fof(abstractness_v11_closure2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(abstractness_v12_aofa_a00,axiom,( ! [A] : ( l5_aofa_a00(A) => ( v12_aofa_a00(A) => A = g5_aofa_a00(u1_struct_0(A),u4_struct_0(A),u1_msualg_1(A),u2_msualg_1(A),u7_aofa_a00(A)) ) ) )).
fof(abstractness_v12_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ( v12_pcs_0(A) => A = g2_pcs_0(u1_struct_0(A),u1_orders_2(A),u1_pcs_0(A)) ) ) )).
fof(abstractness_v15_algstr_0,axiom,( ! [A] : ( l3_algstr_0(A) => ( v15_algstr_0(A) => A = g3_algstr_0(u1_struct_0(A),u2_algstr_0(A)) ) ) )).
fof(abstractness_v15_aofa_a00,axiom,( ! [A] : ( l6_aofa_a00(A) => ( v15_aofa_a00(A) => A = g6_aofa_a00(u1_struct_0(A),u4_struct_0(A),u1_msualg_1(A),u2_msualg_1(A),u8_aofa_a00(A),u7_aofa_a00(A)) ) ) )).
fof(abstractness_v1_algstr_3,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v1_analmetr,axiom,( ! [A] : ( l1_analmetr(A) => ( v1_analmetr(A) => A = g1_analmetr(u1_struct_0(A),u1_analoaf(A),u1_analmetr(A)) ) ) )).
fof(abstractness_v1_analoaf,axiom,( ! [A] : ( l1_analoaf(A) => ( v1_analoaf(A) => A = g1_analoaf(u1_struct_0(A),u1_analoaf(A)) ) ) )).
fof(abstractness_v1_bcialg_4,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v1_bhsp_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v1_cat_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v1_cayldick,axiom,( ! [A] : ( l1_cayldick(A) => ( v1_cayldick(A) => A = g1_cayldick(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),u1_cayldick(A)) ) ) )).
fof(abstractness_v1_cfuncdom,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v1_cgames_1,axiom,( ! [A] : ( l1_cgames_1(A) => ( v1_cgames_1(A) => A = g1_cgames_1(u1_cgames_1(A),u2_cgames_1(A)) ) ) )).
fof(abstractness_v1_clopban2,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v1_clvect_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v1_collsp,axiom,( ! [A] : ( l1_collsp(A) => ( v1_collsp(A) => A = g1_collsp(u1_struct_0(A),u1_collsp(A)) ) ) )).
fof(abstractness_v1_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ( v1_compos_1(A) => A = g1_compos_1(u1_compos_1(A)) ) ) )).
fof(abstractness_v1_conlat_1,axiom,( ! [A] : ( l1_conlat_1(A) => ( v1_conlat_1(A) => A = g1_conlat_1(u1_struct_0(A),u4_struct_0(A),u1_conlat_1(A)) ) ) )).
fof(abstractness_v1_csspace,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v1_e_siec,axiom,( ! [A] : ( l1_e_siec(A) => ( v1_e_siec(A) => A = g1_e_siec(u1_struct_0(A),u1_e_siec(A),u2_e_siec(A)) ) ) )).
fof(abstractness_v1_extpro_1,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(abstractness_v1_fomodel1,axiom,( ! [A] : ( l1_fomodel1(A) => ( v1_fomodel1(A) => A = g1_fomodel1(u1_struct_0(A),u2_struct_0(A),u3_struct_0(A),u1_fomodel1(A)) ) ) )).
fof(abstractness_v1_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(abstractness_v1_funcsdom,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v1_geomtrap,axiom,( ! [A] : ( l1_geomtrap(A) => ( v1_geomtrap(A) => A = g1_geomtrap(u1_struct_0(A),u1_midsp_1(A),u1_analoaf(A)) ) ) )).
fof(abstractness_v1_graph_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v1_grcat_1,axiom,( ! [A] : ( l1_grcat_1(A) => ( v1_grcat_1(A) => A = g1_grcat_1(u1_grcat_1(A),u2_grcat_1(A),u3_grcat_1(A)) ) ) )).
fof(abstractness_v1_incsp_1,axiom,( ! [A] : ( l1_incsp_1(A) => ( v1_incsp_1(A) => A = g1_incsp_1(u1_incsp_1(A),u2_incsp_1(A),u3_incsp_1(A)) ) ) )).
fof(abstractness_v1_lang1,axiom,( ! [A] : ( l1_lang1(A) => ( v1_lang1(A) => A = g1_lang1(u1_struct_0(A),u1_lang1(A)) ) ) )).
fof(abstractness_v1_lattices,axiom,( ! [A] : ( l1_lattices(A) => ( v1_lattices(A) => A = g1_lattices(u1_struct_0(A),u1_lattices(A)) ) ) )).
fof(abstractness_v1_lopban_2,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v1_memstr_0,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(abstractness_v1_metric_1,axiom,( ! [A] : ( l1_metric_1(A) => ( v1_metric_1(A) => A = g1_metric_1(u1_struct_0(A),u1_metric_1(A)) ) ) )).
fof(abstractness_v1_midsp_1,axiom,( ! [A] : ( l1_midsp_1(A) => ( v1_midsp_1(A) => A = g1_midsp_1(u1_struct_0(A),u1_midsp_1(A)) ) ) )).
fof(abstractness_v1_midsp_3,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & 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)) ) ) )).
fof(abstractness_v1_modelc_3,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & 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)) ) ) )).
fof(abstractness_v1_msualg_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v1_normsp_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_orders_2(A) => A = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) )).
fof(abstractness_v1_parsp_1,axiom,( ! [A] : ( l1_parsp_1(A) => ( v1_parsp_1(A) => A = g1_parsp_1(u1_struct_0(A),u1_parsp_1(A)) ) ) )).
fof(abstractness_v1_petri,axiom,( ! [A] : ( l1_petri(A) => ( v1_petri(A) => A = g1_petri(u1_struct_0(A),u4_struct_0(A),u1_petri(A),u2_petri(A)) ) ) )).
fof(abstractness_v1_polyalg1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(abstractness_v1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_pre_topc(A) => A = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) ) ) )).
fof(abstractness_v1_qmax_1,axiom,( ! [A] : ( l1_qmax_1(A) => ( v1_qmax_1(A) => A = g1_qmax_1(u1_qmax_1(A),u2_qmax_1(A),u3_qmax_1(A)) ) ) )).
fof(abstractness_v1_rewrite3,axiom,( ! [A] : ! [B] : ( l1_rewrite3(B,A) => ( v1_rewrite3(B,A) => B = g1_rewrite3(A,u1_struct_0(B),u1_rewrite3(A,B)) ) ) )).
fof(abstractness_v1_rlvect_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v1_sgraph1,axiom,( ! [A] : ( l1_sgraph1(A) => ( v1_sgraph1(A) => A = g1_sgraph1(u1_struct_0(A),u1_sgraph1(A)) ) ) )).
fof(abstractness_v1_stacks_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v1_symsp_1,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) ) )).
fof(abstractness_v1_turing_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v1_unialg_1,axiom,( ! [A] : ( l1_unialg_1(A) => ( v1_unialg_1(A) => A = g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)) ) ) )).
fof(abstractness_v1_waybel_9,axiom,( ! [A] : ( l1_waybel_9(A) => ( v1_waybel_9(A) => A = g1_waybel_9(u1_struct_0(A),u1_orders_2(A),u1_pre_topc(A)) ) ) )).
fof(abstractness_v1_zmodul01,axiom,( ! [A] : ( l1_zmodul01(A) => ( v1_zmodul01(A) => A = g1_zmodul01(u1_struct_0(A),u2_struct_0(A),u1_algstr_0(A),u1_zmodul01(A)) ) ) )).
fof(abstractness_v22_algstr_0,axiom,( ! [A] : ( l4_algstr_0(A) => ( v22_algstr_0(A) => A = g4_algstr_0(u1_struct_0(A),u2_algstr_0(A),u3_struct_0(A)) ) ) )).
fof(abstractness_v29_algstr_0,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v2_armstrng,axiom,( ! [A] : ( l1_armstrng(A) => ( v2_armstrng(A) => A = g1_armstrng(u1_armstrng(A),u2_armstrng(A),u3_armstrng(A)) ) ) )).
fof(abstractness_v2_bcialg_1,axiom,( ! [A] : ( l2_bcialg_1(A) => ( v2_bcialg_1(A) => A = g2_bcialg_1(u1_struct_0(A),u1_bcialg_1(A),u2_struct_0(A)) ) ) )).
fof(abstractness_v2_cat_4,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v2_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(abstractness_v2_group_9,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(abstractness_v2_lang1,axiom,( ! [A] : ( l2_lang1(A) => ( v2_lang1(A) => A = g2_lang1(u1_struct_0(A),u2_lang1(A),u1_lang1(A)) ) ) )).
fof(abstractness_v2_lattices,axiom,( ! [A] : ( l2_lattices(A) => ( v2_lattices(A) => A = g2_lattices(u1_struct_0(A),u2_lattices(A)) ) ) )).
fof(abstractness_v2_mod_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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)) ) ) )).
fof(abstractness_v2_pcs_0,axiom,( ! [A] : ( l1_pcs_0(A) => ( v2_pcs_0(A) => A = g1_pcs_0(u1_struct_0(A),u1_pcs_0(A)) ) ) )).
fof(abstractness_v2_ringcat1,axiom,( ! [A] : ( l1_ringcat1(A) => ( v2_ringcat1(A) => A = g1_ringcat1(u1_ringcat1(A),u2_ringcat1(A),u3_ringcat1(A)) ) ) )).
fof(abstractness_v2_robbins1,axiom,( ! [A] : ( l2_robbins1(A) => ( v2_robbins1(A) => A = g2_robbins1(u1_struct_0(A),u2_lattices(A),u1_robbins1(A)) ) ) )).
fof(abstractness_v2_vectsp_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(abstractness_v36_algstr_0,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v3_abcmiz_0,axiom,( ! [A] : ( l1_abcmiz_0(A) => ( v3_abcmiz_0(A) => A = g1_abcmiz_0(u1_abcmiz_0(A),u2_abcmiz_0(A)) ) ) )).
fof(abstractness_v3_conlat_1,axiom,( ! [A] : ! [B] : ( ( l5_struct_0(A) & l2_conlat_1(B,A) ) => ( v3_conlat_1(B,A) => B = g2_conlat_1(A,u2_conlat_1(A,B),u3_conlat_1(A,B)) ) ) )).
fof(abstractness_v3_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(abstractness_v3_lattices,axiom,( ! [A] : ( l3_lattices(A) => ( v3_lattices(A) => A = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ) ) )).
fof(abstractness_v3_msualg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(abstractness_v3_osalg_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v3_qmax_1,axiom,( ! [A] : ( l2_qmax_1(A) => ( v3_qmax_1(A) => A = g2_qmax_1(u1_struct_0(A),u1_orders_2(A),u1_robbins1(A)) ) ) )).
fof(abstractness_v3_vectsp_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(abstractness_v4_robbins1,axiom,( ! [A] : ( l4_robbins1(A) => ( v4_robbins1(A) => A = g4_robbins1(u1_struct_0(A),u2_lattices(A),u1_lattices(A),u1_robbins1(A)) ) ) )).
fof(abstractness_v4_vectmetr,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v5_cat_4,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v5_closure1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(abstractness_v5_combgras,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(abstractness_v5_rltopsp1,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v6_altcat_1,axiom,( ! [A] : ( l2_altcat_1(A) => ( v6_altcat_1(A) => A = g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(A)) ) ) )).
fof(abstractness_v6_fsm_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(abstractness_v6_robbins3,axiom,( ! [A] : ( l3_robbins3(A) => ( v6_robbins3(A) => A = g3_robbins3(u1_struct_0(A),u2_lattices(A),u1_lattices(A),u1_orders_2(A)) ) ) )).
fof(abstractness_v6_waybel_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(abstractness_v7_abcmiz_0,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v7_clvect_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v7_modelc_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(abstractness_v7_vectsp_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(abstractness_v8_algstr_0,axiom,( ! [A] : ( l2_algstr_0(A) => ( v8_algstr_0(A) => A = g2_algstr_0(u1_struct_0(A),u1_algstr_0(A),u2_struct_0(A)) ) ) )).
fof(abstractness_v9_functor0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(abstractness_v9_modelc_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(abstractness_v9_modelc_2,axiom,( ! [A] : ( 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)) ) ) )).
fof(antisymmetry_r1_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(antisymmetry_r1_polynom3,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_finseq_2(A,k4_ordinal1)) & m1_subset_1(C,k4_finseq_2(A,k4_ordinal1)) ) => ( r1_polynom3(A,B,C) => ~ r1_polynom3(A,C,B) ) ) )).
fof(antisymmetry_r1_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(antisymmetry_r2_hidden,axiom,( ! [A] : ! [B] : ( r2_hidden(A,B) => ~ r2_hidden(B,A) ) )).
fof(antisymmetry_r2_xboole_0,axiom,( ! [A] : ! [B] : ( r2_xboole_0(A,B) => ~ r2_xboole_0(B,A) ) )).
fof(antisymmetry_r3_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(cc10_abcmiz_1,axiom,( ! [A] : ( l1_msualg_1(A) => ! [B] : ( ( v1_relat_1(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) ) ) ) )).
fof(cc10_afinsq_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => ( v5_ordinal1(B) & v1_finset_1(B) ) ) )).
fof(cc10_algstr_0,axiom,( ! [A] : ( l2_algstr_0(A) => ( v14_algstr_0(A) => ( v12_algstr_0(A) & v13_algstr_0(A) ) ) ) )).
fof(cc10_card_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_zfmisc_1(A) ) => v3_card_1(A,1) ) )).
fof(cc10_card_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) ) => ! [C] : ( m1_subset_1(C,k4_card_3(B)) => v4_relat_1(C,A) ) ) )).
fof(cc10_cgames_1,axiom,( ! [A] : ( ( v2_cgames_1(A) & v5_cgames_1(A) & ~ v7_cgames_1(A) ) => ( v2_cgames_1(A) & v9_cgames_1(A) ) ) )).
fof(cc10_closure2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_closure2(B,A) => ( v15_closure2(B,A) => v16_closure2(B,A) ) ) ) )).
fof(cc10_cohsp_1,axiom,( ! [A] : ( v3_cohsp_1(A) => ! [B] : ( ( 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) ) ) ) )).
fof(cc10_compact1,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc10_comput_1,axiom,( ! [A] : ( v7_comput_1(A) => ( v1_relat_1(A) & v1_funct_1(A) ) ) )).
fof(cc10_dilworth,axiom,( ! [A] : ( ( v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_eqrel_1(B,u1_struct_0(A)) => v6_dilworth(B,A) ) ) )).
fof(cc10_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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))) ) ) ) )).
fof(cc10_exchsort,axiom,( ! [A] : ! [B] : ( ( v3_membered(B) & ~ v1_xboole_0(B) ) => ! [C] : ( m1_subset_1(C,k9_funct_2(A,B)) => v3_valued_0(C) ) ) )).
fof(cc10_finseq_1,axiom,( ! [A] : ( v3_finseq_1(A) => ! [B] : ( m1_subset_1(B,A) => v1_finseq_1(B) ) ) )).
fof(cc10_fomodel0,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,k2_xcmplx_0(A,k5_numbers)) & v1_finseq_1(B) ) => ( v1_relat_1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_finseq_1(B) ) ) ) )).
fof(cc10_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_fomodel1(A)) => ( v4_fomodel1(B,A) => ~ v6_fomodel1(B,A) ) ) ) )).
fof(cc10_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) ) => ! [C] : ( 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) ) ) ) )).
fof(cc10_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( v9_fomodel4(E,A,B,k3_xboole_0(C,D)) => v9_fomodel4(E,A,B,C) ) ) )).
fof(cc10_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(cc10_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_funct_2(C,A,B) => v4_funct_1(C) ) )).
fof(cc10_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v4_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => v4_glib_000(B) ) ) )).
fof(cc10_glib_002,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & m1_subset_1(B,k3_glib_002(A)) ) => ! [C] : ( m2_glib_000(C,A,B,k21_glib_000(A,B)) => v4_glib_002(C,A) ) ) )).
fof(cc10_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(cc10_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v19_lattices(B,A) => v21_lattices(B,A) ) ) ) )).
fof(cc10_lfuzzy_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v2_struct_0(A) & v2_lfuzzy_0(A) ) => ( ~ v2_struct_0(A) & v9_waybel_1(A) & v2_lfuzzy_0(A) ) ) ) )).
fof(cc10_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k4_numbers)) => v5_membered(A) ) )).
fof(cc10_monoid_0,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc10_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) & m1_subset_1(D,u1_struct_0(A)) ) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,C),D)) => v3_trees_2(E) ) ) )).
fof(cc10_ordinal1,axiom,( ! [A] : ( v6_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v6_ordinal1(B) ) ) )).
fof(cc10_pcs_0,axiom,( ! [A] : ( 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) ) ) )).
fof(cc10_pre_poly,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k15_pre_poly(A))) => ! [C] : ( m1_subset_1(C,B) => v4_relat_1(C,A) ) ) )).
fof(cc10_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_rewrite1(A) ) => ( v1_relat_1(A) & v4_rewrite1(A) ) ) )).
fof(cc10_scmyciel,axiom,( ! [A] : ( ( v1_finset_1(A) & v4_scmyciel(A) ) => ( v4_scmyciel(A) & v11_scmyciel(A) ) ) )).
fof(cc10_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v1_matroid0(A) & v3_simplex0(A) ) => v3_matroid0(A) ) ) )).
fof(cc10_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => ( ( ~ v2_struct_0(A) & v7_struct_0(A) ) => v13_struct_0(A,1) ) ) )).
fof(cc10_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v1_tsep_1(B,A) => v1_borsuk_1(B,A) ) ) ) )).
fof(cc10_tex_2,axiom,( ! [A] : ( ( v13_struct_0(A,1) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v2_struct_0(B) => ( ~ v2_struct_0(B) & ~ v1_tex_2(B,A) ) ) ) ) )).
fof(cc10_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( v1_tsep_1(B,A) & ~ v2_tex_3(B,A) ) => ~ v1_tex_3(B,A) ) ) ) )).
fof(cc10_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_topalg_6(A)) => ( v5_topalg_6(B,A) => ~ v1_xboole_0(B) ) ) ) )).
fof(cc10_topgen_4,axiom,( ! [A] : ( v1_xboole_0(A) => v4_card_3(A) ) )).
fof(cc10_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_trees_3(B,A) => v3_trees_3(B) ) ) )).
fof(cc10_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v2_struct_0(B) => ( ~ v2_struct_0(B) & v6_pre_topc(B) ) ) ) ) )).
fof(cc10_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( v1_tex_2(B,A) & v2_tsp_2(B,A) ) => ~ v1_borsuk_1(B,A) ) ) ) )).
fof(cc10_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_valued_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_valued_0(B) ) ) )).
fof(cc10_valued_2,axiom,( ! [A] : ( v2_valued_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v2_valued_2(B) ) ) )).
fof(cc10_waybel25,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc10_waybel30,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc10_waybel_0,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc10_waybel_1,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v2_struct_0(A) & v11_waybel_1(A) ) => ( ~ v2_struct_0(A) & v9_waybel_1(A) ) ) ) )).
fof(cc10_xxreal_2,axiom,( ! [A] : ( ( v3_membered(A) & v1_xxreal_2(A) ) => ( v3_membered(A) & v3_xxreal_2(A) ) ) )).
fof(cc10_yellow21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & v3_yellow21(A) & l2_altcat_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc10_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v8_yellow_0(B,A) => v6_yellow_0(B,A) ) ) ) )).
fof(cc11_abcmiz_1,axiom,( ! [A] : ( ( v12_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(cc11_algstr_0,axiom,( ! [A] : ( ( v12_algstr_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v9_algstr_0(B,A) ) ) )).
fof(cc11_card_1,axiom,( ! [A] : ( v3_card_1(A,2) => ~ v1_xboole_0(A) ) )).
fof(cc11_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( m1_subset_1(B,k8_card_3(A)) => v5_funct_1(B,A) ) ) )).
fof(cc11_cgames_1,axiom,( ! [A] : ( ( v2_cgames_1(A) & v8_cgames_1(A) ) => ( v2_cgames_1(A) & ~ v5_cgames_1(A) & ~ v6_cgames_1(A) ) ) )).
fof(cc11_closure2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_closure2(B,A) => ( v13_closure2(B,A) => v17_closure2(B,A) ) ) ) )).
fof(cc11_cohsp_1,axiom,( ! [A] : ( v2_finsub_1(A) => ! [B] : ( ( 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) ) ) ) )).
fof(cc11_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v7_comput_1(A) ) => ( v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v4_valued_0(A) & v2_margrel1(A) ) ) )).
fof(cc11_dilworth,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_dilworth(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v7_dilworth(B,A) => v1_dilworth(B,A) ) ) ) )).
fof(cc11_euclid_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( 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)) ) ) ) )).
fof(cc11_exchsort,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) & v1_exchsort(B) ) => ! [C] : ( m1_exchsort(C,B) => v5_relat_1(C,A) ) ) )).
fof(cc11_finseq_1,axiom,( ! [A] : ( v3_finseq_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v3_finseq_1(B) ) ) )).
fof(cc11_fomodel0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_finseq_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(cc11_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_fomodel1(A)) => ( ( v5_fomodel1(B,A) & v8_fomodel1(B,A) ) => ( v5_fomodel1(B,A) & v6_fomodel1(B,A) ) ) ) ) )).
fof(cc11_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) & v7_ordinal1(C) ) => ! [D] : ( m1_subset_1(D,k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) => ( v3_fomodel2(D,A,k2_xcmplx_0(B,k3_xcmplx_0(k5_numbers,C))) => v3_fomodel2(D,A,k2_xcmplx_0(B,C)) ) ) ) )).
fof(cc11_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( v9_fomodel4(E,A,B,D) => v9_fomodel4(E,A,B,C) ) ) )).
fof(cc11_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v5_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => v5_glib_000(B) ) ) )).
fof(cc11_glib_002,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( 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) ) ) )).
fof(cc11_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc11_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) => v6_membered(A) ) )).
fof(cc11_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_monoid_0(B,A) => ~ v2_struct_0(B) ) ) )).
fof(cc11_msafree4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( l3_msualg_1(C,A) => ( v5_msafree4(C,A,B) => v1_msafree1(C,A) ) ) ) )).
fof(cc11_ordinal1,axiom,( ! [A] : ( v8_ordinal1(A) => v7_ordinal1(A) ) )).
fof(cc11_pcs_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v16_pcs_0(A) ) => ( v1_relat_1(A) & v1_yellow_1(A) & v7_pcs_0(A) ) ) )).
fof(cc11_pre_poly,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k15_pre_poly(A))) ) => ! [C] : ( m1_subset_1(C,B) => ( v1_partfun1(C,A) & v4_valued_0(C) & v2_pre_poly(C) ) ) ) )).
fof(cc11_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_rewrite1(A) & v4_rewrite1(A) ) => ( v1_relat_1(A) & v8_rewrite1(A) ) ) )).
fof(cc11_robbins3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc11_scmyciel,axiom,( ! [A] : ( ( v1_finset_1(A) & v4_scmyciel(A) ) => ( v4_scmyciel(A) & v12_scmyciel(A) ) ) )).
fof(cc11_simplex0,axiom,( ! [A] : ( ( v2_simplex0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_tops_2(B,A) => v1_finset_1(B) ) ) ) )).
fof(cc11_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => ( v13_struct_0(A,1) => ( ~ v2_struct_0(A) & v7_struct_0(A) ) ) ) )).
fof(cc11_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v1_borsuk_1(B,A) => v1_tsep_1(B,A) ) ) ) )).
fof(cc11_tex_2,axiom,( ! [A] : ( ( v13_struct_0(A,1) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & ~ v1_tex_2(B,A) ) => ( ~ v2_struct_0(B) & v7_struct_0(B) ) ) ) ) )).
fof(cc11_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & v1_tsep_1(B,A) ) => ( ~ v2_struct_0(B) & ~ v3_tex_3(B,A) ) ) ) ) )).
fof(cc11_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_topalg_6(A)) => ( v6_topalg_6(B,A) => ~ v1_xboole_0(B) ) ) ) )).
fof(cc11_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc11_trees_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_trees_3(B,A) ) => ! [C] : ( m1_subset_1(C,B) => v5_relat_1(C,A) ) ) )).
fof(cc11_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v6_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & ~ v1_tex_2(B,A) ) => ( ~ v2_struct_0(B) & ~ v6_pre_topc(B) ) ) ) ) )).
fof(cc11_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_valued_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v2_valued_0(B) ) ) )).
fof(cc11_valued_2,axiom,( ! [A] : ( v3_valued_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v3_valued_2(B) ) ) )).
fof(cc11_waybel_0,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc11_xxreal_2,axiom,( ! [A] : ( ( v3_membered(A) & v2_xxreal_2(A) ) => ( v3_membered(A) & v4_xxreal_2(A) ) ) )).
fof(cc11_yellow_0,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc12_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc12_algstr_0,axiom,( ! [A] : ( ( v13_algstr_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v10_algstr_0(B,A) ) ) )).
fof(cc12_card_1,axiom,( ! [A] : ( v3_card_1(A,3) => ~ v1_xboole_0(A) ) )).
fof(cc12_card_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) ) => ! [C] : ( m1_subset_1(C,k8_card_3(B)) => v4_relat_1(C,A) ) ) )).
fof(cc12_cayldick,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_cayldick)) => ( ~ v9_struct_0(A,k3_cayldick) => ( ~ v1_xboole_0(A) & ~ v9_struct_0(A,k3_cayldick) ) ) ) )).
fof(cc12_cgames_1,axiom,( ! [A] : ( ( v2_cgames_1(A) & ~ v5_cgames_1(A) & ~ v6_cgames_1(A) ) => ( v2_cgames_1(A) & v8_cgames_1(A) ) ) )).
fof(cc12_cohsp_1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc12_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k9_comput_1) => v7_comput_1(A) ) )).
fof(cc12_dilworth,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & v5_orders_2(A) & v4_dilworth(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_card_1(B,1) => v7_dilworth(B,A) ) ) ) )).
fof(cc12_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_subset_1(D,k1_funct_2(A,C)) => v5_relat_1(D,B) ) ) )).
fof(cc12_finseq_1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc12_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k9_funct_2(A,k3_finseq_2(B))) => v1_pre_poly(C) ) )).
fof(cc12_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( v12_fomodel1(B,A) => v3_fomodel0(B,k15_fomodel1(A)) ) ) )).
fof(cc12_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(cc12_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( v1_fomodel4(B,A) => v12_fomodel4(B,A) ) ) )).
fof(cc12_glib_000,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m2_glib_000(D,A,B,C) => v2_glib_000(D) ) ) )).
fof(cc12_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(cc12_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xcmplx_0(B) ) ) )).
fof(cc12_monoid_0,axiom,( ! [A] : ( ( v1_monoid_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_monoid_0(B,A) => v1_monoid_0(B) ) ) )).
fof(cc12_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & m3_pboole(B,u1_struct_0(A),k4_equation(A)) & v4_msualg_1(C,A) & v6_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( l3_msualg_1(D,A) => ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) ) => ( v4_msualg_1(D,A) & v6_msafree4(D,A,B) ) ) ) ) )).
fof(cc12_ordinal1,axiom,( ! [A] : ( v8_ordinal1(A) => v1_zfmisc_1(A) ) )).
fof(cc12_pcs_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v17_pcs_0(A) ) => ( v1_relat_1(A) & v16_pcs_0(A) ) ) )).
fof(cc12_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( m1_subset_1(C,k18_pre_poly(A,B)) => v4_valued_0(C) ) ) )).
fof(cc12_rewrite1,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) ) => ( v1_relat_1(A) & v6_rewrite1(A) ) ) )).
fof(cc12_robbins3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc12_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v12_scmyciel(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_tarski(A))) => ( v9_scmyciel(B,A) => ( v1_finset_1(B) & v9_scmyciel(B,A) ) ) ) ) )).
fof(cc12_simplex0,axiom,( ! [A] : ( ( v3_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_tops_2(B,A) => v5_finset_1(B) ) ) ) )).
fof(cc12_struct_0,axiom,( ! [A] : ( l5_struct_0(A) => ( ~ v2_struct_0(A) => v14_struct_0(A) ) ) )).
fof(cc12_tdlat_3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc12_tex_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & v7_struct_0(B) ) => ( ~ v2_struct_0(B) & v1_tex_2(B,A) ) ) ) ) )).
fof(cc12_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & v3_tex_3(B,A) ) => ( ~ v2_struct_0(B) & ~ v1_tsep_1(B,A) ) ) ) ) )).
fof(cc12_topgen_4,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_pre_topc(A) & v7_topgen_4(A) ) => ( v2_pre_topc(A) & v6_pre_topc(A) ) ) ) )).
fof(cc12_trees_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & ~ v1_xboole_0(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc12_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v6_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & v6_pre_topc(B) ) => ( ~ v2_struct_0(B) & v1_tex_2(B,A) ) ) ) ) )).
fof(cc12_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_valued_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v3_valued_0(B) ) ) )).
fof(cc12_valued_2,axiom,( ! [A] : ( v4_valued_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v4_valued_2(B) ) ) )).
fof(cc12_waybel_0,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc12_xxreal_2,axiom,( ! [A] : ( ( v5_membered(A) & v5_xxreal_2(A) ) => ( v5_membered(A) & v1_finset_1(A) ) ) )).
fof(cc12_yellow_0,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc13_algstr_0,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ( v16_algstr_0(B,A) & v17_algstr_0(B,A) ) => v18_algstr_0(B,A) ) ) ) )).
fof(cc13_card_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(B)) => v1_partfun1(C,A) ) ) )).
fof(cc13_cayldick,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_cayldick)) => ( ~ v9_struct_0(A,k3_cayldick) => ( ~ v9_struct_0(A,k3_cayldick) & v18_algstr_0(A,k3_cayldick) ) ) ) )).
fof(cc13_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k9_comput_1) => ( v2_margrel1(A) & v3_margrel1(A,k4_ordinal1) ) ) )).
fof(cc13_finseq_1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc13_fomodel0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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) ) ) ) )).
fof(cc13_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( v3_fomodel0(B,k15_fomodel1(A)) => v12_fomodel1(B,A) ) ) )).
fof(cc13_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k30_fomodel2(A)) => v4_fomodel2(B,A) ) ) )).
fof(cc13_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( v1_fomodel4(B,A) => v12_fomodel4(B,A) ) ) )).
fof(cc13_glib_000,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m2_glib_000(D,A,k6_domain_1(k6_glib_000(A),B),C) => v4_glib_000(D) ) ) )).
fof(cc13_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_isomichi(B,A) => ( ~ v4_isomichi(B,A) & ~ v5_isomichi(B,A) ) ) ) ) )).
fof(cc13_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xxreal_0(B) ) ) )).
fof(cc13_monoid_0,axiom,( ! [A] : ( ( v2_monoid_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_monoid_0(B,A) => v2_monoid_0(B) ) ) )).
fof(cc13_msafree4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( l3_msualg_1(C,A) => ( v4_msafree4(C,A,B) => ( v4_msafree4(C,A,B) & v6_msafree4(C,A,k5_msafree4(A,B)) ) ) ) ) )).
fof(cc13_ordinal1,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ~ v8_ordinal1(A) ) )).
fof(cc13_pcs_0,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc13_pre_poly,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_finseq_1(C,k4_finseq_2(B,A)) => v1_pre_poly(C) ) ) )).
fof(cc13_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_rewrite1(A) & v9_rewrite1(A) ) => ( v1_relat_1(A) & v7_rewrite1(A) ) ) )).
fof(cc13_robbins3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc13_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v6_scmyciel(A) & v12_scmyciel(A) ) => ( v1_finset_1(A) & v4_scmyciel(A) ) ) )).
fof(cc13_simplex0,axiom,( ! [A] : ( ( ~ v5_simplex0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v3_pre_topc(B,A) ) ) ) )).
fof(cc13_struct_0,axiom,( ! [A] : ( l5_struct_0(A) => ( v11_struct_0(A) => v14_struct_0(A) ) ) )).
fof(cc13_tdlat_3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc13_tex_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & ~ v1_tex_2(B,A) ) => ( ~ v2_struct_0(B) & ~ v7_struct_0(B) ) ) ) ) )).
fof(cc13_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v2_tex_3(B,A) => ~ v3_tex_3(B,A) ) ) ) )).
fof(cc13_topgen_4,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_pre_topc(A) & v7_pre_topc(A) ) => ( v2_pre_topc(A) & v7_topgen_4(A) ) ) ) )).
fof(cc13_trees_3,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc13_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k3_numbers) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v5_relat_1(B,k3_numbers) ) ) )).
fof(cc13_valued_2,axiom,( ! [A] : ( v5_valued_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v5_valued_2(B) ) ) )).
fof(cc13_waybel_0,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc13_xxreal_2,axiom,( ! [A] : ( ( v6_membered(A) & v4_xxreal_2(A) ) => ( v6_membered(A) & v1_finset_1(A) & v4_xxreal_2(A) ) ) )).
fof(cc14_algstr_0,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v18_algstr_0(B,A) => ( v16_algstr_0(B,A) & v17_algstr_0(B,A) ) ) ) ) )).
fof(cc14_card_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(B)) => v1_partfun1(C,A) ) ) )).
fof(cc14_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_cayldick(A) & l1_cayldick(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v2_cayldick(B,A) ) ) )).
fof(cc14_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k2_comput_1(k4_ordinal1)) => ( v7_comput_1(A) => v3_margrel1(A,k4_ordinal1) ) ) )).
fof(cc14_fomodel0,axiom,( ! [A] : ( v3_finseq_1(A) => v5_finset_1(A) ) )).
fof(cc14_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) => ~ v1_xboole_0(B) ) ) )).
fof(cc14_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) ) => ! [C] : ( m1_subset_1(C,k32_fomodel2(A,B)) => ~ v5_fomodel2(C,A) ) ) )).
fof(cc14_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_fomodel4(A)) => v12_fomodel4(B,A) ) ) )).
fof(cc14_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => ! [C] : ( m2_glib_000(C,A,k6_domain_1(k6_glib_000(A),B),k1_xboole_0) => ( v2_glib_000(C) & v4_glib_000(C) ) ) ) )).
fof(cc14_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_isomichi(B,A) => ( ~ v3_isomichi(B,A) & ~ v5_isomichi(B,A) ) ) ) ) )).
fof(cc14_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_xreal_0(B) ) ) )).
fof(cc14_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_monoid_0(B,A) => v1_group_1(B) ) ) )).
fof(cc14_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(C) & m3_pboole(C,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B))) & m1_subset_1(D,u1_struct_0(A)) ) => ! [E] : ( m1_subset_1(E,k1_msafree4(u1_struct_0(A),C,D)) => ( v1_relat_1(E) & v1_funct_1(E) ) ) ) )).
fof(cc14_ordinal1,axiom,( ! [A] : ( v1_xboole_0(A) => ~ v10_ordinal1(A) ) )).
fof(cc14_pcs_0,axiom,( ! [A] : ( l1_pcs_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v21_pcs_0(B,A) ) ) ) )).
fof(cc14_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v10_rewrite1(A) ) => ( v1_relat_1(A) & v3_rewrite1(A) & v7_rewrite1(A) ) ) )).
fof(cc14_robbins3,axiom,( ! [A] : ( l3_robbins3(A) => ( ( ~ v2_struct_0(A) & v10_lattices(A) & v10_robbins3(A) ) => ( ~ v2_struct_0(A) & v1_lattice3(A) & v2_lattice3(A) ) ) ) )).
fof(cc14_simplex0,axiom,( ! [A] : ! [B] : ( ( v3_pencil_1(B) & m1_simplex0(B,A) ) => ! [C] : ( m2_simplex0(C,A,B) => v3_pencil_1(C) ) ) )).
fof(cc14_struct_0,axiom,( ! [A] : ( l5_struct_0(A) => ( ( v2_struct_0(A) & v14_struct_0(A) ) => v11_struct_0(A) ) ) )).
fof(cc14_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v4_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & v1_tsep_1(B,A) ) => ( ~ v2_struct_0(B) & v4_tdlat_3(B) ) ) ) ) )).
fof(cc14_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v1_tdlat_3(B) => v2_pre_topc(B) ) ) ) )).
fof(cc14_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v3_tex_3(B,A) => ~ v2_tex_3(B,A) ) ) ) )).
fof(cc14_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(cc14_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_trees_3(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v4_trees_3(A) ) ) )).
fof(cc14_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v5_relat_1(B,k4_numbers) ) ) )).
fof(cc14_valued_2,axiom,( ! [A] : ( v6_valued_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v6_valued_2(B) ) ) )).
fof(cc14_waybel_0,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc14_xxreal_2,axiom,( ! [A] : ( ( v2_membered(A) & v5_xxreal_2(A) ) => ( v2_membered(A) & v3_membered(A) ) ) )).
fof(cc15_algstr_0,axiom,( ! [A] : ( l3_algstr_0(A) => ( ( v19_algstr_0(A) & v20_algstr_0(A) ) => v21_algstr_0(A) ) ) )).
fof(cc15_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v7_comput_1(A) ) => ( v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v2_comput_1(A) ) ) )).
fof(cc15_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k3_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) ) ) ) )).
fof(cc15_fomodel1,axiom,( ! [A] : ( l1_fomodel1(A) => ( ( ~ v6_struct_0(A) & v11_fomodel1(A) ) => ( ~ v6_struct_0(A) & ~ v8_struct_0(A) & v11_fomodel1(A) ) ) ) )).
fof(cc15_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) ) => ! [C] : ( m1_subset_1(C,k33_fomodel2(A,B)) => v5_fomodel2(C,A) ) ) )).
fof(cc15_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( v5_fomodel4(E,C,A,B,D) => v1_fomodel4(E,A) ) ) )).
fof(cc15_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m2_glib_000(C,A,B,k1_xboole_0) => v7_glib_000(C) ) ) )).
fof(cc15_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v5_isomichi(B,A) => ( ~ v3_isomichi(B,A) & ~ v4_isomichi(B,A) ) ) ) ) )).
fof(cc15_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_rat_1(B) ) ) )).
fof(cc15_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_monoid_0(B,A) => v3_group_1(B) ) ) )).
fof(cc15_msafree4,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(A) & v3_rewrite1(A) & v4_rewrite1(A) ) ) )).
fof(cc15_ordinal1,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) ) => ( v1_relat_1(A) & v9_ordinal1(A) ) ) )).
fof(cc15_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_rewrite1(A) & v7_rewrite1(A) ) => ( v1_relat_1(A) & v10_rewrite1(A) ) ) )).
fof(cc15_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_robbins1(A) ) => ! [B] : ( m3_robbins3(B,A) => ~ v2_struct_0(B) ) ) )).
fof(cc15_simplex0,axiom,( ! [A] : ! [B] : ( ( v2_simplex0(B) & m1_simplex0(B,A) ) => ! [C] : ( m2_simplex0(C,A,B) => v2_simplex0(C) ) ) )).
fof(cc15_struct_0,axiom,( ! [A] : ( l5_struct_0(A) => ( ( ~ v11_struct_0(A) & v14_struct_0(A) ) => ~ v2_struct_0(A) ) ) )).
fof(cc15_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v5_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v2_struct_0(B) => ( ~ v2_struct_0(B) & v5_tdlat_3(B) ) ) ) ) )).
fof(cc15_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v2_tdlat_3(B) => v2_pre_topc(B) ) ) ) )).
fof(cc15_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v4_tex_3(B,A) => v3_tex_3(B,A) ) ) ) )).
fof(cc15_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v5_topgen_4(B,A) => v8_topgen_4(B,A) ) ) ) )).
fof(cc15_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_3(A) ) => ! [B] : ( m1_finseq_1(B,A) => v4_trees_3(B) ) ) )).
fof(cc15_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_valued_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v4_valued_0(B) ) ) )).
fof(cc15_valued_2,axiom,( ! [A] : ( v1_valued_2(A) => ! [B] : ( m1_subset_1(B,A) => v1_valued_0(B) ) ) )).
fof(cc15_waybel_0,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc15_xxreal_2,axiom,( ! [A] : ( ( v2_membered(A) & v1_xboole_0(A) ) => ( v2_membered(A) & v6_xxreal_2(A) ) ) )).
fof(cc16_algstr_0,axiom,( ! [A] : ( l3_algstr_0(A) => ( v21_algstr_0(A) => ( v19_algstr_0(A) & v20_algstr_0(A) ) ) ) )).
fof(cc16_comput_1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc16_fomodel0,axiom,( ! [A] : ( v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k3_finseq_2(A)) => v1_xboole_0(B) ) ) )).
fof(cc16_fomodel1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( 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) ) ) ) )).
fof(cc16_fomodel2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( 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) ) ) ) )).
fof(cc16_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( v4_fomodel4(D,A,B,C) => v2_fomodel4(D,A) ) ) )).
fof(cc16_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & m1_subset_1(B,k1_zfmisc_1(k7_glib_000(A))) ) => ! [C] : ( m2_glib_000(C,A,k6_glib_000(A),B) => v9_glib_000(C,A) ) ) )).
fof(cc16_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_isomichi(B,A) => v3_isomichi(B,A) ) ) ) )).
fof(cc16_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,A) => v1_int_1(B) ) ) )).
fof(cc16_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_monoid_0(B,A) => v5_group_1(B) ) ) )).
fof(cc16_msafree4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_msualg_4(C,A,B,B) => ( v3_relat_1(C) => ( v9_msafree4(C,A,B) & v10_msafree4(C,A,B) ) ) ) ) )).
fof(cc16_ordinal1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v10_ordinal1(A) ) => ! [B] : ( m1_subset_1(B,A) => ~ v8_ordinal1(B) ) ) )).
fof(cc16_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v7_lattices(A) & l4_robbins1(A) ) => ! [B] : ( m3_robbins3(B,A) => v7_lattices(B) ) ) )).
fof(cc16_simplex0,axiom,( ! [A] : ! [B] : ( ( v4_matroid0(B) & m1_simplex0(B,A) ) => ! [C] : ( m2_simplex0(C,A,B) => v4_matroid0(C) ) ) )).
fof(cc16_struct_0,axiom,( ! [A] : ( l5_struct_0(A) => ( v11_struct_0(A) => v15_struct_0(A) ) ) )).
fof(cc16_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v2_pre_topc(B) => ~ v1_tdlat_3(B) ) ) ) )).
fof(cc16_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v3_tex_3(B,A) => ~ v4_tex_3(B,A) ) ) ) )).
fof(cc16_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_topgen_4(B,A) => v8_topgen_4(B,A) ) ) ) )).
fof(cc16_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_trees_3(A) ) => ! [B] : ( m1_finseq_1(B,A) => v5_trees_3(B) ) ) )).
fof(cc16_valued_0,axiom,( ! [A] : ! [B] : ( v1_membered(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_valued_0(C) ) ) )).
fof(cc16_valued_2,axiom,( ! [A] : ( v2_valued_2(A) => ! [B] : ( m1_subset_1(B,A) => v2_valued_0(B) ) ) )).
fof(cc16_xxreal_2,axiom,( ! [A] : ( ( v2_membered(A) & v1_xxreal_2(A) ) => ( v2_membered(A) & ~ v1_xboole_0(A) ) ) )).
fof(cc17_algstr_0,axiom,( ! [A] : ( ( v19_algstr_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v16_algstr_0(B,A) ) ) )).
fof(cc17_comput_1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc17_fomodel0,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( ( 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) ) ) ) )).
fof(cc17_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) ) => ! [C] : ( m1_subset_1(C,k1_funct_1(k28_fomodel1(A),B)) => ~ v1_xboole_0(C) ) ) )).
fof(cc17_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & ~ v1_xboole_0(B) ) => ! [C] : ( m1_subset_1(C,k15_fomodel2(A,B)) => v4_relat_1(C,k37_fomodel1(A)) ) ) )).
fof(cc17_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) => ( v13_fomodel4(B,1,A) => v13_fomodel4(B,k5_numbers,A) ) ) ) )).
fof(cc17_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m2_glib_000(B,A,k6_glib_000(A),k1_xboole_0) => v9_glib_000(B,A) ) ) )).
fof(cc17_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_isomichi(B,A) => v3_isomichi(B,A) ) ) ) )).
fof(cc17_membered,axiom,( ! [A] : ( v6_membered(A) => ! [B] : ( m1_subset_1(B,A) => v7_ordinal1(B) ) ) )).
fof(cc17_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_monoid_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_monoid_0(B,A) => v13_monoid_0(B) ) ) )).
fof(cc17_msafree4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_msualg_4(C,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,k1_msafree3(A,B))) => ( v3_relat_1(C) => ( v3_msualg_6(C,A,k1_msafree3(A,B)) & v4_msualg_6(C,A,k1_msafree3(A,B)) & v11_msafree4(C,A,B) ) ) ) ) )).
fof(cc17_ordinal1,axiom,( ! [A] : ( ~ v10_ordinal1(A) => v1_setfam_1(A) ) )).
fof(cc17_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_lattices(A) & l4_robbins1(A) ) => ! [B] : ( m3_robbins3(B,A) => v5_lattices(B) ) ) )).
fof(cc17_simplex0,axiom,( ! [A] : ( v1_int_1(A) => ( v1_finset_1(A) & v1_int_1(A) ) ) )).
fof(cc17_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => ( ~ v7_struct_0(A) => ~ v2_struct_0(A) ) ) )).
fof(cc17_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v2_pre_topc(B) => ~ v2_tdlat_3(B) ) ) ) )).
fof(cc17_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v4_tex_3(B,A) => ~ v1_tex_3(B,A) ) ) ) )).
fof(cc17_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) ) => ! [B] : ( m1_finseq_1(B,A) => v6_trees_3(B) ) ) )).
fof(cc17_valued_0,axiom,( ! [A] : ! [B] : ( v2_membered(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v2_valued_0(C) ) ) )).
fof(cc17_valued_2,axiom,( ! [A] : ( v3_valued_2(A) => ! [B] : ( m1_subset_1(B,A) => v3_valued_0(B) ) ) )).
fof(cc17_xxreal_2,axiom,( ! [A] : ( ( v2_membered(A) & v2_xxreal_2(A) ) => ( v2_membered(A) & ~ v1_xboole_0(A) ) ) )).
fof(cc18_algstr_0,axiom,( ! [A] : ( ( v20_algstr_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v17_algstr_0(B,A) ) ) )).
fof(cc18_comput_1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc18_fomodel0,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_setfam_1(B) ) ) )).
fof(cc18_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k29_fomodel1(A)) => ~ v1_xboole_0(B) ) ) )).
fof(cc18_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & ~ v1_xboole_0(B) ) => ! [C] : ( m1_subset_1(C,k15_fomodel2(A,B)) => ( v4_relat_1(C,k37_fomodel1(A)) => ( v4_relat_1(C,k37_fomodel1(A)) & v1_partfun1(C,k37_fomodel1(A)) ) ) ) ) )).
fof(cc18_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) => ( v13_fomodel4(B,2,A) => v13_fomodel4(B,1,A) ) ) ) )).
fof(cc18_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [C] : ( m2_glib_000(C,A,k6_glib_000(A),k6_subset_1(k7_glib_000(A),k1_tarski(B))) => v9_glib_000(C,A) ) ) )).
fof(cc18_membered,axiom,( ! [A] : ( v1_xboole_0(A) => v6_membered(A) ) )).
fof(cc18_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v16_monoid_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_monoid_0(B,A) => v16_monoid_0(B) ) ) )).
fof(cc18_ordinal1,axiom,( ! [A] : ( v10_ordinal1(A) => ~ v1_setfam_1(A) ) )).
fof(cc18_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_lattices(A) & l4_robbins1(A) ) => ! [B] : ( m3_robbins3(B,A) => v6_lattices(B) ) ) )).
fof(cc18_simplex0,axiom,( ! [A] : ( ( ~ v3_pencil_1(A) & v1_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m3_simplex0(B,A,k2_xxreal_3(1)) => v1_xboole_0(B) ) ) )).
fof(cc18_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v1_tdlat_3(B) => v3_tdlat_3(B) ) ) ) )).
fof(cc18_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v1_tex_3(B,A) => ~ v4_tex_3(B,A) ) ) ) )).
fof(cc18_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v6_trees_3(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) ) )).
fof(cc18_valued_0,axiom,( ! [A] : ! [B] : ( v3_membered(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v3_valued_0(C) ) ) )).
fof(cc18_valued_2,axiom,( ! [A] : ( v4_valued_2(A) => ! [B] : ( m1_subset_1(B,A) => v5_relat_1(B,k3_numbers) ) ) )).
fof(cc19_algstr_0,axiom,( ! [A] : ( l4_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ( v23_algstr_0(B,A) & v24_algstr_0(B,A) ) => v25_algstr_0(B,A) ) ) ) )).
fof(cc19_fomodel0,axiom,( ! [A] : ( ( v1_int_1(A) & v2_xxreal_0(A) ) => ( v7_ordinal1(A) & v1_int_1(A) ) ) )).
fof(cc19_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) => ( v14_fomodel1(B,k5_numbers,A) => v3_card_1(B,1) ) ) ) )).
fof(cc19_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ! [D] : ( m1_subset_1(D,k1_fomodel1(B)) => ( v7_fomodel2(D,C,B) => v7_fomodel2(D,A,B) ) ) ) )).
fof(cc19_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) => ( v13_fomodel4(B,k5_numbers,A) => ( ~ v1_xboole_0(B) & v13_fomodel4(B,k5_numbers,A) ) ) ) ) )).
fof(cc19_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [C] : ( m2_glib_000(C,A,k6_glib_000(A),k6_subset_1(k7_glib_000(A),B)) => v9_glib_000(C,A) ) ) )).
fof(cc19_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_membered(B) ) ) )).
fof(cc19_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v17_monoid_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_monoid_0(B,A) => v17_monoid_0(B) ) ) )).
fof(cc19_ordinal1,axiom,( ! [A] : ( v1_setfam_1(A) => ~ v10_ordinal1(A) ) )).
fof(cc19_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & l4_robbins1(A) ) => ! [B] : ( m3_robbins3(B,A) => v4_lattices(B) ) ) )).
fof(cc19_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v3_tdlat_3(B) => ~ v1_tdlat_3(B) ) ) ) )).
fof(cc19_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( v1_borsuk_1(B,A) & v3_tex_3(B,A) ) => v4_tex_3(B,A) ) ) ) )).
fof(cc19_valued_0,axiom,( ! [A] : ! [B] : ( v4_membered(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v5_relat_1(C,k3_numbers) ) ) )).
fof(cc19_valued_2,axiom,( ! [A] : ( v5_valued_2(A) => ! [B] : ( m1_subset_1(B,A) => v5_relat_1(B,k4_numbers) ) ) )).
fof(cc1_abcmiz_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v13_struct_0(A,1) & v3_orders_2(A) ) => ( v13_struct_0(A,1) & v3_lattice3(A) ) ) ) )).
fof(cc1_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k3_card_3(u3_msualg_1(A,k1_msafree3(A,B)))) => ~ v1_xtuple_0(C) ) ) )).
fof(cc1_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v1_abcmiz_a(A) & l1_msualg_1(A) ) => ! [B] : ( m1_instalg1(B,A) => ( v1_abcmiz_1(B) => ( v1_abcmiz_1(B) & v1_abcmiz_a(B) ) ) ) ) )).
fof(cc1_abian,axiom,( ! [A] : ( v2_setfam_1(A) => v1_zfmisc_1(A) ) )).
fof(cc1_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(A) ) => ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) ) ) )).
fof(cc1_afinsq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( v7_ordinal1(A) & v6_membered(A) ) ) )).
fof(cc1_afvect0,axiom,( ! [A] : ( l1_analoaf(A) => ( ( ~ v2_struct_0(A) & v2_tdgroup(A) ) => ( ~ v2_struct_0(A) & v1_afvect0(A) ) ) ) )).
fof(cc1_algspec1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( m2_algspec1(B,A) => ~ v2_struct_0(B) ) ) )).
fof(cc1_algstr_0,axiom,( ! [A] : ( l1_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ( v2_algstr_0(B,A) & v3_algstr_0(B,A) ) => v4_algstr_0(B,A) ) ) ) )).
fof(cc1_algstr_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_altcat_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_altcat_2,axiom,( ! [A] : ( l2_altcat_1(A) => ( ( ~ v2_struct_0(A) & v12_altcat_1(A) ) => ( ~ v2_struct_0(A) & v1_altcat_2(A) ) ) ) )).
fof(cc1_altcat_5,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) ) => ( v1_relat_1(A) & v4_relat_1(A,k1_xboole_0) ) ) )).
fof(cc1_ami_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( v7_ordinal1(A) & ~ v8_ordinal1(A) & ~ v1_setfam_1(A) ) ) )).
fof(cc1_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( 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) ) ) ) ) )).
fof(cc1_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(k4_amistd_1(A))) => v4_compos_0(B,u1_compos_1(k4_amistd_1(A))) ) ) )).
fof(cc1_amistd_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_compos_1(B)) => v1_amistd_2(C,A,B) ) ) )).
fof(cc1_amistd_5,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_compos_1(B)) => ( v1_amistd_5(C,A,B) => v3_amistd_2(C,A,B) ) ) ) )).
fof(cc1_analmetr,axiom,( ! [A] : ( l1_analmetr(A) => ( ( ~ v2_struct_0(A) & v3_analmetr(A) ) => ( ~ v2_struct_0(A) & v2_analmetr(A) ) ) ) )).
fof(cc1_anproj_2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_aofa_000,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,k4_ordinal1) & ~ v1_xboole_0(B) & v1_freealg(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_freealg(A,B))) => ( v1_relat_1(C) & v1_funct_1(C) ) ) ) )).
fof(cc1_aofa_a00,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( l1_aofa_a00(C,A) => ( v5_msafree4(C,A,B) => v4_msualg_1(C,A) ) ) ) )).
fof(cc1_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( 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) ) ) ) ) )).
fof(cc1_arrow,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k2_arrow(A)) => v1_relat_1(B) ) ) )).
fof(cc1_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ( v3_ordinal1(A) => ( v3_ordinal1(A) & v7_ordinal1(A) ) ) ) )).
fof(cc1_bcialg_1,axiom,( ! [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) ) => ( ~ v2_struct_0(A) & v3_bcialg_1(A) & v4_bcialg_1(A) & v5_bcialg_1(A) & v7_bcialg_1(A) & v13_bcialg_1(A) ) ) ) )).
fof(cc1_bcialg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m4_bcialg_2(C,A,B) => ( v1_partfun1(C,u1_struct_0(A)) & v3_relat_2(C) & v8_relat_2(C) ) ) ) )).
fof(cc1_bcialg_5,axiom,( ! [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) ) => ( ~ 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) ) ) ) )).
fof(cc1_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) => ( ( v1_funct_1(B) & v3_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) ) => ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_bhsp_2(B,A) ) ) ) ) )).
fof(cc1_binari_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v8_ordinal1(A) ) => ( v7_ordinal1(A) & ~ v2_xxreal_0(A) ) ) )).
fof(cc1_binom,axiom,( ! [A] : ( l2_algstr_0(A) => ( ( ~ v2_struct_0(A) & v6_algstr_0(A) & v2_rlvect_1(A) ) => ( ~ v2_struct_0(A) & v5_algstr_0(A) ) ) ) )).
fof(cc1_binop_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_binop_2,axiom,( ! [A] : ( m1_subset_1(A,k3_numbers) => v1_rat_1(A) ) )).
fof(cc1_bintree1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree1(A) ) => ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_trees_2(A) ) ) )).
fof(cc1_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree2(A) ) => ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree1(A) ) ) )).
fof(cc1_borsuk_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( m1_borsuk_2(D,A,B,C) => v5_pre_topc(D,k5_topmetr,A) ) ) )).
fof(cc1_borsuk_3,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_struct_0(A) & v2_pre_topc(A) ) => ( v2_pre_topc(A) & v1_compts_1(A) ) ) ) )).
fof(cc1_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal2(A) => ( ~ v1_zfmisc_1(A) & v1_topreal2(A) ) ) ) )).
fof(cc1_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k3_numbers) => v1_xreal_0(A) ) )).
fof(cc1_borsuk_6,axiom,( ! [A] : ( ( v3_topmetr(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v1_xreal_0(B) ) ) )).
fof(cc1_borsuk_7,axiom,( ! [A] : ( m1_subset_1(A,k1_borsuk_5) => ~ v1_rat_1(A) ) )).
fof(cc1_c0sp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_c0sp1(B,A) => ( v1_ideal_1(B,A) & v1_c0sp1(B,A) ) ) ) ) )).
fof(cc1_cantor_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) ) )).
fof(cc1_card_1,axiom,( ! [A] : ( v1_card_1(A) => v3_ordinal1(A) ) )).
fof(cc1_card_2,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ( v4_ordinal1(A) & v1_card_1(A) ) ) )).
fof(cc1_card_3,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) ) ) )).
fof(cc1_card_5,axiom,( ! [A] : ( ~ v1_finset_1(A) => ~ v1_xboole_0(A) ) )).
fof(cc1_card_fil,axiom,( ! [A] : ( ~ v1_finset_1(A) => ! [B] : ( m1_card_fil(B,A) => ( ( v1_card_fil(B,A) & v3_card_fil(B,A) ) => ~ v2_card_fil(B,A) ) ) ) )).
fof(cc1_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & ~ v1_finset_1(A) & v1_card_1(A) ) => ( v3_ordinal1(A) & v4_ordinal1(A) ) ) )).
fof(cc1_cat_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_cat_5,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_catalan2,axiom,( ! [A] : ! [B] : ( m1_catalan2(B,A) => ! [C] : ( m1_subset_1(C,B) => ( v5_relat_1(C,A) & v5_ordinal1(C) & v1_finset_1(C) ) ) ) )).
fof(cc1_catalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( v4_msualg_1(B,A) => ~ v1_catalg_1(B,A) ) ) ) )).
fof(cc1_cayldick,axiom,( ! [A] : ( l1_algstr_0(A) => ( ( ~ v2_struct_0(A) & v6_algstr_0(A) & v2_rlvect_1(A) ) => ( ~ v2_struct_0(A) & v5_algstr_0(A) & v2_rlvect_1(A) ) ) ) )).
fof(cc1_cayley,axiom,( ! [A] : ( v3_matrix_2(A) => v4_funct_1(A) ) )).
fof(cc1_cfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) => ( ( v1_funct_1(A) & v9_ordinal1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v1_cfdiff_1(A,k5_numbers) ) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) ) ) ) )).
fof(cc1_cgames_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m1_subset_1(B,k2_cgames_1(A)) => v2_cgames_1(B) ) ) )).
fof(cc1_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_chain_1(B,A) => v2_finset_1(B) ) ) )).
fof(cc1_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v4_glib_000(A) ) => ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_chord(A) ) ) )).
fof(cc1_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc1_circcomb,axiom,( ! [A] : ( l1_msualg_1(A) => ( ( ~ v2_struct_0(A) & v3_circcomb(A) ) => ( ~ v2_struct_0(A) & v5_circcomb(A) ) ) ) )).
fof(cc1_circtrm1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(k1_circtrm1(A,B,C))) => ( v1_relat_1(D) & v1_funct_1(D) & v1_finset_1(D) ) ) ) )).
fof(cc1_circuit1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(cc1_classes2,axiom,( ! [A] : ( v2_classes1(A) => v1_classes1(A) ) )).
fof(cc1_clopban1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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] : ( m1_subset_1(C,u1_struct_0(k9_clopban1(A,B))) => ( v1_relat_1(C) & v1_funct_1(C) ) ) ) )).
fof(cc1_clopban2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) => ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_clopban3(B,A) ) => ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v9_clvect_1(B,A) ) ) ) ) )).
fof(cc1_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m2_pboole(C,A,k5_mssubfam(A,B),k5_mssubfam(A,B)) => ( v4_closure1(C,A,B) => v2_closure1(C,A,B) ) ) ) )).
fof(cc1_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) => ( v2_closure2(C,A,B) => v1_closure2(C,A,B) ) ) ) )).
fof(cc1_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k3_coh_sp(A)) => ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) ) )).
fof(cc1_cohsp_1,axiom,( ! [A] : ( v1_cohsp_1(A) => ~ v1_xboole_0(A) ) )).
fof(cc1_compact1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v2_compact1(B,A) ) ) ) )).
fof(cc1_compl_sp,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v2_compl_sp(B,A) ) ) ) )).
fof(cc1_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => v1_xcmplx_0(A) ) )).
fof(cc1_compos_0,axiom,( ! [A] : ( v1_compos_0(A) => v1_relat_1(A) ) )).
fof(cc1_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_zfmisc_1(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) & v4_compos_1(B,A) ) ) ) )).
fof(cc1_compts_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v2_compts_1(B,A) ) ) ) )).
fof(cc1_comput_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_rfunct_3(C,A,B) => ( ~ v1_xboole_0(C) => ( ~ v1_xboole_0(C) & v4_funct_1(C) ) ) ) )).
fof(cc1_comseq_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) => ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) ) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v1_comseq_2(A) ) ) ) )).
fof(cc1_comseq_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) => ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v1_series_1(A) ) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_comseq_2(A) ) ) ) )).
fof(cc1_conlat_1,axiom,( ! [A] : ( ( v2_struct_0(A) & v11_struct_0(A) & l5_struct_0(A) ) => ! [B] : ( l2_conlat_1(B,A) => v4_conlat_1(B,A) ) ) )).
fof(cc1_connsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_connsp_1(B,A) => v2_connsp_1(B,A) ) ) ) )).
fof(cc1_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v1_convex4(B,A) ) ) ) )).
fof(cc1_descip_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k4_finseq_2(A,k6_margrel1)) => v1_margrel1(B) ) ) )).
fof(cc1_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_zfmisc_1(B) => v1_dilworth(B,A) ) ) ) )).
fof(cc1_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k6_dist_1(A)) => ~ v1_xboole_0(B) ) ) )).
fof(cc1_dtconstr,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_trees_3(B,A) ) => ! [C] : ( m1_finseq_1(C,B) => v6_trees_3(C) ) ) )).
fof(cc1_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_dynkin(B,A) => ~ v1_xboole_0(B) ) ) )).
fof(cc1_entropy1,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => ( v1_matrprob(A) => ( ~ v1_xboole_0(A) & v4_partfun3(A) ) ) ) )).
fof(cc1_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ~ v1_xboole_0(B) ) ) )).
fof(cc1_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_euclid(A)) => v3_card_1(B,A) ) ) )).
fof(cc1_euclid_7,axiom,( ! [A] : ( v1_xboole_0(A) => v1_euclid_7(A) ) )).
fof(cc1_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(A))) => v5_relat_1(B,k1_numbers) ) ) )).
fof(cc1_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_exchsort(A) ) ) )).
fof(cc1_facirc_1,axiom,( ! [A] : ( v1_xtuple_0(A) => ~ v1_xboole_0(A) ) )).
fof(cc1_facirc_2,axiom,( ! [A] : ( l1_msualg_1(A) => ( v11_struct_0(A) => ( v1_circcomb(A) & v2_circcomb(A) & v3_circcomb(A) ) ) ) )).
fof(cc1_fcont_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_fcont_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_xboole_0(A) => v2_rcomp_1(A) ) ) )).
fof(cc1_fdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) => ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v1_fdiff_1(A,k5_numbers) ) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_comseq_2(A) ) ) ) )).
fof(cc1_fib_num2,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_setfam_1(B) ) ) )).
fof(cc1_filter_0,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) ) => ( v1_relat_1(A) & v1_finseq_1(A) ) ) )).
fof(cc1_finseq_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) ) => ! [C] : ( m1_subset_1(C,k4_finseq_2(B,A)) => v3_card_1(C,B) ) ) )).
fof(cc1_finseq_4,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_eqrel_1(B,A) => v1_finset_1(B) ) ) )).
fof(cc1_finset_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_finset_1(A) ) )).
fof(cc1_finsub_1,axiom,( ! [A] : ( v4_finsub_1(A) => ( v1_finsub_1(A) & v3_finsub_1(A) ) ) )).
fof(cc1_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v4_fin_topo(B,A) ) ) ) )).
fof(cc1_fomodel0,axiom,( ! [A] : ( v1_xboole_0(A) => v2_setfam_1(A) ) )).
fof(cc1_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_fomodel1(A)) => ( v9_fomodel1(B,A) => v10_fomodel1(B,A) ) ) ) )).
fof(cc1_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_fomodel2(D,A,B,C) => v5_relat_1(D,B) ) ) )).
fof(cc1_fomodel3,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k8_eqrel_1(A,B)) => ~ v1_xboole_0(C) ) ) )).
fof(cc1_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_fomodel4(A))) => v2_fomodel4(B,A) ) ) )).
fof(cc1_frechet,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc1_funcop_1,axiom,( ! [A] : ( v4_funct_1(A) => ! [B] : ( ( 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) ) ) ) )).
fof(cc1_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_funct_1(A) ) )).
fof(cc1_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ( v1_partfun1(C,A) => v1_funct_2(C,A,B) ) ) )).
fof(cc1_funct_7,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) ) )).
fof(cc1_funct_8,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) ) => ( v1_relat_1(A) & v2_funct_8(A) ) ) )).
fof(cc1_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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] : ( m1_functor0(F,A,B,C,D,E) => v1_funcop_1(F) ) ) )).
fof(cc1_functor2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m2_functor0(C,A,B) => ( v8_functor0(C,A,B) & v12_functor0(C,A,B) ) ) ) )).
fof(cc1_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) => ( ( v5_relat_1(B,k1_rcomp_1(k5_numbers,1)) & v1_funct_1(B) & v1_funct_2(B,A,k1_numbers) ) => ( v5_relat_1(B,k1_rcomp_1(k5_numbers,1)) & v1_funct_1(B) & v1_funct_2(B,A,k1_numbers) & v3_valued_0(B) ) ) ) ) )).
fof(cc1_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) => ( ( v5_relat_1(B,k1_rcomp_1(k5_numbers,1)) & v1_funct_1(B) & v1_funct_2(B,A,k1_numbers) ) => ( v5_relat_1(B,k1_rcomp_1(k5_numbers,1)) & v1_funct_1(B) & v1_funct_2(B,A,k1_numbers) ) ) ) ) )).
fof(cc1_fvaluat1,axiom,( ! [A] : ( v1_fvaluat1(A) => v1_xxreal_0(A) ) )).
fof(cc1_fvsum_1,axiom,( ! [A] : ( l2_algstr_0(A) => ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & v4_rlvect_1(A) ) => ( ~ v2_struct_0(A) & v1_algstr_1(A) ) ) ) )).
fof(cc1_gcd_1,axiom,( ! [A] : ( l4_algstr_0(A) => ( ( ~ v2_struct_0(A) & v5_group_1(A) & v3_vectsp_1(A) ) => ( ~ v2_struct_0(A) & v6_vectsp_1(A) ) ) ) )).
fof(cc1_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v5_glib_000(A) ) => ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v6_glib_000(A) ) ) )).
fof(cc1_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v5_glib_001(B,A) => v4_glib_001(B,A) ) ) ) )).
fof(cc1_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v4_glib_000(A) ) => ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_002(A) ) ) )).
fof(cc1_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) ) )).
fof(cc1_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v8_glib_003(A) ) ) )).
fof(cc1_goedcpuc,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ( v1_henmodel(B,A) => v1_goedcpuc(B,A) ) ) ) )).
fof(cc1_gr_cy_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_gr_cy_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_gr_cy_1(A))) => v7_ordinal1(B) ) ) )).
fof(cc1_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => ( v1_xboole_0(B) => v7_graph_1(B,A) ) ) ) )).
fof(cc1_graph_2,axiom,( ! [A] : ! [B] : ( m1_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => v2_finseq_1(C) ) ) )).
fof(cc1_grfunc_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( 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) ) ) ) )).
fof(cc1_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & v1_grnilp_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => v1_grnilp_1(B) ) ) )).
fof(cc1_group_1,axiom,( ! [A] : ( l3_algstr_0(A) => ( v2_group_1(A) => v1_group_1(A) ) ) )).
fof(cc1_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => v3_group_1(B) ) ) )).
fof(cc1_group_6,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(cc1_group_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_group_7(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_pralg_1(A) ) ) )).
fof(cc1_groupp_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(B)) => v1_groupp_1(C,A,B) ) ) )).
fof(cc1_hahnban,axiom,( ! [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) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc1_hahnban1,axiom,( ! [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) & 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] : ( 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) ) ) ) ) )).
fof(cc1_hallmar1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_finseq_1(B,k1_zfmisc_1(A)) => ( ( ~ v1_xboole_0(B) & v1_hallmar1(B,A) ) => ( v2_relat_1(B) & ~ v1_xboole_0(B) ) ) ) ) )).
fof(cc1_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ~ v1_xboole_0(B) ) ) )).
fof(cc1_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(cc1_hilbert1,axiom,( ! [A] : ( v5_hilbert1(A) => ( ~ v1_xboole_0(A) & v1_hilbert1(A) & v2_hilbert1(A) & v3_hilbert1(A) & v4_hilbert1(A) ) ) )).
fof(cc1_hilbert3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & m1_subset_1(B,k1_hilbert1) & m1_subset_1(C,k1_hilbert1) & m1_subset_1(D,k1_hilbert1) ) => ! [E] : ( m1_subset_1(E,k3_hilbert3(A,k3_hilbert1(B,k3_hilbert1(C,D)))) => v1_funcop_1(E) ) ) )).
fof(cc1_idea_1,axiom,( ! [A] : ( m1_subset_1(A,k14_idea_1) => v1_finseq_1(A) ) )).
fof(cc1_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc1_incsp_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_index_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(cc1_instalg1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,k3_msualg_1(A,C,k11_msafree(A,B))) => v6_trees_3(D) ) ) )).
fof(cc1_int_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => v1_int_1(A) ) )).
fof(cc1_int_3,axiom,( ! [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) & 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) ) ) ) )).
fof(cc1_int_6,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc1_integra1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v2_measure5(A) => v1_rcomp_1(A) ) ) )).
fof(cc1_intpro_1,axiom,( ! [A] : ( 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) ) ) )).
fof(cc1_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(B,A) => v1_isomichi(B,A) ) ) ) )).
fof(cc1_jordan,axiom,( ! [A] : ( 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) ) ) )).
fof(cc1_jordan1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) ) )).
fof(cc1_jordan12,axiom,( ! [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v3_topreal1(A) => v1_goboard5(A) ) ) )).
fof(cc1_jordan1h,axiom,( ! [A] : ( m1_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) => ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) ) => ( v2_relat_1(A) & ~ v3_relat_1(A) & ~ v1_xboole_0(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) ) ) ) )).
fof(cc1_jordan21,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_jordan21(A) => ~ v1_xboole_0(A) ) ) )).
fof(cc1_jordan23,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc1_jordan2b,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => v5_relat_1(B,k1_numbers) ) ) )).
fof(cc1_jordan2c,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( 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)) ) ) ) )).
fof(cc1_jordan5a,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_finset_1(A) => v1_rcomp_1(A) ) ) )).
fof(cc1_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_jordan_a(B,A) => ~ v1_zfmisc_1(B) ) ) )).
fof(cc1_knaster,axiom,( ! [A] : ( l3_lattices(A) => ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) ) => ( ~ v2_struct_0(A) & v10_lattices(A) & v15_lattices(A) ) ) ) )).
fof(cc1_kurato_0,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) => ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) ) => ( ~ v1_xboole_0(B) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) ) ) ) )).
fof(cc1_lattice2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_lattice3(A) => ~ v2_struct_0(A) ) ) )).
fof(cc1_lattice6,axiom,( ! [A] : ( l3_lattices(A) => ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v10_lattices(A) ) => ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) ) ) ) )).
fof(cc1_lattices,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & v13_glib_000(A) & v2_lexbfs(A) ) => ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & v3_lexbfs(A) ) ) )).
fof(cc1_lfuzzy_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_lfuzzy_0(A) => ( ~ v2_struct_0(A) & v1_lfuzzy_0(A) ) ) ) )).
fof(cc1_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) => ( ( v5_relat_1(B,k1_rcomp_1(k5_numbers,1)) & v1_funct_1(B) & v1_funct_2(B,A,k1_numbers) ) => ( v5_relat_1(B,k1_rcomp_1(k5_numbers,1)) & v1_funct_1(B) & v1_funct_2(B,A,k1_numbers) & v3_valued_0(B) ) ) ) ) )).
fof(cc1_lopban_1,axiom,( ! [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) & 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] : ( m1_subset_1(C,u1_struct_0(k11_lopban_1(A,B))) => ( v1_relat_1(C) & v1_funct_1(C) ) ) ) )).
fof(cc1_lopban_2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) => ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_lopban_3(B,A) ) => ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v3_normsp_1(B,A) ) ) ) ) )).
fof(cc1_lpspacc1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_membered(B) ) => ! [C] : ( m1_subset_1(C,k3_rfunct_3(A,B)) => v1_valued_0(C) ) ) )).
fof(cc1_lpspace2,axiom,( ! [A] : ( ( v1_xreal_0(A) & v1_lpspace2(A) ) => ( v2_xxreal_0(A) & v1_xreal_0(A) ) ) )).
fof(cc1_ltlaxio4,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) ) => ! [B] : ( m1_subset_1(B,k4_ltlaxio4(A)) => v3_ltlaxio3(B) ) ) )).
fof(cc1_margrel1,axiom,( ! [A] : ( v1_xboole_0(A) => v2_card_3(A) ) )).
fof(cc1_matrix13,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k6_prvect_1(A,B))) => ( v1_relat_1(C) & v1_funct_1(C) ) ) ) )).
fof(cc1_matrix_0,axiom,( ! [A] : ! [B] : ( m1_finseq_1(B,k3_finseq_2(A)) => ( v1_matrix_0(B) => ( v1_funcop_1(B) & v1_matrix_0(B) ) ) ) )).
fof(cc1_matrix_2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) => ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & v1_matrix_1(C,B) ) => ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & v1_matrix_1(C,B) & v1_matrix_2(C,A,B) & v2_matrix_2(C,A,B) ) ) ) ) )).
fof(cc1_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_finseq_1(B,k3_finseq_2(k3_finseq_2(A))) => ( v2_matrixj1(B,A) => v1_matrixj1(B,A) ) ) ) )).
fof(cc1_matrixj2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(cc1_matrlin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_finseq_1(B,k3_finseq_2(A)) => ( v1_matrix_0(B) => ( v1_matrix_0(B) & v1_pre_poly(B) ) ) ) ) )).
fof(cc1_matroid0,axiom,( ! [A] : ( ( ~ v3_pencil_1(A) & v1_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v3_pre_topc(B,A) ) ) ) )).
fof(cc1_matrprob,axiom,( ! [A] : ( m1_finseq_1(A,k3_finseq_2(k1_numbers)) => ( ( v1_matrix_0(A) & v4_matrprob(A) ) => ( v1_matrix_0(A) & v2_matrprob(A) & v3_matrprob(A) ) ) ) )).
fof(cc1_matrtop3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( 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) ) ) ) )).
fof(cc1_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) ) => ! [D] : ( m1_subset_1(D,k3_zfmisc_1(A,B,C)) => v2_xtuple_0(D) ) ) )).
fof(cc1_measure1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( ( v1_finsub_1(B) & v1_prob_1(B,A) ) => v2_finsub_1(B) ) ) )).
fof(cc1_measure5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_measure5(A) => v6_xxreal_2(A) ) ) )).
fof(cc1_measure6,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(cc1_membered,axiom,( ! [A] : ( v6_membered(A) => v5_membered(A) ) )).
fof(cc1_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ~ v1_xboole_0(A) ) )).
fof(cc1_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) => ( ( v1_funct_1(B) & v6_supinf_2(B) ) => ( v1_funct_1(B) & v3_mesfunc5(B) ) ) ) ) )).
fof(cc1_metric_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_metric_2(B,A) => ~ v1_xboole_0(B) ) ) )).
fof(cc1_metrizts,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_struct_0(A) & v2_pre_topc(A) ) => ( v2_pre_topc(A) & v3_pcomps_1(A) ) ) ) )).
fof(cc1_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) ) )).
fof(cc1_midsp_2,axiom,( ! [A] : ( l2_algstr_0(A) => ( ( ~ v2_struct_0(A) & v2_midsp_2(A) ) => ( ~ v2_struct_0(A) & v12_vectsp_1(A) ) ) ) )).
fof(cc1_mmlquer2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( ( v6_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A) ) => v1_mmlquer2(B,A) ) ) )).
fof(cc1_mod_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) & ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc1_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k6_modal_1) => v1_finset_1(A) ) )).
fof(cc1_modcat_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k4_modcat_1(B,k3_modcat_1(A,B))) => v2_mod_2(C,B) ) ) )).
fof(cc1_moebius1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v1_int_2(A) => ~ v1_moebius1(A) ) ) )).
fof(cc1_monoid_0,axiom,( ! [A] : ( ( v1_monoid_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) )).
fof(cc1_msafree1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(cc1_msafree2,axiom,( ! [A] : ( l1_msualg_1(A) => ( ( ~ v2_struct_0(A) & v11_struct_0(A) ) => ( ~ v2_struct_0(A) & v2_msafree2(A) ) ) ) )).
fof(cc1_msafree3,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k3_card_3(u3_msualg_1(A,k1_msafree3(A,B)))) => ( v1_relat_1(C) & v1_funct_1(C) ) ) ) )).
fof(cc1_msafree4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,k1_msaterm(A,B)) & v1_funct_1(C) ) => ( v1_relat_1(C) & v5_relat_1(C,k1_msaterm(A,B)) & v1_funct_1(C) & v2_finset_1(C) ) ) ) )).
fof(cc1_msaterm,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_msaterm(A,B)) => v1_finset_1(C) ) ) )).
fof(cc1_msscyc_1,axiom,( ! [A] : ( l1_graph_1(A) => ( ( ~ v2_struct_0(A) & v11_struct_0(A) ) => ( ~ v2_struct_0(A) & v2_msscyc_1(A) ) ) ) )).
fof(cc1_mssubfam,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(cc1_msualg_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k10_xtuple_0(u3_msualg_1(A,B))) => ~ v1_xboole_0(C) ) ) )).
fof(cc1_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( m1_msualg_4(D,A,B,C) => v2_funcop_1(D) ) ) )).
fof(cc1_msualg_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(cc1_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( v4_msualg_1(B,A) => v1_msualg_6(B,A) ) ) ) )).
fof(cc1_msualg_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m2_nat_lat(B,A) => ( v1_msualg_7(B,A) => v4_lattice3(B) ) ) ) )).
fof(cc1_msualg_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,k3_msualg_1(A,C,B)) => v1_finseq_1(D) ) ) )).
fof(cc1_mycielsk,axiom,( ! [A] : ( l1_orders_2(A) => ( v8_struct_0(A) => v1_mycielsk(A) ) ) )).
fof(cc1_nagata_1,axiom,( ! [A] : ( ~ v4_card_3(A) => ~ v1_xboole_0(A) ) )).
fof(cc1_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( v3_ordinal1(A) & v7_ordinal1(A) ) ) )).
fof(cc1_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ( v7_ordinal1(A) & ~ v8_ordinal1(A) & v1_int_2(A) ) ) )).
fof(cc1_nattra_1,axiom,( ! [A] : ( 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) & v4_nattra_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) & v2_nattra_1(A) & v3_nattra_1(A) ) ) ) )).
fof(cc1_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_prvect_2(A))) => v3_card_1(B,k3_finseq_1(A)) ) ) )).
fof(cc1_neckla_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k4_classes1(A)) => v1_finset_1(B) ) ) )).
fof(cc1_neckla_3,axiom,( ! [A] : ! [B] : ( ( v1_zfmisc_1(A) & v1_zfmisc_1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_zfmisc_1(C) ) ) )).
fof(cc1_necklace,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_zfmisc_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) )).
fof(cc1_nfcont_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc1_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( 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) ) ) ) ) )).
fof(cc1_openlatt,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_oposet_1,axiom,( ! [A] : ( l2_qmax_1(A) => ( ( ~ v2_struct_0(A) & v4_oposet_1(A) ) => ( ~ v2_struct_0(A) & v3_oposet_1(A) ) ) ) )).
fof(cc1_ordeq_01,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ( ( v1_funct_1(B) & v3_funct_1(B) & v1_funct_2(B,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) ) ) ) ) )).
fof(cc1_orders_1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_orders_2(A) => v2_orders_2(A) ) ) )).
fof(cc1_orders_3,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_struct_0(A) => v1_orders_3(A) ) ) )).
fof(cc1_orders_4,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_struct_0(A) => ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) ) ) ) )).
fof(cc1_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => ( v1_ordinal1(A) & v2_ordinal1(A) ) ) )).
fof(cc1_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v5_ordinal1(B) & v1_funct_1(B) ) => ( v1_relat_1(B) & v5_relat_1(B,A) & v5_ordinal1(B) & v1_funct_1(B) & v1_ordinal2(B) ) ) ) )).
fof(cc1_ordinal4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc1_ordinal5,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(A) & v1_ordinal2(A) ) ) )).
fof(cc1_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => v1_ordinal6(A) ) )).
fof(cc1_osalg_1,axiom,( ! [A] : ( l3_osalg_1(A) => ( v4_osalg_1(A) => ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) ) ) ) )).
fof(cc1_osalg_3,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_msualg_2(C,A,B) => ( v12_osalg_1(C,A) => ( v12_osalg_1(C,A) & v13_osalg_1(C,A) ) ) ) ) )).
fof(cc1_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_msualg_4(D,u1_struct_0(A),B,C) => ( v1_osalg_4(D,A,B,C) => v11_osalg_1(D,A) ) ) ) )).
fof(cc1_partfun1,axiom,( ! [A] : ! [B] : ( v1_xboole_0(A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_partfun1(C,A) ) ) )).
fof(cc1_partfun3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_partfun3(A) ) => ( v1_relat_1(A) & v2_relat_1(A) & v4_partfun3(A) ) ) )).
fof(cc1_partit_2,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) ) => ( v1_relat_1(A) & v2_relat_2(A) & v5_relat_2(A) & v8_relat_2(A) ) ) )).
fof(cc1_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(cc1_pcs_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_struct_0(A) => v2_orders_2(A) ) ) )).
fof(cc1_pdiff_3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_pdiff_6,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc1_pencil_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v11_pencil_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_pralg_1(A) ) ) )).
fof(cc1_polynom1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_polynom4,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_polynom8,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_poset_1,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_poset_1(A) => v1_yellow_0(A) ) ) )).
fof(cc1_pralg_2,axiom,( ! [A] : ( ( v4_funct_1(A) & ~ v1_xboole_0(A) & v2_card_3(A) ) => ! [B] : ( m1_subset_1(B,A) => v4_relat_1(B,k9_card_3(A)) ) ) )).
fof(cc1_pre_circ,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k5_trees_3(A)) => v1_finset_1(B) ) ) )).
fof(cc1_pre_poly,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k3_finseq_2(A)) => v1_finseq_1(B) ) )).
fof(cc1_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => v2_pre_topc(B) ) ) )).
fof(cc1_prob_1,axiom,( ! [A] : ! [B] : ( 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) ) ) ) )).
fof(cc1_projdes1,axiom,( ! [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) ) => ( ~ 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) ) ) ) )).
fof(cc1_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) ) => ! [B] : ( m1_prvect_1(B,A) => v1_finseq_1(B) ) ) )).
fof(cc1_prvect_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) ) => ! [C] : ( m1_prvect_2(C,A,B) => v1_finseq_1(C) ) ) )).
fof(cc1_pscomp_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_pua2mss1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( m1_finseq_1(B,A) => v2_relat_1(B) ) ) )).
fof(cc1_pythtrip,axiom,( ! [A] : ( v1_pythtrip(A) => v7_ordinal1(A) ) )).
fof(cc1_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ( v1_relat_1(A) & ~ v1_xboole_0(A) ) ) )).
fof(cc1_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ( v1_henmodel(B,A) => v2_qc_trans(B,A,A) ) ) ) )).
fof(cc1_quantal1,axiom,( ! [A] : ( l3_algstr_0(A) => ( ( ~ v2_struct_0(A) & v6_quantal1(A) ) => ( ~ v2_struct_0(A) & v4_quantal1(A) & v5_quantal1(A) ) ) ) )).
fof(cc1_quatern2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k14_quatern2)) => v1_quaterni(A) ) )).
fof(cc1_quaterni,axiom,( ! [A] : ( m1_subset_1(A,k1_quaterni) => v1_quaterni(A) ) )).
fof(cc1_quofield,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => v1_xreal_0(A) ) )).
fof(cc1_ratfunc1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_rcomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_rcomp_1(A) => v2_rcomp_1(A) ) ) )).
fof(cc1_rcomp_3,axiom,( ! [A] : ( m1_topmetr(A,k7_metric_1) => v3_topmetr(A) ) )).
fof(cc1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => v1_xreal_0(A) ) )).
fof(cc1_realset2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_relat_1(A) ) )).
fof(cc1_relat_2,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc1_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_relat_1(C) ) )).
fof(cc1_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( m1_rewrite1(B,A) => ~ v1_xboole_0(B) ) ) )).
fof(cc1_rewrite2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_rewrite2(A) ) ) )).
fof(cc1_rfunct_1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc1_rfunct_2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_rfunct_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v3_membered(B) ) => ! [C] : ( m1_subset_1(C,k3_rfunct_3(A,B)) => v3_valued_0(C) ) ) )).
fof(cc1_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc1_ringcat1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) & ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc1_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v1_rlaffin1(B,A) ) ) ) )).
fof(cc1_rlaffin3,axiom,( ! [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_rlvect_5(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_rlaffin1(B,A) => ( v1_finset_1(B) & v1_rlaffin1(B,A) ) ) ) ) )).
fof(cc1_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v3_rltopsp1(B,A) ) ) ) )).
fof(cc1_rlvect_1,axiom,( ! [A] : ( l2_algstr_0(A) => ( ( ~ v2_struct_0(A) & v9_rlvect_1(A) ) => ( ~ v2_struct_0(A) & v4_rlvect_1(A) ) ) ) )).
fof(cc1_rlvect_5,axiom,( ! [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_rlvect_5(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_rlsub_1(B,A) => v1_rlvect_5(B) ) ) )).
fof(cc1_robbins1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_robbins2,axiom,( ! [A] : ( l2_robbins1(A) => ( ( ~ v2_struct_0(A) & v1_robbins2(A) ) => ( ~ v2_struct_0(A) & v4_lattices(A) ) ) ) )).
fof(cc1_robbins3,axiom,( ! [A] : ( l3_lattices(A) => ( ( ~ v2_struct_0(A) & v10_lattices(A) ) => ( ~ v2_struct_0(A) & v1_robbins3(A) & v2_robbins3(A) & v3_robbins3(A) ) ) ) )).
fof(cc1_robbins4,axiom,( ! [A] : ( l4_robbins1(A) => ( v13_struct_0(A,1) => ( v13_struct_0(A,1) & v3_robbins3(A) ) ) ) )).
fof(cc1_rpr_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v3_card_1(B,1) => ( v1_finset_1(B) & v3_card_1(B,1) ) ) ) ) )).
fof(cc1_rusub_4,axiom,( ! [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_bhsp_1(A) & v1_rusub_4(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => v1_rusub_4(B) ) ) )).
fof(cc1_rvsum_1,axiom,( ! [A] : ( m1_finseq_1(A,k2_numbers) => v1_valued_0(A) ) )).
fof(cc1_scm_halt,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) ) )).
fof(cc1_scmfsa6b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(cc1_scmfsa7b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) & v1_scmfsa7b(A) ) => ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) ) )).
fof(cc1_scmpds_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) & v2_scmpds_4(A) ) => ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) & v1_scmpds_4(A) ) ) )).
fof(cc1_scmyciel,axiom,( ! [A] : ( v1_scmyciel(A) => v1_finset_1(A) ) )).
fof(cc1_seq_2,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc1_seq_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) => ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v7_valued_0(A) & v1_seq_2(A) ) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_comseq_2(A) ) ) ) )).
fof(cc1_seqm_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) => ( ( v1_funct_1(A) & v3_funct_1(A) ) => ( v1_funct_1(A) & v7_valued_0(A) & v8_valued_0(A) ) ) ) )).
fof(cc1_series_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) => ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_series_1(A) ) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v1_series_1(A) ) ) ) )).
fof(cc1_setfam_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) => ! [B] : ( m1_subset_1(B,A) => ~ v1_xboole_0(B) ) ) )).
fof(cc1_sheffer1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_sheffer2,axiom,( ! [A] : ( l1_sheffer1(A) => ( ( ~ v2_struct_0(A) & v7_struct_0(A) ) => ( ~ v2_struct_0(A) & v1_sheffer2(A) ) ) ) )).
fof(cc1_simplex0,axiom,( ! [A] : ( v1_xboole_0(A) => v1_classes1(A) ) )).
fof(cc1_simplex1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) & ~ v4_simplex0(B) & m1_simplex0(B,u1_struct_0(A)) ) => ! [C] : ( m1_simplex1(C,A,B) => ~ v4_simplex0(C) ) ) )).
fof(cc1_simplex2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_finset_1(B) => v6_tbsp_1(B,A) ) ) ) )).
fof(cc1_sppol_1,axiom,( ! [A] : ( 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) ) ) )).
fof(cc1_sppol_2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_sprect_1,axiom,( ! [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v1_sprect_1(A) => ~ v3_funct_1(A) ) ) )).
fof(cc1_sprect_3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_stacks_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u4_struct_0(k8_stacks_1(A))) => v1_finseq_1(B) ) ) )).
fof(cc1_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k7_card_1(A)) => v7_ordinal1(B) ) ) )).
fof(cc1_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => ( v2_struct_0(A) => v7_struct_0(A) ) ) )).
fof(cc1_subset_1,axiom,( ! [A] : ( v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_xboole_0(B) ) ) )).
fof(cc1_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_substlat(A,B)) => v1_finset_1(C) ) )).
fof(cc1_supinf_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k6_numbers)) => ! [C] : ( 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) ) ) ) ) )).
fof(cc1_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) => ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v2_tbsp_1(B,A) ) => ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v3_tbsp_1(B,A) ) ) ) ) )).
fof(cc1_tdlat_3,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_tdlat_3(A) => v2_pre_topc(A) ) ) )).
fof(cc1_termord,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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) ) ) ) ) )).
fof(cc1_tex_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_tex_2,axiom,( ! [A] : ( v3_card_1(A,1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_subset_1(B,A) => v1_xboole_0(B) ) ) ) )).
fof(cc1_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( v1_borsuk_1(B,A) & v1_tex_3(B,A) ) => ~ v1_tex_2(B,A) ) ) ) )).
fof(cc1_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v4_tex_4(B,A) => v2_tdlat_3(B) ) ) ) )).
fof(cc1_toler_1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc1_topalg_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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] : ( 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)) ) ) )).
fof(cc1_topalg_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_pre_topc(B,k15_euclid(A)) => ( ( ~ v2_struct_0(B) & v1_topalg_2(B,A) ) => ( ~ v2_struct_0(B) & v1_borsuk_2(B) ) ) ) ) )).
fof(cc1_topalg_3,axiom,( ! [A] : ( l1_pre_topc(A) => ( v2_struct_0(A) => v1_connsp_1(A) ) ) )).
fof(cc1_topalg_6,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc1_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_finset_1(B) => v1_topdim_1(B,A) ) ) ) )).
fof(cc1_topdim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v1_finset_1(B) => v1_topdim_2(B,A) ) ) )).
fof(cc1_topgen_1,axiom,( ! [A] : ( l1_struct_0(A) => ( v8_struct_0(A) => v1_orders_4(A) ) ) )).
fof(cc1_topgen_2,axiom,( ! [A] : ( l1_pre_topc(A) => ( v8_struct_0(A) => v1_topgen_2(A) ) ) )).
fof(cc1_topgen_4,axiom,( ! [A] : ( l1_pre_topc(A) => ( v8_struct_0(A) => v5_waybel23(A) ) ) )).
fof(cc1_topgen_5,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_pre_topc(A) & v1_topgen_5(A) ) => ( v2_pre_topc(A) & v9_pre_topc(A) ) ) ) )).
fof(cc1_topgrp_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( m1_connsp_2(C,A,B) => ~ v1_xboole_0(C) ) ) )).
fof(cc1_topmetr,axiom,( ! [A] : ( ( v3_topmetr(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => v3_topmetr(B) ) ) )).
fof(cc1_topreal1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v5_topreal1(A) => ~ v1_xboole_0(A) ) ) )).
fof(cc1_topreal2,axiom,( ! [A] : ( 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)) ) ) ) )).
fof(cc1_topreal5,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_topreal6,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v2_connsp_1(B,A) ) ) ) )).
fof(cc1_topreala,axiom,( ! [A] : ( ( v2_pre_topc(A) & v2_monoid_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => v2_monoid_0(B) ) ) )).
fof(cc1_toprealb,axiom,( ! [A] : ( m1_pre_topc(A,k15_euclid(2)) => ( v1_toprealb(A) => ( ~ v2_struct_0(A) & v1_compts_1(A) & v1_borsuk_2(A) ) ) ) )).
fof(cc1_toprealc,axiom,( ! [A] : ( l1_struct_0(A) => ( v2_toprealc(A) => v1_toprealc(A) ) ) )).
fof(cc1_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v3_pre_topc(B,A) ) ) ) )).
fof(cc1_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ! [B] : ( m4_trees_1(B,A) => v1_finset_1(B) ) ) )).
fof(cc1_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_2(B,A) => ( v2_trees_2(B,A) => ~ v1_xboole_0(B) ) ) ) )).
fof(cc1_trees_3,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_trees_3(A) & v2_trees_3(A) & v3_trees_3(A) ) ) )).
fof(cc1_trees_4,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_finseq_1(C,B) => v6_trees_3(C) ) ) )).
fof(cc1_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_trees_2(A) ) ) )).
fof(cc1_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v2_struct_0(A) & v7_struct_0(A) ) => ( ~ v2_struct_0(A) & v6_pre_topc(A) ) ) ) )).
fof(cc1_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) ) => ( ~ v2_struct_0(B) & v6_pre_topc(B) ) ) ) ) )).
fof(cc1_unialg_3,axiom,( ! [A] : ( ( ~ 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] : ( m1_unialg_2(B,A) => v2_unialg_2(B) ) ) )).
fof(cc1_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_valued_0(A) ) => ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) ) ) )).
fof(cc1_valued_2,axiom,( ! [A] : ( v6_valued_2(A) => v5_valued_2(A) ) )).
fof(cc1_vectsp10,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(cc1_vectsp_1,axiom,( ! [A] : ( l6_algstr_0(A) => ( ( ~ v2_struct_0(A) & v5_vectsp_1(A) ) => ( ~ v2_struct_0(A) & v1_vectsp_1(A) & v2_vectsp_1(A) ) ) ) )).
fof(cc1_vectsp_2,axiom,( ! [A] : ( l4_algstr_0(A) => ( ( ~ v2_struct_0(A) & v5_group_1(A) & v6_vectsp_1(A) ) => ( ~ v2_struct_0(A) & v4_vectsp_1(A) ) ) ) )).
fof(cc1_vectsp_7,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v1_xboole_0(C) => v1_vectsp_7(C,A,B) ) ) ) )).
fof(cc1_vectsp_9,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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] : ( m1_vectsp_4(C,A,B) => v1_matrlin(C,A) ) ) )).
fof(cc1_waybel10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc1_waybel11,axiom,( ! [A] : ( ( v8_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => v1_finset_1(B) ) ) )).
fof(cc1_waybel12,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(cc1_waybel13,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(cc1_waybel15,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_waybel15(B,A) => v6_waybel_6(B,A) ) ) ) )).
fof(cc1_waybel17,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(cc1_waybel18,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_waybel18(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_pralg_1(A) ) ) )).
fof(cc1_waybel19,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_waybel21,axiom,( ! [A] : ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(cc1_waybel22,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(k8_waybel_0(A)))) => ~ v1_xboole_0(B) ) ) )).
fof(cc1_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_waybel23(B,A) => v1_waybel23(B,A) ) ) ) )).
fof(cc1_waybel24,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc1_waybel25,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_waybel26,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(A,B)))) => v1_relat_1(C) ) ) )).
fof(cc1_waybel27,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc1_waybel29,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_waybel30,axiom,( ! [A] : ( ( v13_struct_0(A,1) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => v7_struct_0(B) ) ) )).
fof(cc1_waybel31,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_waybel32,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_waybel33,axiom,( ! [A] : ( l1_waybel_9(A) => ( ( ~ v2_struct_0(A) & v1_waybel33(A) ) => ( ~ v2_struct_0(A) & v2_pre_topc(A) ) ) ) )).
fof(cc1_waybel34,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc1_waybel35,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc1_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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) ) ) ) ) )).
fof(cc1_waybel_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(cc1_waybel_2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v16_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_waybel_0(B,A) & v2_waybel_0(B,A) ) ) ) )).
fof(cc1_waybel_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc1_waybel_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m2_pboole(D,A,C,k7_funcop_1(A,B)) => v2_relat_1(D) ) ) )).
fof(cc1_waybel_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc1_waybel_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc1_waybel_8,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v8_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v2_struct_0(B) => ( ~ v2_struct_0(B) & v8_pre_topc(B) ) ) ) ) )).
fof(cc1_wellord1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc1_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => v7_ordinal1(A) ) )).
fof(cc1_xcmplx_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => v1_xcmplx_0(A) ) )).
fof(cc1_xreal_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => v1_xreal_0(A) ) )).
fof(cc1_xreal_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => v1_xxreal_0(A) ) )).
fof(cc1_xtuple_0,axiom,( ! [A] : ( v2_xtuple_0(A) => v1_xtuple_0(A) ) )).
fof(cc1_xxreal_0,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => v1_xxreal_0(A) ) )).
fof(cc1_xxreal_3,axiom,( ! [A] : ( ( v1_xxreal_0(A) & ~ v3_xxreal_0(A) & ~ v1_xreal_0(A) ) => ( v1_xxreal_0(A) & v2_xxreal_0(A) ) ) )).
fof(cc1_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v1_waybel_6(B,A) ) ) ) )).
fof(cc1_yellow11,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_yellow12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc1_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v7_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_finset_1(B) => v4_pre_topc(B,A) ) ) ) )).
fof(cc1_yellow14,axiom,( ! [A] : ( ( v1_monoid_0(A) & l1_struct_0(A) ) => ! [B] : ( l1_waybel_0(B,A) => v1_yellow14(B,A) ) ) )).
fof(cc1_yellow15,axiom,( ! [A] : ( m1_finseq_1(A,k6_margrel1) => v1_margrel1(A) ) )).
fof(cc1_yellow16,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_yellow16(A) ) => ( v1_relat_1(A) & v1_yellow_1(A) & v5_waybel_3(A) ) ) )).
fof(cc1_yellow18,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_yellow19,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) & ~ v2_struct_0(B) & v3_orders_2(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_yellow19(C,A,B) => ~ v1_xboole_0(C) ) ) )).
fof(cc1_yellow21,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v2_struct_0(A) & v3_lattice3(A) ) => ( ~ v2_struct_0(A) & v1_lattice3(A) & v2_lattice3(A) ) ) ) )).
fof(cc1_yellow_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_yellow_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_pralg_1(A) ) ) )).
fof(cc1_yellow_2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc1_yellow_3,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_struct_0(A) => v1_yellow_3(A) ) ) )).
fof(cc1_yellow_6,axiom,( ! [A] : ! [B] : ( l1_struct_0(B) => ! [C] : ( m3_yellow_6(C,A,B) => v1_yellow_1(C) ) ) )).
fof(cc1_yellow_7,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v2_struct_0(A) & v1_waybel_5(A) ) => ( ~ v2_struct_0(A) & v3_lattice3(A) ) ) ) )).
fof(cc1_yellow_8,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_yellow_8(B,A) => ~ v1_xboole_0(B) ) ) ) )).
fof(cc1_yellow_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => ~ v2_struct_0(B) ) ) )).
fof(cc1_zfmisc_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_zfmisc_1(A) ) )).
fof(cc1_zmodul03,axiom,( ! [A] : ( l1_zmodul01(A) => ( ( ~ 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) & v1_zmodul03(A) ) => ( ~ 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) & v6_zmodul01(A) & v1_zmodul03(A) ) ) ) )).
fof(cc20_algstr_0,axiom,( ! [A] : ( l4_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v25_algstr_0(B,A) => ( v23_algstr_0(B,A) & v24_algstr_0(B,A) ) ) ) ) )).
fof(cc20_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_relat_2(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_partit_2(A) ) ) )).
fof(cc20_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k32_fomodel1(A)) => v15_fomodel1(B,A) ) ) )).
fof(cc20_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( m1_subset_1(D,k1_fomodel1(C)) => ( ~ v7_fomodel2(D,k13_fomodel0(B,A),C) => ~ v7_fomodel2(D,k3_xboole_0(A,B),C) ) ) ) )).
fof(cc20_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v2_membered(B) ) ) )).
fof(cc20_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_monoid_0(A) & l3_algstr_0(A) ) => ! [B] : ( m2_monoid_0(B,A) => ( ~ v2_struct_0(B) => ( ~ v2_struct_0(B) & v1_monoid_0(B) ) ) ) ) )).
fof(cc20_ordinal1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => v10_ordinal1(A) ) )).
fof(cc20_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_lattices(A) & l4_robbins1(A) ) => ! [B] : ( m3_robbins3(B,A) => v8_lattices(B) ) ) )).
fof(cc20_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v2_tdlat_3(B) => v3_tdlat_3(B) ) ) ) )).
fof(cc20_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( v3_tex_3(B,A) & ~ v4_tex_3(B,A) ) => ~ v1_borsuk_1(B,A) ) ) ) )).
fof(cc20_valued_0,axiom,( ! [A] : ! [B] : ( v5_membered(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v5_relat_1(C,k4_numbers) ) ) )).
fof(cc20_valued_2,axiom,( ! [A] : ( v6_valued_2(A) => ! [B] : ( m1_subset_1(B,A) => v4_valued_0(B) ) ) )).
fof(cc21_algstr_0,axiom,( ! [A] : ( l4_algstr_0(A) => ( ( v26_algstr_0(A) & v27_algstr_0(A) ) => v28_algstr_0(A) ) ) )).
fof(cc21_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) ) => ! [B] : ( m1_subset_1(B,A) => v1_xtuple_0(B) ) ) )).
fof(cc21_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k35_fomodel1(A)) => v13_fomodel1(B,A) ) ) )).
fof(cc21_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(A) & ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( 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) ) ) ) ) )).
fof(cc21_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v3_membered(B) ) ) )).
fof(cc21_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_monoid_0(A) & l3_algstr_0(A) ) => ! [B] : ( m3_monoid_0(B,A) => ( ~ v2_struct_0(B) => ( ~ v2_struct_0(B) & v1_monoid_0(B) ) ) ) ) )).
fof(cc21_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v9_lattices(A) & l4_robbins1(A) ) => ! [B] : ( m3_robbins3(B,A) => v9_lattices(B) ) ) )).
fof(cc21_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v3_tdlat_3(B) => ~ v2_tdlat_3(B) ) ) ) )).
fof(cc21_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( v1_borsuk_1(B,A) & ~ v4_tex_3(B,A) ) => ~ v3_tex_3(B,A) ) ) ) )).
fof(cc21_valued_0,axiom,( ! [A] : ! [B] : ( v6_membered(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v4_valued_0(C) ) ) )).
fof(cc21_valued_2,axiom,( ! [A] : ( v1_valued_2(A) => ! [B] : ( ( 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) ) ) ) )).
fof(cc22_algstr_0,axiom,( ! [A] : ( l4_algstr_0(A) => ( v28_algstr_0(A) => ( v26_algstr_0(A) & v27_algstr_0(A) ) ) ) )).
fof(cc22_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v4_fomodel0(A) ) ) )).
fof(cc22_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_fomodel1(A)) => ( ( ~ v7_fomodel1(B,A) & v10_fomodel1(B,A) ) => ( v8_fomodel1(B,A) & v10_fomodel1(B,A) ) ) ) ) )).
fof(cc22_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( v6_fomodel2(B,A) => v9_fomodel2(B,A) ) ) )).
fof(cc22_membered,axiom,( ! [A] : ( v4_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v4_membered(B) ) ) )).
fof(cc22_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_monoid_0(A) & l3_algstr_0(A) ) => ! [B] : ( m2_monoid_0(B,A) => ( ~ v2_struct_0(B) => ( ~ v2_struct_0(B) & v2_monoid_0(B) ) ) ) ) )).
fof(cc22_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v9_robbins3(A) & l4_robbins1(A) ) => ! [B] : ( m3_robbins3(B,A) => v9_robbins3(B) ) ) )).
fof(cc22_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc22_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v2_struct_0(B) => ( ~ v2_struct_0(B) & ~ v3_tex_3(B,A) ) ) ) ) )).
fof(cc22_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_zfmisc_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) ) ) )).
fof(cc22_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v12_valued_2(A) ) => ( v1_relat_1(A) & v11_valued_2(A) ) ) )).
fof(cc23_algstr_0,axiom,( ! [A] : ( ( v26_algstr_0(A) & l4_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v23_algstr_0(B,A) ) ) )).
fof(cc23_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v4_fomodel0(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) )).
fof(cc23_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_fomodel1(A)) => ( ( ~ v4_fomodel1(B,A) & v8_fomodel1(B,A) ) => ( v6_fomodel1(B,A) & v8_fomodel1(B,A) ) ) ) ) )).
fof(cc23_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k40_fomodel2(A)) => ( v4_fomodel2(B,A) & v5_fomodel2(B,A) ) ) ) )).
fof(cc23_membered,axiom,( ! [A] : ( v5_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v5_membered(B) ) ) )).
fof(cc23_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_monoid_0(A) & l3_algstr_0(A) ) => ! [B] : ( m3_monoid_0(B,A) => ( ~ v2_struct_0(B) => ( ~ v2_struct_0(B) & v2_monoid_0(B) ) ) ) ) )).
fof(cc23_robbins3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc23_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc23_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v1_tex_2(B,A) => ~ v1_tex_3(B,A) ) ) ) )).
fof(cc23_valued_0,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc23_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v11_valued_2(A) ) => ( v1_relat_1(A) & v10_valued_2(A) ) ) )).
fof(cc24_algstr_0,axiom,( ! [A] : ( ( v27_algstr_0(A) & l4_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v24_algstr_0(B,A) ) ) )).
fof(cc24_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_fomodel0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v4_fomodel0(B) ) ) )).
fof(cc24_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k16_fomodel1(A)) => v4_fomodel1(B,A) ) ) )).
fof(cc24_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k40_fomodel2(A)) => v4_fomodel2(B,A) ) ) )).
fof(cc24_membered,axiom,( ! [A] : ( v6_membered(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v6_membered(B) ) ) )).
fof(cc24_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_vectsp_1(A) & l4_algstr_0(A) ) => ! [B] : ( m3_monoid_0(B,A) => ( ~ v2_struct_0(B) => ( ~ v2_struct_0(B) & v4_vectsp_1(B) ) ) ) ) )).
fof(cc24_robbins3,axiom,( ! [A] : ( l3_robbins3(A) => ( ( ~ v2_struct_0(A) & v5_lattices(A) & v10_robbins3(A) ) => ( ~ v2_struct_0(A) & v4_orders_2(A) ) ) ) )).
fof(cc24_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc24_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v1_tex_3(B,A) => ~ v1_tex_2(B,A) ) ) ) )).
fof(cc24_valued_0,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc24_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v10_valued_2(A) ) => ( v1_relat_1(A) & v9_valued_2(A) ) ) )).
fof(cc25_algstr_0,axiom,( ! [A] : ( l5_algstr_0(A) => ( ( v30_algstr_0(A) & v31_algstr_0(A) ) => v32_algstr_0(A) ) ) )).
fof(cc25_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & ~ v2_abian(A) ) ) )).
fof(cc25_fomodel1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) & v7_ordinal1(C) ) => ! [D] : ( 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(k5_numbers,C)),A) => v14_fomodel1(D,k2_xcmplx_0(B,C),A) ) ) ) )).
fof(cc25_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k40_fomodel2(A)) => v5_fomodel2(B,A) ) ) )).
fof(cc25_membered,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => v6_membered(A) ) )).
fof(cc25_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_monoid_0(B,A) => ( ~ v2_struct_0(B) => ( ~ v2_struct_0(B) & v5_group_1(B) ) ) ) ) )).
fof(cc25_robbins3,axiom,( ! [A] : ( l3_robbins3(A) => ( ( ~ v2_struct_0(A) & v4_lattices(A) & v10_robbins3(A) ) => ( ~ v2_struct_0(A) & v5_orders_2(A) ) ) ) )).
fof(cc25_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc25_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v2_struct_0(B) => ( ~ v2_struct_0(B) & ~ v4_tex_3(B,A) ) ) ) ) )).
fof(cc25_valued_0,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( m1_valued_0(C,B) => v5_relat_1(C,A) ) ) )).
fof(cc25_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v9_valued_2(A) ) => ( v1_relat_1(A) & v8_valued_2(A) ) ) )).
fof(cc26_algstr_0,axiom,( ! [A] : ( l5_algstr_0(A) => ( v32_algstr_0(A) => ( v30_algstr_0(A) & v31_algstr_0(A) ) ) ) )).
fof(cc26_fomodel0,axiom,( ! [A] : ( v1_xboole_0(A) => v5_fomodel0(A) ) )).
fof(cc26_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_fomodel1(A)) => ( ( ~ v5_fomodel1(B,A) & v9_fomodel1(B,A) ) => ( v4_fomodel1(B,A) & v9_fomodel1(B,A) ) ) ) ) )).
fof(cc26_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( 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) ) ) ) )).
fof(cc26_membered,axiom,( ! [A] : ( v1_xboole_0(A) => v7_membered(A) ) )).
fof(cc26_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m3_monoid_0(B,A) => ( ~ v2_struct_0(B) => ( ~ v2_struct_0(B) & v5_group_1(B) ) ) ) ) )).
fof(cc26_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v10_robbins1(A) & v8_robbins3(A) & v9_robbins3(A) & l4_robbins1(A) ) => ! [B] : ( m3_robbins3(B,A) => v8_robbins3(B) ) ) )).
fof(cc26_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v1_tex_2(B,A) => ( v1_borsuk_1(B,A) & v1_tsep_1(B,A) ) ) ) ) )).
fof(cc26_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v1_tex_2(B,A) => ~ v2_tex_3(B,A) ) ) ) )).
fof(cc26_valued_0,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v3_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ! [C] : ( m1_valued_0(C,B) => v3_funct_1(C) ) ) )).
fof(cc26_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v9_valued_2(A) ) => ( v1_relat_1(A) & v7_valued_2(A) ) ) )).
fof(cc27_algstr_0,axiom,( ! [A] : ( l5_algstr_0(A) => ( ( v33_algstr_0(A) & v34_algstr_0(A) ) => v35_algstr_0(A) ) ) )).
fof(cc27_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v5_fomodel0(A) ) ) )).
fof(cc27_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(cc27_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) & m1_subset_1(C,k15_fomodel2(B,A)) & v10_fomodel2(D,A,B,C) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(D)) => v10_fomodel2(E,A,B,C) ) ) )).
fof(cc27_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_monoid_0(B,A) => ( ~ v2_struct_0(B) => ( ~ v2_struct_0(B) & v3_group_1(B) ) ) ) ) )).
fof(cc27_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v10_robbins1(A) & v8_robbins3(A) & v9_robbins3(A) & l4_robbins1(A) ) => ! [B] : ( m3_robbins3(B,A) => v10_robbins1(B) ) ) )).
fof(cc27_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v1_tsep_1(B,A) => v1_tex_2(B,A) ) ) ) )).
fof(cc27_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v2_tex_3(B,A) => ~ v1_tex_2(B,A) ) ) ) )).
fof(cc27_valued_0,axiom,( ! [A] : ! [B] : ( ( ~ v2_setfam_1(A) & v2_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ! [C] : ( m1_valued_0(C,B) => v2_relat_1(C) ) ) )).
fof(cc27_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) ) => ( v1_relat_1(A) & v12_valued_2(A) ) ) )).
fof(cc28_algstr_0,axiom,( ! [A] : ( l5_algstr_0(A) => ( v35_algstr_0(A) => ( v33_algstr_0(A) & v34_algstr_0(A) ) ) ) )).
fof(cc28_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_fomodel0(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v3_funct_1(A) ) ) )).
fof(cc28_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(cc28_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m3_monoid_0(B,A) => ( ~ v2_struct_0(B) => ( ~ v2_struct_0(B) & v3_group_1(B) ) ) ) ) )).
fof(cc28_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v1_borsuk_1(B,A) => v1_tex_2(B,A) ) ) ) )).
fof(cc28_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & v3_tex_3(B,A) ) => ( ~ v2_struct_0(B) & ~ v1_borsuk_1(B,A) ) ) ) ) )).
fof(cc28_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k2_numbers) ) => ( v1_relat_1(A) & v1_valued_0(A) ) ) )).
fof(cc28_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ( v1_funct_1(C) => ( v1_funct_1(C) & v7_valued_2(C) ) ) ) ) )).
fof(cc29_fomodel0,axiom,( ! [A] : ( v1_zfmisc_1(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) ) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) )).
fof(cc29_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & l1_fomodel1(A) ) => ! [B] : ( l1_fomodel1(B) => ( v16_fomodel1(B,A) => ~ v6_struct_0(B) ) ) ) )).
fof(cc29_robbins3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc29_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & v2_tdlat_3(B) ) => ( ~ v2_struct_0(B) & v7_struct_0(B) ) ) ) ) )).
fof(cc29_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & v1_borsuk_1(B,A) ) => ( ~ v2_struct_0(B) & ~ v3_tex_3(B,A) ) ) ) ) )).
fof(cc29_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k6_numbers) ) => ( v1_relat_1(A) & v2_valued_0(A) ) ) )).
fof(cc29_valued_2,axiom,( ! [A] : ! [B] : ( v2_valued_2(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ( v1_funct_1(C) => ( v1_funct_1(C) & v8_valued_2(C) ) ) ) ) )).
fof(cc2_abcmiz_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v13_struct_0(A,1) => ( v13_struct_0(A,1) & v1_abcmiz_0(A) ) ) ) )).
fof(cc2_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_finseq_1(C,k3_card_3(u3_msualg_1(A,k1_msafree3(A,B)))) => v6_trees_3(C) ) ) )).
fof(cc2_abcmiz_a,axiom,( ! [A] : ( m1_subset_1(A,k2_abcmiz_1) => v1_xtuple_0(A) ) )).
fof(cc2_abian,axiom,( ! [A] : ( ( v1_int_1(A) & ~ v1_abian(A) ) => ( ~ v8_ordinal1(A) & v1_int_1(A) ) ) )).
fof(cc2_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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) ) ) ) )).
fof(cc2_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_valued_0(A) ) => ( v1_relat_1(A) & v4_partfun3(A) ) ) )).
fof(cc2_algspec1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( m2_algspec1(B,A) => ~ v11_struct_0(B) ) ) )).
fof(cc2_algstr_0,axiom,( ! [A] : ( l1_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v4_algstr_0(B,A) => ( v2_algstr_0(B,A) & v3_algstr_0(B,A) ) ) ) ) )).
fof(cc2_algstr_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_altcat_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_altcat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_altcat_2(B,A) => ( ( ~ v2_struct_0(B) & v2_altcat_2(B,A) ) => v2_altcat_1(B) ) ) ) )).
fof(cc2_altcat_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v1_altcat_5(A) & l2_altcat_1(A) & m1_subset_1(B,u1_struct_0(A)) & 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] : ( m1_altcat_5(E,A,B,C,D) => v1_funcop_1(E) ) ) )).
fof(cc2_ami_wstd,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_compos_1(B)) => ( v3_ami_wstd(C,A,B) => ~ v2_extpro_1(C,A,B) ) ) ) )).
fof(cc2_amistd_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_setfam_1(A) & ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ( v4_amistd_1(C,A,B) => ~ v2_extpro_1(C,A,B) ) ) ) )).
fof(cc2_amistd_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_compos_1(B)) => ( v2_extpro_1(C,A,B) => v4_compos_0(C,u1_compos_1(B)) ) ) ) )).
fof(cc2_amistd_5,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_compos_1(B)) => v1_amistd_5(C,A,B) ) ) )).
fof(cc2_aofa_000,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,k4_ordinal1) & ~ v1_xboole_0(B) & v1_freealg(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_freealg(A,B))) => v3_trees_2(C) ) ) )).
fof(cc2_armstrng,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => v1_finset_1(B) ) ) )).
fof(cc2_arrow,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k3_arrow(A)) => v1_relat_1(B) ) ) )).
fof(cc2_asympt_0,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) => ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v4_asympt_0(A) ) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & v5_asympt_0(A) ) ) ) )).
fof(cc2_bcialg_1,axiom,( ! [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) ) => ( ~ v2_struct_0(A) & v3_bcialg_1(A) & v4_bcialg_1(A) & v5_bcialg_1(A) & v7_bcialg_1(A) & v20_bcialg_1(A) ) ) ) )).
fof(cc2_bcialg_5,axiom,( ! [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) ) => ( ~ 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) ) ) ) )).
fof(cc2_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) => ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_bhsp_2(B,A) ) => ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_bhsp_3(B,A) ) ) ) ) )).
fof(cc2_binom,axiom,( ! [A] : ( l2_algstr_0(A) => ( ( ~ v2_struct_0(A) & v5_algstr_0(A) & v2_rlvect_1(A) ) => ( ~ v2_struct_0(A) & v6_algstr_0(A) ) ) ) )).
fof(cc2_bintree1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dtconstr(A) & v2_dtconstr(A) & v3_bintree1(A) & l1_lang1(A) ) => ! [B] : ( m1_subset_1(B,k4_dtconstr(A)) => v2_bintree1(B) ) ) )).
fof(cc2_borsuk_2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_borsuk_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v1_rat_1(A) ) => ( ~ v8_ordinal1(A) & v1_xreal_0(A) ) ) )).
fof(cc2_borsuk_6,axiom,( ! [A] : ( ( v3_topmetr(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => v3_topmetr(B) ) ) )).
fof(cc2_c0sp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_ideal_1(B,A) & v1_c0sp1(B,A) ) => v2_c0sp1(B,A) ) ) ) )).
fof(cc2_card_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_card_1(A) ) )).
fof(cc2_card_3,axiom,( ! [A] : ! [B] : ( v1_setfam_1(B) => ! [C] : ( 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) ) ) ) ) )).
fof(cc2_card_fil,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(cc2_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_xboole_0(A) ) => ( v3_ordinal1(A) & ~ v1_finset_1(A) ) ) )).
fof(cc2_cat_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m3_cat_2(B,A) => v3_cat_5(B) ) ) )).
fof(cc2_catalg_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_cayldick,axiom,( ! [A] : ( l1_algstr_0(A) => ( ( ~ v2_struct_0(A) & v5_algstr_0(A) & v2_rlvect_1(A) ) => ( ~ v2_struct_0(A) & v6_algstr_0(A) & v2_rlvect_1(A) ) ) ) )).
fof(cc2_cgames_1,axiom,( ! [A] : ( l1_cgames_1(A) => ( v2_cgames_1(A) => v1_cgames_1(A) ) ) )).
fof(cc2_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_chord(A) ) => ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v6_chord(A) ) ) )).
fof(cc2_circcmb3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_circcomb,axiom,( ! [A] : ( l1_msualg_1(A) => ( ( ~ v2_struct_0(A) & v1_circcomb(A) ) => ( ~ v2_struct_0(A) & v2_msafree2(A) ) ) ) )).
fof(cc2_circtrm1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(k1_circtrm1(A,B,C))) => v3_trees_2(D) ) ) )).
fof(cc2_circuit1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,k1_funct_1(u3_msualg_1(A,k5_msafree2(A,B)),C)) => v3_trees_2(D) ) ) )).
fof(cc2_classes2,axiom,( ! [A] : ( v1_classes2(A) => ( v1_ordinal1(A) & v2_classes1(A) ) ) )).
fof(cc2_clopban1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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] : ( m1_subset_1(C,u1_struct_0(k14_clopban1(A,B))) => ( v1_relat_1(C) & v1_funct_1(C) ) ) ) )).
fof(cc2_clopban2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_clopban3,axiom,( ! [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_clopban1(A) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) => ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v2_clopban3(B,A) ) => ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_clopban3(B,A) ) ) ) ) )).
fof(cc2_closure1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_closure1(B,A) => ( v7_closure1(B,A) => v6_closure1(B,A) ) ) ) )).
fof(cc2_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) => ( v4_closure2(C,A,B) => v3_closure2(C,A,B) ) ) ) )).
fof(cc2_cohsp_1,axiom,( ! [A] : ( v2_cohsp_1(A) => ~ v1_xboole_0(A) ) )).
fof(cc2_compact1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_compl_sp,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v3_compl_sp(B,A) ) ) ) )).
fof(cc2_compos_0,axiom,( ! [A] : ( v5_compos_0(A) => ~ v1_xboole_0(A) ) )).
fof(cc2_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) ) => ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) & v2_compos_1(B,A) ) ) ) )).
fof(cc2_compts_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v8_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_compts_1(B,A) => v4_pre_topc(B,A) ) ) ) )).
fof(cc2_comput_1,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) ) => ( v1_relat_1(A) & v2_margrel1(A) ) ) )).
fof(cc2_comseq_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) => ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & ~ v1_comseq_2(A) ) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & ~ v2_comseq_2(A) ) ) ) )).
fof(cc2_comseq_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) => ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_series_1(A) ) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v1_series_1(A) ) ) ) )).
fof(cc2_connsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_connsp_1(B,A) => ~ v1_xboole_0(B) ) ) ) )).
fof(cc2_descip_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc2_dilworth,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_dilworth(B,A) => v6_orders_2(B,A) ) ) ) )).
fof(cc2_entropy1,axiom,( ! [A] : ( m1_finseq_1(A,k3_finseq_2(k1_numbers)) => ( ( v1_matrix_0(A) & v3_matrprob(A) ) => ( ~ v3_relat_1(A) & v1_matrix_0(A) ) ) ) )).
fof(cc2_eqrel_1,axiom,( ! [A] : ! [B] : ( m1_eqrel_1(B,A) => v1_setfam_1(B) ) )).
fof(cc2_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => v1_finseq_1(B) ) ) )).
fof(cc2_euclid_7,axiom,( ! [A] : ( v1_xboole_0(A) => v2_euclid_7(A) ) )).
fof(cc2_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(A))) => v3_card_1(B,A) ) ) )).
fof(cc2_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_exchsort(A) ) ) )).
fof(cc2_facirc_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( v7_ordinal1(A) & ~ v1_xtuple_0(A) ) ) )).
fof(cc2_facirc_2,axiom,( ! [A] : ( v1_xboole_0(A) => ~ v1_xtuple_0(A) ) )).
fof(cc2_fcont_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_fcont_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_xboole_0(A) => v3_rcomp_1(A) ) ) )).
fof(cc2_filter_0,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) )).
fof(cc2_finseq_2,axiom,( ! [A] : ! [B] : ( m1_finseq_2(B,A) => v4_funct_1(B) ) )).
fof(cc2_finset_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_finset_1(B) ) ) )).
fof(cc2_finsub_1,axiom,( ! [A] : ( ( v1_finsub_1(A) & v3_finsub_1(A) ) => v4_finsub_1(A) ) )).
fof(cc2_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_fintopo6(B,A) => ( ~ v2_struct_0(B) => ( ~ v2_struct_0(B) & v3_orders_2(B) ) ) ) ) )).
fof(cc2_fomodel0,axiom,( ! [A] : ( v2_setfam_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v2_setfam_1(B) ) ) )).
fof(cc2_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_fomodel1(A)) => ( v7_fomodel1(B,A) => v5_fomodel1(B,A) ) ) ) )).
fof(cc2_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_fomodel1(A)) => ( v4_fomodel1(B,A) => v9_fomodel1(B,A) ) ) ) )).
fof(cc2_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k37_fomodel1(A)) => v9_fomodel1(B,A) ) ) )).
fof(cc2_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_fomodel4(A)) => v1_fomodel4(B,A) ) ) )).
fof(cc2_frechet,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funcop_1(A) ) ) )).
fof(cc2_funct_1,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) ) )).
fof(cc2_funct_2,axiom,( ! [A] : ! [B] : ( v1_xboole_0(A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ( v1_funct_2(C,A,B) => v1_partfun1(C,A) ) ) ) )).
fof(cc2_funct_7,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc2_funct_8,axiom,( ! [A] : ! [B] : ( ( v1_membered(A) & v1_membered(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc2_functor0,axiom,( ! [A] : ( l2_altcat_1(A) => ( ( ~ v2_struct_0(A) & v12_altcat_1(A) ) => ( ~ v2_struct_0(A) & v1_altcat_2(A) ) ) ) )).
fof(cc2_functor2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m2_functor0(C,A,B) => ( v15_functor0(C,A,B) => ( v10_functor0(C,A,B) & v13_functor0(C,A,B) ) ) ) ) )).
fof(cc2_fvaluat1,axiom,( ! [A] : ( v1_int_1(A) => v1_fvaluat1(A) ) )).
fof(cc2_gcd_1,axiom,( ! [A] : ( l6_algstr_0(A) => ( ( ~ v2_struct_0(A) & v5_group_1(A) & v1_vectsp_1(A) ) => ( ~ v2_struct_0(A) & v5_vectsp_1(A) ) ) ) )).
fof(cc2_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v7_glib_000(A) ) => ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_000(A) & v5_glib_000(A) ) ) )).
fof(cc2_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v3_glib_001(B,A) => v5_glib_001(B,A) ) ) ) )).
fof(cc2_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) ) )).
fof(cc2_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => ( ( v2_funct_1(B) & v1_xboole_0(B) ) => ( v2_funct_1(B) & v9_graph_1(B,A) ) ) ) ) )).
fof(cc2_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => ( v1_xboole_0(B) => v2_funct_1(B) ) ) ) )).
fof(cc2_grfunc_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) & v5_funct_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => v5_funct_1(C,A) ) ) )).
fof(cc2_grnilp_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & v5_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => v5_group_1(B) ) ) )).
fof(cc2_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_card_3(k12_pralg_1(k1_tarski(1),k9_finseq_1(A)))) => v1_finseq_1(B) ) ) )).
fof(cc2_groupp_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_group_2(C,B) => v2_group_10(C,A) ) ) )).
fof(cc2_hahnban,axiom,( ! [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) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc2_hahnban1,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc2_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v4_glib_001(B,A) => v5_glib_001(B,A) ) ) ) )).
fof(cc2_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc2_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k13_finseq_1(k4_ordinal1))) => ( ( v1_hilbert1(A) & v2_hilbert1(A) & v3_hilbert1(A) & v4_hilbert1(A) ) => v5_hilbert1(A) ) ) )).
fof(cc2_hilbert3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( v1_hilbert3(A) => v2_hilbert3(A) ) ) )).
fof(cc2_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc2_instalg1,axiom,( ! [A] : ( l1_msualg_1(A) => ( ~ v2_struct_0(A) => v1_instalg1(A) ) ) )).
fof(cc2_int_1,axiom,( ! [A] : ( v7_ordinal1(A) => v1_int_1(A) ) )).
fof(cc2_int_3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_int_6,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc2_integra1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( ( ~ v1_xboole_0(A) & v2_measure5(A) ) => v5_xxreal_2(A) ) ) )).
fof(cc2_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_tops_1(B,A) => ( v1_isomichi(B,A) & v2_isomichi(B,A) ) ) ) ) )).
fof(cc2_jordan,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( v1_xboole_0(B) => v9_rltopsp1(B,k15_euclid(A)) ) ) ) )).
fof(cc2_jordan21,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal2(A) => ( v1_topreal2(A) & v1_jordan21(A) ) ) ) )).
fof(cc2_jordan23,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc2_lattice2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_lattice3(A) => ~ v2_struct_0(A) ) ) )).
fof(cc2_lattice6,axiom,( ! [A] : ( l3_lattices(A) => ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v10_lattices(A) ) => ( ~ v2_struct_0(A) & v10_lattices(A) & v1_lattice6(A) ) ) ) )).
fof(cc2_lattices,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & v3_lexbfs(A) ) => ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & v13_glib_000(A) ) ) )).
fof(cc2_lfuzzy_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_struct_0(A) => v1_lfuzzy_0(A) ) ) )).
fof(cc2_lopban_1,axiom,( ! [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) & 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] : ( m1_subset_1(C,u1_struct_0(k16_lopban_1(A,B))) => ( v1_relat_1(C) & v1_funct_1(C) ) ) ) )).
fof(cc2_lopban_2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_lopban_3,axiom,( ! [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) & v3_lopban_1(A) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) => ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v2_lopban_3(B,A) ) => ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_lopban_3(B,A) ) ) ) ) )).
fof(cc2_ltlaxio4,axiom,( ! [A] : ( ( ~ v2_ltlaxio3(A) & m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) ) => ! [B] : ( m1_subset_1(B,k5_ltlaxio4(A)) => ~ v2_ltlaxio3(B) ) ) )).
fof(cc2_margrel1,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => v1_xboolean(A) ) )).
fof(cc2_matroid0,axiom,( ! [A] : ( l1_pre_topc(A) => ( v4_matroid0(A) => v3_matroid0(A) ) ) )).
fof(cc2_matrprob,axiom,( ! [A] : ( m1_finseq_1(A,k3_finseq_2(k1_numbers)) => ( ( v1_matrix_0(A) & v2_matrprob(A) & v3_matrprob(A) ) => ( v1_matrix_0(A) & v4_matrprob(A) ) ) ) )).
fof(cc2_matrtop3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(cc2_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & ~ v1_xboole_0(D) ) => ! [E] : ( m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) => v3_xtuple_0(E) ) ) )).
fof(cc2_measure1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( ( v2_finsub_1(B) & v1_prob_1(B,A) ) => v1_finsub_1(B) ) ) )).
fof(cc2_measure5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v2_measure5(A) => v6_xxreal_2(A) ) ) )).
fof(cc2_membered,axiom,( ! [A] : ( v5_membered(A) => v4_membered(A) ) )).
fof(cc2_memstr_0,axiom,( ! [A] : ! [B] : ( ( ~ v1_setfam_1(A) & l1_memstr_0(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(cc2_metrizts,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_pre_topc(A) & v3_pcomps_1(A) ) => ( v2_pre_topc(A) & v12_pre_topc(A) ) ) ) )).
fof(cc2_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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) ) ) ) ) )).
fof(cc2_mmlquer2,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) ) => ( v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) ) ) )).
fof(cc2_mod_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) & ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc2_monoid_0,axiom,( ! [A] : ( l1_struct_0(A) => ( v2_monoid_0(A) => v1_monoid_0(A) ) ) )).
fof(cc2_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) ) => ( v4_msualg_1(B,A) & v3_msafree2(B,A) ) ) ) ) )).
fof(cc2_msafree3,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k3_card_3(u3_msualg_1(A,k1_msafree3(A,B)))) => ( v1_finset_1(C) & v3_trees_2(C) ) ) ) )).
fof(cc2_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k3_card_3(u3_msualg_1(A,k3_equation(A)))) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) )).
fof(cc2_msscyc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => v1_xboole_0(B) ) ) )).
fof(cc2_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v2_finset_1(B) ) => ! [C] : ( m3_pboole(C,A,B) => v2_finset_1(C) ) ) )).
fof(cc2_msualg_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k10_xtuple_0(k6_finseq_2(u1_struct_0(A),u3_msualg_1(A,B)))) => ~ v1_xboole_0(C) ) ) )).
fof(cc2_msualg_6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc2_msualg_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m2_nat_lat(B,A) => ( v2_msualg_7(B,A) => v4_lattice3(B) ) ) ) )).
fof(cc2_msualg_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( m1_subset_1(E,k1_funct_1(k10_pralg_2(B,A,D),C)) => ( v1_relat_1(E) & v1_funct_1(E) ) ) ) )).
fof(cc2_mycielsk,axiom,( ! [A] : ( l1_orders_2(A) => ( v8_struct_0(A) => v2_mycielsk(A) ) ) )).
fof(cc2_nat_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ v3_xxreal_0(A) ) )).
fof(cc2_nat_lat,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) => ! [B] : ( m1_subset_1(B,A) => v1_xreal_0(B) ) ) )).
fof(cc2_nattra_1,axiom,( ! [A] : ( 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) & v2_nattra_1(A) & v3_nattra_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) & v4_nattra_1(A) ) ) ) )).
fof(cc2_neckla_2,axiom,( ! [A] : ( m1_subset_1(A,k13_classes2) => v1_finset_1(A) ) )).
fof(cc2_neckla_3,axiom,( ! [A] : ( v1_zfmisc_1(A) => ! [B] : ( 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) ) ) ) )).
fof(cc2_nfcont_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc2_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( 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) ) ) ) ) )).
fof(cc2_openlatt,axiom,( ! [A] : ( l3_lattices(A) => ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) ) => ( ~ v2_struct_0(A) & v10_lattices(A) & v14_lattices(A) ) ) ) )).
fof(cc2_oposet_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_ordeq_01,axiom,( ! [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) & v3_lopban_1(A) & l1_normsp_1(A) ) => ! [B] : ( 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) ) => ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_ordeq_01(B) ) ) ) ) )).
fof(cc2_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v6_orders_2(B,A) ) ) ) )).
fof(cc2_ordinal1,axiom,( ! [A] : ( ( v1_ordinal1(A) & v2_ordinal1(A) ) => v3_ordinal1(A) ) )).
fof(cc2_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m1_subset_1(B,A) => v3_ordinal1(B) ) ) )).
fof(cc2_ordinal5,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc2_ordinal6,axiom,( ! [A] : ( v1_ordinal6(A) => ! [B] : ( m1_subset_1(B,A) => v3_ordinal1(B) ) ) )).
fof(cc2_osalg_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_osalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k2_osalg_4(A)) => ~ v1_xboole_0(B) ) ) )).
fof(cc2_partfun1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_xboole_0(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ~ v1_partfun1(C,A) ) ) )).
fof(cc2_partfun3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_partfun3(A) ) => ( v1_relat_1(A) & v2_relat_1(A) & v3_partfun3(A) ) ) )).
fof(cc2_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(cc2_pdiff_6,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => ! [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))))) => ( ( 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)) ) ) ) ) )).
fof(cc2_pencil_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v14_pencil_1(A) ) => ( v1_relat_1(A) & v4_waybel_3(A) ) ) )).
fof(cc2_polynom1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( 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,B) ) ) ) ) )).
fof(cc2_poset_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(cc2_pralg_2,axiom,( ! [A] : ( ( v4_funct_1(A) & ~ v1_xboole_0(A) & v2_card_3(A) ) => ! [B] : ( m1_subset_1(B,A) => v1_partfun1(B,k9_card_3(A)) ) ) )).
fof(cc2_pre_poly,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k5_finsub_1(A))) ) => ! [C] : ( m1_subset_1(C,B) => v1_finset_1(C) ) ) )).
fof(cc2_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v4_pre_topc(B,A) ) ) ) )).
fof(cc2_prob_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m2_prob_1(C,A,B) => v10_valued_0(C) ) ) )).
fof(cc2_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) ) => ! [B] : ( m2_prvect_1(B,A) => v1_finseq_1(B) ) ) )).
fof(cc2_prvect_2,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc2_pscomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v2_pscomp_1(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc2_pua2mss1,axiom,( ! [A] : ( l1_unialg_1(A) => ( v4_unialg_1(A) => ~ v2_struct_0(A) ) ) )).
fof(cc2_pythtrip,axiom,( ! [A] : ( m1_pythtrip(A) => v1_finset_1(A) ) )).
fof(cc2_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ( v2_qc_trans(B,A,A) => v1_henmodel(B,A) ) ) ) )).
fof(cc2_quantal1,axiom,( ! [A] : ( l3_algstr_0(A) => ( ( ~ v2_struct_0(A) & v4_quantal1(A) & v5_quantal1(A) ) => ( ~ v2_struct_0(A) & v6_quantal1(A) ) ) ) )).
fof(cc2_quatern2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_quatern2)) => v1_quaterni(A) ) )).
fof(cc2_quofield,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) & ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc2_rat_1,axiom,( ! [A] : ( v1_int_1(A) => v1_rat_1(A) ) )).
fof(cc2_ratfunc1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_rcomp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_rcomp_1(B,A) => v3_rcomp_1(B) ) ) )).
fof(cc2_rcomp_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k2_topalg_2))) => ( v2_connsp_1(A,k2_topalg_2) => v6_xxreal_2(A) ) ) )).
fof(cc2_realset2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_relat_1(B) ) ) )).
fof(cc2_relat_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_relat_2(A) & v8_relat_2(A) ) => ( v1_relat_1(A) & v1_relat_2(A) ) ) )).
fof(cc2_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ( v4_relat_1(C,A) & v5_relat_1(C,B) ) ) )).
fof(cc2_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_rewrite1(A) ) => ( v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) ) ) )).
fof(cc2_rewrite2,axiom,( ! [A] : ! [B] : ( m1_finseq_1(B,k8_afinsq_1(A)) => v1_rewrite2(B) ) )).
fof(cc2_rfunct_2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(cc2_ringcat1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) & ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc2_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_rlvect_3(B,A) => v1_rlaffin1(B,A) ) ) ) )).
fof(cc2_rlaffin3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) ) )).
fof(cc2_rltopsp1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_rltopsp1(B,A) => v2_rltopsp1(B,A) ) ) ) )).
fof(cc2_rlvect_1,axiom,( ! [A] : ( l2_algstr_0(A) => ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & v4_rlvect_1(A) ) => ( ~ v2_struct_0(A) & v9_rlvect_1(A) ) ) ) )).
fof(cc2_robbins1,axiom,( ! [A] : ( l2_robbins1(A) => ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) ) => ( ~ v2_struct_0(A) & v7_robbins1(A) ) ) ) )).
fof(cc2_robbins2,axiom,( ! [A] : ( l2_robbins1(A) => ( ( ~ v2_struct_0(A) & v1_robbins2(A) ) => ( ~ v2_struct_0(A) & v5_lattices(A) ) ) ) )).
fof(cc2_robbins3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_robbins4,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_scm_halt,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) ) )).
fof(cc2_scmfsa6b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(cc2_scmyciel,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v3_scmyciel(B,A) => v5_finset_1(B) ) ) )).
fof(cc2_seq_2,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc2_seq_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) => ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v8_valued_0(A) & v2_seq_2(A) ) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_comseq_2(A) ) ) ) )).
fof(cc2_seqm_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) => ( ( v1_funct_1(A) & v7_valued_0(A) & v8_valued_0(A) ) => ( v1_funct_1(A) & v3_funct_1(A) ) ) ) )).
fof(cc2_setfam_1,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ~ v1_xboole_0(A) ) )).
fof(cc2_sheffer1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_simplex0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ~ v1_xboole_0(A) ) )).
fof(cc2_simplex1,axiom,( ! [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) ) => ! [B] : ( m1_simplex0(B,u1_struct_0(A)) => ( v4_simplex0(B) => v1_simplex1(B,A) ) ) ) )).
fof(cc2_simplex2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) & v1_simplex2(C,A) & m1_simplex0(C,B) ) => ! [D] : ( m2_simplex0(D,B,C) => v1_simplex2(D,A) ) ) )).
fof(cc2_sppol_1,axiom,( ! [A] : ( 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) ) ) )).
fof(cc2_sppol_2,axiom,( ! [A] : ( 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) ) ) )).
fof(cc2_sprect_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => ( ~ v7_struct_0(A) => ~ v2_struct_0(A) ) ) )).
fof(cc2_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ~ v1_subset_1(B,A) => ~ v1_xboole_0(B) ) ) ) )).
fof(cc2_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_substlat(A,B)) => v4_funct_1(C) ) )).
fof(cc2_supinf_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k6_numbers)) => ! [C] : ( 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) ) ) ) ) )).
fof(cc2_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v6_tbsp_1(B,A) ) ) ) )).
fof(cc2_tdlat_3,axiom,( ! [A] : ( l1_pre_topc(A) => ( v2_tdlat_3(A) => v2_pre_topc(A) ) ) )).
fof(cc2_tex_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_tex_2,axiom,( ! [A] : ( v3_card_1(A,1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ~ v1_xboole_0(B) => ~ v1_subset_1(B,A) ) ) ) )).
fof(cc2_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( v1_tex_2(B,A) & v1_tex_3(B,A) ) => ~ v1_borsuk_1(B,A) ) ) ) )).
fof(cc2_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v2_tdlat_3(B) => ~ v4_tex_4(B,A) ) ) ) )).
fof(cc2_topalg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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] : ( m1_borsuk_6(G,B,C,D,E,F) => v5_pre_topc(G,k2_borsuk_1(k5_topmetr,k5_topmetr),B) ) ) )).
fof(cc2_topalg_3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_topalg_6,axiom,( ! [A] : ( ( v7_ordinal1(A) & v2_xxreal_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc2_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_xboole_0(B) => v2_topdim_1(B,A) ) ) ) )).
fof(cc2_topdim_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_card_3(B) => v1_topdim_1(B,A) ) ) ) )).
fof(cc2_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc2_topgen_2,axiom,( ! [A] : ( l1_pre_topc(A) => ( ~ v1_topgen_2(A) => ~ v8_struct_0(A) ) ) )).
fof(cc2_topgen_4,axiom,( ! [A] : ( ~ v4_card_3(A) => ~ v1_finset_1(A) ) )).
fof(cc2_topgrp_1,axiom,( ! [A] : ! [B] : ( ( l1_pre_topc(A) & l1_pre_topc(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc2_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ~ v1_sppol_1(A) => ~ v1_xboole_0(A) ) ) )).
fof(cc2_topreala,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_struct_0(A) & v2_pre_topc(A) ) => ( v2_pre_topc(A) & v1_tdlat_3(A) & v2_tdlat_3(A) ) ) ) )).
fof(cc2_toprealc,axiom,( ! [A] : ( ( v2_pre_topc(A) & v1_toprealc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => v1_toprealc(B) ) ) )).
fof(cc2_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v2_tops_1(B,A) ) ) ) )).
fof(cc2_trees_3,axiom,( ! [A] : ( v2_trees_3(A) => v1_trees_3(A) ) )).
fof(cc2_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_trees_2(A) ) => ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_trees_9(A) ) ) )).
fof(cc2_tsp_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & ~ v6_pre_topc(B) ) => ( ~ v2_struct_0(B) & ~ v2_tsp_2(B,A) ) ) ) ) )).
fof(cc2_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) ) => ( v1_relat_1(A) & v5_relat_1(A,k3_numbers) ) ) )).
fof(cc2_valued_2,axiom,( ! [A] : ( v5_valued_2(A) => v4_valued_2(A) ) )).
fof(cc2_vectmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v7_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(cc2_vectsp10,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(cc2_vectsp_1,axiom,( ! [A] : ( l6_algstr_0(A) => ( ( ~ v2_struct_0(A) & v1_vectsp_1(A) & v2_vectsp_1(A) ) => ( ~ v2_struct_0(A) & v5_vectsp_1(A) ) ) ) )).
fof(cc2_vectsp_2,axiom,( ! [A] : ( l4_algstr_0(A) => ( ( ~ v2_struct_0(A) & v5_group_1(A) & v3_vectsp_1(A) ) => ( ~ v2_struct_0(A) & v4_vectsp_1(A) ) ) ) )).
fof(cc2_waybel10,axiom,( ! [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] : ( m1_yellow_0(B,A) => ( v7_yellow_0(B,A) => ~ v2_struct_0(B) ) ) ) )).
fof(cc2_waybel11,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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) ) ) ) ) )).
fof(cc2_waybel12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v3_waybel_3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v12_waybel_0(B,A) => v1_waybel_6(B,A) ) ) ) )).
fof(cc2_waybel17,axiom,( ! [A] : ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(cc2_waybel19,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_waybel21,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_waybel21(C,A,B) => v19_waybel_0(C,A,B) ) ) )).
fof(cc2_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_waybel23(B,A) => v2_waybel23(B,A) ) ) ) )).
fof(cc2_waybel25,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => ( v4_waybel11(B) => v2_waybel18(B) ) ) ) )).
fof(cc2_waybel26,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_pre_topc(k2_borsuk_1(A,B))) => v1_relat_1(C) ) ) )).
fof(cc2_waybel27,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_monoid_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( ~ v2_struct_0(B) => ( ~ v2_struct_0(B) & v1_monoid_0(B) ) ) ) ) )).
fof(cc2_waybel29,axiom,( ! [A] : ( ( ~ 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] : ( m1_yellow_9(B,A) => v24_waybel_0(B) ) ) )).
fof(cc2_waybel30,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_waybel32,axiom,( ! [A] : ( ( ~ 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] : ( m1_yellow_9(B,A) => ( v4_waybel11(B) => v2_pre_topc(B) ) ) ) )).
fof(cc2_waybel33,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_waybel34,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v6_waybel34(B,A) => ( v6_yellow_0(B,A) & v7_waybel34(B,A) ) ) ) ) )).
fof(cc2_waybel35,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(cc2_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v7_yellow_0(B,A) => v3_waybel_0(B,A) ) ) ) )).
fof(cc2_waybel_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(cc2_waybel_2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_waybel_3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_waybel_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(cc2_waybel_5,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_waybel_8,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_wellord1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc2_xcmplx_0,axiom,( ! [A] : ( v7_ordinal1(A) => v1_xcmplx_0(A) ) )).
fof(cc2_xreal_0,axiom,( ! [A] : ( v7_ordinal1(A) => v1_xreal_0(A) ) )).
fof(cc2_xtuple_0,axiom,( ! [A] : ( v3_xtuple_0(A) => v2_xtuple_0(A) ) )).
fof(cc2_xxreal_0,axiom,( ! [A] : ( v7_ordinal1(A) => v1_xxreal_0(A) ) )).
fof(cc2_xxreal_2,axiom,( ! [A] : ( ( v2_membered(A) & v1_finset_1(A) & ~ v1_xboole_0(A) ) => ( v2_membered(A) & ~ v1_xboole_0(A) & v1_xxreal_2(A) & v2_xxreal_2(A) ) ) )).
fof(cc2_xxreal_3,axiom,( ! [A] : ( ( v1_xxreal_0(A) & ~ v2_xxreal_0(A) & ~ v1_xreal_0(A) ) => ( v1_xxreal_0(A) & v3_xxreal_0(A) ) ) )).
fof(cc2_yellow11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( ~ v1_xboole_0(B) & v2_yellow11(B,A) ) => v1_waybel_0(B,A) ) ) ) )).
fof(cc2_yellow12,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc2_yellow13,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_yellow14,axiom,( ! [A] : ! [B] : ( ( l1_orders_2(A) & l1_orders_2(B) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(cc2_yellow18,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_yellow19,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) & v4_orders_2(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_yellow_6(C,A,B) => ( v2_yellow_6(C,A,B) => ( v4_orders_2(C) & v2_yellow_6(C,A,B) ) ) ) ) )).
fof(cc2_yellow21,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_yellow_0,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc2_yellow_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ~ v1_yellow_3(A) => ~ v2_struct_0(A) ) ) )).
fof(cc2_yellow_6,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m3_yellow_6(C,u1_struct_0(B),A) => v4_waybel_3(C) ) ) )).
fof(cc2_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v8_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_yellow_8(B,A) => v1_zfmisc_1(B) ) ) ) )).
fof(cc2_yellow_9,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => v3_orders_2(B) ) ) )).
fof(cc2_zfmisc_1,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ~ v1_xboole_0(A) ) )).
fof(cc2_zmodul03,axiom,( ! [A] : ( ( ~ 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) & v1_zmodul03(A) & v2_zmodul03(A) & l1_zmodul01(A) ) => ! [B] : ( m1_zmodul03(B,A) => v1_finset_1(B) ) ) )).
fof(cc30_fomodel0,axiom,( ! [A] : ( v1_zfmisc_1(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) ) => ( v1_relat_1(B) & v1_funct_1(B) & v3_funct_1(B) ) ) ) )).
fof(cc30_fomodel1,axiom,( ! [A] : ( ( v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( l1_fomodel1(B) => ( v16_fomodel1(B,A) => v11_fomodel1(B) ) ) ) )).
fof(cc30_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & ~ v7_struct_0(B) ) => ( ~ v2_struct_0(B) & ~ v2_tdlat_3(B) ) ) ) ) )).
fof(cc30_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( v1_tex_2(B,A) & v1_tex_3(B,A) ) => ~ v1_tsep_1(B,A) ) ) ) )).
fof(cc30_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k1_numbers) ) => ( v1_relat_1(A) & v3_valued_0(A) ) ) )).
fof(cc30_valued_2,axiom,( ! [A] : ! [B] : ( v3_valued_2(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ( v1_funct_1(C) => ( v1_funct_1(C) & v9_valued_2(C) ) ) ) ) )).
fof(cc31_fomodel0,axiom,( ! [A] : ( v5_fomodel0(A) => v1_funct_1(A) ) )).
fof(cc31_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v16_monoid_0(A) & l3_algstr_0(A) ) => ! [B] : ( m2_monoid_0(B,A) => ( ~ v2_struct_0(B) => ( ~ v2_struct_0(B) & v16_monoid_0(B) ) ) ) ) )).
fof(cc31_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & v1_tdlat_3(B) ) => ( ~ v2_struct_0(B) & v7_struct_0(B) ) ) ) ) )).
fof(cc31_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( v1_tsep_1(B,A) & v1_tex_3(B,A) ) => ~ v1_tex_2(B,A) ) ) ) )).
fof(cc31_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_ordinal1) ) => ( v1_relat_1(A) & v4_valued_0(A) ) ) )).
fof(cc31_valued_2,axiom,( ! [A] : ! [B] : ( v4_valued_2(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ( v1_funct_1(C) => ( v1_funct_1(C) & v10_valued_2(C) ) ) ) ) )).
fof(cc32_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v16_monoid_0(A) & l3_algstr_0(A) ) => ! [B] : ( m3_monoid_0(B,A) => ( ~ v2_struct_0(B) => ( ~ v2_struct_0(B) & v16_monoid_0(B) ) ) ) ) )).
fof(cc32_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & ~ v7_struct_0(B) ) => ( ~ v2_struct_0(B) & ~ v1_tdlat_3(B) ) ) ) ) )).
fof(cc32_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( v1_tsep_1(B,A) & v1_tex_2(B,A) ) => ~ v1_tex_3(B,A) ) ) ) )).
fof(cc32_valued_2,axiom,( ! [A] : ! [B] : ( v5_valued_2(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ( v1_funct_1(C) => ( v1_funct_1(C) & v11_valued_2(C) ) ) ) ) )).
fof(cc33_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_vectsp_1(A) & v17_monoid_0(A) & l4_algstr_0(A) ) => ! [B] : ( m3_monoid_0(B,A) => ( ~ v2_struct_0(B) => ( ~ v2_struct_0(B) & v17_monoid_0(B) ) ) ) ) )).
fof(cc33_tex_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc33_valued_2,axiom,( ! [A] : ! [B] : ( v6_valued_2(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ( v1_funct_1(C) => ( v1_funct_1(C) & v12_valued_2(C) ) ) ) ) )).
fof(cc34_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc34_tex_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc34_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v7_valued_2(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) ) )).
fof(cc35_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & v4_tex_2(B,A) ) => ( ~ v2_struct_0(B) & v1_tdlat_3(B) ) ) ) ) )).
fof(cc35_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v9_valued_2(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) ) )).
fof(cc36_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & ~ v1_tdlat_3(B) ) => ( ~ v2_struct_0(B) & ~ v4_tex_2(B,A) ) ) ) ) )).
fof(cc36_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v8_valued_2(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) ) )).
fof(cc37_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v4_tex_2(B,A) => ~ v1_tex_2(B,A) ) ) ) )).
fof(cc38_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v1_tex_2(B,A) => ~ v4_tex_2(B,A) ) ) ) )).
fof(cc39_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v1_tex_2(B,A) => v4_tex_2(B,A) ) ) ) )).
fof(cc3_abcmiz_0,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_abcmiz_1,axiom,( ! [A] : ( m1_subset_1(A,k4_abcmiz_1) => v2_funct_1(A) ) )).
fof(cc3_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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) ) ) ) )).
fof(cc3_algstr_0,axiom,( ! [A] : ( l1_algstr_0(A) => ( ( v5_algstr_0(A) & v6_algstr_0(A) ) => v7_algstr_0(A) ) ) )).
fof(cc3_algstr_1,axiom,( ! [A] : ( l2_algstr_0(A) => ( ( ~ v2_struct_0(A) & v4_algstr_1(A) ) => ( ~ v2_struct_0(A) & v2_algstr_1(A) ) ) ) )).
fof(cc3_altcat_1,axiom,( ! [A] : ( l2_altcat_1(A) => ( v13_struct_0(A,1) => v13_altcat_1(A) ) ) )).
fof(cc3_altcat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_altcat_2(B,A) => ( ( ~ v2_struct_0(B) & v2_altcat_1(B) ) => ( ~ v2_struct_0(B) & v11_altcat_1(B) ) ) ) ) )).
fof(cc3_altcat_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) & v1_funct_1(B) & v1_funct_2(B,k1_xboole_0,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_xboole_0,u1_struct_0(A)))) & m1_subset_1(C,u1_struct_0(A)) ) => ! [D] : ( m1_altcat_5(D,A,C,k1_xboole_0,B) => v2_altcat_5(D,A,k1_xboole_0,B,C) ) ) )).
fof(cc3_ami_wstd,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_compos_1(B)) => ( v2_extpro_1(C,A,B) => ~ v3_ami_wstd(C,A,B) ) ) ) )).
fof(cc3_amistd_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_setfam_1(A) & ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ( v2_extpro_1(C,A,B) => ~ v4_amistd_1(C,A,B) ) ) ) )).
fof(cc3_amistd_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_compos_1(B)) => ( v4_amistd_1(C,A,B) => v4_compos_0(C,u1_compos_1(B)) ) ) ) )).
fof(cc3_aofa_000,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,k4_ordinal1) & ~ v1_xboole_0(B) & v1_freealg(B) ) => ! [C] : ( m1_finseq_1(C,u1_struct_0(k7_freealg(A,B))) => v6_trees_3(C) ) ) )).
fof(cc3_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & v2_relat_1(D) & m1_msafree(D,A,B) ) => ! [E] : ( m1_subset_1(E,k13_aofa_a00(A,B,C,D)) => ( v1_relat_1(E) & v1_funct_1(E) ) ) ) )).
fof(cc3_aofa_a01,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_finseq_1(B,k8_afinsq_1(A)) => v1_funcop_1(B) ) ) )).
fof(cc3_armstrng,axiom,( ! [A] : ! [B] : ( 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) ) ) ) )).
fof(cc3_asympt_0,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) => ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & v5_asympt_0(A) ) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v4_asympt_0(A) ) ) ) )).
fof(cc3_bcialg_1,axiom,( ! [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) ) => ( ~ v2_struct_0(A) & v3_bcialg_1(A) & v4_bcialg_1(A) & v5_bcialg_1(A) & v7_bcialg_1(A) & v17_bcialg_1(A) ) ) ) )).
fof(cc3_binom,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_c0sp1,axiom,( ! [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) & v2_funcsdom(A) & v3_group_1(A) & v5_group_1(A) & v1_vectsp_1(A) & v3_vectsp_1(A) & l1_funcsdom(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_c0sp1(B,A) => v2_c0sp1(B,A) ) ) ) )).
fof(cc3_card_1,axiom,( ! [A] : ( v7_ordinal1(A) => v1_card_1(A) ) )).
fof(cc3_card_3,axiom,( ! [A] : ( v3_card_3(A) => ( v4_funct_1(A) & v2_card_3(A) ) ) )).
fof(cc3_card_fil,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) & v5_card_fil(A) ) => ( ~ v1_finset_1(A) & v1_card_1(A) & v2_card_1(A) ) ) )).
fof(cc3_card_lar,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) & ~ v2_card_1(A) ) => ( ~ v1_finset_1(A) & v1_card_1(A) & ~ v4_card_3(A) ) ) )).
fof(cc3_catalg_1,axiom,( ! [A] : ! [B] : ( m1_catalg_1(B,A) => v2_catalg_1(B) ) )).
fof(cc3_cayldick,axiom,( ! [A] : ( l2_algstr_0(A) => ( ( ~ v2_struct_0(A) & v12_algstr_0(A) & v2_rlvect_1(A) ) => ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) ) ) ) )).
fof(cc3_cgames_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) ) => ! [B] : ( m1_subset_1(B,k4_finseq_1(A)) => ( v7_ordinal1(B) & ~ v1_xboole_0(B) ) ) ) )).
fof(cc3_chord,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v6_chord(A) ) => ! [C] : ( m2_glib_000(C,A,B,k21_glib_000(A,B)) => v6_chord(C) ) ) )).
fof(cc3_circcmb3,axiom,( ! [A] : ( l1_msualg_1(A) => ( ( ~ v2_struct_0(A) & v4_circcmb3(A) ) => ( ~ v2_struct_0(A) & v5_circcomb(A) ) ) ) )).
fof(cc3_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( v6_circcomb(B,A) => ( v4_msualg_1(B,A) & v4_msafree2(B,A) ) ) ) ) )).
fof(cc3_circtrm1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u4_struct_0(k1_circtrm1(A,B,C))) => ( v1_relat_1(D) & v1_funct_1(D) & v1_finset_1(D) ) ) ) )).
fof(cc3_classes2,axiom,( ! [A] : ( ( v1_ordinal1(A) & v2_classes1(A) ) => v1_classes2(A) ) )).
fof(cc3_clopban3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_closure1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_closure1(B,A) => ( v9_closure1(B,A) => v8_closure1(B,A) ) ) ) )).
fof(cc3_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) => ( v4_closure2(C,A,B) => v5_closure2(C,A,B) ) ) ) )).
fof(cc3_cohsp_1,axiom,( ! [A] : ( v1_classes1(A) => v2_finsub_1(A) ) )).
fof(cc3_compact1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) & v4_compos_1(B,A) ) ) ) )).
fof(cc3_compts_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v8_struct_0(A) & v2_pre_topc(A) ) => ( v2_pre_topc(A) & v1_compts_1(A) ) ) ) )).
fof(cc3_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(k4_ordinal1),k4_ordinal1))) => ( v1_funct_1(A) => ( v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v4_valued_0(A) ) ) ) )).
fof(cc3_comseq_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) => ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v1_comseq_3(A) ) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) ) ) ) )).
fof(cc3_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_connsp_1(B,A) => v4_pre_topc(B,A) ) ) ) )).
fof(cc3_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_zfmisc_1(B) => v2_dilworth(B,A) ) ) ) )).
fof(cc3_entropy1,axiom,( ! [A] : ( m1_finseq_1(A,k3_finseq_2(k1_numbers)) => ( ( v1_matrix_0(A) & v4_matrprob(A) ) => ( ~ v3_relat_1(A) & v1_matrix_0(A) ) ) ) )).
fof(cc3_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => v3_valued_0(B) ) ) )).
fof(cc3_euclid_7,axiom,( ! [A] : ( v3_euclid_7(A) => ( v1_euclid_7(A) & v2_euclid_7(A) ) ) )).
fof(cc3_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_exchsort(A,k5_numbers) ) ) )).
fof(cc3_facirc_1,axiom,( ! [A] : ( v1_xboole_0(A) => ~ v1_facirc_1(A) ) )).
fof(cc3_facirc_2,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_facirc_1(A) ) ) )).
fof(cc3_fcont_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_filter_0,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_finseq_1,axiom,( ! [A] : ! [B] : ( m1_finseq_1(B,A) => v5_relat_1(B,A) ) )).
fof(cc3_finseq_2,axiom,( ! [A] : ! [B] : ( m1_finseq_2(B,A) => v3_finseq_1(B) ) )).
fof(cc3_finset_1,axiom,( ! [A] : ! [B] : ( v1_finset_1(A) => ! [C] : ( 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) ) ) ) ) )).
fof(cc3_finsub_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(A)) => v1_finset_1(B) ) )).
fof(cc3_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v3_fintopo6(B,A) ) ) ) )).
fof(cc3_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k4_finseq_2(1,A))) => v3_fomodel0(B,A) ) ) )).
fof(cc3_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_fomodel1(A)) => ( v6_fomodel1(B,A) => v8_fomodel1(B,A) ) ) ) )).
fof(cc3_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & ~ v1_xboole_0(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(cc3_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k37_fomodel1(A)) => v10_fomodel1(B,A) ) ) )).
fof(cc3_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( v3_fomodel4(B,A) => v1_finset_1(B) ) ) )).
fof(cc3_frechet,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) ) )).
fof(cc3_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_funct_1(B) ) ) )).
fof(cc3_funct_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ( v1_funct_2(C,A,B) => v1_partfun1(C,A) ) ) ) )).
fof(cc3_funct_7,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc3_funct_8,axiom,( ! [A] : ! [B] : ( ( v1_membered(A) & v1_membered(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc3_functor0,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( l1_functor0(C,A,B) => ( v10_functor0(C,A,B) => v6_functor0(C,A,B) ) ) ) )).
fof(cc3_functor2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m2_functor0(C,A,B) => ( ( v10_functor0(C,A,B) & v13_functor0(C,A,B) ) => v15_functor0(C,A,B) ) ) ) )).
fof(cc3_fvaluat1,axiom,( ! [A] : ( ( v1_xreal_0(A) & v1_fvaluat1(A) ) => v1_int_1(A) ) )).
fof(cc3_gcd_1,axiom,( ! [A] : ( l6_algstr_0(A) => ( ( ~ v2_struct_0(A) & v5_group_1(A) & v2_vectsp_1(A) ) => ( ~ v2_struct_0(A) & v5_vectsp_1(A) ) ) ) )).
fof(cc3_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v7_glib_000(A) ) ) )).
fof(cc3_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v3_glib_001(B,A) => v6_glib_001(B,A) ) ) ) )).
fof(cc3_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_002(A) ) => ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v7_glib_000(A) ) ) )).
fof(cc3_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => ( v1_xboole_0(B) => v7_graph_1(B,A) ) ) ) )).
fof(cc3_grnilp_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => v8_struct_0(B) ) ) )).
fof(cc3_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_group_7(k1_tarski(1),k9_finseq_1(A)))) => v1_finseq_1(B) ) ) )).
fof(cc3_groupp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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) ) ) ) ) )).
fof(cc3_hahnban,axiom,( ! [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) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc3_hahnban1,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(cc3_hallmar1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & ~ v1_xboole_0(B) & m1_finseq_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m4_hallmar1(C,A,B) => ~ v1_xboole_0(C) ) ) )).
fof(cc3_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc3_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc3_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => v1_finseq_1(A) ) )).
fof(cc3_instalg1,axiom,( ! [A] : ( l1_msualg_1(A) => ( v11_struct_0(A) => v1_instalg1(A) ) ) )).
fof(cc3_int_1,axiom,( ! [A] : ( v1_int_1(A) => v1_xreal_0(A) ) )).
fof(cc3_int_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ( v7_ordinal1(A) & ~ v8_ordinal1(A) & v1_int_2(A) ) ) )).
fof(cc3_int_6,axiom,( ! [A] : ( ( 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] : ( m1_int_6(B,A) => v5_relat_1(B,k4_numbers) ) ) )).
fof(cc3_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_subset_1(B,k1_integra1(A)) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) )).
fof(cc3_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => v1_finseq_1(A) ) )).
fof(cc3_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_isomichi(B,A) & v2_isomichi(B,A) ) => v4_tops_1(B,A) ) ) ) )).
fof(cc3_jordan,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( ~ v9_rltopsp1(B,k15_euclid(A)) => ~ v1_xboole_0(B) ) ) ) )).
fof(cc3_jordan23,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_jordan23(A) ) ) )).
fof(cc3_lattice2,axiom,( ! [A] : ( l3_lattices(A) => ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v10_lattices(A) ) => ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) ) ) ) )).
fof(cc3_lattice6,axiom,( ! [A] : ( l3_lattices(A) => ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v10_lattices(A) ) => ( ~ v2_struct_0(A) & v10_lattices(A) & v2_lattice6(A) ) ) ) )).
fof(cc3_lattices,axiom,( ! [A] : ( l3_lattices(A) => ( ( ~ v2_struct_0(A) & v13_lattices(A) & v14_lattices(A) ) => ( ~ v2_struct_0(A) & v15_lattices(A) ) ) ) )).
fof(cc3_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_lexbfs(B,A) => ( v4_lexbfs(B,A) => ( v13_glib_000(B) & v2_lexbfs(B) ) ) ) ) )).
fof(cc3_lfuzzy_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_lfuzzy_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v1_xreal_0(B) ) ) )).
fof(cc3_lopban_3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_ltlaxio4,axiom,( ! [A] : ( ( ~ v2_ltlaxio3(A) & m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) ) => ! [B] : ( m1_subset_1(B,k8_ltlaxio4(A)) => ~ v2_ltlaxio3(B) ) ) )).
fof(cc3_margrel1,axiom,( ! [A] : ! [B] : ( 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) ) ) ) )).
fof(cc3_matroid0,axiom,( ! [A] : ( l1_pre_topc(A) => ( v8_struct_0(A) => v4_matroid0(A) ) ) )).
fof(cc3_matrprob,axiom,( ! [A] : ( m1_finseq_1(A,k3_finseq_2(k1_numbers)) => ( ( v1_matrix_0(A) & v6_matrprob(A) ) => ( v1_matrix_0(A) & v2_matrprob(A) & v5_matrprob(A) ) ) ) )).
fof(cc3_matrtop3,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc3_measure1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( ( v2_finsub_1(B) & v1_prob_1(B,A) ) => v3_finsub_1(B) ) ) )).
fof(cc3_measure5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v3_measure5(A) => v6_xxreal_2(A) ) ) )).
fof(cc3_membered,axiom,( ! [A] : ( v4_membered(A) => v3_membered(A) ) )).
fof(cc3_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) => v5_topgen_4(B,A) ) ) ) )).
fof(cc3_mfold_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v2_mfold_1(A,k5_numbers) ) => ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) ) ) ) )).
fof(cc3_mmlquer2,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( ( v1_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A) ) => ( v1_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A) & v1_wellord1(B) ) ) ) ) )).
fof(cc3_monoid_0,axiom,( ! [A] : ( ( v2_monoid_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v1_finseq_1(B) ) ) )).
fof(cc3_msafree2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,k1_funct_1(u3_msualg_1(A,k11_msafree(A,B)),C)) => ( v1_relat_1(D) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) ) ) ) )).
fof(cc3_msafree3,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k3_card_3(u3_msualg_1(A,k1_msafree3(A,B)))) => v3_trees_9(C) ) ) )).
fof(cc3_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_pboole(C,u1_struct_0(A),u3_msualg_1(A,k11_msafree(A,B))) ) => ! [E] : ( m1_subset_1(E,k1_funct_1(C,D)) => ( v1_relat_1(E) & v1_funct_1(E) ) ) ) )).
fof(cc3_msscyc_1,axiom,( ! [A] : ( l1_graph_1(A) => ( ( ~ v2_struct_0(A) & v11_struct_0(A) ) => ( ~ v2_struct_0(A) & v3_msscyc_1(A) ) ) ) )).
fof(cc3_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) => ( v2_mssubfam(C,A,B) => v1_mssubfam(C,A,B) ) ) ) )).
fof(cc3_msualg_6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc3_mycielsk,axiom,( ! [A] : ( m1_mycielsk(A,k5_numbers) => v2_struct_0(A) ) )).
fof(cc3_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( v7_ordinal1(A) & ~ v3_xxreal_0(A) ) ) )).
fof(cc3_nat_lat,axiom,( ! [A] : ( m1_subset_1(A,k6_nat_lat) => ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) ) )).
fof(cc3_nattra_1,axiom,( ! [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) & v4_nattra_1(A) & l1_cat_1(A) ) => ! [B] : ( m3_cat_2(B,A) => v4_nattra_1(B) ) ) )).
fof(cc3_neckla_3,axiom,( ! [A] : ( ( v3_necklace(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v4_yellow_0(B,A) => ( v4_yellow_0(B,A) & v3_necklace(B) ) ) ) ) )).
fof(cc3_nfcont_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc3_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( 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) ) ) ) ) )).
fof(cc3_oposet_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_ordinal1,axiom,( ! [A] : ( v1_xboole_0(A) => v3_ordinal1(A) ) )).
fof(cc3_ordinal5,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc3_ordinal6,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc3_osalg_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => v7_osalg_1(B,A) ) ) )).
fof(cc3_osalg_4,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_partfun1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_relat_2(A) & v8_relat_2(A) ) => ( v1_relat_1(A) & v1_relat_2(A) ) ) )).
fof(cc3_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( m2_pboole(D,A,B,C) => v1_funcop_1(D) ) ) )).
fof(cc3_pcs_0,axiom,( ! [A] : ( l1_pcs_0(A) => ( v4_pcs_0(A) => v3_pcs_0(A) ) ) )).
fof(cc3_pencil_1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc3_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc3_pre_poly,axiom,( ! [A] : ! [B] : ( m1_finseq_1(B,k3_finseq_2(A)) => v1_pre_poly(B) ) )).
fof(cc3_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ( v11_pre_topc(A) => ( v7_pre_topc(A) & v9_pre_topc(A) ) ) ) )).
fof(cc3_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) ) => ! [B] : ( m1_prvect_1(B,A) => v1_funcop_1(B) ) ) )).
fof(cc3_pua2mss1,axiom,( ! [A] : ! [B] : ( m2_pua2mss1(B,A) => ( v2_relat_1(B) & v2_funct_1(B) ) ) )).
fof(cc3_quantal1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_quofield,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) & ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc3_ratfunc1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) => ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & v1_ratfunc1(B,A) ) => ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & v2_ratfunc1(B,A) ) ) ) ) )).
fof(cc3_rcomp_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k2_topalg_2))) => ( v6_xxreal_2(A) => v2_connsp_1(A,k2_topalg_2) ) ) )).
fof(cc3_relat_1,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) ) => ( v1_relat_1(A) & v3_relat_1(A) ) ) )).
fof(cc3_relat_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_2(A) & v8_relat_2(A) ) => ( v1_relat_1(A) & v5_relat_2(A) ) ) )).
fof(cc3_relset_1,axiom,( ! [A] : ! [B] : ( v1_xboole_0(A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => v1_xboole_0(C) ) ) )).
fof(cc3_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_2(A) & v1_rewrite1(A) ) => ( v1_relat_1(A) & v3_rewrite1(A) ) ) )).
fof(cc3_rfunct_2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc3_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_xboole_0(B) => v2_rlaffin1(B,A) ) ) ) )).
fof(cc3_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v9_rltopsp1(B,A) ) ) ) )).
fof(cc3_rlvect_1,axiom,( ! [A] : ( l2_algstr_0(A) => ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) ) => ( ~ v2_struct_0(A) & v12_algstr_0(A) ) ) ) )).
fof(cc3_robbins1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_robbins2,axiom,( ! [A] : ( l2_robbins1(A) => ( ( ~ v2_struct_0(A) & v1_robbins2(A) ) => ( ~ v2_struct_0(A) & v5_robbins1(A) ) ) ) )).
fof(cc3_robbins3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_robbins4,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_roughs_1,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_orders_3(A) => v1_roughs_1(A) ) ) )).
fof(cc3_scm_halt,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & 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) ) ) )).
fof(cc3_scmfsa6b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) ) )).
fof(cc3_scmyciel,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v3_scmyciel(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => v3_scmyciel(C,A) ) ) )).
fof(cc3_seq_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) => ( ( v1_funct_1(A) & v3_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) ) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_comseq_2(A) ) ) ) )).
fof(cc3_seq_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) => ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v1_seqm_3(A) & v1_comseq_2(A) ) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_comseq_2(A) ) ) ) )).
fof(cc3_seqm_3,axiom,( ! [A] : ( m1_finseq_1(A,k4_ordinal1) => v4_valued_0(A) ) )).
fof(cc3_setfam_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) => ~ v2_setfam_1(A) ) )).
fof(cc3_sheffer1,axiom,( ! [A] : ( l1_sheffer1(A) => ( v13_struct_0(A,1) => ( v13_struct_0(A,1) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) ) ) ) )).
fof(cc3_simplex0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) ) => ~ v1_setfam_1(A) ) )).
fof(cc3_simplex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_simplex0(B,u1_struct_0(A)) => ( v4_simplex0(B) => v2_simplex1(B,A) ) ) ) )).
fof(cc3_simplex2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_simplex0(B,u1_struct_0(k15_euclid(A))) => ( v2_simplex2(B,A) => v1_simplex2(B,k14_euclid(A)) ) ) ) )).
fof(cc3_sppol_2,axiom,( ! [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v4_topreal1(A) => ~ v1_xboole_0(A) ) ) )).
fof(cc3_struct_0,axiom,( ! [A] : ( l4_struct_0(A) => ( ~ v6_struct_0(A) => ~ v7_struct_0(A) ) ) )).
fof(cc3_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_xboole_0(B) => v1_subset_1(B,A) ) ) ) )).
fof(cc3_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_finset_1(B) => v6_tbsp_1(B,A) ) ) ) )).
fof(cc3_tdlat_3,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_tdlat_3(A) => v3_tdlat_3(A) ) ) )).
fof(cc3_tex_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_tex_2,axiom,( ! [A] : ( v3_card_1(A,1) => ! [B] : ( 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) ) ) ) ) )).
fof(cc3_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( v1_borsuk_1(B,A) & v1_tex_2(B,A) ) => ~ v1_tex_3(B,A) ) ) ) )).
fof(cc3_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc3_topalg_2,axiom,( ! [A] : ( m1_pre_topc(A,k2_topalg_2) => ( ( ~ v2_struct_0(A) & v2_topalg_2(A) ) => ( ~ v2_struct_0(A) & v1_borsuk_2(A) ) ) ) )).
fof(cc3_topalg_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( m1_borsuk_2(C,A,B,B) => v5_pre_topc(C,k5_topmetr,A) ) ) )).
fof(cc3_topalg_6,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_topdim_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_struct_0(A) & v2_pre_topc(A) ) => ( v2_pre_topc(A) & v3_topdim_1(A) ) ) ) )).
fof(cc3_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(cc3_topgen_4,axiom,( ! [A] : ( ~ v1_finset_1(A) => ~ v1_zfmisc_1(A) ) )).
fof(cc3_topgrp_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) & ~ v2_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc3_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ~ v2_sppol_1(A) => ~ v1_xboole_0(A) ) ) )).
fof(cc3_topreala,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc3_toprealc,axiom,( ! [A] : ( ( v2_pre_topc(A) & v2_toprealc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => v2_toprealc(B) ) ) )).
fof(cc3_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v3_tops_1(B,A) ) ) ) )).
fof(cc3_trees_3,axiom,( ! [A] : ( v1_trees_3(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_trees_3(B) ) ) )).
fof(cc3_trees_9,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc3_tsp_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v2_tsp_2(B,A) => v1_tex_3(B,A) ) ) ) )).
fof(cc3_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) ) => ( v1_relat_1(A) & v3_valued_0(A) ) ) )).
fof(cc3_valued_2,axiom,( ! [A] : ( v4_valued_2(A) => v3_valued_2(A) ) )).
fof(cc3_vectsp10,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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] : ( 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)) ) ) ) ) )).
fof(cc3_vectsp_1,axiom,( ! [A] : ( l4_algstr_0(A) => ( ( ~ v2_struct_0(A) & v4_vectsp_1(A) ) => ( ~ v2_struct_0(A) & v3_vectsp_1(A) & v6_vectsp_1(A) ) ) ) )).
fof(cc3_waybel10,axiom,( ! [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] : ( m1_yellow_0(B,A) => ( v8_yellow_0(B,A) => ~ v2_struct_0(B) ) ) ) )).
fof(cc3_waybel11,axiom,( ! [A] : ( ( v13_struct_0(A,1) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => v13_waybel_0(B,A) ) ) )).
fof(cc3_waybel17,axiom,( ! [A] : ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(cc3_waybel19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => v1_yellow_0(B) ) ) )).
fof(cc3_waybel23,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_waybel23(B,A) => v2_waybel_0(B,A) ) ) ) )).
fof(cc3_waybel25,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(cc3_waybel29,axiom,( ! [A] : ( ( ~ 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] : ( m1_yellow_9(B,A) => ( v4_waybel11(B) => v2_pre_topc(B) ) ) ) )).
fof(cc3_waybel30,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_waybel32,axiom,( ! [A] : ( ( ~ 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] : ( m1_yellow_9(B,A) => v24_waybel_0(B) ) ) )).
fof(cc3_waybel33,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v25_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => v25_waybel_0(B) ) ) )).
fof(cc3_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v8_yellow_0(B,A) => v4_waybel_0(B,A) ) ) ) )).
fof(cc3_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc3_waybel_2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_waybel_3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_waybel_4,axiom,( ! [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] : ( 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) ) ) ) )).
fof(cc3_waybel_5,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_waybel_8,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_xcmplx_0,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => v1_xcmplx_0(A) ) )).
fof(cc3_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xcmplx_0(A) ) )).
fof(cc3_xxreal_0,axiom,( ! [A] : ( ( v1_xxreal_0(A) & v2_xxreal_0(A) ) => ( ~ v8_ordinal1(A) & v1_xxreal_0(A) & ~ v3_xxreal_0(A) ) ) )).
fof(cc3_xxreal_2,axiom,( ! [A] : ( ( v6_membered(A) & ~ v1_xboole_0(A) ) => ( v6_membered(A) & ~ v1_xboole_0(A) & v1_xxreal_2(A) ) ) )).
fof(cc3_yellow11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( ~ v1_xboole_0(B) & v2_yellow11(B,A) ) => v2_waybel_0(B,A) ) ) ) )).
fof(cc3_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v8_struct_0(A) & v2_pre_topc(A) ) => ( v2_pre_topc(A) & v1_compts_1(A) ) ) ) )).
fof(cc3_yellow14,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_struct_0(A) => v3_yellow_0(A) ) ) )).
fof(cc3_yellow18,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc3_yellow21,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc3_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v2_struct_0(A) & v3_lattice3(A) ) => ( ~ v2_struct_0(A) & v3_yellow_0(A) ) ) ) )).
fof(cc3_yellow_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v2_struct_0(A) & v3_orders_2(A) ) => ~ v1_yellow_3(A) ) ) )).
fof(cc3_yellow_6,axiom,( ! [A] : ! [B] : ( l1_struct_0(B) => ! [C] : ( m3_yellow_6(C,A,B) => v4_waybel_3(C) ) ) )).
fof(cc3_yellow_9,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => v4_orders_2(B) ) ) )).
fof(cc40_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v4_tex_2(B,A) => v1_tex_2(B,A) ) ) ) )).
fof(cc41_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & v4_tex_2(B,A) ) => ( ~ v2_struct_0(B) & v7_struct_0(B) ) ) ) ) )).
fof(cc42_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & ~ v7_struct_0(B) ) => ( ~ v2_struct_0(B) & ~ v4_tex_2(B,A) ) ) ) ) )).
fof(cc43_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & v7_struct_0(B) ) => ( ~ v2_struct_0(B) & v4_tex_2(B,A) ) ) ) ) )).
fof(cc44_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & ~ v4_tex_2(B,A) ) => ( ~ v2_struct_0(B) & ~ v7_struct_0(B) ) ) ) ) )).
fof(cc45_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & v4_tex_2(B,A) ) => ( ~ v2_struct_0(B) & v1_tex_2(B,A) ) ) ) ) )).
fof(cc46_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & ~ v1_tex_2(B,A) ) => ( ~ v2_struct_0(B) & ~ v4_tex_2(B,A) ) ) ) ) )).
fof(cc47_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v2_tdlat_3(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & v4_tex_2(B,A) ) => ( ~ v2_struct_0(B) & ~ v7_struct_0(B) ) ) ) ) )).
fof(cc48_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v2_tdlat_3(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( ~ v2_struct_0(B) & v7_struct_0(B) ) => ( ~ v2_struct_0(B) & ~ v4_tex_2(B,A) ) ) ) ) )).
fof(cc4_abcmiz_0,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_abcmiz_1,axiom,( ! [A] : ( l1_msualg_1(A) => ( ( v1_instalg1(A) & v1_abcmiz_1(A) ) => ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_instalg1(A) ) ) ) )).
fof(cc4_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ( v4_abcmiz_a(B,A) => v2_abcmiz_1(B,A) ) ) ) )).
fof(cc4_afinsq_1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc4_algstr_0,axiom,( ! [A] : ( l1_algstr_0(A) => ( v7_algstr_0(A) => ( v5_algstr_0(A) & v6_algstr_0(A) ) ) ) )).
fof(cc4_algstr_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_altcat_1,axiom,( ! [A] : ( l2_altcat_1(A) => ( v13_altcat_1(A) => v2_altcat_1(A) ) ) )).
fof(cc4_altcat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc4_altcat_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) & v1_funct_1(B) & v1_funct_2(B,k1_xboole_0,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_xboole_0,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v5_altcat_5(C,A,k1_xboole_0,B) => v7_altcat_3(C,A) ) ) ) )).
fof(cc4_ami_wstd,axiom,( ! [A] : ! [B] : ( ( ~ v1_setfam_1(A) & ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) & v5_ami_wstd(C,A,B) ) ) ) )).
fof(cc4_amistd_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_compos_1(B)) => ( v4_amistd_1(C,A,B) => v3_amistd_2(C,A,B) ) ) ) )).
fof(cc4_aofa_000,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & v2_relat_1(D) & m1_msafree(D,A,B) ) => ! [E] : ( m1_subset_1(E,k13_aofa_a00(A,B,C,D)) => ( v4_relat_1(E,u1_struct_0(A)) & v1_funcop_1(E) ) ) ) )).
fof(cc4_armstrng,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(cc4_bcialg_1,axiom,( ! [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) ) => ( ~ v2_struct_0(A) & v3_bcialg_1(A) & v4_bcialg_1(A) & v5_bcialg_1(A) & v7_bcialg_1(A) & v16_bcialg_1(A) ) ) ) )).
fof(cc4_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) => ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_bhsp_2(B,A) ) => ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v2_bhsp_3(B,A) ) ) ) ) )).
fof(cc4_card_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => v1_finset_1(A) ) )).
fof(cc4_card_3,axiom,( ! [A] : ( v5_card_3(A) => ( ~ v1_finset_1(A) & v4_card_3(A) ) ) )).
fof(cc4_card_fil,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(cc4_catalg_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_catalg_1(B,A) => ~ v2_struct_0(B) ) ) )).
fof(cc4_cayldick,axiom,( ! [A] : ( l6_algstr_0(A) => ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & v5_group_1(A) & v2_vectsp_1(A) ) => ( ~ v2_struct_0(A) & v2_rlvect_1(A) & v5_group_1(A) & v1_vectsp_1(A) ) ) ) )).
fof(cc4_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ! [B] : ( m1_subset_1(B,k10_cgames_1(A)) => v2_cgames_1(B) ) ) )).
fof(cc4_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m3_chord(B,A) => ~ v1_xboole_0(B) ) ) )).
fof(cc4_circcmb3,axiom,( ! [A] : ( ( v4_circcmb3(A) & l1_msualg_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc4_circtrm1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u4_struct_0(k1_circtrm1(A,B,C))) => v3_trees_2(D) ) ) )).
fof(cc4_closure1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_closure1(B,A) => ( v9_closure1(B,A) => v10_closure1(B,A) ) ) ) )).
fof(cc4_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) => ( v5_closure2(C,A,B) => ~ v1_xboole_0(C) ) ) ) )).
fof(cc4_cohsp_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(cc4_compact1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_compts_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_finset_1(B) => v2_compts_1(B,A) ) ) ) )).
fof(cc4_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(k4_ordinal1),k4_ordinal1))) => ( ( v1_funct_1(A) & v3_margrel1(A,k4_ordinal1) ) => ( v1_funct_1(A) & v2_comput_1(A) ) ) ) )).
fof(cc4_comseq_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) => ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_3(A) ) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v1_comseq_3(A) ) ) ) )).
fof(cc4_connsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v2_connsp_1(B,A) ) ) ) )).
fof(cc4_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ( v8_struct_0(A) => v3_dilworth(A) ) ) )).
fof(cc4_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => v3_card_1(B,A) ) ) )).
fof(cc4_euclid_7,axiom,( ! [A] : ( ( v1_euclid_7(A) & v2_euclid_7(A) ) => v3_euclid_7(A) ) )).
fof(cc4_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_exchsort(A,1) ) ) )).
fof(cc4_facirc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_facirc_1(A) ) => v1_xboole_0(A) ) )).
fof(cc4_fcont_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_filter_0,axiom,( ! [A] : ( l3_lattices(A) => ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) ) => ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) ) ) ) )).
fof(cc4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) ) => ( v1_relat_1(A) & v1_finseq_1(A) ) ) )).
fof(cc4_finset_1,axiom,( ! [A] : ( v1_zfmisc_1(A) => v1_finset_1(A) ) )).
fof(cc4_fomodel0,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,B) ) => ( v1_relat_1(C) & v5_relat_1(C,A) ) ) ) )).
fof(cc4_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_fomodel1(A)) => ( v4_fomodel1(B,A) => v8_fomodel1(B,A) ) ) ) )).
fof(cc4_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_fomodel2(D,A,B,C) => ~ v1_xboole_0(D) ) ) )).
fof(cc4_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(cc4_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v3_fomodel4(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => v3_fomodel4(C,A) ) ) )).
fof(cc4_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) ) => ! [D] : ( 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) ) ) ) ) )).
fof(cc4_funct_1,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v3_funct_1(A) ) ) )).
fof(cc4_funct_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( v1_funct_2(B,A,A) => v1_partfun1(B,A) ) ) )).
fof(cc4_funct_7,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_funct_7(B,A) => ( v2_relat_1(B) & v1_funct_7(B) ) ) ) )).
fof(cc4_funct_8,axiom,( ! [A] : ! [B] : ( ( v1_membered(A) & v1_membered(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc4_functor0,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( l1_functor0(C,A,B) => ( v11_functor0(C,A,B) => v6_functor0(C,A,B) ) ) ) )).
fof(cc4_functor2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m2_functor0(C,A,B) => ( v16_functor0(C,A,B) => ( v11_functor0(C,A,B) & v14_functor0(C,A,B) ) ) ) ) )).
fof(cc4_gcd_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v8_glib_000(A) ) ) )).
fof(cc4_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v6_glib_001(B,A) => v5_glib_001(B,A) ) ) ) )).
fof(cc4_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_002(A) & v2_glib_002(A) ) ) )).
fof(cc4_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc4_group_7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) & ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,k4_card_3(k12_pralg_1(k2_tarski(1,2),k10_finseq_1(A,B)))) => v1_finseq_1(C) ) ) )).
fof(cc4_groupp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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) ) ) ) ) )).
fof(cc4_hahnban,axiom,( ! [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) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc4_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc4_instalg1,axiom,( ! [A] : ( l1_msualg_1(A) => ( ( v2_struct_0(A) & v1_instalg1(A) ) => v11_struct_0(A) ) ) )).
fof(cc4_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_subset_1(B,k1_integra1(A)) => ( v1_finseq_1(B) & v3_valued_0(B) ) ) ) )).
fof(cc4_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_isomichi(B,A) => v1_decomp_1(B,A) ) ) ) )).
fof(cc4_jordan,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( 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))) ) ) ) )).
fof(cc4_jordan23,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc4_lattice2,axiom,( ! [A] : ( l3_lattices(A) => ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v10_lattices(A) ) => ( ~ v2_struct_0(A) & v10_lattices(A) & v14_lattices(A) ) ) ) )).
fof(cc4_lattices,axiom,( ! [A] : ( l3_lattices(A) => ( ( ~ v2_struct_0(A) & v15_lattices(A) ) => ( ~ v2_struct_0(A) & v13_lattices(A) & v14_lattices(A) ) ) ) )).
fof(cc4_lfuzzy_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_lfuzzy_0(A) => ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) ) ) ) )).
fof(cc4_ltlaxio4,axiom,( ! [A] : ( ( ~ v2_ltlaxio3(A) & m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) ) => ! [B] : ( m1_subset_1(B,k9_ltlaxio4(A)) => ~ v2_ltlaxio3(B) ) ) )).
fof(cc4_matroid0,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_tdlat_3(A) => ( v1_tdlat_3(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) ) ) ) )).
fof(cc4_matrprob,axiom,( ! [A] : ( m1_finseq_1(A,k3_finseq_2(k1_numbers)) => ( ( v1_matrix_0(A) & v2_matrprob(A) & v5_matrprob(A) ) => ( v1_matrix_0(A) & v6_matrprob(A) ) ) ) )).
fof(cc4_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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) ) ) ) ) )).
fof(cc4_measure1,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(cc4_measure5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v4_measure5(A) => v6_xxreal_2(A) ) ) )).
fof(cc4_membered,axiom,( ! [A] : ( v3_membered(A) => v2_membered(A) ) )).
fof(cc4_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(B,A) => v6_topgen_4(B,A) ) ) ) )).
fof(cc4_mfold_1,axiom,( ! [A] : ( 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,k5_numbers) ) ) ) )).
fof(cc4_mmlquer2,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( ( v1_relat_2(B) & v4_relat_2(B) & v6_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A) ) => ( v1_relat_2(B) & v4_relat_2(B) & v6_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A) & v2_wellord1(B) ) ) ) ) )).
fof(cc4_monoid_0,axiom,( ! [A] : ( l3_algstr_0(A) => ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) ) => ( ~ v2_struct_0(A) & v13_monoid_0(A) ) ) ) )).
fof(cc4_msafree2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(cc4_msafree3,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc4_msafree4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( l3_msualg_1(C,A) => ( v4_msafree4(C,A,B) => v4_msualg_1(C,A) ) ) ) )).
fof(cc4_msscyc_1,axiom,( ! [A] : ( l1_graph_1(A) => ( ( ~ v2_struct_0(A) & ~ v3_msscyc_1(A) ) => ( ~ v2_struct_0(A) & ~ v11_struct_0(A) ) ) ) )).
fof(cc4_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) => ( v4_mssubfam(C,A,B) => v3_mssubfam(C,A,B) ) ) ) )).
fof(cc4_msualg_6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(cc4_mycielsk,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( m1_mycielsk(B,A) => ~ v2_struct_0(B) ) ) )).
fof(cc4_nat_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v8_ordinal1(A) ) => ( v7_ordinal1(A) & ~ v2_xxreal_0(A) ) ) )).
fof(cc4_nat_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k10_nat_lat)) => ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) ) )).
fof(cc4_neckla_3,axiom,( ! [A] : ( ( v1_necklace(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v4_yellow_0(B,A) => ( v4_yellow_0(B,A) & v1_necklace(B) ) ) ) ) )).
fof(cc4_nfcont_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc4_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( 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) ) ) ) ) )).
fof(cc4_orders_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v16_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) ) => ( ~ v2_struct_0(B) & v16_waybel_0(B) ) ) ) ) )).
fof(cc4_ordinal1,axiom,( ! [A] : ( v1_xboole_0(A) => v5_ordinal1(A) ) )).
fof(cc4_ordinal5,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc4_ordinal6,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc4_osalg_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k2_osalg_4(A)) => v1_waybel_0(B,A) ) ) )).
fof(cc4_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(cc4_pcs_0,axiom,( ! [A] : ( l1_pcs_0(A) => ( v2_struct_0(A) => ( v4_pcs_0(A) & v5_pcs_0(A) & v6_pcs_0(A) ) ) ) )).
fof(cc4_pencil_1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc4_pre_poly,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_pre_poly(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) ) )).
fof(cc4_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v7_pre_topc(A) & v9_pre_topc(A) ) => v11_pre_topc(A) ) ) )).
fof(cc4_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) ) => ! [B] : ( m2_prvect_1(B,A) => v1_funcop_1(B) ) ) )).
fof(cc4_pua2mss1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_pua2mss1(B,A) => ~ v1_xboole_0(B) ) ) )).
fof(cc4_quofield,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) & ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc4_ratfunc1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) => ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & ~ v2_ratfunc1(B,A) ) => ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & ~ v1_ratfunc1(B,A) ) ) ) ) )).
fof(cc4_rcomp_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k1_numbers))) => ! [B] : ( m1_subset_1(B,A) => v3_membered(B) ) ) )).
fof(cc4_relat_1,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) ) => ( v1_relat_1(A) & v2_relat_1(A) ) ) )).
fof(cc4_relat_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_2(A) ) => ( v1_relat_1(A) & v2_relat_2(A) & v4_relat_2(A) ) ) )).
fof(cc4_relset_1,axiom,( ! [A] : ! [B] : ( v1_xboole_0(A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,A))) => v1_xboole_0(C) ) ) )).
fof(cc4_rewrite1,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) ) => ( v1_relat_1(A) & v2_rewrite1(A) & v3_rewrite1(A) ) ) )).
fof(cc4_rfunct_2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(cc4_rltopsp1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_robbins1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_robbins4,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_roughs_1,axiom,( ! [A] : ( l1_orders_2(A) => ( ~ v1_roughs_1(A) => ~ v1_orders_3(A) ) ) )).
fof(cc4_scm_halt,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & 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) ) ) )).
fof(cc4_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ( ~ v1_xboole_0(A) & v1_classes1(A) & v3_scmyciel(A,1) ) ) )).
fof(cc4_seq_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) => ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_comseq_2(A) ) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v1_comseq_2(A) ) ) ) )).
fof(cc4_seqm_3,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => v3_valued_0(A) ) )).
fof(cc4_setfam_1,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ~ v2_setfam_1(A) ) )).
fof(cc4_sheffer1,axiom,( ! [A] : ( l2_lattices(A) => ( v13_struct_0(A,1) => ( v13_struct_0(A,1) & v4_lattices(A) & v5_lattices(A) ) ) ) )).
fof(cc4_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ( ~ v5_simplex0(A) => ~ v3_pencil_1(A) ) ) )).
fof(cc4_simplex1,axiom,( ! [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) & v8_rlvect_1(A) & l1_rlvect_1(A) & v1_simplex1(B,A) & m1_simplex0(B,u1_struct_0(A)) ) => ! [C] : ( m2_simplex0(C,u1_struct_0(A),B) => v1_simplex1(C,A) ) ) )).
fof(cc4_simplex2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_simplex0(B,u1_struct_0(k15_euclid(A))) => ( v2_simplex0(B) => v2_simplex2(B,A) ) ) ) )).
fof(cc4_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal4(A) => ~ v1_xboole_0(A) ) ) )).
fof(cc4_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => ( v2_struct_0(A) => ( v2_struct_0(A) & v8_struct_0(A) ) ) ) )).
fof(cc4_subset_1,axiom,( ! [A] : ( v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ~ v1_subset_1(B,A) ) ) )).
fof(cc4_tdlat_3,axiom,( ! [A] : ( l1_pre_topc(A) => ( v2_tdlat_3(A) => v3_tdlat_3(A) ) ) )).
fof(cc4_tex_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_tex_2,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ! [B] : ( 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) ) ) ) ) )).
fof(cc4_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v2_tex_3(B,A) => v1_tex_3(B,A) ) ) ) )).
fof(cc4_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc4_topalg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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] : ( m1_borsuk_6(F,A,B,C,D,E) => v5_pre_topc(F,k2_borsuk_1(k5_topmetr,k5_topmetr),A) ) ) )).
fof(cc4_topalg_6,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_topdim_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => v1_topdim_1(B,A) ) ) )).
fof(cc4_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v5_topgen_1(B,A) ) ) ) )).
fof(cc4_topgen_4,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m2_topgrp_1(B,A) => v3_tops_2(B,A,A) ) ) )).
fof(cc4_topreal6,axiom,( ! [A] : ( 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)) ) ) ) )).
fof(cc4_topreala,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & l1_pre_topc(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc4_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_tops_1(B,A) => v2_tops_1(B,A) ) ) ) )).
fof(cc4_trees_3,axiom,( ! [A] : ( v2_trees_3(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v2_trees_3(B) ) ) )).
fof(cc4_trees_9,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc4_tsp_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v1_tex_3(B,A) => ~ v2_tsp_2(B,A) ) ) ) )).
fof(cc4_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k3_numbers) ) => ( v1_relat_1(A) & v3_valued_0(A) ) ) )).
fof(cc4_valued_2,axiom,( ! [A] : ( v3_valued_2(A) => v1_valued_2(A) ) )).
fof(cc4_vectsp10,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v6_struct_0(A) & l6_algstr_0(A) & ~ v7_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(cc4_vectsp_1,axiom,( ! [A] : ( l4_algstr_0(A) => ( ( ~ v2_struct_0(A) & v3_vectsp_1(A) & v6_vectsp_1(A) ) => ( ~ v2_struct_0(A) & v1_group_1(A) ) ) ) )).
fof(cc4_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => ( v2_waybel11(B,A) & v3_waybel11(B,A) ) ) ) ) )).
fof(cc4_waybel17,axiom,( ! [A] : ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(cc4_waybel19,axiom,( ! [A] : ( ( ~ 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] : ( m1_yellow_9(B,A) => v3_waybel_3(B) ) ) )).
fof(cc4_waybel23,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_waybel23(B,A) => v1_waybel_0(B,A) ) ) ) )).
fof(cc4_waybel25,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(cc4_waybel30,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_waybel32,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v12_waybel_0(B,A) => v3_waybel11(B,A) ) ) ) )).
fof(cc4_waybel33,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => v2_lattice3(B) ) ) )).
fof(cc4_waybel34,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc4_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc4_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc4_waybel_2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_waybel_3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_waybel_4,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_waybel_5,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_waybel_8,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xxreal_0(A) ) )).
fof(cc4_xxreal_0,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & v1_xxreal_0(A) & ~ v3_xxreal_0(A) ) => ( v1_xxreal_0(A) & v2_xxreal_0(A) ) ) )).
fof(cc4_xxreal_2,axiom,( ! [A] : ( ( v2_membered(A) & v5_xxreal_2(A) ) => ( v2_membered(A) & v3_xxreal_2(A) & v4_xxreal_2(A) ) ) )).
fof(cc4_yellow11,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_yellow13,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_yellow14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_waybel11(A) & l1_waybel_9(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc4_yellow18,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,k1_altcat_1(A,B,C)) => ( v1_relat_1(D) & v1_funct_1(D) ) ) ) )).
fof(cc4_yellow21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & v3_yellow18(A) & l2_altcat_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc4_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_yellow_0(A) => ( v1_yellow_0(A) & v2_yellow_0(A) ) ) ) )).
fof(cc4_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc4_yellow_8,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc4_yellow_9,axiom,( ! [A] : ( ( v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => v5_orders_2(B) ) ) )).
fof(cc5_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_abcmiz_1(B,A,k13_abcmiz_1(A)) => ( v6_abcmiz_1(B,A) => ( ~ v7_abcmiz_1(B,A) & v8_abcmiz_1(B,A) ) ) ) ) )).
fof(cc5_abcmiz_a,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc5_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_ordinal1) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ( v1_relat_1(A) & v5_relat_1(A,k4_ordinal1) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) & v4_valued_0(A) ) ) )).
fof(cc5_algstr_0,axiom,( ! [A] : ( ( v5_algstr_0(A) & l1_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v2_algstr_0(B,A) ) ) )).
fof(cc5_algstr_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v21_algstr_0(A) & v5_algstr_1(A) & l4_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v23_algstr_0(B,A) ) ) )).
fof(cc5_amistd_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_compos_1(B)) => ( v2_extpro_1(C,A,B) => v3_amistd_2(C,A,B) ) ) ) )).
fof(cc5_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_aofa_000(D,A,B,C) => ( v13_aofa_000(D,A,B) & v14_aofa_000(D,A,B) ) ) ) )).
fof(cc5_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & v4_msafree4(C,A,B) & l3_msualg_1(C,A) & v2_relat_1(D) & m1_msafree(D,A,B) ) => ! [E] : ( m1_subset_1(E,k13_aofa_a00(A,B,C,D)) => v1_partfun1(E,u1_struct_0(A)) ) ) )).
fof(cc5_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( ( v4_msualg_1(B,A) & v6_aofa_a01(B,A) ) => ( v4_msualg_1(B,A) & v1_aofa_a01(B,A) ) ) ) ) )).
fof(cc5_armstrng,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(cc5_bcialg_1,axiom,( ! [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) ) => ( ~ v2_struct_0(A) & v3_bcialg_1(A) & v4_bcialg_1(A) & v5_bcialg_1(A) & v7_bcialg_1(A) & v16_bcialg_1(A) ) ) ) )).
fof(cc5_bhsp_3,axiom,( ! [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) & v8_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v2_bhsp_3(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_valued_0(C,B) => v2_bhsp_3(C,A) ) ) )).
fof(cc5_card_1,axiom,( ! [A] : ( v7_ordinal1(A) => v1_finset_1(A) ) )).
fof(cc5_card_3,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v4_card_3(A) ) => v5_card_3(A) ) )).
fof(cc5_card_fil,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) & v6_card_fil(A) ) => ( ~ v1_finset_1(A) & v1_card_1(A) & v4_card_fil(A) ) ) )).
fof(cc5_cayldick,axiom,( ! [A] : ( l6_algstr_0(A) => ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & v5_group_1(A) & v1_vectsp_1(A) ) => ( ~ v2_struct_0(A) & v2_rlvect_1(A) & v5_group_1(A) & v2_vectsp_1(A) ) ) ) )).
fof(cc5_cgames_1,axiom,( ! [A] : ( ( v2_cgames_1(A) & v7_cgames_1(A) ) => ( v2_cgames_1(A) & v5_cgames_1(A) & v6_cgames_1(A) ) ) )).
fof(cc5_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc5_closure1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_closure1(B,A) => ( v7_closure1(B,A) => v11_closure1(B,A) ) ) ) )).
fof(cc5_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) => ( v2_closure2(C,A,B) => v6_closure2(C,A,B) ) ) ) )).
fof(cc5_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_cohsp_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v6_cohsp_1(A) ) ) )).
fof(cc5_compact1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc5_compts_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( v2_struct_0(A) => v8_pre_topc(A) ) ) )).
fof(cc5_comput_1,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) ) => ( v1_relat_1(A) & v3_comput_1(A) ) ) )).
fof(cc5_dilworth,axiom,( ! [A] : ( ( v3_dilworth(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_dilworth(B,A) => ( v1_finset_1(B) & v1_dilworth(B,A) ) ) ) ) )).
fof(cc5_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ( v5_euclid_7(B,A) => ( v3_euclid_7(B) & v4_euclid_7(B,A) ) ) ) ) )).
fof(cc5_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_exchsort(A) & v2_exchsort(A,k5_numbers) ) => ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_exchsort(A) ) ) )).
fof(cc5_fcont_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc5_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finseq_1(A) ) ) )).
fof(cc5_finset_1,axiom,( ! [A] : ( ~ v1_finset_1(A) => ~ v1_zfmisc_1(A) ) )).
fof(cc5_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ( v1_funct_2(C,A,B) => v1_partfun1(C,A) ) ) ) )).
fof(cc5_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_fomodel1(A)) => ( v8_fomodel1(B,A) => v9_fomodel1(B,A) ) ) ) )).
fof(cc5_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) ) => ! [D] : ( 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) ) ) ) ) )).
fof(cc5_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(cc5_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( v8_fomodel4(C,A,B) => v4_fomodel4(C,A,B,k1_xboole_0) ) ) )).
fof(cc5_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v3_funct_1(A) ) => ( ~ v1_zfmisc_1(A) & v1_relat_1(A) & v1_funct_1(A) ) ) )).
fof(cc5_funct_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),A))) => ( v1_funct_2(B,k2_zfmisc_1(A,A),A) => v1_partfun1(B,k2_zfmisc_1(A,A)) ) ) )).
fof(cc5_funct_8,axiom,( ! [A] : ! [B] : ( ( v1_membered(A) & v1_membered(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc5_functor0,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m2_functor0(C,A,B) => ( v15_functor0(C,A,B) => v6_functor0(C,A,B) ) ) ) )).
fof(cc5_functor2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m2_functor0(C,A,B) => ( ( v11_functor0(C,A,B) & v14_functor0(C,A,B) ) => v16_functor0(C,A,B) ) ) ) )).
fof(cc5_gcd_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc5_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v8_glib_000(A) ) => ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_000(A) & v6_glib_000(A) ) ) )).
fof(cc5_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) ) )).
fof(cc5_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v8_glib_003(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc5_group_7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) & ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_group_7(k2_tarski(1,2),k10_finseq_1(A,B)))) => v1_finseq_1(C) ) ) )).
fof(cc5_groupp_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_group_2(C,B) => v2_groupp_1(C,A) ) ) )).
fof(cc5_hahnban,axiom,( ! [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) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc5_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc5_instalg1,axiom,( ! [A] : ( l1_msualg_1(A) => ( ( ~ v11_struct_0(A) & v1_instalg1(A) ) => ~ v2_struct_0(A) ) ) )).
fof(cc5_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_decomp_1(B,A) => v2_isomichi(B,A) ) ) ) )).
fof(cc5_jordan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v8_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v2_struct_0(B) => ( ~ v2_struct_0(B) & v8_pre_topc(B) ) ) ) ) )).
fof(cc5_lattice2,axiom,( ! [A] : ( l3_lattices(A) => ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v10_lattices(A) ) => ( ~ v2_struct_0(A) & v10_lattices(A) & v15_lattices(A) ) ) ) )).
fof(cc5_lattices,axiom,( ! [A] : ( l3_lattices(A) => ( ( ~ v2_struct_0(A) & v17_lattices(A) ) => ( ~ v2_struct_0(A) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A) ) ) ) )).
fof(cc5_lfuzzy_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v2_struct_0(A) & v1_lfuzzy_0(A) ) => ( ~ v2_struct_0(A) & v16_waybel_0(A) & v1_lfuzzy_0(A) ) ) ) )).
fof(cc5_ltlaxio4,axiom,( ! [A] : ( ( ~ v2_ltlaxio3(A) & m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) ) => ! [B] : ( m1_subset_1(B,k9_ltlaxio4(A)) => v3_ltlaxio3(B) ) ) )).
fof(cc5_matroid0,axiom,( ! [A] : ! [B] : ( m1_eqrel_1(B,A) => v4_taxonom2(B) ) )).
fof(cc5_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) ) ) )).
fof(cc5_measure1,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(cc5_measure5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_xboole_0(A) => v1_measure5(A) ) ) )).
fof(cc5_membered,axiom,( ! [A] : ( v3_membered(A) => v1_membered(A) ) )).
fof(cc5_metrizts,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc5_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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) ) ) ) ) )).
fof(cc5_monoid_0,axiom,( ! [A] : ( l3_algstr_0(A) => ( ( ~ v2_struct_0(A) & v3_group_1(A) & v13_monoid_0(A) ) => ( ~ v2_struct_0(A) & v2_group_1(A) ) ) ) )).
fof(cc5_msafree3,axiom,( ! [A] : ! [B] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) & v1_msualg_6(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msualg_2(C,A,B) => v1_msualg_6(C,A) ) ) )).
fof(cc5_msafree4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( l3_msualg_1(C,A) => ( v5_msafree4(C,A,B) => v4_msualg_1(C,A) ) ) ) )).
fof(cc5_msscyc_1,axiom,( ! [A] : ( l1_graph_1(A) => ( ( ~ v2_struct_0(A) & v3_msscyc_1(A) ) => ( ~ v2_struct_0(A) & v2_msscyc_1(A) ) ) ) )).
fof(cc5_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) => ( v4_mssubfam(C,A,B) => v5_mssubfam(C,A,B) ) ) ) )).
fof(cc5_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_mycielsk(B,A) => v8_struct_0(B) ) ) )).
fof(cc5_nat_1,axiom,( ! [A] : ( v1_xboole_0(A) => v8_ordinal1(A) ) )).
fof(cc5_neckla_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v2_struct_0(A) & v7_struct_0(A) & v1_orders_2(A) ) => ( ~ v2_struct_0(A) & v1_neckla_2(A) ) ) ) )).
fof(cc5_nfcont_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc5_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( 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) ) ) ) ) )).
fof(cc5_orders_4,axiom,( ! [A] : ( ( v8_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => v8_struct_0(B) ) ) )).
fof(cc5_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m1_subset_1(B,A) => v3_ordinal1(B) ) ) )).
fof(cc5_ordinal5,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(A) & v2_ordinal2(A) & v1_ordinal5(A) ) ) )).
fof(cc5_ordinal6,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc5_osalg_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc5_osalg_4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(cc5_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(cc5_pcs_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) ) => ( v1_relat_1(A) & v9_pcs_0(A) & v10_pcs_0(A) & v11_pcs_0(A) ) ) )).
fof(cc5_pencil_1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc5_pre_poly,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_pre_poly(A) ) ) )).
fof(cc5_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ( v12_pre_topc(A) => ( v7_pre_topc(A) & v10_pre_topc(A) ) ) ) )).
fof(cc5_quofield,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) & ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc5_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( m1_ratfunc1(B,A) => ( v6_ratfunc1(B,A) => v5_ratfunc1(B,A) ) ) ) )).
fof(cc5_relat_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => v4_relat_1(C,A) ) ) )).
fof(cc5_relat_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v7_relat_2(A) ) => ( v1_relat_1(A) & v1_relat_2(A) & v6_relat_2(A) ) ) )).
fof(cc5_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_rewrite1(A) ) => ( v1_relat_1(A) & v2_rewrite1(A) ) ) )).
fof(cc5_rfunct_2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc5_ring_1,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc5_robbins1,axiom,( ! [A] : ( l4_robbins1(A) => ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v10_robbins1(A) ) => ( ~ v2_struct_0(A) & v6_lattices(A) ) ) ) )).
fof(cc5_robbins4,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc5_roughs_1,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_prob_2(A) ) ) )).
fof(cc5_scm_halt,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & 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) ) ) )).
fof(cc5_scmyciel,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v3_scmyciel(A,1) ) => v4_scmyciel(A) ) )).
fof(cc5_sheffer1,axiom,( ! [A] : ( l1_lattices(A) => ( v13_struct_0(A,1) => ( v13_struct_0(A,1) & v6_lattices(A) & v7_lattices(A) ) ) ) )).
fof(cc5_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ( ~ v4_simplex0(A) => ~ v3_pencil_1(A) ) ) )).
fof(cc5_simplex1,axiom,( ! [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) & v8_rlvect_1(A) & l1_rlvect_1(A) & v2_simplex1(B,A) & m1_simplex0(B,u1_struct_0(A)) ) => ! [C] : ( m2_simplex0(C,u1_struct_0(A),B) => v2_simplex1(C,A) ) ) )).
fof(cc5_simplex2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v2_simplex2(B,A) & m1_simplex0(B,u1_struct_0(k15_euclid(A))) ) => ! [C] : ( m1_simplex1(C,k15_euclid(A),B) => v2_simplex2(C,A) ) ) )).
fof(cc5_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal4(A) => ~ v1_zfmisc_1(A) ) ) )).
fof(cc5_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => ( ~ v8_struct_0(A) => ( ~ v2_struct_0(A) & ~ v8_struct_0(A) ) ) ) )).
fof(cc5_subset_1,axiom,( ! [A] : ( v1_zfmisc_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_zfmisc_1(B) ) ) )).
fof(cc5_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v1_borsuk_1(B,A) & v1_tsep_1(B,A) & v1_tdlat_3(B) ) ) ) )).
fof(cc5_tex_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc5_tex_2,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ! [B] : ( 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) ) ) ) ) )).
fof(cc5_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v1_tex_3(B,A) => ~ v2_tex_3(B,A) ) ) ) )).
fof(cc5_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc5_topalg_6,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc5_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(cc5_topgen_4,axiom,( ! [A] : ! [B] : ( 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) ) ) ) )).
fof(cc5_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( v13_struct_0(A,1) => ( v13_struct_0(A,1) & v1_topgrp_1(A) ) ) ) )).
fof(cc5_topreal6,axiom,( ! [A] : ( 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)) ) ) )).
fof(cc5_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(cc5_trees_3,axiom,( ! [A] : ( v3_trees_3(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v3_trees_3(B) ) ) )).
fof(cc5_trees_9,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k5_trees_3(A))) ) => ! [C] : ( m1_subset_1(C,B) => v1_finset_1(C) ) ) )).
fof(cc5_tsp_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc5_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( v1_tsep_1(B,A) & v2_tsp_2(B,A) ) => ~ v1_tex_2(B,A) ) ) ) )).
fof(cc5_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_valued_0(A) ) => ( v1_relat_1(A) & v2_valued_0(A) ) ) )).
fof(cc5_valued_2,axiom,( ! [A] : ( v3_valued_2(A) => v2_valued_2(A) ) )).
fof(cc5_vectsp_1,axiom,( ! [A] : ( l4_algstr_0(A) => ( ( ~ v2_struct_0(A) & v4_vectsp_1(A) ) => ( ~ v2_struct_0(A) & v1_group_1(A) ) ) ) )).
fof(cc5_waybel11,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => v1_waybel11(B,A) ) ) )).
fof(cc5_waybel19,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc5_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_waybel23(B,A) => ~ v1_xboole_0(B) ) ) ) )).
fof(cc5_waybel25,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( 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))) ) ) ) ) )).
fof(cc5_waybel30,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc5_waybel34,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(cc5_waybel35,axiom,( ! [A] : ! [B] : ( ( l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ( m1_waybel35(C,A,B) => ( v1_zfmisc_1(C) => v3_waybel35(C,A,B) ) ) ) )).
fof(cc5_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc5_waybel_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc5_waybel_2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc5_waybel_3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc5_waybel_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(cc5_xxreal_0,axiom,( ! [A] : ( ( v1_xxreal_0(A) & v3_xxreal_0(A) ) => ( ~ v8_ordinal1(A) & v1_xxreal_0(A) & ~ v2_xxreal_0(A) ) ) )).
fof(cc5_xxreal_2,axiom,( ! [A] : ( ( v2_membered(A) & v3_xxreal_2(A) & v4_xxreal_2(A) ) => ( v2_membered(A) & v5_xxreal_2(A) ) ) )).
fof(cc5_yellow11,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc5_yellow13,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc5_yellow14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_waybel11(A) & l1_waybel_9(A) ) => ! [B] : ( 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) ) ) ) )).
fof(cc5_yellow21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & v2_yellow18(A) & l2_altcat_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc5_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v1_yellow_0(A) & v2_yellow_0(A) ) => v3_yellow_0(A) ) ) )).
fof(cc5_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) => v1_relat_1(B) ) ) )).
fof(cc5_yellow_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => v3_lattice3(B) ) ) )).
fof(cc6_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_abcmiz_1(B,A,k13_abcmiz_1(A)) => ( v7_abcmiz_1(B,A) => ( ~ v6_abcmiz_1(B,A) & v8_abcmiz_1(B,A) ) ) ) ) )).
fof(cc6_abcmiz_a,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc6_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v1_afinsq_1(A) ) ) )).
fof(cc6_algstr_0,axiom,( ! [A] : ( ( v6_algstr_0(A) & l1_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v3_algstr_0(B,A) ) ) )).
fof(cc6_algstr_1,axiom,( ! [A] : ( l5_algstr_0(A) => ( ( ~ v2_struct_0(A) & v7_algstr_1(A) ) => ( ~ v2_struct_0(A) & v32_algstr_0(A) & v6_algstr_1(A) ) ) ) )).
fof(cc6_amistd_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_compos_1(B)) => v3_amistd_2(C,A,B) ) ) )).
fof(cc6_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,k3_msualg_1(A,C,B)) => ( v1_relat_1(D) & v1_funct_1(D) ) ) ) )).
fof(cc6_aofa_a01,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) & v4_msualg_1(B,A) & v17_aofa_a00(B,A) & v22_aofa_a00(B,A,1,1,11) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),k37_aofa_a00(A))) => ( v1_relat_1(C) & v1_funct_1(C) ) ) ) )).
fof(cc6_armstrng,axiom,( ! [A] : ! [B] : ( 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) ) ) ) )).
fof(cc6_bcialg_1,axiom,( ! [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) ) => ( ~ v2_struct_0(A) & v3_bcialg_1(A) & v4_bcialg_1(A) & v5_bcialg_1(A) & v7_bcialg_1(A) & v16_bcialg_1(A) ) ) ) )).
fof(cc6_bhsp_3,axiom,( ! [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) & v8_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_bhsp_2(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_valued_0(C,B) => v1_bhsp_2(C,A) ) ) )).
fof(cc6_card_1,axiom,( ! [A] : ( ( v3_ordinal1(A) & v1_finset_1(A) ) => v7_ordinal1(A) ) )).
fof(cc6_card_3,axiom,( ! [A] : ( v1_finset_1(A) => v4_card_3(A) ) )).
fof(cc6_card_fil,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) & ~ v2_card_1(A) ) => ( ~ v1_finset_1(A) & v1_card_1(A) & v1_card_5(A) ) ) )).
fof(cc6_cayldick,axiom,( ! [A] : ( l5_algstr_0(A) => ( ( ~ v2_struct_0(A) & v33_algstr_0(A) & v5_group_1(A) ) => ( ~ v2_struct_0(A) & v34_algstr_0(A) & v5_group_1(A) ) ) ) )).
fof(cc6_cgames_1,axiom,( ! [A] : ( ( v2_cgames_1(A) & v5_cgames_1(A) & v6_cgames_1(A) ) => ( v2_cgames_1(A) & v7_cgames_1(A) ) ) )).
fof(cc6_circcmb3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & m1_circcmb3(B,A) ) => ! [C] : ( m2_circcmb3(C,A,B) => ( v4_msualg_1(C,B) & v4_circcomb(C,B) ) ) ) )).
fof(cc6_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) => ( v6_closure2(C,A,B) => ~ v1_xboole_0(C) ) ) ) )).
fof(cc6_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v4_cohsp_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v5_cohsp_1(A) ) ) )).
fof(cc6_compact1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc6_compts_1,axiom,( ! [A] : ( ( v8_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => v8_pre_topc(B) ) ) )).
fof(cc6_comput_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k2_comput_1(A)) => v2_margrel1(B) ) )).
fof(cc6_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ( v8_struct_0(A) => v4_dilworth(A) ) ) )).
fof(cc6_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ( ( v3_euclid_7(B) & v4_euclid_7(B,A) ) => v5_euclid_7(B,A) ) ) ) )).
fof(cc6_exchsort,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & v1_xboole_0(B) & v1_funct_1(B) & v1_exchsort(B) ) => ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & v1_xboole_0(B) & v1_funct_1(B) & v1_exchsort(B) & v5_exchsort(B,A) ) ) ) )).
fof(cc6_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) ) ) )).
fof(cc6_finset_1,axiom,( ! [A] : ( v1_xboole_0(A) => v5_finset_1(A) ) )).
fof(cc6_fomodel0,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k3_finseq_2(A)) => v5_relat_1(B,A) ) )).
fof(cc6_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_fomodel1(A)) => ( v6_fomodel1(B,A) => v5_fomodel1(B,A) ) ) ) )).
fof(cc6_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( v2_fomodel2(D,A,B,C) => v1_funct_1(D) ) ) )).
fof(cc6_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k9_funct_2(k30_fomodel2(A),k30_fomodel2(A))) => v1_pre_poly(B) ) ) )).
fof(cc6_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( v4_fomodel4(C,A,B,k1_xboole_0) => v8_fomodel4(C,A,B) ) ) )).
fof(cc6_funct_1,axiom,( ! [A] : ( ( v1_zfmisc_1(A) & v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v3_funct_1(A) ) ) )).
fof(cc6_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) ) ) )).
fof(cc6_functor0,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m2_functor0(C,A,B) => ( v16_functor0(C,A,B) => v6_functor0(C,A,B) ) ) ) )).
fof(cc6_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) ) )).
fof(cc6_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc6_glib_002,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => ! [C] : ( m2_glib_000(C,A,k6_domain_1(k6_glib_000(A),B),k1_xboole_0) => v3_glib_002(C) ) ) )).
fof(cc6_group_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( 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) ) ) )).
fof(cc6_groupp_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc6_hahnban,axiom,( ! [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) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc6_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc6_instalg1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_instalg1(B,A) => v1_instalg1(B) ) ) )).
fof(cc6_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc6_lattice2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc6_lattices,axiom,( ! [A] : ( l3_lattices(A) => ( ( ~ v2_struct_0(A) & v11_lattices(A) & v15_lattices(A) & v16_lattices(A) ) => ( ~ v2_struct_0(A) & v17_lattices(A) ) ) ) )).
fof(cc6_lfuzzy_0,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc6_ltlaxio4,axiom,( ! [A] : ! [B] : ( ( ~ v2_ltlaxio3(A) & m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) & m3_ltlaxio4(B,A) ) => ! [C] : ( m1_subset_1(C,k2_relset_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)),B)) => ~ v2_ltlaxio3(C) ) ) )).
fof(cc6_matroid0,axiom,( ! [A] : ( ( ~ v3_pencil_1(A) & v3_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc6_measure1,axiom,( ! [A] : ! [B] : ( 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) ) ) ) )).
fof(cc6_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_numbers)) => v1_membered(A) ) )).
fof(cc6_metrizts,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc6_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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) ) ) ) ) )).
fof(cc6_monoid_0,axiom,( ! [A] : ( l3_algstr_0(A) => ( ( ~ v2_struct_0(A) & v13_monoid_0(A) ) => ( ~ v2_struct_0(A) & v11_monoid_0(A) & v12_monoid_0(A) ) ) ) )).
fof(cc6_msafree4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_prob_2(B) ) => ! [C] : ( m3_pboole(C,A,B) => v1_prob_2(C) ) ) )).
fof(cc6_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) => ( v5_mssubfam(C,A,B) => v2_relat_1(C) ) ) ) )).
fof(cc6_nat_1,axiom,( ! [A] : ( ~ v8_ordinal1(A) => ~ v1_xboole_0(A) ) )).
fof(cc6_neckla_3,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_struct_0(A) => v1_neckla_3(A) ) ) )).
fof(cc6_oposet_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc6_ordinal1,axiom,( ! [A] : ( v7_ordinal1(A) => v3_ordinal1(A) ) )).
fof(cc6_ordinal5,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal5(A) ) => ( ~ v1_xboole_0(A) & v3_ordinal1(A) & v4_ordinal1(A) ) ) )).
fof(cc6_ordinal6,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) & v3_ordinal1(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc6_osalg_1,axiom,( ! [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) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => v9_osalg_1(B,A) ) ) )).
fof(cc6_osalg_4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(cc6_pcs_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v7_pcs_0(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_pralg_1(A) ) ) )).
fof(cc6_pencil_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(cc6_pre_poly,axiom,( ! [A] : ( m1_finseq_1(A,k4_ordinal1) => v1_card_3(A) ) )).
fof(cc6_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v7_pre_topc(A) & v10_pre_topc(A) ) => v12_pre_topc(A) ) ) )).
fof(cc6_relat_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => v5_relat_1(C,A) ) ) )).
fof(cc6_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v8_rewrite1(A) ) => ( v1_relat_1(A) & v7_rewrite1(A) ) ) )).
fof(cc6_robbins1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc6_robbins4,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc6_roughs_1,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_roughs_1(A) => v3_roughs_1(A) ) ) )).
fof(cc6_scm_halt,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) ) )).
fof(cc6_scmyciel,axiom,( ! [A] : ( ( v1_finset_1(A) & v4_scmyciel(A) ) => ( v4_scmyciel(A) & v6_scmyciel(A) ) ) )).
fof(cc6_sheffer1,axiom,( ! [A] : ( l3_lattices(A) => ( v13_struct_0(A,1) => ( v13_struct_0(A,1) & v8_lattices(A) & v9_lattices(A) & v17_lattices(A) ) ) ) )).
fof(cc6_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_pencil_1(A) & v4_simplex0(A) ) => ~ v5_simplex0(A) ) ) )).
fof(cc6_simplex2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) ) )).
fof(cc6_sppol_2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc6_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => ( v7_struct_0(A) => v8_struct_0(A) ) ) )).
fof(cc6_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => v2_tdlat_3(B) ) ) )).
fof(cc6_tex_2,axiom,( ! [A] : ( ( v13_struct_0(A,1) & l1_struct_0(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(cc6_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v1_tex_2(B,A) => v2_tex_3(B,A) ) ) ) )).
fof(cc6_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc6_topalg_6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( m1_borsuk_2(C,A,B,B) => ( v3_funct_1(C) => v3_topalg_6(C,A,B) ) ) ) )).
fof(cc6_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(cc6_topgen_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v3_topgen_4(B,A) => ~ v1_xboole_0(B) ) ) )).
fof(cc6_topgrp_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc6_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_xboole_0(A) => v1_sppol_1(A) ) ) )).
fof(cc6_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(cc6_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_3(A) ) => ! [B] : ( m1_subset_1(B,A) => ( ~ v1_xboole_0(B) & v1_trees_1(B) ) ) ) )).
fof(cc6_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) ) => ! [B] : ( m1_subset_1(B,k3_trees_9(A)) => v1_finset_1(B) ) ) )).
fof(cc6_tsp_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc6_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( v1_tsep_1(B,A) & v1_tex_2(B,A) ) => ~ v2_tsp_2(B,A) ) ) ) )).
fof(cc6_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_valued_0(A) ) => ( v1_relat_1(A) & v1_valued_0(A) ) ) )).
fof(cc6_valued_2,axiom,( ! [A] : ( v1_xboole_0(A) => v6_valued_2(A) ) )).
fof(cc6_vectsp_1,axiom,( ! [A] : ( l4_algstr_0(A) => ( ( ~ v2_struct_0(A) & v5_group_1(A) & v6_vectsp_1(A) ) => ( ~ v2_struct_0(A) & v3_vectsp_1(A) ) ) ) )).
fof(cc6_waybel11,axiom,( ! [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) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v12_waybel_0(B,A) => v3_waybel11(B,A) ) ) ) )).
fof(cc6_waybel19,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc6_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v7_waybel23(B,A) => ~ v1_xboole_0(B) ) ) ) )).
fof(cc6_waybel25,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc6_waybel30,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc6_waybel34,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc6_waybel_0,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc6_waybel_1,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v2_struct_0(A) & v9_waybel_1(A) ) => ( ~ v2_struct_0(A) & v2_waybel_1(A) ) ) ) )).
fof(cc6_waybel_2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc6_waybel_3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc6_waybel_4,axiom,( ! [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] : ( 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) ) ) ) ) )).
fof(cc6_xxreal_0,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & v1_xxreal_0(A) & ~ v2_xxreal_0(A) ) => ( v1_xxreal_0(A) & v3_xxreal_0(A) ) ) )).
fof(cc6_xxreal_2,axiom,( ! [A] : ( ( v3_membered(A) & v1_finset_1(A) ) => ( v3_membered(A) & v5_xxreal_2(A) ) ) )).
fof(cc6_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_pre_topc(A) & v11_pre_topc(A) ) => ( v2_pre_topc(A) & v8_pre_topc(A) ) ) ) )).
fof(cc6_yellow21,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(cc6_yellow_0,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v4_yellow_0(B,A) => ( v3_orders_2(B) & v4_yellow_0(B,A) ) ) ) ) )).
fof(cc6_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc6_yellow_9,axiom,( ! [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] : ( m1_yellow_9(B,A) => ( v4_waybel11(B) => v2_pre_topc(B) ) ) ) )).
fof(cc7_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc7_afinsq_1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc7_algstr_0,axiom,( ! [A] : ( l2_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ( v9_algstr_0(B,A) & v10_algstr_0(B,A) ) => v11_algstr_0(B,A) ) ) ) )).
fof(cc7_algstr_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc7_aofa_a00,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) & v4_msualg_1(B,A) & v17_aofa_a00(B,A) & v20_aofa_a00(B,4,1,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_funct_1(u3_msualg_1(A,B),1)) => v1_int_1(C) ) ) )).
fof(cc7_aofa_a01,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) & v4_msualg_1(B,A) & v17_aofa_a00(B,A) & v22_aofa_a00(B,A,1,1,11) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),k37_aofa_a00(A))) => ( v5_ordinal1(C) & v1_finset_1(C) ) ) ) )).
fof(cc7_armstrng,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(cc7_bcialg_1,axiom,( ! [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) ) => ( ~ v2_struct_0(A) & v3_bcialg_1(A) & v4_bcialg_1(A) & v5_bcialg_1(A) & v7_bcialg_1(A) & v16_bcialg_1(A) ) ) ) )).
fof(cc7_bhsp_3,axiom,( ! [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) & v8_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_bhsp_3(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_valued_0(C,B) => v1_bhsp_3(C,A) ) ) )).
fof(cc7_card_1,axiom,( ! [A] : ( v3_card_1(A,k5_ordinal1) => v1_xboole_0(A) ) )).
fof(cc7_card_3,axiom,( ! [A] : ( v4_card_3(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v4_card_3(B) ) ) )).
fof(cc7_cayldick,axiom,( ! [A] : ( l5_algstr_0(A) => ( ( ~ v2_struct_0(A) & v34_algstr_0(A) & v5_group_1(A) ) => ( ~ v2_struct_0(A) & v33_algstr_0(A) & v5_group_1(A) ) ) ) )).
fof(cc7_cgames_1,axiom,( ! [A] : ( ( v2_cgames_1(A) & v10_cgames_1(A) ) => ( v2_cgames_1(A) & v6_cgames_1(A) & ~ v7_cgames_1(A) ) ) )).
fof(cc7_circcmb3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v8_struct_0(B) & m1_circcmb3(B,A) ) => ! [C] : ( m2_circcmb3(C,A,B) => v3_circcmb3(C,B) ) ) )).
fof(cc7_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc7_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v8_cohsp_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v5_cohsp_1(A) ) ) )).
fof(cc7_compact1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc7_comput_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_comput_1(A))) ) => ! [C] : ( m1_subset_1(C,B) => v2_margrel1(C) ) ) )).
fof(cc7_dilworth,axiom,( ! [A] : ( ( v4_dilworth(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_dilworth(B,A) => ( v1_finset_1(B) & v2_dilworth(B,A) ) ) ) ) )).
fof(cc7_euclid_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ( v5_euclid_7(B,A) => ( ~ v1_xboole_0(B) & v5_euclid_7(B,A) ) ) ) ) )).
fof(cc7_exchsort,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => v5_relat_1(B,A) ) )).
fof(cc7_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) ) => ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v2_finseq_1(A) ) ) )).
fof(cc7_finset_1,axiom,( ! [A] : ( v5_finset_1(A) => ! [B] : ( m1_subset_1(B,A) => v1_finset_1(B) ) ) )).
fof(cc7_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k1_tarski(k1_xboole_0)) ) => ( v1_relat_1(A) & v3_relat_1(A) ) ) )).
fof(cc7_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_fomodel1(A)) => ( v5_fomodel1(B,A) => v10_fomodel1(B,A) ) ) ) )).
fof(cc7_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & ~ v1_xboole_0(B) ) => ! [C] : ( m1_subset_1(C,k15_fomodel2(A,B)) => v1_fomodel2(C,A,B) ) ) )).
fof(cc7_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( v4_fomodel4(D,A,B,C) => v8_fomodel4(D,A,B) ) ) )).
fof(cc7_funct_1,axiom,( ! [A] : ( v1_xboole_0(A) => v4_funct_1(A) ) )).
fof(cc7_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) ) ) )).
fof(cc7_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) ) )).
fof(cc7_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_002(A) ) => ! [B] : ( m1_glib_000(B,A) => v2_glib_002(B) ) ) )).
fof(cc7_group_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( 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) ) ) )).
fof(cc7_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_tops_1(B,A) => v3_pre_topc(B,A) ) ) ) )).
fof(cc7_lattices,axiom,( ! [A] : ( l3_lattices(A) => ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) ) => ( ~ v2_struct_0(A) & v10_lattices(A) & v12_lattices(A) ) ) ) )).
fof(cc7_lfuzzy_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v2_struct_0(A) & v2_lfuzzy_0(A) ) => ( ~ v2_struct_0(A) & v3_yellow_0(A) ) ) ) )).
fof(cc7_ltlaxio4,axiom,( ! [A] : ! [B] : ( ( ~ v2_ltlaxio3(A) & v3_ltlaxio3(A) & m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) & m3_ltlaxio4(B,A) ) => ! [C] : ( m1_subset_1(C,k2_relset_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)),B)) => v3_ltlaxio3(C) ) ) )).
fof(cc7_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v5_matroid0(B,A) => ( ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ) ) )).
fof(cc7_measure1,axiom,( ! [A] : ! [B] : ( 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) ) ) ) )).
fof(cc7_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k6_numbers)) => v2_membered(A) ) )).
fof(cc7_metrizts,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc7_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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) ) ) ) ) )).
fof(cc7_monoid_0,axiom,( ! [A] : ( l3_algstr_0(A) => ( ( ~ v2_struct_0(A) & v11_monoid_0(A) & v12_monoid_0(A) ) => ( ~ v2_struct_0(A) & v13_monoid_0(A) ) ) ) )).
fof(cc7_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( m1_subset_1(D,k3_card_3(u3_msualg_1(A,C))) => ( v1_relat_1(D) & v1_funct_1(D) ) ) ) )).
fof(cc7_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) => ( v2_mssubfam(C,A,B) => v6_mssubfam(C,A,B) ) ) ) )).
fof(cc7_neckla_3,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v2_struct_0(A) & v16_waybel_0(A) ) => ( ~ v2_struct_0(A) & v1_neckla_3(A) ) ) ) )).
fof(cc7_ordinal1,axiom,( ! [A] : ( v1_xboole_0(A) => v7_ordinal1(A) ) )).
fof(cc7_ordinal5,axiom,( ! [A] : ( ( v3_ordinal1(A) & v5_ordinal5(A) ) => ( ~ v1_xboole_0(A) & v3_ordinal1(A) ) ) )).
fof(cc7_ordinal6,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc7_osalg_1,axiom,( ! [A] : ( ( ~ 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] : ( l3_msualg_1(B,A) => v12_osalg_1(B,A) ) ) )).
fof(cc7_pcs_0,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc7_pre_poly,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_pre_poly(A) ) ) )).
fof(cc7_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ( v7_pre_topc(A) => v6_pre_topc(A) ) ) )).
fof(cc7_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) ) => ( v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,A) ) ) ) )).
fof(cc7_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v7_rewrite1(A) ) => ( v1_relat_1(A) & v8_rewrite1(A) & v9_rewrite1(A) ) ) )).
fof(cc7_robbins1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc7_robbins4,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc7_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_orders_3(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ v4_roughs_1(B,A) ) ) )).
fof(cc7_scm_halt,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & 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) ) ) )).
fof(cc7_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( ~ v3_pencil_1(A) & v1_matroid0(A) ) => ~ v5_simplex0(A) ) ) )).
fof(cc7_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => ( ~ v8_struct_0(A) => ~ v7_struct_0(A) ) ) )).
fof(cc7_tdlat_3,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_pre_topc(A) & v1_tdlat_3(A) ) => ( v2_pre_topc(A) & v3_tdlat_3(A) ) ) ) )).
fof(cc7_tex_2,axiom,( ! [A] : ( ( v13_struct_0(A,1) & l1_struct_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc7_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v2_tex_3(B,A) => v1_tex_2(B,A) ) ) ) )).
fof(cc7_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc7_topalg_6,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_borsuk_2(C,A,B,B) => v3_topalg_6(C,A,B) ) ) )).
fof(cc7_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => v6_topgen_1(B,A) ) ) ) )).
fof(cc7_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(cc7_topgrp_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc7_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_xboole_0(A) => v2_sppol_1(A) ) ) )).
fof(cc7_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_trees_3(A) ) => ! [B] : ( m1_subset_1(B,A) => v1_finset_1(B) ) ) )).
fof(cc7_tsp_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc7_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( v1_tex_2(B,A) & v2_tsp_2(B,A) ) => ~ v1_tsep_1(B,A) ) ) ) )).
fof(cc7_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_valued_0(A) ) => ( v1_relat_1(A) & v5_relat_1(A,k3_numbers) ) ) )).
fof(cc7_valued_2,axiom,( ! [A] : ( v1_valued_2(A) => v4_funct_1(A) ) )).
fof(cc7_waybel23,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v3_waybel_3(A) & l1_orders_2(A) ) => ! [B] : ( m1_waybel23(B,A) => v2_waybel23(B,A) ) ) )).
fof(cc7_waybel25,axiom,( ! [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] : ( m1_yellow_9(B,A) => ( v4_waybel11(B) => ( v4_waybel11(B) & v1_waybel25(B) ) ) ) ) )).
fof(cc7_waybel30,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc7_waybel34,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc7_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc7_waybel_1,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v2_struct_0(A) & v9_waybel_1(A) ) => ( ~ v2_struct_0(A) & v2_yellow_0(A) ) ) ) )).
fof(cc7_waybel_2,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc7_waybel_3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc7_xxreal_0,axiom,( ! [A] : ( ( v8_ordinal1(A) & v1_xxreal_0(A) ) => ( v1_xxreal_0(A) & ~ v2_xxreal_0(A) & ~ v3_xxreal_0(A) ) ) )).
fof(cc7_xxreal_2,axiom,( ! [A] : ( ( v5_membered(A) & ~ v1_xboole_0(A) & v4_xxreal_2(A) ) => ( v5_membered(A) & ~ v1_xboole_0(A) & v2_xxreal_2(A) ) ) )).
fof(cc7_yellow13,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( m1_yellow13(C,A,B) => ~ v1_xboole_0(C) ) ) )).
fof(cc7_yellow21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & v1_yellow21(A) & l2_altcat_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc7_yellow_0,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v4_yellow_0(B,A) => ( v4_orders_2(B) & v4_yellow_0(B,A) ) ) ) ) )).
fof(cc7_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(cc7_yellow_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) & l1_pre_topc(B) ) => ! [C] : ( m3_yellow_9(C,A,B) => ~ v2_struct_0(C) ) ) )).
fof(cc8_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc8_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) ) )).
fof(cc8_algstr_0,axiom,( ! [A] : ( l2_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v11_algstr_0(B,A) => ( v9_algstr_0(B,A) & v10_algstr_0(B,A) ) ) ) ) )).
fof(cc8_algstr_1,axiom,( ! [A] : ( l6_algstr_0(A) => ( ( ~ v2_struct_0(A) & v7_struct_0(A) ) => ( ~ v2_struct_0(A) & v1_vectsp_1(A) & v4_vectsp_1(A) ) ) ) )).
fof(cc8_card_1,axiom,( ! [A] : ( v1_xboole_0(A) => v3_card_1(A,k5_ordinal1) ) )).
fof(cc8_card_3,axiom,( ! [A] : ( v2_card_3(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v2_card_3(B) ) ) )).
fof(cc8_cayldick,axiom,( ! [A] : ( l5_algstr_0(A) => ( ( ~ v2_struct_0(A) & v31_algstr_0(A) & v5_group_1(A) ) => ( ~ v2_struct_0(A) & v30_algstr_0(A) & v5_group_1(A) ) ) ) )).
fof(cc8_cgames_1,axiom,( ! [A] : ( ( v2_cgames_1(A) & v6_cgames_1(A) & ~ v7_cgames_1(A) ) => ( v2_cgames_1(A) & v10_cgames_1(A) ) ) )).
fof(cc8_circcmb3,axiom,( ! [A] : ( ~ v1_facirc_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ~ v1_facirc_1(B) ) ) )).
fof(cc8_closure2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_closure2(B,A) => ( v13_closure2(B,A) => v12_closure2(B,A) ) ) ) )).
fof(cc8_cohsp_1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc8_compact1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc8_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k2_comput_1(k4_ordinal1)) => ( v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v4_valued_0(A) & v2_margrel1(A) ) ) )).
fof(cc8_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v3_dilworth(A) & v4_dilworth(A) ) => v8_struct_0(A) ) ) )).
fof(cc8_euclid_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_real_ns1(A))) => v3_valued_0(B) ) ) )).
fof(cc8_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_exchsort(A) ) => ! [B] : ( m1_exchsort(B,A) => v3_valued_0(B) ) ) )).
fof(cc8_finseq_1,axiom,( ! [A] : ( v1_xboole_0(A) => v3_finseq_1(A) ) )).
fof(cc8_finset_1,axiom,( ! [A] : ( v5_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v5_finset_1(B) ) ) )).
fof(cc8_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_relat_1(A) ) => ( v1_relat_1(A) & v5_relat_1(A,k1_tarski(k1_xboole_0)) ) ) )).
fof(cc8_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_fomodel1(A)) => ( v8_fomodel1(B,A) => ~ v7_fomodel1(B,A) ) ) ) )).
fof(cc8_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) => ( v3_fomodel2(B,A,k5_numbers) => v15_fomodel1(B,A) ) ) ) )).
fof(cc8_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( v9_fomodel4(E,A,B,k6_subset_1(C,D)) => v9_fomodel4(E,A,B,C) ) ) )).
fof(cc8_funct_1,axiom,( ! [A] : ( v4_funct_1(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) )).
fof(cc8_funct_2,axiom,( ! [A] : ! [B] : ( 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) ) ) ) )).
fof(cc8_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => v2_glib_000(B) ) ) )).
fof(cc8_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ( v4_glib_002(B,A) => v1_glib_002(B) ) ) ) )).
fof(cc8_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v5_tops_1(B,A) => v4_pre_topc(B,A) ) ) ) )).
fof(cc8_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) => ( v18_lattices(B,A) & v19_lattices(B,A) ) ) ) ) )).
fof(cc8_lfuzzy_0,axiom,( ! [A] : ( l1_orders_2(A) => ( ( ~ v2_struct_0(A) & v2_lfuzzy_0(A) ) => ( ~ v2_struct_0(A) & v3_lattice3(A) & v2_lfuzzy_0(A) ) ) ) )).
fof(cc8_measure1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) => ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) ) => ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v2_measure1(C,A,B) ) ) ) ) )).
fof(cc8_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => v3_membered(A) ) )).
fof(cc8_metrizts,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_pre_topc(A) & v5_waybel23(A) ) => ( v2_pre_topc(A) & v1_metrizts(A) ) ) ) )).
fof(cc8_mfold_1,axiom,( ! [A] : ( 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,k5_numbers) ) ) ) )).
fof(cc8_monoid_0,axiom,( ! [A] : ( l3_algstr_0(A) => ( ( ~ v2_struct_0(A) & v16_monoid_0(A) ) => ( ~ v2_struct_0(A) & v14_monoid_0(A) & v15_monoid_0(A) ) ) ) )).
fof(cc8_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) & m1_subset_1(D,u1_struct_0(A)) ) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,C),D)) => ( v1_relat_1(E) & v1_funct_1(E) ) ) ) )).
fof(cc8_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) => ( v6_mssubfam(C,A,B) => v2_relat_1(C) ) ) ) )).
fof(cc8_neckla_3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc8_ordinal1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => v7_ordinal1(A) ) )).
fof(cc8_ordinal5,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc8_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,k7_osalg_1(A)) => ~ v1_xboole_0(B) ) ) )).
fof(cc8_pcs_0,axiom,( ! [A] : ( 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) ) ) )).
fof(cc8_pre_poly,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( ( 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) ) ) ) )).
fof(cc8_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ( v8_pre_topc(A) => v7_pre_topc(A) ) ) )).
fof(cc8_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) ) => ( v1_xboole_0(B) & v1_relat_1(B) & v5_relat_1(B,A) ) ) ) )).
fof(cc8_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v6_rewrite1(A) ) => ( v1_relat_1(A) & v7_rewrite1(A) ) ) )).
fof(cc8_robbins1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc8_scmyciel,axiom,( ! [A] : ( ( v1_finset_1(A) & v4_scmyciel(A) ) => ( v4_scmyciel(A) & v8_scmyciel(A) ) ) )).
fof(cc8_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ( v4_simplex0(A) => ( v1_matroid0(A) & v2_simplex0(A) ) ) ) )).
fof(cc8_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => ( v2_struct_0(A) => v13_struct_0(A,k5_ordinal1) ) ) )).
fof(cc8_tdlat_3,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_pre_topc(A) & v2_tdlat_3(A) ) => ( v2_pre_topc(A) & v3_tdlat_3(A) ) ) ) )).
fof(cc8_tex_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(cc8_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( v1_tsep_1(B,A) & v1_tex_3(B,A) ) => v2_tex_3(B,A) ) ) ) )).
fof(cc8_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc8_topalg_6,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_topalg_6(A)) => ( ( v5_topalg_6(B,A) & v6_topalg_6(B,A) ) => v7_topalg_6(B,A) ) ) ) )).
fof(cc8_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) & v4_pre_topc(B,A) ) ) ) )).
fof(cc8_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(cc8_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal2(A) => v2_connsp_1(A,k15_euclid(2)) ) ) )).
fof(cc8_trees_3,axiom,( ! [A] : ( v3_trees_3(A) => v4_funct_1(A) ) )).
fof(cc8_tsp_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc8_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( v1_borsuk_1(B,A) & v2_tsp_2(B,A) ) => ~ v1_tex_2(B,A) ) ) ) )).
fof(cc8_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_valued_0(A) ) => ( v1_relat_1(A) & v3_valued_0(A) ) ) )).
fof(cc8_valued_2,axiom,( ! [A] : ( v2_valued_2(A) => v4_funct_1(A) ) )).
fof(cc8_waybel23,axiom,( ! [A] : ( ( ~ 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] : ( m1_waybel23(B,A) => ~ v1_xboole_0(B) ) ) )).
fof(cc8_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_waybel25(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(cc8_waybel30,axiom,( ! [A] : ( l1_waybel_9(A) => ( ( ~ v2_struct_0(A) & v2_tdlat_3(A) ) => ( ~ v2_struct_0(A) & v1_waybel30(A) & v3_waybel30(A) ) ) ) )).
fof(cc8_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc8_waybel_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc8_xxreal_0,axiom,( ! [A] : ( ( v1_xxreal_0(A) & ~ v2_xxreal_0(A) & ~ v3_xxreal_0(A) ) => ( v8_ordinal1(A) & v1_xxreal_0(A) ) ) )).
fof(cc8_xxreal_2,axiom,( ! [A] : ( ( v5_membered(A) & ~ v1_xboole_0(A) & v3_xxreal_2(A) ) => ( v5_membered(A) & ~ v1_xboole_0(A) & v1_xxreal_2(A) ) ) )).
fof(cc8_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m2_yellow13(B,A) => ~ v1_xboole_0(B) ) ) )).
fof(cc8_yellow21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & v2_yellow21(A) & l2_altcat_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc8_yellow_0,axiom,( ! [A] : ( ( v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v4_yellow_0(B,A) => ( v5_orders_2(B) & v4_yellow_0(B,A) ) ) ) ) )).
fof(cc8_yellow_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) & l1_pre_topc(B) ) => ! [C] : ( m3_yellow_9(C,B,A) => ~ v2_struct_0(C) ) ) )).
fof(cc9_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m3_abcmiz_1(B,A) => v1_xtuple_0(B) ) ) )).
fof(cc9_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) ) ) )).
fof(cc9_algstr_0,axiom,( ! [A] : ( l2_algstr_0(A) => ( ( v12_algstr_0(A) & v13_algstr_0(A) ) => v14_algstr_0(A) ) ) )).
fof(cc9_algstr_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc9_card_1,axiom,( ! [A] : ( v3_card_1(A,1) => ( ~ v1_xboole_0(A) & v1_zfmisc_1(A) ) ) )).
fof(cc9_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( m1_subset_1(B,k4_card_3(A)) => v5_funct_1(B,A) ) ) )).
fof(cc9_cayldick,axiom,( ! [A] : ( l5_algstr_0(A) => ( ( ~ v2_struct_0(A) & v30_algstr_0(A) & v5_group_1(A) ) => ( ~ v2_struct_0(A) & v31_algstr_0(A) & v5_group_1(A) ) ) ) )).
fof(cc9_cgames_1,axiom,( ! [A] : ( ( v2_cgames_1(A) & v9_cgames_1(A) ) => ( v2_cgames_1(A) & v5_cgames_1(A) & ~ v7_cgames_1(A) ) ) )).
fof(cc9_circcmb3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v4_valued_0(A) ) => ( v1_relat_1(A) & v1_funct_1(A) & v2_facirc_1(A) ) ) )).
fof(cc9_closure2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_closure2(B,A) => ( v15_closure2(B,A) => v14_closure2(B,A) ) ) ) )).
fof(cc9_cohsp_1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc9_compact1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc9_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k9_comput_1) => v2_margrel1(A) ) )).
fof(cc9_dilworth,axiom,( ! [A] : ( ( v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_eqrel_1(B,u1_struct_0(A)) => ( v1_xboole_0(B) => v5_dilworth(B,A) ) ) ) )).
fof(cc9_euclid_7,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k10_funcsdom(A))) => v3_valued_0(B) ) )).
fof(cc9_exchsort,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & ~ v1_xboole_0(B) ) => ! [C] : ( m1_subset_1(C,k9_funct_2(A,B)) => v5_ordinal1(C) ) ) )).
fof(cc9_finseq_1,axiom,( ! [A] : ( v3_finseq_1(A) => v4_funct_1(A) ) )).
fof(cc9_finset_1,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) ) => ( v1_relat_1(A) & v2_finset_1(A) ) ) )).
fof(cc9_fomodel0,axiom,( ! [A] : ( ( v1_int_1(A) & ~ v3_xxreal_0(A) ) => ( v7_ordinal1(A) & v1_int_1(A) ) ) )).
fof(cc9_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_fomodel1(A)) => ( v4_fomodel1(B,A) => ~ v7_fomodel1(B,A) ) ) ) )).
fof(cc9_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( 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,k5_numbers) ) ) ) )).
fof(cc9_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( v9_fomodel4(E,A,B,k6_subset_1(C,D)) => v9_fomodel4(E,A,B,k2_xboole_0(C,D)) ) ) )).
fof(cc9_funct_1,axiom,( ! [A] : ( v4_funct_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v4_funct_1(B) ) ) )).
fof(cc9_funct_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc9_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => v3_glib_000(B) ) ) )).
fof(cc9_glib_002,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => ! [C] : ( m2_glib_000(C,A,k1_glib_002(A,B),k21_glib_000(A,k1_glib_002(A,B))) => v4_glib_002(C,A) ) ) )).
fof(cc9_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc9_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v18_lattices(B,A) => v20_lattices(B,A) ) ) ) )).
fof(cc9_lfuzzy_0,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc9_membered,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k3_numbers)) => v4_membered(A) ) )).
fof(cc9_metrizts,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_pre_topc(A) & v9_pre_topc(A) & v1_metrizts(A) ) => ( v2_pre_topc(A) & v10_pre_topc(A) ) ) ) )).
fof(cc9_monoid_0,axiom,( ! [A] : ( l3_algstr_0(A) => ( ( ~ v2_struct_0(A) & v14_monoid_0(A) & v15_monoid_0(A) ) => ( ~ v2_struct_0(A) & v16_monoid_0(A) ) ) ) )).
fof(cc9_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( m1_subset_1(D,k3_card_3(u3_msualg_1(A,C))) => v3_trees_2(D) ) ) )).
fof(cc9_ordinal1,axiom,( ! [A] : ( v1_xboole_0(A) => v6_ordinal1(A) ) )).
fof(cc9_ordinal5,axiom,( ! [A] : ( ( 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) ) ) )).
fof(cc9_pcs_0,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc9_pre_poly,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k15_pre_poly(A))) => v4_funct_1(B) ) )).
fof(cc9_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ( v2_struct_0(A) => v6_pre_topc(A) ) ) )).
fof(cc9_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v8_rewrite1(A) ) => ( v1_relat_1(A) & v5_rewrite1(A) ) ) )).
fof(cc9_robbins1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc9_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_tarski(A))) => ( v1_zfmisc_1(B) => v9_scmyciel(B,A) ) ) ) )).
fof(cc9_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ( v2_simplex0(A) => ( v4_matroid0(A) & v3_simplex0(A) ) ) ) )).
fof(cc9_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => ( v13_struct_0(A,k5_ordinal1) => v2_struct_0(A) ) ) )).
fof(cc9_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ~ v2_struct_0(B) => ( ~ v2_struct_0(B) & v3_tdlat_3(B) ) ) ) ) )).
fof(cc9_tex_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc9_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( v1_tex_3(B,A) & ~ v2_tex_3(B,A) ) => ~ v1_tsep_1(B,A) ) ) ) )).
fof(cc9_topalg_6,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_topalg_6(A)) => ( v7_topalg_6(B,A) => ( v5_topalg_6(B,A) & v6_topalg_6(B,A) ) ) ) ) )).
fof(cc9_topgen_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v2_pre_topc(A) & v1_orders_4(A) ) => ( v2_pre_topc(A) & v7_topgen_1(A) ) ) ) )).
fof(cc9_topgen_4,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(cc9_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) ) => ! [B] : ( m1_subset_1(B,A) => v3_trees_2(B) ) ) )).
fof(cc9_tsp_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc9_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( ( v1_borsuk_1(B,A) & v1_tex_2(B,A) ) => ~ v2_tsp_2(B,A) ) ) ) )).
fof(cc9_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) ) => ( v1_relat_1(A) & v4_valued_0(A) ) ) )).
fof(cc9_valued_2,axiom,( ! [A] : ( v1_valued_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_valued_2(B) ) ) )).
fof(cc9_waybel25,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(cc9_waybel30,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc9_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(cc9_waybel_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc9_xxreal_2,axiom,( ! [A] : ( v6_membered(A) => ( v6_membered(A) & v3_xxreal_2(A) ) ) )).
fof(cc9_yellow13,axiom,( ! [A] : ( 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) ) ) ) )).
fof(cc9_yellow21,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(cc9_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v7_yellow_0(B,A) => v5_yellow_0(B,A) ) ) ) )).
fof(commutativity_k10_arytm_3,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k5_arytm_3) & m1_subset_1(B,k5_arytm_3) ) => k10_arytm_3(A,B) = k10_arytm_3(B,A) ) )).
fof(commutativity_k10_bvfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k10_group_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k10_margrel1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => k10_margrel1(A,B) = k10_margrel1(B,A) ) )).
fof(commutativity_k10_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,u1_struct_0(k15_euclid(A))) ) => k10_toprealc(A,B,C) = k10_toprealc(A,C,B) ) )).
fof(commutativity_k10_xboolean,axiom,( ! [A] : ! [B] : ( ( v1_xboolean(A) & v1_xboolean(B) ) => k10_xboolean(A,B) = k10_xboolean(B,A) ) )).
fof(commutativity_k11_openlatt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k11_pnproc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(commutativity_k11_polynom1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) => k11_polynom1(A,B,C,D) = k11_polynom1(A,B,D,C) ) )).
fof(commutativity_k11_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k11_rvsum_2,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(commutativity_k12_descip_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & 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) ) )).
fof(commutativity_k12_fomodel0,axiom,( ! [A] : ! [B] : k12_fomodel0(A,B) = k12_fomodel0(B,A) )).
fof(commutativity_k12_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k12_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k12_member_1,axiom,( ! [A] : ! [B] : ( ( v2_membered(A) & v2_membered(B) ) => k12_member_1(A,B) = k12_member_1(B,A) ) )).
fof(commutativity_k12_openlatt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k12_rvsum_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k13_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k13_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k13_member_1,axiom,( ! [A] : ! [B] : ( ( v1_membered(A) & v1_membered(B) ) => k13_member_1(A,B) = k13_member_1(B,A) ) )).
fof(commutativity_k13_polynom3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_group_1(A) & l6_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k13_polynom3(A,B,C) = k13_polynom3(A,C,B) ) )).
fof(commutativity_k13_seq_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,k12_seq_4(A)) & m1_subset_1(C,k12_seq_4(A)) ) => k13_seq_4(A,B,C) = k13_seq_4(A,C,B) ) )).
fof(commutativity_k14_margrel1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(commutativity_k14_rvsum_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(commutativity_k15_csspace,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) )).
fof(commutativity_k15_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k15_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k15_rvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k16_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k16_csspace,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k16_csspace(A,B,C) = k16_csspace(A,C,B) ) )).
fof(commutativity_k16_margrel1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k16_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k17_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(commutativity_k18_valued_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(commutativity_k19_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => k19_bvfunc_1(A,B) = k19_bvfunc_1(B,A) ) )).
fof(commutativity_k19_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k19_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(commutativity_k1_arytm_0,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k1_arytm_0(A,B) = k1_arytm_0(B,A) ) )).
fof(commutativity_k1_asympt_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k1_asympt_0(A,B) = k1_asympt_0(B,A) ) )).
fof(commutativity_k1_binarith,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => k1_binarith(A,B) = k1_binarith(B,A) ) )).
fof(commutativity_k1_bvfunc26,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(commutativity_k1_card_2,axiom,( ! [A] : ! [B] : ( ( v1_card_1(A) & v1_card_1(B) ) => k1_card_2(A,B) = k1_card_2(B,A) ) )).
fof(commutativity_k1_euclid_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) & v3_valued_0(B) & v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & v3_valued_0(C) ) => k1_euclid_9(A,B,C) = k1_euclid_9(A,C,B) ) )).
fof(commutativity_k1_extreal1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_numbers) & m1_subset_1(B,k6_numbers) ) => k1_extreal1(A,B) = k1_extreal1(B,A) ) )).
fof(commutativity_k1_extreal2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_numbers) & m1_subset_1(B,k6_numbers) ) => k1_extreal2(A,B) = k1_extreal2(B,A) ) )).
fof(commutativity_k1_finsub_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k1_fuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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) ) )).
fof(commutativity_k1_geomtrap,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) )).
fof(commutativity_k1_grnilp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k1_groeb_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,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,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) ) )).
fof(commutativity_k1_hausdorf,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k1_helly,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(commutativity_k1_jct_misc,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(commutativity_k1_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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) ) )).
fof(commutativity_k1_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v1_membered(B) & m1_subset_1(C,k3_rfunct_3(A,B)) & m1_subset_1(D,k3_rfunct_3(A,B)) ) => k1_lpspacc1(A,B,C,D) = k1_lpspacc1(A,B,D,C) ) )).
fof(commutativity_k1_measure1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(commutativity_k1_nat_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k4_ordinal1) ) => k1_nat_1(A,B) = k1_nat_1(B,A) ) )).
fof(commutativity_k1_normform,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(commutativity_k1_polyform,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v7_ordinal1(B) ) => k1_polyform(A,B) = k1_polyform(B,A) ) )).
fof(commutativity_k1_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) )).
fof(commutativity_k1_series_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_membered(A) & v7_membered(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => k1_series_1(A,B,C) = k1_series_1(A,C,B) ) )).
fof(commutativity_k1_setlim_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k1_setlim_2(A,B,C) = k1_setlim_2(A,C,B) ) )).
fof(commutativity_k1_topreal6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & 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) ) )).
fof(commutativity_k1_tsep_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k1_valued_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(commutativity_k1_xxreal_3,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => k1_xxreal_3(A,B) = k1_xxreal_3(B,A) ) )).
fof(commutativity_k1_yellow20,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => k1_yellow20(A,B) = k1_yellow20(B,A) ) )).
fof(commutativity_k20_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => k20_bvfunc_1(A,B) = k20_bvfunc_1(B,A) ) )).
fof(commutativity_k20_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k20_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(commutativity_k21_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => k21_bvfunc_1(A,B) = k21_bvfunc_1(B,A) ) )).
fof(commutativity_k22_quaterni,axiom,( ! [A] : ! [B] : ( ( v1_quaterni(A) & v1_quaterni(B) ) => k22_quaterni(A,B) = k22_quaterni(B,A) ) )).
fof(commutativity_k22_rvsum_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(commutativity_k22_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(commutativity_k22_zmodul02,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & m1_zmodul02(B,A) & m1_zmodul02(C,A) ) => k22_zmodul02(A,B,C) = k22_zmodul02(A,C,B) ) )).
fof(commutativity_k2_aff_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k2_arytm_0,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k2_arytm_0(A,B) = k2_arytm_0(B,A) ) )).
fof(commutativity_k2_arytm_3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v7_ordinal1(A) & v3_ordinal1(B) & v7_ordinal1(B) ) => k2_arytm_3(A,B) = k2_arytm_3(B,A) ) )).
fof(commutativity_k2_bhsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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) ) )).
fof(commutativity_k2_binarith,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => k2_binarith(A,B) = k2_binarith(B,A) ) )).
fof(commutativity_k2_borsuk_7,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,u1_struct_0(k3_topmetr)) & v1_xreal_0(B) ) => k2_borsuk_7(A,B) = k2_borsuk_7(B,A) ) )).
fof(commutativity_k2_bvfunc26,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(commutativity_k2_bvfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k2_card_2,axiom,( ! [A] : ! [B] : ( ( v1_card_1(A) & v1_card_1(B) ) => k2_card_2(A,B) = k2_card_2(B,A) ) )).
fof(commutativity_k2_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k2_euclid_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k2_fuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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) ) )).
fof(commutativity_k2_fuzzy_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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) ) )).
fof(commutativity_k2_gate_1,axiom,( ! [A] : ! [B] : k2_gate_1(A,B) = k2_gate_1(B,A) )).
fof(commutativity_k2_groeb_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k2_int_2,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_int_1(B) ) => k2_int_2(A,B) = k2_int_2(B,A) ) )).
fof(commutativity_k2_lfuzzy_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k2_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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) ) )).
fof(commutativity_k2_lopclset,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k2_measure1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(commutativity_k2_morph_01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k2_nat_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k4_ordinal1) ) => k2_nat_1(A,B) = k2_nat_1(B,A) ) )).
fof(commutativity_k2_normform,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(commutativity_k2_openlatt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k2_partit1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_eqrel_1(B,A) & m1_eqrel_1(C,A) ) => k2_partit1(A,B,C) = k2_partit1(A,C,B) ) )).
fof(commutativity_k2_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k2_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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) ) )).
fof(commutativity_k2_pnproc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) & v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => k2_pnproc_1(A,B,C) = k2_pnproc_1(A,C,B) ) )).
fof(commutativity_k2_pzfmisc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k2_setfam_1,axiom,( ! [A] : ! [B] : k2_setfam_1(A,B) = k2_setfam_1(B,A) )).
fof(commutativity_k2_setlim_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k2_setlim_2(A,B,C) = k2_setlim_2(A,C,B) ) )).
fof(commutativity_k2_substlat,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(commutativity_k2_tarski,axiom,( ! [A] : ! [B] : k2_tarski(A,B) = k2_tarski(B,A) )).
fof(commutativity_k2_topgen_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k2_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(commutativity_k2_vectsp_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) )).
fof(commutativity_k2_xboole_0,axiom,( ! [A] : ! [B] : k2_xboole_0(A,B) = k2_xboole_0(B,A) )).
fof(commutativity_k2_xcmplx_0,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) )).
fof(commutativity_k2_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k33_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(commutativity_k34_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(commutativity_k34_gate_1,axiom,( ! [A] : ! [B] : k34_gate_1(A,B) = k34_gate_1(B,A) )).
fof(commutativity_k3_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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) ) )).
fof(commutativity_k3_arytm_3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v7_ordinal1(A) & v3_ordinal1(B) & v7_ordinal1(B) ) => k3_arytm_3(A,B) = k3_arytm_3(B,A) ) )).
fof(commutativity_k3_boolealg,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k3_bvfunc26,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k3_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(commutativity_k3_closure3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(commutativity_k3_complsp2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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) ) )).
fof(commutativity_k3_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k3_finance1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k3_finance1(A,B) = k3_finance1(B,A) ) )).
fof(commutativity_k3_finsub_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k3_fuzzy_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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) ) )).
fof(commutativity_k3_gate_1,axiom,( ! [A] : ! [B] : k3_gate_1(A,B) = k3_gate_1(B,A) )).
fof(commutativity_k3_group_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k3_hausdorf,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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) ) )).
fof(commutativity_k3_idea_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) => k3_idea_1(A,B,C) = k3_idea_1(A,C,B) ) )).
fof(commutativity_k3_int_2,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_int_1(B) ) => k3_int_2(A,B) = k3_int_2(B,A) ) )).
fof(commutativity_k3_lattices,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k3_lfuzzy_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k3_lopclset,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k3_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v1_membered(B) & m1_subset_1(C,k3_rfunct_3(A,B)) & m1_subset_1(D,k3_rfunct_3(A,B)) ) => k3_lpspacc1(A,B,C,D) = k3_lpspacc1(A,B,D,C) ) )).
fof(commutativity_k3_member_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_numbers) & m1_subset_1(B,k6_numbers) ) => k3_member_1(A,B) = k3_member_1(B,A) ) )).
fof(commutativity_k3_mesfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k6_numbers) & v1_funct_1(B) & v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,k6_numbers) & v1_funct_1(C) ) => k3_mesfunc1(A,B,C) = k3_mesfunc1(A,C,B) ) )).
fof(commutativity_k3_metric_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v8_metric_1(A) & l1_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k3_metric_1(A,B,C) = k3_metric_1(A,C,B) ) )).
fof(commutativity_k3_midsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k3_nagata_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k3_openlatt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k3_partit1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_eqrel_1(B,A) & m1_eqrel_1(C,A) ) => k3_partit1(A,B,C) = k3_partit1(A,C,B) ) )).
fof(commutativity_k3_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k3_random_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(commutativity_k3_real_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k3_real_1(A,B) = k3_real_1(B,A) ) )).
fof(commutativity_k3_rlvect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k3_rvsum_2,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(commutativity_k3_setfam_1,axiom,( ! [A] : ! [B] : k3_setfam_1(A,B) = k3_setfam_1(B,A) )).
fof(commutativity_k3_setwiseo,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => k3_setwiseo(A,B,C) = k3_setwiseo(A,C,B) ) )).
fof(commutativity_k3_supinf_2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_numbers) & m1_subset_1(B,k6_numbers) ) => k3_supinf_2(A,B) = k3_supinf_2(B,A) ) )).
fof(commutativity_k3_topgen_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k3_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(commutativity_k3_vfunct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(commutativity_k3_xboole_0,axiom,( ! [A] : ! [B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) )).
fof(commutativity_k3_xcmplx_0,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) )).
fof(commutativity_k3_xxreal_0,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => k3_xxreal_0(A,B) = k3_xxreal_0(B,A) ) )).
fof(commutativity_k3_yellow_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k4_bhsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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) ) )).
fof(commutativity_k4_bvfunc26,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k4_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(commutativity_k4_catalan2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k4_catalan2(A,B) = k4_catalan2(B,A) ) )).
fof(commutativity_k4_closure3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(commutativity_k4_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k4_euclid_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k4_gate_1,axiom,( ! [A] : ! [B] : k4_gate_1(A,B) = k4_gate_1(B,A) )).
fof(commutativity_k4_jordan1k,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ 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) ) )).
fof(commutativity_k4_lattices,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k4_matrix13,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => k4_matrix13(A,B) = k4_matrix13(B,A) ) )).
fof(commutativity_k4_msualg_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(commutativity_k4_nat_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => k4_nat_1(A,B) = k4_nat_1(B,A) ) )).
fof(commutativity_k4_quofield,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k4_real_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k4_real_1(A,B) = k4_real_1(B,A) ) )).
fof(commutativity_k4_robbins3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k4_rvsum_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(commutativity_k4_rvsum_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k4_setlim_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k4_setlim_2(A,B,C) = k4_setlim_2(A,C,B) ) )).
fof(commutativity_k4_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k4_xboolean,axiom,( ! [A] : ! [B] : ( ( v1_xboolean(A) & v1_xboolean(B) ) => k4_xboolean(A,B) = k4_xboolean(B,A) ) )).
fof(commutativity_k4_xxreal_0,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => k4_xxreal_0(A,B) = k4_xxreal_0(B,A) ) )).
fof(commutativity_k4_xxreal_3,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => k4_xxreal_3(A,B) = k4_xxreal_3(B,A) ) )).
fof(commutativity_k4_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k5_arytm_2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_arytm_2) & m1_subset_1(B,k1_arytm_2) ) => k5_arytm_2(A,B) = k5_arytm_2(B,A) ) )).
fof(commutativity_k5_asympt_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k5_asympt_0(A,B) = k5_asympt_0(B,A) ) )).
fof(commutativity_k5_bvfunc26,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k5_bvfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k5_classes2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k5_convex4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k5_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k5_gate_1,axiom,( ! [A] : ! [B] : k5_gate_1(A,B) = k5_gate_1(B,A) )).
fof(commutativity_k5_lang1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(commutativity_k5_matrixc1,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k2_numbers) & m1_finseq_1(B,k2_numbers) ) => k5_matrixc1(A,B) = k5_matrixc1(B,A) ) )).
fof(commutativity_k5_mesfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k6_numbers) & v1_funct_1(B) & v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,k6_numbers) & v1_funct_1(C) ) => k5_mesfunc1(A,B,C) = k5_mesfunc1(A,C,B) ) )).
fof(commutativity_k5_nat_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => k5_nat_1(A,B) = k5_nat_1(B,A) ) )).
fof(commutativity_k5_nat_d,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => k5_nat_d(A,B) = k5_nat_d(B,A) ) )).
fof(commutativity_k5_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k5_prob_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_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) ) )).
fof(commutativity_k5_quofield,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k5_rfunct_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(commutativity_k5_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) => k5_rltopsp1(A,B,C) = k5_rltopsp1(A,C,B) ) )).
fof(commutativity_k5_robbins1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k5_robbins3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k5_rvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k5_scmfsa_m,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(commutativity_k5_setwiseo,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k5_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k5_supinf_2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_zfmisc_1(k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => k5_supinf_2(A,B) = k5_supinf_2(B,A) ) )).
fof(commutativity_k5_xboole_0,axiom,( ! [A] : ! [B] : k5_xboole_0(A,B) = k5_xboole_0(B,A) )).
fof(commutativity_k5_xboolean,axiom,( ! [A] : ! [B] : ( ( v1_xboolean(A) & v1_xboolean(B) ) => k5_xboolean(A,B) = k5_xboolean(B,A) ) )).
fof(commutativity_k6_arytm_2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_arytm_2) & m1_subset_1(B,k1_arytm_2) ) => k6_arytm_2(A,B) = k6_arytm_2(B,A) ) )).
fof(commutativity_k6_bhsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k6_bhsp_1(A,B,C) = k6_bhsp_1(A,C,B) ) )).
fof(commutativity_k6_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(commutativity_k6_bvfunc26,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k6_bvfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k6_fuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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) ) )).
fof(commutativity_k6_gate_1,axiom,( ! [A] : ! [B] : k6_gate_1(A,B) = k6_gate_1(B,A) )).
fof(commutativity_k6_nat_d,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => k6_nat_d(A,B) = k6_nat_d(B,A) ) )).
fof(commutativity_k6_polynom1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) => k6_polynom1(A,B,C,D) = k6_polynom1(A,B,D,C) ) )).
fof(commutativity_k6_prob_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_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) ) )).
fof(commutativity_k6_random_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(commutativity_k6_robbins1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k6_vfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(commutativity_k6_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k7_arytm_2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k2_arytm_2) & m1_subset_1(B,k2_arytm_2) ) => k7_arytm_2(A,B) = k7_arytm_2(B,A) ) )).
fof(commutativity_k7_chain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_chain_1(B,A) & m1_subset_1(C,k4_ordinal1) & 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) ) )).
fof(commutativity_k7_classes2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k7_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k7_euclid,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(commutativity_k7_gate_1,axiom,( ! [A] : ! [B] : k7_gate_1(A,B) = k7_gate_1(B,A) )).
fof(commutativity_k7_quaterni,axiom,( ! [A] : ! [B] : ( ( v1_quaterni(A) & v1_quaterni(B) ) => k7_quaterni(A,B) = k7_quaterni(B,A) ) )).
fof(commutativity_k7_rfunct_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(commutativity_k7_rlvect_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k7_rusub_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k7_seq_4,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k2_numbers) & m1_finseq_1(B,k2_numbers) ) => k7_seq_4(A,B) = k7_seq_4(B,A) ) )).
fof(commutativity_k7_xboolean,axiom,( ! [A] : ! [B] : ( ( v1_xboolean(A) & v1_xboolean(B) ) => k7_xboolean(A,B) = k7_xboolean(B,A) ) )).
fof(commutativity_k7_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k8_arytm_2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k2_arytm_2) & m1_subset_1(B,k2_arytm_2) ) => k8_arytm_2(A,B) = k8_arytm_2(B,A) ) )).
fof(commutativity_k8_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(commutativity_k8_group_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(commutativity_k8_matrixc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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) ) )).
fof(commutativity_k8_member_1,axiom,( ! [A] : ! [B] : ( ( v2_membered(A) & v2_membered(B) ) => k8_member_1(A,B) = k8_member_1(B,A) ) )).
fof(commutativity_k8_ordinal3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v7_ordinal1(A) & v3_ordinal1(B) & v7_ordinal1(B) ) => k8_ordinal3(A,B) = k8_ordinal3(B,A) ) )).
fof(commutativity_k8_polynom3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & l2_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k8_polynom3(A,B,C) = k8_polynom3(A,C,B) ) )).
fof(commutativity_k8_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k8_subset_1(A,B,C) = k8_subset_1(A,C,B) ) )).
fof(commutativity_k8_xboolean,axiom,( ! [A] : ! [B] : ( ( v1_xboolean(A) & v1_xboolean(B) ) => k8_xboolean(A,B) = k8_xboolean(B,A) ) )).
fof(commutativity_k9_arytm_3,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k5_arytm_3) & m1_subset_1(B,k5_arytm_3) ) => k9_arytm_3(A,B) = k9_arytm_3(B,A) ) )).
fof(commutativity_k9_member_1,axiom,( ! [A] : ! [B] : ( ( v1_membered(A) & v1_membered(B) ) => k9_member_1(A,B) = k9_member_1(B,A) ) )).
fof(commutativity_k9_ordinal3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v7_ordinal1(A) & v3_ordinal1(B) & v7_ordinal1(B) ) => k9_ordinal3(A,B) = k9_ordinal3(B,A) ) )).
fof(commutativity_k9_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k9_subset_1(A,B,C) = k9_subset_1(A,C,B) ) )).
fof(commutativity_k9_xboolean,axiom,( ! [A] : ! [B] : ( ( v1_xboolean(A) & v1_xboolean(B) ) => k9_xboolean(A,B) = k9_xboolean(B,A) ) )).
fof(connectedness_r1_arytm_2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k2_arytm_2) & m1_subset_1(B,k2_arytm_2) ) => ( r1_arytm_2(A,B) | r1_arytm_2(B,A) ) ) )).
fof(connectedness_r1_ordinal1,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => ( r1_ordinal1(A,B) | r1_ordinal1(B,A) ) ) )).
fof(connectedness_r1_xxreal_0,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => ( r1_xxreal_0(A,B) | r1_xxreal_0(B,A) ) ) )).
fof(connectedness_r3_arytm_3,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k5_arytm_3) & m1_subset_1(B,k5_arytm_3) ) => ( r3_arytm_3(A,B) | r3_arytm_3(B,A) ) ) )).
fof(d10_abcmiz_0,axiom,( ! [A] : ( ( ~ 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(k2_yellow_1(u1_abcmiz_0(A))))) & v20_waybel_0(u3_abcmiz_0(A),A,k7_lattice3(k2_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(k2_yellow_1(u1_abcmiz_0(A))))))) ) ) ) )).
fof(d10_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v10_aff_2(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d10_afinsq_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ( r1_tarski(k4_ordinal1,A) => ( r1_xxreal_0(C,k3_finseq_1(B)) | ! [D] : ( ( 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,k5_numbers) & k1_afinsq_1(D) = C & ! [E] : ( 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] : ( v7_ordinal1(E) => ~ ( ~ r1_xxreal_0(E,k3_finseq_1(B)) & ~ r1_xxreal_0(C,E) & k1_funct_1(D,E) != k5_numbers ) ) ) ) ) ) ) ) ) ) )).
fof(d10_afinsq_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k8_afinsq_1(A)) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ( C = k8_afinsq_2(A,B) <=> ? [D] : ( 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] : ( m1_subset_1(E,k8_afinsq_1(A)) => ! [F] : ( 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) ) ) ) ) )).
fof(d10_afproj,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(d10_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(d10_algstr_0,axiom,( ! [A] : ( l2_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v9_algstr_0(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & k1_algstr_0(A,C,B) = k4_struct_0(A) ) ) ) ) )).
fof(d10_algstr_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l5_algstr_0(A) ) => ( v7_algstr_1(A) <=> ( v6_algstr_1(A) & v32_algstr_0(A) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_algstr_0(A,B,k4_struct_0(A)) = k4_struct_0(A) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_algstr_0(A,k4_struct_0(A),B) = k4_struct_0(A) ) ) ) ) )).
fof(d10_algstr_4,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_algstr_4(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d10_altcat_1,axiom,( ! [A] : ( v4_funct_1(A) => ! [B] : ( v4_funct_1(B) => ! [C] : ( ( 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) ) ) ) )).
fof(d10_altcat_3,axiom,( ! [A] : ( l1_altcat_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v7_altcat_3(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( 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)) ) ) ) ) ) )).
fof(d10_ami_3,axiom,( ! [A] : ( v7_ordinal1(A) => k10_ami_3(A) = k4_tarski(1,A) ) )).
fof(d10_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) ) => ( v5_ami_wstd(C,A,B) <=> ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,C)) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_ami_wstd(A,B,E,D) => r2_hidden(E,k1_relset_1(k4_ordinal1,C)) ) ) ) ) ) ) ) ) )).
fof(d10_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) ) => ( v6_amistd_1(C,A,B) <=> ! [D] : ( ( 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,k5_numbers) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(B)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ( r1_tarski(C,E) => ! [F] : ( v7_ordinal1(F) => r2_hidden(k5_memstr_0(A,B,k5_extpro_1(A,B,E,D,F)),k1_relset_1(k4_ordinal1,C)) ) ) ) ) ) ) ) ) )).
fof(d10_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r5_analmetr(A,B,C,D) <=> r2_analoaf(A,B,C,B,D) ) ) ) ) ) )).
fof(d10_anproj_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_collsp(A) ) => ( v3_anproj_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & B != D & C != D & r1_collsp(A,B,C,D) ) ) ) ) ) )).
fof(d10_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l1_aofa_a00(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_funct_1(u3_msualg_1(A,B),C)) => k11_aofa_a00(A,B,C,D) = k1_funct_1(k1_msafree4(u1_struct_0(A),u1_aofa_a00(A,B),C),D) ) ) ) ) )).
fof(d10_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v19_aofa_a00(D,A) & m1_subset_1(D,u1_struct_0(A)) ) => k7_aofa_a01(A,B,C,D) = k30_aofa_a00(A,C,D,k28_aofa_a00(A,C,D),k28_aofa_a00(A,C,D)) ) ) ) ) )).
fof(d10_aofa_i00,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( v1_int_1(C) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(d10_armstrng,axiom,( ! [A] : k7_armstrng(A) = a_1_1_armstrng(A) )).
fof(d10_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(d10_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k7_asympt_0(A) = a_1_1_asympt_0(A) ) )).
fof(d10_bagorder,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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,k5_numbers,k1_nat_1(A,1),F) != k1_bagorder(B,k5_numbers,k1_nat_1(A,1),G) & r2_hidden(k4_tarski(k1_bagorder(B,k5_numbers,k1_nat_1(A,1),F),k1_bagorder(B,k5_numbers,k1_nat_1(A,1),G)),C) ) | ( k1_bagorder(B,k5_numbers,k1_nat_1(A,1),F) = k1_bagorder(B,k5_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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d10_bcialg_1,axiom,( ! [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] : ( ( ~ 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)) ) ) ) ) )).
fof(d10_bcialg_2,axiom,( ! [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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(k4_tarski(C,D),B) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d10_bcialg_3,axiom,( ! [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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d10_bcialg_4,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => k8_bcialg_4(A,B) = a_2_0_bcialg_4(A,B) ) ) )).
fof(d10_bcialg_6,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ! [C] : ( m5_bcialg_2(C,A,B) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(d10_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d10_binop_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(d10_binop_2,axiom,( ! [A] : ( ( 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 = k10_binop_2 <=> ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k1_binop_1(A,B,C) = k6_xcmplx_0(B,C) ) ) ) ) )).
fof(d10_bor_cant,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k10_bor_cant(A,B,C) = k1_prob_1(A,k9_bor_cant(A,C)) ) ) ) )).
fof(d10_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) ) => ( m1_borsuk_1(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => ! [D] : ( m2_connsp_2(D,A,C) => ? [E] : ( 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] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(F,B) => ( r1_xboole_0(F,E) | r1_tarski(F,E) ) ) ) ) ) ) ) ) ) ) )).
fof(d10_borsuk_6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))) => ( A = k8_borsuk_6 <=> ! [B] : ( r2_hidden(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k5_topmetr)) & ? [D] : ( m1_subset_1(D,u1_struct_0(k5_topmetr)) & B = k4_borsuk_1(k5_topmetr,k5_topmetr,C,D) & r1_xxreal_0(D,k6_xcmplx_0(k3_xcmplx_0(2,C),1)) ) ) ) ) ) )).
fof(d10_borsuk_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(d10_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => k3_funct_2(A,k6_margrel1,B,C) = k7_margrel1 ) ) ) ) )).
fof(d10_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => k7_bvfunc_2(A,B,C,D) = k17_bvfunc_1(A,B,k5_bvfunc_2(A,D,C)) ) ) ) ) )).
fof(d10_c0sp1,axiom,( ! [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) & v2_funcsdom(A) & v3_group_1(A) & v5_group_1(A) & v1_vectsp_1(A) & v3_vectsp_1(A) & l1_funcsdom(A) ) => ! [B] : ( 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] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => r2_hidden(k1_rlvect_1(A,D,C),B) ) ) ) ) ) ) ) )).
fof(d10_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ( r5_calcul_1(A,B,C) <=> ? [D] : ( 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) ) ) ) ) ) )).
fof(d10_card_3,axiom,( ! [A] : ( v2_card_3(A) <=> ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => k9_xtuple_0(B) = k9_xtuple_0(C) ) ) ) ) )).
fof(d10_card_fil,axiom,( ! [A] : ( ~ v1_finset_1(A) => k4_card_fil(A) = a_1_1_card_fil(A) ) )).
fof(d10_card_lar,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(d10_cat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v5_cat_1(A) & v6_cat_1(A) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_cat_1(C,A,B,B) => ( C = k4_cat_1(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( k2_cat_1(A,B,D) != k1_xboole_0 => ! [E] : ( m1_cat_1(E,A,B,D) => k1_cat_1(A,C,E) = E ) ) & ( k2_cat_1(A,D,B) != k1_xboole_0 => ! [E] : ( m1_cat_1(E,A,D,B) => k1_cat_1(A,E,C) = E ) ) ) ) ) ) ) ) )).
fof(d10_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & 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_cat_2(A,B) = k9_funct_3(u4_struct_0(A),u4_struct_0(B)) ) ) )).
fof(d10_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_cat_1(A,B,C) != k1_xboole_0 => ! [D] : ( ( ~ 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] : ( m2_cat_1(E,A,D) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d10_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,D,B) => ! [F] : ( 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] : ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(d10_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(d10_catalg_1,axiom,( ! [A] : ! [B] : ! [C] : k7_catalg_1(A,B,C) = k4_tarski(2,k11_finseq_1(A,B,C)) )).
fof(d10_cc0sp1,axiom,( ! [A] : ( ~ 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)) ) )).
fof(d10_cc0sp2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d10_cfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_numbers)) => ( v5_cfdiff_1(A) <=> ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( r1_tarski(k2_relset_1(k2_numbers,B),A) & v2_comseq_2(B) ) => r2_hidden(k3_comseq_2(B),A) ) ) ) ) )).
fof(d10_cgames_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v3_cgames_1(A) <=> ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => v2_cgames_1(k1_funct_1(A,B)) ) ) ) )).
fof(d10_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_chain_1(B,A) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k4_chain_1(A,B,A)) => ( C = k8_chain_1(A,B) <=> ? [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) & ? [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) & C = k3_chain_1(A,D,E) & ! [F] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(A)) => ( ~ r1_xxreal_0(k1_funct_1(D,F),k1_funct_1(E,F)) & m2_chain_1(k4_tarski(k1_funct_1(D,F),k1_funct_1(E,F)),k2_chain_1(A,B,F)) ) ) ) ) ) ) ) ) )).
fof(d10_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v5_chord(B,A) <=> ? [C] : ( v7_ordinal1(C) & ~ v1_abian(C) & ? [D] : ( 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] : r1_glib_000(A,k1_funct_1(B,C),k1_funct_1(B,D),E) & ! [E] : ~ ( r2_hidden(E,k14_glib_001(A,B)) & r1_glib_000(A,k1_funct_1(B,C),k1_funct_1(B,D),E) ) ) ) ) ) ) )).
fof(d10_circcmb3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_circcmb3(B,A) => ! [C] : ( ( 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 ) ) ) ) ) )).
fof(d10_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( v4_circcomb(B,A) <=> ! [C] : ( r2_hidden(C,u4_struct_0(A)) => C = k4_tarski(k1_xtuple_0(C),k1_funct_1(u4_msualg_1(A,B),C)) ) ) ) ) )).
fof(d10_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ( r2_circtrm1(A,B) <=> ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & v2_funct_1(C) & ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & v2_funct_1(D) & r1_circtrm1(A,B,C,D) ) ) ) ) ) )).
fof(d10_classes1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r2_classes1(A,B) <=> ! [C] : k1_card_1(k10_relat_1(A,C)) = k1_card_1(k10_relat_1(B,C)) ) ) ) )).
fof(d10_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( 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) ) ) ) )).
fof(d10_clopban2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clopban2(A) ) => ( v3_clopban2(A) <=> k2_normsp_0(A,k5_struct_0(A)) = 1 ) ) )).
fof(d10_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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] : ( m1_closure2(D,A,B,k6_closure2(A,B)) => r2_pboole(A,D,k7_closure2(A,B,C,D)) ) ) ) ) )).
fof(d10_clvect_1,axiom,( ! [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) ) => k4_clvect_1(A) = g1_clvect_1(u1_struct_0(A),u2_struct_0(A),u1_algstr_0(A),u1_clvect_1(A)) ) )).
fof(d10_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_clvect_2(B,A) <=> ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k13_csspace(A,k1_normsp_1(A,B,D)),C) ) ) ) ) ) )).
fof(d10_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_coh_sp(A)) => ! [C] : ( 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))) ) ) ) )).
fof(d10_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v5_cohsp_1(A) <=> ! [B] : ( 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)) ) ) ) ) )).
fof(d10_combgras,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( l1_incsp_1(B) => ! [C] : ( l1_combgras(C,A,B) => ! [D] : ( 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) ) ) ) ) )).
fof(d10_compl_sp,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ! [D] : ( ( 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] : ( 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] : ( 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] : ! [H] : ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ( ( E = k4_tarski(G,I) & F = k4_tarski(H,J) ) => ( ( G = H => k2_binop_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,E,F) = k1_metric_1(A,I,J) ) & ( G != H => k2_binop_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,E,F) = k2_xcmplx_0(k1_metric_1(A,I,B),k1_metric_1(A,B,J)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d10_compos_0,axiom,( ! [A] : ( v5_compos_0(A) => k6_compos_0(A) = k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0) ) )).
fof(d10_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( v7_ordinal1(C) => k6_compos_1(A,B,C) = k61_valued_1(k5_compos_1(A,B,C),C) ) ) ) )).
fof(d10_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v4_valued_0(A) & v2_margrel1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ! [E] : ( m2_rfunct_3(E,k3_finseq_2(k4_ordinal1),k4_ordinal1,k2_comput_1(k4_ordinal1)) => ( E = k6_comput_1(A,B,C,D) <=> ? [F] : ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k2_comput_1(k4_ordinal1)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_comput_1(k4_ordinal1)))) & E = k9_nat_1(k2_comput_1(k4_ordinal1),F,k7_partfun1(k4_ordinal1,D,C)) & ( ( r2_hidden(C,k4_finseq_1(D)) & r2_hidden(k2_finseq_3(C,D),k1_relset_1(k3_finseq_2(k4_ordinal1),A)) ) => k9_nat_1(k2_comput_1(k4_ordinal1),F,k5_numbers) = k16_funcop_1(k2_funct_7(k4_ordinal1,D,C,k5_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(k4_ordinal1),A)) ) => k9_nat_1(k2_comput_1(k4_ordinal1),F,k5_numbers) = k1_xboole_0 ) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( ( ( r2_hidden(C,k4_finseq_1(D)) & r2_hidden(k2_funct_7(k4_ordinal1,D,C,G),k1_relset_1(k3_finseq_2(k4_ordinal1),k9_nat_1(k2_comput_1(k4_ordinal1),F,G))) & r2_hidden(k8_finseq_1(k4_ordinal1,k2_funct_7(k4_ordinal1,D,C,G),k12_finseq_1(k4_ordinal1,k1_recdef_1(k9_nat_1(k2_comput_1(k4_ordinal1),F,G),k2_funct_7(k4_ordinal1,D,C,G)))),k1_relset_1(k3_finseq_2(k4_ordinal1),B)) ) => k9_nat_1(k2_comput_1(k4_ordinal1),F,k1_nat_1(G,1)) = k1_funct_4(k9_nat_1(k2_comput_1(k4_ordinal1),F,G),k16_funcop_1(k2_funct_7(k4_ordinal1,D,C,k1_nat_1(G,1)),k1_recdef_1(B,k8_finseq_1(k4_ordinal1,k2_funct_7(k4_ordinal1,D,C,G),k12_finseq_1(k4_ordinal1,k1_recdef_1(k9_nat_1(k2_comput_1(k4_ordinal1),F,G),k2_funct_7(k4_ordinal1,D,C,G))))))) ) & ( ~ ( r2_hidden(C,k4_finseq_1(D)) & r2_hidden(k2_funct_7(k4_ordinal1,D,C,G),k1_relset_1(k3_finseq_2(k4_ordinal1),k9_nat_1(k2_comput_1(k4_ordinal1),F,G))) & r2_hidden(k8_finseq_1(k4_ordinal1,k2_funct_7(k4_ordinal1,D,C,G),k12_finseq_1(k4_ordinal1,k1_recdef_1(k9_nat_1(k2_comput_1(k4_ordinal1),F,G),k2_funct_7(k4_ordinal1,D,C,G)))),k1_relset_1(k3_finseq_2(k4_ordinal1),B)) ) => k9_nat_1(k2_comput_1(k4_ordinal1),F,k1_nat_1(G,1)) = k9_nat_1(k2_comput_1(k4_ordinal1),F,G) ) ) ) ) ) ) ) ) ) ) )).
fof(d10_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( l2_conlat_1(B,A) => ( v7_conlat_1(B,A) <=> u2_conlat_1(A,B) = u1_struct_0(A) ) ) ) )).
fof(d10_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_convex4(B,A) => k8_convex4(A,B) = k7_convex4(A,k4_xcmplx_0(k6_complex1),B) ) ) )).
fof(d10_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) )).
fof(d10_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v2_cqc_the1(B,A) <=> r2_hidden(B,k4_cqc_the1(A)) ) ) ) )).
fof(d10_csspace,axiom,( ! [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) ) => ! [B] : ( 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) ) ) ) ) )).
fof(d10_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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)) ) ) )).
fof(d10_decomp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)) ) ) )).
fof(d10_dickson,axiom,( ! [A] : ( l1_orders_2(A) => ( v4_dickson(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ? [C] : ( r1_dickson(A,B,C) & v1_finset_1(C) ) ) ) ) )).
fof(d10_diff_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k10_diff_1(A,B,C,D) = k7_xcmplx_0(k6_xcmplx_0(k9_diff_1(A,B,C),k9_diff_1(A,C,D)),k6_xcmplx_0(B,D)) ) ) ) ) )).
fof(d10_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( ~ v2_struct_0(A) => ( B = k6_dilworth(A) <=> ! [C] : ( 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 ) ) ) ) ) )).
fof(d10_dist_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_matrprob(B) & m2_finseq_1(B,k1_numbers) ) => ( m1_dist_1(B,A) <=> ( k3_finseq_1(B) = k5_card_1(A) & ? [C] : ( m2_finseq_1(C,A) & k4_dist_1(A,C) = B ) ) ) ) ) )).
fof(d10_dtconstr,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_dtconstr(k5_dtconstr)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_dtconstr(k5_dtconstr)))) ) => ( A = k14_dtconstr <=> ( k9_nat_1(k4_dtconstr(k5_dtconstr),A,k5_numbers) = k2_trees_4(k4_ordinal1,k5_numbers) & ! [B] : ( v7_ordinal1(B) => k9_nat_1(k4_dtconstr(k5_dtconstr),A,k1_nat_1(B,1)) = k13_dtconstr(k9_nat_1(k4_dtconstr(k5_dtconstr),A,B)) ) ) ) ) )).
fof(d10_e_siec,axiom,( ! [A] : ( ( 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)) ) )).
fof(d10_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( 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] : ( 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] : ( 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)) ) ) ) ) ) )).
fof(d10_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,k2_ens_1(A)) => k3_funct_2(k2_ens_1(A),A,B,C) = k4_ens_1(A,C) ) ) ) ) )).
fof(d10_entropy1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => k7_entropy1(A) = k6_entropy1(k2_entropy1(k1_numbers,A)) ) )).
fof(d10_euclid,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => k18_euclid(A) = k1_funct_1(A,2) ) )).
fof(d10_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ( r1_euclid_3(A,B,C) <=> ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( 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 = k5_numbers & E = k5_numbers ) ) ) ) ) ) ) ) )).
fof(d10_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ( v1_euclidlp(B,A) <=> ? [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) & ? [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) & ? [E] : ( 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) ) ) ) ) ) ) )).
fof(d10_exchsort,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_exchsort(B) ) => ( v5_exchsort(B,A) <=> ! [C] : ( v3_ordinal1(C) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d10_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) ) => ! [D] : ( ( 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] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(B)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(B)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( ( r1_tarski(C,E) & r1_tarski(C,F) ) => ! [G] : ( ( 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] : ( ( 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] : ( v7_ordinal1(I) => 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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d10_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(d10_ff_siec,axiom,( ! [A] : ( ( 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))) ) )).
fof(d10_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(d10_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(k4_lattices(A,C,D),B) <=> ( r2_hidden(C,B) | r2_hidden(D,B) ) ) ) ) ) ) ) )).
fof(d10_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k10_fin_topo(A,B) = a_2_3_fin_topo(A,B) ) ) )).
fof(d10_finseq_1,axiom,( ! [A] : ! [B] : ! [C] : k11_finseq_1(A,B,C) = k7_finseq_1(k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)),k9_finseq_1(C)) )).
fof(d10_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( E = k8_finseq_8(A,B,C,D) <=> ( ( E != k5_numbers => ( r1_xxreal_0(D,E) & r1_tarski(C,k2_rfinseq(A,k7_nat_d(E,1),B)) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ( r1_xxreal_0(D,F) & r1_tarski(C,k2_rfinseq(A,k7_nat_d(F,1),B)) ) => ( r1_xxreal_0(F,k5_numbers) | r1_xxreal_0(E,F) ) ) ) ) ) & ~ ( E = k5_numbers & r2_finseq_8(A,B,C,D) ) ) ) ) ) ) ) ) )).
fof(d10_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k9_fintopo2(A,B) = a_2_1_fintopo2(A,B) ) ) )).
fof(d10_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k10_fintopo3(A,B,C) = k7_fintopo3(A,k1_fin_topo(A,C),B) ) ) ) )).
fof(d10_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( v2_fomodel0(C,A,B) <=> ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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 ) ) ) ) ) )).
fof(d10_fomodel1,axiom,( ! [A] : ( l1_fomodel1(A) => k10_fomodel1(A) = k6_subset_1(k1_fomodel1(A),k1_tarski(k8_fomodel1(A))) ) )).
fof(d10_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_fomodel2(C,A,B) ) => k10_fomodel2(A,B,C) = k1_funct_4(C,k16_funcop_1(k18_fomodel1(A),k2_fomodel2(B))) ) ) ) )).
fof(d10_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v10_fomodel1(C,A) & m1_subset_1(C,k1_fomodel1(A)) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,B))) => ! [E] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d10_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( 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)))) => ( v6_fomodel4(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_fomodel4(A))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d10_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ( r5_fsm_1(A,B,C,D,E) <=> ! [F] : ( m2_finseq_1(F,A) => k4_fsm_1(A,B,C,D,F) = k4_fsm_1(A,B,C,E,F) ) ) ) ) ) ) ) )).
fof(d10_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k10_ftacell1(A,B,C,D,E) = k24_gfacirc1(A,B,C) )).
fof(d10_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(d10_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v3_funct_1(A) <=> ! [B] : ! [C] : ( ( r2_hidden(B,k9_xtuple_0(A)) & r2_hidden(C,k9_xtuple_0(A)) ) => k1_funct_1(A,B) = k1_funct_1(A,C) ) ) ) )).
fof(d10_funct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(B))) => ( E = k7_funct_2(A,B,C,D) <=> ! [F] : ( m1_subset_1(F,k1_zfmisc_1(B)) => ( r2_hidden(F,E) <=> ? [G] : ( m1_subset_1(G,k1_zfmisc_1(A)) & r2_hidden(G,D) & F = k7_relset_1(A,B,C,G) ) ) ) ) ) ) ) ) ) )).
fof(d10_funct_7,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_relat_1(C) => ( C = k8_funct_7(A,B) <=> ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(k2_zfmisc_1(k1_relat_1(A),k1_relat_1(A)))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,k9_setfam_1(k2_zfmisc_1(k1_relat_1(A),k1_relat_1(A))),D,k5_numbers),k6_partfun1(k1_relat_1(A))) & ! [E] : ( v7_ordinal1(E) => k3_funct_2(k4_ordinal1,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)) ) ) ) ) ) ) )).
fof(d10_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_altcat_1(B) ) => ! [C] : ( l1_functor0(C,A,B) => ( v6_functor0(C,A,B) <=> ! [D] : ( 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)) ) ) ) ) ) )).
fof(d10_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => ! [C] : ( m1_fvaluat1(C,A) => ( C = k5_fvaluat1(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k6_numbers,B,D) = k4_xxreal_3(k3_funct_2(u1_struct_0(A),k6_numbers,C,D),k1_fvaluat1(k2_relset_1(k6_numbers,B))) ) ) ) ) ) ) )).
fof(d10_gate_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : 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) )).
fof(d10_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v4_vectsp_1(A) & l4_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ( v2_gcd_1(B,A) <=> ! [C] : ( m2_subset_1(C,u1_struct_0(A),B) => ! [D] : ( m2_subset_1(D,u1_struct_0(A),B) => r2_hidden(k6_algstr_0(A,C,D),B) ) ) ) ) ) )).
fof(d10_geomtrap,axiom,( ! [A] : ( l1_geomtrap(A) => k8_geomtrap(A) = g1_analoaf(u1_struct_0(A),u1_analoaf(A)) ) )).
fof(d10_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : k10_gfacirc1(A,B,C) = k8_facirc_1(A,B,C,k14_twoscomp) )).
fof(d10_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) ) => ( v1_glib_000(A) <=> ( r2_hidden(k1_glib_000,k1_relset_1(k4_ordinal1,A)) & r2_hidden(k2_glib_000,k1_relset_1(k4_ordinal1,A)) & r2_hidden(k3_glib_000,k1_relset_1(k4_ordinal1,A)) & r2_hidden(k4_glib_000,k1_relset_1(k4_ordinal1,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)))) ) ) ) )).
fof(d10_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( 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 ) ) ) ) ) )).
fof(d10_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ( v5_glib_002(B,A) <=> ! [C] : ( 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)) ) ) ) ) )).
fof(d10_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(d10_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( ( 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] : ( 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),o_3_0_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),o_3_0_glib_005(A,B,C)),o_3_0_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),o_3_0_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),o_3_0_glib_005(A,B,C)),o_3_0_glib_005(A,B,C))) ) ) ) ) ) )).
fof(d10_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v7_graph_1(B,A) & m2_graph_1(B,A) ) => ( B != k1_xboole_0 => ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(d10_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_2(B,u4_struct_0(A),k9_graph_3(A)) => ! [C] : ( 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] : ( m2_finseq_2(D,u4_struct_0(A),k9_graph_3(A)) => ( D = k11_graph_3(A,B,C) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & E = o_3_2_graph_3(A,B,C) & D = k8_finseq_1(u4_struct_0(A),k10_graph_3(A,E,B),k10_graph_3(A,E,C)) ) ) ) ) ) ) ) ) )).
fof(d10_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v7_graph_1(B,A) & m2_graph_1(B,A) ) => k6_graph_5(A,B) = a_2_3_graph_5(A,B) ) ) )).
fof(d10_graphsp,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( D = k14_graphsp(A,B,C) <=> ( ~ ( A != k1_xboole_0 & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( E = D & r2_hidden(E,A) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r2_hidden(F,A) => r1_xxreal_0(k7_partfun1(k1_numbers,B,k1_nat_1(k2_nat_1(2,C),E)),k7_partfun1(k1_numbers,B,k1_nat_1(k2_nat_1(2,C),F))) ) ) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ( r2_hidden(F,A) & k7_partfun1(k1_numbers,B,k1_nat_1(k2_nat_1(2,C),E)) = k7_partfun1(k1_numbers,B,k1_nat_1(k2_nat_1(2,C),F)) ) => r1_xxreal_0(E,F) ) ) ) ) ) & ( A = k1_xboole_0 => D = k5_numbers ) ) ) ) ) ) ) )).
fof(d10_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ( r6_groeb_2(A,B,C,D,E) <=> ? [F] : ( m2_ideal_1(F,k12_polynom1(A,C),E) & r4_groeb_2(A,B,C,D,E,F) ) ) ) ) ) ) ) )).
fof(d10_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v4_group_1(B,A) <=> ! [C] : ( v7_ordinal1(C) => ( k5_group_1(A,C,B) = k1_group_1(A) => C = k5_numbers ) ) ) ) ) )).
fof(d10_group_10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(B)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(d10_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(d10_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k8_group_3(A,B) = a_2_1_group_3(A,B) ) ) )).
fof(d10_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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] : ( ( v15_algstr_0(C) & m1_group_2(C,A) ) => ! [D] : ( ( v15_algstr_0(D) & m1_group_2(D,A) ) => k1_binop_1(B,C,D) = k8_group_4(A,C,D) ) ) ) ) ) )).
fof(d10_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ( B = k10_group_5(A) <=> u1_struct_0(B) = a_1_0_group_5(A) ) ) ) )).
fof(d10_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(d10_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ( v4_group_9(C,A,B) <=> ! [D] : ( ( 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) ) ) ) ) ) )).
fof(d10_heyting1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k12_normform(A))) => k10_heyting1(A,B) = k1_zfmisc_1(B) ) )).
fof(d10_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => ( v6_hilbert1(A) <=> ( r2_hidden(k2_hilbert1,A) & ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d10_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => k3_hilbert2(A) = k1_funct_1(k2_hilbert2,A) ) )).
fof(d10_hurwitz,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(A,k1_complfld) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => ! [B] : ( 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))) ) ) )).
fof(d10_idea_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v7_ordinal1(B) => ( ( r1_idea_1(A,B) & v1_int_2(k1_nat_1(k5_series_1(2,A),1)) ) => ! [C] : ( v7_ordinal1(C) => ( C = k10_idea_1(A,B) <=> ( k9_idea_1(A,B,C) = 1 & r1_idea_1(A,C) ) ) ) ) ) ) )).
fof(d10_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( m3_ideal_1(C,A,B) <=> ! [D] : ~ ( r2_hidden(D,k1_relset_1(k4_ordinal1,C)) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m2_subset_1(F,u1_struct_0(A),B) => k7_partfun1(u1_struct_0(A),C,D) != k6_algstr_0(A,F,E) ) ) ) ) ) ) ) )).
fof(d10_incsp_1,axiom,( ! [A] : ( l1_incsp_1(A) => ( v7_incsp_1(A) <=> ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) ) )).
fof(d10_index_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B,B),B))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,A,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ? [G] : ( ~ 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] : ( m3_index_1(G,A,B,C,D) => ( m5_index_1(G,A,B,C,D,E,F) <=> ( ! [H] : ( 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] : ( m1_subset_1(H,B) => ! [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)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d10_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( ( B != k5_numbers => k5_int_1(A,B) = k6_xcmplx_0(A,k3_xcmplx_0(k4_int_1(A,B),B)) ) & ( B = k5_numbers => k5_int_1(A,B) = k5_numbers ) ) ) ) )).
fof(d10_int_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ! [B] : ( ( 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] : ( m1_subset_1(C,k7_card_1(A)) => ! [D] : ( m1_subset_1(D,k7_card_1(A)) => k5_binop_1(k7_card_1(A),B,C,D) = k4_nat_d(k3_xcmplx_0(C,D),A) ) ) ) ) ) ) )).
fof(d10_integr15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_euclid(A)))) ) => ! [D] : ( ( 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) ) ) ) )).
fof(d10_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( 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] : ( m1_integra1(D,A) => k1_funct_1(C,D) = k7_integra1(A,B,D) ) ) ) ) ) )).
fof(d10_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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) ) ) )).
fof(d10_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => k3_intpro_1(A,B) = k7_finseq_1(k7_finseq_1(k12_finseq_1(k4_ordinal1,1),A),B) ) ) )).
fof(d10_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & 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] : ( m2_cat_1(C,A,B) & ? [D] : ( 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)) ) ) ) ) ) )).
fof(d10_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,k6_cat_2(B,C)) => ! [E] : ( m2_cat_1(E,A,k6_cat_2(B,C)) => ! [F] : ( m2_nattra_1(F,A,k6_cat_2(B,C),D,E) => k12_isocat_2(A,B,C,D,E,F) = k4_isocat_1(A,k6_cat_2(B,C),C,D,E,F,k13_cat_2(B,C)) ) ) ) ) ) ) )).
fof(d10_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) ) ) )).
fof(d10_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(d10_kolmog01,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( m1_kolmog01(D,A,B,C) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(B))) => ( E = k8_kolmog01(A,B,C,D) <=> ! [F] : ( m1_subset_1(F,k1_zfmisc_1(B)) => ( r2_hidden(F,E) <=> ? [G] : ( v1_finset_1(G) & m1_subset_1(G,k1_zfmisc_1(A)) & r2_hidden(F,k4_kolmog01(A,B,C,D,G)) ) ) ) ) ) ) ) ) )).
fof(d10_lang1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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))) ) ) ) ) )).
fof(d10_laplace,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( 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) ) ) ) )).
fof(d10_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_lattice3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r1_orders_2(A,B,D) & r1_orders_2(A,C,D) & ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d10_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_lattice4(C,A) => ( C = k3_lattice4(A,B) <=> ( r1_tarski(B,C) & ! [D] : ( m2_lattice4(D,A) => ( r1_tarski(B,D) => r1_tarski(C,D) ) ) ) ) ) ) ) )).
fof(d10_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,k4_zfmisc_1(A,A,u1_struct_0(B),u1_struct_0(B))) => ! [E] : ( ( 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] : ( m1_subset_1(F,A) => ! [G] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d10_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v5_lattice6(B,A) <=> r1_lattice6(A,B,k5_lattices(A)) ) ) ) )).
fof(d10_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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] : ( m1_lattice5(F,A,B,C) & D = k7_lattice8(A,B,C) & E = k8_lattice8(A,B,C,F) ) ) ) ) ) ) ) )).
fof(d10_lattices,axiom,( ! [A] : ( ( ~ 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) ) ) ) )).
fof(d10_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(d10_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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)) ) ) )).
fof(d10_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v7_limfunc1(A) <=> ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(B,C) & r2_hidden(C,k1_relset_1(k1_numbers,A)) ) ) & ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_limfunc1(B) & r1_tarski(k10_xtuple_0(B),k1_relset_1(k1_numbers,A)) ) => v1_limfunc1(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,B,A)) ) ) ) ) ) )).
fof(d10_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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),k9_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k7_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k8_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B))) ) ) )).
fof(d10_lopban_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lopban_2(A) ) => ( v3_lopban_2(A) <=> k2_normsp_0(A,k5_struct_0(A)) = 1 ) ) )).
fof(d10_lopban_3,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => k6_lopban_3(A,B,C) = k5_rsspace3(A,k5_lopban_3(A,B),C) ) ) ) )).
fof(d10_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(d10_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => k14_lpspacc1(A,B,C) = g1_clvect_1(k13_lpspacc1(A,B,C),k10_subset_1(k4_struct_0(k12_lpspacc1(A)),k13_lpspacc1(A,B,C)),k1_ideal_1(k12_lpspacc1(A),k13_lpspacc1(A,B,C)),k6_lpspacc1(k12_lpspacc1(A),k13_lpspacc1(A,B,C))) ) ) ) )).
fof(d10_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( 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] : ( m2_subset_1(F,k1_zfmisc_1(A),B) & k3_funct_2(B,k6_numbers,C,F) = k5_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))) ) ) ) ) ) ) ) )).
fof(d10_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v2_xxreal_0(D) & v1_xreal_0(D) ) => ! [E] : ( ( 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] : ( v1_xreal_0(F) => ! [G] : ( m2_subset_1(G,k1_zfmisc_1(k1_lpspace2(A,B,C,D)),k6_lpspace2(A,B,C,D)) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( r2_hidden(H,G) => k1_binop_1(E,F,G) = k5_lpspace2(A,B,C,k26_valued_1(A,k1_numbers,H,F),D) ) ) ) ) ) ) ) ) ) ) )).
fof(d10_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ( v2_ltlaxio3(A) <=> r8_ltlaxio1(k1_subset_1(k1_hilbert1),k1_ltlaxio1(k12_ltlaxio3(A))) ) ) )).
fof(d10_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => k9_ltlaxio4(A) = a_1_6_ltlaxio4(A) ) )).
fof(d10_mathmorp,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_convex1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ( ( r1_xxreal_0(k5_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,k6_xcmplx_0(1,E))),B) ) ) ) ) ) ) ) )).
fof(d10_matrix16,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ( v5_matrix16(B,A) <=> ? [C] : ( m2_finseq_1(C,u1_struct_0(A)) & k3_finseq_1(C) = k1_matrix_0(B) & r3_matrix16(A,B,C) ) ) ) ) )).
fof(d10_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ( v3_relat_1(B) <=> ( k5_numbers = k3_finseq_1(B) | k5_numbers = k1_matrix_0(B) ) ) ) ) )).
fof(d10_matrix_2,axiom,( ! [A] : ( v1_finset_1(A) => k6_matrix_2(A) = A ) )).
fof(d10_matrix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ( D = k13_matrix_3(A,B,C) <=> ( k3_finseq_1(D) = A & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k2_finseq_1(A)) => k1_funct_1(D,E) = k3_matrix_0(u1_struct_0(B),C,E,E) ) ) ) ) ) ) ) ) )).
fof(d10_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ( B = k11_matrixc1(A) <=> ( k3_finseq_1(B) = k1_matrix_0(A) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k2_finseq_1(k1_matrix_0(A))) => k9_matrix_5(B,C) = k17_rvsum_1(k8_matrix_0(k2_numbers,A,C)) ) ) ) ) ) ) )).
fof(d10_matrixj1,axiom,( ! [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] : ( ( v1_matrixj1(B,u1_struct_0(A)) & m2_finseq_1(B,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) => ! [C] : ( ( v1_matrixj1(C,u1_struct_0(A)) & m2_finseq_1(C,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d10_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( B = k10_matrixr1(A) <=> ( k1_matrix_0(B) = k3_finseq_1(A) & k3_finseq_1(B) = 1 & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(A)) => k3_matrix_0(k1_numbers,B,1,C) = k1_funct_1(A,C) ) ) ) ) ) ) )).
fof(d10_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k4_matroid0(A,B) = k3_tarski(a_2_1_matroid0(A,B)) ) ) )).
fof(d10_mcart_1,axiom,( ! [A] : k13_mcart_1(A) = k1_xtuple_0(k1_xtuple_0(A)) )).
fof(d10_measure6,axiom,( ! [A] : ! [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_seq_2(B) <=> v4_xxreal_2(k7_relset_1(A,k1_numbers,B,A)) ) ) )).
fof(d10_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => k13_member_1(A,B) = a_2_5_member_1(A,B) ) ) )).
fof(d10_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [C] : ( v7_ordinal1(C) => k7_memstr_0(A,B,C) = k16_funcop_1(k4_struct_0(B),C) ) ) ) )).
fof(d10_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ! [C] : ( ( 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,k5_numbers)) & ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(d10_mesfunc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k6_numbers) & v1_funct_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( C = k10_mesfunc1(A,B) <=> ( k9_xtuple_0(C) = k9_xtuple_0(B) & ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,k9_xtuple_0(C)) => k12_supinf_2(C,D) = k3_extreal1(k12_supinf_2(B,D)) ) ) ) ) ) ) ) )).
fof(d10_mesfunc5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v9_mesfunc5(A) <=> ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_numbers,B) & ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & ~ r1_xxreal_0(k9_nat_1(k6_numbers,A,D),B) ) ) ) ) ) ) )).
fof(d10_metric_1,axiom,( ! [A] : ! [B] : ( ( 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 = k4_metric_1(A) <=> ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ( k1_binop_1(B,C,C) = k5_numbers & ( C != D => k1_binop_1(B,C,D) = 1 ) ) ) ) ) ) )).
fof(d10_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => k7_metric_2(A) = a_1_3_metric_2(A) ) )).
fof(d10_metric_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))) => ! [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) ) => k2_binop_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,H,I) = k3_square_1(k2_xcmplx_0(k1_square_1(k3_metric_1(A,D,E)),k1_square_1(k3_metric_1(B,F,G)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d10_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(d10_midsp_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( 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 ) ) ) )).
fof(d10_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_nat_1(A,2)) ) => ! [C] : ( ( v4_midsp_2(C,B) & l1_midsp_2(C,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_2(E,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_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))) ) ) ) ) ) )).
fof(d10_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [D] : ( v7_ordinal1(D) => k10_mmlquery(A,B,C,D) = a_4_5_mmlquery(A,B,C,D) ) ) ) )).
fof(d10_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( v3_mod_2(B,A) & l1_mod_2(B,A) ) => ! [C] : ( ( v3_mod_2(C,A) & l1_mod_2(C,A) ) => ( k2_mod_2(A,B) = k3_mod_2(A,C) => ! [D] : ( ( v2_mod_2(D,A) & v3_mod_2(D,A) & l1_mod_2(D,A) ) => ( D = k8_mod_2(A,B,C) <=> ! [E] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d10_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) ) )).
fof(d10_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k6_modal_1) => ! [B] : ( m1_subset_1(B,k6_modal_1) => k12_modal_1(A,B) = k7_trees_2(k7_trees_2(k8_funcop_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k2_trees_1(2),k1_domain_1(k4_ordinal1,k4_ordinal1,2,k5_numbers)),k14_trees_3(k5_numbers),A),k14_trees_3(1),B) ) ) )).
fof(d10_modelc_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => k10_modelc_1(A) = k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,3),A) ) )).
fof(d10_modelc_2,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ( v1_modelc_2(A) <=> m1_subset_1(A,k9_modelc_2) ) ) )).
fof(d10_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v1_group_1(A) <=> v1_setwiseo(u2_algstr_0(A),u1_struct_0(A)) ) ) )).
fof(d10_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => k7_msafree(A,B,C) = a_3_0_msafree(A,B,C) ) ) ) )).
fof(d10_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( ( ~ v11_struct_0(A) => ( v3_msafree2(B,A) <=> ! [C] : ( ( ~ v2_struct_0(C) & ~ v11_struct_0(C) & l1_msualg_1(C) ) => ( C = A => ! [D] : ( l3_msualg_1(D,C) => ~ ( D = B & ! [E] : ( 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)) ) ) ) ) ) )).
fof(d10_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m3_pboole(B,u1_struct_0(A),k4_equation(A)) => ! [C] : ( l3_msualg_1(C,A) => ( v8_msafree4(C,A,B) <=> ? [D] : ( m1_msafree(D,A,C) & v7_msafree4(D,A,C,B) ) ) ) ) ) )).
fof(d10_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( 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] : ( m2_pboole(E,u1_struct_0(A),C,u3_msualg_1(A,B)) => ! [F] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d10_msualg_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(d10_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m3_pboole(C,u1_struct_0(A),u3_msualg_1(A,B)) => ! [D] : ( D = k5_msualg_2(A,B,C) <=> ! [E] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d10_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d10_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_mycielsk(B,k7_nat_d(k3_xcmplx_0(3,k1_newton(2,A)),1)) => ( B = k7_mycielsk(A) <=> ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & B = k1_funct_1(C,A) & k9_xtuple_0(C) = k4_ordinal1 & k1_funct_1(C,k5_numbers) = k5_mycielsk(2) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( m1_mycielsk(E,k7_nat_d(k3_xcmplx_0(3,k1_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,k1_newton(2,D)),1),E) ) ) ) ) ) ) ) )).
fof(d10_nagata_1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) ) )).
fof(d10_nat_lat,axiom,( k10_nat_lat = g3_lattices(k6_nat_lat,k9_nat_lat,k8_nat_lat) )).
fof(d10_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ( r3_nattra_1(A,B,C,D) <=> ( r2_nattra_1(A,B,C,D) & ? [E] : ( m2_nattra_1(E,A,B,C,D) & v1_nattra_1(E,A,B,C,D) ) ) ) ) ) ) ) )).
fof(d10_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ! [C] : ( ( 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] : ( v1_xreal_0(D) & ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r2_hidden(E,B) & r2_hidden(F,B) ) => r1_xxreal_0(k9_complex1(k5_real_1(k7_partfun1(k1_numbers,C,E),k7_partfun1(k1_numbers,C,F))),k3_xcmplx_0(D,k2_normsp_0(A,k5_algstr_0(A,E,F)))) ) ) ) ) ) ) ) ) )).
fof(d10_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(k7_normform(A))) => k9_normform(A,B) = a_2_0_normform(A,B) ) )).
fof(d10_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v9_o_ring_1(B,A) <=> ? [C] : ( 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)) ) ) ) ) )).
fof(d10_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k9_openlatt(A)) => ! [D] : ( m1_subset_1(D,k9_openlatt(A)) => k5_binop_1(k9_openlatt(A),B,C,D) = k12_openlatt(A,C,D) ) ) ) ) ) )).
fof(d10_oposet_1,axiom,( ! [A] : ( ( ~ 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)))) ) ) ) )).
fof(d10_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d10_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r4_orders_1(A,B) <=> ! [C] : ~ ( r1_tarski(C,B) & v3_orders_1(k2_wellord1(A,C)) & ! [D] : ~ ( r2_hidden(D,B) & ! [E] : ( r2_hidden(E,C) => r2_hidden(k4_tarski(E,D),A) ) ) ) ) ) )).
fof(d10_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(d10_ordinal1,axiom,( ! [A] : ! [B] : ( B = k3_ordinal1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( r2_hidden(C,A) & ? [D] : ( v3_ordinal1(D) & C = D & v4_ordinal1(D) ) ) ) ) )).
fof(d10_ordinal2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ( ? [B] : ( v3_ordinal1(B) & r1_ordinal2(B,A) ) => ! [B] : ( v3_ordinal1(B) => ( B = k8_ordinal2(A) <=> r1_ordinal2(B,A) ) ) ) ) )).
fof(d10_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( ( ( r2_hidden(1,B) & r2_hidden(k5_numbers,A) ) => ( C = k5_ordinal5(A,B) <=> ( r1_ordinal1(k12_ordinal2(B,C),A) & ! [D] : ( v3_ordinal1(D) => ( r1_ordinal1(k12_ordinal2(B,D),A) => r1_ordinal1(D,C) ) ) ) ) ) & ( ~ ( r2_hidden(1,B) & r2_hidden(k5_numbers,A) ) => ( C = k5_ordinal5(A,B) <=> C = k5_numbers ) ) ) ) ) ) )).
fof(d10_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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] : ( 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)) ) ) ) ) ) )).
fof(d10_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d10_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_osalg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( E = k8_osalg_2(A,B,C,D) <=> ! [F] : ( r2_hidden(F,E) <=> ? [G] : ( m2_osalg_2(G,A,B) & r2_hidden(G,k5_osalg_2(A,B,C)) & F = k1_funct_1(G,D) ) ) ) ) ) ) ) )).
fof(d10_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v2_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( r2_hidden(F,E) <=> ? [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d10_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) )).
fof(d10_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r6_pboole(A,B,C) <=> ! [D] : ( r2_hidden(D,A) => k1_funct_1(B,D) = k1_funct_1(C,D) ) ) ) ) )).
fof(d10_pcs_0,axiom,( ! [A] : ( l1_pcs_0(A) => ( v5_pcs_0(A) <=> r2_relat_2(u1_pcs_0(A),u1_struct_0(A)) ) ) )).
fof(d10_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(d10_pdiff_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [D] : ( 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,k6_xcmplx_0(k10_pdiff_1(3,2,C,D),k10_pdiff_1(3,3,B,D))),k9_euclid(3,k3_euclid_8,k6_xcmplx_0(k10_pdiff_1(3,3,A,D),k10_pdiff_1(3,1,C,D)))),k9_euclid(3,k4_euclid_8,k6_xcmplx_0(k10_pdiff_1(3,1,B,D),k10_pdiff_1(3,2,A,D)))) ) ) ) ) )).
fof(d10_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r1_pdiff_5(A,B) => ! [C] : ( v1_xreal_0(C) => ( C = k1_pdiff_5(A,B) <=> ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & B = k11_finseq_1(D,E,F) & ? [G] : ( 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] : ( v1_funct_1(H) & v3_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [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_funct_1(H,1) & ! [J] : ( v1_xreal_0(J) => ( r2_hidden(J,G) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,1,k1_pdiff_3(1,3,A),B),J),k1_funct_1(k1_pdiff_2(3,1,k1_pdiff_3(1,3,A),B),D)) = k2_xcmplx_0(k1_funct_1(H,k6_xcmplx_0(J,D)),k1_funct_1(I,k6_xcmplx_0(J,D))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d10_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( r5_pdiff_9(A,B,C,D) <=> ! [E] : ( ( ~ v1_xboole_0(E) & m2_finseq_1(E,k4_ordinal1) ) => ( ( 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) ) ) ) ) ) ) )).
fof(d10_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(d10_petri_2,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(d10_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m2_finseq_2(C,B,k3_finseq_2(B)) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( D = k8_pnproc_1(A,B,C) <=> ? [E] : ( v1_relat_1(E) & v1_funct_1(E) & v1_funcop_1(E) & v1_finseq_1(E) & D = k3_funct_7(k9_funct_2(A,k4_ordinal1),E) & k3_finseq_1(E) = k3_finseq_1(C) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r2_hidden(F,k4_finseq_1(C)) => k1_funct_1(E,F) = k7_pnproc_1(A,k7_partfun1(B,C,F)) ) ) ) ) ) ) ) )).
fof(d10_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => k13_polyform(A) = k11_polyform(A,1) ) )).
fof(d10_polynom1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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 = k10_polynom1(A,B,C,D) <=> ! [F] : ( ( 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] : ( m2_finseq_1(G,u1_struct_0(B)) & k4_polynom1(A,B,E,F) = k4_rlvect_1(B,G) & k3_finseq_1(G) = k3_finseq_1(k21_pre_poly(A,F)) & ! [H] : ( m1_subset_1(H,k4_ordinal1) => ~ ( r2_hidden(H,k4_finseq_1(G)) & ! [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] : ( ( 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),k4_ordinal1,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,k4_polynom1(A,B,C,I),k4_polynom1(A,B,D,J)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d10_polynom3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & v36_algstr_0(B) & l6_algstr_0(B) ) => ( B = k14_polynom3(A) <=> ( ! [C] : ( r2_hidden(C,u1_struct_0(B)) <=> ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( C = E & D = F ) => k1_algstr_0(B,C,D) = k2_normsp_1(A,E,F) ) ) ) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(d10_polynom5,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( C = k7_polynom5(A,B) <=> ! [D] : ( m1_subset_1(D,k4_ordinal1) => k3_funct_2(k4_ordinal1,u1_struct_0(A),C,D) = k3_vectsp_1(A,k3_funct_2(k4_ordinal1,u1_struct_0(A),B,D),k3_funct_2(k4_ordinal1,u1_struct_0(A),B,k7_nat_d(k1_algseq_1(A,B),1))) ) ) ) ) ) )).
fof(d10_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l5_algstr_0(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( 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] : ( ( 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) ) => k4_polynom1(A,B,E,F) = k6_algstr_0(B,k4_polynom1(A,B,C,F),D) ) ) ) ) ) ) )).
fof(d10_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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)) ) ) ) ) ) ) ) )).
fof(d10_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( ( ~ 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) ) ) ) ) ) ) ) ) )).
fof(d10_pralg_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => k1_funct_1(D,E) = k4_card_3(k9_pralg_2(A,B,E,C)) ) ) ) ) ) )).
fof(d10_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(d10_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ( v8_pre_topc(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d10_prob_1,axiom,( ! [A] : ( v1_xxreal_0(A) => k10_prob_1(A) = k4_xxreal_1(k2_xxreal_0,A) ) )).
fof(d10_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v1_prvect_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_finseq_1(B) ) => ( B = k15_prvect_1(A) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & ! [C] : ( m2_subset_1(C,k4_ordinal1,k4_finseq_1(A)) => k1_funct_1(B,C) = u1_struct_0(k14_prvect_1(A,C)) ) ) ) ) ) )).
fof(d10_prvect_2,axiom,( ! [A] : ( v1_relat_1(A) => ( v2_prvect_2(A) <=> ! [B] : ( 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) ) ) ) ) )).
fof(d10_pscomp_1,axiom,( ! [A] : ( 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)) ) )).
fof(d10_pua2mss1,axiom,( ! [A] : ( ( v2_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_eqrel_1(B,u1_struct_0(A)) => ( m3_pua2mss1(B,A) <=> ! [C] : ( 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) ) ) ) ) )).
fof(d10_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v1_qc_lang1(B,A) <=> ( m1_subset_1(B,k1_zfmisc_1(k13_finseq_1(k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))))) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_subset_1(D,k6_qc_lang1(A),k8_qc_lang1(A,C)) => ! [E] : ( ( 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(k5_numbers,k5_numbers)),B) & ! [C] : ( m2_finseq_1(C,k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))) => ( r2_hidden(C,B) => r2_hidden(k7_finseq_1(k9_finseq_1(k4_tarski(1,k5_numbers)),C),B) ) ) & ! [C] : ( m2_finseq_1(C,k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))) => ! [D] : ( m2_finseq_1(D,k2_zfmisc_1(k4_ordinal1,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,k5_numbers)),C),D),B) ) ) ) & ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_finseq_1(D,k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))) => ( r2_hidden(D,B) => r2_hidden(k7_finseq_1(k7_finseq_1(k9_finseq_1(k4_tarski(3,k5_numbers)),k12_finseq_1(k3_qc_lang1(A),C)),D),B) ) ) ) ) ) ) )).
fof(d10_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v1_qc_lang2(B,A) <=> ? [C] : ( m1_subset_1(C,k9_qc_lang1(A)) & ? [D] : ( m1_subset_1(D,k9_qc_lang1(A)) & B = k3_qc_lang2(A,C,D) ) ) ) ) ) )).
fof(d10_qmax_1,axiom,( ! [A] : ( ( v2_qmax_1(A) & l1_qmax_1(A) ) => ! [B] : ( m1_subset_1(B,k5_qmax_1(A)) => ! [C] : ( m1_subset_1(C,k5_qmax_1(A)) => ( r3_qmax_1(A,B,C) <=> ! [D] : ( 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))) ) ) ) ) ) )).
fof(d10_quatern2,axiom,( ! [A] : ( ( v36_algstr_0(A) & l6_algstr_0(A) ) => ( A = k15_quatern2 <=> ( u1_struct_0(A) = k1_quaterni & u1_algstr_0(A) = k9_quatern2 & u2_algstr_0(A) = k11_quatern2 & k5_struct_0(A) = k2_quatern2 & k4_struct_0(A) = k1_quatern2 ) ) ) )).
fof(d10_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( C = k10_quaterni(A,B) <=> ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & ? [I] : ( v1_xreal_0(I) & ? [J] : ( v1_xreal_0(J) & ? [K] : ( v1_xreal_0(K) & A = k6_quaterni(D,E,F,G) & B = k6_quaterni(H,I,J,K) & C = k6_quaterni(k6_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(D,H),k3_xcmplx_0(E,I)),k3_xcmplx_0(F,J)),k3_xcmplx_0(G,K)),k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(D,I),k3_xcmplx_0(E,H)),k3_xcmplx_0(F,K)),k3_xcmplx_0(G,J)),k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(D,J),k3_xcmplx_0(H,F)),k3_xcmplx_0(I,G)),k3_xcmplx_0(K,E)),k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(D,K),k3_xcmplx_0(G,H)),k3_xcmplx_0(E,J)),k3_xcmplx_0(F,I))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d10_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ( C = k13_quofield(A,B) <=> ! [D] : ( m2_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A)) => ( r2_hidden(D,C) <=> ? [E] : ( 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))) ) ) ) ) ) ) ) )).
fof(d10_radix_1,axiom,( ! [A] : ( 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) = k5_numbers ) ) ) )).
fof(d10_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(2,C) => ( ( ~ r1_xxreal_0(A,B) => k9_radix_6(A,B,C) = k5_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) ) ) ) ) ) ) ) )).
fof(d10_random_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ( B = k5_random_3(A) <=> ( k1_funct_1(B,k5_numbers) = k1_funct_1(A,k5_numbers) & ! [C] : ( v7_ordinal1(C) => k1_funct_1(B,k1_nat_1(C,1)) = k2_zfmisc_1(k1_funct_1(B,C),k1_funct_1(A,k1_nat_1(C,1))) ) ) ) ) ) )).
fof(d10_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( m1_ratfunc1(B,A) => ( v5_ratfunc1(B,A) <=> ~ r2_ratfunc1(A,k4_ratfunc1(A,B),k5_ratfunc1(A,B)) ) ) ) )).
fof(d10_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => ( C = k6_relat_1(A,B) <=> ! [D] : ! [E] : ( r2_hidden(k4_tarski(D,E),C) <=> ( r2_hidden(E,A) & r2_hidden(k4_tarski(D,E),B) ) ) ) ) ) )).
fof(d10_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ( v2_relat_2(A) <=> r2_relat_2(A,k1_relat_1(A)) ) ) )).
fof(d10_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r8_rewrite1(A,B,C) <=> ? [D] : ( ( r2_hidden(k4_tarski(D,B),A) | B = D ) & ( r2_hidden(k4_tarski(D,C),A) | C = D ) ) ) ) )).
fof(d10_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ( r2_hidden(D,k1_relset_1(A,C)) => k1_funct_1(C,D) = k1_rfunct_3(k1_funct_1(B,D)) ) ) ) ) ) ) ) )).
fof(d10_ringcat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m1_ringcat1(D,B,C) => ! [E] : ( m1_ringcat1(E,A,B) => ( ( r1_ringcat1(A,B) & r1_ringcat1(B,C) ) => k7_ringcat1(A,B,C,D,E) = k6_ringcat1(D,E) ) ) ) ) ) ) )).
fof(d10_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rltopsp1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d10_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ( v3_rlvect_1(A) & v4_rlvect_1(A) & v13_algstr_0(A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k4_algstr_0(A,B) <=> k1_algstr_0(A,B,C) = k4_struct_0(A) ) ) ) ) ) )).
fof(d10_rlvect_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_rlvect_2(C,A) => ! [D] : ( m1_rlvect_2(D,A) => ( D = k7_rlvect_2(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k1_numbers,D,E) = k3_real_1(k3_funct_2(u1_struct_0(A),k1_numbers,B,E),k3_funct_2(u1_struct_0(A),k1_numbers,C,E)) ) ) ) ) ) ) )).
fof(d10_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_rmod_4(D,A,B) => ! [E] : ( m1_rmod_4(E,A,B) => ( E = k7_rmod_4(A,B,C,D) <=> ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d10_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_robbins1(A) ) => ( v8_robbins1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_lattices(A,k3_robbins1(A,B),B) ) ) ) )).
fof(d10_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_robbins3(A) ) => ( v10_robbins3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_orders_2(A,B,C) <=> k1_lattices(A,B,C) = C ) ) ) ) ) )).
fof(d10_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ( D = k7_roughs_1(A,B,C) <=> ( k1_relset_1(k4_ordinal1,D) = k1_relset_1(k4_ordinal1,B) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k1_relset_1(k4_ordinal1,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) ) ) ) ) ) ) ) ) )).
fof(d10_rsspace,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k6_rsspace))) => ( A = k10_rsspace <=> ! [B] : ( r2_hidden(B,A) <=> ( r2_hidden(B,k1_rsspace) & v1_series_1(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k2_rsspace(B),k2_rsspace(B))) ) ) ) ) )).
fof(d10_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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),k9_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k7_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace4(A,B)) ) ) )).
fof(d10_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(k1_scmfsa_2)) => ( C = k10_scmfsa_2(A,B) <=> ? [D] : ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_ami_3)) & ? [E] : ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_ami_3)) & A = D & B = E & C = k6_ami_3(D,E) ) ) ) ) ) ) )).
fof(d10_scmpds_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => k10_scmpds_2(A,B,C) = k3_xtuple_0(7,k1_xboole_0,k11_finseq_1(A,B,C)) ) ) ) )).
fof(d10_scmpds_4,axiom,( ! [A] : ( 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) ) ) ) ) )).
fof(d10_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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(k1_nat_1(k5_card_1(C),1))),C) ) ) ) )).
fof(d10_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => ( ? [B] : ( m1_subset_1(B,k2_scm_inst) & ? [C] : ( m1_subset_1(C,k2_scm_inst) & ? [D] : ( v1_int_1(D) & ? [E] : ( v1_int_1(E) & ? [F] : ( 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] : ( m1_subset_1(B,k2_scm_inst) => ( B = k11_scmpds_i(A) <=> ? [C] : ( 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) ) ) ) ) ) )).
fof(d10_scmyciel,axiom,( ! [A] : k5_scmyciel(A) = a_1_3_scmyciel(A) )).
fof(d10_seq_4,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => k11_seq_4(A) = k4_finseqop(k2_numbers,k1_numbers,A,k6_seq_4) ) )).
fof(d10_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( D = k10_seqfunc(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k1_funct_1(D,E) = k1_funct_1(k1_seqfunc(A,k1_numbers,B,E),C) ) ) ) ) ) ) )).
fof(d10_seqm_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v3_funct_1(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r2_hidden(B,k4_finseq_1(A)) & r2_hidden(C,k4_finseq_1(A)) ) => k1_funct_1(A,B) = k1_funct_1(A,C) ) ) ) ) ) )).
fof(d10_setfam_1,axiom,( ! [A] : ( v2_setfam_1(A) <=> ! [B] : ( ~ v1_xboole_0(B) => ~ r2_hidden(B,A) ) ) )).
fof(d10_sgraph1,axiom,( ! [A] : ! [B] : ( m1_sgraph1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k5_sgraph1(A,B,C,D) = a_4_0_sgraph1(A,B,C,D) ) ) ) )).
fof(d10_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ( v6_simplex0(B,A) <=> k2_struct_0(B) = A ) ) )).
fof(d10_sin_cos,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k2_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( D = k9_sin_cos(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(E,A) => k9_nat_1(k2_numbers,D,E) = k3_xcmplx_0(k3_xcmplx_0(k9_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) => k9_nat_1(k2_numbers,D,E) = k5_numbers ) ) ) ) ) ) ) ) )).
fof(d10_stacks_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_stacks_1(A) ) => ( v4_stacks_1(A) <=> ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => C = k6_stacks_1(A,k7_stacks_1(A,B,C)) ) ) ) ) )).
fof(d10_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => ( v7_struct_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = C ) ) ) ) )).
fof(d10_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m1_subset_1(C,k1_substut1(A)) => ! [D] : ( D = k16_sublemma(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ? [F] : ( 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) ) ) ) ) ) ) )).
fof(d10_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_substut1(A)) ) => k11_substut1(A,B) = a_2_2_substut1(A,B) ) ) )).
fof(d10_supinf_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_card_3(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( m1_supinf_2(B,A) <=> A = k2_relset_1(k6_numbers,B) ) ) ) )).
fof(d10_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k9_tdlat_1(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(d10_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( ( v1_pre_topc(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ( C = k8_tmap_1(A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( D = u1_struct_0(B) => C = k6_tmap_1(A,D) ) ) ) ) ) ) )).
fof(d10_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(d10_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k4_topgen_4(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,C) <=> r1_topgen_4(A,B,D) ) ) ) ) ) ) )).
fof(d10_topreal1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( B = k4_topreal1(A) <=> ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(d10_toprealb,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k8_toprealb(2))) => ! [B] : ( ( 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)) ) ) ) )).
fof(d10_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(d10_trees_1,axiom,( ! [A] : ( v2_trees_1(A) <=> ( ! [B] : ( r2_hidden(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) & ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(d10_trees_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( ( 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] : ( m2_finseq_1(D,k4_ordinal1) => ( r2_hidden(D,k4_trees_1(k9_xtuple_0(A),B)) => k1_funct_1(C,D) = k1_funct_1(A,k8_finseq_1(k4_ordinal1,B,D)) ) ) ) ) ) ) ) )).
fof(d10_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v5_trees_3(A) <=> v2_trees_3(k10_xtuple_0(A)) ) ) )).
fof(d10_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k1_funct_1(A,k10_finseq_1(B,C)) = k9_margrel1(k1_binarith(B,C)) ) ) ) ) )).
fof(d10_unialg_2,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(d10_uproots,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( C = k9_uproots(A,B) <=> ? [D] : ( m2_finseq_1(D,k3_finseq_2(u1_struct_0(k14_polynom3(A)))) & ? [E] : ( m2_finseq_1(E,u1_struct_0(A)) & k3_finseq_1(D) = k5_card_1(k22_pre_poly(u1_struct_0(A),B)) & E = k19_finseq_1(k22_pre_poly(u1_struct_0(A),B)) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r2_hidden(F,k4_finseq_1(D)) => k1_funct_1(D,F) = k8_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)) ) ) ) ) ) ) )).
fof(d10_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(d10_valued_2,axiom,( ! [A] : ! [B] : ( B = k4_valued_2(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) ) ) )).
fof(d10_vectsp_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( B != k4_struct_0(A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k11_algstr_0(A,B) <=> k8_group_1(A,C,B) = k5_struct_0(A) ) ) ) ) ) )).
fof(d10_vectsp_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ v2_struct_0(C) & l2_vectsp_2(C,A,B) ) => ( v5_vectsp_2(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(d10_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(d10_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d10_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k1_yellow_1(k7_waybel_0(B))),u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_yellow_1(k7_waybel_0(B))),u1_struct_0(A)))) ) => ( C = k3_waybel23(A,B) <=> ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(d10_waybel34,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k4_waybel34(A))) => m1_subset_1(C,u1_struct_0(B)) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(k4_waybel34(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_waybel34(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( E = C & F = D ) => ( k1_altcat_1(k4_waybel34(A),C,D) = k1_xboole_0 | ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d10_waybel35,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ! [C] : ! [D] : ( D = k5_waybel35(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> E = k1_yellow_0(A,k4_waybel35(A,B,C,E)) ) ) ) ) )).
fof(d10_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_waybel_1(C,A,B) => ( v3_waybel_1(C,A,B) <=> ? [D] : ( 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] : ( 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] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d10_waybel_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d10_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [C] : ( 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)) ) ) ) )).
fof(d10_xboole_0,axiom,( ! [A] : ! [B] : ( A = B <=> ( r1_tarski(A,B) & r1_tarski(B,A) ) ) )).
fof(d10_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k9_xboolean(A,B) = k3_xboolean(k5_xboolean(A,B)) ) ) )).
fof(d10_xtuple_0,axiom,( ! [A] : k7_xtuple_0(A) = k1_xtuple_0(k1_xtuple_0(k1_xtuple_0(A))) )).
fof(d10_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ! [D] : ( ( ~ 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 ) ) ) ) )).
fof(d10_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ( v4_xxreal_2(A) <=> ? [B] : ( v1_xreal_0(B) & m1_xxreal_2(B,A) ) ) ) )).
fof(d10_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ( v3_yellow18(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k8_altcat_1(A,B) = k6_partfun1(k3_yellow18(A,B)) ) ) ) )).
fof(d10_yellow21,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ ! [B] : ( m1_subset_1(B,A) => v1_xboole_0(B) ) => ! [B] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d10_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_lattice3(A,B,D) => r1_orders_2(A,D,C) ) ) ) ) ) ) ) )).
fof(d10_yellow_6,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_waybel_0(B,A) => ! [C] : ! [D] : ( ( 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) ) ) ) ) ) )).
fof(d10_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ( v6_zf_fund1(B,A) <=> ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(a_3_2_zf_fund1(A,C,D),B) ) ) ) ) ) ) )).
fof(d10_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v2_zf_lang(A) <=> ? [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) & ? [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) & A = k4_zf_lang(B,C) ) ) ) ) )).
fof(d10_zf_model,axiom,( k10_zf_model = k8_zf_lang(k2_zf_lang(k5_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(k5_numbers)))))))) )).
fof(d10_zfmisc_1,axiom,( ! [A] : ( v1_zfmisc_1(A) <=> ! [B] : ! [C] : ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => B = C ) ) )).
fof(d10_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( 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)) ) ) ) )).
fof(d10_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v2_rlvect_1(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v1_zmodul01(C) & v2_zmodul01(C) & v3_zmodul01(C) & v4_zmodul01(C) & v5_zmodul01(C) & l1_zmodul01(C) ) => ( C = k10_zmodul02(A,B) <=> ( u1_struct_0(C) = k6_zmodul02(A,B) & r1_funct_2(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(C)),u1_struct_0(C),k2_zfmisc_1(k6_zmodul02(A,B),k6_zmodul02(A,B)),k6_zmodul02(A,B),u1_algstr_0(C),k7_zmodul02(A,B)) & k4_struct_0(C) = k8_zmodul02(A,B) & r1_funct_2(k2_zfmisc_1(k4_numbers,u1_struct_0(C)),u1_struct_0(C),k2_zfmisc_1(k4_numbers,k6_zmodul02(A,B)),k6_zmodul02(A,B),u1_zmodul01(C),k9_zmodul02(A,B)) ) ) ) ) ) )).
fof(d11_abcmiz_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l2_abcmiz_0(A) ) => ( v9_abcmiz_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(d11_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ( v2_abcmiz_1(B,A) <=> ( B != k9_abcmiz_1 & B != k10_abcmiz_1 ) ) ) ) )).
fof(d11_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ( v11_aff_2(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d11_afinsq_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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,k5_numbers)) & r2_hidden(k1_funct_1(B,k5_numbers),k1_afinsq_1(B)) ) => ! [C] : ( m2_finseq_1(C,A) => ( C = k12_afinsq_1(A,B) <=> ! [D] : ( v7_ordinal1(D) => ( D = k1_funct_1(B,k5_numbers) => ( k3_finseq_1(C) = D & ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,D) ) => k1_funct_1(C,E) = k1_funct_1(B,E) ) ) ) ) ) ) ) ) ) ) )).
fof(d11_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_afproj(A),k10_afproj(A)))) => ( B = k11_afproj(A) <=> ! [C] : ! [D] : ( r2_hidden(k4_tarski(C,D),B) <=> ~ ( ! [E] : ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d11_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_alg_1(B,A) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d11_algstr_0,axiom,( ! [A] : ( l2_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v10_algstr_0(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & k1_algstr_0(A,B,C) = k4_struct_0(A) ) ) ) ) )).
fof(d11_algstr_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v32_algstr_0(A) & v6_algstr_1(A) & l5_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B != k4_struct_0(A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k11_algstr_0(A,B) <=> k6_algstr_0(A,C,B) = k5_struct_0(A) ) ) ) ) ) )).
fof(d11_algstr_4,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( ( 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) ) ) )).
fof(d11_altcat_2,axiom,( ! [A] : ( l2_altcat_1(A) => ! [B] : ( 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)) ) ) ) ) )).
fof(d11_altcat_3,axiom,( ! [A] : ( l1_altcat_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v8_altcat_3(B,A) <=> ( v6_altcat_3(B,A) & v7_altcat_3(B,A) ) ) ) ) )).
fof(d11_altcat_5,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(k7_altcat_1(B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(k7_altcat_1(B))))) ) => ( r2_hidden(k4_card_3(C),B) => ! [D] : ( m1_altcat_5(D,k7_altcat_1(B),k2_altcat_5(A,B,C),A,C) => ( D = k3_altcat_5(A,B,C) <=> ! [E] : ( r2_hidden(E,A) => k1_funct_1(D,E) = k12_card_3(C,E) ) ) ) ) ) ) )).
fof(d11_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( D = k6_ami_wstd(A,B,C) <=> ? [E] : ( ~ 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)) ) ) ) ) ) ) )).
fof(d11_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) ) => ( v7_amistd_1(C,A,B) <=> ! [D] : ( ( 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,k5_numbers) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(B)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ( r1_tarski(C,E) => r1_extpro_1(A,B,E,D) ) ) ) ) ) ) ) )).
fof(d11_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( D = k4_analmetr(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(E,D) <=> r5_analmetr(A,B,C,E) ) ) ) ) ) ) ) )).
fof(d11_anproj_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d11_armstrng,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ( v3_armstrng(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => r2_hidden(k6_armstrng(A,C,C),B) ) ) ) )).
fof(d11_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( 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))) ) ) )).
fof(d11_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k8_asympt_0(A) = k3_xboole_0(k6_asympt_0(A),k7_asympt_0(A)) ) )).
fof(d11_bagorder,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_orders_2(B) & l1_orders_2(B) ) => ( B = k9_bagorder(A) <=> ( u1_struct_0(B) = k15_pre_poly(A) & ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(d11_bcialg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_bcialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_bcialg_1(A,B,C) <=> k1_bcialg_1(A,B,C) = k4_struct_0(A) ) ) ) ) )).
fof(d11_bcialg_2,axiom,( ! [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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(k4_tarski(C,D),B) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d11_bcialg_3,axiom,( ! [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) ) => ( v10_bcialg_3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d11_bcialg_4,axiom,( ! [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) & l1_bcialg_4(A) ) => ( v4_bcialg_4(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(d11_bcialg_6,axiom,( ! [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] : ( m1_bcialg_1(B,A) => ! [C] : ( ( v12_bcialg_1(C,A) & m2_bcialg_1(C,A) ) => ! [D] : ( m5_bcialg_2(D,A,C) => k7_bcialg_6(A,B,C,D) = k3_tarski(a_4_0_bcialg_6(A,B,C,D)) ) ) ) ) )).
fof(d11_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => v13_vectsp_1(k7_bilinear(A,B,C,D,E),C,A) ) ) ) ) ) ) )).
fof(d11_binop_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(d11_binop_2,axiom,( ! [A] : ( ( 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 = k11_binop_2 <=> ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k1_binop_1(A,B,C) = k3_xcmplx_0(B,C) ) ) ) ) )).
fof(d11_borsuk_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v1_borsuk_1(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = u1_struct_0(B) => v4_pre_topc(C,A) ) ) ) ) ) )).
fof(d11_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ( r3_borsuk_2(A,B,C,D,E) => ! [F] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(k5_topmetr)) => ( k1_binop_1(F,G,k5_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,k5_numbers,G) = B & k1_binop_1(F,1,G) = C ) ) ) ) ) ) ) ) ) ) ) )).
fof(d11_borsuk_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k8_toprealb(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k8_toprealb(2))) => ! [C] : ! [D] : ( 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] : ( ( 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,k5_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] : ( ( 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,k5_numbers) = C ) => r2_funct_2(u1_struct_0(k17_borsuk_1),u1_struct_0(k3_topmetr),E,F) ) ) ) ) ) ) ) ) ) )).
fof(d11_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => k3_funct_2(A,k6_margrel1,B,C) = k8_margrel1 ) ) ) ) )).
fof(d11_c0sp1,axiom,( ! [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) & v2_funcsdom(A) & v3_group_1(A) & v5_group_1(A) & v1_vectsp_1(A) & v3_vectsp_1(A) & l1_funcsdom(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(d11_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_valuat_1(D,A,C) => ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ( r6_calcul_1(A,B,C,D,E) <=> ! [F] : ( m2_subset_1(F,k9_qc_lang1(A),k3_cqc_lang(A)) => ( r2_hidden(F,B) => r1_valuat_1(A,C,F,D,E) ) ) ) ) ) ) ) ) )).
fof(d11_card_3,axiom,( ! [A] : ( v4_funct_1(A) => k9_card_3(A) = k1_setfam_1(a_1_0_card_3(A)) ) )).
fof(d11_card_fil,axiom,( ! [A] : ( ~ v1_finset_1(A) => k5_card_fil(A) = k1_card_fil(A,k4_card_fil(A)) ) )).
fof(d11_card_lar,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(d11_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,B,C) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d11_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => k13_cat_2(A,B) = k10_funct_3(u4_struct_0(A),u4_struct_0(B)) ) ) )).
fof(d11_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k10_cat_4(A,B) = k8_cat_4(A,k1_cat_4(A),B) ) ) )).
fof(d11_catalg_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( ( 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] : ( 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(k5_numbers,k3_relat_1(k2_xtuple_0(E),k7_cat_1(A,B,C))) ) ) ) ) ) ) )).
fof(d11_cfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_numbers)) => ( v6_cfdiff_1(A) <=> v5_cfdiff_1(k3_subset_1(k2_numbers,A)) ) ) )).
fof(d11_cgames_1,axiom,( ! [A] : ( ( 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] : ( m2_subset_1(B,k4_ordinal1,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))) ) ) ) ) )).
fof(d11_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_chain_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( 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) ) ) ) ) )).
fof(d11_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ( v6_chord(A) <=> ! [B] : ( m3_glib_001(B,A) => ( v8_glib_001(B,A) => ( r1_xxreal_0(k15_glib_001(A,B),3) | v5_chord(B,A) ) ) ) ) ) )).
fof(d11_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ( v6_circcmb3(A) <=> ~ v1_facirc_1(k2_msafree2(A)) ) ) )).
fof(d11_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ( v5_circcomb(A) <=> ? [B] : ( l3_msualg_1(B,A) & v4_circcomb(B,A) ) ) ) )).
fof(d11_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(d11_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( 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] : ( r2_hidden(D,k8_clopban1(A,B)) => k1_funct_1(C,D) = k2_seq_4(k12_clopban1(A,B,k11_clopban1(A,B,D))) ) ) ) ) ) )).
fof(d11_clopban2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clopban2(A) ) => ( v4_clopban2(A) <=> ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d11_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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] : ( m1_closure2(D,A,B,k6_closure2(A,B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d11_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_clvect_1(C,A) => k5_clvect_1(A,B,C) = a_3_1_clvect_1(A,B,C) ) ) ) )).
fof(d11_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ( v4_clvect_2(A) <=> ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v2_clvect_2(B,A) => v1_clvect_2(B,A) ) ) ) ) )).
fof(d11_coh_sp,axiom,( ! [A] : ! [B] : ( ( 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] : ( 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) ) ) ) )).
fof(d11_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v6_cohsp_1(A) <=> ! [B] : ! [C] : ( ( 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)) ) ) ) )).
fof(d11_combgras,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( l1_incsp_1(B) => ! [C] : ( l1_combgras(C,A,B) => ! [D] : ( 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) ) ) ) ) )).
fof(d11_compl_sp,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : 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)) ) ) )).
fof(d11_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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))) ) ) ) )).
fof(d11_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v4_valued_0(A) & v2_margrel1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m2_rfunct_3(D,k3_finseq_2(k4_ordinal1),k4_ordinal1,k2_comput_1(k4_ordinal1)) => ( D = k7_comput_1(A,B,C) <=> ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k4_finseq_2(k1_nat_1(k19_margrel1(A),1),k4_ordinal1),k2_comput_1(k4_ordinal1)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(k1_nat_1(k19_margrel1(A),1),k4_ordinal1),k2_comput_1(k4_ordinal1)))) & D = k3_card_3(E) & ! [F] : ( m2_finseq_2(F,k4_ordinal1,k4_finseq_2(k1_nat_1(k19_margrel1(A),1),k4_ordinal1)) => k3_funct_2(k4_finseq_2(k1_nat_1(k19_margrel1(A),1),k4_ordinal1),k2_comput_1(k4_ordinal1),E,F) = k6_comput_1(A,B,C,F) ) ) ) ) ) ) ) )).
fof(d11_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( l2_conlat_1(B,A) => ( v8_conlat_1(B,A) <=> u3_conlat_1(A,B) = u4_struct_0(A) ) ) ) )).
fof(d11_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_convex4(B,A) => ! [C] : ( m1_convex4(C,A) => k9_convex4(A,B,C) = k5_convex4(A,B,k8_convex4(A,C)) ) ) ) )).
fof(d11_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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))) ) ) )).
fof(d11_csspace,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k7_csspace))) => ( A = k11_csspace <=> ( ~ v1_xboole_0(A) & ! [B] : ( r2_hidden(B,A) <=> ( r2_hidden(B,k1_csspace) & v1_series_1(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,k2_csspace(B)),k55_valued_1(k4_ordinal1,k2_numbers,k2_csspace(B)))) ) ) ) ) ) )).
fof(d11_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k6_decomp_1(A) = a_1_0_decomp_1(A) ) )).
fof(d11_diff_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => k11_diff_1(A,B,C,D,E) = k7_xcmplx_0(k6_xcmplx_0(k10_diff_1(A,B,C,D),k10_diff_1(A,C,D,E)),k6_xcmplx_0(B,E)) ) ) ) ) ) )).
fof(d11_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_eqrel_1(B,u1_struct_0(A)) => ( v5_dilworth(B,A) <=> ! [C] : ( r2_hidden(C,B) => ( v1_dilworth(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) )).
fof(d11_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,A) => ( v1_dist_1(B,A) <=> ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(k4_dist_1(A,B))) => k1_funct_1(k4_dist_1(A,B),C) = k7_xcmplx_0(1,k5_card_1(A)) ) ) ) ) ) )).
fof(d11_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => ! [C] : ( m3_dist_2(C,A,B) => k9_dist_2(A,B,C) = k6_dist_2(A,B,k7_dist_2(A,k6_domain_1(A,C))) ) ) ) )).
fof(d11_e_siec,axiom,( ! [A] : ( ( 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)) ) )).
fof(d11_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => k7_ec_pf_1(A) = a_1_0_ec_pf_1(A) ) )).
fof(d11_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,k2_ens_1(A)) => ! [D] : ( 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] : ( m1_subset_1(C,k2_ens_1(A)) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(d11_entropy1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( B = k8_entropy1(A) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => k1_funct_1(B,C) = k6_entropy1(k7_matrix_0(k1_numbers,A,C)) ) ) ) ) ) ) )).
fof(d11_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => k20_euclid(A) = k5_finseq_2(k4_ordinal1,A,1) ) )).
fof(d11_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( 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] : ( v1_xreal_0(F) => ( F = k10_euclid_3(A,B,C,D,E) <=> ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & k2_xcmplx_0(k2_xcmplx_0(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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d11_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k5_euclidlp(A) = a_1_1_euclidlp(A) ) )).
fof(d11_exchsort,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( 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) ) ) )).
fof(d11_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(B)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( r1_tarski(C,F) => r1_extpro_1(A,B,F,E) ) ) ) ) ) ) ) ) ) )).
fof(d11_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(d11_ff_siec,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => k11_ff_siec(A) = u1_struct_0(A) ) )).
fof(d11_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( v1_relat_1(C) => ( C = k8_filter_0(A,B) <=> ( r1_tarski(k1_relat_1(C),u1_struct_0(A)) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d11_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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) ) ) ) )).
fof(d11_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) )).
fof(d11_finance1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ 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] : ( ~ v1_xboole_0(E) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,E) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,E))) ) => ! [G] : ( m1_subset_1(G,C) => k11_finance1(A,B,C,D,E,F,G) = k1_funct_1(k3_series_1(k10_finance1(C,D,E,G,F,B)),A) ) ) ) ) ) ) ) )).
fof(d11_finseq_1,axiom,( ! [A] : ! [B] : ( B = k13_finseq_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> m2_finseq_1(C,A) ) ) )).
fof(d11_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => k9_finseq_8(A,B,C) = k5_finseq_8(A,B,C) ) ) ) )).
fof(d11_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k10_fintopo2(A,B) = a_2_2_fintopo2(A,B) ) ) )).
fof(d11_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k7_fomodel0(A) = k6_fomodel0(A,k2_fomodel0(A)) ) )).
fof(d11_fomodel1,axiom,( ! [A] : ( l1_fomodel1(A) => k11_fomodel1(A) = k4_finseq_2(1,k2_fomodel1(A)) ) )).
fof(d11_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(A),k10_eqrel_1(A)) => ! [C] : ( m1_subset_1(C,A) => ( C = k14_fomodel3(A,B) <=> B = k6_domain_1(A,C) ) ) ) ) )).
fof(d11_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) => ( v7_fomodel4(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_fomodel4(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_fomodel4(A))) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ~ ( r1_tarski(C,D) & r2_hidden(E,B) & ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ~ ( r2_hidden(F,B) & r1_tarski(k1_funct_1(E,C),k1_funct_1(F,D)) ) ) ) ) ) ) ) ) ) )).
fof(d11_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( v7_ordinal1(F) => ( r6_fsm_1(A,B,C,D,E,F) <=> ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d11_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k11_ftacell1(A,B,C,D,E) = k33_gfacirc1(k24_gfacirc1(A,B,C),E,D) )).
fof(d11_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( A = B <=> ( k9_xtuple_0(A) = k9_xtuple_0(B) & ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) ) )).
fof(d11_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [E] : ( ( 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) ) ) ) ) )).
fof(d11_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( ( ( r2_hidden(B,k9_xtuple_0(A)) & r2_hidden(C,k9_xtuple_0(A)) ) => k9_funct_7(A,B,C) = k1_funct_7(k1_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)) ) => k9_funct_7(A,B,C) = A ) ) ) )).
fof(d11_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_altcat_1(B) ) => ! [C] : ( l1_functor0(C,A,B) => ( v8_functor0(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(d11_fvaluat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_fvaluat1(B,A) => k6_fvaluat1(A,B) = a_2_1_fvaluat1(A,B) ) ) )).
fof(d11_gate_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : 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) )).
fof(d11_geomtrap,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_geomtrap(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d11_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : k11_gfacirc1(A,B,C) = k10_facirc_1(A,B,C,k14_twoscomp) )).
fof(d11_glib_000,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [D] : ( ( 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) ) ) ) )).
fof(d11_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(d11_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m2_glib_004(C,A) => ( C = k10_glib_004(A,B) <=> ( k9_glib_004(A,C,k5_numbers) = k8_glib_004(A,B) & ! [D] : ( v7_ordinal1(D) => k9_glib_004(A,C,k1_nat_1(D,1)) = k7_glib_004(A,k9_glib_004(A,C,D)) ) ) ) ) ) ) )).
fof(d11_graph_1,axiom,( ! [A] : ( l1_graph_1(A) => ( v6_graph_1(A) <=> ( v1_finset_1(u1_struct_0(A)) & v1_finset_1(u4_struct_0(A)) ) ) ) )).
fof(d11_graph_2,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(B,C) & r1_xxreal_0(C,k3_finseq_1(A)) ) => ! [D] : ( v7_ordinal1(D) => ( D = k8_graph_2(A,B,C) <=> ? [E] : ( ~ 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)) & k1_nat_1(D,1) = k2_xcmplx_0(k4_finseq_4(k2_graph_2(k4_numbers,A,B,C),k2_xxreal_2(E)),B) ) ) ) ) ) ) ) )).
fof(d11_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( k7_graph_3(A,B,C) != k5_numbers => k12_graph_3(A,B,C) = a_3_3_graph_3(A,B,C) ) ) ) )).
fof(d11_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => k7_graph_5(A) = a_1_0_graph_5(A) ) )).
fof(d11_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( 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 = k15_graphsp(A) <=> ( k9_xtuple_0(B) = k3_finseq_2(k1_numbers) & ! [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => k6_graphsp(B,C) = k2_graphsp(k1_nat_1(k1_nat_1(k2_nat_1(A,A),k2_nat_1(3,A)),1),k14_graphsp(k7_graphsp(C,A),C,A),C,k4_xcmplx_0(1)) ) ) ) ) ) )).
fof(d11_grcat_1,axiom,( ! [A] : ( l1_grcat_1(A) => ( v2_grcat_1(A) <=> v13_vectsp_1(k9_grcat_1(A),k7_grcat_1(A),k8_grcat_1(A)) ) ) )).
fof(d11_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( v4_group_1(B,A) => ( C = k6_group_1(A,B) <=> C = k5_numbers ) ) & ( ~ v4_group_1(B,A) => ( C = k6_group_1(A,B) <=> ( k5_group_1(A,C,B) = k1_group_1(A) & C != k5_numbers & ! [D] : ( v7_ordinal1(D) => ( k5_group_1(A,D,B) = k1_group_1(A) => ( D = k5_numbers | r1_xxreal_0(C,D) ) ) ) ) ) ) ) ) ) ) )).
fof(d11_group_10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,B) => k11_group_10(A,B,C,D) = k10_group_10(A,B,C,k6_domain_1(B,D)) ) ) ) ) )).
fof(d11_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(d11_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ( r5_group_3(A,B,C) <=> ? [D] : ( 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) ) ) ) ) ) )).
fof(d11_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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] : ( ( v15_algstr_0(C) & m1_group_2(C,A) ) => ! [D] : ( ( v15_algstr_0(D) & m1_group_2(D,A) ) => k1_binop_1(B,C,D) = k10_group_2(A,C,D) ) ) ) ) ) )).
fof(d11_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ( r1_group_6(A,B) <=> ? [C] : ( 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)) ) ) ) ) )).
fof(d11_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( C = k6_group_9(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( v2_group_9(D,A) & m1_group_9(D,A,B) ) ) ) ) )).
fof(d11_hahnban1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)),k3_real_1(k3_funct_2(u1_struct_0(B),k1_numbers,C,D),k3_funct_2(u1_struct_0(B),k1_numbers,C,E))) ) ) ) ) ) ) )).
fof(d11_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( ~ 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] : ( ( 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))) ) ) ) )).
fof(d11_heyting1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k12_normform(A))) => ! [C] : ( ( 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] : ( 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) ) ) ) ) )).
fof(d11_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_hilbert1)) => ( B = k5_hilbert1(A) <=> ! [C] : ( m1_subset_1(C,k1_hilbert1) => ( r2_hidden(C,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_hilbert1)) => ( ( v6_hilbert1(D) & r1_tarski(A,D) ) => r2_hidden(C,D) ) ) ) ) ) ) ) )).
fof(d11_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( D = k11_idea_1(A,B,C) <=> ( k3_finseq_1(D) = k3_finseq_1(B) & ! [E] : ( v7_ordinal1(E) => ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d11_incsp_1,axiom,( ! [A] : ( l2_incsp_1(A) => ( v8_incsp_1(A) <=> ! [B] : ( m1_subset_1(B,u4_incsp_1(A)) => ? [C] : ( m1_subset_1(C,u1_incsp_1(A)) & r2_incsp_1(A,C,B) ) ) ) ) )).
fof(d11_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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] : ( m4_index_1(C,u1_struct_0(A),u4_struct_0(A),u1_graph_1(A),u2_graph_1(A),B) => ! [D] : ( m2_cat_1(D,A,C) => ( D = k9_index_1(A,B,C) <=> ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d11_int_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ! [B] : ( ( 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] : ( m1_subset_1(C,k7_card_1(A)) => k1_funct_1(B,C) = k5_int_1(k6_xcmplx_0(A,C),A) ) ) ) ) ) )).
fof(d11_integr15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ! [D] : ( ( 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) ) ) ) )).
fof(d11_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(d11_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => k4_intpro_1(A,B) = k7_finseq_1(k7_finseq_1(k12_finseq_1(k4_ordinal1,2),A),B) ) ) )).
fof(d11_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & 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] : ( m2_cat_1(C,A,B) => ( m1_isocat_1(C,A,B) <=> ? [D] : ( 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)) ) ) ) ) ) ) )).
fof(d11_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,A,C) => ! [G] : ( m2_cat_1(G,A,C) => ( ( r1_nattra_1(A,B,D,E) & r1_nattra_1(A,C,F,G) ) => ! [H] : ( m1_nattra_1(H,A,B,D,E) => ! [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) ) ) ) ) ) ) ) ) ) ) )).
fof(d11_jordan6,axiom,( ! [A] : ( ( 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(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)),2)),k18_pscomp_1(A),k22_pscomp_1(A)) ) )).
fof(d11_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(d11_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_lattice3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r1_orders_2(A,D,B) & r1_orders_2(A,D,C) & ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d11_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(d11_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( v1_card_1(D) => ( D = k7_lattice5(A,B,C) <=> r2_tarski(D,a_3_0_lattice5(A,B,C)) ) ) ) ) ) )).
fof(d11_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v6_lattice6(B,A) <=> r1_lattice6(A,k6_lattices(A),B) ) ) ) )).
fof(d11_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( m1_lattice8(D,A,B,C) <=> ( k9_xtuple_0(D) = k4_ordinal1 & k1_funct_1(D,k5_numbers) = k4_tarski(A,C) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ? [F] : ( ~ v1_xboole_0(F) & ? [G] : ( 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] : ( ~ v1_xboole_0(H) & ? [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,k1_nat_1(E,1)) = k4_tarski(H,I) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d11_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( v11_lattices(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d11_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)))) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ( ( k1_relset_1(k6_glib_000(A),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),B)) = k6_glib_000(A) => ( C = k10_lexbfs(A,B) <=> C = o_1_0_lexbfs(A) ) ) & ( k1_relset_1(k6_glib_000(A),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),B)) != k6_glib_000(A) => ( C = k10_lexbfs(A,B) <=> ? [D] : ( ~ v1_xboole_0(D) & v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(k4_ordinal1))) & ? [E] : ( ~ v1_xboole_0(E) & v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(k15_pre_poly(k4_ordinal1))) & ? [F] : ( v1_relat_1(F) & v1_funct_1(F) & D = k10_xtuple_0(F) & F = k5_relset_1(k6_glib_000(A),k5_finsub_1(k4_ordinal1),k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),B)))) & ! [G] : ( ( v1_finset_1(G) & m1_subset_1(G,k1_zfmisc_1(k4_ordinal1)) ) => ( r2_hidden(G,D) => r2_hidden(k1_uproots(k4_ordinal1,G,1),E) ) ) & ! [G] : ~ ( r2_hidden(G,E) & ! [H] : ( ( v1_finset_1(H) & m1_subset_1(H,k1_zfmisc_1(k4_ordinal1)) ) => ~ ( r2_hidden(H,D) & G = k1_uproots(k4_ordinal1,H,1) ) ) ) & C = o_2_0_lexbfs(E,F) ) ) ) ) ) ) ) ) ) )).
fof(d11_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v8_limfunc1(A) <=> ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(B,C) & r2_hidden(C,k1_relset_1(k1_numbers,A)) ) ) & ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_limfunc1(B) & r1_tarski(k10_xtuple_0(B),k1_relset_1(k1_numbers,A)) ) => v2_limfunc1(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,B,A)) ) ) ) ) ) )).
fof(d11_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( C != k1_xboole_0 => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( m9_lmod_7(D,A,B,C) <=> m1_subset_1(D,C) ) ) ) ) ) ) )).
fof(d11_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( r2_hidden(C,k10_lopban_1(A,B)) => k13_lopban_1(A,B,C) = C ) ) ) )).
fof(d11_lopban_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lopban_2(A) ) => ( v4_lopban_2(A) <=> ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d11_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( 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) ) ) )).
fof(d11_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( r1_lpspacc1(A,B,C,D,E) <=> ? [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) & k12_supinf_2(C,F) = k5_numbers & r2_relset_1(A,k2_numbers,k2_partfun1(A,k2_numbers,D,k3_subset_1(A,F)),k2_partfun1(A,k2_numbers,E,k3_subset_1(A,F))) ) ) ) ) ) ) ) )).
fof(d11_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => k11_lpspace1(A,B,C) = a_3_1_lpspace1(A,B,C) ) ) ) )).
fof(d11_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v2_xxreal_0(D) & v1_xreal_0(D) ) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(d11_ltlaxio1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1))) ) => ( B = k11_ltlaxio1(A) <=> ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,B,k1_domain_1(k4_ordinal1,k1_hilbert1,C,k2_hilbert1)) = k5_ordinal1 & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,B,k1_domain_1(k4_ordinal1,k1_hilbert1,C,k1_hilbert2(D))) = 1 <=> r2_hidden(k1_hilbert2(D),k3_funct_2(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1),A,C)) ) ) & ! [D] : ( m1_subset_1(D,k1_hilbert1) => ! [E] : ( m1_subset_1(E,k1_hilbert1) => ( k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,B,k1_domain_1(k4_ordinal1,k1_hilbert1,C,k3_hilbert1(D,E))) = k6_xboolean(k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,B,k1_domain_1(k4_ordinal1,k1_hilbert1,C,D)),k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,B,k1_domain_1(k4_ordinal1,k1_hilbert1,C,E))) & ~ ( k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,B,k1_domain_1(k4_ordinal1,k1_hilbert1,C,k4_hilbert1(D,E))) = 1 & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( ~ r1_xxreal_0(F,k5_ordinal1) & k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,B,k1_domain_1(k4_ordinal1,k1_hilbert1,k1_nat_1(C,F),E)) = 1 & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( r1_xxreal_0(1,G) => ( r1_xxreal_0(F,G) | k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,B,k1_domain_1(k4_ordinal1,k1_hilbert1,k1_nat_1(C,G),D)) = 1 ) ) ) ) ) ) & ( ? [F] : ( m1_subset_1(F,k4_ordinal1) & ~ r1_xxreal_0(F,k5_ordinal1) & k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,B,k1_domain_1(k4_ordinal1,k1_hilbert1,k1_nat_1(C,F),E)) = 1 & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( r1_xxreal_0(1,G) => ( r1_xxreal_0(F,G) | k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,B,k1_domain_1(k4_ordinal1,k1_hilbert1,k1_nat_1(C,G),D)) = 1 ) ) ) ) => k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,B,k1_domain_1(k4_ordinal1,k1_hilbert1,C,k4_hilbert1(D,E))) = 1 ) ) ) ) ) ) ) ) ) )).
fof(d11_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ( v3_ltlaxio3(A) <=> k5_ltlaxio3(k10_ltlaxio3(A)) = k10_ltlaxio3(A) ) ) )).
fof(d11_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) & v1_funct_1(B) & v3_trees_2(B) & v3_trees_9(B) ) => ( m3_ltlaxio4(B,A) <=> ( k1_funct_1(B,k1_xboole_0) = A & ! [C] : ( m1_trees_1(C,k9_xtuple_0(B)) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ( D = k3_trees_2(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)),B,C) => k2_trees_9(B,C) = o_1_7_ltlaxio4(D) ) ) ) ) ) ) ) )).
fof(d11_margrel1,axiom,( k6_margrel1 = k2_tarski(k5_numbers,1) )).
fof(d11_matrix16,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ( v6_matrix16(B,A) <=> ? [C] : ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(A),k3_finseq_1(B),k3_finseq_1(B)) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) & r3_matrix16(A,C,B) ) ) ) ) )).
fof(d11_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : k10_matrix_0(A,B,C) = k2_finseq_2(A,k2_finseq_2(B,C)) ) ) )).
fof(d11_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => k12_matrixc1(A) = k17_rvsum_1(k10_matrixc1(A)) ) )).
fof(d11_matrixj1,axiom,( ! [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] : ( ( v1_matrixj1(B,u1_struct_0(A)) & m2_finseq_1(B,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) => ! [C] : ( ( v1_matrixj1(C,u1_struct_0(A)) & m2_finseq_1(C,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d11_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( m2_finseq_1(B,k1_numbers) => k11_matrixr1(A,B) = k8_matrix_0(k1_numbers,k6_matrixr1(A,k9_matrixr1(B)),1) ) ) )).
fof(d11_mcart_1,axiom,( ! [A] : k14_mcart_1(A) = k2_xtuple_0(k1_xtuple_0(A)) )).
fof(d11_measure6,axiom,( ! [A] : ! [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))) ) => ( v5_measure6(B,A) <=> v2_xxreal_2(k7_relset_1(A,k1_numbers,B,A)) ) ) )).
fof(d11_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ( v1_measure8(C,A,B) <=> ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & v1_prob_2(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ( r2_hidden(k3_tarski(k2_relset_1(B,D)),B) => k19_supinf_2(k1_partfun1(k4_ordinal1,B,B,k6_numbers,D,C)) = k1_mesfunc9(C,k3_tarski(k2_relset_1(B,D))) ) ) ) ) ) )).
fof(d11_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => k14_member_1(A,B) = k12_member_1(A,k6_member_1(B)) ) ) )).
fof(d11_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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 ) ) ) ) ) ) )).
fof(d11_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( C = k11_mesfun7c(A,B) <=> ! [D] : ( 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] : ( m1_subset_1(E,A) => ( r2_hidden(E,k1_relset_1(A,k4_mesfunc5(A,k1_numbers,C,D))) => k12_supinf_2(k4_mesfunc5(A,k1_numbers,C,D),E) = k12_supinf_2(k7_comseq_3(k9_mesfun7c(A,B,E)),D) ) ) ) ) ) ) ) ) )).
fof(d11_mesfunc1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_valued_0(A) ) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( C = k11_mesfunc1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,k9_xtuple_0(A)) & ~ r1_xxreal_0(B,k1_funct_1(A,D)) ) ) ) ) ) )).
fof(d11_mesfunc5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v10_mesfunc5(A) <=> ~ ( ~ v7_mesfunc5(A) & ~ v8_mesfunc5(A) & ~ v9_mesfunc5(A) ) ) ) )).
fof(d11_metric_1,axiom,( ! [A] : k5_metric_1(A) = g1_metric_1(A,k4_metric_1(A)) )).
fof(d11_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => k8_metric_2(A) = a_1_4_metric_2(A) ) )).
fof(d11_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_nat_1(A,2)) ) => ( m2_midsp_3(B,A) <=> v2_midsp_3(B,A) ) ) ) )).
fof(d11_mmlquer2,axiom,( ! [A] : ! [B] : ( ( v1_relat_2(B) & v4_relat_2(B) & v6_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ! [D] : ( ( v1_relat_1(D) & v5_relat_1(D,A) & v1_funct_1(D) & v5_ordinal1(D) & v1_finset_1(D) ) => ( D = k10_mmlquer2(A,B,C) <=> ( k2_relset_1(A,D) = C & v2_funct_1(D) & ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( ( r2_hidden(E,k1_relset_1(k4_ordinal1,D)) & r2_hidden(F,k1_relset_1(k4_ordinal1,D)) ) => ( r1_xxreal_0(E,F) <=> r1_mmlquery(k1_funct_1(D,E),k1_funct_1(D,F),B) ) ) ) ) ) ) ) ) ) )).
fof(d11_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [D] : ( v7_ordinal1(D) => k11_mmlquery(A,B,C,D) = a_4_6_mmlquery(A,B,C,D) ) ) ) )).
fof(d11_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( m1_mod_2(E,A,C,D) => ! [F] : ( m1_mod_2(F,A,B,C) => k9_mod_2(A,B,C,D,E,F) = k8_mod_2(A,E,F) ) ) ) ) ) ) )).
fof(d11_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) ) )).
fof(d11_modcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_modcat_1(B,A) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d11_modelc_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => k11_modelc_1(A,B) = k8_finseq_1(k4_ordinal1,k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,4),A),B) ) ) )).
fof(d11_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v2_modelc_2(A) <=> ? [B] : ( v7_ordinal1(B) & A = k2_modelc_2(B) ) ) ) )).
fof(d11_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( l1_modelc_3(B,A) => ( v3_modelc_3(B,A) <=> u2_modelc_3(A,B) = k1_xboole_0 ) ) ) )).
fof(d11_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v5_group_1(A) <=> v1_binop_1(u2_algstr_0(A),u1_struct_0(A)) ) ) )).
fof(d11_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => k1_funct_1(C,D) = k7_msafree(A,B,D) ) ) ) ) ) )).
fof(d11_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( v4_msafree2(B,A) <=> v2_finset_1(u3_msualg_1(A,B)) ) ) ) )).
fof(d11_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m3_pboole(C,u1_struct_0(A),k4_equation(A)) => ( C = k5_msafree4(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_msafree4(u1_struct_0(A),C,D) = a_3_0_msafree4(A,B,D) ) ) ) ) ) )).
fof(d11_msualg_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d11_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( C = k6_msualg_2(A,B) <=> ! [D] : ( 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] : ( m3_pboole(E,u1_struct_0(A),u3_msualg_1(A,B)) => ( E = D => v3_msualg_2(E,A,B) ) ) ) ) ) ) ) )).
fof(d11_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ( r5_msualg_3(A,B,C) <=> ? [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) & r4_msualg_3(A,B,C,D) ) ) ) ) ) )).
fof(d11_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msualg_4(C,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,B)) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(d11_nat_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k10_nat_lat)) => k11_nat_lat(A) = A ) )).
fof(d11_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ( r1_nattra_1(A,B,C,D) => ! [E] : ( m1_nattra_1(E,A,B,C,D) => ( v1_nattra_1(E,A,B,C,D) => ! [F] : ( m1_nattra_1(F,A,B,D,C) => ( F = k6_nattra_1(A,B,C,D,E) <=> ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => k2_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),k2_nattra_1(A,B,C,D,E,G)) ) ) ) ) ) ) ) ) ) ) )).
fof(d11_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( r7_ncfcont1(A,B,C,D) <=> ( r1_tarski(D,k1_relset_1(u1_struct_0(A),C)) & ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d11_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(k7_normform(A))) => ! [C] : ( 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)) ) ) )).
fof(d11_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ( v10_o_ring_1(B,A) <=> ( k3_finseq_1(B) != k5_numbers & v9_o_ring_1(k7_partfun1(u1_struct_0(A),B,1),A) & ! [C] : ( v7_ordinal1(C) => ~ ( C != k5_numbers & ~ r1_xxreal_0(k3_finseq_1(B),C) & ! [D] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d11_openlatt,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d11_oposet_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v3_oposet_1(A) <=> ( v2_oposet_1(A) & v4_orders_2(A) ) ) ) )).
fof(d11_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d11_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r5_orders_1(A,B) <=> ! [C] : ~ ( r1_tarski(C,B) & v3_orders_1(k2_wellord1(A,C)) & ! [D] : ~ ( r2_hidden(D,B) & ! [E] : ( r2_hidden(E,C) => r2_hidden(k4_tarski(D,E),A) ) ) ) ) ) )).
fof(d11_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( B != k1_xboole_0 => ( m1_orders_2(C,A,B) <=> ? [D] : ( 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 ) ) ) ) ) ) )).
fof(d11_ordinal1,axiom,( ! [A] : ( A = k4_ordinal1 <=> ( r2_hidden(k1_xboole_0,A) & v4_ordinal1(A) & v3_ordinal1(A) & ! [B] : ( v3_ordinal1(B) => ( ( r2_hidden(k1_xboole_0,B) & v4_ordinal1(B) ) => r1_tarski(A,B) ) ) ) ) )).
fof(d11_ordinal5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) ) => ( v6_ordinal5(A) <=> ( ! [B] : ( v3_ordinal1(B) => ( r2_hidden(B,k9_xtuple_0(A)) => v5_ordinal5(k1_funct_1(A,B)) ) ) & ! [B] : ( v3_ordinal1(B) => ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(d11_ordinal6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v3_ordinal6(A) ) => k7_ordinal6(A) = k2_ordinal6(a_1_1_ordinal6(A)) ) )).
fof(d11_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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)) ) ) )).
fof(d11_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d11_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_osalg_2(C,A,B) => ! [D] : ( m2_osalg_2(D,A,B) => ( D = k9_osalg_2(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k1_funct_1(D,E) = k1_setfam_1(k8_osalg_2(A,B,C,E)) ) ) ) ) ) ) )).
fof(d11_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v2_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => k1_funct_1(D,E) = k6_osalg_4(A,B,C,E) ) ) ) ) ) ) )).
fof(d11_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) ) )).
fof(d11_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r7_pboole(A,B,C) <=> ! [D] : ( ( 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) ) ) ) ) ) )).
fof(d11_pcs_0,axiom,( ! [A] : ( l1_pcs_0(A) => ( v6_pcs_0(A) <=> r3_relat_2(u1_pcs_0(A),u1_struct_0(A)) ) ) )).
fof(d11_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( 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),k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_1(B,A),D)) ) ) ) ) ) )).
fof(d11_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r2_pdiff_5(A,B) => ! [C] : ( v1_xreal_0(C) => ( C = k2_pdiff_5(A,B) <=> ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & B = k11_finseq_1(D,E,F) & ? [G] : ( 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] : ( v1_funct_1(H) & v3_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [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_funct_1(H,1) & ! [J] : ( v1_xreal_0(J) => ( r2_hidden(J,G) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,2,k1_pdiff_3(1,3,A),B),J),k1_funct_1(k1_pdiff_2(3,2,k1_pdiff_3(1,3,A),B),E)) = k2_xcmplx_0(k1_funct_1(H,k6_xcmplx_0(J,E)),k1_funct_1(I,k6_xcmplx_0(J,E))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d11_pencil_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( v10_pencil_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_pencil_1(C,A) & v2_pencil_1(C,A) & ! [D] : ( m2_finseq_1(D,k9_setfam_1(u1_struct_0(A))) => ~ ( C = k1_funct_1(D,1) & r2_hidden(B,k1_funct_1(D,k3_finseq_1(D))) & ! [E] : ( 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] : ( 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))))) ) ) ) ) ) ) ) ) ) ) )).
fof(d11_petri_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ~ ( r2_hidden(B,k9_xtuple_0(u2_petri_2(A))) & ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_petri_2(A))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k8_petri(A,k6_domain_1(u4_struct_0(A),B)))) => ! [E] : ( 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)))) ) ) ) ) ) ) ) ) ) )).
fof(d11_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => k14_polyform(A) = k11_polyform(A,2) ) )).
fof(d11_polynom1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [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] : ( ( ~ v2_struct_0(C) & v36_algstr_0(C) & l6_algstr_0(C) ) => ( C = k12_polynom1(A,B) <=> ( ! [D] : ( 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,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(F,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(G,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) = k5_polynom1(A,B,F,G) ) ) ) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(F,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(G,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) = k10_polynom1(A,B,F,G) ) ) ) ) ) & k4_struct_0(C) = k8_polynom1(A,B) & k5_struct_0(C) = k9_polynom1(A,B) ) ) ) ) ) )).
fof(d11_polynom5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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] : ( 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),k4_ordinal1,u1_struct_0(A),k4_group_1(A),E,C)) ) ) ) ) ) ) )).
fof(d11_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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] : ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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) ) ) ) ) ) ) ) )).
fof(d11_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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)) ) ) )).
fof(d11_pralg_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( ( 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] : ~ ( r2_hidden(E,A) & ! [F] : ( 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 ) ) ) ) ) ) )).
fof(d11_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : r1_xxreal_0(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) )).
fof(d11_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ( v9_pre_topc(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d11_prob_1,axiom,( k11_prob_1 = a_0_0_prob_1 )).
fof(d11_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v1_prvect_1(A) ) => ! [B] : ( m1_prvect_1(B,k15_prvect_1(A)) => ( B = k17_prvect_1(A) <=> ( k3_finseq_1(B) = k3_finseq_1(k15_prvect_1(A)) & ! [C] : ( m2_subset_1(C,k4_ordinal1,k4_finseq_1(k15_prvect_1(A))) => r1_funct_2(k2_zfmisc_1(k1_funct_1(k15_prvect_1(A),C),k1_funct_1(k15_prvect_1(A),C)),k1_funct_1(k15_prvect_1(A),C),k2_zfmisc_1(u1_struct_0(k16_prvect_1(A,C)),u1_struct_0(k16_prvect_1(A,C))),u1_struct_0(k16_prvect_1(A,C)),k9_prvect_1(k15_prvect_1(A),B,C),u1_algstr_0(k16_prvect_1(A,C))) ) ) ) ) ) )).
fof(d11_prvect_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m1_subset_1(B,k4_card_3(k4_prvect_2(A))) => ! [C] : ( 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] : ( m2_subset_1(D,k4_ordinal1,k4_finseq_1(A)) => k1_funct_1(C,D) = k1_funct_1(u1_normsp_0(k11_prvect_2(A,D)),k1_funct_1(B,D)) ) ) ) ) ) ) )).
fof(d11_pscomp_1,axiom,( ! [A] : ( 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)) ) )).
fof(d11_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ( B = k9_qc_lang1(A) <=> ( v1_qc_lang1(B,A) & ! [C] : ( ~ v1_xboole_0(C) => ( v1_qc_lang1(C,A) => r1_tarski(B,C) ) ) ) ) ) ) )).
fof(d11_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v2_qc_lang2(B,A) <=> ? [C] : ( m1_subset_1(C,k9_qc_lang1(A)) & ? [D] : ( m1_subset_1(D,k9_qc_lang1(A)) & B = k2_qc_lang2(A,C,D) ) ) ) ) ) )).
fof(d11_qmax_1,axiom,( ! [A] : ( ( v2_qmax_1(A) & l1_qmax_1(A) ) => ! [B] : ( m1_subset_1(B,k5_qmax_1(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d11_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k17_quatern2(A,B) = k23_quaterni(A,k27_quaterni(B)) ) ) )).
fof(d11_quaterni,axiom,( k11_quaterni = k6_quaterni(k5_numbers,k5_numbers,1,k5_numbers) )).
fof(d11_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ( B != k11_quofield(A) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ( C = k14_quofield(A,B) <=> ! [D] : ( m2_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A)) => ( r2_hidden(D,C) <=> ? [E] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d11_radix_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v7_ordinal1(B) => k12_radix_1(A,B) = k6_xcmplx_0(A,k3_xcmplx_0(k11_radix_1(A),k1_radix_1(B))) ) ) )).
fof(d11_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v3_card_1(D,A) & m2_finseq_1(D,k3_radix_1(C)) ) => ( D = k10_radix_6(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k2_finseq_1(A)) => k4_radix_1(E,C,A,D) = k9_radix_6(E,B,C) ) ) ) ) ) ) ) )).
fof(d11_random_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => k6_random_3(A,B,C) = C ) ) ) )).
fof(d11_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( m1_ratfunc1(B,A) => ( v6_ratfunc1(B,A) <=> ( v5_ratfunc1(B,A) & v3_ratfunc1(k5_ratfunc1(A,B),A) ) ) ) ) )).
fof(d11_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( C = k7_relat_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( r2_hidden(k4_tarski(E,D),A) & r2_hidden(E,B) ) ) ) ) )).
fof(d11_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ( v3_relat_2(A) <=> r3_relat_2(A,k1_relat_1(A)) ) ) )).
fof(d11_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r9_rewrite1(A,B) <=> ? [C] : r4_rewrite1(A,B,C) ) ) )).
fof(d11_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ( r2_hidden(D,k1_relset_1(A,C)) => k1_funct_1(C,D) = k2_rfunct_3(k1_funct_1(B,D)) ) ) ) ) ) ) ) )).
fof(d11_rlvect_1,axiom,( ! [A] : ( l2_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_algstr_0(A,B,C) = k1_algstr_0(A,B,k4_algstr_0(A,C)) ) ) ) )).
fof(d11_rlvect_2,axiom,( ! [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) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_rlvect_2(C,A) => ! [D] : ( m1_rlvect_2(D,A) => ( D = k8_rlvect_2(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k1_numbers,D,E) = k3_xcmplx_0(B,k3_funct_2(u1_struct_0(A),k1_numbers,C,E)) ) ) ) ) ) ) )).
fof(d11_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(d11_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_robbins1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_binop_1(u1_lattices(B),C,D) = k4_robbins1(A,C,D) ) ) ) ) ) ) )).
fof(d11_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(d11_rvsum_1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => k17_rvsum_1(A) = k1_finsop_1(k2_numbers,A,k3_binop_2) ) )).
fof(d11_scm_comp,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_dtconstr(k1_scm_comp),k9_funct_2(k4_ordinal1,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(k4_ordinal1,k8_afinsq_1(u1_compos_1(k1_ami_3)))))) ) => ( A = k14_scm_comp <=> ( ! [B] : ( m2_subset_1(B,u1_struct_0(k1_scm_comp),k6_dtconstr(k1_scm_comp)) => ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k8_afinsq_1(u1_compos_1(k1_ami_3))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k8_afinsq_1(u1_compos_1(k1_ami_3))))) & C = k3_funct_2(k4_dtconstr(k1_scm_comp),k9_funct_2(k4_ordinal1,k8_afinsq_1(u1_compos_1(k1_ami_3))),A,k3_scm_comp(B)) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => k3_funct_2(k4_ordinal1,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] : ( m2_subset_1(B,u1_struct_0(k1_scm_comp),k7_dtconstr(k1_scm_comp)) => ! [C] : ( m1_dtconstr(C,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [D] : ( m1_dtconstr(D,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k1_scm_comp)) => ! [F] : ( 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] : ( ( v1_funct_1(G) & v1_funct_2(G,k4_ordinal1,k8_afinsq_1(u1_compos_1(k1_ami_3))) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k8_afinsq_1(u1_compos_1(k1_ami_3))))) ) => ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,k4_ordinal1,k8_afinsq_1(u1_compos_1(k1_ami_3))) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k8_afinsq_1(u1_compos_1(k1_ami_3))))) ) => ! [I] : ( ( v1_funct_1(I) & v1_funct_2(I,k4_ordinal1,k8_afinsq_1(u1_compos_1(k1_ami_3))) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k8_afinsq_1(u1_compos_1(k1_ami_3))))) ) => ~ ( G = k3_funct_2(k4_dtconstr(k1_scm_comp),k9_funct_2(k4_ordinal1,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(k4_ordinal1,k8_afinsq_1(u1_compos_1(k1_ami_3))),A,C) & I = k3_funct_2(k4_dtconstr(k1_scm_comp),k9_funct_2(k4_ordinal1,k8_afinsq_1(u1_compos_1(k1_ami_3))),A,D) & ! [J] : ( m1_subset_1(J,k4_ordinal1) => k3_funct_2(k4_ordinal1,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(k4_ordinal1,k8_afinsq_1(u1_compos_1(k1_ami_3)),H,J),k3_funct_2(k4_ordinal1,k8_afinsq_1(u1_compos_1(k1_ami_3)),I,k1_nat_1(J,1))),k13_scm_comp(B,J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d11_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => k11_scmfsa_2(A) = k7_ami_3(A) ) )).
fof(d11_scmpds_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => k11_scmpds_2(A,B,C) = k3_xtuple_0(8,k1_xboole_0,k11_finseq_1(A,B,C)) ) ) ) )).
fof(d11_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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,k1_nat_1(k5_card_1(C),1)),C) ) ) ) )).
fof(d11_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => ( ? [B] : ( m1_subset_1(B,k2_scm_inst) & ? [C] : ( m1_subset_1(C,k2_scm_inst) & ? [D] : ( v1_int_1(D) & ? [E] : ( v1_int_1(E) & ? [F] : ( 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] : ( v1_int_1(B) => ( B = k12_scmpds_i(A) <=> ? [C] : ( 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) ) ) ) ) ) )).
fof(d11_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => k6_scmyciel(A) = k6_subset_1(k5_scmyciel(k3_tarski(A)),k1_scmyciel(A)) ) )).
fof(d11_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => k12_seq_4(A) = k4_finseq_2(A,k2_numbers) ) )).
fof(d11_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( r2_seqfunc(A,B,C) <=> ( r1_seqfunc(A,k1_numbers,B,C) & ? [D] : ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) & C = k1_relset_1(A,D) & ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,C) => ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( v7_ordinal1(G) => ? [H] : ( v7_ordinal1(H) & r1_xxreal_0(G,H) & r1_xxreal_0(F,k9_complex1(k6_xcmplx_0(k1_funct_1(k1_seqfunc(A,k1_numbers,B,H),E),k1_funct_1(D,E)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d11_setfam_1,axiom,( ! [A] : ! [B] : ( m1_setfam_1(B,A) <=> r1_tarski(A,k3_tarski(B)) ) )).
fof(d11_sgraph1,axiom,( ! [A] : ! [B] : ( m1_sgraph1(B,A) => ! [C] : ( r4_sgraph1(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & r2_hidden(C,k5_sgraph1(A,B,D,D)) ) ) ) )).
fof(d11_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d11_simplex0,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => k5_simplex0(A,B) = g1_pre_topc(A,k2_simplex0(A,B)) ) )).
fof(d11_sin_cos,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k2_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( D = k10_sin_cos(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(E,A) => k9_nat_1(k2_numbers,D,E) = k3_xcmplx_0(k9_nat_1(k2_numbers,k3_sin_cos(B),E),k9_nat_1(k2_numbers,k10_comseq_3(k3_sin_cos(C)),k7_nat_d(A,E))) ) & ( ~ r1_xxreal_0(E,A) => k9_nat_1(k2_numbers,D,E) = k5_numbers ) ) ) ) ) ) ) ) )).
fof(d11_stacks_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_stacks_1(A) ) => ( v5_stacks_1(A) <=> ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = k5_stacks_1(A,k7_stacks_1(A,B,C)) ) ) ) ) )).
fof(d11_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => ( v8_struct_0(A) <=> v1_finset_1(u1_struct_0(A)) ) ) )).
fof(d11_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_substut1(A)) ) => k12_substut1(A,B,C) = k6_subset_1(k4_ordinal1,k4_subset_1(k1_qc_lang1(A),k10_substut1(A,B),k11_substut1(A,C))) ) ) ) )).
fof(d11_supinf_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_card_3(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( m1_supinf_2(B,A) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( C = k15_supinf_2(A,B) <=> ( k12_supinf_2(C,k5_numbers) = k12_supinf_2(B,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( m1_subset_1(E,k6_numbers) => ( E = k12_supinf_2(C,D) => k12_supinf_2(C,k1_nat_1(D,1)) = k3_supinf_2(E,k12_supinf_2(B,k1_nat_1(D,1))) ) ) ) ) ) ) ) ) )).
fof(d11_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k9_tdlat_1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d11_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) )).
fof(d11_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d11_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( v7_topalg_6(B,A) & m2_subset_1(B,k4_partfun1(k1_numbers,k2_struct_0(A)),k1_topalg_6(A)) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( m1_borsuk_2(F,A,D,E) & ? [G] : ( m1_borsuk_2(G,A,D,E) & F = k3_relat_1(k1_borsuk_6(k5_numbers,1,k2_xxreal_2(k9_xtuple_0(B)),k1_xxreal_2(k9_xtuple_0(B))),B) & G = k3_relat_1(k1_borsuk_6(k5_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) ) ) ) ) ) ) ) ) )).
fof(d11_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_topgen_1(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( ~ v1_xboole_0(C) & r1_tarski(C,B) & v2_topgen_1(C,A) ) ) ) ) ) )).
fof(d11_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(d11_topreal1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( B = k5_topreal1(A) <=> ! [C] : ( 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) ) ) ) ) ) ) )).
fof(d11_toprealb,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => k1_funct_1(A,B) = k19_euclid(k19_sin_cos(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)),k17_sin_cos(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B))) ) ) ) )).
fof(d11_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => C != k3_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) ) ) ) ) ) ) )).
fof(d11_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( v2_trees_1(B) => ( m4_trees_1(B,A) <=> r1_tarski(B,A) ) ) ) )).
fof(d11_trees_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) ) => ( r2_hidden(B,k9_xtuple_0(A)) => ! [D] : ( ( 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] : ( m2_finseq_1(E,k4_ordinal1) => ~ ( 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] : ( m2_finseq_1(F,k4_ordinal1) => ~ ( r2_hidden(F,k9_xtuple_0(C)) & r2_relset_1(k4_ordinal1,k4_ordinal1,E,k8_finseq_1(k4_ordinal1,B,F)) & k1_funct_1(D,E) = k1_funct_1(C,F) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d11_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v6_trees_3(A) <=> v3_trees_3(k10_xtuple_0(A)) ) ) )).
fof(d11_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) ) => k9_trees_9(A) = a_1_2_trees_9(A) ) )).
fof(d11_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(d11_turing_1,axiom,( 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(k4_ordinal1,k4_ordinal1,k3_turing_1(5),k7_domain_1(k4_ordinal1,k5_numbers,1)),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),k5_numbers),k2_turing_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k3_zfmisc_1(k4_ordinal1,k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers),k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers,1))),k2_turing_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k3_zfmisc_1(k4_ordinal1,k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,1),k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,1,k5_numbers,1))),k2_turing_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k3_zfmisc_1(k4_ordinal1,k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,1,1),k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,1,1,1))),k2_turing_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k3_zfmisc_1(k4_ordinal1,k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,1,k5_numbers),k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,2,1,1))),k2_turing_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k3_zfmisc_1(k4_ordinal1,k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,2,1),k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,2,1,1))),k16_funcop_1(k1_domain_1(k4_ordinal1,k4_ordinal1,2,k5_numbers),k3_xtuple_0(3,k5_numbers,k4_xcmplx_0(1)))),k16_funcop_1(k1_domain_1(k4_ordinal1,k4_ordinal1,3,1),k3_xtuple_0(4,k5_numbers,k4_xcmplx_0(1)))),k16_funcop_1(k1_domain_1(k4_ordinal1,k4_ordinal1,4,1),k3_xtuple_0(4,1,k4_xcmplx_0(1)))),k2_turing_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k3_zfmisc_1(k4_ordinal1,k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,4,k5_numbers),k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,5,k5_numbers,k5_numbers))) )).
fof(d11_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k1_funct_1(A,k10_finseq_1(B,C)) = k9_margrel1(k1_binarith(k9_margrel1(B),C)) ) ) ) ) )).
fof(d11_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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] : ( r2_hidden(C,k9_xtuple_0(B)) => k1_funct_1(B,C) = k9_complex1(k1_funct_1(A,C)) ) ) ) ) ) )).
fof(d11_valued_2,axiom,( ! [A] : ! [B] : ( B = k5_valued_2(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( v1_funct_1(C) & v1_funct_2(C,A,k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) ) ) )).
fof(d11_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( 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] : ( ( ~ 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) ) ) ) ) ) )).
fof(d11_vectsp_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_vectsp_1(A,B,C) = k8_group_1(A,B,k11_algstr_0(A,C)) ) ) ) )).
fof(d11_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(d11_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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))) ) ) ) ) ) )).
fof(d11_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k1_yellow_1(k7_waybel_0(B))),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_yellow_1(k7_waybel_0(B))),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))))) ) => ( C = k4_waybel23(A,B) <=> ! [D] : ( ( ~ 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & D = E & k1_funct_1(C,D) = k3_waybel_0(A,E) ) ) ) ) ) ) )).
fof(d11_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k5_waybel34(A))) => m1_subset_1(C,u1_struct_0(B)) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(k5_waybel34(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_waybel34(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( E = C & F = D ) => ( k1_altcat_1(k5_waybel34(A),C,D) = k1_xboole_0 | ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d11_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( r1_waybel_0(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r1_orders_2(B,D,E) => r2_hidden(k2_waybel_0(A,B,E),C) ) ) ) ) ) ) )).
fof(d11_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) )).
fof(d11_waybel_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d11_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k10_xboolean(A,B) = k3_xboolean(k7_xboolean(A,B)) ) ) )).
fof(d11_xtuple_0,axiom,( ! [A] : k8_xtuple_0(A) = k2_xtuple_0(k1_xtuple_0(k1_xtuple_0(A))) )).
fof(d11_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ( v5_xxreal_2(A) <=> ( v3_xxreal_2(A) & v4_xxreal_2(A) ) ) ) )).
fof(d11_yellow21,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) ) ) )).
fof(d11_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => k3_yellow_0(A) = k1_yellow_0(A,k1_xboole_0) ) )).
fof(d11_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( B = k6_yellow_6(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( ~ 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))) ) ) ) ) )).
fof(d11_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ( v7_zf_fund1(B,A) <=> ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(a_3_3_zf_fund1(A,C,D),B) ) ) ) ) ) ) )).
fof(d11_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v3_zf_lang(A) <=> ? [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) & ? [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) & A = k5_zf_lang(B,C) ) ) ) ) )).
fof(d11_zf_model,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => k11_zf_model(A) = k11_zf_lang(k8_zf_lang(k2_zf_lang(3),k13_zf_lang(k2_zf_lang(k5_numbers),k8_zf_lang(k2_zf_lang(4),k12_zf_lang(A,k4_zf_lang(k2_zf_lang(4),k2_zf_lang(k5_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))))))) ) )).
fof(d11_zmodul01,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d11_zmodul02,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(k9_int_3(A)),u1_struct_0(k10_zmodul02(B,k5_zmodul02(B,A)))),u1_struct_0(k10_zmodul02(B,k5_zmodul02(B,A)))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(k9_int_3(A)),u1_struct_0(k10_zmodul02(B,k5_zmodul02(B,A)))),u1_struct_0(k10_zmodul02(B,k5_zmodul02(B,A)))))) ) => ( C = k11_zmodul02(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(A))) => ! [E] : ( v1_int_1(E) => ! [F] : ( m1_subset_1(F,u1_struct_0(k10_zmodul02(B,k5_zmodul02(B,A)))) => ( D = k5_int_1(E,A) => k2_binop_1(u1_struct_0(k9_int_3(A)),u1_struct_0(k10_zmodul02(B,k5_zmodul02(B,A))),u1_struct_0(k10_zmodul02(B,k5_zmodul02(B,A))),C,D,F) = k1_zmodul01(k10_zmodul02(B,k5_zmodul02(B,A)),F,k5_int_1(E,A)) ) ) ) ) ) ) ) ) )).
fof(d12_abcmiz_0,axiom,( ! [A] : ( l2_abcmiz_0(A) => ! [B] : ( m1_subset_1(B,u1_abcmiz_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k3_abcmiz_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & D = E & r2_hidden(B,k2_abcmiz_0(A,E)) ) ) ) ) ) ) )).
fof(d12_abcmiz_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ( v3_abcmiz_1(A) <=> ? [B] : ( m1_subset_1(B,u4_struct_0(A)) & ? [C] : ( 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 ) ) ) ) )).
fof(d12_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v12_aff_2(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d12_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_afinsq_1(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k9_xtuple_0(A)) => ( r1_xxreal_0(C,B) | r2_hidden(B,k9_xtuple_0(A)) ) ) ) ) ) ) )).
fof(d12_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k7_afproj(A),k8_afproj(A)))) => ( B = k12_afproj(A) <=> ! [C] : ! [D] : ( r2_hidden(k4_tarski(C,D),B) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & ? [F] : ( 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) ) ) ) ) ) ) )).
fof(d12_algstr_0,axiom,( ! [A] : ( l2_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v11_algstr_0(B,A) <=> ( v10_algstr_0(B,A) & v9_algstr_0(B,A) ) ) ) ) )).
fof(d12_algstr_4,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v15_algstr_0(C) & m1_algstr_4(C,A) ) => ( C = k9_algstr_4(A,B) <=> ( r1_tarski(B,u1_struct_0(C)) & ! [D] : ( ( v15_algstr_0(D) & m1_algstr_4(D,A) ) => ( r1_tarski(B,u1_struct_0(D)) => m1_algstr_4(C,D) ) ) ) ) ) ) ) )).
fof(d12_altcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ( v9_altcat_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(E,k1_altcat_1(A,B,C)) & ? [F] : ( m1_subset_1(F,k1_altcat_1(A,C,D)) & ? [G] : ( v1_relat_1(G) & v1_funct_1(G) & ? [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d12_altcat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(d12_altcat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_altcat_1(A,B,C)) => ( v9_altcat_3(D,A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( v8_altcat_3(E,A) => ! [F] : ( m1_subset_1(F,k1_altcat_1(A,B,E)) => ! [G] : ( m1_subset_1(G,k1_altcat_1(A,E,C)) => D = k5_altcat_1(A,B,E,C,F,G) ) ) ) ) ) ) ) ) ) )).
fof(d12_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_analmetr(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & C != D & B = k4_analmetr(A,C,D) ) ) ) ) ) )).
fof(d12_anproj_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d12_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & l1_aofa_a00(C,A) ) => ( v3_aofa_a00(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,C),D)) => k1_msafree4(u1_struct_0(A),k11_aofa_a00(A,C,D,F),E) = a_6_0_aofa_a00(A,B,C,D,E,F) ) ) ) ) ) ) ) )).
fof(d12_armstrng,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ( v4_armstrng(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d12_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( 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))) ) ) )).
fof(d12_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : k9_asympt_0(A,B) = a_2_0_asympt_0(A,B) ) )).
fof(d12_bcialg_1,axiom,( ! [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) ) => k4_bcialg_1(A) = a_1_0_bcialg_1(A) ) )).
fof(d12_bcialg_2,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d12_bcialg_3,axiom,( ! [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) ) => ( v11_bcialg_3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_1(A,B,k1_bcialg_1(A,C,B)) = B ) ) ) ) )).
fof(d12_bcialg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_bcialg_4(A) ) => ( v5_bcialg_4(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_bcialg_4(A,B,B) = B ) ) ) )).
fof(d12_bcialg_6,axiom,( ! [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] : ( m1_bcialg_1(B,A) => ! [C] : ( ( v12_bcialg_1(C,A) & m2_bcialg_1(C,A) ) => ! [D] : ( m5_bcialg_2(D,A,C) => ! [E] : ( ( 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] : ( m2_subset_1(F,u1_struct_0(A),k7_bcialg_6(A,B,C,D)) => ! [G] : ( m2_subset_1(G,u1_struct_0(A),k7_bcialg_6(A,B,C,D)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d12_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(C)) => v13_vectsp_1(k8_bilinear(A,B,C,D,E),B,A) ) ) ) ) ) ) )).
fof(d12_binop_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(d12_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_borsuk_1(B,A) => ( v2_borsuk_1(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => v2_compts_1(C,A) ) ) ) ) ) )).
fof(d12_borsuk_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(d12_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( 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 ) ) ) ) ) ) )).
fof(d12_c0sp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ( v5_c0sp1(A) <=> ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( k1_rlvect_1(A,C,B) = k4_struct_0(A) & B != k5_numbers & C != k4_struct_0(A) ) ) ) ) ) )).
fof(d12_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ( r7_calcul_1(A,B,C) <=> ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_valuat_1(E,A,D) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d12_card_3,axiom,( ! [A] : ( v4_funct_1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k10_card_3(A) <=> ( k9_xtuple_0(B) = k9_card_3(A) & ! [C] : ( r2_hidden(C,k9_xtuple_0(B)) => k1_funct_1(B,C) = k5_card_3(C,A) ) ) ) ) ) )).
fof(d12_card_fil,axiom,( r3_card_fil <=> ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => k2_card_1(A) = k3_card_2(2,A) ) )).
fof(d12_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_cat_1(D,A,B,C) => ( v7_cat_1(D,A,B,C) <=> ( k2_cat_1(A,B,C) != k1_xboole_0 & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k2_cat_1(A,E,B) != k1_xboole_0 => ! [F] : ( m1_cat_1(F,A,E,B) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) ) ) )).
fof(d12_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( 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)) ) ) )).
fof(d12_catalg_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( ( 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] : ( 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))) ) ) ) ) ) ) )).
fof(d12_cfdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [B] : ( r2_cfdiff_1(A,B) => ! [C] : ( ( 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] : ( v1_xcmplx_0(D) => ( r2_hidden(D,B) => k7_partfun1(k2_numbers,C,D) = k2_cfdiff_1(A,D) ) ) ) ) ) ) ) )).
fof(d12_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ! [B] : ( B = k10_cgames_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( 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 ) ) ) ) )).
fof(d12_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_chain_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k4_chain_1(A,B,k1_nat_1(C,1)))) => k10_chain_1(A,B,C,D) = a_4_1_chain_1(A,B,C,D) ) ) ) ) )).
fof(d12_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m2_finseq_1(B,k6_glib_000(A)) => ( m3_chord(B,A) <=> ( v2_funct_1(B) & k10_xtuple_0(B) = k6_glib_000(A) ) ) ) ) )).
fof(d12_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v4_msualg_1(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(d12_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(d12_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m2_pboole(C,A,B,B) => ! [D] : ( m3_pboole(D,A,B) => ( D = k5_closure1(A,B,C) <=> ! [E] : ! [F] : ( r2_hidden(F,A) => ( r2_hidden(E,k1_funct_1(D,F)) <=> ? [G] : ( 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 ) ) ) ) ) ) ) )).
fof(d12_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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] : ( 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))) ) ) ) ) )).
fof(d12_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_clvect_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( m2_clvect_1(C,A,B) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & C = k5_clvect_1(A,D,B) ) ) ) ) ) )).
fof(d12_coh_sp,axiom,( ! [A] : ! [B] : ( ( 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] : ( 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) ) ) ) )).
fof(d12_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v7_cohsp_1(A) <=> ! [B] : ! [C] : ( 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)) ) ) ) )).
fof(d12_combgras,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => k6_combgras(A,B) = a_2_2_combgras(A,B) ) )).
fof(d12_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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)) ) ) )).
fof(d12_comput_1,axiom,( ! [A] : ( v4_comput_1(A) <=> ! [B] : ( m2_rfunct_3(B,k3_finseq_2(k4_ordinal1),k4_ordinal1,k2_comput_1(k4_ordinal1)) => ! [C] : ( ( v3_comput_1(C) & m2_finseq_1(C,k2_comput_1(k4_ordinal1)) ) => ( ( r2_hidden(B,A) & k19_margrel1(B) = k3_finseq_1(C) & r1_tarski(k10_xtuple_0(C),A) ) => r2_hidden(k3_relat_1(k5_funct_6(C),B),A) ) ) ) ) )).
fof(d12_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( v3_conlat_1(B,A) & ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) & v7_conlat_1(B,A) & l2_conlat_1(B,A) ) => ( B = k5_conlat_1(A) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & ? [D] : ( 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)) ) ) ) ) ) )).
fof(d12_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( B = k10_convex4(A) <=> ! [C] : ( r2_hidden(C,B) <=> m1_convex4(C,A) ) ) ) )).
fof(d12_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m1_subset_1(E,k1_qc_lang1(A)) => ! [F] : ( m1_subset_1(F,k5_finsub_1(k3_qc_lang1(A))) => ! [G] : ( 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] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( m1_subset_1(F,k1_qc_lang1(A)) => ! [G] : ( m1_subset_1(G,k5_finsub_1(k3_qc_lang1(A))) => ! [H] : ( 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] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [F] : ( m1_subset_1(F,k1_qc_lang1(A)) => ! [G] : ( m1_subset_1(G,k5_finsub_1(k3_qc_lang1(A))) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d12_csspace,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d12_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k7_decomp_1(A) = a_1_1_decomp_1(A) ) )).
fof(d12_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_eqrel_1(B,u1_struct_0(A)) => ( v6_dilworth(B,A) <=> ! [C] : ( r2_hidden(C,B) => ( v2_dilworth(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) )).
fof(d12_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) => ( B = k10_dist_1(A) <=> ! [C] : ( m2_finseq_1(C,A) => ( r2_hidden(C,B) <=> v1_dist_1(C,A) ) ) ) ) ) )).
fof(d12_e_siec,axiom,( ! [A] : ( ( 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))) ) )).
fof(d12_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( 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))) ) ) ) )).
fof(d12_ens_1,axiom,( ! [A] : ( ~ 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)) ) )).
fof(d12_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => k22_euclid(A) = k21_euclid(A) ) )).
fof(d12_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( 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] : ( v1_xreal_0(F) => ( F = k11_euclid_3(A,B,C,D,E) <=> ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & k2_xcmplx_0(k2_xcmplx_0(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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d12_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ( r7_euclidlp(A,B,C) <=> ? [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) & ? [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) & ? [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(d12_exchsort,axiom,( ! [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) ) => ! [B] : ( ( 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) ) ) )).
fof(d12_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & ~ v2_compos_1(C,B) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(d12_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(d12_ff_siec,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => k12_ff_siec(A) = u4_struct_0(A) ) )).
fof(d12_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_filter_0(A,B,C,D) <=> r2_hidden(k7_filter_0(A,C,D),B) ) ) ) ) ) )).
fof(d12_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(d12_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k12_fin_topo(A,B) = a_2_4_fin_topo(A,B) ) ) )).
fof(d12_finance1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ 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] : ( ~ v1_xboole_0(E) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,E) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,E))) ) => ! [G] : ( m1_subset_1(G,C) => k12_finance1(A,B,C,D,E,F,G) = k1_funct_1(k3_series_1(k8_nat_1(k1_numbers,k10_finance1(C,D,E,G,F,B),1)),k6_xcmplx_0(A,1)) ) ) ) ) ) ) ) )).
fof(d12_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_finseq_1(A) <=> ? [B] : ( v7_ordinal1(B) & r1_tarski(k9_xtuple_0(A),k2_finseq_1(B)) ) ) ) )).
fof(d12_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r5_finseq_8(A,B,C) <=> ( ~ r1_xxreal_0(k3_finseq_1(C),k5_numbers) => ( r1_xxreal_0(k3_finseq_1(C),k3_finseq_1(B)) & k8_finseq_8(A,B,C,1) = k7_nat_d(k1_nat_1(k3_finseq_1(B),1),k3_finseq_1(C)) ) ) ) ) ) ) )).
fof(d12_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k11_fintopo2(A,B) = a_2_3_fintopo2(A,B) ) ) )).
fof(d12_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k8_fomodel0(A) = k1_funct_4(k16_funcop_1(k1_xboole_0,k1_xboole_0),k6_fomodel0(k3_finseq_2(A),k11_monoid_0(A))) ) )).
fof(d12_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_fomodel2(C,A,B) ) => ! [D] : ( ( 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))) ) => k12_fomodel2(A,B,C,D) = k1_funct_1(k11_fomodel2(A,B,C,k10_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),k9_fomodel2(A,B,C))) ) ) ) ) )).
fof(d12_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(d12_freealg,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_freealg(B) ) => k7_freealg(A,B) = g1_unialg_1(k4_dtconstr(k3_freealg(A,B)),k6_freealg(A,B)) ) ) )).
fof(d12_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d12_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k12_ftacell1(A,B,C,D,E) = k36_gfacirc1(k24_gfacirc1(A,B,C),E,D) )).
fof(d12_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v3_funct_1(A) => ( v1_xboole_0(A) | ! [B] : ( B = k3_funct_1(A) <=> ? [C] : ( r2_hidden(C,k9_xtuple_0(A)) & B = k1_funct_1(A,C) ) ) ) ) ) )).
fof(d12_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ( m1_funct_2(C,A,B) <=> ! [D] : ( 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))) ) ) ) ) )).
fof(d12_funct_7,axiom,( ! [A] : ! [B] : k10_funct_7(A,B) = k1_funct_7(k7_funcop_1(k4_ordinal1,B),k5_numbers,A) )).
fof(d12_functor0,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(d12_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => ! [C] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(d12_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ ( ~ 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 ) ) )).
fof(d12_gate_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : 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) )).
fof(d12_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v4_vectsp_1(A) & v3_gcd_1(A) & l4_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d12_geomtrap,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_geomtrap(A) ) => ( v2_geomtrap(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( 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] : ( 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] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d12_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : k12_gfacirc1(A,B,C) = k9_facirc_1(A,B,C,k14_twoscomp) )).
fof(d12_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : k13_glib_000(A,B,C) = k1_funct_4(A,k16_funcop_1(B,C)) ) ) )).
fof(d12_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( ( 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 ) ) ) ) ) ) )).
fof(d12_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => k11_glib_004(A,B) = k40_glib_000(k10_glib_004(A,B)) ) ) )).
fof(d12_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m2_glib_005(D,A,B) => ( D = k5_glib_005(A,B,C) <=> ( k4_glib_005(A,B,D,k5_numbers) = k16_funcop_1(C,1) & ! [E] : ( v7_ordinal1(E) => r2_relset_1(k6_glib_000(A),k2_xboole_0(k6_domain_1(k4_ordinal1,1),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))) ) ) ) ) ) ) ) )).
fof(d12_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(d12_graph_2,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r3_graph_2(A,B,C) <=> ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( 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)) ) ) ) ) ) ) ) )).
fof(d12_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => v1_abian(k7_graph_3(A,D,C)) ) => ( k7_graph_3(A,B,C) = k5_numbers | k13_graph_3(A,B,C) = a_3_4_graph_3(A,B,C) ) ) ) ) )).
fof(d12_graph_5,axiom,( k8_graph_5 = a_0_0_graph_5 )).
fof(d12_graphsp,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers)) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k16_graphsp(A,B,C) = k3_real_1(k7_partfun1(k1_numbers,A,k2_xcmplx_0(k2_nat_1(2,B),k7_partfun1(k1_numbers,A,k1_nat_1(k1_nat_1(k2_nat_1(B,B),k2_nat_1(3,B)),1)))),k7_partfun1(k1_numbers,A,k2_xcmplx_0(k2_xcmplx_0(k2_nat_1(2,B),k3_xcmplx_0(B,k7_partfun1(k1_numbers,A,k1_nat_1(k1_nat_1(k2_nat_1(B,B),k2_nat_1(3,B)),1)))),C))) ) ) ) )).
fof(d12_grcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( v2_grcat_1(C) & l1_grcat_1(C) ) => ( m1_grcat_1(C,A,B) <=> ( k7_grcat_1(C) = A & k8_grcat_1(C) = B ) ) ) ) ) )).
fof(d12_group_1,axiom,( ! [A] : ( l3_algstr_0(A) => ( v5_group_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_algstr_0(A,B,C) = k6_algstr_0(A,C,B) ) ) ) ) )).
fof(d12_group_10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l3_algstr_0(A) ) => ! [B] : ! [C] : ( ( 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] : ( m1_subset_1(D,B) => ( r1_group_10(A,B,C,D) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => D = k1_funct_1(k1_group_10(A,B,C,E),D) ) ) ) ) ) )).
fof(d12_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( 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) ) ) ) )).
fof(d12_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_group_3(A))) => ( C = k9_group_3(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( v15_algstr_0(E) & m1_group_2(E,A) & D = E & r5_group_3(A,B,E) ) ) ) ) ) ) )).
fof(d12_group_4,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d12_hahnban1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => k3_funct_2(u1_struct_0(B),k1_numbers,C,k1_algstr_0(B,D,E)) = k3_real_1(k3_funct_2(u1_struct_0(B),k1_numbers,C,D),k3_funct_2(u1_struct_0(B),k1_numbers,C,E)) ) ) ) ) ) ) )).
fof(d12_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k6_vectsp10(k1_complfld,A,k13_bilinear(k1_complfld,A,B,C)))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k6_vectsp10(k1_complfld,B,k14_bilinear(k1_complfld,A,B,k3_hermitan(A,B,C))))) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d12_hilbert1,axiom,( k6_hilbert1 = k5_hilbert1(k1_subset_1(k1_hilbert1)) )).
fof(d12_idea_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( D = k12_idea_1(A,B,C) <=> ( k3_finseq_1(D) = k3_finseq_1(B) & ! [E] : ( v7_ordinal1(E) => ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d12_incproj,axiom,( ! [A] : ( l1_incsp_1(A) => ( v8_incproj(A) <=> ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u1_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u1_incsp_1(A)) => ! [H] : ( m1_subset_1(H,u1_incsp_1(A)) => ! [I] : ( m1_subset_1(I,u2_incsp_1(A)) => ! [J] : ( m1_subset_1(J,u2_incsp_1(A)) => ! [K] : ( m1_subset_1(K,u2_incsp_1(A)) => ! [L] : ( m1_subset_1(L,u2_incsp_1(A)) => ! [M] : ( m1_subset_1(M,u2_incsp_1(A)) => ! [N] : ( m1_subset_1(N,u2_incsp_1(A)) => ! [O] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d12_incsp_1,axiom,( ! [A] : ( l2_incsp_1(A) => ( v9_incsp_1(A) <=> ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ? [E] : ( m1_subset_1(E,u4_incsp_1(A)) & r5_incsp_1(A,k8_domain_1(u1_incsp_1(A),B,C,D),E) ) ) ) ) ) ) )).
fof(d12_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(d12_int_3,axiom,( ! [A] : ( v7_ordinal1(A) => k9_int_3(A) = g6_algstr_0(k7_card_1(A),k3_gr_cy_1(A),k7_int_3(A),k10_subset_1(1,k7_card_1(A)),k10_subset_1(k5_numbers,k7_card_1(A))) ) )).
fof(d12_integr10,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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(k5_numbers) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,k1_relset_1(k1_numbers,B)) => k1_funct_1(B,C) = k3_integr10(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,A,k6_integr10(C)),k5_numbers) ) ) ) ) ) ) )).
fof(d12_integr15,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k4_ordinal1) => ( 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))) ) ) ) ) ) ) )).
fof(d12_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(d12_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => k5_intpro_1(A,B) = k7_finseq_1(k7_finseq_1(k12_finseq_1(k4_ordinal1,3),A),B) ) ) )).
fof(d12_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(d12_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,A,C) => ! [G] : ( m2_cat_1(G,A,C) => ( ( r2_nattra_1(A,B,D,E) & r2_nattra_1(A,C,F,G) ) => ! [H] : ( m2_nattra_1(H,A,B,D,E) => ! [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) ) ) ) ) ) ) ) ) ) ) )).
fof(d12_jordan6,axiom,( ! [A] : ( ( 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(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)),2)),k18_pscomp_1(A),k22_pscomp_1(A)) ) )).
fof(d12_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_lattice3(A) <=> ! [B] : ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r2_lattice3(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_lattice3(A,B,D) => r1_orders_2(A,C,D) ) ) ) ) ) )).
fof(d12_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(d12_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( v12_lattices(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d12_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)))) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( v7_ordinal1(D) => k11_lexbfs(A,B,C,D) = k4_tarski(k1_funct_4(k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),B),k16_funcop_1(C,k7_nat_d(k15_glib_000(A),D))),k1_lexbfs(k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),B),k4_rfunct_3(k6_glib_000(A),k1_zfmisc_1(k4_ordinal1),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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),B))),k6_domain_1(k4_ordinal1,k7_nat_d(k15_glib_000(A),D))))) ) ) ) ) )).
fof(d12_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v3_limfunc1(A) => ! [B] : ( v1_xreal_0(B) => ( B = k4_limfunc1(A) <=> ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_limfunc1(C) & r1_tarski(k10_xtuple_0(C),k1_relset_1(k1_numbers,A)) ) => ( v2_comseq_2(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,C,A)) & k1_seq_2(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,C,A)) = B ) ) ) ) ) ) ) )).
fof(d12_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( D = k7_lmod_7(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & E = k3_vectsp_4(A,B,F,C) ) ) ) ) ) ) )).
fof(d12_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(d12_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => k15_lpspacc1(A,B,C) = a_3_1_lpspacc1(A,B,C) ) ) ) )).
fof(d12_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => k12_lpspace1(A,B,C) = g1_rlvect_1(k11_lpspace1(A,B,C),k10_subset_1(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))) ) ) ) )).
fof(d12_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v2_xxreal_0(D) & v1_xreal_0(D) ) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k10_lpspace2(A,B,C,D))) => ? [G] : ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) & r2_hidden(G,F) & ? [H] : ( v1_xreal_0(H) & H = k1_mesfunc6(A,B,C,k2_mesfun6c(D,A,k56_valued_1(A,k1_numbers,G))) & k3_funct_2(u1_struct_0(k10_lpspace2(A,B,C,D)),k1_numbers,E,F) = k2_power(H,k2_extreal1(1,D)) ) ) ) ) ) ) ) ) ) )).
fof(d12_ltlaxio1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ( r1_ltlaxio1(A,B) <=> ! [C] : ( m1_subset_1(C,k4_ordinal1) => k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(A),k1_domain_1(k4_ordinal1,k1_hilbert1,C,B)) = 1 ) ) ) ) )).
fof(d12_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ! [B] : ( m3_ltlaxio4(B,A) => k11_ltlaxio4(A,B) = a_2_0_ltlaxio4(A,B) ) ) )).
fof(d12_matrix16,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ( v6_matrix16(B,A) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(A),k3_finseq_1(B),k3_finseq_1(B)) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( C = k3_matrix16(A,B) <=> r3_matrix16(A,C,B) ) ) ) ) ) )).
fof(d12_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k12_matrix_0(A,B,C,D) = k10_finseq_1(k10_finseq_1(A,B),k10_finseq_1(C,D)) )).
fof(d12_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k2_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(C) & k3_finseq_1(B) = k1_matrix_0(C) ) => ! [D] : ( ( v1_matrix_0(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_0(D) = k3_finseq_1(B) & ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( r2_hidden(k4_tarski(E,F),k2_matrix_0(C)) => k3_matrix_0(k2_numbers,D,E,F) = k3_xcmplx_0(k3_xcmplx_0(k9_matrix_5(A,E),k3_matrix_0(k2_numbers,C,E,F)),k8_complex1(k9_matrix_5(B,F))) ) ) ) ) ) ) ) ) ) ) )).
fof(d12_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( m2_finseq_1(B,k1_numbers) => k12_matrixr1(A,B) = k7_matrix_0(k1_numbers,k6_matrixr1(k10_matrixr1(B),A),1) ) ) )).
fof(d12_matroid0,axiom,( ! [A] : ( ( ~ v3_pencil_1(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(d12_mcart_1,axiom,( ! [A] : k15_mcart_1(A) = k1_xtuple_0(k2_xtuple_0(A)) )).
fof(d12_measure6,axiom,( ! [A] : ! [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))) ) => ( v6_measure6(B,A) <=> v1_xxreal_2(k7_relset_1(A,k1_numbers,B,A)) ) ) )).
fof(d12_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,k6_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,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,C,k6_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,k6_numbers))) ) => ( r1_measure8(A,B,C,D,E) <=> ! [F] : ( r2_hidden(F,B) => k1_mesfunc9(E,F) = k1_mesfunc9(D,F) ) ) ) ) ) ) )).
fof(d12_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => k15_member_1(A,B) = k13_member_1(A,k7_member_1(B)) ) ) )).
fof(d12_membered,axiom,( ! [A] : ( v6_membered(A) => ! [B] : ( r1_tarski(A,B) <=> ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ) ) )).
fof(d12_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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 ) ) ) ) ) )).
fof(d12_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( C = k12_mesfun7c(A,B) <=> ! [D] : ( 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] : ( m1_subset_1(E,A) => ( r2_hidden(E,k1_relset_1(A,k4_mesfunc5(A,k1_numbers,C,D))) => k12_supinf_2(k4_mesfunc5(A,k1_numbers,C,D),E) = k12_supinf_2(k8_comseq_3(k9_mesfun7c(A,B,E)),D) ) ) ) ) ) ) ) ) )).
fof(d12_mesfunc1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_valued_0(A) ) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( C = k12_mesfunc1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,k9_xtuple_0(A)) & r1_xxreal_0(k1_funct_1(A,D),B) ) ) ) ) ) )).
fof(d12_mesfunc5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v10_mesfunc5(A) => ! [B] : ( m1_subset_1(B,k6_numbers) => ( B = k2_mesfunc5(A) <=> ~ ( ! [C] : ( v1_xreal_0(C) => ~ ( B = C & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(E,F) & r1_xxreal_0(D,k3_extreal1(k4_supinf_2(k9_nat_1(k6_numbers,A,F),B))) ) ) ) ) & v7_mesfunc5(A) ) ) & ~ ( B = k1_supinf_1 & v8_mesfunc5(A) ) & ~ ( B = k2_supinf_1 & v9_mesfunc5(A) ) ) ) ) ) ) )).
fof(d12_metric_1,axiom,( ! [A] : ( ( 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 = k6_metric_1 <=> ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k1_binop_1(A,B,C) = k9_complex1(k6_xcmplx_0(B,C)) ) ) ) ) )).
fof(d12_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => k9_metric_2(A) = a_1_5_metric_2(A) ) )).
fof(d12_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => k10_midsp_1(A) = a_1_1_midsp_1(A) ) )).
fof(d12_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_midsp_1(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(d12_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_midsp_3(B,A) => ! [C] : ( ( v4_midsp_2(C,B) & l1_midsp_2(C,B) ) => ! [D] : ( m2_finseq_2(D,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(u1_midsp_2(B,C)))) => ! [E] : ( m1_subset_1(E,u1_struct_0(u1_midsp_2(B,C))) => ( E = k10_midsp_3(A,B,C,D) <=> ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => E = k9_midsp_3(A,B,C,F,D) ) ) ) ) ) ) ) )).
fof(d12_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [D] : ( v7_ordinal1(D) => k12_mmlquery(A,B,C,D) = a_4_7_mmlquery(A,B,C,D) ) ) ) )).
fof(d12_mod_2,axiom,( ! [A] : ( m1_subset_1(A,k1_enumset1(k5_numbers,1,2)) => ( ( A = k5_numbers => k10_mod_2(A) = k5_numbers ) & ( A = 1 => k10_mod_2(A) = 2 ) & ( A = 2 => k10_mod_2(A) = 1 ) ) ) )).
fof(d12_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) ) )).
fof(d12_modcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_modcat_1(B,A) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d12_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( A = k12_modelc_1 <=> ( ! [B] : ( r2_hidden(B,A) => m2_finseq_1(B,k4_ordinal1) ) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => r2_hidden(k6_modelc_1(B),A) ) & ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ( r2_hidden(B,A) => r2_hidden(k7_modelc_1(B),A) ) ) & ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r2_hidden(k8_modelc_1(B,C),A) ) ) ) & ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ( r2_hidden(B,A) => r2_hidden(k9_modelc_1(B),A) ) ) & ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ( r2_hidden(B,A) => r2_hidden(k10_modelc_1(B),A) ) ) & ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r2_hidden(k11_modelc_1(B,C),A) ) ) ) & ! [B] : ( ~ v1_xboole_0(B) => ( ( ! [C] : ( r2_hidden(C,B) => m2_finseq_1(C,k4_ordinal1) ) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => r2_hidden(k6_modelc_1(C),B) ) & ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( r2_hidden(C,B) => r2_hidden(k7_modelc_1(C),B) ) ) & ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k8_modelc_1(C,D),B) ) ) ) & ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( r2_hidden(C,B) => r2_hidden(k9_modelc_1(C),B) ) ) & ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( r2_hidden(C,B) => r2_hidden(k10_modelc_1(C),B) ) ) & ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k11_modelc_1(C,D),B) ) ) ) ) => r1_tarski(A,B) ) ) ) ) ) )).
fof(d12_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v3_modelc_2(A) <=> ? [B] : ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) & A = k3_modelc_2(B) ) ) ) )).
fof(d12_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v3_group_1(A) <=> v2_binop_1(u2_algstr_0(A),u1_struct_0(A)) ) ) )).
fof(d12_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d12_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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(k5_ordinal1))) ) ) ) )).
fof(d12_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m2_pboole(C,u1_struct_0(A),B,k7_funcop_1(u1_struct_0(A),k4_ordinal1)) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( m1_subset_1(D,k3_card_3(u3_msualg_1(A,k1_msafree3(A,B)))) => ! [E] : ( m1_subset_1(E,k3_card_3(u3_msualg_1(A,k3_equation(A)))) => ( E = k6_msafree4(A,B,C,D) <=> ? [F] : ( v1_relat_1(F) & v4_relat_1(F,k1_msaterm(A,B)) & v1_funct_1(F) & v1_partfun1(F,k1_msaterm(A,B)) & E = k1_funct_1(F,D) & ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_msafree4(H,u1_struct_0(A),B,k1_msafree4(u1_struct_0(A),B,G)) => k1_funct_1(F,k1_trees_4(k4_tarski(H,G))) = k1_trees_4(k4_tarski(k3_funct_2(k1_msafree4(u1_struct_0(A),B,G),k1_funct_1(k7_funcop_1(u1_struct_0(A),k4_ordinal1),G),k2_msafree4(u1_struct_0(A),B,k7_funcop_1(u1_struct_0(A),k4_ordinal1),C,G),H),G)) ) ) & ! [G] : ( m1_subset_1(G,u4_struct_0(A)) => ! [H] : ( m1_msaterm(H,A,B,k2_msaterm(A,B,G)) => k1_msafree4(k1_msaterm(A,B),F,k6_msaterm(A,B,k2_msaterm(A,B,G),H)) = k4_trees_4(k2_msaterm(A,k7_funcop_1(u1_struct_0(A),k4_ordinal1),G),k3_relat_1(H,F)) ) ) ) ) ) ) ) ) ) ) )).
fof(d12_msualg_1,axiom,( ! [A] : ( ( v13_struct_0(A,1) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( C = k10_msualg_1(A,B) <=> m1_subset_1(C,k10_xtuple_0(u3_msualg_1(A,B))) ) ) ) )).
fof(d12_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(d12_msualg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d12_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msualg_4(C,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,B)) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(d12_nat_lat,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) ) ) ) ) )).
fof(d12_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_nattra_1(E,A,B,C,D) => ( ( r2_nattra_1(A,B,C,D) & v1_nattra_1(E,A,B,C,D) ) => k7_nattra_1(A,B,C,D,E) = k6_nattra_1(A,B,C,D,E) ) ) ) ) ) ) )).
fof(d12_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( r8_ncfcont1(A,B,C,D) <=> ( r1_tarski(D,k1_relset_1(u1_struct_0(A),C)) & ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d12_normform,axiom,( ! [A] : ! [B] : ( ( v3_lattices(B) & l3_lattices(B) ) => ( B = k12_normform(A) <=> ( u1_struct_0(B) = k8_normform(A) & ! [C] : ( m2_subset_1(C,k5_finsub_1(k7_normform(A)),k8_normform(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d12_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v11_o_ring_1(B,A) <=> ? [C] : ( 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)) ) ) ) ) )).
fof(d12_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v1_lattice2(A) & l3_lattices(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(d12_oposet_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v4_oposet_1(A) <=> ( v3_orders_2(A) & v4_orders_2(A) ) ) ) )).
fof(d12_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => k12_oppcat_1(A) = k11_oppcat_1(A,A,k10_cat_1(A)) ) )).
fof(d12_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r6_orders_1(A,B) <=> ( r2_hidden(B,k1_relat_1(A)) & ! [C] : ~ ( r2_hidden(C,k1_relat_1(A)) & C != B & r2_hidden(k4_tarski(B,C),A) ) ) ) ) )).
fof(d12_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m2_orders_1(B,k1_orders_1(u1_struct_0(A)),k6_partfun1(k1_orders_1(u1_struct_0(A)))) => ! [C] : ( ( 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] : ( 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 ) ) ) ) ) ) ) )).
fof(d12_ordinal1,axiom,( ! [A] : ( v7_ordinal1(A) <=> r2_hidden(A,k4_ordinal1) ) )).
fof(d12_ordinal2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ( v2_ordinal2(A) <=> ! [B] : ( v3_ordinal1(B) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(d12_ordinal6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v3_ordinal6(A) ) => ! [B] : ( ( 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,k5_numbers)) & ! [C] : ( v3_ordinal1(C) => ( r2_hidden(C,k9_xtuple_0(B)) => k1_funct_1(B,C) = k3_tarski(a_2_0_ordinal6(A,C)) ) ) ) ) ) ) )).
fof(d12_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d12_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ( v9_osalg_1(B,A) <=> ( v7_osalg_1(B,A) & ! [C] : ( 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] : ( m1_subset_1(D,u4_struct_0(A)) => ~ r3_osalg_1(A,B,D,C) ) ) ) ) ) ) ) )).
fof(d12_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_osalg_2(C,A,B) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d12_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v2_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(d12_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_parsp_1(A) ) => ( v2_parsp_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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] : ( m1_subset_1(J,u1_struct_0(A)) & r1_parsp_1(A,B,C,D,J) & r1_parsp_1(A,B,D,C,J) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d12_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ( v3_relat_1(B) <=> ! [C] : ( r2_hidden(C,A) => v1_xboole_0(k1_funct_1(B,C)) ) ) ) )).
fof(d12_pcs_0,axiom,( k5_pcs_0 = g1_pcs_0(k1_xboole_0,k1_partit_2(k1_xboole_0,k1_xboole_0)) )).
fof(d12_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( 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),k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_1(B,A),D)) ) ) ) ) )).
fof(d12_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r3_pdiff_5(A,B) => ! [C] : ( v1_xreal_0(C) => ( C = k3_pdiff_5(A,B) <=> ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & B = k11_finseq_1(D,E,F) & ? [G] : ( 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] : ( v1_funct_1(H) & v3_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [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_funct_1(H,1) & ! [J] : ( v1_xreal_0(J) => ( r2_hidden(J,G) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,3,k1_pdiff_3(1,3,A),B),J),k1_funct_1(k1_pdiff_2(3,3,k1_pdiff_3(1,3,A),B),F)) = k2_xcmplx_0(k1_funct_1(H,k6_xcmplx_0(J,F)),k1_funct_1(I,k6_xcmplx_0(J,F))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d12_petri,axiom,( ! [A] : ( 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))) ) )).
fof(d12_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B))) => ! [D] : ( 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) ) ) ) )).
fof(d12_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( 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) ) ) ) ) )).
fof(d12_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( r10_polyred(A,B,C,D,E) <=> ? [F] : ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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) ) ) ) ) ) ) ) )).
fof(d12_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k6_poset_1(A,A))) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(d12_pralg_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => k12_pralg_2(A,B,C,D) = k1_funct_1(k9_funct_6(k11_pralg_2(A,B,C)),D) ) ) ) )).
fof(d12_pre_poly,axiom,( ! [A] : ! [B] : ( B = k14_pre_poly(A) <=> ! [C] : ( 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) ) ) ) )).
fof(d12_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ( v10_pre_topc(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d12_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_prelamb(A) ) => ! [B] : ( ( 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)),k4_ordinal1)) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) ) => ( m1_prelamb(B,A) <=> ( v1_finset_1(k9_xtuple_0(B)) & ! [C] : ( m1_trees_1(C,k9_xtuple_0(B)) => v2_prelamb(C,A,B) ) ) ) ) ) )).
fof(d12_prob_1,axiom,( k12_prob_1 = k9_prob_1(k1_numbers,k11_prob_1) )).
fof(d12_prvect_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k4_card_3(k4_prvect_2(A))) => k3_funct_2(k4_card_3(k4_prvect_2(A)),k1_numbers,B,C) = k12_euclid(k12_prvect_2(A,C)) ) ) ) ) )).
fof(d12_pscomp_1,axiom,( ! [A] : ( 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)) ) )).
fof(d12_pua2mss1,axiom,( ! [A] : ( l1_msualg_1(A) => ! [B] : ( l1_msualg_1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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] : ! [F] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(d12_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k6_qc_lang1(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(d12_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v3_qc_lang2(B,A) <=> ? [C] : ( m1_subset_1(C,k9_qc_lang1(A)) & ? [D] : ( m1_subset_1(D,k9_qc_lang1(A)) & B = k4_qc_lang2(A,C,D) ) ) ) ) ) )).
fof(d12_qmax_1,axiom,( ! [A] : ( ( v2_qmax_1(A) & l1_qmax_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k5_qmax_1(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d12_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d12_quaterni,axiom,( k12_quaterni = k6_quaterni(k5_numbers,k5_numbers,k5_numbers,1) )).
fof(d12_quofield,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d12_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_radix_1(A,B,C) <=> ~ r1_xxreal_0(k1_newton(k1_radix_1(C),A),B) ) ) ) ) )).
fof(d12_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ( ~ r1_xxreal_0(E,A) => k4_radix_1(E,C,k2_xcmplx_0(B,2),D) = k5_numbers ) ) ) ) ) ) ) )).
fof(d12_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( 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))))) ) ) )).
fof(d12_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( C = k8_relat_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( r2_hidden(k4_tarski(D,E),A) & r2_hidden(E,B) ) ) ) ) )).
fof(d12_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ( v4_relat_2(A) <=> r4_relat_2(A,k1_relat_1(A)) ) ) )).
fof(d12_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ( r9_rewrite1(A,B) & ! [C] : ! [D] : ( ( r4_rewrite1(A,B,C) & r4_rewrite1(A,B,D) ) => C = D ) ) => ! [C] : ( C = k2_rewrite1(A,B) <=> r4_rewrite1(A,B,C) ) ) ) )).
fof(d12_rfunct_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( r2_rfunct_3(A,B) <=> ( r1_tarski(B,k1_relset_1(k1_numbers,A)) & ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(C,1) ) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( r2_hidden(D,B) & r2_hidden(E,B) & r2_hidden(k2_xcmplx_0(k3_xcmplx_0(C,D),k3_xcmplx_0(k6_xcmplx_0(1,C),E)),B) ) => r1_xxreal_0(k1_funct_1(A,k2_xcmplx_0(k3_xcmplx_0(C,D),k3_xcmplx_0(k6_xcmplx_0(1,C),E))),k2_xcmplx_0(k3_xcmplx_0(C,k1_funct_1(A,D)),k3_xcmplx_0(k6_xcmplx_0(1,C),k1_funct_1(A,E)))) ) ) ) ) ) ) ) ) )).
fof(d12_ringcat1,axiom,( ! [A] : ( v5_ringcat1(A) <=> ! [B] : ( r2_hidden(B,A) => ( v2_ringcat1(B) & v3_ringcat1(B) & l1_ringcat1(B) ) ) ) )).
fof(d12_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v9_rltopsp1(B,A) <=> ! [C] : ( m1_connsp_2(C,A,k4_struct_0(A)) => ? [D] : ( v1_xreal_0(D) & ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ( ~ r1_xxreal_0(E,D) => r1_tarski(B,k1_convex1(A,C,E)) ) ) ) ) ) ) ) )).
fof(d12_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k4_rlvect_1(A,B) <=> ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & C = k9_nat_1(u1_struct_0(A),D,k3_finseq_1(B)) & k9_nat_1(u1_struct_0(A),D,k5_numbers) = k4_struct_0(A) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( F = k1_funct_1(B,k1_nat_1(E,1)) => ( r1_xxreal_0(k3_finseq_1(B),E) | k9_nat_1(u1_struct_0(A),D,k1_nat_1(E,1)) = k1_algstr_0(A,k9_nat_1(u1_struct_0(A),D,E),F) ) ) ) ) ) ) ) ) ) )).
fof(d12_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => k9_rlvect_2(A,B) = k8_rlvect_2(A,k4_xcmplx_0(1),B) ) ) )).
fof(d12_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_4(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(d12_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & l2_robbins1(A) ) => ( v6_robbins1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(d12_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(d12_rvsum_1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => k18_rvsum_1(A) = k1_finsop_1(k1_numbers,A,k9_binop_2) ) )).
fof(d12_scm_comp,axiom,( ! [A] : ( m1_dtconstr(A,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k15_scm_comp(A,B) = k1_funct_1(k3_funct_2(k4_dtconstr(k1_scm_comp),k9_funct_2(k4_ordinal1,k8_afinsq_1(u1_compos_1(k1_ami_3))),k14_scm_comp,A),B) ) ) )).
fof(d12_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(k1_scmfsa_2)) => ( C = k12_scmfsa_2(A,B) <=> ? [D] : ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_ami_3)) & B = D & C = k8_ami_3(A,D) ) ) ) ) ) )).
fof(d12_scmpds_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ! [C] : ( v1_int_1(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(d12_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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(k1_nat_1(k5_card_1(C),1))),C) ) ) ) )).
fof(d12_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => ( ? [B] : ( m1_subset_1(B,k2_scm_inst) & ? [C] : ( m1_subset_1(C,k2_scm_inst) & ? [D] : ( v1_int_1(D) & ? [E] : ( v1_int_1(E) & ? [F] : ( 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] : ( v1_int_1(B) => ( B = k13_scmpds_i(A) <=> ? [C] : ( 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) ) ) ) ) ) )).
fof(d12_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : k7_scmyciel(A,B) = k3_xboole_0(A,k1_zfmisc_1(B)) ) )).
fof(d12_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => k14_seq_4(A) = k5_finseq_2(k2_numbers,A,k5_complex1) ) )).
fof(d12_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( r3_seqfunc(A,B,C) <=> ( r1_seqfunc(A,k1_numbers,B,C) & ? [D] : ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) & C = k1_relset_1(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v7_ordinal1(F) => ? [G] : ( v7_ordinal1(G) & ? [H] : ( m1_subset_1(H,A) & r1_xxreal_0(F,G) & r2_hidden(H,C) & r1_xxreal_0(E,k9_complex1(k6_xcmplx_0(k1_funct_1(k1_seqfunc(A,k1_numbers,B,G),H),k1_funct_1(D,H)))) ) ) ) ) ) ) ) ) ) ) )).
fof(d12_setfam_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v3_setfam_1(B,A) <=> ~ r2_hidden(A,B) ) ) )).
fof(d12_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_sheffer1(A) ) => ( v9_sheffer1(A) <=> ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_sheffer1(A,B,B) = k3_robbins1(A,B) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,B,C) = k1_lattices(A,k3_robbins1(A,B),k3_robbins1(A,C)) ) ) ) ) ) )).
fof(d12_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( v1_xxreal_0(B) => ( ( v4_matroid0(A) => ( v3_pencil_1(A) | ( B = k6_simplex0(A) <=> ( ! [C] : ( ( 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] : ( 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 ) ) ) ) ) )).
fof(d12_stacks_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_stacks_1(A) ) => ( v6_stacks_1(A) <=> ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ r1_stacks_1(A,k7_stacks_1(A,B,C)) ) ) ) ) )).
fof(d12_struct_0,axiom,( ! [A] : ( l2_struct_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v9_struct_0(B,A) <=> B = k4_struct_0(A) ) ) ) )).
fof(d12_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_substut1(A)) ) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => k13_substut1(A,B,C) = o_3_0_substut1(A,B,C) ) ) ) )).
fof(d12_tdlat_1,axiom,( ! [A] : ( ( 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)) ) )).
fof(d12_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tex_4(B,A) <=> ! [C] : ( 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))) ) ) ) ) ) )).
fof(d12_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d12_topalg_6,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m2_subset_1(B,k4_partfun1(k1_numbers,k2_struct_0(A)),k1_topalg_6(A)) => ! [C] : ( 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 ) ) ) ) ) )).
fof(d12_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( v1_card_1(B) => ( B = k4_topgen_1(A) <=> ( ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v1_tops_1(C,A) & B = k1_card_1(C) ) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tops_1(C,A) => r1_ordinal1(B,k1_card_1(C)) ) ) ) ) ) ) )).
fof(d12_topreal1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( B = k6_topreal1(A) <=> ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(d12_toprealb,axiom,( ! [A] : ( 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,k2_xcmplx_0(A,1))) ) )).
fof(d12_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(d12_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ! [B] : ( v7_ordinal1(B) => ( B = k6_trees_1(A) <=> ( ? [C] : ( m2_finseq_1(C,k4_ordinal1) & r2_hidden(C,A) & k3_finseq_1(C) = B ) & ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( r2_hidden(C,A) => r1_xxreal_0(k3_finseq_1(C),B) ) ) ) ) ) ) )).
fof(d12_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => k8_trees_2(A,B) = k5_card_1(k1_trees_2(A,B)) ) ) )).
fof(d12_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(d12_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) ) => ! [B] : k12_trees_9(A,B) = a_2_1_trees_9(A,B) ) )).
fof(d12_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( D = u1_struct_0(B) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d12_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( m2_funct_2(B,k4_numbers,u1_turing_1(A),k9_funct_2(k4_numbers,u1_turing_1(A))) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ( r1_turing_1(A,B,C,D) <=> ( k1_funct_1(B,C) = k5_numbers & k1_funct_1(B,D) = k5_numbers & ! [E] : ( v1_int_1(E) => ~ ( ~ r1_xxreal_0(E,C) & ~ r1_xxreal_0(D,E) & k1_funct_1(B,E) != 1 ) ) ) ) ) ) ) ) )).
fof(d12_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( 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))) ) ) ) ) )).
fof(d12_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ~ ( k6_unialg_2(A) = k1_xboole_0 & B = k1_xboole_0 ) => ! [C] : ( ( v1_unialg_1(C) & m1_unialg_2(C,A) ) => ( C = k7_unialg_2(A,B) <=> ( r1_tarski(B,u1_struct_0(C)) & ! [D] : ( m1_unialg_2(D,A) => ( r1_tarski(B,u1_struct_0(D)) => m1_unialg_2(C,D) ) ) ) ) ) ) ) ) )).
fof(d12_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( v7_ordinal1(D) => ( r2_hidden(D,k9_xtuple_0(A)) => k1_funct_1(C,k2_xcmplx_0(D,B)) = k1_funct_1(A,D) ) ) ) ) ) ) ) )).
fof(d12_valued_2,axiom,( ! [A] : ! [B] : ( B = k6_valued_2(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) ) ) )).
fof(d12_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k6_vectsp10(A,B,C))) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d12_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(d12_waybel11,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(d12_waybel23,axiom,( ! [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] : ( ( v6_waybel23(B,A) & m1_waybel23(B,A) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k1_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(k1_yellow_1(k7_waybel_0(k5_yellow_0(A,B))))))) ) => ( C = k5_waybel23(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k1_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) ) ) ) ) ) )).
fof(d12_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) ) ) )).
fof(d12_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( r2_waybel_0(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r1_orders_2(B,D,E) & r2_hidden(k2_waybel_0(A,B,E),C) ) ) ) ) ) )).
fof(d12_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d12_waybel_4,axiom,( ! [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] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))))) ) => ( C = k7_waybel_4(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A))),C,D) = k5_waybel_4(A,D,B) ) ) ) ) ) )).
fof(d12_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k11_xboolean(A,B) = k4_xboolean(A,k3_xboolean(B)) ) ) )).
fof(d12_xtuple_0,axiom,( ! [A] : ! [B] : ( B = k9_xtuple_0(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : r2_hidden(k4_tarski(C,D),A) ) ) )).
fof(d12_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ( v6_xxreal_2(A) <=> ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r1_tarski(k1_xxreal_1(B,C),A) ) ) ) ) ) )).
fof(d12_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( m1_subset_1(H,k1_altcat_1(A,F,G)) & F = C & G = D & k1_altcat_1(A,F,G) != k1_xboole_0 & ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ( k1_altcat_1(A,I,F) != k1_xboole_0 => ! [J] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d12_yellow21,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) ) ) )).
fof(d12_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => k4_yellow_0(A) = k2_yellow_0(A,k1_xboole_0) ) )).
fof(d12_yellow_6,axiom,( ! [A] : ! [B] : ( l1_struct_0(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( m3_yellow_6(C,A,B) <=> ! [D] : ( r2_hidden(D,k10_xtuple_0(C)) => ( ~ v2_struct_0(D) & v4_orders_2(D) & v7_waybel_0(D) & l1_waybel_0(D,B) ) ) ) ) ) )).
fof(d12_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(d12_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v4_zf_lang(A) <=> ? [B] : ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) & A = k6_zf_lang(B) ) ) ) )).
fof(d12_zf_model,axiom,( ! [A] : ( ~ 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] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r1_xboole_0(k1_enumset1(k2_zf_lang(k5_numbers),k2_zf_lang(1),k2_zf_lang(2)),k2_zf_model(B)) => r2_zf_model(A,k11_zf_model(B)) ) ) ) ) ) )).
fof(d12_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_zmodul01(C,A) => k5_zmodul01(A,B,C) = a_3_1_zmodul01(A,B,C) ) ) ) )).
fof(d12_zmodul02,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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) ) => k12_zmodul02(A,B) = g1_vectsp_1(k9_int_3(A),u1_struct_0(k10_zmodul02(B,k5_zmodul02(B,A))),u1_algstr_0(k10_zmodul02(B,k5_zmodul02(B,A))),u2_struct_0(k10_zmodul02(B,k5_zmodul02(B,A))),k11_zmodul02(A,B)) ) ) )).
fof(d13_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_abcmiz_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k4_abcmiz_0(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,C) <=> ! [E] : ( m1_subset_1(E,u1_abcmiz_0(A)) => ( r2_hidden(E,B) => r2_hidden(D,k3_abcmiz_0(A,E)) ) ) ) ) ) ) ) ) )).
fof(d13_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => k12_abcmiz_1(A) = k6_abcmiz_1 ) )).
fof(d13_abcmiz_a,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ( v4_abcmiz_a(B,A) <=> k1_msualg_1(A,B) = k1_xboole_0 ) ) ) )).
fof(d13_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ( v13_aff_2(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d13_afproj,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d13_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d13_algstr_0,axiom,( ! [A] : ( l2_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ( v9_algstr_0(B,A) & v3_algstr_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k4_algstr_0(A,B) <=> k1_algstr_0(A,C,B) = k4_struct_0(A) ) ) ) ) ) )).
fof(d13_algstr_4,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(k1_yellow_6(k2_xboole_0(A,k4_ordinal1)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k1_yellow_6(k2_xboole_0(A,k4_ordinal1)))))) ) => ( B = k10_algstr_4(A) <=> ( k9_nat_1(k9_setfam_1(k1_yellow_6(k2_xboole_0(A,k4_ordinal1))),B,k5_numbers) = k1_xboole_0 & k9_nat_1(k9_setfam_1(k1_yellow_6(k2_xboole_0(A,k4_ordinal1))),B,1) = A & ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(2,C) & ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ~ ( k3_finseq_1(D) = k6_xcmplx_0(C,1) & ! [E] : ( 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(k9_nat_1(k9_setfam_1(k1_yellow_6(k2_xboole_0(A,k4_ordinal1))),B,E),k1_funct_1(B,k6_xcmplx_0(C,E))) ) ) & k9_nat_1(k9_setfam_1(k1_yellow_6(k2_xboole_0(A,k4_ordinal1))),B,C) = k3_card_3(k2_card_3(D)) ) ) ) ) ) ) ) )).
fof(d13_altcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ( v10_altcat_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(d13_altcat_2,axiom,( ! [A] : ( l2_altcat_1(A) => ! [B] : ( m1_altcat_2(B,A) => ( v2_altcat_2(B,A) <=> u1_altcat_1(B) = k1_realset1(u1_altcat_1(A),u1_struct_0(B)) ) ) ) )).
fof(d13_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r6_analmetr(A,B,C,D) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & E != F & D = k4_analmetr(A,E,F) & r4_analmetr(A,B,C,E,F) ) ) ) ) ) ) ) )).
fof(d13_anproj_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d13_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_aofa_a01(D,A,B,C) & l4_aofa_a00(D,A,B,C) ) => ! [E] : ( ( ~ v2_struct_0(E) & v2_unialg_1(E) & v3_unialg_1(E) & v4_unialg_1(E) & v3_aofa_000(E) & v4_aofa_000(E) & v5_aofa_000(E) & v6_aofa_000(E) & ~ v10_aofa_000(E) & v11_aofa_000(E) & v12_aofa_000(E) & l3_aofa_a00(E,A,C,u4_aofa_a00(A,B,C,D)) ) => ( v5_aofa_a01(E,A,B,C,D) <=> r1_tarski(k10_xtuple_0(u3_aofa_a00(A,C,u4_aofa_a00(A,B,C,D),E)),k18_aofa_000(E)) ) ) ) ) ) ) )).
fof(d13_aofa_i00,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( D = k17_aofa_i00(A,B,C) <=> ( ? [E] : ( ! [F] : ( r2_hidden(F,E) <=> ? [G] : ( v1_relat_1(G) & v1_funct_1(G) & r2_hidden(G,k9_xtuple_0(B)) & r2_hidden(F,k10_xtuple_0(G)) ) ) & ! [F] : ( r2_hidden(F,k9_xtuple_0(D)) <=> ( r2_hidden(F,k1_funct_2(A,E)) & ? [G] : ( v1_relat_1(G) & v1_funct_1(G) & F = G & r2_hidden(k3_relat_1(C,G),k9_xtuple_0(B)) ) ) ) ) & ! [E] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(d13_armstrng,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ( v5_armstrng(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d13_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ( r3_arytm_3(A,B) <=> ? [C] : ( m1_subset_1(C,k5_arytm_3) & B = k9_arytm_3(A,C) ) ) ) ) )).
fof(d13_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : k10_asympt_0(A,B) = a_2_1_asympt_0(A,B) ) )).
fof(d13_bagorder,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) => ( ~ v1_xboole_0(B) => ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(d13_bcialg_2,axiom,( ! [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] : ( B = k3_bcialg_2(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( m2_bcialg_1(D,A) & m4_bcialg_2(C,A,D) ) ) ) ) )).
fof(d13_bcialg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_bcialg_4(A) ) => ( v6_bcialg_4(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_4(A,B,C) = k1_bcialg_4(A,C,B) ) ) ) ) )).
fof(d13_bcialg_6,axiom,( ! [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] : ( m1_bcialg_1(B,A) => ! [C] : ( ( v12_bcialg_1(C,A) & m2_bcialg_1(C,A) ) => ! [D] : ( m5_bcialg_2(D,A,C) => k9_bcialg_6(A,B,C,D) = k4_struct_0(A) ) ) ) ) )).
fof(d13_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => v1_hahnban1(k7_bilinear(A,B,C,D,E),A,C) ) ) ) ) ) ) )).
fof(d13_borsuk_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( A = k17_borsuk_1 <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(k7_metric_1)))) => ( B = k1_rcomp_1(k5_numbers,1) => A = k1_pre_topc(k3_pcomps_1(k7_metric_1),B) ) ) ) ) )).
fof(d13_borsuk_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(d13_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ( ( ! [C] : ( 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] : ( m1_subset_1(C,A) => k3_funct_2(A,k6_margrel1,B,C) = k8_margrel1 ) => k13_bvfunc_1(A,B) = k11_bvfunc_1(A) ) ) ) ) )).
fof(d13_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k6_c0sp1(A) = a_1_0_c0sp1(A) ) )).
fof(d13_card_3,axiom,( ! [A] : ( v3_card_3(A) <=> ? [B] : ( v1_relat_1(B) & v1_funct_1(B) & A = k4_card_3(B) ) ) )).
fof(d13_card_fil,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ( v4_card_fil(A) <=> ( v1_card_5(A) & v2_card_1(A) ) ) ) )).
fof(d13_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_cat_1(D,A,B,C) => ( v8_cat_1(D,A,B,C) <=> ( k2_cat_1(A,B,C) != k1_xboole_0 & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k2_cat_1(A,C,E) != k1_xboole_0 => ! [F] : ( m1_cat_1(F,A,C,E) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) ) ) )).
fof(d13_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ! [D] : ( ( 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)) ) ) ) ) )).
fof(d13_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k12_cat_4(A,B) = k7_cat_4(A,B,k1_cat_4(A)) ) ) )).
fof(d13_catalg_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u4_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d13_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => k11_cgames_1(A) = k6_subset_1(k10_cgames_1(A),k1_tarski(A)) ) )).
fof(d13_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m3_chord(B,A) => ( v7_chord(B,A) <=> ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ( r1_xxreal_0(C,k3_finseq_1(B)) => ! [D] : ( m2_glib_000(D,A,k4_chord(A,B,C),k21_glib_000(A,k4_chord(A,B,C))) => ! [E] : ( m1_subset_1(E,k6_glib_000(D)) => ( E = k1_funct_1(B,C) => v3_chord(E,D) ) ) ) ) ) ) ) ) )).
fof(d13_circcomb,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_card_1(D,A) & v1_finseq_1(D) ) => ! [E] : ( ( 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 ) ) ) ) ) ) ) )).
fof(d13_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v4_msualg_1(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(d13_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ( v3_clopban1(A) <=> ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_csspace3(B,A) => v9_clvect_1(B,A) ) ) ) ) )).
fof(d13_closure1,axiom,( ! [A] : ( l1_struct_0(A) => ! [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] : ( ( 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] : ( ( v9_closure1(D,A) & l1_closure1(D,A) ) => ( D = k6_closure1(A,B,C) <=> ? [E] : ( 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) ) ) ) ) ) ) )).
fof(d13_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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] : ( m1_closure2(D,A,B,k6_closure2(A,B)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(d13_clvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_clvect_1(A) ) => ( v8_clvect_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xcmplx_0(D) => ( k2_normsp_0(A,k1_clvect_1(A,B,D)) = k3_xcmplx_0(k9_complex1(D),k2_normsp_0(A,B)) & r1_xxreal_0(k2_normsp_0(A,k1_algstr_0(A,B,C)),k2_xcmplx_0(k2_normsp_0(A,B),k2_normsp_0(A,C))) ) ) ) ) ) ) )).
fof(d13_coh_sp,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,k5_coh_sp(A)) => ! [D] : ( 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] : ( m1_subset_1(C,k5_coh_sp(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d13_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v8_cohsp_1(A) <=> ( v3_cohsp_1(k9_xtuple_0(A)) & v5_cohsp_1(A) ) ) ) )).
fof(d13_combgras,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ( r1_ordinal1(k1_nat_1(A,1),k1_card_1(B)) => ( r1_xxreal_0(A,k5_numbers) | ! [C] : ( v1_finset_1(C) => ( k5_card_1(C) = k6_xcmplx_0(A,1) => k7_combgras(A,B,C) = k6_combgras(B,C) ) ) ) ) ) ) )).
fof(d13_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(A)) => k11_compos_1(A,B) = k10_compos_1(A,k9_compos_1(A,B)) ) ) )).
fof(d13_comput_1,axiom,( ! [A] : ( v5_comput_1(A) <=> ! [B] : ( m2_rfunct_3(B,k3_finseq_2(k4_ordinal1),k4_ordinal1,k2_comput_1(k4_ordinal1)) => ! [C] : ( m2_rfunct_3(C,k3_finseq_2(k4_ordinal1),k4_ordinal1,k2_comput_1(k4_ordinal1)) => ! [D] : ( m2_rfunct_3(D,k3_finseq_2(k4_ordinal1),k4_ordinal1,k2_comput_1(k4_ordinal1)) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_comput_1(B,C,D,E) & r2_hidden(C,A) & r2_hidden(D,A) ) => r2_hidden(B,A) ) ) ) ) ) ) )).
fof(d13_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( v3_conlat_1(B,A) & ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) & v8_conlat_1(B,A) & l2_conlat_1(B,A) ) => ( B = k6_conlat_1(A) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & ? [D] : ( 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) ) ) ) ) ) )).
fof(d13_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,k10_convex4(A)) => k11_convex4(A,B) = B ) ) )).
fof(d13_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d13_csspace,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_csspace(A) ) => ( v2_csspace(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xcmplx_0(E) => ( ( k12_csspace(A,B,B) = k5_numbers => B = k4_struct_0(A) ) & ( B = k4_struct_0(A) => k12_csspace(A,B,B) = k5_numbers ) & r1_xxreal_0(k5_numbers,k3_complex1(k12_csspace(A,B,B))) & k5_numbers = k4_complex1(k12_csspace(A,B,B)) & k12_csspace(A,B,C) = k8_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)) ) ) ) ) ) ) ) )).
fof(d13_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k8_decomp_1(A) = a_1_2_decomp_1(A) ) )).
fof(d13_dist_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => k11_dist_1(A) = k4_dist_1(A,k19_finseq_1(A)) ) )).
fof(d13_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => ! [C] : ( m4_dist_2(C,A,B) => k10_dist_2(A,B,C) = k6_dist_2(A,B,k7_dist_2(A,C)) ) ) ) )).
fof(d13_e_siec,axiom,( ! [A] : ( ( 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))) ) )).
fof(d13_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => k12_ens_1(A,B) = B ) ) )).
fof(d13_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( 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] : ( v1_xreal_0(F) => ( F = k12_euclid_3(A,B,C,D,E) <=> ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & k2_xcmplx_0(k2_xcmplx_0(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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d13_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => k8_euclid_7(A) = a_1_0_euclid_7(A) ) )).
fof(d13_exchsort,axiom,( ! [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) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_exchsort(B) ) => ! [C] : ! [D] : k7_exchsort(A,B,C,D) = k1_funct_4(k15_funct_3(k9_funct_7(k6_partfun1(k9_xtuple_0(B)),C,D),k9_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))))) ) ) )).
fof(d13_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & ~ v2_compos_1(C,B) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(B)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( r1_tarski(C,F) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d13_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(d13_ff_siec,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => k13_ff_siec(A) = k5_relat_1(k1_net_1(A),u4_struct_0(A)) ) )).
fof(d13_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v1_fin_topo(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k1_fin_topo(A,B)) => r2_hidden(B,k1_fin_topo(A,C)) ) ) ) ) ) )).
fof(d13_finseq_1,axiom,( ! [A] : ( ? [B] : ( v7_ordinal1(B) & r1_tarski(A,k2_finseq_1(B)) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ( B = k14_finseq_1(A) <=> ( k10_xtuple_0(B) = A & ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d13_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( 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)) ) ) )).
fof(d13_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => k14_fomodel2(A,B) = a_2_0_fomodel2(A,B) ) ) )).
fof(d13_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,A) => k3_funct_2(A,k8_eqrel_1(A,B),C,D) = k9_eqrel_1(A,B,D) ) ) ) ) ) )).
fof(d13_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) => ! [C] : ! [D] : ( v9_fomodel4(D,A,B,C) <=> ~ ( ~ v8_fomodel4(k1_tarski(k4_tarski(C,D)),A,B) & ! [E] : ~ ( r1_tarski(k1_xtuple_0(E),C) & k2_xtuple_0(E) = D & v8_fomodel4(k1_tarski(E),A,B) ) ) ) ) ) )).
fof(d13_freealg,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_freealg(B) ) => k8_freealg(A,B) = a_2_0_freealg(A,B) ) ) )).
fof(d13_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( v7_ordinal1(D) => k7_fsm_1(A,B,C,D) = k8_eqrel_1(u1_struct_0(C),k6_fsm_1(A,B,C,D)) ) ) ) ) )).
fof(d13_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k13_ftacell1(A,B,C,D,E) = k2_circcomb(k37_gfacirc1(A,B,C),k25_gfacirc1(k36_gfacirc1(A,B,C),E,D)) )).
fof(d13_funct_1,axiom,( ! [A] : ( v4_funct_1(A) <=> ! [B] : ( r2_hidden(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) )).
fof(d13_funct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( r2_hidden(D,A) => k10_funct_2(A,B,C,D) = k1_funct_1(C,D) ) ) ) ) )).
fof(d13_funct_7,axiom,( ! [A] : ! [B] : ! [C] : k12_funct_7(A,B,C) = k1_funct_4(k7_funcop_1(k4_ordinal1,C),k4_funct_4(k5_numbers,1,A,B)) )).
fof(d13_functor0,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(d13_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => k8_fvaluat1(A,B) = a_2_2_fvaluat1(A,B) ) ) ) )).
fof(d13_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ ( 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 ) ) )).
fof(d13_gate_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : 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) )).
fof(d13_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v4_vectsp_1(A) & v3_gcd_1(A) & l4_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d13_geomtrap,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ( v3_geomtrap(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( 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] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d13_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : k13_gfacirc1(A,B,C) = k2_circcomb(k10_gfacirc1(A,B,C),k7_gfacirc1(A,B,C)) )).
fof(d13_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ( 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 ) ) ) ) ) )).
fof(d13_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : 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)) ) ) )).
fof(d13_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k1_zfmisc_1(k6_glib_000(A)),k1_zfmisc_1(k7_glib_000(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k7_glib_000(A))) => ( C = k12_glib_004(A,B) <=> ! [D] : ( 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] : ( 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_funct_1(k5_glib_003(A),D),k1_funct_1(k5_glib_003(A),E)) ) ) ) ) ) ) ) )).
fof(d13_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k6_glib_000(A)) => k6_glib_005(A,B,C) = k40_glib_000(k5_glib_005(A,B,C)) ) ) ) )).
fof(d13_graph_2,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ! [B] : ( v7_ordinal1(B) => ( r4_graph_2(A,B) <=> ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( 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)) ) ) ) ) ) ) ) )).
fof(d13_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_graph_1(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( 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] : ( m2_finseq_2(C,u4_struct_0(A),k9_graph_3(A)) => ( C = k14_graph_3(A,B) <=> ? [D] : ( m2_finseq_2(D,u4_struct_0(A),k9_graph_3(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & E = o_2_1_graph_3(A,B) & D = o_3_5_graph_3(A,B,E) & C = k11_graph_3(A,B,D) ) ) ) ) ) ) ) )).
fof(d13_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( 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))) ) ) ) ) )).
fof(d13_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => ( r1_graphsp(A,B,C) <=> ( ~ ( k1_funct_1(C,k1_nat_1(A,B)) != k4_xcmplx_0(1) & r1_xxreal_0(k7_partfun1(k1_numbers,C,k1_nat_1(k2_nat_1(2,A),B)),k16_graphsp(C,A,B)) ) & r1_xxreal_0(k5_numbers,k7_partfun1(k1_numbers,C,k2_xcmplx_0(k2_xcmplx_0(k2_nat_1(2,A),k3_xcmplx_0(A,k7_partfun1(k1_numbers,C,k1_nat_1(k1_nat_1(k2_nat_1(A,A),k2_nat_1(3,A)),1)))),B))) & k1_funct_1(C,B) != k4_xcmplx_0(1) ) ) ) ) ) )).
fof(d13_grcat_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d13_group_1,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( l3_algstr_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(d13_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k13_group_2(A,B,C) = k4_group_2(A,C,k8_group_2(A,B)) ) ) ) )).
fof(d13_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ( v1_group_3(B,A) <=> ! [C] : ( 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)) ) ) ) ) )).
fof(d13_group_9,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( 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) ) ) ) ) ) )).
fof(d13_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => k3_funct_2(u1_struct_0(A),k1_numbers,B,k4_vectsp_1(k1_complfld,A,k1_hahnban1(D,k5_numbers),C)) = k3_xcmplx_0(D,k3_funct_2(u1_struct_0(A),k1_numbers,B,C)) ) ) ) ) ) )).
fof(d13_idea_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ( B = k13_idea_1(A) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(A)) => k1_recdef_1(B,C) = k15_funcop_1(k4_ordinal1,C,2,k1_recdef_1(A,3),k15_funcop_1(k4_ordinal1,C,3,k1_recdef_1(A,2),k1_recdef_1(A,C))) ) ) ) ) ) ) )).
fof(d13_incproj,axiom,( ! [A] : ( l1_incsp_1(A) => ( v9_incproj(A) <=> ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u1_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u1_incsp_1(A)) => ! [H] : ( m1_subset_1(H,u1_incsp_1(A)) => ! [I] : ( m1_subset_1(I,u1_incsp_1(A)) => ! [J] : ( m1_subset_1(J,u1_incsp_1(A)) => ! [K] : ( m1_subset_1(K,u1_incsp_1(A)) => ! [L] : ( m1_subset_1(L,u2_incsp_1(A)) => ! [M] : ( m1_subset_1(M,u2_incsp_1(A)) => ! [N] : ( m1_subset_1(N,u2_incsp_1(A)) => ! [O] : ( m1_subset_1(O,u2_incsp_1(A)) => ! [P] : ( m1_subset_1(P,u2_incsp_1(A)) => ! [Q] : ( m1_subset_1(Q,u2_incsp_1(A)) => ! [R] : ( m1_subset_1(R,u2_incsp_1(A)) => ! [S] : ( m1_subset_1(S,u2_incsp_1(A)) => ! [T] : ( 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] : ( m1_subset_1(U,u2_incsp_1(A)) => ~ r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),I,J,K),U) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d13_incsp_1,axiom,( ! [A] : ( l2_incsp_1(A) => ( v10_incsp_1(A) <=> ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u4_incsp_1(A)) => ! [F] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(d13_integr15,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k4_ordinal1) => ( 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) ) ) ) ) ) ) )).
fof(d13_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => k10_integra1(A,B) = k3_seq_4(k1_rvsum_1(k8_integra1(A,B))) ) ) )).
fof(d13_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) )).
fof(d13_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => k6_intpro_1(A) = k7_finseq_1(k12_finseq_1(k4_ordinal1,6),A) ) )).
fof(d13_lang1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(d13_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ( v5_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r1_orders_2(A,B,D) & r1_orders_2(A,C,D) & ! [E] : ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d13_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(d13_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v8_lattice6(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & C = k15_lattice3(A,D) ) ) ) ) ) )).
fof(d13_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lattices(A) ) => ( v13_lattices(A) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_lattices(A,B,C) = B & k2_lattices(A,C,B) = B ) ) ) ) ) )).
fof(d13_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)))) => ( ( r1_xxreal_0(k15_glib_000(A),k5_card_1(k1_relset_1(k6_glib_000(A),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),B)))) ) ) ) ) )).
fof(d13_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v6_limfunc1(A) => ! [B] : ( v1_xreal_0(B) => ( B = k5_limfunc1(A) <=> ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_limfunc1(C) & r1_tarski(k10_xtuple_0(C),k1_relset_1(k1_numbers,A)) ) => ( v2_comseq_2(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,C,A)) & k1_seq_2(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,C,A)) = B ) ) ) ) ) ) ) )).
fof(d13_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k8_lmod_7(A,B,C,D) = k3_vectsp_4(A,B,D,C) ) ) ) ) )).
fof(d13_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( r2_hidden(D,k10_lopban_1(A,B)) => k1_funct_1(C,D) = k2_seq_4(k14_lopban_1(A,B,k13_lopban_1(A,B,D))) ) ) ) ) ) )).
fof(d13_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => k16_lpspacc1(A,B,C) = g1_clvect_1(k15_lpspacc1(A,B,C),k10_subset_1(k4_struct_0(k14_lpspacc1(A,B,C)),k15_lpspacc1(A,B,C)),k1_ideal_1(k14_lpspacc1(A,B,C),k15_lpspacc1(A,B,C)),k6_lpspacc1(k14_lpspacc1(A,B,C),k15_lpspacc1(A,B,C))) ) ) ) )).
fof(d13_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(d13_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v2_xxreal_0(D) & v1_xreal_0(D) ) => 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)) ) ) ) ) )).
fof(d13_ltlaxio1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_hilbert1)) => ( r2_ltlaxio1(A,B) <=> ! [C] : ( m1_subset_1(C,k1_hilbert1) => ( r2_hidden(C,B) => r1_ltlaxio1(A,C) ) ) ) ) ) )).
fof(d13_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(B)) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(B)) ) => ( D = k16_matrix_0(A,B,C) <=> ( k3_finseq_1(D) = k3_finseq_1(C) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(C)) => k1_funct_1(D,E) = k2_finseq_3(A,k7_matrix_0(B,C,E)) ) ) ) ) ) ) ) ) )).
fof(d13_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(d13_mcart_1,axiom,( ! [A] : k16_mcart_1(A) = k2_xtuple_0(k2_xtuple_0(A)) )).
fof(d13_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => k16_member_1(A,B) = k8_member_1(k1_tarski(B),A) ) ) )).
fof(d13_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ( A = B <=> ! [C] : ( v1_xcmplx_0(C) => ( r2_hidden(C,A) <=> r2_hidden(C,B) ) ) ) ) ) )).
fof(d13_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => k8_memstr_0(A,B,C) = k1_funct_4(C,k7_memstr_0(A,B,k5_numbers)) ) ) ) )).
fof(d13_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( r1_mesfun7c(A,B,C) <=> ? [D] : ( v1_prob_2(D) & m2_finseq_1(D,B) & k1_relset_1(A,C) = k3_tarski(k2_relset_1(B,D)) & ! [E] : ( v7_ordinal1(E) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d13_mesfunc1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_valued_0(A) ) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( C = k13_mesfunc1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,k9_xtuple_0(A)) & ~ r1_xxreal_0(k1_funct_1(A,D),B) ) ) ) ) ) )).
fof(d13_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k6_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( D = k3_mesfunc5(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k9_nat_1(k6_numbers,D,E) = k12_supinf_2(k1_seqfunc(A,k6_numbers,B,E),C) ) ) ) ) ) ) )).
fof(d13_metric_1,axiom,( k7_metric_1 = g1_metric_1(k1_numbers,k6_metric_1) )).
fof(d13_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k2_metric_2(A)) => ! [D] : ( m1_subset_1(D,k2_metric_2(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r2_hidden(E,C) & r2_hidden(F,D) ) => k2_binop_1(k2_metric_2(A),k2_metric_2(A),k1_numbers,B,C,D) = k3_metric_1(A,E,F) ) ) ) ) ) ) ) ) )).
fof(d13_metric_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ! [I] : ( m1_subset_1(I,u1_struct_0(C)) => ! [J] : ( m1_subset_1(J,u1_struct_0(C)) => ! [K] : ( m1_subset_1(K,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C))) => ! [L] : ( 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) ) => k2_binop_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,K,L) = k3_square_1(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k3_metric_1(A,E,F)),k1_square_1(k3_metric_1(B,G,H))),k1_square_1(k3_metric_1(C,I,J)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d13_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,k10_midsp_1(A)) => ! [C] : ( m1_subset_1(C,k10_midsp_1(A)) => ! [D] : ( m1_subset_1(D,k10_midsp_1(A)) => ( D = k11_midsp_1(A,B,C) <=> ! [E] : ( m1_midsp_1(E,A) => ! [F] : ( m1_midsp_1(F,A) => ( ( B = E & C = F ) => D = k7_midsp_1(A,E,F) ) ) ) ) ) ) ) ) )).
fof(d13_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( l1_midsp_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(d13_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [D] : ( v7_ordinal1(D) => k13_mmlquery(A,B,C,D) = a_4_8_mmlquery(A,B,C,D) ) ) ) )).
fof(d13_mod_2,axiom,( ! [A] : ( m1_subset_1(A,k1_enumset1(k5_numbers,1,2)) => ! [B] : ( m1_subset_1(B,k1_enumset1(k5_numbers,1,2)) => ( ( A = k5_numbers => k11_mod_2(A,B) = B ) & ( B = k5_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) = k5_numbers ) & ( ( A = 2 & B = 1 ) => k11_mod_2(A,B) = k5_numbers ) & ( ( A = 2 & B = 2 ) => k11_mod_2(A,B) = 1 ) ) ) ) )).
fof(d13_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) ) )).
fof(d13_modcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_modcat_1(B,A) => ! [C] : ( ( 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] : ( m4_modcat_1(D,A,k4_modcat_1(A,B)) => ! [E] : ( 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] : ( m4_modcat_1(D,A,k4_modcat_1(A,B)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d13_modelc_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ( v1_modelc_1(A) <=> m1_subset_1(A,k12_modelc_1) ) ) )).
fof(d13_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v4_modelc_2(A) <=> ? [B] : ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) & ? [C] : ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) & A = k4_modelc_2(B,C) ) ) ) ) )).
fof(d13_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => k7_modelc_3(A) = k1_xboole_0 ) )).
fof(d13_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v10_monoid_0(A) <=> v3_binop_1(u2_algstr_0(A),u1_struct_0(A)) ) ) )).
fof(d13_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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] : ( 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)) ) ) ) ) ) )).
fof(d13_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ( v5_msafree2(A) <=> ! [B] : ( ( v4_msualg_1(B,A) & v3_msafree2(B,A) & l3_msualg_1(B,A) ) => v4_msafree2(B,A) ) ) ) )).
fof(d13_msafree4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_msualg_4(C,A,B,B) => ( v9_msafree4(C,A,B) <=> ! [D] : ( r2_hidden(D,A) => v3_rewrite1(k7_msafree4(A,B,B,C,D)) ) ) ) ) )).
fof(d13_msualg_1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v13_struct_0(A,1) & v5_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => k11_msualg_1(A,B) = u4_msualg_1(A,B) ) ) )).
fof(d13_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m3_pboole(C,u1_struct_0(A),u3_msualg_1(A,B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( E = k8_msualg_2(A,B,C,D) <=> ! [F] : ( r2_hidden(F,E) <=> ? [G] : ( 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) ) ) ) ) ) ) ) )).
fof(d13_msualg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d13_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msualg_4(C,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,B)) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(d13_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ( r3_nattra_1(A,B,C,D) => ! [E] : ( m2_nattra_1(E,A,B,C,D) => ( m3_nattra_1(E,A,B,C,D) <=> v1_nattra_1(E,A,B,C,D) ) ) ) ) ) ) ) )).
fof(d13_ncfcont1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( r9_ncfcont1(A,B,C,D) <=> ( r1_tarski(D,k1_relset_1(u1_struct_0(A),C)) & ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d13_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : ! [C] : ( C = k10_net_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r1_tarski(D,k2_net_1(A)) & ? [E] : ( m1_subset_1(E,k2_net_1(A)) & r2_hidden(E,B) & D = k5_net_1(A,E) ) ) ) ) ) )).
fof(d13_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ( v12_o_ring_1(B,A) <=> ( k3_finseq_1(B) != k5_numbers & ! [C] : ( v7_ordinal1(C) => ~ ( C != k5_numbers & r1_xxreal_0(C,k3_finseq_1(B)) & ~ v9_o_ring_1(k7_partfun1(u1_struct_0(A),B,C),A) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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 != k5_numbers & ~ r1_xxreal_0(C,D) & E != k5_numbers & ~ r1_xxreal_0(C,E) ) ) ) ) ) ) ) ) ) )).
fof(d13_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => k13_oppcat_1(A) = k10_oppcat_1(A,A,k10_cat_1(A)) ) )).
fof(d13_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r7_orders_1(A,B) <=> ( r2_hidden(B,k1_relat_1(A)) & ! [C] : ~ ( r2_hidden(C,k1_relat_1(A)) & C != B & r2_hidden(k4_tarski(C,B),A) ) ) ) ) )).
fof(d13_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m2_orders_1(B,k1_orders_1(u1_struct_0(A)),k6_partfun1(k1_orders_1(u1_struct_0(A)))) => ! [C] : ( C = k4_orders_2(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> m2_orders_2(D,A,B) ) ) ) ) )).
fof(d13_ordinal1,axiom,( k5_ordinal1 = k1_xboole_0 )).
fof(d13_ordinal2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ( v3_ordinal2(A) <=> ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( ( r2_hidden(B,k9_xtuple_0(A)) & v4_ordinal1(B) & C = k1_funct_1(A,B) ) => ( B = k5_ordinal1 | r1_ordinal2(C,k5_relat_1(A,B)) ) ) ) ) ) ) )).
fof(d13_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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] : ( m1_trees_4(C,k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) => ! [D] : ( 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] : ( v7_ordinal1(E) => ~ ( r2_hidden(E,k4_finseq_1(C)) & ! [F] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d13_osalg_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => v9_osalg_1(B,A) ) ) ) )).
fof(d13_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v12_osalg_1(C,A) & m1_msualg_2(C,A,B) ) => ! [D] : ( ( v12_osalg_1(D,A) & m1_msualg_2(D,A,B) ) => ! [E] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d13_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( ( v4_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v2_msualg_4(D,A,C) & v3_msualg_4(D,A,C) & m1_osalg_4(D,A,C) ) => ! [E] : ( m1_subset_1(E,k3_msualg_1(A,B,C)) => ! [F] : ( 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] : ( v7_ordinal1(G) => ~ ( r2_hidden(G,k4_finseq_1(k1_msualg_1(A,B))) & ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d13_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ( v2_relat_1(B) <=> ! [C] : ~ ( r2_hidden(C,A) & v1_xboole_0(k1_funct_1(B,C)) ) ) ) )).
fof(d13_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ( r4_pdiff_1(A,B,C,D,E) <=> ? [F] : ( 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] : ( m1_subset_1(G,u1_struct_0(k4_real_ns1(A))) & D = F & E = G & r2_pdiff_1(B,A,C,F,G) ) ) ) ) ) ) ) ) )).
fof(d13_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r4_pdiff_5(A,B) => ! [C] : ( v1_xreal_0(C) => ( C = k4_pdiff_5(A,B) <=> ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & B = k11_finseq_1(D,E,F) & ? [G] : ( 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] : ( v1_funct_1(H) & v3_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [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_funct_1(H,1) & ! [J] : ( v1_xreal_0(J) => ( r2_hidden(J,G) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,1,k1_pdiff_3(2,3,A),B),J),k1_funct_1(k1_pdiff_2(3,1,k1_pdiff_3(2,3,A),B),D)) = k2_xcmplx_0(k1_funct_1(H,k6_xcmplx_0(J,D)),k1_funct_1(I,k6_xcmplx_0(J,D))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d13_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k12_petri(A,B) = B ) ) )).
fof(d13_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B))) => ! [D] : ( 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) ) ) ) )).
fof(d13_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,k8_polyform(A,k6_xcmplx_0(B,1))) => ! [D] : ( m1_subset_1(D,k8_polyform(A,B)) => ( ( r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(B,k7_polyform(A)) ) => k16_polyform(A,B,C,D) = k1_binop_1(k9_polyform(A,B),C,D) ) ) ) ) ) )).
fof(d13_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k8_struct_0(k12_polynom1(A,C)),u1_struct_0(k12_polynom1(A,C))))) => ( E = k3_polyred(A,B,C,D) <=> ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(G,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) ) ) ) ) ) ) ) ) ) )).
fof(d13_pralg_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v2_pralg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( C = k12_pralg_1(A,B) <=> ! [D] : ~ ( r2_hidden(D,A) & ! [E] : ( l1_struct_0(E) => ~ ( E = k1_funct_1(B,D) & k1_funct_1(C,D) = u1_struct_0(E) ) ) ) ) ) ) )).
fof(d13_pralg_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( 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] : ( m1_subset_1(E,u4_struct_0(B)) => k1_funct_1(D,E) = k14_funcop_1(k1_msualg_1(B,E),k1_xboole_0,k9_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) ) ) ) ) ) )).
fof(d13_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(d13_prvect_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( ( ~ 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)) ) ) ) ) )).
fof(d13_pscomp_1,axiom,( ! [A] : ( 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)) ) )).
fof(d13_pua2mss1,axiom,( ! [A] : ( l1_msualg_1(A) => ! [B] : ( l1_msualg_1(B) => ( r4_pua2mss1(A,B) <=> ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & ? [D] : ( 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) ) ) ) ) ) )).
fof(d13_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => k11_qc_lang1(A,B) = B ) ) )).
fof(d13_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v4_qc_lang2(B,A) <=> ? [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) & ? [D] : ( m1_subset_1(D,k9_qc_lang1(A)) & B = k5_qc_lang2(A,C,D) ) ) ) ) ) )).
fof(d13_qmax_1,axiom,( ! [A] : ( ( v2_qmax_1(A) & l1_qmax_1(A) ) => ! [B] : ( 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] : ( m1_subset_1(C,k1_zfmisc_1(k5_qmax_1(A))) => ! [D] : ( 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] : ( m1_subset_1(E,k5_qmax_1(A)) => ! [F] : ( m1_subset_1(F,k5_qmax_1(A)) => ( ( r2_hidden(E,C) & r2_hidden(F,D) ) => r3_qmax_1(A,E,F) ) ) ) ) ) ) ) ) ) ) )).
fof(d13_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( 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))) ) ) ) ) )).
fof(d13_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( ( r2_hidden(A,k2_numbers) => ( B = k13_quaterni(A) <=> ? [C] : ( v1_xcmplx_0(C) & A = C & B = k3_complex1(C) ) ) ) & ( ~ r2_hidden(A,k2_numbers) => ( B = k13_quaterni(A) <=> ? [C] : ( 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_funct_1(C,k5_numbers) ) ) ) ) ) )).
fof(d13_quofield,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d13_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v3_card_1(D,C) & m2_finseq_1(D,k3_radix_1(A)) ) => ! [E] : ( ( 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)))) ) ) ) ) ) ) )).
fof(d13_random_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v2_finset_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v7_random_3(B,A,k7_random_3(A)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( C = k9_random_3(A,B) <=> ( k1_funct_1(C,k5_numbers) = k8_random_3(A,B,k5_numbers) & ! [D] : ( v7_ordinal1(D) => k1_funct_1(C,k1_nat_1(D,1)) = k2_random_2(k1_funct_1(k5_random_3(A),D),k1_funct_1(A,k1_nat_1(D,1)),k6_random_3(k1_funct_1(k5_random_3(A),D),k1_random_1(k1_funct_1(k5_random_3(A),D)),k1_funct_1(C,D)),k8_random_3(A,B,k1_nat_1(D,1))) ) ) ) ) ) ) )).
fof(d13_ratfunc1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & l5_algstr_0(A) ) => k7_ratfunc1(A) = k3_ratfunc1(A,k9_polynom3(A),k10_polynom3(A)) ) )).
fof(d13_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v3_relat_1(A) <=> r1_tarski(k10_xtuple_0(A),k1_tarski(k1_xboole_0)) ) ) )).
fof(d13_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ( v5_relat_2(A) <=> r5_relat_2(A,k1_relat_1(A)) ) ) )).
fof(d13_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_finset_1(k1_relset_1(A,k2_partfun1(A,k1_numbers,B,C))) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(d13_ringcat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ v1_xboole_0(C) & v5_ringcat1(C) ) => ( m4_ringcat1(C,A,B) <=> ! [D] : ( m3_ringcat1(D,C) => m1_ringcat1(D,A,B) ) ) ) ) ) )).
fof(d13_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rltopsp1(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d13_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_rlvect_2(C,A) => k10_rlvect_2(A,B,C) = k7_rlvect_2(A,B,k9_rlvect_2(A,C)) ) ) ) )).
fof(d13_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v1_rmod_4(C,A,B) <=> ! [D] : ( 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 ) ) ) ) ) ) )).
fof(d13_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_robbins1(A) ) => ( v9_robbins1(A) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & k1_lattices(A,B,B) = B ) ) ) )).
fof(d13_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d13_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( v1_xcmplx_0(B) => ( B = k19_rvsum_1(A) <=> ? [C] : ( m2_finseq_1(C,k2_numbers) & C = A & B = k1_finsop_1(k2_numbers,C,k5_binop_2) ) ) ) ) )).
fof(d13_scm_comp,axiom,( ! [A] : ( m2_subset_1(A,u1_struct_0(k1_scm_comp),k6_dtconstr(k1_scm_comp)) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( B = k16_scm_comp(A) <=> k10_ami_3(B) = A ) ) ) )).
fof(d13_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(k1_scmfsa_2)) => ( C = k13_scmfsa_2(A,B) <=> ? [D] : ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_ami_3)) & B = D & C = k9_ami_3(A,D) ) ) ) ) ) )).
fof(d13_scmpds_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ! [C] : ( v1_int_1(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(d13_scmpds_i,axiom,( k14_scmpds_i = k5_numbers )).
fof(d13_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ( v5_scmyciel(A) <=> A = k5_scmyciel(k3_tarski(A)) ) ) )).
fof(d13_seq_4,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => k20_seq_4(A) = k3_square_1(k18_rvsum_1(k12_rvsum_1(k11_seq_4(A)))) ) )).
fof(d13_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( r2_seqfunc(A,B,C) => ! [D] : ( ( 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] : ( m1_subset_1(E,A) => ( r2_hidden(E,k1_relset_1(A,D)) => k1_funct_1(D,E) = k1_seq_2(k10_seqfunc(A,B,E)) ) ) ) ) ) ) ) ) )).
fof(d13_sgraph1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_sgraph1(B,k4_ordinal1) => ( B = k7_sgraph1(A) <=> ? [C] : ( 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) ) ) ) ) )).
fof(d13_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_sheffer1(A) ) => ( v10_sheffer1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,B)) = B ) ) ) )).
fof(d13_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(d13_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k2_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( D = k12_sin_cos(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(E,C) => k9_nat_1(k2_numbers,D,E) = k3_xcmplx_0(k9_nat_1(k2_numbers,k3_sin_cos(A),E),k6_xcmplx_0(k9_nat_1(k2_numbers,k10_comseq_3(k3_sin_cos(B)),C),k9_nat_1(k2_numbers,k10_comseq_3(k3_sin_cos(B)),k7_nat_d(C,E)))) ) & ( ~ r1_xxreal_0(E,C) => k9_nat_1(k2_numbers,D,E) = k5_numbers ) ) ) ) ) ) ) ) )).
fof(d13_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ( C = k9_stacks_1(A,B) <=> ? [D] : ( 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] : ( 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] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(d13_struct_0,axiom,( ! [A] : ( l5_struct_0(A) => ( v11_struct_0(A) <=> v1_xboole_0(u4_struct_0(A)) ) ) )).
fof(d13_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_substut1(A)) ) => ( ? [E] : ( 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))) ) ) ) ) ) ) ) )).
fof(d13_topalg_6,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m2_finseq_1(B,k1_topalg_6(A)) => ! [C] : ( 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] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(d13_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v7_topgen_1(A) <=> r1_ordinal1(k4_topgen_1(A),k4_ordinal1) ) ) )).
fof(d13_topreal1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( B = k7_topreal1(A) <=> ! [C] : ( 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) ) ) ) ) ) ) )).
fof(d13_toprealb,axiom,( ! [A] : ( ( 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(k5_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(k5_numbers,1))))))) ) => ( A = k14_toprealb <=> ! [B] : ( m1_subset_1(B,u1_struct_0(k11_toprealb(k9_toprealb))) => ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & B = k19_euclid(C,D) & ( r1_xxreal_0(k5_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(k5_numbers,1)))),A,B) = k7_xcmplx_0(k4_sin_cos6(C),k3_xcmplx_0(2,k28_sin_cos)) ) & ( r1_xxreal_0(D,k5_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(k5_numbers,1)))),A,B) = k6_xcmplx_0(1,k7_xcmplx_0(k4_sin_cos6(C),k3_xcmplx_0(2,k28_sin_cos))) ) ) ) ) ) ) )).
fof(d13_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ! [B] : ( v7_ordinal1(B) => ( B = k7_trees_1(A) <=> ? [C] : ( m4_trees_1(C,A) & B = k5_card_1(C) & ! [D] : ( m4_trees_1(D,A) => r1_xxreal_0(k5_card_1(D),k5_card_1(C)) ) ) ) ) ) )).
fof(d13_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(d13_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) ) => ( ! [B] : ( m1_subset_1(B,A) => v1_finset_1(B) ) => ! [B] : ! [C] : ( ( 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] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_trees_2(D) ) => ( r2_hidden(D,k12_trees_9(A,B)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d13_turing_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( l1_turing_1(B) => ! [C] : ( 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] : ( m1_subset_1(D,k4_ordinal1) => ( r1_xxreal_0(1,D) => ( r1_xxreal_0(k3_finseq_1(A),D) | r1_turing_1(B,C,k2_xcmplx_0(k1_gr_cy_1(k4_turing_1(D,A)),k3_xcmplx_0(2,k6_xcmplx_0(D,1))),k2_xcmplx_0(k1_gr_cy_1(k4_turing_1(k1_nat_1(D,1),A)),k2_nat_1(2,D))) ) ) ) ) ) ) ) )).
fof(d13_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k1_funct_1(A,k10_finseq_1(B,C)) = k2_binarith(B,C) ) ) ) ) )).
fof(d13_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_unialg_2(B,A) => ! [C] : ( m1_unialg_2(C,A) => ! [D] : ( ( v1_unialg_1(D) & m1_unialg_2(D,A) ) => ( D = k8_unialg_2(A,B,C) <=> ! [E] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(d13_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ( m1_valued_0(B,A) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_ordinal1) & v5_valued_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) & B = k3_relat_1(C,A) ) ) ) ) )).
fof(d13_valued_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_membered(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ( v5_valued_0(B) <=> ! [C] : ( v7_ordinal1(C) => ~ r1_xxreal_0(k9_nat_1(A,B,k1_nat_1(C,1)),k9_nat_1(A,B,C)) ) ) ) ) )).
fof(d13_valued_2,axiom,( ! [A] : ! [B] : ( B = k7_valued_2(A) <=> ! [C] : ( 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))) ) ) ) )).
fof(d13_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( 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) ) ) ) )).
fof(d13_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(d13_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) ) ) )).
fof(d13_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(d13_waybel_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_orders_2(B) & l1_orders_2(B) ) => ( B = k8_waybel_4(A) <=> ! [C] : ( ~ ( r2_hidden(C,u1_struct_0(B)) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))))) ) => ~ ( C = D & v5_orders_3(D,A,k1_yellow_1(k7_waybel_0(A))) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => r1_tarski(k3_funct_2(u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A))),D,E),k5_waybel_0(A,E)) ) ) ) ) & ( ? [D] : ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))))) & C = D & v5_orders_3(D,A,k1_yellow_1(k7_waybel_0(A))) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => r1_tarski(k3_funct_2(u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A))),D,E),k5_waybel_0(A,E)) ) ) => r2_hidden(C,u1_struct_0(B)) ) & ! [D] : ! [E] : ( r2_hidden(k4_tarski(D,E),u1_orders_2(B)) <=> ? [F] : ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))))) & ? [G] : ( v1_funct_1(G) & v1_funct_2(G,u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k1_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),k1_yellow_1(k7_waybel_0(A)),F,G) ) ) ) ) ) ) ) )).
fof(d13_xtuple_0,axiom,( ! [A] : ! [B] : ( B = k10_xtuple_0(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : r2_hidden(k4_tarski(D,C),A) ) ) )).
fof(d13_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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)) ) ) ) ) )).
fof(d13_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m3_yellow_6(C,u1_struct_0(B),A) => ! [D] : ( ( ~ 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,k4_yellow_1(u1_struct_0(B),C)) & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ( ( r2_hidden(E,u1_struct_0(B)) & r2_hidden(F,u1_struct_0(k4_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)) ) ) ) ) ) ) ) ) ) )).
fof(d13_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v5_zf_lang(A) <=> ? [B] : ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) & ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & A = k7_zf_lang(B,C) ) ) ) ) )).
fof(d13_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( m2_zmodul01(C,A,B) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & C = k5_zmodul01(A,D,B) ) ) ) ) ) )).
fof(d13_zmodul02,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => k13_zmodul02(A,B,C) = k5_zmodul01(B,C,k5_zmodul02(B,A)) ) ) ) )).
fof(d14_abcmiz_0,axiom,( ! [A] : ( l2_abcmiz_0(A) => ( v10_abcmiz_0(A) <=> ! [B] : ( 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)))) ) ) ) )).
fof(d14_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => k13_abcmiz_1(A) = k7_abcmiz_1 ) )).
fof(d14_abcmiz_a,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ( v5_abcmiz_a(B,A) <=> k3_finseq_1(k1_msualg_1(A,B)) = 1 ) ) ) )).
fof(d14_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v14_aff_2(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d14_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : 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)) )).
fof(d14_afproj,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d14_algstr_0,axiom,( ! [A] : ( l2_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_algstr_0(A,B,C) = k1_algstr_0(A,B,k4_algstr_0(A,C)) ) ) ) )).
fof(d14_algstr_4,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => k11_algstr_4(A,B) = k9_nat_1(k9_setfam_1(k1_yellow_6(k2_xboole_0(A,k4_ordinal1))),k10_algstr_4(A),B) ) )).
fof(d14_altcat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k1_altcat_1(B,C,D) = k1_funct_2(C,D) ) ) ) ) ) ) )).
fof(d14_altcat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_altcat_2(B,A) => ( ( ~ v2_struct_0(B) => ( v3_altcat_2(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) )).
fof(d14_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( 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)) ) ) ) ) )).
fof(d14_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r7_analmetr(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & D != E & B = k4_analmetr(A,D,E) & r6_analmetr(A,D,E,C) ) ) ) ) ) ) )).
fof(d14_anproj_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & r1_collsp(A,B,C,F) & r1_collsp(A,D,E,F) ) ) ) ) ) ) ) )).
fof(d14_aofa_i00,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(C,k4_numbers))) => ! [E] : ( 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] : ( 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] : ( 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] : ( 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) = k14_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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d14_armstrng,axiom,( ! [A] : ! [B] : ( 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) ) ) ) )).
fof(d14_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : k11_asympt_0(A,B) = a_2_2_asympt_0(A,B) ) )).
fof(d14_bagorder,axiom,( ! [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) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,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(k4_ordinal1,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(k4_ordinal1,B) = k4_ordinal1 & k9_nat_1(k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A)))),B,k5_numbers) = a_1_0_bagorder(A) & ! [C] : ( v7_ordinal1(C) => k9_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) ) ) ) ) ) )).
fof(d14_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v10_bcialg_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_bcialg_1(A,C,B) = k4_struct_0(A) => C = B ) ) ) ) ) )).
fof(d14_bcialg_2,axiom,( ! [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) ) => k4_bcialg_2(A) = a_1_0_bcialg_2(A) ) )).
fof(d14_bcialg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_bcialg_4(A) ) => ( v7_bcialg_4(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(d14_bcialg_6,axiom,( ! [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] : ( m1_bcialg_1(B,A) => ! [C] : ( ( v12_bcialg_1(C,A) & m2_bcialg_1(C,A) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(d14_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(C)) => v1_hahnban1(k8_bilinear(A,B,C,D,E),A,B) ) ) ) ) ) ) )).
fof(d14_borsuk_1,axiom,( k18_borsuk_1 = k5_numbers )).
fof(d14_borsuk_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k15_euclid(A))) & ? [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(A))) & r2_borsuk_7(A,C,F,G,D,E) ) ) ) ) ) ) ) ) )).
fof(d14_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ( ( ! [C] : ( 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] : ( m1_subset_1(C,A) => k3_funct_2(A,k6_margrel1,B,C) = k7_margrel1 ) => k14_bvfunc_1(A,B) = k12_bvfunc_1(A) ) ) ) ) )).
fof(d14_c0sp1,axiom,( ! [A] : ( ~ 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))) ) )).
fof(d14_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_valuat_1(D,A,C) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(d14_card_3,axiom,( ! [A] : ( v4_card_3(A) <=> r1_ordinal1(k1_card_1(A),k4_ordinal1) ) )).
fof(d14_card_fil,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ( v5_card_fil(A) <=> ! [B] : ( v1_card_1(B) => ( r2_hidden(B,A) => r2_hidden(k3_card_2(2,B),A) ) ) ) ) )).
fof(d14_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d14_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(G,u4_struct_0(A)) => ~ ( r2_hidden(G,k2_cat_1(A,E,B)) & ! [H] : ( m1_subset_1(H,u4_struct_0(A)) => ( r2_hidden(H,k2_cat_1(A,E,B)) => ( ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d14_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( 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)) ) ) )).
fof(d14_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ! [B] : ( B = k13_cgames_1(A) <=> ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & k9_xtuple_0(C) = k10_cgames_1(A) & B = k1_funct_1(C,A) & ! [D] : ( 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)) ) ) ) ) ) )).
fof(d14_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_chain_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k4_chain_1(A,B,C))) => ( m3_chain_1(D,A,B,C) <=> ~ ( ~ ( C = k5_numbers & v1_abian(k5_card_1(D)) ) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( C = k1_nat_1(E,1) & ? [F] : ( m1_subset_1(F,k1_zfmisc_1(k4_chain_1(A,B,k1_nat_1(E,1)))) & F = D & k10_chain_1(A,B,E,F) = k5_chain_1(A,B,E) ) ) ) ) ) ) ) ) ) )).
fof(d14_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( v6_circcomb(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_funct_1(u3_msualg_1(A,B),C) = k6_margrel1 ) ) ) ) )).
fof(d14_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msualg_1(D,B) & l3_msualg_1(D,B) ) => ( r6_circtrm1(A,B,C,D) <=> ? [E] : ( v1_relat_1(E) & v1_funct_1(E) & ? [F] : ( v1_relat_1(F) & v1_funct_1(F) & r5_circtrm1(A,B,E,F,C,D) ) ) ) ) ) ) ) )).
fof(d14_closure1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( v9_closure1(B,A) & l1_closure1(B,A) ) => ! [C] : ( ( 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] : ( m1_pboole(D,u1_struct_0(A),k5_mssubfam(u1_struct_0(A),u3_msualg_1(A,B))) => ! [E] : ( ( v2_relat_1(E) & m3_pboole(E,u1_struct_0(A),k1_mboolean(u1_struct_0(A),u3_msualg_1(A,B))) ) => ( ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(d14_clvect_1,axiom,( ! [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) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k6_clvect_1(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k1_normsp_1(A,D,E) = k1_clvect_1(A,k1_normsp_1(A,B,E),C) ) ) ) ) ) ) )).
fof(d14_coh_sp,axiom,( ! [A] : 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)) )).
fof(d14_combgras,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ( r1_ordinal1(k1_nat_1(A,1),k1_card_1(B)) => ( r1_xxreal_0(A,k5_numbers) | ! [C] : ( ( 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] : ( ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d14_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) ) => ( v2_compos_1(B,A) <=> ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(C,k9_xtuple_0(B)) & k1_funct_1(B,C) = k2_compos_1(A) ) ) ) ) ) )).
fof(d14_comput_1,axiom,( ! [A] : ( v6_comput_1(A) <=> ( r2_hidden(k3_comput_1(k5_numbers,k5_numbers),A) & r2_hidden(k4_comput_1(1,1),A) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( 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) ) ) )).
fof(d14_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_convex4(B,A) => k12_convex4(A,B) = B ) ) )).
fof(d14_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(d14_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_csspace(A,B,C) <=> k12_csspace(A,B,C) = k5_numbers ) ) ) ) )).
fof(d14_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k9_decomp_1(A) = a_1_3_decomp_1(A) ) )).
fof(d14_descip_1,axiom,( ! [A] : ( m2_finseq_2(A,k6_margrel1,k4_finseq_2(64,k6_margrel1)) => ! [B] : ( 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) ) ) ) ) )).
fof(d14_dickson,axiom,( k10_dickson = a_0_0_dickson )).
fof(d14_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => ! [C] : ( m4_dist_2(C,A,B) => ! [D] : ( ( v1_setfam_1(D) & m2_subset_1(D,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => ( D = k11_dist_2(A,B,C) <=> ? [E] : ( m1_dist_2(E,A,B) & ? [F] : ( m2_finseq_1(F,A) & ? [G] : ( m1_subset_1(G,k1_zfmisc_1(k4_finseq_1(E))) & G = k8_relset_1(k4_ordinal1,A,E,C) & F = k5_dist_2(A,E,G) & r2_hidden(F,D) ) ) ) ) ) ) ) ) )).
fof(d14_dtconstr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_dtconstr(A) & l1_lang1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k18_dtconstr(A,B) = a_2_0_dtconstr(A,B) ) ) )).
fof(d14_e_siec,axiom,( ! [A] : ( ( v2_e_siec(A) & v3_e_siec(A) & l1_e_siec(A) ) => k12_e_siec(A) = u1_struct_0(A) ) )).
fof(d14_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k11_ens_1(A))) => k13_ens_1(A,B) = B ) ) )).
fof(d14_exchsort,axiom,( ! [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) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_exchsort(B) ) => ! [C] : ( ( v1_relat_1(C) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_exchsort(C) ) => ( m2_exchsort(C,A,B) <=> ( k1_funct_1(C,k1_exchsort(C)) = B & ! [D] : ( 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] : ( v3_ordinal1(D) => ~ ( r2_hidden(D,k9_xtuple_0(C)) & r2_hidden(k1_ordinal1(D),k9_xtuple_0(C)) & ! [E] : ( ( v1_relat_1(E) & v5_relat_1(E,u1_struct_0(A)) & v1_funct_1(E) & v1_exchsort(E) ) => ! [F] : ! [G] : ~ ( r2_hidden(k4_tarski(F,G),k6_exchsort(A,E)) & k1_funct_1(C,D) = E & k1_funct_1(C,k1_ordinal1(D)) = k9_funct_7(E,F,G) ) ) ) ) ) ) ) ) ) )).
fof(d14_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & ~ v2_compos_1(C,B) ) => ! [D] : ( ( 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] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r2_extpro_1(A,B,C,D,E) <=> ! [F] : ~ ( r2_hidden(F,k9_xtuple_0(E)) & ! [G] : ( ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(d14_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : k12_facirc_1(A,B,C) = k9_facirc_1(A,B,C,k1_facirc_1) )).
fof(d14_ff_siec,axiom,( ! [A] : ( ( 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)) ) )).
fof(d14_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v20_lattices(B,A) & v21_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_nat_lat(C,A) => ( C = k10_filter_2(A,B) <=> ? [D] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(d14_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_fin_topo(B,A) <=> B = k8_fin_topo(A,B) ) ) ) )).
fof(d14_finseq_1,axiom,( ! [A] : ( ( 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) ) )).
fof(d14_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( 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)) ) ) )).
fof(d14_fomodel0,axiom,( k4_numbers = k2_xboole_0(k4_ordinal1,k6_subset_1(k2_zfmisc_1(k6_domain_1(k4_ordinal1,k5_numbers),k4_ordinal1),k6_domain_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers)))) )).
fof(d14_fomodel1,axiom,( ! [A] : ( l1_fomodel1(A) => ! [B] : ( m1_subset_1(B,k1_fomodel1(A)) => ( v4_fomodel1(B,A) <=> r2_hidden(B,k2_fomodel1(A)) ) ) ) )).
fof(d14_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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)),k15_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)),k15_fomodel2(A,B),k32_fomodel1(A)),k6_margrel1))) ) => ( C = k16_fomodel2(A,B) <=> ! [D] : ( m2_subset_1(D,k9_funct_2(k37_fomodel1(A),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_fomodel2(A,B)) => ! [E] : ( m2_subset_1(E,k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k32_fomodel1(A)) => k2_binop_1(k15_fomodel2(A,B),k32_fomodel1(A),k6_margrel1,C,D,E) = k13_fomodel2(A,B,D,E) ) ) ) ) ) ) )).
fof(d14_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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))) ) ) ) )).
fof(d14_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) => ! [C] : ! [D] : ( v9_fomodel4(D,A,B,C) <=> ? [E] : ( r1_tarski(k1_xtuple_0(E),C) & k2_xtuple_0(E) = D & v8_fomodel4(k1_tarski(E),A,B) ) ) ) ) )).
fof(d14_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( m1_eqrel_1(D,u1_struct_0(C)) => ( v4_fsm_1(D,A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ( r5_fsm_1(A,B,C,E,F) <=> ? [G] : ( m2_subset_1(G,k1_zfmisc_1(u1_struct_0(C)),D) & r2_hidden(E,G) & r2_hidden(F,G) ) ) ) ) ) ) ) ) ) )).
fof(d14_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : 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)) )).
fof(d14_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( v5_funct_1(B,A) <=> ! [C] : ( r2_hidden(C,k9_xtuple_0(B)) => r2_hidden(k1_funct_1(B,C),k1_funct_1(A,C)) ) ) ) ) )).
fof(d14_functor0,axiom,( ! [A] : ( l1_altcat_1(A) => ! [B] : ( l1_altcat_1(B) => ! [C] : ( l2_functor0(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(d14_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ! [C] : ( ( ~ 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),k6_numbers,B,k6_domain_1(k6_numbers,k7_supinf_2(k7_relset_1(u1_struct_0(A),k6_numbers,B,C)))),C) ) ) ) ) )).
fof(d14_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ ( ~ 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 ) ) )).
fof(d14_gate_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k14_gate_5(A,B,C,D,E) = k10_gate_1(C,D,k11_gate_1(A,B,E)) )).
fof(d14_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v4_vectsp_1(A) & v3_gcd_1(A) & l4_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r6_gcd_1(A,B,C) <=> ? [D] : ( m2_gcd_1(D,A) & k5_gcd_1(A,D,B,C) = k5_struct_0(A) ) ) ) ) ) )).
fof(d14_geomtrap,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ( v4_geomtrap(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(H,u1_struct_0(A)) & r2_analoaf(A,B,C,D,H) ) ) ) ) ) ) ) ) ) ) )).
fof(d14_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(d14_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ( 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 ) ) ) )).
fof(d14_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_glib_001(C,A) => ( C = k11_glib_001(A,B) <=> ( k1_nat_1(k3_finseq_1(B),1) = k2_nat_1(2,k3_finseq_1(C)) & ! [D] : ( 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(k3_xcmplx_0(2,D),1)) ) ) ) ) ) ) ) )).
fof(d14_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) ) )).
fof(d14_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),o_1_0_glib_004(A)),k1_xboole_0) ) )).
fof(d14_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => ! [E] : ( ( 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] : ( ( v7_ordinal1(F) & v1_abian(F) ) => ( r2_hidden(F,k1_relset_1(k4_ordinal1,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(k4_ordinal1,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),E,k1_glib_001(A,C)) ) ) ) ) ) ) ) ) )).
fof(d14_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( m1_graph_1(B,A) <=> ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( 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] : ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & k3_finseq_1(C) = k1_nat_1(k3_finseq_1(B),1) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( 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] : ( m1_subset_1(D,k4_ordinal1) => ~ ( r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(B)) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( E = k1_funct_1(C,D) & F = k1_funct_1(C,k1_nat_1(D,1)) & r2_graph_1(A,E,F,k1_funct_1(B,D)) ) ) ) ) ) ) ) ) ) ) )).
fof(d14_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v2_funct_1(B) & m2_graph_1(B,A) ) => ( v1_graph_3(B,A) <=> k10_xtuple_0(B) = u4_struct_0(A) ) ) ) )).
fof(d14_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( 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))) ) ) ) ) )).
fof(d14_graphsp,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers)) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => ( C = k17_graphsp(A,B) <=> ( k4_finseq_1(C) = k4_finseq_1(A) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k4_finseq_1(A)) => ( ( r1_xxreal_0(D,k2_nat_1(2,B)) => ( r1_xxreal_0(D,B) | ( ( r1_graphsp(B,k7_nat_d(D,B),A) => k1_funct_1(C,D) = k7_partfun1(k1_numbers,A,k1_nat_1(k1_nat_1(k2_nat_1(B,B),k2_nat_1(3,B)),1)) ) & ( ~ r1_graphsp(B,k7_nat_d(D,B),A) => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) ) ) & ( r1_xxreal_0(D,k2_nat_1(3,B)) => ( r1_xxreal_0(D,k2_nat_1(2,B)) | ( ( r1_graphsp(B,k7_nat_d(D,k2_nat_1(2,B)),A) => k1_funct_1(C,D) = k16_graphsp(A,B,k7_nat_d(D,k2_nat_1(2,B))) ) & ( ~ r1_graphsp(B,k7_nat_d(D,k2_nat_1(2,B)),A) => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) ) ) & ( ~ ( ~ r1_xxreal_0(D,B) & r1_xxreal_0(D,k2_nat_1(3,B)) ) => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) ) ) ) ) ) ) ) )).
fof(d14_grcat_1,axiom,( ! [A] : ( ( v2_grcat_1(A) & l1_grcat_1(A) ) => ! [B] : ( ( v2_grcat_1(B) & l1_grcat_1(B) ) => ( k7_grcat_1(A) = k8_grcat_1(B) => ! [C] : ( ( v1_grcat_1(C) & v2_grcat_1(C) & l1_grcat_1(C) ) => ( C = k13_grcat_1(A,B) <=> ! [D] : ( ( ~ v2_struct_0(D) & v13_algstr_0(D) & v3_rlvect_1(D) & v4_rlvect_1(D) & l2_algstr_0(D) ) => ! [E] : ( ( ~ v2_struct_0(E) & v13_algstr_0(E) & v3_rlvect_1(E) & v4_rlvect_1(E) & l2_algstr_0(E) ) => ! [F] : ( ( ~ v2_struct_0(F) & v13_algstr_0(F) & v3_rlvect_1(F) & v4_rlvect_1(F) & l2_algstr_0(F) ) => ! [G] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d14_group_10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l3_algstr_0(A) ) => ! [B] : ! [C] : ( ( 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] : ( m1_subset_1(D,B) => ! [E] : ( m1_subset_1(E,B) => ( r2_group_10(A,B,C,D,E) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & E = k1_funct_1(k1_group_10(A,B,C,F),D) ) ) ) ) ) ) )).
fof(d14_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k14_group_2(A,B,C) = k5_group_2(A,C,k8_group_2(A,B)) ) ) ) )).
fof(d14_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( 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) ) ) ) ) )).
fof(d14_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v4_group_9(C,A,B) & m1_group_9(C,A,B) ) => ! [D] : ( D = k7_group_9(A,B,C) <=> ! [E] : ( ( 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) ) ) ) ) ) )).
fof(d14_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) = k3_xcmplx_0(k9_complex1(D),k3_funct_2(u1_struct_0(A),k1_numbers,B,C)) ) ) ) ) ) )).
fof(d14_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( 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) ) ) )).
fof(d14_idea_1,axiom,( k14_idea_1 = k3_finseq_2(k4_ordinal1) )).
fof(d14_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) ) ) ) )).
fof(d14_incproj,axiom,( ! [A] : ( l1_incsp_1(A) => ( v10_incproj(A) <=> ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u1_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u1_incsp_1(A)) => ! [H] : ( m1_subset_1(H,u1_incsp_1(A)) => ! [I] : ( m1_subset_1(I,u1_incsp_1(A)) => ! [J] : ( m1_subset_1(J,u1_incsp_1(A)) => ! [K] : ( m1_subset_1(K,u1_incsp_1(A)) => ! [L] : ( m1_subset_1(L,u2_incsp_1(A)) => ! [M] : ( m1_subset_1(M,u2_incsp_1(A)) => ! [N] : ( m1_subset_1(N,u2_incsp_1(A)) => ! [O] : ( m1_subset_1(O,u2_incsp_1(A)) => ! [P] : ( m1_subset_1(P,u2_incsp_1(A)) => ! [Q] : ( m1_subset_1(Q,u2_incsp_1(A)) => ! [R] : ( m1_subset_1(R,u2_incsp_1(A)) => ! [S] : ( m1_subset_1(S,u2_incsp_1(A)) => ! [T] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d14_incsp_1,axiom,( ! [A] : ( l2_incsp_1(A) => ( v11_incsp_1(A) <=> ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u4_incsp_1(A)) => ( ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & ? [E] : ( 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) ) ) ) ) ) )).
fof(d14_integr15,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ( D = k10_integr15(A,B,C) <=> ( k4_finseq_1(D) = k2_finseq_1(A) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k2_finseq_1(A)) => k1_funct_1(D,E) = k12_integra1(B,k1_partfun1(B,k1_euclid(A),k1_euclid(A),k1_numbers,C,k1_pdiff_1(E,A))) ) ) ) ) ) ) ) ) )).
fof(d14_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => k11_integra1(A,B) = k2_seq_4(k1_rvsum_1(k9_integra1(A,B))) ) ) )).
fof(d14_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ( v8_intpro_1(A) <=> ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(d14_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ( v5_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r1_orders_2(A,D,B) & r1_orders_2(A,D,C) & ! [E] : ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d14_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m1_lattice5(D,A,B,C) => ! [E] : ( v3_ordinal1(E) => ( r2_hidden(E,k9_xtuple_0(D)) => k9_lattice5(A,B,C,D,E) = k1_funct_1(D,E) ) ) ) ) ) ) )).
fof(d14_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v9_lattice6(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & C = k16_lattice3(A,D) ) ) ) ) ) )).
fof(d14_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_lattices(A) ) => ( v14_lattices(A) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_lattices(A,B,C) = B & k1_lattices(A,C,B) = B ) ) ) ) ) )).
fof(d14_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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),k9_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k7_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k8_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k15_lopban_1(A,B)) ) ) )).
fof(d14_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => k17_lpspacc1(A,B,C,D) = a_4_0_lpspacc1(A,B,C,D) ) ) ) ) )).
fof(d14_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => k14_lpspace1(A,B,C) = a_3_2_lpspace1(A,B,C) ) ) ) )).
fof(d14_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ( r3_ltlaxio1(A,B) <=> ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => ( r2_ltlaxio1(C,A) => r1_ltlaxio1(C,B) ) ) ) ) ) )).
fof(d14_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,D,C,C) & m2_finseq_1(E,k3_finseq_2(D)) ) => k18_matrix_0(A,B,C,D,E) = k16_matrix_0(B,D,k17_matrix_0(D,A,E)) ) ) ) ) ) )).
fof(d14_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k6_matroid0(A,B) = a_2_2_matroid0(A,B) ) ) )).
fof(d14_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => k17_member_1(A,B) = k9_member_1(k1_tarski(B),A) ) ) )).
fof(d14_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ( A = B <=> ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(C,A) <=> r2_hidden(C,B) ) ) ) ) ) )).
fof(d14_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( v7_ordinal1(D) => k9_memstr_0(A,B,C,D) = k1_funct_4(C,k7_memstr_0(A,B,k2_xcmplx_0(k5_memstr_0(A,B,C),D))) ) ) ) ) )).
fof(d14_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( v1_prob_2(D) & m2_finseq_1(D,B) ) => ! [E] : ( 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] : ( v7_ordinal1(F) => ( r2_hidden(F,k4_finseq_1(D)) => ! [G] : ( r2_hidden(G,k1_funct_1(D,F)) => k12_supinf_2(C,G) = k12_supinf_2(E,F) ) ) ) ) ) ) ) ) ) ) )).
fof(d14_mesfunc1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_valued_0(A) ) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( C = k14_mesfunc1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,k9_xtuple_0(A)) & r1_xxreal_0(B,k1_funct_1(A,D)) ) ) ) ) ) )).
fof(d14_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_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 ) ) ) ) ) ) )).
fof(d14_metric_1,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( ~ v2_struct_0(A) => ( D = k8_metric_1(A,B,C) <=> D = a_3_0_metric_1(A,B,C) ) ) & ( v2_struct_0(A) => ( D = k8_metric_1(A,B,C) <=> v1_xboole_0(D) ) ) ) ) ) ) ) )).
fof(d14_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k10_midsp_1(A)) => ! [D] : ( m1_subset_1(D,k10_midsp_1(A)) => k5_binop_1(k10_midsp_1(A),B,C,D) = k11_midsp_1(A,C,D) ) ) ) ) ) )).
fof(d14_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( l1_midsp_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(d14_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [D] : ( v7_ordinal1(D) => k14_mmlquery(A,B,C,D) = a_4_9_mmlquery(A,B,C,D) ) ) ) )).
fof(d14_mod_2,axiom,( ! [A] : ( m1_subset_1(A,k1_enumset1(k5_numbers,1,2)) => ! [B] : ( m1_subset_1(B,k1_enumset1(k5_numbers,1,2)) => ( ( B = k5_numbers => k12_mod_2(A,B) = k5_numbers ) & ( A = k5_numbers => k12_mod_2(A,B) = k5_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 ) ) ) ) )).
fof(d14_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(d14_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k3_modal_1) => k16_modal_1(A) = k8_funcop_1(k3_modal_1,k2_trees_1(k5_numbers),A) ) )).
fof(d14_modcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ 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))) ) ) )).
fof(d14_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v2_modelc_1(A) <=> ? [B] : ( m1_subset_1(B,k4_ordinal1) & A = k6_modelc_1(B) ) ) ) )).
fof(d14_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v5_modelc_2(A) <=> ? [B] : ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) & ? [C] : ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) & A = k5_modelc_2(B,C) ) ) ) ) )).
fof(d14_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => k8_modelc_3(A) = k1_tarski(A) ) )).
fof(d14_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v11_monoid_0(A) <=> v3_monoid_0(u2_algstr_0(A),u1_struct_0(A)) ) ) )).
fof(d14_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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)) ) ) )).
fof(d14_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_funct_1(u3_msualg_1(A,k11_msafree(A,B)),C)) => ! [E] : ( v7_ordinal1(E) => ( E = k8_msafree2(A,B,C,D) <=> ? [F] : ( v1_relat_1(F) & v1_funct_1(F) & v1_finset_1(F) & v3_trees_2(F) & ? [G] : ( ~ v1_xboole_0(G) & v1_finset_1(G) & v1_trees_1(G) & F = D & G = k9_xtuple_0(F) & E = k6_trees_1(G) ) ) ) ) ) ) ) ) )).
fof(d14_msualg_1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v13_struct_0(A,1) & v5_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(d14_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m3_pboole(C,u1_struct_0(A),u3_msualg_1(A,B)) => ! [D] : ( m3_pboole(D,u1_struct_0(A),u3_msualg_1(A,B)) => ( D = k9_msualg_2(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k1_funct_1(D,E) = k1_setfam_1(k8_msualg_2(A,B,C,E)) ) ) ) ) ) ) )).
fof(d14_msualg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(d14_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(d14_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ~ v1_xboole_0(C) => ( m4_nattra_1(C,A,B) <=> ! [D] : ~ ( r2_hidden(D,C) & ! [E] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,A,B) => ! [G] : ( m2_nattra_1(G,A,B,E,F) => ~ ( D = k4_tarski(k4_tarski(E,F),G) & r2_nattra_1(A,B,E,F) ) ) ) ) ) ) ) ) ) )).
fof(d14_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k2_numbers))) ) => ! [C] : ( r10_ncfcont1(A,B,C) <=> ( r1_tarski(C,k1_relset_1(u1_struct_0(A),B)) & ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d14_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : ! [C] : ( C = k11_net_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r1_tarski(D,k2_net_1(A)) & ? [E] : ( m1_subset_1(E,k2_net_1(A)) & r2_hidden(E,B) & D = k6_net_1(A,E) ) ) ) ) ) )).
fof(d14_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v13_o_ring_1(B,A) <=> ? [C] : ( 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)) ) ) ) ) )).
fof(d14_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r8_orders_1(A,B) <=> ( r2_hidden(B,k1_relat_1(A)) & ! [C] : ( r2_hidden(C,k1_relat_1(A)) => ( C = B | r2_hidden(k4_tarski(C,B),A) ) ) ) ) ) )).
fof(d14_osalg_1,axiom,( ! [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) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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] : ( m1_subset_1(D,u4_struct_0(A)) => ( D = k2_osalg_1(A,B,C) <=> r3_osalg_1(A,B,D,C) ) ) ) ) ) ) )).
fof(d14_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( C = k12_osalg_2(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( v3_msualg_1(D,A) & v12_osalg_1(D,A) & m1_msualg_2(D,A,B) ) ) ) ) ) )).
fof(d14_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( ( v4_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v2_msualg_4(D,A,C) & v3_msualg_4(D,A,C) & m1_osalg_4(D,A,C) ) => ! [E] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d14_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( m1_pboole(C,A,B) <=> ! [D] : ( r2_hidden(D,A) => m1_subset_1(k1_funct_1(C,D),k1_funct_1(B,D)) ) ) ) ) )).
fof(d14_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ( r4_pdiff_1(A,B,C,D,E) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(B)) => ( F = k11_pdiff_1(A,B,C,D,E) <=> ? [G] : ( 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] : ( 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(k4_ordinal1,1)) ) ) ) ) ) ) ) ) ) ) )).
fof(d14_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r5_pdiff_5(A,B) => ! [C] : ( v1_xreal_0(C) => ( C = k5_pdiff_5(A,B) <=> ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & B = k11_finseq_1(D,E,F) & ? [G] : ( 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] : ( v1_funct_1(H) & v3_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [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_funct_1(H,1) & ! [J] : ( v1_xreal_0(J) => ( r2_hidden(J,G) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,2,k1_pdiff_3(2,3,A),B),J),k1_funct_1(k1_pdiff_2(3,2,k1_pdiff_3(2,3,A),B),E)) = k2_xcmplx_0(k1_funct_1(H,k6_xcmplx_0(J,E)),k1_funct_1(I,k6_xcmplx_0(J,E))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d14_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k13_petri(A,B) = B ) ) )).
fof(d14_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => k12_pnproc_1(A,B) = k6_domain_1(k3_finseq_2(B),k2_pre_poly(B)) ) )).
fof(d14_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => k17_polyform(A,B) = k7_bspace(k8_polyform(A,B)) ) ) )).
fof(d14_polyred,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r11_polyred(A,B,C,D) <=> r2_hidden(k5_algstr_0(A,C,D),B) ) ) ) ) ) )).
fof(d14_pralg_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( 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)) ) ) )).
fof(d14_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(A,k4_ordinal1))) => ( C = k18_pre_poly(A,B) <=> ! [D] : ( ( 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] : ( r2_hidden(E,A) => r1_xxreal_0(k1_funct_1(D,E),k1_funct_1(B,E)) ) ) ) ) ) ) )).
fof(d14_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v1_prvect_1(A) ) => k20_prvect_1(A) = g2_algstr_0(k4_card_3(k15_prvect_1(A)),k13_prvect_1(k15_prvect_1(A),k17_prvect_1(A)),k19_prvect_1(A)) ) )).
fof(d14_pscomp_1,axiom,( ! [A] : ( 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)) ) )).
fof(d14_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => k12_qc_lang1(A) = k9_finseq_1(k4_tarski(k5_numbers,k5_numbers)) ) )).
fof(d14_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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))) ) ) )).
fof(d14_qmax_1,axiom,( ! [A] : ( ( v2_qmax_1(A) & l1_qmax_1(A) ) => ! [B] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(d14_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( ( r2_hidden(A,k2_numbers) => ( B = k14_quaterni(A) <=> ? [C] : ( v1_xcmplx_0(C) & A = C & B = k4_complex1(C) ) ) ) & ( ~ r2_hidden(A,k2_numbers) => ( B = k14_quaterni(A) <=> ? [C] : ( 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_funct_1(C,1) ) ) ) ) ) )).
fof(d14_quofield,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( 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) ) ) ) ) )).
fof(d14_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k3_radix_1(B)) ) => ! [D] : ( ( v3_card_1(D,A) & m2_finseq_1(D,k3_radix_1(B)) ) => ! [E] : ( ( v3_card_1(E,A) & m2_finseq_1(E,k3_radix_1(B)) ) => ( E = k14_radix_1(A,B,C,D) <=> ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d14_ratfunc1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & l5_algstr_0(A) ) => k8_ratfunc1(A) = k3_ratfunc1(A,k10_polynom3(A),k10_polynom3(A)) ) )).
fof(d14_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : k9_relat_1(A,B) = k7_relat_1(A,k1_tarski(B)) ) )).
fof(d14_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ( v6_relat_2(A) <=> r6_relat_2(A,k1_relat_1(A)) ) ) )).
fof(d14_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ( v2_rewrite1(A) <=> ! [B] : ( r2_hidden(B,k1_relat_1(A)) => r9_rewrite1(A,B) ) ) ) )).
fof(d14_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : k21_rfunct_3(A,B,C) = k18_rvsum_1(k20_rfunct_3(A,B,C)) ) ) )).
fof(d14_rltopsp1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_rltopsp1(A,B,C) = a_3_2_rltopsp1(A,B,C) ) ) ) )).
fof(d14_rlvect_2,axiom,( ! [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) ) => ! [B] : ( B = k11_rlvect_2(A) <=> ! [C] : ( r2_hidden(C,B) <=> m1_rlvect_2(C,A) ) ) ) )).
fof(d14_rmod_4,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(d14_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k9_robbins1(A,B,C) = k3_robbins1(A,k1_lattices(A,k3_robbins1(A,B),C)) ) ) ) )).
fof(d14_rvsum_1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => k20_rvsum_1(A) = k1_finsop_1(k2_numbers,A,k5_binop_2) ) )).
fof(d14_scm_comp,axiom,( ! [A] : ( m1_dtconstr(A,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( B = k17_scm_comp(A) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k4_dtconstr(k1_scm_comp),k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k1_scm_comp),k4_ordinal1))) & B = k3_funct_2(k4_dtconstr(k1_scm_comp),k4_ordinal1,C,A) & ! [D] : ( m2_subset_1(D,u1_struct_0(k1_scm_comp),k6_dtconstr(k1_scm_comp)) => k3_funct_2(k4_dtconstr(k1_scm_comp),k4_ordinal1,C,k3_scm_comp(D)) = k16_scm_comp(D) ) & ! [D] : ( m2_subset_1(D,u1_struct_0(k1_scm_comp),k7_dtconstr(k1_scm_comp)) => ! [E] : ( m1_dtconstr(E,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [F] : ( m1_dtconstr(F,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [G] : ( m1_subset_1(G,u1_struct_0(k1_scm_comp)) => ! [H] : ( 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] : ( m1_subset_1(I,k4_ordinal1) => ! [J] : ( m1_subset_1(J,k4_ordinal1) => ( ( I = k3_funct_2(k4_dtconstr(k1_scm_comp),k4_ordinal1,C,E) & J = k3_funct_2(k4_dtconstr(k1_scm_comp),k4_ordinal1,C,F) ) => k3_funct_2(k4_dtconstr(k1_scm_comp),k4_ordinal1,C,k2_scm_comp(D,E,F)) = k5_nat_1(I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d14_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_scmfsa_2(C) => k14_scmfsa_2(A,B,C) = k3_xtuple_0(9,k1_xboole_0,k11_finseq_1(A,C,B)) ) ) ) )).
fof(d14_scmpds_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ! [C] : ( v1_int_1(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(d14_scmpds_i,axiom,( k15_scmpds_i = 1 )).
fof(d14_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k12_seq_4(A))) => ( v1_seq_4(B,A) <=> ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => ~ ( r2_hidden(C,B) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( m2_finseq_2(E,k2_numbers,k12_seq_4(A)) => ( ~ r1_xxreal_0(D,k20_seq_4(E)) => r2_hidden(k13_seq_4(A,C,E),B) ) ) ) ) ) ) ) ) ) )).
fof(d14_sgraph1,axiom,( k8_sgraph1 = k7_sgraph1(3) )).
fof(d14_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_sheffer1(A) ) => ( v11_sheffer1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(d14_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ! [C] : ( m2_simplex0(C,A,B) => ( v7_simplex0(C,A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) => ( r2_hidden(D,u1_pre_topc(B)) => v3_pre_topc(D,C) ) ) ) ) ) )).
fof(d14_sin_cos,axiom,( ! [A] : ( ( 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] : ( v1_xcmplx_0(B) => k1_funct_1(A,B) = k11_comseq_3(k3_sin_cos(B)) ) ) ) )).
fof(d14_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( r2_stacks_1(A,B,C) <=> k9_stacks_1(A,B) = k9_stacks_1(A,C) ) ) ) ) )).
fof(d14_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( 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) ) ) ) )).
fof(d14_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k1_substut1(A)) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(d14_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tex_4(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d14_topalg_6,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m2_finseq_1(B,k1_topalg_6(A)) => ( ( ~ r1_xxreal_0(k3_finseq_1(B),k5_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),k5_numbers) => k6_topalg_6(A,B) = k1_xboole_0 ) ) ) ) )).
fof(d14_toprealb,axiom,( ! [A] : ( ( 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(k7_xcmplx_0(1,2),k7_xcmplx_0(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(k7_xcmplx_0(1,2),k7_xcmplx_0(3,2)))))))) ) => ( A = k15_toprealb <=> ! [B] : ( m1_subset_1(B,u1_struct_0(k11_toprealb(k10_toprealb))) => ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & B = k19_euclid(C,D) & ( r1_xxreal_0(k5_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(k7_xcmplx_0(1,2),k7_xcmplx_0(3,2))))),A,B) = k2_xcmplx_0(1,k7_xcmplx_0(k4_sin_cos6(C),k3_xcmplx_0(2,k28_sin_cos))) ) & ( r1_xxreal_0(D,k5_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(k7_xcmplx_0(1,2),k7_xcmplx_0(3,2))))),A,B) = k6_xcmplx_0(1,k7_xcmplx_0(k4_sin_cos6(C),k3_xcmplx_0(2,k28_sin_cos))) ) ) ) ) ) ) )).
fof(d14_trees_1,axiom,( k8_trees_1 = a_0_0_trees_1 )).
fof(d14_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ( m4_trees_3(B,A) <=> ! [C] : ( m1_trees_1(C,B) => ~ ( ~ r2_hidden(C,A) & ! [D] : ( m3_trees_3(D,A) => ~ r2_xboole_0(D,C) ) ) ) ) ) ) )).
fof(d14_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => ( v6_pre_topc(B) <=> ( v2_struct_0(B) | ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v4_pre_topc(E,A) & ~ r2_hidden(C,E) & r2_hidden(D,E) ) ) ) ) ) ) ) ) ) )).
fof(d14_turing_1,axiom,( ! [A] : ( ( v1_turing_1(A) & l1_turing_1(A) ) => ( A = k14_turing_1 <=> ( u1_turing_1(A) = k7_domain_1(k4_ordinal1,k5_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),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1)),k8_mcart_1(k4_ordinal1,k4_ordinal1,k3_turing_1(5),k7_domain_1(k4_ordinal1,k5_numbers,1)),k3_zfmisc_1(k3_turing_1(5),k7_domain_1(k4_ordinal1,k5_numbers,1),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1)),u3_turing_1(A),k13_turing_1) & u4_turing_1(A) = k5_numbers & u5_turing_1(A) = 5 ) ) ) )).
fof(d14_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k1_funct_1(A,k10_finseq_1(B,C)) = k2_binarith(k9_margrel1(B),C) ) ) ) ) )).
fof(d14_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( B = k9_unialg_2(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( v1_unialg_1(C) & m1_unialg_2(C,A) ) ) ) ) )).
fof(d14_valued_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ( v3_funct_1(B) <=> ? [C] : ( m1_subset_1(C,A) & ! [D] : ( v7_ordinal1(D) => k9_nat_1(A,B,D) = C ) ) ) ) ) )).
fof(d14_valued_2,axiom,( ! [A] : ! [B] : ( B = k8_valued_2(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k3_numbers))) ) ) ) )).
fof(d14_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ( v8_vectsp_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d14_waybel34,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) ) )).
fof(d14_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(d14_waybel_4,axiom,( ! [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] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k1_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(k1_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A))))) ) => ( B = k9_waybel_4(A) <=> ! [C] : ( ( 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) ) ) ) ) )).
fof(d14_xtuple_0,axiom,( ! [A] : k11_xtuple_0(A) = k9_xtuple_0(k9_xtuple_0(A)) )).
fof(d14_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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)) ) ) ) )).
fof(d14_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k9_yellow_6(A,B) = k7_lattice3(k1_yellow_1(a_2_0_yellow_6(A,B))) ) ) )).
fof(d14_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v6_zf_lang(A) <=> ? [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) & ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & A = k8_zf_lang(B,C) ) ) ) ) )).
fof(d14_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( ( v1_zmodul01(D) & m1_zmodul01(D,A) ) => ( D = k6_zmodul01(A,B,C) <=> u1_struct_0(D) = a_3_2_zmodul01(A,B,C) ) ) ) ) ) )).
fof(d14_zmodul02,axiom,( ! [A] : ( ( ~ 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) ) => k14_zmodul02(A) = u1_zmodul01(A) ) )).
fof(d15_abcmiz_0,axiom,( ! [A] : ( l2_abcmiz_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_abcmiz_0(A)) => ( r1_abcmiz_0(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r2_hidden(D,k3_abcmiz_0(A,C)) & r1_orders_2(A,D,B) ) ) ) ) ) )).
fof(d15_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => k14_abcmiz_1(A) = k8_abcmiz_1 ) )).
fof(d15_abcmiz_a,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ( v6_abcmiz_a(B,A) <=> k3_finseq_1(k1_msualg_1(A,B)) = 2 ) ) ) )).
fof(d15_algstr_4,axiom,( ! [A] : k12_algstr_4(A) = k3_card_3(k2_card_3(k2_partfun1(k4_ordinal1,k9_setfam_1(k1_yellow_6(k2_xboole_0(A,k4_ordinal1))),k10_algstr_4(A),k6_nat_lat))) )).
fof(d15_altcat_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(d15_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r8_analmetr(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d15_anproj_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d15_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v19_aofa_a00(D,A) & m1_subset_1(D,u1_struct_0(A)) ) => ! [E] : ( v1_int_1(E) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,C),D)) => ( F = k10_aofa_a01(A,B,C,D,E) <=> ? [G] : ( v1_funct_1(G) & v1_funct_2(G,k4_numbers,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,C),D)) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_numbers,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,C),D)))) & F = k1_funct_1(G,E) & k1_funct_1(G,k5_numbers) = k27_aofa_a00(A,C,D) & ! [H] : ( v7_ordinal1(H) => ! [I] : ( m1_subset_1(I,k1_funct_1(u3_msualg_1(A,C),D)) => ( k1_funct_1(G,H) = I => ( k1_funct_1(G,k2_xcmplx_0(H,1)) = k30_aofa_a00(A,C,D,I,k28_aofa_a00(A,C,D)) & k1_funct_1(G,k4_xcmplx_0(k2_xcmplx_0(H,1))) = k29_aofa_a00(A,C,D,k30_aofa_a00(A,C,D,I,k28_aofa_a00(A,C,D))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d15_aofa_i00,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) => ! [E] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(A)) & r2_hidden(G,k18_aofa_000(A)) & ! [H] : ( 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) = k14_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)) ) ) ) ) ) ) ) ) ) )).
fof(d15_armstrng,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ( v7_armstrng(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( r1_tarski(D,C) => r2_hidden(k6_armstrng(A,C,D),B) ) ) ) ) ) )).
fof(d15_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( C = k12_asympt_0(A,B) <=> ! [D] : ( m1_subset_1(D,k4_ordinal1) => k9_nat_1(k1_numbers,C,D) = k9_nat_1(k1_numbers,A,k2_nat_1(B,D)) ) ) ) ) ) )).
fof(d15_bagorder,axiom,( ! [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) ) => k13_bagorder(A) = k3_tarski(k10_xtuple_0(k12_bagorder(A))) ) )).
fof(d15_bcialg_1,axiom,( ! [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) ) => k5_bcialg_1(A) = a_1_1_bcialg_1(A) ) )).
fof(d15_bcialg_2,axiom,( ! [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) ) => k5_bcialg_2(A) = a_1_1_bcialg_2(A) ) )).
fof(d15_bcialg_4,axiom,( ! [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) & l1_bcialg_4(A) ) => ( v8_bcialg_4(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_1(A,B,k1_bcialg_1(A,C,B)) = B ) ) ) ) )).
fof(d15_bcialg_6,axiom,( ! [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] : ( m1_bcialg_1(B,A) => ! [C] : ( ( v12_bcialg_1(C,A) & m2_bcialg_1(C,A) ) => ! [D] : ( m5_bcialg_2(D,A,C) => ! [E] : ( m2_subset_1(E,u1_struct_0(A),k7_bcialg_6(A,B,C,D)) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(d15_bilinear,axiom,( ! [A] : ( l2_struct_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(d15_binop_2,axiom,( ! [A] : ( ( 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 = k15_binop_2 <=> ! [B] : ( v1_rat_1(B) => ! [C] : ( v1_rat_1(C) => k1_binop_1(A,B,C) = k2_xcmplx_0(B,C) ) ) ) ) )).
fof(d15_borsuk_1,axiom,( k19_borsuk_1 = 1 )).
fof(d15_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_eqrel_1(C,A) => ( r2_bvfunc_1(A,B,C) <=> ! [D] : ( r2_hidden(D,C) => ! [E] : ! [F] : ( ( r2_hidden(E,D) & r2_hidden(F,D) ) => k1_funct_1(B,E) = k1_funct_1(B,F) ) ) ) ) ) ) )).
fof(d15_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( r2_hidden(B,k6_c0sp1(A)) => ! [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))) ) => ( C = k8_c0sp1(A,B) <=> ( C = B & v1_comseq_2(k2_partfun1(A,k1_numbers,C,A)) ) ) ) ) ) )).
fof(d15_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ( r10_calcul_1(A,B,C) <=> ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_valuat_1(E,A,D) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d15_card_fil,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ( v6_card_fil(A) <=> ( v1_card_5(A) & v5_card_fil(A) ) ) ) )).
fof(d15_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_cat_1(D,A,B,C) => ( v9_cat_1(D,A,B,C) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d15_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u4_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(H,u4_struct_0(A)) => ~ ( r2_hidden(H,k2_cat_1(A,E,B)) & ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d15_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(d15_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ( v5_cgames_1(A) <=> ? [B] : ( r2_hidden(A,B) & ! [C] : ( v2_cgames_1(C) => ( r2_hidden(C,B) => ! [D] : ( v2_cgames_1(D) => ~ ( r2_hidden(D,k7_cgames_1(C)) & ! [E] : ( v2_cgames_1(E) => ~ ( r2_hidden(E,k6_cgames_1(D)) & r2_hidden(E,B) ) ) ) ) ) ) ) ) ) )).
fof(d15_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_chain_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m3_chain_1(D,A,B,k1_nat_1(C,1)) => k10_chain_1(A,B,C,D) = k5_chain_1(A,B,C) ) ) ) ) )).
fof(d15_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k1_msaterm(A,C))) ) => ! [E] : ( ( ~ v2_struct_0(E) & ~ v11_struct_0(E) & v2_msafree2(E) & l1_msualg_1(E) ) => ! [F] : ( ( v4_msualg_1(F,E) & v4_msafree2(F,E) & l3_msualg_1(F,E) ) => ( r7_circtrm1(A,B,C,D,E,F) <=> ? [G] : ( v1_relat_1(G) & v1_funct_1(G) & ? [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d15_clvect_1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v9_clvect_1(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(E,F) & r1_xxreal_0(D,k2_normsp_0(A,k5_algstr_0(A,k1_normsp_1(A,B,F),C))) ) ) ) ) ) ) ) ) )).
fof(d15_coh_sp,axiom,( ! [A] : ! [B] : ( B = k14_coh_sp(A) <=> ! [C] : ( 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))) ) ) ) )).
fof(d15_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v10_cohsp_1(A) <=> ( v9_cohsp_1(A) & v4_cohsp_1(A) ) ) ) )).
fof(d15_comput_1,axiom,( k9_comput_1 = k1_setfam_1(a_0_0_comput_1) )).
fof(d15_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) & l2_conlat_1(B,A) ) => ! [C] : ( ( ~ v4_conlat_1(C,A) & v6_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)) ) ) ) ) )).
fof(d15_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k10_convex4(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d15_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k13_csspace(A,B) = k3_square_1(k9_complex1(k12_csspace(A,B,B))) ) ) )).
fof(d15_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k10_decomp_1(A) = a_1_4_decomp_1(A) ) )).
fof(d15_descip_1,axiom,( ! [A] : ( ( 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] : ( 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) ) ) ) )).
fof(d15_dickson,axiom,( k11_dickson = g1_orders_2(k4_ordinal1,k10_dickson) )).
fof(d15_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => ! [C] : ( m4_dist_2(C,A,B) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,k6_margrel1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => k12_dist_2(A,B,C,D) = k6_dist_2(A,k11_dist_2(A,B,C),D) ) ) ) ) )).
fof(d15_e_siec,axiom,( ! [A] : ( ( 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))) ) )).
fof(d15_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k2_ens_1(A)) => k14_ens_1(A,B) = B ) ) )).
fof(d15_exchsort,axiom,( ! [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) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_exchsort(B) ) => ! [C] : ( m2_exchsort(C,A,B) => ( v6_exchsort(C,A,B) <=> v5_exchsort(k4_exchsort(C),A) ) ) ) ) )).
fof(d15_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ( 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] : ( v7_ordinal1(F) => ( k3_extpro_1(A,B,C,k5_extpro_1(A,B,C,D,F)) = k2_compos_1(B) => r1_xxreal_0(E,F) ) ) ) ) ) ) ) ) ) ) )).
fof(d15_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : k13_facirc_1(A,B,C) = k10_facirc_1(A,B,C,k1_facirc_1) )).
fof(d15_ff_siec,axiom,( ! [A] : ( ( 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))) ) )).
fof(d15_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_fin_topo(B,A) <=> B = k9_fin_topo(A,B) ) ) ) )).
fof(d15_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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)) ) ) )).
fof(d15_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( 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)) ) ) )).
fof(d15_fomodel0,axiom,( ! [A] : ! [B] : k13_fomodel0(A,B) = B )).
fof(d15_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k9_funct_2(k37_fomodel1(A),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_fomodel2(A,B)) => ! [D] : ( ( 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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),k6_margrel1))) ) => ! [E] : ( 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] : ( m1_subset_1(F,B) & ? [G] : ( 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 ) ) => k17_fomodel2(A,B,C,D,E) = k8_margrel1 ) & ( ! [F] : ( m1_subset_1(F,B) => ! [G] : ( ( 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 ) ) ) => k17_fomodel2(A,B,C,D,E) = k7_margrel1 ) ) ) ) ) ) ) )).
fof(d15_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v10_fomodel1(C,A) & m1_subset_1(C,k1_fomodel1(A)) ) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(d15_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) => ! [C] : ( v10_fomodel4(C,A,B) <=> ? [D] : ( 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] : ( 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))) & v9_fomodel4(D,A,B,C) & v9_fomodel4(k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k1_fomodel2(A)),D),E),A,B,C) ) ) ) ) ) )).
fof(d15_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & v8_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( m1_eqrel_1(D,u1_struct_0(C)) => ( D = k8_fsm_1(A,B,C) <=> v4_fsm_1(D,A,B,C) ) ) ) ) ) )).
fof(d15_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k15_ftacell1(A,B,C,D,E) = k33_gfacirc1(A,B,C) )).
fof(d15_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_altcat_1(B) ) => ! [C] : ( ( v10_functor0(C,A,B) & l2_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d15_fvaluat1,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,k4_vectsp_2(A)) => ( m2_fvaluat1(C,A,B) <=> u1_struct_0(C) = B ) ) ) ) )).
fof(d15_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ ( 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 ) ) )).
fof(d15_gate_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : 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))) )).
fof(d15_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v4_vectsp_1(A) & v3_gcd_1(A) & l5_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d15_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ( 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) ) ) ) ) ) )).
fof(d15_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m2_glib_001(C,A) => ( C = k12_glib_001(A,B) <=> ( k3_finseq_1(B) = k1_nat_1(k2_nat_1(2,k3_finseq_1(C)),1) & ! [D] : ( 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,k3_xcmplx_0(2,D)) ) ) ) ) ) ) ) )).
fof(d15_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( 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),o_2_1_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),o_2_1_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(o_2_1_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),o_2_1_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),o_2_1_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(o_2_1_glib_004(A,B)))) ) ) ) ) )).
fof(d15_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v1_glib_005(A) ) => ! [B] : ( ( 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] : ( m3_glib_001(C,A) => ( r5_glib_005(A,B,C) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( D = k8_glib_005(A,B,C) <=> ( k1_relset_1(k4_ordinal1,D) = k1_relset_1(k4_ordinal1,k12_glib_001(A,C)) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k1_relset_1(k4_ordinal1,D)) => ( ( r2_glib_000(A,k1_funct_1(C,k6_xcmplx_0(k3_xcmplx_0(2,E),1)),k1_funct_1(C,k1_nat_1(k3_xcmplx_0(2,E),1)),k1_funct_1(C,k3_xcmplx_0(2,E))) => k1_funct_1(D,E) = k6_xcmplx_0(k1_funct_1(k5_glib_003(A),k1_funct_1(C,k3_xcmplx_0(2,E))),k1_funct_1(B,k1_funct_1(C,k3_xcmplx_0(2,E)))) ) & ( ~ r2_glib_000(A,k1_funct_1(C,k6_xcmplx_0(k3_xcmplx_0(2,E),1)),k1_funct_1(C,k1_nat_1(k3_xcmplx_0(2,E),1)),k1_funct_1(C,k3_xcmplx_0(2,E))) => k1_funct_1(D,E) = k1_funct_1(B,k1_funct_1(C,k3_xcmplx_0(2,E))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d15_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_graph_1(B,A) => ( v7_graph_1(B,A) <=> ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_xxreal_0(1,C) => ( r1_xxreal_0(k3_finseq_1(B),C) | k1_funct_1(u1_graph_1(A),k1_funct_1(B,k1_nat_1(C,1))) = k1_funct_1(u2_graph_1(A),k1_funct_1(B,C)) ) ) ) ) ) ) )).
fof(d15_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u4_struct_0(A)) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r6_graph_5(A,C) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ( D = k9_graph_5(A,B,C) <=> ( k4_finseq_1(B) = k4_finseq_1(D) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k4_finseq_1(B)) => k1_funct_1(D,E) = k1_funct_1(C,k1_funct_1(B,E)) ) ) ) ) ) ) ) ) ) )).
fof(d15_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( 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 = k18_graphsp(A) <=> ( k9_xtuple_0(B) = k3_finseq_2(k1_numbers) & ! [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => k6_graphsp(B,C) = k17_graphsp(C,A) ) ) ) ) ) )).
fof(d15_group_10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,B) => k13_group_10(A,B,C,D) = a_4_1_group_10(A,B,C,D) ) ) ) ) )).
fof(d15_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( C = k15_group_2(A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(D,C) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & D = k13_group_2(A,B,E) ) ) ) ) ) ) ) )).
fof(d15_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => k11_group_3(A,B) = k10_group_3(A,k8_group_2(A,B)) ) ) )).
fof(d15_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v4_group_9(C,A,B) & m1_group_9(C,A,B) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(d15_idea_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( ( 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] : ( m2_finseq_1(D,k4_ordinal1) => k1_funct_1(C,D) = k11_idea_1(A,k13_idea_1(k12_idea_1(A,D,B)),B) ) ) ) ) ) )).
fof(d15_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) ) ) ) )).
fof(d15_incsp_1,axiom,( ! [A] : ( l2_incsp_1(A) => ( v12_incsp_1(A) <=> ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u4_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u4_incsp_1(A)) => ~ ( r2_incsp_1(A,B,C) & r2_incsp_1(A,B,D) & ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ~ ( B != E & r2_incsp_1(A,E,C) & r2_incsp_1(A,E,D) ) ) ) ) ) ) ) ) )).
fof(d15_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ 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] : ( m2_cat_1(C,A,B) => k13_index_1(A,B,C) = k4_tarski(k7_cat_1(A,B,C),k12_mcart_1(C)) ) ) ) )).
fof(d15_integr15,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ( v3_integr15(B,A) <=> ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( 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))) ) ) ) ) ) )).
fof(d15_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(d15_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m2_interva1(B,A) => k14_interva1(A,B) = k1_xtuple_0(B) ) ) )).
fof(d15_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1)) => ( B = k7_intpro_1(A) <=> ! [C] : ( m1_subset_1(C,k1_intpro_1) => ( r2_hidden(C,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_intpro_1)) => ( ( v8_intpro_1(D) & r1_tarski(A,D) ) => r2_hidden(C,D) ) ) ) ) ) ) ) )).
fof(d15_lattice3,axiom,( ! [A] : ( 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] : ( ( ~ 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) ) ) ) ) )).
fof(d15_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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 ) ) ) )).
fof(d15_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => k5_lattice6(A) = a_1_0_lattice6(A) ) )).
fof(d15_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( v15_lattices(A) <=> ( v13_lattices(A) & v14_lattices(A) ) ) ) )).
fof(d15_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m2_lexbfs(B,A) => ! [C] : ( m1_lexbfs(C,A) => ( C = k15_lexbfs(A,B) <=> ! [D] : ( v7_ordinal1(D) => r2_relset_1(k6_glib_000(A),k4_ordinal1,k5_lexbfs(A,C,D),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),k13_lexbfs(A,B,D))) ) ) ) ) ) )).
fof(d15_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_subset_1(D,k7_lmod_7(A,B,C)) => ! [E] : ( m1_subset_1(E,k7_lmod_7(A,B,C)) => ! [F] : ( m1_subset_1(F,k7_lmod_7(A,B,C)) => ( F = k10_lmod_7(A,B,C,D,E) <=> ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d15_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ( v3_lopban_1(A) <=> ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_rsspace3(B,A) => v3_normsp_1(B,A) ) ) ) ) )).
fof(d15_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => k18_lpspacc1(A,B,C) = a_3_2_lpspacc1(A,B,C) ) ) ) )).
fof(d15_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( 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] : ( m2_subset_1(E,k1_zfmisc_1(k9_lpspace1(A,B,C)),k14_lpspace1(A,B,C)) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(k9_lpspace1(A,B,C)),k14_lpspace1(A,B,C)) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [H] : ( ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d15_ltlaxio1,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( m1_subset_1(D,k1_hilbert1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( k3_funct_2(k1_hilbert1,k6_margrel1,B,k2_hilbert1) = k5_ordinal1 & 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)) ) ) ) ) ) ) ) )).
fof(d15_margrel1,axiom,( ! [A] : ( ( ~ r2_hidden(k7_margrel1,A) => k11_margrel1(A) = k8_margrel1 ) & ( r2_hidden(k7_margrel1,A) => k11_margrel1(A) = k7_margrel1 ) ) )).
fof(d15_matroid0,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v5_matroid0(B,A) <=> ( ~ v3_pre_topc(B,A) & ! [C] : ( 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) ) ) ) ) ) ) )).
fof(d15_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => k18_member_1(A,B) = k10_member_1(k1_tarski(B),A) ) ) )).
fof(d15_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( v3_membered(B) => ( A = B <=> ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) <=> r2_hidden(C,B) ) ) ) ) ) )).
fof(d15_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( 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))) ) ) ) ) )).
fof(d15_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( v1_prob_2(D) & m2_finseq_1(D,B) ) => ! [E] : ( 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] : ( v7_ordinal1(F) => ( r2_hidden(F,k4_finseq_1(D)) => ! [G] : ( r2_hidden(G,k1_funct_1(D,F)) => k1_funct_1(C,G) = k1_funct_1(E,F) ) ) ) ) ) ) ) ) ) ) )).
fof(d15_mesfunc1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_valued_0(A) ) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( C = k10_relat_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,k9_xtuple_0(A)) & k12_supinf_2(A,D) = B ) ) ) ) ) )).
fof(d15_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( v6_supinf_2(D) => ( ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ~ ( E = k1_relset_1(A,D) & r1_mesfunc1(A,B,D,E) ) ) | ! [E] : ( m1_subset_1(E,k6_numbers) => ( E = k6_mesfunc5(A,B,C,D) <=> ? [F] : ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) & ? [G] : ( v1_funct_1(G) & v1_funct_2(G,k4_ordinal1,k6_numbers) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) & ! [H] : ( v7_ordinal1(H) => ( r1_mesfunc2(A,B,k4_mesfunc5(A,k6_numbers,F,H)) & k1_relset_1(A,k4_mesfunc5(A,k6_numbers,F,H)) = k1_relset_1(A,D) ) ) & ! [H] : ( v7_ordinal1(H) => v6_supinf_2(k4_mesfunc5(A,k6_numbers,F,H)) ) & ! [H] : ( v7_ordinal1(H) => ! [I] : ( v7_ordinal1(I) => ( r1_xxreal_0(H,I) => ! [J] : ( m1_subset_1(J,A) => ( r2_hidden(J,k1_relset_1(A,D)) => r1_xxreal_0(k12_supinf_2(k4_mesfunc5(A,k6_numbers,F,H),J),k12_supinf_2(k4_mesfunc5(A,k6_numbers,F,I),J)) ) ) ) ) ) & ! [H] : ( 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] : ( v7_ordinal1(H) => k9_nat_1(k6_numbers,G,H) = k5_mesfunc5(A,B,C,k4_mesfunc5(A,k6_numbers,F,H)) ) & v10_mesfunc5(G) & E = k2_mesfunc5(G) ) ) ) ) ) ) ) ) ) ) )).
fof(d15_metric_1,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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_1_metric_1(A,B,C) ) ) & ( v2_struct_0(A) => ( D = k9_metric_1(A,B,C) <=> v1_xboole_0(D) ) ) ) ) ) ) ) )).
fof(d15_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(d15_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( ( v4_midsp_2(B,A) & l1_midsp_2(B,A) ) => k11_midsp_2(A,B) = k4_struct_0(u1_midsp_2(A,B)) ) ) )).
fof(d15_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( C = k18_mmlquery(A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => k2_mmlquery(A,C,D) = k3_tarski(a_3_2_mmlquery(A,B,D)) ) ) ) ) )).
fof(d15_mod_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k1_enumset1(k5_numbers,1,2),k1_enumset1(k5_numbers,1,2)),k1_enumset1(k5_numbers,1,2)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_enumset1(k5_numbers,1,2),k1_enumset1(k5_numbers,1,2)),k1_enumset1(k5_numbers,1,2)))) ) => ( A = k13_mod_2 <=> ! [B] : ( m1_subset_1(B,k1_enumset1(k5_numbers,1,2)) => ! [C] : ( m1_subset_1(C,k1_enumset1(k5_numbers,1,2)) => k5_binop_1(k1_enumset1(k5_numbers,1,2),A,B,C) = k11_mod_2(B,C) ) ) ) ) )).
fof(d15_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(d15_modal_1,axiom,( k17_modal_1 = k8_funcop_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k2_trees_1(k5_numbers),k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers)) )).
fof(d15_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v3_modelc_1(A) <=> ? [B] : ( v1_modelc_1(B) & m2_finseq_1(B,k4_ordinal1) & A = k7_modelc_1(B) ) ) ) )).
fof(d15_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v6_modelc_2(A) <=> ? [B] : ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) & A = k6_modelc_2(B) ) ) ) )).
fof(d15_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v12_monoid_0(A) <=> v4_monoid_0(u2_algstr_0(A),u1_struct_0(A)) ) ) )).
fof(d15_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_funct_1(k8_msafree(A,B),C))) => ( D = k12_msafree(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ? [F] : ( r2_hidden(F,k1_funct_1(B,C)) & E = k1_trees_4(k4_tarski(F,C)) ) ) ) ) ) ) ) )).
fof(d15_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(d15_msualg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d15_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msualg_4(C,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,B)) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(d15_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m4_nattra_1(C,A,B) => ( C = k8_nattra_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( m2_cat_1(E,A,B) & ? [F] : ( m2_cat_1(F,A,B) & ? [G] : ( m2_nattra_1(G,A,B,E,F) & D = k4_tarski(k4_tarski(E,F),G) & r2_nattra_1(A,B,E,F) ) ) ) ) ) ) ) ) )).
fof(d15_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_numbers))) ) => ! [C] : ( r11_ncfcont1(A,B,C) <=> ( r1_tarski(C,k1_relset_1(u1_struct_0(A),B)) & ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d15_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : k12_net_1(A,B) = k3_tarski(k10_net_1(A,B)) ) )).
fof(d15_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r9_orders_1(A,B) <=> ( r2_hidden(B,k1_relat_1(A)) & ! [C] : ( r2_hidden(C,k1_relat_1(A)) => ( C = B | r2_hidden(k4_tarski(B,C),A) ) ) ) ) ) )).
fof(d15_ordinal1,axiom,( ! [A] : ( v1_relat_1(A) => ( v9_ordinal1(A) <=> ~ r2_hidden(k5_ordinal1,k10_xtuple_0(A)) ) ) )).
fof(d15_ordinal6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( 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,k5_numbers) = k6_ordinal6(A,k4_ordinal1) & ! [C] : ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(d15_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ~ v1_xboole_0(B) => k3_osalg_1(A,B) = k7_funcop_1(u1_struct_0(A),B) ) ) )).
fof(d15_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( m2_subset_1(D,k14_msualg_2(A,B),k13_osalg_2(A,B)) => ! [E] : ( m2_subset_1(E,k14_msualg_2(A,B),k13_osalg_2(A,B)) => ! [F] : ( ( v3_msualg_1(F,A) & v12_osalg_1(F,A) & m1_msualg_2(F,A,B) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d15_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( m2_pboole(D,A,B,C) <=> ! [E] : ( 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)))) ) ) ) ) ) ) )).
fof(d15_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(d15_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r6_pdiff_5(A,B) => ! [C] : ( v1_xreal_0(C) => ( C = k6_pdiff_5(A,B) <=> ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & B = k11_finseq_1(D,E,F) & ? [G] : ( 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] : ( v1_funct_1(H) & v3_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [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_funct_1(H,1) & ! [J] : ( v1_xreal_0(J) => ( r2_hidden(J,G) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,3,k1_pdiff_3(2,3,A),B),J),k1_funct_1(k1_pdiff_2(3,3,k1_pdiff_3(2,3,A),B),F)) = k2_xcmplx_0(k1_funct_1(H,k6_xcmplx_0(J,F)),k1_funct_1(I,k6_xcmplx_0(J,F))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d15_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => k18_polyform(A,B) = k1_zfmisc_1(k8_polyform(A,B)) ) ) )).
fof(d15_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( m2_finseq_1(C,k15_pre_poly(A)) => ( C = k20_pre_poly(A,B) <=> ? [D] : ( ~ 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(d15_pscomp_1,axiom,( ! [A] : ( 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) ) )).
fof(d15_pua2mss1,axiom,( ! [A] : ( ( v2_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( l3_msualg_1(C,B) => ! [D] : ( 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] : ( m2_subset_1(E,k4_ordinal1,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)) ) ) ) ) ) ) ) )).
fof(d15_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => k13_qc_lang1(A,B) = k7_finseq_1(k9_finseq_1(k4_tarski(1,k5_numbers)),k11_qc_lang1(A,B)) ) ) )).
fof(d15_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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))) ) ) )).
fof(d15_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_quantal1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_quantal1(A,B,C) = k15_lattice3(A,a_3_6_quantal1(A,B,C)) ) ) ) )).
fof(d15_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( ( r2_hidden(A,k2_numbers) => ( B = k15_quaterni(A) <=> B = k5_numbers ) ) & ( ~ r2_hidden(A,k2_numbers) => ( B = k15_quaterni(A) <=> ? [C] : ( 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_funct_1(C,2) ) ) ) ) ) )).
fof(d15_quofield,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( 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) ) ) ) ) )).
fof(d15_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( m1_ratfunc1(B,A) => ! [C] : ( 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))) ) ) ) )).
fof(d15_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : k10_relat_1(A,B) = k8_relat_1(A,k1_tarski(B)) ) )).
fof(d15_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ( v7_relat_2(A) <=> r7_relat_2(A,k1_relat_1(A)) ) ) )).
fof(d15_ringcat1,axiom,( ! [A] : ! [B] : ( r2_ringcat1(A,B) <=> ? [C] : ? [D] : ? [E] : ? [F] : ? [G] : ? [H] : ( A = k3_xtuple_0(k6_xtuple_0(C,D,E,F),G,H) & ? [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) ) ) ) )).
fof(d15_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k11_rlvect_2(A)) => k12_rlvect_2(A,B) = B ) ) )).
fof(d15_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(d15_rvsum_1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => k21_rvsum_1(A) = k1_finsop_1(k1_numbers,A,k11_binop_2) ) )).
fof(d15_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_scmfsa_2(C) => k15_scmfsa_2(A,B,C) = k3_xtuple_0(10,k1_xboole_0,k11_finseq_1(A,C,B)) ) ) ) )).
fof(d15_scmpds_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ! [C] : ( v1_int_1(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(d15_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v6_scmyciel(A) ) => ! [B] : ( v7_ordinal1(B) => ( B = k8_scmyciel(A) <=> ( ? [C] : ( v1_finset_1(C) & v4_scmyciel(C) & v5_scmyciel(C) & m1_subset_1(C,k1_zfmisc_1(A)) & k2_scmyciel(C) = B ) & ! [C] : ( ( 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) ) ) ) ) ) )).
fof(d15_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k12_seq_4(A))) => ( v2_seq_4(B,A) <=> ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( m2_finseq_2(E,k2_numbers,k12_seq_4(A)) => ~ ( ~ r1_xxreal_0(D,k20_seq_4(E)) & r2_hidden(k13_seq_4(A,C,E),B) ) ) ) ) => r2_hidden(C,B) ) ) ) ) ) )).
fof(d15_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_sheffer1(A) ) => ( v12_sheffer1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d15_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => k14_sin_cos(A) = k1_funct_1(k13_sin_cos,A) ) )).
fof(d15_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( r2_stacks_1(A,B,C) => B = C ) ) ) ) ) )).
fof(d15_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k15_substut1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( m1_subset_1(D,k9_qc_lang1(A)) & ? [E] : ( m1_subset_1(E,k1_substut1(A)) & ? [F] : ( C = k4_tarski(k1_domain_1(k9_qc_lang1(A),k1_substut1(A),D,E),F) & r1_substut1(A,D,E,F) ) ) ) ) ) ) ) )).
fof(d15_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( B = k18_supinf_2(A) <=> ! [C] : ( m1_supinf_2(C,k17_supinf_2(A)) => ( r2_funct_2(k4_ordinal1,k6_numbers,C,A) => r2_funct_2(k4_ordinal1,k6_numbers,B,k15_supinf_2(k17_supinf_2(A),C)) ) ) ) ) ) )).
fof(d15_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(d15_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v4_trees_3(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ( B = k11_trees_3(A) <=> ! [C] : ( r2_hidden(C,B) <=> ~ ( C != k1_xboole_0 & ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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,k1_nat_1(D,1))) & C = k7_finseq_1(k9_finseq_1(D),E) ) ) ) ) ) ) ) ) ) )).
fof(d15_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r3_turing_1(A,B) <=> ! [C] : ( m1_subset_1(C,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k9_funct_2(k4_numbers,u1_turing_1(A)))) => ! [D] : ( m2_funct_2(D,k4_numbers,u1_turing_1(A),k9_funct_2(k4_numbers,u1_turing_1(A))) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m2_finseq_1(F,k4_ordinal1) => ( ( r2_hidden(F,k9_xtuple_0(B)) & C = k4_domain_1(u2_turing_1(A),k4_ordinal1,k9_funct_2(k4_numbers,u1_turing_1(A)),u4_turing_1(A),E,D) & r2_turing_1(k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,E),F),A,D) ) => ( v2_turing_1(C,A) & ? [G] : ( m1_subset_1(G,k4_ordinal1) & ? [H] : ( m1_subset_1(H,k4_ordinal1) & 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(k4_ordinal1,k12_finseq_1(k4_ordinal1,G),k12_finseq_1(k4_ordinal1,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))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d15_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k1_funct_1(A,k10_finseq_1(B,C)) = k2_binarith(k9_margrel1(B),k9_margrel1(C)) ) ) ) ) )).
fof(d15_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k9_unialg_2(A)) => ! [D] : ( m1_subset_1(D,k9_unialg_2(A)) => ! [E] : ( ( v1_unialg_1(E) & m1_unialg_2(E,A) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(d15_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_valued_0(A) ) => ( v10_valued_0(A) <=> k1_funct_1(A,k1_xboole_0) = k5_numbers ) ) )).
fof(d15_valued_2,axiom,( ! [A] : ! [B] : ( B = k9_valued_2(A) <=> ! [C] : ( 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))) ) ) ) )).
fof(d15_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ( v9_vectsp_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d15_waybel34,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => r4_waybel_0(A,B,C,D) ) ) ) ) ) )).
fof(d15_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k3_waybel_0(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,C) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r1_orders_2(A,D,E) & r2_hidden(E,B) ) ) ) ) ) ) ) )).
fof(d15_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(d15_waybel_4,axiom,( ! [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] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k8_waybel_4(A)),u1_struct_0(k1_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(k1_yellow_1(k3_waybel_4(A)))))) ) => ( B = k10_waybel_4(A) <=> ! [C] : ~ ( r2_hidden(C,u1_struct_0(k8_waybel_4(A))) & ! [D] : ( ( 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] : ! [F] : ( r2_hidden(k4_tarski(E,F),D) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & ? [I] : ( v1_funct_1(I) & v1_funct_2(I,u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k1_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(k1_yellow_1(k7_waybel_0(A))),I,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(d15_xtuple_0,axiom,( ! [A] : k12_xtuple_0(A) = k10_xtuple_0(k9_xtuple_0(A)) )).
fof(d15_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( 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 ) ) ) ) )).
fof(d15_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k10_yellow_6(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,C) <=> ! [E] : ( m1_connsp_2(E,A,D) => r1_waybel_0(A,B,E) ) ) ) ) ) ) ) )).
fof(d15_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v7_zf_lang(A) <=> ( v2_zf_lang(A) | v3_zf_lang(A) ) ) ) )).
fof(d15_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(d15_zmodul02,axiom,( ! [A] : ( ( ~ 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) ) => k15_zmodul02(A) = g1_vectsp_1(k1_int_3,u1_struct_0(A),u1_algstr_0(A),u2_struct_0(A),k14_zmodul02(A)) ) )).
fof(d16_abcmiz_0,axiom,( ! [A] : ( l2_abcmiz_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A))) => ( r2_abcmiz_0(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r1_tarski(C,k2_abcmiz_0(A,D)) & r1_orders_2(A,D,B) ) ) ) ) ) )).
fof(d16_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => k15_abcmiz_1(A) = k10_abcmiz_1 ) )).
fof(d16_abcmiz_a,axiom,( ! [A] : ( m1_subset_1(A,k20_abcmiz_1) => k13_abcmiz_a(A) = A ) )).
fof(d16_algstr_0,axiom,( ! [A] : ( l2_algstr_0(A) => ( v13_algstr_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v10_algstr_0(B,A) ) ) ) )).
fof(d16_algstr_4,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,k12_algstr_4(A)) => ! [D] : ( m1_subset_1(D,k12_algstr_4(A)) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( 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 ) ) ) ) )).
fof(d16_altcat_1,axiom,( ! [A] : ( ( ~ 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)) ) ) ) )).
fof(d16_aofa_000,axiom,( ! [A] : ( ( v4_unialg_1(A) & v3_aofa_000(A) & l1_unialg_1(A) ) => k12_aofa_000(A) = k1_funct_1(k2_pua2mss1(A,k10_subset_1(1,k4_finseq_1(u1_unialg_1(A)))),k1_xboole_0) ) )).
fof(d16_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_aofa_a01(D,A,B,C) & l4_aofa_a00(D,A,B,C) ) => ! [E] : ( ( v19_aofa_a00(E,A) & m1_subset_1(E,u1_struct_0(A)) ) => ! [F] : ( ( v3_aofa_a01(F,A,B,C,u4_aofa_a00(A,B,C,D),k37_aofa_a00(A)) & m1_msafree4(F,u1_struct_0(A),u4_aofa_a00(A,B,C,D),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),k37_aofa_a00(A))) ) => ! [G] : ( v1_int_1(G) => k11_aofa_a01(A,B,C,D,E,F,G) = k39_aofa_a00(A,C,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,D),k37_aofa_a00(A),F),E,k10_aofa_a01(A,B,C,E,G)) ) ) ) ) ) ) ) )).
fof(d16_aofa_i00,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) => ( ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r1_aofa_i00(A,E,B,C,D) ) => ! [E] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d16_armstrng,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(d16_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v7_ordinal1(B) => ( r2_asympt_0(A,B) <=> ( v6_asympt_0(A) & r2_hidden(k12_asympt_0(A,B),k6_asympt_0(A)) ) ) ) ) )).
fof(d16_bagorder,axiom,( ! [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) ) => k14_bagorder(A) = g1_orders_2(k5_finsub_1(u1_struct_0(A)),k13_bagorder(A)) ) )).
fof(d16_bcialg_1,axiom,( ! [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) ) => ( v11_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m2_subset_1(C,u1_struct_0(A),k5_bcialg_1(A)) & r1_bcialg_1(A,C,B) ) ) ) ) )).
fof(d16_bcialg_2,axiom,( ! [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) ) => k6_bcialg_2(A) = a_1_2_bcialg_2(A) ) )).
fof(d16_bilinear,axiom,( ! [A] : ( l2_struct_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(d16_binop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(d16_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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 ) ) ) ) ) ) )).
fof(d16_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( ( 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] : ( m1_subset_1(E,A) => ( ( ! [F] : ( 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] : ( 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 ) ) ) ) ) ) ) ) )).
fof(d16_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => k9_c0sp1(A,B) = a_2_0_c0sp1(A,B) ) ) )).
fof(d16_calcul_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r1_calcul_1(A,B) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & r2_hidden(C,k1_relset_1(k4_ordinal1,A)) & k1_funct_1(A,C) = B ) ) ) )).
fof(d16_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k12_card_3(A,B) <=> ( k9_xtuple_0(C) = k4_card_3(A) & ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(d16_card_fil,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ( v7_card_fil(A) <=> ? [B] : ( m1_card_fil(B,A) & r1_card_fil(A,A,B) & ~ v2_card_fil(B,A) & v3_card_fil(B,A) ) ) ) )).
fof(d16_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v10_cat_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_cat_1(A,C,B) != k1_xboole_0 & ? [D] : ( m1_cat_1(D,A,C,B) & ! [E] : ( m1_cat_1(E,A,C,B) => D = E ) ) ) ) ) ) ) )).
fof(d16_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ! [D] : ( ( 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)) ) ) ) ) )).
fof(d16_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( 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)) ) ) )).
fof(d16_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ( v6_cgames_1(A) <=> v5_cgames_1(k13_cgames_1(A)) ) ) )).
fof(d16_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_chain_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ 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] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k4_chain_1(A,B,C))) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d16_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k1_msaterm(A,C))) ) => ! [E] : ( ( ~ v2_struct_0(E) & ~ v11_struct_0(E) & v2_msafree2(E) & l1_msualg_1(E) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(d16_clvect_1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v9_clvect_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k7_clvect_1(A,B) <=> ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(E,F) & r1_xxreal_0(D,k2_normsp_0(A,k5_algstr_0(A,k1_normsp_1(A,B,F),C))) ) ) ) ) ) ) ) ) ) )).
fof(d16_coh_sp,axiom,( ! [A] : k15_coh_sp(A) = k3_tarski(a_1_3_coh_sp(A)) )).
fof(d16_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k5_cohsp_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( v1_finset_1(D) & ? [E] : ( C = k4_tarski(D,E) & r2_hidden(D,k9_xtuple_0(A)) & r2_hidden(E,k1_funct_1(A,D)) ) ) ) ) ) )).
fof(d16_comput_1,axiom,( ! [A] : ( v7_comput_1(A) <=> r2_hidden(A,k9_comput_1) ) )).
fof(d16_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => k7_conlat_1(A) = a_1_0_conlat_1(A) ) )).
fof(d16_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( ( 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] : ( v1_xcmplx_0(C) => ! [D] : ( m1_subset_1(D,k10_convex4(A)) => k1_funct_1(B,k4_tarski(C,D)) = k7_convex4(A,C,k11_convex4(A,D)) ) ) ) ) ) )).
fof(d16_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k14_csspace(A,B,C) = k13_csspace(A,k5_algstr_0(A,B,C)) ) ) ) )).
fof(d16_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k11_decomp_1(A) = a_1_5_decomp_1(A) ) )).
fof(d16_descip_1,axiom,( ! [A] : ( m2_finseq_2(A,k6_margrel1,k4_finseq_2(64,k6_margrel1)) => ! [B] : ( 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) ) ) ) ) )).
fof(d16_e_siec,axiom,( ! [A] : ( ( 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))) ) )).
fof(d16_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u4_struct_0(k11_ens_1(A))) => k15_ens_1(A,B) = B ) ) )).
fof(d16_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : 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))) )).
fof(d16_ff_siec,axiom,( ! [A] : ( ( 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))) ) )).
fof(d16_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_fin_topo(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d16_finseq_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( B = k18_finseq_1(A) <=> ! [C] : ! [D] : ( r2_hidden(k4_tarski(C,D),B) <=> ( r2_hidden(C,k1_relat_1(A)) & r2_hidden(D,k1_relat_1(A)) & ? [E] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d16_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_fintopo2(B,A) <=> B = k10_fintopo2(A,B) ) ) ) )).
fof(d16_fomodel0,axiom,( ! [A] : ! [B] : k14_fomodel0(A,B) = k6_subset_1(A,B) )).
fof(d16_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( 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)),k15_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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),k6_margrel1)) => ! [D] : ( ( 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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),k6_margrel1))) ) => ( D = k18_fomodel2(A,B,C) <=> ( ! [E] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(A),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_fomodel2(A,B)) => ! [F] : ( 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(k15_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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),D)) <=> ? [G] : ( v4_fomodel1(G,A) & m1_subset_1(G,k1_fomodel1(A)) & ? [H] : ( 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(k15_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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),C)) & F = k42_fomodel1(A,k43_fomodel1(A,G),H) ) ) ) ) ) & ! [E] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(A),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_fomodel2(A,B)) => ! [F] : ( 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(k15_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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),D)) => k1_binop_1(D,E,F) = k17_fomodel2(A,B,E,C,F) ) ) ) ) ) ) ) ) ) )).
fof(d16_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) => ! [C] : k7_fomodel4(A,B,C) = a_3_0_fomodel4(A,B,C) ) ) )).
fof(d16_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k16_ftacell1(A,B,C,D,E) = k36_gfacirc1(A,B,C) )).
fof(d16_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_altcat_1(B) ) => ! [C] : ( ( v11_functor0(C,A,B) & l2_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d16_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ ( ~ 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 ) ) )).
fof(d16_gate_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : k16_gate_5(A,B,C,D,E,F,G) = k10_gate_1(E,F,k15_gate_5(A,B,C,D,G)) )).
fof(d16_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(d16_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ( 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) ) ) ) )).
fof(d16_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => k13_glib_001(A,B) = k2_relset_1(k6_glib_000(A),k11_glib_001(A,B)) ) ) )).
fof(d16_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v1_glib_005(A) ) => ! [B] : ( ( 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] : ( m3_glib_001(C,A) => ( r5_glib_005(A,B,C) => ! [D] : ( v7_ordinal1(D) => ( ( ~ v3_glib_001(C,A) => ( D = k9_glib_005(A,B,C) <=> ( r2_hidden(D,k2_relset_1(k4_ordinal1,k8_glib_005(A,B,C))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k2_relset_1(k4_ordinal1,k8_glib_005(A,B,C))) => r1_xxreal_0(D,E) ) ) ) ) ) & ( v3_glib_001(C,A) => ( D = k9_glib_005(A,B,C) <=> D = k5_numbers ) ) ) ) ) ) ) ) )).
fof(d16_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_graph_1(B,A) => ( v2_funct_1(B) <=> ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( 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) ) ) ) ) ) ) )).
fof(d16_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u4_struct_0(A)) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => k10_graph_5(A,B,C) = k18_rvsum_1(k9_graph_5(A,B,C)) ) ) ) )).
fof(d16_graphsp,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_graphsp(A,B,C,D) <=> ( k4_finseq_1(A) = k4_finseq_1(B) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r2_hidden(E,k4_finseq_1(A)) & r1_xxreal_0(C,E) & r1_xxreal_0(E,D) ) => k1_funct_1(A,E) = k1_funct_1(B,E) ) ) ) ) ) ) ) ) )).
fof(d16_grcat_1,axiom,( ! [A] : ( v4_grcat_1(A) <=> ! [B] : ( r2_hidden(B,A) => ( v1_grcat_1(B) & v2_grcat_1(B) & l1_grcat_1(B) ) ) ) )).
fof(d16_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( C = k16_group_2(A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(D,C) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & D = k14_group_2(A,B,E) ) ) ) ) ) ) ) )).
fof(d16_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v4_group_9(C,A,B) & m1_group_9(C,A,B) ) => ! [D] : ( ( 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] : ( 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)))) ) ) ) ) ) ) )).
fof(d16_idea_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( ( 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] : ( m2_finseq_1(D,k4_ordinal1) => k1_funct_1(C,D) = k12_idea_1(A,k11_idea_1(A,k13_idea_1(D),B),B) ) ) ) ) ) )).
fof(d16_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) ) ) ) )).
fof(d16_incsp_1,axiom,( ! [A] : ( l2_incsp_1(A) => ( v13_incsp_1(A) <=> ~ ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => v4_incsp_1(k9_domain_1(u1_incsp_1(A),B,C,D,E),A) ) ) ) ) ) ) )).
fof(d16_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( 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] : ( 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] : ( 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)))) ) ) ) ) ) ) ) ) ) ) )).
fof(d16_integr15,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k4_ordinal1) => ( 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))) ) ) ) ) ) ) )).
fof(d16_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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) ) ) )).
fof(d16_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m2_interva1(B,A) => k15_interva1(A,B) = k2_xtuple_0(B) ) ) )).
fof(d16_intpro_1,axiom,( k8_intpro_1 = k7_intpro_1(k1_subset_1(k1_intpro_1)) )).
fof(d16_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( r3_lattice3(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,C) => r1_lattices(A,B,D) ) ) ) ) ) )).
fof(d16_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => k6_lattice6(A) = a_1_1_lattice6(A) ) )).
fof(d16_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lattices(A) ) => ( v13_lattices(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B = k5_lattices(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_lattices(A,B,C) = B & k2_lattices(A,C,B) = B ) ) ) ) ) ) )).
fof(d16_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m2_lexbfs(B,A) => ( B = k16_lexbfs(A) <=> ( k13_lexbfs(A,B,k5_numbers) = k9_lexbfs(A) & ! [C] : ( v7_ordinal1(C) => k13_lexbfs(A,B,k1_nat_1(C,1)) = k12_lexbfs(A,k13_lexbfs(A,B,C)) ) ) ) ) ) )).
fof(d16_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(k18_lpspacc1(A,B,C),k18_lpspacc1(A,B,C)),k18_lpspacc1(A,B,C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k18_lpspacc1(A,B,C),k18_lpspacc1(A,B,C)),k18_lpspacc1(A,B,C)))) ) => ( D = k19_lpspacc1(A,B,C) <=> ! [E] : ( m2_subset_1(E,k1_zfmisc_1(k13_lpspacc1(A,B,C)),k18_lpspacc1(A,B,C)) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(k13_lpspacc1(A,B,C)),k18_lpspacc1(A,B,C)) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( ( r2_hidden(G,E) & r2_hidden(H,F) ) => k5_binop_1(k18_lpspacc1(A,B,C),D,E,F) = k17_lpspacc1(A,B,C,k2_valued_1(A,k2_numbers,k2_numbers,G,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(d16_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(k9_lpspace1(A,B,C)),k14_lpspace1(A,B,C)) => ( D = k16_lpspace1(A,B,C) <=> ? [E] : ( 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,k5_numbers)) & r2_hidden(E,k9_lpspace1(A,B,C)) & D = k13_lpspace1(A,B,C,E) ) ) ) ) ) ) )).
fof(d16_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( v1_ltlaxio1(A) <=> ! [B] : ( ( 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 ) ) ) )).
fof(d16_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => k19_member_1(A,B) = k11_member_1(k1_tarski(B),A) ) ) )).
fof(d16_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( v2_memstr_0(B,A) & l1_memstr_0(B,A) ) => k11_memstr_0(A,B) = a_2_0_memstr_0(A,B) ) ) )).
fof(d16_mesfunc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( r1_mesfunc1(A,B,C,D) <=> ! [E] : ( v1_xreal_0(E) => r2_hidden(k9_subset_1(A,D,k15_mesfunc1(A,C,E)),B) ) ) ) ) ) ) )).
fof(d16_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_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))) ) ) ) ) )).
fof(d16_metric_1,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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_2_metric_1(A,B,C) ) ) & ( v2_struct_0(A) => ( D = k10_metric_1(A,B,C) <=> v1_xboole_0(D) ) ) ) ) ) ) ) )).
fof(d16_metric_3,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,k1_numbers) => ! [E] : ( m1_subset_1(E,k1_numbers) => ! [F] : ( m1_subset_1(F,k2_zfmisc_1(k1_numbers,k1_numbers)) => ! [G] : ( 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) ) => k2_binop_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers,A,F,G) = k3_real_1(k5_binop_1(k1_numbers,k6_metric_1,B,C),k5_binop_1(k1_numbers,k6_metric_1,D,E)) ) ) ) ) ) ) ) ) ) )).
fof(d16_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => k14_midsp_1(A) = k6_midsp_1(A) ) )).
fof(d16_mod_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k1_enumset1(k5_numbers,1,2),k1_enumset1(k5_numbers,1,2)),k1_enumset1(k5_numbers,1,2)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_enumset1(k5_numbers,1,2),k1_enumset1(k5_numbers,1,2)),k1_enumset1(k5_numbers,1,2)))) ) => ( A = k14_mod_2 <=> ! [B] : ( m1_subset_1(B,k1_enumset1(k5_numbers,1,2)) => ! [C] : ( m1_subset_1(C,k1_enumset1(k5_numbers,1,2)) => k5_binop_1(k1_enumset1(k5_numbers,1,2),A,B,C) = k12_mod_2(B,C) ) ) ) ) )).
fof(d16_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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 ) ) ) )).
fof(d16_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v4_modelc_1(A) <=> ? [B] : ( v1_modelc_1(B) & m2_finseq_1(B,k4_ordinal1) & ? [C] : ( v1_modelc_1(C) & m2_finseq_1(C,k4_ordinal1) & A = k8_modelc_1(B,C) ) ) ) ) )).
fof(d16_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v7_modelc_2(A) <=> ? [B] : ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) & ? [C] : ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) & A = k7_modelc_2(B,C) ) ) ) ) )).
fof(d16_modelc_3,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( ( ( 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)) ) ) ) )).
fof(d16_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v13_monoid_0(A) <=> v5_monoid_0(u2_algstr_0(A),u1_struct_0(A)) ) ) )).
fof(d16_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_msafree(C,A,k11_msafree(A,B)) => ( C = k13_msafree(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_funct_1(C,D) = k12_msafree(A,B,D) ) ) ) ) ) )).
fof(d16_msafree4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v9_msafree4(C,A,B) & v10_msafree4(C,A,B) & m1_msualg_4(C,A,B,B) ) => ! [D] : ( ( v2_relat_1(D) & m3_pboole(D,A,B) ) => ( D = k9_msafree4(A,B,C) <=> ! [E] : ( m1_subset_1(E,A) => k1_msafree4(A,D,E) = a_4_0_msafree4(A,B,C,E) ) ) ) ) ) ) )).
fof(d16_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_msualg_2(C,A,B) => ! [D] : ( m1_msualg_2(D,A,B) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d16_msualg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d16_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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 = k9_nattra_1(A,B) <=> ( u1_struct_0(C) = k4_cat_2(A,B) & u4_struct_0(C) = k8_nattra_1(A,B) & ! [D] : ( 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] : ( m1_subset_1(D,u4_struct_0(C)) => ! [E] : ( m1_subset_1(E,u4_struct_0(C)) => ( k3_graph_1(C,E) = k4_graph_1(C,D) => r2_hidden(k8_cat_2(C,C,E,D),k9_xtuple_0(u1_cat_1(C))) ) ) ) & ! [D] : ( m1_subset_1(D,u4_struct_0(C)) => ! [E] : ( m1_subset_1(E,u4_struct_0(C)) => ~ ( r2_hidden(k8_cat_2(C,C,E,D),k9_xtuple_0(u1_cat_1(C))) & ! [F] : ( m2_cat_1(F,A,B) => ! [G] : ( m2_cat_1(G,A,B) => ! [H] : ( m2_cat_1(H,A,B) => ! [I] : ( m2_nattra_1(I,A,B,F,G) => ! [J] : ( 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),k8_cat_2(C,C,E,D)) = k4_tarski(k4_tarski(F,H),k5_nattra_1(A,B,F,G,H,I,J)) ) ) ) ) ) ) ) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m2_cat_1(E,A,B) => ( E = D => k4_cat_1(C,D) = k4_tarski(k4_tarski(E,E),k4_nattra_1(A,B,E)) ) ) ) ) ) ) ) ) )).
fof(d16_ncfcont1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k2_numbers))) ) => ! [C] : ( r12_ncfcont1(A,B,C) <=> ( r1_tarski(C,k1_relset_1(u1_struct_0(A),B)) & ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d16_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : k13_net_1(A,B) = k3_tarski(k11_net_1(A,B)) ) )).
fof(d16_oposet_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_qmax_1(A) ) => ( v8_oposet_1(A) <=> ( v2_necklace(A) & v4_orders_2(A) ) ) ) )).
fof(d16_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( 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) ) ) )).
fof(d16_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d16_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( m2_subset_1(D,k14_msualg_2(A,B),k13_osalg_2(A,B)) => ! [E] : ( m2_subset_1(E,k14_msualg_2(A,B),k13_osalg_2(A,B)) => ! [F] : ( ( v3_msualg_1(F,A) & v12_osalg_1(F,A) & m1_msualg_2(F,A,B) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d16_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( D = k6_pboole(A,B,C) <=> ! [E] : ( r2_hidden(E,A) => k1_funct_1(D,E) = k2_zfmisc_1(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) )).
fof(d16_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k4_real_ns1(A))) => k12_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)) ) ) ) ) ) ) )).
fof(d16_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r7_pdiff_5(A,B) => ! [C] : ( v1_xreal_0(C) => ( C = k7_pdiff_5(A,B) <=> ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & B = k11_finseq_1(D,E,F) & ? [G] : ( 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] : ( v1_funct_1(H) & v3_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [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_funct_1(H,1) & ! [J] : ( v1_xreal_0(J) => ( r2_hidden(J,G) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,1,k1_pdiff_3(3,3,A),B),J),k1_funct_1(k1_pdiff_2(3,1,k1_pdiff_3(3,3,A),B),D)) = k2_xcmplx_0(k1_funct_1(H,k6_xcmplx_0(J,D)),k1_funct_1(I,k6_xcmplx_0(J,D))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d16_pencil_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v13_pencil_1(A) <=> ! [B] : ( r2_hidden(B,k10_xtuple_0(A)) => v1_zfmisc_1(B) ) ) ) )).
fof(d16_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k11_petri(A))) => k15_petri(A,B) = B ) ) )).
fof(d16_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,k8_polyform(A,k6_xcmplx_0(B,1))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k17_polyform(A,B))) => ! [E] : ( 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] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d16_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( 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] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( 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),k4_ordinal1,k4_finseq_2(2,k15_pre_poly(A)),C,D) = k10_finseq_1(E,k12_pre_poly(A,B,E)) ) ) ) ) ) ) ) ) )).
fof(d16_pscomp_1,axiom,( ! [A] : ( 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) ) )).
fof(d16_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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,k5_numbers)),k11_qc_lang1(A,B)),k11_qc_lang1(A,C)) ) ) ) )).
fof(d16_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => k12_qc_lang2(A,B) = k19_qc_lang1(A,k18_qc_lang1(A,B)) ) ) )).
fof(d16_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_quantal1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_quantal1(A,B,C) = k15_lattice3(A,a_3_7_quantal1(A,B,C)) ) ) ) )).
fof(d16_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( ( r2_hidden(A,k2_numbers) => ( B = k16_quaterni(A) <=> B = k5_numbers ) ) & ( ~ r2_hidden(A,k2_numbers) => ( B = k16_quaterni(A) <=> ? [C] : ( 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_funct_1(C,3) ) ) ) ) ) )).
fof(d16_quofield,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d16_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( m1_ratfunc1(B,A) => ! [C] : ( 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))) ) ) ) )).
fof(d16_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( v4_relat_1(B,A) <=> r1_tarski(k9_xtuple_0(B),A) ) ) )).
fof(d16_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ( v8_relat_2(A) <=> r8_relat_2(A,k1_relat_1(A)) ) ) )).
fof(d16_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_rewrite1(A) <=> ! [B] : ~ ( r1_tarski(B,k1_relat_1(A)) & B != k1_xboole_0 & ! [C] : ~ ( r2_hidden(C,B) & ! [D] : ~ ( r2_hidden(D,B) & C != D & r2_hidden(k4_tarski(C,D),A) ) ) ) ) ) )).
fof(d16_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( B = k9_ringcat1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(D,A) & r2_ringcat1(D,C) ) ) ) ) )).
fof(d16_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => k13_rlvect_2(A,B) = B ) ) )).
fof(d16_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k11_robbins1(A,B) = k3_robbins1(A,k1_lattices(A,k3_robbins1(A,B),B)) ) ) )).
fof(d16_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(d16_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( m1_scmfsa_2(B) => k16_scmfsa_2(A,B) = k3_xtuple_0(11,k1_xboole_0,k10_finseq_1(A,B)) ) ) )).
fof(d16_scmpds_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ! [C] : ( v1_int_1(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(d16_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( m1_eqrel_1(B,k3_tarski(A)) => ( v7_scmyciel(B,A) <=> ! [C] : ( 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)) ) ) ) ) ) )).
fof(d16_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( v1_xreal_0(C) => k21_seq_4(A,B,C) = a_3_0_seq_4(A,B,C) ) ) ) )).
fof(d16_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_sheffer1(A,B) = k5_sheffer1(A,B,B) ) ) )).
fof(d16_simplex0,axiom,( ! [A] : ! [B] : ( ( v1_matroid0(B) & v3_matroid0(B) & m1_simplex0(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( ( 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 ) ) ) ) )).
fof(d16_sin_cos,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => k1_funct_1(A,B) = k4_complex1(k11_comseq_3(k3_sin_cos(k3_xcmplx_0(B,k7_complex1)))) ) ) ) )).
fof(d16_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(A),u4_struct_0(A)))) => ( B = k10_stacks_1(A) <=> ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d16_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => k7_struct_0(A) = k1_card_1(u1_struct_0(A)) ) )).
fof(d16_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v1_substut1(B,A) <=> ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k13_finseq_1(k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))),k1_substut1(A)))) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_subset_1(D,k6_qc_lang1(A),k8_qc_lang1(A,C)) => ! [E] : ( ( v3_card_1(E,C) & m2_finseq_1(E,k2_qc_lang1(A)) ) => ! [F] : ( 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] : ( m1_subset_1(C,k1_substut1(A)) => r2_hidden(k1_domain_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_zfmisc_1(k4_ordinal1,k4_ordinal1))),k1_substut1(A),k12_finseq_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers)),C),B) ) & ! [C] : ( m2_finseq_1(C,k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))) => ! [D] : ( m1_subset_1(D,k1_substut1(A)) => ( r2_hidden(k1_domain_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A)))),k1_substut1(A),C,D),B) => r2_hidden(k4_tarski(k7_finseq_1(k12_finseq_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,1,k5_numbers)),C),D),B) ) ) ) & ! [C] : ( m2_finseq_1(C,k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))) => ! [D] : ( m2_finseq_1(D,k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))) => ! [E] : ( m1_subset_1(E,k1_substut1(A)) => ( ( r2_hidden(k1_domain_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A)))),k1_substut1(A),C,E),B) & r2_hidden(k1_domain_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,2,k5_numbers)),C),D),E),B) ) ) ) ) & ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_finseq_1(D,k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))) => ! [E] : ( 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(k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,3,k5_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(k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,3,k5_numbers)),k12_finseq_1(k3_qc_lang1(A),C)),D),E),B) ) ) ) ) ) ) ) )).
fof(d16_supinf_2,axiom,( ! [A] : ( v1_relat_1(A) => ( v6_supinf_2(A) <=> v5_supinf_2(k10_xtuple_0(A)) ) ) )).
fof(d16_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v4_tex_4(B,A) <=> ( v2_tdlat_3(B) & ! [C] : ( 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) ) ) ) ) ) ) )).
fof(d16_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => k12_trees_3(A) = k11_trees_3(k9_finseq_1(A)) ) )).
fof(d16_turing_1,axiom,( 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(k4_ordinal1,k4_ordinal1,k3_turing_1(4),k7_domain_1(k4_ordinal1,k5_numbers,1)),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),k5_numbers),k2_turing_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k3_zfmisc_1(k4_ordinal1,k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers),k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,1,k5_numbers,1))),k2_turing_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k3_zfmisc_1(k4_ordinal1,k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,1,1),k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,1,1,1))),k2_turing_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k3_zfmisc_1(k4_ordinal1,k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,1,k5_numbers),k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,2,1,1))),k16_funcop_1(k1_domain_1(k4_ordinal1,k4_ordinal1,2,k5_numbers),k3_xtuple_0(3,k5_numbers,k4_xcmplx_0(1)))),k16_funcop_1(k1_domain_1(k4_ordinal1,k4_ordinal1,2,1),k3_xtuple_0(3,k5_numbers,k4_xcmplx_0(1)))),k16_funcop_1(k1_domain_1(k4_ordinal1,k4_ordinal1,3,1),k3_xtuple_0(3,1,k4_xcmplx_0(1)))),k2_turing_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k3_zfmisc_1(k4_ordinal1,k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,3,k5_numbers),k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,4,k5_numbers,k5_numbers))) )).
fof(d16_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => ! [D] : ( m1_subset_1(D,k6_margrel1) => k1_funct_1(A,k11_finseq_1(B,C,D)) = k10_margrel1(k10_margrel1(B,C),D) ) ) ) ) ) )).
fof(d16_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k9_unialg_2(A)) => ! [D] : ( m1_subset_1(D,k9_unialg_2(A)) => ! [E] : ( ( v1_unialg_1(E) & m1_unialg_2(E,A) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(d16_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( v3_funct_1(A) <=> ? [B] : ! [C] : ( v7_ordinal1(C) => k1_funct_1(A,C) = B ) ) ) )).
fof(d16_valued_2,axiom,( ! [A] : ! [B] : ( B = k10_valued_2(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_numbers))) ) ) ) )).
fof(d16_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ( v10_vectsp_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d16_waybel34,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(d16_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k4_waybel_0(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,C) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r1_orders_2(A,E,D) & r2_hidden(E,B) ) ) ) ) ) ) ) )).
fof(d16_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) )).
fof(d16_waybel_4,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))))) ) => ( C = k11_waybel_4(A,B) <=> ! [D] : ( 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(k1_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(k1_yellow_1(k7_waybel_0(A))),C,D) = k5_waybel_0(A,D) ) ) ) ) ) ) ) )).
fof(d16_xtuple_0,axiom,( ! [A] : k13_xtuple_0(A) = k9_xtuple_0(k11_xtuple_0(A)) )).
fof(d16_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v5_yellow_0(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d16_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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 ) ) ) )).
fof(d16_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => k10_zf_lang(A,B) = k6_zf_lang(k7_zf_lang(k6_zf_lang(A),k6_zf_lang(B))) ) ) )).
fof(d16_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( B = k8_zmodul01(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( v1_zmodul01(C) & m1_zmodul01(C,A) ) ) ) ) )).
fof(d16_zmodul02,axiom,( ! [A] : ( ( ~ 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_int_3) & v9_vectsp_1(A,k1_int_3) & v10_vectsp_1(A,k1_int_3) & v11_vectsp_1(A,k1_int_3) & l1_vectsp_1(A,k1_int_3) ) => k16_zmodul02(A) = u1_vectsp_1(k1_int_3,A) ) )).
fof(d17_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(d17_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => k16_abcmiz_1(A) = k9_abcmiz_1 ) )).
fof(d17_abcmiz_a,axiom,( 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))) )).
fof(d17_algstr_4,axiom,( ! [A] : k14_algstr_4(A) = g3_algstr_0(k12_algstr_4(A),k13_algstr_4(A)) )).
fof(d17_altcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_altcat_1(A,B,B)) => ( C = k8_altcat_1(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k1_altcat_1(A,B,D) != k1_xboole_0 => ! [E] : ( m1_subset_1(E,k1_altcat_1(A,B,D)) => k5_altcat_1(A,B,B,D,C,E) = E ) ) ) ) ) ) ) )).
fof(d17_aofa_000,axiom,( ! [A] : ( ( v4_unialg_1(A) & v4_aofa_000(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k13_aofa_000(A,B,C) = k1_funct_1(k2_pua2mss1(A,k10_subset_1(2,k4_finseq_1(u1_unialg_1(A)))),k2_finseq_4(u1_struct_0(A),B,C)) ) ) ) )).
fof(d17_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_aofa_a01(D,A,B,C) & l4_aofa_a00(D,A,B,C) ) => ( v7_aofa_a01(D,A,B,C) <=> ! [E] : ( ( v19_aofa_a00(E,A) & m1_subset_1(E,u1_struct_0(A)) ) => ( r1_tarski(a_5_0_aofa_a01(A,B,C,D,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),E)) & ! [F] : ( ( v3_aofa_a01(F,A,B,C,u4_aofa_a00(A,B,C,D),k37_aofa_a00(A)) & m1_msafree4(F,u1_struct_0(A),u4_aofa_a00(A,B,C,D),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),k37_aofa_a00(A))) ) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),E)) => ! [H] : ( m4_aofa_a00(H,A,B,C,D,E) => ~ ( H = k39_aofa_a00(A,C,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,D),k37_aofa_a00(A),F),E,G) & ! [I] : ( ( v3_aofa_a01(I,A,B,C,u4_aofa_a00(A,B,C,D),E) & m1_msafree4(I,u1_struct_0(A),u4_aofa_a00(A,B,C,D),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),E)) ) => ~ ( ~ r2_hidden(I,k1_msafree4(u1_struct_0(A),k11_aofa_a00(A,C,E,G),E)) & k17_aofa_a00(A,B,C,D,E,H) = I & k1_funct_1(k2_msafree4(u1_struct_0(A),k11_aofa_a00(A,C,E,H),u3_msualg_1(A,C),k18_aofa_a00(A,B,C,D,E,H),k37_aofa_a00(A)),F) = k40_aofa_a00(A,C,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,D),k37_aofa_a00(A),F),E,G,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,D),E,I)) & ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( ( v3_aofa_a01(K,A,B,C,u4_aofa_a00(A,B,C,D),E) & m1_msafree4(K,u1_struct_0(A),u4_aofa_a00(A,B,C,D),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),E)) ) => ( r2_hidden(K,k1_msafree4(u1_struct_0(A),k11_aofa_a00(A,C,E,H),J)) => ( ( J = k37_aofa_a00(A) & K = F ) | k1_funct_1(k2_msafree4(u1_struct_0(A),k11_aofa_a00(A,C,E,H),u3_msualg_1(A,C),k18_aofa_a00(A,B,C,D,E,H),J),K) = K ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d17_aofa_i00,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) => ( ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r1_aofa_i00(A,E,B,C,D) ) => ! [E] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d17_armstrng,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ! [C] : ! [D] : ( r4_armstrng(A,B,C,D) <=> r2_hidden(k4_tarski(C,D),k8_armstrng(A,B)) ) ) )).
fof(d17_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v7_asympt_0(A) <=> ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r1_xxreal_0(2,B) => r2_asympt_0(A,B) ) ) ) ) )).
fof(d17_bagorder,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v16_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ( ( v1_wellfnd1(A) & r1_tarski(B,u1_struct_0(A)) ) => ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(d17_bcialg_1,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => k7_bcialg_1(A,B) = a_2_0_bcialg_1(A,B) ) ) )).
fof(d17_bcialg_2,axiom,( ! [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] : ( m1_bcialg_2(B,A) => ! [C] : ( ( 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] : ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k8_eqrel_1(u1_struct_0(A),B)) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(u1_struct_0(A)),k8_eqrel_1(u1_struct_0(A),B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d17_bilinear,axiom,( ! [A] : ( l2_struct_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(d17_binop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d17_binop_2,axiom,( ! [A] : ( ( 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 = k17_binop_2 <=> ! [B] : ( v1_rat_1(B) => ! [C] : ( v1_rat_1(C) => k1_binop_1(A,B,C) = k3_xcmplx_0(B,C) ) ) ) ) )).
fof(d17_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ( r1_borsuk_1(A,B) <=> ? [C] : ( 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) ) ) ) ) )).
fof(d17_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( ( 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] : ( m1_subset_1(E,A) => ( ( ? [F] : ( 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] : ( 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 ) ) ) ) ) ) ) ) )).
fof(d17_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( r2_hidden(C,k6_c0sp1(A)) => k1_funct_1(B,C) = k2_seq_4(k9_c0sp1(A,k8_c0sp1(A,C))) ) ) ) ) )).
fof(d17_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v11_cat_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_cat_1(A,B,C) != k1_xboole_0 & ? [D] : ( m1_cat_1(D,A,B,C) & ! [E] : ( m1_cat_1(E,A,B,C) => D = E ) ) ) ) ) ) ) )).
fof(d17_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(G,u4_struct_0(A)) => ~ ( r2_hidden(G,k2_cat_1(A,B,E)) & ! [H] : ( m1_subset_1(H,u4_struct_0(A)) => ( r2_hidden(H,k2_cat_1(A,B,E)) => ( ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d17_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(d17_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k1_msaterm(A,B))) ) => ! [E] : ( ( ~ v2_struct_0(E) & ~ v11_struct_0(E) & v2_msafree2(E) & l1_msualg_1(E) ) => ! [F] : ( ( v4_msualg_1(F,E) & v4_msafree2(F,E) & l3_msualg_1(F,E) ) => ( r7_circtrm1(A,C,B,D,E,F) => ! [G] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d17_coh_sp,axiom,( ! [A] : k16_coh_sp(A) = a_1_4_coh_sp(A) )).
fof(d17_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k7_cohsp_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ? [E] : ( C = k4_tarski(D,E) & r2_hidden(D,k9_xtuple_0(A)) & r2_hidden(E,k1_funct_1(A,D)) & ! [F] : ( ( r2_hidden(F,k9_xtuple_0(A)) & r1_tarski(F,D) & r2_hidden(E,k1_funct_1(A,F)) ) => D = F ) ) ) ) ) )).
fof(d17_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( 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] : ( ( v3_conlat_1(C,A) & ~ v4_conlat_1(C,A) & v6_conlat_1(C,A) & l2_conlat_1(C,A) ) => ! [D] : ( ( v3_conlat_1(D,A) & ~ v4_conlat_1(D,A) & v6_conlat_1(D,A) & l2_conlat_1(D,A) ) => ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & ? [F] : ( 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)))) ) ) ) ) ) ) ) )).
fof(d17_convex4,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d17_csspace,axiom,( ! [A] : ( ( 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] : ! [C] : ( ( r2_hidden(B,k11_csspace) & r2_hidden(C,k11_csspace) ) => k1_binop_1(A,B,C) = k11_comseq_3(k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k2_csspace(B),k2_comseq_2(k4_ordinal1,k2_csspace(C)))) ) ) ) )).
fof(d17_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k12_decomp_1(A) = a_1_6_decomp_1(A) ) )).
fof(d17_descip_1,axiom,( ! [A] : ( ( 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] : ( 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) ) ) ) )).
fof(d17_e_siec,axiom,( ! [A] : ( ( 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))))) ) )).
fof(d17_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => k16_ens_1(A) = a_1_3_ens_1(A) ) )).
fof(d17_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : 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)))) )).
fof(d17_ff_siec,axiom,( ! [A] : ( ( 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))) ) )).
fof(d17_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( A = B <=> ( k3_finseq_1(A) = k3_finseq_1(B) & ! [C] : ( 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) ) ) ) ) ) ) )).
fof(d17_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_fintopo2(B,A) <=> B = k9_fintopo2(A,B) ) ) ) )).
fof(d17_fomodel0,axiom,( ! [A] : ! [B] : k15_fomodel0(A,B) = A )).
fof(d17_fomodel1,axiom,( ! [A] : ( l1_fomodel1(A) => ! [B] : ( m1_subset_1(B,k1_fomodel1(A)) => ( v7_fomodel1(B,A) <=> r2_hidden(B,k4_fomodel1(A)) ) ) ) )).
fof(d17_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),k6_margrel1))) ) => ! [D] : ( m2_subset_1(D,k9_funct_2(k37_fomodel1(A),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_fomodel2(A,B)) => ! [E] : ( 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] : ( 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] : ( 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(k15_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)),k15_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 = k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k1_fomodel2(A)),F),G) ) ) => k19_fomodel2(A,B,C,D,E) = k8_margrel1 ) & ( ! [F] : ( 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] : ( 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(k15_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)),k15_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 = k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k1_fomodel2(A)),F),G) ) ) ) => k19_fomodel2(A,B,C,D,E) = k7_margrel1 ) ) ) ) ) ) ) )).
fof(d17_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_fomodel2(D,A,B) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( E = k22_fomodel3(A,B,C,D) <=> ( k9_xtuple_0(E) = k37_fomodel1(A) & ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d17_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) => ! [C] : ( v11_fomodel4(C,A,B) <=> ! [D] : ( v9_fomodel4(D,A,B,C) => r1_tarski(k1_tarski(D),C) ) ) ) ) )).
fof(d17_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k17_ftacell1(A,B,C,D,E) = k21_gfacirc1(k36_gfacirc1(A,B,C),E,D) )).
fof(d17_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_altcat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( k1_altcat_1(B,C,C) != k1_xboole_0 => ! [D] : ( m1_subset_1(D,k1_altcat_1(B,C,C)) => ! [E] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(d17_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ ( 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 ) ) )).
fof(d17_gate_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : 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))) )).
fof(d17_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(d17_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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))) )).
fof(d17_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) ) )).
fof(d17_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => k14_glib_001(A,B) = k2_relset_1(k7_glib_000(A),k12_glib_001(A,B)) ) ) )).
fof(d17_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( m3_glib_004(B,A) => ( B = k16_glib_004(A) <=> ( k15_glib_004(A,B,k5_numbers) = k13_glib_004(A) & ! [C] : ( v7_ordinal1(C) => k15_glib_004(A,B,k1_nat_1(C,1)) = k14_glib_004(A,k15_glib_004(A,B,C)) ) ) ) ) ) )).
fof(d17_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v7_graph_1(D,A) & m2_graph_1(D,A) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r7_graph_5(A,B,C,D,E) <=> ( r1_graph_5(A,D,B,C) & ! [F] : ( ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d17_graphsp,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r3_graphsp(A,B,C,D) <=> ( k1_funct_1(A,k3_finseq_1(A)) = C & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(1,E) => ( r1_xxreal_0(k3_finseq_1(A),E) | k1_funct_1(A,k6_xcmplx_0(k3_finseq_1(A),E)) = k1_funct_1(B,k1_nat_1(D,k7_partfun1(k4_ordinal1,A,k2_xcmplx_0(k6_xcmplx_0(k3_finseq_1(A),E),1)))) ) ) ) ) ) ) ) ) ) )).
fof(d17_grcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v4_grcat_1(C) ) => ( m4_grcat_1(C,A,B) <=> ! [D] : ( m3_grcat_1(D,C) => ( v1_grcat_1(D) & m1_grcat_1(D,A,B) ) ) ) ) ) ) )).
fof(d17_group_10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ( v2_group_10(B,A) <=> ? [C] : ( v7_ordinal1(C) & k7_struct_0(B) = k1_newton(A,C) ) ) ) ) )).
fof(d17_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => k17_group_2(A,B) = k1_card_1(k15_group_2(A,B)) ) ) )).
fof(d17_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( 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)) ) ) )).
fof(d17_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( 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,k5_numbers),D) ) ) ) ) ) ) )).
fof(d17_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k4_ordinal1,B,6) & m2_finseq_1(D,k3_finseq_2(k4_ordinal1)) ) => ! [E] : ( ( 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] : ( v7_ordinal1(F) => ( r2_hidden(F,k4_finseq_1(E)) => k1_funct_1(E,F) = k15_idea_1(C,k7_matrix_0(k4_ordinal1,D,F)) ) ) ) ) ) ) ) ) ) )).
fof(d17_incsp_1,axiom,( ! [A] : ( l2_incsp_1(A) => ( v14_incsp_1(A) <=> ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d17_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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] : ( ( ~ 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] : ( ( ~ 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] : ( m2_cat_1(E,C,D) => ! [F] : ( 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] : ( m4_index_1(G,u1_struct_0(A),u4_struct_0(A),u1_graph_1(A),u2_graph_1(A),B) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d17_integr15,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ( D = k11_integr15(A,B,C) <=> ( k4_finseq_1(D) = k2_finseq_1(A) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k2_finseq_1(A)) => k1_funct_1(D,E) = k2_integra5(B,k1_partfun1(k1_numbers,k1_euclid(A),k1_euclid(A),k1_numbers,C,k1_pdiff_1(E,A))) ) ) ) ) ) ) ) ) )).
fof(d17_integra1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(d17_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m2_interva1(B,A) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d17_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( r4_lattice3(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,C) => r1_lattices(A,D,B) ) ) ) ) ) )).
fof(d17_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(d17_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_lattices(A) ) => ( v14_lattices(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B = k6_lattices(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_lattices(A,B,C) = B & k1_lattices(A,C,B) = B ) ) ) ) ) ) )).
fof(d17_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k6_glib_000(A),k4_ordinal1))) ) => ( v5_lexbfs(B,A) <=> ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => ! [E] : ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d17_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( ( 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] : ( m1_subset_1(E,k7_lmod_7(A,B,C)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d17_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => k20_lpspacc1(A,B,C) = k17_lpspacc1(A,B,C,k8_funcop_1(k2_numbers,A,k5_complex1)) ) ) ) )).
fof(d17_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(k9_lpspace1(A,B,C)),k14_lpspace1(A,B,C)) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( r2_hidden(G,F) => k1_binop_1(D,E,F) = k13_lpspace1(A,B,C,k26_valued_1(A,k1_numbers,G,E)) ) ) ) ) ) ) ) ) ) )).
fof(d17_ltlaxio1,axiom,( ! [A] : ( v2_ltlaxio1(A) <=> ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) ) )).
fof(d17_margrel1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_margrel1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_margrel1(B) ) => ( B = k13_margrel1(A) <=> ( k9_xtuple_0(B) = k9_xtuple_0(A) & ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => k1_funct_1(B,C) = k3_xboolean(k1_funct_1(A,C)) ) ) ) ) ) )).
fof(d17_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => k20_member_1(A,B) = k10_member_1(A,k1_tarski(B)) ) ) )).
fof(d17_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( r1_mesfunc5(A,B,C,D) <=> ( ? [E] : ( 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))) ) ) ) ) ) ) )).
fof(d17_metric_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ~ ( C != D & r1_xxreal_0(k2_binop_1(A,A,k1_numbers,B,C,D),k5_numbers) ) ) ) ) ) ) )).
fof(d17_midsp_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d17_mod_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(D)) => ! [H] : ( 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] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d17_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v5_modelc_1(A) <=> ? [B] : ( v1_modelc_1(B) & m2_finseq_1(B,k4_ordinal1) & A = k9_modelc_1(B) ) ) ) )).
fof(d17_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v8_modelc_2(A) <=> ? [B] : ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) & ? [C] : ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) & A = k8_modelc_2(B,C) ) ) ) ) )).
fof(d17_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => k11_modelc_3(A) = g1_modelc_3(A,k7_modelc_3(A),k7_modelc_3(A),k8_modelc_3(A)) ) )).
fof(d17_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v14_monoid_0(A) <=> v6_monoid_0(u2_algstr_0(A),u1_struct_0(A)) ) ) )).
fof(d17_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d17_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v3_msualg_6(C,A,k1_msafree3(A,B)) & v4_msualg_6(C,A,k1_msafree3(A,B)) & v9_msafree4(C,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B))) & v10_msafree4(C,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B))) & m1_msualg_4(C,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,k1_msafree3(A,B))) ) => ! [D] : ( ( v3_msualg_1(D,A) & v4_msualg_1(D,A) & l3_msualg_1(D,A) ) => ( D = k10_msafree4(A,B,C) <=> ( r8_pboole(u1_struct_0(A),u3_msualg_1(A,D),k9_msafree4(u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),C)) & ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( m1_subset_1(F,k3_msualg_1(A,E,D)) => k3_funct_2(k3_msualg_1(A,E,D),k4_msualg_1(A,E,D),k5_msualg_1(A,E,D),F) = k2_rewrite1(k7_msafree4(u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,k1_msafree3(A,B)),C,k2_msualg_1(A,E)),k1_funct_1(k5_msualg_1(A,E,k1_msafree3(A,B)),F)) ) ) ) ) ) ) ) ) )).
fof(d17_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m3_pboole(C,u1_struct_0(A),u3_msualg_1(A,B)) => ! [D] : ( ( 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] : ( m1_msualg_2(E,A,B) => ( m3_pboole(C,u1_struct_0(A),u3_msualg_1(A,E)) => m1_msualg_2(D,A,E) ) ) ) ) ) ) ) ) )).
fof(d17_msualg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( ( 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] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,B),E)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d17_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ( v2_nattra_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_cat_1(A,B,C) != k1_xboole_0 => B = C ) ) ) ) ) )).
fof(d17_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ! [D] : ( ( 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] : ( v1_xreal_0(E) & ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r2_hidden(F,C) & r2_hidden(G,C) ) => r1_xxreal_0(k2_normsp_0(B,k5_algstr_0(B,k7_partfun1(u1_struct_0(B),D,F),k7_partfun1(u1_struct_0(B),D,G))),k3_xcmplx_0(E,k2_normsp_0(A,k5_algstr_0(A,F,G)))) ) ) ) ) ) ) ) ) ) )).
fof(d17_oposet_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(d17_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r2_ordinal2(A,B) <=> ? [C] : ( v1_relat_1(C) & v5_ordinal1(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) ) ) ) ) )).
fof(d17_ordinal6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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) ) ) )).
fof(d17_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(d17_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( v12_osalg_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d17_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(d17_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( D = k7_pboole(A,B,C) <=> ! [E] : ( r2_hidden(E,A) => k1_funct_1(D,E) = k1_funct_2(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) )).
fof(d17_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [F] : ( 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))),k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_1(C,A),F)) ) ) ) ) ) ) ) )).
fof(d17_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r8_pdiff_5(A,B) => ! [C] : ( v1_xreal_0(C) => ( C = k8_pdiff_5(A,B) <=> ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & B = k11_finseq_1(D,E,F) & ? [G] : ( 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] : ( v1_funct_1(H) & v3_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [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_funct_1(H,1) & ! [J] : ( v1_xreal_0(J) => ( r2_hidden(J,G) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,2,k1_pdiff_3(3,3,A),B),J),k1_funct_1(k1_pdiff_2(3,2,k1_pdiff_3(3,3,A),B),E)) = k2_xcmplx_0(k1_funct_1(H,k6_xcmplx_0(J,E)),k1_funct_1(I,k6_xcmplx_0(J,E))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d17_pencil_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v14_pencil_1(A) <=> ! [B] : ( l1_struct_0(B) => ~ ( r2_hidden(B,k10_xtuple_0(A)) & v7_struct_0(B) ) ) ) ) )).
fof(d17_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k17_polyform(A,B))) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d17_pralg_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k15_pralg_1(A,B) <=> ( k9_xtuple_0(C) = k9_xtuple_0(A) & ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d17_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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) ) => ( v3_relat_1(B) <=> r6_pboole(A,B,k16_pre_poly(A)) ) ) )).
fof(d17_pscomp_1,axiom,( ! [A] : ( 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) ) )).
fof(d17_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( 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,k5_numbers)),k12_finseq_1(k3_qc_lang1(A),B)),k11_qc_lang1(A,C)) ) ) ) )).
fof(d17_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => k13_qc_lang2(A,B) = k12_qc_lang2(A,k19_qc_lang1(A,B)) ) ) )).
fof(d17_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_quantal1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v17_quantal1(B,A) <=> ! [C] : ( 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 ) ) ) ) ) )).
fof(d17_quaterni,axiom,( k17_quaterni = k5_numbers )).
fof(d17_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k20_quofield(A,B,C) = k8_group_1(A,B,k11_algstr_0(A,C)) ) ) ) )).
fof(d17_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( m1_ratfunc1(B,A) => ! [C] : ( m1_ratfunc1(C,A) => ( ( ~ v4_ratfunc1(B,A) => ( C = k11_ratfunc1(A,B) <=> ? [D] : ( m1_ratfunc1(D,A) & ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(E,A) & ~ v1_ratfunc1(E,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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] : ( m2_finseq_1(F,u1_struct_0(k14_polynom3(A))) & E = k3_group_4(k14_polynom3(A),F) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ~ ( r2_hidden(G,k4_finseq_1(F)) & ! [H] : ( 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) ) ) ) ) ) ) )).
fof(d17_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( v5_relat_1(B,A) <=> r1_tarski(k10_xtuple_0(B),A) ) ) )).
fof(d17_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r10_rewrite1(A,B) <=> ! [C] : ! [D] : ! [E] : ~ ( r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(C,E),B) & ! [F] : ~ ( r1_rewrite1(B,D,F) & r1_rewrite1(A,E,F) ) ) ) ) ) )).
fof(d17_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_ringcat1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v5_ringcat1(B) ) => ( B = k10_ringcat1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( m2_ringcat1(D,A) & ? [E] : ( m2_ringcat1(E,A) & r1_ringcat1(D,E) & m1_ringcat1(C,D,E) ) ) ) ) ) ) )).
fof(d17_rlvect_2,axiom,( ! [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) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k11_rlvect_2(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d17_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k12_robbins1(A,B) = k1_lattices(A,B,B) ) ) )).
fof(d17_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => ( r1_rvsum_1(A,B) <=> k22_rvsum_1(A,B) = k5_numbers ) ) ) )).
fof(d17_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( m1_scmfsa_2(B) => k17_scmfsa_2(A,B) = k3_xtuple_0(12,k1_xboole_0,k10_finseq_1(A,B)) ) ) )).
fof(d17_scmpds_2,axiom,( ! [A] : ( ( 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] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( C = k17_scmpds_2(A,B) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & D = k5_memstr_0(2,k1_scmpds_2,A) & C = k1_int_2(k2_xcmplx_0(D,B)) ) ) ) ) ) )).
fof(d17_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ! [C] : ( 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))) ) ) )).
fof(d17_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => k17_sin_cos(A) = k1_funct_1(k16_sin_cos,A) ) )).
fof(d17_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u4_struct_0(A))) => ( C = k11_stacks_1(A,B) <=> ( r2_hidden(B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u4_struct_0(A))) => ( ( r2_hidden(B,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d17_struct_0,axiom,( ! [A] : ( 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))) ) )).
fof(d17_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ( B = k16_substut1(A) <=> ( v1_substut1(B,A) & ! [C] : ( ~ v1_xboole_0(C) => ( v1_substut1(C,A) => r1_tarski(B,C) ) ) ) ) ) ) )).
fof(d17_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => k19_supinf_2(A) = k8_supinf_2(k17_supinf_2(k18_supinf_2(A))) ) )).
fof(d17_tex_4,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_pre_topc(C) & m1_pre_topc(C,A) ) => ( C = k5_tex_4(A,B) <=> u1_struct_0(C) = k2_tex_4(A,B) ) ) ) ) )).
fof(d17_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => k13_trees_3(A,B) = k11_trees_3(k10_finseq_1(A,B)) ) ) )).
fof(d17_turing_1,axiom,( ! [A] : ( ( v1_turing_1(A) & l1_turing_1(A) ) => ( A = k16_turing_1 <=> ( u1_turing_1(A) = k7_domain_1(k4_ordinal1,k5_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),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1)),k8_mcart_1(k4_ordinal1,k4_ordinal1,k3_turing_1(4),k7_domain_1(k4_ordinal1,k5_numbers,1)),k3_zfmisc_1(k3_turing_1(4),k7_domain_1(k4_ordinal1,k5_numbers,1),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1)),u3_turing_1(A),k15_turing_1) & u4_turing_1(A) = k5_numbers & u5_turing_1(A) = 4 ) ) ) )).
fof(d17_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d17_unialg_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d17_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) ) => k62_valued_1(A) = k1_xxreal_2(k1_relset_1(k4_ordinal1,A)) ) )).
fof(d17_valued_2,axiom,( ! [A] : ! [B] : ( B = k11_valued_2(A) <=> ! [C] : ( 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))) ) ) ) )).
fof(d17_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ( v11_vectsp_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k4_vectsp_1(A,B,k5_struct_0(A),C) = C ) ) ) ) )).
fof(d17_waybel34,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & v1_yellow_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(d17_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) )).
fof(d17_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) )).
fof(d17_waybel_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ( v6_waybel_4(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => C = k1_yellow_0(A,k5_waybel_4(A,C,B)) ) ) ) ) )).
fof(d17_xtuple_0,axiom,( ! [A] : k14_xtuple_0(A) = k10_xtuple_0(k11_xtuple_0(A)) )).
fof(d17_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v6_yellow_0(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d17_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v8_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & v3_yellow_6(B,A) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k11_yellow_6(A,B) <=> r2_hidden(C,k10_yellow_6(A,B)) ) ) ) ) )).
fof(d17_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => k11_zf_lang(A,B) = k6_zf_lang(k7_zf_lang(A,k6_zf_lang(B))) ) ) )).
fof(d17_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d17_zmodul02,axiom,( ! [A] : ( ( ~ 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_int_3) & v9_vectsp_1(A,k1_int_3) & v10_vectsp_1(A,k1_int_3) & v11_vectsp_1(A,k1_int_3) & l1_vectsp_1(A,k1_int_3) ) => k17_zmodul02(A) = g1_zmodul01(u1_struct_0(A),u2_struct_0(A),u1_algstr_0(A),k16_zmodul02(A)) ) )).
fof(d18_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(d18_abcmiz_1,axiom,( k17_abcmiz_1 = k2_zfmisc_1(k1_tarski(k6_abcmiz_1),k2_zfmisc_1(k4_abcmiz_1,k4_ordinal1)) )).
fof(d18_abcmiz_a,axiom,( ! [A] : ( m2_finseq_1(A,k2_abcmiz_1) => ! [B] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(d18_algstr_0,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d18_algstr_4,axiom,( ! [A] : ! [B] : ( 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) = k5_numbers ) ) ) )).
fof(d18_altcat_1,axiom,( ! [A] : ( l2_altcat_1(A) => ( v13_altcat_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_altcat_1(A,B,C) != k1_xboole_0 => B = C ) ) ) ) ) )).
fof(d18_aofa_000,axiom,( ! [A] : ( ( v4_unialg_1(A) & v5_aofa_000(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k14_aofa_000(A,B,C,D) = k1_funct_1(k2_pua2mss1(A,k10_subset_1(3,k4_finseq_1(u1_unialg_1(A)))),k3_finseq_4(u1_struct_0(A),B,C,D)) ) ) ) ) )).
fof(d18_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v2_relat_1(C) & m1_msafree(C,A,B) ) => ! [D] : ( ( ~ v2_struct_0(D) & l3_aofa_a00(D,A,B,C) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_msafree4(F,u1_struct_0(A),C,k1_msafree4(u1_struct_0(A),C,E)) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,B),E)) => k12_aofa_a00(A,B,C,D,E,F,G) = k1_funct_1(u3_aofa_a00(A,B,C,D),k4_tarski(F,G)) ) ) ) ) ) ) ) )).
fof(d18_aofa_i00,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d18_armstrng,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ( v8_armstrng(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ? [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) & ? [E] : ( 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) ) ) ) ) ) )).
fof(d18_asympt_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_funct_2(B,A,k1_numbers) => ! [C] : ( m1_funct_2(C,A,k1_numbers) => k13_asympt_0(A,B,C) = a_3_0_asympt_0(A,B,C) ) ) ) )).
fof(d18_bcialg_1,axiom,( ! [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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(d18_bcialg_2,axiom,( ! [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] : ( 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)) ) ) )).
fof(d18_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(d18_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ( r2_borsuk_1(A,B) <=> ? [C] : ( 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] : ( 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] : ( 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 ) ) ) ) ) ) ) ) )).
fof(d18_c0sp1,axiom,( ! [A] : ( ~ 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)) ) )).
fof(d18_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_cat_1(A,B,C) <=> ? [D] : ( m1_cat_1(D,A,B,C) & v9_cat_1(D,A,B,C) ) ) ) ) ) )).
fof(d18_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u4_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(H,u4_struct_0(A)) => ~ ( r2_hidden(H,k2_cat_1(A,B,E)) & ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d18_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(d18_coh_sp,axiom,( ! [A] : k19_coh_sp(A) = k3_tarski(a_1_5_coh_sp(A)) )).
fof(d18_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( C = k9_cohsp_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( 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) ) ) ) ) ) )).
fof(d18_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( 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] : ( ( v3_conlat_1(C,A) & ~ v4_conlat_1(C,A) & v6_conlat_1(C,A) & l2_conlat_1(C,A) ) => ! [D] : ( ( v3_conlat_1(D,A) & ~ v4_conlat_1(D,A) & v6_conlat_1(D,A) & l2_conlat_1(D,A) ) => ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & ? [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(d18_csspace,axiom,( 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) )).
fof(d18_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k13_decomp_1(A) = a_1_7_decomp_1(A) ) )).
fof(d18_e_siec,axiom,( ! [A] : ( ( 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))))) ) )).
fof(d18_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d18_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(d18_finseq_1,axiom,( ! [A] : ( v3_finseq_1(A) <=> ! [B] : ( r2_hidden(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ) )).
fof(d18_fomodel0,axiom,( ! [A] : ( ( 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] : ( v1_xcmplx_0(B) => k1_funct_1(A,B) = k2_xcmplx_0(B,1) ) ) ) )).
fof(d18_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( 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)),k15_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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),k6_margrel1)) => ! [D] : ( ( 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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),k6_margrel1))) ) => ( D = k20_fomodel2(A,B,C) <=> ( ! [E] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(A),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_fomodel2(A,B)) => ! [F] : ( 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(k15_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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),D)) <=> ? [G] : ( 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] : ( 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 = k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k1_fomodel2(A)),G),H) & r2_hidden(k1_domain_1(k15_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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),C)) & r2_hidden(k1_domain_1(k15_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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),C)) ) ) ) ) ) & ! [E] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(A),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_fomodel2(A,B)) => ! [F] : ( 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(k15_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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),D)) => k1_binop_1(D,E,F) = k19_fomodel2(A,B,C,E,F) ) ) ) ) ) ) ) ) ) )).
fof(d18_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_fomodel2(D,A,B) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( E = k22_fomodel3(A,B,C,D) <=> ( k9_xtuple_0(E) = k37_fomodel1(A) & ! [F] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(d18_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) => ! [C] : ( v11_fomodel4(C,A,B) <=> ! [D] : ( v9_fomodel4(D,A,B,C) => r2_hidden(D,C) ) ) ) ) )).
fof(d18_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & v8_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( 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)) ) ) ) ) ) ) )).
fof(d18_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k18_ftacell1(A,B,C,D,E) = k24_gfacirc1(k36_gfacirc1(A,B,C),E,D) )).
fof(d18_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_altcat_1(B) ) => ! [C] : ( ( v10_functor0(C,A,B) & l2_functor0(C,A,B) ) => ( v8_functor0(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(d18_gate_1,axiom,( ! [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) & 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 ) ) )).
fof(d18_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(d18_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(d18_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ( v3_glib_000(A) <=> ! [B] : ~ ( r2_hidden(B,k7_glib_000(A)) & k1_funct_1(k10_glib_000(A),B) = k1_funct_1(k11_glib_000(A),B) ) ) ) )).
fof(d18_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => k15_glib_001(A,B) = k3_finseq_1(k12_glib_001(A,B)) ) ) )).
fof(d18_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(d18_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(d18_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(d18_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) ) ) ) )).
fof(d18_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v7_graph_1(D,A) & m2_graph_1(D,A) ) => ! [E] : ! [F] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d18_graphsp,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r4_graphsp(A,B,C,D) <=> ( k1_funct_1(A,1) = 1 & ~ r1_xxreal_0(k3_finseq_1(A),1) & r3_graphsp(A,B,C,D) & v2_funct_1(A) ) ) ) ) ) ) )).
fof(d18_group_10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(d18_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ( v1_finset_1(k15_group_2(A,B)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( C = k18_group_2(A,B) <=> ? [D] : ( v1_finset_1(D) & D = k15_group_2(A,B) & C = k5_card_1(D) ) ) ) ) ) ) )).
fof(d18_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,A) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(d18_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(d18_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k4_ordinal1,B,6) & m2_finseq_1(D,k3_finseq_2(k4_ordinal1)) ) => ! [E] : ( ( 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] : ( v7_ordinal1(F) => ( r2_hidden(F,k4_finseq_1(E)) => k1_funct_1(E,F) = k16_idea_1(C,k7_matrix_0(k4_ordinal1,D,k1_nat_1(k7_nat_d(A,F),1))) ) ) ) ) ) ) ) ) ) )).
fof(d18_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k10_ideal_1(A,B,C) = a_3_1_ideal_1(A,B,C) ) ) ) )).
fof(d18_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( 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] : ( 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) ) ) ) ) )).
fof(d18_integr15,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(C)))) ) => ! [E] : ( 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] : ( m1_subset_1(F,k4_ordinal1) => ( r2_hidden(F,k2_finseq_1(C)) => k1_funct_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))) ) ) ) ) ) ) ) ) ) )).
fof(d18_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [C] : ( m1_integra1(C,A) => ! [D] : ( v7_ordinal1(D) => ( r1_integra1(B,C) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r2_hidden(D,k4_finseq_1(B)) => ( E = k13_integra1(A,B,C,D) <=> ( r2_hidden(E,k4_finseq_1(C)) & k1_funct_1(B,D) = k1_funct_1(C,E) ) ) ) & ( ~ r2_hidden(D,k4_finseq_1(B)) => ( E = k13_integra1(A,B,C,D) <=> E = k5_numbers ) ) ) ) ) ) ) ) ) )).
fof(d18_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m2_interva1(B,A) => ! [C] : ( 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))) ) ) ) )).
fof(d18_intpro_1,axiom,( k10_intpro_1 = k3_intpro_1(k2_intpro_1,k2_intpro_1) )).
fof(d18_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( v4_lattice3(A) <=> ! [B] : ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r4_lattice3(A,C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r4_lattice3(A,D,B) => r1_lattices(A,C,D) ) ) ) ) ) )).
fof(d18_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m1_lattice5(D,A,B,C) => k14_lattice5(A,B,C,D) = k12_lattice5(A,B,C,D,k7_lattice5(A,B,C)) ) ) ) ) )).
fof(d18_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d18_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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(k4_ordinal1,k6_glib_000(A),k5_numbers)) ) )).
fof(d18_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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))) ) ) ) )).
fof(d18_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(k2_numbers,k18_lpspacc1(A,B,C)),k18_lpspacc1(A,B,C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_numbers,k18_lpspacc1(A,B,C)),k18_lpspacc1(A,B,C)))) ) => ( D = k21_lpspacc1(A,B,C) <=> ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(k13_lpspacc1(A,B,C)),k18_lpspacc1(A,B,C)) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( r2_hidden(G,F) => k1_binop_1(D,E,F) = k17_lpspacc1(A,B,C,k25_valued_1(A,k2_numbers,G,E)) ) ) ) ) ) ) ) ) ) )).
fof(d18_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( ~ 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)) ) ) ) ) ) ) )).
fof(d18_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => ( A = k13_ltlaxio1 <=> ( v2_ltlaxio1(A) & ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_hilbert1)) => ( v2_ltlaxio1(B) => r1_tarski(A,B) ) ) ) ) ) )).
fof(d18_margrel1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_margrel1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_margrel1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_margrel1(C) ) => ( C = k14_margrel1(A,B) <=> ( k9_xtuple_0(C) = k3_xboole_0(k9_xtuple_0(A),k9_xtuple_0(B)) & ! [D] : ( r2_hidden(D,k9_xtuple_0(C)) => k1_funct_1(C,D) = k4_xboolean(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) )).
fof(d18_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => k21_member_1(A,B) = k11_member_1(A,k1_tarski(B)) ) ) )).
fof(d18_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_card_3(k2_memstr_0(A,B)),k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_card_3(k2_memstr_0(A,B)),k4_ordinal1))) ) => ( v7_memstr_0(C,A,B) <=> ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(d18_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => k8_mesfunc5(A,B,C,D,E) = k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,E)) ) ) ) ) ) )).
fof(d18_metric_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ( v11_metric_1(A) <=> v10_metric_1(u1_metric_1(A),u1_struct_0(A)) ) ) )).
fof(d18_metric_3,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,k1_numbers) => ! [E] : ( m1_subset_1(E,k1_numbers) => ! [F] : ( m1_subset_1(F,k2_zfmisc_1(k1_numbers,k1_numbers)) => ! [G] : ( 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) ) => k2_binop_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers,A,F,G) = k3_square_1(k2_xcmplx_0(k1_square_1(k5_binop_1(k1_numbers,k6_metric_1,B,C)),k1_square_1(k5_binop_1(k1_numbers,k6_metric_1,D,E)))) ) ) ) ) ) ) ) ) ) )).
fof(d18_mod_2,axiom,( k16_mod_2 = 1 )).
fof(d18_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v6_modelc_1(A) <=> ? [B] : ( v1_modelc_1(B) & m2_finseq_1(B,k4_ordinal1) & A = k10_modelc_1(B) ) ) ) )).
fof(d18_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ( v3_modelc_2(A) | v6_modelc_2(A) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( ( 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 ) ) ) ) ) ) )).
fof(d18_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( 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)) ) ) )).
fof(d18_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v15_monoid_0(A) <=> v7_monoid_0(u2_algstr_0(A),u1_struct_0(A)) ) ) )).
fof(d18_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m2_pboole(C,u1_struct_0(A),k13_msafree(A,B),B) => ( C = k15_msafree(A,B) <=> ! [D] : ( 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)) ) ) ) ) ) )).
fof(d18_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msualg_2(C,A,B) => ! [D] : ( m1_msualg_2(D,A,B) => ! [E] : ( ( v3_msualg_1(E,A) & m1_msualg_2(E,A,B) ) => ( E = k13_msualg_2(A,B,C,D) <=> ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d18_msualg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d18_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ( v3_nattra_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v1_zfmisc_1(k2_cat_1(A,B,B)) ) ) ) )).
fof(d18_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( 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] : ( v1_xreal_0(E) & ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r2_hidden(F,C) & r2_hidden(G,C) ) => r1_xxreal_0(k2_normsp_0(B,k5_algstr_0(B,k7_partfun1(u1_struct_0(B),D,F),k7_partfun1(u1_struct_0(B),D,G))),k3_xcmplx_0(E,k2_normsp_0(A,k5_algstr_0(A,F,G)))) ) ) ) ) ) ) ) ) ) )).
fof(d18_oposet_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_qmax_1(A) ) => ( v10_oposet_1(A) <=> v9_oposet_1(u1_robbins1(A),A) ) ) )).
fof(d18_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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)) ) ) )).
fof(d18_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(d18_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( ( v4_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v2_msualg_4(D,A,C) & v3_msualg_4(D,A,C) & m1_osalg_4(D,A,C) ) => ! [E] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d18_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(d18_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(A)) => k13_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))),k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_1(C,A),F)) ) ) ) ) ) ) )).
fof(d18_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r9_pdiff_5(A,B) => ! [C] : ( v1_xreal_0(C) => ( C = k9_pdiff_5(A,B) <=> ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & B = k11_finseq_1(D,E,F) & ? [G] : ( 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] : ( v1_funct_1(H) & v3_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [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_funct_1(H,1) & ! [J] : ( v1_xreal_0(J) => ( r2_hidden(J,G) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,3,k1_pdiff_3(3,3,A),B),J),k1_funct_1(k1_pdiff_2(3,3,k1_pdiff_3(3,3,A),B),F)) = k2_xcmplx_0(k1_funct_1(H,k6_xcmplx_0(J,F)),k1_funct_1(I,k6_xcmplx_0(J,F))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d18_pencil_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_pralg_1(A) ) => ( v14_pencil_1(A) <=> ! [B] : ( r2_hidden(B,k10_xtuple_0(A)) => ( ~ v7_struct_0(B) & l1_struct_0(B) ) ) ) ) )).
fof(d18_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d18_pralg_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_funcop_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( D = k16_pralg_1(A,B,C) <=> ( k9_xtuple_0(D) = A & ! [E] : ( r2_hidden(E,A) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(d18_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_prelamb(A) ) => ( v10_prelamb(A) <=> ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_prelamb(A,k12_finseq_1(u1_struct_0(A),B),B) ) & ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d18_pscomp_1,axiom,( ! [A] : ( 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) ) )).
fof(d18_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v2_qc_lang1(B,A) <=> ? [C] : ( v7_ordinal1(C) & ? [D] : ( m2_subset_1(D,k6_qc_lang1(A),k8_qc_lang1(A,C)) & ? [E] : ( v3_card_1(E,C) & m2_finseq_1(E,k2_qc_lang1(A)) & B = k10_qc_lang1(A,D,E) ) ) ) ) ) ) )).
fof(d18_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => k14_qc_lang2(A,B) = k11_qc_lang2(A,k19_qc_lang1(A,B)) ) ) )).
fof(d18_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_quantal1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v18_quantal1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_quantal1(A,C,B) = k2_quantal1(A,C,B) ) ) ) ) )).
fof(d18_quaterni,axiom,( k18_quaterni = 1 )).
fof(d18_quofield,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(d18_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( 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)))) ) ) )).
fof(d18_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r11_rewrite1(A,B) <=> ! [C] : ! [D] : ! [E] : ~ ( r1_rewrite1(A,C,D) & r1_rewrite1(B,C,E) & ! [F] : ~ ( r1_rewrite1(B,D,F) & r1_rewrite1(A,E,F) ) ) ) ) ) )).
fof(d18_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_ringcat1(A) ) => ! [B] : ( m2_ringcat1(B,A) => k13_ringcat1(A,B) = k5_ringcat1(B) ) ) )).
fof(d18_rlvect_2,axiom,( ! [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) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k11_rlvect_2(A)) => k1_funct_1(B,k4_tarski(C,D)) = k8_rlvect_2(A,C,k12_rlvect_2(A,D)) ) ) ) ) ) )).
fof(d18_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k13_robbins1(A,B) = k1_lattices(A,k11_robbins1(A,B),B) ) ) )).
fof(d18_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v8_scmyciel(A) ) => ! [B] : ( v7_ordinal1(B) => ( B = k9_scmyciel(A) <=> ( ? [C] : ( v1_finset_1(C) & v7_scmyciel(C,A) & m1_eqrel_1(C,k3_tarski(A)) & k5_card_1(C) = B ) & ! [C] : ( ( v1_finset_1(C) & v7_scmyciel(C,A) & m1_eqrel_1(C,k3_tarski(A)) ) => r1_xxreal_0(B,k5_card_1(C)) ) ) ) ) ) )).
fof(d18_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k12_seq_4(A))) => ! [C] : ( v1_xreal_0(C) => k23_seq_4(A,B,C) = a_3_2_seq_4(A,B,C) ) ) ) )).
fof(d18_simplex0,axiom,( ! [A] : ( ( ~ v3_pencil_1(A) & v1_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( v1_xreal_0(B) => ( v1_int_1(B) => ! [C] : ( ( 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) ) ) ) ) ) ) ) )).
fof(d18_sin_cos,axiom,( ! [A] : ( ( 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 = k18_sin_cos <=> ! [B] : ( v1_xreal_0(B) => k1_funct_1(A,B) = k3_complex1(k11_comseq_3(k3_sin_cos(k3_xcmplx_0(B,k7_complex1)))) ) ) ) )).
fof(d18_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(A),u4_struct_0(A)))) => ( B = k12_stacks_1(A) <=> ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => D != k7_stacks_1(A,C,E) ) ) ) ) ) ) ) ) )).
fof(d18_struct_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ( v7_struct_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => B = k4_struct_0(A) ) ) ) )).
fof(d18_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k6_qc_lang1(A)) => ! [C] : ( m2_finseq_1(C,k2_qc_lang1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d18_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v7_supinf_2(A) <=> r2_hidden(k19_supinf_2(A),k1_numbers) ) ) )).
fof(d18_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v1_pre_topc(C) & m1_pre_topc(C,A) ) => ( C = k6_tex_4(A,B) <=> u1_struct_0(C) = k3_tex_4(A,B) ) ) ) ) )).
fof(d18_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v6_trees_3(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( B = k15_trees_3(A) <=> ( k1_relset_1(k4_ordinal1,B) = k1_relset_1(k4_ordinal1,A) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r2_hidden(C,k1_relset_1(k4_ordinal1,A)) & ! [D] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d18_turing_1,axiom,( k17_turing_1 = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k12_turing_1(k8_mcart_1(k4_ordinal1,k4_ordinal1,k3_turing_1(4),k7_domain_1(k4_ordinal1,k5_numbers,1)),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),1),k2_turing_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k3_zfmisc_1(k4_ordinal1,k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers),k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,1,k5_numbers,1))),k2_turing_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k3_zfmisc_1(k4_ordinal1,k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,1,1),k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,2,1,1))),k16_funcop_1(k1_domain_1(k4_ordinal1,k4_ordinal1,2,k5_numbers),k3_xtuple_0(3,k5_numbers,k4_xcmplx_0(1)))),k16_funcop_1(k1_domain_1(k4_ordinal1,k4_ordinal1,2,1),k3_xtuple_0(3,k5_numbers,k4_xcmplx_0(1)))),k16_funcop_1(k1_domain_1(k4_ordinal1,k4_ordinal1,3,1),k3_xtuple_0(4,1,k4_xcmplx_0(1)))) )).
fof(d18_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d18_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)))) ) )).
fof(d18_valued_2,axiom,( ! [A] : ! [B] : ( B = k12_valued_2(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) ) ) )).
fof(d18_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ( v12_vectsp_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( k1_algstr_0(A,B,B) = k4_struct_0(A) => B = k4_struct_0(A) ) ) ) ) )).
fof(d18_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) )).
fof(d18_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d18_waybel_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))))) ) => ( v7_waybel_4(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & D = k3_funct_2(u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A))),B,C) & C = k1_yellow_0(A,D) ) ) ) ) ) )).
fof(d18_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v7_yellow_0(B,A) <=> ! [C] : ( 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)) ) ) ) ) ) )).
fof(d18_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) <=> r1_tarski(B,k2_zfmisc_1(k6_yellow_6(A),u1_struct_0(A))) ) ) )).
fof(d18_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => k12_zf_lang(A,B) = k7_zf_lang(k11_zf_lang(A,B),k11_zf_lang(B,A)) ) ) )).
fof(d18_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ( v8_zmodul01(B,A) <=> ? [C] : ( m1_zmodul01(C,A) & r1_zmodul01(A,C,B) ) ) ) ) )).
fof(d18_zmodul02,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( m2_funct_2(B,u1_struct_0(A),k4_numbers,k9_funct_2(u1_struct_0(A),k4_numbers)) => ( m1_zmodul02(B,A) <=> ? [C] : ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ~ r2_hidden(D,C) => k3_funct_2(u1_struct_0(A),k4_numbers,B,D) = k5_numbers ) ) ) ) ) ) )).
fof(d19_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_abcmiz_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ( D = k7_abcmiz_0(A,B,C) <=> ( k3_finseq_1(D) = k1_nat_1(k3_finseq_1(C),1) & k1_funct_1(D,1) = B & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,u1_abcmiz_0(A)) => ! [G] : ( 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,k1_nat_1(E,1)) = k5_abcmiz_0(A,G,F) ) ) ) ) ) ) ) ) ) ) )).
fof(d19_abcmiz_1,axiom,( k18_abcmiz_1 = k2_zfmisc_1(k1_tarski(k7_abcmiz_1),k2_zfmisc_1(k4_abcmiz_1,k4_ordinal1)) )).
fof(d19_algstr_0,axiom,( k7_algstr_0 = g3_algstr_0(k1_tarski(k5_ordinal1),k9_funct_5) )).
fof(d19_algstr_4,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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,k5_numbers) => ( C = k16_algstr_4(A,B) <=> ! [D] : ( 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,k5_numbers) => ( C = k16_algstr_4(A,B) <=> C = k1_xboole_0 ) ) ) ) ) )).
fof(d19_altcat_1,axiom,( ! [A] : ( l2_altcat_1(A) => ( v14_altcat_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v1_zfmisc_1(k1_altcat_1(A,B,B)) ) ) ) )).
fof(d19_aofa_000,axiom,( ! [A] : ( ( v4_unialg_1(A) & v3_aofa_000(A) & v5_aofa_000(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k15_aofa_000(A,B,C) = k14_aofa_000(A,B,C,k12_aofa_000(A)) ) ) ) )).
fof(d19_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v2_relat_1(D) & m1_msafree(D,A,B) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k4_autalg_1(u1_struct_0(A),D,u3_msualg_1(A,C)))) => ( E = k13_aofa_a00(A,B,C,D) <=> ! [F] : ( m2_pboole(F,u1_struct_0(A),D,u3_msualg_1(A,C)) => ( r2_hidden(F,E) <=> ? [G] : ( m2_pboole(G,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) & r1_msualg_3(A,B,C,G) & r8_pboole(u1_struct_0(A),F,k1_msafree(u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C),D,G)) ) ) ) ) ) ) ) ) ) )).
fof(d19_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_aofa_a01(D,A,B,C) & l4_aofa_a00(D,A,B,C) ) => ! [E] : ( ( ~ v2_struct_0(E) & v2_unialg_1(E) & v3_unialg_1(E) & v4_unialg_1(E) & v3_aofa_000(E) & v4_aofa_000(E) & v5_aofa_000(E) & v6_aofa_000(E) & ~ v10_aofa_000(E) & v11_aofa_000(E) & v12_aofa_000(E) & v5_aofa_a01(E,A,B,C,D) & l3_aofa_a00(E,A,C,u4_aofa_a00(A,B,C,D)) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),F)) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),F)) => ( r2_hidden(G,k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),F)) => k13_aofa_a01(A,B,C,D,E,F,G,H) = k1_funct_1(u3_aofa_a00(A,C,u4_aofa_a00(A,B,C,D),E),k4_tarski(G,H)) ) ) ) ) ) ) ) ) ) )).
fof(d19_aofa_i00,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(d19_armstrng,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ( v9_armstrng(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ! [F] : ( 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 ) ) ) ) ) ) ) ) )).
fof(d19_bcialg_1,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( v12_bcialg_1(B,A) <=> ! [C] : ( m2_subset_1(C,u1_struct_0(A),B) => r2_hidden(k2_bcialg_1(A,C),B) ) ) ) ) )).
fof(d19_bcialg_2,axiom,( ! [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] : ( 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)) ) ) )).
fof(d19_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(d19_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k7_xboolean(A,B) = k3_xboolean(k10_xboolean(A,B)) ) ) )).
fof(d19_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( 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] : ( 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] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d19_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_cat_1(F,A,B,C) => ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(d19_coh_sp,axiom,( ! [A] : k20_coh_sp(A) = a_1_6_coh_sp(A) )).
fof(d19_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k10_cohsp_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ? [E] : ( C = k4_tarski(D,E) & r2_hidden(k4_tarski(k1_tarski(D),E),k7_cohsp_1(A)) ) ) ) ) )).
fof(d19_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => k11_conlat_1(A) = g3_lattices(k8_conlat_1(A),k10_conlat_1(A),k9_conlat_1(A)) ) )).
fof(d19_convex4,axiom,( ! [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) ) => ! [B] : ( m1_clvect_1(B,A) => k17_convex4(A,B) = u1_struct_0(B) ) ) )).
fof(d19_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k14_decomp_1(A) = a_1_8_decomp_1(A) ) )).
fof(d19_e_siec,axiom,( ! [A] : ( ( 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))))) ) )).
fof(d19_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d19_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : 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) )).
fof(d19_finseq_1,axiom,( ! [A] : ( v1_finset_1(A) => k19_finseq_1(A) = o_1_1_finseq_1(A) ) )).
fof(d19_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v3_fomodel0(B,A) <=> ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,A) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v5_relat_1(D,A) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v5_relat_1(E,A) & v1_funct_1(E) & v1_finseq_1(E) ) => ! [F] : ( ( 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 ) ) ) ) ) ) ) ) )).
fof(d19_fomodel1,axiom,( ! [A] : ( l1_fomodel1(A) => ! [B] : ( m1_subset_1(B,k1_fomodel1(A)) => ( v9_fomodel1(B,A) <=> r2_hidden(B,k9_fomodel1(A)) ) ) ) )).
fof(d19_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,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)),k15_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(k4_ordinal1,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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),k6_margrel1)))) ) => ( C = k21_fomodel2(A,B) <=> ( k9_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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),k6_margrel1),C,k5_numbers) = k16_fomodel2(A,B) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => k9_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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),k6_margrel1),C,k1_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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),k6_margrel1,k18_fomodel2(A,B,k9_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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),k6_margrel1),C,D)),k20_fomodel2(A,B,k9_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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),k6_margrel1),C,D))),k9_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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),k6_margrel1),C,D)) ) ) ) ) ) ) )).
fof(d19_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v4_fomodel1(B,A) & m1_subset_1(B,k1_fomodel1(A)) ) => ! [C] : ( m2_subset_1(C,k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k35_fomodel1(A)) => ! [D] : ( ( 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(k43_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),D)),k1_funct_1(k21_fomodel1(A),k3_relat_1(k34_fomodel1(A,D),k9_fomodel2(A,k35_fomodel1(A),k34_fomodel2(A,k35_fomodel1(A),k7_fomodel3(A,k1_xboole_0),B,C))))) ) ) ) ) )).
fof(d19_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( ( ~ v2_struct_0(D) & l2_fsm_1(D,A,B) ) => ( r7_fsm_1(A,B,C,D) <=> ? [E] : ( 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] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d19_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k19_ftacell1(A,B,C,D,E) = k2_circcomb(k49_gfacirc1(A,B,C),k49_gfacirc1(k48_gfacirc1(A,B,C),E,D)) )).
fof(d19_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_altcat_1(B) ) => ! [C] : ( ( v11_functor0(C,A,B) & l2_functor0(C,A,B) ) => ( v8_functor0(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(d19_gate_1,axiom,( ! [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) ) => 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 ) ) )).
fof(d19_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(d19_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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)))) )).
fof(d19_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ( v4_glib_000(A) <=> k1_card_1(k6_glib_000(A)) = 1 ) ) )).
fof(d19_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(d19_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( m3_glib_001(B,A) => k10_glib_003(A,B) = k18_rvsum_1(k9_glib_003(A,B)) ) ) )).
fof(d19_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(d19_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( B = k6_graph_1(A) <=> ? [C] : ( v1_finset_1(C) & C = u1_struct_0(A) & B = k5_card_1(C) ) ) ) ) )).
fof(d19_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u4_struct_0(A)) => ! [C] : ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r9_graph_5(A,B,C,D,E) <=> ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_hidden(F,C) & F != D & ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d19_graphsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u4_struct_0(A)) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r5_graphsp(A,B,C) <=> ( k3_finseq_1(C) = k1_nat_1(k3_finseq_1(B),1) & ! [D] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d19_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(d19_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(d19_idea_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( m2_finseq_1(D,k4_ordinal1) => k1_funct_1(C,D) = k11_idea_1(B,D,A) ) ) ) ) ) )).
fof(d19_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(d19_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ( B != C => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d19_integra1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( B = k14_integra1(A) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(A)) => k1_funct_1(B,C) = k18_rvsum_1(k17_finseq_1(k1_numbers,C,A)) ) ) ) ) ) ) )).
fof(d19_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m2_interva1(B,A) => ! [C] : ( 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))) ) ) ) )).
fof(d19_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ( v9_intpro_1(A) <=> ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(d19_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( v5_lattice3(A) <=> ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r4_lattice3(A,C,B) & ! [F] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(d19_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(d19_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( v16_lattices(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r2_lattices(A,C,B) ) ) ) ) )).
fof(d19_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k9_funct_2(k6_glib_000(A),k4_ordinal1))) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ( ( k1_relset_1(k6_glib_000(A),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),B)) = k6_glib_000(A) => ( C = k19_lexbfs(A,B) <=> C = o_1_0_lexbfs(A) ) ) & ( k1_relset_1(k6_glib_000(A),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),B)) != k6_glib_000(A) => ( C = k19_lexbfs(A,B) <=> ? [D] : ( ~ v1_xboole_0(D) & v6_membered(D) & v1_finset_1(D) & ? [E] : ( v1_relat_1(E) & v1_funct_1(E) & D = k10_xtuple_0(E) & E = k5_relset_1(k6_glib_000(A),k4_ordinal1,k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k4_ordinal1,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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),B)))) & C = o_2_1_lexbfs(D,E) ) ) ) ) ) ) ) ) )).
fof(d19_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k14_lmod_7(A,B,C,D) = k8_lmod_7(A,B,C,D) ) ) ) ) )).
fof(d19_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( ~ v2_struct_0(D) & v13_algstr_0(D) & v2_rlvect_1(D) & v3_rlvect_1(D) & v4_rlvect_1(D) & v1_clvect_1(D) & v2_clvect_1(D) & v3_clvect_1(D) & v4_clvect_1(D) & v5_clvect_1(D) & l1_clvect_1(D) ) => ( D = k22_lpspacc1(A,B,C) <=> ( u1_struct_0(D) = k18_lpspacc1(A,B,C) & r1_funct_2(k2_zfmisc_1(u1_struct_0(D),u1_struct_0(D)),u1_struct_0(D),k2_zfmisc_1(k18_lpspacc1(A,B,C),k18_lpspacc1(A,B,C)),k18_lpspacc1(A,B,C),u1_algstr_0(D),k19_lpspacc1(A,B,C)) & k4_struct_0(D) = k20_lpspacc1(A,B,C) & r1_funct_2(k2_zfmisc_1(k2_numbers,u1_struct_0(D)),u1_struct_0(D),k2_zfmisc_1(k2_numbers,k18_lpspacc1(A,B,C)),k18_lpspacc1(A,B,C),u1_clvect_1(D),k21_lpspacc1(A,B,C)) ) ) ) ) ) ) )).
fof(d19_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k18_lpspace1(A,B,C))) => ? [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(d19_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ( r4_ltlaxio1(A,B) <=> B = k2_ltlaxio1(A) ) ) ) )).
fof(d19_margrel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => k3_funct_2(A,k6_margrel1,C,D) = k9_margrel1(k3_funct_2(A,k6_margrel1,B,D)) ) ) ) ) ) )).
fof(d19_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => k22_member_1(A,B) = k12_member_1(k1_tarski(B),A) ) ) )).
fof(d19_mod_2,axiom,( k17_mod_2 = k5_numbers )).
fof(d19_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v7_modelc_1(A) <=> ? [B] : ( v1_modelc_1(B) & m2_finseq_1(B,k4_ordinal1) & ? [C] : ( v1_modelc_1(C) & m2_finseq_1(C,k4_ordinal1) & A = k11_modelc_1(B,C) ) ) ) ) )).
fof(d19_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ~ ( ~ v4_modelc_2(A) & ~ v5_modelc_2(A) & ~ v7_modelc_2(A) & ~ v8_modelc_2(A) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( ( v4_modelc_2(A) => ( B = k11_modelc_2(A) <=> ? [C] : ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) & k4_modelc_2(B,C) = A ) ) ) & ( v5_modelc_2(A) => ( B = k11_modelc_2(A) <=> ? [C] : ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) & k5_modelc_2(B,C) = A ) ) ) & ( v7_modelc_2(A) => ( B = k11_modelc_2(A) <=> ? [C] : ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) & k7_modelc_2(B,C) = A ) ) ) & ~ ( ~ v4_modelc_2(A) & ~ v5_modelc_2(A) & ~ v7_modelc_2(A) & ~ ( B = k11_modelc_2(A) <=> ? [C] : ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) & k8_modelc_2(B,C) = A ) ) ) ) ) ) ) )).
fof(d19_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( r5_modelc_3(A,B) <=> ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,C) & ~ r1_xxreal_0(k3_finseq_1(B),C) & ! [D] : ( ( v1_modelc_3(D,A) & l1_modelc_3(D,A) ) => ! [E] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(d19_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v16_monoid_0(A) <=> v8_monoid_0(u2_algstr_0(A),u1_struct_0(A)) ) ) )).
fof(d19_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( C = k14_msualg_2(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( v3_msualg_1(D,A) & m1_msualg_2(D,A,B) ) ) ) ) ) )).
fof(d19_msualg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_msualg_3(A,B,C,D) => ! [F] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d19_ncfcont1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ 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] : ! [D] : ( ( 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] : ( v1_xreal_0(E) & ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r2_hidden(F,C) & r2_hidden(G,C) ) => r1_xxreal_0(k2_normsp_0(B,k5_algstr_0(B,k7_partfun1(u1_struct_0(B),D,F),k7_partfun1(u1_struct_0(B),D,G))),k3_xcmplx_0(E,k2_normsp_0(A,k5_algstr_0(A,F,G)))) ) ) ) ) ) ) ) ) ) )).
fof(d19_oposet_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( 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))) ) ) ) ) ) ) )).
fof(d19_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(k2_osafree(A,B))) => k17_osafree(A,B,C) = a_3_1_osafree(A,B,C) ) ) ) )).
fof(d19_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v2_msualg_4(C,A,B) & v3_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ! [D] : ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d19_pboole,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) ) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d19_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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] : ( r7_pdiff_1(A,B,C,D,E) <=> ( r1_tarski(E,k1_relset_1(u1_struct_0(k4_real_ns1(A)),D)) & ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d19_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( 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)) ) ) )).
fof(d19_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d19_pscomp_1,axiom,( ! [A] : ( 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)))) ) )).
fof(d19_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v3_qc_lang1(B,A) <=> ? [C] : ( m1_subset_1(C,k9_qc_lang1(A)) & B = k13_qc_lang1(A,C) ) ) ) ) )).
fof(d19_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( r1_qc_lang2(A,B,C) <=> ~ ( C != k13_qc_lang1(A,B) & ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ( C != k14_qc_lang1(A,B,D) & C != k14_qc_lang1(A,D,B) ) ) & ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => C != k15_qc_lang1(A,D,B) ) ) ) ) ) ) )).
fof(d19_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_quantal1(A) ) => ( v20_quantal1(A) <=> v18_quantal1(u1_quantal1(A),A) ) ) )).
fof(d19_quaterni,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( C = k19_quaterni(A,B) <=> ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & B = k6_quaterni(D,E,F,G) & C = k6_quaterni(k2_xcmplx_0(A,D),E,F,G) ) ) ) ) ) ) ) )).
fof(d19_quofield,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(d19_ratfunc1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_ratfunc1(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(d19_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ( v4_rewrite1(A) <=> ! [B] : ! [C] : ( ( r3_rewrite1(A,B) & r3_rewrite1(A,C) & r2_rewrite1(A,B,C) ) => B = C ) ) ) )).
fof(d19_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_ringcat1(A) ) => ! [B] : ( ( 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] : ( m3_ringcat1(C,k10_ringcat1(A)) => k3_funct_2(k10_ringcat1(A),A,B,C) = k11_ringcat1(A,C) ) ) ) ) )).
fof(d19_rlvect_2,axiom,( ! [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) ) => 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)) ) )).
fof(d19_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k14_robbins1(A,B) = k1_lattices(A,k11_robbins1(A,B),k12_robbins1(A,B)) ) ) )).
fof(d19_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_tarski(A))) => ( v9_scmyciel(B,A) <=> ! [C] : ! [D] : ~ ( C != D & r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k2_tarski(C,D),A) ) ) ) ) )).
fof(d19_simplex0,axiom,( ! [A] : ( ( ~ v3_pencil_1(A) & v1_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( v1_xreal_0(B) => ( ( v1_int_1(B) & r1_xxreal_0(B,k6_simplex0(A)) ) => ! [C] : ( m3_simplex0(C,A,B) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d19_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => k19_sin_cos(A) = k1_funct_1(k18_sin_cos,A) ) )).
fof(d19_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( C = k13_stacks_1(A,B) <=> ( r1_stacks_1(A,C) & ? [D] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d19_struct_0,axiom,( ! [A] : ! [B] : ( l1_struct_0(B) => ( v13_struct_0(B,A) <=> v3_card_1(u1_struct_0(B),A) ) ) )).
fof(d19_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => ( v2_substut1(B,A) <=> ? [C] : ( m1_subset_1(C,k1_substut1(A)) & B = k1_domain_1(k3_cqc_lang(A),k1_substut1(A),k5_cqc_lang(A),C) ) ) ) ) )).
fof(d19_turing_1,axiom,( ! [A] : ( ( v1_turing_1(A) & l1_turing_1(A) ) => ( A = k18_turing_1 <=> ( u1_turing_1(A) = k7_domain_1(k4_ordinal1,k5_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),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1)),k8_mcart_1(k4_ordinal1,k4_ordinal1,k3_turing_1(4),k7_domain_1(k4_ordinal1,k5_numbers,1)),k3_zfmisc_1(k3_turing_1(4),k7_domain_1(k4_ordinal1,k5_numbers,1),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1)),u3_turing_1(A),k17_turing_1) & u4_turing_1(A) = k5_numbers & u5_turing_1(A) = 4 ) ) ) )).
fof(d19_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d19_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) ) => k64_valued_1(A) = k2_xxreal_2(k1_relset_1(k4_ordinal1,A)) ) )).
fof(d19_valued_2,axiom,( ! [A] : ! [B] : ( B = k13_valued_2(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) ) ) )).
fof(d19_vectsp_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(d19_waybel34,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v7_waybel34(B,A) <=> r2_hidden(k3_yellow_0(A),u1_struct_0(B)) ) ) ) )).
fof(d19_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v12_waybel_0(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & r1_orders_2(A,D,C) ) => r2_hidden(D,B) ) ) ) ) ) ) )).
fof(d19_waybel_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => v5_waybel_1(k4_waybel_1(A,B),A,A) ) ) ) ) )).
fof(d19_waybel_4,axiom,( ! [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] : ( B = k12_waybel_4(A) <=> ! [C] : ( 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)))) ) ) ) ) )).
fof(d19_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v8_yellow_0(B,A) <=> ! [C] : ( 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)) ) ) ) ) ) )).
fof(d19_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m4_yellow_6(B,A) => ( B = k12_yellow_6(A) <=> ! [C] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(d19_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => k13_zf_lang(A,B) = k6_zf_lang(k8_zf_lang(A,k6_zf_lang(B))) ) ) )).
fof(d19_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ( v8_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ( m3_zmodul01(C,A,B) <=> r1_zmodul01(A,C,B) ) ) ) ) ) )).
fof(d19_zmodul02,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_zmodul02(B,A) => k18_zmodul02(A,B) = a_2_2_zmodul02(A,B) ) ) )).
fof(d1_abcmiz_1,axiom,( ! [A] : ! [B] : ( B = k1_abcmiz_1(A) <=> ( r1_tarski(A,B) & ! [C] : ! [D] : ( r2_hidden(k4_tarski(C,D),B) => r1_tarski(C,B) ) & ! [C] : ( ( r1_tarski(A,C) & ! [D] : ! [E] : ( r2_hidden(k4_tarski(D,E),C) => r1_tarski(D,C) ) ) => r1_tarski(B,C) ) ) ) )).
fof(d1_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => ( v1_abcmiz_a(A) <=> ! [B] : ( 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)) ) ) ) ) ) )).
fof(d1_abian,axiom,( ! [A] : ( v1_int_1(A) => ( v1_abian(A) <=> r1_int_1(2,A) ) ) )).
fof(d1_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k5_numbers,A) => k9_complex1(A) = A ) & ( ~ r1_xxreal_0(k5_numbers,A) => k9_complex1(A) = k4_xcmplx_0(A) ) ) ) )).
fof(d1_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_aff_1(A,B,C,D) <=> r2_analoaf(A,B,C,B,D) ) ) ) ) ) )).
fof(d1_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v1_aff_2(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_aff_3,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v1_aff_3(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ! [L] : ( m1_subset_1(L,u1_struct_0(A)) => ! [M] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(d1_afinsq_1,axiom,( ! [A] : k3_afinsq_1(A) = k16_funcop_1(k5_numbers,A) )).
fof(d1_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ( r2_hidden(C,k1_relset_1(k4_ordinal1,B)) => k1_funct_1(B,C) = k1_funct_1(A,k6_xcmplx_0(k1_afinsq_1(A),k1_nat_1(C,1))) ) ) ) ) ) ) )).
fof(d1_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => k1_afproj(A) = a_1_0_afproj(A) ) )).
fof(d1_afvect0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ( v1_afvect0(A) <=> ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,D) => B = C ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_analoaf(A,B,C,D,E) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r2_analoaf(A,B,D,D,C) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,E) => r2_analoaf(A,B,D,C,E) ) ) ) ) ) ) ) ) )).
fof(d1_afvect01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ( v1_afvect01(A) <=> ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_analoaf(A,B,C,C,B) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_analoaf(A,B,C,B,B) => B = C ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r2_analoaf(A,B,D,D,C) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ~ ( B != D & r2_analoaf(A,B,C,C,D) ) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(u1_unialg_1(A))) => ! [E] : ( m5_margrel1(E,u1_struct_0(A),k1_unialg_2(A)) => ! [F] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_algseq_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_polynom1(B,A) <=> ? [C] : ( v7_ordinal1(C) & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => k1_funct_1(B,D) = k4_struct_0(A) ) ) ) ) ) ) )).
fof(d1_algspec1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => k1_algspec1(A,B) = k1_funct_4(k6_partfun1(A),k5_relat_1(B,A)) ) )).
fof(d1_algstr_0,axiom,( ! [A] : ( l1_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d1_algstr_1,axiom,( ! [A] : k1_algstr_1(A) = A )).
fof(d1_algstr_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_algstr_0(A) & v3_algstr_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k1_algstr_2(A,B) <=> k1_algstr_0(A,B,C) = k4_struct_0(A) ) ) ) ) )).
fof(d1_algstr_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_algstr_3(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(d1_altcat_1,axiom,( ! [A] : ( l1_altcat_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_altcat_1(A,B,C) = k1_binop_1(u1_altcat_1(A),B,C) ) ) ) )).
fof(d1_altcat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_altcat_1(A,B,C)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(d1_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d1_ami_2,axiom,( k1_ami_2 = k2_xboole_0(k1_tarski(k4_ordinal1),k2_scm_inst) )).
fof(d1_ami_3,axiom,( k1_ami_3 = g1_extpro_1(k7_card_1(2),k1_ami_2,k10_subset_1(k4_ordinal1,k1_ami_2),k3_scm_inst,k3_ami_2,k4_ami_2,k9_ami_2) )).
fof(d1_ami_4,axiom,( k1_ami_4 = k1_funct_4(k16_funcop_1(k5_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(k5_numbers),k10_ami_3(1))),k1_funct_4(k16_funcop_1(2,k2_ami_3(k10_ami_3(k5_numbers),k10_ami_3(2))),k1_funct_4(k16_funcop_1(3,k9_ami_3(k5_numbers,k10_ami_3(1))),k16_funcop_1(4,k2_compos_1(k1_ami_3)))))) )).
fof(d1_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r1_ami_wstd(A,B,C,D) <=> ? [E] : ( ~ v1_xboole_0(E) & m2_finseq_1(E,k4_ordinal1) & k7_partfun1(k4_ordinal1,E,1) = C & k7_partfun1(k4_ordinal1,E,k3_finseq_1(E)) = D & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(1,F) => ( r1_xxreal_0(k3_finseq_1(E),F) | r2_hidden(k7_partfun1(k4_ordinal1,E,k1_nat_1(F,1)),k3_amistd_1(A,B,k7_partfun1(k4_ordinal1,E,F))) ) ) ) ) ) ) ) ) ) )).
fof(d1_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_compos_0(u1_compos_1(B))) => ( v1_amistd_1(C,A,B) <=> ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d1_amistd_2,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(d1_amistd_3,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) => ! [D] : ( ( v1_relat_1(D) & v5_relat_1(D,k4_ordinal1) & v5_ordinal1(D) & v1_funct_1(D) ) => ( D = k1_amistd_3(A,B,C) <=> ( k9_xtuple_0(D) = k1_card_1(C) & ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d1_amistd_5,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_compos_1(B)) => ( v1_amistd_5(C,A,B) <=> ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( ( 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)) ) => r6_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)) ) ) ) ) ) ) ) )).
fof(d1_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) <=> ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & D = k3_rlvect_1(A,k1_rlvect_1(A,B,E),k1_rlvect_1(A,C,F)) ) ) ) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( k3_rlvect_1(A,k1_rlvect_1(A,B,D),k1_rlvect_1(A,C,E)) = k4_struct_0(A) => ( D = k5_numbers & E = k5_numbers ) ) ) ) ) ) ) ) ) )).
fof(d1_analoaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_analoaf(A,B,C,D,E) <=> ~ ( B != C & D != E & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ~ r1_xxreal_0(G,k5_numbers) & k1_rlvect_1(A,k5_algstr_0(A,C,B),F) = k1_rlvect_1(A,k5_algstr_0(A,E,D),G) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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,k4_xcmplx_0(k3_geomtrap(A,B,C,D)))) ) ) ) ) )).
fof(d1_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_anproj_1(A,B,C) <=> ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & k1_rlvect_1(A,B,D) = k1_rlvect_1(A,C,E) & D != k5_numbers & E != k5_numbers ) ) ) ) ) ) )).
fof(d1_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d1_aofa_a00,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ! [C] : k2_aofa_a00(A,B,C) = k1_aofa_a00(A,k1_pboole(A),B,k1_tarski(C)) ) )).
fof(d1_aofa_i00,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_funct_1(A) ) => ! [B] : ! [C] : k1_aofa_i00(A,B,C) = a_3_0_aofa_i00(A,B,C) ) )).
fof(d1_armstrng,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( C = k1_armstrng(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> r2_waybel_4(A,D,B) ) ) ) ) )).
fof(d1_arrow,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( B = k2_arrow(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) & ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(k4_tarski(D,E),C) | r2_hidden(k4_tarski(E,D),C) ) ) ) & ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d1_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( 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] : ( m1_subset_1(D,k2_arytm_2) & ? [E] : ( 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(k5_numbers),k2_arytm_2)) ) => ( C = k1_arytm_0(A,B) <=> ? [D] : ( m1_subset_1(D,k2_arytm_2) & ? [E] : ( m1_subset_1(E,k2_arytm_2) & A = D & B = k4_tarski(k5_numbers,E) & C = k2_arytm_1(D,E) ) ) ) ) & ( ( r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) ) => ( C = k1_arytm_0(A,B) <=> ? [D] : ( m1_subset_1(D,k2_arytm_2) & ? [E] : ( m1_subset_1(E,k2_arytm_2) & A = k4_tarski(k5_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(k5_numbers),k2_arytm_2)) ) & ~ ( r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) ) & ~ ( C = k1_arytm_0(A,B) <=> ? [D] : ( m1_subset_1(D,k2_arytm_2) & ? [E] : ( m1_subset_1(E,k2_arytm_2) & A = k4_tarski(k5_numbers,D) & B = k4_tarski(k5_numbers,E) & C = k4_tarski(k5_numbers,k7_arytm_2(D,E)) ) ) ) ) ) ) ) ) )).
fof(d1_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( 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 ) ) ) ) ) ) )).
fof(d1_arytm_2,axiom,( k1_arytm_2 = k6_subset_1(a_0_0_arytm_2,k1_tarski(k5_arytm_3)) )).
fof(d1_arytm_3,axiom,( k1_arytm_3 = 1 )).
fof(d1_asympt_0,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_asympt_0(A) <=> ( ~ r1_xxreal_0(A,k5_numbers) & A != 1 ) ) ) )).
fof(d1_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( D = k1_asympt_1(A,B,C) <=> ! [E] : ( m1_subset_1(E,k4_ordinal1) => k9_nat_1(k1_numbers,D,E) = k2_power(A,k2_xcmplx_0(k3_xcmplx_0(B,E),C)) ) ) ) ) ) ) )).
fof(d1_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) => ( B = k1_autalg_1(A) <=> ! [C] : ( ( 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) ) ) ) ) ) )).
fof(d1_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) => ( B = k1_autgroup(A) <=> ( ! [C] : ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(d1_bagorder,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( 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] : ( m1_subset_1(F,k4_ordinal1) => ( r2_hidden(F,k7_nat_d(C,B)) => k1_funct_1(E,F) = k1_funct_1(D,k1_nat_1(B,F)) ) ) ) ) ) ) ) ) )).
fof(d1_bcialg_1,axiom,( ! [A] : ( l1_bcialg_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d1_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( E = k1_bcialg_2(A,B,C,D) <=> ? [F] : ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & E = k3_funct_2(k4_ordinal1,u1_struct_0(A),F,D) & k3_funct_2(k4_ordinal1,u1_struct_0(A),F,k5_numbers) = B & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( ~ r1_xxreal_0(D,G) => k3_funct_2(k4_ordinal1,u1_struct_0(A),F,k1_nat_1(G,1)) = k1_bcialg_1(A,k3_funct_2(k4_ordinal1,u1_struct_0(A),F,G),C) ) ) ) ) ) ) ) ) ) )).
fof(d1_bcialg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_bcialg_1(A) ) => ( v1_bcialg_3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(d1_bcialg_4,axiom,( ! [A] : ( l1_bcialg_4(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d1_bcialg_5,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => k1_bcialg_5(A,B,C,D,E) = k1_bcialg_2(A,k1_bcialg_2(A,B,k1_bcialg_1(A,B,C),k1_nat_1(D,1)),k1_bcialg_1(A,C,B),E) ) ) ) ) ) )).
fof(d1_bcialg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_bcialg_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),k4_ordinal1),u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_ordinal1),u1_struct_0(A)))) ) => ( B = k2_bcialg_6(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),B,C,k5_numbers) = k4_struct_0(A) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),B,C,k1_nat_1(D,1)) = k1_bcialg_1(A,C,k2_bcialg_1(A,k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),B,C,D))) ) ) ) ) ) ) )).
fof(d1_bciideal,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => k1_bciideal(A,B) = a_2_0_bciideal(A,B) ) ) )).
fof(d1_bhsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(d1_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_bhsp_2(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(E,F) & r1_xxreal_0(D,k4_bhsp_1(A,k1_normsp_1(A,B,F),C)) ) ) ) ) ) ) ) ) )).
fof(d1_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_bhsp_3(B,A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & ? [F] : ( v7_ordinal1(F) & 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))) ) ) ) ) ) ) ) ) )).
fof(d1_bhsp_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( C = k1_bhsp_4(A,B) <=> ( k1_normsp_1(A,C,k5_numbers) = k1_normsp_1(A,B,k5_numbers) & ! [D] : ( v7_ordinal1(D) => k1_normsp_1(A,C,k1_nat_1(D,1)) = k1_algstr_0(A,k1_normsp_1(A,C,D),k1_normsp_1(A,B,k1_nat_1(D,1))) ) ) ) ) ) ) )).
fof(d1_bhsp_6,axiom,( ! [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_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] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k1_bhsp_6(A,B) <=> ? [D] : ( 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)) ) ) ) ) ) ) )).
fof(d1_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( l1_vectsp_1(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(d1_binari_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ( B = k1_binari_2(A) <=> ! [C] : ( 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) ) ) ) ) ) )).
fof(d1_binari_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k6_margrel1) ) => ( C = k1_binari_3(A,B) <=> ! [D] : ( 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),k5_numbers,k7_margrel1,k8_margrel1) ) ) ) ) ) ) )).
fof(d1_binari_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( C = k1_binari_4(A,B) <=> ( r1_xxreal_0(B,k5_series_1(2,C)) & r1_xxreal_0(A,C) & ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(B,k5_series_1(2,D)) & r1_xxreal_0(A,D) ) => r1_xxreal_0(C,D) ) ) ) ) ) ) ) )).
fof(d1_binarith,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k6_margrel1) ) => ( C = k3_binarith(A,B) <=> ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k2_finseq_1(A)) => k7_partfun1(k6_margrel1,C,D) = k9_margrel1(k7_partfun1(k6_margrel1,B,D)) ) ) ) ) ) ) )).
fof(d1_binop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C)) ) )).
fof(d1_binop_2,axiom,( ! [A] : ( ( 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_binop_2 <=> ! [B] : ( v1_xcmplx_0(B) => k1_funct_1(A,B) = k4_xcmplx_0(B) ) ) ) )).
fof(d1_bintree1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) )).
fof(d1_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k2_trees_2(A,B),k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_trees_2(A,B),k4_ordinal1))) ) => ( C = k1_bintree2(A,B) <=> ! [D] : ( m1_bintree2(D,A) => ( r2_hidden(D,k2_trees_2(A,B)) => ! [E] : ( m2_finseq_2(E,k6_margrel1,k4_finseq_2(B,k6_margrel1)) => ( E = k4_finseq_5(k6_margrel1,D) => k1_funct_1(C,D) = k1_nat_1(k6_binarith(B,E),1) ) ) ) ) ) ) ) ) )).
fof(d1_birkhoff,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m2_pboole(D,u1_struct_0(A),B,u3_msualg_1(A,C)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(d1_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_boolealg(A,B,C) = k4_lattices(A,B,k7_lattices(A,C)) ) ) ) )).
fof(d1_boolmark,axiom,( ! [A] : ( l1_petri(A) => k1_boolmark(A) = k9_funct_2(u1_struct_0(A),k6_margrel1) ) )).
fof(d1_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_connsp_2(E,B,k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,D)) => ? [F] : ( m1_connsp_2(F,A,D) & r1_tarski(k7_relset_1(u1_struct_0(A),u1_struct_0(B),C,F),E) ) ) ) ) ) ) ) )).
fof(d1_borsuk_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_borsuk_2(A,B,C) <=> ? [D] : ( 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,k5_numbers) = B & k1_funct_1(D,1) = C ) ) ) ) ) )).
fof(d1_borsuk_4,axiom,( ! [A] : ( ( v1_pre_topc(A) & m1_pre_topc(A,k5_topmetr) ) => ( A = k1_borsuk_4 <=> u1_struct_0(A) = k2_rcomp_1(k5_numbers,1) ) ) )).
fof(d1_borsuk_5,axiom,( k1_borsuk_5 = k6_subset_1(k1_numbers,k3_numbers) )).
fof(d1_borsuk_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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(k5_numbers,1)),u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k4_topmetr(C,D)),k4_treal_1(A,B,k1_treal_1(k5_numbers,1),k2_treal_1(k5_numbers,1)),k3_treal_1(C,D,k1_treal_1(C,D),k2_treal_1(C,D))) ) ) ) ) )).
fof(d1_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : k1_borsuk_7(A,B,C,D,E,F) = k1_funct_4(k4_funct_4(A,B,D,E),k16_funcop_1(C,F)) )).
fof(d1_brouwer,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => k1_brouwer(A,B) = a_2_0_brouwer(A,B) ) ) )).
fof(d1_bspace,axiom,( ! [A] : ( l1_struct_0(A) => k1_bspace(A) = k6_finseq_1(k2_struct_0(A)) ) )).
fof(d1_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ( r1_xxreal_0(A,B) <=> k6_xboolean(A,B) = k8_margrel1 ) ) ) )).
fof(d1_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ( C = k2_bvfunc_2(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( v1_relat_1(E) & v1_funct_1(E) & ? [F] : ( m1_subset_1(F,k1_zfmisc_1(k1_zfmisc_1(A))) & k9_xtuple_0(E) = B & k10_xtuple_0(E) = F & ! [G] : ( r2_hidden(G,B) => r2_hidden(k1_funct_1(E,G),G) ) & D = k8_setfam_1(A,F) & D != k1_xboole_0 ) ) ) ) ) ) ) )).
fof(d1_c0sp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_c0sp1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => r2_hidden(k4_algstr_0(A,C),B) ) ) ) ) ) )).
fof(d1_c0sp2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( v1_xreal_0(B) => k1_c0sp2(A,B) = k7_funcop_1(u1_struct_0(A),B) ) ) )).
fof(d1_calcul_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( ( ~ r1_xxreal_0(k3_finseq_1(B),k5_numbers) => ( C = k1_calcul_1(A,B) <=> ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( k3_finseq_1(B) = k1_nat_1(D,1) => r2_relset_1(k4_ordinal1,A,C,k2_partfun1(k4_ordinal1,A,B,k2_finseq_1(D))) ) ) ) ) & ( r1_xxreal_0(k3_finseq_1(B),k5_numbers) => ( C = k1_calcul_1(A,B) <=> C = k1_xboole_0 ) ) ) ) ) ) )).
fof(d1_calcul_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k1_calcul_2(A,B) = a_2_0_calcul_2(A,B) ) ) )).
fof(d1_cantor_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ( C = k1_cantor_1(A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( r2_hidden(D,C) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(A))) & r1_tarski(E,B) & D = k5_setfam_1(A,E) ) ) ) ) ) ) )).
fof(d1_card_1,axiom,( ! [A] : ( v1_card_1(A) <=> ? [B] : ( v3_ordinal1(B) & A = B & ! [C] : ( v3_ordinal1(C) => ( r2_wellord2(C,B) => r1_ordinal1(B,C) ) ) ) ) )).
fof(d1_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => k1_card_2(A,B) = k1_card_1(k10_ordinal2(A,B)) ) ) )).
fof(d1_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_card_3(A) <=> ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => v1_card_1(k1_funct_1(A,B)) ) ) ) )).
fof(d1_card_5,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ( B = k1_card_5(A) <=> ( r2_ordinal2(A,B) & ! [C] : ( v1_card_1(C) => ( r2_ordinal2(A,C) => r1_ordinal1(B,C) ) ) ) ) ) ) )).
fof(d1_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d1_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k9_funct_2(A,k2_tarski(C,D)))) => ( E = k1_card_fin(A,B,C,D) <=> ! [F] : ( r2_hidden(F,E) <=> ? [G] : ( 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 ) ) ) ) ) ) )).
fof(d1_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( r1_card_lar(A,B) <=> ( r1_tarski(B,A) & k3_ordinal2(B) = A ) ) ) )).
fof(d1_cardfin2,axiom,( ! [A] : ( v1_xreal_0(A) => k1_cardfin2(A) = k1_int_1(k2_xcmplx_0(A,k7_xcmplx_0(1,2))) ) )).
fof(d1_cat_1,axiom,( ! [A] : ( l1_cat_1(A) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(d1_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(d1_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ! [C] : ( ( 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] : ( ( 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] : ( r2_hidden(E,B) => k7_partfun1(u1_struct_0(A),D,E) = k3_graph_1(A,k7_partfun1(u4_struct_0(A),C,E)) ) ) ) ) ) )).
fof(d1_cat_4,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( m1_cat_1(D,A,B,C) & ? [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d1_catalan1,axiom,( ! [A] : ( v7_ordinal1(A) => k1_catalan1(A) = k7_xcmplx_0(k4_newton(k7_nat_d(A,1),k7_nat_d(k3_xcmplx_0(2,A),2)),A) ) )).
fof(d1_catalan2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ( v1_catalan2(A) <=> ( r1_tarski(k2_relset_1(k4_ordinal1,A),k7_domain_1(k4_ordinal1,k5_numbers,1)) & ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(B,k1_relset_1(k4_ordinal1,A)) => r1_xxreal_0(k3_xcmplx_0(2,k7_afinsq_2(k5_relat_1(A,B))),B) ) ) ) ) ) )).
fof(d1_catalg_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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] : ( r2_hidden(E,A) => k1_funct_1(D,E) = k5_relat_1(C,k1_funct_1(B,E)) ) ) ) ) ) )).
fof(d1_cayley,axiom,( ! [A] : k1_cayley(A) = a_1_0_cayley(A) )).
fof(d1_cc0sp1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) )).
fof(d1_cc0sp2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d1_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [B] : ( v1_xcmplx_0(B) => ( r1_cfcont_1(A,B) <=> ( r2_hidden(B,k1_relset_1(k2_numbers,A)) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,k2_numbers,k2_numbers,C,A)) & k7_partfun1(k2_numbers,A,B) = k3_comseq_2(k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,C,A)) ) ) ) ) ) ) ) )).
fof(d1_cfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_cfdiff_1(B,A) <=> ( v2_comseq_2(B) & k3_comseq_2(B) = A ) ) ) ) )).
fof(d1_cfuncdom,axiom,( ! [A] : ! [B] : ( ( 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] : ( m2_funct_2(C,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ! [D] : ( 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,k3_binop_2,C,D)) ) ) ) ) )).
fof(d1_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( 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(k5_numbers)))) & ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,k1_relset_1(A,D)) => k7_partfun1(k2_numbers,D,E) = k3_xcmplx_0(k7_partfun1(k2_numbers,B,E),k5_xcmplx_0(k7_partfun1(k2_numbers,C,E))) ) ) ) ) ) ) ) ) )).
fof(d1_cgames_1,axiom,( k1_cgames_1 = g1_cgames_1(k1_xboole_0,k1_xboole_0) )).
fof(d1_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => k1_chord(A,B) = k10_xtuple_0(k1_graph_2(A,B,k3_finseq_1(A))) ) ) )).
fof(d1_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ( v1_circcmb3(C,A,B) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & v1_circuit2(k5_facirc_1(A,B,C,D),A,B) ) ) ) ) ) )).
fof(d1_circcomb,axiom,( ! [A] : ( l1_msualg_1(A) => ! [B] : ( 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)) ) ) ) ) )).
fof(d1_circled1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_rltopsp1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(k9_complex1(D),1) & r2_hidden(C,B) ) => r2_hidden(k1_rlvect_1(A,C,D),B) ) ) ) ) ) ) )).
fof(d1_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( ~ 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)))))) ) ) ) )).
fof(d1_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d1_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msafree2(C,A,B) => ! [D] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d1_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( r1_ckspace1(A,B,C,D) <=> ( r1_tarski(D,k1_relset_1(k1_euclid(A),B)) & r5_pdiff_9(A,B,C,D) & ! [E] : ( ( ~ v1_xboole_0(E) & m2_finseq_1(E,k4_ordinal1) ) => ( ( r1_xxreal_0(k3_finseq_1(E),C) & r1_tarski(k2_relset_1(k4_ordinal1,E),k2_finseq_1(A)) ) => r1_pdiff_9(A,D,k5_pdiff_9(A,D,E,B)) ) ) ) ) ) ) ) )).
fof(d1_classes1,axiom,( ! [A] : ( v1_classes1(A) <=> ! [B] : ! [C] : ( ( r2_hidden(B,A) & r1_tarski(C,B) ) => r2_hidden(C,A) ) ) )).
fof(d1_classes2,axiom,( ! [A] : ( v1_classes2(A) <=> ( v1_ordinal1(A) & v2_classes1(A) ) ) )).
fof(d1_clopban1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( 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] : ( v1_xcmplx_0(D) => ! [E] : ( m2_funct_2(E,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d1_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(k6_clopban1(A,A)),k8_clopban1(A,A)) => ! [C] : ( 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) ) ) ) )).
fof(d1_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clopban3(B,A) <=> v9_clvect_1(k1_bhsp_4(A,B),A) ) ) ) )).
fof(d1_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( C = k1_clopban4(A,B) <=> ! [D] : ( v7_ordinal1(D) => k1_normsp_1(A,C,D) = k1_clvect_1(A,k6_clopban3(A,B,D),k7_xcmplx_0(k6_complex1,k2_newton(D))) ) ) ) ) ) )).
fof(d1_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m2_pboole(C,A,k5_mssubfam(A,B),k5_mssubfam(A,B)) => ( v1_closure1(C,A,B) <=> ! [D] : ( m1_pboole(D,A,k5_mssubfam(A,B)) => r2_pboole(A,D,k2_closure1(A,B,C,D)) ) ) ) ) )).
fof(d1_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( C = k1_closure2(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> m3_pboole(D,A,B) ) ) ) )).
fof(d1_closure3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) )).
fof(d1_clvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xcmplx_0(C) => k1_clvect_1(A,B,C) = k1_funct_1(u1_clvect_1(A),k4_tarski(C,B)) ) ) ) )).
fof(d1_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clvect_2(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(E,F) & r1_xxreal_0(D,k15_csspace(A,k1_normsp_1(A,B,F),C)) ) ) ) ) ) ) ) ) )).
fof(d1_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clvect_3(B,A) <=> v1_clvect_2(k1_bhsp_4(A,B),A) ) ) ) )).
fof(d1_coh_sp,axiom,( ! [A] : ( v1_coh_sp(A) <=> ! [B] : ( ( r1_tarski(B,A) & ! [C] : ! [D] : ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k2_xboole_0(C,D),A) ) ) => r2_hidden(k3_tarski(B),A) ) ) )).
fof(d1_cohsp_1,axiom,( ! [A] : ( v1_coh_sp(A) <=> ! [B] : ( ! [C] : ! [D] : ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k2_xboole_0(C,D),A) ) => r2_hidden(k3_tarski(B),A) ) ) )).
fof(d1_collsp,axiom,( ! [A] : ! [B] : ( m1_collsp(B,A) <=> r1_tarski(B,k3_zfmisc_1(A,A,A)) ) )).
fof(d1_combgras,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ( r1_ordinal1(k1_nat_1(A,1),k1_card_1(B)) => ( r1_xxreal_0(A,k5_numbers) | ! [C] : ( ( 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))) ) ) ) ) ) ) ) )).
fof(d1_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ( v1_compl_sp(B,A) <=> ! [C] : ( v7_ordinal1(C) => v6_tbsp_1(k9_nat_1(k9_setfam_1(u1_struct_0(A)),B,C),A) ) ) ) ) )).
fof(d1_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( r2_hidden(A,k1_numbers) => ( B = k1_complex1(A) <=> B = A ) ) & ( ~ r2_hidden(A,k1_numbers) => ( B = k1_complex1(A) <=> ? [C] : ( 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,k5_numbers) ) ) ) ) ) )).
fof(d1_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k1_complex2(A,B) = k3_xcmplx_0(A,k8_complex1(B)) ) ) )).
fof(d1_complfld,axiom,( ! [A] : ( ( v36_algstr_0(A) & l6_algstr_0(A) ) => ( A = k1_complfld <=> ( u1_struct_0(A) = k2_numbers & u1_algstr_0(A) = k3_binop_2 & u2_algstr_0(A) = k5_binop_2 & k5_struct_0(A) = k6_complex1 & k4_struct_0(A) = k5_complex1 ) ) ) )).
fof(d1_complsp1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k1_complsp1(A) = g1_pre_topc(k12_seq_4(A),k25_seq_4(A)) ) )).
fof(d1_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ( B = k1_complsp2(A) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(A)) ) => k9_matrix_5(B,C) = k8_complex1(k9_matrix_5(A,C)) ) ) ) ) ) ) )).
fof(d1_compos_0,axiom,( ! [A] : ( v1_compos_0(A) <=> ? [B] : ( ~ v1_xboole_0(B) & r1_tarski(A,k3_zfmisc_1(k4_ordinal1,k13_finseq_1(k4_ordinal1),k13_finseq_1(B))) ) ) )).
fof(d1_compos_1,axiom,( ! [A] : ( ( v1_compos_1(A) & l1_compos_1(A) ) => ( A = k1_compos_1 <=> u1_compos_1(A) = k1_tarski(k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0)) ) ) )).
fof(d1_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) ) ) )).
fof(d1_comptrig,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( A != k5_numbers => ( B = k1_comptrig(A) <=> ( A = k2_xcmplx_0(k3_xcmplx_0(k9_complex1(A),k19_sin_cos(B)),k3_xcmplx_0(k3_xcmplx_0(k9_complex1(A),k17_sin_cos(B)),k7_complex1)) & r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(k3_xcmplx_0(2,k28_sin_cos),B) ) ) ) & ( A = k5_numbers => ( B = k1_comptrig(A) <=> B = k5_numbers ) ) ) ) ) )).
fof(d1_compts_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_compts_1(A) <=> ! [B] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(d1_comput_1,axiom,( ! [A] : ( v1_comput_1(A) <=> ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r1_partfun1(B,C) ) ) ) ) )).
fof(d1_comseq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( B = k1_comseq_3(A) <=> ( k9_nat_1(k2_numbers,B,k5_numbers) = k6_complex1 & ! [C] : ( v7_ordinal1(C) => k9_nat_1(k2_numbers,B,k1_nat_1(C,1)) = k3_xcmplx_0(k9_nat_1(k2_numbers,B,C),A) ) ) ) ) ) )).
fof(d1_conaffm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v1_conaffm(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( r1_conlat_1(A,B,C) <=> r2_hidden(k4_tarski(B,C),u1_conlat_1(A)) ) ) ) ) )).
fof(d1_conmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v1_conmetr(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(A))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_conmetr1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v1_conmetr1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A))) => ! [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_connsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(d1_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(d1_connsp_3,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k1_connsp_3(A,B) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & ! [E] : ( 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 ) ) ) ) ) )).
fof(d1_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v1_xreal_0(C) => k1_convex1(A,B,C) = a_3_0_convex1(A,B,C) ) ) ) )).
fof(d1_convex3,axiom,( ! [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) ) => ! [B] : ( B = k1_convex3(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( v2_convex1(C,A) & m1_rlvect_2(C,A) ) ) ) ) )).
fof(d1_convfun1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_rlvect_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))) => ! [E] : ( m1_subset_1(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ! [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))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k2_qc_lang1(A)) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k5_qc_lang1(A),k2_qc_lang1(A)))) ) => ! [D] : ( m2_finseq_1(D,k2_qc_lang1(A)) => ( D = k1_cqc_lang(A,B,C) <=> ( k3_finseq_1(D) = k3_finseq_1(B) & ! [E] : ( v7_ordinal1(E) => ( ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ( v1_cqc_the1(B,A) <=> ( r2_hidden(k5_cqc_lang(A),B) & ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( m1_subset_1(F,k9_qc_lang1(A)) => ! [G] : ( m2_subset_1(G,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(d1_csspace,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( A = k1_csspace <=> ! [B] : ( r2_hidden(B,A) <=> ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) ) ) ) )).
fof(d1_csspace3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k7_csspace))) => ( A = k1_csspace3 <=> ! [B] : ( r2_hidden(B,A) <=> ( r2_hidden(B,k1_csspace) & v2_comseq_3(k2_csspace(B)) ) ) ) ) )).
fof(d1_csspace4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k7_csspace))) => ( A = k1_csspace4 <=> ! [B] : ( r2_hidden(B,A) <=> ( r2_hidden(B,k1_csspace) & v1_comseq_2(k2_csspace(B)) ) ) ) ) )).
fof(d1_decomp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)))) ) ) ) )).
fof(d1_descip_1,axiom,( ! [A] : ( ( 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))) ) )).
fof(d1_diff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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) = k1_measure6(k1_relset_1(k1_numbers,A),k4_xcmplx_0(B)) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,k1_measure6(k1_relset_1(k1_numbers,A),k4_xcmplx_0(B))) => k1_funct_1(C,D) = k1_funct_1(A,k2_xcmplx_0(D,B)) ) ) ) ) ) ) ) )).
fof(d1_diff_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => k1_diff_2(A,B,C,D,E,F) = k7_xcmplx_0(k6_xcmplx_0(k11_diff_1(A,B,C,D,E),k11_diff_1(A,C,D,E,F)),k6_xcmplx_0(B,F)) ) ) ) ) ) ) )).
fof(d1_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_dilworth(B,A) <=> r6_relat_2(u1_orders_2(A),B) ) ) ) )).
fof(d1_diraf,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),k2_zfmisc_1(A,A)))) => ! [C] : ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_dirort,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ( v1_dirort(A) <=> ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & D != E & r2_analoaf(A,D,E,B,C) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & D != E & r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) )).
fof(d1_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : k2_dist_1(A,B,C) = k5_card_1(k1_dist_1(A,B,C)) ) ) )).
fof(d1_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,A) => k1_dist_2(A,B) = k4_finseq_4(k19_finseq_1(A),B) ) ) )).
fof(d1_dtconstr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k5_trees_3(u1_struct_0(A)))) => ( B = k4_dtconstr(A) <=> ( ! [C] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(C,k1_zfmisc_1(k5_trees_3(u1_struct_0(A)))) => ( ( ! [D] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(d1_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( D = k2_dynkin(A,B,C) <=> ! [E] : ( m1_subset_1(E,k4_ordinal1) => k9_nat_1(k9_setfam_1(A),D,E) = k9_subset_1(A,C,k9_nat_1(k9_setfam_1(A),B,E)) ) ) ) ) ) ) )).
fof(d1_e_siec,axiom,( ! [A] : ( 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) ) ) ) )).
fof(d1_ec_pf_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [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) ) ) ) ) )).
fof(d1_ec_pf_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( v1_ec_pf_2(B,A) <=> r1_xxreal_0(A,B) ) ) ) )).
fof(d1_endalg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) => ( B = k1_endalg(A) <=> ! [C] : ( ( 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) ) ) ) ) ) )).
fof(d1_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k1_ens_1(A) = k3_tarski(a_1_0_ens_1(A)) ) )).
fof(d1_entropy1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( v4_partfun3(A) <=> ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => r1_xxreal_0(k5_numbers,k1_funct_1(A,B)) ) ) ) ) )).
fof(d1_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( D = k1_enumset1(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ~ ( E != A & E != B & E != C ) ) ) )).
fof(d1_eqrel_1,axiom,( ! [A] : k1_eqrel_1(A) = k2_zfmisc_1(A,A) )).
fof(d1_equation,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v1_funcop_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( D = k1_equation(A,B,C) <=> ! [E] : ( r2_hidden(E,A) => k1_funct_1(D,E) = k8_relat_1(k1_funct_1(C,E),k1_funct_1(B,E)) ) ) ) ) ) )).
fof(d1_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => k1_euclid(A) = k4_finseq_2(A,k1_numbers) ) )).
fof(d1_euclid_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k1_euclid_3(A) = k19_euclid(k3_complex1(A),k4_complex1(A)) ) )).
fof(d1_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => k1_euclid_4(A,B,C) = a_3_0_euclid_4(A,B,C) ) ) ) )).
fof(d1_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => k1_euclid_5(A) = k1_funct_1(A,1) ) )).
fof(d1_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => k1_euclid_6(A,B,C) = k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k17_euclid(A),k18_euclid(B)),k3_xcmplx_0(k17_euclid(B),k18_euclid(A))),k6_xcmplx_0(k3_xcmplx_0(k17_euclid(B),k18_euclid(C)),k3_xcmplx_0(k17_euclid(C),k18_euclid(B)))),k6_xcmplx_0(k3_xcmplx_0(k17_euclid(C),k18_euclid(A)),k3_xcmplx_0(k17_euclid(A),k18_euclid(C)))),2) ) ) ) )).
fof(d1_euclid_8,axiom,( k2_euclid_8 = k1_euclid_8(1,k5_numbers,k5_numbers) )).
fof(d1_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) & v3_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & v3_valued_0(C) ) => k1_euclid_9(A,B,C) = o_3_0_euclid_9(A,B,C) ) ) ) )).
fof(d1_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ( r1_euclidlp(A,B,C) <=> ( B != k5_euclid(A) & C != k5_euclid(A) & ? [D] : ( v1_xreal_0(D) & B = k9_euclid(A,C,D) ) ) ) ) ) ) )).
fof(d1_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ( v1_euclmetr(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d1_euler_1,axiom,( ! [A] : ( v7_ordinal1(A) => k1_euler_1(A) = k1_card_1(a_1_0_euler_1(A)) ) )).
fof(d1_euler_2,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( C = k2_euler_2(A,B) <=> ( k3_finseq_1(C) = k3_finseq_1(A) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(A)) => k1_recdef_1(C,D) = k4_nat_d(k1_recdef_1(A,D),B) ) ) ) ) ) ) ) )).
fof(d1_exchsort,axiom,( ! [A] : ( v1_exchsort(A) <=> ? [B] : ( v3_ordinal1(B) & ? [C] : ( v3_ordinal1(C) & k9_xtuple_0(A) = k6_subset_1(B,C) ) ) ) )).
fof(d1_extpro_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( v1_extpro_1(B,A) & l1_extpro_1(B,A) ) => ( B = k1_extpro_1(A) <=> ( u1_struct_0(B) = k6_domain_1(k4_ordinal1,k5_numbers) & u2_struct_0(B) = k5_numbers & u1_compos_1(B) = k1_tarski(k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0)) & u1_memstr_0(A,B) = k16_funcop_1(k5_numbers,k5_numbers) & u2_memstr_0(A,B) = k7_funcop_1(A,k4_ordinal1) & u1_extpro_1(A,B) = k16_funcop_1(k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0),k6_partfun1(k4_card_3(k3_relat_1(k16_funcop_1(k5_numbers,k5_numbers),k7_funcop_1(A,k4_ordinal1))))) ) ) ) ) )).
fof(d1_extreal1,axiom,( ! [A] : ( v1_xxreal_0(A) => ( ( r1_xxreal_0(k5_numbers,A) => k3_extreal1(A) = A ) & ( ~ r1_xxreal_0(k5_numbers,A) => k3_extreal1(A) = k2_xxreal_3(A) ) ) ) )).
fof(d1_facirc_1,axiom,( ! [A] : ( v1_facirc_1(A) <=> ? [B] : ( v1_xtuple_0(B) & r2_hidden(B,A) ) ) )).
fof(d1_facirc_2,axiom,( ! [A] : ! [B] : ( ( v11_struct_0(B) & v1_msualg_1(B) & l1_msualg_1(B) ) => ( B = k1_facirc_2(A) <=> u1_struct_0(B) = k1_tarski(A) ) ) )).
fof(d1_fcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r1_fcont_1(A,B) <=> ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( r1_tarski(k2_relset_1(k1_numbers,C),k1_relset_1(k1_numbers,A)) & v2_comseq_2(C) & k1_seq_2(C) = B ) => ( v2_comseq_2(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,C,A)) & k1_funct_1(A,B) = k1_seq_2(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,C,A)) ) ) ) ) ) ) )).
fof(d1_fcont_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v1_fcont_2(A) <=> ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(D,k1_relset_1(k1_numbers,A)) & r2_hidden(E,k1_relset_1(k1_numbers,A)) & ~ r1_xxreal_0(C,k9_complex1(k6_xcmplx_0(D,E))) & r1_xxreal_0(B,k9_complex1(k6_xcmplx_0(k1_funct_1(A,D),k1_funct_1(A,E)))) ) ) ) ) ) ) ) ) ) )).
fof(d1_fdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_fdiff_1(B,A) <=> ( v2_comseq_2(B) & k1_seq_2(B) = A ) ) ) ) )).
fof(d1_fdiff_9,axiom,( k1_fdiff_9 = k6_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos) )).
fof(d1_ff_siec,axiom,( ! [A] : ! [B] : ( r1_xboole_0(A,B) => k1_ff_siec(A,B) = g1_petri(A,B,k1_partit_2(A,B),k1_partit_2(B,A)) ) )).
fof(d1_fib_num,axiom,( k1_fib_num = k7_xcmplx_0(k2_xcmplx_0(1,k3_square_1(5)),2) )).
fof(d1_fib_num2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ! [B] : ( ( v1_finset_1(B) & v1_setfam_1(B) & v6_membered(B) ) => k1_fib_num2(A,B) = k15_finseq_1(k5_relat_1(A,B)) ) ) )).
fof(d1_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_finseq_1(B,A) => ! [C] : ( m1_finseq_1(C,A) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d1_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => k1_filter_0(A) = u1_struct_0(A) ) )).
fof(d1_filter_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d1_filter_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_filter_2(A,B,C) <=> ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,B) <=> r2_hidden(D,C) ) ) ) ) ) ) )).
fof(d1_fin_topo,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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) ) ) )).
fof(d1_finance1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k1_numbers)))) ) => ( C = k2_finance1(A,B) <=> ( k3_funct_2(k4_ordinal1,k9_setfam_1(k1_numbers),C,k5_numbers) = k1_finance1(A,k2_xcmplx_0(B,1)) & ! [D] : ( v7_ordinal1(D) => k3_funct_2(k4_ordinal1,k9_setfam_1(k1_numbers),C,k1_nat_1(D,1)) = k1_finance1(A,k2_xcmplx_0(B,k7_xcmplx_0(1,k1_nat_1(D,1)))) ) ) ) ) ) ) )).
fof(d1_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => k1_finseq_1(A) = a_1_0_finseq_1(A) ) )).
fof(d1_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => k1_finseq_2(A) = k6_partfun1(k2_finseq_1(A)) ) )).
fof(d1_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : k1_finseq_3(A,B) = k3_relat_1(k14_finseq_1(k7_subset_1(k4_ordinal1,k1_relset_1(k4_ordinal1,A),k8_relat_1(A,B))),A) ) )).
fof(d1_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r1_finseq_4(A,B) <=> k8_relat_1(A,k9_relat_1(A,B)) = k1_tarski(B) ) ) )).
fof(d1_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : k1_finseq_5(A,B,C) = k17_finseq_1(A,k4_finseq_4(B,C),B) ) ) )).
fof(d1_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( v1_finseq_6(B,A) <=> k7_partfun1(A,B,1) = k7_partfun1(A,B,k3_finseq_1(B)) ) ) ) )).
fof(d1_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(d1_finseq_8,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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)) ) ) ) )).
fof(d1_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(d1_finset_1,axiom,( ! [A] : ( v1_finset_1(A) <=> ? [B] : ( v1_relat_1(B) & v1_funct_1(B) & k10_xtuple_0(B) = A & r2_hidden(k9_xtuple_0(B),k4_ordinal1) ) ) )).
fof(d1_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ( ( ( v1_setwiseo(C,A) & k3_finseq_1(B) = k5_numbers ) => ( D = k1_finsop_1(A,B,C) <=> D = k4_binop_1(A,C) ) ) & ( ~ ( v1_setwiseo(C,A) & k3_finseq_1(B) = k5_numbers ) => ( D = k1_finsop_1(A,B,C) <=> ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) & k9_nat_1(A,E,1) = k1_funct_1(B,1) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( k5_numbers != F & ~ r1_xxreal_0(k3_finseq_1(B),F) & k9_nat_1(A,E,k1_nat_1(F,1)) != k1_binop_1(C,k9_nat_1(A,E,F),k1_funct_1(B,k1_nat_1(F,1))) ) ) & D = k9_nat_1(A,E,k3_finseq_1(B)) ) ) ) ) ) ) ) ) ) )).
fof(d1_finsub_1,axiom,( ! [A] : ( v1_finsub_1(A) <=> ! [B] : ! [C] : ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r2_hidden(k2_xboole_0(B,C),A) ) ) )).
fof(d1_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(d1_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k1_fintopo3(A,B) = a_2_0_fintopo3(A,B) ) ) )).
fof(d1_fintopo4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(d1_fintopo5,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) ) )).
fof(d1_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v1_fintopo6(A) <=> v4_fin_topo(k2_struct_0(A),A) ) ) )).
fof(d1_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_catalan2(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_catalan2(A))) => ( D = k6_flang_1(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ? [F] : ( m1_subset_1(F,k3_catalan2(A)) & ? [G] : ( m1_subset_1(G,k3_catalan2(A)) & r2_hidden(F,B) & r2_hidden(G,C) & E = k1_flang_1(A,F,G) ) ) ) ) ) ) ) )).
fof(d1_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k1_flang_2(A,B,C,D) = k3_tarski(a_4_0_flang_2(A,B,C,D)) ) ) ) )).
fof(d1_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => k1_flang_3(A,B,C) = k3_tarski(a_3_0_flang_3(A,B,C)) ) ) )).
fof(d1_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( v1_fomodel0(B,A) <=> v2_funct_1(k5_relat_1(B,A)) ) ) )).
fof(d1_fomodel1,axiom,( ! [A] : ( l1_fomodel1(A) => k1_fomodel1(A) = u1_struct_0(A) ) )).
fof(d1_fomodel2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k2_fomodel2(A) = k10_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)) ) )).
fof(d1_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_fomodel1(A)) => ! [C] : ( m2_subset_1(C,k3_finseq_2(k3_finseq_2(k1_fomodel1(A))),k3_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(k43_fomodel1(A,B),k3_funct_2(k3_finseq_2(k3_finseq_2(k1_fomodel1(A))),k3_finseq_2(k15_fomodel1(A)),k21_fomodel1(A),C)) ) ) ) )).
fof(d1_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k1_fomodel4(A) = a_1_0_fomodel4(A) ) )).
fof(d1_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k1_frechet2(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,C) <=> ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & r1_tarski(k2_relset_1(u1_struct_0(A),E),B) & r2_hidden(D,k2_frechet(A,E)) ) ) ) ) ) ) ) )).
fof(d1_freealg,axiom,( ! [A] : ( v1_freealg(A) <=> r1_xboole_0(A,k4_ordinal1) ) )).
fof(d1_friends1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( m1_subset_1(B,k1_relat_1(A)) => ( v1_friends1(B,A) <=> ! [C] : ( r2_hidden(C,k6_subset_1(k1_relat_1(A),k1_tarski(B))) => r2_hidden(k4_tarski(B,C),A) ) ) ) ) )).
fof(d1_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : k1_fscirc_1(A,B,C) = k9_facirc_1(A,B,C,k1_facirc_1) )).
fof(d1_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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)) ) ) ) ) )).
fof(d1_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ( v1_fsm_2(B,A) <=> ! [C] : ( ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( m2_finseq_1(E,A) => ( ( k1_funct_1(D,1) = k1_funct_1(E,1) & r1_xxreal_0(C,k1_nat_1(k3_finseq_1(D),1)) & r1_xxreal_0(C,k1_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) ) ) ) ) ) ) ) )).
fof(d1_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ v2_struct_0(C) & l1_rewrite3(C,B) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) => ! [F] : ( m1_subset_1(F,k8_afinsq_1(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k1_ftacell1(A,B,C,D,E) = k2_circcomb(k13_gfacirc1(A,B,C),k13_gfacirc1(k12_gfacirc1(A,B,C),E,D)) )).
fof(d1_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k1_funcop_1(A) <=> ( k9_xtuple_0(B) = k9_xtuple_0(A) & ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => ( ! [D] : ! [E] : ( 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] : ! [E] : k1_funct_1(A,C) != k4_tarski(D,E) ) ) ) ) ) ) ) )).
fof(d1_funcsdom,axiom,( ! [A] : ! [B] : ( ( 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] : ( m2_funct_2(C,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [D] : ( 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,k9_binop_2,C,D)) ) ) ) ) )).
fof(d1_funct_1,axiom,( ! [A] : ( v1_funct_1(A) <=> ! [B] : ! [C] : ! [D] : ( ( r2_hidden(k4_tarski(B,C),A) & r2_hidden(k4_tarski(B,D),A) ) => C = D ) ) )).
fof(d1_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( 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 ) ) ) ) )).
fof(d1_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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] : ( r1_tarski(C,k9_xtuple_0(A)) => k1_funct_1(B,C) = k7_relat_1(A,C) ) ) ) ) ) )).
fof(d1_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d1_funct_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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] : ~ ( r2_hidden(C,k9_xtuple_0(k9_xtuple_0(A))) & ! [D] : ( ( 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] : ( r2_hidden(E,k9_xtuple_0(D)) => k1_funct_1(D,E) = k1_binop_1(A,C,E) ) ) ) ) ) ) ) ) )).
fof(d1_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k1_funct_6(A) <=> ( k9_xtuple_0(B) = k9_xtuple_0(A) & ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => k1_funct_1(B,C) = k9_xtuple_0(k1_funct_1(A,C)) ) ) ) ) ) )).
fof(d1_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(d1_funct_8,axiom,( ! [A] : ( v1_funct_8(A) <=> ! [B] : ( v1_xcmplx_0(B) => ( r2_hidden(B,A) => r2_hidden(k4_xcmplx_0(B),A) ) ) ) )).
fof(d1_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( v1_funct_9(B,A) <=> ( A != k5_numbers & ! [C] : ( 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)) ) ) ) ) ) ) ) )).
fof(d1_functor0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( 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)) ) ) ) )).
fof(d1_functor2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( m2_functor0(C,A,B) => ! [D] : ( m2_functor0(D,A,B) => ( r1_functor2(A,B,C,D) <=> ! [E] : ( 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 ) ) ) ) ) ) )).
fof(d1_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ! [F] : ( m1_functor2(F,A,B,D,E) => ! [G] : ( ( v15_functor0(G,B,C) & m2_functor0(G,B,C) ) => ( r1_functor2(A,B,D,E) => ! [H] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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)) ) ) ) )).
fof(d1_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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 = k1_fuzzy_4(A,B,C) <=> ! [E] : ! [F] : ( r2_hidden(k4_tarski(E,F),k2_zfmisc_1(A,B)) => k1_binop_1(D,E,F) = k1_binop_1(C,F,E) ) ) ) ) ) ) )).
fof(d1_fvaluat1,axiom,( ! [A] : ( v1_fvaluat1(A) <=> ( v1_int_1(A) | A = k1_xxreal_0 ) ) )).
fof(d1_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( 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))) ) ) )).
fof(d1_gate_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) => k1_gate_1(A) = k1_xboole_0 ) & ( v1_xboole_0(A) => k1_gate_1(A) = k1_tarski(k1_xboole_0) ) ) )).
fof(d1_gate_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k1_gate_5(A,B,C,D) = k2_gate_1(A,C) )).
fof(d1_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_gcd_1(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & C = k6_algstr_0(A,B,D) ) ) ) ) ) )).
fof(d1_genealg1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_finseq_1(B,k3_card_3(A)) => ( m1_genealg1(B,A) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k4_finseq_1(B)) => r2_hidden(k1_funct_1(B,C),k1_funct_1(A,C)) ) ) ) ) ) ) )).
fof(d1_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d1_gfacirc1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => k1_funct_1(A,k10_binarith(k6_margrel1,B)) = k9_margrel1(B) ) ) ) )).
fof(d1_glib_000,axiom,( k1_glib_000 = 1 )).
fof(d1_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m2_finseq_1(B,k6_glib_000(A)) => ( m1_glib_001(B,A) <=> ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r1_xxreal_0(1,C) & ~ r1_xxreal_0(k3_finseq_1(B),C) & ! [D] : ~ r1_glib_000(A,k1_funct_1(B,C),k1_funct_1(B,k1_nat_1(C,1)),D) ) ) ) ) ) )).
fof(d1_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ( v1_glib_002(A) <=> ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ? [D] : ( m3_glib_001(D,A) & r1_glib_001(A,B,C,D) ) ) ) ) ) )).
fof(d1_glib_003,axiom,( k2_glib_003 = 5 )).
fof(d1_goboard1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( B = k1_goboard1(A) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => k1_funct_1(B,C) = k17_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),A,C)) ) ) ) ) ) ) )).
fof(d1_goboard2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( A != k1_xboole_0 => ! [C] : ( ( v1_matrix_0(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_0(C) = k3_finseq_1(B) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(D,E),k2_matrix_0(C)) => k3_matrix_0(u1_struct_0(k15_euclid(2)),C,D,E) = k19_euclid(k1_funct_1(A,D),k1_funct_1(B,E)) ) ) ) ) ) ) ) ) ) )).
fof(d1_goboard5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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) ) ) ) ) )).
fof(d1_goboard9,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(d1_gobrd10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_gobrd10(A,B) <=> ( B = k1_nat_1(A,1) | A = k1_nat_1(B,1) ) ) ) ) )).
fof(d1_gobrd13,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(A)) & r1_goboard1(u1_struct_0(k15_euclid(2)),A,B) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( D = k2_gobrd13(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ~ ( r2_hidden(k4_tarski(E,F),k2_matrix_0(B)) & r2_hidden(k4_tarski(G,H),k2_matrix_0(B)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),B,E,F) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),B,G,H) & ~ ( E = G & k1_nat_1(F,1) = H & D = k3_goboard5(B,E,F) ) & ~ ( k1_nat_1(E,1) = G & F = H & D = k3_goboard5(B,E,k7_nat_d(F,1)) ) & ~ ( E = k1_nat_1(G,1) & F = H & D = k3_goboard5(B,G,H) ) & ~ ( E = G & F = k1_nat_1(H,1) & D = k3_goboard5(B,k7_nat_d(E,1),H) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_goedcpuc,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ( v1_goedcpuc(B,A) <=> ? [C] : ( ~ v1_xboole_0(C) & ? [D] : ( m1_valuat_1(D,A,C) & ? [E] : ( m2_funct_2(E,k3_qc_lang1(A),C,k2_valuat_1(A,C)) & r6_calcul_1(A,B,C,D,E) ) ) ) ) ) ) )).
fof(d1_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ( v1_goedelcp(B,A) <=> ! [C] : ( 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)) ) ) ) ) ) )).
fof(d1_gr_cy_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_gr_cy_3(A) <=> ? [B] : ( v7_ordinal1(B) & v1_int_2(B) & k1_nat_1(k3_xcmplx_0(2,B),1) = A ) ) ) )).
fof(d1_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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_xcmplx_0(k3_finseq_1(D),B) = k1_nat_1(C,1) & ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(d1_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u4_struct_0(A))) => ( D = k2_graph_3(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ( r2_hidden(E,u4_struct_0(A)) & r2_hidden(E,C) & k1_funct_1(u2_graph_1(A),E) = B ) ) ) ) ) ) )).
fof(d1_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) )).
fof(d1_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(d1_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ! [D] : ( v1_xreal_0(D) => k2_graphsp(A,B,C,D) = k1_graphsp(k1_graphsp(C,A,B),B,D) ) ) ) ) )).
fof(d1_grcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(d1_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( B = k2_grnilp_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( v15_algstr_0(C) & v1_group_3(C,A) & m1_group_2(C,A) ) ) ) ) )).
fof(d1_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => k2_groeb_1(A,B,C,D) = a_4_0_groeb_1(A,B,C,D) ) ) ) ) )).
fof(d1_groeb_2,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(d1_groeb_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( 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] : ( 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(k3_polynom1(k15_pre_poly(A),B,C),D),k4_struct_0(B))) ) ) ) )).
fof(d1_group_1,axiom,( ! [A] : ( l3_algstr_0(A) => ( v1_group_1(A) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k6_algstr_0(A,C,B) = C & k6_algstr_0(A,B,C) = C ) ) ) ) ) )).
fof(d1_group_10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l3_algstr_0(A) ) => ! [B] : ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(d1_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_group_2(C,A) => k1_group_11(A,B,C) = a_3_0_group_11(A,B,C) ) ) ) )).
fof(d1_group_12,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k2_group_7(A,B)))) => ( D = k1_group_12(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k1_group_7(A,B,C))) & E = k1_funct_7(k1_group_1(k2_group_7(A,B)),C,F) ) ) ) ) ) ) ) )).
fof(d1_group_14,axiom,( ! [A] : ( v7_ordinal1(A) => k2_group_14(A) = g2_algstr_0(u1_struct_0(k9_int_3(A)),u1_algstr_0(k9_int_3(A)),u2_struct_0(k9_int_3(A))) ) )).
fof(d1_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k1_group_2(A,B) = a_2_0_group_2(A,B) ) ) )).
fof(d1_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( B = k1_group_3(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( v15_algstr_0(C) & m1_group_2(C,A) ) ) ) ) )).
fof(d1_group_4,axiom,( ! [A] : ( v1_int_1(A) => k2_group_4(A) = A ) )).
fof(d1_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ( D = k1_group_5(A,B,C) <=> ( k3_finseq_1(D) = k3_finseq_1(B) & ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d1_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(d1_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( r1_group_9(A,B,C,D) <=> ! [E] : ( m1_subset_1(E,A) => ! [F] : ( ( 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) ) ) ) ) ) )).
fof(d1_groupp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( v1_groupp_1(C,A,B) <=> ? [D] : ( v7_ordinal1(D) & k6_group_1(B,C) = k1_newton(A,D) ) ) ) ) ) )).
fof(d1_grsolv_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ( v1_grsolv_1(A) <=> ? [B] : ( m2_finseq_1(B,k1_group_3(A)) & ~ r1_xxreal_0(k3_finseq_1(B),k5_numbers) & k1_funct_1(B,1) = k7_group_2(A) & k1_funct_1(B,k3_finseq_1(B)) = k6_group_2(A) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(k1_nat_1(C,1),k4_finseq_1(B)) ) => ! [D] : ( ( v15_algstr_0(D) & m1_group_2(D,A) ) => ! [E] : ( ( v15_algstr_0(E) & m1_group_2(E,A) ) => ( ( D = k1_funct_1(B,C) & E = k1_funct_1(B,k1_nat_1(C,1)) ) => ( v15_algstr_0(E) & v1_group_3(E,D) & m1_group_6(E,A,D) & ! [F] : ( ( v1_group_3(F,D) & m1_group_6(F,A,D) ) => ( F = E => v5_group_1(k5_group_6(D,F)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_hahnban,axiom,( ! [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) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)),k3_real_1(k3_funct_2(u1_struct_0(A),k1_numbers,B,C),k3_funct_2(u1_struct_0(A),k1_numbers,B,D))) ) ) ) ) ) )).
fof(d1_hahnban1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_hahnban1(A,B) = k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1)) ) ) )).
fof(d1_hallmar1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ! [C] : ! [D] : ( D = k1_hallmar1(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ? [F] : ( r2_hidden(F,C) & r2_hidden(F,k4_finseq_1(B)) & r2_hidden(E,k1_funct_1(B,F)) ) ) ) ) )).
fof(d1_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => k1_hausdorf(A,B,C) = k4_xxreal_0(k8_weierstr(A,B,C),k8_weierstr(A,C,B)) ) ) ) )).
fof(d1_heine,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( C = k1_heine(A,B) <=> ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k2_power(B,k9_nat_1(k1_numbers,A,D)) ) ) ) ) ) )).
fof(d1_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ( ( r1_tarski(D,A) & r1_tarski(D,B) ) => r1_tarski(D,C) ) ) ) ) ) ) ) )).
fof(d1_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ( r1_henmodel(A,B,C) <=> ? [D] : ( 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))) ) ) ) ) ) )).
fof(d1_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d1_heyting1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k5_finsub_1(A)) => ! [C] : ( m1_subset_1(C,k5_finsub_1(A)) => ( r1_heyting1(A,B,C) <=> ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,B) => r2_hidden(D,C) ) ) ) ) ) ) )).
fof(d1_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( D = k1_heyting2(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ? [F] : ( v1_relat_1(F) & v1_funct_1(F) & v1_finset_1(F) & r2_hidden(F,C) & r2_hidden(E,k9_xtuple_0(F)) ) ) ) ) ) )).
fof(d1_heyting3,axiom,( ! [A] : ! [B] : k1_heyting3(A,B) = k3_lattice3(k5_substlat(A,B)) )).
fof(d1_hilbasis,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( 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 ) ) ) ) ) ) )).
fof(d1_hilbert1,axiom,( ! [A] : ( v1_hilbert1(A) <=> r2_hidden(k12_finseq_1(k4_ordinal1,k5_numbers),A) ) )).
fof(d1_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k1_hilbert2(A) = k14_trees_3(k1_nat_1(3,A)) ) )).
fof(d1_hilbert3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) => ! [E] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(d1_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( 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] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(d1_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => k1_idea_1(A) = k5_finseq_2(k6_margrel1,A,k7_margrel1) ) )).
fof(d1_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_ideal_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d1_incproj,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => k1_incproj(A) = a_1_0_incproj(A) ) )).
fof(d1_incsp_1,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(d1_instalg1,axiom,( ! [A] : ( l1_msualg_1(A) => ( v1_instalg1(A) <=> ( u1_struct_0(A) = k1_xboole_0 => u4_struct_0(A) = k1_xboole_0 ) ) ) )).
fof(d1_int_1,axiom,( ! [A] : ( A = k4_numbers <=> ! [B] : ( r2_hidden(B,A) <=> ~ ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( B != C & B != k4_xcmplx_0(C) ) ) ) ) )).
fof(d1_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ( C = k2_int_2(A,B) <=> ( r1_int_1(A,C) & r1_int_1(B,C) & ! [D] : ( v1_int_1(D) => ( ( r1_int_1(A,D) & r1_int_1(B,D) ) => r1_int_1(C,D) ) ) ) ) ) ) ) )).
fof(d1_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_numbers,k4_numbers))) => ( B = k1_int_4(A) <=> ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ( r2_hidden(k4_tarski(C,D),B) <=> r2_int_1(C,D,A) ) ) ) ) ) ) )).
fof(d1_int_5,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ! [B] : ( ( 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] : ( m1_subset_1(C,k4_numbers) => ? [D] : ( m2_finseq_1(D,k4_numbers) & k3_finseq_1(D) = k3_finseq_1(A) & ! [E] : ( 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) ) ) ) ) ) )).
fof(d1_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v2_relat_1(A) <=> ! [B] : ( v7_ordinal1(B) => ~ ( r2_hidden(B,k4_finseq_1(A)) & k1_funct_1(A,B) = k5_numbers ) ) ) ) )).
fof(d1_int_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k8_newton) & v1_funct_1(A) & v1_partfun1(A,k8_newton) & v4_valued_0(A) & v2_pre_poly(A) ) => ( v1_int_7(A) <=> ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ~ ( r2_hidden(B,k22_pre_poly(k8_newton,A)) & ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & k1_recdef_1(A,B) = k1_newton(B,C) ) ) ) ) ) ) )).
fof(d1_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => k1_int_8(A) = a_1_0_int_8(A) ) )).
fof(d1_integr10,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_integr10(A,B,C) <=> ( ! [D] : ( v1_xreal_0(D) => ( 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] : ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,k1_relset_1(k1_numbers,D)) => k1_funct_1(D,E) = k4_integra5(B,E,A) ) ) & r1_limfunc2(D,C) ) ) ) ) ) ) )).
fof(d1_integr15,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => ! [C] : ( m1_integra1(C,A) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ( m1_integr15(D,A,B,C) <=> ( k3_finseq_1(D) = k3_finseq_1(C) & ! [E] : ( v7_ordinal1(E) => ~ ( r2_hidden(E,k4_finseq_1(C)) & ! [F] : ( m1_subset_1(F,k1_numbers) => ~ ( r2_hidden(F,k1_rvsum_1(k2_partfun1(A,k1_numbers,B,k2_integra1(A,C,E)))) & k1_funct_1(D,E) = k3_xcmplx_0(F,k3_integra1(k2_integra1(A,C,E))) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_integr16,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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] : ( m1_integra1(C,A) => ! [D] : ( m2_finseq_1(D,k2_numbers) => ( m1_integr16(D,A,B,C) <=> ( k3_finseq_1(D) = k3_finseq_1(C) & ! [E] : ( v7_ordinal1(E) => ~ ( r2_hidden(E,k4_finseq_1(C)) & ! [F] : ( 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) = k3_xcmplx_0(F,k3_integra1(k2_integra1(A,C,E))) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( m1_integra1(D,B) => ! [E] : ( m2_finseq_1(E,u1_struct_0(A)) => ( m1_integr18(E,A,B,C,D) <=> ( k3_finseq_1(E) = k3_finseq_1(D) & ! [F] : ( v7_ordinal1(F) => ~ ( r2_hidden(F,k4_finseq_1(D)) & ! [G] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_integr19,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) & ! [E] : ~ ( r2_hidden(E,k1_relset_1(B,C)) & r1_xxreal_0(D,k2_normsp_0(A,k7_partfun1(u1_struct_0(A),C,E))) ) ) ) ) ) ) )).
fof(d1_integr1c,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k2_zfmisc_1(k1_numbers,k1_numbers)) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d1_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ 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_funct_1(B,k3_finseq_1(B)) = k2_seq_4(A) ) ) ) ) )).
fof(d1_integra2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( v1_integra2(A) <=> ! [B] : ( v7_ordinal1(B) => ( ( r2_hidden(B,k4_finseq_1(A)) & r2_hidden(k1_nat_1(B,1),k4_finseq_1(A)) ) => r1_xxreal_0(k1_funct_1(A,B),k1_funct_1(A,k1_nat_1(B,1))) ) ) ) ) )).
fof(d1_integra3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => k1_integra3(A,B) = k1_xxreal_2(k1_rvsum_1(k4_integra1(A,k7_rfunct_1(A,A),B))) ) ) )).
fof(d1_integra5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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) ) ) ) )).
fof(d1_integra7,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( C = k1_integra7(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( 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)) ) ) ) ) )).
fof(d1_integra8,axiom,( ! [A] : ( v1_xreal_0(A) => k1_integra8(A) = k7_funcop_1(k1_numbers,A) ) )).
fof(d1_integra9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(d1_interva1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k1_interva1(A,B,C) = a_3_0_interva1(A,B,C) ) ) )).
fof(d1_intpro_1,axiom,( ! [A] : ( v1_intpro_1(A) <=> r2_hidden(k12_finseq_1(k4_ordinal1,k5_numbers),A) ) )).
fof(d1_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( B = k1_irrat_1(A) <=> ! [C] : ( v7_ordinal1(C) => k1_funct_1(B,C) = k7_xcmplx_0(k6_xcmplx_0(C,A),C) ) ) ) ) )).
fof(d1_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_cat_1(D,k9_nattra_1(A,B),B) => ( D = k2_isocat_2(A,B,C) <=> ! [E] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,A,B) => ! [G] : ( 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)) = k2_nattra_1(A,B,E,F,G,C) ) ) ) ) ) ) ) ) ) )).
fof(d1_isomichi,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) )).
fof(d1_jct_misc,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ! [C] : ( v1_xreal_0(C) => ( C = k1_jct_misc(A,B) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_numbers)) & D = a_2_0_jct_misc(A,B) & C = k3_seq_4(D) ) ) ) ) ) )).
fof(d1_jgraph_1,axiom,( ! [A] : k1_jgraph_1(A) = g1_graph_1(A,k2_zfmisc_1(A,A),k9_funct_3(A,A),k10_funct_3(A,A)) )).
fof(d1_jgraph_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(d1_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k1_jgraph_6(A,B,C,D) = a_4_0_jgraph_6(A,B,C,D) ) ) ) ) )).
fof(d1_jordan1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_convex1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r1_tarski(k1_rltopsp1(A,C,D),B) ) ) ) ) ) ) )).
fof(d1_jordan10,axiom,( ! [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)))) ) => k1_jordan10(A) = a_1_0_jordan10(A) ) )).
fof(d1_jordan11,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( B = k3_jordan11(A) <=> ( r1_jordan1h(A,B) & ! [C] : ( v7_ordinal1(C) => ( r1_jordan1h(A,C) => r1_xxreal_0(B,C) ) ) ) ) ) ) )).
fof(d1_jordan12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( 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] : ( v7_ordinal1(D) => ( 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))) ) ) ) ) ) ) ) ) )).
fof(d1_jordan13,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( r1_jordan1h(A,B) => ! [C] : ( ( ~ 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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k3_jordan1h(A,B),k5_jordan11(A,B)) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,2) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k7_nat_d(k3_jordan1h(A,B),1),k5_jordan11(A,B)) & ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(k1_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) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => k1_jordan14(A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k3_jordan1h(A,B),k5_jordan11(A,B)) ) ) )).
fof(d1_jordan17,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d1_jordan19,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))))) ) => ( B = k1_jordan19(A) <=> ! [C] : ( v7_ordinal1(C) => k2_kurato_2(k15_euclid(2),B,C) = k8_jordan6(k3_topreal1(2,k2_jordan9(A,C))) ) ) ) ) )).
fof(d1_jordan1a,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k1_jordan1a(A) = k1_nat_1(k3_nat_d(k3_finseq_1(A),2),1) ) )).
fof(d1_jordan1e,axiom,( ! [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] : ( 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)),k2_jordan9(A,B),k18_pscomp_1(k3_topreal1(2,k2_jordan9(A,B)))),k22_pscomp_1(k3_topreal1(2,k2_jordan9(A,B)))) ) ) )).
fof(d1_jordan1h,axiom,( k1_jordan1h = a_0_0_jordan1h )).
fof(d1_jordan1k,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( v1_xreal_0(D) => ( D = k1_jordan1k(A,B,C) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(k14_euclid(A))))) & ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d1_jordan20,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ( r1_jordan20(A,B,C,D,E) <=> ( r1_topreal1(k15_euclid(2),B,C,A) & r2_hidden(D,A) & k17_euclid(D) = E & ? [F] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_jordan21,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_jordan21(A) <=> ~ r1_xboole_0(A,k6_jordan6(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)),2))) ) ) )).
fof(d1_jordan23,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_jordan23(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( 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 ) ) ) ) ) ) )).
fof(d1_jordan24,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d1_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(d1_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(B,k3_topreal1(2,A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( C = k1_jordan3(A,B) <=> ? [D] : ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) & C = k4_seq_4(D) & D = a_2_0_jordan3(A,B) ) ) ) ) ) ) )).
fof(d1_jordan4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ( k4_nat_d(A,k7_nat_d(k3_finseq_1(B),1)) != k5_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)) = k5_numbers => k1_jordan4(A,B) = k7_nat_d(k3_finseq_1(B),1) ) ) ) ) )).
fof(d1_jordan5c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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] : ( 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] : ( ( 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] : ( v1_xreal_0(G) => ( ( v3_tops_2(F,k5_topmetr,k1_pre_topc(k15_euclid(2),A)) & k1_funct_1(F,k5_numbers) = C & k1_funct_1(F,1) = D & k1_funct_1(F,G) = E & r1_xxreal_0(k5_numbers,G) & r1_xxreal_0(G,1) ) => ! [H] : ( v1_xreal_0(H) => ~ ( r1_xxreal_0(k5_numbers,H) & ~ r1_xxreal_0(G,H) & r2_hidden(k1_funct_1(F,H),B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( B = k1_jordan5d(A) <=> ( r2_hidden(k4_tarski(1,B),k2_matrix_0(k2_goboard2(A))) & k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,B) = k18_pscomp_1(k3_topreal1(2,A)) ) ) ) ) )).
fof(d1_jordan7,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d1_jordan8,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(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(k1_newton(2,B),3) & k3_finseq_1(C) = k1_matrix_0(C) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(D,E),k2_matrix_0(C)) => k3_matrix_0(u1_struct_0(k15_euclid(2)),C,D,E) = k19_euclid(k2_xcmplx_0(k6_pscomp_1(A),k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k8_pscomp_1(A),k6_pscomp_1(A)),k1_newton(2,B)),k6_xcmplx_0(D,2))),k2_xcmplx_0(k9_pscomp_1(A),k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k7_pscomp_1(A),k9_pscomp_1(A)),k1_newton(2,B)),k6_xcmplx_0(E,2)))) ) ) ) ) ) ) ) ) )).
fof(d1_jordan9,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( v2_connsp_1(A,k15_euclid(2)) => ! [C] : ( ( ~ 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 = k2_jordan9(A,B) <=> ( r1_goboard1(u1_struct_0(k15_euclid(2)),C,k1_jordan8(A,B)) & ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,1) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),D,k1_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,2) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k1_nat_1(D,1),k1_matrix_0(k1_jordan8(A,B))) & r2_hidden(k20_pscomp_1(A),k3_goboard5(k1_jordan8(A,B),D,k7_nat_d(k1_matrix_0(k1_jordan8(A,B)),1))) & k20_pscomp_1(A) != k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),D,k7_nat_d(k1_matrix_0(k1_jordan8(A,B)),1)) ) & ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(k1_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) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_knaster,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(d1_kolmog01,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m2_prob_1(D,A,B) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(B)) => ( E = k1_kolmog01(A,B,C,D) <=> ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ( r2_hidden(F,E) <=> ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d1_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( C = k3_kurato_0(A,B) <=> ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & C = k1_kurato_0(A,D) & ! [E] : ( v7_ordinal1(E) => k1_funct_1(D,E) = k2_kurato_0(A,k8_nat_1(k9_setfam_1(A),B,E)) ) ) ) ) ) )).
fof(d1_kurato_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))))))) ) ) )).
fof(d1_kurato_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k1_kurato_2(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,C) <=> ! [E] : ( m1_connsp_2(E,A,D) => ? [F] : ( v7_ordinal1(F) & ! [G] : ( v7_ordinal1(G) => ~ ( ~ r1_xxreal_0(G,F) & r1_xboole_0(k1_funct_1(B,G),E) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_lang1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(d1_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(D),C,C) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(D))) ) => ( ( r2_hidden(A,k2_finseq_1(C)) & r2_hidden(B,k2_finseq_1(C)) ) => k2_laplace(A,B,C,D,E) = k18_matrix_0(A,B,C,u1_struct_0(D),E) ) ) ) ) ) ) )).
fof(d1_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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] : ( ( v15_algstr_0(C) & m1_group_2(C,A) ) => k1_funct_1(B,C) = u1_struct_0(C) ) ) ) ) )).
fof(d1_latsum_1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ( r1_latsum_1(A,B) <=> ! [C] : ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(d1_lattice2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => k5_binop_1(A,B,D,k5_binop_1(A,C,D,E)) = D ) ) ) ) ) ) )).
fof(d1_lattice3,axiom,( ! [A] : ! [B] : ( ( v3_lattices(B) & l3_lattices(B) ) => ( B = k1_lattice3(A) <=> ( u1_struct_0(B) = k9_setfam_1(A) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d1_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(d1_lattice5,axiom,( ! [A] : k1_lattice5(A) = k3_lattice3(k2_msualg_5(A)) )).
fof(d1_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k1_lattice6(A,B) = a_2_0_lattice6(A,B) ) ) )).
fof(d1_lattice7,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_lattice7(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => r2_hidden(D,C) ) ) ) ) ) ) )).
fof(d1_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d1_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d1_lfuzzy_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_lfuzzy_0(A) <=> ( r1_tarski(u1_struct_0(A),k1_numbers) & ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) ) ) ) )).
fof(d1_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,B) => r1_xxreal_0(k8_lfuzzy_0(A,B,C,E,F),k8_lfuzzy_0(A,B,D,E,F)) ) ) ) ) ) ) ) )).
fof(d1_limfunc1,axiom,( ! [A] : ( v1_xreal_0(A) => k1_limfunc1(A) = k3_xxreal_1(k2_xxreal_0,A) ) )).
fof(d1_limfunc2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r1_limfunc2(A,B) <=> ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(B,C) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,C) & ~ r1_xxreal_0(B,D) & r2_hidden(D,k1_relset_1(k1_numbers,A)) ) ) ) ) & ? [C] : ( v1_xreal_0(C) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(D) & k1_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(k4_ordinal1,k1_numbers,k1_numbers,D,A)) & k1_seq_2(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,D,A)) = C ) ) ) ) ) ) ) ) )).
fof(d1_limfunc3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r1_limfunc3(A,B) <=> ( ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(B,C) & ~ r1_xxreal_0(D,B) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ~ ( ~ 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] : ( v1_xreal_0(C) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(D) & k1_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(k4_ordinal1,k1_numbers,k1_numbers,D,A)) & k1_seq_2(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,D,A)) = C ) ) ) ) ) ) ) ) )).
fof(d1_lmod_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v1_lmod_5(C,A,B) <=> ! [D] : ( 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 ) ) ) ) ) ) )).
fof(d1_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) ) )).
fof(d1_lopban_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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] : ( m2_funct_2(D,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d1_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(k8_lopban_1(A,A)),k10_lopban_1(A,A)) => ! [C] : ( 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),k7_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),B,C) ) ) ) )).
fof(d1_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_lopban_3(B,A) <=> v3_normsp_1(k1_bhsp_4(A,B),A) ) ) ) )).
fof(d1_lopban_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(d1_lopban_5,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => k1_lopban_5(A,B,C) = a_3_0_lopban_5(A,B,C) ) ) ) )).
fof(d1_lopban_7,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => k3_lopban_7(A,B,C) = C ) ) ) )).
fof(d1_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => k1_lopclset(A) = a_1_0_lopclset(A) ) )).
fof(d1_lp_space,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( C = k1_lp_space(A,B) <=> ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k2_power(k9_complex1(k9_nat_1(k1_numbers,A,D)),B) ) ) ) ) ) )).
fof(d1_lpspacc1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_lpspacc1(B,A) <=> ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => r2_hidden(k1_clvect_1(A,D,C),B) ) ) ) ) ) ) )).
fof(d1_lpspace1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_lpspace1(B,A) <=> ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => r2_hidden(k1_rlvect_1(A,D,C),B) ) ) ) ) ) ) )).
fof(d1_lpspace2,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_lpspace2(A) <=> r1_xxreal_0(1,A) ) ) )).
fof(d1_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => k1_ltlaxio1(A) = k3_hilbert1(A,k2_hilbert1) ) )).
fof(d1_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => k1_ltlaxio2(A,B) = k5_ltlaxio1(B,k4_ltlaxio1(A,k4_hilbert1(A,B))) ) ) )).
fof(d1_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => ( v1_ltlaxio3(A) <=> ! [B] : ( m1_subset_1(B,k1_hilbert1) => ~ ( r2_hidden(B,A) & v2_hilbert2(B) ) ) ) ) )).
fof(d1_margrel1,axiom,( ! [A] : ( v3_finseq_1(A) => ( v2_card_3(A) <=> ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(d1_mathmorp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => k1_mathmorp(A,B,C) = a_3_0_mathmorp(A,B,C) ) ) ) )).
fof(d1_matrix10,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( v1_matrix10(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(k4_tarski(B,C),k2_matrix_0(A)) & r1_xxreal_0(k3_matrix_0(k1_numbers,A,B,C),k5_numbers) ) ) ) ) ) )).
fof(d1_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_matrix_2(C,k3_matrix_2(k1_nat_1(A,2))) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(C),A,B) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(C))) ) => ( G = k1_matrix12(A,B,C,D,E,F) <=> ( k3_finseq_1(G) = k3_finseq_1(D) & ! [H] : ( v7_ordinal1(H) => ! [I] : ( v7_ordinal1(I) => ( ( r2_hidden(H,k4_finseq_1(D)) & r2_hidden(I,k2_finseq_1(k1_matrix_0(D))) ) => ( ( H = E => k3_matrix_0(u1_struct_0(C),G,H,I) = k3_matrix_0(u1_struct_0(C),D,F,I) ) & ( H = F => k3_matrix_0(u1_struct_0(C),G,H,I) = k3_matrix_0(u1_struct_0(C),D,E,I) ) & ~ ( H != E & H != F & k3_matrix_0(u1_struct_0(C),G,H,I) != k3_matrix_0(u1_struct_0(C),D,H,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(C,k4_ordinal1)) => ! [F] : ( m2_finseq_2(F,k4_ordinal1,k4_finseq_2(D,k4_ordinal1)) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,A,C,D) & m2_finseq_1(G,k3_finseq_2(A)) ) => ( G = k1_matrix13(A,B,C,D,E,F) <=> ! [H] : ( v7_ordinal1(H) => ! [I] : ( v7_ordinal1(I) => ( r2_hidden(k4_tarski(H,I),k2_matrix_0(G)) => k3_matrix_0(A,G,H,I) = k3_matrix_0(A,B,k1_funct_1(E,H),k1_funct_1(F,I)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_matrix14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k1_matrix14(A,B) = k5_finseq_2(u1_struct_0(A),B,k4_struct_0(A)) ) ) )).
fof(d1_matrix15,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => k2_matrix15(A,B) = k10_laplace(A,B) ) ) )).
fof(d1_matrix16,axiom,( ! [A] : ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r1_matrix16(A,B,C) <=> ( k3_finseq_1(C) = k1_matrix_0(B) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(D,E),k2_matrix_0(B)) => k3_matrix_0(A,B,D,E) = k1_funct_1(C,k2_xcmplx_0(k5_int_1(k6_xcmplx_0(E,D),k3_finseq_1(C)),1)) ) ) ) ) ) ) ) )).
fof(d1_matrix_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_matrix_0(A) <=> ? [B] : ( v7_ordinal1(B) & ! [C] : ~ ( r2_hidden(C,k10_xtuple_0(A)) & ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ~ ( D = C & k3_finseq_1(D) = B ) ) ) ) ) ) )).
fof(d1_matrix_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => k1_matrix_1(A,B) = k4_finseq_2(B,k4_finseq_2(B,u1_struct_0(A))) ) ) )).
fof(d1_matrix_3,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( 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))) ) ) ) )).
fof(d1_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(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)) ) ) ) )).
fof(d1_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => k1_matrix_5(A) = A ) )).
fof(d1_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r1_matrix_6(A,B,C,D) <=> k4_matrix_3(B,C,D) = k4_matrix_3(B,D,C) ) ) ) ) ) )).
fof(d1_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v1_matrix_8(C,A,B) <=> k4_matrix_3(B,C,C) = C ) ) ) ) )).
fof(d1_matrix_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k3_matrix_2(A),u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k3_matrix_2(A),u1_struct_0(B)))) ) => ( D = k1_matrix_9(A,B,C) <=> ! [E] : ( m1_matrix_2(E,k3_matrix_2(A)) => k3_funct_2(k3_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)) ) ) ) ) ) ) )).
fof(d1_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k2_numbers)) ) => ( B = k1_matrixc1(A) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & k1_matrix_0(B) = k1_matrix_0(A) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k4_tarski(C,D),k2_matrix_0(A)) => k3_matrix_0(k2_numbers,B,C,D) = k8_complex1(k3_matrix_0(k2_numbers,A,C,D)) ) ) ) ) ) ) ) )).
fof(d1_matrixj1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k2_finseq_1(k2_wsierp_1(A))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( C = k1_matrixj1(A,B) <=> ( r1_xxreal_0(B,k2_wsierp_1(k17_finseq_1(k4_ordinal1,C,A))) & r2_hidden(C,k4_finseq_1(A)) & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(B,k2_wsierp_1(k17_finseq_1(k4_ordinal1,D,A))) => r1_xxreal_0(C,D) ) ) ) ) ) ) ) ) )).
fof(d1_matrixj2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(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_0(D) = C & ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( r2_hidden(k4_tarski(E,F),k2_matrix_0(D)) => ( ( E = F => k3_matrix_0(u1_struct_0(A),D,E,F) = B ) & ( k1_nat_1(E,1) = F => k3_matrix_0(u1_struct_0(A),D,E,F) = k1_group_1(A) ) & ~ ( E != F & k1_nat_1(E,1) != F & k3_matrix_0(u1_struct_0(A),D,E,F) != k4_struct_0(A) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => k1_matrixr1(A) = A ) )).
fof(d1_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => k3_matrixr2(A,B) = k12_matrix_3(A,k2_vectsp_1,k2_matrixr2(A,B)) ) ) )).
fof(d1_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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] : ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_vectsp_7(C,A,B) ) ) ) ) )).
fof(d1_matrlin2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( v1_relat_1(B) => k2_matrlin2(A,B) = k5_relat_1(B,u1_struct_0(A)) ) ) )).
fof(d1_matroid0,axiom,( ! [A] : ( l1_pre_topc(A) => k1_matroid0(A) = u1_pre_topc(A) ) )).
fof(d1_matrprob,axiom,( ! [A] : ( m2_finseq_1(A,k3_finseq_2(k1_numbers)) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( B = k3_matrprob(A) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => k1_funct_1(B,C) = k18_rvsum_1(k1_matrprob(k1_numbers,A,C)) ) ) ) ) ) ) )).
fof(d1_matrtop1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => k1_matrtop1(A) = A ) )).
fof(d1_matrtop3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) ) => ( v1_matrtop3(B,A) <=> ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d1_mazurulm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k2_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))) = k2_normsp_0(A,k5_algstr_0(A,D,E)) ) ) ) ) ) ) )).
fof(d1_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( C = k1_mboolean(A,B) <=> ! [D] : ( r2_hidden(D,A) => k1_funct_1(C,D) = k1_zfmisc_1(k1_funct_1(B,D)) ) ) ) ) )).
fof(d1_mcart_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k3_zfmisc_1(A,B,C)) => ! [E] : ( m1_subset_1(E,A) => ( E = k1_mcart_1(A,B,C,D) <=> ! [F] : ! [G] : ! [H] : ( D = k3_xtuple_0(F,G,H) => E = F ) ) ) ) ) ) ) )).
fof(d1_measure1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v1_prob_1(B,A) <=> ! [C] : ( r2_hidden(C,B) => r2_hidden(k6_subset_1(A,C),B) ) ) ) )).
fof(d1_measure2,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( ~ 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) ) ) ) )).
fof(d1_measure3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( r1_measure3(A,B,C) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( ( r2_hidden(E,B) & r1_tarski(D,E) & k12_supinf_2(C,E) = k1_supinf_2 ) => r2_hidden(D,B) ) ) ) ) ) )).
fof(d1_measure4,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k9_setfam_1(A),k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k6_numbers))) ) => ( m1_measure4(B,A) <=> ( v6_supinf_2(B) & v10_valued_0(B) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,k9_setfam_1(A),k9_setfam_1(A),k6_numbers,E,B))) ) ) ) ) ) ) ) ) )).
fof(d1_measure5,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ! [B] : ( m1_subset_1(B,k6_numbers) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_numbers)) => ( C = k1_measure5(A,B) <=> ! [D] : ( m1_subset_1(D,k6_numbers) => ( r2_hidden(D,C) <=> ( ~ r1_xxreal_0(D,A) & ~ r1_xxreal_0(B,D) ) ) ) ) ) ) ) )).
fof(d1_measure7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( C = k1_measure7(A,B) <=> ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( 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 ) ) ) ) ) ) ) )).
fof(d1_member_1,axiom,( ! [A] : ( v2_membered(A) => k4_member_1(A) = a_1_0_member_1(A) ) )).
fof(d1_membered,axiom,( ! [A] : ( v1_membered(A) <=> ! [B] : ( r2_hidden(B,A) => v1_xcmplx_0(B) ) ) )).
fof(d1_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( v1_memstr_0(B,A) & l1_memstr_0(B,A) ) => ( B = k1_memstr_0(A) <=> ( u1_struct_0(B) = k6_domain_1(k4_ordinal1,k5_numbers) & u2_struct_0(B) = k5_numbers & u1_memstr_0(A,B) = k16_funcop_1(k5_numbers,k5_numbers) & u2_memstr_0(A,B) = k7_funcop_1(A,k4_ordinal1) ) ) ) ) )).
fof(d1_menelaus,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(D,A) & r2_hidden(D,B) & r2_hidden(D,C) ) ) ) ) ) ) ) )).
fof(d1_mesfun10,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ( v1_mesfun10(B,A) <=> ? [C] : ( v1_xreal_0(C) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( r2_hidden(E,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers))) => r1_xxreal_0(k3_extreal1(k12_supinf_2(k4_mesfunc5(A,k6_numbers,B,D),E)),C) ) ) ) ) ) )).
fof(d1_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d1_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => k1_mesfun7c(A,B) = B ) ) )).
fof(d1_mesfun9c,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,B)))) ) => ! [D] : ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_partfun1(A,B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,B)))) ) => ( E = k1_mesfun9c(A,B,C,D) <=> ! [F] : ( 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)) ) ) ) ) )).
fof(d1_mesfunc1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( A = k1_mesfunc1 <=> ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & B = k4_xcmplx_0(C) ) ) ) ) ) )).
fof(d1_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( v3_valued_0(B) <=> ! [C] : ( 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))) ) ) ) ) ) )).
fof(d1_mesfunc3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( ( v1_prob_2(D) & m2_finseq_1(D,B) ) => ! [E] : ( m2_finseq_1(E,k6_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] : ( v7_ordinal1(F) => ( r2_hidden(F,k4_finseq_1(D)) => ! [G] : ( r2_hidden(G,k1_funct_1(D,F)) => k1_funct_1(C,G) = k12_supinf_2(E,F) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_mesfunc5,axiom,( ! [A] : ( v1_mesfunc5(A) <=> ! [B] : ( m1_subset_1(B,k6_numbers) => ( r2_hidden(B,A) => r1_xxreal_0(B,k5_numbers) ) ) ) )).
fof(d1_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( r1_mesfunc6(A,B,C,D) <=> r1_mesfunc1(A,B,k1_mesfunc5(A,C),D) ) ) ) ) ) )).
fof(d1_mesfunc7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k6_numbers,k6_numbers),k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k6_numbers,k6_numbers),k6_numbers))) ) => ( A = k1_mesfunc7 <=> ! [B] : ( m1_subset_1(B,k6_numbers) => ! [C] : ( m1_subset_1(C,k6_numbers) => k5_binop_1(k6_numbers,A,B,C) = k1_extreal1(B,C) ) ) ) ) )).
fof(d1_metric_1,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_metric_1(A,B,C) = k1_binop_1(u1_metric_1(A),B,C) ) ) ) )).
fof(d1_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_metric_2(A,B,C) <=> k1_metric_1(A,B,C) = k5_numbers ) ) ) ) )).
fof(d1_metric_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))) => ! [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) ) => k2_binop_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,H,I) = k2_xcmplx_0(k3_metric_1(A,D,E),k3_metric_1(B,F,G)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_metric_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => k2_binop_1(A,A,k1_numbers,C,D,E) = k7_xcmplx_0(k2_binop_1(A,A,k1_numbers,B,D,E),k2_xcmplx_0(1,k2_binop_1(A,A,k1_numbers,B,D,E))) ) ) ) ) ) ) )).
fof(d1_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d1_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( v1_mfold_1(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) & ? [D] : ( v1_xreal_0(D) & B = k1_topreal9(A,C,D) ) ) ) ) ) )).
fof(d1_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d1_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_midsp_2(A,B) = k1_algstr_0(A,B,B) ) ) )).
fof(d1_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_nat_1(A,2)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(B))) => k4_midsp_3(A,B,C,D) = k1_funct_1(u1_midsp_3(k1_nat_1(A,2),B),k3_midsp_3(A,B,1,k1_nat_1(A,1),k2_midsp_3(A,B,C),D)) ) ) ) ) )).
fof(d1_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( r1_mmlquery(A,B,C) <=> r2_hidden(k4_tarski(A,B),C) ) )).
fof(d1_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => k1_mod_2(A) = g1_vectsp_1(A,k1_tarski(k5_numbers),k9_funct_5,k5_funct_5,k10_funct_3(u1_struct_0(A),k1_tarski(k5_numbers))) ) )).
fof(d1_mod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(d1_mod_4,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d1_modal_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => k1_modal_1(A) = k1_xboole_0 ) )).
fof(d1_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ( 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 ) ) ) )).
fof(d1_moebius1,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_moebius1(A) <=> ? [B] : ( v7_ordinal1(B) & v1_int_2(B) & r1_nat_d(k1_newton(B,2),A) ) ) ) )).
fof(d1_monoid_0,axiom,( ! [A] : ( l1_struct_0(A) => ( v1_monoid_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) ) )).
fof(d1_monoid_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : k1_monoid_1(A,B,C,D) = k4_funct_6(A,k4_tarski(B,C),D) ) )).
fof(d1_morph_01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(d1_msafree,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m3_pboole(D,A,B) => ! [E] : ( m2_pboole(E,A,B,C) => ! [F] : ( m2_pboole(F,A,D,C) => ( F = k1_msafree(A,B,C,D,E) <=> ! [G] : ( r2_hidden(G,A) => ! [H] : ( ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d1_msafree1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_prob_2(B) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,C) => ! [E] : ( ( 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] : ( m1_subset_1(F,A) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d1_msafree2,axiom,( ! [A] : ( ( ~ 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 ) ) ) )).
fof(d1_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [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] : ( ( v3_msualg_1(C,A) & l3_msualg_1(C,A) ) => ( C = k1_msafree3(A,B) <=> ? [D] : ( 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(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_numbers)))))) & C = k12_msualg_2(A,k11_msafree(A,k2_pboole(u1_struct_0(A),B,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_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(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_numbers)))))) ) ) ) ) ) )).
fof(d1_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(d1_msinst_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v6_altcat_1(B) & l2_altcat_1(B) ) => ( B = k1_msinst_1(A) <=> ( u1_struct_0(B) = k4_msalimit(A) & ! [C] : ( m3_msalimit(C,k4_msalimit(A)) => ! [D] : ( m3_msalimit(D,k4_msalimit(A)) => k1_binop_1(u1_altcat_1(B),C,D) = k5_msalimit(C,D) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( ( r2_hidden(C,k4_msalimit(A)) & r2_hidden(D,k4_msalimit(A)) & r2_hidden(E,k4_msalimit(A)) ) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) ) => ! [H] : ( ( v1_relat_1(H) & v1_funct_1(H) ) => ! [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)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_msscyc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( 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] : ( m2_finseq_1(C,u1_struct_0(A)) & r1_graph_2(A,C,B) ) ) ) ) ) )).
fof(d1_msscyc_2,axiom,( ! [A] : ( l1_msualg_1(A) => ! [B] : ( B = k1_msscyc_2(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ? [E] : ( C = k4_tarski(D,E) & r2_hidden(D,u4_struct_0(A)) & r2_hidden(E,u1_struct_0(A)) & ? [F] : ( v7_ordinal1(F) & ? [G] : ( 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 ) ) ) ) ) ) )).
fof(d1_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( D = k3_mssubfam(A,B,C) <=> ! [E] : ~ ( r2_hidden(E,A) & ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d1_msualg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( 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) ) ) )).
fof(d1_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_msualg_2(B,A) <=> ? [C] : ( 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 ) ) ) ) )).
fof(d1_msualg_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m2_pboole(C,A,B,B) => ( C = k2_msualg_3(A,B) <=> ! [D] : ( r2_hidden(D,A) => k1_funct_1(C,D) = k6_partfun1(k1_funct_1(B,D)) ) ) ) ) )).
fof(d1_msualg_4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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] : ( 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)))) ) ) ) ) ) )).
fof(d1_msualg_5,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(d1_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( v1_msualg_6(B,A) <=> ! [C] : ( 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 ) ) ) ) ) )).
fof(d1_msualg_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( v4_lattice3(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r4_lattice3(A,C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r4_lattice3(A,D,B) => r1_lattices(A,C,D) ) ) ) ) ) ) )).
fof(d1_msualg_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(d1_msualg_9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v2_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( m2_pboole(E,A,B,k6_pboole(A,C,D)) => ! [F] : ( m2_pboole(F,A,B,C) => ( F = k1_msualg_9(A,B,C,D,E) <=> ! [G] : ( r2_hidden(G,A) => k1_funct_1(F,G) = k11_mcart_1(k1_funct_1(E,G)) ) ) ) ) ) ) ) )).
fof(d1_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(d1_multop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : k1_multop_1(A,B,C,D) = k1_funct_1(A,k3_xtuple_0(B,C,D)) ) )).
fof(d1_mycielsk,axiom,( ! [A] : ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k1_mycielsk(A,B,C) = a_3_0_mycielsk(A,B,C) ) ) )).
fof(d1_nagata_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_nagata_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( v3_pre_topc(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(C,D) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ! [F] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(d1_nagata_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1))) ) => ( A = k1_nagata_2 <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k1_funct_1(A,k4_tarski(B,C)) = k6_xcmplx_0(k2_nat_1(k1_newton(2,B),k1_nat_1(k3_xcmplx_0(2,C),1)),1) ) ) ) ) )).
fof(d1_nat_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) ) => ( B = k3_nat_1(A) <=> ( r2_hidden(B,A) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,A) => r1_xxreal_0(B,C) ) ) ) ) ) & ( ~ ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) ) => ( B = k3_nat_1(A) <=> B = k5_numbers ) ) ) ) )).
fof(d1_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_zfmisc_1(A) <=> ( A = k5_numbers | A = 1 ) ) ) )).
fof(d1_nat_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( r2_hidden(D,k4_finseq_1(C)) => k1_funct_1(C,D) = k1_newton(k1_funct_1(A,D),B) ) ) ) ) ) ) )).
fof(d1_nat_4,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( C = k1_nat_4(A,B) <=> ( k3_finseq_1(C) = k3_finseq_1(A) & ! [D] : ( r2_hidden(D,k4_finseq_1(C)) => k1_recdef_1(C,D) = k11_nat_3(k1_recdef_1(A,D),B) ) ) ) ) ) ) )).
fof(d1_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ( B = k2_nat_5(A) <=> ! [C] : ( v7_ordinal1(C) => k1_recdef_1(B,C) = k1_newton(C,A) ) ) ) ) )).
fof(d1_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( C = k1_nat_d(A,B) <=> ~ ( ! [D] : ( v7_ordinal1(D) => ~ ( A = k2_xcmplx_0(k3_xcmplx_0(B,C),D) & ~ r1_xxreal_0(B,D) ) ) & ~ ( C = k5_numbers & B = k5_numbers ) ) ) ) ) ) )).
fof(d1_nat_lat,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1))) ) => ( A = k1_nat_lat <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k1_binop_1(A,C,B) = k6_nat_d(C,B) ) ) ) ) )).
fof(d1_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ( r1_nattra_1(A,B,C,D) <=> ! [E] : ( 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 ) ) ) ) ) ) )).
fof(d1_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( m1_ncfcont1(C,A,B) <=> ? [D] : ( v1_xreal_0(D) & ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(a_3_0_ncfcont1(A,B,D),C) ) ) ) ) ) )).
fof(d1_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ~ ( r2_hidden(G,A) & r2_hidden(H,A) & ~ r1_xxreal_0(F,k2_normsp_0(B,k5_algstr_0(B,G,H))) & r1_xxreal_0(E,k2_normsp_0(C,k5_algstr_0(C,k7_partfun1(u1_struct_0(C),D,G),k7_partfun1(u1_struct_0(C),D,H)))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_ndiff_1,axiom,( ! [A] : ! [B] : ( l2_struct_0(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(d1_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( 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] : ( ( v9_ordinal1(C) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & v1_fdiff_1(C,k5_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v3_normsp_1(k1_ndiff_1(A,k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,C,B),k37_valued_1(k4_ordinal1,k1_numbers,C)),A) & k6_normsp_1(A,k1_ndiff_1(A,k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,C,B),k37_valued_1(k4_ordinal1,k1_numbers,C))) = k4_struct_0(A) ) ) ) ) ) ) )).
fof(d1_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [C] : ( v1_xreal_0(C) => ( r1_ndiff_4(A,B,C) <=> ? [D] : ( 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) ) ) ) ) ) )).
fof(d1_neckla_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v1_neckla_2(A) <=> ~ r1_necklace(k4_necklace(4),A) ) ) )).
fof(d1_necklace,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ( r1_necklace(A,B) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(d1_net_1,axiom,( ! [A] : ( l1_petri(A) => k1_net_1(A) = k2_xboole_0(u1_petri(A),u2_petri(A)) ) )).
fof(d1_newton,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v7_ordinal1(B) => k1_newton(A,B) = k19_rvsum_1(k2_finseq_2(B,A)) ) ) )).
fof(d1_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( m1_nfcont_1(C,A,B) <=> ? [D] : ( v1_xreal_0(D) & ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(a_3_0_nfcont_1(A,B,D),C) ) ) ) ) ) )).
fof(d1_nfcont_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ~ ( r2_hidden(G,A) & r2_hidden(H,A) & ~ r1_xxreal_0(F,k2_normsp_0(B,k5_algstr_0(B,G,H))) & r1_xxreal_0(E,k2_normsp_0(C,k5_algstr_0(C,k7_partfun1(u1_struct_0(C),D,G),k7_partfun1(u1_struct_0(C),D,H)))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_nfcont_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [C] : ( v1_xreal_0(C) => ( r1_nfcont_3(A,B,C) <=> ( r2_hidden(C,k1_relset_1(k1_numbers,B)) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( r1_tarski(k2_relset_1(k1_numbers,D),k1_relset_1(k1_numbers,B)) & v2_comseq_2(D) & k1_seq_2(D) = C ) => ( v3_normsp_1(k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,D,B),A) & k7_partfun1(u1_struct_0(A),B,C) = k6_normsp_1(A,k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,D,B)) ) ) ) ) ) ) ) ) )).
fof(d1_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [C] : ( v1_xreal_0(C) => ( r1_nfcont_4(A,B,C) <=> ? [D] : ( 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) ) ) ) ) ) )).
fof(d1_normform,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_finsub_1(B) ) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d1_normsp_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_normsp_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_normsp_0(A,B) = k3_funct_2(u1_struct_0(A),k1_numbers,u1_normsp_0(A),B) ) ) )).
fof(d1_normsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_normsp_1(A) ) => ( v2_normsp_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( k2_normsp_0(A,k1_rlvect_1(A,B,D)) = k3_xcmplx_0(k9_complex1(D),k2_normsp_0(A,B)) & r1_xxreal_0(k2_normsp_0(A,k1_algstr_0(A,B,C)),k2_xcmplx_0(k2_normsp_0(A,B),k2_normsp_0(A,C))) ) ) ) ) ) ) )).
fof(d1_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k2_binop_1(u1_struct_0(A),u1_struct_0(A),k1_numbers,B,C,D) = k2_normsp_0(A,k5_algstr_0(A,C,D)) ) ) ) ) ) )).
fof(d1_ntalgo_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => ! [B] : ( m1_subset_1(B,k4_numbers) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( C = k1_ntalgo_1(A,B) <=> ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_ordinal1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) & ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_ordinal1) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) & k9_nat_1(k4_ordinal1,D,k5_numbers) = k1_int_2(A) & k9_nat_1(k4_ordinal1,E,k5_numbers) = k1_int_2(B) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( k9_nat_1(k4_ordinal1,D,k1_nat_1(F,1)) = k9_nat_1(k4_ordinal1,E,F) & k9_nat_1(k4_ordinal1,E,k1_nat_1(F,1)) = k4_nat_d(k9_nat_1(k4_ordinal1,D,F),k9_nat_1(k4_ordinal1,E,F)) ) ) & C = k9_nat_1(k4_ordinal1,D,k3_nat_1(a_1_0_ntalgo_1(E))) ) ) ) ) ) ) )).
fof(d1_numbers,axiom,( k1_numbers = k6_subset_1(k2_xboole_0(k2_arytm_2,k2_zfmisc_1(k1_tarski(k5_ordinal1),k2_arytm_2)),k1_tarski(k4_tarski(k5_ordinal1,k5_ordinal1))) )).
fof(d1_numeral1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( C = k1_numeral1(A,B) <=> ? [D] : ( v1_relat_1(D) & v5_relat_1(D,k4_ordinal1) & v1_funct_1(D) & v5_ordinal1(D) & v1_finset_1(D) & k1_relset_1(k4_ordinal1,D) = k1_relset_1(k4_ordinal1,A) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k1_relset_1(k4_ordinal1,D)) => k1_recdef_1(D,E) = k3_xcmplx_0(k1_recdef_1(A,E),k1_newton(B,E)) ) ) & C = k7_afinsq_2(D) ) ) ) ) ) )).
fof(d1_openlatt,axiom,( ! [A] : ( l1_pre_topc(A) => k1_openlatt(A) = u1_pre_topc(A) ) )).
fof(d1_oposet_1,axiom,( k1_oposet_1 = g2_qmax_1(k1_tarski(k5_ordinal1),k6_partfun1(k1_tarski(k5_ordinal1)),k8_funct_5) )).
fof(d1_oppcat_1,axiom,( ! [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) & 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))) ) )).
fof(d1_ordeq_01,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_ordeq_01(A) <=> ? [B] : ( r1_abian(B,A) & ! [C] : ( r1_abian(C,A) => B = C ) ) ) ) )).
fof(d1_orders_3,axiom,( ! [A] : ( 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))) ) ) )).
fof(d1_ordinal1,axiom,( ! [A] : k1_ordinal1(A) = k2_xboole_0(A,k1_tarski(A)) )).
fof(d1_ordinal2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) ) => k1_ordinal2(A) = k1_funct_1(A,k3_tarski(k9_xtuple_0(A))) ) )).
fof(d1_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_ordinal2(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_ordinal2(C) ) => ( C = k1_ordinal3(A,B) <=> ( k9_xtuple_0(C) = k9_xtuple_0(B) & ! [D] : ( v3_ordinal1(D) => ( r2_hidden(D,k9_xtuple_0(B)) => k1_funct_1(C,D) = k10_ordinal2(A,k1_funct_1(B,D)) ) ) ) ) ) ) ) )).
fof(d1_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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] : ( v3_ordinal1(D) => ( r2_hidden(D,k9_xtuple_0(A)) => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) & ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(d1_ordinal6,axiom,( ! [A] : ( v1_ordinal6(A) <=> ? [B] : ( v3_ordinal1(B) & r1_tarski(A,B) ) ) )).
fof(d1_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m3_pboole(C,u1_struct_0(A),u3_msualg_1(A,B)) => ( m1_osafree(C,A,B) <=> ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d1_osalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r3_orders_2(A,C,D) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d1_osalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [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] : ( ( v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) ) => ! [D] : ( m1_msualg_4(D,u1_struct_0(A),B,C) => ( v1_osalg_4(D,A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( r3_orders_2(A,E,F) => ! [G] : ! [H] : ( ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_papdesaf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ( v1_translac(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d1_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(d1_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & l1_parsp_1(A) ) => ( v1_parsp_2(A) <=> ( ~ ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_parsp_1(A,B,C,B,D) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_partfun1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : k3_partfun1(A,B,C) = k5_relat_1(k6_relat_1(C,A),B) ) )).
fof(d1_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( v3_funct_1(C) <=> ? [D] : ( m1_subset_1(D,B) & ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,k1_relset_1(A,C)) => k1_funct_1(C,E) = D ) ) ) ) ) ) ) )).
fof(d1_partfun3,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_partfun3(A) <=> ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,k10_xtuple_0(A)) & r1_xxreal_0(B,k5_numbers) ) ) ) ) )).
fof(d1_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( r1_partit1(A,B,C) <=> ? [D] : ( r1_tarski(D,B) & D != k1_xboole_0 & C = k3_tarski(D) ) ) ) ) )).
fof(d1_partit_2,axiom,( ! [A] : ! [B] : k1_partit_2(A,B) = k1_xboole_0 )).
fof(d1_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ( v1_pasch(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d1_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r1_pboole(A,B,C) <=> ! [D] : ( r2_hidden(D,A) => r2_hidden(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) )).
fof(d1_pcomps_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_pcomps_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( 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)) ) ) ) ) ) )).
fof(d1_pcs_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v2_pralg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( C = k12_pralg_1(A,B) <=> ! [D] : ( m1_subset_1(D,A) => k1_funct_1(C,D) = u1_struct_0(k10_pralg_1(A,B,D)) ) ) ) ) ) )).
fof(d1_pdiff_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( m2_finseq_2(D,k1_numbers,k1_euclid(B)) => k3_funct_2(k1_euclid(B),k1_numbers,C,D) = k1_funct_1(D,A) ) ) ) ) ) )).
fof(d1_pdiff_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( 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) ) ) ) ) )).
fof(d1_pdiff_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( r1_pdiff_4(A,B) <=> ( r1_tarski(B,k1_relset_1(k1_euclid(3),A)) & ! [C] : ( 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) ) ) ) ) ) )).
fof(d1_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r1_pdiff_5(A,B) <=> ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & B = k11_finseq_1(C,D,E) & ? [F] : ( 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] : ( v1_funct_1(G) & v3_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [H] : ( v1_funct_1(H) & v2_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,F) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,1,k1_pdiff_3(1,3,A),B),I),k1_funct_1(k1_pdiff_2(3,1,k1_pdiff_3(1,3,A),B),C)) = k2_xcmplx_0(k1_funct_1(G,k6_xcmplx_0(I,C)),k1_funct_1(H,k6_xcmplx_0(I,C))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_pdiff_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( m2_finseq_2(D,k1_numbers,k1_euclid(B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d1_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( 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) ) ) ) ) )).
fof(d1_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ! [D] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d1_pencil_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_pencil_1(A,B,C) <=> ~ ( B != C & ! [D] : ( m1_subset_1(D,u1_pre_topc(A)) => ~ r1_tarski(k2_tarski(B,C),D) ) ) ) ) ) ) )).
fof(d1_pencil_2,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) )).
fof(d1_pencil_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(d1_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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] : ( ( 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 ) ) ) ) ) ) ) ) )).
fof(d1_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k2_pepin(A,B,C) = k4_nat_d(k1_newton(B,A),C) ) ) ) )).
fof(d1_petri_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ! [D] : ( ( 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) ) ) ) )).
fof(d1_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ( r1_pnproc_1(A,B,C) <=> ! [D] : ( r2_hidden(D,A) => k1_funct_1(B,D) = k1_funct_1(C,D) ) ) ) ) )).
fof(d1_polyeq_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k1_polyeq_1(A,B,C) = k2_xcmplx_0(k3_xcmplx_0(A,C),B) ) ) ) )).
fof(d1_polyeq_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( 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,k1_square_1(F))),k3_xcmplx_0(D,F)),E) ) ) ) ) ) ) )).
fof(d1_polyeq_4,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( v1_xcmplx_0(F) => ! [G] : ( 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,k1_square_1(G))),k3_xcmplx_0(E,G)),F) ) ) ) ) ) ) ) )).
fof(d1_polyeq_5,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v1_xcmplx_0(B) => k1_polyeq_5(A,B) = k3_xcmplx_0(k1_power(A,k9_complex1(B)),k2_xcmplx_0(k19_sin_cos(k7_xcmplx_0(k1_comptrig(B),A)),k3_xcmplx_0(k17_sin_cos(k7_xcmplx_0(k1_comptrig(B),A)),k7_complex1))) ) ) )).
fof(d1_polynom1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ( D = k9_fvsum_1(A,B,C) <=> ( k4_finseq_1(D) = k4_finseq_1(B) & ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(d1_polynom3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [C] : ( m2_finseq_2(C,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ( r1_polynom3(A,B,C) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & r2_hidden(D,k2_finseq_1(A)) & ~ r1_xxreal_0(k1_recdef_1(C,D),k1_recdef_1(B,D)) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(1,E) => ( r1_xxreal_0(D,E) | k1_recdef_1(B,E) = k1_recdef_1(C,E) ) ) ) ) ) ) ) ) )).
fof(d1_polynom4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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] : ( m1_subset_1(D,k4_ordinal1) => ( D != k7_nat_d(k1_algseq_1(A,B),1) => k1_normsp_1(A,C,D) = k4_struct_0(A) ) ) ) ) ) ) ) )).
fof(d1_polynom5,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( B = k1_polynom5(A) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k4_finseq_1(A)) => k7_partfun1(k1_numbers,B,C) = k9_complex1(k7_partfun1(u1_struct_0(k1_complfld),A,C)) ) ) ) ) ) ) )).
fof(d1_polynom6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( m2_subset_1(C,k14_pre_poly(A),k15_pre_poly(A)) => ! [D] : ( m2_subset_1(D,k14_pre_poly(B),k15_pre_poly(B)) => ! [E] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d1_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( 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 != k8_polynom1(A,B) ) ) ) )).
fof(d1_polynom8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k1_polynom8(A,B) = k5_binom(A,k5_struct_0(A),B) ) ) )).
fof(d1_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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) => ( k4_polynom1(A,C,E,F) = k4_polynom1(A,C,D,k12_pre_poly(A,F,B)) & ! [G] : ( ( 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) => k4_polynom1(A,C,E,G) = k4_struct_0(C) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_poset_1,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_poset_1(A) <=> ( v1_yellow_0(A) & ! [B] : ( ( 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) ) ) ) ) ) )).
fof(d1_power,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ( ( ( r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(1,A) ) => k1_power(A,B) = k2_prepower(A,B) ) & ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ v1_abian(A) & k1_power(A,B) != k4_xcmplx_0(k2_prepower(A,k4_xcmplx_0(B))) ) ) ) ) )).
fof(d1_pralg_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k1_pralg_2(A) <=> ( ! [C] : ( r2_hidden(C,k9_xtuple_0(B)) <=> ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & r2_hidden(D,k9_xtuple_0(A)) & C = k9_funct_6(D) ) ) & ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(C,k9_xtuple_0(B)) => k1_funct_1(B,C) = k1_funct_1(A,k9_funct_6(C)) ) ) ) ) ) ) )).
fof(d1_pralg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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) ) ) ) )).
fof(d1_pre_poly,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k3_finseq_2(A)) => ! [C] : ( m2_finseq_2(C,A,k3_finseq_2(A)) => ( C = k5_pre_poly(A,B) <=> ? [D] : ( 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] : ( m2_finseq_2(E,A,k3_finseq_2(A)) => ! [F] : ( 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) ) ) ) ) )).
fof(d1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ( v2_pre_topc(A) <=> ( r2_hidden(u1_struct_0(A),u1_pre_topc(A)) & ! [B] : ( 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(d1_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_prelamb(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d1_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( B = k1_prepower(A) <=> ! [C] : ( v7_ordinal1(C) => k1_funct_1(B,C) = k1_newton(A,C) ) ) ) ) )).
fof(d1_prgcor_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r1_xxreal_0(k5_numbers,A) => ( r1_xxreal_0(B,k5_numbers) | ! [C] : ( v1_int_1(C) => ( C = k1_prgcor_1(A,B) <=> ? [D] : ( m2_finseq_1(D,k4_numbers) & ? [E] : ( m2_finseq_1(E,k4_numbers) & ? [F] : ( 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 = k5_numbers ) & ( r1_xxreal_0(B,A) => ( k1_funct_1(D,1) = B & ? [G] : ( v1_int_1(G) & r1_xxreal_0(1,G) & r1_xxreal_0(G,A) & ! [H] : ( 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)) = k5_numbers & k1_funct_1(E,k2_xcmplx_0(G,1)) = A & ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_prgcor_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( m2_finseq_1(C,A) => ( r1_prgcor_2(A,B,C) <=> ( r1_tarski(k4_ordinal1,A) & k1_funct_1(B,k5_numbers) = k3_finseq_1(C) & ~ r1_xxreal_0(k1_afinsq_1(B),k3_finseq_1(C)) & ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(d1_prob_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v1_prob_1(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r2_hidden(C,B) => r2_hidden(k3_subset_1(A,C),B) ) ) ) ) )).
fof(d1_prob_2,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k2_prob_2(A,B,C) = k3_prob_1(A,C) ) ) )).
fof(d1_prob_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( C = k1_prob_3(A,B) <=> ( k1_prob_2(A,k9_setfam_1(A),C,k5_numbers) = k1_prob_2(A,k9_setfam_1(A),B,k5_numbers) & ! [D] : ( v7_ordinal1(D) => k1_prob_2(A,k9_setfam_1(A),C,k1_nat_1(D,1)) = k5_prob_1(A,k9_setfam_1(A),k1_prob_2(A,k9_setfam_1(A),C,D),k1_prob_2(A,k9_setfam_1(A),B,k1_nat_1(D,1))) ) ) ) ) ) )).
fof(d1_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => k2_prob_4(A,B,C) = C ) ) ) )).
fof(d1_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_projdes1(A,B,C,D,E) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & r1_collsp(A,B,C,F) & r1_collsp(A,D,E,F) ) ) ) ) ) ) ) )).
fof(d1_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d1_projred1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ~ ( ~ r1_incsp_1(A,D,B) & ~ r1_incsp_1(A,D,C) & ~ ! [E] : ( ( 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] : ( 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] : ( m1_subset_1(F,u1_incsp_1(A)) => ! [G] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_projred2,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ( r1_projred2(A,B,C,D) <=> ? [E] : ( 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) ) ) ) ) ) ) )).
fof(d1_prvect_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ! [D] : ( ( 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] : ( m2_finseq_2(E,A,k4_finseq_2(C,A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d1_prvect_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( m1_prvect_2(C,A,B) <=> ( k9_xtuple_0(C) = k9_xtuple_0(A) & ! [D] : ( 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)))) ) ) ) ) ) ) )).
fof(d1_prvect_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d1_pscomp_1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( 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) = k3_seq_4(k7_relset_1(u1_struct_0(A),k1_numbers,B,u1_struct_0(A))) ) ) )).
fof(d1_pua2mss1,axiom,( ! [A] : ( ( v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(u1_unialg_1(A))) => k2_pua2mss1(A,B) = k1_funct_1(u1_unialg_1(A),B) ) ) )).
fof(d1_pythtrip,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_int_2(A,B) <=> ! [C] : ( v7_ordinal1(C) => ( ( r1_nat_d(C,A) & r1_nat_d(C,B) ) => C = 1 ) ) ) ) ) )).
fof(d1_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( C = k1_pzfmisc1(A,B) <=> ! [D] : ( r2_hidden(D,A) => k1_funct_1(C,D) = k1_tarski(k1_funct_1(B,D)) ) ) ) ) )).
fof(d1_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) <=> ( ~ v1_xboole_0(A) & ? [B] : ( r1_tarski(k4_ordinal1,B) & A = k2_zfmisc_1(k4_ordinal1,B) ) ) ) )).
fof(d1_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => k1_qc_lang2(A) = k13_qc_lang1(A,k12_qc_lang1(A)) ) )).
fof(d1_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k2_qc_lang1(A)) => ! [C] : ( ( ~ 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) ) ) ) )).
fof(d1_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) ) ) )).
fof(d1_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_qc_lang1(B) => ( v1_qc_trans(B,A) <=> r1_tarski(A,B) ) ) ) )).
fof(d1_qmax_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( C = k1_qmax_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> m2_prob_1(D,A,B) ) ) ) ) )).
fof(d1_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_quantal1(B,A) <=> ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r1_lattices(A,k15_lattice3(A,C),D) & r2_hidden(D,B) ) ) ) ) ) )).
fof(d1_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( C = k4_quatern2(A,B) <=> ? [D] : ( m1_subset_1(D,k1_numbers) & ? [E] : ( m1_subset_1(E,k1_numbers) & ? [F] : ( m1_subset_1(F,k1_numbers) & ? [G] : ( m1_subset_1(G,k1_numbers) & ? [H] : ( m1_subset_1(H,k1_numbers) & ? [I] : ( m1_subset_1(I,k1_numbers) & ? [J] : ( m1_subset_1(J,k1_numbers) & ? [K] : ( m1_subset_1(K,k1_numbers) & A = k6_quaterni(D,E,F,G) & B = k6_quaterni(H,I,J,K) & C = k6_quaterni(k7_xcmplx_0(k3_real_1(k3_real_1(k3_real_1(k4_real_1(H,D),k4_real_1(I,E)),k4_real_1(J,F)),k4_real_1(K,G)),k1_square_1(k28_quaterni(B))),k7_xcmplx_0(k3_real_1(k5_real_1(k5_real_1(k4_real_1(H,E),k4_real_1(I,D)),k4_real_1(J,G)),k4_real_1(K,F)),k1_square_1(k28_quaterni(B))),k7_xcmplx_0(k5_real_1(k5_real_1(k3_real_1(k4_real_1(H,F),k4_real_1(I,G)),k4_real_1(J,D)),k4_real_1(K,E)),k1_square_1(k28_quaterni(B))),k7_xcmplx_0(k5_real_1(k3_real_1(k5_real_1(k4_real_1(H,G),k4_real_1(I,F)),k4_real_1(J,E)),k4_real_1(K,D)),k1_square_1(k28_quaterni(B)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k1_quatern3(A) = k23_quaterni(A,A) ) )).
fof(d1_quaterni,axiom,( k1_quaterni = k2_xboole_0(k6_subset_1(k9_funct_2(4,k1_numbers),a_0_0_quaterni),k2_numbers) )).
fof(d1_quin_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k1_quin_1(A,B,C) = k6_xcmplx_0(k1_square_1(B),k3_xcmplx_0(k3_xcmplx_0(4,A),C)) ) ) ) )).
fof(d1_quofield,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ( B = k1_quofield(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( 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) ) ) ) ) ) ) )).
fof(d1_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => k1_radix_1(A) = k2_power(2,A) ) )).
fof(d1_radix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v3_card_1(D,C) & m2_finseq_1(D,k4_ordinal1) ) => k1_radix_2(A,B,C,D) = k2_nat_1(k11_newton(k1_radix_1(B),k7_nat_d(A,1)),k1_recdef_1(D,A)) ) ) ) ) )).
fof(d1_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => k1_radix_3(A) = a_1_0_radix_3(A) ) )).
fof(d1_radix_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v3_card_1(D,B) & m2_finseq_1(D,k4_radix_3(C)) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(d1_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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) = k5_numbers ) ) ) ) ) ) )).
fof(d1_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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) = k5_numbers ) ) ) ) ) ) ) )).
fof(d1_ramsey_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_eqrel_1(D,k3_group_10(A,B)) => ( r1_ramsey_1(A,B,C,D) <=> ? [E] : ( m1_subset_1(E,D) & r1_tarski(k3_group_10(C,B),E) ) ) ) ) )).
fof(d1_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m2_prob_1(B,A,k1_random_1(A)) => ( B = k2_random_1(A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k3_funct_2(k1_zfmisc_1(A),k1_numbers,B,C) = k1_rpr_1(A,C) ) ) ) ) )).
fof(d1_random_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( 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] : ( v1_xreal_0(E) => ( E = k1_random_2(A,B,C,D) <=> ? [F] : ( m1_random_1(F,A,B) & ? [G] : ( m1_random_1(G,A,B) & r1_funct_2(A,k1_numbers,A,k1_tarski(k8_random_1(A,B,C,D)),G,k7_funcop_1(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))) ) ) ) ) ) ) ) ) ) )).
fof(d1_random_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( v1_random_3(E,A,B,C,D) <=> r1_finance1(A,B,C,D,E) ) ) ) ) ) ) )).
fof(d1_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(d1_rat_1,axiom,( ! [A] : ( A = k3_numbers <=> ! [B] : ( r2_hidden(B,A) <=> ? [C] : ( v1_int_1(C) & ? [D] : ( v1_int_1(D) & B = k7_xcmplx_0(C,D) ) ) ) ) )).
fof(d1_ratfunc1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_ratfunc1(B,A) <=> r2_funct_2(k4_ordinal1,u1_struct_0(A),B,k9_polynom3(A)) ) ) ) )).
fof(d1_rcomp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_rcomp_1(A,B) = a_2_0_rcomp_1(A,B) ) ) )).
fof(d1_rcomp_3,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_rcomp_3(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => v2_connsp_1(C,A) ) ) ) ) ) )).
fof(d1_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ( C = k1_real_3(A,B) <=> ( k9_nat_1(k4_ordinal1,C,k5_numbers) = k4_nat_d(A,B) & k9_nat_1(k4_ordinal1,C,1) = k4_nat_d(B,k4_nat_d(A,B)) & ! [D] : ( v7_ordinal1(D) => k9_nat_1(k4_ordinal1,C,k1_nat_1(D,2)) = k4_nat_d(k9_nat_1(k4_ordinal1,C,D),k9_nat_1(k4_ordinal1,C,k1_nat_1(D,1))) ) ) ) ) ) ) )).
fof(d1_real_lat,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k1_binop_1(A,B,C) = k3_xxreal_0(B,C) ) ) ) ) )).
fof(d1_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => k5_binop_1(k1_euclid(A),B,C,D) = k7_euclid(A,C,D) ) ) ) ) ) )).
fof(d1_realset1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( m1_realset1(C,A,B) <=> ! [D] : ( r2_hidden(D,k2_zfmisc_1(C,C)) => r2_hidden(k1_funct_1(B,D),C) ) ) ) ) )).
fof(d1_realset2,axiom,( k1_realset2 = k1_funct_4(k1_funct_4(k1_funct_4(k13_funcop_1(k5_numbers,k5_numbers,k5_numbers),k13_funcop_1(k5_numbers,1,1)),k13_funcop_1(1,k5_numbers,1)),k13_funcop_1(1,1,k5_numbers)) )).
fof(d1_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d1_rearran1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_rearran1(A) <=> ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(A)) ) => ! [C] : ( v1_finset_1(C) => ( C = k1_funct_1(A,B) => k5_card_1(C) = B ) ) ) ) ) ) )).
fof(d1_recdef_2,axiom,( ! [A] : ( v2_xtuple_0(A) => ! [B] : ( B = k4_xtuple_0(A) <=> ! [C] : ! [D] : ! [E] : ( A = k3_xtuple_0(C,D,E) => B = C ) ) ) )).
fof(d1_relat_1,axiom,( ! [A] : ( v1_relat_1(A) <=> ! [B] : ~ ( r2_hidden(B,A) & ! [C] : ! [D] : B != k4_tarski(C,D) ) ) )).
fof(d1_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r1_relat_2(A,B) <=> ! [C] : ( r2_hidden(C,B) => r2_hidden(k4_tarski(C,C),A) ) ) ) )).
fof(d1_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ! [D] : ( r1_relset_1(A,B,C,D) <=> ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,B) => ( r2_hidden(k4_tarski(E,F),C) => r2_hidden(k4_tarski(E,F),D) ) ) ) ) ) )).
fof(d1_relset_2,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k3_relset_2(A,B) <=> ( k9_xtuple_0(C) = k9_setfam_1(A) & ! [D] : ( r1_tarski(D,A) => k1_funct_1(C,D) = k7_relat_1(B,D) ) ) ) ) ) )).
fof(d1_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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] : ( v7_ordinal1(D) & ? [E] : ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) & k3_finseq_1(A) = k1_nat_1(D,1) & E = k5_relat_1(A,k2_finseq_1(D)) & C = k7_finseq_1(E,B) ) ) ) ) ) ) ) ) )).
fof(d1_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(A)) => ! [F] : ( 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] : ( m1_subset_1(G,k8_afinsq_1(A)) => ( k1_flang_1(A,E,G) != F & k1_flang_1(A,F,G) != E ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_rfinseq,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) = k6_xcmplx_0(k3_finseq_1(B),A) & ! [D] : ( 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 ) ) ) ) ) ) )).
fof(d1_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( v7_ordinal1(B) => ( B = k1_rfinseq2(A) <=> ( ( k3_finseq_1(A) = k5_numbers => B = k5_numbers ) & ( ~ r1_xxreal_0(k3_finseq_1(A),k5_numbers) => ( r2_hidden(B,k4_finseq_1(A)) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( r2_hidden(C,k4_finseq_1(A)) & D = k1_funct_1(A,C) & E = k1_funct_1(A,B) ) => r1_xxreal_0(D,E) ) ) ) ) & ! [C] : ( v7_ordinal1(C) => ( ( r2_hidden(C,k4_finseq_1(A)) & k1_funct_1(A,C) = k1_funct_1(A,B) ) => r1_xxreal_0(B,C) ) ) ) ) ) ) ) ) )).
fof(d1_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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(k5_numbers)))) & ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(d1_rfunct_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v5_valued_0(A) <=> ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( 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_funct_1(A,C),k1_funct_1(A,B)) ) ) ) ) ) )).
fof(d1_rfunct_3,axiom,( ! [A] : ( v1_xreal_0(A) => k1_rfunct_3(A) = k4_xxreal_0(A,k5_numbers) ) )).
fof(d1_rfunct_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( r1_rfunct_4(A,B) <=> ( r1_tarski(B,k9_xtuple_0(A)) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(1,C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & r2_hidden(D,B) & r2_hidden(E,B) & r2_hidden(k2_xcmplx_0(k3_xcmplx_0(C,D),k3_xcmplx_0(k6_xcmplx_0(1,C),E)),B) & D != E & r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(C,k1_funct_1(A,D)),k3_xcmplx_0(k6_xcmplx_0(1,C),k1_funct_1(A,E))),k1_funct_1(A,k2_xcmplx_0(k3_xcmplx_0(C,D),k3_xcmplx_0(k6_xcmplx_0(1,C),E)))) ) ) ) ) ) ) ) )).
fof(d1_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k1_rinfsup1(A) = k2_seq_4(k2_relset_1(k1_numbers,A)) ) )).
fof(d1_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => k1_rinfsup2(A) = k8_supinf_2(k17_supinf_2(A)) ) )).
fof(d1_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_ring_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d1_ringcat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(d1_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_rlvect_2(D,A) => ( D = k1_rlaffin1(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k1_numbers,D,E) = k3_funct_2(u1_struct_0(A),k1_numbers,B,k5_algstr_0(A,E,C)) ) ) ) ) ) ) )).
fof(d1_rlaffin2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k1_rlaffin2(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,k3_convex1(A,B)) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_xboole_0(E,B) & r2_hidden(D,k3_convex1(A,E)) ) ) ) ) ) ) ) ) )).
fof(d1_rlaffin3,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( ( 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 ) ) ) )).
fof(d1_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_rlsub_1(B,A) <=> ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => r2_hidden(k1_rlvect_1(A,D,C),B) ) ) ) ) ) ) ) )).
fof(d1_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(d1_rltopsp1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_convex1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ( ( r1_xxreal_0(k5_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,k6_xcmplx_0(1,E))),B) ) ) ) ) ) ) ) )).
fof(d1_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => k1_rlvect_1(A,B,C) = k1_binop_1(u1_rlvect_1(A),C,B) ) ) ) )).
fof(d1_rlvect_2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( r1_struct_0(A,B) => k1_rlvect_2(A,B) = B ) ) )).
fof(d1_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_rlvect_3(B,A) <=> ! [C] : ( m2_rlvect_2(C,A,B) => ( k6_rlvect_2(A,C) = k4_struct_0(A) => k3_rlvect_2(A,C) = k1_xboole_0 ) ) ) ) ) )).
fof(d1_rlvect_5,axiom,( ! [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) ) => ( v1_rlvect_5(A) <=> ? [B] : ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_rlvect_3(B,A) ) ) ) )).
fof(d1_rlvect_x,axiom,( ! [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) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_rlvect_2(C,A) => ! [D] : ( m1_rlvect_2(D,A) => ( D = k1_rlvect_x(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k1_numbers,D,E) = k3_xcmplx_0(B,k3_funct_2(u1_struct_0(A),k1_numbers,C,E)) ) ) ) ) ) ) )).
fof(d1_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v1_rmod_2(C,A,B) <=> ( ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r2_hidden(E,C) => r2_hidden(k5_vectsp_2(A,B,D,E),C) ) ) ) ) ) ) ) ) )).
fof(d1_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(d1_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( D = k1_rmod_4(A,B,C) <=> ? [E] : ( m2_finseq_1(E,u1_struct_0(B)) & k10_xtuple_0(E) = C & v2_funct_1(E) & D = k4_rlvect_1(B,E) ) ) ) ) ) ) )).
fof(d1_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_robbins1(A) ) => ( v1_robbins2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(d1_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_lattices(A) ) => ( v1_robbins3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d1_robbins4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_robbins1(A) ) => ( v1_robbins4(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(d1_roughs_1,axiom,( ! [A] : ( 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))) ) ) )).
fof(d1_rpr_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k1_rpr_1(A,B) = k7_xcmplx_0(k5_card_1(B),k5_card_1(A)) ) ) )).
fof(d1_rsspace,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( A = k1_rsspace <=> ! [B] : ( r2_hidden(B,A) <=> ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) ) ) )).
fof(d1_rsspace3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k6_rsspace))) => ( A = k1_rsspace3 <=> ! [B] : ( r2_hidden(B,A) <=> ( r2_hidden(B,k1_rsspace) & v2_series_1(k2_rsspace(B)) ) ) ) ) )).
fof(d1_rsspace4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k6_rsspace))) => ( A = k1_rsspace4 <=> ! [B] : ( r2_hidden(B,A) <=> ( r2_hidden(B,k1_rsspace) & v1_comseq_2(k2_rsspace(B)) ) ) ) ) )).
fof(d1_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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)) ) ) ) ) )).
fof(d1_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(d1_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( 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) ) ) ) ) )).
fof(d1_rusub_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ( v1_rusub_4(A) <=> ? [B] : ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_rusub_3(B,A) ) ) ) )).
fof(d1_rusub_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( v2_rusub_4(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v2_rusub_4(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( r1_rusub_5(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & B = k6_rusub_4(A,C,k6_domain_1(u1_struct_0(A),D)) ) ) ) ) ) )).
fof(d1_rvsum_1,axiom,( k10_binop_2 = k7_finseqop(k1_numbers,k9_binop_2,k6_partfun1(k1_numbers),k7_binop_2) )).
fof(d1_scm_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ! [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(B,u1_struct_0(k1_ami_3)) ) => ( m1_scm_1(B,A) <=> ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ r1_xxreal_0(k1_afinsq_1(A),C) => k1_funct_1(B,k10_ami_3(C)) = k1_funct_1(A,C) ) ) ) ) ) )).
fof(d1_scm_comp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(d1_scm_halt,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( r1_tarski(A,C) => ! [D] : ( v7_ordinal1(D) => ( r1_tarski(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_3(k4_scmfsa_2(k5_numbers),1)),B) => r2_hidden(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,C,B,D)),k9_xtuple_0(A)) ) ) ) ) ) ) ) )).
fof(d1_scm_inst,axiom,( k2_scm_inst = k2_zfmisc_1(k6_domain_1(k4_ordinal1,1),k4_ordinal1) )).
fof(d1_scmbsort,axiom,( ! [A] : ( 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(k5_numbers)),k6_scmfsa_2(k4_scmfsa_2(3),k4_scmfsa_2(k5_numbers))),k6_scmfsa_2(k4_scmfsa_2(4),k4_scmfsa_2(k5_numbers))),k6_scmfsa_2(k4_scmfsa_2(5),k4_scmfsa_2(k5_numbers))),k6_scmfsa_2(k4_scmfsa_2(6),k4_scmfsa_2(k5_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(k5_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(k5_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))))))) ) )).
fof(d1_scmfsa6a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( v7_ordinal1(B) => k1_scmfsa6a(A,B) = k6_funct_4(A,k2_compos_1(k1_scmfsa_2),k11_scmfsa_2(B)) ) ) )).
fof(d1_scmfsa6b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => k1_scmfsa6b(A,B,C) = k6_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(C,A),k1_scmfsa_m(B)) ) ) ) )).
fof(d1_scmfsa7b,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ( r1_scmfsa7b(A,B) <=> ~ ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(d1_scmfsa8a,axiom,( ! [A] : ( v7_ordinal1(A) => k1_scmfsa8a(A) = k16_funcop_1(k5_numbers,k11_scmfsa_2(A)) ) )).
fof(d1_scmfsa8b,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k1_nat_1(k5_card_1(C),3),A),C),k1_scmfsa8a(k1_nat_1(k5_card_1(B),1))),B),k4_compos_1(k1_scmfsa_2)) ) ) ) )).
fof(d1_scmfsa8c,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k5_numbers) ) )).
fof(d1_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ( r1_scmfsa9a(A,B,C,D) <=> ! [E] : ( v7_ordinal1(E) => ( k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(B,D,C,A),E),C) = k5_numbers => ( r5_scmfsa7b(D,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(B,D,C,A),E),k1_funct_4(A,k1_scmfsa_9(C,D))) & r6_scmfsa7b(D,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(B,D,C,A),E),k1_funct_4(A,k1_scmfsa_9(C,D))) ) ) ) ) ) ) ) ) )).
fof(d1_scmfsa_1,axiom,( k1_scmfsa_1 = k2_xboole_0(k1_ami_2,k1_scmfsa_i) )).
fof(d1_scmfsa_2,axiom,( k1_scmfsa_2 = g1_extpro_1(k7_card_1(3),k1_scmfsa_1,k10_subset_1(k4_ordinal1,k1_scmfsa_1),k2_scmfsa_i,k4_scmfsa_1,k5_scmfsa_1,k12_scmfsa_1) )).
fof(d1_scmfsa_7,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) ) => ( ( ~ r1_xxreal_0(B,k5_numbers) => ( C = k1_scmfsa_7(A,B) <=> ? [D] : ( v7_ordinal1(D) & k1_nat_1(D,1) = B & C = k1_ordinal4(k1_ordinal4(k5_afinsq_1(k6_scmfsa_2(A,k4_scmfsa_2(k5_numbers))),k8_funcop_1(u1_compos_1(k1_scmfsa_2),D,k7_scmfsa_2(A,k4_scmfsa_2(k5_numbers)))),k5_afinsq_1(k2_compos_1(k1_scmfsa_2))) ) ) ) & ( r1_xxreal_0(B,k5_numbers) => ( C = k1_scmfsa_7(A,B) <=> ? [D] : ( v7_ordinal1(D) & k2_xcmplx_0(D,B) = 1 & C = k1_ordinal4(k1_ordinal4(k5_afinsq_1(k6_scmfsa_2(A,k4_scmfsa_2(k5_numbers))),k8_funcop_1(u1_compos_1(k1_scmfsa_2),D,k8_scmfsa_2(A,k4_scmfsa_2(k5_numbers)))),k5_afinsq_1(k2_compos_1(k1_scmfsa_2))) ) ) ) ) ) ) ) )).
fof(d1_scmfsa_9,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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(k5_numbers)),k4_compos_1(k1_scmfsa_2)),k16_funcop_1(k1_nat_1(k5_card_1(B),4),k11_scmfsa_2(k5_numbers))) ) ) )).
fof(d1_scmfsa_i,axiom,( k1_scmfsa_i = k6_subset_1(k4_numbers,k4_ordinal1) )).
fof(d1_scmfsa_m,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) ) => k1_scmfsa_m(A) = k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))) ) )).
fof(d1_scmisort,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2))))) ) => ( E = k1_scmisort(A,B,C,D) <=> ( r8_pboole(u1_struct_0(k1_scmfsa_2),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),E,k5_numbers),A) & ! [F] : ( v7_ordinal1(F) => r8_pboole(u1_struct_0(k1_scmfsa_2),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),E,k1_nat_1(F,1)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(D,k2_scmfsa_9(C,B)),k1_scmfsa_m(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),E,F)),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(k1_funct_4(D,k2_scmfsa_9(C,B)),B),k1_scmfsa_m(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),E,F))),3))) ) ) ) ) ) ) ) ) )).
fof(d1_scmp_gcd,axiom,( ! [A] : ( v7_ordinal1(A) => k1_scmp_gcd(A) = k10_ami_3(A) ) )).
fof(d1_scmpds_2,axiom,( k1_scmpds_2 = g1_extpro_1(k7_card_1(2),k1_ami_2,k10_subset_1(k4_ordinal1,k1_ami_2),k1_scmpds_i,k3_ami_2,k4_ami_2,k6_scmpds_1) )).
fof(d1_scmpds_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & 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))) ) ) )).
fof(d1_scmpds_6,axiom,( ! [A] : ( v1_int_1(A) => k1_scmpds_6(A) = k9_compos_1(k1_scmpds_2,k3_scmpds_2(A)) ) )).
fof(d1_scmpds_7,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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,k1_nat_1(k5_card_1(D),3)),D),k11_scmpds_2(A,B,C)),k3_scmpds_2(k4_xcmplx_0(k1_nat_1(k5_card_1(D),2)))) ) ) ) ) )).
fof(d1_scmpds_8,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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,k1_nat_1(k5_card_1(C),2)),C),k3_scmpds_2(k4_xcmplx_0(k1_nat_1(k5_card_1(C),1)))) ) ) ) )).
fof(d1_scmpds_i,axiom,( k1_scmpds_i = k2_xboole_0(k2_xboole_0(k2_xboole_0(k2_xboole_0(k2_xboole_0(k1_tarski(k3_xtuple_0(k5_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) )).
fof(d1_scmring1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => k1_scmring1(A) = k6_afinsq_1(k4_ordinal1,u1_struct_0(A)) ) )).
fof(d1_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_extpro_1(B,k7_card_1(2)) & l1_extpro_1(B,k7_card_1(2)) ) => ( B = k1_scmring2(A) <=> ( u1_struct_0(B) = k1_ami_2 & u2_struct_0(B) = k4_ordinal1 & u1_compos_1(B) = k1_scmringi(A) & u1_memstr_0(k7_card_1(2),B) = k3_ami_2 & u2_memstr_0(k7_card_1(2),B) = k1_scmring1(A) & u1_extpro_1(k7_card_1(2),B) = k8_scmring1(A) ) ) ) ) )).
fof(d1_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => k2_scmring3(A,B) = k10_ami_3(B) ) ) )).
fof(d1_scmringi,axiom,( ! [A] : ( ( ~ 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(k5_numbers,k1_xboole_0,k1_xboole_0)),a_0_0_scmringi),a_0_1_scmringi),a_0_2_scmringi),a_1_0_scmringi(A)) ) )).
fof(d1_scmyciel,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( B = k1_scmyciel(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( r2_hidden(C,A) & k1_card_1(C) = 2 ) ) ) ) )).
fof(d1_scpisort,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ( r1_scpisort(A,B,C) <=> ! [D] : ( v7_ordinal1(D) => ( ( 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_xcmplx_0(C,D))) ) ) ) ) ) ) )).
fof(d1_scpqsort,axiom,( 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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(2),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(2),k2_scmp_gcd,k5_numbers,6)) )).
fof(d1_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ( v1_semi_af1(A) <=> ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_analoaf(A,B,C,C,B) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_analoaf(A,B,C,D,D) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_analoaf(A,B,C,B,D) => r2_analoaf(A,C,B,C,D) ) ) ) ) & ~ ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_analoaf(A,B,C,B,D) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_analoaf(A,B,C,D,E) & r2_analoaf(A,B,D,C,E) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( r2_analoaf(A,B,C,B,D) & ~ ! [G] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d1_seq_1,axiom,( ! [A] : ( v1_xreal_0(A) => k1_seq_1(A) = k7_funcop_1(k4_ordinal1,A) ) )).
fof(d1_seq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) ) => ( v1_seq_2(A) <=> ? [B] : ( v1_xreal_0(B) & ! [C] : ~ ( r2_hidden(C,k9_xtuple_0(A)) & r1_xxreal_0(B,k1_funct_1(A,C)) ) ) ) ) )).
fof(d1_seq_4,axiom,( ! [A] : ( v3_membered(A) => ( v4_xxreal_2(A) => ( v1_xboole_0(A) | ! [B] : ( v1_xreal_0(B) => ( B = k2_seq_4(A) <=> ( ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => r1_xxreal_0(C,B) ) ) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,A) & ~ r1_xxreal_0(D,k6_xcmplx_0(B,C)) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( D = k2_seqfunc(A,B,C) <=> ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d1_seqm_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v3_valued_0(A) ) => ( v5_valued_0(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(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)) ) ) ) ) ) )).
fof(d1_series_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v1_valued_0(B) ) => ( B = k2_series_1(A) <=> ( k1_funct_1(B,k5_numbers) = k1_funct_1(A,k5_numbers) & ! [C] : ( v7_ordinal1(C) => k1_funct_1(B,k1_nat_1(C,1)) = k2_xcmplx_0(k1_funct_1(B,C),k1_funct_1(A,k1_nat_1(C,1))) ) ) ) ) ) )).
fof(d1_setfam_1,axiom,( ! [A] : ! [B] : ( ( A != k1_xboole_0 => ( B = k1_setfam_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ! [D] : ( r2_hidden(D,A) => r2_hidden(C,D) ) ) ) ) & ( A = k1_xboole_0 => ( B = k1_setfam_1(A) <=> B = k1_xboole_0 ) ) ) )).
fof(d1_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_setlim_1(B,A) <=> ( v3_prob_1(B) | v2_prob_1(B) ) ) ) )).
fof(d1_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( D = k1_setlim_2(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k9_nat_1(k9_setfam_1(A),D,E) = k9_subset_1(A,k9_nat_1(k9_setfam_1(A),B,E),k9_nat_1(k9_setfam_1(A),C,E)) ) ) ) ) ) )).
fof(d1_setwiseo,axiom,( ! [A] : k1_setwiseo(A) = k1_xboole_0 )).
fof(d1_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => k1_setwop_2(A,B,C) = k2_finsop_1(A,k8_funcop_1(A,k4_ordinal1,C),B) ) ) ) )).
fof(d1_sf_mastr,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( 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] : ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) & ? [D] : ( 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] : ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) & ? [D] : ( v7_ordinal1(D) & ( 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] : ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) & ? [D] : ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) & ? [E] : ( 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] : ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) & ? [D] : ( 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 ) ) ) ) ) )).
fof(d1_sfmastr2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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_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(k5_numbers)))) ) ) )).
fof(d1_sfmastr3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(F,u1_struct_0(k1_scmfsa_2)) ) => k1_sfmastr3(A,B,C,D,E,F) = k5_scmfsa_9(k1_funct_7(k1_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(k5_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(k5_numbers))),k9_scmfsa_m(1,k4_subset_1(k2_scmfsa_2,k6_scmfsa_m(B,C,D),k2_sf_mastr(E))),A) ) ) ) ) ) ) )).
fof(d1_sgraph1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k1_sgraph1(A,B) = a_2_0_sgraph1(A,B) ) ) )).
fof(d1_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( v1_sheffer1(A) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_lattices(A,B,C) = C & k2_lattices(A,C,B) = C ) ) ) ) ) )).
fof(d1_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_sheffer1(A) ) => ( v1_sheffer2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) )).
fof(d1_simplex0,axiom,( ! [A] : ! [B] : ( v1_classes1(B) => ( B = k1_simplex0(A) <=> ( r1_tarski(A,B) & ! [C] : ( ( r1_tarski(A,C) & v1_classes1(C) ) => r1_tarski(B,C) ) ) ) ) )).
fof(d1_simplex1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_simplex0(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => k1_simplex1(A,B,C) = C ) ) ) )).
fof(d1_simplex2,axiom,( ! [A] : ( ( ~ 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] : ( 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] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => ( m1_simplex2(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) & r2_hidden(E,B) & r1_tarski(k8_metric_1(A,D,C),E) ) ) ) ) ) ) ) ) )).
fof(d1_sin_cos2,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => k1_funct_1(A,B) = k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_funct_1(k22_sin_cos,k4_xcmplx_0(B))),2) ) ) ) )).
fof(d1_sin_cos3,axiom,( ! [A] : ( ( 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] : ( v1_xcmplx_0(B) => k1_funct_1(A,B) = k7_xcmplx_0(k6_xcmplx_0(k15_sin_cos(k3_xcmplx_0(k7_complex1,B)),k15_sin_cos(k4_xcmplx_0(k3_xcmplx_0(k7_complex1,B)))),k3_xcmplx_0(2,k7_complex1)) ) ) ) )).
fof(d1_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => k1_sin_cos4(A) = k7_xcmplx_0(k17_sin_cos(A),k19_sin_cos(A)) ) )).
fof(d1_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => k1_sin_cos5(A) = k7_xcmplx_0(k4_sin_cos2(A),k2_sin_cos2(A)) ) )).
fof(d1_sin_cos6,axiom,( k1_sin_cos6 = k2_partfun2(k1_numbers,k1_numbers,k5_relset_1(k1_numbers,k1_numbers,k16_sin_cos,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(d1_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => k1_sin_cos7(A) = k3_power(k4_power,k2_xcmplx_0(A,k3_square_1(k2_xcmplx_0(k1_square_1(A),1)))) ) )).
fof(d1_sin_cos9,axiom,( k1_sin_cos9 = k2_partfun2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k26_sin_cos,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(d1_sincos10,axiom,( k1_sincos10 = k2_partfun2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k3_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(d1_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( r1_sppol_1(A,B,C) <=> ( r2_hidden(B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( 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 ) ) ) ) ) ) ) ) )).
fof(d1_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( r1_sppol_2(A,B,C) <=> ( A != B & ? [D] : ( v4_topreal1(D) & m2_finseq_1(D,u1_struct_0(k15_euclid(2))) & ? [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(d1_sprect_1,axiom,( ! [A] : ( 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))) ) )).
fof(d1_sprect_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r1_sprect_2(A,B) <=> ! [C] : ( v7_ordinal1(C) => ( 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))) ) ) ) ) ) ) )).
fof(d1_square_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k1_square_1(A) = k3_xcmplx_0(A,A) ) )).
fof(d1_stacks_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( v1_relat_1(C) => ! [D] : ( ( 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] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,B) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d1_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k7_card_1(A),k7_card_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(A),k7_card_1(B)))) ) => ( v1_stirl2_1(C,A,B) <=> ( ( A = k5_numbers => B = k5_numbers ) & ( B = k5_numbers => A = k5_numbers ) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( r2_hidden(D,k2_relset_1(k7_card_1(B),C)) & r2_hidden(E,k2_relset_1(k7_card_1(B),C)) & ~ r1_xxreal_0(E,D) & r1_xxreal_0(k3_nat_1(k1_stirl2_1(A,k7_card_1(B),C,k1_seq_4(E))),k3_nat_1(k1_stirl2_1(A,k7_card_1(B),C,k1_seq_4(D)))) ) ) ) ) ) ) ) ) )).
fof(d1_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => ( v2_struct_0(A) <=> v1_xboole_0(u1_struct_0(A)) ) ) )).
fof(d1_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k16_substut1(A),k38_substut1(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( 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) ) ) ) ) )).
fof(d1_subset_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) ) )).
fof(d1_substlat,axiom,( ! [A] : ! [B] : k1_substlat(A,B) = a_2_0_substlat(A,B) )).
fof(d1_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => k1_substut1(A) = k4_partfun1(k3_qc_lang1(A),k3_qc_lang1(A)) ) )).
fof(d1_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(d1_supinf_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ( B = k3_supinf_1(A) <=> ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(C,B) <=> m1_xxreal_2(C,A) ) ) ) ) ) )).
fof(d1_supinf_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( ( 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)) ) ) ) )).
fof(d1_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ~ ( C != k4_struct_0(B) & ! [H] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_sysrel,axiom,( ! [A] : ( v1_relat_1(A) => k1_sysrel(A) = k3_xboole_0(A,k4_relat_1(k9_xtuple_0(A))) ) )).
fof(d1_t_0topsp,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ( r1_t_0topsp(A,B) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(d1_t_1topsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => k1_t_1topsp(A) = a_1_0_t_1topsp(A) ) )).
fof(d1_tarski,axiom,( ! [A] : ! [B] : ( B = k1_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> C = A ) ) )).
fof(d1_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ( m1_taxonom1(B,A) <=> ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & ~ r1_setfam_1(C,D) & ~ r1_setfam_1(D,C) ) ) ) ) ) ) )).
fof(d1_taxonom2,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_taxonom2(A) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & r8_orders_1(u1_orders_2(A),B) ) ) ) )).
fof(d1_taylor_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => k1_funct_1(B,C) = k3_prepower(C,A) ) ) ) ) )).
fof(d1_taylor_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ! [C] : ( v1_xreal_0(C) => k1_taylor_2(A,B,C) = k6_taylor_1(A,B,k5_numbers,C) ) ) ) )).
fof(d1_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ( v1_tbsp_1(A) <=> ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(D,C) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => D != k8_metric_1(A,E,B) ) ) ) ) ) ) ) ) ) )).
fof(d1_tdgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ( v1_tdgroup(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & k1_algstr_0(A,C,C) = B ) ) ) ) )).
fof(d1_tdlat_1,axiom,( ! [A] : ( l1_pre_topc(A) => k1_tdlat_1(A) = a_1_0_tdlat_1(A) ) )).
fof(d1_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( C = k1_tdlat_2(A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(D,C) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & D = k1_tops_1(A,E) & r2_hidden(E,B) ) ) ) ) ) ) ) )).
fof(d1_tdlat_3,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_tdlat_3(A) <=> u1_pre_topc(A) = k9_setfam_1(u1_struct_0(A)) ) ) )).
fof(d1_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ( v7_struct_0(A) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & u1_struct_0(A) = k6_domain_1(u1_struct_0(A),B) ) ) ) )).
fof(d1_tex_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => ( v1_tex_2(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = u1_struct_0(B) => v1_subset_1(C,u1_struct_0(A)) ) ) ) ) ) )).
fof(d1_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v1_tex_3(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = u1_struct_0(B) => v1_tops_1(C,A) ) ) ) ) ) )).
fof(d1_tex_4,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tex_4(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d1_tietze,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( r1_tietze(A,B,C) <=> ! [D] : ( r2_hidden(D,k3_xboole_0(C,k9_xtuple_0(A))) => r1_xxreal_0(k9_complex1(k1_funct_1(A,D)),B) ) ) ) ) )).
fof(d1_tmap_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,C,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,B))) ) => ! [F] : ( ( 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] : ( ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(d1_toler_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_toler_1(C,A,B) <=> ! [D] : ! [E] : ( ( r2_hidden(D,C) & r2_hidden(E,C) ) => r2_hidden(k4_tarski(D,E),B) ) ) ) )).
fof(d1_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( D = k1_topalg_1(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> m1_borsuk_2(E,A,B,C) ) ) ) ) ) )).
fof(d1_topalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k5_topalg_1(A,C))) => ? [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d1_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l3_algstr_0(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & l3_algstr_0(D) ) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(H,u1_struct_0(k2_group_7(k2_tarski(1,2),k10_finseq_1(A,B)))) => ? [I] : ( m1_subset_1(I,u1_struct_0(A)) & ? [J] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_topalg_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(d1_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_topalg_6(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v7_struct_0(k5_topalg_1(A,B)) ) ) ) )).
fof(d1_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(k9_setfam_1(u1_struct_0(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k9_setfam_1(u1_struct_0(A)))))) ) => ( B = k1_topdim_1(A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( v7_ordinal1(D) => ( k13_prob_1(u1_struct_0(A),k4_ordinal1,k9_setfam_1(u1_struct_0(A)),B,k5_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),k4_ordinal1,k9_setfam_1(u1_struct_0(A)),B,k1_nat_1(D,1))) & ~ r2_hidden(C,k13_prob_1(u1_struct_0(A),k4_ordinal1,k9_setfam_1(u1_struct_0(A)),B,D)) & ? [E] : ( m1_subset_1(E,u1_struct_0(k1_pre_topc(A,C))) & ? [F] : ( 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] : ( ( 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),k4_ordinal1,k9_setfam_1(u1_struct_0(A)),B,D)) ) ) ) ) ) & ( ( r2_hidden(C,k13_prob_1(u1_struct_0(A),k4_ordinal1,k9_setfam_1(u1_struct_0(A)),B,D)) | ! [E] : ( m1_subset_1(E,u1_struct_0(k1_pre_topc(A,C))) => ! [F] : ( ( 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] : ( ( 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),k4_ordinal1,k9_setfam_1(u1_struct_0(A)),B,D)) ) ) ) ) ) ) => r2_hidden(C,k13_prob_1(u1_struct_0(A),k4_ordinal1,k9_setfam_1(u1_struct_0(A)),B,k1_nat_1(D,1))) ) ) ) ) ) ) ) )).
fof(d1_topdim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v1_topdim_2(B,A) <=> ? [C] : ( v7_ordinal1(C) & ! [D] : ( 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)) ) ) ) ) ) )).
fof(d1_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( C = k1_topgen_1(A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(D,C) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & D = k2_tops_1(A,E) & r2_hidden(E,B) ) ) ) ) ) ) ) )).
fof(d1_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_card_1(C) => ( C = k1_topgen_2(A,B) <=> ( ? [D] : ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(d1_topgen_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v1_topgen_3(B,A) <=> ! [C] : ! [D] : ! [E] : ~ ( r2_hidden(D,B) & r2_hidden(E,B) & r2_hidden(C,k3_xboole_0(D,E)) & ! [F] : ( m1_subset_1(F,k1_zfmisc_1(A)) => ~ ( r2_hidden(F,B) & r2_hidden(C,F) & r1_tarski(F,k3_xboole_0(D,E)) ) ) ) ) ) )).
fof(d1_topgen_4,axiom,( ! [A] : ( l1_struct_0(A) => k1_topgen_4(A) = k1_zfmisc_1(u1_struct_0(A)) ) )).
fof(d1_topgen_5,axiom,( k1_topgen_5 = a_0_0_topgen_5 )).
fof(d1_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d1_topmetr,axiom,( ! [A] : ( ( v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k1_binop_1(u1_metric_1(B),C,D) = k1_binop_1(u1_metric_1(A),C,D) ) ) ) ) ) ) )).
fof(d1_topreal1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r1_topreal1(A,B,C,D) <=> ? [E] : ( 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,k5_numbers) = B & k1_funct_1(E,1) = C ) ) ) ) ) ) )).
fof(d1_topreal2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal2(A) <=> ? [B] : ( 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)) ) ) ) )).
fof(d1_topreal4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( r1_topreal4(A,B,C) <=> ? [D] : ( 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)) ) ) ) ) ) )).
fof(d1_topreal6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( v1_xreal_0(D) => ( D = k1_topreal6(A,B,C) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(A))) & ? [F] : ( m1_subset_1(F,u1_struct_0(k14_euclid(A))) & E = B & F = C & D = k3_metric_1(k14_euclid(A),E,F) ) ) ) ) ) ) ) )).
fof(d1_topreal7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_metric_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( m1_subset_1(H,u1_struct_0(B)) & ? [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_binop_1(u1_metric_1(C),D,E) = k4_xxreal_0(k2_binop_1(u1_struct_0(A),u1_struct_0(A),k1_numbers,u1_metric_1(A),F,G),k2_binop_1(u1_struct_0(B),u1_struct_0(B),k1_numbers,u1_metric_1(B),H,I)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( v1_xreal_0(C) => k1_topreal9(A,B,C) = a_3_0_topreal9(A,B,C) ) ) ) )).
fof(d1_topreala,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k1_topreala(A,B,C,D) = k1_pre_topc(k15_euclid(2),k2_jgraph_6(A,B,C,D)) ) ) ) ) )).
fof(d1_toprealb,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_toprealb(A,B) = a_2_0_toprealb(A,B) ) ) )).
fof(d1_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ( v1_toprns_1(B,A) <=> r1_tarski(k10_xtuple_0(B),k8_struct_0(k15_euclid(A))) ) ) ) )).
fof(d1_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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))) ) ) )).
fof(d1_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_tops_2(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => v3_pre_topc(C,A) ) ) ) ) ) )).
fof(d1_tops_3,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_tops_1(B,A) <=> k1_tops_1(A,B) = k1_xboole_0 ) ) ) )).
fof(d1_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(d1_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ( v1_translac(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d1_treal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => k1_treal_1(A,B) = A ) ) ) )).
fof(d1_trees_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( r1_tarski(A,B) <=> ? [C] : ( v7_ordinal1(C) & A = k5_relat_1(B,k2_finseq_1(C)) ) ) ) ) )).
fof(d1_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ( A = B <=> ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( r2_hidden(C,A) <=> r2_hidden(C,B) ) ) ) ) ) )).
fof(d1_trees_3,axiom,( ! [A] : ( A = k1_trees_3 <=> ! [B] : ( r2_hidden(B,A) <=> ( ~ v1_xboole_0(B) & v1_trees_1(B) ) ) ) )).
fof(d1_trees_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ( A = B <=> ( k9_xtuple_0(A) = k9_xtuple_0(B) & ! [C] : ( m1_trees_1(C,k9_xtuple_0(A)) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) ) )).
fof(d1_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ( v1_zfmisc_1(A) <=> k9_xtuple_0(A) = k2_trees_1(k5_numbers) ) ) )).
fof(d1_trees_a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( m4_trees_1(C,A) => ( C != k1_xboole_0 => ! [D] : ( ( ~ v1_xboole_0(D) & v1_trees_1(D) ) => ( D = k1_trees_a(A,B,C) <=> ! [E] : ( m2_finseq_1(E,k4_ordinal1) => ( r2_hidden(E,D) <=> ~ ( ~ ( r2_hidden(E,A) & ! [F] : ( m2_finseq_1(F,k4_ordinal1) => ~ ( r2_hidden(F,C) & r2_xboole_0(F,E) ) ) ) & ! [F] : ( m2_finseq_1(F,k4_ordinal1) => ! [G] : ( m2_finseq_1(G,k4_ordinal1) => ~ ( r2_hidden(F,C) & r2_hidden(G,B) & E = k8_finseq_1(k4_ordinal1,F,G) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_triang_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(d1_tsep_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => ( v1_tsep_1(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = u1_struct_0(B) => v3_pre_topc(C,A) ) ) ) ) ) )).
fof(d1_tsep_2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d1_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ( m1_pre_topc(B,A) <=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A)) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v3_pre_topc(C,B) <=> ? [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(d1_turing_1,axiom,( ! [A] : ( v7_ordinal1(A) => k3_turing_1(A) = a_1_0_turing_1(A) ) )).
fof(d1_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k1_funct_1(A,k10_finseq_1(B,C)) = k10_margrel1(B,C) ) ) ) ) )).
fof(d1_unialg_1,axiom,( ! [A] : ( l1_unialg_1(A) => ( v2_unialg_1(A) <=> v4_margrel1(u1_unialg_1(A),u1_struct_0(A)) ) ) )).
fof(d1_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(d1_uniform1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_metric_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( ~ r1_xxreal_0(E,k1_metric_1(A,F,G)) & r1_xxreal_0(D,k1_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))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_uniroots,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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)) ) ) ) ) )).
fof(d1_uproots,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k1_uproots(A,B,C) = k1_funct_4(k16_pre_poly(A),k8_funcop_1(k4_ordinal1,B,C)) ) ) )).
fof(d1_urysohn1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( B = k1_urysohn1(A) <=> ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) <=> ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(D,k1_newton(2,A)) & C = k7_xcmplx_0(D,k1_newton(2,A)) ) ) ) ) ) ) )).
fof(d1_urysohn3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( v7_ordinal1(D) => ( ( v10_pre_topc(A) & v4_pre_topc(B,A) & v4_pre_topc(C,A) & r1_xboole_0(B,C) ) => ( B = k1_xboole_0 | ! [E] : ( ( 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,k5_numbers)) & C = k7_subset_1(u1_struct_0(A),k2_struct_0(A),k1_funct_1(E,1)) & ! [F] : ( m2_subset_1(F,k1_numbers,k1_urysohn1(D)) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : k1_valuat_1(A,B) = k1_funct_2(k3_qc_lang1(A),B) ) )).
fof(d1_valued_0,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_valued_0(A) <=> r1_tarski(k10_xtuple_0(A),k2_numbers) ) ) )).
fof(d1_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d1_valued_2,axiom,( ! [A] : ( v4_funct_1(A) => k1_valued_2(A) = k3_tarski(a_1_0_valued_2(A)) ) )).
fof(d1_vectsp11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) & ? [E] : ( 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) ) ) ) ) ) ) )).
fof(d1_vectsp_1,axiom,( k1_vectsp_1 = g2_algstr_0(k1_numbers,k9_binop_2,k10_subset_1(k5_numbers,k1_numbers)) )).
fof(d1_vectsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l5_algstr_0(A) ) => ( v1_vectsp_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d1_vectsp_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v1_vectsp_4(C,A,B) <=> ( ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r2_hidden(E,C) => r2_hidden(k4_vectsp_1(A,B,D,E),C) ) ) ) ) ) ) ) ) )).
fof(d1_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(d1_vectsp_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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] : ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d1_vectsp_7,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v1_vectsp_7(C,A,B) <=> ! [D] : ( 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 ) ) ) ) ) ) )).
fof(d1_vectsp_8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(d1_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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] : ( v7_ordinal1(C) => ( C = k1_vectsp_9(A,B) <=> ! [D] : ( m1_vectsp_7(D,A,B) => C = k1_card_1(D) ) ) ) ) ) ) )).
fof(d1_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d1_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d1_waybel10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_orders_2(B) & v4_yellow_0(B,k6_yellow_1(A,A)) & m1_yellow_0(B,k6_yellow_1(A,A)) ) => ( B = k2_waybel10(A) <=> ! [C] : ( ( 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) ) ) ) ) ) )).
fof(d1_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_waybel11(B,A) <=> ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(d1_waybel14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(d1_waybel15,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_waybel15(B,A) <=> ( r2_orders_2(A,k3_yellow_0(A),B) & ! [C] : ( 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 ) ) ) ) ) ) )).
fof(d1_waybel16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v3_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(d1_waybel17,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ( D = k1_waybel17(A,B,C) <=> ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( ? [F] : ( m1_subset_1(F,k4_ordinal1) & E = k2_nat_1(2,F) ) => k3_funct_2(k4_ordinal1,A,D,E) = B ) & ( ! [F] : ( m1_subset_1(F,k4_ordinal1) => E != k2_nat_1(2,F) ) => k3_funct_2(k4_ordinal1,A,D,E) = C ) ) ) ) ) ) ) ) )).
fof(d1_waybel19,axiom,( ! [A] : ( ( ~ 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)))) ) ) ) )).
fof(d1_waybel20,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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 ) ) ) )).
fof(d1_waybel21,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => r3_waybel_0(A,B,C,D) ) ) ) ) ) ) )).
fof(d1_waybel22,axiom,( ! [A] : ( ( ~ 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] : ( r1_waybel22(A,B) <=> ! [C] : ( ( ~ 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] : ( ( 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] : ( m1_waybel16(E,A,C) & k2_partfun1(u1_struct_0(A),u1_struct_0(C),E,B) = D & ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d1_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_waybel23(B,A) <=> v5_yellow_0(k5_yellow_0(A,B),A) ) ) ) )).
fof(d1_waybel24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => k1_waybel24(A,B,C,D,E) = k1_funct_1(k1_funct_5(D),E) ) ) ) ) ) )).
fof(d1_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( r1_waybel18(A,B) <=> ? [C] : ( 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] : ( 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)) ) ) ) ) ) )).
fof(d1_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => k1_waybel26(A,B) = k3_waybel24(A,k1_waybel25(B)) ) ) )).
fof(d1_waybel27,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_waybel27(A) <=> ( ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => ( v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) ) ) & ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(B,k9_xtuple_0(A)) => k1_funct_1(A,B) = k2_funct_5(B) ) ) ) ) ) )).
fof(d1_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => r1_orders_2(A,C,k2_yellow_6(u1_struct_0(A),A,B,C)) ) ) ) ) )).
fof(d1_waybel29,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_waybel_9(B) & v4_waybel11(B) & m1_yellow_9(B,A) ) => B = k1_waybel29(A) ) ) )).
fof(d1_waybel30,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k1_waybel30(A,B) = a_2_1_waybel30(A,B) ) ) )).
fof(d1_waybel31,axiom,( ! [A] : ( ( 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)) ) )).
fof(d1_waybel32,axiom,( ! [A] : ( ( ~ 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)))) ) ) ) )).
fof(d1_waybel33,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_waybel_0(C,k2_yellow_1(B)) & v13_waybel_0(C,k2_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(B)))) ) => k1_waybel33(A,B,C) = k1_yellow_0(A,a_3_0_waybel33(A,B,C)) ) ) ) )).
fof(d1_waybel34,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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) ) ) ) ) ) ) )).
fof(d1_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_waybel_0(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,B) & r1_orders_2(A,C,E) & r1_orders_2(A,D,E) ) ) ) ) ) ) ) ) )).
fof(d1_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(d1_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( l1_waybel_0(B,A) => k1_waybel_2(A,B) = k4_yellow_2(A,u1_waybel_0(A,B)) ) ) )).
fof(d1_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_waybel_3(A,B,C) <=> ! [D] : ( ( ~ 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] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,D) & r3_orders_2(A,B,E) ) ) ) ) ) ) ) ) )).
fof(d1_waybel_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ( B = k1_waybel_4(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d1_waybel_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) ) => ! [C] : ( ( 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] : ( r2_hidden(D,k9_xtuple_0(B)) => k1_funct_1(C,D) = k4_yellow_2(A,k1_funct_1(B,D)) ) ) ) ) ) )).
fof(d1_waybel_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_waybel_6(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,B) & r1_waybel_3(A,D,C) ) ) ) ) ) ) ) )).
fof(d1_waybel_7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(k12_lattice3(A,C,D),B) & ~ r2_hidden(C,B) & ~ r2_hidden(D,B) ) ) ) ) ) ) )).
fof(d1_waybel_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_orders_2(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ( B = k1_waybel_8(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,u1_struct_0(B)) <=> v1_waybel_3(C,A) ) ) ) ) ) )).
fof(d1_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(d1_weddwitt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v15_algstr_0(C) & m1_group_2(C,A) ) => ( C = k1_weddwitt(A,B) <=> u1_struct_0(C) = a_2_0_weddwitt(A,B) ) ) ) ) )).
fof(d1_weierstr,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => k1_weierstr(A) = A ) )).
fof(d1_wellfnd1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v12_waybel_0(B,A) <=> ! [C] : ! [D] : ( ( r2_hidden(C,B) & r2_hidden(k4_tarski(D,C),u1_orders_2(A)) ) => r2_hidden(D,B) ) ) ) ) )).
fof(d1_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : k1_wellord1(A,B) = k6_subset_1(k10_relat_1(A,B),k1_tarski(B)) ) )).
fof(d1_wellord2,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( B = k1_wellord2(A) <=> ( k1_relat_1(B) = A & ! [C] : ! [D] : ( ( r2_hidden(C,A) & r2_hidden(D,A) ) => ( r2_hidden(k4_tarski(C,D),B) <=> r1_tarski(C,D) ) ) ) ) ) )).
fof(d1_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) <=> ( k1_nat_1(k3_finseq_1(C),1) = k3_finseq_1(B) & ! [D] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_xboole_0,axiom,( ! [A] : ( v1_xboole_0(A) <=> ! [B] : ~ r2_hidden(B,A) ) )).
fof(d1_xboolean,axiom,( k1_xboolean = k5_numbers )).
fof(d1_xcmplx_0,axiom,( k1_xcmplx_0 = k5_funct_4(k4_ordinal1,k5_numbers,1,k5_numbers,1) )).
fof(d1_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) <=> r2_hidden(A,k1_numbers) ) )).
fof(d1_xtuple_0,axiom,( ! [A] : ( v1_xtuple_0(A) <=> ? [B] : ? [C] : A = k4_tarski(B,C) ) )).
fof(d1_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) <=> r2_hidden(A,k6_numbers) ) )).
fof(d1_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k1_xxreal_1(A,B) = a_2_0_xxreal_1(A,B) ) ) )).
fof(d1_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => ( m1_xxreal_2(B,A) <=> ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(C,A) => r1_xxreal_0(C,B) ) ) ) ) ) )).
fof(d1_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( ( ( r2_hidden(A,k1_numbers) & r2_hidden(B,k1_numbers) ) => ( r1_xxreal_0(A,B) <=> ? [C] : ( m1_subset_1(C,k1_numbers) & ? [D] : ( 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 ) ) ) ) ) ) )).
fof(d1_yellow11,axiom,( k1_yellow11 = k1_yellow_1(k3_enumset1(k5_numbers,k6_subset_1(3,1),2,k6_subset_1(3,2),3)) )).
fof(d1_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( m1_yellow13(C,A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(B,k1_tops_1(A,D)) & ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d1_yellow14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ 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) ) ) ) ) ) )).
fof(d1_yellow15,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k9_setfam_1(A)) => ! [C] : ( m2_finseq_1(C,k6_margrel1) => ! [D] : ( m2_finseq_1(D,k9_setfam_1(A)) => ( D = k1_yellow15(A,B,C) <=> ( k3_finseq_1(D) = k3_finseq_1(B) & ! [E] : ( 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))) ) ) ) ) ) ) ) )).
fof(d1_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(d1_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_yellow19(A,B) = a_2_0_yellow19(A,B) ) ) )).
fof(d1_yellow20,axiom,( ! [A] : ( l2_altcat_1(A) => ! [B] : ( l2_altcat_1(B) => ( r1_yellow20(A,B) <=> ! [C] : ! [D] : ! [E] : 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))) ) ) ) )).
fof(d1_yellow21,axiom,( ! [A] : ( ( l1_struct_0(A) => k1_yellow21(A) = A ) & ( ~ l1_struct_0(A) => k1_yellow21(A) = o_0_0_yellow21 ) ) )).
fof(d1_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v3_orders_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_orders_2(A,B,B) ) ) ) )).
fof(d1_yellow_1,axiom,( ! [A] : k1_yellow_1(A) = g1_orders_2(A,k2_orders_1(A)) )).
fof(d1_yellow_2,axiom,( ! [A] : ! [B] : ( l1_orders_2(B) => ! [C] : ( ( 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] : ( ( 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] : ~ ( r2_hidden(E,A) & ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d1_yellow_3,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => ( C = k1_yellow_3(A,B) <=> ! [D] : ! [E] : ( r2_hidden(k4_tarski(D,E),C) <=> ? [F] : ? [G] : ? [H] : ? [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) ) ) ) ) ) ) )).
fof(d1_yellow_4,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_yellow_4(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,B) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,C) & r1_orders_2(A,D,E) ) ) ) ) ) ) ) ) )).
fof(d1_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_yellow_5(A,B,C) = k11_lattice3(A,B,k7_waybel_1(A,C)) ) ) ) )).
fof(d1_yellow_6,axiom,( ! [A] : k1_yellow_6(A) = k1_classes1(k5_classes1(A)) )).
fof(d1_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v3_pre_topc(D,A) & r2_hidden(B,D) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(E,C) & r1_tarski(E,D) ) ) ) ) ) ) ) ) ) )).
fof(d1_yellow_9,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(d1_yoneda_1,axiom,( ! [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) & l1_cat_1(A) ) => k1_yoneda_1(A) = k11_ens_1(k16_ens_1(A)) ) )).
fof(d1_zf_fund1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k4_ordinal1) => k3_funct_2(k4_ordinal1,k1_zf_lang,A,B) = k2_zf_lang(k5_card_1(B)) ) ) ) )).
fof(d1_zf_fund2,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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(k5_numbers),k2_zf_model(A)) => k1_zf_fund2(A,B,C) = a_3_0_zf_fund2(A,B,C) ) & ( ~ r2_hidden(k2_zf_lang(k5_numbers),k2_zf_model(A)) => k1_zf_fund2(A,B,C) = k1_xboole_0 ) ) ) ) ) )).
fof(d1_zf_lang,axiom,( k1_zf_lang = a_0_0_zf_lang )).
fof(d1_zf_model,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( B = k1_zf_model(A) <=> ? [C] : ( ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ! [E] : ( m2_subset_1(E,k4_ordinal1,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] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( 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] : ~ ( E = F & r2_hidden(k4_tarski(k20_zf_lang(D),F),C) ) ) & ~ ( v5_zf_lang(D) & ! [F] : ! [G] : ~ ( 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] : ~ ( 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) ) ) ) ) ) ) ) ) )).
fof(d1_zf_refle,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) ) => ! [C] : ( ( 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)))) ) ) ) )).
fof(d1_zfmisc_1,axiom,( ! [A] : ! [B] : ( B = k1_zfmisc_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> r1_tarski(C,A) ) ) )).
fof(d1_zfmodel1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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(k5_numbers),k8_zf_lang(k2_zf_lang(4),k12_zf_lang(A,k4_zf_lang(k2_zf_lang(4),k2_zf_lang(k5_numbers))))))) => ( r2_hidden(k2_zf_lang(k5_numbers),k2_zf_model(A)) | ! [D] : ( ( 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] : ( ( 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] : ( m2_subset_1(F,k4_ordinal1,k1_zf_lang) => ~ ( k3_funct_2(k1_zf_lang,B,E,F) != k3_funct_2(k1_zf_lang,B,C,F) & k2_zf_lang(k5_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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d1_zfrefle1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_zf_lang)) => ( r1_zfrefle1(A,B) <=> ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ( r2_hidden(C,B) => r2_zf_model(A,C) ) ) ) ) ) )).
fof(d1_zmodul01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_zmodul01(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_int_1(C) => k1_zmodul01(A,B,C) = k1_binop_1(u1_zmodul01(A),C,B) ) ) ) )).
fof(d1_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( v1_int_1(B) => k1_zmodul02(A,B) = a_2_0_zmodul02(A,B) ) ) )).
fof(d20_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_abcmiz_0(A)) => k8_abcmiz_0(A,B,C) = k1_funct_1(k7_abcmiz_0(A,B,C),k1_nat_1(k3_finseq_1(C),1)) ) ) ) )).
fof(d20_abcmiz_1,axiom,( k19_abcmiz_1 = k2_zfmisc_1(k1_tarski(k8_abcmiz_1),k2_zfmisc_1(k4_abcmiz_1,k4_ordinal1)) )).
fof(d20_abcmiz_a,axiom,( ! [A] : ( 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))) ) )).
fof(d20_algstr_0,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v16_algstr_0(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k6_algstr_0(A,B,C) = k6_algstr_0(A,B,D) => C = D ) ) ) ) ) ) )).
fof(d20_altcat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => k1_altcat_1(B,C,C) = k1_tarski(k4_relat_1(C)) ) ) ) ) ) )).
fof(d20_aofa_000,axiom,( ! [A] : ( ( v4_unialg_1(A) & v6_aofa_000(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k16_aofa_000(A,B,C) = k1_funct_1(k2_pua2mss1(A,k10_subset_1(4,k4_finseq_1(u1_unialg_1(A)))),k2_finseq_4(u1_struct_0(A),B,C)) ) ) ) )).
fof(d20_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v2_relat_1(D) & m1_msafree(D,A,B) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_msafree4(F,u1_struct_0(A),D,k1_msafree4(u1_struct_0(A),D,E)) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),E)) => ! [H] : ( m1_subset_1(H,k1_zfmisc_1(k13_aofa_a00(A,B,C,D))) => ( H = k14_aofa_a00(A,B,C,D,E,F,G) <=> ! [I] : ( m2_pboole(I,u1_struct_0(A),D,u3_msualg_1(A,C)) => ( r2_hidden(I,H) <=> ( r2_hidden(I,k13_aofa_a00(A,B,C,D)) & k1_msafree4(k1_msafree4(u1_struct_0(A),D,E),k2_msafree4(u1_struct_0(A),D,u3_msualg_1(A,C),I,E),F) != G ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d20_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ( v8_aofa_a01(C,A,B) <=> ~ ! [D] : ( ( v19_aofa_a00(D,A) & m1_subset_1(D,u1_struct_0(A)) ) => ! [E] : ( m1_msafree4(E,u1_struct_0(A),k1_aofa_a01(A,B,C),k1_msafree4(u1_struct_0(A),k1_aofa_a01(A,B,C),k37_aofa_a00(A))) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,C),D)) => k39_aofa_a00(A,C,k4_aofa_a01(A,C,k1_aofa_a01(A,B,C),k37_aofa_a00(A),E),D,F) = k4_trees_4(k2_msaterm(A,B,k10_subset_1(k1_funct_1(u7_aofa_a00(A),11),u4_struct_0(A))),k10_finseq_1(E,F)) ) ) ) ) ) ) ) )).
fof(d20_aofa_i00,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => k24_aofa_i00(A,B) = k8_funcop_1(A,k9_funct_2(A,k4_numbers),B) ) ) )).
fof(d20_armstrng,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ( v10_armstrng(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d20_asympt_0,axiom,( ! [A] : ( m1_funct_2(A,k4_ordinal1,k1_numbers) => ! [B] : ( m1_funct_2(B,k4_ordinal1,k1_numbers) => k15_asympt_0(A,B) = a_2_3_asympt_0(A,B) ) ) )).
fof(d20_bcialg_1,axiom,( ! [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) ) => ( v13_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d20_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k6_vectsp10(A,B,k13_bilinear(A,B,C,D)))) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d20_binop_2,axiom,( ! [A] : ( ( 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 = k20_binop_2 <=> ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => k1_binop_1(A,B,C) = k2_xcmplx_0(B,C) ) ) ) ) )).
fof(d20_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(d20_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k20_coh_sp(A)) => k21_coh_sp(A,B) = k1_xtuple_0(k1_xtuple_0(B)) ) )).
fof(d20_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( C = k12_cohsp_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( 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) ) ) ) ) ) )).
fof(d20_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k11_conlat_1(A))) => k12_conlat_1(A,B) = B ) ) )).
fof(d20_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_convex4(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xcmplx_0(E) => ( ( v1_xreal_0(E) & 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) ) ) ) ) ) ) ) )).
fof(d20_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k15_decomp_1(A) = a_1_9_decomp_1(A) ) )).
fof(d20_descip_1,axiom,( ! [A] : ( m2_finseq_2(A,k6_margrel1,k4_finseq_2(48,k6_margrel1)) => ! [B] : ( 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) ) ) ) ) )).
fof(d20_e_siec,axiom,( ! [A] : ( 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)))) ) )).
fof(d20_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(d20_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(d20_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => k17_fomodel0(A,B,C) = k6_funct_4(C,A,B) ) )).
fof(d20_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( 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)),k15_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)),k15_fomodel2(A,C),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),k6_margrel1)) => ( D = k22_fomodel2(A,B,C) <=> ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( B = E => D = k9_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)),k15_fomodel2(A,C),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),k6_margrel1),k21_fomodel2(A,C),E) ) ) ) ) ) ) ) )).
fof(d20_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v4_fomodel1(B,A) & m1_subset_1(B,k1_fomodel1(A)) ) => ! [C] : ( ( 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] : ( v7_ordinal1(D) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_pre_poly(E) ) => ! [F] : ( ( 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))) ) => ( ( k29_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(k43_fomodel1(A,k1_fomodel2(A)),k1_funct_1(E,k37_fomodel2(A,F))),k1_funct_1(E,k38_fomodel2(A,F))) ) ) & ( ( k29_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(k43_fomodel1(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),k37_fomodel2(A,F)))) ) ) & ~ ( ~ ( k29_fomodel2(A,F) = k1_nat_1(D,1) & ~ v5_fomodel2(F,A) ) & ~ ( k29_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) ) ) ) ) ) ) ) ) )).
fof(d20_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) => ! [C] : ! [D] : ( v9_fomodel4(D,A,B,C) <=> ? [E] : ? [F] : ( v7_ordinal1(F) & r1_tarski(E,C) & v5_fomodel4(k4_tarski(E,D),F,A,B,k1_xboole_0) ) ) ) ) )).
fof(d20_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ( v5_fsm_1(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ~ ( D != E & r5_fsm_1(A,B,C,D,E) ) ) ) ) ) ) ) )).
fof(d20_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : 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)) )).
fof(d20_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( l2_functor0(C,A,B) => ( v12_functor0(C,A,B) <=> ! [D] : ( 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)) ) ) ) ) ) )).
fof(d20_gate_1,axiom,( ! [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) ) => 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 ) ) )).
fof(d20_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(d20_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ( v5_glib_000(A) <=> ! [B] : ! [C] : ! [D] : ! [E] : ( ( r1_glib_000(A,D,E,B) & r1_glib_000(A,D,E,C) ) => B = C ) ) ) )).
fof(d20_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(d20_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(d20_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m3_glib_005(D,A) => ( D = k12_glib_005(A,B,C) <=> ( r6_pboole(k7_glib_000(A),k1_funct_1(D,k5_numbers),k8_funcop_1(k4_ordinal1,k7_glib_000(A),k5_numbers)) & ! [E] : ( v7_ordinal1(E) => r6_pboole(k7_glib_000(A),k1_funct_1(D,k1_nat_1(E,1)),k11_glib_005(A,k1_funct_1(D,E),C,B)) ) ) ) ) ) ) ) )).
fof(d20_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( B = k7_graph_1(A) <=> ? [C] : ( v1_finset_1(C) & C = u4_struct_0(A) & B = k5_card_1(C) ) ) ) ) )).
fof(d20_graphsp,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers)) => ! [B] : ( ( ~ v2_struct_0(B) & v2_graph_1(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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) = k1_nat_1(k1_nat_1(k2_nat_1(C,C),k2_nat_1(3,C)),1) & k2_finseq_1(C) = u1_struct_0(B) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,C) ) => ( k1_funct_1(A,E) = 1 & k1_funct_1(A,k1_nat_1(k2_nat_1(2,C),E)) = k5_numbers ) ) ) & k1_funct_1(A,k1_nat_1(C,1)) = k5_numbers & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(2,E) & r1_xxreal_0(E,C) ) => k1_funct_1(A,k1_nat_1(C,E)) = k4_xcmplx_0(1) ) ) & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ! [H] : ( m1_subset_1(H,k4_ordinal1) => ( ( G = E & H = F ) => k1_funct_1(A,k1_nat_1(k1_nat_1(k2_nat_1(2,C),k2_nat_1(C,G)),H)) = k11_graphsp(B,E,F,D) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d20_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v4_group_9(C,A,B) & m1_group_9(C,A,B) ) => ! [D] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(d20_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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 ) ) )).
fof(d20_idea_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( m2_finseq_1(D,k4_ordinal1) => k1_funct_1(C,D) = k11_idea_1(B,D,A) ) ) ) ) ) )).
fof(d20_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(d20_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ( ~ v3_incsp_1(k8_domain_1(u1_incsp_1(A),B,C,D),A) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d20_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( B = k18_interva1(A) <=> ! [C] : ( r2_hidden(C,B) <=> m2_interva1(C,A) ) ) ) )).
fof(d20_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1)) => ( B = k11_intpro_1(A) <=> ! [C] : ( m1_subset_1(C,k1_intpro_1) => ( r2_hidden(C,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_intpro_1)) => ( ( v9_intpro_1(D) & r1_tarski(A,D) ) => r2_hidden(C,D) ) ) ) ) ) ) ) )).
fof(d20_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( v6_lattice3(A) <=> ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r3_lattice3(A,C,B) & ! [F] : ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d20_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( m2_lattice5(D,A,B,C) <=> ( k9_xtuple_0(D) = k4_ordinal1 & k1_funct_1(D,k5_numbers) = k4_tarski(A,C) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ? [F] : ( ~ v1_xboole_0(F) & ? [G] : ( 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] : ( ~ v1_xboole_0(H) & ? [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,k1_nat_1(E,1)) = k4_tarski(H,I) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d20_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( v17_lattices(A) <=> ( v15_lattices(A) & v16_lattices(A) & v11_lattices(A) ) ) ) )).
fof(d20_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k9_funct_2(k6_glib_000(A),k4_ordinal1))) => ! [C] : k20_lexbfs(A,B,C) = k4_tarski(k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),B),k3_lexbfs(k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k4_ordinal1,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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),B))),1)) ) ) )).
fof(d20_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k13_lmod_7(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k13_lmod_7(A,B,C))) => ( F = k15_lmod_7(A,B,C,D,E) <=> ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d20_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(k22_lpspacc1(A,B,C)),k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k22_lpspacc1(A,B,C)),k1_numbers))) ) => ( D = k23_lpspacc1(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(k22_lpspacc1(A,B,C))) => ? [F] : ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) & r2_hidden(F,E) & k12_supinf_2(D,E) = k1_mesfunc6(A,B,C,k56_valued_1(A,k2_numbers,F)) ) ) ) ) ) ) ) )).
fof(d20_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_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)) ) ) ) )).
fof(d20_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ( r5_ltlaxio1(A,B,C) <=> B = k3_hilbert1(A,C) ) ) ) ) )).
fof(d20_margrel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d20_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => k23_member_1(A,B) = k13_member_1(k1_tarski(B),A) ) ) )).
fof(d20_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ( r1_xboole_0(A,B) <=> ! [C] : ( v1_xxreal_0(C) => ~ ( r2_hidden(C,A) & r2_hidden(C,B) ) ) ) ) ) )).
fof(d20_metric_1,axiom,( k11_metric_1 = k8_funcop_1(k4_ordinal1,k2_zfmisc_1(2,2),k5_numbers) )).
fof(d20_metric_3,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,k1_numbers) => ! [E] : ( m1_subset_1(E,k1_numbers) => ! [F] : ( m1_subset_1(F,k1_numbers) => ! [G] : ( m1_subset_1(G,k1_numbers) => ! [H] : ( m1_subset_1(H,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)) => ! [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) ) => k2_binop_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k1_numbers,A,H,I) = k3_real_1(k3_real_1(k5_binop_1(k1_numbers,k6_metric_1,B,C),k5_binop_1(k1_numbers,k6_metric_1,D,E)),k5_binop_1(k1_numbers,k6_metric_1,F,G)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d20_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( D = k23_mmlquery(A,B,C) <=> ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => k2_mmlquery(A,D,E) = k3_tarski(a_4_13_mmlquery(A,B,C,E)) ) ) ) ) ) )).
fof(d20_mod_2,axiom,( k18_mod_2 = g6_algstr_0(k1_enumset1(k5_numbers,1,2),k13_mod_2,k14_mod_2,k16_mod_2,k17_mod_2) )).
fof(d20_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_1(B) & m2_finseq_1(B,k4_ordinal1) ) => k13_modelc_1(A,B) = k7_modelc_1(k8_modelc_1(k7_modelc_1(A),k7_modelc_1(B))) ) ) )).
fof(d20_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ~ ( ~ v4_modelc_2(A) & ~ v5_modelc_2(A) & ~ v7_modelc_2(A) & ~ v8_modelc_2(A) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( ( v4_modelc_2(A) => ( B = k12_modelc_2(A) <=> ? [C] : ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) & k4_modelc_2(C,B) = A ) ) ) & ( v5_modelc_2(A) => ( B = k12_modelc_2(A) <=> ? [C] : ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) & k5_modelc_2(C,B) = A ) ) ) & ( v7_modelc_2(A) => ( B = k12_modelc_2(A) <=> ? [C] : ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) & k7_modelc_2(C,B) = A ) ) ) & ~ ( ~ v4_modelc_2(A) & ~ v5_modelc_2(A) & ~ v7_modelc_2(A) & ~ ( B = k12_modelc_2(A) <=> ? [C] : ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) & k8_modelc_2(C,B) = A ) ) ) ) ) ) ) )).
fof(d20_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_3(B,A) & l1_modelc_3(B,A) ) => ! [C] : ( ( 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] : ( 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 ) ) ) ) ) ) )).
fof(d20_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v17_monoid_0(A) <=> v9_monoid_0(u2_algstr_0(A),u1_struct_0(A)) ) ) )).
fof(d20_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k14_msualg_2(A,B)) => ! [E] : ( m1_subset_1(E,k14_msualg_2(A,B)) => ! [F] : ( ( v3_msualg_1(F,A) & m1_msualg_2(F,A,B) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d20_msualg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [E] : ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(d20_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( v1_cat_1(B) & m3_cat_2(B,A) ) => ( B = k10_nattra_1(A) <=> ( u1_struct_0(B) = u1_struct_0(A) & u4_struct_0(B) = a_1_0_nattra_1(A) ) ) ) ) )).
fof(d20_oposet_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_qmax_1(A) ) => ( v11_oposet_1(A) <=> ? [B] : ( 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) ) ) ) )).
fof(d20_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(k2_osafree(A,B))) => ! [D] : ( 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) ) ) ) ) )).
fof(d20_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(d20_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(d20_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v1_funcop_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( D = k9_pboole(A,B,C) <=> ! [E] : ( r2_hidden(E,A) => k1_funct_1(D,E) = k7_relat_1(k1_funct_1(C,E),k1_funct_1(B,E)) ) ) ) ) ) )).
fof(d20_pcs_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v7_pcs_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( C = k7_pcs_0(A,B) <=> ! [D] : ( m1_subset_1(D,A) => k1_funct_1(C,D) = u1_pcs_0(k6_pcs_0(A,B,D)) ) ) ) ) ) )).
fof(d20_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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] : ( r7_pdiff_1(A,B,C,D,E) => ! [F] : ( ( 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 = k14_pdiff_1(A,B,C,D,E) <=> ( k1_relset_1(u1_struct_0(k4_real_ns1(A)),F) = E & ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d20_pencil_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ( v16_pencil_1(B,A) <=> ? [C] : ( m1_subset_1(C,A) & ! [D] : ( m1_subset_1(D,A) => ( C != D => v3_card_1(k1_funct_1(B,D),1) ) ) ) ) ) )).
fof(d20_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => k23_polyform(A,B) = k2_struct_0(k22_polyform(A,B)) ) ) )).
fof(d20_pscomp_1,axiom,( ! [A] : ( 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)))) ) )).
fof(d20_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v4_qc_lang1(B,A) <=> ? [C] : ( m1_subset_1(C,k9_qc_lang1(A)) & ? [D] : ( m1_subset_1(D,k9_qc_lang1(A)) & B = k14_qc_lang1(A,C,D) ) ) ) ) ) )).
fof(d20_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( r2_qc_lang2(A,B,C) <=> ? [D] : ( v7_ordinal1(D) & ? [E] : ( 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] : ( v7_ordinal1(F) => ~ ( r1_xxreal_0(1,F) & ~ r1_xxreal_0(D,F) & ! [G] : ( m1_subset_1(G,k9_qc_lang1(A)) => ! [H] : ( m1_subset_1(H,k9_qc_lang1(A)) => ~ ( k1_funct_1(E,F) = G & k1_funct_1(E,k1_nat_1(F,1)) = H & r1_qc_lang2(A,G,H) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d20_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_quantal1(A) ) => ( v21_quantal1(A) <=> v17_quantal1(u1_quantal1(A),A) ) ) )).
fof(d20_quaterni,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_quaterni(B) => k20_quaterni(A,B) = k19_quaterni(A,k8_quaterni(B)) ) ) )).
fof(d20_quofield,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(d20_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_ringcat1(A) ) => ! [B] : ( ( 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] : ( m3_ringcat1(C,k10_ringcat1(A)) => k3_funct_2(k10_ringcat1(A),A,B,C) = k12_ringcat1(A,C) ) ) ) ) )).
fof(d20_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_robbins1(A) ) => ! [B] : ( 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)) ) ) )).
fof(d20_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( m1_eqrel_1(B,k3_tarski(A)) => ( v10_scmyciel(B,A) <=> ! [C] : ( r2_hidden(C,B) => ( v9_scmyciel(C,A) & m1_subset_1(C,k1_zfmisc_1(k3_tarski(A))) ) ) ) ) ) )).
fof(d20_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => k25_seq_4(A) = a_1_0_seq_4(A) ) )).
fof(d20_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_pre_topc(D) & m1_simplex0(D,A) ) => ( D = k10_simplex0(A,B,C) <=> ( k2_struct_0(D) = k2_struct_0(B) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(D))) => ( v3_pre_topc(E,D) <=> ? [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d20_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( m2_orders_1(C,k8_eqrel_1(u4_struct_0(A),k10_stacks_1(A)),k6_partfun1(k8_eqrel_1(u4_struct_0(A),k10_stacks_1(A)))) => u4_stacks_1(B) = k1_funct_7(k3_relat_1(C,u4_stacks_1(A)),u1_stacks_1(A),o_1_1_stacks_1(A)) ) ) ) ) ) )).
fof(d20_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) )).
fof(d20_turing_1,axiom,( k19_turing_1 = k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k1_funct_4(k12_turing_1(k8_mcart_1(k4_ordinal1,k4_ordinal1,k3_turing_1(3),k7_domain_1(k4_ordinal1,k5_numbers,1)),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),k5_numbers),k2_turing_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k3_zfmisc_1(k4_ordinal1,k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers),k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,1,k5_numbers,1))),k2_turing_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k3_zfmisc_1(k4_ordinal1,k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,1,1),k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,1,k5_numbers,1))),k2_turing_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k3_zfmisc_1(k4_ordinal1,k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,1,k5_numbers),k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,2,k5_numbers,1))),k2_turing_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k3_zfmisc_1(k4_ordinal1,k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,2,1),k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,2,k5_numbers,1))),k2_turing_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k3_zfmisc_1(k4_ordinal1,k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,2,k5_numbers),k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,3,k5_numbers,k5_numbers))) )).
fof(d20_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d20_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d20_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v13_waybel_0(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & r1_orders_2(A,C,D) ) => r2_hidden(D,B) ) ) ) ) ) ) )).
fof(d20_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v9_waybel_1(A) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(d20_waybel_4,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ( v8_waybel_4(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(k4_tarski(C,D),B) & C != D & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(k4_tarski(C,E),B) & r2_hidden(k4_tarski(E,D),B) & C != E ) ) ) ) ) ) ) ) )).
fof(d20_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) => ( v4_yellow_6(B,A) <=> ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(d20_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v8_zf_lang(A) <=> ? [B] : ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) & ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & A = k10_zf_lang(B,C) ) ) ) ) )).
fof(d20_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( m1_zmodul01(D,A) => ( r1_zmodul01(A,C,D) => ! [E] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d20_zmodul02,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_zmodul02(B,A) => ( B = k19_zmodul02(A) <=> k18_zmodul02(A,B) = k1_xboole_0 ) ) ) )).
fof(d21_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_abcmiz_0(A)) => ( r3_abcmiz_0(A,B,C) <=> ! [D] : ( v7_ordinal1(D) => ! [E] : ( m1_subset_1(E,u1_abcmiz_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d21_abcmiz_1,axiom,( k20_abcmiz_1 = k2_xboole_0(k2_xboole_0(k17_abcmiz_1,k18_abcmiz_1),k19_abcmiz_1) )).
fof(d21_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [C] : ( 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] : ( 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) ) ) ) ) ) )).
fof(d21_algstr_0,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v17_algstr_0(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k6_algstr_0(A,C,B) = k6_algstr_0(A,D,B) => C = D ) ) ) ) ) ) )).
fof(d21_algstr_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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)))) ) ) ) ) ) ) )).
fof(d21_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(d21_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & l3_msualg_1(D,A) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,C),E)) => ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) & v1_funcop_1(G) ) => ( ? [H] : ( m2_pboole(H,u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D)) & ? [I] : ( m1_msafree(I,A,C) & r1_msualg_3(A,C,D,H) & I = k1_funct_6(G) & G = k1_msafree(u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D),I,H) ) ) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,D),E)) => ( H = k15_aofa_a00(A,B,C,D,E,F,G) <=> ? [I] : ( m2_pboole(I,u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D)) & ? [J] : ( m1_msafree(J,A,C) & r1_msualg_3(A,C,D,I) & J = k1_funct_6(G) & G = k1_msafree(u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D),J,I) & H = k1_msafree4(k1_funct_1(u3_msualg_1(A,C),E),k2_msafree4(u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D),I,E),F) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d21_aofa_i00,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_int_1(B) => k25_aofa_i00(A,B) = k7_funcop_1(k9_funct_2(A,k4_numbers),B) ) ) )).
fof(d21_armstrng,axiom,( ! [A] : ! [B] : ( 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) ) )).
fof(d21_bcialg_1,axiom,( ! [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) ) => ( v14_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_bcialg_1(A,k2_bcialg_1(A,B)) = k2_bcialg_1(A,B) ) ) ) )).
fof(d21_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k6_vectsp10(A,C,k14_bilinear(A,B,C,D)))) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d21_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( 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) ) ) ) ) )).
fof(d21_cat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l2_cat_4(A) ) => k19_cat_4(A) = u5_cat_4(A) ) )).
fof(d21_closure2,axiom,( ! [A] : ( l1_struct_0(A) => ! [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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(d21_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k20_coh_sp(A)) => k22_coh_sp(A,B) = k2_xtuple_0(k1_xtuple_0(B)) ) )).
fof(d21_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => k13_cohsp_1(A) = a_1_0_cohsp_1(A) ) )).
fof(d21_comput_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_margrel1(B) ) => ( v8_comput_1(B,A) <=> k18_margrel1(B) = A ) ) )).
fof(d21_convex4,axiom,( ! [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) ) => k18_convex4(A) = g1_clvect_1(u1_struct_0(A),u2_struct_0(A),u1_algstr_0(A),u1_clvect_1(A)) ) )).
fof(d21_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k16_decomp_1(A) = a_1_10_decomp_1(A) ) )).
fof(d21_e_siec,axiom,( ! [A] : ( 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)))) ) )).
fof(d21_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(d21_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : k19_facirc_1(A,B,C) = k2_circcomb(k8_facirc_1(A,B,C,k1_facirc_1),k15_facirc_1(A,B,C)) )).
fof(d21_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,k1_funct_7(k6_partfun1(A),B,C)) ) )).
fof(d21_fomodel1,axiom,( ! [A] : ( l4_struct_0(A) => ! [B] : ( 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) = k5_numbers ) ) ) ) )).
fof(d21_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_subset_1(D,k9_funct_2(k37_fomodel1(A),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_fomodel2(A,B)) => k23_fomodel2(A,B,C,D) = k1_funct_1(k1_funct_5(k22_fomodel2(A,C,B)),D) ) ) ) ) )).
fof(d21_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v4_fomodel1(B,A) & m1_subset_1(B,k1_fomodel1(A)) ) => ! [C] : ( ( 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] : ( v7_ordinal1(D) => ! [E] : ( m2_funct_2(E,k30_fomodel2(A),k30_fomodel2(A),k9_funct_2(k30_fomodel2(A),k30_fomodel2(A))) => ! [F] : ( m2_funct_2(F,k30_fomodel2(A),k30_fomodel2(A),k9_funct_2(k30_fomodel2(A),k30_fomodel2(A))) => ( F = k31_fomodel3(A,B,C,D,E) <=> ! [G] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(d21_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( v12_fomodel4(C,B) => ( r1_fomodel4(A,B,C) <=> r2_hidden(k2_xtuple_0(C),k1_xtuple_0(C)) ) ) ) )).
fof(d21_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ( v6_fsm_1(D,A,B,C) <=> ? [E] : ( m2_finseq_1(E,A) & r1_fsm_1(A,C,E,u2_fsm_1(A,C),D) ) ) ) ) ) ) )).
fof(d21_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k21_ftacell1(A,B,C,D,E) = k45_gfacirc1(A,B,C) )).
fof(d21_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l2_altcat_1(B) ) => ! [C] : ( l2_functor0(C,A,B) => ( v13_functor0(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(G,k1_altcat_1(A,D,E)) & ? [H] : ( m1_subset_1(H,k1_altcat_1(A,E,F)) & ! [I] : ( m1_subset_1(I,k1_altcat_1(B,k3_functor0(A,B,C,D),k3_functor0(A,B,C,E))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d21_gate_1,axiom,( ! [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) & 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 ) ) )).
fof(d21_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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) )).
fof(d21_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ( v6_glib_000(A) <=> ! [B] : ! [C] : ! [D] : ! [E] : ( ( r2_glib_000(A,D,E,B) & r2_glib_000(A,D,E,C) ) => B = C ) ) ) )).
fof(d21_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( ( 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] : ( ( ~ v1_abian(E) & m1_subset_1(E,k4_ordinal1) ) => ( ( 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) ) ) ) ) ) ) )).
fof(d21_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_003(A) ) => ! [B] : ! [C] : ( ( 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 ) ) ) )).
fof(d21_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => k13_glib_005(A,B,C) = k40_glib_000(k12_glib_005(A,C,B)) ) ) ) )).
fof(d21_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( C = k8_graph_1(A,B) <=> ? [D] : ( v1_finset_1(D) & ! [E] : ( 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) ) ) ) ) ) )).
fof(d21_grcat_1,axiom,( ! [A] : ! [B] : ( r1_grcat_1(A,B) <=> ? [C] : ? [D] : ? [E] : ? [F] : ( A = k6_xtuple_0(C,D,E,F) & ? [G] : ( ~ 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) ) ) ) )).
fof(d21_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(d21_idea_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( ( 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] : ( m2_finseq_1(D,k4_ordinal1) => k1_funct_1(C,D) = k11_idea_1(A,k12_idea_1(A,D,B),B) ) ) ) ) ) )).
fof(d21_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(d21_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ( ~ r1_incsp_1(A,B,C) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(d21_intpro_1,axiom,( k12_intpro_1 = k11_intpro_1(k1_subset_1(k1_intpro_1)) )).
fof(d21_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k15_lattice3(A,B) <=> ( r4_lattice3(A,C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r4_lattice3(A,D,B) => r1_lattices(A,C,D) ) ) ) ) ) ) ) )).
fof(d21_lattice5,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(d21_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k7_lattices(A,B) <=> r2_lattices(A,C,B) ) ) ) ) ) )).
fof(d21_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k9_funct_2(k6_glib_000(A),k4_ordinal1))) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( m1_subset_1(E,k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k9_funct_2(k6_glib_000(A),k4_ordinal1))) => ( E = k21_lexbfs(A,B,C,D) <=> ? [F] : ( m1_subset_1(F,k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k9_funct_2(k6_glib_000(A),k4_ordinal1))) & F = k4_tarski(k1_funct_4(k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),B),k16_funcop_1(C,k7_nat_d(k15_glib_000(A),D))),k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k4_ordinal1,k6_glib_000(A),B)) & E = k20_lexbfs(A,F,C) ) ) ) ) ) ) ) )).
fof(d21_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d21_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => k24_lpspacc1(A,B,C) = g2_clvect_1(u1_struct_0(k22_lpspacc1(A,B,C)),u2_struct_0(k22_lpspacc1(A,B,C)),u1_algstr_0(k22_lpspacc1(A,B,C)),u1_clvect_1(k22_lpspacc1(A,B,C)),k23_lpspacc1(A,B,C)) ) ) ) )).
fof(d21_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ( r6_ltlaxio1(A,B,C) <=> ? [D] : ( m1_subset_1(D,k1_hilbert1) & ? [E] : ( 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)) ) ) ) ) ) ) )).
fof(d21_margrel1,axiom,( ! [A] : ( v1_relat_1(A) => ( v2_margrel1(A) <=> v2_card_3(k9_xtuple_0(A)) ) ) )).
fof(d21_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => k24_member_1(A,B) = k14_member_1(k1_tarski(B),A) ) ) )).
fof(d21_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( v3_membered(B) => ( r1_xboole_0(A,B) <=> ! [C] : ( v1_xreal_0(C) => ~ ( r2_hidden(C,A) & r2_hidden(C,B) ) ) ) ) ) )).
fof(d21_mmlquery,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(d21_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ~ ( ~ v3_modelc_1(A) & ~ v5_modelc_1(A) & ~ v6_modelc_1(A) ) => ! [B] : ( ( v1_modelc_1(B) & m2_finseq_1(B,k4_ordinal1) ) => ( ( 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 ) ) ) ) ) ) )).
fof(d21_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r1_modelc_2(A,B) <=> ~ ( B != k3_modelc_2(A) & B != k6_modelc_2(A) & ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ( 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) ) ) ) ) ) ) )).
fof(d21_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_modelc_3(A))) => k13_modelc_3(A,B) = B ) ) )).
fof(d21_monoid_0,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(d21_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k14_msualg_2(A,B)) => ! [E] : ( m1_subset_1(E,k14_msualg_2(A,B)) => ! [F] : ( ( v3_msualg_1(F,A) & m1_msualg_2(F,A,B) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d21_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ! [C] : ( ( 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] : ( v1_xreal_0(D) & ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r2_hidden(E,B) & r2_hidden(F,B) ) => r1_xxreal_0(k9_complex1(k5_real_1(k7_partfun1(k1_numbers,C,E),k7_partfun1(k1_numbers,C,F))),k3_xcmplx_0(D,k2_normsp_0(A,k5_algstr_0(A,E,F)))) ) ) ) ) ) ) ) ) )).
fof(d21_oposet_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d21_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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] : ( ( 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] : ( 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] : ( m1_subset_1(D,u1_struct_0(k2_osafree(A,B))) => ! [E] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d21_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ( v13_osalg_1(B,A) <=> ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d21_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v2_msualg_4(C,A,B) & v3_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d21_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r8_pboole(A,B,C) <=> ! [D] : ( m1_subset_1(D,A) => k1_funct_1(B,D) = k1_funct_1(C,D) ) ) ) ) ) )).
fof(d21_pcs_0,axiom,( ! [A] : ( l1_pcs_0(A) => ! [B] : ( 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))) ) ) )).
fof(d21_pencil_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ( C = k3_pencil_1(A,B) <=> ~ v1_zfmisc_1(k1_funct_1(B,C)) ) ) ) ) )).
fof(d21_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( 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))) ) ) )).
fof(d21_pscomp_1,axiom,( ! [A] : ( 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)) ) )).
fof(d21_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v5_qc_lang1(B,A) <=> ? [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) & ? [D] : ( m1_subset_1(D,k9_qc_lang1(A)) & B = k15_qc_lang1(A,C,D) ) ) ) ) ) )).
fof(d21_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( r3_qc_lang2(A,B,C) <=> ( r2_qc_lang2(A,B,C) & B != C ) ) ) ) ) )).
fof(d21_quantal1,axiom,( ! [A] : ( l3_quantal1(A) => k3_quantal1(A) = u1_quantal1(A) ) )).
fof(d21_quaterni,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( C = k21_quaterni(A,B) <=> ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & B = k6_quaterni(D,E,F,G) & C = k6_quaterni(k3_xcmplx_0(A,D),k3_xcmplx_0(A,E),k3_xcmplx_0(A,F),k3_xcmplx_0(A,G)) ) ) ) ) ) ) ) )).
fof(d21_quofield,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(d21_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ( v6_rewrite1(A) <=> ! [B] : ! [C] : ! [D] : ( ( r2_hidden(k4_tarski(B,C),A) & r2_hidden(k4_tarski(B,D),A) ) => r7_rewrite1(A,C,D) ) ) ) )).
fof(d21_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_ringcat1(A) ) => ! [B] : ( ( 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] : ( m3_ringcat1(C,k10_ringcat1(A)) => ! [D] : ( 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] : ( m3_ringcat1(C,k10_ringcat1(A)) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(d21_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_robbins1(A) ) => ! [B] : ( 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))) ) ) )).
fof(d21_seq_4,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v5_valued_0(B) & m2_finseq_1(B,k1_numbers) ) => ( B = k26_seq_4(A) <=> ( k1_rvsum_1(B) = k1_rvsum_1(A) & k3_finseq_1(B) = k5_card_1(k1_rvsum_1(A)) ) ) ) ) )).
fof(d21_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( m1_simplex0(E,A) => ( E = k11_simplex0(A,B,C,D) <=> ? [F] : ( v1_relat_1(F) & v1_funct_1(F) & k1_funct_1(F,k5_numbers) = B & k1_funct_1(F,D) = E & k9_xtuple_0(F) = k4_ordinal1 & ! [G] : ( v7_ordinal1(G) => ! [H] : ( m1_simplex0(H,A) => ( H = k1_funct_1(F,G) => k1_funct_1(F,k1_nat_1(G,1)) = k10_simplex0(A,H,C) ) ) ) ) ) ) ) ) ) )).
fof(d21_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( B = k21_sin_cos(A) <=> ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,B,C) = k7_xcmplx_0(k3_xcmplx_0(k1_newton(k4_xcmplx_0(1),C),k1_newton(A,k3_xcmplx_0(2,C))),k2_newton(k3_xcmplx_0(2,C))) ) ) ) ) )).
fof(d21_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d21_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(d21_turing_1,axiom,( ! [A] : ( ( v1_turing_1(A) & l1_turing_1(A) ) => ( A = k20_turing_1 <=> ( u1_turing_1(A) = k7_domain_1(k4_ordinal1,k5_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),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1)),k8_mcart_1(k4_ordinal1,k4_ordinal1,k3_turing_1(3),k7_domain_1(k4_ordinal1,k5_numbers,1)),k3_zfmisc_1(k3_turing_1(3),k7_domain_1(k4_ordinal1,k5_numbers,1),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1)),u3_turing_1(A),k19_turing_1) & u4_turing_1(A) = k5_numbers & u5_turing_1(A) = 3 ) ) ) )).
fof(d21_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d21_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) & r2_hidden(C,B) & r2_lattice3(A,B,C) ) ) ) ) )).
fof(d21_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d21_waybel_4,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ( v9_waybel_4(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(k4_tarski(C,D),B) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(k4_tarski(C,E),B) & r2_hidden(k4_tarski(E,D),B) ) ) ) ) ) ) ) ) )).
fof(d21_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) => ( v5_yellow_6(B,A) <=> ! [C] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ! [D] : ( m2_yellow_6(D,A,C) => ( r2_hidden(D,k6_yellow_6(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(k4_tarski(C,E),B) => r2_hidden(k4_tarski(D,E),B) ) ) ) ) ) ) ) ) )).
fof(d21_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v9_zf_lang(A) <=> ? [B] : ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) & ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & A = k11_zf_lang(B,C) ) ) ) ) )).
fof(d21_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(C,k8_zmodul01(A)) => ! [D] : ( m1_subset_1(D,k8_zmodul01(A)) => ! [E] : ( m1_zmodul01(E,A) => ! [F] : ( m1_zmodul01(F,A) => ( ( C = E & D = F ) => k5_binop_1(k8_zmodul01(A),B,C,D) = k6_zmodul01(A,E,F) ) ) ) ) ) ) ) ) )).
fof(d21_zmodul02,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_zmodul02(C,A) => ( m2_zmodul02(C,A,B) <=> r1_tarski(k18_zmodul02(A,C),B) ) ) ) ) )).
fof(d22_abcmiz_1,axiom,( ! [A] : ( m1_subset_1(A,k20_abcmiz_1) => k25_abcmiz_1(A) = k21_abcmiz_1(k24_abcmiz_1(A)) ) )).
fof(d22_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k38_abcmiz_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k38_abcmiz_1(A))) => ( r2_abcmiz_a(A,B,C) <=> ? [D] : ( 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) ) ) ) ) ) )).
fof(d22_aofa_000,axiom,( ! [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) & 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,k10_subset_1(3,k4_finseq_1(u1_unialg_1(A)))))),k2_relset_1(u1_struct_0(A),k2_pua2mss1(A,k10_subset_1(4,k4_finseq_1(u1_unialg_1(A)))))),a_1_1_aofa_000(A)) ) )).
fof(d22_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( l4_aofa_a00(D,A,B,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,C),E)) => ( m4_aofa_a00(F,A,B,C,D,E) <=> r2_hidden(F,k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),E)) ) ) ) ) ) ) ) )).
fof(d22_aofa_i00,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) => ( v1_aofa_i00(D,A,B,C) <=> ( ! [E] : ( m2_aofa_i00(E,A,B,C,D) => ! [F] : ( m3_aofa_i00(F,A,B,C,D) => r2_aofa_i00(A,B,C,D,E,F) ) ) & ! [E] : ( v1_int_1(E) => m3_aofa_i00(k25_aofa_i00(B,E),A,B,C,D) ) & ! [E] : ( m2_aofa_i00(E,A,B,C,D) => m3_aofa_i00(k23_aofa_i00(B,E),A,B,C,D) ) & ! [E] : ( m1_subset_1(E,B) => m2_aofa_i00(k24_aofa_i00(B,E),A,B,C,D) ) & ? [E] : ( 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] : ( 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] : ( 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] : ( m3_aofa_i00(E,A,B,C,D) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d22_armstrng,axiom,( ! [A] : ! [B] : k10_armstrng(A,B) = a_2_5_armstrng(A,B) )).
fof(d22_bcialg_1,axiom,( ! [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) ) => ( v15_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)))) ) ) ) ) )).
fof(d22_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k6_vectsp10(A,B,k13_bilinear(A,B,C,D)))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k6_vectsp10(A,C,k14_bilinear(A,B,C,D)))) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ! [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d22_binop_2,axiom,( ! [A] : ( ( 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 = k22_binop_2 <=> ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => k1_binop_1(A,B,C) = k3_xcmplx_0(B,C) ) ) ) ) )).
fof(d22_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => k10_cat_1(A) = k6_partfun1(u4_struct_0(A)) ) )).
fof(d22_cat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d22_closure2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( v15_closure2(B,A) & l1_closure2(B,A) ) => ! [C] : ( m3_pboole(C,u1_struct_0(A),u3_msualg_1(A,B)) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(d22_coh_sp,axiom,( ! [A] : ! [B] : ( 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))) ) )).
fof(d22_cohsp_1,axiom,( ! [A] : ! [B] : k14_cohsp_1(A,B) = k3_card_3(k2_card_3(k10_finseq_1(A,B))) )).
fof(d22_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k14_comput_1(A) = k3_relat_1(k5_funct_6(k10_finseq_1(k5_comput_1(3,1),k5_comput_1(3,3))),A) ) )).
fof(d22_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v1_xcmplx_0(C) => k19_convex4(A,B,C) = a_3_0_convex4(A,B,C) ) ) ) )).
fof(d22_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k17_decomp_1(A) = a_1_11_decomp_1(A) ) )).
fof(d22_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(d22_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(d22_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(d22_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & l4_struct_0(A) ) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(d22_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0)))) => ( C = k24_fomodel2(A,B) <=> ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(A),k3_rfunct_3(k3_finseq_2(D),k2_xboole_0(D,k6_margrel1))),k15_fomodel2(A,D)) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( B = F => C = k1_relset_1(k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0)),k23_fomodel2(A,D,F,E)) ) ) ) ) ) ) ) ) )).
fof(d22_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v4_fomodel1(B,A) & m1_subset_1(B,k1_fomodel1(A)) ) => ! [C] : ( ( 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] : ( m2_funct_2(D,k30_fomodel2(A),k30_fomodel2(A),k9_funct_2(k30_fomodel2(A),k30_fomodel2(A))) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k9_funct_2(k30_fomodel2(A),k30_fomodel2(A))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_funct_2(k30_fomodel2(A),k30_fomodel2(A))))) ) => ( E = k32_fomodel3(A,B,C,D) <=> ( k9_nat_1(k9_funct_2(k30_fomodel2(A),k30_fomodel2(A)),E,k5_numbers) = D & ! [F] : ( v7_ordinal1(F) => k9_nat_1(k9_funct_2(k30_fomodel2(A),k30_fomodel2(A)),E,k1_nat_1(F,1)) = k31_fomodel3(A,B,C,F,k9_nat_1(k9_funct_2(k30_fomodel2(A),k30_fomodel2(A)),E,F)) ) ) ) ) ) ) ) ) )).
fof(d22_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( v12_fomodel4(C,B) => ( r2_fomodel4(A,B,C) <=> ? [D] : ( r2_hidden(D,A) & r1_tarski(k1_xtuple_0(D),k1_xtuple_0(C)) & k2_xtuple_0(C) = k2_xtuple_0(D) ) ) ) ) )).
fof(d22_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ( v7_fsm_1(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => v6_fsm_1(D,A,B,C) ) ) ) ) ) )).
fof(d22_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k22_ftacell1(A,B,C,D,E) = k48_gfacirc1(A,B,C) )).
fof(d22_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l2_altcat_1(B) ) => ! [C] : ( l2_functor0(C,A,B) => ( v14_functor0(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(G,k1_altcat_1(A,D,E)) & ? [H] : ( m1_subset_1(H,k1_altcat_1(A,E,F)) & ! [I] : ( m1_subset_1(I,k1_altcat_1(B,k3_functor0(A,B,C,E),k3_functor0(A,B,C,D))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d22_gate_1,axiom,( ! [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) & 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 ) ) )).
fof(d22_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : k22_gfacirc1(A,B,C) = k8_facirc_1(A,B,C,k4_gfacirc1) )).
fof(d22_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ( v7_glib_000(A) <=> ( v3_glib_000(A) & v5_glib_000(A) ) ) ) )).
fof(d22_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( ( 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] : ( ( ~ v1_abian(E) & m1_subset_1(E,k4_ordinal1) ) => ( ( 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) ) ) ) ) ) ) ) )).
fof(d22_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_003(A) ) => ! [B] : ! [C] : ( ( 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 ) ) ) )).
fof(d22_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( C = k9_graph_1(A,B) <=> ? [D] : ( v1_finset_1(D) & ! [E] : ( 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) ) ) ) ) ) )).
fof(d22_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( B = k17_grcat_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(D,A) & r1_grcat_1(D,C) ) ) ) ) )).
fof(d22_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(d22_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(d22_idea_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( ( 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] : ( m2_finseq_1(D,k4_ordinal1) => k1_funct_1(C,D) = k12_idea_1(A,k11_idea_1(A,D,B),B) ) ) ) ) ) )).
fof(d22_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(d22_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ~ ( B != C & ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & r1_incsp_1(A,D,B) & r1_incsp_1(A,D,C) ) & ~ ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(d22_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ( v10_intpro_1(A) <=> ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(d22_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ! [B] : k16_lattice3(A,B) = k15_lattice3(A,a_2_1_lattice3(A,B)) ) )).
fof(d22_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v18_lattices(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r3_lattices(A,C,D) & r2_hidden(D,B) ) => r2_hidden(C,B) ) ) ) ) ) ) )).
fof(d22_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k9_funct_2(k6_glib_000(A),k4_ordinal1))) => ( ( r1_xxreal_0(k15_glib_000(A),k5_card_1(k1_relset_1(k6_glib_000(A),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),B)))) ) ) ) ) )).
fof(d22_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(d22_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( v3_ltlaxio1(A) <=> ? [B] : ( m1_subset_1(B,k1_hilbert1) & A = k3_hilbert1(k1_ltlaxio1(k2_ltlaxio1(B)),k2_ltlaxio1(k1_ltlaxio1(B))) ) ) ) )).
fof(d22_margrel1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(A),A))) ) => ( v3_margrel1(B,A) <=> ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d22_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => k25_member_1(A,B) = k15_member_1(k1_tarski(B),A) ) ) )).
fof(d22_metric_1,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_metric_1(A,B,C,D) <=> ( B != C & B != D & C != D & k1_metric_1(A,B,D) = k2_xcmplx_0(k1_metric_1(A,B,C),k1_metric_1(A,C,D)) ) ) ) ) ) ) )).
fof(d22_metric_3,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,k1_numbers) => ! [E] : ( m1_subset_1(E,k1_numbers) => ! [F] : ( m1_subset_1(F,k1_numbers) => ! [G] : ( m1_subset_1(G,k1_numbers) => ! [H] : ( m1_subset_1(H,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)) => ! [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) ) => k2_binop_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k1_numbers,A,H,I) = k3_square_1(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k5_binop_1(k1_numbers,k6_metric_1,B,C)),k1_square_1(k5_binop_1(k1_numbers,k6_metric_1,D,E))),k1_square_1(k5_binop_1(k1_numbers,k6_metric_1,F,G)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d22_mmlquery,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : k24_mmlquery(A,B) = k1_card_1(a_2_0_mmlquery(A,B)) ) )).
fof(d22_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ( v4_modelc_1(A) | v7_modelc_1(A) ) => ! [B] : ( ( v1_modelc_1(B) & m2_finseq_1(B,k4_ordinal1) ) => ( ( v4_modelc_1(A) => ( B = k15_modelc_1(A) <=> ? [C] : ( v1_modelc_1(C) & m2_finseq_1(C,k4_ordinal1) & k8_modelc_1(B,C) = A ) ) ) & ( ~ v4_modelc_1(A) => ( B = k15_modelc_1(A) <=> ? [C] : ( v1_modelc_1(C) & m2_finseq_1(C,k4_ordinal1) & k11_modelc_1(B,C) = A ) ) ) ) ) ) ) )).
fof(d22_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r2_modelc_2(A,B) <=> ? [C] : ( v7_ordinal1(C) & ? [D] : ( 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] : ( v7_ordinal1(E) => ~ ( r1_xxreal_0(1,E) & ~ r1_xxreal_0(C,E) & ! [F] : ( ( v1_modelc_2(F) & m2_finseq_1(F,k4_ordinal1) ) => ! [G] : ( ( v1_modelc_2(G) & m2_finseq_1(G,k4_ordinal1) ) => ~ ( k1_funct_1(D,E) = F & k1_funct_1(D,k1_nat_1(E,1)) = G & r1_modelc_2(F,G) ) ) ) ) ) ) ) ) ) ) )).
fof(d22_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( 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)))) ) ) )).
fof(d22_monoid_0,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(d22_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(d22_oposet_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_qmax_1(A) ) => ( v12_oposet_1(A) <=> ? [B] : ( 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) ) ) ) )).
fof(d22_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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] : ( ( v2_msualg_4(C,A,k8_osafree(A,B)) & m1_osalg_4(C,A,k8_osafree(A,B)) ) => ( C = k20_osafree(A,B) <=> ! [D] : ( r2_hidden(D,u1_struct_0(A)) => k1_funct_1(C,D) = a_3_2_osafree(A,B,D) ) ) ) ) ) )).
fof(d22_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d22_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v2_msualg_4(C,A,B) & v3_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ! [D] : ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d22_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ( v13_pcs_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d22_pencil_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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] : ( r2_hidden(D,C) <=> ? [E] : ( v16_pencil_1(E,A) & m3_pboole(E,A,k12_pralg_1(A,B)) & D = k4_card_3(E) & ? [F] : ( m1_subset_1(F,A) & m1_subset_1(k1_funct_1(E,F),u1_pre_topc(k1_pencil_1(A,B,F))) ) ) ) ) ) ) ) )).
fof(d22_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => k25_polyform(A,B) = k2_struct_0(k24_polyform(A,B)) ) ) )).
fof(d22_pscomp_1,axiom,( ! [A] : ( 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)) ) )).
fof(d22_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v2_qc_lang1(B,A) => ! [C] : ( m1_subset_1(C,k6_qc_lang1(A)) => ( C = k16_qc_lang1(A,B) <=> ? [D] : ( v7_ordinal1(D) & ? [E] : ( v3_card_1(E,D) & m2_finseq_1(E,k2_qc_lang1(A)) & ? [F] : ( m2_subset_1(F,k6_qc_lang1(A),k8_qc_lang1(A,D)) & C = F & B = k10_qc_lang1(A,F,E) ) ) ) ) ) ) ) ) )).
fof(d22_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( C = k15_qc_lang2(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( m1_subset_1(E,k9_qc_lang1(A)) & E = D & r2_qc_lang2(A,E,B) ) ) ) ) ) )).
fof(d22_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_quantal1(A) ) => k4_quantal1(A) = k1_quantal1(A,k3_quantal1(A),k3_quantal1(A)) ) )).
fof(d22_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => k26_quaterni(A) = k22_quaterni(k22_quaterni(k19_quaterni(k13_quaterni(A),k21_quaterni(k4_xcmplx_0(k14_quaterni(A)),k1_xcmplx_0)),k21_quaterni(k4_xcmplx_0(k15_quaterni(A)),k11_quaterni)),k21_quaterni(k4_xcmplx_0(k16_quaterni(A)),k12_quaterni)) ) )).
fof(d22_quofield,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ( r1_quofield(A,B) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(d22_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ( v7_rewrite1(A) <=> ! [B] : ! [C] : ( r6_rewrite1(A,B,C) => r5_rewrite1(A,B,C) ) ) ) )).
fof(d22_ringcat1,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(d22_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( 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))) ) ) )).
fof(d22_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v11_scmyciel(A) ) => ! [B] : ( v7_ordinal1(B) => ( B = k10_scmyciel(A) <=> ( ? [C] : ( v1_finset_1(C) & v10_scmyciel(C,A) & m1_eqrel_1(C,k3_tarski(A)) & k5_card_1(C) = B ) & ! [C] : ( ( v1_finset_1(C) & v10_scmyciel(C,A) & m1_eqrel_1(C,k3_tarski(A)) ) => r1_xxreal_0(B,k5_card_1(C)) ) ) ) ) ) )).
fof(d22_sin_cos,axiom,( ! [A] : ( ( 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 = k22_sin_cos <=> ! [B] : ( v1_xreal_0(B) => k1_funct_1(A,B) = k4_series_1(k4_sin_cos(B)) ) ) ) )).
fof(d22_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( v1_relat_1(C) & v1_funct_1(C) & ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & r3_stacks_1(A,B,C,D) ) ) ) ) ) )).
fof(d22_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k16_substut1(A),k3_qc_lang1(A))) => ( v3_substut1(B,A) <=> ? [C] : ( 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)) ) ) ) ) )).
fof(d22_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( 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))) ) ) )).
fof(d22_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d22_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) & r2_hidden(C,B) & r1_lattice3(A,B,C) ) ) ) ) )).
fof(d22_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k7_waybel_1(A,B) = k6_waybel_1(A,B,k3_yellow_0(A)) ) ) )).
fof(d22_waybel_4,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(D,B) & r2_hidden(E,B) & ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d22_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) => ( v6_yellow_6(B,A) <=> ! [C] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(C,k6_yellow_6(A)) & ~ r2_hidden(k4_tarski(C,D),B) & ! [E] : ( m2_yellow_6(E,A,C) => ~ ( r2_hidden(E,k6_yellow_6(A)) & ! [F] : ( m2_yellow_6(F,A,E) => ~ r2_hidden(k4_tarski(F,D),B) ) ) ) ) ) ) ) ) ) )).
fof(d22_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v10_zf_lang(A) <=> ? [B] : ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) & ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & A = k12_zf_lang(B,C) ) ) ) ) )).
fof(d22_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(C,k8_zmodul01(A)) => ! [D] : ( m1_subset_1(D,k8_zmodul01(A)) => ! [E] : ( m1_zmodul01(E,A) => ! [F] : ( m1_zmodul01(F,A) => ( ( C = E & D = F ) => k5_binop_1(k8_zmodul01(A),B,C,D) = k7_zmodul01(A,E,F) ) ) ) ) ) ) ) ) )).
fof(d22_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k4_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_numbers))) ) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ( D = k20_zmodul02(A,B,C) <=> ( k3_finseq_1(D) = k3_finseq_1(B) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k4_finseq_1(D)) => k1_funct_1(D,E) = k1_zmodul01(A,k7_partfun1(u1_struct_0(A),B,E),k3_funct_2(u1_struct_0(A),k4_numbers,C,k7_partfun1(u1_struct_0(A),B,E))) ) ) ) ) ) ) ) ) )).
fof(d23_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v4_abcmiz_0(A) & l3_abcmiz_0(A) ) => ! [B] : ( 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) ) ) )).
fof(d23_abcmiz_1,axiom,( ! [A] : ( m1_subset_1(A,k20_abcmiz_1) => k26_abcmiz_1(A) = k22_abcmiz_1(k24_abcmiz_1(A)) ) )).
fof(d23_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m3_abcmiz_1(B,A) => ! [C] : ( m3_abcmiz_1(C,A) => ( r3_abcmiz_a(A,B,C) <=> ? [D] : ( 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) ) ) ) ) ) )).
fof(d23_algstr_0,axiom,( ! [A] : ( l3_algstr_0(A) => ( v19_algstr_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v16_algstr_0(B,A) ) ) ) )).
fof(d23_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( l4_aofa_a00(D,A,B,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k16_aofa_a00(A,B,C,D,E) = k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),E) ) ) ) ) ) )).
fof(d23_armstrng,axiom,( ! [A] : ! [B] : ( 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) ) )).
fof(d23_bcialg_1,axiom,( ! [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) ) => ( v16_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d23_bilinear,axiom,( ! [A] : ( l2_struct_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(d23_binop_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1))) ) => ( A = k23_binop_2 <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k1_binop_1(A,B,C) = k2_xcmplx_0(B,C) ) ) ) ) )).
fof(d23_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d23_cat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d23_closure2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( v15_closure2(B,A) & l1_closure2(B,A) ) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(d23_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k20_coh_sp(A)) => ! [C] : ( 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))) ) ) ) )).
fof(d23_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => k15_cohsp_1(A,B) = a_2_0_cohsp_1(A,B) ) ) )).
fof(d23_comput_1,axiom,( k15_comput_1 = k7_comput_1(k5_comput_1(1,1),k4_comput_1(3,3),2) )).
fof(d23_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_convex4(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xcmplx_0(E) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => ( ! [F] : ( v1_xreal_0(F) => ~ ( E = F & ~ r1_xxreal_0(F,k5_numbers) & ~ 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) ) ) ) ) ) ) ) ) )).
fof(d23_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k18_decomp_1(A) = a_1_12_decomp_1(A) ) )).
fof(d23_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u4_struct_0(k6_cat_2(A,A)),k2_ens_1(k16_ens_1(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(k6_cat_2(A,A)),k2_ens_1(k16_ens_1(A))))) ) => ( B = k22_ens_1(A) <=> ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => k3_funct_2(u4_struct_0(k6_cat_2(A,A)),k2_ens_1(k16_ens_1(A)),B,k8_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)) ) ) ) ) ) )).
fof(d23_fomodel0,axiom,( ! [A] : ( v4_funct_1(A) => k21_fomodel0(A) = k3_tarski(a_1_3_fomodel0(A)) ) )).
fof(d23_fomodel1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(d23_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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,k24_fomodel2(A,B)) ) ) ) ) )).
fof(d23_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( v12_fomodel4(C,B) => ( r3_fomodel4(A,B,C) <=> ( v1_xboole_0(k1_xtuple_0(C)) & ? [D] : ( 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) = k42_fomodel1(B,k42_fomodel1(B,k43_fomodel1(B,k31_fomodel2(B)),D),D) ) ) ) ) ) )).
fof(d23_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => k12_fsm_1(A,B,C) = a_3_0_fsm_1(A,B,C) ) ) ) )).
fof(d23_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k23_ftacell1(A,B,C,D,E) = k45_gfacirc1(k48_gfacirc1(A,B,C),E,D) )).
fof(d23_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l2_altcat_1(B) ) => ! [C] : ( ( v8_functor0(C,A,B) & v10_functor0(C,A,B) & l2_functor0(C,A,B) ) => ( v13_functor0(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(G,k1_altcat_1(A,D,E)) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d23_gate_1,axiom,( ! [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) ) => 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 ) ) )).
fof(d23_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : k23_gfacirc1(A,B,C) = k10_facirc_1(A,B,C,k4_gfacirc1) )).
fof(d23_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ( m3_glib_001(D,A) => ( r1_glib_001(A,B,C,D) <=> ( k3_glib_001(A,D) = B & k4_glib_001(A,D) = C ) ) ) ) )).
fof(d23_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(d23_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k10_graph_1(A,B) = k1_nat_1(k8_graph_1(A,B),k9_graph_1(A,B)) ) ) )).
fof(d23_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_grcat_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_grcat_1(B) ) => ( B = k18_grcat_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( v8_algstr_0(D) & m2_grcat_1(D,A) & ? [E] : ( v8_algstr_0(E) & m2_grcat_1(E,A) & v1_grcat_1(C) & m1_grcat_1(C,D,E) ) ) ) ) ) ) )).
fof(d23_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => k15_group_9(A,B,C) = u1_struct_0(C) ) ) )).
fof(d23_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(d23_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(d23_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_lattices(B) & l3_lattices(B) ) => ( B = k21_interva1(A) <=> ( u1_struct_0(B) = k18_interva1(A) & ! [C] : ( m1_subset_1(C,k18_interva1(A)) => ! [D] : ( m1_subset_1(D,k18_interva1(A)) => ! [E] : ( m2_interva1(E,A) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d23_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1)) => ( B = k13_intpro_1(A) <=> ! [C] : ( m1_subset_1(C,k1_intpro_1) => ( r2_hidden(C,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_intpro_1)) => ( ( v10_intpro_1(D) & r1_tarski(A,D) ) => r2_hidden(C,D) ) ) ) ) ) ) ) )).
fof(d23_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v19_lattices(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r3_lattices(A,C,D) & r2_hidden(C,B) ) => r2_hidden(D,B) ) ) ) ) ) ) )).
fof(d23_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k18_lmod_7(A,B,C,D) = k14_lmod_7(A,B,C,D) ) ) ) ) )).
fof(d23_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( v4_ltlaxio1(A) <=> ? [B] : ( m1_subset_1(B,k1_hilbert1) & A = k3_hilbert1(k2_ltlaxio1(k1_ltlaxio1(B)),k1_ltlaxio1(k2_ltlaxio1(B))) ) ) ) )).
fof(d23_margrel1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k4_partfun1(k3_finseq_2(A),A)) => ( v4_margrel1(B,A) <=> ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(d23_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => k26_member_1(A,B) = k14_member_1(A,k1_tarski(B)) ) ) )).
fof(d23_metric_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k13_metric_1(A,B,C) = a_3_6_metric_1(A,B,C) ) ) ) )).
fof(d23_mmlquery,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ( B = k25_mmlquery(A) <=> ( ! [C] : r1_xxreal_0(k24_mmlquery(A,C),B) & ! [C] : ( v7_ordinal1(C) => ( ! [D] : r1_xxreal_0(k24_mmlquery(A,D),C) => r1_xxreal_0(B,C) ) ) ) ) ) ) )).
fof(d23_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ( v4_modelc_1(A) | v7_modelc_1(A) ) => ! [B] : ( ( v1_modelc_1(B) & m2_finseq_1(B,k4_ordinal1) ) => ( ( v4_modelc_1(A) => ( B = k16_modelc_1(A) <=> ? [C] : ( v1_modelc_1(C) & m2_finseq_1(C,k4_ordinal1) & k8_modelc_1(C,B) = A ) ) ) & ( ~ v4_modelc_1(A) => ( B = k16_modelc_1(A) <=> ? [C] : ( v1_modelc_1(C) & m2_finseq_1(C,k4_ordinal1) & k11_modelc_1(C,B) = A ) ) ) ) ) ) ) )).
fof(d23_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r3_modelc_2(A,B) <=> ( r2_modelc_2(A,B) & A != B ) ) ) ) )).
fof(d23_monoid_0,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( l3_algstr_0(B) => ( m2_monoid_0(B,A) <=> r1_tarski(u2_algstr_0(B),u2_algstr_0(A)) ) ) ) )).
fof(d23_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( r2_hidden(E,D) <=> ? [F] : ( r2_hidden(F,k1_funct_1(B,C)) & E = k1_trees_4(k4_tarski(F,C)) ) ) ) ) ) ) ) )).
fof(d23_osalg_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d23_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d23_pencil_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(d23_pscomp_1,axiom,( ! [A] : ( 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)))) ) )).
fof(d23_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v2_qc_lang1(B,A) => ! [C] : ( m2_finseq_1(C,k2_qc_lang1(A)) => ( C = k17_qc_lang1(A,B) <=> ? [D] : ( v7_ordinal1(D) & ? [E] : ( m2_subset_1(E,k6_qc_lang1(A),k8_qc_lang1(A,D)) & ? [F] : ( v3_card_1(F,D) & m2_finseq_1(F,k2_qc_lang1(A)) & C = F & B = k10_qc_lang1(A,E,F) ) ) ) ) ) ) ) ) )).
fof(d23_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_quantal1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_quantal1(A,B) = k1_quantal1(A,B,k3_quantal1(A)) ) ) )).
fof(d23_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => k28_quaterni(A) = k3_square_1(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k13_quaterni(A)),k1_square_1(k14_quaterni(A))),k1_square_1(k15_quaterni(A))),k1_square_1(k16_quaterni(A)))) ) )).
fof(d23_quofield,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ( r2_quofield(A,B) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(d23_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ( v8_rewrite1(A) <=> ! [B] : ! [C] : ( r2_rewrite1(A,B,C) => r5_rewrite1(A,B,C) ) ) ) )).
fof(d23_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_robbins1(A) ) => ( v10_robbins1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(d23_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => k23_sin_cos(A) = k1_funct_1(k22_sin_cos,A) ) )).
fof(d23_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k16_substut1(A),k3_qc_lang1(A))) => ( v3_substut1(B,A) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(d23_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( l1_turing_1(B) => ! [C] : ( m1_subset_1(C,k3_zfmisc_1(u2_turing_1(A),u1_turing_1(A),k1_enumset1(k4_xcmplx_0(1),k5_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),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),k1_domain_1(u2_turing_1(A),u2_turing_1(B),k1_mcart_1(u2_turing_1(A),u1_turing_1(A),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),C),u4_turing_1(B)),k2_mcart_1(u2_turing_1(A),u1_turing_1(A),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),C),k3_mcart_1(u2_turing_1(A),u1_turing_1(A),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),C)) ) ) ) )).
fof(d23_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(d23_waybel_0,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(d23_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d23_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r2_waybel_4(A,B,C) <=> ( r2_hidden(B,A) & ! [D] : ~ ( r2_hidden(D,A) & D != B & r2_hidden(k4_tarski(B,D),C) ) ) ) ) )).
fof(d23_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v11_zf_lang(A) <=> ? [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) & ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & A = k13_zf_lang(B,C) ) ) ) ) )).
fof(d23_zmodul01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k4_numbers) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r1_xxreal_0(k5_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(k5_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)) ) ) ) ) ) ) ) )).
fof(d23_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k21_zmodul02(A,B) <=> ? [D] : ( m2_finseq_1(D,u1_struct_0(A)) & v2_funct_1(D) & k2_relset_1(u1_struct_0(A),D) = k18_zmodul02(A,B) & C = k4_rlvect_1(A,k20_zmodul02(A,D,B)) ) ) ) ) ) )).
fof(d24_abcmiz_1,axiom,( ! [A] : ( ( 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] : ( 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))) ) ) ) ) ) ) )).
fof(d24_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [C] : ( m1_subset_1(C,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(d24_algstr_0,axiom,( ! [A] : ( l3_algstr_0(A) => ( v20_algstr_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v17_algstr_0(B,A) ) ) ) )).
fof(d24_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( l4_aofa_a00(D,A,B,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m4_aofa_a00(F,A,B,C,D,E) => k17_aofa_a00(A,B,C,D,E,F) = k1_funct_1(k2_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),k13_msafree(A,B),u5_aofa_a00(A,B,C,D),E),F) ) ) ) ) ) ) )).
fof(d24_aofa_i00,axiom,( k26_aofa_i00 = k2_zfmisc_1(k9_funct_2(k9_funct_2(k4_ordinal1,k4_numbers),k4_ordinal1),k9_funct_2(k9_funct_2(k4_ordinal1,k4_numbers),k4_numbers)) )).
fof(d24_armstrng,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d24_bcialg_1,axiom,( ! [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) ) => ( v17_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(d24_bilinear,axiom,( ! [A] : ( l2_struct_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(d24_binop_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1))) ) => ( A = k24_binop_2 <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k1_binop_1(A,B,C) = k3_xcmplx_0(B,C) ) ) ) ) )).
fof(d24_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ( v13_cat_1(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( 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] : ( m1_cat_1(G,A,D,E) & F = k3_funct_2(u4_struct_0(A),u4_struct_0(B),C,G) ) ) ) ) ) ) ) ) ) ) )).
fof(d24_cat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d24_coh_sp,axiom,( ! [A] : ! [B] : ( ( 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] : ( 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) ) ) ) )).
fof(d24_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(d24_comput_1,axiom,( k16_comput_1 = k7_comput_1(k3_comput_1(1,k5_numbers),k14_comput_1(k15_comput_1),2) )).
fof(d24_convex4,axiom,( ! [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) ) => ! [B] : ( m1_convex4(B,A) => ( v3_convex4(B,A) <=> ? [C] : ( 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] : ( m2_finseq_1(D,k1_numbers) & k3_finseq_1(D) = k3_finseq_1(C) & k18_rvsum_1(D) = 1 & ! [E] : ( 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(k5_numbers,k1_funct_1(D,E)) ) ) ) ) ) ) ) ) )).
fof(d24_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k19_decomp_1(A) = a_1_13_decomp_1(A) ) )).
fof(d24_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(d24_fomodel0,axiom,( ! [A] : ( v4_funct_1(A) => k21_fomodel0(A) = k3_tarski(a_1_4_fomodel0(A)) ) )).
fof(d24_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v10_fomodel1(B,A) & m1_subset_1(B,k1_fomodel1(A)) ) => k19_fomodel1(A,B) = k1_funct_1(u1_fomodel1(A),B) ) ) )).
fof(d24_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( 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] : ( v7_ordinal1(C) & v3_fomodel2(B,A,C) ) ) ) ) )).
fof(d24_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v4_fomodel1(B,A) & m1_subset_1(B,k1_fomodel1(A)) ) => ! [C] : ( ( 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(k30_fomodel2(A)),k33_fomodel3(A,B,C)) ) ) ) )).
fof(d24_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( v12_fomodel4(C,B) => ( r4_fomodel4(A,B,C) <=> ? [D] : ( 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] : ( 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] : ( 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))) & C = k1_domain_1(k1_zfmisc_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)),k7_domain_1(k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0)),k42_fomodel1(B,k42_fomodel1(B,k43_fomodel1(B,k31_fomodel2(B)),D),E),k42_fomodel1(B,k42_fomodel1(B,k43_fomodel1(B,k31_fomodel2(B)),E),F)),k42_fomodel1(B,k42_fomodel1(B,k43_fomodel1(B,k31_fomodel2(B)),D),F)) ) ) ) ) ) ) )).
fof(d24_fsm_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( ( ~ v2_struct_0(D) & l2_fsm_1(D,A,B) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(d24_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k24_ftacell1(A,B,C,D,E) = k48_gfacirc1(k48_gfacirc1(A,B,C),E,D) )).
fof(d24_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l2_altcat_1(B) ) => ! [C] : ( ( v8_functor0(C,A,B) & v11_functor0(C,A,B) & l2_functor0(C,A,B) ) => ( v14_functor0(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(G,k1_altcat_1(A,D,E)) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d24_gate_1,axiom,( ! [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) ) => 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 ) ) )).
fof(d24_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : k24_gfacirc1(A,B,C) = k9_facirc_1(A,B,C,k4_gfacirc1) )).
fof(d24_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => k14_glib_000(A) = k1_card_1(k6_glib_000(A)) ) )).
fof(d24_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v1_glib_001(B,A) <=> k3_glib_001(A,B) = k4_glib_001(A,B) ) ) ) )).
fof(d24_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ( r4_graph_1(A,B) <=> m3_graph_1(A,B) ) ) ) )).
fof(d24_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_grcat_1(A) ) => ! [B] : ( m2_grcat_1(B,A) => k21_grcat_1(A,B) = k11_grcat_1(B) ) ) )).
fof(d24_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( 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)) ) ) ) )).
fof(d24_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k17_ideal_1(A,B) = a_2_1_ideal_1(A,B) ) ) )).
fof(d24_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => k22_interva1(A) = k4_tarski(k1_xboole_0,k1_xboole_0) ) )).
fof(d24_intpro_1,axiom,( k14_intpro_1 = k13_intpro_1(k1_subset_1(k1_intpro_1)) )).
fof(d24_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v20_lattices(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k4_lattices(A,C,D),B) ) ) ) ) ) ) )).
fof(d24_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m3_lexbfs(B,A) => ! [C] : ( m1_lexbfs(C,A) => ( C = k25_lexbfs(A,B) <=> ! [D] : ( v7_ordinal1(D) => r2_relset_1(k6_glib_000(A),k4_ordinal1,k5_lexbfs(A,C,D),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),k23_lexbfs(A,B,D))) ) ) ) ) ) )).
fof(d24_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( v5_ltlaxio1(A) <=> ? [B] : ( m1_subset_1(B,k1_hilbert1) & ? [C] : ( m1_subset_1(C,k1_hilbert1) & A = k3_hilbert1(k2_ltlaxio1(k3_hilbert1(B,C)),k3_hilbert1(k2_ltlaxio1(B),k2_ltlaxio1(C))) ) ) ) ) )).
fof(d24_margrel1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k4_partfun1(k3_finseq_2(A),A)) => ( v5_margrel1(B,A) <=> ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(d24_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => k27_member_1(A,B) = k15_member_1(A,k1_tarski(B)) ) ) )).
fof(d24_metric_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k14_metric_1(A,B,C) = k2_xboole_0(a_3_6_metric_1(A,B,C),k2_tarski(B,C)) ) ) ) )).
fof(d24_mmlquery,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k9_setfam_1(A)) => ! [C] : ( v7_ordinal1(C) => ( A != k1_xboole_0 => k26_mmlquery(A,B,C) = a_3_3_mmlquery(A,B,C) ) ) ) )).
fof(d24_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( B = k13_modelc_2(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( v1_modelc_2(D) & m2_finseq_1(D,k4_ordinal1) & D = C & r2_modelc_2(D,A) ) ) ) ) )).
fof(d24_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k13_modelc_2(A))) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( D = k16_modelc_3(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(k1_funct_1(C,E),B) => k1_funct_1(D,E) = k3_finseq_1(k14_modelc_2(k1_funct_1(C,E))) ) & ( ~ r2_hidden(k1_funct_1(C,E),B) => k1_funct_1(D,E) = k5_numbers ) ) ) ) ) ) ) ) )).
fof(d24_monoid_0,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( l4_algstr_0(B) => ( m3_monoid_0(B,A) <=> ( r1_tarski(u2_algstr_0(B),u2_algstr_0(A)) & ! [C] : ( l4_algstr_0(C) => ( A = C => k5_struct_0(B) = k5_struct_0(C) ) ) ) ) ) ) )).
fof(d24_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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] : ( m3_pboole(C,u1_struct_0(A),u3_msualg_1(A,k8_osafree(A,B))) => ( C = k22_osafree(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_funct_1(C,D) = k21_osafree(A,B,D) ) ) ) ) ) )).
fof(d24_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( 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) ) ) )).
fof(d24_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r1_msualg_3(A,B,C,D) & v1_osalg_3(D,A) ) => ! [F] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d24_pscomp_1,axiom,( ! [A] : ( 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)))) ) )).
fof(d24_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v3_qc_lang1(B,A) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( C = k18_qc_lang1(A,B) <=> B = k13_qc_lang1(A,C) ) ) ) ) ) )).
fof(d24_quofield,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(d24_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ( v9_rewrite1(A) <=> ! [B] : ! [C] : ! [D] : ( ( r2_hidden(k4_tarski(B,C),A) & r2_hidden(k4_tarski(B,D),A) ) => r5_rewrite1(A,C,D) ) ) ) )).
fof(d24_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v12_scmyciel(A) ) => ! [B] : ( v7_ordinal1(B) => ( B = k11_scmyciel(A) <=> ( ? [C] : ( v1_finset_1(C) & v9_scmyciel(C,A) & m1_subset_1(C,k1_zfmisc_1(k3_tarski(A))) & k5_card_1(C) = B ) & ! [C] : ( ( 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) ) ) ) ) ) )).
fof(d24_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( B = k24_sin_cos(A) <=> ! [C] : ( v7_ordinal1(C) => k9_nat_1(k2_numbers,B,C) = k7_xcmplx_0(k1_newton(A,k1_nat_1(C,1)),k2_newton(k1_nat_1(C,2))) ) ) ) ) )).
fof(d24_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k16_substut1(A),k3_qc_lang1(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(d24_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( l1_turing_1(B) => ! [C] : ( m1_subset_1(C,k3_zfmisc_1(u2_turing_1(B),u1_turing_1(B),k1_enumset1(k4_xcmplx_0(1),k5_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),k1_enumset1(k4_xcmplx_0(1),k5_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),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),C)),k2_mcart_1(u2_turing_1(B),u1_turing_1(B),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),C),k3_mcart_1(u2_turing_1(B),u1_turing_1(B),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),C)) ) ) ) )).
fof(d24_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => ! [D] : ( m1_subset_1(D,k6_margrel1) => k1_funct_1(A,k11_finseq_1(B,C,D)) = k1_binarith(k1_binarith(B,C),D) ) ) ) ) ) )).
fof(d24_waybel_0,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(d24_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v10_waybel_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r6_waybel_1(A,B,C) ) ) ) ) )).
fof(d24_waybel_4,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_waybel_4(A,B,C) <=> r2_waybel_4(B,C,u1_orders_2(A)) ) ) ) )).
fof(d24_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(d24_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => k14_zf_lang(A,B,C) = k8_zf_lang(A,k8_zf_lang(B,C)) ) ) ) )).
fof(d24_zmodul02,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_zmodul02(B,A) => ! [C] : ( m1_zmodul02(C,A) => ( r1_zmodul02(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k4_numbers,B,D) = k3_funct_2(u1_struct_0(A),k4_numbers,C,D) ) ) ) ) ) )).
fof(d25_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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 ) ) ) ) )).
fof(d25_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [C] : ( 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] : ( 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) ) ) ) ) ) )).
fof(d25_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ( v11_aofa_000(A) <=> m1_freealg(k18_aofa_000(A),A) ) ) )).
fof(d25_aofa_i00,axiom,( ! [A] : ( m1_aofa_000(A,k7_freealg(k19_aofa_000,k26_aofa_i00),k9_funct_2(k4_ordinal1,k4_numbers),k1_aofa_i00(k9_funct_2(k4_ordinal1,k4_numbers),k5_numbers,k5_numbers)) => ( m4_aofa_i00(A) <=> ! [B] : ( m2_funct_2(B,k4_ordinal1,k4_numbers,k9_funct_2(k4_ordinal1,k4_numbers)) => ! [C] : ( m2_funct_2(C,k9_funct_2(k4_ordinal1,k4_numbers),k4_ordinal1,k9_funct_2(k9_funct_2(k4_ordinal1,k4_numbers),k4_ordinal1)) => ! [D] : ( m2_funct_2(D,k9_funct_2(k4_ordinal1,k4_numbers),k4_numbers,k9_funct_2(k9_funct_2(k4_ordinal1,k4_numbers),k4_numbers)) => k1_binop_1(A,B,k1_trees_4(k4_tarski(C,D))) = k14_funct_7(k4_ordinal1,k4_numbers,B,k21_aofa_i00(k9_funct_2(k4_ordinal1,k4_numbers),k4_ordinal1,C,B),k21_aofa_i00(k9_funct_2(k4_ordinal1,k4_numbers),k4_numbers,D,B)) ) ) ) ) ) )).
fof(d25_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) ) ) )).
fof(d25_bilinear,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_vectsp_1(B,A) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => k1_binop_1(C,D,E) = k1_binop_1(C,E,D) ) ) ) ) ) ) )).
fof(d25_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ( v14_cat_1(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k2_cat_1(A,D,E) != k1_xboole_0 => ! [F] : ( m1_cat_1(F,A,D,E) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(d25_cat_4,axiom,( ! [A] : ! [B] : 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)) )).
fof(d25_coh_sp,axiom,( ! [A] : ! [B] : ( ( 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] : ( 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) ) ) ) )).
fof(d25_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(d25_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( C = k20_convex4(A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(D,C) <=> ( v2_convex4(D,A) & r1_tarski(B,D) ) ) ) ) ) ) ) )).
fof(d25_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k20_decomp_1(A) = a_1_14_decomp_1(A) ) )).
fof(d25_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(d25_fomodel0,axiom,( ! [A] : k22_fomodel0(A) = A )).
fof(d25_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k20_fomodel1(A) = k11_monoid_0(k15_fomodel1(A)) ) )).
fof(d25_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k9_funct_2(k37_fomodel1(A),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_fomodel2(A,B)) => ! [D] : ( ( 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] : ( m1_subset_1(E,k6_margrel1) => ( E = k25_fomodel2(A,B,C,D) <=> ! [F] : ( v7_ordinal1(F) => ( v3_fomodel2(D,A,F) => E = k1_funct_1(k23_fomodel2(A,B,F,C),D) ) ) ) ) ) ) ) ) )).
fof(d25_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v4_fomodel1(B,A) & m1_subset_1(B,k1_fomodel1(A)) ) => ! [C] : ( ( 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] : ( ( 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(k9_nat_1(k9_funct_2(k30_fomodel2(A),k30_fomodel2(A)),k32_fomodel3(A,B,C,k36_fomodel3(A,B,C)),k29_fomodel2(A,D)),D) ) ) ) ) )).
fof(d25_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( v12_fomodel4(C,B) => ( r5_fomodel4(A,B,C) <=> ? [D] : ( 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] : ( 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)),k42_fomodel1(B,k42_fomodel1(B,k43_fomodel1(B,k31_fomodel2(B)),D),E)) & k2_xtuple_0(C) = k42_fomodel1(B,k42_fomodel1(B,k43_fomodel1(B,k31_fomodel2(B)),E),D) ) ) ) ) ) )).
fof(d25_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( 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) ) ) ) ) ) ) ) )).
fof(d25_gate_1,axiom,( ! [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) & 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 ) ) )).
fof(d25_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : k25_gfacirc1(A,B,C) = k2_circcomb(k22_gfacirc1(A,B,C),k19_gfacirc1(A,B,C)) )).
fof(d25_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => k16_glib_000(A) = k1_card_1(k7_glib_000(A)) ) )).
fof(d25_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v2_glib_001(B,A) <=> ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( ~ r1_xxreal_0(k3_finseq_1(B),C) => k1_funct_1(k10_glib_000(A),k1_funct_1(B,k1_nat_1(C,1))) = k1_funct_1(B,C) ) ) ) ) ) )).
fof(d25_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( B = k11_graph_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( v1_graph_1(C) & m3_graph_1(C,A) ) ) ) ) )).
fof(d25_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_grcat_1(A) ) => ! [B] : ( ( 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] : ( m3_grcat_1(C,k18_grcat_1(A)) => k3_funct_2(k18_grcat_1(A),A,B,C) = k19_grcat_1(A,C) ) ) ) ) )).
fof(d25_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( m1_group_9(D,A,B) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(d25_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ~ 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) ) ) ) ) )).
fof(d25_interva1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d25_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v21_lattices(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k3_lattices(A,C,D),B) ) ) ) ) ) ) )).
fof(d25_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m3_lexbfs(B,A) => ( B = k26_lexbfs(A) <=> ( k23_lexbfs(A,B,k5_numbers) = k18_lexbfs(A) & ! [C] : ( v7_ordinal1(C) => k23_lexbfs(A,B,k1_nat_1(C,1)) = k22_lexbfs(A,k23_lexbfs(A,B,C)) ) ) ) ) ) )).
fof(d25_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( v6_ltlaxio1(A) <=> ? [B] : ( m1_subset_1(B,k1_hilbert1) & A = k3_hilbert1(k6_ltlaxio1(B),k4_ltlaxio1(B,k2_ltlaxio1(k6_ltlaxio1(B)))) ) ) ) )).
fof(d25_margrel1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_margrel1(A) ) => ! [B] : ( v7_ordinal1(B) => ( ( ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & r2_hidden(C,k9_xtuple_0(A)) ) => ( B = k18_margrel1(A) <=> ! [C] : ( ( 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] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ~ r2_hidden(C,k9_xtuple_0(A)) ) => ( B = k18_margrel1(A) <=> B = k5_numbers ) ) ) ) ) )).
fof(d25_mmlquery,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k9_setfam_1(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( A != k1_xboole_0 => k27_mmlquery(A,B,C,D) = a_4_14_mmlquery(A,B,C,D) ) ) ) ) )).
fof(d25_modelc_1,axiom,( k18_modelc_1 = a_0_0_modelc_1 )).
fof(d25_modelc_2,axiom,( ! [A] : ( ( r2_hidden(A,k9_modelc_2) => k14_modelc_2(A) = A ) & ( ~ r2_hidden(A,k9_modelc_2) => k14_modelc_2(A) = k2_modelc_2(k5_numbers) ) ) )).
fof(d25_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k13_modelc_2(A))) => ! [C] : ( ( 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)) ) ) ) )).
fof(d25_monoid_0,axiom,( ! [A] : ( l4_algstr_0(A) => ! [B] : ( 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) ) ) ) ) )).
fof(d25_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( r2_hidden(E,D) <=> ? [F] : ( 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))) ) ) ) ) ) ) ) )).
fof(d25_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [E] : ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(d25_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ( v5_polyform(A) <=> ! [B] : ( v1_int_1(B) => k23_polyform(A,B) = k25_polyform(A,B) ) ) ) )).
fof(d25_pscomp_1,axiom,( ! [A] : ( 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)) ) )).
fof(d25_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v4_qc_lang1(B,A) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( C = k19_qc_lang1(A,B) <=> ? [D] : ( m1_subset_1(D,k9_qc_lang1(A)) & B = k14_qc_lang1(A,C,D) ) ) ) ) ) ) )).
fof(d25_quofield,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( 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))) ) ) ) ) )).
fof(d25_scmyciel,axiom,( ! [A] : ( 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)) ) )).
fof(d25_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => ( v4_substut1(B,A) <=> ? [C] : ( v7_ordinal1(C) & ? [D] : ( m2_subset_1(D,k6_qc_lang1(A),k8_qc_lang1(A,C)) & ? [E] : ( v3_card_1(E,C) & m2_finseq_1(E,k2_qc_lang1(A)) & ? [F] : ( m1_subset_1(F,k1_substut1(A)) & B = k17_substut1(A,D,E,F) ) ) ) ) ) ) ) )).
fof(d25_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( l1_turing_1(B) => ! [C] : ( 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)) ) ) ) )).
fof(d25_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d25_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r4_waybel_4(A,B,C) <=> ( r2_hidden(B,A) & ! [D] : ~ ( r2_hidden(D,A) & D != B & r2_hidden(k4_tarski(D,B),C) ) ) ) ) )).
fof(d25_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => k15_zf_lang(A,B,C) = k13_zf_lang(A,k13_zf_lang(B,C)) ) ) ) )).
fof(d25_zmodul02,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_zmodul02(B,A) => ! [C] : ( m1_zmodul02(C,A) => ! [D] : ( m1_zmodul02(D,A) => ( D = k22_zmodul02(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k4_numbers,D,E) = k2_xcmplx_0(k3_funct_2(u1_struct_0(A),k4_numbers,B,E),k3_funct_2(u1_struct_0(A),k4_numbers,C,E)) ) ) ) ) ) ) )).
fof(d26_abcmiz_1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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] : ( 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 ) ) ) ) )).
fof(d26_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [C] : ( 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] : ( 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)) ) ) ) ) ) )).
fof(d26_algstr_0,axiom,( k8_algstr_0 = g4_algstr_0(k1_tarski(k5_ordinal1),k9_funct_5,k5_funct_5) )).
fof(d26_aofa_000,axiom,( k19_aofa_000 = k8_finseq_1(k4_ordinal1,k2_finseq_4(k4_ordinal1,k5_numbers,2),k2_finseq_4(k4_ordinal1,3,2)) )).
fof(d26_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & l3_msualg_1(D,A) ) => ! [E] : ( l4_aofa_a00(E,A,B,C) => ( v11_aofa_a00(E,A,B,C,D) <=> ( m3_pboole(k13_msafree(A,B),u1_struct_0(A),u4_aofa_a00(A,B,C,E)) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( k9_xtuple_0(k1_msafree4(u1_struct_0(A),u6_aofa_a00(A,B,C,E),F)) = k16_aofa_a00(A,B,C,E,F) & ! [G] : ( m4_aofa_a00(G,A,B,C,E,F) => ( m2_pboole(k1_funct_1(k1_msafree4(u1_struct_0(A),u6_aofa_a00(A,B,C,E),F),G),u1_struct_0(A),k11_aofa_a00(A,C,F,G),u3_msualg_1(A,C)) & ( r2_hidden(G,k1_msafree4(u1_struct_0(A),k13_msafree(A,B),F)) => ( r8_pboole(u1_struct_0(A),k18_aofa_a00(A,B,C,E,F,G),k2_msualg_3(u1_struct_0(A),k2_aofa_a00(u1_struct_0(A),F,G))) & k17_aofa_a00(A,B,C,E,F,G) = G ) ) & ! [H] : ( m2_subset_1(H,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => ( k1_funct_1(k1_msafree4(u1_struct_0(A),H,F),k17_aofa_a00(A,B,C,E,F,G)) = k1_funct_1(k1_msafree4(u1_struct_0(A),H,F),G) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_msafree4(J,u1_struct_0(A),k13_msafree(A,B),k1_msafree4(u1_struct_0(A),k13_msafree(A,B),I)) => ! [K] : ( m1_msafree4(K,u1_struct_0(A),u3_msualg_1(A,C),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,C),I)) => ( ( r2_hidden(J,k1_msafree4(u1_struct_0(A),k11_aofa_a00(A,C,F,G),I)) & K = k1_funct_1(k2_msafree4(u1_struct_0(A),k11_aofa_a00(A,C,F,G),u3_msualg_1(A,C),k18_aofa_a00(A,B,C,E,F,G),I),J) ) => k1_funct_1(k1_msafree4(u1_struct_0(A),H,I),J) = k15_aofa_a00(A,B,C,D,I,K,H) ) ) ) ) ) ) & ( ~ r2_hidden(G,k1_msafree4(u1_struct_0(A),k13_msafree(A,B),F)) => ! [H] : ( m3_pboole(H,u1_struct_0(A),u4_aofa_a00(A,B,C,E)) => ( r8_pboole(u1_struct_0(A),H,k13_msafree(A,B)) => ! [I] : ( m1_subset_1(I,k1_funct_1(u3_msualg_1(A,D),F)) => ! [J] : ( m2_pboole(J,u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)) => ( r2_hidden(J,k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => ! [K] : ( m2_pboole(K,u1_struct_0(A),k13_msafree(A,B),u3_msualg_1(A,D)) => ( ! [L] : ( m1_subset_1(L,u1_struct_0(A)) => ! [M] : ( m1_msafree4(M,u1_struct_0(A),k13_msafree(A,B),k1_msafree4(u1_struct_0(A),k13_msafree(A,B),L)) => ( r2_hidden(M,k1_msafree4(u1_struct_0(A),k11_aofa_a00(A,C,F,G),L)) => ! [N] : ( m1_subset_1(N,k1_funct_1(u3_msualg_1(A,C),L)) => ( N = k1_funct_1(k2_msafree4(u1_struct_0(A),k11_aofa_a00(A,C,F,G),u3_msualg_1(A,C),k18_aofa_a00(A,B,C,E,F,G),L),M) => k1_msafree4(k1_msafree4(u1_struct_0(A),k13_msafree(A,B),L),k2_msafree4(u1_struct_0(A),k13_msafree(A,B),u3_msualg_1(A,D),K,L),M) = k15_aofa_a00(A,B,C,D,L,N,k3_aofa_a00(u1_struct_0(A),H,u3_msualg_1(A,D),k1_msafree(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D),H,J),F,k17_aofa_a00(A,B,C,E,F,G),I)) ) ) ) ) ) => ! [L] : ( m3_pboole(L,u1_struct_0(A),u3_msualg_1(A,C)) => ( r8_pboole(u1_struct_0(A),L,k13_msafree(A,B)) => ! [M] : ( m2_pboole(M,u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D)) => ( ( r1_msualg_3(A,C,D,M) & r8_pboole(u1_struct_0(A),k1_msafree(u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D),L,M),K) ) => I = k1_msafree4(k1_funct_1(u3_msualg_1(A,C),F),k2_msafree4(u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D),M,F),G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d26_armstrng,axiom,( ! [A] : ! [B] : ( 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) ) )).
fof(d26_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_1(A,B,k1_bcialg_1(A,B,C)) = C ) ) ) ) )).
fof(d26_bilinear,axiom,( ! [A] : ( l2_struct_0(A) => ! [B] : ( l1_vectsp_1(B,A) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => k1_binop_1(C,D,D) = k4_struct_0(A) ) ) ) ) ) )).
fof(d26_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(d26_cat_4,axiom,( ! [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) & l2_cat_4(A) ) => ( v6_cat_4(A) <=> ( v11_cat_1(u5_cat_4(A),A) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(d26_coh_sp,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,k20_coh_sp(A)) => ! [D] : ( 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] : ( m1_subset_1(C,k20_coh_sp(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d26_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(d26_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) ) )).
fof(d26_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & 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) ) ) ) )).
fof(d26_fomodel0,axiom,( ! [A] : k23_fomodel0(A) = k2_zfmisc_1(k4_ordinal1,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))) )).
fof(d26_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k21_fomodel1(A) = k9_fomodel0(k15_fomodel1(A)) ) )).
fof(d26_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k26_fomodel2(A) = a_1_0_fomodel2(A) ) )).
fof(d26_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( v12_fomodel4(C,B) => ( r6_fomodel4(A,B,C) <=> ? [D] : ( v5_fomodel1(D,B) & m1_subset_1(D,k1_fomodel1(B)) & ? [E] : ( 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))),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0)),k35_fomodel1(B))) & ? [F] : ( 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))),k3_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) = k42_fomodel1(B,k42_fomodel1(B,k43_fomodel1(B,k31_fomodel2(B)),k1_fomodel3(B,D,E)),k1_fomodel3(B,D,F)) ) ) ) ) ) ) )).
fof(d26_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( m2_functor0(C,A,B) => ( v15_functor0(C,A,B) <=> ( v10_functor0(C,A,B) & v13_functor0(C,A,B) ) ) ) ) ) )).
fof(d26_gate_1,axiom,( ! [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) & 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 ) ) )).
fof(d26_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(d26_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k7_glib_000(A))) => ( C = k18_glib_000(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,k7_glib_000(A)) & r2_hidden(k1_funct_1(k11_glib_000(A),D),B) ) ) ) ) ) )).
fof(d26_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v3_glib_001(B,A) <=> k15_glib_001(A,B) = k5_numbers ) ) ) )).
fof(d26_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_grcat_1(A) ) => ! [B] : ( ( 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] : ( m3_grcat_1(C,k18_grcat_1(A)) => k3_funct_2(k18_grcat_1(A),A,B,C) = k20_grcat_1(A,C) ) ) ) ) )).
fof(d26_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( ( 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] : ( ( v2_group_9(E,A) & m1_group_9(E,A,B) ) => ( r1_tarski(C,u1_struct_0(E)) => m1_group_9(D,A,E) ) ) ) ) ) ) ) )).
fof(d26_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ( v6_ideal_1(A) <=> ! [B] : ( ( ~ 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) ) ) ) )).
fof(d26_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k6_glib_000(A),k4_ordinal1))) ) => ( v6_lexbfs(B,A) <=> ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => ! [E] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d26_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( v7_ltlaxio1(A) <=> ? [B] : ( m1_subset_1(B,k1_hilbert1) & ? [C] : ( 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))))) ) ) ) ) )).
fof(d26_modelc_1,axiom,( ! [A] : ( l2_modelc_1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( v1_modelc_1(D) & m2_finseq_1(D,k4_ordinal1) ) => ( ( 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))) ) ) ) ) ) ) ) )).
fof(d26_modelc_2,axiom,( k15_modelc_2 = a_0_0_modelc_2 )).
fof(d26_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k13_modelc_2(A))) => ! [C] : ( v1_xreal_0(C) => ( C = k18_modelc_3(A,B) <=> ? [D] : ( 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) ) ) ) ) ) )).
fof(d26_monoid_0,axiom,( k2_monoid_0 = g3_algstr_0(k1_numbers,k9_binop_2) )).
fof(d26_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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] : ( m1_osafree(C,A,k16_osafree(A,B)) => ( C = k24_osafree(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_funct_1(C,D) = k23_osafree(A,B,D) ) ) ) ) ) )).
fof(d26_osalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v2_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ( v3_osalg_4(C,A,B) <=> ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ( r6_osalg_1(A,D,E) => ! [F] : ( m1_subset_1(F,k3_msualg_1(A,D,B)) => ! [G] : ( m1_subset_1(G,k3_msualg_1(A,E,B)) => ( ! [H] : ( 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))) ) ) ) ) ) ) ) ) ) ) )).
fof(d26_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( m2_finseq_1(B,k4_numbers) => ( B = k28_polyform(A) <=> ( k3_finseq_1(B) = k2_xcmplx_0(k7_polyform(A),2) & ! [C] : ( 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))) ) ) ) ) ) ) )).
fof(d26_pscomp_1,axiom,( ! [A] : ( 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)) ) )).
fof(d26_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v4_qc_lang1(B,A) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( C = k20_qc_lang1(A,B) <=> ? [D] : ( m1_subset_1(D,k9_qc_lang1(A)) & B = k14_qc_lang1(A,D,C) ) ) ) ) ) ) )).
fof(d26_quofield,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d26_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r12_rewrite1(A,B) <=> ! [C] : ! [D] : ( r2_rewrite1(A,C,D) <=> r2_rewrite1(B,C,D) ) ) ) ) )).
fof(d26_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ( B = k13_scmyciel(A) <=> ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & B = C & k1_funct_1(C,k5_numbers) = A & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v4_scmyciel(E) => ( E = k1_funct_1(C,D) => k1_funct_1(C,k1_nat_1(D,1)) = k12_scmyciel(E) ) ) ) ) ) ) ) )).
fof(d26_sin_cos,axiom,( k26_sin_cos = k3_rfunct_1(k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos) )).
fof(d26_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => ( v5_substut1(B,A) <=> ? [C] : ( m1_subset_1(C,k16_substut1(A)) & B = k20_substut1(A,C) ) ) ) ) )).
fof(d26_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( l1_turing_1(B) => ! [C] : ( 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)) ) ) ) )).
fof(d26_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d26_waybel_4,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r5_waybel_4(A,B,C) <=> r4_waybel_4(B,C,u1_orders_2(A)) ) ) ) )).
fof(d26_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => k16_zf_lang(A,B,C,D) = k8_zf_lang(A,k14_zf_lang(B,C,D)) ) ) ) ) )).
fof(d26_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( v1_int_1(B) => ! [C] : ( m1_zmodul02(C,A) => ! [D] : ( m1_zmodul02(D,A) => ( D = k23_zmodul02(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k4_numbers,D,E) = k3_xcmplx_0(B,k3_funct_2(u1_struct_0(A),k4_numbers,C,E)) ) ) ) ) ) ) )).
fof(d27_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v4_abcmiz_0(A) & l3_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d27_abcmiz_1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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] : ( 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)))) ) ) ) ) )).
fof(d27_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [C] : ( m1_subset_1(C,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(d27_algstr_0,axiom,( ! [A] : ( l4_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v23_algstr_0(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & k6_algstr_0(A,C,B) = k5_struct_0(A) ) ) ) ) )).
fof(d27_aofa_000,axiom,( ! [A] : ( ( ~ 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 ) ) )).
fof(d27_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & l3_msualg_1(D,A) ) => ! [E] : ( l4_aofa_a00(E,A,B,C) => ( v11_aofa_a00(E,A,B,C,D) => ! [F] : ( m2_subset_1(F,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,D),G)) => ! [I] : ( m4_aofa_a00(I,A,B,C,E,G) => ! [J] : ( m2_subset_1(J,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => ( J = k19_aofa_a00(A,B,C,D,E,F,G,H,I) <=> ( k1_funct_1(k1_msafree4(u1_struct_0(A),J,G),I) = H & ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ! [L] : ( m1_msafree4(L,u1_struct_0(A),k13_msafree(A,B),k1_msafree4(u1_struct_0(A),k13_msafree(A,B),K)) => ( ~ ( K = G & L = I ) => ( ( ~ r2_hidden(L,k1_msafree4(u1_struct_0(A),k11_aofa_a00(A,C,G,I),K)) => k1_funct_1(k1_msafree4(u1_struct_0(A),J,K),L) = k1_funct_1(k1_msafree4(u1_struct_0(A),F,K),L) ) & ! [M] : ( m2_pboole(M,u1_struct_0(A),k13_msafree(A,B),u3_msualg_1(A,D)) => ! [N] : ( m3_pboole(N,u1_struct_0(A),u4_aofa_a00(A,B,C,E)) => ( r8_pboole(u1_struct_0(A),N,k13_msafree(A,B)) => ! [O] : ( m2_pboole(O,u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)) => ( ( r8_pboole(u1_struct_0(A),O,F) & r8_pboole(u1_struct_0(A),M,k3_aofa_a00(u1_struct_0(A),N,u3_msualg_1(A,D),k1_msafree(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D),N,O),G,k17_aofa_a00(A,B,C,E,G,I),H)) & r2_hidden(L,k1_msafree4(u1_struct_0(A),k11_aofa_a00(A,C,G,I),K)) ) => ! [P] : ( m1_subset_1(P,k1_funct_1(u3_msualg_1(A,C),K)) => ( P = k1_funct_1(k2_msafree4(u1_struct_0(A),k11_aofa_a00(A,C,G,I),u3_msualg_1(A,C),k18_aofa_a00(A,B,C,E,G,I),K),L) => k1_funct_1(k1_msafree4(u1_struct_0(A),J,K),L) = k15_aofa_a00(A,B,C,D,K,P,M) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d27_armstrng,axiom,( ! [A] : ( v11_armstrng(A) <=> ! [B] : ! [C] : ( ( r2_hidden(B,A) & r2_hidden(C,A) & r1_tarski(B,C) ) => B = C ) ) )).
fof(d27_bcialg_1,axiom,( ! [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) ) => ( v20_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(d27_coh_sp,axiom,( ! [A] : 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)) )).
fof(d27_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) ) )).
fof(d27_fomodel0,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k24_fomodel0(A,B) = k5_relat_1(B,A) ) )).
fof(d27_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k22_fomodel1(A) = k7_fomodel0(k15_fomodel1(A)) ) )).
fof(d27_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0)))) => ( C = k24_fomodel2(A,B) <=> ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(A),k3_rfunct_3(k3_finseq_2(D),k2_xboole_0(D,k6_margrel1))),k15_fomodel2(A,D)) => C = k1_relset_1(k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0)),k23_fomodel2(A,D,B,E)) ) ) ) ) ) ) )).
fof(d27_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( v12_fomodel4(C,B) => ( r7_fomodel4(A,B,C) <=> ? [D] : ( v7_fomodel1(D,B) & m1_subset_1(D,k1_fomodel1(B)) & ? [E] : ( 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))),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0)),k35_fomodel1(B))) & ? [F] : ( 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))),k3_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) ) ) ) ) ) ) )).
fof(d27_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( m2_functor0(C,A,B) => ( v16_functor0(C,A,B) <=> ( v11_functor0(C,A,B) & v14_functor0(C,A,B) ) ) ) ) ) )).
fof(d27_gate_1,axiom,( ! [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) ) => 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 ) ) )).
fof(d27_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k7_glib_000(A))) => ( C = k19_glib_000(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,k7_glib_000(A)) & r2_hidden(k1_funct_1(k10_glib_000(A),D),B) ) ) ) ) ) )).
fof(d27_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v4_glib_001(B,A) <=> v2_funct_1(k12_glib_001(A,B)) ) ) ) )).
fof(d27_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_grcat_1(A) ) => ! [B] : ( ( 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] : ( m3_grcat_1(C,k18_grcat_1(A)) => ! [D] : ( 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] : ( m3_grcat_1(C,k18_grcat_1(A)) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(d27_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( 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))) ) ) ) )).
fof(d27_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) & B = k7_ideal_1(A,k6_domain_1(u1_struct_0(A),C)) ) ) ) ) )).
fof(d27_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( v8_ltlaxio1(A) <=> ? [B] : ( m1_subset_1(B,k1_hilbert1) & ? [C] : ( 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)) ) ) ) ) )).
fof(d27_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => k29_mmlquery(A,B,C) = C ) ) )).
fof(d27_modelc_1,axiom,( ! [A] : ( l2_modelc_1(A) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,k4_ordinal1) => ( r2_modelc_1(A,B,C,D) <=> ! [E] : ( ( v1_modelc_1(E) & m2_finseq_1(E,k4_ordinal1) ) => ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(d27_modelc_2,axiom,( ! [A] : ( l1_modelc_2(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( v1_modelc_2(D) & m2_finseq_1(D,k4_ordinal1) ) => ( ( 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))) ) ) ) ) ) ) ) )).
fof(d27_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r2_hidden(B,k1_modelc_3(A)) => k19_modelc_3(A,B) = k2_modelc_3(B) ) ) ) )).
fof(d27_monoid_0,axiom,( ! [A] : ( ( ~ 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) = k4_ordinal1 ) ) )).
fof(d27_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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] : ( ( 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] : ( 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] : ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d27_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [E] : ( ( v2_msualg_4(E,A,B) & v3_msualg_4(E,A,B) & m1_osalg_4(E,A,B) ) => ! [F] : ( 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] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d27_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( m2_finseq_1(B,k4_numbers) => ( B = k29_polyform(A) <=> ( k3_finseq_1(B) = k7_polyform(A) & ! [C] : ( 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))) ) ) ) ) ) ) )).
fof(d27_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v5_qc_lang1(B,A) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ( C = k21_qc_lang1(A,B) <=> ? [D] : ( m1_subset_1(D,k9_qc_lang1(A)) & B = k15_qc_lang1(A,C,D) ) ) ) ) ) ) )).
fof(d27_quantal1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(d27_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r13_rewrite1(A,B,C) <=> ( r8_rewrite1(A,B,C) & ~ r5_rewrite1(A,B,C) ) ) ) )).
fof(d27_sin_cos,axiom,( k27_sin_cos = k3_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos,k16_sin_cos) )).
fof(d27_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => ( v6_substut1(B,A) <=> ? [C] : ( m1_subset_1(C,k16_substut1(A)) & ? [D] : ( m1_subset_1(D,k16_substut1(A)) & B = k21_substut1(A,C,D) & k19_substut1(A,C) = k19_substut1(A,D) ) ) ) ) ) )).
fof(d27_turing_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(A,k2_xboole_0(B,C))) => ( ? [E] : ? [F] : ( 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) ) ) ) ) ) )).
fof(d27_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d27_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k11_waybel_0(A,B) = a_2_2_waybel_0(A,B) ) ) )).
fof(d27_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => k17_zf_lang(A,B,C,D) = k13_zf_lang(A,k15_zf_lang(B,C,D)) ) ) ) ) )).
fof(d27_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => k24_zmodul02(A,B) = k23_zmodul02(A,k4_xcmplx_0(1),B) ) ) )).
fof(d28_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l3_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_abcmiz_0(A)) => ( r5_abcmiz_0(A,B,C) <=> ! [D] : ( v7_ordinal1(D) => ! [E] : ( m1_subset_1(E,u1_abcmiz_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d28_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(d28_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,B) => k2_binop_1(B,u1_struct_0(A),B,C,D,k12_aofa_000(A)) = D ) ) ) ) ) )).
fof(d28_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & l3_msualg_1(D,A) ) => ! [E] : ( l4_aofa_a00(E,A,B,C) => ! [F] : ( ( ~ v2_struct_0(F) & v2_unialg_1(F) & v3_unialg_1(F) & v4_unialg_1(F) & v3_aofa_000(F) & v4_aofa_000(F) & v5_aofa_000(F) & v6_aofa_000(F) & l3_aofa_a00(F,A,C,u4_aofa_a00(A,B,C,E)) ) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_msafree4(H,u1_struct_0(A),u4_aofa_a00(A,B,C,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),G)) => ! [I] : ( m1_subset_1(I,k1_funct_1(u3_msualg_1(A,D),G)) => ! [J] : ( m1_subset_1(J,k1_zfmisc_1(k9_funct_2(k2_zfmisc_1(k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E)),u1_struct_0(F)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))))) => ( J = k20_aofa_a00(A,B,C,D,E,F,G,H,I) <=> ! [K] : ( ( v1_funct_1(K) & v1_funct_2(K,k2_zfmisc_1(k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E)),u1_struct_0(F)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) & m1_subset_1(K,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E)),u1_struct_0(F)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))))) ) => ( r2_hidden(K,J) <=> ( m1_aofa_000(K,F,k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E)),k14_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E),G,H,I)) & ! [L] : ( m2_subset_1(L,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => ! [M] : ( m1_subset_1(M,u1_struct_0(A)) => ! [N] : ( m1_msafree4(N,u1_struct_0(A),u4_aofa_a00(A,B,C,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),M)) => ! [O] : ( m4_aofa_a00(O,A,B,C,E,M) => ( O = N => ! [P] : ( m1_subset_1(P,k1_funct_1(u3_msualg_1(A,C),M)) => r8_pboole(u1_struct_0(A),k2_binop_1(k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E)),u1_struct_0(F),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E)),K,L,k12_aofa_a00(A,C,u4_aofa_a00(A,B,C,E),F,M,N,P)),k19_aofa_a00(A,B,C,D,E,L,M,k15_aofa_a00(A,B,C,D,M,P,L),O)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d28_aofa_i00,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(A,k4_numbers))) => ! [C] : ( ( 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),k4_ordinal1) => ! [D] : ( 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] : ( m2_funct_2(E,A,k4_numbers,k9_funct_2(A,k4_numbers)) => ! [F] : ( m2_funct_2(F,k9_funct_2(A,k4_numbers),A,k9_funct_2(k9_funct_2(A,k4_numbers),A)) => ! [G] : ( 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(k4_ordinal1,k1_partfun1(k9_funct_2(A,k4_numbers),A,A,k1_card_1(A),F,C),C),k17_aofa_i00(k4_ordinal1,G,C)))) = k14_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)) ) ) ) ) ) ) ) ) ) )).
fof(d28_armstrng,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ( v12_armstrng(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(d28_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,B,D) => ! [F] : ( 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] : ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(d28_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) ) )).
fof(d28_fomodel0,axiom,( ! [A] : ! [B] : k25_fomodel0(A,B) = k3_xboole_0(B,k2_zfmisc_1(A,k10_xtuple_0(B))) )).
fof(d28_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( v7_ordinal1(B) => k27_fomodel2(A,B) = a_2_1_fomodel2(A,B) ) ) )).
fof(d28_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( v12_fomodel4(C,B) => ( r8_fomodel4(A,B,C) <=> ? [D] : ( v4_fomodel1(D,B) & m1_subset_1(D,k1_fomodel1(B)) & ? [E] : ( 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] : ( 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) = k42_fomodel1(B,k43_fomodel1(B,D),E) ) ) ) ) ) ) )).
fof(d28_functor0,axiom,( ! [A] : ( l2_altcat_1(A) => ! [B] : ( m1_altcat_2(B,A) => ! [C] : ( ( 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))) ) ) ) ) ) )).
fof(d28_gate_1,axiom,( ! [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) ) => 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 ) ) )).
fof(d28_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : k20_glib_000(A,B) = k4_subset_1(k7_glib_000(A),k18_glib_000(A,B),k19_glib_000(A,B)) ) )).
fof(d28_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v5_glib_001(B,A) <=> ( v4_glib_001(B,A) & ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d28_grcat_1,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(d28_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( 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] : ( v7_ordinal1(D) => ( ( r2_hidden(D,k4_finseq_1(C)) & r2_hidden(k1_nat_1(D,1),k4_finseq_1(C)) ) => ! [E] : ( m1_group_9(E,A,B) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d28_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ( v8_ideal_1(A) <=> ! [B] : ( ( ~ 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) ) ) ) )).
fof(d28_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( v9_ltlaxio1(A) <=> ? [B] : ( m1_subset_1(B,k1_hilbert1) & ? [C] : ( m1_subset_1(C,k1_hilbert1) & A = k3_hilbert1(k4_hilbert1(B,C),k2_ltlaxio1(k7_ltlaxio1(C))) ) ) ) ) )).
fof(d28_mmlquery,axiom,( ! [A] : ( l1_mmlquery(A) => ! [B] : ( 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) ) ) )).
fof(d28_modelc_2,axiom,( ! [A] : ( l1_modelc_2(A) => ! [B] : ( ( 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] : ( ( 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] : ( v7_ordinal1(D) => ( r5_modelc_2(A,B,C,D) <=> ! [E] : ( ( v1_modelc_2(E) & m2_finseq_1(E,k4_ordinal1) ) => ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(d28_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r2_hidden(B,k1_modelc_3(A)) => k20_modelc_3(A,B) = k3_modelc_3(B) ) ) ) )).
fof(d28_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [E] : ( ( v2_msualg_4(E,A,B) & v3_msualg_4(E,A,B) & m1_osalg_4(E,A,B) ) => ! [F] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d28_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( m2_finseq_1(B,k4_numbers) => ( B = k30_polyform(A) <=> ( k3_finseq_1(B) = k2_xcmplx_0(k7_polyform(A),1) & ! [C] : ( 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))) ) ) ) ) ) ) )).
fof(d28_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v5_qc_lang1(B,A) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( C = k22_qc_lang1(A,B) <=> ? [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) & B = k15_qc_lang1(A,D,C) ) ) ) ) ) ) )).
fof(d28_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ( v1_relat_1(B) & v10_rewrite1(B) ) => ( m2_rewrite1(B,A) <=> ! [C] : ! [D] : ( r2_rewrite1(A,C,D) <=> r5_rewrite1(B,C,D) ) ) ) ) )).
fof(d28_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( A = k28_sin_cos <=> ( k1_funct_1(k26_sin_cos,k7_xcmplx_0(A,4)) = 1 & r2_hidden(A,k2_rcomp_1(k5_numbers,4)) ) ) ) )).
fof(d28_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => ( v7_substut1(B,A) <=> ? [C] : ( m1_subset_1(C,k2_zfmisc_1(k16_substut1(A),k3_qc_lang1(A))) & ? [D] : ( m1_substut1(D,A,C) & B = k24_substut1(A,C,D) & v3_substut1(C,A) ) ) ) ) ) )).
fof(d28_turing_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(A,k2_xboole_0(B,C))) => ( ? [E] : ? [F] : ( 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) ) ) ) ) ) )).
fof(d28_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d28_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k12_waybel_0(A,B) = a_2_3_waybel_0(A,B) ) ) )).
fof(d28_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v7_zf_lang(A) => k18_zf_lang(A) = k1_funct_1(A,2) ) ) )).
fof(d28_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( m1_zmodul02(C,A) => k25_zmodul02(A,B,C) = k22_zmodul02(A,B,k24_zmodul02(A,C)) ) ) ) )).
fof(d29_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l3_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A))) => ( r6_abcmiz_0(A,B,C) <=> ? [D] : ( m2_finseq_1(D,u1_abcmiz_0(A)) & k2_relset_1(u1_abcmiz_0(A),D) = C & r5_abcmiz_0(A,B,D) ) ) ) ) ) )).
fof(d29_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_abcmiz_1(B,A) & m1_subset_1(B,u4_struct_0(A)) ) => ( k3_finseq_1(k1_msualg_1(A,B)) = k5_numbers => k29_abcmiz_1(A,B) = k4_trees_4(k4_tarski(B,u1_struct_0(A)),k1_xboole_0) ) ) ) )).
fof(d29_abcmiz_a,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k2_abcmiz_1) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d29_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,B) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d29_aofa_a00,axiom,( ! [A] : ( l5_aofa_a00(A) => ( v13_aofa_a00(A) <=> v2_funct_1(u7_aofa_a00(A)) ) ) )).
fof(d29_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m3_aofa_i00(E,A,B,C,D) => ! [F] : ( m3_aofa_i00(F,A,B,C,D) => ! [G] : ( m3_aofa_i00(G,A,B,C,D) => ( G = k35_aofa_i00(A,B,C,D,E,F) <=> ! [H] : ( 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) = k4_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)) ) ) ) ) ) ) ) ) ) )).
fof(d29_armstrng,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ( v13_armstrng(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d29_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( 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)) ) ) )).
fof(d29_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) ) )).
fof(d29_fomodel0,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => k26_fomodel0(A,B) = k2_xboole_0(k6_subset_1(A,k2_zfmisc_1(k9_xtuple_0(B),k10_xtuple_0(A))),B) ) ) )).
fof(d29_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v10_fomodel1(B,A) & m1_subset_1(B,k1_fomodel1(A)) ) => ! [C] : k23_fomodel1(A,B,C) = a_3_0_fomodel1(A,B,C) ) ) )).
fof(d29_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( v7_ordinal1(B) => k28_fomodel2(A,B) = a_2_2_fomodel2(A,B) ) ) )).
fof(d29_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( v12_fomodel4(C,B) => ( r9_fomodel4(A,B,C) <=> ? [D] : ( v4_fomodel1(D,B) & m1_subset_1(D,k1_fomodel1(B)) & ? [E] : ( v4_fomodel1(E,B) & m1_subset_1(E,k1_fomodel1(B)) & ? [F] : ? [G] : ( 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(k43_fomodel1(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) ) ) ) ) ) ) )).
fof(d29_functor0,axiom,( ! [A] : ( l1_altcat_1(A) => ! [B] : ( ( 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))) ) ) ) ) )).
fof(d29_gate_1,axiom,( ! [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) & 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 ) ) )).
fof(d29_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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))) )).
fof(d29_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : k21_glib_000(A,B) = k9_subset_1(k7_glib_000(A),k18_glib_000(A,B),k19_glib_000(A,B)) ) )).
fof(d29_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v6_glib_001(B,A) <=> ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( ( 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 ) ) ) ) ) ) )).
fof(d29_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => k26_grcat_1(A) = a_1_0_grcat_1(A) ) )).
fof(d29_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v8_group_9(C,A,B) & m2_finseq_1(C,k6_group_9(A,B)) ) => ! [D] : ( ( v8_group_9(D,A,B) & m2_finseq_1(D,k6_group_9(A,B)) ) => ( r4_group_9(A,B,C,D) <=> ? [E] : ( r1_tarski(E,k4_finseq_1(C)) & r2_relset_1(k4_ordinal1,k6_group_9(A,B),D,k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k6_group_9(A,B),k14_finseq_1(E),C)) ) ) ) ) ) )).
fof(d29_ltlaxio1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k1_hilbert1) => ! [C] : ( 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] : ( v7_ordinal1(D) => ! [E] : ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(d29_mmlquery,axiom,( ! [A] : ( l1_mmlquery(A) => ! [B] : ( 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) ) ) )).
fof(d29_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( 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))) ) ) )).
fof(d29_monoid_0,axiom,( k23_binop_2 = u2_algstr_0(k4_monoid_0) )).
fof(d29_polyform,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(d29_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k2_qc_lang1(A)) => k23_qc_lang1(A,B) = a_2_1_qc_lang1(A,B) ) ) )).
fof(d29_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => ( v4_substut1(B,A) => ! [C] : ( m2_finseq_1(C,k2_qc_lang1(A)) => ( C = k26_substut1(A,B) <=> ? [D] : ( v7_ordinal1(D) & ? [E] : ( m2_subset_1(E,k6_qc_lang1(A),k8_qc_lang1(A,D)) & ? [F] : ( v3_card_1(F,D) & m2_finseq_1(F,k2_qc_lang1(A)) & ? [G] : ( m1_subset_1(G,k1_substut1(A)) & r2_relset_1(k4_ordinal1,k2_qc_lang1(A),C,F) & B = k17_substut1(A,E,F,G) ) ) ) ) ) ) ) ) ) )).
fof(d29_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( l1_turing_1(B) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(k21_turing_1(A,B),k2_xboole_0(u1_turing_1(A),u1_turing_1(B)))) => ( ( ? [D] : ( m1_subset_1(D,u2_turing_1(A)) & ? [E] : ( 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),k1_enumset1(k4_xcmplx_0(1),k5_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] : ( m1_subset_1(D,u2_turing_1(B)) & ? [E] : ( 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),k1_enumset1(k4_xcmplx_0(1),k5_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] : ( m1_subset_1(D,u2_turing_1(A)) => ! [E] : ( 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] : ( m1_subset_1(D,u2_turing_1(B)) => ! [E] : ( 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) = k3_xtuple_0(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),k4_xcmplx_0(1)) ) ) ) ) ) )).
fof(d29_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d29_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v16_waybel_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_orders_2(A,B,C) | r1_orders_2(A,C,B) ) ) ) ) ) )).
fof(d29_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v7_zf_lang(A) => k19_zf_lang(A) = k1_funct_1(A,3) ) ) )).
fof(d29_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( B = k26_zmodul02(A) <=> ! [C] : ( r2_hidden(C,B) <=> m1_zmodul02(C,A) ) ) ) )).
fof(d2_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v1_abcmiz_0(A) <=> ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r2_hidden(C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,B) & r2_orders_2(A,C,D) ) ) ) ) ) ) )).
fof(d2_abcmiz_1,axiom,( ! [A] : ( A = k2_abcmiz_1 <=> ? [B] : ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & A = k3_card_3(B) & k1_funct_1(B,k5_numbers) = a_0_0_abcmiz_1 & ! [C] : ( v7_ordinal1(C) => k1_funct_1(B,k1_nat_1(C,1)) = a_2_0_abcmiz_1(B,C) ) ) ) )).
fof(d2_abian,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_abian(A) <=> ? [B] : ( m1_subset_1(B,k4_ordinal1) & A = k2_nat_1(2,B) ) ) ) )).
fof(d2_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( ~ r1_xxreal_0(A,k5_numbers) => k1_absvalue(A) = 1 ) & ( ~ r1_xxreal_0(k5_numbers,A) => k1_absvalue(A) = k4_xcmplx_0(1) ) & ( ( r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k5_numbers,A) ) => k1_absvalue(A) = k5_numbers ) ) ) )).
fof(d2_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( D = k1_aff_1(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(E,D) <=> r1_aff_1(A,B,C,E) ) ) ) ) ) ) ) )).
fof(d2_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ( v2_aff_2(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_aff_3,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v2_aff_3(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ! [L] : ( m1_subset_1(L,u1_struct_0(A)) => ! [M] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_aff_4(B,A) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & ? [D] : ( 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) ) ) ) ) ) )).
fof(d2_afinsq_1,axiom,( ! [A] : k4_afinsq_1(A) = k1_xboole_0 )).
fof(d2_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( v7_ordinal1(D) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,C)) => k1_funct_1(C,D) = k1_funct_1(A,k2_xcmplx_0(D,B)) ) ) ) ) ) ) ) )).
fof(d2_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => k2_afproj(A) = a_1_1_afproj(A) ) )).
fof(d2_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_afvect0(A,B,C) <=> ( r2_analoaf(A,B,C,C,B) & B != C ) ) ) ) ) )).
fof(d2_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect01(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_afvect01(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( 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) ) ) ) ) ) ) )).
fof(d2_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(d2_algseq_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => ( r1_algseq_1(A,B,C) <=> ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => k1_funct_1(B,D) = k4_struct_0(A) ) ) ) ) ) ) )).
fof(d2_algspec1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(d2_algstr_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ( v1_algstr_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_algstr_0(A,k4_struct_0(A),B) = B ) ) ) )).
fof(d2_algstr_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_algstr_0(A) & v3_algstr_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_algstr_2(A,B,C) = k1_algstr_0(A,B,k1_algstr_2(A,C)) ) ) ) )).
fof(d2_algstr_3,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k1_multop_1(A,B,C,D) = k2_xcmplx_0(k3_xcmplx_0(B,C),D) ) ) ) ) ) )).
fof(d2_algstr_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(d2_altcat_1,axiom,( ! [A] : ( l1_altcat_1(A) => ( v2_altcat_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(d2_altcat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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] : ( r2_hidden(E,A) => r1_tarski(k1_funct_1(C,E),k1_funct_1(D,E)) ) ) ) ) ) )).
fof(d2_altcat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_altcat_1(A,B,C)) => ( v1_altcat_3(D,A,B,C) <=> ? [E] : ( m1_subset_1(E,k1_altcat_1(A,C,B)) & r1_altcat_3(A,B,C,D,E) ) ) ) ) ) ) )).
fof(d2_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d2_altcat_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ! [D] : ( ( 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] : ( ( v1_relat_1(E) & v4_relat_1(E,C) & v1_funct_1(E) & v1_partfun1(E,C) ) => ( m1_altcat_5(E,A,B,C,D) <=> ! [F] : ~ ( r2_hidden(F,C) & ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( G = k1_funct_1(D,F) & m1_subset_1(k1_funct_1(E,F),k1_altcat_1(A,B,G)) ) ) ) ) ) ) ) ) )).
fof(d2_ami_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k1_ami_2,k7_card_1(2)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_ami_2,k7_card_1(2)))) ) => ( A = k3_ami_2 <=> ! [B] : ( m1_subset_1(B,k1_ami_2) => ( ( B = k4_ordinal1 => k3_funct_2(k1_ami_2,k7_card_1(2),A,B) = k5_numbers ) & ( r2_hidden(B,k2_ami_2) => k3_funct_2(k1_ami_2,k7_card_1(2),A,B) = 1 ) ) ) ) ) )).
fof(d2_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( 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)) ) ) )).
fof(d2_ami_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k11_memstr_0(k7_card_1(2),k1_ami_3),k11_memstr_0(k7_card_1(2),k1_ami_3)))) ) => ( A = k2_ami_4 <=> ! [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(k7_card_1(2),k1_ami_3)) & v1_finset_1(B) ) => ! [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(k7_card_1(2),k1_ami_3)) & v1_finset_1(C) ) => ( r2_hidden(k4_tarski(B,C),A) <=> ? [D] : ( v1_int_1(D) & ? [E] : ( v1_int_1(E) & ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(E,k5_numbers) & B = k12_ami_3(k10_ami_3(k5_numbers),k10_ami_3(1),D,E) & C = k11_ami_3(k10_ami_3(k5_numbers),k3_int_2(D,E)) ) ) ) ) ) ) ) )).
fof(d2_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_ami_wstd(A,B,C,D) & r1_ami_wstd(A,B,D,C) ) => C = D ) ) ) ) ) ) )).
fof(d2_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(d2_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_analmetr(A,B,C,D,E) <=> ? [F] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & ? [I] : ( v1_xreal_0(I) & 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)) & k2_xcmplx_0(k3_xcmplx_0(F,H),k3_xcmplx_0(G,I)) = k5_numbers ) ) ) ) ) ) ) ) ) ) )).
fof(d2_analoaf,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d2_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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,k4_xcmplx_0(k2_geomtrap(A,B,C,D)))) ) ) ) ) )).
fof(d2_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_anproj_1(A,B,C,D) <=> ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & 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 = k5_numbers & F = k5_numbers & G = k5_numbers ) ) ) ) ) ) ) ) ) )).
fof(d2_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d2_aofa_a00,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,C) => ! [E] : ( r2_hidden(E,A) => ! [F] : ( r2_hidden(F,k1_funct_1(B,E)) => ! [G] : ( r2_hidden(G,k1_funct_1(C,E)) => ! [H] : ( m2_pboole(H,A,B,C) => ( H = k3_aofa_a00(A,B,C,D,E,F,G) <=> ( k2_msafree4(A,B,C,H,E) = k1_funct_7(k2_msafree4(A,B,C,D,E),F,G) & ! [I] : ( r2_hidden(I,A) => ( I = E | r2_funct_2(k1_funct_1(B,I),k1_funct_1(C,I),k2_msafree4(A,B,C,H,I),k2_msafree4(A,B,C,D,I)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => k1_aofa_a01(A,B,C) = k13_msafree(A,B) ) ) ) )).
fof(d2_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ( m1_subset_1(E,A) => m1_aofa_i00(E,A,B,C,D) ) ) )).
fof(d2_arrow,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_arrow(A))) => ( B = k3_arrow(A) <=> ! [C] : ( m1_subset_1(C,k2_arrow(A)) => ( r2_hidden(C,B) <=> ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ( ( r2_hidden(k4_tarski(D,E),C) & r2_hidden(k4_tarski(E,D),C) ) => D = E ) ) ) ) ) ) ) ) )).
fof(d2_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( 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] : ( m1_subset_1(D,k2_arytm_2) & ? [E] : ( 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(k5_numbers),k2_arytm_2)) ) => ( A = k5_numbers | ( C = k2_arytm_0(A,B) <=> ? [D] : ( m1_subset_1(D,k2_arytm_2) & ? [E] : ( m1_subset_1(E,k2_arytm_2) & A = D & B = k4_tarski(k5_numbers,E) & C = k4_tarski(k5_numbers,k8_arytm_2(D,E)) ) ) ) ) ) & ( ( r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) ) => ( B = k5_numbers | ( C = k2_arytm_0(A,B) <=> ? [D] : ( m1_subset_1(D,k2_arytm_2) & ? [E] : ( m1_subset_1(E,k2_arytm_2) & A = k4_tarski(k5_numbers,D) & B = E & C = k4_tarski(k5_numbers,k8_arytm_2(E,D)) ) ) ) ) ) & ( ( r2_hidden(A,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) & r2_hidden(B,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) ) => ( C = k2_arytm_0(A,B) <=> ? [D] : ( m1_subset_1(D,k2_arytm_2) & ? [E] : ( m1_subset_1(E,k2_arytm_2) & A = k4_tarski(k5_numbers,D) & B = k4_tarski(k5_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(k5_numbers),k2_arytm_2)) & A != k5_numbers ) & ~ ( r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) & B != k5_numbers ) & ~ ( r2_hidden(A,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) & r2_hidden(B,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) ) & ~ ( C = k2_arytm_0(A,B) <=> C = k5_numbers ) ) ) ) ) ) )).
fof(d2_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( 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)) ) ) ) ) )).
fof(d2_arytm_2,axiom,( k2_arytm_2 = k6_subset_1(k2_xboole_0(k5_arytm_3,k1_arytm_2),a_0_1_arytm_2) )).
fof(d2_arytm_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r1_arytm_3(A,B) <=> ! [C] : ( v3_ordinal1(C) => ! [D] : ( v3_ordinal1(D) => ! [E] : ( v3_ordinal1(E) => ( ( A = k11_ordinal2(C,D) & B = k11_ordinal2(C,E) ) => C = 1 ) ) ) ) ) ) ) )).
fof(d2_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_asympt_0(A) <=> ? [B] : ( v7_ordinal1(B) & ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,A,C)) ) ) ) ) ) )).
fof(d2_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( A = k2_asympt_1 <=> ( k9_nat_1(k1_numbers,A,k5_numbers) = k5_numbers & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(B,k5_numbers) => k9_nat_1(k1_numbers,A,B) = k3_power(2,B) ) ) ) ) ) )).
fof(d2_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( 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] : ( m2_funct_2(C,u1_struct_0(A),u1_struct_0(A),k1_autalg_1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d2_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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] : ( m2_funct_2(C,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d2_bcialg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_bcialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_bcialg_1(A,B) = k1_bcialg_1(A,k4_struct_0(A),B) ) ) )).
fof(d2_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_bcialg_2(B,A) <=> r1_bcialg_1(A,k4_struct_0(A),B) ) ) ) )).
fof(d2_bcialg_3,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v2_bcialg_3(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_1(A,C,B) = k4_struct_0(A) ) ) ) ) )).
fof(d2_bcialg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_bcialg_4(A) ) => ( v2_bcialg_4(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d2_bcialg_6,axiom,( ! [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] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( r1_xxreal_0(k5_numbers,B) => k3_bcialg_6(A,B,C) = k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k2_bcialg_6(A),C,k1_int_2(B)) ) & ( ~ r1_xxreal_0(k5_numbers,B) => k3_bcialg_6(A,B,C) = k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k2_bcialg_6(A),k2_bcialg_1(A,C),k1_int_2(B)) ) ) ) ) ) )).
fof(d2_bhsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_bhsp_1(A) ) => ( v2_bhsp_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ( ( k1_bhsp_1(A,B,B) = k5_numbers => B = k4_struct_0(A) ) & ( B = k4_struct_0(A) => k1_bhsp_1(A,B,B) = k5_numbers ) & r1_xxreal_0(k5_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) = k2_xcmplx_0(k1_bhsp_1(A,B,D),k1_bhsp_1(A,C,D)) & k1_bhsp_1(A,k1_rlvect_1(A,B,E),C) = k3_xcmplx_0(E,k1_bhsp_1(A,B,C)) ) ) ) ) ) ) ) )).
fof(d2_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_bhsp_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k1_bhsp_2(A,B) <=> ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(E,F) & r1_xxreal_0(D,k4_bhsp_1(A,k1_normsp_1(A,B,F),C)) ) ) ) ) ) ) ) ) ) )).
fof(d2_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r1_bhsp_3(A,B,C) <=> ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & 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))) ) ) ) ) ) ) ) ) )).
fof(d2_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_bhsp_4(B,A) <=> v1_bhsp_2(k1_bhsp_4(A,B),A) ) ) ) )).
fof(d2_bhsp_6,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_bhsp_6(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( ~ v1_xboole_0(E) & r1_tarski(E,B) & ! [F] : ( ( 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)))) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d2_binari_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(d2_binari_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_int_1(B) => ( ( ~ r1_xxreal_0(k5_numbers,B) => k2_binari_4(A,B) = k1_binari_3(A,k1_int_2(k2_xcmplx_0(k5_series_1(2,k1_binari_4(A,k1_int_2(B))),B))) ) & ( r1_xxreal_0(k5_numbers,B) => k2_binari_4(A,B) = k1_binari_3(A,k1_int_2(B)) ) ) ) ) )).
fof(d2_binarith,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k6_margrel1) ) => ! [D] : ( ( 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] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(d2_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => k2_binom(A,B,C) = k1_binop_1(k4_group_1(A),B,C) ) ) ) )).
fof(d2_binop_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => k3_binop_1(A,B,C,D) = k3_binop_1(A,B,D,C) ) ) ) ) )).
fof(d2_bintree1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ( v1_bintree1(A) <=> ! [B] : ( m1_trees_1(B,A) => ( ~ r2_hidden(B,k3_trees_1(A)) => k1_trees_2(A,B) = k2_tarski(k8_finseq_1(k4_ordinal1,B,k14_trees_3(k5_numbers)),k8_finseq_1(k4_ordinal1,B,k14_trees_3(1))) ) ) ) ) )).
fof(d2_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ( v1_bintree2(A) <=> A = k3_finseq_2(k7_domain_1(k4_ordinal1,k5_numbers,1)) ) ) )).
fof(d2_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(d2_boolmark,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m2_funct_2(B,u1_struct_0(A),k6_margrel1,k1_boolmark(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(d2_borsuk_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(d2_borsuk_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_borsuk_2(A,B,C) => ! [D] : ( ( 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,k5_numbers) = B & k1_funct_1(D,1) = C ) ) ) ) ) ) ) )).
fof(d2_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k2_borsuk_5(A,B) = k9_subset_1(k1_numbers,k3_numbers,k2_rcomp_1(A,B)) ) ) )).
fof(d2_borsuk_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_borsuk_7(A) <=> ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(d2_brouwer,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( v1_xreal_0(C) => k2_brouwer(A,B,C) = k1_pre_topc(k15_euclid(A),k2_topreal9(A,B,C)) ) ) ) )).
fof(d2_bspace,axiom,( k2_bspace = k9_int_3(2) )).
fof(d2_bvfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_margrel1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_margrel1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_margrel1(C) ) => ( C = k3_bvfunc_1(A,B) <=> ( k9_xtuple_0(C) = k3_xboole_0(k9_xtuple_0(A),k9_xtuple_0(B)) & ! [D] : ( r2_hidden(D,k9_xtuple_0(C)) => k1_funct_1(C,D) = k5_xboolean(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) )).
fof(d2_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( r1_bvfunc_2(A,B,C) <=> ( ! [D] : ( m1_eqrel_1(D,A) => ( r2_hidden(D,B) => r1_partit1(A,D,C) ) ) & ! [D] : ( ( r1_tarski(D,C) & ! [E] : ( m1_eqrel_1(E,A) => ( r2_hidden(E,B) => r1_partit1(A,E,D) ) ) ) => D = C ) ) ) ) ) )).
fof(d2_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => k2_c0sp2(A) = a_1_0_c0sp2(A) ) )).
fof(d2_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ( ( ~ r1_xxreal_0(k3_finseq_1(B),k5_numbers) => k2_calcul_1(A,B) = k1_funct_1(B,k3_finseq_1(B)) ) & ( r1_xxreal_0(k3_finseq_1(B),k5_numbers) => k2_calcul_1(A,B) = k5_cqc_lang(A) ) ) ) ) )).
fof(d2_calcul_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)) & v3_funct_2(C,k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)))) ) => k3_calcul_2(A,B,C) = k4_relset_1(k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B),k4_ordinal1,A,C,B) ) ) ) )).
fof(d2_cantor_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)) ) ) ) )).
fof(d2_card_1,axiom,( ! [A] : ! [B] : ( v1_card_1(B) => ( B = k1_card_1(A) <=> r2_wellord2(A,B) ) ) )).
fof(d2_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => k2_card_2(A,B) = k1_card_1(k2_zfmisc_1(A,B)) ) ) )).
fof(d2_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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] : ( r2_hidden(C,k9_xtuple_0(A)) => k1_funct_1(B,C) = k1_card_1(k1_funct_1(A,C)) ) ) ) ) ) )).
fof(d2_card_5,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_card_3(C) ) => ( C = k2_card_5(A,B) <=> ( ! [D] : ( r2_hidden(D,k9_xtuple_0(C)) <=> ( r2_hidden(D,A) & v1_card_1(D) ) ) & ! [D] : ( v1_card_1(D) => ( r2_hidden(D,A) => k1_funct_1(C,D) = k3_card_2(D,B) ) ) ) ) ) ) ) )).
fof(d2_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d2_card_fin,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_tarski(k10_xtuple_0(A)))) => ( D = k2_card_fin(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ( r2_hidden(E,k3_tarski(k10_xtuple_0(A))) & ! [F] : ( ( r2_hidden(F,k9_xtuple_0(B)) & k1_funct_1(B,F) = C ) => r2_hidden(E,k1_funct_1(A,F)) ) ) ) ) ) ) ) )).
fof(d2_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( r2_card_lar(A,B) <=> ( r1_tarski(B,A) & ! [C] : ( ( 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) ) ) ) ) ) )).
fof(d2_cardfin2,axiom,( ! [A] : k2_cardfin2(A) = a_1_0_cardfin2(A) )).
fof(d2_cat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_cat_1(A,B,C) = a_3_0_cat_1(A,B,C) ) ) ) )).
fof(d2_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( C = k2_cat_2(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> m2_cat_1(D,A,B) ) ) ) ) )).
fof(d2_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ! [C] : ( ( 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] : ( ( 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] : ( r2_hidden(E,B) => k7_partfun1(u1_struct_0(A),D,E) = k4_graph_1(A,k7_partfun1(u4_struct_0(A),C,E)) ) ) ) ) ) )).
fof(d2_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ~ ( ? [C] : ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(B)) ) & ~ ! [C] : ( ( ~ 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)) ) ) ) ) ) ) )).
fof(d2_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(k7_domain_1(k4_ordinal1,k5_numbers,1)))) => ( C = k2_catalan2(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( v1_relat_1(E) & v5_relat_1(E,k4_ordinal1) & v1_funct_1(E) & v5_ordinal1(E) & v1_finset_1(E) & E = D & v1_catalan2(E) & k1_relset_1(k4_ordinal1,E) = A & k7_afinsq_2(E) = B ) ) ) ) ) ) )).
fof(d2_catalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( v1_catalg_1(B,A) <=> v3_relat_1(u3_msualg_1(A,B)) ) ) ) )).
fof(d2_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_cayldick(A,B) = k3_funct_2(u1_struct_0(A),u1_struct_0(A),u1_cayldick(A),B) ) ) )).
fof(d2_cayley,axiom,( ! [A] : ! [B] : ( ( v15_algstr_0(B) & v1_monoid_0(B) & l3_algstr_0(B) ) => ( B = k2_cayley(A) <=> ( u1_struct_0(B) = k1_cayley(A) & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k6_algstr_0(B,C,D) = k3_relat_1(C,D) ) ) ) ) ) )).
fof(d2_cc0sp1,axiom,( ! [A] : ( ( ~ 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] : ( 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] : ( v1_xcmplx_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => r2_hidden(k1_clvect_1(A,D,C),B) ) ) ) ) ) ) ) )).
fof(d2_cc0sp2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( v1_xcmplx_0(B) => k1_cc0sp2(A,B) = k7_funcop_1(u1_struct_0(A),B) ) ) )).
fof(d2_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [B] : ( r2_cfcont_1(A,B) <=> ( r1_tarski(B,k1_relset_1(k2_numbers,A)) & ! [C] : ( v1_xcmplx_0(C) => ( r2_hidden(C,B) => r1_cfcont_1(k5_relset_1(k2_numbers,k2_numbers,A,B),C) ) ) ) ) ) )).
fof(d2_cfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( B = k1_cfdiff_1(A) <=> ! [C] : ( v7_ordinal1(C) => k9_nat_1(k2_numbers,B,C) = k7_xcmplx_0(1,k2_xcmplx_0(C,A)) ) ) ) ) )).
fof(d2_cfuncdom,axiom,( ! [A] : ! [B] : ( ( 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] : ( m2_funct_2(C,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ! [D] : ( 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,k5_binop_2,C,D)) ) ) ) ) )).
fof(d2_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( 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(k5_numbers))) & ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,k1_relset_1(A,C)) => k7_partfun1(k2_numbers,C,D) = k5_xcmplx_0(k7_partfun1(k2_numbers,B,D)) ) ) ) ) ) ) ) )).
fof(d2_cgames_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( B = k2_cgames_1(A) <=> ? [C] : ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & r2_hidden(A,k9_xtuple_0(C)) & k1_funct_1(C,A) = B & ! [D] : ( v3_ordinal1(D) => ( r2_hidden(D,k9_xtuple_0(C)) => k1_funct_1(C,D) = a_2_0_cgames_1(C,D) ) ) ) ) ) )).
fof(d2_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v8_ordinal1(A) <=> ~ r1_xxreal_0(1,A) ) ) )).
fof(d2_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v1_chord(B,A) <=> ! [C] : ( 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)) ) ) ) ) ) )).
fof(d2_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ( v2_circcmb3(B,A) <=> ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => v1_circcmb3(C,A,B) ) ) ) ) )).
fof(d2_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ 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)) ) ) ) ) ) )).
fof(d2_circled1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( C = k1_circled1(A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(D,C) <=> ( v3_rltopsp1(D,A) & r1_tarski(B,D) ) ) ) ) ) ) ) )).
fof(d2_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_circtrm1(A,B,C))) => ! [E] : ( l3_msualg_1(E,A) => ! [F] : ( F = k2_circtrm1(A,B,C,D,E) <=> ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d2_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ( v1_msafree2(A) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_pboole(C,k2_msafree2(A),k7_funcop_1(k2_msafree2(A),k4_ordinal1),k5_relat_1(u3_msualg_1(A,B),k2_msafree2(A))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k2_circuit1(A,B,C,D) = k1_funct_1(k9_funct_6(C),D) ) ) ) ) ) )).
fof(d2_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msafree2(C,A,B) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d2_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_pdiff_7(C,A) & m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) ) => k1_ckspace1(A,B,C) = a_3_0_ckspace1(A,B,C) ) ) ) )).
fof(d2_classes1,axiom,( ! [A] : ( v2_classes1(A) <=> ( v1_classes1(A) & ! [B] : ( r2_hidden(B,A) => r2_hidden(k9_setfam_1(B),A) ) & ! [B] : ~ ( r1_tarski(B,A) & ~ r2_tarski(B,A) & ~ r2_hidden(B,A) ) ) ) )).
fof(d2_classes2,axiom,( k13_classes2 = k1_classes1(k1_xboole_0) )).
fof(d2_clopban1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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)) ) ) )).
fof(d2_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(k6_clopban1(A,A)),k8_clopban1(A,A)) => ! [C] : ( 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)) ) ) ) )).
fof(d2_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k1_clopban3(A,B) = k7_clvect_1(A,k1_bhsp_4(A,B)) ) ) )).
fof(d2_clopban4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( E = k2_clopban4(A,B,C,D) <=> ! [F] : ( v7_ordinal1(F) => ( ( r1_xxreal_0(F,A) => k1_normsp_1(B,E,F) = k6_algstr_0(B,k1_clvect_1(B,k6_clopban3(B,C,F),k9_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) ) ) ) ) ) ) ) ) ) )).
fof(d2_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m2_pboole(C,A,k5_mssubfam(A,B),k5_mssubfam(A,B)) => ( v2_closure1(C,A,B) <=> ! [D] : ( m1_pboole(D,A,k5_mssubfam(A,B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d2_closure2,axiom,( ! [A] : ( v4_funct_1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( A != k1_xboole_0 => ( B = k3_closure2(A) <=> ? [C] : ( ~ v1_xboole_0(C) & v4_funct_1(C) & C = A & k9_xtuple_0(B) = k1_setfam_1(a_1_0_closure2(C)) & ! [D] : ( 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 ) ) ) ) ) )).
fof(d2_closure3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) => ! [D] : ( m3_pboole(D,A,B) => ( D = k2_closure3(A,B,C) <=> ! [E] : ( r2_hidden(E,A) => k1_funct_1(D,E) = k3_tarski(a_4_0_closure3(A,B,C,E)) ) ) ) ) ) )).
fof(d2_clvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ( v2_clvect_1(A) <=> ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d2_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clvect_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k1_clvect_2(A,B) <=> ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(E,F) & r1_xxreal_0(D,k15_csspace(A,k1_normsp_1(A,B,F),C)) ) ) ) ) ) ) ) ) ) )).
fof(d2_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k1_clvect_3(A,B) = k1_clvect_2(A,k1_bhsp_4(A,B)) ) ) )).
fof(d2_coh_sp,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( 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] : ! [D] : ( r2_hidden(k4_tarski(C,D),B) <=> ? [E] : ( r2_hidden(E,A) & r2_hidden(C,E) & r2_hidden(D,E) ) ) ) ) ) )).
fof(d2_cohsp_1,axiom,( ! [A] : k1_cohsp_1(A) = k2_coh_sp(A,k6_partfun1(A)) )).
fof(d2_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d2_combgras,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_incsp_1(A))) => ( v1_combgras(B,A) <=> ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & ! [E] : ( m1_subset_1(E,u2_incsp_1(A)) => ~ r4_incsp_1(A,k7_domain_1(u1_incsp_1(A),C,D),E) ) ) ) ) ) ) ) )).
fof(d2_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( C = k1_compl_sp(A,B) <=> ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k3_tbsp_1(A,k9_nat_1(k9_setfam_1(u1_struct_0(A)),B,D)) ) ) ) ) ) )).
fof(d2_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( r2_hidden(A,k1_numbers) => ( B = k2_complex1(A) <=> B = k5_numbers ) ) & ( ~ r2_hidden(A,k1_numbers) => ( B = k2_complex1(A) <=> ? [C] : ( 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) ) ) ) ) ) )).
fof(d2_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xreal_0(B) => k2_complex2(A,B) = k2_xcmplx_0(k3_xcmplx_0(k9_complex1(A),k19_sin_cos(k2_xcmplx_0(B,k1_comptrig(A)))),k3_xcmplx_0(k3_xcmplx_0(k9_complex1(A),k17_sin_cos(k2_xcmplx_0(B,k1_comptrig(A)))),k7_complex1)) ) ) )).
fof(d2_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_complfld)) => ( m1_complfld(C,A,B) <=> k2_binop_1(u1_struct_0(k1_complfld),k4_ordinal1,u1_struct_0(k1_complfld),k4_group_1(k1_complfld),C,B) = A ) ) ) ) )).
fof(d2_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => k6_complsp2(A) = k10_seq_4(k7_seq_4(A,k1_complsp2(A)),k7_xcmplx_0(1,2)) ) )).
fof(d2_compos_0,axiom,( ! [A] : ( v1_compos_0(A) => k1_compos_0(A) = k11_xtuple_0(A) ) )).
fof(d2_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => k2_compos_1(A) = k6_compos_0(u1_compos_1(A)) ) )).
fof(d2_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( 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)) ) ) ) )).
fof(d2_comptrig,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( v1_xcmplx_0(C) => ( m1_comptrig(C,A,B) <=> k1_newton(C,B) = A ) ) ) ) )).
fof(d2_compts_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v9_pre_topc(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d2_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) ) => ( v2_comput_1(A) <=> ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & r2_hidden(B,k1_relset_1(k3_finseq_2(k4_ordinal1),A)) ) => r2_hidden(C,k1_relset_1(k3_finseq_2(k4_ordinal1),A)) ) ) ) ) ) )).
fof(d2_comseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,A) => k3_funct_2(A,k2_numbers,C,D) = k8_complex1(k3_funct_2(A,k2_numbers,B,D)) ) ) ) ) ) ) )).
fof(d2_comseq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v7_ordinal1(B) => k2_comseq_3(A,B) = k9_nat_1(k2_numbers,k1_comseq_3(A),B) ) ) )).
fof(d2_conaffm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v2_conaffm(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(d2_conmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v2_conmetr(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(A))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_conmetr1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v2_conmetr1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,k1_zfmisc_1(u1_struct_0(A))) => ! [L] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_connsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_connsp_1(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d2_connsp_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(d2_connsp_3,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( m1_connsp_3(B,A) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & ! [D] : ( 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) ) ) ) ) )).
fof(d2_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_convex1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => ( r1_xxreal_0(E,k5_numbers) | r1_xxreal_0(1,E) | r2_hidden(k1_algstr_0(A,k1_rlvect_1(A,C,E),k1_rlvect_1(A,D,k6_xcmplx_0(1,E))),B) ) ) ) ) ) ) ) ) )).
fof(d2_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( 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) ) ) )).
fof(d2_convfun1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_rlvect_1(B) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ( E = k1_domain_1(u1_struct_0(A),u1_struct_0(B),F,G) => k1_binop_1(C,D,E) = k4_tarski(k1_funct_1(u1_rlvect_1(A),k4_tarski(D,F)),k1_funct_1(u1_rlvect_1(B),k4_tarski(D,G))) ) ) ) ) ) ) ) ) ) )).
fof(d2_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => k3_cqc_lang(A) = a_1_0_cqc_lang(A) ) )).
fof(d2_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( 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] : ( m1_subset_1(E,B) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d2_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ( C = k1_cqc_the1(A,B) <=> ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ( r2_hidden(D,C) <=> ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k3_cqc_lang(A))) => ( ( v1_cqc_the1(E,A) & r1_tarski(B,E) ) => r2_hidden(D,E) ) ) ) ) ) ) ) ) )).
fof(d2_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ( r2_cqc_the3(A,B,C) <=> ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ( r2_hidden(D,C) => r3_cqc_the1(A,B,D) ) ) ) ) ) ) )).
fof(d2_csspace,axiom,( ! [A] : ( r2_hidden(A,k1_csspace) => k2_csspace(A) = A ) )).
fof(d2_csspace3,axiom,( ! [A] : ( ( 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] : ( r2_hidden(B,k1_csspace3) => k1_funct_1(A,B) = k4_series_1(k55_valued_1(k4_ordinal1,k2_numbers,k2_csspace(B))) ) ) ) )).
fof(d2_csspace4,axiom,( ! [A] : ( ( 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] : ( r2_hidden(B,k1_csspace4) => k1_funct_1(A,B) = k2_seq_4(k2_relset_1(k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,k2_csspace(B)))) ) ) ) )).
fof(d2_decomp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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))) ) ) ) )).
fof(d2_descip_1,axiom,( ! [A] : ( ( 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)) ) )).
fof(d2_diff_1,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_funct_1(A,k2_xcmplx_0(D,B)) ) ) ) ) ) )).
fof(d2_diff_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => k2_diff_2(A,B,C,D,E,F,G) = k7_xcmplx_0(k6_xcmplx_0(k1_diff_2(A,B,C,D,E,F),k1_diff_2(A,C,D,E,F,G)),k6_xcmplx_0(B,G)) ) ) ) ) ) ) ) )).
fof(d2_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_dilworth(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d2_diraf,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(d2_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : k3_dist_1(A,B,C) = k7_xcmplx_0(k2_dist_1(A,B,C),k3_finseq_1(B)) ) ) )).
fof(d2_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => k2_dist_2(A,B) = k3_funct_2(k6_dist_1(A),k3_finseq_2(k1_numbers),k7_dist_1(A),B) ) ) )).
fof(d2_dtconstr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_lang1(A) & l1_lang1(A) ) => ( A = k5_dtconstr <=> ( u1_struct_0(A) = k7_domain_1(k4_ordinal1,k5_numbers,1) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( r1_lang1(A,B,C) <=> ( B = 1 & ( C = k3_pre_poly(k4_ordinal1,k5_numbers) | C = k3_pre_poly(k4_ordinal1,1) ) ) ) ) ) ) ) ) )).
fof(d2_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_prob_2(B) <=> ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ~ r1_xxreal_0(D,C) => r1_xboole_0(k9_nat_1(k9_setfam_1(A),B,C),k9_nat_1(k9_setfam_1(A),B,D)) ) ) ) ) ) ) )).
fof(d2_e_siec,axiom,( ! [A] : ( 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 ) ) ) )).
fof(d2_ec_pf_2,axiom,( ! [A] : ( ( 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) ) )).
fof(d2_endalg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( 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] : ( m2_funct_2(C,u1_struct_0(A),u1_struct_0(A),k1_endalg(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d2_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k2_ens_1(A) = a_1_1_ens_1(A) ) )).
fof(d2_entropy1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( v7_ordinal1(B) => ( r1_entropy1(A,B) <=> ( r2_hidden(B,k4_finseq_1(A)) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(A)) => ( C = B | k1_funct_1(A,C) = k5_numbers ) ) ) ) ) ) ) )).
fof(d2_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( E = k2_enumset1(A,B,C,D) <=> ! [F] : ( r2_hidden(F,E) <=> ~ ( F != A & F != B & F != C & F != D ) ) ) )).
fof(d2_eqrel_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(d2_euclid,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => k1_funct_1(A,B) = k9_complex1(B) ) ) ) )).
fof(d2_euclid_3,axiom,( ! [A] : ( 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)) ) )).
fof(d2_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ( v1_euclid_4(B,A) <=> ? [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) & ? [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) & C != D & B = k2_euclid_4(A,C,D) ) ) ) ) ) )).
fof(d2_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => k2_euclid_5(A) = k1_funct_1(A,2) ) )).
fof(d2_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => k2_euclid_6(A,B,C) = k2_xcmplx_0(k2_xcmplx_0(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))) ) ) ) )).
fof(d2_euclid_7,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( 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),k4_ordinal1,A,C,B) ) ) )).
fof(d2_euclid_8,axiom,( k3_euclid_8 = k1_euclid_8(k5_numbers,1,k5_numbers) )).
fof(d2_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ( r3_euclidlp(A,B,C) <=> ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( k7_euclid(A,k9_euclid(A,B,D),k9_euclid(A,C,E)) = k5_euclid(A) => ( D = k5_numbers & E = k5_numbers ) ) ) ) ) ) ) ) )).
fof(d2_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ( v2_euclmetr(A) <=> v2_aff_2(k3_analmetr(A)) ) ) )).
fof(d2_exchsort,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v2_exchsort(B,A) <=> ! [C] : ( v3_ordinal1(C) => ( r2_hidden(C,k9_xtuple_0(B)) => ( r2_hidden(A,k9_xtuple_0(B)) & r1_ordinal1(A,C) ) ) ) ) ) )).
fof(d2_extpro_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( v2_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ! [D] : ( ( 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) ) ) ) ) )).
fof(d2_extreal1,axiom,( ! [A] : ( m2_finseq_1(A,k6_numbers) => ! [B] : ( m1_subset_1(B,k6_numbers) => ( B = k4_extreal1(A) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) & B = k12_supinf_2(C,k3_finseq_1(A)) & k12_supinf_2(C,k5_numbers) = k1_supinf_2 & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ~ r1_xxreal_0(k3_finseq_1(A),D) => k12_supinf_2(C,k1_nat_1(D,1)) = k3_supinf_2(k12_supinf_2(C,D),k12_supinf_2(A,k1_nat_1(D,1))) ) ) ) ) ) ) )).
fof(d2_facirc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_facirc_1(A) <=> ! [B] : ~ ( r2_hidden(B,k9_xtuple_0(A)) & v1_xtuple_0(k1_funct_1(A,B)) ) ) ) )).
fof(d2_fcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v1_fcont_1(A) <=> ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,k1_relset_1(k1_numbers,A)) => r1_fcont_1(A,B) ) ) ) ) )).
fof(d2_fdiff_1,axiom,( ! [A] : ( ( 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] : ( ( v1_funct_1(B) & v9_ordinal1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v1_fdiff_1(B,k5_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,B),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,B,A))) & k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,B),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,B,A))) = k5_numbers ) ) ) ) ) )).
fof(d2_fdiff_9,axiom,( k2_fdiff_9 = k6_rfunct_1(k1_numbers,k1_numbers,k16_sin_cos) )).
fof(d2_ff_siec,axiom,( ! [A] : k2_ff_siec(A) = k1_ff_siec(A,k1_xboole_0) )).
fof(d2_fib_num,axiom,( k2_fib_num = k7_xcmplx_0(k6_xcmplx_0(1,k3_square_1(5)),2) )).
fof(d2_fib_num2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ( A = k2_fib_num2 <=> ! [B] : ( m1_subset_1(B,k4_ordinal1) => k3_funct_2(k4_ordinal1,k4_ordinal1,A,B) = k1_pre_ff(B) ) ) ) )).
fof(d2_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_filter_0(A,B) = a_2_0_filter_0(A,B) ) ) )).
fof(d2_filter_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d2_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_filter_2(A,B) = B ) ) )).
fof(d2_fin_topo,axiom,( ! [A] : k3_fin_topo(A) = k1_tarski(k4_tarski(A,A)) )).
fof(d2_finseq_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_finseq_1(A) <=> ? [B] : ( v7_ordinal1(B) & k9_xtuple_0(A) = k2_finseq_1(B) ) ) ) )).
fof(d2_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : k2_finseq_2(A,B) = k7_funcop_1(k2_finseq_1(A),B) ) )).
fof(d2_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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(k4_ordinal1,k1_relset_1(k4_ordinal1,B),k1_tarski(A))),B) ) ) )).
fof(d2_finseq_4,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r2_finseq_4(A,B) <=> k1_card_1(k10_relat_1(A,B)) = 1 ) ) )).
fof(d2_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(d2_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( 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 ) ) ) ) ) )).
fof(d2_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(d2_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( 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,k1_nat_1(k7_nat_d(k3_finseq_1(B),k3_finseq_1(D)),1),k3_finseq_1(B)) & ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(E,k3_finseq_1(C)) & k3_finseq_8(A,C,1,E) = k3_finseq_8(A,B,k1_nat_1(k7_nat_d(k3_finseq_1(B),E),1),k3_finseq_1(B)) ) => r1_xxreal_0(E,k3_finseq_1(D)) ) ) ) ) ) ) ) ) )).
fof(d2_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(d2_finsub_1,axiom,( ! [A] : ( v2_finsub_1(A) <=> ! [B] : ! [C] : ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r2_hidden(k3_xboole_0(B,C),A) ) ) )).
fof(d2_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(d2_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(u1_struct_0(A))))) ) => ( C = k2_fintopo3(A,B) <=> ( ! [D] : ( v7_ordinal1(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( E = k1_funct_1(C,D) => k3_funct_2(k4_ordinal1,k1_zfmisc_1(u1_struct_0(A)),C,k1_nat_1(D,1)) = k9_fin_topo(A,E) ) ) ) & k3_funct_2(k4_ordinal1,k1_zfmisc_1(u1_struct_0(A)),C,k5_numbers) = B ) ) ) ) ) )).
fof(d2_fintopo4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,k4_ordinal1) => ( r2_fintopo4(A,B,C,D) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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,k5_numbers,E)),k10_fintopo3(B,D,F)) ) ) ) ) ) ) ) ) )).
fof(d2_fintopo5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( 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] : ( r2_hidden(D,k2_zfmisc_1(k2_finseq_1(A),k2_finseq_1(B))) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( 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)) ) ) ) ) ) ) ) ) )).
fof(d2_fintopo6,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ( m1_fintopo6(B,A) <=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A)) & ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(d2_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_catalan2(A))) => ( D = k7_flang_1(A,B,C) <=> ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k9_setfam_1(k3_catalan2(A))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k3_catalan2(A))))) & D = k5_flang_1(k3_catalan2(A),E,C) & k5_flang_1(k3_catalan2(A),E,k5_numbers) = k4_flang_1(A,k2_flang_1(A)) & ! [F] : ( v7_ordinal1(F) => k5_flang_1(k3_catalan2(A),E,k1_nat_1(F,1)) = k6_flang_1(A,k5_flang_1(k3_catalan2(A),E,F),B) ) ) ) ) ) ) )).
fof(d2_flang_2,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(d2_flang_3,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(d2_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( v2_fomodel0(C,A,B) <=> v1_fomodel0(B,k2_zfmisc_1(C,A)) ) ) ) )).
fof(d2_fomodel1,axiom,( ! [A] : ( 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(k4_ordinal1,k5_numbers)) ) )).
fof(d2_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v10_fomodel1(C,A) & m1_subset_1(C,k1_fomodel1(A)) ) => ! [D] : ( ( 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))) ) ) ) ) ) ) ) )).
fof(d2_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_fomodel1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k3_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(k3_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] : ( m2_subset_1(D,k3_finseq_2(k3_finseq_2(k1_fomodel1(A))),k3_fomodel0(k3_finseq_2(k1_fomodel1(A)),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0)))) => k3_funct_2(k3_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) ) ) ) ) ) )).
fof(d2_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( v1_fomodel4(B,A) <=> r2_hidden(B,k1_fomodel4(A)) ) ) )).
fof(d2_frechet,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ( v1_frechet(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( 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) ) ) ) ) )).
fof(d2_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & k2_frechet(A,B) = k6_domain_1(u1_struct_0(A),C) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k2_frechet2(A,B) <=> r1_frechet(A,B,C) ) ) ) ) ) )).
fof(d2_friends1,axiom,( ! [A] : ( v1_relat_1(A) => ( v2_friends1(A) <=> ? [B] : ( m1_subset_1(B,k1_relat_1(A)) & v1_friends1(B,A) ) ) ) )).
fof(d2_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : k2_fscirc_1(A,B,C) = k10_facirc_1(A,B,C,k1_facirc_1) )).
fof(d2_fscirc_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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] : ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) & ? [F] : ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) & ? [G] : ( v1_relat_1(G) & v4_relat_1(G,k4_ordinal1) & v1_funct_1(G) & v1_partfun1(G,k4_ordinal1) & k1_fscirc_2(A,B,C) = k1_funct_1(E,A) & D = k1_funct_1(F,A) & k1_funct_1(E,k5_numbers) = k5_circcomb(k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k8_margrel1),k1_xboole_0) & k1_funct_1(F,k5_numbers) = k7_circcomb(k5_ordinal1,k6_margrel1,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k8_margrel1),k1_xboole_0) & k1_funct_1(G,k5_numbers) = k4_tarski(k1_xboole_0,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k8_margrel1)) & ! [H] : ( v7_ordinal1(H) => ! [I] : ( ( ~ v2_struct_0(I) & l1_msualg_1(I) ) => ! [J] : ( ( v4_msualg_1(J,I) & l3_msualg_1(J,I) ) => ! [K] : ( ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( 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) = k1_nat_1(k3_finseq_1(D),1) & ! [F] : ( v7_ordinal1(F) => ~ ( r1_xxreal_0(1,F) & r1_xxreal_0(F,k3_finseq_1(D)) & ! [G] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,A) => ( r1_fsm_2(A,B,C,D) <=> ? [E] : ( 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) ) ) ) ) ) ) )).
fof(d2_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : 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)) )).
fof(d2_funcop_1,axiom,( ! [A] : ! [B] : k2_funcop_1(A,B) = k2_zfmisc_1(A,k1_tarski(B)) )).
fof(d2_funcsdom,axiom,( ! [A] : ! [B] : ( ( 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] : ( m2_funct_2(C,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [D] : ( 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,k11_binop_2,C,D)) ) ) ) ) )).
fof(d2_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( ( 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 ) ) ) ) )).
fof(d2_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( C = k1_funct_2(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( v1_relat_1(E) & v1_funct_1(E) & D = E & k9_xtuple_0(E) = A & r1_tarski(k10_xtuple_0(E),B) ) ) ) )).
fof(d2_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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] : ( r1_tarski(C,k10_xtuple_0(A)) => k1_funct_1(B,C) = k8_relat_1(A,C) ) ) ) ) ) )).
fof(d2_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k2_funct_4(A) <=> ( ! [C] : ( r2_hidden(C,k9_xtuple_0(B)) <=> ? [D] : ? [E] : ( C = k4_tarski(E,D) & r2_hidden(k4_tarski(D,E),k9_xtuple_0(A)) ) ) & ! [C] : ! [D] : ( r2_hidden(k4_tarski(C,D),k9_xtuple_0(A)) => k1_binop_1(B,D,C) = k1_binop_1(A,C,D) ) ) ) ) ) )).
fof(d2_funct_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k2_funct_5(A) <=> ( ! [C] : ( r2_hidden(C,k9_xtuple_0(B)) <=> ? [D] : ? [E] : ( v1_relat_1(E) & v1_funct_1(E) & ? [F] : ( 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] : ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(d2_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k2_funct_6(A) <=> ( k9_xtuple_0(B) = k9_xtuple_0(A) & ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => k1_funct_1(B,C) = k10_xtuple_0(k1_funct_1(A,C)) ) ) ) ) ) )).
fof(d2_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( ( r2_hidden(B,k9_xtuple_0(A)) => k1_funct_7(A,B,C) = k1_funct_4(A,k16_funcop_1(B,C)) ) & ( ~ r2_hidden(B,k9_xtuple_0(A)) => k1_funct_7(A,B,C) = A ) ) ) )).
fof(d2_funct_8,axiom,( ! [A] : ( v1_relat_1(A) => ( v2_funct_8(A) <=> v1_funct_8(k9_xtuple_0(A)) ) ) )).
fof(d2_funct_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_9(A) <=> ? [B] : ( v1_xreal_0(B) & v1_funct_9(A,B) ) ) ) )).
fof(d2_functor0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( 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))) ) ) ) )).
fof(d2_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v15_functor0(D,B,C) & m2_functor0(D,B,C) ) => ! [E] : ( ( v15_functor0(E,B,C) & m2_functor0(E,B,C) ) => ! [F] : ( ( v15_functor0(F,A,B) & m2_functor0(F,A,B) ) => ! [G] : ( m1_functor2(G,B,C,D,E) => ( r1_functor2(B,C,D,E) => ! [H] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( m1_subset_1(D,A) => r1_xxreal_0(k3_funct_2(A,k1_numbers,B,D),k3_funct_2(A,k1_numbers,C,D)) ) ) ) ) ) )).
fof(d2_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( m1_subset_1(E,A) => k3_funct_2(A,k1_numbers,D,E) = k4_real_1(k3_funct_2(A,k1_numbers,B,E),k3_funct_2(A,k1_numbers,C,E)) ) ) ) ) ) ) )).
fof(d2_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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] : ! [G] : ( ( r2_hidden(F,A) & r2_hidden(G,C) ) => ! [H] : ( ( v5_relat_1(H,k1_rcomp_1(k5_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 = k2_fuzzy_4(A,B,C,D,E,F,G) <=> ! [I] : ( m1_subset_1(I,B) => k1_funct_1(H,I) = k3_xxreal_0(k1_funct_1(D,k4_tarski(F,I)),k1_funct_1(E,k4_tarski(I,G))) ) ) ) ) ) ) ) ) ) )).
fof(d2_fvaluat1,axiom,( ! [A] : ( v2_membered(A) => ( ? [B] : ( v2_xxreal_0(B) & v1_fvaluat1(B) & r2_hidden(B,A) ) => ! [B] : ( ( v2_xxreal_0(B) & v1_fvaluat1(B) ) => ( B = k1_fvaluat1(A) <=> ( r2_hidden(B,A) & ! [C] : ( ( v2_xxreal_0(C) & v1_fvaluat1(C) ) => ( r2_hidden(C,A) => r1_xxreal_0(B,C) ) ) ) ) ) ) ) )).
fof(d2_fvsum_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d2_gate_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_gate_5(A,B,C,D) = k10_gate_1(k2_gate_1(B,C),k2_gate_1(A,D),k1_xboole_0) )).
fof(d2_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_gcd_1(B,A) <=> r1_gcd_1(A,B,k5_struct_0(A)) ) ) ) )).
fof(d2_genealg1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_finseq_1(B,k3_card_3(A)) => ! [C] : ( m2_finseq_1(C,k3_card_3(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => 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)) ) ) ) ) )).
fof(d2_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d2_gfacirc1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => k1_funct_1(A,k10_binarith(k6_margrel1,B)) = B ) ) ) )).
fof(d2_gfacirc2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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] : ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) & ? [F] : ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) & ? [G] : ( v1_relat_1(G) & v4_relat_1(G,k4_ordinal1) & v1_funct_1(G) & v1_partfun1(G,k4_ordinal1) & k1_gfacirc2(A,B,C) = k1_funct_1(E,A) & D = k1_funct_1(F,A) & k1_funct_1(E,k5_numbers) = k5_circcomb(k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1),k1_xboole_0) & k1_funct_1(F,k5_numbers) = k7_circcomb(k5_ordinal1,k6_margrel1,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1),k1_xboole_0) & k1_funct_1(G,k5_numbers) = k4_tarski(k1_xboole_0,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1)) & ! [H] : ( v7_ordinal1(H) => ! [I] : ( ( ~ v2_struct_0(I) & l1_msualg_1(I) ) => ! [J] : ( ( v4_msualg_1(J,I) & l3_msualg_1(J,I) ) => ! [K] : ( ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_glib_000,axiom,( k2_glib_000 = 2 )).
fof(d2_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m2_finseq_1(B,k7_glib_000(A)) => ( m2_glib_001(B,A) <=> ? [C] : ( m2_finseq_1(C,k6_glib_000(A)) & k3_finseq_1(C) = k1_nat_1(k3_finseq_1(B),1) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( 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,k1_nat_1(D,1)),k1_funct_1(B,D)) ) ) ) ) ) ) )).
fof(d2_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ( v2_glib_002(A) <=> ! [B] : ( m3_glib_001(B,A) => ~ v8_glib_001(B,A) ) ) ) )).
fof(d2_glib_003,axiom,( k3_glib_003 = 6 )).
fof(d2_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( ( v2_glib_001(B,A) & v5_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ! [D] : ( r2_glib_004(A,B,C,D) <=> ( r1_glib_001(A,C,D,B) & ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(d2_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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] : ! [D] : ( r1_glib_005(A,B,C,D) <=> ( m1_subset_1(C,k6_glib_000(A)) & m1_subset_1(D,k6_glib_000(A)) & ! [E] : ( r2_hidden(E,k7_glib_000(A)) => ( r1_xxreal_0(k5_numbers,k1_funct_1(B,E)) & r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(k5_glib_003(A),E)) ) ) & ! [E] : ( m1_subset_1(E,k6_glib_000(A)) => ~ ( E != C & E != D & k2_uproots(k26_glib_000(A,E),k5_relat_1(B,k26_glib_000(A,E))) != k2_uproots(k27_glib_000(A,E),k5_relat_1(B,k27_glib_000(A,E))) ) ) ) ) ) ) )).
fof(d2_goboard1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( B = k2_goboard1(A) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => k1_funct_1(B,C) = k18_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),A,C)) ) ) ) ) ) ) )).
fof(d2_goboard2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => k2_goboard2(A) = k1_goboard2(k26_seq_4(k1_goboard1(A)),k26_seq_4(k2_goboard1(A))) ) )).
fof(d2_goboard4,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_goboard4(A,B,C) <=> ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(A)) => ( r1_xxreal_0(B,k1_funct_1(A,D)) & r1_xxreal_0(k1_funct_1(A,D),C) ) ) ) ) ) ) ) )).
fof(d2_goboard5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) => ( r1_xxreal_0(k1_matrix_0(A),B) | k2_goboard5(A,B) = a_2_3_goboard5(A,B) ) ) & ( r1_xxreal_0(k1_matrix_0(A),B) => k2_goboard5(A,B) = a_2_4_goboard5(A,B) ) & ~ ( ~ ( r1_xxreal_0(1,B) & ~ r1_xxreal_0(k1_matrix_0(A),B) ) & ~ r1_xxreal_0(k1_matrix_0(A),B) & k2_goboard5(A,B) != a_2_5_goboard5(A,B) ) ) ) ) )).
fof(d2_goboard9,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(d2_gobrd10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_gobrd10(A,B,C,D) <=> ( ( r1_gobrd10(A,C) & B = D ) | ( A = C & r1_gobrd10(B,D) ) ) ) ) ) ) ) )).
fof(d2_gobrd13,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(A)) & r1_goboard1(u1_struct_0(k15_euclid(2)),A,B) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( D = k3_gobrd13(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ~ ( r2_hidden(k4_tarski(E,F),k2_matrix_0(B)) & r2_hidden(k4_tarski(G,H),k2_matrix_0(B)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),B,E,F) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),B,G,H) & ~ ( E = G & k1_nat_1(F,1) = H & D = k3_goboard5(B,k7_nat_d(E,1),F) ) & ~ ( k1_nat_1(E,1) = G & F = H & D = k3_goboard5(B,E,F) ) & ~ ( E = k1_nat_1(G,1) & F = H & D = k3_goboard5(B,G,k7_nat_d(H,1)) ) & ~ ( E = G & F = k1_nat_1(H,1) & D = k3_goboard5(B,E,H) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ( v2_goedelcp(B,A) <=> ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ? [E] : ( 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))) ) ) ) ) ) ) )).
fof(d2_gr_cy_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => k1_gr_cy_1(A) = k1_finsop_1(k4_numbers,A,k20_binop_2) ) )).
fof(d2_gr_cy_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( v2_gr_cy_3(A) <=> ( v7_ordinal1(k1_nat_1(k3_xcmplx_0(2,A),1)) & v1_int_2(k1_nat_1(k3_xcmplx_0(2,A),1)) ) ) ) )).
fof(d2_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(d2_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u4_struct_0(A))) => ( D = k3_graph_3(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ( r2_hidden(E,u4_struct_0(A)) & r2_hidden(E,C) & k1_funct_1(u1_graph_1(A),E) = B ) ) ) ) ) ) )).
fof(d2_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u4_struct_0(A)) => k2_graph_5(A,B) = a_2_2_graph_5(A,B) ) ) )).
fof(d2_graphsp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_funct_2(A,A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_funct_2(A,A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_funct_2(A,A)))) ) => ( C = k5_graphsp(A,B) <=> ( k9_nat_1(k1_funct_2(A,A),C,k5_numbers) = k11_cqc_sim1(A) & ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_funct_2(A,A),C,k1_nat_1(D,1)) = k3_graphsp(A,k9_nat_1(k1_funct_2(A,A),C,D),B) ) ) ) ) ) )).
fof(d2_grcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(d2_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ( v1_grnilp_1(A) <=> ? [B] : ( m2_finseq_1(B,k2_grnilp_1(A)) & ~ r1_xxreal_0(k3_finseq_1(B),k5_numbers) & k1_funct_1(B,1) = k7_group_2(A) & k1_funct_1(B,k3_finseq_1(B)) = k6_group_2(A) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(k2_xcmplx_0(C,1),k4_finseq_1(B)) ) => ! [D] : ( ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) ) => ! [E] : ( ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(d2_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k15_pre_poly(A))) => k3_groeb_1(A,B) = a_2_0_groeb_1(A,B) ) ) )).
fof(d2_groeb_2,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : k1_funct_1(D,E) = k4_xxreal_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) )).
fof(d2_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(E,k5_card_1(k3_polynom1(k15_pre_poly(A),C,D))) => ! [F] : ( ( 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,k3_polynom1(k15_pre_poly(A),C,D)) & k5_card_1(F) = E & ! [G] : ( ( 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] : ( ( 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,k3_polynom1(k15_pre_poly(A),C,D)) & r1_termord(A,B,G,H) ) => r2_hidden(H,F) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_group_1,axiom,( ! [A] : ( l3_algstr_0(A) => ( v2_group_1(A) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k6_algstr_0(A,C,B) = C & k6_algstr_0(A,B,C) = C & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & k6_algstr_0(A,C,D) = B & k6_algstr_0(A,D,C) = B ) ) ) ) ) ) )).
fof(d2_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_group_2(C,A) => k2_group_11(A,B,C) = a_3_1_group_11(A,B,C) ) ) ) )).
fof(d2_group_12,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(d2_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(d2_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d2_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( 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)) ) ) )).
fof(d2_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d2_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ( v7_struct_0(A) <=> ? [B] : u1_struct_0(A) = k1_tarski(B) ) ) )).
fof(d2_group_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_group_7(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k4_card_3(k12_pralg_1(A,B))) => ! [E] : ( m1_subset_1(E,k4_card_3(k12_pralg_1(A,B))) => ! [F] : ~ ( r2_hidden(F,A) & ! [G] : ( ( ~ v2_struct_0(G) & l3_algstr_0(G) ) => ! [H] : ( ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_groupp_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ( v2_group_10(B,A) => ! [C] : ( v7_ordinal1(C) => ( C = k1_groupp_1(A,B) <=> k7_struct_0(B) = k1_newton(A,C) ) ) ) ) ) )).
fof(d2_grsolv_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(d2_hahnban,axiom,( ! [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) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k1_numbers,B,k3_rlvect_1(A,C,D)) = k3_real_1(k3_funct_2(u1_struct_0(A),k1_numbers,B,C),k3_funct_2(u1_struct_0(A),k1_numbers,B,D)) ) ) ) ) ) )).
fof(d2_hahnban1,axiom,( k2_hahnban1 = k7_complex1 )).
fof(d2_hallmar1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ! [E] : ( m2_finseq_1(E,k1_zfmisc_1(A)) => ( E = k2_hallmar1(A,B,C,D) <=> ( k4_finseq_1(E) = k4_finseq_1(B) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( ( v5_glib_001(D,A) & m3_glib_001(D,A) ) => ( D = k2_helly(A,B,C) <=> r1_glib_001(A,B,C,D) ) ) ) ) ) )).
fof(d2_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ( v1_henmodel(B,A) <=> ! [C] : ( 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)) ) ) ) ) ) )).
fof(d2_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(d2_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => k2_heyting2(A,B,C) = a_3_0_heyting2(A,B,C) ) ) )).
fof(d2_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_partfun1(k4_ordinal1,k6_domain_1(k4_ordinal1,B))) => ( C = k2_heyting3(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ~ ( ! [E] : ( ( ~ v1_abian(E) & m1_subset_1(E,k4_ordinal1) ) => ~ ( r1_xxreal_0(E,k2_nat_1(2,A)) & k1_domain_1(k4_ordinal1,k4_ordinal1,E,B) = D ) ) & k1_domain_1(k4_ordinal1,k4_ordinal1,k2_nat_1(2,A),B) != D ) ) ) ) ) ) )).
fof(d2_hilbasis,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => k2_hilbasis(A,B) = k1_funct_7(k16_pre_poly(A),B,1) ) )).
fof(d2_hilbert3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k4_ordinal1) => k1_funct_1(B,k1_hilbert2(C)) = k1_funct_1(A,C) ) & ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(d2_hurwitz,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k2_hurwitz(A,B) = k6_xcmplx_0(k1_algseq_1(A,B),1) ) ) )).
fof(d2_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k6_margrel1) ) => ! [D] : ( ( v3_card_1(D,A) & m2_finseq_1(D,k6_margrel1) ) => ( D = k2_idea_1(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ( 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)) ) ) ) ) ) ) ) )).
fof(d2_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_ideal_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => r2_hidden(k6_algstr_0(A,C,D),B) ) ) ) ) ) ) )).
fof(d2_incproj,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_incproj(A)))) => ( B = k2_incproj(A) <=> ! [C] : ! [D] : ( r2_hidden(k4_tarski(C,D),B) <=> ( r2_hidden(C,u1_struct_0(A)) & r2_hidden(D,k1_incproj(A)) & ? [E] : ( D = E & r2_hidden(C,E) ) ) ) ) ) ) )).
fof(d2_index_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_index_1(A) ) => ! [B] : ( ( 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] : ( r2_hidden(C,k9_xtuple_0(A)) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(d2_instalg1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( l1_msualg_1(B) => ( m1_instalg1(B,A) <=> r3_pua2mss1(B,A,k6_partfun1(u1_struct_0(B)),k6_partfun1(u4_struct_0(B))) ) ) ) )).
fof(d2_int_1,axiom,( ! [A] : ( v1_int_1(A) <=> r2_hidden(A,k4_numbers) ) )).
fof(d2_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ( C = k3_int_2(A,B) <=> ( r1_int_1(C,A) & r1_int_1(C,B) & ! [D] : ( v1_int_1(D) => ( ( r1_int_1(D,A) & r1_int_1(D,B) ) => r1_int_1(D,C) ) ) ) ) ) ) ) )).
fof(d2_int_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( r1_int_4(A,B) <=> ? [C] : ( m2_finseq_1(C,k4_numbers) & B = k1_rvsum_1(C) & k3_finseq_1(C) = A & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,C)) => r2_hidden(k1_funct_1(C,D),k6_eqrel_1(k4_numbers,k4_numbers,k1_int_4(A),k7_nat_d(D,1))) ) ) ) ) ) )).
fof(d2_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_int_5(A,B) <=> ? [C] : ( v1_int_1(C) & k5_int_1(k6_xcmplx_0(k1_pepin(C),A),B) = k5_numbers ) ) ) ) )).
fof(d2_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_int_6(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(d2_int_7,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,1) => k1_int_7(A) = k7_subset_1(k4_ordinal1,k7_card_1(A),k6_domain_1(k4_ordinal1,k5_numbers)) ) ) )).
fof(d2_int_8,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r1_int_8(A,B) <=> ? [C] : ( m2_finseq_1(C,k4_numbers) & k3_finseq_1(C) = k3_finseq_1(k14_finseq_1(k2_int_8(B))) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,C)) => r2_hidden(k1_funct_1(C,D),k6_eqrel_1(k4_numbers,k4_numbers,k1_int_4(B),k1_funct_1(k14_finseq_1(k2_int_8(B)),D))) ) ) & A = k2_relset_1(k4_numbers,C) ) ) ) )).
fof(d2_integr10,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r2_integr10(A,B,C) <=> ( ! [D] : ( v1_xreal_0(D) => ( 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] : ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,k1_relset_1(k1_numbers,D)) => k1_funct_1(D,E) = k4_integra5(E,C,A) ) ) & r4_limfunc2(D,B) ) ) ) ) ) ) )).
fof(d2_integr15,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => ! [C] : ( m1_integra1(C,A) => ! [D] : ( m1_integr15(D,A,B,C) => k1_integr15(A,B,C,D) = k18_rvsum_1(D) ) ) ) ) )).
fof(d2_integr16,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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] : ( m1_integra1(C,A) => ! [D] : ( m1_integr16(D,A,B,C) => k3_integr16(A,B,C,D) = k17_rvsum_1(D) ) ) ) ) )).
fof(d2_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( m1_integra1(D,B) => ! [E] : ( m1_integr18(E,A,B,C,D) => k1_integr18(A,B,C,D,E) = k4_rlvect_1(A,E) ) ) ) ) ) )).
fof(d2_integr1c,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k1_numbers)) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [G] : ( v1_xcmplx_0(G) => ( G = k2_integr1c(A,B,C,D,E,F) <=> ? [H] : ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( B = k1_integra1(A) <=> ! [C] : ( r2_hidden(C,B) <=> m1_integra1(C,A) ) ) ) )).
fof(d2_integra2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_integra1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( D = k3_integra2(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k1_funct_1(D,E) = k6_integra1(A,B,k2_integra2(A,C,E)) ) ) ) ) ) ) )).
fof(d2_integra3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_integra1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( C = k2_integra3(A,B) <=> ! [D] : ( m1_subset_1(D,k4_ordinal1) => k3_funct_2(k4_ordinal1,k1_numbers,C,D) = k1_integra3(A,k2_integra2(A,B,D)) ) ) ) ) ) )).
fof(d2_integra5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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)) ) ) )).
fof(d2_integra7,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(d2_integra9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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) = k5_numbers ) ) ) ) )).
fof(d2_interva1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( m1_interva1(B,A) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) & ? [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) & B = k1_interva1(A,C,D) ) ) ) ) )).
fof(d2_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( B = k2_irrat_1(A) <=> ! [C] : ( v7_ordinal1(C) => k1_funct_1(B,C) = k3_xcmplx_0(k4_newton(A,C),k2_power(C,k4_xcmplx_0(A))) ) ) ) ) )).
fof(d2_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ( v12_cat_1(C,A,B) => k1_isocat_1(A,B,C) = k2_funct_1(C) ) ) ) ) )).
fof(d2_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,k6_cat_2(A,B),C) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => k3_isocat_2(A,B,C,D,E) = k1_funct_1(k1_funct_5(D),E) ) ) ) ) ) )).
fof(d2_isomichi,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) )).
fof(d2_jgraph_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ( 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,k1_nat_1(C,1))) ) ) ) ) ) ) ) )).
fof(d2_jgraph_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( 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(k2_xcmplx_0(k3_xcmplx_0(A,k17_euclid(F)),B),k2_xcmplx_0(k3_xcmplx_0(C,k18_euclid(F)),D)) ) ) ) ) ) ) ) )).
fof(d2_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k2_jgraph_6(A,B,C,D) = a_4_1_jgraph_6(A,B,C,D) ) ) ) ) )).
fof(d2_jordan1,axiom,( ! [A] : ( 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ? [C] : ( 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] : ( 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] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(d2_jordan10,axiom,( ! [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)))) ) => k2_jordan10(A) = a_1_1_jordan10(A) ) )).
fof(d2_jordan11,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( B = k4_jordan11(A) <=> ( ~ r1_xxreal_0(k1_matrix_0(k1_jordan8(A,k3_jordan11(A))),B) & r1_tarski(k3_goboard5(k1_jordan8(A,k3_jordan11(A)),k7_nat_d(k3_jordan1h(A,k3_jordan11(A)),1),B),k1_jordan2c(2,A)) & ! [C] : ( v7_ordinal1(C) => ( r1_tarski(k3_goboard5(k1_jordan8(A,k3_jordan11(A)),k7_nat_d(k3_jordan1h(A,k3_jordan11(A)),1),C),k1_jordan2c(2,A)) => ( r1_xxreal_0(k1_matrix_0(k1_jordan8(A,k3_jordan11(A))),C) | r1_xxreal_0(B,C) ) ) ) ) ) ) ) )).
fof(d2_jordan12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d2_jordan19,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))))) ) => ( B = k2_jordan19(A) <=> ! [C] : ( v7_ordinal1(C) => k2_kurato_2(k15_euclid(2),B,C) = k9_jordan6(k3_topreal1(2,k2_jordan9(A,C))) ) ) ) ) )).
fof(d2_jordan1e,axiom,( ! [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] : ( 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)),k2_jordan9(A,B),k18_pscomp_1(k3_topreal1(2,k2_jordan9(A,B)))),k22_pscomp_1(k3_topreal1(2,k2_jordan9(A,B)))) ) ) )).
fof(d2_jordan1h,axiom,( ! [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] : ( v7_ordinal1(B) => k3_jordan1h(A,B) = k1_nat_1(k11_newton(2,k7_nat_d(B,1)),2) ) ) )).
fof(d2_jordan1k,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( 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) ) ) ) )).
fof(d2_jordan20,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ( r2_jordan20(A,B,C,D,E) <=> ( r1_topreal1(k15_euclid(2),B,C,A) & r2_hidden(D,A) & k17_euclid(D) = E & ? [F] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_jordan21,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k1_jordan21(A) = k19_euclid(k7_xcmplx_0(k2_xcmplx_0(k8_pscomp_1(A),k6_pscomp_1(A)),2),k2_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(k7_xcmplx_0(k2_xcmplx_0(k8_pscomp_1(A),k6_pscomp_1(A)),2)))))) ) )).
fof(d2_jordan23,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v2_jordan23(A) <=> ! [B] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(1,B) & ~ r1_xxreal_0(k3_finseq_1(A),B) & k1_funct_1(A,B) = k1_funct_1(A,k1_nat_1(B,1)) ) ) ) ) )).
fof(d2_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(d2_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(d2_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r1_jordan4(A,B,C,D) <=> ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(A)) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_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] : ( 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_xcmplx_0(C,E),1),A)) ) ) ) ) ) ) ) ) )).
fof(d2_jordan5c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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] : ( 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] : ( ( 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] : ( v1_xreal_0(G) => ( ( v3_tops_2(F,k5_topmetr,k1_pre_topc(k15_euclid(2),A)) & k1_funct_1(F,k5_numbers) = C & k1_funct_1(F,1) = D & k1_funct_1(F,G) = E & r1_xxreal_0(k5_numbers,G) & r1_xxreal_0(G,1) ) => ! [H] : ( v1_xreal_0(H) => ~ ( r1_xxreal_0(H,1) & ~ r1_xxreal_0(H,G) & r2_hidden(k1_funct_1(F,H),B) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( B = k2_jordan5d(A) <=> ( r2_hidden(k4_tarski(1,B),k2_matrix_0(k2_goboard2(A))) & k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,B) = k19_pscomp_1(k3_topreal1(2,A)) ) ) ) ) )).
fof(d2_knaster,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(d2_kolmog01,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( 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] : ( 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))) ) ) ) ) ) ) )).
fof(d2_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( C = k4_kurato_0(A,B) <=> ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & C = k2_kurato_0(A,D) & ! [E] : ( v7_ordinal1(E) => k1_funct_1(D,E) = k1_kurato_0(A,k8_nat_1(k9_setfam_1(A),B,E)) ) ) ) ) ) )).
fof(d2_kurato_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))))))))) ) ) )).
fof(d2_kurato_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k3_kurato_2(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( m2_valued_0(E,k9_setfam_1(u1_struct_0(A)),B) & r2_hidden(D,k1_kurato_2(A,E)) ) ) ) ) ) ) )).
fof(d2_lang1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => k1_lang1(A) = a_1_0_lang1(A) ) )).
fof(d2_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,D,B,C) & m2_finseq_1(E,k3_finseq_2(D)) ) => ! [F] : ( m2_finseq_1(F,D) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,D,B,C) & m2_finseq_1(G,k3_finseq_2(D)) ) => ( ( 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_0(G) = k1_matrix_0(E) & ! [H] : ( v7_ordinal1(H) => ! [I] : ( v7_ordinal1(I) => ( r2_hidden(k4_tarski(H,I),k2_matrix_0(E)) => ( ( I != A => k3_matrix_0(D,G,H,I) = k3_matrix_0(D,E,H,I) ) & ( I = A => k3_matrix_0(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 ) ) ) ) ) ) ) ) ) ) )).
fof(d2_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_group_3(A))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(d2_latsum_1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( ( 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))) ) ) ) ) ) )).
fof(d2_lattice2,axiom,( ! [A] : ( l3_lattices(A) => k1_lattice2(A) = g3_lattices(u1_struct_0(A),u1_lattices(A),u2_lattices(A)) ) )).
fof(d2_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => k3_lattice3(A) = g1_orders_2(u1_struct_0(A),k2_lattice3(A)) ) )).
fof(d2_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ( r1_filter_1(A,B) <=> ? [C] : ( m1_lattice4(C,A,B) & v3_funct_2(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) )).
fof(d2_lattice5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v3_lattice3(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r1_lattice3(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_lattice3(A,B,D) => r1_orders_2(A,D,C) ) ) ) ) ) ) )).
fof(d2_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_lattice3(A)))) => k2_lattice6(A,B) = a_2_1_lattice6(A,B) ) ) )).
fof(d2_lattice7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_orders_2(A,B,C) => ! [D] : ( ( ~ 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] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(E,D) => ( r3_orders_2(A,B,E) & r3_orders_2(A,E,C) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_lattice8,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k4_ordinal1) => ( r1_lattice8(A,B) <=> ? [C] : ( ~ v1_zfmisc_1(C) & ? [D] : ( 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] : ( 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) ) ) ) ) ) )).
fof(d2_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d2_lexbfs,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_lexbfs(A) <=> r1_tarski(k10_xtuple_0(A),k1_zfmisc_1(k4_ordinal1)) ) ) )).
fof(d2_limfunc1,axiom,( ! [A] : ( v1_xreal_0(A) => k2_limfunc1(A) = k2_xxreal_1(A,k1_xxreal_0) ) )).
fof(d2_limfunc2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r2_limfunc2(A,B) <=> ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(B,C) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,C) & ~ r1_xxreal_0(B,D) & r2_hidden(D,k1_relset_1(k1_numbers,A)) ) ) ) ) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(C) & k1_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(k4_ordinal1,k1_numbers,k1_numbers,C,A)) ) ) ) ) ) ) )).
fof(d2_limfunc3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r2_limfunc3(A,B) <=> ( ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(B,C) & ~ r1_xxreal_0(D,B) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ~ ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(C) & k1_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(k4_ordinal1,k1_numbers,k1_numbers,C,A)) ) ) ) ) ) ) )).
fof(d2_lmod_5,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(d2_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v7_vectsp_1(C,A) & m1_vectsp_4(C,A,B) ) => k1_lmod_6(A,B,C) = C ) ) ) )).
fof(d2_lopban_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( m2_funct_2(E,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => ! [F] : ( m1_subset_1(F,A) => k1_funct_1(k1_funct_1(C,k4_tarski(D,E)),F) = k1_rlvect_1(B,k3_funct_2(A,u1_struct_0(B),E,F),D) ) ) ) ) ) ) ) )).
fof(d2_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(k8_lopban_1(A,A)),k10_lopban_1(A,A)) => ! [C] : ( 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)) ) ) ) )).
fof(d2_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k1_lopban_3(A,B) = k6_normsp_1(A,k1_bhsp_4(A,B)) ) ) )).
fof(d2_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( C = k1_lopban_4(A,B) <=> ! [D] : ( v7_ordinal1(D) => k9_nat_1(u1_struct_0(A),C,D) = k1_rlvect_1(A,k6_lopban_3(A,B,D),k7_xcmplx_0(1,k2_newton(D))) ) ) ) ) ) )).
fof(d2_lopban_5,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k16_lopban_1(A,B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k16_lopban_1(A,B))))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( E = k2_lopban_5(A,B,C,D) <=> ! [F] : ( v7_ordinal1(F) => k5_rsspace3(B,E,F) = k17_lopban_1(A,B,k5_rsspace3(k16_lopban_1(A,B),C,F),D) ) ) ) ) ) ) ) )).
fof(d2_lopban_7,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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)))) ) => k4_lopban_7(A,B,C) = k17_funct_3(u1_struct_0(k7_prvect_3(A,B)),k1_numbers,u1_normsp_0(k7_prvect_3(A,B)),k3_lopban_7(A,B,C)) ) ) ) )).
fof(d2_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k1_lopclset(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d2_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k6_rsspace))) ) => ( B = k2_lp_space(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( r2_hidden(C,k1_rsspace) & v1_series_1(k1_lp_space(k2_rsspace(C),A)) ) ) ) ) ) ) )).
fof(d2_lpspacc1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_lpspacc1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => k6_lpspacc1(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)) ) ) )).
fof(d2_lpspace1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(d2_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v2_xxreal_0(D) & v1_xreal_0(D) ) => k1_lpspace2(A,B,C,D) = a_4_0_lpspace2(A,B,C,D) ) ) ) ) )).
fof(d2_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => k2_ltlaxio1(A) = k4_hilbert1(k2_hilbert1,A) ) )).
fof(d2_ltlaxio2,axiom,( ! [A] : ( m2_finseq_1(A,k1_hilbert1) => ! [B] : ( m2_finseq_1(B,k1_hilbert1) => ( ( ~ r1_xxreal_0(k3_finseq_1(A),k5_numbers) => ( B = k2_ltlaxio2(A) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & k1_funct_1(B,1) = k1_funct_1(A,1) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_xxreal_0(1,C) => ( r1_xxreal_0(k3_finseq_1(A),C) | k1_funct_1(B,k1_nat_1(C,1)) = k4_ltlaxio1(k7_partfun1(k1_hilbert1,B,C),k7_partfun1(k1_hilbert1,A,k1_nat_1(C,1))) ) ) ) ) ) ) & ( r1_xxreal_0(k3_finseq_1(A),k5_numbers) => ( B = k2_ltlaxio2(A) <=> B = k12_finseq_1(k1_hilbert1,k3_ltlaxio1) ) ) ) ) ) )).
fof(d2_ltlaxio3,axiom,( ! [A] : ! [B] : ( B = k1_ltlaxio3(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( v2_funct_1(C) & m2_finseq_1(C,A) ) ) ) )).
fof(d2_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( v1_ltlaxio4(A) <=> ? [B] : ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) & ? [C] : ( m1_subset_1(C,k4_ordinal1) & k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(B),k1_domain_1(k4_ordinal1,k1_hilbert1,C,A)) = 1 ) ) ) ) )).
fof(d2_mathmorp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k2_mathmorp(A,B) = a_2_0_mathmorp(A,B) ) ) )).
fof(d2_matrix10,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( v2_matrix10(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(k4_tarski(B,C),k2_matrix_0(A)) & r1_xxreal_0(k5_numbers,k3_matrix_0(k1_numbers,A,B,C)) ) ) ) ) ) )).
fof(d2_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_matrix_2(C,k3_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),k6_matrix_2(k2_sgraph1(k2_finseq_1(k1_nat_1(A,2)))),k1_matrix11(A,B,C)) ) ) ) )).
fof(d2_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(C),A,B) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(C))) ) => ( G = k2_matrix12(A,B,C,D,E,F) <=> ( k3_finseq_1(G) = k3_finseq_1(D) & ! [H] : ( v7_ordinal1(H) => ! [I] : ( v7_ordinal1(I) => ( ( r2_hidden(H,k4_finseq_1(D)) & r2_hidden(I,k2_finseq_1(k1_matrix_0(D))) ) => ( ( H = E => k3_matrix_0(u1_struct_0(C),G,H,I) = k8_group_1(C,F,k3_matrix_0(u1_struct_0(C),D,E,I)) ) & ( H != E => k3_matrix_0(u1_struct_0(C),G,H,I) = k3_matrix_0(u1_struct_0(C),D,H,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( ( v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => k6_matrix13(A,B,C,D) = k1_matrix13(A,B,k5_card_1(C),k5_card_1(D),k5_matrix13(C),k5_matrix13(D)) ) ) ) ) )).
fof(d2_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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)) ) ) ) )).
fof(d2_matrix15,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => k3_matrix15(A,B) = k4_matrix_0(A,k10_laplace(A,B)) ) ) )).
fof(d2_matrix16,axiom,( ! [A] : ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ( v1_matrix16(B,A) <=> ? [C] : ( m2_finseq_1(C,A) & k3_finseq_1(C) = k1_matrix_0(B) & r1_matrix16(A,B,C) ) ) ) )).
fof(d2_matrix17,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(A),B,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( v2_matrix17(C,A,B) <=> ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ( ( r2_hidden(k4_tarski(D,E),k2_matrix_0(C)) & F = k6_xcmplx_0(k2_xcmplx_0(B,1),E) & G = k6_xcmplx_0(k2_xcmplx_0(B,1),D) ) => k3_matrix_0(u1_struct_0(A),C,D,E) = k4_algstr_0(A,k3_matrix_0(u1_struct_0(A),C,F,G)) ) ) ) ) ) ) ) ) ) )).
fof(d2_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(A)) ) => ( v2_matrix_0(D,A,B,C) <=> ( k3_finseq_1(D) = B & ! [E] : ( m2_finseq_1(E,A) => ( r2_hidden(E,k10_xtuple_0(D)) => k3_finseq_1(E) = C ) ) ) ) ) ) ) ) )).
fof(d2_matrix_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => k2_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))) ) ) )).
fof(d2_matrix_3,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(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_0(C) = k1_matrix_0(B) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(D,E),k2_matrix_0(B)) => k3_matrix_0(u1_struct_0(A),C,D,E) = k4_algstr_0(A,k3_matrix_0(u1_struct_0(A),B,D,E)) ) ) ) ) ) ) ) ) )).
fof(d2_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k1_complfld))) ) => k2_matrix_5(A) = A ) )).
fof(d2_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( 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) = k3_matrix_1(B,A) ) ) ) ) ) ) )).
fof(d2_matrix_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v1_matrix_1(C,B) <=> ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(D,k2_finseq_1(A)) & r2_hidden(E,k2_finseq_1(A)) ) => ( D = E | k3_matrix_0(u1_struct_0(B),C,D,E) = k4_struct_0(B) ) ) ) ) ) ) ) ) )).
fof(d2_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v2_matrix_8(C,A,B) <=> k4_matrix_3(B,C,C) = k2_matrix_1(B,A) ) ) ) ) )).
fof(d2_matrix_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => k2_matrix_9(A,B,C) = k7_setwiseo(k3_matrix_2(A),u1_struct_0(B),u1_algstr_0(B),k6_matrix_2(k3_matrix_2(A)),k1_matrix_9(A,B,C)) ) ) ) )).
fof(d2_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => k2_matrixc1(A) = k1_matrixc1(k4_matrix_0(k2_numbers,A)) ) )).
fof(d2_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,k3_finseq_2(k3_finseq_2(A))) => ( v1_matrixj1(B,A) <=> ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => ( v1_matrix_0(k1_funct_1(B,C)) & m2_finseq_1(k1_funct_1(B,C),k3_finseq_2(A)) ) ) ) ) ) ) )).
fof(d2_matrixj2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) => ( v1_matrixj2(B,A) <=> ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(C,k4_finseq_1(B)) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v7_ordinal1(E) => k1_funct_1(B,C) != k2_matrixj2(A,D,E) ) ) ) ) ) ) ) )).
fof(d2_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => k2_matrixr1(A) = A ) )).
fof(d2_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => k4_matrixr2(A) = k2_matrixr1(k3_matrix_1(k2_vectsp_1,A)) ) )).
fof(d2_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( 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) ) ) ) ) ) )).
fof(d2_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( ( 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] : ( m2_finseq_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d2_matroid0,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) <=> r2_hidden(B,k1_matroid0(A)) ) ) ) )).
fof(d2_matrprob,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( B = k4_matrprob(A) <=> ( k3_finseq_1(B) = k1_matrix_0(A) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k2_finseq_1(k1_matrix_0(A))) => k1_funct_1(B,C) = k18_rvsum_1(k8_matrix_0(k1_numbers,A,C)) ) ) ) ) ) ) )).
fof(d2_matrtop1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k2_vectsp_1)) => k2_matrtop1(A) = A ) )).
fof(d2_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k2_finseq_1(A)) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,A) & v1_matrix_6(C,A,k2_vectsp_1) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( C = k1_matrtop3(A,B) <=> ( k3_matrix_0(u1_struct_0(k2_vectsp_1),C,B,B) = k4_algstr_0(k2_vectsp_1,k5_struct_0(k2_vectsp_1)) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(D,E),k2_matrix_0(C)) => ( ( D = E => ( D = B | k3_matrix_0(u1_struct_0(k2_vectsp_1),C,D,D) = k5_struct_0(k2_vectsp_1) ) ) & ( D != E => k3_matrix_0(u1_struct_0(k2_vectsp_1),C,D,E) = k4_struct_0(k2_vectsp_1) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_mazurulm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_rlvect_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ( ( r1_xxreal_0(k5_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,k3_xxreal_3(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),k3_xxreal_3(1,F)),k1_rlvect_1(B,k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,E),F)) ) ) ) ) ) ) ) ) )).
fof(d2_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( C = k2_mboolean(A,B) <=> ! [D] : ( r2_hidden(D,A) => k1_funct_1(C,D) = k3_tarski(k1_funct_1(B,D)) ) ) ) ) )).
fof(d2_mcart_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k3_zfmisc_1(A,B,C)) => ! [E] : ( m1_subset_1(E,B) => ( E = k2_mcart_1(A,B,C,D) <=> ! [F] : ! [G] : ! [H] : ( D = k3_xtuple_0(F,G,H) => E = G ) ) ) ) ) ) ) )).
fof(d2_measure1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( v6_supinf_2(B) <=> ! [C] : ( m1_subset_1(C,A) => r1_xxreal_0(k1_supinf_2,k12_supinf_2(B,C)) ) ) ) ) )).
fof(d2_measure3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( m1_measure3(D,A,B,C) <=> ? [E] : ( r2_hidden(E,B) & r1_tarski(D,E) & k12_supinf_2(C,E) = k1_supinf_2 ) ) ) ) ) )).
fof(d2_measure4,axiom,( ! [A] : ! [B] : ( m1_measure4(B,A) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ( C = k1_measure4(A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( r2_hidden(D,C) <=> ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ! [F] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(d2_measure5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_measure5(A) <=> ? [B] : ( m1_subset_1(B,k6_numbers) & ? [C] : ( m1_subset_1(C,k6_numbers) & A = k1_measure5(B,C) ) ) ) ) )).
fof(d2_measure6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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 = k2_measure6(A,B,C) <=> ! [E] : ( 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) ) ) ) ) )).
fof(d2_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( m2_measure8(C,A,B) <=> ! [D] : ( v7_ordinal1(D) => r2_hidden(k9_nat_1(k9_setfam_1(A),C,D),B) ) ) ) ) )).
fof(d2_member_1,axiom,( ! [A] : ( v1_membered(A) => k5_member_1(A) = a_1_1_member_1(A) ) )).
fof(d2_membered,axiom,( ! [A] : ( v2_membered(A) <=> ! [B] : ( r2_hidden(B,A) => v1_xxreal_0(B) ) ) )).
fof(d2_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( l1_memstr_0(B,A) => k2_memstr_0(A,B) = k3_relat_1(u1_memstr_0(A,B),u2_memstr_0(A,B)) ) ) )).
fof(d2_mesfun10,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( r1_mesfun10(A,B,C) <=> ( v1_mesfunc8(B,A,k6_numbers) & k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers)) = k1_relset_1(A,C) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & ? [G] : ( r1_xxreal_0(E,F) & r2_hidden(G,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers))) & r1_xxreal_0(D,k3_extreal1(k4_supinf_2(k12_supinf_2(k4_mesfunc5(A,k6_numbers,B,F),G),k12_supinf_2(C,G)))) ) ) ) ) ) ) ) ) ) )).
fof(d2_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(d2_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => k2_mesfun7c(A,B) = k1_mesfunc8(A,k1_mesfun7c(A,B)) ) ) )).
fof(d2_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( C = k1_mesfunc2(A,B) <=> ( k1_relset_1(A,C) = k1_relset_1(A,B) & ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(d2_mesfunc5,axiom,( ! [A] : ( v1_relat_1(A) => ( v2_mesfunc5(A) <=> v1_mesfunc5(k10_xtuple_0(A)) ) ) )).
fof(d2_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( r2_mesfunc6(A,B,C) <=> ? [D] : ( v1_prob_2(D) & m2_finseq_1(D,B) & k1_relset_1(A,C) = k3_tarski(k2_relset_1(B,D)) & ! [E] : ( v7_ordinal1(E) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d2_mesfunc7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_valued_0(A) ) => ! [B] : ( m1_subset_1(B,k6_numbers) => ( B = k2_mesfunc7(A) <=> ? [C] : ( m2_finseq_1(C,k6_numbers) & C = A & B = k1_finsop_1(k6_numbers,C,k1_mesfunc7) ) ) ) ) )).
fof(d2_mesfunc8,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,B)))) ) => ( v1_mesfunc8(C,A,B) <=> ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => k1_relset_1(A,k4_mesfunc5(A,B,C,D)) = k1_relset_1(A,k4_mesfunc5(A,B,C,E)) ) ) ) ) )).
fof(d2_mesfunc9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_valued_0(A) ) => ( v1_mesfunc9(A) <=> v10_mesfunc5(k2_mesfunc9(A)) ) ) )).
fof(d2_metric_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) => k1_binop_1(B,C,C) = k5_numbers ) ) ) )).
fof(d2_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_metric_2(A,B) = a_2_0_metric_2(A,B) ) ) )).
fof(d2_metric_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_metric_6(A,B,C) <=> ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(E,F) & r1_xxreal_0(D,k1_metric_1(A,k2_tbsp_1(A,B,F),C)) ) ) ) ) ) ) ) ) )).
fof(d2_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_metrizts(A) <=> ! [B] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(d2_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( v1_xreal_0(C) => k1_mfold_1(A,B,C) = k1_pre_topc(k15_euclid(A),k1_topreal9(A,B,C)) ) ) ) )).
fof(d2_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => k2_mfold_2(A,B,C) = a_3_0_mfold_2(A,B,C) ) ) ) )).
fof(d2_midsp_1,axiom,( k2_midsp_1 = g1_midsp_1(k1_tarski(k5_ordinal1),k9_funct_5) )).
fof(d2_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_midsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d2_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( m1_midsp_3(B,A) <=> ( r1_xxreal_0(1,B) & r1_xxreal_0(B,k1_nat_1(A,1)) ) ) ) ) )).
fof(d2_mmlquer2,axiom,( ! [A] : ( v1_relat_1(A) => ( v4_relat_2(A) <=> ! [B] : ! [C] : ( ( r1_mmlquery(B,C,A) & r1_mmlquery(C,B,A) ) => B = C ) ) ) )).
fof(d2_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k2_mmlquery(A,B,C) = k3_tarski(a_3_0_mmlquery(A,B,C)) ) ) )).
fof(d2_mod_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(d2_mod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(d2_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( v2_vectsp_2(C,k2_mod_4(A)) & l1_vectsp_2(C,k2_mod_4(A)) ) => ( C = k3_mod_4(A,B) <=> ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(d2_modal_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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))) ) ) )).
fof(d2_modcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ( m3_modcat_1(B,A) <=> ! [C] : ( m1_subset_1(C,B) => ( v2_mod_2(C,A) & v3_mod_2(C,A) & l1_mod_2(C,A) ) ) ) ) ) )).
fof(d2_modelc_2,axiom,( ! [A] : ( v7_ordinal1(A) => k2_modelc_2(A) = k9_finseq_1(k2_xcmplx_0(6,A)) ) )).
fof(d2_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ( 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 ) ) ) )).
fof(d2_moebius1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) => ( A = k1_moebius1 <=> ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,A) <=> ~ v1_moebius1(B) ) ) ) ) )).
fof(d2_monoid_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ! [F] : ( ( 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] : ( m2_funct_2(G,E,A,k9_funct_2(E,A)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d2_morph_01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d2_msafree,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( r2_hidden(C,A) => ! [D] : ( D = k2_msafree(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ? [F] : ( r2_hidden(F,k1_funct_1(B,C)) & E = k4_tarski(F,C) ) ) ) ) ) )).
fof(d2_msafree1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( v1_msafree1(B,A) <=> v1_prob_2(u3_msualg_1(A,B)) ) ) ) )).
fof(d2_msafree2,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(d2_msafree3,axiom,( ! [A] : ( l1_msualg_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) ) => ! [C] : ( ( 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] : ( r2_hidden(D,u1_struct_0(A)) => k1_funct_1(C,D) = a_2_0_msafree3(B,D) ) ) ) ) ) )).
fof(d2_msalimit,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_msalimit(C,A,B) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( r1_orders_2(A,F,E) & r1_orders_2(A,G,F) & ! [H] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m2_subset_1(C,u1_struct_0(k5_msafree(A,B)),k7_dtconstr(k5_msafree(A,B))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d2_msinst_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( C = k2_msinst_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( v3_msualg_1(E,A) & v1_msualg_6(E,A) & l3_msualg_1(E,A) & D = E & ! [F] : ( m1_subset_1(F,k10_xtuple_0(u3_msualg_1(A,E))) => r1_tarski(F,B) ) ) ) ) ) ) )).
fof(d2_msscyc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => ( v1_msscyc_1(B,A) <=> ? [C] : ( 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)) ) ) ) ) )).
fof(d2_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) => ( v1_mssubfam(C,A,B) <=> ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(d2_msualg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( 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) ) ) )).
fof(d2_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ( v2_msualg_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v1_msualg_2(B,A) ) ) ) )).
fof(d2_msualg_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_msualg_3(A) <=> ! [B] : ! [C] : ( ( 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) ) ) ) ) )).
fof(d2_msualg_4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_msualg_4(C,A,B,B) => ( v1_msualg_4(C,A,B) <=> ! [D] : ! [E] : ( 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)))) ) ) ) ) ) ) )).
fof(d2_msualg_5,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(d2_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(d2_msualg_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m2_nat_lat(B,A) => ( v1_msualg_7(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => r2_hidden(k16_lattice3(A,C),u1_struct_0(B)) ) ) ) ) )).
fof(d2_msualg_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(d2_msualg_9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v2_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( m2_pboole(E,A,B,k6_pboole(A,C,D)) => ! [F] : ( m2_pboole(F,A,B,D) => ( F = k2_msualg_9(A,B,C,D,E) <=> ! [G] : ( r2_hidden(G,A) => k1_funct_1(F,G) = k12_mcart_1(k1_funct_1(E,G)) ) ) ) ) ) ) ) )).
fof(d2_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v1_msualg_1(B) & l1_msualg_1(B) ) => ! [C] : ( ( v3_msualg_1(C,B) & v4_msualg_1(C,B) & l3_msualg_1(C,B) ) => ( r1_msuhom_1(A,B) => ! [D] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(d2_multop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : k3_multop_1(A,B,C,D,E) = k1_funct_1(A,k6_xtuple_0(B,C,D,E)) ) )).
fof(d2_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) ) => ( v2_nagata_1(B,A) <=> ! [C] : ( m1_subset_1(C,k4_ordinal1) => v1_nagata_1(k1_nagata_1(A,B,C),A) ) ) ) ) )).
fof(d2_nagata_2,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( ( 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] : ( m1_subset_1(E,A) => k1_funct_1(D,E) = k1_binop_1(B,C,E) ) ) ) ) ) )).
fof(d2_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => k1_ordinal1(A) = k1_nat_1(A,1) ) )).
fof(d2_nat_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v3_valued_0(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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] : k1_funct_1(D,E) = k3_xcmplx_0(C,k1_funct_1(B,E)) ) ) ) ) )).
fof(d2_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( B != k5_numbers => ( C = k3_nat_5(A,B) <=> ! [D] : ( ( v7_ordinal1(D) & ~ v8_ordinal1(D) ) => ( B = D => C = k2_uproots(k3_moebius1(D),k1_nat_5(k4_ordinal1,k2_nat_5(A),k3_moebius1(D))) ) ) ) ) & ( B = k5_numbers => ( C = k3_nat_5(A,B) <=> C = k5_numbers ) ) ) ) ) ) )).
fof(d2_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( C = k2_nat_d(A,B) <=> ~ ( ! [D] : ( v7_ordinal1(D) => ~ ( A = k2_xcmplx_0(k3_xcmplx_0(B,D),C) & ~ r1_xxreal_0(B,C) ) ) & ~ ( C = k5_numbers & B = k5_numbers ) ) ) ) ) ) )).
fof(d2_nat_lat,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1))) ) => ( A = k2_nat_lat <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k1_binop_1(A,C,B) = k5_nat_d(C,B) ) ) ) ) )).
fof(d2_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ( r1_nattra_1(A,B,C,D) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d2_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ! [H] : ( m1_subset_1(H,u1_struct_0(C)) => ~ ( r2_hidden(G,A) & r2_hidden(H,A) & ~ r1_xxreal_0(F,k2_normsp_0(C,k5_algstr_0(C,G,H))) & r1_xxreal_0(E,k2_normsp_0(B,k5_algstr_0(B,k7_partfun1(u1_struct_0(B),D,G),k7_partfun1(u1_struct_0(B),D,H)))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_ndiff_1,axiom,( ! [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) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k1_ndiff_1(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k1_normsp_1(A,D,E) = k1_rlvect_1(A,k1_normsp_1(A,B,E),k9_nat_1(k1_numbers,C,E)) ) ) ) ) ) ) )).
fof(d2_ndiff_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(k16_lopban_1(A,B))) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(d2_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) & ! [D] : ( v1_xreal_0(D) => k10_funct_2(k1_numbers,u1_struct_0(A),B,D) = k1_rlvect_1(A,C,D) ) ) ) ) ) )).
fof(d2_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ( D = k1_ndiff_4(A,B,C) <=> ? [E] : ( 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) ) ) ) ) ) ) )).
fof(d2_ndiff_5,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_ndiff_5(A,B,C) = a_3_0_ndiff_5(A,B,C) ) ) ) )).
fof(d2_neckla_2,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(d2_necklace,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ( r3_necklace(A,B) <=> ( r2_necklace(B,A) & r2_necklace(A,B) ) ) ) ) )).
fof(d2_net_1,axiom,( ! [A] : ( 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)))) ) ) ) )).
fof(d2_newton,axiom,( ! [A] : ( v7_ordinal1(A) => k2_newton(A) = k19_rvsum_1(k1_finseq_2(A)) ) )).
fof(d2_nfcont_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ~ ( r2_hidden(F,A) & r2_hidden(G,A) & ~ r1_xxreal_0(E,k2_normsp_0(B,k5_algstr_0(B,F,G))) & r1_xxreal_0(D,k9_complex1(k5_real_1(k7_partfun1(k1_numbers,C,F),k7_partfun1(k1_numbers,C,G)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_nfcont_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ( r2_hidden(C,k1_relset_1(k1_numbers,B)) => r1_nfcont_3(A,B,C) ) ) ) ) ) )).
fof(d2_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_euclid(A)))) ) => ! [D] : ( ( 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] : ( r2_hidden(E,k1_relset_1(B,D)) => k7_partfun1(k1_numbers,D,E) = k12_euclid(k7_partfun1(k1_euclid(A),C,E)) ) ) ) ) ) ) )).
fof(d2_normform,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_finsub_1(B) ) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ! [D] : ( 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))) ) ) ) ) )).
fof(d2_normsp_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_normsp_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k3_normsp_0(A,B) <=> ( k9_xtuple_0(C) = k9_xtuple_0(B) & ! [D] : ( r2_hidden(D,k9_xtuple_0(C)) => k1_funct_1(C,D) = k2_normsp_0(A,k7_partfun1(u1_struct_0(A),B,D)) ) ) ) ) ) ) )).
fof(d2_normsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k2_normsp_1(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k1_normsp_1(A,D,E) = k1_algstr_0(A,k1_normsp_1(A,B,E),k1_normsp_1(A,C,E)) ) ) ) ) ) ) )).
fof(d2_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => k2_normsp_2(A) = g1_metric_1(u1_struct_0(A),k1_normsp_2(A)) ) )).
fof(d2_ntalgo_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => ! [B] : ( m1_subset_1(B,k4_numbers) => ! [C] : ( m1_subset_1(C,k3_zfmisc_1(k4_numbers,k4_numbers,k4_numbers)) => ( C = k2_ntalgo_1(A,B) <=> ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_numbers))) & ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_numbers))) & ? [F] : ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k4_numbers) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_numbers))) & ? [G] : ( v1_funct_1(G) & v1_funct_2(G,k4_ordinal1,k4_numbers) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_numbers))) & ? [H] : ( v1_funct_1(H) & v1_funct_2(H,k4_ordinal1,k4_numbers) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_numbers))) & ? [I] : ( v1_funct_1(I) & v1_funct_2(I,k4_ordinal1,k4_numbers) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_numbers))) & ? [J] : ( v1_funct_1(J) & v1_funct_2(J,k4_ordinal1,k4_numbers) & m1_subset_1(J,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_numbers))) & ? [K] : ( v1_funct_1(K) & v1_funct_2(K,k4_ordinal1,k4_numbers) & m1_subset_1(K,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_numbers))) & ? [L] : ( m1_subset_1(L,k4_ordinal1) & k9_nat_1(k4_numbers,H,k5_numbers) = 1 & k9_nat_1(k4_numbers,I,k5_numbers) = k5_numbers & k9_nat_1(k4_numbers,D,k5_numbers) = A & k9_nat_1(k4_numbers,F,k5_numbers) = k5_numbers & k9_nat_1(k4_numbers,K,k5_numbers) = k5_numbers & k9_nat_1(k4_numbers,J,k5_numbers) = 1 & k9_nat_1(k4_numbers,E,k5_numbers) = B & k9_nat_1(k4_numbers,G,k5_numbers) = k5_numbers & ! [M] : ( m1_subset_1(M,k4_ordinal1) => ( k9_nat_1(k4_numbers,F,k1_nat_1(M,1)) = k4_int_1(k9_nat_1(k4_numbers,D,M),k9_nat_1(k4_numbers,E,M)) & k9_nat_1(k4_numbers,G,k1_nat_1(M,1)) = k5_int_1(k9_nat_1(k4_numbers,D,M),k9_nat_1(k4_numbers,E,M)) & k9_nat_1(k4_numbers,H,k1_nat_1(M,1)) = k9_nat_1(k4_numbers,K,M) & k9_nat_1(k4_numbers,I,k1_nat_1(M,1)) = k9_nat_1(k4_numbers,J,M) & k9_nat_1(k4_numbers,D,k1_nat_1(M,1)) = k9_nat_1(k4_numbers,E,M) & k9_nat_1(k4_numbers,K,k1_nat_1(M,1)) = k6_xcmplx_0(k9_nat_1(k4_numbers,H,M),k3_xcmplx_0(k9_nat_1(k4_numbers,F,k1_nat_1(M,1)),k9_nat_1(k4_numbers,K,M))) & k9_nat_1(k4_numbers,J,k1_nat_1(M,1)) = k6_xcmplx_0(k9_nat_1(k4_numbers,I,M),k3_xcmplx_0(k9_nat_1(k4_numbers,F,k1_nat_1(M,1)),k9_nat_1(k4_numbers,J,M))) & k9_nat_1(k4_numbers,E,k1_nat_1(M,1)) = k9_nat_1(k4_numbers,G,k1_nat_1(M,1)) ) ) & L = k3_nat_1(a_1_1_ntalgo_1(E)) & ( r1_xxreal_0(k5_numbers,k9_nat_1(k4_numbers,D,L)) => C = k3_xtuple_0(k9_nat_1(k4_numbers,H,L),k9_nat_1(k4_numbers,I,L),k9_nat_1(k4_numbers,D,L)) ) & ( ~ r1_xxreal_0(k5_numbers,k9_nat_1(k4_numbers,D,L)) => C = k3_xtuple_0(k4_xcmplx_0(k9_nat_1(k4_numbers,H,L)),k4_xcmplx_0(k9_nat_1(k4_numbers,I,L)),k4_xcmplx_0(k9_nat_1(k4_numbers,D,L))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_numbers,axiom,( k2_numbers = k2_xboole_0(k6_subset_1(k9_funct_2(k2_tarski(k5_ordinal1,1),k1_numbers),a_0_0_numbers),k1_numbers) )).
fof(d2_numeral1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,1) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v5_ordinal1(C) & v1_finset_1(C) ) => ( ( A != k5_numbers => ( C = k2_numeral1(A,B) <=> ( k1_numeral1(C,B) = A & k1_recdef_1(C,k6_xcmplx_0(k1_afinsq_1(C),1)) != k5_numbers & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,C)) => ( r1_xxreal_0(k5_numbers,k1_recdef_1(C,D)) & ~ r1_xxreal_0(B,k1_recdef_1(C,D)) ) ) ) ) ) ) & ( A = k5_numbers => ( C = k2_numeral1(A,B) <=> C = k5_afinsq_1(k5_numbers) ) ) ) ) ) ) ) )).
fof(d2_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k1_openlatt(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d2_oposet_1,axiom,( k2_oposet_1 = g2_qmax_1(k1_tarski(k5_ordinal1),k1_partit_2(k1_tarski(k5_ordinal1),k1_tarski(k5_ordinal1)),k8_funct_5) )).
fof(d2_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_oppcat_1(A,B) = B ) ) )).
fof(d2_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_rsspace4(A,B)))) => ( C = k1_ordeq_01(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( v1_funct_1(E) & v1_nfcont_3(E,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) & D = E & k1_relset_1(k1_numbers,E) = A ) ) ) ) ) ) )).
fof(d2_orders_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( m2_orders_1(C,A,B) <=> ! [D] : ( r2_hidden(D,A) => k1_funct_1(C,D) = o_3_0_orders_1(A,B,D) ) ) ) ) )).
fof(d2_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_orders_2(A) <=> r1_relat_2(u1_orders_2(A),u1_struct_0(A)) ) ) )).
fof(d2_orders_3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_orders_3(B,A) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & ? [D] : ( 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)) ) ) ) ) ) )).
fof(d2_orders_4,axiom,( ! [A] : ( l1_struct_0(A) => ( v1_orders_4(A) <=> v4_card_3(u1_struct_0(A)) ) ) )).
fof(d2_ordinal1,axiom,( ! [A] : ( v1_ordinal1(A) <=> ! [B] : ( r2_hidden(B,A) => r1_tarski(B,A) ) ) )).
fof(d2_ordinal2,axiom,( ! [A] : k2_ordinal2(A) = k1_setfam_1(k2_ordinal1(A)) )).
fof(d2_ordinal4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => k2_ordinal4(A) = k1_xboole_0 ) )).
fof(d2_ordinal5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) ) => ( v2_ordinal5(A) <=> ! [B] : ( v3_ordinal1(B) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(d2_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( ~ r1_orders_2(B,D,C) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( F = k1_ortsp_1(A,B,C,D,E) <=> ! [G] : ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(d2_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( r1_osalg_1(A,B,C) <=> r2_hidden(k4_tarski(B,C),u1_osalg_1(A)) ) ) ) ) )).
fof(d2_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d2_osalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ( r1_osalg_3(A,B,C) <=> ? [D] : ( 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) ) ) ) ) ) )).
fof(d2_osalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(d2_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(d2_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_parsp_2(A,B,C,D) <=> r1_parsp_1(A,B,C,B,D) ) ) ) ) ) )).
fof(d2_partfun1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) ) => ( v1_partfun1(B,A) <=> k1_relset_1(A,B) = A ) ) )).
fof(d2_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( r2_partit1(A,B,C,D) <=> ( r1_partit1(A,B,D) & r1_partit1(A,C,D) & ! [E] : ( ( r1_tarski(E,D) & r1_partit1(A,B,E) & r1_partit1(A,C,E) ) => E = D ) ) ) ) ) ) )).
fof(d2_partit_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_partit_2(A) <=> ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => k1_funct_1(A,k1_funct_1(A,B)) = B ) ) ) )).
fof(d2_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ( v2_pasch(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d2_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r2_pboole(A,B,C) <=> ! [D] : ( r2_hidden(D,A) => r1_tarski(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) )).
fof(d2_pcomps_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( C = k1_pcomps_1(A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(D,C) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & D = k2_pre_topc(A,E) & r2_hidden(E,B) ) ) ) ) ) ) ) )).
fof(d2_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(C,D))) => ! [G] : ( 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] : ( r2_hidden(k4_tarski(H,I),G) <=> ? [J] : ? [K] : ? [L] : ? [M] : ( 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) ) ) ) ) ) ) ) )).
fof(d2_pdiff_1,axiom,( ! [A] : ( ( 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)))) ) )).
fof(d2_pdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( r1_pdiff_2(A,B) <=> ( r1_tarski(B,k1_relset_1(k1_euclid(2),A)) & ! [C] : ( 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) ) ) ) ) ) )).
fof(d2_pdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(2)) => ( r1_pdiff_3(A,B) <=> ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & B = k10_finseq_1(C,D) & ? [E] : ( 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] : ( v1_funct_1(F) & v3_fdiff_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [G] : ( v1_funct_1(G) & v2_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,E) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(2,1,k1_pdiff_3(1,2,A),B),H),k1_funct_1(k1_pdiff_2(2,1,k1_pdiff_3(1,2,A),B),C)) = k2_xcmplx_0(k1_funct_1(F,k6_xcmplx_0(H,C)),k1_funct_1(G,k6_xcmplx_0(H,C))) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_pdiff_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( r2_pdiff_4(A,B) <=> ( r1_tarski(B,k1_relset_1(k1_euclid(3),A)) & ! [C] : ( 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) ) ) ) ) ) )).
fof(d2_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r2_pdiff_5(A,B) <=> ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & B = k11_finseq_1(C,D,E) & ? [F] : ( 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] : ( v1_funct_1(G) & v3_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [H] : ( v1_funct_1(H) & v2_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,F) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,2,k1_pdiff_3(1,3,A),B),I),k1_funct_1(k1_pdiff_2(3,2,k1_pdiff_3(1,3,A),B),D)) = k2_xcmplx_0(k1_funct_1(G,k6_xcmplx_0(I,D)),k1_funct_1(H,k6_xcmplx_0(I,D))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_pdiff_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( m2_finseq_2(D,k1_numbers,k1_euclid(B)) => ! [E] : ( v1_xreal_0(E) => 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) ) ) ) ) ) ) )).
fof(d2_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( 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)) ) ) ) )).
fof(d2_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ! [C] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d2_pencil_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_pencil_1(B,A) <=> ! [C] : ( 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) ) ) ) ) ) )).
fof(d2_pencil_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pencil_1(A,B)))) => ( m1_pencil_2(C,A,B) <=> ? [D] : ( ~ 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))) ) ) ) ) ) )).
fof(d2_pencil_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v15_pencil_1(B) ) => ! [C] : ( m1_pencil_2(C,A,B) => ! [D] : ( m1_pencil_2(D,A,B) => ( r1_pencil_3(A,B,C,D) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(k5_pencil_1(A,B))) => ~ ( r2_hidden(E,C) & ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d2_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( 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))) ) ) ) ) )).
fof(d2_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_int_2(A,B) => ( r1_xxreal_0(B,1) | ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( C = k3_pepin(A,B) <=> ( ~ r1_xxreal_0(C,k5_numbers) & k4_nat_d(k1_newton(A,C),B) = 1 & ! [D] : ( v7_ordinal1(D) => ( k4_nat_d(k1_newton(A,D),B) = 1 => ( r1_xxreal_0(D,k5_numbers) | ( ~ r1_xxreal_0(C,k5_numbers) & r1_xxreal_0(C,D) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_petri_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,A))) ) => ( m1_petri_2(C,A,B) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & ? [E] : ( 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) ) ) ) ) ) )).
fof(d2_pnproc_1,axiom,( ! [A] : k1_pnproc_1(A) = k8_funcop_1(k4_ordinal1,A,k5_numbers) )).
fof(d2_polyalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_polyalg1(B,A) & l1_polyalg1(B,A) ) => ( B = k1_polyalg1(A) <=> ( ! [C] : ( r2_hidden(C,u1_struct_0(B)) <=> ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( C = E & D = F ) => k1_algstr_0(B,C,D) = k2_normsp_1(A,E,F) ) ) ) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( C = E & D = F ) => k6_algstr_0(B,C,D) = k11_polynom3(A,E,F) ) ) ) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(d2_polyeq_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => k2_polyeq_1(A,B,C,D) = k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k1_square_1(D)),k3_xcmplx_0(B,D)),C) ) ) ) ) )).
fof(d2_polyeq_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(d2_polyeq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_polyeq_3(A) = k3_xcmplx_0(k1_square_1(A),A) ) )).
fof(d2_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( ( k6_xcmplx_0(k3_xcmplx_0(3,B),k1_newton(C,2)) = k5_numbers => ( D = k2_polyeq_5(A,B,C) <=> ? [E] : ( v1_xcmplx_0(E) & ? [F] : ( v1_xcmplx_0(F) & E = k7_xcmplx_0(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,k7_xcmplx_0(C,3)) ) ) ) ) & ( k6_xcmplx_0(k3_xcmplx_0(3,B),k1_newton(C,2)) != k5_numbers => ( D = k2_polyeq_5(A,B,C) <=> ? [E] : ( v1_xcmplx_0(E) & ? [F] : ( v1_xcmplx_0(F) & ? [G] : ( v1_xcmplx_0(G) & ? [H] : ( v1_xcmplx_0(H) & ? [I] : ( v1_xcmplx_0(I) & E = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(3,B),k1_newton(C,2)),9) & F = k7_xcmplx_0(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 = k4_xcmplx_0(k7_xcmplx_0(E,H)) & D = k6_xcmplx_0(k2_xcmplx_0(H,I),k7_xcmplx_0(C,3)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_polynom1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ( D = k1_polynom1(A,B,C) <=> ( k4_finseq_1(D) = k4_finseq_1(B) & ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d2_polynom2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ( E = k2_polynom2(A,B,C,D) <=> ? [F] : ( m2_finseq_1(F,u1_struct_0(B)) & k3_finseq_1(F) = k3_finseq_1(k7_pre_poly(k15_pre_poly(A),k3_polynom1(k15_pre_poly(A),B,C),k17_pre_poly(A))) & E = k4_rlvect_1(B,F) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( ( 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(k4_ordinal1,k15_pre_poly(A),k15_pre_poly(A),u1_struct_0(B),k7_pre_poly(k15_pre_poly(A),k3_polynom1(k15_pre_poly(A),B,C),k17_pre_poly(A)),C),G),k1_polynom2(A,k7_partfun1(k15_pre_poly(A),k7_pre_poly(k15_pre_poly(A),k3_polynom1(k15_pre_poly(A),B,C),k17_pre_poly(A)),G),B,D)) ) ) ) ) ) ) ) ) ) )).
fof(d2_polynom3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [C] : ( m2_finseq_2(C,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ( r2_polynom3(A,B,C) <=> ( r1_polynom3(A,B,C) | B = C ) ) ) ) ) )).
fof(d2_polynom4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( D = k2_polynom4(A,B,C) <=> ? [E] : ( m2_finseq_1(E,u1_struct_0(A)) & D = k4_rlvect_1(A,E) & k3_finseq_1(E) = k1_algseq_1(A,B) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( 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),k4_ordinal1,u1_struct_0(A),k4_group_1(A),C,k7_nat_d(F,1))) ) ) ) ) ) ) ) ) )).
fof(d2_polynom5,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => k2_polynom5(A,B,C) = k1_binop_1(k4_group_1(k14_polynom3(A)),B,C) ) ) ) )).
fof(d2_polynom8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k2_polynom8(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k9_nat_1(u1_struct_0(A),D,E) = k6_algstr_0(A,k9_nat_1(u1_struct_0(A),B,E),k9_nat_1(u1_struct_0(A),C,E)) ) ) ) ) ) ) )).
fof(d2_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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(k3_polynom1(k15_pre_poly(A),C,D),k3_polynom1(k15_pre_poly(A),C,E)),k13_bagorder(g1_orders_2(k15_pre_poly(A),B))) ) ) ) ) ) ) )).
fof(d2_poset_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => k1_poset_1(A,B,C) = a_3_0_poset_1(A,B,C) ) ) ) )).
fof(d2_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( ~ r1_xxreal_0(A,k5_numbers) => ( C = k2_power(A,B) <=> C = k6_prepower(A,B) ) ) & ( A = k5_numbers => ( r1_xxreal_0(B,k5_numbers) | ( C = k2_power(A,B) <=> C = k5_numbers ) ) ) & ( v1_int_1(B) => ( C = k2_power(A,B) <=> ? [D] : ( v1_int_1(D) & D = B & C = k3_prepower(A,D) ) ) ) ) ) ) ) )).
fof(d2_pralg_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_card_3(k1_funct_6(A))) & v1_funct_1(B) & v1_partfun1(B,k4_card_3(k1_funct_6(A))) & v1_funcop_1(B) ) => ( B = k2_pralg_2(A) <=> ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(C,k4_card_3(k1_funct_6(A))) => k1_funct_1(B,C) = k15_pralg_1(A,C) ) ) ) ) ) )).
fof(d2_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d2_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( 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] : ( m2_finseq_1(D,A) => ( D = k7_pre_poly(A,B,C) <=> ( k2_relset_1(A,D) = B & ! [E] : ( v7_ordinal1(E) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) <=> r2_hidden(B,u1_pre_topc(A)) ) ) ) )).
fof(d2_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_prelamb(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d2_prepower,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(1,A) => ! [C] : ( v1_xreal_0(C) => ( ( ~ r1_xxreal_0(B,k5_numbers) => ( C = k2_prepower(A,B) <=> ( k1_newton(C,A) = B & ~ r1_xxreal_0(C,k5_numbers) ) ) ) & ( B = k5_numbers => ( C = k2_prepower(A,B) <=> C = k5_numbers ) ) ) ) ) ) ) )).
fof(d2_prgcor_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( C = k2_prgcor_1(A,B) <=> ? [D] : ( v1_int_1(D) & ( B = k5_numbers => C = k5_numbers ) & ( B != k5_numbers => ( ( r1_xxreal_0(k5_numbers,A) => ( r1_xxreal_0(B,k5_numbers) | C = k1_prgcor_1(A,B) ) ) & ( ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,k5_numbers) ) => ( ( r1_xxreal_0(k5_numbers,A) => ( r1_xxreal_0(k5_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(k5_numbers,A) & ~ r1_xxreal_0(k5_numbers,B) ) => ( ~ ( ~ r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,k5_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(k5_numbers,A) & ~ r1_xxreal_0(B,k5_numbers) ) => C = k1_prgcor_1(k4_xcmplx_0(A),k4_xcmplx_0(B)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_prob_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( C = k2_prob_1(A,B) <=> ! [D] : ( v7_ordinal1(D) => k9_nat_1(k9_setfam_1(A),C,D) = k3_subset_1(A,k9_nat_1(k9_setfam_1(A),B,D)) ) ) ) ) )).
fof(d2_prob_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_prob_2(A) <=> ! [B] : ! [C] : ( B != C => r1_xboole_0(k1_funct_1(A,B),k1_funct_1(A,C)) ) ) ) )).
fof(d2_prob_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( C = k2_prob_3(A,B) <=> ( k1_prob_2(A,k9_setfam_1(A),C,k5_numbers) = k1_prob_2(A,k9_setfam_1(A),B,k5_numbers) & ! [D] : ( v7_ordinal1(D) => k1_prob_2(A,k9_setfam_1(A),C,k1_nat_1(D,1)) = k6_prob_1(A,k9_setfam_1(A),k1_prob_2(A,k9_setfam_1(A),C,D),k1_prob_2(A,k9_setfam_1(A),B,k1_nat_1(D,1))) ) ) ) ) ) )).
fof(d2_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( k1_funct_1(C,A) = 1 => k3_prob_4(A,B,C) = C ) ) ) ) )).
fof(d2_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d2_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d2_projred2,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => k1_projred2(A,B) = a_2_0_projred2(A,B) ) ) )).
fof(d2_prvect_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(d2_prvect_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_prvect_2(C,A,B) => ! [D] : ( ( 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] : ( m1_subset_1(E,B) => ! [F] : ( m1_subset_1(F,k4_card_3(A)) => ! [G] : ( m2_subset_1(G,k4_ordinal1,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)) ) ) ) ) ) ) ) ) )).
fof(d2_prvect_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_rlvect_1(B) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => k1_binop_1(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)) ) ) ) ) ) ) ) )).
fof(d2_pscomp_1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( 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) = k2_seq_4(k7_relset_1(u1_struct_0(A),k1_numbers,B,u1_struct_0(A))) ) ) )).
fof(d2_pua2mss1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( m2_pua2mss1(B,A) <=> ( m1_eqrel_1(k10_xtuple_0(B),A) & v2_funct_1(B) ) ) ) )).
fof(d2_pythtrip,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_int_2(A,B) <=> ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => ~ ( r1_nat_d(C,A) & r1_nat_d(C,B) ) ) ) ) ) )).
fof(d2_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( D = k2_pzfmisc1(A,B,C) <=> ! [E] : ( r2_hidden(E,A) => k1_funct_1(D,E) = k2_tarski(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) )).
fof(d2_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => k1_qc_lang1(A) = k10_xtuple_0(A) ) )).
fof(d2_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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))) ) ) ) )).
fof(d2_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_qc_lang1(A)) => k2_qc_lang3(A,B) = k4_tarski(4,B) ) ) )).
fof(d2_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d2_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_qc_lang1(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ( v2_qc_trans(C,A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_cqc_lang(B))) => ( C = D => v1_henmodel(D,B) ) ) ) ) ) ) )).
fof(d2_qmax_1,axiom,( ! [A] : ( l1_qmax_1(A) => k2_qmax_1(A) = u1_qmax_1(A) ) )).
fof(d2_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v4_quantal1(A) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_algstr_0(A,B,C) = B ) ) ) ) )).
fof(d2_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => k6_quatern2(A) = k5_quatern2(k2_quatern2,A) ) )).
fof(d2_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k3_quatern3(A) = k23_quaterni(k23_quaterni(A,A),A) ) )).
fof(d2_quaterni,axiom,( ! [A] : ( v1_quaterni(A) <=> r2_hidden(A,k1_quaterni) ) )).
fof(d2_quofield,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v6_struct_0(A) & v1_vectsp_2(A) & l6_algstr_0(A) ) => ! [B] : ( m2_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A)) => ! [C] : ( 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))) ) ) ) )).
fof(d2_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => k2_radix_1(A) = a_1_0_radix_1(A) ) )).
fof(d2_radix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v3_card_1(D,A) & m2_finseq_1(D,k4_ordinal1) ) => ( D = k2_radix_2(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k2_finseq_1(A)) => k7_partfun1(k4_ordinal1,D,E) = k1_radix_2(E,B,A,C) ) ) ) ) ) ) ) )).
fof(d2_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => k2_radix_3(A) = a_1_1_radix_3(A) ) )).
fof(d2_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v3_card_1(D,A) & m2_finseq_1(D,k3_radix_1(C)) ) => ( D = k2_radix_5(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k2_finseq_1(A)) => k4_radix_1(E,C,A,D) = k1_radix_5(E,B,C) ) ) ) ) ) ) ) )).
fof(d2_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,k2_xcmplx_0(A,2)) & m2_finseq_1(C,k3_radix_1(B)) ) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d2_ramsey_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ! [D] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,k3_group_10(B,A)) => k1_funct_1(E,F) = k7_relat_1(D,F) ) ) ) ) ) ) ) )).
fof(d2_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [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))) ) => ( m1_random_1(C,A,B) <=> ? [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) & D = A & r1_mesfunc6(A,B,C,D) ) ) ) ) ) )).
fof(d2_random_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( m2_prob_1(C,A,k1_random_1(A)) => ! [D] : ( m2_prob_1(D,B,k1_random_1(B)) => ! [E] : ( 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] : ( 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] : ! [H] : ( ( r2_hidden(G,A) & r2_hidden(H,B) ) => k1_binop_1(F,G,H) = k1_extreal1(k12_supinf_2(C,k1_tarski(G)),k12_supinf_2(D,k1_tarski(H))) ) & ! [G] : ( ( v1_finset_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => k12_supinf_2(E,G) = k5_bhsp_5(k1_numbers,k2_zfmisc_1(A,B),k9_binop_2,G,F) ) ) ) ) ) ) ) ) )).
fof(d2_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(d2_rat_1,axiom,( ! [A] : ( v1_rat_1(A) <=> r2_hidden(A,k3_numbers) ) )).
fof(d2_rcomp_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k2_rcomp_1(A,B) = a_2_1_rcomp_1(A,B) ) ) )).
fof(d2_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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] : ( 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] : ( 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(k3_seq_4(k7_partfun1(k9_setfam_1(k1_numbers),D,E)),k3_seq_4(k7_partfun1(k9_setfam_1(k1_numbers),D,k1_nat_1(E,1)))) & r1_xxreal_0(k2_seq_4(k7_partfun1(k9_setfam_1(k1_numbers),D,E)),k2_seq_4(k7_partfun1(k9_setfam_1(k1_numbers),D,k1_nat_1(E,1)))) & ~ r1_xxreal_0(k2_seq_4(k7_partfun1(k9_setfam_1(k1_numbers),D,E)),k3_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(k2_seq_4(k7_partfun1(k9_setfam_1(k1_numbers),D,E)),k3_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] : ( 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] : ( 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] : ( v7_ordinal1(E) => ~ ( ~ r1_xxreal_0(E,1) & ~ r1_xxreal_0(k3_finseq_1(D),E) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ( C = k2_real_3(A,B) <=> ( k9_nat_1(k4_ordinal1,C,k5_numbers) = k3_nat_d(A,B) & k9_nat_1(k4_ordinal1,C,1) = k3_nat_d(B,k4_nat_d(A,B)) & ! [D] : ( v7_ordinal1(D) => k9_nat_1(k4_ordinal1,C,k1_nat_1(D,2)) = k3_nat_d(k9_nat_1(k4_ordinal1,k1_real_3(A,B),D),k9_nat_1(k4_ordinal1,k1_real_3(A,B),k1_nat_1(D,1))) ) ) ) ) ) ) )).
fof(d2_real_lat,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k1_binop_1(A,B,C) = k4_xxreal_0(B,C) ) ) ) ) )).
fof(d2_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => k1_binop_1(B,C,D) = k9_euclid(A,D,C) ) ) ) ) ) )).
fof(d2_realset1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : k1_realset1(A,B) = k5_relat_1(A,k2_zfmisc_1(B,B)) ) )).
fof(d2_realset2,axiom,( k2_realset2 = k1_funct_4(k1_funct_4(k1_funct_4(k13_funcop_1(k5_numbers,k5_numbers,k5_numbers),k13_funcop_1(k5_numbers,1,k5_numbers)),k13_funcop_1(1,k5_numbers,k5_numbers)),k13_funcop_1(1,1,1)) )).
fof(d2_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d2_rearran1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v2_rearran1(A) <=> ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(B,k6_xcmplx_0(k3_finseq_1(A),1)) ) => r1_tarski(k1_funct_1(A,B),k1_funct_1(A,k1_nat_1(B,1))) ) ) ) ) )).
fof(d2_recdef_2,axiom,( ! [A] : ( v2_xtuple_0(A) => ! [B] : ( B = k5_xtuple_0(A) <=> ! [C] : ! [D] : ! [E] : ( A = k3_xtuple_0(C,D,E) => B = D ) ) ) )).
fof(d2_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( A = B <=> ! [C] : ! [D] : ( r2_hidden(k4_tarski(C,D),A) <=> r2_hidden(k4_tarski(C,D),B) ) ) ) ) )).
fof(d2_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r2_relat_2(A,B) <=> ! [C] : ~ ( r2_hidden(C,B) & r2_hidden(k4_tarski(C,C),A) ) ) ) )).
fof(d2_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ( r2_relset_1(A,B,C,D) <=> ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,B) => ( r2_hidden(k4_tarski(E,F),C) <=> r2_hidden(k4_tarski(E,F),D) ) ) ) ) ) ) )).
fof(d2_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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))) ) ) )).
fof(d2_revrot_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( r1_revrot_1(A,B,C) <=> ? [D] : ( r2_hidden(D,k4_finseq_1(B)) & C = k7_partfun1(A,B,D) & ! [E] : ~ ( r2_hidden(E,k4_finseq_1(B)) & E != D & k7_partfun1(A,B,E) = C ) ) ) ) ) )).
fof(d2_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( m1_rewrite1(B,A) <=> ( ~ r1_xxreal_0(k3_finseq_1(B),k5_numbers) & ! [C] : ( v7_ordinal1(C) => ( ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(k1_nat_1(C,1),k4_finseq_1(B)) ) => r2_hidden(k4_tarski(k1_funct_1(B,C),k1_funct_1(B,k1_nat_1(C,1))),A) ) ) ) ) ) ) )).
fof(d2_rewrite2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_rewrite2(B) ) => ! [C] : ( ( 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] : ( r2_hidden(D,k9_xtuple_0(B)) => k1_funct_1(C,D) = k1_ordinal4(A,k1_funct_1(B,D)) ) ) ) ) ) ) )).
fof(d2_rewrite3,axiom,( ! [A] : ! [B] : ( l1_rewrite3(B,A) => ! [C] : ! [D] : ! [E] : ( r1_rewrite3(A,B,C,D,E) <=> r2_hidden(k4_tarski(k4_tarski(C,D),E),u1_rewrite3(A,B)) ) ) )).
fof(d2_rfinseq,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( B = k3_rfinseq(A) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & k1_funct_1(B,k3_finseq_1(B)) = k1_funct_1(A,k3_finseq_1(A)) & ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k6_xcmplx_0(k3_finseq_1(B),1)) ) => k1_funct_1(B,C) = k6_xcmplx_0(k1_funct_1(A,C),k1_funct_1(A,k1_nat_1(C,1))) ) ) ) ) ) ) )).
fof(d2_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( v7_ordinal1(B) => ( B = k2_rfinseq2(A) <=> ( ( k3_finseq_1(A) = k5_numbers => B = k5_numbers ) & ( ~ r1_xxreal_0(k3_finseq_1(A),k5_numbers) => ( r2_hidden(B,k4_finseq_1(A)) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( r2_hidden(C,k4_finseq_1(A)) & D = k1_funct_1(A,C) & E = k1_funct_1(A,B) ) => r1_xxreal_0(E,D) ) ) ) ) & ! [C] : ( v7_ordinal1(C) => ( ( r2_hidden(C,k4_finseq_1(A)) & k1_funct_1(A,C) = k1_funct_1(A,B) ) => r1_xxreal_0(B,C) ) ) ) ) ) ) ) ) )).
fof(d2_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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(k5_numbers))) & ! [C] : ( r2_hidden(C,k9_xtuple_0(B)) => k1_funct_1(B,C) = k5_xcmplx_0(k1_funct_1(A,C)) ) ) ) ) ) )).
fof(d2_rfunct_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v6_valued_0(A) <=> ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( 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_funct_1(A,B),k1_funct_1(A,C)) ) ) ) ) ) )).
fof(d2_rfunct_3,axiom,( ! [A] : ( v1_xreal_0(A) => k2_rfunct_3(A) = k4_xxreal_0(k4_xcmplx_0(A),k5_numbers) ) )).
fof(d2_rfunct_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( r2_rfunct_4(A,B) <=> ( r1_tarski(B,k9_xtuple_0(A)) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(1,C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & r2_hidden(D,B) & r2_hidden(E,B) & r2_hidden(k2_xcmplx_0(k3_xcmplx_0(C,D),k3_xcmplx_0(k6_xcmplx_0(1,C),E)),B) & ~ r1_xxreal_0(k1_funct_1(A,k2_xcmplx_0(k3_xcmplx_0(C,D),k3_xcmplx_0(k6_xcmplx_0(1,C),E))),k4_xxreal_0(k1_funct_1(A,D),k1_funct_1(A,E))) ) ) ) ) ) ) ) )).
fof(d2_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k2_rinfsup1(A) = k3_seq_4(k2_relset_1(k1_numbers,A)) ) )).
fof(d2_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => k2_rinfsup2(A) = k7_supinf_2(k17_supinf_2(A)) ) )).
fof(d2_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(d2_ringcat1,axiom,( ! [A] : ( l1_ringcat1(A) => k1_ringcat1(A) = u1_ringcat1(A) ) )).
fof(d2_rlaffin1,axiom,( ! [A] : ( ( ~ 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] : ( m1_rlvect_2(B,A) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_rlvect_2(D,A) => ( ( C != k5_numbers => ( D = k2_rlaffin1(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k1_numbers,D,E) = k3_funct_2(u1_struct_0(A),k1_numbers,B,k1_rlvect_1(A,E,k5_xcmplx_0(C))) ) ) ) & ( C = k5_numbers => ( D = k2_rlaffin1(A,B,C) <=> r1_rlvect_2(A,D,k4_rlvect_2(A)) ) ) ) ) ) ) ) )).
fof(d2_rlaffin2,axiom,( ! [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) ) => ! [B] : ( ( 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] : ( ( ~ 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),k7_xcmplx_0(1,k5_card_1(C))) ) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ~ v1_finset_1(C) => k1_funct_1(B,C) = k4_struct_0(A) ) ) ) ) ) ) )).
fof(d2_rlaffin3,axiom,( ! [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) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_rlaffin3(C,A,B) => ! [D] : k1_rlaffin3(A,B,C,D) = k4_finseqop(u1_struct_0(A),k1_numbers,C,k5_rlaffin1(A,B,D)) ) ) ) )).
fof(d2_rlsub_1,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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))) ) ) ) ) )).
fof(d2_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(d2_rltopsp1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_rltopsp1(A,B,C) = a_3_1_rltopsp1(A,B,C) ) ) ) )).
fof(d2_rlvect_1,axiom,( ! [A] : ( l1_algstr_0(A) => ( v2_rlvect_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_algstr_0(A,B,C) = k1_algstr_0(A,C,B) ) ) ) ) )).
fof(d2_rlvect_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k2_rlvect_2(A,B) <=> ? [D] : ( 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) ) ) ) ) ) ) )).
fof(d2_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( 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) ) ) ) ) )).
fof(d2_rlvect_5,axiom,( ! [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) ) => ( v1_rlvect_5(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( B = k1_rlvect_5(A) <=> ! [C] : ( m1_rlvect_3(C,A) => B = k1_card_1(C) ) ) ) ) ) )).
fof(d2_rlvect_x,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k2_rlvect_x(A,B) = a_2_0_rlvect_x(A,B) ) ) )).
fof(d2_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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))) ) ) ) ) ) )).
fof(d2_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(d2_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_robbins1(A) ) => ( v2_robbins2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_lattices(A,k3_robbins1(A,k1_lattices(A,k3_robbins1(A,B),C)),B) = B ) ) ) ) )).
fof(d2_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lattices(A) ) => ( v2_robbins3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d2_robbins4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_robbins1(A) ) => ( v2_robbins4(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(d2_rpr_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k2_rpr_1(A,B,C) = k7_xcmplx_0(k1_rpr_1(A,k9_subset_1(A,C,B)),k1_rpr_1(A,B)) ) ) ) )).
fof(d2_rsspace,axiom,( ! [A] : ( r2_hidden(A,k1_rsspace) => k2_rsspace(A) = A ) )).
fof(d2_rsspace3,axiom,( ! [A] : ( ( 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] : ( r2_hidden(B,k1_rsspace3) => k1_funct_1(A,B) = k4_series_1(k56_valued_1(k4_ordinal1,k1_numbers,k2_rsspace(B))) ) ) ) )).
fof(d2_rsspace4,axiom,( ! [A] : ( ( 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] : ( r2_hidden(B,k1_rsspace4) => k1_funct_1(A,B) = k2_seq_4(k2_relset_1(k1_numbers,k56_valued_1(k4_ordinal1,k1_numbers,k2_rsspace(B)))) ) ) ) )).
fof(d2_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(d2_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(d2_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(d2_rusub_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ( v1_rusub_4(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( B = k1_rusub_4(A) <=> ! [C] : ( m1_rusub_3(C,A) => B = k1_card_1(C) ) ) ) ) ) )).
fof(d2_rusub_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(d2_rvsum_1,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => k1_funct_1(A,B) = k1_square_1(B) ) ) ) )).
fof(d2_rvsum_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_valued_0(B) ) => k3_rvsum_2(A,B) = k3_funcop_1(k3_binop_2,A,B) ) ) )).
fof(d2_scm_comp,axiom,( ! [A] : ( m2_subset_1(A,u1_struct_0(k1_scm_comp),k6_dtconstr(k1_scm_comp)) => k4_scm_comp(A) = A ) )).
fof(d2_scm_halt,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ( r1_tarski(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_3(k4_scmfsa_2(k5_numbers),1)),B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( r1_tarski(A,C) => r1_extpro_1(k7_card_1(3),k1_scmfsa_2,C,B) ) ) ) ) ) ) )).
fof(d2_scm_inst,axiom,( 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) )).
fof(d2_scmbsort,axiom,( k2_scmbsort = k1_scmbsort(k5_scmfsa_2(k5_numbers)) )).
fof(d2_scmfsa6a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(d2_scmfsa6b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(B,k7_card_1(3),k1_scmfsa_2,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( r1_tarski(A,C) => ! [D] : ( v7_ordinal1(D) => k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,C,B,D),k4_scmfsa_2(k5_numbers)) = k1_funct_1(B,k4_scmfsa_2(k5_numbers)) ) ) ) ) ) ) )).
fof(d2_scmfsa7b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ( r2_scmfsa7b(A,B) <=> ? [C] : ( m1_subset_1(C,u1_compos_1(k1_scmfsa_2)) & r2_hidden(C,k10_xtuple_0(A)) & r1_scmfsa7b(C,B) ) ) ) ) )).
fof(d2_scmfsa8a,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( v7_ordinal1(D) & k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),D)) = k5_card_1(C) & ! [E] : ( v7_ordinal1(E) => ( ~ r1_xxreal_0(D,E) => r2_hidden(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),E)),k2_afinsq_1(C)) ) ) ) ) ) ) ) )).
fof(d2_scmfsa8b,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k1_nat_1(k5_card_1(C),3),A),C),k1_scmfsa8a(k1_nat_1(k5_card_1(B),1))),B),k4_compos_1(k1_scmfsa_2)) ) ) ) )).
fof(d2_scmfsa8c,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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(k5_numbers))))),k4_compos_1(k1_scmfsa_2)) ) ) )).
fof(d2_scmfsa_1,axiom,( k4_scmfsa_1 = k1_funct_4(k8_funcop_1(k4_ordinal1,k1_scmfsa_1,2),k3_ami_2) )).
fof(d2_scmfsa_2,axiom,( k3_scmfsa_2 = k3_scmfsa_1 )).
fof(d2_scmfsa_7,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ( ( ~ r1_xxreal_0(B,k5_numbers) => ( C = k2_scmfsa_7(A,B) <=> ? [D] : ( v7_ordinal1(D) & k1_nat_1(D,1) = B & C = k1_ordinal4(k5_afinsq_1(k6_scmfsa_2(A,k4_scmfsa_2(k5_numbers))),k8_funcop_1(u1_compos_1(k1_scmfsa_2),D,k7_scmfsa_2(A,k4_scmfsa_2(k5_numbers)))) ) ) ) & ( r1_xxreal_0(B,k5_numbers) => ( C = k2_scmfsa_7(A,B) <=> ? [D] : ( v7_ordinal1(D) & k2_xcmplx_0(D,B) = 1 & C = k1_ordinal4(k5_afinsq_1(k6_scmfsa_2(A,k4_scmfsa_2(k5_numbers))),k8_funcop_1(u1_compos_1(k1_scmfsa_2),D,k8_scmfsa_2(A,k4_scmfsa_2(k5_numbers)))) ) ) ) ) ) ) ) )).
fof(d2_scmfsa_9,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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(k5_numbers)),k4_compos_1(k1_scmfsa_2)),k16_funcop_1(k1_nat_1(k5_card_1(B),4),k11_scmfsa_2(k5_numbers))) ) ) )).
fof(d2_scmfsa_i,axiom,( k2_scmfsa_i = k2_xboole_0(k2_xboole_0(k3_scm_inst,a_0_0_scmfsa_i),a_0_1_scmfsa_i) )).
fof(d2_scmfsa_m,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ( v1_scmfsa_m(A) <=> A = k4_scmfsa_2(k5_numbers) ) ) )).
fof(d2_scmisort,axiom,( ! [A] : ( 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(k5_numbers)),k6_scmfsa_2(k4_scmfsa_2(3),k4_scmfsa_2(k5_numbers))),k6_scmfsa_2(k4_scmfsa_2(4),k4_scmfsa_2(k5_numbers))),k6_scmfsa_2(k4_scmfsa_2(5),k4_scmfsa_2(k5_numbers))),k6_scmfsa_2(k4_scmfsa_2(6),k4_scmfsa_2(k5_numbers))),k16_scmfsa_2(k4_scmfsa_2(1),A)),k8_scmfsa_2(k4_scmfsa_2(1),k4_scmfsa_2(k5_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(k5_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(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(2),k4_scmfsa_2(k5_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(k5_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)))))) ) )).
fof(d2_scmp_gcd,axiom,( k2_scmp_gcd = k1_scmp_gcd(k5_numbers) )).
fof(d2_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => k2_scmpds_2(A,B) = k4_tarski(1,k1_int_2(k2_xcmplx_0(A,B))) ) ) )).
fof(d2_scmpds_4,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & 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) ) ) )).
fof(d2_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( r1_scmpds_6(A,B,C) <=> ! [D] : ( v7_ordinal1(D) => 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))) ) ) ) ) ) )).
fof(d2_scmpds_7,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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,k1_nat_1(k5_card_1(D),3)),D),k11_scmpds_2(A,B,k4_xcmplx_0(C))),k3_scmpds_2(k4_xcmplx_0(k1_nat_1(k5_card_1(D),2)))) ) ) ) ) )).
fof(d2_scmpds_8,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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,k1_nat_1(k5_card_1(C),2)),C),k3_scmpds_2(k4_xcmplx_0(k1_nat_1(k5_card_1(C),1)))) ) ) ) )).
fof(d2_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => ( ? [B] : ( m1_subset_1(B,k2_scm_inst) & ? [C] : ( 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] : ( m1_subset_1(B,k2_scm_inst) => ( B = k3_scmpds_i(A) <=> ? [C] : ( m2_finseq_1(C,k2_scm_inst) & C = k2_xtuple_0(A) & B = k7_partfun1(k2_scm_inst,C,1) ) ) ) ) ) )).
fof(d2_scmring1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k4_card_3(k3_relat_1(k3_ami_2,k1_scmring1(A)))) => k2_scmring1(A,B) = k1_funct_1(B,k4_ordinal1) ) ) )).
fof(d2_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(d2_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_scmringi(A)) => ( ? [C] : ( m1_subset_1(C,k2_scm_inst) & ? [D] : ( m1_subset_1(D,k2_scm_inst) & ? [E] : ( 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] : ( m1_subset_1(C,k2_scm_inst) => ( C = k2_scmringi(A,B) <=> ? [D] : ( m2_finseq_1(D,k2_scm_inst) & D = k2_xtuple_0(B) & C = k7_partfun1(k2_scm_inst,D,1) ) ) ) ) ) ) )).
fof(d2_scmyciel,axiom,( ! [A] : ( v1_scmyciel(A) <=> A = k1_tarski(k1_xboole_0) ) )).
fof(d2_scpisort,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k1_scpisort(A,B) = k1_scmpds_4(k3_scmpds_4(k3_scmpds_4(k4_scmpds_4(k5_scmpds_2(k2_scmp_gcd,k5_numbers),k10_scmpds_2(k2_scmp_gcd,1,k5_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,k5_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),k5_numbers)),k16_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,k5_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,k5_numbers)))))))) ) ) )).
fof(d2_scpqsort,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k2_scpqsort(A,B) = k1_scmpds_4(k3_scmpds_4(k3_scmpds_4(k4_scmpds_4(k5_scmpds_2(k2_scmp_gcd,k5_numbers),k5_scmpds_2(k3_scmp_gcd,1)),k10_scmpds_2(k3_scmp_gcd,k2_xcmplx_0(B,A),k1_nat_1(B,1))),k10_scmpds_2(k3_scmp_gcd,k1_nat_1(k2_xcmplx_0(B,A),1),k2_xcmplx_0(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,k1_nat_1(k2_xcmplx_0(B,A),1)),k13_scmpds_2(k2_scmp_gcd,k3_scmp_gcd,2,k2_xcmplx_0(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_xcmplx_0(B,A)),k16_scmpds_2(k2_scmp_gcd,k3_scmp_gcd,4,k1_nat_1(k2_xcmplx_0(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,k1_nat_1(k2_xcmplx_0(B,A),3),k1_nat_1(k2_xcmplx_0(B,A),1)),k16_scmpds_2(k3_scmp_gcd,k2_scmp_gcd,k1_nat_1(k2_xcmplx_0(B,A),1),4)),k16_scmpds_2(k3_scmp_gcd,k2_scmp_gcd,k1_nat_1(k2_xcmplx_0(B,A),2),4)),k11_scmpds_2(k3_scmp_gcd,k1_nat_1(k2_xcmplx_0(B,A),1),k4_xcmplx_0(1))),k11_scmpds_2(k3_scmp_gcd,k1_nat_1(k2_xcmplx_0(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))))))) ) ) )).
fof(d2_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_semi_af1(A,B,C,D) <=> r2_analoaf(A,B,C,B,D) ) ) ) ) ) )).
fof(d2_seq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) ) => ( v2_seq_2(A) <=> ? [B] : ( v1_xreal_0(B) & ! [C] : ~ ( r2_hidden(C,k9_xtuple_0(A)) & r1_xxreal_0(k1_funct_1(A,C),B) ) ) ) ) )).
fof(d2_seq_4,axiom,( ! [A] : ( v3_membered(A) => ( v3_xxreal_2(A) => ( v1_xboole_0(A) | ! [B] : ( v1_xreal_0(B) => ( B = k3_seq_4(A) <=> ( ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => r1_xxreal_0(B,C) ) ) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,A) & ~ r1_xxreal_0(k2_xcmplx_0(B,C),D) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( C = k3_seqfunc(A,B) <=> ! [D] : ( 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))) ) ) ) ) ) )).
fof(d2_seqm_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v3_valued_0(A) ) => ( v6_valued_0(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(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)) ) ) ) ) ) )).
fof(d2_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_series_1(A) <=> v2_comseq_2(k3_series_1(A)) ) ) )).
fof(d2_setfam_1,axiom,( ! [A] : ! [B] : ( r1_setfam_1(A,B) <=> ! [C] : ~ ( r2_hidden(C,A) & ! [D] : ~ ( r2_hidden(D,B) & r1_tarski(C,D) ) ) ) )).
fof(d2_setlim_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k1_setlim_1(A) <=> ( k9_xtuple_0(B) = k4_ordinal1 & ! [C] : ( v7_ordinal1(C) => k1_funct_1(B,C) = k1_setfam_1(a_2_1_setlim_1(A,C)) ) ) ) ) ) )).
fof(d2_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( D = k2_setlim_2(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k9_nat_1(k9_setfam_1(A),D,E) = k4_subset_1(A,k9_nat_1(k9_setfam_1(A),B,E),k9_nat_1(k9_setfam_1(A),C,E)) ) ) ) ) ) )).
fof(d2_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) & r3_binop_1(A,C,B) ) ) ) ) )).
fof(d2_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( 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(k4_ordinal1,A,C,k3_finsop_1(B),k1_setwop_2(A,B,k4_binop_1(A,C))) ) ) ) ) ) )).
fof(d2_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_scmfsa_2)) => ( B = k2_sf_mastr(A) <=> ? [C] : ( 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] : ( 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)) ) ) ) ) )).
fof(d2_sfmastr2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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_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)) ) ) )).
fof(d2_sfmastr3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(F,u1_struct_0(k1_scmfsa_2)) ) => ( r1_sfmastr3(A,B,C,D,E,F) <=> ! [G] : ( v7_ordinal1(G) => ( ~ r1_xxreal_0(k2_xcmplx_0(k6_xcmplx_0(k1_funct_1(F,D),k1_funct_1(F,C)),1),G) => ( r5_scmfsa7b(E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(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(k5_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(k5_numbers)))))) & r6_scmfsa7b(E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(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(k5_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(k5_numbers)))))) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_sgraph1,axiom,( ! [A] : k2_sgraph1(A) = a_1_0_sgraph1(A) )).
fof(d2_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( v1_sheffer1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B = k1_sheffer1(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_lattices(A,B,C) = C & k2_lattices(A,C,B) = C ) ) ) ) ) ) )).
fof(d2_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) => ( D = k3_simplex0(A,B,C) <=> ! [E] : ( 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)) ) ) ) ) ) )).
fof(d2_simplex1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_simplex0(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) => k2_simplex1(A,B,C) = C ) ) ) )).
fof(d2_simplex2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( l1_pre_topc(B) => ( v1_simplex2(B,A) <=> ? [C] : ( v1_xreal_0(C) & ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(d2_sin_cos,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( A = k2_sin_cos <=> ( k9_nat_1(k1_numbers,A,k5_numbers) = 1 & ! [B] : ( v7_ordinal1(B) => k9_nat_1(k1_numbers,A,k1_nat_1(B,1)) = k3_xcmplx_0(k9_nat_1(k1_numbers,A,B),k1_nat_1(B,1)) ) ) ) ) )).
fof(d2_sin_cos2,axiom,( ! [A] : k2_sin_cos2(A) = k1_funct_1(k1_sin_cos2,A) )).
fof(d2_sin_cos3,axiom,( ! [A] : ( ( 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] : ( v1_xcmplx_0(B) => k1_funct_1(A,B) = k7_xcmplx_0(k2_xcmplx_0(k15_sin_cos(k3_xcmplx_0(k7_complex1,B)),k15_sin_cos(k4_xcmplx_0(k3_xcmplx_0(k7_complex1,B)))),2) ) ) ) )).
fof(d2_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => k2_sin_cos4(A) = k7_xcmplx_0(k19_sin_cos(A),k17_sin_cos(A)) ) )).
fof(d2_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => k2_sin_cos5(A) = k7_xcmplx_0(1,k4_sin_cos2(A)) ) )).
fof(d2_sin_cos6,axiom,( ! [A] : k2_sin_cos6(A) = k1_funct_1(k1_sin_cos6,A) )).
fof(d2_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => k2_sin_cos7(A) = k3_power(k4_power,k2_xcmplx_0(A,k3_square_1(k6_xcmplx_0(k1_square_1(A),1)))) ) )).
fof(d2_sin_cos9,axiom,( k2_sin_cos9 = k2_partfun2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k27_sin_cos,k2_rcomp_1(k5_numbers,k28_sin_cos))) )).
fof(d2_sincos10,axiom,( k2_sincos10 = k2_partfun2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k4_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos))) )).
fof(d2_sppol_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_sppol_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => k18_euclid(B) = k18_euclid(C) ) ) ) ) ) )).
fof(d2_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal4(A) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & r1_sppol_2(B,C,A) ) ) ) ) )).
fof(d2_sprect_1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v1_sprect_1(A) <=> ? [B] : ( ~ 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) ) ) ) )).
fof(d2_sprect_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) ) )).
fof(d2_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k5_numbers,A) => ! [B] : ( v1_xreal_0(B) => ( B = k3_square_1(A) <=> ( r1_xxreal_0(k5_numbers,B) & k1_square_1(B) = A ) ) ) ) ) )).
fof(d2_stacks_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ! [G] : ! [H] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(d2_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k3_stirl2_1(A,B) = k1_card_1(a_2_0_stirl2_1(A,B)) ) ) )).
fof(d2_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => k1_struct_0(A) = k1_xboole_0 ) )).
fof(d2_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k16_substut1(A),k38_substut1(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [E] : ( m1_valuat_1(E,A,C) => ( r1_sublemma(A,B,C,D,E) <=> r1_valuat_1(A,C,k2_sublemma(A,B),E,D) ) ) ) ) ) ) )).
fof(d2_subset_1,axiom,( ! [A] : k1_subset_1(A) = k1_xboole_0 )).
fof(d2_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => k3_substlat(A,B,C) = a_3_0_substlat(A,B,C) ) )).
fof(d2_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_substut1(A)) => k2_substut1(A,B) = B ) ) )).
fof(d2_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => k6_substut2(A) = k5_relat_1(k15_substut1(A),k38_substut1(A)) ) )).
fof(d2_supinf_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ( B = k4_supinf_1(A) <=> ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(C,B) <=> m2_xxreal_2(C,A) ) ) ) ) ) )).
fof(d2_supinf_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( ( 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)) ) ) ) )).
fof(d2_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( ~ r1_orders_2(B,D,C) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( F = k1_symsp_1(A,B,C,D,E) <=> ! [G] : ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(d2_t_0topsp,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) ) )).
fof(d2_t_1topsp,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(d2_tarski,axiom,( ! [A] : ! [B] : ! [C] : ( C = k2_tarski(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( D = A | D = B ) ) ) )).
fof(d2_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) ) ) )).
fof(d2_taxonom2,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_taxonom2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( ? [D] : ( 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) ) ) ) ) ) )).
fof(d2_taylor_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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(k5_numbers) & ! [C] : ( m2_subset_1(C,k1_numbers,k3_limfunc1(k5_numbers)) => k1_funct_1(B,C) = k3_power(A,C) ) ) ) ) ) )).
fof(d2_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v2_tbsp_1(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(E,F) & r1_xxreal_0(D,k1_metric_1(A,k9_nat_1(u1_struct_0(A),B,F),C)) ) ) ) ) ) ) ) ) )).
fof(d2_tdgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d2_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k1_tdlat_1(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d2_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_tdlat_2(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => v4_tops_1(C,A) ) ) ) ) ) )).
fof(d2_tdlat_3,axiom,( ! [A] : ( l1_pre_topc(A) => ( v2_tdlat_3(A) <=> u1_pre_topc(A) = k2_tarski(k1_xboole_0,u1_struct_0(A)) ) ) )).
fof(d2_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(d2_tex_1,axiom,( ! [A] : k1_tex_1(A) = k2_tarski(k1_xboole_0,A) )).
fof(d2_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(d2_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v2_tex_3(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = u1_struct_0(B) => v1_tops_3(C,A) ) ) ) ) ) )).
fof(d2_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tex_4(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d2_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_tmap_1(A,B,C,D) <=> ! [E] : ( m1_connsp_2(E,B,k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,D)) => ? [F] : ( m1_connsp_2(F,A,D) & r1_tarski(k7_relset_1(u1_struct_0(A),u1_struct_0(B),C,F),E) ) ) ) ) ) ) ) )).
fof(d2_toler_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_toler_1(C,A,B) => ( v1_toler_1(C,A,B) <=> ! [D] : ~ ( ~ r2_hidden(D,C) & r2_hidden(D,A) & ! [E] : ~ ( r2_hidden(E,C) & ~ r2_hidden(k4_tarski(D,E),B) ) ) ) ) ) )).
fof(d2_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_topalg_1(A,B) = k1_topalg_1(A,B,B) ) ) )).
fof(d2_topalg_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v1_topalg_2(B,A) & m1_pre_topc(B,k15_euclid(A)) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k5_topmetr)) => ! [G] : ( m1_subset_1(G,u1_struct_0(k5_topmetr)) => ! [H] : ( m1_subset_1(H,u1_struct_0(k15_euclid(A))) => ! [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,k6_xcmplx_0(1,G)),k1_rlvect_1(k15_euclid(A),I,G)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k5_topalg_1(k2_borsuk_1(A,B),k4_borsuk_1(A,B,C,D)))) => ? [G] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(d2_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v2_topalg_6(A) <=> ( v1_topalg_6(A) & v1_borsuk_2(A) ) ) ) )).
fof(d2_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_topdim_1(B,A) <=> ? [C] : ( v7_ordinal1(C) & r2_hidden(B,k13_prob_1(u1_struct_0(A),k4_ordinal1,k9_setfam_1(u1_struct_0(A)),k1_topdim_1(A),C)) ) ) ) ) )).
fof(d2_topdim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( v1_xxreal_0(C) => ( ( v1_topdim_2(B,A) => ( C = k1_topdim_2(A,B) <=> ( ! [D] : ( 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] : ( 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 ) ) ) ) ) )).
fof(d2_topgen_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( r1_topgen_1(A,B,C) <=> r2_hidden(C,k2_pre_topc(A,k7_subset_1(u1_struct_0(A),B,k1_tarski(C)))) ) ) ) )).
fof(d2_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( v1_card_1(B) => ( B = k2_topgen_2(A) <=> ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_ordinal1(k1_topgen_2(A,C),B) ) & ! [C] : ( v1_card_1(C) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_ordinal1(k1_topgen_2(A,D),C) ) => r1_ordinal1(B,C) ) ) ) ) ) ) )).
fof(d2_topgen_3,axiom,( ! [A] : ( ( ~ 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] : ( 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 ) ) ) ) )).
fof(d2_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_topgen_4(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(C,A) => r2_hidden(C,B) ) ) ) ) ) )).
fof(d2_topgen_5,axiom,( k2_topgen_5 = a_0_1_topgen_5 )).
fof(d2_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d2_topmetr,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v1_metric_1(C) & m1_topmetr(C,A) ) => ( C = k1_topmetr(A,B) <=> u1_struct_0(C) = B ) ) ) ) )).
fof(d2_topreal1,axiom,( 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(k5_numbers,k5_numbers),k19_euclid(k5_numbers,1)),k1_rltopsp1(k15_euclid(2),k19_euclid(k5_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,k5_numbers)),k1_rltopsp1(k15_euclid(2),k19_euclid(1,k5_numbers),k19_euclid(k5_numbers,k5_numbers)))) )).
fof(d2_topreal4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal4(A) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ? [E] : ( 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) ) ) ) ) ) ) )).
fof(d2_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( v1_xreal_0(C) => k2_topreal9(A,B,C) = a_3_1_topreal9(A,B,C) ) ) ) )).
fof(d2_topreala,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k1_funct_1(A,k4_tarski(B,C)) = k10_finseq_1(B,C) ) ) ) ) )).
fof(d2_toprealb,axiom,( ! [A] : ( v1_xreal_0(A) => k4_toprealb(A) = A ) )).
fof(d2_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => k1_toprns_1(A,B,C) = k1_vfunct_1(k4_ordinal1,k15_euclid(A),B,C) ) ) ) )).
fof(d2_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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))) ) ) )).
fof(d2_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v2_tops_2(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => v4_pre_topc(C,A) ) ) ) ) ) )).
fof(d2_tops_3,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) )).
fof(d2_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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] : ( m1_subset_1(D,A) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(d2_treal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => k2_treal_1(A,B) = B ) ) ) )).
fof(d2_trees_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( B = k1_trees_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) & C = D & r2_xboole_0(D,A) ) ) ) ) )).
fof(d2_trees_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_trees_3)) => ( A = k2_trees_3 <=> ! [B] : ( r2_hidden(B,A) <=> ( ~ v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) ) ) ) ) )).
fof(d2_trees_4,axiom,( ! [A] : k1_trees_4(A) = k7_funcop_1(k2_trees_1(k5_numbers),A) )).
fof(d2_trees_a,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( m4_trees_1(B,k9_xtuple_0(A)) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) ) => ( B != k1_xboole_0 => ! [D] : ( ( 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] : ( m2_finseq_1(E,k4_ordinal1) => ~ ( r2_hidden(E,k1_trees_a(k9_xtuple_0(A),k9_xtuple_0(C),B)) & ? [F] : ( m2_finseq_1(F,k4_ordinal1) & r2_hidden(F,B) & ~ ( ~ r1_tarski(F,E) & k1_funct_1(D,E) = k1_funct_1(A,E) ) ) & ! [F] : ( m2_finseq_1(F,k4_ordinal1) => ! [G] : ( m2_finseq_1(G,k4_ordinal1) => ~ ( r2_hidden(F,B) & r2_hidden(G,k9_xtuple_0(C)) & E = k8_finseq_1(k4_ordinal1,F,G) & k1_funct_1(D,E) = k1_funct_1(C,G) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ 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)) ) ) ) ) ) )).
fof(d2_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_pre_topc(C,A) => ( r3_tsep_2(A,B,C) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d2_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ( m1_pre_topc(B,A) <=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A)) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v4_pre_topc(C,B) <=> ? [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(d2_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tsp_1(B,A) <=> ! [C] : ( 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) ) ) ) ) ) )).
fof(d2_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( m2_funct_2(B,k4_numbers,u1_turing_1(A),k9_funct_2(k4_numbers,u1_turing_1(A))) => ! [C] : ( v1_int_1(C) => ! [D] : ( m1_subset_1(D,u1_turing_1(A)) => k5_turing_1(A,B,C,D) = k1_funct_4(B,k16_funcop_1(C,D)) ) ) ) ) )).
fof(d2_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k1_funct_1(A,k10_finseq_1(B,C)) = k10_margrel1(k9_margrel1(B),C) ) ) ) ) )).
fof(d2_unialg_1,axiom,( ! [A] : ( l1_unialg_1(A) => ( v3_unialg_1(A) <=> v5_margrel1(u1_unialg_1(A),u1_struct_0(A)) ) ) )).
fof(d2_unialg_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d2_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => k2_uniroots(A) = a_1_0_uniroots(A) ) )).
fof(d2_uproots,axiom,( ! [A] : ! [B] : ( ( 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] : ( v1_xreal_0(C) => ( C = k2_uproots(A,B) <=> ? [D] : ( m2_finseq_1(D,k1_numbers) & C = k18_rvsum_1(D) & D = k3_relat_1(k19_finseq_1(k13_pre_poly(B)),B) ) ) ) ) )).
fof(d2_urysohn1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( A = k2_urysohn1 <=> ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) <=> ? [C] : ( v7_ordinal1(C) & r2_hidden(B,k1_urysohn1(C)) ) ) ) ) ) )).
fof(d2_urysohn3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(k2_urysohn1,k9_setfam_1(u1_struct_0(A)))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(k2_urysohn1,k9_setfam_1(u1_struct_0(A)))))) ) => ( m2_urysohn3(D,A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ( m1_urysohn3(k2_urysohn3(k2_urysohn1,k9_setfam_1(u1_struct_0(A)),D,E),A,B,C,E) & ! [F] : ( m1_subset_1(F,k9_xtuple_0(k2_urysohn3(k2_urysohn1,k9_setfam_1(u1_struct_0(A)),D,E))) => k1_funct_1(k2_urysohn3(k2_urysohn1,k9_setfam_1(u1_struct_0(A)),D,E),F) = k1_funct_1(k2_urysohn3(k2_urysohn1,k9_setfam_1(u1_struct_0(A)),D,k1_nat_1(E,1)),F) ) ) ) ) ) ) ) ) ) ) )).
fof(d2_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_funct_2(D,k2_valuat_1(A,B),k6_margrel1,k9_funct_2(k2_valuat_1(A,B),k6_margrel1)) => ! [E] : ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(d2_valued_0,axiom,( ! [A] : ( v1_relat_1(A) => ( v2_valued_0(A) <=> r1_tarski(k10_xtuple_0(A),k6_numbers) ) ) )).
fof(d2_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k7_valued_1(A,B) <=> ( k9_xtuple_0(C) = k9_xtuple_0(A) & ! [D] : ( r2_hidden(D,k9_xtuple_0(C)) => k1_funct_1(C,D) = k2_xcmplx_0(B,k1_funct_1(A,D)) ) ) ) ) ) ) )).
fof(d2_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => k2_vectsp10(A,B,C) = a_3_0_vectsp10(A,B,C) ) ) ) )).
fof(d2_vectsp11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ( m1_vectsp11(D,A,B,C) <=> ? [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d2_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ( v1_vectsp_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d2_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( B != k4_struct_0(A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k11_algstr_0(A,B) <=> k6_algstr_0(A,C,B) = k5_struct_0(A) ) ) ) ) ) )).
fof(d2_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ 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))) ) ) ) ) ) )).
fof(d2_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(d2_vectsp_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => k1_vectsp_6(A,B,C) = a_3_0_vectsp_6(A,B,C) ) ) ) )).
fof(d2_vectsp_7,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(d2_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( v7_ordinal1(C) => ! [D] : ( D = k2_vectsp_9(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ? [F] : ( v7_vectsp_1(F,A) & m1_vectsp_4(F,A,B) & F = E & k1_vectsp_9(A,F) = C ) ) ) ) ) ) )).
fof(d2_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d2_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d2_waybel10,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( ~ v2_struct_0(B) & v1_orders_2(B) & l1_orders_2(B) ) => ( B = k3_waybel10(A) <=> ( ! [C] : ( m1_subset_1(C,u1_struct_0(B)) <=> ( v1_orders_2(C) & m1_yellow_0(C,A) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r1_orders_2(B,C,D) <=> ? [E] : ( l1_orders_2(E) & D = E & m1_yellow_0(C,E) ) ) ) ) ) ) ) ) )).
fof(d2_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_waybel11(B,A) <=> ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(d2_waybel12,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_waybel12(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => v1_tops_1(C,A) ) ) ) ) ) )).
fof(d2_waybel15,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( B = k1_waybel15(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) <=> v1_waybel15(C,A) ) ) ) ) ) )).
fof(d2_waybel17,axiom,( ! [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) & v4_waybel11(A) & l1_waybel_9(A) ) => ! [B] : ( ( 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] : ( ( v1_orders_2(C) & v4_yellow_0(C,k6_yellow_1(A,B)) & m1_yellow_0(C,k6_yellow_1(A,B)) ) => ( C = k2_waybel17(A,B) <=> ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(d2_waybel18,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_waybel18(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(k4_card_3(k12_pralg_1(A,B))))) => ( C = k2_waybel18(A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k4_card_3(k12_pralg_1(A,B)))) => ( r2_hidden(D,C) <=> ? [E] : ? [F] : ( l1_pre_topc(F) & ? [G] : ( 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(k1_funct_7(k12_pralg_1(A,B),E,G)) ) ) ) ) ) ) ) )).
fof(d2_waybel19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( B = k1_waybel19(A) <=> ! [C] : ( ( v2_pre_topc(C) & v1_waybel19(C) & m1_yellow_9(C,A) ) => B = u1_pre_topc(C) ) ) ) ) )).
fof(d2_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(d2_waybel22,axiom,( ! [A] : k1_waybel22(A) = a_1_0_waybel22(A) )).
fof(d2_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_waybel23(B,A) <=> v6_yellow_0(k5_yellow_0(A,B),A) ) ) ) )).
fof(d2_waybel24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => k2_waybel24(A,B,C,D,E) = k1_funct_1(k3_funct_5(D),E) ) ) ) ) ) )).
fof(d2_waybel25,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r1_orders_2(B,C,D) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & E = k1_tarski(D) & r2_hidden(C,k2_pre_topc(A,E)) ) ) ) ) ) ) ) ) )).
fof(d2_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(d2_waybel27,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_waybel27(A) <=> ( ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => ( v1_relat_1(B) & v1_funct_1(B) & v1_relat_1(k9_xtuple_0(B)) ) ) & ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(B,k9_xtuple_0(A)) => k1_funct_1(A,B) = k1_funct_5(B) ) ) ) ) ) )).
fof(d2_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( ( 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] : ( ( ~ 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))) ) ) ) ) ) ) )).
fof(d2_waybel29,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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 ) ) ) )).
fof(d2_waybel31,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(d2_waybel32,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_orders_2(A) & l1_waybel_9(A) ) => ( v2_waybel32(A) <=> ! [B] : ( 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] : ( ( ~ 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] : ( m1_connsp_2(D,A,B) => r1_waybel_0(A,C,D) ) ) ) ) ) ) ) )).
fof(d2_waybel33,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_waybel_9(A) ) => ( v1_waybel33(A) <=> u1_pre_topc(A) = k4_waybel28(A) ) ) )).
fof(d2_waybel34,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(d2_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_waybel_0(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,B) & r1_orders_2(A,E,C) & r1_orders_2(A,E,D) ) ) ) ) ) ) ) ) )).
fof(d2_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(d2_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ! [C] : ( ( 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] : ( ( ~ v2_struct_0(D) & v7_waybel_0(D) & l1_waybel_0(D,A) ) => ( D = k2_waybel_2(A,B,C) <=> ? [E] : ( 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] : ( 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),k2_orders_1(k5_finsub_1(B)),E) ) ) ) ) ) ) ) )).
fof(d2_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_waybel_3(B,A) <=> r1_waybel_3(A,B,B) ) ) ) )).
fof(d2_waybel_4,axiom,( ! [A] : ( l1_orders_2(A) => k2_waybel_4(A) = u1_orders_2(A) ) )).
fof(d2_waybel_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) ) => ! [C] : ( ( 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] : ( r2_hidden(D,k9_xtuple_0(B)) => k1_funct_1(C,D) = k5_yellow_2(A,k1_funct_1(B,D)) ) ) ) ) ) )).
fof(d2_waybel_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v2_waybel_6(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( B = k11_lattice3(A,C,D) & C != B & D != B ) ) ) ) ) ) )).
fof(d2_waybel_7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(k13_lattice3(A,C,D),B) & ~ r2_hidden(C,B) & ~ r2_hidden(D,B) ) ) ) ) ) ) )).
fof(d2_waybel_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_waybel_8(A,B) = a_2_0_waybel_8(A,B) ) ) )).
fof(d2_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( l1_waybel_0(B,A) => k1_waybel_9(A,B) = k5_yellow_2(A,u1_waybel_0(A,B)) ) ) )).
fof(d2_weddwitt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d2_weierstr,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => k2_weierstr(A) = k2_seq_4(k1_weierstr(A)) ) )).
fof(d2_wellfnd1,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_wellfnd1(A) <=> r1_wellord1(u1_orders_2(A),u1_struct_0(A)) ) ) )).
fof(d2_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_wellord1(A) <=> ! [B] : ~ ( r1_tarski(B,k1_relat_1(A)) & B != k1_xboole_0 & ! [C] : ~ ( r2_hidden(C,B) & r1_xboole_0(k1_wellord1(A,C),B) ) ) ) ) )).
fof(d2_wellord2,axiom,( ! [A] : ( v1_relat_1(A) => ( v2_wellord1(A) => ! [B] : ( v3_ordinal1(B) => ( B = k2_wellord2(A) <=> r4_wellord1(A,k1_wellord2(B)) ) ) ) ) )).
fof(d2_xboole_0,axiom,( k1_xboole_0 = o_0_0_xboole_0 )).
fof(d2_xboolean,axiom,( k2_xboolean = 1 )).
fof(d2_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) <=> r2_hidden(A,k2_numbers) ) )).
fof(d2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,k6_xcmplx_0(A,B)) => k1_xreal_0(A,B) = k6_xcmplx_0(A,B) ) & ( ~ r1_xxreal_0(k5_numbers,k6_xcmplx_0(A,B)) => k1_xreal_0(A,B) = k5_numbers ) ) ) ) )).
fof(d2_xtuple_0,axiom,( ! [A] : ( v1_xtuple_0(A) => ! [B] : ( B = k1_xtuple_0(A) <=> ! [C] : ! [D] : ( A = k4_tarski(C,D) => B = C ) ) ) )).
fof(d2_xxreal_0,axiom,( k1_xxreal_0 = k1_numbers )).
fof(d2_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k2_xxreal_1(A,B) = a_2_1_xxreal_1(A,B) ) ) )).
fof(d2_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => ( m2_xxreal_2(B,A) <=> ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(C,A) => r1_xxreal_0(B,C) ) ) ) ) ) )).
fof(d2_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( C = k1_xxreal_3(A,B) <=> ? [D] : ( v1_xcmplx_0(D) & ? [E] : ( 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 = k5_numbers ) ) ) ) ) ) )).
fof(d2_yellow11,axiom,( k2_yellow11 = k1_yellow_1(k3_enumset1(k5_numbers,1,k6_subset_1(2,1),k6_subset_1(3,2),3)) )).
fof(d2_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( m1_yellow13(C,A,B) <=> ! [D] : ( m1_connsp_2(D,A,B) => ? [E] : ( m1_connsp_2(E,A,B) & r2_hidden(E,C) & r1_tarski(E,D) ) ) ) ) ) ) )).
fof(d2_yellow15,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ( C = k2_yellow15(A,B) <=> ? [D] : ( 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) ) ) ) ) )).
fof(d2_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(d2_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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] : ( v15_functor0(C,A,B) & m2_functor0(C,A,B) & ? [D] : ( 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)) ) ) ) ) ) )).
fof(d2_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( m1_yellow19(C,A,B) <=> ? [D] : ( 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))) ) ) ) ) ) )).
fof(d2_yellow20,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d2_yellow21,axiom,( ! [A] : ! [B] : ( B = k2_yellow21(A) <=> ! [C] : ( 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) ) ) ) )).
fof(d2_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v4_orders_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d2_yellow_1,axiom,( ! [A] : k2_yellow_1(A) = k3_lattice3(k1_lattice3(A)) )).
fof(d2_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) )).
fof(d2_yellow_3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(d2_yellow_4,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_yellow_4(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,B) & r1_orders_2(A,E,D) ) ) ) ) ) ) ) ) )).
fof(d2_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(d2_yellow_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_pralg_1(A) ) => ( v4_waybel_3(A) <=> ! [B] : ( r2_hidden(B,k10_xtuple_0(A)) => ( ~ v2_struct_0(B) & l1_struct_0(B) ) ) ) ) )).
fof(d2_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v2_yellow_8(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ~ ( v4_card_3(B) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => v1_tops_3(C,A) ) ) & ! [C] : ( 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) ) ) ) ) ) ) )).
fof(d2_yellow_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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))) ) ) )).
fof(d2_yoneda_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_yoneda_1(A,B) = k19_ens_1(A,B) ) ) )).
fof(d2_zf_fund1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( B = k3_zf_fund1(A) <=> k2_zf_lang(B) = A ) ) ) )).
fof(d2_zf_fund2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_zf_fund2(A) <=> ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(d2_zf_lang,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k2_zf_lang(A) = k1_nat_1(5,A) ) )).
fof(d2_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => k3_zf_lang1(A) = k6_subset_1(k10_xtuple_0(A),k3_enumset1(k5_numbers,1,2,3,4)) ) )).
fof(d2_zf_model,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k3_zf_model(A) = k9_funct_2(k1_zf_lang,A) ) )).
fof(d2_zf_refle,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(d2_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( C = k2_zfmisc_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ? [F] : ( r2_hidden(E,A) & r2_hidden(F,B) & D = k4_tarski(E,F) ) ) ) )).
fof(d2_zfmodel1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ 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(k5_numbers),k8_zf_lang(k2_zf_lang(4),k12_zf_lang(A,k4_zf_lang(k2_zf_lang(4),k2_zf_lang(k5_numbers))))))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(d2_zfrefle1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ( r2_zfrefle1(A,B) <=> ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ( k2_zf_model(C) = k1_xboole_0 => ( r2_zf_model(A,C) <=> r2_zf_model(B,C) ) ) ) ) ) ) )).
fof(d2_zmodul01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_zmodul01(A) ) => ( v2_zmodul01(A) <=> ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d2_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( v1_int_1(B) => k2_zmodul02(A,B) = k4_struct_0(A) ) ) )).
fof(d2_zmodul03,axiom,( ! [A] : ( ( ~ 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) & v1_zmodul03(A) & l1_zmodul01(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( m1_zmodul03(B,A) <=> ( v1_zmodul02(B,A) & k33_zmodul02(A,B) = g1_zmodul01(u1_struct_0(A),u2_struct_0(A),u1_algstr_0(A),u1_zmodul01(A)) ) ) ) ) )).
fof(d30_abcmiz_0,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( ( 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 ) ) ) ) ) ) ) ) )).
fof(d30_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ( k3_finseq_1(k1_msualg_1(A,B)) = 1 => ! [C] : ( m1_subset_1(C,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ( ? [D] : ( 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)) ) ) ) ) ) )).
fof(d30_abcmiz_a,axiom,( ! [A] : ( m2_finseq_2(A,k2_abcmiz_1,k4_abcmiz_1) => ! [B] : ( ( 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) ) ) ) ) )).
fof(d30_algstr_0,axiom,( ! [A] : ( l4_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ( v23_algstr_0(B,A) & v17_algstr_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k9_algstr_0(A,B) <=> k6_algstr_0(A,C,B) = k5_struct_0(A) ) ) ) ) ) )).
fof(d30_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( ( 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] : ( m1_subset_1(E,B) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d30_aofa_a00,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( l5_aofa_a00(B) => ( v14_aofa_a00(B,A) <=> k3_finseq_1(u7_aofa_a00(B)) = A ) ) ) )).
fof(d30_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m3_aofa_i00(E,A,B,C,D) => ! [F] : ( m3_aofa_i00(F,A,B,C,D) => ! [G] : ( m3_aofa_i00(G,A,B,C,D) => ( G = k36_aofa_i00(A,B,C,D,E,F) <=> ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d30_armstrng,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ( v14_armstrng(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(d30_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_cat_1(F,A,B,D) => ! [G] : ( 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))) ) ) ) ) ) ) ) )).
fof(d30_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) ) )).
fof(d30_descip_1,axiom,( ! [A] : ( m2_finseq_2(A,k4_finseq_2(48,k6_margrel1),k4_finseq_2(16,k4_finseq_2(48,k6_margrel1))) => ! [B] : ( ( 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] : ( ( 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] : ( m2_finseq_2(D,k6_margrel1,k4_finseq_2(64,k6_margrel1)) => ! [E] : ( m2_finseq_2(E,k6_margrel1,k4_finseq_2(64,k6_margrel1)) => ( E = k41_descip_1(A,B,C,D) <=> ? [F] : ( v1_funct_1(F) & v1_funct_2(F,k4_finseq_2(k2_nat_1(2,32),k6_margrel1),k4_finseq_2(k2_nat_1(2,32),k6_margrel1)) & v3_funct_2(F,k4_finseq_2(k2_nat_1(2,32),k6_margrel1),k4_finseq_2(k2_nat_1(2,32),k6_margrel1)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(k2_nat_1(2,32),k6_margrel1),k4_finseq_2(k2_nat_1(2,32),k6_margrel1)))) & ? [G] : ( m2_finseq_2(G,k6_margrel1,k4_finseq_2(k2_nat_1(2,32),k6_margrel1)) & r1_funct_2(k4_finseq_2(k2_nat_1(2,32),k6_margrel1),k4_finseq_2(k2_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) ) ) ) ) ) ) ) ) )).
fof(d30_fomodel0,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => k27_fomodel0(A,B) = k2_xboole_0(k5_relat_1(A,k6_subset_1(k9_xtuple_0(A),k9_xtuple_0(B))),B) ) ) )).
fof(d30_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k25_fomodel1(A) <=> ( k9_xtuple_0(B) = k4_ordinal1 & k1_funct_1(B,k5_numbers) = k11_fomodel1(A) & ! [C] : ( 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)) ) ) ) ) ) )).
fof(d30_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ( C = k29_fomodel2(A,B) <=> ( v3_fomodel2(B,A,C) & ! [D] : ( v7_ordinal1(D) => ( v3_fomodel2(B,A,D) => r1_xxreal_0(C,D) ) ) ) ) ) ) ) )).
fof(d30_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( v12_fomodel4(C,B) => ( r10_fomodel4(A,B,C) <=> ? [D] : ? [E] : ? [F] : ( 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] : ( 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) = k42_fomodel1(B,k42_fomodel1(B,k43_fomodel1(B,k1_fomodel2(B)),F),F) & k2_xtuple_0(E) = k42_fomodel1(B,k42_fomodel1(B,k43_fomodel1(B,k1_fomodel2(B)),G),G) & k2_xtuple_0(C) = k42_fomodel1(B,k42_fomodel1(B,k43_fomodel1(B,k1_fomodel2(B)),F),G) ) ) ) ) ) )).
fof(d30_functor0,axiom,( ! [A] : ( l1_altcat_1(A) => ! [B] : ( l1_altcat_1(B) => ! [C] : ( l2_functor0(C,A,B) => ( v17_functor0(C,A,B) <=> v1_msualg_3(u2_functor0(A,B,C)) ) ) ) ) )).
fof(d30_gate_1,axiom,( ! [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) & 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 ) ) )).
fof(d30_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(d30_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k7_glib_000(A))) => ( D = k22_glib_000(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> r3_glib_000(A,B,C,E) ) ) ) ) )).
fof(d30_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => k27_grcat_1(A) = k5_grcat_1(k25_grcat_1(A),k26_grcat_1(A)) ) )).
fof(d30_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v8_group_9(C,A,B) & m2_finseq_1(C,k6_group_9(A,B)) ) => ( v9_group_9(C,A,B) <=> ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(D,k4_finseq_1(C)) & r2_hidden(k1_nat_1(D,1),k4_finseq_1(C)) ) => ! [E] : ( m1_group_9(E,A,B) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(d30_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ( r8_ltlaxio1(A,B) <=> ? [C] : ( m2_finseq_1(C,k1_hilbert1) & k1_funct_1(C,k3_finseq_1(C)) = B & r1_xxreal_0(1,k3_finseq_1(C)) & ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(C)) ) => r7_ltlaxio1(D,C,A) ) ) ) ) ) ) )).
fof(d30_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ( B = k22_modelc_3(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( v1_modelc_3(D,A) & l1_modelc_3(D,A) & C = D ) ) ) ) ) )).
fof(d30_monoid_0,axiom,( k6_monoid_0 = g3_algstr_0(k1_numbers,k11_binop_2) )).
fof(d30_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_qc_lang1(A))) => ( C = k24_qc_lang1(A,B) <=> ? [D] : ( 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] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(d30_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => ( v5_substut1(B,A) => ! [C] : ( m1_subset_1(C,k16_substut1(A)) => ( C = k27_substut1(A,B) <=> B = k20_substut1(A,C) ) ) ) ) ) )).
fof(d30_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( l1_turing_1(B) => ! [C] : ( ( 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)),k1_enumset1(k4_xcmplx_0(1),k5_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)),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1))))) ) => ( C = k31_turing_1(A,B) <=> ! [D] : ( 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)),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1)),C,D) = k30_turing_1(A,B,D) ) ) ) ) ) )).
fof(d30_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d30_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) ) ) )).
fof(d30_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v4_zf_lang(A) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( B = k20_zf_lang(A) <=> k6_zf_lang(B) = A ) ) ) ) )).
fof(d30_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k26_zmodul02(A)) => k27_zmodul02(A,B) = B ) ) )).
fof(d31_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l3_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ( B = k11_abcmiz_0(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( 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 ) ) ) ) ) ) ) )).
fof(d31_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ( k3_finseq_1(k1_msualg_1(A,B)) = 2 => ! [C] : ( m1_subset_1(C,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [D] : ( m1_subset_1(D,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ( ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( 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)) ) ) ) ) ) ) )).
fof(d31_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( ( 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] : ( m1_subset_1(E,B) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d31_aofa_a00,axiom,( ! [A] : ( l6_aofa_a00(A) => ( v16_aofa_a00(A) <=> ( r1_xxreal_0(3,k3_finseq_1(u7_aofa_a00(A))) & r1_aofa_a00(A,k1_funct_1(u7_aofa_a00(A),1),k1_xboole_0,u8_aofa_a00(A)) & r1_aofa_a00(A,k1_funct_1(u7_aofa_a00(A),2),k9_finseq_1(u8_aofa_a00(A)),u8_aofa_a00(A)) & r1_aofa_a00(A,k1_funct_1(u7_aofa_a00(A),3),k10_finseq_1(u8_aofa_a00(A),u8_aofa_a00(A)),u8_aofa_a00(A)) ) ) ) )).
fof(d31_armstrng,axiom,( ! [A] : ! [B] : ( 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) ) )).
fof(d31_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) ) )).
fof(d31_descip_1,axiom,( ! [A] : ( m2_finseq_2(A,k6_margrel1,k4_finseq_2(64,k6_margrel1)) => ! [B] : ( 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) ) ) )).
fof(d31_fomodel0,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => k28_fomodel0(A,B) = k2_xboole_0(k6_subset_1(k5_relat_1(A,k9_xtuple_0(A)),k5_relat_1(A,k9_xtuple_0(B))),B) ) ) )).
fof(d31_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k27_fomodel1(A) = k3_tarski(k10_xtuple_0(k25_fomodel1(A))) ) )).
fof(d31_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( v12_fomodel4(C,B) => ( r11_fomodel4(A,B,C) <=> ? [D] : ? [E] : ( 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] : ( 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) = k42_fomodel1(B,k42_fomodel1(B,k43_fomodel1(B,k1_fomodel2(B)),E),F) & k2_xtuple_0(C) = k42_fomodel1(B,k42_fomodel1(B,k43_fomodel1(B,k1_fomodel2(B)),F),E) ) ) ) ) ) )).
fof(d31_gate_1,axiom,( ! [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) ) => 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 ) ) )).
fof(d31_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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)))) )).
fof(d31_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k7_glib_000(A))) => ( D = k23_glib_000(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> r4_glib_000(A,B,C,E) ) ) ) ) )).
fof(d31_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(d31_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => k28_grcat_1(A) = a_1_1_grcat_1(A) ) )).
fof(d31_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(d31_mmlquery,axiom,( ! [A] : ( l1_mmlquery(A) => ! [B] : ( m2_finseq_1(B,u1_mmlquery(A)) => ( u1_struct_0(A) != k1_xboole_0 => k32_mmlquery(A,B) = a_2_1_mmlquery(A,B) ) ) ) )).
fof(d31_modelc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_modelc_1(A) & l2_modelc_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k4_ordinal1) => k21_modelc_1(A,B,C) = a_3_0_modelc_1(A,B,C) ) ) ) )).
fof(d31_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => k23_modelc_3(A) = a_1_0_modelc_3(A) ) )).
fof(d31_monoid_0,axiom,( ! [A] : ( ( ~ 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) = k4_ordinal1 ) ) )).
fof(d31_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ( v6_polyform(A) <=> k16_rvsum_1(k28_polyform(A)) = k5_numbers ) ) )).
fof(d31_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v6_qc_lang1(B,A) <=> k24_qc_lang1(A,B) = k1_xboole_0 ) ) ) )).
fof(d31_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => ( v6_substut1(B,A) => ! [C] : ( m1_subset_1(C,k16_substut1(A)) => ( C = k28_substut1(A,B) <=> ? [D] : ( m1_subset_1(D,k16_substut1(A)) & B = k21_substut1(A,C,D) & k19_substut1(A,C) = k19_substut1(A,D) ) ) ) ) ) ) )).
fof(d31_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( l1_turing_1(B) => ! [C] : ( ( 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),k1_enumset1(k4_xcmplx_0(1),k5_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)),k1_enumset1(k4_xcmplx_0(1),k5_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)) ) ) ) ) ) )).
fof(d31_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(d31_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) ) ) )).
fof(d31_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ( v5_zf_lang(A) | v8_zf_lang(A) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( ( v5_zf_lang(A) => ( B = k21_zf_lang(A) <=> ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & k7_zf_lang(B,C) = A ) ) ) & ( ~ v5_zf_lang(A) => ( B = k21_zf_lang(A) <=> ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & k10_zf_lang(B,C) = A ) ) ) ) ) ) ) )).
fof(d31_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => k28_zmodul02(A,B) = B ) ) )).
fof(d32_abcmiz_0,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k12_abcmiz_0(A,B) = k2_rewrite1(k11_abcmiz_0(A),B) ) ) )).
fof(d32_abcmiz_1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ? [C] : ( m1_subset_1(C,u4_struct_0(A)) & k2_msualg_1(A,C) = B ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( m2_abcmiz_1(C,A,B) <=> k2_msualg_1(A,C) = B ) ) ) ) ) )).
fof(d32_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(d32_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l6_aofa_a00(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( v17_aofa_a00(B,A) <=> ( k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),u8_aofa_a00(A)) = k6_margrel1 & k1_funct_1(k5_msualg_1(A,k10_subset_1(k1_funct_1(u7_aofa_a00(A),1),u4_struct_0(A)),B),k1_xboole_0) = k8_margrel1 & ! [C] : ( v1_xboolean(C) => ! [D] : ( v1_xboolean(D) => ( k1_funct_1(k5_msualg_1(A,k10_subset_1(k1_funct_1(u7_aofa_a00(A),2),u4_struct_0(A)),B),k9_finseq_1(C)) = k3_xboolean(C) & k1_funct_1(k5_msualg_1(A,k10_subset_1(k1_funct_1(u7_aofa_a00(A),3),u4_struct_0(A)),B),k10_finseq_1(C,D)) = k4_xboolean(C,D) ) ) ) ) ) ) ) )).
fof(d32_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ( r6_armstrng(A,B,C) <=> ( ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( r1_tarski(B,D) => ( D = A | r2_hidden(D,k14_armstrng(A,C)) ) ) ) & ! [D] : ~ ( r2_xboole_0(D,B) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ~ ( r1_tarski(D,E) & E != A & ~ r2_hidden(E,k14_armstrng(A,C)) ) ) ) ) ) ) )).
fof(d32_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) ) )).
fof(d32_descip_1,axiom,( ! [A] : ( m2_finseq_2(A,k6_margrel1,k4_finseq_2(64,k6_margrel1)) => ! [B] : ( 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) ) ) )).
fof(d32_fomodel0,axiom,( ! [A] : ! [B] : k29_fomodel0(A,B) = k2_xboole_0(k1_tarski(A),k1_tarski(B)) )).
fof(d32_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(d32_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m2_subset_1(B,k3_finseq_2(k15_fomodel1(A)),k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) => k35_fomodel2(A,B) = k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k1_fomodel2(A)),B),B) ) ) )).
fof(d32_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( v12_fomodel4(C,B) => ( r12_fomodel4(A,B,C) <=> ? [D] : ? [E] : ? [F] : ( 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] : ( 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] : ( 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) = k42_fomodel1(B,k42_fomodel1(B,k43_fomodel1(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) = k42_fomodel1(B,k42_fomodel1(B,k43_fomodel1(B,k1_fomodel2(B)),F),F) ) ) ) ) ) ) )).
fof(d32_functor0,axiom,( ! [A] : ( l1_altcat_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_altcat_1(B) ) => ! [C] : ( l2_functor0(C,A,B) => ( v18_functor0(C,A,B) <=> ? [D] : ( 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))) ) ) ) ) ) )).
fof(d32_gate_1,axiom,( ! [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) ) => 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 ) ) )).
fof(d32_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(d32_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( 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) ) ) ) ) ) ) )).
fof(d32_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k12_glib_001(A,B))) & k12_glib_001(A,C) = k15_finseq_1(D) ) ) ) ) ) ) )).
fof(d32_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => k29_grcat_1(A) = k5_grcat_1(k27_grcat_1(A),k28_grcat_1(A)) ) )).
fof(d32_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( ( v8_group_9(D,A,B) & m2_finseq_1(D,k6_group_9(A,B)) ) => ! [E] : ( ( 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] : ( v7_ordinal1(F) => ~ ( k1_nat_1(F,1) = k3_finseq_1(D) & ! [G] : ( ( 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] : ( m1_group_9(H,A,B) & ? [I] : ( m1_group_9(I,A,C) & ? [J] : ( v4_group_9(J,A,H) & m1_group_9(J,A,H) & ? [K] : ( v4_group_9(K,A,I) & m1_group_9(K,A,I) & ? [L] : ( v7_ordinal1(L) & ? [M] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d32_mmlquery,axiom,( ! [A] : ( l1_mmlquery(A) => ! [B] : ( m2_finseq_1(B,u1_mmlquery(A)) => ( u1_struct_0(A) != k1_xboole_0 => k33_mmlquery(A,B) = a_2_2_mmlquery(A,B) ) ) ) )).
fof(d32_modelc_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_modelc_2(A) & l1_modelc_2(A) ) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => k18_modelc_2(A,B,C) = a_3_0_modelc_2(A,B,C) ) ) ) )).
fof(d32_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k25_modelc_2(k43_modelc_2)) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r7_modelc_3(A,B,C) <=> ! [D] : ( ( 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))) ) ) ) ) ) ) ) )).
fof(d32_osafree,axiom,( ! [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) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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 ) ) ) ) )).
fof(d32_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v1_relat_1(B) => ( m2_qc_lang1(B,A) <=> r2_wellord1(B,k6_subset_1(k1_qc_lang1(A),k4_ordinal1)) ) ) ) )).
fof(d32_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => ( v6_substut1(B,A) => ! [C] : ( m1_subset_1(C,k16_substut1(A)) => ( C = k29_substut1(A,B) <=> ? [D] : ( m1_subset_1(D,k16_substut1(A)) & B = k21_substut1(A,D,C) & k19_substut1(A,D) = k19_substut1(A,C) ) ) ) ) ) ) )).
fof(d32_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => ! [D] : ( m1_subset_1(D,k6_margrel1) => k1_funct_1(A,k11_finseq_1(B,C,D)) = k2_binarith(k2_binarith(B,C),D) ) ) ) ) ) )).
fof(d32_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( v1_xcmplx_0(B) => k14_valued_2(A,B) = k24_valued_1(A,k7_xcmplx_0(1,B)) ) ) )).
fof(d32_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => r3_waybel_0(A,B,C,D) ) ) ) ) ) )).
fof(d32_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ( v5_zf_lang(A) | v8_zf_lang(A) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( ( v5_zf_lang(A) => ( B = k22_zf_lang(A) <=> ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & k7_zf_lang(C,B) = A ) ) ) & ( ~ v5_zf_lang(A) => ( B = k22_zf_lang(A) <=> ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & k10_zf_lang(C,B) = A ) ) ) ) ) ) ) )).
fof(d32_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(k26_zmodul02(A),k26_zmodul02(A)),k26_zmodul02(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k26_zmodul02(A),k26_zmodul02(A)),k26_zmodul02(A)))) ) => ( B = k29_zmodul02(A) <=> ! [C] : ( m1_subset_1(C,k26_zmodul02(A)) => ! [D] : ( m1_subset_1(D,k26_zmodul02(A)) => k5_binop_1(k26_zmodul02(A),B,C,D) = k22_zmodul02(A,k27_zmodul02(A,C),k27_zmodul02(A,D)) ) ) ) ) ) )).
fof(d33_abcmiz_1,axiom,( ! [A] : ( ( 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)) ) )).
fof(d33_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(C)) => ! [F] : ( m1_aofa_000(F,A,C,E) => ( r4_aofa_000(A,B,C,D,E,F) <=> ? [G] : ( ~ 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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d33_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & l6_aofa_a00(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => k21_aofa_a00(A,B) = k1_funct_1(k5_msualg_1(A,k10_subset_1(k1_funct_1(u7_aofa_a00(A),1),u4_struct_0(A)),B),k1_xboole_0) ) ) )).
fof(d33_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) ) )).
fof(d33_fomodel0,axiom,( ! [A] : ! [B] : k30_fomodel0(A,B) = k10_xtuple_0(k25_fomodel0(B,A)) )).
fof(d33_fomodel1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(d33_functor0,axiom,( ! [A] : ( l1_altcat_1(A) => ! [B] : ( l1_altcat_1(B) => ! [C] : ( l2_functor0(C,A,B) => ( v19_functor0(C,A,B) <=> ( v4_functor0(C,A,B) & v17_functor0(C,A,B) ) ) ) ) ) )).
fof(d33_gate_1,axiom,( ! [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) & 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 ) ) )).
fof(d33_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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) )).
fof(d33_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ( v9_glib_000(B,A) <=> k24_glib_000(A,B) = k6_glib_000(A) ) ) ) )).
fof(d33_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v8_group_9(C,A,B) & m2_finseq_1(C,k6_group_9(A,B)) ) => ! [D] : ( ( 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) = k1_nat_1(k3_finseq_1(D),1) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(D)) => ! [F] : ( m1_group_9(F,A,B) => ! [G] : ( ( 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 ) ) ) ) ) ) )).
fof(d33_mmlquery,axiom,( ! [A] : ( l1_mmlquery(A) => ! [B] : ( m2_finseq_1(B,u1_mmlquery(A)) => ( u1_struct_0(A) != k1_xboole_0 => k34_mmlquery(A,B) = a_2_3_mmlquery(A,B) ) ) ) )).
fof(d33_modelc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_modelc_1(A) & l2_modelc_1(A) ) => ! [B] : ( ( 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] : ( ~ v1_xboole_0(C) => ( C = k23_modelc_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,k1_zfmisc_1(k9_funct_2(k12_modelc_1,u1_struct_0(A)))) & ? [E] : ( m1_subset_1(E,k4_ordinal1) & D = k21_modelc_1(A,B,E) ) ) ) ) ) ) ) )).
fof(d33_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k25_modelc_2(k43_modelc_2)) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r8_modelc_3(A,B,C) <=> ! [D] : ( ( 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))) ) ) ) ) ) ) )).
fof(d33_monoid_0,axiom,( k24_binop_2 = u2_algstr_0(k7_monoid_0) )).
fof(d33_osafree,axiom,( ! [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) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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)) ) ) )).
fof(d33_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k1_qc_lang1(A)) => ( ( ( r2_hidden(B,k4_ordinal1) & r2_hidden(C,k4_ordinal1) ) => ( r1_qc_lang1(A,B,C) <=> ? [D] : ( v7_ordinal1(D) & ? [E] : ( v7_ordinal1(E) & D = B & E = C & r1_xxreal_0(D,E) ) ) ) ) & ~ ( ~ r2_hidden(B,k4_ordinal1) & ~ r2_hidden(C,k4_ordinal1) & ~ ( r1_qc_lang1(A,B,C) <=> r2_hidden(k4_tarski(B,C),o_1_1_qc_lang1(A)) ) ) & ~ ( ~ ( r2_hidden(B,k4_ordinal1) & r2_hidden(C,k4_ordinal1) ) & ~ ( ~ r2_hidden(B,k4_ordinal1) & ~ r2_hidden(C,k4_ordinal1) ) & ~ ( r1_qc_lang1(A,B,C) <=> r2_hidden(C,k4_ordinal1) ) ) ) ) ) ) )).
fof(d33_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => ( v7_substut1(B,A) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ( C = k30_substut1(A,B) <=> ? [D] : ( m1_subset_1(D,k2_zfmisc_1(k16_substut1(A),k3_qc_lang1(A))) & ? [E] : ( m1_substut1(E,A,D) & B = k24_substut1(A,D,E) & k23_substut1(A,D) = C & v3_substut1(D,A) ) ) ) ) ) ) ) )).
fof(d33_twoscomp,axiom,( ! [A] : ! [B] : k34_twoscomp(A,B) = k5_circcomb(k15_twoscomp,k10_finseq_1(A,B)) )).
fof(d33_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v7_valued_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k15_valued_2(A) <=> ( k9_xtuple_0(B) = k9_xtuple_0(A) & ! [C] : ( r2_hidden(C,k9_xtuple_0(B)) => k1_funct_1(B,C) = k30_valued_1(k1_funct_1(A,C)) ) ) ) ) ) )).
fof(d33_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => r4_waybel_0(A,B,C,D) ) ) ) ) ) )).
fof(d33_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ( v6_zf_lang(A) | v11_zf_lang(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ( ( v6_zf_lang(A) => ( B = k23_zf_lang(A) <=> ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & k8_zf_lang(B,C) = A ) ) ) & ( ~ v6_zf_lang(A) => ( B = k23_zf_lang(A) <=> ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & k13_zf_lang(B,C) = A ) ) ) ) ) ) ) )).
fof(d33_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(k4_numbers,k26_zmodul02(A)),k26_zmodul02(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_numbers,k26_zmodul02(A)),k26_zmodul02(A)))) ) => ( B = k30_zmodul02(A) <=> ! [C] : ( v1_int_1(C) => ! [D] : ( m1_subset_1(D,k26_zmodul02(A)) => k1_funct_1(B,k4_tarski(C,D)) = k23_zmodul02(A,C,k27_zmodul02(A,D)) ) ) ) ) ) )).
fof(d34_abcmiz_1,axiom,( ! [A] : ( m1_subset_1(A,k2_abcmiz_1) => ! [B] : ( ( 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)) ) ) )).
fof(d34_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(C)) => ! [F] : ( m1_aofa_000(F,A,C,E) => ! [G] : ( m1_subset_1(G,k6_numbers) => ( ( r4_aofa_000(A,B,C,D,E,F) => ( G = k20_aofa_000(A,B,C,D,E,F) <=> ? [H] : ( ~ 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] : ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(d34_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & l6_aofa_a00(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_funct_1(u3_msualg_1(A,B),u8_aofa_a00(A))) => k22_aofa_a00(A,B,C) = k1_funct_1(k5_msualg_1(A,k10_subset_1(k1_funct_1(u7_aofa_a00(A),2),u4_struct_0(A)),B),k12_finseq_1(k1_funct_1(u3_msualg_1(A,B),u8_aofa_a00(A)),C)) ) ) ) )).
fof(d34_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m2_aofa_i00(E,A,B,C,D) => k40_aofa_i00(A,B,C,D,E) = k23_aofa_i00(B,E) ) ) ) ) ) )).
fof(d34_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) ) )).
fof(d34_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(d34_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( 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] : ( ( ~ v15_fomodel1(B,A) => ( C = k36_fomodel2(A,B) <=> ? [D] : ( 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] : ( 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(k42_fomodel1(A,k43_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)),D),E) ) ) ) ) & ( v15_fomodel1(B,A) => ( C = k36_fomodel2(A,B) <=> C = k4_tarski(B,k1_xboole_0) ) ) ) ) ) )).
fof(d34_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(k1_fomodel4(A)),k1_fomodel4(A)))) => ( B = k10_fomodel4(A) <=> ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d34_functor0,axiom,( ! [A] : ( l1_altcat_1(A) => ! [B] : ( l1_altcat_1(B) => ! [C] : ( l2_functor0(C,A,B) => ( v20_functor0(C,A,B) <=> ( v18_functor0(C,A,B) & v5_functor0(C,A,B) ) ) ) ) ) )).
fof(d34_gate_1,axiom,( ! [A] : ! [B] : ( ~ ( ~ ( 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 ) ) )).
fof(d34_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : k34_gfacirc1(A,B,C) = k8_facirc_1(A,B,C,k4_gfacirc1) )).
fof(d34_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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)) ) ) ) ) )).
fof(d34_group_9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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] : ( ( ~ v2_struct_0(E) & v2_group_1(E) & v3_group_1(E) & v3_group_9(E,A) & l1_group_9(E,A) ) => ! [F] : ( ( ~ v2_struct_0(F) & v2_group_1(F) & v3_group_1(F) & v3_group_9(F,A) & l1_group_9(F,A) ) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d34_mmlquery,axiom,( ! [A] : ( l1_mmlquery(A) => ! [B] : ( m2_finseq_1(B,u1_mmlquery(A)) => ! [C] : ( v7_ordinal1(C) => ( u1_struct_0(A) != k1_xboole_0 => k35_mmlquery(A,B,C) = a_3_4_mmlquery(A,B,C) ) ) ) ) )).
fof(d34_modelc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_modelc_1(A) & l2_modelc_1(A) ) => ! [B] : ( ( 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] : ( ( v1_modelc_1(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( D = k24_modelc_1(A,B,C) <=> ? [E] : ( 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) ) ) ) ) ) ) )).
fof(d34_modelc_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_modelc_2(A) & l1_modelc_2(A) ) => ! [B] : ( ( 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] : ( ~ v1_xboole_0(C) => ( C = k20_modelc_2(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,k1_zfmisc_1(k9_funct_2(k9_modelc_2,u1_struct_0(A)))) & ? [E] : ( v7_ordinal1(E) & D = k18_modelc_2(A,B,E) ) ) ) ) ) ) ) )).
fof(d34_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_orders_1(B,k1_orders_1(k1_modelc_3(A)),k6_partfun1(k1_orders_1(k1_modelc_3(A)))) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(d34_monoid_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k6_algstr_0(B,C,D) = k7_finseq_1(C,D) ) ) ) ) ) ) )).
fof(d34_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ( 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)) ) ) ) ) )).
fof(d34_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k1_qc_lang1(A)) => ( r2_qc_lang1(A,B,C) <=> ( r1_qc_lang1(A,B,C) & B != C ) ) ) ) ) )).
fof(d34_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => ( v7_substut1(B,A) => ! [C] : ( m1_subset_1(C,k16_substut1(A)) => ( C = k31_substut1(A,B) <=> ? [D] : ( m1_subset_1(D,k2_zfmisc_1(k16_substut1(A),k3_qc_lang1(A))) & ? [E] : ( m1_substut1(E,A,D) & B = k24_substut1(A,D,E) & k22_substut1(A,D) = C & v3_substut1(D,A) ) ) ) ) ) ) ) )).
fof(d34_twoscomp,axiom,( ! [A] : ! [B] : k35_twoscomp(A,B) = k6_facirc_1(A,B,k15_twoscomp) )).
fof(d34_valued_2,axiom,( ! [A] : ( v1_valued_2(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(d34_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => r3_waybel_0(A,B,C,k7_domain_1(u1_struct_0(A),D,E)) ) ) ) ) ) ) )).
fof(d34_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ( v6_zf_lang(A) | v11_zf_lang(A) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( ( v6_zf_lang(A) => ( B = k24_zf_lang(A) <=> ? [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) & k8_zf_lang(C,B) = A ) ) ) & ( ~ v6_zf_lang(A) => ( B = k24_zf_lang(A) <=> ? [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) & k13_zf_lang(C,B) = A ) ) ) ) ) ) ) )).
fof(d34_zmodul02,axiom,( ! [A] : ( ( ~ 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) ) => k31_zmodul02(A) = g1_zmodul01(k26_zmodul02(A),k28_zmodul02(A,k19_zmodul02(A)),k29_zmodul02(A),k30_zmodul02(A)) ) )).
fof(d35_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_abcmiz_1(B,A) & m1_subset_1(B,u4_struct_0(A)) ) => ! [C] : ( 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) ) ) ) ) )).
fof(d35_algstr_0,axiom,( ! [A] : ( l5_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( ( v23_algstr_0(B,A) & v17_algstr_0(B,A) ) => ( C = k11_algstr_0(A,B) <=> k6_algstr_0(A,C,B) = k5_struct_0(A) ) ) & ( ~ ( v23_algstr_0(B,A) & v17_algstr_0(B,A) ) => ( C = k11_algstr_0(A,B) <=> C = k4_struct_0(A) ) ) ) ) ) ) )).
fof(d35_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_aofa_000(D,A,B,C) => ! [E] : ( 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] : ( m1_subset_1(F,B) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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] : ( ( ~ 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] : ( 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] : ( 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] : ( m1_subset_1(G,B) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( 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] : ( ( ~ 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d35_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & l6_aofa_a00(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_funct_1(u3_msualg_1(A,B),u8_aofa_a00(A))) => ! [D] : ( m1_subset_1(D,k1_funct_1(u3_msualg_1(A,B),u8_aofa_a00(A))) => k23_aofa_a00(A,B,C,D) = k1_funct_1(k5_msualg_1(A,k10_subset_1(k1_funct_1(u7_aofa_a00(A),3),u4_struct_0(A)),B),k2_finseq_4(k1_funct_1(u3_msualg_1(A,B),u8_aofa_a00(A)),C,D)) ) ) ) ) )).
fof(d35_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m1_subset_1(E,B) => k41_aofa_i00(A,B,C,D,E) = k24_aofa_i00(B,E) ) ) ) ) ) )).
fof(d35_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) ) )).
fof(d35_fomodel0,axiom,( ! [A] : k32_fomodel0(A) = k9_xtuple_0(k9_subset_1(k2_zfmisc_1(k9_xtuple_0(A),k9_xtuple_0(A)),A,k6_partfun1(k9_xtuple_0(A)))) )).
fof(d35_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( 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] : ( v7_fomodel1(C,A) & m1_subset_1(C,k1_fomodel1(A)) & ? [D] : ( v3_card_1(D,k1_int_2(k19_fomodel1(A,C))) & m2_subset_1(D,k3_finseq_2(k3_finseq_2(k15_fomodel1(A))),k3_fomodel0(k3_finseq_2(k15_fomodel1(A)),k29_fomodel1(A))) & B = k7_finseq_1(k12_finseq_1(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)) ) ) ) ) ) )).
fof(d35_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( 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))) ) => k37_fomodel2(A,B) = k1_xtuple_0(k36_fomodel2(A,B)) ) ) )).
fof(d35_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(k1_fomodel4(A)),k1_fomodel4(A)))) => ( B = k11_fomodel4(A) <=> ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d35_functor0,axiom,( ! [A] : ( l1_altcat_1(A) => ! [B] : ( l1_altcat_1(B) => ! [C] : ( l2_functor0(C,A,B) => ( v21_functor0(C,A,B) <=> ( v19_functor0(C,A,B) & v20_functor0(C,A,B) ) ) ) ) ) )).
fof(d35_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k35_gate_1(A,B,C,D,E) = k10_gate_1(C,D,k11_gate_1(A,B,E)) )).
fof(d35_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : k35_gfacirc1(A,B,C) = k10_facirc_1(A,B,C,k4_gfacirc1) )).
fof(d35_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ( r6_glib_000(A,B) <=> m1_glib_000(A,B) ) ) ) )).
fof(d35_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v8_group_9(C,A,B) & m2_finseq_1(C,k6_group_9(A,B)) ) => ! [D] : ( ( 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] : ( ( v8_group_9(E,A,B) & m2_finseq_1(E,k6_group_9(A,B)) ) => ( E = k21_group_9(A,B,C,D) <=> ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ! [I] : ( m1_group_9(I,A,B) => ! [J] : ( m1_group_9(J,A,B) => ! [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d35_mmlquery,axiom,( ! [A] : ( ( v3_mmlquery(A) & l1_mmlquery(A) ) => ! [B] : ( m2_finseq_1(B,u1_mmlquery(A)) => ! [C] : ( v7_ordinal1(C) => ( u1_struct_0(A) != k1_xboole_0 => k36_mmlquery(A,B,C) = a_3_5_mmlquery(A,B,C) ) ) ) ) )).
fof(d35_modelc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_modelc_1(A) & l2_modelc_1(A) ) => ! [B] : ( 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) ) ) )).
fof(d35_modelc_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_modelc_2(A) & l1_modelc_2(A) ) => ! [B] : ( ( 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] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( D = k21_modelc_2(A,B,C) <=> ? [E] : ( 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) ) ) ) ) ) ) )).
fof(d35_modelc_3,axiom,( ! [A] : ( m1_subset_1(A,k25_modelc_2(k43_modelc_2)) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m2_orders_1(C,k1_orders_1(k1_modelc_3(B)),k6_partfun1(k1_orders_1(k1_modelc_3(B)))) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(d35_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1(A))) ) => ! [C] : ( m1_subset_1(C,k1_qc_lang1(A)) => ( C = k25_qc_lang1(A,B) <=> ( r2_hidden(C,B) & ! [D] : ( m1_subset_1(D,k1_qc_lang1(A)) => ( r2_hidden(D,B) => r1_qc_lang1(A,C,D) ) ) ) ) ) ) ) )).
fof(d35_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => k32_substut1(A,B) = B ) ) )).
fof(d35_twoscomp,axiom,( ! [A] : ! [B] : k36_twoscomp(A,B) = k4_tarski(k10_finseq_1(A,B),k15_twoscomp) )).
fof(d35_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v7_valued_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k21_valued_2(A) <=> ( k9_xtuple_0(B) = k9_xtuple_0(A) & ! [C] : ( r2_hidden(C,k9_xtuple_0(B)) => k1_funct_1(B,C) = k35_valued_1(k1_funct_1(A,C)) ) ) ) ) ) )).
fof(d35_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => r4_waybel_0(A,B,C,k7_domain_1(u1_struct_0(A),D,E)) ) ) ) ) ) ) )).
fof(d35_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v9_zf_lang(A) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( B = k25_zf_lang(A) <=> ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & A = k11_zf_lang(B,C) ) ) ) ) ) )).
fof(d36_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_abcmiz_1(B,A,k13_abcmiz_1(A)) => ( ( ? [C] : ( 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(k4_ordinal1,k5_numbers)) ) & ( ! [C] : ( 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) ) ) ) ) )).
fof(d36_algstr_0,axiom,( ! [A] : ( l5_algstr_0(A) => ( v30_algstr_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B != k4_struct_0(A) => v16_algstr_0(B,A) ) ) ) ) )).
fof(d36_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v15_aofa_000(B,A) <=> ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(C)) => ! [F] : ( m1_aofa_000(F,A,C,E) => r2_hidden(k4_tarski(D,B),k21_aofa_000(A,C,E,F)) ) ) ) ) ) ) ) )).
fof(d36_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(d36_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) ) )).
fof(d36_fomodel0,axiom,( ! [A] : k33_fomodel0(A) = k9_xtuple_0(k9_subset_1(k2_zfmisc_1(k3_xboole_0(k9_xtuple_0(A),k10_xtuple_0(A)),k3_xboole_0(k9_xtuple_0(A),k10_xtuple_0(A))),A,k6_partfun1(k3_xboole_0(k9_xtuple_0(A),k10_xtuple_0(A))))) )).
fof(d36_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k31_fomodel1(A) = a_1_0_fomodel1(A) ) )).
fof(d36_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( 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))) ) => k38_fomodel2(A,B) = k2_xtuple_0(k36_fomodel2(A,B)) ) ) )).
fof(d36_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(k1_fomodel4(A)),k1_fomodel4(A)))) => ( B = k12_fomodel4(A) <=> ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d36_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l1_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_altcat_2(C) & l1_altcat_1(C) ) => ! [D] : ( ( v8_functor0(D,A,B) & l2_functor0(D,A,B) ) => ! [E] : ( l2_functor0(E,B,C) => ! [F] : ( ( 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)))) ) ) ) ) ) ) ) ) )).
fof(d36_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k36_gate_1(A,B,C,D,E) = k11_gate_1(C,D,k11_gate_1(A,B,E)) )).
fof(d36_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : k36_gfacirc1(A,B,C) = k9_facirc_1(A,B,C,k4_gfacirc1) )).
fof(d36_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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) ) ) ) ) )).
fof(d36_mmlquery,axiom,( ! [A] : ( ( v3_mmlquery(A) & l1_mmlquery(A) ) => ! [B] : ( m2_finseq_1(B,u1_mmlquery(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( u1_struct_0(A) != k1_xboole_0 => k37_mmlquery(A,B,C,D) = a_4_15_mmlquery(A,B,C,D) ) ) ) ) ) )).
fof(d36_modelc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_modelc_1(A) & l2_modelc_1(A) ) => ! [B] : ( 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) ) ) )).
fof(d36_modelc_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_modelc_2(A) & l1_modelc_2(A) ) => ! [B] : ( 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) ) ) )).
fof(d36_modelc_3,axiom,( ! [A] : ( m1_subset_1(A,k25_modelc_2(k43_modelc_2)) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m2_orders_1(C,k1_orders_1(k1_modelc_3(B)),k6_partfun1(k1_orders_1(k1_modelc_3(B)))) => ! [D] : ( ( 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] : ( r2_hidden(E,k22_modelc_3(B)) => k1_funct_1(D,E) = k25_modelc_3(A,B,C,k10_modelc_3(E,B)) ) ) ) ) ) ) )).
fof(d36_monoid_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k11_monoid_0(A) = u2_algstr_0(k9_monoid_0(A)) ) )).
fof(d36_pcs_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v16_pcs_0(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(d36_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_qc_lang1(A)) => ( B = k26_qc_lang1(A) <=> ! [C] : ( m1_subset_1(C,k1_qc_lang1(A)) => r1_qc_lang1(A,B,C) ) ) ) ) )).
fof(d36_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) ) ) )).
fof(d36_twoscomp,axiom,( ! [A] : ! [B] : k37_twoscomp(A,B) = k5_circcomb(k3_twoscomp,k10_finseq_1(A,B)) )).
fof(d36_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v7_valued_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k25_valued_2(A) <=> ( k9_xtuple_0(B) = k9_xtuple_0(A) & ! [C] : ( r2_hidden(C,k9_xtuple_0(B)) => k1_funct_1(B,C) = k54_valued_1(k1_funct_1(A,C)) ) ) ) ) ) )).
fof(d36_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) ) ) )).
fof(d36_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v9_zf_lang(A) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( B = k26_zf_lang(A) <=> ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & A = k11_zf_lang(C,B) ) ) ) ) ) )).
fof(d36_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_zmodul02(B,A) <=> ! [C] : ( m2_zmodul02(C,A,B) => ( k21_zmodul02(A,C) = k4_struct_0(A) => k18_zmodul02(A,C) = k1_xboole_0 ) ) ) ) ) )).
fof(d37_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_abcmiz_1(B,A,k13_abcmiz_1(A)) => ( v6_abcmiz_1(B,A) <=> ! [C] : ( m1_abcmiz_1(C,A,k13_abcmiz_1(A)) => B != k30_abcmiz_1(A,k32_abcmiz_1(A),C) ) ) ) ) )).
fof(d37_algstr_0,axiom,( ! [A] : ( l5_algstr_0(A) => ( v31_algstr_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B != k4_struct_0(A) => v17_algstr_0(B,A) ) ) ) ) )).
fof(d37_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_aofa_000(E,A,B,C) => ( r5_aofa_000(A,B,C,D,E) <=> ! [F] : ( m1_subset_1(F,B) => r2_hidden(k4_tarski(F,D),k21_aofa_000(A,B,C,E)) ) ) ) ) ) ) ) )).
fof(d37_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( v1_int_1(E) => k43_aofa_i00(A,B,C,D,E) = k25_aofa_i00(B,E) ) ) ) ) ) )).
fof(d37_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) ) )).
fof(d37_fomodel0,axiom,( ! [A] : ( v5_fomodel0(A) <=> v1_zfmisc_1(k10_xtuple_0(A)) ) )).
fof(d37_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( 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] : ( m2_subset_1(C,k3_finseq_2(k3_finseq_2(k15_fomodel1(A))),k3_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(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)),k3_funct_2(k3_finseq_2(k3_finseq_2(k15_fomodel1(A))),k3_finseq_2(k15_fomodel1(A)),k21_fomodel1(A),C)) ) ) ) ) ) )).
fof(d37_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( 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))) ) ) ) )).
fof(d37_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(k1_fomodel4(A)),k1_fomodel4(A)))) => ( B = k13_fomodel4(A) <=> ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d37_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_altcat_2(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_altcat_2(C,A) ) => ! [D] : ( l2_functor0(D,A,B) => k14_functor0(A,B,C,D) = k13_functor0(C,A,B,k10_functor0(A,C),D) ) ) ) ) )).
fof(d37_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : k37_gate_1(A,B,C,D,E,F,G) = k10_gate_1(E,F,k36_gate_1(A,B,C,D,G)) )).
fof(d37_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : k37_gfacirc1(A,B,C) = k2_circcomb(k34_gfacirc1(A,B,C),k31_gfacirc1(A,B,C)) )).
fof(d37_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ( 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) ) ) ) ) ) )).
fof(d37_modelc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_modelc_1(A) & l2_modelc_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d37_modelc_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_modelc_2(A) & l1_modelc_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d37_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v5_modelc_3(A) <=> ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( ( r2_modelc_2(B,A) & v3_modelc_2(B) ) => v2_modelc_2(k10_modelc_2(B)) ) ) ) ) )).
fof(d37_monoid_0,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k6_algstr_0(B,C,D) = k3_relat_1(C,D) ) ) ) ) ) )).
fof(d37_pcs_0,axiom,( ! [A] : ! [B] : k18_pcs_0(A,B) = k6_afinsq_1(A,B) )).
fof(d37_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_qc_lang1(A)) => k27_qc_lang1(A,B) = a_2_3_qc_lang1(A,B) ) ) )).
fof(d37_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => ! [C] : ( 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) ) ) ) )).
fof(d37_twoscomp,axiom,( ! [A] : ! [B] : k38_twoscomp(A,B) = k6_facirc_1(A,B,k3_twoscomp) )).
fof(d37_valued_2,axiom,( ! [A] : ( v1_valued_2(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) ) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( D = k30_valued_2(A,B,C) <=> ( k9_xtuple_0(D) = k9_xtuple_0(B) & ! [E] : ( r2_hidden(E,k9_xtuple_0(D)) => k1_funct_1(D,E) = k7_valued_1(k1_funct_1(B,E),C) ) ) ) ) ) ) ) )).
fof(d37_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) ) ) )).
fof(d37_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v10_zf_lang(A) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( B = k27_zf_lang(A) <=> ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & A = k12_zf_lang(B,C) ) ) ) ) ) )).
fof(d37_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v1_zmodul01(C) & m1_zmodul01(C,A) ) => ( C = k33_zmodul02(A,B) <=> u1_struct_0(C) = a_2_4_zmodul02(A,B) ) ) ) ) )).
fof(d38_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_abcmiz_1(B,A,k13_abcmiz_1(A)) => ( v7_abcmiz_1(B,A) <=> ? [C] : ( m1_abcmiz_1(C,A,k13_abcmiz_1(A)) & v6_abcmiz_1(C,A) & B = k30_abcmiz_1(A,k32_abcmiz_1(A),C) ) ) ) ) )).
fof(d38_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_aofa_000(E,A,B,C) => ! [F] : ( r6_aofa_000(A,B,C,D,E,F) <=> ! [G] : ( m1_subset_1(G,B) => ( r2_hidden(G,F) => r2_hidden(k4_tarski(G,D),k21_aofa_000(A,B,C,E)) ) ) ) ) ) ) ) ) )).
fof(d38_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m2_aofa_i00(E,A,B,C,D) => ! [F] : ( m3_aofa_i00(F,A,B,C,D) => k44_aofa_i00(A,B,C,D,E,F) = o_6_0_aofa_i00(A,B,C,D,E,F) ) ) ) ) ) ) )).
fof(d38_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) ) )).
fof(d38_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( 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] : ( ( 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))),k3_fomodel0(k3_finseq_2(k15_fomodel1(A)),k29_fomodel1(A))) ) => ( C = k34_fomodel1(A,B) <=> B = k7_finseq_1(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)),k3_funct_2(k3_finseq_2(k3_finseq_2(k15_fomodel1(A))),k3_finseq_2(k15_fomodel1(A)),k21_fomodel1(A),C)) ) ) ) ) )).
fof(d38_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_fomodel1(A)) => ! [C] : ( v8_fomodel2(C,A,B) <=> r2_hidden(B,k21_fomodel0(k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k3_xboole_0(k1_tarski(k1_xboole_0),C)))) ) ) ) )).
fof(d38_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(k1_fomodel4(A)),k1_fomodel4(A)))) => ( B = k14_fomodel4(A) <=> ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d38_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_altcat_1(B) ) => ! [C] : ( l2_functor0(C,A,B) => ( v21_functor0(C,A,B) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d38_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : k38_gate_1(A,B,C,D,E,F,G) = k11_gate_1(E,F,k36_gate_1(A,B,C,D,G)) )).
fof(d38_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(d38_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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)) ) ) )).
fof(d38_modelc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_modelc_1(A) & l2_modelc_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(d38_modelc_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_modelc_2(A) & l1_modelc_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d38_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v6_modelc_3(A) <=> ~ ( ~ v2_modelc_2(A) & ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ~ ( v2_modelc_2(B) & A = k3_modelc_2(B) ) ) ) ) ) )).
fof(d38_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ( l2_pcs_0(B) => k19_pcs_0(A,B) = k17_pcs_0(k7_domain_1(k4_ordinal1,k5_numbers,1),k18_pcs_0(A,B)) ) ) )).
fof(d38_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_qc_lang1(A)) => k28_qc_lang1(A,B) = k25_qc_lang1(A,k27_qc_lang1(A,B)) ) ) )).
fof(d38_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( C = k37_substut1(A,B) <=> ? [D] : ( 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] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(d38_twoscomp,axiom,( ! [A] : ! [B] : k39_twoscomp(A,B) = k4_tarski(k10_finseq_1(A,B),k3_twoscomp) )).
fof(d38_valued_2,axiom,( ! [A] : ( v1_valued_2(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) ) => ! [C] : ( v1_xcmplx_0(C) => k36_valued_2(A,B,C) = k30_valued_2(A,B,k4_xcmplx_0(C)) ) ) ) )).
fof(d38_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) ) ) )).
fof(d38_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v10_zf_lang(A) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( B = k28_zf_lang(A) <=> ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & A = k12_zf_lang(C,B) ) ) ) ) ) )).
fof(d39_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_abcmiz_1(B,A,k13_abcmiz_1(A)) => ( v8_abcmiz_1(B,A) <=> ( v6_abcmiz_1(B,A) | v7_abcmiz_1(B,A) ) ) ) ) )).
fof(d39_algstr_0,axiom,( ! [A] : ( l5_algstr_0(A) => ( v33_algstr_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B != k4_struct_0(A) => v23_algstr_0(B,A) ) ) ) ) )).
fof(d39_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_aofa_000(E,A,B,C) => ! [F] : ( r7_aofa_000(A,B,C,D,E,F) <=> ! [G] : ( m1_subset_1(G,B) => ( r2_hidden(G,F) => r2_hidden(k2_binop_1(B,u1_struct_0(A),B,E,G,D),F) ) ) ) ) ) ) ) ) )).
fof(d39_aofa_a00,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( l6_aofa_a00(C) => ( v18_aofa_a00(C,A,B) <=> ( r1_xxreal_0(k2_xcmplx_0(A,6),k3_finseq_1(u7_aofa_a00(C))) & ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & D = B & D != u8_aofa_a00(C) & r1_aofa_a00(C,k1_funct_1(u7_aofa_a00(C),A),k1_xboole_0,D) & r1_aofa_a00(C,k1_funct_1(u7_aofa_a00(C),k2_xcmplx_0(A,1)),k1_xboole_0,D) & k1_funct_1(u7_aofa_a00(C),A) != k1_funct_1(u7_aofa_a00(C),k2_xcmplx_0(A,1)) & r1_aofa_a00(C,k1_funct_1(u7_aofa_a00(C),k2_xcmplx_0(A,2)),k9_finseq_1(D),D) & r1_aofa_a00(C,k1_funct_1(u7_aofa_a00(C),k2_xcmplx_0(A,3)),k10_finseq_1(D,D),D) & r1_aofa_a00(C,k1_funct_1(u7_aofa_a00(C),k2_xcmplx_0(A,4)),k10_finseq_1(D,D),D) & r1_aofa_a00(C,k1_funct_1(u7_aofa_a00(C),k2_xcmplx_0(A,5)),k10_finseq_1(D,D),D) & k1_funct_1(u7_aofa_a00(C),k2_xcmplx_0(A,3)) != k1_funct_1(u7_aofa_a00(C),k2_xcmplx_0(A,4)) & k1_funct_1(u7_aofa_a00(C),k2_xcmplx_0(A,3)) != k1_funct_1(u7_aofa_a00(C),k2_xcmplx_0(A,5)) & k1_funct_1(u7_aofa_a00(C),k2_xcmplx_0(A,4)) != k1_funct_1(u7_aofa_a00(C),k2_xcmplx_0(A,5)) & r1_aofa_a00(C,k1_funct_1(u7_aofa_a00(C),k2_xcmplx_0(A,6)),k10_finseq_1(D,D),u8_aofa_a00(C)) ) ) ) ) ) )).
fof(d39_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) ) )).
fof(d39_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k35_fomodel1(A),k3_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),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k35_fomodel1(A))))) ) => ( B = k36_fomodel1(A) <=> ! [C] : ( 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),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k35_fomodel1(A)),B,C) = k33_fomodel1(A,C) ) ) ) ) )).
fof(d39_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(k1_fomodel4(A)),k1_fomodel4(A)))) => ( B = k15_fomodel4(A) <=> ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d39_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ( r1_functor0(A,B) <=> ? [C] : ( m2_functor0(C,A,B) & v21_functor0(C,A,B) & v15_functor0(C,A,B) ) ) ) ) )).
fof(d39_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [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)) )).
fof(d39_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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)) ) ) )).
fof(d39_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ( m1_modelc_1(C,A,B) <=> ! [D] : ( m1_subset_1(D,k4_ordinal1) => r2_hidden(k4_tarski(k3_funct_2(k4_ordinal1,A,C,D),k3_funct_2(k4_ordinal1,A,C,k1_nat_1(D,1))),B) ) ) ) ) ) )).
fof(d39_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k25_modelc_2(A) = k9_funct_2(k4_ordinal1,A) ) )).
fof(d39_monoid_0,axiom,( ! [A] : k14_monoid_0(A) = u2_algstr_0(k12_monoid_0(A)) )).
fof(d39_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ! [C] : ( ( v12_pcs_0(C) & l2_pcs_0(C) ) => ( C = k20_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)) ) ) ) ) )).
fof(d39_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => k38_substut1(A) = a_1_0_substut1(A) ) )).
fof(d39_twoscomp,axiom,( ! [A] : ! [B] : k40_twoscomp(A,B) = k2_circcomb(k34_twoscomp(A,B),k37_twoscomp(A,B)) )).
fof(d39_valued_2,axiom,( ! [A] : ( v1_valued_2(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) ) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( D = k41_valued_2(A,B,C) <=> ( k9_xtuple_0(D) = k9_xtuple_0(B) & ! [E] : ( r2_hidden(E,k9_xtuple_0(D)) => k1_funct_1(D,E) = k24_valued_1(k1_funct_1(B,E),C) ) ) ) ) ) ) ) )).
fof(d39_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ( v24_waybel_0(A) <=> ! [B] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r2_lattice3(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_lattice3(A,B,D) => r3_orders_2(A,C,D) ) ) ) ) ) ) )).
fof(d39_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r1_zf_lang(A,B) <=> ~ ( B != k6_zf_lang(A) & ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ( B != k7_zf_lang(A,C) & B != k7_zf_lang(C,A) ) ) & ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => B != k8_zf_lang(C,A) ) ) ) ) ) )).
fof(d3_abcmiz_1,axiom,( ! [A] : ( m1_finseq_2(A,k2_abcmiz_1) => ( A = k4_abcmiz_1 <=> ! [B] : ( m2_finseq_1(B,k2_abcmiz_1) => ( r2_hidden(B,A) <=> ( v2_funct_1(B) & ! [C] : ( 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))) ) ) ) ) ) ) ) )).
fof(d3_abian,axiom,( ! [A] : ! [B] : ( ( 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) ) ) ) )).
fof(d3_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_aff_1(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & C != D & B = k2_aff_1(A,C,D) ) ) ) ) ) )).
fof(d3_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v3_aff_2(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_aff_3,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v3_aff_3(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ! [L] : ( m1_subset_1(L,u1_struct_0(A)) => ! [M] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v1_aff_1(C,A) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(d3_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) ) => ( C = k1_ordinal4(A,B) <=> ( k9_xtuple_0(C) = k1_nat_1(k1_afinsq_1(A),k1_afinsq_1(B)) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k2_afinsq_1(A)) => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k2_afinsq_1(B)) => k1_funct_1(C,k2_xcmplx_0(k1_afinsq_1(A),D)) = k1_funct_1(B,D) ) ) ) ) ) ) ) )).
fof(d3_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k3_afinsq_2(A,B,C) = k2_afinsq_2(k5_relat_1(A,C),k7_nat_d(B,1)) ) ) ) )).
fof(d3_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => k3_afproj(A) = a_1_2_afproj(A) ) )).
fof(d3_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_afvect0(A,B,C,D) <=> r2_analoaf(A,B,C,C,D) ) ) ) ) ) )).
fof(d3_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(d3_algseq_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( C = k1_algseq_1(A,B) <=> ( r1_algseq_1(A,B,C) & ! [D] : ( v7_ordinal1(D) => ( r1_algseq_1(A,B,D) => r1_xxreal_0(C,D) ) ) ) ) ) ) ) )).
fof(d3_algspec1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r1_algspec1(A,B,C) <=> ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d3_algstr_0,axiom,( ! [A] : ( l1_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v2_algstr_0(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k1_algstr_0(A,B,C) = k1_algstr_0(A,B,D) => C = D ) ) ) ) ) ) )).
fof(d3_algstr_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ( v2_algstr_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & k1_algstr_0(A,D,B) = C ) ) ) ) ) )).
fof(d3_algstr_3,axiom,( k3_algstr_3 = g1_algstr_3(k1_numbers,k10_subset_1(k5_numbers,k1_numbers),k10_subset_1(1,k1_numbers),k2_algstr_3) )).
fof(d3_algstr_4,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(d3_altcat_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : ! [E] : ! [F] : ( ( 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) ) ) ) ) )).
fof(d3_altcat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_cat_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_binop_1(B,C,D) = k2_cat_1(A,C,D) ) ) ) ) ) )).
fof(d3_altcat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_altcat_1(A,B,C)) => ( v2_altcat_3(D,A,B,C) <=> ? [E] : ( m1_subset_1(E,k1_altcat_1(A,C,B)) & r1_altcat_3(A,C,B,E,D) ) ) ) ) ) ) )).
fof(d3_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d3_ami_2,axiom,( k4_ami_2 = k6_afinsq_1(k4_ordinal1,k4_numbers) )).
fof(d3_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( 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)) ) ) )).
fof(d3_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) & v3_funct_2(C,k4_ordinal1,k4_ordinal1) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(D,E) <=> r1_ami_wstd(A,B,k3_funct_2(k4_ordinal1,k4_ordinal1,C,D),k3_funct_2(k4_ordinal1,k4_ordinal1,C,E)) ) ) ) ) ) ) ) )).
fof(d3_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,u1_compos_1(B)) => k1_amistd_1(A,B,C,D) = a_4_0_amistd_1(A,B,C,D) ) ) ) ) )).
fof(d3_amistd_2,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_compos_1(B)) => ( v3_amistd_2(C,A,B) <=> ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( ( 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_xcmplx_0(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))) ) ) ) ) ) ) ) )).
fof(d3_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( D = k2_amistd_4(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r2_hidden(E,D) <=> ~ ! [F] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(d3_amistd_5,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) & ~ v2_compos_1(C,B) ) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(d3_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d3_analoaf,axiom,( ! [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) ) => ! [B] : ( 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] : ! [D] : ( r2_hidden(k4_tarski(C,D),B) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d3_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d3_anproj_1,axiom,( ! [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) ) => ! [B] : ( ( 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] : ! [D] : ( r2_hidden(k4_tarski(C,D),B) <=> ( r2_hidden(C,k8_struct_0(A)) & r2_hidden(D,k8_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & C = E & D = F & r1_anproj_1(A,E,F) ) ) ) ) ) ) ) )).
fof(d3_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : k4_aofa_a00(A,B,C,D,E,F,G,H) = k1_funct_4(k1_borsuk_7(A,B,C,E,F,G),k16_funcop_1(D,H)) )).
fof(d3_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( m1_msafree(D,A,C) => ( v2_aofa_a01(D,A,B,C) <=> r2_pboole(u1_struct_0(A),k1_aofa_a01(A,B,C),D) ) ) ) ) ) )).
fof(d3_armstrng,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( B = k2_armstrng(A) <=> ! [C] : ( r2_hidden(C,B) <=> r1_armstrng(C,A) ) ) ) ) )).
fof(d3_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ( B = k3_arytm_0(A) <=> k1_arytm_0(A,B) = k5_numbers ) ) ) )).
fof(d3_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( 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] : ( 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 ) ) ) ) ) )).
fof(d3_arytm_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r2_arytm_3(A,B) <=> ? [C] : ( v3_ordinal1(C) & B = k11_ordinal2(A,C) ) ) ) ) )).
fof(d3_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( B = k3_asympt_1(A) <=> ( k9_nat_1(k1_numbers,B,k5_numbers) = k5_numbers & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ r1_xxreal_0(C,k5_numbers) => k9_nat_1(k1_numbers,B,C) = k2_power(C,A) ) ) ) ) ) ) )).
fof(d3_autalg_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d3_autgroup,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d3_bcialg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_bcialg_1(A) ) => ( v3_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d3_bcialg_4,axiom,( k2_bcialg_4 = g1_bcialg_4(k1_tarski(k5_numbers),k9_funct_5,k9_funct_5,k5_funct_5) )).
fof(d3_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( ~ 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] : ( m1_subset_1(F,u1_struct_0(E)) => ! [G] : ( m1_subset_1(G,u1_struct_0(E)) => k1_bcialg_5(E,F,G,A,B) = k1_bcialg_5(E,G,F,C,D) ) ) ) ) ) ) ) ) )).
fof(d3_bcialg_6,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_bcialg_6(A,B,C) = k1_binop_1(k2_bcialg_6(A),C,B) ) ) ) )).
fof(d3_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_bhsp_1(A,B,C) <=> k2_bhsp_1(A,B,C) = k5_numbers ) ) ) ) )).
fof(d3_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( C = k2_bhsp_2(A,B) <=> ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k3_bhsp_1(A,k1_normsp_1(A,B,D)) ) ) ) ) ) )).
fof(d3_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v2_bhsp_3(B,A) <=> ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k3_bhsp_1(A,k1_normsp_1(A,B,D)),C) ) ) ) ) ) )).
fof(d3_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k2_bhsp_4(A,B) = k1_bhsp_2(A,k1_bhsp_4(A,B)) ) ) )).
fof(d3_bhsp_6,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_bhsp_6(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k2_bhsp_6(A,B) <=> ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( ~ v1_xboole_0(E) & r1_tarski(E,B) & ! [F] : ( ( 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)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d3_binari_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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) = k6_xcmplx_0(k6_binarith(A,B),k5_series_1(2,A)) ) ) ) ) )).
fof(d3_binarith,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k4_ordinal1) ) => ( C = k5_binarith(A,B) <=> ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k2_finseq_1(A)) => k7_partfun1(k4_ordinal1,C,D) = k15_funcop_1(k4_ordinal1,k7_partfun1(k6_margrel1,B,D),k7_margrel1,k5_numbers,k5_series_1(2,k7_nat_d(D,1))) ) ) ) ) ) ) )).
fof(d3_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)),u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)),u1_struct_0(A)))) ) => ( B = k3_binom(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_binop_1(k4_ordinal1,u1_struct_0(A),u1_struct_0(A),B,k5_numbers,C) = k4_struct_0(A) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => k2_binop_1(k4_ordinal1,u1_struct_0(A),u1_struct_0(A),B,k1_nat_1(D,1),C) = k1_algstr_0(A,C,k2_binop_1(k4_ordinal1,u1_struct_0(A),u1_struct_0(A),B,D,C)) ) ) ) ) ) ) )).
fof(d3_binop_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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) ) ) ) ) ) )).
fof(d3_binop_2,axiom,( ! [A] : ( ( 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 = k3_binop_2 <=> ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k1_binop_1(A,B,C) = k2_xcmplx_0(B,C) ) ) ) ) )).
fof(d3_bintree1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ( v2_bintree1(A) <=> v1_bintree1(k9_xtuple_0(A)) ) ) )).
fof(d3_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => k2_bintree2(A,B) = k2_funct_1(k1_bintree2(A,B)) ) ) )).
fof(d3_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_boolealg(A,B,C) <=> ( r3_lattices(A,B,C) & r3_lattices(A,C,B) ) ) ) ) ) )).
fof(d3_boolmark,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m2_funct_2(B,u1_struct_0(A),k6_margrel1,k1_boolmark(A)) => ! [C] : ( 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)) ) ) ) )).
fof(d3_borsuk_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( 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) ) ) ) )).
fof(d3_borsuk_2,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_borsuk_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_borsuk_2(A,B,C) ) ) ) ) )).
fof(d3_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k3_borsuk_5(A,B) = k9_subset_1(k1_numbers,k1_borsuk_5,k2_rcomp_1(A,B)) ) ) )).
fof(d3_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( m1_borsuk_2(E,A,C,B) => ( E = k2_borsuk_2(A,B,C,D) <=> ! [F] : ( 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,k6_xcmplx_0(1,F)) ) ) ) ) ) ) ) )).
fof(d3_borsuk_7,axiom,( k8_borsuk_7 = k4_euclid_5(1,k5_numbers,k5_numbers) )).
fof(d3_brouwer,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( ( v1_xreal_0(E) & ~ v3_xxreal_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] : ( 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(k15_euclid(A),C,D),k3_topreal9(A,B,E))) & F != C ) ) ) ) ) ) ) ) ) ) )).
fof(d3_bspace,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(d3_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d3_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ( ( B != k1_xboole_0 => ( C = k3_bvfunc_2(A,B) <=> ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d3_c0sp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(d3_c0sp2,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(d3_calcul_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r1_calcul_1(A,B) <=> r2_hidden(B,k10_xtuple_0(A)) ) ) )).
fof(d3_cantor_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ( C = k2_cantor_1(A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( r2_hidden(D,C) <=> ? [E] : ( 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) ) ) ) ) ) ) )).
fof(d3_card_1,axiom,( ! [A] : ! [B] : ( v1_card_1(B) => ( B = k2_card_1(A) <=> ( r2_hidden(k1_card_1(A),B) & ! [C] : ( v1_card_1(C) => ( r2_hidden(k1_card_1(A),C) => r1_ordinal1(B,C) ) ) ) ) ) )).
fof(d3_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => k3_card_2(A,B) = k1_card_1(k1_funct_2(B,A)) ) ) )).
fof(d3_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k2_card_3(A) <=> ( k9_xtuple_0(B) = k9_xtuple_0(A) & ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => k1_funct_1(B,C) = k2_zfmisc_1(k1_funct_1(A,C),k1_tarski(C)) ) ) ) ) ) )).
fof(d3_card_5,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ( v1_card_5(A) <=> k1_card_5(A) = A ) ) )).
fof(d3_card_fin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_finset_1(B) ) => ( v1_finset_1(k9_xtuple_0(B)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( C = k3_card_fin(A,B) <=> ! [D] : ! [E] : ! [F] : ( v1_finset_1(F) => ! [G] : ( ( 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] : ( ( v1_relat_1(H) & v5_relat_1(H,k4_ordinal1) & v5_ordinal1(H) & v1_funct_1(H) & v1_finset_1(H) ) => ~ ( k1_relset_1(k4_ordinal1,H) = k1_relset_1(k5_card_1(k1_card_fin(F,A,D,E)),G) & ! [I] : ! [J] : ( ( v1_relat_1(J) & v1_funct_1(J) ) => ( ( r2_hidden(I,k1_relset_1(k4_ordinal1,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) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( r3_card_lar(A,B) <=> ( r2_card_lar(A,B) & r1_card_lar(A,B) ) ) ) )).
fof(d3_cat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_cat_1(A,B,C) != k1_xboole_0 => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ( m1_cat_1(D,A,B,C) <=> r2_hidden(D,k2_cat_1(A,B,C)) ) ) ) ) ) ) )).
fof(d3_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(d3_cat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_cat_4(A) ) => k1_cat_4(A) = u1_cat_4(A) ) )).
fof(d3_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d3_catalg_1,axiom,( ! [A] : ! [B] : ( ( v1_msualg_1(B) & l1_msualg_1(B) ) => ( B = k2_catalg_1(A) <=> ( u1_struct_0(B) = k2_zfmisc_1(k1_tarski(k5_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] : ( 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(k5_numbers,k10_finseq_1(C,C)) ) ) & ! [C] : ! [D] : ! [E] : ( ( 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(k5_numbers,k10_finseq_1(D,E)),k4_tarski(k5_numbers,k10_finseq_1(C,D))) & k1_funct_1(u2_msualg_1(B),k4_tarski(2,k11_finseq_1(C,D,E))) = k4_tarski(k5_numbers,k10_finseq_1(C,E)) ) ) ) ) ) )).
fof(d3_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ( ~ v9_struct_0(B,A) => ( v2_cayldick(B,A) <=> k6_algstr_0(A,k2_cayldick(A,B),B) = k1_rlvect_1(A,k5_struct_0(A),k1_square_1(k2_normsp_0(A,B))) ) ) & ( v9_struct_0(B,A) => ( v2_cayldick(B,A) <=> v9_struct_0(k2_cayldick(A,B),A) ) ) ) ) ) )).
fof(d3_cayley,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d3_cc0sp1,axiom,( ! [A] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(d3_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => k2_cc0sp2(A) = a_1_0_cc0sp2(A) ) )).
fof(d3_cfdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ( v2_cfdiff_1(A) <=> ! [B] : ( ( v1_funct_1(B) & v9_ordinal1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & v1_cfdiff_1(B,k5_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v2_comseq_2(k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k36_valued_1(k4_ordinal1,k2_numbers,B),k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,B,A))) & k3_comseq_2(k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k36_valued_1(k4_ordinal1,k2_numbers,B),k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,B,A))) = k5_numbers ) ) ) ) )).
fof(d3_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( v1_xcmplx_0(C) => ! [D] : ( m2_funct_2(D,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ! [E] : ( m1_subset_1(E,A) => k1_funct_1(k1_funct_1(B,k4_tarski(C,D)),E) = k3_xcmplx_0(C,k3_funct_2(A,k2_numbers,D,E)) ) ) ) ) ) ) )).
fof(d3_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) <=> ? [B] : ( v3_ordinal1(B) & r2_hidden(A,k2_cgames_1(B)) ) ) )).
fof(d3_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_finseq_2(B,k1_numbers) => ( B = k1_euclid(A) <=> ! [C] : ( 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))) ) ) ) ) ) )).
fof(d3_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ( r1_chord(A,B,C) <=> ? [D] : r1_glib_000(A,B,C,D) ) ) ) ) )).
fof(d3_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d3_circled1,axiom,( ! [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) ) => ! [B] : ( 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)) ) ) )).
fof(d3_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) => ( m3_msaterm(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(k1_circtrm1(A,B,C))) => ! [E] : ( l3_msualg_1(E,A) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ( F = k3_circtrm1(A,B,C,D,E) <=> ! [G] : ( m3_msaterm(G,A,B) => ( G = C => ! [H] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => k3_circuit1(A,B,C,D) = k3_relat_1(k1_msualg_1(A,D),C) ) ) ) ) )).
fof(d3_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_msafree2(D,A,B) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,k5_msafree2(A,B)),C)) => ( E = k4_circuit2(A,B,C,D) <=> ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d3_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_pdiff_7(C,A) & m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) ) => k2_ckspace1(A,B,C) = g1_funcsdom(k1_ckspace1(A,B,C),k2_c0sp1(k12_funcsdom(C),k1_ckspace1(A,B,C)),k1_c0sp1(k12_funcsdom(C),k1_ckspace1(A,B,C)),k5_c0sp1(k12_funcsdom(C),k1_ckspace1(A,B,C)),k4_c0sp1(k12_funcsdom(C),k1_ckspace1(A,B,C)),k3_c0sp1(k12_funcsdom(C),k1_ckspace1(A,B,C))) ) ) ) )).
fof(d3_classes1,axiom,( ! [A] : ! [B] : ( r1_classes1(A,B) <=> ( r2_hidden(A,B) & v2_classes1(B) ) ) )).
fof(d3_classes2,axiom,( k14_classes2 = k1_classes1(k13_classes2) )).
fof(d3_clopban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_clvect_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(d3_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(k6_clopban1(A,A)),k8_clopban1(A,A)) => ! [C] : ( v1_xcmplx_0(C) => k4_clopban2(A,B,C) = k1_binop_1(k9_csspace(k6_clopban1(A,A),k8_clopban1(A,A)),C,B) ) ) ) )).
fof(d3_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v2_clopban3(B,A) <=> v1_series_1(k5_normsp_0(A,B)) ) ) ) )).
fof(d3_clopban4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( E = k3_clopban4(A,B,C,D) <=> ! [F] : ( v7_ordinal1(F) => ( ( r1_xxreal_0(F,A) => k1_normsp_1(B,E,F) = k6_algstr_0(B,k1_clvect_1(B,k6_clopban3(B,C,F),k9_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) ) ) ) ) ) ) ) ) ) )).
fof(d3_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m2_pboole(C,A,k5_mssubfam(A,B),k5_mssubfam(A,B)) => ( v3_closure1(C,A,B) <=> ! [D] : ( 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))) ) ) ) ) )).
fof(d3_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(d3_clvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ( v3_clvect_1(A) <=> ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d3_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( C = k2_clvect_2(A,B) <=> ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k13_csspace(A,k1_normsp_1(A,B,D)) ) ) ) ) ) )).
fof(d3_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => k2_clvect_3(A,B,C) = k1_normsp_0(A,k1_bhsp_4(A,B),C) ) ) ) )).
fof(d3_coh_sp,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & v1_classes1(C) & v1_coh_sp(C) ) => ( C = k2_coh_sp(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ! [E] : ! [F] : ( ( r2_hidden(E,D) & r2_hidden(F,D) ) => r2_hidden(k4_tarski(E,F),B) ) ) ) ) ) )).
fof(d3_cohsp_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( B = k2_cohsp_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( r2_hidden(C,A) & v1_finset_1(C) ) ) ) ) )).
fof(d3_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_collsp(A) ) => ( v2_collsp(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d3_combgras,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_incsp_1(A))) => ( v2_combgras(B,A) <=> ( v1_combgras(B,A) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_incsp_1(A))) => ( ( v1_combgras(C,A) & r1_tarski(B,C) ) => C = B ) ) ) ) ) ) )).
fof(d3_compl_sp,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_compl_sp(B,A) <=> r2_hidden(B,k2_pcomps_1(A)) ) ) ) )).
fof(d3_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( A = B <=> ( k3_complex1(A) = k3_complex1(B) & k4_complex1(A) = k4_complex1(B) ) ) ) ) )).
fof(d3_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( ( ~ ( k1_comptrig(A) != k5_numbers & B = k5_numbers ) => k3_complex2(A,B) = k1_comptrig(k2_complex2(B,k4_xcmplx_0(k1_comptrig(A)))) ) & ~ ( k1_comptrig(A) != k5_numbers & B = k5_numbers & k3_complex2(A,B) != k6_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k1_comptrig(A)) ) ) ) ) )).
fof(d3_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => k7_complsp2(A) = k10_seq_4(k8_seq_4(A,k1_complsp2(A)),k4_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,2),k7_complex1))) ) )).
fof(d3_compos_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_compos_0(A) ) => ! [B] : ( m1_subset_1(B,k1_compos_0(A)) => k3_compos_0(A,B) = a_2_0_compos_0(A,B) ) ) )).
fof(d3_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(d3_compts_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v10_pre_topc(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d3_comput_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v3_comput_1(A) <=> ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ~ 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_comseq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ( v1_comseq_2(A) <=> ? [B] : ( v1_xreal_0(B) & ! [C] : ~ ( r2_hidden(C,k9_xtuple_0(A)) & r1_xxreal_0(B,k9_complex1(k1_funct_1(A,C))) ) ) ) ) )).
fof(d3_comseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k3_comseq_3(A) <=> ( k9_xtuple_0(B) = k9_xtuple_0(A) & ! [C] : ( r2_hidden(C,k9_xtuple_0(B)) => k1_funct_1(B,C) = k3_complex1(k1_funct_1(A,C)) ) ) ) ) ) )).
fof(d3_conaffm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v3_conaffm(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( ~ r5_analmetr(A,B,C,D) & ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d3_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(d3_conmetr1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v3_conmetr1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A))) => ! [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_connsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_connsp_1(B,A) <=> v1_connsp_1(k1_pre_topc(A,B)) ) ) ) )).
fof(d3_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r1_connsp_2(A,B) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( m1_connsp_2(C,A,B) & ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(d3_connsp_3,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => k2_connsp_3(A,B,C) = C ) ) ) ) )).
fof(d3_convex1,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ( v2_convex1(B,A) <=> ? [C] : ( m2_finseq_1(C,u1_struct_0(A)) & v2_funct_1(C) & k10_xtuple_0(C) = k3_rlvect_2(A,B) & ? [D] : ( m2_finseq_1(D,k1_numbers) & k3_finseq_1(D) = k3_finseq_1(C) & k18_rvsum_1(D) = 1 & ! [E] : ( 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(k5_numbers,k1_funct_1(D,E)) ) ) ) ) ) ) ) ) )).
fof(d3_convex3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_convex3(B,A) <=> ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => ( r1_xxreal_0(C,k5_numbers) | r2_hidden(k1_rlvect_1(A,D,C),B) ) ) ) ) ) ) ) )).
fof(d3_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_convex4(B,A) => ( B = k2_convex4(A) <=> k1_convex4(A,B) = k1_xboole_0 ) ) ) )).
fof(d3_convfun1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(d3_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ( D = k13_cqc_lang(A,B,C) <=> ? [E] : ( 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] : ( 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,k5_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)))) ) ) ) ) ) ) ) ) ) )).
fof(d3_cqc_the1,axiom,( k2_cqc_the1 = a_0_0_cqc_the1 )).
fof(d3_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ( r3_cqc_the3(A,B) <=> ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ( r2_hidden(C,B) => v2_cqc_the1(C,A) ) ) ) ) ) )).
fof(d3_csspace,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_csspace(A) = A ) )).
fof(d3_csspace3,axiom,( 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) )).
fof(d3_csspace4,axiom,( 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) )).
fof(d3_decomp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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))) ) ) ) )).
fof(d3_descip_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v1_int_1(C) => ( r1_xxreal_0(1,k3_finseq_1(B)) => ! [D] : ( m2_finseq_1(D,A) => ( D = k8_descip_1(A,B,C) <=> ( k3_finseq_1(D) = k3_finseq_1(B) & ! [E] : ( 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(k5_int_1(k2_xcmplx_0(k6_xcmplx_0(E,1),C),k3_finseq_1(B)),1)) ) ) ) ) ) ) ) ) ) )).
fof(d3_dickson,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_dickson(A) <=> ( v3_orders_2(A) & v4_orders_2(A) ) ) ) )).
fof(d3_diff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => k3_diff_1(A,B) = k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_diff_1(A,B),A) ) ) )).
fof(d3_diraf,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_diraf(A,B,C,D) <=> r2_analoaf(A,B,C,C,D) ) ) ) ) ) )).
fof(d3_dirort,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dirort(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_dirort(A,B,C,D,E) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & F != G & r2_analoaf(A,F,G,B,C) & r2_analoaf(A,F,G,D,E) ) ) ) ) ) ) ) ) )).
fof(d3_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ( C = k4_dist_1(A,B) <=> ( k4_finseq_1(C) = k2_finseq_1(k5_card_1(A)) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(C)) => k1_funct_1(C,D) = k3_dist_1(A,B,k1_funct_1(k19_finseq_1(A),D)) ) ) ) ) ) ) ) )).
fof(d3_dist_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k6_margrel1) & v1_funct_1(A) ) => k3_dist_2(A) = k8_relat_1(A,k6_domain_1(k6_margrel1,k8_margrel1)) ) )).
fof(d3_dtconstr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => ( v1_dtconstr(A) <=> k1_lang1(A) != k1_xboole_0 ) ) )).
fof(d3_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( v7_ordinal1(C) => k3_dynkin(A,B,C) = k7_subset_1(A,k9_nat_1(k9_setfam_1(A),B,C),k3_tarski(k10_xtuple_0(k5_relat_1(B,C)))) ) ) ) )).
fof(d3_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ( v2_ec_pf_1(B,A) <=> ( B != k5_numbers & ? [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) & k2_binom(k9_int_3(A),C,2) = B ) ) ) ) ) )).
fof(d3_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m2_subset_1(D,k3_ec_pf_1(k9_int_3(A)),k6_ec_pf_1(A,B,C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(A))) => ( E = k4_ec_pf_2(A,B,C,D) <=> ! [F] : ! [G] : ! [H] : ( D = k3_xtuple_0(F,G,H) => E = F ) ) ) ) ) ) ) )).
fof(d3_endalg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(d3_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k2_ens_1(A)) => k3_ens_1(A,B) = k1_xtuple_0(k1_xtuple_0(B)) ) ) )).
fof(d3_entropy1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( v1_entropy1(B,A) <=> ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k4_tarski(C,D),k2_matrix_0(B)) => ( k3_matrix_0(k1_numbers,B,C,D) = k5_numbers | C = D ) ) ) ) ) ) ) )).
fof(d3_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( F = k3_enumset1(A,B,C,D,E) <=> ! [G] : ( r2_hidden(G,F) <=> ~ ( G != A & G != B & G != C & G != D & G != E ) ) ) )).
fof(d3_eqrel_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ( C = k7_eqrel_1(A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( r2_hidden(D,C) <=> ? [E] : ( r2_hidden(E,A) & D = k6_eqrel_1(A,A,B,E) ) ) ) ) ) ) )).
fof(d3_equation,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => k3_equation(A) = k11_msafree(A,k7_funcop_1(u1_struct_0(A),k4_ordinal1)) ) )).
fof(d3_euclid,axiom,( ! [A] : ( ( 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) ) )).
fof(d3_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => k3_euclid_3(A) = k1_comptrig(k2_euclid_3(A)) ) )).
fof(d3_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => k3_euclid_4(A,B,C) = a_3_1_euclid_4(A,B,C) ) ) ) )).
fof(d3_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => k3_euclid_5(A) = k1_funct_1(A,3) ) )).
fof(d3_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(d3_euclid_7,axiom,( ! [A] : ( v1_euclid_7(A) <=> ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v3_valued_0(B) ) => ! [C] : ( ( 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 | k22_rvsum_1(B,C) = k5_numbers ) ) ) ) ) )).
fof(d3_euclid_8,axiom,( k4_euclid_8 = k1_euclid_8(k5_numbers,k5_numbers,1) )).
fof(d3_euclid_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k3_euclid_9(A,B) <=> ( k9_xtuple_0(C) = k9_xtuple_0(A) & ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d3_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d3_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ( v3_euclmetr(A) <=> v4_aff_2(k3_analmetr(A)) ) ) )).
fof(d3_exchsort,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_exchsort(B,A) <=> A = k3_ordinal2(k9_xtuple_0(B)) ) ) )).
fof(d3_extpro_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( v2_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ( v2_extpro_1(C,A,B) <=> ! [D] : ( ( 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 ) ) ) ) ) )).
fof(d3_facirc_1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k1_funct_1(A,k10_finseq_1(B,C)) = k2_binarith(B,C) ) ) ) ) )).
fof(d3_fcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v2_fcont_1(A) <=> ? [B] : ( v1_xreal_0(B) & ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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(k9_complex1(k6_xcmplx_0(k1_funct_1(A,C),k1_funct_1(A,D))),k3_xcmplx_0(B,k9_complex1(k6_xcmplx_0(C,D)))) ) ) ) ) ) ) )).
fof(d3_fdiff_1,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) & ! [C] : ( v1_xreal_0(C) => k1_funct_1(A,C) = k3_xcmplx_0(B,C) ) ) ) ) ) )).
fof(d3_fdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r3_fdiff_3(A,B) <=> ( ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,k5_numbers) & r1_tarski(k1_rcomp_1(B,k2_xcmplx_0(B,C)),k1_relset_1(k1_numbers,A)) ) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & v9_ordinal1(C) & v1_fdiff_1(C,k5_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v3_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k10_xtuple_0(D) = k1_tarski(B) & r1_tarski(k10_xtuple_0(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,D)),k1_relset_1(k1_numbers,A)) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ r1_xxreal_0(k3_funct_2(k4_ordinal1,k1_numbers,C,E),k5_numbers) ) ) => v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,C),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,D),A),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,D,A)))) ) ) ) ) ) ) ) )).
fof(d3_ff_siec,axiom,( ! [A] : k3_ff_siec(A) = k1_ff_siec(k1_xboole_0,A) )).
fof(d3_fib_fusc,axiom,( 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(k5_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(k5_numbers))),k5_afinsq_1(k3_ami_3(k10_ami_3(2),k10_ami_3(3)))),k5_afinsq_1(k7_ami_3(k5_numbers))),k5_afinsq_1(k2_compos_1(k1_ami_3))) )).
fof(d3_fib_num2,axiom,( k3_fib_num2 = a_0_0_fib_num2 )).
fof(d3_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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 ) ) ) ) ) ) ) )).
fof(d3_filter_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(d3_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_lattice2(A))) => k2_filter_2(A,B) = B ) ) )).
fof(d3_fin_topo,axiom,( k4_fin_topo = g1_orders_2(k6_domain_1(k4_ordinal1,k5_numbers),k3_fin_topo(k5_numbers)) )).
fof(d3_finance1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k4_finance1(A,B,C) = k1_funct_1(k3_series_1(k3_finance1(B,C)),A) ) ) ) )).
fof(d3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( B = k3_finseq_1(A) <=> k2_finseq_1(B) = k9_xtuple_0(A) ) ) ) )).
fof(d3_finseq_2,axiom,( ! [A] : ! [B] : ( m1_finseq_2(B,A) <=> ! [C] : ( r2_hidden(C,B) => m2_finseq_1(C,A) ) ) )).
fof(d3_finseq_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( 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] : ( m2_finseq_1(D,A) => ! [E] : ( m2_finseq_1(E,A) => ( r2_hidden(k4_tarski(D,E),C) <=> ( k3_finseq_1(D) = k3_finseq_1(E) & ! [F] : ( v7_ordinal1(F) => ( r2_hidden(F,k1_relset_1(k4_ordinal1,D)) => r2_hidden(k4_tarski(k1_funct_1(D,F),k1_funct_1(E,F)),B) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r2_finseq_4(A,B) => ! [C] : ( C = k1_finseq_4(A,B) <=> ( r2_hidden(C,k9_xtuple_0(A)) & k1_funct_1(A,C) = B ) ) ) ) )).
fof(d3_finseq_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d3_finseq_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(B,C) => k2_finseq_6(A,B,C) = k16_finseq_1(k1_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(k1_nat_1(k7_nat_d(B,C),1),k1_rfinseq(k7_nat_d(C,1),A))) ) ) ) ) ) )).
fof(d3_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(d3_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(d3_finset_1,axiom,( ! [A] : ( v3_finset_1(A) <=> ( A != k1_xboole_0 & ! [B] : ~ ( B != k1_xboole_0 & r1_tarski(B,A) & v1_finset_1(B) & k1_setfam_1(B) = k1_xboole_0 ) ) ) )).
fof(d3_finsub_1,axiom,( ! [A] : ( v3_finsub_1(A) <=> ! [B] : ! [C] : ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r2_hidden(k6_subset_1(B,C),A) ) ) )).
fof(d3_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) ) )).
fof(d3_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v7_ordinal1(C) => k3_fintopo3(A,B,C) = k1_funct_1(k2_fintopo3(A,B),C) ) ) ) )).
fof(d3_fintopo4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(A),k2_finseq_1(A)))) => ( B = k1_fintopo4(A) <=> ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k2_finseq_1(A)) => k9_relat_1(B,C) = k1_enumset1(C,k5_nat_1(k7_nat_d(C,1),1),k3_xxreal_0(k1_nat_1(C,1),A)) ) ) ) ) ) )).
fof(d3_fintopo5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k3_fintopo5(A,B) = g1_orders_2(k2_zfmisc_1(k2_finseq_1(A),k2_finseq_1(B)),k2_fintopo5(A,B)) ) ) )).
fof(d3_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_orders_2(C) & m1_fintopo6(C,A) ) => ( C = k1_fintopo6(A,B) <=> k2_struct_0(C) = B ) ) ) ) )).
fof(d3_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => k8_flang_1(A,B) = k3_tarski(a_2_0_flang_1(A,B)) ) )).
fof(d3_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v3_fomodel0(B,A) <=> v2_fomodel0(B,k3_finseq_2(A),k11_monoid_0(A)) ) ) )).
fof(d3_fomodel1,axiom,( ! [A] : ( 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),k6_subset_1(k4_ordinal1,k6_domain_1(k4_ordinal1,k5_numbers))) ) )).
fof(d3_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( m3_fomodel2(C,A,B) <=> ! [D] : ( ( v9_fomodel1(D,A) & m1_subset_1(D,k1_fomodel1(A)) ) => m2_fomodel2(k1_funct_1(C,D),A,B,D) ) ) ) ) ) )).
fof(d3_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v10_fomodel1(B,A) & m1_subset_1(B,k1_fomodel1(A)) ) => ! [C] : ( ( ~ v7_fomodel1(B,A) => k3_fomodel3(A,B,C) = k2_partfun1(k3_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(k3_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))),k10_fomodel0(C,k32_fomodel1(A))) ) ) ) ) )).
fof(d3_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( v2_fomodel4(B,A) <=> r1_tarski(B,k1_fomodel4(A)) ) ) )).
fof(d3_frechet,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_frechet(A,B,C) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v3_pre_topc(D,A) & r2_hidden(C,D) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(E,F) & ~ r2_hidden(k1_funct_1(B,F),D) ) ) ) ) ) ) ) ) )).
fof(d3_frechet2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_frechet2(A,B,C) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( v7_ordinal1(E) => ~ ( v3_pre_topc(D,A) & r2_hidden(C,D) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( r1_xxreal_0(E,F) & r2_hidden(k9_nat_1(u1_struct_0(A),B,F),D) ) ) ) ) ) ) ) ) ) )).
fof(d3_friends1,axiom,( ! [A] : ( v1_relat_1(A) => ( v3_friends1(A) <=> ! [B] : ! [C] : ~ ( r2_hidden(B,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) & B != C & ! [D] : k3_xboole_0(k9_relat_1(A,B),k10_relat_1(A,C)) != k1_tarski(D) ) ) ) )).
fof(d3_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : 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))) )).
fof(d3_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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),k1_nat_1(k3_finseq_1(C),1)) = E ) ) ) ) ) ) )).
fof(d3_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( v2_fsm_2(C,A,B) <=> ? [D] : ( m2_finseq_1(D,A) & r1_fsm_1(A,B,D,u2_fsm_1(A,B),C) ) ) ) ) ) )).
fof(d3_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ v2_struct_0(C) & l1_fsm_3(C,A,B) ) => ! [D] : ( ( 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))) ) ) ) ) ) ) )).
fof(d3_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k3_ftacell1(A,B,C,D,E) = k9_gfacirc1(A,B,C) )).
fof(d3_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => k3_funcop_1(A,B,C) = k3_relat_1(k13_funct_3(B,C),A) ) ) ) )).
fof(d3_funcsdom,axiom,( ! [A] : ! [B] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( m2_funct_2(D,A,k1_numbers,k9_funct_2(A,k1_numbers)) => k1_binop_1(B,C,D) = k5_funcop_1(k11_binop_2,C,D) ) ) ) ) )).
fof(d3_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k10_xtuple_0(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(D,k9_xtuple_0(A)) & C = k1_funct_1(A,D) ) ) ) ) )).
fof(d3_funct_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) ) => ( v2_funct_2(B,A) <=> k2_relset_1(A,B) = A ) ) )).
fof(d3_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k4_funct_3(A,B) <=> ( k9_xtuple_0(C) = B & ! [D] : ( 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 ) ) ) ) ) ) )).
fof(d3_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k3_funct_4(A,B) <=> ( ! [D] : ( r2_hidden(D,k9_xtuple_0(C)) <=> ? [E] : ? [F] : ? [G] : ? [H] : ( 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] : ! [E] : ! [F] : ! [G] : ( ( 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)) ) ) ) ) ) ) )).
fof(d3_funct_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k3_funct_5(A) = k1_funct_5(k2_funct_4(A)) ) )).
fof(d3_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k3_funct_6(A) = k1_setfam_1(k10_xtuple_0(A)) ) )).
fof(d3_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k3_funct_7(A,B) <=> ? [D] : ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) & v1_funcop_1(D) & C = k1_funct_1(D,k3_finseq_1(B)) & k1_funct_1(D,k5_numbers) = k6_partfun1(A) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k1_nat_1(E,1),k4_finseq_1(B)) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) ) => ( ( F = k1_funct_1(D,E) & G = k1_funct_1(B,k1_nat_1(E,1)) ) => k1_funct_1(D,k1_nat_1(E,1)) = k3_relat_1(F,G) ) ) ) ) ) ) ) ) ) )).
fof(d3_funct_8,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( v3_funct_8(C,A,B) <=> ! [D] : ( v1_xreal_0(D) => ( ( r2_hidden(D,k1_relset_1(A,C)) & r2_hidden(k4_xcmplx_0(D),k1_relset_1(A,C)) ) => k1_funct_1(C,k4_xcmplx_0(D)) = k1_funct_1(C,D) ) ) ) ) ) ) )).
fof(d3_functor0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,B) & v1_funct_1(E) & v1_partfun1(E,B) ) => ! [F] : ( ( 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] : ( ~ v1_xboole_0(G) & ? [H] : ( v1_relat_1(H) & v4_relat_1(H,G) & v1_funct_1(H) & v1_partfun1(H,G) & ? [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)) ) ) ) ) ) ) ) )).
fof(d3_functor2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( m2_functor0(C,A,B) => ! [D] : ( m1_functor2(D,A,B,C,C) => ( D = k1_functor2(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k1_funct_1(D,E) = k8_altcat_1(B,k3_functor0(A,B,C,E)) ) ) ) ) ) ) )).
fof(d3_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ! [F] : ( ( v15_functor0(F,B,C) & m2_functor0(F,B,C) ) => ! [G] : ( ( v15_functor0(G,B,C) & m2_functor0(G,B,C) ) => ! [H] : ( m1_functor2(H,A,B,D,E) => ! [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)) ) ) ) ) ) ) ) ) ) )).
fof(d3_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( m1_subset_1(E,A) => k3_funct_2(A,k1_numbers,D,E) = k3_xxreal_0(k3_funct_2(A,k1_numbers,B,E),k3_funct_2(A,k1_numbers,C,E)) ) ) ) ) ) ) )).
fof(d3_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( m1_subset_1(E,A) => k3_funct_2(A,k1_numbers,D,E) = k5_real_1(k3_real_1(k3_funct_2(A,k1_numbers,B,E),k3_funct_2(A,k1_numbers,C,E)),k4_real_1(k3_funct_2(A,k1_numbers,B,E),k3_funct_2(A,k1_numbers,C,E))) ) ) ) ) ) ) )).
fof(d3_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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] : ( ( v5_relat_1(F,k1_rcomp_1(k5_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 = k3_fuzzy_4(A,B,C,D,E) <=> ! [G] : ! [H] : ( r2_hidden(k4_tarski(G,H),k2_zfmisc_1(A,C)) => k1_binop_1(F,G,H) = k2_seq_4(k2_relset_1(k1_numbers,k2_fuzzy_4(A,B,C,D,E,G,H))) ) ) ) ) ) ) ) ) )).
fof(d3_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d3_gate_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : 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) )).
fof(d3_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d3_genealg1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_finseq_1(B,k3_card_3(A)) => ! [C] : ( m2_finseq_1(C,k3_card_3(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => k2_genealg1(A,B,C,D,E) = k1_genealg1(A,k1_genealg1(A,B,C,D),k1_genealg1(A,C,B,D),E) ) ) ) ) ) )).
fof(d3_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d3_gfacirc1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k1_funct_1(A,k10_finseq_1(B,C)) = k10_margrel1(B,k9_margrel1(C)) ) ) ) ) )).
fof(d3_glib_000,axiom,( k3_glib_000 = 3 )).
fof(d3_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( ~ r1_xxreal_0(k3_finseq_1(B),C) => r1_glib_000(A,k1_funct_1(B,C),k1_funct_1(B,k1_nat_1(C,2)),k1_funct_1(B,k1_nat_1(C,1))) ) ) ) ) ) ) )).
fof(d3_glib_003,axiom,( k4_glib_003 = 7 )).
fof(d3_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ! [C] : ! [D] : ( v1_xreal_0(D) => ( ( ? [E] : ( 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] : ( 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] : ( ( 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 = k5_numbers ) ) ) ) ) )).
fof(d3_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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] : ! [D] : k1_glib_005(A,B,C,D) = k6_xcmplx_0(k2_uproots(k18_glib_000(A,k1_tarski(D)),k5_relat_1(B,k18_glib_000(A,k1_tarski(D)))),k2_uproots(k19_glib_000(A,k1_tarski(D)),k5_relat_1(B,k19_glib_000(A,k1_tarski(D))))) ) ) )).
fof(d3_goboard1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( v1_goboard1(A) <=> ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => v3_funct_1(k1_goboard1(k7_matrix_0(u1_struct_0(k15_euclid(2)),A,B))) ) ) ) ) )).
fof(d3_goboard5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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)) ) ) ) )).
fof(d3_gobrd13,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(A)) & r1_goboard1(u1_struct_0(k15_euclid(2)),A,B) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( D = k4_gobrd13(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ~ ( r2_hidden(k4_tarski(E,F),k2_matrix_0(B)) & r2_hidden(k4_tarski(G,H),k2_matrix_0(B)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),B,E,F) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),B,G,H) & ~ ( E = G & k1_nat_1(F,1) = H & D = k3_goboard5(B,G,H) ) & ~ ( k1_nat_1(E,1) = G & F = H & D = k3_goboard5(B,G,k7_nat_d(H,1)) ) & ~ ( E = k1_nat_1(G,1) & F = H & D = k3_goboard5(B,k7_nat_d(G,1),H) ) & ~ ( E = G & F = k1_nat_1(H,1) & D = k3_goboard5(B,k7_nat_d(G,1),k7_nat_d(H,1)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_goedcpuc,axiom,( ! [A] : ( m1_qc_lang1(A) => k1_goedcpuc(A) = k2_zfmisc_1(k4_ordinal1,k2_xboole_0(k1_qc_lang1(A),a_1_0_goedcpuc(A))) ) )).
fof(d3_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ( B = k1_goedelcp(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) & ? [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) & C = k12_cqc_lang(A,D,E) ) ) ) ) ) ) )).
fof(d3_gr_cy_1,axiom,( k2_gr_cy_1 = g3_algstr_0(k4_numbers,k20_binop_2) )).
fof(d3_gr_cy_3,axiom,( ! [A] : ( v7_ordinal1(A) => k1_gr_cy_3(A) = k6_xcmplx_0(k1_newton(2,A),1) ) )).
fof(d3_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( 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) ) ) )).
fof(d3_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_graph_2(A) <=> k5_card_1(k10_xtuple_0(A)) = 2 ) ) )).
fof(d3_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : 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)) ) ) )).
fof(d3_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : k1_graph_4(A,B) = a_2_0_graph_4(A,B) ) )).
fof(d3_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v7_graph_1(B,A) & m2_graph_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(d3_graphsp,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers)) => ! [B] : ( v7_ordinal1(B) => k7_graphsp(A,B) = a_2_0_graphsp(A,B) ) ) )).
fof(d3_grcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(d3_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( r1_groeb_1(A,B,C,D) <=> v9_rewrite1(k3_polyred(A,B,C,D)) ) ) ) ) ) )).
fof(d3_groeb_2,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : ( k1_funct_1(B,D) = k5_numbers | k1_funct_1(C,D) = k5_numbers ) ) ) ) )).
fof(d3_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => k4_groeb_3(A,B,C,D,E) = k4_xboole_0(k3_polynom1(k15_pre_poly(A),C,D),k3_groeb_3(A,B,C,D,E)) ) ) ) ) ) )).
fof(d3_group_1,axiom,( ! [A] : ( l3_algstr_0(A) => ( v3_group_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d3_group_10,axiom,( ! [A] : ! [B] : k3_group_10(A,B) = a_2_0_group_10(A,B) )).
fof(d3_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => k3_group_11(A,B,C) = a_3_2_group_11(A,B,C) ) ) ) )).
fof(d3_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d3_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(d3_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,k4_numbers) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ( D = k4_group_4(A,B,C) <=> ( k3_finseq_1(D) = k3_finseq_1(C) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( 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)) ) ) ) ) ) ) ) ) )).
fof(d3_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(d3_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k15_group_2(A,B)) => ! [E] : ( m1_subset_1(E,k15_group_2(A,B)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d3_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( m2_finseq_1(D,A) => ! [E] : ( ( 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) = k5_numbers => ( E = k2_group_9(A,B,C,D) <=> r2_funct_2(B,B,E,k6_partfun1(B)) ) ) & ( k3_finseq_1(D) != k5_numbers => ( E = k2_group_9(A,B,C,D) <=> ? [F] : ( 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] : ( v7_ordinal1(G) => ~ ( G != k5_numbers & ~ r1_xxreal_0(k3_finseq_1(D),G) & ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,B,B) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) => ! [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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_groupp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ( v2_groupp_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d3_grsolv_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v15_algstr_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( m1_group_2(D,A) => k2_grsolv_1(A,B,C,D) = k10_group_6(D,B,k1_grsolv_1(A,B,C,D)) ) ) ) ) )).
fof(d3_hahnban,axiom,( ! [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) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => k3_funct_2(u1_struct_0(A),k1_numbers,B,k1_rlvect_1(A,C,D)) = k3_xcmplx_0(D,k3_funct_2(u1_struct_0(A),k1_numbers,B,C)) ) ) ) ) ) )).
fof(d3_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(d3_hallmar1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ! [C] : ( r1_hallmar1(A,B,C) <=> ? [D] : ( m2_finseq_1(D,A) & D = C & k4_finseq_1(B) = k4_finseq_1(D) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k4_finseq_1(D)) => r2_hidden(k1_funct_1(D,E),k1_funct_1(B,E)) ) ) & v2_funct_1(D) ) ) ) ) )).
fof(d3_hausdorf,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( v1_xreal_0(D) => ( D = k3_hausdorf(A,B,C) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(k14_euclid(A))))) & ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d3_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(d3_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ( v2_henmodel(B,A) <=> ! [C] : ( 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)))) ) ) ) ) ) )).
fof(d3_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( 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) ) ) )).
fof(d3_heyting1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k12_normform(A))) => k3_heyting1(A,B) = B ) )).
fof(d3_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( 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)) ) ) ) )).
fof(d3_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_partfun1(k4_ordinal1,k6_domain_1(k4_ordinal1,B))) => ( C = k3_heyting3(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( ~ v1_abian(E) & m1_subset_1(E,k4_ordinal1) & r1_xxreal_0(E,k1_nat_1(k2_nat_1(2,A),1)) & k1_domain_1(k4_ordinal1,k4_ordinal1,E,B) = D ) ) ) ) ) ) )).
fof(d3_hilbasis,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ v2_struct_0(C) & v1_group_1(C) & l5_algstr_0(C) ) => k3_hilbasis(A,B,C) = k14_funct_7(k15_pre_poly(A),u1_struct_0(C),k8_polynom1(A,C),k2_hilbasis(A,B),k1_group_1(C)) ) ) )).
fof(d3_hilbert3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => k3_hilbert3(A,B) = k1_funct_1(k2_hilbert3(A),B) ) ) )).
fof(d3_hurwitz,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k3_hurwitz(A,B,C) = k1_funct_4(k9_polynom3(A),k5_funct_4(u1_struct_0(A),k5_numbers,C,k4_algstr_0(A,k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k4_group_1(A),B,C)),k1_group_1(A))) ) ) ) )).
fof(d3_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_idea_1(A,B) <=> ~ r1_xxreal_0(k5_series_1(2,A),B) ) ) ) )).
fof(d3_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_ideal_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => r2_hidden(k6_algstr_0(A,D,C),B) ) ) ) ) ) ) )).
fof(d3_incproj,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d3_index_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_index_1(A) ) => ! [B] : ( ( 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] : ( r2_hidden(C,k9_xtuple_0(A)) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(d3_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( l3_msualg_1(C,B) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r3_pua2mss1(A,B,D,E) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d3_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r1_int_1(A,B) <=> ? [C] : ( v1_int_1(C) & B = k3_xcmplx_0(A,C) ) ) ) ) )).
fof(d3_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r1_int_2(A,B) <=> k3_int_2(A,B) = 1 ) ) ) )).
fof(d3_int_3,axiom,( k1_int_3 = g6_algstr_0(k4_numbers,k20_binop_2,k22_binop_2,k10_subset_1(1,k4_numbers),k10_subset_1(k5_numbers,k4_numbers)) )).
fof(d3_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ( ( r1_int_5(A,B) => ( k5_int_1(A,B) = k5_numbers | k2_int_5(A,B) = 1 ) ) & ( ( r1_int_5(A,B) & k5_int_1(A,B) = k5_numbers ) => k2_int_5(A,B) = k5_numbers ) & ~ ( ~ ( r1_int_5(A,B) & k5_int_1(A,B) != k5_numbers ) & ~ ( r1_int_5(A,B) & k5_int_1(A,B) = k5_numbers ) & k2_int_5(A,B) != k4_xcmplx_0(1) ) ) ) ) )).
fof(d3_int_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k4_numbers) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(C)) => k1_funct_1(C,D) = k5_int_1(A,k1_funct_1(B,D)) ) ) ) ) ) ) ) )).
fof(d3_int_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => k2_int_7(A) = k1_realset1(k7_int_3(A),k1_int_7(A)) ) )).
fof(d3_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_int_8(A,B) <=> k3_pepin(A,B) = k1_euler_1(B) ) ) ) )).
fof(d3_integr10,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_integr10(A,B,C) => ! [D] : ( v1_xreal_0(D) => ( D = k1_integr10(A,B,C) <=> ? [E] : ( 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] : ( v1_xreal_0(F) => ( r2_hidden(F,k1_relset_1(k1_numbers,E)) => k1_funct_1(E,F) = k4_integra5(B,F,A) ) ) & r1_limfunc2(E,C) & D = k1_limfunc2(E,C) ) ) ) ) ) ) ) )).
fof(d3_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_integra1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(B)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k3_finseq_2(u1_struct_0(A))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k3_finseq_2(u1_struct_0(A))))) ) => ( m2_integr18(E,A,B,C,D) <=> ! [F] : ( m1_subset_1(F,k4_ordinal1) => m1_integr18(k9_nat_1(k3_finseq_2(u1_struct_0(A)),E,F),A,B,C,k2_integra2(B,D,F)) ) ) ) ) ) ) ) )).
fof(d3_integr1c,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k2_numbers))) ) => ( v1_integr1c(A) <=> ? [B] : ( v1_xreal_0(B) & ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [E] : ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [F] : ( 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))) ) ) ) ) ) ) ) )).
fof(d3_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => ! [D] : ( ( ~ v1_xboole_0(D) & v2_measure5(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( C = 1 => ( D = k2_integra1(A,B,C) <=> ( k3_seq_4(D) = k3_seq_4(A) & k2_seq_4(D) = k1_funct_1(B,C) ) ) ) & ( C != 1 => ( D = k2_integra1(A,B,C) <=> ( k3_seq_4(D) = k1_funct_1(B,k6_xcmplx_0(C,1)) & k2_seq_4(D) = k1_funct_1(B,C) ) ) ) ) ) ) ) ) ) )).
fof(d3_integra2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_integra1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( D = k4_integra2(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k1_funct_1(D,E) = k7_integra1(A,B,k2_integra2(A,C,E)) ) ) ) ) ) ) )).
fof(d3_integra5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => k3_integra5(A,B) = k1_rcomp_1(A,B) ) ) ) )).
fof(d3_integra9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => k2_integra9(A,B) = k3_square_1(k1_integra9(A,B,B)) ) ) )).
fof(d3_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_interva1(C,A) ) => k3_interva1(A,B,C) = k3_setfam_1(B,C) ) ) ) )).
fof(d3_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( B = k3_irrat_1(A) <=> ! [C] : ( v7_ordinal1(C) => k1_funct_1(B,C) = k3_xcmplx_0(k4_newton(C,A),k2_power(A,k4_xcmplx_0(C))) ) ) ) ) )).
fof(d3_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d3_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,k6_cat_2(A,B),C) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(d3_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(d3_jgraph_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k4_jgraph_1(A,B))) & ? [E] : ( m1_subset_1(E,k1_zfmisc_1(B)) & ? [F] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d3_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k3_jgraph_6(A,B,C,D) = a_4_2_jgraph_6(A,B,C,D) ) ) ) ) )).
fof(d3_jordan11,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( r1_jordan1h(A,B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( C = k5_jordan11(A,B) <=> ( r1_xxreal_0(C,k1_matrix_0(k1_jordan8(A,B))) & ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(C,D) & r1_xxreal_0(D,k1_nat_1(k2_nat_1(k11_newton(2,k7_nat_d(B,k3_jordan11(A))),k7_nat_d(k4_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] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(D,k1_matrix_0(k1_jordan8(A,B))) & ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(D,E) & r1_xxreal_0(E,k1_nat_1(k2_nat_1(k11_newton(2,k7_nat_d(B,k3_jordan11(A))),k7_nat_d(k4_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) ) ) ) ) ) ) ) ) )).
fof(d3_jordan18,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(A))) => ( r1_jordan18(A,B,C,D,E,F) <=> ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d3_jordan19,axiom,( ! [A] : ( ( 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)) ) )).
fof(d3_jordan1h,axiom,( ! [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] : ( v7_ordinal1(B) => ( r1_jordan1h(A,B) <=> ? [C] : ( v7_ordinal1(C) & ~ r1_xxreal_0(k1_matrix_0(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)) ) ) ) ) )).
fof(d3_jordan20,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ( r3_jordan20(A,B,C,D,E) <=> ( r1_topreal1(k15_euclid(2),B,C,A) & r2_hidden(D,A) & k17_euclid(D) = E & ? [F] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_jordan21,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k2_jordan21(A) = k19_euclid(k7_xcmplx_0(k2_xcmplx_0(k8_pscomp_1(A),k6_pscomp_1(A)),2),k3_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(k7_xcmplx_0(k2_xcmplx_0(k8_pscomp_1(A),k6_pscomp_1(A)),2)))))) ) )).
fof(d3_jordan23,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( ( k3_finseq_1(A) != 2 => ( v3_jordan23(A) <=> ! [B] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(1,B) & ~ r1_xxreal_0(k3_finseq_1(A),B) & k1_funct_1(A,B) = k1_funct_1(A,k1_nat_1(B,1)) ) ) ) ) & ( k3_finseq_1(A) = 2 => v3_jordan23(A) ) ) ) )).
fof(d3_jordan24,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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] : ( 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))) ) ) ) ) )).
fof(d3_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) )).
fof(d3_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( ( B != k1_funct_1(A,k1_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,k1_nat_1(k1_jordan3(A,B),1),k3_finseq_1(A))) ) & ( B = k1_funct_1(A,k1_nat_1(k1_jordan3(A,B),1)) => k2_jordan3(A,B) = k3_finseq_6(u1_struct_0(k15_euclid(2)),A,k1_nat_1(k1_jordan3(A,B),1),k3_finseq_1(A)) ) ) ) ) )).
fof(d3_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_jordan4(A,B,C,D) <=> ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(A)) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_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] : ( 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_xcmplx_0(k3_finseq_1(A),C),E),A)) ) ) ) ) ) ) ) ) )).
fof(d3_jordan5c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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] : ( ( 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] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ( ( v3_tops_2(F,k5_topmetr,k1_pre_topc(k15_euclid(2),A)) & k1_funct_1(F,k5_numbers) = B & k1_funct_1(F,1) = C & k1_funct_1(F,G) = D & r1_xxreal_0(k5_numbers,G) & r1_xxreal_0(G,1) & k1_funct_1(F,H) = E & r1_xxreal_0(k5_numbers,H) & r1_xxreal_0(H,1) ) => r1_xxreal_0(G,H) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( B = k3_jordan5d(A) <=> ( r2_hidden(k4_tarski(k3_finseq_1(k2_goboard2(A)),B),k2_matrix_0(k2_goboard2(A))) & k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k3_finseq_1(k2_goboard2(A)),B) = k23_pscomp_1(k3_topreal1(2,A)) ) ) ) ) )).
fof(d3_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => k3_jordan6(A,B,C,D) = a_4_0_jordan6(A,B,C,D) ) ) ) ) )).
fof(d3_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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] : ( v7_ordinal1(C) => ( 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,k1_nat_1(C,1))) ) ) ) & ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(1,C) => ( r1_xxreal_0(k3_finseq_1(B),k1_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,k1_nat_1(C,1))),k1_jordan7(A,k7_partfun1(u1_struct_0(k15_euclid(2)),B,k1_nat_1(C,1)),k7_partfun1(u1_struct_0(k15_euclid(2)),B,k1_nat_1(C,2)))) = k1_tarski(k7_partfun1(u1_struct_0(k15_euclid(2)),B,k1_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] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( 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,k1_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,k1_nat_1(D,1)))) ) ) ) ) & ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(C,1) & ~ r1_xxreal_0(k3_finseq_1(B),k1_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,k1_nat_1(C,1)))) ) ) ) ) ) ) )).
fof(d3_knaster,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(d3_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v2_prob_1(B) <=> ! [C] : ( v7_ordinal1(C) => r1_tarski(k3_funct_2(k4_ordinal1,k9_setfam_1(A),B,k1_nat_1(C,1)),k1_funct_1(B,C)) ) ) ) )).
fof(d3_kurato_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))))))) ) ) )).
fof(d3_lang1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => k2_lang1(A) = a_1_1_lang1(A) ) )).
fof(d3_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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] : ( ( v15_algstr_0(E) & m1_group_2(E,A) ) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d3_lattice2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( m1_subset_1(C,k5_finsub_1(A)) => ! [D] : ( ( 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) ) ) ) ) )).
fof(d3_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k4_lattice3(A,B) = B ) ) )).
fof(d3_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( m1_lattice4(C,A,B) => ( r1_lattice4(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d3_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,A) ) => ! [C] : ! [D] : ! [E] : ( v1_relat_1(E) => ! [F] : ( 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] : ( m1_subset_1(G,k4_ordinal1) => ( 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,k1_nat_1(G,1))),E) ) & ( v1_abian(G) => r2_hidden(k4_tarski(k1_funct_1(B,G),k1_funct_1(B,k1_nat_1(G,1))),F) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( v1_lattice6(A) <=> v1_wellfnd1(k3_lattice3(A)) ) ) )).
fof(d3_lattice7,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( C = k1_lattice7(A,B) <=> ( ? [D] : ( m1_lattice7(D,A,k3_yellow_0(A),B) & C = k5_card_1(D) ) & ! [D] : ( m1_lattice7(D,A,k3_yellow_0(A),B) => r1_xxreal_0(k5_card_1(D),C) ) ) ) ) ) ) )).
fof(d3_lattice8,axiom,( ! [A] : k1_lattice8(A) = k2_xboole_0(A,k2_tarski(k1_tarski(A),k1_tarski(k1_tarski(A)))) )).
fof(d3_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_lattices(A,B,C) <=> k1_lattices(A,B,C) = C ) ) ) ) )).
fof(d3_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v4_valued_0(A) ) => ! [B] : ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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] : ( ( ( r2_hidden(E,B) & r2_hidden(E,k9_xtuple_0(A)) ) => k1_funct_1(D,E) = k2_xcmplx_0(k1_funct_1(A,E),C) ) & ( ~ r2_hidden(E,B) => k1_funct_1(D,E) = k1_funct_1(A,E) ) ) ) ) ) ) ) )).
fof(d3_lfuzzy_0,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( ( v1_orders_2(B) & v1_lfuzzy_0(B) & l1_orders_2(B) ) => ( B = k1_lfuzzy_0(A) <=> u1_struct_0(B) = A ) ) ) )).
fof(d3_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( m1_subset_1(C,A) => k8_lfuzzy_0(A,A,B,C,C) = 1 ) ) ) ) )).
fof(d3_limfunc1,axiom,( ! [A] : ( v1_xreal_0(A) => k3_limfunc1(A) = k4_xxreal_1(A,k1_xxreal_0) ) )).
fof(d3_limfunc2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r3_limfunc2(A,B) <=> ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(B,C) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,C) & ~ r1_xxreal_0(B,D) & r2_hidden(D,k1_relset_1(k1_numbers,A)) ) ) ) ) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(C) & k1_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(k4_ordinal1,k1_numbers,k1_numbers,C,A)) ) ) ) ) ) ) )).
fof(d3_limfunc3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r3_limfunc3(A,B) <=> ( ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(B,C) & ~ r1_xxreal_0(D,B) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ~ ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(C) & k1_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(k4_ordinal1,k1_numbers,k1_numbers,C,A)) ) ) ) ) ) ) )).
fof(d3_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) => k2_lmod_6(A,B,C,D) = D ) ) ) ) )).
fof(d3_lopban_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(d3_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(k8_lopban_1(A,A)),k10_lopban_1(A,A)) => ! [C] : ( v1_xreal_0(C) => k4_lopban_2(A,B,C) = k1_binop_1(k8_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),C,B) ) ) ) )).
fof(d3_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v2_lopban_3(B,A) <=> v1_series_1(k5_normsp_0(A,B)) ) ) ) )).
fof(d3_lopban_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( B = k2_lopban_4(A) <=> ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(C,A) => k9_nat_1(k1_numbers,B,C) = k7_xcmplx_0(k2_newton(A),k3_xcmplx_0(k2_newton(C),k2_newton(k7_nat_d(A,C)))) ) & ( ~ r1_xxreal_0(C,A) => k9_nat_1(k1_numbers,B,C) = k5_numbers ) ) ) ) ) ) )).
fof(d3_lopban_7,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ( v1_lopban_7(C,A,B) <=> v2_nfcont_1(k3_lopban_7(A,B,C),k7_prvect_3(A,B)) ) ) ) ) )).
fof(d3_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k1_lopclset(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d3_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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] : ( r2_hidden(C,k2_lp_space(A)) => k1_funct_1(B,C) = k2_power(k4_series_1(k1_lp_space(k2_rsspace(C),A)),k7_xcmplx_0(1,A)) ) ) ) ) )).
fof(d3_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(k3_rfunct_3(A,k2_numbers),k3_rfunct_3(A,k2_numbers)),k3_rfunct_3(A,k2_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k3_rfunct_3(A,k2_numbers),k3_rfunct_3(A,k2_numbers)),k3_rfunct_3(A,k2_numbers)))) ) => ( B = k7_lpspacc1(A) <=> ! [C] : ( m2_rfunct_3(C,A,k2_numbers,k3_rfunct_3(A,k2_numbers)) => ! [D] : ( m2_rfunct_3(D,A,k2_numbers,k3_rfunct_3(A,k2_numbers)) => r2_relset_1(A,k2_numbers,k2_lpspace1(A,k2_numbers,B,C,D),k3_lpspacc1(A,k2_numbers,C,D)) ) ) ) ) ) )).
fof(d3_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m2_rfunct_3(C,A,k1_numbers,k3_rfunct_3(A,k1_numbers)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d3_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v2_xxreal_0(D) & v1_xreal_0(D) ) => k2_lpspace2(A,B,C,D) = g1_rlvect_1(k1_lpspace2(A,B,C,D),k10_subset_1(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))) ) ) ) ) )).
fof(d3_ltlaxio1,axiom,( k3_ltlaxio1 = k1_ltlaxio1(k2_hilbert1) )).
fof(d3_ltlaxio3,axiom,( ! [A] : ! [B] : ( ( v2_funct_1(B) & m2_finseq_1(B,A) ) => ! [C] : ( ( v2_funct_1(C) & m2_finseq_1(C,A) ) => ( r1_xboole_0(k2_relset_1(A,B),k2_relset_1(A,C)) => k3_ltlaxio3(A,B,C) = k8_finseq_1(A,B,C) ) ) ) )).
fof(d3_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)))) => k3_ltlaxio4(A) = a_1_0_ltlaxio4(A) ) )).
fof(d3_mathmorp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => k3_mathmorp(A,B,C) = a_3_1_mathmorp(A,B,C) ) ) ) )).
fof(d3_matrix10,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( v3_matrix10(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k4_tarski(B,C),k2_matrix_0(A)) => r1_xxreal_0(k3_matrix_0(k1_numbers,A,B,C),k5_numbers) ) ) ) ) ) )).
fof(d3_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,D,B,C) & m2_finseq_1(E,k3_finseq_2(D)) ) => ! [F] : ( m2_finseq_1(F,D) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,D,B,C) & m2_finseq_1(G,k3_finseq_2(D)) ) => ( ( k3_finseq_1(F) = k1_matrix_0(E) => ( G = k3_matrix11(A,B,C,D,E,F) <=> ( k3_finseq_1(G) = k3_finseq_1(E) & k1_matrix_0(G) = k1_matrix_0(E) & ! [H] : ( v7_ordinal1(H) => ! [I] : ( v7_ordinal1(I) => ( r2_hidden(k4_tarski(H,I),k2_matrix_0(E)) => ( ( H != A => k3_matrix_0(D,G,H,I) = k3_matrix_0(D,E,H,I) ) & ( H = A => k3_matrix_0(D,G,A,I) = k1_funct_1(F,I) ) ) ) ) ) ) ) ) & ( k3_finseq_1(F) != k1_matrix_0(E) => ( G = k3_matrix11(A,B,C,D,E,F) <=> G = E ) ) ) ) ) ) ) ) ) ) )).
fof(d3_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ( r2_hidden(F,k4_finseq_1(D)) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(C),A,B) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(C))) ) => ( H = k3_matrix12(A,B,C,D,E,F,G) <=> ( k3_finseq_1(H) = k3_finseq_1(D) & ! [I] : ( v7_ordinal1(I) => ! [J] : ( v7_ordinal1(J) => ( ( r2_hidden(I,k4_finseq_1(D)) & r2_hidden(J,k2_finseq_1(k1_matrix_0(D))) ) => ( ( I = E => k3_matrix_0(u1_struct_0(C),H,I,J) = k1_algstr_0(C,k8_group_1(C,G,k3_matrix_0(u1_struct_0(C),D,F,J)),k3_matrix_0(u1_struct_0(C),D,E,J)) ) & ( I != E => k3_matrix_0(u1_struct_0(C),H,I,J) = k3_matrix_0(u1_struct_0(C),D,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( ( v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ( k5_card_1(C) = k5_card_1(D) => k7_matrix13(A,B,C,D) = k6_matrix13(A,B,C,D) ) ) ) ) ) )).
fof(d3_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( v7_ordinal1(C) => k4_matrix14(A,B,C) = k2_finseq_7(k3_finseq_2(u1_struct_0(A)),k3_matrix_1(A,B),1,C) ) ) ) )).
fof(d3_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => k4_matrix15(A,B,C) = a_3_0_matrix15(A,B,C) ) ) ) )).
fof(d3_matrix16,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( v2_matrix16(B,A) <=> ? [C] : ( v1_matrix_0(C) & v2_matrix_0(C,A,k3_finseq_1(B),k3_finseq_1(B)) & m2_finseq_1(C,k3_finseq_2(A)) & r1_matrix16(A,C,B) ) ) ) ) )).
fof(d3_matrix_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_matrix_0(A) ) => ! [B] : ( v7_ordinal1(B) => ( ( ~ r1_xxreal_0(k3_finseq_1(A),k5_numbers) => ( B = k1_matrix_0(A) <=> ? [C] : ( 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),k5_numbers) => ( B = k1_matrix_0(A) <=> B = k5_numbers ) ) ) ) ) )).
fof(d3_matrix_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(A),B,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( C = k3_matrix_1(A,B) <=> ( ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k4_tarski(D,D),k2_matrix_0(C)) => k3_matrix_0(u1_struct_0(A),C,D,D) = k5_struct_0(A) ) ) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(D,E),k2_matrix_0(C)) => ( D = E | k3_matrix_0(u1_struct_0(A),C,D,E) = k4_struct_0(A) ) ) ) ) ) ) ) ) ) )).
fof(d3_matrix_2,axiom,( ! [A] : ( v3_matrix_2(A) <=> ? [B] : ( v7_ordinal1(B) & ! [C] : ( 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)))) ) ) ) ) )).
fof(d3_matrix_3,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(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_0(D) = k1_matrix_0(B) & ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( r2_hidden(k4_tarski(E,F),k2_matrix_0(B)) => k3_matrix_0(u1_struct_0(A),D,E,F) = k3_rlvect_1(A,k3_matrix_0(u1_struct_0(A),B,E,F),k3_matrix_0(u1_struct_0(A),C,E,F)) ) ) ) ) ) ) ) ) ) )).
fof(d3_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ! [B] : ( ( v1_matrix_0(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))) ) ) )).
fof(d3_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v1_matrix_6(C,A,B) <=> ? [D] : ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) & r2_matrix_6(A,B,C,D) ) ) ) ) ) )).
fof(d3_matrix_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( C = k4_matrix_7(A,B) <=> ( k3_finseq_1(C) = k3_finseq_1(B) & ! [D] : ( v7_ordinal1(D) => ( 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)) ) ) ) ) ) ) ) )).
fof(d3_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v3_matrix_8(C,A,B) <=> k4_matrix_3(B,C,C) = k3_matrix_1(B,A) ) ) ) ) )).
fof(d3_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrixj1(B,A) & m2_finseq_1(B,k3_finseq_2(k3_finseq_2(A))) ) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( C = k8_matrixj1(A,B) <=> ( k4_finseq_1(C) = k4_finseq_1(B) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(C)) => k1_funct_1(C,D) = k3_finseq_1(k2_matrixj1(A,B,D)) ) ) ) ) ) ) ) )).
fof(d3_matrixj2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_matrixj2(C,A) & m2_finseq_1(C,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) => ( m1_matrixj2(C,A,B) <=> ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(D,k4_finseq_1(C)) & ! [E] : ( v7_ordinal1(E) => k14_matrixj1(u1_struct_0(A),C,D) != k2_matrixj2(A,B,E) ) ) ) ) ) ) ) )).
fof(d3_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(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))) ) ) )).
fof(d3_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => k5_matrixr2(A) = k8_matrixr1(A,A) ) )).
fof(d3_matrlin,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d3_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( m1_matrlin(D,A,B) => ! [E] : ( m2_finseq_1(E,u1_struct_0(C)) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(A),k3_finseq_1(D),k3_finseq_1(E)) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(A))) ) => ! [G] : ( ( 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] : ( 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,k7_matrix_0(u1_struct_0(A),k4_matrix_3(A,k2_matrix15(u1_struct_0(A),k9_matrlin(A,B,D,H)),F),1),E)) ) ) ) ) ) ) ) ) ) )).
fof(d3_matroid0,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_matroid0(A) <=> v1_classes1(k1_matroid0(A)) ) ) )).
fof(d3_matrprob,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => k5_matrprob(A) = k18_rvsum_1(k3_matrprob(A)) ) )).
fof(d3_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ! [D] : ( ( 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 != k5_numbers => ( D = k3_matrtop1(A,B,C) <=> ! [E] : ( ( 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) = k7_matrix_0(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 = k5_numbers => ( D = k3_matrtop1(A,B,C) <=> ! [E] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(d3_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(D,A) ) => ( r1_xxreal_0(D,C) | ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(k2_vectsp_1),A,A) & v1_matrix_6(E,A,k2_vectsp_1) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( E = k2_matrtop3(A,B,C,D) <=> ( k3_matrix_0(u1_struct_0(k2_vectsp_1),E,C,C) = k19_sin_cos(B) & k3_matrix_0(u1_struct_0(k2_vectsp_1),E,D,D) = k19_sin_cos(B) & k3_matrix_0(u1_struct_0(k2_vectsp_1),E,C,D) = k17_sin_cos(B) & k3_matrix_0(u1_struct_0(k2_vectsp_1),E,D,C) = k4_xcmplx_0(k17_sin_cos(B)) & ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ( r2_hidden(k4_tarski(F,G),k2_matrix_0(E)) => ( ( F = G => ( F = C | F = D | k3_matrix_0(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_0(u1_struct_0(k2_vectsp_1),E,F,G) != k4_struct_0(k2_vectsp_1) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_mazurulm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_rlvect_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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),k6_xxreal_3(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)),k6_xxreal_3(1,2)) ) ) ) ) ) ) )).
fof(d3_mcart_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k3_zfmisc_1(A,B,C)) => ! [E] : ( m1_subset_1(E,C) => ( E = k3_mcart_1(A,B,C,D) <=> ! [F] : ! [G] : ! [H] : ( D = k3_xtuple_0(F,G,H) => E = H ) ) ) ) ) ) ) )).
fof(d3_measure1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( v2_measure1(C,A,B) <=> ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d3_measure3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ( D = k2_measure3(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ? [F] : ( r2_hidden(F,B) & ? [G] : ( m1_measure3(G,A,B,C) & E = k2_xboole_0(F,G) ) ) ) ) ) ) ) )).
fof(d3_measure4,axiom,( ! [A] : ! [B] : ( m1_measure4(B,A) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k1_measure4(A,B),k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_measure4(A,B),k6_numbers))) ) => ( C = k3_measure4(A,B) <=> ! [D] : ( 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) ) ) ) ) ) )).
fof(d3_measure5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v2_measure5(A) <=> ? [B] : ( v1_xreal_0(B) & ? [C] : ( v1_xreal_0(C) & A = k1_rcomp_1(B,C) ) ) ) ) )).
fof(d3_measure6,axiom,( ! [A] : ( v3_membered(A) => ( v2_xxreal_2(A) <=> ( v4_xxreal_2(A) & r2_hidden(k2_seq_4(A),A) ) ) ) )).
fof(d3_measure8,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( ~ 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] : ( 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))) ) ) ) ) )).
fof(d3_member_1,axiom,( ! [A] : ( v2_membered(A) => k6_member_1(A) = a_1_2_member_1(A) ) )).
fof(d3_membered,axiom,( ! [A] : ( v3_membered(A) <=> ! [B] : ( r2_hidden(B,A) => v1_xreal_0(B) ) ) )).
fof(d3_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( r2_mesfun6c(A,B,C,D) => ! [E] : ( v1_xcmplx_0(E) => ( E = k1_mesfun6c(A,B,C,D) <=> ? [F] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & 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)) ) ) ) ) ) ) ) ) ) )).
fof(d3_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => k3_mesfun7c(A,B) = k2_mesfunc8(A,k1_mesfun7c(A,B)) ) ) )).
fof(d3_mesfunc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k6_numbers) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,k6_numbers) & v1_funct_1(C) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d3_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( C = k2_mesfunc2(A,B) <=> ( k1_relset_1(A,C) = k1_relset_1(A,B) & ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(d3_mesfunc5,axiom,( ! [A] : ( v1_relat_1(A) => ( v3_mesfunc5(A) <=> ~ r2_hidden(k2_supinf_1,k10_xtuple_0(A)) ) ) )).
fof(d3_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(d3_mesfunc7,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ! [B] : ( v7_ordinal1(B) => k3_mesfunc7(A,B) = k2_mesfunc7(k5_finseq_2(k6_numbers,B,A)) ) ) )).
fof(d3_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( C = k1_mesfunc8(A,B) <=> ( k1_relset_1(A,C) = k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers)) & ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(d3_mesfunc9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_valued_0(A) ) => k3_mesfunc9(A) = k2_mesfunc5(k2_mesfunc9(A)) ) )).
fof(d3_metric_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ( k1_binop_1(B,C,D) = k5_numbers => C = D ) ) ) ) ) )).
fof(d3_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( m1_metric_2(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & B = k1_metric_2(A,C) ) ) ) ) )).
fof(d3_metric_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_tbsp_1(B,A) <=> ? [C] : ( v1_xreal_0(C) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ~ r1_xxreal_0(C,k5_numbers) & r1_tarski(B,k8_metric_1(A,D,C)) ) ) ) ) ) )).
fof(d3_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_metrizts(A,B,C,D) <=> ? [E] : ( v3_pre_topc(E,A) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & ? [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(d3_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => k2_mfold_1(A) = k1_mfold_1(A,k4_struct_0(k15_euclid(A)),1) ) )).
fof(d3_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( 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)) ) ) ) )).
fof(d3_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_midsp_1(A) ) => ( v2_midsp_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_subset_1(F,u1_struct_0(A)) & k1_midsp_1(A,F,B) = C ) ) ) ) ) ) ) ) )).
fof(d3_midsp_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ? [F] : ( m1_subset_1(F,A) & k2_binop_1(A,A,u1_struct_0(B),C,D,F) = E ) ) ) & ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d3_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_nat_1(A,2)) ) => ( v2_midsp_3(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(B))) => ! [F] : ( m2_finseq_2(F,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(B))) => ( ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d3_mmlquer2,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => k1_mmlquer2(A,B) = k2_xboole_0(A,k6_subset_1(B,k2_relat_1(A))) ) ) )).
fof(d3_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k3_mmlquery(A,B,C) = k1_setfam_1(a_3_0_mmlquery(A,B,C)) ) ) )).
fof(d3_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( l1_mod_2(B,A) => k2_mod_2(A,B) = u1_mod_2(A,B) ) ) )).
fof(d3_mod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v1_mod_3(C,A,B) ) ) ) ) )).
fof(d3_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(d3_modal_1,axiom,( k3_modal_1 = k2_zfmisc_1(k6_domain_1(k4_ordinal1,3),k4_ordinal1) )).
fof(d3_modcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m3_modcat_1(D,A) => ( m5_modcat_1(D,A,B,C) <=> ! [E] : ( m4_modcat_1(E,A,D) => ( v2_mod_2(E,A) & m1_mod_2(E,A,B,C) ) ) ) ) ) ) ) )).
fof(d3_modelc_2,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => k3_modelc_2(A) = k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,k5_numbers),A) ) )).
fof(d3_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ( 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 ) ) ) )).
fof(d3_moebius1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ( ( v1_moebius1(A) => ( B = k2_moebius1(A) <=> B = k5_numbers ) ) & ( ~ v1_moebius1(A) => ( B = k2_moebius1(A) <=> ? [C] : ( v7_ordinal1(C) & ~ v8_ordinal1(C) & C = A & B = k1_newton(k4_xcmplx_0(1),k5_card_1(k22_pre_poly(k8_newton,k13_nat_3(C)))) ) ) ) ) ) ) )).
fof(d3_monoid_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ? [E] : ( m1_subset_1(E,A) & k5_binop_1(A,B,E,C) = D ) ) ) ) ) ) )).
fof(d3_monoid_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(d3_morph_01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d3_msafree,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k3_msafree(A,B) <=> ( k9_xtuple_0(C) = A & ! [D] : ( r2_hidden(D,A) => k1_funct_1(C,D) = k2_msafree(A,B,D) ) ) ) ) ) )).
fof(d3_msafree1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v3_msualg_1(B,A) & l3_msualg_1(B,A) ) => ( B = k2_msafree1(A) <=> ! [C] : ( r2_hidden(C,u1_struct_0(A)) => k1_funct_1(u3_msualg_1(A,B),C) = k1_tarski(C) ) ) ) ) )).
fof(d3_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => k3_msafree2(A) = k2_relset_1(u1_struct_0(A),u2_msualg_1(A)) ) )).
fof(d3_msafree3,axiom,( ! [A] : ( l1_msualg_1(A) => ! [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] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) ) => k3_msafree3(A,B,C) = k3_pboole(u1_struct_0(A),B,k2_msafree3(A,C)) ) ) ) )).
fof(d3_msalimit,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_msalimit(C,A,B) => ! [D] : ( m2_msalimit(D,A,B,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d3_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(d3_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) => ( v2_mssubfam(C,A,B) <=> ! [D] : ( m3_pboole(D,A,k1_mboolean(A,B)) => ( r2_pboole(A,D,C) => r1_pboole(A,k2_mboolean(A,D),C) ) ) ) ) ) )).
fof(d3_msualg_1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l2_msualg_1(B,A) => ( v4_msualg_1(B,A) <=> v2_relat_1(u3_msualg_1(A,B)) ) ) ) )).
fof(d3_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( ~ 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 ) ) ) ) ) ) ) )).
fof(d3_msualg_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,C) => ( v2_msualg_3(D,A,B,C) <=> ! [E] : ( r2_hidden(E,A) => k10_xtuple_0(k1_funct_1(D,E)) = k1_funct_1(C,E) ) ) ) ) ) )).
fof(d3_msualg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(d3_msualg_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_msualg_4(C,A,B,B) => ! [D] : ( ( v1_msualg_4(D,A,B) & m1_msualg_4(D,A,B,B) ) => ( D = k3_msualg_5(A,B,C) <=> ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(d3_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ( B = k3_msualg_6(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(k4_tarski(C,D),B) <=> ? [E] : ( m1_subset_1(E,u4_struct_0(A)) & k2_msualg_1(A,E) = D & ? [F] : ( m1_subset_1(F,k4_ordinal1) & r2_hidden(F,k4_finseq_1(k1_msualg_1(A,E))) & k7_partfun1(u1_struct_0(A),k1_msualg_1(A,E),F) = C ) ) ) ) ) ) ) ) )).
fof(d3_msualg_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m2_nat_lat(B,A) => ( v2_msualg_7(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => r2_hidden(k15_lattice3(A,C),u1_struct_0(B)) ) ) ) ) )).
fof(d3_msualg_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_msualg_5(A,B)))) => ! [E] : ( 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] : ( r2_hidden(F,E) <=> ? [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d3_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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(k5_numbers,C) ) ) ) ) )).
fof(d3_mycielsk,axiom,( ! [A] : ( ( v1_mycielsk(A) & l1_orders_2(A) ) => ! [B] : ( v7_ordinal1(B) => ( B = k2_mycielsk(A) <=> ( ? [C] : ( v1_finset_1(C) & v6_dilworth(C,A) & m1_eqrel_1(C,u1_struct_0(A)) & k5_card_1(C) = B ) & ! [C] : ( ( v1_finset_1(C) & v6_dilworth(C,A) & m1_eqrel_1(C,u1_struct_0(A)) ) => r1_xxreal_0(B,k5_card_1(C)) ) ) ) ) ) )).
fof(d3_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) ) => ( v3_nagata_1(B,A) <=> ! [C] : ( m1_subset_1(C,k4_ordinal1) => v1_pcomps_1(k1_nagata_1(A,B,C),A) ) ) ) ) )).
fof(d3_nagata_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( ( 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] : ( m1_subset_1(E,A) => k3_funct_2(A,k1_numbers,D,E) = k3_seq_4(k7_relset_1(A,k1_numbers,k2_nagata_2(A,B,E),C)) ) ) ) ) ) ) )).
fof(d3_nat_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( C = k7_nat_1(A,B) <=> ! [D] : ( v7_ordinal1(D) => k1_funct_1(C,D) = k1_funct_1(A,k2_xcmplx_0(D,B)) ) ) ) ) ) )).
fof(d3_nat_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v3_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v3_valued_0(C) ) => ! [D] : ( ( 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] : ( ( r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(C,E)) => k1_funct_1(D,E) = k1_funct_1(B,E) ) & ( ~ r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(C,E)) => k1_funct_1(D,E) = k1_funct_1(C,E) ) ) ) ) ) ) )).
fof(d3_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ( B = k4_nat_5(A) <=> ! [C] : ( v7_ordinal1(C) => k1_recdef_1(B,C) = k3_nat_5(A,C) ) ) ) ) )).
fof(d3_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_nat_d(A,B) <=> ? [C] : ( v7_ordinal1(C) & B = k3_xcmplx_0(A,C) ) ) ) ) )).
fof(d3_nat_lat,axiom,( k3_nat_lat = g3_lattices(k4_ordinal1,k2_nat_lat,k1_nat_lat) )).
fof(d3_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m1_nattra_1(D,A,B,C,C) => ( D = k1_nattra_1(A,B,C) <=> ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d3_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_ncfcont1(B,A) <=> ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) ) )).
fof(d3_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ~ ( r2_hidden(G,A) & r2_hidden(H,A) & ~ r1_xxreal_0(F,k2_normsp_0(B,k5_algstr_0(B,G,H))) & r1_xxreal_0(E,k2_normsp_0(C,k5_algstr_0(C,k7_partfun1(u1_struct_0(C),D,G),k7_partfun1(u1_struct_0(C),D,H)))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_ndiff_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k2_ndiff_1(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k1_normsp_1(A,D,E) = k1_rlvect_1(A,B,k9_nat_1(k1_numbers,C,E)) ) ) ) ) ) ) )).
fof(d3_ndiff_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_ndiff_2(A,B,C,D,E) <=> ? [F] : ( m1_nfcont_1(F,A,D) & r1_tarski(F,k1_relset_1(u1_struct_0(A),C)) & ? [G] : ( m1_subset_1(G,u1_struct_0(B)) & ! [H] : ( v1_xreal_0(H) => ~ ( ~ r1_xxreal_0(H,k5_numbers) & ! [I] : ( v1_xreal_0(I) => ~ ( ~ r1_xxreal_0(I,k5_numbers) & ! [J] : ( v1_xreal_0(J) => ~ ( ~ r1_xxreal_0(I,k9_complex1(J)) & J != k5_numbers & r2_hidden(k3_rlvect_1(A,k1_rlvect_1(A,E,J),D),F) & r1_xxreal_0(H,k2_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)),k5_xcmplx_0(J)),G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [C] : ( v1_xreal_0(C) => ( r1_ndiff_3(A,B,C) <=> ? [D] : ( m1_rcomp_1(D,C) & r1_tarski(D,k1_relset_1(k1_numbers,B)) & ? [E] : ( 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] : ( 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] : ( v1_xreal_0(G) => ( 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,k10_funct_2(k1_numbers,u1_struct_0(A),E,k6_xcmplx_0(G,C)),k7_partfun1(u1_struct_0(A),F,k6_xcmplx_0(G,C))) ) ) ) ) ) ) ) ) ) )).
fof(d3_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [C] : ( r2_ndiff_4(A,B,C) <=> ( r1_tarski(C,k1_relset_1(k1_numbers,B)) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => r1_ndiff_4(A,k2_partfun1(k1_numbers,k1_euclid(A),B,C),D) ) ) ) ) ) ) )).
fof(d3_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(A)) => ! [C] : ( ( 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] : ( m1_subset_1(D,k4_card_3(k4_prvect_2(A))) => k1_funct_1(C,D) = k1_ndiff_5(A,D,B) ) ) ) ) ) )).
fof(d3_neckla_2,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( ( 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))) ) ) ) ) ) )).
fof(d3_neckla_3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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) ) ) )).
fof(d3_necklace,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_necklace(A) <=> r3_relat_2(u1_orders_2(A),u1_struct_0(A)) ) ) )).
fof(d3_net_1,axiom,( ! [A] : ( l1_petri(A) => k2_net_1(A) = k2_xboole_0(u1_struct_0(A),u4_struct_0(A)) ) )).
fof(d3_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( r1_xxreal_0(A,B) => ( C = k3_newton(A,B) <=> ! [D] : ( v7_ordinal1(D) => ( D = k6_xcmplx_0(B,A) => C = k7_xcmplx_0(k2_newton(B),k3_xcmplx_0(k2_newton(A),k2_newton(D))) ) ) ) ) & ( ~ r1_xxreal_0(A,B) => ( C = k3_newton(A,B) <=> C = k5_numbers ) ) ) ) ) )).
fof(d3_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_nfcont_1(B,A) <=> ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) ) )).
fof(d3_nfcont_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_normsp_1(A) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(1,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => r1_xxreal_0(k2_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))),k3_xcmplx_0(C,k2_normsp_0(A,k5_algstr_0(A,D,E)))) ) ) ) ) ) ) )).
fof(d3_nfcont_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( 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(k2_normsp_0(A,k5_algstr_0(A,k7_partfun1(u1_struct_0(A),B,D),k7_partfun1(u1_struct_0(A),B,E))),k3_xcmplx_0(C,k9_complex1(k6_xcmplx_0(D,E)))) ) ) ) ) ) ) ) )).
fof(d3_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_euclid(A)))) ) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(d3_normform,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_finsub_1(B) ) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ! [D] : ( 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))) ) ) ) ) )).
fof(d3_normsp_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_normsp_0(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( D = k4_normsp_0(A,B,C) <=> ( k9_xtuple_0(D) = k9_xtuple_0(C) & ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,k9_xtuple_0(D)) => k1_funct_1(D,E) = k2_normsp_0(B,k7_partfun1(u1_struct_0(B),C,E)) ) ) ) ) ) ) ) ) )).
fof(d3_normsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k3_normsp_1(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k1_normsp_1(A,D,E) = k5_algstr_0(A,k1_normsp_1(A,B,E),k1_normsp_1(A,C,E)) ) ) ) ) ) ) )).
fof(d3_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => k3_normsp_2(A) = k3_pcomps_1(k2_normsp_2(A)) ) )).
fof(d3_ntalgo_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => ! [B] : ( m1_subset_1(B,k4_numbers) => ! [C] : ( m1_subset_1(C,k4_numbers) => ( C = k3_ntalgo_1(A,B) <=> ! [D] : ( m1_subset_1(D,k4_numbers) => ( D = k5_int_1(A,B) => ( ( k3_mcart_1(k4_numbers,k4_numbers,k4_numbers,k2_ntalgo_1(B,D)) = 1 => ( ~ ( ~ r1_xxreal_0(k5_numbers,k2_mcart_1(k4_numbers,k4_numbers,k4_numbers,k2_ntalgo_1(B,D))) & ! [E] : ( 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(k5_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 ) ) ) ) ) ) ) ) )).
fof(d3_numbers,axiom,( k3_numbers = k6_subset_1(k2_xboole_0(k5_arytm_3,k2_zfmisc_1(k1_tarski(k5_ordinal1),k5_arytm_3)),k1_tarski(k4_tarski(k5_ordinal1,k5_ordinal1))) )).
fof(d3_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ( v2_o_ring_1(B,A) <=> ( k3_finseq_1(B) != k5_numbers & v1_o_ring_1(k7_partfun1(u1_struct_0(A),B,1),A) & ! [C] : ( v7_ordinal1(C) => ~ ( C != k5_numbers & ~ r1_xxreal_0(k3_finseq_1(B),C) & ! [D] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d3_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k1_openlatt(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d3_oposet_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_qmax_1(A) ) => ( v1_oposet_1(A) <=> ? [B] : ( 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) ) ) ) )).
fof(d3_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_oppcat_1(A))) => k4_oppcat_1(A,B) = k3_oppcat_1(k2_oppcat_1(A),B) ) ) )).
fof(d3_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => k2_ordeq_01(A,B) = g1_rlvect_1(k1_ordeq_01(A,B),k9_rsspace(k5_rsspace4(A,B),k1_ordeq_01(A,B)),k7_rsspace(k5_rsspace4(A,B),k1_ordeq_01(A,B)),k8_rsspace(k5_rsspace4(A,B),k1_ordeq_01(A,B))) ) ) )).
fof(d3_orders_1,axiom,( ! [A] : k1_orders_1(A) = k7_subset_1(k1_zfmisc_1(A),k9_setfam_1(A),k1_tarski(k1_xboole_0)) )).
fof(d3_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => ( v4_orders_2(A) <=> r8_relat_2(u1_orders_2(A),u1_struct_0(A)) ) ) )).
fof(d3_orders_3,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_orders_3(A) <=> v2_orders_3(k2_struct_0(A),A) ) ) )).
fof(d3_orders_4,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ! [C] : ( r1_orders_4(A,B,C) <=> ( k2_xboole_0(B,C) = u1_struct_0(A) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r2_hidden(D,B) & r2_hidden(E,C) ) => r2_orders_2(A,D,E) ) ) ) ) ) ) )).
fof(d3_ordinal1,axiom,( ! [A] : ( v2_ordinal1(A) <=> ! [B] : ! [C] : ~ ( r2_hidden(B,A) & r2_hidden(C,A) & ~ r2_hidden(B,C) & B != C & ~ r2_hidden(C,B) ) ) )).
fof(d3_ordinal2,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => ( B = k3_ordinal2(A) <=> ( r1_tarski(k2_ordinal1(A),B) & ! [C] : ( v3_ordinal1(C) => ( r1_tarski(k2_ordinal1(A),C) => r1_ordinal1(B,C) ) ) ) ) ) )).
fof(d3_ordinal4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => k3_ordinal4(A) = 1 ) )).
fof(d3_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ~ r1_orders_2(B,F,E) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( ? [H] : ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & v13_osalg_1(B,A) & l3_msualg_1(B,A) ) => ( v2_osafree(B,A) <=> ? [C] : ( m1_osafree(C,A,B) & v1_osafree(C,A,B) ) ) ) ) )).
fof(d3_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_osalg_1(A) ) => ( v5_osalg_1(A) <=> ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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 ) ) ) ) ) )).
fof(d3_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_osalg_2(A,B,C) = k3_tarski(a_3_0_osalg_2(A,B,C)) ) ) ) )).
fof(d3_osalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ! [D] : ( r2_hidden(k4_tarski(C,D),B) <=> ( r2_hidden(C,u1_struct_0(A)) & r2_hidden(D,u1_struct_0(A)) & ? [E] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d3_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( 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] : ( 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))) ) ) ) ) )).
fof(d3_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d3_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( C = k4_partfun1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( v1_relat_1(E) & v1_funct_1(E) & D = E & r1_tarski(k9_xtuple_0(E),A) & r1_tarski(k10_xtuple_0(E),B) ) ) ) )).
fof(d3_partit1,axiom,( ! [A] : ! [B] : ( B = k1_partit1(A) <=> ! [C] : ( r2_hidden(C,B) <=> m1_eqrel_1(C,A) ) ) )).
fof(d3_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => k3_funct_2(A,A,B,k3_funct_2(A,A,B,C)) = C ) ) ) ) )).
fof(d3_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ( v3_pasch(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_pboole,axiom,( ! [A] : k1_pboole(A) = k7_funcop_1(A,k1_xboole_0) )).
fof(d3_pcomps_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( v2_pcomps_1(A) <=> ! [B] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(d3_pcs_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(C,D))) => ! [G] : ( 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] : ( m1_subset_1(H,A) => ! [I] : ( m1_subset_1(I,B) => ! [J] : ( m1_subset_1(J,C) => ! [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_pdiff_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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))) ) ) )).
fof(d3_pdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( r2_pdiff_2(A,B) <=> ( r1_tarski(B,k1_relset_1(k1_euclid(2),A)) & ! [C] : ( 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) ) ) ) ) ) )).
fof(d3_pdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(2)) => ( r2_pdiff_3(A,B) <=> ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & B = k10_finseq_1(C,D) & ? [E] : ( 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] : ( v1_funct_1(F) & v3_fdiff_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [G] : ( v1_funct_1(G) & v2_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,E) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(2,2,k1_pdiff_3(1,2,A),B),H),k1_funct_1(k1_pdiff_2(2,2,k1_pdiff_3(1,2,A),B),D)) = k2_xcmplx_0(k1_funct_1(F,k6_xcmplx_0(H,D)),k1_funct_1(G,k6_xcmplx_0(H,D))) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_pdiff_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( r3_pdiff_4(A,B) <=> ( r1_tarski(B,k1_relset_1(k1_euclid(3),A)) & ! [C] : ( 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) ) ) ) ) ) )).
fof(d3_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r3_pdiff_5(A,B) <=> ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & B = k11_finseq_1(C,D,E) & ? [F] : ( 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] : ( v1_funct_1(G) & v3_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [H] : ( v1_funct_1(H) & v2_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,F) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,3,k1_pdiff_3(1,3,A),B),I),k1_funct_1(k1_pdiff_2(3,3,k1_pdiff_3(1,3,A),B),E)) = k2_xcmplx_0(k1_funct_1(G,k6_xcmplx_0(I,E)),k1_funct_1(H,k6_xcmplx_0(I,E))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ( v1_pdiff_7(B,A) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_real_ns1(A)))) & C = B & v3_nfcont_1(C,k4_real_ns1(A)) ) ) ) ) )).
fof(d3_pdiff_9,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d3_pencil_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_pencil_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r1_pencil_1(A,C,D) ) ) ) ) ) ) )).
fof(d3_pencil_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_pencil_2(A,B,C) <=> ? [D] : ( 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] : ( 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] : ( m1_subset_1(E,k4_ordinal1) => ( 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,k1_nat_1(E,1))))) ) ) ) ) ) ) ) ) )).
fof(d3_pencil_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v15_pencil_1(B) ) => ( ! [C] : ( m1_subset_1(C,A) => v10_pencil_1(k2_pencil_1(A,B,C)) ) => ! [C] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ( k3_funct_2(A,A,D,E) = F <=> ! [G] : ( m1_pencil_2(G,A,B) => ! [H] : ( ( ~ v13_pencil_1(H) & v16_pencil_1(H,A) & m3_pboole(H,A,k12_pralg_1(A,B)) ) => ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(d3_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => k4_pepin(A) = k1_nat_1(k1_newton(2,k1_newton(2,A)),1) ) )).
fof(d3_petri_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : k2_petri_2(A,B) = a_2_0_petri_2(A,B) ) )).
fof(d3_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ( r2_pnproc_1(A,B,C) <=> ! [D] : ( r2_hidden(D,A) => r1_xxreal_0(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) )).
fof(d3_polyalg1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_polyalg1(B,A) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(d3_polyeq_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => k3_polyeq_1(A,B,C,D) = k3_xcmplx_0(A,k3_xcmplx_0(k6_xcmplx_0(B,C),k6_xcmplx_0(B,D))) ) ) ) ) )).
fof(d3_polyeq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => k4_polyeq_1(A,B,C,D,E) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k3_polyeq_3(E)),k3_xcmplx_0(B,k1_square_1(E))),k3_xcmplx_0(C,E)),D) ) ) ) ) ) )).
fof(d3_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( ( k6_xcmplx_0(k3_xcmplx_0(3,B),k1_newton(C,2)) = k5_numbers => ( D = k3_polyeq_5(A,B,C) <=> ? [E] : ( v1_xcmplx_0(E) & ? [F] : ( v1_xcmplx_0(F) & E = k7_xcmplx_0(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 = k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(F,2)),k7_xcmplx_0(C,3)),k7_xcmplx_0(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)) != k5_numbers => ( D = k3_polyeq_5(A,B,C) <=> ? [E] : ( v1_xcmplx_0(E) & ? [F] : ( v1_xcmplx_0(F) & ? [G] : ( v1_xcmplx_0(G) & ? [H] : ( v1_xcmplx_0(H) & ? [I] : ( v1_xcmplx_0(I) & E = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(3,B),k1_newton(C,2)),9) & F = k7_xcmplx_0(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 = k4_xcmplx_0(k7_xcmplx_0(E,H)) & D = k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(H,I),2)),k7_xcmplx_0(C,3)),k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(H,I),k1_polyeq_5(2,3)),k7_complex1),2)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_polyform,axiom,( ! [A] : ( l1_polyform(A) => ( v4_polyform(A) <=> ! [B] : ( 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)) ) ) ) ) ) )).
fof(d3_polynom3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_partfun1(B,k4_finseq_2(A,k4_ordinal1)) & 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,k4_ordinal1),k4_finseq_2(A,k4_ordinal1)))) ) => ( B = k5_polynom3(A) <=> ! [C] : ( m2_finseq_2(C,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [D] : ( m2_finseq_2(D,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ( r2_hidden(k4_tarski(C,D),B) <=> r2_polynom3(A,C,D) ) ) ) ) ) ) )).
fof(d3_polynom5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k3_polynom5(A,B,C) <=> ! [E] : ( m1_subset_1(E,k4_ordinal1) => k3_funct_2(k4_ordinal1,u1_struct_0(A),D,E) = k6_algstr_0(A,C,k3_funct_2(k4_ordinal1,u1_struct_0(A),B,E)) ) ) ) ) ) ) )).
fof(d3_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( 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] : ( 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] : ( ( 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 => k4_polynom1(A,B,C,E) = k4_struct_0(B) ) ) ) ) ) ) )).
fof(d3_polynom8,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_int_1(C) => ( ( r1_xxreal_0(k5_numbers,C) => k3_polynom8(A,B,C) = k1_binop_1(k4_group_1(A),B,C) ) & ( ~ r1_xxreal_0(k5_numbers,C) => k3_polynom8(A,B,C) = k11_algstr_0(A,k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k4_group_1(A),B,k1_int_2(C))) ) ) ) ) ) )).
fof(d3_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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) & k3_polynom1(k15_pre_poly(A),C,D) != k3_polynom1(k15_pre_poly(A),C,E) ) ) ) ) ) ) ) )).
fof(d3_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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)) ) ) )).
fof(d3_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & A != 1 & ~ r1_xxreal_0(B,k5_numbers) & ~ ! [C] : ( v1_xreal_0(C) => ( C = k3_power(A,B) <=> k2_power(A,C) = B ) ) ) ) ) )).
fof(d3_pralg_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_pre_poly,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_pre_poly(A) <=> ! [B] : ( 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)) ) ) ) ) )).
fof(d3_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) )).
fof(d3_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_prelamb(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d3_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ( ( r1_xxreal_0(k5_numbers,B) => k3_prepower(A,B) = k1_newton(A,k1_int_2(B)) ) & ( ~ r1_xxreal_0(k5_numbers,B) => k3_prepower(A,B) = k5_xcmplx_0(k1_newton(A,k1_int_2(B))) ) ) ) ) )).
fof(d3_prgcor_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k1_numbers) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k1_numbers) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ( v7_ordinal1(k1_funct_1(B,k5_numbers)) => ( r1_xxreal_0(k1_afinsq_1(A),k1_funct_1(B,k5_numbers)) | ! [C] : ( v1_xreal_0(C) => ( C = k2_prgcor_2(A,B) <=> ? [D] : ( v1_relat_1(D) & v5_relat_1(D,k1_numbers) & v5_ordinal1(D) & v1_funct_1(D) & v1_finset_1(D) & ? [E] : ( v1_int_1(E) & k1_afinsq_1(D) = k1_afinsq_1(A) & k1_funct_1(D,k5_numbers) = k5_numbers & E = k1_funct_1(B,k5_numbers) & ( E != k5_numbers => ! [F] : ( v7_ordinal1(F) => ( ~ r1_xxreal_0(E,F) => k1_funct_1(D,k1_nat_1(F,1)) = k2_xcmplx_0(k1_funct_1(D,F),k3_xcmplx_0(k1_funct_1(A,k1_nat_1(F,1)),k1_funct_1(B,k1_nat_1(F,1)))) ) ) ) & C = k1_funct_1(D,E) ) ) ) ) ) ) ) ) )).
fof(d3_prob_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k3_prob_1(A,B) = k3_subset_1(A,k1_prob_1(A,k2_prob_1(A,B))) ) )).
fof(d3_prob_2,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_prob_2(C) <=> ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( D != E => r1_xboole_0(k1_prob_2(A,B,C,D),k1_prob_2(A,B,C,E)) ) ) ) ) ) ) )).
fof(d3_prob_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( C = k3_prob_3(A,B) <=> ( k1_prob_2(A,k9_setfam_1(A),C,k5_numbers) = k1_prob_2(A,k9_setfam_1(A),B,k5_numbers) & ! [D] : ( v7_ordinal1(D) => k1_prob_2(A,k9_setfam_1(A),C,k1_nat_1(D,1)) = k7_prob_1(A,k9_setfam_1(A),k1_prob_2(A,k9_setfam_1(A),B,k1_nat_1(D,1)),k1_prob_2(A,k9_setfam_1(A),k2_prob_3(A,B),D)) ) ) ) ) ) )).
fof(d3_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ( r1_prob_4(A,B,C) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( ( r2_hidden(E,B) & r1_tarski(D,E) & k1_funct_1(C,E) = k5_numbers ) => r2_hidden(D,B) ) ) ) ) ) ) )).
fof(d3_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d3_projred2,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( m1_subset_1(C,u1_incsp_1(A)) & ? [D] : ( m1_subset_1(D,u2_incsp_1(A)) & ? [E] : ( 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) ) ) ) ) ) ) )).
fof(d3_prvect_2,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_prvect_2(A) <=> ! [B] : ( 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) ) ) ) ) )).
fof(d3_prvect_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(d3_pscomp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d3_pua2mss1,axiom,( ! [A] : ! [B] : ( m2_pua2mss1(B,A) => ! [C] : ( r2_hidden(C,A) => ! [D] : ( D = k5_pua2mss1(A,B,C) <=> ( r2_hidden(D,k9_xtuple_0(B)) & r2_hidden(C,k1_funct_1(B,D)) ) ) ) ) )).
fof(d3_pythtrip,axiom,( ! [A] : ( v1_pythtrip(A) <=> ? [B] : ( v7_ordinal1(B) & A = k1_pepin(B) ) ) )).
fof(d3_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r1_pzfmisc1(A,B,C) <=> ! [D] : ( ( r2_hidden(D,A) & k1_funct_1(C,D) = k1_xboole_0 ) => k1_funct_1(B,D) = k1_xboole_0 ) ) ) ) )).
fof(d3_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => k2_qc_lang1(A) = k2_xboole_0(k2_zfmisc_1(k1_tarski(6),k4_ordinal1),k2_zfmisc_1(k2_tarski(4,5),k1_qc_lang1(A))) ) )).
fof(d3_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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))) ) ) ) )).
fof(d3_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => k3_qc_lang3(A,B) = k4_tarski(6,B) ) ) )).
fof(d3_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m4_trees_1(D,k9_xtuple_0(k2_qc_lang4(A,B))) => ( D = k3_qc_lang4(A,B,C) <=> ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(d3_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_qc_trans(B,A) & m1_qc_lang1(B) ) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => k1_qc_trans(A,B,C) = C ) ) ) )).
fof(d3_qmax_1,axiom,( ! [A] : ( l1_qmax_1(A) => k3_qmax_1(A) = u2_qmax_1(A) ) )).
fof(d3_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v5_quantal1(A) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_algstr_0(A,C,B) = B ) ) ) ) )).
fof(d3_quaterni,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : 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)) )).
fof(d3_quofield,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v6_struct_0(A) & v1_vectsp_2(A) & l6_algstr_0(A) ) => ! [B] : ( m2_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A)) => ! [C] : ( 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))) ) ) ) )).
fof(d3_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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 = k5_numbers => k4_radix_1(A,B,C,D) = k5_numbers ) ) ) ) ) ) )).
fof(d3_radix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k4_ordinal1) ) => k3_radix_2(A,B,C) = k2_wsierp_1(k2_radix_2(A,B,C)) ) ) ) )).
fof(d3_radix_3,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( 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) = k5_numbers ) ) ) ) ) )).
fof(d3_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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) = k5_numbers ) ) ) ) ) ) )).
fof(d3_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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) ) ) ) ) ) ) ) )).
fof(d3_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_random_1(C,A,B) => ! [D] : ( m2_prob_1(D,A,B) => ( r1_random_1(A,B,C,D) <=> r3_mesfunc6(A,B,k2_prob_4(A,B,D),C) ) ) ) ) ) )).
fof(d3_random_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => k3_random_2(A,B) = a_2_0_random_2(A,B) ) ) )).
fof(d3_ranknull,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( 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) ) ) )).
fof(d3_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( B = k1_rat_1(A) <=> ( B != k5_numbers & ? [C] : ( v1_int_1(C) & A = k7_xcmplx_0(C,B) ) & ! [C] : ( v1_int_1(C) => ! [D] : ( v7_ordinal1(D) => ( A = k7_xcmplx_0(C,D) => ( D = k5_numbers | r1_xxreal_0(B,D) ) ) ) ) ) ) ) ) )).
fof(d3_ratfunc1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_ratfunc1(A,B,C,D) <=> ( r1_polynom5(A,B,D) & r1_polynom5(A,C,D) ) ) ) ) ) ) )).
fof(d3_rcomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_rcomp_1(A) <=> ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( r1_tarski(k10_xtuple_0(B),A) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( m2_valued_0(C,k1_numbers,B) & v2_comseq_2(C) & r2_hidden(k1_seq_2(C),A) ) ) ) ) ) ) )).
fof(d3_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B))))) => ! [D] : ( 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] : ( m2_finseq_1(E,k1_numbers) => ( m2_rcomp_3(E,A,B,C,D) <=> ( k3_finseq_1(E) = k1_nat_1(k3_finseq_1(D),1) & k1_funct_1(E,1) = A & k1_funct_1(E,k3_finseq_1(E)) = B & ! [F] : ( 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(k3_seq_4(k7_partfun1(k9_setfam_1(k1_numbers),D,k1_nat_1(F,1))),k2_seq_4(k7_partfun1(k9_setfam_1(k1_numbers),D,F)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( B = k3_real_3(A) <=> ( k9_nat_1(k1_numbers,B,k5_numbers) = A & ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,B,k1_nat_1(C,1)) = k7_xcmplx_0(1,k3_int_1(k9_nat_1(k1_numbers,B,C))) ) ) ) ) ) )).
fof(d3_real_lat,axiom,( k3_real_lat = g3_lattices(k1_numbers,k2_real_lat,k1_real_lat) )).
fof(d3_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => k3_funct_2(k1_euclid(A),k1_numbers,B,C) = k12_euclid(C) ) ) ) ) )).
fof(d3_rearran1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ( v3_rearran1(B,A) <=> ? [C] : ( v1_finset_1(C) & C = k3_tarski(A) & k3_finseq_1(B) = k5_card_1(C) ) ) ) )).
fof(d3_recdef_2,axiom,( ! [A] : ( v2_xtuple_0(A) => ! [B] : ( B = k2_xtuple_0(A) <=> ! [C] : ! [D] : ! [E] : ( A = k3_xtuple_0(C,D,E) => B = E ) ) ) )).
fof(d3_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r1_tarski(A,B) <=> ! [C] : ! [D] : ( r2_hidden(k4_tarski(C,D),A) => r2_hidden(k4_tarski(C,D),B) ) ) ) )).
fof(d3_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r3_relat_2(A,B) <=> ! [C] : ! [D] : ( ( r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) ) => r2_hidden(k4_tarski(D,C),A) ) ) ) )).
fof(d3_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r1_rewrite1(A,B,C) <=> ? [D] : ( m1_rewrite1(D,A) & k1_funct_1(D,1) = B & k1_funct_1(D,k3_finseq_1(D)) = C ) ) ) )).
fof(d3_rewrite2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_rewrite2(B) ) => ! [C] : ( ( 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] : ( r2_hidden(D,k9_xtuple_0(B)) => k1_funct_1(C,D) = k1_ordinal4(k1_funct_1(B,D),A) ) ) ) ) ) ) )).
fof(d3_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( l1_rewrite3(C,B) => ! [D] : ! [E] : ! [F] : ! [G] : ( r2_rewrite3(A,B,C,D,E,F,G) <=> ? [H] : ( m1_subset_1(H,k8_afinsq_1(A)) & ? [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) ) ) ) ) ) ) )).
fof(d3_rfinseq,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => ( v8_valued_0(A) <=> ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( r2_hidden(B,k4_finseq_1(A)) & r2_hidden(k1_nat_1(B,1),k4_finseq_1(A)) ) => r1_xxreal_0(k1_funct_1(A,k1_nat_1(B,1)),k1_funct_1(A,B)) ) ) ) ) )).
fof(d3_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => k3_rfinseq2(A) = k1_funct_1(A,k1_rfinseq2(A)) ) )).
fof(d3_rfunct_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v7_valued_0(A) <=> ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( 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_funct_1(A,B),k1_funct_1(A,C)) ) ) ) ) ) ) )).
fof(d3_rfunct_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( r3_rfunct_4(A,B) <=> ( r1_tarski(B,k9_xtuple_0(A)) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(1,C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & r2_hidden(D,B) & r2_hidden(E,B) & r2_hidden(k2_xcmplx_0(k3_xcmplx_0(C,D),k3_xcmplx_0(k6_xcmplx_0(1,C),E)),B) & k1_funct_1(A,D) != k1_funct_1(A,E) & r1_xxreal_0(k4_xxreal_0(k1_funct_1(A,D),k1_funct_1(A,E)),k1_funct_1(A,k2_xcmplx_0(k3_xcmplx_0(C,D),k3_xcmplx_0(k6_xcmplx_0(1,C),E)))) ) ) ) ) ) ) ) )).
fof(d3_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v4_partfun3(A) <=> ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k5_numbers,k1_funct_1(A,B)) ) ) ) )).
fof(d3_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v1_rinfsup2(A) <=> v3_xxreal_2(k17_supinf_2(A)) ) ) )).
fof(d3_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_ring_1(B,A) <=> ! [C] : ( ( ~ 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)) ) ) ) ) ) )).
fof(d3_ringcat1,axiom,( ! [A] : ( l1_ringcat1(A) => k2_ringcat1(A) = u2_ringcat1(A) ) )).
fof(d3_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( v1_xreal_0(C) => ( C = k3_rlaffin1(A,B) <=> ? [D] : ( 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)) ) ) ) ) ) )).
fof(d3_rlaffin3,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ! [D] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d3_rlsub_1,axiom,( ! [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) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(d3_rlsub_2,axiom,( ! [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) ) => ! [B] : ( B = k3_rlsub_2(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( v1_rlvect_1(C) & m1_rlsub_1(C,A) ) ) ) ) )).
fof(d3_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_rltopsp1(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => v1_convex1(C,A) ) ) ) ) ) )).
fof(d3_rlvect_1,axiom,( ! [A] : ( l1_algstr_0(A) => ( v3_rlvect_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d3_rlvect_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( 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] : ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ~ r2_hidden(D,C) => k3_funct_2(u1_struct_0(A),k1_numbers,B,D) = k5_numbers ) ) ) ) ) ) )).
fof(d3_rlvect_3,axiom,( ! [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) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(d3_rlvect_5,axiom,( ! [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_rlvect_5(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( C = k2_rlvect_5(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( v1_rlvect_1(E) & m1_rlsub_1(E,A) & E = D & k1_rlvect_5(E) = B ) ) ) ) ) )).
fof(d3_rlvect_x,axiom,( ! [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) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => k3_rlvect_x(A,B) = a_2_1_rlvect_x(A,B) ) ) )).
fof(d3_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( 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)) ) ) ) ) )).
fof(d3_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( C = k3_rmod_3(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( v2_vectsp_2(E,A) & m1_rmod_2(E,A,B) & E = D ) ) ) ) ) )).
fof(d3_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_4(C,A,B) => k2_rmod_4(A,B,C) = a_3_0_rmod_4(A,B,C) ) ) ) )).
fof(d3_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_robbins1(A) ) => ! [B] : ( 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) ) ) )).
fof(d3_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_robbins1(A) ) => ( v3_robbins2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d3_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( v3_robbins3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_lattices(A,B,k2_lattices(A,B,C)) = B ) ) ) ) )).
fof(d3_robbins4,axiom,( k1_robbins4 = k1_yellow_1(k4_enumset1(k5_numbers,1,k6_subset_1(3,1),2,k6_subset_1(3,2),3)) )).
fof(d3_rpr_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_rpr_1(A,B,C) <=> k1_rpr_1(A,k9_subset_1(A,B,C)) = k3_xcmplx_0(k1_rpr_1(A,B),k1_rpr_1(A,C)) ) ) ) ) )).
fof(d3_rsspace,axiom,( ! [A] : ( ( 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 = k3_rsspace <=> ! [B] : ( m1_subset_1(B,k1_rsspace) => ! [C] : ( 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)) ) ) ) ) )).
fof(d3_rsspace3,axiom,( k3_rsspace3 = g1_normsp_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3),k2_rsspace3) )).
fof(d3_rsspace4,axiom,( k3_rsspace4 = g1_normsp_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4),k2_rsspace4) )).
fof(d3_rusub_1,axiom,( ! [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_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)) ) )).
fof(d3_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( B = k3_rusub_2(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( v1_bhsp_1(C) & m1_rusub_1(C,A) ) ) ) ) )).
fof(d3_rusub_4,axiom,( ! [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_bhsp_1(A) & v1_rusub_4(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( C = k2_rusub_4(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( v1_bhsp_1(E) & m1_rusub_1(E,A) & E = D & k1_rusub_4(E) = B ) ) ) ) ) )).
fof(d3_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( ( 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) ) ) ) ) )).
fof(d3_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => k3_rvsum_1(A) = k5_funcop_1(k11_binop_2,A,k6_partfun1(k1_numbers)) ) )).
fof(d3_rvsum_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => k5_rvsum_2(A) = k3_relat_1(A,k1_binop_2) ) )).
fof(d3_scm_comp,axiom,( ! [A] : ( m1_dtconstr(A,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [B] : ( 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(k5_numbers,k5_numbers),A,B) ) ) )).
fof(d3_scm_halt,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ( r1_tarski(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_3(k4_scmfsa_2(k5_numbers),1)),B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( r1_tarski(A,C) => ! [D] : ( v7_ordinal1(D) => k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,C,B,D),k4_scmfsa_2(k5_numbers)) = 1 ) ) ) ) ) ) ) )).
fof(d3_scm_inst,axiom,( ! [A] : ( m1_subset_1(A,k3_scm_inst) => ( ? [B] : ( m1_subset_1(B,k2_scm_inst) & ? [C] : ( m1_subset_1(C,k2_scm_inst) & ? [D] : ( m2_subset_1(D,k4_ordinal1,k7_card_1(9)) & A = k3_xtuple_0(D,k1_xboole_0,k2_finseq_4(k2_scm_inst,B,C)) ) ) ) => ! [B] : ( m1_subset_1(B,k2_scm_inst) => ( B = k4_scm_inst(A) <=> ? [C] : ( m2_finseq_1(C,k2_scm_inst) & C = k2_xtuple_0(A) & B = k7_partfun1(k2_scm_inst,C,1) ) ) ) ) ) )).
fof(d3_scmfsa6a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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))) ) ) )).
fof(d3_scmfsa6c,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( 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))))) ) ) )).
fof(d3_scmfsa7b,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ( r3_scmfsa7b(A,B) <=> ~ ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(d3_scmfsa8a,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( v7_ordinal1(D) => ( D = k2_scmfsa8a(A,B,C) <=> ( k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),D)) = k5_card_1(C) & ! [E] : ( v7_ordinal1(E) => ( ~ r2_hidden(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),E)),k2_afinsq_1(C)) => r1_xxreal_0(D,E) ) ) ) ) ) ) ) ) ) )).
fof(d3_scmfsa8b,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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)) ) ) ) )).
fof(d3_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ( r2_scmfsa9a(A,B,C,D) => ( ( ~ r1_scmfsa9a(A,B,C,D) & ~ v7_amistd_1(D,k7_card_1(3),k1_scmfsa_2) ) | ! [E] : ( v7_ordinal1(E) => ( E = k1_scmfsa9a(A,B,C,D) <=> ? [F] : ( v7_ordinal1(F) & E = F & k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(B,D,C,A),F),C) != k5_numbers & ! [G] : ( v7_ordinal1(G) => ( k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(B,D,C,A),G),C) != k5_numbers => r1_xxreal_0(F,G) ) ) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa_9(C,D)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa_9(C,D)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B)))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(B,D,C,A),F)) ) ) ) ) ) ) ) ) ) )).
fof(d3_scmfsa_1,axiom,( k5_scmfsa_1 = k7_afinsq_1(k4_ordinal1,k4_numbers,k3_finseq_2(k4_numbers)) )).
fof(d3_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) => ( m1_scmfsa_2(A) <=> r2_hidden(A,k3_scmfsa_1) ) ) )).
fof(d3_scmfsa_9,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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(k5_numbers)))),k16_funcop_1(k1_nat_1(k5_card_1(B),4),k11_scmfsa_2(k5_numbers))) ) ) )).
fof(d3_scmfsa_m,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ( B = k2_scmfsa_m(A) <=> ? [C] : ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) & B = k4_scmfsa_2(k4_seq_4(C)) & C = a_1_0_scmfsa_m(A) ) ) ) ) )).
fof(d3_scmisort,axiom,( k3_scmisort = k2_scmisort(k5_scmfsa_2(k5_numbers)) )).
fof(d3_scmp_gcd,axiom,( k3_scmp_gcd = k1_scmp_gcd(1) )).
fof(d3_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => k3_scmpds_2(A) = k3_xtuple_0(14,k1_xboole_0,k9_finseq_1(A)) ) )).
fof(d3_scmpds_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(d3_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( 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)) ) ) ) ) )).
fof(d3_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => ( ? [B] : ( v1_int_1(B) & ? [C] : ( m2_subset_1(C,k4_ordinal1,k7_card_1(15)) & A = k3_xtuple_0(C,k1_xboole_0,k9_finseq_1(B)) ) ) => ! [B] : ( v1_int_1(B) => ( B = k4_scmpds_i(A) <=> ? [C] : ( m2_finseq_1(C,k4_numbers) & C = k2_xtuple_0(A) & B = k7_partfun1(k4_numbers,C,1) ) ) ) ) ) )).
fof(d3_scmring1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k4_card_3(k3_relat_1(k3_ami_2,k1_scmring1(A)))) => ! [C] : ( v7_ordinal1(C) => k3_scmring1(A,B,C) = k1_funct_4(B,k16_funcop_1(k4_ordinal1,C)) ) ) ) )).
fof(d3_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(d3_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_scmringi(A)) => ( ? [C] : ( m1_subset_1(C,k2_scm_inst) & ? [D] : ( m1_subset_1(D,k2_scm_inst) & ? [E] : ( 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] : ( m1_subset_1(C,k2_scm_inst) => ( C = k3_scmringi(A,B) <=> ? [D] : ( m2_finseq_1(D,k2_scm_inst) & D = k2_xtuple_0(B) & C = k7_partfun1(k2_scm_inst,D,2) ) ) ) ) ) ) )).
fof(d3_scmyciel,axiom,( ! [A] : ( v2_scmyciel(A) <=> v1_xboole_0(k1_scmyciel(A)) ) )).
fof(d3_scpinvar,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k1_nat_1(k5_card_1(C),2))),C),k3_scmpds_2(k4_xcmplx_0(k1_nat_1(k5_card_1(C),2)))) ) ) ) )).
fof(d3_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d3_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_seq_2(A) <=> ? [B] : ( v1_xreal_0(B) & ! [C] : ( v7_ordinal1(C) => ~ r1_xxreal_0(B,k1_funct_1(A,C)) ) ) ) ) )).
fof(d3_seq_4,axiom,( k4_binop_2 = k7_finseqop(k2_numbers,k3_binop_2,k6_partfun1(k2_numbers),k1_binop_2) )).
fof(d3_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( C = k4_seqfunc(A,B) <=> ! [D] : ( 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))) ) ) ) ) ) )).
fof(d3_seqm_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v3_valued_0(A) ) => ( v7_valued_0(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(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)) ) ) ) ) ) )).
fof(d3_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k4_series_1(A) = k1_seq_2(k3_series_1(A)) ) )).
fof(d3_setfam_1,axiom,( ! [A] : ! [B] : ( r2_setfam_1(A,B) <=> ! [C] : ~ ( r2_hidden(C,B) & ! [D] : ~ ( r2_hidden(D,A) & r1_tarski(D,C) ) ) ) )).
fof(d3_setlim_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k3_setlim_1(A) <=> ( k9_xtuple_0(B) = k4_ordinal1 & ! [C] : ( v7_ordinal1(C) => k1_funct_1(B,C) = k3_tarski(a_2_1_setlim_1(A,C)) ) ) ) ) ) )).
fof(d3_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( D = k3_setlim_2(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k9_nat_1(k9_setfam_1(A),D,E) = k7_subset_1(A,k9_nat_1(k9_setfam_1(A),B,E),k9_nat_1(k9_setfam_1(A),C,E)) ) ) ) ) ) )).
fof(d3_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,k5_finsub_1(A)) => ! [E] : ( ( 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] : ( m1_subset_1(F,B) => ( F = k7_setwiseo(A,B,C,D,E) <=> ? [G] : ( 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] : ( m1_subset_1(H,B) => ( r3_binop_1(B,H,C) => k1_funct_1(G,k1_xboole_0) = H ) ) & ! [H] : ( m1_subset_1(H,A) => k1_funct_1(G,k1_tarski(H)) = k3_funct_2(A,B,E,H) ) & ! [H] : ( m1_subset_1(H,k5_finsub_1(A)) => ( r1_tarski(H,D) => ( H = k1_xboole_0 | ! [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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_sf_mastr,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( 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] : ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) & ? [D] : ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) & ? [E] : ( 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] : ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) & ? [D] : ( 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 ) ) ) ) ) )).
fof(d3_sfmastr2,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( 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(k7_card_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(k5_numbers))),k9_scmfsa_m(1,k4_subset_1(k2_scmfsa_2,k4_scmfsa_m(D),k2_sf_mastr(C))),A) ) ) ) ) )).
fof(d3_sfmastr3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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(k5_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(k5_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(k5_numbers))))) ) ) ) ) )).
fof(d3_sgraph1,axiom,( ! [A] : k3_sgraph1(A) = a_1_1_sgraph1(A) )).
fof(d3_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( v2_sheffer1(A) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_lattices(A,B,C) = C & k1_lattices(A,C,B) = C ) ) ) ) ) )).
fof(d3_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_simplex0(B,A) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(C,A) & r2_hidden(B,C) ) ) ) ) )).
fof(d3_simplex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_simplex0(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k3_simplex1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( 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))) ) ) ) ) ) ) )).
fof(d3_simplex2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( l1_pre_topc(B) => ( v1_simplex2(B,A) => ! [C] : ( v1_xreal_0(C) => ( ( ~ r1_xboole_0(u1_pre_topc(B),k9_setfam_1(k2_struct_0(A))) => ( C = k1_simplex2(A,B) <=> ( ! [D] : ( 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] : ( v1_xreal_0(D) => ( ! [E] : ( 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 = k5_numbers ) ) ) ) ) ) ) )).
fof(d3_sin_cos,axiom,( ! [A] : ( v7_ordinal1(A) => k2_newton(A) = k9_nat_1(k1_numbers,k2_sin_cos,A) ) )).
fof(d3_sin_cos2,axiom,( ! [A] : ( ( 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 = k3_sin_cos2 <=> ! [B] : ( v1_xreal_0(B) => k1_funct_1(A,B) = k7_xcmplx_0(k2_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_funct_1(k22_sin_cos,k4_xcmplx_0(B))),2) ) ) ) )).
fof(d3_sin_cos3,axiom,( ! [A] : ( ( 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] : ( v1_xcmplx_0(B) => k1_funct_1(A,B) = k7_xcmplx_0(k6_xcmplx_0(k15_sin_cos(B),k15_sin_cos(k4_xcmplx_0(B))),2) ) ) ) )).
fof(d3_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => k3_sin_cos4(A) = k7_xcmplx_0(1,k17_sin_cos(A)) ) )).
fof(d3_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => k3_sin_cos5(A) = k7_xcmplx_0(1,k2_sin_cos2(A)) ) )).
fof(d3_sin_cos6,axiom,( k3_sin_cos6 = k2_partfun2(k1_numbers,k1_numbers,k5_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k5_numbers,k28_sin_cos))) )).
fof(d3_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => k3_sin_cos7(A) = k4_xcmplx_0(k3_power(k4_power,k2_xcmplx_0(A,k3_square_1(k6_xcmplx_0(k1_square_1(A),1))))) ) )).
fof(d3_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => k3_sin_cos9(A) = k1_funct_1(k1_sin_cos9,A) ) )).
fof(d3_sincos10,axiom,( k3_sincos10 = k2_partfun2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers))) )).
fof(d3_sppol_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v2_sppol_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => k17_euclid(B) = k17_euclid(C) ) ) ) ) ) )).
fof(d3_sppol_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)))) ) ) ) ) )).
fof(d3_sprect_1,axiom,( ! [A] : ( 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ? [C] : ( 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) ) ) ) ) ) )).
fof(d3_sprect_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) ) )).
fof(d3_stacks_1,axiom,( ! [A] : ( l1_stacks_1(A) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ( r1_stacks_1(A,B) <=> r2_hidden(B,u1_stacks_1(A)) ) ) ) )).
fof(d3_stirl2_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k4_ordinal1)) => ! [C] : ( ( 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] : ( v7_ordinal1(D) => ! [E] : ( 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(k3_nat_1(k8_relset_1(A,B,C,k1_seq_4(E))),k3_nat_1(k8_relset_1(A,B,C,k1_seq_4(D)))) ) ) ) ) ) ) ) )).
fof(d3_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => k2_struct_0(A) = u1_struct_0(A) ) )).
fof(d3_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k16_substut1(A),k38_substut1(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(d3_subset_1,axiom,( ! [A] : k2_subset_1(A) = A )).
fof(d3_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( 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) ) ) )).
fof(d3_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k2_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k1_substut1(A)) => ! [D] : ( m2_finseq_1(D,k2_qc_lang1(A)) => ( D = k3_substut1(A,B,C) <=> ( k3_finseq_1(D) = k3_finseq_1(B) & ! [E] : ( v7_ordinal1(E) => ( ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(d3_supinf_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_setfam_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k6_numbers))) ) => ! [B] : ( v2_membered(B) => ( B = k5_supinf_1(A) <=> ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(C,B) <=> ? [D] : ( ~ v1_xboole_0(D) & v2_membered(D) & r2_hidden(D,A) & C = k1_xxreal_2(D) ) ) ) ) ) ) )).
fof(d3_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( ? [H] : ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_t_0topsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(k4_tarski(C,D),B) <=> ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(E,A) => ( r2_hidden(C,E) <=> r2_hidden(D,E) ) ) ) ) ) ) ) ) ) )).
fof(d3_tarski,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) ) )).
fof(d3_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( D = k1_taxonom1(A,B,C) <=> ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ( r2_hidden(k4_tarski(E,F),D) <=> r1_xxreal_0(k1_binop_1(B,E,F),C) ) ) ) ) ) ) ) ) )).
fof(d3_taxonom2,axiom,( ! [A] : ( v3_taxonom2(A) <=> ! [B] : ! [C] : ~ ( r2_hidden(B,A) & r2_hidden(C,A) & ~ r1_tarski(B,C) & ~ r1_tarski(C,B) & ~ r1_xboole_0(B,C) ) ) )).
fof(d3_taylor_1,axiom,( k3_taylor_1 = k2_taylor_1(k4_power) )).
fof(d3_tbsp_1,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v2_tbsp_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k1_tbsp_1(A,B) <=> ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(E,F) & r1_xxreal_0(D,k3_metric_1(A,k9_nat_1(u1_struct_0(A),B,F),C)) ) ) ) ) ) ) ) ) ) )).
fof(d3_tdgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => k2_tdgroup(A) = g1_analoaf(u1_struct_0(A),k1_tdgroup(A)) ) )).
fof(d3_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k1_tdlat_1(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d3_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v2_tdlat_2(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => v5_tops_1(C,A) ) ) ) ) ) )).
fof(d3_tdlat_3,axiom,( ! [A] : ( l1_pre_topc(A) => ( v3_tdlat_3(A) <=> ! [B] : ( 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)) ) ) ) ) )).
fof(d3_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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 ) ) ) ) ) ) )).
fof(d3_tex_1,axiom,( ! [A] : k2_tex_1(A) = g1_pre_topc(A,k1_tex_1(A)) )).
fof(d3_tex_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_tex_2(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r1_tarski(C,B) & ! [D] : ( 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 ) ) ) ) ) ) ) )).
fof(d3_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v3_tex_3(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = u1_struct_0(B) => v2_tops_1(C,A) ) ) ) ) ) )).
fof(d3_tex_4,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tex_4(B,A) <=> ! [C] : ( 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) ) ) ) ) ) )).
fof(d3_tmap_1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) )).
fof(d3_toler_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( C = k3_toler_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> m1_toler_1(D,A,B) ) ) ) )).
fof(d3_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_borsuk_6(A,B,C) => ! [D] : ( 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] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ( r2_hidden(k4_tarski(E,F),D) <=> r3_borsuk_2(A,B,C,E,F) ) ) ) ) ) ) ) ) ) )).
fof(d3_topalg_2,axiom,( ! [A] : ( ( v3_topmetr(A) & l1_pre_topc(A) ) => ( v2_topalg_2(A) <=> v6_xxreal_2(k2_struct_0(A)) ) ) )).
fof(d3_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_borsuk_2(C,A,B,B) => ( v3_topalg_6(C,A,B) <=> ? [D] : ( v3_funct_1(D) & m1_borsuk_2(D,A,B,B) & r3_borsuk_2(A,B,B,C,D) ) ) ) ) ) )).
fof(d3_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v2_topdim_1(B,A) <=> ? [C] : ( v7_ordinal1(C) & r1_tarski(B,k13_prob_1(u1_struct_0(A),k4_ordinal1,k9_setfam_1(u1_struct_0(A)),k1_topdim_1(A),C)) ) ) ) ) )).
fof(d3_topgen_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k2_topgen_1(A,B) <=> ! [D] : ( r2_hidden(D,u1_struct_0(A)) => ( r2_hidden(D,C) <=> r1_topgen_1(A,B,D) ) ) ) ) ) ) )).
fof(d3_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( 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)))) ) ) ) ) ) )).
fof(d3_topgen_3,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r1_topgen_3(A,B) <=> ( r2_hidden(B,A) & ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(B,C) & r1_xboole_0(k2_rcomp_1(C,B),A) ) ) ) ) )).
fof(d3_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v2_topgen_4(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(C,A) => r2_hidden(C,B) ) ) ) ) ) )).
fof(d3_topgen_5,axiom,( ! [A] : ( ( ~ 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] : ( m1_topgen_2(B,A) & ! [C] : ( v1_xreal_0(C) => k1_funct_1(B,k19_euclid(C,k5_numbers)) = a_1_0_topgen_5(C) ) & ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ~ r1_xxreal_0(D,k5_numbers) => k1_funct_1(B,k19_euclid(C,D)) = a_2_0_topgen_5(C,D) ) ) ) ) ) ) ) )).
fof(d3_topmetr,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => ! [C] : ( ( ~ v2_struct_0(C) & v1_metric_1(C) & m1_topmetr(C,k7_metric_1) ) => ( C = k2_topmetr(A,B) <=> ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k7_metric_1))) ) => ( D = k1_rcomp_1(A,B) => C = k1_topmetr(k7_metric_1,D) ) ) ) ) ) ) ) )).
fof(d3_topreal1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(d3_topreal4,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) ) )).
fof(d3_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( v1_xreal_0(C) => k3_topreal9(A,B,C) = a_3_2_topreal9(A,B,C) ) ) ) )).
fof(d3_toprealb,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => k5_toprealb(A) = A ) )).
fof(d3_toprealc,axiom,( ! [A] : ( v1_valued_2(A) => ! [B] : ( v1_valued_2(B) => ( B = k2_toprealc(A) <=> ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_valued_0(C) ) => ( r2_hidden(k30_valued_1(C),B) <=> r2_hidden(C,A) ) ) ) ) ) )).
fof(d3_toprns_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(B))))) ) => k2_toprns_1(A,B,C) = k4_vfunct_1(k4_ordinal1,k15_euclid(B),C,A) ) ) ) )).
fof(d3_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) )).
fof(d3_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [D] : ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k1_pre_topc(A,B)))) => ( r2_hidden(E,D) <=> ? [F] : ( 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 ) ) ) ) ) ) ) ) )).
fof(d3_tops_3,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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 ) ) ) )).
fof(d3_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d3_treal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_topmetr(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_topmetr(A,B))) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k4_topmetr(A,B))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k4_topmetr(A,B))))) ) => ( E = k3_treal_1(A,B,C,D) <=> ! [F] : ( m1_subset_1(F,u1_struct_0(k4_topmetr(k5_numbers,1))) => k3_funct_2(u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k4_topmetr(A,B)),E,F) = k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(1,F),C),k3_xcmplx_0(F,D)) ) ) ) ) ) ) ) ) )).
fof(d3_trees_1,axiom,( ! [A] : ( v1_trees_1(A) <=> ( r1_tarski(A,k3_finseq_2(k4_ordinal1)) & ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ( r2_hidden(B,A) => r1_tarski(k1_trees_1(B),A) ) ) & ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(k7_finseq_1(B,k9_finseq_1(C)),A) & r1_xxreal_0(D,C) ) => r2_hidden(k7_finseq_1(B,k9_finseq_1(D)),A) ) ) ) ) ) ) )).
fof(d3_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( m1_trees_2(B,A) <=> ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r3_xboole_0(C,D) ) ) ) ) ) ) )).
fof(d3_trees_3,axiom,( ! [A] : ( v1_trees_3(A) <=> ! [B] : ( r2_hidden(B,A) => ( ~ v1_xboole_0(B) & v1_trees_1(B) ) ) ) )).
fof(d3_trees_4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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] : ( v7_ordinal1(D) => ( ~ r1_xxreal_0(k3_finseq_1(B),D) => k1_funct_1(C,k14_trees_3(D)) = k1_funct_1(B,k1_nat_1(D,1)) ) ) ) ) ) ) )).
fof(d3_tsep_1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => ( r1_tsep_1(A,B) <=> r1_xboole_0(u1_struct_0(A),u1_struct_0(B)) ) ) ) )).
fof(d3_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( v6_pre_topc(A) <=> ( v2_struct_0(A) | ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v3_pre_topc(D,A) & ~ r2_hidden(B,D) & r2_hidden(C,D) ) ) ) ) ) ) ) ) )).
fof(d3_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),u1_turing_1(A),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1))) => k6_turing_1(A,B) = k3_mcart_1(u2_turing_1(A),u1_turing_1(A),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),B) ) ) )).
fof(d3_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k1_funct_1(A,k10_finseq_1(B,C)) = k10_margrel1(k9_margrel1(B),k9_margrel1(C)) ) ) ) ) )).
fof(d3_unialg_1,axiom,( ! [A] : ( l1_unialg_1(A) => ( v4_unialg_1(A) <=> ( u1_unialg_1(A) != k1_xboole_0 & v2_relat_1(u1_unialg_1(A)) ) ) ) )).
fof(d3_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m5_margrel1(C,u1_struct_0(A),k1_unialg_2(A)) => ( r2_unialg_2(A,B,C) <=> ! [D] : ( m2_finseq_1(D,B) => ( k3_finseq_1(D) = k19_margrel1(C) => r2_hidden(k1_funct_1(C,D),B) ) ) ) ) ) ) )).
fof(d3_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ 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)) ) ) ) ) )).
fof(d3_uproots,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,k4_ordinal1) => ( C = k3_uproots(A,B) <=> ? [D] : ( m2_finseq_1(D,k4_ordinal1) & C = k2_wsierp_1(D) & D = k3_relat_1(k19_finseq_1(k22_pre_poly(A,B)),B) ) ) ) ) )).
fof(d3_urysohn1,axiom,( k3_urysohn1 = k4_subset_1(k1_numbers,k4_subset_1(k1_numbers,k10_prob_1(k5_numbers),k2_urysohn1),k3_limfunc1(1)) )).
fof(d3_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v5_relat_1(D,k3_qc_lang1(A)) & v3_card_1(D,C) & m2_finseq_1(D,k2_qc_lang1(A)) ) => ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [F] : ( m2_finseq_1(F,B) => ( F = k4_valuat_1(A,B,C,D,E) <=> ( k3_finseq_1(F) = C & ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_valued_0,axiom,( ! [A] : ( v1_relat_1(A) => ( v3_valued_0(A) <=> r1_tarski(k10_xtuple_0(A),k1_numbers) ) ) )).
fof(d3_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( v1_xcmplx_0(B) => k13_valued_1(A,B) = k7_valued_1(A,k4_xcmplx_0(B)) ) ) )).
fof(d3_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( ( 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] : ( m2_subset_1(E,k1_zfmisc_1(u1_struct_0(B)),k2_vectsp10(A,B,C)) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(u1_struct_0(B)),k2_vectsp10(A,B,C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_vectsp11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( v1_vectsp11(C,A,B) & m1_vectsp11(D,A,B,C) ) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d3_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ( v2_vectsp_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d3_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_vectsp_2(A,B,C) = k6_algstr_0(A,B,k11_algstr_0(A,C)) ) ) ) )).
fof(d3_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(d3_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( C = k3_vectsp_5(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( v7_vectsp_1(E,A) & m1_vectsp_4(E,A,B) & E = D ) ) ) ) ) )).
fof(d3_vectsp_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => ( C = k2_vectsp_6(A,B) <=> k1_vectsp_6(A,B,C) = k1_xboole_0 ) ) ) ) )).
fof(d3_vectsp_7,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(d3_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_rlvect_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ( ( 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] : ( 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_funct_1(C,F)) ) ) ) ) ) ) ) ) ) )).
fof(d3_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( r1_vfunct_2(A,B,C,D) <=> ? [E] : ( v1_xreal_0(E) & ! [F] : ( m1_subset_1(F,A) => ( r2_hidden(F,k9_subset_1(A,D,k1_relset_1(A,C))) => r1_xxreal_0(k2_normsp_0(B,k7_partfun1(u1_struct_0(B),C,F)),E) ) ) ) ) ) ) ) )).
fof(d3_waybel10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( ( 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) ) ) ) ) ) ) )).
fof(d3_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_waybel11(B,A) <=> ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r2_hidden(E,C) & r1_orders_2(A,D,E) ) => r2_hidden(E,B) ) ) ) ) ) ) ) ) ) )).
fof(d3_waybel12,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(d3_waybel16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(d3_waybel17,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ v2_struct_0(D) & v6_waybel_0(D,A) & l1_waybel_0(D,A) ) => ( D = k3_waybel17(A,B,C) <=> ( u1_struct_0(D) = k4_ordinal1 & r1_funct_2(u1_struct_0(D),u1_struct_0(A),k4_ordinal1,u1_struct_0(A),u1_waybel_0(A,D),k1_waybel17(u1_struct_0(A),B,C)) & ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ! [H] : ( m1_subset_1(H,k4_ordinal1) => ( ( E = G & F = H ) => ( r1_orders_2(D,E,F) <=> r1_xxreal_0(G,H) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_waybel18,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(d3_waybel19,axiom,( ! [A] : ( ( ~ 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)))) ) ) ) )).
fof(d3_waybel20,axiom,( ! [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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) ) => ( v1_waybel20(B,A) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d3_waybel21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_waybel_0(C,A) ) => ( m2_yellow_6(C,A,B) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ? [F] : ( m1_subset_1(F,u1_struct_0(C)) & ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_waybel22,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(k1_yellow_1(k8_waybel_0(k2_yellow_1(A)))),u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_yellow_1(k8_waybel_0(k2_yellow_1(A)))),u1_struct_0(B)))) ) => ( D = k2_waybel22(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(k1_yellow_1(k8_waybel_0(k2_yellow_1(A))))) => k3_funct_2(u1_struct_0(k1_yellow_1(k8_waybel_0(k2_yellow_1(A)))),u1_struct_0(B),D,E) = k1_yellow_0(B,a_4_0_waybel22(A,B,C,E)) ) ) ) ) ) )).
fof(d3_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_waybel23(B,A) <=> v7_yellow_0(k5_yellow_0(A,B),A) ) ) ) )).
fof(d3_waybel24,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_9(B) ) => ! [C] : ( ( v1_orders_2(C) & l1_orders_2(C) ) => ( C = k3_waybel24(A,B) <=> ( v4_yellow_0(C,k5_yellow_1(u1_struct_0(A),B)) & m1_yellow_0(C,k5_yellow_1(u1_struct_0(A),B)) & ! [D] : ( r2_hidden(D,u1_struct_0(C)) <=> ? [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d3_waybel25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v4_orders_2(D) & v7_waybel_0(D) & l1_waybel_0(D,C) ) => ! [E] : ( m1_subset_1(E,A) => ( r1_tarski(u1_struct_0(C),u1_struct_0(k5_yellow_1(A,B))) => ! [F] : ( ( ~ 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(k9_funct_6(u1_waybel_0(C,D)),E) ) ) ) ) ) ) ) ) ) )).
fof(d3_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(d3_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m4_yellow_6(B,A) => ( B = k3_waybel28(A) <=> ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(k4_tarski(C,D),B) <=> ! [E] : ( m2_yellow_6(E,A,C) => D = k1_waybel11(A,E) ) ) ) ) ) ) ) ) )).
fof(d3_waybel29,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k1_yellow_1(u1_pre_topc(k2_borsuk_1(A,B)))),u1_struct_0(k3_waybel24(A,k1_waybel29(k1_yellow_1(u1_pre_topc(B)))))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_yellow_1(u1_pre_topc(k2_borsuk_1(A,B)))),u1_struct_0(k3_waybel24(A,k1_waybel29(k1_yellow_1(u1_pre_topc(B)))))))) ) => ( C = k3_waybel29(A,B) <=> ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(d3_waybel30,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_waybel_9(A) ) => ( v2_waybel30(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_yellow13(C,A,B) & ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(d3_waybel32,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( 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] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(d3_waybel34,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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 ) ) ) )).
fof(d3_waybel35,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( m1_waybel35(C,A,B) <=> ! [D] : ! [E] : ~ ( r2_hidden(D,C) & r2_hidden(E,C) & ~ r2_hidden(k4_tarski(D,E),B) & D != E & ~ r2_hidden(k4_tarski(E,D),B) ) ) ) ) ) )).
fof(d3_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v3_waybel_0(B,A) <=> ! [C] : ( ( 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)) ) ) ) ) ) ) )).
fof(d3_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v2_waybel_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d3_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ v2_struct_0(C) & l1_waybel_0(C,A) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(D)) => ? [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d3_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_waybel_3(A,B) = a_2_0_waybel_3(A,B) ) ) )).
fof(d3_waybel_4,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ( v1_waybel_4(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(k4_tarski(C,D),B) => r1_orders_2(A,C,D) ) ) ) ) ) ) )).
fof(d3_waybel_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v1_waybel_5(A) <=> ( v3_lattice3(A) & ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) ) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(d3_waybel_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v3_waybel_6(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( B = k10_lattice3(A,C,D) & C != B & D != B ) ) ) ) ) ) )).
fof(d3_waybel_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(d3_waybel_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ( v1_waybel_8(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => B = k1_yellow_0(A,k2_waybel_8(A,B)) ) ) ) )).
fof(d3_waybel_9,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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))) ) ) ) )).
fof(d3_weddwitt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => k3_weddwitt(A) = a_1_0_weddwitt(A) ) )).
fof(d3_weierstr,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => k3_weierstr(A) = k3_seq_4(k1_weierstr(A)) ) )).
fof(d3_wellfnd1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_wellfnd1(B,A) <=> r1_wellord1(u1_orders_2(A),B) ) ) ) )).
fof(d3_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r1_wellord1(A,B) <=> ! [C] : ~ ( r1_tarski(C,B) & C != k1_xboole_0 & ! [D] : ~ ( r2_hidden(D,C) & r1_xboole_0(k1_wellord1(A,D),C) ) ) ) ) )).
fof(d3_xboole_0,axiom,( ! [A] : ! [B] : ! [C] : ( C = k2_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) | r2_hidden(D,B) ) ) ) )).
fof(d3_xboolean,axiom,( ! [A] : ( v1_xboolean(A) <=> ( A = k1_xboolean | A = k2_xboolean ) ) )).
fof(d3_xtuple_0,axiom,( ! [A] : ( v1_xtuple_0(A) => ! [B] : ( B = k2_xtuple_0(A) <=> ! [C] : ! [D] : ( A = k4_tarski(C,D) => B = D ) ) ) )).
fof(d3_xxreal_0,axiom,( k2_xxreal_0 = k4_tarski(k5_numbers,k1_numbers) )).
fof(d3_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k3_xxreal_1(A,B) = a_2_2_xxreal_1(A,B) ) ) )).
fof(d3_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => ( B = k1_xxreal_2(A) <=> ( m1_xxreal_2(B,A) & ! [C] : ( m1_xxreal_2(C,A) => r1_xxreal_0(B,C) ) ) ) ) ) )).
fof(d3_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( ( v1_xreal_0(A) => ( B = k2_xxreal_3(A) <=> ? [C] : ( 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 ) ) ) ) ) )).
fof(d3_yellow11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v1_yellow11(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d3_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_yellow13(C,A,B) => ( v1_yellow13(C,A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(D,C) <=> r2_hidden(B,k1_tops_1(A,D)) ) ) ) ) ) ) )).
fof(d3_yellow15,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(d3_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(d3_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d3_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => k2_yellow19(A,B) = a_2_1_yellow19(A,B) ) ) )).
fof(d3_yellow20,axiom,( ! [A] : ( l2_altcat_1(A) => ! [B] : ( l2_altcat_1(B) => ( r1_yellow20(A,B) => ! [C] : ( ( 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)) ) ) ) ) ) ) )).
fof(d3_yellow21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ( v1_yellow21(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( l1_struct_0(C) & B = C & k3_yellow18(A,B) = u1_struct_0(C) ) ) ) ) )).
fof(d3_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v5_orders_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( r1_orders_2(A,B,C) & r1_orders_2(A,C,B) ) => B = C ) ) ) ) ) )).
fof(d3_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k1_yellow_1(k7_waybel_0(A))),u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_yellow_1(k7_waybel_0(A))),u1_struct_0(A)))) ) => ( B = k2_yellow_2(A) <=> ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(d3_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(d3_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_yellow_5(A,B,C) <=> k11_lattice3(A,B,C) != k3_yellow_0(A) ) ) ) ) )).
fof(d3_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v7_waybel_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r1_orders_2(A,B,D) & r1_orders_2(A,C,D) ) ) ) ) ) )).
fof(d3_yellow_8,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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 ) ) ) ) ) ) ) )).
fof(d3_yellow_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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))) ) ) )).
fof(d3_zf_fund1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_zf_lang)) => k4_zf_fund1(A) = k7_relat_1(k2_funct_1(k2_zf_fund1),A) ) )).
fof(d3_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => k4_zf_lang(A,B) = k8_finseq_1(k4_ordinal1,k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,k5_numbers),k3_zf_lang(A)),k3_zf_lang(B)) ) ) )).
fof(d3_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( D = k5_zf_lang1(A,B,C) <=> ( k9_xtuple_0(D) = k4_finseq_1(A) & ! [E] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d3_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : k3_zfmisc_1(A,B,C) = k2_zfmisc_1(k2_zfmisc_1(A,B),C) )).
fof(d3_zfmodel1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ( r1_zfmodel1(A,B) <=> ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & 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(k5_numbers),k8_zf_lang(k2_zf_lang(4),k12_zf_lang(C,k4_zf_lang(k2_zf_lang(4),k2_zf_lang(k5_numbers))))))) & A = k2_zfmodel1(C,B) ) ) ) ) )).
fof(d3_zfrefle1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ( r3_zfrefle1(A,B) <=> ( r1_tarski(A,B) & ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( 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) ) ) ) ) ) ) ) )).
fof(d3_zmodul01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_zmodul01(A) ) => ( v3_zmodul01(A) <=> ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d3_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( v1_int_1(B) => k3_zmodul02(A,B) = k2_partfun1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A),u1_algstr_0(A),k2_zfmisc_1(k1_zmodul02(A,B),k1_zmodul02(A,B))) ) ) )).
fof(d40_abcmiz_1,axiom,( ! [A] : ( ( 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) ) )).
fof(d40_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l6_aofa_a00(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v19_aofa_a00(B,A) <=> B = 1 ) ) ) )).
fof(d40_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) ) )).
fof(d40_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ( C = k38_fomodel1(A,B) <=> ( v14_fomodel1(B,C,A) & ! [D] : ( v7_ordinal1(D) => ( v14_fomodel1(B,D,A) => r1_xxreal_0(C,D) ) ) ) ) ) ) ) )).
fof(d40_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k40_fomodel2(A) = a_1_2_fomodel2(A) ) )).
fof(d40_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(k1_fomodel4(A)),k1_fomodel4(A)))) => ( B = k16_fomodel4(A) <=> ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d40_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ( r2_functor0(A,B) <=> ? [C] : ( m2_functor0(C,A,B) & v21_functor0(C,A,B) & v16_functor0(C,A,B) ) ) ) ) )).
fof(d40_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [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)) )).
fof(d40_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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)) ) ) )).
fof(d40_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k30_modelc_1(A) = k9_funct_2(A,k6_margrel1) ) )).
fof(d40_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => k26_modelc_2(A,B) = B ) ) )).
fof(d40_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & v5_modelc_3(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_3(B,A) & l1_modelc_3(B,A) ) => k27_modelc_3(A,B) = a_2_0_modelc_3(A,B) ) ) )).
fof(d40_monoid_0,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(d40_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ( ( v12_pcs_0(B) & l2_pcs_0(B) ) => ( B = k21_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)) ) ) ) ) )).
fof(d40_twoscomp,axiom,( ! [A] : ! [B] : k41_twoscomp(A,B) = k3_circcomb(k34_twoscomp(A,B),k37_twoscomp(A,B),k35_twoscomp(A,B),k38_twoscomp(A,B)) )).
fof(d40_valued_2,axiom,( ! [A] : ( v1_valued_2(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) ) => ! [C] : ( v1_xcmplx_0(C) => k47_valued_2(A,B,C) = k41_valued_2(A,B,k5_xcmplx_0(C)) ) ) ) )).
fof(d40_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ( v25_waybel_0(A) <=> ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r1_lattice3(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_lattice3(A,B,D) => r1_orders_2(A,D,C) ) ) ) ) ) ) )).
fof(d40_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r2_zf_lang(A,B) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & ? [D] : ( 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] : ( m1_subset_1(E,k4_ordinal1) => ~ ( r1_xxreal_0(1,E) & ~ r1_xxreal_0(C,E) & ! [F] : ( ( v1_zf_lang(F) & m2_finseq_1(F,k4_ordinal1) ) => ! [G] : ( ( v1_zf_lang(G) & m2_finseq_1(G,k4_ordinal1) ) => ~ ( k1_funct_1(D,E) = F & k1_funct_1(D,k1_nat_1(E,1)) = G & r1_zf_lang(F,G) ) ) ) ) ) ) ) ) ) ) )).
fof(d41_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_abcmiz_1(B,A,k12_abcmiz_1(A)) => ( v9_abcmiz_1(B,A) <=> ! [C] : ( m1_abcmiz_1(C,A,k13_abcmiz_1(A)) => ! [D] : ( m1_abcmiz_1(D,A,k12_abcmiz_1(A)) => B != k31_abcmiz_1(A,k33_abcmiz_1(A),C,D) ) ) ) ) ) )).
fof(d41_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v19_aofa_a00(C,A) & m1_subset_1(C,u1_struct_0(A)) ) => k27_aofa_a00(A,B,C) = k1_funct_1(k5_msualg_1(A,k10_subset_1(k1_funct_1(u7_aofa_a00(A),4),u4_struct_0(A)),B),k1_xboole_0) ) ) ) )).
fof(d41_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(d41_fomodel1,axiom,( ! [A] : ( l1_fomodel1(A) => ! [B] : ( 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) ) ) ) ) )).
fof(d41_fomodel2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m2_subset_1(C,k9_funct_2(k37_fomodel1(B),k3_rfunct_3(k3_finseq_2(A),k2_xboole_0(A,k6_margrel1))),k15_fomodel2(B,A)) => ! [D] : ( v10_fomodel2(D,A,B,C) <=> ! [E] : ( ( 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) => k25_fomodel2(B,A,C,E) = 1 ) ) ) ) ) ) )).
fof(d41_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(k1_fomodel4(A)),k1_fomodel4(A)))) => ( B = k17_fomodel4(A) <=> ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d41_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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))) )).
fof(d41_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( ( ( 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 ) ) ) ) )).
fof(d41_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(d41_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k25_modelc_2(A)) => k27_modelc_2(A,B) = B ) ) )).
fof(d41_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & v5_modelc_3(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_3(B,A) & l1_modelc_3(B,A) ) => k28_modelc_3(A,B) = a_2_1_modelc_3(A,B) ) ) )).
fof(d41_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ( l2_pcs_0(B) => k22_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))) ) ) )).
fof(d41_valued_2,axiom,( ! [A] : ( v1_valued_2(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_valued_0(C) ) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(d41_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r3_zf_lang(A,B) <=> ( r2_zf_lang(A,B) & A != B ) ) ) ) )).
fof(d42_abcmiz_1,axiom,( ! [A] : ( ( 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) ) )).
fof(d42_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v19_aofa_a00(C,A) & m1_subset_1(C,u1_struct_0(A)) ) => k28_aofa_a00(A,B,C) = k1_funct_1(k5_msualg_1(A,k10_subset_1(k1_funct_1(u7_aofa_a00(A),5),u4_struct_0(A)),B),k1_xboole_0) ) ) ) )).
fof(d42_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(d42_fomodel1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fomodel1(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(d42_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ! [D] : ( m2_subset_1(D,k9_funct_2(k37_fomodel1(A),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_fomodel2(A,B)) => ( v11_fomodel2(D,A,B,C) <=> v10_fomodel2(C,B,A,D) ) ) ) ) )).
fof(d42_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(k1_fomodel4(A)),k1_fomodel4(A)))) => ( B = k18_fomodel4(A) <=> ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d42_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(d42_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => k30_glib_000(A,B) = k1_card_1(k26_glib_000(A,B)) ) ) )).
fof(d42_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,k30_modelc_1(A)) => ( C = k32_modelc_1(A,B) <=> ! [D] : ( 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 ) ) ) ) ) )).
fof(d42_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( v7_ordinal1(C) => k28_modelc_2(A,B,C) = k26_modelc_2(A,k8_nat_1(A,k27_modelc_2(A,B),C)) ) ) )).
fof(d42_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & v5_modelc_3(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_3(B,A) & l1_modelc_3(B,A) ) => k29_modelc_3(A,B) = a_2_2_modelc_3(A,B) ) ) )).
fof(d42_monoid_0,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( 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))) ) ) ) ) ) )).
fof(d42_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ( l2_pcs_0(B) => k23_pcs_0(A,B) = k22_pcs_0(k21_pcs_0(A),B) ) ) )).
fof(d42_valued_2,axiom,( ! [A] : ( v1_valued_2(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(d42_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( B = k29_zf_lang(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) & D = C & r2_zf_lang(D,A) ) ) ) ) )).
fof(d43_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m3_abcmiz_1(B,A) <=> r2_hidden(B,k39_abcmiz_1(A)) ) ) )).
fof(d43_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v19_aofa_a00(C,A) & m1_subset_1(C,u1_struct_0(A)) ) => ! [D] : ( m1_msafree4(D,u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) => k29_aofa_a00(A,B,C,D) = k1_funct_1(k5_msualg_1(A,k10_subset_1(k1_funct_1(u7_aofa_a00(A),6),u4_struct_0(A)),B),k12_finseq_1(k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C),D)) ) ) ) ) )).
fof(d43_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( v4_funct_1(B) => k41_fomodel1(A,B) = k40_fomodel1(k8_funcop_1(k4_ordinal1,k23_fomodel0(k2_xboole_0(k15_fomodel1(A),k21_fomodel0(B))),k5_numbers),A) ) ) )).
fof(d43_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(k1_fomodel4(A)),k1_fomodel4(A)))) => ( B = k19_fomodel4(A) <=> ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d43_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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)))) )).
fof(d43_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => k31_glib_000(A,B) = k1_card_1(k27_glib_000(A,B)) ) ) )).
fof(d43_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( r2_hidden(C,k30_modelc_1(A)) => k1_funct_1(B,C) = k32_modelc_1(A,C) ) ) ) ) )).
fof(d43_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k25_modelc_2(A)) => ! [C] : ( v7_ordinal1(C) => k29_modelc_2(A,B,C) = k28_modelc_2(A,B,C) ) ) ) )).
fof(d43_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & v5_modelc_3(A) & m2_finseq_1(A,k4_ordinal1) ) => k30_modelc_3(A) = a_1_1_modelc_3(A) ) )).
fof(d43_valued_2,axiom,( ! [A] : ( v1_valued_2(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_valued_0(C) ) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(d44_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m3_abcmiz_1(B,A) => ! [C] : ( ( 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)) ) ) ) )).
fof(d44_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v19_aofa_a00(C,A) & m1_subset_1(C,u1_struct_0(A)) ) => ! [D] : ( m1_msafree4(D,u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) => ! [E] : ( m1_msafree4(E,u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) => k30_aofa_a00(A,B,C,D,E) = k1_funct_1(k5_msualg_1(A,k10_subset_1(k1_funct_1(u7_aofa_a00(A),7),u4_struct_0(A)),B),k2_finseq_4(k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C),D,E)) ) ) ) ) ) )).
fof(d44_fomodel1,axiom,( ! [A] : ( l4_struct_0(A) => ( v6_struct_0(A) <=> u2_struct_0(A) = u3_struct_0(A) ) ) )).
fof(d44_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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] : ( ~ v1_xboole_0(D) => ! [E] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(B),k3_rfunct_3(k3_finseq_2(D),k2_xboole_0(D,k6_margrel1))),k15_fomodel2(B,D)) => ( v10_fomodel2(A,D,B,E) => k25_fomodel2(B,D,E,C) = 1 ) ) ) ) ) ) )).
fof(d44_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(k1_fomodel4(A)),k1_fomodel4(A)))) => ( B = k20_fomodel4(A) <=> ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d44_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(d44_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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)) ) ) )).
fof(d44_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( 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] : ( ( r2_hidden(D,A) => ( ! [E] : ( m1_modelc_1(E,A,B) => ~ ( k3_funct_2(k4_ordinal1,A,E,k5_numbers) = D & k3_funct_2(A,k6_margrel1,C,k3_funct_2(k4_ordinal1,A,E,1)) = k8_margrel1 ) ) | k34_modelc_1(A,B,C,D) = k8_margrel1 ) ) & ( ~ ( r2_hidden(D,A) & ? [E] : ( m1_modelc_1(E,A,B) & k3_funct_2(k4_ordinal1,A,E,k5_numbers) = D & k3_funct_2(A,k6_margrel1,C,k3_funct_2(k4_ordinal1,A,E,1)) = k8_margrel1 ) ) => k34_modelc_1(A,B,C,D) = k7_margrel1 ) ) ) ) ) )).
fof(d44_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,k30_modelc_1(k25_modelc_2(A))) => ( C = k30_modelc_2(A,B) <=> ! [D] : ( 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 ) ) ) ) ) )).
fof(d44_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & v5_modelc_3(A) & m2_finseq_1(A,k4_ordinal1) ) => k31_modelc_3(A) = k1_tarski(k11_modelc_3(A)) ) )).
fof(d44_valued_2,axiom,( ! [A] : ( v1_valued_2(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(d45_abcmiz_1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(d45_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v19_aofa_a00(C,A) & m1_subset_1(C,u1_struct_0(A)) ) => ! [D] : ( m1_msafree4(D,u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) => ! [E] : ( m1_msafree4(E,u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) => k31_aofa_a00(A,B,C,D,E) = k1_funct_1(k5_msualg_1(A,k10_subset_1(k1_funct_1(u7_aofa_a00(A),8),u4_struct_0(A)),B),k2_finseq_4(k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C),D,E)) ) ) ) ) ) )).
fof(d45_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(d45_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(k1_fomodel4(A)),k1_fomodel4(A)))) => ( B = k21_fomodel4(A) <=> ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d45_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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) )).
fof(d45_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => k35_glib_000(A,B) = k1_nat_1(k32_glib_000(A,B),k33_glib_000(A,B)) ) ) )).
fof(d45_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ! [D] : ( m1_subset_1(D,k30_modelc_1(A)) => ( D = k35_modelc_1(A,B,C) <=> ! [E] : ( 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 ) ) ) ) ) ) )).
fof(d45_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( r2_hidden(C,k30_modelc_1(k25_modelc_2(A))) => k1_funct_1(B,C) = k30_modelc_2(A,C) ) ) ) ) )).
fof(d45_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & v5_modelc_3(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => k32_modelc_3(A,B) = a_2_3_modelc_3(A,B) ) ) )).
fof(d45_pcs_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) => ( C = k24_pcs_0(A,B) <=> ! [D] : ! [E] : ( r2_hidden(k4_tarski(D,E),C) <=> ( r2_hidden(D,B) & r2_hidden(E,B) & ! [F] : ~ ( r2_hidden(F,D) & ! [G] : ~ ( r2_hidden(G,E) & r2_hidden(k4_tarski(F,G),u1_orders_2(A)) ) ) ) ) ) ) ) )).
fof(d45_valued_2,axiom,( ! [A] : ( v1_valued_2(A) => ! [B] : ( v1_valued_2(B) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,A) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v5_relat_1(D,B) & v1_funct_1(D) ) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d46_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(d46_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v19_aofa_a00(C,A) & m1_subset_1(C,u1_struct_0(A)) ) => ! [D] : ( m1_msafree4(D,u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) => ! [E] : ( m1_msafree4(E,u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) => k32_aofa_a00(A,B,C,D,E) = k1_funct_1(k5_msualg_1(A,k10_subset_1(k1_funct_1(u7_aofa_a00(A),9),u4_struct_0(A)),B),k2_finseq_4(k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C),D,E)) ) ) ) ) ) )).
fof(d46_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : k46_gfacirc1(A,B,C) = k8_facirc_1(A,B,C,k14_twoscomp) )).
fof(d46_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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)) ) ) )).
fof(d46_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( 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] : ( r2_hidden(D,k30_modelc_1(A)) => k1_funct_1(C,D) = k35_modelc_1(A,B,D) ) ) ) ) ) )).
fof(d46_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( ( 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 ) ) ) ) )).
fof(d46_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & v5_modelc_3(A) & m2_finseq_1(A,k4_ordinal1) ) => k33_modelc_3(A) = a_1_2_modelc_3(A) ) )).
fof(d46_pcs_0,axiom,( ! [A] : ( l1_pcs_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) => ( C = k25_pcs_0(A,B) <=> ! [D] : ! [E] : ( r2_hidden(k4_tarski(D,E),C) <=> ( r2_hidden(D,B) & r2_hidden(E,B) & ! [F] : ! [G] : ( ( r2_hidden(F,D) & r2_hidden(G,E) ) => r2_hidden(k4_tarski(F,G),u1_pcs_0(A)) ) ) ) ) ) ) )).
fof(d46_valued_2,axiom,( ! [A] : ( v1_valued_2(A) => ! [B] : ( v1_valued_2(B) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,A) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v5_relat_1(D,B) & v1_funct_1(D) ) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d47_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(d47_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v19_aofa_a00(C,A) & m1_subset_1(C,u1_struct_0(A)) ) => ! [D] : ( m1_msafree4(D,u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) => ! [E] : ( m1_msafree4(E,u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) => k33_aofa_a00(A,B,C,D,E) = k1_funct_1(k5_msualg_1(A,k10_subset_1(k1_funct_1(u7_aofa_a00(A),10),u4_struct_0(A)),B),k2_finseq_4(k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C),D,E)) ) ) ) ) ) )).
fof(d47_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(d47_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(k1_fomodel4(A)),k1_fomodel4(A)))) => ! [C] : ( 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 = k23_fomodel4(A,B) <=> ! [D] : ( r2_hidden(D,k9_setfam_1(k1_fomodel4(A))) => k1_funct_1(C,D) = a_3_1_fomodel4(A,B,D) ) ) ) ) ) )).
fof(d47_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : k47_gfacirc1(A,B,C) = k10_facirc_1(A,B,C,k14_twoscomp) )).
fof(d47_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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)) ) ) )).
fof(d47_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( 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] : ( ( r2_hidden(D,A) => ( ! [E] : ( m1_modelc_1(E,A,B) => ~ ( k3_funct_2(k4_ordinal1,A,E,k5_numbers) = D & ! [F] : ( m1_subset_1(F,k4_ordinal1) => k3_funct_2(A,k6_margrel1,C,k3_funct_2(k4_ordinal1,A,E,F)) = k8_margrel1 ) ) ) | k37_modelc_1(A,B,C,D) = k8_margrel1 ) ) & ( ~ ( r2_hidden(D,A) & ? [E] : ( m1_modelc_1(E,A,B) & k3_funct_2(k4_ordinal1,A,E,k5_numbers) = D & ! [F] : ( m1_subset_1(F,k4_ordinal1) => k3_funct_2(A,k6_margrel1,C,k3_funct_2(k4_ordinal1,A,E,F)) = k8_margrel1 ) ) ) => k37_modelc_1(A,B,C,D) = k7_margrel1 ) ) ) ) ) )).
fof(d47_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,k30_modelc_1(k25_modelc_2(A))) => ( C = k33_modelc_2(A,B) <=> ! [D] : ( 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 ) ) ) ) ) )).
fof(d47_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & v5_modelc_3(A) & m2_finseq_1(A,k4_ordinal1) ) => 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)) ) )).
fof(d47_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : k26_pcs_0(A,B) = g2_pcs_0(B,k24_pcs_0(A,B),k25_pcs_0(A,B)) ) )).
fof(d47_valued_2,axiom,( ! [A] : ( v1_valued_2(A) => ! [B] : ( v1_valued_2(B) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,A) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v5_relat_1(D,B) & v1_funct_1(D) ) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d48_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( 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))) ) ) )).
fof(d48_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v19_aofa_a00(C,A) & m1_subset_1(C,u1_struct_0(A)) ) => ! [D] : ( m1_subset_1(D,k1_funct_1(u3_msualg_1(A,B),C)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,B),C)) => k34_aofa_a00(A,B,C,D,E) = k30_aofa_a00(A,B,C,D,k29_aofa_a00(A,B,C,E)) ) ) ) ) ) )).
fof(d48_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(d48_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k24_fomodel4(A) = k23_fomodel4(A,k10_fomodel4(A)) ) )).
fof(d48_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : k48_gfacirc1(A,B,C) = k9_facirc_1(A,B,C,k14_twoscomp) )).
fof(d48_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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)) ) ) )).
fof(d48_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ! [D] : ( m1_subset_1(D,k30_modelc_1(A)) => ( D = k38_modelc_1(A,B,C) <=> ! [E] : ( 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 ) ) ) ) ) ) )).
fof(d48_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( r2_hidden(C,k30_modelc_1(k25_modelc_2(A))) => k1_funct_1(B,C) = k33_modelc_2(A,C) ) ) ) ) )).
fof(d48_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => k27_pcs_0(A) = a_1_0_pcs_0(A) ) )).
fof(d48_valued_2,axiom,( ! [A] : ( v1_valued_2(A) => ! [B] : ( v1_valued_2(B) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,A) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v5_relat_1(D,B) & v1_funct_1(D) ) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d49_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m3_abcmiz_1(B,A) => k48_abcmiz_1(A,B) = k1_abcmiz_1(k47_abcmiz_1(A,B)) ) ) )).
fof(d49_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v19_aofa_a00(C,A) & m1_subset_1(C,u1_struct_0(A)) ) => ! [D] : ( m1_subset_1(D,k1_funct_1(u3_msualg_1(A,B),C)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,B),C)) => k35_aofa_a00(A,B,C,D,E) = k30_aofa_a00(A,B,C,D,k29_aofa_a00(A,B,C,k31_aofa_a00(A,B,C,k32_aofa_a00(A,B,C,D,E),E))) ) ) ) ) ) )).
fof(d49_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(d49_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k25_fomodel4(A) = k23_fomodel4(A,k11_fomodel4(A)) ) )).
fof(d49_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : k49_gfacirc1(A,B,C) = k2_circcomb(k46_gfacirc1(A,B,C),k43_gfacirc1(A,B,C)) )).
fof(d49_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ( v10_glib_000(B,A) <=> k28_glib_000(A,B) = k1_xboole_0 ) ) ) )).
fof(d49_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( 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] : ( r2_hidden(D,k30_modelc_1(A)) => k1_funct_1(C,D) = k38_modelc_1(A,B,D) ) ) ) ) ) )).
fof(d49_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k30_modelc_1(k25_modelc_2(A))) => ( D = k35_modelc_2(A,B,C) <=> ! [E] : ( 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 ) ) ) ) ) )).
fof(d4_abcmiz_0,axiom,( ! [A] : ( l1_abcmiz_0(A) => ( v4_abcmiz_0(A) <=> v1_xboole_0(u1_abcmiz_0(A)) ) ) )).
fof(d4_abcmiz_1,axiom,( k6_abcmiz_1 = k5_numbers )).
fof(d4_abian,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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) ) ) ) ) )).
fof(d4_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_aff_1(A,B,C,D) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & E != F & D = k2_aff_1(A,E,F) & r2_analoaf(A,B,C,E,F) ) ) ) ) ) ) ) )).
fof(d4_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ( v4_aff_2(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_aff_3,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v4_aff_3(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ! [L] : ( m1_subset_1(L,u1_struct_0(A)) => ! [M] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_aff_4(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d4_afinsq_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k5_afinsq_1(A) <=> ( k9_xtuple_0(B) = 1 & k1_funct_1(B,k5_numbers) = A ) ) ) )).
fof(d4_afinsq_2,axiom,( ! [A] : ( ( v1_finset_1(A) & v6_membered(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ( B = k4_afinsq_2(A) <=> ( k2_relset_1(k4_ordinal1,B) = A & ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d4_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => k4_afproj(A) = a_1_3_afproj(A) ) )).
fof(d4_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( D = k1_afvect0(A,B,C) <=> r2_afvect0(A,C,B,D) ) ) ) ) ) )).
fof(d4_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(d4_algseq_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( C = k2_algseq_1(A,B) <=> ( r1_xxreal_0(k1_algseq_1(A,C),1) & k3_funct_2(k4_ordinal1,u1_struct_0(A),C,k5_numbers) = B ) ) ) ) ) )).
fof(d4_algspec1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r1_algspec1(A,B,C) => ! [D] : ( ( ~ 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)) ) ) ) ) ) ) ) )).
fof(d4_algstr_0,axiom,( ! [A] : ( l1_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v3_algstr_0(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k1_algstr_0(A,C,B) = k1_algstr_0(A,D,B) => C = D ) ) ) ) ) ) )).
fof(d4_algstr_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ( v3_algstr_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & k1_algstr_0(A,B,D) = C ) ) ) ) ) )).
fof(d4_altcat_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ! [F] : ! [G] : ( ( 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)) ) ) ) ) ) )).
fof(d4_altcat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(d4_altcat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d4_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d4_altcat_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_altcat_5(E,A,D,B,C) => ( v2_altcat_5(E,A,B,C,D) <=> ! [F] : ~ ( r2_hidden(F,B) & ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( G = k1_funct_1(C,F) & r2_hidden(k1_funct_1(E,F),k1_altcat_1(A,D,G)) ) ) ) ) ) ) ) ) )).
fof(d4_ami_2,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k3_ami_2,k4_ami_2))) => k5_ami_2(A) = k1_funct_1(A,k4_ordinal1) ) )).
fof(d4_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( 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)) ) ) )).
fof(d4_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( D = k1_ami_wstd(A,B,C) <=> ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_ordinal1) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) & v3_funct_2(E,k4_ordinal1,k4_ordinal1) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( r1_xxreal_0(F,G) <=> r1_ami_wstd(A,B,k3_funct_2(k4_ordinal1,k4_ordinal1,E,F),k3_funct_2(k4_ordinal1,k4_ordinal1,E,G)) ) ) ) & D = k1_funct_1(E,C) ) ) ) ) ) ) )).
fof(d4_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(d4_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( D = k3_amistd_4(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r2_hidden(E,D) <=> ! [F] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d4_amistd_5,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) & ~ v2_compos_1(C,B) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(B)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( r1_tarski(C,F) => ! [G] : ( v7_ordinal1(G) => r2_hidden(k5_memstr_0(A,B,k5_extpro_1(A,B,F,E,G)),k9_xtuple_0(C)) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ! [F] : ( r2_hidden(k4_tarski(E,F),D) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & ? [I] : ( m1_subset_1(I,u1_struct_0(A)) & ? [J] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_analoaf,axiom,( ! [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) ) => k2_analoaf(A) = g1_analoaf(u1_struct_0(A),k1_analoaf(A)) ) )).
fof(d4_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d4_anproj_1,axiom,( ! [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) ) => ! [B] : ( 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) ) ) )).
fof(d4_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_aofa_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : k2_aofa_000(A,B,C) = k1_funct_4(B,k5_relat_1(A,C)) ) ) )).
fof(d4_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : k5_aofa_a00(A,B,C,D,E,F) = k7_finseq_1(k8_finseq_4(A,B,C,D,E),k9_finseq_1(F)) )).
fof(d4_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( m1_msafree(D,A,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_msafree4(u1_struct_0(A),D,E)) => ( v3_aofa_a01(F,A,B,C,D,E) <=> r2_hidden(F,k1_msafree4(u1_struct_0(A),k1_aofa_a01(A,B,C),E)) ) ) ) ) ) ) ) )).
fof(d4_armstrng,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v1_armstrng(B,A) <=> r2_hidden(A,B) ) ) )).
fof(d4_arrow,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r1_arrow(A,B,C) <=> r2_hidden(k4_tarski(B,C),A) ) ) )).
fof(d4_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ( ( A != k5_numbers => ( B = k4_arytm_0(A) <=> k2_arytm_0(A,B) = 1 ) ) & ( A = k5_numbers => ( B = k4_arytm_0(A) <=> B = k5_numbers ) ) ) ) ) )).
fof(d4_arytm_2,axiom,( ! [A] : ( m2_subset_1(A,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ( ( ? [C] : ( m1_subset_1(C,k5_arytm_3) & ! [D] : ( m1_subset_1(D,k5_arytm_3) => ( r2_hidden(D,A) <=> ~ r3_arytm_3(C,D) ) ) ) => ( B = k4_arytm_2(A) <=> ? [C] : ( m1_subset_1(C,k5_arytm_3) & B = C & ! [D] : ( m1_subset_1(D,k5_arytm_3) => ( r2_hidden(D,A) <=> ~ r3_arytm_3(C,D) ) ) ) ) ) & ( ! [C] : ( m1_subset_1(C,k5_arytm_3) => ~ ! [D] : ( m1_subset_1(D,k5_arytm_3) => ( r2_hidden(D,A) <=> ~ r3_arytm_3(C,D) ) ) ) => ( B = k4_arytm_2(A) <=> B = A ) ) ) ) ) )).
fof(d4_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( C = k2_arytm_3(A,B) <=> ( r2_arytm_3(A,C) & r2_arytm_3(B,C) & ! [D] : ( ( v3_ordinal1(D) & v7_ordinal1(D) ) => ( ( r2_arytm_3(A,D) & r2_arytm_3(B,D) ) => r2_arytm_3(C,D) ) ) ) ) ) ) ) )).
fof(d4_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v4_asympt_0(A) <=> ? [B] : ( v7_ordinal1(B) & ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(B,C) & r1_xxreal_0(k9_nat_1(k1_numbers,A,C),k5_numbers) ) ) ) ) ) )).
fof(d4_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( B = k4_asympt_1(A) <=> ! [C] : ( m1_subset_1(C,k4_ordinal1) => k9_nat_1(k1_numbers,B,C) = k7_newton(k1_nat_1(C,A)) ) ) ) ) )).
fof(d4_autalg_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(d4_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) => ( B = k4_autgroup(A) <=> ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) & ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d4_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ( C = k3_bagorder(A,B) <=> ? [D] : ( m2_finseq_1(D,k4_ordinal1) & C = k2_wsierp_1(D) & D = k23_pre_poly(A,k7_pre_poly(A,k22_pre_poly(A,B),k2_orders_1(A)),B) ) ) ) ) ) )).
fof(d4_bcialg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_bcialg_1(A) ) => ( v4_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d4_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v3_bcialg_2(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_bcialg_1(A,B,C) => C = B ) ) ) ) ) )).
fof(d4_bcialg_3,axiom,( ! [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) ) => ( v4_bcialg_3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(d4_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_bcialg_4(A,B,C) = a_3_0_bcialg_4(A,B,C) ) ) ) )).
fof(d4_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k2_bcialg_5(A,B,C,D) = k4_nat_1(k4_nat_1(A,B),k4_nat_1(C,D)) ) ) ) ) )).
fof(d4_bcialg_6,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_bcialg_6(B,A) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & C != k5_numbers & r2_hidden(k3_bcialg_6(A,C,B),k4_bcialg_1(A)) ) ) ) ) )).
fof(d4_bciideal,axiom,( ! [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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d4_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_bhsp_1(A,B) = k3_square_1(k2_bhsp_1(A,B,B)) ) ) )).
fof(d4_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( D = k3_bhsp_2(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k9_nat_1(k1_numbers,D,E) = k4_bhsp_1(A,k1_normsp_1(A,B,E),C) ) ) ) ) ) ) )).
fof(d4_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ( v3_bhsp_3(A) <=> ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_bhsp_3(B,A) => v1_bhsp_2(B,A) ) ) ) ) )).
fof(d4_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => k3_bhsp_4(A,B,C) = k1_normsp_1(A,k1_bhsp_4(A,B),C) ) ) ) )).
fof(d4_bhsp_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [D] : ( m2_finseq_1(D,B) => k4_bhsp_5(A,B,C,D) = k3_relat_1(D,C) ) ) ) ) )).
fof(d4_bhsp_6,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_xxreal_0(k9_complex1(k3_funct_2(u1_struct_0(A),k1_numbers,B,D)),k3_xcmplx_0(C,k3_bhsp_1(A,D))) ) ) ) ) ) )).
fof(d4_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d4_binari_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(d4_binarith,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => k6_binarith(A,B) = k1_finsop_1(k4_ordinal1,k5_binarith(A,B),k23_binop_2) ) ) )).
fof(d4_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),k4_ordinal1),u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_ordinal1),u1_struct_0(A)))) ) => ( B = k4_binom(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),B,C,k5_numbers) = k4_struct_0(A) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),B,C,k1_nat_1(D,1)) = k1_algstr_0(A,k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),B,C,D),C) ) ) ) ) ) ) )).
fof(d4_binop_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) => k3_binop_1(A,B,C,C) = C ) ) ) )).
fof(d4_binop_2,axiom,( ! [A] : ( ( 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 = k4_binop_2 <=> ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k1_binop_1(A,B,C) = k6_xcmplx_0(B,C) ) ) ) ) )).
fof(d4_bintree1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => ( v3_bintree1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ~ ( r1_lang1(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => C != k4_pre_poly(u1_struct_0(A),D,E) ) ) ) ) ) ) ) )).
fof(d4_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_boolealg(A,B,C) <=> k4_lattices(A,B,C) != k5_lattices(A) ) ) ) ) )).
fof(d4_boolmark,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m2_funct_2(B,u1_struct_0(A),k6_margrel1,k1_boolmark(A)) => ! [C] : ( m2_finseq_1(C,u4_struct_0(A)) => ( r2_boolmark(A,B,C) <=> ~ ( C != k1_xboole_0 & ! [D] : ( 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] : ( m1_subset_1(E,k4_ordinal1) => ~ ( ~ r1_xxreal_0(k3_finseq_1(C),E) & ~ r1_xxreal_0(E,k5_numbers) & ~ ( r1_boolmark(A,k7_partfun1(k1_boolmark(A),D,E),k7_partfun1(u4_struct_0(A),C,k1_nat_1(E,1))) & k7_partfun1(k1_boolmark(A),D,k1_nat_1(E,1)) = k2_boolmark(A,k7_partfun1(k1_boolmark(A),D,E),k7_partfun1(u4_struct_0(A),C,k1_nat_1(E,1))) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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))) ) ) )).
fof(d4_borsuk_2,axiom,( ! [A] : ( ( v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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,k5_numbers) = B & k1_funct_1(D,1) = C ) ) ) ) ) ) )).
fof(d4_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( ( 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,k5_numbers) = k5_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) ) ) ) ) ) ) )).
fof(d4_borsuk_7,axiom,( k9_borsuk_7 = k4_euclid_5(k4_xcmplx_0(1),k5_numbers,k5_numbers) )).
fof(d4_brouwer,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( ( v1_xreal_0(C) & ~ v3_xxreal_0(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_brouwer(A,B,C))) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k7_toprealb(A,B,C))) => ( F = k4_brouwer(A,B,C,D,E) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(A))) & ? [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_bspace,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k2_bspace)) => ! [C] : ( 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) ) ) ) ) )).
fof(d4_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d4_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d4_c0sp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l5_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_c0sp1(B,A) <=> ( r2_hidden(k5_struct_0(A),B) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(d4_c0sp2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d4_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => ( r2_calcul_1(A,B,C) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) & r1_relset_1(k4_ordinal1,k3_cqc_lang(A),B,k15_finseq_1(k2_partfun1(k4_ordinal1,k3_cqc_lang(A),C,D))) ) ) ) ) ) )).
fof(d4_cantor_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v2_cantor_1(B,A) <=> ? [C] : ( 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)) ) ) ) ) )).
fof(d4_card_1,axiom,( ! [A] : ( v1_card_1(A) => ( v2_card_1(A) <=> ! [B] : ( v1_card_1(B) => A != k2_card_1(B) ) ) ) )).
fof(d4_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k3_card_3(A) = k3_tarski(k10_xtuple_0(A)) ) )).
fof(d4_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_card_1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ( r2_card_fil(A,B,C) <=> ! [D] : ( ~ v1_xboole_0(D) => ( ( r1_tarski(D,C) & r2_hidden(k1_card_1(D),B) ) => r2_hidden(k3_tarski(D),C) ) ) ) ) ) ) )).
fof(d4_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_card_lar(B,A) <=> k3_ordinal2(B) = A ) ) ) )).
fof(d4_cardfin2,axiom,( ! [A] : ! [B] : k4_cardfin2(A,B) = a_2_0_cardfin2(A,B) )).
fof(d4_cat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_cat_1(A) ) => ( v2_cat_1(A) <=> ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d4_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( C = D => k4_cat_1(B,C) = k4_cat_1(A,D) ) ) ) ) ) ) ) )).
fof(d4_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(d4_cat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d4_cat_5,axiom,( ! [A] : ( v2_cat_5(A) <=> ! [B] : ( 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) ) ) ) )).
fof(d4_catalan2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( C = k4_catalan2(A,B) <=> ! [D] : ( v7_ordinal1(D) => ? [E] : ( v1_relat_1(E) & v5_relat_1(E,k1_numbers) & v1_funct_1(E) & v5_ordinal1(E) & v1_finset_1(E) & k1_relset_1(k4_ordinal1,E) = k1_nat_1(D,1) & ! [F] : ( v7_ordinal1(F) => ( r2_hidden(F,k1_nat_1(D,1)) => k1_funct_1(E,F) = k4_real_1(k9_nat_1(k1_numbers,A,F),k3_funct_2(k4_ordinal1,k1_numbers,B,k7_nat_d(D,F))) ) ) & k7_afinsq_2(E) = k9_nat_1(k1_numbers,C,D) ) ) ) ) ) ) )).
fof(d4_catalg_1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ( v2_catalg_1(A) <=> ? [B] : ( m1_instalg1(k2_catalg_1(B),A) & u1_struct_0(A) = k2_zfmisc_1(k1_tarski(k5_numbers),k4_finseq_2(2,B)) ) ) ) )).
fof(d4_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k2_cc0sp1(A) = a_1_0_cc0sp1(A) ) )).
fof(d4_cc0sp2,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(d4_cfdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ( v3_cfdiff_1(A) <=> ? [B] : ( v1_xcmplx_0(B) & ! [C] : ( v1_xcmplx_0(C) => k7_partfun1(k2_numbers,A,C) = k3_xcmplx_0(B,C) ) ) ) ) )).
fof(d4_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k4_cfuncdom(A) = k7_funcop_1(A,k5_numbers) ) )).
fof(d4_cgames_1,axiom,( k4_cgames_1 = g1_cgames_1(k1_tarski(k3_cgames_1),k1_xboole_0) )).
fof(d4_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : k2_chord(A,B) = a_2_0_chord(A,B) ) )).
fof(d4_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ( v1_circcmb3(C,A,B) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(A,B))) => ( D = k1_circcmb3(A,B,C) <=> ( v1_circuit2(D,A,B) & ? [E] : ( m1_subset_1(E,k4_ordinal1) & r8_pboole(u1_struct_0(A),D,k5_facirc_1(A,B,C,E)) ) ) ) ) ) ) ) ) )).
fof(d4_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msualg_1(D,B) & l3_msualg_1(D,B) ) => ( r1_partfun1(u3_msualg_1(A,C),u3_msualg_1(B,D)) => ! [E] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(d4_circled1,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ( v1_circled1(B,A) <=> ? [C] : ( m2_finseq_1(C,u1_struct_0(A)) & v2_funct_1(C) & k10_xtuple_0(C) = k3_rlvect_2(A,B) & ? [D] : ( m2_finseq_1(D,k1_numbers) & k3_finseq_1(D) = k3_finseq_1(C) & k18_rvsum_1(D) = 1 & ! [E] : ( 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(k5_numbers,k1_funct_1(D,E)) ) ) ) ) ) ) ) ) )).
fof(d4_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) => ! [D] : ( l3_msualg_1(D,A) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k1_circtrm1(A,B,C))) => k1_funct_1(E,F) = k2_circtrm1(A,B,C,F,D) ) ) ) ) ) ) ) )).
fof(d4_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v7_ordinal1(D) => ( D = k4_circuit1(A,B,C) <=> ? [E] : ( ~ v1_xboole_0(E) & v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) & E = a_3_0_circuit1(A,B,C) & D = k1_xxreal_2(E) ) ) ) ) ) ) )).
fof(d4_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(d4_classes1,axiom,( ! [A] : ! [B] : ( B = k1_classes1(A) <=> ( r1_classes1(A,B) & ! [C] : ( r1_classes1(A,C) => r1_tarski(B,C) ) ) ) )).
fof(d4_clopban1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_clopban1(u1_struct_0(A),B)))) => ( C = k5_clopban1(A,B) <=> ! [D] : ( 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)))) ) ) ) ) ) ) )).
fof(d4_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( 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] : ( m2_subset_1(C,u1_struct_0(k6_clopban1(A,A)),k8_clopban1(A,A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d4_clopban3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clopban2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k2_clopban3(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k1_normsp_0(A,D,E) = k6_algstr_0(A,C,k1_normsp_0(A,B,E)) ) ) ) ) ) ) )).
fof(d4_clopban4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( E = k4_clopban4(A,B,C,D) <=> ! [F] : ( v7_ordinal1(F) => ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d4_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m2_pboole(C,A,k5_mssubfam(A,B),k5_mssubfam(A,B)) => ( v4_closure1(C,A,B) <=> ! [D] : ( m1_pboole(D,A,k5_mssubfam(A,B)) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(d4_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) => ( v1_closure2(C,A,B) <=> ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(d4_clvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ( v4_clvect_1(A) <=> ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d4_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( D = k3_clvect_2(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k9_nat_1(k1_numbers,D,E) = k15_csspace(A,k1_normsp_1(A,B,E),C) ) ) ) ) ) ) )).
fof(d4_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k3_clvect_3(A,B,C,D) = k5_algstr_0(A,k2_clvect_3(A,B,C),k2_clvect_3(A,B,D)) ) ) ) ) )).
fof(d4_coh_sp,axiom,( ! [A] : k3_coh_sp(A) = a_1_0_coh_sp(A) )).
fof(d4_cohsp_1,axiom,( ! [A] : ( v1_cohsp_1(A) <=> ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : ( r1_tarski(k3_tarski(B),C) & r2_hidden(C,A) ) ) ) )).
fof(d4_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_collsp(A) ) => ( v3_collsp(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d4_combgras,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_incsp_1(k1_combgras(A,B)))) => ( v3_combgras(C,A,B) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & k1_card_1(D) = k6_xcmplx_0(A,1) & C = a_3_0_combgras(A,B,D) ) ) ) ) ) )).
fof(d4_compl_sp,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( 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) ) ) ) )).
fof(d4_complex1,axiom,( k6_complex1 = 1 )).
fof(d4_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( ( r1_xxreal_0(k5_numbers,k6_xcmplx_0(k1_comptrig(k6_xcmplx_0(C,B)),k1_comptrig(k6_xcmplx_0(A,B)))) => k4_complex2(A,B,C) = k6_xcmplx_0(k1_comptrig(k6_xcmplx_0(C,B)),k1_comptrig(k6_xcmplx_0(A,B))) ) & ( ~ r1_xxreal_0(k5_numbers,k6_xcmplx_0(k1_comptrig(k6_xcmplx_0(C,B)),k1_comptrig(k6_xcmplx_0(A,B)))) => k4_complex2(A,B,C) = k2_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k6_xcmplx_0(k1_comptrig(k6_xcmplx_0(C,B)),k1_comptrig(k6_xcmplx_0(A,B)))) ) ) ) ) ) )).
fof(d4_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => k8_complsp2(A,B) = k2_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k22_rvsum_1(k6_complsp2(A),k6_complsp2(B)),k3_xcmplx_0(k7_complex1,k22_rvsum_1(k6_complsp2(A),k7_complsp2(B)))),k3_xcmplx_0(k7_complex1,k22_rvsum_1(k7_complsp2(A),k6_complsp2(B)))),k22_rvsum_1(k7_complsp2(A),k7_complsp2(B))) ) ) )).
fof(d4_compos_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( r1_compos_2(A,B) <=> r1_tarski(k63_valued_1(A),B) ) ) )).
fof(d4_compts_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_compts_1(B,A) <=> ! [C] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d4_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_comput_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & v2_margrel1(C) & r2_hidden(C,k10_xtuple_0(A)) ) => ( B = k1_comput_1(A) <=> ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_margrel1(C) ) => ( r2_hidden(C,k10_xtuple_0(A)) => B = k19_margrel1(C) ) ) ) ) & ( ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_margrel1(C) ) => ~ r2_hidden(C,k10_xtuple_0(A)) ) => ( B = k1_comput_1(A) <=> B = k5_numbers ) ) ) ) ) )).
fof(d4_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_comseq_2(A) <=> ? [B] : ( v1_xreal_0(B) & ! [C] : ( v7_ordinal1(C) => ~ r1_xxreal_0(B,k9_complex1(k9_nat_1(k2_numbers,A,C))) ) ) ) ) )).
fof(d4_comseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k4_comseq_3(A) <=> ( k9_xtuple_0(B) = k9_xtuple_0(A) & ! [C] : ( r2_hidden(C,k9_xtuple_0(B)) => k1_funct_1(B,C) = k4_complex1(k1_funct_1(A,C)) ) ) ) ) ) )).
fof(d4_conaffm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v4_conaffm(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => k3_conlat_1(A) = k1_conlat_1(A) ) )).
fof(d4_conmetr1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v4_conmetr1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A))) => ! [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_connsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_connsp_1(A,B,C) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v2_connsp_1(D,A) & r2_hidden(B,D) & r2_hidden(C,D) ) ) ) ) ) )).
fof(d4_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_connsp_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_connsp_2(A,B) ) ) ) )).
fof(d4_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( C = k2_convex1(A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(D,C) <=> ( v1_convex1(D,A) & r1_tarski(B,D) ) ) ) ) ) ) ) )).
fof(d4_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_convex4(C,A) => ( m2_convex4(C,A,B) <=> r1_tarski(k1_convex4(A,C),B) ) ) ) ) )).
fof(d4_convfun1,axiom,( k4_convfun1 = g1_rlvect_1(k1_numbers,k10_subset_1(k5_numbers,k1_numbers),k9_binop_2,k11_binop_2) )).
fof(d4_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k2_zfmisc_1(k3_cqc_lang(A),k2_cqc_the1)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_cqc_lang(A))) => ( ( k2_xtuple_0(k1_funct_1(B,C)) = k5_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] : ( 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] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) & ? [F] : ( 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] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) & ? [F] : ( m2_subset_1(F,k9_qc_lang1(A),k3_cqc_lang(A)) & ? [G] : ( 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] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) & ? [F] : ( 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] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) & ? [F] : ( 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] : ( v7_ordinal1(E) & ? [F] : ( v7_ordinal1(F) & ? [G] : ( m2_subset_1(G,k9_qc_lang1(A),k3_cqc_lang(A)) & ? [H] : ( 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] : ( v7_ordinal1(E) & ? [F] : ( m2_subset_1(F,k9_qc_lang1(A),k3_cqc_lang(A)) & ? [G] : ( m2_subset_1(G,k9_qc_lang1(A),k3_cqc_lang(A)) & ? [H] : ( 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] : ( v7_ordinal1(E) & ? [F] : ( m2_subset_1(F,k2_qc_lang1(A),k3_qc_lang1(A)) & ? [G] : ( m2_subset_1(G,k2_qc_lang1(A),k3_qc_lang1(A)) & ? [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ( r4_cqc_the3(A,B,C) <=> ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ( r3_cqc_the1(A,B,D) <=> r3_cqc_the1(A,C,D) ) ) ) ) ) ) )).
fof(d4_csspace,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k1_csspace) => ! [C] : ( 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)) ) ) ) ) )).
fof(d4_csspace3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k4_csspace3(A,B,C) = k2_normsp_0(A,k5_algstr_0(A,B,C)) ) ) ) )).
fof(d4_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( 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] : ( v1_xreal_0(D) & r1_xxreal_0(k5_numbers,D) & ! [E] : ( m1_subset_1(E,A) => r1_xxreal_0(k2_normsp_0(B,k3_funct_2(A,u1_struct_0(B),C,E)),D) ) ) ) ) ) ) )).
fof(d4_decomp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)))) ) ) ) )).
fof(d4_descip_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1)) => ! [C] : ( m2_finseq_2(C,k6_margrel1,k4_finseq_2(A,k6_margrel1)) => ! [D] : ( m2_finseq_2(D,k6_margrel1,k4_finseq_2(A,k6_margrel1)) => ( D = k12_descip_1(A,B,C) <=> ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(d4_dickson,axiom,( ! [A] : ( 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))) ) ) )).
fof(d4_diff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( 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))) ) ) )).
fof(d4_dilworth,axiom,( ! [A] : ( ( v3_dilworth(A) & l1_orders_2(A) ) => ! [B] : ( v7_ordinal1(B) => ( B = k1_dilworth(A) <=> ( ? [C] : ( 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] : ( ( 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) ) ) ) ) ) )).
fof(d4_diraf,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d4_dirort,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dirort(A) & l1_analoaf(A) ) => ( v2_dirort(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r1_dist_1(A,B,C) <=> ! [D] : k3_dist_1(A,B,D) = k3_dist_1(A,C,D) ) ) ) ) )).
fof(d4_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => ! [C] : ( m1_dist_2(C,A,B) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,k6_margrel1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => k4_dist_2(A,B,C,D) = k7_xcmplx_0(k5_card_1(k3_dist_2(k1_partfun1(k4_ordinal1,A,A,k6_margrel1,C,D))),k3_finseq_1(C)) ) ) ) ) )).
fof(d4_dtconstr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => ( v2_dtconstr(A) <=> k2_lang1(A) != k1_xboole_0 ) ) )).
fof(d4_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( C = k4_dynkin(A,B) <=> ! [D] : ( v7_ordinal1(D) => k9_nat_1(k9_setfam_1(A),C,D) = k3_dynkin(A,B,D) ) ) ) ) ) )).
fof(d4_e_siec,axiom,( ! [A] : k2_e_siec(A) = g1_e_siec(A,k4_relat_1(A),k4_relat_1(A)) )).
fof(d4_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ( v3_ec_pf_1(B,A) <=> ( B != k5_numbers & ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => k2_binom(k9_int_3(A),C,2) != B ) ) ) ) ) )).
fof(d4_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m2_subset_1(D,k3_ec_pf_1(k9_int_3(A)),k6_ec_pf_1(A,B,C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(A))) => ( E = k5_ec_pf_2(A,B,C,D) <=> ! [F] : ! [G] : ! [H] : ( D = k3_xtuple_0(F,G,H) => E = G ) ) ) ) ) ) ) )).
fof(d4_endalg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( ~ 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] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d4_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k2_ens_1(A)) => k4_ens_1(A,B) = k2_xtuple_0(k1_xtuple_0(B)) ) ) )).
fof(d4_entropy1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,k3_finseq_1(A),k3_finseq_1(A)) & v1_entropy1(B,k3_finseq_1(A)) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( B = k1_entropy1(A) <=> ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(A)) => k3_matrix_0(k1_numbers,B,C,C) = k1_funct_1(A,C) ) ) ) ) ) )).
fof(d4_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( G = k4_enumset1(A,B,C,D,E,F) <=> ! [H] : ( r2_hidden(H,G) <=> ~ ( H != A & H != B & H != C & H != D & H != E & H != F ) ) ) )).
fof(d4_eqrel_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( m1_eqrel_1(B,A) <=> ( k5_setfam_1(A,B) = A & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r2_hidden(C,B) => ( C != k1_xboole_0 & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ~ ( r2_hidden(D,B) & C != D & ~ r1_xboole_0(C,D) ) ) ) ) ) ) ) ) )).
fof(d4_equation,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(d4_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => k4_euclid(A) = k5_finseq_2(k1_numbers,A,k10_subset_1(k5_numbers,k1_numbers)) ) )).
fof(d4_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) )).
fof(d4_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( v2_euclid_4(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) & ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) & C != D & B = k4_euclid_4(A,C,D) ) ) ) ) ) )).
fof(d4_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(3))) => k5_euclid_5(A,B) = k4_euclid_5(k6_xcmplx_0(k3_xcmplx_0(k2_euclid_5(A),k3_euclid_5(B)),k3_xcmplx_0(k3_euclid_5(A),k2_euclid_5(B))),k6_xcmplx_0(k3_xcmplx_0(k3_euclid_5(A),k1_euclid_5(B)),k3_xcmplx_0(k1_euclid_5(A),k3_euclid_5(B))),k6_xcmplx_0(k3_xcmplx_0(k1_euclid_5(A),k2_euclid_5(B)),k3_xcmplx_0(k2_euclid_5(A),k1_euclid_5(B)))) ) ) )).
fof(d4_euclid_7,axiom,( ! [A] : ( v2_euclid_7(A) <=> ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v3_valued_0(B) ) => ( r2_hidden(B,A) => k12_euclid(B) = 1 ) ) ) )).
fof(d4_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => k5_euclid_8(A,B) = k1_euclid_8(k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(A,2),k1_funct_1(B,3)),k3_xcmplx_0(k1_funct_1(A,3),k1_funct_1(B,2))),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(A,3),k1_funct_1(B,1)),k3_xcmplx_0(k1_funct_1(A,1),k1_funct_1(B,3))),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(A,1),k1_funct_1(B,2)),k3_xcmplx_0(k1_funct_1(A,2),k1_funct_1(B,1)))) ) ) )).
fof(d4_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(A))) => ! [C] : ( v1_xreal_0(C) => k4_euclid_9(A,B,C) = k4_card_3(k3_euclid_9(B,C)) ) ) ) )).
fof(d4_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k1_euclidlp(A) = a_1_0_euclidlp(A) ) )).
fof(d4_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ( v4_euclmetr(A) <=> v1_translac(k3_analmetr(A)) ) ) )).
fof(d4_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( v3_ordinal1(B) => ( ( ? [C] : ( v3_ordinal1(C) & r2_hidden(C,k9_xtuple_0(A)) ) => ( B = k1_exchsort(A) <=> v2_exchsort(A,B) ) ) & ( ! [C] : ( v3_ordinal1(C) => ~ r2_hidden(C,k9_xtuple_0(A)) ) => ( B = k1_exchsort(A) <=> B = k5_numbers ) ) ) ) ) )).
fof(d4_facirc_1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k1_funct_1(A,k10_finseq_1(B,C)) = k1_binarith(B,C) ) ) ) ) )).
fof(d4_facirc_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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] : ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) & ? [F] : ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) & ? [G] : ( v1_relat_1(G) & v4_relat_1(G,k4_ordinal1) & v1_funct_1(G) & v1_partfun1(G,k4_ordinal1) & k3_facirc_2(A,B,C) = k1_funct_1(E,A) & D = k1_funct_1(F,A) & k1_funct_1(E,k5_numbers) = k5_circcomb(k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1),k1_xboole_0) & k1_funct_1(F,k5_numbers) = k7_circcomb(k5_ordinal1,k6_margrel1,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1),k1_xboole_0) & k1_funct_1(G,k5_numbers) = k4_tarski(k1_xboole_0,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1)) & ! [H] : ( v7_ordinal1(H) => ! [I] : ( ( ~ v2_struct_0(I) & l1_msualg_1(I) ) => ! [J] : ( ( v4_msualg_1(J,I) & l3_msualg_1(J,I) ) => ! [K] : ( ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_fcont_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k2_xcmplx_0(k3_xcmplx_0(A,D),B) ) ) ) ) ) )).
fof(d4_fdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r1_fdiff_1(A,B) <=> ? [C] : ( m1_rcomp_1(C,B) & r1_tarski(C,k1_relset_1(k1_numbers,A)) & ? [D] : ( v1_funct_1(D) & v3_fdiff_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [E] : ( v1_funct_1(E) & v2_fdiff_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,C) => k6_xcmplx_0(k1_funct_1(A,F),k1_funct_1(A,B)) = k2_xcmplx_0(k1_funct_1(D,k6_xcmplx_0(F,B)),k1_funct_1(E,k6_xcmplx_0(F,B))) ) ) ) ) ) ) ) ) )).
fof(d4_fdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r4_fdiff_3(A,B) <=> ( ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,k5_numbers) & r1_tarski(k1_rcomp_1(k6_xcmplx_0(B,C),B),k1_relset_1(k1_numbers,A)) ) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & v9_ordinal1(C) & v1_fdiff_1(C,k5_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v3_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k10_xtuple_0(D) = k1_tarski(B) & r1_tarski(k10_xtuple_0(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,D)),k1_relset_1(k1_numbers,A)) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ r1_xxreal_0(k5_numbers,k3_funct_2(k4_ordinal1,k1_numbers,C,E)) ) ) => v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,C),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,D),A),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,D,A)))) ) ) ) ) ) ) ) )).
fof(d4_ff_siec,axiom,( ! [A] : k4_ff_siec(A) = k1_ff_siec(k1_xboole_0,k1_tarski(A)) )).
fof(d4_fib_num2,axiom,( k4_fib_num2 = a_0_1_fib_num2 )).
fof(d4_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(d4_filter_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ! [F] : ! [G] : ! [H] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(d4_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k3_filter_2(A,B) = B ) ) )).
fof(d4_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v3_orders_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_hidden(B,k1_fin_topo(A,B)) ) ) ) )).
fof(d4_finance1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k5_finance1(A,B,C) = k1_funct_1(k3_series_1(k8_nat_1(k1_numbers,k3_finance1(B,C),1)),k6_xcmplx_0(A,1)) ) ) ) )).
fof(d4_finseq_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( m1_finseq_1(B,A) <=> r1_tarski(k10_xtuple_0(B),A) ) ) )).
fof(d4_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : k4_finseq_2(A,B) = a_2_0_finseq_2(A,B) ) )).
fof(d4_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : k4_finseq_4(A,B) = k1_funct_1(k14_finseq_1(k8_relat_1(A,k1_tarski(B))),1) ) )).
fof(d4_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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)) ) ) ) ) )).
fof(d4_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( 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) ) ) ) )).
fof(d4_finseqop,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => k6_finseqop(A,B,C) = k3_relat_1(k15_funct_3(B,C),A) ) ) ) )).
fof(d4_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) ) )).
fof(d4_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(u1_struct_0(A))))) ) => ( C = k4_fintopo3(A,B) <=> ( ! [D] : ( v7_ordinal1(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( E = k1_funct_1(C,D) => k3_funct_2(k4_ordinal1,k1_zfmisc_1(u1_struct_0(A)),C,k1_nat_1(D,1)) = k8_fin_topo(A,E) ) ) ) & k3_funct_2(k4_ordinal1,k1_zfmisc_1(u1_struct_0(A)),C,k5_numbers) = B ) ) ) ) ) )).
fof(d4_fintopo4,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k2_fintopo4(A) = g1_orders_2(k2_finseq_1(A),k1_fintopo4(A)) ) ) )).
fof(d4_fintopo5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( 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] : ( r2_hidden(D,k2_zfmisc_1(k2_finseq_1(A),k2_finseq_1(B))) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( 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))) ) ) ) ) ) ) ) ) )).
fof(d4_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( r1_fintopo6(A,B) <=> ( v4_fin_topo(B,A) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v4_fin_topo(C,A) & r1_tarski(B,C) ) => B = C ) ) ) ) ) ) )).
fof(d4_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ( B = k9_flang_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( m1_subset_1(D,A) & r2_hidden(D,A) & C = k5_afinsq_1(D) ) ) ) ) )).
fof(d4_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k1_fomodel0(A,B) <=> ( k9_xtuple_0(C) = k3_xboole_0(k9_xtuple_0(A),k9_xtuple_0(B)) & ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d4_fomodel1,axiom,( ! [A] : ( 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,k4_ordinal1)) ) )).
fof(d4_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( v1_fomodel2(C,A,B) <=> ( m3_fomodel2(C,A,B) & v1_funcop_1(C) ) ) ) ) ) )).
fof(d4_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k5_fomodel3(A,B) <=> ( k9_xtuple_0(C) = k37_fomodel1(A) & ! [D] : ( ( v9_fomodel1(D,A) & m1_subset_1(D,k1_fomodel1(A)) ) => k1_funct_1(C,D) = k4_fomodel3(A,D,B) ) ) ) ) ) )).
fof(d4_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( v3_fomodel4(B,A) <=> ( r1_tarski(B,k30_fomodel2(A)) & v1_finset_1(B) ) ) ) )).
fof(d4_frechet,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v2_frechet(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r1_frechet(A,B,C) ) ) ) ) )).
fof(d4_freealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( m1_freealg(B,A) <=> ! [C] : ( 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) ) ) ) ) ) )).
fof(d4_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : 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)))) )).
fof(d4_fscirc_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( 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] : ( m1_subset_1(F,k4_ordinal1) & A = k1_nat_1(F,1) & E = k1_fscirc_1(k1_funct_1(C,A),k1_funct_1(D,A),k3_fscirc_2(F,C,D)) ) ) ) ) ) ) ) ) )).
fof(d4_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ( r2_fsm_1(A,B,C,D) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & E = k1_funct_1(D,1) & k2_fsm_1(A,B,E,C) = D ) ) ) ) ) ) )).
fof(d4_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ( v3_fsm_2(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => v2_fsm_2(C,A,B) ) ) ) ) )).
fof(d4_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ v2_struct_0(C) & l1_fsm_3(C,A,B) ) => ! [D] : ( 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) ) ) ) ) )).
fof(d4_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k4_ftacell1(A,B,C,D,E) = k12_gfacirc1(A,B,C) )).
fof(d4_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : k4_funcop_1(A,B,C) = k3_relat_1(k13_funct_3(B,k2_funcop_1(k9_xtuple_0(B),C)),A) ) ) )).
fof(d4_funcsdom,axiom,( ! [A] : k8_funcsdom(A) = k8_funcop_1(k4_ordinal1,A,k5_numbers) )).
fof(d4_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) <=> ! [B] : ! [C] : ( ( 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 ) ) ) )).
fof(d4_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) ) )).
fof(d4_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k7_funct_3(A,B) <=> ( k9_xtuple_0(C) = k2_zfmisc_1(A,B) & ! [D] : ! [E] : ( ( r2_hidden(D,A) & r2_hidden(E,B) ) => k1_binop_1(C,D,E) = D ) ) ) ) )).
fof(d4_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k4_funct_4(A,B,C,D) = k1_funct_4(k16_funcop_1(A,C),k16_funcop_1(B,D)) )).
fof(d4_funct_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k4_funct_5(A) = k2_funct_4(k2_funct_5(A)) ) )).
fof(d4_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : k4_funct_6(A,B,C) = k1_binop_1(k2_funct_5(A),B,C) ) )).
fof(d4_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( C = k4_funct_7(A,B) <=> ( k3_finseq_1(C) = k1_nat_1(k3_finseq_1(A),1) & k1_funct_1(C,1) = B & ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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,k1_nat_1(D,1)) = k1_funct_1(E,k1_funct_1(C,D)) ) ) ) ) ) ) ) )).
fof(d4_functor0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,B) & v1_funct_1(E) & v1_partfun1(E,B) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) )).
fof(d4_functor2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( m2_functor0(C,A,B) => ! [D] : ( m2_functor0(D,A,B) => ( r1_functor2(A,B,C,D) => ! [E] : ( m1_functor2(E,A,B,C,D) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d4_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( 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] : ( m2_functor2(E,A,B,C,D) & ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d4_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( m1_subset_1(E,A) => k3_funct_2(A,k1_numbers,D,E) = k4_xxreal_0(k3_funct_2(A,k1_numbers,B,E),k3_funct_2(A,k1_numbers,C,E)) ) ) ) ) ) ) )).
fof(d4_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => k4_fuzzy_2(A,B) = k5_funct_3(k1_xboole_0,k2_zfmisc_1(A,B)) ) ) )).
fof(d4_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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 = k4_fuzzy_4(A,B) <=> ! [D] : ! [E] : ( r2_hidden(k4_tarski(D,E),k2_zfmisc_1(A,B)) => ( ( D = E => k1_binop_1(C,D,E) = 1 ) & ( D != E => k1_binop_1(C,D,E) = k5_numbers ) ) ) ) ) ) ) )).
fof(d4_fvaluat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( C = k5_numbers => ( D = k2_fvaluat1(A,B,C) <=> D = u1_struct_0(A) ) ) & ( C != k5_numbers => ( D = k2_fvaluat1(A,B,C) <=> ? [E] : ( 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] : ( v7_ordinal1(F) => ( ( r2_hidden(F,k4_finseq_1(E)) & r2_hidden(k2_xcmplx_0(F,1),k4_finseq_1(E)) ) => k1_funct_1(E,k2_xcmplx_0(F,1)) = k14_ideal_1(A,B,k7_partfun1(k1_zfmisc_1(u1_struct_0(A)),E,F)) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( 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)) ) ) )).
fof(d4_gate_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : 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) )).
fof(d4_gcd_1,axiom,( ! [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) & v1_vectsp_2(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_gcd_1(A,C,B) => ( C = k4_struct_0(A) | ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( D = k1_gcd_1(A,B,C) <=> k8_group_1(A,D,C) = B ) ) ) ) ) ) ) )).
fof(d4_genealg1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_finseq_1(B,k3_card_3(A)) => ! [C] : ( m2_finseq_1(C,k3_card_3(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => 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) ) ) ) ) ) ) )).
fof(d4_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [E] : ( v1_xreal_0(E) => ( E = k2_geomtrap(A,B,C,D) <=> ? [F] : ( v1_xreal_0(F) & D = k3_rlvect_1(A,k1_rlvect_1(A,B,E),k1_rlvect_1(A,C,F)) ) ) ) ) ) ) ) ) )).
fof(d4_gfacirc1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k1_funct_1(A,k10_finseq_1(B,C)) = k2_binarith(B,k9_margrel1(C)) ) ) ) ) )).
fof(d4_gfacirc2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d4_glib_000,axiom,( k4_glib_000 = 4 )).
fof(d4_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => k1_glib_001(A,B) = k12_finseq_1(k6_glib_000(A),B) ) ) )).
fof(d4_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( r1_glib_002(A,B) <=> ( v3_glib_002(A) & ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ? [D] : ( v2_glib_001(D,A) & m3_glib_001(D,A) & r1_glib_001(A,B,C,D) ) ) ) ) ) )).
fof(d4_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) ) => ( v1_glib_003(A) <=> ( r2_hidden(k2_glib_003,k1_relset_1(k4_ordinal1,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)) ) ) ) )).
fof(d4_glib_004,axiom,( k2_glib_004 = k10_domain_1(k4_ordinal1,k1_glib_000,k2_glib_000,k3_glib_000,k4_glib_000,k2_glib_003) )).
fof(d4_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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] : ! [D] : ( r2_glib_005(A,B,C,D) <=> ( r1_glib_005(A,B,C,D) & ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(d4_goboard1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( v2_goboard1(A) <=> ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k2_finseq_1(k1_matrix_0(A))) => v3_funct_1(k2_goboard1(k8_matrix_0(u1_struct_0(k15_euclid(2)),A,B))) ) ) ) ) )).
fof(d4_goboard5,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v1_goboard5(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(C,k1_nat_1(B,1)) & ~ ( ~ ( ~ r1_xxreal_0(B,1) & ~ r1_xxreal_0(k3_finseq_1(A),C) ) & r1_xxreal_0(k3_finseq_1(A),k1_nat_1(C,1)) ) & ~ r1_xboole_0(k2_topreal1(2,A,B),k2_topreal1(2,A,C)) ) ) ) ) ) )).
fof(d4_gobrd13,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(A)) & r1_goboard1(u1_struct_0(k15_euclid(2)),A,B) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( D = k5_gobrd13(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ~ ( r2_hidden(k4_tarski(E,F),k2_matrix_0(B)) & r2_hidden(k4_tarski(G,H),k2_matrix_0(B)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),B,E,F) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),B,G,H) & ~ ( E = G & k1_nat_1(F,1) = H & D = k3_goboard5(B,k7_nat_d(G,1),H) ) & ~ ( k1_nat_1(E,1) = G & F = H & D = k3_goboard5(B,G,H) ) & ~ ( E = k1_nat_1(G,1) & F = H & D = k3_goboard5(B,k7_nat_d(G,1),k7_nat_d(H,1)) ) & ~ ( E = G & F = k1_nat_1(H,1) & D = k3_goboard5(B,G,k7_nat_d(H,1)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v4_qc_lang2(B,A) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ( C = k2_goedelcp(A,B) <=> ? [D] : ( m1_subset_1(D,k9_qc_lang1(A)) & B = k5_qc_lang2(A,C,D) ) ) ) ) ) ) )).
fof(d4_gr_cy_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ! [B] : ( ( 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] : ( m1_subset_1(C,k7_card_1(A)) => ! [D] : ( m1_subset_1(D,k7_card_1(A)) => k5_binop_1(k7_card_1(A),B,C,D) = k4_nat_d(k2_xcmplx_0(C,D),A) ) ) ) ) ) ) )).
fof(d4_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( 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) ) ) )).
fof(d4_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v2_graph_2(A) <=> ! [B] : ( 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)) ) ) ) ) )).
fof(d4_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_graph_3(A,B) = k2_graph_3(A,B,u4_struct_0(A)) ) ) )).
fof(d4_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : k2_graph_4(A,B) = a_2_1_graph_4(A,B) ) )).
fof(d4_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v7_graph_1(D,A) & m2_graph_1(D,A) ) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(d4_graphsp,axiom,( ! [A] : ( 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] : ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) => ! [C] : ( v7_ordinal1(C) => ( ? [D] : ( m1_subset_1(D,k4_ordinal1) & k7_graphsp(k6_graphsp(k9_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] : ( m1_subset_1(D,k4_ordinal1) => ( D = k8_graphsp(A,B,C) <=> ( k7_graphsp(k6_graphsp(k9_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] : ( v7_ordinal1(E) => ( k7_graphsp(k6_graphsp(k9_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) ) ) ) ) ) ) ) ) ) )).
fof(d4_grcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(d4_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( r2_groeb_1(A,B,C,D,E) <=> ( k7_ideal_1(k12_polynom1(A,C),D) = E & v9_rewrite1(k3_polyred(A,B,C,D)) ) ) ) ) ) ) ) )).
fof(d4_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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) = k7_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))) ) ) ) ) ) )).
fof(d4_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => k5_groeb_3(A,B,C,D,E) = k2_groeb_3(A,C,D,k3_groeb_3(A,B,C,D,E)) ) ) ) ) ) )).
fof(d4_group_1,axiom,( ! [A] : ( l3_algstr_0(A) => ( v1_group_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B = k1_group_1(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k6_algstr_0(A,C,B) = C & k6_algstr_0(A,B,C) = C ) ) ) ) ) ) )).
fof(d4_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => k4_group_11(A,B,C) = a_3_3_group_11(A,B,C) ) ) ) )).
fof(d4_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(d4_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(d4_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v15_algstr_0(C) & m1_group_2(C,A) ) => ( C = k5_group_4(A,B) <=> ( r1_tarski(B,u1_struct_0(C)) & ! [D] : ( ( v15_algstr_0(D) & m1_group_2(D,A) ) => ( r1_tarski(B,u1_struct_0(D)) => m1_group_2(C,D) ) ) ) ) ) ) ) )).
fof(d4_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(d4_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(d4_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( 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)))) ) ) ) ) ) ) )).
fof(d4_hahnban,axiom,( ! [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) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( ~ r1_xxreal_0(D,k5_numbers) => k3_funct_2(u1_struct_0(A),k1_numbers,B,k1_rlvect_1(A,C,D)) = k3_xcmplx_0(D,k3_funct_2(u1_struct_0(A),k1_numbers,B,C)) ) ) ) ) ) ) )).
fof(d4_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d4_hallmar1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ( v1_hallmar1(B,A) <=> ! [C] : ( 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))) ) ) ) ) ) )).
fof(d4_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => k1_henmodel(A) = k3_qc_lang1(A) ) )).
fof(d4_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,k1_complfld) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => v1_hermitan(k7_bilinear(k1_complfld,A,B,C,D),B) ) ) ) ) ) )).
fof(d4_heyting1,axiom,( ! [A] : ! [B] : ( ( 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] : ( 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) ) ) ) )).
fof(d4_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(k5_substlat(A,B))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d4_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(k4_ordinal1,k6_domain_1(k4_ordinal1,B)))) => ( C = k4_heyting3(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ~ ( ! [E] : ( ( ~ v8_ordinal1(E) & m1_subset_1(E,k4_ordinal1) ) => ~ ( r1_xxreal_0(E,A) & D = k2_heyting3(E,B) ) ) & D != k3_heyting3(A,B) ) ) ) ) ) ) )).
fof(d4_hilbasis,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) )).
fof(d4_hurwitz,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k4_hurwitz(A,B,C) <=> ( ! [E] : ( v7_ordinal1(E) => ( ~ r1_xxreal_0(C,E) => k1_normsp_1(A,D,E) = k1_binop_1(k4_group_1(A),B,k6_xcmplx_0(k6_xcmplx_0(C,E),1)) ) ) & ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(C,E) => k1_normsp_1(A,D,E) = k4_struct_0(A) ) ) ) ) ) ) ) ) )).
fof(d4_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k4_idea_1(A,B,C) = k4_nat_d(k2_xcmplx_0(B,C),k5_series_1(2,A)) ) ) ) )).
fof(d4_incproj,axiom,( ! [A] : ( l1_incsp_1(A) => ( v1_incproj(A) <=> ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(d4_incsp_1,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_incsp_1(A))) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ( r4_incsp_1(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ( r2_hidden(D,B) => r1_incsp_1(A,D,C) ) ) ) ) ) ) )).
fof(d4_index_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_index_1(C,A,B) <=> ? [D] : ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) & ? [E] : ( v1_relat_1(E) & v4_relat_1(E,B) & v1_funct_1(E) & v1_partfun1(E,B) & C = k4_tarski(D,E) ) ) ) )).
fof(d4_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( 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))) ) ) ) )).
fof(d4_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( r2_int_1(A,B,C) <=> r1_int_1(C,k6_xcmplx_0(A,B)) ) ) ) ) )).
fof(d4_int_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_int_2(A) <=> ( ~ r1_xxreal_0(A,1) & ! [B] : ( v7_ordinal1(B) => ~ ( r1_int_1(B,A) & B != 1 & B != A ) ) ) ) ) )).
fof(d4_int_6,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( v7_ordinal1(C) => ~ ( r2_hidden(C,k4_finseq_1(B)) & ! [D] : ( v1_int_1(D) => ! [E] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(d4_int_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => k3_int_7(A) = g3_algstr_0(k1_int_7(A),k2_int_7(A)) ) )).
fof(d4_integr10,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r2_integr10(A,B,C) => ! [D] : ( v1_xreal_0(D) => ( D = k2_integr10(A,B,C) <=> ? [E] : ( 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] : ( v1_xreal_0(F) => ( r2_hidden(F,k1_relset_1(k1_numbers,E)) => k1_funct_1(E,F) = k4_integra5(F,C,A) ) ) & r4_limfunc2(E,B) & D = k2_limfunc2(E,B) ) ) ) ) ) ) ) )).
fof(d4_integr15,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_integra1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) ) => ! [D] : ( m2_integr15(D,A,B,C) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( E = k3_integr15(A,B,C,D) <=> ! [F] : ( m1_subset_1(F,k4_ordinal1) => k3_funct_2(k4_ordinal1,k1_numbers,E,F) = k1_integr15(A,B,k2_integra2(A,C,F),k2_integr15(A,B,C,D,F)) ) ) ) ) ) ) ) )).
fof(d4_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_integra1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(B)))) ) => ! [E] : ( m2_integr18(E,A,B,C,D) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( F = k3_integr18(A,B,C,D,E) <=> ! [G] : ( v7_ordinal1(G) => k1_normsp_1(A,F,G) = k1_integr18(A,B,C,k2_integra2(B,D,G),k2_integr18(A,B,C,D,E,G)) ) ) ) ) ) ) ) ) )).
fof(d4_integr1c,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [B] : ( ( 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] : ( v1_xcmplx_0(C) => ( C = k3_integr1c(A,B) <=> ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [G] : ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_integra1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => k3_integra1(A) = k6_xcmplx_0(k2_seq_4(A),k3_seq_4(A)) ) )).
fof(d4_integra5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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) = k4_xcmplx_0(k2_integra5(k3_integra5(B,A),C)) ) ) ) ) ) )).
fof(d4_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_interva1(C,A) ) => k4_interva1(A,B,C) = k2_setfam_1(B,C) ) ) ) )).
fof(d4_irrat_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( A = k4_irrat_1 <=> ! [B] : ( v7_ordinal1(B) => k1_funct_1(A,B) = k2_power(k2_xcmplx_0(1,k7_xcmplx_0(1,B)),B) ) ) ) )).
fof(d4_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & 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] : ( m2_cat_1(C,A,B) & v12_cat_1(C,A,B) ) ) ) ) )).
fof(d4_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,k6_cat_2(A,B),C) => ! [E] : ( m2_cat_1(E,A,k9_nattra_1(B,C)) => ( E = k5_isocat_2(A,B,C,D) <=> ! [F] : ( m1_subset_1(F,u4_struct_0(A)) => k3_funct_2(u4_struct_0(A),u4_struct_0(k9_nattra_1(B,C)),E,F) = k4_tarski(k4_tarski(k10_cat_2(A,B,C,D,k3_graph_1(A,F)),k10_cat_2(A,B,C,D,k4_graph_1(A,F))),k4_isocat_2(A,B,C,D,F)) ) ) ) ) ) ) ) )).
fof(d4_isomichi,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)) ) ) )).
fof(d4_jgraph_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(A))) => ( v1_jgraph_1(B,A) <=> ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( ~ 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,k1_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,k1_nat_1(C,1))) & ( k1_funct_1(B,k1_nat_1(C,1)) = k1_funct_1(B,D) | k1_funct_1(B,k1_nat_1(C,1)) = k1_funct_1(B,k1_nat_1(D,1)) ) ) & k2_topreal1(A,B,C) != k2_topreal1(A,B,D) ) ) ) ) ) ) )).
fof(d4_jordan19,axiom,( ! [A] : ( ( 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)) ) )).
fof(d4_jordan20,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ( r4_jordan20(A,B,C,D,E) <=> ( r1_topreal1(k15_euclid(2),B,C,A) & r2_hidden(D,A) & k17_euclid(D) = E & ? [F] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_jordan24,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) ) )).
fof(d4_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) )).
fof(d4_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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) ) ) ) ) )).
fof(d4_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r3_jordan4(A,B,C,D) <=> ( r1_jordan4(A,B,C,D) | r2_jordan4(A,B,C,D) ) ) ) ) ) ) )).
fof(d4_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( B = k4_jordan5d(A) <=> ( r2_hidden(k4_tarski(k3_finseq_1(k2_goboard2(A)),B),k2_matrix_0(k2_goboard2(A))) & k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k3_finseq_1(k2_goboard2(A)),B) = k22_pscomp_1(k3_topreal1(2,A)) ) ) ) ) )).
fof(d4_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => k4_jordan6(A,B,C,D) = a_4_1_jordan6(A,B,C,D) ) ) ) ) )).
fof(d4_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(d4_kurato_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)))))))) ) ) )).
fof(d4_lang1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => ! [B] : ( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ! [C] : ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ( r2_lang1(A,B,C) <=> ? [D] : ( m2_finseq_2(D,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) & ? [E] : ( m2_finseq_2(E,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) & ? [F] : ( m2_finseq_2(F,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & r2_relset_1(k4_ordinal1,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(k4_ordinal1,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) ) ) ) ) ) ) ) ) )).
fof(d4_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(D),C,C) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(D))) ) => k5_laplace(A,B,C,D,E) = k12_matrix_3(k7_nat_d(C,1),D,k2_laplace(A,B,C,D,E)) ) ) ) ) ) )).
fof(d4_lattice2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( m1_subset_1(C,k5_finsub_1(A)) => ! [D] : ( ( 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) ) ) ) ) )).
fof(d4_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_lattice3(A))) => k5_lattice3(A,B) = B ) ) )).
fof(d4_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(d4_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_yellow_0(B,k1_lattice5(A)) & v6_yellow_0(B,k1_lattice5(A)) & m1_yellow_0(B,k1_lattice5(A)) ) => ~ ( ? [C] : ( 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] : ( m1_subset_1(C,k4_ordinal1) & ! [D] : ( ( 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] : ( ( 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] : ! [G] : ~ ( 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] : ( ( ~ v1_xboole_0(H) & m2_finseq_1(H,A) ) => ~ ( k3_finseq_1(H) = C & r1_lattice5(A,H,F,G,D,E) ) ) ) ) ) ) & ~ ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( C = k2_lattice5(A,B) <=> ( ! [D] : ( ( 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] : ( ( 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] : ! [G] : ~ ( 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] : ( ( ~ v1_xboole_0(H) & m2_finseq_1(H,A) ) => ~ ( k3_finseq_1(H) = k1_nat_1(C,2) & r1_lattice5(A,H,F,G,D,E) ) ) ) ) ) & ? [D] : ( 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] : ( 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] : ? [G] : ( 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] : ( ( ~ v1_xboole_0(H) & m2_finseq_1(H,A) ) => ~ ( k3_finseq_1(H) = k1_nat_1(C,1) & r1_lattice5(A,H,F,G,D,E) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( v2_lattice6(A) <=> v1_wellfnd1(k7_lattice3(k3_lattice3(A))) ) ) )).
fof(d4_lattice7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_lattice7(A,B,C) <=> ( r2_orders_2(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_orders_2(A,B,D) & r2_orders_2(A,D,C) ) ) ) ) ) ) ) )).
fof(d4_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,k4_zfmisc_1(A,A,u1_struct_0(B),u1_struct_0(B))) => ! [E] : ( ( 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] : ( m1_subset_1(F,A) => ! [G] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d4_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_lattices(A) ) => ( v4_lattices(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_lattices(A,B,C) = k1_lattices(A,C,B) ) ) ) ) )).
fof(d4_lexbfs,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k15_pre_poly(A))) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(d4_lfuzzy_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k4_lfuzzy_0(A) = k5_yellow_1(A,k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1))) ) )).
fof(d4_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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,k1_fuzzy_4(A,A,B),B) ) ) ) )).
fof(d4_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_limfunc1(A) <=> ! [B] : ( v1_xreal_0(B) => ? [C] : ( v7_ordinal1(C) & ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(C,D) & r1_xxreal_0(k1_funct_1(A,D),B) ) ) ) ) ) ) )).
fof(d4_limfunc2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r4_limfunc2(A,B) <=> ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,B) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(C,D) & ~ r1_xxreal_0(D,B) & r2_hidden(D,k1_relset_1(k1_numbers,A)) ) ) ) ) & ? [C] : ( v1_xreal_0(C) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(D) & k1_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(k4_ordinal1,k1_numbers,k1_numbers,D,A)) & k1_seq_2(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,D,A)) = C ) ) ) ) ) ) ) ) )).
fof(d4_limfunc3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r1_limfunc3(A,B) => ! [C] : ( v1_xreal_0(C) => ( C = k1_limfunc3(A,B) <=> ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(D) & k1_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(k4_ordinal1,k1_numbers,k1_numbers,D,A)) & k1_seq_2(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,D,A)) = C ) ) ) ) ) ) ) ) )).
fof(d4_lopban_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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)) ) ) )).
fof(d4_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( 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] : ( m2_subset_1(C,u1_struct_0(k8_lopban_1(A,A)),k10_lopban_1(A,A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d4_lopban_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v4_vectsp_1(A) & l4_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v25_algstr_0(B,A) <=> ? [C] : ( 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) ) ) ) ) )).
fof(d4_lopban_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( B = k3_lopban_4(A) <=> ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(C,A) => k9_nat_1(k1_numbers,B,C) = k7_xcmplx_0(1,k3_xcmplx_0(k2_newton(C),k2_newton(k7_nat_d(A,C)))) ) & ( ~ r1_xxreal_0(C,A) => k9_nat_1(k1_numbers,B,C) = k5_numbers ) ) ) ) ) ) )).
fof(d4_lopban_7,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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)))) ) => k5_lopban_7(A,B,C) = g1_normsp_1(k3_lopban_7(A,B,C),k9_rsspace(k7_prvect_3(A,B),k3_lopban_7(A,B,C)),k7_rsspace(k7_prvect_3(A,B),k3_lopban_7(A,B,C)),k8_rsspace(k7_prvect_3(A,B),k3_lopban_7(A,B,C)),k4_lopban_7(A,B,C)) ) ) ) )).
fof(d4_lopclset,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d4_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(k2_numbers,k3_rfunct_3(A,k2_numbers)),k3_rfunct_3(A,k2_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_numbers,k3_rfunct_3(A,k2_numbers)),k3_rfunct_3(A,k2_numbers)))) ) => ( B = k8_lpspacc1(A) <=> ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( m2_rfunct_3(D,A,k2_numbers,k3_rfunct_3(A,k2_numbers)) => k1_binop_1(B,C,D) = k5_lpspacc1(A,k2_numbers,D,C) ) ) ) ) ) )).
fof(d4_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( m2_rfunct_3(D,A,k1_numbers,k3_rfunct_3(A,k1_numbers)) => k1_binop_1(B,C,D) = k12_rfunct_3(A,k1_numbers,D,C) ) ) ) ) ) )).
fof(d4_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v2_xxreal_0(D) & v1_xreal_0(D) ) => k3_lpspace2(A,B,C,D) = a_4_1_lpspace2(A,B,C,D) ) ) ) ) )).
fof(d4_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => k4_ltlaxio1(A,B) = k1_ltlaxio1(k3_hilbert1(A,k1_ltlaxio1(B))) ) ) )).
fof(d4_ltlaxio2,axiom,( ! [A] : ( m2_finseq_1(A,k1_hilbert1) => ! [B] : ( m2_finseq_1(B,k1_hilbert1) => ( B = k4_ltlaxio2(A) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(A)) ) => k1_funct_1(B,C) = k1_ltlaxio1(k7_partfun1(k1_hilbert1,A,C)) ) ) ) ) ) ) )).
fof(d4_ltlaxio3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k1_hilbert1,k9_setfam_1(k1_hilbert1)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_hilbert1,k9_setfam_1(k1_hilbert1)))) ) => ( A = k4_ltlaxio3 <=> ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),A,k2_hilbert1) = k6_domain_1(k1_hilbert1,k2_hilbert1) & k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),A,k1_hilbert2(D)) = k6_domain_1(k1_hilbert1,k1_hilbert2(D)) & k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),A,k3_hilbert1(B,C)) = k4_subset_1(k1_hilbert1,k4_subset_1(k1_hilbert1,k6_domain_1(k1_hilbert1,k3_hilbert1(B,C)),k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),A,B)),k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),A,C)) & k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),A,k4_hilbert1(B,C)) = k6_domain_1(k1_hilbert1,k4_hilbert1(B,C)) ) ) ) ) ) ) )).
fof(d4_ltlaxio4,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) ) => k4_ltlaxio4(A) = a_1_1_ltlaxio4(A) ) )).
fof(d4_margrel1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v3_finseq_1(B) & v2_card_3(B) ) => ( m1_margrel1(B,A) <=> ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(C,B) => k3_finseq_1(C) = A ) ) ) ) ) )).
fof(d4_mathmorp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(d4_matrix10,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( v4_matrix10(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k4_tarski(B,C),k2_matrix_0(A)) => r1_xxreal_0(k5_numbers,k3_matrix_0(k1_numbers,A,B,C)) ) ) ) ) ) )).
fof(d4_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( ( v1_matrix_0(E) & v2_matrix_0(E,C,A,B) & m2_finseq_1(E,k3_finseq_2(C)) ) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,C,A,B) & m2_finseq_1(F,k3_finseq_2(C)) ) => ( F = k4_matrix11(A,B,C,D,E) <=> ( k3_finseq_1(F) = k3_finseq_1(E) & k1_matrix_0(F) = k1_matrix_0(E) & ! [G] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ! [I] : ( v7_ordinal1(I) => ( ( r2_hidden(k4_tarski(G,H),k2_matrix_0(E)) & k1_funct_1(D,G) = I ) => k3_matrix_0(C,F,G,H) = k3_matrix_0(C,E,I,H) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( ( r2_hidden(E,k2_finseq_1(k1_matrix_0(D))) & r2_hidden(F,k2_finseq_1(k1_matrix_0(D))) ) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(B,k5_numbers) | ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(C),A,B) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(C))) ) => ( G = k4_matrix12(A,B,C,D,E,F) <=> ( k3_finseq_1(G) = k3_finseq_1(D) & ! [H] : ( v7_ordinal1(H) => ! [I] : ( v7_ordinal1(I) => ( ( r2_hidden(H,k4_finseq_1(D)) & r2_hidden(I,k2_finseq_1(k1_matrix_0(D))) ) => ( ( I = E => k3_matrix_0(u1_struct_0(C),G,H,I) = k3_matrix_0(u1_struct_0(C),D,H,F) ) & ( I = F => k3_matrix_0(u1_struct_0(C),G,H,I) = k3_matrix_0(u1_struct_0(C),D,H,E) ) & ~ ( I != E & I != F & k3_matrix_0(u1_struct_0(C),G,H,I) != k3_matrix_0(u1_struct_0(C),D,H,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_matrix13,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( C = k8_matrix13(A,B) <=> ( ? [D] : ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) & ? [E] : ( v1_finset_1(E) & v1_setfam_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) & r1_tarski(k2_zfmisc_1(D,E),k2_matrix_0(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] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ! [E] : ( ( v1_finset_1(E) & v1_setfam_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ( ( r1_tarski(k2_zfmisc_1(D,E),k2_matrix_0(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) ) ) ) ) ) ) ) ) ) )).
fof(d4_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => k5_matrix15(A,B,C) = a_3_2_matrix15(A,B,C) ) ) ) )).
fof(d4_matrix16,axiom,( ! [A] : ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( ( 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] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(D,E),k2_matrix_0(B)) => k3_matrix_0(A,B,D,E) = k1_funct_1(C,k2_xcmplx_0(k5_int_1(k6_xcmplx_0(D,E),k3_finseq_1(C)),1)) ) ) ) ) ) ) ) )).
fof(d4_matrix17,axiom,( ! [A] : ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r1_matrix17(A,B,C) <=> ( k3_finseq_1(C) = k1_matrix_0(B) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(D,E),k2_matrix_0(B)) => ( k2_xcmplx_0(D,E) = k2_xcmplx_0(k3_finseq_1(C),1) | k3_matrix_0(A,B,D,E) = k1_funct_1(C,k5_int_1(k6_xcmplx_0(k2_xcmplx_0(D,E),1),k3_finseq_1(C))) ) ) ) ) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(k4_tarski(D,E),k2_matrix_0(B)) & k2_xcmplx_0(D,E) = k2_xcmplx_0(k3_finseq_1(C),1) ) => k3_matrix_0(A,B,D,E) = k1_funct_1(C,k3_finseq_1(C)) ) ) ) ) ) ) ) )).
fof(d4_matrix_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_matrix_0(A) ) => k2_matrix_0(A) = k2_zfmisc_1(k4_finseq_1(A),k2_finseq_1(k1_matrix_0(A))) ) )).
fof(d4_matrix_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(A),B,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(A),B,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ( D = k4_matrix_1(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( r2_hidden(k4_tarski(E,F),k2_matrix_0(C)) => k3_matrix_0(u1_struct_0(A),D,E,F) = k4_algstr_0(A,k3_matrix_0(u1_struct_0(A),C,E,F)) ) ) ) ) ) ) ) ) )).
fof(d4_matrix_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_matrix_2(A) ) => ! [B] : ( v7_ordinal1(B) => ( B = k1_matrix_2(A) <=> ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & r2_hidden(C,A) & B = k3_finseq_1(C) ) ) ) ) )).
fof(d4_matrix_3,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( k1_matrix_0(B) = k3_finseq_1(C) => ! [D] : ( ( v1_matrix_0(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_0(D) = k1_matrix_0(C) & ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( r2_hidden(k4_tarski(E,F),k2_matrix_0(D)) => k3_matrix_0(u1_struct_0(A),D,E,F) = k13_fvsum_1(A,k7_matrix_0(u1_struct_0(A),B,E),k8_matrix_0(u1_struct_0(A),C,F)) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(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))) ) )).
fof(d4_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v1_matrix_6(C,A,B) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( D = k1_matrix_6(A,B,C) <=> r2_matrix_6(A,B,D,C) ) ) ) ) ) ) )).
fof(d4_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v4_matrix_8(C,A,B) <=> ( v1_matrix_6(C,A,B) & k1_matrix_6(A,B,C) = C ) ) ) ) ) )).
fof(d4_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrixj1(B,A) & m2_finseq_1(B,k3_finseq_2(k3_finseq_2(A))) ) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( C = k9_matrixj1(A,B) <=> ( k4_finseq_1(C) = k4_finseq_1(B) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(C)) => k1_funct_1(C,D) = k1_matrix_0(k2_matrixj1(A,B,D)) ) ) ) ) ) ) ) )).
fof(d4_matrixj2,axiom,( ! [A] : ( l6_algstr_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( v7_ordinal1(D) & ! [E] : ( 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) ) ) ) ) ) ) )).
fof(d4_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => k4_matrixr1(A) = k2_matrixr1(k2_matrix_3(k2_vectsp_1,k1_matrixr1(A))) ) )).
fof(d4_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k6_matrixr2(A,B) = k2_funct_7(k4_ordinal1,k5_finseq_2(k4_ordinal1,A,k5_numbers),B,1) ) ) )).
fof(d4_matrlin,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d4_matroid0,axiom,( ! [A] : ( l1_pre_topc(A) => ( v2_matroid0(A) <=> ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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) = k1_nat_1(k5_card_1(B),1) & ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(d4_matrprob,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(C) & k3_finseq_1(B) = k1_matrix_0(C) ) => ! [D] : ( ( v1_matrix_0(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_0(D) = k3_finseq_1(B) & ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( r2_hidden(k4_tarski(E,F),k2_matrix_0(C)) => k3_matrix_0(k1_numbers,D,E,F) = k3_xcmplx_0(k3_xcmplx_0(k1_funct_1(A,E),k3_matrix_0(k1_numbers,C,E,F)),k1_funct_1(B,F)) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(d4_mazurulm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d4_mcart_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) => ! [F] : ( m1_subset_1(F,A) => ( F = k4_mcart_1(A,B,C,D,E) <=> ! [G] : ! [H] : ! [I] : ! [J] : ( E = k6_xtuple_0(G,H,I,J) => F = G ) ) ) ) ) ) ) ) )).
fof(d4_measure1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( m1_measure1(D,A,B,C) <=> k12_supinf_2(C,D) = k1_supinf_2 ) ) ) ) )).
fof(d4_measure3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),k2_measure3(A,B,C)) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ( E = k3_measure3(A,B,C,D) <=> ! [F] : ( r2_hidden(F,E) <=> ( r2_hidden(F,B) & r1_tarski(F,D) & m1_measure3(k7_subset_1(A,D,F),A,B,C) ) ) ) ) ) ) ) )).
fof(d4_measure5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v3_measure5(A) <=> ? [B] : ( v1_xreal_0(B) & ? [C] : ( m1_subset_1(C,k6_numbers) & A = k3_rcomp_1(B,C) ) ) ) ) )).
fof(d4_measure6,axiom,( ! [A] : ( v3_membered(A) => ( v1_xxreal_2(A) <=> ( v3_xxreal_2(A) & r2_hidden(k3_seq_4(A),A) ) ) ) )).
fof(d4_measure7,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( m1_measure7(B,A) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( C = k3_measure7(A,B) <=> ! [D] : ( m1_subset_1(D,k4_ordinal1) => k12_supinf_2(C,D) = k2_measure5(k2_measure7(A,B,D)) ) ) ) ) ) )).
fof(d4_member_1,axiom,( ! [A] : ( v1_membered(A) => k7_member_1(A) = a_1_3_member_1(A) ) )).
fof(d4_membered,axiom,( ! [A] : ( v4_membered(A) <=> ! [B] : ( r2_hidden(B,A) => v1_rat_1(B) ) ) )).
fof(d4_mesfun6c,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,B) => ( r2_hidden(E,k1_relset_1(B,D)) => k12_supinf_2(D,E) = k2_power(k12_supinf_2(C,E),A) ) ) ) ) ) ) ) ) )).
fof(d4_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => k4_mesfun7c(A,B) = k3_mesfunc8(A,k1_mesfun7c(A,B)) ) ) )).
fof(d4_mesfun9c,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( v1_mesfun9c(B,A) <=> ? [C] : ( v1_xreal_0(C) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,k1_relset_1(A,k4_mesfunc5(A,k1_numbers,B,k5_numbers))) => r1_xxreal_0(k9_complex1(k1_mesfunc9(k4_mesfunc5(A,k1_numbers,B,D),E)),C) ) ) ) ) ) ) )).
fof(d4_mesfunc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k6_numbers) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,k6_numbers) & v1_funct_1(C) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d4_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( r1_mesfunc2(A,B,C) <=> ( v3_valued_0(C) & ? [D] : ( v1_prob_2(D) & m2_finseq_1(D,B) & k1_relset_1(A,C) = k3_tarski(k2_relset_1(B,D)) & ! [E] : ( v7_ordinal1(E) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_mesfunc5,axiom,( ! [A] : ( v1_relat_1(A) => ( v4_mesfunc5(A) <=> ~ r2_hidden(k1_supinf_1,k10_xtuple_0(A)) ) ) )).
fof(d4_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(d4_mesfunc7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( D = k5_mesfunc7(A,B,C) <=> ( k1_relset_1(B,D) = k1_relset_1(B,C) & ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d4_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( C = k2_mesfunc8(A,B) <=> ( k1_relset_1(A,C) = k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers)) & ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(d4_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ( C = k4_mesfunc9(A,B) <=> ( r2_relset_1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,C,k5_numbers),k4_mesfunc5(A,k6_numbers,B,k5_numbers)) & ! [D] : ( v7_ordinal1(D) => r2_relset_1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,C,k1_nat_1(D,1)),k3_mesfunc1(A,k4_mesfunc5(A,k6_numbers,C,D),k4_mesfunc5(A,k6_numbers,B,k1_nat_1(D,1)))) ) ) ) ) ) ) )).
fof(d4_metric_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => k1_binop_1(B,C,D) = k1_binop_1(B,D,C) ) ) ) ) )).
fof(d4_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => k2_metric_2(A) = a_1_0_metric_2(A) ) )).
fof(d4_metric_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ! [I] : ( m1_subset_1(I,u1_struct_0(C)) => ! [J] : ( m1_subset_1(J,u1_struct_0(C)) => ! [K] : ( m1_subset_1(K,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C))) => ! [L] : ( 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) ) => k2_binop_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,K,L) = k2_xcmplx_0(k2_xcmplx_0(k3_metric_1(A,E,F),k3_metric_1(B,G,H)),k3_metric_1(C,I,J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_metric_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_metric_6(B,A) <=> ? [C] : ( v1_xreal_0(C) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ~ r1_xxreal_0(C,k5_numbers) & r1_tarski(k10_xtuple_0(B),k8_metric_1(A,D,C)) ) ) ) ) ) )).
fof(d4_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( v2_mfold_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ? [D] : ( m1_connsp_2(D,B,C) & ? [E] : ( 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) ) ) ) ) ) ) )).
fof(d4_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => k4_mfold_2(A) = k8_toprealb(k2_xcmplx_0(A,1)) ) )).
fof(d4_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(d4_midsp_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r1_midsp_2(A,B,C) => ! [F] : ( 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 ) ) ) ) ) ) ) ) )).
fof(d4_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v2_struct_0(C) & v2_midsp_1(C) & l1_midsp_3(C,k1_nat_1(A,2)) ) => ( r1_midsp_3(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(C))) => k4_midsp_3(A,C,D,k6_midsp_3(A,C,E,B,D)) = D ) ) ) ) ) ) )).
fof(d4_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k4_mmlquery(A,B,C) = a_3_1_mmlquery(A,B,C) ) ) )).
fof(d4_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( l1_mod_2(B,A) => k3_mod_2(A,B) = u2_mod_2(A,B) ) ) )).
fof(d4_mod_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( m1_mod_3(C,A,B) <=> v1_mod_3(C,A,B) ) ) ) ) )).
fof(d4_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_2(B,A) ) => ! [C] : ( ( v7_vectsp_1(C,k2_mod_4(A)) & l1_vectsp_1(C,k2_mod_4(A)) ) => ( C = k5_mod_4(A,B) <=> ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(d4_modal_1,axiom,( k4_modal_1 = k2_zfmisc_1(k8_domain_1(k4_ordinal1,k5_numbers,1,2),k4_ordinal1) )).
fof(d4_modelc_1,axiom,( ! [A] : ( ( v1_xboolean(A) => k4_modelc_1(A) = A ) & ( ~ v1_xboolean(A) => k4_modelc_1(A) = k7_margrel1 ) ) )).
fof(d4_modelc_2,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => k4_modelc_2(A,B) = k8_finseq_1(k4_ordinal1,k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,1),A),B) ) ) )).
fof(d4_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( l1_modelc_3(B,A) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ( r2_hidden(C,u2_modelc_3(A,B)) => ! [D] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(d4_moebius1,axiom,( ! [A] : ( v7_ordinal1(A) => k3_moebius1(A) = a_1_0_moebius1(A) ) )).
fof(d4_monoid_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ? [E] : ( m1_subset_1(E,A) & k5_binop_1(A,B,C,E) = D ) ) ) ) ) ) )).
fof(d4_monoid_1,axiom,( ! [A] : k13_monoid_1(A) = k12_monoid_1(k5_monoid_0,A) )).
fof(d4_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(d4_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ( v1_msafree2(A) <=> k2_msafree2(A) != k1_xboole_0 ) ) )).
fof(d4_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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) ) ) ) )).
fof(d4_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( l3_msualg_1(C,A) => ( v4_msafree4(C,A,B) <=> ? [D] : ( v4_msualg_1(D,A) & l3_msualg_1(D,A) & ? [E] : ( m2_pboole(E,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,D)) & r1_msualg_3(A,B,D,E) & g3_msualg_1(A,u3_msualg_1(A,C),u4_msualg_1(A,C)) = k6_msualg_3(A,B,D,E) ) ) ) ) ) ) )).
fof(d4_msalimit,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_msalimit(C,A,B) => ! [D] : ( m2_msalimit(D,A,B,C) => ( v1_msalimit(D,A,B,C) <=> ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(d4_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(C,D)) => k5_msaterm(A,B,C,D,E) = k1_trees_4(k4_tarski(E,D)) ) ) ) ) ) )).
fof(d4_msinst_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,k2_msinst_1(A,B)) => ! [E] : ( 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) & v1_funcop_1(G) ) => ! [H] : ( ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_msscyc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ( v3_msscyc_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,k4_ordinal1) & ! [D] : ( ( v7_graph_1(D,A) & m1_graph_1(D,A) ) => ( k1_funct_1(k7_graph_2(A,D),k1_nat_1(k3_finseq_1(D),1)) = B => ( v1_xboole_0(D) | r1_xxreal_0(k3_finseq_1(D),C) ) ) ) ) ) ) ) )).
fof(d4_msscyc_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d4_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) => ( v3_mssubfam(C,A,B) <=> ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(d4_msualg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d4_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m3_pboole(C,u1_struct_0(A),u3_msualg_1(A,B)) => ( C = k2_msualg_2(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_funct_1(C,D) = k1_msualg_2(A,B,D) ) ) ) ) ) )).
fof(d4_msualg_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,C) => ( ( v1_msualg_3(D) & v2_msualg_3(D,A,B,C) ) => ! [E] : ( m2_pboole(E,A,C,B) => ( E = k4_msualg_3(A,B,C,D) <=> ! [F] : ( r2_hidden(F,A) => k1_funct_1(E,F) = k2_funct_1(k1_funct_1(D,F)) ) ) ) ) ) ) ) )).
fof(d4_msualg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( m1_subset_1(E,k3_msualg_1(A,D,B)) => ! [F] : ( m1_subset_1(F,k3_msualg_1(A,D,B)) => ( ! [G] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(d4_msualg_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_msualg_4(C,A,B) & m1_msualg_4(C,A,B,B) ) => ! [D] : ( ( v1_msualg_4(D,A,B) & m1_msualg_4(D,A,B,B) ) => ! [E] : ( ( v1_msualg_4(E,A,B) & m1_msualg_4(E,A,B,B) ) => ( E = k4_msualg_5(A,B,C,D) <=> ? [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(d4_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( l3_msualg_1(D,A) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ! [F] : ( ( 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] : ( 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),k1_funct_7(E,C,G)) ) ) ) ) ) ) ) ) ) )).
fof(d4_msualg_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => ! [C] : ( ( ~ 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)) ) ) ) ) ) ) )).
fof(d4_nat_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v3_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v3_valued_0(C) ) => ! [D] : ( ( 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] : ( ( r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(C,E)) => k1_funct_1(D,E) = k1_funct_1(C,E) ) & ( ~ r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(C,E)) => k1_funct_1(D,E) = k1_funct_1(B,E) ) ) ) ) ) ) )).
fof(d4_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => k5_nat_5(A) = k3_nat_5(1,A) ) )).
fof(d4_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( C = k2_int_2(A,B) <=> ( r1_nat_d(A,C) & r1_nat_d(B,C) & ! [D] : ( v7_ordinal1(D) => ( ( r1_nat_d(A,D) & r1_nat_d(B,D) ) => r1_nat_d(C,D) ) ) ) ) ) ) ) )).
fof(d4_nat_lat,axiom,( k4_nat_lat = 1 )).
fof(d4_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ( r1_nattra_1(A,B,C,D) => ! [E] : ( m1_nattra_1(E,A,B,C,D) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => k2_nattra_1(A,B,C,D,E,F) = k3_funct_2(u1_struct_0(A),u4_struct_0(B),E,F) ) ) ) ) ) ) ) )).
fof(d4_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ~ ( r2_hidden(F,A) & r2_hidden(G,A) & ~ r1_xxreal_0(E,k2_normsp_0(B,k5_algstr_0(B,F,G))) & r1_xxreal_0(D,k9_complex1(k6_xcmplx_0(k7_partfun1(k2_numbers,C,F),k7_partfun1(k2_numbers,C,G)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_ndiff_1(C,A,B) <=> ( v3_normsp_1(C,A) & k6_normsp_1(A,C) = B ) ) ) ) ) )).
fof(d4_ndiff_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_ndiff_2(A,B,C,D,E) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( F = k3_ndiff_2(A,B,C,D,E) <=> ? [G] : ( m1_nfcont_1(G,A,D) & r1_tarski(G,k1_relset_1(u1_struct_0(A),C)) & ! [H] : ( v1_xreal_0(H) => ~ ( ~ r1_xxreal_0(H,k5_numbers) & ! [I] : ( v1_xreal_0(I) => ~ ( ~ r1_xxreal_0(I,k5_numbers) & ! [J] : ( v1_xreal_0(J) => ~ ( ~ r1_xxreal_0(I,k9_complex1(J)) & J != k5_numbers & r2_hidden(k3_rlvect_1(A,k1_rlvect_1(A,E,J),D),G) & r1_xxreal_0(H,k2_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)),k5_xcmplx_0(J)),F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [C] : ( v1_xreal_0(C) => ( r1_ndiff_3(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( D = k1_ndiff_3(A,B,C) <=> ? [E] : ( m1_rcomp_1(E,C) & r1_tarski(E,k1_relset_1(k1_numbers,B)) & ? [F] : ( 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] : ( 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 = k10_funct_2(k1_numbers,u1_struct_0(A),F,1) & ! [H] : ( v1_xreal_0(H) => ( 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,k10_funct_2(k1_numbers,u1_struct_0(A),F,k6_xcmplx_0(H,C)),k7_partfun1(u1_struct_0(A),G,k6_xcmplx_0(H,C))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [C] : ( r2_ndiff_4(A,B,C) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(D,E) = k1_ndiff_4(A,B,E) ) ) ) ) ) ) ) ) )).
fof(d4_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_prvect_2(A))) => ! [D] : ( ( 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] : ( 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) = k1_funct_7(C,B,E) ) ) ) ) ) ) )).
fof(d4_neckla_2,axiom,( ! [A] : ( A = k3_neckla_2 <=> ! [B] : ( r2_hidden(B,A) <=> ? [C] : ( v1_orders_2(C) & l1_orders_2(C) & B = C & r2_hidden(u1_struct_0(C),k13_classes2) ) ) ) )).
fof(d4_necklace,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_necklace(A) <=> v5_relat_2(u1_orders_2(A)) ) ) )).
fof(d4_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : ! [C] : ( r1_net_1(A,B,C) <=> ( r2_hidden(k4_tarski(C,B),k1_net_1(A)) & r2_hidden(B,u4_struct_0(A)) ) ) ) )).
fof(d4_newton,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ( D = k5_newton(A,B,C) <=> ( k3_finseq_1(D) = k1_nat_1(C,1) & ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ( ( r2_hidden(E,k4_finseq_1(D)) & G = k6_xcmplx_0(E,1) & F = k6_xcmplx_0(C,G) ) => k1_funct_1(D,E) = k3_xcmplx_0(k3_xcmplx_0(k4_newton(G,C),k1_newton(A,F)),k1_newton(B,G)) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(d4_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( m1_subset_1(C,k1_euclid(A)) => ( r2_nfcont_4(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k4_real_ns1(A))) & ? [E] : ( 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) ) ) ) ) ) ) )).
fof(d4_normform,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_finsub_1(B) ) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ! [D] : ( 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))) ) ) ) ) )).
fof(d4_normsp_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_normsp_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( C = k5_normsp_0(A,B) <=> ! [D] : ( v7_ordinal1(D) => k1_funct_1(C,D) = k2_normsp_0(A,k1_normsp_0(A,B,D)) ) ) ) ) ) )).
fof(d4_normsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k4_normsp_1(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k1_normsp_1(A,D,E) = k5_algstr_0(A,k1_normsp_1(A,B,E),C) ) ) ) ) ) ) )).
fof(d4_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ 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)) ) ) ) ) )).
fof(d4_numbers,axiom,( k4_numbers = k6_subset_1(k2_xboole_0(k4_ordinal1,k2_zfmisc_1(k1_tarski(k5_ordinal1),k4_ordinal1)),k1_tarski(k4_tarski(k5_ordinal1,k5_ordinal1))) )).
fof(d4_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v3_o_ring_1(B,A) <=> ? [C] : ( 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)) ) ) ) ) )).
fof(d4_openlatt,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d4_oposet_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v2_oposet_1(A) <=> v1_relat_2(u1_orders_2(A)) ) ) )).
fof(d4_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => k5_oppcat_1(A,B) = B ) ) )).
fof(d4_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => k3_ordeq_01(A,B) = k2_partfun1(k4_rsspace4(A,B),k1_numbers,k8_rsspace4(A,B),k1_ordeq_01(A,B)) ) ) )).
fof(d4_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_orders_1(A) <=> ( v1_relat_2(A) & v8_relat_2(A) ) ) ) )).
fof(d4_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => ( v5_orders_2(A) <=> r4_relat_2(u1_orders_2(A),u1_struct_0(A)) ) ) )).
fof(d4_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) <=> ( v1_ordinal1(A) & v2_ordinal1(A) ) ) )).
fof(d4_ordinal2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_ordinal2(A) <=> ? [B] : ( v3_ordinal1(B) & r1_tarski(k10_xtuple_0(A),B) ) ) ) )).
fof(d4_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_ordinal2(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_ordinal2(C) ) => ( C = k4_ordinal3(A,B) <=> ( k9_xtuple_0(C) = k9_xtuple_0(B) & ! [D] : ( v3_ordinal1(D) => ( r2_hidden(D,k9_xtuple_0(B)) => k1_funct_1(C,D) = k11_ordinal2(k1_funct_1(B,D),A) ) ) ) ) ) ) ) )).
fof(d4_ordinal6,axiom,( ! [A] : k1_ordinal6(A) = k2_wellord2(k1_wellord2(k2_ordinal1(A))) )).
fof(d4_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [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] : ( 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] : ( 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] : ( 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] : ( 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] : ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_osalg_1,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(d4_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => k1_funct_1(C,D) = k3_tarski(a_3_1_osalg_2(A,B,D)) ) ) ) ) ) )).
fof(d4_osalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_osalg_4(A,B,C) <=> r2_hidden(k4_tarski(B,C),k1_osalg_4(A)) ) ) ) ) )).
fof(d4_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) )).
fof(d4_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r3_parsp_2(A,B,C,D,E) <=> ~ ( ~ ( B = C & D = E ) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( r2_parsp_2(A,F,G,B,C) & r2_parsp_2(A,F,G,D,E) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_partfun1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_partfun1(A,B) <=> ! [C] : ( r2_hidden(C,k3_xboole_0(k9_xtuple_0(A),k9_xtuple_0(B))) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) )).
fof(d4_partfun3,axiom,( ! [A] : ( v1_relat_1(A) => ( v4_partfun3(A) <=> ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,k10_xtuple_0(A)) => r1_xxreal_0(k5_numbers,B) ) ) ) ) )).
fof(d4_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => k2_partit1(A,B,C) = k6_subset_1(k3_setfam_1(B,C),k1_tarski(k1_xboole_0)) ) ) ) )).
fof(d4_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ( v4_pasch(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(H,u1_struct_0(A)) => ~ ( r1_diraf(A,B,H,D) & r1_diraf(A,H,F,E) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( D = k2_pboole(A,B,C) <=> ! [E] : ( r2_hidden(E,A) => k1_funct_1(D,E) = k2_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) )).
fof(d4_pcomps_1,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( B = k2_pcomps_1(A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & r1_tarski(k8_metric_1(A,D,E),C) ) ) ) ) ) ) ) ) ) )).
fof(d4_pdiff_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( 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) = k9_finseq_1(k1_funct_1(k1_pdiff_1(A,B),D)) ) ) ) ) ) )).
fof(d4_pdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(2)) => ( r3_pdiff_3(A,B) <=> ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & B = k10_finseq_1(C,D) & ? [E] : ( 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] : ( v1_funct_1(F) & v3_fdiff_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [G] : ( v1_funct_1(G) & v2_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,E) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(2,1,k1_pdiff_3(2,2,A),B),H),k1_funct_1(k1_pdiff_2(2,1,k1_pdiff_3(2,2,A),B),C)) = k2_xcmplx_0(k1_funct_1(F,k6_xcmplx_0(H,C)),k1_funct_1(G,k6_xcmplx_0(H,C))) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r4_pdiff_5(A,B) <=> ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & B = k11_finseq_1(C,D,E) & ? [F] : ( 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] : ( v1_funct_1(G) & v3_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [H] : ( v1_funct_1(H) & v2_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,F) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,1,k1_pdiff_3(2,3,A),B),I),k1_funct_1(k1_pdiff_2(3,1,k1_pdiff_3(2,3,A),B),C)) = k2_xcmplx_0(k1_funct_1(G,k6_xcmplx_0(I,C)),k1_funct_1(H,k6_xcmplx_0(I,C))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_pdiff_6,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d4_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [E] : ( r2_pdiff_7(A,B,C,D,E) <=> ( r1_tarski(E,k1_relset_1(k1_euclid(A),D)) & ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d4_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ! [C] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d4_pencil_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( v3_pencil_1(A) <=> v1_xboole_0(u1_pre_topc(A)) ) ) )).
fof(d4_pencil_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(d4_pencil_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v15_pencil_1(B) ) => ( ! [C] : ( m1_subset_1(C,A) => v10_pencil_1(k2_pencil_1(A,B,C)) ) => ! [C] : ( ( 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] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(k2_vectsp_9(A,B,C)))) => ( D = k4_pencil_4(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ? [F] : ( m1_vectsp_4(F,A,B) & ? [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d4_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k6_petri(A,B) = a_2_0_petri(A,B) ) ) )).
fof(d4_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,k4_ordinal1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ( D = k2_pnproc_1(A,B,C) <=> ! [E] : ( r2_hidden(E,A) => k1_funct_1(D,E) = k2_xcmplx_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) )).
fof(d4_polyalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_polyalg1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v3_polyalg1(C,A,B) <=> ( v1_vectsp_4(C,A,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(d4_polyeq_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => k4_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,k1_square_1(E))),k3_xcmplx_0(C,E)),D) ) ) ) ) ) )).
fof(d4_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( ( k6_xcmplx_0(k3_xcmplx_0(3,B),k1_newton(C,2)) = k5_numbers => ( D = k4_polyeq_5(A,B,C) <=> ? [E] : ( v1_xcmplx_0(E) & ? [F] : ( v1_xcmplx_0(F) & E = k7_xcmplx_0(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(k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(F,2)),k7_xcmplx_0(C,3)),k7_xcmplx_0(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)) != k5_numbers => ( D = k4_polyeq_5(A,B,C) <=> ? [E] : ( v1_xcmplx_0(E) & ? [F] : ( v1_xcmplx_0(F) & ? [G] : ( v1_xcmplx_0(G) & ? [H] : ( v1_xcmplx_0(H) & ? [I] : ( v1_xcmplx_0(I) & E = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(3,B),k1_newton(C,2)),9) & F = k7_xcmplx_0(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 = k4_xcmplx_0(k7_xcmplx_0(E,H)) & D = k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(H,I),2)),k7_xcmplx_0(C,3)),k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(H,I),k1_polyeq_5(2,3)),k7_complex1),2)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => k7_polyform(A) = k3_finseq_1(u1_polyform(A)) ) )).
fof(d4_polynom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( D = k3_polynom1(A,B,C) <=> ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,D) <=> k3_funct_2(A,u1_struct_0(B),C,E) != k4_struct_0(B) ) ) ) ) ) ) ) )).
fof(d4_polynom3,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_finseq_2(A,k4_ordinal1)) => ( C = k6_polynom3(A,B) <=> ? [D] : ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_finseq_2(A,k4_ordinal1))) & C = k7_pre_poly(k4_finseq_2(A,k4_ordinal1),D,k5_polynom3(A)) & ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ( r2_hidden(E,D) <=> k2_wsierp_1(E) = B ) ) ) ) ) ) ) )).
fof(d4_polynom5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k4_polynom5(A,B,C) = k14_funct_7(k4_ordinal1,u1_struct_0(A),k14_funct_7(k4_ordinal1,u1_struct_0(A),k9_polynom3(A),k5_numbers,B),1,C) ) ) ) )).
fof(d4_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( 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) = k14_funct_7(k15_pre_poly(A),u1_struct_0(B),k8_polynom1(A,B),D,C) ) ) ) )).
fof(d4_polynom8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,1) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( D = k4_polynom8(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,A) ) => k3_matrix_0(u1_struct_0(B),D,E,1) = k1_funct_1(C,k6_xcmplx_0(E,1)) ) ) ) ) ) ) ) )).
fof(d4_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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) = k3_polynom1(k15_pre_poly(A),C,D) ) ) ) ) )).
fof(d4_poset_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(d4_power,axiom,( ! [A] : ( v1_xreal_0(A) => ( A = k4_power <=> ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => k9_nat_1(k1_numbers,B,C) = k2_power(k2_xcmplx_0(1,k7_xcmplx_0(1,k1_nat_1(C,1))),k1_nat_1(C,1)) ) => A = k1_seq_2(B) ) ) ) ) )).
fof(d4_pralg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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] : ( 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] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(C)) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_pre_poly,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_pre_poly(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_pre_poly(B) ) => ! [C] : ( ( 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] : ( r2_hidden(D,k9_xtuple_0(C)) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d4_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ( m1_pre_topc(B,A) <=> ( r1_tarski(k2_struct_0(B),k2_struct_0(A)) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( r2_hidden(C,u1_pre_topc(B)) <=> ? [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(d4_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_prelamb(A) ) => ! [B] : ( ( 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)),k4_ordinal1)) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) ) => ! [C] : ( 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)),k4_ordinal1),B,C)) = k5_numbers => ( v2_prelamb(C,A,B) <=> ( k8_trees_2(k9_xtuple_0(B),C) = k5_numbers & ? [D] : ( 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)),k4_ordinal1),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)),k4_ordinal1),B,C)) = 1 => ( v2_prelamb(C,A,B) <=> ( k8_trees_2(k9_xtuple_0(B),C) = 1 & ? [D] : ( m2_finseq_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( 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)),k4_ordinal1),B,C)) = k4_tarski(D,k2_prelamb(A,E,F)) & k1_xtuple_0(k1_funct_1(B,k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,k5_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)),k4_ordinal1),B,C)) = 2 => ( v2_prelamb(C,A,B) <=> ( k8_trees_2(k9_xtuple_0(B),C) = 1 & ? [D] : ( m2_finseq_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( 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)),k4_ordinal1),B,C)) = k4_tarski(D,k1_prelamb(A,F,E)) & k1_xtuple_0(k1_funct_1(B,k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,k5_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)),k4_ordinal1),B,C)) = 3 => ( v2_prelamb(C,A,B) <=> ( k8_trees_2(k9_xtuple_0(B),C) = 2 & ? [D] : ( m2_finseq_1(D,u1_struct_0(A)) & ? [E] : ( m2_finseq_1(E,u1_struct_0(A)) & ? [F] : ( m2_finseq_1(F,u1_struct_0(A)) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & ? [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)),k4_ordinal1),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(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,k5_numbers)))) = k4_tarski(D,H) & k1_xtuple_0(k1_funct_1(B,k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,1)))) = 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)),k4_ordinal1),B,C)) = 4 => ( v2_prelamb(C,A,B) <=> ( k8_trees_2(k9_xtuple_0(B),C) = 2 & ? [D] : ( m2_finseq_1(D,u1_struct_0(A)) & ? [E] : ( m2_finseq_1(E,u1_struct_0(A)) & ? [F] : ( m2_finseq_1(F,u1_struct_0(A)) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & ? [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)),k4_ordinal1),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(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,k5_numbers)))) = k4_tarski(D,H) & k1_xtuple_0(k1_funct_1(B,k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,1)))) = 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)),k4_ordinal1),B,C)) = 5 => ( v2_prelamb(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k8_trees_2(k9_xtuple_0(B),C) = 1 & ? [E] : ( m2_finseq_1(E,u1_struct_0(A)) & ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( 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)),k4_ordinal1),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(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,k5_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)),k4_ordinal1),B,C)) = 6 => ( v2_prelamb(C,A,B) <=> ( k8_trees_2(k9_xtuple_0(B),C) = 2 & ? [D] : ( m2_finseq_1(D,u1_struct_0(A)) & ? [E] : ( m2_finseq_1(E,u1_struct_0(A)) & ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( 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)),k4_ordinal1),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(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,k5_numbers)))) = k4_tarski(D,F) & k1_xtuple_0(k1_funct_1(B,k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,1)))) = 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)),k4_ordinal1),B,C)) = 7 => ( v2_prelamb(C,A,B) <=> ( k8_trees_2(k9_xtuple_0(B),C) = 2 & ? [D] : ( m2_finseq_1(D,u1_struct_0(A)) & ? [E] : ( m2_finseq_1(E,u1_struct_0(A)) & ? [F] : ( m2_finseq_1(F,u1_struct_0(A)) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( 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)),k4_ordinal1),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(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,k5_numbers)))) = k4_tarski(D,G) & k1_xtuple_0(k1_funct_1(B,k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,1)))) = 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)),k4_ordinal1),B,C)) != k5_numbers & k2_xtuple_0(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k4_ordinal1),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)),k4_ordinal1),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)),k4_ordinal1),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)),k4_ordinal1),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)),k4_ordinal1),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)),k4_ordinal1),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)),k4_ordinal1),B,C)) != 7 & ~ ( v2_prelamb(C,A,B) <=> ~ $true ) ) ) ) ) ) )).
fof(d4_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => k4_prepower(A,B) = k2_prepower(k1_rat_1(B),k3_prepower(A,k2_rat_1(B))) ) ) )).
fof(d4_prgcor_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k1_numbers) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k1_numbers) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_int_1(D) => ( r2_prgcor_2(A,B,C,D) <=> ( k1_afinsq_1(B) = D & k1_afinsq_1(A) = D & ? [E] : ( v1_int_1(E) & k1_funct_1(B,k5_numbers) = k1_funct_1(A,k5_numbers) & E = k1_funct_1(A,k5_numbers) & ( E != k5_numbers => ! [F] : ( v7_ordinal1(F) => ( ( r1_xxreal_0(1,F) & r1_xxreal_0(F,E) ) => k1_funct_1(B,F) = k3_xcmplx_0(C,k1_funct_1(A,F)) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_prob_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_prob_1(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => r1_tarski(k1_funct_1(A,C),k1_funct_1(A,B)) ) ) ) ) ) )).
fof(d4_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m1_prob_1(E,A,B) => ( r1_prob_2(A,B,C,D,E) <=> k3_funct_2(B,k1_numbers,C,k5_prob_1(A,B,D,E)) = k4_real_1(k3_funct_2(B,k1_numbers,C,D),k3_funct_2(B,k1_numbers,C,E)) ) ) ) ) ) ) )).
fof(d4_prob_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_prob_2(B) <=> ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( C != D => r1_xboole_0(k1_prob_2(A,k9_setfam_1(A),B,C),k1_prob_2(A,k9_setfam_1(A),B,D)) ) ) ) ) ) )).
fof(d4_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( m1_prob_4(D,A,B,C) <=> ? [E] : ( r2_hidden(E,B) & r1_tarski(D,E) & k1_funct_1(C,E) = k5_numbers ) ) ) ) ) ) )).
fof(d4_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ( v1_projpl_1(A) <=> ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(d4_prvect_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v1_prvect_2(A) ) => ! [B] : ( ( 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] : ( m2_subset_1(C,k4_ordinal1,k4_finseq_1(A)) => k1_funct_1(B,C) = u1_struct_0(k3_prvect_2(A,C)) ) ) ) ) ) )).
fof(d4_prvect_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(d4_pua2mss1,axiom,( ! [A] : ( ( v2_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ( B = k6_pua2mss1(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(k4_tarski(C,D),B) <=> ! [E] : ( 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] : ( ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_pythtrip,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) => ( m1_pythtrip(A) <=> ? [B] : ( m1_subset_1(B,k4_ordinal1) & ? [C] : ( m1_subset_1(C,k4_ordinal1) & ? [D] : ( m1_subset_1(D,k4_ordinal1) & k1_nat_1(k1_pepin(B),k1_pepin(C)) = k1_pepin(D) & A = k8_domain_1(k4_ordinal1,B,C,D) ) ) ) ) ) )).
fof(d4_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => k3_qc_lang1(A) = k2_zfmisc_1(k1_tarski(4),k1_qc_lang1(A)) ) )).
fof(d4_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) )).
fof(d4_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( m1_qc_lang4(C,A,B) <=> r2_qc_lang2(A,C,B) ) ) ) ) )).
fof(d4_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_qc_trans(B,A) & m1_qc_lang1(B) ) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => k2_qc_trans(A,B,C) = C ) ) ) )).
fof(d4_qmax_1,axiom,( ! [A] : ( l1_qmax_1(A) => ! [B] : ( m1_subset_1(B,k2_qmax_1(A)) => ! [C] : ( 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)) ) ) ) )).
fof(d4_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v6_quantal1(A) <=> ( v4_quantal1(A) & v5_quantal1(A) ) ) ) )).
fof(d4_quaterni,axiom,( k4_quaterni = k3_quaterni(k4_ordinal1,k5_numbers,1,2,3,k5_numbers,k5_numbers,1,k5_numbers) )).
fof(d4_quofield,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v6_struct_0(A) & l5_algstr_0(A) ) => ! [B] : ( m2_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_quofield(A))) => ( C = k6_quofield(A,B) <=> ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d4_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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) ) ) ) ) )).
fof(d4_radix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k4_radix_2(A,B,C) = k3_nat_d(k4_nat_d(C,k1_newton(k1_radix_1(B),A)),k11_newton(k1_radix_1(B),k7_nat_d(A,1))) ) ) ) )).
fof(d4_radix_3,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v7_ordinal1(B) => k6_radix_3(A,B) = k6_xcmplx_0(A,k3_xcmplx_0(k1_radix_1(B),k5_radix_3(A,B))) ) ) )).
fof(d4_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v3_card_1(D,A) & m2_finseq_1(D,k3_radix_1(C)) ) => ( D = k4_radix_5(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k2_finseq_1(A)) => k4_radix_1(E,C,A,D) = k3_radix_5(E,B,C) ) ) ) ) ) ) ) )).
fof(d4_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,k2_xcmplx_0(A,2)) & m2_finseq_1(C,k3_radix_1(B)) ) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d4_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d4_random_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( v4_random_3(C,A,B) <=> ! [D] : ~ ( r2_hidden(D,k9_xtuple_0(C)) & ! [E] : ( m2_prob_1(E,A,B) => k1_funct_1(C,D) != E ) ) ) ) ) ) )).
fof(d4_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_6(C,A,B) => ! [D] : ( 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))) ) ) ) ) )).
fof(d4_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => k2_rat_1(A) = k3_xcmplx_0(k1_rat_1(A),A) ) )).
fof(d4_ratfunc1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r2_ratfunc1(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r1_ratfunc1(A,B,C,D) ) ) ) ) ) )).
fof(d4_rcomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v2_rcomp_1(A) <=> ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( r1_tarski(k10_xtuple_0(B),A) & v2_comseq_2(B) ) => r2_hidden(k1_seq_2(B),A) ) ) ) ) )).
fof(d4_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v5_relat_1(B,k4_numbers) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( B = k4_real_3(A) <=> ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,B,C) = k1_int_1(k9_nat_1(k1_numbers,k3_real_3(A),C)) ) ) ) ) )).
fof(d4_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m2_funct_2(C,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d4_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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)) ) ) ) ) )).
fof(d4_realset1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( 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] : ( r2_hidden(D,k2_zfmisc_1(B,B)) => r2_hidden(k1_funct_1(C,D),B) ) ) ) ) )).
fof(d4_recdef_2,axiom,( ! [A] : ( v3_xtuple_0(A) => ! [B] : ( B = k7_xtuple_0(A) <=> ! [C] : ! [D] : ! [E] : ! [F] : ( A = k6_xtuple_0(C,D,E,F) => B = C ) ) ) )).
fof(d4_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => k1_relat_1(A) = k2_xboole_0(k9_xtuple_0(A),k10_xtuple_0(A)) ) )).
fof(d4_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r4_relat_2(A,B) <=> ! [C] : ! [D] : ( ( r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,C),A) ) => C = D ) ) ) )).
fof(d4_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r2_rewrite1(A,B,C) <=> r1_rewrite1(k2_xboole_0(A,k2_relat_1(A)),B,C) ) ) )).
fof(d4_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(d4_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ v2_struct_0(C) & l1_rewrite3(C,B) ) => ! [D] : ( 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] : ! [F] : ! [G] : ! [H] : ( r2_hidden(k4_tarski(k4_tarski(E,F),k4_tarski(G,H)),D) <=> r2_rewrite3(A,B,C,E,F,G,H) ) ) ) ) ) ) )).
fof(d4_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => k4_rfinseq2(A) = k1_funct_1(A,k2_rfinseq2(A)) ) )).
fof(d4_rfunct_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v8_valued_0(A) <=> ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( 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_funct_1(A,C),k1_funct_1(A,B)) ) ) ) ) ) ) )).
fof(d4_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m2_rfunct_3(C,A,k1_numbers,k3_rfunct_3(A,k1_numbers)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d4_rfunct_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( r4_rfunct_4(A,B) <=> ( r1_tarski(B,k9_xtuple_0(A)) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(1,C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & r2_hidden(D,B) & r2_hidden(E,B) & r2_hidden(k2_xcmplx_0(k3_xcmplx_0(C,D),k3_xcmplx_0(k6_xcmplx_0(1,C),E)),B) & D != E & r1_xxreal_0(k4_xxreal_0(k1_funct_1(A,D),k1_funct_1(A,E)),k1_funct_1(A,k2_xcmplx_0(k3_xcmplx_0(C,D),k3_xcmplx_0(k6_xcmplx_0(1,C),E)))) ) ) ) ) ) ) ) )).
fof(d4_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( B = k3_rinfsup1(A) <=> ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_numbers)) => ( D = a_2_0_rinfsup1(A,C) => k1_funct_1(B,C) = k3_seq_4(D) ) ) ) ) ) ) )).
fof(d4_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v2_rinfsup2(A) <=> v4_xxreal_2(k17_supinf_2(A)) ) ) )).
fof(d4_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(d4_ringcat1,axiom,( ! [A] : ( l1_ringcat1(A) => k3_ringcat1(A) = u3_ringcat1(A) ) )).
fof(d4_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_rlaffin1(B,A) <=> ~ ( ~ v1_xboole_0(B) & ! [C] : ( 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) ) ) ) ) ) ) )).
fof(d4_rlsub_1,axiom,( ! [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) ) => k2_rlsub_1(A) = g1_rlvect_1(u1_struct_0(A),u2_struct_0(A),u1_algstr_0(A),u1_rlvect_1(A)) ) )).
fof(d4_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d4_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k2_rltopsp1(A,B) = k1_convex1(A,B,k4_xcmplx_0(1)) ) ) )).
fof(d4_rlvect_1,axiom,( ! [A] : ( l2_algstr_0(A) => ( v4_rlvect_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_algstr_0(A,B,k4_struct_0(A)) = B ) ) ) )).
fof(d4_rlvect_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( 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) ) ) )).
fof(d4_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(d4_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d4_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_4(C,A,B) => ( C = k3_rmod_4(A,B) <=> k2_rmod_4(A,B,C) = k1_xboole_0 ) ) ) ) )).
fof(d4_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(d4_robbins3,axiom,( k1_robbins3 = g3_robbins3(k1_tarski(k5_ordinal1),k9_funct_5,k9_funct_5,k6_partfun1(k1_tarski(k5_ordinal1))) )).
fof(d4_robbins4,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(3)) => ( B = C => k1_funct_1(u1_robbins1(A),B) = k3_subset_1(3,C) ) ) ) ) ) ) )).
fof(d4_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k3_roughs_1(A,B) = a_2_0_roughs_1(A,B) ) ) )).
fof(d4_rsspace,axiom,( ! [A] : ( ( 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 = k4_rsspace <=> ! [B] : ! [C] : ( ( r2_hidden(B,k1_numbers) & r2_hidden(C,k1_rsspace) ) => k1_binop_1(A,B,C) = k26_valued_1(k4_ordinal1,k1_numbers,k2_rsspace(C),k10_subset_1(B,k1_numbers)) ) ) ) )).
fof(d4_rsspace3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k4_rsspace3(A,B,C) = k2_normsp_0(A,k5_algstr_0(A,B,C)) ) ) ) )).
fof(d4_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) & r1_xxreal_0(k5_numbers,D) & ! [E] : ( m1_subset_1(E,A) => r1_xxreal_0(k2_normsp_0(B,k3_funct_2(A,u1_struct_0(B),C,E)),D) ) ) ) ) ) ) )).
fof(d4_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rusub_1(C,A) => k3_rusub_1(A,B,C) = a_3_0_rusub_1(A,B,C) ) ) ) )).
fof(d4_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d4_rusub_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_rusub_4(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k1_algstr_0(A,k1_rlvect_1(A,C,k6_xcmplx_0(1,E)),k1_rlvect_1(A,D,E)),B) ) ) ) ) ) ) ) )).
fof(d4_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(d4_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => k4_rvsum_1(A,B) = k3_funcop_1(k9_binop_2,A,B) ) ) )).
fof(d4_rvsum_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_valued_0(B) ) => k7_rvsum_2(A,B) = k3_funcop_1(k4_binop_2,A,B) ) ) )).
fof(d4_scm_comp,axiom,( ! [A] : ( m1_dtconstr(A,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [B] : ( 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(k5_numbers,1),A,B) ) ) )).
fof(d4_scm_halt,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( r1_scm_halt(A,B,C) <=> ! [D] : ( v7_ordinal1(D) => r2_hidden(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(C,A),k1_scmfsa_m(B),D)),k9_xtuple_0(A)) ) ) ) ) ) )).
fof(d4_scm_inst,axiom,( ! [A] : ( m1_subset_1(A,k3_scm_inst) => ( ? [B] : ( m1_subset_1(B,k2_scm_inst) & ? [C] : ( m1_subset_1(C,k2_scm_inst) & ? [D] : ( m2_subset_1(D,k4_ordinal1,k7_card_1(9)) & A = k3_xtuple_0(D,k1_xboole_0,k2_finseq_4(k2_scm_inst,B,C)) ) ) ) => ! [B] : ( m1_subset_1(B,k2_scm_inst) => ( B = k5_scm_inst(A) <=> ? [C] : ( m2_finseq_1(C,k2_scm_inst) & C = k2_xtuple_0(A) & B = k7_partfun1(k2_scm_inst,C,2) ) ) ) ) ) )).
fof(d4_scmfsa6a,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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) ) ) )).
fof(d4_scmfsa7b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ( r4_scmfsa7b(A,B) <=> ? [C] : ( m1_subset_1(C,u1_compos_1(k1_scmfsa_2)) & r2_hidden(C,k10_xtuple_0(A)) & r3_scmfsa7b(C,B) ) ) ) ) )).
fof(d4_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ( r3_scmfsa9a(A,B,C,D) <=> ! [E] : ( v7_ordinal1(E) => ( ~ r1_xxreal_0(k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(B,D,C,A),E),C),k5_numbers) => ( r5_scmfsa7b(D,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(B,D,C,A),E),k1_funct_4(A,k2_scmfsa_9(C,D))) & r6_scmfsa7b(D,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(B,D,C,A),E),k1_funct_4(A,k2_scmfsa_9(C,D))) ) ) ) ) ) ) ) ) )).
fof(d4_scmfsa_1,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k4_scmfsa_1,k5_scmfsa_1))) => ! [B] : ( v7_ordinal1(B) => k6_scmfsa_1(A,B) = k1_funct_4(A,k16_funcop_1(k4_ordinal1,B)) ) ) )).
fof(d4_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => k4_scmfsa_2(A) = k10_ami_3(A) ) )).
fof(d4_scmfsa_7,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( 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))) ) ) )).
fof(d4_scmfsa_9,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2))))) ) => ( E = k4_scmfsa_9(A,B,C,D) <=> ( r6_pboole(u1_struct_0(k1_scmfsa_2),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),E,k5_numbers),A) & ! [F] : ( v7_ordinal1(F) => r6_pboole(u1_struct_0(k1_scmfsa_2),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),E,k1_nat_1(F,1)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(D,k1_scmfsa_9(C,B)),k1_funct_4(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),E,F),k7_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_numbers)),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(k1_funct_4(D,k1_scmfsa_9(C,B)),B),k1_funct_4(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),E,F),k7_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_numbers))),3))) ) ) ) ) ) ) ) ) )).
fof(d4_scmfsa_m,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k3_scmfsa_2)) ) => ! [B] : ( m1_scmfsa_2(B) => ( B = k3_scmfsa_m(A) <=> ? [C] : ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) & B = k5_scmfsa_2(k4_seq_4(C)) & C = a_1_1_scmfsa_m(A) ) ) ) ) )).
fof(d4_scmp_gcd,axiom,( 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,k5_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,k1_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)) )).
fof(d4_scmpds_2,axiom,( ! [A] : ( ( 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)) ) )).
fof(d4_scmpds_4,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( 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)) ) ) )).
fof(d4_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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,k1_nat_1(k5_card_1(C),2)),C),k1_scmpds_6(k1_nat_1(k5_card_1(D),1))),D) ) ) ) ) )).
fof(d4_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => ( ? [B] : ( m1_subset_1(B,k2_scm_inst) & ? [C] : ( v1_int_1(C) & ? [D] : ( m2_subset_1(D,k4_ordinal1,k7_card_1(15)) & A = k3_xtuple_0(D,k1_xboole_0,k2_scmpds_i(B,C)) ) ) ) => ! [B] : ( m1_subset_1(B,k2_scm_inst) => ( B = k5_scmpds_i(A) <=> ? [C] : ( 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) ) ) ) ) ) )).
fof(d4_scmring1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k4_card_3(k3_relat_1(k3_ami_2,k1_scmring1(A)))) => ! [C] : ( m2_subset_1(C,k1_ami_2,k2_ami_2) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k4_scmring1(A,B,C,D) = k1_funct_4(B,k16_funcop_1(C,D)) ) ) ) ) )).
fof(d4_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(d4_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_scmringi(A)) => ( ? [C] : ( m1_subset_1(C,k4_ordinal1) & ? [D] : ( m2_subset_1(D,k4_ordinal1,k7_card_1(8)) & B = k3_xtuple_0(D,k12_finseq_1(k4_ordinal1,C),k1_xboole_0) ) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( C = k4_scmringi(A,B) <=> ? [D] : ( m2_finseq_1(D,k4_ordinal1) & D = k5_xtuple_0(B) & C = k7_partfun1(k4_ordinal1,D,1) ) ) ) ) ) ) )).
fof(d4_scmyciel,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v3_scmyciel(B,A) <=> ! [C] : ( r2_hidden(C,B) => r1_ordinal1(k1_card_1(C),k1_nat_1(A,1)) ) ) ) )).
fof(d4_scpinvar,axiom,( k5_scpinvar = k1_scmpds_4(k3_scmpds_4(k4_scmpds_4(k5_scmpds_2(k2_scmp_gcd,k5_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)))) )).
fof(d4_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r3_semi_af1(A,B,C,D,E) <=> ~ ( ~ ( B = C & D = E ) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( r2_semi_af1(A,F,G,B,C) & r2_semi_af1(A,F,G,D,E) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_seq_2(A) <=> ? [B] : ( v1_xreal_0(B) & ! [C] : ( v7_ordinal1(C) => ~ r1_xxreal_0(k1_funct_1(A,C),B) ) ) ) ) )).
fof(d4_seq_4,axiom,( ! [A] : ( v1_xcmplx_0(A) => k5_seq_4(A) = k5_funcop_1(k5_binop_2,A,k6_partfun1(k2_numbers)) ) )).
fof(d4_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( C = k5_seqfunc(A,B) <=> ! [D] : ( 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))) ) ) ) ) ) )).
fof(d4_seqm_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v3_valued_0(A) ) => ( v8_valued_0(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(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)) ) ) ) ) ) )).
fof(d4_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_series_1(A) <=> v1_series_1(k56_valued_1(k4_ordinal1,k1_numbers,A)) ) ) )).
fof(d4_setfam_1,axiom,( ! [A] : ! [B] : ! [C] : ( C = k2_setfam_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ? [F] : ( r2_hidden(E,A) & r2_hidden(F,B) & D = k2_xboole_0(E,F) ) ) ) )).
fof(d4_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k3_kurato_0(A,B) = k1_kurato_0(A,k2_setlim_1(A,B)) ) )).
fof(d4_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( D = k4_setlim_2(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k9_nat_1(k9_setfam_1(A),D,E) = k5_subset_1(A,k9_nat_1(k9_setfam_1(A),B,E),k9_nat_1(k9_setfam_1(A),C,E)) ) ) ) ) ) )).
fof(d4_setwiseo,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,k5_finsub_1(A)) => ! [D] : ( m1_subset_1(D,k5_finsub_1(A)) => k5_binop_1(k5_finsub_1(A),B,C,D) = k5_setwiseo(A,C,D) ) ) ) ) )).
fof(d4_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_scmfsa_2)) => ( B = k4_sf_mastr(A) <=> ? [C] : ( 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] : ( 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)) ) ) ) ) )).
fof(d4_sfmastr2,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ( r1_sfmastr2(A,B,C,D) <=> ! [E] : ( v7_ordinal1(E) => ( ~ r1_xxreal_0(k1_funct_1(B,C),E) => ( r5_scmfsa7b(D,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k3_sfmastr2(A,B,D,C),E),k1_funct_4(A,k1_sfmastr2(C,D))) & r6_scmfsa7b(D,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k3_sfmastr2(A,B,D,C),E),k1_funct_4(A,k1_sfmastr2(C,D))) ) ) ) ) ) ) ) ) )).
fof(d4_sfmastr3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( 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))))) ) ) ) ) )).
fof(d4_sgraph1,axiom,( ! [A] : ! [B] : ( ( v1_sgraph1(B) & l1_sgraph1(B) ) => ( m1_sgraph1(B,A) <=> m1_subset_1(B,k3_sgraph1(A)) ) ) )).
fof(d4_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( v2_sheffer1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B = k2_sheffer1(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_lattices(A,B,C) = C & k1_lattices(A,C,B) = C ) ) ) ) ) ) )).
fof(d4_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( B = k4_simplex0(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) <=> v1_simplex0(C,A) ) ) ) ) ) )).
fof(d4_simplex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_simplex0(B,u1_struct_0(A)) => ! [C] : ( m1_simplex0(C,u1_struct_0(A)) => ( m1_simplex1(C,A,B) <=> ( r1_tarski(k3_simplex1(A,B),k3_simplex1(A,C)) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) => ~ ( v3_pre_topc(D,C) & ! [E] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(d4_simplex2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( ( ~ v3_pencil_1(B) & v1_matroid0(B) & v1_simplex2(B,A) & l1_pre_topc(B) ) => ! [C] : ( v1_xreal_0(C) => ( C = k2_simplex2(A,B) <=> ( ! [D] : ( 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] : ( v1_xreal_0(D) => ( ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d4_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( B = k3_sin_cos(A) <=> ! [C] : ( v7_ordinal1(C) => k9_nat_1(k2_numbers,B,C) = k7_xcmplx_0(k2_comseq_3(A,C),k2_newton(C)) ) ) ) ) )).
fof(d4_sin_cos2,axiom,( ! [A] : k4_sin_cos2(A) = k1_funct_1(k3_sin_cos2,A) )).
fof(d4_sin_cos3,axiom,( ! [A] : ( ( 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] : ( v1_xcmplx_0(B) => k1_funct_1(A,B) = k7_xcmplx_0(k2_xcmplx_0(k15_sin_cos(B),k15_sin_cos(k4_xcmplx_0(B))),2) ) ) ) )).
fof(d4_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => k4_sin_cos4(A) = k7_xcmplx_0(1,k19_sin_cos(A)) ) )).
fof(d4_sin_cos6,axiom,( ! [A] : k4_sin_cos6(A) = k1_funct_1(k3_sin_cos6,A) )).
fof(d4_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => k4_sin_cos7(A) = k3_xcmplx_0(k7_xcmplx_0(1,2),k3_power(k4_power,k7_xcmplx_0(k2_xcmplx_0(1,A),k6_xcmplx_0(1,A)))) ) )).
fof(d4_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => k4_sin_cos9(A) = k1_funct_1(k2_sin_cos9,A) ) )).
fof(d4_sincos10,axiom,( k4_sincos10 = k2_partfun2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k4_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(d4_sppol_1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v3_sppol_1(A) <=> ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_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,k1_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,k1_nat_1(B,2))) ) ) ) ) ) )).
fof(d4_sprect_2,axiom,( ! [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,k20_pscomp_1(k3_topreal1(2,A))),2),k15_pscomp_1(k3_topreal1(2,A))) ) ) )).
fof(d4_stacks_1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & l1_stacks_1(A) ) => ! [B] : ( 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) ) ) )).
fof(d4_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => k3_struct_0(A) = k6_partfun1(u1_struct_0(A)) ) )).
fof(d4_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k3_subset_1(A,B) = k4_xboole_0(A,B) ) )).
fof(d4_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_lattices(C) & l3_lattices(C) ) => ( C = k5_substlat(A,B) <=> ( u1_struct_0(C) = k1_substlat(A,B) & ! [D] : ( m2_subset_1(D,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d4_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_qc_lang1(A)) => k4_substut1(A,B) = B ) ) )).
fof(d4_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k1_substut1(A)) => k8_substut2(A,B,C,D) = D ) ) ) ) )).
fof(d4_supinf_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_setfam_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k6_numbers))) ) => ! [B] : ( v2_membered(B) => ( B = k6_supinf_1(A) <=> ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(C,B) <=> ? [D] : ( ~ v1_xboole_0(D) & v2_membered(D) & r2_hidden(D,A) & C = k2_xxreal_2(D) ) ) ) ) ) ) )).
fof(d4_supinf_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,A) => k12_supinf_2(D,E) = k2_supinf_2(k12_supinf_2(C,E)) ) ) ) ) ) ) )).
fof(d4_t_0topsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => k2_t_0topsp(A) = k8_eqrel_1(u1_struct_0(A),k1_t_0topsp(A)) ) )).
fof(d4_tarski,axiom,( ! [A] : ! [B] : ( B = k3_tarski(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( r2_hidden(C,D) & r2_hidden(D,A) ) ) ) )).
fof(d4_taxonom1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => r1_xxreal_0(k5_numbers,k1_binop_1(B,C,D)) ) ) ) ) )).
fof(d4_taylor_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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(k5_numbers) & ! [C] : ( m2_subset_1(C,k1_numbers,k3_limfunc1(k5_numbers)) => k1_funct_1(B,C) = k6_prepower(C,A) ) ) ) ) ) )).
fof(d4_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_tbsp_1(B,A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(D,E) & r1_xxreal_0(D,F) & r1_xxreal_0(C,k1_metric_1(A,k9_nat_1(u1_struct_0(A),B,E),k9_nat_1(u1_struct_0(A),B,F))) ) ) ) ) ) ) ) ) )).
fof(d4_tdgroup,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(d4_tdlat_1,axiom,( ! [A] : ( ( 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)) ) )).
fof(d4_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v3_tdlat_2(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => v6_tops_1(C,A) ) ) ) ) ) )).
fof(d4_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v4_tdlat_3(A) <=> ! [B] : ( 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) ) ) ) ) )).
fof(d4_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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 ) ) ) ) ) ) )).
fof(d4_tex_1,axiom,( ! [A] : ! [B] : ( 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))) ) )).
fof(d4_tex_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_tex_2(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r1_tarski(C,B) & ! [D] : ( 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 ) ) ) ) ) ) ) )).
fof(d4_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v4_tex_3(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = u1_struct_0(B) => v3_tops_1(C,A) ) ) ) ) ) )).
fof(d4_tex_4,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tex_4(B,A) <=> ! [C] : ( 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) ) ) ) ) ) )).
fof(d4_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) )).
fof(d4_toler_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( C = k4_toler_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( v1_toler_1(D,A,B) & m1_toler_1(D,A,B) ) ) ) ) )).
fof(d4_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k4_topalg_1(A,B) = k3_topalg_1(A,B,B) ) ) )).
fof(d4_topalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_topalg_2(A) & m1_pre_topc(A,k2_topalg_2) ) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k5_topmetr)) => ! [F] : ( m1_subset_1(F,u1_struct_0(k5_topmetr)) => k1_binop_1(D,E,F) = k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(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))) ) ) ) ) ) ) ) )).
fof(d4_topalg_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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] : ( 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(k19_sin_cos(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A),C)),k17_sin_cos(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A),C))) ) ) ) ) )).
fof(d4_topalg_6,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( 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] : ( m1_pre_topc(C,k2_topalg_2) & ? [D] : ( 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) ) ) ) ) ) ) )).
fof(d4_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v3_topdim_1(A) <=> v1_topdim_1(k2_struct_0(A),A) ) ) )).
fof(d4_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( r2_topgen_1(A,B,C) <=> ( r2_hidden(C,B) & ~ r1_topgen_1(A,B,C) ) ) ) ) )).
fof(d4_topgen_3,axiom,( k3_topgen_3 = k1_card_1(k1_numbers) )).
fof(d4_topgen_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v3_topgen_4(B,A) <=> ! [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) ) ) ) ) )).
fof(d4_topgen_5,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_topgen_5(A) <=> ! [B] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,k3_subset_1(u1_struct_0(A),B)) & ! [D] : ( ( 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) = k5_numbers & r1_tarski(k7_relset_1(u1_struct_0(A),u1_struct_0(k5_topmetr),D,B),k6_domain_1(k4_ordinal1,1)) ) ) ) ) ) ) ) )).
fof(d4_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( 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) ) ) ) )).
fof(d4_topmetr,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_topmetr(B,A) <=> ! [C] : ~ ( r2_hidden(C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => C != k8_metric_1(A,D,E) ) ) ) ) ) ) )).
fof(d4_topreal1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(A))) => k3_topreal1(A,B) = k3_tarski(a_2_0_topreal1(A,B)) ) ) )).
fof(d4_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d4_toprealb,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => k6_toprealb(A) = A ) )).
fof(d4_toprealc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( v3_membered(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ! [E] : ( ( 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 = k14_toprealc(A,B,C,D) <=> ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(d4_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => k3_toprns_1(A,B) = k5_vfunct_1(k4_ordinal1,k15_euclid(A),B) ) ) )).
fof(d4_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) )).
fof(d4_tops_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(d4_tops_3,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) )).
fof(d4_transgeo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(d4_treal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_topmetr(k5_numbers,1))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_topmetr(k5_numbers,1))) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(k5_numbers,1))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(k5_numbers,1))))) ) => ( E = k4_treal_1(A,B,C,D) <=> ! [F] : ( 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(k5_numbers,1)),E,F) = k7_xcmplx_0(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)) ) ) ) ) ) ) ) ) )).
fof(d4_trees_1,axiom,( ! [A] : ( v7_ordinal1(A) => k2_trees_1(A) = k2_xboole_0(a_1_0_trees_1(A),k1_tarski(k1_xboole_0)) ) )).
fof(d4_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( m2_trees_2(B,A) <=> ? [C] : ( v7_ordinal1(C) & B = a_2_0_trees_2(A,C) ) ) ) ) )).
fof(d4_trees_3,axiom,( ! [A] : ( v2_trees_3(A) <=> ! [B] : ( r2_hidden(B,A) => ( ~ v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) ) ) ) )).
fof(d4_trees_4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v6_trees_3(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) ) => ( C = k4_trees_4(A,B) <=> ( ? [D] : ( 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(k1_funct_6(D)) ) & k1_funct_1(C,k1_xboole_0) = A & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ~ r1_xxreal_0(k3_finseq_1(B),D) => k5_trees_2(C,k14_trees_3(D)) = k1_funct_1(B,k1_nat_1(D,1)) ) ) ) ) ) ) ) )).
fof(d4_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( ~ r1_tsep_1(B,C) => ! [D] : ( ( ~ 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)) ) ) ) ) ) ) )).
fof(d4_tsp_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tsp_2(B,A) <=> ( v1_tsp_1(B,A) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_tsp_1(C,A) & r1_tarski(B,C) ) => B = C ) ) ) ) ) ) )).
fof(d4_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( 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) ) ) )).
fof(d4_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k1_funct_1(A,k10_finseq_1(B,C)) = k9_margrel1(k10_margrel1(B,C)) ) ) ) ) )).
fof(d4_unialg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ( B = k1_unialg_1(A) <=> ( k3_finseq_1(B) = k3_finseq_1(u1_unialg_1(A)) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => ! [D] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(d4_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_unialg_2(B,A) <=> ! [C] : ( m5_margrel1(C,u1_struct_0(A),k1_unialg_2(A)) => r2_unialg_2(A,B,C) ) ) ) ) )).
fof(d4_unialg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( 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] : ( m2_unialg_3(C,A,k1_unialg_3(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d4_uniroots,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v6_vectsp_1(B) & l6_algstr_0(B) ) => k4_uniroots(A,B) = k14_funct_7(k4_ordinal1,u1_struct_0(B),k14_funct_7(k4_ordinal1,u1_struct_0(B),k9_polynom3(B),k5_numbers,k4_algstr_0(B,k1_group_1(B))),A,k1_group_1(B)) ) ) )).
fof(d4_uproots,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_uproots(B,A) <=> B != k9_polynom3(A) ) ) ) )).
fof(d4_urysohn1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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(k1_newton(2,A),1)) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => k1_funct_1(B,C) = k7_xcmplx_0(k6_xcmplx_0(C,1),k1_newton(2,A)) ) ) ) ) ) ) )).
fof(d4_urysohn3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( m2_urysohn3(D,A,B,C) => ! [E] : ( ( 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 = k4_urysohn3(A,B,C,D) <=> ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,k3_urysohn1) => ( ( r2_hidden(F,k10_prob_1(k5_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] : ( v7_ordinal1(G) => ( r2_hidden(F,k1_urysohn1(G)) => k1_funct_1(E,F) = k1_funct_1(k2_urysohn3(k2_urysohn1,k9_setfam_1(u1_struct_0(A)),D,G),F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v5_relat_1(D,k3_qc_lang1(A)) & v3_card_1(D,C) & m2_finseq_1(D,k2_qc_lang1(A)) ) => ! [E] : ( m1_subset_1(E,k3_margrel1(B)) => ! [F] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_valued_0,axiom,( ! [A] : ( v1_relat_1(A) => ( v4_valued_0(A) <=> r1_tarski(k10_xtuple_0(A),k4_ordinal1) ) ) )).
fof(d4_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d4_vectmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( B = k1_vectmetr(A) <=> ! [C] : ( 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)))) ) ) ) ) )).
fof(d4_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => k4_vectsp10(A,B,C) = u1_struct_0(C) ) ) ) )).
fof(d4_vectsp11,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(d4_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ( v3_vectsp_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_algstr_0(A,B,k5_struct_0(A)) = B ) ) ) )).
fof(d4_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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)) ) ) )).
fof(d4_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d4_vectsp_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_vectsp_6(D,A,B) => ( m2_vectsp_6(D,A,B,C) <=> r1_tarski(k1_vectsp_6(A,B,D),C) ) ) ) ) ) )).
fof(d4_vectsp_8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( 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] : ( m2_vectsp_8(D,A,B,k2_vectsp_8(A,B)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d4_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_rlvect_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d4_waybel10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(d4_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_waybel_9(A) ) => ( v4_waybel11(A) <=> ! [B] : ( 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) ) ) ) ) ) )).
fof(d4_waybel12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v2_waybel12(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( C != k3_yellow_0(A) & k11_lattice3(A,B,C) = k3_yellow_0(A) ) ) ) ) ) )).
fof(d4_waybel16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( B = k1_waybel16(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) <=> v1_waybel16(C,A) ) ) ) ) ) )).
fof(d4_waybel17,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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),k17_funct_3(u1_struct_0(A),u1_struct_0(A),k6_partfun1(u1_struct_0(A)),B)) ) ) )).
fof(d4_waybel18,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => k6_waybel18(A,B,C) = k12_card_3(k12_pralg_1(A,B),C) ) ) ) )).
fof(d4_waybel19,axiom,( ! [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] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( B = k2_waybel19(A) <=> ! [C] : ( ( v2_pre_topc(C) & v2_waybel19(C) & m1_yellow_9(C,A) ) => B = u1_pre_topc(C) ) ) ) ) )).
fof(d4_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(d4_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_waybel23(B,A) <=> v8_yellow_0(k5_yellow_0(A,B),A) ) ) ) )).
fof(d4_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_waybel25(A) <=> ! [B] : ( ( ~ 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] : ( ( 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) ) ) ) ) ) ) )).
fof(d4_waybel26,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k5_waybel26(A) = k2_relat_1(k3_card_3(k2_card_3(A))) ) )).
fof(d4_waybel27,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_orders_2(C) & l1_orders_2(C) ) => ( C = k2_waybel27(A,B) <=> ( v4_yellow_0(C,k5_yellow_1(u1_struct_0(A),B)) & m1_yellow_0(C,k5_yellow_1(u1_struct_0(A),B)) & ! [D] : ( 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)))) ) ) ) ) ) ) ) )).
fof(d4_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => k4_waybel28(A) = u1_pre_topc(k13_yellow_6(A,k3_waybel28(A))) ) )).
fof(d4_waybel29,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k1_waybel26(A,k9_waybel18)),u1_struct_0(k1_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(k1_yellow_1(u1_pre_topc(A)))))) ) => ( B = k4_waybel29(A) <=> ! [C] : ( ( 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)) ) ) ) ) )).
fof(d4_waybel30,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_waybel_9(A) ) => ( v3_waybel30(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(D,C) => v5_yellow_0(k5_yellow_0(A,D),A) ) ) ) ) ) ) )).
fof(d4_waybel32,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v6_waybel_0(C,A) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ( C = k2_waybel32(A,B) <=> ? [D] : ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d4_waybel34,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ ! [B] : ( m1_subset_1(B,A) => v1_xboole_0(B) ) => ! [B] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d4_waybel35,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ! [C] : ( m1_waybel35(C,A,B) => ( v2_waybel35(C,A,B) <=> ! [D] : ( m1_waybel35(D,A,B) => ( r1_lattice7(A,C,D) => C = D ) ) ) ) ) ) )).
fof(d4_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ( v4_waybel_0(B,A) <=> ! [C] : ( ( 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)) ) ) ) ) ) ) )).
fof(d4_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( r1_waybel_1(A,B) <=> ( r2_yellow_0(A,B) & r2_hidden(k2_yellow_0(A,B),B) ) ) ) )).
fof(d4_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_binop_1(B,C,D) = k11_lattice3(A,C,D) ) ) ) ) ) )).
fof(d4_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_waybel_3(A,B) = a_2_1_waybel_3(A,B) ) ) )).
fof(d4_waybel_4,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ( v2_waybel_4(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d4_waybel_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( B = k3_waybel_6(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) <=> v2_waybel_6(C,A) ) ) ) ) ) )).
fof(d4_waybel_7,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ! [C] : ( r1_waybel_7(A,B,C) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( v3_pre_topc(D,A) & r2_hidden(C,D) ) => ! [E] : ~ ( r2_hidden(E,B) & r1_xboole_0(D,E) ) ) ) ) ) )).
fof(d4_waybel_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ( v2_waybel_8(A) <=> ( ! [B] : ( 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) ) ) ) )).
fof(d4_waybel_9,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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))) ) ) ) )).
fof(d4_weddwitt,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [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) ) ) ) ) )).
fof(d4_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => k1_funct_1(C,D) = k3_metric_1(A,D,B) ) ) ) ) ) )).
fof(d4_wellfnd1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( B = k1_wellfnd1(A) <=> B = k3_tarski(a_1_0_wellfnd1(A)) ) ) ) )).
fof(d4_wellord1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(d4_wellord2,axiom,( ! [A] : ! [B] : ( r2_wellord2(A,B) <=> ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & v2_funct_1(C) & k9_xtuple_0(C) = A & k10_xtuple_0(C) = B ) ) )).
fof(d4_xboole_0,axiom,( ! [A] : ! [B] : ! [C] : ( C = k3_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & r2_hidden(D,B) ) ) ) )).
fof(d4_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => k3_xboolean(A) = k6_xcmplx_0(1,A) ) )).
fof(d4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( C = k3_xcmplx_0(A,B) <=> ? [D] : ( m1_subset_1(D,k1_numbers) & ? [E] : ( m1_subset_1(E,k1_numbers) & ? [F] : ( m1_subset_1(F,k1_numbers) & ? [G] : ( 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))) ) ) ) ) ) ) ) )).
fof(d4_xtuple_0,axiom,( ! [A] : ! [B] : ! [C] : k3_xtuple_0(A,B,C) = k4_tarski(k4_tarski(A,B),C) )).
fof(d4_xxreal_0,axiom,( k6_numbers = k2_xboole_0(k1_numbers,k2_tarski(k1_xxreal_0,k2_xxreal_0)) )).
fof(d4_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k4_xxreal_1(A,B) = a_2_3_xxreal_1(A,B) ) ) )).
fof(d4_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => ( B = k2_xxreal_2(A) <=> ( m2_xxreal_2(B,A) & ! [C] : ( m2_xxreal_2(C,A) => r1_xxreal_0(C,B) ) ) ) ) ) )).
fof(d4_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k3_xxreal_3(A,B) = k1_xxreal_3(A,k2_xxreal_3(B)) ) ) )).
fof(d4_yellow11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( D = k3_yellow11(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(E,D) <=> ( r1_orders_2(A,B,E) & r1_orders_2(A,E,C) ) ) ) ) ) ) ) ) )).
fof(d4_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( m2_yellow13(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => m1_yellow13(B,A,C) ) ) ) ) )).
fof(d4_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(d4_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v6_altcat_1(B) & l2_altcat_1(B) ) => ( B = k1_yellow18(A) <=> r2_yellow18(A,B) ) ) ) )).
fof(d4_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_waybel_0(C,k2_yellow_1(B)) & v13_waybel_0(C,k2_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(B)))) ) => ! [D] : ( ( ~ 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] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( 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] : ( m1_subset_1(E,u1_struct_0(D)) => k2_waybel_0(A,D,E) = k1_xtuple_0(E) ) ) ) ) ) ) ) )).
fof(d4_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( l2_functor0(C,A,B) => ! [D] : ( ( ~ v2_struct_0(D) & v2_altcat_1(D) & v11_altcat_1(D) & v12_altcat_1(D) & l2_altcat_1(D) ) => ! [E] : ( ( ~ 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] : ( v15_functor0(F,D,E) & m2_functor0(F,D,E) & v21_functor0(F,D,E) & ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( G = H => k3_functor0(D,E,F,G) = k3_functor0(A,B,C,H) ) ) ) & ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => ! [H] : ( m1_subset_1(H,u1_struct_0(D)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ( ( G = I & H = J ) => ( k1_altcat_1(D,G,H) = k1_xboole_0 | ! [K] : ( m1_subset_1(K,k1_altcat_1(D,G,H)) => ! [L] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_yellow21,axiom,( ! [A] : ( ( ~ 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] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v3_orders_2(D) & v4_orders_2(D) & v5_orders_2(D) & v1_lattice3(D) & v2_lattice3(D) & l1_orders_2(D) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(d4_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_yellow_0(A) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & r1_lattice3(A,u1_struct_0(A),B) ) ) ) )).
fof(d4_yellow_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_yellow_1(B) ) => ! [C] : ( ( v1_orders_2(C) & l1_orders_2(C) ) => ( C = k4_yellow_1(A,B) <=> ( u1_struct_0(C) = k4_card_3(k12_pralg_1(A,B)) & ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( 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] : ( v1_relat_1(F) & v1_funct_1(F) & ? [G] : ( v1_relat_1(G) & v1_funct_1(G) & F = D & G = E & ! [H] : ~ ( r2_hidden(H,A) & ! [I] : ( l1_orders_2(I) => ! [J] : ( m1_subset_1(J,u1_struct_0(I)) => ! [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d4_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))))) ) => ( B = k3_yellow_2(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A))),B,C) = k5_waybel_0(A,C) ) ) ) ) )).
fof(d4_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(d4_yellow_6,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_waybel_0(B,A) => ( v1_yellow_6(B,A) <=> v3_funct_1(u1_waybel_0(A,B)) ) ) ) )).
fof(d4_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(d4_yellow_9,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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)) ) ) ) )).
fof(d4_zf_fund1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( C = k5_zf_fund1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( 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)) ) ) ) ) ) )).
fof(d4_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => k5_zf_lang(A,B) = k8_finseq_1(k4_ordinal1,k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,1),k3_zf_lang(A)),k3_zf_lang(B)) ) ) )).
fof(d4_zf_model,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ( r1_zf_model(A,B,C) <=> r2_hidden(B,k5_zf_model(C,A)) ) ) ) ) )).
fof(d4_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k4_zfmisc_1(A,B,C,D) = k2_zfmisc_1(k3_zfmisc_1(A,B,C),D) )).
fof(d4_zfmodel1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ( r2_zfmodel1(A,B) <=> ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & ? [D] : ( 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(k5_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(k5_numbers),k8_zf_lang(k2_zf_lang(4),k12_zf_lang(C,k4_zf_lang(k2_zf_lang(4),k2_zf_lang(k5_numbers))))))) & A = k1_zfmodel1(C,B,D) ) ) ) ) ) )).
fof(d4_zfrefle1,axiom,( ! [A] : ( A = k1_zfrefle1 <=> ! [B] : ( 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] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ~ ( r1_xboole_0(k1_enumset1(k2_zf_lang(k5_numbers),k2_zf_lang(1),k2_zf_lang(2)),k2_zf_model(C)) & B = k11_zf_model(C) ) ) ) ) ) ) )).
fof(d4_zmodul01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_zmodul01(A) ) => ( v4_zmodul01(A) <=> ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d4_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( v1_int_1(B) => k4_zmodul02(A,B) = k2_partfun1(k2_zfmisc_1(k4_numbers,u1_struct_0(A)),u1_struct_0(A),u1_zmodul01(A),k2_zfmisc_1(k4_numbers,k1_zmodul02(A,B))) ) ) )).
fof(d50_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m3_abcmiz_1(B,A) => ( v10_abcmiz_1(B,A) <=> k47_abcmiz_1(A,B) = k1_xboole_0 ) ) ) )).
fof(d50_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(d50_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k26_fomodel4(A) = k23_fomodel4(A,k12_fomodel4(A)) ) )).
fof(d50_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(d50_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k30_modelc_1(A)) => ( D = k40_modelc_1(A,B,C) <=> ! [E] : ( 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 ) ) ) ) ) )).
fof(d50_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ! [D] : ( ( 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) ) ) ) ) )).
fof(d51_abcmiz_1,axiom,( k49_abcmiz_1 = k7_lattice3(k1_yellow_1(a_0_2_abcmiz_1)) )).
fof(d51_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ( v7_ordinal1(C) => ! [D] : ( l5_aofa_a00(D) => ( v21_aofa_a00(D,A,B,C) <=> ( r1_xxreal_0(k2_xcmplx_0(C,3),k3_finseq_1(u7_aofa_a00(D))) & ? [E] : ( m1_subset_1(E,u1_struct_0(D)) & ? [F] : ( m1_subset_1(F,u1_struct_0(D)) & ? [G] : ( m1_subset_1(G,u1_struct_0(D)) & G = A & F = B & E != G & E != F & r1_aofa_a00(D,k1_funct_1(u7_aofa_a00(D),C),k10_finseq_1(E,F),G) & r1_aofa_a00(D,k1_funct_1(u7_aofa_a00(D),k2_xcmplx_0(C,1)),k11_finseq_1(E,F,G),E) & r1_aofa_a00(D,k1_funct_1(u7_aofa_a00(D),k2_xcmplx_0(C,2)),k9_finseq_1(E),F) & r1_aofa_a00(D,k1_funct_1(u7_aofa_a00(D),k2_xcmplx_0(C,3)),k10_finseq_1(F,G),E) ) ) ) ) ) ) ) )).
fof(d51_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(d51_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k27_fomodel4(A) = k23_fomodel4(A,k13_fomodel4(A)) ) )).
fof(d51_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ( v11_glib_000(B,A) <=> ? [C] : ( k28_glib_000(A,B) = k1_tarski(C) & ~ r1_glib_000(A,B,B,C) ) ) ) ) )).
fof(d51_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ! [D] : ( ( 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) ) ) ) ) )).
fof(d51_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( m1_subset_1(D,k25_modelc_2(A)) => ( ! [E] : ( v7_ordinal1(E) => ~ ( ! [F] : ( 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] : ( v7_ordinal1(E) & ! [F] : ( 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 ) ) ) ) ) )).
fof(d52_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l5_aofa_a00(A) ) => ! [B] : ! [C] : ! [D] : ( v7_ordinal1(D) => ! [E] : ( l3_msualg_1(E,A) => ( v22_aofa_a00(E,A,B,C,D) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & G = B & r1_aofa_a00(A,k1_funct_1(u7_aofa_a00(A),D),k10_finseq_1(F,C),G) & k1_msafree4(u1_struct_0(A),u3_msualg_1(A,E),F) = k8_afinsq_1(k1_msafree4(u1_struct_0(A),u3_msualg_1(A,E),G)) & k1_funct_1(u3_msualg_1(A,E),C) = k4_numbers & ! [H] : ( ( v1_relat_1(H) & v5_relat_1(H,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,E),G)) & v1_funct_1(H) & v1_finset_1(H) & v1_exchsort(H) & v2_exchsort(H,k5_numbers) ) => ( ! [I] : ( v1_int_1(I) => ( r2_hidden(I,k2_afinsq_1(H)) => ( k1_funct_1(k5_msualg_1(A,k7_partfun1(u4_struct_0(A),u7_aofa_a00(A),D),E),k10_finseq_1(H,I)) = k1_funct_1(H,I) & ! [J] : ( m1_subset_1(J,k1_funct_1(u3_msualg_1(A,E),G)) => k1_funct_1(k5_msualg_1(A,k7_partfun1(u4_struct_0(A),u7_aofa_a00(A),k2_xcmplx_0(D,1)),E),k11_finseq_1(H,I,J)) = k1_funct_7(H,I,J) ) ) ) ) & k1_funct_1(k5_msualg_1(A,k7_partfun1(u4_struct_0(A),u7_aofa_a00(A),k2_xcmplx_0(D,2)),E),k9_finseq_1(H)) = k5_card_1(H) ) ) & ! [H] : ( v1_int_1(H) => ! [I] : ( m1_subset_1(I,k1_funct_1(u3_msualg_1(A,E),G)) => ( r1_xxreal_0(k5_numbers,H) => k1_funct_1(k5_msualg_1(A,k7_partfun1(u4_struct_0(A),u7_aofa_a00(A),k2_xcmplx_0(D,3)),E),k10_finseq_1(H,I)) = k7_funcop_1(H,I) ) ) ) ) ) ) ) ) ) )).
fof(d52_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(d52_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k28_fomodel4(A) = k23_fomodel4(A,k14_fomodel4(A)) ) )).
fof(d52_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( r2_hidden(E,A) => ( ! [F] : ( m1_modelc_1(F,A,B) => ~ ( k3_funct_2(k4_ordinal1,A,F,k5_numbers) = E & ? [G] : ( m1_subset_1(G,k4_ordinal1) & ! [H] : ( m1_subset_1(H,k4_ordinal1) => ( ~ r1_xxreal_0(G,H) => k3_funct_2(A,k6_margrel1,C,k3_funct_2(k4_ordinal1,A,F,H)) = k8_margrel1 ) ) & k3_funct_2(A,k6_margrel1,D,k3_funct_2(k4_ordinal1,A,F,G)) = k8_margrel1 ) ) ) | k42_modelc_1(A,B,C,D,E) = k8_margrel1 ) ) & ( ~ ( r2_hidden(E,A) & ? [F] : ( m1_modelc_1(F,A,B) & k3_funct_2(k4_ordinal1,A,F,k5_numbers) = E & ? [G] : ( m1_subset_1(G,k4_ordinal1) & ! [H] : ( m1_subset_1(H,k4_ordinal1) => ( ~ r1_xxreal_0(G,H) => k3_funct_2(A,k6_margrel1,C,k3_funct_2(k4_ordinal1,A,F,H)) = k8_margrel1 ) ) & k3_funct_2(A,k6_margrel1,D,k3_funct_2(k4_ordinal1,A,F,G)) = k8_margrel1 ) ) ) => k42_modelc_1(A,B,C,D,E) = k7_margrel1 ) ) ) ) ) ) )).
fof(d52_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k30_modelc_1(k25_modelc_2(A))) => ( D = k38_modelc_2(A,B,C) <=> ! [E] : ( 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 ) ) ) ) ) )).
fof(d53_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_aofa_a00(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l5_aofa_a00(B) ) => ! [C] : ( ( v15_aofa_a00(C) & l6_aofa_a00(C) ) => ( C = k36_aofa_a00(A,B) <=> ( g1_msualg_1(u1_struct_0(C),u4_struct_0(C),u1_msualg_1(C),u2_msualg_1(C)) = k2_circcomb(A,B) & u8_aofa_a00(C) = u8_aofa_a00(A) & u7_aofa_a00(C) = k7_finseq_1(u7_aofa_a00(A),u7_aofa_a00(B)) ) ) ) ) ) )).
fof(d53_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(d53_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k29_fomodel4(A) = k23_fomodel4(A,k15_fomodel4(A)) ) )).
fof(d53_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ! [D] : ! [E] : ( m1_subset_1(E,k30_modelc_1(A)) => ( E = k43_modelc_1(A,B,C,D) <=> ! [F] : ( 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 ) ) ) ) ) ) )).
fof(d53_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ! [D] : ( ( 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) ) ) ) ) )).
fof(d54_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(d54_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k30_fomodel4(A) = k23_fomodel4(A,k16_fomodel4(A)) ) )).
fof(d54_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( v13_glib_000(A) <=> ? [B] : ( v7_ordinal1(B) & k1_funct_1(A,B) = k1_funct_1(A,k1_nat_1(B,1)) ) ) ) )).
fof(d54_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( 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] : ! [E] : ( ( 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) ) ) ) ) ) )).
fof(d54_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ! [D] : ( ( 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))) ) ) ) ) )).
fof(d55_abcmiz_1,axiom,( ! [A] : ( l1_msualg_1(A) => ! [B] : ( ( 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))) ) ) ) )).
fof(d55_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v21_aofa_a00(A,1,1,11) & l6_aofa_a00(A) ) => k37_aofa_a00(A) = k1_funct_1(u2_msualg_1(A),k1_funct_1(u7_aofa_a00(A),12)) ) )).
fof(d55_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k31_fomodel4(A) = k23_fomodel4(A,k17_fomodel4(A)) ) )).
fof(d55_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( v13_glib_000(A) => ( B = k39_glib_000(A) <=> ( k1_funct_1(A,B) = k1_funct_1(A,k1_nat_1(B,1)) & ! [C] : ( 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 = k5_numbers ) ) ) ) ) )).
fof(d55_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) => ( D = k45_modelc_1(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ( r2_hidden(E,B) & ? [F] : ( 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 ) ) ) ) ) ) ) )).
fof(d55_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ! [D] : ( ( 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))) ) ) ) ) )).
fof(d56_abcmiz_1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(d56_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msafree4(C,u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),k37_aofa_a00(A))) => ! [D] : ( ( v19_aofa_a00(D,A) & m1_subset_1(D,u1_struct_0(A)) ) => k38_aofa_a00(A,B,C,D) = k1_funct_1(k5_msualg_1(A,k10_subset_1(k1_funct_1(u7_aofa_a00(A),13),u4_struct_0(A)),B),k12_finseq_1(k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),k37_aofa_a00(A)),C)) ) ) ) ) )).
fof(d56_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k32_fomodel4(A) = k23_fomodel4(A,k18_fomodel4(A)) ) )).
fof(d56_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => k40_glib_000(A) = k1_funct_1(A,k39_glib_000(A)) ) )).
fof(d56_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [C] : ( ( 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] : ( r2_hidden(D,A) => k1_funct_1(C,D) = k45_modelc_1(A,B,D) ) ) ) ) ) )).
fof(d56_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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)) ) ) )).
fof(d57_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msafree4(C,u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),k37_aofa_a00(A))) => ! [D] : ( ( v19_aofa_a00(D,A) & m1_subset_1(D,u1_struct_0(A)) ) => ! [E] : ( m1_msafree4(E,u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),D)) => k39_aofa_a00(A,B,C,D,E) = k1_funct_1(k5_msualg_1(A,k10_subset_1(k1_funct_1(u7_aofa_a00(A),11),u4_struct_0(A)),B),k2_finseq_4(k3_card_3(u3_msualg_1(A,B)),C,E)) ) ) ) ) ) )).
fof(d57_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k33_fomodel4(A) = k23_fomodel4(A,k19_fomodel4(A)) ) )).
fof(d57_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k30_modelc_1(k25_modelc_2(A)))) ) => ! [C] : ( m1_subset_1(C,k25_modelc_2(A)) => ! [D] : ( 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 ) ) ) ) ) )).
fof(d58_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msafree4(C,u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),k37_aofa_a00(A))) => ! [D] : ( ( v19_aofa_a00(D,A) & m1_subset_1(D,u1_struct_0(A)) ) => ! [E] : ( m1_msafree4(E,u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),D)) => ! [F] : ( m1_msafree4(F,u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),D)) => k40_aofa_a00(A,B,C,D,E,F) = k1_funct_1(k5_msualg_1(A,k10_subset_1(k1_funct_1(u7_aofa_a00(A),12),u4_struct_0(A)),B),k3_finseq_4(k3_card_3(u3_msualg_1(A,B)),C,E,F)) ) ) ) ) ) ) )).
fof(d58_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k34_fomodel4(A) = k23_fomodel4(A,k20_fomodel4(A)) ) )).
fof(d58_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(d58_modelc_2,axiom,( k43_modelc_2 = k1_zfmisc_1(k15_modelc_2) )).
fof(d59_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_abcmiz_1)) => k54_abcmiz_1(A,B) = a_2_7_abcmiz_1(A,B) ) ) )).
fof(d59_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v19_aofa_a00(C,A) & m1_subset_1(C,u1_struct_0(A)) ) => ! [D] : ( m1_msafree4(D,u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) => ! [E] : ( m1_msafree4(E,u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) => k41_aofa_a00(A,B,C,D,E) = k1_funct_1(k5_msualg_1(A,k10_subset_1(k1_funct_1(u7_aofa_a00(A),14),u4_struct_0(A)),B),k2_finseq_4(k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C),D,E)) ) ) ) ) ) )).
fof(d59_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_aofa_i00(D,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) ) => ! [E] : ( m3_aofa_i00(E,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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,k5_numbers),D,C,k36_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,E,k43_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,2))) ) ) ) ) ) )).
fof(d59_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k35_fomodel4(A) = k23_fomodel4(A,k21_fomodel4(A)) ) )).
fof(d59_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(d59_modelc_2,axiom,( ! [A] : ! [B] : ( ( ( r2_hidden(B,k25_modelc_2(k43_modelc_2)) & r2_hidden(A,k9_nat_1(k43_modelc_2,k27_modelc_2(k43_modelc_2,B),k5_numbers)) ) => k44_modelc_2(A,B) = k8_margrel1 ) & ( ~ ( r2_hidden(B,k25_modelc_2(k43_modelc_2)) & r2_hidden(A,k9_nat_1(k43_modelc_2,k27_modelc_2(k43_modelc_2,B),k5_numbers)) ) => k44_modelc_2(A,B) = k7_margrel1 ) ) )).
fof(d5_abcmiz_0,axiom,( ! [A] : ( l1_abcmiz_0(A) => ! [B] : ( m1_subset_1(B,u1_abcmiz_0(A)) => k1_abcmiz_0(A,B) = k1_funct_1(u2_abcmiz_0(A),B) ) ) )).
fof(d5_abcmiz_1,axiom,( k7_abcmiz_1 = 1 )).
fof(d5_abcmiz_a,axiom,( k4_abcmiz_a = k39_abcmiz_1(k27_abcmiz_1) )).
fof(d5_abian,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_abian(A) <=> ? [B] : r1_abian(B,A) ) ) )).
fof(d5_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r3_aff_1(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & B = k2_aff_1(A,D,E) & D != E & r2_aff_1(A,D,E,C) ) ) ) ) ) ) )).
fof(d5_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v5_aff_2(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_aff_3,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v5_aff_3(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ! [L] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_aff_4(A,B,C,D) <=> ? [E] : ( 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) ) ) ) ) ) ) )).
fof(d5_afinsq_1,axiom,( ! [A] : ! [B] : k6_afinsq_1(A,B) = k1_ordinal4(k5_afinsq_1(A),k5_afinsq_1(B)) )).
fof(d5_afinsq_2,axiom,( ! [A] : ! [B] : ( r1_afinsq_2(A,B) <=> ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(C,A) & r2_hidden(D,B) & r1_xxreal_0(D,C) ) ) ) ) )).
fof(d5_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( 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) ) ) )).
fof(d5_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( E = k2_afvect0(A,B,C,D) <=> r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) )).
fof(d5_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(d5_algspec1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_instalg1(B) & l1_msualg_1(B) ) => ( m2_algspec1(B,A) <=> m1_instalg1(A,B) ) ) ) )).
fof(d5_algstr_0,axiom,( ! [A] : ( l1_algstr_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v4_algstr_0(B,A) <=> ( v3_algstr_0(B,A) & v2_algstr_0(B,A) ) ) ) ) )).
fof(d5_algstr_1,axiom,( ! [A] : ( ( ~ 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) ) ) ) )).
fof(d5_algstr_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_algstr_3(A) ) => ( v2_algstr_3(A) <=> ( k4_struct_0(A) != k5_struct_0(A) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_algstr_3(A,B,k5_struct_0(A),k4_struct_0(A)) = B ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_algstr_3(A,k5_struct_0(A),B,k4_struct_0(A)) = B ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_algstr_3(A,B,k4_struct_0(A),C) = C ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_algstr_3(A,k4_struct_0(A),B,C) = C ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & k1_algstr_3(A,B,C,E) = D ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( B != C => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( B != C => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & k1_algstr_3(A,B,F,D) = k1_algstr_3(A,C,F,E) ) ) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(d5_algstr_4,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(d5_altcat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ! [H] : ! [I] : ! [J] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d5_altcat_2,axiom,( ! [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) & l1_cat_1(A) ) => k4_altcat_2(A) = g2_altcat_1(u1_struct_0(A),k2_altcat_2(A),k3_altcat_2(A)) ) )).
fof(d5_altcat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d5_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d5_ami_2,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k3_ami_2,k4_ami_2))) => ! [B] : ( v7_ordinal1(B) => k6_ami_2(A,B) = k1_funct_4(A,k16_funcop_1(k4_ordinal1,B)) ) ) )).
fof(d5_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( 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)) ) ) )).
fof(d5_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( D = k2_ami_wstd(A,B,C) <=> k1_ami_wstd(A,B,D) = C ) ) ) ) ) )).
fof(d5_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( v7_ordinal1(C) => k3_amistd_1(A,B,C) = k3_tarski(a_3_1_amistd_1(A,B,C)) ) ) ) )).
fof(d5_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( D = k4_amistd_4(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r2_hidden(E,D) <=> ~ ! [F] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d5_amistd_5,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(B)) & v1_funct_1(D) & v1_finset_1(D) & ~ v2_compos_1(D,B) ) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( v1_relat_1(H) & v4_relat_1(H,k4_ordinal1) & v5_relat_1(H,u1_compos_1(B)) & v1_funct_1(H) & v1_partfun1(H,k4_ordinal1) ) => ! [I] : ( ( v1_relat_1(I) & v4_relat_1(I,k4_ordinal1) & v5_relat_1(I,u1_compos_1(B)) & v1_funct_1(I) & v1_partfun1(I,k4_ordinal1) ) => ( ( r1_tarski(D,H) & r1_tarski(k6_compos_1(B,D,C),I) ) => ! [J] : ( v7_ordinal1(J) => 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d5_analoaf,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ( v2_analoaf(A) <=> ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ~ r2_analoaf(A,B,C,D,E) & ~ r2_analoaf(A,B,C,E,D) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( B != D & r2_analoaf(A,D,B,B,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_analoaf(A,C,B,B,F) & r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ! [F] : ( r2_hidden(k4_tarski(E,F),D) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & ? [I] : ( m1_subset_1(I,u1_struct_0(A)) & ? [J] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_anproj_1,axiom,( ! [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) ) => ! [B] : ( B = k3_anproj_1(A) <=> ? [C] : ( 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 ) ) ) )).
fof(d5_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_aofa_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : k5_aofa_000(A,B) = a_2_0_aofa_000(A,B) ) )).
fof(d5_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : k7_aofa_a00(A,B,C,D,E,F,G) = k7_finseq_1(k8_finseq_4(A,B,C,D,E),k10_finseq_1(F,G)) )).
fof(d5_armstrng,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k6_margrel1) ) => ! [D] : ( ( v3_card_1(D,A) & m2_finseq_1(D,k6_margrel1) ) => ( D = k3_armstrng(A,B,C) <=> ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d5_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ( ( B = k5_numbers => k5_arytm_0(A,B) = A ) & ( B != k5_numbers => k5_arytm_0(A,B) = k5_funct_4(k1_numbers,k5_numbers,1,A,B) ) ) ) ) )).
fof(d5_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( 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] : ( m1_subset_1(C,k5_arytm_3) & ? [D] : ( 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) ) ) ) ) ) )).
fof(d5_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( C = k3_arytm_3(A,B) <=> ( r2_arytm_3(C,A) & r2_arytm_3(C,B) & ! [D] : ( ( v3_ordinal1(D) & v7_ordinal1(D) ) => ( ( r2_arytm_3(D,A) & r2_arytm_3(D,B) ) => r2_arytm_3(D,C) ) ) ) ) ) ) ) )).
fof(d5_asympt_1,axiom,( k5_asympt_1 = a_0_0_asympt_1 )).
fof(d5_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( ~ 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] : ( 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) ) ) ) ) ) ) )).
fof(d5_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(d5_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(d5_bcialg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_bcialg_1(A) ) => ( v5_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_bcialg_1(A,B,B) = k4_struct_0(A) ) ) ) )).
fof(d5_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v4_bcialg_2(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_bcialg_1(A,C,B) ) ) ) ) )).
fof(d5_bcialg_3,axiom,( ! [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_3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(d5_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k3_bcialg_5(A,B,C,D) = k5_nat_1(k5_nat_1(A,B),k5_nat_1(C,D)) ) ) ) ) )).
fof(d5_bcialg_6,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_bcialg_6(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( C = k4_bcialg_6(A,B) <=> ( r2_hidden(k3_bcialg_6(A,C,B),k4_bcialg_1(A)) & C != k5_numbers & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(k3_bcialg_6(A,D,B),k4_bcialg_1(A)) => ( D = k5_numbers | r1_xxreal_0(C,D) ) ) ) ) ) ) ) ) ) )).
fof(d5_bciideal,axiom,( ! [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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d5_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k4_bhsp_1(A,B,C) = k3_bhsp_1(A,k5_algstr_0(A,B,C)) ) ) ) )).
fof(d5_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => k4_bhsp_2(A,B,C) = a_3_0_bhsp_2(A,B,C) ) ) ) )).
fof(d5_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k4_bhsp_4(A,B,C,D) = k5_algstr_0(A,k3_bhsp_4(A,B,C),k3_bhsp_4(A,B,D)) ) ) ) ) )).
fof(d5_bhsp_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ! [E] : ( ( 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] : ( m1_subset_1(F,A) => ( F = k5_bhsp_5(A,B,C,D,E) <=> ? [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_bhsp_6,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_bhsp_6(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ! [D] : ( ( 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] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( ( v1_finset_1(F) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( ~ v1_xboole_0(F) & r1_tarski(F,B) & ! [G] : ( ( 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,k9_complex1(k3_funct_2(u1_struct_0(A),k1_numbers,D,k5_algstr_0(A,C,k1_bhsp_6(A,G))))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_bilinear,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(d5_binari_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(d5_binarith,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k6_margrel1) ) => ! [D] : ( ( v3_card_1(D,A) & m2_finseq_1(D,k6_margrel1) ) => ( D = k7_binarith(A,B,C) <=> ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(d5_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k5_binom(A,B,C) = k2_binop_1(k4_ordinal1,u1_struct_0(A),u1_struct_0(A),k3_binom(A),C,B) ) ) ) )).
fof(d5_binop_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( m1_subset_1(D,A) => k1_binop_1(C,B,D) = D ) ) ) )).
fof(d5_binop_2,axiom,( ! [A] : ( ( 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 = k5_binop_2 <=> ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k1_binop_1(A,B,C) = k3_xcmplx_0(B,C) ) ) ) ) )).
fof(d5_boolmark,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m2_funct_2(B,u1_struct_0(A),k6_margrel1,k1_boolmark(A)) => ! [C] : ( m2_finseq_1(C,u4_struct_0(A)) => ! [D] : ( 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] : ( 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] : ( m1_subset_1(F,k4_ordinal1) => ~ ( ~ r1_xxreal_0(k3_finseq_1(C),F) & ~ r1_xxreal_0(F,k5_numbers) & k7_partfun1(k1_boolmark(A),E,k1_nat_1(F,1)) != k2_boolmark(A,k7_partfun1(k1_boolmark(A),E,F),k7_partfun1(u4_struct_0(A),C,k1_nat_1(F,1))) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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))) ) ) )).
fof(d5_borsuk_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( m1_borsuk_2(F,A,C,D) => ( ( r2_borsuk_2(A,B,C) & r2_borsuk_2(A,C,D) ) => ! [G] : ( m1_borsuk_2(G,A,B,D) => ( G = k1_borsuk_2(A,B,C,D,E,F) <=> ! [H] : ( m1_subset_1(H,u1_struct_0(k5_topmetr)) => ( ( r1_xxreal_0(H,k7_xcmplx_0(1,2)) => k3_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),G,H) = k1_funct_1(E,k3_xcmplx_0(2,H)) ) & ( r1_xxreal_0(k7_xcmplx_0(1,2),H) => k3_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),G,H) = k1_funct_1(F,k6_xcmplx_0(k3_xcmplx_0(2,H),1)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_borsuk_6,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(k5_topmetr)) => ( ( r1_xxreal_0(B,k7_xcmplx_0(1,2)) => k3_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,B) = k3_xcmplx_0(2,B) ) & ( ~ r1_xxreal_0(B,k7_xcmplx_0(1,2)) => k3_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,B) = 1 ) ) ) ) ) )).
fof(d5_borsuk_7,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xxreal_0(A) ) => ! [B] : ( v1_xreal_0(B) => 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)) ) ) )).
fof(d5_brouwer,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_xreal_0(B) & ~ v3_xxreal_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d5_bspace,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => k5_binop_1(k1_zfmisc_1(A),B,C,D) = k5_subset_1(A,C,D) ) ) ) ) )).
fof(d5_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d5_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ( v2_bvfunc_2(B,A) <=> ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) => ~ ( k9_xtuple_0(C) = B & k10_xtuple_0(C) = D & ! [E] : ( r2_hidden(E,B) => r2_hidden(k1_funct_1(C,E),E) ) & k8_setfam_1(A,D) = k1_xboole_0 ) ) ) ) ) ) )).
fof(d5_c0sp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(d5_c0sp2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d5_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_qc_lang1(A))) => ( C = k3_calcul_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & ? [F] : ( m2_subset_1(F,k9_qc_lang1(A),k3_cqc_lang(A)) & r2_hidden(E,k1_relset_1(k4_ordinal1,B)) & F = k1_funct_1(B,E) & r2_hidden(D,k24_qc_lang1(A,F)) ) ) ) ) ) ) ) )).
fof(d5_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k4_card_3(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & C = D & k9_xtuple_0(D) = k9_xtuple_0(A) & ! [E] : ( r2_hidden(E,k9_xtuple_0(A)) => r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)) ) ) ) ) ) )).
fof(d5_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_card_fil(B,A) => ( v1_card_fil(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r2_hidden(C,B) => k1_card_1(C) = k1_card_1(A) ) ) ) ) ) )).
fof(d5_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v2_card_lar(B,A) <=> ! [C] : ( ( 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) ) ) ) ) ) )).
fof(d5_cat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_cat_1(A) ) => ( v3_cat_1(A) <=> ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) ) )).
fof(d5_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m3_cat_2(B,A) => k5_cat_2(A,B) = k10_cat_1(B) ) ) )).
fof(d5_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ! [C] : ( ( 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] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d5_cat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d5_cat_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v2_cat_5(A) <=> ! [B] : ( 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) ) ) ) ) )).
fof(d5_catalg_1,axiom,( ! [A] : ! [B] : ( ( 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(k5_numbers),k4_finseq_2(2,A)) ) ) ) )).
fof(d5_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ( v4_cayldick(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_cayldick(A,k1_algstr_0(A,B,C)) = k1_algstr_0(A,k2_cayldick(A,B),k2_cayldick(A,C)) ) ) ) ) )).
fof(d5_cc0sp2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d5_cfdiff_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_numbers)) => ( m1_cfdiff_1(B,A) <=> ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,k5_numbers) & r1_tarski(a_2_0_cfdiff_1(A,C),B) ) ) ) ) )).
fof(d5_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k5_cfuncdom(A) = k8_funcop_1(k2_numbers,A,k6_complex1) ) )).
fof(d5_cgames_1,axiom,( k5_cgames_1 = g1_cgames_1(k1_tarski(k3_cgames_1),k1_tarski(k3_cgames_1)) )).
fof(d5_chain_1,axiom,( ! [A] : ( ( ~ v1_zfmisc_1(A) & v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k1_numbers,k1_numbers)) => ( m2_chain_1(B,A) <=> ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & B = k4_tarski(C,D) & r2_hidden(C,A) & r2_hidden(D,A) & ( ( ~ r1_xxreal_0(D,C) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,A) & ~ r1_xxreal_0(E,C) & ~ r1_xxreal_0(D,E) ) ) ) | ( ~ r1_xxreal_0(C,D) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,A) => ( r1_xxreal_0(E,C) & r1_xxreal_0(D,E) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( 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))) ) ) ) ) )).
fof(d5_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ( v1_circcmb3(C,A,B) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( D = k2_circcmb3(A,B,C) <=> ( v1_circuit2(k5_facirc_1(A,B,C,D),A,B) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( ~ r1_xxreal_0(D,E) & v1_circuit2(k5_facirc_1(A,B,C,E),A,B) ) ) ) ) ) ) ) ) ) )).
fof(d5_circcomb,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ! [D] : ( ( ~ 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 ) ) ) ) )).
fof(d5_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) => ! [D] : ( ( v4_msualg_1(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d5_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_funct_1(u3_msualg_1(A,k5_msafree2(A,B)),C)) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( E = k5_circuit1(A,B,C,D) <=> ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d5_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(A,B))) => ( D = k6_circuit2(A,B,C) <=> ! [E] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(d5_clopban1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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))) ) ) )).
fof(d5_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => k6_clopban2(A) = k6_partfun1(u1_struct_0(A)) ) )).
fof(d5_clopban3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clopban2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k3_clopban3(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k1_normsp_0(A,D,E) = k6_algstr_0(A,k1_normsp_0(A,B,E),C) ) ) ) ) ) ) )).
fof(d5_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( E = k5_clopban4(A,B,C,D) <=> ! [F] : ( v7_ordinal1(F) => ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d5_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) => ( v2_closure2(C,A,B) <=> ! [D] : ( 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) ) ) ) ) ) )).
fof(d5_clvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ( v5_clvect_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_clvect_1(A,B,k6_complex1) = B ) ) ) )).
fof(d5_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => k4_clvect_2(A,B,C) = a_3_0_clvect_2(A,B,C) ) ) ) )).
fof(d5_coh_sp,axiom,( ! [A] : k4_coh_sp(A) = k3_tarski(a_1_1_coh_sp(A)) )).
fof(d5_cohsp_1,axiom,( ! [A] : ( v2_cohsp_1(A) <=> ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : ( ! [D] : ( r2_hidden(D,B) => r1_tarski(C,D) ) & r2_hidden(C,A) ) ) ) )).
fof(d5_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_collsp(A,B,C) = a_3_0_collsp(A,B,C) ) ) ) )).
fof(d5_combgras,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_incsp_1(k1_combgras(A,B)))) => ( v4_combgras(C,A,B) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & k1_card_1(D) = k1_nat_1(A,1) & C = a_3_1_combgras(A,B,D) ) ) ) ) ) )).
fof(d5_compl_sp,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ( v4_compl_sp(B,A) <=> ! [C] : ( v7_ordinal1(C) => v3_pre_topc(k9_nat_1(k9_setfam_1(u1_struct_0(A)),B,C),A) ) ) ) ) )).
fof(d5_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k8_complex1(A) = k6_xcmplx_0(k3_complex1(A),k3_xcmplx_0(k4_complex1(A),k7_complex1)) ) )).
fof(d5_compos_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_compos_0(A) ) => ( v2_compos_0(A) <=> ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(d5_compts_1,axiom,( ! [A] : k1_compts_1(A) = g1_pre_topc(A,k2_subset_1(k9_setfam_1(A))) )).
fof(d5_comput_1,axiom,( ! [A] : k2_comput_1(A) = a_1_2_comput_1(A) )).
fof(d5_comseq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & v1_valued_0(A) ) => ( v2_comseq_2(A) <=> ? [B] : ( v1_xcmplx_0(B) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(D,E) & r1_xxreal_0(C,k9_complex1(k6_xcmplx_0(k1_funct_1(A,E),B))) ) ) ) ) ) ) ) )).
fof(d5_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( B = k7_comseq_3(A) <=> ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,B,C) = k3_complex1(k9_nat_1(k2_numbers,A,C)) ) ) ) ) )).
fof(d5_conaffm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v5_conaffm(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => k4_conlat_1(A) = k2_conlat_1(A) ) )).
fof(d5_conmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v5_conmetr(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_conmetr1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v5_conmetr1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A))) => ! [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_connsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_connsp_1(B,A) <=> ( v2_connsp_1(B,A) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v2_connsp_1(C,A) & r1_tarski(B,C) ) => B = C ) ) ) ) ) ) )).
fof(d5_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_connsp_2(A,B,C) <=> ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( B = D & ! [E] : ( m1_subset_1(E,u1_struct_0(k1_pre_topc(A,D))) => ~ ( E = C & r1_connsp_2(k1_pre_topc(A,D),E) ) ) ) ) ) ) ) ) )).
fof(d5_connsp_3,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(d5_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(d5_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( m2_finseq_1(D,u1_struct_0(A)) => ( D = k3_convex4(A,B,C) <=> ( k3_finseq_1(D) = k3_finseq_1(B) & ! [E] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(d5_convfun1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k6_numbers))) ) => k5_convfun1(A,B) = a_2_0_convfun1(A,B) ) ) )).
fof(d5_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( 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] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(C)) ) => r1_cqc_the1(A,C,D,B) ) ) ) ) ) ) ) )).
fof(d5_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d5_csspace,axiom,( ! [A] : ( ( 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] : ! [C] : ( ( v1_xcmplx_0(B) & r2_hidden(C,k1_csspace) ) => k1_binop_1(A,B,C) = k25_valued_1(k4_ordinal1,k2_numbers,k2_csspace(C),k3_csspace(B)) ) ) ) )).
fof(d5_csspace3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_csspace3(B,A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(D,E) & r1_xxreal_0(D,F) & r1_xxreal_0(C,k4_csspace3(A,k1_normsp_0(A,B,E),k1_normsp_0(A,B,F))) ) ) ) ) ) ) ) ) )).
fof(d5_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_clopban1(A,B)))) => ( C = k4_csspace4(A,B) <=> ! [D] : ( 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)))) ) ) ) ) ) ) )).
fof(d5_decomp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)))) ) ) ) )).
fof(d5_descip_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => k3_funct_2(A,k2_finseq_1(A),B,C) = k16_descip_1(A,C) ) ) ) ) )).
fof(d5_dickson,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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] : ! [D] : ( r2_hidden(k4_tarski(C,D),B) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( 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) ) ) ) ) ) ) )).
fof(d5_diff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => k5_diff_1(A,B) = k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_diff_1(A,k7_xcmplx_0(B,2)),k1_diff_1(A,k4_xcmplx_0(k7_xcmplx_0(B,2)))) ) ) )).
fof(d5_diraf,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r3_diraf(A,B,C,D) <=> r2_diraf(A,B,C,B,D) ) ) ) ) ) )).
fof(d5_dirort,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dirort(A) & l1_analoaf(A) ) => ( v3_dirort(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,A) => k5_dist_1(A,B) = a_2_0_dist_1(A,B) ) ) )).
fof(d5_dist_2,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k4_finseq_1(B))) => k5_dist_2(A,B,C) = k1_partfun1(k4_ordinal1,C,k4_ordinal1,A,k19_finseq_1(C),B) ) ) )).
fof(d5_dtconstr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => ( v3_dtconstr(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ( r2_hidden(B,k2_lang1(A)) & ! [C] : ( 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)) ) ) ) ) ) )).
fof(d5_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( m1_dynkin(B,A) <=> ( ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ( r1_tarski(k10_xtuple_0(C),B) & v1_prob_2(C) ) => r2_hidden(k1_prob_1(A,C),B) ) ) & ! [C] : ( 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) ) ) ) ) )).
fof(d5_e_siec,axiom,( ! [A] : k3_e_siec(A) = g1_e_siec(A,k1_xboole_0,k1_xboole_0) )).
fof(d5_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ( ( B = k5_numbers => k2_ec_pf_1(A,B) = k5_numbers ) & ( v2_ec_pf_1(B,A) => k2_ec_pf_1(A,B) = 1 ) & ~ ( B != k5_numbers & ~ v2_ec_pf_1(B,A) & k2_ec_pf_1(A,B) != k4_xcmplx_0(1) ) ) ) ) )).
fof(d5_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m2_subset_1(D,k3_ec_pf_1(k9_int_3(A)),k6_ec_pf_1(A,B,C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(A))) => ( E = k6_ec_pf_2(A,B,C,D) <=> ! [F] : ! [G] : ! [H] : ( D = k3_xtuple_0(F,G,H) => E = H ) ) ) ) ) ) ) )).
fof(d5_endalg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( m1_autalg_1(D,u1_struct_0(A),u3_msualg_1(A,B),k4_endalg(A,B)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(d5_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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)) ) ) )).
fof(d5_entropy1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( m2_finseq_1(C,A) => ( ( k3_finseq_1(B) = k5_numbers => ( C = k2_entropy1(A,B) <=> C = k1_xboole_0 ) ) & ( k3_finseq_1(B) != k5_numbers => ( C = k2_entropy1(A,B) <=> ? [D] : ( 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] : ( v7_ordinal1(E) => ( r1_xxreal_0(1,E) => ( r1_xxreal_0(k3_finseq_1(B),E) | k1_matrprob(A,D,k1_nat_1(E,1)) = k8_finseq_1(A,k1_matrprob(A,D,E),k1_matrprob(A,B,k1_nat_1(E,1))) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( H = k5_enumset1(A,B,C,D,E,F,G) <=> ! [I] : ( r2_hidden(I,H) <=> ~ ( I != A & I != B & I != C & I != D & I != E & I != F & I != G ) ) ) )).
fof(d5_eqrel_1,axiom,( ! [A] : k10_eqrel_1(A) = k8_eqrel_1(A,k6_partfun1(A)) )).
fof(d5_equation,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_funct_1(k4_equation(A),C)) => ( r1_equation(A,B,C,D) <=> ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(d5_euclid,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => k12_euclid(A) = k3_square_1(k18_rvsum_1(k12_rvsum_1(A))) ) )).
fof(d5_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(d5_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(3))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(3))) => k6_euclid_5(A,B,C) = k22_rvsum_1(A,k5_euclid_5(B,C)) ) ) ) )).
fof(d5_euclid_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => k1_funct_1(D,E) = k1_euclid_8(k1_funct_1(A,E),k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) )).
fof(d5_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( 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) ) ) ) )).
fof(d5_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ( v5_euclmetr(A) <=> v7_aff_2(k3_analmetr(A)) ) ) )).
fof(d5_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( v3_ordinal1(B) => ( ( ? [C] : ( v3_ordinal1(C) & r2_hidden(C,k9_xtuple_0(A)) ) => ( B = k2_exchsort(A) <=> v3_exchsort(A,B) ) ) & ( ! [C] : ( v3_ordinal1(C) => ~ r2_hidden(C,k9_xtuple_0(A)) ) => ( B = k2_exchsort(A) <=> B = k5_numbers ) ) ) ) ) )).
fof(d5_extpro_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(d5_facirc_1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k1_funct_1(A,k10_finseq_1(B,C)) = k10_margrel1(B,C) ) ) ) ) )).
fof(d5_fdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r1_fdiff_1(A,B) => ! [C] : ( v1_xreal_0(C) => ( C = k1_fdiff_1(A,B) <=> ? [D] : ( m1_rcomp_1(D,B) & r1_tarski(D,k1_relset_1(k1_numbers,A)) & ? [E] : ( v1_funct_1(E) & v3_fdiff_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [F] : ( v1_funct_1(F) & v2_fdiff_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & C = k1_funct_1(E,1) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,D) => k6_xcmplx_0(k1_funct_1(A,G),k1_funct_1(A,B)) = k2_xcmplx_0(k1_funct_1(E,k6_xcmplx_0(G,B)),k1_funct_1(F,k6_xcmplx_0(G,B))) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_fdiff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r4_fdiff_3(B,A) => ! [C] : ( v1_xreal_0(C) => ( C = k1_fdiff_3(A,B) <=> ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v9_ordinal1(D) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k10_xtuple_0(E) = k1_tarski(A) & r1_tarski(k10_xtuple_0(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),k1_relset_1(k1_numbers,B)) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ r1_xxreal_0(k5_numbers,k3_funct_2(k4_ordinal1,k1_numbers,D,F)) ) ) => C = k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),B),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,B)))) ) ) ) ) ) ) ) ) )).
fof(d5_ff_siec,axiom,( ! [A] : k5_ff_siec(A) = k1_ff_siec(k1_tarski(A),k1_xboole_0) )).
fof(d5_fib_num2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k5_fib_num2(A) = k1_fib_num2(k2_fib_num2,k3_xboole_0(k3_fib_num2,k2_finseq_1(A))) ) )).
fof(d5_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(k3_lattices(A,C,D),B) <=> ( r2_hidden(C,B) | r2_hidden(D,B) ) ) ) ) ) ) ) )).
fof(d5_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ v2_struct_0(C) & v3_lattices(C) & v10_lattices(C) & l3_lattices(C) ) => ( C = k4_filter_1(A,B) <=> ! [D] : ( ( 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))) ) ) ) ) ) ) ) )).
fof(d5_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) => k4_filter_2(A,B) = B ) ) )).
fof(d5_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k5_fin_topo(A,B) = a_2_0_fin_topo(A,B) ) ) )).
fof(d5_finance1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r1_finance1(A,B,C,D,E) <=> ! [F] : ( r2_hidden(F,D) => r2_hidden(k8_relat_1(E,F),C) ) ) ) ) ) )).
fof(d5_finseq_1,axiom,( ! [A] : k5_finseq_1(A) = k1_tarski(k4_tarski(1,A)) )).
fof(d5_finseq_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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] : ( m2_finseq_2(D,A,k3_finseq_2(A)) => k1_funct_1(C,D) = k4_card_3(k3_relat_1(D,B)) ) ) ) ) )).
fof(d5_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_hidden(B,k10_xtuple_0(A)) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( C = k5_finseq_4(A,B) <=> ? [D] : ( v7_ordinal1(D) & D = k6_xcmplx_0(k4_finseq_4(A,B),1) & C = k5_relat_1(A,k2_finseq_1(D)) ) ) ) ) ) )).
fof(d5_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => k7_finseq_8(A,B,C) = k2_rfinseq(A,k3_finseq_1(k4_finseq_8(A,B,C)),C) ) ) ) )).
fof(d5_finset_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) ) => ( v2_finset_1(B) <=> ! [C] : ( r2_hidden(C,A) => v1_finset_1(k1_funct_1(B,C)) ) ) ) )).
fof(d5_finsub_1,axiom,( ! [A] : ! [B] : ( v4_finsub_1(B) => ( B = k5_finsub_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( r1_tarski(C,A) & v1_finset_1(C) ) ) ) ) )).
fof(d5_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) ) )).
fof(d5_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v7_ordinal1(C) => k5_fintopo3(A,B,C) = k1_funct_1(k4_fintopo3(A,B),C) ) ) ) )).
fof(d5_fintopo4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(A),k2_finseq_1(A)))) => ( B = k3_fintopo4(A) <=> ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( 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),k1_nat_1(C,1)) ) & ( C = 1 => ( r1_xxreal_0(A,C) | k9_relat_1(B,C) = k1_enumset1(C,A,k1_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) ) ) ) ) ) ) ) )).
fof(d5_fintopo5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k5_fintopo5(A,B) = g1_orders_2(k2_zfmisc_1(k2_finseq_1(A),k2_finseq_1(B)),k4_fintopo5(A,B)) ) ) )).
fof(d5_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_fintopo6(A,B,C) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k1_fintopo6(A,B)))) & D = C & r1_fintopo6(k1_fintopo6(A,B),D) ) ) ) ) ) )).
fof(d5_fomodel0,axiom,( ! [A] : k2_fomodel0(A) = k9_funct_3(A,A) )).
fof(d5_fomodel1,axiom,( ! [A] : ( 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),k4_ordinal1) ) )).
fof(d5_fomodel2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : k5_fomodel2(A,B,C) = k1_funct_4(A,k16_funcop_1(B,k16_funcop_1(k1_xboole_0,C))) ) )).
fof(d5_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ! [D] : ( v7_ordinal1(D) => k8_fomodel3(A,B,C,D) = a_4_0_fomodel3(A,B,C,D) ) ) ) ) )).
fof(d5_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) => ! [C] : ( 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 = k4_fomodel4(A,B) <=> ! [D] : ( 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))) ) ) ) ) ) )).
fof(d5_frechet,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k2_frechet(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,C) <=> r1_frechet(A,B,D) ) ) ) ) ) ) )).
fof(d5_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(d5_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( E = k3_fsm_1(A,B,C,D) <=> r1_fsm_1(A,B,D,C,E) ) ) ) ) ) ) )).
fof(d5_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ v2_struct_0(C) & l1_fsm_2(C,A) ) => ( r2_fsm_2(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & r1_fsm_2(A,C,D,B) & r2_hidden(D,u1_fsm_2(A,C)) ) ) ) ) ) )).
fof(d5_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k5_ftacell1(A,B,C,D,E) = k9_gfacirc1(k12_gfacirc1(A,B,C),E,D) )).
fof(d5_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( ( 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) ) ) )).
fof(d5_funcsdom,axiom,( ! [A] : k9_funcsdom(A) = k8_funcop_1(k4_ordinal1,A,1) )).
fof(d5_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) => k2_funct_1(A) = k2_relat_1(A) ) ) )).
fof(d5_funct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(d5_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k8_funct_3(A,B) <=> ( k9_xtuple_0(C) = k2_zfmisc_1(A,B) & ! [D] : ! [E] : ( ( r2_hidden(D,A) & r2_hidden(E,B) ) => k1_binop_1(C,D,E) = E ) ) ) ) )).
fof(d5_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : k6_funct_4(A,B,C) = k1_funct_4(A,k3_relat_1(A,k16_funcop_1(B,C))) ) )).
fof(d5_funct_5,axiom,( k6_funct_5 = k16_funcop_1(k5_ordinal1,k5_ordinal1) )).
fof(d5_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => k5_funct_6(A) = k1_funct_5(k5_relat_1(k4_funct_5(A),k2_zfmisc_1(k3_funct_6(k1_funct_6(A)),k9_xtuple_0(A)))) ) )).
fof(d5_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_xboole_0(A) => ( B = k5_funct_7(A) <=> v1_xboole_0(B) ) ) & ( ~ v1_xboole_0(A) => ( B = k5_funct_7(A) <=> B = k9_xtuple_0(k1_funct_1(A,1)) ) ) ) ) )).
fof(d5_funct_8,axiom,( ! [A] : ! [B] : ( v1_membered(B) => ! [C] : ( v1_membered(C) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(d5_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_altcat_1(B) ) => ! [C] : ( l1_functor0(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(d5_functor2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( m2_functor0(C,A,B) => ! [D] : ( m2_functor0(D,A,B) => ! [E] : ( m2_functor0(E,A,B) => ( ( r1_functor2(A,B,C,D) & r1_functor2(A,B,D,E) ) => ! [F] : ( m1_functor2(F,A,B,C,D) => ! [G] : ( m1_functor2(G,A,B,D,E) => ! [H] : ( m1_functor2(H,A,B,C,E) => ( H = k3_functor2(A,B,C,D,E,F,G) <=> ! [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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ( r1_functor3(A,B,C,D) => ! [E] : ( m2_functor2(E,A,B,C,D) => ( m1_functor3(E,A,B,C,D) <=> ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d5_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( m1_subset_1(D,A) => k3_funct_2(A,k1_numbers,C,D) = k6_xcmplx_0(1,k3_funct_2(A,k1_numbers,B,D)) ) ) ) ) ) )).
fof(d5_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => k5_fuzzy_2(A,B) = k5_funct_3(k2_zfmisc_1(A,B),k2_zfmisc_1(A,B)) ) ) )).
fof(d5_fvaluat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_int_1(C) => ( ( r1_xxreal_0(k5_numbers,C) => k3_fvaluat1(A,B,C) = k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k4_group_1(A),B,k1_int_2(C)) ) & ( ~ r1_xxreal_0(k5_numbers,C) => k3_fvaluat1(A,B,C) = k11_algstr_0(A,k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k4_group_1(A),B,k1_int_2(C))) ) ) ) ) ) )).
fof(d5_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d5_gate_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k5_gate_5(A,B,C,D,E) = k2_gate_1(A,D) )).
fof(d5_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k2_gcd_1(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,C) <=> r3_gcd_1(A,D,B) ) ) ) ) ) ) )).
fof(d5_genealg1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_finseq_1(B,k3_card_3(A)) => ! [C] : ( m2_finseq_1(C,k3_card_3(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => 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) ) ) ) ) ) ) ) )).
fof(d5_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [E] : ( v1_xreal_0(E) => ( E = k3_geomtrap(A,B,C,D) <=> ? [F] : ( v1_xreal_0(F) & D = k3_rlvect_1(A,k1_rlvect_1(A,B,F),k1_rlvect_1(A,C,E)) ) ) ) ) ) ) ) ) )).
fof(d5_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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))) )).
fof(d5_glib_000,axiom,( k5_glib_000 = k9_domain_1(k4_ordinal1,k1_glib_000,k2_glib_000,k3_glib_000,k4_glib_000) )).
fof(d5_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ( ( 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,o_1_0_glib_001(A)) ) ) ) )).
fof(d5_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k6_glib_000(A))) ) => ( C = k1_glib_002(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( m3_glib_001(E,A) & r1_glib_001(A,B,D,E) ) ) ) ) ) ) )).
fof(d5_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) ) => ( v2_glib_003(A) <=> ( r2_hidden(k3_glib_003,k1_relset_1(k4_ordinal1,A)) & ? [B] : ( 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)) ) ) ) ) )).
fof(d5_goboard1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( v3_goboard1(A) <=> ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => v5_valued_0(k2_goboard1(k7_matrix_0(u1_struct_0(k15_euclid(2)),A,B))) ) ) ) ) )).
fof(d5_goboard5,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(d5_gobrd13,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ! [D] : ( v7_ordinal1(D) => ( r1_gobrd13(A,B,C,D) <=> ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ~ ( r2_hidden(k4_tarski(E,F),k2_matrix_0(C)) & r2_hidden(k4_tarski(G,H),k2_matrix_0(C)) & k7_partfun1(A,B,D) = k3_matrix_0(A,C,E,F) & k7_partfun1(A,B,k1_nat_1(D,1)) = k3_matrix_0(A,C,G,H) & ~ ( E = G & k1_nat_1(F,1) = H & r2_hidden(k4_tarski(k1_nat_1(G,1),H),k2_matrix_0(C)) & k7_partfun1(A,B,k1_nat_1(D,2)) = k3_matrix_0(A,C,k1_nat_1(G,1),H) ) & ~ ( k1_nat_1(E,1) = G & F = H & r2_hidden(k4_tarski(G,k7_nat_d(H,1)),k2_matrix_0(C)) & k7_partfun1(A,B,k1_nat_1(D,2)) = k3_matrix_0(A,C,G,k7_nat_d(H,1)) ) & ~ ( E = k1_nat_1(G,1) & F = H & r2_hidden(k4_tarski(G,k1_nat_1(H,1)),k2_matrix_0(C)) & k7_partfun1(A,B,k1_nat_1(D,2)) = k3_matrix_0(A,C,G,k1_nat_1(H,1)) ) & ~ ( E = G & F = k1_nat_1(H,1) & r2_hidden(k4_tarski(k7_nat_d(G,1),H),k2_matrix_0(C)) & k7_partfun1(A,B,k1_nat_1(D,2)) = k3_matrix_0(A,C,k7_nat_d(G,1),H) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ( v4_qc_lang2(B,A) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ( C = k3_goedelcp(A,B) <=> ? [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) & B = k12_cqc_lang(A,D,C) ) ) ) ) ) ) )).
fof(d5_gr_cy_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => k4_gr_cy_1(A) = g3_algstr_0(k7_card_1(A),k3_gr_cy_1(A)) ) )).
fof(d5_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d5_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : k5_graph_2(A,B) = a_2_2_graph_2(A,B) ) )).
fof(d5_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_graph_3(A,B) = k3_graph_3(A,B,u4_struct_0(A)) ) ) )).
fof(d5_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r3_graph_4(A,B,C) <=> ( k3_finseq_1(B) = k1_nat_1(k3_finseq_1(C),1) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( 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,k1_nat_1(D,1)),k1_funct_1(C,D)) ) ) ) ) ) ) ) )).
fof(d5_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_graph_5(A,B,C) = a_3_0_graph_5(A,B,C) ) ) ) )).
fof(d5_grcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(d5_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => k6_groeb_3(A,B,C,D,E) = k2_groeb_3(A,C,D,k4_groeb_3(A,B,C,D,E)) ) ) ) ) ) )).
fof(d5_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d5_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) ) ) )).
fof(d5_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(d5_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_group_4(B,A) <=> ? [C] : ( 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)) ) ) ) ) )).
fof(d5_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(d5_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_group_6(A,B))) => k6_group_6(A,B,C) = C ) ) ) )).
fof(d5_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_group_9(B,A) ) => ( v3_group_9(B,A) <=> ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & l3_algstr_0(C) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(d5_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(d5_hallmar1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k1_zfmisc_1(A)) => ( m1_hallmar1(D,A,B,C) <=> ( k4_finseq_1(D) = k4_finseq_1(B) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( 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)) ) ) ) ) ) )).
fof(d5_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_henmodel(B,A) & m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) ) => ! [C] : ( m1_valuat_1(C,A,k1_henmodel(A)) => ( m1_henmodel(C,A,B) <=> ! [D] : ( m1_subset_1(D,k6_qc_lang1(A)) => ! [E] : ( 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] : ( r2_hidden(F,E) <=> ? [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d5_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d5_heyting1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))) => ! [D] : ( 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) ) ) ) ) )).
fof(d5_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(k5_substlat(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_substlat(A,B))) => ! [F] : ( m2_subset_1(F,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B)) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d5_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A))))) => ( B = k5_heyting3(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( ~ v8_ordinal1(D) & m1_subset_1(D,k4_ordinal1) & C = k4_heyting3(D,A) ) ) ) ) ) )).
fof(d5_hilbasis,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k5_hilbasis(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ( ( E = B => k1_normsp_1(A,D,E) = C ) & ( E != B => k1_normsp_1(A,D,E) = k4_struct_0(A) ) ) ) ) ) ) ) ) )).
fof(d5_hilbert1,axiom,( ! [A] : ( v5_hilbert1(A) <=> ( r1_tarski(A,k13_finseq_1(k4_ordinal1)) & v1_hilbert1(A) & v2_hilbert1(A) & v3_hilbert1(A) & v4_hilbert1(A) ) ) )).
fof(d5_hilbert3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( m1_hilbert3(B,A) => ! [C] : ( 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] : ( m1_subset_1(D,k4_ordinal1) => k1_msualg_3(k1_hilbert1,k2_hilbert3(A),k2_hilbert3(A),C,k1_hilbert2(D)) = k1_funct_1(B,D) ) & ! [D] : ( m1_subset_1(D,k1_hilbert1) => ! [E] : ( m1_subset_1(E,k1_hilbert1) => ? [F] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d5_hurwitz,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( C != k9_polynom3(A) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k5_hurwitz(A,B,C) <=> ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(E,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & r2_funct_2(k4_ordinal1,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)) ) ) ) ) ) ) ) )).
fof(d5_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_idea_1(A,B) => k5_idea_1(A,B) = k6_xcmplx_0(k5_series_1(2,A),B) ) ) ) )).
fof(d5_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(d5_incproj,axiom,( ! [A] : ( l1_incsp_1(A) => ( v6_incsp_1(A) <=> ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ? [D] : ( m1_subset_1(D,u2_incsp_1(A)) & r1_incsp_1(A,B,D) & r1_incsp_1(A,C,D) ) ) ) ) ) )).
fof(d5_incsp_1,axiom,( ! [A] : ( l2_incsp_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_incsp_1(A))) => ! [C] : ( m1_subset_1(C,u4_incsp_1(A)) => ( r5_incsp_1(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ( r2_hidden(D,B) => r2_incsp_1(A,D,C) ) ) ) ) ) ) )).
fof(d5_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r3_pua2mss1(A,B,D,E) => ! [F] : ( 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] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( r2_int_1(A,B,C) <=> ? [D] : ( v1_int_1(D) & k3_xcmplx_0(C,D) = k6_xcmplx_0(A,B) ) ) ) ) ) )).
fof(d5_int_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(k1_int_3),k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_int_3),k4_ordinal1))) ) => ( A = k3_int_3 <=> ! [B] : ( m1_subset_1(B,u1_struct_0(k1_int_3)) => k3_funct_2(u1_struct_0(k1_int_3),k4_ordinal1,A,B) = k1_funct_1(k2_euclid,B) ) ) ) )).
fof(d5_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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] : ( v1_int_1(C) => ( C = k2_int_6(A,B) <=> ! [D] : ( m1_int_6(D,B) => C = k5_int_1(k16_rvsum_1(k18_valued_1(A,D)),k19_rvsum_1(B)) ) ) ) ) ) ) )).
fof(d5_integr10,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r3_integr10(A,B) <=> ( ! [C] : ( v1_xreal_0(C) => ( 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] : ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,k1_relset_1(k1_numbers,C)) => k1_funct_1(C,D) = k4_integra5(B,D,A) ) ) & v3_limfunc1(C) ) ) ) ) ) )).
fof(d5_integr15,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( m1_integra1(D,B) => ! [E] : ( m2_finseq_1(E,k1_euclid(A)) => ( m3_integr15(E,A,B,C,D) <=> ( k3_finseq_1(E) = k3_finseq_1(D) & ! [F] : ( v7_ordinal1(F) => ~ ( r2_hidden(F,k4_finseq_1(D)) & ! [G] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_integr16,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(d5_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) & ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_integra1(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(B)))) ) => ! [F] : ( m2_integr18(F,A,B,C,E) => ( ( v2_comseq_2(k2_integra3(B,E)) & k1_seq_2(k2_integra3(B,E)) = k5_numbers ) => ( v3_normsp_1(k3_integr18(A,B,C,E,F),A) & k6_normsp_1(A,k3_integr18(A,B,C,E,F)) = D ) ) ) ) ) ) ) ) ) )).
fof(d5_integr1c,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k1_numbers)) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [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)))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( m1_integra1(C,A) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ( D = k4_integra1(A,B,C) <=> ( k3_finseq_1(D) = k3_finseq_1(C) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(C)) => k1_funct_1(D,E) = k3_xcmplx_0(k2_seq_4(k1_rvsum_1(k2_partfun1(A,k1_numbers,B,k2_integra1(A,C,E)))),k3_integra1(k2_integra1(A,C,E))) ) ) ) ) ) ) ) ) )).
fof(d5_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( C = k5_interva1(A,B) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) & B = k2_interva1(A,C,D) ) ) ) ) ) )).
fof(d5_irrat_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( A = k5_irrat_1 <=> ! [B] : ( v7_ordinal1(B) => k1_funct_1(A,B) = k7_xcmplx_0(1,k7_newton(B)) ) ) ) )).
fof(d5_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ( r1_nattra_1(A,B,D,E) => ! [F] : ( m1_nattra_1(F,A,B,D,E) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d5_isomichi,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k1_isomichi(A,B) = k1_tops_1(A,k2_tops_1(A,B)) ) ) )).
fof(d5_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k5_jgraph_6(A,B,C) = a_3_0_jgraph_6(A,B,C) ) ) ) )).
fof(d5_jordan20,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ( r5_jordan20(A,B,C,D,E) <=> ( r1_topreal1(k15_euclid(2),B,C,A) & r2_hidden(D,A) & k17_euclid(D) = E & ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & r1_jordan5c(A,B,C,F,D) & ! [G] : ( 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] : ( m1_subset_1(G,u1_struct_0(k15_euclid(2))) => ( r1_jordan5c(A,B,C,G,F) => ( G = F | ( ? [H] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_jordan3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( ( r1_xxreal_0(k5_numbers,E) & r1_xxreal_0(E,1) & C = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),A,k6_xcmplx_0(1,E)),k1_rlvect_1(k15_euclid(2),B,E)) & r1_xxreal_0(k5_numbers,F) & r1_xxreal_0(F,1) & D = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),A,k6_xcmplx_0(1,F)),k1_rlvect_1(k15_euclid(2),B,F)) ) => r1_xxreal_0(E,F) ) ) ) ) ) ) ) ) ) )).
fof(d5_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( B = k5_jordan5d(A) <=> ( r2_hidden(k4_tarski(B,1),k2_matrix_0(k2_goboard2(A))) & k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),B,1) = k25_pscomp_1(k3_topreal1(2,A)) ) ) ) ) )).
fof(d5_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(d5_jordan_a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( v1_xreal_0(C) => ( C = k3_jordan_a(A,B) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k14_euclid(A)))) & D = B & C = k3_tbsp_1(k14_euclid(A),D) ) ) ) ) ) )).
fof(d5_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_kurato_0(B,A) <=> k4_kurato_0(A,B) = k3_kurato_0(A,B) ) ) )).
fof(d5_kurato_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)))) ) ) )).
fof(d5_lang1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => ! [B] : ( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ! [C] : ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ( r3_lang1(A,B,C) <=> ? [D] : ( 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] : ( m1_subset_1(E,k4_ordinal1) => ~ ( r1_xxreal_0(1,E) & ~ r1_xxreal_0(k3_finseq_1(D),E) & ! [F] : ( m2_finseq_2(F,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ! [G] : ( 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,k1_nat_1(E,1)) = G & r2_lang1(A,F,G) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(D),C,C) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(D))) ) => 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)) ) ) ) ) ) )).
fof(d5_lattice3,axiom,( ! [A] : ( 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))) ) )).
fof(d5_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(d5_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( l1_struct_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => k3_lattice5(A,B,C,D,E) = k3_lattice5(A,B,C,E,D) ) ) ) ) ) ) )).
fof(d5_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_lattice6(A,B,C) <=> ( B != C & r3_lattices(A,C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r3_lattices(A,C,D) & r3_lattices(A,D,B) & D != B & D != C ) ) ) ) ) ) ) )).
fof(d5_lattice7,axiom,( ! [A] : ( ( 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] : ( ( ~ v1_xboole_0(B) & v6_orders_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k2_lattice7(A,B) <=> ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => r3_orders_2(A,D,C) ) ) & r2_hidden(C,B) ) ) ) ) ) )).
fof(d5_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_lattices(A) ) => ( v5_lattices(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d5_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( v2_lexbfs(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(d5_lfuzzy_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_lfuzzy_0(A))) => k5_lfuzzy_0(A,B) = B ) ) )).
fof(d5_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => k8_lfuzzy_0(A,A,B,C,D) = k8_lfuzzy_0(A,A,B,D,C) ) ) ) ) ) )).
fof(d5_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_limfunc1(A) <=> ! [B] : ( v1_xreal_0(B) => ? [C] : ( v7_ordinal1(C) & ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(C,D) & r1_xxreal_0(B,k1_funct_1(A,D)) ) ) ) ) ) ) )).
fof(d5_limfunc2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r5_limfunc2(A,B) <=> ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,B) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(C,D) & ~ r1_xxreal_0(D,B) & r2_hidden(D,k1_relset_1(k1_numbers,A)) ) ) ) ) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(C) & k1_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(k4_ordinal1,k1_numbers,k1_numbers,C,A)) ) ) ) ) ) ) )).
fof(d5_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) )).
fof(d5_lopban_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_rlvect_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => 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) ) ) ) ) ) ) )).
fof(d5_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => k6_lopban_2(A) = k6_partfun1(u1_struct_0(A)) ) )).
fof(d5_lopban_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lopban_2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k2_lopban_3(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k5_rsspace3(A,D,E) = k6_algstr_0(A,C,k5_rsspace3(A,B,E)) ) ) ) ) ) ) )).
fof(d5_lopban_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( C = k4_lopban_4(A,B) <=> ( k9_nat_1(u1_struct_0(A),C,k5_numbers) = k4_struct_0(A) & ! [D] : ( v7_ordinal1(D) => k9_nat_1(u1_struct_0(A),C,k1_nat_1(D,1)) = k9_nat_1(u1_struct_0(A),B,D) ) ) ) ) ) ) )).
fof(d5_lopclset,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(d5_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(k3_rfunct_3(A,k2_numbers),k3_rfunct_3(A,k2_numbers)),k3_rfunct_3(A,k2_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k3_rfunct_3(A,k2_numbers),k3_rfunct_3(A,k2_numbers)),k3_rfunct_3(A,k2_numbers)))) ) => ( B = k9_lpspacc1(A) <=> ! [C] : ( m2_rfunct_3(C,A,k2_numbers,k3_rfunct_3(A,k2_numbers)) => ! [D] : ( m2_rfunct_3(D,A,k2_numbers,k3_rfunct_3(A,k2_numbers)) => r2_relset_1(A,k2_numbers,k2_lpspace1(A,k2_numbers,B,C,D),k1_lpspacc1(A,k2_numbers,C,D)) ) ) ) ) ) )).
fof(d5_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k5_lpspace1(A) = k8_funcop_1(k4_ordinal1,A,k5_numbers) ) )).
fof(d5_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v2_xxreal_0(D) & v1_xreal_0(D) ) => k4_lpspace2(A,B,C,D) = g1_rlvect_1(k3_lpspace2(A,B,C,D),k10_subset_1(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))) ) ) ) ) )).
fof(d5_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => k5_ltlaxio1(A,B) = k1_ltlaxio1(k4_ltlaxio1(k1_ltlaxio1(A),k1_ltlaxio1(B))) ) ) )).
fof(d5_ltlaxio2,axiom,( ! [A] : ( m2_finseq_1(A,k1_hilbert1) => ! [B] : ( m2_finseq_1(B,k1_hilbert1) => ( B = k5_ltlaxio2(A) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(A)) ) => k1_funct_1(B,C) = k2_ltlaxio1(k7_partfun1(k1_hilbert1,A,C)) ) ) ) ) ) ) )).
fof(d5_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_hilbert1)) => ( B = k5_ltlaxio3(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( m1_subset_1(D,k1_hilbert1) & r2_hidden(D,A) & r2_hidden(C,k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,D)) ) ) ) ) ) )).
fof(d5_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ( r1_ltlaxio4(A,B) <=> ( r1_tarski(k2_relset_1(k1_hilbert1,k8_ltlaxio3(A)),k2_relset_1(k1_hilbert1,k8_ltlaxio3(B))) & r1_tarski(k2_relset_1(k1_hilbert1,k9_ltlaxio3(A)),k2_relset_1(k1_hilbert1,k9_ltlaxio3(B))) & k5_ltlaxio3(k10_ltlaxio3(A)) = k10_ltlaxio3(B) ) ) ) ) )).
fof(d5_margrel1,axiom,( ! [A] : ! [B] : ( ( v3_finseq_1(B) & v2_card_3(B) ) => ( m2_margrel1(B,A) <=> ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(C,B) => r1_tarski(k10_xtuple_0(C),A) ) ) ) ) )).
fof(d5_mathmorp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(d5_matrix10,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( r1_matrix10(A,B) <=> ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(k4_tarski(C,D),k2_matrix_0(A)) & r1_xxreal_0(k3_matrix_0(k1_numbers,B,C,D),k3_matrix_0(k1_numbers,A,C,D)) ) ) ) ) ) ) )).
fof(d5_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ( r2_hidden(E,k2_finseq_1(k1_matrix_0(D))) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(B,k5_numbers) | ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(C),A,B) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(C))) ) => ( G = k5_matrix12(A,B,C,D,E,F) <=> ( k3_finseq_1(G) = k3_finseq_1(D) & ! [H] : ( v7_ordinal1(H) => ! [I] : ( v7_ordinal1(I) => ( ( r2_hidden(H,k4_finseq_1(D)) & r2_hidden(I,k2_finseq_1(k1_matrix_0(D))) ) => ( ( I = E => k3_matrix_0(u1_struct_0(C),G,H,I) = k8_group_1(C,F,k3_matrix_0(u1_struct_0(C),D,H,E)) ) & ( I != E => k3_matrix_0(u1_struct_0(C),G,H,I) = k3_matrix_0(u1_struct_0(C),D,H,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_matrix13,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k6_prvect_1(A,B))) => k10_matrix13(A,B,C) = C ) ) ) )).
fof(d5_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ( ( k1_matrix_0(B) = k5_numbers => k3_finseq_1(B) = k5_numbers ) => ! [C] : ( ( v7_vectsp_1(C,A) & m1_vectsp_4(C,A,k6_prvect_1(A,k1_matrix_0(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))) ) ) ) ) ) )).
fof(d5_matrix16,axiom,( ! [A] : ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ( v3_matrix16(B,A) <=> ? [C] : ( m2_finseq_1(C,A) & k3_finseq_1(C) = k3_finseq_1(B) & r2_matrix16(A,B,C) ) ) ) )).
fof(d5_matrix17,axiom,( ! [A] : ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ( v4_matrix17(B,A) <=> ? [C] : ( m2_finseq_1(C,A) & k3_finseq_1(C) = k1_matrix_0(B) & r1_matrix17(A,B,C) ) ) ) )).
fof(d5_matrix_0,axiom,( ! [A] : ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k4_tarski(C,D),k2_matrix_0(B)) => ! [E] : ( m1_subset_1(E,A) => ( E = k3_matrix_0(A,B,C,D) <=> ? [F] : ( m2_finseq_1(F,A) & F = k1_funct_1(B,C) & E = k1_funct_1(F,D) ) ) ) ) ) ) ) )).
fof(d5_matrix_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(A),B,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(A),B,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(A),B,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(A))) ) => ( E = k5_matrix_1(A,B,C,D) <=> ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ( r2_hidden(k4_tarski(F,G),k2_matrix_0(C)) => k3_matrix_0(u1_struct_0(A),E,F,G) = k1_algstr_0(A,k3_matrix_0(u1_struct_0(A),C,F,G),k3_matrix_0(u1_struct_0(A),D,F,G)) ) ) ) ) ) ) ) ) ) )).
fof(d5_matrix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( B = k3_matrix_2(A) <=> ! [C] : ( 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)))) ) ) ) ) )).
fof(d5_matrix_3,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_matrix_0(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_0(D) = k1_matrix_0(B) & ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( r2_hidden(k4_tarski(E,F),k2_matrix_0(B)) => k3_matrix_0(u1_struct_0(A),D,E,F) = k8_group_1(A,C,k3_matrix_0(u1_struct_0(A),B,E,F)) ) ) ) ) ) ) ) ) ) )).
fof(d5_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ! [B] : ( ( v1_matrix_0(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))) ) ) )).
fof(d5_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v2_matrix_6(C,A,B) <=> k4_matrix_0(u1_struct_0(B),C) = C ) ) ) ) )).
fof(d5_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r1_matrix_8(A,B,C,D) <=> ? [E] : ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) & v1_matrix_6(E,A,B) & C = k4_matrix_3(B,k4_matrix_3(B,k1_matrix_6(A,B,E),D),E) ) ) ) ) ) ) )).
fof(d5_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => k5_matrixc1(A,B) = k1_finseqop(k2_numbers,k2_numbers,k2_numbers,k5_binop_2,A,B) ) ) )).
fof(d5_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_matrixj1(C,A) & m2_finseq_1(C,k3_finseq_2(k3_finseq_2(A))) ) => ! [D] : ( ( v1_matrix_0(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_0(D) = k2_wsierp_1(k11_matrixj1(A,C)) & ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( r2_hidden(k4_tarski(E,F),k2_matrix_0(D)) => ( ( ~ ( ~ r1_xxreal_0(F,k2_wsierp_1(k17_finseq_1(k4_ordinal1,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(k4_ordinal1,k1_matrixj1(k10_matrixj1(A,C),E),k11_matrixj1(A,C)))) ) => k3_matrix_0(A,D,E,F) = B ) & ( r1_xxreal_0(F,k2_wsierp_1(k17_finseq_1(k4_ordinal1,k1_matrixj1(k10_matrixj1(A,C),E),k11_matrixj1(A,C)))) => ( r1_xxreal_0(F,k2_wsierp_1(k17_finseq_1(k4_ordinal1,k7_nat_d(k1_matrixj1(k10_matrixj1(A,C),E),1),k11_matrixj1(A,C)))) | k3_matrix_0(A,D,E,F) = k3_matrix_0(A,k2_matrixj1(A,C,k1_matrixj1(k10_matrixj1(A,C),E)),k7_nat_d(E,k2_wsierp_1(k17_finseq_1(k4_ordinal1,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(k4_ordinal1,k7_nat_d(k1_matrixj1(k10_matrixj1(A,C),E),1),k11_matrixj1(A,C))))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_matrixj2,axiom,( ! [A] : ( l6_algstr_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d5_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(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))) ) ) )).
fof(d5_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( v1_matrixr2(B,A) <=> ? [C] : ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) & k1_matrixr2(A,C,B) = k4_matrixr2(A) & k1_matrixr2(A,B,C) = k4_matrixr2(A) ) ) ) ) )).
fof(d5_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(d5_matrprob,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( v1_matrprob(A) <=> ( ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => r1_xxreal_0(k5_numbers,k1_funct_1(A,B)) ) ) & k18_rvsum_1(A) = 1 ) ) ) )).
fof(d5_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( 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] : ( v7_ordinal1(D) => ~ ( r2_hidden(D,k4_finseq_1(C)) & ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_mcart_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) => ! [F] : ( m1_subset_1(F,B) => ( F = k5_mcart_1(A,B,C,D,E) <=> ! [G] : ! [H] : ! [I] : ! [J] : ( E = k6_xtuple_0(G,H,I,J) => F = H ) ) ) ) ) ) ) ) )).
fof(d5_measure1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v3_measure1(B,A) <=> ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(d5_measure3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k2_measure3(A,B,C),k6_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),k6_numbers))) ) => ( D = k4_measure3(A,B,C) <=> ! [E] : ( r2_hidden(E,B) => ! [F] : ( m1_measure3(F,A,B,C) => k12_supinf_2(D,k2_xboole_0(E,F)) = k12_supinf_2(C,E) ) ) ) ) ) ) )).
fof(d5_measure5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v4_measure5(A) <=> ? [B] : ( m1_subset_1(B,k6_numbers) & ? [C] : ( v1_xreal_0(C) & A = k4_rcomp_1(B,C) ) ) ) ) )).
fof(d5_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ! [D] : ( m2_measure8(D,A,B) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k6_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( E = k2_measure8(A,B,C,D) <=> ! [F] : ( v7_ordinal1(F) => k1_mesfunc9(E,F) = k1_mesfunc9(C,k1_measure8(A,B,D,F)) ) ) ) ) ) ) )).
fof(d5_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => k8_member_1(A,B) = a_2_0_member_1(A,B) ) ) )).
fof(d5_membered,axiom,( ! [A] : ( v5_membered(A) <=> ! [B] : ( r2_hidden(B,A) => v1_int_1(B) ) ) )).
fof(d5_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_memstr_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k4_memstr_0(A,B,C) = k1_funct_1(k2_memstr_0(A,B),C) ) ) ) )).
fof(d5_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(d5_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => k5_mesfun7c(A,B) = k4_mesfunc8(A,k1_mesfun7c(A,B)) ) ) )).
fof(d5_mesfun9c,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( 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,k5_numbers)) = k1_relset_1(A,C) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & ? [G] : ( m1_subset_1(G,A) & r1_xxreal_0(E,F) & r2_hidden(G,k1_relset_1(A,k4_mesfunc5(A,k1_numbers,B,k5_numbers))) & r1_xxreal_0(D,k9_complex1(k4_supinf_2(k1_mesfunc9(k4_mesfunc5(A,k1_numbers,B,F),G),k1_mesfunc9(C,G)))) ) ) ) ) ) ) ) ) ) )).
fof(d5_mesfunc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k6_numbers) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,k6_numbers) & v1_funct_1(C) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( D = k5_mesfunc1(A,B,C) <=> ( k9_xtuple_0(D) = k3_xboole_0(k9_xtuple_0(B),k9_xtuple_0(C)) & ! [E] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d5_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( v3_mesfunc5(B) <=> ! [C] : ~ r1_xxreal_0(k1_funct_1(B,C),k2_supinf_1) ) ) ) )).
fof(d5_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(d5_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k6_numbers)) & v1_mesfunc8(C,A,k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ( C = k3_mesfunc8(A,B) <=> ! [D] : ( v7_ordinal1(D) => ( k1_relset_1(A,k4_mesfunc5(A,k6_numbers,C,D)) = k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers)) & ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,C,D))) => k12_supinf_2(k4_mesfunc5(A,k6_numbers,C,D),E) = k9_nat_1(k6_numbers,k3_rinfsup2(k3_mesfunc5(A,B,E)),D) ) ) ) ) ) ) ) ) )).
fof(d5_mesfunc9,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ( v2_mesfunc9(B,A) <=> ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( C != D => ! [E] : ~ ( r2_hidden(E,k9_subset_1(A,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,C)),k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,D)))) & k1_mesfunc9(k4_mesfunc5(A,k6_numbers,B,C),E) = k1_supinf_1 & k1_mesfunc9(k4_mesfunc5(A,k6_numbers,B,D),E) = k2_supinf_1 ) ) ) ) ) ) )).
fof(d5_metric_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => r1_xxreal_0(k1_binop_1(B,C,E),k2_xcmplx_0(k1_binop_1(B,C,D),k1_binop_1(B,D,E))) ) ) ) ) ) )).
fof(d5_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k2_metric_2(A)) => ! [C] : ( m1_subset_1(C,k2_metric_2(A)) => ! [D] : ( v1_xreal_0(D) => ( r4_metric_2(A,B,C,D) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r2_hidden(E,B) & r2_hidden(F,C) ) => k1_metric_1(A,E,F) = D ) ) ) ) ) ) ) ) )).
fof(d5_metric_6,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r2_metric_6(A,B,C) <=> ? [D] : ( v7_ordinal1(D) & ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(D,E) => r2_hidden(k2_tbsp_1(A,C,E),B) ) ) ) ) ) ) ) )).
fof(d5_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(d5_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v2_struct_0(C) & v2_midsp_1(C) & l1_midsp_3(C,k1_nat_1(A,2)) ) => ( r2_midsp_3(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m2_finseq_2(F,u1_struct_0(C),k4_finseq_2(k1_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)) ) ) ) ) ) ) ) ) )).
fof(d5_mmlquer2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( C = k3_mmlquer2(A,B) <=> ! [D] : ! [E] : ( r1_mmlquery(D,E,C) <=> ( r2_hidden(D,A) & r2_hidden(E,A) & ~ r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(B,D)) ) ) ) ) ) )).
fof(d5_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( l1_mod_2(B,A) => k4_mod_2(A,B) = u3_mod_2(A,B) ) ) )).
fof(d5_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_2(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(d5_modal_1,axiom,( ! [A] : ( m1_trees_3(A,k2_zfmisc_1(k4_ordinal1,k4_ordinal1)) => ( A = k6_modal_1 <=> ( ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k2_zfmisc_1(k4_ordinal1,k4_ordinal1)) & v1_funct_1(B) & v3_trees_2(B) ) => ( r2_hidden(B,A) => v1_finset_1(B) ) ) & ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k2_zfmisc_1(k4_ordinal1,k4_ordinal1)) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) ) => ( r2_hidden(B,A) <=> ! [C] : ( 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) = k5_numbers & k3_trees_2(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),B,C) != k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers) & ! [D] : ( v7_ordinal1(D) => k3_trees_2(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),B,C) != k4_tarski(3,D) ) ) & ~ ( k5_modal_1(k9_xtuple_0(B),C) = 1 & k3_trees_2(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),B,C) != k1_domain_1(k4_ordinal1,k4_ordinal1,1,k5_numbers) & k3_trees_2(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),B,C) != k1_domain_1(k4_ordinal1,k4_ordinal1,1,1) ) & ( k5_modal_1(k9_xtuple_0(B),C) = 2 => k3_trees_2(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),B,C) = k1_domain_1(k4_ordinal1,k4_ordinal1,2,k5_numbers) ) ) ) ) ) ) ) ) )).
fof(d5_modcat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ? [E] : ( A = k4_tarski(D,E) & ? [F] : ( ~ 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) ) ) ) ) )).
fof(d5_modelc_2,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => k5_modelc_2(A,B) = k8_finseq_1(k4_ordinal1,k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,2),A),B) ) ) )).
fof(d5_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( l1_modelc_3(B,A) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ( r2_hidden(C,u2_modelc_3(A,B)) => ! [D] : ( ( 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) ) ) ) ) ) ) ) )).
fof(d5_moebius1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ( B = k4_moebius1(A) <=> ( k13_pre_poly(B) = k9_subset_1(k4_ordinal1,A,k1_moebius1) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k13_pre_poly(B)) => k1_funct_1(B,C) = k2_moebius1(C) ) ) ) ) ) )).
fof(d5_monoid_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ? [E] : ( m1_subset_1(E,A) & ? [F] : ( m1_subset_1(F,A) & k5_binop_1(A,B,C,E) = D & k5_binop_1(A,B,F,C) = D ) ) ) ) ) ) ) )).
fof(d5_monoid_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => k18_monoid_1(A,B) = k16_monoid_1(k6_domain_1(A,B),A) ) ) )).
fof(d5_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_msafree(C,A,B) => ( v1_msafree(C,A,B) <=> ! [D] : ( ( v4_msualg_1(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( m2_pboole(E,u1_struct_0(A),C,u3_msualg_1(A,D)) => ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d5_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d5_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) ) => ! [D] : ( m3_pboole(D,u1_struct_0(A),u3_msualg_1(A,k11_msafree(A,B))) => ( D = k5_msafree3(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k1_funct_1(D,E) = a_4_0_msafree3(A,B,C,E) ) ) ) ) ) ) )).
fof(d5_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ( v4_msafree4(C,A,B) <=> ? [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) & r2_msualg_3(A,B,C,D) ) ) ) ) ) )).
fof(d5_msalimit,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_msalimit(C,A,B) => ! [D] : ( m2_msalimit(D,A,B,C) => ! [E] : ( m2_msalimit(E,A,B,C) => ( E = k2_msalimit(A,B,C,D) <=> ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(d5_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ( D = k7_msaterm(A,B,C) <=> r2_hidden(C,k7_msafree(A,B,D)) ) ) ) ) ) )).
fof(d5_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) => ( v4_mssubfam(C,A,B) <=> ! [D] : ( m3_pboole(D,A,k1_mboolean(A,B)) => ( r2_pboole(A,D,C) => r1_pboole(A,k4_mssubfam(A,B,D),C) ) ) ) ) ) )).
fof(d5_msualg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d5_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d5_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( m2_pboole(E,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d5_msualg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(d5_msualg_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v3_lattices(C) & v10_lattices(C) & l3_lattices(C) ) => ( C = k5_msualg_5(A,B) <=> ( ! [D] : ( r2_hidden(D,u1_struct_0(C)) <=> ( v1_msualg_4(D,A,B) & m1_msualg_4(D,A,B,B) ) ) & ! [D] : ( ( v1_msualg_4(D,A,B) & m1_msualg_4(D,A,B,B) ) => ! [E] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(d5_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( l3_msualg_1(D,A) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r1_msualg_6(A,B,C,D,E) <=> ? [F] : ( m1_subset_1(F,u4_struct_0(A)) & k2_msualg_1(A,F) = C & ? [G] : ( m1_subset_1(G,k4_ordinal1) & 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d5_mycielsk,axiom,( ! [A] : ( ( v2_mycielsk(A) & l1_orders_2(A) ) => ! [B] : ( v7_ordinal1(B) => ( B = k3_mycielsk(A) <=> ( ? [C] : ( v1_finset_1(C) & v5_dilworth(C,A) & m1_eqrel_1(C,u1_struct_0(A)) & k5_card_1(C) = B ) & ! [C] : ( ( v1_finset_1(C) & v5_dilworth(C,A) & m1_eqrel_1(C,u1_struct_0(A)) ) => r1_xxreal_0(B,k5_card_1(C)) ) ) ) ) ) )).
fof(d5_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)))) ) ) ) ) )).
fof(d5_nat_3,axiom,( ! [A] : ! [B] : ( ( 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] : ( v1_xcmplx_0(C) => ( C = k7_nat_3(A,B) <=> ? [D] : ( m2_finseq_1(D,k2_numbers) & C = k20_rvsum_1(D) & D = k3_relat_1(k19_finseq_1(k13_pre_poly(B)),B) ) ) ) ) )).
fof(d5_nat_5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ( v1_nat_5(A) <=> ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ( r1_int_2(B,C) => k1_recdef_1(A,k3_xcmplx_0(B,C)) = k2_nat_1(k1_recdef_1(A,B),k1_recdef_1(A,C)) ) ) ) ) ) )).
fof(d5_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( C = k3_int_2(A,B) <=> ( r1_nat_d(C,A) & r1_nat_d(C,B) & ! [D] : ( v7_ordinal1(D) => ( ( r1_nat_d(D,A) & r1_nat_d(D,B) ) => r1_nat_d(D,C) ) ) ) ) ) ) ) )).
fof(d5_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ( ( r1_nattra_1(A,B,C,D) & r1_nattra_1(A,B,D,E) ) => ! [F] : ( m1_nattra_1(F,A,B,C,D) => ! [G] : ( m1_nattra_1(G,A,B,D,E) => ! [H] : ( m1_nattra_1(H,A,B,C,E) => ( H = k3_nattra_1(A,B,C,D,E,F,G) <=> ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => k2_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),k2_nattra_1(A,B,C,D,F,I),k2_nattra_1(A,B,D,E,G,I)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,C)) ) ) ) ) ) ) ) ) ) )).
fof(d5_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ~ ( r2_hidden(F,A) & r2_hidden(G,A) & ~ r1_xxreal_0(E,k2_normsp_0(B,k5_algstr_0(B,F,G))) & r1_xxreal_0(D,k9_complex1(k5_real_1(k7_partfun1(k1_numbers,C,F),k7_partfun1(k1_numbers,C,G)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_ndiff_1(D,A,k4_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v12_struct_0(D,k4_ordinal1,A) => ( v3_normsp_1(k1_ndiff_1(B,k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),D,C),k37_valued_1(k4_ordinal1,k1_numbers,k5_normsp_0(A,D))),B) & k6_normsp_1(B,k1_ndiff_1(B,k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),D,C),k37_valued_1(k4_ordinal1,k1_numbers,k5_normsp_0(A,D)))) = k4_struct_0(B) ) ) ) ) ) ) ) ) )).
fof(d5_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [C] : ( r2_ndiff_3(A,B,C) <=> ( r1_tarski(C,k1_relset_1(k1_numbers,B)) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => r1_ndiff_3(A,k2_partfun1(k1_numbers,u1_struct_0(A),B,C),D) ) ) ) ) ) ) )).
fof(d5_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(d5_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( r2_hidden(B,k4_finseq_1(A)) => k5_ndiff_5(A,B) = B ) ) )).
fof(d5_neckla_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k3_neckla_2)) => ( A = k4_neckla_2 <=> ( ! [B] : ( ( 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] : ( ( v1_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(B,k1_zfmisc_1(k3_neckla_2)) => ( ( ! [C] : ( ( 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] : ( ( v1_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(d5_necklace,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_necklace(A) <=> ! [B] : ~ ( r2_hidden(B,u1_struct_0(A)) & r2_hidden(k4_tarski(B,B),u1_orders_2(A)) ) ) ) )).
fof(d5_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : ! [C] : ( r2_net_1(A,B,C) <=> ( r2_hidden(k4_tarski(B,C),k1_net_1(A)) & r2_hidden(B,u4_struct_0(A)) ) ) ) )).
fof(d5_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( B = k6_newton(A) <=> ( k3_finseq_1(B) = k1_nat_1(A,1) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(C,k4_finseq_1(B)) & D = k6_xcmplx_0(C,1) ) => k1_funct_1(B,C) = k4_newton(D,A) ) ) ) ) ) ) ) )).
fof(d5_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,C)) ) ) ) ) ) ) ) ) ) )).
fof(d5_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ( r2_hidden(C,k1_relset_1(k1_numbers,B)) => r1_nfcont_4(A,B,C) ) ) ) ) ) )).
fof(d5_normsp_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_normsp_0(A) ) => ( v3_normsp_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( k2_normsp_0(A,B) = k5_numbers => B = k4_struct_0(A) ) ) ) ) )).
fof(d5_normsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k5_normsp_1(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k1_normsp_1(A,D,E) = k1_rlvect_1(A,k1_normsp_1(A,B,E),C) ) ) ) ) ) ) )).
fof(d5_numbers,axiom,( k6_numbers = k2_xboole_0(k1_numbers,k2_tarski(k1_numbers,k4_tarski(k5_numbers,k1_numbers))) )).
fof(d5_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ( v4_o_ring_1(B,A) <=> ( k3_finseq_1(B) != k5_numbers & v1_o_ring_1(k7_partfun1(u1_struct_0(A),B,1),A) & ! [C] : ( v7_ordinal1(C) => ~ ( C != k5_numbers & ~ r1_xxreal_0(k3_finseq_1(B),C) & ! [D] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d5_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => k7_openlatt(A) = a_1_0_openlatt(A) ) )).
fof(d5_oposet_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v3_necklace(A) <=> v2_relat_2(u1_orders_2(A)) ) ) )).
fof(d5_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(k2_oppcat_1(A))) => k6_oppcat_1(A,B) = k5_oppcat_1(k2_oppcat_1(A),B) ) ) )).
fof(d5_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( r2_hidden(C,k1_ordeq_01(A,B)) => ! [D] : ( ( v1_funct_1(D) & v1_nfcont_3(D,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ( D = k4_ordeq_01(A,B,C) <=> ( D = C & k1_relset_1(k1_numbers,D) = A ) ) ) ) ) ) )).
fof(d5_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v2_orders_1(A) <=> ( v1_relat_2(A) & v8_relat_2(A) & v4_relat_2(A) ) ) ) )).
fof(d5_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_orders_2(A,B,C) <=> r2_hidden(k4_tarski(B,C),u1_orders_2(A)) ) ) ) ) )).
fof(d5_orders_3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_orders_2(A,D,E) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r1_ordinal1(A,B) <=> ! [C] : ( v3_ordinal1(C) => ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ) ) ) )).
fof(d5_ordinal2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) ) => k4_ordinal2(A) = k3_ordinal2(k10_xtuple_0(A)) ) )).
fof(d5_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( 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 ) ) ) ) ) ) )).
fof(d5_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ( v4_ordinal5(A) <=> k12_ordinal2(k4_ordinal1,A) = A ) ) )).
fof(d5_ordinal6,axiom,( ! [A] : ( v1_ordinal6(A) => k1_ordinal6(A) = k2_wellord2(k1_wellord2(A)) ) )).
fof(d5_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(d5_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ 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)) ) ) ) ) )).
fof(d5_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_osalg_2(C,A,B) => ( C = k3_osalg_2(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_funct_1(C,D) = k1_osalg_2(A,B,D) ) ) ) ) ) )).
fof(d5_osalg_4,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d5_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( D = k5_partfun1(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ? [F] : ( 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) ) ) ) ) )).
fof(d5_partfun3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k1_partfun3(A) <=> ( k9_xtuple_0(B) = k9_xtuple_0(A) & ! [C] : ( r2_hidden(C,k9_xtuple_0(B)) => k1_funct_1(B,C) = k3_square_1(k1_funct_1(A,C)) ) ) ) ) ) )).
fof(d5_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ( D = k3_partit1(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> r2_partit1(A,B,C,E) ) ) ) ) ) ) )).
fof(d5_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ( v5_pasch(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(H,u1_struct_0(A)) => ~ ( r1_diraf(A,C,H,D) & r1_diraf(A,F,H,E) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( D = k3_pboole(A,B,C) <=> ! [E] : ( r2_hidden(E,A) => k1_funct_1(D,E) = k3_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) )).
fof(d5_pcomps_1,axiom,( ! [A] : ( l1_metric_1(A) => k3_pcomps_1(A) = g1_pre_topc(u1_struct_0(A),k2_pcomps_1(A)) ) )).
fof(d5_pdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k5_pdiff_1(A,B) <=> ( k9_xtuple_0(C) = k1_numbers & ! [D] : ( m1_subset_1(D,k1_numbers) => k1_funct_1(C,D) = k1_finseq_7(k1_numbers,B,A,D) ) ) ) ) ) ) )).
fof(d5_pdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(2)) => ( r4_pdiff_3(A,B) <=> ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & B = k10_finseq_1(C,D) & ? [E] : ( 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] : ( v1_funct_1(F) & v3_fdiff_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [G] : ( v1_funct_1(G) & v2_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,E) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(2,2,k1_pdiff_3(2,2,A),B),H),k1_funct_1(k1_pdiff_2(2,2,k1_pdiff_3(2,2,A),B),D)) = k2_xcmplx_0(k1_funct_1(F,k6_xcmplx_0(H,D)),k1_funct_1(G,k6_xcmplx_0(H,D))) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r5_pdiff_5(A,B) <=> ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & B = k11_finseq_1(C,D,E) & ? [F] : ( 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] : ( v1_funct_1(G) & v3_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [H] : ( v1_funct_1(H) & v2_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,F) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,2,k1_pdiff_3(2,3,A),B),I),k1_funct_1(k1_pdiff_2(3,2,k1_pdiff_3(2,3,A),B),D)) = k2_xcmplx_0(k1_funct_1(G,k6_xcmplx_0(I,D)),k1_funct_1(H,k6_xcmplx_0(I,D))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [E] : ( r2_pdiff_7(A,B,C,D,E) => ! [F] : ( ( 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] : ( m2_finseq_2(G,k1_numbers,k1_euclid(A)) => ( r2_hidden(G,E) => k7_partfun1(k1_euclid(B),F,G) = k11_pdiff_1(A,B,C,D,G) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d5_pencil_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( v4_pencil_1(A) <=> m1_subset_1(u1_struct_0(A),u1_pre_topc(A)) ) ) )).
fof(d5_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( v7_ordinal1(C) => k5_pencil_4(A,B,C) = g1_pre_topc(k2_vectsp_9(A,B,C),k4_pencil_4(A,B,C)) ) ) ) )).
fof(d5_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k7_petri(A,B) = a_2_1_petri(A,B) ) ) )).
fof(d5_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ( r2_pnproc_1(A,C,B) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,k4_ordinal1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ( D = k3_pnproc_1(A,B,C) <=> ! [E] : ( r2_hidden(E,A) => k1_funct_1(D,E) = k6_xcmplx_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) )).
fof(d5_polyalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_polyalg1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( ( ~ 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] : ( m1_polyalg1(E,A,B) => ( r1_tarski(C,u1_struct_0(E)) => r1_tarski(u1_struct_0(D),u1_struct_0(E)) ) ) ) ) ) ) ) ) )).
fof(d5_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( 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)) = k5_numbers => ( E = k5_polyeq_5(A,B,C,D) <=> ? [F] : ( v1_xcmplx_0(F) & ? [G] : ( v1_xcmplx_0(G) & ? [H] : ( v1_xcmplx_0(H) & F = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(8,C),k3_xcmplx_0(3,k1_newton(D,2))),32) & G = k7_xcmplx_0(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)))),k7_xcmplx_0(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)) != k5_numbers => ( E = k5_polyeq_5(A,B,C,D) <=> ? [F] : ( v1_xcmplx_0(F) & ? [G] : ( v1_xcmplx_0(G) & ? [H] : ( v1_xcmplx_0(H) & ? [I] : ( v1_xcmplx_0(I) & ? [J] : ( v1_xcmplx_0(J) & ? [K] : ( v1_xcmplx_0(K) & F = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(8,C),k3_xcmplx_0(3,k1_newton(D,2))),32) & G = k7_xcmplx_0(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 = k7_xcmplx_0(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 = k4_xcmplx_0(k7_xcmplx_0(G,k3_xcmplx_0(I,J))) & E = k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(I,J),K),k7_xcmplx_0(D,4)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( 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 ) ) ) ) ) ) )).
fof(d5_polynom1,axiom,( ! [A] : ( l2_struct_0(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) ) => ( v1_polynom1(B,A) <=> v1_finset_1(k2_polynom1(A,B)) ) ) ) )).
fof(d5_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( m2_finseq_1(E,k4_finseq_2(3,k4_ordinal1)) => ! [F] : ( 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] : ( m1_subset_1(G,k4_ordinal1) => ( 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(k4_ordinal1,k9_pre_poly(k4_ordinal1,k4_ordinal1,k4_finseq_2(3,k4_ordinal1),E,G),1)),k1_normsp_1(A,C,k7_partfun1(k4_ordinal1,k9_pre_poly(k4_ordinal1,k4_ordinal1,k4_finseq_2(3,k4_ordinal1),E,G),2))),k1_normsp_1(A,D,k7_partfun1(k4_ordinal1,k9_pre_poly(k4_ordinal1,k4_ordinal1,k4_finseq_2(3,k4_ordinal1),E,G),3))) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_polynom5,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k5_polynom5(A,B,C) <=> ? [E] : ( 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] : ( m1_subset_1(F,k4_ordinal1) => ( 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(k4_ordinal1,u1_struct_0(A),B,k7_nat_d(F,1))) ) ) ) ) ) ) ) ) )).
fof(d5_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( 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] : ( ( 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) <=> ~ ( k4_polynom1(A,B,C,D) = k4_struct_0(B) & ~ ( k3_polynom1(k15_pre_poly(A),B,C) = k1_xboole_0 & D = k16_pre_poly(A) ) ) ) ) ) ) )).
fof(d5_polynom8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( C = k5_polynom8(A,B) <=> ( ! [D] : ( v7_ordinal1(D) => ( ~ r1_xxreal_0(k3_finseq_1(B),D) => k9_nat_1(u1_struct_0(A),C,D) = k3_matrix_0(u1_struct_0(A),B,k1_nat_1(D,1),1) ) ) & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(k3_finseq_1(B),D) => k9_nat_1(u1_struct_0(A),C,D) = k4_struct_0(A) ) ) ) ) ) ) ) )).
fof(d5_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [G] : ( ( 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 != k8_polynom1(A,C) & E != k8_polynom1(A,C) & r2_hidden(G,k3_polynom1(k15_pre_poly(A),C,D)) & ? [H] : ( 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,k7_polynom1(A,C,D,k5_polynom7(A,C,k1_polyred(A,H,C,E),k3_vectsp_1(C,k4_polynom1(A,C,D,G),k4_termord(A,B,C,E))))) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k3_poset_1(A,B) <=> ( r2_abian(u1_struct_0(A),C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_abian(u1_struct_0(A),D,B) => r3_orders_2(A,C,D) ) ) ) ) ) ) ) ) )).
fof(d5_pralg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(d5_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v1_valued_0(C) ) => ! [D] : ( ( 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] : k1_funct_1(D,E) = k2_xcmplx_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) )).
fof(d5_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v1_pre_topc(C) & m1_pre_topc(C,A) ) => ( C = k1_pre_topc(A,B) <=> k2_struct_0(C) = B ) ) ) ) )).
fof(d5_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v5_relat_1(B,k3_numbers) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( C = k5_prepower(A,B) <=> ! [D] : ( v7_ordinal1(D) => k1_funct_1(C,D) = k4_prepower(A,k1_funct_1(B,D)) ) ) ) ) ) )).
fof(d5_prgcor_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k1_numbers) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k1_numbers) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( v1_int_1(C) => ( r3_prgcor_2(A,B,C) <=> ( k1_afinsq_1(B) = C & k1_afinsq_1(A) = C & ? [D] : ( v1_int_1(D) & k1_funct_1(B,k5_numbers) = k1_funct_1(A,k5_numbers) & D = k1_funct_1(A,k5_numbers) & ( D != k5_numbers => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,D) ) => k1_funct_1(B,E) = k4_xcmplx_0(k1_funct_1(A,E)) ) ) ) ) ) ) ) ) ) )).
fof(d5_prob_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v3_prob_1(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => r1_tarski(k1_funct_1(A,B),k1_funct_1(A,C)) ) ) ) ) ) )).
fof(d5_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m1_prob_1(E,A,B) => ! [F] : ( m1_prob_1(F,A,B) => ( r2_prob_2(A,B,C,D,E,F) <=> ( k3_funct_2(B,k1_numbers,C,k5_prob_1(A,B,k5_prob_1(A,B,D,E),F)) = k4_real_1(k4_real_1(k3_funct_2(B,k1_numbers,C,D),k3_funct_2(B,k1_numbers,C,E)),k3_funct_2(B,k1_numbers,C,F)) & k3_funct_2(B,k1_numbers,C,k5_prob_1(A,B,D,E)) = k4_real_1(k3_funct_2(B,k1_numbers,C,D),k3_funct_2(B,k1_numbers,C,E)) & k3_funct_2(B,k1_numbers,C,k5_prob_1(A,B,D,F)) = k4_real_1(k3_funct_2(B,k1_numbers,C,D),k3_funct_2(B,k1_numbers,C,F)) & k3_funct_2(B,k1_numbers,C,k5_prob_1(A,B,E,F)) = k4_real_1(k3_funct_2(B,k1_numbers,C,E),k3_funct_2(B,k1_numbers,C,F)) ) ) ) ) ) ) ) ) )).
fof(d5_prob_3,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k9_setfam_1(A)) => ! [C] : ( m2_finseq_1(C,k9_setfam_1(A)) => ( C = k6_prob_3(A,B) <=> ( k3_finseq_1(C) = k3_finseq_1(B) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,C)) => k4_prob_3(A,C,D) = k3_subset_1(A,k4_prob_3(A,B,D)) ) ) ) ) ) ) )).
fof(d5_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ( D = k4_prob_4(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ? [F] : ( r2_hidden(F,B) & ? [G] : ( m1_prob_4(G,A,B,C) & E = k2_xboole_0(F,G) ) ) ) ) ) ) ) ) )).
fof(d5_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ( r4_projpl_1(A,B,C,D) <=> ? [E] : ( m1_subset_1(E,u2_incsp_1(A)) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),B,C,D),E) ) ) ) ) ) ) )).
fof(d5_prvect_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v1_prvect_2(A) ) => ! [B] : ( 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] : ( m2_subset_1(C,k4_ordinal1,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))) ) ) ) ) ) )).
fof(d5_prvect_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(d5_pscomp_1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => k3_funct_2(u1_struct_0(k15_euclid(2)),k1_numbers,A,B) = k17_euclid(B) ) ) ) )).
fof(d5_pua2mss1,axiom,( ! [A] : ( ( v2_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ( C = k7_pua2mss1(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(k4_tarski(D,E),C) <=> ( r2_hidden(k4_tarski(D,E),B) & ! [F] : ( 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] : ( ( v1_relat_1(G) & v1_funct_1(G) & v1_finseq_1(G) ) => ! [H] : ( ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_pythtrip,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) => ( m1_pythtrip(A) <=> ? [B] : ( m1_subset_1(B,k4_ordinal1) & ? [C] : ( m1_subset_1(C,k4_ordinal1) & ? [D] : ( m1_subset_1(D,k4_ordinal1) & r1_xxreal_0(C,D) & A = k1_enumset1(k3_xcmplx_0(B,k6_xcmplx_0(k1_pepin(D),k1_pepin(C))),k2_nat_1(B,k2_nat_1(k2_nat_1(2,C),D)),k2_nat_1(B,k1_nat_1(k1_pepin(D),k1_pepin(C)))) ) ) ) ) ) )).
fof(d5_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => k4_qc_lang1(A) = k2_zfmisc_1(k1_tarski(5),k1_qc_lang1(A)) ) )).
fof(d5_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( 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))) ) ) ) )).
fof(d5_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => k5_qc_lang3(A,B) = k4_qc_lang3(A,k5_qc_lang1(A),B) ) ) )).
fof(d5_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_qc_lang4(C,A,B) => ! [D] : ( 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 ) ) ) ) ) )).
fof(d5_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_qc_trans(B,A) & m1_qc_lang1(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_subset_1(D,k6_qc_lang1(A),k8_qc_lang1(A,C)) => k3_qc_trans(A,B,C,D) = D ) ) ) ) )).
fof(d5_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_quantal1(A) ) => ( v7_quantal1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : k6_algstr_0(A,B,k15_lattice3(A,C)) = k15_lattice3(A,a_3_0_quantal1(A,B,C)) ) ) ) )).
fof(d5_quaterni,axiom,( k5_quaterni = k3_quaterni(k4_ordinal1,k5_numbers,1,2,3,k5_numbers,k5_numbers,k5_numbers,1) )).
fof(d5_quofield,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v6_struct_0(A) & l5_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(k1_quofield(A)))) => ( B = k7_quofield(A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_quofield(A))) => ( r2_hidden(C,B) <=> ? [D] : ( m2_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A)) & C = k6_quofield(A,D) ) ) ) ) ) ) )).
fof(d5_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v3_card_1(D,C) & m2_finseq_1(D,k3_radix_1(B)) ) => k6_radix_1(A,B,C,D) = k3_xcmplx_0(k11_newton(k1_radix_1(B),k7_nat_d(A,1)),k5_radix_1(A,B,C,D)) ) ) ) ) )).
fof(d5_radix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v3_card_1(D,B) & m2_finseq_1(D,k4_ordinal1) ) => ( D = k5_radix_2(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k2_finseq_1(B)) => k1_recdef_1(D,E) = k4_radix_2(E,A,C) ) ) ) ) ) ) ) )).
fof(d5_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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 = k5_numbers => k7_radix_3(A,B,C,D) = k5_numbers ) ) ) ) ) ) )).
fof(d5_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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) = k5_numbers ) ) ) ) ) ) )).
fof(d5_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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) ) ) ) ) ) ) ) )).
fof(d5_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m1_vectsp_6(D,A,B) => ! [E] : ( ( 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] : ( m1_vectsp_6(F,A,C) => ( F = k8_ranknull(A,B,C,D,E) <=> ! [G] : ( 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)))) ) ) ) ) ) ) ) ) )).
fof(d5_rcomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v3_rcomp_1(A) <=> v2_rcomp_1(k3_subset_1(k1_numbers,A)) ) ) )).
fof(d5_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( B = k5_real_3(A) <=> ( k9_nat_1(k1_numbers,B,k5_numbers) = k9_nat_1(k1_numbers,k4_real_3(A),k5_numbers) & k9_nat_1(k1_numbers,B,1) = k2_xcmplx_0(k4_real_1(k9_nat_1(k1_numbers,k4_real_3(A),1),k9_nat_1(k1_numbers,k4_real_3(A),k5_numbers)),1) & ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,B,k1_nat_1(C,2)) = k3_real_1(k4_real_1(k9_nat_1(k1_numbers,k4_real_3(A),k1_nat_1(C,2)),k9_nat_1(k1_numbers,B,k1_nat_1(C,1))),k9_nat_1(k1_numbers,B,C)) ) ) ) ) ) )).
fof(d5_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m2_funct_2(C,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d5_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d5_realset2,axiom,( ! [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) & l6_algstr_0(A) ) => k4_realset2(A) = u2_algstr_0(A) ) )).
fof(d5_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_rearran1(C) & v2_rearran1(C) & v3_rearran1(C,k1_zfmisc_1(B)) & m2_finseq_1(C,k1_zfmisc_1(B)) ) => ! [D] : ( ( 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)))) ) ) ) ) )).
fof(d5_recdef_2,axiom,( ! [A] : ( v3_xtuple_0(A) => ! [B] : ( B = k8_xtuple_0(A) <=> ! [C] : ! [D] : ! [E] : ! [F] : ( A = k6_xtuple_0(C,D,E,F) => B = D ) ) ) )).
fof(d5_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( B = k2_relat_1(A) <=> ! [C] : ! [D] : ( r2_hidden(k4_tarski(C,D),B) <=> r2_hidden(k4_tarski(D,C),A) ) ) ) ) )).
fof(d5_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r5_relat_2(A,B) <=> ! [C] : ! [D] : ~ ( r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(D,C),A) ) ) ) )).
fof(d5_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r3_rewrite1(A,B) <=> ! [C] : ~ r2_hidden(k4_tarski(B,C),A) ) ) )).
fof(d5_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ( r2_rewrite2(A,B,C,D) <=> ? [E] : ( m1_subset_1(E,k8_afinsq_1(A)) & ? [F] : ( m1_subset_1(F,k8_afinsq_1(A)) & ? [G] : ( m1_subset_1(G,k8_afinsq_1(A)) & ? [H] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d5_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v8_valued_0(B) & m2_finseq_1(B,k1_numbers) ) => ( B = k5_rfinseq2(A) <=> r2_classes1(A,B) ) ) ) )).
fof(d5_rfunct_2,axiom,( ! [A] : ( ( 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) ) ) ) )).
fof(d5_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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)) ) ) )).
fof(d5_rfunct_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r5_rfunct_4(A,B) <=> ( r2_hidden(B,k9_xtuple_0(A)) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_xtuple_0(A)) & ~ r1_xxreal_0(D,k9_complex1(k6_xcmplx_0(E,B))) & r1_xxreal_0(C,k6_xcmplx_0(k1_funct_1(A,B),k1_funct_1(A,E))) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( B = k4_rinfsup1(A) <=> ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_numbers)) => ( D = a_2_0_rinfsup1(A,C) => k1_funct_1(B,C) = k2_seq_4(D) ) ) ) ) ) ) )).
fof(d5_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v3_rinfsup2(A) <=> ( v2_rinfsup2(A) & v1_rinfsup2(A) ) ) ) )).
fof(d5_ring_1,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d5_ringcat1,axiom,( ! [A] : ( l1_ringcat1(A) => ( v3_ringcat1(A) <=> v1_ringcat1(k3_ringcat1(A),u1_ringcat1(A),u2_ringcat1(A)) ) ) )).
fof(d5_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v2_rlaffin1(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => v1_rlaffin1(C,A) ) ) ) ) ) )).
fof(d5_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rlsub_1(C,A) => k3_rlsub_1(A,B,C) = a_3_1_rlsub_1(A,B,C) ) ) ) )).
fof(d5_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ( m1_rlsub_2(C,A,B) <=> r1_rlsub_2(A,C,B) ) ) ) ) )).
fof(d5_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_rltopsp1(B,A) <=> B = k2_rltopsp1(A,B) ) ) ) )).
fof(d5_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ( v5_rlvect_1(A) <=> ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d5_rlvect_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_rlvect_2(B,A) => ( B = k4_rlvect_2(A) <=> k3_rlvect_2(A,B) = k1_xboole_0 ) ) ) )).
fof(d5_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_rmod_2(D,A,B) => k3_rmod_2(A,B,C,D) = a_4_1_rmod_2(A,B,C,D) ) ) ) ) )).
fof(d5_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( m1_rmod_2(E,A,B) => ( r1_rmod_3(A,B,D,E) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d5_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_rmod_4(D,A,B) => ( m2_rmod_4(D,A,B,C) <=> r1_tarski(k2_rmod_4(A,B,D),C) ) ) ) ) ) )).
fof(d5_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_robbins1(A) ) => ( v5_robbins1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(d5_robbins4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v10_robbins1(A) & v8_robbins3(A) & v9_robbins3(A) & l4_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_robbins4(A,B,C) <=> r3_lattices(A,B,k3_robbins1(A,C)) ) ) ) ) )).
fof(d5_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k4_roughs_1(A,B) = a_2_1_roughs_1(A,B) ) ) )).
fof(d5_rsspace,axiom,( ! [A] : ( m1_subset_1(A,k1_rsspace) => ( A = k5_rsspace <=> ! [B] : ( v7_ordinal1(B) => k1_funct_1(k2_rsspace(A),B) = k5_numbers ) ) ) )).
fof(d5_rsspace3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_rsspace3(B,A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(D,E) & r1_xxreal_0(D,F) & r1_xxreal_0(C,k4_rsspace3(A,k5_rsspace3(A,B,E),k5_rsspace3(A,B,F))) ) ) ) ) ) ) ) ) )).
fof(d5_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_lopban_1(A,B)))) => ( C = k4_rsspace4(A,B) <=> ! [D] : ( 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)))) ) ) ) ) ) ) )).
fof(d5_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( m2_rusub_1(C,A,B) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & C = k3_rusub_1(A,D,B) ) ) ) ) ) )).
fof(d5_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ( m1_rusub_2(C,A,B) <=> r1_rusub_2(A,C,B) ) ) ) ) )).
fof(d5_rusub_4,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => k3_rusub_4(A,B) = u1_struct_0(B) ) ) )).
fof(d5_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( B = k4_rusub_5(A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & r1_tarski(k4_bhsp_2(A,D,E),C) ) ) ) ) ) ) ) ) ) )).
fof(d5_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => k6_rvsum_1(A) = k3_relat_1(A,k7_binop_2) ) )).
fof(d5_rvsum_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( v1_xcmplx_0(B) => k9_rvsum_2(A,B) = k3_relat_1(A,k5_seq_4(B)) ) ) )).
fof(d5_scm_comp,axiom,( ! [A] : ( m1_dtconstr(A,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [B] : ( 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(k5_numbers,2),A,B) ) ) )).
fof(d5_scm_halt,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( r2_scm_halt(A,B,C) <=> r1_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(C,A),k1_scmfsa_m(B)) ) ) ) ) )).
fof(d5_scm_inst,axiom,( ! [A] : ( m1_subset_1(A,k3_scm_inst) => ( ? [B] : ( v7_ordinal1(B) & ? [C] : ( m2_subset_1(C,k4_ordinal1,k7_card_1(9)) & A = k3_xtuple_0(C,k9_finseq_1(B),k1_xboole_0) ) ) => ! [B] : ( v7_ordinal1(B) => ( B = k6_scm_inst(A) <=> ? [C] : ( m2_finseq_1(C,k4_ordinal1) & C = k5_xtuple_0(A) & B = k7_partfun1(k4_ordinal1,C,1) ) ) ) ) ) )).
fof(d5_scmfsa6a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => k5_scmfsa6a(A,B) = k3_scmfsa6a(A,k11_compos_1(k1_scmfsa_2,B)) ) ) )).
fof(d5_scmfsa7b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) ) => ( v1_scmfsa7b(A) <=> ~ r4_scmfsa7b(A,k4_scmfsa_2(k5_numbers)) ) ) )).
fof(d5_scmfsa8b,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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)) ) ) ) ) )).
fof(d5_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ( r4_scmfsa9a(A,B,C,D) <=> ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1))) & ! [F] : ( v7_ordinal1(F) => ~ ( r1_xxreal_0(k3_funct_2(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(B,D,C,A),F)),k3_funct_2(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(B,D,C,A),k1_nat_1(F,1)))) & ~ r1_xxreal_0(k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(B,D,C,A),F),C),k5_numbers) ) ) ) ) ) ) ) ) )).
fof(d5_scmfsa_1,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k4_scmfsa_1,k5_scmfsa_1))) => ! [B] : ( m2_subset_1(B,k1_scmfsa_1,k2_scmfsa_1) => ! [C] : ( v1_int_1(C) => k7_scmfsa_1(A,B,C) = k1_funct_4(A,k16_funcop_1(B,C)) ) ) ) )).
fof(d5_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => k5_scmfsa_2(A) = k4_xcmplx_0(k1_nat_1(A,1)) ) )).
fof(d5_scmfsa_9,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2))))) ) => ( E = k5_scmfsa_9(A,B,C,D) <=> ( r6_pboole(u1_struct_0(k1_scmfsa_2),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),E,k5_numbers),A) & ! [F] : ( v7_ordinal1(F) => r6_pboole(u1_struct_0(k1_scmfsa_2),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),E,k1_nat_1(F,1)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(D,k2_scmfsa_9(C,B)),k1_funct_4(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),E,F),k7_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_numbers)),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(k1_funct_4(D,k2_scmfsa_9(C,B)),B),k1_funct_4(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),E,F),k7_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_numbers))),3))) ) ) ) ) ) ) ) ) )).
fof(d5_scmfsa_m,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_zfmisc_1(k4_ordinal1)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k4_ordinal1)))) ) => ( B = k8_scmfsa_m(A) <=> ( k3_funct_2(k4_ordinal1,k1_zfmisc_1(k4_ordinal1),B,k5_numbers) = a_1_2_scmfsa_m(A) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ( k9_nat_1(k1_zfmisc_1(k4_ordinal1),B,C) = D => k3_funct_2(k4_ordinal1,k1_zfmisc_1(k4_ordinal1),B,k1_nat_1(C,1)) = k7_subset_1(k4_ordinal1,D,k6_domain_1(k4_ordinal1,k4_seq_4(D))) ) ) ) & ! [C] : ( v7_ordinal1(C) => ~ v1_finset_1(k9_nat_1(k1_zfmisc_1(k4_ordinal1),B,C)) ) ) ) ) ) )).
fof(d5_scmpds_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => k5_scmpds_2(A,B) = k3_xtuple_0(2,k1_xboole_0,k10_finseq_1(A,B)) ) ) )).
fof(d5_scmpds_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => 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) ) ) ) )).
fof(d5_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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,k1_nat_1(k5_card_1(C),2)),C),k1_scmpds_6(k1_nat_1(k5_card_1(D),1))),D) ) ) ) ) )).
fof(d5_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => ( ? [B] : ( m1_subset_1(B,k2_scm_inst) & ? [C] : ( v1_int_1(C) & ? [D] : ( m2_subset_1(D,k4_ordinal1,k7_card_1(15)) & A = k3_xtuple_0(D,k1_xboole_0,k2_scmpds_i(B,C)) ) ) ) => ! [B] : ( v1_int_1(B) => ( B = k6_scmpds_i(A) <=> ? [C] : ( 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) ) ) ) ) ) )).
fof(d5_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(d5_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_scmringi(A)) => ( ? [C] : ( m1_subset_1(C,k4_ordinal1) & ? [D] : ( m1_subset_1(D,k2_scm_inst) & ? [E] : ( m2_subset_1(E,k4_ordinal1,k7_card_1(8)) & B = k3_xtuple_0(E,k12_finseq_1(k4_ordinal1,C),k12_finseq_1(k2_scm_inst,D)) ) ) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( C = k5_scmringi(A,B) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & k12_finseq_1(k4_ordinal1,D) = k5_xtuple_0(B) & C = k7_partfun1(k4_ordinal1,k12_finseq_1(k4_ordinal1,D),1) ) ) ) ) ) ) )).
fof(d5_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( E = k1_semi_af1(A,B,C,D) <=> r3_semi_af1(A,D,B,C,E) ) ) ) ) ) ) )).
fof(d5_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(A) <=> ? [B] : ( v1_xreal_0(B) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(D,E) & r1_xxreal_0(C,k9_complex1(k6_xcmplx_0(k1_funct_1(A,E),B))) ) ) ) ) ) ) ) )).
fof(d5_seq_4,axiom,( ! [A] : ( ( 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 = k6_seq_4 <=> ! [B] : ( m1_subset_1(B,k2_numbers) => k3_funct_2(k2_numbers,k1_numbers,A,B) = k9_complex1(B) ) ) ) )).
fof(d5_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( D = k6_seqfunc(A,B,C) <=> ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(d5_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_seqm_3(A) <=> ( v7_valued_0(A) | v8_valued_0(A) ) ) ) )).
fof(d5_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v7_ordinal1(B) => k6_series_1(A,B) = k9_nat_1(k1_numbers,k3_series_1(A),B) ) ) )).
fof(d5_setfam_1,axiom,( ! [A] : ! [B] : ! [C] : ( C = k3_setfam_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ? [F] : ( r2_hidden(E,A) & r2_hidden(F,B) & D = k3_xboole_0(E,F) ) ) ) )).
fof(d5_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k4_kurato_0(A,B) = k3_prob_1(A,k4_setlim_1(A,B)) ) )).
fof(d5_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( D = k5_setlim_2(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k9_nat_1(k9_setfam_1(A),D,E) = k9_subset_1(A,C,k9_nat_1(k9_setfam_1(A),B,E)) ) ) ) ) ) )).
fof(d5_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(A)) => ! [D] : ( ( 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) ) ) ) )).
fof(d5_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ( B = k5_sf_mastr(A) <=> ? [C] : ( 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(k5_numbers))) & B = k2_scmfsa_m(C) ) ) ) ) )).
fof(d5_sfmastr2,axiom,( ! [A] : ( ( 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(k5_numbers)))) ) )).
fof(d5_sfmastr3,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(d5_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( v3_sheffer1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d5_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ( v2_simplex0(A) <=> v1_finset_1(k4_simplex0(A)) ) ) )).
fof(d5_simplex1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(d5_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( B = k4_sin_cos(A) <=> ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,B,C) = k7_xcmplx_0(k1_newton(A,C),k2_newton(C)) ) ) ) ) )).
fof(d5_sin_cos2,axiom,( ! [A] : ( ( 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 = k5_sin_cos2 <=> ! [B] : ( v1_xreal_0(B) => k1_funct_1(A,B) = k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_funct_1(k22_sin_cos,k4_xcmplx_0(B))),k2_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_funct_1(k22_sin_cos,k4_xcmplx_0(B)))) ) ) ) )).
fof(d5_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => k5_sin_cos7(A) = k3_xcmplx_0(k7_xcmplx_0(1,2),k3_power(k4_power,k7_xcmplx_0(k2_xcmplx_0(A,1),k6_xcmplx_0(A,1)))) ) )).
fof(d5_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => k5_sincos10(A) = k1_funct_1(k1_sincos10,A) ) )).
fof(d5_sppol_1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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,k6_xcmplx_0(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,k6_xcmplx_0(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)) ) ) ) ) ) )).
fof(d5_stacks_1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & l1_stacks_1(A) ) => ! [B] : ( 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) ) ) )).
fof(d5_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( r1_struct_0(A,B) <=> r2_hidden(B,u1_struct_0(A)) ) ) )).
fof(d5_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_sublemma(B,A) & m1_subset_1(B,k2_zfmisc_1(k16_substut1(A),k3_qc_lang1(A))) ) => ! [C] : ( m1_substut1(C,A,B) => ( v3_substut1(B,A) => k9_sublemma(A,B,C) = k24_substut1(A,B,C) ) ) ) ) )).
fof(d5_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k1_substut1(A)) => k5_substut1(A,B,C) = k3_substut1(A,k4_substut1(A,B),C) ) ) ) )).
fof(d5_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( r2_qc_lang2(A,B,C) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ~ ( r1_xxreal_0(1,E) & ~ r1_xxreal_0(k3_finseq_1(D),E) & ! [F] : ( m1_subset_1(F,k9_qc_lang1(A)) => ! [G] : ( m1_subset_1(G,k9_qc_lang1(A)) => ~ ( k1_funct_1(D,E) = F & k1_funct_1(D,k1_nat_1(E,1)) = G & r1_qc_lang2(A,F,G) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_supinf_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k6_numbers)) => ! [C] : ( ( 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(k6_numbers,A,B,C)) ) ) ) )).
fof(d5_t_0topsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => k3_t_0topsp(A) = k11_borsuk_1(A,k2_t_0topsp(A)) ) )).
fof(d5_tarski,axiom,( ! [A] : ! [B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) )).
fof(d5_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),k1_numbers))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_partit1(A))) => ( C = k2_taxonom1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( ~ v3_xxreal_0(E) & v1_xreal_0(E) & ? [F] : ( 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 ) ) ) ) ) ) ) )).
fof(d5_taxonom2,axiom,( ! [A] : ( v4_taxonom2(A) <=> ! [B] : ! [C] : ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => ( B = C | r1_xboole_0(B,C) ) ) ) )).
fof(d5_taylor_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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,k5_numbers),k2_partfun1(k1_numbers,k1_numbers,A,B)) & ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d5_tdgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ( v2_tdgroup(A) <=> ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,D) => B = C ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_analoaf(A,B,C,D,E) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r2_analoaf(A,B,D,D,C) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,E) => r2_analoaf(A,B,D,C,E) ) ) ) ) ) ) ) ) )).
fof(d5_tdlat_1,axiom,( ! [A] : ( l1_pre_topc(A) => k5_tdlat_1(A) = a_1_1_tdlat_1(A) ) )).
fof(d5_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v5_tdlat_3(A) <=> ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => v4_tdlat_3(B) ) ) ) )).
fof(d5_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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 ) ) ) ) ) ) )).
fof(d5_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_tdlat_3(A) <=> ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ v2_tops_1(B,A) ) ) ) )).
fof(d5_tex_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_tex_2(B,A) <=> ( v2_tex_2(B,A) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v2_tex_2(C,A) & r1_tarski(B,C) ) => B = C ) ) ) ) ) ) )).
fof(d5_tex_4,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v2_tex_4(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => v1_tex_4(C,A) ) ) ) ) ) )).
fof(d5_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_pre_topc(C,A) => ! [D] : ( m1_pre_topc(D,A) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(d5_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ? [F] : ( m1_borsuk_2(F,A,B,B) & ? [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d5_topalg_5,axiom,( ! [A] : ( ( 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] : ( 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)) ) ) ) )).
fof(d5_topalg_6,axiom,( ! [A] : ( l1_pre_topc(A) => k1_topalg_6(A) = a_1_0_topalg_6(A) ) )).
fof(d5_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_topdim_1(B,A) => ! [C] : ( v1_int_1(C) => ( C = k2_topdim_1(A,B) <=> ( r2_hidden(B,k13_prob_1(u1_struct_0(A),k4_ordinal1,k9_setfam_1(u1_struct_0(A)),k1_topdim_1(A),k2_xcmplx_0(C,1))) & ~ r2_hidden(B,k13_prob_1(u1_struct_0(A),k4_ordinal1,k9_setfam_1(u1_struct_0(A)),k1_topdim_1(A),C)) ) ) ) ) ) ) )).
fof(d5_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_topgen_1(B,A) <=> r2_topgen_1(A,k2_struct_0(A),B) ) ) ) )).
fof(d5_topgen_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) ) )).
fof(d5_topgen_3,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( C = k4_topgen_3(A,B) <=> ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(D,A) & k9_nat_1(k1_numbers,C,D) = k1_newton(B,D) ) | ( ~ r2_hidden(D,A) & k9_nat_1(k1_numbers,C,D) = k5_numbers ) ) ) ) ) ) )).
fof(d5_topgen_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v4_topgen_4(B,A) <=> ! [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) ) ) ) ) )).
fof(d5_topgen_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( 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,k5_numbers)) = k5_numbers & ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( v1_xreal_0(E) & ~ v3_xxreal_0(E) ) => ( ~ ( ~ ( D = A & E = k5_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)) = k7_xcmplx_0(k1_square_1(k12_euclid(k5_algstr_0(k15_euclid(2),k19_euclid(A,k5_numbers),k19_euclid(D,E)))),k3_xcmplx_0(k3_xcmplx_0(2,B),E)) ) ) ) ) ) ) ) ) ) )).
fof(d5_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( v15_algstr_0(B) & l3_algstr_0(B) ) => ( B = k5_topgrp_1(A) <=> ! [C] : ( ( 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] : ( m3_topgrp_1(D,A) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(d5_topreal1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v1_topreal1(A) <=> ! [B] : ( 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))) ) ) ) ) )).
fof(d5_topreal9,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k4_topreal9(A,B,C) = a_3_3_topreal9(A,B,C) ) ) ) )).
fof(d5_toprealb,axiom,( ! [A] : ( 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)))) ) ) ) )).
fof(d5_toprealc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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 = k15_toprealc(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => k5_toprealc(k15_euclid(A),k15_euclid(A),k15_euclid(A),B,C,D) = k10_toprealc(A,C,D) ) ) ) ) ) )).
fof(d5_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => k4_toprns_1(A,B,C) = k1_toprns_1(A,B,k3_toprns_1(A,C)) ) ) ) )).
fof(d5_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) )).
fof(d5_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(d5_tops_3,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) )).
fof(d5_transgeo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ( v1_transgeo(A) <=> ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_analoaf(A,B,B,C,D) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,E) => r2_analoaf(A,D,E,B,C) ) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_analoaf(A,B,C,B,C) ) ) ) ) ) )).
fof(d5_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( B = k3_trees_1(A) <=> ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( r2_hidden(C,B) <=> ( r2_hidden(C,A) & ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ~ ( r2_hidden(D,A) & r2_xboole_0(C,D) ) ) ) ) ) ) ) ) )).
fof(d5_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => k1_trees_2(A,B) = a_2_1_trees_2(A,B) ) ) )).
fof(d5_trees_3,axiom,( ! [A] : ( v3_trees_3(A) <=> ! [B] : ( r2_hidden(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) ) ) )).
fof(d5_trees_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(d5_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_trees_9(A) ) => ! [B] : ( m1_trees_1(B,A) => ! [C] : ( ( 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] : ( v7_ordinal1(D) => ( ~ r1_xxreal_0(k3_finseq_1(C),D) => k1_funct_1(C,k1_nat_1(D,1)) = k8_finseq_1(k4_ordinal1,B,k14_trees_3(D)) ) ) ) ) ) ) ) )).
fof(d5_tsep_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(d5_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v6_pre_topc(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(d5_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(d5_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( 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)))) ) ) )).
fof(d5_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k1_funct_1(A,k10_finseq_1(B,C)) = k9_margrel1(k10_margrel1(k9_margrel1(B),C)) ) ) ) ) )).
fof(d5_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(d5_unialg_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_unialg_3(A))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(d5_uniroots,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(B,k1_complfld) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => ( B = k5_uniroots(A) <=> ? [C] : ( ~ 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(k4_ordinal1,u1_struct_0(k1_complfld),B,k9_uproots(k1_complfld,k1_uproots(u1_struct_0(k1_complfld),C,1))) ) ) ) ) )).
fof(d5_uproots,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k4_uproots(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k1_normsp_1(A,D,E) = k1_normsp_1(A,B,k2_xcmplx_0(C,E)) ) ) ) ) ) ) )).
fof(d5_urysohn1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_subset_1(B,k1_numbers,k1_urysohn1(A)) => ! [C] : ( v7_ordinal1(C) => ( C = k6_urysohn1(A,B) <=> B = k7_xcmplx_0(C,k1_newton(2,A)) ) ) ) ) )).
fof(d5_urysohn3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m2_urysohn3(D,A,B,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k6_numbers)) => ( F = k6_urysohn3(A,B,C,D,E) <=> ! [G] : ( r2_hidden(G,F) <=> ( r2_hidden(G,k2_urysohn1) & ! [H] : ( v1_xreal_0(H) => ~ ( H = G & r2_hidden(E,k1_funct_1(k4_urysohn3(A,B,C,D),H)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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)))) ) => ( m1_valuat_1(C,A,B) <=> ! [D] : ( m1_subset_1(D,k6_qc_lang1(A)) => ! [E] : ( m1_subset_1(E,k3_margrel1(B)) => ~ ( r1_margrel1(B,k3_funct_2(k6_qc_lang1(A),k3_margrel1(B),C,D),E) & ~ r1_margrel1(B,E,k4_margrel1(B)) & k7_qc_lang1(A,D) != k5_margrel1(B,E) ) ) ) ) ) ) ) )).
fof(d5_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_valued_0(A) <=> ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => v1_xcmplx_0(k1_funct_1(A,B)) ) ) ) )).
fof(d5_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k24_valued_1(A,B) <=> ( k9_xtuple_0(C) = k9_xtuple_0(A) & ! [D] : ( r2_hidden(D,k9_xtuple_0(C)) => k1_funct_1(C,D) = k3_xcmplx_0(B,k1_funct_1(A,D)) ) ) ) ) ) ) )).
fof(d5_vectmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectmetr(A) ) => ( v5_vectmetr(A) <=> ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_metric_1(A,k1_rlvect_1(A,C,B),k1_rlvect_1(A,D,B)) = k3_xcmplx_0(k9_complex1(B),k1_metric_1(A,C,D)) ) ) ) ) ) )).
fof(d5_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(u1_struct_0(B)),k2_vectsp10(A,B,C)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d5_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(d5_vectsp_1,axiom,( k2_vectsp_1 = g6_algstr_0(k1_numbers,k9_binop_2,k11_binop_2,k10_subset_1(1,k1_numbers),k10_subset_1(k5_numbers,k1_numbers)) )).
fof(d5_vectsp_2,axiom,( ! [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) & 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)) ) )).
fof(d5_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_vectsp_4(D,A,B) => k3_vectsp_4(A,B,C,D) = a_4_1_vectsp_4(A,B,C,D) ) ) ) ) )).
fof(d5_vectsp_5,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( m1_vectsp_5(D,A,B,C) <=> r1_vectsp_5(A,B,D,C) ) ) ) ) ) )).
fof(d5_vectsp_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d5_vectsp_8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_vectsp_8(A,B))) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(d5_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d5_waybel10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_0(B,A) => ! [C] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(d5_waybel12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_waybel12(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => v2_waybel12(C,A) ) ) ) ) ) )).
fof(d5_waybel18,axiom,( ! [A] : ( l1_pre_topc(A) => ( v2_waybel18(A) <=> ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( ( ~ v2_struct_0(D) & v2_pre_topc(D) & l1_pre_topc(D) ) => ~ ( m1_pre_topc(B,D) & ! [E] : ( ( 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 ) ) ) ) ) ) ) ) ) )).
fof(d5_waybel20,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) ) => ( v1_waybel20(B,A) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d5_waybel23,axiom,( ! [A] : ( l1_pre_topc(A) => k2_waybel23(A) = k1_setfam_1(a_1_0_waybel23(A)) ) )).
fof(d5_waybel26,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k6_waybel26(A,B) <=> ( k9_xtuple_0(C) = B & ! [D] : ( r2_hidden(D,B) => k1_funct_1(C,D) = k9_relat_1(A,D) ) ) ) ) ) )).
fof(d5_waybel27,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v3_orders_2(D) & v5_orders_2(D) & l1_orders_2(D) ) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_waybel34,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ ! [B] : ( m1_subset_1(B,A) => v1_xboole_0(B) ) => ! [B] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d5_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_orders_2(A,D,E) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( r2_waybel_1(A,B) <=> ( r1_yellow_0(A,B) & r2_hidden(k1_yellow_0(A,B),B) ) ) ) )).
fof(d5_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_binop_1(B,C,D) = k10_lattice3(A,C,D) ) ) ) ) ) )).
fof(d5_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ( v2_waybel_3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => B = k1_yellow_0(A,k1_waybel_3(A,B)) ) ) ) )).
fof(d5_waybel_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ( v3_waybel_4(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d5_waybel_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_waybel_6(B,A) <=> ! [C] : ( 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)) ) ) ) ) ) )).
fof(d5_waybel_7,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ! [C] : ( r2_waybel_7(A,B,C) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( v3_pre_topc(D,A) & r2_hidden(C,D) ) => r2_hidden(D,B) ) ) ) ) )).
fof(d5_waybel_8,axiom,( ! [A] : ( ( ~ 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) ) ) ) )).
fof(d5_waybel_9,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( 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) ) ) ) ) )).
fof(d5_weddwitt,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(d5_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(d5_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( 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) ) ) ) )).
fof(d5_xboole_0,axiom,( ! [A] : ! [B] : ! [C] : ( C = k4_xboole_0(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,A) & ~ r2_hidden(D,B) ) ) ) )).
fof(d5_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k4_xboolean(A,B) = k3_xcmplx_0(A,B) ) ) )).
fof(d5_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( B = k4_xcmplx_0(A) <=> k2_xcmplx_0(A,B) = k5_numbers ) ) ) )).
fof(d5_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( ( ( r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_arytm_2) ) => ( r1_xxreal_0(A,B) <=> ? [C] : ( m1_subset_1(C,k2_arytm_2) & ? [D] : ( m1_subset_1(D,k2_arytm_2) & A = C & B = D & r1_arytm_2(C,D) ) ) ) ) & ( ( r2_hidden(A,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) & r2_hidden(B,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) ) => ( r1_xxreal_0(A,B) <=> ? [C] : ( m1_subset_1(C,k2_arytm_2) & ? [D] : ( m1_subset_1(D,k2_arytm_2) & A = k4_tarski(k5_numbers,C) & B = k4_tarski(k5_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(k5_numbers),k2_arytm_2)) & r2_hidden(B,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) ) & ~ ( r1_xxreal_0(A,B) <=> ~ ( ~ ( r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) ) & A != k2_xxreal_0 & B != k1_xxreal_0 ) ) ) ) ) ) )).
fof(d5_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ( v1_xxreal_2(A) <=> r2_hidden(k2_xxreal_2(A),A) ) ) )).
fof(d5_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( C = k4_xxreal_3(A,B) <=> ? [D] : ( v1_xcmplx_0(D) & ? [E] : ( 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 = k5_numbers ) ) ) ) ) ) )).
fof(d5_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_waybel_9(A) ) => ( v2_yellow13(A) <=> ! [B] : ( ( 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) ) ) ) ) )).
fof(d5_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v9_functor0(C,A,B) & v16_functor0(C,A,B) & m2_functor0(C,A,B) ) => ( C = k2_yellow18(A,B) <=> ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k3_functor0(A,B,C,D) = D ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k1_altcat_1(A,D,E) != k1_xboole_0 => ! [F] : ( m1_subset_1(F,k1_altcat_1(A,D,E)) => k8_functor0(A,B,C,D,E,F) = F ) ) ) ) ) ) ) ) ) ) )).
fof(d5_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ( v1_yellow19(B,A) <=> ! [C] : ( 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)) ) ) ) ) ) )).
fof(d5_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( l2_functor0(C,A,B) => ! [D] : ( ( ~ v2_struct_0(D) & v2_altcat_1(D) & v11_altcat_1(D) & v12_altcat_1(D) & l2_altcat_1(D) ) => ! [E] : ( ( ~ 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] : ( v16_functor0(F,D,E) & m2_functor0(F,D,E) & v21_functor0(F,D,E) & ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( G = H => k3_functor0(D,E,F,G) = k3_functor0(A,B,C,H) ) ) ) & ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => ! [H] : ( m1_subset_1(H,u1_struct_0(D)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ( ( G = I & H = J ) => ( k1_altcat_1(D,G,H) = k1_xboole_0 | ! [K] : ( m1_subset_1(K,k1_altcat_1(D,G,H)) => ! [L] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d5_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_yellow_0(A) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & r2_lattice3(A,u1_struct_0(A),B) ) ) ) )).
fof(d5_yellow_1,axiom,( ! [A] : ! [B] : ( l1_orders_2(B) => k5_yellow_1(A,B) = k4_yellow_1(A,k7_funcop_1(A,B)) ) )).
fof(d5_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( v1_relat_1(B) => k4_yellow_2(A,B) = k1_yellow_0(A,k10_xtuple_0(B)) ) ) )).
fof(d5_yellow_6,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(d5_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v4_yellow_8(A) <=> ! [B] : ( ( v3_yellow_8(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r1_yellow_8(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_yellow_8(A,B,D) => C = D ) ) ) ) ) ) )).
fof(d5_yellow_9,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(d5_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ( v1_zf_fund1(B,A) <=> ! [C] : ( m1_subset_1(C,A) => ( r2_hidden(C,B) => r2_hidden(a_2_0_zf_fund1(A,C),B) ) ) ) ) ) )).
fof(d5_zf_lang,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => k6_zf_lang(A) = k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,2),A) ) )).
fof(d5_zf_model,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r2_zf_model(A,B) <=> ! [C] : ( ( 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) ) ) ) ) )).
fof(d5_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_zfmisc_1(A,B,C) <=> ( A != B & A != C & B != C ) ) )).
fof(d5_zmodul01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_zmodul01(A) ) => ( v5_zmodul01(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_zmodul01(A,B,1) = B ) ) ) )).
fof(d5_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( v1_int_1(B) => k5_zmodul02(A,B) = g1_zmodul01(k1_zmodul02(A,B),k2_zmodul02(A,B),k3_zmodul02(A,B),k4_zmodul02(A,B)) ) ) )).
fof(d5_zmodul03,axiom,( ! [A] : ( ( ~ 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) & v1_zmodul03(A) & v2_zmodul03(A) & l1_zmodul01(A) ) => ! [B] : ( v7_ordinal1(B) => ( B = k2_zmodul03(A) <=> ! [C] : ( m1_zmodul03(C,A) => B = k5_card_1(C) ) ) ) ) )).
fof(d60_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_abcmiz_1,k34_abcmiz_1(A)))) ) => ! [C] : ( m4_abcmiz_1(C,A,k28_abcmiz_1(A)) => ( C = k55_abcmiz_1(A,B) <=> ( ! [D] : ( 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] : ( ( v2_abcmiz_1(D,A) & m1_subset_1(D,u4_struct_0(A)) ) => ! [E] : ( m1_trees_4(E,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A)))),k34_abcmiz_1(A)) => ! [F] : ( 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] : ( 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] : ( m1_abcmiz_1(D,A,k13_abcmiz_1(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(d60_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_aofa_a00(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l5_aofa_a00(B) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msualg_1(D,B) & l3_msualg_1(D,B) ) => k42_aofa_a00(A,B,C,D) = k3_circcomb(A,B,C,D) ) ) ) ) )).
fof(d60_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_aofa_i00(D,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) ) => ! [E] : ( m3_aofa_i00(E,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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,k5_numbers),D,C,k36_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,k29_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,E,1),k43_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,2))) ) ) ) ) ) )).
fof(d60_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k36_fomodel4(A) = k23_fomodel4(A,k22_fomodel4(A)) ) )).
fof(d60_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,A) => ! [F] : ( ( v1_modelc_1(F) & m2_finseq_1(F,k4_ordinal1) ) => ( 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)) ) ) ) ) ) ) ) )).
fof(d60_modelc_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k30_modelc_1(k25_modelc_2(k43_modelc_2))) => ( B = k45_modelc_2(A) <=> ! [C] : ( 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) ) ) ) )).
fof(d61_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_abcmiz_1,k34_abcmiz_1(A)))) ) => ! [C] : ( 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) ) ) ) )).
fof(d61_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_aofa_i00(D,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) ) => ! [E] : ( m3_aofa_i00(E,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D) => ! [F] : ( m3_aofa_i00(F,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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,k5_numbers),D,C,k37_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,E,F)) ) ) ) ) ) ) )).
fof(d61_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( ( 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))),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k35_fomodel1(A))) ) => ! [D] : ( ( 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))),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k35_fomodel1(A))) ) => k37_fomodel4(A,B,C,D) = a_4_2_fomodel4(A,B,C,D) ) ) ) ) )).
fof(d61_modelc_2,axiom,( k46_modelc_2 = a_0_1_modelc_2 )).
fof(d62_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_aofa_i00(D,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) ) => ! [E] : ( m3_aofa_i00(E,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D) => ! [F] : ( m3_aofa_i00(F,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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,k5_numbers),D,C,k38_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,E,F)) ) ) ) ) ) ) )).
fof(d62_fomodel4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ( ( A = k5_numbers => ( v13_fomodel4(C,A,B) <=> ( r2_hidden(k24_fomodel4(B),C) & r2_hidden(k26_fomodel4(B),C) & r2_hidden(k27_fomodel4(B),C) & r2_hidden(k28_fomodel4(B),C) ) ) ) & ( A = 1 => ( v13_fomodel4(C,A,B) <=> ( r2_hidden(k24_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) ) ) ) & ( A = 2 => ( v13_fomodel4(C,A,B) <=> ( 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) & r2_hidden(k34_fomodel4(B),C) & r2_hidden(k35_fomodel4(B),C) ) ) ) & ~ ( A != k5_numbers & A != 1 & A != 2 & ~ ( v13_fomodel4(C,A,B) <=> C = k1_xboole_0 ) ) ) ) ) ) )).
fof(d62_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k50_modelc_1(A,B,C) = a_3_1_modelc_1(A,B,C) ) ) ) )).
fof(d62_modelc_2,axiom,( ! [A] : ( ( 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] : ( r2_hidden(B,k15_modelc_2) => k1_funct_1(A,B) = k45_modelc_2(B) ) ) ) )).
fof(d63_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_abcmiz_1,k34_abcmiz_1(A)))) ) => ! [C] : ( 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)) ) ) ) )).
fof(d63_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k39_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))),k24_fomodel4(A),k25_fomodel4(A),k26_fomodel4(A),k27_fomodel4(A),k28_fomodel4(A),k29_fomodel4(A),k30_fomodel4(A),k31_fomodel4(A)),k9_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))),k32_fomodel4(A),k33_fomodel4(A),k34_fomodel4(A),k35_fomodel4(A))) ) )).
fof(d63_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( 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) ) ) ) ) )).
fof(d63_modelc_2,axiom,( ! [A] : ( m1_subset_1(A,k25_modelc_2(k43_modelc_2)) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( 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)) ) ) ) )).
fof(d64_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_abcmiz_1,k34_abcmiz_1(A)))) ) => ! [C] : ( 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) ) ) ) )).
fof(d64_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v13_fomodel4(B,k5_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] : ( v11_fomodel4(C,A,B) => k40_fomodel4(A,B,C) = k22_fomodel3(A,k35_fomodel1(A),k8_fomodel4(A,B,C),k7_fomodel3(A,C)) ) ) ) )).
fof(d64_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k48_modelc_1(A,B,C))) => ( E = k52_modelc_1(A,B,C,D) <=> ! [F] : ( r2_hidden(F,A) => k1_funct_1(k31_modelc_1(A,E),F) = k1_funct_1(k5_funct_3(D,A),F) ) ) ) ) ) ) ) )).
fof(d64_modelc_2,axiom,( ! [A] : ( m1_subset_1(A,k25_modelc_2(k43_modelc_2)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_modelc_2)) => ( r8_modelc_2(A,B) <=> ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ( r2_hidden(C,B) => r7_modelc_2(A,C) ) ) ) ) ) )).
fof(d65_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_abcmiz_1,k34_abcmiz_1(A)))) ) => ! [C] : ( 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))) ) ) ) )).
fof(d65_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( v14_fomodel4(B,A) <=> ! [C] : ( ( v4_fomodel1(C,A) & m1_subset_1(C,k1_fomodel1(A)) ) => ! [D] : ( ( 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(k42_fomodel1(A,k43_fomodel1(A,C),D),B) & ! [E] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(d65_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(d65_modelc_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k9_modelc_2)) => k48_modelc_2(A) = a_1_0_modelc_2(A) ) )).
fof(d66_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_aofa_i00(D,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) ) => ! [E] : ( 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,k5_numbers),D,E)) ) ) ) ) ) )).
fof(d66_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) => ! [C] : ( v4_funct_1(C) => ! [D] : ( m2_subset_1(D,k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0)),k40_fomodel2(A)) => ( ~ ( ~ v10_fomodel4(k2_xboole_0(C,k6_domain_1(k40_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)),k37_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),k37_fomodel2(A,D)))) ) & ( ~ ( ~ v10_fomodel4(k2_xboole_0(C,k6_domain_1(k40_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)),k37_fomodel2(A,D)))))) != k1_xboole_0 ) => k42_fomodel4(A,B,C,D) = C ) ) ) ) ) ) )).
fof(d66_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(d67_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_aofa_i00(D,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) ) => ! [E] : ( 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,k5_numbers),D,E)) ) ) ) ) ) )).
fof(d67_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) => ( v15_fomodel4(B,A) <=> ! [C] : ( ( 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] : ( v9_fomodel4(C,A,B,D) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m2_subset_1(F,k9_funct_2(k37_fomodel1(A),k3_rfunct_3(k3_finseq_2(E),k2_xboole_0(E,k6_margrel1))),k15_fomodel2(A,E)) => ( v10_fomodel2(D,E,A,F) => k25_fomodel2(A,E,F,C) = 1 ) ) ) ) ) ) ) ) )).
fof(d67_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m1_modelc_1(C,A,B) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_modelc_1(E,A,B) => ( E = k55_modelc_1(A,B,C,D) <=> ! [F] : ( m1_subset_1(F,k4_ordinal1) => k3_funct_2(k4_ordinal1,A,E,F) = k3_funct_2(k4_ordinal1,A,C,k1_nat_1(F,D)) ) ) ) ) ) ) ) )).
fof(d68_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_aofa_i00(D,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( 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,k5_numbers),D,E),k42_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,F)) ) ) ) ) ) ) )).
fof(d68_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( 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)))) => ( v16_fomodel4(B,A) <=> ! [C] : ( v12_fomodel2(C,A) => v12_fomodel2(k1_funct_1(B,C),A) ) ) ) ) )).
fof(d68_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m1_modelc_1(C,A,B) => ! [D] : ( m1_modelc_1(D,A,B) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ( ~ r1_xxreal_0(F,E) => k56_modelc_1(A,B,C,D,E,F) = k3_funct_2(k4_ordinal1,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)) ) ) ) ) ) ) ) ) )).
fof(d69_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_aofa_i00(D,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( 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,k5_numbers),D,E),k42_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,F)) ) ) ) ) ) ) )).
fof(d69_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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))) ) => ( v17_fomodel4(C,A,B) <=> v9_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))),k36_fomodel4(B)),k39_fomodel4(B)),A) ) ) ) )).
fof(d69_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m1_modelc_1(C,A,B) => ! [D] : ( m1_modelc_1(D,A,B) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,A) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ( F = k57_modelc_1(A,B,C,D,E) <=> ! [G] : ( m1_subset_1(G,k4_ordinal1) => k3_funct_2(k4_ordinal1,A,F,G) = k56_modelc_1(A,B,C,D,G,E) ) ) ) ) ) ) ) ) )).
fof(d6_abcmiz_0,axiom,( ! [A] : ( l1_abcmiz_0(A) => ( v5_abcmiz_0(A) <=> ! [B] : ( m1_subset_1(B,u1_abcmiz_0(A)) => k1_abcmiz_0(A,k1_abcmiz_0(A,B)) = B ) ) ) )).
fof(d6_abcmiz_1,axiom,( k8_abcmiz_1 = 2 )).
fof(d6_abcmiz_a,axiom,( k8_abcmiz_a = k4_tarski(k6_abcmiz_1,k4_tarski(k1_xboole_0,k5_numbers)) )).
fof(d6_abian,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ( v3_abian(B,A) <=> k3_tarski(B) = k3_tarski(k3_tarski(A)) ) ) )).
fof(d6_aff_3,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v6_aff_3(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ! [L] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v1_aff_4(C,A) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(d6_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : k7_afinsq_1(A,B,C) = k1_ordinal4(k1_ordinal4(k5_afinsq_1(A),k5_afinsq_1(B)),k5_afinsq_1(C)) )).
fof(d6_afinsq_2,axiom,( ! [A] : ! [B] : ( r2_afinsq_2(A,B) <=> ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(C,A) & r2_hidden(D,B) ) => r1_xxreal_0(C,D) ) ) ) ) )).
fof(d6_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( 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) ) ) )).
fof(d6_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k5_binop_1(u1_struct_0(A),C,D,E) = k2_afvect0(A,B,D,E) ) ) ) ) ) ) )).
fof(d6_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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)) ) ) ) ) ) ) )).
fof(d6_algspec1,axiom,( ! [A] : ( m3_algspec1(A) <=> ? [B] : ( ~ v11_struct_0(B) & v1_instalg1(B) & l1_msualg_1(B) & v1_msualg_6(A,B) & l3_msualg_1(A,B) ) ) )).
fof(d6_algstr_0,axiom,( ! [A] : ( l1_algstr_0(A) => ( v5_algstr_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v2_algstr_0(B,A) ) ) ) )).
fof(d6_algstr_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ( v5_algstr_1(A) <=> ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & k6_algstr_0(A,B,D) = C ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & k6_algstr_0(A,D,B) = C ) ) ) ) ) ) )).
fof(d6_algstr_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d6_altcat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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] : ( m1_subset_1(D,A) => ? [E] : ( r2_hidden(E,k1_binop_1(B,D,D)) & ! [F] : ( m1_subset_1(F,A) => ! [G] : ( r2_hidden(G,k1_binop_1(B,D,F)) => k1_binop_1(k4_altcat_1(A,B,C,D,D,F),G,E) = G ) ) ) ) ) ) ) ) )).
fof(d6_altcat_2,axiom,( ! [A] : ( l1_altcat_1(A) => ( v1_altcat_2(A) <=> ! [B] : ~ ( r2_hidden(B,u1_struct_0(A)) & k1_binop_1(u1_altcat_1(A),B,B) = k1_xboole_0 ) ) ) )).
fof(d6_altcat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( m1_subset_1(D,k1_altcat_1(A,B,C)) & v3_altcat_3(D,A,B,C) ) ) ) ) ) ) )).
fof(d6_altcat_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_altcat_5(E,A,D,B,C) => ( v3_altcat_5(E,A,B,C,D) <=> ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_altcat_5(G,A,F,B,C) => ~ ( v2_altcat_5(G,A,B,C,F) & ! [H] : ( m1_subset_1(H,k1_altcat_1(A,F,D)) => ~ ( r2_hidden(H,k1_altcat_1(A,F,D)) & ! [I] : ~ ( r2_hidden(I,B) & ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,k1_altcat_1(A,D,J)) => ~ ( J = k1_funct_1(C,I) & K = k1_funct_1(E,I) & k1_funct_1(G,I) = k5_altcat_1(A,F,D,J,H,K) ) ) ) ) & ! [I] : ( m1_subset_1(I,k1_altcat_1(A,F,D)) => ( ! [J] : ~ ( r2_hidden(J,B) & ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ! [L] : ( m1_subset_1(L,k1_altcat_1(A,D,K)) => ~ ( K = k1_funct_1(C,J) & L = k1_funct_1(E,J) & k1_funct_1(G,J) = k5_altcat_1(A,F,D,K,I,L) ) ) ) ) => H = I ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_ami_2,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k3_ami_2,k4_ami_2))) => ! [B] : ( m2_subset_1(B,k1_ami_2,k2_ami_2) => ! [C] : ( v1_int_1(C) => k7_ami_2(A,B,C) = k1_funct_4(A,k16_funcop_1(B,C)) ) ) ) )).
fof(d6_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( 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)) ) ) )).
fof(d6_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( v7_ordinal1(D) => k4_ami_wstd(A,B,C,D) = k1_ami_wstd(A,B,k2_xcmplx_0(k3_ami_wstd(A,B,C),D)) ) ) ) ) )).
fof(d6_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(d6_amistd_5,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(B)) & v1_funct_1(D) & v1_finset_1(D) & ~ v2_compos_1(D,B) ) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( v1_relat_1(H) & v4_relat_1(H,k4_ordinal1) & v5_relat_1(H,u1_compos_1(B)) & v1_funct_1(H) & v1_partfun1(H,k4_ordinal1) ) => ! [I] : ( ( v1_relat_1(I) & v4_relat_1(I,k4_ordinal1) & v5_relat_1(I,u1_compos_1(B)) & v1_funct_1(I) & v1_partfun1(I,k4_ordinal1) ) => ( ( r1_tarski(D,H) & r1_tarski(k6_compos_1(B,D,C),I) ) => ! [J] : ( v7_ordinal1(J) => 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))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(d6_analoaf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ( v3_analoaf(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( ~ r2_analoaf(A,B,C,D,E) & ~ r2_analoaf(A,B,C,E,D) & ! [F] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ! [F] : ( r2_hidden(k4_tarski(E,F),D) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & ? [I] : ( m1_subset_1(I,u1_struct_0(A)) & ? [J] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_anproj_1,axiom,( ! [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) & l1_rlvect_1(A) ) => ! [B] : ( m1_collsp(B,k3_anproj_1(A)) => ( B = k4_anproj_1(A) <=> ! [C] : ! [D] : ! [E] : ( r2_hidden(k3_xtuple_0(C,D,E),B) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( 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) ) ) ) ) ) ) ) )).
fof(d6_anproj_2,axiom,( ! [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) ) => ( v1_anproj_2(A) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( 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 = k5_numbers & F = k5_numbers & G = k5_numbers ) ) ) ) ) ) ) ) ) ) )).
fof(d6_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : k9_aofa_a00(A,B,C,D,E,F,G,H) = k7_finseq_1(k8_finseq_4(A,B,C,D,E),k11_finseq_1(F,G,H)) )).
fof(d6_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & l6_aofa_a00(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => k2_aofa_a01(A,B) = k22_aofa_a00(A,B,k21_aofa_a00(A,B)) ) ) )).
fof(d6_armstrng,axiom,( ! [A] : k4_armstrng(A) = k8_mcart_1(k1_zfmisc_1(A),k1_zfmisc_1(A),k9_setfam_1(A),k9_setfam_1(A)) )).
fof(d6_arytm_2,axiom,( ! [A] : ( m2_subset_1(A,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) => ! [B] : ( 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) ) ) )).
fof(d6_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => k4_arytm_3(A,B) = k6_ordinal3(A,k3_arytm_3(A,B)) ) ) )).
fof(d6_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v6_asympt_0(A) <=> ? [B] : ( v7_ordinal1(B) & ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => r1_xxreal_0(k9_nat_1(k1_numbers,A,C),k9_nat_1(k1_numbers,A,k1_nat_1(C,1))) ) ) ) ) ) )).
fof(d6_asympt_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( A != k5_numbers => ( B = k6_asympt_1(A) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & r1_xxreal_0(k7_newton(C),A) & ~ r1_xxreal_0(k7_newton(k1_nat_1(C,1)),A) & B = k7_newton(C) ) ) ) & ( A = k5_numbers => ( B = k6_asympt_1(A) <=> B = k5_numbers ) ) ) ) ) )).
fof(d6_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( m1_autalg_1(D,u1_struct_0(A),u3_msualg_1(A,B),k5_autalg_1(A,B)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(d6_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_funct_2(C,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) => ( C = k6_autgroup(A,B) <=> ! [D] : ( 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) ) ) ) ) ) )).
fof(d6_bcialg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_bcialg_1(A) ) => ( v6_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_1(A,k1_bcialg_1(A,B,C),B) = k4_struct_0(A) ) ) ) ) )).
fof(d6_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v5_bcialg_2(B,A) <=> ? [C] : ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) & k1_bcialg_2(A,k4_struct_0(A),B,C) = k4_struct_0(A) ) ) ) ) )).
fof(d6_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),k4_ordinal1),u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_ordinal1),u1_struct_0(A)))) ) => ( B = k5_bcialg_4(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),B,C,k5_numbers) = k4_struct_0(A) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),B,C,k1_nat_1(D,1)) = k1_bcialg_4(A,k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),B,C,D),C) ) ) ) ) ) ) )).
fof(d6_bcialg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_bcialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l2_bcialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d6_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( v3_bciideal(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d6_bhsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k5_bhsp_1(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k1_normsp_1(A,D,E) = k1_algstr_0(A,k1_normsp_1(A,B,E),C) ) ) ) ) ) ) )).
fof(d6_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => k5_bhsp_2(A,B,C) = a_3_1_bhsp_2(A,B,C) ) ) ) )).
fof(d6_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v2_bhsp_4(B,A) <=> v1_series_1(k2_bhsp_2(A,B)) ) ) ) )).
fof(d6_bhsp_6,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( 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] : ( v1_xreal_0(D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( ( v1_finset_1(F) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( ~ v1_xboole_0(F) & r1_tarski(F,B) & ! [G] : ( ( 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,k9_complex1(k6_xcmplx_0(D,k5_bhsp_5(k1_numbers,u1_struct_0(A),k9_binop_2,G,C)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(d6_binari_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k6_margrel1) ) => ! [D] : ( ( v3_card_1(D,A) & m2_finseq_1(D,k6_margrel1) ) => ( D = k6_binari_2(A,B,C) <=> ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(d6_binarith,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(d6_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k6_binom(A,B,C) = k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k4_binom(A),B,C) ) ) ) )).
fof(d6_binop_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( m1_subset_1(D,A) => k1_binop_1(C,D,B) = D ) ) ) )).
fof(d6_borsuk_1,axiom,( ! [A] : ( l1_struct_0(A) => k10_borsuk_1(A) = k8_eqrel_1(u1_struct_0(A),k6_partfun1(u1_struct_0(A))) ) )).
fof(d6_borsuk_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ( r2_borsuk_2(A,B,C) => ! [E] : ( m1_borsuk_2(E,A,C,B) => ( E = k2_borsuk_2(A,B,C,D) <=> ! [F] : ( 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,k6_xcmplx_0(1,F)) ) ) ) ) ) ) ) ) )).
fof(d6_borsuk_6,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(k5_topmetr)) => ( ( r1_xxreal_0(B,k7_xcmplx_0(1,2)) => k3_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,B) = k5_numbers ) & ( ~ r1_xxreal_0(B,k7_xcmplx_0(1,2)) => k3_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,B) = k6_xcmplx_0(k3_xcmplx_0(2,B),1) ) ) ) ) ) )).
fof(d6_borsuk_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( ( v1_xreal_0(C) & ~ v3_xxreal_0(C) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k8_toprealb(A))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d6_bspace,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k2_bspace)) => ! [D] : ( 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) ) ) ) ) )).
fof(d6_c0sp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l5_algstr_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(d6_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => k6_c0sp2(A) = a_1_1_c0sp2(A) ) )).
fof(d6_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( B = k4_calcul_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> m2_finseq_1(C,k3_cqc_lang(A)) ) ) ) )).
fof(d6_card_1,axiom,( ! [A] : ( v7_ordinal1(A) => k6_card_1(A) = A ) )).
fof(d6_card_3,axiom,( ! [A] : ! [B] : ! [C] : ( C = k5_card_3(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( v1_relat_1(E) & v1_funct_1(E) & r2_hidden(E,B) & D = k1_funct_1(E,A) ) ) ) )).
fof(d6_cat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_cat_1(A) ) => ( v4_cat_1(A) <=> ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d6_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m3_cat_2(B,A) => ( v1_cat_2(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( C = E & D = F ) => k2_cat_1(B,C,D) = k2_cat_1(A,E,F) ) ) ) ) ) ) ) ) )).
fof(d6_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ! [C] : ( ( 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] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(d6_cat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d6_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ( v3_cat_5(A) <=> ( v2_cat_5(u1_struct_0(A)) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( m2_cat_1(E,C,D) => B != k4_tarski(k4_tarski(C,D),E) ) ) ) ) ) & ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( m2_cat_1(G,D,E) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_catalg_1,axiom,( ! [A] : ( l1_msualg_1(A) => ( ! [B] : ( r2_hidden(B,k10_xtuple_0(k2_xboole_0(u1_struct_0(A),u4_struct_0(A)))) => ( v1_relat_1(B) & v1_funct_1(B) ) ) => ! [B] : ( B = k4_catalg_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ? [E] : ( 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)) ) ) ) ) ) )).
fof(d6_cc0sp1,axiom,( ! [A] : ( ~ 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))) ) )).
fof(d6_cc0sp2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d6_cfdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [B] : ( v1_xcmplx_0(B) => ( r1_cfdiff_1(A,B) <=> ? [C] : ( m1_cfdiff_1(C,B) & r1_tarski(C,k1_relset_1(k2_numbers,A)) & ? [D] : ( 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] : ( 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] : ( v1_xcmplx_0(F) => ( r2_hidden(F,C) => k6_xcmplx_0(k7_partfun1(k2_numbers,A,F),k7_partfun1(k2_numbers,A,B)) = k2_xcmplx_0(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))) ) ) ) ) ) ) ) ) )).
fof(d6_cfuncdom,axiom,( ! [A] : ( ~ 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)) ) )).
fof(d6_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ! [B] : ( B = k6_cgames_1(A) <=> ? [C] : ( l1_cgames_1(C) & A = C & B = u1_cgames_1(C) ) ) ) )).
fof(d6_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => k3_chain_1(A,B,C) = a_3_0_chain_1(A,B,C) ) ) ) )).
fof(d6_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ( v2_chord(A) <=> ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ( B != C => r1_chord(A,B,C) ) ) ) ) ) )).
fof(d6_circcmb3,axiom,( ! [A] : ( l1_msualg_1(A) => ( v4_circcmb3(A) <=> ? [B] : ( ~ v1_xboole_0(B) & v1_finset_1(B) & ? [C] : ( m1_subset_1(C,k4_ordinal1) & ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & v3_card_1(D,C) & v1_finseq_1(D) & ? [E] : ( 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) ) ) ) ) ) ) )).
fof(d6_circcomb,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(d6_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(d6_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v7_ordinal1(D) => ( D = k6_circuit1(A,B,C) <=> ? [E] : ( ~ v1_xboole_0(E) & v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) & E = a_3_1_circuit1(A,B,C) & D = k1_xxreal_2(E) ) ) ) ) ) ) )).
fof(d6_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(d6_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( 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] : ( v1_xreal_0(D) & r1_xxreal_0(k5_numbers,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => r1_xxreal_0(k2_normsp_0(B,k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)),k3_xcmplx_0(D,k2_normsp_0(A,E))) ) ) ) ) ) ) )).
fof(d6_clopban2,axiom,( ! [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) & 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))) ) )).
fof(d6_clopban3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clopban2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k4_clopban3(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k1_normsp_0(A,D,E) = k6_algstr_0(A,k1_normsp_0(A,B,E),k1_normsp_0(A,C,E)) ) ) ) ) ) ) )).
fof(d6_clopban4,axiom,( ! [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) & 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] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(d6_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) => ( v3_closure2(C,A,B) <=> ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(d6_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => k5_clvect_2(A,B,C) = a_3_1_clvect_2(A,B,C) ) ) ) )).
fof(d6_coh_sp,axiom,( ! [A] : k5_coh_sp(A) = a_1_2_coh_sp(A) )).
fof(d6_cohsp_1,axiom,( ! [A] : ( v3_cohsp_1(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_cohsp_1(B) => r2_hidden(k3_tarski(B),A) ) ) ) )).
fof(d6_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_collsp(A) ) => ( v4_collsp(A) <=> ~ ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_collsp(A,B,C,D) ) ) ) ) ) )).
fof(d6_combgras,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( l1_incsp_1(B) => ! [C] : ( l1_combgras(C,A,B) => ! [D] : ( 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) ) ) ) ) )).
fof(d6_compact1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v5_compact1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_connsp_2(C,A,B) & v2_compts_1(C,A) ) ) ) ) )).
fof(d6_compl_sp,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ( v5_compl_sp(B,A) <=> ! [C] : ( v7_ordinal1(C) => v4_pre_topc(k9_nat_1(k9_setfam_1(u1_struct_0(A)),B,C),A) ) ) ) ) )).
fof(d6_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k9_complex1(A) = k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A)))) ) )).
fof(d6_compos_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_compos_0(A) ) => ( v3_compos_0(A) <=> ! [B] : ( m1_subset_1(B,k1_compos_0(A)) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v4_valued_0(C) ) => ! [D] : ( ( 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] : ( r2_hidden(k3_xtuple_0(B,C,E),A) => r2_hidden(k3_xtuple_0(B,D,E),A) ) ) ) ) ) ) ) )).
fof(d6_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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) ) ) ) )).
fof(d6_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k3_comput_1(A,B) = k8_funcop_1(k4_ordinal1,k4_finseq_2(A,k4_ordinal1),B) ) ) )).
fof(d6_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v2_comseq_2(A) => ! [B] : ( v1_xcmplx_0(B) => ( B = k3_comseq_2(A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(D,E) & r1_xxreal_0(C,k9_complex1(k6_xcmplx_0(k9_nat_1(k2_numbers,A,E),B))) ) ) ) ) ) ) ) ) )).
fof(d6_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( B = k8_comseq_3(A) <=> ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,B,C) = k4_complex1(k9_nat_1(k2_numbers,A,C)) ) ) ) ) )).
fof(d6_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_waybel_1(C,A,B) => ( v2_conlat_1(C,A,B) <=> ? [D] : ( 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] : ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ! [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))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_conlat_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d6_conmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v6_conmetr(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A))) => ! [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_conmetr1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v6_conmetr1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,k1_zfmisc_1(u1_struct_0(A))) => ! [L] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_connsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r3_connsp_1(A,B,C) <=> ? [D] : ( 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)) ) ) ) ) ) )).
fof(d6_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(d6_connsp_3,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_pre_topc(A,B)))) => k5_connsp_3(A,B,C) = C ) ) ) )).
fof(d6_convex4,axiom,( ! [A] : ( ( ~ 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] : ( m1_convex4(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k4_convex4(A,B) <=> ? [D] : ( 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)) ) ) ) ) ) )).
fof(d6_convfun1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k6_numbers))) ) => ( v1_convfun1(B,A) <=> v1_convex1(k5_convfun1(A,B),k3_convfun1(A,k4_convfun1)) ) ) ) )).
fof(d6_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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))) ) ) ) )).
fof(d6_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ( r6_cqc_the3(A,B,C) <=> ( v6_qc_lang1(B,A) & ? [D] : ( m1_subset_1(D,k4_ordinal1) & r1_xxreal_0(1,D) & ? [E] : ( 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] : ( m1_subset_1(F,k4_ordinal1) => ~ ( r1_xxreal_0(1,F) & ~ r1_xxreal_0(D,F) & ! [G] : ( m2_subset_1(G,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [H] : ( m2_subset_1(H,k9_qc_lang1(A),k3_cqc_lang(A)) => ~ ( H = k1_funct_1(E,F) & k1_funct_1(E,k1_nat_1(F,1)) = k11_cqc_lang(A,G,H) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_csspace,axiom,( ! [A] : ( m1_subset_1(A,k1_csspace) => ( A = k6_csspace <=> ! [B] : ( v7_ordinal1(B) => k9_nat_1(k2_numbers,k2_csspace(A),B) = k5_complex1 ) ) ) )).
fof(d6_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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))) ) ) )).
fof(d6_decomp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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))) ) ) )).
fof(d6_dickson,axiom,( ! [A] : ( v1_relat_1(A) => k3_dickson(A) = k6_subset_1(A,k2_relat_1(A)) ) )).
fof(d6_diff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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,k5_numbers),A) & ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d6_dilworth,axiom,( ! [A] : ( ( v4_dilworth(A) & l1_orders_2(A) ) => ! [B] : ( v7_ordinal1(B) => ( B = k2_dilworth(A) <=> ( ? [C] : ( 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] : ( ( 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) ) ) ) ) ) )).
fof(d6_diraf,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ( v1_diraf(A) <=> ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_analoaf(A,B,C,B,D) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_analoaf(A,B,D,C,E) & C != E ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_analoaf(A,B,C,D,E) & r2_analoaf(A,B,D,C,E) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_analoaf(A,D,B,B,E) & B != D & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_analoaf(A,C,B,B,F) & r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_dirort,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dirort(A) & l1_analoaf(A) ) => ( v4_dirort(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(k3_finseq_2(A)))) => ( B = k6_dist_1(A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(A))) => ( r2_hidden(C,B) <=> ? [D] : ( m2_finseq_1(D,A) & C = k5_dist_1(A,D) ) ) ) ) ) ) )).
fof(d6_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( D = k6_dist_2(A,B,C) <=> ! [E] : ( m1_dist_2(E,A,B) => D = k4_dist_2(A,B,E,C) ) ) ) ) ) ) )).
fof(d6_dtconstr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_dtconstr(A) & v3_dtconstr(A) & l1_lang1(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(A),k7_dtconstr(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(d6_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( m1_dynkin(C,A) => ( C = k5_dynkin(A,B) <=> ( r1_tarski(B,C) & ! [D] : ( m1_dynkin(D,A) => ( r1_tarski(B,D) => r1_tarski(C,D) ) ) ) ) ) ) ) )).
fof(d6_e_siec,axiom,( ! [A] : k4_e_siec(A) = g1_e_siec(k1_tarski(A),k4_relat_1(k1_tarski(A)),k4_relat_1(k1_tarski(A))) )).
fof(d6_ec_pf_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)))) ) )).
fof(d6_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( 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] : ( ( 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)) ) ) ) ) )).
fof(d6_endalg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(d6_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k2_ens_1(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(d6_entropy1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( v4_partfun3(B) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ( C = k3_entropy1(A,B) <=> ( k3_finseq_1(C) = k3_finseq_1(B) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(C)) => ( ( ~ r1_xxreal_0(k1_funct_1(B,D),k5_numbers) => k1_funct_1(C,D) = k3_power(A,k1_funct_1(B,D)) ) & ( k1_funct_1(B,D) = k5_numbers => k1_funct_1(C,D) = k5_numbers ) ) ) ) ) ) ) ) ) ) )).
fof(d6_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ( I = k6_enumset1(A,B,C,D,E,F,G,H) <=> ! [J] : ( r2_hidden(J,I) <=> ~ ( J != A & J != B & J != C & J != D & J != E & J != F & J != G & J != H ) ) ) )).
fof(d6_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( D = k11_eqrel_1(A,B,C) <=> ( r2_hidden(B,D) & r2_hidden(D,C) ) ) ) ) ) ) )).
fof(d6_equation,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m3_pboole(C,u1_struct_0(A),k4_equation(A)) => ( r2_equation(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d6_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d6_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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) ) ) ) ) )).
fof(d6_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ( v4_euclid_7(B,A) <=> ! [C] : ( ( v3_euclid_7(C) & m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) ) => ( r1_tarski(B,C) => C = B ) ) ) ) ) )).
fof(d6_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => k7_euclid_8(A,B,C) = k22_rvsum_1(A,k5_euclid_8(B,C)) ) ) ) )).
fof(d6_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => k3_euclidlp(A,B,C) = k3_seq_4(k2_euclidlp(A,B,C)) ) ) ) )).
fof(d6_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ( v6_euclmetr(A) <=> v11_aff_2(k3_analmetr(A)) ) ) )).
fof(d6_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k3_exchsort(A) = k5_ordinal3(k2_exchsort(A),k1_exchsort(A)) ) )).
fof(d6_extpro_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [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_partfun1(C,u1_struct_0(B)) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(d6_facirc_1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => ! [D] : ( m1_subset_1(D,k6_margrel1) => k1_funct_1(A,k11_finseq_1(B,C,D)) = k1_binarith(k1_binarith(B,C),D) ) ) ) ) ) )).
fof(d6_facirc_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( 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] : ( m1_subset_1(F,k4_ordinal1) & A = k1_nat_1(F,1) & E = k12_facirc_1(k1_funct_1(C,A),k1_funct_1(D,A),k5_facirc_2(F,C,D)) ) ) ) ) ) ) ) ) )).
fof(d6_fdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( r2_fdiff_1(A,B) <=> ( r1_tarski(B,k1_relset_1(k1_numbers,A)) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => r1_fdiff_1(k2_partfun1(k1_numbers,k1_numbers,A,B),C) ) ) ) ) ) )).
fof(d6_fdiff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r3_fdiff_3(B,A) => ! [C] : ( v1_xreal_0(C) => ( C = k2_fdiff_3(A,B) <=> ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v9_ordinal1(D) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k10_xtuple_0(E) = k1_tarski(A) & r1_tarski(k10_xtuple_0(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),k1_relset_1(k1_numbers,B)) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ r1_xxreal_0(k3_funct_2(k4_ordinal1,k1_numbers,D,F),k5_numbers) ) ) => C = k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),B),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,B)))) ) ) ) ) ) ) ) ) )).
fof(d6_ff_siec,axiom,( k6_ff_siec = k1_ff_siec(k1_xboole_0,k1_xboole_0) )).
fof(d6_fib_num2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k6_fib_num2(A) = k1_fib_num2(k2_fib_num2,k3_xboole_0(k4_fib_num2,k2_finseq_1(A))) ) )).
fof(d6_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( v3_filter_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r1_lattices(A,k2_lattices(A,B,D),C) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_lattices(A,k2_lattices(A,B,E),C) => r1_lattices(A,E,D) ) ) ) ) ) ) ) )).
fof(d6_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_filter_1(A,B))) => ( D = k5_filter_1(A,B,C) <=> ! [E] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(d6_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => k5_filter_2(A) = u1_struct_0(A) ) )).
fof(d6_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) )).
fof(d6_finance1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( ~ 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) ) ) )).
fof(d6_finseq_1,axiom,( ! [A] : k6_finseq_1(A) = k1_xboole_0 )).
fof(d6_finseq_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k3_finseq_2(k1_tarski(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k3_finseq_2(k1_tarski(A))))) ) => ( B = k7_finseq_2(A) <=> ! [C] : ( v7_ordinal1(C) => k1_funct_1(B,C) = k2_finseq_2(C,A) ) ) ) )).
fof(d6_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_hidden(B,k10_xtuple_0(A)) => ! [C] : ( ( 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(d6_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( r1_finseq_8(A,B) <=> ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(k7_nat_d(k1_nat_1(E,k3_finseq_1(B)),1),k3_finseq_1(C)) & k3_finseq_8(A,C,D,k7_nat_d(k1_nat_1(D,k3_finseq_1(B)),1)) = k3_finseq_8(A,C,E,k7_nat_d(k1_nat_1(E,k3_finseq_1(B)),1)) & k3_finseq_8(A,C,D,k7_nat_d(k1_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)) ) ) ) ) ) ) ) ) )).
fof(d6_finset_1,axiom,( ! [A] : ( v5_finset_1(A) <=> ! [B] : ( r2_hidden(B,A) => v1_finset_1(B) ) ) )).
fof(d6_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( 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) ) ) )).
fof(d6_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(u1_struct_0(A))))) ) => ( C = k6_fintopo3(A,B) <=> ( ! [D] : ( v7_ordinal1(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( E = k1_funct_1(C,D) => k3_funct_2(k4_ordinal1,k1_zfmisc_1(u1_struct_0(A)),C,k1_nat_1(D,1)) = k12_fin_topo(A,E) ) ) ) & k3_funct_2(k4_ordinal1,k1_zfmisc_1(u1_struct_0(A)),C,k5_numbers) = B ) ) ) ) ) )).
fof(d6_fintopo4,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k4_fintopo4(A) = g1_orders_2(k2_finseq_1(A),k3_fintopo4(A)) ) ) )).
fof(d6_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ( v2_fintopo6(B,A) <=> ( r1_xxreal_0(1,k3_finseq_1(B)) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d6_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( v1_fomodel0(B,A) <=> ! [C] : ! [D] : ( ( 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 ) ) ) )).
fof(d6_fomodel1,axiom,( ! [A] : ( 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(k4_ordinal1,k5_numbers))) ) )).
fof(d6_fomodel2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k6_fomodel2(A,B) <=> ( k9_xtuple_0(C) = k9_xtuple_0(A) & ! [D] : ( r2_hidden(D,k9_xtuple_0(A)) => k1_funct_1(C,D) = k3_relat_1(k1_funct_1(A,D),B) ) ) ) ) ) ) )).
fof(d6_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( v7_ordinal1(C) => k9_fomodel3(A,B,C) = k8_fomodel3(A,A,B,C) ) ) ) )).
fof(d6_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) => ! [C] : ( v7_ordinal1(C) => k5_fomodel4(A,B,C) = k8_funct_7(k4_fomodel4(A,B),C) ) ) ) )).
fof(d6_frechet,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ( v3_frechet(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,k2_pre_topc(A,B)) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( r1_tarski(k2_relset_1(u1_struct_0(A),D),B) & r2_hidden(C,k2_frechet(A,D)) ) ) ) ) ) ) ) )).
fof(d6_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : 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) )).
fof(d6_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m2_finseq_1(E,A) => ! [F] : ( m2_finseq_1(F,B) => ( F = k4_fsm_1(A,B,C,D,E) <=> ( k3_finseq_1(F) = k3_finseq_1(E) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( 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))) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_2(B,A) ) => ( v5_fsm_2(B,A) <=> ! [C] : ( m1_subset_1(C,A) => r2_fsm_2(A,C,B) ) ) ) ) )).
fof(d6_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_3(C,A,B) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(d6_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k6_ftacell1(A,B,C,D,E) = k12_gfacirc1(k12_gfacirc1(A,B,C),E,D) )).
fof(d6_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_funcop_1(A) <=> ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => ( v1_relat_1(k1_funct_1(A,B)) & v1_funct_1(k1_funct_1(A,B)) ) ) ) ) )).
fof(d6_funcsdom,axiom,( ! [A] : k10_funcsdom(A) = g1_rlvect_1(k9_funct_2(A,k1_numbers),k8_funcsdom(A),k5_funcsdom(A),k7_funcsdom(A)) )).
fof(d6_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( C = k7_relat_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( r2_hidden(E,k9_xtuple_0(A)) & r2_hidden(E,B) & D = k1_funct_1(A,E) ) ) ) ) )).
fof(d6_funct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(d6_funct_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k11_funct_3(A) <=> ( k9_xtuple_0(B) = A & ! [C] : ( r2_hidden(C,A) => k1_funct_1(B,C) = k4_tarski(C,C) ) ) ) ) )).
fof(d6_funct_5,axiom,( k7_funct_5 = k17_funcop_1(k5_ordinal1,k5_ordinal1,k5_ordinal1) )).
fof(d6_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k6_funct_6(A) <=> ( k9_xtuple_0(B) = k4_card_3(k1_funct_6(A)) & ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ~ ( r2_hidden(C,k4_card_3(k1_funct_6(A))) & ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ~ ( k1_funct_1(B,C) = D & k9_xtuple_0(D) = k9_xtuple_0(A) & ! [E] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d6_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_xboole_0(A) => ( B = k6_funct_7(A) <=> v1_xboole_0(B) ) ) & ( ~ v1_xboole_0(A) => ( B = k6_funct_7(A) <=> B = k10_xtuple_0(k1_funct_1(A,k3_finseq_1(A))) ) ) ) ) )).
fof(d6_funct_8,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( v5_funct_8(C,A,B) <=> ! [D] : ( v1_xreal_0(D) => ( ( r2_hidden(D,k1_relset_1(A,C)) & r2_hidden(k4_xcmplx_0(D),k1_relset_1(A,C)) ) => k1_funct_1(C,k4_xcmplx_0(D)) = k4_xcmplx_0(k1_funct_1(C,D)) ) ) ) ) ) ) )).
fof(d6_functor0,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => ! [C] : ( l1_functor0(C,A,B) => ( v4_functor0(C,A,B) <=> v2_funct_1(u1_functor0(A,B,C)) ) ) ) ) )).
fof(d6_functor2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ( r2_functor2(A,B,C,D) <=> ( r1_functor2(A,B,C,D) & ? [E] : ( m1_functor2(E,A,B,C,D) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( k1_altcat_1(A,F,G) != k1_xboole_0 => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( m1_functor3(E,A,B,C,D) => ( r1_functor3(A,B,C,D) => ! [F] : ( m1_functor3(F,A,B,D,C) => ( F = k8_functor3(A,B,C,D,E) <=> ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d6_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k4_fuzzy_1(A) = k7_rfunct_1(k1_xboole_0,A) ) )).
fof(d6_fvaluat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => k3_fvaluat1(A,B,C) = k1_binop_1(k4_group_1(A),B,C) ) ) ) )).
fof(d6_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(d6_gate_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k6_gate_5(A,B,C,D,E) = k10_gate_1(k2_gate_1(B,D),k2_gate_1(A,E),k1_xboole_0) )).
fof(d6_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( B = k3_gcd_1(A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & C = k2_gcd_1(A,D) ) ) ) ) ) ) )).
fof(d6_genealg1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_finseq_1(B,k3_card_3(A)) => ! [C] : ( m2_finseq_1(C,k3_card_3(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ! [H] : ( m1_subset_1(H,k4_ordinal1) => 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) ) ) ) ) ) ) ) ) )).
fof(d6_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k4_geomtrap(A,B,C,D,E) = k2_xcmplx_0(k3_xcmplx_0(k2_geomtrap(A,B,C,D),k2_geomtrap(A,B,C,E)),k3_xcmplx_0(k3_geomtrap(A,B,C,D),k3_geomtrap(A,B,C,E))) ) ) ) ) ) )).
fof(d6_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(d6_gfacirc2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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] : ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) & ? [F] : ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) & ? [G] : ( v1_relat_1(G) & v4_relat_1(G,k4_ordinal1) & v1_funct_1(G) & v1_partfun1(G,k4_ordinal1) & k5_gfacirc2(A,B,C) = k1_funct_1(E,A) & D = k1_funct_1(F,A) & k1_funct_1(E,k5_numbers) = k5_circcomb(k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k8_margrel1),k1_xboole_0) & k1_funct_1(F,k5_numbers) = k7_circcomb(k5_ordinal1,k6_margrel1,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k8_margrel1),k1_xboole_0) & k1_funct_1(G,k5_numbers) = k4_tarski(k1_xboole_0,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k8_margrel1)) & ! [H] : ( v7_ordinal1(H) => ! [I] : ( ( ~ v2_struct_0(I) & l1_msualg_1(I) ) => ! [J] : ( ( v4_msualg_1(J,I) & l3_msualg_1(J,I) ) => ! [K] : ( ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) ) => k6_glib_000(A) = k1_funct_1(A,k1_glib_000) ) )).
fof(d6_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => k3_glib_001(A,B) = k1_funct_1(B,1) ) ) )).
fof(d6_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k6_glib_000(A))) ) => ( C = k2_glib_002(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( v2_glib_001(E,A) & m3_glib_001(E,A) & r1_glib_001(A,B,D,E) ) ) ) ) ) ) )).
fof(d6_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) ) => ( v3_glib_003(A) <=> ( r2_hidden(k4_glib_003,k1_relset_1(k4_ordinal1,A)) & ? [B] : ( 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)) ) ) ) ) )).
fof(d6_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) = k2_uproots(k7_glib_000(A),k5_glib_003(A)) ) )).
fof(d6_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( ( 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] : ( m1_glib_005(C,A,B) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d6_goboard1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( v4_goboard1(A) <=> ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k2_finseq_1(k1_matrix_0(A))) => v5_valued_0(k1_goboard1(k8_matrix_0(u1_struct_0(k15_euclid(2)),A,B))) ) ) ) ) )).
fof(d6_goboard5,axiom,( ! [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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k3_finseq_1(A)) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( C = k4_goboard5(A,B) <=> ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ~ ( r2_hidden(k4_tarski(D,E),k2_matrix_0(k2_goboard2(A))) & r2_hidden(k4_tarski(F,G),k2_matrix_0(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),D,E) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),F,G) & ~ ( D = F & k1_nat_1(E,1) = G & C = k3_goboard5(k2_goboard2(A),D,E) ) & ~ ( k1_nat_1(D,1) = F & E = G & C = k3_goboard5(k2_goboard2(A),D,k7_nat_d(E,1)) ) & ~ ( D = k1_nat_1(F,1) & E = G & C = k3_goboard5(k2_goboard2(A),F,G) ) & ~ ( D = F & E = k1_nat_1(G,1) & C = k3_goboard5(k2_goboard2(A),k7_nat_d(D,1),G) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_gobrd13,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ! [D] : ( v7_ordinal1(D) => ( r2_gobrd13(A,B,C,D) <=> ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ~ ( r2_hidden(k4_tarski(E,F),k2_matrix_0(C)) & r2_hidden(k4_tarski(G,H),k2_matrix_0(C)) & k7_partfun1(A,B,D) = k3_matrix_0(A,C,E,F) & k7_partfun1(A,B,k1_nat_1(D,1)) = k3_matrix_0(A,C,G,H) & ~ ( E = G & k1_nat_1(F,1) = H & r2_hidden(k4_tarski(k7_nat_d(G,1),H),k2_matrix_0(C)) & k7_partfun1(A,B,k1_nat_1(D,2)) = k3_matrix_0(A,C,k7_nat_d(G,1),H) ) & ~ ( k1_nat_1(E,1) = G & F = H & r2_hidden(k4_tarski(G,k1_nat_1(H,1)),k2_matrix_0(C)) & k7_partfun1(A,B,k1_nat_1(D,2)) = k3_matrix_0(A,C,G,k1_nat_1(H,1)) ) & ~ ( E = k1_nat_1(G,1) & F = H & r2_hidden(k4_tarski(G,k7_nat_d(H,1)),k2_matrix_0(C)) & k7_partfun1(A,B,k1_nat_1(D,2)) = k3_matrix_0(A,C,G,k7_nat_d(H,1)) ) & ~ ( E = G & F = k1_nat_1(H,1) & r2_hidden(k4_tarski(k1_nat_1(G,1),H),k2_matrix_0(C)) & k7_partfun1(A,B,k1_nat_1(D,2)) = k3_matrix_0(A,C,k1_nat_1(G,1),H) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_gr_cy_1,axiom,( ! [A] : ( v1_int_1(A) => k5_gr_cy_1(A) = A ) )).
fof(d6_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(d6_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r1_graph_2(A,B,C) <=> ( k3_finseq_1(B) = k1_nat_1(k3_finseq_1(C),1) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( 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,k1_nat_1(D,1)),k1_funct_1(C,D)) ) ) ) ) ) ) ) )).
fof(d6_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : k7_graph_3(A,B,C) = k1_nat_1(k5_card_1(k2_graph_3(A,B,C)),k5_card_1(k3_graph_3(A,B,C))) ) ) )).
fof(d6_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v7_graph_1(B,A) & m2_graph_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d6_graphsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ? [D] : ( r2_hidden(D,u4_struct_0(A)) & r1_graph_4(A,B,C,D) ) => ! [D] : ( D = k10_graphsp(A,B,C) <=> ? [E] : ( D = E & r2_hidden(E,u4_struct_0(A)) & r1_graph_4(A,B,C,E) ) ) ) ) ) ) )).
fof(d6_grcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(d6_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l5_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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) ) ) ) ) ) )).
fof(d6_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [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] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,B)))) ) => ! [E] : ( m2_ideal_1(E,k12_polynom1(A,B),D) => ( r2_groeb_2(A,B,C,D,E) <=> ( k4_rlvect_1(k12_polynom1(A,B),E) = C & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( r2_hidden(F,k4_finseq_1(E)) & ! [G] : ( ( 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] : ( ( v1_funct_1(H) & v1_funct_2(H,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(H,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(k12_polynom1(A,B)),E,F) = k10_polynom1(A,B,G,H) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(d6_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ! [C] : ( ( v15_algstr_0(C) & m1_group_2(C,A) ) => ( r1_group_2(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_struct_0(B,D) <=> r1_struct_0(C,D) ) ) ) ) ) ) )).
fof(d6_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(d6_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(d6_group_5,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d6_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d6_group_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => v2_group_1(k1_group_7(A,B,C)) ) ) ) ) )).
fof(d6_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(d6_hahnban,axiom,( ! [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) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => k3_funct_2(u1_struct_0(A),k1_numbers,B,k1_rlvect_1(A,C,D)) = k3_xcmplx_0(k9_complex1(D),k3_funct_2(u1_struct_0(A),k1_numbers,B,C)) ) ) ) ) ) )).
fof(d6_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(d6_hallmar1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ! [C] : ( m2_finseq_1(C,k1_zfmisc_1(A)) => ( m2_hallmar1(C,A,B) <=> ( k4_finseq_1(C) = k4_finseq_1(B) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k4_finseq_1(B)) => r1_tarski(k1_funct_1(C,D),k1_funct_1(B,D)) ) ) ) ) ) ) )).
fof(d6_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => k3_henmodel(A) = k11_cqc_sim1(k3_qc_lang1(A)) ) )).
fof(d6_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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] : ( 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)) = k5_numbers ) ) ) ) )).
fof(d6_heyting1,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(d6_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_substlat(A,B))) => k6_heyting2(A,B,C) = k1_zfmisc_1(C) ) ) )).
fof(d6_hilbasis,axiom,( ! [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] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k14_polynom3(k12_polynom1(B,A))),u1_struct_0(k12_polynom1(k1_nat_1(B,1),A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k14_polynom3(k12_polynom1(B,A))),u1_struct_0(k12_polynom1(k1_nat_1(B,1),A))))) ) => ( C = k6_hilbasis(A,B) <=> ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(k12_polynom1(B,A))) & v1_polynom1(D,k12_polynom1(B,A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k12_polynom1(B,A))))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(B),u1_struct_0(A)) & v1_polynom1(E,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(A)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(k1_nat_1(B,1)),u1_struct_0(A)) & v1_polynom1(F,A) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(k1_nat_1(B,1)),u1_struct_0(A)))) ) => ! [G] : ( ( v1_relat_1(G) & v4_relat_1(G,k1_nat_1(B,1)) & v1_funct_1(G) & v1_partfun1(G,k1_nat_1(B,1)) & v4_valued_0(G) & v2_pre_poly(G) ) => ( ( F = k1_funct_1(C,D) & E = k1_normsp_1(k12_polynom1(B,A),D,k1_recdef_1(G,B)) ) => k4_polynom1(k1_nat_1(B,1),A,F,G) = k1_funct_1(E,k5_relat_1(G,B)) ) ) ) ) ) ) ) ) ) )).
fof(d6_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( v1_hilbert2(A) <=> ? [B] : ( m1_subset_1(B,k1_hilbert1) & ? [C] : ( m1_subset_1(C,k1_hilbert1) & A = k4_hilbert1(B,C) ) ) ) ) )).
fof(d6_hilbert3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( m1_hilbert3(B,A) => ! [C] : ( 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) ) ) ) )).
fof(d6_hurwitz,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k6_hurwitz(A,B,C) = k3_normsp_1(A,B,k13_polynom3(A,k5_hurwitz(A,B,C),C)) ) ) ) )).
fof(d6_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k6_idea_1(A,B) = k4_nat_d(k5_idea_1(A,B),k5_series_1(2,A)) ) ) )).
fof(d6_incproj,axiom,( ! [A] : ( l1_incsp_1(A) => ( v2_incproj(A) <=> ~ ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => r1_incsp_1(A,B,C) ) ) ) ) )).
fof(d6_incsp_1,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_incsp_1(A))) => ( v3_incsp_1(B,A) <=> ? [C] : ( m1_subset_1(C,u2_incsp_1(A)) & r4_incsp_1(A,B,C) ) ) ) ) )).
fof(d6_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ( B = k1_int_1(A) <=> ( r1_xxreal_0(B,A) & ~ r1_xxreal_0(B,k6_xcmplx_0(A,1)) ) ) ) ) )).
fof(d6_int_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_int_3)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_int_3)) => ( B != k4_struct_0(k1_int_3) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_int_3)) => ( C = k4_int_3(A,B) <=> ? [D] : ( 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) ) ) ) ) ) ) )).
fof(d6_integr10,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r4_integr10(A,B) <=> ( ! [C] : ( v1_xreal_0(C) => ( 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] : ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,k1_relset_1(k1_numbers,C)) => k1_funct_1(C,D) = k4_integra5(D,B,A) ) ) & v6_limfunc1(C) ) ) ) ) ) )).
fof(d6_integr15,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( m1_integra1(D,B) => ! [E] : ( m3_integr15(E,A,B,C,D) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(A)) => ( F = k4_integr15(A,B,C,D,E) <=> ! [G] : ( m1_subset_1(G,k4_ordinal1) => ~ ( r2_hidden(G,k2_finseq_1(A)) & ! [H] : ( m2_finseq_1(H,k1_numbers) => ~ ( H = k4_finseqop(k1_euclid(A),k1_numbers,E,k1_pdiff_1(G,A)) & k1_funct_1(F,G) = k18_rvsum_1(H) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_integr16,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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) = k2_xcmplx_0(k12_integra1(A,k5_comseq_3(A,B)),k3_xcmplx_0(k12_integra1(A,k6_comseq_3(A,B)),k7_complex1)) ) ) )).
fof(d6_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ( D = k4_integr18(A,B,C) <=> ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_integra1(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(B)))) ) => ! [F] : ( m2_integr18(F,A,B,C,E) => ( ( v2_comseq_2(k2_integra3(B,E)) & k1_seq_2(k2_integra3(B,E)) = k5_numbers ) => ( v3_normsp_1(k3_integr18(A,B,C,E,F),A) & k6_normsp_1(A,k3_integr18(A,B,C,E,F)) = D ) ) ) ) ) ) ) ) ) ) )).
fof(d6_integr1c,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k1_numbers)) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [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))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( m1_integra1(C,A) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ( D = k5_integra1(A,B,C) <=> ( k3_finseq_1(D) = k3_finseq_1(C) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(C)) => k1_funct_1(D,E) = k3_xcmplx_0(k3_seq_4(k1_rvsum_1(k2_partfun1(A,k1_numbers,B,k2_integra1(A,C,E)))),k3_integra1(k2_integra1(A,C,E))) ) ) ) ) ) ) ) ) )).
fof(d6_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( C = k6_interva1(A,B) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) & B = k2_interva1(A,D,C) ) ) ) ) ) )).
fof(d6_irrat_1,axiom,( k4_power = k4_series_1(k5_irrat_1) )).
fof(d6_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,B,C) => ! [E] : ( m2_cat_1(E,B,C) => ( r1_nattra_1(B,C,D,E) => ! [F] : ( m2_cat_1(F,A,B) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d6_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(d6_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k6_jgraph_6(A,B,C) = a_3_1_jgraph_6(A,B,C) ) ) ) )).
fof(d6_jordan20,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ( r6_jordan20(A,B,C,D,E) <=> ( r1_topreal1(k15_euclid(2),B,C,A) & r2_hidden(D,A) & k17_euclid(D) = E & ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & r1_jordan5c(A,B,C,D,F) & ! [G] : ( 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] : ( m1_subset_1(G,u1_struct_0(k15_euclid(2))) => ( r1_jordan5c(A,B,C,F,G) => ( G = F | ( ? [H] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_jordan3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( r3_jordan3(A,B,C,D) <=> ( r2_jordan3(A,B,C,D) & C != D ) ) ) ) ) ) )).
fof(d6_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( B = k6_jordan5d(A) <=> ( r2_hidden(k4_tarski(B,1),k2_matrix_0(k2_goboard2(A))) & k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),B,1) = k24_pscomp_1(k3_topreal1(2,A)) ) ) ) ) )).
fof(d6_jordan6,axiom,( ! [A] : ( v1_xreal_0(A) => k6_jordan6(A) = a_1_2_jordan6(A) ) )).
fof(d6_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_jordan_a(B,A) => ! [C] : ( v1_xreal_0(C) => ( C = k4_jordan_a(A,B) <=> ? [D] : ( ~ 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) ) ) ) ) ) )).
fof(d6_kolmog01,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( m1_kolmog01(D,A,B,C) => ! [E] : ( 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))) ) ) ) ) )).
fof(d6_kurato_1,axiom,( 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)) )).
fof(d6_lang1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_lang1(A) ) => k3_lang1(A) = a_1_2_lang1(A) ) )).
fof(d6_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( D = k7_laplace(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( r2_hidden(k4_tarski(E,F),k2_matrix_0(D)) => k3_matrix_0(u1_struct_0(B),D,E,F) = k6_laplace(E,F,A,B,C) ) ) ) ) ) ) ) ) )).
fof(d6_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k8_lattice3(A,B) = B ) ) )).
fof(d6_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( m1_lattice4(C,A,B) => ( r4_lattice4(A,B,C) <=> ! [D] : ( 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)) ) ) ) ) ) )).
fof(d6_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,A) => k3_lattice5(A,B,C,D,D) = k3_yellow_0(B) ) ) ) ) ) )).
fof(d6_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_lattice6(A,B) = k16_lattice3(A,a_2_2_lattice6(A,B)) ) ) )).
fof(d6_lattice7,axiom,( ! [A] : ( ( 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) ) )).
fof(d6_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m1_lattice5(D,A,B,C) => ! [E] : ( v3_ordinal1(E) => ( r2_hidden(E,k9_xtuple_0(D)) => k4_lattice8(A,B,C,D,E) = k1_funct_1(D,E) ) ) ) ) ) ) )).
fof(d6_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lattices(A) ) => ( v6_lattices(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_lattices(A,B,C) = k2_lattices(A,C,B) ) ) ) ) )).
fof(d6_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( v3_lexbfs(A) <=> ? [B] : ( v7_ordinal1(B) & ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => k1_funct_1(A,B) = k1_funct_1(A,C) ) ) ) ) ) )).
fof(d6_lfuzzy_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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 ) ) )).
fof(d6_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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(k3_fuzzy_4(A,A,A,B,B),B) ) ) ) )).
fof(d6_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v3_limfunc1(A) <=> ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,B) & r2_hidden(C,k1_relset_1(k1_numbers,A)) ) ) & ? [B] : ( v1_xreal_0(B) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_limfunc1(C) & r1_tarski(k10_xtuple_0(C),k1_relset_1(k1_numbers,A)) ) => ( v2_comseq_2(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,C,A)) & k1_seq_2(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,C,A)) = B ) ) ) ) ) ) ) )).
fof(d6_limfunc2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r6_limfunc2(A,B) <=> ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,B) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(C,D) & ~ r1_xxreal_0(D,B) & r2_hidden(D,k1_relset_1(k1_numbers,A)) ) ) ) ) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(C) & k1_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(k4_ordinal1,k1_numbers,k1_numbers,C,A)) ) ) ) ) ) ) )).
fof(d6_lopban_1,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( 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] : ( 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)))) ) ) ) ) ) ) )).
fof(d6_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => k7_lopban_2(A) = g6_algstr_0(k10_lopban_1(A,A),k7_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),k5_lopban_2(A),k6_lopban_2(A),k9_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A))) ) )).
fof(d6_lopban_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lopban_2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k3_lopban_3(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k5_rsspace3(A,D,E) = k6_algstr_0(A,k5_rsspace3(A,B,E),C) ) ) ) ) ) ) )).
fof(d6_lopban_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( E = k5_lopban_4(A,B,C,D) <=> ! [F] : ( v7_ordinal1(F) => ( ( r1_xxreal_0(F,A) => k9_nat_1(u1_struct_0(B),E,F) = k6_algstr_0(B,k1_rlvect_1(B,k6_lopban_3(B,C,F),k9_nat_1(k1_numbers,k2_lopban_4(A),F)),k6_lopban_3(B,D,k7_nat_d(A,F))) ) & ( ~ r1_xxreal_0(F,A) => k9_nat_1(u1_struct_0(B),E,F) = k4_struct_0(B) ) ) ) ) ) ) ) ) ) )).
fof(d6_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k8_lopclset(A) <=> ( k9_xtuple_0(B) = u1_struct_0(A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_funct_1(B,C) = a_2_0_lopclset(A,C) ) ) ) ) ) )).
fof(d6_lpspacc1,axiom,( ! [A] : k10_lpspacc1(A) = k8_funcop_1(k2_numbers,A,k5_complex1) )).
fof(d6_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k6_lpspace1(A) = k8_funcop_1(k4_ordinal1,A,1) ) )).
fof(d6_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v2_xxreal_0(E) & v1_xreal_0(E) ) => k5_lpspace2(A,B,C,D,E) = a_5_0_lpspace2(A,B,C,D,E) ) ) ) ) ) )).
fof(d6_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => k6_ltlaxio1(A) = k1_ltlaxio1(k5_ltlaxio1(k1_ltlaxio1(A),k4_hilbert1(k3_ltlaxio1,k1_ltlaxio1(A)))) ) )).
fof(d6_ltlaxio3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k1_hilbert1,k9_setfam_1(k1_hilbert1)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_hilbert1,k9_setfam_1(k1_hilbert1)))) ) => ( A = k6_ltlaxio3 <=> ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),A,k2_hilbert1) = k6_domain_1(k1_hilbert1,k2_hilbert1) & k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),A,k1_hilbert2(D)) = k6_domain_1(k1_hilbert1,k1_hilbert2(D)) & k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),A,k3_hilbert1(B,C)) = k4_subset_1(k1_hilbert1,k4_subset_1(k1_hilbert1,k6_domain_1(k1_hilbert1,k3_hilbert1(B,C)),k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),A,B)),k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),A,C)) & k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),A,k4_hilbert1(B,C)) = k4_subset_1(k1_hilbert1,k4_subset_1(k1_hilbert1,k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,k1_ltlaxio2(B,C)),k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),A,B)),k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),A,C)) ) ) ) ) ) ) )).
fof(d6_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => k5_ltlaxio4(A) = a_1_2_ltlaxio4(A) ) )).
fof(d6_mathmorp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_rlvect_1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => k6_mathmorp(A,B,C) = a_3_2_mathmorp(A,B,C) ) ) ) )).
fof(d6_matrix10,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( r2_matrix10(A,B) <=> ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k4_tarski(C,D),k2_matrix_0(A)) => r1_xxreal_0(k3_matrix_0(k1_numbers,A,C,D),k3_matrix_0(k1_numbers,B,C,D)) ) ) ) ) ) ) )).
fof(d6_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ( ( r2_hidden(E,k2_finseq_1(k1_matrix_0(D))) & r2_hidden(F,k2_finseq_1(k1_matrix_0(D))) ) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(B,k5_numbers) | ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(C),A,B) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(C))) ) => ( H = k6_matrix12(A,B,C,D,E,F,G) <=> ( k3_finseq_1(H) = k3_finseq_1(D) & ! [I] : ( v7_ordinal1(I) => ! [J] : ( v7_ordinal1(J) => ( ( r2_hidden(I,k4_finseq_1(D)) & r2_hidden(J,k2_finseq_1(k1_matrix_0(D))) ) => ( ( J = E => k3_matrix_0(u1_struct_0(C),H,I,J) = k1_algstr_0(C,k8_group_1(C,G,k3_matrix_0(u1_struct_0(C),D,I,F)),k3_matrix_0(u1_struct_0(C),D,I,E)) ) & ( J != E => k3_matrix_0(u1_struct_0(C),H,I,J) = k3_matrix_0(u1_struct_0(C),D,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_matrix13,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(A),B,C) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => k11_matrix13(A,B,C,D) = D ) ) ) ) )).
fof(d6_matrix16,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( v4_matrix16(B,A) <=> ? [C] : ( v1_matrix_0(C) & v2_matrix_0(C,A,k3_finseq_1(B),k3_finseq_1(B)) & m2_finseq_1(C,k3_finseq_2(A)) & r2_matrix16(A,C,B) ) ) ) ) )).
fof(d6_matrix17,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( v5_matrix17(B,A) <=> ? [C] : ( v1_matrix_0(C) & v2_matrix_0(C,A,k3_finseq_1(B),k3_finseq_1(B)) & m2_finseq_1(C,k3_finseq_2(A)) & r1_matrix17(A,C,B) ) ) ) ) )).
fof(d6_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ( C = k4_matrix_0(A,B) <=> ( k3_finseq_1(C) = k1_matrix_0(B) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(D,E),k2_matrix_0(C)) <=> r2_hidden(k4_tarski(E,D),k2_matrix_0(B)) ) ) ) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(E,D),k2_matrix_0(B)) => k3_matrix_0(A,C,D,E) = k3_matrix_0(A,B,E,D) ) ) ) ) ) ) ) ) )).
fof(d6_matrix_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ( v1_matrix_1(B,A) <=> ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k4_tarski(C,D),k2_matrix_0(B)) => ( k3_matrix_0(u1_struct_0(A),B,C,D) = k4_struct_0(A) | C = D ) ) ) ) ) ) ) )).
fof(d6_matrix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v15_algstr_0(B) & l3_algstr_0(B) ) => ( B = k4_matrix_2(A) <=> ( u1_struct_0(B) = k3_matrix_2(A) & ! [C] : ( m1_matrix_2(C,k3_matrix_2(A)) => ! [D] : ( m1_matrix_2(D,k3_matrix_2(A)) => k1_binop_1(u2_algstr_0(B),C,D) = k1_partfun1(k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),C,D) ) ) ) ) ) ) )).
fof(d6_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ! [B] : ( ( v1_matrix_0(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))) ) ) )).
fof(d6_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v3_matrix_6(C,A,B) <=> k4_matrix_0(u1_struct_0(B),C) = k2_matrix_3(B,C) ) ) ) ) )).
fof(d6_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r2_matrix_8(A,B,C,D) <=> ? [E] : ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) & v1_matrix_6(E,A,B) & C = k4_matrix_3(B,k4_matrix_3(B,k4_matrix_0(u1_struct_0(B),E),D),E) ) ) ) ) ) ) )).
fof(d6_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( m2_finseq_1(C,k2_numbers) => ( C = k6_matrixc1(A,B) <=> ( k3_finseq_1(C) = k3_finseq_1(A) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k2_finseq_1(k3_finseq_1(A))) => k9_matrix_5(C,D) = k17_rvsum_1(k5_matrixc1(k7_matrix_0(k2_numbers,A,D),B)) ) ) ) ) ) ) ) )).
fof(d6_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,k3_finseq_2(k3_finseq_2(A))) => ( v2_matrixj1(B,A) <=> ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(C,k4_finseq_1(B)) & ! [D] : ( v7_ordinal1(D) => ~ ( v1_matrix_0(k1_funct_1(B,C)) & v2_matrix_0(k1_funct_1(B,C),A,D,D) & m2_finseq_1(k1_funct_1(B,C),k3_finseq_2(A)) ) ) ) ) ) ) ) )).
fof(d6_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(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))) ) ) )).
fof(d6_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( v1_matrixr2(B,A) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( C = k7_matrixr2(A,B) <=> ( k1_matrixr2(A,C,B) = k4_matrixr2(A) & k1_matrixr2(A,B,C) = k4_matrixr2(A) ) ) ) ) ) ) )).
fof(d6_matrlin,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( C = k6_matrlin(A,B) <=> ( k3_finseq_1(C) = k3_finseq_1(B) & ! [D] : ( 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),k4_ordinal1,k3_finseq_2(u1_struct_0(A)),B,D)) ) ) ) ) ) ) ) )).
fof(d6_matroid0,axiom,( ! [A] : ( l1_pre_topc(A) => ( v4_matroid0(A) <=> ( v3_matroid0(A) & ? [B] : ( v7_ordinal1(B) & ! [C] : ( ( 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) ) ) ) ) ) ) )).
fof(d6_matrprob,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( v2_matrprob(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k4_tarski(B,C),k2_matrix_0(A)) => r1_xxreal_0(k5_numbers,k3_matrix_0(k1_numbers,A,B,C)) ) ) ) ) ) )).
fof(d6_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( 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)) ) ) ) ) )).
fof(d6_mcart_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) => ! [F] : ( m1_subset_1(F,C) => ( F = k6_mcart_1(A,B,C,D,E) <=> ! [G] : ! [H] : ! [I] : ! [J] : ( E = k6_xtuple_0(G,H,I,J) => F = I ) ) ) ) ) ) ) ) )).
fof(d6_measure1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( v4_measure1(C,A,B) <=> ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & v1_prob_2(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => k19_supinf_2(k1_partfun1(k4_ordinal1,B,B,k6_numbers,D,C)) = k12_supinf_2(C,k5_setfam_1(A,k4_measure1(A,B,D))) ) ) ) ) )).
fof(d6_measure5,axiom,( ! [A] : ( 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 ) ) ) )).
fof(d6_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k1_numbers))) => ( v2_measure6(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( r2_hidden(B,A) => v2_rcomp_1(B) ) ) ) ) )).
fof(d6_measure7,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( m1_measure7(B,A) => k6_measure7(A,B) = k19_supinf_2(k3_measure7(A,B)) ) ) )).
fof(d6_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,k6_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,k6_numbers))) ) => ! [E] : ( m4_measure8(E,A,B,C) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k6_numbers) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( F = k4_measure8(A,B,C,D,E) <=> ! [G] : ( v7_ordinal1(G) => k1_mesfunc9(F,G) = k19_supinf_2(k2_measure8(A,B,D,k3_measure8(A,B,C,E,G))) ) ) ) ) ) ) ) )).
fof(d6_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => k9_member_1(A,B) = a_2_1_member_1(A,B) ) ) )).
fof(d6_membered,axiom,( ! [A] : ( v6_membered(A) <=> ! [B] : ( r2_hidden(B,A) => v7_ordinal1(B) ) ) )).
fof(d6_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_memstr_0(B,A) ) => ( v3_memstr_0(B,A) <=> k4_memstr_0(A,B,k4_struct_0(B)) = k4_ordinal1 ) ) ) )).
fof(d6_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => k6_mesfun7c(A,B) = k5_mesfunc8(A,k1_mesfun7c(A,B)) ) ) )).
fof(d6_mesfunc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k6_numbers) & v1_funct_1(B) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( D = k6_mesfunc1(A,B,C) <=> ( k9_xtuple_0(D) = k9_xtuple_0(B) & ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,k9_xtuple_0(D)) => k12_supinf_2(D,E) = k4_xxreal_3(C,k12_supinf_2(B,E)) ) ) ) ) ) ) ) ) )).
fof(d6_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( v4_mesfunc5(B) <=> ! [C] : ~ r1_xxreal_0(k1_supinf_1,k1_funct_1(B,C)) ) ) ) )).
fof(d6_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k6_numbers)) & v1_mesfunc8(C,A,k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ( C = k4_mesfunc8(A,B) <=> ! [D] : ( v7_ordinal1(D) => ( k1_relset_1(A,k4_mesfunc5(A,k6_numbers,C,D)) = k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers)) & ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,C,D))) => k12_supinf_2(k4_mesfunc5(A,k6_numbers,C,D),E) = k9_nat_1(k6_numbers,k4_rinfsup2(k3_mesfunc5(A,B,E)),D) ) ) ) ) ) ) ) ) )).
fof(d6_metric_1,axiom,( ! [A] : ( l1_metric_1(A) => ( v6_metric_1(A) <=> v2_metric_1(u1_metric_1(A),u1_struct_0(A)) ) ) )).
fof(d6_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k2_metric_2(A)) => ! [C] : ( m1_subset_1(C,k2_metric_2(A)) => k3_metric_2(A,B,C) = a_3_0_metric_2(A,B,C) ) ) ) )).
fof(d6_metric_6,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( D = k2_metric_6(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k9_nat_1(k1_numbers,D,E) = k3_metric_1(A,k2_tbsp_1(A,B,E),C) ) ) ) ) ) ) )).
fof(d6_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( 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) ) ) )).
fof(d6_midsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k3_midsp_2(A,B) <=> k1_midsp_2(A,C) = B ) ) ) ) )).
fof(d6_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v2_struct_0(C) & v2_midsp_1(C) & l1_midsp_3(C,k1_nat_1(A,2)) ) => ( r3_midsp_3(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m2_finseq_2(G,u1_struct_0(C),k4_finseq_2(k1_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))) ) ) ) ) ) ) ) ) ) )).
fof(d6_mmlquer2,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ( C = k4_mmlquer2(A,B) <=> ! [D] : ( m1_subset_1(D,A) => k1_funct_1(C,D) = k5_card_1(k1_mmlquery(A,B,D)) ) ) ) ) ) )).
fof(d6_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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) ) ) ) )).
fof(d6_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d6_modcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ 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] : ( C = k2_modcat_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( r2_hidden(E,a_2_1_modcat_1(A,B)) & r1_modcat_1(E,D,B) ) ) ) ) ) )).
fof(d6_modelc_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k6_modelc_1(A) = k12_finseq_1(k4_ordinal1,k1_nat_1(5,A)) ) )).
fof(d6_modelc_2,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => k6_modelc_2(A) = k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,3),A) ) )).
fof(d6_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( l1_modelc_3(B,A) => ! [C] : ( l1_modelc_3(C,A) => ! [D] : ( ( v1_modelc_2(D) & m2_finseq_1(D,k4_ordinal1) ) => ( 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) ) ) ) ) ) ) ) ) )).
fof(d6_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k8_newton) & v1_funct_1(B) & v1_partfun1(B,k8_newton) ) => ( B = k5_moebius1(A) <=> ( k13_pre_poly(B) = k22_pre_poly(k8_newton,k12_nat_3(A)) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k22_pre_poly(k8_newton,k12_nat_3(A))) => k1_funct_1(B,C) = C ) ) ) ) ) ) )).
fof(d6_monoid_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ( k5_binop_1(A,B,C,D) = k5_binop_1(A,B,C,E) => D = E ) ) ) ) ) ) ) )).
fof(d6_monoid_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v22_algstr_0(B) & m3_monoid_0(B,k13_monoid_1(A)) ) => ( B = k19_monoid_1(A) <=> ! [C] : ( 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,k6_subset_1(k4_ordinal1,k6_domain_1(k4_ordinal1,k5_numbers)))) ) ) ) ) )).
fof(d6_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( v2_msafree(B,A) <=> ? [C] : ( m1_msafree(C,A,B) & v1_msafree(C,A,B) ) ) ) ) )).
fof(d6_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ( v2_msafree2(A) <=> ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ( B = A => ! [C] : ( m1_subset_1(C,u4_struct_0(B)) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ( k2_msualg_1(B,C) = k2_msualg_1(B,D) => C = D ) ) ) ) ) ) ) )).
fof(d6_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( l3_msualg_1(C,A) => ( v5_msafree4(C,A,B) <=> ( m3_pboole(u3_msualg_1(A,C),u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B))) & m3_pboole(k13_msafree(A,B),u1_struct_0(A),u3_msualg_1(A,C)) & ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ( ( r2_hidden(E,k3_msualg_1(A,D,k1_msafree3(A,B))) & r2_hidden(k1_funct_1(k5_msualg_1(A,D,k1_msafree3(A,B)),E),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,C),k2_msualg_1(A,D))) ) => ( 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,k1_msafree3(A,B)),E) ) ) ) ) & ! [D] : ( m2_pboole(D,u1_struct_0(A),k13_msafree(A,B),u3_msualg_1(A,C)) => ! [E] : ( m3_pboole(E,u1_struct_0(A),u3_msualg_1(A,C)) => ~ ( r8_pboole(u1_struct_0(A),E,k13_msafree(A,B)) & ! [F] : ( m2_pboole(F,u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,C)) => ~ ( r1_msualg_3(A,C,C,F) & r8_pboole(u1_struct_0(A),D,k1_msafree(u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,C),E,F)) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_msalimit,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_msalimit(C,A,B) => ! [D] : ( m2_msalimit(D,A,B,C) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( 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] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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)))) ) ) ) ) )).
fof(d6_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) => ( v5_mssubfam(C,A,B) <=> r1_pboole(A,B,C) ) ) ) )).
fof(d6_msualg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( l3_msualg_1(C,A) => k5_msualg_1(A,B,C) = k1_funct_1(u4_msualg_1(A,C),B) ) ) ) )).
fof(d6_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m3_pboole(C,u1_struct_0(A),u3_msualg_1(A,B)) => ( v3_msualg_2(C,A,B) <=> ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => r1_msualg_2(A,B,D,C) ) ) ) ) ) )).
fof(d6_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( m2_pboole(E,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [F] : ( m1_subset_1(F,k3_msualg_1(A,D,B)) => ! [G] : ( m1_subset_1(G,k3_msualg_1(A,D,C)) => ( G = k5_msualg_3(A,B,C,D,E,F) <=> ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_msualg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d6_msualg_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d6_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_rewrite1(k3_msualg_6(A),C,D) => ! [E] : ( ( 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] : ( m1_rewrite1(F,k3_msualg_6(A)) & ? [G] : ( v1_relat_1(G) & v1_funct_1(G) & v1_finseq_1(G) & v1_funcop_1(G) & E = k3_funct_7(k1_funct_1(u3_msualg_1(A,B),C),G) & k3_finseq_1(F) = k1_nat_1(k3_finseq_1(G),1) & C = k1_funct_1(F,1) & D = k1_funct_1(F,k3_finseq_1(F)) & ! [H] : ( m1_subset_1(H,k4_ordinal1) => ! [I] : ( ( v1_relat_1(I) & v1_funct_1(I) ) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( 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,k1_nat_1(H,1)) ) => r1_msualg_6(A,J,K,B,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)))) ) ) ) ) )).
fof(d6_nat_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v3_valued_0(B) ) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ! [D] : ( ( 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] : k1_funct_1(D,E) = k1_newton(k1_funct_1(B,E),C) ) ) ) ) ) )).
fof(d6_nat_5,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( v2_nat_5(A) <=> k5_nat_5(A) = k3_xcmplx_0(2,A) ) ) )).
fof(d6_nat_lat,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) => ( A = k6_nat_lat <=> ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,A) <=> ~ r1_xxreal_0(B,k5_numbers) ) ) ) ) )).
fof(d6_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ( r2_nattra_1(A,B,C,D) <=> ( r1_nattra_1(A,B,C,D) & ? [E] : ( m1_nattra_1(E,A,B,C,D) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( k2_cat_1(A,F,G) != k1_xboole_0 => ! [H] : ( 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),k2_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),k2_nattra_1(A,B,C,D,E,F),k9_cat_3(A,F,G,B,D,H)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,C)) ) ) ) ) ) ) ) ) ) )).
fof(d6_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ~ ( r2_hidden(F,A) & r2_hidden(G,A) & ~ r1_xxreal_0(E,k2_normsp_0(B,k5_algstr_0(B,F,G))) & r1_xxreal_0(D,k9_complex1(k6_xcmplx_0(k7_partfun1(k2_numbers,C,F),k7_partfun1(k2_numbers,C,G)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_ndiff_1(A,B,C,D) <=> ? [E] : ( m1_nfcont_1(E,A,D) & r1_tarski(E,k1_relset_1(u1_struct_0(A),C)) & ? [F] : ( m1_subset_1(F,u1_struct_0(k16_lopban_1(A,B))) & ? [G] : ( 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] : ( 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))) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [C] : ( r2_ndiff_3(A,B,C) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(D,E) = k1_ndiff_3(A,B,E) ) ) ) ) ) ) ) ) )).
fof(d6_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(A)),k1_numbers))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(A))) => ( r3_ndiff_4(A,B,C) <=> ? [D] : ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) & ? [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) & B = D & C = E & r1_pdiff_7(A,D,E) ) ) ) ) ) ) )).
fof(d6_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(d6_necklace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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) ) ) ) ) )).
fof(d6_net_1,axiom,( ! [A] : ( l1_petri(A) => ! [B] : ( m1_subset_1(B,k2_net_1(A)) => ! [C] : ( C = k3_net_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,k2_net_1(A)) & r2_hidden(k4_tarski(D,B),k1_net_1(A)) ) ) ) ) ) )).
fof(d6_newton,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) => ( A = k8_newton <=> ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,A) <=> v1_int_2(B) ) ) ) ) )).
fof(d6_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_numbers))) ) => ! [C] : ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,k1_numbers,u1_struct_0(A),D,B)) & k7_partfun1(k1_numbers,B,C) = k1_seq_2(k8_funct_2(k4_ordinal1,k1_numbers,u1_struct_0(A),D,B)) ) ) ) ) ) ) ) ) )).
fof(d6_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(d6_normform,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))) => ! [D] : ( 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) ) ) ) ) )).
fof(d6_normsp_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_normsp_0(A) ) => ( v4_normsp_0(A) <=> k2_normsp_0(A,k4_struct_0(A)) = k5_numbers ) ) )).
fof(d6_normsp_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_normsp_1(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(E,F) & r1_xxreal_0(D,k2_normsp_0(A,k5_algstr_0(A,k1_normsp_1(A,B,F),C))) ) ) ) ) ) ) ) ) )).
fof(d6_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v5_o_ring_1(B,A) <=> ? [C] : ( 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)) ) ) ) ) )).
fof(d6_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k8_openlatt(A) <=> ! [C] : ( 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) ) ) ) ) ) )).
fof(d6_oposet_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v3_necklace(A) <=> r2_relat_2(u1_orders_2(A),u1_struct_0(A)) ) ) )).
fof(d6_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_cat_1(A,B,C) != k1_xboole_0 => ! [D] : ( m1_cat_1(D,A,B,C) => k7_oppcat_1(A,B,C,D) = D ) ) ) ) ) )).
fof(d6_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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_ordeq_01(A,B) = g1_normsp_1(k1_ordeq_01(A,B),k9_rsspace(k5_rsspace4(A,B),k1_ordeq_01(A,B)),k7_rsspace(k5_rsspace4(A,B),k1_ordeq_01(A,B)),k8_rsspace(k5_rsspace4(A,B),k1_ordeq_01(A,B)),k3_ordeq_01(A,B)) ) ) )).
fof(d6_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v3_orders_1(A) <=> ( v1_relat_2(A) & v8_relat_2(A) & v4_relat_2(A) & v6_relat_2(A) ) ) ) )).
fof(d6_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_orders_2(A,B,C) <=> ( r1_orders_2(A,B,C) & B != C ) ) ) ) ) )).
fof(d6_orders_3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( C = k1_orders_3(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( 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) ) ) ) ) ) )).
fof(d6_ordinal1,axiom,( ! [A] : ( v4_ordinal1(A) <=> A = k3_tarski(A) ) )).
fof(d6_ordinal2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) ) => k5_ordinal2(A) = k2_ordinal2(k10_xtuple_0(A)) ) )).
fof(d6_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( ( B != k1_xboole_0 => ( C = k6_ordinal3(A,B) <=> ? [D] : ( 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 ) ) ) ) ) ) )).
fof(d6_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v3_ordinal1(B) & v4_ordinal5(B) ) => ( B = k2_ordinal5(A) <=> ( r2_hidden(A,B) & ! [C] : ( ( v3_ordinal1(C) & v4_ordinal5(C) ) => ( r2_hidden(A,C) => r1_ordinal1(B,C) ) ) ) ) ) ) )).
fof(d6_ordinal6,axiom,( ! [A] : k2_ordinal6(A) = k3_wellord1(k1_wellord2(k1_ordinal6(A)),k1_wellord2(k2_ordinal1(A))) )).
fof(d6_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u4_struct_0(A)) => k3_osafree(A,B,C) = k4_tarski(C,u1_struct_0(A)) ) ) ) )).
fof(d6_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ! [C] : ( 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] : ( r2_hidden(D,k4_finseq_1(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d6_osalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) )).
fof(d6_papdesaf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ( v5_papdesaf(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d6_partfun1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) ) => ! [C] : ( r2_hidden(C,k9_xtuple_0(B)) => k7_partfun1(A,B,C) = k1_funct_1(B,C) ) ) )).
fof(d6_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( ( 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] : ! [E] : ( r2_hidden(k4_tarski(D,E),C) <=> ? [F] : ( m1_subset_1(F,k1_zfmisc_1(A)) & r2_hidden(F,B) & r2_hidden(D,F) & r2_hidden(E,F) ) ) ) ) ) ) )).
fof(d6_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ( v6_pasch(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_diraf(A,B,F,E) & r1_diraf(A,C,F,D) ) ) ) ) ) ) ) ) ) )).
fof(d6_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( D = k4_pboole(A,B,C) <=> ! [E] : ( r2_hidden(E,A) => k1_funct_1(D,E) = k6_subset_1(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) )).
fof(d6_pcomps_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ( ( k1_binop_1(B,C,D) = k5_numbers => C = D ) & ( C = D => k1_binop_1(B,C,D) = k5_numbers ) & k1_binop_1(B,C,D) = k1_binop_1(B,D,C) & r1_xxreal_0(k1_binop_1(B,C,E),k2_xcmplx_0(k1_binop_1(B,C,D),k1_binop_1(B,D,E))) ) ) ) ) ) ) )).
fof(d6_pcs_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_yellow_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( C = k4_pcs_0(A,B) <=> ! [D] : ( m1_subset_1(D,A) => k1_funct_1(C,D) = u1_orders_2(k3_waybel_3(A,B,D)) ) ) ) ) ) )).
fof(d6_pdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(A))) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(1))) => ? [F] : ( m1_subset_1(F,k1_numbers) & ? [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d6_pdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(2)) => ( r1_pdiff_3(A,B) => ! [C] : ( v1_xreal_0(C) => ( C = k2_pdiff_3(A,B) <=> ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & B = k10_finseq_1(D,E) & ? [F] : ( 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] : ( v1_funct_1(G) & v3_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [H] : ( v1_funct_1(H) & v2_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & C = k1_funct_1(G,1) & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,F) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(2,1,k1_pdiff_3(1,2,A),B),I),k1_funct_1(k1_pdiff_2(2,1,k1_pdiff_3(1,2,A),B),D)) = k2_xcmplx_0(k1_funct_1(G,k6_xcmplx_0(I,D)),k1_funct_1(H,k6_xcmplx_0(I,D))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r6_pdiff_5(A,B) <=> ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & B = k11_finseq_1(C,D,E) & ? [F] : ( 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] : ( v1_funct_1(G) & v3_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [H] : ( v1_funct_1(H) & v2_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,F) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,3,k1_pdiff_3(2,3,A),B),I),k1_funct_1(k1_pdiff_2(3,3,k1_pdiff_3(2,3,A),B),E)) = k2_xcmplx_0(k1_funct_1(G,k6_xcmplx_0(I,E)),k1_funct_1(H,k6_xcmplx_0(I,E))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ( r3_pdiff_7(A,B,C,D) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(A))) & ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d6_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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] : ( ( 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] : ( m2_finseq_2(F,k1_numbers,k1_euclid(A)) => ( r2_hidden(F,B) => k7_partfun1(k1_numbers,E,F) = k10_pdiff_1(A,C,D,F) ) ) ) ) ) ) ) ) ) )).
fof(d6_pencil_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( v5_pencil_1(A) <=> ! [B] : ( m1_subset_1(B,u1_pre_topc(A)) => r1_ordinal1(2,k1_card_1(B)) ) ) ) )).
fof(d6_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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] : ( r2_hidden(F,E) <=> ? [G] : ( m1_vectsp_4(G,A,B) & k1_vectsp_9(A,G) = D & F = k2_vectsp_9(A,G,C) ) ) ) ) ) ) ) ) )).
fof(d6_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u4_struct_0(A))) => k8_petri(A,B) = a_2_4_petri(A,B) ) ) )).
fof(d6_polyalg1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & v1_polyalg1(B,A) & l1_polyalg1(B,A) ) => ( B = k3_polyalg1(A) <=> ? [C] : ( ~ 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) ) ) ) ) )).
fof(d6_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( 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)) = k5_numbers => ( E = k6_polyeq_5(A,B,C,D) <=> ? [F] : ( v1_xcmplx_0(F) & ? [G] : ( v1_xcmplx_0(G) & ? [H] : ( v1_xcmplx_0(H) & F = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(8,C),k3_xcmplx_0(3,k1_newton(D,2))),32) & G = k7_xcmplx_0(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))))),k7_xcmplx_0(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)) != k5_numbers => ( E = k6_polyeq_5(A,B,C,D) <=> ? [F] : ( v1_xcmplx_0(F) & ? [G] : ( v1_xcmplx_0(G) & ? [H] : ( v1_xcmplx_0(H) & ? [I] : ( v1_xcmplx_0(I) & ? [J] : ( v1_xcmplx_0(J) & ? [K] : ( v1_xcmplx_0(K) & F = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(8,C),k3_xcmplx_0(3,k1_newton(D,2))),32) & G = k7_xcmplx_0(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 = k7_xcmplx_0(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 = k4_xcmplx_0(k7_xcmplx_0(G,k3_xcmplx_0(I,J))) & E = k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(I),J),K),k7_xcmplx_0(D,4)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( 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(k5_numbers,B) => C = k1_xboole_0 ) & ( B = k5_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,k5_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,k5_numbers)),k5_struct_0(k2_bspace))) ) & ~ ( ~ r1_xxreal_0(B,k5_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 ) ) ) ) ) ) )).
fof(d6_polynom1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( 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) = k1_vfunct_1(k15_pre_poly(A),B,C,D) ) ) ) )).
fof(d6_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k3_normsp_1(A,B,C) = k2_normsp_1(A,B,k5_vfunct_1(k4_ordinal1,A,C)) ) ) ) )).
fof(d6_polynom5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_polynom5(A,B,C) <=> k2_polynom4(A,B,C) = k4_struct_0(A) ) ) ) ) )).
fof(d6_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( 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) = k4_polynom1(A,B,C,k2_polynom7(A,B,C)) ) ) )).
fof(d6_polynom8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_polynom8(A,B,C) <=> ( C != k5_numbers & k2_binom(A,B,C) = k5_struct_0(A) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(C,D) & k2_binom(A,B,D) = k5_struct_0(A) ) ) ) ) ) ) ) )).
fof(d6_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d6_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) )).
fof(d6_pralg_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(d6_pralg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => k6_pralg_2(A,B) = k3_tarski(k10_xtuple_0(u3_msualg_1(A,B))) ) ) )).
fof(d6_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v4_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v4_valued_0(C) ) => ! [D] : ( ( 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] : k1_funct_1(D,E) = k7_nat_d(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) )).
fof(d6_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) ) )).
fof(d6_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(A,k5_numbers) => ! [C] : ( v1_xreal_0(C) => ( C = k6_prepower(A,B) <=> ? [D] : ( v5_relat_1(D,k3_numbers) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v2_comseq_2(D) & k1_seq_2(D) = B & v2_comseq_2(k5_prepower(A,D)) & k1_seq_2(k5_prepower(A,D)) = C ) ) ) ) ) ) )).
fof(d6_prgcor_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k1_numbers) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k1_numbers) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,k1_numbers) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ! [D] : ( 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] : ( v1_int_1(E) & k1_funct_1(C,k5_numbers) = k1_funct_1(B,k5_numbers) & E = k1_funct_1(B,k5_numbers) & ( E != k5_numbers => ! [F] : ( v7_ordinal1(F) => ( ( r1_xxreal_0(1,F) & r1_xxreal_0(F,E) ) => k1_funct_1(C,F) = k2_xcmplx_0(k1_funct_1(A,F),k1_funct_1(B,F)) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_prob_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v4_prob_1(B,A) <=> ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( r1_tarski(k10_xtuple_0(C),B) => r2_hidden(k3_prob_1(A,C),B) ) ) ) ) )).
fof(d6_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ( ~ r1_xxreal_0(k3_funct_2(B,k1_numbers,C,D),k5_numbers) => ! [E] : ( m2_prob_1(E,A,B) => ( E = k3_prob_2(A,B,C,D) <=> ! [F] : ( m1_prob_1(F,A,B) => k3_funct_2(B,k1_numbers,E,F) = k6_real_1(k3_funct_2(B,k1_numbers,C,k5_prob_1(A,B,F,D)),k3_funct_2(B,k1_numbers,C,D)) ) ) ) ) ) ) ) ) )).
fof(d6_prob_3,axiom,( ! [A] : ! [B] : ( 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 ) ) ) )).
fof(d6_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),k4_prob_4(A,B,C)) => k5_prob_4(A,B,C,D) = D ) ) ) ) )).
fof(d6_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d6_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( m1_prvect_1(B,A) <=> ( k9_xtuple_0(B) = k9_xtuple_0(A) & ! [C] : ( 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)))) ) ) ) ) ) ) )).
fof(d6_prvect_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ? [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(2)) & F = k10_finseq_1(k2_normsp_0(A,D),k2_normsp_0(B,E)) & k2_binop_1(u1_struct_0(A),u1_struct_0(B),k1_numbers,C,D,E) = k12_euclid(F) ) ) ) ) ) ) ) )).
fof(d6_pscomp_1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => k3_funct_2(u1_struct_0(k15_euclid(2)),k1_numbers,A,B) = k18_euclid(B) ) ) ) )).
fof(d6_pua2mss1,axiom,( ! [A] : ( ( v2_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( 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] : ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) & D = k1_funct_1(E,C) & k1_funct_1(E,k5_numbers) = B & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( 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,k1_nat_1(F,1)) = k7_pua2mss1(A,G) ) ) ) ) ) ) ) ) ) )).
fof(d6_pythtrip,axiom,( ! [A] : ( m1_pythtrip(A) => ( v2_pythtrip(A) <=> r2_hidden(k5_numbers,A) ) ) )).
fof(d6_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => k5_qc_lang1(A) = k2_zfmisc_1(k1_tarski(6),k4_ordinal1) ) )).
fof(d6_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(d6_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => k6_qc_lang3(A,B) = k4_qc_lang3(A,k4_qc_lang1(A),B) ) ) )).
fof(d6_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_qc_lang4(C,A,B) => k4_qc_lang4(A,B,C) = k3_qc_lang4(A,B,C) ) ) ) )).
fof(d6_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_qc_trans(B,A) & m1_qc_lang1(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v5_relat_1(D,k3_qc_lang1(A)) & v3_card_1(D,C) & m2_finseq_1(D,k2_qc_lang1(A)) ) => k4_qc_trans(A,B,C,D) = D ) ) ) ) )).
fof(d6_qmax_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) => k1_funct_1(B,k1_funct_1(B,C)) = C ) ) ) )).
fof(d6_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_quantal1(A) ) => ( v8_quantal1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : k6_algstr_0(A,k15_lattice3(A,C),B) = k15_lattice3(A,a_3_1_quantal1(A,B,C)) ) ) ) )).
fof(d6_quaterni,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k1_quaterni) => ( ( ( C = k5_numbers & D = k5_numbers ) => ( E = k6_quaterni(A,B,C,D) <=> ? [F] : ( m1_subset_1(F,k1_numbers) & ? [G] : ( m1_subset_1(G,k1_numbers) & F = A & G = B & E = k5_arytm_0(F,G) ) ) ) ) & ( ~ ( C = k5_numbers & D = k5_numbers ) => ( E = k6_quaterni(A,B,C,D) <=> E = k2_quaterni(k5_numbers,1,2,3,A,B,C,D) ) ) ) ) ) ) ) ) )).
fof(d6_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ( D = k8_quofield(A,B,C) <=> ! [E] : ( m2_subset_1(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A)) => ( r2_hidden(E,D) <=> ? [F] : ( m2_subset_1(F,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A)) & ? [G] : ( 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)))) ) ) ) ) ) ) ) ) ) )).
fof(d6_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k3_radix_1(B)) ) => ! [D] : ( ( v3_card_1(D,A) & m2_finseq_1(D,k4_numbers) ) => ( D = k7_radix_1(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k2_finseq_1(A)) => k7_partfun1(k4_numbers,D,E) = k6_radix_1(E,B,A,C) ) ) ) ) ) ) ) )).
fof(d6_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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) != k5_numbers ) ) ) ) ) ) )).
fof(d6_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v3_card_1(D,A) & m2_finseq_1(D,k3_radix_1(C)) ) => ( D = k6_radix_5(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k2_finseq_1(A)) => k4_radix_1(E,C,A,D) = k5_radix_5(E,B,C) ) ) ) ) ) ) ) )).
fof(d6_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,k2_xcmplx_0(A,2)) & m2_finseq_1(C,k3_radix_1(B)) ) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d6_random_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(E) & v1_funct_2(E,C,k6_numbers) & v10_valued_0(E) & v6_supinf_2(E) & v2_measure1(E,A,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,k6_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,A,B) & v1_random_3(F,A,B,C,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,D,k6_numbers) & v10_valued_0(G) & v6_supinf_2(G) & v2_measure1(G,B,D) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(D,k6_numbers))) ) => ( G = k1_random_3(A,B,C,D,E,F) <=> ! [H] : ( m2_subset_1(H,k1_zfmisc_1(B),D) => k12_supinf_2(G,H) = k12_supinf_2(E,k8_relset_1(A,B,F,H)) ) ) ) ) ) ) ) ) ) )).
fof(d6_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( ( 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(d6_ratfunc1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k2_ratfunc1(A,B) = k1_normsp_1(A,B,k7_nat_d(k1_algseq_1(A,B),1)) ) ) )).
fof(d6_rcomp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( m1_rcomp_1(B,A) <=> ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,k5_numbers) & B = k2_rcomp_1(k6_xcmplx_0(A,C),k2_xcmplx_0(A,C)) ) ) ) ) )).
fof(d6_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( B = k6_real_3(A) <=> ( k9_nat_1(k1_numbers,B,k5_numbers) = 1 & k9_nat_1(k1_numbers,B,1) = k9_nat_1(k1_numbers,k4_real_3(A),1) & ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,B,k1_nat_1(C,2)) = k3_real_1(k4_real_1(k9_nat_1(k1_numbers,k4_real_3(A),k1_nat_1(C,2)),k9_nat_1(k1_numbers,B,k1_nat_1(C,1))),k9_nat_1(k1_numbers,B,C)) ) ) ) ) ) )).
fof(d6_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k6_real_lat(A) = g3_lattices(k9_funct_2(A,k1_numbers),k4_real_lat(A),k5_real_lat(A)) ) )).
fof(d6_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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)) ) ) ) ) )).
fof(d6_realset1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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] : ( 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))) ) ) ) ) )).
fof(d6_realset2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(d6_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_rearran1(C) & v2_rearran1(C) & v3_rearran1(C,k1_zfmisc_1(B)) & m2_finseq_1(C,k1_zfmisc_1(B)) ) => ! [D] : ( ( 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)))) ) ) ) ) )).
fof(d6_recdef_2,axiom,( ! [A] : ( v3_xtuple_0(A) => ! [B] : ( B = k5_xtuple_0(A) <=> ! [C] : ! [D] : ! [E] : ! [F] : ( A = k6_xtuple_0(C,D,E,F) => B = E ) ) ) )).
fof(d6_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( C = k3_relat_1(A,B) <=> ! [D] : ! [E] : ( r2_hidden(k4_tarski(D,E),C) <=> ? [F] : ( r2_hidden(k4_tarski(D,F),A) & r2_hidden(k4_tarski(F,E),B) ) ) ) ) )).
fof(d6_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r6_relat_2(A,B) <=> ! [C] : ! [D] : ~ ( r2_hidden(C,B) & r2_hidden(D,B) & C != D & ~ r2_hidden(k4_tarski(C,D),A) & ~ r2_hidden(k4_tarski(D,C),A) ) ) ) )).
fof(d6_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r4_rewrite1(A,B,C) <=> ( r3_rewrite1(A,C) & r1_rewrite1(A,B,C) ) ) ) )).
fof(d6_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ( C = k7_rewrite2(A,B) <=> ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(d6_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ v2_struct_0(C) & l1_rewrite3(C,B) ) => ! [D] : ! [E] : ! [F] : ! [G] : ( r3_rewrite3(A,B,C,D,E,F,G) <=> r1_rewrite1(k1_rewrite3(A,B,C),k4_tarski(D,E),k4_tarski(F,G)) ) ) ) ) )).
fof(d6_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_integra2(B) & m2_finseq_1(B,k1_numbers) ) => ( B = k6_rfinseq2(A) <=> r2_classes1(A,B) ) ) ) )).
fof(d6_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( 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] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k4_finseq_1(C)) => k1_funct_1(C,D) = k7_rfunct_1(k1_funct_1(B,D),A) ) ) ) ) ) ) ) )).
fof(d6_rfunct_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( r6_rfunct_4(A,B) <=> ( r1_tarski(B,k9_xtuple_0(A)) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => r5_rfunct_4(k2_partfun1(k1_numbers,k1_numbers,A,B),C) ) ) ) ) ) )).
fof(d6_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k5_rinfsup1(A) = k2_rinfsup1(k4_rinfsup1(A)) ) )).
fof(d6_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( B = k3_rinfsup2(A) <=> ! [C] : ( v7_ordinal1(C) => ? [D] : ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k6_numbers)) & D = a_2_0_rinfsup2(A,C) & k12_supinf_2(B,C) = k7_supinf_2(D) ) ) ) ) ) )).
fof(d6_ring_1,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d6_ringcat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) ) )).
fof(d6_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k4_rlaffin1(A,B) = k1_setfam_1(a_2_0_rlaffin1(A,B)) ) ) )).
fof(d6_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( m2_rlsub_1(C,A,B) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & C = k3_rlsub_1(A,D,B) ) ) ) ) ) )).
fof(d6_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( m1_rlsub_1(D,A) => ( r1_rlsub_2(A,C,D) => ! [E] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d6_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_rltopsp1(B,A) <=> ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k9_complex1(C),1) => r1_tarski(k1_convex1(A,B,C),B) ) ) ) ) ) )).
fof(d6_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ( v6_rlvect_1(A) <=> ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d6_rlvect_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_rlvect_2(C,A) => ( m2_rlvect_2(C,A,B) <=> r1_tarski(k3_rlvect_2(A,C),B) ) ) ) ) )).
fof(d6_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( m2_rmod_2(D,A,B,C) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & D = k3_rmod_2(A,B,E,C) ) ) ) ) ) ) )).
fof(d6_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(D,k3_rmod_3(A,B)) => ! [E] : ( m1_subset_1(E,k3_rmod_3(A,B)) => ! [F] : ( m1_rmod_2(F,A,B) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d6_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d6_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_robbins1(A) ) => ( v6_robbins1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(d6_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_robbins1(A) ) => ( v8_robbins3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_robbins1(A,k3_robbins1(A,B)) = B ) ) ) )).
fof(d6_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) )).
fof(d6_rsspace,axiom,( k6_rsspace = g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace) )).
fof(d6_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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),k9_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k7_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B))) ) ) )).
fof(d6_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( m1_rusub_1(D,A) => ( r1_rusub_2(A,C,D) => ! [E] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d6_rusub_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => k4_rusub_4(A,B) = u1_struct_0(B) ) ) )).
fof(d6_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => k5_rusub_5(A) = g1_pre_topc(u1_struct_0(A),k4_rusub_5(A)) ) )).
fof(d6_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => k8_rvsum_1(A,B) = k3_funcop_1(k10_binop_2,A,B) ) ) )).
fof(d6_rvsum_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_valued_0(B) ) => k11_rvsum_2(A,B) = k3_funcop_1(k5_binop_2,A,B) ) ) )).
fof(d6_scm_comp,axiom,( ! [A] : ( m1_dtconstr(A,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [B] : ( 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(k5_numbers,3),A,B) ) ) )).
fof(d6_scm_inst,axiom,( ! [A] : ( m1_subset_1(A,k3_scm_inst) => ( ? [B] : ( v7_ordinal1(B) & ? [C] : ( m1_subset_1(C,k2_scm_inst) & ? [D] : ( m2_subset_1(D,k4_ordinal1,k7_card_1(9)) & A = k3_xtuple_0(D,k9_finseq_1(B),k12_finseq_1(k2_scm_inst,C)) ) ) ) => ! [B] : ( v7_ordinal1(B) => ( B = k7_scm_inst(A) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & k12_finseq_1(k4_ordinal1,C) = k5_xtuple_0(A) & B = k7_partfun1(k4_ordinal1,k12_finseq_1(k4_ordinal1,C),1) ) ) ) ) ) )).
fof(d6_scmfsa6a,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( 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)) ) ) )).
fof(d6_scmfsa7b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( r5_scmfsa7b(A,B,C) <=> ! [D] : ( v7_ordinal1(D) => r2_hidden(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(C,A),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),D)),k2_afinsq_1(A)) ) ) ) ) ) )).
fof(d6_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ( r4_scmfsa9a(A,B,C,D) => ( ( ~ r3_scmfsa9a(A,B,C,D) & ~ v7_amistd_1(D,k7_card_1(3),k1_scmfsa_2) ) | ! [E] : ( v7_ordinal1(E) => ( E = k2_scmfsa9a(A,B,C,D) <=> ? [F] : ( v7_ordinal1(F) & E = F & r1_xxreal_0(k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(B,D,C,A),F),C),k5_numbers) & ! [G] : ( v7_ordinal1(G) => ( r1_xxreal_0(k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(B,D,C,A),G),C),k5_numbers) => r1_xxreal_0(F,G) ) ) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa_9(C,D)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa_9(C,D)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B)))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(B,D,C,A),F)) ) ) ) ) ) ) ) ) ) )).
fof(d6_scmfsa_1,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k4_scmfsa_1,k5_scmfsa_1))) => ! [B] : ( m2_subset_1(B,k1_scmfsa_1,k3_scmfsa_1) => ! [C] : ( m2_finseq_1(C,k4_numbers) => k8_scmfsa_1(A,B,C) = k1_funct_4(A,k16_funcop_1(B,C)) ) ) ) )).
fof(d6_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(k1_scmfsa_2)) => ( C = k6_scmfsa_2(A,B) <=> ? [D] : ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_ami_3)) & ? [E] : ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_ami_3)) & A = D & B = E & C = k2_ami_3(D,E) ) ) ) ) ) ) )).
fof(d6_scmfsa_m,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_scmfsa_2)) ) => k9_scmfsa_m(A,B) = k4_scmfsa_2(k4_seq_4(k3_funct_2(k4_ordinal1,k1_zfmisc_1(k4_ordinal1),k8_scmfsa_m(B),A))) ) ) )).
fof(d6_scmpds_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => k6_scmpds_2(A,B) = k3_xtuple_0(3,k1_xboole_0,k10_finseq_1(A,B)) ) ) )).
fof(d6_scmpds_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ( v1_scmpds_4(A) <=> ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ( 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))) ) ) ) ) ) ) )).
fof(d6_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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,k1_nat_1(k5_card_1(C),2)),C),k1_scmpds_6(k1_nat_1(k5_card_1(D),1))),D) ) ) ) ) )).
fof(d6_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => ( ? [B] : ( m1_subset_1(B,k2_scm_inst) & ? [C] : ( v1_int_1(C) & ? [D] : ( v1_int_1(D) & ? [E] : ( 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] : ( m1_subset_1(B,k2_scm_inst) => ( B = k7_scmpds_i(A) <=> ? [C] : ( 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) ) ) ) ) ) )).
fof(d6_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( 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)) ) ) ) )).
fof(d6_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_scmringi(A)) => ( ? [C] : ( m1_subset_1(C,k4_ordinal1) & ? [D] : ( m1_subset_1(D,k2_scm_inst) & ? [E] : ( m2_subset_1(E,k4_ordinal1,k7_card_1(8)) & B = k3_xtuple_0(E,k12_finseq_1(k4_ordinal1,C),k12_finseq_1(k2_scm_inst,D)) ) ) ) => ! [C] : ( m1_subset_1(C,k2_scm_inst) => ( C = k6_scmringi(A,B) <=> ? [D] : ( 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) ) ) ) ) ) ) )).
fof(d6_scmyciel,axiom,( ! [A] : ( ( v1_finset_1(A) & v5_finset_1(A) ) => k2_scmyciel(A) = k5_card_1(k3_tarski(A)) ) )).
fof(d6_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( D = k2_semi_af1(A,B,C) <=> k1_semi_af1(A,B,D,C) = C ) ) ) ) ) )).
fof(d6_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(A) => ! [B] : ( v1_xreal_0(B) => ( B = k1_seq_2(A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(D,E) & r1_xxreal_0(C,k9_complex1(k6_xcmplx_0(k1_funct_1(A,E),B))) ) ) ) ) ) ) ) ) )).
fof(d6_seq_4,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => k7_seq_4(A,B) = k1_finseqop(k2_numbers,k2_numbers,k2_numbers,k3_binop_2,A,B) ) ) )).
fof(d6_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => k7_seqfunc(A,B,C) = k6_seqfunc(A,B,k4_seqfunc(A,C)) ) ) ) )).
fof(d6_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v5_valued_0(A) <=> ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,A,k1_nat_1(B,1)),k9_nat_1(k1_numbers,A,B)) ) ) ) )).
fof(d6_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k7_series_1(A,B,C) = k6_xcmplx_0(k6_series_1(A,B),k6_series_1(A,C)) ) ) ) )).
fof(d6_setfam_1,axiom,( ! [A] : ! [B] : ! [C] : ( C = k4_setfam_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ? [F] : ( r2_hidden(E,A) & r2_hidden(F,B) & D = k6_subset_1(E,F) ) ) ) )).
fof(d6_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( D = k6_setlim_2(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k9_nat_1(k9_setfam_1(A),D,E) = k4_subset_1(A,C,k9_nat_1(k9_setfam_1(A),B,E)) ) ) ) ) ) )).
fof(d6_setwiseo,axiom,( ! [A] : ! [B] : ( ( 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] : ( r2_hidden(C,A) => k1_funct_1(B,C) = k1_tarski(C) ) ) ) )).
fof(d6_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( m1_scmfsa_2(B) => ( B = k6_sf_mastr(A) <=> ? [C] : ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k3_scmfsa_2)) & C = k4_sf_mastr(A) & B = k3_scmfsa_m(C) ) ) ) ) )).
fof(d6_sgraph1,axiom,( ! [A] : ! [B] : ( r2_sgraph1(A,B) <=> ( r2_hidden(g1_sgraph1(k1_xboole_0,k1_subset_1(k2_sgraph1(k1_xboole_0))),B) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_sgraph1(C))) => ! [E] : ! [F] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_sgraph1(C))) => ! [E] : ! [F] : ~ ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(d6_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d6_simplex1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( ~ 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) ) ) ) ) )).
fof(d6_simplex2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_simplex0(B,u1_struct_0(k15_euclid(A))) => k3_simplex2(A,B) = k1_simplex2(k14_euclid(A),B) ) ) )).
fof(d6_sin_cos,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( B = k5_sin_cos(A) <=> ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(C,A) => k9_nat_1(k2_numbers,B,C) = k7_xcmplx_0(k2_newton(A),k3_xcmplx_0(k2_newton(C),k2_newton(k7_nat_d(A,C)))) ) & ( ~ r1_xxreal_0(C,A) => k9_nat_1(k2_numbers,B,C) = k5_numbers ) ) ) ) ) ) )).
fof(d6_sin_cos2,axiom,( ! [A] : k6_sin_cos2(A) = k1_funct_1(k5_sin_cos2,A) )).
fof(d6_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => k6_sin_cos7(A) = k3_power(k4_power,k7_xcmplx_0(k2_xcmplx_0(1,k3_square_1(k6_xcmplx_0(1,k1_square_1(A)))),A)) ) )).
fof(d6_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => k6_sincos10(A) = k1_funct_1(k2_sincos10,A) ) )).
fof(d6_stacks_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_stacks_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d6_struct_0,axiom,( ! [A] : ( l2_struct_0(A) => k4_struct_0(A) = u2_struct_0(A) ) )).
fof(d6_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k16_substut1(A),k38_substut1(A)) => ( v7_substut1(B,A) => k10_sublemma(A,B) = k31_substut1(A,B) ) ) ) )).
fof(d6_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_zfmisc_1(A) <=> ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => B = C ) ) ) ) )).
fof(d6_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(d6_supinf_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k6_numbers)) => ! [C] : ( ( 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(k6_numbers,A,B,C),k2_supinf_1) ) ) ) )).
fof(d6_t_0topsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => k4_t_0topsp(A) = k12_borsuk_1(A,k2_t_0topsp(A)) ) )).
fof(d6_tarski,axiom,( ! [A] : ! [B] : ( r2_tarski(A,B) <=> ? [C] : ( ! [D] : ~ ( r2_hidden(D,A) & ! [E] : ~ ( r2_hidden(E,B) & r2_hidden(k4_tarski(D,E),C) ) ) & ! [D] : ~ ( r2_hidden(D,B) & ! [E] : ~ ( r2_hidden(E,A) & r2_hidden(k4_tarski(E,D),C) ) ) & ! [D] : ! [E] : ! [F] : ! [G] : ( ( r2_hidden(k4_tarski(D,E),C) & r2_hidden(k4_tarski(F,G),C) ) => ( D = F <=> E = G ) ) ) ) )).
fof(d6_taxonom1,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_taxonom1(A,B,C,D) <=> r1_xxreal_0(k1_metric_1(A,C,D),B) ) ) ) ) ) )).
fof(d6_taxonom2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v5_taxonom2(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r2_hidden(C,B) => ! [D] : ( m1_subset_1(D,A) => ~ ( ~ r2_hidden(D,C) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ~ ( r2_hidden(D,E) & r2_hidden(E,B) & r1_xboole_0(C,E) ) ) ) ) ) ) ) ) )).
fof(d6_taylor_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_numbers)) => ( r1_taylor_1(A,B,C) <=> ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(D,k6_xcmplx_0(B,1)) => r2_fdiff_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(A,C),D),C) ) ) ) ) ) ) )).
fof(d6_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ( v5_tbsp_1(A) <=> ? [B] : ( v1_xreal_0(B) & ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_xxreal_0(k1_metric_1(A,C,D),B) ) ) ) ) ) )).
fof(d6_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k5_tdlat_1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d6_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m2_subset_1(E,k14_pre_poly(A),k15_pre_poly(A)) => ( E = k3_termord(A,B,C,D) <=> ( ( k3_polynom1(k15_pre_poly(A),C,D) = k1_xboole_0 & r6_pboole(A,E,k16_pre_poly(A)) ) | ( r2_hidden(E,k3_polynom1(k15_pre_poly(A),C,D)) & ! [F] : ( ( 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,k3_polynom1(k15_pre_poly(A),C,D)) => r1_termord(A,B,F,E) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v3_tdlat_3(A) <=> ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ v3_tops_1(B,A) ) ) ) )).
fof(d6_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v4_tex_2(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = u1_struct_0(B) => v3_tex_2(C,A) ) ) ) ) ) )).
fof(d6_tex_4,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_tex_4(A,B) = a_2_3_tex_4(A,B) ) ) )).
fof(d6_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => k4_tmap_1(A,B) = k2_tmap_1(A,A,k3_struct_0(A),B) ) ) )).
fof(d6_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ( r1_borsuk_6(A,B,C) => ! [E] : ( ( 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] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(d6_topalg_6,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)) ) ) ) )).
fof(d6_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v2_topdim_1(B,A) => ! [C] : ( v1_int_1(C) => ( C = k3_topdim_1(A,B) <=> ( r1_tarski(B,k13_prob_1(u1_struct_0(A),k4_ordinal1,k9_setfam_1(u1_struct_0(A)),k1_topdim_1(A),k2_xcmplx_0(C,1))) & r1_xxreal_0(k4_xcmplx_0(1),C) & ! [D] : ( v1_int_1(D) => ( ( r1_xxreal_0(k4_xcmplx_0(1),D) & r1_tarski(B,k13_prob_1(u1_struct_0(A),k4_ordinal1,k9_setfam_1(u1_struct_0(A)),k1_topdim_1(A),k2_xcmplx_0(D,1))) ) => r1_xxreal_0(C,D) ) ) ) ) ) ) ) ) )).
fof(d6_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( C = k3_topgen_1(A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(D,C) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & D = k2_topgen_1(A,E) & r2_hidden(E,B) ) ) ) ) ) ) ) )).
fof(d6_topgen_3,axiom,( ! [A] : ! [B] : ( ( v1_pre_topc(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( B = k5_topgen_3(A) <=> ( u1_struct_0(B) = A & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v4_pre_topc(C,B) <=> ( v1_finset_1(C) | C = A ) ) ) ) ) ) )).
fof(d6_topgen_4,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v5_topgen_4(B,A) <=> ? [C] : ( 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) ) ) ) ) )).
fof(d6_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_topgrp_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m3_topgrp_1(D,A) & k1_funct_1(D,B) = C ) ) ) ) ) )).
fof(d6_topmetr,axiom,( k3_topmetr = k3_pcomps_1(k7_metric_1) )).
fof(d6_topreal1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v2_topreal1(A) <=> ! [B] : ( 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))) ) ) ) ) )).
fof(d6_toprealb,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( v1_xreal_0(C) => k7_toprealb(A,B,C) = k1_pre_topc(k15_euclid(A),k3_topreal9(A,B,C)) ) ) ) )).
fof(d6_toprealc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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 = k16_toprealc(A,B) <=> ! [D] : ( 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) ) ) ) ) ) )).
fof(d6_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( C = k5_toprns_1(A,B) <=> ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k12_euclid(k9_nat_1(u1_struct_0(k15_euclid(A)),B,D)) ) ) ) ) ) )).
fof(d6_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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))) ) ) ) ) )).
fof(d6_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(d6_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ( r2_hidden(B,A) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_trees_1(C) ) => ( C = k4_trees_1(A,B) <=> ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( r2_hidden(D,C) <=> r2_hidden(k8_finseq_1(k4_ordinal1,B,D),A) ) ) ) ) ) ) ) )).
fof(d6_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( v7_ordinal1(B) => k2_trees_2(A,B) = a_2_0_trees_2(A,B) ) ) )).
fof(d6_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ( m1_trees_3(B,A) <=> ! [C] : ( r2_hidden(C,B) => ( v1_relat_1(C) & v5_relat_1(C,A) & v1_funct_1(C) & v3_trees_2(C) ) ) ) ) ) )).
fof(d6_trees_4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ! [C] : ( ( 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)) ) ) )).
fof(d6_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v3_trees_9(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( r2_hidden(B,k9_xtuple_0(A)) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( C = k2_trees_9(A,B) <=> ? [D] : ( m1_trees_1(D,k9_xtuple_0(A)) & D = B & C = k3_relat_1(k1_trees_9(k9_xtuple_0(A),D),A) ) ) ) ) ) ) )).
fof(d6_tsep_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_pre_topc(C,A) => ( r3_tsep_1(A,B,C) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d6_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v6_pre_topc(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(d6_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tsp_2(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( 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) ) ) ) ) ) )).
fof(d6_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( 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),k1_enumset1(k4_xcmplx_0(1),k5_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),k1_enumset1(k4_xcmplx_0(1),k5_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 ) ) ) ) )).
fof(d6_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( 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))) ) ) ) ) )).
fof(d6_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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] : ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d6_unialg_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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] : ( ( v1_unialg_1(E) & m1_unialg_2(E,A) ) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d6_uproots,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r1_polynom5(A,C,B) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( ~ r1_xxreal_0(k1_algseq_1(A,C),k5_numbers) => ( D = k5_uproots(A,B,C) <=> ( k1_nat_1(k1_algseq_1(A,D),1) = k1_algseq_1(A,C) & ! [E] : ( v7_ordinal1(E) => k1_normsp_1(A,D,E) = k2_polynom4(A,k4_uproots(A,C,k1_nat_1(E,1)),B) ) ) ) ) & ( r1_xxreal_0(k1_algseq_1(A,C),k5_numbers) => ( D = k5_uproots(A,B,C) <=> r2_funct_2(k4_ordinal1,u1_struct_0(A),D,k9_polynom3(A)) ) ) ) ) ) ) ) ) )).
fof(d6_urysohn3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m2_urysohn3(D,A,B,C) => ! [E] : ( ( 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 = k7_urysohn3(A,B,C,D) <=> ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( k6_urysohn3(A,B,C,D,F) = k1_xboole_0 => k12_supinf_2(E,F) = k5_numbers ) & ! [G] : ( ( ~ v1_xboole_0(G) & m1_subset_1(G,k1_zfmisc_1(k6_numbers)) ) => ( G = k6_urysohn3(A,B,C,D,F) => k12_supinf_2(E,F) = k8_supinf_2(G) ) ) ) ) ) ) ) ) ) ) )).
fof(d6_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_valued_0(A) <=> ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => v1_xxreal_0(k1_funct_1(A,B)) ) ) ) )).
fof(d6_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => k30_valued_1(A) = k24_valued_1(A,k4_xcmplx_0(1)) ) )).
fof(d6_vectmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectmetr(A) ) => ( v6_vectmetr(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_metric_1(A,D,C) = k1_metric_1(A,k1_algstr_0(A,D,B),k1_algstr_0(A,C,B)) ) ) ) ) ) )).
fof(d6_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( ( ~ 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)) ) ) ) ) ) ) )).
fof(d6_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ( v4_vectsp_1(A) <=> ! [B] : ( 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 ) ) ) ) )).
fof(d6_vectsp_2,axiom,( ! [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) & 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)) ) )).
fof(d6_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( m2_vectsp_4(D,A,B,C) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & D = k3_vectsp_4(A,B,E,C) ) ) ) ) ) ) )).
fof(d6_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m1_vectsp_4(E,A,B) => ( r1_vectsp_5(A,B,D,E) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d6_vectsp_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => ( ( v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v13_algstr_0(B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( D = k4_vectsp_6(A,B,C) <=> ? [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(d6_vectsp_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( v4_lattice3(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r3_lattice3(A,C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r3_lattice3(A,D,B) => r1_lattices(A,D,C) ) ) ) ) ) ) )).
fof(d6_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( r1_vfunct_1(A,B,C,D) <=> ? [E] : ( v1_xreal_0(E) & ! [F] : ( m1_subset_1(F,A) => ( r2_hidden(F,k9_subset_1(A,D,k1_relset_1(A,C))) => r1_xxreal_0(k2_normsp_0(B,k7_partfun1(u1_struct_0(B),C,F)),E) ) ) ) ) ) ) ) )).
fof(d6_waybel10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( ( 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) ) ) ) ) ) )).
fof(d6_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(d6_waybel12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v2_yellow_8(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ~ ( v4_card_3(B) & ! [C] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(d6_waybel18,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) )).
fof(d6_waybel23,axiom,( ! [A] : ( l1_pre_topc(A) => ( v5_waybel23(A) <=> r1_ordinal1(k2_waybel23(A),k4_ordinal1) ) ) )).
fof(d6_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( ( 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] : ( 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] : ( m1_subset_1(C,u1_struct_0(k4_waybel34(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_waybel34(A))) => ( k1_altcat_1(k4_waybel34(A),C,D) != k1_xboole_0 => ! [E] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d6_waybel35,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ( r1_waybel35(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( 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 ) ) ) ) ) ) ) ) )).
fof(d6_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v7_waybel_0(A) <=> v1_waybel_0(k2_struct_0(A),A) ) ) )).
fof(d6_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(d6_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ( v1_waybel_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(d6_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ( v3_waybel_3(A) <=> ( ! [B] : ( 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) ) ) ) )).
fof(d6_waybel_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ( v4_waybel_4(B,A) <=> ! [C] : ( 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) ) ) ) ) )).
fof(d6_waybel_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v5_waybel_6(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d6_waybel_7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v4_waybel_7(B,A) <=> ? [C] : ( ~ 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) ) ) ) ) )).
fof(d6_waybel_9,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( 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) ) ) ) ) )).
fof(d6_weddwitt,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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))) ) ) ) ) )).
fof(d6_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(d6_wellfnd1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_wellfnd1(B,A) <=> ! [C] : ( v7_ordinal1(C) => ( k3_funct_2(k4_ordinal1,u1_struct_0(A),B,k1_nat_1(C,1)) != k9_nat_1(u1_struct_0(A),B,C) & r2_hidden(k4_tarski(k3_funct_2(k4_ordinal1,u1_struct_0(A),B,k1_nat_1(C,1)),k9_nat_1(u1_struct_0(A),B,C)),u1_orders_2(A)) ) ) ) ) ) )).
fof(d6_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : k2_wellord1(A,B) = k3_xboole_0(A,k2_zfmisc_1(B,B)) ) )).
fof(d6_xboole_0,axiom,( ! [A] : ! [B] : k5_xboole_0(A,B) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A)) )).
fof(d6_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k5_xboolean(A,B) = k3_xboolean(k4_xboolean(k3_xboolean(A),k3_xboolean(B))) ) ) )).
fof(d6_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( ( A != k5_numbers => ( B = k5_xcmplx_0(A) <=> k3_xcmplx_0(A,B) = 1 ) ) & ( A = k5_numbers => ( B = k5_xcmplx_0(A) <=> B = k5_numbers ) ) ) ) ) )).
fof(d6_xtuple_0,axiom,( ! [A] : k4_xtuple_0(A) = k1_xtuple_0(k1_xtuple_0(A)) )).
fof(d6_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ( v2_xxreal_0(A) <=> ~ r1_xxreal_0(A,k5_numbers) ) ) )).
fof(d6_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ( v2_xxreal_2(A) <=> r2_hidden(k1_xxreal_2(A),A) ) ) )).
fof(d6_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( ( v1_xreal_0(A) => ( B = k5_xxreal_3(A) <=> ? [C] : ( v1_xcmplx_0(C) & A = C & B = k5_xcmplx_0(C) ) ) ) & ( ~ v1_xreal_0(A) => ( B = k5_xxreal_3(A) <=> B = k5_numbers ) ) ) ) ) )).
fof(d6_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( r5_yellow16(A,B,C) <=> ( r1_yellow_0(B,C) => r2_hidden(k1_yellow_0(B,C),u1_struct_0(A)) ) ) ) ) )).
fof(d6_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(d6_yellow21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & v2_yellow21(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_yellow21(A,B) = B ) ) )).
fof(d6_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_yellow_0(A) <=> ( v1_yellow_0(A) & v2_yellow_0(A) ) ) ) )).
fof(d6_yellow_1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( ( v1_orders_2(C) & v4_yellow_0(C,k5_yellow_1(u1_struct_0(A),B)) & m1_yellow_0(C,k5_yellow_1(u1_struct_0(A),B)) ) => ( C = k6_yellow_1(A,B) <=> ! [D] : ( ( 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) ) ) ) ) ) ) ) )).
fof(d6_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( v1_relat_1(B) => k5_yellow_2(A,B) = k2_yellow_0(A,k10_xtuple_0(B)) ) ) )).
fof(d6_yellow_6,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_waybel_0(B,A) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(d6_yellow_8,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) ) )).
fof(d6_yellow_9,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( ( 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)))) ) ) ) ) ) )).
fof(d6_yoneda_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_oppcat_1(C,A,B) => ( v1_yoneda_1(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k2_cat_1(A,D,E) != k1_xboole_0 => ! [F] : ( m1_cat_1(F,A,D,E) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(d6_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ( v2_zf_fund1(B,A) <=> ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k5_classes2(A,C,D),B) ) ) ) ) ) ) )).
fof(d6_zf_lang,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => k7_zf_lang(A,B) = k8_finseq_1(k4_ordinal1,k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,3),A),B) ) ) )).
fof(d6_zf_model,axiom,( k6_zf_model = k14_zf_lang(k2_zf_lang(k5_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(k5_numbers)),k5_zf_lang(k2_zf_lang(2),k2_zf_lang(1)))),k4_zf_lang(k2_zf_lang(k5_numbers),k2_zf_lang(1)))) )).
fof(d6_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r2_zfmisc_1(A,B,C,D) <=> ( A != B & A != C & A != D & B != C & B != D & C != D ) ) )).
fof(d6_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => k6_zmodul02(A,B) = a_2_1_zmodul02(A,B) ) ) )).
fof(d70_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_aofa_i00(D,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( 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,k5_numbers),D,E),k43_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,F)) ) ) ) ) ) ) )).
fof(d70_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d71_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_aofa_i00(D,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( 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,k5_numbers),D,F),k42_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,E)) ) ) ) ) ) ) )).
fof(d71_fomodel4,axiom,( ! [A] : ( v4_funct_1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k40_fomodel2(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k40_fomodel2(B)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k9_setfam_1(k2_xboole_0(A,k30_fomodel2(B)))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k2_xboole_0(A,k30_fomodel2(B)))))) ) => ( E = k44_fomodel4(A,B,C,D) <=> ( k9_nat_1(k9_setfam_1(k2_xboole_0(A,k30_fomodel2(B))),E,k5_numbers) = A & ! [F] : ( m1_subset_1(F,k4_ordinal1) => k9_nat_1(k9_setfam_1(k2_xboole_0(A,k30_fomodel2(B))),E,k2_xcmplx_0(F,1)) = k43_fomodel4(B,C,k9_nat_1(k9_setfam_1(k2_xboole_0(A,k30_fomodel2(B))),E,F),k9_nat_1(k40_fomodel2(B),D,F)) ) ) ) ) ) ) ) ) )).
fof(d71_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k48_modelc_1(A,B,C))) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(d72_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_aofa_i00(D,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( 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,k5_numbers),D,E),k43_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,F)) ) ) ) ) ) ) )).
fof(d72_fomodel4,axiom,( ! [A] : ( v4_funct_1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k40_fomodel2(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k40_fomodel2(B)))) ) => k45_fomodel4(A,B,C,D) = k3_tarski(k10_xtuple_0(k44_fomodel4(A,B,C,D))) ) ) ) ) )).
fof(d72_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k48_modelc_1(A,B,C))) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(d73_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_aofa_i00(D,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( 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,k5_numbers),D,F),k42_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,E)) ) ) ) ) ) ) )).
fof(d73_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ! [D] : ( m2_subset_1(D,k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0)),k30_fomodel2(B)) => ( ( ~ v9_fomodel4(k35_fomodel2(B,D),B,C,A) => k46_fomodel4(A,B,C,D) = k2_xboole_0(A,k6_domain_1(k30_fomodel2(B),D)) ) & ( v9_fomodel4(k35_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)),k35_fomodel2(B,D))) ) ) ) ) ) )).
fof(d73_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k48_modelc_1(A,B,C))) => ! [F] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d74_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k30_fomodel2(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k30_fomodel2(B)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k9_setfam_1(k2_xboole_0(A,k30_fomodel2(B)))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k2_xboole_0(A,k30_fomodel2(B)))))) ) => ( E = k48_fomodel4(A,B,C,D) <=> ( k9_nat_1(k9_setfam_1(k2_xboole_0(A,k30_fomodel2(B))),E,k5_numbers) = A & ! [F] : ( v7_ordinal1(F) => k9_nat_1(k9_setfam_1(k2_xboole_0(A,k30_fomodel2(B))),E,k2_xcmplx_0(F,1)) = k47_fomodel4(k9_nat_1(k9_setfam_1(k2_xboole_0(A,k30_fomodel2(B))),E,F),B,C,k9_nat_1(k30_fomodel2(B),D,F)) ) ) ) ) ) ) ) )).
fof(d75_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(d75_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k30_fomodel2(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k30_fomodel2(B)))) ) => k49_fomodel4(A,B,C,D) = k3_tarski(k10_xtuple_0(k48_fomodel4(A,B,C,D))) ) ) ) )).
fof(d76_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(d77_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(d78_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(d7_abcmiz_0,axiom,( ! [A] : ( l1_abcmiz_0(A) => ( v6_abcmiz_0(A) <=> ! [B] : ( m1_subset_1(B,u1_abcmiz_0(A)) => k1_abcmiz_0(A,B) != B ) ) ) )).
fof(d7_abcmiz_1,axiom,( k9_abcmiz_1 = k5_numbers )).
fof(d7_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [C] : ( 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)) ) ) ) ) )).
fof(d7_abian,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( 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] : ! [E] : ( ( r2_hidden(D,A) & r2_hidden(E,A) ) => ( r2_hidden(k4_tarski(D,E),C) <=> ? [F] : ( m1_subset_1(F,k4_ordinal1) & ? [G] : ( m1_subset_1(G,k4_ordinal1) & k1_funct_1(k1_abian(A,B,F),D) = k1_funct_1(k1_abian(A,B,G),E) ) ) ) ) ) ) ) )).
fof(d7_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ( v7_aff_2(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_aff_3,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v7_aff_3(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ! [L] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_afinsq_1,axiom,( ! [A] : ! [B] : ( B = k8_afinsq_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( v1_relat_1(C) & v5_relat_1(C,A) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) ) ) )).
fof(d7_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ! [B] : k5_afinsq_2(A,B) = k3_relat_1(k4_afinsq_2(k3_xboole_0(B,k1_afinsq_1(A))),A) ) )).
fof(d7_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => k7_afproj(A) = k8_eqrel_1(k1_afproj(A),k3_afproj(A)) ) )).
fof(d7_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d7_algspec1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( m3_algspec1(B) => ( m4_algspec1(B,A) <=> ? [C] : ( ~ v11_struct_0(C) & m2_algspec1(C,A) & v1_msualg_6(B,C) & l3_msualg_1(B,C) ) ) ) ) )).
fof(d7_algstr_0,axiom,( ! [A] : ( l1_algstr_0(A) => ( v6_algstr_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v3_algstr_0(B,A) ) ) ) )).
fof(d7_algstr_4,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(d7_altcat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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] : ( m1_subset_1(D,A) => ? [E] : ( r2_hidden(E,k1_binop_1(B,D,D)) & ! [F] : ( m1_subset_1(F,A) => ! [G] : ( r2_hidden(G,k1_binop_1(B,F,D)) => k1_binop_1(k4_altcat_1(A,B,C,F,D,D),E,G) = G ) ) ) ) ) ) ) ) )).
fof(d7_altcat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ( v1_altcat_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_altcat_1(A,B,B) != k1_xboole_0 ) ) ) )).
fof(d7_altcat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_altcat_1(A,B,C)) => ( v4_altcat_3(D,A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k1_altcat_1(A,E,B) != k1_xboole_0 => ! [F] : ( m1_subset_1(F,k1_altcat_1(A,E,B)) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(d7_ami_3,axiom,( ! [A] : ( v7_ordinal1(A) => k7_ami_3(A) = k3_xtuple_0(6,k9_finseq_1(A),k1_xboole_0) ) )).
fof(d7_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k4_ordinal1) => k5_ami_wstd(A,B,C) = k4_ami_wstd(A,B,C,1) ) ) ) )).
fof(d7_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( v1_extpro_1(B,A) & l1_extpro_1(B,A) ) => ( B = k4_amistd_1(A) <=> ( u1_struct_0(B) = k6_domain_1(k4_ordinal1,k5_numbers) & u2_struct_0(B) = k5_numbers & u1_compos_1(B) = k2_tarski(k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers,k5_numbers),k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,1,k5_numbers,k5_numbers)) & u1_memstr_0(A,B) = k16_funcop_1(k5_numbers,k5_numbers) & r8_pboole(A,u2_memstr_0(A,B),k7_funcop_1(A,k4_ordinal1)) & ? [C] : ( 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] : ( m1_subset_1(D,k4_card_3(k2_memstr_0(A,B))) => k1_funct_1(C,D) = k1_funct_4(D,k16_funcop_1(k5_numbers,k1_ordinal1(k1_funct_1(D,k5_numbers)))) ) & u1_extpro_1(A,B) = k1_funct_4(k16_funcop_1(k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,1,k5_numbers,k5_numbers),C),k16_funcop_1(k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers,k5_numbers),k6_partfun1(k4_card_3(k2_memstr_0(A,B))))) ) ) ) ) ) )).
fof(d7_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analmetr(A) ) => k3_analmetr(A) = g1_analoaf(u1_struct_0(A),u1_analoaf(A)) ) )).
fof(d7_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_analort(A,B,C) = g1_analoaf(u1_struct_0(A),k3_analort(A,B,C)) ) ) ) )).
fof(d7_anproj_1,axiom,( ! [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) & l1_rlvect_1(A) ) => k5_anproj_1(A) = g1_collsp(k3_anproj_1(A),k4_anproj_1(A)) ) )).
fof(d7_anproj_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_collsp(A) ) => ( v2_collsp(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d7_aofa_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( r1_tarski(k10_xtuple_0(A),k9_xtuple_0(A)) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( D = k7_aofa_000(A,B,C) <=> ( k9_xtuple_0(D) = k9_xtuple_0(A) & ! [E] : ( 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] : ( v7_ordinal1(F) => ( ! [G] : ( v7_ordinal1(G) => ( ~ r1_xxreal_0(F,G) => r2_hidden(k1_funct_1(k8_funct_7(A,G),E),B) ) ) => ( r2_hidden(k1_funct_1(k8_funct_7(A,F),E),B) | k1_funct_1(D,E) = k1_funct_1(k8_funct_7(A,F),E) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v2_relat_1(C) & m1_msafree(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_msafree4(E,u1_struct_0(A),C,k1_msafree4(u1_struct_0(A),C,D)) => k4_aofa_a01(A,B,C,D,E) = E ) ) ) ) ) )).
fof(d7_armstrng,axiom,( ! [A] : ( l1_armstrng(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_armstrng(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_armstrng(A))) => ( r2_armstrng(A,B,C) <=> ! [D] : ( m1_subset_1(D,u3_armstrng(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d7_arytm_2,axiom,( ! [A] : ( m2_subset_1(A,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) => ! [B] : ( 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) ) ) )).
fof(d7_arytm_3,axiom,( k5_arytm_3 = k2_xboole_0(k6_subset_1(a_0_0_arytm_3,a_0_1_arytm_3),k4_ordinal1) )).
fof(d7_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( C = k5_asympt_0(A,B) <=> ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k4_xxreal_0(k9_nat_1(k1_numbers,A,D),k9_nat_1(k1_numbers,B,D)) ) ) ) ) ) )).
fof(d7_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(d7_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_bcialg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_bcialg_1(A) ) => ( v7_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) ) )).
fof(d7_bcialg_3,axiom,( ! [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) & v6_bcialg_3(A) & l2_bcialg_1(A) ) => ( v7_bcialg_3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v2_bcialg_3(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_1(A,B,k1_bcialg_1(A,B,C)) = C ) ) ) ) ) )).
fof(d7_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k6_bcialg_4(A,B,C) = k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k5_bcialg_4(A),B,C) ) ) ) )).
fof(d7_bciideal,axiom,( ! [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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d7_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => k6_bhsp_2(A,B,C) = a_3_2_bhsp_2(A,B,C) ) ) ) )).
fof(d7_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k5_bhsp_4(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k1_normsp_1(A,D,E) = k1_rlvect_1(A,k1_normsp_1(A,B,E),k9_nat_1(k1_numbers,C,E)) ) ) ) ) ) ) )).
fof(d7_bhsp_6,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( D = k3_bhsp_6(A,B,C) <=> ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( ( v1_finset_1(F) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( ~ v1_xboole_0(F) & r1_tarski(F,B) & ! [G] : ( ( 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,k9_complex1(k6_xcmplx_0(D,k5_bhsp_5(k1_numbers,u1_struct_0(A),k9_binop_2,G,C)))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d7_binarith,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k6_margrel1) ) => ( r1_binarith(A,B,C) <=> k8_binarith(A,B,C) = k7_margrel1 ) ) ) ) )).
fof(d7_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m2_finseq_1(E,u1_struct_0(A)) => ( E = k8_binom(A,B,C,D) <=> ( k3_finseq_1(E) = k1_nat_1(D,1) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ! [H] : ( m1_subset_1(H,k4_ordinal1) => ( ( r2_hidden(F,k1_relset_1(k4_ordinal1,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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_binop_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) ) )).
fof(d7_binop_2,axiom,( ! [A] : ( ( 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_binop_2 <=> ! [B] : ( v1_xreal_0(B) => k1_funct_1(A,B) = k4_xcmplx_0(B) ) ) ) )).
fof(d7_bor_cant,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( C = k7_bor_cant(A,B) <=> ! [D] : ( v7_ordinal1(D) => k1_funct_1(C,D) = k1_prob_1(A,k1_valued_0(k9_setfam_1(A),B,D)) ) ) ) ) )).
fof(d7_borsuk_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_eqrel_1(B,u1_struct_0(A)) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(d7_borsuk_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ( r3_borsuk_2(A,B,C,D,E) <=> ? [F] : ( 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] : ( m1_subset_1(G,u1_struct_0(k5_topmetr)) => ( k1_binop_1(F,G,k5_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,k5_numbers,G) = B & k1_binop_1(F,1,G) = C ) ) ) ) ) ) ) ) ) )).
fof(d7_borsuk_6,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(k5_topmetr)) => ( ( r1_xxreal_0(B,k7_xcmplx_0(1,2)) => k3_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,B) = k3_xcmplx_0(k7_xcmplx_0(1,2),B) ) & ( r1_xxreal_0(B,k7_xcmplx_0(3,4)) => ( r1_xxreal_0(B,k7_xcmplx_0(1,2)) | k3_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,B) = k6_xcmplx_0(B,k7_xcmplx_0(1,4)) ) ) & ( ~ r1_xxreal_0(B,k7_xcmplx_0(3,4)) => k3_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr),A,B) = k6_xcmplx_0(k3_xcmplx_0(2,B),1) ) ) ) ) ) )).
fof(d7_borsuk_7,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => k1_funct_1(A,B) = k4_euclid_5(k19_sin_cos(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)),k17_sin_cos(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)),k5_numbers) ) ) ) )).
fof(d7_bspace,axiom,( ! [A] : k7_bspace(A) = g1_vectsp_1(k2_bspace,k1_zfmisc_1(A),k5_bspace(A),k1_subset_1(A),k6_bspace(A)) )).
fof(d7_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( 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))) ) ) ) )).
fof(d7_c0sp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(d7_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => k7_c0sp2(A) = g1_rlvect_1(k6_c0sp2(A),k9_rsspace(k10_funcsdom(u1_struct_0(A)),k6_c0sp2(A)),k7_rsspace(k10_funcsdom(u1_struct_0(A)),k6_c0sp2(A)),k8_rsspace(k10_funcsdom(u1_struct_0(A)),k6_c0sp2(A))) ) )).
fof(d7_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k2_zfmisc_1(k4_calcul_1(A),k2_cqc_the1)) => ! [C] : ( v7_ordinal1(C) => ( ( k2_xtuple_0(k1_funct_1(B,C)) = k5_numbers => ( r3_calcul_1(A,B,C) <=> ? [D] : ( 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] : ( 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] : ( m1_subset_1(D,k4_ordinal1) & ? [E] : ( m2_finseq_1(E,k3_cqc_lang(A)) & ? [F] : ( 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] : ( m1_subset_1(D,k4_ordinal1) & ? [E] : ( m1_subset_1(E,k4_ordinal1) & ? [F] : ( m2_finseq_1(F,k3_cqc_lang(A)) & ? [G] : ( 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(k4_ordinal1,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] : ( m1_subset_1(D,k4_ordinal1) & ? [E] : ( m1_subset_1(E,k4_ordinal1) & ? [F] : ( m2_finseq_1(F,k3_cqc_lang(A)) & ? [G] : ( m2_finseq_1(G,k3_cqc_lang(A)) & ? [H] : ( 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(k4_ordinal1,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] : ( m1_subset_1(D,k4_ordinal1) & ? [E] : ( m1_subset_1(E,k4_ordinal1) & ? [F] : ( m2_finseq_1(F,k3_cqc_lang(A)) & ? [G] : ( 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(k4_ordinal1,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] : ( m1_subset_1(D,k4_ordinal1) & ? [E] : ( m2_finseq_1(E,k3_cqc_lang(A)) & ? [F] : ( m2_subset_1(F,k9_qc_lang1(A),k3_cqc_lang(A)) & ? [G] : ( 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] : ( m1_subset_1(D,k4_ordinal1) & ? [E] : ( m2_finseq_1(E,k3_cqc_lang(A)) & ? [F] : ( m2_subset_1(F,k9_qc_lang1(A),k3_cqc_lang(A)) & ? [G] : ( 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] : ( m1_subset_1(D,k4_ordinal1) & ? [E] : ( m2_finseq_1(E,k3_cqc_lang(A)) & ? [F] : ( m2_subset_1(F,k9_qc_lang1(A),k3_cqc_lang(A)) & ? [G] : ( m2_subset_1(G,k2_qc_lang1(A),k3_qc_lang1(A)) & ? [H] : ( 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] : ( m1_subset_1(D,k4_ordinal1) & ? [E] : ( m2_finseq_1(E,k3_cqc_lang(A)) & ? [F] : ( m2_subset_1(F,k9_qc_lang1(A),k3_cqc_lang(A)) & ? [G] : ( m2_subset_1(G,k2_qc_lang1(A),k3_qc_lang1(A)) & ? [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_card_1,axiom,( ! [A] : ! [B] : ( v3_card_1(B,A) <=> k1_card_1(B) = A ) )).
fof(d7_card_3,axiom,( ! [A] : ( ( 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))) ) )).
fof(d7_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_card_fil(B,A) => ( v3_card_fil(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r2_hidden(C,B) | r2_hidden(k6_subset_1(A,C),B) ) ) ) ) ) )).
fof(d7_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v3_card_lar(B,A) <=> ! [C] : ( 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)) ) ) ) ) ) )).
fof(d7_cat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_cat_1(A) ) => ( v5_cat_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_cat_1(A,B,B) != k1_xboole_0 ) ) ) )).
fof(d7_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => k6_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)),k16_funct_3(u4_struct_0(A),u4_struct_0(B),u1_struct_0(A),u1_struct_0(B),u1_graph_1(A),u1_graph_1(B)),k16_funct_3(u4_struct_0(A),u4_struct_0(B),u1_struct_0(A),u1_struct_0(B),u2_graph_1(A),u2_graph_1(B)),k8_funct_4(u4_struct_0(A),u4_struct_0(B),u1_cat_1(A),u1_cat_1(B))) ) ) )).
fof(d7_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d7_cat_4,axiom,( ! [A] : ! [B] : 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)) )).
fof(d7_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => k7_cat_5(A) = A ) )).
fof(d7_catalg_1,axiom,( ! [A] : ( l1_msualg_1(A) => ( v3_catalg_1(A) <=> ? [B] : ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) & ! [C] : ~ ( r2_hidden(C,u1_struct_0(A)) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ~ ( C = k4_tarski(D,E) & k3_finseq_1(E) = k3_funct_2(k4_ordinal1,k4_ordinal1,B,D) & r1_tarski(k2_zfmisc_1(k1_tarski(D),k4_finseq_2(k3_funct_2(k4_ordinal1,k4_ordinal1,B,D),k4_catalg_1(A))),u1_struct_0(A)) ) ) ) ) & ! [C] : ~ ( r2_hidden(C,u4_struct_0(A)) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ~ ( C = k4_tarski(D,E) & k3_finseq_1(E) = k3_funct_2(k4_ordinal1,k4_ordinal1,B,D) & r1_tarski(k2_zfmisc_1(k1_tarski(D),k4_finseq_2(k3_funct_2(k4_ordinal1,k4_ordinal1,B,D),k4_catalg_1(A))),u4_struct_0(A)) ) ) ) ) ) ) ) )).
fof(d7_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( r2_hidden(B,k2_cc0sp1(A)) => ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(d7_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => k6_cc0sp2(A) = a_1_1_cc0sp2(A) ) )).
fof(d7_cfdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [B] : ( v1_xcmplx_0(B) => ( r1_cfdiff_1(A,B) => ! [C] : ( m1_subset_1(C,k2_numbers) => ( C = k2_cfdiff_1(A,B) <=> ? [D] : ( m1_cfdiff_1(D,B) & r1_tarski(D,k1_relset_1(k2_numbers,A)) & ? [E] : ( 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] : ( 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] : ( v1_xcmplx_0(G) => ( r2_hidden(G,D) => k6_xcmplx_0(k7_partfun1(k2_numbers,A,G),k7_partfun1(k2_numbers,A,B)) = k2_xcmplx_0(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))) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_cfuncdom,axiom,( ! [A] : ( ~ 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)) ) )).
fof(d7_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ! [B] : ( B = k7_cgames_1(A) <=> ? [C] : ( l1_cgames_1(C) & A = C & B = u2_cgames_1(C) ) ) ) )).
fof(d7_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_chain_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_xxreal_0(C,A) => k4_chain_1(A,B,C) = a_3_1_chain_1(A,B,C) ) ) ) ) )).
fof(d7_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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] : ( m1_chord(C,A,k6_domain_1(k6_glib_000(A),B)) => v2_chord(C) ) ) ) ) ) )).
fof(d7_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( v5_circcmb3(B,A) <=> ? [C] : ( ~ v1_xboole_0(C) & v1_finset_1(C) & ? [D] : ( m1_subset_1(D,k4_ordinal1) & ? [E] : ( v1_relat_1(E) & v1_funct_1(E) & v3_card_1(E,D) & v1_finseq_1(E) & ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d7_circcomb,axiom,( ! [A] : ( l1_msualg_1(A) => ( v1_circcomb(A) <=> u2_msualg_1(A) = k6_partfun1(u4_struct_0(A)) ) ) )).
fof(d7_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( v7_ordinal1(C) => ( C = k7_circuit1(A,B) <=> ? [D] : ( ~ v1_xboole_0(D) & v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) & D = a_2_0_circuit1(A,B) & C = k1_xxreal_2(D) ) ) ) ) ) )).
fof(d7_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( m1_msafree2(D,A,B) => k7_circuit2(A,B,C,D) = k6_circuit2(A,B,k1_circuit2(A,B,C,D)) ) ) ) ) )).
fof(d7_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_clopban1(A,B)))) => ( C = k8_clopban1(A,B) <=> ! [D] : ( 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)))) ) ) ) ) ) ) )).
fof(d7_clopban2,axiom,( ! [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) & 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))) ) )).
fof(d7_clopban3,axiom,( ! [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) & l1_clopban2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( C = k5_clopban3(A,B) <=> ( k1_normsp_0(A,C,k5_numbers) = k5_struct_0(A) & ! [D] : ( v7_ordinal1(D) => k1_normsp_0(A,C,k1_nat_1(D,1)) = k6_algstr_0(A,k1_normsp_0(A,C,D),B) ) ) ) ) ) ) )).
fof(d7_clopban4,axiom,( ! [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) & 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] : ( 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) ) ) )).
fof(d7_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) => ( v4_closure2(C,A,B) <=> ! [D] : ( 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) ) ) ) ) ) )).
fof(d7_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_clvect_1(B,A) <=> ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( v1_xcmplx_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => r2_hidden(k1_clvect_1(A,D,C),B) ) ) ) ) ) ) ) )).
fof(d7_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => k6_clvect_2(A,B,C) = a_3_2_clvect_2(A,B,C) ) ) ) )).
fof(d7_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v2_clvect_3(B,A) <=> v1_series_1(k2_clvect_2(A,B)) ) ) ) )).
fof(d7_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_coh_sp(A)) => k6_coh_sp(A,B) = k1_xtuple_0(k1_xtuple_0(B)) ) )).
fof(d7_cohsp_1,axiom,( ! [A] : ! [B] : ( r1_cohsp_1(A,B) <=> ! [C] : ! [D] : ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => ( r2_hidden(k3_xboole_0(C,D),A) & r2_hidden(k2_xboole_0(C,D),A) ) ) ) )).
fof(d7_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m2_collsp(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & C != D & B = k1_collsp(A,C,D) ) ) ) ) )).
fof(d7_combgras,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( l1_incsp_1(B) => ! [C] : ( l1_combgras(C,A,B) => ! [D] : ( 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) ) ) ) ) )).
fof(d7_compact1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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))) ) ) ) ) ) )).
fof(d7_compl_sp,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ( v6_compl_sp(B,A) <=> ! [C] : ( v7_ordinal1(C) => v2_compl_sp(k9_nat_1(k9_setfam_1(u1_struct_0(A)),B,C),A) ) ) ) ) )).
fof(d7_compos_0,axiom,( ! [A] : ( v1_compos_0(A) => ! [B] : ( m1_subset_1(B,A) => ( v4_compos_0(B,A) <=> v1_xboole_0(k5_xtuple_0(B)) ) ) ) )).
fof(d7_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) ) => ( v4_compos_1(B,A) <=> ! [C] : ( v7_ordinal1(C) => ( ( k1_funct_1(B,C) = k2_compos_1(A) & r2_hidden(C,k9_xtuple_0(B)) ) => C = k62_valued_1(B) ) ) ) ) ) )).
fof(d7_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k3_finseq_2(k4_ordinal1)) & v1_funct_1(C) & v4_valued_0(C) & v2_margrel1(C) ) => ( C = k4_comput_1(A,B) <=> ( k1_relset_1(k3_finseq_2(k4_ordinal1),C) = k4_finseq_2(A,k4_ordinal1) & ! [D] : ( m2_finseq_2(D,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => k1_recdef_1(C,D) = k1_nat_1(k7_partfun1(k4_ordinal1,D,B),1) ) ) ) ) ) ) )).
fof(d7_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => k11_comseq_3(A) = k3_comseq_2(k10_comseq_3(A)) ) )).
fof(d7_conlat_1,axiom,( ! [A] : ( l5_struct_0(A) => ! [B] : ( l2_conlat_1(B,A) => ( v4_conlat_1(B,A) <=> ( v1_xboole_0(u2_conlat_1(A,B)) & v1_xboole_0(u3_conlat_1(A,B)) ) ) ) ) )).
fof(d7_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(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))) ) )).
fof(d7_connsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k1_connsp_1(A,B) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & ! [E] : ( 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 ) ) ) ) ) )).
fof(d7_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k1_connsp_2(A,B) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & ! [E] : ( 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 ) ) ) ) ) )).
fof(d7_connsp_3,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( D = k6_connsp_3(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(k1_pre_topc(A,B))) => ( E = C => D = k1_connsp_1(k1_pre_topc(A,B),E) ) ) ) ) ) ) ) ) )).
fof(d7_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_convex4(B,A) => ! [C] : ( m1_convex4(C,A) => ( r1_convex4(A,B,C) <=> ! [D] : ( 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) ) ) ) ) ) )).
fof(d7_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ! [D] : ( ( v5_relat_1(D,k3_qc_lang1(A)) & v3_card_1(D,C) & m2_finseq_1(D,k2_qc_lang1(A)) ) => ! [E] : ( 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] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d7_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => k4_cqc_the1(A) = k1_cqc_the1(A,k1_subset_1(k3_cqc_lang(A))) ) )).
fof(d7_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(d7_csspace,axiom,( k7_csspace = g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace) )).
fof(d7_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( r2_hidden(C,k4_csspace4(A,B)) => k6_csspace4(A,B,C) = C ) ) ) )).
fof(d7_decomp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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))) ) ) )).
fof(d7_dickson,axiom,( ! [A] : ( l1_orders_2(A) => k5_dickson(A) = g1_orders_2(u1_struct_0(A),k4_dickson(u1_struct_0(A),u1_orders_2(A))) ) )).
fof(d7_diff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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,k5_numbers),A) & ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d7_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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)) ) ) )).
fof(d7_diraf,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ( v2_diraf(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( ~ r2_analoaf(A,B,C,D,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_analoaf(A,B,C,B,F) & r2_analoaf(A,D,E,D,F) ) ) ) ) ) ) ) ) ) )).
fof(d7_dirort,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dirort(A) & l1_analoaf(A) ) => ( v5_dirort(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,E) => r2_analoaf(A,D,E,C,B) ) ) ) ) ) ) ) )).
fof(d7_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( ( 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] : ( m2_subset_1(C,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) => ? [D] : ( 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) ) ) ) ) ) )).
fof(d7_dist_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k7_dist_2(A,B) = k5_funct_3(B,A) ) )).
fof(d7_dtconstr,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => k11_dtconstr(A) = k1_nat_1(k1_funct_1(A,1),1) ) )).
fof(d7_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) => ( D = k6_dynkin(A,B,C) <=> ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ( r2_hidden(E,D) <=> r2_hidden(k9_subset_1(A,E,C),B) ) ) ) ) ) ) )).
fof(d7_e_siec,axiom,( ! [A] : k5_e_siec(A) = g1_e_siec(k1_tarski(A),k1_xboole_0,k1_xboole_0) )).
fof(d7_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(A))) => ( D = k4_ec_pf_1(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(A))) => ! [F] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(d7_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( 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) != k5_numbers => k7_ec_pf_2(A,B) = k4_domain_1(u1_struct_0(k9_int_3(A)),u1_struct_0(k9_int_3(A)),k4_ordinal1,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) = k5_numbers => k7_ec_pf_2(A,B) = k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k5_numbers,1,k5_numbers) ) ) ) ) )).
fof(d7_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => k7_ens_1(A,B,C) = a_3_0_ens_1(A,B,C) ) ) ) )).
fof(d7_entropy1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => k4_entropy1(A) = k14_rvsum_1(A,k3_entropy1(2,A)) ) )).
fof(d7_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ( J = k7_enumset1(A,B,C,D,E,F,G,H,I) <=> ! [K] : ( r2_hidden(K,J) <=> ~ ( K != A & K != B & K != C & K != D & K != E & K != F & K != G & K != H & K != I ) ) ) )).
fof(d7_eqrel_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(k9_setfam_1(A)))) => ( v1_eqrel_1(B,A) <=> ! [C] : ( r2_hidden(C,B) => m1_eqrel_1(C,A) ) ) ) )).
fof(d7_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => k14_euclid(A) = g1_metric_1(k1_euclid(A),k13_euclid(A)) ) )).
fof(d7_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(d7_euclid_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( v1_xreal_0(D) => 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)) ) ) ) ) )).
fof(d7_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ( r5_euclidlp(A,B,C) <=> ? [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) & ? [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) & ? [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(A)) & ? [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d7_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ( v7_euclmetr(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_exchsort(A) ) => k4_exchsort(A) = k1_funct_1(A,k3_tarski(k9_xtuple_0(A))) ) )).
fof(d7_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( m1_subset_1(E,k4_card_3(u3_msualg_1(A,B))) => ( E = k5_facirc_1(A,B,C,D) <=> ? [F] : ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k4_card_3(u3_msualg_1(A,B))) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_card_3(u3_msualg_1(A,B))))) & E = k9_nat_1(k4_card_3(u3_msualg_1(A,B)),F,D) & k9_nat_1(k4_card_3(u3_msualg_1(A,B)),F,k5_numbers) = C & ! [G] : ( v7_ordinal1(G) => k9_nat_1(k4_card_3(u3_msualg_1(A,B)),F,k1_nat_1(G,1)) = k6_circuit2(A,B,k9_nat_1(k4_card_3(u3_msualg_1(A,B)),F,G)) ) ) ) ) ) ) ) ) )).
fof(d7_fdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( r2_fdiff_1(A,B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(C,D) = k1_fdiff_1(A,D) ) ) ) ) ) ) ) )).
fof(d7_ff_siec,axiom,( ! [A] : ( ( 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))) ) )).
fof(d7_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ( r3_lattices(A,k4_lattices(A,B,E),C) => r3_lattices(A,E,D) ) ) ) ) ) ) ) ) ) )).
fof(d7_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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))) ) ) )).
fof(d7_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_filter_2(A,B) = a_2_0_filter_2(A,B) ) ) )).
fof(d7_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) )).
fof(d7_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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(k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(A)) => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(B)) => k1_funct_1(C,k2_xcmplx_0(k3_finseq_1(A),D)) = k1_funct_1(B,D) ) ) ) ) ) ) ) )).
fof(d7_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k7_finseq_4(A,B,C,D) = k7_finseq_1(k11_finseq_1(A,B,C),k9_finseq_1(D)) )).
fof(d7_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_finseq_8(A,B,C,D) <=> ~ ( ~ r1_xxreal_0(k3_finseq_1(C),k5_numbers) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( r1_xxreal_0(D,E) & r1_xxreal_0(E,k3_finseq_1(B)) & k3_finseq_6(A,B,E,k1_nat_1(k7_nat_d(E,1),k3_finseq_1(C))) = C ) ) ) ) ) ) ) ) )).
fof(d7_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v7_ordinal1(C) => k7_fintopo3(A,B,C) = k1_funct_1(k6_fintopo3(A,B),C) ) ) ) )).
fof(d7_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_fintopo6(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & ! [E] : ( 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 ) ) ) ) ) ) ) ) )).
fof(d7_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m2_finseq_1(C,A) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( D = k4_fomodel0(A,B,C) <=> ( k9_xtuple_0(D) = k4_ordinal1 & k1_funct_1(D,k5_numbers) = k1_funct_1(C,1) & ! [E] : ( 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))) ) ) ) ) ) ) ) )).
fof(d7_fomodel1,axiom,( ! [A] : ( l1_fomodel1(A) => k7_fomodel1(A) = u2_struct_0(A) ) )).
fof(d7_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_fomodel2(D,A,B) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k9_funct_2(k35_fomodel1(A),B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_funct_2(k35_fomodel1(A),B)))) ) => ( E = k7_fomodel2(A,B,C,D) <=> ( r2_relset_1(k35_fomodel1(A),B,k10_funct_5(k4_ordinal1,k35_fomodel1(A),B,k9_funct_2(k35_fomodel1(A),B),E,k5_numbers),k8_funcop_1(B,k35_fomodel1(A),C)) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => k10_funct_5(k4_ordinal1,k35_fomodel1(A),B,k9_funct_2(k35_fomodel1(A),B),E,k1_nat_1(F,1)) = k1_fomodel0(k3_relat_1(k22_fomodel1(A),D),k6_fomodel2(k36_fomodel1(A),k10_funct_5(k4_ordinal1,k35_fomodel1(A),B,k9_funct_2(k35_fomodel1(A),B),E,F))) ) ) ) ) ) ) ) ) )).
fof(d7_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( ( v7_ordinal1(C) & v8_ordinal1(C) ) => k10_fomodel3(A,B,C) = k1_tarski(k4_tarski(k1_xboole_0,k1_xboole_0)) ) ) ) )).
fof(d7_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) => ! [C] : ! [D] : ( v4_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)),k4_fomodel4(A,B)),k1_tarski(C)))) ) ) ) )).
fof(d7_frechet,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ( v4_frechet(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(B,A) <=> ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) ) ) )).
fof(d7_freealg,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ! [C] : ( 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] : ( m1_subset_1(D,k2_xboole_0(k4_finseq_1(A),B)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d7_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(d7_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l3_fsm_1(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m2_finseq_1(E,A) => ! [F] : ( m2_finseq_1(F,B) => ( F = k5_fsm_1(A,B,C,D,E) <=> ( k3_finseq_1(F) = k1_nat_1(k3_finseq_1(E),1) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( r2_hidden(G,k2_finseq_1(k1_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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ! [D] : ! [E] : ( ( 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] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(d7_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_3(C,A,B) ) => ! [D] : ( 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) ) ) ) ) )).
fof(d7_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k7_ftacell1(A,B,C,D,E) = k2_circcomb(k25_gfacirc1(A,B,C),k37_gfacirc1(k24_gfacirc1(A,B,C),E,D)) )).
fof(d7_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : k13_funcop_1(A,B,C) = k7_funcop_1(k1_tarski(k4_tarski(A,B)),C) )).
fof(d7_funcsdom,axiom,( ! [A] : ( ~ 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)) ) )).
fof(d7_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( C = k8_relat_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,k9_xtuple_0(A)) & r2_hidden(k1_funct_1(A,D),B) ) ) ) ) )).
fof(d7_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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] : ( r2_hidden(D,k9_xtuple_0(C)) => k1_funct_1(C,D) = k4_tarski(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) )).
fof(d7_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k7_funct_6(A,B) <=> ( k9_xtuple_0(C) = k9_xtuple_0(A) & ! [D] : ( r2_hidden(D,k9_xtuple_0(A)) => k1_funct_1(C,D) = k1_funct_2(k1_funct_1(A,D),B) ) ) ) ) ) )).
fof(d7_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_funct_7(A) <=> ? [B] : ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & k3_finseq_1(B) = k1_nat_1(k3_finseq_1(A),1) & ! [C] : ( v7_ordinal1(C) => ( 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,k1_nat_1(C,1)))) ) ) ) ) ) )).
fof(d7_functor0,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => ! [C] : ( 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))) ) ) ) ) )).
fof(d7_functor2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ( r2_functor2(A,B,C,D) => ! [E] : ( m1_functor2(E,A,B,C,D) => ( m2_functor2(E,A,B,C,D) <=> ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( k1_altcat_1(A,F,G) != k1_xboole_0 => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k5_fuzzy_1(A) = k7_rfunct_1(A,A) ) )).
fof(d7_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(d7_gate_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : 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) )).
fof(d7_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v4_vectsp_1(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( m1_gcd_1(B,A) <=> ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m2_subset_1(D,u1_struct_0(A),B) & r4_gcd_1(A,D,C) ) ) & ! [C] : ( m2_subset_1(C,u1_struct_0(A),B) => ! [D] : ( m2_subset_1(D,u1_struct_0(A),B) => ~ ( C != D & r3_gcd_1(A,C,D) ) ) ) ) ) ) ) )).
fof(d7_genealg1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_finseq_1(B,k3_card_3(A)) => ! [C] : ( m2_finseq_1(C,k3_card_3(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ! [H] : ( m1_subset_1(H,k4_ordinal1) => ! [I] : ( m1_subset_1(I,k4_ordinal1) => 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) ) ) ) ) ) ) ) ) ) )).
fof(d7_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ! [F] : ( r2_hidden(k4_tarski(E,F),D) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & ? [I] : ( m1_subset_1(I,u1_struct_0(A)) & ? [J] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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)))) )).
fof(d7_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) ) => k7_glib_000(A) = k1_funct_1(A,k2_glib_000) ) )).
fof(d7_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => k4_glib_001(A,B) = k1_funct_1(B,k3_finseq_1(B)) ) ) )).
fof(d7_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ( v4_glib_002(B,A) <=> ( v1_glib_002(B) & ! [C] : ( ( v1_glib_002(C) & m1_glib_000(C,A) ) => ~ r7_glib_000(B,C) ) ) ) ) ) )).
fof(d7_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(d7_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k1_numbers),k1_zfmisc_1(k7_glib_000(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k7_glib_000(A))) => ( C = k6_glib_004(A,B) <=> ! [D] : ( 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] : ( 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_funct_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_funct_1(k5_glib_003(A),D)),k2_xcmplx_0(k1_funct_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_funct_1(k5_glib_003(A),E))) ) ) ) ) ) ) ) )).
fof(d7_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( ( 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] : ( m1_glib_005(C,A,B) => ! [D] : ( 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),k5_numbers) ) ) ) ) ) )).
fof(d7_goboard1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ( r1_goboard1(A,B,C) <=> ( ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(D,k4_finseq_1(B)) & ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ~ ( r2_hidden(k4_tarski(E,F),k2_matrix_0(C)) & k7_partfun1(A,B,D) = k3_matrix_0(A,C,E,F) ) ) ) ) ) & ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(D,k4_finseq_1(B)) & r2_hidden(k1_nat_1(D,1),k4_finseq_1(B)) ) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ( ( r2_hidden(k4_tarski(E,F),k2_matrix_0(C)) & r2_hidden(k4_tarski(G,H),k2_matrix_0(C)) & k7_partfun1(A,B,D) = k3_matrix_0(A,C,E,F) & k7_partfun1(A,B,k1_nat_1(D,1)) = k3_matrix_0(A,C,G,H) ) => k2_xcmplx_0(k9_complex1(k6_xcmplx_0(E,G)),k9_complex1(k6_xcmplx_0(F,H))) = 1 ) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_goboard5,axiom,( ! [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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k3_finseq_1(A)) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( C = k5_goboard5(A,B) <=> ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ~ ( r2_hidden(k4_tarski(D,E),k2_matrix_0(k2_goboard2(A))) & r2_hidden(k4_tarski(F,G),k2_matrix_0(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),D,E) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),F,G) & ~ ( D = F & k1_nat_1(E,1) = G & C = k3_goboard5(k2_goboard2(A),k7_nat_d(D,1),E) ) & ~ ( k1_nat_1(D,1) = F & E = G & C = k3_goboard5(k2_goboard2(A),D,E) ) & ~ ( D = k1_nat_1(F,1) & E = G & C = k3_goboard5(k2_goboard2(A),F,k7_nat_d(G,1)) ) & ~ ( D = F & E = k1_nat_1(G,1) & C = k3_goboard5(k2_goboard2(A),D,G) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_gobrd13,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ! [D] : ( v7_ordinal1(D) => ( r3_gobrd13(A,B,C,D) <=> ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ~ ( r2_hidden(k4_tarski(E,F),k2_matrix_0(C)) & r2_hidden(k4_tarski(G,H),k2_matrix_0(C)) & k7_partfun1(A,B,D) = k3_matrix_0(A,C,E,F) & k7_partfun1(A,B,k1_nat_1(D,1)) = k3_matrix_0(A,C,G,H) & ~ ( E = G & k1_nat_1(F,1) = H & r2_hidden(k4_tarski(G,k1_nat_1(H,1)),k2_matrix_0(C)) & k7_partfun1(A,B,k1_nat_1(D,2)) = k3_matrix_0(A,C,G,k1_nat_1(H,1)) ) & ~ ( k1_nat_1(E,1) = G & F = H & r2_hidden(k4_tarski(k1_nat_1(G,1),H),k2_matrix_0(C)) & k7_partfun1(A,B,k1_nat_1(D,2)) = k3_matrix_0(A,C,k1_nat_1(G,1),H) ) & ~ ( E = k1_nat_1(G,1) & F = H & r2_hidden(k4_tarski(k7_nat_d(G,1),H),k2_matrix_0(C)) & k7_partfun1(A,B,k1_nat_1(D,2)) = k3_matrix_0(A,C,k7_nat_d(G,1),H) ) & ~ ( E = G & F = k1_nat_1(H,1) & r2_hidden(k4_tarski(G,k7_nat_d(H,1)),k2_matrix_0(C)) & k7_partfun1(A,B,k1_nat_1(D,2)) = k3_matrix_0(A,C,G,k7_nat_d(H,1)) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_goedcpuc,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,k1_nat_1(B,1)) & v1_finseq_1(C) ) => ( m2_goedcpuc(C,A,B) <=> ( ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(D,k1_nat_1(B,1)) & r1_xxreal_0(1,D) ) => m1_qc_lang1(k1_funct_1(C,D)) ) ) & k1_funct_1(C,1) = A & ! [D] : ( v7_ordinal1(D) => ~ ( ~ r1_xxreal_0(k1_nat_1(B,1),D) & r1_xxreal_0(1,D) & ! [E] : ( m1_qc_lang1(E) => ~ ( k1_funct_1(C,D) = E & k1_funct_1(C,k1_nat_1(D,1)) = k1_goedcpuc(E) ) ) ) ) ) ) ) ) ) )).
fof(d7_gr_cy_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ( v1_gr_cy_1(A) <=> ? [B] : ( 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)) ) ) ) )).
fof(d7_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ( v2_graph_1(A) <=> ! [B] : ! [C] : ( ( 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 ) ) ) )).
fof(d7_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k4_ordinal1) => ~ ( 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)) ) ) ) ) ) ) )).
fof(d7_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ 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)) ) ) ) ) ) ) )).
fof(d7_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v7_graph_1(B,A) & m2_graph_1(B,A) ) => ( v1_graph_4(B,A) <=> ? [C] : ( m2_finseq_1(C,u1_struct_0(A)) & r3_graph_4(A,C,B) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d7_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v7_graph_1(B,A) & m2_graph_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( r4_graph_5(A,B,C,D,E) <=> ( v1_graph_4(B,A) & r2_graph_5(A,C,D,B,E) ) ) ) ) ) ) )).
fof(d7_graphsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( ( ? [E] : ( 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] : ~ ( r2_hidden(E,u4_struct_0(A)) & r1_graph_4(A,B,C,E) ) => k11_graphsp(A,B,C,D) = k4_xcmplx_0(1) ) ) ) ) ) ) )).
fof(d7_grcat_1,axiom,( ! [A] : ( l1_grcat_1(A) => k7_grcat_1(A) = u1_grcat_1(A) ) )).
fof(d7_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( r4_groeb_1(A,B,C,D) <=> ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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(k12_polynom1(A,C)),D,k1_groeb_1(A,C,E))) ) ) ) ) ) ) ) ) )).
fof(d7_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ! [F] : ( m2_ideal_1(F,k12_polynom1(A,C),E) => ! [G] : ( ( 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(k12_polynom1(A,C),F) = D & ! [H] : ( m1_subset_1(H,k4_ordinal1) => ~ ( r2_hidden(H,k4_finseq_1(F)) & ! [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] : ( ( v1_funct_1(J) & v1_funct_2(J,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(J,A,C) & v1_polynom1(J,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(k12_polynom1(A,C)),F,H) = k10_polynom1(A,C,I,J) & r1_termord(A,B,k3_termord(A,B,C,k10_polynom1(A,C,I,J)),G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),k4_ordinal1),u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_ordinal1),u1_struct_0(A)))) ) => ( B = k4_group_1(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),B,C,k5_numbers) = k1_group_1(A) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),B,C,k1_nat_1(D,1)) = k6_algstr_0(A,k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),B,C,D),C) ) ) ) ) ) ) )).
fof(d7_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(d7_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_group_3(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & B = k2_group_3(A,C,D) ) ) ) ) ) )).
fof(d7_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ( ( ? [C] : ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(d7_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(d7_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) )).
fof(d7_group_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => v3_group_1(k1_group_7(A,B,C)) ) ) ) ) )).
fof(d7_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ 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] : ( 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)) ) ) ) ) ) )).
fof(d7_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( l1_vectsp_1(B,A) => k7_hahnban1(A,B) = k8_funcop_1(u1_struct_0(A),k2_struct_0(B),k4_struct_0(A)) ) ) )).
fof(d7_hallmar1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k4_finseq_1(B)) => ( k1_funct_1(B,C) = k1_xboole_0 | ! [D] : ( m2_hallmar1(D,A,B) => ( m3_hallmar1(D,A,B,C) <=> k1_card_1(k1_funct_1(D,C)) = 1 ) ) ) ) ) ) )).
fof(d7_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k5_numbers,k3_complex1(k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(k1_complfld),B,C,C))) ) ) ) ) )).
fof(d7_heyting1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(k7_normform(A))) => ! [C] : ( 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)) ) ) )).
fof(d7_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_substlat(A,B))) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d7_hilbasis,axiom,( ! [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] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k12_polynom1(k1_nat_1(B,1),A)),u1_struct_0(k14_polynom3(k12_polynom1(B,A)))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k12_polynom1(k1_nat_1(B,1),A)),u1_struct_0(k14_polynom3(k12_polynom1(B,A)))))) ) => ( C = k7_hilbasis(A,B) <=> ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(k1_nat_1(B,1)),u1_struct_0(A)) & v1_polynom1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(k1_nat_1(B,1)),u1_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(B),u1_struct_0(A)) & v1_polynom1(E,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(A)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,u1_struct_0(k12_polynom1(B,A))) & v1_polynom1(F,k12_polynom1(B,A)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k12_polynom1(B,A))))) ) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ! [H] : ( ( 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(k12_polynom1(B,A),F,G) ) => k4_polynom1(B,A,E,H) = k4_polynom1(k1_nat_1(B,1),A,D,k1_hilbasis(B,G,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_hilbert1,axiom,( k2_hilbert1 = k12_finseq_1(k4_ordinal1,k5_numbers) )).
fof(d7_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( v2_hilbert2(A) <=> ? [B] : ( m1_subset_1(B,k1_hilbert1) & ? [C] : ( m1_subset_1(C,k1_hilbert1) & A = k3_hilbert1(B,C) ) ) ) ) )).
fof(d7_hilbert3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( v1_hilbert3(A) <=> ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ? [C] : ! [D] : ( m1_hilbert3(D,B) => r1_abian(C,k5_hilbert3(B,D,A)) ) ) ) ) )).
fof(d7_hurwitz,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r1_hurwitz(A,B,C) <=> r2_funct_2(k4_ordinal1,u1_struct_0(A),k6_hurwitz(A,B,C),k9_polynom3(A)) ) ) ) ) )).
fof(d7_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( B = k5_numbers => k7_idea_1(A,B) = k5_series_1(2,A) ) & ( B != k5_numbers => k7_idea_1(A,B) = B ) ) ) ) )).
fof(d7_incproj,axiom,( ! [A] : ( l1_incsp_1(A) => ( v3_incproj(A) <=> ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ? [C] : ( m1_subset_1(C,u1_incsp_1(A)) & ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & ? [E] : ( 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) ) ) ) ) ) ) )).
fof(d7_incsp_1,axiom,( ! [A] : ( l2_incsp_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_incsp_1(A))) => ( v4_incsp_1(B,A) <=> ? [C] : ( m1_subset_1(C,u4_incsp_1(A)) & r5_incsp_1(A,B,C) ) ) ) ) )).
fof(d7_index_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_index_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v1_index_1(C) ) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d7_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ( B = k2_int_1(A) <=> ( r1_xxreal_0(A,B) & ~ r1_xxreal_0(k2_xcmplx_0(A,1),B) ) ) ) ) )).
fof(d7_int_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_int_3)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_int_3)) => ( B != k4_struct_0(k1_int_3) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_int_3)) => ( C = k5_int_3(A,B) <=> ? [D] : ( 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) ) ) ) ) ) ) )).
fof(d7_integr10,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r3_integr10(A,B) => ! [C] : ( v1_xreal_0(C) => ( C = k3_integr10(A,B) <=> ? [D] : ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,k1_relset_1(k1_numbers,D)) => k1_funct_1(D,E) = k4_integra5(B,E,A) ) ) & v3_limfunc1(D) & C = k4_limfunc1(D) ) ) ) ) ) ) )).
fof(d7_integr15,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_integra1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(B)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k3_finseq_2(k1_euclid(A))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k3_finseq_2(k1_euclid(A))))) ) => ( m4_integr15(E,A,B,C,D) <=> ! [F] : ( m1_subset_1(F,k4_ordinal1) => m3_integr15(k3_funct_2(k4_ordinal1,k3_finseq_2(k1_euclid(A)),E,F),A,B,C,k2_integra2(B,D,F)) ) ) ) ) ) ) ) )).
fof(d7_integr16,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(d7_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d7_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( m1_integra1(C,A) => k6_integra1(A,B,C) = k18_rvsum_1(k4_integra1(A,B,C)) ) ) ) )).
fof(d7_intpro_1,axiom,( ! [A] : ( v7_intpro_1(A) <=> ( r1_tarski(A,k13_finseq_1(k4_ordinal1)) & v1_intpro_1(A) & v2_intpro_1(A) & v3_intpro_1(A) & v4_intpro_1(A) & v5_intpro_1(A) & v6_intpro_1(A) ) ) )).
fof(d7_irrat_1,axiom,( k4_power = k23_sin_cos(1) )).
fof(d7_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ( r2_nattra_1(A,B,D,E) => ! [F] : ( m2_nattra_1(F,A,B,D,E) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d7_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,k6_cat_2(B,C)) => k9_isocat_2(A,B,C,D) = k9_cat_1(A,k6_cat_2(B,C),B,D,k12_cat_2(B,C)) ) ) ) ) )).
fof(d7_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(d7_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k7_jgraph_6(A,B,C) = a_3_2_jgraph_6(A,B,C) ) ) ) )).
fof(d7_jordan,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( ( v1_xreal_0(D) & v2_xxreal_0(D) ) => ( m1_subset_1(C,u1_struct_0(k2_brouwer(A,B,D))) => ! [E] : ( ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d7_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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,k1_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,k1_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)) ) ) ) ) ) )).
fof(d7_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( B = k7_jordan5d(A) <=> ( r2_hidden(k4_tarski(B,k1_matrix_0(k2_goboard2(A))),k2_matrix_0(k2_goboard2(A))) & k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),B,k1_matrix_0(k2_goboard2(A))) = k20_pscomp_1(k3_topreal1(2,A)) ) ) ) ) )).
fof(d7_jordan6,axiom,( ! [A] : ( v1_xreal_0(A) => k7_jordan6(A) = a_1_5_jordan6(A) ) )).
fof(d7_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_jordan_a(B,A) => ! [C] : ( v1_xreal_0(C) => ( C = k5_jordan_a(A,B) <=> ? [D] : ( ~ v1_xboole_0(D) & v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) & ? [E] : ( ~ 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)) ) ) ) ) ) ) )).
fof(d7_kolmog01,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( m1_kolmog01(D,A,B,C) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(k9_setfam_1(B)))) => ( E = k5_kolmog01(A,B,C,D) <=> ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k1_zfmisc_1(B))) => ( r2_hidden(F,E) <=> ? [G] : ( v1_finset_1(G) & m1_subset_1(G,k1_zfmisc_1(A)) & F = k4_kolmog01(A,B,C,D,k6_subset_1(A,G)) ) ) ) ) ) ) ) ) )).
fof(d7_lang1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) ) )).
fof(d7_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ! [E] : ( m2_finseq_1(E,u1_struct_0(C)) => ( E = k8_laplace(A,B,C,D) <=> ( k3_finseq_1(E) = A & ! [F] : ( v7_ordinal1(F) => ( r2_hidden(F,k4_finseq_1(E)) => k1_funct_1(E,F) = k8_group_1(C,k3_matrix_0(u1_struct_0(C),D,B,F),k6_laplace(B,F,A,C,D)) ) ) ) ) ) ) ) ) ) )).
fof(d7_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_lattice3(A))) => k9_lattice3(A,B) = B ) ) )).
fof(d7_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( 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)) ) ) )).
fof(d7_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( 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))) ) ) ) ) ) ) ) )).
fof(d7_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k4_lattice6(A,B) = k15_lattice3(A,a_2_3_lattice6(A,B)) ) ) )).
fof(d7_lattice7,axiom,( ! [A] : ( l1_orders_2(A) => k4_lattice7(A) = a_1_1_lattice7(A) ) )).
fof(d7_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lattices(A) ) => ( v7_lattices(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d7_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => r1_orders_2(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),k12_lattice3(k1_lfuzzy_0(k1_rcomp_1(k5_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))) ) ) ) ) ) ) )).
fof(d7_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v4_limfunc1(A) <=> ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,B) & r2_hidden(C,k1_relset_1(k1_numbers,A)) ) ) & ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_limfunc1(B) & r1_tarski(k10_xtuple_0(B),k1_relset_1(k1_numbers,A)) ) => v1_limfunc1(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,B,A)) ) ) ) ) ) )).
fof(d7_limfunc2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r1_limfunc2(A,B) => ! [C] : ( v1_xreal_0(C) => ( C = k1_limfunc2(A,B) <=> ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(D) & k1_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(k4_ordinal1,k1_numbers,k1_numbers,D,A)) & k1_seq_2(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,D,A)) = C ) ) ) ) ) ) ) ) )).
fof(d7_lopban_1,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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),k9_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k7_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))) ) ) )).
fof(d7_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => k8_lopban_2(A) = g1_funcsdom(k10_lopban_1(A,A),k5_lopban_2(A),k7_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),k8_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),k6_lopban_2(A),k9_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A))) ) )).
fof(d7_lopban_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lopban_2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k4_lopban_3(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k5_rsspace3(A,D,E) = k6_algstr_0(A,k5_rsspace3(A,B,E),k5_rsspace3(A,C,E)) ) ) ) ) ) ) )).
fof(d7_lopban_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( E = k6_lopban_4(A,B,C,D) <=> ! [F] : ( v7_ordinal1(F) => ( ( r1_xxreal_0(F,A) => k9_nat_1(u1_struct_0(B),E,F) = k6_algstr_0(B,k1_rlvect_1(B,k6_lopban_3(B,C,F),k9_nat_1(k1_numbers,k3_lopban_4(A),F)),k6_lopban_3(B,D,k7_nat_d(A,F))) ) & ( ~ r1_xxreal_0(F,A) => k9_nat_1(u1_struct_0(B),E,F) = k4_struct_0(B) ) ) ) ) ) ) ) ) ) )).
fof(d7_lopclset,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d7_lpspacc1,axiom,( ! [A] : k11_lpspacc1(A) = k8_funcop_1(k2_numbers,A,k6_complex1) )).
fof(d7_lpspace1,axiom,( ! [A] : ( ~ 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)) ) )).
fof(d7_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v2_xxreal_0(D) & v1_xreal_0(D) ) => k6_lpspace2(A,B,C,D) = a_4_2_lpspace2(A,B,C,D) ) ) ) ) )).
fof(d7_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => k7_ltlaxio1(A) = k1_ltlaxio1(k6_ltlaxio1(k1_ltlaxio1(A))) ) )).
fof(d7_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => k7_ltlaxio3(A) = a_1_1_ltlaxio3(A) ) )).
fof(d7_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)))) => k6_ltlaxio4(A) = k3_tarski(a_1_3_ltlaxio4(A)) ) )).
fof(d7_margrel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( B = k3_margrel1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( r1_tarski(C,k3_finseq_2(A)) & ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( m2_finseq_1(E,A) => ( ( r2_hidden(D,C) & r2_hidden(E,C) ) => k3_finseq_1(D) = k3_finseq_1(E) ) ) ) ) ) ) ) )).
fof(d7_mathmorp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(d7_matrix10,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( B = k1_matrix10(A) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & k1_matrix_0(B) = k1_matrix_0(A) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k4_tarski(C,D),k2_matrix_0(A)) => k3_matrix_0(k1_numbers,B,C,D) = k9_complex1(k3_matrix_0(k1_numbers,A,C,D)) ) ) ) ) ) ) ) )).
fof(d7_matrix16,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( v2_matrix16(B,A) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,A,k3_finseq_1(B),k3_finseq_1(B)) & m2_finseq_1(C,k3_finseq_2(A)) ) => ( C = k1_matrix16(A,B) <=> r1_matrix16(A,C,B) ) ) ) ) ) )).
fof(d7_matrix17,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( v5_matrix17(B,A) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,A,k3_finseq_1(B),k3_finseq_1(B)) & m2_finseq_1(C,k3_finseq_2(A)) ) => ( C = k1_matrix17(A,B) <=> r1_matrix17(A,C,B) ) ) ) ) ) )).
fof(d7_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,A) => ( D = k5_matrix_0(A,B,C) <=> ( k3_finseq_1(D) = k1_matrix_0(B) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k2_finseq_1(k1_matrix_0(B))) => k1_funct_1(D,E) = k3_matrix_0(A,B,C,E) ) ) ) ) ) ) ) ) )).
fof(d7_matrix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( m1_matrix_2(D,k3_matrix_2(A)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(B)) => ( E = k10_matrix_3(A,B,C,D) <=> ( k3_finseq_1(E) = A & ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ( ( r2_hidden(F,k4_finseq_1(E)) & G = k1_funct_1(D,F) ) => k1_funct_1(E,F) = k3_matrix_0(u1_struct_0(B),C,F,G) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_matrix_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k2_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k2_numbers)) ) => ( C = k7_matrix_5(A,B) <=> ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d7_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v4_matrix_6(C,A,B) <=> ( v1_matrix_6(C,A,B) & k4_matrix_0(u1_struct_0(B),C) = k1_matrix_6(A,B,C) ) ) ) ) ) )).
fof(d7_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => k1_matrix_8(A,B,C) = k4_rlvect_1(B,k13_matrix_3(A,B,C)) ) ) ) )).
fof(d7_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ! [B] : ( v1_xcmplx_0(B) => k7_matrixc1(A,B) = k7_matrix_5(B,A) ) ) )).
fof(d7_matrixj1,axiom,( ! [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] : ( ( v2_matrixj1(B,u1_struct_0(A)) & m2_finseq_1(B,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( C = k21_matrixj1(A,B) <=> ( k4_finseq_1(C) = k4_finseq_1(B) & ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(d7_matrixr1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( C = k7_matrixr1(A,B) <=> ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d7_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_matrlin(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(A)) => ( E = k9_matrlin(A,B,C,D) <=> ( k3_finseq_1(E) = k3_finseq_1(C) & ? [F] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_matroid0,axiom,( ! [A] : ! [B] : ( ( 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) ) ) ) )).
fof(d7_matrprob,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( v3_matrprob(A) <=> k5_matrprob(A) = 1 ) ) )).
fof(d7_mcart_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) => ! [F] : ( m1_subset_1(F,D) => ( F = k7_mcart_1(A,B,C,D,E) <=> ! [G] : ! [H] : ! [I] : ! [J] : ( E = k6_xtuple_0(G,H,I,J) => F = J ) ) ) ) ) ) ) ) )).
fof(d7_measure1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( m2_measure1(D,A,B,C) <=> k12_supinf_2(C,D) = k1_supinf_2 ) ) ) ) )).
fof(d7_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => k4_measure6(A) = a_1_0_measure6(A) ) )).
fof(d7_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k9_setfam_1(k1_numbers)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k1_numbers)))) ) => ! [B] : ( m2_measure7(B,A) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( C = k7_measure7(A,B) <=> ! [D] : ( m1_subset_1(D,k4_ordinal1) => k12_supinf_2(C,D) = k6_measure7(k9_nat_1(k9_setfam_1(k1_numbers),A,D),k4_measure7(A,B,D)) ) ) ) ) ) )).
fof(d7_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k6_numbers)) => ( E = k5_measure8(A,B,C,D) <=> ! [F] : ( m1_subset_1(F,k6_numbers) => ( r2_hidden(F,E) <=> ? [G] : ( m3_measure8(G,A,D,B) & F = k19_supinf_2(k2_measure8(A,B,C,G)) ) ) ) ) ) ) ) ) )).
fof(d7_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => k10_member_1(A,B) = k8_member_1(A,k4_member_1(B)) ) ) )).
fof(d7_membered,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( r1_tarski(A,B) <=> ! [C] : ( v1_xcmplx_0(C) => ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ) ) )).
fof(d7_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => k5_memstr_0(A,B,C) = k1_funct_1(C,k4_struct_0(B)) ) ) ) )).
fof(d7_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => k7_mesfun7c(A,B) = k6_mesfunc8(A,k1_mesfun7c(A,B)) ) ) )).
fof(d7_mesfunc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k6_numbers) & v1_funct_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( C = k7_mesfunc1(A,B) <=> ( k9_xtuple_0(C) = k9_xtuple_0(B) & ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(d7_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => k1_mesfunc5(A,B) = B ) ) )).
fof(d7_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( C = k5_mesfunc8(A,B) <=> ( k1_relset_1(A,C) = k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers)) & ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(d7_metric_1,axiom,( ! [A] : ( l1_metric_1(A) => ( v7_metric_1(A) <=> v3_metric_1(u1_metric_1(A),u1_struct_0(A)) ) ) )).
fof(d7_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => k4_metric_2(A,B) = a_2_1_metric_2(A,B) ) ) )).
fof(d7_metric_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ! [I] : ( m1_subset_1(I,u1_struct_0(B)) => ! [J] : ( m1_subset_1(J,u1_struct_0(C)) => ! [K] : ( m1_subset_1(K,u1_struct_0(C)) => ! [L] : ( m1_subset_1(L,u1_struct_0(D)) => ! [M] : ( m1_subset_1(M,u1_struct_0(D)) => ! [N] : ( m1_subset_1(N,k4_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),u1_struct_0(D))) => ! [O] : ( 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) ) => k2_binop_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,N,O) = k2_xcmplx_0(k2_xcmplx_0(k3_metric_1(A,F,G),k3_metric_1(B,H,I)),k2_xcmplx_0(k3_metric_1(C,J,K),k3_metric_1(D,L,M))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_metric_6,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( D = k3_metric_6(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k9_nat_1(k1_numbers,D,E) = k3_metric_1(A,k2_tbsp_1(A,B,E),k2_tbsp_1(A,C,E)) ) ) ) ) ) ) )).
fof(d7_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) & B = k4_midsp_1(A,C) ) ) ) ) )).
fof(d7_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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) ) ) ) )).
fof(d7_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(d7_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(d7_modal_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) & v3_trees_2(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,A) & v1_funct_1(C) & v3_trees_2(C) ) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( r2_hidden(D,k9_xtuple_0(B)) => k9_modal_1(A,B,C,D) = k7_trees_2(B,D,C) ) ) ) ) ) )).
fof(d7_modcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_modcat_1(B,A) => ! [C] : ( m3_modcat_1(C,A) => ( C = k4_modcat_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( v7_vectsp_1(E,A) & m2_modcat_1(E,A,B) & ? [F] : ( v7_vectsp_1(F,A) & m2_modcat_1(F,A,B) & v2_mod_2(D,A) & m1_mod_2(D,A,E,F) ) ) ) ) ) ) ) )).
fof(d7_modelc_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => k7_modelc_1(A) = k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,k5_numbers),A) ) )).
fof(d7_modelc_2,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => k7_modelc_2(A,B) = k8_finseq_1(k4_ordinal1,k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,4),A),B) ) ) )).
fof(d7_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( l1_modelc_3(B,A) => ! [C] : ( l1_modelc_3(C,A) => ( r2_modelc_3(A,B,C) <=> ? [D] : ( v1_modelc_2(D) & m2_finseq_1(D,k4_ordinal1) & r2_hidden(D,u2_modelc_3(A,B)) & C = k5_modelc_3(A,B,D) ) ) ) ) ) )).
fof(d7_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => k6_moebius1(A) = k8_nat_3(k8_newton,k5_moebius1(A)) ) )).
fof(d7_monoid_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ( k5_binop_1(A,B,D,C) = k5_binop_1(A,B,E,C) => D = E ) ) ) ) ) ) ) )).
fof(d7_monoid_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(k13_monoid_1(A))) => ( C = k20_monoid_1(A,B) <=> ! [D] : ( m1_subset_1(D,A) => k15_monoid_1(A,C,D) = k5_card_1(k1_relset_1(k4_ordinal1,k6_relset_1(k4_ordinal1,A,k6_domain_1(A,D),B))) ) ) ) ) ) )).
fof(d7_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [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] : ( 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] : ( 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] : ( 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] : ( 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] : ( 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] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r2_hidden(B,k3_msafree2(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( C = k4_msafree2(A,B) <=> k2_msualg_1(A,C) = B ) ) ) ) ) )).
fof(d7_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,C)) => ( D = k4_msafree4(A,B,C) <=> ( r1_msualg_3(A,k1_msafree3(A,B),C,D) & ! [E] : ( m1_msafree(E,A,k1_msafree3(A,B)) => ( r8_pboole(u1_struct_0(A),E,k13_msafree(A,B)) => r8_pboole(u1_struct_0(A),k2_msualg_3(u1_struct_0(A),E),k1_msafree(u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,C),E,D)) ) ) ) ) ) ) ) ) )).
fof(d7_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) => ( m3_msaterm(C,A,B) <=> ? [D] : ( m2_msaterm(D,A,B) & r2_hidden(D,C) ) ) ) ) ) )).
fof(d7_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) => ( v6_mssubfam(C,A,B) <=> r1_pboole(A,k1_pboole(A),C) ) ) ) )).
fof(d7_msualg_1,axiom,( ! [A] : ( l1_msualg_1(A) => ( v5_msualg_1(A) <=> ? [B] : ( v7_ordinal1(B) & u4_struct_0(A) = k2_finseq_1(B) ) ) ) )).
fof(d7_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d7_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( 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] : ( m1_subset_1(E,u4_struct_0(A)) => ( k3_msualg_1(A,E,B) != k1_xboole_0 => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d7_msualg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,k3_msualg_1(A,B,C)) => ! [F] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d7_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_ordinal1) => ( 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))) ) ) ) ) ) ) ) ) )).
fof(d7_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_orders_2(B) & l1_orders_2(B) ) => ( m1_mycielsk(B,A) <=> u1_struct_0(B) = A ) ) ) )).
fof(d7_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k1_numbers,D,E) = k3_real_1(k3_funct_2(u1_struct_0(A),k1_numbers,B,E),k3_funct_2(u1_struct_0(A),k1_numbers,C,E)) ) ) ) ) ) ) )).
fof(d7_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( B != 1 & A != k5_numbers & ~ ! [C] : ( v7_ordinal1(C) => ( C = k10_nat_3(A,B) <=> ( r1_nat_d(k1_newton(B,C),A) & ~ r1_nat_d(k1_newton(B,k2_xcmplx_0(C,1)),A) ) ) ) ) ) ) )).
fof(d7_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ( r2_nattra_1(A,B,C,D) => ! [E] : ( m1_nattra_1(E,A,B,C,D) => ( m2_nattra_1(E,A,B,C,D) <=> ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( k2_cat_1(A,F,G) != k1_xboole_0 => ! [H] : ( 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),k2_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),k2_nattra_1(A,B,C,D,E,F),k9_cat_3(A,F,G,B,D,H)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_ncfcont1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,C)) ) ) ) ) ) ) ) ) ) )).
fof(d7_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_ndiff_1(A,B,C,D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k16_lopban_1(A,B))) => ( E = k3_ndiff_1(A,B,C,D) <=> ? [F] : ( m1_nfcont_1(F,A,D) & r1_tarski(F,k1_relset_1(u1_struct_0(A),C)) & ? [G] : ( 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] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(d7_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(A)),k1_numbers))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(A))) => ! [D] : ( ( 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] : ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) & ? [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(d7_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(d7_necklace,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( 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))) ) ) ) ) )).
fof(d7_net_1,axiom,( ! [A] : ( l1_petri(A) => ! [B] : ( m1_subset_1(B,k2_net_1(A)) => ! [C] : ( C = k4_net_1(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,k2_net_1(A)) & r2_hidden(k4_tarski(B,D),k1_net_1(A)) ) ) ) ) ) )).
fof(d7_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k4_ordinal1)) => ( B = k9_newton(A) <=> ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,B) <=> ( ~ r1_xxreal_0(A,C) & v1_int_2(C) ) ) ) ) ) ) )).
fof(d7_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( r3_nfcont_1(A,B,C,D) <=> ( r1_tarski(D,k1_relset_1(u1_struct_0(A),C)) & ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d7_normform,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(A)) => ! [D] : ( ( 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) ) ) ) )).
fof(d7_normsp_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_normsp_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k6_normsp_1(A,B) <=> ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(E,F) & r1_xxreal_0(D,k2_normsp_0(A,k5_algstr_0(A,k1_normsp_1(A,B,F),C))) ) ) ) ) ) ) ) ) ) )).
fof(d7_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ( v6_o_ring_1(B,A) <=> ( k3_finseq_1(B) != k5_numbers & v5_o_ring_1(k7_partfun1(u1_struct_0(A),B,1),A) & ! [C] : ( v7_ordinal1(C) => ~ ( C != k5_numbers & ~ r1_xxreal_0(k3_finseq_1(B),C) & ! [D] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d7_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => k9_openlatt(A) = k10_xtuple_0(k8_openlatt(A)) ) )).
fof(d7_oposet_1,axiom,( ! [A] : ( ( ~ 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)))) ) ) ) )).
fof(d7_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( 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 ) ) ) ) ) )).
fof(d7_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(A))) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A))))) ) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( r1_xxreal_0(D,E) & r3_nfcont_1(k4_real_ns1(A),k4_real_ns1(A),C,k1_relset_1(u1_struct_0(k4_real_ns1(A)),C)) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(k5_ordeq_01(k3_integra5(D,E),k4_real_ns1(A))),u1_struct_0(k5_ordeq_01(k3_integra5(D,E),k4_real_ns1(A)))) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_ordeq_01(k3_integra5(D,E),k4_real_ns1(A))),u1_struct_0(k5_ordeq_01(k3_integra5(D,E),k4_real_ns1(A)))))) ) => ( F = k6_ordeq_01(A,B,C,D,E) <=> ! [G] : ( m1_subset_1(G,u1_struct_0(k5_ordeq_01(k3_integra5(D,E),k4_real_ns1(A)))) => ? [H] : ( v1_funct_1(H) & v1_nfcont_3(H,k4_real_ns1(A)) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) & ? [I] : ( v1_funct_1(I) & v1_nfcont_3(I,k4_real_ns1(A)) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) & ? [J] : ( v1_funct_1(J) & v1_nfcont_3(J,k4_real_ns1(A)) & m1_subset_1(J,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) & G = H & k3_funct_2(u1_struct_0(k5_ordeq_01(k3_integra5(D,E),k4_real_ns1(A))),u1_struct_0(k5_ordeq_01(k3_integra5(D,E),k4_real_ns1(A))),F,G) = I & k1_relset_1(k1_numbers,H) = k3_integra5(D,E) & k1_relset_1(k1_numbers,I) = k3_integra5(D,E) & r2_relset_1(k1_numbers,u1_struct_0(k4_real_ns1(A)),J,k1_partfun1(k1_numbers,u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A)),H,C)) & ! [K] : ( v1_xreal_0(K) => ( r2_hidden(K,k3_integra5(D,E)) => k1_funct_1(I,K) = k3_rlvect_1(k4_real_ns1(A),B,k6_integr18(k4_real_ns1(A),J,D,K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r1_orders_1(A,B) <=> ( r1_relat_2(A,B) & r8_relat_2(A,B) ) ) ) )).
fof(d7_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_orders_2(B,A) <=> r7_relat_2(u1_orders_2(A),B) ) ) ) )).
fof(d7_orders_3,axiom,( ! [A] : ! [B] : ( B = k2_orders_3(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( l1_struct_0(D) & r2_hidden(D,A) & C = u1_struct_0(D) ) ) ) )).
fof(d7_ordinal1,axiom,( ! [A] : ( v5_ordinal1(A) <=> v3_ordinal1(k9_xtuple_0(A)) ) )).
fof(d7_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => k7_ordinal3(A,B) = k5_ordinal3(A,k11_ordinal2(k6_ordinal3(A,B),B)) ) ) )).
fof(d7_ordinal6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) ) => k3_ordinal6(A) = k2_ordinal6(a_1_0_ordinal6(A)) ) )).
fof(d7_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => k4_osafree(A,B,C) = a_3_0_osafree(A,B,C) ) ) ) )).
fof(d7_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ( v7_osalg_1(B,A) <=> ! [C] : ( 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)) ) ) ) ) ) )).
fof(d7_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_osalg_2(C,A,B) => k5_osalg_2(A,B,C) = a_3_2_osalg_2(A,B,C) ) ) ) )).
fof(d7_osalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [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] : ( 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)) ) ) ) )).
fof(d7_papdesaf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ( v6_papdesaf(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) ) )).
fof(d7_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r4_pboole(A,B,C) <=> ! [D] : ~ ( r2_hidden(D,A) & r1_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) )).
fof(d7_pcomps_1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(d7_pcs_0,axiom,( ! [A] : ( l1_pcs_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_pcs_0(A,B,C) <=> r2_hidden(k4_tarski(B,C),u1_pcs_0(A)) ) ) ) ) )).
fof(d7_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ( r1_pdiff_1(A,B,C,D) <=> ? [E] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d7_pdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(2)) => ( r2_pdiff_3(A,B) => ! [C] : ( v1_xreal_0(C) => ( C = k3_pdiff_3(A,B) <=> ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & B = k10_finseq_1(D,E) & ? [F] : ( 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] : ( v1_funct_1(G) & v3_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [H] : ( v1_funct_1(H) & v2_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & C = k1_funct_1(G,1) & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,F) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(2,2,k1_pdiff_3(1,2,A),B),I),k1_funct_1(k1_pdiff_2(2,2,k1_pdiff_3(1,2,A),B),E)) = k2_xcmplx_0(k1_funct_1(G,k6_xcmplx_0(I,E)),k1_funct_1(H,k6_xcmplx_0(I,E))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_pdiff_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( 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,k10_pdiff_1(3,1,A,B)),k9_euclid(3,k3_euclid_8,k10_pdiff_1(3,2,A,B))),k9_euclid(3,k4_euclid_8,k10_pdiff_1(3,3,A,B))) ) ) )).
fof(d7_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r7_pdiff_5(A,B) <=> ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & B = k11_finseq_1(C,D,E) & ? [F] : ( 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] : ( v1_funct_1(G) & v3_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [H] : ( v1_funct_1(H) & v2_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,F) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,1,k1_pdiff_3(3,3,A),B),I),k1_funct_1(k1_pdiff_2(3,1,k1_pdiff_3(3,3,A),B),C)) = k2_xcmplx_0(k1_funct_1(G,k6_xcmplx_0(I,C)),k1_funct_1(H,k6_xcmplx_0(I,C))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [D] : ( r4_pdiff_7(A,B,C,D) <=> ( r1_tarski(D,k1_relset_1(k1_euclid(A),C)) & ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d7_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_partfun1(k1_euclid(A),k1_numbers)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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,k5_numbers),D) & ! [F] : ( v7_ordinal1(F) => r2_relset_1(k1_euclid(A),k1_numbers,k1_seqfunc(k1_euclid(A),k1_numbers,E,k1_nat_1(F,1)),k3_pdiff_9(A,B,k7_partfun1(k4_ordinal1,C,k1_nat_1(F,1)),k1_seqfunc(k1_euclid(A),k1_numbers,E,F))) ) ) ) ) ) ) ) )).
fof(d7_pencil_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( v6_pencil_1(A) <=> ! [B] : ( m1_subset_1(B,u1_pre_topc(A)) => ! [C] : ( m1_subset_1(C,u1_pre_topc(A)) => ( r1_ordinal1(2,k1_card_1(k3_xboole_0(B,C))) => B = C ) ) ) ) ) )).
fof(d7_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(d7_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u4_struct_0(A))) => k9_petri(A,B) = a_2_5_petri(A,B) ) ) )).
fof(d7_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( 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 ) ) ) ) )).
fof(d7_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( 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)) = k5_numbers => ( E = k7_polyeq_5(A,B,C,D) <=> ? [F] : ( v1_xcmplx_0(F) & ? [G] : ( v1_xcmplx_0(G) & ? [H] : ( v1_xcmplx_0(H) & F = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(8,C),k3_xcmplx_0(3,k1_newton(D,2))),32) & G = k7_xcmplx_0(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)))),k7_xcmplx_0(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)) != k5_numbers => ( E = k7_polyeq_5(A,B,C,D) <=> ? [F] : ( v1_xcmplx_0(F) & ? [G] : ( v1_xcmplx_0(G) & ? [H] : ( v1_xcmplx_0(H) & ? [I] : ( v1_xcmplx_0(I) & ? [J] : ( v1_xcmplx_0(J) & ? [K] : ( v1_xcmplx_0(K) & F = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(8,C),k3_xcmplx_0(3,k1_newton(D,2))),32) & G = k7_xcmplx_0(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 = k7_xcmplx_0(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 = k4_xcmplx_0(k7_xcmplx_0(G,k3_xcmplx_0(I,J))) & E = k6_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(I),J),K),k7_xcmplx_0(D,4)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( 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) ) ) ) ) ) ) )).
fof(d7_polynom1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( 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)))) ) => k7_polynom1(A,B,C,D) = k5_polynom1(A,B,C,k5_vfunct_1(k15_pre_poly(A),B,D)) ) ) ) )).
fof(d7_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => k9_polynom3(A) = k8_funcop_1(u1_struct_0(A),k4_ordinal1,k4_struct_0(A)) ) )).
fof(d7_polynom5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_polynom5(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r1_polynom5(A,B,C) ) ) ) ) )).
fof(d7_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( 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] : ( ( 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) => k4_polynom1(A,B,C,D) = k4_struct_0(B) ) ) ) ) ) )).
fof(d7_polynom8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v4_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(E,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( E = k6_polynom8(A,B,C,D) <=> ( ! [F] : ( v7_ordinal1(F) => ( ~ r1_xxreal_0(A,F) => k9_nat_1(u1_struct_0(B),E,F) = k2_polynom4(B,C,k2_binom(B,D,F)) ) ) & ! [F] : ( v7_ordinal1(F) => ( r1_xxreal_0(A,F) => k9_nat_1(u1_struct_0(B),E,F) = k4_struct_0(B) ) ) ) ) ) ) ) ) ) )).
fof(d7_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( r5_polyred(A,B,C,D,E,F) <=> ? [G] : ( v1_funct_1(G) & v1_funct_2(G,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(G,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) ) ) ) ) ) ) ) ) )).
fof(d7_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( 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] : ! [E] : ( r2_hidden(k4_tarski(D,E),C) <=> ( r2_hidden(D,k4_poset_1(A,B)) & r2_hidden(E,k4_poset_1(A,B)) & ? [F] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d7_pralg_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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) ) ) ) ) )).
fof(d7_pralg_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => k7_pralg_2(A,B,C) = k3_tarski(a_3_0_pralg_2(A,B,C)) ) ) ) )).
fof(d7_pre_poly,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k13_pre_poly(A) <=> ! [C] : ( r2_hidden(C,B) <=> k1_funct_1(A,C) != k5_numbers ) ) ) )).
fof(d7_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k2_pre_topc(A,B) <=> ! [D] : ( r2_hidden(D,u1_struct_0(A)) => ( r2_hidden(D,C) <=> ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d7_prgcor_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k1_numbers) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k1_numbers) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,k1_numbers) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ! [D] : ( 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] : ( v1_int_1(E) & k1_funct_1(C,k5_numbers) = k1_funct_1(B,k5_numbers) & E = k1_funct_1(B,k5_numbers) & ( E != k5_numbers => ! [F] : ( v7_ordinal1(F) => ( ( r1_xxreal_0(1,F) & r1_xxreal_0(F,E) ) => k1_funct_1(C,F) = k6_xcmplx_0(k1_funct_1(A,F),k1_funct_1(B,F)) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_prob_1,axiom,( ! [A] : ! [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))) ) => k4_prob_1(A,B) = A ) )).
fof(d7_prob_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v2_prob_3(B,A) <=> ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(d7_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),k4_prob_4(A,B,C)) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ( E = k6_prob_4(A,B,C,D) <=> ! [F] : ( r2_hidden(F,E) <=> ( r2_hidden(F,B) & r1_tarski(F,D) & m1_prob_4(k7_subset_1(A,D,F),A,B,C) ) ) ) ) ) ) ) ) )).
fof(d7_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( m2_prvect_1(B,A) <=> ( k9_xtuple_0(B) = k9_xtuple_0(A) & ! [C] : ( 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)))) ) ) ) ) ) ) )).
fof(d7_prvect_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v1_prvect_2(A) ) => ! [B] : ( m1_subset_1(B,k4_card_3(k4_prvect_2(A))) => ( B = k8_prvect_2(A) <=> ! [C] : ( m2_subset_1(C,k4_ordinal1,k4_finseq_1(k4_prvect_2(A))) => k8_prvect_1(k4_prvect_2(A),B,C) = u2_struct_0(k5_prvect_2(A,C)) ) ) ) ) )).
fof(d7_prvect_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_normsp_1(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(d7_pscomp_1,axiom,( ! [A] : ( 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)) ) )).
fof(d7_pua2mss1,axiom,( ! [A] : ( ( v2_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ( B = k9_pua2mss1(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(k4_tarski(C,D),B) <=> ! [E] : ( m1_subset_1(E,k4_ordinal1) => r2_hidden(k4_tarski(C,D),k8_pua2mss1(A,k6_pua2mss1(A),E)) ) ) ) ) ) ) ) )).
fof(d7_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => k6_qc_lang1(A) = a_1_0_qc_lang1(A) ) )).
fof(d7_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(d7_qmax_1,axiom,( ! [A] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(d7_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( C = k7_quaterni(A,B) <=> ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & ? [I] : ( v1_xreal_0(I) & ? [J] : ( v1_xreal_0(J) & ? [K] : ( v1_xreal_0(K) & A = k6_quaterni(D,E,F,G) & B = k6_quaterni(H,I,J,K) & C = k6_quaterni(k2_xcmplx_0(D,H),k2_xcmplx_0(E,I),k2_xcmplx_0(F,J),k2_xcmplx_0(G,K)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ( D = k9_quofield(A,B,C) <=> ! [E] : ( m2_subset_1(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A)) => ( r2_hidden(E,D) <=> ? [F] : ( m2_subset_1(F,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A)) & ? [G] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(d7_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(d7_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(d7_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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) = k5_numbers ) ) ) ) ) ) )).
fof(d7_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_int_1(C) => ( r1_radix_6(A,B,C) <=> ( ~ r1_xxreal_0(k1_newton(k1_radix_1(B),A),C) & r1_xxreal_0(k11_newton(k1_radix_1(B),k7_nat_d(A,1)),C) ) ) ) ) ) )).
fof(d7_random_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( m2_prob_1(E,A,C) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,A,B) & v1_random_3(F,A,B,C,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => k2_random_3(A,B,C,D,E,F) = k3_prob_4(B,D,k1_random_3(A,B,C,D,k2_prob_4(A,C,E),F)) ) ) ) ) ) ) )).
fof(d7_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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)) ) ) ) ) )).
fof(d7_ratfunc1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_ratfunc1(B,A) <=> k2_ratfunc1(A,B) = k5_struct_0(A) ) ) ) )).
fof(d7_rcomp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k3_rcomp_1(A,B) = a_2_2_rcomp_1(A,B) ) ) )).
fof(d7_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => k7_real_3(A) = k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k5_real_3(A),k6_real_3(A)) ) )).
fof(d7_realset1,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m3_realset1(C,A,B) => k4_realset1(A,B,C) = k1_realset1(C,k6_subset_1(A,k6_domain_1(A,B))) ) ) ) )).
fof(d7_recdef_2,axiom,( ! [A] : ( v3_xtuple_0(A) => ! [B] : ( B = k2_xtuple_0(A) <=> ! [C] : ! [D] : ! [E] : ! [F] : ( A = k6_xtuple_0(C,D,E,F) => B = F ) ) ) )).
fof(d7_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v2_relat_1(A) <=> ~ r2_hidden(k1_xboole_0,k10_xtuple_0(A)) ) ) )).
fof(d7_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r7_relat_2(A,B) <=> ! [C] : ! [D] : ~ ( r2_hidden(C,B) & r2_hidden(D,B) & ~ r2_hidden(k4_tarski(C,D),A) & ~ r2_hidden(k4_tarski(D,C),A) ) ) ) )).
fof(d7_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r5_rewrite1(A,B,C) <=> ? [D] : ( r1_rewrite1(A,B,D) & r1_rewrite1(A,C,D) ) ) ) )).
fof(d7_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ( r3_rewrite2(A,B,C,D) <=> r1_rewrite1(k7_rewrite2(A,B),C,D) ) ) ) ) )).
fof(d7_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ v2_struct_0(C) & l1_rewrite3(C,B) ) => ! [D] : ! [E] : ! [F] : ( r4_rewrite3(A,B,C,D,E,F) <=> r3_rewrite3(A,B,C,D,E,F,k2_flang_1(A)) ) ) ) ) )).
fof(d7_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,k3_rfunct_3(A,k1_numbers)) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ! [D] : ( m2_finseq_1(D,k3_rfunct_3(A,k1_numbers)) => ( D = k16_rfunct_3(A,B,C) <=> ( k3_finseq_1(D) = k4_nat_1(k3_finseq_1(C),k3_finseq_1(B)) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k4_finseq_1(D)) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [G] : ( v1_xreal_0(G) => ( ( G = k1_funct_1(C,E) & F = k1_funct_1(B,E) ) => k1_funct_1(D,E) = k26_valued_1(A,k1_numbers,F,G) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_rfunct_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r7_rfunct_4(A,B) <=> ( r2_hidden(B,k9_xtuple_0(A)) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_xtuple_0(A)) & ~ r1_xxreal_0(D,k9_complex1(k6_xcmplx_0(E,B))) & r1_xxreal_0(C,k6_xcmplx_0(k1_funct_1(A,E),k1_funct_1(A,B))) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k6_rinfsup1(A) = k1_rinfsup1(k3_rinfsup1(A)) ) )).
fof(d7_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( B = k4_rinfsup2(A) <=> ! [C] : ( v7_ordinal1(C) => ? [D] : ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k6_numbers)) & D = a_2_0_rinfsup2(A,C) & k12_supinf_2(B,C) = k8_supinf_2(D) ) ) ) ) ) )).
fof(d7_ringcat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( v3_ringcat1(C) & l1_ringcat1(C) & k1_ringcat1(C) = A & k2_ringcat1(C) = B ) ) ) ) )).
fof(d7_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_rlaffin1(B,A) => ! [C] : ( r2_hidden(C,k4_rlaffin1(A,B)) => ! [D] : ( m2_rlvect_2(D,A,B) => ( D = k5_rlaffin1(A,B,C) <=> ( k6_rlvect_2(A,D) = C & k3_rlaffin1(A,D) = 1 ) ) ) ) ) ) ) )).
fof(d7_rlsub_2,axiom,( ! [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) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k3_rlsub_2(A)) => ! [D] : ( m1_subset_1(D,k3_rlsub_2(A)) => ! [E] : ( m1_rlsub_1(E,A) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d7_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v4_rltopsp1(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => v3_rltopsp1(C,A) ) ) ) ) ) )).
fof(d7_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ( v7_rlvect_1(A) <=> ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d7_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( m2_finseq_1(D,u1_struct_0(A)) => ( D = k5_rlvect_2(A,B,C) <=> ( k3_finseq_1(D) = k3_finseq_1(B) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k1_relset_1(k4_ordinal1,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))) ) ) ) ) ) ) ) ) )).
fof(d7_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(D,k3_rmod_3(A,B)) => ! [E] : ( m1_subset_1(E,k3_rmod_3(A,B)) => ! [F] : ( m1_rmod_2(F,A,B) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d7_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_4(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( D = k5_rmod_4(A,B,C) <=> ? [E] : ( 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)) ) ) ) ) ) ) )).
fof(d7_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_lattices(A) ) => ( v7_robbins1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_lattices(A,B,B) = B ) ) ) )).
fof(d7_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_robbins1(A) ) => ( v9_robbins3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_lattices(A,B,k3_robbins1(A,B)) = k1_lattices(A,C,k3_robbins1(A,C)) ) ) ) ) )).
fof(d7_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_roughs_1(B,A) <=> k5_roughs_1(A,B) != k1_xboole_0 ) ) ) )).
fof(d7_rsspace,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_rlsub_1(B,A) => ( v1_xboole_0(B) | k7_rsspace(A,B) = k1_realset1(u1_algstr_0(A),B) ) ) ) ) )).
fof(d7_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( r2_hidden(C,k4_rsspace4(A,B)) => k6_rsspace4(A,B,C) = C ) ) ) )).
fof(d7_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k3_rusub_2(A)) => ! [D] : ( m1_subset_1(D,k3_rusub_2(A)) => ! [E] : ( m1_rusub_1(E,A) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d7_rusub_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d7_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( v1_xreal_0(B) => k10_rvsum_1(A,B) = k3_relat_1(A,k3_rvsum_1(B)) ) ) )).
fof(d7_scm_comp,axiom,( ! [A] : ( m1_dtconstr(A,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [B] : ( 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(k5_numbers,4),A,B) ) ) )).
fof(d7_scm_inst,axiom,( ! [A] : ( m1_subset_1(A,k3_scm_inst) => ( ? [B] : ( v7_ordinal1(B) & ? [C] : ( m1_subset_1(C,k2_scm_inst) & ? [D] : ( m2_subset_1(D,k4_ordinal1,k7_card_1(9)) & A = k3_xtuple_0(D,k9_finseq_1(B),k12_finseq_1(k2_scm_inst,C)) ) ) ) => ! [B] : ( m1_subset_1(B,k2_scm_inst) => ( B = k8_scm_inst(A) <=> ? [C] : ( 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) ) ) ) ) ) )).
fof(d7_scmfsa7b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( r6_scmfsa7b(A,B,C) <=> r1_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(C,A),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B)) ) ) ) ) )).
fof(d7_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(k1_scmfsa_2)) => ( C = k7_scmfsa_2(A,B) <=> ? [D] : ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_ami_3)) & ? [E] : ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_ami_3)) & A = D & B = E & C = k3_ami_3(D,E) ) ) ) ) ) ) )).
fof(d7_scmfsa_m,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k11_memstr_0(k7_card_1(3),k1_scmfsa_2),k11_memstr_0(k7_card_1(3),k1_scmfsa_2)))) ) => ( A = k10_scmfsa_m <=> ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_finset_1(B) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_finset_1(C) ) => ( r2_hidden(k4_tarski(B,C),A) <=> ? [D] : ( m2_finseq_1(D,k4_numbers) & ? [E] : ( 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(k5_numbers),D) & C = k16_funcop_1(k5_scmfsa_2(k5_numbers),E) ) ) ) ) ) ) ) )).
fof(d7_scmpds_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => k7_scmpds_2(A,B,C) = k3_xtuple_0(4,k1_xboole_0,k11_finseq_1(A,B,C)) ) ) ) )).
fof(d7_scmpds_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ( v2_scmpds_4(A) <=> ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( r1_tarski(k10_compos_1(k1_scmpds_2,A),C) => r1_extpro_1(2,k1_scmpds_2,C,B) ) ) ) ) ) )).
fof(d7_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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,k1_nat_1(k5_card_1(C),1)),C) ) ) ) )).
fof(d7_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => ( ? [B] : ( m1_subset_1(B,k2_scm_inst) & ? [C] : ( v1_int_1(C) & ? [D] : ( v1_int_1(D) & ? [E] : ( 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] : ( v1_int_1(B) => ( B = k8_scmpds_i(A) <=> ? [C] : ( 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) ) ) ) ) ) )).
fof(d7_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => k8_scmring2(A,B) = k3_xtuple_0(6,k9_finseq_1(B),k1_xboole_0) ) ) )).
fof(d7_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_scmringi(A)) => ( ? [C] : ( m1_subset_1(C,k2_scm_inst) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m2_subset_1(E,k4_ordinal1,k7_card_1(8)) & B = k3_xtuple_0(E,k1_xboole_0,k7_scmringi(A,C,D)) ) ) ) => ! [C] : ( m1_subset_1(C,k2_scm_inst) => ( C = k8_scmringi(A,B) <=> ? [D] : ( 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) ) ) ) ) ) ) )).
fof(d7_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(d7_seq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) ) => ( v1_comseq_2(A) <=> ( v1_seq_2(A) & v2_seq_2(A) ) ) ) )).
fof(d7_seq_4,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => k8_seq_4(A,B) = k1_finseqop(k2_numbers,k2_numbers,k2_numbers,k4_binop_2,A,B) ) ) )).
fof(d7_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( D = k8_seqfunc(A,B,C) <=> ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(d7_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v6_valued_0(A) <=> ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,A,k1_nat_1(B,1))) ) ) ) )).
fof(d7_setfam_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ( C = k7_setfam_1(A,B) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( r2_hidden(D,C) <=> r2_hidden(k3_subset_1(A,D),B) ) ) ) ) ) )).
fof(d7_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( D = k7_setlim_2(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k9_nat_1(k9_setfam_1(A),D,E) = k7_subset_1(A,C,k9_nat_1(k9_setfam_1(A),B,E)) ) ) ) ) ) )).
fof(d7_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( v4_sheffer1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r1_sheffer1(A,C,B) ) ) ) ) )).
fof(d7_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ( v4_simplex0(A) <=> v2_setfam_1(u1_pre_topc(A)) ) ) )).
fof(d7_simplex1,axiom,( ! [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) ) => ! [B] : ( m1_simplex0(B,u1_struct_0(A)) => ( v1_simplex1(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v3_pre_topc(C,B) => v1_rlaffin1(k1_simplex1(A,B,C),A) ) ) ) ) ) )).
fof(d7_sin_cos,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( B = k6_sin_cos(A) <=> ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(C,A) => k9_nat_1(k2_numbers,B,C) = k7_xcmplx_0(k6_complex1,k3_xcmplx_0(k2_newton(C),k2_newton(k7_nat_d(A,C)))) ) & ( ~ r1_xxreal_0(C,A) => k9_nat_1(k2_numbers,B,C) = k5_numbers ) ) ) ) ) ) )).
fof(d7_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => k7_sin_cos7(A) = k4_xcmplx_0(k3_power(k4_power,k7_xcmplx_0(k2_xcmplx_0(1,k3_square_1(k6_xcmplx_0(1,k1_square_1(A)))),A))) ) )).
fof(d7_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => k7_sincos10(A) = k1_funct_1(k3_sincos10,A) ) )).
fof(d7_struct_0,axiom,( ! [A] : ( l3_struct_0(A) => k5_struct_0(A) = u3_struct_0(A) ) )).
fof(d7_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k16_substut1(A),k38_substut1(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(d7_subset_1,axiom,( ! [A] : ! [B] : ( r2_hidden(A,B) => k10_subset_1(A,B) = A ) )).
fof(d7_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k2_qc_lang1(A)) => k8_substut1(A,B) = a_2_0_substut1(A,B) ) ) )).
fof(d7_t_0topsp,axiom,( ! [A] : ( l1_pre_topc(A) => ( v6_pre_topc(A) <=> ( v2_struct_0(A) | ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d7_taxonom1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ( C = k3_taxonom1(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(k4_tarski(D,E),C) <=> r1_taxonom1(A,B,D,E) ) ) ) ) ) ) ) )).
fof(d7_taylor_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( E = k6_taylor_1(A,B,C,D) <=> ! [F] : ( v7_ordinal1(F) => k9_nat_1(k1_numbers,E,F) = k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(A,B),F),C),k1_newton(k6_xcmplx_0(D,C),F)),k2_newton(F)) ) ) ) ) ) ) ) )).
fof(d7_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_tbsp_1(B,A) <=> ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r2_hidden(D,B) & r2_hidden(E,B) ) => r1_xxreal_0(k1_metric_1(A,D,E),C) ) ) ) ) ) ) ) )).
fof(d7_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k5_tdlat_1(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(d7_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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_polynom1(A,C,D,k3_termord(A,B,C,D)) ) ) ) ) )).
fof(d7_tex_4,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_tex_4(B,A) <=> ( v1_tex_4(B,A) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_tex_4(C,A) & r1_tarski(B,C) ) => B = C ) ) ) ) ) ) )).
fof(d7_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k5_tmap_1(A,B) = a_2_0_tmap_1(A,B) ) ) )).
fof(d7_topalg_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k17_borsuk_1)) => ! [F] : ( 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),k6_xcmplx_0(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)) ) ) ) ) ) ) ) )).
fof(d7_topalg_6,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)) ) ) ) )).
fof(d7_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k4_topdim_1(A) = k2_topdim_1(A,k2_struct_0(A)) ) )).
fof(d7_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_topgen_1(B,A) <=> r1_tarski(B,k2_topgen_1(A,B)) ) ) ) )).
fof(d7_topgen_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_pre_topc(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ( C = k6_topgen_3(A,B) <=> ( u1_struct_0(C) = A & ! [D] : ( 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))) ) ) ) ) )).
fof(d7_topgen_4,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_topgen_4(B,A) <=> ? [C] : ( 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) ) ) ) ) )).
fof(d7_topgrp_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(d7_topmetr,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k4_topmetr(A,B) = k3_pcomps_1(k2_topmetr(A,B)) ) ) )).
fof(d7_topreal1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v3_topreal1(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(d7_toprealb,axiom,( ! [A] : ( v7_ordinal1(A) => k8_toprealb(A) = k7_toprealb(A,k4_struct_0(k15_euclid(A)),1) ) )).
fof(d7_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ( v2_toprns_1(B,A) <=> ? [C] : ( v1_xreal_0(C) & ! [D] : ( v7_ordinal1(D) => ~ r1_xxreal_0(C,k12_euclid(k9_nat_1(u1_struct_0(k15_euclid(A)),B,D))) ) ) ) ) ) )).
fof(d7_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)) ) ) ) )).
fof(d7_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(d7_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_2(B,A) => ( v2_trees_2(B,A) <=> ( ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( r2_hidden(C,B) => r1_tarski(k1_trees_1(C),B) ) ) & ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ~ ( r2_hidden(C,A) & ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( r2_hidden(D,B) => r2_xboole_0(D,C) ) ) ) ) ) ) ) ) )).
fof(d7_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_trees_3(B,A) => ( B = k4_trees_3(A) <=> ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,A) & v1_funct_1(C) & v3_trees_2(C) ) => r2_hidden(C,B) ) ) ) ) )).
fof(d7_trees_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ! [C] : ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_trees_2(D) ) => ( D = k9_trees_4(A,B,C) <=> ( ! [E] : ( ( 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] : ( m1_trees_1(F,k9_xtuple_0(A)) => ! [G] : ( 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(k4_ordinal1,F,G) ) ) ) ) ) ) & ! [E] : ( 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] : ( m1_trees_1(E,k9_xtuple_0(A)) => ! [F] : ( 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(k4_ordinal1,E,F)) = k1_funct_1(B,F) ) ) ) ) ) ) ) ) )).
fof(d7_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => k3_trees_9(A) = a_1_0_trees_9(A) ) )).
fof(d7_tsep_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_pre_topc(C,A) => ( r4_tsep_1(A,B,C) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d7_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v2_tsp_2(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = u1_struct_0(B) => v1_tsp_2(C,A) ) ) ) ) ) )).
fof(d7_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k9_funct_2(k4_numbers,u1_turing_1(A)))) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,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(k4_ordinal1,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k9_funct_2(k4_numbers,u1_turing_1(A)))))) ) => ( C = k10_turing_1(A,B) <=> ( k9_nat_1(k3_zfmisc_1(u2_turing_1(A),k4_numbers,k9_funct_2(k4_numbers,u1_turing_1(A))),C,k5_numbers) = B & ! [D] : ( v7_ordinal1(D) => k9_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,k9_nat_1(k3_zfmisc_1(u2_turing_1(A),k4_numbers,k9_funct_2(k4_numbers,u1_turing_1(A))),C,D)) ) ) ) ) ) ) )).
fof(d7_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k1_funct_1(A,k10_finseq_1(B,C)) = k1_binarith(B,C) ) ) ) ) )).
fof(d7_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(d7_uproots,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & v1_uproots(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( D = k6_uproots(A,B,C) <=> ? [E] : ( ~ v1_xboole_0(E) & v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) & E = a_3_0_uproots(A,B,C) & D = k1_xxreal_2(E) ) ) ) ) ) ) )).
fof(d7_urysohn1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v7_pre_topc(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d7_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m1_valuat_1(D,A,B) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(d7_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v3_valued_0(A) <=> ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => v1_xreal_0(k1_funct_1(A,B)) ) ) ) )).
fof(d7_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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] : ( r2_hidden(C,k9_xtuple_0(B)) => k1_funct_1(B,C) = k5_xcmplx_0(k1_funct_1(A,C)) ) ) ) ) ) )).
fof(d7_vectmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_vectmetr(A,B) = k1_metric_1(A,k4_struct_0(A),B) ) ) )).
fof(d7_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ( v5_vectsp_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d7_vectsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(d7_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k3_vectsp_5(A,B)) => ! [E] : ( m1_subset_1(E,k3_vectsp_5(A,B)) => ! [F] : ( m1_vectsp_4(F,A,B) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d7_vectsp_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => ! [D] : ( m1_vectsp_6(D,A,B) => ( r1_vectsp_6(A,B,C,D) <=> ! [E] : ( 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) ) ) ) ) ) ) )).
fof(d7_vectsp_8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( ( v7_vectsp_1(F,A) & m1_vectsp_4(F,A,B) ) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d7_waybel10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( ( 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) ) ) ) ) ) )).
fof(d7_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_waybel11(A,B,C) <=> r3_orders_2(A,C,k1_waybel11(A,B)) ) ) ) ) )).
fof(d7_waybel18,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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 ) ) ) )).
fof(d7_waybel23,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v3_waybel_3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( m1_waybel23(B,A) <=> ( v2_waybel23(B,A) & ! [C] : ( 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)) ) ) ) ) ) )).
fof(d7_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( ( 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] : ( 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] : ( m1_subset_1(C,u1_struct_0(k5_waybel34(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_waybel34(A))) => ( k1_altcat_1(k5_waybel34(A),C,D) != k1_xboole_0 => ! [E] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d7_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => k1_waybel_0(A,B) = u1_waybel_0(A,B) ) ) )).
fof(d7_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(d7_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ( v2_waybel_2(A) <=> ( v24_waybel_0(A) & v1_waybel_2(A) ) ) ) )).
fof(d7_waybel_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( B = k4_waybel_6(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) <=> v5_waybel_6(C,A) ) ) ) ) ) )).
fof(d7_waybel_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ( v5_waybel_7(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d7_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( v6_waybel_0(D,A) & l1_waybel_0(D,A) ) => ( D = k4_waybel_9(A,B,C) <=> ( ! [E] : ( r2_hidden(E,u1_struct_0(D)) <=> ? [F] : ( 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)) ) ) ) ) ) ) )).
fof(d7_weddwitt,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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)))) ) ) ) ) ) )).
fof(d7_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [C] : ( 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)) ) ) ) )).
fof(d7_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( ( 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] : ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d7_xboole_0,axiom,( ! [A] : ! [B] : ( r1_xboole_0(A,B) <=> k3_xboole_0(A,B) = k1_xboole_0 ) )).
fof(d7_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k6_xboolean(A,B) = k5_xboolean(k3_xboolean(A),B) ) ) )).
fof(d7_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k6_xcmplx_0(A,B) = k2_xcmplx_0(A,k4_xcmplx_0(B)) ) ) )).
fof(d7_xtuple_0,axiom,( ! [A] : k5_xtuple_0(A) = k2_xtuple_0(k1_xtuple_0(A)) )).
fof(d7_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ( v3_xxreal_0(A) <=> ~ r1_xxreal_0(k5_numbers,A) ) ) )).
fof(d7_xxreal_2,axiom,( ! [A] : ( ( v2_membered(A) & v1_xxreal_2(A) ) => ! [B] : ( v1_xxreal_0(B) => ( B = k2_xxreal_2(A) <=> ( r2_hidden(B,A) & ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(C,A) => r1_xxreal_0(B,C) ) ) ) ) ) ) )).
fof(d7_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k6_xxreal_3(A,B) = k4_xxreal_3(A,k5_xxreal_3(B)) ) ) )).
fof(d7_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( r6_yellow16(A,B,C) <=> ( r2_yellow_0(B,C) => r2_hidden(k2_yellow_0(B,C),u1_struct_0(A)) ) ) ) ) )).
fof(d7_yellow21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & v2_yellow21(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_altcat_1(A,B,C) != k1_xboole_0 => ! [D] : ( m1_subset_1(D,k1_altcat_1(A,B,C)) => k5_yellow21(A,B,C,D) = D ) ) ) ) ) )).
fof(d7_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( r1_yellow_0(A,B) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r2_lattice3(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_lattice3(A,B,D) => r1_orders_2(A,C,D) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_lattice3(A,B,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_lattice3(A,B,E) => r1_orders_2(A,D,E) ) ) ) => D = C ) ) ) ) ) )).
fof(d7_yellow_6,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_waybel_0(B,A) => ! [C] : ( m1_yellow_6(C,A,B) => ( v2_yellow_6(C,A,B) <=> ( v4_yellow_0(C,B) & m1_yellow_0(C,B) ) ) ) ) ) )).
fof(d7_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ( v3_zf_fund1(B,A) <=> ! [C] : ( m1_subset_1(C,A) => ( r2_hidden(C,B) => r2_hidden(k3_classes2(A,C),B) ) ) ) ) ) )).
fof(d7_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => k8_zf_lang(A,B) = k8_finseq_1(k4_ordinal1,k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,4),k3_zf_lang(A)),B) ) ) )).
fof(d7_zf_model,axiom,( k7_zf_model = k14_zf_lang(k2_zf_lang(k5_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(k5_numbers)),k4_zf_lang(k2_zf_lang(3),k2_zf_lang(1))))))) )).
fof(d7_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( 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 ) ) )).
fof(d7_zmodul01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_zmodul01(A) ) => ( v6_zmodul01(A) <=> ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( k1_zmodul01(A,C,B) = k4_struct_0(A) & B != k5_numbers & C != k4_struct_0(A) ) ) ) ) ) )).
fof(d7_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(k6_zmodul02(A,B),k6_zmodul02(A,B)),k6_zmodul02(A,B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k6_zmodul02(A,B),k6_zmodul02(A,B)),k6_zmodul02(A,B)))) ) => ( C = k7_zmodul02(A,B) <=> ! [D] : ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k6_zmodul02(A,B)) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(u1_struct_0(A)),k6_zmodul02(A,B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( D = k5_zmodul01(A,F,B) & E = k5_zmodul01(A,G,B) ) => k5_binop_1(k6_zmodul02(A,B),C,D,E) = k5_zmodul01(A,k3_rlvect_1(A,F,G),B) ) ) ) ) ) ) ) ) ) )).
fof(d8_abcmiz_0,axiom,( ! [A] : ( l2_abcmiz_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_abcmiz_0(A,B) = k1_funct_1(u3_abcmiz_0(A),B) ) ) )).
fof(d8_abcmiz_1,axiom,( k10_abcmiz_1 = 1 )).
fof(d8_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(d8_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v8_aff_2(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d8_aff_3,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v8_aff_3(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ! [L] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d8_afinsq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ( v5_relat_1(B,A) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ( ( ( v1_setwiseo(C,A) & k1_afinsq_1(B) = k5_numbers ) => ( D = k6_afinsq_2(A,B,C) <=> D = k4_binop_1(A,C) ) ) & ( ~ ( v1_setwiseo(C,A) & k1_afinsq_1(B) = k5_numbers ) => ( D = k6_afinsq_2(A,B,C) <=> ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) & k3_funct_2(k4_ordinal1,A,E,k5_numbers) = k1_funct_1(B,k5_numbers) & ! [F] : ( v7_ordinal1(F) => ( ~ r1_xxreal_0(k1_afinsq_1(B),k1_nat_1(F,1)) => k3_funct_2(k4_ordinal1,A,E,k1_nat_1(F,1)) = k1_binop_1(C,k9_nat_1(A,E,F),k1_funct_1(B,k1_nat_1(F,1))) ) ) & D = k1_funct_1(E,k6_xcmplx_0(k1_afinsq_1(B),1)) ) ) ) ) ) ) ) ) ) ) )).
fof(d8_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => k8_afproj(A) = k8_eqrel_1(k2_afproj(A),k4_afproj(A)) ) )).
fof(d8_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_afvect0(A,B) = g2_algstr_0(u1_struct_0(A),k3_afvect0(A,B),B) ) ) )).
fof(d8_algstr_1,axiom,( k3_algstr_1 = g5_algstr_0(k1_numbers,k11_binop_2,k10_subset_1(k5_numbers,k1_numbers),k10_subset_1(1,k1_numbers)) )).
fof(d8_algstr_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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] : ! [F] : ( 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) ) ) ) ) ) )).
fof(d8_altcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(E,k1_altcat_1(A,B,C)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d8_altcat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_altcat_1(A,B,C)) => ( v5_altcat_3(D,A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k1_altcat_1(A,C,E) != k1_xboole_0 => ! [F] : ( m1_subset_1(F,k1_altcat_1(A,C,E)) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(d8_altcat_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ( v4_altcat_5(A) <=> ! [B] : ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_altcat_5(E,A,D,B,C) & v2_altcat_5(E,A,B,C,D) & v3_altcat_5(E,A,B,C,D) ) ) ) ) ) )).
fof(d8_ami_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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)) ) ) )).
fof(d8_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ( v4_amistd_1(C,A,B) <=> ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(d8_analmetr,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( B != C & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_analoaf(A,B,C,B,E) & r4_analmetr(A,B,C,E,D) ) ) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r4_analmetr(A,B,C,D,E) & D != E ) ) ) ) ) ) ) )).
fof(d8_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_analort(A,B,C) = g1_analoaf(u1_struct_0(A),k4_analort(A,B,C)) ) ) ) )).
fof(d8_anproj_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_collsp(A) ) => ( v3_collsp(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d8_aofa_000,axiom,( ! [A] : ( ( v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( D = k9_aofa_000(A,B,C) <=> ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) & D = k9_nat_1(k9_setfam_1(u1_struct_0(A)),E,C) & k9_nat_1(k9_setfam_1(u1_struct_0(A)),E,k5_numbers) = B & ! [F] : ( v7_ordinal1(F) => k9_nat_1(k9_setfam_1(u1_struct_0(A)),E,k1_nat_1(F,1)) = k2_xboole_0(k9_nat_1(k9_setfam_1(u1_struct_0(A)),E,F),a_3_0_aofa_000(A,E,F)) ) ) ) ) ) ) ) )).
fof(d8_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_aofa_a01(D,A,B,C) & l4_aofa_a00(D,A,B,C) ) => ! [E] : ( ( ~ v2_struct_0(E) & v2_unialg_1(E) & v3_unialg_1(E) & v4_unialg_1(E) & v3_aofa_000(E) & v4_aofa_000(E) & v5_aofa_000(E) & v6_aofa_000(E) & ~ v10_aofa_000(E) & v11_aofa_000(E) & v12_aofa_000(E) & l3_aofa_a00(E,A,C,u4_aofa_a00(A,B,C,D)) ) => ! [F] : ( ( v3_aofa_a01(F,A,B,C,u4_aofa_a00(A,B,C,D),u8_aofa_a00(A)) & m1_msafree4(F,u1_struct_0(A),u4_aofa_a00(A,B,C,D),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),u8_aofa_a00(A))) ) => ! [G] : ( ( v19_aofa_a00(G,A) & m1_subset_1(G,u1_struct_0(A)) ) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),G)) => ! [I] : ( m1_subset_1(I,k1_funct_1(u3_msualg_1(A,C),G)) => k5_aofa_a01(A,B,C,D,E,F,G,H,I) = k12_aofa_a00(A,C,u4_aofa_a00(A,B,C,D),E,u8_aofa_a00(A),F,k33_aofa_a00(A,C,G,H,I)) ) ) ) ) ) ) ) ) ) )).
fof(d8_aofa_i00,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( v1_int_1(C) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(d8_armstrng,axiom,( ! [A] : ( l1_armstrng(A) => k5_armstrng(A) = a_1_0_armstrng(A) ) )).
fof(d8_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( 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))) ) ) ) ) )).
fof(d8_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( 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] : ( v3_ordinal1(C) & v7_ordinal1(C) & A = k4_tarski(B,C) ) ) ) ) ) ) )).
fof(d8_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r1_asympt_0(A,B) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r1_xxreal_0(C,D) => r1_xxreal_0(k9_nat_1(k1_numbers,A,D),k9_nat_1(k1_numbers,B,D)) ) ) ) ) ) ) )).
fof(d8_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => k6_bagorder(A) = k5_bagorder(A,k17_pre_poly(A)) ) )).
fof(d8_bcialg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_bcialg_1(A) ) => ( v8_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_bcialg_1(A,B) = k4_struct_0(A) ) ) ) )).
fof(d8_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v5_bcialg_2(B,A) => ! [C] : ( ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) ) => ( C = k2_bcialg_2(A,B) <=> ( k1_bcialg_2(A,k4_struct_0(A),B,C) = k4_struct_0(A) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( k1_bcialg_2(A,k4_struct_0(A),B,D) = k4_struct_0(A) => ( D = k5_numbers | r1_xxreal_0(C,D) ) ) ) ) ) ) ) ) ) )).
fof(d8_bcialg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_bcialg_4(A) ) => ! [B] : ( 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)) ) ) )).
fof(d8_bcialg_6,axiom,( ! [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] : ( ( ~ 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] : ( ( 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) ) ) ) )).
fof(d8_bciideal,axiom,( ! [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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d8_bhsp_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v3_bhsp_4(A) <=> ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(C,D) & r1_xxreal_0(C,E) & r1_xxreal_0(B,k9_complex1(k5_real_1(k9_nat_1(k1_numbers,A,D),k9_nat_1(k1_numbers,A,E)))) ) ) ) ) ) ) ) )).
fof(d8_bhsp_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( m1_bhsp_5(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => ( C = D | k2_bhsp_1(A,C,D) = k5_numbers ) ) ) ) ) ) ) )).
fof(d8_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d8_binop_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) & r3_binop_1(A,C,B) ) => ! [C] : ( m1_subset_1(C,A) => ( C = k4_binop_1(A,B) <=> r3_binop_1(A,C,B) ) ) ) ) )).
fof(d8_bor_cant,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k8_bor_cant(A,B,C) = k2_prob_2(A,B,k7_bor_cant(A,C)) ) ) ) )).
fof(d8_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(d8_borsuk_6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))) => ( A = k6_borsuk_6 <=> ! [B] : ( r2_hidden(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k5_topmetr)) & ? [D] : ( m1_subset_1(D,u1_struct_0(k5_topmetr)) & B = k4_borsuk_1(k5_topmetr,k5_topmetr,C,D) & r1_xxreal_0(D,k6_xcmplx_0(1,k3_xcmplx_0(2,C))) ) ) ) ) ) )).
fof(d8_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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] : ( 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(k19_sin_cos(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A),C)),k17_sin_cos(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A),C)),k5_numbers) ) ) ) ) )).
fof(d8_bspace,axiom,( ! [A] : k8_bspace(A) = a_1_0_bspace(A) )).
fof(d8_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d8_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ( r3_bvfunc_2(A,B,C,D) <=> r2_bvfunc_1(A,B,k5_bvfunc_2(A,D,C)) ) ) ) ) ) )).
fof(d8_c0sp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l5_algstr_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(d8_c0sp2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d8_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k2_zfmisc_1(k4_calcul_1(A),k2_cqc_the1)) => ( v1_calcul_1(B,A) <=> ( B != k1_xboole_0 & ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(B)) ) => r3_calcul_1(A,B,C) ) ) ) ) ) ) )).
fof(d8_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) ) => k7_card_3(A) = k1_card_1(k4_card_3(A)) ) )).
fof(d8_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_card_fil(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k2_card_fil(A,B,C) = a_3_0_card_fil(A,B,C) ) ) ) )).
fof(d8_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( r4_card_lar(A,B) <=> ( r1_tarski(B,A) & ! [C] : ( 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)) ) ) ) ) ) )).
fof(d8_cat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_cat_1(A) ) => ( v6_cat_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_cat_1(C,A,B,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( k2_cat_1(A,B,D) != k1_xboole_0 => ! [E] : ( m1_cat_1(E,A,B,D) => k1_cat_1(A,C,E) = E ) ) & ( k2_cat_1(A,D,B) != k1_xboole_0 => ! [E] : ( m1_cat_1(E,A,D,B) => k1_cat_1(A,E,C) = E ) ) ) ) ) ) ) ) )).
fof(d8_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,k6_cat_2(A,B),C) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k10_cat_2(A,B,C,D,E) = k1_funct_1(k1_funct_5(D),k4_cat_1(A,E)) ) ) ) ) ) )).
fof(d8_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_cat_1(E,A,C,B) & k5_cat_1(A,C,B,C,E,D) = k4_cat_1(A,C) ) ) ) ) ) ) ) )).
fof(d8_cat_4,axiom,( ! [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) & l1_cat_4(A) ) => ( v3_cat_4(A) <=> ( v10_cat_1(u1_cat_4(A),A) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(d8_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ( v4_cat_5(A) <=> ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,B,C) => m1_subset_1(k4_tarski(k4_tarski(B,C),D),u4_struct_0(A)) ) ) ) ) ) ) )).
fof(d8_catalg_1,axiom,( ! [A] : k5_catalg_1(A) = k4_tarski(1,k9_finseq_1(A)) )).
fof(d8_cayldick,axiom,( k3_cayldick = g1_cayldick(k1_numbers,k11_binop_2,k9_binop_2,k11_binop_2,k10_subset_1(1,k1_numbers),k10_subset_1(k5_numbers,k1_numbers),k2_euclid,k6_partfun1(k1_numbers)) )).
fof(d8_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) )).
fof(d8_cc0sp2,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(d8_cfdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ( v4_cfdiff_1(A) <=> ! [B] : ( v1_xcmplx_0(B) => ( r2_hidden(B,k1_relset_1(k2_numbers,A)) => r1_cfdiff_1(A,B) ) ) ) ) )).
fof(d8_cfuncdom,axiom,( ! [A] : ( ~ 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)) ) )).
fof(d8_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => k8_cgames_1(A) = k2_xboole_0(k6_cgames_1(A),k7_cgames_1(A)) ) )).
fof(d8_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_chain_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k5_chain_1(A,B,C) = k1_xboole_0 ) ) ) )).
fof(d8_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ~ ( B != C & ~ r1_chord(A,B,C) & ~ ! [D] : ( 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] : ( 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] : ( m3_glib_001(F,E) => ~ r1_glib_001(E,B,C,F) ) ) ) ) ) ) ) ) ) )).
fof(d8_circcmb3,axiom,( ! [A] : ( ( v4_circcmb3(A) & l1_msualg_1(A) ) => k3_circcmb3(A) = k3_tarski(u4_struct_0(A)) ) )).
fof(d8_circcomb,axiom,( ! [A] : ( l1_msualg_1(A) => ( v2_circcomb(A) <=> ! [B] : ( r2_hidden(B,u4_struct_0(A)) => B = k4_tarski(k1_funct_1(u1_msualg_1(A),B),k2_xtuple_0(B)) ) ) ) )).
fof(d8_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m3_msaterm(C,A,B) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( m1_subset_1(E,k4_card_3(u3_msualg_1(k1_circtrm1(A,B,C),k6_circtrm1(A,B,C,D)))) => ! [F] : ( m2_pboole(F,u1_struct_0(A),B,u3_msualg_1(A,D)) => ( m1_circtrm1(F,A,B,C,D,E) <=> ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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))) ) ) ) ) ) ) ) ) ) ) )).
fof(d8_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_pboole(C,k2_msafree2(A),k7_funcop_1(k2_msafree2(A),k4_ordinal1),k5_relat_1(u3_msualg_1(A,B),k2_msafree2(A))) => ! [D] : ( 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,k5_numbers)),k1_circuit1(A,B)) ) ) ) ) )).
fof(d8_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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))) ) ) )).
fof(d8_clopban2,axiom,( ! [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) & 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)) ) )).
fof(d8_clopban3,axiom,( ! [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) & l1_clopban2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => k6_clopban3(A,B,C) = k1_normsp_0(A,k5_clopban3(A,B),C) ) ) ) )).
fof(d8_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) => ( v5_closure2(C,A,B) <=> r2_hidden(B,C) ) ) ) )).
fof(d8_clvect_1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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))) ) ) ) ) )).
fof(d8_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v2_clvect_2(B,A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & ? [F] : ( v7_ordinal1(F) & 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))) ) ) ) ) ) ) ) ) )).
fof(d8_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k6_clvect_3(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k1_normsp_0(A,D,E) = k1_clvect_1(A,k1_normsp_0(A,B,E),k9_nat_1(k2_numbers,C,E)) ) ) ) ) ) ) )).
fof(d8_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_coh_sp(A)) => k7_coh_sp(A,B) = k2_xtuple_0(k1_xtuple_0(B)) ) )).
fof(d8_cohsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_cohsp_1(A,B,C) <=> r1_cohsp_1(A,k2_tarski(B,C)) ) )).
fof(d8_combgras,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( l1_incsp_1(B) => ! [C] : ( l1_combgras(C,A,B) => ( v6_combgras(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(d8_compact1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(d8_compl_sp,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ( v7_compl_sp(B,A) <=> ! [C] : ( v7_ordinal1(C) => v3_compl_sp(k9_nat_1(k9_setfam_1(u1_struct_0(A)),B,C),A) ) ) ) ) )).
fof(d8_compos_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_compos_0(A) & v2_compos_0(A) & v3_compos_0(A) ) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d8_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => k4_compos_1(A) = k3_afinsq_1(k2_compos_1(A)) ) )).
fof(d8_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k5_comput_1(A,B) = k12_card_3(k2_finseq_2(A,k4_ordinal1),B) ) ) )).
fof(d8_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_comseq_3(A) <=> v2_comseq_2(k10_comseq_3(A)) ) ) )).
fof(d8_conlat_1,axiom,( ! [A] : ( l5_struct_0(A) => ! [B] : ( 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)) ) ) ) ) )).
fof(d8_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( l2_conlat_1(B,A) => ! [C] : ( ( v3_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) ) ) ) ) ) )).
fof(d8_conmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v8_conmetr(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d8_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_convex4(B,A) => ! [C] : ( m1_convex4(C,A) => ! [D] : ( m1_convex4(D,A) => ( D = k5_convex4(A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k2_numbers,D,E) = k2_xcmplx_0(k3_funct_2(u1_struct_0(A),k2_numbers,B,E),k3_funct_2(u1_struct_0(A),k2_numbers,C,E)) ) ) ) ) ) ) )).
fof(d8_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m1_subset_1(C,k1_qc_lang1(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(d8_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( r3_cqc_the1(A,B,C) <=> r2_hidden(C,k1_cqc_the1(A,B)) ) ) ) ) )).
fof(d8_csspace,axiom,( ! [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) ) => ! [B] : ( 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) ) ) ) )).
fof(d8_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( 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) ) ) ) )).
fof(d8_decomp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)))) ) ) )).
fof(d8_dickson,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( C = k6_dickson(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( 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) ) ) ) ) ) ) )).
fof(d8_diff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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,k5_numbers),A) & ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d8_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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)) ) ) )).
fof(d8_dirort,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dirort(A) & l1_analoaf(A) ) => ( v6_dirort(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,E) => r2_analoaf(A,D,E,B,C) ) ) ) ) ) ) ) )).
fof(d8_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( ( v1_matrprob(B) & m2_finseq_1(B,k1_numbers) ) => ( ? [C] : ( m2_finseq_1(C,A) & k4_dist_1(A,C) = B ) => ! [C] : ( 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 ) ) ) ) ) )).
fof(d8_dtconstr,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_dtconstr(k5_dtconstr),k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k5_dtconstr),k4_ordinal1))) ) => ( A = k12_dtconstr <=> ( ! [B] : ( 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)) = k5_numbers ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(k5_dtconstr)) => ! [C] : ( 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),k4_ordinal1,C,A)) ) ) ) ) ) ) )).
fof(d8_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( ( 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] : ( 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)))) ) ) ) ) ) ) )).
fof(d8_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(d8_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) ) )).
fof(d8_entropy1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( v2_matrprob(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( B = k5_entropy1(A) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & k1_matrix_0(B) = k1_matrix_0(A) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => k1_matrprob(k1_numbers,B,C) = k14_rvsum_1(k7_matrix_0(k1_numbers,A,C),k3_entropy1(2,k7_matrix_0(k1_numbers,A,C))) ) ) ) ) ) ) ) )).
fof(d8_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ( K = k8_enumset1(A,B,C,D,E,F,G,H,I,J) <=> ! [L] : ( r2_hidden(L,K) <=> ~ ( L != A & L != B & L != C & L != D & L != E & L != F & L != G & L != H & L != I & L != J ) ) ) )).
fof(d8_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_eqrel_1(B,A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(k9_setfam_1(A)))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_eqrel_1(C,A) ) => ( C = k12_eqrel_1(A,B) <=> ! [D] : ( m1_subset_1(D,A) => k11_eqrel_1(A,D,C) = k1_setfam_1(a_3_0_eqrel_1(A,B,D)) ) ) ) ) ) )).
fof(d8_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(d8_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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) ) ) ) ) )).
fof(d8_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ( v6_euclid_7(B,A) <=> ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m1_subset_1(E,k1_numbers) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d8_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ( r6_euclidlp(A,B,C) <=> ? [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) & ? [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) & ? [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(A)) & ? [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d8_extpro_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) ) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(d8_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( r1_facirc_1(A,B,C,D) <=> ! [E] : ( v7_ordinal1(E) => k1_funct_1(k5_facirc_1(A,B,C,E),D) = k1_funct_1(C,D) ) ) ) ) ) )).
fof(d8_fdiff_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(d8_ff_siec,axiom,( ! [A] : ( ( 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))) ) )).
fof(d8_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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) ) ) ) )).
fof(d8_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => k8_filter_1(A) = a_1_0_filter_1(A) ) )).
fof(d8_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(d8_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k8_fin_topo(A,B) = a_2_1_fin_topo(A,B) ) ) )).
fof(d8_finseq_1,axiom,( ! [A] : ! [B] : ( ( 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 ) ) ) )).
fof(d8_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k8_finseq_4(A,B,C,D,E) = k7_finseq_1(k11_finseq_1(A,B,C),k10_finseq_1(D,E)) )).
fof(d8_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r3_finseq_8(A,B,C) <=> ( ~ r1_xxreal_0(k3_finseq_1(B),k5_numbers) => ( r1_xxreal_0(1,k3_finseq_1(C)) & k3_finseq_6(A,C,1,k3_finseq_1(B)) = B ) ) ) ) ) ) )).
fof(d8_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ( v2_fintopo2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,k6_fintopo2(A,B)) => r2_hidden(B,C) ) ) ) ) ) )).
fof(d8_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(u1_struct_0(A))))) ) => ( C = k8_fintopo3(A,B) <=> ( ! [D] : ( v7_ordinal1(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( E = k1_funct_1(C,D) => k3_funct_2(k4_ordinal1,k1_zfmisc_1(u1_struct_0(A)),C,k1_nat_1(D,1)) = k1_fintopo3(A,E) ) ) ) & k3_funct_2(k4_ordinal1,k1_zfmisc_1(u1_struct_0(A)),C,k5_numbers) = B ) ) ) ) ) )).
fof(d8_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d8_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m2_subset_1(C,k3_finseq_2(A),k6_subset_1(k3_finseq_2(A),k1_tarski(k1_xboole_0))) => k5_fomodel0(A,B,C) = k4_fomodel0(A,B,C) ) ) ) )).
fof(d8_fomodel1,axiom,( ! [A] : ( l1_fomodel1(A) => k8_fomodel1(A) = u3_struct_0(A) ) )).
fof(d8_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_fomodel2(C,A,B) ) => ! [D] : ( m2_subset_1(D,k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k35_fomodel1(A)) => ! [E] : ( m1_subset_1(E,B) => ( E = k8_fomodel2(A,B,C,D) <=> ! [F] : ( m1_subset_1(F,B) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( r2_hidden(D,k9_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(k4_ordinal1,k35_fomodel1(A),B,k9_funct_2(k35_fomodel1(A),B),k7_fomodel2(A,B,F,C),k1_nat_1(G,1)),D) ) ) ) ) ) ) ) ) ) )).
fof(d8_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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] : ( v1_relat_1(E) => k11_fomodel3(A,B,C,D,E) = a_5_0_fomodel3(A,B,C,D,E) ) ) ) ) ) )).
fof(d8_fomodel4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ! [D] : ! [E] : ( v5_fomodel4(E,A,B,C,D) <=> r2_hidden(E,k1_funct_1(k5_fomodel4(B,C,A),D)) ) ) ) ) )).
fof(d8_frechet,axiom,( ! [A] : ( ( ~ 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,k4_ordinal1),k1_tarski(k1_numbers)) & ? [B] : ( 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(k4_ordinal1,k1_numbers)) & ! [C] : ( 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) ) ) ) ) ) ) )).
fof(d8_freealg,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : k3_freealg(A,B) = g1_lang1(k2_xboole_0(k4_finseq_1(A),B),k2_freealg(A,B)) ) )).
fof(d8_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : k8_fscirc_1(A,B,C) = k2_circcomb(k8_facirc_1(A,B,C,k1_facirc_1),k4_fscirc_1(A,B,C)) )).
fof(d8_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_2(C,A,B) ) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( r3_fsm_2(A,B,C,D,E) <=> ? [F] : ( ~ v8_ordinal1(F) & m1_subset_1(F,k4_ordinal1) & ! [G] : ( m2_finseq_1(G,A) => ( k1_funct_1(G,1) = D => ( ( r1_xxreal_0(F,k1_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] : ( ( ~ v8_ordinal1(H) & m1_subset_1(H,k4_ordinal1) ) => ~ ( ~ r1_xxreal_0(F,H) & r1_xxreal_0(H,k1_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d8_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_3(C,A,B) ) => k6_fsm_3(A,B,C) = a_3_0_fsm_3(A,B,C) ) ) ) )).
fof(d8_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : 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)) )).
fof(d8_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( A = B => k14_funcop_1(A,B,C,D) = C ) & ( A != B => k14_funcop_1(A,B,C,D) = D ) ) )).
fof(d8_funcsdom,axiom,( ! [A] : 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)) )).
fof(d8_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v3_relat_1(A) <=> ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => v1_xboole_0(k1_funct_1(A,B)) ) ) ) )).
fof(d8_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,A) => k1_funct_1(C,E) = k1_funct_1(D,E) ) ) ) ) )).
fof(d8_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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] : ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(d8_funct_6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k8_funct_6(A,B) <=> ( k9_xtuple_0(C) = k9_xtuple_0(B) & ! [D] : ( r2_hidden(D,k9_xtuple_0(B)) => k1_funct_1(C,D) = k1_funct_2(A,k1_funct_1(B,D)) ) ) ) ) ) )).
fof(d8_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(B) => v1_xboole_0(A) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v1_funct_7(C) ) => ( m1_funct_7(C,A,B) <=> ( k5_funct_7(C) = A & r1_tarski(k6_funct_7(C),B) ) ) ) ) )).
fof(d8_funct_8,axiom,( ! [A] : ! [B] : ( v1_membered(B) => ! [C] : ( v1_membered(C) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(d8_functor2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ( ( r2_functor2(A,B,C,D) & r2_functor2(A,B,D,E) ) => ! [F] : ( m2_functor2(F,A,B,C,D) => ! [G] : ( m2_functor2(G,A,B,D,E) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d8_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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)) ) ) ) )).
fof(d8_fvaluat1,axiom,( ! [A] : ( l6_algstr_0(A) => ( v3_fvaluat1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k6_numbers) & v2_fvaluat1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k6_numbers))) ) => ( m1_fvaluat1(B,A) <=> ( k1_funct_1(B,k4_struct_0(A)) = k1_xxreal_0 & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C != k4_struct_0(A) => r2_hidden(k1_funct_1(B,C),k4_numbers) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_xxreal_0(k5_numbers,k1_funct_1(B,C)) => r1_xxreal_0(k5_numbers,k1_funct_1(B,k1_algstr_0(A,k5_struct_0(A),C))) ) ) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & k1_funct_1(B,C) != k5_numbers & k1_funct_1(B,C) != k1_xxreal_0 ) ) ) ) ) ) )).
fof(d8_fvsum_1,axiom,( ! [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) ) => ! [B] : ( 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)) ) ) )).
fof(d8_gate_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : 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) )).
fof(d8_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v4_vectsp_1(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(d8_geomtrap,axiom,( ! [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) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k5_binop_1(u1_struct_0(A),B,C,D) = k1_geomtrap(A,C,D) ) ) ) ) ) )).
fof(d8_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(d8_gfacirc2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d8_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) ) => k8_glib_000(A) = k1_funct_1(A,k3_glib_000) ) )).
fof(d8_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( 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) ) ) ) ) ) )).
fof(d8_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(k6_glib_000(A)))) ) => ( B = k3_glib_002(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( m1_subset_1(D,k6_glib_000(A)) & C = k1_glib_002(A,D) ) ) ) ) ) )).
fof(d8_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(d8_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( 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),o_2_0_glib_004(A,B)),k2_xcmplx_0(k1_funct_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),o_2_0_glib_004(A,B))),k1_funct_1(k5_glib_003(A),o_2_0_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(o_2_0_glib_004(A,B)))) ) ) ) ) )).
fof(d8_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( ( 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] : ( m3_glib_001(C,A) => ( r5_glib_005(A,B,C) <=> ! [D] : ( ( 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))),k5_numbers) ) ) ) ) ) ) ) ) )).
fof(d8_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => k6_goedelcp(A,B) = k3_tarski(a_2_0_goedelcp(A,B)) ) ) )).
fof(d8_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ( v3_graph_1(A) <=> ! [B] : ! [C] : ( ( 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 ) ) ) ) )).
fof(d8_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_graph_1(B,A) => ( ( k1_card_1(u1_struct_0(A)) = 1 | ( B != k1_xboole_0 & ~ r2_graph_2(A,B) ) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( C = k6_graph_2(A,B) <=> r1_graph_2(A,C,B) ) ) ) ) ) )).
fof(d8_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_finseq_2(B,u4_struct_0(A)) => ( B = k9_graph_3(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( v2_funct_1(C) & v1_msscyc_1(C,A) & m2_graph_1(C,A) ) ) ) ) ) )).
fof(d8_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k4_graph_5(A,B,C) = a_3_1_graph_5(A,B,C) ) ) ) )).
fof(d8_graphsp,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers)) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k12_graphsp(A,B) = a_2_1_graphsp(A,B) ) ) )).
fof(d8_grcat_1,axiom,( ! [A] : ( l1_grcat_1(A) => k8_grcat_1(A) = u2_grcat_1(A) ) )).
fof(d8_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ! [F] : ( m2_ideal_1(F,k12_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)) ) ) ) ) ) ) ) )).
fof(d8_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( r1_xxreal_0(k5_numbers,B) => k5_group_1(A,B,C) = k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k4_group_1(A),C,k1_int_2(B)) ) & ( ~ r1_xxreal_0(k5_numbers,B) => k5_group_1(A,B,C) = k2_group_1(A,k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k4_group_1(A),C,k1_int_2(B))) ) ) ) ) ) )).
fof(d8_group_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d8_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) )).
fof(d8_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(d8_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(d8_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d8_group_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => v5_group_1(k1_group_7(A,B,C)) ) ) ) ) )).
fof(d8_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(d8_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d8_hallmar1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ( v2_relat_1(B) => ! [C] : ( m2_hallmar1(C,A,B) => ( m4_hallmar1(C,A,B) <=> ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k4_finseq_1(B)) => k1_card_1(k1_funct_1(C,D)) = 1 ) ) ) ) ) ) ) )).
fof(d8_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,k1_complfld) ) => ! [C] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(d8_heyting1,axiom,( ! [A] : ! [B] : ( ( 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] : ( 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))) ) ) ) )).
fof(d8_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(d8_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => k3_hilbert1(A,B) = k7_finseq_1(k7_finseq_1(k12_finseq_1(k4_ordinal1,1),A),B) ) ) )).
fof(d8_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( v3_hilbert2(A) <=> ? [B] : ( m1_subset_1(B,k4_ordinal1) & A = k1_hilbert2(B) ) ) ) )).
fof(d8_hilbert3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( v2_hilbert3(A) <=> ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( m1_hilbert3(C,B) => ? [D] : r1_abian(D,k5_hilbert3(B,C,A)) ) ) ) ) )).
fof(d8_hurwitz,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(A,k1_complfld) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => ( v1_hurwitz(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ~ ( r1_polynom5(k1_complfld,A,B) & r1_xxreal_0(k5_numbers,k3_complex1(B)) ) ) ) ) )).
fof(d8_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( B = k5_series_1(2,A) => k8_idea_1(A,B) = k5_numbers ) & ( B != k5_series_1(2,A) => k8_idea_1(A,B) = B ) ) ) ) )).
fof(d8_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( m1_ideal_1(C,A,B) <=> ! [D] : ~ ( r2_hidden(D,k1_relset_1(k4_ordinal1,C)) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d8_incproj,axiom,( ! [A] : ( l1_incsp_1(A) => ( v4_incproj(A) <=> ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u1_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u1_incsp_1(A)) => ! [H] : ( m1_subset_1(H,u2_incsp_1(A)) => ! [I] : ( m1_subset_1(I,u2_incsp_1(A)) => ! [J] : ( m1_subset_1(J,u2_incsp_1(A)) => ! [K] : ( 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] : ( m1_subset_1(L,u1_incsp_1(A)) => ~ ( r1_incsp_1(A,L,J) & r1_incsp_1(A,L,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d8_incsp_1,axiom,( ! [A] : ( l1_incsp_1(A) => ( v5_incsp_1(A) <=> ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ? [C] : ( m1_subset_1(C,u1_incsp_1(A)) & ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & C != D & r4_incsp_1(A,k7_domain_1(u1_incsp_1(A),C,D),B) ) ) ) ) ) )).
fof(d8_index_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( ( 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))) ) ) ) ) ) ) )).
fof(d8_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => k3_int_1(A) = k6_xcmplx_0(A,k1_int_1(A)) ) )).
fof(d8_int_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ( v1_int_3(A) <=> ? [B] : ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_ordinal1))) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( D != k4_struct_0(A) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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),k4_ordinal1,B,D),k3_funct_2(u1_struct_0(A),k4_ordinal1,B,F)) ) ) ) ) ) ) ) ) ) ) )).
fof(d8_integr10,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r4_integr10(A,B) => ! [C] : ( v1_xreal_0(C) => ( C = k4_integr10(A,B) <=> ? [D] : ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,k1_relset_1(k1_numbers,D)) => k1_funct_1(D,E) = k4_integra5(E,B,A) ) ) & v6_limfunc1(D) & C = k5_limfunc1(D) ) ) ) ) ) ) )).
fof(d8_integr15,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_integra1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(B)))) ) => ! [E] : ( m4_integr15(E,A,B,C,D) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,u1_struct_0(k4_real_ns1(A))) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k4_real_ns1(A))))) ) => ( F = k6_integr15(A,B,C,D,E) <=> ! [G] : ( m1_subset_1(G,k4_ordinal1) => 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)) ) ) ) ) ) ) ) ) )).
fof(d8_integr16,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k2_numbers))) ) => k7_integr16(A,B) = k2_xcmplx_0(k2_integra5(A,k5_comseq_3(k1_numbers,B)),k3_xcmplx_0(k2_integra5(A,k6_comseq_3(k1_numbers,B)),k7_complex1)) ) ) )).
fof(d8_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ( D = k5_integr18(A,B,C) <=> ? [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d8_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( m1_integra1(C,A) => k7_integra1(A,B,C) = k18_rvsum_1(k5_integra1(A,B,C)) ) ) ) )).
fof(d8_interva1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v1_interva1(B,A) <=> ? [C] : ? [D] : ( r2_hidden(C,B) & r2_hidden(D,B) & ! [E] : ( r2_hidden(E,B) <=> ( r1_tarski(C,E) & r1_tarski(E,D) ) ) ) ) ) )).
fof(d8_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,B,C) => ! [E] : ( m2_cat_1(E,B,C) => ( r2_nattra_1(B,C,D,E) => ! [F] : ( m2_cat_1(F,A,B) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d8_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,k6_cat_2(B,C)) => k10_isocat_2(A,B,C,D) = k9_cat_1(A,k6_cat_2(B,C),C,D,k13_cat_2(B,C)) ) ) ) ) )).
fof(d8_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(d8_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k8_jgraph_6(A,B,C) = a_3_3_jgraph_6(A,B,C) ) ) ) )).
fof(d8_jordan,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( ( v1_xreal_0(D) & v2_xxreal_0(D) ) => ( r2_hidden(C,k1_topreal9(A,B,D)) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k7_toprealb(A,B,D))) => ? [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d8_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( B = k8_jordan5d(A) <=> ( r2_hidden(k4_tarski(B,k1_matrix_0(k2_goboard2(A))),k2_matrix_0(k2_goboard2(A))) & k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),B,k1_matrix_0(k2_goboard2(A))) = k21_pscomp_1(k3_topreal1(2,A)) ) ) ) ) )).
fof(d8_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal2(A) => ! [B] : ( ( ~ 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] : ( ~ 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(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)),2)),k18_pscomp_1(A),k22_pscomp_1(A))),k18_euclid(k2_jordan5c(C,k6_jordan6(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)),2)),k22_pscomp_1(A),k18_pscomp_1(A)))) ) ) ) ) ) ) )).
fof(d8_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_knaster(B,A) & v3_knaster(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v2_struct_0(C) & v3_lattices(C) & v10_lattices(C) & l3_lattices(C) ) => ( C = k7_knaster(A,B) <=> ( u1_struct_0(C) = B & ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d8_kolmog01,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(d8_lang1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) ) )).
fof(d8_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ! [E] : ( m2_finseq_1(E,u1_struct_0(C)) => ( E = k9_laplace(A,B,C,D) <=> ( k3_finseq_1(E) = A & ! [F] : ( v7_ordinal1(F) => ( r2_hidden(F,k4_finseq_1(E)) => k1_funct_1(E,F) = k8_group_1(C,k3_matrix_0(u1_struct_0(C),D,F,B),k6_laplace(F,B,A,C,D)) ) ) ) ) ) ) ) ) ) )).
fof(d8_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_lattice3(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => r1_orders_2(A,C,D) ) ) ) ) ) )).
fof(d8_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( 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)) ) ) )).
fof(d8_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ? [F] : ( 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] : ( m1_subset_1(G,A) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d8_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v3_lattice6(B,A) <=> k3_lattice6(A,B) != B ) ) ) )).
fof(d8_lattice7,axiom,( ! [A] : ( m2_lattice7(A) <=> r1_cohsp_1(A,A) ) )).
fof(d8_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(d8_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( v8_lattices(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_lattices(A,k2_lattices(A,B,C),C) = C ) ) ) ) )).
fof(d8_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_lexbfs(B,A) => ( v4_lexbfs(B,A) <=> ( k5_lexbfs(A,B,k5_numbers) = k1_xboole_0 & v2_lexbfs(B) & v13_glib_000(B) & k39_glib_000(B) = k15_glib_000(A) & ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(k39_glib_000(B),C) & ! [D] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(d8_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ~ ( k8_lfuzzy_0(A,A,B,C,D) != k5_numbers & k8_lfuzzy_0(A,A,B,D,C) != k5_numbers & C != D ) ) ) ) ) ) )).
fof(d8_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v5_limfunc1(A) <=> ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,B) & r2_hidden(C,k1_relset_1(k1_numbers,A)) ) ) & ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_limfunc1(B) & r1_tarski(k10_xtuple_0(B),k1_relset_1(k1_numbers,A)) ) => v2_limfunc1(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,B,A)) ) ) ) ) ) )).
fof(d8_limfunc2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r4_limfunc2(A,B) => ! [C] : ( v1_xreal_0(C) => ( C = k2_limfunc2(A,B) <=> ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(D) & k1_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(k4_ordinal1,k1_numbers,k1_numbers,D,A)) & k1_seq_2(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,D,A)) = C ) ) ) ) ) ) ) ) )).
fof(d8_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) & r1_xxreal_0(k5_numbers,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => r1_xxreal_0(k2_normsp_0(B,k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)),k3_xcmplx_0(D,k2_normsp_0(A,E))) ) ) ) ) ) ) )).
fof(d8_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => k9_lopban_2(A) = g1_lopban_2(k10_lopban_1(A,A),k5_lopban_2(A),k7_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),k8_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),k6_lopban_2(A),k9_rsspace(k8_lopban_1(A,A),k10_lopban_1(A,A)),k15_lopban_1(A,A)) ) )).
fof(d8_lopban_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v4_vectsp_1(A) & l4_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v25_algstr_0(B,A) => ! [C] : ( 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) ) ) ) ) ) ) )).
fof(d8_lopban_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( E = k7_lopban_4(A,B,C,D) <=> ! [F] : ( v7_ordinal1(F) => ( ( r1_xxreal_0(F,A) => k9_nat_1(u1_struct_0(B),E,F) = k6_algstr_0(B,k9_nat_1(u1_struct_0(B),k1_lopban_4(B,C),F),k9_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) => k9_nat_1(u1_struct_0(B),E,F) = k4_struct_0(B) ) ) ) ) ) ) ) ) ) )).
fof(d8_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(d8_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k12_lpspacc1(A) = g1_clvect_1(k3_rfunct_3(A,k2_numbers),k10_lpspacc1(A),k9_lpspacc1(A),k8_lpspacc1(A)) ) )).
fof(d8_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => k9_lpspace1(A,B,C) = a_3_0_lpspace1(A,B,C) ) ) ) )).
fof(d8_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v2_xxreal_0(D) & v1_xreal_0(D) ) => ! [E] : ( ( 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] : ( m2_subset_1(F,k1_zfmisc_1(k1_lpspace2(A,B,C,D)),k6_lpspace2(A,B,C,D)) => ! [G] : ( m2_subset_1(G,k1_zfmisc_1(k1_lpspace2(A,B,C,D)),k6_lpspace2(A,B,C,D)) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d8_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => k8_ltlaxio1(A,B) = k5_ltlaxio1(B,k4_ltlaxio1(A,k4_hilbert1(A,B))) ) ) )).
fof(d8_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => k10_ltlaxio3(A) = k4_subset_1(k1_hilbert1,k2_relset_1(k1_hilbert1,k8_ltlaxio3(A)),k2_relset_1(k1_hilbert1,k9_ltlaxio3(A))) ) )).
fof(d8_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => k7_ltlaxio4(A) = a_1_4_ltlaxio4(A) ) )).
fof(d8_mathmorp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(d8_matrix16,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( v4_matrix16(B,A) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,A,k3_finseq_1(B),k3_finseq_1(B)) & m2_finseq_1(C,k3_finseq_2(A)) ) => ( C = k2_matrix16(A,B) <=> r2_matrix16(A,C,B) ) ) ) ) ) )).
fof(d8_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,A) => ( D = k6_matrix_0(A,B,C) <=> ( k3_finseq_1(D) = k3_finseq_1(B) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(B)) => k1_funct_1(D,E) = k3_matrix_0(A,B,E,C) ) ) ) ) ) ) ) ) )).
fof(d8_matrix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m2_finseq_1(C,u1_struct_0(k4_matrix_2(A))) & k4_nat_d(k3_finseq_1(C),2) = k5_numbers & B = k3_group_4(k4_matrix_2(A),C) & ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(D,k4_finseq_1(C)) & ! [E] : ( m1_matrix_2(E,k3_matrix_2(A)) => ~ ( k1_funct_1(C,D) = E & v4_matrix_2(E,k2_matrix_2(k3_matrix_2(A))) ) ) ) ) ) ) ) ) )).
fof(d8_matrix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k3_matrix_2(A),u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k3_matrix_2(A),u1_struct_0(B)))) ) => ( D = k11_matrix_3(A,B,C) <=> ! [E] : ( m1_matrix_2(E,k3_matrix_2(A)) => k3_funct_2(k3_matrix_2(A),u1_struct_0(B),D,E) = k5_matrix_2(B,A,k1_finsop_1(u1_struct_0(B),k10_matrix_3(A,B,C,E),u2_algstr_0(B)),E) ) ) ) ) ) ) )).
fof(d8_matrix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k8_matrix_5(A,B) = k2_matrix_5(k1_matrix_3(k1_complfld,A,B)) ) ) )).
fof(d8_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => k9_matrixc1(A) = A ) )).
fof(d8_matrixj1,axiom,( ! [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] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( ( 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] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(C)) => k14_matrixj1(u1_struct_0(A),C,D) = k3_matrix_1(A,k1_funct_1(B,D)) ) ) ) ) ) ) ) )).
fof(d8_matrixr1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k8_matrixr1(A,B) = k2_matrixr1(k1_matrix_3(k2_vectsp_1,A,B)) ) ) )).
fof(d8_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( ( 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] : ( m2_finseq_1(E,u1_struct_0(B)) => ! [F] : ( m1_matrlin(F,A,C) => ! [G] : ( ( v1_matrix_0(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] : ( v7_ordinal1(H) => ( r2_hidden(H,k9_xtuple_0(E)) => k9_pre_poly(u1_struct_0(A),k4_ordinal1,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))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d8_matroid0,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( 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) ) ) ) ) ) )).
fof(d8_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => k5_measure6(A) = k1_setfam_1(a_1_1_measure6(A)) ) )).
fof(d8_measure7,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k6_numbers)) => ( B = k8_measure7(A) <=> ! [C] : ( m1_subset_1(C,k6_numbers) => ( r2_hidden(C,B) <=> ? [D] : ( m1_measure7(D,A) & C = k6_measure7(A,D) ) ) ) ) ) ) )).
fof(d8_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k9_setfam_1(A),k6_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k6_numbers))) ) => ( D = k6_measure8(A,B,C) <=> ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => k1_mesfunc9(D,E) = k7_supinf_2(k5_measure8(A,B,C,E)) ) ) ) ) ) )).
fof(d8_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => k11_member_1(A,B) = k9_member_1(A,k5_member_1(B)) ) ) )).
fof(d8_membered,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( r1_tarski(A,B) <=> ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ) ) )).
fof(d8_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( l1_memstr_0(B,A) => ! [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)) ) => k6_memstr_0(A,B,C) = k5_relat_1(C,k8_struct_0(B)) ) ) ) )).
fof(d8_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => k8_mesfun7c(A,B) = k7_mesfunc8(A,k1_mesfun7c(A,B)) ) ) )).
fof(d8_mesfunc1,axiom,( k8_mesfunc1 = 1 )).
fof(d8_mesfunc5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v7_mesfunc5(A) <=> ? [B] : ( v1_xreal_0(B) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(D,E) & r1_xxreal_0(C,k3_extreal1(k3_xxreal_3(k9_nat_1(k6_numbers,A,E),B))) ) ) ) ) ) ) ) )).
fof(d8_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( C = k6_mesfunc8(A,B) <=> ( k1_relset_1(A,C) = k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers)) & ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(d8_metric_1,axiom,( ! [A] : ( l1_metric_1(A) => ( v8_metric_1(A) <=> v4_metric_1(u1_metric_1(A),u1_struct_0(A)) ) ) )).
fof(d8_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => k5_metric_2(A) = a_1_1_metric_2(A) ) )).
fof(d8_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => k6_midsp_1(A) = a_1_0_midsp_1(A) ) )).
fof(d8_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(d8_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_nat_1(A,2)) ) => ! [C] : ( ( v4_midsp_2(C,B) & l1_midsp_2(C,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_2(E,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(u1_midsp_2(B,C)))) => ! [F] : ( m2_finseq_2(F,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(B))) => ( F = k7_midsp_3(A,B,C,D,E) <=> ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d8_mmlquer2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : k6_mmlquer2(A,B) = k1_setfam_1(k8_relat_1(A,k1_tarski(B))) ) )).
fof(d8_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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) ) ) ) )).
fof(d8_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ 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] : ( ( 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 ) ) ) ) ) ) )).
fof(d8_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(d8_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k6_modal_1) => k10_modal_1(A) = k7_trees_2(k8_funcop_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k2_trees_1(1),k1_domain_1(k4_ordinal1,k4_ordinal1,1,k5_numbers)),k14_trees_3(k5_numbers),A) ) )).
fof(d8_modcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_modcat_1(B,A) => ! [C] : ( m4_modcat_1(C,A,k4_modcat_1(A,B)) => k5_modcat_1(A,B,C) = k2_mod_2(A,C) ) ) ) )).
fof(d8_modelc_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => k8_modelc_1(A,B) = k8_finseq_1(k4_ordinal1,k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,1),A),B) ) ) )).
fof(d8_modelc_2,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => k8_modelc_2(A,B) = k8_finseq_1(k4_ordinal1,k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,5),A),B) ) ) )).
fof(d8_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( l1_modelc_3(B,A) => ! [C] : ( l1_modelc_3(C,A) => ( r3_modelc_3(A,B,C) <=> ? [D] : ( v1_modelc_2(D) & m2_finseq_1(D,k4_ordinal1) & 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) ) ) ) ) ) )).
fof(d8_monoid_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(d8_monoid_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(d8_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(d8_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => k5_msafree2(A,B) = k11_msafree(A,u3_msualg_1(A,B)) ) ) )).
fof(d8_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m3_pboole(B,u1_struct_0(A),k4_equation(A)) => ! [C] : ( l3_msualg_1(C,A) => ( v6_msafree4(C,A,B) <=> r2_equation(A,C,B) ) ) ) ) )).
fof(d8_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(d8_msualg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( 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(k5_numbers) & u4_struct_0(B) = k4_finseq_1(k1_unialg_1(A)) & u1_msualg_1(B) = k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k3_finseq_2(k1_tarski(k5_numbers)),k1_unialg_1(A),k7_finseq_2(k5_numbers)) & u2_msualg_1(B) = k1_margrel1(k4_ordinal1,k4_finseq_1(k1_unialg_1(A)),k5_numbers) ) ) ) ) )).
fof(d8_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m3_pboole(C,u1_struct_0(A),u3_msualg_1(A,B)) => ! [D] : ( 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] : ( m1_subset_1(E,u4_struct_0(A)) => k1_funct_1(D,E) = k3_msualg_2(A,B,E,C) ) ) ) ) ) ) )).
fof(d8_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d8_msualg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d8_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ( r1_msualg_6(A,D,E,B,F) => ! [G] : ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d8_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_mycielsk(B,A) => ( B = k5_mycielsk(A) <=> u1_orders_2(B) = k6_subset_1(k2_zfmisc_1(A,A),k4_relat_1(A)) ) ) ) )).
fof(d8_nagata_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(d8_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k8_newton) & v1_funct_1(B) & v1_partfun1(B,k8_newton) ) => ( B = k12_nat_3(A) <=> ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => k1_funct_1(B,C) = k11_nat_3(A,C) ) ) ) ) )).
fof(d8_nat_lat,axiom,( ! [A] : ( ( 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] : ( m2_subset_1(B,k4_ordinal1,k6_nat_lat) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k6_nat_lat) => k5_binop_1(k6_nat_lat,A,B,C) = k6_nat_d(B,C) ) ) ) ) )).
fof(d8_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ( ( r2_nattra_1(A,B,C,D) & r2_nattra_1(A,B,D,E) ) => ! [F] : ( m2_nattra_1(F,A,B,C,D) => ! [G] : ( m2_nattra_1(G,A,B,D,E) => k5_nattra_1(A,B,C,D,E,F,G) = k3_nattra_1(A,B,C,D,E,F,G) ) ) ) ) ) ) ) ) )).
fof(d8_ndiff_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d8_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( 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] : ( r2_ndiff_5(A,B,C,D,E) <=> ( r1_tarski(E,k1_relset_1(u1_struct_0(k14_prvect_2(A)),D)) & ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(d8_necklace,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( 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))) ) ) ) ) )).
fof(d8_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k2_net_1(A)) => ( k2_net_1(A) != k1_xboole_0 => ! [C] : ( 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) ) ) ) ) ) ) )).
fof(d8_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_int_2(B) & m1_subset_1(B,k4_ordinal1) ) => ( B = k10_newton(A) <=> A = k5_card_1(k9_newton(B)) ) ) ) )).
fof(d8_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_numbers))) ) => ! [C] : ( r4_nfcont_1(A,B,C) <=> ( r1_tarski(C,k1_relset_1(u1_struct_0(A),B)) & ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d8_normform,axiom,( ! [A] : k7_normform(A) = a_1_0_normform(A) )).
fof(d8_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v7_o_ring_1(B,A) <=> ? [C] : ( 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)) ) ) ) ) )).
fof(d8_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k10_openlatt(A,B) = a_2_1_openlatt(A,B) ) ) )).
fof(d8_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d8_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r2_orders_1(A,B) <=> ( r1_relat_2(A,B) & r8_relat_2(A,B) & r4_relat_2(A,B) ) ) ) )).
fof(d8_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k1_orders_2(A,B) = a_2_0_orders_2(A,B) ) ) )).
fof(d8_ordinal1,axiom,( ! [A] : ( v6_ordinal1(A) <=> ! [B] : ! [C] : ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r3_xboole_0(B,C) ) ) )).
fof(d8_ordinal5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) & v1_ordinal2(A) ) => ! [B] : ( v3_ordinal1(B) => ( B = k4_ordinal5(A) <=> ? [C] : ( 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,k5_numbers) = k5_numbers & ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d8_ordinal6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( v3_ordinal1(B) => ( r2_hidden(B,A) => ! [C] : ( ( 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] : ( ( v3_ordinal1(D) & m1_subset_1(D,A) ) => k4_ordinal6(A,k2_ordinal1(A),C,D) = k12_ordinal2(B,D) ) ) ) ) ) ) )).
fof(d8_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => k1_funct_1(C,D) = k4_osafree(A,B,D) ) ) ) ) ) )).
fof(d8_osalg_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => v7_osalg_1(B,A) ) ) ) )).
fof(d8_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => k6_osalg_2(A,B) = a_2_0_osalg_2(A,B) ) ) )).
fof(d8_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k1_zfmisc_1(u1_struct_0(A)),k2_osalg_4(A)) => v1_waybel_0(B,A) ) ) ) )).
fof(d8_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) ) )).
fof(d8_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k6_partit1(A) = k1_tarski(A) ) )).
fof(d8_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r5_pboole(A,B,C) <=> ! [D] : ( r2_hidden(D,A) => r1_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) )).
fof(d8_pcomps_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( v3_pcomps_1(A) <=> ? [B] : ( 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) ) ) ) )).
fof(d8_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ( r1_pdiff_1(A,B,C,D) => ! [E] : ( ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d8_pdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(2)) => ( r3_pdiff_3(A,B) => ! [C] : ( v1_xreal_0(C) => ( C = k4_pdiff_3(A,B) <=> ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & B = k10_finseq_1(D,E) & ? [F] : ( 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] : ( v1_funct_1(G) & v3_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [H] : ( v1_funct_1(H) & v2_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & C = k1_funct_1(G,1) & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,F) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(2,1,k1_pdiff_3(2,2,A),B),I),k1_funct_1(k1_pdiff_2(2,1,k1_pdiff_3(2,2,A),B),D)) = k2_xcmplx_0(k1_funct_1(G,k6_xcmplx_0(I,D)),k1_funct_1(H,k6_xcmplx_0(I,D))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d8_pdiff_4,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => k5_pdiff_4(A) = k1_euclid_8(k7_xcmplx_0(k1_funct_1(A,1),k3_square_1(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k1_funct_1(A,1)),k1_square_1(k1_funct_1(A,2))),k1_square_1(k1_funct_1(A,3))))),k7_xcmplx_0(k1_funct_1(A,2),k3_square_1(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k1_funct_1(A,1)),k1_square_1(k1_funct_1(A,2))),k1_square_1(k1_funct_1(A,3))))),k7_xcmplx_0(k1_funct_1(A,3),k3_square_1(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k1_funct_1(A,1)),k1_square_1(k1_funct_1(A,2))),k1_square_1(k1_funct_1(A,3)))))) ) )).
fof(d8_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r8_pdiff_5(A,B) <=> ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & B = k11_finseq_1(C,D,E) & ? [F] : ( 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] : ( v1_funct_1(G) & v3_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [H] : ( v1_funct_1(H) & v2_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,F) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,2,k1_pdiff_3(3,3,A),B),I),k1_funct_1(k1_pdiff_2(3,2,k1_pdiff_3(3,3,A),B),D)) = k2_xcmplx_0(k1_funct_1(G,k6_xcmplx_0(I,D)),k1_funct_1(H,k6_xcmplx_0(I,D))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d8_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( ( 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] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(E,k6_xcmplx_0(k3_finseq_1(C),1)) => r3_pdiff_9(A,B,k7_partfun1(k4_ordinal1,C,k1_nat_1(E,1)),k1_seqfunc(k1_euclid(A),k1_numbers,k4_pdiff_9(A,B,C,D),E)) ) ) ) ) ) ) )).
fof(d8_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(d8_pnproc_1,axiom,( ! [A] : ! [B] : ( m1_pnproc_1(B,A) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k7_pnproc_1(A,B) <=> ( k9_xtuple_0(C) = k9_funct_2(A,k4_ordinal1) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,k4_ordinal1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => k1_funct_1(C,D) = k6_pnproc_1(A,D,B) ) ) ) ) ) )).
fof(d8_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( 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)) = k5_numbers => ( E = k8_polyeq_5(A,B,C,D) <=> ? [F] : ( v1_xcmplx_0(F) & ? [G] : ( v1_xcmplx_0(G) & ? [H] : ( v1_xcmplx_0(H) & F = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(8,C),k3_xcmplx_0(3,k1_newton(D,2))),32) & G = k7_xcmplx_0(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))))),k7_xcmplx_0(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)) != k5_numbers => ( E = k8_polyeq_5(A,B,C,D) <=> ? [F] : ( v1_xcmplx_0(F) & ? [G] : ( v1_xcmplx_0(G) & ? [H] : ( v1_xcmplx_0(H) & ? [I] : ( v1_xcmplx_0(I) & ? [J] : ( v1_xcmplx_0(J) & ? [K] : ( v1_xcmplx_0(K) & F = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(8,C),k3_xcmplx_0(3,k1_newton(D,2))),32) & G = k7_xcmplx_0(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 = k7_xcmplx_0(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 = k4_xcmplx_0(k7_xcmplx_0(G,k3_xcmplx_0(I,J))) & E = k6_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(I,J),K),k7_xcmplx_0(D,4)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d8_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => k11_polyform(A,B) = k5_card_1(k8_polyform(A,B)) ) ) )).
fof(d8_polynom1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => k8_polynom1(A,B) = k8_funcop_1(u1_struct_0(B),k15_pre_poly(A),k4_struct_0(B)) ) )).
fof(d8_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l5_algstr_0(A) ) => k10_polynom3(A) = k14_funct_7(k4_ordinal1,u1_struct_0(A),k9_polynom3(A),k5_numbers,k5_struct_0(A)) ) )).
fof(d8_polynom5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l6_algstr_0(A) ) => ( v2_polynom5(A) <=> ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ~ r1_xxreal_0(k1_algseq_1(A,B),1) => v1_polynom5(B,A) ) ) ) ) )).
fof(d8_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k4_polynom7(A,B,C) = k14_funct_7(k15_pre_poly(A),u1_struct_0(B),k8_polynom1(A,B),k16_pre_poly(A),C) ) ) )).
fof(d8_polynom8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(A),B,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ( D = k7_polynom8(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ! [F] : ( 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_0(u1_struct_0(A),D,E,F) = k3_polynom8(A,C,k3_xcmplx_0(k6_xcmplx_0(E,1),k6_xcmplx_0(F,1))) ) ) ) ) ) ) ) ) )).
fof(d8_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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] : ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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) ) ) ) ) ) ) ) )).
fof(d8_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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)) ) ) )).
fof(d8_pralg_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( 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] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => ! [D] : ( v7_ordinal1(D) => ( D = k1_funct_1(A,C) => k1_funct_1(B,C) = k7_pralg_1(D) ) ) ) ) ) ) ) ) )).
fof(d8_pre_poly,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_pre_poly(A) <=> v1_finset_1(k13_pre_poly(A)) ) ) )).
fof(d8_prob_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( 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] : ( m1_prob_1(D,A,B) => r1_xxreal_0(k5_numbers,k3_funct_2(B,k1_numbers,C,D)) ) & k1_funct_1(C,A) = 1 & ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m1_prob_1(E,A,B) => ( r1_xboole_0(D,E) => k3_funct_2(B,k1_numbers,C,k6_prob_1(A,B,D,E)) = k3_real_1(k3_funct_2(B,k1_numbers,C,D),k3_funct_2(B,k1_numbers,C,E)) ) ) ) & ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v2_prob_1(D) => ( v2_comseq_2(k8_prob_1(A,B,D,C)) & k1_seq_2(k8_prob_1(A,B,D,C)) = k1_funct_1(C,k3_prob_1(A,D)) ) ) ) ) ) ) ) ) )).
fof(d8_prob_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v3_prob_3(B,A) <=> ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(d8_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m2_prob_1(D,A,k4_prob_4(A,B,C)) => ( D = k7_prob_4(A,B,C) <=> ! [E] : ( r2_hidden(E,B) => ! [F] : ( m2_prob_4(F,A,B,C) => k1_funct_1(D,k2_xboole_0(E,F)) = k1_funct_1(C,E) ) ) ) ) ) ) ) )).
fof(d8_projpl_1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ( B != C => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d8_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) ) => ! [B] : ( m1_prvect_1(B,A) => ! [C] : ( ( 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] : ( m1_subset_1(D,k4_card_3(A)) => ! [E] : ( m1_subset_1(E,k4_card_3(A)) => ! [F] : ( m2_subset_1(F,k4_ordinal1,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)) ) ) ) ) ) ) ) )).
fof(d8_prvect_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v1_prvect_2(A) ) => ! [B] : ( 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] : ( m2_subset_1(C,k4_ordinal1,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))) ) ) ) ) ) )).
fof(d8_pscomp_1,axiom,( ! [A] : ( 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)) ) )).
fof(d8_pua2mss1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(A),A))) ) => ! [C] : ( m1_eqrel_1(C,A) => ( r1_pua2mss1(A,B,C) <=> ! [D] : ( m2_finseq_1(D,C) => ? [E] : ( 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) ) ) ) ) ) ) )).
fof(d8_pythtrip,axiom,( ! [A] : ( m1_pythtrip(A) => ( v3_pythtrip(A) <=> ? [B] : ( m1_subset_1(B,k4_ordinal1) & ? [C] : ( m1_subset_1(C,k4_ordinal1) & r2_hidden(B,A) & r2_hidden(C,A) & r1_int_2(B,C) ) ) ) ) )).
fof(d8_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k6_qc_lang1(A)) => ! [C] : ( v7_ordinal1(C) => ( C = k7_qc_lang1(A,B) <=> k1_xtuple_0(B) = k2_xcmplx_0(7,C) ) ) ) ) )).
fof(d8_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(d8_qmax_1,axiom,( ! [A] : ( ( v2_qmax_1(A) & l1_qmax_1(A) ) => k5_qmax_1(A) = k2_zfmisc_1(k2_qmax_1(A),k12_prob_1) ) )).
fof(d8_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ( B = k8_quaterni(A) <=> k7_quaterni(A,B) = k5_numbers ) ) ) )).
fof(d8_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ( B = k11_quofield(A) <=> ! [C] : ( 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) ) ) ) ) ) )).
fof(d8_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k9_radix_1(A,B,C) = k3_nat_d(k4_nat_d(C,k1_newton(k1_radix_1(B),A)),k11_newton(k1_radix_1(B),k7_nat_d(A,1))) ) ) ) )).
fof(d8_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k3_radix_1(B)) ) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d8_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v3_card_1(D,A) & m2_finseq_1(D,k3_radix_1(C)) ) => ( D = k8_radix_5(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k2_finseq_1(A)) => k4_radix_1(E,C,A,D) = k7_radix_5(E,B,C) ) ) ) ) ) ) ) )).
fof(d8_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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) = k5_numbers ) ) ) ) ) ) ) )).
fof(d8_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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)) ) ) ) ) )).
fof(d8_ratfunc1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & l5_algstr_0(A) ) => ! [B] : ( m1_ratfunc1(B,A) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & ~ v1_ratfunc1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & B = k4_tarski(C,D) ) ) ) ) )).
fof(d8_rcomp_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xreal_0(B) => k4_rcomp_1(A,B) = a_2_3_rcomp_1(A,B) ) ) )).
fof(d8_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( B = k4_relat_1(A) <=> ! [C] : ! [D] : ( r2_hidden(k4_tarski(C,D),B) <=> ( r2_hidden(C,A) & C = D ) ) ) ) )).
fof(d8_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r8_relat_2(A,B) <=> ! [C] : ! [D] : ! [E] : ( ( 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) ) ) ) )).
fof(d8_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r6_rewrite1(A,B,C) <=> ? [D] : ( r1_rewrite1(A,D,B) & r1_rewrite1(A,D,C) ) ) ) )).
fof(d8_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => k8_rewrite2(A,B,C) = a_3_0_rewrite2(A,B,C) ) ) )).
fof(d8_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ v2_struct_0(C) & l1_rewrite3(C,B) ) => ! [D] : ! [E] : k3_rewrite3(A,B,C,D,E) = a_5_0_rewrite3(A,B,C,D,E) ) ) ) )).
fof(d8_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,k3_rfunct_3(A,k1_numbers)) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ( D = k17_rfunct_3(A,B,C) <=> ( k3_finseq_1(D) = k3_finseq_1(B) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k4_finseq_1(D)) => k1_funct_1(D,E) = k1_funct_1(k1_funct_1(B,E),C) ) ) ) ) ) ) ) ) )).
fof(d8_rfunct_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( r8_rfunct_4(A,B) <=> ( r1_tarski(B,k9_xtuple_0(A)) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => r7_rfunct_4(k2_partfun1(k1_numbers,k1_numbers,A,B),C) ) ) ) ) ) )).
fof(d8_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => k5_rinfsup2(A) = k2_rinfsup2(k4_rinfsup2(A)) ) )).
fof(d8_ringcat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v2_ringcat1(C) & v3_ringcat1(C) & l1_ringcat1(C) ) => ( m1_ringcat1(C,A,B) <=> ( k1_ringcat1(C) = A & k2_ringcat1(C) = B ) ) ) ) ) ) )).
fof(d8_rlsub_2,axiom,( ! [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) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k3_rlsub_2(A)) => ! [D] : ( m1_subset_1(D,k3_rlsub_2(A)) => ! [E] : ( m1_rlsub_1(E,A) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d8_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rltopsp1(A) ) => ( v6_rltopsp1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d8_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ( v8_rlvect_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_rlvect_1(A,B,1) = B ) ) ) )).
fof(d8_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k6_rlvect_2(A,B) <=> ? [D] : ( 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)) ) ) ) ) ) )).
fof(d8_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_4(C,A,B) => ! [D] : ( m1_rmod_4(D,A,B) => ( r1_rmod_4(A,B,C,D) <=> ! [E] : ( 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) ) ) ) ) ) ) )).
fof(d8_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & v7_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B = k6_lattices(A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & B = k5_robbins1(A,C,k3_robbins1(A,C)) ) ) ) ) )).
fof(d8_rsspace,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_rlsub_1(B,A) => ( v1_xboole_0(B) | k8_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)) ) ) ) ) )).
fof(d8_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(d8_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k3_rusub_2(A)) => ! [D] : ( m1_subset_1(D,k3_rusub_2(A)) => ! [E] : ( m1_rusub_1(E,A) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d8_rusub_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_rusub_4(A,B,C) = a_3_0_rusub_4(A,B,C) ) ) ) )).
fof(d8_rvsum_1,axiom,( ! [A] : ( ( 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) ) )).
fof(d8_scm_comp,axiom,( ! [A] : ( m2_subset_1(A,u1_struct_0(k1_scm_comp),k7_dtconstr(k1_scm_comp)) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( A = k4_tarski(k5_numbers,k5_numbers) => k10_scm_comp(A,B,C) = k2_xcmplx_0(B,C) ) & ( A = k4_tarski(k5_numbers,1) => k10_scm_comp(A,B,C) = k6_xcmplx_0(B,C) ) & ( A = k4_tarski(k5_numbers,2) => k10_scm_comp(A,B,C) = k3_xcmplx_0(B,C) ) & ( A = k4_tarski(k5_numbers,3) => k10_scm_comp(A,B,C) = k4_int_1(B,C) ) & ( A = k4_tarski(k5_numbers,4) => k10_scm_comp(A,B,C) = k5_int_1(B,C) ) ) ) ) ) )).
fof(d8_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(k1_scmfsa_2)) => ( C = k8_scmfsa_2(A,B) <=> ? [D] : ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_ami_3)) & ? [E] : ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_ami_3)) & A = D & B = E & C = k4_ami_3(D,E) ) ) ) ) ) ) )).
fof(d8_scmpds_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => k8_scmpds_2(A,B,C) = k3_xtuple_0(5,k1_xboole_0,k11_finseq_1(A,B,C)) ) ) ) )).
fof(d8_scmpds_4,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( v7_ordinal1(B) => ( r1_scmpds_4(A,B) <=> ( ~ ( k2_compos_0(u1_compos_1(k1_scmpds_2),A) = 14 & ! [C] : ( v1_int_1(C) => ~ ( A = k3_scmpds_2(C) & r1_xxreal_0(k5_numbers,k2_xcmplx_0(B,C)) ) ) ) & ~ ( k2_compos_0(u1_compos_1(k1_scmpds_2),A) = 4 & ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmpds_2)) ) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => ~ ( A = k7_scmpds_2(C,D,E) & r1_xxreal_0(k5_numbers,k2_xcmplx_0(B,E)) ) ) ) ) ) & ~ ( k2_compos_0(u1_compos_1(k1_scmpds_2),A) = 5 & ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmpds_2)) ) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => ~ ( A = k8_scmpds_2(C,D,E) & r1_xxreal_0(k5_numbers,k2_xcmplx_0(B,E)) ) ) ) ) ) & ~ ( k2_compos_0(u1_compos_1(k1_scmpds_2),A) = 6 & ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmpds_2)) ) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => ~ ( A = k9_scmpds_2(C,D,E) & r1_xxreal_0(k5_numbers,k2_xcmplx_0(B,E)) ) ) ) ) ) ) ) ) ) )).
fof(d8_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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(k1_nat_1(k5_card_1(C),1))),C) ) ) ) )).
fof(d8_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => ( ? [B] : ( m1_subset_1(B,k2_scm_inst) & ? [C] : ( v1_int_1(C) & ? [D] : ( v1_int_1(D) & ? [E] : ( 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] : ( v1_int_1(B) => ( B = k9_scmpds_i(A) <=> ? [C] : ( 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) ) ) ) ) ) )).
fof(d8_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => k9_scmring2(A,B,C) = k3_xtuple_0(7,k9_finseq_1(B),k12_finseq_1(u1_struct_0(k1_scmring2(A)),C)) ) ) ) )).
fof(d8_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_scmringi(A)) => ( ? [C] : ( m1_subset_1(C,k2_scm_inst) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m2_subset_1(E,k4_ordinal1,k7_card_1(8)) & B = k3_xtuple_0(E,k1_xboole_0,k7_scmringi(A,C,D)) ) ) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k9_scmringi(A,B) <=> ? [D] : ( 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) ) ) ) ) ) ) )).
fof(d8_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( m1_subset_1(B,k3_tarski(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_tarski(A))) => ( C = k4_scmyciel(A,B) <=> ! [D] : ( m1_subset_1(D,k3_tarski(A)) => ( r2_hidden(D,C) <=> r2_hidden(k2_tarski(B,D),k1_scmyciel(A)) ) ) ) ) ) ) )).
fof(d8_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d8_seq_4,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => k9_seq_4(A) = k4_finseqop(k2_numbers,k2_numbers,A,k1_binop_2) ) )).
fof(d8_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => k9_seqfunc(A,B,C) = k8_seqfunc(A,C,k3_seqfunc(A,B)) ) ) ) )).
fof(d8_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v7_valued_0(A) <=> ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,A,k1_nat_1(B,1))) ) ) ) )).
fof(d8_setfam_1,axiom,( ! [A] : ( v1_setfam_1(A) <=> ~ r2_hidden(k1_xboole_0,A) ) )).
fof(d8_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( D = k8_setlim_2(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k9_nat_1(k9_setfam_1(A),D,E) = k7_subset_1(A,k9_nat_1(k9_setfam_1(A),B,E),C) ) ) ) ) ) )).
fof(d8_sgraph1,axiom,( ! [A] : ! [B] : ( m1_sgraph1(B,A) => ! [C] : ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( D = k4_sgraph1(A,B,C) <=> ? [E] : ( v1_finset_1(E) & ! [F] : ( r2_hidden(F,E) <=> ( r2_hidden(F,u1_sgraph1(B)) & r2_hidden(C,F) ) ) & D = k5_card_1(E) ) ) ) ) )).
fof(d8_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ( v4_sheffer1(A) & v11_lattices(A) & v1_sheffer1(A) & v6_lattices(A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = k3_sheffer1(A,B) <=> r1_sheffer1(A,C,B) ) ) ) ) ) )).
fof(d8_simplex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_simplex0(B,u1_struct_0(A)) => ( v2_simplex1(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(d8_sin_cos,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( B = k7_sin_cos(A) <=> ( k9_nat_1(k2_numbers,B,k5_numbers) = k5_numbers & ! [C] : ( v7_ordinal1(C) => k9_nat_1(k2_numbers,B,k1_nat_1(C,1)) = k9_nat_1(k2_numbers,A,C) ) ) ) ) ) )).
fof(d8_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( ~ r1_xxreal_0(A,k5_numbers) => k8_sin_cos7(A) = k3_power(k4_power,k7_xcmplx_0(k2_xcmplx_0(1,k3_square_1(k2_xcmplx_0(1,k1_square_1(A)))),A)) ) & ( ~ r1_xxreal_0(k5_numbers,A) => k8_sin_cos7(A) = k3_power(k4_power,k7_xcmplx_0(k6_xcmplx_0(1,k3_square_1(k2_xcmplx_0(1,k1_square_1(A)))),A)) ) ) ) )).
fof(d8_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => k8_sincos10(A) = k1_funct_1(k4_sincos10,A) ) )).
fof(d8_struct_0,axiom,( ! [A] : ( l4_struct_0(A) => ( v6_struct_0(A) <=> k4_struct_0(A) = k5_struct_0(A) ) ) )).
fof(d8_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k16_substut1(A),k38_substut1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m1_substut1(D,A,k7_sublemma(A,B,C)) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(d8_supinf_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v4_card_3(B) <=> ~ ( ~ v1_xboole_0(B) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => B != k2_relset_1(A,C) ) ) ) ) ) )).
fof(d8_taxonom1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(u1_struct_0(A)))) => ( B = k4_taxonom1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( ~ v3_xxreal_0(D) & v1_xreal_0(D) & ? [E] : ( 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 ) ) ) ) ) ) )).
fof(d8_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_tbsp_1(B,A) => ! [C] : ( v1_xreal_0(C) => ( ( B != k1_xboole_0 => ( C = k3_tbsp_1(A,B) <=> ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r2_hidden(D,B) & r2_hidden(E,B) ) => r1_xxreal_0(k1_metric_1(A,D,E),C) ) ) ) & ! [D] : ( v1_xreal_0(D) => ( ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r2_hidden(E,B) & r2_hidden(F,B) ) => r1_xxreal_0(k1_metric_1(A,E,F),D) ) ) ) => r1_xxreal_0(C,D) ) ) ) ) ) & ( B = k1_xboole_0 => ( C = k3_tbsp_1(A,B) <=> C = k5_numbers ) ) ) ) ) ) ) )).
fof(d8_tdlat_1,axiom,( ! [A] : ( ( 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)) ) )).
fof(d8_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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)) ) ) ) ) )).
fof(d8_tex_4,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)) ) ) )).
fof(d8_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) )).
fof(d8_topgen_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_pre_topc(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ( C = k7_topgen_3(A,B) <=> ( u1_struct_0(C) = A & ! [D] : ( 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)) ) ) ) ) )).
fof(d8_topgen_4,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v7_topgen_4(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => v4_pre_topc(k2_topgen_1(A,B),A) ) ) ) )).
fof(d8_topgrp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_topgrp_1(A) ) => ( v4_topgrp_1(A) <=> ! [B] : ( ( 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) ) ) ) ) )).
fof(d8_topmetr,axiom,( ! [A] : ( l1_struct_0(A) => ( v3_topmetr(A) <=> v3_membered(u1_struct_0(A)) ) ) )).
fof(d8_topreal1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(d8_toprealb,axiom,( k9_toprealb = k19_euclid(1,k5_numbers) )).
fof(d8_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ( v3_toprns_1(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(E,F) & r1_xxreal_0(D,k12_euclid(k5_algstr_0(k15_euclid(A),k9_nat_1(u1_struct_0(k15_euclid(A)),B,F),C))) ) ) ) ) ) ) ) ) )).
fof(d8_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)) ) ) ) )).
fof(d8_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(d8_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_trees_3(B,A) => ( B = k5_trees_3(A) <=> ! [C] : ( ( 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) ) ) ) ) ) )).
fof(d8_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => k6_trees_9(A) = a_1_1_trees_9(A) ) )).
fof(d8_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tsp_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & C != D & ! [E] : ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v3_pre_topc(E,A) & ~ r2_hidden(C,E) & r2_hidden(D,E) ) ) ) ) ) ) ) ) )).
fof(d8_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( 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] : ( m1_subset_1(C,k4_ordinal1) & k1_mcart_1(u2_turing_1(A),k4_numbers,k9_funct_2(k4_numbers,u1_turing_1(A)),k9_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) ) ) ) ) )).
fof(d8_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k1_funct_1(A,k10_finseq_1(B,C)) = k1_binarith(k9_margrel1(B),C) ) ) ) ) )).
fof(d8_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(d8_uproots,axiom,( ! [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) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & v1_uproots(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( 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 = k7_uproots(A,B) <=> ( k22_pre_poly(u1_struct_0(A),C) = k6_polynom5(A,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_recdef_1(C,D) = k6_uproots(A,D,B) ) ) ) ) ) ) )).
fof(d8_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_valuat_1(C,A,B) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ( r2_valuat_1(A,B,C,D) <=> ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => r1_valuat_1(A,B,D,C,E) ) ) ) ) ) ) )).
fof(d8_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v4_valued_0(A) <=> ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => v7_ordinal1(k1_funct_1(A,B)) ) ) ) )).
fof(d8_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => k39_valued_1(A) = k18_valued_1(A,A) ) )).
fof(d8_valued_2,axiom,( ! [A] : ! [B] : ( B = k2_valued_2(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) ) ) )).
fof(d8_vectmetr,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ 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] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => k1_binop_1(u1_algstr_0(B),C,D) = k7_euclid(A,C,D) ) ) & ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m1_subset_1(D,k1_numbers) => k1_binop_1(u1_rlvect_1(B),D,C) = k9_euclid(A,C,D) ) ) ) ) ) ) )).
fof(d8_vectsp10,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(d8_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ( v6_vectsp_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_algstr_0(A,k5_struct_0(A),B) = B ) ) ) )).
fof(d8_vectsp_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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,k1_tarski(k5_ordinal1),k9_funct_5,k5_funct_5,k10_funct_3(u1_struct_0(A),k1_tarski(k5_ordinal1)),k9_funct_3(k1_tarski(k5_ordinal1),u1_struct_0(B))) ) ) )).
fof(d8_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k3_vectsp_5(A,B)) => ! [E] : ( m1_subset_1(E,k3_vectsp_5(A,B)) => ! [F] : ( m1_vectsp_4(F,A,B) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d8_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => ! [D] : ( m1_vectsp_6(D,A,B) => k5_vectsp_6(A,B,C,D) = k1_vfunct_1(u1_struct_0(B),A,C,D) ) ) ) ) )).
fof(d8_vectsp_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d8_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m4_yellow_6(B,A) => ( B = k2_waybel11(A) <=> ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(k4_tarski(C,D),B) <=> r1_waybel11(A,C,D) ) ) ) ) ) ) ) )).
fof(d8_waybel18,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ( r1_waybel18(A,B) <=> ? [C] : ( 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) ) ) ) ) )).
fof(d8_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_waybel23(B,A) <=> r2_hidden(k3_yellow_0(A),B) ) ) ) )).
fof(d8_waybel34,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(d8_waybel35,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : k3_waybel35(A,B,C) = k3_xboole_0(k8_relat_1(A,k1_tarski(C)),B) ) )).
fof(d8_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(d8_waybel_1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ( r5_waybel_1(A,B) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(d8_waybel_4,axiom,( ! [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] : ( B = k3_waybel_4(A) <=> ! [C] : ( 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)))) ) ) ) ) )).
fof(d8_waybel_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v6_waybel_6(B,A) <=> v5_waybel_6(k8_lattice3(A,B),k7_lattice3(A)) ) ) ) )).
fof(d8_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( l1_struct_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( l1_waybel_0(D,A) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(d8_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [C] : ( 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)) ) ) ) )).
fof(d8_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r4_wellord1(A,B) <=> ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & r3_wellord1(A,B,C) ) ) ) ) )).
fof(d8_xboole_0,axiom,( ! [A] : ! [B] : ( r2_xboole_0(A,B) <=> ( r1_tarski(A,B) & A != B ) ) )).
fof(d8_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k7_xboolean(A,B) = k4_xboolean(k6_xboolean(A,B),k6_xboolean(B,A)) ) ) )).
fof(d8_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k7_xcmplx_0(A,B) = k3_xcmplx_0(A,k5_xcmplx_0(B)) ) ) )).
fof(d8_xtuple_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k6_xtuple_0(A,B,C,D) = k4_tarski(k3_xtuple_0(A,B,C),D) )).
fof(d8_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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 ) ) ) ) )).
fof(d8_xxreal_2,axiom,( ! [A] : ( ( v2_membered(A) & v2_xxreal_2(A) ) => ! [B] : ( v1_xxreal_0(B) => ( B = k1_xxreal_2(A) <=> ( r2_hidden(B,A) & ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(C,A) => r1_xxreal_0(C,B) ) ) ) ) ) ) )).
fof(d8_yellow21,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(d8_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( r2_yellow_0(A,B) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r1_lattice3(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_lattice3(A,B,D) => r1_orders_2(A,D,C) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r1_lattice3(A,B,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_lattice3(A,B,E) => r1_orders_2(A,E,D) ) ) ) => D = C ) ) ) ) ) )).
fof(d8_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(d8_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ( v4_zf_fund1(B,A) <=> ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(a_3_0_zf_fund1(A,C,D),B) ) ) ) ) ) ) )).
fof(d8_zf_lang,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( A = k9_zf_lang <=> ( ! [B] : ( r2_hidden(B,A) => m2_finseq_1(B,k4_ordinal1) ) & ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ( r2_hidden(k4_zf_lang(B,C),A) & r2_hidden(k5_zf_lang(B,C),A) ) ) ) & ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ( r2_hidden(B,A) => r2_hidden(k6_zf_lang(B),A) ) ) & ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r2_hidden(k7_zf_lang(B,C),A) ) ) ) & ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( r2_hidden(C,A) => r2_hidden(k8_zf_lang(B,C),A) ) ) ) & ! [B] : ( ~ v1_xboole_0(B) => ( ( ! [C] : ( r2_hidden(C,B) => m2_finseq_1(C,k4_ordinal1) ) & ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ( r2_hidden(k4_zf_lang(C,D),B) & r2_hidden(k5_zf_lang(C,D),B) ) ) ) & ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( r2_hidden(C,B) => r2_hidden(k6_zf_lang(C),B) ) ) & ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k7_zf_lang(C,D),B) ) ) ) & ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( r2_hidden(D,B) => r2_hidden(k8_zf_lang(C,D),B) ) ) ) ) => r1_tarski(A,B) ) ) ) ) ) )).
fof(d8_zf_model,axiom,( k8_zf_model = k8_zf_lang(k2_zf_lang(k5_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(k5_numbers)))))))) )).
fof(d8_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( 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 ) ) )).
fof(d8_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v7_zmodul01(B,A) <=> ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( v1_int_1(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => r2_hidden(k1_zmodul01(A,D,C),B) ) ) ) ) ) ) ) )).
fof(d8_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => k8_zmodul02(A,B) = u1_struct_0(B) ) ) )).
fof(d9_abcmiz_0,axiom,( ! [A] : ( l2_abcmiz_0(A) => ( v8_abcmiz_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(d9_abcmiz_1,axiom,( ! [A] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(d9_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( 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 ) ) ) ) )).
fof(d9_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v9_aff_2(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d9_afinsq_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( m2_finseq_1(C,A) => ( C = k10_afinsq_1(A,B) <=> ( k3_finseq_1(C) = k1_afinsq_1(B) & ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d9_afinsq_2,axiom,( ! [A] : ( ( 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,k3_binop_2) ) )).
fof(d9_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => k9_afproj(A) = k2_xboole_0(u1_struct_0(A),k7_afproj(A)) ) )).
fof(d9_algstr_0,axiom,( k3_algstr_0 = g2_algstr_0(k1_tarski(k5_ordinal1),k9_funct_5,k5_funct_5) )).
fof(d9_algstr_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l5_algstr_0(A) ) => ( v6_algstr_1(A) <=> ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != k4_struct_0(A) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k6_algstr_0(A,B,D) != C ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != k4_struct_0(A) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k6_algstr_0(A,D,B) != C ) ) ) ) ) ) ) )).
fof(d9_algstr_4,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( 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)) ) ) ) ) )).
fof(d9_altcat_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v7_altcat_1(A) <=> ! [B] : ~ ( r2_hidden(B,k9_xtuple_0(A)) & ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ~ ( B = k4_tarski(D,C) & k1_funct_1(A,B) = k3_relat_1(C,D) ) ) ) ) ) ) )).
fof(d9_altcat_3,axiom,( ! [A] : ( l1_altcat_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v6_altcat_3(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( 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)) ) ) ) ) ) )).
fof(d9_altcat_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ( v5_altcat_5(D,A,B,C) <=> ? [E] : ( m1_altcat_5(E,A,D,B,C) & v2_altcat_5(E,A,B,C,D) & v3_altcat_5(E,A,B,C,D) ) ) ) ) ) )).
fof(d9_ami_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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)) ) ) )).
fof(d9_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) ) => ( v4_ami_wstd(C,A,B) <=> ! [D] : ( ( 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,k5_numbers) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => r2_hidden(k5_memstr_0(A,B,k5_extpro_1(A,B,C,D,E)),k1_relset_1(k4_ordinal1,C)) ) ) ) ) ) ) ) )).
fof(d9_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) ) => ( v5_amistd_1(C,A,B) <=> ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,C)) => r1_tarski(k1_amistd_1(A,B,D,k7_partfun1(u1_compos_1(B),C,D)),k1_relset_1(k4_ordinal1,C)) ) ) ) ) ) ) )).
fof(d9_analmetr,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r4_analmetr(A,B,C,D,E) & D != E ) ) ) ) ) ) ) )).
fof(d9_anproj_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_collsp(A) ) => ( v2_anproj_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_collsp(A,B,C,E) & r1_collsp(A,C,D,F) & ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( r1_collsp(A,B,D,G) & r1_collsp(A,E,F,G) ) ) ) ) ) ) ) ) ) ) )).
fof(d9_aofa_000,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(d9_aofa_a00,axiom,( ! [A] : ( l1_msualg_1(A) => ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_aofa_a00(A,B,C,D) <=> ( k1_funct_1(u1_msualg_1(A),B) = C & k1_funct_1(u2_msualg_1(A),B) = D ) ) ) ) )).
fof(d9_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_aofa_a01(D,A,B,C) & l4_aofa_a00(D,A,B,C) ) => ! [E] : ( ( ~ v2_struct_0(E) & v2_unialg_1(E) & v3_unialg_1(E) & v4_unialg_1(E) & v3_aofa_000(E) & v4_aofa_000(E) & v5_aofa_000(E) & v6_aofa_000(E) & ~ v10_aofa_000(E) & v11_aofa_000(E) & v12_aofa_000(E) & l3_aofa_a00(E,A,C,u4_aofa_a00(A,B,C,D)) ) => ! [F] : ( ( v3_aofa_a01(F,A,B,C,u4_aofa_a00(A,B,C,D),u8_aofa_a00(A)) & m1_msafree4(F,u1_struct_0(A),u4_aofa_a00(A,B,C,D),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),u8_aofa_a00(A))) ) => ! [G] : ( ( v19_aofa_a00(G,A) & m1_subset_1(G,u1_struct_0(A)) ) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),G)) => ! [I] : ( m1_subset_1(I,k1_funct_1(u3_msualg_1(A,C),G)) => k6_aofa_a01(A,B,C,D,E,F,G,H,I) = k12_aofa_a00(A,C,u4_aofa_a00(A,B,C,D),E,u8_aofa_a00(A),F,k22_aofa_a00(A,C,k33_aofa_a00(A,C,G,H,I))) ) ) ) ) ) ) ) ) ) )).
fof(d9_armstrng,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_armstrng(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(d9_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( 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))) ) ) )).
fof(d9_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( 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] : ( v3_ordinal1(C) & v7_ordinal1(C) & A = k4_tarski(C,B) ) ) ) ) ) ) )).
fof(d9_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k6_asympt_0(A) = a_1_0_asympt_0(A) ) )).
fof(d9_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => k7_bagorder(A) = k5_bagorder(A,k4_bagorder(A)) ) )).
fof(d9_bcialg_2,axiom,( ! [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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d9_bcialg_4,axiom,( ! [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) & l1_bcialg_4(A) ) => ( v3_bcialg_4(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(d9_bcialg_6,axiom,( ! [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] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(d9_bhsp_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( m2_bhsp_5(B,A) <=> ( m1_bhsp_5(B,A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => k2_bhsp_1(A,C,C) = 1 ) ) ) ) ) ) )).
fof(d9_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(d9_binop_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(d9_binop_2,axiom,( ! [A] : ( ( 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 = k9_binop_2 <=> ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k1_binop_1(A,B,C) = k2_xcmplx_0(B,C) ) ) ) ) )).
fof(d9_bor_cant,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( C = k9_bor_cant(A,B) <=> ! [D] : ( v7_ordinal1(D) => k1_funct_1(C,D) = k3_prob_1(A,k1_valued_0(k9_setfam_1(A),B,D)) ) ) ) ) )).
fof(d9_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(d9_borsuk_6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))) => ( A = k7_borsuk_6 <=> ! [B] : ( r2_hidden(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k5_topmetr)) & ? [D] : ( m1_subset_1(D,u1_struct_0(k5_topmetr)) & B = k4_borsuk_1(k5_topmetr,k5_topmetr,C,D) & r1_xxreal_0(k6_xcmplx_0(1,k3_xcmplx_0(2,C)),D) & r1_xxreal_0(k6_xcmplx_0(k3_xcmplx_0(2,C),1),D) ) ) ) ) ) )).
fof(d9_borsuk_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ( B != k4_struct_0(k15_euclid(A)) => k15_borsuk_7(A,B) = k9_toprealc(A,B,k12_euclid(B)) ) ) ) )).
fof(d9_bspace,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k7_bspace(A))) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k2_bspace)) => ( D = k11_bspace(A,B,C) <=> ( k3_finseq_1(D) = k3_finseq_1(B) & ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d9_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) ) )).
fof(d9_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => k6_bvfunc_2(A,B,C,D) = k16_bvfunc_1(A,B,k5_bvfunc_2(A,D,C)) ) ) ) ) )).
fof(d9_c0sp1,axiom,( ! [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) & v2_funcsdom(A) & v3_group_1(A) & v5_group_1(A) & v1_vectsp_1(A) & v3_vectsp_1(A) & l1_funcsdom(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & 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) ) ) ) ) )).
fof(d9_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => k9_c0sp2(A) = g1_normsp_1(k6_c0sp2(A),k9_rsspace(k10_funcsdom(u1_struct_0(A)),k6_c0sp2(A)),k7_rsspace(k10_funcsdom(u1_struct_0(A)),k6_c0sp2(A)),k8_rsspace(k10_funcsdom(u1_struct_0(A)),k6_c0sp2(A)),k8_c0sp2(A)) ) )).
fof(d9_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ( r4_calcul_1(A,B) <=> ? [C] : ( 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))) ) ) ) ) )).
fof(d9_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( B = k8_card_3(A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & C = D & r1_tarski(k9_xtuple_0(D),k9_xtuple_0(A)) & ! [E] : ( r2_hidden(E,k9_xtuple_0(D)) => r2_hidden(k1_funct_1(D,E),k1_funct_1(A,E)) ) ) ) ) ) )).
fof(d9_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k3_card_fil(A) = a_1_0_card_fil(A) ) )).
fof(d9_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k2_card_lar(A,B) = a_2_0_card_lar(A,B) ) ) )).
fof(d9_cat_1,axiom,( ! [A] : ! [B] : 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)) )).
fof(d9_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,k6_cat_2(A,B),C) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => k11_cat_2(A,B,C,D,E) = k1_funct_1(k3_funct_5(D),k4_cat_1(B,E)) ) ) ) ) ) )).
fof(d9_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_cat_1(E,A,C,B) & k5_cat_1(A,B,C,B,D,E) = k4_cat_1(A,B) ) ) ) ) ) ) ) )).
fof(d9_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(d9_catalg_1,axiom,( ! [A] : ! [B] : k6_catalg_1(A,B) = k4_tarski(k5_numbers,k10_finseq_1(A,B)) )).
fof(d9_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ! [B] : ( ( v1_cayldick(B) & l1_cayldick(B) ) => ( B = k4_cayldick(A) <=> ( u1_struct_0(B) = k4_card_3(k6_afinsq_1(u1_struct_0(A),u1_struct_0(A))) & u2_struct_0(B) = k6_afinsq_1(k4_struct_0(A),k4_struct_0(A)) & u3_struct_0(B) = k6_afinsq_1(k5_struct_0(A),k4_struct_0(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( k1_binop_1(u1_algstr_0(B),k6_afinsq_1(C,E),k6_afinsq_1(D,F)) = k6_afinsq_1(k1_algstr_0(A,C,D),k1_algstr_0(A,E,F)) & k1_binop_1(u2_algstr_0(B),k6_afinsq_1(C,E),k6_afinsq_1(D,F)) = k6_afinsq_1(k5_algstr_0(A,k6_algstr_0(A,C,D),k6_algstr_0(A,k2_cayldick(A,F),E)),k1_algstr_0(A,k6_algstr_0(A,F,C),k6_algstr_0(A,E,k2_cayldick(A,D)))) ) ) ) ) ) & ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k1_binop_1(u1_rlvect_1(B),C,k6_afinsq_1(D,E)) = k6_afinsq_1(k1_rlvect_1(A,D,C),k1_rlvect_1(A,E,C)) ) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k1_funct_1(u1_normsp_0(B),k6_afinsq_1(C,D)) = k3_square_1(k2_xcmplx_0(k1_square_1(k2_normsp_0(A,C)),k1_square_1(k2_normsp_0(A,D)))) & k1_funct_1(u1_cayldick(B),k6_afinsq_1(C,D)) = k6_afinsq_1(k2_cayldick(A,C),k4_algstr_0(A,D)) ) ) ) ) ) ) ) )).
fof(d9_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( r2_hidden(C,k2_cc0sp1(A)) => k1_funct_1(B,C) = k2_seq_4(k5_cc0sp1(A,k4_cc0sp1(A,C))) ) ) ) ) )).
fof(d9_cc0sp2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d9_cfdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [B] : ( 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)) ) ) ) )).
fof(d9_cfuncdom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cfuncdom(A) ) => ( v2_cfuncdom(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xcmplx_0(D) => k1_clvect_1(A,k6_algstr_0(A,B,C),D) = k6_algstr_0(A,k1_clvect_1(A,B,D),C) ) ) ) ) ) )).
fof(d9_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ! [B] : ( v3_ordinal1(B) => ( B = k9_cgames_1(A) <=> ( r2_hidden(A,k2_cgames_1(B)) & ! [C] : ( v3_ordinal1(C) => ~ ( r2_hidden(C,B) & r2_hidden(A,k2_cgames_1(C)) ) ) ) ) ) ) )).
fof(d9_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_chain_1(B,A) => k6_chain_1(A,B) = k4_chain_1(A,B,A) ) ) )).
fof(d9_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m2_chord(D,A,B,C) => ( v4_chord(D,A,B,C) <=> ! [E] : ( m1_subset_1(E,k1_zfmisc_1(D)) => ~ ( E != D & m2_chord(E,A,B,C) ) ) ) ) ) ) ) )).
fof(d9_circcmb3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(d9_circcomb,axiom,( ! [A] : ( l1_msualg_1(A) => ( v3_circcomb(A) <=> ! [B] : ( r2_hidden(B,u4_struct_0(A)) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ~ ( C = k1_funct_1(u1_msualg_1(A),B) & ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(d9_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(d9_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_pboole(C,k2_msafree2(A),k7_funcop_1(k2_msafree2(A),k4_ordinal1),k5_relat_1(u3_msualg_1(A,B),k2_msafree2(A))) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(A,B))) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_card_3(u3_msualg_1(A,B))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_card_3(u3_msualg_1(A,B))))) ) => ( E = k9_circuit2(A,B,C,D) <=> ( r8_pboole(u1_struct_0(A),k9_nat_1(k4_card_3(u3_msualg_1(A,B)),E,k5_numbers),k8_circuit2(A,B,C,D)) & ! [F] : ( v7_ordinal1(F) => r8_pboole(u1_struct_0(A),k9_nat_1(k4_card_3(u3_msualg_1(A,B)),E,k1_nat_1(F,1)),k7_circuit2(A,B,k9_nat_1(k4_card_3(u3_msualg_1(A,B)),E,F),k2_circuit1(A,B,C,k1_nat_1(F,1)))) ) ) ) ) ) ) ) ) )).
fof(d9_classes1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => ( B = k6_classes1(A) <=> ( r1_tarski(A,k4_classes1(B)) & ! [C] : ( v3_ordinal1(C) => ( r1_tarski(A,k4_classes1(C)) => r1_ordinal1(B,C) ) ) ) ) ) )).
fof(d9_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( r2_hidden(C,k8_clopban1(A,B)) => k11_clopban1(A,B,C) = C ) ) ) )).
fof(d9_clopban2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clopban2(A) ) => ( v2_clopban2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k2_normsp_0(A,k6_algstr_0(A,B,C)),k3_xcmplx_0(k2_normsp_0(A,B),k2_normsp_0(A,C))) ) ) ) ) )).
fof(d9_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) => ( v6_closure2(C,A,B) <=> r2_hidden(k1_pboole(A),C) ) ) ) )).
fof(d9_clvect_1,axiom,( ! [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) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(d9_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r1_clvect_2(A,B,C) <=> ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(E,F) & r1_xxreal_0(D,k15_csspace(A,k1_normsp_1(A,B,F),k1_normsp_1(A,C,F))) ) ) ) ) ) ) ) ) )).
fof(d9_clvect_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v3_clvect_3(A) <=> ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(C,D) & r1_xxreal_0(C,E) & r1_xxreal_0(B,k9_complex1(k6_xcmplx_0(k9_nat_1(k2_numbers,A,D),k9_nat_1(k2_numbers,A,E)))) ) ) ) ) ) ) ) )).
fof(d9_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k3_coh_sp(A)) => k8_coh_sp(A,B) = k4_tarski(k4_tarski(B,B),k6_partfun1(k3_tarski(B))) ) )).
fof(d9_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v4_cohsp_1(A) <=> ! [B] : ( 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)) ) ) ) ) )).
fof(d9_combgras,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( 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) ) ) ) ) )).
fof(d9_compact1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(d9_compl_sp,axiom,( ! [A] : ( l1_pre_topc(A) => ( v8_compl_sp(A) <=> ! [B] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(d9_compos_0,axiom,( ! [A] : ( v5_compos_0(A) <=> r2_hidden(k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0),A) ) )).
fof(d9_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d9_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v4_valued_0(A) & v2_margrel1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k3_finseq_2(k4_ordinal1)) & v1_funct_1(C) & v4_valued_0(C) & v2_margrel1(C) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r1_comput_1(A,B,C,D) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & r1_tarski(k1_relset_1(k3_finseq_2(k4_ordinal1),A),k4_finseq_2(E,k4_ordinal1)) & r1_xxreal_0(1,D) & r1_xxreal_0(D,E) & k1_nat_1(k19_margrel1(B),1) = E & k1_nat_1(E,1) = k19_margrel1(C) & ! [F] : ( m2_finseq_1(F,k4_ordinal1) => ( k3_finseq_1(F) = E => ( ( r2_hidden(k2_funct_7(k4_ordinal1,F,D,k5_numbers),k1_relset_1(k3_finseq_2(k4_ordinal1),A)) => r2_hidden(k2_finseq_3(D,F),k1_relset_1(k3_finseq_2(k4_ordinal1),B)) ) & ( r2_hidden(k2_finseq_3(D,F),k1_relset_1(k3_finseq_2(k4_ordinal1),B)) => r2_hidden(k2_funct_7(k4_ordinal1,F,D,k5_numbers),k1_relset_1(k3_finseq_2(k4_ordinal1),A)) ) & ( r2_hidden(k2_funct_7(k4_ordinal1,F,D,k5_numbers),k1_relset_1(k3_finseq_2(k4_ordinal1),A)) => k1_recdef_1(A,k2_funct_7(k4_ordinal1,F,D,k5_numbers)) = k1_recdef_1(B,k2_finseq_3(D,F)) ) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( ( r2_hidden(k2_funct_7(k4_ordinal1,F,D,k1_nat_1(G,1)),k1_relset_1(k3_finseq_2(k4_ordinal1),A)) => ( r2_hidden(k2_funct_7(k4_ordinal1,F,D,G),k1_relset_1(k3_finseq_2(k4_ordinal1),A)) & r2_hidden(k8_finseq_1(k4_ordinal1,k2_funct_7(k4_ordinal1,F,D,G),k12_finseq_1(k4_ordinal1,k1_recdef_1(A,k2_funct_7(k4_ordinal1,F,D,G)))),k1_relset_1(k3_finseq_2(k4_ordinal1),C)) ) ) & ( ( r2_hidden(k2_funct_7(k4_ordinal1,F,D,G),k1_relset_1(k3_finseq_2(k4_ordinal1),A)) & r2_hidden(k8_finseq_1(k4_ordinal1,k2_funct_7(k4_ordinal1,F,D,G),k12_finseq_1(k4_ordinal1,k1_recdef_1(A,k2_funct_7(k4_ordinal1,F,D,G)))),k1_relset_1(k3_finseq_2(k4_ordinal1),C)) ) => r2_hidden(k2_funct_7(k4_ordinal1,F,D,k1_nat_1(G,1)),k1_relset_1(k3_finseq_2(k4_ordinal1),A)) ) & ( r2_hidden(k2_funct_7(k4_ordinal1,F,D,k1_nat_1(G,1)),k1_relset_1(k3_finseq_2(k4_ordinal1),A)) => k1_recdef_1(A,k2_funct_7(k4_ordinal1,F,D,k1_nat_1(G,1))) = k1_recdef_1(C,k8_finseq_1(k4_ordinal1,k2_funct_7(k4_ordinal1,F,D,G),k12_finseq_1(k4_ordinal1,k1_recdef_1(A,k2_funct_7(k4_ordinal1,F,D,G))))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d9_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v2_comseq_3(A) <=> v1_series_1(k55_valued_1(k4_ordinal1,k2_numbers,A)) ) ) )).
fof(d9_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( l2_conlat_1(B,A) => ( v6_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) ) ) ) ) )).
fof(d9_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( m1_convex4(C,A) => ! [D] : ( m1_convex4(D,A) => ( D = k7_convex4(A,B,C) <=> ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d9_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => k12_cqc_sim1(A,B) = a_2_0_cqc_sim1(A,B) ) ) )).
fof(d9_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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) ) ) ) )).
fof(d9_csspace,axiom,( ! [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) ) => ! [B] : ( 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)) ) ) ) )).
fof(d9_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( 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] : ( r2_hidden(D,k4_csspace4(A,B)) => k1_funct_1(C,D) = k2_seq_4(k7_csspace4(A,B,k6_csspace4(A,B,D))) ) ) ) ) ) )).
fof(d9_decomp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)))) ) ) )).
fof(d9_dickson,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( r1_dickson(A,B,C) <=> ( r1_tarski(C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,B) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,C) & r1_orders_2(A,E,D) ) ) ) ) ) ) ) ) )).
fof(d9_diff_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k9_diff_1(A,B,C) = k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(A,B),k1_funct_1(A,C)),k6_xcmplx_0(B,C)) ) ) ) )).
fof(d9_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( ~ v2_struct_0(A) => ( B = k5_dilworth(A) <=> ! [C] : ( 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 ) ) ) ) ) )).
fof(d9_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( C = k9_dist_1(A,B) <=> ( k4_finseq_1(C) = k2_finseq_1(k5_card_1(A)) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(C)) => k1_funct_1(C,D) = k3_xcmplx_0(k3_finseq_1(B),k1_funct_1(k4_dist_1(A,B),D)) ) ) ) ) ) ) ) )).
fof(d9_dtconstr,axiom,( ! [A] : ( 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)) ) )).
fof(d9_e_siec,axiom,( ! [A] : ( ( v2_e_siec(A) & v3_e_siec(A) & l1_e_siec(A) ) => k7_e_siec(A) = k10_xtuple_0(u1_e_siec(A)) ) )).
fof(d9_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( 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) ) ) ) )).
fof(d9_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,k2_ens_1(A)) => k3_funct_2(k2_ens_1(A),A,B,C) = k3_ens_1(A,C) ) ) ) ) )).
fof(d9_entropy1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => k6_entropy1(A) = k4_xcmplx_0(k18_rvsum_1(k4_entropy1(A))) ) )).
fof(d9_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_eqrel_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => r2_hidden(D,k3_funct_2(A,B,C,D)) ) ) ) ) ) )).
fof(d9_euclid,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => k17_euclid(A) = k1_funct_1(A,1) ) )).
fof(d9_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(d9_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => k4_euclidlp(A,B,C,D) = a_4_1_euclidlp(A,B,C,D) ) ) ) ) )).
fof(d9_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_exchsort(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_exchsort(B) ) => ( m1_exchsort(B,A) <=> ? [C] : ( 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) ) ) ) ) )).
fof(d9_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) ) => ! [D] : ( ( 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] : ( ( 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] : ( v7_ordinal1(F) & E = k5_extpro_1(A,B,C,D,F) & k3_extpro_1(A,B,C,E) = k2_compos_1(B) ) ) ) ) ) ) ) ) )).
fof(d9_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(d9_ff_siec,axiom,( ! [A] : ( ( 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))) ) )).
fof(d9_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v2_struct_0(C) & v10_lattices(C) & l3_lattices(C) ) => ( C = k6_filter_0(A,B) <=> ? [D] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(d9_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(d9_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(d9_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k9_fin_topo(A,B) = a_2_2_fin_topo(A,B) ) ) )).
fof(d9_finseq_1,axiom,( ! [A] : ! [B] : k10_finseq_1(A,B) = k7_finseq_1(k9_finseq_1(A),k9_finseq_1(B)) )).
fof(d9_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r4_finseq_8(A,B,C) <=> r1_tarski(k4_finseq_5(A,C),k4_finseq_5(A,B)) ) ) ) ) )).
fof(d9_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k8_fintopo2(A,B) = a_2_0_fintopo2(A,B) ) ) )).
fof(d9_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v7_ordinal1(C) => k9_fintopo3(A,B,C) = k1_funct_1(k8_fintopo3(A,B),C) ) ) ) )).
fof(d9_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ( v4_fintopo6(B,A) <=> ( r1_xxreal_0(1,k3_finseq_1(B)) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d9_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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 = k6_fomodel0(A,B) <=> ! [D] : ( 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(k5_fomodel0(A,B,D),k6_xcmplx_0(k3_finseq_1(D),1)) ) ) ) ) ) )).
fof(d9_fomodel1,axiom,( ! [A] : ( l1_fomodel1(A) => k9_fomodel1(A) = k6_subset_1(u1_struct_0(A),k2_tarski(u2_struct_0(A),u3_struct_0(A))) ) )).
fof(d9_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_fomodel2(C,A,B) ) => ! [D] : ( ( 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 = k9_fomodel2(A,B,C) <=> ! [E] : ( 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) = k8_fomodel2(A,B,C,E) ) ) ) ) ) ) )).
fof(d9_fomodel3,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( v1_fomodel3(C,A,B) <=> ! [D] : ! [E] : ( r2_hidden(k4_tarski(D,E),A) => r2_hidden(k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E)),B) ) ) ) ) ) )).
fof(d9_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( 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) = a_2_0_fomodel4(A,B) ) ) )).
fof(d9_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(d9_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( ( ~ v2_struct_0(D) & l2_fsm_1(D,A,B) ) => ( r4_fsm_1(A,B,C,D) <=> ! [E] : ( 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) ) ) ) ) ) ) )).
fof(d9_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & v1_fsm_2(C,A) & v5_fsm_2(C,A) & l2_fsm_2(C,A,B) ) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,B) => ( E = k2_fsm_2(A,B,C,D) <=> r3_fsm_2(A,B,C,D,E) ) ) ) ) ) ) )).
fof(d9_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k9_ftacell1(A,B,C,D,E) = k21_gfacirc1(A,B,C) )).
fof(d9_funcop_1,axiom,( ! [A] : ! [B] : k16_funcop_1(A,B) = k7_funcop_1(k1_tarski(A),B) )).
fof(d9_funcsdom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_funcsdom(A) ) => ( v2_funcsdom(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => k1_rlvect_1(A,k6_algstr_0(A,B,C),D) = k6_algstr_0(A,k1_rlvect_1(A,B,D),C) ) ) ) ) ) )).
fof(d9_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_relat_1(A) <=> ! [B] : ~ ( r2_hidden(B,k9_xtuple_0(A)) & v1_xboole_0(k1_funct_1(A,B)) ) ) ) )).
fof(d9_funct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(B))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(A))) => ( E = k6_funct_2(A,B,C,D) <=> ! [F] : ( m1_subset_1(F,k1_zfmisc_1(A)) => ( r2_hidden(F,E) <=> ? [G] : ( m1_subset_1(G,k1_zfmisc_1(B)) & r2_hidden(G,D) & F = k8_relset_1(A,B,C,G) ) ) ) ) ) ) ) ) ) )).
fof(d9_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k9_funct_6(A) = k3_funct_5(k2_funct_5(A)) ) )).
fof(d9_funct_7,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( m2_funct_7(B,A) <=> ( k1_nat_1(k3_finseq_1(B),1) = k3_finseq_1(A) & ! [C] : ( v7_ordinal1(C) => ( 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,k1_nat_1(C,1)))) ) ) ) ) ) ) )).
fof(d9_funct_8,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => k1_funct_1(A,B) = k2_absvalue(B) ) ) ) )).
fof(d9_functor0,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => ! [C] : ( 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)))) ) ) ) ) )).
fof(d9_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => k4_fvaluat1(A,B) = o_2_0_fvaluat1(A,B) ) ) ) )).
fof(d9_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => k13_fvsum_1(A,B,C) = k4_rlvect_1(A,k11_fvsum_1(A,B,C)) ) ) ) )).
fof(d9_gate_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : 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) )).
fof(d9_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v4_vectsp_1(A) & l4_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d9_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(d9_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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) )).
fof(d9_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) ) => k9_glib_000(A) = k1_funct_1(A,k4_glib_000) ) )).
fof(d9_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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) ) ) )).
fof(d9_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => k4_glib_002(A) = k1_card_1(k3_glib_002(A)) ) )).
fof(d9_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(d9_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => k8_glib_004(A,B) = k4_tarski(k16_funcop_1(B,k5_numbers),k1_xboole_0) ) ) )).
fof(d9_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( ( 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] : ( m1_glib_005(C,A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k7_glib_000(A))) => ( D = k2_glib_005(A,B,C) <=> ! [E] : ( r2_hidden(E,D) <=> ( r3_glib_005(A,B,C,E) | r4_glib_005(A,B,C,E) ) ) ) ) ) ) ) )).
fof(d9_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ( v4_graph_1(A) <=> ! [B] : ~ ( r2_hidden(B,u4_struct_0(A)) & k1_funct_1(u1_graph_1(A),B) = k1_funct_1(u2_graph_1(A),B) ) ) ) )).
fof(d9_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_graph_1(B,A) => ( v3_graph_2(B,A) <=> ? [C] : ( m2_finseq_1(C,u1_struct_0(A)) & r1_graph_2(A,C,B) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d9_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) = o_3_1_graph_3(A,B,C) ) ) ) ) )).
fof(d9_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : k5_graph_5(A,B,C,D) = a_4_0_graph_5(A,B,C,D) ) ) ) )).
fof(d9_graphsp,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k3_finseq_2(k1_numbers)) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k13_graphsp(A,B) = a_2_2_graphsp(A,B) ) ) )).
fof(d9_grcat_1,axiom,( ! [A] : ( l1_grcat_1(A) => k9_grcat_1(A) = u3_grcat_1(A) ) )).
fof(d9_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_group_1(A,B,C) = k1_binop_1(k4_group_1(A),C,B) ) ) ) )).
fof(d9_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => k8_group_2(A,B) = u1_struct_0(B) ) ) )).
fof(d9_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r3_group_3(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & B = k4_group_3(A,C,D) ) ) ) ) ) )).
fof(d9_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( 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))) ) ) ) )).
fof(d9_group_5,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d9_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(d9_group_9,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(d9_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(d9_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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] : ( 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)) ) ) ) )).
fof(d9_heyting1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k12_normform(A))) => ! [D] : ( 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))) ) ) ) ) )).
fof(d9_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => k4_hilbert1(A,B) = k7_finseq_1(k7_finseq_1(k12_finseq_1(k4_ordinal1,2),A),B) ) ) )).
fof(d9_hilbert2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k4_ordinal1) => k1_funct_1(A,k1_hilbert2(B)) = k2_trees_4(k1_hilbert1,k1_hilbert2(B)) ) & ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ? [D] : ( v1_relat_1(D) & v5_relat_1(D,k1_hilbert1) & v1_funct_1(D) & v3_trees_2(D) & ? [E] : ( 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) ) ) ) ) ) ) ) )).
fof(d9_hurwitz,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(A,k1_complfld) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(B,k1_complfld) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => ( B = k7_hurwitz(A) <=> ! [C] : ( m1_subset_1(C,k4_ordinal1) => k1_normsp_1(k1_complfld,B,C) = k8_group_1(k1_complfld,k2_binop_1(u1_struct_0(k1_complfld),k4_ordinal1,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))) ) ) ) ) )).
fof(d9_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k9_idea_1(A,B,C) = k8_idea_1(A,k4_nat_d(k3_xcmplx_0(k7_idea_1(A,B),k7_idea_1(A,C)),k1_nat_1(k5_series_1(2,A),1))) ) ) ) )).
fof(d9_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( m2_ideal_1(C,A,B) <=> ! [D] : ~ ( r2_hidden(D,k1_relset_1(k4_ordinal1,C)) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m2_subset_1(F,u1_struct_0(A),B) => k7_partfun1(u1_struct_0(A),C,D) != k6_algstr_0(A,E,F) ) ) ) ) ) ) ) )).
fof(d9_incproj,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) ) => ( v5_incproj(A) <=> ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & r1_incsp_1(A,D,B) & r1_incsp_1(A,D,C) ) ) ) ) ) )).
fof(d9_incsp_1,axiom,( ! [A] : ( l1_incsp_1(A) => ( v6_incsp_1(A) <=> ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ? [D] : ( m1_subset_1(D,u2_incsp_1(A)) & r4_incsp_1(A,k7_domain_1(u1_incsp_1(A),B,C),D) ) ) ) ) ) )).
fof(d9_index_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( m3_index_1(E,A,B,C,D) => ! [F] : ( ( ~ 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] : ( m1_subset_1(G,A) => m1_subset_1(k2_index_1(A,k1_xtuple_0(E),G),u1_struct_0(F)) ) & ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d9_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => k4_int_1(A,B) = k1_int_1(k7_xcmplx_0(A,B)) ) ) )).
fof(d9_int_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_int_3(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_ordinal1))) ) => ( m1_int_3(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( D != k4_struct_0(A) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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),k4_ordinal1,B,D),k3_funct_2(u1_struct_0(A),k4_ordinal1,B,F)) ) ) ) ) ) ) ) ) ) ) )).
fof(d9_integr15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_euclid(A)))) ) => ! [D] : ( ( 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) ) ) ) )).
fof(d9_integr16,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k2_numbers))) ) => k8_integr16(A,B,C) = k2_xcmplx_0(k4_integra5(A,B,k5_comseq_3(k1_numbers,C)),k3_xcmplx_0(k4_integra5(A,B,k6_comseq_3(k1_numbers,C)),k7_complex1)) ) ) ) )).
fof(d9_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d9_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( 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] : ( m1_integra1(D,A) => k1_funct_1(C,D) = k6_integra1(A,B,D) ) ) ) ) ) )).
fof(d9_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_interva1(C,A) ) => k9_interva1(A,B,C) = k4_setfam_1(B,C) ) ) ) )).
fof(d9_intpro_1,axiom,( k2_intpro_1 = k12_finseq_1(k4_ordinal1,k5_numbers) )).
fof(d9_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,B,C) => ! [G] : ( m2_cat_1(G,B,C) => ! [H] : ( m2_nattra_1(H,A,B,D,E) => ! [I] : ( m2_nattra_1(I,B,C,F,G) => k6_isocat_1(A,B,C,D,E,F,G,H,I) = k5_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)) ) ) ) ) ) ) ) ) ) )).
fof(d9_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,k6_cat_2(B,C)) => ! [E] : ( m2_cat_1(E,A,k6_cat_2(B,C)) => ! [F] : ( m2_nattra_1(F,A,k6_cat_2(B,C),D,E) => k11_isocat_2(A,B,C,D,E,F) = k4_isocat_1(A,k6_cat_2(B,C),B,D,E,F,k12_cat_2(B,C)) ) ) ) ) ) ) )).
fof(d9_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k9_jgraph_6(A,B,C) = a_3_4_jgraph_6(A,B,C) ) ) ) )).
fof(d9_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal2(A) => ! [B] : ( ( ~ 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(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)),2)),k18_pscomp_1(A),k22_pscomp_1(A))),k18_euclid(k2_jordan5c(B,k6_jordan6(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)),2)),k22_pscomp_1(A),k18_pscomp_1(A)))) ) ) ) ) ) )).
fof(d9_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v3_lattices(C) & v10_lattices(C) & l3_lattices(C) ) => ( C = k8_knaster(A,B) <=> ? [D] : ( ~ 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) ) ) ) ) ) ) )).
fof(d9_lang1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) ) )).
fof(d9_laplace,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => k11_laplace(A,B,C) = k4_matrix_3(A,B,k4_matrix_0(u1_struct_0(A),k10_laplace(u1_struct_0(A),C))) ) ) ) )).
fof(d9_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_lattice3(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => r1_orders_2(A,D,C) ) ) ) ) ) )).
fof(d9_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( m2_lattice4(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(d9_lattice5,axiom,( ! [A] : k5_lattice5(A) = k2_xboole_0(A,k1_enumset1(k1_tarski(A),k1_tarski(k1_tarski(A)),k1_tarski(k1_tarski(k1_tarski(A))))) )).
fof(d9_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v4_lattice6(B,A) <=> k4_lattice6(A,B) != B ) ) ) )).
fof(d9_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m1_lattice5(D,A,B,C) => k8_lattice8(A,B,C,D) = k6_lattice8(A,B,C,D,k7_lattice5(A,B,C)) ) ) ) ) )).
fof(d9_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( v9_lattices(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_lattices(A,B,k1_lattices(A,B,C)) = B ) ) ) ) )).
fof(d9_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( ( v4_lexbfs(B,A) & m1_lexbfs(B,A) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( r1_xxreal_0(k39_glib_000(B),C) => ( D = k6_lexbfs(A,B,C) <=> D = o_1_0_lexbfs(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))) ) ) ) ) ) ) ) )).
fof(d9_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( v7_ordinal1(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k9_funct_2(k2_zfmisc_1(A,A),k1_rcomp_1(k5_numbers,1))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_funct_2(k2_zfmisc_1(A,A),k1_rcomp_1(k5_numbers,1))))) & D = k9_nat_1(k9_funct_2(k2_zfmisc_1(A,A),k1_rcomp_1(k5_numbers,1)),E,C) & k9_nat_1(k9_funct_2(k2_zfmisc_1(A,A),k1_rcomp_1(k5_numbers,1)),E,k5_numbers) = k4_fuzzy_4(A,A) & ! [F] : ( v7_ordinal1(F) => ? [G] : ( v5_relat_1(G,k1_rcomp_1(k5_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))) & k9_nat_1(k9_funct_2(k2_zfmisc_1(A,A),k1_rcomp_1(k5_numbers,1)),E,F) = G & k9_nat_1(k9_funct_2(k2_zfmisc_1(A,A),k1_rcomp_1(k5_numbers,1)),E,k1_nat_1(F,1)) = k3_fuzzy_4(A,A,A,G,B) ) ) ) ) ) ) ) ) )).
fof(d9_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v6_limfunc1(A) <=> ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(B,C) & r2_hidden(C,k1_relset_1(k1_numbers,A)) ) ) & ? [B] : ( v1_xreal_0(B) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_limfunc1(C) & r1_tarski(k10_xtuple_0(C),k1_relset_1(k1_numbers,A)) ) => ( v2_comseq_2(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,C,A)) & k1_seq_2(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,C,A)) = B ) ) ) ) ) ) ) )).
fof(d9_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k8_lopban_1(A,B)))) => ( C = k10_lopban_1(A,B) <=> ! [D] : ( 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)))) ) ) ) ) ) ) )).
fof(d9_lopban_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lopban_2(A) ) => ( v2_lopban_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k2_normsp_0(A,k6_algstr_0(A,B,C)),k3_xcmplx_0(k2_normsp_0(A,B),k2_normsp_0(A,C))) ) ) ) ) )).
fof(d9_lopban_3,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( C = k5_lopban_3(A,B) <=> ( k5_rsspace3(A,C,k5_numbers) = k5_struct_0(A) & ! [D] : ( v7_ordinal1(D) => k5_rsspace3(A,C,k1_nat_1(D,1)) = k6_algstr_0(A,k5_rsspace3(A,C,D),B) ) ) ) ) ) ) )).
fof(d9_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( E = k8_lopban_4(A,B,C,D) <=> ! [F] : ( v7_ordinal1(F) => ( ( r1_xxreal_0(F,D) => k9_nat_1(u1_struct_0(A),E,F) = k6_algstr_0(A,k9_nat_1(u1_struct_0(A),k1_lopban_4(A,B),F),k5_algstr_0(A,k9_nat_1(u1_struct_0(A),k1_bhsp_4(A,k1_lopban_4(A,C)),D),k9_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) => k9_nat_1(u1_struct_0(A),E,F) = k4_struct_0(A) ) ) ) ) ) ) ) ) ) )).
fof(d9_lopclset,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(d9_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => k13_lpspacc1(A,B,C) = a_3_0_lpspacc1(A,B,C) ) ) ) )).
fof(d9_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => k10_lpspace1(A,B,C) = g1_rlvect_1(k9_lpspace1(A,B,C),k10_subset_1(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))) ) ) ) )).
fof(d9_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v2_xxreal_0(D) & v1_xreal_0(D) ) => k8_lpspace2(A,B,C,D) = k5_lpspace2(A,B,C,k8_lpspace1(A,k5_numbers),D) ) ) ) ) )).
fof(d9_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => k12_ltlaxio3(A) = k4_ltlaxio1(k7_partfun1(k1_hilbert1,k2_ltlaxio2(k8_ltlaxio3(A)),k3_finseq_1(k2_ltlaxio2(k8_ltlaxio3(A)))),k7_partfun1(k1_hilbert1,k2_ltlaxio2(k4_ltlaxio2(k9_ltlaxio3(A))),k3_finseq_1(k2_ltlaxio2(k4_ltlaxio2(k9_ltlaxio3(A)))))) ) )).
fof(d9_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => k8_ltlaxio4(A) = a_1_5_ltlaxio4(A) ) )).
fof(d9_margrel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k3_margrel1(A)) => ( B = k4_margrel1(A) <=> ! [C] : ( m2_finseq_1(C,A) => ~ r2_hidden(C,B) ) ) ) ) )).
fof(d9_mathmorp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(d9_matrix16,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( r3_matrix16(A,B,C) <=> ( k3_finseq_1(C) = k1_matrix_0(B) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(k4_tarski(D,E),k2_matrix_0(B)) & r1_xxreal_0(D,E) ) => k3_matrix_0(u1_struct_0(A),B,D,E) = k1_funct_1(C,k2_xcmplx_0(k5_int_1(k6_xcmplx_0(E,D),k3_finseq_1(C)),1)) ) ) ) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(k4_tarski(D,E),k2_matrix_0(B)) & r1_xxreal_0(E,D) ) => k3_matrix_0(u1_struct_0(A),B,D,E) = k1_funct_1(k5_fvsum_1(A,C),k2_xcmplx_0(k5_int_1(k6_xcmplx_0(E,D),k3_finseq_1(C)),1)) ) ) ) ) ) ) ) ) )).
fof(d9_matrix_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => k9_matrix_0(A) = k3_card_3(k2_funct_6(A)) ) )).
fof(d9_matrix_2,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_matrix_2(D,k3_matrix_2(B)) => ( ( v5_matrix_2(D,k2_matrix_2(k3_matrix_2(B))) => k5_matrix_2(A,B,C,D) = C ) & ( ~ v5_matrix_2(D,k2_matrix_2(k3_matrix_2(B))) => k5_matrix_2(A,B,C,D) = k4_algstr_0(A,C) ) ) ) ) ) ) )).
fof(d9_matrix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => k12_matrix_3(A,B,C) = k7_setwiseo(k3_matrix_2(A),u1_struct_0(B),u1_algstr_0(B),k6_matrix_2(k3_matrix_2(A)),k11_matrix_3(A,B,C)) ) ) ) )).
fof(d9_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ( B = k10_matrixc1(A) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k2_finseq_1(k3_finseq_1(A))) => k9_matrix_5(B,C) = k17_rvsum_1(k7_matrix_0(k2_numbers,A,C)) ) ) ) ) ) ) )).
fof(d9_matrixj1,axiom,( ! [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] : ( ( v1_matrixj1(B,u1_struct_0(A)) & m2_finseq_1(B,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d9_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( ~ r1_xxreal_0(k3_finseq_1(A),k5_numbers) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( B = k9_matrixr1(A) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & k1_matrix_0(B) = 1 & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(A)) => k1_funct_1(B,C) = k9_finseq_1(k1_funct_1(A,C)) ) ) ) ) ) ) ) )).
fof(d9_matroid0,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( 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 ) ) ) ) ) ) ) )).
fof(d9_matrprob,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( v5_matrprob(A) <=> ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => k18_rvsum_1(k1_matrprob(k1_numbers,A,B)) = 1 ) ) ) ) )).
fof(d9_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => k12_member_1(A,B) = a_2_4_member_1(A,B) ) ) )).
fof(d9_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( r1_tarski(A,B) <=> ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => r2_hidden(C,B) ) ) ) ) )).
fof(d9_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k2_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( D = k9_mesfun7c(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k1_funct_1(D,E) = k1_funct_1(k4_mesfunc5(A,k2_numbers,B,E),C) ) ) ) ) ) ) )).
fof(d9_mesfunc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k6_numbers) & v1_funct_1(B) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_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] : ( m1_subset_1(E,A) => ( r2_hidden(E,k9_xtuple_0(D)) => k12_supinf_2(D,E) = k2_extreal1(C,k12_supinf_2(B,E)) ) ) ) ) ) ) ) ) )).
fof(d9_mesfunc5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v8_mesfunc5(A) <=> ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & ~ r1_xxreal_0(B,k9_nat_1(k6_numbers,A,D)) ) ) ) ) ) ) )).
fof(d9_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( C = k7_mesfunc8(A,B) <=> ( k1_relset_1(A,C) = k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers)) & ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(d9_metric_1,axiom,( ! [A] : ( l1_metric_1(A) => ( v9_metric_1(A) <=> v5_metric_1(u1_metric_1(A),u1_struct_0(A)) ) ) )).
fof(d9_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => k6_metric_2(A) = a_1_2_metric_2(A) ) )).
fof(d9_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_midsp_1(B,A) => ! [C] : ( m1_midsp_1(C,A) => ! [D] : ( m1_midsp_1(D,A) => ( D = k7_midsp_1(A,B,C) <=> ? [E] : ( m1_subset_1(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) & ? [F] : ( 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))) ) ) ) ) ) ) ) )).
fof(d9_midsp_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,A) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d9_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_nat_1(A,2)) ) => ! [C] : ( ( v4_midsp_2(C,B) & l1_midsp_2(C,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(B))) => ! [F] : ( m2_finseq_2(F,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(u1_midsp_2(B,C)))) => ( F = k8_midsp_3(A,B,C,D,E) <=> ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d9_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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) ) ) ) )).
fof(d9_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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)) ) ) )).
fof(d9_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(d9_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k6_modal_1) => k11_modal_1(A) = k7_trees_2(k8_funcop_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k2_trees_1(1),k1_domain_1(k4_ordinal1,k4_ordinal1,1,1)),k14_trees_3(k5_numbers),A) ) )).
fof(d9_modcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_modcat_1(B,A) => ! [C] : ( m4_modcat_1(C,A,k4_modcat_1(A,B)) => k6_modcat_1(A,B,C) = k3_mod_2(A,C) ) ) ) )).
fof(d9_modelc_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => k9_modelc_1(A) = k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,2),A) ) )).
fof(d9_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( A = k9_modelc_2 <=> ( ! [B] : ( r2_hidden(B,A) => m2_finseq_1(B,k4_ordinal1) ) & ! [B] : ( v7_ordinal1(B) => r2_hidden(k2_modelc_2(B),A) ) & ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ( r2_hidden(B,A) => r2_hidden(k3_modelc_2(B),A) ) ) & ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r2_hidden(k4_modelc_2(B,C),A) ) ) ) & ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r2_hidden(k5_modelc_2(B,C),A) ) ) ) & ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ( r2_hidden(B,A) => r2_hidden(k6_modelc_2(B),A) ) ) & ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r2_hidden(k7_modelc_2(B,C),A) ) ) ) & ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r2_hidden(k8_modelc_2(B,C),A) ) ) ) & ! [B] : ( ~ v1_xboole_0(B) => ( ( ! [C] : ( r2_hidden(C,B) => m2_finseq_1(C,k4_ordinal1) ) & ! [C] : ( v7_ordinal1(C) => r2_hidden(k2_modelc_2(C),B) ) & ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( r2_hidden(C,B) => r2_hidden(k3_modelc_2(C),B) ) ) & ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k4_modelc_2(C,D),B) ) ) ) & ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k5_modelc_2(C,D),B) ) ) ) & ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( r2_hidden(C,B) => r2_hidden(k6_modelc_2(C),B) ) ) & ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k7_modelc_2(C,D),B) ) ) ) & ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k8_modelc_2(C,D),B) ) ) ) ) => r1_tarski(A,B) ) ) ) ) ) )).
fof(d9_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( l1_modelc_3(B,A) => ! [C] : ( l1_modelc_3(C,A) => ( r4_modelc_3(A,B,C) <=> ( r2_modelc_3(A,B,C) | r3_modelc_3(A,B,C) ) ) ) ) ) )).
fof(d9_monoid_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d9_monoid_1,axiom,( ! [A] : ( ( ~ 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))) ) ) ) )).
fof(d9_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u4_struct_0(A)) => k6_msafree(A,B,C) = k4_tarski(C,u1_struct_0(A)) ) ) ) )).
fof(d9_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ! [F] : ( ( 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 ) ) ) ) ) ) ) )).
fof(d9_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m3_pboole(C,u1_struct_0(A),k4_equation(A)) => ! [D] : ( m1_msafree(D,A,B) => ( v7_msafree4(D,A,B,C) <=> ! [E] : ( ( v4_msualg_1(E,A) & v6_msafree4(E,A,C) & l3_msualg_1(E,A) ) => ! [F] : ( m2_pboole(F,u1_struct_0(A),D,u3_msualg_1(A,E)) => ? [G] : ( m2_pboole(G,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,E)) & r1_msualg_3(A,B,E,G) & r8_pboole(u1_struct_0(A),k1_msafree(u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,E),D,G),F) ) ) ) ) ) ) ) ) )).
fof(d9_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( 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] : ( m2_pboole(E,u1_struct_0(A),C,u3_msualg_1(A,B)) => ! [F] : ( ( 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] : ( m1_trees_1(G,k9_xtuple_0(F)) => ( ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d9_msualg_1,axiom,( ! [A] : ( ( ~ 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(k5_numbers,u1_struct_0(A)) ) )).
fof(d9_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d9_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d9_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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] : ( m1_msualg_6(D,A,B) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(d9_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_mycielsk(B,A) => ! [C] : ( 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)))) ) ) ) ) )).
fof(d9_nagata_1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ! [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))) ) => ! [D] : ( ( 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] : ( r2_hidden(E,A) => k1_funct_1(D,E) = k3_xxreal_0(B,k1_funct_1(C,E)) ) ) ) ) ) )).
fof(d9_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k8_newton) & v1_funct_1(B) & v1_partfun1(B,k8_newton) ) => ( B = k13_nat_3(A) <=> ( k13_pre_poly(B) = k22_pre_poly(k8_newton,k12_nat_3(A)) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k22_pre_poly(k8_newton,k12_nat_3(A))) => k1_funct_1(B,C) = k1_newton(C,k11_nat_3(A,C)) ) ) ) ) ) ) )).
fof(d9_nat_lat,axiom,( ! [A] : ( ( 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] : ( m2_subset_1(B,k4_ordinal1,k6_nat_lat) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k6_nat_lat) => k5_binop_1(k6_nat_lat,A,B,C) = k5_nat_d(B,C) ) ) ) ) )).
fof(d9_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( m1_nattra_1(E,A,B,C,D) => ( v1_nattra_1(E,A,B,C,D) <=> ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => v9_cat_1(k2_nattra_1(A,B,C,D,E,F),B,k8_cat_1(A,B,C,F),k8_cat_1(A,B,D,F)) ) ) ) ) ) ) ) )).
fof(d9_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_numbers))) ) => ! [C] : ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,k1_numbers,u1_struct_0(A),D,B)) & k7_partfun1(k1_numbers,B,C) = k1_seq_2(k8_funct_2(k4_ordinal1,k1_numbers,u1_struct_0(A),D,B)) ) ) ) ) ) ) ) ) )).
fof(d9_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( r2_ndiff_1(D,A,B,C) => ! [E] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d9_necklace,axiom,( ! [A] : ( v7_ordinal1(A) => k4_necklace(A) = k2_necklace(k1_necklace(A)) ) )).
fof(d9_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k2_net_1(A)) => ( k2_net_1(A) != k1_xboole_0 => ! [C] : ( 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) ) ) ) ) ) ) )).
fof(d9_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( 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] : ( v1_xreal_0(E) & ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r2_hidden(F,C) & r2_hidden(G,C) ) => r1_xxreal_0(k2_normsp_0(B,k5_algstr_0(B,k7_partfun1(u1_struct_0(B),D,F),k7_partfun1(u1_struct_0(B),D,G))),k3_xcmplx_0(E,k2_normsp_0(A,k5_algstr_0(A,F,G)))) ) ) ) ) ) ) ) ) ) )).
fof(d9_normform,axiom,( ! [A] : k8_normform(A) = a_1_1_normform(A) )).
fof(d9_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ( v8_o_ring_1(B,A) <=> ( k3_finseq_1(B) != k5_numbers & ! [C] : ( v7_ordinal1(C) => ~ ( C != k5_numbers & r1_xxreal_0(C,k3_finseq_1(B)) & ~ v5_o_ring_1(k7_partfun1(u1_struct_0(A),B,C),A) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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 != k5_numbers & ~ r1_xxreal_0(C,D) & E != k5_numbers & ~ r1_xxreal_0(C,E) ) ) ) ) ) ) ) ) ) )).
fof(d9_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k9_openlatt(A)) => ! [D] : ( m1_subset_1(D,k9_openlatt(A)) => k5_binop_1(k9_openlatt(A),B,C,D) = k11_openlatt(A,C,D) ) ) ) ) ) )).
fof(d9_oposet_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v2_necklace(A) <=> r5_relat_2(u1_orders_2(A),u1_struct_0(A)) ) ) )).
fof(d9_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( 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] : ( 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] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d9_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( 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) ) ) ) )).
fof(d9_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k2_orders_2(A,B) = a_2_1_orders_2(A,B) ) ) )).
fof(d9_orders_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_orders_3(A) ) => ! [B] : ( ( v6_altcat_1(B) & l2_altcat_1(B) ) => ( B = k4_orders_3(A) <=> ( u1_struct_0(B) = A & ! [C] : ( m1_orders_3(C,A) => ! [D] : ( m1_orders_3(D,A) => ( k1_binop_1(u1_altcat_1(B),C,D) = k1_orders_3(C,D) & ! [E] : ( m1_orders_3(E,A) => ! [F] : ( m1_orders_3(F,A) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(d9_ordinal1,axiom,( ! [A] : ! [B] : ( B = k2_ordinal1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( r2_hidden(C,A) & v3_ordinal1(C) ) ) ) )).
fof(d9_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_ordinal2(B) ) => ( ( A = k5_ordinal1 => ( r1_ordinal2(A,B) <=> ? [C] : ( v3_ordinal1(C) & r2_hidden(C,k9_xtuple_0(B)) & ! [D] : ( v3_ordinal1(D) => ( ( r1_ordinal1(C,D) & r2_hidden(D,k9_xtuple_0(B)) ) => k1_funct_1(B,D) = k5_ordinal1 ) ) ) ) ) & ( A != k5_ordinal1 => ( r1_ordinal2(A,B) <=> ! [C] : ( v3_ordinal1(C) => ! [D] : ( v3_ordinal1(D) => ~ ( r2_hidden(C,A) & r2_hidden(A,D) & ! [E] : ( v3_ordinal1(E) => ~ ( r2_hidden(E,k9_xtuple_0(B)) & ! [F] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d9_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ( v5_ordinal5(A) <=> ? [B] : ( v3_ordinal1(B) & ? [C] : ( v7_ordinal1(C) & r2_hidden(k5_numbers,C) & A = k11_ordinal2(C,k12_ordinal2(k4_ordinal1,B)) ) ) ) ) )).
fof(d9_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d9_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d9_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v2_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k2_osalg_4(A)) => ! [E] : ( ( 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] : ! [G] : ( r2_hidden(k4_tarski(F,G),E) <=> ? [H] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(d9_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( B = k7_parsp_1(A) <=> ! [C] : ( r2_hidden(C,B) <=> ( r2_hidden(C,k6_parsp_1(A)) & ? [D] : ( m1_subset_1(D,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) & ? [E] : ( m1_subset_1(E,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) & ? [F] : ( m1_subset_1(F,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) & ? [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(d9_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) )).
fof(d9_pcs_0,axiom,( ! [A] : ( l1_pcs_0(A) => ( v4_pcs_0(A) <=> r1_relat_2(u1_pcs_0(A),u1_struct_0(A)) ) ) )).
fof(d9_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(d9_pdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(2)) => ( r4_pdiff_3(A,B) => ! [C] : ( v1_xreal_0(C) => ( C = k5_pdiff_3(A,B) <=> ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & B = k10_finseq_1(D,E) & ? [F] : ( 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] : ( v1_funct_1(G) & v3_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [H] : ( v1_funct_1(H) & v2_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & C = k1_funct_1(G,1) & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,F) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(2,2,k1_pdiff_3(2,2,A),B),I),k1_funct_1(k1_pdiff_2(2,2,k1_pdiff_3(2,2,A),B),E)) = k2_xcmplx_0(k1_funct_1(G,k6_xcmplx_0(I,E)),k1_funct_1(H,k6_xcmplx_0(I,E))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d9_pdiff_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => k6_pdiff_4(A,B,C) = k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k10_pdiff_1(3,1,A,B),k1_funct_1(k5_pdiff_4(C),1)),k3_xcmplx_0(k10_pdiff_1(3,2,A,B),k1_funct_1(k5_pdiff_4(C),2))),k3_xcmplx_0(k10_pdiff_1(3,3,A,B),k1_funct_1(k5_pdiff_4(C),3))) ) ) ) )).
fof(d9_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r9_pdiff_5(A,B) <=> ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & B = k11_finseq_1(C,D,E) & ? [F] : ( 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] : ( v1_funct_1(G) & v3_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [H] : ( v1_funct_1(H) & v2_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,F) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,3,k1_pdiff_3(3,3,A),B),I),k1_funct_1(k1_pdiff_2(3,3,k1_pdiff_3(3,3,A),B),E)) = k2_xcmplx_0(k1_funct_1(G,k6_xcmplx_0(I,E)),k1_funct_1(H,k6_xcmplx_0(I,E))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d9_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( ( 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)) ) ) ) )).
fof(d9_pencil_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( v8_pencil_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,u1_pre_topc(A)) & r2_hidden(B,C) ) ) ) ) )).
fof(d9_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => k12_polyform(A) = k11_polyform(A,k5_numbers) ) )).
fof(d9_polynom1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_vectsp_1(B) & l5_algstr_0(B) ) => k9_polynom1(A,B) = k14_funct_7(k15_pre_poly(A),u1_struct_0(B),k8_polynom1(A,B),k16_pre_poly(A),k5_struct_0(B)) ) )).
fof(d9_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( D = k11_polynom3(A,B,C) <=> ! [E] : ( m1_subset_1(E,k4_ordinal1) => ? [F] : ( m2_finseq_1(F,u1_struct_0(A)) & k3_finseq_1(F) = k1_nat_1(E,1) & k1_normsp_1(A,D,E) = k4_rlvect_1(A,F) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( 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(k1_nat_1(E,1),G))) ) ) ) ) ) ) ) ) ) )).
fof(d9_polynom5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k6_polynom5(A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,C) <=> r1_polynom5(A,B,D) ) ) ) ) ) ) )).
fof(d9_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l5_algstr_0(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( 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] : ( ( 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) ) => k4_polynom1(A,B,E,F) = k6_algstr_0(B,D,k4_polynom1(A,B,C,F)) ) ) ) ) ) ) )).
fof(d9_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( r7_polyred(A,B,C,D,E) <=> ? [F] : ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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) ) ) ) ) ) ) ) )).
fof(d9_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(A)) => k7_poset_1(A,B,C,D) = a_4_0_poset_1(A,B,C,D) ) ) ) ) )).
fof(d9_pralg_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_pralg_2(D,A,B) => ! [E] : ( ( 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] : ~ ( r2_hidden(F,A) & ! [G] : ( 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 ) ) ) ) ) ) ) )).
fof(d9_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( v3_ordinal1(D) & ~ r1_xxreal_0(k1_funct_1(C,D),k1_funct_1(B,D)) & ! [E] : ( v3_ordinal1(E) => ( r2_hidden(E,D) => k1_funct_1(B,E) = k1_funct_1(C,E) ) ) ) ) ) ) ) )).
fof(d9_prob_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( ( ~ 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] : ( ( 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) ) ) ) ) ) ) )).
fof(d9_prob_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(d9_projpl_1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & v5_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ( B != C => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ( D = k2_projpl_1(A,B,C) <=> r2_projpl_1(A,D,B,C) ) ) ) ) ) ) )).
fof(d9_prvect_2,axiom,( ! [A] : ( ( 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))) ) )).
fof(d9_pscomp_1,axiom,( ! [A] : ( 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)) ) )).
fof(d9_pua2mss1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(A),A))) ) => ! [C] : ( m1_eqrel_1(C,A) => ( r2_pua2mss1(A,B,C) <=> ( r1_pua2mss1(A,B,C) & ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(d9_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => k8_qc_lang1(A,B) = a_2_0_qc_lang1(A,B) ) ) )).
fof(d9_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(d9_qmax_1,axiom,( ! [A] : ( ( v2_qmax_1(A) & l1_qmax_1(A) ) => ! [B] : ( 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))) ) ) )).
fof(d9_quantal1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v11_quantal1(A) <=> k3_relat_1(A,A) = A ) ) )).
fof(d9_quatern2,axiom,( ! [A] : ( ( v8_algstr_0(A) & l2_algstr_0(A) ) => ( A = k14_quatern2 <=> ( u1_struct_0(A) = k1_quaterni & u1_algstr_0(A) = k9_quatern2 & k4_struct_0(A) = k1_quatern2 ) ) ) )).
fof(d9_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k9_quaterni(A,B) = k7_quaterni(A,k8_quaterni(B)) ) ) )).
fof(d9_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ( B = k12_quofield(A) <=> ! [C] : ( 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) ) ) ) ) ) )).
fof(d9_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v3_card_1(D,B) & m2_finseq_1(D,k3_radix_1(A)) ) => ( D = k10_radix_1(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k2_finseq_1(B)) => k4_radix_1(E,A,B,D) = k9_radix_1(E,A,C) ) ) ) ) ) ) ) )).
fof(d9_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,k2_xcmplx_0(A,2)) & m2_finseq_1(C,k3_radix_1(B)) ) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(d9_ratfunc1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & l5_algstr_0(A) ) => ! [B] : ( m1_ratfunc1(B,A) => ( v4_ratfunc1(B,A) <=> r2_funct_2(k4_ordinal1,u1_struct_0(A),k4_ratfunc1(A,B),k9_polynom3(A)) ) ) ) )).
fof(d9_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( v1_relat_1(C) => ( C = k5_relat_1(A,B) <=> ! [D] : ! [E] : ( r2_hidden(k4_tarski(D,E),C) <=> ( r2_hidden(D,B) & r2_hidden(k4_tarski(D,E),A) ) ) ) ) ) )).
fof(d9_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_relat_2(A) <=> r1_relat_2(A,k1_relat_1(A)) ) ) )).
fof(d9_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r7_rewrite1(A,B,C) <=> ? [D] : ( ( r2_hidden(k4_tarski(B,D),A) | B = D ) & ( r2_hidden(k4_tarski(C,D),A) | C = D ) ) ) ) )).
fof(d9_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ( r4_rewrite2(A,B,C,D) <=> k8_rewrite2(A,B,D) = k8_rewrite2(A,C,D) ) ) ) ) )).
fof(d9_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,k3_rfunct_3(A,B)) => ! [D] : ( m1_subset_1(D,A) => ( r1_rfunct_3(A,B,C,D) <=> ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k4_finseq_1(C)) => r2_hidden(D,k9_xtuple_0(k1_funct_1(C,E))) ) ) ) ) ) ) ) )).
fof(d9_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => k6_rinfsup2(A) = k1_rinfsup2(k3_rinfsup2(A)) ) )).
fof(d9_ringcat1,axiom,( ! [A] : ( ( v3_ringcat1(A) & l1_ringcat1(A) ) => ! [B] : ( ( v3_ringcat1(B) & l1_ringcat1(B) ) => ( k1_ringcat1(A) = k2_ringcat1(B) => ! [C] : ( ( v2_ringcat1(C) & v3_ringcat1(C) & l1_ringcat1(C) ) => ( C = k6_ringcat1(A,B) <=> ! [D] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d9_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rltopsp1(A) ) => ( v7_rltopsp1(A) <=> ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( ( v2_xxreal_0(E) & v1_xreal_0(E) ) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v3_pre_topc(F,A) & r2_hidden(C,F) & ! [G] : ( v1_xreal_0(G) => ( ~ r1_xxreal_0(E,k9_complex1(k6_xcmplx_0(G,B))) => r1_tarski(k1_convex1(A,F,G),D) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d9_rlvect_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_rlvect_2(C,A) => ( r1_rlvect_2(A,B,C) <=> ! [D] : ( 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) ) ) ) ) ) )).
fof(d9_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_4(C,A,B) => ! [D] : ( m1_rmod_4(D,A,B) => ! [E] : ( m1_rmod_4(E,A,B) => ( E = k6_rmod_4(A,B,C,D) <=> ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(d9_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & v7_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B = k7_robbins1(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_robbins1(A,B,C) = B ) ) ) ) )).
fof(d9_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(d9_rsspace,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_rlsub_1(B,A) => ( v1_xboole_0(B) | k9_rsspace(A,B) = k4_struct_0(A) ) ) ) ) )).
fof(d9_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( r2_hidden(D,k4_rsspace4(A,B)) => k1_funct_1(C,D) = k2_seq_4(k7_rsspace4(A,B,k6_rsspace4(A,B,D))) ) ) ) ) ) )).
fof(d9_rusub_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(d9_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => k14_rvsum_1(A,B) = k3_funcop_1(k11_binop_2,A,B) ) ) )).
fof(d9_scm_comp,axiom,( ! [A] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( m1_dtconstr(B,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [C] : ( v1_int_1(C) => ( C = k12_scm_comp(A,B) <=> ? [D] : ( 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] : ( 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] : ( m2_subset_1(E,u1_struct_0(k1_scm_comp),k7_dtconstr(k1_scm_comp)) => ! [F] : ( m1_dtconstr(F,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [G] : ( m1_dtconstr(G,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [H] : ( m1_subset_1(H,u1_struct_0(k1_scm_comp)) => ! [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] : ( m1_subset_1(J,k4_numbers) => ! [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d9_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(k1_scmfsa_2)) => ( C = k9_scmfsa_2(A,B) <=> ? [D] : ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_ami_3)) & ? [E] : ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_ami_3)) & A = D & B = E & C = k5_ami_3(D,E) ) ) ) ) ) ) )).
fof(d9_scmpds_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => k9_scmpds_2(A,B,C) = k3_xtuple_0(6,k1_xboole_0,k11_finseq_1(A,B,C)) ) ) ) )).
fof(d9_scmpds_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ( v3_scmpds_4(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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) ) ) ) ) ) ) )).
fof(d9_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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,k1_nat_1(k5_card_1(C),1)),C) ) ) ) )).
fof(d9_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => ( ? [B] : ( m1_subset_1(B,k2_scm_inst) & ? [C] : ( m1_subset_1(C,k2_scm_inst) & ? [D] : ( v1_int_1(D) & ? [E] : ( v1_int_1(E) & ? [F] : ( 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] : ( m1_subset_1(B,k2_scm_inst) => ( B = k10_scmpds_i(A) <=> ? [C] : ( 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) ) ) ) ) ) )).
fof(d9_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r5_semi_af1(A,B,C) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(d9_seq_4,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( v1_xcmplx_0(B) => k10_seq_4(A,B) = k4_finseqop(k2_numbers,k2_numbers,A,k5_seq_4(B)) ) ) )).
fof(d9_seqfunc,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,B)))) ) => ! [D] : ( r1_seqfunc(A,B,C,D) <=> ( D != k1_xboole_0 & ! [E] : ( v7_ordinal1(E) => r1_tarski(D,k1_relset_1(A,k1_seqfunc(A,B,C,E))) ) ) ) ) )).
fof(d9_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v8_valued_0(A) <=> ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_nat_1(k1_numbers,A,k1_nat_1(B,1)),k9_nat_1(k1_numbers,A,B)) ) ) ) )).
fof(d9_setfam_1,axiom,( ! [A] : ! [B] : ( 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 ) ) ) )).
fof(d9_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( D = k9_setlim_2(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => k9_nat_1(k9_setfam_1(A),D,E) = k5_subset_1(A,C,k9_nat_1(k9_setfam_1(A),B,E)) ) ) ) ) ) )).
fof(d9_sgraph1,axiom,( ! [A] : ! [B] : ( m1_sgraph1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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] : ( m1_subset_1(F,k4_ordinal1) => ( 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,k1_nat_1(F,1))),u1_sgraph1(B)) ) ) ) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( 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,k1_nat_1(F,1))) != k2_tarski(k1_funct_1(E,G),k1_funct_1(E,k1_nat_1(G,1))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d9_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lattices(A) ) => ( v5_sheffer1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_lattices(A,B,B) = B ) ) ) )).
fof(d9_simplex0,axiom,( ! [A] : ! [B] : ( l1_pre_topc(B) => ( m1_simplex0(B,A) <=> r1_tarski(k2_struct_0(B),A) ) ) )).
fof(d9_sin_cos,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k2_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( D = k8_sin_cos(A,B,C) <=> ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(E,A) => k9_nat_1(k2_numbers,D,E) = k3_xcmplx_0(k3_xcmplx_0(k9_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) => k9_nat_1(k2_numbers,D,E) = k5_numbers ) ) ) ) ) ) ) ) )).
fof(d9_stacks_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_stacks_1(A) ) => ( v3_stacks_1(A) <=> ! [B] : ( 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)) ) ) ) ) )).
fof(d9_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( C = k15_sublemma(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( m2_subset_1(E,k2_qc_lang1(A),k3_qc_lang1(A)) & E = D & ~ r2_hidden(E,k24_qc_lang1(A,B)) ) ) ) ) ) )).
fof(d9_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => k10_substut1(A,B) = a_2_1_substut1(A,B) ) ) )).
fof(d9_supinf_2,axiom,( ! [A] : ( v5_supinf_2(A) <=> ! [B] : ( v1_xxreal_0(B) => ( r2_hidden(B,A) => r1_xxreal_0(k1_supinf_2,B) ) ) ) )).
fof(d9_tdlat_1,axiom,( ! [A] : ( l1_pre_topc(A) => k9_tdlat_1(A) = a_1_2_tdlat_1(A) ) )).
fof(d9_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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) = k7_polynom1(A,C,D,k5_termord(A,B,C,D)) ) ) ) ) )).
fof(d9_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_tex_4(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r2_hidden(C,B) & B = k2_tex_4(A,C) ) ) ) ) )).
fof(d9_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k7_tmap_1(A,B) = k6_partfun1(u1_struct_0(A)) ) ) )).
fof(d9_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(d9_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v4_topgen_1(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => v2_topgen_1(C,A) ) ) ) ) ) )).
fof(d9_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_topgen_4(A,B,C) <=> ! [D] : ( m1_connsp_2(D,A,C) => ~ v4_card_3(k9_subset_1(u1_struct_0(A),D,B)) ) ) ) ) ) )).
fof(d9_topreal1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v5_topreal1(A) <=> ? [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) & v4_topreal1(B) & A = k3_topreal1(2,B) ) ) ) )).
fof(d9_toprealb,axiom,( k10_toprealb = k19_euclid(k4_xcmplx_0(1),k5_numbers) )).
fof(d9_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ( v3_toprns_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ( C = k6_toprns_1(A,B) <=> ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(E,F) & r1_xxreal_0(D,k12_euclid(k5_algstr_0(k15_euclid(A),k9_nat_1(u1_struct_0(k15_euclid(A)),B,F),C))) ) ) ) ) ) ) ) ) ) )).
fof(d9_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => C != k3_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) ) ) ) ) ) ) )).
fof(d9_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_trees_1(C) ) => ( r2_hidden(B,A) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_trees_1(D) ) => ( D = k5_trees_1(A,B,C) <=> ! [E] : ( m2_finseq_1(E,k4_ordinal1) => ( r2_hidden(E,D) <=> ~ ( ~ ( r2_hidden(E,A) & ~ r2_xboole_0(B,E) ) & ! [F] : ( m2_finseq_1(F,k4_ordinal1) => ~ ( r2_hidden(F,C) & E = k8_finseq_1(k4_ordinal1,B,F) ) ) ) ) ) ) ) ) ) ) ) )).
fof(d9_trees_2,axiom,( ! [A] : ( ( 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))) ) )).
fof(d9_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v4_trees_3(A) <=> v1_trees_3(k10_xtuple_0(A)) ) ) )).
fof(d9_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : k7_trees_9(A,B) = a_2_0_trees_9(A,B) ) )).
fof(d9_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tsp_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & C != D & ! [E] : ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v4_pre_topc(E,A) & ~ r2_hidden(C,E) & r2_hidden(D,E) ) ) ) ) ) ) ) ) )).
fof(d9_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(d9_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( 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] : ( 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] : ( m1_subset_1(D,k4_ordinal1) & C = k9_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)),k9_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) ) ) ) ) ) ) )).
fof(d9_twoscomp,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k1_funct_1(A,k10_finseq_1(B,C)) = k1_binarith(k9_margrel1(B),k9_margrel1(C)) ) ) ) ) )).
fof(d9_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_unialg_2(B,A) => ! [C] : ( m1_unialg_2(C,A) => ( ~ r2_subset_1(u1_struct_0(B),u1_struct_0(C)) => ! [D] : ( ( 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] : ( ( ~ 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) ) ) ) ) ) ) ) ) ) ) )).
fof(d9_uproots,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k14_polynom3(A))) => ( D = k8_uproots(A,B,C) <=> ( k3_finseq_1(D) = C & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k4_finseq_1(D)) => k1_funct_1(D,E) = k4_polynom5(A,k4_algstr_0(A,B),k5_struct_0(A)) ) ) ) ) ) ) ) ) )).
fof(d9_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(d9_valued_2,axiom,( ! [A] : ! [B] : ( B = k3_valued_2(A) <=> ! [C] : ( 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))) ) ) ) )).
fof(d9_vectmetr,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v15_algstr_0(B) & l3_algstr_0(B) ) => ( B = k5_vectmetr(A) <=> ( u1_struct_0(B) = k2_vectmetr(k4_vectmetr(A)) & ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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) ) ) ) ) ) ) ) )).
fof(d9_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(d9_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l5_algstr_0(A) ) => ( v33_algstr_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ( B != k4_struct_0(A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_algstr_0(A,C,B) != k5_struct_0(A) ) ) ) ) ) )).
fof(d9_vectsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_2(B,A) ) => ( v4_vectsp_2(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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 ) ) ) ) ) ) ) ) )).
fof(d9_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_vectsp_6(D,A,B) => ! [E] : ( m1_vectsp_6(E,A,B) => ( E = k6_vectsp_6(A,B,C,D) <=> ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(d9_vectsp_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(d9_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ( v8_waybel_0(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(d9_waybel18,axiom,( ! [A] : ( ( v1_pre_topc(A) & l1_pre_topc(A) ) => ( A = k9_waybel18 <=> ( u1_struct_0(A) = k2_tarski(k5_numbers,1) & u1_pre_topc(A) = k1_enumset1(k1_xboole_0,k1_tarski(1),k2_tarski(k5_numbers,1)) ) ) ) )).
fof(d9_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v7_waybel23(B,A) <=> r2_hidden(k4_yellow_0(A),B) ) ) ) )).
fof(d9_waybel34,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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))))) ) ) ) ) ) ) )).
fof(d9_waybel35,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_waybel35(B,A) <=> ! [C] : ( 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) ) ) ) ) ) )).
fof(d9_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ( v8_waybel_0(B,A) <=> v5_orders_3(k1_waybel_0(A,B),B,A) ) ) ) )).
fof(d9_waybel_1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( m1_waybel_1(C,A,B) <=> ? [D] : ( 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] : ( 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) ) ) ) ) ) )).
fof(d9_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v6_waybel_3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(B,C) & v3_pre_topc(C,A) & ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(d9_waybel_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ( B = k4_waybel_4(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(d9_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_waybel_9(A,B,C) <=> ! [D] : ( m1_connsp_2(D,A,C) => r2_waybel_0(A,B,D) ) ) ) ) ) )).
fof(d9_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [C] : ( 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)) ) ) ) )).
fof(d9_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( ( v2_wellord1(A) & r4_wellord1(A,B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k3_wellord1(A,B) <=> r3_wellord1(A,B,C) ) ) ) ) ) )).
fof(d9_xboole_0,axiom,( ! [A] : ! [B] : ( r3_xboole_0(A,B) <=> ( r1_tarski(A,B) | r1_tarski(B,A) ) ) )).
fof(d9_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k8_xboolean(A,B) = k3_xboolean(k4_xboolean(A,B)) ) ) )).
fof(d9_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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 ) ) ) ) )).
fof(d9_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ( v3_xxreal_2(A) <=> ? [B] : ( v1_xreal_0(B) & m2_xxreal_2(B,A) ) ) ) )).
fof(d9_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_yellow18(A,B) = k9_xtuple_0(k8_altcat_1(A,B)) ) ) )).
fof(d9_yellow21,axiom,( ! [A] : ( v1_relat_1(A) => ( v5_yellow21(A) <=> ? [B] : ! [C] : ( r2_hidden(C,k1_relat_1(A)) => r2_hidden(k4_tarski(C,B),A) ) ) ) )).
fof(d9_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_lattice3(A,B,D) => r1_orders_2(A,C,D) ) ) ) ) ) ) ) )).
fof(d9_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ( m2_yellow_6(C,A,B) <=> ? [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ? [F] : ( m1_subset_1(F,u1_struct_0(C)) & ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(d9_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ( v5_zf_fund1(B,A) <=> ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(a_3_1_zf_fund1(A,C,D),B) ) ) ) ) ) ) )).
fof(d9_zf_lang,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ( v1_zf_lang(A) <=> m1_subset_1(A,k9_zf_lang) ) ) )).
fof(d9_zf_model,axiom,( k9_zf_model = k15_zf_lang(k2_zf_lang(k5_numbers),k2_zf_lang(1),k7_zf_lang(k5_zf_lang(k2_zf_lang(1),k2_zf_lang(k5_numbers)),k8_zf_lang(k2_zf_lang(2),k11_zf_lang(k5_zf_lang(k2_zf_lang(2),k2_zf_lang(k5_numbers)),k13_zf_lang(k2_zf_lang(3),k7_zf_lang(k7_zf_lang(k5_zf_lang(k2_zf_lang(3),k2_zf_lang(k5_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)))))))))) )).
fof(d9_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( 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 ) ) )).
fof(d9_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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))) ) ) ) ) )).
fof(d9_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(k4_numbers,k6_zmodul02(A,B)),k6_zmodul02(A,B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_numbers,k6_zmodul02(A,B)),k6_zmodul02(A,B)))) ) => ( C = k9_zmodul02(A,B) <=> ! [D] : ( v1_int_1(D) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(u1_struct_0(A)),k6_zmodul02(A,B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( E = k5_zmodul01(A,F,B) => k1_binop_1(C,D,E) = k5_zmodul01(A,k1_zmodul01(A,F,D),B) ) ) ) ) ) ) ) ) )).
fof(dt_g1_abcmiz_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_g1_algstr_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_g1_analmetr,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_g1_analoaf,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(dt_g1_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_g1_bcialg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_g1_bhsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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)) ) ) )).
fof(dt_g1_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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)) ) ) )).
fof(dt_g1_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [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)) ) ) )).
fof(dt_g1_cayldick,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( 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_funct_1(H) & v1_funct_2(H,A,A) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( v1_cayldick(g1_cayldick(A,B,C,D,E,F,G,H)) & l1_cayldick(g1_cayldick(A,B,C,D,E,F,G,H)) ) ) )).
fof(dt_g1_cfuncdom,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)) ) ) )).
fof(dt_g1_cgames_1,axiom,( ! [A] : ! [B] : ( v1_cgames_1(g1_cgames_1(A,B)) & l1_cgames_1(g1_cgames_1(A,B)) ) )).
fof(dt_g1_clopban2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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)) ) ) )).
fof(dt_g1_closure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_g1_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_g1_clvect_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_g1_collsp,axiom,( ! [A] : ! [B] : ( m1_collsp(B,A) => ( v1_collsp(g1_collsp(A,B)) & l1_collsp(g1_collsp(A,B)) ) ) )).
fof(dt_g1_combgras,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(dt_g1_compos_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_g1_conlat_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ( v1_conlat_1(g1_conlat_1(A,B,C)) & l1_conlat_1(g1_conlat_1(A,B,C)) ) ) )).
fof(dt_g1_csspace,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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)) ) ) )).
fof(dt_g1_e_siec,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_g1_extpro_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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) ) ) )).
fof(dt_g1_fomodel1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_g1_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(dt_g1_funcsdom,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)) ) ) )).
fof(dt_g1_geomtrap,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_g1_graph_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_g1_grcat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_g1_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(dt_g1_incsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_g1_lang1,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(dt_g1_lattices,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_g1_lopban_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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)) ) ) )).
fof(dt_g1_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) ) )).
fof(dt_g1_metric_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_g1_midsp_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_g1_midsp_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & 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) ) ) )).
fof(dt_g1_mod_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) ) )).
fof(dt_g1_modelc_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( 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)) ) ) )).
fof(dt_g1_modelc_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & 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) ) ) )).
fof(dt_g1_msualg_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_g1_normsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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)) ) ) )).
fof(dt_g1_orders_2,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(dt_g1_parsp_1,axiom,( ! [A] : ! [B] : ( m1_parsp_1(B,A) => ( v1_parsp_1(g1_parsp_1(A,B)) & l1_parsp_1(g1_parsp_1(A,B)) ) ) )).
fof(dt_g1_pcs_0,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(dt_g1_petri,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_g1_polyalg1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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) ) ) )).
fof(dt_g1_pre_topc,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(dt_g1_qmax_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_g1_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) ) )).
fof(dt_g1_ringcat1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) ) ) )).
fof(dt_g1_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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)) ) ) )).
fof(dt_g1_rlvect_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_g1_sgraph1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_sgraph1(A))) => ( v1_sgraph1(g1_sgraph1(A,B)) & l1_sgraph1(g1_sgraph1(A,B)) ) ) )).
fof(dt_g1_stacks_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)) ) ) )).
fof(dt_g1_symsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) ) )).
fof(dt_g1_turing_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k1_enumset1(k4_xcmplx_0(1),k5_numbers,1))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B,A),k3_zfmisc_1(B,A,k1_enumset1(k4_xcmplx_0(1),k5_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)) ) ) )).
fof(dt_g1_unialg_1,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(dt_g1_vectmetr,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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)) ) ) )).
fof(dt_g1_vectsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) ) )).
fof(dt_g1_vectsp_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) ) )).
fof(dt_g1_waybel_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(dt_g1_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_g1_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_g2_abcmiz_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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)) ) ) )).
fof(dt_g2_algstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_g2_altcat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_g2_bcialg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_g2_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [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)) ) ) )).
fof(dt_g2_clvect_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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)) ) ) )).
fof(dt_g2_conlat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) => ( v3_conlat_1(g2_conlat_1(A,B,C),A) & l2_conlat_1(g2_conlat_1(A,B,C),A) ) ) )).
fof(dt_g2_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) ) )).
fof(dt_g2_fsm_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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) ) ) )).
fof(dt_g2_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) ) )).
fof(dt_g2_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(dt_g2_lang1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_g2_lattices,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_g2_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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)) ) ) )).
fof(dt_g2_modelc_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(dt_g2_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_g2_qmax_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_g2_robbins1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_g2_vectsp_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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) ) ) )).
fof(dt_g3_algstr_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_g3_lattices,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_g3_msualg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_g3_osalg_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)) ) ) )).
fof(dt_g3_robbins3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_g4_algstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_g4_robbins1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_g5_algstr_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_g5_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k13_finseq_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k13_finseq_1(A)))) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) & m1_finseq_1(E,B) ) => ( v12_aofa_a00(g5_aofa_a00(A,B,C,D,E)) & l5_aofa_a00(g5_aofa_a00(A,B,C,D,E)) ) ) )).
fof(dt_g6_algstr_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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)) ) ) )).
fof(dt_g6_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k13_finseq_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k13_finseq_1(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) & m1_finseq_1(F,B) ) => ( v15_aofa_a00(g6_aofa_a00(A,B,C,D,E,F)) & l6_aofa_a00(g6_aofa_a00(A,B,C,D,E,F)) ) ) )).
fof(dt_k10_abcmiz_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k10_afinsq_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k10_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ~ v1_xboole_0(k10_afproj(A)) ) )).
fof(dt_k10_algstr_4,axiom,( ! [A] : ( v1_funct_1(k10_algstr_4(A)) & v1_funct_2(k10_algstr_4(A),k4_ordinal1,k9_setfam_1(k1_yellow_6(k2_xboole_0(A,k4_ordinal1)))) & m1_subset_1(k10_algstr_4(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k1_yellow_6(k2_xboole_0(A,k4_ordinal1)))))) ) )).
fof(dt_k10_ami_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_ami_2(k10_ami_3(A)) & m1_subset_1(k10_ami_3(A),u1_struct_0(k1_ami_3)) ) ) )).
fof(dt_k10_aofa_000,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(dt_k10_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [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) ) => m2_finseq_1(k10_aofa_a00(A,B,C,D,E,F,G,H,I),A) ) )).
fof(dt_k10_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(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) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) & v19_aofa_a00(D,A) & m1_subset_1(D,u1_struct_0(A)) & v1_int_1(E) ) => m1_subset_1(k10_aofa_a01(A,B,C,D,E),k1_funct_1(u3_msualg_1(A,C),D)) ) )).
fof(dt_k10_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k10_armstrng,axiom,( ! [A] : ! [B] : m1_subset_1(k10_armstrng(A,B),k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) )).
fof(dt_k10_arytm_3,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k10_asympt_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => m1_funct_2(k10_asympt_0(A,B),k4_ordinal1,k1_numbers) ) )).
fof(dt_k10_bcialg_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k10_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k10_binarith,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k10_binop_2,axiom,( v1_funct_1(k10_binop_2) & v1_funct_2(k10_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & m1_subset_1(k10_binop_2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers))) )).
fof(dt_k10_bor_cant,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => m1_prob_1(k10_bor_cant(A,B,C),A,B) ) )).
fof(dt_k10_borsuk_1,axiom,( ! [A] : ( l1_struct_0(A) => m1_eqrel_1(k10_borsuk_1(A),u1_struct_0(A)) ) )).
fof(dt_k10_borsuk_7,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & ~ v3_xxreal_0(A) & v1_xreal_0(B) ) => ( 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))))) ) ) )).
fof(dt_k10_bspace,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) ) )).
fof(dt_k10_bvfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k10_c0sp1,axiom,( ! [A] : ( ~ 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))) ) ) )).
fof(dt_k10_card_3,axiom,( ! [A] : ( v4_funct_1(A) => ( v1_relat_1(k10_card_3(A)) & v1_funct_1(k10_card_3(A)) ) ) )).
fof(dt_k10_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => m2_cat_1(k10_cat_1(A),A,A) ) )).
fof(dt_k10_cat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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,k6_cat_2(A,B),C) & m1_subset_1(E,u1_struct_0(A)) ) => m2_cat_1(k10_cat_2(A,B,C,D,E),B,C) ) )).
fof(dt_k10_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) )).
fof(dt_k10_cat_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ 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) ) )).
fof(dt_k10_cat_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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))) ) )).
fof(dt_k10_catalg_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k10_chain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_chain_1(B,A) & m1_subset_1(C,k4_ordinal1) & m1_subset_1(D,k1_zfmisc_1(k4_chain_1(A,B,k1_nat_1(C,1)))) ) => m1_subset_1(k10_chain_1(A,B,C,D),k1_zfmisc_1(k4_chain_1(A,B,C))) ) )).
fof(dt_k10_clopban1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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)) ) )).
fof(dt_k10_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k10_coh_sp,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k10_compos_1,axiom,( ! [A] : ! [B] : ( ( l1_compos_1(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k10_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_funct_1(k10_comseq_3(A)) & v1_funct_2(k10_comseq_3(A),k4_ordinal1,k2_numbers) & m1_subset_1(k10_comseq_3(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) ) )).
fof(dt_k10_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(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)))) ) ) )).
fof(dt_k10_cqc_lang,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k10_cqc_sim1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k10_csspace,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) )).
fof(dt_k10_decomp_1,axiom,( ! [A] : ( ( 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)))) ) )).
fof(dt_k10_descip_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_finseq_2(A,k6_margrel1)) & v7_ordinal1(C) ) => m1_subset_1(k10_descip_1(A,B,C),k6_margrel1) ) )).
fof(dt_k10_dickson,axiom,( m1_subset_1(k10_dickson,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) )).
fof(dt_k10_diff_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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(k10_diff_1(A,B,C,D)) ) )).
fof(dt_k10_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => m2_subset_1(k10_dist_1(A),k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) )).
fof(dt_k10_dist_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_setfam_1(B) & m1_subset_1(B,k6_dist_1(A)) & m4_dist_2(C,A,B) ) => v1_xreal_0(k10_dist_2(A,B,C)) ) )).
fof(dt_k10_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) )).
fof(dt_k10_e_siec,axiom,( ! [A] : ( ( v2_e_siec(A) & v3_e_siec(A) & l1_e_siec(A) ) => v1_relat_1(k10_e_siec(A)) ) )).
fof(dt_k10_ens_1,axiom,( ! [A] : ( ~ 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)))) ) ) )).
fof(dt_k10_eqrel_1,axiom,( ! [A] : m1_eqrel_1(k10_eqrel_1(A),A) )).
fof(dt_k10_euclid,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k10_euclid_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(A,k4_ordinal1) & 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))) ) => v1_xreal_0(k10_euclid_3(A,B,C,D,E)) ) )).
fof(dt_k10_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_k10_ff_siec,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => v1_relat_1(k10_ff_siec(A)) ) )).
fof(dt_k10_filter_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k10_filter_2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k10_fin_topo,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k10_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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,k4_ordinal1,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,C))) & v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k1_numbers) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_funct_1(k10_finance1(A,B,C,D,E,F)) & v1_funct_2(k10_finance1(A,B,C,D,E,F),k4_ordinal1,k1_numbers) & m1_subset_1(k10_finance1(A,B,C,D,E,F),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k10_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(dt_k10_fintopo2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k10_fintopo3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k10_fomodel0,axiom,( ! [A] : ! [B] : ( v1_funct_1(k10_fomodel0(A,B)) & v1_funct_2(k10_fomodel0(A,B),B,k6_margrel1) & m1_subset_1(k10_fomodel0(A,B),k1_zfmisc_1(k2_zfmisc_1(B,k6_margrel1))) ) )).
fof(dt_k10_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k10_fomodel2(A,B,C)) & v1_funct_1(k10_fomodel2(A,B,C)) ) ) )).
fof(dt_k10_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) & v7_ordinal1(C) & v8_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)))) ) )).
fof(dt_k10_fomodel4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k10_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : m1_subset_1(k10_ftacell1(A,B,C,D,E),k3_msafree2(k7_ftacell1(A,B,C,D,E))) )).
fof(dt_k10_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))) ) ) )).
fof(dt_k10_funcsdom,axiom,( ! [A] : ( ~ 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)) ) )).
fof(dt_k10_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k10_funct_3,axiom,( ! [A] : ! [B] : ( 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))) ) )).
fof(dt_k10_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(dt_k10_functor0,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(dt_k10_fvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & ~ 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))) ) )).
fof(dt_k10_genealg1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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,k4_ordinal1) & m1_subset_1(E,k4_ordinal1) & m1_subset_1(F,k4_ordinal1) & m1_subset_1(G,k4_ordinal1) ) => m1_genealg1(k10_genealg1(A,B,C,D,E,F,G),A) ) )).
fof(dt_k10_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ 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)) ) )).
fof(dt_k10_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)))) ) ) )).
fof(dt_k10_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(dt_k10_glib_003,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) => v1_xreal_0(k10_glib_003(A,B)) ) )).
fof(dt_k10_glib_004,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(dt_k10_glib_005,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(dt_k10_graph_1,axiom,( ! [A] : ! [B] : ( ( ~ 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),k4_ordinal1) ) )).
fof(dt_k10_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k10_graph_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) & m1_finseq_1(B,u4_struct_0(A)) & v1_relat_1(C) & v1_funct_1(C) ) => v1_xreal_0(k10_graph_5(A,B,C)) ) )).
fof(dt_k10_group_10,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(dt_k10_group_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k10_group_3,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k10_group_4,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k10_group_5,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(dt_k10_group_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k10_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k10_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ( v1_rlvect_1(k10_hahnban1(A)) & l1_rlvect_1(k10_hahnban1(A)) ) ) )).
fof(dt_k10_heyting1,axiom,( ! [A] : ! [B] : ( 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)))) ) )).
fof(dt_k10_idea_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) & v7_ordinal1(B) ) => v7_ordinal1(k10_idea_1(A,B)) ) )).
fof(dt_k10_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k10_index_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) ) )).
fof(dt_k10_integr15,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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)) ) )).
fof(dt_k10_integra1,axiom,( ! [A] : ! [B] : ( ( ~ 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_xreal_0(k10_integra1(A,B)) ) )).
fof(dt_k10_interva1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k10_intpro_1,axiom,( m1_subset_1(k10_intpro_1,k1_intpro_1) )).
fof(dt_k10_isocat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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,k6_cat_2(B,C)) ) => m2_cat_1(k10_isocat_2(A,B,C,D),A,C) ) )).
fof(dt_k10_jordan,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,u1_struct_0(k15_euclid(A))) & v1_xreal_0(D) & v2_xxreal_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))))) ) ) )).
fof(dt_k10_jordan6,axiom,( ! [A] : ( ( 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))) ) )).
fof(dt_k10_knaster,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k10_laplace,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) ) => ( v1_matrix_0(k10_laplace(A,B)) & v2_matrix_0(k10_laplace(A,B),A,1,k3_finseq_1(B)) & m2_finseq_1(k10_laplace(A,B),k3_finseq_2(A)) ) ) )).
fof(dt_k10_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k10_lattice5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k10_lexbfs,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1),k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)))) ) => m1_subset_1(k10_lexbfs(A,B),k6_glib_000(A)) ) )).
fof(dt_k10_lmod_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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)) ) )).
fof(dt_k10_lopban_1,axiom,( ! [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) & 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)))) ) )).
fof(dt_k10_lopban_4,axiom,( ! [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) & 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)) ) )).
fof(dt_k10_lpspacc1,axiom,( ! [A] : m2_rfunct_3(k10_lpspacc1(A),A,k2_numbers,k3_rfunct_3(A,k2_numbers)) )).
fof(dt_k10_lpspace1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( ~ v2_struct_0(k10_lpspace1(A,B,C)) & l1_rlvect_1(k10_lpspace1(A,B,C)) ) ) )).
fof(dt_k10_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v2_xxreal_0(D) & v1_xreal_0(D) ) => ( v1_rlvect_1(k10_lpspace2(A,B,C,D)) & l1_rlvect_1(k10_lpspace2(A,B,C,D)) ) ) )).
fof(dt_k10_ltlaxio1,axiom,( m1_subset_1(k10_ltlaxio1,k1_zfmisc_1(k1_hilbert1)) )).
fof(dt_k10_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ( v1_finset_1(k10_ltlaxio3(A)) & m1_subset_1(k10_ltlaxio3(A),k1_zfmisc_1(k1_hilbert1)) ) ) )).
fof(dt_k10_margrel1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => m1_subset_1(k10_margrel1(A,B),k6_margrel1) ) )).
fof(dt_k10_matrix13,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) => ( v1_matrix_0(k10_matrix13(A,B,C)) & v2_matrix_0(k10_matrix13(A,B,C),u1_struct_0(A),k3_finseq_1(C),B) & m2_finseq_1(k10_matrix13(A,B,C),k3_finseq_2(u1_struct_0(A))) ) ) )).
fof(dt_k10_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => ( v1_relat_1(k10_matrix_0(A,B,C)) & v1_funct_1(k10_matrix_0(A,B,C)) & v1_finseq_1(k10_matrix_0(A,B,C)) & v1_matrix_0(k10_matrix_0(A,B,C)) ) ) )).
fof(dt_k10_matrix_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & m1_subset_1(D,k3_matrix_2(A)) ) => m2_finseq_1(k10_matrix_3(A,B,C,D),u1_struct_0(B)) ) )).
fof(dt_k10_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k2_numbers)) ) => m2_finseq_1(k10_matrixc1(A),k2_numbers) ) )).
fof(dt_k10_matrixj1,axiom,( ! [A] : ! [B] : ( ( ~ 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),k4_ordinal1,k4_finseq_2(k3_finseq_1(B),k4_ordinal1)) ) )).
fof(dt_k10_matrixr1,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => ( v1_matrix_0(k10_matrixr1(A)) & m2_finseq_1(k10_matrixr1(A),k3_finseq_2(k1_numbers)) ) ) )).
fof(dt_k10_matrlin,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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_0(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))) ) ) )).
fof(dt_k10_measure8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( v1_funct_1(k10_measure8(A,B,C,D)) & v1_funct_2(k10_measure8(A,B,C,D),k4_ordinal1,k6_numbers) & m1_subset_1(k10_measure8(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) ) )).
fof(dt_k10_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(dt_k10_mesfun7c,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) ) ) )).
fof(dt_k10_mesfunc1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k6_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,k6_numbers))) ) ) )).
fof(dt_k10_metric_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k10_metric_2,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(dt_k10_metric_3,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k10_midsp_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k10_midsp_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & m2_midsp_3(B,A) & v4_midsp_2(C,B) & l1_midsp_2(C,B) & m1_subset_1(D,k4_finseq_2(k1_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))) ) )).
fof(dt_k10_mmlquer2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_2(B) & v4_relat_2(B) & v6_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ( v1_relat_1(k10_mmlquer2(A,B,C)) & v5_relat_1(k10_mmlquer2(A,B,C),A) & v1_funct_1(k10_mmlquer2(A,B,C)) & v5_ordinal1(k10_mmlquer2(A,B,C)) & v1_finset_1(k10_mmlquer2(A,B,C)) ) ) )).
fof(dt_k10_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k10_mod_2,axiom,( ! [A] : ( m1_subset_1(A,k1_enumset1(k5_numbers,1,2)) => m1_subset_1(k10_mod_2(A),k1_enumset1(k5_numbers,1,2)) ) )).
fof(dt_k10_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k6_modal_1) => m1_subset_1(k10_modal_1(A),k6_modal_1) ) )).
fof(dt_k10_modcat_1,axiom,( ! [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) & 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)))) ) ) )).
fof(dt_k10_modelc_1,axiom,( ! [A] : ( m1_finseq_1(A,k4_ordinal1) => m2_finseq_1(k10_modelc_1(A),k4_ordinal1) ) )).
fof(dt_k10_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => ( v1_modelc_2(k10_modelc_2(A)) & m2_finseq_1(k10_modelc_2(A),k4_ordinal1) ) ) )).
fof(dt_k10_modelc_3,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(B) & m1_finseq_1(B,k4_ordinal1) ) => ( v1_modelc_3(k10_modelc_3(A,B),B) & l1_modelc_3(k10_modelc_3(A,B),B) ) ) )).
fof(dt_k10_monoid_0,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(dt_k10_monoid_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k10_msafree,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k10_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_6(C,A,k1_msafree3(A,B)) & v4_msualg_6(C,A,k1_msafree3(A,B)) & v9_msafree4(C,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B))) & v10_msafree4(C,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B))) & m1_msualg_4(C,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,k1_msafree3(A,B))) ) => ( v3_msualg_1(k10_msafree4(A,B,C),A) & v4_msualg_1(k10_msafree4(A,B,C),A) & l3_msualg_1(k10_msafree4(A,B,C),A) ) ) )).
fof(dt_k10_msualg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k10_msualg_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k10_nat_3,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => v7_ordinal1(k10_nat_3(A,B)) ) )).
fof(dt_k10_nat_lat,axiom,( v3_lattices(k10_nat_lat) & l3_lattices(k10_nat_lat) )).
fof(dt_k10_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ( v1_cat_1(k10_nattra_1(A)) & m3_cat_2(k10_nattra_1(A),A) ) ) )).
fof(dt_k10_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_int_2(k10_newton(A)) & m1_subset_1(k10_newton(A),k4_ordinal1) ) ) )).
fof(dt_k10_normform,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k10_openlatt,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k10_oppcat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)))) ) ) )).
fof(dt_k10_ordinal2,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => v3_ordinal1(k10_ordinal2(A,B)) ) )).
fof(dt_k10_osafree,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k10_osalg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k10_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k10_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k10_pdiff_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) & 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)) ) )).
fof(dt_k10_petri,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k10_pnproc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k10_polyform,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k10_polynom1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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(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)))) ) ) )).
fof(dt_k10_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l5_algstr_0(A) ) => ( v1_funct_1(k10_polynom3(A)) & v1_funct_2(k10_polynom3(A),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k10_polynom3(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k10_poset_1,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k10_pralg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k10_pralg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k10_pre_poly,axiom,( ! [A] : ! [B] : ( m1_finseq_1(B,k3_finseq_2(A)) => ( v1_card_3(k10_pre_poly(A,B)) & m2_finseq_1(k10_pre_poly(A,B),k4_ordinal1) ) ) )).
fof(dt_k10_prob_1,axiom,( ! [A] : ( v1_xxreal_0(A) => m1_subset_1(k10_prob_1(A),k1_zfmisc_1(k1_numbers)) ) )).
fof(dt_k10_prob_3,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k10_prvect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) ) )).
fof(dt_k10_prvect_2,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k10_pscomp_1,axiom,( ! [A] : ( 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))) ) )).
fof(dt_k10_pua2mss1,axiom,( ! [A] : ! [B] : ( ( v2_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) & m4_pua2mss1(B,A) ) => m3_pua2mss1(k10_pua2mss1(A,B),A) ) )).
fof(dt_k10_qc_lang1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k10_qc_lang2,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k9_qc_lang1(A)) ) => m1_subset_1(k10_qc_lang2(A,B),k9_qc_lang1(A)) ) )).
fof(dt_k10_qmax_1,axiom,( ! [A] : ( ( 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))))) ) )).
fof(dt_k10_quofield,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k10_radix_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k10_radix_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k10_radix_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k10_ranknull,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) )).
fof(dt_k10_ratfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k10_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_ringcat1(A) ) => ( ~ v1_xboole_0(k10_ringcat1(A)) & v5_ringcat1(k10_ringcat1(A)) ) ) )).
fof(dt_k10_rlvect_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) )).
fof(dt_k10_rmod_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k10_robbins1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k10_rsspace,axiom,( m1_subset_1(k10_rsspace,k1_zfmisc_1(u1_struct_0(k6_rsspace))) )).
fof(dt_k10_rvsum_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k10_rvsum_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k10_scm_comp,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k10_scmfsa_1,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k4_scmfsa_1,k5_scmfsa_1))) => m1_subset_1(k10_scmfsa_1(A),k4_ordinal1) ) )).
fof(dt_k10_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k10_scmfsa_m,axiom,( v1_funct_1(k10_scmfsa_m) & m1_subset_1(k10_scmfsa_m,k1_zfmisc_1(k2_zfmisc_1(k11_memstr_0(k7_card_1(3),k1_scmfsa_2),k11_memstr_0(k7_card_1(3),k1_scmfsa_2)))) )).
fof(dt_k10_scmpds_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k10_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) & v1_int_1(B) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ( v1_relat_1(k10_scmpds_6(A,B,C)) & v4_relat_1(k10_scmpds_6(A,B,C),k4_ordinal1) & v5_relat_1(k10_scmpds_6(A,B,C),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k10_scmpds_6(A,B,C)) & 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)) ) ) )).
fof(dt_k10_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => m1_subset_1(k10_scmpds_i(A),k2_scm_inst) ) )).
fof(dt_k10_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v11_scmyciel(A) ) => v7_ordinal1(k10_scmyciel(A)) ) )).
fof(dt_k10_seq_4,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k2_numbers) & v1_xcmplx_0(B) ) => m2_finseq_1(k10_seq_4(A,B),k2_numbers) ) )).
fof(dt_k10_seqfunc,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,k1_numbers) & m1_subset_1(k10_seqfunc(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k10_setwiseo,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k10_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k10_sin_cos,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => ( v1_funct_1(k10_sin_cos(A,B,C)) & v1_funct_2(k10_sin_cos(A,B,C),k4_ordinal1,k2_numbers) & m1_subset_1(k10_sin_cos(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) ) )).
fof(dt_k10_stacks_1,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k10_sublemma,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k38_substut1(A)) ) => m2_subset_1(k10_sublemma(A,B),k16_substut1(A),k38_substut1(A)) ) )).
fof(dt_k10_subset_1,axiom,( ! [A] : ! [B] : m1_subset_1(k10_subset_1(A,B),B) )).
fof(dt_k10_substut1,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k10_supinf_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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),k6_numbers) ) )).
fof(dt_k10_tdlat_1,axiom,( ! [A] : ( ( 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)))) ) ) )).
fof(dt_k10_tmap_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)))) ) ) )).
fof(dt_k10_topalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(dt_k10_toprealb,axiom,( m1_subset_1(k10_toprealb,u1_struct_0(k8_toprealb(2))) )).
fof(dt_k10_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(k10_toprealc(A,B,C),u1_struct_0(k15_euclid(A))) ) )).
fof(dt_k10_turing_1,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1,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(k4_ordinal1,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k9_funct_2(k4_numbers,u1_turing_1(A)))))) ) ) )).
fof(dt_k10_twoscomp,axiom,( 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))) )).
fof(dt_k10_unialg_2,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k10_vectsp10,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)))) ) ) )).
fof(dt_k10_waybel34,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(dt_k10_waybel_4,axiom,( ! [A] : ( ( 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(k1_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(k1_yellow_1(k3_waybel_4(A)))))) ) ) )).
fof(dt_k10_weierstr,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) => v1_xreal_0(k10_weierstr(A,B,C)) ) )).
fof(dt_k10_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) ) )).
fof(dt_k10_yellow_6,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k10_zf_lang,axiom,( ! [A] : ! [B] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) & v1_zf_lang(B) & m1_finseq_1(B,k4_ordinal1) ) => ( v1_zf_lang(k10_zf_lang(A,B)) & m2_finseq_1(k10_zf_lang(A,B),k4_ordinal1) ) ) )).
fof(dt_k10_zf_model,axiom,( v1_zf_lang(k10_zf_model) & m2_finseq_1(k10_zf_model,k4_ordinal1) )).
fof(dt_k10_zmodul01,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k10_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) => ( ~ v2_struct_0(k10_zmodul02(A,B)) & v13_algstr_0(k10_zmodul02(A,B)) & v2_rlvect_1(k10_zmodul02(A,B)) & v3_rlvect_1(k10_zmodul02(A,B)) & v4_rlvect_1(k10_zmodul02(A,B)) & v1_zmodul01(k10_zmodul02(A,B)) & v2_zmodul01(k10_zmodul02(A,B)) & v3_zmodul01(k10_zmodul02(A,B)) & v4_zmodul01(k10_zmodul02(A,B)) & v5_zmodul01(k10_zmodul02(A,B)) & l1_zmodul01(k10_zmodul02(A,B)) ) ) )).
fof(dt_k11_abcmiz_0,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k11_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k11_afproj,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k11_algstr_0,axiom,( ! [A] : ! [B] : ( ( l5_algstr_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k11_algstr_0(A,B),u1_struct_0(A)) ) )).
fof(dt_k11_ami_3,axiom,( ! [A] : ! [B] : ( ( 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(k7_card_1(2),k1_ami_3)) ) ) )).
fof(dt_k11_aofa_000,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(dt_k11_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & v4_msualg_1(B,A) & l1_aofa_a00(B,A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,k1_funct_1(u3_msualg_1(A,B),C)) ) => m3_pboole(k11_aofa_a00(A,B,C,D),u1_struct_0(A),u3_msualg_1(A,B)) ) )).
fof(dt_k11_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(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) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) & v4_aofa_a01(D,A,B,C) & l4_aofa_a00(D,A,B,C) & v19_aofa_a00(E,A) & m1_subset_1(E,u1_struct_0(A)) & v3_aofa_a01(F,A,B,C,u4_aofa_a00(A,B,C,D),k37_aofa_a00(A)) & m1_subset_1(F,k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),k37_aofa_a00(A))) & v1_int_1(G) ) => m1_subset_1(k11_aofa_a01(A,B,C,D,E,F,G),k1_funct_1(u3_msualg_1(A,C),E)) ) )).
fof(dt_k11_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k11_armstrng,axiom,( ! [A] : ! [B] : ( 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))) ) )).
fof(dt_k11_arytm_3,axiom,( m1_subset_1(k11_arytm_3,k5_arytm_3) )).
fof(dt_k11_asympt_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => m1_funct_2(k11_asympt_0(A,B),k4_ordinal1,k1_numbers) ) )).
fof(dt_k11_bagorder,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k11_bcialg_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) )).
fof(dt_k11_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k11_binop_2,axiom,( v1_funct_1(k11_binop_2) & v1_funct_2(k11_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & m1_subset_1(k11_binop_2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers))) )).
fof(dt_k11_borsuk_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k11_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v8_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))))) ) ) )).
fof(dt_k11_bspace,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k11_bvfunc_1,axiom,( ! [A] : ( ~ 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))) ) ) )).
fof(dt_k11_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => l1_lopban_2(k11_c0sp1(A)) ) )).
fof(dt_k11_card_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k11_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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))))) ) ) )).
fof(dt_k11_cat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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,k6_cat_2(A,B),C) & m1_subset_1(E,u1_struct_0(B)) ) => m2_cat_1(k11_cat_2(A,B,C,D,E),A,C) ) )).
fof(dt_k11_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) )).
fof(dt_k11_cat_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ 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)) ) )).
fof(dt_k11_catalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)))))) ) ) )).
fof(dt_k11_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => m1_subset_1(k11_cgames_1(A),k1_zfmisc_1(k10_cgames_1(A))) ) )).
fof(dt_k11_chain_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_chain_1(B,A) & m1_subset_1(C,k4_ordinal1) ) => m3_chain_1(k11_chain_1(A,B,C),A,B,C) ) )).
fof(dt_k11_clopban1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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)))) ) ) )).
fof(dt_k11_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k11_coh_sp,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k11_cohsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) )).
fof(dt_k11_compos_1,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k11_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => m1_subset_1(k11_comseq_3(A),k2_numbers) ) )).
fof(dt_k11_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ( ~ v2_struct_0(k11_conlat_1(A)) & v3_lattices(k11_conlat_1(A)) & l3_lattices(k11_conlat_1(A)) ) ) )).
fof(dt_k11_convex4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) & m1_subset_1(B,k10_convex4(A)) ) => m1_convex4(k11_convex4(A,B),A) ) )).
fof(dt_k11_cqc_lang,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k11_cqc_sim1,axiom,( ! [A] : m1_subset_1(k11_cqc_sim1(A),k1_funct_2(A,A)) )).
fof(dt_k11_csspace,axiom,( m1_subset_1(k11_csspace,k1_zfmisc_1(u1_struct_0(k7_csspace))) )).
fof(dt_k11_decomp_1,axiom,( ! [A] : ( ( 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)))) ) )).
fof(dt_k11_dickson,axiom,( ~ v2_struct_0(k11_dickson) & l1_orders_2(k11_dickson) )).
fof(dt_k11_diff_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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(k11_diff_1(A,B,C,D,E)) ) )).
fof(dt_k11_dist_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => m1_dist_1(k11_dist_1(A),A) ) )).
fof(dt_k11_dist_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_setfam_1(B) & m1_subset_1(B,k6_dist_1(A)) & m4_dist_2(C,A,B) ) => ( v1_setfam_1(k11_dist_2(A,B,C)) & m2_subset_1(k11_dist_2(A,B,C),k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) ) )).
fof(dt_k11_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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)) ) )).
fof(dt_k11_dtconstr,axiom,( ! [A] : ( m1_finseq_1(A,k4_ordinal1) => m1_subset_1(k11_dtconstr(A),k4_ordinal1) ) )).
fof(dt_k11_e_siec,axiom,( ! [A] : ( ( v2_e_siec(A) & v3_e_siec(A) & l1_e_siec(A) ) => v1_relat_1(k11_e_siec(A)) ) )).
fof(dt_k11_ens_1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(dt_k11_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k11_euclid,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k11_euclid_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(A,k4_ordinal1) & 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))) ) => v1_xreal_0(k11_euclid_3(A,B,C,D,E)) ) )).
fof(dt_k11_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k11_filter_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k11_fin_topo,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k11_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( v7_ordinal1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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,k4_ordinal1,E) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,E))) & m1_subset_1(G,C) ) => v1_xreal_0(k11_finance1(A,B,C,D,E,F,G)) ) )).
fof(dt_k11_fintopo2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k11_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(k11_fomodel2(A,B,C,D,E),A,B,E) ) )).
fof(dt_k11_fomodel4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k11_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k11_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : m1_subset_1(k11_ftacell1(A,B,C,D,E),k3_msafree2(k7_ftacell1(A,B,C,D,E))) )).
fof(dt_k11_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k11_funcsdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v36_algstr_0(k11_funcsdom(A)) & l6_algstr_0(k11_funcsdom(A)) ) ) )).
fof(dt_k11_funct_3,axiom,( ! [A] : ( v1_relat_1(k11_funct_3(A)) & v1_funct_1(k11_funct_3(A)) ) )).
fof(dt_k11_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k11_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => ( v1_funct_1(k11_funct_7(A,B,C)) & v1_funct_2(k11_funct_7(A,B,C),k4_ordinal1,A) & m1_subset_1(k11_funct_7(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) ) )).
fof(dt_k11_functor0,axiom,( ! [A] : ( l1_altcat_1(A) => ( v9_functor0(k11_functor0(A),A,A) & l2_functor0(k11_functor0(A),A,A) ) ) )).
fof(dt_k11_fvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k11_genealg1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( ~ 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,k4_ordinal1) & m1_subset_1(E,k4_ordinal1) & m1_subset_1(F,k4_ordinal1) & m1_subset_1(G,k4_ordinal1) & m1_subset_1(H,k4_ordinal1) ) => m1_genealg1(k11_genealg1(A,B,C,D,E,F,G,H),A) ) )).
fof(dt_k11_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k11_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)))) ) ) )).
fof(dt_k11_glib_001,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(dt_k11_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) )).
fof(dt_k11_glib_004,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)))) ) )).
fof(dt_k11_glib_005,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(dt_k11_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k11_grcat_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(dt_k11_group_10,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(dt_k11_group_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k11_group_3,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k11_group_4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k11_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)))) ) ) )).
fof(dt_k11_hahnban1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k11_heyting1,axiom,( ! [A] : ! [B] : ( 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))))) ) ) )).
fof(dt_k11_idea_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_finseq_1(B,k4_ordinal1) & m1_finseq_1(C,k4_ordinal1) ) => m2_finseq_1(k11_idea_1(A,B,C),k4_ordinal1) ) )).
fof(dt_k11_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k11_integr15,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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)) ) )).
fof(dt_k11_integra1,axiom,( ! [A] : ! [B] : ( ( ~ 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_xreal_0(k11_integra1(A,B)) ) )).
fof(dt_k11_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => m1_subset_1(k11_intpro_1(A),k1_zfmisc_1(k1_intpro_1)) ) )).
fof(dt_k11_isocat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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,k6_cat_2(B,C)) & m2_cat_1(E,A,k6_cat_2(B,C)) & m2_nattra_1(F,A,k6_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)) ) )).
fof(dt_k11_jordan6,axiom,( ! [A] : ( ( 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))) ) )).
fof(dt_k11_lang1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k11_laplace,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_0(B) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(A))) & m1_finseq_1(C,u1_struct_0(A)) ) => ( v1_matrix_0(k11_laplace(A,B,C)) & m2_finseq_1(k11_laplace(A,B,C),k3_finseq_2(u1_struct_0(A))) ) ) )).
fof(dt_k11_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k11_lexbfs,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1),k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)))) & 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),k4_ordinal1),k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)))) ) )).
fof(dt_k11_lopban_1,axiom,( ! [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) & 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)) ) ) )).
fof(dt_k11_lopclset,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k11_lpspacc1,axiom,( ! [A] : m2_rfunct_3(k11_lpspacc1(A),A,k2_numbers,k3_rfunct_3(A,k2_numbers)) )).
fof(dt_k11_lpspace1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_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)))) ) ) )).
fof(dt_k11_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v2_xxreal_0(D) & v1_xreal_0(D) ) => ( 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))) ) ) )).
fof(dt_k11_ltlaxio1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => ( v1_funct_1(k11_ltlaxio1(A)) & v1_funct_2(k11_ltlaxio1(A),k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1) & m1_subset_1(k11_ltlaxio1(A),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1))) ) ) )).
fof(dt_k11_ltlaxio3,axiom,( ! [A] : ! [B] : ( ( v2_funct_1(A) & m1_finseq_1(A,k1_hilbert1) & v2_funct_1(B) & m1_finseq_1(B,k1_hilbert1) ) => m1_subset_1(k11_ltlaxio3(A,B),k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) ) )).
fof(dt_k11_ltlaxio4,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) & m3_ltlaxio4(B,A) ) => ( v1_finset_1(k11_ltlaxio4(A,B)) & m1_subset_1(k11_ltlaxio4(A,B),k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)))) ) ) )).
fof(dt_k11_matrix13,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(A),B,C) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => m2_finseq_1(k11_matrix13(A,B,C,D),u1_struct_0(k6_prvect_1(A,C))) ) )).
fof(dt_k11_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & v7_ordinal1(C) & m1_subset_1(D,A) ) => ( v1_matrix_0(k11_matrix_0(A,B,C,D)) & v2_matrix_0(k11_matrix_0(A,B,C,D),A,B,C) & m2_finseq_1(k11_matrix_0(A,B,C,D),k3_finseq_2(A)) ) ) )).
fof(dt_k11_matrix_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v1_funct_1(k11_matrix_3(A,B,C)) & v1_funct_2(k11_matrix_3(A,B,C),k3_matrix_2(A),u1_struct_0(B)) & m1_subset_1(k11_matrix_3(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k3_matrix_2(A),u1_struct_0(B)))) ) ) )).
fof(dt_k11_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k2_numbers)) ) => m2_finseq_1(k11_matrixc1(A),k2_numbers) ) )).
fof(dt_k11_matrixj1,axiom,( ! [A] : ! [B] : ( ( ~ 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),k4_ordinal1,k4_finseq_2(k3_finseq_1(B),k4_ordinal1)) ) )).
fof(dt_k11_matrixr1,axiom,( ! [A] : ! [B] : ( ( v1_matrix_0(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) ) )).
fof(dt_k11_mcart_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k11_mcart_1(A)) & v1_funct_1(k11_mcart_1(A)) ) ) )).
fof(dt_k11_measure7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k9_setfam_1(k1_numbers)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k1_numbers)))) & m2_measure7(B,A) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_zfmisc_1(k4_ordinal1,k4_ordinal1)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_zfmisc_1(k4_ordinal1,k4_ordinal1)))) ) => m1_measure7(k11_measure7(A,B,C),k5_setfam_1(k1_numbers,k2_relset_1(k9_setfam_1(k1_numbers),A))) ) )).
fof(dt_k11_measure8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & v1_funct_1(D) & v1_funct_2(D,B,k6_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( v1_funct_1(k11_measure8(A,B,C,D)) & v1_funct_2(k11_measure8(A,B,C,D),k4_ordinal1,k6_numbers) & m1_subset_1(k11_measure8(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) ) )).
fof(dt_k11_memstr_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k11_mesfun7c,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ( v1_funct_1(k11_mesfun7c(A,B)) & v1_funct_2(k11_mesfun7c(A,B),k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(k11_mesfun7c(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) ) )).
fof(dt_k11_metric_1,axiom,( v1_funct_1(k11_metric_1) & v1_funct_2(k11_metric_1,k2_zfmisc_1(2,2),k1_numbers) & m1_subset_1(k11_metric_1,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(2,2),k1_numbers))) )).
fof(dt_k11_midsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k11_midsp_2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k11_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k11_mod_2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_enumset1(k5_numbers,1,2)) & m1_subset_1(B,k1_enumset1(k5_numbers,1,2)) ) => m1_subset_1(k11_mod_2(A,B),k1_enumset1(k5_numbers,1,2)) ) )).
fof(dt_k11_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k6_modal_1) => m1_subset_1(k11_modal_1(A),k6_modal_1) ) )).
fof(dt_k11_modcat_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k11_modelc_1,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k4_ordinal1) & m1_finseq_1(B,k4_ordinal1) ) => m2_finseq_1(k11_modelc_1(A,B),k4_ordinal1) ) )).
fof(dt_k11_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => ( v1_modelc_2(k11_modelc_2(A)) & m2_finseq_1(k11_modelc_2(A),k4_ordinal1) ) ) )).
fof(dt_k11_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => ( v1_modelc_3(k11_modelc_3(A),A) & v3_modelc_3(k11_modelc_3(A),A) & l1_modelc_3(k11_modelc_3(A),A) ) ) )).
fof(dt_k11_monoid_0,axiom,( ! [A] : ( ~ 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)))) ) ) )).
fof(dt_k11_monoid_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k11_msafree,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k11_msualg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k11_msualg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(dt_k11_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k11_nat_3,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => m1_subset_1(k11_nat_3(A,B),k4_ordinal1) ) )).
fof(dt_k11_nat_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k10_nat_lat)) => m2_subset_1(k11_nat_lat(A),k4_ordinal1,k6_nat_lat) ) )).
fof(dt_k11_newton,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => m1_subset_1(k11_newton(A,B),k4_ordinal1) ) )).
fof(dt_k11_openlatt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k11_oppcat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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))))) ) ) )).
fof(dt_k11_ordinal2,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => v3_ordinal1(k11_ordinal2(A,B)) ) )).
fof(dt_k11_ordinal6,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k11_osafree,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k11_osalg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(dt_k11_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k11_pdiff_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & 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(k11_pdiff_1(A,B,C,D,E),k1_numbers,k1_euclid(B)) ) )).
fof(dt_k11_petri,axiom,( ! [A] : ( l1_petri(A) => ( v1_petri(k11_petri(A)) & l1_petri(k11_petri(A)) ) ) )).
fof(dt_k11_pnproc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k11_polyform,axiom,( ! [A] : ! [B] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) & v1_int_1(B) ) => m1_subset_1(k11_polyform(A,B),k4_ordinal1) ) )).
fof(dt_k11_polynom1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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(k11_polynom1(A,B,C,D)) & v1_funct_2(k11_polynom1(A,B,C,D),k15_pre_poly(A),u1_struct_0(B)) & m1_subset_1(k11_polynom1(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) ) )).
fof(dt_k11_polynom3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k11_polynom3(A,B,C)) & v1_funct_2(k11_polynom3(A,B,C),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k11_polynom3(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k11_pralg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k11_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k11_prob_1,axiom,( m1_subset_1(k11_prob_1,k1_zfmisc_1(k1_zfmisc_1(k1_numbers))) )).
fof(dt_k11_prvect_1,axiom,( ! [A] : ! [B] : ( ( 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)))) ) ) )).
fof(dt_k11_prvect_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k11_pscomp_1,axiom,( ! [A] : ( 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))) ) )).
fof(dt_k11_qc_lang1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k9_qc_lang1(A)) ) => m2_finseq_1(k11_qc_lang1(A,B),k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))) ) )).
fof(dt_k11_qc_lang2,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k9_qc_lang1(A)) ) => m1_subset_1(k11_qc_lang2(A,B),k9_qc_lang1(A)) ) )).
fof(dt_k11_qmax_1,axiom,( ! [A] : ( ( 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))))) ) ) )).
fof(dt_k11_quatern2,axiom,( v1_funct_1(k11_quatern2) & v1_funct_2(k11_quatern2,k2_zfmisc_1(k1_quaterni,k1_quaterni),k1_quaterni) & m1_subset_1(k11_quatern2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_quaterni,k1_quaterni),k1_quaterni))) )).
fof(dt_k11_quaterni,axiom,( m1_subset_1(k11_quaterni,k1_quaterni) )).
fof(dt_k11_quofield,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(dt_k11_radix_1,axiom,( ! [A] : ( v1_int_1(A) => v1_int_1(k11_radix_1(A)) ) )).
fof(dt_k11_ranknull,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) )).
fof(dt_k11_ratfunc1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k11_ringcat1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v4_ringcat1(A) & m1_subset_1(B,k10_ringcat1(A)) ) => m2_ringcat1(k11_ringcat1(A,B),A) ) )).
fof(dt_k11_robbins1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k11_rvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k11_rvsum_2,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k11_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k11_scmfsa_2(A),u1_compos_1(k1_scmfsa_2)) ) )).
fof(dt_k11_scmpds_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k11_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => m1_subset_1(k11_scmpds_i(A),k2_scm_inst) ) )).
fof(dt_k11_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v12_scmyciel(A) ) => v7_ordinal1(k11_scmyciel(A)) ) )).
fof(dt_k11_seq_4,axiom,( ! [A] : ( m1_finseq_1(A,k2_numbers) => m2_finseq_1(k11_seq_4(A),k1_numbers) ) )).
fof(dt_k11_seqfunc,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) ) ) )).
fof(dt_k11_setwiseo,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k11_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_simplex0(B,A) & v1_relat_1(C) & v1_funct_1(C) & v7_ordinal1(D) ) => m1_simplex0(k11_simplex0(A,B,C,D),A) ) )).
fof(dt_k11_stacks_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k11_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k11_substut1,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k11_supinf_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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),k6_numbers) ) )).
fof(dt_k11_tdlat_1,axiom,( ! [A] : ( ( 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)))) ) ) )).
fof(dt_k11_topalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))))))) ) ) )).
fof(dt_k11_toprealb,axiom,( ! [A] : ( 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)) ) ) )).
fof(dt_k11_toprealc,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) ) => m1_subset_1(k11_toprealc(A,B),u1_struct_0(k15_euclid(A))) ) )).
fof(dt_k11_trees_3,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k11_turing_1,axiom,( ! [A] : ! [B] : ( ( 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)))) ) )).
fof(dt_k11_twoscomp,axiom,( 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))) )).
fof(dt_k11_unialg_2,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k11_vectsp10,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)))) ) ) )).
fof(dt_k11_waybel34,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(dt_k11_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k11_waybel_4,axiom,( ! [A] : ! [B] : ( ( 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(k1_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(k1_yellow_1(k7_waybel_0(A)))))) ) ) )).
fof(dt_k11_yellow_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k11_zf_lang,axiom,( ! [A] : ! [B] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) & v1_zf_lang(B) & m1_finseq_1(B,k4_ordinal1) ) => ( v1_zf_lang(k11_zf_lang(A,B)) & m2_finseq_1(k11_zf_lang(A,B),k4_ordinal1) ) ) )).
fof(dt_k11_zf_model,axiom,( ! [A] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) ) => ( v1_zf_lang(k11_zf_model(A)) & m2_finseq_1(k11_zf_model(A),k4_ordinal1) ) ) )).
fof(dt_k11_zmodul01,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k11_zmodul02,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_int_2(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) ) => ( v1_funct_1(k11_zmodul02(A,B)) & v1_funct_2(k11_zmodul02(A,B),k2_zfmisc_1(u1_struct_0(k9_int_3(A)),u1_struct_0(k10_zmodul02(B,k5_zmodul02(B,A)))),u1_struct_0(k10_zmodul02(B,k5_zmodul02(B,A)))) & m1_subset_1(k11_zmodul02(A,B),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(k9_int_3(A)),u1_struct_0(k10_zmodul02(B,k5_zmodul02(B,A)))),u1_struct_0(k10_zmodul02(B,k5_zmodul02(B,A)))))) ) ) )).
fof(dt_k12_abcmiz_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k12_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => m1_subset_1(k12_abcmiz_1(A),u1_struct_0(A)) ) )).
fof(dt_k12_abcmiz_a,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k12_afinsq_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k12_afproj,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k12_ami_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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(k7_card_1(2),k1_ami_3)) ) ) )).
fof(dt_k12_aofa_000,axiom,( ! [A] : ( ( v4_unialg_1(A) & v3_aofa_000(A) & l1_unialg_1(A) ) => m1_subset_1(k12_aofa_000(A),u1_struct_0(A)) ) )).
fof(dt_k12_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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_msafree(C,A,B) & ~ v2_struct_0(D) & l3_aofa_a00(D,A,B,C) & m1_subset_1(E,u1_struct_0(A)) & m1_subset_1(F,k1_msafree4(u1_struct_0(A),C,E)) & m1_subset_1(G,k1_funct_1(u3_msualg_1(A,B),E)) ) => m1_subset_1(k12_aofa_a00(A,B,C,D,E,F,G),u1_struct_0(D)) ) )).
fof(dt_k12_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k12_armstrng,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k12_arytm_3,axiom,( ~ v1_xboole_0(k12_arytm_3) & v3_ordinal1(k12_arytm_3) & m1_subset_1(k12_arytm_3,k5_arytm_3) )).
fof(dt_k12_asympt_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v7_ordinal1(B) ) => ( v1_funct_1(k12_asympt_0(A,B)) & v1_funct_2(k12_asympt_0(A,B),k4_ordinal1,k1_numbers) & m1_subset_1(k12_asympt_0(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k12_bagorder,axiom,( ! [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) ) => ( v1_funct_1(k12_bagorder(A)) & v1_funct_2(k12_bagorder(A),k4_ordinal1,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(k4_ordinal1,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(A)),k5_finsub_1(u1_struct_0(A))))))) ) ) )).
fof(dt_k12_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k12_borsuk_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))))) ) ) )).
fof(dt_k12_borsuk_7,axiom,( 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))))) )).
fof(dt_k12_bvfunc_1,axiom,( ! [A] : ( ~ 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))) ) ) )).
fof(dt_k12_card_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k12_card_3(A,B)) & v1_funct_1(k12_card_3(A,B)) ) ) )).
fof(dt_k12_cat_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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(k12_cat_2(A,B),k6_cat_2(A,B),A) ) )).
fof(dt_k12_cat_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ 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) ) )).
fof(dt_k12_catalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)))))) ) ) )).
fof(dt_k12_cgames_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k12_clopban1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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)) ) ) )).
fof(dt_k12_closure2,axiom,( ! [A] : ! [B] : ( ( 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))))) ) ) )).
fof(dt_k12_coh_sp,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k12_conlat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) & m1_subset_1(B,u1_struct_0(k11_conlat_1(A))) ) => ( v3_conlat_1(k12_conlat_1(A,B),A) & ~ v4_conlat_1(k12_conlat_1(A,B),A) & v6_conlat_1(k12_conlat_1(A,B),A) & l2_conlat_1(k12_conlat_1(A,B),A) ) ) )).
fof(dt_k12_convex4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) & m1_convex4(B,A) ) => m1_subset_1(k12_convex4(A,B),k10_convex4(A)) ) )).
fof(dt_k12_cqc_lang,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k12_cqc_sim1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k12_csspace,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k12_decomp_1,axiom,( ! [A] : ( ( 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)))) ) )).
fof(dt_k12_descip_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & 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)) ) )).
fof(dt_k12_diff_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)) & v1_diff_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)))) & m1_subset_1(B,k4_ordinal1) ) => ( v1_funct_1(k12_diff_1(A,B)) & v1_funct_2(k12_diff_1(A,B),k4_ordinal1,k1_numbers) & m1_subset_1(k12_diff_1(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k12_dist_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_setfam_1(B) & m1_subset_1(B,k6_dist_1(A)) & m4_dist_2(C,A,B) & v1_funct_1(D) & v1_funct_2(D,A,k6_margrel1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => v1_xreal_0(k12_dist_2(A,B,C,D)) ) )).
fof(dt_k12_dtconstr,axiom,( v1_funct_1(k12_dtconstr) & v1_funct_2(k12_dtconstr,k4_dtconstr(k5_dtconstr),k4_ordinal1) & m1_subset_1(k12_dtconstr,k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k5_dtconstr),k4_ordinal1))) )).
fof(dt_k12_ens_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m1_subset_1(k12_ens_1(A,B),u1_struct_0(k11_ens_1(A))) ) )).
fof(dt_k12_eqrel_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k12_euclid,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => v1_xreal_0(k12_euclid(A)) ) )).
fof(dt_k12_euclid_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(A,k4_ordinal1) & 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))) ) => v1_xreal_0(k12_euclid_3(A,B,C,D,E)) ) )).
fof(dt_k12_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : 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))) )).
fof(dt_k12_fin_topo,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k12_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( v7_ordinal1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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,k4_ordinal1,E) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,E))) & m1_subset_1(G,C) ) => v1_xreal_0(k12_finance1(A,B,C,D,E,F,G)) ) )).
fof(dt_k12_finseq_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m2_finseq_1(k12_finseq_1(A,B),A) ) )).
fof(dt_k12_fintopo2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k12_fomodel0,axiom,( ! [A] : ! [B] : m1_subset_1(k12_fomodel0(A,B),k1_zfmisc_1(A)) )).
fof(dt_k12_fomodel1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k12_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) )).
fof(dt_k12_fomodel4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k12_freealg,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,k4_ordinal1) & ~ 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)) ) ) )).
fof(dt_k12_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : m1_subset_1(k12_ftacell1(A,B,C,D,E),k3_msafree2(k7_ftacell1(A,B,C,D,E))) )).
fof(dt_k12_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k12_funcsdom,axiom,( ! [A] : ( v1_funcsdom(k12_funcsdom(A)) & l1_funcsdom(k12_funcsdom(A)) ) )).
fof(dt_k12_funct_3,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k12_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k12_functor0,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(dt_k12_fvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & ~ 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))) ) )).
fof(dt_k12_genealg1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [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,k4_ordinal1) & m1_subset_1(E,k4_ordinal1) & m1_subset_1(F,k4_ordinal1) & m1_subset_1(G,k4_ordinal1) & m1_subset_1(H,k4_ordinal1) & m1_subset_1(I,k4_ordinal1) ) => m1_genealg1(k12_genealg1(A,B,C,D,E,F,G,H,I),A) ) )).
fof(dt_k12_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : m2_subset_1(k12_gfacirc1(A,B,C),u1_struct_0(k10_gfacirc1(A,B,C)),k3_msafree2(k10_gfacirc1(A,B,C))) )).
fof(dt_k12_glib_000,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k12_glib_001,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(dt_k12_glib_003,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k12_glib_004,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) )).
fof(dt_k12_glib_005,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(dt_k12_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k12_graphsp,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k3_finseq_2(k1_numbers)) & m1_subset_1(B,k4_ordinal1) ) => m1_subset_1(k12_graphsp(A,B),k1_zfmisc_1(k4_ordinal1)) ) )).
fof(dt_k12_group_10,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k12_group_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k12_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))))) ) ) )).
fof(dt_k12_hahnban1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k12_idea_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) & m1_finseq_1(B,k4_ordinal1) & m1_finseq_1(C,k4_ordinal1) ) => m2_finseq_1(k12_idea_1(A,B,C),k4_ordinal1) ) )).
fof(dt_k12_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k12_integr15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & m1_subset_1(C,k4_ordinal1) & 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)) ) )).
fof(dt_k12_integra1,axiom,( ! [A] : ! [B] : ( ( ~ 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_xreal_0(k12_integra1(A,B)) ) )).
fof(dt_k12_intpro_1,axiom,( m1_subset_1(k12_intpro_1,k1_zfmisc_1(k1_intpro_1)) )).
fof(dt_k12_isocat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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,k6_cat_2(B,C)) & m2_cat_1(E,A,k6_cat_2(B,C)) & m2_nattra_1(F,A,k6_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)) ) )).
fof(dt_k12_lang1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k12_laplace,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_0(B) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(A))) & m1_finseq_1(C,u1_struct_0(A)) ) => ( v1_matrix_0(k12_laplace(A,B,C)) & m2_finseq_1(k12_laplace(A,B,C),k3_finseq_2(u1_struct_0(A))) ) ) )).
fof(dt_k12_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k12_lattice5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k12_lexbfs,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1),k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)))) ) => m1_subset_1(k12_lexbfs(A,B),k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)))) ) )).
fof(dt_k12_lmod_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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)))) ) ) )).
fof(dt_k12_lopban_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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)) ) )).
fof(dt_k12_lopclset,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k12_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v2_struct_0(k12_lpspacc1(A)) & l1_clvect_1(k12_lpspacc1(A)) ) ) )).
fof(dt_k12_lpspace1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( ~ v2_struct_0(k12_lpspace1(A,B,C)) & l1_rlvect_1(k12_lpspace1(A,B,C)) ) ) )).
fof(dt_k12_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v2_xxreal_0(D) & v1_xreal_0(D) ) => ( ~ v2_struct_0(k12_lpspace2(A,B,C,D)) & l1_normsp_1(k12_lpspace2(A,B,C,D)) ) ) )).
fof(dt_k12_ltlaxio1,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(dt_k12_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => m1_subset_1(k12_ltlaxio3(A),k1_hilbert1) ) )).
fof(dt_k12_margrel1,axiom,( ! [A] : m1_subset_1(k12_margrel1(A),k6_margrel1) )).
fof(dt_k12_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v1_relat_1(k12_matrix_0(A,B,C,D)) & v1_funct_1(k12_matrix_0(A,B,C,D)) & v1_finseq_1(k12_matrix_0(A,B,C,D)) & v1_matrix_0(k12_matrix_0(A,B,C,D)) ) )).
fof(dt_k12_matrix_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => m1_subset_1(k12_matrix_3(A,B,C),u1_struct_0(B)) ) )).
fof(dt_k12_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k2_numbers)) ) => m1_subset_1(k12_matrixc1(A),k2_numbers) ) )).
fof(dt_k12_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_0(k12_matrixj1(A,B,C)) & m2_finseq_1(k12_matrixj1(A,B,C),k3_finseq_2(A)) ) ) )).
fof(dt_k12_matrixr1,axiom,( ! [A] : ! [B] : ( ( v1_matrix_0(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) ) )).
fof(dt_k12_mcart_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k12_mcart_1(A)) & v1_funct_1(k12_mcart_1(A)) ) ) )).
fof(dt_k12_mesfun7c,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ( v1_funct_1(k12_mesfun7c(A,B)) & v1_funct_2(k12_mesfun7c(A,B),k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(k12_mesfun7c(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) ) )).
fof(dt_k12_midsp_1,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k12_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k12_mod_2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_enumset1(k5_numbers,1,2)) & m1_subset_1(B,k1_enumset1(k5_numbers,1,2)) ) => m1_subset_1(k12_mod_2(A,B),k1_enumset1(k5_numbers,1,2)) ) )).
fof(dt_k12_modal_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k12_modelc_1,axiom,( ~ v1_xboole_0(k12_modelc_1) )).
fof(dt_k12_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => ( v1_modelc_2(k12_modelc_2(A)) & m2_finseq_1(k12_modelc_2(A),k4_ordinal1) ) ) )).
fof(dt_k12_modelc_3,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & l1_modelc_3(B,A) ) => ( v1_modelc_3(k12_modelc_3(A,B),A) & l1_modelc_3(k12_modelc_3(A,B),A) ) ) )).
fof(dt_k12_monoid_0,axiom,( ! [A] : ( v15_algstr_0(k12_monoid_0(A)) & v1_monoid_0(k12_monoid_0(A)) & l3_algstr_0(k12_monoid_0(A)) ) )).
fof(dt_k12_monoid_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k12_msafree,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k12_msualg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k12_msualg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k12_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k12_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_relat_1(k12_nat_3(A)) & v4_relat_1(k12_nat_3(A),k8_newton) & v1_funct_1(k12_nat_3(A)) & v1_partfun1(k12_nat_3(A),k8_newton) ) ) )).
fof(dt_k12_normform,axiom,( ! [A] : ( v3_lattices(k12_normform(A)) & l3_lattices(k12_normform(A)) ) )).
fof(dt_k12_openlatt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k12_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => m1_oppcat_1(k12_oppcat_1(A),A,k2_oppcat_1(A)) ) )).
fof(dt_k12_ordinal2,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => v3_ordinal1(k12_ordinal2(A,B)) ) )).
fof(dt_k12_ordinal6,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => v3_ordinal1(k12_ordinal6(A,B)) ) )).
fof(dt_k12_pdiff_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) & 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(k12_pdiff_1(A,B,C,D,E,F),u1_struct_0(k16_lopban_1(k4_real_ns1(1),k4_real_ns1(1)))) ) )).
fof(dt_k12_petri,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k12_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ( ~ v1_xboole_0(k12_pnproc_1(A,B)) & m1_subset_1(k12_pnproc_1(A,B),k1_zfmisc_1(k3_finseq_2(B))) ) ) )).
fof(dt_k12_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => m1_subset_1(k12_polyform(A),k4_ordinal1) ) )).
fof(dt_k12_polynom1,axiom,( ! [A] : ! [B] : ( ( 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(k12_polynom1(A,B)) & v36_algstr_0(k12_polynom1(A,B)) & l6_algstr_0(k12_polynom1(A,B)) ) ) )).
fof(dt_k12_polynom3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => m2_finseq_2(k12_polynom3(A),k4_ordinal1,k4_finseq_2(1,k4_ordinal1)) ) )).
fof(dt_k12_pralg_1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(dt_k12_pralg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(dt_k12_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k12_prob_1,axiom,( ~ 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))) )).
fof(dt_k12_prvect_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(dt_k12_prvect_2,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k12_pscomp_1,axiom,( ! [A] : ( 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))) ) )).
fof(dt_k12_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => m1_subset_1(k12_qc_lang1(A),k9_qc_lang1(A)) ) )).
fof(dt_k12_qc_lang2,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k9_qc_lang1(A)) ) => m1_subset_1(k12_qc_lang2(A,B),k9_qc_lang1(A)) ) )).
fof(dt_k12_quaterni,axiom,( m1_subset_1(k12_quaterni,k1_quaterni) )).
fof(dt_k12_quofield,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(dt_k12_radix_1,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v7_ordinal1(B) ) => v1_int_1(k12_radix_1(A,B)) ) )).
fof(dt_k12_ratfunc1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k12_rfunct_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k12_ringcat1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v4_ringcat1(A) & m1_subset_1(B,k10_ringcat1(A)) ) => m2_ringcat1(k12_ringcat1(A,B),A) ) )).
fof(dt_k12_rlvect_2,axiom,( ! [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) & 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) ) )).
fof(dt_k12_robbins1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k12_rvsum_1,axiom,( ! [A] : ( ( 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) ) )).
fof(dt_k12_rvsum_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k12_scm_comp,axiom,( ! [A] : ! [B] : ( ( 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(k7_card_1(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)) ) )).
fof(dt_k12_scmfsa_1,axiom,( 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)))))) )).
fof(dt_k12_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & 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)) ) )).
fof(dt_k12_scmpds_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k12_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => v1_int_1(k12_scmpds_i(A)) ) )).
fof(dt_k12_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => v4_scmyciel(k12_scmyciel(A)) ) )).
fof(dt_k12_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => m1_finseq_2(k12_seq_4(A),k2_numbers) ) )).
fof(dt_k12_sin_cos,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v7_ordinal1(C) ) => ( v1_funct_1(k12_sin_cos(A,B,C)) & v1_funct_2(k12_sin_cos(A,B,C),k4_ordinal1,k2_numbers) & m1_subset_1(k12_sin_cos(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) ) )).
fof(dt_k12_stacks_1,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k12_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) )).
fof(dt_k12_substut1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k12_supinf_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_valued_0(A) ) => m1_subset_1(k12_supinf_2(A,B),k6_numbers) ) )).
fof(dt_k12_tdlat_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k12_toprealb,axiom,( 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))))) )).
fof(dt_k12_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(k12_toprealc(A,B,C),u1_struct_0(k15_euclid(A))) ) )).
fof(dt_k12_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ( ~ v1_xboole_0(k12_trees_3(A)) & v1_trees_1(k12_trees_3(A)) ) ) )).
fof(dt_k12_trees_9,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) ) => m1_subset_1(k12_trees_9(A,B),k1_zfmisc_1(k9_trees_9(A))) ) )).
fof(dt_k12_turing_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k12_twoscomp,axiom,( 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))) )).
fof(dt_k12_unialg_2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k12_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k12_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) ) )).
fof(dt_k12_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => m4_yellow_6(k12_yellow_6(A),A) ) )).
fof(dt_k12_zf_lang,axiom,( ! [A] : ! [B] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) & v1_zf_lang(B) & m1_finseq_1(B,k4_ordinal1) ) => ( v1_zf_lang(k12_zf_lang(A,B)) & m2_finseq_1(k12_zf_lang(A,B),k4_ordinal1) ) ) )).
fof(dt_k12_zmodul01,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k12_zmodul02,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_int_2(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) ) => ( ~ v2_struct_0(k12_zmodul02(A,B)) & v7_vectsp_1(k12_zmodul02(A,B),k9_int_3(A)) & l1_vectsp_1(k12_zmodul02(A,B),k9_int_3(A)) ) ) )).
fof(dt_k13_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => m1_subset_1(k13_abcmiz_1(A),u1_struct_0(A)) ) )).
fof(dt_k13_abcmiz_a,axiom,( ! [A] : ( 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)) ) ) )).
fof(dt_k13_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ( v1_incsp_1(k13_afproj(A)) & l1_incsp_1(k13_afproj(A)) ) ) )).
fof(dt_k13_algstr_4,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k13_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k13_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & v2_relat_1(D) & m1_msafree(D,A,B) ) => m1_subset_1(k13_aofa_a00(A,B,C,D),k1_zfmisc_1(k4_autalg_1(u1_struct_0(A),D,u3_msualg_1(A,C)))) ) )).
fof(dt_k13_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(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) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) & v4_aofa_a01(D,A,B,C) & l4_aofa_a00(D,A,B,C) & ~ v2_struct_0(E) & v2_unialg_1(E) & v3_unialg_1(E) & v4_unialg_1(E) & v3_aofa_000(E) & v4_aofa_000(E) & v5_aofa_000(E) & v6_aofa_000(E) & ~ v10_aofa_000(E) & v11_aofa_000(E) & v12_aofa_000(E) & v5_aofa_a01(E,A,B,C,D) & l3_aofa_a00(E,A,C,u4_aofa_a00(A,B,C,D)) & m1_subset_1(F,u1_struct_0(A)) & m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),F)) & m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),F)) ) => ( v15_aofa_000(k13_aofa_a01(A,B,C,D,E,F,G,H),E) & m1_subset_1(k13_aofa_a01(A,B,C,D,E,F,G,H),u1_struct_0(E)) ) ) )).
fof(dt_k13_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k13_armstrng,axiom,( ! [A] : ! [B] : ( 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))) ) )).
fof(dt_k13_asympt_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k13_bagorder,axiom,( ! [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) ) => ( 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))))) ) ) )).
fof(dt_k13_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) ) )).
fof(dt_k13_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k13_borsuk_7,axiom,( ! [A] : ( 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))))) ) ) )).
fof(dt_k13_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k13_cat_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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(k13_cat_2(A,B),k6_cat_2(A,B),B) ) )).
fof(dt_k13_cat_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ 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))) ) )).
fof(dt_k13_catalg_1,axiom,( ! [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) & 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))) ) ) )).
fof(dt_k13_classes2,axiom,( ~ v1_xboole_0(k13_classes2) & v1_classes2(k13_classes2) )).
fof(dt_k13_clopban1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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))) ) ) )).
fof(dt_k13_coh_sp,axiom,( ! [A] : ( ~ 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)) ) )).
fof(dt_k13_convex4,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k13_cqc_lang,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k13_cqc_sim1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k3_cqc_lang(A)) ) => m1_subset_1(k13_cqc_sim1(A,B),k1_qc_lang1(A)) ) )).
fof(dt_k13_csspace,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) ) => v1_xreal_0(k13_csspace(A,B)) ) )).
fof(dt_k13_decomp_1,axiom,( ! [A] : ( ( 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)))) ) )).
fof(dt_k13_descip_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & 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)) ) )).
fof(dt_k13_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [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)) ) )).
fof(dt_k13_dtconstr,axiom,( ! [A] : ( 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)) ) )).
fof(dt_k13_e_siec,axiom,( ! [A] : ( ( v2_e_siec(A) & v3_e_siec(A) & l1_e_siec(A) ) => v1_relat_1(k13_e_siec(A)) ) )).
fof(dt_k13_ens_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,u1_struct_0(k11_ens_1(A))) ) => m1_subset_1(k13_ens_1(A,B),A) ) )).
fof(dt_k13_eqrel_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k13_euclid,axiom,( ! [A] : ( 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))) ) ) )).
fof(dt_k13_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k13_ff_siec,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => v1_relat_1(k13_ff_siec(A)) ) )).
fof(dt_k13_fintopo2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k13_fomodel1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k13_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k13_fomodel2(A,B,C,D),k6_margrel1) ) )).
fof(dt_k13_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k13_fomodel4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k13_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(dt_k13_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ~ 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)) ) )).
fof(dt_k13_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(k13_funcop_1(A,B,C)) & v1_funct_1(k13_funcop_1(A,B,C)) ) )).
fof(dt_k13_funct_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k13_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k13_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(D,A) ) => ( v1_funct_1(k13_funct_7(A,B,C,D)) & v1_funct_2(k13_funct_7(A,B,C,D),k4_ordinal1,A) & m1_subset_1(k13_funct_7(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) ) )).
fof(dt_k13_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(dt_k13_fvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k13_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ 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)) ) )).
fof(dt_k13_glib_000,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & v1_funct_1(k13_glib_000(A,B,C)) & v1_finset_1(k13_glib_000(A,B,C)) ) ) )).
fof(dt_k13_glib_001,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) ) )).
fof(dt_k13_glib_003,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k13_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)))) ) )).
fof(dt_k13_glib_005,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(dt_k13_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k13_graphsp,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k3_finseq_2(k1_numbers)) & m1_subset_1(B,k4_ordinal1) ) => m1_subset_1(k13_graphsp(A,B),k1_zfmisc_1(k4_ordinal1)) ) )).
fof(dt_k13_grcat_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k13_group_10,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k13_group_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k13_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(dt_k13_hahnban1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k13_idea_1,axiom,( ! [A] : ( m1_finseq_1(A,k4_ordinal1) => m2_finseq_1(k13_idea_1(A),k4_ordinal1) ) )).
fof(dt_k13_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k13_index_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) )).
fof(dt_k13_integra1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) => m1_subset_1(k13_integra1(A,B,C,D),k4_ordinal1) ) )).
fof(dt_k13_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => m1_subset_1(k13_intpro_1(A),k1_zfmisc_1(k1_intpro_1)) ) )).
fof(dt_k13_isocat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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,k6_cat_2(B,C),k8_isocat_2(A,B,C,D,F),k8_isocat_2(A,B,C,E,G)) ) )).
fof(dt_k13_lang1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k13_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k13_lexbfs,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1),k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)))) ) )).
fof(dt_k13_lmod_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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)) ) ) )).
fof(dt_k13_lopban_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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)))) ) ) )).
fof(dt_k13_lopclset,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(dt_k13_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( ~ v1_xboole_0(k13_lpspacc1(A,B,C)) & m1_subset_1(k13_lpspacc1(A,B,C),k1_zfmisc_1(u1_struct_0(k12_lpspacc1(A)))) ) ) )).
fof(dt_k13_lpspace1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_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))) ) )).
fof(dt_k13_ltlaxio1,axiom,( m1_subset_1(k13_ltlaxio1,k1_zfmisc_1(k1_hilbert1)) )).
fof(dt_k13_margrel1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k13_matrix_0,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m2_finseq_2(k13_matrix_0(A,B),A,k4_finseq_2(1,A)) ) )).
fof(dt_k13_matrix_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => m2_finseq_1(k13_matrix_3(A,B,C),u1_struct_0(B)) ) )).
fof(dt_k13_matrixc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(A,k2_numbers) & m1_finseq_1(B,k2_numbers) & v1_matrix_0(C) & m1_finseq_1(C,k3_finseq_2(k2_numbers)) ) => ( v1_matrix_0(k13_matrixc1(A,B,C)) & m2_finseq_1(k13_matrixc1(A,B,C),k3_finseq_2(k2_numbers)) ) ) )).
fof(dt_k13_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_0(k13_matrixj1(A,B,C)) & v2_matrix_0(k13_matrixj1(A,B,C),A,k2_wsierp_1(k10_matrixj1(A,C)),k2_wsierp_1(k11_matrixj1(A,C))) & m2_finseq_1(k13_matrixj1(A,B,C),k3_finseq_2(A)) ) ) )).
fof(dt_k13_metric_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k13_metric_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k13_metric_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k13_midsp_1,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k13_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k13_mod_2,axiom,( v1_funct_1(k13_mod_2) & v1_funct_2(k13_mod_2,k2_zfmisc_1(k1_enumset1(k5_numbers,1,2),k1_enumset1(k5_numbers,1,2)),k1_enumset1(k5_numbers,1,2)) & m1_subset_1(k13_mod_2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_enumset1(k5_numbers,1,2),k1_enumset1(k5_numbers,1,2)),k1_enumset1(k5_numbers,1,2)))) )).
fof(dt_k13_modelc_1,axiom,( ! [A] : ! [B] : ( ( v1_modelc_1(A) & m1_finseq_1(A,k4_ordinal1) & v1_modelc_1(B) & m1_finseq_1(B,k4_ordinal1) ) => ( v1_modelc_1(k13_modelc_1(A,B)) & m2_finseq_1(k13_modelc_1(A,B),k4_ordinal1) ) ) )).
fof(dt_k13_modelc_3,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & 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)) ) )).
fof(dt_k13_monoid_1,axiom,( ! [A] : ( ~ 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)) ) )).
fof(dt_k13_msafree,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k13_msualg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(dt_k13_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k13_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( v1_relat_1(k13_nat_3(A)) & v4_relat_1(k13_nat_3(A),k8_newton) & v1_funct_1(k13_nat_3(A)) & v1_partfun1(k13_nat_3(A),k8_newton) ) ) )).
fof(dt_k13_openlatt,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k13_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => m1_oppcat_1(k13_oppcat_1(A),k2_oppcat_1(A),A) ) )).
fof(dt_k13_ordinal6,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v3_ordinal1(B) ) => v3_ordinal1(k13_ordinal6(A,B)) ) )).
fof(dt_k13_osalg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k13_pdiff_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) & 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(k13_pdiff_1(A,B,C,D,E,F)) ) )).
fof(dt_k13_petri,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k13_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => m1_subset_1(k13_polyform(A),k4_ordinal1) ) )).
fof(dt_k13_polynom3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_group_1(A) & l6_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k13_polynom3(A,B,C)) & v1_funct_2(k13_polynom3(A,B,C),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k13_polynom3(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k13_pralg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k13_prob_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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))) ) )).
fof(dt_k13_prvect_1,axiom,( ! [A] : ! [B] : ( ( 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)))) ) ) )).
fof(dt_k13_prvect_2,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(dt_k13_pscomp_1,axiom,( ! [A] : ( 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))) ) )).
fof(dt_k13_qc_lang1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k9_qc_lang1(A)) ) => m1_subset_1(k13_qc_lang1(A,B),k9_qc_lang1(A)) ) )).
fof(dt_k13_qc_lang2,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k9_qc_lang1(A)) ) => m1_subset_1(k13_qc_lang2(A,B),k9_qc_lang1(A)) ) )).
fof(dt_k13_quofield,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k13_radix_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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)) ) )).
fof(dt_k13_ratfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) ) )).
fof(dt_k13_rfunct_3,axiom,( ! [A] : ( ~ 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)))) ) ) )).
fof(dt_k13_ringcat1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k13_rlvect_2,axiom,( ! [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) & 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)) ) )).
fof(dt_k13_robbins1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k13_rvsum_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k13_scm_comp,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k7_dtconstr(k1_scm_comp)) & m1_subset_1(B,k4_ordinal1) ) => ( 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)) ) ) )).
fof(dt_k13_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & 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)) ) )).
fof(dt_k13_scmpds_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k13_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => v1_int_1(k13_scmpds_i(A)) ) )).
fof(dt_k13_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ( v1_relat_1(k13_scmyciel(A)) & v4_relat_1(k13_scmyciel(A),k4_ordinal1) & v1_funct_1(k13_scmyciel(A)) & v1_partfun1(k13_scmyciel(A),k4_ordinal1) ) ) )).
fof(dt_k13_seq_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,k12_seq_4(A)) & m1_subset_1(C,k12_seq_4(A)) ) => m2_finseq_2(k13_seq_4(A,B,C),k2_numbers,k12_seq_4(A)) ) )).
fof(dt_k13_sin_cos,axiom,( 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))) )).
fof(dt_k13_stacks_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k13_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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))) ) ) )).
fof(dt_k13_substut1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k13_supinf_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k6_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)))) ) ) )).
fof(dt_k13_toprealb,axiom,( ! [A] : ( 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,k2_xcmplx_0(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,k2_xcmplx_0(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)))))) ) ) )).
fof(dt_k13_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(D) ) => m1_subset_1(k13_toprealc(A,B,C,D),u1_struct_0(k15_euclid(A))) ) )).
fof(dt_k13_trees_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k13_trees_9,axiom,( ! [A] : ! [B] : ( ( ~ 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))))) ) ) )).
fof(dt_k13_turing_1,axiom,( v1_funct_1(k13_turing_1) & v1_funct_2(k13_turing_1,k8_mcart_1(k4_ordinal1,k4_ordinal1,k3_turing_1(5),k7_domain_1(k4_ordinal1,k5_numbers,1)),k3_zfmisc_1(k3_turing_1(5),k7_domain_1(k4_ordinal1,k5_numbers,1),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1))) & m1_subset_1(k13_turing_1,k1_zfmisc_1(k2_zfmisc_1(k8_mcart_1(k4_ordinal1,k4_ordinal1,k3_turing_1(5),k7_domain_1(k4_ordinal1,k5_numbers,1)),k3_zfmisc_1(k3_turing_1(5),k7_domain_1(k4_ordinal1,k5_numbers,1),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1))))) )).
fof(dt_k13_twoscomp,axiom,( 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))) )).
fof(dt_k13_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k13_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) ) )).
fof(dt_k13_yellow_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k13_zf_lang,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_zf_lang) & v1_zf_lang(B) & m1_finseq_1(B,k4_ordinal1) ) => ( v1_zf_lang(k13_zf_lang(A,B)) & m2_finseq_1(k13_zf_lang(A,B),k4_ordinal1) ) ) )).
fof(dt_k13_zmodul02,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_int_2(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) & m1_subset_1(C,u1_struct_0(B)) ) => m1_subset_1(k13_zmodul02(A,B,C),u1_struct_0(k12_zmodul02(A,B))) ) )).
fof(dt_k14_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => m1_subset_1(k14_abcmiz_1(A),u1_struct_0(A)) ) )).
fof(dt_k14_abcmiz_a,axiom,( ! [A] : ( 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)) ) ) )).
fof(dt_k14_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ( v1_incsp_1(k14_afproj(A)) & l1_incsp_1(k14_afproj(A)) ) ) )).
fof(dt_k14_algstr_4,axiom,( ! [A] : l3_algstr_0(k14_algstr_4(A)) )).
fof(dt_k14_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k14_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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) & v2_relat_1(D) & m1_msafree(D,A,B) & m1_subset_1(E,u1_struct_0(A)) & m1_subset_1(F,k1_msafree4(u1_struct_0(A),D,E)) & m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),E)) ) => m1_subset_1(k14_aofa_a00(A,B,C,D,E,F,G),k1_zfmisc_1(k13_aofa_a00(A,B,C,D))) ) )).
fof(dt_k14_bagorder,axiom,( ! [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) ) => ( v3_orders_2(k14_bagorder(A)) & v4_orders_2(k14_bagorder(A)) & v5_orders_2(k14_bagorder(A)) & l1_orders_2(k14_bagorder(A)) ) ) )).
fof(dt_k14_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) ) )).
fof(dt_k14_borsuk_7,axiom,( ! [A] : ( v1_int_1(A) => m1_borsuk_2(k14_borsuk_7(A),k8_toprealb(3),k8_borsuk_7,k8_borsuk_7) ) )).
fof(dt_k14_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k14_cat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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(k14_cat_2(A,B,C,D,E),A,k6_cat_2(B,C)) ) )).
fof(dt_k14_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ 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)) ) )).
fof(dt_k14_classes2,axiom,( ~ v1_xboole_0(k14_classes2) & v1_classes2(k14_classes2) )).
fof(dt_k14_clopban1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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)) ) ) )).
fof(dt_k14_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k14_comput_1(A)) & v1_funct_1(k14_comput_1(A)) ) ) )).
fof(dt_k14_convex4,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k14_cqc_sim1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k14_csspace,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) ) => v1_xreal_0(k14_csspace(A,B,C)) ) )).
fof(dt_k14_decomp_1,axiom,( ! [A] : ( ( 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)))) ) )).
fof(dt_k14_dtconstr,axiom,( v1_funct_1(k14_dtconstr) & v1_funct_2(k14_dtconstr,k4_ordinal1,k4_dtconstr(k5_dtconstr)) & m1_subset_1(k14_dtconstr,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_dtconstr(k5_dtconstr)))) )).
fof(dt_k14_e_siec,axiom,( ! [A] : ( ( v2_e_siec(A) & v3_e_siec(A) & l1_e_siec(A) ) => v1_relat_1(k14_e_siec(A)) ) )).
fof(dt_k14_ens_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k14_euclid,axiom,( ! [A] : ( 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)) ) ) )).
fof(dt_k14_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ 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)) ) )).
fof(dt_k14_ff_siec,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => v1_relat_1(k14_ff_siec(A)) ) )).
fof(dt_k14_finseq_1,axiom,( ! [A] : m2_finseq_1(k14_finseq_1(A),k4_ordinal1) )).
fof(dt_k14_fintopo2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k14_fomodel0,axiom,( ! [A] : ! [B] : m1_subset_1(k14_fomodel0(A,B),k1_zfmisc_1(A)) )).
fof(dt_k14_fomodel1,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(dt_k14_fomodel3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k10_eqrel_1(A)) ) => m1_subset_1(k14_fomodel3(A,B),A) ) )).
fof(dt_k14_fomodel4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k14_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( 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)) ) )).
fof(dt_k14_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k14_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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(k14_funct_7(A,B,C,D,E)) & v1_funct_2(k14_funct_7(A,B,C,D,E),A,B) & m1_subset_1(k14_funct_7(A,B,C,D,E),k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ) )).
fof(dt_k14_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k14_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k14_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => v1_card_1(k14_glib_000(A)) ) )).
fof(dt_k14_glib_001,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) ) )).
fof(dt_k14_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) )).
fof(dt_k14_glib_004,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)))) ) )).
fof(dt_k14_graph_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k14_graphsp,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) & m1_subset_1(B,k3_finseq_2(k1_numbers)) & m1_subset_1(C,k4_ordinal1) ) => m1_subset_1(k14_graphsp(A,B,C),k4_ordinal1) ) )).
fof(dt_k14_grcat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(dt_k14_group_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k14_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(dt_k14_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k14_index_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) )).
fof(dt_k14_integra1,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => m2_finseq_1(k14_integra1(A),k1_numbers) ) )).
fof(dt_k14_interva1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k14_intpro_1,axiom,( m1_subset_1(k14_intpro_1,k1_zfmisc_1(k1_intpro_1)) )).
fof(dt_k14_isocat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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,k6_cat_2(B,C),k8_isocat_2(A,B,C,D,F),k8_isocat_2(A,B,C,E,G)) ) )).
fof(dt_k14_lattice3,axiom,( ! [A] : ( 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)) ) ) )).
fof(dt_k14_lexbfs,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1),k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)))) ) )).
fof(dt_k14_lmod_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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))) ) )).
fof(dt_k14_lopban_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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)) ) ) )).
fof(dt_k14_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( ~ v2_struct_0(k14_lpspacc1(A,B,C)) & l1_clvect_1(k14_lpspacc1(A,B,C)) ) ) )).
fof(dt_k14_lpspace1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_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)))) ) ) )).
fof(dt_k14_margrel1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k14_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & m1_subset_1(C,k4_finseq_2(B,A)) ) => ( v1_matrix_0(k14_matrix_0(A,B,C)) & v2_matrix_0(k14_matrix_0(A,B,C),A,1,B) & m2_finseq_1(k14_matrix_0(A,B,C),k3_finseq_2(A)) ) ) )).
fof(dt_k14_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v2_matrixj1(B,A) & m1_finseq_1(B,k3_finseq_2(k3_finseq_2(A))) ) => ( v1_matrix_0(k14_matrixj1(A,B,C)) & v2_matrix_0(k14_matrixj1(A,B,C),A,k3_finseq_1(k2_matrixj1(A,B,C)),k3_finseq_1(k2_matrixj1(A,B,C))) & m2_finseq_1(k14_matrixj1(A,B,C),k3_finseq_2(A)) ) ) )).
fof(dt_k14_metric_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k14_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => m1_subset_1(k14_midsp_1(A),k10_midsp_1(A)) ) )).
fof(dt_k14_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k14_mod_2,axiom,( v1_funct_1(k14_mod_2) & v1_funct_2(k14_mod_2,k2_zfmisc_1(k1_enumset1(k5_numbers,1,2),k1_enumset1(k5_numbers,1,2)),k1_enumset1(k5_numbers,1,2)) & m1_subset_1(k14_mod_2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_enumset1(k5_numbers,1,2),k1_enumset1(k5_numbers,1,2)),k1_enumset1(k5_numbers,1,2)))) )).
fof(dt_k14_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m1_finseq_1(A,k4_ordinal1) ) => ( v1_modelc_1(k14_modelc_1(A)) & m2_finseq_1(k14_modelc_1(A),k4_ordinal1) ) ) )).
fof(dt_k14_modelc_2,axiom,( ! [A] : ( v1_modelc_2(k14_modelc_2(A)) & m2_finseq_1(k14_modelc_2(A),k4_ordinal1) ) )).
fof(dt_k14_modelc_3,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & v1_modelc_3(B,A) & l1_modelc_3(B,A) ) => m1_subset_1(k14_modelc_3(A,B),k1_zfmisc_1(k9_modelc_2)) ) )).
fof(dt_k14_monoid_0,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k14_msafree,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k14_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k14_openlatt,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k14_osalg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k14_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k14_pdiff_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & 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(k14_pdiff_1(A,B,C,D,E)) & m1_subset_1(k14_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)))))) ) ) )).
fof(dt_k14_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => m1_subset_1(k14_polyform(A),k4_ordinal1) ) )).
fof(dt_k14_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ( ~ v2_struct_0(k14_polynom3(A)) & v36_algstr_0(k14_polynom3(A)) & l6_algstr_0(k14_polynom3(A)) ) ) )).
fof(dt_k14_pralg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k14_prvect_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v1_prvect_1(A) & m1_subset_1(B,k4_finseq_1(A)) ) => ( ~ v2_struct_0(k14_prvect_1(A,B)) & v13_algstr_0(k14_prvect_1(A,B)) & v2_rlvect_1(k14_prvect_1(A,B)) & v3_rlvect_1(k14_prvect_1(A,B)) & v4_rlvect_1(k14_prvect_1(A,B)) & l2_algstr_0(k14_prvect_1(A,B)) ) ) )).
fof(dt_k14_prvect_2,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k14_pscomp_1,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k14_qc_lang1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k14_qc_lang2,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k9_qc_lang1(A)) ) => m1_subset_1(k14_qc_lang2(A,B),k9_qc_lang1(A)) ) )).
fof(dt_k14_quatern2,axiom,( v8_algstr_0(k14_quatern2) & l2_algstr_0(k14_quatern2) )).
fof(dt_k14_quofield,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k14_radix_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_k14_rfunct_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k14_ringcat1,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(dt_k14_rlvect_2,axiom,( ! [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) ) => ( 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)))) ) ) )).
fof(dt_k14_robbins1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k14_rvsum_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k14_scm_comp,axiom,( v1_funct_1(k14_scm_comp) & v1_funct_2(k14_scm_comp,k4_dtconstr(k1_scm_comp),k9_funct_2(k4_ordinal1,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(k4_ordinal1,k8_afinsq_1(u1_compos_1(k1_ami_3)))))) )).
fof(dt_k14_scmfsa_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k14_scmpds_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k14_scmpds_i,axiom,( m1_subset_1(k14_scmpds_i,k4_ordinal1) )).
fof(dt_k14_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => m2_finseq_1(k14_seq_4(A),k2_numbers) ) )).
fof(dt_k14_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k14_sin_cos(A)) ) )).
fof(dt_k14_stacks_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k14_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) )).
fof(dt_k14_substut1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k14_supinf_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_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)))) ) ) )).
fof(dt_k14_toprealb,axiom,( 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(k5_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(k5_numbers,1))))))) )).
fof(dt_k14_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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(k14_toprealc(A,B,C,D)) & v1_funct_2(k14_toprealc(A,B,C,D),B,u1_struct_0(k15_euclid(A))) & m1_subset_1(k14_toprealc(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(B,u1_struct_0(k15_euclid(A))))) ) ) )).
fof(dt_k14_trees_3,axiom,( ! [A] : ( v7_ordinal1(A) => m2_finseq_1(k14_trees_3(A),k4_ordinal1) ) )).
fof(dt_k14_turing_1,axiom,( v1_turing_1(k14_turing_1) & l1_turing_1(k14_turing_1) )).
fof(dt_k14_twoscomp,axiom,( 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))) )).
fof(dt_k14_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) )).
fof(dt_k14_valued_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k14_zf_lang,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k1_zf_lang) & m1_subset_1(B,k1_zf_lang) & v1_zf_lang(C) & m1_finseq_1(C,k4_ordinal1) ) => ( v1_zf_lang(k14_zf_lang(A,B,C)) & m2_finseq_1(k14_zf_lang(A,B,C),k4_ordinal1) ) ) )).
fof(dt_k14_zmodul02,axiom,( ! [A] : ( ( ~ 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(k14_zmodul02(A)) & v1_funct_2(k14_zmodul02(A),k2_zfmisc_1(u1_struct_0(k1_int_3),u1_struct_0(A)),u1_struct_0(A)) & m1_subset_1(k14_zmodul02(A),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_int_3),u1_struct_0(A)),u1_struct_0(A)))) ) ) )).
fof(dt_k15_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => m1_subset_1(k15_abcmiz_1(A),u4_struct_0(A)) ) )).
fof(dt_k15_abcmiz_a,axiom,( m3_abcmiz_1(k15_abcmiz_a,k27_abcmiz_1) )).
fof(dt_k15_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k15_algstr_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k14_algstr_4(A))) => v7_ordinal1(k15_algstr_4(A,B)) ) )).
fof(dt_k15_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k15_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) & v4_msualg_1(D,A) & v4_msafree4(D,A,C) & l3_msualg_1(D,A) & m1_subset_1(E,u1_struct_0(A)) & m1_subset_1(F,k1_funct_1(u3_msualg_1(A,C),E)) & v1_relat_1(G) & v1_funct_1(G) & v1_funcop_1(G) ) => m1_subset_1(k15_aofa_a00(A,B,C,D,E,F,G),k1_funct_1(u3_msualg_1(A,D),E)) ) )).
fof(dt_k15_asympt_0,axiom,( ! [A] : ! [B] : ( ( m1_funct_2(A,k4_ordinal1,k1_numbers) & m1_funct_2(B,k4_ordinal1,k1_numbers) ) => m1_funct_2(k15_asympt_0(A,B),k4_ordinal1,k1_numbers) ) )).
fof(dt_k15_bagorder,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k15_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)))) ) ) )).
fof(dt_k15_binop_2,axiom,( v1_funct_1(k15_binop_2) & v1_funct_2(k15_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & m1_subset_1(k15_binop_2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers))) )).
fof(dt_k15_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k15_borsuk_7,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k15_bvfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k15_cat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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(k15_cat_2(A,B,C,D,E,F),k6_cat_2(A,B),k6_cat_2(C,D)) ) )).
fof(dt_k15_cat_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ 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)) ) )).
fof(dt_k15_chain_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_chain_1(B,A) & m1_subset_1(C,k4_ordinal1) ) => ( ~ 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)) ) ) )).
fof(dt_k15_classes2,axiom,( ! [A] : ( ~ v1_xboole_0(k15_classes2(A)) & v1_classes2(k15_classes2(A)) ) )).
fof(dt_k15_clopban1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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)) ) )).
fof(dt_k15_comput_1,axiom,( 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) )).
fof(dt_k15_convex4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k15_cqc_sim1,axiom,( ! [A] : ! [B] : ( ( 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))))) ) )).
fof(dt_k15_csspace,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) ) => v1_xreal_0(k15_csspace(A,B,C)) ) )).
fof(dt_k15_decomp_1,axiom,( ! [A] : ( ( 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)))) ) )).
fof(dt_k15_dtconstr,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k15_e_siec,axiom,( ! [A] : ( ( v2_e_siec(A) & v3_e_siec(A) & l1_e_siec(A) ) => v1_relat_1(k15_e_siec(A)) ) )).
fof(dt_k15_ens_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k15_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ( v5_rltopsp1(k15_euclid(A)) & l1_rltopsp1(k15_euclid(A)) ) ) )).
fof(dt_k15_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ 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)) ) )).
fof(dt_k15_ff_siec,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => v1_relat_1(k15_ff_siec(A)) ) )).
fof(dt_k15_finseq_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k15_fomodel0,axiom,( ! [A] : ! [B] : m1_subset_1(k15_fomodel0(A,B),k1_zfmisc_1(k2_xboole_0(A,B))) )).
fof(dt_k15_fomodel1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fomodel1(A) ) => ~ v1_xboole_0(k15_fomodel1(A)) ) )).
fof(dt_k15_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & ~ v1_xboole_0(B) ) => m1_subset_1(k15_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))))) ) )).
fof(dt_k15_fomodel3,axiom,( ! [A] : ( ~ 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))) ) ) )).
fof(dt_k15_fomodel4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k15_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : m1_subset_1(k15_ftacell1(A,B,C,D,E),k3_msafree2(k13_ftacell1(A,B,C,D,E))) )).
fof(dt_k15_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(D,A) & m1_subset_1(E,A) ) => m1_subset_1(k15_funcop_1(A,B,C,D,E),A) ) )).
fof(dt_k15_funct_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k15_functor0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k15_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ( ~ v8_ordinal1(k15_glib_000(A)) & m1_subset_1(k15_glib_000(A),k4_ordinal1) ) ) )).
fof(dt_k15_glib_001,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) ) )).
fof(dt_k15_glib_004,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)))) ) )).
fof(dt_k15_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => m2_funct_2(k15_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))) ) )).
fof(dt_k15_group_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k15_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k15_hahnban1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k15_idea_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) & m1_finseq_1(B,k4_ordinal1) ) => ( 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))) ) ) )).
fof(dt_k15_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k15_index_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) )).
fof(dt_k15_interva1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k15_isocat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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),k9_nattra_1(A,k6_cat_2(B,C)),k6_cat_2(k9_nattra_1(A,B),k9_nattra_1(A,C))) ) )).
fof(dt_k15_lattice3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => m1_subset_1(k15_lattice3(A,B),u1_struct_0(A)) ) )).
fof(dt_k15_lattice5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k15_lexbfs,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(dt_k15_lmod_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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))) ) )).
fof(dt_k15_lopban_1,axiom,( ! [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) & 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))) ) ) )).
fof(dt_k15_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( ~ v1_xboole_0(k15_lpspacc1(A,B,C)) & m1_subset_1(k15_lpspacc1(A,B,C),k1_zfmisc_1(u1_struct_0(k14_lpspacc1(A,B,C)))) ) ) )).
fof(dt_k15_lpspace1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_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)))) ) ) )).
fof(dt_k15_margrel1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k15_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(D,A) & m1_subset_1(E,A) ) => ( v1_matrix_0(k15_matrix_0(A,B,C,D,E)) & v2_matrix_0(k15_matrix_0(A,B,C,D,E),A,2,2) & m2_finseq_1(k15_matrix_0(A,B,C,D,E),k3_finseq_2(A)) ) ) )).
fof(dt_k15_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k15_mesfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) & v1_xxreal_0(C) ) => m1_subset_1(k15_mesfunc1(A,B,C),k1_zfmisc_1(A)) ) )).
fof(dt_k15_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => l2_algstr_0(k15_midsp_1(A)) ) )).
fof(dt_k15_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k15_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m1_finseq_1(A,k4_ordinal1) ) => ( v1_modelc_1(k15_modelc_1(A)) & m2_finseq_1(k15_modelc_1(A),k4_ordinal1) ) ) )).
fof(dt_k15_modelc_2,axiom,( m1_subset_1(k15_modelc_2,k1_zfmisc_1(k9_modelc_2)) )).
fof(dt_k15_monoid_0,axiom,( ! [A] : ( v15_algstr_0(k15_monoid_0(A)) & m2_monoid_0(k15_monoid_0(A),k12_monoid_0(A)) ) )).
fof(dt_k15_monoid_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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),k4_ordinal1) ) )).
fof(dt_k15_msafree,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k15_msualg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k15_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k15_openlatt,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k15_osafree,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k15_osalg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k15_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k15_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k15_petri,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k15_polyform,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k15_pralg_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k15_pre_poly,axiom,( ! [A] : m1_subset_1(k15_pre_poly(A),k1_zfmisc_1(k14_pre_poly(A))) )).
fof(dt_k15_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v1_prvect_1(A) ) => ( v1_relat_1(k15_prvect_1(A)) & v2_relat_1(k15_prvect_1(A)) & v1_funct_1(k15_prvect_1(A)) & ~ v1_xboole_0(k15_prvect_1(A)) & v1_finseq_1(k15_prvect_1(A)) ) ) )).
fof(dt_k15_pscomp_1,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k15_qc_lang1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k15_quatern2,axiom,( v36_algstr_0(k15_quatern2) & l6_algstr_0(k15_quatern2) )).
fof(dt_k15_quofield,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k15_rfunct_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k15_ringcat1,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(dt_k15_rlvect_2,axiom,( ! [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) ) => ( 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)))) ) ) )).
fof(dt_k15_robbins1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k15_rvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k15_scm_comp,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_dtconstr(k1_scm_comp)) & m1_subset_1(B,k4_ordinal1) ) => ( 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)) ) ) )).
fof(dt_k15_scmfsa_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k15_scmpds_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k15_scmpds_i,axiom,( m1_subset_1(k15_scmpds_i,k4_ordinal1) )).
fof(dt_k15_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => m2_finseq_2(k15_seq_4(A),k2_numbers,k12_seq_4(A)) ) )).
fof(dt_k15_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => m1_subset_1(k15_sin_cos(A),k2_numbers) ) )).
fof(dt_k15_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ( v1_relat_1(k15_substut1(A)) & v1_funct_1(k15_substut1(A)) ) ) )).
fof(dt_k15_supinf_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v4_card_3(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) & m1_supinf_2(B,A) ) => ( v1_funct_1(k15_supinf_2(A,B)) & v1_funct_2(k15_supinf_2(A,B),k4_ordinal1,k6_numbers) & m1_subset_1(k15_supinf_2(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) ) )).
fof(dt_k15_toprealb,axiom,( 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(k7_xcmplx_0(1,2),k7_xcmplx_0(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(k7_xcmplx_0(1,2),k7_xcmplx_0(3,2)))))))) )).
fof(dt_k15_toprealc,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_funct_1(k15_toprealc(A)) & v1_funct_2(k15_toprealc(A),u1_struct_0(k2_borsuk_1(k15_euclid(A),k15_euclid(A))),u1_struct_0(k15_euclid(A))) & m1_subset_1(k15_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))))) ) ) )).
fof(dt_k15_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(k15_trees_3(A)) & v1_funct_1(k15_trees_3(A)) & v1_finseq_1(k15_trees_3(A)) ) ) )).
fof(dt_k15_turing_1,axiom,( v1_funct_1(k15_turing_1) & v1_funct_2(k15_turing_1,k8_mcart_1(k4_ordinal1,k4_ordinal1,k3_turing_1(4),k7_domain_1(k4_ordinal1,k5_numbers,1)),k3_zfmisc_1(k3_turing_1(4),k7_domain_1(k4_ordinal1,k5_numbers,1),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1))) & m1_subset_1(k15_turing_1,k1_zfmisc_1(k2_zfmisc_1(k8_mcart_1(k4_ordinal1,k4_ordinal1,k3_turing_1(4),k7_domain_1(k4_ordinal1,k5_numbers,1)),k3_zfmisc_1(k3_turing_1(4),k7_domain_1(k4_ordinal1,k5_numbers,1),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1))))) )).
fof(dt_k15_twoscomp,axiom,( 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))) )).
fof(dt_k15_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) )).
fof(dt_k15_valued_2,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k15_zf_lang,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k1_zf_lang) & m1_subset_1(B,k1_zf_lang) & v1_zf_lang(C) & m1_finseq_1(C,k4_ordinal1) ) => ( v1_zf_lang(k15_zf_lang(A,B,C)) & m2_finseq_1(k15_zf_lang(A,B,C),k4_ordinal1) ) ) )).
fof(dt_k15_zmodul02,axiom,( ! [A] : ( ( ~ 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(k15_zmodul02(A)) & v7_vectsp_1(k15_zmodul02(A),k1_int_3) & l1_vectsp_1(k15_zmodul02(A),k1_int_3) ) ) )).
fof(dt_k16_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => m1_subset_1(k16_abcmiz_1(A),u4_struct_0(A)) ) )).
fof(dt_k16_abcmiz_a,axiom,( ! [A] : ( 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)) ) )).
fof(dt_k16_algstr_4,axiom,( ! [A] : ! [B] : ( 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))))) ) ) )).
fof(dt_k16_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k16_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) & l4_aofa_a00(D,A,B,C) & m1_subset_1(E,u1_struct_0(A)) ) => m1_subset_1(k16_aofa_a00(A,B,C,D,E),k10_xtuple_0(u4_aofa_a00(A,B,C,D))) ) )).
fof(dt_k16_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k16_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)))) ) ) )).
fof(dt_k16_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k16_borsuk_7,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v8_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))))) ) ) )).
fof(dt_k16_bvfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k16_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ 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))) ) )).
fof(dt_k16_comput_1,axiom,( 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) )).
fof(dt_k16_csspace,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k16_csspace(A,B,C)) & v1_funct_2(k16_csspace(A,B,C),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k16_csspace(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k16_decomp_1,axiom,( ! [A] : ( ( 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)))) ) )).
fof(dt_k16_descip_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) & m1_subset_1(B,A) ) => m2_subset_1(k16_descip_1(A,B),k4_ordinal1,k2_finseq_1(A)) ) )).
fof(dt_k16_e_siec,axiom,( ! [A] : ( ( v2_e_siec(A) & v3_e_siec(A) & l1_e_siec(A) ) => v1_relat_1(k16_e_siec(A)) ) )).
fof(dt_k16_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k16_euclid(A),u1_struct_0(k15_euclid(A))) ) )).
fof(dt_k16_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k16_ff_siec,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => v1_relat_1(k16_ff_siec(A)) ) )).
fof(dt_k16_finseq_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k16_fomodel0,axiom,( 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))) )).
fof(dt_k16_fomodel1,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(dt_k16_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & ~ v1_xboole_0(B) ) => ( v1_funct_1(k16_fomodel2(A,B)) & v1_funct_2(k16_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)),k15_fomodel2(A,B),k32_fomodel1(A)),k6_margrel1) & m1_subset_1(k16_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)),k15_fomodel2(A,B),k32_fomodel1(A)),k6_margrel1))) ) ) )).
fof(dt_k16_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k16_fomodel4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k16_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : m1_subset_1(k16_ftacell1(A,B,C,D,E),k3_msafree2(k13_ftacell1(A,B,C,D,E))) )).
fof(dt_k16_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)))) ) ) )).
fof(dt_k16_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => v1_card_1(k16_glib_000(A)) ) )).
fof(dt_k16_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) ) ) )).
fof(dt_k16_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(dt_k16_graphsp,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k3_finseq_2(k1_numbers)) & m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) ) => v1_xreal_0(k16_graphsp(A,B,C)) ) )).
fof(dt_k16_group_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k16_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k16_hahnban1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k16_idea_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) & m1_finseq_1(B,k4_ordinal1) ) => ( 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))) ) ) )).
fof(dt_k16_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k16_index_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) )).
fof(dt_k16_interva1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k16_lattice3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => m1_subset_1(k16_lattice3(A,B),u1_struct_0(A)) ) )).
fof(dt_k16_lattice5,axiom,( ! [A] : ( ( 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)))) ) ) )).
fof(dt_k16_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => m2_lexbfs(k16_lexbfs(A),A) ) )).
fof(dt_k16_lmod_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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))))) ) ) )).
fof(dt_k16_lopban_1,axiom,( ! [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) & 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)) ) ) )).
fof(dt_k16_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( ~ v2_struct_0(k16_lpspacc1(A,B,C)) & l1_clvect_1(k16_lpspacc1(A,B,C)) ) ) )).
fof(dt_k16_lpspace1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => m2_subset_1(k16_lpspace1(A,B,C),k1_zfmisc_1(k9_lpspace1(A,B,C)),k14_lpspace1(A,B,C)) ) )).
fof(dt_k16_margrel1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k16_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v1_xboole_0(B) & v1_matrix_0(C) & m1_finseq_1(C,k3_finseq_2(B)) ) => ( v1_matrix_0(k16_matrix_0(A,B,C)) & m2_finseq_1(k16_matrix_0(A,B,C),k3_finseq_2(B)) ) ) )).
fof(dt_k16_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & v1_matrix_0(C) & v2_matrix_0(C,A,B,B) & m1_finseq_1(C,k3_finseq_2(A)) ) => ( v2_matrixj1(k16_matrixj1(A,B,C),A) & m2_finseq_1(k16_matrixj1(A,B,C),k3_finseq_2(k3_finseq_2(A))) ) ) )).
fof(dt_k16_mesfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) & v1_xxreal_0(C) ) => m1_subset_1(k16_mesfunc1(A,B,C),k1_zfmisc_1(A)) ) )).
fof(dt_k16_metric_3,axiom,( 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))) )).
fof(dt_k16_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k16_mod_2,axiom,( m1_subset_1(k16_mod_2,k1_enumset1(k5_numbers,1,2)) )).
fof(dt_k16_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k3_modal_1) => m1_subset_1(k16_modal_1(A),k6_modal_1) ) )).
fof(dt_k16_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m1_finseq_1(A,k4_ordinal1) ) => ( v1_modelc_1(k16_modelc_1(A)) & m2_finseq_1(k16_modelc_1(A),k4_ordinal1) ) ) )).
fof(dt_k16_modelc_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & 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),k4_ordinal1,k1_numbers) & m1_subset_1(k16_modelc_3(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k16_monoid_0,axiom,( ! [A] : ( 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)) ) )).
fof(dt_k16_monoid_1,axiom,( ! [A] : ! [B] : m1_subset_1(k16_monoid_1(A,B),u1_struct_0(k13_monoid_1(B))) )).
fof(dt_k16_msualg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k16_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k16_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => m1_lattice4(k16_openlatt(A),A,k15_openlatt(A)) ) )).
fof(dt_k16_osafree,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k16_osalg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k16_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k16_polyform,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k16_pralg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k16_pre_poly,axiom,( ! [A] : m2_subset_1(k16_pre_poly(A),k14_pre_poly(A),k15_pre_poly(A)) )).
fof(dt_k16_prvect_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v1_prvect_1(A) & m1_subset_1(B,k4_finseq_1(k15_prvect_1(A))) ) => ( ~ v2_struct_0(k16_prvect_1(A,B)) & v13_algstr_0(k16_prvect_1(A,B)) & v2_rlvect_1(k16_prvect_1(A,B)) & v3_rlvect_1(k16_prvect_1(A,B)) & v4_rlvect_1(k16_prvect_1(A,B)) & l2_algstr_0(k16_prvect_1(A,B)) ) ) )).
fof(dt_k16_pscomp_1,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k16_qc_lang1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k9_qc_lang1(A)) ) => m1_subset_1(k16_qc_lang1(A,B),k6_qc_lang1(A)) ) )).
fof(dt_k16_quatern2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_quatern2)) => m1_subset_1(k16_quatern2(A),u1_struct_0(k15_quatern2)) ) )).
fof(dt_k16_quofield,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k16_rfunct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k16_ringcat1,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k16_rlvect_2,axiom,( ! [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) ) => l1_rlvect_1(k16_rlvect_2(A)) ) )).
fof(dt_k16_robbins1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k16_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) & v1_finseq_1(A) ) => v1_xcmplx_0(k16_rvsum_1(A)) ) )).
fof(dt_k16_scm_comp,axiom,( ! [A] : ( m1_subset_1(A,k6_dtconstr(k1_scm_comp)) => m1_subset_1(k16_scm_comp(A),k4_ordinal1) ) )).
fof(dt_k16_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k16_scmpds_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k16_seq_4,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k12_seq_4(A)) ) => m2_finseq_2(k16_seq_4(A,B),k2_numbers,k12_seq_4(A)) ) )).
fof(dt_k16_sin_cos,axiom,( 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))) )).
fof(dt_k16_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ~ v1_xboole_0(k16_substut1(A)) ) )).
fof(dt_k16_toprealc,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => ( v1_funct_1(k16_toprealc(A,B)) & v1_funct_2(k16_toprealc(A,B),u1_struct_0(k15_euclid(A)),u1_struct_0(k3_topmetr)) & m1_subset_1(k16_toprealc(A,B),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(A)),u1_struct_0(k3_topmetr)))) ) ) )).
fof(dt_k16_turing_1,axiom,( v1_turing_1(k16_turing_1) & l1_turing_1(k16_turing_1) )).
fof(dt_k16_twoscomp,axiom,( 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))) )).
fof(dt_k16_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))))) ) ) )).
fof(dt_k16_zf_lang,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,k4_ordinal1) ) => ( v1_zf_lang(k16_zf_lang(A,B,C,D)) & m2_finseq_1(k16_zf_lang(A,B,C,D),k4_ordinal1) ) ) )).
fof(dt_k16_zmodul02,axiom,( ! [A] : ( ( ~ 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_int_3) & v9_vectsp_1(A,k1_int_3) & v10_vectsp_1(A,k1_int_3) & v11_vectsp_1(A,k1_int_3) & l1_vectsp_1(A,k1_int_3) ) => ( v1_funct_1(k16_zmodul02(A)) & v1_funct_2(k16_zmodul02(A),k2_zfmisc_1(k4_numbers,u1_struct_0(A)),u1_struct_0(A)) & m1_subset_1(k16_zmodul02(A),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_numbers,u1_struct_0(A)),u1_struct_0(A)))) ) ) )).
fof(dt_k17_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) )).
fof(dt_k17_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) & l4_aofa_a00(D,A,B,C) & m1_subset_1(E,u1_struct_0(A)) & m4_aofa_a00(F,A,B,C,D,E) ) => m1_msafree4(k17_aofa_a00(A,B,C,D,E,F),u1_struct_0(A),k13_msafree(A,B),k1_msafree4(u1_struct_0(A),k13_msafree(A,B),E)) ) )).
fof(dt_k17_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k17_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)))) ) ) )).
fof(dt_k17_binop_2,axiom,( v1_funct_1(k17_binop_2) & v1_funct_2(k17_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & m1_subset_1(k17_binop_2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers))) )).
fof(dt_k17_borsuk_1,axiom,( l1_pre_topc(k17_borsuk_1) )).
fof(dt_k17_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) ) )).
fof(dt_k17_bvfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k17_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ 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)) ) )).
fof(dt_k17_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k16_coh_sp(A)) => m1_subset_1(k17_coh_sp(A,B),k1_zfmisc_1(A)) ) )).
fof(dt_k17_convex4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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))) ) )).
fof(dt_k17_csspace,axiom,( 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))) )).
fof(dt_k17_decomp_1,axiom,( ! [A] : ( ( 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)))) ) )).
fof(dt_k17_e_siec,axiom,( ! [A] : ( ( v2_e_siec(A) & v3_e_siec(A) & l1_e_siec(A) ) => v1_relat_1(k17_e_siec(A)) ) )).
fof(dt_k17_ens_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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))))) ) ) )).
fof(dt_k17_euclid,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => v1_xreal_0(k17_euclid(A)) ) )).
fof(dt_k17_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : 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))) )).
fof(dt_k17_ff_siec,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => v1_relat_1(k17_ff_siec(A)) ) )).
fof(dt_k17_finseq_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & m1_finseq_1(C,A) ) => m2_finseq_1(k17_finseq_1(A,B,C),A) ) )).
fof(dt_k17_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k17_fomodel1,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(dt_k17_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & ~ v1_xboole_0(B) & m1_subset_1(C,k15_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)),k15_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(k17_fomodel2(A,B,C,D,E),k6_margrel1) ) )).
fof(dt_k17_fomodel3,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k17_fomodel4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k17_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : m1_subset_1(k17_ftacell1(A,B,C,D,E),k3_msafree2(k13_ftacell1(A,B,C,D,E))) )).
fof(dt_k17_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)))) ) )).
fof(dt_k17_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k17_funct_3(A,B,C,D)) & v1_funct_2(k17_funct_3(A,B,C,D),D,B) & m1_subset_1(k17_funct_3(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(D,B))) ) ) )).
fof(dt_k17_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ 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)) ) )).
fof(dt_k17_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => m1_subset_1(k17_glib_000(A),k4_ordinal1) ) )).
fof(dt_k17_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & m3_glib_001(B,A) & m1_subset_1(C,k4_ordinal1) ) => ( ~ v1_abian(k17_glib_001(A,B,C)) & m1_subset_1(k17_glib_001(A,B,C),k4_ordinal1) ) ) )).
fof(dt_k17_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)))) ) )).
fof(dt_k17_graphsp,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k3_finseq_2(k1_numbers)) & m1_subset_1(B,k4_ordinal1) ) => m2_finseq_2(k17_graphsp(A,B),k1_numbers,k3_finseq_2(k1_numbers)) ) )).
fof(dt_k17_group_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k17_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(dt_k17_idea_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) & ~ v8_ordinal1(C) & v1_matrix_0(D) & v2_matrix_0(D,k4_ordinal1,B,6) & m1_finseq_1(D,k3_finseq_2(k4_ordinal1)) ) => ( 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)) ) ) )).
fof(dt_k17_ideal_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k17_interva1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k17_lexbfs,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_k17_lmod_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) ) )).
fof(dt_k17_lopban_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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)) ) )).
fof(dt_k17_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => m1_subset_1(k17_lpspacc1(A,B,C,D),k1_zfmisc_1(k13_lpspacc1(A,B,C))) ) )).
fof(dt_k17_lpspace1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_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)))) ) ) )).
fof(dt_k17_margrel1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k17_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & v1_matrix_0(C) & m1_finseq_1(C,k3_finseq_2(A)) ) => ( v1_matrix_0(k17_matrix_0(A,B,C)) & m2_finseq_1(k17_matrix_0(A,B,C),k3_finseq_2(A)) ) ) )).
fof(dt_k17_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & v7_ordinal1(C) & v1_matrix_0(D) & v2_matrix_0(D,A,B,B) & m1_finseq_1(D,k3_finseq_2(A)) & v1_matrix_0(E) & v2_matrix_0(E,A,C,C) & m1_finseq_1(E,k3_finseq_2(A)) ) => ( 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))) ) ) )).
fof(dt_k17_mesfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) & v1_xxreal_0(C) ) => m1_subset_1(k17_mesfunc1(A,B,C),k1_zfmisc_1(A)) ) )).
fof(dt_k17_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k17_mod_2,axiom,( m1_subset_1(k17_mod_2,k1_enumset1(k5_numbers,1,2)) )).
fof(dt_k17_modal_1,axiom,( m1_subset_1(k17_modal_1,k6_modal_1) )).
fof(dt_k17_modelc_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k13_modelc_2(A))) & v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => v1_xreal_0(k17_modelc_3(A,B,C)) ) )).
fof(dt_k17_monoid_0,axiom,( ! [A] : ( ~ 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)) ) )).
fof(dt_k17_monoid_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => m1_subset_1(k17_monoid_1(A,B),u1_struct_0(k13_monoid_1(A))) ) )).
fof(dt_k17_msualg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k17_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(dt_k17_openlatt,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k17_osafree,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) )).
fof(dt_k17_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k17_pcs_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k17_polyform,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(dt_k17_pre_poly,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_k17_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v1_prvect_1(A) ) => m1_prvect_1(k17_prvect_1(A),k15_prvect_1(A)) ) )).
fof(dt_k17_pscomp_1,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k17_qc_lang1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k9_qc_lang1(A)) ) => m2_finseq_1(k17_qc_lang1(A,B),k2_qc_lang1(A)) ) )).
fof(dt_k17_quatern2,axiom,( ! [A] : ! [B] : ( ( v1_quaterni(A) & v1_quaterni(B) ) => m1_subset_1(k17_quatern2(A,B),k1_quaterni) ) )).
fof(dt_k17_quaterni,axiom,( v1_quaterni(k17_quaterni) )).
fof(dt_k17_quofield,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k17_rfunct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k17_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => l1_cat_1(k17_ringcat1(A)) ) )).
fof(dt_k17_robbins1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k17_rvsum_1,axiom,( ! [A] : ( m1_finseq_1(A,k2_numbers) => m1_subset_1(k17_rvsum_1(A),k2_numbers) ) )).
fof(dt_k17_scm_comp,axiom,( ! [A] : ( m1_subset_1(A,k4_dtconstr(k1_scm_comp)) => m1_subset_1(k17_scm_comp(A),k4_ordinal1) ) )).
fof(dt_k17_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k17_scmpds_2,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) ) )).
fof(dt_k17_seq_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,k12_seq_4(A)) & m1_subset_1(C,k12_seq_4(A)) ) => m2_finseq_2(k17_seq_4(A,B,C),k2_numbers,k12_seq_4(A)) ) )).
fof(dt_k17_substut1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k17_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_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(k6_numbers)) ) ) )).
fof(dt_k17_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_xreal_0(B) & ~ v3_xxreal_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(k17_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)))) ) )).
fof(dt_k17_turing_1,axiom,( v1_funct_1(k17_turing_1) & v1_funct_2(k17_turing_1,k8_mcart_1(k4_ordinal1,k4_ordinal1,k3_turing_1(4),k7_domain_1(k4_ordinal1,k5_numbers,1)),k3_zfmisc_1(k3_turing_1(4),k7_domain_1(k4_ordinal1,k5_numbers,1),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1))) & m1_subset_1(k17_turing_1,k1_zfmisc_1(k2_zfmisc_1(k8_mcart_1(k4_ordinal1,k4_ordinal1,k3_turing_1(4),k7_domain_1(k4_ordinal1,k5_numbers,1)),k3_zfmisc_1(k3_turing_1(4),k7_domain_1(k4_ordinal1,k5_numbers,1),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1))))) )).
fof(dt_k17_twoscomp,axiom,( 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))) )).
fof(dt_k17_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))))) ) ) )).
fof(dt_k17_zf_lang,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,k4_ordinal1) ) => ( v1_zf_lang(k17_zf_lang(A,B,C,D)) & m2_finseq_1(k17_zf_lang(A,B,C,D),k4_ordinal1) ) ) )).
fof(dt_k17_zmodul02,axiom,( ! [A] : ( ( ~ 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_int_3) & v9_vectsp_1(A,k1_int_3) & v10_vectsp_1(A,k1_int_3) & v11_vectsp_1(A,k1_int_3) & l1_vectsp_1(A,k1_int_3) ) => ( ~ v2_struct_0(k17_zmodul02(A)) & v1_zmodul01(k17_zmodul02(A)) & l1_zmodul01(k17_zmodul02(A)) ) ) )).
fof(dt_k18_algstr_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))))) ) ) )).
fof(dt_k18_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => m1_subset_1(k18_aofa_000(A),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k18_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) & v5_msafree4(C,A,B) & l1_aofa_a00(C,A) & l4_aofa_a00(D,A,B,C) & m1_subset_1(E,u1_struct_0(A)) & m4_aofa_a00(F,A,B,C,D,E) ) => m2_pboole(k18_aofa_a00(A,B,C,D,E,F),u1_struct_0(A),k11_aofa_a00(A,C,E,F),u3_msualg_1(A,C)) ) )).
fof(dt_k18_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) )).
fof(dt_k18_borsuk_1,axiom,( m1_subset_1(k18_borsuk_1,u1_struct_0(k17_borsuk_1)) )).
fof(dt_k18_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ v2_struct_0(A) & ~ 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)) ) )).
fof(dt_k18_coh_sp,axiom,( ! [A] : ! [B] : ( 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)))) ) ) )).
fof(dt_k18_convex4,axiom,( ! [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) ) => ( v1_clvect_1(k18_convex4(A)) & m1_clvect_1(k18_convex4(A),A) ) ) )).
fof(dt_k18_csspace,axiom,( ~ v2_struct_0(k18_csspace) & l1_csspace(k18_csspace) )).
fof(dt_k18_decomp_1,axiom,( ! [A] : ( ( 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)))) ) )).
fof(dt_k18_dtconstr,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k18_e_siec,axiom,( ! [A] : ( l1_e_siec(A) => v1_relat_1(k18_e_siec(A)) ) )).
fof(dt_k18_ens_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)))) ) ) )).
fof(dt_k18_euclid,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => v1_xreal_0(k18_euclid(A)) ) )).
fof(dt_k18_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k18_finseq_1,axiom,( ! [A] : ( v1_relat_1(A) => v1_relat_1(k18_finseq_1(A)) ) )).
fof(dt_k18_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_k18_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => m1_subset_1(k18_fomodel1(A),k1_fomodel1(A)) ) )).
fof(dt_k18_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),k6_margrel1)) ) => ( v1_funct_1(k18_fomodel2(A,B,C)) & m1_subset_1(k18_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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),k6_margrel1))) ) ) )).
fof(dt_k18_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))))) ) )).
fof(dt_k18_fomodel4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k18_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : m1_subset_1(k18_ftacell1(A,B,C,D,E),k3_msafree2(k13_ftacell1(A,B,C,D,E))) )).
fof(dt_k18_funcop_1,axiom,( ! [A] : ! [B] : ( 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)))) ) )).
fof(dt_k18_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k18_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) )).
fof(dt_k18_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) ) ) )).
fof(dt_k18_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => m2_funct_2(k18_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))) ) )).
fof(dt_k18_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_grcat_1(A) ) => ( ~ v1_xboole_0(k18_grcat_1(A)) & v4_grcat_1(k18_grcat_1(A)) ) ) )).
fof(dt_k18_group_2,axiom,( ! [A] : ! [B] : ( ( ~ 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),k4_ordinal1) ) )).
fof(dt_k18_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k18_idea_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) & ~ v8_ordinal1(C) & v1_matrix_0(D) & v2_matrix_0(D,k4_ordinal1,B,6) & m1_finseq_1(D,k3_finseq_2(k4_ordinal1)) ) => ( 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)) ) ) )).
fof(dt_k18_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1),k9_funct_2(k6_glib_000(A),k4_ordinal1))) ) )).
fof(dt_k18_lmod_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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))) ) )).
fof(dt_k18_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( ~ v1_xboole_0(k18_lpspacc1(A,B,C)) & m1_subset_1(k18_lpspacc1(A,B,C),k1_zfmisc_1(k1_zfmisc_1(k13_lpspacc1(A,B,C)))) ) ) )).
fof(dt_k18_lpspace1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_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)) ) ) )).
fof(dt_k18_margrel1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_margrel1(A) ) => v7_ordinal1(k18_margrel1(A)) ) )).
fof(dt_k18_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) & ~ v1_xboole_0(D) & v1_matrix_0(E) & v2_matrix_0(E,D,C,C) & m1_finseq_1(E,k3_finseq_2(D)) ) => ( v1_matrix_0(k18_matrix_0(A,B,C,D,E)) & m2_finseq_1(k18_matrix_0(A,B,C,D,E),k3_finseq_2(D)) ) ) )).
fof(dt_k18_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k18_mesfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) & v1_xxreal_0(C) ) => m1_subset_1(k18_mesfunc1(A,B,C),k1_zfmisc_1(A)) ) )).
fof(dt_k18_metric_3,axiom,( 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))) )).
fof(dt_k18_mmlquery,axiom,( ! [A] : ! [B] : ( 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))) ) )).
fof(dt_k18_mod_2,axiom,( v36_algstr_0(k18_mod_2) & l6_algstr_0(k18_mod_2) )).
fof(dt_k18_modelc_1,axiom,( m1_subset_1(k18_modelc_1,k1_zfmisc_1(k12_modelc_1)) )).
fof(dt_k18_modelc_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k18_modelc_3,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k13_modelc_2(A))) ) => v1_xreal_0(k18_modelc_3(A,B)) ) )).
fof(dt_k18_monoid_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m1_subset_1(k18_monoid_1(A,B),u1_struct_0(k13_monoid_1(A))) ) )).
fof(dt_k18_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k18_openlatt,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(dt_k18_osafree,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) )).
fof(dt_k18_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k18_pcs_0,axiom,( ! [A] : ! [B] : ( v1_relat_1(k18_pcs_0(A,B)) & v4_relat_1(k18_pcs_0(A,B),k7_domain_1(k4_ordinal1,k5_numbers,1)) & v1_funct_1(k18_pcs_0(A,B)) & v1_partfun1(k18_pcs_0(A,B),k7_domain_1(k4_ordinal1,k5_numbers,1)) ) )).
fof(dt_k18_polyform,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k18_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => m1_subset_1(k18_pre_poly(A,B),k1_zfmisc_1(k9_funct_2(A,k4_ordinal1))) ) )).
fof(dt_k18_pscomp_1,axiom,( ! [A] : ( 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))) ) )).
fof(dt_k18_qc_lang1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k9_qc_lang1(A)) ) => m1_subset_1(k18_qc_lang1(A,B),k9_qc_lang1(A)) ) )).
fof(dt_k18_quaterni,axiom,( v1_quaterni(k18_quaterni) )).
fof(dt_k18_quofield,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k18_rfunct_3,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k18_rvsum_1,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => v1_xreal_0(k18_rvsum_1(A)) ) )).
fof(dt_k18_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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(k7_card_1(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) ) )).
fof(dt_k18_seq_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,k12_seq_4(A)) & m1_subset_1(C,k2_numbers) ) => m2_finseq_2(k18_seq_4(A,B,C),k2_numbers,k12_seq_4(A)) ) )).
fof(dt_k18_sin_cos,axiom,( v1_funct_1(k18_sin_cos) & v1_funct_2(k18_sin_cos,k1_numbers,k1_numbers) & m1_subset_1(k18_sin_cos,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) )).
fof(dt_k18_substut1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k16_substut1(A)) ) => m1_subset_1(k18_substut1(A,B),k9_qc_lang1(A)) ) )).
fof(dt_k18_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v1_funct_1(k18_supinf_2(A)) & v1_funct_2(k18_supinf_2(A),k4_ordinal1,k6_numbers) & m1_subset_1(k18_supinf_2(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) ) )).
fof(dt_k18_turing_1,axiom,( v1_turing_1(k18_turing_1) & l1_turing_1(k18_turing_1) )).
fof(dt_k18_twoscomp,axiom,( 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))) )).
fof(dt_k18_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k18_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) ) => m2_subset_1(k18_zf_lang(A),k4_ordinal1,k1_zf_lang) ) )).
fof(dt_k18_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & m1_zmodul02(B,A) ) => ( v1_finset_1(k18_zmodul02(A,B)) & m1_subset_1(k18_zmodul02(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_k19_aofa_000,axiom,( ~ v1_xboole_0(k19_aofa_000) & m2_finseq_1(k19_aofa_000,k4_ordinal1) )).
fof(dt_k19_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [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)) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & l1_aofa_a00(C,A) & v4_msualg_1(D,A) & v4_msafree4(D,A,C) & l3_msualg_1(D,A) & l4_aofa_a00(E,A,B,C) & m1_subset_1(F,k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) & m1_subset_1(G,u1_struct_0(A)) & m1_subset_1(H,k1_funct_1(u3_msualg_1(A,D),G)) & m4_aofa_a00(I,A,B,C,E,G) ) => m2_subset_1(k19_aofa_a00(A,B,C,D,E,F,G,H,I),k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) ) )).
fof(dt_k19_borsuk_1,axiom,( m1_subset_1(k19_borsuk_1,u1_struct_0(k17_borsuk_1)) )).
fof(dt_k19_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => m1_subset_1(k19_bvfunc_1(A,B),k6_margrel1) ) )).
fof(dt_k19_cat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l2_cat_4(A) ) => m1_subset_1(k19_cat_4(A),u1_struct_0(A)) ) )).
fof(dt_k19_convex4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k19_decomp_1,axiom,( ! [A] : ( ( 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)))) ) )).
fof(dt_k19_e_siec,axiom,( ! [A] : ( l1_e_siec(A) => v1_relat_1(k19_e_siec(A)) ) )).
fof(dt_k19_ens_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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))))) ) ) )).
fof(dt_k19_euclid,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => m1_subset_1(k19_euclid(A,B),u1_struct_0(k15_euclid(2))) ) )).
fof(dt_k19_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ 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)) ) )).
fof(dt_k19_finseq_1,axiom,( ! [A] : ( v1_finset_1(A) => m2_finseq_1(k19_finseq_1(A),A) ) )).
fof(dt_k19_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) => m1_fomodel0(k19_fomodel0(A,B,C,D),A) ) )).
fof(dt_k19_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k19_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),k6_margrel1))) & m1_subset_1(D,k15_fomodel2(A,B)) & m1_subset_1(E,k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))) ) => m1_subset_1(k19_fomodel2(A,B,C,D,E),k6_margrel1) ) )).
fof(dt_k19_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))))) ) ) )).
fof(dt_k19_fomodel4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k19_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ~ 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)) ) )).
fof(dt_k19_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ 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)) ) )).
fof(dt_k19_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) )).
fof(dt_k19_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & m3_glib_001(B,A) & m1_subset_1(C,k4_ordinal1) ) => ( ~ v1_abian(k19_glib_001(A,B,C)) & m1_subset_1(k19_glib_001(A,B,C),k4_ordinal1) ) ) )).
fof(dt_k19_grcat_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k19_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(dt_k19_idea_1,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k4_ordinal1) & v7_ordinal1(B) ) => ( 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))) ) ) )).
fof(dt_k19_lexbfs,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1),k9_funct_2(k6_glib_000(A),k4_ordinal1))) ) => m1_subset_1(k19_lexbfs(A,B),k6_glib_000(A)) ) )).
fof(dt_k19_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( v1_funct_1(k19_lpspacc1(A,B,C)) & v1_funct_2(k19_lpspacc1(A,B,C),k2_zfmisc_1(k18_lpspacc1(A,B,C),k18_lpspacc1(A,B,C)),k18_lpspacc1(A,B,C)) & m1_subset_1(k19_lpspacc1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k18_lpspacc1(A,B,C),k18_lpspacc1(A,B,C)),k18_lpspacc1(A,B,C)))) ) ) )).
fof(dt_k19_lpspace1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_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))) ) ) )).
fof(dt_k19_margrel1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_margrel1(A) ) => m1_subset_1(k19_margrel1(A),k4_ordinal1) ) )).
fof(dt_k19_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k19_mesfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) & v1_xxreal_0(C) ) => m1_subset_1(k19_mesfunc1(A,B,C),k1_zfmisc_1(A)) ) )).
fof(dt_k19_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k19_modelc_3,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & v1_modelc_2(B) & m1_finseq_1(B,k4_ordinal1) ) => m1_subset_1(k19_modelc_3(A,B),k1_zfmisc_1(k1_modelc_3(A))) ) )).
fof(dt_k19_monoid_1,axiom,( ! [A] : ( ~ 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)) ) )).
fof(dt_k19_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k19_osafree,axiom,( ! [A] : ! [B] : ( ( ~ 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)))))) ) ) )).
fof(dt_k19_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(dt_k19_pcs_0,axiom,( ! [A] : ! [B] : ( ( l2_pcs_0(A) & l2_pcs_0(B) ) => l2_pcs_0(k19_pcs_0(A,B)) ) )).
fof(dt_k19_polyform,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k19_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v1_prvect_1(A) ) => m1_subset_1(k19_prvect_1(A),k4_card_3(k15_prvect_1(A))) ) )).
fof(dt_k19_pscomp_1,axiom,( ! [A] : ( 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))) ) )).
fof(dt_k19_qc_lang1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k9_qc_lang1(A)) ) => m1_subset_1(k19_qc_lang1(A,B),k9_qc_lang1(A)) ) )).
fof(dt_k19_quofield,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k19_rfunct_3,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k19_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) & v1_finseq_1(A) ) => v1_xcmplx_0(k19_rvsum_1(A)) ) )).
fof(dt_k19_seq_4,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k12_seq_4(A)) ) => m2_finseq_2(k19_seq_4(A,B),k1_numbers,k4_finseq_2(A,k1_numbers)) ) )).
fof(dt_k19_substut1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k16_substut1(A)) ) => m1_subset_1(k19_substut1(A,B),k1_substut1(A)) ) )).
fof(dt_k19_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => m1_subset_1(k19_supinf_2(A),k6_numbers) ) )).
fof(dt_k19_turing_1,axiom,( v1_funct_1(k19_turing_1) & v1_funct_2(k19_turing_1,k8_mcart_1(k4_ordinal1,k4_ordinal1,k3_turing_1(3),k7_domain_1(k4_ordinal1,k5_numbers,1)),k3_zfmisc_1(k3_turing_1(3),k7_domain_1(k4_ordinal1,k5_numbers,1),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1))) & m1_subset_1(k19_turing_1,k1_zfmisc_1(k2_zfmisc_1(k8_mcart_1(k4_ordinal1,k4_ordinal1,k3_turing_1(3),k7_domain_1(k4_ordinal1,k5_numbers,1)),k3_zfmisc_1(k3_turing_1(3),k7_domain_1(k4_ordinal1,k5_numbers,1),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1))))) )).
fof(dt_k19_twoscomp,axiom,( 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))) )).
fof(dt_k19_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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))) ) ) )).
fof(dt_k19_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) ) => m2_subset_1(k19_zf_lang(A),k4_ordinal1,k1_zf_lang) ) )).
fof(dt_k19_zmodul02,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => m1_zmodul02(k19_zmodul02(A),A) ) )).
fof(dt_k1_abcmiz_0,axiom,( ! [A] : ! [B] : ( ( l1_abcmiz_0(A) & m1_subset_1(B,u1_abcmiz_0(A)) ) => m1_subset_1(k1_abcmiz_0(A,B),u1_abcmiz_0(A)) ) )).
fof(dt_k1_abian,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(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))) ) ) )).
fof(dt_k1_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k1_absvalue(A)) ) )).
fof(dt_k1_aff_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k1_aff_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k1_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => m1_subset_1(k1_afinsq_1(A),k4_ordinal1) ) )).
fof(dt_k1_afinsq_2,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k1_afproj,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k1_afvect0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k1_alg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k1_algseq_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => m1_subset_1(k1_algseq_1(A,B),k4_ordinal1) ) )).
fof(dt_k1_algspec1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(dt_k1_algstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k1_algstr_1,axiom,( ! [A] : m1_subset_1(k1_algstr_1(A),k1_tarski(A)) )).
fof(dt_k1_algstr_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k1_algstr_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k1_altcat_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k1_altcat_4,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(dt_k1_altcat_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) & m1_subset_1(B,u1_struct_0(A)) & ~ v1_xboole_0(C) & 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)))) & m1_altcat_5(E,A,B,C,D) & m1_subset_1(F,C) ) => m1_subset_1(k1_altcat_5(A,B,C,D,E,F),k1_altcat_1(A,B,k3_funct_2(C,u1_struct_0(A),D,F))) ) )).
fof(dt_k1_ami_3,axiom,( v1_extpro_1(k1_ami_3,k7_card_1(2)) & l1_extpro_1(k1_ami_3,k7_card_1(2)) )).
fof(dt_k1_ami_4,axiom,( v1_relat_1(k1_ami_4) & v4_relat_1(k1_ami_4,k4_ordinal1) & v5_relat_1(k1_ami_4,u1_compos_1(k1_ami_3)) & v1_funct_1(k1_ami_4) & v1_finset_1(k1_ami_4) )).
fof(dt_k1_ami_wstd,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) => m1_subset_1(k1_ami_wstd(A,B,C),k4_ordinal1) ) )).
fof(dt_k1_amistd_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k4_ordinal1)) ) )).
fof(dt_k1_amistd_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k4_ordinal1)) ) => ( v1_relat_1(k1_amistd_3(A,B,C)) & v5_relat_1(k1_amistd_3(A,B,C),k4_ordinal1) & v5_ordinal1(k1_amistd_3(A,B,C)) & v1_funct_1(k1_amistd_3(A,B,C)) ) ) )).
fof(dt_k1_amistd_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) ) )).
fof(dt_k1_analmetr,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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))))) ) )).
fof(dt_k1_analoaf,axiom,( ! [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) ) => 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))))) ) )).
fof(dt_k1_analort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) )).
fof(dt_k1_anproj_1,axiom,( ! [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) ) => ( 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)))) ) ) )).
fof(dt_k1_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k1_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ( v1_relat_1(k1_aofa_a00(A,B,C,D)) & v4_relat_1(k1_aofa_a00(A,B,C,D),A) & v1_funct_1(k1_aofa_a00(A,B,C,D)) & v1_partfun1(k1_aofa_a00(A,B,C,D),A) ) ) )).
fof(dt_k1_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ( v2_relat_1(k1_aofa_a01(A,B,C)) & m1_msafree(k1_aofa_a01(A,B,C),A,C) ) ) )).
fof(dt_k1_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v4_funct_1(A) ) => m1_subset_1(k1_aofa_i00(A,B,C),k1_zfmisc_1(A)) ) )).
fof(dt_k1_armstrng,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => m1_subset_1(k1_armstrng(A,B),k1_zfmisc_1(A)) ) )).
fof(dt_k1_arytm_0,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k1_arytm_0(A,B),k1_numbers) ) )).
fof(dt_k1_arytm_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k1_arytm_2,axiom,( m1_subset_1(k1_arytm_2,k1_zfmisc_1(k1_zfmisc_1(k5_arytm_3))) )).
fof(dt_k1_asympt_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_funct_1(k1_asympt_0(A,B)) & v1_funct_2(k1_asympt_0(A,B),k4_ordinal1,k1_numbers) & v2_asympt_0(k1_asympt_0(A,B)) & m1_subset_1(k1_asympt_0(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k1_asympt_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) ) => ( v1_funct_1(k1_asympt_1(A,B,C)) & v1_funct_2(k1_asympt_1(A,B,C),k4_ordinal1,k1_numbers) & m1_subset_1(k1_asympt_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k1_autalg_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(dt_k1_autgroup,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(dt_k1_bagorder,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_k1_bcialg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k1_bcialg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k4_ordinal1) ) => m1_subset_1(k1_bcialg_2(A,B,C,D),u1_struct_0(A)) ) )).
fof(dt_k1_bcialg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k1_bcialg_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k4_ordinal1) & m1_subset_1(E,k4_ordinal1) ) => m1_subset_1(k1_bcialg_5(A,B,C,D,E),u1_struct_0(A)) ) )).
fof(dt_k1_bhsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_bhsp_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => v1_xreal_0(k1_bhsp_1(A,B,C)) ) )).
fof(dt_k1_bhsp_2,axiom,( ! [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) & v8_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => m1_subset_1(k1_bhsp_2(A,B),u1_struct_0(A)) ) )).
fof(dt_k1_bhsp_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k1_bhsp_4(A,B)) & v1_funct_2(k1_bhsp_4(A,B),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k1_bhsp_4(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k1_bhsp_6,axiom,( ! [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) & 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)) ) )).
fof(dt_k1_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k1_binari_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( v3_card_1(k1_binari_2(A),A) & m2_finseq_1(k1_binari_2(A),k6_margrel1) ) ) )).
fof(dt_k1_binari_3,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(dt_k1_binari_4,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => v7_ordinal1(k1_binari_4(A,B)) ) )).
fof(dt_k1_binarith,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => m1_subset_1(k1_binarith(A,B),k6_margrel1) ) )).
fof(dt_k1_binom,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k1_binop_2,axiom,( v1_funct_1(k1_binop_2) & v1_funct_2(k1_binop_2,k2_numbers,k2_numbers) & m1_subset_1(k1_binop_2,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) )).
fof(dt_k1_bintree1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k1_bintree2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree1(A) & v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( v1_funct_1(k1_bintree2(A,B)) & v1_funct_2(k1_bintree2(A,B),k2_trees_2(A,B),k4_ordinal1) & m1_subset_1(k1_bintree2(A,B),k1_zfmisc_1(k2_zfmisc_1(k2_trees_2(A,B),k4_ordinal1))) ) ) )).
fof(dt_k1_birkhoff,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k1_boolealg,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k1_boolmark,axiom,( ! [A] : ( l1_petri(A) => m1_funct_2(k1_boolmark(A),u1_struct_0(A),k6_margrel1) ) )).
fof(dt_k1_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))) ) )).
fof(dt_k1_borsuk_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(dt_k1_borsuk_4,axiom,( v1_pre_topc(k1_borsuk_4) & m1_pre_topc(k1_borsuk_4,k5_topmetr) )).
fof(dt_k1_borsuk_5,axiom,( m1_subset_1(k1_borsuk_5,k1_zfmisc_1(k1_numbers)) )).
fof(dt_k1_borsuk_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))))) ) ) )).
fof(dt_k1_brouwer,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k1_bspace,axiom,( ! [A] : ( l1_struct_0(A) => m2_finseq_1(k1_bspace(A),u1_struct_0(A)) ) )).
fof(dt_k1_bvfunc26,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k1_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k1_bvfunc_2,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k1_c0sp1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k1_c0sp2,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k1_calcul_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) ) => m2_finseq_1(k1_calcul_1(A,B),A) ) )).
fof(dt_k1_cantor_1,axiom,( ! [A] : ! [B] : ( 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))) ) )).
fof(dt_k1_card_1,axiom,( ! [A] : v1_card_1(k1_card_1(A)) )).
fof(dt_k1_card_2,axiom,( ! [A] : ! [B] : ( ( v1_card_1(A) & v1_card_1(B) ) => v1_card_1(k1_card_2(A,B)) ) )).
fof(dt_k1_card_3,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k1_card_5,axiom,( ! [A] : ( v1_card_1(A) => v1_card_1(k1_card_5(A)) ) )).
fof(dt_k1_card_fil,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_card_fil(B,A) ) => m2_card_fil(k1_card_fil(A,B),A) ) )).
fof(dt_k1_card_fin,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) )).
fof(dt_k1_cardfin2,axiom,( ! [A] : ( v1_xreal_0(A) => v1_int_1(k1_cardfin2(A)) ) )).
fof(dt_k1_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k1_cat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) )).
fof(dt_k1_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k1_cat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_cat_4(A) ) => m1_subset_1(k1_cat_4(A),u1_struct_0(A)) ) )).
fof(dt_k1_cat_5,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k1_catalan1,axiom,( ! [A] : ( v7_ordinal1(A) => v1_xreal_0(k1_catalan1(A)) ) )).
fof(dt_k1_catalan2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) & v1_relat_1(B) & v5_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ( v1_relat_1(k1_catalan2(A,B)) & v5_relat_1(k1_catalan2(A,B),k4_ordinal1) & v1_funct_1(k1_catalan2(A,B)) & v5_ordinal1(k1_catalan2(A,B)) & v1_finset_1(k1_catalan2(A,B)) ) ) )).
fof(dt_k1_catalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k1_cc0sp1,axiom,( ! [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) & 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))) ) ) )).
fof(dt_k1_cc0sp2,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k1_cfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_funct_1(k1_cfdiff_1(A)) & v1_funct_2(k1_cfdiff_1(A),k4_ordinal1,k2_numbers) & m1_subset_1(k1_cfdiff_1(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) ) )).
fof(dt_k1_cfuncdom,axiom,( ! [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)))) ) )).
fof(dt_k1_cfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k1_chain_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => m1_subset_1(k1_chain_1(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) )).
fof(dt_k1_chord,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v7_ordinal1(B) ) => v1_finset_1(k1_chord(A,B)) ) )).
fof(dt_k1_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k1_circcomb,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( 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)) ) )).
fof(dt_k1_circled1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k1_circtrm1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k1_circuit1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k1_circuit2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k1_ckspace1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) & ~ v1_xboole_0(C) & v1_pdiff_7(C,A) & m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) ) => ( ~ v1_xboole_0(k1_ckspace1(A,B,C)) & m1_subset_1(k1_ckspace1(A,B,C),k1_zfmisc_1(u1_struct_0(k12_funcsdom(C)))) ) ) )).
fof(dt_k1_classes2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) ) => m1_subset_1(k1_classes2(A,B),A) ) )).
fof(dt_k1_clopban2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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)))) ) ) )).
fof(dt_k1_clopban3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => m1_subset_1(k1_clopban3(A,B),u1_struct_0(A)) ) )).
fof(dt_k1_clopban4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & 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),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k1_clopban4(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k1_closure1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(dt_k1_clvect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k1_clvect_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => m1_subset_1(k1_clvect_2(A,B),u1_struct_0(A)) ) )).
fof(dt_k1_clvect_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => m1_subset_1(k1_clvect_3(A,B),u1_struct_0(A)) ) )).
fof(dt_k1_coh_sp,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k1_combgras,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ 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)) ) ) )).
fof(dt_k1_compact1,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_pre_topc(k1_compact1(A)) & l1_pre_topc(k1_compact1(A)) ) ) )).
fof(dt_k1_compl_sp,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ( v1_funct_1(k1_compl_sp(A,B)) & v1_funct_2(k1_compl_sp(A,B),k4_ordinal1,k1_numbers) & m1_subset_1(k1_compl_sp(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k1_complex2,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => m1_subset_1(k1_complex2(A,B),k2_numbers) ) )).
fof(dt_k1_complfld,axiom,( v36_algstr_0(k1_complfld) & l6_algstr_0(k1_complfld) )).
fof(dt_k1_complsp1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v1_pre_topc(k1_complsp1(A)) & v2_pre_topc(k1_complsp1(A)) & l1_pre_topc(k1_complsp1(A)) ) ) )).
fof(dt_k1_complsp2,axiom,( ! [A] : ( m1_finseq_1(A,k2_numbers) => m2_finseq_1(k1_complsp2(A),k2_numbers) ) )).
fof(dt_k1_compos_1,axiom,( v1_compos_1(k1_compos_1) & l1_compos_1(k1_compos_1) )).
fof(dt_k1_compos_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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,k4_ordinal1) & 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),k4_ordinal1) & 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) ) ) )).
fof(dt_k1_comptrig,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xreal_0(k1_comptrig(A)) ) )).
fof(dt_k1_compts_1,axiom,( ! [A] : l1_pre_topc(k1_compts_1(A)) )).
fof(dt_k1_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_comput_1(A) ) => m1_subset_1(k1_comput_1(A),k4_ordinal1) ) )).
fof(dt_k1_comseq_2,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k1_comseq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( v1_funct_1(k1_comseq_3(A)) & v1_funct_2(k1_comseq_3(A),k4_ordinal1,k2_numbers) & m1_subset_1(k1_comseq_3(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) ) )).
fof(dt_k1_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(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))))) ) ) )).
fof(dt_k1_connsp_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k1_connsp_2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k1_connsp_3,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k1_convex1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xreal_0(C) ) => m1_subset_1(k1_convex1(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k1_convex4,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k1_convfun1,axiom,( ! [A] : ! [B] : ( ( ~ 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))))) ) ) )).
fof(dt_k1_cqc_lang,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k1_cqc_the1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k1_csspace,axiom,( ~ v1_xboole_0(k1_csspace) )).
fof(dt_k1_csspace3,axiom,( m1_subset_1(k1_csspace3,k1_zfmisc_1(u1_struct_0(k7_csspace))) )).
fof(dt_k1_csspace4,axiom,( m1_subset_1(k1_csspace4,k1_zfmisc_1(u1_struct_0(k7_csspace))) )).
fof(dt_k1_decomp_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k1_descip_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k1_dickson,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_k1_diff_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k1_diff_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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(k1_diff_2(A,B,C,D,E,F)) ) )).
fof(dt_k1_dilworth,axiom,( ! [A] : ( ( v3_dilworth(A) & l1_orders_2(A) ) => v7_ordinal1(k1_dilworth(A)) ) )).
fof(dt_k1_diraf,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k1_dist_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_finseq_1(B,A) => m1_subset_1(k1_dist_1(A,B,C),k1_zfmisc_1(k9_xtuple_0(B))) ) )).
fof(dt_k1_dist_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & m1_subset_1(B,A) ) => m1_subset_1(k1_dist_2(A,B),k4_ordinal1) ) )).
fof(dt_k1_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k1_dtconstr,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_trees_3(B,A) & m1_finseq_1(C,B) ) => m2_finseq_1(k1_dtconstr(A,B,C),A) ) )).
fof(dt_k1_dynkin,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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),k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(k1_dynkin(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) )).
fof(dt_k1_ec_pf_1,axiom,( ! [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) ) => m1_subset_1(k1_ec_pf_1(A),k4_ordinal1) ) )).
fof(dt_k1_ec_pf_2,axiom,( ! [A] : ( ( 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))))) ) )).
fof(dt_k1_endalg,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(dt_k1_entropy1,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => ( v1_matrix_0(k1_entropy1(A)) & v2_matrix_0(k1_entropy1(A),k1_numbers,k3_finseq_1(A),k3_finseq_1(A)) & v1_entropy1(k1_entropy1(A),k3_finseq_1(A)) & m2_finseq_1(k1_entropy1(A),k3_finseq_2(k1_numbers)) ) ) )).
fof(dt_k1_eqrel_1,axiom,( ! [A] : m1_subset_1(k1_eqrel_1(A),k1_zfmisc_1(k2_zfmisc_1(A,A))) )).
fof(dt_k1_equation,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k1_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => m1_finseq_2(k1_euclid(A),k1_numbers) ) )).
fof(dt_k1_euclid_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => m1_subset_1(k1_euclid_3(A),u1_struct_0(k15_euclid(2))) ) )).
fof(dt_k1_euclid_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k1_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => v1_xreal_0(k1_euclid_5(A)) ) )).
fof(dt_k1_euclid_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k1_euclid_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_1(k1_euclid_7(A,B,C),k2_zfmisc_1(A,A)) ) )).
fof(dt_k1_euclid_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k1_euclid_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) & v3_valued_0(B) & v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & v3_valued_0(C) ) => v7_ordinal1(k1_euclid_9(A,B,C)) ) )).
fof(dt_k1_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => m1_subset_1(k1_euclidlp(A),k1_zfmisc_1(k1_zfmisc_1(k1_euclid(A)))) ) )).
fof(dt_k1_euler_1,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k1_euler_1(A),k4_ordinal1) ) )).
fof(dt_k1_euler_2,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k4_ordinal1) & v7_ordinal1(B) ) => m2_finseq_1(k1_euler_2(A,B),k4_ordinal1) ) )).
fof(dt_k1_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v3_ordinal1(k1_exchsort(A)) ) )).
fof(dt_k1_extpro_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ( v1_extpro_1(k1_extpro_1(A),A) & l1_extpro_1(k1_extpro_1(A),A) ) ) )).
fof(dt_k1_extreal1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_numbers) & m1_subset_1(B,k6_numbers) ) => m1_subset_1(k1_extreal1(A,B),k6_numbers) ) )).
fof(dt_k1_extreal2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_numbers) & m1_subset_1(B,k6_numbers) ) => m1_subset_1(k1_extreal2(A,B),k6_numbers) ) )).
fof(dt_k1_facirc_1,axiom,( 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))) )).
fof(dt_k1_facirc_2,axiom,( ! [A] : ( v11_struct_0(k1_facirc_2(A)) & v1_msualg_1(k1_facirc_2(A)) & l1_msualg_1(k1_facirc_2(A)) ) )).
fof(dt_k1_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k1_fdiff_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & v1_xreal_0(B) ) => v1_xreal_0(k1_fdiff_1(A,B)) ) )).
fof(dt_k1_fdiff_3,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => v1_xreal_0(k1_fdiff_3(A,B)) ) )).
fof(dt_k1_fdiff_9,axiom,( v1_funct_1(k1_fdiff_9) & m1_subset_1(k1_fdiff_9,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) )).
fof(dt_k1_ff_siec,axiom,( ! [A] : ! [B] : ( v1_petri(k1_ff_siec(A,B)) & v1_net_1(k1_ff_siec(A,B)) & l1_petri(k1_ff_siec(A,B)) ) )).
fof(dt_k1_fib_num,axiom,( v1_xreal_0(k1_fib_num) )).
fof(dt_k1_fib_num2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) & v1_finset_1(B) & v1_setfam_1(B) & v6_membered(B) ) => m2_finseq_1(k1_fib_num2(A,B),k4_ordinal1) ) )).
fof(dt_k1_fib_num3,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k1_fib_num3(A),k4_ordinal1) ) )).
fof(dt_k1_filter_0,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(dt_k1_filter_2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k1_fin_topo,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k1_finance1,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => m1_subset_1(k1_finance1(A,B),k1_zfmisc_1(k1_numbers)) ) )).
fof(dt_k1_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_relat_1(k1_finseq_2(A)) & v1_funct_1(k1_finseq_2(A)) & v1_finseq_1(k1_finseq_2(A)) ) ) )).
fof(dt_k1_finseq_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k1_finseq_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) ) => m2_finseq_1(k1_finseq_5(A,B,C),A) ) )).
fof(dt_k1_finseq_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) & m1_subset_1(C,A) ) => m2_finseq_1(k1_finseq_6(A,B,C),A) ) )).
fof(dt_k1_finseq_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k1_finseq_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_1(k1_finseq_8(A,B,C),A) ) )).
fof(dt_k1_finseqop,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(dt_k1_finsop_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k1_finsub_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k1_fintopo2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k1_fintopo3,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k1_fintopo4,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k1_fintopo4(A),k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(A),k2_finseq_1(A)))) ) )).
fof(dt_k1_fintopo5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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)) ) )).
fof(dt_k1_fintopo6,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k1_flang_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k1_flang_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k1_flang_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k1_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k1_fomodel0(A,B)) & v1_funct_1(k1_fomodel0(A,B)) ) ) )).
fof(dt_k1_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => m1_subset_1(k1_fomodel2(A),k1_fomodel1(A)) ) )).
fof(dt_k1_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & m1_subset_1(B,k1_fomodel1(A)) & m1_subset_1(C,k3_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))) ) )).
fof(dt_k1_frechet,axiom,( ! [A] : ! [B] : ( ( ~ 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))))) ) )).
fof(dt_k1_frechet2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k1_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : 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))) )).
fof(dt_k1_fscirc_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k1_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k1_fsm_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(dt_k1_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k1_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ~ 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)) ) )).
fof(dt_k1_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k1_funcop_1(A)) & v1_funct_1(k1_funcop_1(A)) ) ) )).
fof(dt_k1_funcsdom,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) )).
fof(dt_k1_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k1_funct_3(A)) & v1_funct_1(k1_funct_3(A)) ) ) )).
fof(dt_k1_funct_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k1_funct_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k1_funct_5(A)) & v1_funct_1(k1_funct_5(A)) ) ) )).
fof(dt_k1_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ( v1_relat_1(k1_funct_6(A)) & v1_funct_1(k1_funct_6(A)) ) ) )).
fof(dt_k1_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k1_funct_7(A,B,C)) & v1_funct_1(k1_funct_7(A,B,C)) ) ) )).
fof(dt_k1_funct_8,axiom,( 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))) )).
fof(dt_k1_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) )).
fof(dt_k1_functor2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k1_functor3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(dt_k1_fuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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(k5_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))) ) ) )).
fof(dt_k1_fuzzy_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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(k5_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))) ) ) )).
fof(dt_k1_fuzzy_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v5_relat_1(C,k1_rcomp_1(k5_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(k1_fuzzy_4(A,B,C),k1_rcomp_1(k5_numbers,1)) & v1_funct_1(k1_fuzzy_4(A,B,C)) & v1_funct_2(k1_fuzzy_4(A,B,C),k2_zfmisc_1(A,B),k1_numbers) & m1_subset_1(k1_fuzzy_4(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),k1_numbers))) ) ) )).
fof(dt_k1_fvaluat1,axiom,( ! [A] : ( v2_membered(A) => ( v2_xxreal_0(k1_fvaluat1(A)) & v1_fvaluat1(k1_fvaluat1(A)) ) ) )).
fof(dt_k1_fvsum_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k1_gcd_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k1_genealg1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k4_ordinal1) ) => m2_finseq_1(k1_genealg1(A,B,C,D),k3_card_3(A)) ) )).
fof(dt_k1_geomtrap,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) )).
fof(dt_k1_gfacirc1,axiom,( 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))) )).
fof(dt_k1_gfacirc2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k1_glib_000,axiom,( m1_subset_1(k1_glib_000,k4_ordinal1) )).
fof(dt_k1_glib_001,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(dt_k1_glib_002,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) ) )).
fof(dt_k1_glib_003,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,A) & m1_subset_1(C,k1_zfmisc_1(B)) ) => m2_finseq_1(k1_glib_003(A,B,C),A) ) )).
fof(dt_k1_glib_004,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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_xreal_0(k1_glib_004(A,B,C)) ) )).
fof(dt_k1_glib_005,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(dt_k1_goboard1,axiom,( ! [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) => m2_finseq_1(k1_goboard1(A),k1_numbers) ) )).
fof(dt_k1_goboard2,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k1_numbers) & m1_finseq_1(B,k1_numbers) ) => ( v1_matrix_0(k1_goboard2(A,B)) & m2_finseq_1(k1_goboard2(A,B),k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) ) )).
fof(dt_k1_goboard5,axiom,( ! [A] : ! [B] : ( ( v1_matrix_0(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)))) ) )).
fof(dt_k1_goboard9,axiom,( ! [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_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))) ) ) )).
fof(dt_k1_goedcpuc,axiom,( ! [A] : ( m1_qc_lang1(A) => ( v1_qc_trans(k1_goedcpuc(A),A) & m1_qc_lang1(k1_goedcpuc(A)) ) ) )).
fof(dt_k1_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => m1_subset_1(k1_goedelcp(A),k1_zfmisc_1(k3_cqc_lang(A))) ) )).
fof(dt_k1_gr_cy_1,axiom,( ! [A] : ( m1_finseq_1(A,k4_numbers) => m1_subset_1(k1_gr_cy_1(A),k4_numbers) ) )).
fof(dt_k1_gr_cy_3,axiom,( ! [A] : ( v7_ordinal1(A) => v7_ordinal1(k1_gr_cy_3(A)) ) )).
fof(dt_k1_graph_1,axiom,( ! [A] : ! [B] : ( ( l1_graph_1(A) & m1_subset_1(B,u4_struct_0(A)) ) => m1_subset_1(k1_graph_1(A,B),u1_struct_0(A)) ) )).
fof(dt_k1_graph_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k1_graph_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => m1_subset_1(k1_graph_3(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k1_graphsp,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(A,k1_numbers) & v1_xreal_0(C) ) => m2_finseq_1(k1_graphsp(A,B,C),k1_numbers) ) )).
fof(dt_k1_grcat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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))) ) )).
fof(dt_k1_grnilp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k1_groeb_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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,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(k12_polynom1(A,B)))) ) )).
fof(dt_k1_groeb_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k1_groeb_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,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,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(k12_polynom1(A,B)))) ) )).
fof(dt_k1_group_1,axiom,( ! [A] : ( l3_algstr_0(A) => m1_subset_1(k1_group_1(A),u1_struct_0(A)) ) )).
fof(dt_k1_group_10,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k1_group_11,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k1_group_12,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) )).
fof(dt_k1_group_14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) & 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(k1_group_14(A,B,C,D,E)) & v1_funct_2(k1_group_14(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C)) & v13_vectsp_1(k1_group_14(A,B,C,D,E),A,C) & m1_subset_1(k1_group_14(A,B,C,D,E),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(C)))) ) ) )).
fof(dt_k1_group_2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k1_group_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k1_group_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k1_group_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k1_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k1_groupp_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k1_grsolv_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k1_hahnban1,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => m1_subset_1(k1_hahnban1(A,B),u1_struct_0(k1_complfld)) ) )).
fof(dt_k1_hausdorf,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) => v1_xreal_0(k1_hausdorf(A,B,C)) ) )).
fof(dt_k1_heine,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v7_ordinal1(B) ) => ( v1_funct_1(k1_heine(A,B)) & v1_funct_2(k1_heine(A,B),k4_ordinal1,k1_numbers) & m1_subset_1(k1_heine(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k1_helly,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k1_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => ~ v1_xboole_0(k1_henmodel(A)) ) )).
fof(dt_k1_hermitan,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k1_heyting1,axiom,( ! [A] : ~ v1_xboole_0(k1_heyting1(A)) )).
fof(dt_k1_heyting3,axiom,( ! [A] : ! [B] : l1_orders_2(k1_heyting3(A,B)) )).
fof(dt_k1_hilbasis,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k1_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => m1_subset_1(k1_hilbert2(A),k1_hilbert1) ) )).
fof(dt_k1_hilbert3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k1_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( v3_card_1(k1_idea_1(A),A) & m2_finseq_1(k1_idea_1(A),k6_margrel1) ) ) )).
fof(dt_k1_ideal_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k1_incsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k1_index_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ 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)) ) )).
fof(dt_k1_instalg1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(dt_k1_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => v1_int_1(k1_int_1(A)) ) )).
fof(dt_k1_int_2,axiom,( ! [A] : ( v1_int_1(A) => m1_subset_1(k1_int_2(A),k4_ordinal1) ) )).
fof(dt_k1_int_3,axiom,( l6_algstr_0(k1_int_3) )).
fof(dt_k1_int_4,axiom,( ! [A] : ( v1_int_1(A) => m1_subset_1(k1_int_4(A),k1_zfmisc_1(k2_zfmisc_1(k4_numbers,k4_numbers))) ) )).
fof(dt_k1_int_5,axiom,( ! [A] : ( 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))) ) ) )).
fof(dt_k1_int_6,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k1_int_7,axiom,( ! [A] : ( 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(k4_ordinal1)) ) ) )).
fof(dt_k1_integr10,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & v1_xreal_0(B) & v1_xreal_0(C) ) => v1_xreal_0(k1_integr10(A,B,C)) ) )).
fof(dt_k1_integr15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) => v1_xreal_0(k1_integr15(A,B,C,D)) ) )).
fof(dt_k1_integr16,axiom,( ! [A] : ( m1_finseq_1(A,k2_numbers) => m2_finseq_1(k1_integr16(A),k1_numbers) ) )).
fof(dt_k1_integr18,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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)) ) )).
fof(dt_k1_integr1c,axiom,( 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))) )).
fof(dt_k1_integra2,axiom,( ! [A] : ! [B] : ( ( v3_membered(A) & v1_xreal_0(B) ) => m1_subset_1(k1_integra2(A,B),k1_zfmisc_1(k1_numbers)) ) )).
fof(dt_k1_integra3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & m1_integra1(B,A) ) => v1_xreal_0(k1_integra3(A,B)) ) )).
fof(dt_k1_integra5,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k1_integra8,axiom,( ! [A] : ( v1_xreal_0(A) => ( 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))) ) ) )).
fof(dt_k1_integra9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) => v1_xreal_0(k1_integra9(A,B,C)) ) )).
fof(dt_k1_interva1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k1_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_funct_1(k1_irrat_1(A)) & v1_funct_2(k1_irrat_1(A),k4_ordinal1,k1_numbers) & m1_subset_1(k1_irrat_1(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k1_isocat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) )).
fof(dt_k1_isocat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k1_isomichi,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k1_jct_misc,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k1_jgraph_1,axiom,( ! [A] : l1_graph_1(k1_jgraph_1(A)) )).
fof(dt_k1_jgraph_3,axiom,( 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))))) )).
fof(dt_k1_jgraph_4,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_k1_jgraph_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) )).
fof(dt_k1_jordan11,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) & v7_ordinal1(C) ) => m1_subset_1(k1_jordan11(A,B,C),u1_struct_0(k15_euclid(A))) ) )).
fof(dt_k1_jordan13,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) & v7_ordinal1(B) ) => ( ~ 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))) ) ) )).
fof(dt_k1_jordan14,axiom,( ! [A] : ! [B] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & v7_ordinal1(B) ) => m1_subset_1(k1_jordan14(A,B),u1_struct_0(k15_euclid(2))) ) )).
fof(dt_k1_jordan19,axiom,( ! [A] : ( ( 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),k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(k1_jordan19(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))))) ) ) )).
fof(dt_k1_jordan1a,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => v7_ordinal1(k1_jordan1a(A)) ) )).
fof(dt_k1_jordan1e,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k1_jordan1h,axiom,( m1_subset_1(k1_jordan1h,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) )).
fof(dt_k1_jordan1k,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & 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)))) ) => v1_xreal_0(k1_jordan1k(A,B,C)) ) )).
fof(dt_k1_jordan21,axiom,( ! [A] : ( 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))) ) )).
fof(dt_k1_jordan24,axiom,( ! [A] : ( v1_xreal_0(A) => ( 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))))) ) ) )).
fof(dt_k1_jordan2b,axiom,( ! [A] : ( v1_xreal_0(A) => m1_subset_1(k1_jordan2b(A),u1_struct_0(k15_euclid(1))) ) )).
fof(dt_k1_jordan2c,axiom,( ! [A] : ! [B] : ( ( 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)))) ) )).
fof(dt_k1_jordan3,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) ) )).
fof(dt_k1_jordan4,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => v7_ordinal1(k1_jordan4(A,B)) ) )).
fof(dt_k1_jordan5c,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k1_jordan5d,axiom,( ! [A] : ( ( ~ 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))) ) => v7_ordinal1(k1_jordan5d(A)) ) )).
fof(dt_k1_jordan7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) )).
fof(dt_k1_jordan8,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & v7_ordinal1(B) ) => ( v1_matrix_0(k1_jordan8(A,B)) & m2_finseq_1(k1_jordan8(A,B),k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) ) )).
fof(dt_k1_knaster,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k1_kolmog01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k1_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => m1_subset_1(k1_kurato_0(A,B),k1_zfmisc_1(A)) ) )).
fof(dt_k1_kurato_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => m1_subset_1(k1_kurato_2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k1_laplace,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),k4_ordinal1),u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_ordinal1),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)) ) )).
fof(dt_k1_latsubgr,axiom,( ! [A] : ( ( ~ 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))))) ) ) )).
fof(dt_k1_latsum_1,axiom,( ! [A] : ! [B] : ( ( l1_orders_2(A) & l1_orders_2(B) ) => ( v1_orders_2(k1_latsum_1(A,B)) & l1_orders_2(k1_latsum_1(A,B)) ) ) )).
fof(dt_k1_lattice2,axiom,( ! [A] : ( l3_lattices(A) => ( v3_lattices(k1_lattice2(A)) & l3_lattices(k1_lattice2(A)) ) ) )).
fof(dt_k1_lattice3,axiom,( ! [A] : ( v3_lattices(k1_lattice3(A)) & l3_lattices(k1_lattice3(A)) ) )).
fof(dt_k1_lattice4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k1_lattice5,axiom,( ! [A] : ( v3_orders_2(k1_lattice5(A)) & v4_orders_2(k1_lattice5(A)) & v5_orders_2(k1_lattice5(A)) & l1_orders_2(k1_lattice5(A)) ) )).
fof(dt_k1_lattice6,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k1_lattice7,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) ) )).
fof(dt_k1_lattices,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k1_lexbfs,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k1_lfuzzy_0,axiom,( ! [A] : ( v3_membered(A) => ( v1_orders_2(k1_lfuzzy_0(A)) & v1_lfuzzy_0(k1_lfuzzy_0(A)) & l1_orders_2(k1_lfuzzy_0(A)) ) ) )).
fof(dt_k1_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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(k5_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))) ) ) )).
fof(dt_k1_limfunc1,axiom,( ! [A] : ( v1_xreal_0(A) => m1_subset_1(k1_limfunc1(A),k1_zfmisc_1(k1_numbers)) ) )).
fof(dt_k1_limfunc2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & v1_xreal_0(B) ) => v1_xreal_0(k1_limfunc2(A,B)) ) )).
fof(dt_k1_limfunc3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & v1_xreal_0(B) ) => v1_xreal_0(k1_limfunc3(A,B)) ) )).
fof(dt_k1_lmod_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k1_lmod_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) ) )).
fof(dt_k1_lmod_7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) )).
fof(dt_k1_lopban_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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)))) ) ) )).
fof(dt_k1_lopban_3,axiom,( ! [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) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => m1_subset_1(k1_lopban_3(A,B),u1_struct_0(A)) ) )).
fof(dt_k1_lopban_4,axiom,( ! [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) & 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),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k1_lopban_4(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k1_lopban_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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))) ) )).
fof(dt_k1_lopban_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & l1_normsp_1(A) & ~ v2_struct_0(B) & l1_normsp_1(B) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) ) => m1_subset_1(k1_lopban_7(A,B,C,D),u1_struct_0(k7_prvect_3(A,B))) ) )).
fof(dt_k1_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => m1_subset_1(k1_lopclset(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).
fof(dt_k1_lp_space,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_xreal_0(B) ) => ( v1_funct_1(k1_lp_space(A,B)) & v1_funct_2(k1_lp_space(A,B),k4_ordinal1,k1_numbers) & m1_subset_1(k1_lp_space(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k1_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v1_membered(B) & m1_subset_1(C,k3_rfunct_3(A,B)) & m1_subset_1(D,k3_rfunct_3(A,B)) ) => m2_rfunct_3(k1_lpspacc1(A,B,C,D),A,k2_numbers,k3_rfunct_3(A,k2_numbers)) ) )).
fof(dt_k1_lpspace1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k1_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v2_xxreal_0(D) & v1_xreal_0(D) ) => ( ~ 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)))) ) ) )).
fof(dt_k1_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => m1_subset_1(k1_ltlaxio1(A),k1_hilbert1) ) )).
fof(dt_k1_ltlaxio2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_hilbert1) & m1_subset_1(B,k1_hilbert1) ) => m1_subset_1(k1_ltlaxio2(A,B),k1_hilbert1) ) )).
fof(dt_k1_margrel1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k1_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k1_matrix10,axiom,( ! [A] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( v1_matrix_0(k1_matrix10(A)) & m2_finseq_1(k1_matrix10(A),k3_finseq_2(k1_numbers)) ) ) )).
fof(dt_k1_matrix11,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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,k3_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)))) ) ) )).
fof(dt_k1_matrix12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & ~ 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) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(C))) & v7_ordinal1(E) & v7_ordinal1(F) ) => ( v1_matrix_0(k1_matrix12(A,B,C,D,E,F)) & v2_matrix_0(k1_matrix12(A,B,C,D,E,F),u1_struct_0(C),A,B) & m2_finseq_1(k1_matrix12(A,B,C,D,E,F),k3_finseq_2(u1_struct_0(C))) ) ) )).
fof(dt_k1_matrix13,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(A) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(A)) & v7_ordinal1(C) & v7_ordinal1(D) & m1_subset_1(E,k4_finseq_2(C,k4_ordinal1)) & m1_subset_1(F,k4_finseq_2(D,k4_ordinal1)) ) => ( v1_matrix_0(k1_matrix13(A,B,C,D,E,F)) & v2_matrix_0(k1_matrix13(A,B,C,D,E,F),A,C,D) & m2_finseq_1(k1_matrix13(A,B,C,D,E,F),k3_finseq_2(A)) ) ) )).
fof(dt_k1_matrix14,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) & m1_subset_1(B,k4_ordinal1) ) => m2_finseq_1(k1_matrix14(A,B),u1_struct_0(A)) ) )).
fof(dt_k1_matrix15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & v7_ordinal1(C) & v7_ordinal1(D) & v1_matrix_0(E) & v2_matrix_0(E,A,B,C) & m1_finseq_1(E,k3_finseq_2(A)) & v1_matrix_0(F) & v2_matrix_0(F,A,B,D) & m1_finseq_1(F,k3_finseq_2(A)) ) => ( v1_matrix_0(k1_matrix15(A,B,C,D,E,F)) & v2_matrix_0(k1_matrix15(A,B,C,D,E,F),A,B,k2_xcmplx_0(k1_matrix_0(E),k1_matrix_0(F))) & m2_finseq_1(k1_matrix15(A,B,C,D,E,F),k3_finseq_2(A)) ) ) )).
fof(dt_k1_matrix16,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) ) => ( v1_matrix_0(k1_matrix16(A,B)) & v2_matrix_0(k1_matrix16(A,B),A,k3_finseq_1(B),k3_finseq_1(B)) & m2_finseq_1(k1_matrix16(A,B),k3_finseq_2(A)) ) ) )).
fof(dt_k1_matrix17,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) ) => ( v1_matrix_0(k1_matrix17(A,B)) & v2_matrix_0(k1_matrix17(A,B),A,k3_finseq_1(B),k3_finseq_1(B)) & m2_finseq_1(k1_matrix17(A,B),k3_finseq_2(A)) ) ) )).
fof(dt_k1_matrix_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_matrix_0(A) ) => v7_ordinal1(k1_matrix_0(A)) ) )).
fof(dt_k1_matrix_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_matrix_2(A) ) => v7_ordinal1(k1_matrix_2(A)) ) )).
fof(dt_k1_matrix_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) => ( v1_matrix_0(k1_matrix_3(A,B,C)) & v2_matrix_0(k1_matrix_3(A,B,C),u1_struct_0(A),B,C) & m2_finseq_1(k1_matrix_3(A,B,C),k3_finseq_2(u1_struct_0(A))) ) ) )).
fof(dt_k1_matrix_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_0(B) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(A))) & v1_matrix_0(C) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( v1_matrix_0(k1_matrix_4(A,B,C)) & m2_finseq_1(k1_matrix_4(A,B,C),k3_finseq_2(u1_struct_0(A))) ) ) )).
fof(dt_k1_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ( v1_matrix_0(k1_matrix_5(A)) & m2_finseq_1(k1_matrix_5(A),k3_finseq_2(u1_struct_0(k1_complfld))) ) ) )).
fof(dt_k1_matrix_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v1_matrix_0(k1_matrix_6(A,B,C)) & v2_matrix_0(k1_matrix_6(A,B,C),u1_struct_0(B),A,A) & m2_finseq_1(k1_matrix_6(A,B,C),k3_finseq_2(u1_struct_0(B))) ) ) )).
fof(dt_k1_matrix_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( v1_matrix_0(k1_matrix_7(A,B,C,D)) & v2_matrix_0(k1_matrix_7(A,B,C,D),u1_struct_0(B),A,A) & m2_finseq_1(k1_matrix_7(A,B,C,D),k3_finseq_2(u1_struct_0(B))) ) ) )).
fof(dt_k1_matrix_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => m1_subset_1(k1_matrix_8(A,B,C),u1_struct_0(B)) ) )).
fof(dt_k1_matrix_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v1_funct_1(k1_matrix_9(A,B,C)) & v1_funct_2(k1_matrix_9(A,B,C),k3_matrix_2(A),u1_struct_0(B)) & m1_subset_1(k1_matrix_9(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k3_matrix_2(A),u1_struct_0(B)))) ) ) )).
fof(dt_k1_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ( v1_matrix_0(k1_matrixc1(A)) & m2_finseq_1(k1_matrixc1(A),k3_finseq_2(k2_numbers)) ) ) )).
fof(dt_k1_matrixj1,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k4_ordinal1) & v7_ordinal1(B) ) => m1_subset_1(k1_matrixj1(A,B),k4_ordinal1) ) )).
fof(dt_k1_matrixj2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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_0(k1_matrixj2(A,B,C)) & m2_finseq_1(k1_matrixj2(A,B,C),k3_finseq_2(u1_struct_0(A))) ) ) )).
fof(dt_k1_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( v1_matrix_0(k1_matrixr1(A)) & m2_finseq_1(k1_matrixr1(A),k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) ) )).
fof(dt_k1_matrixr2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m1_finseq_1(B,k3_finseq_2(k1_numbers)) & v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m1_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( v1_matrix_0(k1_matrixr2(A,B,C)) & v2_matrix_0(k1_matrixr2(A,B,C),k1_numbers,A,A) & m2_finseq_1(k1_matrixr2(A,B,C),k3_finseq_2(k1_numbers)) ) ) )).
fof(dt_k1_matrlin,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & v1_matrix_0(C) & m1_finseq_1(C,k3_finseq_2(A)) ) => ( v1_matrix_0(k1_matrlin(A,B,C)) & m2_finseq_1(k1_matrlin(A,B,C),k3_finseq_2(A)) ) ) )).
fof(dt_k1_matrlin2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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_0(k1_matrlin2(A,B,C,D,E,F)) & v2_matrix_0(k1_matrlin2(A,B,C,D,E,F),u1_struct_0(A),k3_finseq_1(E),k3_finseq_1(F)) & m2_finseq_1(k1_matrlin2(A,B,C,D,E,F),k3_finseq_2(u1_struct_0(A))) ) ) )).
fof(dt_k1_matroid0,axiom,( ! [A] : ( l1_pre_topc(A) => m1_subset_1(k1_matroid0(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).
fof(dt_k1_matrprob,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,k3_finseq_2(A)) & v7_ordinal1(C) ) => m2_finseq_1(k1_matrprob(A,B,C),A) ) )).
fof(dt_k1_matrtop1,axiom,( ! [A] : ( ( 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)) ) )).
fof(dt_k1_matrtop3,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => ( v1_matrix_0(k1_matrtop3(A,B)) & v2_matrix_0(k1_matrtop3(A,B),u1_struct_0(k2_vectsp_1),A,A) & v1_matrix_6(k1_matrtop3(A,B),A,k2_vectsp_1) & m2_finseq_1(k1_matrtop3(A,B),k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) ) )).
fof(dt_k1_mazurulm,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k1_mboolean,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(dt_k1_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k1_measure1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k1_measure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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) ) )).
fof(dt_k1_measure3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => m1_measure2(k1_measure3(A,B,C),A,B) ) )).
fof(dt_k1_measure4,axiom,( ! [A] : ! [B] : ( 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))) ) ) )).
fof(dt_k1_measure5,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_numbers) & m1_subset_1(B,k6_numbers) ) => m1_subset_1(k1_measure5(A,B),k1_zfmisc_1(k1_numbers)) ) )).
fof(dt_k1_measure6,axiom,( ! [A] : ! [B] : ( ( v3_membered(A) & v1_xreal_0(B) ) => m1_subset_1(k1_measure6(A,B),k1_zfmisc_1(k1_numbers)) ) )).
fof(dt_k1_measure7,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,A,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( v1_funct_1(k1_measure7(A,B)) & v1_funct_2(k1_measure7(A,B),k4_ordinal1,k6_numbers) & m1_subset_1(k1_measure7(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) ) )).
fof(dt_k1_measure8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k1_member_1,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => m1_subset_1(k1_member_1(A),k6_numbers) ) )).
fof(dt_k1_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ( v1_memstr_0(k1_memstr_0(A),A) & l1_memstr_0(k1_memstr_0(A),A) ) ) )).
fof(dt_k1_mesfun6c,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_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)) ) )).
fof(dt_k1_mesfun7c,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( v1_funct_1(k1_mesfun7c(A,B)) & v1_funct_2(k1_mesfun7c(A,B),k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(k1_mesfun7c(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) ) )).
fof(dt_k1_mesfun9c,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,B)))) ) => ( v1_funct_1(k1_mesfun9c(A,B,C,D)) & v1_funct_2(k1_mesfun9c(A,B,C,D),k4_ordinal1,k4_partfun1(A,B)) & m1_subset_1(k1_mesfun9c(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,B)))) ) ) )).
fof(dt_k1_mesfunc1,axiom,( m1_subset_1(k1_mesfunc1,k1_zfmisc_1(k1_numbers)) )).
fof(dt_k1_mesfunc2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( v1_funct_1(k1_mesfunc2(A,B)) & m1_subset_1(k1_mesfunc2(A,B),k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) ) )).
fof(dt_k1_mesfunc3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => m1_subset_1(k1_mesfunc3(A,B,C,D),k6_numbers) ) )).
fof(dt_k1_mesfunc5,axiom,( ! [A] : ! [B] : ( ( ~ 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,k6_numbers))) ) ) )).
fof(dt_k1_mesfunc6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_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),k6_numbers) ) )).
fof(dt_k1_mesfunc7,axiom,( v1_funct_1(k1_mesfunc7) & v1_funct_2(k1_mesfunc7,k2_zfmisc_1(k6_numbers,k6_numbers),k6_numbers) & m1_subset_1(k1_mesfunc7,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k6_numbers,k6_numbers),k6_numbers))) )).
fof(dt_k1_mesfunc8,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ( v1_funct_1(k1_mesfunc8(A,B)) & m1_subset_1(k1_mesfunc8(A,B),k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) ) )).
fof(dt_k1_mesfunc9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_valued_0(A) ) => m1_subset_1(k1_mesfunc9(A,B),k6_numbers) ) )).
fof(dt_k1_metric_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => v1_xreal_0(k1_metric_1(A,B,C)) ) )).
fof(dt_k1_metric_2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k1_metric_3,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k1_metric_6,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k1_mfold_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k1_midsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k1_midsp_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k1_midsp_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_finseq_2(B,A)) & m1_subset_1(D,k4_ordinal1) & m1_subset_1(E,A) ) => m2_finseq_2(k1_midsp_3(A,B,C,D,E),A,k4_finseq_2(B,A)) ) )).
fof(dt_k1_mmlquer2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k1_mmlquer2(A,B)) ) )).
fof(dt_k1_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k1_mod_2,axiom,( ! [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) & 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) ) ) )).
fof(dt_k1_mod_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) ) )).
fof(dt_k1_mod_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k1_modal_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => m1_trees_1(k1_modal_1(A),A) ) )).
fof(dt_k1_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => m1_subset_1(k1_modelc_3(A),k1_zfmisc_1(k9_modelc_2)) ) )).
fof(dt_k1_moebius1,axiom,( m1_subset_1(k1_moebius1,k1_zfmisc_1(k4_ordinal1)) )).
fof(dt_k1_monoid_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_2(k1_monoid_0(A,B,C),A,k3_finseq_2(A)) ) )).
fof(dt_k1_morph_01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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))) ) )).
fof(dt_k1_msafree,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(dt_k1_msafree1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k1_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => m1_subset_1(k1_msafree2(A),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k1_msafree3,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k1_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(k1_msafree4(A,B,C),k10_xtuple_0(B)) ) )).
fof(dt_k1_msalimit,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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))) ) )).
fof(dt_k1_msaterm,axiom,( ! [A] : ! [B] : ( ( ~ 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))))) ) )).
fof(dt_k1_msinst_1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(dt_k1_mssubfam,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k1_msualg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k1_msualg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k1_msualg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k1_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) )).
fof(dt_k1_msualg_5,axiom,( ! [A] : ! [B] : ( 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))) ) ) )).
fof(dt_k1_msualg_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(dt_k1_msualg_7,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( ~ 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)) ) ) )).
fof(dt_k1_msualg_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k1_msualg_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(dt_k1_msuhom_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k1_mycielsk,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_eqrel_1(B,A) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_eqrel_1(k1_mycielsk(A,B,C),C) ) )).
fof(dt_k1_nagata_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) & m1_subset_1(C,k4_ordinal1) ) => m1_subset_1(k1_nagata_1(A,B,C),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).
fof(dt_k1_nagata_2,axiom,( v1_funct_1(k1_nagata_2) & v1_funct_2(k1_nagata_2,k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1) & m1_subset_1(k1_nagata_2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1))) )).
fof(dt_k1_nat_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k4_ordinal1) ) => m1_subset_1(k1_nat_1(A,B),k4_ordinal1) ) )).
fof(dt_k1_nat_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k1_nat_4,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k4_ordinal1) & v7_ordinal1(B) & v1_int_2(B) ) => m2_finseq_1(k1_nat_4(A,B),k4_ordinal1) ) )).
fof(dt_k1_nat_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) & 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)) ) ) )).
fof(dt_k1_nat_d,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => v7_ordinal1(k1_nat_d(A,B)) ) )).
fof(dt_k1_nat_lat,axiom,( v1_funct_1(k1_nat_lat) & v1_funct_2(k1_nat_lat,k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1) & m1_subset_1(k1_nat_lat,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1))) )).
fof(dt_k1_nattra_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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(k1_nattra_1(A,B,C),A,B,C,C) ) )).
fof(dt_k1_ndiff_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_funct_1(k1_ndiff_1(A,B,C)) & v1_funct_2(k1_ndiff_1(A,B,C),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k1_ndiff_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k1_ndiff_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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)) ) )).
fof(dt_k1_ndiff_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & 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)) ) )).
fof(dt_k1_ndiff_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & ~ v1_xboole_0(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))) ) )).
fof(dt_k1_neckla_2,axiom,( ! [A] : ! [B] : ( ( l1_orders_2(A) & l1_orders_2(B) ) => ( v1_orders_2(k1_neckla_2(A,B)) & l1_orders_2(k1_neckla_2(A,B)) ) ) )).
fof(dt_k1_neckla_3,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k1_necklace,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_orders_2(k1_necklace(A)) & l1_orders_2(k1_necklace(A)) ) ) )).
fof(dt_k1_nfcont_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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))) ) ) )).
fof(dt_k1_normform,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k1_normsp_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v7_ordinal1(C) ) => m1_subset_1(k1_normsp_0(A,B,C),u1_struct_0(A)) ) )).
fof(dt_k1_normsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v7_ordinal1(C) ) => m1_subset_1(k1_normsp_1(A,B,C),u1_struct_0(A)) ) )).
fof(dt_k1_normsp_2,axiom,( ! [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) & 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))) ) ) )).
fof(dt_k1_ntalgo_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_numbers) & m1_subset_1(B,k4_numbers) ) => m1_subset_1(k1_ntalgo_1(A,B),k4_ordinal1) ) )).
fof(dt_k1_numeral1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) & v7_ordinal1(B) ) => v7_ordinal1(k1_numeral1(A,B)) ) )).
fof(dt_k1_openlatt,axiom,( ! [A] : ( l1_pre_topc(A) => m1_subset_1(k1_openlatt(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).
fof(dt_k1_oposet_1,axiom,( v3_qmax_1(k1_oposet_1) & l2_qmax_1(k1_oposet_1) )).
fof(dt_k1_oppcat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k1_ordeq_01,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_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) & l1_normsp_1(B) ) => m1_subset_1(k1_ordeq_01(A,B),k1_zfmisc_1(u1_struct_0(k5_rsspace4(A,B)))) ) )).
fof(dt_k1_orders_2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k1_ordinal3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_ordinal2(B) ) => ( v1_relat_1(k1_ordinal3(A,B)) & v5_ordinal1(k1_ordinal3(A,B)) & v1_funct_1(k1_ordinal3(A,B)) & v1_ordinal2(k1_ordinal3(A,B)) ) ) )).
fof(dt_k1_ordinal4,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k1_ordinal5,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => v3_ordinal1(k1_ordinal5(A,B)) ) )).
fof(dt_k1_ordinal6,axiom,( ! [A] : v3_ordinal1(k1_ordinal6(A)) )).
fof(dt_k1_ortsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) )).
fof(dt_k1_osafree,axiom,( ! [A] : ! [B] : ( ( ~ 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))))))) ) )).
fof(dt_k1_osalg_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k1_osalg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k1_osalg_4,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k1_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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))))) ) ) )).
fof(dt_k1_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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))) ) ) )).
fof(dt_k1_partfun2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k1_partfun3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) ) => ( v1_relat_1(k1_partfun3(A)) & v1_funct_1(k1_partfun3(A)) ) ) )).
fof(dt_k1_partit_2,axiom,( ! [A] : ! [B] : m1_subset_1(k1_partit_2(A,B),k1_zfmisc_1(k2_zfmisc_1(A,B))) )).
fof(dt_k1_pboole,axiom,( ! [A] : ( 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) ) )).
fof(dt_k1_pcomps_1,axiom,( ! [A] : ! [B] : ( ( 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)))) ) )).
fof(dt_k1_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(dt_k1_pdiff_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k1_pdiff_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) & 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))) ) ) )).
fof(dt_k1_pdiff_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & 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))) ) ) )).
fof(dt_k1_pdiff_5,axiom,( ! [A] : ! [B] : ( ( 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)) ) => v1_xreal_0(k1_pdiff_5(A,B)) ) )).
fof(dt_k1_pdiff_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k1_pdiff_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & 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))) ) ) )).
fof(dt_k1_pdiff_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & 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))))) ) ) )).
fof(dt_k1_pencil_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k1_pencil_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_finseq_1(B,A) & v7_ordinal1(C) & v7_ordinal1(D) ) => m2_finseq_1(k1_pencil_2(A,B,C,D),A) ) )).
fof(dt_k1_pencil_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k1_pencil_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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))) ) )).
fof(dt_k1_pepin,axiom,( ! [A] : ( v1_int_1(A) => m1_subset_1(k1_pepin(A),k4_ordinal1) ) )).
fof(dt_k1_petri_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k1_pnproc_1,axiom,( ! [A] : ( v1_funct_1(k1_pnproc_1(A)) & v1_funct_2(k1_pnproc_1(A),A,k4_ordinal1) & m1_subset_1(k1_pnproc_1(A),k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) )).
fof(dt_k1_polyalg1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(dt_k1_polyeq_5,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) & v1_xcmplx_0(B) ) => v1_xcmplx_0(k1_polyeq_5(A,B)) ) )).
fof(dt_k1_polyform,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v7_ordinal1(B) ) => m1_subset_1(k1_polyform(A,B),k4_numbers) ) )).
fof(dt_k1_polynom1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k1_polynom2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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(k1_polynom2(A,B,C,D),u1_struct_0(C)) ) )).
fof(dt_k1_polynom3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k4_ordinal1) & m1_finseq_1(C,A) ) => m2_finseq_1(k1_polynom3(A,B,C),A) ) )).
fof(dt_k1_polynom4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k1_polynom4(A,B)) & v1_funct_2(k1_polynom4(A,B),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k1_polynom4(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k1_polynom5,axiom,( ! [A] : ( m1_finseq_1(A,u1_struct_0(k1_complfld)) => m2_finseq_1(k1_polynom5(A),k1_numbers) ) )).
fof(dt_k1_polynom6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k1_polynom7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k1_polynom8,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v4_vectsp_1(A) & l6_algstr_0(A) & m1_subset_1(B,k4_ordinal1) ) => m1_subset_1(k1_polynom8(A,B),u1_struct_0(A)) ) )).
fof(dt_k1_polyred,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) ) )).
fof(dt_k1_poset_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k1_power,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_xreal_0(B) ) => v1_xreal_0(k1_power(A,B)) ) )).
fof(dt_k1_pralg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k1_pralg_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k1_pralg_2(A)) & v1_funct_1(k1_pralg_2(A)) ) ) )).
fof(dt_k1_pre_ff,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k1_pre_ff(A),k4_ordinal1) ) )).
fof(dt_k1_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k1_pre_topc,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(dt_k1_prelamb,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k1_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_funct_1(k1_prepower(A)) & v1_funct_2(k1_prepower(A),k4_ordinal1,k1_numbers) & m1_subset_1(k1_prepower(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k1_prgcor_1,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_int_1(B) ) => v1_int_1(k1_prgcor_1(A,B)) ) )).
fof(dt_k1_prob_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => m1_subset_1(k1_prob_1(A,B),k1_zfmisc_1(A)) ) )).
fof(dt_k1_prob_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & v7_ordinal1(D) ) => m1_prob_1(k1_prob_2(A,B,C,D),A,B) ) )).
fof(dt_k1_prob_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_funct_1(k1_prob_3(A,B)) & v1_funct_2(k1_prob_3(A,B),k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(k1_prob_3(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) )).
fof(dt_k1_prob_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & m1_subset_1(D,k4_ordinal1) ) => m2_subset_1(k1_prob_4(A,B,C,D),k1_zfmisc_1(A),B) ) )).
fof(dt_k1_projpl_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k1_projred1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) ) )).
fof(dt_k1_projred2,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k1_prvect_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) )).
fof(dt_k1_prvect_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) ) )).
fof(dt_k1_prvect_3,axiom,( ! [A] : ! [B] : ( ( ~ 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))))) ) ) )).
fof(dt_k1_pscomp_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) => v1_xreal_0(k1_pscomp_1(A,B)) ) )).
fof(dt_k1_pua2mss1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k1_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(dt_k1_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ~ v1_xboole_0(k1_qc_lang1(A)) ) )).
fof(dt_k1_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => m1_subset_1(k1_qc_lang2(A),k9_qc_lang1(A)) ) )).
fof(dt_k1_qc_lang3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k1_qc_lang4,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k9_qc_lang1(A)) ) => m2_finseq_1(k1_qc_lang4(A,B),k9_qc_lang1(A)) ) )).
fof(dt_k1_qc_trans,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(A) & v1_qc_trans(B,A) & m1_qc_lang1(B) & m1_subset_1(C,k3_cqc_lang(A)) ) => m2_subset_1(k1_qc_trans(A,B,C),k9_qc_lang1(B),k3_cqc_lang(B)) ) )).
fof(dt_k1_quantal1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k1_quatern2,axiom,( m1_subset_1(k1_quatern2,k1_quaterni) )).
fof(dt_k1_quofield,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k1_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k1_radix_1(A),k4_ordinal1) ) )).
fof(dt_k1_radix_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) & v3_card_1(D,C) & m1_finseq_1(D,k4_ordinal1) ) => m1_subset_1(k1_radix_2(A,B,C,D),k4_ordinal1) ) )).
fof(dt_k1_radix_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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)) ) )).
fof(dt_k1_radix_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) ) => m2_subset_1(k1_radix_5(A,B,C),k4_numbers,k3_radix_1(C)) ) )).
fof(dt_k1_radix_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k1_ramsey_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) ) )).
fof(dt_k1_random_1,axiom,( ! [A] : ( ~ 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))) ) ) )).
fof(dt_k1_random_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) => v1_xreal_0(k1_random_2(A,B,C,D)) ) )).
fof(dt_k1_random_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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_funct_1(E) & v1_funct_2(E,C,k6_numbers) & v10_valued_0(E) & v6_supinf_2(E) & v2_measure1(E,A,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,k6_numbers))) & v1_funct_1(F) & v1_funct_2(F,A,B) & v1_random_3(F,A,B,C,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( v1_funct_1(k1_random_3(A,B,C,D,E,F)) & v1_funct_2(k1_random_3(A,B,C,D,E,F),D,k6_numbers) & v10_valued_0(k1_random_3(A,B,C,D,E,F)) & v6_supinf_2(k1_random_3(A,B,C,D,E,F)) & v2_measure1(k1_random_3(A,B,C,D,E,F),B,D) & m1_subset_1(k1_random_3(A,B,C,D,E,F),k1_zfmisc_1(k2_zfmisc_1(D,k6_numbers))) ) ) )).
fof(dt_k1_ranknull,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) ) )).
fof(dt_k1_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => m1_subset_1(k1_rat_1(A),k4_ordinal1) ) )).
fof(dt_k1_rcomp_1,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => m1_subset_1(k1_rcomp_1(A,B),k1_zfmisc_1(k1_numbers)) ) )).
fof(dt_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => m1_subset_1(k1_real_1(A),k1_numbers) ) )).
fof(dt_k1_real_3,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => ( v1_funct_1(k1_real_3(A,B)) & v1_funct_2(k1_real_3(A,B),k4_ordinal1,k4_ordinal1) & m1_subset_1(k1_real_3(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) ) )).
fof(dt_k1_real_lat,axiom,( 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))) )).
fof(dt_k1_real_ns1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_k1_realset2,axiom,( 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))) )).
fof(dt_k1_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)))) ) ) )).
fof(dt_k1_rearran1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v3_membered(B) & v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) & v1_xreal_0(D) ) => m2_rfunct_3(k1_rearran1(A,B,C,D),A,k1_numbers,k3_rfunct_3(A,k1_numbers)) ) )).
fof(dt_k1_recdef_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v4_valued_0(A) ) => m1_subset_1(k1_recdef_1(A,B),k4_ordinal1) ) )).
fof(dt_k1_relset_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) ) => m1_subset_1(k1_relset_1(A,B),k1_zfmisc_1(A)) ) )).
fof(dt_k1_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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)) ) )).
fof(dt_k1_rewrite1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k1_rewrite2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v5_ordinal1(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)) ) ) )).
fof(dt_k1_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))))) ) )).
fof(dt_k1_rfinseq,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k1_rfinseq2,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => v7_ordinal1(k1_rfinseq2(A)) ) )).
fof(dt_k1_rfunct_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k1_rfunct_3,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k1_rfunct_3(A)) ) )).
fof(dt_k1_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => v1_xreal_0(k1_rinfsup1(A)) ) )).
fof(dt_k1_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => m1_subset_1(k1_rinfsup2(A),k6_numbers) ) )).
fof(dt_k1_ring_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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)))) ) )).
fof(dt_k1_ringcat1,axiom,( ! [A] : ( 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)) ) ) )).
fof(dt_k1_rlaffin1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k1_rlaffin2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k1_rlaffin3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) )).
fof(dt_k1_rlsub_1,axiom,( ! [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) ) => ( v1_rlvect_1(k1_rlsub_1(A)) & m1_rlsub_1(k1_rlsub_1(A),A) ) ) )).
fof(dt_k1_rlsub_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) ) )).
fof(dt_k1_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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))) ) )).
fof(dt_k1_rlvect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k1_rlvect_2,axiom,( ! [A] : ! [B] : ( l1_struct_0(A) => m1_subset_1(k1_rlvect_2(A,B),u1_struct_0(A)) ) )).
fof(dt_k1_rlvect_3,axiom,( ! [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) & 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) ) ) )).
fof(dt_k1_rlvect_5,axiom,( ! [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) ) => m1_subset_1(k1_rlvect_5(A),k4_ordinal1) ) )).
fof(dt_k1_rlvect_x,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) )).
fof(dt_k1_rmod_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) ) )).
fof(dt_k1_rmod_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) ) )).
fof(dt_k1_rmod_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) ) )).
fof(dt_k1_robbins3,axiom,( l3_robbins3(k1_robbins3) )).
fof(dt_k1_robbins4,axiom,( l1_orders_2(k1_robbins4) )).
fof(dt_k1_roughs_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,k1_zfmisc_1(A)) & v7_ordinal1(C) ) => m1_subset_1(k1_roughs_1(A,B,C),k1_zfmisc_1(A)) ) )).
fof(dt_k1_rpr_1,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => v1_xreal_0(k1_rpr_1(A,B)) ) )).
fof(dt_k1_rsspace,axiom,( ~ v1_xboole_0(k1_rsspace) )).
fof(dt_k1_rsspace3,axiom,( m1_subset_1(k1_rsspace3,k1_zfmisc_1(u1_struct_0(k6_rsspace))) )).
fof(dt_k1_rsspace4,axiom,( m1_subset_1(k1_rsspace4,k1_zfmisc_1(u1_struct_0(k6_rsspace))) )).
fof(dt_k1_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ( v1_bhsp_1(k1_rusub_1(A)) & m1_rusub_1(k1_rusub_1(A),A) ) ) )).
fof(dt_k1_rusub_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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) ) ) )).
fof(dt_k1_rusub_3,axiom,( ! [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) & 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) ) ) )).
fof(dt_k1_rusub_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => m1_subset_1(k1_rusub_4(A),k4_ordinal1) ) )).
fof(dt_k1_rusub_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k1_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_valued_0(A) ) => m1_subset_1(k1_rvsum_1(A),k1_zfmisc_1(k1_numbers)) ) )).
fof(dt_k1_rvsum_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_valued_0(A) ) => m1_subset_1(k1_rvsum_2(A),k1_zfmisc_1(k2_numbers)) ) )).
fof(dt_k1_scm_comp,axiom,( ~ 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) )).
fof(dt_k1_scm_inst,axiom,( m2_subset_1(k1_scm_inst,k4_ordinal1,k7_card_1(9)) )).
fof(dt_k1_scmbsort,axiom,( ! [A] : ( m1_scmfsa_2(A) => ( v1_relat_1(k1_scmbsort(A)) & v4_relat_1(k1_scmbsort(A),k4_ordinal1) & 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)) ) ) )).
fof(dt_k1_scmfsa6a,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v7_ordinal1(B) ) => ( v1_relat_1(k1_scmfsa6a(A,B)) & v4_relat_1(k1_scmfsa6a(A,B),k4_ordinal1) & 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)) ) ) )).
fof(dt_k1_scmfsa6b,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(k1_scmfsa6b(A,B,C),u1_struct_0(k1_scmfsa_2)) ) ) )).
fof(dt_k1_scmfsa6c,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k1_scmfsa8a,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ v1_xboole_0(k1_scmfsa8a(A)) & v1_relat_1(k1_scmfsa8a(A)) & v4_relat_1(k1_scmfsa8a(A),k4_ordinal1) & 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)) ) ) )).
fof(dt_k1_scmfsa8b,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k1_scmfsa8c,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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) ) ) )).
fof(dt_k1_scmfsa9a,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & 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(k7_card_1(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_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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_ordinal1(k1_scmfsa9a(A,B,C,D)) ) )).
fof(dt_k1_scmfsa_2,axiom,( v1_extpro_1(k1_scmfsa_2,k7_card_1(3)) & l1_extpro_1(k1_scmfsa_2,k7_card_1(3)) )).
fof(dt_k1_scmfsa_3,axiom,( ! [A] : ! [B] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_finset_1(k1_scmfsa_3(A,B)) ) ) )).
fof(dt_k1_scmfsa_7,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k1_scmfsa_9,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k1_scmfsa_m,axiom,( ! [A] : ( ( 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(k7_card_1(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(k7_card_1(3),k1_scmfsa_2)) ) ) )).
fof(dt_k1_scmisort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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(k7_card_1(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,k4_ordinal1) & 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,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ( v1_funct_1(k1_scmisort(A,B,C,D)) & v1_funct_2(k1_scmisort(A,B,C,D),k4_ordinal1,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2))) & m1_subset_1(k1_scmisort(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2))))) ) ) )).
fof(dt_k1_scmp_gcd,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_ami_2(k1_scmp_gcd(A)) & m1_subset_1(k1_scmp_gcd(A),u1_struct_0(k1_scmpds_2)) ) ) )).
fof(dt_k1_scmpds_2,axiom,( v1_extpro_1(k1_scmpds_2,2) & l1_extpro_1(k1_scmpds_2,2) )).
fof(dt_k1_scmpds_4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_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,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ( v1_relat_1(k1_scmpds_4(A,B)) & v4_relat_1(k1_scmpds_4(A,B),k4_ordinal1) & v5_relat_1(k1_scmpds_4(A,B),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k1_scmpds_4(A,B)) & v1_funct_1(k1_scmpds_4(A,B)) & v1_finset_1(k1_scmpds_4(A,B)) & v1_afinsq_1(k1_scmpds_4(A,B)) ) ) )).
fof(dt_k1_scmpds_6,axiom,( ! [A] : ( v1_int_1(A) => ( v1_relat_1(k1_scmpds_6(A)) & v4_relat_1(k1_scmpds_6(A),k4_ordinal1) & v5_relat_1(k1_scmpds_6(A),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k1_scmpds_6(A)) & v1_funct_1(k1_scmpds_6(A)) & v1_finset_1(k1_scmpds_6(A)) & v1_afinsq_1(k1_scmpds_6(A)) ) ) )).
fof(dt_k1_scmpds_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) & v1_int_1(B) & v7_ordinal1(C) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ( v1_relat_1(k1_scmpds_7(A,B,C,D)) & v4_relat_1(k1_scmpds_7(A,B,C,D),k4_ordinal1) & v5_relat_1(k1_scmpds_7(A,B,C,D),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k1_scmpds_7(A,B,C,D)) & 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)) ) ) )).
fof(dt_k1_scmpds_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k1_scmring1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ( v1_relat_1(k1_scmring1(A)) & v4_relat_1(k1_scmring1(A),k7_card_1(2)) & v1_funct_1(k1_scmring1(A)) & v1_partfun1(k1_scmring1(A),k7_card_1(2)) ) ) )).
fof(dt_k1_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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),k7_card_1(2)) & l1_extpro_1(k1_scmring2(A),k7_card_1(2)) ) ) )).
fof(dt_k1_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(k1_scmringi(A)) ) )).
fof(dt_k1_scmyciel,axiom,( ! [A] : m1_subset_1(k1_scmyciel(A),k1_zfmisc_1(A)) )).
fof(dt_k1_scpisort,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => ( ~ v1_xboole_0(k1_scpisort(A,B)) & v1_relat_1(k1_scpisort(A,B)) & v4_relat_1(k1_scpisort(A,B),k4_ordinal1) & 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)) ) ) )).
fof(dt_k1_scpqsort,axiom,( v1_relat_1(k1_scpqsort) & v4_relat_1(k1_scpqsort,k4_ordinal1) & v5_relat_1(k1_scpqsort,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k1_scpqsort) & v1_funct_1(k1_scpqsort) & v1_finset_1(k1_scpqsort) & v1_afinsq_1(k1_scpqsort) )).
fof(dt_k1_semi_af1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k1_seq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_funct_1(k1_seq_1(A)) & v1_funct_2(k1_seq_1(A),k4_ordinal1,k1_numbers) & m1_subset_1(k1_seq_1(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k1_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => v1_xreal_0(k1_seq_2(A)) ) )).
fof(dt_k1_seq_4,axiom,( ! [A] : ( v1_xreal_0(A) => m1_subset_1(k1_seq_4(A),k1_zfmisc_1(k1_numbers)) ) )).
fof(dt_k1_seqfunc,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) ) ) )).
fof(dt_k1_series_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_membered(A) & v7_membered(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ( v1_funct_1(k1_series_1(A,B,C)) & v1_funct_2(k1_series_1(A,B,C),k4_ordinal1,A) & m1_subset_1(k1_series_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) ) )).
fof(dt_k1_series_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_funct_1(k1_series_3(A)) & v1_funct_2(k1_series_3(A),k4_ordinal1,k1_numbers) & m1_subset_1(k1_series_3(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k1_setlim_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k1_setlim_1(A)) & v1_funct_1(k1_setlim_1(A)) ) ) )).
fof(dt_k1_setlim_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_funct_1(k1_setlim_2(A,B,C)) & v1_funct_2(k1_setlim_2(A,B,C),k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(k1_setlim_2(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) )).
fof(dt_k1_setwiseo,axiom,( ! [A] : ( v1_xboole_0(k1_setwiseo(A)) & m1_subset_1(k1_setwiseo(A),k5_finsub_1(A)) ) )).
fof(dt_k1_setwop_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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),k4_ordinal1,A) & m1_subset_1(k1_setwop_2(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) ) )).
fof(dt_k1_sf_mastr,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => m1_subset_1(k1_sf_mastr(A),k5_finsub_1(k2_scmfsa_2)) ) )).
fof(dt_k1_sfmastr2,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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_sfmastr2(A,B)) & v4_relat_1(k1_sfmastr2(A,B),k4_ordinal1) & v5_relat_1(k1_sfmastr2(A,B),u1_compos_1(k1_scmfsa_2)) & ~ v1_xboole_0(k1_sfmastr2(A,B)) & v1_funct_1(k1_sfmastr2(A,B)) & v1_finset_1(k1_sfmastr2(A,B)) & v1_afinsq_1(k1_sfmastr2(A,B)) ) ) )).
fof(dt_k1_sfmastr3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & 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,k4_ordinal1) & 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(k7_card_1(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),k4_ordinal1,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2))) & m1_subset_1(k1_sfmastr3(A,B,C,D,E,F),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2))))) ) ) )).
fof(dt_k1_sgraph1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => m1_subset_1(k1_sgraph1(A,B),k1_zfmisc_1(k4_ordinal1)) ) )).
fof(dt_k1_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => m1_subset_1(k1_sheffer1(A),u1_struct_0(A)) ) )).
fof(dt_k1_simplex0,axiom,( ! [A] : v1_classes1(k1_simplex0(A)) )).
fof(dt_k1_simplex1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k1_simplex2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) & l1_pre_topc(B) ) => v1_xreal_0(k1_simplex2(A,B)) ) )).
fof(dt_k1_sin_cos2,axiom,( 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))) )).
fof(dt_k1_sin_cos3,axiom,( 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))) )).
fof(dt_k1_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k1_sin_cos4(A)) ) )).
fof(dt_k1_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k1_sin_cos5(A)) ) )).
fof(dt_k1_sin_cos6,axiom,( v1_funct_1(k1_sin_cos6) & m1_subset_1(k1_sin_cos6,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) )).
fof(dt_k1_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k1_sin_cos7(A)) ) )).
fof(dt_k1_sin_cos9,axiom,( v1_funct_1(k1_sin_cos9) & m1_subset_1(k1_sin_cos9,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) )).
fof(dt_k1_sincos10,axiom,( v1_funct_1(k1_sincos10) & m1_subset_1(k1_sincos10,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) )).
fof(dt_k1_sppol_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) )).
fof(dt_k1_sprect_1,axiom,( ! [A] : ( 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))) ) )).
fof(dt_k1_stacks_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_2(k1_stacks_1(A,B,C),A,k3_finseq_2(A)) ) )).
fof(dt_k1_stirl2_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & v1_funct_1(C) & v1_funct_2(C,k7_card_1(A),B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(A),B))) ) => m1_subset_1(k1_stirl2_1(A,B,C,D),k1_zfmisc_1(k4_ordinal1)) ) )).
fof(dt_k1_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => m1_subset_1(k1_struct_0(A),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k1_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k1_subset_1,axiom,( ! [A] : m1_subset_1(k1_subset_1(A),k1_zfmisc_1(A)) )).
fof(dt_k1_substlat,axiom,( ! [A] : ! [B] : m1_subset_1(k1_substlat(A,B),k1_zfmisc_1(k5_finsub_1(k4_partfun1(A,B)))) )).
fof(dt_k1_substut2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k1_supinf_1,axiom,( m1_subset_1(k1_supinf_1,k6_numbers) )).
fof(dt_k1_supinf_2,axiom,( m1_subset_1(k1_supinf_2,k6_numbers) )).
fof(dt_k1_symsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) )).
fof(dt_k1_sysrel,axiom,( ! [A] : ( v1_relat_1(A) => v1_relat_1(k1_sysrel(A)) ) )).
fof(dt_k1_t_0topsp,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k1_t_1topsp,axiom,( ! [A] : ( ( ~ 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))))) ) ) )).
fof(dt_k1_taxonom1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k1_taylor_1,axiom,( ! [A] : ( 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))) ) ) )).
fof(dt_k1_taylor_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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),k4_ordinal1,k1_numbers) & m1_subset_1(k1_taylor_2(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k1_tbsp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => m1_subset_1(k1_tbsp_1(A,B),u1_struct_0(A)) ) )).
fof(dt_k1_tdgroup,axiom,( ! [A] : ( ( ~ 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))))) ) )).
fof(dt_k1_tdlat_1,axiom,( ! [A] : ( l1_pre_topc(A) => m1_subset_1(k1_tdlat_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).
fof(dt_k1_tdlat_2,axiom,( ! [A] : ! [B] : ( ( 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)))) ) )).
fof(dt_k1_termord,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_k1_tex_1,axiom,( ! [A] : m1_subset_1(k1_tex_1(A),k1_zfmisc_1(k1_zfmisc_1(A))) )).
fof(dt_k1_tex_2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k1_tex_4,axiom,( ! [A] : ! [B] : ( ( 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)))) ) )).
fof(dt_k1_tmap_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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))) ) ) )).
fof(dt_k1_toler_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(A) => m1_subset_1(k1_toler_1(A,B),k1_zfmisc_1(k2_zfmisc_1(B,B))) ) )).
fof(dt_k1_topalg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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)))) ) ) )).
fof(dt_k1_topalg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) )).
fof(dt_k1_topalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)))))) ) ) )).
fof(dt_k1_topalg_5,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_k1_topalg_6,axiom,( ! [A] : ( l1_pre_topc(A) => m1_subset_1(k1_topalg_6(A),k1_zfmisc_1(k4_partfun1(k1_numbers,k2_struct_0(A)))) ) )).
fof(dt_k1_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_funct_1(k1_topdim_1(A)) & v1_funct_2(k1_topdim_1(A),k4_ordinal1,k9_setfam_1(k9_setfam_1(u1_struct_0(A)))) & m1_subset_1(k1_topdim_1(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k9_setfam_1(u1_struct_0(A)))))) ) ) )).
fof(dt_k1_topdim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => v1_xxreal_0(k1_topdim_2(A,B)) ) )).
fof(dt_k1_topgen_1,axiom,( ! [A] : ! [B] : ( ( 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)))) ) )).
fof(dt_k1_topgen_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => v1_card_1(k1_topgen_2(A,B)) ) )).
fof(dt_k1_topgen_3,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(dt_k1_topgen_4,axiom,( ! [A] : ( l1_struct_0(A) => m1_subset_1(k1_topgen_4(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).
fof(dt_k1_topgen_5,axiom,( m1_subset_1(k1_topgen_5,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) )).
fof(dt_k1_topgrp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k1_topmetr,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k1_topreal1,axiom,( m1_subset_1(k1_topreal1,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) )).
fof(dt_k1_topreal6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,u1_struct_0(k15_euclid(A))) ) => v1_xreal_0(k1_topreal6(A,B,C)) ) )).
fof(dt_k1_topreal7,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k1_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) )).
fof(dt_k1_topreala,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k1_toprns_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ( v1_funct_1(k1_toprns_1(A,B,C)) & v1_funct_2(k1_toprns_1(A,B,C),k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(k1_toprns_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) ) )).
fof(dt_k1_tops_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k1_tops_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))))) ) )).
fof(dt_k1_transgeo,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k1_treal_1,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => m1_subset_1(k1_treal_1(A,B),u1_struct_0(k4_topmetr(A,B))) ) )).
fof(dt_k1_trees_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k1_trees_4,axiom,( ! [A] : ( v1_relat_1(k1_trees_4(A)) & v1_funct_1(k1_trees_4(A)) & v3_trees_2(k1_trees_4(A)) ) )).
fof(dt_k1_trees_9,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k1_trees_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k1_triang_1,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k1_tsep_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k1_tsp_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k1_twoscomp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k1_unialg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => m2_finseq_1(k1_unialg_1(A),k4_ordinal1) ) )).
fof(dt_k1_unialg_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(dt_k1_unialg_3,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(dt_k1_uniroots,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k1_uproots,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k4_ordinal1) ) => m2_subset_1(k1_uproots(A,B,C),k14_pre_poly(A),k15_pre_poly(A)) ) )).
fof(dt_k1_urysohn1,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k1_urysohn1(A),k1_zfmisc_1(k1_numbers)) ) )).
fof(dt_k1_valued_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) & v7_ordinal1(C) ) => m2_valued_0(k1_valued_0(A,B,C),A,B) ) )).
fof(dt_k1_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k1_vectsp11,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) ) )).
fof(dt_k1_vectsp_1,axiom,( v8_algstr_0(k1_vectsp_1) & l2_algstr_0(k1_vectsp_1) )).
fof(dt_k1_vectsp_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k1_vectsp_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) ) )).
fof(dt_k1_vectsp_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) ) )).
fof(dt_k1_vectsp_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k1_vectsp_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) ) )).
fof(dt_k1_vectsp_8,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) ) ) )).
fof(dt_k1_vectsp_9,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) ) )).
fof(dt_k1_vfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k1_vfunct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k1_waybel10,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k1_waybel11,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k1_waybel15,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => m1_subset_1(k1_waybel15(A),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k1_waybel16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => m1_subset_1(k1_waybel16(A),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k1_waybel17,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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),k4_ordinal1,A) & m1_subset_1(k1_waybel17(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) ) )).
fof(dt_k1_waybel19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => m1_subset_1(k1_waybel19(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).
fof(dt_k1_waybel20,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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))))) ) ) )).
fof(dt_k1_waybel22,axiom,( ! [A] : m1_subset_1(k1_waybel22(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k2_yellow_1(A))))) )).
fof(dt_k1_waybel23,axiom,( ! [A] : ! [B] : ( ( ~ 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(k1_yellow_1(k7_waybel_0(A))))) ) => m1_subset_1(k1_waybel23(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k1_waybel24,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k1_waybel25,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_waybel_9(k1_waybel25(A)) & l1_waybel_9(k1_waybel25(A)) ) ) )).
fof(dt_k1_waybel26,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k1_waybel27,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(k5_yellow_1(A,B))) & m1_subset_1(D,A) ) => m1_subset_1(k1_waybel27(A,B,C,D),u1_struct_0(B)) ) )).
fof(dt_k1_waybel28,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k1_waybel29,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(dt_k1_waybel30,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k1_waybel31,axiom,( ! [A] : ( ( 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)) ) )).
fof(dt_k1_waybel32,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k1_waybel33,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k2_yellow_1(B)) & v13_waybel_0(C,k2_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(B)))) ) => m1_subset_1(k1_waybel33(A,B,C),u1_struct_0(A)) ) )).
fof(dt_k1_waybel34,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) ) )).
fof(dt_k1_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k1_waybel_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(dt_k1_waybel_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k1_waybel_3,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k1_waybel_4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k1_waybel_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))) ) ) )).
fof(dt_k1_waybel_8,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(dt_k1_waybel_9,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k1_weddwitt,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k1_weierstr,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => m1_subset_1(k1_weierstr(A),k1_zfmisc_1(k1_numbers)) ) )).
fof(dt_k1_wellfnd1,axiom,( ! [A] : ( l1_orders_2(A) => m1_subset_1(k1_wellfnd1(A),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k1_wellord2,axiom,( ! [A] : v1_relat_1(k1_wellord2(A)) )).
fof(dt_k1_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => v1_xxreal_0(k1_xxreal_2(A)) ) )).
fof(dt_k1_xxreal_3,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => v1_xxreal_0(k1_xxreal_3(A,B)) ) )).
fof(dt_k1_yellow11,axiom,( l1_orders_2(k1_yellow11) )).
fof(dt_k1_yellow12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k1_yellow15,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k1_yellow16,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k5_yellow_1(A,B)))) ) => m1_subset_1(k1_yellow16(A,B,C,D),k1_zfmisc_1(u1_struct_0(B))) ) )).
fof(dt_k1_yellow18,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k1_yellow19,axiom,( ! [A] : ! [B] : ( ( ~ 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(k2_yellow_1(k2_struct_0(A))))) ) )).
fof(dt_k1_yellow20,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k1_yellow21,axiom,( ! [A] : l1_struct_0(k1_yellow21(A)) )).
fof(dt_k1_yellow_0,axiom,( ! [A] : ! [B] : ( l1_orders_2(A) => m1_subset_1(k1_yellow_0(A,B),u1_struct_0(A)) ) )).
fof(dt_k1_yellow_1,axiom,( ! [A] : ( v1_orders_2(k1_yellow_1(A)) & l1_orders_2(k1_yellow_1(A)) ) )).
fof(dt_k1_yellow_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k1_yellow_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k1_yellow_3(A,B)) ) )).
fof(dt_k1_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k1_yellow_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k1_yellow_7,axiom,( ! [A] : ( ( ~ 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))))) ) ) )).
fof(dt_k1_yellow_8,axiom,( ! [A] : ( v1_pre_topc(k1_yellow_8(A)) & l1_pre_topc(k1_yellow_8(A)) ) )).
fof(dt_k1_yellow_9,axiom,( ! [A] : ! [B] : ( ( 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)))) ) ) )).
fof(dt_k1_yoneda_1,axiom,( ! [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) & 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)) ) ) )).
fof(dt_k1_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k1_zf_fund2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) & ~ 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)) ) )).
fof(dt_k1_zf_lang,axiom,( m1_subset_1(k1_zf_lang,k1_zfmisc_1(k4_ordinal1)) )).
fof(dt_k1_zf_lang1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k1_zfmodel1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) & ~ 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))) ) ) )).
fof(dt_k1_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k1_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ 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_int_1(B) ) => ( ~ v1_xboole_0(k1_zmodul02(A,B)) & m1_subset_1(k1_zmodul02(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_k1_zmodul03,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) & l1_vectsp_1(B,A) & m1_vectsp_6(C,A,B) & m1_subset_1(D,u1_struct_0(B)) ) => m1_subset_1(k1_zmodul03(A,B,C,D),u1_struct_0(A)) ) )).
fof(dt_k20_abcmiz_1,axiom,( ~ v1_xboole_0(k20_abcmiz_1) )).
fof(dt_k20_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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),k6_numbers) ) )).
fof(dt_k20_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [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)) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & l1_aofa_a00(C,A) & v4_msualg_1(D,A) & v4_msafree4(D,A,C) & l3_msualg_1(D,A) & l4_aofa_a00(E,A,B,C) & ~ v2_struct_0(F) & v2_unialg_1(F) & v3_unialg_1(F) & v4_unialg_1(F) & v3_aofa_000(F) & v4_aofa_000(F) & v5_aofa_000(F) & v6_aofa_000(F) & l3_aofa_a00(F,A,C,u4_aofa_a00(A,B,C,E)) & m1_subset_1(G,u1_struct_0(A)) & m1_subset_1(H,k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),G)) & m1_subset_1(I,k1_funct_1(u3_msualg_1(A,D),G)) ) => m1_subset_1(k20_aofa_a00(A,B,C,D,E,F,G,H,I),k1_zfmisc_1(k9_funct_2(k2_zfmisc_1(k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E)),u1_struct_0(F)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))))) ) )).
fof(dt_k20_binop_2,axiom,( v1_funct_1(k20_binop_2) & v1_funct_2(k20_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & m1_subset_1(k20_binop_2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers))) )).
fof(dt_k20_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => m1_subset_1(k20_bvfunc_1(A,B),k6_margrel1) ) )).
fof(dt_k20_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k20_convex4,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k20_decomp_1,axiom,( ! [A] : ( ( 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)))) ) )).
fof(dt_k20_ens_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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))))) ) ) )).
fof(dt_k20_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => m2_finseq_1(k20_euclid(A),k1_numbers) ) )).
fof(dt_k20_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k20_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k20_fomodel1,axiom,( ! [A] : ( ( ~ 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))))) ) ) )).
fof(dt_k20_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),k6_margrel1)) ) => ( v1_funct_1(k20_fomodel2(A,B,C)) & m1_subset_1(k20_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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),k6_margrel1))) ) ) )).
fof(dt_k20_fomodel4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k20_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( 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)) ) )).
fof(dt_k20_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k20_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) )).
fof(dt_k20_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & m3_glib_001(B,A) & m1_subset_1(C,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => m4_glib_001(k20_glib_001(A,B,C,D),A,B) ) )).
fof(dt_k20_grcat_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k20_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k20_idea_1,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k4_ordinal1) & v7_ordinal1(B) ) => ( 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))) ) ) )).
fof(dt_k20_lexbfs,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1),k9_funct_2(k6_glib_000(A),k4_ordinal1))) ) => m1_subset_1(k20_lexbfs(A,B,C),k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k9_funct_2(k6_glib_000(A),k4_ordinal1))) ) )).
fof(dt_k20_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => m2_subset_1(k20_lpspacc1(A,B,C),k1_zfmisc_1(k13_lpspacc1(A,B,C)),k18_lpspacc1(A,B,C)) ) )).
fof(dt_k20_lpspace1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( ~ v2_struct_0(k20_lpspace1(A,B,C)) & l1_normsp_1(k20_lpspace1(A,B,C)) ) ) )).
fof(dt_k20_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & v2_matrixj1(C,A) & m1_finseq_1(C,k3_finseq_2(k3_finseq_2(A))) ) => ( v1_matrix_0(k20_matrixj1(A,B,C)) & v2_matrix_0(k20_matrixj1(A,B,C),A,k2_wsierp_1(k10_matrixj1(A,C)),k2_wsierp_1(k10_matrixj1(A,C))) & m2_finseq_1(k20_matrixj1(A,B,C),k3_finseq_2(A)) ) ) )).
fof(dt_k20_metric_3,axiom,( 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))) )).
fof(dt_k20_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k20_modelc_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k20_modelc_3,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & v1_modelc_2(B) & m1_finseq_1(B,k4_ordinal1) ) => m1_subset_1(k20_modelc_3(A,B),k1_zfmisc_1(k1_modelc_3(A))) ) )).
fof(dt_k20_monoid_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) ) => m1_subset_1(k20_monoid_1(A,B),u1_struct_0(k13_monoid_1(A))) ) )).
fof(dt_k20_osafree,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k20_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k20_pcs_0,axiom,( ! [A] : ! [B] : ( l2_pcs_0(A) => ( v12_pcs_0(k20_pcs_0(A,B)) & l2_pcs_0(k20_pcs_0(A,B)) ) ) )).
fof(dt_k20_polyform,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) )).
fof(dt_k20_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k20_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v1_prvect_1(A) ) => ( ~ v2_struct_0(k20_prvect_1(A)) & v8_algstr_0(k20_prvect_1(A)) & v13_algstr_0(k20_prvect_1(A)) & v2_rlvect_1(k20_prvect_1(A)) & v3_rlvect_1(k20_prvect_1(A)) & v4_rlvect_1(k20_prvect_1(A)) & l2_algstr_0(k20_prvect_1(A)) ) ) )).
fof(dt_k20_pscomp_1,axiom,( ! [A] : ( 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))) ) )).
fof(dt_k20_qc_lang1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k9_qc_lang1(A)) ) => m1_subset_1(k20_qc_lang1(A,B),k9_qc_lang1(A)) ) )).
fof(dt_k20_quofield,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k20_rfunct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k20_rvsum_1,axiom,( ! [A] : ( m1_finseq_1(A,k2_numbers) => m1_subset_1(k20_rvsum_1(A),k2_numbers) ) )).
fof(dt_k20_seq_4,axiom,( ! [A] : ( m1_finseq_1(A,k2_numbers) => v1_xreal_0(k20_seq_4(A)) ) )).
fof(dt_k20_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_funct_1(k20_sin_cos(A)) & v1_funct_2(k20_sin_cos(A),k4_ordinal1,k1_numbers) & m1_subset_1(k20_sin_cos(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k20_substut1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k16_substut1(A)) ) => m1_subset_1(k20_substut1(A,B),k16_substut1(A)) ) )).
fof(dt_k20_turing_1,axiom,( v1_turing_1(k20_turing_1) & l1_turing_1(k20_turing_1) )).
fof(dt_k20_twoscomp,axiom,( 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))) )).
fof(dt_k20_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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))) ) ) )).
fof(dt_k20_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k20_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) ) => ( v1_zf_lang(k20_zf_lang(A)) & m2_finseq_1(k20_zf_lang(A),k4_ordinal1) ) ) )).
fof(dt_k20_zmodul02,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_finseq_1(B,u1_struct_0(A)) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k4_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_numbers))) ) => m2_finseq_1(k20_zmodul02(A,B,C),u1_struct_0(A)) ) )).
fof(dt_k21_abcmiz_1,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k4_abcmiz_1,k4_ordinal1)) => m2_finseq_2(k21_abcmiz_1(A),k2_abcmiz_1,k4_abcmiz_1) ) )).
fof(dt_k21_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) )).
fof(dt_k21_aofa_a00,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & l6_aofa_a00(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => m1_subset_1(k21_aofa_a00(A,B),k1_funct_1(u3_msualg_1(A,B),u8_aofa_a00(A))) ) )).
fof(dt_k21_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k21_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => m1_subset_1(k21_bvfunc_1(A,B),k6_margrel1) ) )).
fof(dt_k21_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k21_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k20_coh_sp(A)) => m1_subset_1(k21_coh_sp(A,B),k16_coh_sp(A)) ) )).
fof(dt_k21_convex4,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k21_ens_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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))))) ) ) )).
fof(dt_k21_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => m2_finseq_2(k21_euclid(A),k1_numbers,k1_euclid(A)) ) )).
fof(dt_k21_fomodel1,axiom,( ! [A] : ( ( ~ 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))))) ) ) )).
fof(dt_k21_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & ~ v1_xboole_0(B) ) => ( v1_funct_1(k21_fomodel2(A,B)) & v1_funct_2(k21_fomodel2(A,B),k4_ordinal1,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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),k6_margrel1)) & m1_subset_1(k21_fomodel2(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)),k15_fomodel2(A,B),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),k6_margrel1)))) ) ) )).
fof(dt_k21_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(dt_k21_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => m1_subset_1(k21_fomodel4(A),k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(k1_fomodel4(A)),k1_fomodel4(A)))) ) )).
fof(dt_k21_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : m1_subset_1(k21_ftacell1(A,B,C,D,E),k3_msafree2(k19_ftacell1(A,B,C,D,E))) )).
fof(dt_k21_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : m2_subset_1(k21_gfacirc1(A,B,C),u1_struct_0(k19_gfacirc1(A,B,C)),k3_msafree2(k19_gfacirc1(A,B,C))) )).
fof(dt_k21_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) )).
fof(dt_k21_grcat_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k21_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(dt_k21_idea_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) & m1_finseq_1(B,k4_ordinal1) ) => ( 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))) ) ) )).
fof(dt_k21_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ( v3_lattices(k21_interva1(A)) & l3_lattices(k21_interva1(A)) ) ) )).
fof(dt_k21_lexbfs,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1),k9_funct_2(k6_glib_000(A),k4_ordinal1))) & 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),k4_ordinal1),k9_funct_2(k6_glib_000(A),k4_ordinal1))) ) )).
fof(dt_k21_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( v1_funct_1(k21_lpspacc1(A,B,C)) & v1_funct_2(k21_lpspacc1(A,B,C),k2_zfmisc_1(k2_numbers,k18_lpspacc1(A,B,C)),k18_lpspacc1(A,B,C)) & m1_subset_1(k21_lpspacc1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_numbers,k18_lpspacc1(A,B,C)),k18_lpspacc1(A,B,C)))) ) ) )).
fof(dt_k21_matrixj1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k21_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k21_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1) ) => ~ v1_xboole_0(k21_modelc_1(A,B,C)) ) )).
fof(dt_k21_modelc_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1) ) => m1_subset_1(k21_modelc_2(A,B,C),u1_struct_0(A)) ) )).
fof(dt_k21_modelc_3,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & v1_modelc_3(B,A) & l1_modelc_3(B,A) ) => v7_ordinal1(k21_modelc_3(A,B)) ) )).
fof(dt_k21_monoid_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k21_osafree,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k21_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k21_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ( v12_pcs_0(k21_pcs_0(A)) & l2_pcs_0(k21_pcs_0(A)) ) ) )).
fof(dt_k21_polyform,axiom,( ! [A] : ! [B] : ( ( 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)))))) ) ) )).
fof(dt_k21_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k21_pscomp_1,axiom,( ! [A] : ( 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))) ) )).
fof(dt_k21_qc_lang1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k21_quofield,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k21_rfunct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => v1_xreal_0(k21_rfunct_3(A,B,C)) ) )).
fof(dt_k21_rvsum_1,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => v1_xreal_0(k21_rvsum_1(A)) ) )).
fof(dt_k21_seq_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,k12_seq_4(A)) & v1_xreal_0(C) ) => m1_subset_1(k21_seq_4(A,B,C),k1_zfmisc_1(k12_seq_4(A))) ) )).
fof(dt_k21_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_funct_1(k21_sin_cos(A)) & v1_funct_2(k21_sin_cos(A),k4_ordinal1,k1_numbers) & m1_subset_1(k21_sin_cos(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k21_substut1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k21_turing_1,axiom,( ! [A] : ! [B] : ( ( l1_turing_1(A) & l1_turing_1(B) ) => ( ~ v1_xboole_0(k21_turing_1(A,B)) & v1_finset_1(k21_turing_1(A,B)) ) ) )).
fof(dt_k21_twoscomp,axiom,( 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))) )).
fof(dt_k21_valued_2,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k21_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) ) => ( v1_zf_lang(k21_zf_lang(A)) & m2_finseq_1(k21_zf_lang(A),k4_ordinal1) ) ) )).
fof(dt_k21_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ 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_zmodul02(B,A) ) => m1_subset_1(k21_zmodul02(A,B),u1_struct_0(A)) ) )).
fof(dt_k22_abcmiz_1,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k4_abcmiz_1,k4_ordinal1)) => m1_subset_1(k22_abcmiz_1(A),k4_ordinal1) ) )).
fof(dt_k22_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & l6_aofa_a00(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) & m1_subset_1(C,k1_funct_1(u3_msualg_1(A,B),u8_aofa_a00(A))) ) => m1_subset_1(k22_aofa_a00(A,B,C),k1_funct_1(u3_msualg_1(A,B),u8_aofa_a00(A))) ) )).
fof(dt_k22_aofa_i00,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k22_binop_2,axiom,( v1_funct_1(k22_binop_2) & v1_funct_2(k22_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & m1_subset_1(k22_binop_2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers))) )).
fof(dt_k22_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k22_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k20_coh_sp(A)) => m1_subset_1(k22_coh_sp(A,B),k16_coh_sp(A)) ) )).
fof(dt_k22_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => ( v1_funct_1(k22_ens_1(A)) & v1_funct_2(k22_ens_1(A),u4_struct_0(k6_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(k6_cat_2(A,A)),k2_ens_1(k16_ens_1(A))))) ) ) )).
fof(dt_k22_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k22_euclid(A),u1_struct_0(k15_euclid(A))) ) )).
fof(dt_k22_fomodel1,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k22_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) & ~ v1_xboole_0(C) ) => m2_rfunct_3(k22_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)),k15_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)),k15_fomodel2(A,C),k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0))),k6_margrel1)) ) )).
fof(dt_k22_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(dt_k22_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => m1_subset_1(k22_fomodel4(A),k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(k1_fomodel4(A)),k1_fomodel4(A)))) ) )).
fof(dt_k22_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : m1_subset_1(k22_ftacell1(A,B,C,D,E),k3_msafree2(k19_ftacell1(A,B,C,D,E))) )).
fof(dt_k22_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ 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)) ) )).
fof(dt_k22_glib_000,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) )).
fof(dt_k22_grcat_1,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(dt_k22_idea_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) & m1_finseq_1(B,k4_ordinal1) ) => ( 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))) ) ) )).
fof(dt_k22_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => m2_interva1(k22_interva1(A),A) ) )).
fof(dt_k22_lexbfs,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1),k9_funct_2(k6_glib_000(A),k4_ordinal1))) ) => m1_subset_1(k22_lexbfs(A,B),k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k9_funct_2(k6_glib_000(A),k4_ordinal1))) ) )).
fof(dt_k22_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( ~ v2_struct_0(k22_lpspacc1(A,B,C)) & v13_algstr_0(k22_lpspacc1(A,B,C)) & v2_rlvect_1(k22_lpspacc1(A,B,C)) & v3_rlvect_1(k22_lpspacc1(A,B,C)) & v4_rlvect_1(k22_lpspacc1(A,B,C)) & v1_clvect_1(k22_lpspacc1(A,B,C)) & v2_clvect_1(k22_lpspacc1(A,B,C)) & v3_clvect_1(k22_lpspacc1(A,B,C)) & v4_clvect_1(k22_lpspacc1(A,B,C)) & v5_clvect_1(k22_lpspacc1(A,B,C)) & l1_clvect_1(k22_lpspacc1(A,B,C)) ) ) )).
fof(dt_k22_matrixj1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k22_metric_3,axiom,( 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))) )).
fof(dt_k22_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k22_modelc_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k22_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => ~ v1_xboole_0(k22_modelc_3(A)) ) )).
fof(dt_k22_monoid_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => l3_algstr_0(k22_monoid_1(A)) ) )).
fof(dt_k22_osafree,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k22_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)))) ) ) )).
fof(dt_k22_pcs_0,axiom,( ! [A] : ! [B] : ( ( l2_pcs_0(A) & l2_pcs_0(B) ) => l2_pcs_0(k22_pcs_0(A,B)) ) )).
fof(dt_k22_polyform,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k22_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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(k22_pre_poly(A,B)) & m1_subset_1(k22_pre_poly(A,B),k1_zfmisc_1(A)) ) ) )).
fof(dt_k22_pscomp_1,axiom,( ! [A] : ( 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))) ) )).
fof(dt_k22_qc_lang1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k9_qc_lang1(A)) ) => m1_subset_1(k22_qc_lang1(A,B),k9_qc_lang1(A)) ) )).
fof(dt_k22_quaterni,axiom,( ! [A] : ! [B] : ( ( v1_quaterni(A) & v1_quaterni(B) ) => m1_subset_1(k22_quaterni(A,B),k1_quaterni) ) )).
fof(dt_k22_quofield,axiom,( ! [A] : ( ( ~ 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))))) ) ) )).
fof(dt_k22_rvsum_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k22_seq_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,k12_seq_4(A)) & m1_subset_1(C,k1_zfmisc_1(k12_seq_4(A))) ) => v1_xreal_0(k22_seq_4(A,B,C)) ) )).
fof(dt_k22_sin_cos,axiom,( v1_funct_1(k22_sin_cos) & v1_funct_2(k22_sin_cos,k1_numbers,k1_numbers) & m1_subset_1(k22_sin_cos,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) )).
fof(dt_k22_substut1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k22_turing_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_turing_1(A) & l1_turing_1(B) & m1_subset_1(C,k3_zfmisc_1(u2_turing_1(A),u1_turing_1(A),k1_enumset1(k4_xcmplx_0(1),k5_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)),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1))) ) )).
fof(dt_k22_twoscomp,axiom,( 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))) )).
fof(dt_k22_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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))) ) ) )).
fof(dt_k22_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))))) ) ) )).
fof(dt_k22_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) ) => ( v1_zf_lang(k22_zf_lang(A)) & m2_finseq_1(k22_zf_lang(A),k4_ordinal1) ) ) )).
fof(dt_k22_zmodul02,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & m1_zmodul02(B,A) & m1_zmodul02(C,A) ) => m1_zmodul02(k22_zmodul02(A,B,C),A) ) )).
fof(dt_k23_abcmiz_1,axiom,( ! [A] : ( 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)) ) )).
fof(dt_k23_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & l6_aofa_a00(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) & m1_subset_1(C,k1_funct_1(u3_msualg_1(A,B),u8_aofa_a00(A))) & m1_subset_1(D,k1_funct_1(u3_msualg_1(A,B),u8_aofa_a00(A))) ) => m1_subset_1(k23_aofa_a00(A,B,C,D),k1_funct_1(u3_msualg_1(A,B),u8_aofa_a00(A))) ) )).
fof(dt_k23_aofa_i00,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k23_binop_2,axiom,( v1_funct_1(k23_binop_2) & v1_funct_2(k23_binop_2,k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1) & m1_subset_1(k23_binop_2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1))) )).
fof(dt_k23_cat_4,axiom,( ! [A] : ! [B] : ( v5_cat_4(k23_cat_4(A,B)) & l2_cat_4(k23_cat_4(A,B)) ) )).
fof(dt_k23_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k16_coh_sp(A)) => m1_subset_1(k23_coh_sp(A,B),k20_coh_sp(A)) ) )).
fof(dt_k23_ens_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k23_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & ~ v1_xboole_0(B) & v7_ordinal1(C) & m1_subset_1(D,k15_fomodel2(A,B)) ) => m2_rfunct_3(k23_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)) ) )).
fof(dt_k23_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))),k15_fomodel2(A,k8_eqrel_1(B,C))) ) )).
fof(dt_k23_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ 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(k23_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)))) ) )).
fof(dt_k23_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : m1_subset_1(k23_ftacell1(A,B,C,D,E),k3_msafree2(k19_ftacell1(A,B,C,D,E))) )).
fof(dt_k23_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k23_glib_000,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) )).
fof(dt_k23_grcat_1,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(dt_k23_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => m2_interva1(k23_interva1(A),A) ) )).
fof(dt_k23_lexbfs,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1),k9_funct_2(k6_glib_000(A),k4_ordinal1))) ) )).
fof(dt_k23_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( v1_funct_1(k23_lpspacc1(A,B,C)) & v1_funct_2(k23_lpspacc1(A,B,C),u1_struct_0(k22_lpspacc1(A,B,C)),k1_numbers) & m1_subset_1(k23_lpspacc1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k22_lpspacc1(A,B,C)),k1_numbers))) ) ) )).
fof(dt_k23_matrixj1,axiom,( ! [A] : ! [B] : ( ( ~ 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,k4_ordinal1) ) => ( 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)))) ) ) )).
fof(dt_k23_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k23_modelc_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k23_modelc_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k23_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => ~ v1_xboole_0(k23_modelc_3(A)) ) )).
fof(dt_k23_monoid_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k23_osafree,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k23_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) )).
fof(dt_k23_pcs_0,axiom,( ! [A] : ! [B] : ( ( l2_pcs_0(A) & l2_pcs_0(B) ) => l2_pcs_0(k23_pcs_0(A,B)) ) )).
fof(dt_k23_polyform,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k23_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(k23_pre_poly(A,B,C)) & m1_subset_1(k23_pre_poly(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) ) )).
fof(dt_k23_pscomp_1,axiom,( ! [A] : ( 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))) ) )).
fof(dt_k23_qc_lang1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k23_quaterni,axiom,( ! [A] : ! [B] : ( ( v1_quaterni(A) & v1_quaterni(B) ) => m1_subset_1(k23_quaterni(A,B),k1_quaterni) ) )).
fof(dt_k23_seq_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,k1_zfmisc_1(k12_seq_4(A))) & v1_xreal_0(C) ) => m1_subset_1(k23_seq_4(A,B,C),k1_zfmisc_1(k12_seq_4(A))) ) )).
fof(dt_k23_substut1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k23_turing_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_turing_1(A) & l1_turing_1(B) & m1_subset_1(C,k3_zfmisc_1(u2_turing_1(B),u1_turing_1(B),k1_enumset1(k4_xcmplx_0(1),k5_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)),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1))) ) )).
fof(dt_k23_twoscomp,axiom,( 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))) )).
fof(dt_k23_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) ) => m2_subset_1(k23_zf_lang(A),k4_ordinal1,k1_zf_lang) ) )).
fof(dt_k23_zmodul02,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_int_1(B) & m1_zmodul02(C,A) ) => m1_zmodul02(k23_zmodul02(A,B,C),A) ) )).
fof(dt_k24_abcmiz_1,axiom,( ! [A] : ( m1_subset_1(A,k20_abcmiz_1) => m1_subset_1(k24_abcmiz_1(A),k2_zfmisc_1(k4_abcmiz_1,k4_ordinal1)) ) )).
fof(dt_k24_aofa_i00,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k24_binop_2,axiom,( v1_funct_1(k24_binop_2) & v1_funct_2(k24_binop_2,k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1) & m1_subset_1(k24_binop_2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1))) )).
fof(dt_k24_cat_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ 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) ) )).
fof(dt_k24_coh_sp,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k24_ens_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k24_fomodel0,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => m1_subset_1(k24_fomodel0(A,B),k1_zfmisc_1(B)) ) )).
fof(dt_k24_fomodel1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) )).
fof(dt_k24_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) ) => m1_subset_1(k24_fomodel2(A,B),k1_zfmisc_1(k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0)))) ) )).
fof(dt_k24_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k24_fomodel4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k24_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : m1_subset_1(k24_ftacell1(A,B,C,D,E),k3_msafree2(k19_ftacell1(A,B,C,D,E))) )).
fof(dt_k24_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : m2_subset_1(k24_gfacirc1(A,B,C),u1_struct_0(k22_gfacirc1(A,B,C)),k3_msafree2(k22_gfacirc1(A,B,C))) )).
fof(dt_k24_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) ) )).
fof(dt_k24_grcat_1,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k24_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( ~ v2_struct_0(k24_lpspacc1(A,B,C)) & l2_clvect_1(k24_lpspacc1(A,B,C)) ) ) )).
fof(dt_k24_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k24_mmlquery,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => v7_ordinal1(k24_mmlquery(A,B)) ) )).
fof(dt_k24_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1) ) => m1_subset_1(k24_modelc_1(A,B,C),u1_struct_0(A)) ) )).
fof(dt_k24_modelc_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k24_modelc_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & m1_orders_1(B,k6_partfun1(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),k4_ordinal1) ) ) )).
fof(dt_k24_osafree,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k24_pcs_0,axiom,( ! [A] : ! [B] : ( l1_orders_2(A) => m1_subset_1(k24_pcs_0(A,B),k1_zfmisc_1(k2_zfmisc_1(B,B))) ) )).
fof(dt_k24_polyform,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k24_pscomp_1,axiom,( ! [A] : ( 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))) ) )).
fof(dt_k24_qc_lang1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k24_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => m1_subset_1(k24_quaterni(A),k1_quaterni) ) )).
fof(dt_k24_seq_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,k1_zfmisc_1(k12_seq_4(A))) & m1_subset_1(C,k1_zfmisc_1(k12_seq_4(A))) ) => v1_xreal_0(k24_seq_4(A,B,C)) ) )).
fof(dt_k24_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( v1_funct_1(k24_sin_cos(A)) & v1_funct_2(k24_sin_cos(A),k4_ordinal1,k2_numbers) & m1_subset_1(k24_sin_cos(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) ) )).
fof(dt_k24_substut1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k24_turing_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k24_twoscomp,axiom,( 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))) )).
fof(dt_k24_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k24_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) ) => ( v1_zf_lang(k24_zf_lang(A)) & m2_finseq_1(k24_zf_lang(A),k4_ordinal1) ) ) )).
fof(dt_k24_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ 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_zmodul02(B,A) ) => m1_zmodul02(k24_zmodul02(A,B),A) ) )).
fof(dt_k25_abcmiz_1,axiom,( ! [A] : ( m1_subset_1(A,k20_abcmiz_1) => m2_finseq_2(k25_abcmiz_1(A),k2_abcmiz_1,k4_abcmiz_1) ) )).
fof(dt_k25_aofa_i00,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k25_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ 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)) ) )).
fof(dt_k25_coh_sp,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k25_descip_1,axiom,( ! [A] : ( 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)) ) )).
fof(dt_k25_ens_1,axiom,( ! [A] : ! [B] : ( ( ~ 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),k6_cat_2(k2_oppcat_1(B),B),k11_ens_1(A)) ) )).
fof(dt_k25_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ( v1_relat_1(k25_fomodel1(A)) & v1_funct_1(k25_fomodel1(A)) ) ) )).
fof(dt_k25_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & ~ v1_xboole_0(B) & m1_subset_1(C,k15_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(k25_fomodel2(A,B,C,D),k6_margrel1) ) )).
fof(dt_k25_fomodel4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k25_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ 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)) ) )).
fof(dt_k25_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) )).
fof(dt_k25_grcat_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k25_lexbfs,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(dt_k25_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k25_mmlquery,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => v7_ordinal1(k25_mmlquery(A)) ) )).
fof(dt_k25_modelc_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k25_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k25_modelc_2(A)) ) )).
fof(dt_k25_modelc_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k25_modelc_2(k43_modelc_2)) & v1_modelc_2(B) & m1_finseq_1(B,k4_ordinal1) & m1_orders_1(C,k6_partfun1(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) ) ) )).
fof(dt_k25_osafree,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k25_pcs_0,axiom,( ! [A] : ! [B] : ( l1_pcs_0(A) => m1_subset_1(k25_pcs_0(A,B),k1_zfmisc_1(k2_zfmisc_1(B,B))) ) )).
fof(dt_k25_polyform,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k25_pscomp_1,axiom,( ! [A] : ( 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))) ) )).
fof(dt_k25_qc_lang1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k25_quaterni,axiom,( ! [A] : ! [B] : ( ( v1_quaterni(A) & v1_quaterni(B) ) => m1_subset_1(k25_quaterni(A,B),k1_quaterni) ) )).
fof(dt_k25_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k25_seq_4(A),k1_zfmisc_1(k1_zfmisc_1(k12_seq_4(A)))) ) )).
fof(dt_k25_substut1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k25_turing_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k25_twoscomp,axiom,( 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))) )).
fof(dt_k25_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) )).
fof(dt_k25_valued_2,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k25_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) ) => ( v1_zf_lang(k25_zf_lang(A)) & m2_finseq_1(k25_zf_lang(A),k4_ordinal1) ) ) )).
fof(dt_k25_zmodul02,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_zmodul02(B,A) & m1_zmodul02(C,A) ) => m1_zmodul02(k25_zmodul02(A,B,C),A) ) )).
fof(dt_k26_abcmiz_1,axiom,( ! [A] : ( m1_subset_1(A,k20_abcmiz_1) => v7_ordinal1(k26_abcmiz_1(A)) ) )).
fof(dt_k26_aofa_i00,axiom,( ~ v1_finset_1(k26_aofa_i00) & v1_freealg(k26_aofa_i00) )).
fof(dt_k26_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ 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)) ) )).
fof(dt_k26_coh_sp,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k26_descip_1,axiom,( 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)))) )).
fof(dt_k26_fomodel1,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k26_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(dt_k26_fomodel4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k26_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k26_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) )).
fof(dt_k26_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => m1_subset_1(k26_grcat_1(A),k1_zfmisc_1(u1_struct_0(k25_grcat_1(A)))) ) )).
fof(dt_k26_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => m3_lexbfs(k26_lexbfs(A),A) ) )).
fof(dt_k26_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k26_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,k9_setfam_1(A)) & v7_ordinal1(C) ) => m1_subset_1(k26_mmlquery(A,B,C),k1_zfmisc_1(A)) ) )).
fof(dt_k26_modelc_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k26_modelc_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => m1_subset_1(k26_modelc_2(A,B),k25_modelc_2(A)) ) )).
fof(dt_k26_modelc_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k25_modelc_2(k43_modelc_2)) & v1_modelc_2(B) & m1_finseq_1(B,k4_ordinal1) & m1_orders_1(C,k6_partfun1(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)))) ) ) )).
fof(dt_k26_pcs_0,axiom,( ! [A] : ! [B] : ( l2_pcs_0(A) => l2_pcs_0(k26_pcs_0(A,B)) ) )).
fof(dt_k26_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => m1_subset_1(k26_qc_lang1(A),k1_qc_lang1(A)) ) )).
fof(dt_k26_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => v1_quaterni(k26_quaterni(A)) ) )).
fof(dt_k26_seq_4,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => ( v5_valued_0(k26_seq_4(A)) & m2_finseq_1(k26_seq_4(A),k1_numbers) ) ) )).
fof(dt_k26_sin_cos,axiom,( v1_funct_1(k26_sin_cos) & m1_subset_1(k26_sin_cos,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) )).
fof(dt_k26_substut1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k16_substut1(A)) ) => m2_finseq_1(k26_substut1(A,B),k2_qc_lang1(A)) ) )).
fof(dt_k26_turing_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k26_twoscomp,axiom,( 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))) )).
fof(dt_k26_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) )).
fof(dt_k26_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))))) ) ) )).
fof(dt_k26_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) ) => ( v1_zf_lang(k26_zf_lang(A)) & m2_finseq_1(k26_zf_lang(A),k4_ordinal1) ) ) )).
fof(dt_k27_abcmiz_1,axiom,( v1_msualg_1(k27_abcmiz_1) & v1_instalg1(k27_abcmiz_1) & v1_abcmiz_1(k27_abcmiz_1) & l1_msualg_1(k27_abcmiz_1) )).
fof(dt_k27_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) & v19_aofa_a00(C,A) & m1_subset_1(C,u1_struct_0(A)) ) => m1_msafree4(k27_aofa_a00(A,B,C),u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) ) )).
fof(dt_k27_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ 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)) ) )).
fof(dt_k27_coh_sp,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k27_descip_1,axiom,( ! [A] : ( 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)) ) )).
fof(dt_k27_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k27_fomodel4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k27_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) )).
fof(dt_k27_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => m3_cat_2(k27_grcat_1(A),k25_grcat_1(A)) ) )).
fof(dt_k27_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k27_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k27_modelc_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(A) => ( v1_funct_1(k27_modelc_2(A,B)) & v1_funct_2(k27_modelc_2(A,B),k4_ordinal1,A) & m1_subset_1(k27_modelc_2(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) ) )).
fof(dt_k27_modelc_3,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(A) & v5_modelc_3(A) & m1_finseq_1(A,k4_ordinal1) & v1_modelc_3(B,A) & l1_modelc_3(B,A) ) => m1_subset_1(k27_modelc_3(A,B),k1_zfmisc_1(k9_modelc_2)) ) )).
fof(dt_k27_qc_lang1,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k27_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => m1_subset_1(k27_quaterni(A),k1_quaterni) ) )).
fof(dt_k27_sin_cos,axiom,( v1_funct_1(k27_sin_cos) & m1_subset_1(k27_sin_cos,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) )).
fof(dt_k27_substut1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k16_substut1(A)) ) => m1_subset_1(k27_substut1(A,B),k16_substut1(A)) ) )).
fof(dt_k27_turing_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k27_twoscomp,axiom,( 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))) )).
fof(dt_k27_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) ) => ( v1_zf_lang(k27_zf_lang(A)) & m2_finseq_1(k27_zf_lang(A),k4_ordinal1) ) ) )).
fof(dt_k27_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ 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,k26_zmodul02(A)) ) => m1_zmodul02(k27_zmodul02(A,B),A) ) )).
fof(dt_k28_abcmiz_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k28_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) & v19_aofa_a00(C,A) & m1_subset_1(C,u1_struct_0(A)) ) => m1_msafree4(k28_aofa_a00(A,B,C),u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) ) )).
fof(dt_k28_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ 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)) ) )).
fof(dt_k28_coh_sp,axiom,( ! [A] : ( ~ 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)) ) )).
fof(dt_k28_descip_1,axiom,( 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)))) )).
fof(dt_k28_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ( v1_funct_1(k28_fomodel1(A)) & v1_funct_2(k28_fomodel1(A),k4_ordinal1,k9_setfam_1(k3_finseq_2(k15_fomodel1(A)))) & m1_subset_1(k28_fomodel1(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k3_finseq_2(k15_fomodel1(A)))))) ) ) )).
fof(dt_k28_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) ) )).
fof(dt_k28_fomodel4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k28_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) )).
fof(dt_k28_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => m1_subset_1(k28_grcat_1(A),k1_zfmisc_1(u1_struct_0(k27_grcat_1(A)))) ) )).
fof(dt_k28_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k28_modelc_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(C) ) => m1_subset_1(k28_modelc_2(A,B,C),k25_modelc_2(A)) ) )).
fof(dt_k28_modelc_3,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(A) & v5_modelc_3(A) & m1_finseq_1(A,k4_ordinal1) & v1_modelc_3(B,A) & l1_modelc_3(B,A) ) => m1_subset_1(k28_modelc_3(A,B),k1_zfmisc_1(k9_modelc_2)) ) )).
fof(dt_k28_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => m2_finseq_1(k28_polyform(A),k4_numbers) ) )).
fof(dt_k28_qc_lang1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k1_qc_lang1(A)) ) => m1_subset_1(k28_qc_lang1(A,B),k1_qc_lang1(A)) ) )).
fof(dt_k28_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => v1_xreal_0(k28_quaterni(A)) ) )).
fof(dt_k28_sin_cos,axiom,( v1_xreal_0(k28_sin_cos) )).
fof(dt_k28_substut1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k16_substut1(A)) ) => m1_subset_1(k28_substut1(A,B),k16_substut1(A)) ) )).
fof(dt_k28_turing_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k28_twoscomp,axiom,( 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))) )).
fof(dt_k28_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) ) => ( v1_zf_lang(k28_zf_lang(A)) & m2_finseq_1(k28_zf_lang(A),k4_ordinal1) ) ) )).
fof(dt_k28_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ 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_zmodul02(B,A) ) => m1_subset_1(k28_zmodul02(A,B),k26_zmodul02(A)) ) )).
fof(dt_k29_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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))))) ) )).
fof(dt_k29_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) & v19_aofa_a00(C,A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) ) => m1_msafree4(k29_aofa_a00(A,B,C,D),u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) ) )).
fof(dt_k29_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(dt_k29_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(A) & ~ 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) ) )).
fof(dt_k29_fomodel1,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k29_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ 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(k29_fomodel2(A,B)) ) )).
fof(dt_k29_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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(k30_fomodel2(A),k30_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))) ) ) )).
fof(dt_k29_fomodel4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k29_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ 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)) ) )).
fof(dt_k29_glib_000,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(dt_k29_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => m3_cat_2(k29_grcat_1(A),k27_grcat_1(A)) ) )).
fof(dt_k29_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k29_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k29_modelc_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k29_osafree,axiom,( ! [A] : ! [B] : ( ( ~ 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))))) ) ) )).
fof(dt_k29_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => m2_finseq_1(k29_polyform(A),k4_numbers) ) )).
fof(dt_k29_substut1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k16_substut1(A)) ) => m1_subset_1(k29_substut1(A,B),k16_substut1(A)) ) )).
fof(dt_k29_turing_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k29_twoscomp,axiom,( 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))) )).
fof(dt_k29_zmodul02,axiom,( ! [A] : ( ( ~ 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(k29_zmodul02(A)) & v1_funct_2(k29_zmodul02(A),k2_zfmisc_1(k26_zmodul02(A),k26_zmodul02(A)),k26_zmodul02(A)) & m1_subset_1(k29_zmodul02(A),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k26_zmodul02(A),k26_zmodul02(A)),k26_zmodul02(A)))) ) ) )).
fof(dt_k2_abcmiz_0,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k2_abian,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k2_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k2_absvalue(A)) ) )).
fof(dt_k2_aff_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k2_aff_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k2_afinsq_1,axiom,( ! [A] : ( ( 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(k4_ordinal1)) ) )).
fof(dt_k2_afinsq_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k2_afproj,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k2_afvect0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k2_algseq_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( v1_funct_1(k2_algseq_1(A,B)) & v1_funct_2(k2_algseq_1(A,B),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k2_algseq_1(A,B),A) & m1_subset_1(k2_algseq_1(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k2_algspec1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k2_algstr_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k2_algstr_3,axiom,( 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))) )).
fof(dt_k2_altcat_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k2_altcat_2,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(dt_k2_altcat_4,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(dt_k2_altcat_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(k7_altcat_1(B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(k7_altcat_1(B))))) ) => m1_subset_1(k2_altcat_5(A,B,C),u1_struct_0(k7_altcat_1(B))) ) )).
fof(dt_k2_ami_2,axiom,( m1_subset_1(k2_ami_2,k1_zfmisc_1(k1_ami_2)) )).
fof(dt_k2_ami_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k2_ami_4,axiom,( v1_funct_1(k2_ami_4) & m1_subset_1(k2_ami_4,k1_zfmisc_1(k2_zfmisc_1(k11_memstr_0(k7_card_1(2),k1_ami_3),k11_memstr_0(k7_card_1(2),k1_ami_3)))) )).
fof(dt_k2_ami_wstd,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k2_amistd_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k4_ordinal1)) ) )).
fof(dt_k2_amistd_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k2_analmetr,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) ) )).
fof(dt_k2_analoaf,axiom,( ! [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) ) => ( v1_analoaf(k2_analoaf(A)) & l1_analoaf(k2_analoaf(A)) ) ) )).
fof(dt_k2_analort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) )).
fof(dt_k2_anproj_1,axiom,( ! [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) & 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))) ) )).
fof(dt_k2_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k2_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(B,A) => ( v1_relat_1(k2_aofa_a00(A,B,C)) & v4_relat_1(k2_aofa_a00(A,B,C),A) & v1_funct_1(k2_aofa_a00(A,B,C)) & v1_partfun1(k2_aofa_a00(A,B,C),A) ) ) )).
fof(dt_k2_aofa_a01,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & l6_aofa_a00(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => m1_subset_1(k2_aofa_a01(A,B),k1_funct_1(u3_msualg_1(A,B),u8_aofa_a00(A))) ) )).
fof(dt_k2_aofa_i00,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k2_armstrng,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(k2_armstrng(A),k1_zfmisc_1(A)) ) )).
fof(dt_k2_arytm_0,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k2_arytm_0(A,B),k1_numbers) ) )).
fof(dt_k2_arytm_3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v7_ordinal1(A) & v3_ordinal1(B) & v7_ordinal1(B) ) => m1_subset_1(k2_arytm_3(A,B),k4_ordinal1) ) )).
fof(dt_k2_asympt_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v2_xxreal_0(B) & v1_xreal_0(B) ) => ( v1_funct_1(k2_asympt_0(A,B)) & v1_funct_2(k2_asympt_0(A,B),k4_ordinal1,k1_numbers) & v2_asympt_0(k2_asympt_0(A,B)) & m1_subset_1(k2_asympt_0(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k2_asympt_1,axiom,( v1_funct_1(k2_asympt_1) & v1_funct_2(k2_asympt_1,k4_ordinal1,k1_numbers) & m1_subset_1(k2_asympt_1,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) )).
fof(dt_k2_autalg_1,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k2_autgroup,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k2_bcialg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k2_bcialg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) => ( ~ v8_ordinal1(k2_bcialg_2(A,B)) & m1_subset_1(k2_bcialg_2(A,B),k4_ordinal1) ) ) )).
fof(dt_k2_bcialg_4,axiom,( l1_bcialg_4(k2_bcialg_4) )).
fof(dt_k2_bcialg_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => v1_xxreal_0(k2_bcialg_5(A,B,C,D)) ) )).
fof(dt_k2_bcialg_6,axiom,( ! [A] : ( ( ~ 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),k4_ordinal1),u1_struct_0(A)) & m1_subset_1(k2_bcialg_6(A),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_ordinal1),u1_struct_0(A)))) ) ) )).
fof(dt_k2_bhsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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)) ) => v1_xreal_0(k2_bhsp_1(A,B,C)) ) )).
fof(dt_k2_bhsp_2,axiom,( ! [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) & v8_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k2_bhsp_2(A,B)) & v1_funct_2(k2_bhsp_2(A,B),k4_ordinal1,k1_numbers) & m1_subset_1(k2_bhsp_2(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k2_bhsp_4,axiom,( ! [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) & v8_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => m1_subset_1(k2_bhsp_4(A,B),u1_struct_0(A)) ) )).
fof(dt_k2_bhsp_6,axiom,( ! [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) & 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)) ) )).
fof(dt_k2_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k2_binari_2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v8_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) ) ) )).
fof(dt_k2_binari_4,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(dt_k2_binarith,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => m1_subset_1(k2_binarith(A,B),k6_margrel1) ) )).
fof(dt_k2_binom,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k2_binop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(dt_k2_bintree2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree2(A) & v7_ordinal1(B) & ~ v8_ordinal1(B) ) => m2_finseq_1(k2_bintree2(A,B),k2_trees_2(A,B)) ) )).
fof(dt_k2_boolealg,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k2_boolmark,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k2_borsuk_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k2_borsuk_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k2_borsuk_5,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => m1_subset_1(k2_borsuk_5(A,B),k1_zfmisc_1(k1_numbers)) ) )).
fof(dt_k2_borsuk_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(dt_k2_borsuk_7,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k2_brouwer,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & 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)) ) )).
fof(dt_k2_bspace,axiom,( ~ 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) )).
fof(dt_k2_bvfunc26,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k2_bvfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k2_bvfunc_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) ) => m1_eqrel_1(k2_bvfunc_2(A,B),A) ) )).
fof(dt_k2_c0sp1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k2_c0sp2,axiom,( ! [A] : ( ( ~ 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))))) ) )).
fof(dt_k2_calcul_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k2_calcul_2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => m1_subset_1(k2_calcul_2(A,B),k1_zfmisc_1(k4_ordinal1)) ) )).
fof(dt_k2_cantor_1,axiom,( ! [A] : ! [B] : ( 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))) ) )).
fof(dt_k2_card_1,axiom,( ! [A] : v1_card_1(k2_card_1(A)) )).
fof(dt_k2_card_2,axiom,( ! [A] : ! [B] : ( ( v1_card_1(A) & v1_card_1(B) ) => v1_card_1(k2_card_2(A,B)) ) )).
fof(dt_k2_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k2_card_3(A)) & v1_funct_1(k2_card_3(A)) ) ) )).
fof(dt_k2_card_5,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k2_card_fil,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k2_card_fin,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) )).
fof(dt_k2_card_lar,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k2_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k2_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)))) ) ) )).
fof(dt_k2_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k2_cat_5,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k2_catalan2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => m1_subset_1(k2_catalan2(A,B),k1_zfmisc_1(k8_afinsq_1(k7_domain_1(k4_ordinal1,k5_numbers,1)))) ) )).
fof(dt_k2_catalg_1,axiom,( ! [A] : ( v1_msualg_1(k2_catalg_1(A)) & l1_msualg_1(k2_catalg_1(A)) ) )).
fof(dt_k2_cayldick,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k2_cayldick(A,B),u1_struct_0(A)) ) )).
fof(dt_k2_cayley,axiom,( ! [A] : ( v15_algstr_0(k2_cayley(A)) & v1_monoid_0(k2_cayley(A)) & l3_algstr_0(k2_cayley(A)) ) )).
fof(dt_k2_cc0sp1,axiom,( ! [A] : ( ~ 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)))) ) ) )).
fof(dt_k2_cc0sp2,axiom,( ! [A] : ( ( ~ 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))))) ) )).
fof(dt_k2_cfdiff_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k2_cfuncdom,axiom,( ! [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)))) ) )).
fof(dt_k2_cfunct_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k2_chain_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & 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)) ) ) )).
fof(dt_k2_chord,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) )).
fof(dt_k2_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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),k4_ordinal1) ) )).
fof(dt_k2_circcomb,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k2_circled1,axiom,( ! [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) & 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))) ) ) )).
fof(dt_k2_circuit1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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),k4_ordinal1),k5_relat_1(u3_msualg_1(A,B),k2_msafree2(A))) & m1_subset_1(D,k4_ordinal1) ) => m1_msafree2(k2_circuit1(A,B,C,D),A,B) ) )).
fof(dt_k2_circuit2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k2_ckspace1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) & ~ v1_xboole_0(C) & v1_pdiff_7(C,A) & m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) ) => m2_c0sp1(k2_ckspace1(A,B,C),k12_funcsdom(C)) ) )).
fof(dt_k2_classes2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) ) => m1_subset_1(k2_classes2(A,B),A) ) )).
fof(dt_k2_clopban1,axiom,( ! [A] : ! [B] : ( ( ~ 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))))) ) ) )).
fof(dt_k2_clopban2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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)) ) )).
fof(dt_k2_clopban3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_clopban2(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k2_clopban3(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k2_clopban4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(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) & 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),k4_ordinal1,u1_struct_0(B)) & m1_subset_1(k2_clopban4(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) ) )).
fof(dt_k2_closure1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k2_closure2,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k2_closure3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(dt_k2_clvect_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k2_clvect_2(A,B)) & v1_funct_2(k2_clvect_2(A,B),k4_ordinal1,k1_numbers) & m1_subset_1(k2_clvect_2(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k2_clvect_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v7_ordinal1(C) ) => m1_subset_1(k2_clvect_3(A,B,C),u1_struct_0(A)) ) )).
fof(dt_k2_coh_sp,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k2_cohsp_1,axiom,( ! [A] : m1_subset_1(k2_cohsp_1(A),k1_zfmisc_1(A)) )).
fof(dt_k2_combgras,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k2_compl_sp,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k2_complex2,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v1_xreal_0(B) ) => m1_subset_1(k2_complex2(A,B),k2_numbers) ) )).
fof(dt_k2_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => m1_subset_1(k2_complfld(A),u1_struct_0(k1_complfld)) ) )).
fof(dt_k2_complsp2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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)) ) )).
fof(dt_k2_compos_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k2_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => m1_subset_1(k2_compos_1(A),u1_compos_1(A)) ) )).
fof(dt_k2_compos_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_amistd_4(A) & l1_compos_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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),k4_ordinal1) & 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) ) ) )).
fof(dt_k2_comput_1,axiom,( ! [A] : ( ~ v1_xboole_0(k2_comput_1(A)) & m1_rfunct_3(k2_comput_1(A),k3_finseq_2(A),A) ) )).
fof(dt_k2_comseq_2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k2_comseq_3,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v7_ordinal1(B) ) => m1_subset_1(k2_comseq_3(A,B),k2_numbers) ) )).
fof(dt_k2_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(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))))) ) ) )).
fof(dt_k2_connsp_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k2_convex1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k2_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => m1_convex4(k2_convex4(A),A) ) )).
fof(dt_k2_convfun1,axiom,( ! [A] : ! [B] : ( ( ~ 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))))) ) ) )).
fof(dt_k2_cqc_lang,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) ) )).
fof(dt_k2_cqc_sim1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k2_csspace,axiom,( ! [A] : ( v1_funct_1(k2_csspace(A)) & v1_funct_2(k2_csspace(A),k4_ordinal1,k2_numbers) & m1_subset_1(k2_csspace(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) )).
fof(dt_k2_csspace3,axiom,( 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))) )).
fof(dt_k2_csspace4,axiom,( 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))) )).
fof(dt_k2_decomp_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k2_descip_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & m1_finseq_1(C,A) ) => m2_finseq_1(k2_descip_1(A,B,C),A) ) )).
fof(dt_k2_dickson,axiom,( ! [A] : ( 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))))) ) )).
fof(dt_k2_diff_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k2_diff_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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) ) => v1_xreal_0(k2_diff_2(A,B,C,D,E,F,G)) ) )).
fof(dt_k2_dilworth,axiom,( ! [A] : ( ( v4_dilworth(A) & l1_orders_2(A) ) => v7_ordinal1(k2_dilworth(A)) ) )).
fof(dt_k2_diraf,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ( v1_analoaf(k2_diraf(A)) & l1_analoaf(k2_diraf(A)) ) ) )).
fof(dt_k2_dist_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(A) & m1_finseq_1(B,A) ) => v7_ordinal1(k2_dist_1(A,B,C)) ) )).
fof(dt_k2_dist_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_setfam_1(B) & m1_subset_1(B,k6_dist_1(A)) ) => m1_dist_1(k2_dist_2(A,B),A) ) )).
fof(dt_k2_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k2_dtconstr,axiom,( ! [A] : ! [B] : ! [C] : ( m1_finseq_1(C,k2_zfmisc_1(A,B)) => m2_finseq_1(k2_dtconstr(A,B,C),A) ) )).
fof(dt_k2_dynkin,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(k2_dynkin(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) )).
fof(dt_k2_e_siec,axiom,( ! [A] : ( 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)) ) )).
fof(dt_k2_ec_pf_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k2_ec_pf_2,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k2_endalg,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k2_entropy1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(A)) ) => m2_finseq_1(k2_entropy1(A,B),A) ) )).
fof(dt_k2_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k2_euclid,axiom,( 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))) )).
fof(dt_k2_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => m1_subset_1(k2_euclid_3(A),k2_numbers) ) )).
fof(dt_k2_euclid_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k2_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => v1_xreal_0(k2_euclid_5(A)) ) )).
fof(dt_k2_euclid_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k2_euclid_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(dt_k2_euclid_8,axiom,( m2_finseq_2(k2_euclid_8,k1_numbers,k1_euclid(3)) )).
fof(dt_k2_euclidlp,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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)) ) )).
fof(dt_k2_euler_2,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k4_ordinal1) & v7_ordinal1(B) ) => m2_finseq_1(k2_euler_2(A,B),k4_ordinal1) ) )).
fof(dt_k2_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v3_ordinal1(k2_exchsort(A)) ) )).
fof(dt_k2_extpro_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(dt_k2_extreal1,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => m1_subset_1(k2_extreal1(A,B),k6_numbers) ) )).
fof(dt_k2_facirc_1,axiom,( 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))) )).
fof(dt_k2_facirc_2,axiom,( ! [A] : ( 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)) ) )).
fof(dt_k2_fdiff_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k2_fdiff_3,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => v1_xreal_0(k2_fdiff_3(A,B)) ) )).
fof(dt_k2_fdiff_9,axiom,( v1_funct_1(k2_fdiff_9) & m1_subset_1(k2_fdiff_9,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) )).
fof(dt_k2_ff_siec,axiom,( ! [A] : ( v1_petri(k2_ff_siec(A)) & v1_net_1(k2_ff_siec(A)) & l1_petri(k2_ff_siec(A)) ) )).
fof(dt_k2_fib_num,axiom,( v1_xreal_0(k2_fib_num) )).
fof(dt_k2_fib_num2,axiom,( v1_funct_1(k2_fib_num2) & v1_funct_2(k2_fib_num2,k4_ordinal1,k4_ordinal1) & m1_subset_1(k2_fib_num2,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) )).
fof(dt_k2_filter_0,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k2_filter_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k2_filter_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k2_finance1,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_funct_1(k2_finance1(A,B)) & v1_funct_2(k2_finance1(A,B),k4_ordinal1,k9_setfam_1(k1_numbers)) & m1_subset_1(k2_finance1(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k1_numbers)))) ) ) )).
fof(dt_k2_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k2_finseq_1(A),k1_zfmisc_1(k4_ordinal1)) ) )).
fof(dt_k2_finseq_2,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(dt_k2_finseq_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k2_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => m2_finseq_1(k2_finseq_4(A,B,C),A) ) )).
fof(dt_k2_finseq_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) & m1_subset_1(C,A) ) => m2_finseq_1(k2_finseq_5(A,B,C),A) ) )).
fof(dt_k2_finseq_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k2_finseq_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k2_finseq_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k2_finseqop,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(dt_k2_finsop_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) & m1_finseq_1(C,A) ) => ( v1_funct_1(k2_finsop_1(A,B,C)) & v1_funct_2(k2_finsop_1(A,B,C),k4_ordinal1,A) & m1_subset_1(k2_finsop_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) ) )).
fof(dt_k2_finsub_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k2_fintopo2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k2_fintopo3,axiom,( ! [A] : ! [B] : ( ( ~ 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),k4_ordinal1,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(k2_fintopo3(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(u1_struct_0(A))))) ) ) )).
fof(dt_k2_fintopo4,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ v2_struct_0(k2_fintopo4(A)) & l1_orders_2(k2_fintopo4(A)) ) ) )).
fof(dt_k2_fintopo5,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => 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))))) ) )).
fof(dt_k2_flang_1,axiom,( ! [A] : m1_subset_1(k2_flang_1(A),k3_catalan2(A)) )).
fof(dt_k2_flang_2,axiom,( ! [A] : ! [B] : ( 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))) ) )).
fof(dt_k2_flang_3,axiom,( ! [A] : ! [B] : ( 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))) ) )).
fof(dt_k2_fomodel0,axiom,( ! [A] : ( v1_funct_1(k2_fomodel0(A)) & v1_funct_2(k2_fomodel0(A),k2_zfmisc_1(A,A),A) & m1_subset_1(k2_fomodel0(A),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),A))) ) )).
fof(dt_k2_fomodel2,axiom,( ! [A] : ( ~ 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))) ) ) )).
fof(dt_k2_fomodel3,axiom,( ! [A] : ! [B] : ( ( ~ 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),k3_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(k3_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))))) ) ) )).
fof(dt_k2_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k2_fomodel4(A,B,C),k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) ) )).
fof(dt_k2_frechet,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => m1_subset_1(k2_frechet(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k2_frechet2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => m1_subset_1(k2_frechet2(A,B),u1_struct_0(A)) ) )).
fof(dt_k2_freealg,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,k4_ordinal1) ) => 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))))) ) )).
fof(dt_k2_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k2_fscirc_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k2_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k2_fsm_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k2_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k2_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( 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)) ) )).
fof(dt_k2_funcsdom,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) )).
fof(dt_k2_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k2_funct_1(A)) & v1_funct_1(k2_funct_1(A)) ) ) )).
fof(dt_k2_funct_2,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k2_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k2_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k2_funct_4(A)) & v1_funct_1(k2_funct_4(A)) ) ) )).
fof(dt_k2_funct_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k2_funct_5(A)) & v1_funct_1(k2_funct_5(A)) ) ) )).
fof(dt_k2_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ( v1_relat_1(k2_funct_6(A)) & v1_funct_1(k2_funct_6(A)) ) ) )).
fof(dt_k2_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_finseq_1(B,A) & v7_ordinal1(C) & m1_subset_1(D,A) ) => m2_finseq_1(k2_funct_7(A,B,C,D),A) ) )).
fof(dt_k2_functor2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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))) ) )).
fof(dt_k2_functor3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(dt_k2_fuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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(k5_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))) ) ) )).
fof(dt_k2_fuzzy_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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(k5_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))) ) ) )).
fof(dt_k2_fuzzy_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & v5_relat_1(D,k1_rcomp_1(k5_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(k5_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(k2_fuzzy_4(A,B,C,D,E,F,G),k1_rcomp_1(k5_numbers,1)) & v1_funct_1(k2_fuzzy_4(A,B,C,D,E,F,G)) & v1_funct_2(k2_fuzzy_4(A,B,C,D,E,F,G),B,k1_numbers) & m1_subset_1(k2_fuzzy_4(A,B,C,D,E,F,G),k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) ) )).
fof(dt_k2_fvaluat1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k2_fvsum_1,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k2_gcd_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k2_genealg1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k4_ordinal1) & m1_subset_1(E,k4_ordinal1) ) => m2_finseq_1(k2_genealg1(A,B,C,D,E),k3_card_3(A)) ) )).
fof(dt_k2_geomtrap,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) => v1_xreal_0(k2_geomtrap(A,B,C,D)) ) )).
fof(dt_k2_gfacirc1,axiom,( 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))) )).
fof(dt_k2_gfacirc2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k2_glib_000,axiom,( m1_subset_1(k2_glib_000,k4_ordinal1) )).
fof(dt_k2_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => m3_glib_001(k2_glib_001(A,B,C,D),A) ) )).
fof(dt_k2_glib_002,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) ) )).
fof(dt_k2_glib_003,axiom,( m1_subset_1(k2_glib_003,k4_ordinal1) )).
fof(dt_k2_glib_004,axiom,( ~ v1_xboole_0(k2_glib_004) & v1_finset_1(k2_glib_004) & m1_subset_1(k2_glib_004,k1_zfmisc_1(k4_ordinal1)) )).
fof(dt_k2_glib_005,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) )).
fof(dt_k2_goboard1,axiom,( ! [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) => m2_finseq_1(k2_goboard1(A),k1_numbers) ) )).
fof(dt_k2_goboard2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ( v1_matrix_0(k2_goboard2(A)) & m2_finseq_1(k2_goboard2(A),k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) ) )).
fof(dt_k2_goboard5,axiom,( ! [A] : ! [B] : ( ( v1_matrix_0(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)))) ) )).
fof(dt_k2_goboard9,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k2_gobrd13,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) & v7_ordinal1(C) ) => m1_subset_1(k2_gobrd13(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) )).
fof(dt_k2_goedelcp,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k2_gr_cy_1,axiom,( ~ v2_struct_0(k2_gr_cy_1) & v15_algstr_0(k2_gr_cy_1) & l3_algstr_0(k2_gr_cy_1) )).
fof(dt_k2_graph_1,axiom,( ! [A] : ! [B] : ( ( l1_graph_1(A) & m1_subset_1(B,u4_struct_0(A)) ) => m1_subset_1(k2_graph_1(A,B),u1_struct_0(A)) ) )).
fof(dt_k2_graph_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_finseq_1(B,A) & v7_ordinal1(C) & v7_ordinal1(D) ) => m2_finseq_1(k2_graph_2(A,B,C,D),A) ) )).
fof(dt_k2_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k2_graph_5,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k2_graphsp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) & m1_finseq_1(C,k1_numbers) & v1_xreal_0(D) ) => m2_finseq_1(k2_graphsp(A,B,C,D),k1_numbers) ) )).
fof(dt_k2_grcat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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))) ) ) )).
fof(dt_k2_groeb_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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(k12_polynom1(A,C)))) ) => m1_subset_1(k2_groeb_1(A,B,C,D),k1_zfmisc_1(k15_pre_poly(A))) ) )).
fof(dt_k2_groeb_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k2_groeb_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k2_group_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k2_group_11,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k2_group_12,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k2_group_14,axiom,( ! [A] : ( v7_ordinal1(A) => l2_algstr_0(k2_group_14(A)) ) )).
fof(dt_k2_group_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k2_group_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k2_group_4,axiom,( ! [A] : ( v1_int_1(A) => m1_subset_1(k2_group_4(A),k4_numbers) ) )).
fof(dt_k2_group_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k2_group_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k2_group_7,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k2_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) )).
fof(dt_k2_groupp_1,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) ) )).
fof(dt_k2_grsolv_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(dt_k2_hahnban1,axiom,( m1_subset_1(k2_hahnban1,u1_struct_0(k1_complfld)) )).
fof(dt_k2_hallmar1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_finset_1(A) & m1_finseq_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k4_ordinal1) ) => m2_finseq_1(k2_hallmar1(A,B,C,D),k1_zfmisc_1(A)) ) )).
fof(dt_k2_helly,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) ) )).
fof(dt_k2_henmodel,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k2_hermitan,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k2_heyting1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k7_normform(A)) => m2_subset_1(k2_heyting1(A,B),k5_finsub_1(k7_normform(A)),k8_normform(A)) ) )).
fof(dt_k2_heyting2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k2_heyting3,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => m1_subset_1(k2_heyting3(A,B),k4_partfun1(k4_ordinal1,k6_domain_1(k4_ordinal1,B))) ) )).
fof(dt_k2_hilbasis,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => m2_subset_1(k2_hilbasis(A,B),k14_pre_poly(A),k15_pre_poly(A)) ) )).
fof(dt_k2_hilbert1,axiom,( m1_subset_1(k2_hilbert1,k1_hilbert1) )).
fof(dt_k2_hilbert2,axiom,( v1_relat_1(k2_hilbert2) & v4_relat_1(k2_hilbert2,k1_hilbert1) & v1_funct_1(k2_hilbert2) & v1_partfun1(k2_hilbert2,k1_hilbert1) )).
fof(dt_k2_hilbert3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( 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) ) ) )).
fof(dt_k2_hurwitz,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => v1_int_1(k2_hurwitz(A,B)) ) )).
fof(dt_k2_idea_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(k2_idea_1(A,B,C),A) & m2_finseq_1(k2_idea_1(A,B,C),k6_margrel1) ) ) )).
fof(dt_k2_incproj,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k2_incsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k2_index_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k2_instalg1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k2_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => v1_int_1(k2_int_1(A)) ) )).
fof(dt_k2_int_2,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_int_1(B) ) => v7_ordinal1(k2_int_2(A,B)) ) )).
fof(dt_k2_int_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_int_3)) => m1_subset_1(k2_int_3(A),u1_struct_0(k1_int_3)) ) )).
fof(dt_k2_int_5,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v7_ordinal1(B) & v1_int_2(B) ) => v1_int_1(k2_int_5(A,B)) ) )).
fof(dt_k2_int_6,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k2_int_7,axiom,( ! [A] : ( ( 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)))) ) ) )).
fof(dt_k2_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k2_int_8(A),k1_zfmisc_1(k4_ordinal1)) ) )).
fof(dt_k2_integr10,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & v1_xreal_0(B) & v1_xreal_0(C) ) => v1_xreal_0(k2_integr10(A,B,C)) ) )).
fof(dt_k2_integr15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k4_ordinal1,k1_integra1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) & m2_integr15(D,A,B,C) & m1_subset_1(E,k4_ordinal1) ) => m1_integr15(k2_integr15(A,B,C,D,E),A,B,k2_integra2(A,C,E)) ) )).
fof(dt_k2_integr16,axiom,( ! [A] : ( m1_finseq_1(A,k2_numbers) => m2_finseq_1(k2_integr16(A),k1_numbers) ) )).
fof(dt_k2_integr18,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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,k4_ordinal1,k1_integra1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(B)))) & m2_integr18(E,A,B,C,D) & v7_ordinal1(F) ) => m1_integr18(k2_integr18(A,B,C,D,E,F),A,B,C,k2_integra2(B,D,F)) ) )).
fof(dt_k2_integr1c,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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))) & 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)) ) )).
fof(dt_k2_integra1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k2_integra2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_integra1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) & v7_ordinal1(C) ) => m1_integra1(k2_integra2(A,B,C),A) ) )).
fof(dt_k2_integra3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_integra1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) ) => ( v1_funct_1(k2_integra3(A,B)) & v1_funct_2(k2_integra3(A,B),k4_ordinal1,k1_numbers) & m1_subset_1(k2_integra3(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k2_integra5,axiom,( ! [A] : ! [B] : ( ( ~ 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_xreal_0(k2_integra5(A,B)) ) )).
fof(dt_k2_integra9,axiom,( ! [A] : ! [B] : ( ( ~ 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_xreal_0(k2_integra9(A,B)) ) )).
fof(dt_k2_interva1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => m1_interva1(k2_interva1(A,B,C),A) ) )).
fof(dt_k2_intpro_1,axiom,( m1_subset_1(k2_intpro_1,k1_intpro_1) )).
fof(dt_k2_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_funct_1(k2_irrat_1(A)) & v1_funct_2(k2_irrat_1(A),k4_ordinal1,k1_numbers) & m1_subset_1(k2_irrat_1(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k2_isocat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) )).
fof(dt_k2_isocat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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),k9_nattra_1(A,B),B) ) )).
fof(dt_k2_jgraph_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k2_jgraph_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))))) ) ) )).
fof(dt_k2_jgraph_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) )).
fof(dt_k2_jordan19,axiom,( ! [A] : ( ( 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),k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(k2_jordan19(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))))) ) ) )).
fof(dt_k2_jordan1e,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k2_jordan1h,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,k3_finseq_2(A)) ) => m1_subset_1(k2_jordan1h(A,B),k1_zfmisc_1(A)) ) )).
fof(dt_k2_jordan21,axiom,( ! [A] : ( 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))) ) )).
fof(dt_k2_jordan2c,axiom,( ! [A] : ! [B] : ( ( 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)))) ) )).
fof(dt_k2_jordan3,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k2_jordan5c,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k2_jordan5d,axiom,( ! [A] : ( ( ~ 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))) ) => v7_ordinal1(k2_jordan5d(A)) ) )).
fof(dt_k2_jordan9,axiom,( ! [A] : ! [B] : ( ( ~ 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(k2_jordan9(A,B)) & ~ v3_funct_1(k2_jordan9(A,B)) & v1_finseq_6(k2_jordan9(A,B),u1_struct_0(k15_euclid(2))) & v1_topreal1(k2_jordan9(A,B)) & v2_topreal1(k2_jordan9(A,B)) & v1_goboard5(k2_jordan9(A,B)) & v2_goboard5(k2_jordan9(A,B)) & v1_sprect_2(k2_jordan9(A,B)) & m2_finseq_1(k2_jordan9(A,B),u1_struct_0(k15_euclid(2))) ) ) )).
fof(dt_k2_jordan_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) )).
fof(dt_k2_knaster,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k2_kolmog01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k2_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => m1_subset_1(k2_kurato_0(A,B),k1_zfmisc_1(A)) ) )).
fof(dt_k2_kurato_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k2_kurato_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) & v7_ordinal1(C) ) => m1_subset_1(k2_kurato_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k2_laplace,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) & ~ 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) & v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(D),C,C) & m1_finseq_1(E,k3_finseq_2(u1_struct_0(D))) ) => ( v1_matrix_0(k2_laplace(A,B,C,D,E)) & v2_matrix_0(k2_laplace(A,B,C,D,E),u1_struct_0(D),k7_nat_d(C,1),k7_nat_d(C,1)) & m2_finseq_1(k2_laplace(A,B,C,D,E),k3_finseq_2(u1_struct_0(D))) ) ) )).
fof(dt_k2_latsubgr,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k2_lattice2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k2_lattice3,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k2_lattice4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k2_lattice5,axiom,( ! [A] : ! [B] : ( ( ~ 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),k4_ordinal1) ) )).
fof(dt_k2_lattice6,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k2_lattice7,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k2_lattice8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k2_lattices,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k2_lfuzzy_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k2_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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(k5_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))) ) ) )).
fof(dt_k2_limfunc1,axiom,( ! [A] : ( v1_xreal_0(A) => m1_subset_1(k2_limfunc1(A),k1_zfmisc_1(k1_numbers)) ) )).
fof(dt_k2_limfunc2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & v1_xreal_0(B) ) => v1_xreal_0(k2_limfunc2(A,B)) ) )).
fof(dt_k2_lmod_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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))) ) )).
fof(dt_k2_lopban_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))))) ) ) )).
fof(dt_k2_lopban_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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)) ) )).
fof(dt_k2_lopban_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_lopban_2(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k2_lopban_3(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k2_lopban_4,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_funct_1(k2_lopban_4(A)) & v1_funct_2(k2_lopban_4(A),k4_ordinal1,k1_numbers) & m1_subset_1(k2_lopban_4(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k2_lopban_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(k16_lopban_1(A,B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,u1_struct_0(B)) & m1_subset_1(k2_lopban_5(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) ) )).
fof(dt_k2_lopban_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & l1_normsp_1(A) & ~ v2_struct_0(B) & l1_normsp_1(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( v1_funct_1(k2_lopban_7(A,B,C,D)) & v1_funct_2(k2_lopban_7(A,B,C,D),k4_ordinal1,u1_struct_0(k7_prvect_3(A,B))) & m1_subset_1(k2_lopban_7(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k7_prvect_3(A,B))))) ) ) )).
fof(dt_k2_lopclset,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k2_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ v1_xboole_0(k2_lp_space(A)) & m1_subset_1(k2_lp_space(A),k1_zfmisc_1(u1_struct_0(k6_rsspace))) ) ) )).
fof(dt_k2_lpspace1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) )).
fof(dt_k2_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v2_xxreal_0(D) & v1_xreal_0(D) ) => ( ~ 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)) ) ) )).
fof(dt_k2_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => m1_subset_1(k2_ltlaxio1(A),k1_hilbert1) ) )).
fof(dt_k2_ltlaxio2,axiom,( ! [A] : ( m1_finseq_1(A,k1_hilbert1) => m2_finseq_1(k2_ltlaxio2(A),k1_hilbert1) ) )).
fof(dt_k2_mathmorp,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k2_matrix10,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m1_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( v1_matrix_0(k2_matrix10(A,B)) & v2_matrix_0(k2_matrix10(A,B),k1_numbers,A,A) & m2_finseq_1(k2_matrix10(A,B),k3_finseq_2(k1_numbers)) ) ) )).
fof(dt_k2_matrix11,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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,k3_matrix_2(k1_nat_1(A,2))) ) => m1_subset_1(k2_matrix11(A,B,C),u1_struct_0(B)) ) )).
fof(dt_k2_matrix12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & ~ 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) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(C))) & v7_ordinal1(E) & m1_subset_1(F,u1_struct_0(C)) ) => ( v1_matrix_0(k2_matrix12(A,B,C,D,E,F)) & v2_matrix_0(k2_matrix12(A,B,C,D,E,F),u1_struct_0(C),A,B) & m2_finseq_1(k2_matrix12(A,B,C,D,E,F),k3_finseq_2(u1_struct_0(C))) ) ) )).
fof(dt_k2_matrix13,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & ~ 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) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(C))) & m1_subset_1(E,u1_struct_0(C)) ) => ( v1_matrix_0(k2_matrix13(A,B,C,D,E)) & v2_matrix_0(k2_matrix13(A,B,C,D,E),u1_struct_0(C),A,B) & m2_finseq_1(k2_matrix13(A,B,C,D,E),k3_finseq_2(u1_struct_0(C))) ) ) )).
fof(dt_k2_matrix14,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) & m1_subset_1(B,k4_ordinal1) ) => m2_finseq_2(k2_matrix14(A,B),u1_struct_0(A),k4_finseq_2(B,u1_struct_0(A))) ) )).
fof(dt_k2_matrix15,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) ) => ( v1_matrix_0(k2_matrix15(A,B)) & v2_matrix_0(k2_matrix15(A,B),A,1,k3_finseq_1(B)) & m2_finseq_1(k2_matrix15(A,B),k3_finseq_2(A)) ) ) )).
fof(dt_k2_matrix16,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) ) => ( v1_matrix_0(k2_matrix16(A,B)) & v2_matrix_0(k2_matrix16(A,B),A,k3_finseq_1(B),k3_finseq_1(B)) & m2_finseq_1(k2_matrix16(A,B),k3_finseq_2(A)) ) ) )).
fof(dt_k2_matrix_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) & v7_ordinal1(B) ) => ( v1_matrix_0(k2_matrix_1(A,B)) & v2_matrix_0(k2_matrix_1(A,B),u1_struct_0(A),B,B) & m2_finseq_1(k2_matrix_1(A,B),k3_finseq_2(u1_struct_0(A))) ) ) )).
fof(dt_k2_matrix_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_matrix_2(A) ) => m1_subset_1(k2_matrix_2(A),k4_ordinal1) ) )).
fof(dt_k2_matrix_3,axiom,( ! [A] : ! [B] : ( ( ~ 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_0(B) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ( v1_matrix_0(k2_matrix_3(A,B)) & m2_finseq_1(k2_matrix_3(A,B),k3_finseq_2(u1_struct_0(A))) ) ) )).
fof(dt_k2_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(u1_struct_0(k1_complfld))) ) => ( v1_matrix_0(k2_matrix_5(A)) & m2_finseq_1(k2_matrix_5(A),k3_finseq_2(k2_numbers)) ) ) )).
fof(dt_k2_matrix_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => m1_subset_1(k2_matrix_9(A,B,C),u1_struct_0(B)) ) )).
fof(dt_k2_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ( v1_matrix_0(k2_matrixc1(A)) & m2_finseq_1(k2_matrixc1(A),k3_finseq_2(k2_numbers)) ) ) )).
fof(dt_k2_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_matrixj1(B,A) & m1_finseq_1(B,k3_finseq_2(k3_finseq_2(A))) ) => ( v1_matrix_0(k2_matrixj1(A,B,C)) & m2_finseq_1(k2_matrixj1(A,B,C),k3_finseq_2(A)) ) ) )).
fof(dt_k2_matrixj2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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_0(k2_matrixj2(A,B,C)) & v2_matrix_0(k2_matrixj2(A,B,C),u1_struct_0(A),C,C) & v1_matrix_2(k2_matrixj2(A,B,C),C,A) & m2_finseq_1(k2_matrixj2(A,B,C),k3_finseq_2(u1_struct_0(A))) ) ) )).
fof(dt_k2_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( v1_matrix_0(k2_matrixr1(A)) & m2_finseq_1(k2_matrixr1(A),k3_finseq_2(k1_numbers)) ) ) )).
fof(dt_k2_matrixr2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m1_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( v1_matrix_0(k2_matrixr2(A,B)) & v2_matrix_0(k2_matrixr2(A,B),u1_struct_0(k2_vectsp_1),A,A) & m2_finseq_1(k2_matrixr2(A,B),k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) ) )).
fof(dt_k2_matrlin,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) ) => ( v1_matrix_0(k2_matrlin(A,B)) & v2_matrix_0(k2_matrlin(A,B),A,1,k3_finseq_1(B)) & m2_finseq_1(k2_matrlin(A,B),k3_finseq_2(A)) ) ) )).
fof(dt_k2_matroid0,axiom,( ! [A] : ( v1_pre_topc(k2_matroid0(A)) & l1_pre_topc(k2_matroid0(A)) ) )).
fof(dt_k2_matrprob,axiom,( ! [A] : ( v1_xreal_0(A) => m2_finseq_1(k2_matrprob(A),k1_numbers) ) )).
fof(dt_k2_matrtop1,axiom,( ! [A] : ( m1_finseq_1(A,u1_struct_0(k2_vectsp_1)) => m2_finseq_1(k2_matrtop1(A),k1_numbers) ) )).
fof(dt_k2_matrtop3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & v1_xreal_0(B) & v7_ordinal1(C) & v7_ordinal1(D) ) => ( v1_matrix_0(k2_matrtop3(A,B,C,D)) & v2_matrix_0(k2_matrtop3(A,B,C,D),u1_struct_0(k2_vectsp_1),A,A) & v1_matrix_6(k2_matrtop3(A,B,C,D),A,k2_vectsp_1) & m2_finseq_1(k2_matrtop3(A,B,C,D),k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) ) )).
fof(dt_k2_mboolean,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(dt_k2_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k2_measure1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k2_measure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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) ) )).
fof(dt_k2_measure3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( ~ v1_xboole_0(k2_measure3(A,B,C)) & m1_subset_1(k2_measure3(A,B,C),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) )).
fof(dt_k2_measure4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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) ) )).
fof(dt_k2_measure5,axiom,( ! [A] : ( v2_membered(A) => m1_subset_1(k2_measure5(A),k6_numbers) ) )).
fof(dt_k2_measure6,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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_measure6(A,B,C)) & v1_funct_2(k2_measure6(A,B,C),k9_setfam_1(B),k9_setfam_1(A)) & m1_subset_1(k2_measure6(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(B),k9_setfam_1(A)))) ) ) )).
fof(dt_k2_measure7,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & m1_measure7(B,A) & m1_subset_1(C,k4_ordinal1) ) => ( v6_xxreal_2(k2_measure7(A,B,C)) & m1_subset_1(k2_measure7(A,B,C),k1_zfmisc_1(k1_numbers)) ) ) )).
fof(dt_k2_measure8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_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,k6_numbers))) & m2_measure8(D,A,B) ) => ( v1_funct_1(k2_measure8(A,B,C,D)) & v1_funct_2(k2_measure8(A,B,C,D),k4_ordinal1,k6_numbers) & m1_subset_1(k2_measure8(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) ) )).
fof(dt_k2_member_1,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => m1_subset_1(k2_member_1(A),k6_numbers) ) )).
fof(dt_k2_memstr_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k2_mesfun6c,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k2_mesfun7c,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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,k6_numbers))) ) ) )).
fof(dt_k2_mesfun9c,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( v1_funct_1(k2_mesfun9c(A,B)) & v1_funct_2(k2_mesfun9c(A,B),k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(k2_mesfun9c(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) ) )).
fof(dt_k2_mesfunc2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( v1_funct_1(k2_mesfunc2(A,B)) & m1_subset_1(k2_mesfunc2(A,B),k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) ) )).
fof(dt_k2_mesfunc5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => m1_subset_1(k2_mesfunc5(A),k6_numbers) ) )).
fof(dt_k2_mesfunc6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_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),k6_numbers) ) )).
fof(dt_k2_mesfunc7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_valued_0(A) ) => m1_subset_1(k2_mesfunc7(A),k6_numbers) ) )).
fof(dt_k2_mesfunc8,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ( v1_funct_1(k2_mesfunc8(A,B)) & m1_subset_1(k2_mesfunc8(A,B),k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) ) )).
fof(dt_k2_mesfunc9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_valued_0(A) ) => ( v1_funct_1(k2_mesfunc9(A)) & v1_funct_2(k2_mesfunc9(A),k4_ordinal1,k6_numbers) & m1_subset_1(k2_mesfunc9(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) ) )).
fof(dt_k2_metric_1,axiom,( v1_funct_1(k2_metric_1) & v1_funct_2(k2_metric_1,k2_zfmisc_1(1,1),k1_numbers) & m1_subset_1(k2_metric_1,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(1,1),k1_numbers))) )).
fof(dt_k2_metric_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,k1_numbers) & m1_subset_1(k2_metric_6(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k2_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => m1_pre_topc(k2_mfold_1(A),k15_euclid(A)) ) )).
fof(dt_k2_mfold_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) )).
fof(dt_k2_midsp_1,axiom,( l1_midsp_1(k2_midsp_1) )).
fof(dt_k2_midsp_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(dt_k2_midsp_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_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))) ) )).
fof(dt_k2_mmlquer2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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_mmlquer2(A,B,C),k1_zfmisc_1(k2_zfmisc_1(A,A))) ) )).
fof(dt_k2_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k2_mod_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) ) )).
fof(dt_k2_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ( v36_algstr_0(k2_mod_4(A)) & l6_algstr_0(k2_mod_4(A)) ) ) )).
fof(dt_k2_modal_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k2_modelc_2,axiom,( ! [A] : ( v7_ordinal1(A) => m2_finseq_1(k2_modelc_2(A),k4_ordinal1) ) )).
fof(dt_k2_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => m1_subset_1(k2_modelc_3(A),k1_zfmisc_1(k1_modelc_3(A))) ) )).
fof(dt_k2_moebius1,axiom,( ! [A] : ( v7_ordinal1(A) => v1_xreal_0(k2_moebius1(A)) ) )).
fof(dt_k2_monoid_0,axiom,( ~ v2_struct_0(k2_monoid_0) & l3_algstr_0(k2_monoid_0) )).
fof(dt_k2_morph_01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k2_msafree1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ( v3_msualg_1(k2_msafree1(A),A) & l3_msualg_1(k2_msafree1(A),A) ) ) )).
fof(dt_k2_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => m1_subset_1(k2_msafree2(A),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k2_msafree3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k2_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) => ( v1_funct_1(k2_msafree4(A,B,C,D,E)) & v1_funct_2(k2_msafree4(A,B,C,D,E),k1_funct_1(B,E),k1_funct_1(C,E)) & m1_subset_1(k2_msafree4(A,B,C,D,E),k1_zfmisc_1(k2_zfmisc_1(k1_funct_1(B,E),k1_funct_1(C,E)))) ) ) )).
fof(dt_k2_msalimit,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k2_msaterm,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k2_msscyc_2,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_k2_mssubfam,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) )).
fof(dt_k2_msualg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k2_msualg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k2_msualg_3,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k2_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k2_msualg_5,axiom,( ! [A] : ( ~ 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)) ) )).
fof(dt_k2_msualg_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k2_msualg_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(dt_k2_msuhom_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) )).
fof(dt_k2_multop_1,axiom,( ! [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_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) ) )).
fof(dt_k2_mycielsk,axiom,( ! [A] : ( ( v1_mycielsk(A) & l1_orders_2(A) ) => v7_ordinal1(k2_mycielsk(A)) ) )).
fof(dt_k2_nagata_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)))) ) )).
fof(dt_k2_nagata_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k2_nat_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k4_ordinal1) ) => m1_subset_1(k2_nat_1(A,B),k4_ordinal1) ) )).
fof(dt_k2_nat_3,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k1_numbers) & v7_ordinal1(B) ) => m2_finseq_1(k2_nat_3(A,B),k1_numbers) ) )).
fof(dt_k2_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_funct_1(k2_nat_5(A)) & v1_funct_2(k2_nat_5(A),k4_ordinal1,k4_ordinal1) & m1_subset_1(k2_nat_5(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) ) )).
fof(dt_k2_nat_d,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => v7_ordinal1(k2_nat_d(A,B)) ) )).
fof(dt_k2_nat_lat,axiom,( v1_funct_1(k2_nat_lat) & v1_funct_2(k2_nat_lat,k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1) & m1_subset_1(k2_nat_lat,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1))) )).
fof(dt_k2_nattra_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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(k2_nattra_1(A,B,C,D,E,F),B,k8_cat_1(A,B,C,F),k8_cat_1(A,B,D,F)) ) )).
fof(dt_k2_ndiff_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_funct_1(k2_ndiff_1(A,B,C)) & v1_funct_2(k2_ndiff_1(A,B,C),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k2_ndiff_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k2_ndiff_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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))) ) )).
fof(dt_k2_ndiff_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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)))) ) ) )).
fof(dt_k2_ndiff_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & 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)))) ) ) )).
fof(dt_k2_ndiff_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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))) ) )).
fof(dt_k2_neckla_2,axiom,( ! [A] : ! [B] : ( ( l1_orders_2(A) & l1_orders_2(B) ) => ( v1_orders_2(k2_neckla_2(A,B)) & l1_orders_2(k2_neckla_2(A,B)) ) ) )).
fof(dt_k2_necklace,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_orders_2(k2_necklace(A)) & l1_orders_2(k2_necklace(A)) ) ) )).
fof(dt_k2_nfcont_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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)))) ) ) )).
fof(dt_k2_normform,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k2_normsp_0,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_normsp_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => v1_xreal_0(k2_normsp_0(A,B)) ) )).
fof(dt_k2_normsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k2_normsp_1(A,B,C)) & v1_funct_2(k2_normsp_1(A,B,C),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k2_normsp_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k2_normsp_2,axiom,( ! [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) & 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)) ) ) )).
fof(dt_k2_ntalgo_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k2_numeral1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => ( v1_relat_1(k2_numeral1(A,B)) & v5_relat_1(k2_numeral1(A,B),k4_ordinal1) & v1_funct_1(k2_numeral1(A,B)) & v5_ordinal1(k2_numeral1(A,B)) & v1_finset_1(k2_numeral1(A,B)) ) ) )).
fof(dt_k2_openlatt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k2_oposet_1,axiom,( v3_qmax_1(k2_oposet_1) & l2_qmax_1(k2_oposet_1) )).
fof(dt_k2_oppcat_1,axiom,( ! [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) & 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)) ) ) )).
fof(dt_k2_ordeq_01,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_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) & l1_normsp_1(B) ) => ( ~ v2_struct_0(k2_ordeq_01(A,B)) & v13_algstr_0(k2_ordeq_01(A,B)) & v1_rlvect_1(k2_ordeq_01(A,B)) & v2_rlvect_1(k2_ordeq_01(A,B)) & v3_rlvect_1(k2_ordeq_01(A,B)) & v4_rlvect_1(k2_ordeq_01(A,B)) & v5_rlvect_1(k2_ordeq_01(A,B)) & v6_rlvect_1(k2_ordeq_01(A,B)) & v7_rlvect_1(k2_ordeq_01(A,B)) & v8_rlvect_1(k2_ordeq_01(A,B)) & l1_rlvect_1(k2_ordeq_01(A,B)) ) ) )).
fof(dt_k2_orders_1,axiom,( ! [A] : ( v1_relat_2(k2_orders_1(A)) & v4_relat_2(k2_orders_1(A)) & v8_relat_2(k2_orders_1(A)) & v1_partfun1(k2_orders_1(A),A) & m1_subset_1(k2_orders_1(A),k1_zfmisc_1(k2_zfmisc_1(A,A))) ) )).
fof(dt_k2_orders_2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k2_ordinal2,axiom,( ! [A] : v3_ordinal1(k2_ordinal2(A)) )).
fof(dt_k2_ordinal4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ( v3_ordinal1(k2_ordinal4(A)) & m1_subset_1(k2_ordinal4(A),A) ) ) )).
fof(dt_k2_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ( v3_ordinal1(k2_ordinal5(A)) & v4_ordinal5(k2_ordinal5(A)) ) ) )).
fof(dt_k2_ordinal6,axiom,( ! [A] : ( v1_relat_1(k2_ordinal6(A)) & v1_funct_1(k2_ordinal6(A)) & v5_ordinal1(k2_ordinal6(A)) & v1_ordinal2(k2_ordinal6(A)) ) )).
fof(dt_k2_ortsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) )).
fof(dt_k2_osafree,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k2_osalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k2_osalg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k2_osalg_4,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k2_parsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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))) ) )).
fof(dt_k2_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) )).
fof(dt_k2_partfun2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k2_partit1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_eqrel_1(B,A) & m1_eqrel_1(C,A) ) => m1_eqrel_1(k2_partit1(A,B,C),A) ) )).
fof(dt_k2_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k2_pcomps_1,axiom,( ! [A] : ( l1_metric_1(A) => m1_subset_1(k2_pcomps_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).
fof(dt_k2_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)))) ) )).
fof(dt_k2_pdiff_1,axiom,( ! [A] : ( ( 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)))) ) ) )).
fof(dt_k2_pdiff_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) => v1_xreal_0(k2_pdiff_3(A,B)) ) )).
fof(dt_k2_pdiff_5,axiom,( ! [A] : ! [B] : ( ( 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)) ) => v1_xreal_0(k2_pdiff_5(A,B)) ) )).
fof(dt_k2_pdiff_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & 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)))) ) ) )).
fof(dt_k2_pdiff_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & 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)))) ) ) )).
fof(dt_k2_pencil_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k2_pencil_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k2_pencil_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k2_pencil_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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))) ) )).
fof(dt_k2_pepin,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) ) => m1_subset_1(k2_pepin(A,B,C),k4_ordinal1) ) )).
fof(dt_k2_petri,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k2_petri_2,axiom,( ! [A] : ! [B] : ( ~ 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)))) ) ) )).
fof(dt_k2_pnproc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) & v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ( v1_funct_1(k2_pnproc_1(A,B,C)) & v1_funct_2(k2_pnproc_1(A,B,C),A,k4_ordinal1) & m1_subset_1(k2_pnproc_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) ) )).
fof(dt_k2_polyalg1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k2_polyeq_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) & v1_xcmplx_0(D) ) => m1_subset_1(k2_polyeq_3(A,B,C,D),k2_numbers) ) )).
fof(dt_k2_polyeq_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => v1_xcmplx_0(k2_polyeq_5(A,B,C)) ) )).
fof(dt_k2_polyform,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v7_ordinal1(B) ) => m1_subset_1(k2_polyform(A,B),k4_numbers) ) )).
fof(dt_k2_polynom2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,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(k2_polynom2(A,B,C,D),u1_struct_0(B)) ) )).
fof(dt_k2_polynom3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k2_polynom4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l6_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k2_polynom4(A,B,C),u1_struct_0(A)) ) )).
fof(dt_k2_polynom5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v7_ordinal1(C) ) => ( v1_funct_1(k2_polynom5(A,B,C)) & v1_funct_2(k2_polynom5(A,B,C),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k2_polynom5(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k2_polynom7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k2_polynom8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k2_polynom8(A,B,C)) & v1_funct_2(k2_polynom8(A,B,C),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k2_polynom8(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k2_polyred,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,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)))) ) )).
fof(dt_k2_poset_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k2_power,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => v1_xreal_0(k2_power(A,B)) ) )).
fof(dt_k2_pralg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k2_pralg_2,axiom,( ! [A] : ( ( 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(k1_funct_6(A))) & v1_funct_1(k2_pralg_2(A)) & v1_partfun1(k2_pralg_2(A),k4_card_3(k1_funct_6(A))) & v1_funcop_1(k2_pralg_2(A)) ) ) )).
fof(dt_k2_pralg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k2_pre_ff,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k3_finseq_2(k4_ordinal1)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k3_finseq_2(k4_ordinal1)))) & v7_ordinal1(B) ) => m2_finseq_1(k2_pre_ff(A,B),k4_ordinal1) ) )).
fof(dt_k2_pre_poly,axiom,( ! [A] : ( v1_xboole_0(k2_pre_poly(A)) & m2_finseq_2(k2_pre_poly(A),A,k3_finseq_2(A)) ) )).
fof(dt_k2_pre_topc,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k2_prelamb,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k2_prepower,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_xreal_0(B) ) => v1_xreal_0(k2_prepower(A,B)) ) )).
fof(dt_k2_prgcor_1,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_int_1(B) ) => v1_int_1(k2_prgcor_1(A,B)) ) )).
fof(dt_k2_prgcor_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v5_relat_1(A,k1_numbers) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_relat_1(B) & v5_relat_1(B,k1_numbers) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => v1_xreal_0(k2_prgcor_2(A,B)) ) )).
fof(dt_k2_prob_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_funct_1(k2_prob_1(A,B)) & v1_funct_2(k2_prob_1(A,B),k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(k2_prob_1(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) )).
fof(dt_k2_prob_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => m1_prob_1(k2_prob_2(A,B,C),A,B) ) )).
fof(dt_k2_prob_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_funct_1(k2_prob_3(A,B)) & v1_funct_2(k2_prob_3(A,B),k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(k2_prob_3(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) )).
fof(dt_k2_prob_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_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,k6_numbers))) ) ) )).
fof(dt_k2_projpl_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k2_prvect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k2_prvect_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) ) )).
fof(dt_k2_prvect_3,axiom,( ! [A] : ! [B] : ( ( ~ 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))))) ) ) )).
fof(dt_k2_pscomp_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) => v1_xreal_0(k2_pscomp_1(A,B)) ) )).
fof(dt_k2_pua2mss1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k2_pzfmisc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k2_qc_lang2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k2_qc_lang3,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k2_qc_lang4,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k2_qc_trans,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(A) & v1_qc_trans(B,A) & m1_qc_lang1(B) & m1_subset_1(C,k3_qc_lang1(A)) ) => m2_subset_1(k2_qc_trans(A,B,C),k2_qc_lang1(B),k3_qc_lang1(B)) ) )).
fof(dt_k2_quantal1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k2_quatern2,axiom,( m1_subset_1(k2_quatern2,k1_quaterni) )).
fof(dt_k2_quatern3,axiom,( ! [A] : ( m1_subset_1(A,k1_quaterni) => m1_subset_1(k2_quatern3(A),k1_quaterni) ) )).
fof(dt_k2_quofield,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k2_radix_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v3_card_1(C,A) & m1_finseq_1(C,k4_ordinal1) ) => ( v3_card_1(k2_radix_2(A,B,C),A) & m2_finseq_1(k2_radix_2(A,B,C),k4_ordinal1) ) ) )).
fof(dt_k2_radix_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k2_radix_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k2_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => m2_prob_1(k2_random_1(A),A,k1_random_1(A)) ) )).
fof(dt_k2_random_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k2_random_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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))) & m2_prob_1(E,A,C) & v1_funct_1(F) & v1_funct_2(F,A,B) & v1_random_3(F,A,B,C,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => m2_prob_1(k2_random_3(A,B,C,D,E,F),B,D) ) )).
fof(dt_k2_ranknull,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k2_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => v1_int_1(k2_rat_1(A)) ) )).
fof(dt_k2_ratfunc1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => m1_subset_1(k2_ratfunc1(A,B),u1_struct_0(A)) ) )).
fof(dt_k2_rcomp_1,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => m1_subset_1(k2_rcomp_1(A,B),k1_zfmisc_1(k1_numbers)) ) )).
fof(dt_k2_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => m1_subset_1(k2_real_1(A),k1_numbers) ) )).
fof(dt_k2_real_3,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => ( v1_funct_1(k2_real_3(A,B)) & v1_funct_2(k2_real_3(A,B),k4_ordinal1,k4_ordinal1) & m1_subset_1(k2_real_3(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) ) )).
fof(dt_k2_real_lat,axiom,( 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))) )).
fof(dt_k2_real_ns1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_k2_realset2,axiom,( 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))) )).
fof(dt_k2_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)))) ) ) )).
fof(dt_k2_rearran1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k2_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => v1_relat_1(k2_relat_1(A)) ) )).
fof(dt_k2_relset_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) ) => m1_subset_1(k2_relset_1(A,B),k1_zfmisc_1(A)) ) )).
fof(dt_k2_rewrite2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v5_ordinal1(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)) ) ) )).
fof(dt_k2_rfinseq,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & m1_finseq_1(C,A) ) => m2_finseq_1(k2_rfinseq(A,B,C),A) ) )).
fof(dt_k2_rfinseq2,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => v7_ordinal1(k2_rfinseq2(A)) ) )).
fof(dt_k2_rfunct_3,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k2_rfunct_3(A)) ) )).
fof(dt_k2_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => v1_xreal_0(k2_rinfsup1(A)) ) )).
fof(dt_k2_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => m1_subset_1(k2_rinfsup2(A),k6_numbers) ) )).
fof(dt_k2_ring_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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)) ) ) )).
fof(dt_k2_ringcat1,axiom,( ! [A] : ( 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)) ) ) )).
fof(dt_k2_rlaffin1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & v1_xreal_0(C) ) => m1_rlvect_2(k2_rlaffin1(A,B,C),A) ) )).
fof(dt_k2_rlaffin2,axiom,( ! [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) ) => ( 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)))) ) ) )).
fof(dt_k2_rlaffin3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)))) ) ) )).
fof(dt_k2_rlsub_1,axiom,( ! [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) ) => ( v1_rlvect_1(k2_rlsub_1(A)) & m1_rlsub_1(k2_rlsub_1(A),A) ) ) )).
fof(dt_k2_rlsub_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) ) )).
fof(dt_k2_rltopsp1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k2_rlvect_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k2_rlvect_x,axiom,( ! [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) & 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))) ) )).
fof(dt_k2_rmod_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) ) )).
fof(dt_k2_rmod_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) ) )).
fof(dt_k2_rmod_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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))) ) ) )).
fof(dt_k2_robbins3,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k2_robbins4,axiom,( v4_robbins1(k2_robbins4) & l4_robbins1(k2_robbins4) )).
fof(dt_k2_rpr_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(A) & m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => v1_xreal_0(k2_rpr_1(A,B,C)) ) )).
fof(dt_k2_rsspace,axiom,( ! [A] : ( v1_funct_1(k2_rsspace(A)) & v1_funct_2(k2_rsspace(A),k4_ordinal1,k1_numbers) & m1_subset_1(k2_rsspace(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) )).
fof(dt_k2_rsspace3,axiom,( 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))) )).
fof(dt_k2_rsspace4,axiom,( 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))) )).
fof(dt_k2_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ( v1_bhsp_1(k2_rusub_1(A)) & m1_rusub_1(k2_rusub_1(A),A) ) ) )).
fof(dt_k2_rusub_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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) ) ) )).
fof(dt_k2_rusub_5,axiom,( ! [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) & 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) ) ) )).
fof(dt_k2_rvsum_1,axiom,( 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))) )).
fof(dt_k2_scm_comp,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k2_scmbsort,axiom,( v1_relat_1(k2_scmbsort) & v4_relat_1(k2_scmbsort,k4_ordinal1) & 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) )).
fof(dt_k2_scmfsa6a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & v5_relat_1(k2_scmfsa6a(A),u1_compos_1(k1_scmfsa_2)) & v1_funct_1(k2_scmfsa6a(A)) & v1_finset_1(k2_scmfsa6a(A)) ) ) )).
fof(dt_k2_scmfsa8a,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => v7_ordinal1(k2_scmfsa8a(A,B,C)) ) )).
fof(dt_k2_scmfsa8b,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k2_scmfsa8c,axiom,( ! [A] : ! [B] : ( ( 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k2_scmfsa9a,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & 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(k7_card_1(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_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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_ordinal1(k2_scmfsa9a(A,B,C,D)) ) )).
fof(dt_k2_scmfsa_1,axiom,( m1_subset_1(k2_scmfsa_1,k1_zfmisc_1(k1_scmfsa_1)) )).
fof(dt_k2_scmfsa_2,axiom,( m1_subset_1(k2_scmfsa_2,k1_zfmisc_1(u1_struct_0(k1_scmfsa_2))) )).
fof(dt_k2_scmfsa_7,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) & v1_int_1(B) ) => ( v1_relat_1(k2_scmfsa_7(A,B)) & v5_relat_1(k2_scmfsa_7(A,B),u1_compos_1(k1_scmfsa_2)) & v5_ordinal1(k2_scmfsa_7(A,B)) & v1_funct_1(k2_scmfsa_7(A,B)) & v1_finset_1(k2_scmfsa_7(A,B)) ) ) )).
fof(dt_k2_scmfsa_9,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k2_scmfsa_i,axiom,( ~ v1_xboole_0(k2_scmfsa_i) )).
fof(dt_k2_scmfsa_m,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k2_scmisort,axiom,( ! [A] : ( m1_scmfsa_2(A) => ( ~ v1_xboole_0(k2_scmisort(A)) & v1_relat_1(k2_scmisort(A)) & v4_relat_1(k2_scmisort(A),k4_ordinal1) & 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)) ) ) )).
fof(dt_k2_scmp_gcd,axiom,( v1_ami_2(k2_scmp_gcd) & m1_subset_1(k2_scmp_gcd,u1_struct_0(k1_scmpds_2)) )).
fof(dt_k2_scmpds_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k2_scmpds_4,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ( v1_relat_1(k2_scmpds_4(A,B)) & v4_relat_1(k2_scmpds_4(A,B),k4_ordinal1) & v5_relat_1(k2_scmpds_4(A,B),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k2_scmpds_4(A,B)) & v1_funct_1(k2_scmpds_4(A,B)) & v1_finset_1(k2_scmpds_4(A,B)) & v1_afinsq_1(k2_scmpds_4(A,B)) ) ) )).
fof(dt_k2_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) & v1_int_1(B) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ( v1_relat_1(k2_scmpds_6(A,B,C,D)) & v4_relat_1(k2_scmpds_6(A,B,C,D),k4_ordinal1) & v5_relat_1(k2_scmpds_6(A,B,C,D),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k2_scmpds_6(A,B,C,D)) & 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)) ) ) )).
fof(dt_k2_scmpds_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) & v1_int_1(B) & v7_ordinal1(C) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ( v1_relat_1(k2_scmpds_7(A,B,C,D)) & v4_relat_1(k2_scmpds_7(A,B,C,D),k4_ordinal1) & v5_relat_1(k2_scmpds_7(A,B,C,D),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k2_scmpds_7(A,B,C,D)) & 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)) ) ) )).
fof(dt_k2_scmpds_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k2_scmpds_i,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k2_scmring1,axiom,( ! [A] : ! [B] : ( ( ~ 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),k4_ordinal1) ) )).
fof(dt_k2_scmring2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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(k7_card_1(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)) ) )).
fof(dt_k2_scmring3,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) & v7_ordinal1(B) ) => ( v1_ami_2(k2_scmring3(A,B)) & m1_subset_1(k2_scmring3(A,B),u1_struct_0(k1_scmring2(A))) ) ) )).
fof(dt_k2_scmringi,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k2_scmyciel,axiom,( ! [A] : ( ( v1_finset_1(A) & v5_finset_1(A) ) => v7_ordinal1(k2_scmyciel(A)) ) )).
fof(dt_k2_scpqsort,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => ( v1_relat_1(k2_scpqsort(A,B)) & v4_relat_1(k2_scpqsort(A,B),k4_ordinal1) & v5_relat_1(k2_scpqsort(A,B),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k2_scpqsort(A,B)) & v1_funct_1(k2_scpqsort(A,B)) & v1_finset_1(k2_scpqsort(A,B)) & v1_afinsq_1(k2_scpqsort(A,B)) ) ) )).
fof(dt_k2_semi_af1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k2_seq_4,axiom,( ! [A] : ( v3_membered(A) => v1_xreal_0(k2_seq_4(A)) ) )).
fof(dt_k2_seqfunc,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(k2_seqfunc(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) ) )).
fof(dt_k2_series_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & v1_valued_0(A) ) => ( v1_relat_1(k2_series_1(A)) & v4_relat_1(k2_series_1(A),k4_ordinal1) & v1_funct_1(k2_series_1(A)) & v1_partfun1(k2_series_1(A),k4_ordinal1) & v1_valued_0(k2_series_1(A)) ) ) )).
fof(dt_k2_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_funct_1(k2_setlim_1(A,B)) & v1_funct_2(k2_setlim_1(A,B),k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(k2_setlim_1(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) )).
fof(dt_k2_setlim_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_funct_1(k2_setlim_2(A,B,C)) & v1_funct_2(k2_setlim_2(A,B,C),k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(k2_setlim_2(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) )).
fof(dt_k2_setwiseo,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m1_subset_1(k2_setwiseo(A,B),k5_finsub_1(A)) ) )).
fof(dt_k2_setwop_2,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k2_setwop_2(A),k5_finsub_1(k4_ordinal1)) ) )).
fof(dt_k2_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => m1_subset_1(k2_sf_mastr(A),k1_zfmisc_1(k2_scmfsa_2)) ) )).
fof(dt_k2_sfmastr2,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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_sfmastr2(A,B)) & v4_relat_1(k2_sfmastr2(A,B),k4_ordinal1) & v5_relat_1(k2_sfmastr2(A,B),u1_compos_1(k1_scmfsa_2)) & ~ v1_xboole_0(k2_sfmastr2(A,B)) & v1_funct_1(k2_sfmastr2(A,B)) & v1_finset_1(k2_sfmastr2(A,B)) & v1_afinsq_1(k2_sfmastr2(A,B)) ) ) )).
fof(dt_k2_sfmastr3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k2_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => m1_subset_1(k2_sheffer1(A),u1_struct_0(A)) ) )).
fof(dt_k2_simplex0,axiom,( ! [A] : ! [B] : ( 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))) ) ) )).
fof(dt_k2_simplex1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) )).
fof(dt_k2_simplex2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) => v1_xreal_0(k2_simplex2(A,B)) ) )).
fof(dt_k2_sin_cos,axiom,( v1_funct_1(k2_sin_cos) & v1_funct_2(k2_sin_cos,k4_ordinal1,k1_numbers) & m1_subset_1(k2_sin_cos,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) )).
fof(dt_k2_sin_cos3,axiom,( 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))) )).
fof(dt_k2_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k2_sin_cos4(A)) ) )).
fof(dt_k2_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k2_sin_cos5(A)) ) )).
fof(dt_k2_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k2_sin_cos7(A)) ) )).
fof(dt_k2_sin_cos9,axiom,( v1_funct_1(k2_sin_cos9) & m1_subset_1(k2_sin_cos9,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) )).
fof(dt_k2_sincos10,axiom,( v1_funct_1(k2_sincos10) & m1_subset_1(k2_sincos10,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) )).
fof(dt_k2_stacks_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & m1_finseq_1(C,A) ) => m2_finseq_2(k2_stacks_1(A,B,C),A,k3_finseq_2(A)) ) )).
fof(dt_k2_stirl2_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v1_funct_1(C) & v1_funct_2(C,A,k7_card_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k7_card_1(B)))) ) => m1_subset_1(k2_stirl2_1(A,B,C,D),k7_card_1(B)) ) )).
fof(dt_k2_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => m1_subset_1(k2_struct_0(A),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k2_sublemma,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k2_subset_1,axiom,( ! [A] : m1_subset_1(k2_subset_1(A),k1_zfmisc_1(A)) )).
fof(dt_k2_substlat,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k2_substut1,axiom,( ! [A] : ! [B] : ( ( 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)))) ) ) )).
fof(dt_k2_substut2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k2_supinf_1,axiom,( m1_subset_1(k2_supinf_1,k6_numbers) )).
fof(dt_k2_supinf_2,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => m1_subset_1(k2_supinf_2(A),k6_numbers) ) )).
fof(dt_k2_symsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) )).
fof(dt_k2_t_0topsp,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k2_t_1topsp,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k2_taxonom1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k2_taylor_1,axiom,( ! [A] : ( 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))) ) ) )).
fof(dt_k2_tbsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v7_ordinal1(C) ) => m1_subset_1(k2_tbsp_1(A,B,C),u1_struct_0(A)) ) )).
fof(dt_k2_tdgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ( v1_analoaf(k2_tdgroup(A)) & l1_analoaf(k2_tdgroup(A)) ) ) )).
fof(dt_k2_tdlat_1,axiom,( ! [A] : ( ( 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)))) ) ) )).
fof(dt_k2_termord,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_k2_tex_1,axiom,( ! [A] : l1_pre_topc(k2_tex_1(A)) )).
fof(dt_k2_tex_4,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k2_tmap_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) ) )).
fof(dt_k2_toler_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k2_topalg_2,axiom,( v2_topalg_2(k2_topalg_2) & m1_pre_topc(k2_topalg_2,k3_topmetr) )).
fof(dt_k2_topalg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) )).
fof(dt_k2_topalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))))) ) ) )).
fof(dt_k2_topalg_5,axiom,( ! [A] : ( v1_xreal_0(A) => m1_borsuk_2(k2_topalg_5(A),k2_topalg_2,k4_toprealb(k5_numbers),k4_toprealb(A)) ) )).
fof(dt_k2_topalg_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k2_topdim_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k2_topgen_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k2_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => v1_card_1(k2_topgen_2(A)) ) )).
fof(dt_k2_topgen_3,axiom,( ~ v2_struct_0(k2_topgen_3) & v1_pre_topc(k2_topgen_3) & v2_pre_topc(k2_topgen_3) & l1_pre_topc(k2_topgen_3) )).
fof(dt_k2_topgen_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k2_topgen_5,axiom,( m1_subset_1(k2_topgen_5,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) )).
fof(dt_k2_topgrp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k2_topmetr,axiom,( ! [A] : ! [B] : ( ( 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),k7_metric_1) ) ) )).
fof(dt_k2_topreal1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) )).
fof(dt_k2_topreal7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k2_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) )).
fof(dt_k2_topreala,axiom,( 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))))) )).
fof(dt_k2_toprealc,axiom,( ! [A] : ( v1_valued_2(A) => v1_valued_2(k2_toprealc(A)) ) )).
fof(dt_k2_toprns_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(A) & v7_ordinal1(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(B))))) ) => ( v1_funct_1(k2_toprns_1(A,B,C)) & v1_funct_2(k2_toprns_1(A,B,C),k4_ordinal1,u1_struct_0(k15_euclid(B))) & m1_subset_1(k2_toprns_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(B))))) ) ) )).
fof(dt_k2_tops_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k2_tops_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k2_transgeo,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k2_treal_1,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => m1_subset_1(k2_treal_1(A,B),u1_struct_0(k4_topmetr(A,B))) ) )).
fof(dt_k2_trees_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ v1_xboole_0(k2_trees_1(A)) & v1_trees_1(k2_trees_1(A)) ) ) )).
fof(dt_k2_trees_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v7_ordinal1(B) ) => m2_trees_2(k2_trees_2(A,B),A) ) )).
fof(dt_k2_trees_3,axiom,( m1_subset_1(k2_trees_3,k1_zfmisc_1(k1_trees_3)) )).
fof(dt_k2_trees_4,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m1_subset_1(k2_trees_4(A,B),k5_trees_3(A)) ) )).
fof(dt_k2_trees_9,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k2_trees_a,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & m1_subset_1(B,A) ) => m4_trees_1(k2_trees_a(A,B),A) ) )).
fof(dt_k2_tsep_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k2_turing_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k2_twoscomp,axiom,( 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))) )).
fof(dt_k2_unialg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k2_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => m1_subset_1(k2_uniroots(A),k1_zfmisc_1(u1_struct_0(k1_complfld))) ) )).
fof(dt_k2_uproots,axiom,( ! [A] : ! [B] : ( ( 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(k2_uproots(A,B)) ) )).
fof(dt_k2_urysohn1,axiom,( m1_subset_1(k2_urysohn1,k1_zfmisc_1(k1_numbers)) )).
fof(dt_k2_urysohn3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,B)))) & v7_ordinal1(D) ) => m1_subset_1(k2_urysohn3(A,B,C,D),k4_partfun1(A,B)) ) )).
fof(dt_k2_valuat_1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & ~ v1_xboole_0(B) ) => m1_funct_2(k2_valuat_1(A,B),k3_qc_lang1(A),B) ) )).
fof(dt_k2_valued_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_ordinal1) & v5_valued_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => m2_valued_0(k2_valued_0(A,B,C),A,C) ) )).
fof(dt_k2_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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))) ) ) )).
fof(dt_k2_vectmetr,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k2_vectsp10,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)))) ) ) )).
fof(dt_k2_vectsp11,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) ) )).
fof(dt_k2_vectsp_1,axiom,( v36_algstr_0(k2_vectsp_1) & l6_algstr_0(k2_vectsp_1) )).
fof(dt_k2_vectsp_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) ) )).
fof(dt_k2_vectsp_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) ) )).
fof(dt_k2_vectsp_6,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k2_vectsp_8,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) ) )).
fof(dt_k2_vfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k2_vfunct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k2_waybel10,axiom,( ! [A] : ( ( ~ 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),k6_yellow_1(A,A)) & m1_yellow_0(k2_waybel10(A),k6_yellow_1(A,A)) ) ) )).
fof(dt_k2_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => m4_yellow_6(k2_waybel11(A),A) ) )).
fof(dt_k2_waybel17,axiom,( ! [A] : ! [B] : ( ( 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),k6_yellow_1(A,B)) & m1_yellow_0(k2_waybel17(A,B),k6_yellow_1(A,B)) ) ) )).
fof(dt_k2_waybel18,axiom,( ! [A] : ! [B] : ( ( 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))))) ) )).
fof(dt_k2_waybel19,axiom,( ! [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) ) => m1_subset_1(k2_waybel19(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).
fof(dt_k2_waybel20,axiom,( ! [A] : ! [B] : ( ( 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)))) ) ) )).
fof(dt_k2_waybel22,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k1_yellow_1(k8_waybel_0(k2_yellow_1(A)))),u1_struct_0(B)) & m1_subset_1(k2_waybel22(A,B,C),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_yellow_1(k8_waybel_0(k2_yellow_1(A)))),u1_struct_0(B)))) ) ) )).
fof(dt_k2_waybel23,axiom,( ! [A] : ( l1_pre_topc(A) => v1_card_1(k2_waybel23(A)) ) )).
fof(dt_k2_waybel24,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k2_waybel25,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(dt_k2_waybel26,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) )).
fof(dt_k2_waybel27,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k2_waybel28,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k2_waybel29,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))))) ) ) )).
fof(dt_k2_waybel31,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k2_waybel32,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k2_waybel34,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) ) )).
fof(dt_k2_waybel_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k2_waybel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))))) ) ) )).
fof(dt_k2_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k2_waybel_3,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k2_waybel_4,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k2_waybel_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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(k1_funct_6(D)),k7_funcop_1(k4_card_3(k1_funct_6(D)),A),k7_funcop_1(k4_card_3(k1_funct_6(D)),B)) ) )).
fof(dt_k2_waybel_8,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k2_waybel_9,axiom,( ! [A] : ( l1_orders_2(A) => ( v6_waybel_0(k2_waybel_9(A),A) & l1_waybel_0(k2_waybel_9(A),A) ) ) )).
fof(dt_k2_weddwitt,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k2_weierstr,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => v1_xreal_0(k2_weierstr(A)) ) )).
fof(dt_k2_wellord1,axiom,( ! [A] : ! [B] : ( v1_relat_1(A) => v1_relat_1(k2_wellord1(A,B)) ) )).
fof(dt_k2_wellord2,axiom,( ! [A] : ( v1_relat_1(A) => v3_ordinal1(k2_wellord2(A)) ) )).
fof(dt_k2_wsierp_1,axiom,( ! [A] : ( m1_finseq_1(A,k4_ordinal1) => m1_subset_1(k2_wsierp_1(A),k4_ordinal1) ) )).
fof(dt_k2_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => v1_xxreal_0(k2_xxreal_2(A)) ) )).
fof(dt_k2_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => v1_xxreal_0(k2_xxreal_3(A)) ) )).
fof(dt_k2_yellow11,axiom,( l1_orders_2(k2_yellow11) )).
fof(dt_k2_yellow14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k2_yellow15,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k2_yellow16,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k2_yellow18,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k2_yellow19,axiom,( ! [A] : ! [B] : ( ( ~ 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(k2_yellow_1(k2_struct_0(A))))) ) )).
fof(dt_k2_yellow20,axiom,( ! [A] : ! [B] : ( ( l2_altcat_1(A) & l2_altcat_1(B) ) => ( v6_altcat_1(k2_yellow20(A,B)) & l2_altcat_1(k2_yellow20(A,B)) ) ) )).
fof(dt_k2_yellow_0,axiom,( ! [A] : ! [B] : ( l1_orders_2(A) => m1_subset_1(k2_yellow_0(A,B),u1_struct_0(A)) ) )).
fof(dt_k2_yellow_1,axiom,( ! [A] : ( v1_orders_2(k2_yellow_1(A)) & l1_orders_2(k2_yellow_1(A)) ) )).
fof(dt_k2_yellow_2,axiom,( ! [A] : ( ( ~ 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(k1_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(k1_yellow_1(k7_waybel_0(A))),u1_struct_0(A)))) ) ) )).
fof(dt_k2_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)))) ) )).
fof(dt_k2_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k2_yellow_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k2_yellow_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k2_yellow_9,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k2_yoneda_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) )).
fof(dt_k2_zf_fund1,axiom,( 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))) )).
fof(dt_k2_zf_lang,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => m2_subset_1(k2_zf_lang(A),k4_ordinal1,k1_zf_lang) ) )).
fof(dt_k2_zf_lang1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k2_zf_model,axiom,( ! [A] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) ) => m1_subset_1(k2_zf_model(A),k1_zfmisc_1(k1_zf_lang)) ) )).
fof(dt_k2_zf_refle,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k2_zfmodel1,axiom,( ! [A] : ! [B] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) & ~ 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))) ) ) )).
fof(dt_k2_zfrefle1,axiom,( m1_subset_1(k2_zfrefle1,k1_zfmisc_1(k9_zf_lang)) )).
fof(dt_k2_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ 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_int_1(B) ) => m2_subset_1(k2_zmodul02(A,B),u1_struct_0(A),k1_zmodul02(A,B)) ) )).
fof(dt_k2_zmodul03,axiom,( ! [A] : ( ( ~ 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) & v1_zmodul03(A) & v2_zmodul03(A) & l1_zmodul01(A) ) => v7_ordinal1(k2_zmodul03(A)) ) )).
fof(dt_k30_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))))) ) )).
fof(dt_k30_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) & v19_aofa_a00(C,A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) & m1_subset_1(E,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) ) => m1_msafree4(k30_aofa_a00(A,B,C,D,E),u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) ) )).
fof(dt_k30_cat_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ 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) ) )).
fof(dt_k30_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k30_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => m1_subset_1(k30_fomodel2(A),k1_zfmisc_1(k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0)))) ) )).
fof(dt_k30_fomodel4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k30_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k30_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(dt_k30_mmlquery,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k30_modelc_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(A) => m1_subset_1(k30_modelc_2(A,B),k30_modelc_1(k25_modelc_2(A))) ) )).
fof(dt_k30_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & v5_modelc_3(A) & m1_finseq_1(A,k4_ordinal1) ) => 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)))) ) )).
fof(dt_k30_osafree,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k30_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => m2_finseq_1(k30_polyform(A),k4_numbers) ) )).
fof(dt_k30_qc_lang1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k1_qc_lang1(A)) & v7_ordinal1(C) ) => m1_subset_1(k30_qc_lang1(A,B,C),k1_qc_lang1(A)) ) )).
fof(dt_k30_substut1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k30_turing_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1))) ) )).
fof(dt_k30_twoscomp,axiom,( 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))) )).
fof(dt_k30_valued_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k30_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k30_zmodul02,axiom,( ! [A] : ( ( ~ 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(k30_zmodul02(A)) & v1_funct_2(k30_zmodul02(A),k2_zfmisc_1(k4_numbers,k26_zmodul02(A)),k26_zmodul02(A)) & m1_subset_1(k30_zmodul02(A),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_numbers,k26_zmodul02(A)),k26_zmodul02(A)))) ) ) )).
fof(dt_k31_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))))) ) )).
fof(dt_k31_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) & v19_aofa_a00(C,A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) & m1_subset_1(E,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) ) => m1_msafree4(k31_aofa_a00(A,B,C,D,E),u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) ) )).
fof(dt_k31_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(dt_k31_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ v2_struct_0(A) & ~ 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)) ) )).
fof(dt_k31_descip_1,axiom,( ! [A] : ( 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))) ) )).
fof(dt_k31_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => m1_subset_1(k31_fomodel2(A),k1_fomodel1(A)) ) )).
fof(dt_k31_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(k30_fomodel2(A),k30_fomodel2(A))) ) => m2_funct_2(k31_fomodel3(A,B,C,D,E),k30_fomodel2(A),k30_fomodel2(A),k9_funct_2(k30_fomodel2(A),k30_fomodel2(A))) ) )).
fof(dt_k31_fomodel4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k31_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ 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)) ) )).
fof(dt_k31_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(dt_k31_mmlquery,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k31_modelc_1,axiom,( ! [A] : ! [B] : ( ~ 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))) ) ) )).
fof(dt_k31_modelc_2,axiom,( ! [A] : ( ~ 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))))) ) ) )).
fof(dt_k31_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & v5_modelc_3(A) & m1_finseq_1(A,k4_ordinal1) ) => m1_subset_1(k31_modelc_3(A),k1_zfmisc_1(k23_modelc_3(A))) ) )).
fof(dt_k31_substut1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k16_substut1(A)) ) => m1_subset_1(k31_substut1(A,B),k16_substut1(A)) ) )).
fof(dt_k31_turing_1,axiom,( ! [A] : ! [B] : ( ( 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)),k1_enumset1(k4_xcmplx_0(1),k5_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)),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1))))) ) ) )).
fof(dt_k31_twoscomp,axiom,( 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))) )).
fof(dt_k31_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k31_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))))) ) ) )).
fof(dt_k31_zmodul02,axiom,( ! [A] : ( ( ~ 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) ) => l1_zmodul01(k31_zmodul02(A)) ) )).
fof(dt_k32_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => m2_abcmiz_1(k32_abcmiz_1(A),A,k13_abcmiz_1(A)) ) )).
fof(dt_k32_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) & v19_aofa_a00(C,A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) & m1_subset_1(E,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) ) => m1_msafree4(k32_aofa_a00(A,B,C,D,E),u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) ) )).
fof(dt_k32_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(dt_k32_fomodel1,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k32_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) ) => m1_subset_1(k32_fomodel2(A,B),k1_zfmisc_1(k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0)))) ) )).
fof(dt_k32_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k30_fomodel2(A),k30_fomodel2(A))) ) => ( v1_funct_1(k32_fomodel3(A,B,C,D)) & v1_funct_2(k32_fomodel3(A,B,C,D),k4_ordinal1,k9_funct_2(k30_fomodel2(A),k30_fomodel2(A))) & m1_subset_1(k32_fomodel3(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_funct_2(k30_fomodel2(A),k30_fomodel2(A))))) ) ) )).
fof(dt_k32_fomodel4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k32_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k32_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) ) )).
fof(dt_k32_mmlquery,axiom,( ! [A] : ! [B] : ( ( l1_mmlquery(A) & m1_finseq_1(B,u1_mmlquery(A)) ) => m1_subset_1(k32_mmlquery(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k32_modelc_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(A) => m1_subset_1(k32_modelc_1(A,B),k30_modelc_1(A)) ) )).
fof(dt_k32_modelc_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k32_modelc_3,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(A) & v5_modelc_3(A) & m1_finseq_1(A,k4_ordinal1) & v1_modelc_2(B) & m1_finseq_1(B,k4_ordinal1) ) => m1_subset_1(k32_modelc_3(A,B),k1_zfmisc_1(k23_modelc_3(A))) ) )).
fof(dt_k32_substut1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k32_turing_1,axiom,( ! [A] : ! [B] : ( ( l1_turing_1(A) & l1_turing_1(B) ) => ( v1_turing_1(k32_turing_1(A,B)) & l1_turing_1(k32_turing_1(A,B)) ) ) )).
fof(dt_k32_twoscomp,axiom,( 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))) )).
fof(dt_k32_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k32_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))))) ) ) )).
fof(dt_k33_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => m2_abcmiz_1(k33_abcmiz_1(A),A,k12_abcmiz_1(A)) ) )).
fof(dt_k33_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) & v19_aofa_a00(C,A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) & m1_subset_1(E,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) ) => m1_msafree4(k33_aofa_a00(A,B,C,D,E),u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),u8_aofa_a00(A))) ) )).
fof(dt_k33_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(dt_k33_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ 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))),k3_fomodel0(k3_finseq_2(k15_fomodel1(A)),k29_fomodel1(A))) ) )).
fof(dt_k33_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) ) => m1_subset_1(k33_fomodel2(A,B),k1_zfmisc_1(k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0)))) ) )).
fof(dt_k33_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k33_fomodel4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k33_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : m2_subset_1(k33_gfacirc1(A,B,C),u1_struct_0(k31_gfacirc1(A,B,C)),k3_msafree2(k31_gfacirc1(A,B,C))) )).
fof(dt_k33_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) ) )).
fof(dt_k33_mmlquery,axiom,( ! [A] : ! [B] : ( ( l1_mmlquery(A) & m1_finseq_1(B,u1_mmlquery(A)) ) => m1_subset_1(k33_mmlquery(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k33_modelc_1,axiom,( ! [A] : ( ~ 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)))) ) ) )).
fof(dt_k33_modelc_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(A) => m1_subset_1(k33_modelc_2(A,B),k30_modelc_1(k25_modelc_2(A))) ) )).
fof(dt_k33_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & v5_modelc_3(A) & m1_finseq_1(A,k4_ordinal1) ) => m1_subset_1(k33_modelc_3(A),k1_zfmisc_1(k1_zfmisc_1(k23_modelc_3(A)))) ) )).
fof(dt_k33_substut1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k33_twoscomp,axiom,( 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))) )).
fof(dt_k33_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ 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,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_zmodul01(k33_zmodul02(A,B)) & m1_zmodul01(k33_zmodul02(A,B),A) ) ) )).
fof(dt_k34_abcmiz_1,axiom,( ! [A] : ( ( 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)))))) ) )).
fof(dt_k34_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) & v19_aofa_a00(C,A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,k1_funct_1(u3_msualg_1(A,B),C)) & m1_subset_1(E,k1_funct_1(u3_msualg_1(A,B),C)) ) => m1_subset_1(k34_aofa_a00(A,B,C,D,E),k1_funct_1(u3_msualg_1(A,B),C)) ) )).
fof(dt_k34_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(dt_k34_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ 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))),k3_fomodel0(k3_finseq_2(k15_fomodel1(A)),k29_fomodel1(A))) ) ) )).
fof(dt_k34_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & ~ v1_xboole_0(B) & m1_subset_1(C,k15_fomodel2(A,B)) & v4_fomodel1(D,A) & m1_subset_1(D,k1_fomodel1(A)) & m1_subset_1(E,B) ) => m2_subset_1(k34_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))),k15_fomodel2(A,B)) ) )).
fof(dt_k34_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k34_fomodel4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k34_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ 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)) ) )).
fof(dt_k34_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(dt_k34_mmlquery,axiom,( ! [A] : ! [B] : ( ( l1_mmlquery(A) & m1_finseq_1(B,u1_mmlquery(A)) ) => m1_subset_1(k34_mmlquery(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k34_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k34_modelc_2,axiom,( ! [A] : ( ~ 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))))) ) ) )).
fof(dt_k34_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & v5_modelc_3(A) & m1_finseq_1(A,k4_ordinal1) ) => l2_modelc_3(k34_modelc_3(A),k43_modelc_2) ) )).
fof(dt_k34_substut1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k34_twoscomp,axiom,( ! [A] : ! [B] : ( ~ 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)) ) )).
fof(dt_k34_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k35_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k35_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) & v19_aofa_a00(C,A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,k1_funct_1(u3_msualg_1(A,B),C)) & m1_subset_1(E,k1_funct_1(u3_msualg_1(A,B),C)) ) => m1_subset_1(k35_aofa_a00(A,B,C,D,E),k1_funct_1(u3_msualg_1(A,B),C)) ) )).
fof(dt_k35_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(dt_k35_descip_1,axiom,( 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)))) )).
fof(dt_k35_fomodel1,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k35_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ 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(k35_fomodel2(A,B),k3_finseq_2(k15_fomodel1(A)),k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) ) )).
fof(dt_k35_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => m2_funct_2(k35_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)))) ) )).
fof(dt_k35_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k35_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) ) )).
fof(dt_k35_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k35_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k35_modelc_2,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(A) => m1_subset_1(k35_modelc_2(A,B,C),k30_modelc_1(k25_modelc_2(A))) ) )).
fof(dt_k35_substut1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k35_twoscomp,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(dt_k35_valued_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k36_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))))) ) ) )).
fof(dt_k36_aofa_a00,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l6_aofa_a00(A) & ~ v2_struct_0(B) & l5_aofa_a00(B) ) => ( v15_aofa_a00(k36_aofa_a00(A,B)) & l6_aofa_a00(k36_aofa_a00(A,B)) ) ) )).
fof(dt_k36_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(dt_k36_fomodel1,axiom,( ! [A] : ( ( ~ 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),k3_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),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k35_fomodel1(A))))) ) ) )).
fof(dt_k36_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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),k30_fomodel2(A),k30_fomodel2(A),k9_funct_2(k30_fomodel2(A),k30_fomodel2(A))) ) )).
fof(dt_k36_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => m2_funct_2(k36_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)))) ) )).
fof(dt_k36_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : m2_subset_1(k36_gfacirc1(A,B,C),u1_struct_0(k34_gfacirc1(A,B,C)),k3_msafree2(k34_gfacirc1(A,B,C))) )).
fof(dt_k36_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) )).
fof(dt_k36_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k36_modelc_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k36_modelc_2,axiom,( ! [A] : ( ~ 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))))) ) ) )).
fof(dt_k36_substut1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k36_twoscomp,axiom,( ! [A] : ! [B] : m1_subset_1(k36_twoscomp(A,B),k3_msafree2(k34_twoscomp(A,B))) )).
fof(dt_k36_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k36_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k37_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k37_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v21_aofa_a00(A,1,1,11) & l6_aofa_a00(A) ) => m1_subset_1(k37_aofa_a00(A),u1_struct_0(A)) ) )).
fof(dt_k37_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(dt_k37_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => m1_subset_1(k37_fomodel1(A),k1_zfmisc_1(k15_fomodel1(A))) ) )).
fof(dt_k37_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ 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(k37_fomodel2(A,B),A) & m2_subset_1(k37_fomodel2(A,B),k3_finseq_2(k15_fomodel1(A)),k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) ) ) )).
fof(dt_k37_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k37_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ 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)) ) )).
fof(dt_k37_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) )).
fof(dt_k37_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k37_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k37_modelc_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k37_substut1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k16_substut1(A)) ) => m1_subset_1(k37_substut1(A,B),k9_qc_lang1(A)) ) )).
fof(dt_k37_twoscomp,axiom,( ! [A] : ! [B] : ( ~ 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)) ) )).
fof(dt_k37_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k37_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))))) ) ) )).
fof(dt_k38_abcmiz_1,axiom,( ! [A] : ( ( 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)))))) ) )).
fof(dt_k38_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & l6_aofa_a00(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) & m1_subset_1(C,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),k37_aofa_a00(A))) & v19_aofa_a00(D,A) & m1_subset_1(D,u1_struct_0(A)) ) => m1_msafree4(k38_aofa_a00(A,B,C,D),u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),D)) ) )).
fof(dt_k38_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(dt_k38_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k38_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ 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(k38_fomodel2(A,B),k1_fomodel1(A),k3_finseq_2(k1_fomodel1(A))) ) )).
fof(dt_k38_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) & ~ v8_ordinal1(B) & v3_card_1(C,B) & m1_subset_1(C,k3_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,k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k35_fomodel1(A))) ) => m1_subset_1(k38_fomodel4(A,B,C,D),k1_zfmisc_1(k30_fomodel2(A))) ) )).
fof(dt_k38_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k38_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) )).
fof(dt_k38_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k38_modelc_2,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(A) => m1_subset_1(k38_modelc_2(A,B,C),k30_modelc_1(k25_modelc_2(A))) ) )).
fof(dt_k38_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => m1_subset_1(k38_substut1(A),k1_zfmisc_1(k16_substut1(A))) ) )).
fof(dt_k38_twoscomp,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(dt_k38_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))))) ) ) )).
fof(dt_k39_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & l6_aofa_a00(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) & m1_subset_1(C,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),k37_aofa_a00(A))) & v19_aofa_a00(D,A) & m1_subset_1(D,u1_struct_0(A)) & m1_subset_1(E,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),D)) ) => m1_msafree4(k39_aofa_a00(A,B,C,D,E),u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),D)) ) )).
fof(dt_k39_descip_1,axiom,( ! [A] : ( 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))) ) )).
fof(dt_k39_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ( v1_funct_1(k39_fomodel1(A)) & v1_funct_2(k39_fomodel1(A),k4_ordinal1,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(k4_ordinal1,k9_setfam_1(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)))))) ) ) )).
fof(dt_k39_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ 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(k39_fomodel2(A,B),A) & m2_subset_1(k39_fomodel2(A,B),k3_finseq_2(k15_fomodel1(A)),k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) ) ) )).
fof(dt_k39_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => m1_subset_1(k39_fomodel4(A),k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) ) )).
fof(dt_k39_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => m1_subset_1(k39_glib_000(A),k4_ordinal1) ) )).
fof(dt_k39_modelc_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k39_modelc_2,axiom,( ! [A] : ( ~ 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))))) ) ) )).
fof(dt_k39_substut1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k39_twoscomp,axiom,( ! [A] : ! [B] : m1_subset_1(k39_twoscomp(A,B),k3_msafree2(k37_twoscomp(A,B))) )).
fof(dt_k39_valued_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k3_abcmiz_0,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k3_abcmiz_1,axiom,( ! [A] : ( m1_subset_1(A,k2_abcmiz_1) => m1_subset_1(k3_abcmiz_1(A),k1_zfmisc_1(k2_abcmiz_1)) ) )).
fof(dt_k3_aff_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k3_afinsq_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k3_afproj,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k3_afvect0,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k3_alg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k3_algstr_0,axiom,( l2_algstr_0(k3_algstr_0) )).
fof(dt_k3_algstr_1,axiom,( v29_algstr_0(k3_algstr_1) & l5_algstr_0(k3_algstr_1) )).
fof(dt_k3_algstr_3,axiom,( v1_algstr_3(k3_algstr_3) & l1_algstr_3(k3_algstr_3) )).
fof(dt_k3_algstr_4,axiom,( ! [A] : ! [B] : ( ( 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)))) ) ) )).
fof(dt_k3_altcat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k3_altcat_2,axiom,( ! [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) & 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))) ) )).
fof(dt_k3_altcat_4,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(dt_k3_altcat_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(k7_altcat_1(B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(k7_altcat_1(B))))) ) => m1_altcat_5(k3_altcat_5(A,B,C),k7_altcat_1(B),k2_altcat_5(A,B,C),A,C) ) )).
fof(dt_k3_ami_2,axiom,( v1_funct_1(k3_ami_2) & v1_funct_2(k3_ami_2,k1_ami_2,k7_card_1(2)) & m1_subset_1(k3_ami_2,k1_zfmisc_1(k2_zfmisc_1(k1_ami_2,k7_card_1(2)))) )).
fof(dt_k3_ami_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k3_ami_wstd,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) => m1_subset_1(k3_ami_wstd(A,B,C),k4_ordinal1) ) )).
fof(dt_k3_amistd_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k4_ordinal1)) ) )).
fof(dt_k3_amistd_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k3_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analmetr(A) ) => ( v1_analoaf(k3_analmetr(A)) & l1_analoaf(k3_analmetr(A)) ) ) )).
fof(dt_k3_analort,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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))))) ) )).
fof(dt_k3_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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(k3_aofa_a00(A,B,C,D,E,F,G),A,B,C) ) )).
fof(dt_k3_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & l6_aofa_a00(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)) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) & l4_aofa_a00(D,A,B,C) & m1_subset_1(E,k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),u8_aofa_a00(A))) & v4_msualg_1(F,A) & v4_msafree4(F,A,C) & l3_msualg_1(F,A) & ~ v2_struct_0(G) & v2_unialg_1(G) & v3_unialg_1(G) & v4_unialg_1(G) & v3_aofa_000(G) & v4_aofa_000(G) & v5_aofa_000(G) & v6_aofa_000(G) & l1_unialg_1(G) & m1_aofa_000(H,G,k13_aofa_a00(A,C,F,u4_aofa_a00(A,B,C,D)),k14_aofa_a00(A,C,F,u4_aofa_a00(A,B,C,D),u8_aofa_a00(A),E,k2_aofa_a01(A,F))) & m1_subset_1(I,k13_aofa_a00(A,C,F,u4_aofa_a00(A,B,C,D))) & m1_subset_1(J,u1_struct_0(G)) ) => m2_subset_1(k3_aofa_a01(A,B,C,D,E,F,G,H,I,J),k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,D),u3_msualg_1(A,F)),k13_aofa_a00(A,C,F,u4_aofa_a00(A,B,C,D))) ) )).
fof(dt_k3_aofa_i00,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k3_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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) ) ) )).
fof(dt_k3_arrow,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(k3_arrow(A),k1_zfmisc_1(k2_arrow(A))) ) )).
fof(dt_k3_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => m1_subset_1(k3_arytm_0(A),k1_numbers) ) )).
fof(dt_k3_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => m2_subset_1(k3_arytm_2(A),k1_zfmisc_1(k5_arytm_3),k1_arytm_2) ) )).
fof(dt_k3_arytm_3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v7_ordinal1(A) & v3_ordinal1(B) & v7_ordinal1(B) ) => m1_subset_1(k3_arytm_3(A,B),k4_ordinal1) ) )).
fof(dt_k3_asympt_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & ~ v3_xxreal_0(B) & v1_xreal_0(B) ) => ( v1_funct_1(k3_asympt_0(A,B)) & v1_funct_2(k3_asympt_0(A,B),k4_ordinal1,k1_numbers) & v2_asympt_0(k3_asympt_0(A,B)) & m1_subset_1(k3_asympt_0(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k3_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_funct_1(k3_asympt_1(A)) & v1_funct_2(k3_asympt_1(A),k4_ordinal1,k1_numbers) & m1_subset_1(k3_asympt_1(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k3_autalg_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k3_autgroup,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k3_bagorder,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k3_bcialg_4,axiom,( ! [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) & 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))) ) ) )).
fof(dt_k3_bcialg_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => v1_xxreal_0(k3_bcialg_5(A,B,C,D)) ) )).
fof(dt_k3_bcialg_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k3_bhsp_1,axiom,( ! [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) & v8_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) & m1_subset_1(B,u1_struct_0(A)) ) => v1_xreal_0(k3_bhsp_1(A,B)) ) )).
fof(dt_k3_bhsp_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,k1_numbers) & m1_subset_1(k3_bhsp_2(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k3_bhsp_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v7_ordinal1(C) ) => m1_subset_1(k3_bhsp_4(A,B,C),u1_struct_0(A)) ) )).
fof(dt_k3_bhsp_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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))) ) => v1_xreal_0(k3_bhsp_6(A,B,C)) ) )).
fof(dt_k3_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k3_binari_2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v3_card_1(B,A) & m1_finseq_1(B,k6_margrel1) ) => v1_int_1(k3_binari_2(A,B)) ) )).
fof(dt_k3_binarith,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(dt_k3_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ( v1_funct_1(k3_binom(A)) & v1_funct_2(k3_binom(A),k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)),u1_struct_0(A)) & m1_subset_1(k3_binom(A),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)),u1_struct_0(A)))) ) ) )).
fof(dt_k3_binop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(dt_k3_binop_2,axiom,( v1_funct_1(k3_binop_2) & v1_funct_2(k3_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & m1_subset_1(k3_binop_2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers))) )).
fof(dt_k3_boolealg,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k3_boolmark,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k3_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) )).
fof(dt_k3_borsuk_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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))))) ) ) )).
fof(dt_k3_borsuk_5,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => m1_subset_1(k3_borsuk_5(A,B),k1_zfmisc_1(k1_numbers)) ) )).
fof(dt_k3_borsuk_6,axiom,( 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)))) )).
fof(dt_k3_borsuk_7,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k3_brouwer,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & 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))) & v1_xreal_0(E) & ~ v3_xxreal_0(E) ) => m1_subset_1(k3_brouwer(A,B,C,D,E),u1_struct_0(k15_euclid(A))) ) )).
fof(dt_k3_bspace,axiom,( ! [A] : ! [B] : m1_subset_1(k3_bspace(A,B),u1_struct_0(k2_bspace)) )).
fof(dt_k3_bvfunc26,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k3_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k3_bvfunc_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) ) => m1_eqrel_1(k3_bvfunc_2(A,B),A) ) )).
fof(dt_k3_c0sp1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k3_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => l1_funcsdom(k3_c0sp2(A)) ) )).
fof(dt_k3_calcul_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k3_calcul_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) & v1_funct_1(C) & v1_funct_2(C,k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)) & v3_funct_2(C,k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)))) ) => m2_finseq_1(k3_calcul_2(A,B,C),A) ) )).
fof(dt_k3_card_2,axiom,( ! [A] : ! [B] : ( ( v1_card_1(A) & v1_card_1(B) ) => v1_card_1(k3_card_2(A,B)) ) )).
fof(dt_k3_card_fil,axiom,( ! [A] : ( ~ 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)))) ) ) )).
fof(dt_k3_card_fin,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_relat_1(B) & v1_funct_1(B) & v2_finset_1(B) ) => m1_subset_1(k3_card_fin(A,B),k4_ordinal1) ) )).
fof(dt_k3_cat_1,axiom,( ! [A] : ! [B] : ( v1_cat_1(k3_cat_1(A,B)) & l1_cat_1(k3_cat_1(A,B)) ) )).
fof(dt_k3_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)))) ) ) )).
fof(dt_k3_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k3_cat_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) ) )).
fof(dt_k3_catalan2,axiom,( ! [A] : m1_catalan2(k3_catalan2(A),A) )).
fof(dt_k3_catalg_1,axiom,( ! [A] : ( v1_msualg_1(k3_catalg_1(A)) & m1_catalg_1(k3_catalg_1(A),A) ) )).
fof(dt_k3_cayldick,axiom,( v1_cayldick(k3_cayldick) & l1_cayldick(k3_cayldick) )).
fof(dt_k3_cayley,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))))) ) ) )).
fof(dt_k3_cc0sp1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(dt_k3_cc0sp2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k3_cfdiff_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k3_cfuncdom,axiom,( ! [A] : ( ~ 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)))) ) ) )).
fof(dt_k3_cgames_1,axiom,( m1_subset_1(k3_cgames_1,k2_cgames_1(k5_ordinal1)) )).
fof(dt_k3_chain_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & 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))) ) ) )).
fof(dt_k3_chord,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) => ( ~ v8_ordinal1(k3_chord(A,B,C)) & m1_subset_1(k3_chord(A,B,C),k4_ordinal1) ) ) )).
fof(dt_k3_circcmb3,axiom,( ! [A] : ( ( v4_circcmb3(A) & l1_msualg_1(A) ) => m1_subset_1(k3_circcmb3(A),u1_struct_0(A)) ) )).
fof(dt_k3_circcomb,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(dt_k3_circtrm1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) ) )).
fof(dt_k3_circuit1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k3_circuit2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k3_classes1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => m1_subset_1(k3_classes1(A,B),k1_zfmisc_1(k1_classes1(A))) ) )).
fof(dt_k3_classes2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) ) => m1_subset_1(k3_classes2(A,B),A) ) )).
fof(dt_k3_clopban1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k3_clopban2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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)) ) )).
fof(dt_k3_clopban3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_clopban2(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k3_clopban3(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k3_clopban4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(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) & 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),k4_ordinal1,u1_struct_0(B)) & m1_subset_1(k3_clopban4(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) ) )).
fof(dt_k3_closure1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k3_closure2,axiom,( ! [A] : ( v4_funct_1(A) => ( v1_relat_1(k3_closure2(A)) & v1_funct_1(k3_closure2(A)) ) ) )).
fof(dt_k3_closure3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k3_clvect_1,axiom,( ! [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) ) => ( v1_clvect_1(k3_clvect_1(A)) & m1_clvect_1(k3_clvect_1(A),A) ) ) )).
fof(dt_k3_clvect_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,k1_numbers) & m1_subset_1(k3_clvect_2(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k3_clvect_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v7_ordinal1(C) & v7_ordinal1(D) ) => m1_subset_1(k3_clvect_3(A,B,C,D),u1_struct_0(A)) ) )).
fof(dt_k3_cohsp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k3_combgras,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k3_compl_sp,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k3_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => m1_subset_1(k3_complex1(A),k1_numbers) ) )).
fof(dt_k3_complex2,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_xreal_0(k3_complex2(A,B)) ) )).
fof(dt_k3_complsp2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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)) ) )).
fof(dt_k3_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_compos_1(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v7_ordinal1(C) ) => m1_subset_1(k3_compos_1(A,B,C),u1_compos_1(A)) ) )).
fof(dt_k3_compos_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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),k4_ordinal1) & 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) ) ) )).
fof(dt_k3_comput_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => ( v1_relat_1(k3_comput_1(A,B)) & v4_relat_1(k3_comput_1(A,B),k3_finseq_2(k4_ordinal1)) & v1_funct_1(k3_comput_1(A,B)) & v4_valued_0(k3_comput_1(A,B)) & v2_margrel1(k3_comput_1(A,B)) ) ) )).
fof(dt_k3_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => v1_xcmplx_0(k3_comseq_2(A)) ) )).
fof(dt_k3_comseq_3,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k3_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ( v1_funct_1(k3_conlat_1(A)) & v1_funct_2(k3_conlat_1(A),u1_struct_0(k2_yellow_1(u1_struct_0(A))),u1_struct_0(k2_yellow_1(u4_struct_0(A)))) & m1_subset_1(k3_conlat_1(A),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_yellow_1(u1_struct_0(A))),u1_struct_0(k2_yellow_1(u4_struct_0(A)))))) ) ) )).
fof(dt_k3_convex1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k3_convex4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k3_convfun1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) & ~ v2_struct_0(B) & l1_rlvect_1(B) ) => l1_rlvect_1(k3_convfun1(A,B)) ) )).
fof(dt_k3_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => m1_subset_1(k3_cqc_lang(A),k1_zfmisc_1(k9_qc_lang1(A))) ) )).
fof(dt_k3_cqc_sim1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) & v7_ordinal1(D) ) => 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))) ) )).
fof(dt_k3_cqc_the1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k3_csspace,axiom,( ! [A] : v1_xcmplx_0(k3_csspace(A)) )).
fof(dt_k3_csspace3,axiom,( ~ v2_struct_0(k3_csspace3) & l2_clvect_1(k3_csspace3) )).
fof(dt_k3_csspace4,axiom,( ~ v2_struct_0(k3_csspace4) & l2_clvect_1(k3_csspace4) )).
fof(dt_k3_decomp_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k3_descip_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & m1_finseq_1(C,A) ) => m2_finseq_1(k3_descip_1(A,B,C),A) ) )).
fof(dt_k3_dickson,axiom,( ! [A] : ( v1_relat_1(A) => v1_relat_1(k3_dickson(A)) ) )).
fof(dt_k3_diff_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k3_dilworth,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k3_dist_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(A) & m1_finseq_1(B,A) ) => v1_xreal_0(k3_dist_1(A,B,C)) ) )).
fof(dt_k3_dist_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k6_margrel1) & v1_funct_1(A) ) => m1_subset_1(k3_dist_2(A),k1_zfmisc_1(k9_xtuple_0(A))) ) )).
fof(dt_k3_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k3_dtconstr,axiom,( ! [A] : ! [B] : ! [C] : ( m1_finseq_1(C,k2_zfmisc_1(A,B)) => m2_finseq_1(k3_dtconstr(A,B,C),B) ) )).
fof(dt_k3_dynkin,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & v7_ordinal1(C) ) => m1_subset_1(k3_dynkin(A,B,C),k1_zfmisc_1(A)) ) )).
fof(dt_k3_e_siec,axiom,( ! [A] : ( 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)) ) )).
fof(dt_k3_ec_pf_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)))) ) ) )).
fof(dt_k3_ec_pf_2,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k3_endalg,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k3_ens_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k2_ens_1(A)) ) => m1_subset_1(k3_ens_1(A,B),A) ) )).
fof(dt_k3_entropy1,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & m1_finseq_1(B,k1_numbers) ) => m2_finseq_1(k3_entropy1(A,B),k1_numbers) ) )).
fof(dt_k3_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k3_equation,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => l3_msualg_1(k3_equation(A),A) ) )).
fof(dt_k3_euclid,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => m2_finseq_1(k3_euclid(A),k1_numbers) ) )).
fof(dt_k3_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => v1_xreal_0(k3_euclid_3(A)) ) )).
fof(dt_k3_euclid_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) )).
fof(dt_k3_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => v1_xreal_0(k3_euclid_5(A)) ) )).
fof(dt_k3_euclid_8,axiom,( m2_finseq_2(k3_euclid_8,k1_numbers,k1_euclid(3)) )).
fof(dt_k3_euclid_9,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k3_euclidlp,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k1_euclid(A)) & m1_subset_1(C,k1_euclidlp(A)) ) => v1_xreal_0(k3_euclidlp(A,B,C)) ) )).
fof(dt_k3_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v3_ordinal1(k3_exchsort(A)) ) )).
fof(dt_k3_extpro_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k3_extreal1,axiom,( ! [A] : ( v1_xxreal_0(A) => m1_subset_1(k3_extreal1(A),k6_numbers) ) )).
fof(dt_k3_facirc_1,axiom,( 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))) )).
fof(dt_k3_facirc_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k3_ff_siec,axiom,( ! [A] : ( v1_petri(k3_ff_siec(A)) & v1_net_1(k3_ff_siec(A)) & l1_petri(k3_ff_siec(A)) ) )).
fof(dt_k3_fib_fusc,axiom,( v1_relat_1(k3_fib_fusc) & v5_relat_1(k3_fib_fusc,u1_compos_1(k1_ami_3)) & v5_ordinal1(k3_fib_fusc) & v1_funct_1(k3_fib_fusc) & v1_finset_1(k3_fib_fusc) )).
fof(dt_k3_fib_num2,axiom,( m1_subset_1(k3_fib_num2,k1_zfmisc_1(k4_ordinal1)) )).
fof(dt_k3_fib_num3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) ) => m1_subset_1(k3_fib_num3(A,B,C),k4_ordinal1) ) )).
fof(dt_k3_filter_0,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k3_filter_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k3_filter_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k3_fin_topo,axiom,( ! [A] : m1_subset_1(k3_fin_topo(A),k1_zfmisc_1(k2_zfmisc_1(k1_tarski(A),k1_tarski(A)))) )).
fof(dt_k3_finance1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_funct_1(k3_finance1(A,B)) & v1_funct_2(k3_finance1(A,B),k4_ordinal1,k1_numbers) & m1_subset_1(k3_finance1(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k3_finseq_1(A),k4_ordinal1) ) )).
fof(dt_k3_finseq_2,axiom,( ! [A] : m1_finseq_2(k3_finseq_2(A),A) )).
fof(dt_k3_finseq_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k3_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k3_finseq_5,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k3_finseq_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k3_finseq_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_finseq_1(B,A) & v7_ordinal1(C) & v7_ordinal1(D) ) => m2_finseq_1(k3_finseq_8(A,B,C,D),A) ) )).
fof(dt_k3_finseqop,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(dt_k3_finsop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k3_finsop_1(A),k5_finsub_1(k4_ordinal1)) ) )).
fof(dt_k3_finsub_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k3_fintopo2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k3_fintopo3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k3_fintopo4,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k3_fintopo4(A),k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(A),k2_finseq_1(A)))) ) )).
fof(dt_k3_fintopo5,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => ( v1_orders_2(k3_fintopo5(A,B)) & l1_orders_2(k3_fintopo5(A,B)) ) ) )).
fof(dt_k3_flang_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m1_subset_1(k3_flang_1(A,B),k3_catalan2(A)) ) )).
fof(dt_k3_fomodel0,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ~ v1_xboole_0(k3_fomodel0(A,B)) & m1_subset_1(k3_fomodel0(A,B),k1_zfmisc_1(k3_finseq_2(A))) ) ) )).
fof(dt_k3_fomodel2,axiom,( ! [A] : ( 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))) ) )).
fof(dt_k3_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v3_fomodel4(B,A) & v3_fomodel4(C,A) ) => m1_subset_1(k3_fomodel4(A,B,C),k1_zfmisc_1(k30_fomodel2(A))) ) )).
fof(dt_k3_frechet,axiom,( ~ v2_struct_0(k3_frechet) & v1_pre_topc(k3_frechet) & v2_pre_topc(k3_frechet) & l1_pre_topc(k3_frechet) )).
fof(dt_k3_freealg,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,k4_ordinal1) ) => ( v1_lang1(k3_freealg(A,B)) & l1_lang1(k3_freealg(A,B)) ) ) )).
fof(dt_k3_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ 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)) ) )).
fof(dt_k3_fscirc_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k3_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k3_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k3_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : m1_subset_1(k3_ftacell1(A,B,C,D,E),k3_msafree2(k1_ftacell1(A,B,C,D,E))) )).
fof(dt_k3_funcsdom,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) )).
fof(dt_k3_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k3_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k3_funct_3(A)) & v1_funct_1(k3_funct_3(A)) ) ) )).
fof(dt_k3_funct_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k3_funct_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k3_funct_5(A)) & v1_funct_1(k3_funct_5(A)) ) ) )).
fof(dt_k3_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) & v1_finseq_1(B) ) => ( v1_relat_1(k3_funct_7(A,B)) & v1_funct_1(k3_funct_7(A,B)) ) ) )).
fof(dt_k3_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k3_functor2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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) ) )).
fof(dt_k3_functor3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(dt_k3_fuzzy_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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))) ) ) )).
fof(dt_k3_fuzzy_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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(k5_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))) ) ) )).
fof(dt_k3_fuzzy_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & v5_relat_1(D,k1_rcomp_1(k5_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(k5_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),k1_rcomp_1(k5_numbers,1)) & v1_funct_1(k3_fuzzy_4(A,B,C,D,E)) & v1_funct_2(k3_fuzzy_4(A,B,C,D,E),k2_zfmisc_1(A,C),k1_numbers) & m1_subset_1(k3_fuzzy_4(A,B,C,D,E),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,C),k1_numbers))) ) ) )).
fof(dt_k3_fvaluat1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k3_fvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k3_gcd_1,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k3_genealg1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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,k4_ordinal1) & m1_subset_1(E,k4_ordinal1) & m1_subset_1(F,k4_ordinal1) ) => m2_finseq_1(k3_genealg1(A,B,C,D,E,F),k3_card_3(A)) ) )).
fof(dt_k3_geomtrap,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) => v1_xreal_0(k3_geomtrap(A,B,C,D)) ) )).
fof(dt_k3_gfacirc1,axiom,( 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))) )).
fof(dt_k3_gfacirc2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k3_glib_000,axiom,( m1_subset_1(k3_glib_000,k4_ordinal1) )).
fof(dt_k3_glib_001,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(dt_k3_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)))) ) ) )).
fof(dt_k3_glib_003,axiom,( m1_subset_1(k3_glib_003,k4_ordinal1) )).
fof(dt_k3_glib_005,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(dt_k3_goboard5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_matrix_0(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)))) ) )).
fof(dt_k3_goboard9,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k3_gobrd13,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) & v7_ordinal1(C) ) => m1_subset_1(k3_gobrd13(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) )).
fof(dt_k3_goedelcp,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k3_gr_cy_1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_k3_graph_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k3_graph_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k3_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k3_graph_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) )).
fof(dt_k3_graphsp,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k3_grcat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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))) ) ) )).
fof(dt_k3_groeb_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k3_groeb_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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,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,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),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)))) ) ) )).
fof(dt_k3_groeb_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) & m1_subset_1(E,k4_ordinal1) ) => ( 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))) ) ) )).
fof(dt_k3_group_1,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k3_group_10,axiom,( ! [A] : ! [B] : m1_subset_1(k3_group_10(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) )).
fof(dt_k3_group_11,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k3_group_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k3_group_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k3_group_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k3_group_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k3_group_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k3_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k3_hahnban1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k3_hausdorf,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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)))) ) => v1_xreal_0(k3_hausdorf(A,B,C)) ) )).
fof(dt_k3_helly,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(dt_k3_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => m2_funct_2(k3_henmodel(A),k3_qc_lang1(A),k1_henmodel(A),k2_valuat_1(A,k1_henmodel(A))) ) )).
fof(dt_k3_hermitan,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k3_heyting1,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(dt_k3_heyting2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k3_heyting3,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => m1_subset_1(k3_heyting3(A,B),k4_partfun1(k4_ordinal1,k6_domain_1(k4_ordinal1,B))) ) )).
fof(dt_k3_hilbasis,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) ) )).
fof(dt_k3_hilbert1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_hilbert1) & m1_subset_1(B,k1_hilbert1) ) => m1_subset_1(k3_hilbert1(A,B),k1_hilbert1) ) )).
fof(dt_k3_hilbert2,axiom,( ! [A] : ( 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)) ) ) )).
fof(dt_k3_hurwitz,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l6_algstr_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,k4_ordinal1) ) => ( v1_funct_1(k3_hurwitz(A,B,C)) & v1_funct_2(k3_hurwitz(A,B,C),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k3_hurwitz(A,B,C),A) & m1_subset_1(k3_hurwitz(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k3_idea_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(k3_idea_1(A,B,C),A) & m2_finseq_1(k3_idea_1(A,B,C),k6_margrel1) ) ) )).
fof(dt_k3_incproj,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => l1_incsp_1(k3_incproj(A)) ) )).
fof(dt_k3_incsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k3_index_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k3_instalg1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))) ) )).
fof(dt_k3_int_2,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_int_1(B) ) => v7_ordinal1(k3_int_2(A,B)) ) )).
fof(dt_k3_int_3,axiom,( v1_funct_1(k3_int_3) & v1_funct_2(k3_int_3,u1_struct_0(k1_int_3),k4_ordinal1) & m1_subset_1(k3_int_3,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_int_3),k4_ordinal1))) )).
fof(dt_k3_int_5,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) ) ) )).
fof(dt_k3_int_7,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k3_integr10,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & v1_xreal_0(B) ) => v1_xreal_0(k3_integr10(A,B)) ) )).
fof(dt_k3_integr15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k4_ordinal1,k1_integra1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,k1_numbers) & m1_subset_1(k3_integr15(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k3_integr16,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k3_integr18,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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,k4_ordinal1,k1_integra1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k3_integr18(A,B,C,D,E),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k3_integr1c,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k3_integra1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => v1_xreal_0(k3_integra1(A)) ) )).
fof(dt_k3_integra2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,k1_integra1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) ) => ( v1_funct_1(k3_integra2(A,B,C)) & v1_funct_2(k3_integra2(A,B,C),k4_ordinal1,k1_numbers) & m1_subset_1(k3_integra2(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k3_integra5,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k3_interva1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k3_intpro_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k3_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_funct_1(k3_irrat_1(A)) & v1_funct_2(k3_irrat_1(A),k4_ordinal1,k1_numbers) & m1_subset_1(k3_irrat_1(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k3_isocat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) )).
fof(dt_k3_isocat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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,k6_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)))) ) ) )).
fof(dt_k3_jgraph_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) ) => m2_finseq_1(k3_jgraph_1(A,B),u4_struct_0(k1_jgraph_1(A))) ) )).
fof(dt_k3_jgraph_4,axiom,( ! [A] : ( 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))))) ) ) )).
fof(dt_k3_jgraph_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) )).
fof(dt_k3_jordan10,axiom,( ! [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)))) ) => m1_subset_1(k3_jordan10(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) ) )).
fof(dt_k3_jordan11,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => m1_subset_1(k3_jordan11(A),k4_ordinal1) ) )).
fof(dt_k3_jordan19,axiom,( ! [A] : ( ( 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)))) ) )).
fof(dt_k3_jordan1h,axiom,( ! [A] : ! [B] : ( ( 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) ) => v7_ordinal1(k3_jordan1h(A,B)) ) )).
fof(dt_k3_jordan3,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k3_jordan5d,axiom,( ! [A] : ( ( ~ 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))) ) => v7_ordinal1(k3_jordan5d(A)) ) )).
fof(dt_k3_jordan6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) )).
fof(dt_k3_jordan_a,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => v1_xreal_0(k3_jordan_a(A,B)) ) )).
fof(dt_k3_kolmog01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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))) ) )).
fof(dt_k3_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => m1_subset_1(k3_kurato_0(A,B),k1_zfmisc_1(A)) ) )).
fof(dt_k3_kurato_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k3_kurato_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => m1_subset_1(k3_kurato_2(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k3_laplace,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) & ~ v1_xboole_0(D) & v1_matrix_0(E) & v2_matrix_0(E,D,B,C) & m1_finseq_1(E,k3_finseq_2(D)) & m1_finseq_1(F,D) ) => ( v1_matrix_0(k3_laplace(A,B,C,D,E,F)) & v2_matrix_0(k3_laplace(A,B,C,D,E,F),D,B,C) & m2_finseq_1(k3_laplace(A,B,C,D,E,F),k3_finseq_2(D)) ) ) )).
fof(dt_k3_latsubgr,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))))) ) ) )).
fof(dt_k3_lattice2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k3_lattice3,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k3_lattice4,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k3_lattice5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) )).
fof(dt_k3_lattice6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k3_lattice7,axiom,( ! [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(k3_lattice7(A),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k3_lattices,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k3_lexbfs,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k3_lfuzzy_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k3_lfuzzy_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( v5_relat_1(k3_lfuzzy_1(A,B),k1_rcomp_1(k5_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))) ) ) )).
fof(dt_k3_limfunc1,axiom,( ! [A] : ( v1_xreal_0(A) => m1_subset_1(k3_limfunc1(A),k1_zfmisc_1(k1_numbers)) ) )).
fof(dt_k3_lopban_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))))) ) ) )).
fof(dt_k3_lopban_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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)) ) )).
fof(dt_k3_lopban_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_lopban_2(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k3_lopban_3(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k3_lopban_4,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_funct_1(k3_lopban_4(A)) & v1_funct_2(k3_lopban_4(A),k4_ordinal1,k1_numbers) & m1_subset_1(k3_lopban_4(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k3_lopban_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => m1_subset_1(k3_lopban_7(A,B,C),k1_zfmisc_1(u1_struct_0(k7_prvect_3(A,B)))) ) )).
fof(dt_k3_lopclset,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k3_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ( 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))) ) ) )).
fof(dt_k3_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v1_membered(B) & m1_subset_1(C,k3_rfunct_3(A,B)) & m1_subset_1(D,k3_rfunct_3(A,B)) ) => m2_rfunct_3(k3_lpspacc1(A,B,C,D),A,k2_numbers,k3_rfunct_3(A,k2_numbers)) ) )).
fof(dt_k3_lpspace1,axiom,( ! [A] : ( ~ 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)))) ) ) )).
fof(dt_k3_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v2_xxreal_0(D) & v1_xreal_0(D) ) => ( ~ 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)))) ) ) )).
fof(dt_k3_ltlaxio1,axiom,( m1_subset_1(k3_ltlaxio1,k1_hilbert1) )).
fof(dt_k3_ltlaxio3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_funct_1(B) & m1_finseq_1(B,A) & v2_funct_1(C) & m1_finseq_1(C,A) ) => ( v2_funct_1(k3_ltlaxio3(A,B,C)) & m2_finseq_1(k3_ltlaxio3(A,B,C),A) ) ) )).
fof(dt_k3_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)))) => m1_subset_1(k3_ltlaxio4(A),k1_zfmisc_1(k1_hilbert1)) ) )).
fof(dt_k3_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k3_matrix10,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m1_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( v1_matrix_0(k3_matrix10(A,B)) & v2_matrix_0(k3_matrix10(A,B),k1_numbers,A,A) & m2_finseq_1(k3_matrix10(A,B),k3_finseq_2(k1_numbers)) ) ) )).
fof(dt_k3_matrix11,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) & ~ v1_xboole_0(D) & v1_matrix_0(E) & v2_matrix_0(E,D,B,C) & m1_finseq_1(E,k3_finseq_2(D)) & m1_finseq_1(F,D) ) => ( v1_matrix_0(k3_matrix11(A,B,C,D,E,F)) & v2_matrix_0(k3_matrix11(A,B,C,D,E,F),D,B,C) & m2_finseq_1(k3_matrix11(A,B,C,D,E,F),k3_finseq_2(D)) ) ) )).
fof(dt_k3_matrix12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & ~ 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) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(C))) & v7_ordinal1(E) & v7_ordinal1(F) & m1_subset_1(G,u1_struct_0(C)) ) => ( v1_matrix_0(k3_matrix12(A,B,C,D,E,F,G)) & v2_matrix_0(k3_matrix12(A,B,C,D,E,F,G),u1_struct_0(C),A,B) & m2_finseq_1(k3_matrix12(A,B,C,D,E,F,G),k3_finseq_2(u1_struct_0(C))) ) ) )).
fof(dt_k3_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k3_matrix13(A),k1_zfmisc_1(k4_ordinal1)) ) )).
fof(dt_k3_matrix14,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) )).
fof(dt_k3_matrix15,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) ) => ( v1_matrix_0(k3_matrix15(A,B)) & v2_matrix_0(k3_matrix15(A,B),A,k3_finseq_1(B),1) & m2_finseq_1(k3_matrix15(A,B),k3_finseq_2(A)) ) ) )).
fof(dt_k3_matrix16,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) => ( v1_matrix_0(k3_matrix16(A,B)) & v2_matrix_0(k3_matrix16(A,B),u1_struct_0(A),k3_finseq_1(B),k3_finseq_1(B)) & m2_finseq_1(k3_matrix16(A,B),k3_finseq_2(u1_struct_0(A))) ) ) )).
fof(dt_k3_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(A)) & v7_ordinal1(C) & v7_ordinal1(D) ) => m1_subset_1(k3_matrix_0(A,B,C,D),A) ) )).
fof(dt_k3_matrix_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) & v7_ordinal1(B) ) => ( v1_matrix_0(k3_matrix_1(A,B)) & v2_matrix_0(k3_matrix_1(A,B),u1_struct_0(A),B,B) & m2_finseq_1(k3_matrix_1(A,B),k3_finseq_2(u1_struct_0(A))) ) ) )).
fof(dt_k3_matrix_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_0(B) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(A))) & v1_matrix_0(C) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( v1_matrix_0(k3_matrix_3(A,B,C)) & m2_finseq_1(k3_matrix_3(A,B,C),k3_finseq_2(u1_struct_0(A))) ) ) )).
fof(dt_k3_matrix_5,axiom,( ! [A] : ! [B] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k2_numbers)) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(k2_numbers)) ) => ( v1_matrix_0(k3_matrix_5(A,B)) & m2_finseq_1(k3_matrix_5(A,B),k3_finseq_2(k2_numbers)) ) ) )).
fof(dt_k3_matrix_7,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k3_matrix_2(A)) ) => m1_matrix_2(k3_matrix_7(A,B),k3_matrix_2(A)) ) )).
fof(dt_k3_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k3_matrixr1,axiom,( ! [A] : ! [B] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k1_numbers)) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( v1_matrix_0(k3_matrixr1(A,B)) & m2_finseq_1(k3_matrixr1(A,B),k3_finseq_2(k1_numbers)) ) ) )).
fof(dt_k3_matrixr2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m1_finseq_1(B,k3_finseq_2(k1_numbers)) ) => v1_xreal_0(k3_matrixr2(A,B)) ) )).
fof(dt_k3_matrlin,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k3_matrlin2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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_0(k3_matrlin2(A,B,C,D,E,F)) & v2_matrix_0(k3_matrlin2(A,B,C,D,E,F),u1_struct_0(A),k3_finseq_1(E),k3_finseq_1(E)) & m2_finseq_1(k3_matrlin2(A,B,C,D,E,F),k3_finseq_2(u1_struct_0(A))) ) ) )).
fof(dt_k3_matroid0,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) ) )).
fof(dt_k3_matrprob,axiom,( ! [A] : ( m1_finseq_1(A,k3_finseq_2(k1_numbers)) => m2_finseq_1(k3_matrprob(A),k1_numbers) ) )).
fof(dt_k3_matrtop1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,B) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( 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))))) ) ) )).
fof(dt_k3_matrtop3,axiom,( ! [A] : ! [B] : ( ( 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))))) ) => ( v1_matrix_0(k3_matrtop3(A,B)) & v2_matrix_0(k3_matrtop3(A,B),u1_struct_0(k2_vectsp_1),A,A) & m2_finseq_1(k3_matrtop3(A,B),k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) ) )).
fof(dt_k3_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k3_measure1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k3_measure3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_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))) ) ) )).
fof(dt_k3_measure4,axiom,( ! [A] : ! [B] : ( m1_measure4(B,A) => ( v1_funct_1(k3_measure4(A,B)) & v1_funct_2(k3_measure4(A,B),k1_measure4(A,B),k6_numbers) & m1_subset_1(k3_measure4(A,B),k1_zfmisc_1(k2_zfmisc_1(k1_measure4(A,B),k6_numbers))) ) ) )).
fof(dt_k3_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => m1_subset_1(k3_measure6(A),k1_zfmisc_1(k1_numbers)) ) )).
fof(dt_k3_measure7,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1,k6_numbers) & m1_subset_1(k3_measure7(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) ) )).
fof(dt_k3_measure8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & m4_measure8(D,A,B,C) & v7_ordinal1(E) ) => m3_measure8(k3_measure8(A,B,C,D,E),A,k9_nat_1(k9_setfam_1(A),C,E),B) ) )).
fof(dt_k3_member_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_numbers) & m1_subset_1(B,k6_numbers) ) => m1_subset_1(k3_member_1(A,B),k6_numbers) ) )).
fof(dt_k3_mesfun6c,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_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)) ) )).
fof(dt_k3_mesfun7c,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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,k6_numbers))) ) ) )).
fof(dt_k3_mesfun9c,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ( v1_funct_1(k3_mesfun9c(A,B)) & v1_funct_2(k3_mesfun9c(A,B),k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(k3_mesfun9c(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) ) )).
fof(dt_k3_mesfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k6_numbers) & v1_funct_1(B) & v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,k6_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,k6_numbers))) ) ) )).
fof(dt_k3_mesfunc2,axiom,( ! [A] : ! [B] : ( v1_funct_1(k3_mesfunc2(A,B)) & m1_subset_1(k3_mesfunc2(A,B),k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) )).
fof(dt_k3_mesfunc5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) & m1_subset_1(C,A) ) => ( v1_funct_1(k3_mesfunc5(A,B,C)) & v1_funct_2(k3_mesfunc5(A,B,C),k4_ordinal1,k6_numbers) & m1_subset_1(k3_mesfunc5(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) ) )).
fof(dt_k3_mesfunc8,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ( v1_funct_1(k3_mesfunc8(A,B)) & v1_funct_2(k3_mesfunc8(A,B),k4_ordinal1,k4_partfun1(A,k6_numbers)) & v1_mesfunc8(k3_mesfunc8(A,B),A,k6_numbers) & m1_subset_1(k3_mesfunc8(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) ) )).
fof(dt_k3_mesfunc9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_valued_0(A) ) => m1_subset_1(k3_mesfunc9(A),k6_numbers) ) )).
fof(dt_k3_metric_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v8_metric_1(A) & l1_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => v1_xreal_0(k3_metric_1(A,B,C)) ) )).
fof(dt_k3_metric_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k3_metric_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k3_metric_6(A,B,C)) & v1_funct_2(k3_metric_6(A,B,C),k4_ordinal1,k1_numbers) & m1_subset_1(k3_metric_6(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k3_mfold_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k3_midsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k3_midsp_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k3_midsp_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( m1_subset_1(A,k4_ordinal1) & ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_nat_1(A,2)) & m1_subset_1(C,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) & 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(k1_nat_1(C,D),u1_struct_0(B))) ) )).
fof(dt_k3_mmlquer2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => m1_subset_1(k3_mmlquer2(A,B),k1_zfmisc_1(k2_zfmisc_1(A,A))) ) )).
fof(dt_k3_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k3_mod_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) ) )).
fof(dt_k3_mod_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k3_modcat_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k3_modelc_2,axiom,( ! [A] : ( m1_finseq_1(A,k4_ordinal1) => m2_finseq_1(k3_modelc_2(A),k4_ordinal1) ) )).
fof(dt_k3_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => m1_subset_1(k3_modelc_3(A),k1_zfmisc_1(k1_modelc_3(A))) ) )).
fof(dt_k3_moebius1,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k3_moebius1(A),k1_zfmisc_1(k4_ordinal1)) ) )).
fof(dt_k3_monoid_0,axiom,( ~ v2_struct_0(k3_monoid_0) & v15_algstr_0(k3_monoid_0) & m2_monoid_0(k3_monoid_0,k2_monoid_0) )).
fof(dt_k3_monoid_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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)) ) )).
fof(dt_k3_morph_01,axiom,( ! [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) & 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))))) ) ) )).
fof(dt_k3_msafree,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k3_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => m1_subset_1(k3_msafree2(A),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k3_msafree3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(dt_k3_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( v1_relat_1(k3_msafree4(A,B,C,D)) & v4_relat_1(k3_msafree4(A,B,C,D),B) & v1_funct_1(k3_msafree4(A,B,C,D)) & v1_partfun1(k3_msafree4(A,B,C,D),B) ) ) )).
fof(dt_k3_msalimit,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(dt_k3_msaterm,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k3_msscyc_2,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_k3_mssubfam,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k3_msualg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) )).
fof(dt_k3_msualg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k3_msualg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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) ) )).
fof(dt_k3_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))) ) )).
fof(dt_k3_msualg_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k3_msualg_6,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k3_msualg_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))))) ) )).
fof(dt_k3_mycielsk,axiom,( ! [A] : ( ( v2_mycielsk(A) & l1_orders_2(A) ) => v7_ordinal1(k3_mycielsk(A)) ) )).
fof(dt_k3_nagata_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k3_nagata_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k3_nat_1,axiom,( ! [A] : m1_subset_1(k3_nat_1(A),k4_ordinal1) )).
fof(dt_k3_nat_5,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => m1_subset_1(k3_nat_5(A,B),k4_ordinal1) ) )).
fof(dt_k3_nat_d,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => m1_subset_1(k3_nat_d(A,B),k4_ordinal1) ) )).
fof(dt_k3_nat_lat,axiom,( ~ v2_struct_0(k3_nat_lat) & v3_lattices(k3_nat_lat) & l3_lattices(k3_nat_lat) )).
fof(dt_k3_nattra_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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(k3_nattra_1(A,B,C,D,E,F,G),A,B,C,E) ) )).
fof(dt_k3_ndiff_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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) & 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))) ) )).
fof(dt_k3_ndiff_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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) & 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)) ) )).
fof(dt_k3_ndiff_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & 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))) ) ) )).
fof(dt_k3_ndiff_5,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & ~ v1_xboole_0(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))))) ) ) )).
fof(dt_k3_necklace,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_orders_2(k3_necklace(A)) & l1_orders_2(k3_necklace(A)) ) ) )).
fof(dt_k3_normform,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k3_normsp_0,axiom,( ! [A] : ! [B] : ( ( ~ 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(k3_normsp_0(A,B)) & v1_funct_1(k3_normsp_0(A,B)) ) ) )).
fof(dt_k3_normsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k3_normsp_1(A,B,C)) & v1_funct_2(k3_normsp_1(A,B,C),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k3_normsp_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k3_normsp_2,axiom,( ! [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) & 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)) ) ) )).
fof(dt_k3_ntalgo_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_numbers) & m1_subset_1(B,k4_numbers) ) => m1_subset_1(k3_ntalgo_1(A,B),k4_numbers) ) )).
fof(dt_k3_openlatt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k3_oppcat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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))) ) )).
fof(dt_k3_ordeq_01,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_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) & l1_normsp_1(B) ) => ( v1_funct_1(k3_ordeq_01(A,B)) & v1_funct_2(k3_ordeq_01(A,B),k1_ordeq_01(A,B),k1_numbers) & m1_subset_1(k3_ordeq_01(A,B),k1_zfmisc_1(k2_zfmisc_1(k1_ordeq_01(A,B),k1_numbers))) ) ) )).
fof(dt_k3_orders_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k3_ordinal2,axiom,( ! [A] : v3_ordinal1(k3_ordinal2(A)) )).
fof(dt_k3_ordinal4,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(dt_k3_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => v3_ordinal1(k3_ordinal5(A)) ) )).
fof(dt_k3_ordinal6,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k3_osafree,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k3_osalg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k3_osalg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k3_osalg_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k3_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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))))) ) ) )).
fof(dt_k3_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k3_partfun2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k3_partit1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_eqrel_1(B,A) & m1_eqrel_1(C,A) ) => m1_eqrel_1(k3_partit1(A,B,C),A) ) )).
fof(dt_k3_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k3_pcomps_1,axiom,( ! [A] : ( l1_metric_1(A) => l1_pre_topc(k3_pcomps_1(A)) ) )).
fof(dt_k3_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)))) ) )).
fof(dt_k3_pdiff_1,axiom,( ! [A] : ! [B] : ( ( 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)))) ) ) )).
fof(dt_k3_pdiff_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) => v1_xreal_0(k3_pdiff_3(A,B)) ) )).
fof(dt_k3_pdiff_5,axiom,( ! [A] : ! [B] : ( ( 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)) ) => v1_xreal_0(k3_pdiff_5(A,B)) ) )).
fof(dt_k3_pdiff_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & 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))) ) ) )).
fof(dt_k3_pencil_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k3_pencil_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k3_pencil_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))))))) ) ) )).
fof(dt_k3_pencil_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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))) ) )).
fof(dt_k3_pepin,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => m1_subset_1(k3_pepin(A,B),k4_ordinal1) ) )).
fof(dt_k3_petri,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k3_pnproc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) & v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ( v1_funct_1(k3_pnproc_1(A,B,C)) & v1_funct_2(k3_pnproc_1(A,B,C),A,k4_ordinal1) & m1_subset_1(k3_pnproc_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) ) )).
fof(dt_k3_polyalg1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(dt_k3_polyeq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => m1_subset_1(k3_polyeq_3(A),k2_numbers) ) )).
fof(dt_k3_polyeq_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => v1_xcmplx_0(k3_polyeq_5(A,B,C)) ) )).
fof(dt_k3_polyform,axiom,( ! [A] : ( v1_int_1(A) => m2_finseq_1(k3_polyform(A),k4_numbers) ) )).
fof(dt_k3_polynom1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v2_struct_0(B) & 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(k3_polynom1(A,B,C),k1_zfmisc_1(A)) ) )).
fof(dt_k3_polynom5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k3_polynom5(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k3_polynom7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k3_polynom8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k3_polyred,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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(k12_polynom1(A,C)))) ) => m1_subset_1(k3_polyred(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k8_struct_0(k12_polynom1(A,C)),u1_struct_0(k12_polynom1(A,C))))) ) )).
fof(dt_k3_poset_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k3_power,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => v1_xreal_0(k3_power(A,B)) ) )).
fof(dt_k3_pralg_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k3_pre_ff,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k3_pre_ff(A),k4_ordinal1) ) )).
fof(dt_k3_pre_poly,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m2_finseq_2(k3_pre_poly(A,B),A,k3_finseq_2(A)) ) )).
fof(dt_k3_prelamb,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k3_prob_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => m1_subset_1(k3_prob_1(A,B),k1_zfmisc_1(A)) ) )).
fof(dt_k3_prob_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k3_prob_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_funct_1(k3_prob_3(A,B)) & v1_funct_2(k3_prob_3(A,B),k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(k3_prob_3(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) )).
fof(dt_k3_prob_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => m2_prob_1(k3_prob_4(A,B,C),A,B) ) )).
fof(dt_k3_prvect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k3_prvect_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k3_prvect_3,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k3_pscomp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k3_pua2mss1,axiom,( ! [A] : ! [B] : ( m2_pua2mss1(B,A) => m1_eqrel_1(k3_pua2mss1(A,B),A) ) )).
fof(dt_k3_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => m1_subset_1(k3_qc_lang1(A),k1_zfmisc_1(k2_qc_lang1(A))) ) )).
fof(dt_k3_qc_lang2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k3_qc_lang3,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & v7_ordinal1(B) ) => m2_subset_1(k3_qc_lang3(A,B),k2_qc_lang1(A),k5_qc_lang1(A)) ) )).
fof(dt_k3_qc_lang4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k3_qc_trans,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(A) & v1_qc_trans(B,A) & m1_qc_lang1(B) & v7_ordinal1(C) & m1_subset_1(D,k8_qc_lang1(A,C)) ) => m2_subset_1(k3_qc_trans(A,B,C,D),k6_qc_lang1(B),k8_qc_lang1(B,C)) ) )).
fof(dt_k3_quantal1,axiom,( ! [A] : ( l3_quantal1(A) => m1_subset_1(k3_quantal1(A),u1_struct_0(A)) ) )).
fof(dt_k3_quatern2,axiom,( m1_subset_1(k3_quatern2,k1_quaterni) )).
fof(dt_k3_quaterni,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [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))) ) ) )).
fof(dt_k3_quofield,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k3_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ v1_xboole_0(k3_radix_1(A)) & m1_subset_1(k3_radix_1(A),k1_zfmisc_1(k4_numbers)) ) ) )).
fof(dt_k3_radix_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v3_card_1(C,A) & m1_finseq_1(C,k4_ordinal1) ) => m1_subset_1(k3_radix_2(A,B,C),k4_ordinal1) ) )).
fof(dt_k3_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ v1_xboole_0(k3_radix_3(A)) & m1_subset_1(k3_radix_3(A),k1_zfmisc_1(k4_numbers)) ) ) )).
fof(dt_k3_radix_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) ) => m2_subset_1(k3_radix_5(A,B,C),k4_numbers,k3_radix_1(C)) ) )).
fof(dt_k3_radix_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k3_random_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k3_random_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k3_ranknull,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) ) )).
fof(dt_k3_ratfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v7_struct_0(A) & l5_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & ~ v1_ratfunc1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => m1_ratfunc1(k3_ratfunc1(A,B,C),A) ) )).
fof(dt_k3_rcomp_1,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xxreal_0(B) ) => m1_subset_1(k3_rcomp_1(A,B),k1_zfmisc_1(k1_numbers)) ) )).
fof(dt_k3_real_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k3_real_1(A,B),k1_numbers) ) )).
fof(dt_k3_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_funct_1(k3_real_3(A)) & v1_funct_2(k3_real_3(A),k4_ordinal1,k1_numbers) & m1_subset_1(k3_real_3(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k3_real_lat,axiom,( v3_lattices(k3_real_lat) & l3_lattices(k3_real_lat) )).
fof(dt_k3_real_ns1,axiom,( ! [A] : ( 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))) ) ) )).
fof(dt_k3_rearran1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k3_relat_1,axiom,( ! [A] : ! [B] : v1_relat_1(k3_relat_1(A,B)) )).
fof(dt_k3_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(dt_k3_relset_2,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( v1_relat_1(k3_relset_2(A,B)) & v1_funct_1(k3_relset_2(A,B)) ) ) )).
fof(dt_k3_rewrite2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,k8_afinsq_1(A)) & v7_ordinal1(C) ) => m1_subset_1(k3_rewrite2(A,B,C),k8_afinsq_1(A)) ) )).
fof(dt_k3_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))) ) )).
fof(dt_k3_rfinseq,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => m2_finseq_1(k3_rfinseq(A),k1_numbers) ) )).
fof(dt_k3_rfinseq2,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => v1_xreal_0(k3_rfinseq2(A)) ) )).
fof(dt_k3_rfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) )).
fof(dt_k3_rfunct_3,axiom,( ! [A] : ! [B] : m1_rfunct_3(k3_rfunct_3(A,B),A,B) )).
fof(dt_k3_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_funct_1(k3_rinfsup1(A)) & v1_funct_2(k3_rinfsup1(A),k4_ordinal1,k1_numbers) & m1_subset_1(k3_rinfsup1(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k3_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v1_funct_1(k3_rinfsup2(A)) & v1_funct_2(k3_rinfsup2(A),k4_ordinal1,k6_numbers) & m1_subset_1(k3_rinfsup2(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) ) )).
fof(dt_k3_ringcat1,axiom,( ! [A] : ( 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))))) ) ) )).
fof(dt_k3_rlaffin1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & m1_rlvect_2(B,A) ) => v1_xreal_0(k3_rlaffin1(A,B)) ) )).
fof(dt_k3_rlsub_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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))) ) )).
fof(dt_k3_rltopsp1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k3_rlvect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k3_rlvect_2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k3_rlvect_x,axiom,( ! [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) & 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))) ) )).
fof(dt_k3_rmod_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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))) ) )).
fof(dt_k3_rmod_4,axiom,( ! [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) & 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) ) )).
fof(dt_k3_robbins1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k3_roughs_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k3_rsspace,axiom,( v1_funct_1(k3_rsspace) & v1_funct_2(k3_rsspace,k2_zfmisc_1(k1_rsspace,k1_rsspace),k1_rsspace) & m1_subset_1(k3_rsspace,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_rsspace,k1_rsspace),k1_rsspace))) )).
fof(dt_k3_rsspace3,axiom,( ~ v2_struct_0(k3_rsspace3) & l1_normsp_1(k3_rsspace3) )).
fof(dt_k3_rsspace4,axiom,( ~ v2_struct_0(k3_rsspace4) & l1_normsp_1(k3_rsspace4) )).
fof(dt_k3_rusub_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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))) ) )).
fof(dt_k3_rusub_4,axiom,( ! [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) & 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))) ) ) )).
fof(dt_k3_rusub_5,axiom,( ! [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) & 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) ) ) )).
fof(dt_k3_rvsum_1,axiom,( ! [A] : ( 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))) ) ) )).
fof(dt_k3_rvsum_2,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k3_scm_comp,axiom,( ! [A] : ( 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)) ) )).
fof(dt_k3_scm_inst,axiom,( ~ v1_xboole_0(k3_scm_inst) )).
fof(dt_k3_scmfsa6a,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k3_scmfsa8b,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k3_scmfsa_1,axiom,( m1_subset_1(k3_scmfsa_1,k1_zfmisc_1(k1_scmfsa_1)) )).
fof(dt_k3_scmfsa_2,axiom,( m1_subset_1(k3_scmfsa_2,k1_zfmisc_1(u1_struct_0(k1_scmfsa_2))) )).
fof(dt_k3_scmfsa_7,axiom,( ! [A] : ! [B] : ( ( m1_scmfsa_2(A) & m1_finseq_1(B,k4_numbers) ) => ( v1_relat_1(k3_scmfsa_7(A,B)) & v5_relat_1(k3_scmfsa_7(A,B),u1_compos_1(k1_scmfsa_2)) & v5_ordinal1(k3_scmfsa_7(A,B)) & v1_funct_1(k3_scmfsa_7(A,B)) & v1_finset_1(k3_scmfsa_7(A,B)) ) ) )).
fof(dt_k3_scmfsa_9,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k3_scmfsa_m,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k3_scmfsa_2)) ) => m1_scmfsa_2(k3_scmfsa_m(A)) ) )).
fof(dt_k3_scmisort,axiom,( ~ v1_xboole_0(k3_scmisort) & v1_relat_1(k3_scmisort) & v4_relat_1(k3_scmisort,k4_ordinal1) & 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) )).
fof(dt_k3_scmp_gcd,axiom,( v1_ami_2(k3_scmp_gcd) & m1_subset_1(k3_scmp_gcd,u1_struct_0(k1_scmpds_2)) )).
fof(dt_k3_scmpds_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k3_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => m1_subset_1(k3_scmpds_2(A),u1_compos_1(k1_scmpds_2)) ) )).
fof(dt_k3_scmpds_4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_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_scmpds_2)) ) => ( v1_relat_1(k3_scmpds_4(A,B)) & v4_relat_1(k3_scmpds_4(A,B),k4_ordinal1) & v5_relat_1(k3_scmpds_4(A,B),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k3_scmpds_4(A,B)) & v1_funct_1(k3_scmpds_4(A,B)) & v1_finset_1(k3_scmpds_4(A,B)) & v1_afinsq_1(k3_scmpds_4(A,B)) ) ) )).
fof(dt_k3_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) & v1_int_1(B) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ( v1_relat_1(k3_scmpds_6(A,B,C,D)) & v4_relat_1(k3_scmpds_6(A,B,C,D),k4_ordinal1) & v5_relat_1(k3_scmpds_6(A,B,C,D),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k3_scmpds_6(A,B,C,D)) & 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)) ) ) )).
fof(dt_k3_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => m1_subset_1(k3_scmpds_i(A),k2_scm_inst) ) )).
fof(dt_k3_scmring1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) )).
fof(dt_k3_scmring2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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))) ) )).
fof(dt_k3_scmringi,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k3_semi_af1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k3_seq_4,axiom,( ! [A] : ( v3_membered(A) => v1_xreal_0(k3_seq_4(A)) ) )).
fof(dt_k3_seqfunc,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( v1_funct_1(k3_seqfunc(A,B)) & v1_funct_2(k3_seqfunc(A,B),k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(k3_seqfunc(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) ) )).
fof(dt_k3_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_funct_1(k3_series_1(A)) & v1_funct_2(k3_series_1(A),k4_ordinal1,k1_numbers) & m1_subset_1(k3_series_1(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k3_setlim_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k3_setlim_1(A)) & v1_funct_1(k3_setlim_1(A)) ) ) )).
fof(dt_k3_setlim_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_funct_1(k3_setlim_2(A,B,C)) & v1_funct_2(k3_setlim_2(A,B,C),k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(k3_setlim_2(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) )).
fof(dt_k3_setwiseo,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k3_sf_mastr,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => m1_subset_1(k3_sf_mastr(A),k5_finsub_1(k3_scmfsa_2)) ) )).
fof(dt_k3_sfmastr2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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_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),k4_ordinal1,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2))) & m1_subset_1(k3_sfmastr2(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2))))) ) ) )).
fof(dt_k3_sfmastr3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k3_sheffer1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k3_simplex0,axiom,( ! [A] : ! [B] : ! [C] : m1_subset_1(k3_simplex0(A,B,C),k1_zfmisc_1(k1_zfmisc_1(A))) )).
fof(dt_k3_simplex1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k3_simplex2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_simplex0(B,u1_struct_0(k15_euclid(A))) ) => v1_xreal_0(k3_simplex2(A,B)) ) )).
fof(dt_k3_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( v1_funct_1(k3_sin_cos(A)) & v1_funct_2(k3_sin_cos(A),k4_ordinal1,k2_numbers) & m1_subset_1(k3_sin_cos(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) ) )).
fof(dt_k3_sin_cos2,axiom,( v1_funct_1(k3_sin_cos2) & v1_funct_2(k3_sin_cos2,k1_numbers,k1_numbers) & m1_subset_1(k3_sin_cos2,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) )).
fof(dt_k3_sin_cos3,axiom,( 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))) )).
fof(dt_k3_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k3_sin_cos4(A)) ) )).
fof(dt_k3_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k3_sin_cos5(A)) ) )).
fof(dt_k3_sin_cos6,axiom,( v1_funct_1(k3_sin_cos6) & m1_subset_1(k3_sin_cos6,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) )).
fof(dt_k3_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k3_sin_cos7(A)) ) )).
fof(dt_k3_sincos10,axiom,( v1_funct_1(k3_sincos10) & m1_subset_1(k3_sincos10,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) )).
fof(dt_k3_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k3_square_1(A)) ) )).
fof(dt_k3_stacks_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k3_struct_0,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_k3_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) )).
fof(dt_k3_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => m1_subset_1(k3_subset_1(A,B),k1_zfmisc_1(A)) ) )).
fof(dt_k3_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k3_substut1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k3_substut2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k3_supinf_1,axiom,( ! [A] : ( v2_membered(A) => v2_membered(k3_supinf_1(A)) ) )).
fof(dt_k3_supinf_2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_numbers) & m1_subset_1(B,k6_numbers) ) => m1_subset_1(k3_supinf_2(A,B),k6_numbers) ) )).
fof(dt_k3_t_0topsp,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k3_taxonom1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k3_taylor_1,axiom,( v1_funct_1(k3_taylor_1) & m1_subset_1(k3_taylor_1,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) )).
fof(dt_k3_tbsp_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v1_xreal_0(k3_tbsp_1(A,B)) ) )).
fof(dt_k3_tdlat_1,axiom,( ! [A] : ( ( 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)))) ) ) )).
fof(dt_k3_termord,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,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)) ) )).
fof(dt_k3_tex_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => l1_pre_topc(k3_tex_1(A,B)) ) )).
fof(dt_k3_tex_4,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k3_tmap_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k3_topalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) )).
fof(dt_k3_topalg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k3_topalg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))))) ) ) )).
fof(dt_k3_topalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k3_topalg_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k3_topalg_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k3_topdim_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k3_topgen_1,axiom,( ! [A] : ! [B] : ( ( 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)))) ) )).
fof(dt_k3_topgen_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k3_topgen_3,axiom,( ~ v1_finset_1(k3_topgen_3) & v1_card_1(k3_topgen_3) )).
fof(dt_k3_topgen_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k3_topgen_5,axiom,( ~ v2_struct_0(k3_topgen_5) & v1_pre_topc(k3_topgen_5) & v2_pre_topc(k3_topgen_5) & l1_pre_topc(k3_topgen_5) )).
fof(dt_k3_topmetr,axiom,( v2_pre_topc(k3_topmetr) & l1_pre_topc(k3_topmetr) )).
fof(dt_k3_topreal1,axiom,( ! [A] : ! [B] : ( ( 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)))) ) )).
fof(dt_k3_topreal7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k3_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) )).
fof(dt_k3_toprealb,axiom,( ! [A] : ! [B] : ( ( 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)))) ) ) )).
fof(dt_k3_toprns_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ( v1_funct_1(k3_toprns_1(A,B)) & v1_funct_2(k3_toprns_1(A,B),k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(k3_toprns_1(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) ) )).
fof(dt_k3_treal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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(k5_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(k5_numbers,1)),u1_struct_0(k4_topmetr(A,B))))) ) ) )).
fof(dt_k3_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => m1_subset_1(k3_trees_1(A),k1_zfmisc_1(A)) ) )).
fof(dt_k3_trees_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k3_trees_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k3_trees_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k3_turing_1,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k3_turing_1(A),k1_zfmisc_1(k4_ordinal1)) ) )).
fof(dt_k3_twoscomp,axiom,( 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))) )).
fof(dt_k3_unialg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k3_unialg_3,axiom,( ! [A] : ( ( ~ 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))))) ) ) )).
fof(dt_k3_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ( ~ 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)) ) ) )).
fof(dt_k3_uproots,axiom,( ! [A] : ! [B] : ( ( 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) ) => m1_subset_1(k3_uproots(A,B),k4_ordinal1) ) )).
fof(dt_k3_urysohn1,axiom,( m1_subset_1(k3_urysohn1,k1_zfmisc_1(k1_numbers)) )).
fof(dt_k3_urysohn3,axiom,( ! [A] : ( v1_xreal_0(A) => v7_ordinal1(k3_urysohn3(A)) ) )).
fof(dt_k3_valuat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k3_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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))) ) ) )).
fof(dt_k3_vectmetr,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_vectmetr(A) & m1_subset_1(B,u1_struct_0(A)) ) => v1_xreal_0(k3_vectmetr(A,B)) ) )).
fof(dt_k3_vectsp10,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)))) ) ) )).
fof(dt_k3_vectsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k3_vectsp_2,axiom,( ! [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) & 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) ) ) )).
fof(dt_k3_vectsp_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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))) ) )).
fof(dt_k3_vectsp_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k3_vfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k3_vfunct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k3_waybel10,axiom,( ! [A] : ( l1_orders_2(A) => ( ~ v2_struct_0(k3_waybel10(A)) & v1_orders_2(k3_waybel10(A)) & l1_orders_2(k3_waybel10(A)) ) ) )).
fof(dt_k3_waybel11,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k3_waybel17,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k3_waybel18,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k3_waybel20,axiom,( ! [A] : ! [B] : ( ( 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)))) ) ) )).
fof(dt_k3_waybel23,axiom,( ! [A] : ! [B] : ( ( ~ 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(k1_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(k1_yellow_1(k7_waybel_0(B))),u1_struct_0(A)))) ) ) )).
fof(dt_k3_waybel24,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k3_waybel26,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))))) ) ) )).
fof(dt_k3_waybel27,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k3_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => m4_yellow_6(k3_waybel28(A),A) ) )).
fof(dt_k3_waybel29,axiom,( ! [A] : ! [B] : ( ( ~ 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(k1_yellow_1(u1_pre_topc(k2_borsuk_1(A,B)))),u1_struct_0(k3_waybel24(A,k1_waybel29(k1_yellow_1(u1_pre_topc(B)))))) & m1_subset_1(k3_waybel29(A,B),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_yellow_1(u1_pre_topc(k2_borsuk_1(A,B)))),u1_struct_0(k3_waybel24(A,k1_waybel29(k1_yellow_1(u1_pre_topc(B)))))))) ) ) )).
fof(dt_k3_waybel34,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))))) ) ) )).
fof(dt_k3_waybel_0,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k3_waybel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k3_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k3_waybel_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k3_waybel_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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(k1_funct_6(D)),k7_funcop_1(k4_card_3(k1_funct_6(D)),A),k7_funcop_1(k4_card_3(k1_funct_6(D)),B)) & m1_subset_1(F,k4_card_3(k1_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))) ) ) )).
fof(dt_k3_waybel_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => m1_subset_1(k3_waybel_6(A),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k3_waybel_9,axiom,( ! [A] : ( l1_orders_2(A) => ( v6_waybel_0(k3_waybel_9(A),A) & l1_waybel_0(k3_waybel_9(A),A) ) ) )).
fof(dt_k3_weddwitt,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(dt_k3_weierstr,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => v1_xreal_0(k3_weierstr(A)) ) )).
fof(dt_k3_wellord1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => ( v1_relat_1(k3_wellord1(A,B)) & v1_funct_1(k3_wellord1(A,B)) ) ) )).
fof(dt_k3_wsierp_1,axiom,( ! [A] : ( m1_finseq_1(A,k4_ordinal1) => m1_subset_1(k3_wsierp_1(A),k4_ordinal1) ) )).
fof(dt_k3_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => v1_xboolean(k3_xboolean(A)) ) )).
fof(dt_k3_xxreal_3,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => v1_xxreal_0(k3_xxreal_3(A,B)) ) )).
fof(dt_k3_yellow11,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k3_yellow19,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k2_yellow_1(B)) & v13_waybel_0(C,k2_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_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) ) ) )).
fof(dt_k3_yellow20,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k3_yellow21,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k3_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => m1_subset_1(k3_yellow_0(A),u1_struct_0(A)) ) )).
fof(dt_k3_yellow_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_yellow_1(A,B,C)) ) )).
fof(dt_k3_yellow_2,axiom,( ! [A] : ( ( ~ 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(k1_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(k1_yellow_1(k7_waybel_0(A)))))) ) ) )).
fof(dt_k3_yellow_3,axiom,( ! [A] : ! [B] : ( ( l1_orders_2(A) & l1_orders_2(B) ) => ( v1_orders_2(k3_yellow_3(A,B)) & l1_orders_2(k3_yellow_3(A,B)) ) ) )).
fof(dt_k3_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k3_yellow_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k3_yellow_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k3_yellow_9,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k3_yoneda_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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))) ) )).
fof(dt_k3_zf_fund1,axiom,( ! [A] : ( m1_subset_1(A,k1_zf_lang) => m1_subset_1(k3_zf_fund1(A),k4_ordinal1) ) )).
fof(dt_k3_zf_lang,axiom,( ! [A] : ( m1_subset_1(A,k1_zf_lang) => m2_finseq_1(k3_zf_lang(A),k4_ordinal1) ) )).
fof(dt_k3_zmodul01,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(dt_k3_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ 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_int_1(B) ) => ( v1_funct_1(k3_zmodul02(A,B)) & v1_funct_2(k3_zmodul02(A,B),k2_zfmisc_1(k1_zmodul02(A,B),k1_zmodul02(A,B)),k1_zmodul02(A,B)) & m1_subset_1(k3_zmodul02(A,B),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_zmodul02(A,B),k1_zmodul02(A,B)),k1_zmodul02(A,B)))) ) ) )).
fof(dt_k40_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(dt_k40_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & l6_aofa_a00(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) & m1_subset_1(C,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),k37_aofa_a00(A))) & v19_aofa_a00(D,A) & m1_subset_1(D,u1_struct_0(A)) & m1_subset_1(E,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),D)) & m1_subset_1(F,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),D)) ) => m1_msafree4(k40_aofa_a00(A,B,C,D,E,F),u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),k37_aofa_a00(A))) ) )).
fof(dt_k40_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(dt_k40_descip_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) & 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(k2_nat_1(2,A),k6_margrel1),k4_finseq_2(k2_nat_1(2,A),k6_margrel1)) & v3_funct_2(F,k4_finseq_2(k2_nat_1(2,A),k6_margrel1),k4_finseq_2(k2_nat_1(2,A),k6_margrel1)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(k2_nat_1(2,A),k6_margrel1),k4_finseq_2(k2_nat_1(2,A),k6_margrel1)))) & m1_subset_1(G,k4_finseq_2(k2_nat_1(2,A),k6_margrel1)) ) => m2_finseq_2(k40_descip_1(A,B,C,D,E,F,G),k6_margrel1,k4_finseq_2(k2_nat_1(2,A),k6_margrel1)) ) )).
fof(dt_k40_fomodel1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k40_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => m1_subset_1(k40_fomodel2(A),k1_zfmisc_1(k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0)))) ) )).
fof(dt_k40_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v13_fomodel4(B,k5_numbers,A) & m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) & v11_fomodel4(C,A,B) ) => ( v1_relat_1(k40_fomodel4(A,B,C)) & v1_funct_1(k40_fomodel4(A,B,C)) ) ) )).
fof(dt_k40_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(A) => m1_subset_1(k40_modelc_1(A,B,C),k30_modelc_1(A)) ) )).
fof(dt_k40_modelc_2,axiom,( ! [A] : ( ~ 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))))) ) ) )).
fof(dt_k40_twoscomp,axiom,( ! [A] : ! [B] : ( ~ 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)) ) )).
fof(dt_k41_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k41_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & l6_aofa_a00(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) & v19_aofa_a00(C,A) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) & m1_subset_1(E,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) ) => m1_msafree4(k41_aofa_a00(A,B,C,D,E),u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),k37_aofa_a00(A))) ) )).
fof(dt_k41_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(dt_k41_descip_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k41_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k41_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v13_fomodel4(B,k5_numbers,A) & v13_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))))) & v11_fomodel4(C,A,B) ) => m2_subset_1(k41_fomodel4(A,B,C),k9_funct_2(k37_fomodel1(A),k3_rfunct_3(k3_finseq_2(k8_eqrel_1(k35_fomodel1(A),k8_fomodel4(A,B,C))),k2_xboole_0(k8_eqrel_1(k35_fomodel1(A),k8_fomodel4(A,B,C)),k6_margrel1))),k15_fomodel2(A,k8_eqrel_1(k35_fomodel1(A),k8_fomodel4(A,B,C)))) ) )).
fof(dt_k41_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ 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)) ) )).
fof(dt_k41_modelc_1,axiom,( ! [A] : ( ~ 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)))) ) ) )).
fof(dt_k41_modelc_2,axiom,( ! [A] : ( ~ 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))))) ) ) )).
fof(dt_k41_twoscomp,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(dt_k41_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k41_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k42_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k42_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & l6_aofa_a00(A) & ~ v2_struct_0(B) & l5_aofa_a00(B) & v4_msualg_1(C,A) & l3_msualg_1(C,A) & v4_msualg_1(D,B) & l3_msualg_1(D,B) ) => ( v3_msualg_1(k42_aofa_a00(A,B,C,D),k36_aofa_a00(A,B)) & v4_msualg_1(k42_aofa_a00(A,B,C,D),k36_aofa_a00(A,B)) & l3_msualg_1(k42_aofa_a00(A,B,C,D),k36_aofa_a00(A,B)) ) ) )).
fof(dt_k42_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(dt_k42_descip_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k42_fomodel1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k42_fomodel1(A,B,C),k3_finseq_2(k15_fomodel1(A)),k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) ) )).
fof(dt_k42_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k42_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(dt_k42_modelc_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k42_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))))) ) ) )).
fof(dt_k43_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(dt_k43_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(dt_k43_descip_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k43_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & m1_subset_1(B,k1_fomodel1(A)) ) => m2_subset_1(k43_fomodel1(A,B),k3_finseq_2(k15_fomodel1(A)),k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) ) )).
fof(dt_k43_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k40_fomodel2(A)) ) => m1_subset_1(k43_fomodel4(A,B,C,D),k1_zfmisc_1(k2_xboole_0(C,k30_fomodel2(A)))) ) )).
fof(dt_k43_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ 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)) ) )).
fof(dt_k43_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k43_modelc_2,axiom,( ~ v1_xboole_0(k43_modelc_2) )).
fof(dt_k43_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))))) ) ) )).
fof(dt_k44_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))))) ) ) )).
fof(dt_k44_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) )).
fof(dt_k44_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,k4_ordinal1,k40_fomodel2(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k40_fomodel2(B)))) ) => ( v1_funct_1(k44_fomodel4(A,B,C,D)) & v1_funct_2(k44_fomodel4(A,B,C,D),k4_ordinal1,k9_setfam_1(k2_xboole_0(A,k30_fomodel2(B)))) & m1_subset_1(k44_fomodel4(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k2_xboole_0(A,k30_fomodel2(B)))))) ) ) )).
fof(dt_k44_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k44_modelc_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k44_modelc_2,axiom,( ! [A] : ! [B] : m1_subset_1(k44_modelc_2(A,B),k6_margrel1) )).
fof(dt_k45_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k45_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,k4_ordinal1,k40_fomodel2(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k40_fomodel2(B)))) ) => m1_subset_1(k45_fomodel4(A,B,C,D),k1_zfmisc_1(k2_xboole_0(A,k30_fomodel2(B)))) ) )).
fof(dt_k45_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : m2_subset_1(k45_gfacirc1(A,B,C),u1_struct_0(k43_gfacirc1(A,B,C)),k3_msafree2(k43_gfacirc1(A,B,C))) )).
fof(dt_k45_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k45_modelc_2,axiom,( ! [A] : m1_subset_1(k45_modelc_2(A),k30_modelc_1(k25_modelc_2(k43_modelc_2))) )).
fof(dt_k45_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k46_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k46_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ 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)) ) )).
fof(dt_k46_modelc_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k46_modelc_2,axiom,( ~ v1_xboole_0(k46_modelc_2) & m1_subset_1(k46_modelc_2,k1_zfmisc_1(k30_modelc_1(k25_modelc_2(k43_modelc_2)))) )).
fof(dt_k46_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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))) ) ) )).
fof(dt_k47_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k47_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) ) )).
fof(dt_k47_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k30_fomodel2(B)) ) => m1_subset_1(k47_fomodel4(A,B,C,D),k1_zfmisc_1(k2_xboole_0(A,k30_fomodel2(B)))) ) )).
fof(dt_k47_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k47_modelc_2,axiom,( 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))))) )).
fof(dt_k47_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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))) ) ) )).
fof(dt_k47_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k48_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k48_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) ) )).
fof(dt_k48_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k4_ordinal1,k30_fomodel2(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k30_fomodel2(B)))) ) => ( v1_funct_1(k48_fomodel4(A,B,C,D)) & v1_funct_2(k48_fomodel4(A,B,C,D),k4_ordinal1,k9_setfam_1(k2_xboole_0(A,k30_fomodel2(B)))) & m1_subset_1(k48_fomodel4(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k2_xboole_0(A,k30_fomodel2(B)))))) ) ) )).
fof(dt_k48_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : m2_subset_1(k48_gfacirc1(A,B,C),u1_struct_0(k46_gfacirc1(A,B,C)),k3_msafree2(k46_gfacirc1(A,B,C))) )).
fof(dt_k48_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k48_modelc_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k9_modelc_2)) => m1_subset_1(k48_modelc_2(A),k1_zfmisc_1(k9_modelc_2)) ) )).
fof(dt_k48_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))))) ) ) )).
fof(dt_k49_abcmiz_1,axiom,( ~ 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) )).
fof(dt_k49_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k4_ordinal1,k30_fomodel2(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k30_fomodel2(B)))) ) => m1_subset_1(k49_fomodel4(A,B,C,D),k1_zfmisc_1(k2_xboole_0(A,k30_fomodel2(B)))) ) )).
fof(dt_k49_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ 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)) ) )).
fof(dt_k49_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))))) ) ) )).
fof(dt_k4_abcmiz_0,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k4_abcmiz_1,axiom,( m1_finseq_2(k4_abcmiz_1,k2_abcmiz_1) )).
fof(dt_k4_afinsq_1,axiom,( ! [A] : ( 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)) ) )).
fof(dt_k4_afinsq_2,axiom,( ! [A] : ( ( v1_finset_1(A) & v6_membered(A) ) => ( v1_relat_1(k4_afinsq_2(A)) & v5_relat_1(k4_afinsq_2(A),k4_ordinal1) & v1_funct_1(k4_afinsq_2(A)) & v5_ordinal1(k4_afinsq_2(A)) & v1_finset_1(k4_afinsq_2(A)) ) ) )).
fof(dt_k4_afproj,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k4_afvect0,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k4_alg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k4_algstr_0,axiom,( ! [A] : ! [B] : ( ( l2_algstr_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k4_algstr_0(A,B),u1_struct_0(A)) ) )).
fof(dt_k4_algstr_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k4_altcat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)))) ) ) )).
fof(dt_k4_altcat_2,axiom,( ! [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) & 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)) ) ) )).
fof(dt_k4_altcat_4,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(dt_k4_ami_2,axiom,( v1_relat_1(k4_ami_2) & v4_relat_1(k4_ami_2,k7_card_1(2)) & v1_funct_1(k4_ami_2) & v1_partfun1(k4_ami_2,k7_card_1(2)) )).
fof(dt_k4_ami_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k4_ami_wstd,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k4_ordinal1) & v7_ordinal1(D) ) => m1_subset_1(k4_ami_wstd(A,B,C,D),k4_ordinal1) ) )).
fof(dt_k4_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ( v1_extpro_1(k4_amistd_1(A),A) & l1_extpro_1(k4_amistd_1(A),A) ) ) )).
fof(dt_k4_amistd_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k4_analmetr,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k4_analort,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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))))) ) )).
fof(dt_k4_anproj_1,axiom,( ! [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) & l1_rlvect_1(A) ) => m1_collsp(k4_anproj_1(A),k3_anproj_1(A)) ) )).
fof(dt_k4_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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_msafree(C,A,B) & m1_subset_1(D,u1_struct_0(A)) & m1_subset_1(E,k1_msafree4(u1_struct_0(A),C,D)) ) => m1_subset_1(k4_aofa_a01(A,B,C,D,E),k1_funct_1(u3_msualg_1(A,B),D)) ) )).
fof(dt_k4_aofa_i00,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k4_armstrng,axiom,( ! [A] : m1_subset_1(k4_armstrng(A),k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) )).
fof(dt_k4_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => m1_subset_1(k4_arytm_0(A),k1_numbers) ) )).
fof(dt_k4_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k1_arytm_2) => m1_subset_1(k4_arytm_2(A),k2_arytm_2) ) )).
fof(dt_k4_arytm_3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v7_ordinal1(A) & v3_ordinal1(B) & v7_ordinal1(B) ) => m1_subset_1(k4_arytm_3(A,B),k4_ordinal1) ) )).
fof(dt_k4_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v1_funct_1(k4_asympt_1(A)) & v1_funct_2(k4_asympt_1(A),k4_ordinal1,k1_numbers) & m1_subset_1(k4_asympt_1(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k4_autalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k4_autgroup,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(dt_k4_bagorder,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_k4_bcialg_1,axiom,( ! [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) ) => ( ~ v1_xboole_0(k4_bcialg_1(A)) & m1_subset_1(k4_bcialg_1(A),k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_k4_bcialg_6,axiom,( ! [A] : ! [B] : ( ( ~ 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),k4_ordinal1) ) )).
fof(dt_k4_bhsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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)) ) => v1_xreal_0(k4_bhsp_1(A,B,C)) ) )).
fof(dt_k4_bhsp_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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)) & v1_xreal_0(C) ) => m1_subset_1(k4_bhsp_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k4_bhsp_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v7_ordinal1(C) & v7_ordinal1(D) ) => m1_subset_1(k4_bhsp_4(A,B,C,D),u1_struct_0(A)) ) )).
fof(dt_k4_bhsp_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k4_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k4_binari_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v8_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) ) )).
fof(dt_k4_binarith,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v8_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) ) ) )).
fof(dt_k4_binom,axiom,( ! [A] : ( ( ~ 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),k4_ordinal1),u1_struct_0(A)) & m1_subset_1(k4_binom(A),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_ordinal1),u1_struct_0(A)))) ) ) )).
fof(dt_k4_binop_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k4_binop_2,axiom,( v1_funct_1(k4_binop_2) & v1_funct_2(k4_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & m1_subset_1(k4_binop_2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers))) )).
fof(dt_k4_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k4_borsuk_6,axiom,( 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)))) )).
fof(dt_k4_brouwer,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) & ~ v3_xxreal_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))) ) )).
fof(dt_k4_bspace,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k4_bvfunc26,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k4_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k4_bvfunc_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_eqrel_1(B,A) ) => m1_subset_1(k4_bvfunc_2(A,B),k1_zfmisc_1(k1_bvfunc_2(A))) ) )).
fof(dt_k4_c0sp1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k4_c0sp2,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(dt_k4_card_1,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k4_card_1(A),k4_ordinal1) ) )).
fof(dt_k4_card_fil,axiom,( ! [A] : ( ~ v1_finset_1(A) => m1_card_fil(k4_card_fil(A),A) ) )).
fof(dt_k4_cardfin2,axiom,( ! [A] : ! [B] : m1_subset_1(k4_cardfin2(A,B),k1_zfmisc_1(k1_funct_2(A,B))) )).
fof(dt_k4_cat_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k4_cat_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) )).
fof(dt_k4_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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))))) ) ) )).
fof(dt_k4_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k4_cat_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) ) )).
fof(dt_k4_catalan2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_funct_1(k4_catalan2(A,B)) & v1_funct_2(k4_catalan2(A,B),k4_ordinal1,k1_numbers) & m1_subset_1(k4_catalan2(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k4_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ( v1_cayldick(k4_cayldick(A)) & l1_cayldick(k4_cayldick(A)) ) ) )).
fof(dt_k4_cayley,axiom,( ! [A] : ( ( ~ 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)))))) ) ) )).
fof(dt_k4_cc0sp1,axiom,( ! [A] : ! [B] : ( ~ 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))) ) ) )).
fof(dt_k4_cc0sp2,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(dt_k4_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m2_funct_2(k4_cfuncdom(A),A,k2_numbers,k9_funct_2(A,k2_numbers)) ) )).
fof(dt_k4_cgames_1,axiom,( m1_subset_1(k4_cgames_1,k2_cgames_1(1)) )).
fof(dt_k4_chain_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_chain_1(B,A) & m1_subset_1(C,k4_ordinal1) ) => ( ~ 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)))) ) ) )).
fof(dt_k4_chord,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) )).
fof(dt_k4_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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) ) ) )).
fof(dt_k4_circcomb,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k4_circtrm1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k4_circuit1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k4_circuit2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k4_clopban1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k4_clopban2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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)) ) )).
fof(dt_k4_clopban3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_clopban2(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k4_clopban3(A,B,C)) & v1_funct_2(k4_clopban3(A,B,C),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k4_clopban3(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k4_clopban4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(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) & 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),k4_ordinal1,u1_struct_0(B)) & m1_subset_1(k4_clopban4(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) ) )).
fof(dt_k4_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k4_closure3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k4_clvect_1,axiom,( ! [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) ) => ( v1_clvect_1(k4_clvect_1(A)) & m1_clvect_1(k4_clvect_1(A),A) ) ) )).
fof(dt_k4_clvect_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) & v1_xreal_0(C) ) => m1_subset_1(k4_clvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k4_cohsp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k4_combgras,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k4_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => m1_subset_1(k4_complex1(A),k1_numbers) ) )).
fof(dt_k4_complex2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => v1_xreal_0(k4_complex2(A,B,C)) ) )).
fof(dt_k4_complsp2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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)) ) )).
fof(dt_k4_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ( v1_relat_1(k4_compos_1(A)) & v4_relat_1(k4_compos_1(A),k4_ordinal1) & 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)) ) ) )).
fof(dt_k4_comput_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => ( v1_relat_1(k4_comput_1(A,B)) & v4_relat_1(k4_comput_1(A,B),k3_finseq_2(k4_ordinal1)) & v1_funct_1(k4_comput_1(A,B)) & v4_valued_0(k4_comput_1(A,B)) & v2_margrel1(k4_comput_1(A,B)) ) ) )).
fof(dt_k4_comseq_3,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k4_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ( v1_funct_1(k4_conlat_1(A)) & v1_funct_2(k4_conlat_1(A),u1_struct_0(k2_yellow_1(u4_struct_0(A))),u1_struct_0(k2_yellow_1(u1_struct_0(A)))) & m1_subset_1(k4_conlat_1(A),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_yellow_1(u4_struct_0(A))),u1_struct_0(k2_yellow_1(u1_struct_0(A)))))) ) ) )).
fof(dt_k4_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(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))))) ) ) )).
fof(dt_k4_connsp_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) )).
fof(dt_k4_convex4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k4_convfun1,axiom,( ~ v2_struct_0(k4_convfun1) & l1_rlvect_1(k4_convfun1) )).
fof(dt_k4_cqc_lang,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & 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)) ) )).
fof(dt_k4_cqc_sim1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k4_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => m1_subset_1(k4_cqc_the1(A),k1_zfmisc_1(k3_cqc_lang(A))) ) )).
fof(dt_k4_csspace,axiom,( 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))) )).
fof(dt_k4_csspace3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l2_clvect_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => v1_xreal_0(k4_csspace3(A,B,C)) ) )).
fof(dt_k4_csspace4,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k4_decomp_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k4_descip_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & m1_subset_1(C,k4_finseq_2(k3_xcmplx_0(2,B),A)) ) => m2_finseq_2(k4_descip_1(A,B,C),A,k4_finseq_2(B,A)) ) )).
fof(dt_k4_dickson,axiom,( ! [A] : ! [B] : ( 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))) ) )).
fof(dt_k4_diff_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k4_dilworth,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k4_dist_1,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & m1_finseq_1(B,A) ) => m2_finseq_1(k4_dist_1(A,B),k1_numbers) ) )).
fof(dt_k4_dist_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_setfam_1(B) & m1_subset_1(B,k6_dist_1(A)) & m1_subset_1(C,B) & v1_funct_1(D) & v1_funct_2(D,A,k6_margrel1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => v1_xreal_0(k4_dist_2(A,B,C,D)) ) )).
fof(dt_k4_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) )).
fof(dt_k4_dtconstr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => m1_subset_1(k4_dtconstr(A),k1_zfmisc_1(k5_trees_3(u1_struct_0(A)))) ) )).
fof(dt_k4_dynkin,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_funct_1(k4_dynkin(A,B)) & v1_funct_2(k4_dynkin(A,B),k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(k4_dynkin(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) )).
fof(dt_k4_e_siec,axiom,( ! [A] : ( 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)) ) )).
fof(dt_k4_ec_pf_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k4_ec_pf_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k4_endalg,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k4_ens_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k2_ens_1(A)) ) => m1_subset_1(k4_ens_1(A,B),A) ) )).
fof(dt_k4_entropy1,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => m2_finseq_1(k4_entropy1(A),k1_numbers) ) )).
fof(dt_k4_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k4_equation,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k4_euclid,axiom,( ! [A] : ( 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)) ) ) )).
fof(dt_k4_euclid_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(k4_euclid_3(A,B,C)) ) )).
fof(dt_k4_euclid_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) )).
fof(dt_k4_euclid_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k4_euclid_8,axiom,( m2_finseq_2(k4_euclid_8,k1_numbers,k1_euclid(3)) )).
fof(dt_k4_euclid_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))))) ) )).
fof(dt_k4_euclidlp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & 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))) ) )).
fof(dt_k4_extpro_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(dt_k4_extreal1,axiom,( ! [A] : ( m1_finseq_1(A,k6_numbers) => m1_subset_1(k4_extreal1(A),k6_numbers) ) )).
fof(dt_k4_facirc_1,axiom,( 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))) )).
fof(dt_k4_facirc_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k4_ff_siec,axiom,( ! [A] : ( v1_petri(k4_ff_siec(A)) & v1_net_1(k4_ff_siec(A)) & l1_petri(k4_ff_siec(A)) ) )).
fof(dt_k4_fib_num2,axiom,( m1_subset_1(k4_fib_num2,k1_zfmisc_1(k4_ordinal1)) )).
fof(dt_k4_filter_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k4_filter_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k4_filter_2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k4_fin_topo,axiom,( v1_orders_2(k4_fin_topo) & l1_orders_2(k4_fin_topo) )).
fof(dt_k4_finance1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => v1_xreal_0(k4_finance1(A,B,C)) ) )).
fof(dt_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_1(A),k1_zfmisc_1(k4_ordinal1)) ) )).
fof(dt_k4_finseq_2,axiom,( ! [A] : ! [B] : ( v7_ordinal1(A) => m1_finseq_2(k4_finseq_2(A,B),B) ) )).
fof(dt_k4_finseq_4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(k4_finseq_4(A,B),k4_ordinal1) ) )).
fof(dt_k4_finseq_5,axiom,( ! [A] : ! [B] : ( m1_finseq_1(B,A) => m2_finseq_1(k4_finseq_5(A,B),A) ) )).
fof(dt_k4_finseq_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_1(k4_finseq_8(A,B,C),A) ) )).
fof(dt_k4_finseqop,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(dt_k4_fintopo2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k4_fintopo3,axiom,( ! [A] : ! [B] : ( ( ~ 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),k4_ordinal1,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(k4_fintopo3(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(u1_struct_0(A))))) ) ) )).
fof(dt_k4_fintopo4,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ v2_struct_0(k4_fintopo4(A)) & l1_orders_2(k4_fintopo4(A)) ) ) )).
fof(dt_k4_fintopo5,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => 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))))) ) )).
fof(dt_k4_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k3_catalan2(A)) => m1_subset_1(k4_flang_1(A,B),k1_zfmisc_1(k3_catalan2(A))) ) )).
fof(dt_k4_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k4_fomodel0(A,B,C)) & v1_funct_1(k4_fomodel0(A,B,C)) ) ) )).
fof(dt_k4_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k4_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k4_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ 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(k4_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)))) ) )).
fof(dt_k4_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ 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)) ) )).
fof(dt_k4_fscirc_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) & 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))) ) )).
fof(dt_k4_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(dt_k4_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k4_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : m1_subset_1(k4_ftacell1(A,B,C,D,E),k3_msafree2(k1_ftacell1(A,B,C,D,E))) )).
fof(dt_k4_funcsdom,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) )).
fof(dt_k4_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k4_funct_3,axiom,( ! [A] : ! [B] : ( v1_relat_1(k4_funct_3(A,B)) & v1_funct_1(k4_funct_3(A,B)) ) )).
fof(dt_k4_funct_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k4_funct_5(A)) & v1_funct_1(k4_funct_5(A)) ) ) )).
fof(dt_k4_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(k4_funct_7(A,B)) & v1_funct_1(k4_funct_7(A,B)) & v1_finseq_1(k4_funct_7(A,B)) ) ) )).
fof(dt_k4_functor2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k4_functor3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(dt_k4_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v5_relat_1(k4_fuzzy_1(A),k1_rcomp_1(k5_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))) ) ) )).
fof(dt_k4_fuzzy_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( v5_relat_1(k4_fuzzy_2(A,B),k1_rcomp_1(k5_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))) ) ) )).
fof(dt_k4_fuzzy_4,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( v5_relat_1(k4_fuzzy_4(A,B),k1_rcomp_1(k5_numbers,1)) & v1_funct_1(k4_fuzzy_4(A,B)) & v1_funct_2(k4_fuzzy_4(A,B),k2_zfmisc_1(A,B),k1_numbers) & m1_subset_1(k4_fuzzy_4(A,B),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),k1_numbers))) ) ) )).
fof(dt_k4_fvaluat1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k4_fvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & ~ 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))) ) )).
fof(dt_k4_gcd_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k4_genealg1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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,k4_ordinal1) & m1_subset_1(E,k4_ordinal1) & m1_subset_1(F,k4_ordinal1) & m1_subset_1(G,k4_ordinal1) ) => m2_finseq_1(k4_genealg1(A,B,C,D,E,F,G),k3_card_3(A)) ) )).
fof(dt_k4_geomtrap,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) => v1_xreal_0(k4_geomtrap(A,B,C,D,E)) ) )).
fof(dt_k4_gfacirc1,axiom,( 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))) )).
fof(dt_k4_gfacirc2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k4_glib_000,axiom,( m1_subset_1(k4_glib_000,k4_ordinal1) )).
fof(dt_k4_glib_001,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(dt_k4_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => v1_card_1(k4_glib_002(A)) ) )).
fof(dt_k4_glib_003,axiom,( m1_subset_1(k4_glib_003,k4_ordinal1) )).
fof(dt_k4_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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_xreal_0(k4_glib_004(A)) ) )).
fof(dt_k4_glib_005,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(dt_k4_goboard5,axiom,( ! [A] : ! [B] : ( ( ~ 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))) & v7_ordinal1(B) ) => m1_subset_1(k4_goboard5(A,B),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) )).
fof(dt_k4_gobrd13,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) & v7_ordinal1(C) ) => m1_subset_1(k4_gobrd13(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) )).
fof(dt_k4_gr_cy_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(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)) ) ) )).
fof(dt_k4_graph_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k4_graph_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_1(k4_graph_2(A,B,C),A) ) )).
fof(dt_k4_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k4_graph_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) )).
fof(dt_k4_graphsp,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k1_funct_2(A,A)) & m1_subset_1(C,A) ) => m1_subset_1(k4_graphsp(A,B,C),A) ) )).
fof(dt_k4_grcat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)))) ) ) )).
fof(dt_k4_groeb_1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_k4_groeb_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) & m1_subset_1(E,k4_ordinal1) ) => ( 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))) ) ) )).
fof(dt_k4_group_1,axiom,( ! [A] : ( ( ~ 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),k4_ordinal1),u1_struct_0(A)) & m1_subset_1(k4_group_1(A),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_ordinal1),u1_struct_0(A)))) ) ) )).
fof(dt_k4_group_11,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k4_group_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k4_group_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k4_group_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k4_group_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k4_group_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k4_group_7,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k4_group_9,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k4_hahnban1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k4_hermitan,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k4_heyting1,axiom,( ! [A] : ( 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))))) ) )).
fof(dt_k4_heyting2,axiom,( ! [A] : ! [B] : ( 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))))) ) ) )).
fof(dt_k4_heyting3,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => m1_subset_1(k4_heyting3(A,B),k5_finsub_1(k4_partfun1(k4_ordinal1,k6_domain_1(k4_ordinal1,B)))) ) )).
fof(dt_k4_hilbasis,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k4_hilbert1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_hilbert1) & m1_subset_1(B,k1_hilbert1) ) => m1_subset_1(k4_hilbert1(A,B),k1_hilbert1) ) )).
fof(dt_k4_hilbert3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & m1_hilbert3(B,A) ) => m2_pboole(k4_hilbert3(A,B),k1_hilbert1,k2_hilbert3(A),k2_hilbert3(A)) ) )).
fof(dt_k4_hurwitz,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k4_hurwitz(A,B,C),A) & m1_subset_1(k4_hurwitz(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k4_idea_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) ) => v7_ordinal1(k4_idea_1(A,B,C)) ) )).
fof(dt_k4_incsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k4_index_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k4_int_1,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_int_1(B) ) => v1_int_1(k4_int_1(A,B)) ) )).
fof(dt_k4_int_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k4_integr10,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & v1_xreal_0(B) ) => v1_xreal_0(k4_integr10(A,B)) ) )).
fof(dt_k4_integr15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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)) ) )).
fof(dt_k4_integr18,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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)) ) )).
fof(dt_k4_integra1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k4_integra2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,k1_integra1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) ) => ( v1_funct_1(k4_integra2(A,B,C)) & v1_funct_2(k4_integra2(A,B,C),k4_ordinal1,k1_numbers) & m1_subset_1(k4_integra2(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k4_integra5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) => v1_xreal_0(k4_integra5(A,B,C)) ) )).
fof(dt_k4_interva1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k4_intpro_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k4_irrat_1,axiom,( v1_funct_1(k4_irrat_1) & v1_funct_2(k4_irrat_1,k4_ordinal1,k1_numbers) & m1_subset_1(k4_irrat_1,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) )).
fof(dt_k4_isocat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) )).
fof(dt_k4_isocat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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,k6_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,k10_cat_2(A,B,C,D,k3_graph_1(A,E)),k10_cat_2(A,B,C,D,k4_graph_1(A,E))) ) )).
fof(dt_k4_jgraph_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k4_jordan10,axiom,( ! [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)))) ) => m1_subset_1(k4_jordan10(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) ) )).
fof(dt_k4_jordan11,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => m1_subset_1(k4_jordan11(A),k4_ordinal1) ) )).
fof(dt_k4_jordan19,axiom,( ! [A] : ( ( 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)))) ) )).
fof(dt_k4_jordan1k,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ 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)))) ) => v1_xreal_0(k4_jordan1k(A,B,C)) ) )).
fof(dt_k4_jordan3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k4_jordan5d,axiom,( ! [A] : ( ( ~ 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))) ) => v7_ordinal1(k4_jordan5d(A)) ) )).
fof(dt_k4_jordan6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) )).
fof(dt_k4_jordan_a,axiom,( ! [A] : ! [B] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_jordan_a(B,A) ) => v1_xreal_0(k4_jordan_a(A,B)) ) )).
fof(dt_k4_kolmog01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))) ) ) )).
fof(dt_k4_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => m1_subset_1(k4_kurato_0(A,B),k1_zfmisc_1(A)) ) )).
fof(dt_k4_kurato_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k4_lang1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k4_lattice3,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k4_lattice4,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k4_lattice5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))))) ) ) )).
fof(dt_k4_lattice6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k4_lattice7,axiom,( ! [A] : ( l1_orders_2(A) => ~ v1_xboole_0(k4_lattice7(A)) ) )).
fof(dt_k4_lattice8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))) ) )).
fof(dt_k4_lattices,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k4_lexbfs,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k4_lfuzzy_0,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(dt_k4_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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))) ) ) )).
fof(dt_k4_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => v1_xreal_0(k4_limfunc1(A)) ) )).
fof(dt_k4_lopban_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k4_lopban_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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)) & v1_xreal_0(C) ) => m2_subset_1(k4_lopban_2(A,B,C),u1_struct_0(k8_lopban_1(A,A)),k10_lopban_1(A,A)) ) )).
fof(dt_k4_lopban_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_lopban_2(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k4_lopban_3(A,B,C)) & v1_funct_2(k4_lopban_3(A,B,C),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k4_lopban_3(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k4_lopban_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k4_lopban_4(A,B)) & v1_funct_2(k4_lopban_4(A,B),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k4_lopban_4(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k4_lopban_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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_funct_1(k4_lopban_7(A,B,C)) & v1_funct_2(k4_lopban_7(A,B,C),k3_lopban_7(A,B,C),k1_numbers) & m1_subset_1(k4_lopban_7(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k3_lopban_7(A,B,C),k1_numbers))) ) ) )).
fof(dt_k4_lopclset,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k4_lpspace1,axiom,( ! [A] : ( ~ 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)))) ) ) )).
fof(dt_k4_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v2_xxreal_0(D) & v1_xreal_0(D) ) => ( ~ v2_struct_0(k4_lpspace2(A,B,C,D)) & l1_rlvect_1(k4_lpspace2(A,B,C,D)) ) ) )).
fof(dt_k4_ltlaxio1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_hilbert1) & m1_subset_1(B,k1_hilbert1) ) => m1_subset_1(k4_ltlaxio1(A,B),k1_hilbert1) ) )).
fof(dt_k4_ltlaxio2,axiom,( ! [A] : ( m1_finseq_1(A,k1_hilbert1) => m2_finseq_1(k4_ltlaxio2(A),k1_hilbert1) ) )).
fof(dt_k4_ltlaxio3,axiom,( v1_funct_1(k4_ltlaxio3) & v1_funct_2(k4_ltlaxio3,k1_hilbert1,k9_setfam_1(k1_hilbert1)) & m1_subset_1(k4_ltlaxio3,k1_zfmisc_1(k2_zfmisc_1(k1_hilbert1,k9_setfam_1(k1_hilbert1)))) )).
fof(dt_k4_ltlaxio4,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) ) => ( ~ v1_xboole_0(k4_ltlaxio4(A)) & v1_finset_1(k4_ltlaxio4(A)) & m1_subset_1(k4_ltlaxio4(A),k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)))) ) ) )).
fof(dt_k4_margrel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(k4_margrel1(A),k3_margrel1(A)) ) )).
fof(dt_k4_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k4_matrix10,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m1_finseq_1(B,k3_finseq_2(k1_numbers)) & v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m1_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( v1_matrix_0(k4_matrix10(A,B,C)) & v2_matrix_0(k4_matrix10(A,B,C),k1_numbers,A,A) & m2_finseq_1(k4_matrix10(A,B,C),k3_finseq_2(k1_numbers)) ) ) )).
fof(dt_k4_matrix11,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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)))) & v1_matrix_0(E) & v2_matrix_0(E,C,A,B) & m1_finseq_1(E,k3_finseq_2(C)) ) => ( v1_matrix_0(k4_matrix11(A,B,C,D,E)) & v2_matrix_0(k4_matrix11(A,B,C,D,E),C,A,B) & m2_finseq_1(k4_matrix11(A,B,C,D,E),k3_finseq_2(C)) ) ) )).
fof(dt_k4_matrix12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & ~ 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) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(C))) & v7_ordinal1(E) & v7_ordinal1(F) ) => ( v1_matrix_0(k4_matrix12(A,B,C,D,E,F)) & v2_matrix_0(k4_matrix12(A,B,C,D,E,F),u1_struct_0(C),A,B) & m2_finseq_1(k4_matrix12(A,B,C,D,E,F),k3_finseq_2(u1_struct_0(C))) ) ) )).
fof(dt_k4_matrix13,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => m1_subset_1(k4_matrix13(A,B),k1_zfmisc_1(k4_ordinal1)) ) )).
fof(dt_k4_matrix14,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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,k4_ordinal1) & v7_ordinal1(C) ) => ( v1_matrix_0(k4_matrix14(A,B,C)) & v2_matrix_0(k4_matrix14(A,B,C),u1_struct_0(A),B,B) & m2_finseq_1(k4_matrix14(A,B,C),k3_finseq_2(u1_struct_0(A))) ) ) )).
fof(dt_k4_matrix_0,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(A)) ) => ( v1_matrix_0(k4_matrix_0(A,B)) & m2_finseq_1(k4_matrix_0(A,B),k3_finseq_2(A)) ) ) )).
fof(dt_k4_matrix_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) & v7_ordinal1(B) & v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(A),B,B) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( v1_matrix_0(k4_matrix_1(A,B,C)) & v2_matrix_0(k4_matrix_1(A,B,C),u1_struct_0(A),B,B) & m2_finseq_1(k4_matrix_1(A,B,C),k3_finseq_2(u1_struct_0(A))) ) ) )).
fof(dt_k4_matrix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( v15_algstr_0(k4_matrix_2(A)) & l3_algstr_0(k4_matrix_2(A)) ) ) )).
fof(dt_k4_matrix_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_0(B) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(A))) & v1_matrix_0(C) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( v1_matrix_0(k4_matrix_3(A,B,C)) & m2_finseq_1(k4_matrix_3(A,B,C),k3_finseq_2(u1_struct_0(A))) ) ) )).
fof(dt_k4_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ( v1_matrix_0(k4_matrix_5(A)) & m2_finseq_1(k4_matrix_5(A),k3_finseq_2(k2_numbers)) ) ) )).
fof(dt_k4_matrix_7,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k4_matrixj1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_matrix_0(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))) ) ) )).
fof(dt_k4_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( v1_matrix_0(k4_matrixr1(A)) & m2_finseq_1(k4_matrixr1(A),k3_finseq_2(k1_numbers)) ) ) )).
fof(dt_k4_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_matrix_0(k4_matrixr2(A)) & v2_matrix_0(k4_matrixr2(A),k1_numbers,A,A) & m2_finseq_1(k4_matrixr2(A),k3_finseq_2(k1_numbers)) ) ) )).
fof(dt_k4_matrlin,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k4_matrlin2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) & v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(A),k3_finseq_1(D),k3_finseq_1(E)) & m1_finseq_1(F,k3_finseq_2(u1_struct_0(A))) ) => ( 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)))) ) ) )).
fof(dt_k4_matroid0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k4_matrprob,axiom,( ! [A] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k1_numbers)) ) => m2_finseq_1(k4_matrprob(A),k1_numbers) ) )).
fof(dt_k4_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(dt_k4_measure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ( ~ v1_xboole_0(k4_measure1(A,B,C)) & m1_subset_1(k4_measure1(A,B,C),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) )).
fof(dt_k4_measure3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( v1_funct_1(k4_measure3(A,B,C)) & v1_funct_2(k4_measure3(A,B,C),k2_measure3(A,B,C),k6_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),k6_numbers))) ) ) )).
fof(dt_k4_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => m1_subset_1(k4_measure6(A),k1_zfmisc_1(k1_numbers)) ) )).
fof(dt_k4_measure7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k9_setfam_1(k1_numbers)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k1_numbers)))) & m2_measure7(B,A) & m1_subset_1(C,k4_ordinal1) ) => m1_measure7(k4_measure7(A,B,C),k9_nat_1(k9_setfam_1(k1_numbers),A,C)) ) )).
fof(dt_k4_measure8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & v1_funct_1(D) & v1_funct_2(D,B,k6_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,k6_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),k4_ordinal1,k6_numbers) & m1_subset_1(k4_measure8(A,B,C,D,E),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) ) )).
fof(dt_k4_member_1,axiom,( ! [A] : ( v2_membered(A) => v2_membered(k4_member_1(A)) ) )).
fof(dt_k4_mesfun7c,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( v1_funct_1(k4_mesfun7c(A,B)) & v1_funct_2(k4_mesfun7c(A,B),k4_ordinal1,k4_partfun1(A,k6_numbers)) & v1_mesfunc8(k4_mesfun7c(A,B),A,k6_numbers) & m1_subset_1(k4_mesfun7c(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) ) )).
fof(dt_k4_mesfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k6_numbers) & v1_funct_1(B) & v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,k6_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,k6_numbers))) ) ) )).
fof(dt_k4_mesfunc5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k3_rfunct_3(A,B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) ) ) )).
fof(dt_k4_mesfunc7,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_numbers) & v7_ordinal1(B) ) => m1_subset_1(k4_mesfunc7(A,B),k6_numbers) ) )).
fof(dt_k4_mesfunc8,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ( v1_funct_1(k4_mesfunc8(A,B)) & v1_funct_2(k4_mesfunc8(A,B),k4_ordinal1,k4_partfun1(A,k6_numbers)) & v1_mesfunc8(k4_mesfunc8(A,B),A,k6_numbers) & m1_subset_1(k4_mesfunc8(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) ) )).
fof(dt_k4_mesfunc9,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ( v1_funct_1(k4_mesfunc9(A,B)) & v1_funct_2(k4_mesfunc9(A,B),k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(k4_mesfunc9(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) ) )).
fof(dt_k4_metric_1,axiom,( ! [A] : ( v1_funct_1(k4_metric_1(A)) & v1_funct_2(k4_metric_1(A),k2_zfmisc_1(A,A),k1_numbers) & m1_subset_1(k4_metric_1(A),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),k1_numbers))) ) )).
fof(dt_k4_metric_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k4_metric_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k4_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( v2_pre_topc(k4_mfold_2(A)) & l1_pre_topc(k4_mfold_2(A)) ) ) )).
fof(dt_k4_midsp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k4_midsp_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_nat_1(A,2)) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,k4_finseq_2(k1_nat_1(A,1),u1_struct_0(B))) ) => m1_subset_1(k4_midsp_3(A,B,C,D),u1_struct_0(B)) ) )).
fof(dt_k4_mmlquer2,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( v1_funct_1(k4_mmlquer2(A,B)) & v1_funct_2(k4_mmlquer2(A,B),A,k4_ordinal1) & m1_subset_1(k4_mmlquer2(A,B),k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) ) )).
fof(dt_k4_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k4_mod_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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))))) ) ) )).
fof(dt_k4_mod_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))))) ) ) )).
fof(dt_k4_modcat_1,axiom,( ! [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) & 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) ) )).
fof(dt_k4_modelc_1,axiom,( ! [A] : v1_xboolean(k4_modelc_1(A)) )).
fof(dt_k4_modelc_2,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k4_ordinal1) & m1_finseq_1(B,k4_ordinal1) ) => m2_finseq_1(k4_modelc_2(A,B),k4_ordinal1) ) )).
fof(dt_k4_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => m1_subset_1(k4_modelc_3(A),k1_zfmisc_1(k1_modelc_3(A))) ) )).
fof(dt_k4_moebius1,axiom,( ! [A] : ( v1_relat_1(k4_moebius1(A)) & v4_relat_1(k4_moebius1(A),k4_ordinal1) & v1_funct_1(k4_moebius1(A)) & v1_partfun1(k4_moebius1(A),k4_ordinal1) ) )).
fof(dt_k4_monoid_0,axiom,( ~ 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) )).
fof(dt_k4_morph_01,axiom,( ! [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) & 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))))) ) ) )).
fof(dt_k4_msafree,axiom,( ! [A] : ! [B] : ( ( ~ 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))))))) ) )).
fof(dt_k4_msafree2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k4_msafree3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k4_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => m2_pboole(k4_msafree4(A,B,C),u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,C)) ) )).
fof(dt_k4_msaterm,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))) ) )).
fof(dt_k4_msinst_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k4_msscyc_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ( ~ v2_struct_0(k4_msscyc_2(A)) & l1_graph_1(k4_msscyc_2(A)) ) ) )).
fof(dt_k4_mssubfam,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(dt_k4_msualg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k4_msualg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k4_msualg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(dt_k4_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k4_msualg_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(dt_k4_msualg_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & m1_subset_1(B,u4_struct_0(A)) & m1_subset_1(C,k4_ordinal1) & 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)) ) ) )).
fof(dt_k4_multop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ( ( ~ 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) ) )).
fof(dt_k4_nagata_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k4_nat_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => m1_subset_1(k4_nat_1(A,B),k4_ordinal1) ) )).
fof(dt_k4_nat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k4_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_funct_1(k4_nat_5(A)) & v1_funct_2(k4_nat_5(A),k4_ordinal1,k4_ordinal1) & m1_subset_1(k4_nat_5(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) ) )).
fof(dt_k4_nat_d,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => m1_subset_1(k4_nat_d(A,B),k4_ordinal1) ) )).
fof(dt_k4_nat_lat,axiom,( m1_subset_1(k4_nat_lat,u1_struct_0(k3_nat_lat)) )).
fof(dt_k4_nattra_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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(k4_nattra_1(A,B,C),A,B,C,C) ) )).
fof(dt_k4_ndiff_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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) & 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))))) ) ) )).
fof(dt_k4_ndiff_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & ~ v1_xboole_0(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))))) ) ) )).
fof(dt_k4_neckla_2,axiom,( m1_subset_1(k4_neckla_2,k1_zfmisc_1(k3_neckla_2)) )).
fof(dt_k4_necklace,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_orders_2(k4_necklace(A)) & l1_orders_2(k4_necklace(A)) ) ) )).
fof(dt_k4_newton,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => m1_subset_1(k4_newton(A,B),k4_ordinal1) ) )).
fof(dt_k4_normsp_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k4_normsp_0(A,B,C)) & m1_subset_1(k4_normsp_0(A,B,C),k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) ) )).
fof(dt_k4_normsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k4_normsp_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k4_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ( ~ v2_struct_0(k4_normsp_2(A)) & v5_rltopsp1(k4_normsp_2(A)) & l1_rltopsp1(k4_normsp_2(A)) ) ) )).
fof(dt_k4_ntalgo_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,k2_zfmisc_1(k4_numbers,k4_numbers)) ) => m1_subset_1(k4_ntalgo_1(A),k4_numbers) ) )).
fof(dt_k4_openlatt,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k4_oppcat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) )).
fof(dt_k4_ordeq_01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_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) & l1_normsp_1(B) ) => ( v1_funct_1(k4_ordeq_01(A,B,C)) & v1_nfcont_3(k4_ordeq_01(A,B,C),B) & m1_subset_1(k4_ordeq_01(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) ) )).
fof(dt_k4_orders_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_orders_3(A) ) => ( v6_altcat_1(k4_orders_3(A)) & l2_altcat_1(k4_orders_3(A)) ) ) )).
fof(dt_k4_ordinal2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) ) => v3_ordinal1(k4_ordinal2(A)) ) )).
fof(dt_k4_ordinal3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_ordinal2(B) ) => ( v1_relat_1(k4_ordinal3(A,B)) & v5_ordinal1(k4_ordinal3(A,B)) & v1_funct_1(k4_ordinal3(A,B)) & v1_ordinal2(k4_ordinal3(A,B)) ) ) )).
fof(dt_k4_ordinal4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k4_ordinal5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) & v1_ordinal2(A) ) => v3_ordinal1(k4_ordinal5(A)) ) )).
fof(dt_k4_ordinal6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(dt_k4_osafree,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) )).
fof(dt_k4_osalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k4_parsp_1,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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))) ) )).
fof(dt_k4_partfun2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k4_partit1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k4_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k4_pcomps_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k4_pcs_0,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(dt_k4_pdiff_1,axiom,( ! [A] : ! [B] : ( ( 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))))) ) ) )).
fof(dt_k4_pdiff_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) => v1_xreal_0(k4_pdiff_3(A,B)) ) )).
fof(dt_k4_pdiff_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k4_pdiff_5,axiom,( ! [A] : ! [B] : ( ( 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)) ) => v1_xreal_0(k4_pdiff_5(A,B)) ) )).
fof(dt_k4_pdiff_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_finseq_1(C,k4_ordinal1) & 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),k4_ordinal1,k4_partfun1(k1_euclid(A),k1_numbers)) & m1_subset_1(k4_pdiff_9(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(k1_euclid(A),k1_numbers)))) ) ) )).
fof(dt_k4_pencil_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))))) ) )).
fof(dt_k4_pencil_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)))) ) )).
fof(dt_k4_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k4_pepin(A),k4_ordinal1) ) )).
fof(dt_k4_petri,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k4_pnproc_1,axiom,( ! [A] : ! [B] : ( m1_pnproc_1(B,A) => ( v1_funct_1(k4_pnproc_1(A,B)) & v1_funct_2(k4_pnproc_1(A,B),A,k4_ordinal1) & m1_subset_1(k4_pnproc_1(A,B),k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) ) )).
fof(dt_k4_polyeq_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => v1_xcmplx_0(k4_polyeq_5(A,B,C)) ) )).
fof(dt_k4_polyform,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_int_1(B) ) => m2_finseq_1(k4_polyform(A,B),k4_numbers) ) )).
fof(dt_k4_polynom1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k4_polynom1(A,B,C,D),u1_struct_0(B)) ) )).
fof(dt_k4_polynom5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k4_polynom5(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k4_polynom7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k4_polynom8,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v2_struct_0(B) & l2_struct_0(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( v1_matrix_0(k4_polynom8(A,B,C)) & v2_matrix_0(k4_polynom8(A,B,C),u1_struct_0(B),A,1) & m2_finseq_1(k4_polynom8(A,B,C),k3_finseq_2(u1_struct_0(B))) ) ) )).
fof(dt_k4_poset_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k4_power,axiom,( v1_xreal_0(k4_power) )).
fof(dt_k4_pralg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k4_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k4_prob_1,axiom,( ! [A] : ! [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))) ) => m1_prob_1(k4_prob_1(A,B),A,B) ) )).
fof(dt_k4_prob_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,k9_setfam_1(A)) & v7_ordinal1(C) ) => m1_subset_1(k4_prob_3(A,B,C),k1_zfmisc_1(A)) ) )).
fof(dt_k4_prob_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k4_prvect_2,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k4_prvect_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k4_pscomp_1,axiom,( 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))) )).
fof(dt_k4_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => m1_subset_1(k4_qc_lang1(A),k1_zfmisc_1(k2_qc_lang1(A))) ) )).
fof(dt_k4_qc_lang2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k4_qc_lang3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k4_qc_lang4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k4_qc_trans,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(A) & v1_qc_trans(B,A) & m1_qc_lang1(B) & v7_ordinal1(C) & v5_relat_1(D,k3_qc_lang1(A)) & v3_card_1(D,C) & m1_finseq_1(D,k2_qc_lang1(A)) ) => ( v5_relat_1(k4_qc_trans(A,B,C,D),k3_qc_lang1(B)) & v3_card_1(k4_qc_trans(A,B,C,D),C) & m2_finseq_1(k4_qc_trans(A,B,C,D),k2_qc_lang1(B)) ) ) )).
fof(dt_k4_qmax_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(dt_k4_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_quantal1(A) ) => m1_subset_1(k4_quantal1(A),u1_struct_0(A)) ) )).
fof(dt_k4_quatern3,axiom,( ! [A] : ( m1_subset_1(A,k1_quaterni) => m1_subset_1(k4_quatern3(A),k1_quaterni) ) )).
fof(dt_k4_quofield,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k4_radix_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k4_radix_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) ) => m1_subset_1(k4_radix_2(A,B,C),k4_ordinal1) ) )).
fof(dt_k4_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ v1_xboole_0(k4_radix_3(A)) & m1_subset_1(k4_radix_3(A),k1_zfmisc_1(k4_numbers)) ) ) )).
fof(dt_k4_radix_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k4_radix_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k4_random_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k4_ranknull,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k4_ratfunc1,axiom,( ! [A] : ! [B] : ( ( ~ 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),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k4_ratfunc1(A,B),A) & m1_subset_1(k4_ratfunc1(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k4_rcomp_1,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xreal_0(B) ) => m1_subset_1(k4_rcomp_1(A,B),k1_zfmisc_1(k1_numbers)) ) )).
fof(dt_k4_real_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k4_real_1(A,B),k1_numbers) ) )).
fof(dt_k4_real_3,axiom,( ! [A] : ( 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),k4_ordinal1,k1_numbers) & m1_subset_1(k4_real_3(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k4_real_lat,axiom,( ! [A] : ( ~ 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)))) ) ) )).
fof(dt_k4_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ v2_struct_0(k4_real_ns1(A)) & v1_normsp_1(k4_real_ns1(A)) & l1_normsp_1(k4_real_ns1(A)) ) ) )).
fof(dt_k4_realset1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))))) ) ) )).
fof(dt_k4_realset2,axiom,( ! [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) & l6_algstr_0(A) ) => m3_realset1(k4_realset2(A),u1_struct_0(A),k4_struct_0(A)) ) )).
fof(dt_k4_rearran1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k4_relat_1,axiom,( ! [A] : v1_relat_1(k4_relat_1(A)) )).
fof(dt_k4_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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))) ) )).
fof(dt_k4_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( 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)))) ) ) )).
fof(dt_k4_rewrite2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k4_rfinseq2,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => v1_xreal_0(k4_rfinseq2(A)) ) )).
fof(dt_k4_rfunct_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k4_rfunct_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k4_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_funct_1(k4_rinfsup1(A)) & v1_funct_2(k4_rinfsup1(A),k4_ordinal1,k1_numbers) & m1_subset_1(k4_rinfsup1(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k4_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v1_funct_1(k4_rinfsup2(A)) & v1_funct_2(k4_rinfsup2(A),k4_ordinal1,k6_numbers) & m1_subset_1(k4_rinfsup2(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) ) )).
fof(dt_k4_ringcat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) ) ) )).
fof(dt_k4_rlaffin1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k4_rlsub_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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))) ) )).
fof(dt_k4_rltopsp1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_rltopsp1(A) & v1_xreal_0(B) ) => ( 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)))) ) ) )).
fof(dt_k4_rlvect_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k4_rlvect_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => m1_rlvect_2(k4_rlvect_2(A),A) ) )).
fof(dt_k4_rmod_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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))) ) )).
fof(dt_k4_rmod_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) ) )).
fof(dt_k4_robbins1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k4_robbins3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k4_roughs_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k4_rsspace,axiom,( v1_funct_1(k4_rsspace) & v1_funct_2(k4_rsspace,k2_zfmisc_1(k1_numbers,k1_rsspace),k1_rsspace) & m1_subset_1(k4_rsspace,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_rsspace),k1_rsspace))) )).
fof(dt_k4_rsspace3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_normsp_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => v1_xreal_0(k4_rsspace3(A,B,C)) ) )).
fof(dt_k4_rsspace4,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k4_rusub_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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))) ) )).
fof(dt_k4_rusub_4,axiom,( ! [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) & 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))) ) ) )).
fof(dt_k4_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => m1_subset_1(k4_rusub_5(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).
fof(dt_k4_rvsum_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k4_rvsum_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k4_scm_comp,axiom,( ! [A] : ( 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)) ) ) )).
fof(dt_k4_scm_inst,axiom,( ! [A] : ( m1_subset_1(A,k3_scm_inst) => m1_subset_1(k4_scm_inst(A),k2_scm_inst) ) )).
fof(dt_k4_scmfsa6a,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k4_scmfsa_1,axiom,( v1_funct_1(k4_scmfsa_1) & v1_funct_2(k4_scmfsa_1,k1_scmfsa_1,k7_card_1(3)) & m1_subset_1(k4_scmfsa_1,k1_zfmisc_1(k2_zfmisc_1(k1_scmfsa_1,k7_card_1(3)))) )).
fof(dt_k4_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_ami_2(k4_scmfsa_2(A)) & m1_subset_1(k4_scmfsa_2(A),u1_struct_0(k1_scmfsa_2)) ) ) )).
fof(dt_k4_scmfsa_7,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k4_scmfsa_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ( v1_funct_1(k4_scmfsa_9(A,B,C,D)) & v1_funct_2(k4_scmfsa_9(A,B,C,D),k4_ordinal1,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2))) & m1_subset_1(k4_scmfsa_9(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2))))) ) ) )).
fof(dt_k4_scmfsa_m,axiom,( ! [A] : ( ( 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)) ) )).
fof(dt_k4_scmp_gcd,axiom,( ~ v1_xboole_0(k4_scmp_gcd) & v1_relat_1(k4_scmp_gcd) & v4_relat_1(k4_scmp_gcd,k4_ordinal1) & 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) )).
fof(dt_k4_scmpds_2,axiom,( ! [A] : ( ( 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)) ) )).
fof(dt_k4_scmpds_4,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) & m1_subset_1(B,u1_compos_1(k1_scmpds_2)) ) => ( v1_relat_1(k4_scmpds_4(A,B)) & v4_relat_1(k4_scmpds_4(A,B),k4_ordinal1) & v5_relat_1(k4_scmpds_4(A,B),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k4_scmpds_4(A,B)) & v1_funct_1(k4_scmpds_4(A,B)) & v1_finset_1(k4_scmpds_4(A,B)) & v1_afinsq_1(k4_scmpds_4(A,B)) ) ) )).
fof(dt_k4_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) & v1_int_1(B) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ( v1_relat_1(k4_scmpds_6(A,B,C,D)) & v4_relat_1(k4_scmpds_6(A,B,C,D),k4_ordinal1) & v5_relat_1(k4_scmpds_6(A,B,C,D),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k4_scmpds_6(A,B,C,D)) & 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)) ) ) )).
fof(dt_k4_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => v1_int_1(k4_scmpds_i(A)) ) )).
fof(dt_k4_scmring1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) )).
fof(dt_k4_scmring2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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))) ) )).
fof(dt_k4_scmringi,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,k1_scmringi(A)) ) => m1_subset_1(k4_scmringi(A,B),k4_ordinal1) ) )).
fof(dt_k4_scmyciel,axiom,( ! [A] : ! [B] : ( ( v4_scmyciel(A) & m1_subset_1(B,k3_tarski(A)) ) => m1_subset_1(k4_scmyciel(A,B),k1_zfmisc_1(k3_tarski(A))) ) )).
fof(dt_k4_scpinvar,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k4_seq_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_membered(A) ) => m1_subset_1(k4_seq_4(A),k4_ordinal1) ) )).
fof(dt_k4_seqfunc,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( v1_funct_1(k4_seqfunc(A,B)) & v1_funct_2(k4_seqfunc(A,B),k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(k4_seqfunc(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) ) )).
fof(dt_k4_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => v1_xreal_0(k4_series_1(A)) ) )).
fof(dt_k4_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_funct_1(k4_setlim_1(A,B)) & v1_funct_2(k4_setlim_1(A,B),k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(k4_setlim_1(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) )).
fof(dt_k4_setlim_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_funct_1(k4_setlim_2(A,B,C)) & v1_funct_2(k4_setlim_2(A,B,C),k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(k4_setlim_2(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) )).
fof(dt_k4_setwiseo,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k4_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => m1_subset_1(k4_sf_mastr(A),k1_zfmisc_1(k3_scmfsa_2)) ) )).
fof(dt_k4_sfmastr2,axiom,( ! [A] : ( ( v1_ami_2(A) & ~ v1_scmfsa_m(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ( v1_relat_1(k4_sfmastr2(A)) & v4_relat_1(k4_sfmastr2(A),k4_ordinal1) & v5_relat_1(k4_sfmastr2(A),u1_compos_1(k1_scmfsa_2)) & ~ v1_xboole_0(k4_sfmastr2(A)) & v1_funct_1(k4_sfmastr2(A)) & v1_finset_1(k4_sfmastr2(A)) & v1_afinsq_1(k4_sfmastr2(A)) ) ) )).
fof(dt_k4_sfmastr3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k4_sgraph1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_sgraph1(B,A) => m1_subset_1(k4_sgraph1(A,B,C),k4_ordinal1) ) )).
fof(dt_k4_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => m1_subset_1(k4_simplex0(A),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k4_simplex1,axiom,( ! [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) & 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) ) ) )).
fof(dt_k4_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_funct_1(k4_sin_cos(A)) & v1_funct_2(k4_sin_cos(A),k4_ordinal1,k1_numbers) & m1_subset_1(k4_sin_cos(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k4_sin_cos3,axiom,( 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))) )).
fof(dt_k4_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k4_sin_cos4(A)) ) )).
fof(dt_k4_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k4_sin_cos7(A)) ) )).
fof(dt_k4_sincos10,axiom,( v1_funct_1(k4_sincos10) & m1_subset_1(k4_sincos10,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) )).
fof(dt_k4_stacks_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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))) ) ) )).
fof(dt_k4_struct_0,axiom,( ! [A] : ( l2_struct_0(A) => m1_subset_1(k4_struct_0(A),u1_struct_0(A)) ) )).
fof(dt_k4_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(A) & 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)) ) )).
fof(dt_k4_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k4_substlat,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k4_substut1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_finseq_1(B,k3_qc_lang1(A)) ) => m2_finseq_1(k4_substut1(A,B),k2_qc_lang1(A)) ) )).
fof(dt_k4_substut2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k4_supinf_1,axiom,( ! [A] : ( v2_membered(A) => v2_membered(k4_supinf_1(A)) ) )).
fof(dt_k4_supinf_2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_numbers) & m1_subset_1(B,k6_numbers) ) => m1_subset_1(k4_supinf_2(A,B),k6_numbers) ) )).
fof(dt_k4_t_0topsp,axiom,( ! [A] : ( ( ~ 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))))) ) ) )).
fof(dt_k4_taxonom1,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k4_taylor_1,axiom,( ! [A] : ( 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))) ) ) )).
fof(dt_k4_tdlat_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k4_termord,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,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)) ) )).
fof(dt_k4_tex_4,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k4_tmap_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k4_topalg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k4_topalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k4_topalg_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k4_topalg_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k4_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => v1_int_1(k4_topdim_1(A)) ) )).
fof(dt_k4_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => v1_card_1(k4_topgen_1(A)) ) )).
fof(dt_k4_topgen_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k4_topgen_3,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( v1_funct_1(k4_topgen_3(A,B)) & v1_funct_2(k4_topgen_3(A,B),k4_ordinal1,k1_numbers) & m1_subset_1(k4_topgen_3(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k4_topgen_4,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k4_topgen_5,axiom,( ! [A] : ! [B] : ( ( 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)))) ) ) )).
fof(dt_k4_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => m3_topgrp_1(k4_topgrp_1(A),A) ) )).
fof(dt_k4_topmetr,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(dt_k4_topreal1,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k4_topreal7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k4_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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_topreal9(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k4_toprealb,axiom,( ! [A] : ( v1_xreal_0(A) => m1_subset_1(k4_toprealb(A),u1_struct_0(k2_topalg_2)) ) )).
fof(dt_k4_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(k4_toprealc(A,B,C,D,E),u1_struct_0(C)) ) )).
fof(dt_k4_toprns_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ( v1_funct_1(k4_toprns_1(A,B,C)) & v1_funct_2(k4_toprns_1(A,B,C),k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(k4_toprns_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) ) )).
fof(dt_k4_treal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & m1_subset_1(C,u1_struct_0(k4_topmetr(k5_numbers,1))) & m1_subset_1(D,u1_struct_0(k4_topmetr(k5_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(k5_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(k5_numbers,1))))) ) ) )).
fof(dt_k4_trees_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & m1_finseq_1(B,k4_ordinal1) ) => ( ~ v1_xboole_0(k4_trees_1(A,B)) & v1_trees_1(k4_trees_1(A,B)) ) ) )).
fof(dt_k4_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_trees_3(k4_trees_3(A),A) ) )).
fof(dt_k4_trees_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k4_turing_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_finseq_1(B,k4_ordinal1) ) => m2_finseq_1(k4_turing_1(A,B),k4_numbers) ) )).
fof(dt_k4_twoscomp,axiom,( 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))) )).
fof(dt_k4_unialg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k4_unialg_3,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k4_uniroots,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(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),k4_ordinal1,u1_struct_0(B)) & v1_polynom1(k4_uniroots(A,B),B) & m1_subset_1(k4_uniroots(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) ) )).
fof(dt_k4_uproots,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v7_ordinal1(C) ) => ( v1_funct_1(k4_uproots(A,B,C)) & v1_funct_2(k4_uproots(A,B,C),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k4_uproots(A,B,C),A) & m1_subset_1(k4_uproots(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k4_urysohn1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k4_urysohn3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k4_urysohn3(A,B,C,D)) & v1_funct_2(k4_urysohn3(A,B,C,D),k3_urysohn1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(k4_urysohn3(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k3_urysohn1,k9_setfam_1(u1_struct_0(A))))) ) ) )).
fof(dt_k4_valuat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_qc_lang1(A) & ~ v1_xboole_0(B) & v7_ordinal1(C) & 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) ) )).
fof(dt_k4_vectmetr,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( ~ 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)) ) ) )).
fof(dt_k4_vectsp10,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) ) )).
fof(dt_k4_vectsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k4_vectsp_2,axiom,( ! [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) & 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) ) ) )).
fof(dt_k4_vectsp_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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))) ) )).
fof(dt_k4_vectsp_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k4_vectsp_8,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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))))) ) ) )).
fof(dt_k4_vfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) & v1_xreal_0(D) ) => ( 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)))) ) ) )).
fof(dt_k4_waybel10,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k4_waybel11,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k4_waybel17,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k4_waybel18,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k4_waybel20,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k4_waybel23,axiom,( ! [A] : ! [B] : ( ( ~ 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(k1_yellow_1(k7_waybel_0(B))),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) & m1_subset_1(k4_waybel23(A,B),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_yellow_1(k7_waybel_0(B))),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))))) ) ) )).
fof(dt_k4_waybel26,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))))) ) ) )).
fof(dt_k4_waybel27,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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))))) ) ) )).
fof(dt_k4_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => m1_subset_1(k4_waybel28(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).
fof(dt_k4_waybel29,axiom,( ! [A] : ( ( ~ 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(k1_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(k1_yellow_1(u1_pre_topc(A)))))) ) ) )).
fof(dt_k4_waybel34,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(dt_k4_waybel35,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k4_waybel_0,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k4_waybel_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k4_waybel_2,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k4_waybel_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k4_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))) ) )).
fof(dt_k4_waybel_4,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k4_waybel_5,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k4_waybel_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => m1_subset_1(k4_waybel_6(A),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k4_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k4_weddwitt,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(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)) ) ) )).
fof(dt_k4_weierstr,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k4_wsierp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & m1_finseq_1(C,A) ) => m2_finseq_1(k4_wsierp_1(A,B,C),A) ) )).
fof(dt_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k4_xcmplx_0(A)) ) )).
fof(dt_k4_xxreal_3,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => v1_xxreal_0(k4_xxreal_3(A,B)) ) )).
fof(dt_k4_yellow18,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k4_yellow20,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(dt_k4_yellow21,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k4_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => m1_subset_1(k4_yellow_0(A),u1_struct_0(A)) ) )).
fof(dt_k4_yellow_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_yellow_1(B) ) => ( v1_orders_2(k4_yellow_1(A,B)) & l1_orders_2(k4_yellow_1(A,B)) ) ) )).
fof(dt_k4_yellow_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & v1_relat_1(B) ) => m1_subset_1(k4_yellow_2(A,B),u1_struct_0(A)) ) )).
fof(dt_k4_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k4_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k4_yellow_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k4_zf_fund1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_zf_lang)) => m1_subset_1(k4_zf_fund1(A),k1_zfmisc_1(k4_ordinal1)) ) )).
fof(dt_k4_zf_lang,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_zf_lang) & m1_subset_1(B,k1_zf_lang) ) => m2_finseq_1(k4_zf_lang(A,B),k4_ordinal1) ) )).
fof(dt_k4_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) ) => ( ~ v1_xboole_0(k4_zf_lang1(A)) & m1_subset_1(k4_zf_lang1(A),k1_zfmisc_1(k1_zf_lang)) ) ) )).
fof(dt_k4_zf_refle,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k4_zmodul01,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(dt_k4_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ 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_int_1(B) ) => ( v1_funct_1(k4_zmodul02(A,B)) & v1_funct_2(k4_zmodul02(A,B),k2_zfmisc_1(k4_numbers,k1_zmodul02(A,B)),k1_zmodul02(A,B)) & m1_subset_1(k4_zmodul02(A,B),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_numbers,k1_zmodul02(A,B)),k1_zmodul02(A,B)))) ) ) )).
fof(dt_k50_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k50_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k50_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k51_abcmiz_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => m1_subset_1(k51_abcmiz_1(A),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k51_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) ) )).
fof(dt_k51_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k51_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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))) ) ) )).
fof(dt_k51_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k52_abcmiz_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => m1_subset_1(k52_abcmiz_1(A),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k52_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k52_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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))) ) ) )).
fof(dt_k52_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))))) ) ) )).
fof(dt_k53_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) ) )).
fof(dt_k53_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))) ) )).
fof(dt_k53_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))))) ) ) )).
fof(dt_k54_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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)))) ) ) )).
fof(dt_k54_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) ) )).
fof(dt_k54_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) )).
fof(dt_k54_valued_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k55_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k55_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) ) )).
fof(dt_k55_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k4_ordinal1) ) => m1_modelc_1(k55_modelc_1(A,B,C,D),A,B) ) )).
fof(dt_k55_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k56_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))))) ) )).
fof(dt_k56_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) ) )).
fof(dt_k56_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k57_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k57_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) ) )).
fof(dt_k57_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k4_ordinal1) ) => ( v1_funct_1(k57_modelc_1(A,B,C,D,E)) & v1_funct_2(k57_modelc_1(A,B,C,D,E),k4_ordinal1,A) & m1_subset_1(k57_modelc_1(A,B,C,D,E),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) ) )).
fof(dt_k57_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k58_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k58_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) ) )).
fof(dt_k58_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k58_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))))) ) ) )).
fof(dt_k59_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) ) )).
fof(dt_k59_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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))) ) )).
fof(dt_k59_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))))) ) ) )).
fof(dt_k5_abcmiz_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k5_abcmiz_a,axiom,( ~ v1_xboole_0(k5_abcmiz_a) & m1_subset_1(k5_abcmiz_a,k1_zfmisc_1(k20_abcmiz_1)) )).
fof(dt_k5_afinsq_1,axiom,( ! [A] : ( v1_relat_1(k5_afinsq_1(A)) & v1_funct_1(k5_afinsq_1(A)) ) )).
fof(dt_k5_afinsq_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k5_afproj,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k5_afvect0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k5_alg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))))) ) ) )).
fof(dt_k5_algstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k5_algstr_4,axiom,( ! [A] : ! [B] : ( ( ~ 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))))) ) ) )).
fof(dt_k5_altcat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) )).
fof(dt_k5_altcat_2,axiom,( v6_altcat_1(k5_altcat_2) & l2_altcat_1(k5_altcat_2) )).
fof(dt_k5_altcat_4,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(dt_k5_ami_2,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k3_ami_2,k4_ami_2))) => m1_subset_1(k5_ami_2(A),k4_ordinal1) ) )).
fof(dt_k5_ami_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k5_ami_wstd,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1) ) => m1_subset_1(k5_ami_wstd(A,B,C),k4_ordinal1) ) )).
fof(dt_k5_amistd_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k5_analort,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) ) )).
fof(dt_k5_anproj_1,axiom,( ! [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) & l1_rlvect_1(A) ) => ( v1_collsp(k5_anproj_1(A)) & l1_collsp(k5_anproj_1(A)) ) ) )).
fof(dt_k5_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( v1_relat_1(k5_aofa_a00(A,B,C,D,E,F)) & v1_funct_1(k5_aofa_a00(A,B,C,D,E,F)) & v1_finseq_1(k5_aofa_a00(A,B,C,D,E,F)) ) )).
fof(dt_k5_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(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) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) & v4_aofa_a01(D,A,B,C) & l4_aofa_a00(D,A,B,C) & ~ v2_struct_0(E) & v2_unialg_1(E) & v3_unialg_1(E) & v4_unialg_1(E) & v3_aofa_000(E) & v4_aofa_000(E) & v5_aofa_000(E) & v6_aofa_000(E) & ~ v10_aofa_000(E) & v11_aofa_000(E) & v12_aofa_000(E) & l3_aofa_a00(E,A,C,u4_aofa_a00(A,B,C,D)) & v3_aofa_a01(F,A,B,C,u4_aofa_a00(A,B,C,D),u8_aofa_a00(A)) & m1_subset_1(F,k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),u8_aofa_a00(A))) & v19_aofa_a00(G,A) & m1_subset_1(G,u1_struct_0(A)) & m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),G)) & m1_subset_1(I,k1_funct_1(u3_msualg_1(A,C),G)) ) => m1_subset_1(k5_aofa_a01(A,B,C,D,E,F,G,H,I),u1_struct_0(E)) ) )).
fof(dt_k5_aofa_i00,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k5_armstrng,axiom,( ! [A] : ( 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))))) ) )).
fof(dt_k5_arytm_0,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k5_arytm_0(A,B),k2_numbers) ) )).
fof(dt_k5_arytm_2,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k5_asympt_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_funct_1(k5_asympt_0(A,B)) & v1_funct_2(k5_asympt_0(A,B),k4_ordinal1,k1_numbers) & m1_subset_1(k5_asympt_0(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k5_asympt_1,axiom,( ~ v1_xboole_0(k5_asympt_1) & m1_subset_1(k5_asympt_1,k1_zfmisc_1(k4_ordinal1)) )).
fof(dt_k5_autalg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k5_autgroup,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k5_bagorder,axiom,( ! [A] : ! [B] : ( ( 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)))) ) ) )).
fof(dt_k5_bcialg_1,axiom,( ! [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) ) => ( ~ v1_xboole_0(k5_bcialg_1(A)) & m1_subset_1(k5_bcialg_1(A),k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_k5_bcialg_4,axiom,( ! [A] : ( ( ~ 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),k4_ordinal1),u1_struct_0(A)) & m1_subset_1(k5_bcialg_4(A),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_ordinal1),u1_struct_0(A)))) ) ) )).
fof(dt_k5_bhsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k5_bhsp_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k5_bhsp_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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)) & v1_xreal_0(C) ) => m1_subset_1(k5_bhsp_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k5_bhsp_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_funct_1(k5_bhsp_4(A,B,C)) & v1_funct_2(k5_bhsp_4(A,B,C),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k5_bhsp_4(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k5_bhsp_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(dt_k5_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k5_binari_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v8_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) ) )).
fof(dt_k5_binarith,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) ) ) )).
fof(dt_k5_binom,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,k4_ordinal1) ) => m1_subset_1(k5_binom(A,B,C),u1_struct_0(A)) ) )).
fof(dt_k5_binop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(dt_k5_binop_2,axiom,( v1_funct_1(k5_binop_2) & v1_funct_2(k5_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & m1_subset_1(k5_binop_2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers))) )).
fof(dt_k5_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) )).
fof(dt_k5_borsuk_6,axiom,( 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)))) )).
fof(dt_k5_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) ) )).
fof(dt_k5_brouwer,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & v1_xreal_0(B) & ~ v3_xxreal_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))))) ) ) )).
fof(dt_k5_bspace,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k5_bvfunc26,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k5_bvfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k5_bvfunc_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k5_c0sp1,axiom,( ! [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) & 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))) ) ) )).
fof(dt_k5_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => l1_lopban_2(k5_c0sp2(A)) ) )).
fof(dt_k5_calcul_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k5_card_1,axiom,( ! [A] : ( v1_finset_1(A) => m1_subset_1(k5_card_1(A),k4_ordinal1) ) )).
fof(dt_k5_card_fil,axiom,( ! [A] : ( ~ v1_finset_1(A) => m2_card_fil(k5_card_fil(A),A) ) )).
fof(dt_k5_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) )).
fof(dt_k5_cat_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) )).
fof(dt_k5_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)))) ) ) )).
fof(dt_k5_cat_4,axiom,( ! [A] : ! [B] : ( v2_cat_4(k5_cat_4(A,B)) & l1_cat_4(k5_cat_4(A,B)) ) )).
fof(dt_k5_cat_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ 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)) ) ) )).
fof(dt_k5_cayldick,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(k5_cayldick(A,B,C),u1_struct_0(k4_cayldick(A))) ) )).
fof(dt_k5_cc0sp1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k5_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => l1_clopban2(k5_cc0sp2(A)) ) )).
fof(dt_k5_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m2_funct_2(k5_cfuncdom(A),A,k2_numbers,k9_funct_2(A,k2_numbers)) ) )).
fof(dt_k5_cgames_1,axiom,( m1_subset_1(k5_cgames_1,k2_cgames_1(1)) )).
fof(dt_k5_chain_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_chain_1(B,A) & m1_subset_1(C,k4_ordinal1) ) => m1_subset_1(k5_chain_1(A,B,C),k1_zfmisc_1(k4_chain_1(A,B,C))) ) )).
fof(dt_k5_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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)) ) ) )).
fof(dt_k5_circcomb,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k5_circtrm1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k5_circuit1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) => m1_subset_1(k5_circuit1(A,B,C,D),k4_ordinal1) ) )).
fof(dt_k5_circuit2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k5_classes2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k5_clopban1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)))) ) )).
fof(dt_k5_clopban2,axiom,( ! [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) & 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)))) ) ) )).
fof(dt_k5_clopban3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & 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),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k5_clopban3(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k5_clopban4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & 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)) & v7_ordinal1(D) ) => ( v1_funct_1(k5_clopban4(A,B,C,D)) & v1_funct_2(k5_clopban4(A,B,C,D),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k5_clopban4(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k5_closure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(dt_k5_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k5_clvect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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))) ) )).
fof(dt_k5_clvect_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) & v1_xreal_0(C) ) => m1_subset_1(k5_clvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k5_combgras,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k5_complex1,axiom,( m1_subset_1(k5_complex1,k2_numbers) )).
fof(dt_k5_complsp2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & 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)) ) )).
fof(dt_k5_compos_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k5_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_compos_1(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k5_comput_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => ( v1_relat_1(k5_comput_1(A,B)) & v4_relat_1(k5_comput_1(A,B),k3_finseq_2(k4_ordinal1)) & v1_funct_1(k5_comput_1(A,B)) & v4_valued_0(k5_comput_1(A,B)) & v2_margrel1(k5_comput_1(A,B)) ) ) )).
fof(dt_k5_comseq_3,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k5_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ( v3_conlat_1(k5_conlat_1(A),A) & ~ v4_conlat_1(k5_conlat_1(A),A) & v6_conlat_1(k5_conlat_1(A),A) & v7_conlat_1(k5_conlat_1(A),A) & l2_conlat_1(k5_conlat_1(A),A) ) ) )).
fof(dt_k5_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(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))))) ) ) )).
fof(dt_k5_connsp_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k5_convex4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & m1_convex4(B,A) & m1_convex4(C,A) ) => m1_convex4(k5_convex4(A,B,C),A) ) )).
fof(dt_k5_convfun1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k6_numbers))) ) => m1_subset_1(k5_convfun1(A,B),k1_zfmisc_1(u1_struct_0(k3_convfun1(A,k4_convfun1)))) ) )).
fof(dt_k5_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => m2_subset_1(k5_cqc_lang(A),k9_qc_lang1(A),k3_cqc_lang(A)) ) )).
fof(dt_k5_csspace,axiom,( 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))) )).
fof(dt_k5_csspace4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k5_decomp_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k5_descip_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_finseq_2(k2_nat_1(2,B),A)) ) => m2_finseq_2(k5_descip_1(A,B,C),A,k4_finseq_2(B,A)) ) )).
fof(dt_k5_dickson,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_orders_2(k5_dickson(A)) & l1_orders_2(k5_dickson(A)) ) ) )).
fof(dt_k5_diff_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k5_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => m1_subset_1(k5_dilworth(A),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k5_dist_1,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & m1_finseq_1(B,A) ) => m1_subset_1(k5_dist_1(A,B),k1_zfmisc_1(k3_finseq_2(A))) ) )).
fof(dt_k5_dist_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,A) & m1_subset_1(C,k1_zfmisc_1(k4_finseq_1(B))) ) => m2_finseq_1(k5_dist_2(A,B,C),A) ) )).
fof(dt_k5_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( ~ 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)) ) )).
fof(dt_k5_dtconstr,axiom,( ~ v2_struct_0(k5_dtconstr) & v1_lang1(k5_dtconstr) & l1_lang1(k5_dtconstr) )).
fof(dt_k5_dynkin,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => m1_dynkin(k5_dynkin(A,B),A) ) )).
fof(dt_k5_e_siec,axiom,( ! [A] : ( 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)) ) )).
fof(dt_k5_ec_pf_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))))) ) ) )).
fof(dt_k5_ec_pf_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k5_endalg,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k5_ens_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m1_subset_1(k5_ens_1(A,B),k2_ens_1(A)) ) )).
fof(dt_k5_entropy1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( v1_matrix_0(k5_entropy1(A)) & m2_finseq_1(k5_entropy1(A),k3_finseq_2(k1_numbers)) ) ) )).
fof(dt_k5_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k5_equation,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,k1_funct_1(u3_msualg_1(A,k3_equation(A)),B)) & m1_subset_1(D,k1_funct_1(u3_msualg_1(A,k3_equation(A)),B)) ) => m1_subset_1(k5_equation(A,B,C,D),k1_funct_1(k4_equation(A),B)) ) )).
fof(dt_k5_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => m2_finseq_2(k5_euclid(A),k1_numbers,k1_euclid(A)) ) )).
fof(dt_k5_euclid_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & 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)))) ) )).
fof(dt_k5_euclid_5,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k5_euclid_7,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_finseq_1(B,k1_euclid(A)) ) => m2_finseq_2(k5_euclid_7(A,B),k1_numbers,k1_euclid(A)) ) )).
fof(dt_k5_euclid_8,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k5_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => m1_subset_1(k5_euclidlp(A),k1_zfmisc_1(k1_zfmisc_1(k1_euclid(A)))) ) )).
fof(dt_k5_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))) ) ) )).
fof(dt_k5_extpro_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k4_ordinal1) & 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)) ) ) )).
fof(dt_k5_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k5_facirc_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k5_ff_siec,axiom,( ! [A] : ( v1_petri(k5_ff_siec(A)) & v1_net_1(k5_ff_siec(A)) & l1_petri(k5_ff_siec(A)) ) )).
fof(dt_k5_fib_num2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => m2_finseq_1(k5_fib_num2(A),k4_ordinal1) ) )).
fof(dt_k5_filter_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k5_filter_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k5_filter_2,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(dt_k5_fin_topo,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k5_finance1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => v1_xreal_0(k5_finance1(A,B,C)) ) )).
fof(dt_k5_finseq_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k5_finseq_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k5_finseq_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k5_finseq_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_1(k5_finseq_8(A,B,C),A) ) )).
fof(dt_k5_finseqop,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k5_finsub_1,axiom,( ! [A] : v4_finsub_1(k5_finsub_1(A)) )).
fof(dt_k5_fintopo2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k5_fintopo3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k5_fintopo5,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => ( v1_orders_2(k5_fintopo5(A,B)) & l1_orders_2(k5_fintopo5(A,B)) ) ) )).
fof(dt_k5_flang_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & v7_ordinal1(C) ) => m1_subset_1(k5_flang_1(A,B,C),k1_zfmisc_1(A)) ) )).
fof(dt_k5_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k5_fomodel0(A,B,C)) & v1_funct_1(k5_fomodel0(A,B,C)) ) ) )).
fof(dt_k5_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k5_fomodel2(A,B,C)) & v1_funct_1(k5_fomodel2(A,B,C)) ) ) )).
fof(dt_k5_fomodel3,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ( v1_relat_1(k5_fomodel3(A,B)) & v1_funct_1(k5_fomodel3(A,B)) ) ) )).
fof(dt_k5_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k5_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)))) ) )).
fof(dt_k5_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k5_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(dt_k5_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k5_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : m1_subset_1(k5_ftacell1(A,B,C,D,E),k3_msafree2(k1_ftacell1(A,B,C,D,E))) )).
fof(dt_k5_funcsdom,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k5_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k5_funct_3,axiom,( ! [A] : ! [B] : ( 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)))) ) )).
fof(dt_k5_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))) ) ) )).
fof(dt_k5_funct_5,axiom,( m1_subset_1(k5_funct_5,k1_tarski(k5_ordinal1)) )).
fof(dt_k5_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ( v1_relat_1(k5_funct_6(A)) & v1_funct_1(k5_funct_6(A)) ) ) )).
fof(dt_k5_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))))) ) ) )).
fof(dt_k5_functor2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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) ) )).
fof(dt_k5_functor3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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)) ) )).
fof(dt_k5_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v5_relat_1(k5_fuzzy_1(A),k1_rcomp_1(k5_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))) ) ) )).
fof(dt_k5_fuzzy_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( v5_relat_1(k5_fuzzy_2(A,B),k1_rcomp_1(k5_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))) ) ) )).
fof(dt_k5_fvaluat1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k5_fvsum_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k5_gcd_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k5_genealg1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( ~ 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,k4_ordinal1) & m1_subset_1(E,k4_ordinal1) & m1_subset_1(F,k4_ordinal1) & m1_subset_1(G,k4_ordinal1) & m1_subset_1(H,k4_ordinal1) ) => m2_finseq_1(k5_genealg1(A,B,C,D,E,F,G,H),k3_card_3(A)) ) )).
fof(dt_k5_geomtrap,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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))))) ) )).
fof(dt_k5_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ 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)) ) )).
fof(dt_k5_gfacirc2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k5_glib_000,axiom,( ~ v1_xboole_0(k5_glib_000) & m1_subset_1(k5_glib_000,k1_zfmisc_1(k4_ordinal1)) )).
fof(dt_k5_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(dt_k5_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(dt_k5_glib_004,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k5_glib_005,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(dt_k5_goboard5,axiom,( ! [A] : ! [B] : ( ( ~ 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))) & v7_ordinal1(B) ) => m1_subset_1(k5_goboard5(A,B),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) )).
fof(dt_k5_gobrd13,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) & v7_ordinal1(C) ) => m1_subset_1(k5_gobrd13(A,B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) )).
fof(dt_k5_gr_cy_1,axiom,( ! [A] : ( v1_int_1(A) => m1_subset_1(k5_gr_cy_1(A),u1_struct_0(k2_gr_cy_1)) ) )).
fof(dt_k5_graph_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k5_graph_3,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k5_graph_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) )).
fof(dt_k5_graphsp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_funct_2(A,A)) => ( v1_funct_1(k5_graphsp(A,B)) & v1_funct_2(k5_graphsp(A,B),k4_ordinal1,k1_funct_2(A,A)) & m1_subset_1(k5_graphsp(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_funct_2(A,A)))) ) ) )).
fof(dt_k5_grcat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) )).
fof(dt_k5_groeb_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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(k12_polynom1(A,B)))) & m2_ideal_1(D,k12_polynom1(A,B),C) & m2_ideal_1(E,k12_polynom1(A,B),C) ) => m2_ideal_1(k5_groeb_2(A,B,C,D,E),k12_polynom1(A,B),C) ) )).
fof(dt_k5_groeb_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) & m1_subset_1(E,k4_ordinal1) ) => ( 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),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)))) ) ) )).
fof(dt_k5_group_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k5_group_10,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))))) ) ) )).
fof(dt_k5_group_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k5_group_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k5_group_4,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k5_group_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k5_group_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k5_group_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) )).
fof(dt_k5_group_9,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k5_hahnban1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k5_heyting1,axiom,( ! [A] : ( 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))))) ) )).
fof(dt_k5_heyting2,axiom,( ! [A] : ! [B] : ( 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))))) ) ) )).
fof(dt_k5_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => m1_subset_1(k5_heyting3(A),k1_zfmisc_1(u1_struct_0(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A))))) ) )).
fof(dt_k5_hilbasis,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k5_hilbasis(A,B,C),A) & m1_subset_1(k5_hilbasis(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k5_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => m1_subset_1(k5_hilbert1(A),k1_zfmisc_1(k1_hilbert1)) ) )).
fof(dt_k5_hilbert3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & 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)))) ) ) )).
fof(dt_k5_hurwitz,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k5_hurwitz(A,B,C)) & v1_funct_2(k5_hurwitz(A,B,C),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k5_hurwitz(A,B,C),A) & m1_subset_1(k5_hurwitz(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k5_idea_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => v7_ordinal1(k5_idea_1(A,B)) ) )).
fof(dt_k5_index_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(dt_k5_int_1,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_int_1(B) ) => v1_int_1(k5_int_1(A,B)) ) )).
fof(dt_k5_int_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k5_integr15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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,k4_ordinal1,k1_integra1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(B)))) & m4_integr15(E,A,B,C,D) & m1_subset_1(F,k4_ordinal1) ) => m3_integr15(k5_integr15(A,B,C,D,E,F),A,B,C,k2_integra2(B,D,F)) ) )).
fof(dt_k5_integr18,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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)) ) )).
fof(dt_k5_integra1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k5_interva1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_interva1(B,A) ) => m1_subset_1(k5_interva1(A,B),k1_zfmisc_1(A)) ) )).
fof(dt_k5_intpro_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k5_irrat_1,axiom,( v1_funct_1(k5_irrat_1) & v1_funct_2(k5_irrat_1,k4_ordinal1,k1_numbers) & m1_subset_1(k5_irrat_1,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) )).
fof(dt_k5_isocat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) )).
fof(dt_k5_isocat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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,k6_cat_2(A,B),C) ) => m2_cat_1(k5_isocat_2(A,B,C,D),A,k9_nattra_1(B,C)) ) )).
fof(dt_k5_jgraph_4,axiom,( ! [A] : ( 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))))) ) ) )).
fof(dt_k5_jgraph_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) )).
fof(dt_k5_jordan11,axiom,( ! [A] : ! [B] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & v7_ordinal1(B) ) => m1_subset_1(k5_jordan11(A,B),k4_ordinal1) ) )).
fof(dt_k5_jordan1k,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => v1_xreal_0(k5_jordan1k(A,B,C)) ) )).
fof(dt_k5_jordan5d,axiom,( ! [A] : ( ( ~ 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))) ) => v7_ordinal1(k5_jordan5d(A)) ) )).
fof(dt_k5_jordan6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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)))) ) )).
fof(dt_k5_jordan_a,axiom,( ! [A] : ! [B] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_jordan_a(B,A) ) => v1_xreal_0(k5_jordan_a(A,B)) ) )).
fof(dt_k5_knaster,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k5_kolmog01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) )).
fof(dt_k5_kurato_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k5_lang1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k5_laplace,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) & ~ 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) & v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(D),C,C) & m1_finseq_1(E,k3_finseq_2(u1_struct_0(D))) ) => m1_subset_1(k5_laplace(A,B,C,D,E),u1_struct_0(D)) ) )).
fof(dt_k5_lattice3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k5_lattice4,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k5_lattice6,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(dt_k5_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lattices(A) ) => m1_subset_1(k5_lattices(A),u1_struct_0(A)) ) )).
fof(dt_k5_lexbfs,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1))) ) ) )).
fof(dt_k5_lfuzzy_0,axiom,( ! [A] : ! [B] : ( ( ~ 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(k5_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))) ) ) )).
fof(dt_k5_lfuzzy_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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))) ) ) )).
fof(dt_k5_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => v1_xreal_0(k5_limfunc1(A)) ) )).
fof(dt_k5_lopban_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k5_lopban_2,axiom,( ! [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) & 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)))) ) ) )).
fof(dt_k5_lopban_3,axiom,( ! [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) & 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),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k5_lopban_3(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k5_lopban_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) & 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),k4_ordinal1,u1_struct_0(B)) & m1_subset_1(k5_lopban_4(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) ) )).
fof(dt_k5_lopban_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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)))) ) => ( ~ v2_struct_0(k5_lopban_7(A,B,C)) & l1_normsp_1(k5_lopban_7(A,B,C)) ) ) )).
fof(dt_k5_lopclset,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k5_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v1_membered(B) & m1_subset_1(C,k3_rfunct_3(A,B)) & v1_xcmplx_0(D) ) => m2_rfunct_3(k5_lpspacc1(A,B,C,D),A,k2_numbers,k3_rfunct_3(A,k2_numbers)) ) )).
fof(dt_k5_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m2_rfunct_3(k5_lpspace1(A),A,k1_numbers,k3_rfunct_3(A,k1_numbers)) ) )).
fof(dt_k5_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) & v2_xxreal_0(E) & v1_xreal_0(E) ) => m1_subset_1(k5_lpspace2(A,B,C,D,E),k1_zfmisc_1(k1_lpspace2(A,B,C,E))) ) )).
fof(dt_k5_ltlaxio1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_hilbert1) & m1_subset_1(B,k1_hilbert1) ) => m1_subset_1(k5_ltlaxio1(A,B),k1_hilbert1) ) )).
fof(dt_k5_ltlaxio2,axiom,( ! [A] : ( m1_finseq_1(A,k1_hilbert1) => m2_finseq_1(k5_ltlaxio2(A),k1_hilbert1) ) )).
fof(dt_k5_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => m1_subset_1(k5_ltlaxio3(A),k1_zfmisc_1(k1_hilbert1)) ) )).
fof(dt_k5_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ( v1_finset_1(k5_ltlaxio4(A)) & m1_subset_1(k5_ltlaxio4(A),k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)))) ) ) )).
fof(dt_k5_margrel1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k3_margrel1(A)) ) => m1_subset_1(k5_margrel1(A,B),k4_ordinal1) ) )).
fof(dt_k5_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k5_matrix10,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m1_finseq_1(B,k3_finseq_2(k1_numbers)) & v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m1_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( v1_matrix_0(k5_matrix10(A,B,C)) & v2_matrix_0(k5_matrix10(A,B,C),k1_numbers,A,A) & m2_finseq_1(k5_matrix10(A,B,C),k3_finseq_2(k1_numbers)) ) ) )).
fof(dt_k5_matrix12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & ~ 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) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(C))) & v7_ordinal1(E) & m1_subset_1(F,u1_struct_0(C)) ) => ( v1_matrix_0(k5_matrix12(A,B,C,D,E,F)) & v2_matrix_0(k5_matrix12(A,B,C,D,E,F),u1_struct_0(C),A,B) & m2_finseq_1(k5_matrix12(A,B,C,D,E,F),k3_finseq_2(u1_struct_0(C))) ) ) )).
fof(dt_k5_matrix13,axiom,( ! [A] : ( ( v1_finset_1(A) & v1_setfam_1(A) & m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) ) => m2_finseq_2(k5_matrix13(A),k4_ordinal1,k4_finseq_2(k5_card_1(A),k4_ordinal1)) ) )).
fof(dt_k5_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(A)) & v7_ordinal1(C) ) => m2_finseq_1(k5_matrix_0(A,B,C),A) ) )).
fof(dt_k5_matrix_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) & v7_ordinal1(B) & v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(A),B,B) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(A))) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(A),B,B) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ( v1_matrix_0(k5_matrix_1(A,B,C,D)) & v2_matrix_0(k5_matrix_1(A,B,C,D),u1_struct_0(A),B,B) & m2_finseq_1(k5_matrix_1(A,B,C,D),k3_finseq_2(u1_struct_0(A))) ) ) )).
fof(dt_k5_matrix_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k3_matrix_2(B)) ) => m1_subset_1(k5_matrix_2(A,B,C,D),u1_struct_0(A)) ) )).
fof(dt_k5_matrix_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) & ~ 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) & v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(D),A,B) & m1_finseq_1(E,k3_finseq_2(u1_struct_0(D))) & v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(D),k1_matrix_0(E),C) & m1_finseq_1(F,k3_finseq_2(u1_struct_0(D))) ) => ( v1_matrix_0(k5_matrix_3(A,B,C,D,E,F)) & v2_matrix_0(k5_matrix_3(A,B,C,D,E,F),u1_struct_0(D),k3_finseq_1(E),k1_matrix_0(F)) & m2_finseq_1(k5_matrix_3(A,B,C,D,E,F),k3_finseq_2(u1_struct_0(D))) ) ) )).
fof(dt_k5_matrix_5,axiom,( ! [A] : ! [B] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k2_numbers)) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(k2_numbers)) ) => ( v1_matrix_0(k5_matrix_5(A,B)) & m2_finseq_1(k5_matrix_5(A,B),k3_finseq_2(k2_numbers)) ) ) )).
fof(dt_k5_matrixc1,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k2_numbers) & m1_finseq_1(B,k2_numbers) ) => m2_finseq_1(k5_matrixc1(A,B),k2_numbers) ) )).
fof(dt_k5_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(A)) & v1_matrix_0(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))) ) ) )).
fof(dt_k5_matrixr1,axiom,( ! [A] : ! [B] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k1_numbers)) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( v1_matrix_0(k5_matrixr1(A,B)) & m2_finseq_1(k5_matrixr1(A,B),k3_finseq_2(k1_numbers)) ) ) )).
fof(dt_k5_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_matrix_0(k5_matrixr2(A)) & v2_matrix_0(k5_matrixr2(A),k1_numbers,A,A) & m2_finseq_1(k5_matrixr2(A),k3_finseq_2(k1_numbers)) ) ) )).
fof(dt_k5_matrlin,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) ) )).
fof(dt_k5_matrlin2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & ~ 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) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(C))) & v1_matrix_0(E) & m1_finseq_1(E,k3_finseq_2(u1_struct_0(C))) ) => ( v1_matrix_0(k5_matrlin2(A,B,C,D,E)) & v2_matrix_0(k5_matrlin2(A,B,C,D,E),u1_struct_0(C),A,B) & m2_finseq_1(k5_matrlin2(A,B,C,D,E),k3_finseq_2(u1_struct_0(C))) ) ) )).
fof(dt_k5_matrprob,axiom,( ! [A] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k1_numbers)) ) => v1_xreal_0(k5_matrprob(A)) ) )).
fof(dt_k5_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(dt_k5_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => m1_subset_1(k5_measure6(A),k1_zfmisc_1(k1_numbers)) ) )).
fof(dt_k5_measure8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_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,k6_numbers))) & m1_subset_1(D,k1_zfmisc_1(A)) ) => m1_subset_1(k5_measure8(A,B,C,D),k1_zfmisc_1(k6_numbers)) ) )).
fof(dt_k5_member_1,axiom,( ! [A] : ( v1_membered(A) => v1_membered(k5_member_1(A)) ) )).
fof(dt_k5_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) => m1_subset_1(k5_memstr_0(A,B,C),k4_ordinal1) ) )).
fof(dt_k5_mesfun7c,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( v1_funct_1(k5_mesfun7c(A,B)) & v1_funct_2(k5_mesfun7c(A,B),k4_ordinal1,k4_partfun1(A,k6_numbers)) & v1_mesfunc8(k5_mesfun7c(A,B),A,k6_numbers) & m1_subset_1(k5_mesfun7c(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) ) )).
fof(dt_k5_mesfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k6_numbers) & v1_funct_1(B) & v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,k6_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,k6_numbers))) ) ) )).
fof(dt_k5_mesfunc5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => m1_subset_1(k5_mesfunc5(A,B,C,D),k6_numbers) ) )).
fof(dt_k5_mesfunc7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v1_xboole_0(B) & v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( v1_funct_1(k5_mesfunc7(A,B,C)) & m1_subset_1(k5_mesfunc7(A,B,C),k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) ) )).
fof(dt_k5_mesfunc8,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ( v1_funct_1(k5_mesfunc8(A,B)) & m1_subset_1(k5_mesfunc8(A,B),k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) ) )).
fof(dt_k5_metric_1,axiom,( ! [A] : ( v1_metric_1(k5_metric_1(A)) & l1_metric_1(k5_metric_1(A)) ) )).
fof(dt_k5_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => m1_subset_1(k5_metric_2(A),k1_zfmisc_1(k1_numbers)) ) )).
fof(dt_k5_mfold_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))))))) ) ) )).
fof(dt_k5_midsp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k5_midsp_2,axiom,( ! [A] : ( ( ~ 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))))) ) ) )).
fof(dt_k5_midsp_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & ~ v1_xboole_0(B) & m1_subset_1(C,k4_finseq_2(k1_nat_1(A,1),B)) & m1_midsp_3(D,A) ) => m1_subset_1(k5_midsp_3(A,B,C,D),B) ) )).
fof(dt_k5_mod_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k5_modal_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) & m1_subset_1(B,A) ) => v7_ordinal1(k5_modal_1(A,B)) ) )).
fof(dt_k5_modcat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) )).
fof(dt_k5_modelc_2,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k4_ordinal1) & m1_finseq_1(B,k4_ordinal1) ) => m2_finseq_1(k5_modelc_2(A,B),k4_ordinal1) ) )).
fof(dt_k5_modelc_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & l1_modelc_3(B,A) & v1_modelc_2(C) & m1_finseq_1(C,k4_ordinal1) ) => ( v1_modelc_3(k5_modelc_3(A,B,C),A) & l1_modelc_3(k5_modelc_3(A,B,C),A) ) ) )).
fof(dt_k5_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( v1_relat_1(k5_moebius1(A)) & v4_relat_1(k5_moebius1(A),k8_newton) & v1_funct_1(k5_moebius1(A)) & v1_partfun1(k5_moebius1(A),k8_newton) ) ) )).
fof(dt_k5_monoid_0,axiom,( ~ 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) )).
fof(dt_k5_monoid_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k5_msafree,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k5_msafree2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k5_msafree3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k5_msafree4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => m3_pboole(k5_msafree4(A,B),u1_struct_0(A),k4_equation(A)) ) )).
fof(dt_k5_msaterm,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))) ) )).
fof(dt_k5_mssubfam,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k5_msualg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k5_msualg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) )).
fof(dt_k5_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k5_msualg_5,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k5_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => m1_mycielsk(k5_mycielsk(A),A) ) )).
fof(dt_k5_nagata_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(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(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))) ) ) )).
fof(dt_k5_nat_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => m1_subset_1(k5_nat_1(A,B),k4_ordinal1) ) )).
fof(dt_k5_nat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k5_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k5_nat_5(A),k4_ordinal1) ) )).
fof(dt_k5_nat_d,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => m1_subset_1(k5_nat_d(A,B),k4_ordinal1) ) )).
fof(dt_k5_nattra_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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(k5_nattra_1(A,B,C,D,E,F,G),A,B,C,E) ) )).
fof(dt_k5_ndiff_5,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => m2_subset_1(k5_ndiff_5(A,B),k4_ordinal1,k4_finseq_1(A)) ) )).
fof(dt_k5_newton,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v7_ordinal1(C) ) => m2_finseq_1(k5_newton(A,B,C),k1_numbers) ) )).
fof(dt_k5_normform,axiom,( ! [A] : ( 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))))) ) )).
fof(dt_k5_normsp_0,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_normsp_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k5_normsp_0(A,B)) & v1_funct_2(k5_normsp_0(A,B),k4_ordinal1,k1_numbers) & m1_subset_1(k5_normsp_0(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k5_normsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_xreal_0(C) ) => ( v1_funct_1(k5_normsp_1(A,B,C)) & v1_funct_2(k5_normsp_1(A,B,C),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k5_normsp_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k5_numbers,axiom,( m1_subset_1(k5_numbers,k4_ordinal1) )).
fof(dt_k5_openlatt,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k5_oppcat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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))) ) )).
fof(dt_k5_ordeq_01,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_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) & l1_normsp_1(B) ) => ( ~ v2_struct_0(k5_ordeq_01(A,B)) & v1_normsp_1(k5_ordeq_01(A,B)) & l1_normsp_1(k5_ordeq_01(A,B)) ) ) )).
fof(dt_k5_ordinal2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) ) => v3_ordinal1(k5_ordinal2(A)) ) )).
fof(dt_k5_ordinal3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => v3_ordinal1(k5_ordinal3(A,B)) ) )).
fof(dt_k5_ordinal5,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => v3_ordinal1(k5_ordinal5(A,B)) ) )).
fof(dt_k5_osafree,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k5_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k5_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k5_pcs_0,axiom,( l1_pcs_0(k5_pcs_0) )).
fof(dt_k5_pdiff_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_finseq_1(B,k1_numbers) ) => ( v1_relat_1(k5_pdiff_1(A,B)) & v1_funct_1(k5_pdiff_1(A,B)) ) ) )).
fof(dt_k5_pdiff_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) => v1_xreal_0(k5_pdiff_3(A,B)) ) )).
fof(dt_k5_pdiff_4,axiom,( ! [A] : ( m1_subset_1(A,k1_euclid(3)) => m2_finseq_2(k5_pdiff_4(A),k1_numbers,k1_euclid(3)) ) )).
fof(dt_k5_pdiff_5,axiom,( ! [A] : ! [B] : ( ( 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)) ) => v1_xreal_0(k5_pdiff_5(A,B)) ) )).
fof(dt_k5_pdiff_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_finseq_1(C,k4_ordinal1) & 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))) ) ) )).
fof(dt_k5_pencil_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k5_pencil_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) ) ) )).
fof(dt_k5_petri,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k5_pnproc_1,axiom,( ! [A] : ! [B] : ( m1_pnproc_1(B,A) => ( v1_funct_1(k5_pnproc_1(A,B)) & v1_funct_2(k5_pnproc_1(A,B),A,k4_ordinal1) & m1_subset_1(k5_pnproc_1(A,B),k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) ) )).
fof(dt_k5_polyeq_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k5_polyform,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_int_1(A) & v1_int_1(B) & v1_int_1(C) ) => m2_finseq_1(k5_polyform(A,B,C),k4_numbers) ) )).
fof(dt_k5_polynom1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(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)))) ) ) )).
fof(dt_k5_polynom3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v1_partfun1(k5_polynom3(A),k4_finseq_2(A,k4_ordinal1)) & 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,k4_ordinal1),k4_finseq_2(A,k4_ordinal1)))) ) ) )).
fof(dt_k5_polynom5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k5_polynom5(A,B,C)) & v1_funct_2(k5_polynom5(A,B,C),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k5_polynom5(A,B,C),A) & m1_subset_1(k5_polynom5(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k5_polynom7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k5_polynom8,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) & v1_matrix_0(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),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k5_polynom8(A,B),A) & m1_subset_1(k5_polynom8(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k5_poset_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k5_pralg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k5_pralg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(dt_k5_pre_poly,axiom,( ! [A] : ! [B] : ( m1_finseq_1(B,k3_finseq_2(A)) => m2_finseq_2(k5_pre_poly(A,B),A,k3_finseq_2(A)) ) )).
fof(dt_k5_prepower,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v5_relat_1(B,k3_numbers) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_funct_1(k5_prepower(A,B)) & v1_funct_2(k5_prepower(A,B),k4_ordinal1,k1_numbers) & m1_subset_1(k5_prepower(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k5_prob_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_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) ) )).
fof(dt_k5_prob_3,axiom,( ! [A] : ! [B] : ( m1_finseq_1(B,k9_setfam_1(A)) => m1_subset_1(k5_prob_3(A,B),k1_zfmisc_1(A)) ) )).
fof(dt_k5_prob_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k5_prvect_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k5_prvect_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k5_pscomp_1,axiom,( 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))) )).
fof(dt_k5_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => m1_subset_1(k5_qc_lang1(A),k1_zfmisc_1(k2_qc_lang1(A))) ) )).
fof(dt_k5_qc_lang2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k5_qc_lang3,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k5_quantal1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k5_quatern2,axiom,( ! [A] : ! [B] : ( ( v1_quaterni(A) & v1_quaterni(B) ) => m1_subset_1(k5_quatern2(A,B),k1_quaterni) ) )).
fof(dt_k5_quofield,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k5_radix_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(dt_k5_radix_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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),k4_ordinal1) ) ) )).
fof(dt_k5_radix_3,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v7_ordinal1(B) ) => v1_int_1(k5_radix_3(A,B)) ) )).
fof(dt_k5_radix_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) ) => m2_subset_1(k5_radix_5(A,B,C),k4_numbers,k3_radix_1(C)) ) )).
fof(dt_k5_radix_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k5_random_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_xreal_0(D) ) => m1_random_1(k5_random_1(A,B,C,D),A,B) ) )).
fof(dt_k5_random_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( v1_relat_1(k5_random_3(A)) & v4_relat_1(k5_random_3(A),k4_ordinal1) & v1_funct_1(k5_random_3(A)) & v1_partfun1(k5_random_3(A),k4_ordinal1) ) ) )).
fof(dt_k5_ranknull,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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))) ) )).
fof(dt_k5_ratfunc1,axiom,( ! [A] : ! [B] : ( ( ~ 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),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(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(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k5_real_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k5_real_1(A,B),k1_numbers) ) )).
fof(dt_k5_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_funct_1(k5_real_3(A)) & v1_funct_2(k5_real_3(A),k4_ordinal1,k1_numbers) & m1_subset_1(k5_real_3(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k5_real_lat,axiom,( ! [A] : ( ~ 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)))) ) ) )).
fof(dt_k5_realset2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)))) ) ) )).
fof(dt_k5_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(A) => v1_relat_1(k5_relat_1(A,B)) ) )).
fof(dt_k5_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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))) ) )).
fof(dt_k5_rewrite2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k5_rfinseq2,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => ( v8_valued_0(k5_rfinseq2(A)) & m2_finseq_1(k5_rfinseq2(A),k1_numbers) ) ) )).
fof(dt_k5_rfunct_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k5_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => v1_xreal_0(k5_rinfsup1(A)) ) )).
fof(dt_k5_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => m1_subset_1(k5_rinfsup2(A),k6_numbers) ) )).
fof(dt_k5_ringcat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) ) )).
fof(dt_k5_rlaffin1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) )).
fof(dt_k5_rlsub_2,axiom,( ! [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) ) => ( 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)))) ) ) )).
fof(dt_k5_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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_rltopsp1(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k5_rlvect_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) )).
fof(dt_k5_rmod_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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)))) ) ) )).
fof(dt_k5_rmod_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) ) )).
fof(dt_k5_robbins1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k5_robbins3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k5_roughs_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k5_rsspace,axiom,( m1_subset_1(k5_rsspace,k1_rsspace) )).
fof(dt_k5_rsspace3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_normsp_1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v7_ordinal1(C) ) => m1_subset_1(k5_rsspace3(A,B,C),u1_struct_0(A)) ) )).
fof(dt_k5_rsspace4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k5_rusub_2,axiom,( ! [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_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)))) ) ) )).
fof(dt_k5_rusub_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k5_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => l1_pre_topc(k5_rusub_5(A)) ) )).
fof(dt_k5_rvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k5_rvsum_2,axiom,( ! [A] : ( ( 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) ) )).
fof(dt_k5_scm_comp,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k5_scm_inst,axiom,( ! [A] : ( m1_subset_1(A,k3_scm_inst) => m1_subset_1(k5_scm_inst(A),k2_scm_inst) ) )).
fof(dt_k5_scmfsa6a,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k5_scmfsa8b,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k5_scmfsa_1,axiom,( v1_relat_1(k5_scmfsa_1) & v4_relat_1(k5_scmfsa_1,k7_card_1(3)) & v1_funct_1(k5_scmfsa_1) & v1_partfun1(k5_scmfsa_1,k7_card_1(3)) )).
fof(dt_k5_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => m1_scmfsa_2(k5_scmfsa_2(A)) ) )).
fof(dt_k5_scmfsa_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ( v1_funct_1(k5_scmfsa_9(A,B,C,D)) & v1_funct_2(k5_scmfsa_9(A,B,C,D),k4_ordinal1,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2))) & m1_subset_1(k5_scmfsa_9(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2))))) ) ) )).
fof(dt_k5_scmfsa_m,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k5_scmpds_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k5_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) & v1_int_1(B) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ( v1_relat_1(k5_scmpds_6(A,B,C)) & v4_relat_1(k5_scmpds_6(A,B,C),k4_ordinal1) & v5_relat_1(k5_scmpds_6(A,B,C),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k5_scmpds_6(A,B,C)) & 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)) ) ) )).
fof(dt_k5_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => m1_subset_1(k5_scmpds_i(A),k2_scm_inst) ) )).
fof(dt_k5_scmring2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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))) ) )).
fof(dt_k5_scmringi,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,k1_scmringi(A)) ) => m1_subset_1(k5_scmringi(A,B),k4_ordinal1) ) )).
fof(dt_k5_scmyciel,axiom,( ! [A] : m1_scmyciel(k5_scmyciel(A),A) )).
fof(dt_k5_scpinvar,axiom,( ~ v1_xboole_0(k5_scpinvar) & v1_relat_1(k5_scpinvar) & v4_relat_1(k5_scpinvar,k4_ordinal1) & 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) )).
fof(dt_k5_seq_4,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( v1_funct_1(k5_seq_4(A)) & v1_funct_2(k5_seq_4(A),k2_numbers,k2_numbers) & m1_subset_1(k5_seq_4(A),k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) ) )).
fof(dt_k5_seqfunc,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( v1_funct_1(k5_seqfunc(A,B)) & v1_funct_2(k5_seqfunc(A,B),k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(k5_seqfunc(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) ) )).
fof(dt_k5_series_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => m1_subset_1(k5_series_1(A,B),k4_ordinal1) ) )).
fof(dt_k5_setfam_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k5_setfam_1(A,B),k1_zfmisc_1(A)) ) )).
fof(dt_k5_setlim_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(k5_setlim_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) )).
fof(dt_k5_setlim_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(k5_setlim_2(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) )).
fof(dt_k5_setwiseo,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k5_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(dt_k5_sgraph1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) )).
fof(dt_k5_sheffer1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k5_simplex0,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(dt_k5_simplex1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k5_sin_cos,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_funct_1(k5_sin_cos(A)) & v1_funct_2(k5_sin_cos(A),k4_ordinal1,k2_numbers) & m1_subset_1(k5_sin_cos(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) ) )).
fof(dt_k5_sin_cos2,axiom,( v1_funct_1(k5_sin_cos2) & v1_funct_2(k5_sin_cos2,k1_numbers,k1_numbers) & m1_subset_1(k5_sin_cos2,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) )).
fof(dt_k5_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k5_sin_cos7(A)) ) )).
fof(dt_k5_stacks_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k5_struct_0,axiom,( ! [A] : ( l3_struct_0(A) => m1_subset_1(k5_struct_0(A),u1_struct_0(A)) ) )).
fof(dt_k5_sublemma,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k38_substut1(A)) ) => m2_subset_1(k5_sublemma(A,B),k16_substut1(A),k38_substut1(A)) ) )).
fof(dt_k5_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k5_substlat,axiom,( ! [A] : ! [B] : ( v3_lattices(k5_substlat(A,B)) & l3_lattices(k5_substlat(A,B)) ) )).
fof(dt_k5_substut1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k5_substut2,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k16_substut1(A)) ) => m1_subset_1(k5_substut2(A,B),k1_substut1(A)) ) )).
fof(dt_k5_supinf_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_setfam_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k6_numbers))) ) => v2_membered(k5_supinf_1(A)) ) )).
fof(dt_k5_supinf_2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_zfmisc_1(k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => m1_subset_1(k5_supinf_2(A,B),k1_zfmisc_1(k6_numbers)) ) )).
fof(dt_k5_taylor_1,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)) & m1_subset_1(k5_taylor_1(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)))) ) ) )).
fof(dt_k5_tdlat_1,axiom,( ! [A] : ( l1_pre_topc(A) => m1_subset_1(k5_tdlat_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).
fof(dt_k5_termord,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,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)))) ) ) )).
fof(dt_k5_tex_4,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(dt_k5_tmap_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k5_topalg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k5_topalg_5,axiom,( ! [A] : ( 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))))) ) ) )).
fof(dt_k5_topalg_6,axiom,( ! [A] : ! [B] : ( ( l1_pre_topc(A) & m1_finseq_1(B,k1_topalg_6(A)) ) => m2_finseq_1(k5_topalg_6(A,B),k1_topalg_6(A)) ) )).
fof(dt_k5_topgen_2,axiom,( ! [A] : ! [B] : ( v1_pre_topc(k5_topgen_2(A,B)) & l1_pre_topc(k5_topgen_2(A,B)) ) )).
fof(dt_k5_topgen_3,axiom,( ! [A] : ( v1_pre_topc(k5_topgen_3(A)) & v2_pre_topc(k5_topgen_3(A)) & l1_pre_topc(k5_topgen_3(A)) ) )).
fof(dt_k5_topgen_4,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k5_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( v15_algstr_0(k5_topgrp_1(A)) & l3_algstr_0(k5_topgrp_1(A)) ) ) )).
fof(dt_k5_topmetr,axiom,( m1_pre_topc(k5_topmetr,k3_topmetr) )).
fof(dt_k5_topreal1,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k5_toprealb,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => m1_subset_1(k5_toprealb(A),k1_zfmisc_1(u1_struct_0(k2_topalg_2))) ) )).
fof(dt_k5_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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(k5_toprealc(A,B,C,D,E,F),u1_struct_0(C)) ) )).
fof(dt_k5_toprns_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ( v1_funct_1(k5_toprns_1(A,B)) & v1_funct_2(k5_toprns_1(A,B),k4_ordinal1,k1_numbers) & m1_subset_1(k5_toprns_1(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k5_trees_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & m1_finseq_1(B,k4_ordinal1) & ~ 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)) ) ) )).
fof(dt_k5_trees_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & m1_finseq_1(B,k4_ordinal1) ) => ( v1_relat_1(k5_trees_2(A,B)) & v1_funct_1(k5_trees_2(A,B)) & v3_trees_2(k5_trees_2(A,B)) ) ) )).
fof(dt_k5_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_trees_3(k5_trees_3(A),A) ) )).
fof(dt_k5_trees_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k5_trees_9,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) ) => ( ~ v1_xboole_0(k5_trees_9(A,B)) & m1_subset_1(k5_trees_9(A,B),k1_zfmisc_1(k5_trees_3(A))) ) ) )).
fof(dt_k5_turing_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k5_twoscomp,axiom,( 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))) )).
fof(dt_k5_unialg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k5_unialg_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))))) ) ) )).
fof(dt_k5_uniroots,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( v1_funct_1(k5_uniroots(A)) & v1_funct_2(k5_uniroots(A),k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(k5_uniroots(A),k1_complfld) & m1_subset_1(k5_uniroots(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) ) )).
fof(dt_k5_uproots,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k5_uproots(A,B,C)) & v1_funct_2(k5_uproots(A,B,C),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k5_uproots(A,B,C),A) & m1_subset_1(k5_uproots(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k5_urysohn1,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_relat_1(k5_urysohn1(A)) & v1_funct_1(k5_urysohn1(A)) & v1_finseq_1(k5_urysohn1(A)) ) ) )).
fof(dt_k5_urysohn3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k5_urysohn3(A,B,C,D),k1_zfmisc_1(u1_struct_0(B))) ) )).
fof(dt_k5_valuat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_qc_lang1(A) & ~ v1_xboole_0(B) & v7_ordinal1(C) & 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)) ) )).
fof(dt_k5_vectmetr,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v15_algstr_0(k5_vectmetr(A)) & l3_algstr_0(k5_vectmetr(A)) ) ) )).
fof(dt_k5_vectsp10,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)))) ) ) )).
fof(dt_k5_vectsp_1,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k5_vectsp_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k5_vectsp_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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)))) ) ) )).
fof(dt_k5_vectsp_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) )).
fof(dt_k5_vectsp_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) ) )).
fof(dt_k5_vfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k5_waybel10,axiom,( ! [A] : ( ( ~ 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)))))) ) ) )).
fof(dt_k5_waybel11,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k5_waybel18,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k5_waybel20,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k5_waybel23,axiom,( ! [A] : ! [B] : ( ( 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(k1_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(k1_yellow_1(k7_waybel_0(k5_yellow_0(A,B))))))) ) ) )).
fof(dt_k5_waybel26,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v1_relat_1(k5_waybel26(A)) ) )).
fof(dt_k5_waybel34,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(dt_k5_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k5_waybel_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k5_waybel_2,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k5_waybel_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k4_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)))) ) )).
fof(dt_k5_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k5_waybel_5,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k5_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k5_weddwitt,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v6_struct_0(A) & 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)) ) ) )).
fof(dt_k5_weierstr,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k5_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k5_xcmplx_0(A)) ) )).
fof(dt_k5_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => v1_xxreal_0(k5_xxreal_3(A)) ) )).
fof(dt_k5_yellow18,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k5_yellow20,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(dt_k5_yellow21,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))))) ) ) )).
fof(dt_k5_yellow_0,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(dt_k5_yellow_1,axiom,( ! [A] : ! [B] : ( l1_orders_2(B) => ( v1_orders_2(k5_yellow_1(A,B)) & l1_orders_2(k5_yellow_1(A,B)) ) ) )).
fof(dt_k5_yellow_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & v1_relat_1(B) ) => m1_subset_1(k5_yellow_2(A,B),u1_struct_0(A)) ) )).
fof(dt_k5_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k5_yellow_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k5_zf_lang,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_zf_lang) & m1_subset_1(B,k1_zf_lang) ) => m2_finseq_1(k5_zf_lang(A,B),k4_ordinal1) ) )).
fof(dt_k5_zf_lang1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) & 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)) ) ) )).
fof(dt_k5_zf_model,axiom,( ! [A] : ! [B] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) & ~ v1_xboole_0(B) ) => m1_subset_1(k5_zf_model(A,B),k1_zfmisc_1(k3_zf_model(B))) ) )).
fof(dt_k5_zf_refle,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k5_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k5_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ 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_int_1(B) ) => m1_zmodul01(k5_zmodul02(A,B),A) ) )).
fof(dt_k60_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k60_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) ) )).
fof(dt_k60_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) )).
fof(dt_k61_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k61_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k61_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k62_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k62_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) ) => m1_subset_1(k62_valued_1(A),k4_ordinal1) ) )).
fof(dt_k62_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k63_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k63_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(dt_k63_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))))) ) ) )).
fof(dt_k64_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(dt_k64_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) ) => m1_subset_1(k64_valued_1(A),k4_ordinal1) ) )).
fof(dt_k64_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))))) ) ) )).
fof(dt_k65_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) ) )).
fof(dt_k65_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & m3_aofa_i00(E,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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)) ) ) )).
fof(dt_k66_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & m3_aofa_i00(E,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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)) ) ) )).
fof(dt_k67_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & m3_aofa_i00(E,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D) & m3_aofa_i00(F,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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)) ) ) )).
fof(dt_k68_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & m3_aofa_i00(E,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D) & m3_aofa_i00(F,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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)) ) ) )).
fof(dt_k68_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k69_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))))) ) ) )).
fof(dt_k6_abcmiz_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k6_afinsq_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k6_afproj,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k6_alg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k6_algstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k6_algstr_4,axiom,( ! [A] : ! [B] : ( ( 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)))) ) ) )).
fof(dt_k6_altcat_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k6_altcat_2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k6_ami_2,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k6_ami_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k6_ami_wstd,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) ) => m1_subset_1(k6_ami_wstd(A,B,C),k4_ordinal1) ) )).
fof(dt_k6_analort,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) ) )).
fof(dt_k6_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(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) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) & v4_aofa_a01(D,A,B,C) & l4_aofa_a00(D,A,B,C) & ~ v2_struct_0(E) & v2_unialg_1(E) & v3_unialg_1(E) & v4_unialg_1(E) & v3_aofa_000(E) & v4_aofa_000(E) & v5_aofa_000(E) & v6_aofa_000(E) & ~ v10_aofa_000(E) & v11_aofa_000(E) & v12_aofa_000(E) & l3_aofa_a00(E,A,C,u4_aofa_a00(A,B,C,D)) & v3_aofa_a01(F,A,B,C,u4_aofa_a00(A,B,C,D),u8_aofa_a00(A)) & m1_subset_1(F,k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),u8_aofa_a00(A))) & v19_aofa_a00(G,A) & m1_subset_1(G,u1_struct_0(A)) & m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),G)) & m1_subset_1(I,k1_funct_1(u3_msualg_1(A,C),G)) ) => m1_subset_1(k6_aofa_a01(A,B,C,D,E,F,G,H,I),u1_struct_0(E)) ) )).
fof(dt_k6_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k6_arytm_2,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k6_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => m1_subset_1(k6_arytm_3(A),k4_ordinal1) ) )).
fof(dt_k6_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => m1_funct_2(k6_asympt_0(A),k4_ordinal1,k1_numbers) ) )).
fof(dt_k6_asympt_1,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k6_asympt_1(A),k4_ordinal1) ) )).
fof(dt_k6_autalg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k6_autgroup,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k6_bagorder,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_k6_bcialg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k6_bcialg_4,axiom,( ! [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) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,k4_ordinal1) ) => m1_subset_1(k6_bcialg_4(A,B,C),u1_struct_0(A)) ) )).
fof(dt_k6_bcialg_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))))) ) ) )).
fof(dt_k6_bhsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k6_bhsp_1(A,B,C)) & v1_funct_2(k6_bhsp_1(A,B,C),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k6_bhsp_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k6_bhsp_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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)) & v1_xreal_0(C) ) => m1_subset_1(k6_bhsp_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k6_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k6_binari_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v8_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) ) ) )).
fof(dt_k6_binarith,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v3_card_1(B,A) & m1_finseq_1(B,k6_margrel1) ) => m1_subset_1(k6_binarith(A,B),k4_ordinal1) ) )).
fof(dt_k6_binom,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,k4_ordinal1) ) => m1_subset_1(k6_binom(A,B,C),u1_struct_0(A)) ) )).
fof(dt_k6_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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))) ) )).
fof(dt_k6_borsuk_6,axiom,( m1_subset_1(k6_borsuk_6,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))) )).
fof(dt_k6_bspace,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k6_bvfunc26,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k6_bvfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k6_bvfunc_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k6_c0sp1,axiom,( ! [A] : ( ~ 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)))) ) ) )).
fof(dt_k6_c0sp2,axiom,( ! [A] : ( ( ~ 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))))) ) ) )).
fof(dt_k6_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) ) => v1_card_1(k6_card_3(A)) ) )).
fof(dt_k6_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) )).
fof(dt_k6_cat_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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(k6_cat_2(A,B)) & ~ v11_struct_0(k6_cat_2(A,B)) & v2_cat_1(k6_cat_2(A,B)) & v3_cat_1(k6_cat_2(A,B)) & v4_cat_1(k6_cat_2(A,B)) & v5_cat_1(k6_cat_2(A,B)) & v6_cat_1(k6_cat_2(A,B)) & l1_cat_1(k6_cat_2(A,B)) ) ) )).
fof(dt_k6_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)))) ) ) )).
fof(dt_k6_cat_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ 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)) ) )).
fof(dt_k6_cat_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ 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)) ) ) )).
fof(dt_k6_cc0sp1,axiom,( ! [A] : ( ~ 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))) ) ) )).
fof(dt_k6_cc0sp2,axiom,( ! [A] : ( ( ~ 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))))) ) ) )).
fof(dt_k6_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v2_struct_0(k6_cfuncdom(A)) & v1_clvect_1(k6_cfuncdom(A)) & l1_clvect_1(k6_cfuncdom(A)) ) ) )).
fof(dt_k6_chain_1,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_chain_1(B,A) ) => m1_subset_1(k6_chain_1(A,B),k1_zfmisc_1(k4_chain_1(A,B,A))) ) )).
fof(dt_k6_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k6_circtrm1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(dt_k6_circuit1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k6_circuit2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k6_classes1,axiom,( ! [A] : v3_ordinal1(k6_classes1(A)) )).
fof(dt_k6_classes2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k6_clopban1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) ) ) )).
fof(dt_k6_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => m2_subset_1(k6_clopban2(A),u1_struct_0(k6_clopban1(A,A)),k8_clopban1(A,A)) ) )).
fof(dt_k6_clopban3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & 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)) & v7_ordinal1(C) ) => m1_subset_1(k6_clopban3(A,B,C),u1_struct_0(A)) ) )).
fof(dt_k6_clopban4,axiom,( ! [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) & 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)))) ) ) )).
fof(dt_k6_closure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k6_closure2,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k6_clvect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k6_clvect_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k6_clvect_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) & v1_xreal_0(C) ) => m1_subset_1(k6_clvect_2(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k6_clvect_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_funct_1(k6_clvect_3(A,B,C)) & v1_funct_2(k6_clvect_3(A,B,C),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k6_clvect_3(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k6_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_coh_sp(A)) => m1_subset_1(k6_coh_sp(A,B),k3_coh_sp(A)) ) )).
fof(dt_k6_cohsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) )).
fof(dt_k6_combgras,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => m1_subset_1(k6_combgras(A,B),k1_zfmisc_1(k9_setfam_1(A))) ) )).
fof(dt_k6_complex1,axiom,( m1_subset_1(k6_complex1,k2_numbers) )).
fof(dt_k6_complsp2,axiom,( ! [A] : ( m1_finseq_1(A,k2_numbers) => m2_finseq_1(k6_complsp2(A),k1_numbers) ) )).
fof(dt_k6_compos_0,axiom,( ! [A] : ( v5_compos_0(A) => m1_subset_1(k6_compos_0(A),A) ) )).
fof(dt_k6_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_compos_1(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k6_comput_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v4_valued_0(A) & v2_margrel1(A) & v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) & m1_subset_1(C,k4_ordinal1) & m1_finseq_1(D,k4_ordinal1) ) => m2_rfunct_3(k6_comput_1(A,B,C,D),k3_finseq_2(k4_ordinal1),k4_ordinal1,k2_comput_1(k4_ordinal1)) ) )).
fof(dt_k6_comseq_3,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k6_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ( v3_conlat_1(k6_conlat_1(A),A) & ~ v4_conlat_1(k6_conlat_1(A),A) & v6_conlat_1(k6_conlat_1(A),A) & v8_conlat_1(k6_conlat_1(A),A) & l2_conlat_1(k6_conlat_1(A),A) ) ) )).
fof(dt_k6_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( ~ v2_struct_0(k6_conlat_2(A)) & ~ v11_struct_0(k6_conlat_2(A)) & v1_conlat_1(k6_conlat_2(A)) & l1_conlat_1(k6_conlat_2(A)) ) ) )).
fof(dt_k6_connsp_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k6_cqc_lang,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k6_cqc_sim1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(A) & v7_ordinal1(B) & 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))) ) )).
fof(dt_k6_csspace,axiom,( m1_subset_1(k6_csspace,k1_csspace) )).
fof(dt_k6_csspace4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k6_decomp_1,axiom,( ! [A] : ( ( 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)))) ) )).
fof(dt_k6_descip_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k6_dickson,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k6_diff_1,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)) & m1_subset_1(k6_diff_1(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)))) ) ) )).
fof(dt_k6_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => m1_subset_1(k6_dilworth(A),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k6_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => m1_subset_1(k6_dist_1(A),k1_zfmisc_1(k1_zfmisc_1(k3_finseq_2(A)))) ) )).
fof(dt_k6_dist_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_setfam_1(B) & m1_subset_1(B,k6_dist_1(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_xreal_0(k6_dist_2(A,B,C)) ) )).
fof(dt_k6_domain_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m1_subset_1(k6_domain_1(A,B),k1_zfmisc_1(A)) ) )).
fof(dt_k6_dtconstr,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(dt_k6_dynkin,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k6_ec_pf_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) ) )).
fof(dt_k6_ec_pf_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k6_endalg,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k6_ens_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k6_entropy1,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => v1_xreal_0(k6_entropy1(A)) ) )).
fof(dt_k6_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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)) ) )).
fof(dt_k6_euclid,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k1_euclid(A)) ) => m2_finseq_2(k6_euclid(A,B),k1_numbers,k1_euclid(A)) ) )).
fof(dt_k6_euclid_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & 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)))) ) )).
fof(dt_k6_euclid_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k6_euclid_7,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => m2_finseq_2(k6_euclid_7(A,B),k1_numbers,k1_euclid(A)) ) )).
fof(dt_k6_euclid_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) ) )).
fof(dt_k6_extpro_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k4_ordinal1) & 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)) ) ) )).
fof(dt_k6_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k6_facirc_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k6_ff_siec,axiom,( v1_petri(k6_ff_siec) & v1_net_1(k6_ff_siec) & l1_petri(k6_ff_siec) )).
fof(dt_k6_fib_num2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => m2_finseq_1(k6_fib_num2(A),k4_ordinal1) ) )).
fof(dt_k6_filter_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k6_filter_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) ) )).
fof(dt_k6_filter_2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k6_fin_topo,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k6_finseq_1,axiom,( ! [A] : m2_finseq_1(k6_finseq_1(A),A) )).
fof(dt_k6_finseq_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k6_finseq_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k6_finseq_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_1(k6_finseq_8(A,B,C),A) ) )).
fof(dt_k6_finseqop,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k6_fintopo2,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k6_fintopo3,axiom,( ! [A] : ! [B] : ( ( ~ 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),k4_ordinal1,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(k6_fintopo3(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(u1_struct_0(A))))) ) ) )).
fof(dt_k6_flang_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k6_fomodel0,axiom,( ! [A] : ! [B] : ( ( ~ 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(k6_fomodel0(A,B)) & v1_funct_2(k6_fomodel0(A,B),k6_subset_1(k3_finseq_2(A),k1_tarski(k1_xboole_0)),A) & m1_subset_1(k6_fomodel0(A,B),k1_zfmisc_1(k2_zfmisc_1(k6_subset_1(k3_finseq_2(A),k1_tarski(k1_xboole_0)),A))) ) ) )).
fof(dt_k6_fomodel2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k6_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ 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),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)))))) ) )).
fof(dt_k6_freealg,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,k4_ordinal1) & ~ 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)))) ) )).
fof(dt_k6_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : 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))) )).
fof(dt_k6_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k6_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k6_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : m1_subset_1(k6_ftacell1(A,B,C,D,E),k3_msafree2(k1_ftacell1(A,B,C,D,E))) )).
fof(dt_k6_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))) ) ) )).
fof(dt_k6_funcsdom,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k6_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k6_funct_3,axiom,( ! [A] : ! [B] : ( 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))) ) ) )).
fof(dt_k6_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ( v1_relat_1(k6_funct_6(A)) & v1_funct_1(k6_funct_6(A)) ) ) )).
fof(dt_k6_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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))) ) )).
fof(dt_k6_functor3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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)) ) )).
fof(dt_k6_fuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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(k5_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))) ) ) )).
fof(dt_k6_fvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ 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))) ) )).
fof(dt_k6_gcd_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) )).
fof(dt_k6_genealg1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [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,k4_ordinal1) & m1_subset_1(E,k4_ordinal1) & m1_subset_1(F,k4_ordinal1) & m1_subset_1(G,k4_ordinal1) & m1_subset_1(H,k4_ordinal1) & m1_subset_1(I,k4_ordinal1) ) => m2_finseq_1(k6_genealg1(A,B,C,D,E,F,G,H,I),k3_card_3(A)) ) )).
fof(dt_k6_geomtrap,axiom,( ! [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) ) => ( 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)))) ) ) )).
fof(dt_k6_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k6_gfacirc2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k6_glib_001,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(dt_k6_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(dt_k6_glib_004,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) )).
fof(dt_k6_glib_005,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(dt_k6_goedelcp,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k6_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => m1_subset_1(k6_graph_1(A),k4_ordinal1) ) )).
fof(dt_k6_graph_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k6_graph_3,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k6_graph_5,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k6_graphsp,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k6_grcat_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k6_groeb_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) & m1_subset_1(E,k4_ordinal1) ) => ( 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),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)))) ) ) )).
fof(dt_k6_group_1,axiom,( ! [A] : ! [B] : ( ( ~ 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(k6_group_1(A,B),k4_ordinal1) ) )).
fof(dt_k6_group_2,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(dt_k6_group_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k6_group_4,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(dt_k6_group_5,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(dt_k6_group_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k6_group_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)))) ) )).
fof(dt_k6_hahnban1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k6_hermitan,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k6_heyting1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(k7_normform(A))) => m1_subset_1(k6_heyting1(A,B),k5_finsub_1(k7_normform(A))) ) )).
fof(dt_k6_heyting2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) )).
fof(dt_k6_hilbasis,axiom,( ! [A] : ! [B] : ( ( ~ 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,k4_ordinal1) ) => ( v1_funct_1(k6_hilbasis(A,B)) & v1_funct_2(k6_hilbasis(A,B),u1_struct_0(k14_polynom3(k12_polynom1(B,A))),u1_struct_0(k12_polynom1(k1_nat_1(B,1),A))) & m1_subset_1(k6_hilbasis(A,B),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k14_polynom3(k12_polynom1(B,A))),u1_struct_0(k12_polynom1(k1_nat_1(B,1),A))))) ) ) )).
fof(dt_k6_hilbert1,axiom,( m1_subset_1(k6_hilbert1,k1_zfmisc_1(k1_hilbert1)) )).
fof(dt_k6_hurwitz,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k6_hurwitz(A,B,C)) & v1_funct_2(k6_hurwitz(A,B,C),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k6_hurwitz(A,B,C),A) & m1_subset_1(k6_hurwitz(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k6_idea_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => v7_ordinal1(k6_idea_1(A,B)) ) )).
fof(dt_k6_index_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(dt_k6_integr10,axiom,( ! [A] : ( 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))) ) ) )).
fof(dt_k6_integr15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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,k4_ordinal1,k1_integra1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,u1_struct_0(k4_real_ns1(A))) & m1_subset_1(k6_integr15(A,B,C,D,E),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k4_real_ns1(A))))) ) ) )).
fof(dt_k6_integr16,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k6_integr18,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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)) ) )).
fof(dt_k6_integra1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_xreal_0(k6_integra1(A,B,C)) ) )).
fof(dt_k6_interva1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_interva1(B,A) ) => m1_subset_1(k6_interva1(A,B),k1_zfmisc_1(A)) ) )).
fof(dt_k6_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => m1_subset_1(k6_intpro_1(A),k1_intpro_1) ) )).
fof(dt_k6_isocat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) )).
fof(dt_k6_jgraph_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) )).
fof(dt_k6_jordan5d,axiom,( ! [A] : ( ( ~ 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))) ) => v7_ordinal1(k6_jordan5d(A)) ) )).
fof(dt_k6_jordan6,axiom,( ! [A] : ( v1_xreal_0(A) => m1_subset_1(k6_jordan6(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) )).
fof(dt_k6_knaster,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k6_kolmog01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k6_kurato_1,axiom,( m1_subset_1(k6_kurato_1,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )).
fof(dt_k6_lang1,axiom,( ! [A] : ( v2_lang1(k6_lang1(A)) & l2_lang1(k6_lang1(A)) ) )).
fof(dt_k6_laplace,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) & ~ 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) & v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(D),C,C) & m1_finseq_1(E,k3_finseq_2(u1_struct_0(D))) ) => m1_subset_1(k6_laplace(A,B,C,D,E),u1_struct_0(D)) ) )).
fof(dt_k6_lattice3,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k6_lattice5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k6_lattice6,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(dt_k6_lattice8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k6_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_lattices(A) ) => m1_subset_1(k6_lattices(A),u1_struct_0(A)) ) )).
fof(dt_k6_lfuzzy_0,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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))) ) )).
fof(dt_k6_lopban_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k6_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => m2_subset_1(k6_lopban_2(A),u1_struct_0(k8_lopban_1(A,A)),k10_lopban_1(A,A)) ) )).
fof(dt_k6_lopban_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & 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)) & v7_ordinal1(C) ) => m1_subset_1(k6_lopban_3(A,B,C),u1_struct_0(A)) ) )).
fof(dt_k6_lopban_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) & 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),k4_ordinal1,u1_struct_0(B)) & m1_subset_1(k6_lopban_4(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) ) )).
fof(dt_k6_lopclset,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k6_lpspacc1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) & ~ v1_xboole_0(B) & v1_lpspacc1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_funct_1(k6_lpspacc1(A,B)) & v1_funct_2(k6_lpspacc1(A,B),k2_zfmisc_1(k2_numbers,B),B) & m1_subset_1(k6_lpspacc1(A,B),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_numbers,B),B))) ) ) )).
fof(dt_k6_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m2_rfunct_3(k6_lpspace1(A),A,k1_numbers,k3_rfunct_3(A,k1_numbers)) ) )).
fof(dt_k6_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v2_xxreal_0(D) & v1_xreal_0(D) ) => ( ~ 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)))) ) ) )).
fof(dt_k6_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => m1_subset_1(k6_ltlaxio1(A),k1_hilbert1) ) )).
fof(dt_k6_ltlaxio3,axiom,( v1_funct_1(k6_ltlaxio3) & v1_funct_2(k6_ltlaxio3,k1_hilbert1,k9_setfam_1(k1_hilbert1)) & m1_subset_1(k6_ltlaxio3,k1_zfmisc_1(k2_zfmisc_1(k1_hilbert1,k9_setfam_1(k1_hilbert1)))) )).
fof(dt_k6_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)))) => m1_subset_1(k6_ltlaxio4(A),k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)))) ) )).
fof(dt_k6_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k6_matrix10,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_xreal_0(B) & v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m1_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( v1_matrix_0(k6_matrix10(A,B,C)) & v2_matrix_0(k6_matrix10(A,B,C),k1_numbers,A,A) & m2_finseq_1(k6_matrix10(A,B,C),k3_finseq_2(k1_numbers)) ) ) )).
fof(dt_k6_matrix12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & ~ 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) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(C))) & v7_ordinal1(E) & v7_ordinal1(F) & m1_subset_1(G,u1_struct_0(C)) ) => ( v1_matrix_0(k6_matrix12(A,B,C,D,E,F,G)) & v2_matrix_0(k6_matrix12(A,B,C,D,E,F,G),u1_struct_0(C),A,B) & m2_finseq_1(k6_matrix12(A,B,C,D,E,F,G),k3_finseq_2(u1_struct_0(C))) ) ) )).
fof(dt_k6_matrix13,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(A)) & v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) & v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ( v1_matrix_0(k6_matrix13(A,B,C,D)) & v2_matrix_0(k6_matrix13(A,B,C,D),A,k5_card_1(C),k5_card_1(D)) & m2_finseq_1(k6_matrix13(A,B,C,D),k3_finseq_2(A)) ) ) )).
fof(dt_k6_matrix15,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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_0(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_0(B))))) ) )).
fof(dt_k6_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(A)) & v7_ordinal1(C) ) => m2_finseq_1(k6_matrix_0(A,B,C),A) ) )).
fof(dt_k6_matrix_2,axiom,( ! [A] : m1_subset_1(k6_matrix_2(A),k5_finsub_1(A)) )).
fof(dt_k6_matrix_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_0(B) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(A))) & m1_subset_1(C,u1_struct_0(A)) ) => ( v1_matrix_0(k6_matrix_3(A,B,C)) & m2_finseq_1(k6_matrix_3(A,B,C),k3_finseq_2(u1_struct_0(A))) ) ) )).
fof(dt_k6_matrix_5,axiom,( ! [A] : ! [B] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k2_numbers)) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(k2_numbers)) ) => ( v1_matrix_0(k6_matrix_5(A,B)) & m2_finseq_1(k6_matrix_5(A,B),k3_finseq_2(k2_numbers)) ) ) )).
fof(dt_k6_matrixc1,axiom,( ! [A] : ! [B] : ( ( v1_matrix_0(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) ) )).
fof(dt_k6_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k6_matrixr1,axiom,( ! [A] : ! [B] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k1_numbers)) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( v1_matrix_0(k6_matrixr1(A,B)) & m2_finseq_1(k6_matrixr1(A,B),k3_finseq_2(k1_numbers)) ) ) )).
fof(dt_k6_matrixr2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => m2_finseq_1(k6_matrixr2(A,B),k1_numbers) ) )).
fof(dt_k6_matrlin,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k6_matrlin2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)))) ) ) )).
fof(dt_k6_matroid0,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k6_matrprob,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(A,k1_numbers) & m1_finseq_1(B,k1_numbers) & v1_matrix_0(C) & m1_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( v1_matrix_0(k6_matrprob(A,B,C)) & m2_finseq_1(k6_matrprob(A,B,C),k3_finseq_2(k1_numbers)) ) ) )).
fof(dt_k6_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(dt_k6_measure6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_membered(B) & v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( v1_funct_1(k6_measure6(A,B,C)) & m1_subset_1(k6_measure6(A,B,C),k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) ) )).
fof(dt_k6_measure7,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & m1_measure7(B,A) ) => m1_subset_1(k6_measure7(A,B),k6_numbers) ) )).
fof(dt_k6_measure8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_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,k6_numbers))) ) => ( v1_funct_1(k6_measure8(A,B,C)) & v1_funct_2(k6_measure8(A,B,C),k9_setfam_1(A),k6_numbers) & m1_subset_1(k6_measure8(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k6_numbers))) ) ) )).
fof(dt_k6_member_1,axiom,( ! [A] : ( v2_membered(A) => v2_membered(k6_member_1(A)) ) )).
fof(dt_k6_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k6_mesfun7c,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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,k6_numbers))) ) ) )).
fof(dt_k6_mesfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k6_numbers) & v1_funct_1(B) & v1_xreal_0(C) ) => ( v1_funct_1(k6_mesfunc1(A,B,C)) & m1_subset_1(k6_mesfunc1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) ) )).
fof(dt_k6_mesfunc5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => m1_subset_1(k6_mesfunc5(A,B,C,D),k6_numbers) ) )).
fof(dt_k6_mesfunc8,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ( v1_funct_1(k6_mesfunc8(A,B)) & m1_subset_1(k6_mesfunc8(A,B),k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) ) )).
fof(dt_k6_metric_1,axiom,( v1_funct_1(k6_metric_1) & v1_funct_2(k6_metric_1,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & m1_subset_1(k6_metric_1,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers))) )).
fof(dt_k6_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => m1_subset_1(k6_metric_2(A),k1_zfmisc_1(k2_metric_2(A))) ) )).
fof(dt_k6_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => m1_midsp_1(k6_midsp_1(A),A) ) )).
fof(dt_k6_midsp_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k6_midsp_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(A,k4_ordinal1) & ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_nat_1(A,2)) & m1_subset_1(C,k4_finseq_2(k1_nat_1(A,1),u1_struct_0(B))) & m1_subset_1(D,k4_ordinal1) & 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(k1_nat_1(A,1),u1_struct_0(B))) ) )).
fof(dt_k6_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k6_mod_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) ) )).
fof(dt_k6_mod_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))))) ) ) )).
fof(dt_k6_modal_1,axiom,( m1_trees_3(k6_modal_1,k2_zfmisc_1(k4_ordinal1,k4_ordinal1)) )).
fof(dt_k6_modcat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) )).
fof(dt_k6_modelc_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => m2_finseq_1(k6_modelc_1(A),k4_ordinal1) ) )).
fof(dt_k6_modelc_2,axiom,( ! [A] : ( m1_finseq_1(A,k4_ordinal1) => m2_finseq_1(k6_modelc_2(A),k4_ordinal1) ) )).
fof(dt_k6_modelc_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & l1_modelc_3(B,A) & v1_modelc_2(C) & m1_finseq_1(C,k4_ordinal1) ) => ( v1_modelc_3(k6_modelc_3(A,B,C),A) & l1_modelc_3(k6_modelc_3(A,B,C),A) ) ) )).
fof(dt_k6_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => m1_subset_1(k6_moebius1(A),k4_ordinal1) ) )).
fof(dt_k6_monoid_0,axiom,( ~ 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) )).
fof(dt_k6_monoid_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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)) ) )).
fof(dt_k6_msafree,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k6_msafree2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k6_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(C,u1_struct_0(A),B,k7_funcop_1(u1_struct_0(A),k4_ordinal1)) & v1_relat_1(D) & v1_funct_1(D) ) => m1_subset_1(k6_msafree4(A,B,C,D),k3_card_3(u3_msualg_1(A,k3_equation(A)))) ) )).
fof(dt_k6_msaterm,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k6_msualg_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k6_msualg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(dt_k6_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) )).
fof(dt_k6_msualg_5,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k6_msualg_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k6_mycielsk,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_mycielsk(B,A) ) => m1_mycielsk(k6_mycielsk(A,B),k2_xcmplx_0(k3_xcmplx_0(2,A),1)) ) )).
fof(dt_k6_nat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) & v7_ordinal1(C) ) => m1_subset_1(k6_nat_1(A,B,C),A) ) )).
fof(dt_k6_nat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k6_nat_d,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => m1_subset_1(k6_nat_d(A,B),k4_ordinal1) ) )).
fof(dt_k6_nat_lat,axiom,( m1_subset_1(k6_nat_lat,k1_zfmisc_1(k4_ordinal1)) )).
fof(dt_k6_nattra_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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(k6_nattra_1(A,B,C,D,E),A,B,D,C) ) )).
fof(dt_k6_ndiff_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(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(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))) ) )).
fof(dt_k6_newton,axiom,( ! [A] : ( v7_ordinal1(A) => m2_finseq_1(k6_newton(A),k1_numbers) ) )).
fof(dt_k6_normform,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k6_normsp_1,axiom,( ! [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) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => m1_subset_1(k6_normsp_1(A,B),u1_struct_0(A)) ) )).
fof(dt_k6_openlatt,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k6_oppcat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) )).
fof(dt_k6_ordeq_01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,u1_struct_0(k4_real_ns1(A))) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A))))) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( v1_funct_1(k6_ordeq_01(A,B,C,D,E)) & v1_funct_2(k6_ordeq_01(A,B,C,D,E),u1_struct_0(k5_ordeq_01(k3_integra5(D,E),k4_real_ns1(A))),u1_struct_0(k5_ordeq_01(k3_integra5(D,E),k4_real_ns1(A)))) & m1_subset_1(k6_ordeq_01(A,B,C,D,E),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_ordeq_01(k3_integra5(D,E),k4_real_ns1(A))),u1_struct_0(k5_ordeq_01(k3_integra5(D,E),k4_real_ns1(A)))))) ) ) )).
fof(dt_k6_ordinal3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => v3_ordinal1(k6_ordinal3(A,B)) ) )).
fof(dt_k6_ordinal4,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k6_ordinal6,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k6_osafree,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k6_osalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k6_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))))) ) )).
fof(dt_k6_partfun1,axiom,( ! [A] : ( v1_partfun1(k6_partfun1(A),A) & m1_subset_1(k6_partfun1(A),k1_zfmisc_1(k2_zfmisc_1(A,A))) ) )).
fof(dt_k6_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_eqrel_1(k6_partit1(A),A) ) )).
fof(dt_k6_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k6_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k6_pdiff_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) & 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)))) ) ) )).
fof(dt_k6_pdiff_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) => v1_xreal_0(k6_pdiff_4(A,B,C)) ) )).
fof(dt_k6_pdiff_5,axiom,( ! [A] : ! [B] : ( ( 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)) ) => v1_xreal_0(k6_pdiff_5(A,B)) ) )).
fof(dt_k6_pencil_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)))) ) )).
fof(dt_k6_petri,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k6_pnproc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) & m1_pnproc_1(C,A) ) => ( v1_funct_1(k6_pnproc_1(A,B,C)) & v1_funct_2(k6_pnproc_1(A,B,C),A,k4_ordinal1) & m1_subset_1(k6_pnproc_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) ) )).
fof(dt_k6_polyeq_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k6_polyform,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k4_numbers) & m1_finseq_1(B,k4_numbers) ) => m2_finseq_1(k6_polyform(A,B),k4_numbers) ) )).
fof(dt_k6_polynom1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(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)))) ) ) )).
fof(dt_k6_polynom3,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => m2_finseq_1(k6_polynom3(A,B),k4_finseq_2(A,k4_ordinal1)) ) )).
fof(dt_k6_polynom5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l6_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => m1_subset_1(k6_polynom5(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k6_polynom7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k6_polynom8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & ~ v2_struct_0(B) & v4_vectsp_1(B) & l6_algstr_0(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,u1_struct_0(B)) & v1_polynom1(k6_polynom8(A,B,C,D),B) & m1_subset_1(k6_polynom8(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) ) )).
fof(dt_k6_poset_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k6_pralg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k6_prelamb,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k6_prepower,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => v1_xreal_0(k6_prepower(A,B)) ) )).
fof(dt_k6_prob_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_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) ) )).
fof(dt_k6_prob_3,axiom,( ! [A] : ! [B] : ( m1_finseq_1(B,k9_setfam_1(A)) => m2_finseq_1(k6_prob_3(A,B),k9_setfam_1(A)) ) )).
fof(dt_k6_prob_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k6_prvect_1,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) ) )).
fof(dt_k6_prvect_2,axiom,( ! [A] : ( ( 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)) ) )).
fof(dt_k6_prvect_3,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k6_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => v1_xreal_0(k6_pscomp_1(A)) ) )).
fof(dt_k6_pua2mss1,axiom,( ! [A] : ( ( 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)))) ) )).
fof(dt_k6_qc_lang2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k6_qc_lang3,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k6_qmax_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k6_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => v1_quaterni(k6_quatern2(A)) ) )).
fof(dt_k6_quaterni,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(dt_k6_quofield,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k6_radix_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(dt_k6_radix_3,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v7_ordinal1(B) ) => v1_int_1(k6_radix_3(A,B)) ) )).
fof(dt_k6_radix_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k6_radix_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k6_random_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k6_random_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k6_random_3(A,B,C),A,B) ) )).
fof(dt_k6_ranknull,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) )).
fof(dt_k6_ratfunc1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k6_real_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => m1_subset_1(k6_real_1(A,B),k1_numbers) ) )).
fof(dt_k6_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_funct_1(k6_real_3(A)) & v1_funct_2(k6_real_3(A),k4_ordinal1,k1_numbers) & m1_subset_1(k6_real_3(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k6_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v2_struct_0(k6_real_lat(A)) & v3_lattices(k6_real_lat(A)) & l3_lattices(k6_real_lat(A)) ) ) )).
fof(dt_k6_real_ns1,axiom,( ! [A] : ( 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))) ) ) )).
fof(dt_k6_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => v1_relat_1(k6_relat_1(A,B)) ) )).
fof(dt_k6_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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))) ) )).
fof(dt_k6_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k6_rewrite2,axiom,( ! [A] : m1_subset_1(k6_rewrite2(A),k1_zfmisc_1(k2_zfmisc_1(A,A))) )).
fof(dt_k6_rfinseq2,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => ( v1_integra2(k6_rfinseq2(A)) & m2_finseq_1(k6_rfinseq2(A),k1_numbers) ) ) )).
fof(dt_k6_rfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k6_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => v1_xreal_0(k6_rinfsup1(A)) ) )).
fof(dt_k6_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => m1_subset_1(k6_rinfsup2(A),k6_numbers) ) )).
fof(dt_k6_ringcat1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k6_rlsub_2,axiom,( ! [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) ) => ( 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)))) ) ) )).
fof(dt_k6_rlvect_2,axiom,( ! [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) & 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)) ) )).
fof(dt_k6_rmod_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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)))) ) ) )).
fof(dt_k6_rmod_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) )).
fof(dt_k6_robbins1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k6_roughs_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k6_rsspace,axiom,( l1_rlvect_1(k6_rsspace) )).
fof(dt_k6_rsspace4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k6_rusub_2,axiom,( ! [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_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)))) ) ) )).
fof(dt_k6_rusub_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k6_rvsum_1,axiom,( ! [A] : ( ( 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) ) )).
fof(dt_k6_rvsum_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k6_scm_comp,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k6_scm_inst,axiom,( ! [A] : ( m1_subset_1(A,k3_scm_inst) => v7_ordinal1(k6_scm_inst(A)) ) )).
fof(dt_k6_scmfsa6a,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k6_scmfsa_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k6_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k6_scmfsa_m,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k6_scmpds_1,axiom,( 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)))))) )).
fof(dt_k6_scmpds_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k6_scmpds_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_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_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,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( 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)) ) ) )).
fof(dt_k6_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) & v1_int_1(B) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ( v1_relat_1(k6_scmpds_6(A,B,C)) & v4_relat_1(k6_scmpds_6(A,B,C),k4_ordinal1) & v5_relat_1(k6_scmpds_6(A,B,C),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k6_scmpds_6(A,B,C)) & 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)) ) ) )).
fof(dt_k6_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => v1_int_1(k6_scmpds_i(A)) ) )).
fof(dt_k6_scmring1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k6_scmring2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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))) ) )).
fof(dt_k6_scmringi,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k6_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => v4_scmyciel(k6_scmyciel(A)) ) )).
fof(dt_k6_seq_4,axiom,( v1_funct_1(k6_seq_4) & v1_funct_2(k6_seq_4,k2_numbers,k1_numbers) & m1_subset_1(k6_seq_4,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k1_numbers))) )).
fof(dt_k6_seqfunc,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( v1_funct_1(k6_seqfunc(A,B,C)) & v1_funct_2(k6_seqfunc(A,B,C),k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(k6_seqfunc(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) ) )).
fof(dt_k6_series_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v7_ordinal1(B) ) => v1_xreal_0(k6_series_1(A,B)) ) )).
fof(dt_k6_setfam_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k6_setfam_1(A,B),k1_zfmisc_1(A)) ) )).
fof(dt_k6_setlim_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(k6_setlim_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) )).
fof(dt_k6_setlim_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(k6_setlim_2(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) )).
fof(dt_k6_setwiseo,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k6_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(dt_k6_sheffer1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k6_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => v1_xxreal_0(k6_simplex0(A)) ) )).
fof(dt_k6_sin_cos,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_funct_1(k6_sin_cos(A)) & v1_funct_2(k6_sin_cos(A),k4_ordinal1,k2_numbers) & m1_subset_1(k6_sin_cos(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) ) )).
fof(dt_k6_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k6_sin_cos7(A)) ) )).
fof(dt_k6_stacks_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k6_struct_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) ) )).
fof(dt_k6_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k6_subset_1,axiom,( ! [A] : ! [B] : m1_subset_1(k6_subset_1(A,B),k1_zfmisc_1(A)) )).
fof(dt_k6_substut1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k1_substut1(A)) ) => m1_subset_1(k6_substut1(A,B,C),k1_substut1(A)) ) )).
fof(dt_k6_substut2,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_k6_supinf_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_setfam_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k6_numbers))) ) => v2_membered(k6_supinf_1(A)) ) )).
fof(dt_k6_supinf_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k6_numbers)) => m1_subset_1(k6_supinf_2(A),k1_zfmisc_1(k6_numbers)) ) )).
fof(dt_k6_taylor_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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),k4_ordinal1,k1_numbers) & m1_subset_1(k6_taylor_1(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k6_tdlat_1,axiom,( ! [A] : ( ( 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)))) ) ) )).
fof(dt_k6_termord,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,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),C) & m1_subset_1(k6_termord(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) ) )).
fof(dt_k6_tex_4,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k6_tmap_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k6_topalg_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))))) ) ) )).
fof(dt_k6_topalg_5,axiom,( ! [A] : ( v1_int_1(A) => m1_borsuk_2(k6_topalg_5(A),k8_toprealb(2),k9_toprealb,k9_toprealb) ) )).
fof(dt_k6_topalg_6,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k6_topgen_3,axiom,( ! [A] : ! [B] : ( v1_pre_topc(k6_topgen_3(A,B)) & v2_pre_topc(k6_topgen_3(A,B)) & l1_pre_topc(k6_topgen_3(A,B)) ) )).
fof(dt_k6_topgrp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k6_topreal1,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k6_toprealb,axiom,( ! [A] : ( ( 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))))))) ) ) )).
fof(dt_k6_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => m1_subset_1(k6_toprealc(A,B,C),u1_struct_0(k15_euclid(A))) ) )).
fof(dt_k6_toprns_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => m1_subset_1(k6_toprns_1(A,B),u1_struct_0(k15_euclid(A))) ) )).
fof(dt_k6_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => v7_ordinal1(k6_trees_1(A)) ) )).
fof(dt_k6_trees_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k6_trees_3,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k6_trees_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k6_trees_9,axiom,( ! [A] : ( ( 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)))) ) )).
fof(dt_k6_turing_1,axiom,( ! [A] : ! [B] : ( ( l1_turing_1(A) & m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),u1_turing_1(A),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1))) ) => v1_int_1(k6_turing_1(A,B)) ) )).
fof(dt_k6_twoscomp,axiom,( 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))) )).
fof(dt_k6_unialg_2,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(dt_k6_uproots,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & v1_uproots(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => m1_subset_1(k6_uproots(A,B,C),k4_ordinal1) ) )).
fof(dt_k6_urysohn1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k1_urysohn1(A)) ) => v7_ordinal1(k6_urysohn1(A,B)) ) )).
fof(dt_k6_urysohn3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(k6_urysohn3(A,B,C,D,E),k1_zfmisc_1(k6_numbers)) ) )).
fof(dt_k6_vectsp10,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) ) )).
fof(dt_k6_vectsp_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) ) )).
fof(dt_k6_vectsp_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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)))) ) ) )).
fof(dt_k6_vectsp_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) )).
fof(dt_k6_vectsp_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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))))) ) ) )).
fof(dt_k6_vfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k6_waybel10,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k6_waybel18,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))))) ) ) )).
fof(dt_k6_waybel26,axiom,( ! [A] : ! [B] : ( v1_relat_1(A) => ( v1_relat_1(k6_waybel26(A,B)) & v1_funct_1(k6_waybel26(A,B)) ) ) )).
fof(dt_k6_waybel34,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(dt_k6_waybel35,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k6_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k6_waybel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k6_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k6_waybel_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k6_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(dt_k6_weddwitt,axiom,( ! [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) & 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)) ) ) )).
fof(dt_k6_weierstr,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k6_xxreal_3,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => v1_xxreal_0(k6_xxreal_3(A,B)) ) )).
fof(dt_k6_yellow21,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(dt_k6_yellow_1,axiom,( ! [A] : ! [B] : ( ( l1_orders_2(A) & l1_orders_2(B) ) => ( v1_orders_2(k6_yellow_1(A,B)) & v4_yellow_0(k6_yellow_1(A,B),k5_yellow_1(u1_struct_0(A),B)) & m1_yellow_0(k6_yellow_1(A,B),k5_yellow_1(u1_struct_0(A),B)) ) ) )).
fof(dt_k6_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) )).
fof(dt_k6_zf_lang,axiom,( ! [A] : ( m1_finseq_1(A,k4_ordinal1) => m2_finseq_1(k6_zf_lang(A),k4_ordinal1) ) )).
fof(dt_k6_zf_lang1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) & 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),k4_ordinal1) ) ) )).
fof(dt_k6_zf_model,axiom,( v1_zf_lang(k6_zf_model) & m2_finseq_1(k6_zf_model,k4_ordinal1) )).
fof(dt_k6_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k6_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) => ( ~ v1_xboole_0(k6_zmodul02(A,B)) & m1_subset_1(k6_zmodul02(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) )).
fof(dt_k70_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))))) ) ) )).
fof(dt_k72_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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)) ) ) )).
fof(dt_k72_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_k73_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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)) ) ) )).
fof(dt_k73_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)))))) ) ) )).
fof(dt_k74_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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)) ) ) )).
fof(dt_k74_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)))))) ) ) )).
fof(dt_k75_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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)) ) ) )).
fof(dt_k76_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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)) ) ) )).
fof(dt_k77_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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)) ) ) )).
fof(dt_k78_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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)) ) ) )).
fof(dt_k78_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_k79_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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)) ) ) )).
fof(dt_k79_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)))))) ) ) )).
fof(dt_k7_abcmiz_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k7_abcmiz_a,axiom,( ~ v1_xboole_0(k7_abcmiz_a) & m1_subset_1(k7_abcmiz_a,k1_zfmisc_1(k20_abcmiz_1)) )).
fof(dt_k7_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => m1_subset_1(k7_afinsq_2(A),k2_numbers) ) )).
fof(dt_k7_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ~ v1_xboole_0(k7_afproj(A)) ) )).
fof(dt_k7_alg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k7_algstr_0,axiom,( l3_algstr_0(k7_algstr_0) )).
fof(dt_k7_algstr_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k7_altcat_1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(dt_k7_ami_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k7_ami_3,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k7_ami_3(A),u1_compos_1(k1_ami_3)) ) )).
fof(dt_k7_ami_wstd,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k4_ordinal1) & v7_ordinal1(D) ) => m1_subset_1(k7_ami_wstd(A,B,C,D),k4_ordinal1) ) )).
fof(dt_k7_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k7_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( v1_relat_1(k7_aofa_a00(A,B,C,D,E,F,G)) & v1_funct_1(k7_aofa_a00(A,B,C,D,E,F,G)) & v1_finseq_1(k7_aofa_a00(A,B,C,D,E,F,G)) ) )).
fof(dt_k7_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(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) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) & v19_aofa_a00(D,A) & m1_subset_1(D,u1_struct_0(A)) ) => m1_subset_1(k7_aofa_a01(A,B,C,D),k1_funct_1(u3_msualg_1(A,C),D)) ) )).
fof(dt_k7_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k7_armstrng,axiom,( ! [A] : m1_subset_1(k7_armstrng(A),k1_zfmisc_1(k2_zfmisc_1(k4_armstrng(A),k4_armstrng(A)))) )).
fof(dt_k7_arytm_2,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k7_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => m1_subset_1(k7_arytm_3(A),k4_ordinal1) ) )).
fof(dt_k7_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => m1_funct_2(k7_asympt_0(A),k4_ordinal1,k1_numbers) ) )).
fof(dt_k7_autalg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k7_bagorder,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_k7_bcialg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k7_bcialg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k7_bcialg_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k7_bcialg_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k7_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k7_binarith,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v8_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) ) ) )).
fof(dt_k7_binom,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => m1_subset_1(k7_binom(A,B),k4_ordinal1) ) )).
fof(dt_k7_binop_2,axiom,( v1_funct_1(k7_binop_2) & v1_funct_2(k7_binop_2,k1_numbers,k1_numbers) & m1_subset_1(k7_binop_2,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) )).
fof(dt_k7_bor_cant,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_funct_1(k7_bor_cant(A,B)) & v1_funct_2(k7_bor_cant(A,B),k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(k7_bor_cant(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) )).
fof(dt_k7_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))))) ) )).
fof(dt_k7_borsuk_6,axiom,( m1_subset_1(k7_borsuk_6,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))) )).
fof(dt_k7_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k7_bspace,axiom,( ! [A] : ( ~ v2_struct_0(k7_bspace(A)) & l1_vectsp_1(k7_bspace(A),k2_bspace) ) )).
fof(dt_k7_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k7_bvfunc_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k7_c0sp1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(dt_k7_c0sp2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k7_card_1,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k7_card_1(A),k1_zfmisc_1(k4_ordinal1)) ) )).
fof(dt_k7_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) ) => v1_card_1(k7_card_3(A)) ) )).
fof(dt_k7_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)))) ) ) )).
fof(dt_k7_cat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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(k7_cat_2(A,B,C,D),u1_struct_0(k6_cat_2(A,B))) ) )).
fof(dt_k7_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)))) ) ) )).
fof(dt_k7_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ 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) ) )).
fof(dt_k7_cat_5,axiom,( ! [A] : ( ~ 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)) ) )).
fof(dt_k7_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => l1_clopban2(k7_cc0sp1(A)) ) )).
fof(dt_k7_cc0sp2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k7_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => l6_algstr_0(k7_cfuncdom(A)) ) )).
fof(dt_k7_chain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_chain_1(B,A) & m1_subset_1(C,k4_ordinal1) & 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))) ) )).
fof(dt_k7_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) ) )).
fof(dt_k7_circcomb,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_k7_circuit1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k7_circuit2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k7_classes2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k7_clopban1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) ) )).
fof(dt_k7_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => l6_algstr_0(k7_clopban2(A)) ) )).
fof(dt_k7_clopban4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & 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)) ) )).
fof(dt_k7_closure1,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k7_closure2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k7_clvect_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => m1_subset_1(k7_clvect_1(A,B),u1_struct_0(A)) ) )).
fof(dt_k7_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_coh_sp(A)) => m1_subset_1(k7_coh_sp(A,B),k3_coh_sp(A)) ) )).
fof(dt_k7_combgras,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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)))) ) )).
fof(dt_k7_complex1,axiom,( m1_subset_1(k7_complex1,k2_numbers) )).
fof(dt_k7_complsp2,axiom,( ! [A] : ( m1_finseq_1(A,k2_numbers) => m2_finseq_1(k7_complsp2(A),k1_numbers) ) )).
fof(dt_k7_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_compos_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k7_comput_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v4_valued_0(A) & v2_margrel1(A) & v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) & m1_subset_1(C,k4_ordinal1) ) => m2_rfunct_3(k7_comput_1(A,B,C),k3_finseq_2(k4_ordinal1),k4_ordinal1,k2_comput_1(k4_ordinal1)) ) )).
fof(dt_k7_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_funct_1(k7_comseq_3(A)) & v1_funct_2(k7_comseq_3(A),k4_ordinal1,k1_numbers) & m1_subset_1(k7_comseq_3(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k7_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ~ v1_xboole_0(k7_conlat_1(A)) ) )).
fof(dt_k7_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ( ~ v2_struct_0(k7_conlat_2(A)) & ~ v11_struct_0(k7_conlat_2(A)) & v1_conlat_1(k7_conlat_2(A)) & l1_conlat_1(k7_conlat_2(A)) ) ) )).
fof(dt_k7_convex4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) & v1_xcmplx_0(B) & m1_convex4(C,A) ) => m1_convex4(k7_convex4(A,B,C),A) ) )).
fof(dt_k7_cqc_lang,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k7_cqc_sim1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k3_cqc_lang(A)) ) => m1_subset_1(k7_cqc_sim1(A,B),k4_ordinal1) ) )).
fof(dt_k7_csspace,axiom,( ~ v2_struct_0(k7_csspace) & v1_clvect_1(k7_csspace) & l1_clvect_1(k7_csspace) )).
fof(dt_k7_csspace4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k7_decomp_1,axiom,( ! [A] : ( ( 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)))) ) )).
fof(dt_k7_descip_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k7_diff_1,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)) & m1_subset_1(k7_diff_1(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)))) ) ) )).
fof(dt_k7_dist_1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_k7_dist_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_funct_1(k7_dist_2(A,B)) & v1_funct_2(k7_dist_2(A,B),A,k6_margrel1) & m1_subset_1(k7_dist_2(A,B),k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) ) )).
fof(dt_k7_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k7_dtconstr,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(dt_k7_dynkin,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_dynkin(B,A) & m1_subset_1(C,B) ) => m1_dynkin(k7_dynkin(A,B,C),A) ) )).
fof(dt_k7_ec_pf_1,axiom,( ! [A] : ( ( 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))))) ) )).
fof(dt_k7_ec_pf_2,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k7_entropy1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k1_numbers)) ) => v1_xreal_0(k7_entropy1(A)) ) )).
fof(dt_k7_eqrel_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k7_euclid,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k7_euclid_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & 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)))) ) )).
fof(dt_k7_euclid_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k7_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(dt_k7_extpro_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k4_ordinal1) & 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)) ) ) )).
fof(dt_k7_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) )).
fof(dt_k7_ff_siec,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => v1_relat_1(k7_ff_siec(A)) ) )).
fof(dt_k7_filter_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k7_filter_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k7_filter_2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k7_fin_topo,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k7_finseq_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k7_finseq_2,axiom,( ! [A] : ( v1_funct_1(k7_finseq_2(A)) & v1_funct_2(k7_finseq_2(A),k4_ordinal1,k3_finseq_2(k1_tarski(A))) & m1_subset_1(k7_finseq_2(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k3_finseq_2(k1_tarski(A))))) ) )).
fof(dt_k7_finseq_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_1(k7_finseq_8(A,B,C),A) ) )).
fof(dt_k7_finseqop,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k7_fintopo3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k7_flang_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k7_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_funct_1(k7_fomodel0(A)) & v1_funct_2(k7_fomodel0(A),k6_subset_1(k3_finseq_2(A),k1_tarski(k1_xboole_0)),A) & m1_subset_1(k7_fomodel0(A),k1_zfmisc_1(k2_zfmisc_1(k6_subset_1(k3_finseq_2(A),k1_tarski(k1_xboole_0)),A))) ) ) )).
fof(dt_k7_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k7_fomodel2(A,B,C,D)) & v1_funct_2(k7_fomodel2(A,B,C,D),k4_ordinal1,k9_funct_2(k35_fomodel1(A),B)) & m1_subset_1(k7_fomodel2(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_funct_2(k35_fomodel1(A),B)))) ) ) )).
fof(dt_k7_fomodel3,axiom,( ! [A] : ! [B] : ( ( ~ 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))),k15_fomodel2(A,k35_fomodel1(A))) ) )).
fof(dt_k7_freealg,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,k4_ordinal1) & ~ 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)) ) ) )).
fof(dt_k7_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k7_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(dt_k7_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ~ 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)) ) )).
fof(dt_k7_funcop_1,axiom,( ! [A] : ! [B] : ( 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)))) ) )).
fof(dt_k7_funcsdom,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k7_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k7_funct_3,axiom,( ! [A] : ! [B] : ( v1_relat_1(k7_funct_3(A,B)) & v1_funct_1(k7_funct_3(A,B)) ) )).
fof(dt_k7_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) )).
fof(dt_k7_funct_6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k7_funct_6(A,B)) & v1_funct_1(k7_funct_6(A,B)) ) ) )).
fof(dt_k7_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))))) ) ) )).
fof(dt_k7_functor3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [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)) ) )).
fof(dt_k7_fvaluat1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k7_fvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k7_gcd_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) )).
fof(dt_k7_genealg1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k4_ordinal1) ) => m1_genealg1(k7_genealg1(A,B,C,D),A) ) )).
fof(dt_k7_geomtrap,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) ) )).
fof(dt_k7_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ 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)) ) )).
fof(dt_k7_gfacirc2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k7_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(dt_k7_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(dt_k7_glib_004,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)))) ) )).
fof(dt_k7_glib_005,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) ) )).
fof(dt_k7_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => m1_subset_1(k7_graph_1(A),k4_ordinal1) ) )).
fof(dt_k7_graph_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k7_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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),k4_ordinal1) ) )).
fof(dt_k7_graph_5,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k7_graphsp,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k3_finseq_2(k1_numbers)) & v7_ordinal1(B) ) => m1_subset_1(k7_graphsp(A,B),k1_zfmisc_1(k4_ordinal1)) ) )).
fof(dt_k7_grcat_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(dt_k7_group_1,axiom,( ! [A] : ( ( v8_struct_0(A) & l1_struct_0(A) ) => m1_subset_1(k7_group_1(A),k4_ordinal1) ) )).
fof(dt_k7_group_10,axiom,( ! [A] : ! [B] : ( ( ~ 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))))) ) ) )).
fof(dt_k7_group_2,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(dt_k7_group_3,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k7_group_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k7_group_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k7_group_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k7_hahnban1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k7_hermitan,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k7_heyting1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k7_heyting2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))))) ) ) )).
fof(dt_k7_hilbasis,axiom,( ! [A] : ! [B] : ( ( ~ 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,k4_ordinal1) ) => ( v1_funct_1(k7_hilbasis(A,B)) & v1_funct_2(k7_hilbasis(A,B),u1_struct_0(k12_polynom1(k1_nat_1(B,1),A)),u1_struct_0(k14_polynom3(k12_polynom1(B,A)))) & m1_subset_1(k7_hilbasis(A,B),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k12_polynom1(k1_nat_1(B,1),A)),u1_struct_0(k14_polynom3(k12_polynom1(B,A)))))) ) ) )).
fof(dt_k7_hurwitz,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(A,k1_complfld) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => ( v1_funct_1(k7_hurwitz(A)) & v1_funct_2(k7_hurwitz(A),k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(k7_hurwitz(A),k1_complfld) & m1_subset_1(k7_hurwitz(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) ) )).
fof(dt_k7_idea_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => v7_ordinal1(k7_idea_1(A,B)) ) )).
fof(dt_k7_ideal_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k7_index_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) )).
fof(dt_k7_int_3,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_k7_integr10,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(dt_k7_integr15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) ) )).
fof(dt_k7_integr16,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k7_integra1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_xreal_0(k7_integra1(A,B,C)) ) )).
fof(dt_k7_interva1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k7_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => m1_subset_1(k7_intpro_1(A),k1_zfmisc_1(k1_intpro_1)) ) )).
fof(dt_k7_isocat_1,axiom,( ! [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) & 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)))) ) ) )).
fof(dt_k7_isocat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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),k9_nattra_1(k6_cat_2(A,B),C),k9_nattra_1(A,k9_nattra_1(B,C))) ) )).
fof(dt_k7_jgraph_4,axiom,( ! [A] : ( 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))))) ) ) )).
fof(dt_k7_jgraph_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) )).
fof(dt_k7_jordan5d,axiom,( ! [A] : ( ( ~ 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))) ) => v7_ordinal1(k7_jordan5d(A)) ) )).
fof(dt_k7_jordan6,axiom,( ! [A] : ( v1_xreal_0(A) => m1_subset_1(k7_jordan6(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) )).
fof(dt_k7_knaster,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k7_kolmog01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))) ) )).
fof(dt_k7_lang1,axiom,( ! [A] : ! [B] : ( v2_lang1(k7_lang1(A,B)) & l2_lang1(k7_lang1(A,B)) ) )).
fof(dt_k7_laplace,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v1_matrix_0(k7_laplace(A,B,C)) & v2_matrix_0(k7_laplace(A,B,C),u1_struct_0(B),A,A) & m2_finseq_1(k7_laplace(A,B,C),k3_finseq_2(u1_struct_0(B))) ) ) )).
fof(dt_k7_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_orders_2(k7_lattice3(A)) & l1_orders_2(k7_lattice3(A)) ) ) )).
fof(dt_k7_lattice5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k7_lattices,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k7_lexbfs,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k7_lfuzzy_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_numbers,1)))) ) )).
fof(dt_k7_lopban_1,axiom,( ! [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) & 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)))) ) )).
fof(dt_k7_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => l6_algstr_0(k7_lopban_2(A)) ) )).
fof(dt_k7_lopban_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) & 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),k4_ordinal1,u1_struct_0(B)) & m1_subset_1(k7_lopban_4(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) ) )).
fof(dt_k7_lopclset,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k7_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_funct_1(k7_lpspacc1(A)) & v1_funct_2(k7_lpspacc1(A),k2_zfmisc_1(k3_rfunct_3(A,k2_numbers),k3_rfunct_3(A,k2_numbers)),k3_rfunct_3(A,k2_numbers)) & m1_subset_1(k7_lpspacc1(A),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k3_rfunct_3(A,k2_numbers),k3_rfunct_3(A,k2_numbers)),k3_rfunct_3(A,k2_numbers)))) ) ) )).
fof(dt_k7_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v2_struct_0(k7_lpspace1(A)) & l1_rlvect_1(k7_lpspace1(A)) ) ) )).
fof(dt_k7_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v2_xxreal_0(D) & v1_xreal_0(D) ) => ( 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)))) ) ) )).
fof(dt_k7_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => m1_subset_1(k7_ltlaxio1(A),k1_hilbert1) ) )).
fof(dt_k7_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => m1_subset_1(k7_ltlaxio3(A),k1_zfmisc_1(k9_setfam_1(k1_hilbert1))) ) )).
fof(dt_k7_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => m1_subset_1(k7_ltlaxio4(A),k1_zfmisc_1(k1_hilbert1)) ) )).
fof(dt_k7_margrel1,axiom,( m1_subset_1(k7_margrel1,k6_margrel1) )).
fof(dt_k7_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k7_matrix13,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(A)) & v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) & v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ( v1_matrix_0(k7_matrix13(A,B,C,D)) & v2_matrix_0(k7_matrix13(A,B,C,D),A,k5_card_1(C),k5_card_1(C)) & m2_finseq_1(k7_matrix13(A,B,C,D),k3_finseq_2(A)) ) ) )).
fof(dt_k7_matrix15,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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_0(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_0(B))) ) ) )).
fof(dt_k7_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(A)) & v7_ordinal1(C) ) => m2_finseq_2(k7_matrix_0(A,B,C),A,k4_finseq_2(k1_matrix_0(B),A)) ) )).
fof(dt_k7_matrix_5,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(k2_numbers)) ) => ( v1_matrix_0(k7_matrix_5(A,B)) & m2_finseq_1(k7_matrix_5(A,B),k3_finseq_2(k2_numbers)) ) ) )).
fof(dt_k7_matrixc1,axiom,( ! [A] : ! [B] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k2_numbers)) & v1_xcmplx_0(B) ) => ( v1_matrix_0(k7_matrixc1(A,B)) & m2_finseq_1(k7_matrixc1(A,B),k3_finseq_2(k2_numbers)) ) ) )).
fof(dt_k7_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k7_matrixj2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) )).
fof(dt_k7_matrixr1,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( v1_matrix_0(k7_matrixr1(A,B)) & m2_finseq_1(k7_matrixr1(A,B),k3_finseq_2(k1_numbers)) ) ) )).
fof(dt_k7_matrixr2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m1_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( v1_matrix_0(k7_matrixr2(A,B)) & v2_matrix_0(k7_matrixr2(A,B),k1_numbers,A,A) & m2_finseq_1(k7_matrixr2(A,B),k3_finseq_2(k1_numbers)) ) ) )).
fof(dt_k7_matrlin,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(A)) & v1_matrix_0(C) & m1_finseq_1(C,k3_finseq_2(A)) ) => ( v1_matrix_0(k7_matrlin(A,B,C)) & m2_finseq_1(k7_matrlin(A,B,C),k3_finseq_2(A)) ) ) )).
fof(dt_k7_matrlin2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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)))) ) ) )).
fof(dt_k7_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(dt_k7_measure7,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k9_setfam_1(k1_numbers)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k1_numbers)))) & m2_measure7(B,A) ) => ( v1_funct_1(k7_measure7(A,B)) & v1_funct_2(k7_measure7(A,B),k4_ordinal1,k6_numbers) & m1_subset_1(k7_measure7(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) ) )).
fof(dt_k7_member_1,axiom,( ! [A] : ( v1_membered(A) => v1_membered(k7_member_1(A)) ) )).
fof(dt_k7_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k7_mesfun7c,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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,k6_numbers))) ) ) )).
fof(dt_k7_mesfunc1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k6_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,k6_numbers))) ) ) )).
fof(dt_k7_mesfunc5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => m1_subset_1(k7_mesfunc5(A,B,C,D),k6_numbers) ) )).
fof(dt_k7_mesfunc8,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ( v1_funct_1(k7_mesfunc8(A,B)) & m1_subset_1(k7_mesfunc8(A,B),k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) ) )).
fof(dt_k7_metric_1,axiom,( v1_metric_1(k7_metric_1) & l1_metric_1(k7_metric_1) )).
fof(dt_k7_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => m1_subset_1(k7_metric_2(A),k1_zfmisc_1(k2_metric_2(A))) ) )).
fof(dt_k7_metric_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k7_midsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k7_midsp_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k7_midsp_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(A,k4_ordinal1) & ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_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(k1_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(k1_nat_1(A,1),u1_struct_0(B))) ) )).
fof(dt_k7_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k7_mod_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))))) ) ) )).
fof(dt_k7_modelc_1,axiom,( ! [A] : ( m1_finseq_1(A,k4_ordinal1) => m2_finseq_1(k7_modelc_1(A),k4_ordinal1) ) )).
fof(dt_k7_modelc_2,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k4_ordinal1) & m1_finseq_1(B,k4_ordinal1) ) => m2_finseq_1(k7_modelc_2(A,B),k4_ordinal1) ) )).
fof(dt_k7_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => m1_subset_1(k7_modelc_3(A),k1_zfmisc_1(k1_modelc_3(A))) ) )).
fof(dt_k7_monoid_0,axiom,( ~ 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) )).
fof(dt_k7_monoid_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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)) ) )).
fof(dt_k7_msafree,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) )).
fof(dt_k7_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ( v3_msualg_1(k7_msafree2(A),A) & l3_msualg_1(k7_msafree2(A),A) ) ) )).
fof(dt_k7_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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(k7_msafree4(A,B,C,D,E),k1_zfmisc_1(k2_zfmisc_1(k1_funct_1(B,E),k1_funct_1(C,E)))) ) )).
fof(dt_k7_msaterm,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k7_msualg_1,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(dt_k7_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k7_msualg_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k7_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => m1_mycielsk(k7_mycielsk(A),k7_nat_d(k3_xcmplx_0(3,k1_newton(2,A)),1)) ) )).
fof(dt_k7_nat_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & v7_ordinal1(B) ) => ( v1_relat_1(k7_nat_1(A,B)) & v4_relat_1(k7_nat_1(A,B),k4_ordinal1) & v1_funct_1(k7_nat_1(A,B)) & v1_partfun1(k7_nat_1(A,B),k4_ordinal1) ) ) )).
fof(dt_k7_nat_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k7_nat_d,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => m1_subset_1(k7_nat_d(A,B),k4_ordinal1) ) )).
fof(dt_k7_nattra_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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(k7_nattra_1(A,B,C,D,E),A,B,D,C) ) )).
fof(dt_k7_newton,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k7_newton(A),k4_ordinal1) ) )).
fof(dt_k7_normform,axiom,( ! [A] : m1_subset_1(k7_normform(A),k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)))) )).
fof(dt_k7_oppcat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) )).
fof(dt_k7_ordinal3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => v3_ordinal1(k7_ordinal3(A,B)) ) )).
fof(dt_k7_ordinal6,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k7_osafree,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k7_osalg_1,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k7_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k7_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) ) => m1_subset_1(k7_partfun1(A,B,C),A) ) )).
fof(dt_k7_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k7_pcs_0,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(dt_k7_pdiff_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) & 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))))) ) ) )).
fof(dt_k7_pdiff_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k7_pdiff_5,axiom,( ! [A] : ! [B] : ( ( 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)) ) => v1_xreal_0(k7_pdiff_5(A,B)) ) )).
fof(dt_k7_pencil_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) ) ) )).
fof(dt_k7_petri,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k7_pnproc_1,axiom,( ! [A] : ! [B] : ( m1_pnproc_1(B,A) => ( v1_relat_1(k7_pnproc_1(A,B)) & v1_funct_1(k7_pnproc_1(A,B)) ) ) )).
fof(dt_k7_polyeq_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k7_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => m1_subset_1(k7_polyform(A),k4_ordinal1) ) )).
fof(dt_k7_polynom1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k7_polynom1(A,B,C,D)) & v1_funct_2(k7_polynom1(A,B,C,D),k15_pre_poly(A),u1_struct_0(B)) & m1_subset_1(k7_polynom1(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) ) )).
fof(dt_k7_polynom3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & m1_finseq_1(E,k4_finseq_2(3,k4_ordinal1)) ) => m2_finseq_2(k7_polynom3(A,B,C,D,E),u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) ) )).
fof(dt_k7_polynom5,axiom,( ! [A] : ! [B] : ( ( ~ 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,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k7_polynom5(A,B)) & v1_funct_2(k7_polynom5(A,B),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k7_polynom5(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k7_polynom8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) => ( v1_matrix_0(k7_polynom8(A,B,C)) & v2_matrix_0(k7_polynom8(A,B,C),u1_struct_0(A),B,B) & m2_finseq_1(k7_polynom8(A,B,C),k3_finseq_2(u1_struct_0(A))) ) ) )).
fof(dt_k7_poset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(dt_k7_pralg_1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_k7_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(dt_k7_prob_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_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) ) )).
fof(dt_k7_prob_3,axiom,( ! [A] : ! [B] : ( m1_finseq_1(B,k9_setfam_1(A)) => m1_subset_1(k7_prob_3(A,B),k1_zfmisc_1(A)) ) )).
fof(dt_k7_prob_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k7_prvect_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k7_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => v1_xreal_0(k7_pscomp_1(A)) ) )).
fof(dt_k7_pua2mss1,axiom,( ! [A] : ! [B] : ( ( 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)))) ) )).
fof(dt_k7_qc_lang1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k6_qc_lang1(A)) ) => v7_ordinal1(k7_qc_lang1(A,B)) ) )).
fof(dt_k7_qc_lang2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k7_qmax_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k7_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => m1_subset_1(k7_quatern2(A),k1_quaterni) ) )).
fof(dt_k7_quofield,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k7_radix_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k7_radix_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k7_radix_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) ) => m2_subset_1(k7_radix_5(A,B,C),k4_numbers,k3_radix_1(C)) ) )).
fof(dt_k7_radix_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k7_random_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k7_random_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v2_finset_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( v1_relat_1(k7_random_3(A)) & v4_relat_1(k7_random_3(A),k4_ordinal1) & v1_funct_1(k7_random_3(A)) & v1_partfun1(k7_random_3(A),k4_ordinal1) & v6_random_3(k7_random_3(A),A) ) ) )).
fof(dt_k7_ranknull,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k7_ratfunc1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & l5_algstr_0(A) ) => m1_ratfunc1(k7_ratfunc1(A),A) ) )).
fof(dt_k7_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_funct_1(k7_real_3(A)) & v1_funct_2(k7_real_3(A),k4_ordinal1,k1_numbers) & m1_subset_1(k7_real_3(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k7_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ v2_struct_0(k7_real_ns1(A)) & v1_bhsp_1(k7_real_ns1(A)) & l1_bhsp_1(k7_real_ns1(A)) ) ) )).
fof(dt_k7_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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)) ) )).
fof(dt_k7_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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))) ) )).
fof(dt_k7_rewrite2,axiom,( ! [A] : ! [B] : ( 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)))) ) )).
fof(dt_k7_rfunct_1,axiom,( ! [A] : ! [B] : ( 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))) ) )).
fof(dt_k7_rfunct_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k7_ringcat1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) ) )).
fof(dt_k7_rlvect_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k7_rmod_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) )).
fof(dt_k7_robbins1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(dt_k7_roughs_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k7_rsspace,axiom,( ! [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) & v8_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_funct_1(k7_rsspace(A,B)) & v1_funct_2(k7_rsspace(A,B),k2_zfmisc_1(B,B),B) & m1_subset_1(k7_rsspace(A,B),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B,B),B))) ) ) )).
fof(dt_k7_rsspace4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k7_rusub_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k7_rvsum_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k7_rvsum_2,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k7_scm_comp,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k7_scm_inst,axiom,( ! [A] : ( m1_subset_1(A,k3_scm_inst) => v7_ordinal1(k7_scm_inst(A)) ) )).
fof(dt_k7_scmfsa_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k7_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k7_scmfsa_m,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k7_scmpds_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k7_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) & v1_int_1(B) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ( v1_relat_1(k7_scmpds_6(A,B,C)) & v4_relat_1(k7_scmpds_6(A,B,C),k4_ordinal1) & v5_relat_1(k7_scmpds_6(A,B,C),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k7_scmpds_6(A,B,C)) & 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)) ) ) )).
fof(dt_k7_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => m1_subset_1(k7_scmpds_i(A),k2_scm_inst) ) )).
fof(dt_k7_scmring2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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))) ) )).
fof(dt_k7_scmringi,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k7_scmyciel,axiom,( ! [A] : ! [B] : ( v4_scmyciel(A) => m1_subset_1(k7_scmyciel(A,B),k1_zfmisc_1(A)) ) )).
fof(dt_k7_seq_4,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k2_numbers) & m1_finseq_1(B,k2_numbers) ) => m2_finseq_1(k7_seq_4(A,B),k2_numbers) ) )).
fof(dt_k7_seqfunc,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( v1_funct_1(k7_seqfunc(A,B,C)) & v1_funct_2(k7_seqfunc(A,B,C),k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(k7_seqfunc(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) ) )).
fof(dt_k7_series_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v7_ordinal1(B) & v7_ordinal1(C) ) => v1_xreal_0(k7_series_1(A,B,C)) ) )).
fof(dt_k7_setfam_1,axiom,( ! [A] : ! [B] : ( 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))) ) )).
fof(dt_k7_setlim_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(k7_setlim_2(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) )).
fof(dt_k7_setwiseo,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(dt_k7_sgraph1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => m1_sgraph1(k7_sgraph1(A),k4_ordinal1) ) )).
fof(dt_k7_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k7_sin_cos,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_funct_1(k7_sin_cos(A)) & v1_funct_2(k7_sin_cos(A),k4_ordinal1,k2_numbers) & m1_subset_1(k7_sin_cos(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) ) )).
fof(dt_k7_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k7_sin_cos7(A)) ) )).
fof(dt_k7_stacks_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k7_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => v1_card_1(k7_struct_0(A)) ) )).
fof(dt_k7_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(dt_k7_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(B,k1_zfmisc_1(A)) => m1_subset_1(k7_subset_1(A,B,C),k1_zfmisc_1(A)) ) )).
fof(dt_k7_substut1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_k7_substut2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) )).
fof(dt_k7_supinf_2,axiom,( ! [A] : ( v2_membered(A) => m1_subset_1(k7_supinf_2(A),k6_numbers) ) )).
fof(dt_k7_tdlat_1,axiom,( ! [A] : ( ( 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)))) ) ) )).
fof(dt_k7_tmap_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))))) ) ) )).
fof(dt_k7_topalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))))) ) ) )).
fof(dt_k7_topalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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) ) )).
fof(dt_k7_topalg_5,axiom,( 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))))) )).
fof(dt_k7_topgen_3,axiom,( ! [A] : ! [B] : ( v1_pre_topc(k7_topgen_3(A,B)) & v2_pre_topc(k7_topgen_3(A,B)) & l1_pre_topc(k7_topgen_3(A,B)) ) )).
fof(dt_k7_topgrp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k7_topreal1,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k7_toprealb,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k7_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k7_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => v7_ordinal1(k7_trees_1(A)) ) )).
fof(dt_k7_trees_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & m1_finseq_1(B,k4_ordinal1) & 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)) ) ) )).
fof(dt_k7_trees_3,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k7_trees_4,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,k5_trees_3(A)) ) => m2_finseq_1(k7_trees_4(A,B),k2_trees_3) ) )).
fof(dt_k7_trees_9,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k7_turing_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k7_twoscomp,axiom,( 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))) )).
fof(dt_k7_unialg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k7_uproots,axiom,( ! [A] : ! [B] : ( ( ~ 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,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & v1_uproots(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_relat_1(k7_uproots(A,B)) & v4_relat_1(k7_uproots(A,B),u1_struct_0(A)) & v1_funct_1(k7_uproots(A,B)) & v1_partfun1(k7_uproots(A,B),u1_struct_0(A)) & v4_valued_0(k7_uproots(A,B)) & v2_pre_poly(k7_uproots(A,B)) ) ) )).
fof(dt_k7_urysohn3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k7_urysohn3(A,B,C,D)) & v1_funct_2(k7_urysohn3(A,B,C,D),u1_struct_0(A),u1_struct_0(k3_topmetr)) & m1_subset_1(k7_urysohn3(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k3_topmetr)))) ) ) )).
fof(dt_k7_valuat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_qc_lang1(A) & ~ v1_xboole_0(B) & v7_ordinal1(C) & 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)) ) )).
fof(dt_k7_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k7_vectsp10,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)))) ) ) )).
fof(dt_k7_vectsp_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) )).
fof(dt_k7_waybel10,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k7_waybel18,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(dt_k7_waybel34,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(dt_k7_waybel_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k7_waybel_4,axiom,( ! [A] : ! [B] : ( ( 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(k1_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(k1_yellow_1(k7_waybel_0(A)))))) ) ) )).
fof(dt_k7_waybel_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k7_weddwitt,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v6_struct_0(A) & 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)) ) ) )).
fof(dt_k7_weierstr,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) => v1_xreal_0(k7_weierstr(A,B,C)) ) )).
fof(dt_k7_yellow21,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(dt_k7_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k7_yellow_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(dt_k7_zf_lang,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k4_ordinal1) & m1_finseq_1(B,k4_ordinal1) ) => m2_finseq_1(k7_zf_lang(A,B),k4_ordinal1) ) )).
fof(dt_k7_zf_model,axiom,( v1_zf_lang(k7_zf_model) & m2_finseq_1(k7_zf_model,k4_ordinal1) )).
fof(dt_k7_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k7_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) => ( v1_funct_1(k7_zmodul02(A,B)) & v1_funct_2(k7_zmodul02(A,B),k2_zfmisc_1(k6_zmodul02(A,B),k6_zmodul02(A,B)),k6_zmodul02(A,B)) & m1_subset_1(k7_zmodul02(A,B),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k6_zmodul02(A,B),k6_zmodul02(A,B)),k6_zmodul02(A,B)))) ) ) )).
fof(dt_k80_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)))))) ) ) )).
fof(dt_k81_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) ) )).
fof(dt_k82_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) ) )).
fof(dt_k83_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) ) )).
fof(dt_k83_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_k84_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) ) )).
fof(dt_k84_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)))))) ) ) )).
fof(dt_k85_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)))))) ) ) )).
fof(dt_k89_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) )).
fof(dt_k89_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_k8_abcmiz_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k8_abcmiz_a,axiom,( m2_subset_1(k8_abcmiz_a,k20_abcmiz_1,k5_abcmiz_a) )).
fof(dt_k8_afinsq_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k8_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ~ v1_xboole_0(k8_afproj(A)) ) )).
fof(dt_k8_algstr_0,axiom,( l4_algstr_0(k8_algstr_0) )).
fof(dt_k8_algstr_4,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(dt_k8_altcat_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k8_ami_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k8_armstrng,axiom,( ! [A] : ! [B] : ( 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)))) ) )).
fof(dt_k8_arytm_2,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k8_arytm_3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v7_ordinal1(A) & v3_ordinal1(B) & v7_ordinal1(B) ) => m1_subset_1(k8_arytm_3(A,B),k5_arytm_3) ) )).
fof(dt_k8_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => m1_funct_2(k8_asympt_0(A),k4_ordinal1,k1_numbers) ) )).
fof(dt_k8_bagorder,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) ) )).
fof(dt_k8_bcialg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k8_bcialg_4,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k8_bcialg_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(dt_k8_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k8_binarith,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v8_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) ) )).
fof(dt_k8_binom,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k4_ordinal1) ) => m2_finseq_1(k8_binom(A,B,C,D),u1_struct_0(A)) ) )).
fof(dt_k8_bor_cant,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => m1_prob_1(k8_bor_cant(A,B,C),A,B) ) )).
fof(dt_k8_borsuk_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))))) ) ) )).
fof(dt_k8_borsuk_6,axiom,( m1_subset_1(k8_borsuk_6,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))) )).
fof(dt_k8_borsuk_7,axiom,( m1_subset_1(k8_borsuk_7,u1_struct_0(k8_toprealb(3))) )).
fof(dt_k8_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k8_c0sp1,axiom,( ! [A] : ! [B] : ( ~ 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))) ) ) )).
fof(dt_k8_c0sp2,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(dt_k8_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) )).
fof(dt_k8_cat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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(k8_cat_2(A,B,C,D),u4_struct_0(k6_cat_2(A,B))) ) )).
fof(dt_k8_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)))) ) ) )).
fof(dt_k8_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ 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) ) )).
fof(dt_k8_cat_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ 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))) ) )).
fof(dt_k8_catalg_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m1_subset_1(k8_catalg_1(A,B),u4_struct_0(k3_catalg_1(A))) ) )).
fof(dt_k8_cc0sp2,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(dt_k8_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_cfuncdom(k8_cfuncdom(A)) & l1_cfuncdom(k8_cfuncdom(A)) ) ) )).
fof(dt_k8_chain_1,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & 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)) ) )).
fof(dt_k8_circuit2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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),k4_ordinal1),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))) ) )).
fof(dt_k8_clopban1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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)))) ) )).
fof(dt_k8_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => l1_cfuncdom(k8_clopban2(A)) ) )).
fof(dt_k8_closure2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) ) )).
fof(dt_k8_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k3_coh_sp(A)) => m1_subset_1(k8_coh_sp(A,B),k5_coh_sp(A)) ) )).
fof(dt_k8_cohsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) )).
fof(dt_k8_combgras,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ 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)) ) ) )).
fof(dt_k8_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k8_complex1(A)) ) )).
fof(dt_k8_complsp2,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k2_numbers) & m1_finseq_1(B,k2_numbers) ) => m1_subset_1(k8_complsp2(A,B),k2_numbers) ) )).
fof(dt_k8_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_compos_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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) ) ) )).
fof(dt_k8_comput_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & m1_subset_1(B,k4_finseq_2(A,k4_ordinal1)) & m1_subset_1(C,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => m2_finseq_2(k8_comput_1(A,B,C,D),k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) ) )).
fof(dt_k8_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_funct_1(k8_comseq_3(A)) & v1_funct_2(k8_comseq_3(A),k4_ordinal1,k1_numbers) & m1_subset_1(k8_comseq_3(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k8_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => m1_conlat_1(k8_conlat_1(A),A) ) )).
fof(dt_k8_conlat_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) & l2_conlat_1(B,A) ) => ( v3_conlat_1(k8_conlat_2(A,B),k7_conlat_2(A)) & l2_conlat_1(k8_conlat_2(A,B),k7_conlat_2(A)) ) ) )).
fof(dt_k8_convex4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) & m1_convex4(B,A) ) => m1_convex4(k8_convex4(A,B),A) ) )).
fof(dt_k8_cqc_lang,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k8_cqc_sim1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k8_csspace,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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))) ) ) )).
fof(dt_k8_csspace4,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k8_decomp_1,axiom,( ! [A] : ( ( 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)))) ) )).
fof(dt_k8_descip_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) & v1_int_1(C) ) => m2_finseq_1(k8_descip_1(A,B,C),A) ) )).
fof(dt_k8_diff_1,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)) & m1_subset_1(k8_diff_1(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)))) ) ) )).
fof(dt_k8_dist_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k8_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k8_dtconstr,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k8_ec_pf_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) ) )).
fof(dt_k8_ec_pf_2,axiom,( ! [A] : ! [B] : ( ( 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))))) ) ) )).
fof(dt_k8_ens_1,axiom,( ! [A] : ( ~ 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))) ) ) )).
fof(dt_k8_entropy1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k1_numbers)) ) => m2_finseq_1(k8_entropy1(A),k1_numbers) ) )).
fof(dt_k8_eqrel_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k8_euclid,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k8_euclid_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & 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)))) ) )).
fof(dt_k8_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k8_euclid_7(A),k1_zfmisc_1(k1_euclid(A))) ) )).
fof(dt_k8_euclid_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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_xreal_0(D) ) => m2_finseq_2(k8_euclid_8(A,B,C,D),k1_numbers,k1_euclid(3)) ) )).
fof(dt_k8_extpro_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k4_ordinal1) & 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(k8_extpro_1(A,B,C,D)) ) )).
fof(dt_k8_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(dt_k8_ff_siec,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => v1_relat_1(k8_ff_siec(A)) ) )).
fof(dt_k8_filter_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k8_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => v1_relat_1(k8_filter_1(A)) ) )).
fof(dt_k8_filter_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k8_fin_topo,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k8_finseq_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_1(k8_finseq_1(A,B,C),A) ) )).
fof(dt_k8_finseq_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) & m1_finseq_1(C,A) & m1_subset_1(D,k4_ordinal1) ) => m1_subset_1(k8_finseq_8(A,B,C,D),k4_ordinal1) ) )).
fof(dt_k8_fintopo2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k8_fintopo3,axiom,( ! [A] : ! [B] : ( ( ~ 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),k4_ordinal1,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(k8_fintopo3(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(u1_struct_0(A))))) ) ) )).
fof(dt_k8_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => m1_subset_1(k8_flang_1(A,B),k1_zfmisc_1(k3_catalan2(A))) ) )).
fof(dt_k8_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_relat_1(k8_fomodel0(A)) & v1_funct_1(k8_fomodel0(A)) ) ) )).
fof(dt_k8_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k8_fomodel2(A,B,C,D),B) ) )).
fof(dt_k8_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) )).
fof(dt_k8_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k8_fomodel4(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k35_fomodel1(A),k35_fomodel1(A)))) ) )).
fof(dt_k8_freealg,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,k4_ordinal1) & ~ v1_xboole_0(B) & v1_freealg(B) ) => m1_subset_1(k8_freealg(A,B),k1_zfmisc_1(u1_struct_0(k7_freealg(A,B)))) ) )).
fof(dt_k8_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ 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)) ) )).
fof(dt_k8_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k8_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( 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)) ) )).
fof(dt_k8_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k8_funcsdom,axiom,( ! [A] : m2_funct_2(k8_funcsdom(A),A,k1_numbers,k9_funct_2(A,k1_numbers)) )).
fof(dt_k8_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))) ) ) )).
fof(dt_k8_funct_3,axiom,( ! [A] : ! [B] : ( v1_relat_1(k8_funct_3(A,B)) & v1_funct_1(k8_funct_3(A,B)) ) )).
fof(dt_k8_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k8_funct_4(A,B,C,D)) & m1_subset_1(k8_funct_4(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)))) ) ) )).
fof(dt_k8_funct_5,axiom,( v1_funct_1(k8_funct_5) & v1_funct_2(k8_funct_5,k1_tarski(k5_ordinal1),k1_tarski(k5_ordinal1)) & m1_subset_1(k8_funct_5,k1_zfmisc_1(k2_zfmisc_1(k1_tarski(k5_ordinal1),k1_tarski(k5_ordinal1)))) )).
fof(dt_k8_funct_6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k8_funct_6(A,B)) & v1_funct_1(k8_funct_6(A,B)) ) ) )).
fof(dt_k8_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v7_ordinal1(B) ) => v1_relat_1(k8_funct_7(A,B)) ) )).
fof(dt_k8_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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))) ) )).
fof(dt_k8_functor3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(dt_k8_fvaluat1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k8_fvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & ~ 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))) ) )).
fof(dt_k8_gcd_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) )).
fof(dt_k8_genealg1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k4_ordinal1) & m1_subset_1(E,k4_ordinal1) ) => m1_genealg1(k8_genealg1(A,B,C,D,E),A) ) )).
fof(dt_k8_geomtrap,axiom,( ! [A] : ( l1_geomtrap(A) => ( v1_analoaf(k8_geomtrap(A)) & l1_analoaf(k8_geomtrap(A)) ) ) )).
fof(dt_k8_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k8_gfacirc2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k8_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(dt_k8_glib_003,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(dt_k8_glib_004,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)))) ) )).
fof(dt_k8_glib_005,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) ) )).
fof(dt_k8_graph_1,axiom,( ! [A] : ! [B] : ( ( ~ 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),k4_ordinal1) ) )).
fof(dt_k8_graph_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(A,k4_numbers) & v7_ordinal1(B) & v7_ordinal1(C) ) => v7_ordinal1(k8_graph_2(A,B,C)) ) )).
fof(dt_k8_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k8_graph_5,axiom,( m1_subset_1(k8_graph_5,k1_zfmisc_1(k1_numbers)) )).
fof(dt_k8_graphsp,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) => m1_subset_1(k8_graphsp(A,B,C),k4_ordinal1) ) )).
fof(dt_k8_grcat_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(dt_k8_group_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k8_group_2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k8_group_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_k8_group_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k8_group_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k8_group_6,axiom,( ! [A] : ! [B] : ( ( ~ 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))))) ) ) )).
fof(dt_k8_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k8_hermitan,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k8_heyting1,axiom,( ! [A] : ( 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))))) ) )).
fof(dt_k8_heyting2,axiom,( ! [A] : ! [B] : ( 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))))) ) ) )).
fof(dt_k8_hurwitz,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(A,k1_complfld) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(k8_hurwitz(A,B),k1_complfld) & m1_subset_1(k8_hurwitz(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) ) )).
fof(dt_k8_idea_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => v7_ordinal1(k8_idea_1(A,B)) ) )).
fof(dt_k8_ideal_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k8_index_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))) ) )).
fof(dt_k8_int_3,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_k8_integr15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) ) )).
fof(dt_k8_integr16,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(dt_k8_integra1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k8_interva1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k8_intpro_1,axiom,( m1_subset_1(k8_intpro_1,k1_zfmisc_1(k1_intpro_1)) )).
fof(dt_k8_isocat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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,k6_cat_2(B,C)) ) )).
fof(dt_k8_jgraph_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) )).
fof(dt_k8_jordan5d,axiom,( ! [A] : ( ( ~ 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))) ) => v7_ordinal1(k8_jordan5d(A)) ) )).
fof(dt_k8_jordan6,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_k8_knaster,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k8_kolmog01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k8_lang1,axiom,( ! [A] : ! [B] : ( v2_lang1(k8_lang1(A,B)) & l2_lang1(k8_lang1(A,B)) ) )).
fof(dt_k8_laplace,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & ~ 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) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,A) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => m2_finseq_1(k8_laplace(A,B,C,D),u1_struct_0(C)) ) )).
fof(dt_k8_lattice3,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k8_lexbfs,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k8_lfuzzy_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v5_relat_1(C,k1_rcomp_1(k5_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(k5_numbers,1)))) ) )).
fof(dt_k8_lmod_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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)) ) )).
fof(dt_k8_lopban_1,axiom,( ! [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) & 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)) ) ) )).
fof(dt_k8_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => l1_funcsdom(k8_lopban_2(A)) ) )).
fof(dt_k8_lopban_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & 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)) & v7_ordinal1(D) ) => ( v1_funct_1(k8_lopban_4(A,B,C,D)) & v1_funct_2(k8_lopban_4(A,B,C,D),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k8_lopban_4(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k8_lopclset,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k8_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_funct_1(k8_lpspacc1(A)) & v1_funct_2(k8_lpspacc1(A),k2_zfmisc_1(k2_numbers,k3_rfunct_3(A,k2_numbers)),k3_rfunct_3(A,k2_numbers)) & m1_subset_1(k8_lpspacc1(A),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k2_numbers,k3_rfunct_3(A,k2_numbers)),k3_rfunct_3(A,k2_numbers)))) ) ) )).
fof(dt_k8_lpspace1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(B) ) => ( v1_funct_1(k8_lpspace1(A,B)) & m1_subset_1(k8_lpspace1(A,B),k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) ) )).
fof(dt_k8_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v2_xxreal_0(D) & v1_xreal_0(D) ) => m2_subset_1(k8_lpspace2(A,B,C,D),k1_zfmisc_1(k1_lpspace2(A,B,C,D)),k6_lpspace2(A,B,C,D)) ) )).
fof(dt_k8_ltlaxio1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_hilbert1) & m1_subset_1(B,k1_hilbert1) ) => m1_subset_1(k8_ltlaxio1(A,B),k1_hilbert1) ) )).
fof(dt_k8_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ( v2_funct_1(k8_ltlaxio3(A)) & m2_finseq_1(k8_ltlaxio3(A),k1_hilbert1) ) ) )).
fof(dt_k8_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ( ~ v1_xboole_0(k8_ltlaxio4(A)) & v1_finset_1(k8_ltlaxio4(A)) & m1_subset_1(k8_ltlaxio4(A),k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)))) ) ) )).
fof(dt_k8_margrel1,axiom,( m1_subset_1(k8_margrel1,k6_margrel1) )).
fof(dt_k8_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k8_matrix13,axiom,( ! [A] : ! [B] : ( ( ~ 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_0(B) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => m1_subset_1(k8_matrix13(A,B),k4_ordinal1) ) )).
fof(dt_k8_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(A)) & v7_ordinal1(C) ) => m2_finseq_2(k8_matrix_0(A,B,C),A,k4_finseq_2(k3_finseq_1(B),A)) ) )).
fof(dt_k8_matrix_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k8_matrix_5,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => ( v1_matrix_0(k8_matrix_5(A,B)) & m2_finseq_1(k8_matrix_5(A,B),k3_finseq_2(k2_numbers)) ) ) )).
fof(dt_k8_matrixc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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)) ) )).
fof(dt_k8_matrixj1,axiom,( ! [A] : ! [B] : ( ( ~ 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),k4_ordinal1) ) )).
fof(dt_k8_matrixr1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => ( v1_matrix_0(k8_matrixr1(A,B)) & m2_finseq_1(k8_matrixr1(A,B),k3_finseq_2(k1_numbers)) ) ) )).
fof(dt_k8_matrlin,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & v7_ordinal1(C) & v7_ordinal1(D) & v1_matrix_0(E) & v2_matrix_0(E,A,B,D) & m1_finseq_1(E,k3_finseq_2(A)) & v1_matrix_0(F) & v2_matrix_0(F,A,C,D) & m1_finseq_1(F,k3_finseq_2(A)) ) => ( v1_matrix_0(k8_matrlin(A,B,C,D,E,F)) & v2_matrix_0(k8_matrlin(A,B,C,D,E,F),A,k2_xcmplx_0(B,C),D) & m2_finseq_1(k8_matrlin(A,B,C,D,E,F),k3_finseq_2(A)) ) ) )).
fof(dt_k8_matrlin2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)))) ) ) )).
fof(dt_k8_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k8_measure7,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => m1_subset_1(k8_measure7(A),k1_zfmisc_1(k6_numbers)) ) )).
fof(dt_k8_measure8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) )).
fof(dt_k8_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k8_mesfun7c,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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,k6_numbers))) ) ) )).
fof(dt_k8_mesfunc1,axiom,( m1_subset_1(k8_mesfunc1,k6_numbers) )).
fof(dt_k8_mesfunc5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) & m1_subset_1(E,B) ) => m1_subset_1(k8_mesfunc5(A,B,C,D,E),k6_numbers) ) )).
fof(dt_k8_metric_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & v1_xreal_0(C) ) => m1_subset_1(k8_metric_1(A,B,C),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k8_metric_2,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(dt_k8_midsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k8_midsp_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(A,k4_ordinal1) & ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_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(k1_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(k1_nat_1(A,1),u1_struct_0(u1_midsp_2(B,C)))) ) )).
fof(dt_k8_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k8_mod_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) ) )).
fof(dt_k8_modcat_1,axiom,( ! [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) & 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))) ) ) )).
fof(dt_k8_modelc_1,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k4_ordinal1) & m1_finseq_1(B,k4_ordinal1) ) => m2_finseq_1(k8_modelc_1(A,B),k4_ordinal1) ) )).
fof(dt_k8_modelc_2,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k4_ordinal1) & m1_finseq_1(B,k4_ordinal1) ) => m2_finseq_1(k8_modelc_2(A,B),k4_ordinal1) ) )).
fof(dt_k8_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => m1_subset_1(k8_modelc_3(A),k1_zfmisc_1(k1_modelc_3(A))) ) )).
fof(dt_k8_monoid_0,axiom,( ~ 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) )).
fof(dt_k8_monoid_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k8_msafree,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k8_msafree2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k8_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v3_rewrite1(B) & v4_rewrite1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) & m1_subset_1(C,A) ) => m1_subset_1(k8_msafree4(A,B,C),A) ) )).
fof(dt_k8_msaterm,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k8_msualg_1,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(dt_k8_msualg_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k8_nat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) & v7_ordinal1(C) ) => ( v1_funct_1(k8_nat_1(A,B,C)) & v1_funct_2(k8_nat_1(A,B,C),k4_ordinal1,A) & m1_subset_1(k8_nat_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) ) )).
fof(dt_k8_nat_3,axiom,( ! [A] : ! [B] : ( ( 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) ) => m1_subset_1(k8_nat_3(A,B),k4_ordinal1) ) )).
fof(dt_k8_nat_lat,axiom,( 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))) )).
fof(dt_k8_nattra_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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(k8_nattra_1(A,B),A,B) ) )).
fof(dt_k8_newton,axiom,( m1_subset_1(k8_newton,k1_zfmisc_1(k4_ordinal1)) )).
fof(dt_k8_normform,axiom,( ! [A] : m1_subset_1(k8_normform(A),k1_zfmisc_1(k5_finsub_1(k7_normform(A)))) )).
fof(dt_k8_openlatt,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k8_oppcat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) )).
fof(dt_k8_ordinal2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => v3_ordinal1(k8_ordinal2(A)) ) )).
fof(dt_k8_ordinal3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v7_ordinal1(A) & v3_ordinal1(B) & v7_ordinal1(B) ) => v3_ordinal1(k8_ordinal3(A,B)) ) )).
fof(dt_k8_ordinal6,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k8_osafree,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(dt_k8_osalg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k8_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) )).
fof(dt_k8_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) ) )).
fof(dt_k8_pboole,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k8_pcs_0,axiom,( ! [A] : ! [B] : ( ( l1_pcs_0(A) & l1_pcs_0(B) ) => l1_pcs_0(k8_pcs_0(A,B)) ) )).
fof(dt_k8_pdiff_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & 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)))) ) ) )).
fof(dt_k8_pdiff_5,axiom,( ! [A] : ! [B] : ( ( 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)) ) => v1_xreal_0(k8_pdiff_5(A,B)) ) )).
fof(dt_k8_petri,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k8_petri_2,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(dt_k8_pnproc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k8_polyeq_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k8_polyform,axiom,( ! [A] : ! [B] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) & v1_int_1(B) ) => v1_finset_1(k8_polyform(A,B)) ) )).
fof(dt_k8_polynom1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_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)))) ) ) )).
fof(dt_k8_polynom3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & l2_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k8_polynom3(A,B,C)) & v1_funct_2(k8_polynom3(A,B,C),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k8_polynom3(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k8_polynom5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l3_algstr_0(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,k4_ordinal1) ) => ( 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)))) ) ) )).
fof(dt_k8_poset_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k8_pralg_1,axiom,( ! [A] : ( m1_finseq_1(A,k4_ordinal1) => m2_finseq_1(k8_pralg_1(A),k4_partfun1(k3_finseq_2(k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0))) ) )).
fof(dt_k8_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_k8_prob_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,k1_numbers) & m1_subset_1(k8_prob_1(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_k8_prob_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_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) ) )).
fof(dt_k8_prvect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k8_prvect_2,axiom,( ! [A] : ( ( 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))) ) )).
fof(dt_k8_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => v1_xreal_0(k8_pscomp_1(A)) ) )).
fof(dt_k8_pua2mss1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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,k4_ordinal1) ) => m1_subset_1(k8_pua2mss1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) )).
fof(dt_k8_qc_lang1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & v7_ordinal1(B) ) => m1_subset_1(k8_qc_lang1(A,B),k1_zfmisc_1(k6_qc_lang1(A))) ) )).
fof(dt_k8_qc_lang2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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)) ) )).
fof(dt_k8_qmax_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k8_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => v1_quaterni(k8_quaterni(A)) ) )).
fof(dt_k8_quofield,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k8_radix_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k8_radix_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k8_radix_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k8_radix_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k8_random_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) => v1_xreal_0(k8_random_1(A,B,C,D)) ) )).
fof(dt_k8_random_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v2_finset_1(A) & v1_partfun1(A,k4_ordinal1) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v7_random_3(B,A,k7_random_3(A)) & v7_ordinal1(C) ) => m2_prob_1(k8_random_3(A,B,C),k1_funct_1(A,C),k1_random_1(k1_funct_1(A,C))) ) )).
fof(dt_k8_ranknull,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) )).
fof(dt_k8_ratfunc1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & l5_algstr_0(A) ) => m1_ratfunc1(k8_ratfunc1(A),A) ) )).
fof(dt_k8_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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)) ) )).
fof(dt_k8_rewrite2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k8_rlvect_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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_xreal_0(B) & m1_rlvect_2(C,A) ) => m1_rlvect_2(k8_rlvect_2(A,B,C),A) ) )).
fof(dt_k8_rmod_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) )).
fof(dt_k8_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_robbins1(A) ) => ( v4_robbins1(k8_robbins1(A)) & l4_robbins1(k8_robbins1(A)) ) ) )).
fof(dt_k8_rsspace,axiom,( ! [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) & 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(k1_numbers,B),B) & m1_subset_1(k8_rsspace(A,B),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_numbers,B),B))) ) ) )).
fof(dt_k8_rsspace4,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k8_rvsum_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k8_rvsum_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k8_scm_comp,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k8_scm_inst,axiom,( ! [A] : ( m1_subset_1(A,k3_scm_inst) => m1_subset_1(k8_scm_inst(A),k2_scm_inst) ) )).
fof(dt_k8_scmfsa_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k8_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k8_scmfsa_m,axiom,( ! [A] : ( ( 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),k4_ordinal1,k1_zfmisc_1(k4_ordinal1)) & m1_subset_1(k8_scmfsa_m(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k4_ordinal1)))) ) ) )).
fof(dt_k8_scmpds_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k8_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) & v1_int_1(B) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ( v1_relat_1(k8_scmpds_6(A,B,C)) & v4_relat_1(k8_scmpds_6(A,B,C),k4_ordinal1) & v5_relat_1(k8_scmpds_6(A,B,C),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k8_scmpds_6(A,B,C)) & 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)) ) ) )).
fof(dt_k8_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => v1_int_1(k8_scmpds_i(A)) ) )).
fof(dt_k8_scmring1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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))))))) ) ) )).
fof(dt_k8_scmring2,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) & v7_ordinal1(B) ) => m1_subset_1(k8_scmring2(A,B),u1_compos_1(k1_scmring2(A))) ) )).
fof(dt_k8_scmringi,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(dt_k8_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v6_scmyciel(A) ) => v7_ordinal1(k8_scmyciel(A)) ) )).
fof(dt_k8_seq_4,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k2_numbers) & m1_finseq_1(B,k2_numbers) ) => m2_finseq_1(k8_seq_4(A,B),k2_numbers) ) )).
fof(dt_k8_seqfunc,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( v1_funct_1(k8_seqfunc(A,B,C)) & v1_funct_2(k8_seqfunc(A,B,C),k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(k8_seqfunc(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) ) )).
fof(dt_k8_setfam_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(k8_setfam_1(A,B),k1_zfmisc_1(A)) ) )).
fof(dt_k8_setlim_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(k8_setlim_2(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) )).
fof(dt_k8_setwiseo,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k8_sgraph1,axiom,( m1_sgraph1(k8_sgraph1,k4_ordinal1) )).
fof(dt_k8_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_simplex0(B,A) & v1_xreal_0(C) ) => m1_simplex0(k8_simplex0(A,B,C),A) ) )).
fof(dt_k8_sin_cos,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => ( v1_funct_1(k8_sin_cos(A,B,C)) & v1_funct_2(k8_sin_cos(A,B,C),k4_ordinal1,k2_numbers) & m1_subset_1(k8_sin_cos(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) ) )).
fof(dt_k8_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k8_sin_cos7(A)) ) )).
fof(dt_k8_stacks_1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(dt_k8_struct_0,axiom,( ! [A] : ( l2_struct_0(A) => m1_subset_1(k8_struct_0(A),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_k8_sublemma,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k8_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(B,k1_zfmisc_1(A)) => m1_subset_1(k8_subset_1(A,B,C),k1_zfmisc_1(A)) ) )).
fof(dt_k8_substut1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k8_substut2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k8_supinf_2,axiom,( ! [A] : ( v2_membered(A) => m1_subset_1(k8_supinf_2(A),k6_numbers) ) )).
fof(dt_k8_tdlat_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(dt_k8_tmap_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k8_topalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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) ) )).
fof(dt_k8_topgrp_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(dt_k8_toprealb,axiom,( ! [A] : ( v7_ordinal1(A) => m1_pre_topc(k8_toprealb(A),k15_euclid(A)) ) )).
fof(dt_k8_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k8_trees_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k8_trees_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k8_turing_1,axiom,( ! [A] : ! [B] : ( ( 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),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1))) ) )).
fof(dt_k8_twoscomp,axiom,( 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))) )).
fof(dt_k8_unialg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k8_uproots,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1) ) => m2_finseq_1(k8_uproots(A,B,C),u1_struct_0(k14_polynom3(A))) ) )).
fof(dt_k8_valuat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k8_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) )).
fof(dt_k8_vectsp10,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k8_vectsp_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) )).
fof(dt_k8_waybel10,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k8_waybel18,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))))) ) ) )).
fof(dt_k8_waybel34,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(dt_k8_waybel_4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k8_weierstr,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) => v1_xreal_0(k8_weierstr(A,B,C)) ) )).
fof(dt_k8_yellow21,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(dt_k8_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k8_yellow_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k8_zf_lang,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_zf_lang) & m1_finseq_1(B,k4_ordinal1) ) => m2_finseq_1(k8_zf_lang(A,B),k4_ordinal1) ) )).
fof(dt_k8_zf_model,axiom,( v1_zf_lang(k8_zf_model) & m2_finseq_1(k8_zf_model,k4_ordinal1) )).
fof(dt_k8_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) => m2_subset_1(k8_zmodul02(A,B),k1_zfmisc_1(u1_struct_0(A)),k6_zmodul02(A,B)) ) )).
fof(dt_k90_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)))))) ) ) )).
fof(dt_k91_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)))))) ) ) )).
fof(dt_k9_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ~ v1_xboole_0(k9_afproj(A)) ) )).
fof(dt_k9_algstr_0,axiom,( ! [A] : ! [B] : ( ( l4_algstr_0(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(k9_algstr_0(A,B),u1_struct_0(A)) ) )).
fof(dt_k9_algstr_4,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(dt_k9_altcat_1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(dt_k9_ami_2,axiom,( 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)))))) )).
fof(dt_k9_ami_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k9_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k9_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( v1_relat_1(k9_aofa_a00(A,B,C,D,E,F,G,H)) & v1_funct_1(k9_aofa_a00(A,B,C,D,E,F,G,H)) & v1_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H)) ) )).
fof(dt_k9_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k9_armstrng,axiom,( ! [A] : ! [B] : ( 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))) ) )).
fof(dt_k9_arytm_3,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k9_asympt_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => m1_funct_2(k9_asympt_0(A,B),k4_ordinal1,k1_numbers) ) )).
fof(dt_k9_bagorder,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_orders_2(k9_bagorder(A)) & l1_orders_2(k9_bagorder(A)) ) ) )).
fof(dt_k9_bcialg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k9_bcialg_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(dt_k9_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) ) )).
fof(dt_k9_binarith,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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),k2_xcmplx_0(A,B)) & m2_finseq_1(k9_binarith(A,B,C,D,E),C) ) ) )).
fof(dt_k9_binop_2,axiom,( v1_funct_1(k9_binop_2) & v1_funct_2(k9_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & m1_subset_1(k9_binop_2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers))) )).
fof(dt_k9_bor_cant,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_funct_1(k9_bor_cant(A,B)) & v1_funct_2(k9_bor_cant(A,B),k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(k9_bor_cant(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) )).
fof(dt_k9_borsuk_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))))) ) ) )).
fof(dt_k9_borsuk_7,axiom,( m1_subset_1(k9_borsuk_7,u1_struct_0(k8_toprealb(3))) )).
fof(dt_k9_bspace,axiom,( ! [A] : m1_subset_1(k9_bspace(A),k1_zfmisc_1(u1_struct_0(k7_bspace(A)))) )).
fof(dt_k9_bvfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k9_c0sp1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k9_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ~ v2_struct_0(k9_c0sp2(A)) & l1_normsp_1(k9_c0sp2(A)) ) ) )).
fof(dt_k9_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) )).
fof(dt_k9_cat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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,k6_cat_2(A,B),C) & m1_subset_1(E,u4_struct_0(A)) & m1_subset_1(F,u4_struct_0(B)) ) => m1_subset_1(k9_cat_2(A,B,C,D,E,F),u4_struct_0(C)) ) )).
fof(dt_k9_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) )).
fof(dt_k9_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(A) & ~ 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)) ) )).
fof(dt_k9_cat_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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))) ) )).
fof(dt_k9_catalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k9_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => l2_clvect_1(k9_cc0sp2(A)) ) )).
fof(dt_k9_cgames_1,axiom,( ! [A] : v3_ordinal1(k9_cgames_1(A)) )).
fof(dt_k9_chain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_chain_1(B,A) & m1_subset_1(C,k4_ordinal1) & 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,k1_nat_1(C,1)))) ) )).
fof(dt_k9_circuit2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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),k4_ordinal1),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),k4_ordinal1,k4_card_3(u3_msualg_1(A,B))) & m1_subset_1(k9_circuit2(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_card_3(u3_msualg_1(A,B))))) ) ) )).
fof(dt_k9_classes2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k9_clopban1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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)) ) ) )).
fof(dt_k9_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => l1_clopban2(k9_clopban2(A)) ) )).
fof(dt_k9_coh_sp,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k9_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xreal_0(k9_complex1(A)) ) )).
fof(dt_k9_compos_1,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) & 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)) ) ) )).
fof(dt_k9_comput_1,axiom,( m1_subset_1(k9_comput_1,k1_zfmisc_1(k2_comput_1(k4_ordinal1))) )).
fof(dt_k9_comseq_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_ordinal1) & v5_valued_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_funct_1(k9_comseq_3(A,B)) & v1_funct_2(k9_comseq_3(A,B),k4_ordinal1,k2_numbers) & m1_subset_1(k9_comseq_3(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) ) )).
fof(dt_k9_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(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)))) ) ) )).
fof(dt_k9_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => m1_lattice4(k9_conlat_2(A),k1_lattice2(k11_conlat_1(A)),k11_conlat_1(k7_conlat_2(A))) ) )).
fof(dt_k9_convex4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) & m1_convex4(B,A) & m1_convex4(C,A) ) => m1_convex4(k9_convex4(A,B,C),A) ) )).
fof(dt_k9_cqc_lang,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k9_cqc_sim1,axiom,( ! [A] : ( 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))))) ) ) )).
fof(dt_k9_csspace,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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))) ) ) )).
fof(dt_k9_csspace4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k9_decomp_1,axiom,( ! [A] : ( ( 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)))) ) )).
fof(dt_k9_diff_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_xreal_0(B) & v1_xreal_0(C) ) => v1_xreal_0(k9_diff_1(A,B,C)) ) )).
fof(dt_k9_dist_1,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & m1_finseq_1(B,A) ) => m2_finseq_1(k9_dist_1(A,B),k4_ordinal1) ) )).
fof(dt_k9_dist_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_setfam_1(B) & m1_subset_1(B,k6_dist_1(A)) & m3_dist_2(C,A,B) ) => v1_xreal_0(k9_dist_2(A,B,C)) ) )).
fof(dt_k9_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) )).
fof(dt_k9_dtconstr,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k9_e_siec,axiom,( ! [A] : ( ( v2_e_siec(A) & v3_e_siec(A) & l1_e_siec(A) ) => v1_relat_1(k9_e_siec(A)) ) )).
fof(dt_k9_ec_pf_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k9_ens_1,axiom,( ! [A] : ( ~ 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))) ) ) )).
fof(dt_k9_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k9_euclid,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k9_euclid_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & 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)))) ) )).
fof(dt_k9_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(dt_k9_ff_siec,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => v1_relat_1(k9_ff_siec(A)) ) )).
fof(dt_k9_filter_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k9_filter_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k9_filter_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_k9_fin_topo,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k9_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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,k4_ordinal1,F) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) ) ) )).
fof(dt_k9_finseq_1,axiom,( ! [A] : ( v1_relat_1(k9_finseq_1(A)) & v1_funct_1(k9_finseq_1(A)) ) )).
fof(dt_k9_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(dt_k9_finseq_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => m2_finseq_1(k9_finseq_8(A,B,C),A) ) )).
fof(dt_k9_fintopo2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k9_fintopo3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k9_flang_1,axiom,( ! [A] : m1_subset_1(k9_flang_1(A),k1_zfmisc_1(k3_catalan2(A))) )).
fof(dt_k9_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_funct_1(k9_fomodel0(A)) & v1_funct_2(k9_fomodel0(A),k3_finseq_2(k3_finseq_2(A)),k3_finseq_2(A)) & m1_subset_1(k9_fomodel0(A),k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(k3_finseq_2(A)),k3_finseq_2(A)))) ) ) )).
fof(dt_k9_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k9_fomodel2(A,B,C)) & v1_funct_2(k9_fomodel2(A,B,C),k35_fomodel1(A),B) & m1_subset_1(k9_fomodel2(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k35_fomodel1(A),B))) ) ) )).
fof(dt_k9_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) )).
fof(dt_k9_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k9_fomodel4(A,B,C),k1_fomodel4(A)) ) )).
fof(dt_k9_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(dt_k9_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : m1_subset_1(k9_ftacell1(A,B,C,D,E),k3_msafree2(k7_ftacell1(A,B,C,D,E))) )).
fof(dt_k9_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))) ) ) )).
fof(dt_k9_funcsdom,axiom,( ! [A] : m2_funct_2(k9_funcsdom(A),A,k1_numbers,k9_funct_2(A,k1_numbers)) )).
fof(dt_k9_funct_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => m1_funct_2(k9_funct_2(A,B),A,B) ) )).
fof(dt_k9_funct_3,axiom,( ! [A] : ! [B] : ( 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))) ) )).
fof(dt_k9_funct_5,axiom,( v1_funct_1(k9_funct_5) & v1_funct_2(k9_funct_5,k2_zfmisc_1(k1_tarski(k5_ordinal1),k1_tarski(k5_ordinal1)),k1_tarski(k5_ordinal1)) & m1_subset_1(k9_funct_5,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_tarski(k5_ordinal1),k1_tarski(k5_ordinal1)),k1_tarski(k5_ordinal1)))) )).
fof(dt_k9_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k9_funct_6(A)) & v1_funct_1(k9_funct_6(A)) & v1_funcop_1(k9_funct_6(A)) ) ) )).
fof(dt_k9_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(dt_k9_functor3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k9_fvaluat1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) )).
fof(dt_k9_fvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k9_gcd_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) )).
fof(dt_k9_genealg1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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,k4_ordinal1) & m1_subset_1(E,k4_ordinal1) & m1_subset_1(F,k4_ordinal1) ) => m1_genealg1(k9_genealg1(A,B,C,D,E,F),A) ) )).
fof(dt_k9_geomtrap,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k9_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : m2_subset_1(k9_gfacirc1(A,B,C),u1_struct_0(k7_gfacirc1(A,B,C)),k3_msafree2(k7_gfacirc1(A,B,C))) )).
fof(dt_k9_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & m3_glib_001(B,A) & m1_subset_1(C,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => m3_glib_001(k9_glib_001(A,B,C,D),A) ) )).
fof(dt_k9_glib_003,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(dt_k9_glib_004,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)))) ) )).
fof(dt_k9_glib_005,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(dt_k9_graph_1,axiom,( ! [A] : ! [B] : ( ( ~ 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),k4_ordinal1) ) )).
fof(dt_k9_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => m1_finseq_2(k9_graph_3(A),u4_struct_0(A)) ) )).
fof(dt_k9_graph_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k9_grcat_1,axiom,( ! [A] : ( 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))))) ) ) )).
fof(dt_k9_group_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k9_group_3,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k9_group_4,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(dt_k9_group_5,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(dt_k9_group_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(dt_k9_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))))) ) ) )).
fof(dt_k9_heyting1,axiom,( ! [A] : ( 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))))) ) )).
fof(dt_k9_idea_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) ) => v7_ordinal1(k9_idea_1(A,B,C)) ) )).
fof(dt_k9_ideal_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k9_index_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) )).
fof(dt_k9_int_3,axiom,( ! [A] : ( v7_ordinal1(A) => l6_algstr_0(k9_int_3(A)) ) )).
fof(dt_k9_integr15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) ) )).
fof(dt_k9_integra1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k9_interva1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k9_isocat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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,k6_cat_2(B,C)) ) => m2_cat_1(k9_isocat_2(A,B,C,D),A,B) ) )).
fof(dt_k9_jgraph_4,axiom,( ! [A] : ( 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))))) ) ) )).
fof(dt_k9_jgraph_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) )).
fof(dt_k9_jordan,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,u1_struct_0(k15_euclid(A))) & v1_xreal_0(D) & v2_xxreal_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))))) ) ) )).
fof(dt_k9_jordan6,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_k9_knaster,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k9_lang1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v2_lang1(k9_lang1(A)) & l2_lang1(k9_lang1(A)) ) ) )).
fof(dt_k9_laplace,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & ~ 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) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,A) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => m2_finseq_1(k9_laplace(A,B,C,D),u1_struct_0(C)) ) )).
fof(dt_k9_lattice3,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k9_lattice5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))) ) )).
fof(dt_k9_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1),k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)))) ) )).
fof(dt_k9_lfuzzy_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k5_numbers,1)))) ) )).
fof(dt_k9_lopban_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) )).
fof(dt_k9_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => l1_lopban_2(k9_lopban_2(A)) ) )).
fof(dt_k9_lopban_4,axiom,( ! [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) & 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)))) ) ) )).
fof(dt_k9_lopclset,axiom,( ! [A] : ( ( ~ 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))))) ) ) )).
fof(dt_k9_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_funct_1(k9_lpspacc1(A)) & v1_funct_2(k9_lpspacc1(A),k2_zfmisc_1(k3_rfunct_3(A,k2_numbers),k3_rfunct_3(A,k2_numbers)),k3_rfunct_3(A,k2_numbers)) & m1_subset_1(k9_lpspacc1(A),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k3_rfunct_3(A,k2_numbers),k3_rfunct_3(A,k2_numbers)),k3_rfunct_3(A,k2_numbers)))) ) ) )).
fof(dt_k9_lpspace1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_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)))) ) ) )).
fof(dt_k9_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v2_xxreal_0(D) & v1_xreal_0(D) ) => ( 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)))) ) ) )).
fof(dt_k9_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ( v2_funct_1(k9_ltlaxio3(A)) & m2_finseq_1(k9_ltlaxio3(A),k1_hilbert1) ) ) )).
fof(dt_k9_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ( v1_finset_1(k9_ltlaxio4(A)) & m1_subset_1(k9_ltlaxio4(A),k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)))) ) ) )).
fof(dt_k9_margrel1,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => m1_subset_1(k9_margrel1(A),k6_margrel1) ) )).
fof(dt_k9_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k9_matrix13,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(A),B,C) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => m1_subset_1(k9_matrix13(A,B,C,D),k1_zfmisc_1(u1_struct_0(k6_prvect_1(A,C)))) ) )).
fof(dt_k9_matrix_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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))) ) ) )).
fof(dt_k9_matrix_5,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => m1_subset_1(k9_matrix_5(A,B),k2_numbers) ) )).
fof(dt_k9_matrixc1,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => m2_finseq_1(k9_matrixc1(A),k2_numbers) ) )).
fof(dt_k9_matrixj1,axiom,( ! [A] : ! [B] : ( ( ~ 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),k4_ordinal1) ) )).
fof(dt_k9_matrixj2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k9_matrixr1,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => ( v1_matrix_0(k9_matrixr1(A)) & m2_finseq_1(k9_matrixr1(A),k3_finseq_2(k1_numbers)) ) ) )).
fof(dt_k9_matrlin,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) ) )).
fof(dt_k9_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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))) ) )).
fof(dt_k9_measure8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_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,k6_numbers))) ) => m1_measure4(k9_measure8(A,B,C),A) ) )).
fof(dt_k9_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(dt_k9_mesfun7c,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,k2_numbers) & m1_subset_1(k9_mesfun7c(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) ) )).
fof(dt_k9_mesfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k6_numbers) & v1_funct_1(B) & v1_xreal_0(C) ) => ( v1_funct_1(k9_mesfunc1(A,B,C)) & m1_subset_1(k9_mesfunc1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) ) )).
fof(dt_k9_metric_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k9_metric_2,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(dt_k9_midsp_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k9_midsp_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(A,k4_ordinal1) & ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_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(k1_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))) ) )).
fof(dt_k9_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k9_mod_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) ) )).
fof(dt_k9_modal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k4_ordinal1) ) => ( 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)) ) ) )).
fof(dt_k9_modcat_1,axiom,( ! [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) & 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))) ) ) )).
fof(dt_k9_modelc_1,axiom,( ! [A] : ( m1_finseq_1(A,k4_ordinal1) => m2_finseq_1(k9_modelc_1(A),k4_ordinal1) ) )).
fof(dt_k9_modelc_2,axiom,( ~ v1_xboole_0(k9_modelc_2) )).
fof(dt_k9_monoid_0,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(dt_k9_monoid_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => l3_algstr_0(k9_monoid_1(A,B)) ) )).
fof(dt_k9_msafree,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(dt_k9_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & v9_msafree4(C,A,B) & v10_msafree4(C,A,B) & m1_msualg_4(C,A,B,B) ) => ( v2_relat_1(k9_msafree4(A,B,C)) & m3_pboole(k9_msafree4(A,B,C),A,B) ) ) )).
fof(dt_k9_msaterm,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))) ) )).
fof(dt_k9_msualg_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(dt_k9_msualg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k9_msualg_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k9_nat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) & v7_ordinal1(C) ) => m1_subset_1(k9_nat_1(A,B,C),A) ) )).
fof(dt_k9_nat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v3_valued_0(B) & v7_ordinal1(C) & ~ v8_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) ) ) )).
fof(dt_k9_nat_lat,axiom,( 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))) )).
fof(dt_k9_nattra_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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(k9_nattra_1(A,B)) & ~ v11_struct_0(k9_nattra_1(A,B)) & v1_cat_1(k9_nattra_1(A,B)) & v2_cat_1(k9_nattra_1(A,B)) & v3_cat_1(k9_nattra_1(A,B)) & v4_cat_1(k9_nattra_1(A,B)) & v5_cat_1(k9_nattra_1(A,B)) & v6_cat_1(k9_nattra_1(A,B)) & l1_cat_1(k9_nattra_1(A,B)) ) ) )).
fof(dt_k9_newton,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k9_newton(A),k1_zfmisc_1(k4_ordinal1)) ) )).
fof(dt_k9_normform,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(dt_k9_oppcat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)))) ) ) )).
fof(dt_k9_ordinal3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v7_ordinal1(A) & v3_ordinal1(B) & v7_ordinal1(B) ) => v3_ordinal1(k9_ordinal3(A,B)) ) )).
fof(dt_k9_osafree,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_k9_osalg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k9_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)))) ) )).
fof(dt_k9_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) ) )).
fof(dt_k9_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(dt_k9_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k9_pdiff_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & 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)))) ) )).
fof(dt_k9_pdiff_5,axiom,( ! [A] : ! [B] : ( ( 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)) ) => v1_xreal_0(k9_pdiff_5(A,B)) ) )).
fof(dt_k9_petri,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k9_polyform,axiom,( ! [A] : ! [B] : ( ( 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)))) ) )).
fof(dt_k9_polynom1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_vectsp_1(B) & l5_algstr_0(B) ) => ( v1_funct_1(k9_polynom1(A,B)) & v1_funct_2(k9_polynom1(A,B),k15_pre_poly(A),u1_struct_0(B)) & m1_subset_1(k9_polynom1(A,B),k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) ) )).
fof(dt_k9_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ( v1_funct_1(k9_polynom3(A)) & v1_funct_2(k9_polynom3(A),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k9_polynom3(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k9_poset_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(dt_k9_pralg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(dt_k9_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(dt_k9_prob_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(dt_k9_prob_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(dt_k9_prvect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) ) )).
fof(dt_k9_prvect_2,axiom,( ! [A] : ( ( 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) ) )).
fof(dt_k9_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => v1_xreal_0(k9_pscomp_1(A)) ) )).
fof(dt_k9_pua2mss1,axiom,( ! [A] : ( ( 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)))) ) )).
fof(dt_k9_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ~ v1_xboole_0(k9_qc_lang1(A)) ) )).
fof(dt_k9_qc_lang2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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)) ) )).
fof(dt_k9_qmax_1,axiom,( ! [A] : ( ( 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)))) ) ) )).
fof(dt_k9_quantal1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k9_quatern2,axiom,( v1_funct_1(k9_quatern2) & v1_funct_2(k9_quatern2,k2_zfmisc_1(k1_quaterni,k1_quaterni),k1_quaterni) & m1_subset_1(k9_quatern2,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k1_quaterni,k1_quaterni),k1_quaterni))) )).
fof(dt_k9_quofield,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k9_radix_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) ) => m2_subset_1(k9_radix_1(A,B,C),k4_numbers,k3_radix_1(B)) ) )).
fof(dt_k9_radix_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(dt_k9_radix_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) ) => m1_subset_1(k9_radix_6(A,B,C),k3_radix_1(C)) ) )).
fof(dt_k9_random_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v2_finset_1(A) & v1_partfun1(A,k4_ordinal1) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v7_random_3(B,A,k7_random_3(A)) ) => ( v1_relat_1(k9_random_3(A,B)) & v4_relat_1(k9_random_3(A,B),k4_ordinal1) & v1_funct_1(k9_random_3(A,B)) & v1_partfun1(k9_random_3(A,B),k4_ordinal1) ) ) )).
fof(dt_k9_ranknull,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) )).
fof(dt_k9_ratfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(dt_k9_rlvect_2,axiom,( ! [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) & v8_rlvect_1(A) & l1_rlvect_1(A) & m1_rlvect_2(B,A) ) => m1_rlvect_2(k9_rlvect_2(A,B),A) ) )).
fof(dt_k9_rmod_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) )).
fof(dt_k9_robbins1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k9_rsspace,axiom,( ! [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) & v8_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(k9_rsspace(A,B),B) ) )).
fof(dt_k9_rsspace4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_k9_rvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k9_rvsum_2,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k9_scm_comp,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k9_scmfsa_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(dt_k9_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(dt_k9_scmfsa_m,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & 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)) ) ) )).
fof(dt_k9_scmpds_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k9_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) & v1_int_1(B) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ( v1_relat_1(k9_scmpds_6(A,B,C)) & v4_relat_1(k9_scmpds_6(A,B,C),k4_ordinal1) & v5_relat_1(k9_scmpds_6(A,B,C),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k9_scmpds_6(A,B,C)) & 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)) ) ) )).
fof(dt_k9_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => v1_int_1(k9_scmpds_i(A)) ) )).
fof(dt_k9_scmring2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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_ordinal1(B) & 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))) ) )).
fof(dt_k9_scmringi,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k9_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v8_scmyciel(A) ) => v7_ordinal1(k9_scmyciel(A)) ) )).
fof(dt_k9_seq_4,axiom,( ! [A] : ( m1_finseq_1(A,k2_numbers) => m2_finseq_1(k9_seq_4(A),k2_numbers) ) )).
fof(dt_k9_seqfunc,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( v1_funct_1(k9_seqfunc(A,B,C)) & v1_funct_2(k9_seqfunc(A,B,C),k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(k9_seqfunc(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) ) )).
fof(dt_k9_setfam_1,axiom,( ! [A] : m1_subset_1(k9_setfam_1(A),k1_zfmisc_1(k1_zfmisc_1(A))) )).
fof(dt_k9_setlim_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(k9_setlim_2(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) )).
fof(dt_k9_setwiseo,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_k9_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_matroid0(B) & m1_simplex0(B,A) & v1_int_1(C) ) => m2_simplex0(k9_simplex0(A,B,C),A,B) ) )).
fof(dt_k9_sin_cos,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => ( v1_funct_1(k9_sin_cos(A,B,C)) & v1_funct_2(k9_sin_cos(A,B,C),k4_ordinal1,k2_numbers) & m1_subset_1(k9_sin_cos(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) ) )).
fof(dt_k9_stacks_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_k9_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_k9_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => m1_subset_1(k9_subset_1(A,B,C),k1_zfmisc_1(A)) ) )).
fof(dt_k9_substut1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_k9_supinf_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_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(k6_numbers)) ) ) )).
fof(dt_k9_tdlat_1,axiom,( ! [A] : ( l1_pre_topc(A) => m1_subset_1(k9_tdlat_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).
fof(dt_k9_tmap_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))))) ) ) )).
fof(dt_k9_topalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(dt_k9_toprealb,axiom,( m1_subset_1(k9_toprealb,u1_struct_0(k8_toprealb(2))) )).
fof(dt_k9_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(dt_k9_trees_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(dt_k9_trees_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(dt_k9_turing_1,axiom,( ! [A] : ! [B] : ( ( 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)))) ) )).
fof(dt_k9_twoscomp,axiom,( 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))) )).
fof(dt_k9_uproots,axiom,( ! [A] : ! [B] : ( ( ~ 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(k9_uproots(A,B)) & v1_funct_2(k9_uproots(A,B),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k9_uproots(A,B),A) & m1_subset_1(k9_uproots(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) )).
fof(dt_k9_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) )).
fof(dt_k9_vectsp10,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) ) )).
fof(dt_k9_waybel18,axiom,( v1_pre_topc(k9_waybel18) & l1_pre_topc(k9_waybel18) )).
fof(dt_k9_waybel34,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(dt_k9_waybel_4,axiom,( ! [A] : ( ( 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(k1_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(k1_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A))))) ) ) )).
fof(dt_k9_weierstr,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) => v1_xreal_0(k9_weierstr(A,B,C)) ) )).
fof(dt_k9_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(dt_k9_yellow_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(dt_k9_zf_lang,axiom,( ~ v1_xboole_0(k9_zf_lang) )).
fof(dt_k9_zf_model,axiom,( v1_zf_lang(k9_zf_model) & m2_finseq_1(k9_zf_model,k4_ordinal1) )).
fof(dt_k9_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(dt_k9_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) => ( v1_funct_1(k9_zmodul02(A,B)) & v1_funct_2(k9_zmodul02(A,B),k2_zfmisc_1(k4_numbers,k6_zmodul02(A,B)),k6_zmodul02(A,B)) & m1_subset_1(k9_zmodul02(A,B),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_numbers,k6_zmodul02(A,B)),k6_zmodul02(A,B)))) ) ) )).
fof(dt_l1_algstr_0,axiom,( ! [A] : ( l1_algstr_0(A) => l1_struct_0(A) ) )).
fof(dt_l1_algstr_3,axiom,( ! [A] : ( l1_algstr_3(A) => l4_struct_0(A) ) )).
fof(dt_l1_altcat_1,axiom,( ! [A] : ( l1_altcat_1(A) => l1_struct_0(A) ) )).
fof(dt_l1_analmetr,axiom,( ! [A] : ( l1_analmetr(A) => l1_analoaf(A) ) )).
fof(dt_l1_analoaf,axiom,( ! [A] : ( l1_analoaf(A) => l1_struct_0(A) ) )).
fof(dt_l1_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l1_aofa_a00(B,A) => l3_msualg_1(B,A) ) ) )).
fof(dt_l1_bcialg_1,axiom,( ! [A] : ( l1_bcialg_1(A) => l1_struct_0(A) ) )).
fof(dt_l1_bcialg_4,axiom,( ! [A] : ( l1_bcialg_4(A) => ( l2_bcialg_1(A) & l2_struct_0(A) ) ) )).
fof(dt_l1_bhsp_1,axiom,( ! [A] : ( l1_bhsp_1(A) => l1_rlvect_1(A) ) )).
fof(dt_l1_cat_1,axiom,( ! [A] : ( l1_cat_1(A) => l1_graph_1(A) ) )).
fof(dt_l1_cat_4,axiom,( ! [A] : ( l1_cat_4(A) => l1_cat_1(A) ) )).
fof(dt_l1_cayldick,axiom,( ! [A] : ( l1_cayldick(A) => l1_lopban_2(A) ) )).
fof(dt_l1_cfuncdom,axiom,( ! [A] : ( l1_cfuncdom(A) => ( l6_algstr_0(A) & l1_clvect_1(A) ) ) )).
fof(dt_l1_clopban2,axiom,( ! [A] : ( l1_clopban2(A) => ( l1_cfuncdom(A) & l2_clvect_1(A) ) ) )).
fof(dt_l1_closure1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_closure1(B,A) => l2_msualg_1(B,A) ) ) )).
fof(dt_l1_closure2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_closure2(B,A) => l2_msualg_1(B,A) ) ) )).
fof(dt_l1_clvect_1,axiom,( ! [A] : ( l1_clvect_1(A) => l2_algstr_0(A) ) )).
fof(dt_l1_collsp,axiom,( ! [A] : ( l1_collsp(A) => l1_struct_0(A) ) )).
fof(dt_l1_conlat_1,axiom,( ! [A] : ( l1_conlat_1(A) => l5_struct_0(A) ) )).
fof(dt_l1_csspace,axiom,( ! [A] : ( l1_csspace(A) => l1_clvect_1(A) ) )).
fof(dt_l1_e_siec,axiom,( ! [A] : ( l1_e_siec(A) => l1_struct_0(A) ) )).
fof(dt_l1_extpro_1,axiom,( ! [A] : ! [B] : ( l1_extpro_1(B,A) => ( l1_memstr_0(B,A) & l1_compos_1(B) ) ) )).
fof(dt_l1_fintopo2,axiom,( ! [A] : ( l1_fintopo2(A) => l1_struct_0(A) ) )).
fof(dt_l1_fomodel1,axiom,( ! [A] : ( l1_fomodel1(A) => l4_struct_0(A) ) )).
fof(dt_l1_fsm_1,axiom,( ! [A] : ! [B] : ( l1_fsm_1(B,A) => l1_struct_0(B) ) )).
fof(dt_l1_fsm_2,axiom,( ! [A] : ! [B] : ( l1_fsm_2(B,A) => l1_fsm_1(B,A) ) )).
fof(dt_l1_fsm_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) ) => ! [C] : ( l1_fsm_3(C,A,B) => l1_rewrite3(C,B) ) ) )).
fof(dt_l1_funcsdom,axiom,( ! [A] : ( l1_funcsdom(A) => ( l6_algstr_0(A) & l1_rlvect_1(A) ) ) )).
fof(dt_l1_geomtrap,axiom,( ! [A] : ( l1_geomtrap(A) => ( l1_analoaf(A) & l1_midsp_1(A) ) ) )).
fof(dt_l1_graph_1,axiom,( ! [A] : ( l1_graph_1(A) => l5_struct_0(A) ) )).
fof(dt_l1_group_9,axiom,( ! [A] : ! [B] : ( l1_group_9(B,A) => l3_algstr_0(B) ) )).
fof(dt_l1_lang1,axiom,( ! [A] : ( l1_lang1(A) => l1_struct_0(A) ) )).
fof(dt_l1_lattices,axiom,( ! [A] : ( l1_lattices(A) => l1_struct_0(A) ) )).
fof(dt_l1_lopban_2,axiom,( ! [A] : ( l1_lopban_2(A) => ( l1_funcsdom(A) & l1_normsp_1(A) ) ) )).
fof(dt_l1_memstr_0,axiom,( ! [A] : ! [B] : ( l1_memstr_0(B,A) => l2_struct_0(B) ) )).
fof(dt_l1_metric_1,axiom,( ! [A] : ( l1_metric_1(A) => l1_struct_0(A) ) )).
fof(dt_l1_midsp_1,axiom,( ! [A] : ( l1_midsp_1(A) => l1_struct_0(A) ) )).
fof(dt_l1_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( l1_midsp_3(B,A) => l1_midsp_1(B) ) ) )).
fof(dt_l1_mmlquery,axiom,( ! [A] : ( l1_mmlquery(A) => l1_struct_0(A) ) )).
fof(dt_l1_modelc_2,axiom,( ! [A] : ( l1_modelc_2(A) => l4_robbins1(A) ) )).
fof(dt_l1_msualg_1,axiom,( ! [A] : ( l1_msualg_1(A) => l5_struct_0(A) ) )).
fof(dt_l1_normsp_0,axiom,( ! [A] : ( l1_normsp_0(A) => l1_struct_0(A) ) )).
fof(dt_l1_normsp_1,axiom,( ! [A] : ( l1_normsp_1(A) => ( l1_rlvect_1(A) & l2_normsp_0(A) ) ) )).
fof(dt_l1_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => l1_struct_0(A) ) )).
fof(dt_l1_osalg_1,axiom,( ! [A] : ( l1_osalg_1(A) => l1_msualg_1(A) ) )).
fof(dt_l1_parsp_1,axiom,( ! [A] : ( l1_parsp_1(A) => l1_struct_0(A) ) )).
fof(dt_l1_pcs_0,axiom,( ! [A] : ( l1_pcs_0(A) => l1_struct_0(A) ) )).
fof(dt_l1_petri,axiom,( ! [A] : ( l1_petri(A) => l5_struct_0(A) ) )).
fof(dt_l1_petri_2,axiom,( ! [A] : ( l1_petri_2(A) => l1_petri(A) ) )).
fof(dt_l1_polyalg1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_polyalg1(B,A) => ( l6_algstr_0(B) & l1_vectsp_1(B,A) ) ) ) )).
fof(dt_l1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => l1_struct_0(A) ) )).
fof(dt_l1_prelamb,axiom,( ! [A] : ( l1_prelamb(A) => l1_struct_0(A) ) )).
fof(dt_l1_quantal1,axiom,( ! [A] : ( l1_quantal1(A) => ( l3_lattices(A) & l3_algstr_0(A) ) ) )).
fof(dt_l1_rewrite3,axiom,( ! [A] : ! [B] : ( l1_rewrite3(B,A) => l1_struct_0(B) ) )).
fof(dt_l1_rltopsp1,axiom,( ! [A] : ( l1_rltopsp1(A) => ( l1_rlvect_1(A) & l1_pre_topc(A) ) ) )).
fof(dt_l1_rlvect_1,axiom,( ! [A] : ( l1_rlvect_1(A) => l2_algstr_0(A) ) )).
fof(dt_l1_robbins1,axiom,( ! [A] : ( l1_robbins1(A) => l1_struct_0(A) ) )).
fof(dt_l1_robbins3,axiom,( ! [A] : ( l1_robbins3(A) => ( l2_lattices(A) & l1_orders_2(A) ) ) )).
fof(dt_l1_sgraph1,axiom,( ! [A] : ( l1_sgraph1(A) => l1_struct_0(A) ) )).
fof(dt_l1_sheffer1,axiom,( ! [A] : ( l1_sheffer1(A) => l1_struct_0(A) ) )).
fof(dt_l1_stacks_1,axiom,( ! [A] : ( l1_stacks_1(A) => l5_struct_0(A) ) )).
fof(dt_l1_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( l1_symsp_1(B,A) => ( l1_orders_2(B) & l1_vectsp_1(B,A) ) ) ) )).
fof(dt_l1_topgrp_1,axiom,( ! [A] : ( l1_topgrp_1(A) => ( l3_algstr_0(A) & l1_pre_topc(A) ) ) )).
fof(dt_l1_unialg_1,axiom,( ! [A] : ( l1_unialg_1(A) => l1_struct_0(A) ) )).
fof(dt_l1_vectmetr,axiom,( ! [A] : ( l1_vectmetr(A) => ( l1_rlvect_1(A) & l1_metric_1(A) ) ) )).
fof(dt_l1_vectsp_1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_vectsp_1(B,A) => l2_algstr_0(B) ) ) )).
fof(dt_l1_vectsp_2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_vectsp_2(B,A) => l2_algstr_0(B) ) ) )).
fof(dt_l1_waybel_0,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_waybel_0(B,A) => l1_orders_2(B) ) ) )).
fof(dt_l1_waybel_9,axiom,( ! [A] : ( l1_waybel_9(A) => ( l1_pre_topc(A) & l1_orders_2(A) ) ) )).
fof(dt_l1_zmodul01,axiom,( ! [A] : ( l1_zmodul01(A) => l2_algstr_0(A) ) )).
fof(dt_l2_abcmiz_0,axiom,( ! [A] : ( l2_abcmiz_0(A) => ( l1_orders_2(A) & l1_abcmiz_0(A) ) ) )).
fof(dt_l2_algstr_0,axiom,( ! [A] : ( l2_algstr_0(A) => ( l2_struct_0(A) & l1_algstr_0(A) ) ) )).
fof(dt_l2_altcat_1,axiom,( ! [A] : ( l2_altcat_1(A) => l1_altcat_1(A) ) )).
fof(dt_l2_bcialg_1,axiom,( ! [A] : ( l2_bcialg_1(A) => ( l1_bcialg_1(A) & l2_struct_0(A) ) ) )).
fof(dt_l2_cat_4,axiom,( ! [A] : ( l2_cat_4(A) => l1_cat_1(A) ) )).
fof(dt_l2_clvect_1,axiom,( ! [A] : ( l2_clvect_1(A) => ( l1_clvect_1(A) & l2_normsp_0(A) ) ) )).
fof(dt_l2_fsm_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( l2_fsm_1(C,A,B) => l1_fsm_1(C,A) ) ) )).
fof(dt_l2_fsm_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( l2_fsm_2(C,A,B) => ( l1_fsm_2(C,A) & l3_fsm_1(C,A,B) ) ) ) )).
fof(dt_l2_fsm_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) ) => ! [C] : ( l2_fsm_3(C,A,B) => l1_fsm_3(C,A,B) ) ) )).
fof(dt_l2_functor0,axiom,( ! [A] : ! [B] : ( ( l1_altcat_1(A) & l1_altcat_1(B) ) => ! [C] : ( l2_functor0(C,A,B) => l1_functor0(C,A,B) ) ) )).
fof(dt_l2_incsp_1,axiom,( ! [A] : ( l2_incsp_1(A) => l1_incsp_1(A) ) )).
fof(dt_l2_lang1,axiom,( ! [A] : ( l2_lang1(A) => l1_lang1(A) ) )).
fof(dt_l2_lattices,axiom,( ! [A] : ( l2_lattices(A) => l1_struct_0(A) ) )).
fof(dt_l2_modelc_1,axiom,( ! [A] : ( l2_modelc_1(A) => l3_robbins1(A) ) )).
fof(dt_l2_modelc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( l2_modelc_3(B,A) => l1_struct_0(B) ) ) )).
fof(dt_l2_normsp_0,axiom,( ! [A] : ( l2_normsp_0(A) => ( l1_normsp_0(A) & l2_struct_0(A) ) ) )).
fof(dt_l2_osalg_1,axiom,( ! [A] : ( l2_osalg_1(A) => ( l1_msualg_1(A) & l1_orders_2(A) ) ) )).
fof(dt_l2_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ( l1_orders_2(A) & l1_pcs_0(A) ) ) )).
fof(dt_l2_prelamb,axiom,( ! [A] : ( l2_prelamb(A) => l1_prelamb(A) ) )).
fof(dt_l2_qmax_1,axiom,( ! [A] : ( l2_qmax_1(A) => ( l1_orders_2(A) & l1_robbins1(A) ) ) )).
fof(dt_l2_quantal1,axiom,( ! [A] : ( l2_quantal1(A) => ( l1_quantal1(A) & l4_algstr_0(A) ) ) )).
fof(dt_l2_robbins1,axiom,( ! [A] : ( l2_robbins1(A) => ( l2_lattices(A) & l1_robbins1(A) ) ) )).
fof(dt_l2_robbins3,axiom,( ! [A] : ( l2_robbins3(A) => ( l1_lattices(A) & l1_orders_2(A) ) ) )).
fof(dt_l2_struct_0,axiom,( ! [A] : ( l2_struct_0(A) => l1_struct_0(A) ) )).
fof(dt_l2_vectsp_2,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & l1_struct_0(B) ) => ! [C] : ( l2_vectsp_2(C,A,B) => ( l1_vectsp_1(C,A) & l1_vectsp_2(C,B) ) ) ) )).
fof(dt_l3_abcmiz_0,axiom,( ! [A] : ( l3_abcmiz_0(A) => l2_abcmiz_0(A) ) )).
fof(dt_l3_algstr_0,axiom,( ! [A] : ( l3_algstr_0(A) => l1_struct_0(A) ) )).
fof(dt_l3_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & m1_msafree(C,A,B) ) => ! [D] : ( l3_aofa_a00(D,A,B,C) => l1_unialg_1(D) ) ) )).
fof(dt_l3_fsm_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( l3_fsm_1(C,A,B) => l1_fsm_1(C,A) ) ) )).
fof(dt_l3_lattices,axiom,( ! [A] : ( l3_lattices(A) => ( l1_lattices(A) & l2_lattices(A) ) ) )).
fof(dt_l3_msualg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => l2_msualg_1(B,A) ) ) )).
fof(dt_l3_osalg_1,axiom,( ! [A] : ( l3_osalg_1(A) => ( l1_osalg_1(A) & l2_osalg_1(A) ) ) )).
fof(dt_l3_quantal1,axiom,( ! [A] : ( l3_quantal1(A) => l2_quantal1(A) ) )).
fof(dt_l3_robbins1,axiom,( ! [A] : ( l3_robbins1(A) => ( l1_lattices(A) & l1_robbins1(A) ) ) )).
fof(dt_l3_robbins3,axiom,( ! [A] : ( l3_robbins3(A) => ( l2_robbins3(A) & l1_robbins3(A) & l3_lattices(A) ) ) )).
fof(dt_l3_sheffer1,axiom,( ! [A] : ( l3_sheffer1(A) => ( l1_sheffer1(A) & l4_robbins1(A) ) ) )).
fof(dt_l3_struct_0,axiom,( ! [A] : ( l3_struct_0(A) => l1_struct_0(A) ) )).
fof(dt_l4_algstr_0,axiom,( ! [A] : ( l4_algstr_0(A) => ( l3_struct_0(A) & l3_algstr_0(A) ) ) )).
fof(dt_l4_robbins1,axiom,( ! [A] : ( l4_robbins1(A) => ( l2_robbins1(A) & l3_lattices(A) ) ) )).
fof(dt_l4_robbins3,axiom,( ! [A] : ( l4_robbins3(A) => ( l3_robbins3(A) & l4_robbins1(A) & l2_qmax_1(A) ) ) )).
fof(dt_l4_struct_0,axiom,( ! [A] : ( l4_struct_0(A) => ( l2_struct_0(A) & l3_struct_0(A) ) ) )).
fof(dt_l5_algstr_0,axiom,( ! [A] : ( l5_algstr_0(A) => ( l4_algstr_0(A) & l4_struct_0(A) ) ) )).
fof(dt_l5_aofa_a00,axiom,( ! [A] : ( l5_aofa_a00(A) => l1_msualg_1(A) ) )).
fof(dt_l5_struct_0,axiom,( ! [A] : ( l5_struct_0(A) => l1_struct_0(A) ) )).
fof(dt_l6_algstr_0,axiom,( ! [A] : ( l6_algstr_0(A) => ( l2_algstr_0(A) & l5_algstr_0(A) ) ) )).
fof(dt_l6_aofa_a00,axiom,( ! [A] : ( l6_aofa_a00(A) => l5_aofa_a00(A) ) )).
fof(dt_m1_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( m1_abcmiz_1(C,A,B) => m1_subset_1(C,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) ) ) )).
fof(dt_m1_abcmiz_a,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_abcmiz_a(C,A,B) => m1_subset_1(C,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) ) ) )).
fof(dt_m1_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( 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)))) ) ) ) )).
fof(dt_m1_algspec1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( m1_algspec1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) )).
fof(dt_m1_algstr_4,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( m1_algstr_4(B,A) => l3_algstr_0(B) ) ) )).
fof(dt_m1_altcat_2,axiom,( ! [A] : ( l2_altcat_1(A) => ! [B] : ( m1_altcat_2(B,A) => l2_altcat_1(B) ) ) )).
fof(dt_m1_altcat_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) & m1_subset_1(B,u1_struct_0(A)) & 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] : ( m1_altcat_5(E,A,B,C,D) => ( v1_relat_1(E) & v4_relat_1(E,C) & v1_funct_1(E) & v1_partfun1(E,C) ) ) ) )).
fof(dt_m1_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( 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))) ) ) ) )).
fof(dt_m1_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m1_aofa_a00(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) ) ) ) )).
fof(dt_m1_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ( m1_aofa_i00(E,A,B,C,D) => m1_subset_1(E,A) ) ) )).
fof(dt_m1_armstrng,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) ) => ! [C] : ( m1_armstrng(C,A,B) => m1_subset_1(C,k4_armstrng(A)) ) ) )).
fof(dt_m1_autalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( m1_autalg_1(D,A,B,C) => m2_pboole(D,A,B,B) ) ) )).
fof(dt_m1_bcialg_1,axiom,( ! [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] : ( 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) ) ) ) )).
fof(dt_m1_bcialg_2,axiom,( ! [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] : ( 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)))) ) ) ) )).
fof(dt_m1_bcialg_3,axiom,( ! [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] : ( m1_bcialg_3(B,A) => ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).
fof(dt_m1_bcialg_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => ! [E] : ( 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) ) ) ) )).
fof(dt_m1_bciideal,axiom,( ! [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] : ( m1_bciideal(B,A) => ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).
fof(dt_m1_bhsp_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_bhsp_5(B,A) => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_m1_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree1(A) ) => ! [B] : ( m1_bintree2(B,A) => m2_finseq_1(B,k6_margrel1) ) ) )).
fof(dt_m1_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_borsuk_1(B,A) => ( ~ v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) ) ) ) )).
fof(dt_m1_borsuk_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ! [D] : ( 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)))) ) ) ) )).
fof(dt_m1_borsuk_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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] : ( 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)))) ) ) ) )).
fof(dt_m1_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_eqrel_1(B,A) ) => ! [C] : ( m1_bvfunc_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(A)) ) ) )).
fof(dt_m1_c0sp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(dt_m1_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_card_fil(B,A) => ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ) )).
fof(dt_m1_card_lar,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( m1_card_lar(C,A,B) => m1_subset_1(C,k1_zfmisc_1(A)) ) ) )).
fof(dt_m1_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_cat_1(D,A,B,C) => m1_subset_1(D,u4_struct_0(A)) ) ) )).
fof(dt_m1_cat_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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] : ( m1_cat_2(C,A,B) => ~ v1_xboole_0(C) ) ) )).
fof(dt_m1_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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] : ( 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)))) ) ) ) )).
fof(dt_m1_cat_5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_cat_5(A) ) => ! [B] : ( 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) ) ) ) )).
fof(dt_m1_catalan2,axiom,( ! [A] : ! [B] : ( m1_catalan2(B,A) => ( v4_funct_1(B) & ~ v1_xboole_0(B) ) ) )).
fof(dt_m1_catalg_1,axiom,( ! [A] : ! [B] : ( m1_catalg_1(B,A) => ( v1_instalg1(B) & l1_msualg_1(B) ) ) )).
fof(dt_m1_cc0sp1,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(dt_m1_cfdiff_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( m1_cfdiff_1(B,A) => m1_subset_1(B,k1_zfmisc_1(k2_numbers)) ) ) )).
fof(dt_m1_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( 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)))) ) ) ) )).
fof(dt_m1_chord,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [C] : ( m1_chord(C,A,B) => m1_glib_000(C,A) ) ) )).
fof(dt_m1_circcmb3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(dt_m1_circtrm1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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] : ( m1_circtrm1(F,A,B,C,D,E) => m2_pboole(F,u1_struct_0(A),B,u3_msualg_1(A,D)) ) ) )).
fof(dt_m1_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( m1_closure2(D,A,B,C) => m3_pboole(D,A,B) ) ) )).
fof(dt_m1_clvect_1,axiom,( ! [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) ) => ! [B] : ( 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) ) ) ) )).
fof(dt_m1_complfld,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,u1_struct_0(k1_complfld)) & ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_complfld(C,A,B) => m1_subset_1(C,u1_struct_0(k1_complfld)) ) ) )).
fof(dt_m1_comptrig,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( m1_comptrig(C,A,B) => v1_xcmplx_0(C) ) ) )).
fof(dt_m1_comput_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( m1_comput_1(E,A,B,C,D) => m2_rfunct_3(E,A,B,C) ) ) )).
fof(dt_m1_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( m1_conlat_1(B,A) => ~ v1_xboole_0(B) ) ) )).
fof(dt_m1_connsp_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( m1_connsp_2(C,A,B) => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_m1_connsp_3,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_connsp_3(B,A) => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_m1_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_convex4(B,A) => m2_funct_2(B,u1_struct_0(A),k2_numbers,k9_funct_2(u1_struct_0(A),k2_numbers)) ) ) )).
fof(dt_m1_decomp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_decomp_1(B,A) => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_m1_dist_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_dist_1(B,A) => ( v1_matrprob(B) & m2_finseq_1(B,k1_numbers) ) ) ) )).
fof(dt_m1_dist_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & m1_subset_1(B,k6_dist_1(A)) ) => ! [C] : ( m1_dist_2(C,A,B) => m2_finseq_1(C,A) ) ) )).
fof(dt_m1_dtconstr,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_dtconstr(D,A,B,C) => m1_subset_1(D,B) ) ) )).
fof(dt_m1_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_dynkin(B,A) => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ) )).
fof(dt_m1_ec_pf_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_ec_pf_1(B,A) => ( ~ 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) ) ) ) )).
fof(dt_m1_eqrel_1,axiom,( ! [A] : ! [B] : ( m1_eqrel_1(B,A) => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) )).
fof(dt_m1_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_exchsort(A) ) => ! [B] : ( m1_exchsort(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_exchsort(B) ) ) ) )).
fof(dt_m1_extpro_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & ~ v2_compos_1(C,B) ) => ! [D] : ( 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) ) ) ) )).
fof(dt_m1_filter_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_relat_1(B) ) => ! [C] : ( 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))) ) ) ) )).
fof(dt_m1_finance1,axiom,( ! [A] : ( m1_finance1(A) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) )).
fof(dt_m1_finseq_1,axiom,( ! [A] : ! [B] : ( m1_finseq_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) )).
fof(dt_m1_fintopo6,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_fintopo6(B,A) => l1_orders_2(B) ) ) )).
fof(dt_m1_fomodel0,axiom,( ! [A] : ! [B] : ( m1_fomodel0(B,A) => m2_finseq_2(B,A,k3_finseq_2(A)) ) )).
fof(dt_m1_freealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_freealg(B,A) => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_m1_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_funct_2(C,A,B) => ~ v1_xboole_0(C) ) )).
fof(dt_m1_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ( m1_funct_7(C,A,B) => ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v1_funct_7(C) ) ) )).
fof(dt_m1_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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] : ( 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) ) ) ) )).
fof(dt_m1_functor2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(dt_m1_functor3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( m1_functor3(E,A,B,C,D) => m2_functor2(E,A,B,C,D) ) ) )).
fof(dt_m1_fvaluat1,axiom,( ! [A] : ( l6_algstr_0(A) => ! [B] : ( m1_fvaluat1(B,A) => ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k6_numbers) & v2_fvaluat1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k6_numbers))) ) ) ) )).
fof(dt_m1_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v4_vectsp_1(A) & l4_algstr_0(A) ) => ! [B] : ( m1_gcd_1(B,A) => ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).
fof(dt_m1_genealg1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_genealg1(B,A) => m2_finseq_1(B,k3_card_3(A)) ) ) )).
fof(dt_m1_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) ) ) )).
fof(dt_m1_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_001(B,A) => m2_finseq_1(B,k6_glib_000(A)) ) ) )).
fof(dt_m1_glib_005,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( 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(k4_ordinal1,1),k7_glib_000(A))))) ) ) ) )).
fof(dt_m1_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ) )).
fof(dt_m1_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ! [D] : ( m1_graph_3(D,A,B,C) => m2_finseq_1(D,A) ) ) )).
fof(dt_m1_grcat_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_grcat_1(C,A,B) => ( v2_grcat_1(C) & l1_grcat_1(C) ) ) ) )).
fof(dt_m1_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ( ~ v2_struct_0(B) & v2_group_1(B) & l3_algstr_0(B) ) ) ) )).
fof(dt_m1_group_6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) & m1_group_2(B,A) ) => ! [C] : ( m1_group_6(C,A,B) => m1_group_2(C,A) ) ) )).
fof(dt_m1_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(dt_m1_hallmar1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( m1_hallmar1(D,A,B,C) => m2_finseq_1(D,k1_zfmisc_1(A)) ) ) )).
fof(dt_m1_henmodel,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & v1_henmodel(B,A) & m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) ) => ! [C] : ( m1_henmodel(C,A,B) => m1_valuat_1(C,A,k1_henmodel(A)) ) ) )).
fof(dt_m1_hilbert3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( m1_hilbert3(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) )).
fof(dt_m1_ideal_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_ideal_1(C,A,B) => m2_finseq_1(C,u1_struct_0(A)) ) ) )).
fof(dt_m1_incproj,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_incproj(B,A) => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_m1_instalg1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_instalg1(B,A) => l1_msualg_1(B) ) ) )).
fof(dt_m1_int_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_int_3(A) & l6_algstr_0(A) ) => ! [B] : ( m1_int_3(B,A) => ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_ordinal1))) ) ) ) )).
fof(dt_m1_int_6,axiom,( ! [A] : ( ( 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] : ( m1_int_6(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ) )).
fof(dt_m1_integr15,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_integr15(D,A,B,C) => m2_finseq_1(D,k1_numbers) ) ) )).
fof(dt_m1_integr16,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_integr16(D,A,B,C) => m2_finseq_1(D,k2_numbers) ) ) )).
fof(dt_m1_integr18,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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] : ( m1_integr18(E,A,B,C,D) => m2_finseq_1(E,u1_struct_0(A)) ) ) )).
fof(dt_m1_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ( ~ v1_xboole_0(B) & v5_valued_0(B) & m2_finseq_1(B,k1_numbers) ) ) ) )).
fof(dt_m1_interva1,axiom,( ! [A] : ! [B] : ( m1_interva1(B,A) => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) )).
fof(dt_m1_isocat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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] : ( m1_isocat_1(C,A,B) => m2_cat_1(C,A,B) ) ) )).
fof(dt_m1_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_jordan_a(B,A) => m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) ) )).
fof(dt_m1_kolmog01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( 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)))) ) ) ) )).
fof(dt_m1_lattice4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) & ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( 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)))) ) ) ) )).
fof(dt_m1_lattice5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(dt_m1_lattice7,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( 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))) ) ) ) )).
fof(dt_m1_lattice8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_lattice8(D,A,B,C) => ( v1_relat_1(D) & v1_funct_1(D) ) ) ) )).
fof(dt_m1_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_lexbfs(B,A) => ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) ) ) )).
fof(dt_m1_lmod_7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : ( m1_lmod_7(C,A,B) => ~ v1_xboole_0(C) ) ) )).
fof(dt_m1_margrel1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_margrel1(B,A) => ( v3_finseq_1(B) & v2_card_3(B) ) ) ) )).
fof(dt_m1_matrix_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_matrix_2(A) ) => ! [B] : ( m1_matrix_2(B,A) => ( v1_funct_1(B) & v1_funct_2(B,k2_finseq_1(k2_matrix_2(A)),k2_finseq_1(k2_matrix_2(A))) & v3_funct_2(B,k2_finseq_1(k2_matrix_2(A)),k2_finseq_1(k2_matrix_2(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(k2_matrix_2(A)),k2_finseq_1(k2_matrix_2(A))))) ) ) ) )).
fof(dt_m1_matrixj2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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] : ( m1_matrixj2(C,A,B) => ( v1_matrixj2(C,A) & m2_finseq_1(C,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) ) ) )).
fof(dt_m1_matrlin,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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] : ( m1_matrlin(C,A,B) => m2_finseq_1(C,u1_struct_0(B)) ) ) )).
fof(dt_m1_matroid0,axiom,( ! [A] : ( ( ~ v3_pencil_1(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_matroid0(B,A) => ( v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).
fof(dt_m1_measure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_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,k6_numbers))) ) => ! [D] : ( m1_measure1(D,A,B,C) => m2_subset_1(D,k1_zfmisc_1(A),B) ) ) )).
fof(dt_m1_measure2,axiom,( ! [A] : ! [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))) ) => ! [C] : ( m1_measure2(C,A,B) => ( ~ v1_xboole_0(C) & v4_card_3(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ) )).
fof(dt_m1_measure3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m1_measure3(D,A,B,C) => m1_subset_1(D,k1_zfmisc_1(A)) ) ) )).
fof(dt_m1_measure4,axiom,( ! [A] : ! [B] : ( m1_measure4(B,A) => ( v1_funct_1(B) & v1_funct_2(B,k9_setfam_1(A),k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k6_numbers))) ) ) )).
fof(dt_m1_measure7,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( m1_measure7(B,A) => ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k1_numbers)))) ) ) ) )).
fof(dt_m1_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( m1_metric_2(B,A) => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_m1_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( 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)))) ) ) ) )).
fof(dt_m1_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_midsp_3(B,A) => m1_subset_1(B,k4_ordinal1) ) ) )).
fof(dt_m1_mod_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : ( m1_mod_2(D,A,B,C) => ( v3_mod_2(D,A) & l1_mod_2(D,A) ) ) ) )).
fof(dt_m1_mod_3,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_mod_3(C,A,B) => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) ) )).
fof(dt_m1_mod_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : ( 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)))) ) ) ) )).
fof(dt_m1_modcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_modcat_1(B,A) => ~ v1_xboole_0(B) ) ) )).
fof(dt_m1_modelc_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m1_modelc_1(C,A,B) => ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) ) ) )).
fof(dt_m1_monoid_0,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( m1_monoid_0(B,A) => l4_algstr_0(B) ) ) )).
fof(dt_m1_msafree,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msafree(C,A,B) => m3_pboole(C,u1_struct_0(A),u3_msualg_1(A,B)) ) ) )).
fof(dt_m1_msafree2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(dt_m1_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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,k10_xtuple_0(B)) ) => ! [D] : ( m1_msafree4(D,A,B,C) => m1_subset_1(D,k3_card_3(B)) ) ) )).
fof(dt_m1_msalimit,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_msalimit(C,A,B) => m1_pralg_2(C,u1_struct_0(A),B) ) ) )).
fof(dt_m1_msaterm,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_msaterm(D,A,B,C) => m1_trees_4(D,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) ) ) )).
fof(dt_m1_msualg_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msualg_2(C,A,B) => l3_msualg_1(C,A) ) ) )).
fof(dt_m1_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( m1_msualg_4(D,A,B,C) => ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) ) ) )).
fof(dt_m1_msualg_6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msualg_6(C,A,B) => m2_pboole(C,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,B)) ) ) )).
fof(dt_m1_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_mycielsk(B,A) => ( v1_orders_2(B) & l1_orders_2(B) ) ) ) )).
fof(dt_m1_nattra_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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] : ( 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)))) ) ) ) )).
fof(dt_m1_ncfcont1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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] : ( m1_ncfcont1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_m1_nfcont_1,axiom,( ! [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) & 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] : ( m1_nfcont_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_m1_oppcat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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] : ( 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)))) ) ) ) )).
fof(dt_m1_orders_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( m1_orders_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) )).
fof(dt_m1_orders_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_orders_2(C,A,B) => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_m1_orders_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_orders_3(A) ) => ! [B] : ( 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) ) ) ) )).
fof(dt_m1_osafree,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_osafree(C,A,B) => m3_pboole(C,u1_struct_0(A),u3_msualg_1(A,B)) ) ) )).
fof(dt_m1_osalg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_osalg_1(C,A,B) => m1_subset_1(C,u4_struct_0(A)) ) ) )).
fof(dt_m1_osalg_4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_osalg_4(C,A,B) => m1_msualg_4(C,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,B)) ) ) )).
fof(dt_m1_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_pboole(C,A,B) => ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) ) ) )).
fof(dt_m1_pencil_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_pencil_2(C,A,B) => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_pencil_1(A,B)))) ) ) )).
fof(dt_m1_petri,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_petri(D,A,B,C) => m1_subset_1(D,k2_zfmisc_1(A,B)) ) ) )).
fof(dt_m1_petri_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(A) => ! [C] : ( m1_petri_2(C,A,B) => ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,A))) ) ) ) )).
fof(dt_m1_polyalg1,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & l1_polyalg1(B,A) ) => ! [C] : ( m1_polyalg1(C,A,B) => l1_polyalg1(C,A) ) ) )).
fof(dt_m1_pralg_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) ) ) )).
fof(dt_m1_pre_poly,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k5_finsub_1(A))) ) => ! [C] : ( m1_pre_poly(C,A,B) => m1_subset_1(C,k1_zfmisc_1(A)) ) ) )).
fof(dt_m1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => l1_pre_topc(B) ) ) )).
fof(dt_m1_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_prelamb(A) ) => ! [B] : ( 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)),k4_ordinal1)) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) ) ) ) )).
fof(dt_m1_prob_1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(A)) ) ) )).
fof(dt_m1_prob_3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( m1_prob_3(C,A,B) => m2_finseq_1(C,k9_setfam_1(A)) ) ) )).
fof(dt_m1_prob_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_prob_4(D,A,B,C) => m1_subset_1(D,k1_zfmisc_1(A)) ) ) )).
fof(dt_m1_projred2,axiom,( ! [A] : ( ( 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] : ( 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)))) ) ) ) )).
fof(dt_m1_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) ) => ! [B] : ( m1_prvect_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) )).
fof(dt_m1_prvect_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [C] : ( m1_prvect_2(C,A,B) => ( v1_relat_1(C) & v1_funct_1(C) ) ) ) )).
fof(dt_m1_pua2mss1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k4_partfun1(A,B))) ) => ! [D] : ( m1_pua2mss1(D,A,B,C) => ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ) ) )).
fof(dt_m1_pythtrip,axiom,( ! [A] : ( m1_pythtrip(A) => m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) ) )).
fof(dt_m1_qc_lang4,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k9_qc_lang1(A)) ) => ! [C] : ( m1_qc_lang4(C,A,B) => m1_subset_1(C,k9_qc_lang1(A)) ) ) )).
fof(dt_m1_random_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( 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))) ) ) ) )).
fof(dt_m1_rcomp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_rcomp_1(B,A) => m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) ) )).
fof(dt_m1_rcomp_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( m1_rcomp_3(D,A,B,C) => m2_finseq_1(D,k9_setfam_1(k1_numbers)) ) ) )).
fof(dt_m1_realset1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_realset1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(A)) ) ) )).
fof(dt_m1_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( m1_rewrite1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ) )).
fof(dt_m1_ringcat1,axiom,( ! [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) & 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] : ( m1_ringcat1(C,A,B) => ( v2_ringcat1(C) & v3_ringcat1(C) & l1_ringcat1(C) ) ) ) )).
fof(dt_m1_rlaffin3,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_rlaffin3(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finseq_1(B) ) ) ) )).
fof(dt_m1_rlsub_1,axiom,( ! [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) ) => ! [B] : ( 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) ) ) ) )).
fof(dt_m1_rlsub_2,axiom,( ! [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) & v8_rlvect_1(A) & l1_rlvect_1(A) & m1_rlsub_1(B,A) ) => ! [C] : ( m1_rlsub_2(C,A,B) => m1_rlsub_1(C,A) ) ) )).
fof(dt_m1_rlvect_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( m1_rlvect_2(B,A) => m2_funct_2(B,u1_struct_0(A),k1_numbers,k9_funct_2(u1_struct_0(A),k1_numbers)) ) ) )).
fof(dt_m1_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_3(B,A) => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_m1_rmod_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : ( 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) ) ) ) )).
fof(dt_m1_rmod_4,axiom,( ! [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) & 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] : ( 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))) ) ) )).
fof(dt_m1_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(dt_m1_rusub_2,axiom,( ! [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) & v8_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) & m1_rusub_1(B,A) ) => ! [C] : ( m1_rusub_2(C,A,B) => m1_rusub_1(C,A) ) ) )).
fof(dt_m1_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_3(B,A) => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_m1_scm_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ! [B] : ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(B,u1_struct_0(k1_ami_3)) ) ) ) )).
fof(dt_m1_scmfsa_2,axiom,( ! [A] : ( m1_scmfsa_2(A) => m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) )).
fof(dt_m1_scmyciel,axiom,( ! [A] : ! [B] : ( m1_scmyciel(B,A) => v4_scmyciel(B) ) )).
fof(dt_m1_sgraph1,axiom,( ! [A] : ! [B] : ( m1_sgraph1(B,A) => ( v1_sgraph1(B) & l1_sgraph1(B) ) ) )).
fof(dt_m1_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => l1_pre_topc(B) ) )).
fof(dt_m1_simplex1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) & m1_simplex0(B,u1_struct_0(A)) ) => ! [C] : ( m1_simplex1(C,A,B) => m1_simplex0(C,u1_struct_0(A)) ) ) )).
fof(dt_m1_simplex2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_simplex2(C,A,B) => ( v1_xreal_0(C) & v2_xxreal_0(C) ) ) ) )).
fof(dt_m1_stacks_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_relat_1(C) ) => ! [D] : ( 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))) ) ) ) )).
fof(dt_m1_substut1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k2_zfmisc_1(k16_substut1(A),k3_qc_lang1(A))) ) => ! [C] : ( m1_substut1(C,A,B) => m1_subset_1(C,k1_substut1(A)) ) ) )).
fof(dt_m1_substut2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k9_qc_lang1(A)) & m1_subset_1(C,k9_qc_lang1(A)) ) => ! [D] : ( m1_substut2(D,A,B,C) => ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) ) ) )).
fof(dt_m1_supinf_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_card_3(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( m1_supinf_2(B,A) => ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) ) ) )).
fof(dt_m1_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_taxonom1(B,A) => m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) ) ) )).
fof(dt_m1_taxonom2,axiom,( ! [A] : ! [B] : ( m1_taxonom2(B,A) => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) )).
fof(dt_m1_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(dt_m1_topgrp_1,axiom,( ! [A] : ! [B] : ( ( l1_pre_topc(A) & l1_pre_topc(B) ) => ! [C] : ( 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)))) ) ) ) )).
fof(dt_m1_topmetr,axiom,( ! [A] : ( ( v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_topmetr(B,A) => ( v6_metric_1(B) & v7_metric_1(B) & v8_metric_1(B) & v9_metric_1(B) & l1_metric_1(B) ) ) ) )).
fof(dt_m1_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => m2_finseq_1(B,k4_ordinal1) ) ) )).
fof(dt_m1_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_2(B,A) => m1_subset_1(B,k1_zfmisc_1(A)) ) ) )).
fof(dt_m1_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_trees_3(B,A) => ~ v1_xboole_0(B) ) ) )).
fof(dt_m1_trees_4,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_trees_4(C,A,B) => m2_finseq_1(C,A) ) ) )).
fof(dt_m1_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(dt_m1_urysohn3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) & v7_ordinal1(D) ) => ! [E] : ( 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))))) ) ) ) )).
fof(dt_m1_valuat_1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & ~ v1_xboole_0(B) ) => ! [C] : ( 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)))) ) ) ) )).
fof(dt_m1_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( m1_valued_0(B,A) => ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) ) ) )).
fof(dt_m1_vectsp11,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_vectsp11(D,A,B,C) => m1_subset_1(D,u1_struct_0(A)) ) ) )).
fof(dt_m1_vectsp_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : ( 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) ) ) ) )).
fof(dt_m1_vectsp_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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] : ( m1_vectsp_5(D,A,B,C) => m1_vectsp_4(D,A,B) ) ) )).
fof(dt_m1_vectsp_6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) & ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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))) ) ) )).
fof(dt_m1_vectsp_7,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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] : ( m1_vectsp_7(C,A,B) => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) ) )).
fof(dt_m1_waybel12,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_waybel12(C,A,B) => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_m1_waybel16,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( 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)))) ) ) ) )).
fof(dt_m1_waybel21,axiom,( ! [A] : ! [B] : ( ( 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] : ( 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)))) ) ) ) )).
fof(dt_m1_waybel23,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v3_waybel_3(A) & l1_orders_2(A) ) => ! [B] : ( m1_waybel23(B,A) => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_m1_waybel35,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ( m1_waybel35(C,A,B) => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_m1_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m1_xxreal_2(B,A) => v1_xxreal_0(B) ) ) )).
fof(dt_m1_yellow13,axiom,( ! [A] : ! [B] : ( ( l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( m1_yellow13(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) )).
fof(dt_m1_yellow19,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) & ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_yellow19(C,A,B) => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_m1_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_yellow_0(B,A) => l1_orders_2(B) ) ) )).
fof(dt_m1_yellow_6,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & l1_waybel_0(B,A) ) => ! [C] : ( m1_yellow_6(C,A,B) => l1_waybel_0(C,A) ) ) )).
fof(dt_m1_yellow_9,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_yellow_9(B,A) => l1_waybel_9(B) ) ) )).
fof(dt_m1_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(dt_m1_zmodul02,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( m1_zmodul02(B,A) => m2_funct_2(B,u1_struct_0(A),k4_numbers,k9_funct_2(u1_struct_0(A),k4_numbers)) ) ) )).
fof(dt_m1_zmodul03,axiom,( ! [A] : ( ( ~ 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) & v1_zmodul03(A) & l1_zmodul01(A) ) => ! [B] : ( m1_zmodul03(B,A) => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_m2_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( m2_abcmiz_1(C,A,B) => m1_subset_1(C,u4_struct_0(A)) ) ) )).
fof(dt_m2_abcmiz_a,axiom,( ! [A] : ( m1_subset_1(A,k4_abcmiz_1) => ! [B] : ( 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))) ) ) ) )).
fof(dt_m2_algspec1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( m2_algspec1(B,A) => ( v1_instalg1(B) & l1_msualg_1(B) ) ) ) )).
fof(dt_m2_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) => ! [E] : ( m2_aofa_a00(E,A,B,C,D) => m1_aofa_a00(E,A,B,C) ) ) )).
fof(dt_m2_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( 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))) ) ) ) )).
fof(dt_m2_bcialg_1,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).
fof(dt_m2_bcialg_2,axiom,( ! [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] : ( 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)))) ) ) ) )).
fof(dt_m2_bciideal,axiom,( ! [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] : ( m2_bciideal(B,A) => ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).
fof(dt_m2_bhsp_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m2_bhsp_5(B,A) => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_m2_c0sp1,axiom,( ! [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) & v2_funcsdom(A) & v3_group_1(A) & v5_group_1(A) & v1_vectsp_1(A) & v3_vectsp_1(A) & l1_funcsdom(A) ) => ! [B] : ( 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) ) ) ) )).
fof(dt_m2_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_card_fil(B,A) => ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ) )).
fof(dt_m2_cat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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] : ( 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)))) ) ) ) )).
fof(dt_m2_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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] : ( 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)))) ) ) ) )).
fof(dt_m2_chain_1,axiom,( ! [A] : ( ( ~ v1_zfmisc_1(A) & v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m2_chain_1(B,A) => m1_subset_1(B,k2_zfmisc_1(k1_numbers,k1_numbers)) ) ) )).
fof(dt_m2_chord,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m2_chord(D,A,B,C) => m1_subset_1(D,k1_zfmisc_1(k6_glib_000(A))) ) ) )).
fof(dt_m2_circcmb3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & m1_circcmb3(B,A) ) => ! [C] : ( m2_circcmb3(C,A,B) => ( v4_msafree2(C,B) & l3_msualg_1(C,B) ) ) ) )).
fof(dt_m2_circtrm1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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] : ( m2_circtrm1(G,A,B,C,D,E,F) => ( v1_relat_1(G) & v1_funct_1(G) & v2_funct_1(G) ) ) ) )).
fof(dt_m2_clvect_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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] : ( m2_clvect_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_m2_conlat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) & m1_conlat_1(B,A) ) => ! [C] : ( m2_conlat_1(C,A,B) => ( ~ v4_conlat_1(C,A) & v6_conlat_1(C,A) & l2_conlat_1(C,A) ) ) ) )).
fof(dt_m2_connsp_2,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_connsp_2(C,A,B) => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_m2_convex4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_convex4(C,A,B) => m1_convex4(C,A) ) ) )).
fof(dt_m2_dtconstr,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_dtconstr(A) & v3_dtconstr(A) & l1_lang1(A) & m1_subset_1(B,k7_dtconstr(A)) ) => ! [C] : ( m2_dtconstr(C,A,B) => m1_trees_4(C,k5_trees_3(u1_struct_0(A)),k4_dtconstr(A)) ) ) )).
fof(dt_m2_exchsort,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m2_exchsort(C,A,B) => ( v1_relat_1(C) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_exchsort(C) ) ) ) )).
fof(dt_m2_filter_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_relat_1(B) ) => ! [C] : ( 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))) ) ) ) )).
fof(dt_m2_finseq_1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ( v1_funct_1(B) & v1_finseq_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) ) )).
fof(dt_m2_finseq_2,axiom,( ! [A] : ! [B] : ( m1_finseq_2(B,A) => ! [C] : ( m2_finseq_2(C,A,B) => m2_finseq_1(C,A) ) ) )).
fof(dt_m2_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( 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)))) ) ) ) )).
fof(dt_m2_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & m1_funct_2(C,A,B) ) => ! [D] : ( 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))) ) ) ) )).
fof(dt_m2_funct_7,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_funct_7(B,A) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ) )).
fof(dt_m2_functor0,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m2_functor0(C,A,B) => l2_functor0(C,A,B) ) ) )).
fof(dt_m2_functor2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( m2_functor2(E,A,B,C,D) => m1_functor2(E,A,B,C,D) ) ) )).
fof(dt_m2_fvaluat1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : ( m2_fvaluat1(C,A,B) => m1_rmod_2(C,A,k4_vectsp_2(A)) ) ) )).
fof(dt_m2_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v4_vectsp_1(A) & l4_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).
fof(dt_m2_glib_000,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [D] : ( m2_glib_000(D,A,B,C) => m1_glib_000(D,A) ) ) )).
fof(dt_m2_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m2_glib_001(B,A) => m2_finseq_1(B,k7_glib_000(A)) ) ) )).
fof(dt_m2_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( m2_glib_004(B,A) => ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) ) ) )).
fof(dt_m2_glib_005,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m2_glib_005(C,A,B) => ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) ) ) )).
fof(dt_m2_goedcpuc,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & v7_ordinal1(B) ) => ! [C] : ( m2_goedcpuc(C,A,B) => ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,k1_nat_1(B,1)) & v1_finseq_1(C) ) ) ) )).
fof(dt_m2_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_graph_1(B,A) => m2_finseq_1(B,u4_struct_0(A)) ) ) )).
fof(dt_m2_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_grcat_1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(dt_m2_hallmar1,axiom,( ! [A] : ! [B] : ( m1_finseq_1(B,k1_zfmisc_1(A)) => ! [C] : ( m2_hallmar1(C,A,B) => m2_finseq_1(C,k1_zfmisc_1(A)) ) ) )).
fof(dt_m2_ideal_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_ideal_1(C,A,B) => m2_finseq_1(C,u1_struct_0(A)) ) ) )).
fof(dt_m2_index_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(dt_m2_integr15,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,k1_integra1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) ) => ! [D] : ( m2_integr15(D,A,B,C) => ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k3_finseq_2(k1_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k3_finseq_2(k1_numbers)))) ) ) ) )).
fof(dt_m2_integr18,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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,k4_ordinal1,k1_integra1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(B)))) ) => ! [E] : ( m2_integr18(E,A,B,C,D) => ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k3_finseq_2(u1_struct_0(A))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k3_finseq_2(u1_struct_0(A))))) ) ) ) )).
fof(dt_m2_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( 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)))) ) ) )).
fof(dt_m2_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m2_lattice4(B,A) => ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).
fof(dt_m2_lattice5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m2_lattice5(D,A,B,C) => ( v1_relat_1(D) & v1_funct_1(D) ) ) ) )).
fof(dt_m2_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m2_lexbfs(B,A) => ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) ) ) )).
fof(dt_m2_lmod_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : ( m2_lmod_7(D,A,B,C) => ( v7_vectsp_1(D,A) & m1_vectsp_4(D,A,B) ) ) ) )).
fof(dt_m2_ltlaxio4,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_ltlaxio4(C,A,B) => ( v2_funct_1(C) & m2_finseq_1(C,A) ) ) ) )).
fof(dt_m2_margrel1,axiom,( ! [A] : ! [B] : ( m2_margrel1(B,A) => ( v3_finseq_1(B) & v2_card_3(B) ) ) )).
fof(dt_m2_measure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m2_measure1(D,A,B,C) => m2_subset_1(D,k1_zfmisc_1(A),B) ) ) )).
fof(dt_m2_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k9_setfam_1(k1_numbers)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k1_numbers)))) ) => ! [B] : ( m2_measure7(B,A) => ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_funct_2(k4_ordinal1,k9_setfam_1(k1_numbers))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_funct_2(k4_ordinal1,k9_setfam_1(k1_numbers))))) ) ) ) )).
fof(dt_m2_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m2_measure8(C,A,B) => ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) ) )).
fof(dt_m2_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_midsp_3(B,A) => ( ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_nat_1(A,2)) ) ) ) )).
fof(dt_m2_modcat_1,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) & m1_modcat_1(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(dt_m2_monoid_0,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( m2_monoid_0(B,A) => l3_algstr_0(B) ) ) )).
fof(dt_m2_msalimit,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(dt_m2_msaterm,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( 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)) ) ) )).
fof(dt_m2_msualg_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( 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)))) ) ) ) )).
fof(dt_m2_nat_lat,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m2_nat_lat(B,A) => ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) ) ) )).
fof(dt_m2_nattra_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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] : ( m2_nattra_1(E,A,B,C,D) => m1_nattra_1(E,A,B,C,D) ) ) )).
fof(dt_m2_orders_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m2_orders_1(C,A,B) => ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) ) ) )).
fof(dt_m2_orders_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) & m1_orders_1(B,k6_partfun1(k1_orders_1(u1_struct_0(A)))) ) => ! [C] : ( m2_orders_2(C,A,B) => ( v6_orders_2(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).
fof(dt_m2_osafree,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( 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))) ) ) )).
fof(dt_m2_osalg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m2_osalg_2(C,A,B) => m3_pboole(C,u1_struct_0(A),u3_msualg_1(A,B)) ) ) )).
fof(dt_m2_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( m2_pboole(D,A,B,C) => ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) ) ) )).
fof(dt_m2_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ~ v1_xboole_0(B) ) )).
fof(dt_m2_prob_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( 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))) ) ) ) )).
fof(dt_m2_prob_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m2_prob_4(D,A,B,C) => m1_prob_1(D,A,k4_prob_4(A,B,C)) ) ) )).
fof(dt_m2_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) ) => ! [B] : ( m2_prvect_1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) )).
fof(dt_m2_pua2mss1,axiom,( ! [A] : ! [B] : ( m2_pua2mss1(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) )).
fof(dt_m2_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_qc_lang1(B,A) => v1_relat_1(B) ) ) )).
fof(dt_m2_qc_lang4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k9_qc_lang1(A)) & m1_qc_lang4(C,A,B) ) => ! [D] : ( m2_qc_lang4(D,A,B,C) => m1_trees_1(D,k9_xtuple_0(k2_qc_lang4(A,B))) ) ) )).
fof(dt_m2_rcomp_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ( m2_rcomp_3(E,A,B,C,D) => m2_finseq_1(E,k1_numbers) ) ) )).
fof(dt_m2_realset1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( 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))) ) ) ) )).
fof(dt_m2_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( m2_rewrite1(B,A) => ( v1_relat_1(B) & v10_rewrite1(B) ) ) ) )).
fof(dt_m2_rfunct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(C) & m1_rfunct_3(C,A,B) ) => ! [D] : ( m2_rfunct_3(D,A,B,C) => ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ) ) )).
fof(dt_m2_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_ringcat1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(dt_m2_rlaffin3,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_rlaffin3(C,A,B) => ( v2_funct_1(C) & m2_finseq_1(C,u1_struct_0(A)) ) ) ) )).
fof(dt_m2_rlsub_1,axiom,( ! [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) & v8_rlvect_1(A) & l1_rlvect_1(A) & m1_rlsub_1(B,A) ) => ! [C] : ( m2_rlsub_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_m2_rlvect_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_rlvect_2(C,A,B) => m1_rlvect_2(C,A) ) ) )).
fof(dt_m2_rmod_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : ( m2_rmod_2(D,A,B,C) => m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) ) )).
fof(dt_m2_rmod_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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] : ( m2_rmod_4(D,A,B,C) => m1_rmod_4(D,A,B) ) ) )).
fof(dt_m2_rusub_1,axiom,( ! [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) & v8_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) & m1_rusub_1(B,A) ) => ! [C] : ( m2_rusub_1(C,A,B) => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_m2_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ! [C] : ( m2_simplex0(C,A,B) => ( v1_matroid0(C) & v3_matroid0(C) & m1_simplex0(C,A) ) ) ) )).
fof(dt_m2_subset_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) => m1_subset_1(C,A) ) ) )).
fof(dt_m2_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_taxonom1(B,A) => m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) ) ) )).
fof(dt_m2_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)))) ) ) ) )).
fof(dt_m2_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m2_trees_1(B,A) => m1_trees_1(B,A) ) ) )).
fof(dt_m2_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m2_trees_2(B,A) => m1_subset_1(B,k1_zfmisc_1(A)) ) ) )).
fof(dt_m2_trees_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_trees_3(C,A,B) => m1_trees_1(C,A) ) ) )).
fof(dt_m2_unialg_3,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m2_unialg_3(C,A,B) => m1_unialg_2(C,A) ) ) )).
fof(dt_m2_urysohn3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m2_urysohn3(D,A,B,C) => ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(k2_urysohn1,k9_setfam_1(u1_struct_0(A)))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(k2_urysohn1,k9_setfam_1(u1_struct_0(A)))))) ) ) ) )).
fof(dt_m2_valued_0,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ! [C] : ( m2_valued_0(C,A,B) => ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) ) ) )).
fof(dt_m2_vectsp11,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( m2_vectsp11(E,A,B,C,D) => m1_subset_1(E,u1_struct_0(B)) ) ) )).
fof(dt_m2_vectsp_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : ( m2_vectsp_4(D,A,B,C) => m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) ) )).
fof(dt_m2_vectsp_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m2_vectsp_6(D,A,B,C) => m1_vectsp_6(D,A,B) ) ) )).
fof(dt_m2_vectsp_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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] : ( m2_vectsp_8(D,A,B,C) => m1_vectsp_4(D,A,B) ) ) )).
fof(dt_m2_waybel21,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( 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)))) ) ) ) )).
fof(dt_m2_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( m2_xxreal_2(B,A) => v1_xxreal_0(B) ) ) )).
fof(dt_m2_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m2_yellow13(B,A) => m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) )).
fof(dt_m2_yellow_6,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m2_yellow_6(C,A,B) => ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) ) ) )).
fof(dt_m2_yellow_9,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m2_yellow_9(B,A) => ( v2_pre_topc(B) & l1_pre_topc(B) ) ) ) )).
fof(dt_m2_zmodul01,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m2_zmodul01(C,A,B) => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_m2_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_zmodul02(C,A,B) => m1_zmodul02(C,A) ) ) )).
fof(dt_m3_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( 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))) ) ) ) )).
fof(dt_m3_bcialg_2,axiom,( ! [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] : ( 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)))) ) ) ) )).
fof(dt_m3_bciideal,axiom,( ! [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] : ( m3_bciideal(B,A) => ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).
fof(dt_m3_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(dt_m3_chain_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_chain_1(B,A) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( m3_chain_1(D,A,B,C) => m1_subset_1(D,k1_zfmisc_1(k4_chain_1(A,B,C))) ) ) )).
fof(dt_m3_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m3_chord(B,A) => m2_finseq_1(B,k6_glib_000(A)) ) ) )).
fof(dt_m3_conlat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) ) => ! [C] : ( m3_conlat_1(C,A,B) => ( ~ v4_conlat_1(C,A) & v6_conlat_1(C,A) & l2_conlat_1(C,A) ) ) ) )).
fof(dt_m3_dist_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_setfam_1(B) & m1_subset_1(B,k6_dist_1(A)) ) => ! [C] : ( m3_dist_2(C,A,B) => m1_subset_1(C,A) ) ) )).
fof(dt_m3_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & ~ v1_xboole_0(B) ) => ! [C] : ( m3_fomodel2(C,A,B) => ( v1_relat_1(C) & v1_funct_1(C) ) ) ) )).
fof(dt_m3_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => m2_finseq_1(B,k2_xboole_0(k6_glib_000(A),k7_glib_000(A))) ) ) )).
fof(dt_m3_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( m3_glib_004(B,A) => ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) ) ) )).
fof(dt_m3_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_005(B,A) => ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) ) ) )).
fof(dt_m3_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m3_graph_1(B,A) => ( ~ v2_struct_0(B) & l1_graph_1(B) ) ) ) )).
fof(dt_m3_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_grcat_1(A) ) => ! [B] : ( m3_grcat_1(B,A) => ( v2_grcat_1(B) & l1_grcat_1(B) ) ) ) )).
fof(dt_m3_hallmar1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( m3_hallmar1(D,A,B,C) => m2_hallmar1(D,A,B) ) ) )).
fof(dt_m3_ideal_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m3_ideal_1(C,A,B) => m2_finseq_1(C,u1_struct_0(A)) ) ) )).
fof(dt_m3_index_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( m3_index_1(E,A,B,C,D) => ( v2_index_1(E,A,B) & m1_index_1(E,A,B) ) ) ) )).
fof(dt_m3_integr15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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] : ( m3_integr15(E,A,B,C,D) => m2_finseq_1(E,k1_euclid(A)) ) ) )).
fof(dt_m3_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_lexbfs(B,A) => ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) ) ) )).
fof(dt_m3_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ! [B] : ( m3_ltlaxio4(B,A) => ( v1_relat_1(B) & v5_relat_1(B,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) & v1_funct_1(B) & v3_trees_2(B) & v3_trees_9(B) ) ) ) )).
fof(dt_m3_measure8,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( m3_measure8(D,A,B,C) => m2_measure8(D,A,C) ) ) )).
fof(dt_m3_modcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m3_modcat_1(B,A) => ~ v1_xboole_0(B) ) ) )).
fof(dt_m3_monoid_0,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( m3_monoid_0(B,A) => l4_algstr_0(B) ) ) )).
fof(dt_m3_msalimit,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_msalimit(A) ) => ! [B] : ( m3_msalimit(B,A) => ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v1_msualg_1(B) & l1_msualg_1(B) ) ) ) )).
fof(dt_m3_msaterm,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m3_msaterm(C,A,B) => ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) ) ) )).
fof(dt_m3_nattra_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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] : ( m3_nattra_1(E,A,B,C,D) => m2_nattra_1(E,A,B,C,D) ) ) )).
fof(dt_m3_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,B) => ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) ) ) )).
fof(dt_m3_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m3_pnproc_1(C,A,B) => m1_pnproc_1(C,A) ) ) )).
fof(dt_m3_pua2mss1,axiom,( ! [A] : ( ( v2_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m3_pua2mss1(B,A) => m1_eqrel_1(B,u1_struct_0(A)) ) ) )).
fof(dt_m3_realset1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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))) ) ) ) )).
fof(dt_m3_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v5_ringcat1(A) ) => ! [B] : ( m3_ringcat1(B,A) => ( v3_ringcat1(B) & l1_ringcat1(B) ) ) ) )).
fof(dt_m3_robbins3,axiom,( ! [A] : ( l4_robbins1(A) => ! [B] : ( m3_robbins3(B,A) => l4_robbins3(B) ) ) )).
fof(dt_m3_simplex0,axiom,( ! [A] : ! [B] : ( ( ~ v3_pencil_1(A) & v1_matroid0(A) & l1_pre_topc(A) & v1_xreal_0(B) ) => ! [C] : ( 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))) ) ) ) )).
fof(dt_m3_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m3_topgrp_1(B,A) => m1_topgrp_1(B,A,A) ) ) )).
fof(dt_m3_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ! [B] : ( m3_trees_3(B,A) => m2_trees_3(B,A,k3_trees_1(A)) ) ) )).
fof(dt_m3_vectsp_8,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) & ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( 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)))) ) ) ) )).
fof(dt_m3_yellow_6,axiom,( ! [A] : ! [B] : ( l1_struct_0(B) => ! [C] : ( m3_yellow_6(C,A,B) => ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) ) ) )).
fof(dt_m3_yellow_9,axiom,( ! [A] : ! [B] : ( ( l1_pre_topc(A) & l1_pre_topc(B) ) => ! [C] : ( m3_yellow_9(C,A,B) => ( v2_pre_topc(C) & l1_pre_topc(C) ) ) ) )).
fof(dt_m3_zmodul01,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m3_zmodul01(C,A,B) => m1_zmodul01(C,A) ) ) )).
fof(dt_m4_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( 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)))))) ) ) ) )).
fof(dt_m4_algspec1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( m4_algspec1(B,A) => m3_algspec1(B) ) ) )).
fof(dt_m4_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) & l4_aofa_a00(D,A,B,C) & m1_subset_1(E,u1_struct_0(A)) ) => ! [F] : ( m4_aofa_a00(F,A,B,C,D,E) => m1_subset_1(F,k1_funct_1(u3_msualg_1(A,C),E)) ) ) )).
fof(dt_m4_aofa_i00,axiom,( ! [A] : ( m4_aofa_i00(A) => m1_aofa_000(A,k7_freealg(k19_aofa_000,k26_aofa_i00),k9_funct_2(k4_ordinal1,k4_numbers),k1_aofa_i00(k9_funct_2(k4_ordinal1,k4_numbers),k5_numbers,k5_numbers)) ) )).
fof(dt_m4_bcialg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m4_bcialg_2(C,A,B) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) ) )).
fof(dt_m4_bciideal,axiom,( ! [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] : ( m4_bciideal(B,A) => ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).
fof(dt_m4_dist_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_setfam_1(B) & m1_subset_1(B,k6_dist_1(A)) ) => ! [C] : ( m4_dist_2(C,A,B) => ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) ) ) )).
fof(dt_m4_glib_001,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & m3_glib_001(B,A) ) => ! [C] : ( m4_glib_001(C,A,B) => m3_glib_001(C,A) ) ) )).
fof(dt_m4_grcat_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m4_grcat_1(C,A,B) => ( ~ v1_xboole_0(C) & v4_grcat_1(C) ) ) ) )).
fof(dt_m4_hallmar1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m4_hallmar1(C,A,B) => m2_hallmar1(C,A,B) ) ) )).
fof(dt_m4_index_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(dt_m4_integr15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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,k4_ordinal1,k1_integra1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(B)))) ) => ! [E] : ( m4_integr15(E,A,B,C,D) => ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k3_finseq_2(k1_euclid(A))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k3_finseq_2(k1_euclid(A))))) ) ) ) )).
fof(dt_m4_margrel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m4_margrel1(B,A) => ~ v1_xboole_0(B) ) ) )).
fof(dt_m4_measure8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( m4_measure8(D,A,B,C) => ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_funct_2(k4_ordinal1,k9_setfam_1(A))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_funct_2(k4_ordinal1,k9_setfam_1(A))))) ) ) ) )).
fof(dt_m4_modcat_1,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) & m3_modcat_1(B,A) ) => ! [C] : ( m4_modcat_1(C,A,B) => ( v3_mod_2(C,A) & l1_mod_2(C,A) ) ) ) )).
fof(dt_m4_msaterm,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(dt_m4_nattra_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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] : ( m4_nattra_1(C,A,B) => ~ v1_xboole_0(C) ) ) )).
fof(dt_m4_pua2mss1,axiom,( ! [A] : ( ( v2_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m4_pua2mss1(B,A) => m2_pua2mss1(B,u1_struct_0(A)) ) ) )).
fof(dt_m4_ringcat1,axiom,( ! [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) & 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] : ( m4_ringcat1(C,A,B) => ( ~ v1_xboole_0(C) & v5_ringcat1(C) ) ) ) )).
fof(dt_m4_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v3_pencil_1(A) & v1_matroid0(A) & l1_pre_topc(A) & v1_xreal_0(B) & m3_simplex0(C,A,B) ) => ! [D] : ( m4_simplex0(D,A,B,C) => m3_simplex0(D,A,k4_xxreal_0(k3_xxreal_3(B,1),k2_xxreal_3(1))) ) ) )).
fof(dt_m4_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m4_trees_1(B,A) => v2_trees_1(B) ) ) )).
fof(dt_m4_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ! [B] : ( m4_trees_3(B,A) => ( ~ v1_xboole_0(B) & v1_trees_1(B) ) ) ) )).
fof(dt_m4_vectsp_8,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) & ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( 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)))) ) ) ) )).
fof(dt_m5_bcialg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m5_bcialg_2(C,A,B) => m1_bcialg_2(C,A) ) ) )).
fof(dt_m5_index_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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] : ( m5_index_1(G,A,B,C,D,E,F) => m3_index_1(G,A,B,C,D) ) ) )).
fof(dt_m5_margrel1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m4_margrel1(B,A) ) => ! [C] : ( 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))) ) ) ) )).
fof(dt_m5_modcat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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] : ( m5_modcat_1(D,A,B,C) => m3_modcat_1(D,A) ) ) )).
fof(dt_m5_monoid_0,axiom,( ! [A] : ! [B] : ( ( l3_algstr_0(A) & m2_monoid_0(B,A) ) => ! [C] : ( m5_monoid_0(C,A,B) => m2_monoid_0(C,A) ) ) )).
fof(dt_m6_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( 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) ) ) )).
fof(dt_m6_monoid_0,axiom,( ! [A] : ! [B] : ( ( l3_algstr_0(A) & m3_monoid_0(B,A) ) => ! [C] : ( m6_monoid_0(C,A,B) => m2_monoid_0(C,A) ) ) )).
fof(dt_m7_monoid_0,axiom,( ! [A] : ! [B] : ( ( l3_algstr_0(A) & m3_monoid_0(B,A) ) => ! [C] : ( m7_monoid_0(C,A,B) => m3_monoid_0(C,A) ) ) )).
fof(dt_m9_lmod_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : ( m9_lmod_7(D,A,B,C) => m1_subset_1(D,u1_struct_0(B)) ) ) )).
fof(dt_o_0_0_afvect01,axiom,( ~ v7_struct_0(o_0_0_afvect01) & v1_afvect0(o_0_0_afvect01) & l1_analoaf(o_0_0_afvect01) )).
fof(dt_o_0_0_ami_6,axiom,( v1_ami_2(o_0_0_ami_6) & m1_subset_1(o_0_0_ami_6,u1_struct_0(k1_ami_3)) )).
fof(dt_o_0_0_aofa_i00,axiom,( v1_funct_1(o_0_0_aofa_i00) & v1_funct_2(o_0_0_aofa_i00,k9_funct_2(k4_ordinal1,k4_numbers),k4_numbers) & m1_subset_1(o_0_0_aofa_i00,k1_zfmisc_1(k2_zfmisc_1(k9_funct_2(k4_ordinal1,k4_numbers),k4_numbers))) )).
fof(dt_o_0_0_bor_cant,axiom,( v7_ordinal1(o_0_0_bor_cant) )).
fof(dt_o_0_0_cc0sp2,axiom,( m1_subset_1(o_0_0_cc0sp2,k4_ordinal1) )).
fof(dt_o_0_0_descip_1,axiom,( v1_funct_1(o_0_0_descip_1) & v1_funct_2(o_0_0_descip_1,64,k2_finseq_1(64)) & v1_descip_1(o_0_0_descip_1,64) & m1_subset_1(o_0_0_descip_1,k1_zfmisc_1(k2_zfmisc_1(64,k2_finseq_1(64)))) )).
fof(dt_o_0_0_fomodel2,axiom,( ~ v1_xboole_0(o_0_0_fomodel2) )).
fof(dt_o_0_0_funct_5,axiom,( m1_subset_1(o_0_0_funct_5,k9_xtuple_0(k2_funct_5(k1_xboole_0))) )).
fof(dt_o_0_0_goboard9,axiom,( m1_subset_1(o_0_0_goboard9,u1_struct_0(k15_euclid(2))) )).
fof(dt_o_0_0_henmodel,axiom,( ~ v1_xboole_0(o_0_0_henmodel) )).
fof(dt_o_0_0_matrix11,axiom,( ~ v6_struct_0(o_0_0_matrix11) & v13_algstr_0(o_0_0_matrix11) & v33_algstr_0(o_0_0_matrix11) & v3_group_1(o_0_0_matrix11) & v5_group_1(o_0_0_matrix11) & v2_rlvect_1(o_0_0_matrix11) & v3_rlvect_1(o_0_0_matrix11) & v4_rlvect_1(o_0_0_matrix11) & v4_vectsp_1(o_0_0_matrix11) & v5_vectsp_1(o_0_0_matrix11) & v12_vectsp_1(o_0_0_matrix11) & l6_algstr_0(o_0_0_matrix11) )).
fof(dt_o_0_0_moebius1,axiom,( v7_ordinal1(o_0_0_moebius1) & v1_int_2(o_0_0_moebius1) )).
fof(dt_o_0_0_pardepap,axiom,( ~ v7_struct_0(o_0_0_pardepap) & v1_diraf(o_0_0_pardepap) & v2_diraf(o_0_0_pardepap) & v2_aff_2(o_0_0_pardepap) & v4_aff_2(o_0_0_pardepap) & v11_aff_2(o_0_0_pardepap) & v1_translac(o_0_0_pardepap) & l1_analoaf(o_0_0_pardepap) )).
fof(dt_o_0_0_pdiff_2,axiom,( m1_subset_1(o_0_0_pdiff_2,k1_numbers) )).
fof(dt_o_0_0_pdiff_4,axiom,( m1_subset_1(o_0_0_pdiff_4,k1_numbers) )).
fof(dt_o_0_0_scmfsa10,axiom,( v1_ami_2(o_0_0_scmfsa10) & m1_subset_1(o_0_0_scmfsa10,u1_struct_0(k1_scmfsa_2)) )).
fof(dt_o_0_0_topalg_5,axiom,( v1_xreal_0(o_0_0_topalg_5) & v2_xxreal_0(o_0_0_topalg_5) )).
fof(dt_o_0_0_waybel22,axiom,( ~ v2_struct_0(o_0_0_waybel22) & v3_orders_2(o_0_0_waybel22) & v4_orders_2(o_0_0_waybel22) & v5_orders_2(o_0_0_waybel22) & v3_lattice3(o_0_0_waybel22) & v3_waybel_3(o_0_0_waybel22) & l1_orders_2(o_0_0_waybel22) )).
fof(dt_o_0_0_waybel26,axiom,( v1_waybel_9(o_0_0_waybel26) & v4_waybel11(o_0_0_waybel26) & m1_yellow_9(o_0_0_waybel26,k2_yellow_1(k1_tarski(k5_numbers))) )).
fof(dt_o_0_0_xboole_0,axiom,( v1_xboole_0(o_0_0_xboole_0) )).
fof(dt_o_0_0_yellow21,axiom,( l1_struct_0(o_0_0_yellow21) )).
fof(dt_o_0_12_topreal1,axiom,( m1_subset_1(o_0_12_topreal1,k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,k5_numbers),k19_euclid(1,k5_numbers)),k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,1),k19_euclid(1,1)))) )).
fof(dt_o_0_13_topreal1,axiom,( m1_subset_1(o_0_13_topreal1,k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,k5_numbers),k19_euclid(k5_numbers,1)),k1_rltopsp1(k15_euclid(2),k19_euclid(1,k5_numbers),k19_euclid(1,1)))) )).
fof(dt_o_0_1_ami_3,axiom,( v1_relat_1(o_0_1_ami_3) & v4_relat_1(o_0_1_ami_3,u1_struct_0(k1_ami_3)) & v1_funct_1(o_0_1_ami_3) & v5_funct_1(o_0_1_ami_3,k2_memstr_0(k7_card_1(2),k1_ami_3)) & v1_partfun1(o_0_1_ami_3,u1_struct_0(k1_ami_3)) )).
fof(dt_o_0_1_aofa_i00,axiom,( v1_funct_1(o_0_1_aofa_i00) & v1_funct_2(o_0_1_aofa_i00,k9_funct_2(k4_ordinal1,k4_numbers),k4_ordinal1) & m1_subset_1(o_0_1_aofa_i00,k1_zfmisc_1(k2_zfmisc_1(k9_funct_2(k4_ordinal1,k4_numbers),k4_ordinal1))) )).
fof(dt_o_0_1_bor_cant,axiom,( m1_subset_1(o_0_1_bor_cant,k4_ordinal1) )).
fof(dt_o_0_1_groeb_1,axiom,( m1_subset_1(o_0_1_groeb_1,a_0_0_groeb_1) )).
fof(dt_o_0_1_simplex2,axiom,( v1_xreal_0(o_0_1_simplex2) )).
fof(dt_o_0_1_topalg_5,axiom,( m1_subset_1(o_0_1_topalg_5,u1_struct_0(k15_euclid(2))) )).
fof(dt_o_0_1_trees_1,axiom,( m1_subset_1(o_0_1_trees_1,k1_trees_1(k1_xboole_0)) )).
fof(dt_o_0_1_waybel27,axiom,( v1_waybel_9(o_0_1_waybel27) & v4_waybel11(o_0_1_waybel27) & m1_yellow_9(o_0_1_waybel27,k2_yellow_1(k1_tarski(k5_numbers))) )).
fof(dt_o_0_1_zmodul03,axiom,( v7_ordinal1(o_0_1_zmodul03) & v1_int_2(o_0_1_zmodul03) )).
fof(dt_o_0_2_scm_comp,axiom,( m1_dtconstr(o_0_2_scm_comp,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) )).
fof(dt_o_0_2_scmfsa10,axiom,( m1_scmfsa_2(o_0_2_scmfsa10) )).
fof(dt_o_0_2_topalg_5,axiom,( m1_subset_1(o_0_2_topalg_5,u1_struct_0(k7_toprealb(2,o_0_1_topalg_5,o_0_0_topalg_5))) )).
fof(dt_o_0_3_fomodel1,axiom,( ~ v6_struct_0(o_0_3_fomodel1) & ~ v8_struct_0(o_0_3_fomodel1) & l4_struct_0(o_0_3_fomodel1) )).
fof(dt_o_0_3_geomtrap,axiom,( ~ v2_struct_0(o_0_3_geomtrap) & v2_geomtrap(o_0_3_geomtrap) & l1_geomtrap(o_0_3_geomtrap) )).
fof(dt_o_0_3_scm_inst,axiom,( m1_subset_1(o_0_3_scm_inst,k2_scm_inst) )).
fof(dt_o_0_3_scmfsa_i,axiom,( m1_subset_1(o_0_3_scmfsa_i,k2_scm_inst) )).
fof(dt_o_0_3_trees_1,axiom,( m1_subset_1(o_0_3_trees_1,a_0_2_trees_1) )).
fof(dt_o_0_4_scmfsa_i,axiom,( m1_subset_1(o_0_4_scmfsa_i,k1_scmfsa_i) )).
fof(dt_o_0_5_bhsp_1,axiom,( ~ v2_struct_0(o_0_5_bhsp_1) & v13_algstr_0(o_0_5_bhsp_1) & v2_rlvect_1(o_0_5_bhsp_1) & v3_rlvect_1(o_0_5_bhsp_1) & v4_rlvect_1(o_0_5_bhsp_1) & v5_rlvect_1(o_0_5_bhsp_1) & v6_rlvect_1(o_0_5_bhsp_1) & v7_rlvect_1(o_0_5_bhsp_1) & v8_rlvect_1(o_0_5_bhsp_1) & l1_rlvect_1(o_0_5_bhsp_1) )).
fof(dt_o_0_5_clvect_1,axiom,( ~ v2_struct_0(o_0_5_clvect_1) & v13_algstr_0(o_0_5_clvect_1) & v2_rlvect_1(o_0_5_clvect_1) & v3_rlvect_1(o_0_5_clvect_1) & v4_rlvect_1(o_0_5_clvect_1) & v2_clvect_1(o_0_5_clvect_1) & v3_clvect_1(o_0_5_clvect_1) & v4_clvect_1(o_0_5_clvect_1) & v5_clvect_1(o_0_5_clvect_1) & l1_clvect_1(o_0_5_clvect_1) )).
fof(dt_o_0_5_normsp_1,axiom,( ~ v2_struct_0(o_0_5_normsp_1) & v13_algstr_0(o_0_5_normsp_1) & v2_rlvect_1(o_0_5_normsp_1) & v3_rlvect_1(o_0_5_normsp_1) & v4_rlvect_1(o_0_5_normsp_1) & v5_rlvect_1(o_0_5_normsp_1) & v6_rlvect_1(o_0_5_normsp_1) & v7_rlvect_1(o_0_5_normsp_1) & v8_rlvect_1(o_0_5_normsp_1) & l1_rlvect_1(o_0_5_normsp_1) )).
fof(dt_o_0_6_abcmiz_1,axiom,( v1_finset_1(o_0_6_abcmiz_1) & m1_subset_1(o_0_6_abcmiz_1,k1_zfmisc_1(k2_abcmiz_1)) )).
fof(dt_o_0_6_csspace,axiom,( ~ v2_struct_0(o_0_6_csspace) & v13_algstr_0(o_0_6_csspace) & v2_rlvect_1(o_0_6_csspace) & v3_rlvect_1(o_0_6_csspace) & v4_rlvect_1(o_0_6_csspace) & v2_clvect_1(o_0_6_csspace) & v3_clvect_1(o_0_6_csspace) & v4_clvect_1(o_0_6_csspace) & v5_clvect_1(o_0_6_csspace) & l1_clvect_1(o_0_6_csspace) )).
fof(dt_o_0_7_scmpds_2,axiom,( v1_relat_1(o_0_7_scmpds_2) & v4_relat_1(o_0_7_scmpds_2,u1_struct_0(k1_scmpds_2)) & v1_funct_1(o_0_7_scmpds_2) & v5_funct_1(o_0_7_scmpds_2,k2_memstr_0(2,k1_scmpds_2)) & v1_partfun1(o_0_7_scmpds_2,u1_struct_0(k1_scmpds_2)) )).
fof(dt_o_0_8_trees_3,axiom,( m3_trees_3(o_0_8_trees_3,k2_trees_1(k5_numbers)) )).
fof(dt_o_1_0_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_tdgroup(A) & l1_analoaf(A) ) => m1_subset_1(o_1_0_afvect0(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_algspec1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => m1_algspec1(o_1_0_algspec1(A),A) ) )).
fof(dt_o_1_0_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ( v1_relat_1(o_1_0_amistd_1(A)) & v4_relat_1(o_1_0_amistd_1(A),u1_struct_0(k4_amistd_1(A))) & v1_funct_1(o_1_0_amistd_1(A)) & v5_funct_1(o_1_0_amistd_1(A),k2_memstr_0(A,k4_amistd_1(A))) & v1_partfun1(o_1_0_amistd_1(A),u1_struct_0(k4_amistd_1(A))) ) ) )).
fof(dt_o_1_0_analort,axiom,( ! [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) ) => m1_subset_1(o_1_0_analort(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_aofa_i00,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_0_aofa_i00(A),A) ) )).
fof(dt_o_1_0_borsuk_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => m1_subset_1(o_1_0_borsuk_3(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_borsuk_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => m1_subset_1(o_1_0_borsuk_4(A),A) ) )).
fof(dt_o_1_0_bvfunc_2,axiom,( ! [A] : m1_subset_1(o_1_0_bvfunc_2(A),A) )).
fof(dt_o_1_0_calcul_2,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(o_1_0_calcul_2(A),k2_calcul_2(A,k5_numbers)) ) )).
fof(dt_o_1_0_card_2,axiom,( ! [A] : ( v1_finset_1(A) => m1_subset_1(o_1_0_card_2(A),A) ) )).
fof(dt_o_1_0_cat_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_0_cat_5(A),A) ) )).
fof(dt_o_1_0_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_0_cfuncdom(A),A) ) )).
fof(dt_o_1_0_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => m2_subset_1(o_1_0_chain_1(A),k4_ordinal1,k2_finseq_1(A)) ) )).
fof(dt_o_1_0_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & v6_chord(A) ) => m1_subset_1(o_1_0_chord(A),k6_glib_000(A)) ) )).
fof(dt_o_1_0_classes2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => m1_subset_1(o_1_0_classes2(A),A) ) )).
fof(dt_o_1_0_clvect_1,axiom,( ! [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) ) => m1_subset_1(o_1_0_clvect_1(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_collsp,axiom,( ! [A] : m1_subset_1(o_1_0_collsp(A),A) )).
fof(dt_o_1_0_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => m1_subset_1(o_1_0_connsp_1(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_dirort,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dirort(A) & l1_analoaf(A) ) => m1_subset_1(o_1_0_dirort(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_0_dynkin(A),A) ) )).
fof(dt_o_1_0_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => m1_subset_1(o_1_0_exchsort(A),k2_ordinal1(k9_xtuple_0(A))) ) )).
fof(dt_o_1_0_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(o_1_0_finseq_3(A),k8_subset_1(k4_ordinal1,k2_finseq_1(A),k1_tarski(k1_nat_1(A,1)))) ) )).
fof(dt_o_1_0_finseqop,axiom,( ! [A] : m1_subset_1(o_1_0_finseqop(A),A) )).
fof(dt_o_1_0_finsub_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) ) => m1_subset_1(o_1_0_finsub_1(A),A) ) )).
fof(dt_o_1_0_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => m1_subset_1(o_1_0_fintopo6(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => m1_subset_1(o_1_0_frechet2(A),k1_frechet2(A,k1_struct_0(A))) ) )).
fof(dt_o_1_0_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => m1_subset_1(o_1_0_funcop_1(A),k9_xtuple_0(A)) ) )).
fof(dt_o_1_0_funcsdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_0_funcsdom(A),A) ) )).
fof(dt_o_1_0_funct_3,axiom,( ! [A] : m1_subset_1(o_1_0_funct_3(A),A) )).
fof(dt_o_1_0_funct_4,axiom,( ! [A] : m1_subset_1(o_1_0_funct_4(A),A) )).
fof(dt_o_1_0_funct_5,axiom,( ! [A] : m1_subset_1(o_1_0_funct_5(A),A) )).
fof(dt_o_1_0_funct_6,axiom,( ! [A] : m1_subset_1(o_1_0_funct_6(A),A) )).
fof(dt_o_1_0_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => m1_subset_1(o_1_0_glib_001(A),k6_glib_000(A)) ) )).
fof(dt_o_1_0_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => m1_subset_1(o_1_0_glib_004(A),k6_glib_000(A)) ) )).
fof(dt_o_1_0_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => m2_subset_1(o_1_0_goedelcp(A),k2_qc_lang1(A),k3_qc_lang1(A)) ) )).
fof(dt_o_1_0_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => m1_subset_1(o_1_0_graph_3(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => m1_subset_1(o_1_0_graph_4(A),k1_graph_4(A,k1_xboole_0)) ) )).
fof(dt_o_1_0_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ( v1_partfun1(o_1_0_groeb_3(A),k15_pre_poly(A)) & v1_relat_2(o_1_0_groeb_3(A)) & v4_relat_2(o_1_0_groeb_3(A)) & v6_relat_2(o_1_0_groeb_3(A)) & v8_relat_2(o_1_0_groeb_3(A)) & m1_subset_1(o_1_0_groeb_3(A),k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),k15_pre_poly(A)))) ) ) )).
fof(dt_o_1_0_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => m1_subset_1(o_1_0_group_1(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_hahnban,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => m2_subset_1(o_1_0_hahnban(A),k6_numbers,A) ) )).
fof(dt_o_1_0_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ( v4_msualg_1(o_1_0_instalg1(A),A) & l3_msualg_1(o_1_0_instalg1(A),A) ) ) )).
fof(dt_o_1_0_int_6,axiom,( ! [A] : ( ( 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) ) => m1_int_6(o_1_0_int_6(A),A) ) )).
fof(dt_o_1_0_integra4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => m1_subset_1(o_1_0_integra4(A),k1_integra1(A)) ) )).
fof(dt_o_1_0_kolmog01,axiom,( ! [A] : m1_subset_1(o_1_0_kolmog01(A),A) )).
fof(dt_o_1_0_lattice4,axiom,( ! [A] : m1_subset_1(o_1_0_lattice4(A),A) )).
fof(dt_o_1_0_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => m1_subset_1(o_1_0_lexbfs(A),k6_glib_000(A)) ) )).
fof(dt_o_1_0_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_0_lpspacc1(A),A) ) )).
fof(dt_o_1_0_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_0_lpspace1(A),A) ) )).
fof(dt_o_1_0_margrel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_0_margrel1(A),k4_margrel1(A)) ) )).
fof(dt_o_1_0_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(o_1_0_matrtop1(A),u1_struct_0(k15_euclid(A))) ) )).
fof(dt_o_1_0_membered,axiom,( ! [A] : ( v3_membered(A) => m1_subset_1(o_1_0_membered(A),A) ) )).
fof(dt_o_1_0_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => m1_subset_1(o_1_0_midsp_2(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_msscyc_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ( v4_msualg_1(o_1_0_msscyc_2(A),A) & v4_msafree2(o_1_0_msscyc_2(A),A) & l3_msualg_1(o_1_0_msscyc_2(A),A) ) ) )).
fof(dt_o_1_0_msualg_7,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => m2_subset_1(o_1_0_msualg_7(A),k6_numbers,A) ) )).
fof(dt_o_1_0_orders_1,axiom,( ! [A] : m1_subset_1(o_1_0_orders_1(A),A) )).
fof(dt_o_1_0_orders_2,axiom,( ! [A] : m1_subset_1(o_1_0_orders_2(A),A) )).
fof(dt_o_1_0_ordinal1,axiom,( ! [A] : m1_subset_1(o_1_0_ordinal1(A),A) )).
fof(dt_o_1_0_ordinal3,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => m1_subset_1(o_1_0_ordinal3(A),k9_xtuple_0(A)) ) )).
fof(dt_o_1_0_ordinal5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v2_ordinal5(A) ) => m1_subset_1(o_1_0_ordinal5(A),k9_xtuple_0(A)) ) )).
fof(dt_o_1_0_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_0_partfun2(A),A) ) )).
fof(dt_o_1_0_pboole,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => m1_subset_1(o_1_0_pboole(A),k9_xtuple_0(A)) ) )).
fof(dt_o_1_0_pcomps_1,axiom,( ! [A] : m1_subset_1(o_1_0_pcomps_1(A),A) )).
fof(dt_o_1_0_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => m1_subset_1(o_1_0_petri(A),k6_petri(A,k1_subset_1(u1_struct_0(A)))) ) )).
fof(dt_o_1_0_polynom5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l6_algstr_0(A) ) => m1_subset_1(o_1_0_polynom5(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => m1_subset_1(o_1_0_projpl_1(A),u1_incsp_1(A)) ) )).
fof(dt_o_1_0_rfinseq,axiom,( ! [A] : ( v1_finset_1(A) => m1_subset_1(o_1_0_rfinseq(A),A) ) )).
fof(dt_o_1_0_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => m1_subset_1(o_1_0_rfunct_1(A),k8_relat_1(k4_rfunct_1(A),k1_tarski(k5_numbers))) ) )).
fof(dt_o_1_0_rlsub_1,axiom,( ! [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) ) => m1_subset_1(o_1_0_rlsub_1(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_rlvect_5,axiom,( ! [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) ) => m1_rlvect_3(o_1_0_rlvect_5(A),A) ) )).
fof(dt_o_1_0_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & v7_robbins1(A) & l2_robbins1(A) ) => m1_subset_1(o_1_0_robbins1(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => m1_subset_1(o_1_0_robbins2(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_rpr_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_0_rpr_1(A),A) ) )).
fof(dt_o_1_0_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => m1_subset_1(o_1_0_rusub_1(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_rusub_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => m1_rusub_3(o_1_0_rusub_4(A),A) ) )).
fof(dt_o_1_0_setfam_1,axiom,( ! [A] : m1_subset_1(o_1_0_setfam_1(A),A) )).
fof(dt_o_1_0_taxonom1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => m2_subset_1(o_1_0_taxonom1(A),k1_numbers,A) ) )).
fof(dt_o_1_0_topdim_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & v5_waybel23(A) & v3_topdim_1(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => m1_subset_1(o_1_0_topdim_2(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_tops_2(o_1_0_topgen_4(A),A) & v1_cantor_1(o_1_0_topgen_4(A),A) & m1_subset_1(o_1_0_topgen_4(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) )).
fof(dt_o_1_0_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => m1_subset_1(o_1_0_translac(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_treal_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => m1_subset_1(o_1_0_treal_1(A),A) ) )).
fof(dt_o_1_0_waybel20,axiom,( ! [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) & l1_orders_2(A) ) => m1_subset_1(o_1_0_waybel20(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => m1_subset_1(o_1_0_waybel26(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_waybel27,axiom,( ! [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) ) => ( v4_waybel11(o_1_0_waybel27(A)) & m1_yellow_9(o_1_0_waybel27(A),A) ) ) )).
fof(dt_o_1_0_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => m1_subset_1(o_1_0_waybel_1(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ( ~ v1_xboole_0(o_1_0_waybel_2(A)) & v1_waybel_0(o_1_0_waybel_2(A),A) & m1_subset_1(o_1_0_waybel_2(A),k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_o_1_0_waybel_6,axiom,( ! [A] : m1_subset_1(o_1_0_waybel_6(A),A) )).
fof(dt_o_1_0_waybel_7,axiom,( ! [A] : m1_subset_1(o_1_0_waybel_7(A),A) )).
fof(dt_o_1_0_waybel_8,axiom,( ! [A] : ( ( 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) ) => m1_subset_1(o_1_0_waybel_8(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_wellset1,axiom,( ! [A] : m1_subset_1(o_1_0_wellset1(A),A) )).
fof(dt_o_1_0_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => m1_subset_1(o_1_0_yellow10(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => m1_subset_1(o_1_0_yellow13(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_yellow17,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => m1_subset_1(o_1_0_yellow17(A),k4_card_3(A)) ) )).
fof(dt_o_1_0_yellow_2,axiom,( ! [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) ) => m1_subset_1(o_1_0_yellow_2(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => m1_subset_1(o_1_0_yellow_3(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_yellow_9,axiom,( ! [A] : ( ( v13_struct_0(A,1) & v2_pre_topc(A) & l1_pre_topc(A) ) => m1_subset_1(o_1_0_yellow_9(A),u1_struct_0(A)) ) )).
fof(dt_o_1_0_zf_fund2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_0_zf_fund2(A),A) ) )).
fof(dt_o_1_0_zf_lang1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_funct_1(o_1_0_zf_lang1(A)) & v1_funct_2(o_1_0_zf_lang1(A),k1_zf_lang,A) & m1_subset_1(o_1_0_zf_lang1(A),k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang,A))) ) ) )).
fof(dt_o_1_0_zfmodel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_funct_1(o_1_0_zfmodel1(A)) & v1_funct_2(o_1_0_zfmodel1(A),k1_zf_lang,A) & m1_subset_1(o_1_0_zfmodel1(A),k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang,A))) ) ) )).
fof(dt_o_1_0_zfmodel2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_funct_1(o_1_0_zfmodel2(A)) & v1_funct_2(o_1_0_zfmodel2(A),k1_zf_lang,A) & m1_subset_1(o_1_0_zfmodel2(A),k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang,A))) ) ) )).
fof(dt_o_1_0_zmodul01,axiom,( ! [A] : ( ( ~ 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(o_1_0_zmodul01(A),u1_struct_0(A)) ) )).
fof(dt_o_1_10_card_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_card_3(A) ) => m1_subset_1(o_1_10_card_3(A),A) ) )).
fof(dt_o_1_10_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v4_valued_0(A) & v2_margrel1(A) ) => m2_finseq_2(o_1_10_comput_1(A),k4_ordinal1,k4_finseq_2(k1_nat_1(k19_margrel1(A),1),k4_ordinal1)) ) )).
fof(dt_o_1_10_jordan2c,axiom,( ! [A] : ( ( ~ 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)))) ) => m1_subset_1(o_1_10_jordan2c(A),k2_jordan2c(2,k3_topreal1(2,k1_sprect_1(A)))) ) )).
fof(dt_o_1_10_waybel19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v2_pre_topc(o_1_10_waybel19(A)) & v1_waybel19(o_1_10_waybel19(A)) & m1_yellow_9(o_1_10_waybel19(A),A) ) ) )).
fof(dt_o_1_11_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => m1_subset_1(o_1_11_card_3(A),k4_card_3(A)) ) )).
fof(dt_o_1_11_member_1,axiom,( ! [A] : ( v1_membered(A) => m1_subset_1(o_1_11_member_1(A),A) ) )).
fof(dt_o_1_12_jordan2c,axiom,( ! [A] : ( ( ~ 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)))) ) => m1_subset_1(o_1_12_jordan2c(A),k1_jordan2c(2,k3_topreal1(2,k1_sprect_1(A)))) ) )).
fof(dt_o_1_12_waybel30,axiom,( ! [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) & l1_waybel_9(A) ) => ( v4_waybel11(o_1_12_waybel30(A)) & m1_yellow_9(o_1_12_waybel30(A),A) ) ) )).
fof(dt_o_1_13_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ( v5_card_3(o_1_13_fomodel4(A)) & m1_subset_1(o_1_13_fomodel4(A),k1_zfmisc_1(k16_fomodel1(A))) ) ) )).
fof(dt_o_1_14_waybel30,axiom,( ! [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_waybel_2(A) & l1_waybel_9(A) ) => ( v4_waybel11(o_1_14_waybel30(A)) & m1_yellow_9(o_1_14_waybel30(A),A) ) ) )).
fof(dt_o_1_15_waybel30,axiom,( ! [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) & l1_waybel_9(A) ) => ( v3_lattice3(o_1_15_waybel30(A)) & v4_waybel11(o_1_15_waybel30(A)) & m1_yellow_9(o_1_15_waybel30(A),A) ) ) )).
fof(dt_o_1_16_waybel30,axiom,( ! [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_waybel_2(A) & l1_waybel_9(A) ) => ( v3_lattice3(o_1_16_waybel30(A)) & v4_waybel11(o_1_16_waybel30(A)) & m1_yellow_9(o_1_16_waybel30(A),A) ) ) )).
fof(dt_o_1_17_abcmiz_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k49_abcmiz_1))) ) => m2_subset_1(o_1_17_abcmiz_1(A),u1_struct_0(k49_abcmiz_1),A) ) )).
fof(dt_o_1_17_jordan6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => m1_subset_1(o_1_17_jordan6(A),A) ) )).
fof(dt_o_1_18_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => m1_subset_1(o_1_18_jordan6(A),A) ) )).
fof(dt_o_1_19_waybel19,axiom,( ! [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) & l1_waybel_9(A) ) => ( v2_pre_topc(o_1_19_waybel19(A)) & v1_waybel19(o_1_19_waybel19(A)) & m1_yellow_9(o_1_19_waybel19(A),A) ) ) )).
fof(dt_o_1_1_aofa_i00,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_funct_1(o_1_1_aofa_i00(A)) & v2_funct_1(o_1_1_aofa_i00(A)) & v1_funct_2(o_1_1_aofa_i00(A),A,k1_card_1(A)) & v2_funct_2(o_1_1_aofa_i00(A),k1_card_1(A)) & m1_subset_1(o_1_1_aofa_i00(A),k1_zfmisc_1(k2_zfmisc_1(A,k1_card_1(A)))) ) ) )).
fof(dt_o_1_1_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => m1_subset_1(o_1_1_autalg_1(A),u1_struct_0(k3_autalg_1(A))) ) )).
fof(dt_o_1_1_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => m1_subset_1(o_1_1_autgroup(A),u1_struct_0(k3_autgroup(A))) ) )).
fof(dt_o_1_1_card_3,axiom,( ! [A] : m1_subset_1(o_1_1_card_3(A),A) )).
fof(dt_o_1_1_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => m1_subset_1(o_1_1_cat_5(A),u1_struct_0(A)) ) )).
fof(dt_o_1_1_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_1_cc0sp1(A),A) ) )).
fof(dt_o_1_1_closure2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_funct_1(A) ) => m1_subset_1(o_1_1_closure2(A),A) ) )).
fof(dt_o_1_1_eqrel_1,axiom,( ! [A] : m1_subset_1(o_1_1_eqrel_1(A),A) )).
fof(dt_o_1_1_euclid_7,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_euclid(k5_numbers))) => m1_subset_1(o_1_1_euclid_7(A),A) ) )).
fof(dt_o_1_1_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_exchsort(A) ) => m1_subset_1(o_1_1_exchsort(A),k9_xtuple_0(A)) ) )).
fof(dt_o_1_1_finseq_1,axiom,( ! [A] : ( v1_finset_1(A) => ( v2_funct_1(o_1_1_finseq_1(A)) & v2_funct_2(o_1_1_finseq_1(A),A) & m2_finseq_1(o_1_1_finseq_1(A),A) ) ) )).
fof(dt_o_1_1_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(o_1_1_finseq_3(A),k10_xtuple_0(A)) ) )).
fof(dt_o_1_1_freealg,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_freealg(A) ) => m1_subset_1(o_1_1_freealg(A),A) ) )).
fof(dt_o_1_1_funcop_1,axiom,( ! [A] : m1_subset_1(o_1_1_funcop_1(A),A) )).
fof(dt_o_1_1_funct_5,axiom,( ! [A] : m1_subset_1(o_1_1_funct_5(A),k10_xtuple_0(A)) )).
fof(dt_o_1_1_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => m1_subset_1(o_1_1_funct_6(A),k10_xtuple_0(k1_funct_6(A))) ) )).
fof(dt_o_1_1_functor0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_1_functor0(A),A) ) )).
fof(dt_o_1_1_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => m1_subset_1(o_1_1_glib_002(A),k6_glib_000(A)) ) )).
fof(dt_o_1_1_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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(o_1_1_glib_004(A),k6_glib_000(A)) ) )).
fof(dt_o_1_1_goedcpuc,axiom,( ! [A] : ( m1_qc_lang1(A) => m1_goedcpuc(o_1_1_goedcpuc(A),A) ) )).
fof(dt_o_1_1_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => m2_subset_1(o_1_1_goedelcp(A),k9_qc_lang1(A),k3_cqc_lang(A)) ) )).
fof(dt_o_1_1_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => m1_subset_1(o_1_1_graph_1(A),u1_struct_0(A)) ) )).
fof(dt_o_1_1_graph_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_1_graph_2(A),A) ) )).
fof(dt_o_1_1_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => m1_subset_1(o_1_1_graph_4(A),k2_graph_4(A,k1_xboole_0)) ) )).
fof(dt_o_1_1_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => m1_subset_1(o_1_1_graph_5(A),u1_struct_0(A)) ) )).
fof(dt_o_1_1_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & l1_struct_0(A) ) => m1_subset_1(o_1_1_group_1(A),u1_struct_0(A)) ) )).
fof(dt_o_1_1_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => m1_subset_1(o_1_1_group_2(A),u1_struct_0(A)) ) )).
fof(dt_o_1_1_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => m1_valuat_1(o_1_1_henmodel(A),A,o_0_0_henmodel) ) )).
fof(dt_o_1_1_heyting1,axiom,( ! [A] : m1_subset_1(o_1_1_heyting1(A),k2_xtuple_0(A)) )).
fof(dt_o_1_1_hilbert3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => m1_hilbert3(o_1_1_hilbert3(A),A) ) )).
fof(dt_o_1_1_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => m1_subset_1(o_1_1_incsp_1(A),u4_incsp_1(A)) ) )).
fof(dt_o_1_1_int_3,axiom,( ! [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) & l6_algstr_0(A) ) => ( v1_funct_1(o_1_1_int_3(A)) & v1_funct_2(o_1_1_int_3(A),u1_struct_0(A),k4_ordinal1) & m1_subset_1(o_1_1_int_3(A),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_ordinal1))) ) ) )).
fof(dt_o_1_1_integra2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => m1_integra1(o_1_1_integra2(A),A) ) )).
fof(dt_o_1_1_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v1_xboole_0(o_1_1_interva1(A)) & m1_subset_1(o_1_1_interva1(A),k1_zfmisc_1(A)) ) ) )).
fof(dt_o_1_1_jordan1b,axiom,( ! [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)))) ) => m2_subset_1(o_1_1_jordan1b(A),u1_struct_0(k15_euclid(2)),A) ) )).
fof(dt_o_1_1_jordan24,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => m1_subset_1(o_1_1_jordan24(A),k3_subset_1(u1_struct_0(k15_euclid(2)),A)) ) )).
fof(dt_o_1_1_kolmog01,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_finset_1(o_1_1_kolmog01(A)) & m1_subset_1(o_1_1_kolmog01(A),k1_zfmisc_1(A)) ) ) )).
fof(dt_o_1_1_matrix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_funct_1(o_1_1_matrix_2(A)) & v1_funct_2(o_1_1_matrix_2(A),k2_finseq_1(A),k2_finseq_1(A)) & v3_funct_2(o_1_1_matrix_2(A),k2_finseq_1(A),k2_finseq_1(A)) & m1_subset_1(o_1_1_matrix_2(A),k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(A),k2_finseq_1(A)))) ) ) )).
fof(dt_o_1_1_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_relat_1(o_1_1_matrtop1(A)) & v1_funct_1(o_1_1_matrtop1(A)) & v3_card_1(o_1_1_matrtop1(A),A) & v1_finseq_1(o_1_1_matrtop1(A)) & v3_valued_0(o_1_1_matrtop1(A)) ) ) )).
fof(dt_o_1_1_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ v1_xboole_0(o_1_1_mfold_1(A)) & v1_mfold_1(o_1_1_mfold_1(A),A) & m1_subset_1(o_1_1_mfold_1(A),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ) )).
fof(dt_o_1_1_orders_1,axiom,( ! [A] : m1_subset_1(o_1_1_orders_1(A),k3_tarski(A)) )).
fof(dt_o_1_1_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => m2_orders_1(o_1_1_orders_2(A),k1_orders_1(u1_struct_0(A)),k6_partfun1(k1_orders_1(u1_struct_0(A)))) ) )).
fof(dt_o_1_1_ordinal2,axiom,( ! [A] : m1_subset_1(o_1_1_ordinal2(A),k2_ordinal1(A)) )).
fof(dt_o_1_1_partit1,axiom,( ! [A] : m1_subset_1(o_1_1_partit1(A),A) )).
fof(dt_o_1_1_pencil_1,axiom,( ! [A] : m1_subset_1(o_1_1_pencil_1(A),A) )).
fof(dt_o_1_1_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => m1_subset_1(o_1_1_petri(A),k7_petri(A,k1_subset_1(u1_struct_0(A)))) ) )).
fof(dt_o_1_1_pre_circ,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_1_pre_circ(A),A) ) )).
fof(dt_o_1_1_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => m2_qc_lang1(o_1_1_qc_lang1(A),A) ) )).
fof(dt_o_1_1_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => m1_subset_1(o_1_1_relat_1(A),A) ) )).
fof(dt_o_1_1_rlvect_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_1_rlvect_3(A),A) ) )).
fof(dt_o_1_1_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => m1_subset_1(o_1_1_robbins1(A),u1_struct_0(A)) ) )).
fof(dt_o_1_1_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => m1_subset_1(o_1_1_rpr_1(A),A) ) )).
fof(dt_o_1_1_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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(o_1_1_scmring2(A)) & v4_relat_1(o_1_1_scmring2(A),u1_struct_0(k1_scmring2(A))) & v1_funct_1(o_1_1_scmring2(A)) & v5_funct_1(o_1_1_scmring2(A),k2_memstr_0(k7_card_1(2),k1_scmring2(A))) & v1_partfun1(o_1_1_scmring2(A),u1_struct_0(k1_scmring2(A))) ) ) )).
fof(dt_o_1_1_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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(o_1_1_scmring3(A)) & m1_subset_1(o_1_1_scmring3(A),u1_struct_0(k1_scmring2(A))) ) ) )).
fof(dt_o_1_1_seq_4,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => m1_subset_1(o_1_1_seq_4(A),A) ) )).
fof(dt_o_1_1_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v9_sheffer1(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l3_sheffer1(A) ) => m1_subset_1(o_1_1_sheffer1(A),u1_struct_0(A)) ) )).
fof(dt_o_1_1_stacks_1,axiom,( ! [A] : ( ( ~ 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(o_1_1_stacks_1(A),u1_struct_0(A)) ) )).
fof(dt_o_1_1_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => m1_trees_1(o_1_1_trees_1(A),A) ) )).
fof(dt_o_1_1_waybel21,axiom,( ! [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) & l1_waybel_9(A) ) => ( v2_cantor_1(o_1_1_waybel21(A),A) & v1_tops_2(o_1_1_waybel21(A),A) & m1_subset_1(o_1_1_waybel21(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) )).
fof(dt_o_1_1_waybel22,axiom,( ! [A] : ( v1_funct_1(o_1_1_waybel22(A)) & v1_funct_2(o_1_1_waybel22(A),A,u1_struct_0(o_0_0_waybel22)) & m1_subset_1(o_1_1_waybel22(A),k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(o_0_0_waybel22)))) ) )).
fof(dt_o_1_1_waybel25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v4_waybel11(o_1_1_waybel25(A)) & m1_yellow_9(o_1_1_waybel25(A),k4_yellow_1(A,k7_funcop_1(A,k2_yellow_1(k1_tarski(k5_numbers))))) ) ) )).
fof(dt_o_1_1_waybel27,axiom,( ! [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) & l1_orders_2(A) ) => ( v4_waybel11(o_1_1_waybel27(A)) & m1_yellow_9(o_1_1_waybel27(A),A) ) ) )).
fof(dt_o_1_1_waybel28,axiom,( ! [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) ) => ( v4_waybel11(o_1_1_waybel28(A)) & m1_yellow_9(o_1_1_waybel28(A),A) ) ) )).
fof(dt_o_1_1_waybel30,axiom,( ! [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) ) => ( v2_pre_topc(o_1_1_waybel30(A)) & v4_waybel11(o_1_1_waybel30(A)) & m1_yellow_9(o_1_1_waybel30(A),A) ) ) )).
fof(dt_o_1_1_waybel34,axiom,( ! [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) ) => ( v4_waybel11(o_1_1_waybel34(A)) & m1_yellow_9(o_1_1_waybel34(A),A) ) ) )).
fof(dt_o_1_1_yellow10,axiom,( ! [A] : ( ( v5_orders_2(A) & v3_yellow_0(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => m1_subset_1(o_1_1_yellow10(A),u1_struct_0(A)) ) )).
fof(dt_o_1_1_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => m1_subset_1(o_1_1_yellow16(A),u1_struct_0(A)) ) )).
fof(dt_o_1_1_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => m1_subset_1(o_1_1_yellow_3(A),u1_struct_0(A)) ) )).
fof(dt_o_1_1_yellow_9,axiom,( ! [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) ) => ( v2_pre_topc(o_1_1_yellow_9(A)) & v4_waybel11(o_1_1_yellow_9(A)) & m1_yellow_9(o_1_1_yellow_9(A),A) ) ) )).
fof(dt_o_1_1_zf_colla,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_funct_1(o_1_1_zf_colla(A)) & v1_funct_2(o_1_1_zf_colla(A),k1_zf_lang,A) & m1_subset_1(o_1_1_zf_colla(A),k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang,A))) ) ) )).
fof(dt_o_1_1_zf_lang1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_1_zf_lang1(A),A) ) )).
fof(dt_o_1_1_zfrefle1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_funct_1(o_1_1_zfrefle1(A)) & v1_funct_2(o_1_1_zfrefle1(A),k1_zf_lang,A) & m1_subset_1(o_1_1_zfrefle1(A),k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang,A))) ) ) )).
fof(dt_o_1_20_waybel19,axiom,( ! [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) & l1_waybel_9(A) ) => ( v4_waybel11(o_1_20_waybel19(A)) & m1_yellow_9(o_1_20_waybel19(A),A) ) ) )).
fof(dt_o_1_23_waybel19,axiom,( ! [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) ) => ( v2_pre_topc(o_1_23_waybel19(A)) & v2_waybel19(o_1_23_waybel19(A)) & m1_yellow_9(o_1_23_waybel19(A),A) ) ) )).
fof(dt_o_1_25_waybel19,axiom,( ! [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) & l1_waybel_9(A) ) => ( v4_waybel11(o_1_25_waybel19(A)) & m1_yellow_9(o_1_25_waybel19(A),A) ) ) )).
fof(dt_o_1_2_aofa_i00,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_card_3(A) ) => ( v1_funct_1(o_1_2_aofa_i00(A)) & v1_funct_2(o_1_2_aofa_i00(A),k9_funct_2(A,k4_numbers),k4_numbers) & m1_subset_1(o_1_2_aofa_i00(A),k1_zfmisc_1(k2_zfmisc_1(k9_funct_2(A,k4_numbers),k4_numbers))) ) ) )).
fof(dt_o_1_2_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => m1_subset_1(o_1_2_card_3(A),k4_card_3(A)) ) )).
fof(dt_o_1_2_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => m1_subset_1(o_1_2_card_lar(A),A) ) )).
fof(dt_o_1_2_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => m1_subset_1(o_1_2_filter_1(A),u1_struct_0(A)) ) )).
fof(dt_o_1_2_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(o_1_2_finseq_1(A),k8_subset_1(k4_ordinal1,k2_finseq_1(A),k1_tarski(k1_nat_1(A,1)))) ) )).
fof(dt_o_1_2_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(o_1_2_finseq_3(A),k8_subset_1(k4_ordinal1,k2_finseq_1(k3_finseq_1(A)),k1_tarski(k1_nat_1(k3_finseq_1(A),1)))) ) )).
fof(dt_o_1_2_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_2_fomodel3(A),A) ) )).
fof(dt_o_1_2_frechet,axiom,( ! [A] : m1_subset_1(o_1_2_frechet(A),k3_xboole_0(k4_ordinal1,A)) )).
fof(dt_o_1_2_funct_5,axiom,( ! [A] : m1_subset_1(o_1_2_funct_5(A),k9_xtuple_0(A)) )).
fof(dt_o_1_2_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & ~ v4_glib_000(A) ) => m1_subset_1(o_1_2_glib_000(A),k6_glib_000(A)) ) )).
fof(dt_o_1_2_graph_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_2_graph_3(A),A) ) )).
fof(dt_o_1_2_group_9,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_funct_1(o_1_2_group_9(A)) & v1_funct_2(o_1_2_group_9(A),k2_finseq_1(A),k2_finseq_1(A)) & v3_funct_2(o_1_2_group_9(A),k2_finseq_1(A),k2_finseq_1(A)) & m1_subset_1(o_1_2_group_9(A),k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(A),k2_finseq_1(A)))) ) ) )).
fof(dt_o_1_2_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => m2_funct_2(o_1_2_henmodel(A),k3_qc_lang1(A),o_0_0_henmodel,k2_valuat_1(A,o_0_0_henmodel)) ) )).
fof(dt_o_1_2_heyting1,axiom,( ! [A] : m1_subset_1(o_1_2_heyting1(A),k1_xtuple_0(A)) )).
fof(dt_o_1_2_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => m1_subset_1(o_1_2_incsp_1(A),u2_incsp_1(A)) ) )).
fof(dt_o_1_2_lattice7,axiom,( ! [A] : ( ( 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) ) => m1_subset_1(o_1_2_lattice7(A),k9_subset_1(u1_struct_0(A),k6_domain_1(u1_struct_0(A),k3_yellow_0(A)),k3_lattice7(A))) ) )).
fof(dt_o_1_2_matrix_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_matrix_2(A) ) => m1_matrix_2(o_1_2_matrix_2(A),A) ) )).
fof(dt_o_1_2_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v1_lattice2(A) & l3_lattices(A) ) => m1_subset_1(o_1_2_openlatt(A),k3_funct_2(u1_struct_0(A),u1_struct_0(k15_openlatt(A)),k16_openlatt(A),k5_lattices(A))) ) )).
fof(dt_o_1_2_ordinal5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_2_ordinal5(A),A) ) )).
fof(dt_o_1_2_ordinal6,axiom,( ! [A] : m1_subset_1(o_1_2_ordinal6(A),A) )).
fof(dt_o_1_2_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_2_pboole(A),A) ) )).
fof(dt_o_1_2_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => m1_subset_1(o_1_2_petri(A),k8_petri(A,k1_subset_1(u4_struct_0(A)))) ) )).
fof(dt_o_1_2_pua2mss1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => m1_subset_1(o_1_2_pua2mss1(A),k4_card_3(A)) ) )).
fof(dt_o_1_2_qc_trans,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_2_qc_trans(A),A) ) )).
fof(dt_o_1_2_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_quantal1(A) ) => m1_subset_1(o_1_2_quantal1(A),u1_struct_0(A)) ) )).
fof(dt_o_1_2_rltopsp1,axiom,( ! [A] : ( ( ~ 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_connsp_2(o_1_2_rltopsp1(A),A,k4_struct_0(A)) ) )).
fof(dt_o_1_2_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & v15_lattices(A) & v8_robbins1(A) & l4_robbins1(A) ) => m1_subset_1(o_1_2_robbins1(A),u1_struct_0(A)) ) )).
fof(dt_o_1_2_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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(o_1_2_scmring3(A),u1_struct_0(A)) ) )).
fof(dt_o_1_2_setfam_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_2_setfam_1(A),A) ) )).
fof(dt_o_1_2_simplex0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_2_simplex0(A),A) ) )).
fof(dt_o_1_2_simplex2,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(o_1_2_simplex2(A),u1_struct_0(k14_euclid(A))) ) )).
fof(dt_o_1_2_tex_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_2_tex_1(A),A) ) )).
fof(dt_o_1_2_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & v2_unialg_2(A) & l1_unialg_1(A) ) => m2_subset_1(o_1_2_unialg_2(A),u1_struct_0(A),k6_unialg_2(A)) ) )).
fof(dt_o_1_2_waybel21,axiom,( ! [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) & l1_waybel_9(A) ) => ( v4_waybel11(o_1_2_waybel21(A)) & m1_yellow_9(o_1_2_waybel21(A),A) ) ) )).
fof(dt_o_1_2_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & v2_waybel18(A) & l1_pre_topc(A) ) => ( v4_waybel11(o_1_2_waybel25(A)) & m1_yellow_9(o_1_2_waybel25(A),k1_waybel25(A)) ) ) )).
fof(dt_o_1_2_waybel27,axiom,( ! [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) & l1_orders_2(A) ) => ( v4_waybel11(o_1_2_waybel27(A)) & m1_yellow_9(o_1_2_waybel27(A),A) ) ) )).
fof(dt_o_1_2_waybel30,axiom,( ! [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) ) => ( v2_pre_topc(o_1_2_waybel30(A)) & v1_waybel19(o_1_2_waybel30(A)) & m1_yellow_9(o_1_2_waybel30(A),A) ) ) )).
fof(dt_o_1_2_weddwitt,axiom,( ! [A] : ( ( ~ 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_vectsp_7(o_1_2_weddwitt(A),k4_weddwitt(A),k6_weddwitt(A)) ) )).
fof(dt_o_1_2_yellow10,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => m1_subset_1(o_1_2_yellow10(A),u1_struct_0(A)) ) )).
fof(dt_o_1_2_yellow14,axiom,( ! [A] : ( l1_orders_2(A) => m1_subset_1(o_1_2_yellow14(A),u1_struct_0(A)) ) )).
fof(dt_o_1_2_yellow21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => m1_subset_1(o_1_2_yellow21(A),u1_struct_0(A)) ) )).
fof(dt_o_1_2_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ( ~ v1_xboole_0(o_1_2_yellow_3(A)) & m1_subset_1(o_1_2_yellow_3(A),k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_o_1_2_zfrefle1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ( v3_ordinal1(o_1_2_zfrefle1(A)) & m1_subset_1(o_1_2_zfrefle1(A),A) ) ) )).
fof(dt_o_1_3_abcmiz_a,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => m1_subset_1(o_1_3_abcmiz_a(A),A) ) )).
fof(dt_o_1_3_afinsq_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_3_afinsq_1(A),A) ) )).
fof(dt_o_1_3_aofa_i00,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_card_3(A) ) => ( v1_funct_1(o_1_3_aofa_i00(A)) & v1_funct_2(o_1_3_aofa_i00(A),k9_funct_2(A,k4_numbers),A) & m1_subset_1(o_1_3_aofa_i00(A),k1_zfmisc_1(k2_zfmisc_1(k9_funct_2(A,k4_numbers),A))) ) ) )).
fof(dt_o_1_3_card_3,axiom,( ! [A] : m1_subset_1(o_1_3_card_3(A),k5_card_3(A,k1_xboole_0)) )).
fof(dt_o_1_3_cohsp_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_3_cohsp_1(A),A) ) )).
fof(dt_o_1_3_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v15_lattices(A) & l3_lattices(A) ) => m1_subset_1(o_1_3_filter_1(A),u1_struct_0(A)) ) )).
fof(dt_o_1_3_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(o_1_3_finseq_3(A),k1_relset_1(k4_ordinal1,A)) ) )).
fof(dt_o_1_3_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => m2_subset_1(o_1_3_fomodel3(A),k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k35_fomodel1(A)) ) )).
fof(dt_o_1_3_funct_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => m1_subset_1(o_1_3_funct_5(A),k9_xtuple_0(k2_funct_5(A))) ) )).
fof(dt_o_1_3_glib_000,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_3_glib_000(A),A) ) )).
fof(dt_o_1_3_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) => m1_subset_1(o_1_3_glib_004(A),k6_glib_000(A)) ) )).
fof(dt_o_1_3_heyting1,axiom,( ! [A] : m2_funct_2(o_1_3_heyting1(A),k7_normform(A),k1_heyting1(A),k9_funct_2(k7_normform(A),k1_heyting1(A))) )).
fof(dt_o_1_3_lattice6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_3_lattice6(A),A) ) )).
fof(dt_o_1_3_matrix_2,axiom,( ! [A] : ( v7_ordinal1(A) => m1_matrix_2(o_1_3_matrix_2(A),k3_matrix_2(A)) ) )).
fof(dt_o_1_3_matroid0,axiom,( ! [A] : ( ( ~ v3_pencil_1(A) & v1_matroid0(A) & l1_pre_topc(A) ) => ( v3_pre_topc(o_1_3_matroid0(A),A) & m1_subset_1(o_1_3_matroid0(A),k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_o_1_3_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => m1_subset_1(o_1_3_midsp_1(A),u1_struct_0(A)) ) )).
fof(dt_o_1_3_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => m1_subset_1(o_1_3_petri(A),k9_petri(A,k1_subset_1(u4_struct_0(A)))) ) )).
fof(dt_o_1_3_polynom7,axiom,( ! [A] : ( v1_relat_1(o_1_3_polynom7(A)) & v4_relat_1(o_1_3_polynom7(A),A) & v1_funct_1(o_1_3_polynom7(A)) & v1_partfun1(o_1_3_polynom7(A),A) & v4_valued_0(o_1_3_polynom7(A)) & v2_pre_poly(o_1_3_polynom7(A)) ) )).
fof(dt_o_1_3_polyred,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_3_polyred(A),A) ) )).
fof(dt_o_1_3_tex_1,axiom,( ! [A] : m1_subset_1(o_1_3_tex_1(A),A) )).
fof(dt_o_1_3_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => m1_trees_1(o_1_3_trees_2(A),A) ) )).
fof(dt_o_1_3_unialg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & v2_unialg_2(A) & l1_unialg_1(A) ) => m2_subset_1(o_1_3_unialg_3(A),u1_struct_0(A),k6_unialg_2(A)) ) )).
fof(dt_o_1_3_waybel10,axiom,( ! [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) ) => m1_subset_1(o_1_3_waybel10(A),u1_struct_0(A)) ) )).
fof(dt_o_1_3_waybel29,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & l1_pre_topc(A) ) => ( v4_waybel11(o_1_3_waybel29(A)) & m1_yellow_9(o_1_3_waybel29(A),k1_yellow_1(u1_pre_topc(A))) ) ) )).
fof(dt_o_1_3_waybel33,axiom,( ! [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) ) => ( v2_pre_topc(o_1_3_waybel33(A)) & v1_waybel19(o_1_3_waybel33(A)) & m1_yellow_9(o_1_3_waybel33(A),A) ) ) )).
fof(dt_o_1_3_yellow10,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => m1_subset_1(o_1_3_yellow10(A),u1_struct_0(A)) ) )).
fof(dt_o_1_3_zmodul03,axiom,( ! [A] : ( ( ~ 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) & v1_zmodul03(A) & v2_zmodul03(A) & l1_zmodul01(A) ) => m1_zmodul03(o_1_3_zmodul03(A),A) ) )).
fof(dt_o_1_4_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => m1_subset_1(o_1_4_afproj(A),u1_struct_0(A)) ) )).
fof(dt_o_1_4_cat_5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_cat_5(A) ) => m1_cat_5(o_1_4_cat_5(A),A) ) )).
fof(dt_o_1_4_fcont_3,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => m1_rcomp_1(o_1_4_fcont_3(A),A) ) )).
fof(dt_o_1_4_finseq_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_4_finseq_1(A),A) ) )).
fof(dt_o_1_4_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_4_finseq_2(A),A) ) )).
fof(dt_o_1_4_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => m2_subset_1(o_1_4_fomodel2(A),k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k32_fomodel1(A)) ) )).
fof(dt_o_1_4_funct_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => m1_subset_1(o_1_4_funct_5(A),k9_xtuple_0(A)) ) )).
fof(dt_o_1_4_heyting1,axiom,( ! [A] : m2_funct_2(o_1_4_heyting1(A),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)))) )).
fof(dt_o_1_4_lang1,axiom,( ! [A] : m1_subset_1(o_1_4_lang1(A),k1_lang1(k6_lang1(A))) )).
fof(dt_o_1_4_nat_1,axiom,( ! [A] : ( v1_finset_1(A) => m1_subset_1(o_1_4_nat_1(A),A) ) )).
fof(dt_o_1_4_relat_1,axiom,( ! [A] : m1_subset_1(o_1_4_relat_1(A),A) )).
fof(dt_o_1_4_topgen_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k1_numbers))) => m1_subset_1(o_1_4_topgen_3(A),k6_subset_1(k1_numbers,a_1_1_topgen_3(A))) ) )).
fof(dt_o_1_4_waybel21,axiom,( ! [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) & l1_waybel_9(A) ) => ( v2_pre_topc(o_1_4_waybel21(A)) & v1_waybel19(o_1_4_waybel21(A)) & m1_yellow_9(o_1_4_waybel21(A),A) ) ) )).
fof(dt_o_1_4_waybel29,axiom,( ! [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) ) => ( v4_waybel11(o_1_4_waybel29(A)) & m1_yellow_9(o_1_4_waybel29(A),A) ) ) )).
fof(dt_o_1_4_waybel33,axiom,( ! [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) ) => ( v1_waybel33(o_1_4_waybel33(A)) & m1_yellow_9(o_1_4_waybel33(A),A) ) ) )).
fof(dt_o_1_4_waybel_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_4_waybel_4(A),A) ) )).
fof(dt_o_1_4_yellow10,axiom,( ! [A] : ( ( ~ 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) ) => m1_subset_1(o_1_4_yellow10(A),u1_struct_0(A)) ) )).
fof(dt_o_1_5_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => m1_subset_1(o_1_5_card_3(A),k9_xtuple_0(A)) ) )).
fof(dt_o_1_5_catalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_instalg1(A) & v2_catalg_1(A) & v3_catalg_1(A) & l1_msualg_1(A) ) => m1_subset_1(o_1_5_catalg_1(A),u1_struct_0(A)) ) )).
fof(dt_o_1_5_fomodel0,axiom,( ! [A] : m2_subset_1(o_1_5_fomodel0(A),k1_zfmisc_1(k10_xtuple_0(A)),k7_subset_1(k1_zfmisc_1(k10_xtuple_0(A)),k9_setfam_1(k10_xtuple_0(A)),k10_xtuple_0(A))) )).
fof(dt_o_1_5_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => m2_subset_1(o_1_5_fomodel2(A),k9_funct_2(k37_fomodel1(A),k3_rfunct_3(k3_finseq_2(o_0_0_fomodel2),k2_xboole_0(o_0_0_fomodel2,k6_margrel1))),k15_fomodel2(A,o_0_0_fomodel2)) ) )).
fof(dt_o_1_5_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_5_lattice5(A),A) ) )).
fof(dt_o_1_5_lfuzzy_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_5_lfuzzy_0(A),A) ) )).
fof(dt_o_1_5_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => m2_subset_1(o_1_5_lopclset(A),k1_zfmisc_1(u1_struct_0(k11_lopclset(A))),k1_lopclset(k11_lopclset(A))) ) )).
fof(dt_o_1_5_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => m2_orders_1(o_1_5_modelc_3(A),k1_orders_1(k1_modelc_3(A)),k6_partfun1(k1_orders_1(k1_modelc_3(A)))) ) )).
fof(dt_o_1_5_pua2mss1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_5_pua2mss1(A),A) ) )).
fof(dt_o_1_5_stacks_1,axiom,( ! [A] : ( ( ~ 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) ) => m2_orders_1(o_1_5_stacks_1(A),k8_eqrel_1(u4_struct_0(A),k10_stacks_1(A)),k6_partfun1(k8_eqrel_1(u4_struct_0(A),k10_stacks_1(A)))) ) )).
fof(dt_o_1_5_trees_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_5_trees_2(A),A) ) )).
fof(dt_o_1_5_waybel32,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ( v4_waybel11(o_1_5_waybel32(A)) & m1_yellow_9(o_1_5_waybel32(A),A) ) ) )).
fof(dt_o_1_5_waybel_4,axiom,( ! [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) ) => ( ~ v1_xboole_0(o_1_5_waybel_4(A)) & v1_waybel_0(o_1_5_waybel_4(A),A) & v12_waybel_0(o_1_5_waybel_4(A),A) & m1_subset_1(o_1_5_waybel_4(A),k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_o_1_5_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => m1_subset_1(o_1_5_yellow10(A),u1_struct_0(A)) ) )).
fof(dt_o_1_6_cat_5,axiom,( ! [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) & v4_cat_5(A) & l1_cat_1(A) ) => m1_subset_1(o_1_6_cat_5(A),u4_struct_0(A)) ) )).
fof(dt_o_1_6_lopclset,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_6_lopclset(A),A) ) )).
fof(dt_o_1_6_waybel31,axiom,( ! [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) ) => ( v2_pre_topc(o_1_6_waybel31(A)) & v2_waybel19(o_1_6_waybel31(A)) & m1_yellow_9(o_1_6_waybel31(A),A) ) ) )).
fof(dt_o_1_6_waybel33,axiom,( ! [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) ) => ( v2_pre_topc(o_1_6_waybel33(A)) & v2_waybel19(o_1_6_waybel33(A)) & m1_yellow_9(o_1_6_waybel33(A),A) ) ) )).
fof(dt_o_1_6_waybel_4,axiom,( ! [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) & l1_orders_2(A) ) => ( v5_waybel_4(o_1_6_waybel_4(A),A) & v6_waybel_4(o_1_6_waybel_4(A),A) & m1_subset_1(o_1_6_waybel_4(A),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) ) )).
fof(dt_o_1_7_conlat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_subset_1(o_1_7_conlat_1(A),A) ) )).
fof(dt_o_1_7_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => m1_subset_1(o_1_7_lopclset(A),k3_funct_2(u1_struct_0(A),k9_setfam_1(k7_lopclset(A)),k9_lopclset(A),k5_lattices(A))) ) )).
fof(dt_o_1_7_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => m2_ltlaxio4(o_1_7_ltlaxio4(A),k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)),k9_ltlaxio4(A)) ) )).
fof(dt_o_1_7_waybel30,axiom,( ! [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) ) => ( ~ v2_struct_0(o_1_7_waybel30(A)) & v2_pre_topc(o_1_7_waybel30(A)) & v1_waybel19(o_1_7_waybel30(A)) & m1_yellow_9(o_1_7_waybel30(A),A) ) ) )).
fof(dt_o_1_7_waybel31,axiom,( ! [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) ) => ( v4_waybel11(o_1_7_waybel31(A)) & m1_yellow_9(o_1_7_waybel31(A),A) ) ) )).
fof(dt_o_1_7_waybel33,axiom,( ! [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) ) => ( v4_waybel11(o_1_7_waybel33(A)) & m1_yellow_9(o_1_7_waybel33(A),A) ) ) )).
fof(dt_o_1_7_waybel_4,axiom,( ! [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) & l1_orders_2(A) ) => ( ~ v1_xboole_0(o_1_7_waybel_4(A)) & v1_waybel_0(o_1_7_waybel_4(A),A) & v12_waybel_0(o_1_7_waybel_4(A),A) & m1_subset_1(o_1_7_waybel_4(A),k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(dt_o_1_8_cat_5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_cat_5(A) ) => m2_cat_1(o_1_8_cat_5(A),o_1_4_cat_5(A),o_1_4_cat_5(A)) ) )).
fof(dt_o_1_8_waybel30,axiom,( ! [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) ) => ( ~ v2_struct_0(o_1_8_waybel30(A)) & v2_pre_topc(o_1_8_waybel30(A)) & v4_waybel11(o_1_8_waybel30(A)) & m1_yellow_9(o_1_8_waybel30(A),A) ) ) )).
fof(dt_o_1_8_waybel33,axiom,( ! [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) & v1_waybel33(A) & l1_waybel_9(A) ) => ( v2_pre_topc(o_1_8_waybel33(A)) & v2_waybel19(o_1_8_waybel33(A)) & m1_yellow_9(o_1_8_waybel33(A),A) ) ) )).
fof(dt_o_1_9_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => m1_subset_1(o_1_9_cohsp_1(A),A) ) )).
fof(dt_o_1_9_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => m2_finseq_2(o_1_9_comput_1(A),k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) ) )).
fof(dt_o_1_9_waybel30,axiom,( ! [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_waybel_2(A) & l1_waybel_9(A) ) => ( v2_pre_topc(o_1_9_waybel30(A)) & v2_waybel19(o_1_9_waybel30(A)) & m1_yellow_9(o_1_9_waybel30(A),k3_yellow_3(A,A)) ) ) )).
fof(dt_o_2_0_aff_4,axiom,( ! [A] : ! [B] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(o_2_0_aff_4(A,B),B) ) )).
fof(dt_o_2_0_afinsq_2,axiom,( ! [A] : ! [B] : m1_subset_1(o_2_0_afinsq_2(A,B),k3_xboole_0(k3_xboole_0(A,B),k4_ordinal1)) )).
fof(dt_o_2_0_afproj,axiom,( ! [A] : ! [B] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(o_2_0_afproj(A,B),B) ) )).
fof(dt_o_2_0_algspec1,axiom,( ! [A] : ! [B] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => m1_algspec1(o_2_0_algspec1(A,B),k1_algspec1(u4_struct_0(A),B)) ) )).
fof(dt_o_2_0_altcat_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,u1_struct_0(k7_altcat_1(A))) ) => m1_subset_1(o_2_0_altcat_3(A,B),B) ) )).
fof(dt_o_2_0_altcat_4,axiom,( ! [A] : ! [B] : ( ( ~ 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(o_2_0_altcat_4(A,B),k1_altcat_1(A,B,B)) ) )).
fof(dt_o_2_0_amistd_1,axiom,( ! [A] : ! [B] : ( ( ~ 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(o_2_0_amistd_1(A,B)) & v4_relat_1(o_2_0_amistd_1(A,B),u1_struct_0(B)) & v1_funct_1(o_2_0_amistd_1(A,B)) & v5_funct_1(o_2_0_amistd_1(A,B),k2_memstr_0(A,B)) & v1_partfun1(o_2_0_amistd_1(A,B),u1_struct_0(B)) ) ) )).
fof(dt_o_2_0_amistd_4,axiom,( ! [A] : ! [B] : ( ( ~ v1_setfam_1(A) & ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & v2_amistd_4(B,A) & l1_extpro_1(B,A) ) => ( v1_relat_1(o_2_0_amistd_4(A,B)) & v4_relat_1(o_2_0_amistd_4(A,B),u1_struct_0(B)) & v1_funct_1(o_2_0_amistd_4(A,B)) & v5_funct_1(o_2_0_amistd_4(A,B),k2_memstr_0(A,B)) & v1_partfun1(o_2_0_amistd_4(A,B),u1_struct_0(B)) ) ) )).
fof(dt_o_2_0_amistd_5,axiom,( ! [A] : ! [B] : ( ( ~ 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_5(B,A) & v4_amistd_5(B,A) & l1_extpro_1(B,A) ) => ( v1_relat_1(o_2_0_amistd_5(A,B)) & v4_relat_1(o_2_0_amistd_5(A,B),k4_ordinal1) & v5_relat_1(o_2_0_amistd_5(A,B),u1_compos_1(B)) & v1_funct_1(o_2_0_amistd_5(A,B)) & v1_partfun1(o_2_0_amistd_5(A,B),k4_ordinal1) ) ) )).
fof(dt_o_2_0_autalg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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(o_2_0_autalg_1(A,B),u1_struct_0(k7_autalg_1(A,B))) ) )).
fof(dt_o_2_0_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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_3(o_2_0_cat_3(A,B),A,B,k1_xboole_0) ) )).
fof(dt_o_2_0_cfunct_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => m1_subset_1(o_2_0_cfunct_1(A,B),k8_relset_1(A,k2_numbers,k2_cfunct_1(A,B),k1_tarski(k5_complex1))) ) )).
fof(dt_o_2_0_clvect_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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(o_2_0_clvect_1(A,B),B) ) )).
fof(dt_o_2_0_dist_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => m1_dist_2(o_2_0_dist_2(A,B),A,B) ) )).
fof(dt_o_2_0_ens_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,u1_struct_0(k11_ens_1(A))) ) => m1_subset_1(o_2_0_ens_1(A,B),k13_ens_1(A,B)) ) )).
fof(dt_o_2_0_fintopo4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(o_2_0_fintopo4(A,B),B) ) )).
fof(dt_o_2_0_fvaluat1,axiom,( ! [A] : ! [B] : ( ( ~ 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(o_2_0_fvaluat1(A,B),k8_relset_1(u1_struct_0(A),k6_numbers,B,k1_tarski(k1_fvaluat1(k2_relset_1(k6_numbers,B))))) ) )).
fof(dt_o_2_0_glib_002,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & ~ v4_glib_000(A) & v1_glib_002(A) & m3_glib_001(B,A) ) => ( v4_glib_001(o_2_0_glib_002(A,B),A) & m4_glib_001(o_2_0_glib_002(A,B),A,B) ) ) )).
fof(dt_o_2_0_glib_004,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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(o_2_0_glib_004(A,B),k6_glib_004(A,B)) ) )).
fof(dt_o_2_0_group_5,axiom,( ! [A] : ! [B] : ( ( ~ 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(o_2_0_group_5(A,B),B) ) )).
fof(dt_o_2_0_hahnban,axiom,( ! [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) & v8_rlvect_1(A) & l1_rlvect_1(A) & m1_rlsub_1(B,A) ) => m1_subset_1(o_2_0_hahnban(A,B),u1_struct_0(B)) ) )).
fof(dt_o_2_0_interva1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_interva1(B,A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => m2_subset_1(o_2_0_interva1(A,B),k1_zfmisc_1(A),B) ) )).
fof(dt_o_2_0_jgraph_7,axiom,( ! [A] : ! [B] : ( ( 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))))) & 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))))) ) => m1_subset_1(o_2_0_jgraph_7(A,B),k9_subset_1(u1_struct_0(k15_euclid(2)),k2_relset_1(u1_struct_0(k15_euclid(2)),B),k2_relset_1(u1_struct_0(k15_euclid(2)),A))) ) )).
fof(dt_o_2_0_jordan20,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & v1_xreal_0(B) ) => m1_subset_1(o_2_0_jordan20(A,B),k9_subset_1(u1_struct_0(k15_euclid(2)),A,k6_jordan6(B))) ) )).
fof(dt_o_2_0_kurato_2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) ) => m1_connsp_2(o_2_0_kurato_2(A,B),k15_euclid(A),B) ) )).
fof(dt_o_2_0_latsubgr,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) => m2_subset_1(o_2_0_latsubgr(A,B),k1_group_3(A),B) ) )).
fof(dt_o_2_0_lexbfs,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k15_pre_poly(k4_ordinal1))) & v1_relat_1(B) & v1_funct_1(B) ) => m1_subset_1(o_2_0_lexbfs(A,B),k8_relat_1(B,k6_domain_1(k1_zfmisc_1(k4_ordinal1),k22_pre_poly(k4_ordinal1,k4_lexbfs(k4_ordinal1,k4_bagorder(k4_ordinal1),A))))) ) )).
fof(dt_o_2_0_midsp_3,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m2_midsp_3(B,A) ) => m1_subset_1(o_2_0_midsp_3(A,B),u1_struct_0(B)) ) )).
fof(dt_o_2_0_mssublat,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v1_unialg_1(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) & v1_unialg_1(B) & v4_unialg_1(B) & m1_unialg_2(B,A) ) => m1_subset_1(o_2_0_mssublat(A,B),u1_struct_0(B)) ) )).
fof(dt_o_2_0_msualg_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => m2_pboole(o_2_0_msualg_9(A,B),u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,k7_msafree2(A))) ) )).
fof(dt_o_2_0_ordinal1,axiom,( ! [A] : ! [B] : ( ( v1_ordinal1(A) & v3_ordinal1(B) ) => m1_subset_1(o_2_0_ordinal1(A,B),k6_subset_1(B,A)) ) )).
fof(dt_o_2_0_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ( v1_relat_1(o_2_0_pboole(A,B)) & v4_relat_1(o_2_0_pboole(A,B),A) & v1_funct_1(o_2_0_pboole(A,B)) & v5_funct_1(o_2_0_pboole(A,B),B) & v1_partfun1(o_2_0_pboole(A,B),A) ) ) )).
fof(dt_o_2_0_pcomps_1,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(o_2_0_pcomps_1(A,B),B) ) )).
fof(dt_o_2_0_pencil_3,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) => m1_subset_1(o_2_0_pencil_3(A,B),u1_struct_0(k5_pencil_1(A,B))) ) )).
fof(dt_o_2_0_polynom2,axiom,( ! [A] : ! [B] : ( ( 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) ) => m1_subset_1(o_2_0_polynom2(A,B),k3_polynom1(k15_pre_poly(A),B,k8_polynom1(A,B))) ) )).
fof(dt_o_2_0_pre_topc,axiom,( ! [A] : ! [B] : ( ( l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(o_2_0_pre_topc(A,B),B) ) )).
fof(dt_o_2_0_ranknull,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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_7(o_2_0_ranknull(A,B),A,B) ) )).
fof(dt_o_2_0_rearran1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => m1_subset_1(o_2_0_rearran1(A,B),k3_xboole_0(k10_xtuple_0(A),k1_tarski(B))) ) )).
fof(dt_o_2_0_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => m1_subset_1(o_2_0_relat_1(A,B),k7_relat_1(B,A)) ) )).
fof(dt_o_2_0_rfunct_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => m1_subset_1(o_2_0_rfunct_3(A,B),k3_xboole_0(k10_xtuple_0(A),k1_tarski(B))) ) )).
fof(dt_o_2_0_rlsub_1,axiom,( ! [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) & v8_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(o_2_0_rlsub_1(A,B),B) ) )).
fof(dt_o_2_0_rmod_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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(o_2_0_rmod_2(A,B),u1_struct_0(B)) ) )).
fof(dt_o_2_0_rpr_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v3_card_1(B,1) & m1_subset_1(B,k1_zfmisc_1(A)) ) => m2_subset_1(o_2_0_rpr_1(A,B),A,B) ) )).
fof(dt_o_2_0_rusub_4,axiom,( ! [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) & v8_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) & m1_rusub_1(B,A) ) => m1_rusub_3(o_2_0_rusub_4(A,B),B) ) )).
fof(dt_o_2_0_setfam_1,axiom,( ! [A] : ! [B] : m1_subset_1(o_2_0_setfam_1(A,B),k3_xboole_0(A,B)) )).
fof(dt_o_2_0_setwiseo,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k5_finsub_1(A)) ) => m1_subset_1(o_2_0_setwiseo(A,B),B) ) )).
fof(dt_o_2_0_termord,axiom,( ! [A] : ! [B] : ( ( ~ 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) & m2_finseq_1(B,u1_struct_0(A)) ) => m1_subset_1(o_2_0_termord(A,B),k4_finseq_1(B)) ) )).
fof(dt_o_2_0_topalg_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( v3_funct_1(o_2_0_topalg_1(A,B)) & m1_borsuk_2(o_2_0_topalg_1(A,B),A,B,B) ) ) )).
fof(dt_o_2_0_topalg_6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( v3_funct_1(o_2_0_topalg_6(A,B)) & m1_borsuk_2(o_2_0_topalg_6(A,B),A,B,B) ) ) )).
fof(dt_o_2_0_topgen_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( v1_yellow_8(o_2_0_topgen_1(A,B),A,B) & v1_tops_2(o_2_0_topgen_1(A,B),A) & m1_subset_1(o_2_0_topgen_1(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) )).
fof(dt_o_2_0_tops_1,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(o_2_0_tops_1(A,B),k1_tops_1(A,k2_tops_1(A,k2_tops_1(A,B)))) ) )).
fof(dt_o_2_0_tops_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) => m1_subset_1(o_2_0_tops_2(A,B),k5_setfam_1(u1_struct_0(A),B)) ) )).
fof(dt_o_2_0_unialg_3,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) => m2_subset_1(o_2_0_unialg_3(A,B),k1_unialg_3(A),B) ) )).
fof(dt_o_2_0_vectsp11,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & 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) & ~ 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) ) => m1_matrlin(o_2_0_vectsp11(A,B),A,B) ) )).
fof(dt_o_2_0_vectsp_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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(o_2_0_vectsp_4(A,B),u1_struct_0(B)) ) )).
fof(dt_o_2_0_vectsp_9,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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_7(o_2_0_vectsp_9(A,B),A,B) ) )).
fof(dt_o_2_0_waybel20,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v3_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(o_2_0_waybel20(A,B),B) ) )).
fof(dt_o_2_0_waybel25,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m2_subset_1(o_2_0_waybel25(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_0_waybel_7,axiom,( ! [A] : ! [B] : ( ( 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))) ) => m2_subset_1(o_2_0_waybel_7(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_0_wellord1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => m1_subset_1(o_2_0_wellord1(A,B),k1_wellord1(B,A)) ) )).
fof(dt_o_2_0_yellow_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(A)))) ) => m2_subset_1(o_2_0_yellow_1(A,B),u1_struct_0(k2_yellow_1(A)),B) ) )).
fof(dt_o_2_0_yellow_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m2_subset_1(o_2_0_yellow_3(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_0_zf_lang1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(A) => m1_subset_1(o_2_0_zf_lang1(A,B),k3_xboole_0(B,A)) ) )).
fof(dt_o_2_0_zfmodel1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m1_subset_1(o_2_0_zfmodel1(A,B),B) ) )).
fof(dt_o_2_0_zmodul01,axiom,( ! [A] : ! [B] : ( ( ~ 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,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(o_2_0_zmodul01(A,B),B) ) )).
fof(dt_o_2_10_glib_002,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & m3_glib_001(B,A) ) => m2_glib_000(o_2_10_glib_002(A,B),A,k6_glib_000(A),k6_subset_1(k7_glib_000(A),k1_tarski(o_2_9_glib_002(A,B)))) ) )).
fof(dt_o_2_10_waybel30,axiom,( ! [A] : ! [B] : ( ( 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) ) => ( ~ v2_struct_0(o_2_10_waybel30(A,B)) & v2_pre_topc(o_2_10_waybel30(A,B)) & v2_waybel19(o_2_10_waybel30(A,B)) & m1_yellow_9(o_2_10_waybel30(A,B),k3_yellow_3(A,B)) ) ) )).
fof(dt_o_2_10_waybel_0,axiom,( ! [A] : ! [B] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_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))) ) => m2_subset_1(o_2_10_waybel_0(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_11_waybel_0,axiom,( ! [A] : ! [B] : ( ( 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))) ) => m2_subset_1(o_2_11_waybel_0(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_12_conlat_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u4_struct_0(A)))) ) => m1_subset_1(o_2_12_conlat_2(A,B),a_2_1_conlat_2(A,B)) ) )).
fof(dt_o_2_12_waybel11,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_subset_1(o_2_12_waybel11(A,B),u1_struct_0(k4_waybel11(A,B))) ) )).
fof(dt_o_2_12_yellow19,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v1_xboole_0(B) & v2_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v3_waybel_7(B,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))))) ) => m2_subset_1(o_2_12_yellow19(A,B),u1_struct_0(k2_yellow_1(k2_struct_0(A))),B) ) )).
fof(dt_o_2_13_conlat_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u4_struct_0(A)))) ) => m2_subset_1(o_2_13_conlat_2(A,B),k1_zfmisc_1(u4_struct_0(A)),B) ) )).
fof(dt_o_2_13_yellow19,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v1_xboole_0(B) & v2_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v3_waybel_7(B,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))))) ) => m1_subset_1(o_2_13_yellow19(A,B),k10_yellow_6(A,k3_yellow19(A,k2_struct_0(A),B))) ) )).
fof(dt_o_2_14_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v6_trees_3(B) ) => m1_subset_1(o_2_14_abcmiz_1(A,B),a_2_2_abcmiz_1(A,B)) ) )).
fof(dt_o_2_14_waybel11,axiom,( ! [A] : ! [B] : ( ( 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_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => m1_subset_1(o_2_14_waybel11(A,B),u1_struct_0(B)) ) )).
fof(dt_o_2_15_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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(o_2_15_abcmiz_1(A,B),k3_card_3(k2_msafree3(A,B))) ) )).
fof(dt_o_2_16_ideal_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v5_algstr_0(A) & v4_rlvect_1(A) & v2_vectsp_1(A) & l6_algstr_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m2_subset_1(o_2_16_ideal_1(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_1_afinsq_2,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & v6_membered(A) & v1_finset_1(B) & v6_membered(B) ) => m1_subset_1(o_2_1_afinsq_2(A,B),k3_xboole_0(A,B)) ) )).
fof(dt_o_2_1_ami_wstd,axiom,( ! [A] : ! [B] : ( ( ~ 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(o_2_1_ami_wstd(A,B)) & v4_relat_1(o_2_1_ami_wstd(A,B),u1_struct_0(B)) & v1_funct_1(o_2_1_ami_wstd(A,B)) & v5_funct_1(o_2_1_ami_wstd(A,B),k2_memstr_0(A,B)) & v1_partfun1(o_2_1_ami_wstd(A,B),u1_struct_0(B)) ) ) )).
fof(dt_o_2_1_amistd_1,axiom,( ! [A] : ! [B] : ( ( ~ 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(o_2_1_amistd_1(A,B)) & v4_relat_1(o_2_1_amistd_1(A,B),k4_ordinal1) & v5_relat_1(o_2_1_amistd_1(A,B),u1_compos_1(B)) & v1_funct_1(o_2_1_amistd_1(A,B)) & v1_partfun1(o_2_1_amistd_1(A,B),k4_ordinal1) ) ) )).
fof(dt_o_2_1_amistd_4,axiom,( ! [A] : ! [B] : ( ( ~ 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(o_2_1_amistd_4(A,B)) & v4_relat_1(o_2_1_amistd_4(A,B),u1_struct_0(B)) & v1_funct_1(o_2_1_amistd_4(A,B)) & v5_funct_1(o_2_1_amistd_4(A,B),k2_memstr_0(A,B)) & v1_partfun1(o_2_1_amistd_4(A,B),u1_struct_0(B)) ) ) )).
fof(dt_o_2_1_bintree1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & m1_trees_1(B,A) ) => m1_subset_1(o_2_1_bintree1(A,B),k1_trees_2(A,B)) ) )).
fof(dt_o_2_1_card_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => m1_subset_1(o_2_1_card_3(A,B),k1_funct_1(A,B)) ) )).
fof(dt_o_2_1_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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_3(o_2_1_cat_3(A,B),A,B,k1_xboole_0) ) )).
fof(dt_o_2_1_chord,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & m3_glib_001(B,A) ) => ( v5_glib_001(o_2_1_chord(A,B),A) & m4_glib_001(o_2_1_chord(A,B),A,B) ) ) )).
fof(dt_o_2_1_dist_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => m1_dist_2(o_2_1_dist_2(A,B),A,B) ) )).
fof(dt_o_2_1_eqrel_1,axiom,( ! [A] : ! [B] : ( ( 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(o_2_1_eqrel_1(A,B),k7_eqrel_1(A,B)) ) )).
fof(dt_o_2_1_filter_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v10_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))) ) => m2_subset_1(o_2_1_filter_2(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_1_frechet,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) => m1_subset_1(o_2_1_frechet(A,B),B) ) )).
fof(dt_o_2_1_frechet2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => m1_subset_1(o_2_1_frechet2(A,B),k2_frechet(A,B)) ) )).
fof(dt_o_2_1_funct_2,axiom,( ! [A] : ! [B] : m1_subset_1(o_2_1_funct_2(A,B),k3_xboole_0(A,B)) )).
fof(dt_o_2_1_glib_002,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) ) => m2_glib_000(o_2_1_glib_002(A,B),A,B,k21_glib_000(A,B)) ) )).
fof(dt_o_2_1_glib_004,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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(o_2_1_glib_004(A,B),k12_glib_004(A,B)) ) )).
fof(dt_o_2_1_graph_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v5_graph_1(A) & v6_graph_1(A) & l1_graph_1(A) & m2_finseq_2(B,u4_struct_0(A),k9_graph_3(A)) ) => m1_subset_1(o_2_1_graph_3(A,B),a_2_0_graph_3(A,B)) ) )).
fof(dt_o_2_1_group_2,axiom,( ! [A] : ! [B] : ( ( ~ 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(o_2_1_group_2(A,B),k1_group_2(A,B)) ) )).
fof(dt_o_2_1_jgraph_7,axiom,( ! [A] : ! [B] : ( ( 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))))) & 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))))) ) => m1_subset_1(o_2_1_jgraph_7(A,B),k9_subset_1(u1_struct_0(k15_euclid(2)),k2_relset_1(u1_struct_0(k15_euclid(2)),A),k2_relset_1(u1_struct_0(k15_euclid(2)),B))) ) )).
fof(dt_o_2_1_lexbfs,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v6_membered(A) & v1_finset_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => m1_subset_1(o_2_1_lexbfs(A,B),k8_relat_1(B,k1_tarski(k1_xxreal_2(A)))) ) )).
fof(dt_o_2_1_mfold_2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_rlvect_1(B) & m1_rlsub_1(B,k15_euclid(A)) ) => m1_rlvect_3(o_2_1_mfold_2(A,B),B) ) )).
fof(dt_o_2_1_orders_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(A) => m1_subset_1(o_2_1_orders_1(A,B),k1_funct_1(k6_partfun1(A),B)) ) )).
fof(dt_o_2_1_pboole,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( v1_relat_1(o_2_1_pboole(A,B)) & v4_relat_1(o_2_1_pboole(A,B),A) & v5_relat_1(o_2_1_pboole(A,B),B) & v1_funct_1(o_2_1_pboole(A,B)) & v1_partfun1(o_2_1_pboole(A,B),A) ) ) )).
fof(dt_o_2_1_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => m1_subset_1(o_2_1_relat_1(A,B),k8_relat_1(B,A)) ) )).
fof(dt_o_2_1_rlsub_2,axiom,( ! [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) & v8_rlvect_1(A) & l1_rlvect_1(A) & m1_rlsub_1(B,A) ) => ( v1_rlvect_1(o_2_1_rlsub_2(A,B)) & m1_rlsub_2(o_2_1_rlsub_2(A,B),A,B) ) ) )).
fof(dt_o_2_1_rlvect_3,axiom,( ! [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) & v8_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(o_2_1_rlvect_3(A,B),B) ) )).
fof(dt_o_2_1_rlvect_5,axiom,( ! [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) & v8_rlvect_1(A) & l1_rlvect_1(A) & m1_rlsub_1(B,A) ) => m1_rlvect_3(o_2_1_rlvect_5(A,B),B) ) )).
fof(dt_o_2_1_rpr_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => m1_subset_1(o_2_1_rpr_1(A,B),B) ) )).
fof(dt_o_2_1_rusub_2,axiom,( ! [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) & v8_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) & m1_rusub_1(B,A) ) => ( v1_bhsp_1(o_2_1_rusub_2(A,B)) & m1_rusub_2(o_2_1_rusub_2(A,B),A,B) ) ) )).
fof(dt_o_2_1_rusub_3,axiom,( ! [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) & 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(o_2_1_rusub_3(A,B),B) ) )).
fof(dt_o_2_1_rusub_4,axiom,( ! [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) & v8_rlvect_1(A) & v2_bhsp_1(A) & v1_rusub_4(A) & l1_bhsp_1(A) & m1_rusub_1(B,A) ) => m1_rusub_3(o_2_1_rusub_4(A,B),B) ) )).
fof(dt_o_2_1_setfam_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => m1_subset_1(o_2_1_setfam_1(A,B),B) ) )).
fof(dt_o_2_1_tbsp_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(o_2_1_tbsp_1(A,B),B) ) )).
fof(dt_o_2_1_tdlat_3,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(o_2_1_tdlat_3(A,B),B) ) )).
fof(dt_o_2_1_topreal1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m2_finseq_1(B,u1_struct_0(k15_euclid(A))) ) => m1_subset_1(o_2_1_topreal1(A,B),a_2_0_topreal1(A,B)) ) )).
fof(dt_o_2_1_tops_1,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(o_2_1_tops_1(A,B),B) ) )).
fof(dt_o_2_1_tops_2,axiom,( ! [A] : ! [B] : ( ( ~ 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(o_2_1_tops_2(A,B),B) ) )).
fof(dt_o_2_1_waybel19,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) & ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & l1_orders_2(B) ) => ( v2_pre_topc(o_2_1_waybel19(A,B)) & v1_waybel19(o_2_1_waybel19(A,B)) & m1_yellow_9(o_2_1_waybel19(A,B),k3_yellow_3(A,B)) ) ) )).
fof(dt_o_2_1_waybel28,axiom,( ! [A] : ! [B] : ( ( 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_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => m1_subset_1(o_2_1_waybel28(A,B),u1_struct_0(B)) ) )).
fof(dt_o_2_1_waybel34,axiom,( ! [A] : ! [B] : ( ( 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)) & v7_waybel_1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ( v4_waybel11(o_2_1_waybel34(A,B)) & m1_yellow_9(o_2_1_waybel34(A,B),k1_yellow_2(A,A,B)) ) ) )).
fof(dt_o_2_1_waybel_7,axiom,( ! [A] : ! [B] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_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))) ) => m2_subset_1(o_2_1_waybel_7(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_1_yellow13,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( v1_yellow_8(o_2_1_yellow13(A,B),A,B) & v1_tops_2(o_2_1_yellow13(A,B),A) & m1_subset_1(o_2_1_yellow13(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) )).
fof(dt_o_2_1_yellow_3,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) => m2_subset_1(o_2_1_yellow_3(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_20_ideal_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v5_algstr_0(A) & v4_rlvect_1(A) & v2_vectsp_1(A) & v1_algstr_1(A) & l6_algstr_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m2_subset_1(o_2_20_ideal_1(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_26_ideal_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v1_algstr_1(A) & v1_int_3(A) & l6_algstr_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m2_subset_1(o_2_26_ideal_1(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_2_card_fil,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_card_fil(B,A) ) => m2_subset_1(o_2_2_card_fil(A,B),k1_zfmisc_1(A),B) ) )).
fof(dt_o_2_2_cat_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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))) ) => m2_subset_1(o_2_2_cat_2(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_2_dickson,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m2_subset_1(o_2_2_dickson(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_2_eqrel_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => m1_subset_1(o_2_2_eqrel_1(A,B),B) ) )).
fof(dt_o_2_2_exchsort,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => m1_subset_1(o_2_2_exchsort(A,B),k6_subset_1(A,B)) ) )).
fof(dt_o_2_2_filter_0,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) => m2_subset_1(o_2_2_filter_0(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_2_finseq_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => m1_subset_1(o_2_2_finseq_3(A,B),k3_xboole_0(k1_tarski(k1_nat_1(k3_finseq_1(A),1)),k8_relat_1(A,B))) ) )).
fof(dt_o_2_2_fintopo6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(o_2_2_fintopo6(A,B),B) ) )).
fof(dt_o_2_2_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & 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))) ) => m2_subset_1(o_2_2_fomodel4(A,B),k15_fomodel1(A),k9_subset_1(k15_fomodel1(A),k10_xtuple_0(B),k16_fomodel1(A))) ) )).
fof(dt_o_2_2_frechet,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) & v1_xreal_0(B) ) => m1_subset_1(o_2_2_frechet(A,B),k9_subset_1(u1_struct_0(k3_topmetr),k2_rcomp_1(k6_xcmplx_0(B,k7_xcmplx_0(1,4)),k2_xcmplx_0(B,k7_xcmplx_0(1,4))),A)) ) )).
fof(dt_o_2_2_glib_002,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => m2_glib_000(o_2_2_glib_002(A,B),A,k1_glib_002(A,B),k21_glib_000(A,k1_glib_002(A,B))) ) )).
fof(dt_o_2_2_graph_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k9_graph_3(A))) ) => m1_graph_3(o_2_2_graph_3(A,B),u4_struct_0(A),k9_graph_3(A),B) ) )).
fof(dt_o_2_2_group_2,axiom,( ! [A] : ! [B] : ( ( ~ 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(o_2_2_group_2(A,B),B) ) )).
fof(dt_o_2_2_ideal_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) => m2_subset_1(o_2_2_ideal_1(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_2_ltlaxio4,axiom,( ! [A] : ! [B] : ( ( ~ v2_ltlaxio3(A) & v3_ltlaxio3(A) & m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) & m3_ltlaxio4(B,A) ) => m2_ltlaxio4(o_2_2_ltlaxio4(A,B),k1_hilbert1,k3_ltlaxio4(k11_ltlaxio4(A,B))) ) )).
fof(dt_o_2_2_monoid_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => m1_subset_1(o_2_2_monoid_1(A,B),B) ) )).
fof(dt_o_2_2_msscyc_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & v4_msualg_1(B,A) & v3_msafree2(B,A) & l3_msualg_1(B,A) ) => ( v2_relat_1(o_2_2_msscyc_2(A,B)) & v2_finset_1(o_2_2_msscyc_2(A,B)) & m1_msafree(o_2_2_msscyc_2(A,B),A,B) ) ) )).
fof(dt_o_2_2_pencil_1,axiom,( ! [A] : ! [B] : ( ( ~ 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_relat_1(o_2_2_pencil_1(A,B)) & v13_pencil_1(o_2_2_pencil_1(A,B)) & m3_pboole(o_2_2_pencil_1(A,B),A,k12_pralg_1(A,B)) ) ) )).
fof(dt_o_2_2_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k15_pre_poly(A))) ) => m2_subset_1(o_2_2_polynom7(A,B),k15_pre_poly(A),B) ) )).
fof(dt_o_2_2_ramsey_1,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & m1_eqrel_1(B,k3_group_10(A,2)) ) => m1_subset_1(o_2_2_ramsey_1(A,B),B) ) )).
fof(dt_o_2_2_rlvect_5,axiom,( ! [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) & v8_rlvect_1(A) & v1_rlvect_5(A) & l1_rlvect_1(A) & m1_rlsub_1(B,A) ) => m1_rlvect_3(o_2_2_rlvect_5(A,B),B) ) )).
fof(dt_o_2_2_tbsp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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(o_2_2_tbsp_1(A,B),B) ) )).
fof(dt_o_2_2_tops_1,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(o_2_2_tops_1(A,B),k1_tops_1(A,k2_tops_1(A,B))) ) )).
fof(dt_o_2_2_waybel10,axiom,( ! [A] : ! [B] : ( ( 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(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(o_2_2_waybel10(A,B),B) ) )).
fof(dt_o_2_2_waybel34,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m2_subset_1(o_2_2_waybel34(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_2_waybel_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v1_yellow_0(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))) ) => m2_subset_1(o_2_2_waybel_3(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_2_yellow_4,axiom,( ! [A] : ! [B] : ( ( v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m2_subset_1(o_2_2_yellow_4(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_2_yellow_6,axiom,( ! [A] : ! [B] : ( ( ~ 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(o_2_2_yellow_6(A,B),u1_struct_0(B)) ) )).
fof(dt_o_2_2_zf_fund1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => m2_subset_1(o_2_2_zf_fund1(A,B),A,B) ) )).
fof(dt_o_2_3_aofa_000,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v1_xboole_0(B) ) => m2_finseq_2(o_2_3_aofa_000(A,B),B,k4_finseq_2(A,B)) ) )).
fof(dt_o_2_3_card_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) ) => m1_subset_1(o_2_3_card_3(A,B),k4_card_3(B)) ) )).
fof(dt_o_2_3_card_fil,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m2_card_fil(B,A) ) => m2_subset_1(o_2_3_card_fil(A,B),k1_zfmisc_1(A),B) ) )).
fof(dt_o_2_3_cqc_sim1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) ) => m1_subset_1(o_2_3_cqc_sim1(A,B),k24_qc_lang1(A,B)) ) )).
fof(dt_o_2_3_eqrel_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => m1_subset_1(o_2_3_eqrel_1(A,B),B) ) )).
fof(dt_o_2_3_filter_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v10_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))) ) => m1_subset_1(o_2_3_filter_2(A,B),u1_struct_0(k10_filter_2(A,B))) ) )).
fof(dt_o_2_3_glib_002,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_002(A) & m1_subset_1(B,k6_glib_000(A)) ) => m2_glib_000(o_2_3_glib_002(A,B),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)))) ) )).
fof(dt_o_2_3_glib_004,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k1_numbers),k1_zfmisc_1(k7_glib_000(A)))) ) => m1_subset_1(o_2_3_glib_004(A,B),k6_glib_004(A,B)) ) )).
fof(dt_o_2_3_group_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(o_2_3_group_2(A,B),B) ) )).
fof(dt_o_2_3_ideal_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v6_algstr_0(A) & v1_vectsp_1(A) & v1_algstr_1(A) & l6_algstr_0(A) & ~ v1_xboole_0(B) & v3_ideal_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m2_subset_1(o_2_3_ideal_1(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_3_ltlaxio4,axiom,( ! [A] : ! [B] : ( ( ~ v2_ltlaxio3(A) & v3_ltlaxio3(A) & m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) & m2_subset_1(B,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)),k8_ltlaxio4(A)) ) => m2_ltlaxio4(o_2_3_ltlaxio4(A,B),k1_hilbert1,k3_ltlaxio4(k5_ltlaxio4(B))) ) )).
fof(dt_o_2_3_matroid0,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => m1_subset_1(o_2_3_matroid0(A,B),B) ) )).
fof(dt_o_2_3_modal_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v5_relat_1(A,k2_zfmisc_1(k4_ordinal1,k4_ordinal1)) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) & m1_trees_1(B,k9_xtuple_0(A)) ) => m1_subset_1(o_2_3_modal_1(A,B),k1_trees_2(k9_xtuple_0(A),B)) ) )).
fof(dt_o_2_3_openlatt,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) => m1_subset_1(o_2_3_openlatt(A,B),B) ) )).
fof(dt_o_2_3_pua2mss1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k10_eqrel_1(A)) => m1_subset_1(o_2_3_pua2mss1(A,B),k4_card_3(B)) ) )).
fof(dt_o_2_3_ramsey_1,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => m1_subset_1(o_2_3_ramsey_1(A,B),k3_group_10(B,2)) ) )).
fof(dt_o_2_3_topgen_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_connsp_2(o_2_3_topgen_4(A,B),A,B) ) )).
fof(dt_o_2_3_waybel21,axiom,( ! [A] : ! [B] : ( ( ~ 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) & v7_waybel_0(B) & v8_waybel_0(B,A) & l1_waybel_0(B,A) ) => m1_subset_1(o_2_3_waybel21(A,B),u1_struct_0(B)) ) )).
fof(dt_o_2_3_waybel_3,axiom,( ! [A] : ! [B] : ( ( 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) & ~ 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))) ) => m2_subset_1(o_2_3_waybel_3(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_3_waybel_4,axiom,( ! [A] : ! [B] : ( ( 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(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_yellow_1(k3_waybel_4(A))))) ) => m2_subset_1(o_2_3_waybel_4(A,B),u1_struct_0(k1_yellow_1(k3_waybel_4(A))),B) ) )).
fof(dt_o_2_3_waybel_7,axiom,( ! [A] : ! [B] : ( ( 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_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m2_subset_1(o_2_3_waybel_7(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_3_yellow19,axiom,( ! [A] : ! [B] : ( ( ~ 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(o_2_3_yellow19(A,B),k7_subset_1(u1_struct_0(A),B,k1_tops_1(A,B))) ) )).
fof(dt_o_2_3_yellow_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m2_subset_1(o_2_3_yellow_4(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_4_chord,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => m1_chord(o_2_4_chord(A,B),A,k6_domain_1(k6_glib_000(A),B)) ) )).
fof(dt_o_2_4_conlat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(o_2_4_conlat_1(A,B),B) ) )).
fof(dt_o_2_4_finseq_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) ) => m2_finseq_2(o_2_4_finseq_3(A,B),A,B) ) )).
fof(dt_o_2_4_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k16_fomodel1(A))) ) => m2_subset_1(o_2_4_fomodel4(A,B),k16_fomodel1(A),B) ) )).
fof(dt_o_2_4_group_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(o_2_4_group_2(A,B),k2_group_2(A,B,k1_subset_1(u1_struct_0(A)))) ) )).
fof(dt_o_2_4_group_3,axiom,( ! [A] : ! [B] : ( ( ~ 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(o_2_4_group_3(A,B),B) ) )).
fof(dt_o_2_4_mathmorp,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => m2_subset_1(o_2_4_mathmorp(A,B),u1_struct_0(k15_euclid(A)),B) ) )).
fof(dt_o_2_4_matroid0,axiom,( ! [A] : ! [B] : ( ( v4_taxonom2(A) & m1_subset_1(B,A) ) => m1_subset_1(o_2_4_matroid0(A,B),B) ) )).
fof(dt_o_2_4_tex_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => m1_subset_1(o_2_4_tex_1(A,B),k6_subset_1(A,B)) ) )).
fof(dt_o_2_4_topgen_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ( v1_tops_2(o_2_4_topgen_2(A,B),A) & v1_yellow_8(o_2_4_topgen_2(A,B),A,B) & m1_subset_1(o_2_4_topgen_2(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) )).
fof(dt_o_2_4_treal_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => m1_subset_1(o_2_4_treal_1(A,B),k9_subset_1(k1_numbers,A,B)) ) )).
fof(dt_o_2_4_trees_9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k3_trees_9(A))) ) => m2_subset_1(o_2_4_trees_9(A,B),k3_trees_9(A),B) ) )).
fof(dt_o_2_4_waybel19,axiom,( ! [A] : ! [B] : ( ( 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) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m2_subset_1(o_2_4_waybel19(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_4_waybel_4,axiom,( ! [A] : ! [B] : ( ( ~ 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_xboole_0(B) & v1_waybel_0(B,A) & v12_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m2_subset_1(o_2_4_waybel_4(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_4_waybel_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) & ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => m1_subset_1(o_2_4_waybel_9(A,B),u1_struct_0(B)) ) )).
fof(dt_o_2_4_yellow_2,axiom,( ! [A] : ! [B] : ( ( 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))) ) => m2_subset_1(o_2_4_yellow_2(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_4_zf_fund1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) ) => m1_subset_1(o_2_4_zf_fund1(A,B),a_2_3_zf_fund1(A,B)) ) )).
fof(dt_o_2_5_aofa_a00,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) ) => m2_finseq_2(o_2_5_aofa_a00(A,B),A,k4_finseq_2(B,A)) ) )).
fof(dt_o_2_5_borsuk_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => m1_connsp_2(o_2_5_borsuk_1(A,B),A,B) ) )).
fof(dt_o_2_5_conlat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) & m1_subset_1(B,k1_zfmisc_1(u4_struct_0(A))) ) => m1_subset_1(o_2_5_conlat_1(A,B),B) ) )).
fof(dt_o_2_5_exchsort,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) => m1_subset_1(o_2_5_exchsort(A,B),k6_exchsort(A,B)) ) )).
fof(dt_o_2_5_group_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(o_2_5_group_2(A,B),k2_group_2(A,k1_subset_1(u1_struct_0(A)),B)) ) )).
fof(dt_o_2_5_group_9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v7_ordinal1(B) ) => ( v1_funct_1(o_2_5_group_9(A,B)) & v1_funct_2(o_2_5_group_9(A,B),k4_finseq_1(k2_finseq_3(B,A)),k4_finseq_1(k2_finseq_3(B,A))) & v3_funct_2(o_2_5_group_9(A,B),k4_finseq_1(k2_finseq_3(B,A)),k4_finseq_1(k2_finseq_3(B,A))) & m1_subset_1(o_2_5_group_9(A,B),k1_zfmisc_1(k2_zfmisc_1(k4_finseq_1(k2_finseq_3(B,A)),k4_finseq_1(k2_finseq_3(B,A))))) ) ) )).
fof(dt_o_2_5_heyting1,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A)) => m1_subset_1(o_2_5_heyting1(A,B),a_2_4_heyting1(A,B)) ) )).
fof(dt_o_2_5_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => m1_subset_1(o_2_5_mmlquery(A,B),B) ) )).
fof(dt_o_2_5_modal_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_modal_1) & m1_trees_1(B,k9_xtuple_0(A)) ) => m1_subset_1(o_2_5_modal_1(A,B),k1_trees_2(k9_xtuple_0(A),B)) ) )).
fof(dt_o_2_5_tbsp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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(A))) ) => m1_subset_1(o_2_5_tbsp_1(A,B),B) ) )).
fof(dt_o_2_5_tex_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => m1_subset_1(o_2_5_tex_1(A,B),k6_subset_1(A,k6_domain_1(A,B))) ) )).
fof(dt_o_2_5_treal_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k17_borsuk_1))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k17_borsuk_1))) ) => m1_subset_1(o_2_5_treal_1(A,B),k9_subset_1(u1_struct_0(k17_borsuk_1),k2_pre_topc(k17_borsuk_1,A),B)) ) )).
fof(dt_o_2_5_trees_9,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k9_trees_9(A))) ) => m2_subset_1(o_2_5_trees_9(A,B),k9_trees_9(A),B) ) )).
fof(dt_o_2_5_waybel21,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) & ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => m1_subset_1(o_2_5_waybel21(A,B),u1_struct_0(B)) ) )).
fof(dt_o_2_5_waybel_2,axiom,( ! [A] : ! [B] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & v1_lattice3(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))) ) => m2_subset_1(o_2_5_waybel_2(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_5_waybel_4,axiom,( ! [A] : ! [B] : ( ( ~ 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(B) & v2_waybel_0(B,A) & v13_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m2_subset_1(o_2_5_waybel_4(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_6_glib_004,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) ) => m1_subset_1(o_2_6_glib_004(A,B),k12_glib_004(A,k15_glib_004(A,k16_glib_004(A),B))) ) )).
fof(dt_o_2_6_group_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) & m1_group_2(B,A) ) => m1_subset_1(o_2_6_group_2(A,B),u1_struct_0(B)) ) )).
fof(dt_o_2_6_jordan2c,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => m1_subset_1(o_2_6_jordan2c(A,B),k9_subset_1(u1_struct_0(k15_euclid(A)),k1_jordan2c(A,B),k2_jordan2c(A,B))) ) )).
fof(dt_o_2_6_matroid0,axiom,( ! [A] : ! [B] : ( ( ~ 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(o_2_6_matroid0(A,B),B) ) )).
fof(dt_o_2_6_treal_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k17_borsuk_1))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k17_borsuk_1))) ) => m1_subset_1(o_2_6_treal_1(A,B),k9_subset_1(u1_struct_0(k17_borsuk_1),A,B)) ) )).
fof(dt_o_2_6_waybel19,axiom,( ! [A] : ! [B] : ( ( 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_xboole_0(B) & v2_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(o_2_6_waybel19(A,B),u1_struct_0(k3_yellow_9(A,B))) ) )).
fof(dt_o_2_6_waybel21,axiom,( ! [A] : ! [B] : ( ( 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) & ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & v11_waybel_0(B,A) & l1_waybel_0(B,A) ) => m1_subset_1(o_2_6_waybel21(A,B),u1_struct_0(B)) ) )).
fof(dt_o_2_6_waybel30,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & v1_waybel_0(B,k1_yellow_1(k7_waybel_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_yellow_1(k7_waybel_0(A))))) ) => m2_subset_1(o_2_6_waybel30(A,B),u1_struct_0(k1_yellow_1(k7_waybel_0(A))),B) ) )).
fof(dt_o_2_6_weddwitt,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) => m1_vectsp_7(o_2_6_weddwitt(A,B),k4_weddwitt(A),k7_weddwitt(A,B)) ) )).
fof(dt_o_2_6_yellow19,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(o_2_6_yellow19(A,B),B) ) )).
fof(dt_o_2_6_yellow_6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & v1_yellow_6(B,A) & l1_waybel_0(B,A) ) => m1_subset_1(o_2_6_yellow_6(A,B),u1_struct_0(B)) ) )).
fof(dt_o_2_7_classes1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => m1_subset_1(o_2_7_classes1(A,B),k6_subset_1(A,k4_classes1(B))) ) )).
fof(dt_o_2_7_glib_002,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_002(A) & m3_glib_001(B,A) ) => ( v5_glib_001(o_2_7_glib_002(A,B),A) & m4_glib_001(o_2_7_glib_002(A,B),A,B) ) ) )).
fof(dt_o_2_7_goedelcp,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & v1_henmodel(B,A) & m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) ) => m1_henmodel(o_2_7_goedelcp(A,B),A,B) ) )).
fof(dt_o_2_7_group_2,axiom,( ! [A] : ! [B] : ( ( ~ 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(o_2_7_group_2(A,B),u1_struct_0(g3_algstr_0(A,B))) ) )).
fof(dt_o_2_7_heyting1,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A)) => m1_subset_1(o_2_7_heyting1(A,B),a_2_6_heyting1(A,B)) ) )).
fof(dt_o_2_7_matroid0,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) & ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m2_subset_1(o_2_7_matroid0(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_7_msafree4,axiom,( ! [A] : ! [B] : ( ( ~ 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_msafree4(B,u1_struct_0(A)) ) => ( v1_msualg_3(o_2_7_msafree4(A,B)) & m2_pboole(o_2_7_msafree4(A,B),u1_struct_0(A),B,k7_funcop_1(u1_struct_0(A),k4_ordinal1)) ) ) )).
fof(dt_o_2_7_tdlat_2,axiom,( ! [A] : ! [B] : ( ( 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(o_2_7_tdlat_2(A,B),B) ) )).
fof(dt_o_2_7_treal_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k17_borsuk_1))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k17_borsuk_1))) ) => m1_subset_1(o_2_7_treal_1(A,B),k9_subset_1(u1_struct_0(k17_borsuk_1),k2_pre_topc(k17_borsuk_1,B),A)) ) )).
fof(dt_o_2_7_trees_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v2_trees_2(B,A) & m1_trees_2(B,A) ) => m2_subset_1(o_2_7_trees_2(A,B),A,B) ) )).
fof(dt_o_2_7_waybel30,axiom,( ! [A] : ! [B] : ( ( ~ 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) & v12_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m2_subset_1(o_2_7_waybel30(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_7_waybel_0,axiom,( ! [A] : ! [B] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & v12_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m2_subset_1(o_2_7_waybel_0(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_7_yellow_2,axiom,( ! [A] : ! [B] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v1_yellow_0(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))) ) => m2_subset_1(o_2_7_yellow_2(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_8_conlat_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) => m1_subset_1(o_2_8_conlat_2(A,B),a_2_0_conlat_2(A,B)) ) )).
fof(dt_o_2_8_glib_002,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) ) => m2_glib_000(o_2_8_glib_002(A,B),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)))) ) )).
fof(dt_o_2_8_heyting1,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A)) => m1_subset_1(o_2_8_heyting1(A,B),k10_normform(A,B,k6_heyting1(A,B))) ) )).
fof(dt_o_2_8_tdlat_2,axiom,( ! [A] : ! [B] : ( ( 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(o_2_8_tdlat_2(A,B),k1_tdlat_2(A,B)) ) )).
fof(dt_o_2_8_waybel21,axiom,( ! [A] : ! [B] : ( ( 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) & ~ v2_struct_0(B) & v4_yellow_0(B,A) & v7_yellow_0(B,A) & v4_waybel_0(B,A) & v3_lattice3(B) & m1_yellow_0(B,A) ) => ( v2_pre_topc(o_2_8_waybel21(A,B)) & v2_waybel19(o_2_8_waybel21(A,B)) & m1_yellow_9(o_2_8_waybel21(A,B),B) ) ) )).
fof(dt_o_2_8_waybel30,axiom,( ! [A] : ! [B] : ( ( 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) ) => ( ~ v2_struct_0(o_2_8_waybel30(A,B)) & v2_pre_topc(o_2_8_waybel30(A,B)) & v4_waybel11(o_2_8_waybel30(A,B)) & m1_yellow_9(o_2_8_waybel30(A,B),k3_yellow_3(A,B)) ) ) )).
fof(dt_o_2_8_waybel33,axiom,( ! [A] : ! [B] : ( ( 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) & v2_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v3_waybel_7(B,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))))) ) => m2_subset_1(o_2_8_waybel33(A,B),u1_struct_0(k2_yellow_1(k2_struct_0(A))),B) ) )).
fof(dt_o_2_8_waybel_0,axiom,( ! [A] : ! [B] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) & ~ v1_xboole_0(B) & v13_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m2_subset_1(o_2_8_waybel_0(A,B),u1_struct_0(A),B) ) )).
fof(dt_o_2_8_yellow_9,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => m2_subset_1(o_2_8_yellow_9(A,B),k1_zfmisc_1(A),B) ) )).
fof(dt_o_2_8_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ 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,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(o_2_8_zmodul02(A,B),B) ) )).
fof(dt_o_2_9_conlat_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) => m2_subset_1(o_2_9_conlat_2(A,B),k1_zfmisc_1(u1_struct_0(A)),B) ) )).
fof(dt_o_2_9_glib_002,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & m3_glib_001(B,A) ) => m1_subset_1(o_2_9_glib_002(A,B),k14_glib_001(A,B)) ) )).
fof(dt_o_2_9_waybel11,axiom,( ! [A] : ! [B] : ( ( 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_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & v1_yellow_6(B,A) & l1_waybel_0(B,A) ) => m1_subset_1(o_2_9_waybel11(A,B),u1_struct_0(B)) ) )).
fof(dt_o_2_9_waybel30,axiom,( ! [A] : ! [B] : ( ( 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) ) => ( ~ v2_struct_0(o_2_9_waybel30(A,B)) & v2_pre_topc(o_2_9_waybel30(A,B)) & v1_waybel19(o_2_9_waybel30(A,B)) & m1_yellow_9(o_2_9_waybel30(A,B),k3_yellow_3(A,B)) ) ) )).
fof(dt_o_2_9_waybel33,axiom,( ! [A] : ! [B] : ( ( 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(B,u1_struct_0(k2_yellow_1(k2_struct_0(A)))) ) => m1_subset_1(o_2_9_waybel33(A,B),B) ) )).
fof(dt_o_2_9_yellow19,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & 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(o_2_9_yellow19(A,B),k6_setfam_1(u1_struct_0(A),B)) ) )).
fof(dt_o_3_0_altcat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,u1_struct_0(k7_altcat_1(A))) & m1_subset_1(C,u1_struct_0(k7_altcat_1(A))) ) => m1_subset_1(o_3_0_altcat_3(A,B,C),k1_funct_2(B,C)) ) )).
fof(dt_o_3_0_altcat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(o_3_0_altcat_4(A,B,C),k1_altcat_1(A,C,B)) ) )).
fof(dt_o_3_0_amistd_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_setfam_1(A) & ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & v2_amistd_4(B,A) & l1_extpro_1(B,A) & m1_subset_1(C,u1_struct_0(B)) ) => m1_subset_1(o_3_0_amistd_4(A,B,C),k4_memstr_0(A,B,C)) ) )).
fof(dt_o_3_0_brouwer,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) & m1_subset_1(B,u1_struct_0(k15_euclid(2))) & ~ v2_struct_0(C) & m1_pre_topc(C,k2_brouwer(2,B,A)) ) => m1_subset_1(o_3_0_brouwer(A,B,C),u1_struct_0(C)) ) )).
fof(dt_o_3_0_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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(o_3_0_cat_3(A,B,C),A,C,B) ) )).
fof(dt_o_3_0_euclid_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) & v3_valued_0(B) & v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & v3_valued_0(C) ) => m1_subset_1(o_3_0_euclid_9(A,B,C),k8_relset_1(k4_ordinal1,k1_numbers,k3_euclid(k8_rvsum_1(B,C)),k1_tarski(k1_xxreal_2(k1_rvsum_1(k3_euclid(k8_rvsum_1(B,C))))))) ) )).
fof(dt_o_3_0_fintopo4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(o_3_0_fintopo4(A,B,C),k9_subset_1(u1_struct_0(A),k1_fin_topo(A,C),B)) ) )).
fof(dt_o_3_0_fintopo6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(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(o_3_0_fintopo6(A,B,C),k9_subset_1(u1_struct_0(A),k1_fin_topo(A,C),B)) ) )).
fof(dt_o_3_0_glib_005,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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(o_3_0_glib_005(A,B,C),k2_glib_005(A,B,C)) ) )).
fof(dt_o_3_0_integr15,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,k1_integra1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) ) => m2_integr15(o_3_0_integr15(A,B,C),A,B,C) ) )).
fof(dt_o_3_0_jordan6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & 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(o_3_0_jordan6(A,B,C),k7_subset_1(u1_struct_0(k15_euclid(A)),C,B)) ) )).
fof(dt_o_3_0_ltlaxio4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) & m3_ltlaxio4(B,A) & m1_trees_1(C,k9_xtuple_0(B)) ) => m2_ltlaxio4(o_3_0_ltlaxio4(A,B,C),k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)),k9_ltlaxio4(k3_trees_2(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)),B,C))) ) )).
fof(dt_o_3_0_mssublat,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & m1_subset_1(C,u4_struct_0(A)) ) => m2_finseq_2(o_3_0_mssublat(A,B,C),k10_msualg_1(A,B),k4_finseq_2(k3_finseq_1(k1_msualg_1(A,C)),k10_msualg_1(A,B))) ) )).
fof(dt_o_3_0_msualg_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) => m1_subset_1(o_3_0_msualg_6(A,B,C),k3_msualg_1(A,C,B)) ) )).
fof(dt_o_3_0_orders_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => m1_subset_1(o_3_0_orders_1(A,B,C),k1_funct_1(B,C)) ) )).
fof(dt_o_3_0_orders_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(o_3_0_orders_2(A,B,C),k9_subset_1(u1_struct_0(A),k1_wellord1(u1_orders_2(A),C),k6_domain_1(u1_struct_0(A),B))) ) )).
fof(dt_o_3_0_pencil_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(C,A) ) => m1_subset_1(o_3_0_pencil_1(A,B,C),u1_pre_topc(k1_pencil_1(A,B,C))) ) )).
fof(dt_o_3_0_pencil_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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_7(o_3_0_pencil_4(A,B,C),A,C) ) )).
fof(dt_o_3_0_polynom7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(o_3_0_polynom7(A,B,C),k3_polynom1(k15_pre_poly(A),B,C)) ) )).
fof(dt_o_3_0_prelamb,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_prelamb(A) & m1_prelamb(B,A) & m1_trees_1(C,k9_xtuple_0(B)) ) => m1_subset_1(o_3_0_prelamb(A,B,C),k1_trees_2(k9_xtuple_0(B),C)) ) )).
fof(dt_o_3_0_ramsey_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(B)) ) => m1_subset_1(o_3_0_ramsey_1(A,B,C),k3_group_10(C,A)) ) )).
fof(dt_o_3_0_rfinseq,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(B) ) => m1_subset_1(o_3_0_rfinseq(A,B,C),k8_relat_1(k9_finseq_1(k1_funct_1(A,o_1_0_rfinseq(B))),k1_tarski(C))) ) )).
fof(dt_o_3_0_rfunct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => m1_subset_1(o_3_0_rfunct_2(A,B,C),k9_subset_1(k1_numbers,k3_xboole_0(B,A),k1_relset_1(k1_numbers,C))) ) )).
fof(dt_o_3_0_rfunct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) & v1_xreal_0(C) ) => m1_subset_1(o_3_0_rfunct_3(A,B,C),k8_relset_1(A,k1_numbers,k56_valued_1(A,k1_numbers,B),k1_tarski(C))) ) )).
fof(dt_o_3_0_rmod_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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,k1_zfmisc_1(u1_struct_0(B))) ) => m1_subset_1(o_3_0_rmod_2(A,B,C),C) ) )).
fof(dt_o_3_0_substut1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(A) & v1_finset_1(B) & m1_subset_1(B,k1_substut1(A)) & m1_subset_1(C,k9_qc_lang1(A)) ) => m2_subset_1(o_3_0_substut1(A,B,C),k1_qc_lang1(A),k12_substut1(A,C,B)) ) )).
fof(dt_o_3_0_topgen_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => m1_subset_1(o_3_0_topgen_3(A,B,C),k1_funct_1(B,C)) ) )).
fof(dt_o_3_0_topreal4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) & v7_ordinal1(B) & v7_ordinal1(C) ) => m1_subset_1(o_3_0_topreal4(A,B,C),k9_subset_1(u1_struct_0(k15_euclid(2)),k2_topreal1(2,A,B),k2_topreal1(2,A,C))) ) )).
fof(dt_o_3_0_trees_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & m4_trees_1(B,A) & m1_trees_2(C,A) ) => m1_subset_1(o_3_0_trees_2(A,B,C),k9_subset_1(A,B,C)) ) )).
fof(dt_o_3_0_vectsp_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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))) ) => m1_subset_1(o_3_0_vectsp_4(A,B,C),C) ) )).
fof(dt_o_3_0_vectsp_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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))) ) => m2_subset_1(o_3_0_vectsp_8(A,B,C),k2_vectsp_8(A,B),C) ) )).
fof(dt_o_3_0_vectsp_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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_7(o_3_0_vectsp_9(A,B,C),A,C) ) )).
fof(dt_o_3_10_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_mmlquery(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) & m1_subset_1(C,A) ) => m1_subset_1(o_3_10_mmlquery(A,B,C),k1_mmlquery(A,B,C)) ) )).
fof(dt_o_3_11_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v1_orders_4(A) & v11_fomodel1(A) & l1_fomodel1(A) & m1_subset_1(B,k1_zfmisc_1(k30_fomodel2(A))) & ~ v1_xboole_0(C) & v4_card_3(C) ) => ( v1_relat_1(o_3_11_fomodel4(A,B,C)) & v1_funct_1(o_3_11_fomodel4(A,B,C)) & v1_fomodel2(o_3_11_fomodel4(A,B,C),k41_fomodel1(A,B),C) ) ) )).
fof(dt_o_3_12_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v1_orders_4(A) & v11_fomodel1(A) & l1_fomodel1(A) & ~ v6_struct_0(B) & v11_fomodel1(B) & v16_fomodel1(B,A) & l1_fomodel1(B) & ~ v1_xboole_0(C) & v4_card_3(C) ) => m2_subset_1(o_3_12_fomodel4(A,B,C),k9_funct_2(k37_fomodel1(B),k3_rfunct_3(k3_finseq_2(C),k2_xboole_0(C,k6_margrel1))),k15_fomodel2(B,C)) ) )).
fof(dt_o_3_15_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v5_graph_1(A) & v6_graph_1(A) & l1_graph_1(A) & ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(C,u1_struct_0(A)) ) => m1_graph_3(o_3_15_graph_3(A,B,C),u4_struct_0(A),k9_graph_3(A),k13_graph_3(A,C,B)) ) )).
fof(dt_o_3_16_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v5_graph_1(A) & v6_graph_1(A) & l1_graph_1(A) & m2_finseq_2(B,u4_struct_0(A),k9_graph_3(A)) & m2_finseq_2(C,u4_struct_0(A),k9_graph_3(A)) ) => m1_subset_1(o_3_16_graph_3(A,B,C),k9_subset_1(u1_struct_0(A),k1_graph_3(A,k10_xtuple_0(B)),k1_graph_3(A,k10_xtuple_0(C)))) ) )).
fof(dt_o_3_1_aff_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(o_3_1_aff_4(A,B,C),k1_aff_4(A,B,C)) ) )).
fof(dt_o_3_1_altcat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(o_3_1_altcat_4(A,B,C),k1_altcat_1(A,B,C)) ) )).
fof(dt_o_3_1_brouwer,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) & m1_subset_1(B,u1_struct_0(k15_euclid(2))) & m1_subset_1(C,u1_struct_0(k2_brouwer(2,B,A))) ) => ( v3_funct_1(o_3_1_brouwer(A,B,C)) & m1_borsuk_2(o_3_1_brouwer(A,B,C),k2_brouwer(2,B,A),C,C) ) ) )).
fof(dt_o_3_1_card_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => m1_subset_1(o_3_1_card_3(A,B,C),k3_xboole_0(k1_funct_1(k2_card_3(C),A),k1_funct_1(k2_card_3(C),B))) ) )).
fof(dt_o_3_1_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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(o_3_1_cat_1(A,B,C),A,C,B) ) )).
fof(dt_o_3_1_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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(o_3_1_cat_3(A,B,C),A,B,C) ) )).
fof(dt_o_3_1_ens_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,u1_struct_0(k11_ens_1(A))) & m1_subset_1(C,u1_struct_0(k11_ens_1(A))) ) => m1_subset_1(o_3_1_ens_1(A,B,C),k7_ens_1(A,k13_ens_1(A,B),k13_ens_1(A,C))) ) )).
fof(dt_o_3_1_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => m1_subset_1(o_3_1_fsm_1(A,B,C),u1_struct_0(C)) ) )).
fof(dt_o_3_1_glib_002,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & m1_subset_1(B,k6_glib_000(A)) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_finset_1(C) & v1_glib_000(C) & v4_glib_000(C) ) => m2_glib_000(o_3_1_glib_002(A,B,C),C,k6_subset_1(k6_glib_000(C),k1_tarski(B)),k21_glib_000(C,k6_subset_1(k6_glib_000(C),k1_tarski(B)))) ) )).
fof(dt_o_3_1_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) & m1_subset_1(B,u1_struct_0(A)) & m2_finseq_2(C,u4_struct_0(A),k9_graph_3(A)) ) => m1_subset_1(o_3_1_graph_3(A,B,C),a_3_0_graph_3(A,B,C)) ) )).
fof(dt_o_3_1_group_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(o_3_1_group_2(A,B,C),k2_group_2(A,B,C)) ) )).
fof(dt_o_3_1_group_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(o_3_1_group_3(A,B,C),k3_group_3(A,B,C)) ) )).
fof(dt_o_3_1_jordan6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(2),A)))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(2),A)))) ) => m1_subset_1(o_3_1_jordan6(A,B,C),k7_subset_1(u1_struct_0(k1_pre_topc(k15_euclid(2),A)),B,C)) ) )).
fof(dt_o_3_1_mod_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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))) ) => m1_subset_1(o_3_1_mod_3(A,B,C),C) ) )).
fof(dt_o_3_1_msafree3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) & m1_subset_1(C,u4_struct_0(A)) ) => m1_msaterm(o_3_1_msafree3(A,B,C),A,k2_pboole(u1_struct_0(A),B,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_numbers))),k2_msaterm(A,k2_pboole(u1_struct_0(A),B,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_numbers))),C)) ) )).
fof(dt_o_3_1_normform,axiom,( ! [A] : ! [B] : ! [C] : ( ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) & m2_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) ) => m1_subset_1(o_3_1_normform(A,B,C),k3_finsub_1(k5_finsub_1(A),k2_domain_1(k5_finsub_1(A),k5_finsub_1(A),k1_normform(k5_finsub_1(A),k5_finsub_1(A),B,C)),k3_domain_1(k5_finsub_1(A),k5_finsub_1(A),k1_normform(k5_finsub_1(A),k5_finsub_1(A),B,C)))) ) )).
fof(dt_o_3_1_pencil_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & ~ v13_pencil_1(C) & v16_pencil_1(C,A) & m3_pboole(C,A,k12_pralg_1(A,B)) ) => m1_subset_1(o_3_1_pencil_3(A,B,C),u1_pre_topc(k2_pencil_1(A,B,k3_pencil_1(A,C)))) ) )).
fof(dt_o_3_1_pencil_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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_5(o_3_1_pencil_4(A,B,C),A,B,C) ) )).
fof(dt_o_3_1_polynom7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l2_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)))) ) => m1_subset_1(o_3_1_polynom7(A,B,C),k3_polynom1(k15_pre_poly(A),B,C)) ) )).
fof(dt_o_3_1_pralg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & m5_margrel1(C,u1_struct_0(A),k1_unialg_2(A)) ) => m2_finseq_2(o_3_1_pralg_1(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)),k4_finseq_2(k19_margrel1(C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) )).
fof(dt_o_3_1_rfinseq,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(B) ) => m1_subset_1(o_3_1_rfinseq(A,B,C),k8_relat_1(k5_relat_1(A,k1_tarski(o_1_0_rfinseq(B))),k1_tarski(C))) ) )).
fof(dt_o_3_1_tbsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) => m1_subset_1(o_3_1_tbsp_1(A,B,C),k8_metric_1(A,B,C)) ) )).
fof(dt_o_3_1_topalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(o_3_1_topalg_1(A,B,C),A,C,B) ) )).
fof(dt_o_3_1_urysohn3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v10_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))) ) => m2_urysohn3(o_3_1_urysohn3(A,B,C),A,B,C) ) )).
fof(dt_o_3_1_vectsp_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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))) ) => m1_subset_1(o_3_1_vectsp_7(A,B,C),C) ) )).
fof(dt_o_3_1_vectsp_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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_7(o_3_1_vectsp_9(A,B,C),A,C) ) )).
fof(dt_o_3_2_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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(o_3_2_cat_1(A,B,C),A,B,C) ) )).
fof(dt_o_3_2_clvect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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(B) & m1_clvect_1(B,A) & v1_clvect_1(C) & m1_clvect_1(C,A) ) => m1_subset_1(o_3_2_clvect_1(A,B,C),k6_subset_1(u1_struct_0(B),u1_struct_0(C))) ) )).
fof(dt_o_3_2_ens_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,u1_struct_0(k11_ens_1(A))) & m1_subset_1(C,u1_struct_0(k11_ens_1(A))) ) => ( v1_funct_1(o_3_2_ens_1(A,B,C)) & v1_funct_2(o_3_2_ens_1(A,B,C),k13_ens_1(A,C),k13_ens_1(A,B)) & m1_subset_1(o_3_2_ens_1(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k13_ens_1(A,C),k13_ens_1(A,B)))) ) ) )).
fof(dt_o_3_2_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_eqrel_1(B,A) & m2_subset_1(C,k1_zfmisc_1(A),B) ) => m2_subset_1(o_3_2_finseq_4(A,B,C),A,C) ) )).
fof(dt_o_3_2_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v4_funct_1(B) & m2_subset_1(C,k6_subset_1(k3_finseq_2(k1_fomodel1(A)),k1_tarski(k1_xboole_0)),k40_fomodel2(A)) ) => m1_subset_1(o_3_2_fomodel4(A,B,C),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(B,k6_domain_1(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k37_fomodel2(A,C))))))) ) )).
fof(dt_o_3_2_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) & m2_finseq_2(B,u4_struct_0(A),k9_graph_3(A)) & m2_finseq_2(C,u4_struct_0(A),k9_graph_3(A)) ) => m1_subset_1(o_3_2_graph_3(A,B,C),k9_subset_1(u1_struct_0(A),k1_graph_3(A,k10_xtuple_0(B)),k1_graph_3(A,k10_xtuple_0(C)))) ) )).
fof(dt_o_3_2_group_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_group_2(C,A) ) => m1_subset_1(o_3_2_group_2(A,B,C),k13_group_2(A,C,B)) ) )).
fof(dt_o_3_2_jgraph_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(o_3_2_jgraph_1(A,B,C),k9_subset_1(u1_struct_0(k3_pcomps_1(A)),B,C)) ) )).
fof(dt_o_3_2_jordan6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(2),A)))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(2),A)))) ) => m1_subset_1(o_3_2_jordan6(A,B,C),k7_subset_1(u1_struct_0(k1_pre_topc(k15_euclid(2),A)),C,B)) ) )).
fof(dt_o_3_2_lmod_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) => m1_subset_1(o_3_2_lmod_5(A,B,C),C) ) )).
fof(dt_o_3_2_matrtop1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & ~ 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) ) => ( v1_matrix_0(o_3_2_matrtop1(A,B,C)) & v2_matrix_0(o_3_2_matrtop1(A,B,C),u1_struct_0(C),A,k7_nat_d(A,B)) & m2_finseq_1(o_3_2_matrtop1(A,B,C),k3_finseq_2(u1_struct_0(C))) ) ) )).
fof(dt_o_3_2_pua2mss1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_eqrel_1(B,A) & m2_subset_1(C,k1_zfmisc_1(A),B) ) => m2_subset_1(o_3_2_pua2mss1(A,B,C),A,C) ) )).
fof(dt_o_3_2_rlsub_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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(B) & m1_rlsub_1(B,A) & v1_rlvect_1(C) & m1_rlsub_1(C,A) ) => m1_subset_1(o_3_2_rlsub_1(A,B,C),k6_subset_1(u1_struct_0(B),u1_struct_0(C))) ) )).
fof(dt_o_3_2_rusub_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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(B) & m1_rusub_1(B,A) & v1_bhsp_1(C) & m1_rusub_1(C,A) ) => m1_subset_1(o_3_2_rusub_1(A,B,C),k6_subset_1(u1_struct_0(B),u1_struct_0(C))) ) )).
fof(dt_o_3_2_substut2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(A) & m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) & m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) ) => m1_substut2(o_3_2_substut2(A,B,C),A,C,B) ) )).
fof(dt_o_3_2_tbsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v6_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(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(o_3_2_tbsp_1(A,B,C),k9_subset_1(u1_struct_0(A),B,C)) ) )).
fof(dt_o_3_2_topalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(o_3_2_topalg_1(A,B,C),A,C,B) ) )).
fof(dt_o_3_2_vectsp_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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(C,A) & m1_vectsp_4(C,A,B) ) => m1_vectsp_5(o_3_2_vectsp_5(A,B,C),A,B,C) ) )).
fof(dt_o_3_2_yellow_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & m2_yellow_6(C,A,B) ) => m1_subset_1(o_3_2_yellow_6(A,B,C),u1_struct_0(C)) ) )).
fof(dt_o_3_3_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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(o_3_3_cat_1(A,B,C),k2_cat_1(A,B,C)) ) )).
fof(dt_o_3_3_chord,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v6_chord(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) & m1_subset_1(C,k6_glib_000(A)) ) => m2_glib_000(o_3_3_chord(A,B,C),A,k4_subset_1(k6_glib_000(A),B,k6_domain_1(k6_glib_000(A),C)),k21_glib_000(A,k4_subset_1(k6_glib_000(A),B,k6_domain_1(k6_glib_000(A),C)))) ) )).
fof(dt_o_3_3_clvect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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(B) & m1_clvect_1(B,A) & v1_clvect_1(C) & m1_clvect_1(C,A) ) => m1_subset_1(o_3_3_clvect_1(A,B,C),k6_subset_1(u1_struct_0(C),u1_struct_0(B))) ) )).
fof(dt_o_3_3_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) & v15_algstr_0(C) & v1_group_3(C,B) & m1_group_2(C,B) ) => m1_subset_1(o_3_3_group_9(A,B,C),u1_struct_0(C)) ) )).
fof(dt_o_3_3_lattice6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v10_lattices(A) & l3_lattices(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,u1_struct_0(k3_lattice3(A))) ) => m1_subset_1(o_3_3_lattice6(A,B,C),k9_subset_1(u1_struct_0(A),k1_wellord1(u1_orders_2(k7_lattice3(k3_lattice3(A))),C),B)) ) )).
fof(dt_o_3_3_rlsub_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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(B) & m1_rlsub_1(B,A) & v1_rlvect_1(C) & m1_rlsub_1(C,A) ) => m1_subset_1(o_3_3_rlsub_1(A,B,C),k6_subset_1(u1_struct_0(C),u1_struct_0(B))) ) )).
fof(dt_o_3_3_rusub_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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(B) & m1_rusub_1(B,A) & v1_bhsp_1(C) & m1_rusub_1(C,A) ) => m1_subset_1(o_3_3_rusub_1(A,B,C),k6_subset_1(u1_struct_0(C),u1_struct_0(B))) ) )).
fof(dt_o_3_3_waybel28,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & v1_yellow_6(B,A) & l1_waybel_0(B,A) & m2_yellow_6(C,A,B) ) => m2_subset_1(o_3_3_waybel28(A,B,C),u1_struct_0(C),k1_relset_1(u1_struct_0(C),u1_waybel_0(A,C))) ) )).
fof(dt_o_3_3_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(B) & m1_zmodul01(B,A) & v1_zmodul01(C) & m1_zmodul01(C,A) ) => m1_subset_1(o_3_3_zmodul01(A,B,C),k6_subset_1(u1_struct_0(B),u1_struct_0(C))) ) )).
fof(dt_o_3_4_glib_004,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) & m1_subset_1(C,k1_zfmisc_1(k21_glib_000(A,B))) ) => m2_glib_000(o_3_4_glib_004(A,B,C),A,B,C) ) )).
fof(dt_o_3_4_simplex1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) & v7_ordinal1(C) ) => m3_simplex0(o_3_4_simplex1(A,B,C),B,C) ) )).
fof(dt_o_3_4_waybel21,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) & m2_yellow_6(C,A,B) ) => m2_waybel21(o_3_4_waybel21(A,B,C),A,B,C) ) )).
fof(dt_o_3_4_waybel28,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m2_yellow_6(C,A,k4_waybel17(A,B)) ) => m1_subset_1(o_3_4_waybel28(A,B,C),u1_struct_0(C)) ) )).
fof(dt_o_3_4_waybel_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(o_3_4_waybel_5(A,B,C),a_3_1_waybel_5(A,B,C)) ) )).
fof(dt_o_3_4_yellow19,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & m2_yellow_6(C,A,B) ) => m1_subset_1(o_3_4_yellow19(A,B,C),k10_yellow_6(A,C)) ) )).
fof(dt_o_3_4_zf_fund2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) & ~ 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(o_3_4_zf_fund2(A,B,C),a_3_1_zf_fund2(A,B,C)) ) )).
fof(dt_o_3_4_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(B) & m1_zmodul01(B,A) & v1_zmodul01(C) & m1_zmodul01(C,A) ) => m1_subset_1(o_3_4_zmodul01(A,B,C),k6_subset_1(u1_struct_0(C),u1_struct_0(B))) ) )).
fof(dt_o_3_5_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(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_msafree4(B,u1_struct_0(A)) & v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ( v4_msualg_1(o_3_5_aofa_a01(A,B,C),A) & v4_msafree4(o_3_5_aofa_a01(A,B,C),A,C) & v17_aofa_a00(o_3_5_aofa_a01(A,B,C),A) & v20_aofa_a00(o_3_5_aofa_a01(A,B,C),4,1,A) & v22_aofa_a00(o_3_5_aofa_a01(A,B,C),A,1,1,11) & l3_msualg_1(o_3_5_aofa_a01(A,B,C),A) ) ) )).
fof(dt_o_3_5_chord,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & m3_chord(B,A) & v7_ordinal1(C) ) => m2_glib_000(o_3_5_chord(A,B,C),A,k4_chord(A,B,C),k21_glib_000(A,k4_chord(A,B,C))) ) )).
fof(dt_o_3_5_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : m1_subset_1(o_3_5_finseq_3(A,B,C),k3_xboole_0(k2_tarski(A,B),k1_tarski(C))) )).
fof(dt_o_3_5_glib_005,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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(o_3_5_glib_005(A,B,C),k2_glib_005(A,B,k6_glib_005(A,B,C))) ) )).
fof(dt_o_3_5_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v5_graph_1(A) & v6_graph_1(A) & l1_graph_1(A) & m2_finseq_2(B,u4_struct_0(A),k9_graph_3(A)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_graph_3(o_3_5_graph_3(A,B,C),u4_struct_0(A),k9_graph_3(A),k13_graph_3(A,C,k6_subset_1(u4_struct_0(A),k10_xtuple_0(B)))) ) )).
fof(dt_o_3_5_msafree3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) & m1_subset_1(C,u1_struct_0(A)) ) => m1_subset_1(o_3_5_msafree3(A,B,C),k1_funct_1(B,C)) ) )).
fof(dt_o_3_5_rmod_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) => m1_subset_1(o_3_5_rmod_4(A,B,C),C) ) )).
fof(dt_o_3_6_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(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_msafree4(B,u1_struct_0(A)) & v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => m2_pboole(o_3_6_aofa_a01(A,B,C),u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,o_3_5_aofa_a01(A,B,C))) ) )).
fof(dt_o_3_6_chord,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) => m2_glib_000(o_3_6_chord(A,B,C),A,k4_chord(A,B,k3_chord(A,B,C)),k21_glib_000(A,k4_chord(A,B,k3_chord(A,B,C)))) ) )).
fof(dt_o_3_6_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => m1_subset_1(o_3_6_mmlquery(A,B,C),k1_mmlquery(A,C,B)) ) )).
fof(dt_o_3_7_jordan2c,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k14_euclid(A)))) ) => m1_subset_1(o_3_7_jordan2c(A,B,C),k9_subset_1(u1_struct_0(k15_euclid(A)),C,B)) ) )).
fof(dt_o_3_7_topgen_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) ) => m2_subset_1(o_3_7_topgen_2(A,B,C),k1_zfmisc_1(B),C) ) )).
fof(dt_o_3_8_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & m2_finseq_1(C,k6_group_9(A,B)) ) => ( v1_funct_1(o_3_8_group_9(A,B,C)) & v1_funct_2(o_3_8_group_9(A,B,C),k4_finseq_1(k20_group_9(A,B,C)),k4_finseq_1(k20_group_9(A,B,C))) & v3_funct_2(o_3_8_group_9(A,B,C),k4_finseq_1(k20_group_9(A,B,C)),k4_finseq_1(k20_group_9(A,B,C))) & m1_subset_1(o_3_8_group_9(A,B,C),k1_zfmisc_1(k2_zfmisc_1(k4_finseq_1(k20_group_9(A,B,C)),k4_finseq_1(k20_group_9(A,B,C))))) ) ) )).
fof(dt_o_3_8_pua2mss1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) & m4_pua2mss1(B,A) & m2_finseq_2(C,k10_pua2mss1(A,B),k3_finseq_2(k10_pua2mss1(A,B))) ) => m1_subset_1(o_3_8_pua2mss1(A,B,C),k4_card_3(C)) ) )).
fof(dt_o_4_0_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(C,u1_struct_0(k5_cat_4(A,B))) & m1_subset_1(D,u1_struct_0(k5_cat_4(A,B))) ) => m1_cat_1(o_4_0_cat_4(A,B,C,D),k5_cat_4(A,B),D,C) ) )).
fof(dt_o_4_0_chord,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) & m2_glib_000(C,A,B,k21_glib_000(A,B)) & m1_subset_1(D,k6_glib_000(C)) ) => m1_chord(o_4_0_chord(A,B,C,D),C,k6_domain_1(k6_glib_000(C),D)) ) )).
fof(dt_o_4_0_isocat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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(o_4_0_isocat_1(A,B,C,D),A,B,C,D) ) )).
fof(dt_o_4_0_isocat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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(o_4_0_isocat_2(A,B,C,D),A,B,C,D) ) )).
fof(dt_o_4_0_jordan7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(D,u1_struct_0(k15_euclid(2))) ) => m1_subset_1(o_4_0_jordan7(A,B,C,D),k9_subset_1(u1_struct_0(k15_euclid(2)),k1_jordan7(A,B,C),k1_jordan7(A,D,k18_pscomp_1(A)))) ) )).
fof(dt_o_4_0_lmod_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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))) & m2_vectsp_6(D,A,B,C) ) => m1_subset_1(o_4_0_lmod_7(A,B,C,D),k1_vectsp_6(A,B,D)) ) )).
fof(dt_o_4_0_orders_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) & m2_orders_1(B,k1_orders_1(u1_struct_0(A)),k6_partfun1(k1_orders_1(u1_struct_0(A)))) & m2_orders_2(C,A,B) & m1_subset_1(D,u1_struct_0(A)) ) => m1_subset_1(o_4_0_orders_2(A,B,C,D),k9_subset_1(u1_struct_0(A),k2_orders_2(A,k6_domain_1(u1_struct_0(A),D)),C)) ) )).
fof(dt_o_4_0_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) => m1_subset_1(o_4_0_partfun1(A,B,C,D),k3_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D))) ) )).
fof(dt_o_4_0_partfun2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => m1_subset_1(o_4_0_partfun2(A,B,C,D),k9_subset_1(B,A,k1_relset_1(B,D))) ) )).
fof(dt_o_4_0_pencil_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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,C) ) => m1_vectsp_5(o_4_0_pencil_4(A,B,C,D),A,C,D) ) )).
fof(dt_o_4_0_polynom2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,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,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => m1_subset_1(o_4_0_polynom2(A,B,C,D),k3_polynom1(k15_pre_poly(A),B,k11_polynom1(A,B,C,D))) ) )).
fof(dt_o_4_0_rfunct_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => m1_subset_1(o_4_0_rfunct_3(A,B,C,D),k8_relat_1(k9_finseq_1(k1_funct_1(B,C)),k1_tarski(D))) ) )).
fof(dt_o_4_0_yellow20,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v2_altcat_1(A) & l2_altcat_1(A) & v2_altcat_1(B) & l2_altcat_1(B) & m1_subset_1(C,u1_struct_0(k2_yellow20(A,B))) & m1_subset_1(D,u1_struct_0(k2_yellow20(A,B))) ) => m1_subset_1(o_4_0_yellow20(A,B,C,D),k1_altcat_1(k2_yellow20(A,B),C,D)) ) )).
fof(dt_o_4_0_zf_fund2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) & ~ 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(D,B) ) => m1_subset_1(o_4_0_zf_fund2(A,B,C,D),k7_relset_1(B,B,k1_zfmodel1(A,B,C),D)) ) )).
fof(dt_o_4_1_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(C,u1_struct_0(k23_cat_4(A,B))) & m1_subset_1(D,u1_struct_0(k23_cat_4(A,B))) ) => m1_cat_1(o_4_1_cat_4(A,B,C,D),k23_cat_4(A,B),C,D) ) )).
fof(dt_o_4_1_chord,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) & m2_chord(D,A,B,C) ) => m2_glib_000(o_4_1_chord(A,B,C,D),A,k6_subset_1(k6_glib_000(A),D),k21_glib_000(A,k6_subset_1(k6_glib_000(A),D))) ) )).
fof(dt_o_4_1_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & m2_subset_1(C,k3_finseq_2(k15_fomodel1(A)),k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) & 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))) ) => m2_subset_1(o_4_1_fomodel3(A,B,C,D),k15_fomodel1(A),k7_subset_1(k15_fomodel1(A),k16_fomodel1(A),k2_xboole_0(k2_xboole_0(k10_xtuple_0(C),k10_xtuple_0(k37_fomodel2(A,D))),k6_domain_1(k1_fomodel1(A),B)))) ) )).
fof(dt_o_4_1_msafree3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( l1_msualg_1(A) => m1_subset_1(o_4_1_msafree3(A,B,C,D),k1_funct_1(k2_msafree3(A,k1_trees_4(k4_tarski(C,B))),D)) ) )).
fof(dt_o_4_1_orders_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_orders_1(C,k1_orders_1(u1_struct_0(A)),k6_partfun1(k1_orders_1(u1_struct_0(A)))) & m2_orders_2(D,A,C) ) => m1_subset_1(o_4_1_orders_2(A,B,C,D),k9_subset_1(u1_struct_0(A),k2_orders_2(A,k6_domain_1(u1_struct_0(A),B)),D)) ) )).
fof(dt_o_4_1_partfun2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => m1_subset_1(o_4_1_partfun2(A,B,C,D),k9_subset_1(B,k1_tarski(A),k1_relset_1(B,D))) ) )).
fof(dt_o_4_1_pencil_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) & v7_vectsp_1(D,A) & m1_vectsp_4(D,A,C) ) => m1_vectsp_7(o_4_1_pencil_4(A,B,C,D),A,D) ) )).
fof(dt_o_4_1_ranknull,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)))) ) => ( v1_finset_1(o_4_1_ranknull(A,B,C,D)) & m1_vectsp_7(o_4_1_ranknull(A,B,C,D),A,k1_ranknull(A,B,C,D)) ) ) )).
fof(dt_o_4_1_rfunct_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => m1_subset_1(o_4_1_rfunct_3(A,B,C,D),k8_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,B,k1_tarski(C)),k1_tarski(D))) ) )).
fof(dt_o_4_1_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(A) & m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) & m2_subset_1(C,k16_substut1(A),k38_substut1(A)) & m1_substut1(D,A,k7_sublemma(A,C,B)) ) => m2_subset_1(o_4_1_sublemma(A,B,C,D),k1_qc_lang1(A),k12_substut1(A,k22_qc_lang1(A,k2_sublemma(A,k9_sublemma(A,k7_sublemma(A,C,B),D))),k7_substut1(A,k21_qc_lang1(A,k2_sublemma(A,k9_sublemma(A,k7_sublemma(A,C,B),D))),k2_sublemma(A,k9_sublemma(A,k7_sublemma(A,C,B),D)),k19_substut1(A,k9_sublemma(A,k7_sublemma(A,C,B),D))))) ) )).
fof(dt_o_4_1_yellow17,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v1_funct_1(A) & m1_subset_1(D,k1_zfmisc_1(k1_funct_1(A,B))) ) => m1_subset_1(o_4_1_yellow17(A,B,C,D),k3_xboole_0(k8_relat_1(k12_card_3(A,B),k1_tarski(C)),k8_relat_1(k12_card_3(A,B),D))) ) )).
fof(dt_o_4_2_chord,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v6_chord(A) & m1_subset_1(B,k6_glib_000(A)) & m1_subset_1(C,k6_glib_000(A)) & m2_chord(D,A,B,C) ) => m2_glib_000(o_4_2_chord(A,B,C,D),A,k6_subset_1(k6_glib_000(A),D),k21_glib_000(A,k6_subset_1(k6_glib_000(A),D))) ) )).
fof(dt_o_4_2_index_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) & 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)) ) => m4_index_1(o_4_2_index_1(A,B,C,D),u1_struct_0(A),u4_struct_0(A),u1_graph_1(A),u2_graph_1(A),k14_index_1(A,B,B,C,D)) ) )).
fof(dt_o_4_2_rmod_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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(C,A) & m1_rmod_2(C,A,B) & v2_vectsp_2(D,A) & m1_rmod_2(D,A,B) ) => m1_subset_1(o_4_2_rmod_2(A,B,C,D),k6_subset_1(u1_struct_0(C),u1_struct_0(D))) ) )).
fof(dt_o_4_2_vectsp_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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(C,A) & m1_vectsp_4(C,A,B) & v7_vectsp_1(D,A) & m1_vectsp_4(D,A,B) ) => m1_subset_1(o_4_2_vectsp_4(A,B,C,D),k6_subset_1(u1_struct_0(C),u1_struct_0(D))) ) )).
fof(dt_o_4_3_chord,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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(C,k6_glib_000(A)) & m2_chord(D,A,C,B) ) => m2_glib_000(o_4_3_chord(A,B,C,D),A,D,k21_glib_000(A,D)) ) )).
fof(dt_o_4_3_orders_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) & m2_orders_1(C,k1_orders_1(u1_struct_0(A)),k6_partfun1(k1_orders_1(u1_struct_0(A)))) & m2_orders_2(D,A,C) ) => m1_subset_1(o_4_3_orders_2(A,B,C,D),k7_subset_1(u1_struct_0(A),B,D)) ) )).
fof(dt_o_4_3_qc_lang4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k9_qc_lang1(A)) & m1_qc_lang4(C,A,B) & m1_qc_lang4(D,A,C) ) => m2_qc_lang4(o_4_3_qc_lang4(A,B,C,D),A,C,D) ) )).
fof(dt_o_4_3_rmod_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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(C,A) & m1_rmod_2(C,A,B) & v2_vectsp_2(D,A) & m1_rmod_2(D,A,B) ) => m1_subset_1(o_4_3_rmod_2(A,B,C,D),k6_subset_1(u1_struct_0(D),u1_struct_0(C))) ) )).
fof(dt_o_4_3_vectsp_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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(C,A) & m1_vectsp_4(C,A,B) & v7_vectsp_1(D,A) & m1_vectsp_4(D,A,B) ) => m1_subset_1(o_4_3_vectsp_4(A,B,C,D),k6_subset_1(u1_struct_0(D),u1_struct_0(C))) ) )).
fof(dt_o_4_3_yellow12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_pre_topc(o_4_3_yellow12(A,B,C,D)) & m3_yellow_9(o_4_3_yellow12(A,B,C,D),k2_borsuk_1(A,C),k2_borsuk_1(B,D)) ) ) )).
fof(dt_o_4_8_msafree3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) & v1_msualg_6(B,A) & l3_msualg_1(B,A) & m1_msualg_2(C,A,B) & m1_subset_1(D,u4_struct_0(A)) ) => m1_subset_1(o_4_8_msafree3(A,B,C,D),k3_msualg_1(A,D,C)) ) )).
fof(dt_o_5_0_chord,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v6_chord(A) & m1_subset_1(B,k6_glib_000(A)) & m1_subset_1(C,k6_glib_000(A)) & m2_chord(D,A,B,C) & m1_subset_1(E,k6_glib_000(o_4_2_chord(A,B,C,D))) ) => m2_glib_000(o_5_0_chord(A,B,C,D,E),o_4_2_chord(A,B,C,D),k1_glib_002(o_4_2_chord(A,B,C,D),E),k21_glib_000(o_4_2_chord(A,B,C,D),k1_glib_002(o_4_2_chord(A,B,C,D),E))) ) )).
fof(dt_o_5_0_glib_004,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & v1_glib_003(A) & v8_glib_003(A) & v2_glib_001(B,A) & v5_glib_001(B,A) & m3_glib_001(B,A) & m1_subset_1(C,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) & v2_glib_001(E,A) & v5_glib_001(E,A) & m3_glib_001(E,A) ) => ( v2_glib_001(o_5_0_glib_004(A,B,C,D,E),A) & v5_glib_001(o_5_0_glib_004(A,B,C,D,E),A) & m4_glib_001(o_5_0_glib_004(A,B,C,D,E),A,k7_glib_001(A,k7_glib_001(A,k8_glib_001(A,B,1,C),E),k8_glib_001(A,B,D,k3_finseq_1(B)))) ) ) )).
fof(dt_o_5_0_groeb_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) & m1_subset_1(E,k4_ordinal1) ) => m1_subset_1(o_5_0_groeb_3(A,B,C,D,E),k3_xboole_0(k3_groeb_3(A,B,C,D,E),k4_xboole_0(k3_polynom1(k15_pre_poly(A),C,D),k3_groeb_3(A,B,C,D,E)))) ) )).
fof(dt_o_5_0_index_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) & ~ 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) ) => m4_index_1(o_5_0_index_1(A,B,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)) ) )).
fof(dt_o_5_0_jordan7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(D,u1_struct_0(k15_euclid(2))) & m1_subset_1(E,u1_struct_0(k15_euclid(2))) ) => m1_subset_1(o_5_0_jordan7(A,B,C,D,E),k9_subset_1(u1_struct_0(k15_euclid(2)),k1_jordan7(A,B,C),k1_jordan7(A,D,E))) ) )).
fof(dt_o_5_0_msafree3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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(o_5_0_msafree3(A,B,C,D,E),k1_funct_1(k3_msafree3(A,B,k1_trees_4(k4_tarski(D,C))),E)) ) )).
fof(dt_o_5_0_partfun2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(C) & ~ v1_xboole_0(D) & v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,D))) ) => m1_subset_1(o_5_0_partfun2(A,B,C,D,E),k9_subset_1(C,k3_xboole_0(A,B),k1_relset_1(C,E))) ) )).
fof(dt_o_5_0_rlsub_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) & m2_rlsub_1(D,A,B) & m2_rlsub_1(E,A,C) ) => m1_subset_1(o_5_0_rlsub_2(A,B,C,D,E),k9_subset_1(u1_struct_0(A),D,E)) ) )).
fof(dt_o_5_0_rlvect_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) & m2_rlvect_2(E,A,k8_domain_1(u1_struct_0(A),B,C,D)) ) => m1_subset_1(o_5_0_rlvect_4(A,B,C,D,E),k3_rlvect_2(A,E)) ) )).
fof(dt_o_5_0_rusub_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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) & m2_rusub_1(D,A,B) & m2_rusub_1(E,A,C) ) => m1_subset_1(o_5_0_rusub_2(A,B,C,D,E),k9_subset_1(u1_struct_0(A),D,E)) ) )).
fof(dt_o_5_0_topalg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) => m1_borsuk_6(o_5_0_topalg_3(A,B,C,D,E),A,B,C,D,E) ) )).
fof(dt_o_5_0_yellow19,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(C,u1_struct_0(A)) & m1_connsp_2(D,A,C) & m1_yellow19(E,A,B) ) => m1_subset_1(o_5_0_yellow19(A,B,C,D,E),k9_subset_1(u1_struct_0(A),E,k1_tops_1(A,D))) ) )).
fof(dt_o_5_0_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) & m2_zmodul01(D,A,B) & m2_zmodul01(E,A,C) ) => m1_subset_1(o_5_0_zmodul01(A,B,C,D,E),k9_subset_1(u1_struct_0(A),D,E)) ) )).
fof(dt_o_5_1_groeb_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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,C) & v1_polynom7(D,A,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) & m1_subset_1(E,k4_ordinal1) ) => m1_subset_1(o_5_1_groeb_3(A,B,C,D,E),k3_groeb_3(A,B,C,D,E)) ) )).
fof(dt_o_5_1_topalg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & v2_pre_topc(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(B)) & 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(o_5_1_topalg_3(A,B,C,D,E),B,D,k3_funct_2(u1_struct_0(A),u1_struct_0(B),E,C)) ) )).
fof(dt_o_5_2_groeb_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) & m1_subset_1(D,k4_ordinal1) & v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & v1_polynom7(E,A,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => m1_subset_1(o_5_2_groeb_3(A,B,C,D,E),k3_xboole_0(k1_tarski(k3_termord(A,B,C,E)),k4_groeb_3(A,B,C,E,D))) ) )).
fof(dt_o_5_3_groeb_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) & m1_subset_1(E,k4_ordinal1) ) => m1_subset_1(o_5_3_groeb_3(A,B,C,D,E),k3_polynom1(k15_pre_poly(A),C,k5_groeb_3(A,B,C,D,E))) ) )).
fof(dt_o_5_4_groeb_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) & v2_bagorder(B,A) & 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,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) & m1_subset_1(E,k4_ordinal1) ) => m1_subset_1(o_5_4_groeb_3(A,B,C,D,E),k3_xboole_0(k1_tarski(k3_termord(A,B,C,k6_groeb_3(A,B,C,D,E))),k3_polynom1(k15_pre_poly(A),C,k6_groeb_3(A,B,C,D,k1_nat_1(E,1))))) ) )).
fof(dt_o_6_0_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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(o_6_0_aofa_i00(A,B,C,D,E,F),a_6_1_aofa_i00(A,B,C,D,E,F)) ) )).
fof(dt_o_6_0_rmod_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) & m2_rmod_2(E,A,B,C) & m2_rmod_2(F,A,B,D) ) => m1_subset_1(o_6_0_rmod_3(A,B,C,D,E,F),k9_subset_1(u1_struct_0(B),E,F)) ) )).
fof(dt_o_6_0_vectsp_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) & m2_vectsp_4(E,A,B,C) & m2_vectsp_4(F,A,B,D) ) => m1_subset_1(o_6_0_vectsp_5(A,B,C,D,E,F),k9_subset_1(u1_struct_0(B),E,F)) ) )).
fof(dt_o_8_0_chord,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v6_chord(A) & m1_subset_1(B,k6_glib_000(A)) & m1_subset_1(C,k6_glib_000(A)) & m2_chord(D,A,B,C) & ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(k6_glib_000(A))) & m2_glib_000(F,A,D,k21_glib_000(A,D)) & m1_subset_1(G,k6_glib_000(F)) & m1_subset_1(H,k6_glib_000(F)) ) => m2_glib_000(o_8_0_chord(A,B,C,D,E,F,G,H),A,k2_xboole_0(k2_xboole_0(E,k6_domain_1(k6_glib_000(F),G)),k6_domain_1(k6_glib_000(F),H)),k21_glib_000(A,k2_xboole_0(k2_xboole_0(E,k6_domain_1(k6_glib_000(F),G)),k6_domain_1(k6_glib_000(F),H)))) ) )).
fof(dt_u1_algstr_0,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u1_algstr_3,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u1_altcat_1,axiom,( ! [A] : ( 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))) ) ) )).
fof(dt_u1_analmetr,axiom,( ! [A] : ( 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))))) ) )).
fof(dt_u1_analoaf,axiom,( ! [A] : ( 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))))) ) )).
fof(dt_u1_aofa_a00,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & l1_aofa_a00(B,A) ) => m2_aofa_a00(u1_aofa_a00(A,B),u1_struct_0(A),u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,B)) ) )).
fof(dt_u1_armstrng,axiom,( ! [A] : ( l1_armstrng(A) => ( ~ v1_xboole_0(u1_armstrng(A)) & v1_finset_1(u1_armstrng(A)) ) ) )).
fof(dt_u1_bcialg_1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u1_bcialg_4,axiom,( ! [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)) & 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)))) ) ) )).
fof(dt_u1_bhsp_1,axiom,( ! [A] : ( 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))) ) ) )).
fof(dt_u1_cat_1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u1_cat_4,axiom,( ! [A] : ( l1_cat_4(A) => m1_subset_1(u1_cat_4(A),u1_struct_0(A)) ) )).
fof(dt_u1_cayldick,axiom,( ! [A] : ( l1_cayldick(A) => ( v1_funct_1(u1_cayldick(A)) & v1_funct_2(u1_cayldick(A),u1_struct_0(A),u1_struct_0(A)) & m1_subset_1(u1_cayldick(A),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) ) )).
fof(dt_u1_closure1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(dt_u1_closure2,axiom,( ! [A] : ! [B] : ( ( 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)))) ) )).
fof(dt_u1_clvect_1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u1_collsp,axiom,( ! [A] : ( l1_collsp(A) => m1_collsp(u1_collsp(A),u1_struct_0(A)) ) )).
fof(dt_u1_combgras,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) ) )).
fof(dt_u1_compos_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(dt_u1_conlat_1,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_u1_csspace,axiom,( ! [A] : ( 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))) ) ) )).
fof(dt_u1_e_siec,axiom,( ! [A] : ( l1_e_siec(A) => v1_relat_1(u1_e_siec(A)) ) )).
fof(dt_u1_extpro_1,axiom,( ! [A] : ! [B] : ( 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))))))) ) ) )).
fof(dt_u1_fintopo2,axiom,( ! [A] : ( 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)))))) ) ) )).
fof(dt_u1_fomodel1,axiom,( ! [A] : ( 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))) ) ) )).
fof(dt_u1_fsm_1,axiom,( ! [A] : ! [B] : ( 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)))) ) ) )).
fof(dt_u1_fsm_2,axiom,( ! [A] : ! [B] : ( l1_fsm_2(B,A) => m1_subset_1(u1_fsm_2(A,B),k1_zfmisc_1(u1_struct_0(B))) ) )).
fof(dt_u1_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_u1_functor0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))))) ) ) )).
fof(dt_u1_graph_1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u1_grcat_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(dt_u1_group_9,axiom,( ! [A] : ! [B] : ( 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))))) ) ) )).
fof(dt_u1_incsp_1,axiom,( ! [A] : ( l1_incsp_1(A) => ~ v1_xboole_0(u1_incsp_1(A)) ) )).
fof(dt_u1_lang1,axiom,( ! [A] : ( 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))))) ) )).
fof(dt_u1_lattices,axiom,( ! [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)) & 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)))) ) ) )).
fof(dt_u1_memstr_0,axiom,( ! [A] : ! [B] : ( 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))) ) ) )).
fof(dt_u1_metric_1,axiom,( ! [A] : ( 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))) ) ) )).
fof(dt_u1_midsp_1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u1_midsp_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(dt_u1_midsp_3,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & 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)))) ) ) )).
fof(dt_u1_mmlquery,axiom,( ! [A] : ( l1_mmlquery(A) => m1_subset_1(u1_mmlquery(A),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_u1_mod_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) ) )).
fof(dt_u1_modelc_2,axiom,( ! [A] : ( l1_modelc_2(A) => m1_subset_1(u1_modelc_2(A),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_u1_modelc_3,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & l1_modelc_3(B,A) ) => m1_subset_1(u1_modelc_3(A,B),k1_zfmisc_1(k1_modelc_3(A))) ) )).
fof(dt_u1_msualg_1,axiom,( ! [A] : ( 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))))) ) ) )).
fof(dt_u1_normsp_0,axiom,( ! [A] : ( 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))) ) ) )).
fof(dt_u1_orders_2,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_u1_osalg_1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u1_parsp_1,axiom,( ! [A] : ( l1_parsp_1(A) => m1_parsp_1(u1_parsp_1(A),u1_struct_0(A)) ) )).
fof(dt_u1_pcs_0,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_u1_petri,axiom,( ! [A] : ( l1_petri(A) => m1_subset_1(u1_petri(A),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u4_struct_0(A)))) ) )).
fof(dt_u1_petri_2,axiom,( ! [A] : ( l1_petri_2(A) => ( ~ v1_xboole_0(u1_petri_2(A)) & v1_finset_1(u1_petri_2(A)) ) ) )).
fof(dt_u1_polyform,axiom,( ! [A] : ( 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)) ) ) )).
fof(dt_u1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => m1_subset_1(u1_pre_topc(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).
fof(dt_u1_prelamb,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u1_qmax_1,axiom,( ! [A] : ( l1_qmax_1(A) => ~ v1_xboole_0(u1_qmax_1(A)) ) )).
fof(dt_u1_quantal1,axiom,( ! [A] : ( l3_quantal1(A) => m1_subset_1(u1_quantal1(A),u1_struct_0(A)) ) )).
fof(dt_u1_rewrite3,axiom,( ! [A] : ! [B] : ( 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)))) ) )).
fof(dt_u1_ringcat1,axiom,( ! [A] : ( 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)) ) ) )).
fof(dt_u1_rlvect_1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u1_robbins1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u1_sgraph1,axiom,( ! [A] : ( l1_sgraph1(A) => m1_subset_1(u1_sgraph1(A),k1_zfmisc_1(k2_sgraph1(u1_struct_0(A)))) ) )).
fof(dt_u1_sheffer1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u1_stacks_1,axiom,( ! [A] : ( l1_stacks_1(A) => m1_subset_1(u1_stacks_1(A),k1_zfmisc_1(u4_struct_0(A))) ) )).
fof(dt_u1_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ( ~ v1_xboole_0(u1_turing_1(A)) & v1_finset_1(u1_turing_1(A)) ) ) )).
fof(dt_u1_unialg_1,axiom,( ! [A] : ( l1_unialg_1(A) => m2_finseq_1(u1_unialg_1(A),k4_partfun1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A))) ) )).
fof(dt_u1_vectsp_1,axiom,( ! [A] : ! [B] : ( ( 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)))) ) ) )).
fof(dt_u1_vectsp_2,axiom,( ! [A] : ! [B] : ( ( 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)))) ) ) )).
fof(dt_u1_waybel_0,axiom,( ! [A] : ! [B] : ( ( 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)))) ) ) )).
fof(dt_u1_zmodul01,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u2_abcmiz_0,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u2_algstr_0,axiom,( ! [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)) & 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)))) ) ) )).
fof(dt_u2_altcat_1,axiom,( ! [A] : ( 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))) ) )).
fof(dt_u2_armstrng,axiom,( ! [A] : ( 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)) ) ) )).
fof(dt_u2_cat_4,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u2_combgras,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) ) )).
fof(dt_u2_conlat_1,axiom,( ! [A] : ! [B] : ( ( l5_struct_0(A) & l2_conlat_1(B,A) ) => m1_subset_1(u2_conlat_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_u2_e_siec,axiom,( ! [A] : ( l1_e_siec(A) => v1_relat_1(u2_e_siec(A)) ) )).
fof(dt_u2_fsm_1,axiom,( ! [A] : ! [B] : ( l1_fsm_1(B,A) => m1_subset_1(u2_fsm_1(A,B),u1_struct_0(B)) ) )).
fof(dt_u2_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(dt_u2_functor0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(dt_u2_graph_1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u2_grcat_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(dt_u2_incsp_1,axiom,( ! [A] : ( l1_incsp_1(A) => ~ v1_xboole_0(u2_incsp_1(A)) ) )).
fof(dt_u2_lang1,axiom,( ! [A] : ( l2_lang1(A) => m1_subset_1(u2_lang1(A),u1_struct_0(A)) ) )).
fof(dt_u2_lattices,axiom,( ! [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)) & 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)))) ) ) )).
fof(dt_u2_memstr_0,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(dt_u2_midsp_2,axiom,( ! [A] : ! [B] : ( ( ~ 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))))) ) ) )).
fof(dt_u2_mmlquery,axiom,( ! [A] : ( l1_mmlquery(A) => m1_subset_1(u2_mmlquery(A),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_mmlquery(A)))) ) )).
fof(dt_u2_mod_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) ) )).
fof(dt_u2_modelc_2,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u2_modelc_3,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & l1_modelc_3(B,A) ) => m1_subset_1(u2_modelc_3(A,B),k1_zfmisc_1(k1_modelc_3(A))) ) )).
fof(dt_u2_msualg_1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u2_petri,axiom,( ! [A] : ( l1_petri(A) => m1_subset_1(u2_petri(A),k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(A),u1_struct_0(A)))) ) )).
fof(dt_u2_petri_2,axiom,( ! [A] : ( l1_petri_2(A) => ( v1_relat_1(u2_petri_2(A)) & v1_funct_1(u2_petri_2(A)) ) ) )).
fof(dt_u2_polyform,axiom,( ! [A] : ( 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)) ) ) )).
fof(dt_u2_prelamb,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u2_qmax_1,axiom,( ! [A] : ( l1_qmax_1(A) => ~ v1_xboole_0(u2_qmax_1(A)) ) )).
fof(dt_u2_ringcat1,axiom,( ! [A] : ( 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)) ) ) )).
fof(dt_u2_stacks_1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u2_struct_0,axiom,( ! [A] : ( l2_struct_0(A) => m1_subset_1(u2_struct_0(A),u1_struct_0(A)) ) )).
fof(dt_u2_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ( ~ v1_xboole_0(u2_turing_1(A)) & v1_finset_1(u2_turing_1(A)) ) ) )).
fof(dt_u3_abcmiz_0,axiom,( ! [A] : ( 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))))) ) ) )).
fof(dt_u3_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & m1_msafree(C,A,B) & l3_aofa_a00(D,A,B,C) ) => ( v1_funct_1(u3_aofa_a00(A,B,C,D)) & v1_funct_2(u3_aofa_a00(A,B,C,D),k3_card_3(k6_pboole(u1_struct_0(A),C,u3_msualg_1(A,B))),u1_struct_0(D)) & m1_subset_1(u3_aofa_a00(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k3_card_3(k6_pboole(u1_struct_0(A),C,u3_msualg_1(A,B))),u1_struct_0(D)))) ) ) )).
fof(dt_u3_armstrng,axiom,( ! [A] : ( l1_armstrng(A) => m1_subset_1(u3_armstrng(A),k1_zfmisc_1(k4_card_3(u2_armstrng(A)))) ) )).
fof(dt_u3_cat_4,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u3_conlat_1,axiom,( ! [A] : ! [B] : ( ( l5_struct_0(A) & l2_conlat_1(B,A) ) => m1_subset_1(u3_conlat_1(A,B),k1_zfmisc_1(u4_struct_0(A))) ) )).
fof(dt_u3_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_u3_grcat_1,axiom,( ! [A] : ( 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))))) ) ) )).
fof(dt_u3_incsp_1,axiom,( ! [A] : ( 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)))) ) )).
fof(dt_u3_mod_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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))))) ) ) )).
fof(dt_u3_modelc_1,axiom,( ! [A] : ( l2_modelc_1(A) => m1_subset_1(u3_modelc_1(A),k1_zfmisc_1(u1_struct_0(A))) ) )).
fof(dt_u3_modelc_2,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u3_modelc_3,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & l1_modelc_3(B,A) ) => m1_subset_1(u3_modelc_3(A,B),k1_zfmisc_1(k1_modelc_3(A))) ) )).
fof(dt_u3_msualg_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(dt_u3_prelamb,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u3_qmax_1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u3_ringcat1,axiom,( ! [A] : ( 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))))) ) ) )).
fof(dt_u3_stacks_1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u3_struct_0,axiom,( ! [A] : ( l3_struct_0(A) => m1_subset_1(u3_struct_0(A),u1_struct_0(A)) ) )).
fof(dt_u3_turing_1,axiom,( ! [A] : ( 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),k1_enumset1(k4_xcmplx_0(1),k5_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),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1))))) ) ) )).
fof(dt_u4_abcmiz_0,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u4_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) & l4_aofa_a00(D,A,B,C) ) => ( v2_relat_1(u4_aofa_a00(A,B,C,D)) & m1_msafree(u4_aofa_a00(A,B,C,D),A,C) ) ) )).
fof(dt_u4_cat_4,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u4_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(dt_u4_incsp_1,axiom,( ! [A] : ( l2_incsp_1(A) => ~ v1_xboole_0(u4_incsp_1(A)) ) )).
fof(dt_u4_modelc_1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u4_modelc_2,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u4_modelc_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_u4_msualg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(dt_u4_stacks_1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u4_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => m1_subset_1(u4_turing_1(A),u2_turing_1(A)) ) )).
fof(dt_u5_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) & l4_aofa_a00(D,A,B,C) ) => m2_pboole(u5_aofa_a00(A,B,C,D),u1_struct_0(A),u4_aofa_a00(A,B,C,D),k13_msafree(A,B)) ) )).
fof(dt_u5_cat_4,axiom,( ! [A] : ( l2_cat_4(A) => m1_subset_1(u5_cat_4(A),u1_struct_0(A)) ) )).
fof(dt_u5_modelc_1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u5_modelc_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & l2_modelc_3(B,A) ) => m1_subset_1(u5_modelc_3(A,B),k1_zfmisc_1(u1_struct_0(B))) ) )).
fof(dt_u5_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => m1_subset_1(u5_turing_1(A),u2_turing_1(A)) ) )).
fof(dt_u6_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) & l4_aofa_a00(D,A,B,C) ) => m1_aofa_a00(u6_aofa_a00(A,B,C,D),u1_struct_0(A),u1_struct_0(A),u4_aofa_a00(A,B,C,D)) ) )).
fof(dt_u6_cat_4,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u6_modelc_1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u6_modelc_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(dt_u7_aofa_a00,axiom,( ! [A] : ( l5_aofa_a00(A) => m2_finseq_1(u7_aofa_a00(A),u4_struct_0(A)) ) )).
fof(dt_u7_cat_4,axiom,( ! [A] : ( 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)))) ) ) )).
fof(dt_u8_aofa_a00,axiom,( ! [A] : ( l6_aofa_a00(A) => m1_subset_1(u8_aofa_a00(A),u1_struct_0(A)) ) )).
fof(dt_u8_cat_4,axiom,( ! [A] : ( 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)))) ) ) )).
fof(existence_l1_abcmiz_0,axiom,( ? [A] : l1_abcmiz_0(A) )).
fof(existence_l1_algstr_0,axiom,( ? [A] : l1_algstr_0(A) )).
fof(existence_l1_algstr_3,axiom,( ? [A] : l1_algstr_3(A) )).
fof(existence_l1_altcat_1,axiom,( ? [A] : l1_altcat_1(A) )).
fof(existence_l1_analmetr,axiom,( ? [A] : l1_analmetr(A) )).
fof(existence_l1_analoaf,axiom,( ? [A] : l1_analoaf(A) )).
fof(existence_l1_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ? [B] : l1_aofa_a00(B,A) ) )).
fof(existence_l1_armstrng,axiom,( ? [A] : l1_armstrng(A) )).
fof(existence_l1_bcialg_1,axiom,( ? [A] : l1_bcialg_1(A) )).
fof(existence_l1_bcialg_4,axiom,( ? [A] : l1_bcialg_4(A) )).
fof(existence_l1_bhsp_1,axiom,( ? [A] : l1_bhsp_1(A) )).
fof(existence_l1_cat_1,axiom,( ? [A] : l1_cat_1(A) )).
fof(existence_l1_cat_4,axiom,( ? [A] : l1_cat_4(A) )).
fof(existence_l1_cayldick,axiom,( ? [A] : l1_cayldick(A) )).
fof(existence_l1_cfuncdom,axiom,( ? [A] : l1_cfuncdom(A) )).
fof(existence_l1_cgames_1,axiom,( ? [A] : l1_cgames_1(A) )).
fof(existence_l1_clopban2,axiom,( ? [A] : l1_clopban2(A) )).
fof(existence_l1_closure1,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : l1_closure1(B,A) ) )).
fof(existence_l1_closure2,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : l1_closure2(B,A) ) )).
fof(existence_l1_clvect_1,axiom,( ? [A] : l1_clvect_1(A) )).
fof(existence_l1_collsp,axiom,( ? [A] : l1_collsp(A) )).
fof(existence_l1_combgras,axiom,( ! [A] : ! [B] : ( ( l1_incsp_1(A) & l1_incsp_1(B) ) => ? [C] : l1_combgras(C,A,B) ) )).
fof(existence_l1_compos_1,axiom,( ? [A] : l1_compos_1(A) )).
fof(existence_l1_conlat_1,axiom,( ? [A] : l1_conlat_1(A) )).
fof(existence_l1_csspace,axiom,( ? [A] : l1_csspace(A) )).
fof(existence_l1_e_siec,axiom,( ? [A] : l1_e_siec(A) )).
fof(existence_l1_extpro_1,axiom,( ! [A] : ? [B] : l1_extpro_1(B,A) )).
fof(existence_l1_fintopo2,axiom,( ? [A] : l1_fintopo2(A) )).
fof(existence_l1_fomodel1,axiom,( ? [A] : l1_fomodel1(A) )).
fof(existence_l1_fsm_1,axiom,( ! [A] : ? [B] : l1_fsm_1(B,A) )).
fof(existence_l1_fsm_2,axiom,( ! [A] : ? [B] : l1_fsm_2(B,A) )).
fof(existence_l1_fsm_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) ) => ? [C] : l1_fsm_3(C,A,B) ) )).
fof(existence_l1_funcsdom,axiom,( ? [A] : l1_funcsdom(A) )).
fof(existence_l1_functor0,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & l1_struct_0(B) ) => ? [C] : l1_functor0(C,A,B) ) )).
fof(existence_l1_geomtrap,axiom,( ? [A] : l1_geomtrap(A) )).
fof(existence_l1_graph_1,axiom,( ? [A] : l1_graph_1(A) )).
fof(existence_l1_grcat_1,axiom,( ? [A] : l1_grcat_1(A) )).
fof(existence_l1_group_9,axiom,( ! [A] : ? [B] : l1_group_9(B,A) )).
fof(existence_l1_incsp_1,axiom,( ? [A] : l1_incsp_1(A) )).
fof(existence_l1_lang1,axiom,( ? [A] : l1_lang1(A) )).
fof(existence_l1_lattices,axiom,( ? [A] : l1_lattices(A) )).
fof(existence_l1_lopban_2,axiom,( ? [A] : l1_lopban_2(A) )).
fof(existence_l1_memstr_0,axiom,( ! [A] : ? [B] : l1_memstr_0(B,A) )).
fof(existence_l1_metric_1,axiom,( ? [A] : l1_metric_1(A) )).
fof(existence_l1_midsp_1,axiom,( ? [A] : l1_midsp_1(A) )).
fof(existence_l1_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_midsp_1(A) ) => ? [B] : l1_midsp_2(B,A) ) )).
fof(existence_l1_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ? [B] : l1_midsp_3(B,A) ) )).
fof(existence_l1_mmlquery,axiom,( ? [A] : l1_mmlquery(A) )).
fof(existence_l1_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ? [B] : l1_mod_2(B,A) ) )).
fof(existence_l1_modelc_2,axiom,( ? [A] : l1_modelc_2(A) )).
fof(existence_l1_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => ? [B] : l1_modelc_3(B,A) ) )).
fof(existence_l1_msualg_1,axiom,( ? [A] : l1_msualg_1(A) )).
fof(existence_l1_normsp_0,axiom,( ? [A] : l1_normsp_0(A) )).
fof(existence_l1_normsp_1,axiom,( ? [A] : l1_normsp_1(A) )).
fof(existence_l1_orders_2,axiom,( ? [A] : l1_orders_2(A) )).
fof(existence_l1_osalg_1,axiom,( ? [A] : l1_osalg_1(A) )).
fof(existence_l1_parsp_1,axiom,( ? [A] : l1_parsp_1(A) )).
fof(existence_l1_pcs_0,axiom,( ? [A] : l1_pcs_0(A) )).
fof(existence_l1_petri,axiom,( ? [A] : l1_petri(A) )).
fof(existence_l1_petri_2,axiom,( ? [A] : l1_petri_2(A) )).
fof(existence_l1_polyalg1,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : l1_polyalg1(B,A) ) )).
fof(existence_l1_polyform,axiom,( ? [A] : l1_polyform(A) )).
fof(existence_l1_pre_topc,axiom,( ? [A] : l1_pre_topc(A) )).
fof(existence_l1_prelamb,axiom,( ? [A] : l1_prelamb(A) )).
fof(existence_l1_qmax_1,axiom,( ? [A] : l1_qmax_1(A) )).
fof(existence_l1_quantal1,axiom,( ? [A] : l1_quantal1(A) )).
fof(existence_l1_rewrite3,axiom,( ! [A] : ? [B] : l1_rewrite3(B,A) )).
fof(existence_l1_ringcat1,axiom,( ? [A] : l1_ringcat1(A) )).
fof(existence_l1_rltopsp1,axiom,( ? [A] : l1_rltopsp1(A) )).
fof(existence_l1_rlvect_1,axiom,( ? [A] : l1_rlvect_1(A) )).
fof(existence_l1_robbins1,axiom,( ? [A] : l1_robbins1(A) )).
fof(existence_l1_robbins3,axiom,( ? [A] : l1_robbins3(A) )).
fof(existence_l1_sgraph1,axiom,( ? [A] : l1_sgraph1(A) )).
fof(existence_l1_sheffer1,axiom,( ? [A] : l1_sheffer1(A) )).
fof(existence_l1_stacks_1,axiom,( ? [A] : l1_stacks_1(A) )).
fof(existence_l1_struct_0,axiom,( ? [A] : l1_struct_0(A) )).
fof(existence_l1_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ? [B] : l1_symsp_1(B,A) ) )).
fof(existence_l1_topgrp_1,axiom,( ? [A] : l1_topgrp_1(A) )).
fof(existence_l1_turing_1,axiom,( ? [A] : l1_turing_1(A) )).
fof(existence_l1_unialg_1,axiom,( ? [A] : l1_unialg_1(A) )).
fof(existence_l1_vectmetr,axiom,( ? [A] : l1_vectmetr(A) )).
fof(existence_l1_vectsp_1,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : l1_vectsp_1(B,A) ) )).
fof(existence_l1_vectsp_2,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : l1_vectsp_2(B,A) ) )).
fof(existence_l1_waybel_0,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : l1_waybel_0(B,A) ) )).
fof(existence_l1_waybel_9,axiom,( ? [A] : l1_waybel_9(A) )).
fof(existence_l1_zmodul01,axiom,( ? [A] : l1_zmodul01(A) )).
fof(existence_l2_abcmiz_0,axiom,( ? [A] : l2_abcmiz_0(A) )).
fof(existence_l2_algstr_0,axiom,( ? [A] : l2_algstr_0(A) )).
fof(existence_l2_altcat_1,axiom,( ? [A] : l2_altcat_1(A) )).
fof(existence_l2_bcialg_1,axiom,( ? [A] : l2_bcialg_1(A) )).
fof(existence_l2_cat_4,axiom,( ? [A] : l2_cat_4(A) )).
fof(existence_l2_clvect_1,axiom,( ? [A] : l2_clvect_1(A) )).
fof(existence_l2_conlat_1,axiom,( ! [A] : ( l5_struct_0(A) => ? [B] : l2_conlat_1(B,A) ) )).
fof(existence_l2_fsm_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ? [C] : l2_fsm_1(C,A,B) ) )).
fof(existence_l2_fsm_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ? [C] : l2_fsm_2(C,A,B) ) )).
fof(existence_l2_fsm_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) ) => ? [C] : l2_fsm_3(C,A,B) ) )).
fof(existence_l2_functor0,axiom,( ! [A] : ! [B] : ( ( l1_altcat_1(A) & l1_altcat_1(B) ) => ? [C] : l2_functor0(C,A,B) ) )).
fof(existence_l2_incsp_1,axiom,( ? [A] : l2_incsp_1(A) )).
fof(existence_l2_lang1,axiom,( ? [A] : l2_lang1(A) )).
fof(existence_l2_lattices,axiom,( ? [A] : l2_lattices(A) )).
fof(existence_l2_modelc_1,axiom,( ? [A] : l2_modelc_1(A) )).
fof(existence_l2_modelc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : l2_modelc_3(B,A) ) )).
fof(existence_l2_msualg_1,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : l2_msualg_1(B,A) ) )).
fof(existence_l2_normsp_0,axiom,( ? [A] : l2_normsp_0(A) )).
fof(existence_l2_osalg_1,axiom,( ? [A] : l2_osalg_1(A) )).
fof(existence_l2_pcs_0,axiom,( ? [A] : l2_pcs_0(A) )).
fof(existence_l2_prelamb,axiom,( ? [A] : l2_prelamb(A) )).
fof(existence_l2_qmax_1,axiom,( ? [A] : l2_qmax_1(A) )).
fof(existence_l2_quantal1,axiom,( ? [A] : l2_quantal1(A) )).
fof(existence_l2_robbins1,axiom,( ? [A] : l2_robbins1(A) )).
fof(existence_l2_robbins3,axiom,( ? [A] : l2_robbins3(A) )).
fof(existence_l2_struct_0,axiom,( ? [A] : l2_struct_0(A) )).
fof(existence_l2_vectsp_2,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & l1_struct_0(B) ) => ? [C] : l2_vectsp_2(C,A,B) ) )).
fof(existence_l3_abcmiz_0,axiom,( ? [A] : l3_abcmiz_0(A) )).
fof(existence_l3_algstr_0,axiom,( ? [A] : l3_algstr_0(A) )).
fof(existence_l3_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) & m1_msafree(C,A,B) ) => ? [D] : l3_aofa_a00(D,A,B,C) ) )).
fof(existence_l3_fsm_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ? [C] : l3_fsm_1(C,A,B) ) )).
fof(existence_l3_lattices,axiom,( ? [A] : l3_lattices(A) )).
fof(existence_l3_msualg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ? [B] : l3_msualg_1(B,A) ) )).
fof(existence_l3_osalg_1,axiom,( ? [A] : l3_osalg_1(A) )).
fof(existence_l3_quantal1,axiom,( ? [A] : l3_quantal1(A) )).
fof(existence_l3_robbins1,axiom,( ? [A] : l3_robbins1(A) )).
fof(existence_l3_robbins3,axiom,( ? [A] : l3_robbins3(A) )).
fof(existence_l3_sheffer1,axiom,( ? [A] : l3_sheffer1(A) )).
fof(existence_l3_struct_0,axiom,( ? [A] : l3_struct_0(A) )).
fof(existence_l4_algstr_0,axiom,( ? [A] : l4_algstr_0(A) )).
fof(existence_l4_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ? [D] : l4_aofa_a00(D,A,B,C) ) )).
fof(existence_l4_robbins1,axiom,( ? [A] : l4_robbins1(A) )).
fof(existence_l4_robbins3,axiom,( ? [A] : l4_robbins3(A) )).
fof(existence_l4_struct_0,axiom,( ? [A] : l4_struct_0(A) )).
fof(existence_l5_algstr_0,axiom,( ? [A] : l5_algstr_0(A) )).
fof(existence_l5_aofa_a00,axiom,( ? [A] : l5_aofa_a00(A) )).
fof(existence_l5_struct_0,axiom,( ? [A] : l5_struct_0(A) )).
fof(existence_l6_algstr_0,axiom,( ? [A] : l6_algstr_0(A) )).
fof(existence_l6_aofa_a00,axiom,( ? [A] : l6_aofa_a00(A) )).
fof(existence_m1_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_struct_0(A)) ) => ? [C] : m1_abcmiz_1(C,A,B) ) )).
fof(existence_m1_abcmiz_a,axiom,( ! [A] : ! [B] : ( ( 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] : m1_abcmiz_a(C,A,B) ) )).
fof(existence_m1_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ? [B] : m1_alg_1(B,A) ) )).
fof(existence_m1_algspec1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ? [B] : m1_algspec1(B,A) ) )).
fof(existence_m1_algstr_4,axiom,( ! [A] : ( l3_algstr_0(A) => ? [B] : m1_algstr_4(B,A) ) )).
fof(existence_m1_altcat_2,axiom,( ! [A] : ( l2_altcat_1(A) => ? [B] : m1_altcat_2(B,A) ) )).
fof(existence_m1_altcat_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) & m1_subset_1(B,u1_struct_0(A)) & 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] : m1_altcat_5(E,A,B,C,D) ) )).
fof(existence_m1_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : m1_aofa_000(D,A,B,C) ) )).
fof(existence_m1_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ? [D] : m1_aofa_a00(D,A,B,C) ) )).
fof(existence_m1_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : m1_aofa_i00(E,A,B,C,D) ) )).
fof(existence_m1_armstrng,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) ) => ? [C] : m1_armstrng(C,A,B) ) )).
fof(existence_m1_autalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : m1_autalg_1(D,A,B,C) ) )).
fof(existence_m1_bcialg_1,axiom,( ! [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] : m1_bcialg_1(B,A) ) )).
fof(existence_m1_bcialg_2,axiom,( ! [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] : m1_bcialg_2(B,A) ) )).
fof(existence_m1_bcialg_3,axiom,( ! [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] : m1_bcialg_3(B,A) ) )).
fof(existence_m1_bcialg_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => ? [E] : m1_bcialg_5(E,A,B,C,D) ) )).
fof(existence_m1_bciideal,axiom,( ! [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] : m1_bciideal(B,A) ) )).
fof(existence_m1_bhsp_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ? [B] : m1_bhsp_5(B,A) ) )).
fof(existence_m1_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree1(A) ) => ? [B] : m1_bintree2(B,A) ) )).
fof(existence_m1_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : m1_borsuk_1(B,A) ) )).
fof(existence_m1_borsuk_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ? [D] : m1_borsuk_2(D,A,B,C) ) )).
fof(existence_m1_borsuk_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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] : m1_borsuk_6(F,A,B,C,D,E) ) )).
fof(existence_m1_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_eqrel_1(B,A) ) => ? [C] : m1_bvfunc_1(C,A,B) ) )).
fof(existence_m1_c0sp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ? [B] : m1_c0sp1(B,A) ) )).
fof(existence_m1_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : m1_card_fil(B,A) ) )).
fof(existence_m1_card_lar,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ? [C] : m1_card_lar(C,A,B) ) )).
fof(existence_m1_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : m1_cat_1(D,A,B,C) ) )).
fof(existence_m1_cat_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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] : m1_cat_2(C,A,B) ) )).
fof(existence_m1_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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] : m1_cat_3(D,A,B,C) ) )).
fof(existence_m1_cat_5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_cat_5(A) ) => ? [B] : m1_cat_5(B,A) ) )).
fof(existence_m1_catalan2,axiom,( ! [A] : ? [B] : m1_catalan2(B,A) )).
fof(existence_m1_catalg_1,axiom,( ! [A] : ? [B] : m1_catalg_1(B,A) )).
fof(existence_m1_cc0sp1,axiom,( ! [A] : ( ( ~ 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] : m1_cc0sp1(B,A) ) )).
fof(existence_m1_cfdiff_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ? [B] : m1_cfdiff_1(B,A) ) )).
fof(existence_m1_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ? [B] : m1_chain_1(B,A) ) )).
fof(existence_m1_chord,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ? [C] : m1_chord(C,A,B) ) )).
fof(existence_m1_circcmb3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ? [B] : m1_circcmb3(B,A) ) )).
fof(existence_m1_circtrm1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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] : m1_circtrm1(F,A,B,C,D,E) ) )).
fof(existence_m1_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : m1_closure2(D,A,B,C) ) )).
fof(existence_m1_clvect_1,axiom,( ! [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) ) => ? [B] : m1_clvect_1(B,A) ) )).
fof(existence_m1_collsp,axiom,( ! [A] : ? [B] : m1_collsp(B,A) )).
fof(existence_m1_complfld,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,u1_struct_0(k1_complfld)) & ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ? [C] : m1_complfld(C,A,B) ) )).
fof(existence_m1_comptrig,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ? [C] : m1_comptrig(C,A,B) ) )).
fof(existence_m1_comput_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : m1_comput_1(E,A,B,C,D) ) )).
fof(existence_m1_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ? [B] : m1_conlat_1(B,A) ) )).
fof(existence_m1_connsp_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ? [C] : m1_connsp_2(C,A,B) ) )).
fof(existence_m1_connsp_3,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : m1_connsp_3(B,A) ) )).
fof(existence_m1_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ? [B] : m1_convex4(B,A) ) )).
fof(existence_m1_decomp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : m1_decomp_1(B,A) ) )).
fof(existence_m1_dist_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ? [B] : m1_dist_1(B,A) ) )).
fof(existence_m1_dist_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & m1_subset_1(B,k6_dist_1(A)) ) => ? [C] : m1_dist_2(C,A,B) ) )).
fof(existence_m1_dtconstr,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : m1_dtconstr(D,A,B,C) ) )).
fof(existence_m1_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : m1_dynkin(B,A) ) )).
fof(existence_m1_ec_pf_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ? [B] : m1_ec_pf_1(B,A) ) )).
fof(existence_m1_eqrel_1,axiom,( ! [A] : ? [B] : m1_eqrel_1(B,A) )).
fof(existence_m1_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_exchsort(A) ) => ? [B] : m1_exchsort(B,A) ) )).
fof(existence_m1_extpro_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & ~ v2_compos_1(C,B) ) => ? [D] : m1_extpro_1(D,A,B,C) ) )).
fof(existence_m1_filter_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_relat_1(B) ) => ? [C] : m1_filter_1(C,A,B) ) )).
fof(existence_m1_finance1,axiom,( ? [A] : m1_finance1(A) )).
fof(existence_m1_finseq_1,axiom,( ! [A] : ? [B] : m1_finseq_1(B,A) )).
fof(existence_m1_finseq_2,axiom,( ! [A] : ? [B] : m1_finseq_2(B,A) )).
fof(existence_m1_fintopo6,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : m1_fintopo6(B,A) ) )).
fof(existence_m1_fomodel0,axiom,( ! [A] : ? [B] : m1_fomodel0(B,A) )).
fof(existence_m1_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : m1_fomodel2(D,A,B,C) ) )).
fof(existence_m1_freealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ? [B] : m1_freealg(B,A) ) )).
fof(existence_m1_funct_2,axiom,( ! [A] : ! [B] : ? [C] : m1_funct_2(C,A,B) )).
fof(existence_m1_funct_7,axiom,( ! [A] : ! [B] : ? [C] : m1_funct_7(C,A,B) )).
fof(existence_m1_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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] : m1_functor0(F,A,B,C,D,E) ) )).
fof(existence_m1_functor2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : m1_functor2(E,A,B,C,D) ) )).
fof(existence_m1_functor3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : m1_functor3(E,A,B,C,D) ) )).
fof(existence_m1_fvaluat1,axiom,( ! [A] : ( l6_algstr_0(A) => ? [B] : m1_fvaluat1(B,A) ) )).
fof(existence_m1_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v4_vectsp_1(A) & l4_algstr_0(A) ) => ? [B] : m1_gcd_1(B,A) ) )).
fof(existence_m1_genealg1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ? [B] : m1_genealg1(B,A) ) )).
fof(existence_m1_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ? [B] : m1_glib_000(B,A) ) )).
fof(existence_m1_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ? [B] : m1_glib_001(B,A) ) )).
fof(existence_m1_glib_005,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : m1_glib_005(C,A,B) ) )).
fof(existence_m1_goedcpuc,axiom,( ! [A] : ( m1_qc_lang1(A) => ? [B] : m1_goedcpuc(B,A) ) )).
fof(existence_m1_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ? [B] : m1_graph_1(B,A) ) )).
fof(existence_m1_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ? [D] : m1_graph_3(D,A,B,C) ) )).
fof(existence_m1_grcat_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m1_grcat_1(C,A,B) ) )).
fof(existence_m1_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & l3_algstr_0(A) ) => ? [B] : m1_group_2(B,A) ) )).
fof(existence_m1_group_6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) & m1_group_2(B,A) ) => ? [C] : m1_group_6(C,A,B) ) )).
fof(existence_m1_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ? [C] : m1_group_9(C,A,B) ) )).
fof(existence_m1_hallmar1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k4_ordinal1) ) => ? [D] : m1_hallmar1(D,A,B,C) ) )).
fof(existence_m1_henmodel,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & v1_henmodel(B,A) & m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) ) => ? [C] : m1_henmodel(C,A,B) ) )).
fof(existence_m1_hilbert3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ? [B] : m1_hilbert3(B,A) ) )).
fof(existence_m1_ideal_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : m1_ideal_1(C,A,B) ) )).
fof(existence_m1_incproj,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ? [B] : m1_incproj(B,A) ) )).
fof(existence_m1_index_1,axiom,( ! [A] : ! [B] : ? [C] : m1_index_1(C,A,B) )).
fof(existence_m1_instalg1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ? [B] : m1_instalg1(B,A) ) )).
fof(existence_m1_int_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_int_3(A) & l6_algstr_0(A) ) => ? [B] : m1_int_3(B,A) ) )).
fof(existence_m1_int_6,axiom,( ! [A] : ( ( 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] : m1_int_6(B,A) ) )).
fof(existence_m1_integr15,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : m1_integr15(D,A,B,C) ) )).
fof(existence_m1_integr16,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : m1_integr16(D,A,B,C) ) )).
fof(existence_m1_integr18,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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] : m1_integr18(E,A,B,C,D) ) )).
fof(existence_m1_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ? [B] : m1_integra1(B,A) ) )).
fof(existence_m1_interva1,axiom,( ! [A] : ? [B] : m1_interva1(B,A) )).
fof(existence_m1_isocat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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] : m1_isocat_1(C,A,B) ) )).
fof(existence_m1_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ? [B] : m1_jordan_a(B,A) ) )).
fof(existence_m1_kolmog01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : m1_kolmog01(D,A,B,C) ) )).
fof(existence_m1_lattice4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) & ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ? [C] : m1_lattice4(C,A,B) ) )).
fof(existence_m1_lattice5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : m1_lattice5(D,A,B,C) ) )).
fof(existence_m1_lattice7,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : m1_lattice7(D,A,B,C) ) )).
fof(existence_m1_lattice8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : m1_lattice8(D,A,B,C) ) )).
fof(existence_m1_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ? [B] : m1_lexbfs(B,A) ) )).
fof(existence_m1_lmod_7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : m1_lmod_7(C,A,B) ) )).
fof(existence_m1_margrel1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ? [B] : m1_margrel1(B,A) ) )).
fof(existence_m1_matrix_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_matrix_2(A) ) => ? [B] : m1_matrix_2(B,A) ) )).
fof(existence_m1_matrixj2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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] : m1_matrixj2(C,A,B) ) )).
fof(existence_m1_matrlin,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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] : m1_matrlin(C,A,B) ) )).
fof(existence_m1_matroid0,axiom,( ! [A] : ( ( ~ v3_pencil_1(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ? [B] : m1_matroid0(B,A) ) )).
fof(existence_m1_measure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_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,k6_numbers))) ) => ? [D] : m1_measure1(D,A,B,C) ) )).
fof(existence_m1_measure2,axiom,( ! [A] : ! [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))) ) => ? [C] : m1_measure2(C,A,B) ) )).
fof(existence_m1_measure3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ? [D] : m1_measure3(D,A,B,C) ) )).
fof(existence_m1_measure4,axiom,( ! [A] : ? [B] : m1_measure4(B,A) )).
fof(existence_m1_measure7,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ? [B] : m1_measure7(B,A) ) )).
fof(existence_m1_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ? [B] : m1_metric_2(B,A) ) )).
fof(existence_m1_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ? [B] : m1_midsp_1(B,A) ) )).
fof(existence_m1_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ? [B] : m1_midsp_3(B,A) ) )).
fof(existence_m1_mod_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : m1_mod_2(D,A,B,C) ) )).
fof(existence_m1_mod_3,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m1_mod_3(C,A,B) ) )).
fof(existence_m1_mod_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : m1_mod_4(F,A,B,C,D,E) ) )).
fof(existence_m1_modcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ? [B] : m1_modcat_1(B,A) ) )).
fof(existence_m1_modelc_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ? [C] : m1_modelc_1(C,A,B) ) )).
fof(existence_m1_monoid_0,axiom,( ! [A] : ( l3_algstr_0(A) => ? [B] : m1_monoid_0(B,A) ) )).
fof(existence_m1_msafree,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ? [C] : m1_msafree(C,A,B) ) )).
fof(existence_m1_msafree2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : m1_msafree2(C,A,B) ) )).
fof(existence_m1_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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,k10_xtuple_0(B)) ) => ? [D] : m1_msafree4(D,A,B,C) ) )).
fof(existence_m1_msalimit,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m1_msalimit(C,A,B) ) )).
fof(existence_m1_msaterm,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : m1_msaterm(D,A,B,C) ) )).
fof(existence_m1_msualg_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ? [C] : m1_msualg_2(C,A,B) ) )).
fof(existence_m1_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : m1_msualg_4(D,A,B,C) ) )).
fof(existence_m1_msualg_6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ? [C] : m1_msualg_6(C,A,B) ) )).
fof(existence_m1_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : m1_mycielsk(B,A) ) )).
fof(existence_m1_nattra_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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] : m1_nattra_1(E,A,B,C,D) ) )).
fof(existence_m1_ncfcont1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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] : m1_ncfcont1(C,A,B) ) )).
fof(existence_m1_nfcont_1,axiom,( ! [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) & 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] : m1_nfcont_1(C,A,B) ) )).
fof(existence_m1_oppcat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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] : m1_oppcat_1(C,A,B) ) )).
fof(existence_m1_orders_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ? [B] : m1_orders_1(B,A) ) )).
fof(existence_m1_orders_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m1_orders_2(C,A,B) ) )).
fof(existence_m1_orders_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_orders_3(A) ) => ? [B] : m1_orders_3(B,A) ) )).
fof(existence_m1_osafree,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m1_osafree(C,A,B) ) )).
fof(existence_m1_osalg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m1_osalg_1(C,A,B) ) )).
fof(existence_m1_osalg_4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m1_osalg_4(C,A,B) ) )).
fof(existence_m1_parsp_1,axiom,( ! [A] : ? [B] : m1_parsp_1(B,A) )).
fof(existence_m1_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ? [C] : m1_pboole(C,A,B) ) )).
fof(existence_m1_pencil_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m1_pencil_2(C,A,B) ) )).
fof(existence_m1_petri,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : m1_petri(D,A,B,C) ) )).
fof(existence_m1_petri_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(A) => ? [C] : m1_petri_2(C,A,B) ) )).
fof(existence_m1_pnproc_1,axiom,( ! [A] : ? [B] : m1_pnproc_1(B,A) )).
fof(existence_m1_polyalg1,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & l1_polyalg1(B,A) ) => ? [C] : m1_polyalg1(C,A,B) ) )).
fof(existence_m1_pralg_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ? [C] : m1_pralg_2(C,A,B) ) )).
fof(existence_m1_pre_poly,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k5_finsub_1(A))) ) => ? [C] : m1_pre_poly(C,A,B) ) )).
fof(existence_m1_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : m1_pre_topc(B,A) ) )).
fof(existence_m1_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_prelamb(A) ) => ? [B] : m1_prelamb(B,A) ) )).
fof(existence_m1_prob_1,axiom,( ! [A] : ! [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))) ) => ? [C] : m1_prob_1(C,A,B) ) )).
fof(existence_m1_prob_3,axiom,( ! [A] : ! [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))) ) => ? [C] : m1_prob_3(C,A,B) ) )).
fof(existence_m1_prob_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : m1_prob_4(D,A,B,C) ) )).
fof(existence_m1_projred2,axiom,( ! [A] : ( ( 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] : m1_projred2(B,A) ) )).
fof(existence_m1_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) ) => ? [B] : m1_prvect_1(B,A) ) )).
fof(existence_m1_prvect_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ? [C] : m1_prvect_2(C,A,B) ) )).
fof(existence_m1_pua2mss1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k4_partfun1(A,B))) ) => ? [D] : m1_pua2mss1(D,A,B,C) ) )).
fof(existence_m1_pythtrip,axiom,( ? [A] : m1_pythtrip(A) )).
fof(existence_m1_qc_lang1,axiom,( ? [A] : m1_qc_lang1(A) )).
fof(existence_m1_qc_lang4,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k9_qc_lang1(A)) ) => ? [C] : m1_qc_lang4(C,A,B) ) )).
fof(existence_m1_random_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m1_random_1(C,A,B) ) )).
fof(existence_m1_ratfunc1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & l5_algstr_0(A) ) => ? [B] : m1_ratfunc1(B,A) ) )).
fof(existence_m1_rcomp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ? [B] : m1_rcomp_1(B,A) ) )).
fof(existence_m1_rcomp_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : m1_rcomp_3(D,A,B,C) ) )).
fof(existence_m1_realset1,axiom,( ! [A] : ! [B] : ( ( 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] : m1_realset1(C,A,B) ) )).
fof(existence_m1_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ? [B] : m1_rewrite1(B,A) ) )).
fof(existence_m1_rfunct_3,axiom,( ! [A] : ! [B] : ? [C] : m1_rfunct_3(C,A,B) )).
fof(existence_m1_ringcat1,axiom,( ! [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) & 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] : m1_ringcat1(C,A,B) ) )).
fof(existence_m1_rlaffin3,axiom,( ! [A] : ( v1_finset_1(A) => ? [B] : m1_rlaffin3(B,A) ) )).
fof(existence_m1_rlsub_1,axiom,( ! [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) ) => ? [B] : m1_rlsub_1(B,A) ) )).
fof(existence_m1_rlsub_2,axiom,( ! [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) & v8_rlvect_1(A) & l1_rlvect_1(A) & m1_rlsub_1(B,A) ) => ? [C] : m1_rlsub_2(C,A,B) ) )).
fof(existence_m1_rlvect_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ? [B] : m1_rlvect_2(B,A) ) )).
fof(existence_m1_rlvect_3,axiom,( ! [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) ) => ? [B] : m1_rlvect_3(B,A) ) )).
fof(existence_m1_rmod_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : m1_rmod_2(C,A,B) ) )).
fof(existence_m1_rmod_4,axiom,( ! [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) & 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] : m1_rmod_4(C,A,B) ) )).
fof(existence_m1_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ? [B] : m1_rusub_1(B,A) ) )).
fof(existence_m1_rusub_2,axiom,( ! [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) & v8_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) & m1_rusub_1(B,A) ) => ? [C] : m1_rusub_2(C,A,B) ) )).
fof(existence_m1_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ? [B] : m1_rusub_3(B,A) ) )).
fof(existence_m1_scm_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ? [B] : m1_scm_1(B,A) ) )).
fof(existence_m1_scmfsa_2,axiom,( ? [A] : m1_scmfsa_2(A) )).
fof(existence_m1_scmyciel,axiom,( ! [A] : ? [B] : m1_scmyciel(B,A) )).
fof(existence_m1_setfam_1,axiom,( ! [A] : ? [B] : m1_setfam_1(B,A) )).
fof(existence_m1_sgraph1,axiom,( ! [A] : ? [B] : m1_sgraph1(B,A) )).
fof(existence_m1_simplex0,axiom,( ! [A] : ? [B] : m1_simplex0(B,A) )).
fof(existence_m1_simplex1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) & m1_simplex0(B,u1_struct_0(A)) ) => ? [C] : m1_simplex1(C,A,B) ) )).
fof(existence_m1_simplex2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m1_simplex2(C,A,B) ) )).
fof(existence_m1_stacks_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_relat_1(C) ) => ? [D] : m1_stacks_1(D,A,B,C) ) )).
fof(existence_m1_subset_1,axiom,( ! [A] : ? [B] : m1_subset_1(B,A) )).
fof(existence_m1_substut1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k2_zfmisc_1(k16_substut1(A),k3_qc_lang1(A))) ) => ? [C] : m1_substut1(C,A,B) ) )).
fof(existence_m1_substut2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k9_qc_lang1(A)) & m1_subset_1(C,k9_qc_lang1(A)) ) => ? [D] : m1_substut2(D,A,B,C) ) )).
fof(existence_m1_supinf_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_card_3(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ? [B] : m1_supinf_2(B,A) ) )).
fof(existence_m1_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : m1_taxonom1(B,A) ) )).
fof(existence_m1_taxonom2,axiom,( ! [A] : ? [B] : m1_taxonom2(B,A) )).
fof(existence_m1_toler_1,axiom,( ! [A] : ! [B] : ( ( 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] : m1_toler_1(C,A,B) ) )).
fof(existence_m1_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : m1_topgen_2(B,A) ) )).
fof(existence_m1_topgrp_1,axiom,( ! [A] : ! [B] : ( ( l1_pre_topc(A) & l1_pre_topc(B) ) => ? [C] : m1_topgrp_1(C,A,B) ) )).
fof(existence_m1_topmetr,axiom,( ! [A] : ( ( v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ? [B] : m1_topmetr(B,A) ) )).
fof(existence_m1_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ? [B] : m1_trees_1(B,A) ) )).
fof(existence_m1_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ? [B] : m1_trees_2(B,A) ) )).
fof(existence_m1_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : m1_trees_3(B,A) ) )).
fof(existence_m1_trees_4,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m1_trees_4(C,A,B) ) )).
fof(existence_m1_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ? [B] : m1_unialg_2(B,A) ) )).
fof(existence_m1_unialg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ? [B] : m1_unialg_3(B,A) ) )).
fof(existence_m1_urysohn3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) & v7_ordinal1(D) ) => ? [E] : m1_urysohn3(E,A,B,C,D) ) )).
fof(existence_m1_valuat_1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & ~ v1_xboole_0(B) ) => ? [C] : m1_valuat_1(C,A,B) ) )).
fof(existence_m1_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ? [B] : m1_valued_0(B,A) ) )).
fof(existence_m1_vectsp11,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : m1_vectsp11(D,A,B,C) ) )).
fof(existence_m1_vectsp_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : m1_vectsp_4(C,A,B) ) )).
fof(existence_m1_vectsp_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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] : m1_vectsp_5(D,A,B,C) ) )).
fof(existence_m1_vectsp_6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) & ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ? [C] : m1_vectsp_6(C,A,B) ) )).
fof(existence_m1_vectsp_7,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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] : m1_vectsp_7(C,A,B) ) )).
fof(existence_m1_vectsp_8,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) => ? [C] : m1_vectsp_8(C,A,B) ) )).
fof(existence_m1_waybel12,axiom,( ! [A] : ! [B] : ( ( 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] : m1_waybel12(C,A,B) ) )).
fof(existence_m1_waybel16,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m1_waybel16(C,A,B) ) )).
fof(existence_m1_waybel21,axiom,( ! [A] : ! [B] : ( ( 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] : m1_waybel21(C,A,B) ) )).
fof(existence_m1_waybel23,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v3_waybel_3(A) & l1_orders_2(A) ) => ? [B] : m1_waybel23(B,A) ) )).
fof(existence_m1_waybel35,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ? [C] : m1_waybel35(C,A,B) ) )).
fof(existence_m1_waybel_1,axiom,( ! [A] : ! [B] : ( ( l1_orders_2(A) & l1_orders_2(B) ) => ? [C] : m1_waybel_1(C,A,B) ) )).
fof(existence_m1_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ? [B] : m1_xxreal_2(B,A) ) )).
fof(existence_m1_yellow13,axiom,( ! [A] : ! [B] : ( ( l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ? [C] : m1_yellow13(C,A,B) ) )).
fof(existence_m1_yellow19,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) & ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ? [C] : m1_yellow19(C,A,B) ) )).
fof(existence_m1_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : m1_yellow_0(B,A) ) )).
fof(existence_m1_yellow_6,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & l1_waybel_0(B,A) ) => ? [C] : m1_yellow_6(C,A,B) ) )).
fof(existence_m1_yellow_9,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : m1_yellow_9(B,A) ) )).
fof(existence_m1_zmodul01,axiom,( ! [A] : ( ( ~ 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] : m1_zmodul01(B,A) ) )).
fof(existence_m1_zmodul02,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ? [B] : m1_zmodul02(B,A) ) )).
fof(existence_m1_zmodul03,axiom,( ! [A] : ( ( ~ 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) & v1_zmodul03(A) & l1_zmodul01(A) ) => ? [B] : m1_zmodul03(B,A) ) )).
fof(existence_m2_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) & m1_subset_1(B,u1_struct_0(A)) ) => ? [C] : m2_abcmiz_1(C,A,B) ) )).
fof(existence_m2_abcmiz_a,axiom,( ! [A] : ( m1_subset_1(A,k4_abcmiz_1) => ? [B] : m2_abcmiz_a(B,A) ) )).
fof(existence_m2_algspec1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ? [B] : m2_algspec1(B,A) ) )).
fof(existence_m2_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) => ? [E] : m2_aofa_a00(E,A,B,C,D) ) )).
fof(existence_m2_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : m2_aofa_i00(E,A,B,C,D) ) )).
fof(existence_m2_bcialg_1,axiom,( ! [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] : m2_bcialg_1(B,A) ) )).
fof(existence_m2_bcialg_2,axiom,( ! [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] : m2_bcialg_2(B,A) ) )).
fof(existence_m2_bciideal,axiom,( ! [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] : m2_bciideal(B,A) ) )).
fof(existence_m2_bhsp_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ? [B] : m2_bhsp_5(B,A) ) )).
fof(existence_m2_c0sp1,axiom,( ! [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) & v2_funcsdom(A) & v3_group_1(A) & v5_group_1(A) & v1_vectsp_1(A) & v3_vectsp_1(A) & l1_funcsdom(A) ) => ? [B] : m2_c0sp1(B,A) ) )).
fof(existence_m2_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : m2_card_fil(B,A) ) )).
fof(existence_m2_cat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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] : m2_cat_1(C,A,B) ) )).
fof(existence_m2_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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] : m2_cat_3(D,A,B,C) ) )).
fof(existence_m2_chain_1,axiom,( ! [A] : ( ( ~ v1_zfmisc_1(A) & v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ? [B] : m2_chain_1(B,A) ) )).
fof(existence_m2_chord,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : m2_chord(D,A,B,C) ) )).
fof(existence_m2_circcmb3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & m1_circcmb3(B,A) ) => ? [C] : m2_circcmb3(C,A,B) ) )).
fof(existence_m2_circtrm1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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] : m2_circtrm1(G,A,B,C,D,E,F) ) )).
fof(existence_m2_clvect_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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] : m2_clvect_1(C,A,B) ) )).
fof(existence_m2_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ? [B] : m2_collsp(B,A) ) )).
fof(existence_m2_conlat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) & m1_conlat_1(B,A) ) => ? [C] : m2_conlat_1(C,A,B) ) )).
fof(existence_m2_connsp_2,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : m2_connsp_2(C,A,B) ) )).
fof(existence_m2_convex4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : m2_convex4(C,A,B) ) )).
fof(existence_m2_dtconstr,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_dtconstr(A) & v3_dtconstr(A) & l1_lang1(A) & m1_subset_1(B,k7_dtconstr(A)) ) => ? [C] : m2_dtconstr(C,A,B) ) )).
fof(existence_m2_exchsort,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m2_exchsort(C,A,B) ) )).
fof(existence_m2_filter_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_relat_1(B) ) => ? [C] : m2_filter_1(C,A,B) ) )).
fof(existence_m2_finseq_1,axiom,( ! [A] : ? [B] : m2_finseq_1(B,A) )).
fof(existence_m2_finseq_2,axiom,( ! [A] : ! [B] : ( m1_finseq_2(B,A) => ? [C] : m2_finseq_2(C,A,B) ) )).
fof(existence_m2_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : m2_fomodel2(D,A,B,C) ) )).
fof(existence_m2_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & m1_funct_2(C,A,B) ) => ? [D] : m2_funct_2(D,A,B,C) ) )).
fof(existence_m2_funct_7,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ? [B] : m2_funct_7(B,A) ) )).
fof(existence_m2_functor0,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m2_functor0(C,A,B) ) )).
fof(existence_m2_functor2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : m2_functor2(E,A,B,C,D) ) )).
fof(existence_m2_fvaluat1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : m2_fvaluat1(C,A,B) ) )).
fof(existence_m2_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v4_vectsp_1(A) & l4_algstr_0(A) ) => ? [B] : m2_gcd_1(B,A) ) )).
fof(existence_m2_glib_000,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ? [D] : m2_glib_000(D,A,B,C) ) )).
fof(existence_m2_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ? [B] : m2_glib_001(B,A) ) )).
fof(existence_m2_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ? [B] : m2_glib_004(B,A) ) )).
fof(existence_m2_glib_005,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : m2_glib_005(C,A,B) ) )).
fof(existence_m2_goedcpuc,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & v7_ordinal1(B) ) => ? [C] : m2_goedcpuc(C,A,B) ) )).
fof(existence_m2_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ? [B] : m2_graph_1(B,A) ) )).
fof(existence_m2_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_grcat_1(A) ) => ? [B] : m2_grcat_1(B,A) ) )).
fof(existence_m2_hallmar1,axiom,( ! [A] : ! [B] : ( m1_finseq_1(B,k1_zfmisc_1(A)) => ? [C] : m2_hallmar1(C,A,B) ) )).
fof(existence_m2_ideal_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : m2_ideal_1(C,A,B) ) )).
fof(existence_m2_index_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : m2_index_1(D,A,B,C) ) )).
fof(existence_m2_integr15,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,k1_integra1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) ) => ? [D] : m2_integr15(D,A,B,C) ) )).
fof(existence_m2_integr18,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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,k4_ordinal1,k1_integra1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(B)))) ) => ? [E] : m2_integr18(E,A,B,C,D) ) )).
fof(existence_m2_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ? [B] : m2_interva1(B,A) ) )).
fof(existence_m2_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ? [B] : m2_lattice4(B,A) ) )).
fof(existence_m2_lattice5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : m2_lattice5(D,A,B,C) ) )).
fof(existence_m2_lattice7,axiom,( ? [A] : m2_lattice7(A) )).
fof(existence_m2_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ? [B] : m2_lexbfs(B,A) ) )).
fof(existence_m2_lmod_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : m2_lmod_7(D,A,B,C) ) )).
fof(existence_m2_ltlaxio4,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m2_ltlaxio4(C,A,B) ) )).
fof(existence_m2_margrel1,axiom,( ! [A] : ? [B] : m2_margrel1(B,A) )).
fof(existence_m2_measure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ? [D] : m2_measure1(D,A,B,C) ) )).
fof(existence_m2_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k9_setfam_1(k1_numbers)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k1_numbers)))) ) => ? [B] : m2_measure7(B,A) ) )).
fof(existence_m2_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m2_measure8(C,A,B) ) )).
fof(existence_m2_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ? [B] : m2_midsp_3(B,A) ) )).
fof(existence_m2_modcat_1,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) & m1_modcat_1(B,A) ) => ? [C] : m2_modcat_1(C,A,B) ) )).
fof(existence_m2_monoid_0,axiom,( ! [A] : ( l3_algstr_0(A) => ? [B] : m2_monoid_0(B,A) ) )).
fof(existence_m2_msalimit,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : m2_msalimit(D,A,B,C) ) )).
fof(existence_m2_msaterm,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m2_msaterm(C,A,B) ) )).
fof(existence_m2_msualg_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : m2_msualg_6(E,A,B,C,D) ) )).
fof(existence_m2_nat_lat,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ? [B] : m2_nat_lat(B,A) ) )).
fof(existence_m2_nattra_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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] : m2_nattra_1(E,A,B,C,D) ) )).
fof(existence_m2_orders_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ? [C] : m2_orders_1(C,A,B) ) )).
fof(existence_m2_orders_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) & m1_orders_1(B,k6_partfun1(k1_orders_1(u1_struct_0(A)))) ) => ? [C] : m2_orders_2(C,A,B) ) )).
fof(existence_m2_osafree,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m2_osafree(C,A,B) ) )).
fof(existence_m2_osalg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m2_osalg_2(C,A,B) ) )).
fof(existence_m2_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : m2_pboole(D,A,B,C) ) )).
fof(existence_m2_pnproc_1,axiom,( ! [A] : ? [B] : m2_pnproc_1(B,A) )).
fof(existence_m2_prob_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m2_prob_1(C,A,B) ) )).
fof(existence_m2_prob_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : m2_prob_4(D,A,B,C) ) )).
fof(existence_m2_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) ) => ? [B] : m2_prvect_1(B,A) ) )).
fof(existence_m2_pua2mss1,axiom,( ! [A] : ? [B] : m2_pua2mss1(B,A) )).
fof(existence_m2_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ? [B] : m2_qc_lang1(B,A) ) )).
fof(existence_m2_qc_lang4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k9_qc_lang1(A)) & m1_qc_lang4(C,A,B) ) => ? [D] : m2_qc_lang4(D,A,B,C) ) )).
fof(existence_m2_rcomp_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : m2_rcomp_3(E,A,B,C,D) ) )).
fof(existence_m2_realset1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ? [C] : m2_realset1(C,A,B) ) )).
fof(existence_m2_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ? [B] : m2_rewrite1(B,A) ) )).
fof(existence_m2_rfunct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(C) & m1_rfunct_3(C,A,B) ) => ? [D] : m2_rfunct_3(D,A,B,C) ) )).
fof(existence_m2_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_ringcat1(A) ) => ? [B] : m2_ringcat1(B,A) ) )).
fof(existence_m2_rlaffin3,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : m2_rlaffin3(C,A,B) ) )).
fof(existence_m2_rlsub_1,axiom,( ! [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) & v8_rlvect_1(A) & l1_rlvect_1(A) & m1_rlsub_1(B,A) ) => ? [C] : m2_rlsub_1(C,A,B) ) )).
fof(existence_m2_rlvect_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : m2_rlvect_2(C,A,B) ) )).
fof(existence_m2_rmod_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : m2_rmod_2(D,A,B,C) ) )).
fof(existence_m2_rmod_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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] : m2_rmod_4(D,A,B,C) ) )).
fof(existence_m2_rusub_1,axiom,( ! [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) & v8_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) & m1_rusub_1(B,A) ) => ? [C] : m2_rusub_1(C,A,B) ) )).
fof(existence_m2_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ? [C] : m2_simplex0(C,A,B) ) )).
fof(existence_m2_subset_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m2_subset_1(C,A,B) ) )).
fof(existence_m2_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : m2_taxonom1(B,A) ) )).
fof(existence_m2_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : m2_topgrp_1(B,A) ) )).
fof(existence_m2_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ? [B] : m2_trees_1(B,A) ) )).
fof(existence_m2_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ? [B] : m2_trees_2(B,A) ) )).
fof(existence_m2_trees_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : m2_trees_3(C,A,B) ) )).
fof(existence_m2_unialg_3,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m2_unialg_3(C,A,B) ) )).
fof(existence_m2_urysohn3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : m2_urysohn3(D,A,B,C) ) )).
fof(existence_m2_valued_0,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ? [C] : m2_valued_0(C,A,B) ) )).
fof(existence_m2_vectsp11,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : m2_vectsp11(E,A,B,C,D) ) )).
fof(existence_m2_vectsp_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : m2_vectsp_4(D,A,B,C) ) )).
fof(existence_m2_vectsp_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : m2_vectsp_6(D,A,B,C) ) )).
fof(existence_m2_vectsp_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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] : m2_vectsp_8(D,A,B,C) ) )).
fof(existence_m2_waybel21,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : m2_waybel21(D,A,B,C) ) )).
fof(existence_m2_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ? [B] : m2_xxreal_2(B,A) ) )).
fof(existence_m2_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : m2_yellow13(B,A) ) )).
fof(existence_m2_yellow_6,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m2_yellow_6(C,A,B) ) )).
fof(existence_m2_yellow_9,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : m2_yellow_9(B,A) ) )).
fof(existence_m2_zmodul01,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m2_zmodul01(C,A,B) ) )).
fof(existence_m2_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : m2_zmodul02(C,A,B) ) )).
fof(existence_m3_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ? [B] : m3_abcmiz_1(B,A) ) )).
fof(existence_m3_algspec1,axiom,( ? [A] : m3_algspec1(A) )).
fof(existence_m3_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : m3_aofa_i00(E,A,B,C,D) ) )).
fof(existence_m3_bcialg_2,axiom,( ! [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] : m3_bcialg_2(B,A) ) )).
fof(existence_m3_bciideal,axiom,( ! [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] : m3_bciideal(B,A) ) )).
fof(existence_m3_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ? [B] : m3_cat_2(B,A) ) )).
fof(existence_m3_chain_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_chain_1(B,A) & m1_subset_1(C,k4_ordinal1) ) => ? [D] : m3_chain_1(D,A,B,C) ) )).
fof(existence_m3_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ? [B] : m3_chord(B,A) ) )).
fof(existence_m3_conlat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) ) => ? [C] : m3_conlat_1(C,A,B) ) )).
fof(existence_m3_dist_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_setfam_1(B) & m1_subset_1(B,k6_dist_1(A)) ) => ? [C] : m3_dist_2(C,A,B) ) )).
fof(existence_m3_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & ~ v1_xboole_0(B) ) => ? [C] : m3_fomodel2(C,A,B) ) )).
fof(existence_m3_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ? [B] : m3_glib_001(B,A) ) )).
fof(existence_m3_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ? [B] : m3_glib_004(B,A) ) )).
fof(existence_m3_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ? [B] : m3_glib_005(B,A) ) )).
fof(existence_m3_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ? [B] : m3_graph_1(B,A) ) )).
fof(existence_m3_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_grcat_1(A) ) => ? [B] : m3_grcat_1(B,A) ) )).
fof(existence_m3_hallmar1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k4_ordinal1) ) => ? [D] : m3_hallmar1(D,A,B,C) ) )).
fof(existence_m3_ideal_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : m3_ideal_1(C,A,B) ) )).
fof(existence_m3_index_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : m3_index_1(E,A,B,C,D) ) )).
fof(existence_m3_integr15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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] : m3_integr15(E,A,B,C,D) ) )).
fof(existence_m3_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ? [B] : m3_lexbfs(B,A) ) )).
fof(existence_m3_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ? [B] : m3_ltlaxio4(B,A) ) )).
fof(existence_m3_measure8,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : m3_measure8(D,A,B,C) ) )).
fof(existence_m3_modcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ? [B] : m3_modcat_1(B,A) ) )).
fof(existence_m3_monoid_0,axiom,( ! [A] : ( l3_algstr_0(A) => ? [B] : m3_monoid_0(B,A) ) )).
fof(existence_m3_msalimit,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_msalimit(A) ) => ? [B] : m3_msalimit(B,A) ) )).
fof(existence_m3_msaterm,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m3_msaterm(C,A,B) ) )).
fof(existence_m3_nattra_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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] : m3_nattra_1(E,A,B,C,D) ) )).
fof(existence_m3_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ? [C] : m3_pboole(C,A,B) ) )).
fof(existence_m3_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ? [C] : m3_pnproc_1(C,A,B) ) )).
fof(existence_m3_pua2mss1,axiom,( ! [A] : ( ( v2_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ? [B] : m3_pua2mss1(B,A) ) )).
fof(existence_m3_realset1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ? [C] : m3_realset1(C,A,B) ) )).
fof(existence_m3_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v5_ringcat1(A) ) => ? [B] : m3_ringcat1(B,A) ) )).
fof(existence_m3_robbins3,axiom,( ! [A] : ( l4_robbins1(A) => ? [B] : m3_robbins3(B,A) ) )).
fof(existence_m3_simplex0,axiom,( ! [A] : ! [B] : ( ( ~ v3_pencil_1(A) & v1_matroid0(A) & l1_pre_topc(A) & v1_xreal_0(B) ) => ? [C] : m3_simplex0(C,A,B) ) )).
fof(existence_m3_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : m3_topgrp_1(B,A) ) )).
fof(existence_m3_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ? [B] : m3_trees_3(B,A) ) )).
fof(existence_m3_vectsp_8,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) & ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ? [C] : m3_vectsp_8(C,A,B) ) )).
fof(existence_m3_yellow_6,axiom,( ! [A] : ! [B] : ( l1_struct_0(B) => ? [C] : m3_yellow_6(C,A,B) ) )).
fof(existence_m3_yellow_9,axiom,( ! [A] : ! [B] : ( ( l1_pre_topc(A) & l1_pre_topc(B) ) => ? [C] : m3_yellow_9(C,A,B) ) )).
fof(existence_m3_zmodul01,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m3_zmodul01(C,A,B) ) )).
fof(existence_m4_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m4_abcmiz_1(C,A,B) ) )).
fof(existence_m4_algspec1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ? [B] : m4_algspec1(B,A) ) )).
fof(existence_m4_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) & l4_aofa_a00(D,A,B,C) & m1_subset_1(E,u1_struct_0(A)) ) => ? [F] : m4_aofa_a00(F,A,B,C,D,E) ) )).
fof(existence_m4_aofa_i00,axiom,( ? [A] : m4_aofa_i00(A) )).
fof(existence_m4_bcialg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m4_bcialg_2(C,A,B) ) )).
fof(existence_m4_bciideal,axiom,( ! [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] : m4_bciideal(B,A) ) )).
fof(existence_m4_dist_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_setfam_1(B) & m1_subset_1(B,k6_dist_1(A)) ) => ? [C] : m4_dist_2(C,A,B) ) )).
fof(existence_m4_glib_001,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & m3_glib_001(B,A) ) => ? [C] : m4_glib_001(C,A,B) ) )).
fof(existence_m4_grcat_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m4_grcat_1(C,A,B) ) )).
fof(existence_m4_hallmar1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,k1_zfmisc_1(A)) ) => ? [C] : m4_hallmar1(C,A,B) ) )).
fof(existence_m4_index_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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] : m4_index_1(F,A,B,C,D,E) ) )).
fof(existence_m4_integr15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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,k4_ordinal1,k1_integra1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(B)))) ) => ? [E] : m4_integr15(E,A,B,C,D) ) )).
fof(existence_m4_margrel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : m4_margrel1(B,A) ) )).
fof(existence_m4_measure8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ? [D] : m4_measure8(D,A,B,C) ) )).
fof(existence_m4_modcat_1,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) & m3_modcat_1(B,A) ) => ? [C] : m4_modcat_1(C,A,B) ) )).
fof(existence_m4_msaterm,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ? [C] : m4_msaterm(C,A,B) ) )).
fof(existence_m4_nattra_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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] : m4_nattra_1(C,A,B) ) )).
fof(existence_m4_pua2mss1,axiom,( ! [A] : ( ( v2_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ? [B] : m4_pua2mss1(B,A) ) )).
fof(existence_m4_ringcat1,axiom,( ! [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) & 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] : m4_ringcat1(C,A,B) ) )).
fof(existence_m4_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v3_pencil_1(A) & v1_matroid0(A) & l1_pre_topc(A) & v1_xreal_0(B) & m3_simplex0(C,A,B) ) => ? [D] : m4_simplex0(D,A,B,C) ) )).
fof(existence_m4_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ? [B] : m4_trees_1(B,A) ) )).
fof(existence_m4_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ? [B] : m4_trees_3(B,A) ) )).
fof(existence_m4_vectsp_8,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) & ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ? [C] : m4_vectsp_8(C,A,B) ) )).
fof(existence_m4_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ? [B] : m4_yellow_6(B,A) ) )).
fof(existence_m5_bcialg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : m5_bcialg_2(C,A,B) ) )).
fof(existence_m5_index_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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] : m5_index_1(G,A,B,C,D,E,F) ) )).
fof(existence_m5_margrel1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m4_margrel1(B,A) ) => ? [C] : m5_margrel1(C,A,B) ) )).
fof(existence_m5_modcat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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] : m5_modcat_1(D,A,B,C) ) )).
fof(existence_m5_monoid_0,axiom,( ! [A] : ! [B] : ( ( l3_algstr_0(A) & m2_monoid_0(B,A) ) => ? [C] : m5_monoid_0(C,A,B) ) )).
fof(existence_m6_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : m6_aofa_i00(D,A,B,C) ) )).
fof(existence_m6_monoid_0,axiom,( ! [A] : ! [B] : ( ( l3_algstr_0(A) & m3_monoid_0(B,A) ) => ? [C] : m6_monoid_0(C,A,B) ) )).
fof(existence_m7_monoid_0,axiom,( ! [A] : ! [B] : ( ( l3_algstr_0(A) & m3_monoid_0(B,A) ) => ? [C] : m7_monoid_0(C,A,B) ) )).
fof(existence_m9_lmod_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : m9_lmod_7(D,A,B,C) ) )).
fof(fc100_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) ) => v1_xboole_0(k4_xboole_0(k7_subset_1(A,C,B),k6_subset_1(A,D))) ) )).
fof(fc100_member_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v2_membered(A) & v1_xxreal_0(B) ) => ~ v1_xboole_0(k24_member_1(A,B)) ) )).
fof(fc100_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc101_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => v1_xboole_0(k4_xboole_0(k7_subset_1(A,C,B),k6_subset_1(A,B))) ) )).
fof(fc101_member_1,axiom,( ! [A] : ! [B] : ( ( v2_membered(A) & v1_xxreal_0(B) ) => v2_membered(k24_member_1(A,B)) ) )).
fof(fc101_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc102_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) ) => v1_xboole_0(k4_xboole_0(k6_subset_1(k2_xboole_0(C,D),B),A)) ) )).
fof(fc102_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_xcmplx_0(B) ) => v1_xboole_0(k25_member_1(A,B)) ) )).
fof(fc102_valued_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc103_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_zfmisc_1(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => v1_xboole_0(k5_xboole_0(B,C)) ) )).
fof(fc103_member_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_membered(A) & v1_xcmplx_0(B) ) => ~ v1_xboole_0(k25_member_1(A,B)) ) )).
fof(fc103_valued_1,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) & v1_funct_1(k61_valued_1(A,B)) ) ) )).
fof(fc104_fomodel0,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_xboole_0(k4_xboole_0(k9_xtuple_0(B),k9_xtuple_0(A))) ) )).
fof(fc104_member_1,axiom,( ! [A] : ! [B] : ( ( v1_membered(A) & v1_xcmplx_0(B) ) => v1_membered(k25_member_1(A,B)) ) )).
fof(fc104_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc105_fomodel0,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_xboole_0(k4_xboole_0(k10_xtuple_0(B),k10_xtuple_0(A))) ) )).
fof(fc105_member_1,axiom,( ! [A] : ! [B] : ( ( v3_membered(A) & v1_xreal_0(B) ) => v3_membered(k25_member_1(A,B)) ) )).
fof(fc105_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc106_fomodel0,axiom,( ! [A] : ! [B] : v1_xboole_0(k4_xboole_0(k9_xtuple_0(k2_zfmisc_1(A,B)),A)) )).
fof(fc106_member_1,axiom,( ! [A] : ! [B] : ( ( v4_membered(A) & v1_rat_1(B) ) => v4_membered(k25_member_1(A,B)) ) )).
fof(fc106_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc107_fomodel0,axiom,( ! [A] : ! [B] : v1_xboole_0(k5_xboole_0(k3_xboole_0(k9_xtuple_0(k2_zfmisc_1(A,B)),A),k9_xtuple_0(k2_zfmisc_1(A,B)))) )).
fof(fc107_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_xxreal_0(B) ) => v1_xboole_0(k26_member_1(A,B)) ) )).
fof(fc107_valued_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(fc108_fomodel0,axiom,( ! [A] : ! [B] : v1_xboole_0(k4_xboole_0(k10_xtuple_0(k2_zfmisc_1(A,B)),B)) )).
fof(fc108_member_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v2_membered(A) & v1_xxreal_0(B) ) => ~ v1_xboole_0(k26_member_1(A,B)) ) )).
fof(fc108_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) ) => v6_membered(k9_xtuple_0(A)) ) )).
fof(fc109_fomodel0,axiom,( ! [A] : ! [B] : v1_xboole_0(k5_xboole_0(k3_xboole_0(k10_xtuple_0(k2_zfmisc_1(A,B)),B),k10_xtuple_0(k2_zfmisc_1(A,B)))) )).
fof(fc109_member_1,axiom,( ! [A] : ! [B] : ( ( v2_membered(A) & v1_xxreal_0(B) ) => v2_membered(k26_member_1(A,B)) ) )).
fof(fc109_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & v1_funct_1(k63_valued_1(A)) & v1_finset_1(k63_valued_1(A)) ) ) )).
fof(fc10_abcmiz_1,axiom,( v1_msualg_1(k27_abcmiz_1) & v1_instalg1(k27_abcmiz_1) & v1_abcmiz_1(k27_abcmiz_1) & v3_abcmiz_1(k27_abcmiz_1) )).
fof(fc10_abcmiz_a,axiom,( v2_abcmiz_1(k13_abcmiz_a(k8_abcmiz_a),k27_abcmiz_1) & v4_abcmiz_a(k13_abcmiz_a(k8_abcmiz_a),k27_abcmiz_1) )).
fof(fc10_abian,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) & ~ v1_abian(B) ) => ~ v1_abian(k2_xcmplx_0(A,B)) ) )).
fof(fc10_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(k7_afinsq_1(A,B,C)) & v1_funct_1(k7_afinsq_1(A,B,C)) ) )).
fof(fc10_algstr_0,axiom,( v7_algstr_0(k3_algstr_0) )).
fof(fc10_algstr_4,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ~ v1_xboole_0(k11_algstr_4(A,B)) ) )).
fof(fc10_ami_6,axiom,( ! [A] : ! [B] : ( ( 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(k7_card_1(2),k1_ami_3,k5_ami_3(A,B))) ) )).
fof(fc10_aofa_000,axiom,( ! [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) & v9_aofa_000(A) & l1_unialg_1(A) ) => ~ v1_finset_1(k18_aofa_000(A)) ) )).
fof(fc10_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & v4_msafree4(C,A,B) & l3_msualg_1(C,A) & v2_relat_1(D) & m1_msafree(D,A,B) ) => ~ v1_xboole_0(k13_aofa_a00(A,B,C,D)) ) )).
fof(fc10_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xboolean(C) & v1_xboolean(D) ) => v1_xboolean(k5_xxreal_0(A,B,C,D)) ) )).
fof(fc10_bagorder,axiom,( ! [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) ) => ( v3_orders_2(k14_bagorder(A)) & v4_orders_2(k14_bagorder(A)) & v5_orders_2(k14_bagorder(A)) & v16_waybel_0(k14_bagorder(A)) ) ) )).
fof(fc10_bhsp_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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_xreal_0(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v2_bhsp_3(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k5_normsp_1(A,C,B)) & v1_funct_2(k5_normsp_1(A,C,B),k4_ordinal1,u1_struct_0(A)) & v2_bhsp_3(k5_normsp_1(A,C,B),A) ) ) )).
fof(fc10_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc10_binop_2,axiom,( v1_funct_1(k24_binop_2) & v1_funct_2(k24_binop_2,k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1) & v1_binop_1(k24_binop_2,k4_ordinal1) & v2_binop_1(k24_binop_2,k4_ordinal1) )).
fof(fc10_borsuk_5,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(A) & v1_rat_1(A) & v1_xreal_0(B) & ~ v1_rat_1(B) ) => ~ v1_rat_1(k3_xcmplx_0(A,B)) ) )).
fof(fc10_borsuk_6,axiom,( ~ v1_xboole_0(k8_borsuk_6) & v4_pre_topc(k8_borsuk_6,k2_borsuk_1(k5_topmetr,k5_topmetr)) )).
fof(fc10_c0sp2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc10_card_1,axiom,( ! [A] : ( ~ v1_finset_1(A) => ( ~ v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A)) ) ) )).
fof(fc10_card_3,axiom,( v5_card_3(k4_ordinal1) )).
fof(fc10_card_5,axiom,( ! [A] : ! [B] : ( v6_membered(A) => v7_ordinal1(k1_funct_1(k3_wellord1(k1_wellord2(k2_wellord2(k1_wellord2(A))),k1_wellord2(A)),B)) ) )).
fof(fc10_catalg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc10_cayldick,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( 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) & v2_binop_1(C,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_funct_1(H) & v1_funct_2(H,A,A) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( v3_group_1(g1_cayldick(A,C,B,D,E,F,G,H)) & v1_cayldick(g1_cayldick(A,C,B,D,E,F,G,H)) ) ) )).
fof(fc10_cc0sp2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc10_cfdiff_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc10_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => v2_cgames_1(k13_cgames_1(A)) ) )).
fof(fc10_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_circcomb(A) & v2_circcomb(A) & l1_msualg_1(A) ) => v1_relat_1(k3_msafree2(A)) ) )).
fof(fc10_circcomb,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc10_clopban1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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)) ) ) )).
fof(fc10_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => v1_group_1(k9_clopban2(A)) ) )).
fof(fc10_closure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc10_closure2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc10_coh_sp,axiom,( ! [A] : ( v4_funct_1(k19_coh_sp(A)) & ~ v1_xboole_0(k19_coh_sp(A)) ) )).
fof(fc10_cohsp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc10_compos_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc10_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_compos_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc10_comput_1,axiom,( ~ v1_xboole_0(k9_comput_1) & v6_comput_1(k9_comput_1) )).
fof(fc10_comseq_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v1_comseq_3(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & v1_comseq_3(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_funct_1(k1_valued_1(A,B)) & v1_funct_2(k1_valued_1(A,B),k4_ordinal1,k2_numbers) & v1_comseq_3(k1_valued_1(A,B)) ) ) )).
fof(fc10_dickson,axiom,( ~ v2_struct_0(k11_dickson) & v16_waybel_0(k11_dickson) )).
fof(fc10_dilworth,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc10_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => v3_valued_2(k1_euclid(A)) ) )).
fof(fc10_euclid_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( ~ v2_struct_0(k7_real_ns1(A)) & v2_monoid_0(k7_real_ns1(A)) & v1_bhsp_1(k7_real_ns1(A)) ) ) )).
fof(fc10_euclid_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) & v1_valued_0(B) & v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & v1_valued_0(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) ) ) )).
fof(fc10_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_exchsort(A) ) => v1_exchsort(k9_funct_7(A,B,C)) ) )).
fof(fc10_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xtuple_0(A) & v1_xtuple_0(B) & v1_xtuple_0(C) ) => v1_relat_1(k1_enumset1(A,B,C)) ) )).
fof(fc10_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc10_filter_2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc10_finseq_1,axiom,( ! [A] : ! [B] : v1_finseq_1(k10_finseq_1(A,B)) )).
fof(fc10_finset_1,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => v1_finset_1(k3_xboole_0(A,B)) ) )).
fof(fc10_fomodel0,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_xboole_0(B) ) => v3_fomodel0(k3_xboole_0(B,A),A) ) )).
fof(fc10_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ~ v1_xboole_0(k27_fomodel1(A)) ) )).
fof(fc10_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k10_fomodel2(A,B,C)) & v1_funct_1(k10_fomodel2(A,B,C)) & v1_fomodel2(k10_fomodel2(A,B,C),A,B) ) ) )).
fof(fc10_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) & v7_ordinal1(D) & v8_ordinal1(D) ) => v1_funct_1(k8_fomodel3(A,B,C,D)) ) )).
fof(fc10_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k30_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) ) )).
fof(fc10_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc10_funcop_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => v2_relat_1(k2_funcop_1(A,B)) ) )).
fof(fc10_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => v1_setfam_1(k10_xtuple_0(A)) ) )).
fof(fc10_funct_2,axiom,( ! [A] : ! [B] : v4_funct_1(k1_funct_2(A,B)) )).
fof(fc10_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc10_funct_7,axiom,( ! [A] : ! [B] : ( v1_relat_1(k10_funct_7(A,B)) & v1_funct_1(k10_funct_7(A,B)) ) )).
fof(fc10_funct_9,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc10_gate_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & ~ v1_xboole_0(B) ) => v1_xboole_0(k5_gate_1(A,B)) ) )).
fof(fc10_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(fc10_gr_cy_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(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)) ) ) )).
fof(fc10_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc10_group_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc10_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & l3_algstr_0(A) ) => v3_group_7(k5_finseq_1(A),k1_tarski(1)) ) )).
fof(fc10_hilbert3,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_hilbert1) & m1_subset_1(B,k1_hilbert1) ) => v1_hilbert3(k3_hilbert1(A,k3_hilbert1(B,A))) ) )).
fof(fc10_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc10_index_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_index_1(C,A,B) => v4_relat_1(k1_xtuple_0(C),A) ) )).
fof(fc10_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ( v3_lattices(k21_interva1(A)) & v11_lattices(k21_interva1(A)) ) ) )).
fof(fc10_jordan,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & 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)) ) )).
fof(fc10_kurato_1,axiom,( v1_setfam_1(k4_kurato_1(k3_topmetr,k6_kurato_1)) )).
fof(fc10_lattice2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc10_lopban_1,axiom,( ! [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) & 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)) ) ) )).
fof(fc10_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => v1_group_1(k9_lopban_2(A)) ) )).
fof(fc10_ltlaxio3,axiom,( v3_ltlaxio3(k4_tarski(k6_finseq_1(k1_hilbert1),k6_finseq_1(k1_hilbert1))) )).
fof(fc10_ltlaxio4,axiom,( ! [A] : ! [B] : ( ( ~ v2_ltlaxio3(A) & m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) & m3_ltlaxio4(B,A) ) => ( ~ v1_xboole_0(k11_ltlaxio4(A,B)) & v1_finset_1(k11_ltlaxio4(A,B)) ) ) )).
fof(fc10_lukasi_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc10_matrtop1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,B) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( v1_relat_1(k1_funct_1(k3_matrtop1(A,B,C),D)) & v1_funct_1(k1_funct_1(k3_matrtop1(A,B,C),D)) ) ) )).
fof(fc10_mazurulm,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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) ) ) )).
fof(fc10_member_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k6_member_1(A)) & v2_membered(k6_member_1(A)) ) ) )).
fof(fc10_membered,axiom,( ! [A] : ( v1_rat_1(A) => v4_membered(k1_tarski(A)) ) )).
fof(fc10_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc10_metrizts,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc10_mod_4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc10_modelc_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_modelc_2(A) & l1_modelc_2(A) ) => ~ v1_xboole_0(u1_modelc_2(A)) ) )).
fof(fc10_msafree,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc10_msafree4,axiom,( ! [A] : ! [B] : ( v4_card_3(B) => ( 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) & v1_msafree4(k2_funcop_1(A,B),A) ) ) )).
fof(fc10_mssubfam,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc10_msualg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc10_mycielsk,axiom,( ! [A] : ( ( v1_necklace(A) & v4_dilworth(A) & l1_orders_2(A) ) => ( v1_orders_2(k3_necklace(A)) & v3_dilworth(k3_necklace(A)) ) ) )).
fof(fc10_nat_1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(A) => v5_ordinal1(k2_funcop_1(A,B)) ) )).
fof(fc10_nat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc10_neckla_3,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_orders_2(k3_necklace(A)) & v3_necklace(k3_necklace(A)) ) ) )).
fof(fc10_newton,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => v7_ordinal1(k3_newton(A,B)) ) )).
fof(fc10_nfcont_3,axiom,( ! [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) & 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(k3_normsp_0(A,B)) & v2_fcont_1(k3_normsp_0(A,B)) ) ) )).
fof(fc10_openlatt,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc10_oposet_1,axiom,( v3_qmax_1(k1_oposet_1) & v4_oposet_1(k1_oposet_1) )).
fof(fc10_ordinal1,axiom,( ! [A] : ( ( v1_relat_1(A) & v9_ordinal1(A) ) => ~ v10_ordinal1(k10_xtuple_0(A)) ) )).
fof(fc10_ordinal6,axiom,( ! [A] : ( v1_xboole_0(A) => ( v3_ordinal1(k2_wellord2(A)) & v1_xboole_0(k2_wellord2(A)) ) ) )).
fof(fc10_osafree,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc10_partfun3,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(B) & ~ v3_xxreal_0(B) ) => v4_partfun3(k2_funcop_1(A,B)) ) )).
fof(fc10_polynom1,axiom,( ! [A] : ! [B] : ( ( 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(k12_polynom1(A,B)) & v13_algstr_0(k12_polynom1(A,B)) & v36_algstr_0(k12_polynom1(A,B)) ) ) )).
fof(fc10_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ( ~ v2_struct_0(k14_polynom3(A)) & v36_algstr_0(k14_polynom3(A)) & v3_rlvect_1(k14_polynom3(A)) ) ) )).
fof(fc10_pralg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc10_pre_poly,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => ( 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)) ) ) )).
fof(fc10_prvect_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc10_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => v1_xreal_0(k15_quaterni(A)) ) )).
fof(fc10_quofield,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc10_ratfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & ~ v1_ratfunc1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,u1_struct_0(A)) & ~ v1_ratfunc1(k3_polynom5(A,B,C),A) ) ) )).
fof(fc10_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ( v3_xxreal_2(k3_limfunc1(A)) & ~ v4_xxreal_2(k3_limfunc1(A)) & v6_xxreal_2(k3_limfunc1(A)) ) ) )).
fof(fc10_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A)) ) )).
fof(fc10_relat_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v3_relat_2(A) & v1_relat_1(B) & v3_relat_2(B) ) => v3_relat_2(k2_xboole_0(A,B)) ) )).
fof(fc10_relset_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc10_rfunct_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc10_rlaffin1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc10_rltopsp1,axiom,( ! [A] : ! [B] : ( ( ~ 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_ordinal1(B) & v1_xreal_0(B) ) => ( 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) ) ) )).
fof(fc10_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_lattices(A) & l2_robbins1(A) ) => ( v5_lattices(k8_robbins1(A)) & v4_robbins1(k8_robbins1(A)) ) ) )).
fof(fc10_rsspace4,axiom,( ! [A] : ! [B] : ( ( ~ 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) & v3_lopban_1(B) & l1_normsp_1(B) ) => ( ~ v2_struct_0(k9_rsspace4(A,B)) & v3_lopban_1(k9_rsspace4(A,B)) ) ) )).
fof(fc10_rvsum_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_valued_0(k5_finseq_1(A)) ) )).
fof(fc10_scm_halt,axiom,( v1_relat_1(k4_compos_1(k1_scmfsa_2)) & v4_relat_1(k4_compos_1(k1_scmfsa_2),k4_ordinal1) & 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)) )).
fof(fc10_scmfsa10,axiom,( ! [A] : ! [B] : ( ( 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(k7_card_1(3),k1_scmfsa_2,k9_scmfsa_2(A,B))) ) )).
fof(fc10_scmfsa6c,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc10_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc10_scmfsa_4,axiom,( v1_extpro_1(k1_scmfsa_2,k7_card_1(3)) & v2_amistd_5(k1_scmfsa_2,k7_card_1(3)) )).
fof(fc10_scmfsa_m,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & 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)) ) ) )).
fof(fc10_scmpds_4,axiom,( ! [A] : ( ( v4_scmpds_4(A) & m1_subset_1(A,u1_compos_1(k1_scmpds_2)) ) => ( v1_relat_1(k3_afinsq_1(A)) & v4_relat_1(k3_afinsq_1(A),k4_ordinal1) & v5_relat_1(k3_afinsq_1(A),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k3_afinsq_1(A)) & 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)) ) ) )).
fof(fc10_scmpds_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc10_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & 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_relat_1(k6_scmpds_6(B,C,A)) & v4_relat_1(k6_scmpds_6(B,C,A),k4_ordinal1) & v5_relat_1(k6_scmpds_6(B,C,A),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k6_scmpds_6(B,C,A)) & 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) ) ) )).
fof(fc10_scmring2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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),k7_card_1(2),k1_scmring2(A)) ) )).
fof(fc10_scmring3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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(k7_card_1(2),k1_scmring2(A),k6_scmring2(A,B,C))) ) )).
fof(fc10_scmyciel,axiom,( ! [A] : ( v1_finset_1(A) => v1_finset_1(k5_scmyciel(A)) ) )).
fof(fc10_sfmastr1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc10_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ( v1_classes1(B) => v1_classes1(k3_simplex0(A,B,C)) ) )).
fof(fc10_simplex1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) ) )).
fof(fc10_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k16_sin_cos,k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos)))) & v2_funct_1(k5_relat_1(k16_sin_cos,k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos)))) )).
fof(fc10_sincos10,axiom,( v1_funct_1(k2_sincos10) & v2_funct_1(k2_sincos10) )).
fof(fc10_sppol_2,axiom,( ! [A] : ! [B] : ( ( v1_topreal1(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & v7_ordinal1(B) ) => v1_topreal1(k1_rfinseq(B,A)) ) )).
fof(fc10_sprect_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(fc10_stacks_1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc10_struct_0,axiom,( ! [A] : ( l2_struct_0(A) => v9_struct_0(k4_struct_0(A),A) ) )).
fof(fc10_subset_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) )).
fof(fc10_tex_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc10_topalg_5,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc10_topalg_6,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(fc10_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => v9_rltopsp1(k3_topreal9(A,B,C),k15_euclid(A)) ) )).
fof(fc10_topreala,axiom,( ! [A] : ! [B] : ( ( ~ v2_xxreal_0(A) & v1_xreal_0(A) & v2_xxreal_0(B) & v1_xreal_0(B) ) => ~ v1_xboole_0(k2_xxreal_1(A,B)) ) )).
fof(fc10_toprealb,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ~ v1_xboole_0(k5_toprealb(A)) ) )).
fof(fc10_toprealc,axiom,( v7_struct_0(k15_euclid(k5_numbers)) & v5_rltopsp1(k15_euclid(k5_numbers)) )).
fof(fc10_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => v3_pre_topc(k2_struct_0(A),A) ) )).
fof(fc10_trees_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc10_trees_9,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc10_valued_0,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc10_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc10_vectsp10,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc10_waybel10,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc10_waybel11,axiom,( ! [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) ) => v4_yellow_6(k2_waybel11(A),A) ) )).
fof(fc10_waybel18,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v2_struct_0(B) & v5_orders_2(B) & l1_orders_2(B) ) => ( v1_orders_2(k4_yellow_1(A,k7_funcop_1(A,B))) & v5_orders_2(k4_yellow_1(A,k7_funcop_1(A,B))) ) ) )).
fof(fc10_waybel23,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc10_waybel24,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc10_waybel25,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc10_waybel30,axiom,( ! [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) & l1_waybel_9(A) ) => ( v1_orders_2(k1_yellow_1(k5_waybel11(A))) & v3_waybel_3(k1_yellow_1(k5_waybel11(A))) ) ) )).
fof(fc10_waybel34,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc10_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc10_waybel_2,axiom,( ! [A] : ( ( 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(k1_yellow_1(k7_waybel_0(A))),u1_struct_0(A)) & v19_waybel_0(k2_yellow_2(A),k1_yellow_1(k7_waybel_0(A)),A) & v20_waybel_0(k2_yellow_2(A),k1_yellow_1(k7_waybel_0(A)),A) ) ) )).
fof(fc10_waybel_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc10_waybel_4,axiom,( ! [A] : ( ( 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(k1_yellow_1(k3_waybel_4(A))) & v3_lattice3(k1_yellow_1(k3_waybel_4(A))) ) ) )).
fof(fc10_waybel_8,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(fc10_waybel_9,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ( v3_orders_2(k2_waybel_9(A)) & v6_waybel_0(k2_waybel_9(A),A) ) ) )).
fof(fc10_xboolean,axiom,( ! [A] : ! [B] : ( ( v1_xboolean(A) & v1_xboolean(B) ) => v1_xboolean(k11_xboolean(A,B)) ) )).
fof(fc10_xreal_0,axiom,( ! [A] : ! [B] : ( ( ~ v2_xxreal_0(A) & v1_xreal_0(A) & ~ v2_xxreal_0(B) & v1_xreal_0(B) ) => ~ v2_xxreal_0(k2_xcmplx_0(A,B)) ) )).
fof(fc10_xxreal_1,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xxreal_0(B) ) => v3_membered(k2_xxreal_1(A,B)) ) )).
fof(fc10_xxreal_2,axiom,( ! [A] : ( ( v6_membered(A) & v2_xxreal_2(A) ) => ( v1_xxreal_0(k1_xxreal_2(A)) & v7_ordinal1(k1_xxreal_2(A)) ) ) )).
fof(fc10_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc10_yellow10,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc10_yellow_1,axiom,( ! [A] : ! [B] : ( l1_orders_2(B) => v1_yellow_1(k2_funcop_1(A,B)) ) )).
fof(fc10_yellow_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc10_yellow_6,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc10_yellow_7,axiom,( ! [A] : ( ( v2_yellow_0(A) & l1_orders_2(A) ) => ( v1_orders_2(k7_lattice3(A)) & v1_yellow_0(k7_lattice3(A)) ) ) )).
fof(fc110_fomodel0,axiom,( ! [A] : ! [B] : v1_xboole_0(k5_xboole_0(k2_xboole_0(k10_xtuple_0(A),k10_xtuple_0(B)),k10_xtuple_0(k2_xboole_0(A,B)))) )).
fof(fc110_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_xcmplx_0(B) ) => v1_xboole_0(k27_member_1(A,B)) ) )).
fof(fc110_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(fc111_fomodel0,axiom,( ! [A] : ! [B] : v1_xboole_0(k5_xboole_0(k2_xboole_0(k9_xtuple_0(A),k9_xtuple_0(B)),k9_xtuple_0(k2_xboole_0(A,B)))) )).
fof(fc111_member_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_membered(A) & v1_xcmplx_0(B) ) => ~ v1_xboole_0(k27_member_1(A,B)) ) )).
fof(fc111_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc112_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => v1_xboole_0(k3_xboole_0(k6_subset_1(A,B),C)) ) )).
fof(fc112_member_1,axiom,( ! [A] : ! [B] : ( ( v1_membered(A) & v1_xcmplx_0(B) ) => v1_membered(k27_member_1(A,B)) ) )).
fof(fc112_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc113_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => v1_xboole_0(k5_xboole_0(k9_xtuple_0(k2_zfmisc_1(A,B)),A)) ) )).
fof(fc113_member_1,axiom,( ! [A] : ! [B] : ( ( v3_membered(A) & v1_xreal_0(B) ) => v3_membered(k27_member_1(A,B)) ) )).
fof(fc113_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc114_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => v1_xboole_0(k5_xboole_0(k10_xtuple_0(k2_zfmisc_1(B,A)),A)) ) )).
fof(fc114_member_1,axiom,( ! [A] : ! [B] : ( ( v4_membered(A) & v1_rat_1(B) ) => v4_membered(k27_member_1(A,B)) ) )).
fof(fc114_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc115_fomodel0,axiom,( ! [A] : ! [B] : ( v1_relat_1(A) => v1_xboole_0(k4_xboole_0(k7_relat_1(A,B),k10_xtuple_0(A))) ) )).
fof(fc115_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc116_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : v1_xboole_0(k4_xboole_0(k2_zfmisc_1(A,B),k2_zfmisc_1(k2_xboole_0(A,C),k2_xboole_0(B,D)))) )).
fof(fc116_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc117_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : v1_xboole_0(k5_xboole_0(k3_xboole_0(k3_xboole_0(A,B),C),k3_xboole_0(A,k3_xboole_0(B,C)))) )).
fof(fc117_valued_1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc118_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => v1_xboole_0(k4_xboole_0(k4_subset_1(A,B,C),A)) ) )).
fof(fc118_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc119_fomodel0,axiom,( ! [A] : ( v1_relat_1(k4_relat_1(A)) & v2_funct_2(k4_relat_1(A),A) ) )).
fof(fc119_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc11_abcmiz_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc11_abian,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) & ~ v1_abian(B) ) => ~ v1_abian(k2_xcmplx_0(B,A)) ) )).
fof(fc11_afinsq_1,axiom,( ! [A] : ! [B] : ( v5_ordinal1(k6_afinsq_1(A,B)) & v1_finset_1(k6_afinsq_1(A,B)) ) )).
fof(fc11_algstr_0,axiom,( v14_algstr_0(k3_algstr_0) )).
fof(fc11_algstr_4,axiom,( ! [A] : ( v1_xboole_0(A) => v1_xboole_0(k12_algstr_4(A)) ) )).
fof(fc11_ami_6,axiom,( ! [A] : ! [B] : ( ( 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(k7_card_1(2),k1_ami_3,k6_ami_3(A,B))) ) )).
fof(fc11_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => v15_aofa_000(k12_aofa_000(A),A) ) )).
fof(fc11_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & v4_msualg_1(B,A) & v2_msafree(B,A) & l3_msualg_1(B,A) & v4_msualg_1(C,A) & l3_msualg_1(C,A) & v2_relat_1(D) & m1_msafree(D,A,B) ) => ~ v1_xboole_0(k13_aofa_a00(A,B,C,D)) ) )).
fof(fc11_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(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) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) & v4_aofa_a01(D,A,B,C) & l4_aofa_a00(D,A,B,C) & ~ v2_struct_0(E) & v2_unialg_1(E) & v3_unialg_1(E) & v4_unialg_1(E) & v3_aofa_000(E) & v4_aofa_000(E) & v5_aofa_000(E) & v6_aofa_000(E) & ~ v10_aofa_000(E) & v11_aofa_000(E) & v12_aofa_000(E) & v5_aofa_a01(E,A,B,C,D) & l3_aofa_a00(E,A,C,u4_aofa_a00(A,B,C,D)) & m1_subset_1(F,u1_struct_0(A)) & m1_subset_1(G,k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),F)) & m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),F)) ) => v15_aofa_000(k12_aofa_a00(A,C,u4_aofa_a00(A,B,C,D),E,F,G,H),E) ) )).
fof(fc11_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc11_binop_2,axiom,( v1_funct_1(k3_binop_2) & v1_funct_2(k3_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & v1_setwiseo(k3_binop_2,k2_numbers) )).
fof(fc11_borsuk_5,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(A) & v1_rat_1(A) & v1_xreal_0(B) & ~ v1_rat_1(B) ) => ~ v1_rat_1(k3_xcmplx_0(B,A)) ) )).
fof(fc11_card_1,axiom,( ! [A] : ( v8_ordinal1(A) => v1_xboole_0(k6_card_1(A)) ) )).
fof(fc11_card_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc11_catalg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc11_cayldick,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( 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) & v1_binop_1(C,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_funct_1(H) & v1_funct_2(H,A,A) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( v5_group_1(g1_cayldick(A,C,B,D,E,F,G,H)) & v1_cayldick(g1_cayldick(A,C,B,D,E,F,G,H)) ) ) )).
fof(fc11_cfdiff_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc11_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_circcomb(A) & v5_circcomb(A) & l1_msualg_1(A) ) => v1_relat_1(k3_msafree2(A)) ) )).
fof(fc11_circcomb,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc11_clopban2,axiom,( ! [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) & 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)) ) ) )).
fof(fc11_closure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc11_closure2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc11_coh_sp,axiom,( ! [A] : ~ v1_xboole_0(k20_coh_sp(A)) )).
fof(fc11_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v1_relat_1(k10_cohsp_1(A)) ) )).
fof(fc11_compos_0,axiom,( v2_compos_0(k1_tarski(k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0))) & v3_compos_0(k1_tarski(k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0))) )).
fof(fc11_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_compos_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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) ) ) )).
fof(fc11_comput_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ( v1_relat_1(k5_comput_1(A,1)) & v4_relat_1(k5_comput_1(A,1),k3_finseq_2(k4_ordinal1)) & 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)) ) ) )).
fof(fc11_comseq_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v1_comseq_3(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & v1_comseq_3(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_funct_1(k45_valued_1(A,B)) & v1_funct_2(k45_valued_1(A,B),k4_ordinal1,k2_numbers) & v1_comseq_3(k45_valued_1(A,B)) ) ) )).
fof(fc11_dickson,axiom,( ~ v2_struct_0(k11_dickson) & v4_dickson(k11_dickson) )).
fof(fc11_dilworth,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc11_euclid_7,axiom,( ! [A] : ( ~ 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)) ) )).
fof(fc11_euclid_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) & v1_valued_0(B) & v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & v1_valued_0(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) ) ) )).
fof(fc11_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_exchsort(A) ) => ( v1_relat_1(k9_funct_7(A,B,C)) & v1_funct_1(k9_funct_7(A,B,C)) & v3_valued_0(k9_funct_7(A,B,C)) & v1_exchsort(k9_funct_7(A,B,C)) ) ) )).
fof(fc11_facirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => v2_facirc_1(k5_finseq_1(A)) ) )).
fof(fc11_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc11_filter_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc11_finseq_1,axiom,( ! [A] : ! [B] : ! [C] : v1_finseq_1(k11_finseq_1(A,B,C)) )).
fof(fc11_finset_1,axiom,( ! [A] : ! [B] : ( v1_finset_1(A) => v1_finset_1(k3_xboole_0(A,B)) ) )).
fof(fc11_fomodel0,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_xboole_0(B) ) => v1_xboole_0(k1_funct_1(k9_fomodel0(A),B)) ) )).
fof(fc11_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) ) => ~ v1_xboole_0(k1_funct_1(k28_fomodel1(A),B)) ) )).
fof(fc11_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(fc11_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc11_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc11_funcop_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(k16_funcop_1(A,B)) & v1_funct_1(k16_funcop_1(A,B)) ) )).
fof(fc11_funct_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc11_funct_2,axiom,( ! [A] : ( 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) ) )).
fof(fc11_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc11_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(k12_funct_7(A,B,C)) & v1_funct_1(k12_funct_7(A,B,C)) ) )).
fof(fc11_functor0,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc11_gate_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_xboole_0(B) ) => ~ v1_xboole_0(k5_gate_1(A,B)) ) )).
fof(fc11_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(fc11_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc11_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ~ v1_xboole_0(k17_grcat_1(A)) ) )).
fof(fc11_group_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc11_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_group_1(A) & l3_algstr_0(A) ) => v4_group_7(k5_finseq_1(A),k1_tarski(1)) ) )).
fof(fc11_hilbert3,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_hilbert1) & m1_subset_1(B,k1_hilbert1) ) => v1_hilbert3(k3_hilbert1(k4_hilbert1(A,B),A)) ) )).
fof(fc11_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc11_index_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_index_1(C,A,B) => v4_relat_1(k2_xtuple_0(C),B) ) )).
fof(fc11_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ( v3_lattices(k21_interva1(A)) & v15_lattices(k21_interva1(A)) ) ) )).
fof(fc11_jordan,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & 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)) ) )).
fof(fc11_kurato_1,axiom,( v2_tops_2(k3_kurato_1(k3_topmetr,k6_kurato_1),k3_topmetr) )).
fof(fc11_lopban_1,axiom,( ! [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) & 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)) ) ) )).
fof(fc11_lopban_2,axiom,( ! [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) & 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)) ) ) )).
fof(fc11_ltlaxio3,axiom,( ! [A] : ( ( ~ v2_ltlaxio3(A) & m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) ) => ~ v2_ltlaxio3(k4_tarski(k8_ltlaxio3(A),k9_ltlaxio3(A))) ) )).
fof(fc11_lukasi_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc11_matrtop1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,B) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( v1_finseq_1(k1_funct_1(k3_matrtop1(A,B,C),D)) & v3_valued_0(k1_funct_1(k3_matrtop1(A,B,C),D)) ) ) )).
fof(fc11_mazurulm,axiom,( ! [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) & 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) ) ) )).
fof(fc11_member_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_membered(A) ) => ( ~ v1_xboole_0(k6_member_1(A)) & v2_membered(k6_member_1(A)) ) ) )).
fof(fc11_membered,axiom,( ! [A] : ( v1_int_1(A) => v5_membered(k1_tarski(A)) ) )).
fof(fc11_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc11_mod_4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc11_modelc_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc11_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_msafree4(B,A) ) => v4_card_3(k1_funct_1(B,C)) ) )).
fof(fc11_mssubfam,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc11_msualg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc11_mycielsk,axiom,( ! [A] : ( ( v1_mycielsk(A) & l1_orders_2(A) ) => ( v1_orders_2(k3_necklace(A)) & v2_mycielsk(k3_necklace(A)) ) ) )).
fof(fc11_nat_1,axiom,( ! [A] : ( ~ v8_ordinal1(A) => v1_setfam_1(k1_tarski(A)) ) )).
fof(fc11_nat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc11_neckla_3,axiom,( ! [A] : ( ( v1_necklace(A) & l1_orders_2(A) ) => ( v1_orders_2(k3_necklace(A)) & v1_necklace(k3_necklace(A)) ) ) )).
fof(fc11_newton,axiom,( ! [A] : ( v7_ordinal1(A) => v1_finset_1(k9_newton(A)) ) )).
fof(fc11_oposet_1,axiom,( v3_qmax_1(k1_oposet_1) & v5_oposet_1(k1_oposet_1) )).
fof(fc11_ordinal1,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v9_ordinal1(A) ) => v10_ordinal1(k10_xtuple_0(A)) ) )).
fof(fc11_ordinal6,axiom,( ! [A] : ( 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)) ) )).
fof(fc11_partfun3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v2_relat_1(k2_funcop_1(A,k5_numbers)) ) )).
fof(fc11_pcs_0,axiom,( v2_struct_0(k5_pcs_0) & v2_pcs_0(k5_pcs_0) )).
fof(fc11_polynom1,axiom,( ! [A] : ! [B] : ( ( 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(k12_polynom1(A,B)) & v36_algstr_0(k12_polynom1(A,B)) & v5_group_1(k12_polynom1(A,B)) ) ) )).
fof(fc11_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ( ~ v2_struct_0(k14_polynom3(A)) & v36_algstr_0(k14_polynom3(A)) & v4_rlvect_1(k14_polynom3(A)) ) ) )).
fof(fc11_pralg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc11_pre_poly,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc11_prvect_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc11_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => v1_xreal_0(k16_quaterni(A)) ) )).
fof(fc11_ratfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & ~ v1_ratfunc1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & ~ v1_ratfunc1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k11_polynom3(A,B,C)) & v1_funct_2(k11_polynom3(A,B,C),k4_ordinal1,u1_struct_0(A)) & ~ v1_ratfunc1(k11_polynom3(A,B,C),A) ) ) )).
fof(fc11_rcomp_3,axiom,( ~ v3_xxreal_2(k2_subset_1(k1_numbers)) & ~ v4_xxreal_2(k2_subset_1(k1_numbers)) & v6_xxreal_2(k2_subset_1(k1_numbers)) )).
fof(fc11_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A)) ) )).
fof(fc11_relat_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v3_relat_2(A) & v1_relat_1(B) & v3_relat_2(B) ) => v3_relat_2(k3_xboole_0(A,B)) ) )).
fof(fc11_relset_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc11_rfunct_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc11_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) & v1_xreal_0(C) ) => v9_rltopsp1(k1_convex1(A,B,C),A) ) )).
fof(fc11_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & l2_robbins1(A) ) => ( v6_lattices(k8_robbins1(A)) & v4_robbins1(k8_robbins1(A)) ) ) )).
fof(fc11_rvsum_1,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_valued_0(k10_finseq_1(A,B)) ) )).
fof(fc11_scm_halt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc11_scmfsa10,axiom,( ! [A] : ! [B] : ( ( 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(k7_card_1(3),k1_scmfsa_2,k10_scmfsa_2(A,B))) ) )).
fof(fc11_scmfsa6c,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc11_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => ~ v2_extpro_1(k11_scmfsa_2(A),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc11_scmfsa_m,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_ami_2(k4_scmfsa_2(k1_nat_1(A,1))) & ~ v1_scmfsa_m(k4_scmfsa_2(k1_nat_1(A,1))) ) ) )).
fof(fc11_scmpds_4,axiom,( ! [A] : ! [B] : ( ( v4_scmpds_4(A) & m1_subset_1(A,u1_compos_1(k1_scmpds_2)) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) & v3_scmpds_4(B) ) => ( v1_relat_1(k2_scmpds_4(A,B)) & v4_relat_1(k2_scmpds_4(A,B),k4_ordinal1) & v5_relat_1(k2_scmpds_4(A,B),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k2_scmpds_4(A,B)) & 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)) ) ) )).
fof(fc11_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) & v2_scmpds_4(A) & v3_scmpds_4(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & 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_relat_1(k3_scmpds_6(C,D,A,B)) & v4_relat_1(k3_scmpds_6(C,D,A,B),k4_ordinal1) & v5_relat_1(k3_scmpds_6(C,D,A,B),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k3_scmpds_6(C,D,A,B)) & 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)) ) ) )).
fof(fc11_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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),k7_card_1(2)) & v3_extpro_1(k1_scmring2(A),k7_card_1(2)) ) ) )).
fof(fc11_scmring3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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(k7_card_1(2),k1_scmring2(A),k7_scmring2(A,B,C))) ) )).
fof(fc11_scmyciel,axiom,( ! [A] : ! [B] : ( v4_scmyciel(A) => v4_scmyciel(k7_scmyciel(A,B)) ) )).
fof(fc11_sfmastr1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc11_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_setfam_1(B) => ~ v1_setfam_1(k3_simplex0(A,B,C)) ) )).
fof(fc11_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k16_sin_cos,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers))) & v2_funct_1(k5_relat_1(k16_sin_cos,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers))) )).
fof(fc11_sincos10,axiom,( v1_funct_1(k3_sincos10) & v2_funct_1(k3_sincos10) )).
fof(fc11_sppol_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc11_sprect_1,axiom,( ! [A] : ( ( v1_sprect_1(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => v1_jordan1(k3_topreal1(2,A)) ) )).
fof(fc11_stacks_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc11_struct_0,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & l4_struct_0(A) ) => ~ v9_struct_0(k5_struct_0(A),A) ) )).
fof(fc11_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) ) => ~ v1_xboole_0(k3_zfmisc_1(A,B,C)) ) )).
fof(fc11_tex_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc11_topalg_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc11_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc11_topreala,axiom,( ! [A] : ! [B] : ( ( ~ v2_xxreal_0(A) & v1_xreal_0(A) & v2_xxreal_0(B) & v1_xreal_0(B) ) => ~ v1_xboole_0(k3_xxreal_1(A,B)) ) )).
fof(fc11_toprealb,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => v3_pre_topc(k5_toprealb(A),k2_topalg_2) ) )).
fof(fc11_toprealc,axiom,( ! [A] : ( ( v1_toprealc(A) & l1_struct_0(A) ) => v1_valued_2(u1_struct_0(A)) ) )).
fof(fc11_tops_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc11_trees_3,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ 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)) ) ) )).
fof(fc11_valued_0,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc11_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc11_vectsp10,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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))) ) ) )).
fof(fc11_waybel10,axiom,( ! [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) ) => ( 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)))) ) ) )).
fof(fc11_waybel11,axiom,( ! [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) ) => v5_yellow_6(k2_waybel11(A),A) ) )).
fof(fc11_waybel18,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v2_struct_0(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( v1_orders_2(k4_yellow_1(A,k7_funcop_1(A,B))) & v4_orders_2(k4_yellow_1(A,k7_funcop_1(A,B))) ) ) )).
fof(fc11_waybel23,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc11_waybel24,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ( v1_monoid_0(k5_yellow_1(A,B)) & v1_orders_2(k5_yellow_1(A,B)) ) ) )).
fof(fc11_waybel25,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc11_waybel30,axiom,( ! [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_waybel_8(A) & v2_waybel19(A) & v2_waybel_2(A) & l1_waybel_9(A) ) => ( v1_orders_2(k1_yellow_1(k5_waybel11(A))) & v2_waybel_8(k1_yellow_1(k5_waybel11(A))) ) ) )).
fof(fc11_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc11_waybel_2,axiom,( ! [A] : ( ( 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) ) ) )).
fof(fc11_waybel_3,axiom,( ! [A] : ! [B] : ( ( ~ 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(k4_yellow_1(A,B)) & v3_orders_2(k4_yellow_1(A,B)) ) ) )).
fof(fc11_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc11_waybel_8,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(fc11_waybel_9,axiom,( ! [A] : ( ( v5_orders_2(A) & l1_orders_2(A) ) => ( v5_orders_2(k2_waybel_9(A)) & v6_waybel_0(k2_waybel_9(A),A) ) ) )).
fof(fc11_xreal_0,axiom,( ! [A] : ! [B] : ( ( v2_xxreal_0(A) & v1_xreal_0(A) & ~ v3_xxreal_0(B) & v1_xreal_0(B) ) => v2_xxreal_0(k2_xcmplx_0(A,B)) ) )).
fof(fc11_xxreal_1,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xxreal_0(B) ) => v3_membered(k3_xxreal_1(B,A)) ) )).
fof(fc11_xxreal_2,axiom,( ~ v3_xxreal_2(k1_numbers) & ~ v4_xxreal_2(k1_numbers) )).
fof(fc11_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc11_yellow10,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc11_yellow_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ( ~ v2_struct_0(k5_yellow_1(A,B)) & v1_orders_2(k5_yellow_1(A,B)) ) ) )).
fof(fc11_yellow_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc11_yellow_7,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc120_fomodel0,axiom,( ! [A] : ! [B] : v5_relat_1(k2_zfmisc_1(A,B),B) )).
fof(fc120_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc121_fomodel0,axiom,( ! [A] : ! [B] : ( v1_relat_1(k1_funct_4(k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k2_zfmisc_1(k1_tarski(B),k1_tarski(A)))) & v1_funct_1(k1_funct_4(k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k2_zfmisc_1(k1_tarski(B),k1_tarski(A)))) & v3_relat_2(k1_funct_4(k2_zfmisc_1(k1_tarski(A),k1_tarski(B)),k2_zfmisc_1(k1_tarski(B),k1_tarski(A)))) ) )).
fof(fc121_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc122_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & m1_subset_1(C,k1_zfmisc_1(A)) ) => v1_xboole_0(k4_xboole_0(k8_relat_1(B,C),k8_relat_1(B,A))) ) )).
fof(fc122_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc123_fomodel0,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => v1_xboole_0(k5_xboole_0(k8_relat_1(B,k2_xboole_0(A,k10_xtuple_0(B))),k9_xtuple_0(B))) ) )).
fof(fc123_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc124_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_partfun1(B,A) ) => v1_xboole_0(k5_xboole_0(A,k1_relset_1(A,B))) ) )).
fof(fc124_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc125_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,A) ) => v1_xboole_0(k4_xboole_0(k1_tarski(C),k9_funct_2(A,B))) ) )).
fof(fc125_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc126_fomodel0,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => v1_xboole_0(k4_xboole_0(k2_relset_1(A,B),k1_relset_1(A,B))) ) )).
fof(fc126_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc127_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => v1_xboole_0(k5_xboole_0(k7_subset_1(A,C,k6_subset_1(A,B)),k8_subset_1(A,C,B))) ) )).
fof(fc127_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc128_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_relat_1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) & m1_subset_1(C,k15_funct_3(A,B)) ) => v1_xtuple_0(k1_xtuple_0(C)) ) )).
fof(fc128_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc129_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_relat_1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) & m1_subset_1(C,k15_funct_3(A,B)) ) => v1_xtuple_0(k2_xtuple_0(C)) ) )).
fof(fc129_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc12_abcmiz_1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(fc12_abian,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & ~ v1_abian(A) & v1_int_1(B) & ~ v1_abian(B) ) => v1_abian(k2_xcmplx_0(A,B)) ) )).
fof(fc12_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ( v5_ordinal1(k7_afinsq_1(A,B,C)) & v1_finset_1(k7_afinsq_1(A,B,C)) ) )).
fof(fc12_algstr_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc12_algstr_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k12_algstr_4(A)) ) )).
fof(fc12_ami_6,axiom,( ! [A] : ( v7_ordinal1(A) => v3_card_1(k2_amistd_1(k7_card_1(2),k1_ami_3,k7_ami_3(A)),1) ) )).
fof(fc12_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc12_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) & v4_msualg_1(D,A) & v4_msafree4(D,A,C) & l3_msualg_1(D,A) & v2_relat_1(E) & m1_msafree(E,A,C) ) => ~ v1_xboole_0(k13_aofa_a00(A,C,D,E)) ) )).
fof(fc12_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,k8_afinsq_1(A)) & v7_ordinal1(C) ) => ( v1_relat_1(k1_funct_1(B,C)) & v5_ordinal1(k1_funct_1(B,C)) & v1_funct_1(k1_funct_1(B,C)) & v1_finset_1(k1_funct_1(B,C)) ) ) )).
fof(fc12_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc12_binop_2,axiom,( v1_funct_1(k9_binop_2) & v1_funct_2(k9_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_setwiseo(k9_binop_2,k1_numbers) )).
fof(fc12_borsuk_5,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(A) & v1_rat_1(A) & v1_xreal_0(B) & ~ v1_rat_1(B) ) => ~ v1_rat_1(k7_xcmplx_0(A,B)) ) )).
fof(fc12_card_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ~ v1_xboole_0(k6_card_1(A)) ) )).
fof(fc12_card_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc12_catalg_1,axiom,( ! [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) & 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))) ) ) )).
fof(fc12_cayldick,axiom,( ~ v6_struct_0(k3_cayldick) & v2_rlvect_1(k3_cayldick) & v3_rlvect_1(k3_cayldick) & v3_group_1(k3_cayldick) & v5_group_1(k3_cayldick) & v3_topmetr(k3_cayldick) & v1_cayldick(k3_cayldick) )).
fof(fc12_cfdiff_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc12_circcmb3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc12_circcomb,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc12_closure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc12_closure2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc12_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k20_coh_sp(A)) => ( v1_relat_1(k2_xtuple_0(B)) & v1_funct_1(k2_xtuple_0(B)) ) ) )).
fof(fc12_cohsp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc12_compos_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc12_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_compos_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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) ) ) )).
fof(fc12_comput_1,axiom,( v1_relat_1(k5_comput_1(2,2)) & v4_relat_1(k5_comput_1(2,2),k3_finseq_2(k4_ordinal1)) & 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)) )).
fof(fc12_comseq_3,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k2_numbers) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & v1_comseq_3(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_funct_1(k24_valued_1(B,A)) & v1_funct_2(k24_valued_1(B,A),k4_ordinal1,k2_numbers) & v1_comseq_3(k24_valued_1(B,A)) ) ) )).
fof(fc12_dickson,axiom,( ~ v2_struct_0(k11_dickson) & v3_dickson(k11_dickson) )).
fof(fc12_euclid_7,axiom,( ! [A] : ( 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))) ) ) )).
fof(fc12_euclid_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) & v1_valued_0(B) & v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & v1_valued_0(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) ) ) )).
fof(fc12_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => ( v4_relat_1(k9_funct_7(k6_partfun1(A),B,C),A) & v5_relat_1(k9_funct_7(k6_partfun1(A),B,C),A) & v2_funct_1(k9_funct_7(k6_partfun1(A),B,C)) ) ) )).
fof(fc12_facirc_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xtuple_0(A) & ~ v1_xtuple_0(B) ) => v2_facirc_1(k10_finseq_1(A,B)) ) )).
fof(fc12_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc12_filter_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc12_finseq_1,axiom,( ! [A] : ~ v1_xboole_0(k13_finseq_1(A)) )).
fof(fc12_finset_1,axiom,( ! [A] : ! [B] : ( v1_finset_1(A) => v1_finset_1(k4_xboole_0(A,B)) ) )).
fof(fc12_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v14_fomodel1(B,k5_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) ) )).
fof(fc12_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc12_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc12_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(fc12_funcop_1,axiom,( ! [A] : ! [B] : v2_funct_1(k16_funcop_1(A,B)) )).
fof(fc12_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_funct_1(A) ) => v1_zfmisc_1(k10_xtuple_0(A)) ) )).
fof(fc12_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(fc12_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k1_funct_7(B,C,D)) & v5_relat_1(k1_funct_7(B,C,D),A) & v1_funct_1(k1_funct_7(B,C,D)) ) ) )).
fof(fc12_funct_9,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc12_functor0,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc12_gate_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k5_gate_1(A,B)) ) )).
fof(fc12_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => v2_glib_001(k8_glib_001(A,B,C,D),A) ) )).
fof(fc12_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ~ v1_xboole_0(k9_graph_3(A)) ) )).
fof(fc12_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => v3_grcat_1(k17_grcat_1(A)) ) )).
fof(fc12_group_7,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc12_hermitan,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc12_hilbert3,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_hilbert1) & m1_subset_1(B,k1_hilbert1) ) => v1_hilbert3(k3_hilbert1(k4_hilbert1(A,B),B)) ) )).
fof(fc12_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc12_index_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) ) )).
fof(fc12_jordan,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc12_kurato_1,axiom,( v1_tops_2(k4_kurato_1(k3_topmetr,k6_kurato_1),k3_topmetr) )).
fof(fc12_lukasi_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc12_matrix17,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_matrix_0(k10_matrix_0(A,A,C)) & v2_matrix_0(k10_matrix_0(A,A,C),u1_struct_0(B),A,A) & v3_matrix17(k10_matrix_0(A,A,C),B,A) ) ) )).
fof(fc12_matrtop1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,B) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) & 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) ) )).
fof(fc12_mazurulm,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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) ) ) )).
fof(fc12_member_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k7_member_1(A)) & v1_membered(k7_member_1(A)) ) ) )).
fof(fc12_membered,axiom,( ! [A] : ( v7_ordinal1(A) => v6_membered(k1_tarski(A)) ) )).
fof(fc12_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc12_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc12_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v13_pencil_1(B) ) => v1_zfmisc_1(k1_funct_1(B,C)) ) )).
fof(fc12_mssubfam,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc12_msualg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc12_mycielsk,axiom,( ! [A] : ( ( v1_necklace(A) & v2_mycielsk(A) & l1_orders_2(A) ) => ( v1_orders_2(k3_necklace(A)) & v1_mycielsk(k3_necklace(A)) ) ) )).
fof(fc12_nat_1,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(A) & ~ v8_ordinal1(B) ) => v1_setfam_1(k2_tarski(A,B)) ) )).
fof(fc12_nat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc12_newton,axiom,( ~ v1_xboole_0(k8_newton) )).
fof(fc12_oposet_1,axiom,( v3_qmax_1(k1_oposet_1) & v7_oposet_1(k1_oposet_1) )).
fof(fc12_ordinal1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v9_ordinal1(A) & v1_relat_1(B) ) => ( v1_relat_1(k3_relat_1(B,A)) & v9_ordinal1(k3_relat_1(B,A)) ) ) )).
fof(fc12_ordinal6,axiom,( ! [A] : ! [B] : ( ( v1_ordinal6(A) & v1_ordinal6(B) ) => v1_ordinal6(k2_xboole_0(A,B)) ) )).
fof(fc12_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc12_pcs_0,axiom,( ! [A] : ( ( v3_pcs_0(A) & l1_pcs_0(A) ) => v1_partfun1(u1_pcs_0(A),u1_struct_0(A)) ) )).
fof(fc12_polyalg1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc12_polynom1,axiom,( ! [A] : ! [B] : ( ( 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(k12_polynom1(A,B)) & v36_algstr_0(k12_polynom1(A,B)) & v3_group_1(k12_polynom1(A,B)) ) ) )).
fof(fc12_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ( ~ v2_struct_0(k14_polynom3(A)) & v13_algstr_0(k14_polynom3(A)) & v36_algstr_0(k14_polynom3(A)) ) ) )).
fof(fc12_pre_poly,axiom,( ! [A] : v1_pre_poly(k6_finseq_1(A)) )).
fof(fc12_prvect_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc12_quaterni,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_quaterni(B) ) => v1_quaterni(k19_quaterni(A,B)) ) )).
fof(fc12_ratfunc1,axiom,( ! [A] : ! [B] : ( ( ~ v7_struct_0(A) & l2_struct_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & ~ v1_ratfunc1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v7_ordinal1(k2_hurwitz(A,B)) & v1_int_1(k2_hurwitz(A,B)) ) ) )).
fof(fc12_rcomp_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc12_relat_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_relat_1(B) ) => ( v1_xboole_0(k3_relat_1(A,B)) & v1_relat_1(k3_relat_1(A,B)) ) ) )).
fof(fc12_relat_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v3_relat_2(A) & v1_relat_1(B) & v3_relat_2(B) ) => v3_relat_2(k4_xboole_0(A,B)) ) )).
fof(fc12_rfunct_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc12_rltopsp1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc12_robbins1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc12_rvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => v1_valued_0(k11_finseq_1(A,B,C)) ) )).
fof(fc12_scm_halt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc12_scmfsa10,axiom,( ! [A] : ( v7_ordinal1(A) => v3_card_1(k2_amistd_1(k7_card_1(3),k1_scmfsa_2,k11_scmfsa_2(A)),1) ) )).
fof(fc12_scmfsa6c,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc12_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) & v7_ordinal1(B) ) => ~ v2_extpro_1(k12_scmfsa_2(B,A),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc12_scmfsa_m,axiom,( ! [A] : ! [B] : ( ( m1_scmfsa_2(A) & m1_finseq_1(B,k4_numbers) ) => v5_funct_1(k16_funcop_1(A,B),k2_memstr_0(k7_card_1(3),k1_scmfsa_2)) ) )).
fof(fc12_scmpds_4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & 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_relat_1(k3_scmpds_4(A,B)) & v4_relat_1(k3_scmpds_4(A,B),k4_ordinal1) & v5_relat_1(k3_scmpds_4(A,B),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k3_scmpds_4(A,B)) & 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)) ) ) )).
fof(fc12_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) & v2_compos_1(A,k1_scmpds_2) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & 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_relat_1(k3_scmpds_6(C,D,A,B)) & v4_relat_1(k3_scmpds_6(C,D,A,B),k4_ordinal1) & v5_relat_1(k3_scmpds_6(C,D,A,B),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k3_scmpds_6(C,D,A,B)) & 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) ) ) )).
fof(fc12_scmring3,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) & v7_ordinal1(B) ) => v3_card_1(k2_amistd_1(k7_card_1(2),k1_scmring2(A),k8_scmring2(A,B)),1) ) )).
fof(fc12_scmyciel,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & v4_scmyciel(A) ) => v1_finset_1(k7_scmyciel(A,B)) ) )).
fof(fc12_setfam_1,axiom,( ! [A] : ! [B] : ( ( v1_setfam_1(A) & v1_setfam_1(B) ) => v1_setfam_1(k2_xboole_0(A,B)) ) )).
fof(fc12_sfmastr1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc12_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc12_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k16_sin_cos,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) & v2_funct_1(k5_relat_1(k16_sin_cos,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(fc12_sincos10,axiom,( v1_funct_1(k4_sincos10) & v2_funct_1(k4_sincos10) )).
fof(fc12_sppol_2,axiom,( ! [A] : ( ( v4_topreal1(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => v4_topreal1(k3_finseq_5(A)) ) )).
fof(fc12_sprect_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(fc12_stacks_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc12_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => ~ v1_subset_1(k2_struct_0(A),u1_struct_0(A)) ) )).
fof(fc12_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc12_tex_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc12_topalg_6,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(fc12_topgrp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc12_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc12_topreala,axiom,( ! [A] : ! [B] : ( ( ~ v2_xxreal_0(A) & v1_xreal_0(A) & v2_xxreal_0(B) & v1_xreal_0(B) ) => ~ v1_xboole_0(k1_xxreal_1(A,B)) ) )).
fof(fc12_toprealb,axiom,( ! [A] : ( ( v2_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => v4_pre_topc(k5_toprealb(A),k2_topalg_2) ) )).
fof(fc12_toprealc,axiom,( ! [A] : ( ( v2_toprealc(A) & l1_struct_0(A) ) => v3_valued_2(u1_struct_0(A)) ) )).
fof(fc12_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => v1_tops_1(k2_struct_0(A),A) ) )).
fof(fc12_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => v5_trees_3(k5_finseq_1(A)) ) )).
fof(fc12_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_valued_0(A) & v1_relat_1(B) & v4_valued_0(B) ) => v4_valued_0(k2_xboole_0(A,B)) ) )).
fof(fc12_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc12_vectsp10,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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))) ) ) )).
fof(fc12_waybel10,axiom,( ! [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) ) => ( 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))) ) ) )).
fof(fc12_waybel11,axiom,( ! [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) & l1_orders_2(A) ) => v8_yellow_6(k2_waybel11(A),A) ) )).
fof(fc12_waybel18,axiom,( ! [A] : ! [B] : ( ( ~ 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(k4_yellow_1(A,k7_funcop_1(A,B))) & v1_lattice3(k4_yellow_1(A,k7_funcop_1(A,B))) & v3_lattice3(k4_yellow_1(A,k7_funcop_1(A,B))) ) ) )).
fof(fc12_waybel23,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc12_waybel24,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc12_waybel25,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc12_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc12_waybel_2,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc12_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc12_waybel_8,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(fc12_waybel_9,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ( v4_orders_2(k2_waybel_9(A)) & v6_waybel_0(k2_waybel_9(A),A) ) ) )).
fof(fc12_xreal_0,axiom,( ! [A] : ! [B] : ( ( v2_xxreal_0(A) & v1_xreal_0(A) & ~ v3_xxreal_0(B) & v1_xreal_0(B) ) => v2_xxreal_0(k2_xcmplx_0(B,A)) ) )).
fof(fc12_xxreal_1,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => v3_membered(k1_xxreal_1(A,B)) ) )).
fof(fc12_xxreal_2,axiom,( v6_xxreal_2(k6_numbers) )).
fof(fc12_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc12_yellow10,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc12_yellow_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ( v1_orders_2(k5_yellow_1(A,B)) & v3_orders_2(k5_yellow_1(A,B)) ) ) )).
fof(fc12_yellow_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc12_yellow_7,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(fc130_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_fomodel0(A) ) => ( v1_relat_1(k2_relat_1(A)) & v1_funct_1(k2_relat_1(A)) ) ) )).
fof(fc130_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc131_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc132_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc133_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_relat_1(k4_relat_1(A)) & v2_abian(k4_relat_1(A)) ) ) )).
fof(fc133_valued_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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)) ) ) )).
fof(fc134_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_abian(A) ) => ~ v1_xboole_0(k9_xtuple_0(A)) ) )).
fof(fc134_valued_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) & v7_ordinal1(B) ) => ( v1_relat_1(k61_valued_1(A,B)) & v1_funct_1(k61_valued_1(A,B)) & v2_finseq_1(k61_valued_1(A,B)) ) ) )).
fof(fc135_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_abian(A) ) => ~ v1_xboole_0(k32_fomodel0(A)) ) )).
fof(fc136_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v2_abian(A) ) => v1_xboole_0(k32_fomodel0(A)) ) )).
fof(fc137_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_relat_1(B) & v5_fomodel0(B) ) => ( v1_relat_1(k3_relat_1(A,B)) & v5_fomodel0(k3_relat_1(A,B)) ) ) )).
fof(fc138_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_relat_1(B) & v5_fomodel0(B) ) => ( v1_relat_1(k3_relat_1(A,B)) & v1_funct_1(k3_relat_1(A,B)) ) ) )).
fof(fc139_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( v1_zfmisc_1(C) => ( v1_relat_1(k3_relat_1(k2_zfmisc_1(A,B),k2_zfmisc_1(B,C))) & v1_funct_1(k3_relat_1(k2_zfmisc_1(A,B),k2_zfmisc_1(B,C))) ) ) )).
fof(fc13_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc13_abian,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) & ~ v1_abian(B) ) => ~ v1_abian(k6_xcmplx_0(A,B)) ) )).
fof(fc13_afinsq_1,axiom,( ! [A] : v3_card_1(k3_afinsq_1(A),1) )).
fof(fc13_afinsq_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc13_algstr_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc13_algstr_4,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k12_algstr_4(A)) ) => ( v7_ordinal1(k2_xtuple_0(B)) & ~ v8_ordinal1(k2_xtuple_0(B)) ) ) )).
fof(fc13_ami_6,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) & v7_ordinal1(B) ) => v3_card_1(k2_amistd_1(k7_card_1(2),k1_ami_3,k8_ami_3(B,A)),1) ) )).
fof(fc13_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(fc13_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & l5_aofa_a00(A) ) => v2_funct_1(u7_aofa_a00(A)) ) )).
fof(fc13_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_exchsort(B) & v2_exchsort(B,A) ) => ( v1_relat_1(k1_funct_7(B,C,D)) & v1_funct_1(k1_funct_7(B,C,D)) & v1_finset_1(k1_funct_7(B,C,D)) & v1_exchsort(k1_funct_7(B,C,D)) & v2_exchsort(k1_funct_7(B,C,D),A) ) ) )).
fof(fc13_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) ) )).
fof(fc13_binop_2,axiom,( v1_funct_1(k15_binop_2) & v1_funct_2(k15_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & v1_setwiseo(k15_binop_2,k3_numbers) )).
fof(fc13_borsuk_5,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(A) & v1_rat_1(A) & v1_xreal_0(B) & ~ v1_rat_1(B) ) => ~ v1_rat_1(k7_xcmplx_0(B,A)) ) )).
fof(fc13_c0sp2,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(fc13_card_1,axiom,( ! [A] : ( ~ v1_finset_1(A) => ~ v1_finset_1(k1_zfmisc_1(A)) ) )).
fof(fc13_card_3,axiom,( ! [A] : ! [B] : ( ~ v1_finset_1(A) => ~ v1_finset_1(k2_funcop_1(A,B)) ) )).
fof(fc13_cayldick,axiom,( v6_algstr_0(k3_cayldick) & v13_algstr_0(k3_cayldick) & v1_cayldick(k3_cayldick) )).
fof(fc13_cc0sp2,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(fc13_cfdiff_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v9_ordinal1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & v7_ordinal1(B) ) => ( v1_relat_1(k7_nat_1(A,B)) & v4_relat_1(k7_nat_1(A,B),k4_ordinal1) & v1_funct_1(k7_nat_1(A,B)) & v1_partfun1(k7_nat_1(A,B),k4_ordinal1) & v9_ordinal1(k7_nat_1(A,B)) ) ) )).
fof(fc13_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v6_circcmb3(B) & m1_circcmb3(B,A) & m1_subset_1(C,u1_struct_0(B)) & v1_funct_1(D) & v1_funct_2(D,k4_finseq_2(1,A),A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(1,A),A))) ) => ( ~ v2_struct_0(k2_circcomb(B,k4_circcmb3(1,A,D,k12_finseq_1(u1_struct_0(B),C)))) & v1_msualg_1(k2_circcomb(B,k4_circcmb3(1,A,D,k12_finseq_1(u1_struct_0(B),C)))) & v6_circcmb3(k2_circcomb(B,k4_circcmb3(1,A,D,k12_finseq_1(u1_struct_0(B),C)))) ) ) )).
fof(fc13_circcomb,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(fc13_closure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc13_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc13_coh_sp,axiom,( ! [A] : ( ~ 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)) ) )).
fof(fc13_cohsp_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc13_compos_0,axiom,( ! [A] : ! [B] : ( ( ~ 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),k4_ordinal1) & v1_funct_1(k5_xtuple_0(B)) ) ) )).
fof(fc13_compos_1,axiom,( ! [A] : ! [B] : ( ( l1_compos_1(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc13_comput_1,axiom,( v1_relat_1(k4_comput_1(1,1)) & v4_relat_1(k4_comput_1(1,1),k3_finseq_2(k4_ordinal1)) & 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)) )).
fof(fc13_comseq_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v1_comseq_3(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & v7_ordinal1(B) ) => ( v1_funct_1(k7_nat_1(A,B)) & v1_funct_2(k7_nat_1(A,B),k4_ordinal1,k2_numbers) & v1_comseq_3(k7_nat_1(A,B)) ) ) )).
fof(fc13_dickson,axiom,( ~ v2_struct_0(k11_dickson) & v5_orders_2(k11_dickson) )).
fof(fc13_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => v1_finset_1(k8_euclid_7(A)) ) )).
fof(fc13_euclid_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xcmplx_0(A) & v7_ordinal1(B) & v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,B) & v1_finseq_1(C) & v1_valued_0(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) ) ) )).
fof(fc13_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => ( v1_partfun1(k9_funct_7(k6_partfun1(A),B,C),A) & v2_funct_2(k9_funct_7(k6_partfun1(A),B,C),A) ) ) )).
fof(fc13_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xtuple_0(A) & ~ v1_xtuple_0(B) & ~ v1_xtuple_0(C) ) => v2_facirc_1(k11_finseq_1(A,B,C)) ) )).
fof(fc13_fcont_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc13_filter_2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc13_finseq_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc13_finset_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(B) ) => v1_finset_1(k7_relat_1(A,B)) ) )).
fof(fc13_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc13_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc13_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc13_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k30_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) ) )).
fof(fc13_funcop_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc13_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v3_funct_1(A) ) => ~ v1_zfmisc_1(k10_xtuple_0(A)) ) )).
fof(fc13_funct_4,axiom,( ! [A] : ! [B] : v1_zfmisc_1(k16_funcop_1(A,B)) )).
fof(fc13_funct_9,axiom,( v1_funct_1(k16_sin_cos) & v1_funct_2(k16_sin_cos,k1_numbers,k1_numbers) & v2_funct_9(k16_sin_cos) )).
fof(fc13_functor0,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc13_gate_1,axiom,( ! [A] : ! [B] : ( v1_xboole_0(A) => ~ v1_xboole_0(k6_gate_1(A,B)) ) )).
fof(fc13_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => v3_glib_001(k8_glib_001(A,B,C,D),A) ) )).
fof(fc13_grcat_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc13_group_7,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc13_hermitan,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc13_hilbert3,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_hilbert1) & m1_subset_1(B,k1_hilbert1) ) => v1_hilbert3(k3_hilbert1(A,k3_hilbert1(B,k4_hilbert1(A,B)))) ) )).
fof(fc13_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc13_index_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) ) )).
fof(fc13_jordan,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) & v1_xreal_0(B) ) => v1_compts_1(k2_brouwer(2,A,B)) ) )).
fof(fc13_kurato_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc13_lukasi_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc13_matrtop1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_matrix_0(B) & v2_matrix_0(B,u1_struct_0(k2_vectsp_1),A,A) & v1_matrix_6(B,A,k2_vectsp_1) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( 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)) ) ) )).
fof(fc13_mazurulm,axiom,( ! [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) & 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) ) ) )).
fof(fc13_member_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_membered(A) ) => ( ~ v1_xboole_0(k7_member_1(A)) & v1_membered(k7_member_1(A)) ) ) )).
fof(fc13_membered,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_membered(k2_tarski(A,B)) ) )).
fof(fc13_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k5_numbers) ) ) )).
fof(fc13_mod_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc13_msafree4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & v3_msafree4(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)) & v13_pencil_1(u3_msualg_1(A,B)) ) ) )).
fof(fc13_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_necklace(k5_mycielsk(A)) & v3_necklace(k5_mycielsk(A)) ) ) )).
fof(fc13_nat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & ~ v8_ordinal1(B) & ~ v8_ordinal1(C) ) => v1_setfam_1(k1_enumset1(A,B,C)) ) )).
fof(fc13_nat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc13_newton,axiom,( v1_xboole_0(k9_newton(2)) )).
fof(fc13_ordinal6,axiom,( ! [A] : ! [B] : ( v1_ordinal6(A) => v1_ordinal6(k4_xboole_0(A,B)) ) )).
fof(fc13_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc13_pcs_0,axiom,( ! [A] : ( ( v4_pcs_0(A) & l1_pcs_0(A) ) => v1_relat_2(u1_pcs_0(A)) ) )).
fof(fc13_polynom1,axiom,( ! [A] : ! [B] : ( ( 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(k12_polynom1(A,B)) & v36_algstr_0(k12_polynom1(A,B)) & v1_vectsp_1(k12_polynom1(A,B)) & v4_vectsp_1(k12_polynom1(A,B)) ) ) )).
fof(fc13_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_group_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ( ~ v2_struct_0(k14_polynom3(A)) & v36_algstr_0(k14_polynom3(A)) & v5_group_1(k14_polynom3(A)) ) ) )).
fof(fc13_pre_poly,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => v1_pre_poly(k5_finseq_1(A)) ) )).
fof(fc13_prvect_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc13_quaterni,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_quaterni(B) ) => v1_quaterni(k21_quaterni(A,B)) ) )).
fof(fc13_ratfunc1,axiom,( ! [A] : ! [B] : ( ( ~ v7_struct_0(A) & l6_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & ~ v1_ratfunc1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ v9_struct_0(k2_ratfunc1(A,B),A) ) )).
fof(fc13_rcomp_3,axiom,( ! [A] : ( ( v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => v6_xxreal_2(k5_toprealb(A)) ) )).
fof(fc13_relat_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_relat_1(B) ) => ( v1_xboole_0(k3_relat_1(B,A)) & v1_relat_1(k3_relat_1(B,A)) ) ) )).
fof(fc13_relat_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_2(A) ) => ( v1_relat_1(k2_relat_1(A)) & v5_relat_2(k2_relat_1(A)) ) ) )).
fof(fc13_rfunct_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc13_rltopsp1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc13_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_robbins1(A) & l2_robbins1(A) ) => ( v4_robbins1(k8_robbins1(A)) & v6_robbins1(k8_robbins1(A)) ) ) )).
fof(fc13_rvsum_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_xcmplx_0(B) ) => ( v1_relat_1(k2_finseq_2(A,B)) & v1_funct_1(k2_finseq_2(A,B)) & v1_valued_0(k2_finseq_2(A,B)) & v1_finseq_1(k2_finseq_2(A,B)) ) ) )).
fof(fc13_scm_halt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & 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(k3_scmfsa8b(C,A,B)) & v1_relat_1(k3_scmfsa8b(C,A,B)) & v4_relat_1(k3_scmfsa8b(C,A,B),k4_ordinal1) & v5_relat_1(k3_scmfsa8b(C,A,B),u1_compos_1(k1_scmfsa_2)) & v1_funct_1(k3_scmfsa8b(C,A,B)) & v1_finset_1(k3_scmfsa8b(C,A,B)) & v1_afinsq_1(k3_scmfsa8b(C,A,B)) & v2_scm_halt(k3_scmfsa8b(C,A,B)) ) ) )).
fof(fc13_scmfsa10,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) & v7_ordinal1(B) ) => v3_card_1(k2_amistd_1(k7_card_1(3),k1_scmfsa_2,k12_scmfsa_2(B,A)),1) ) )).
fof(fc13_scmfsa6c,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc13_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) & v7_ordinal1(B) ) => ~ v2_extpro_1(k13_scmfsa_2(B,A),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc13_scmpds_4,axiom,( ! [A] : ! [B] : ( ( 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_relat_1(k4_scmpds_4(A,B)) & v4_relat_1(k4_scmpds_4(A,B),k4_ordinal1) & v5_relat_1(k4_scmpds_4(A,B),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k4_scmpds_4(A,B)) & 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)) ) ) )).
fof(fc13_scmpds_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc13_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & 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_relat_1(k7_scmpds_6(B,C,A)) & v4_relat_1(k7_scmpds_6(B,C,A),k4_ordinal1) & v5_relat_1(k7_scmpds_6(B,C,A),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k7_scmpds_6(B,C,A)) & 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)) ) ) )).
fof(fc13_scmring3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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))) & v7_ordinal1(C) ) => v3_card_1(k2_amistd_1(k7_card_1(2),k1_scmring2(A),k9_scmring2(A,C,B)),1) ) )).
fof(fc13_scmyciel,axiom,( ! [A] : ! [B] : ( ( v4_scmyciel(A) & v1_finset_1(B) ) => v1_finset_1(k7_scmyciel(A,B)) ) )).
fof(fc13_setfam_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) => ~ v1_xboole_0(k3_tarski(A)) ) )).
fof(fc13_sfmastr1,axiom,( ! [A] : ( ( 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),k4_ordinal1) & 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)) ) ) )).
fof(fc13_simplex0,axiom,( ! [A] : ( ( ~ v4_simplex0(A) & l1_pre_topc(A) ) => ~ v1_xboole_0(k4_simplex0(A)) ) )).
fof(fc13_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k16_sin_cos,k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos))) & v2_funct_1(k5_relat_1(k16_sin_cos,k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos))) )).
fof(fc13_sincos10,axiom,( v1_relat_1(k5_relat_1(k1_fdiff_9,k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,4)))) & v2_funct_1(k5_relat_1(k1_fdiff_9,k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,4)))) )).
fof(fc13_sppol_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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)) ) )).
fof(fc13_sprect_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(fc13_struct_0,axiom,( ! [A] : ( ( v11_struct_0(A) & l5_struct_0(A) ) => v1_xboole_0(u4_struct_0(A)) ) )).
fof(fc13_subset_1,axiom,( ! [A] : v1_xboole_0(k1_subset_1(A)) )).
fof(fc13_tex_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc13_topgrp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc13_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ( 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) ) ) )).
fof(fc13_topreala,axiom,( ! [A] : ! [B] : ( ( v3_xxreal_0(A) & v1_xreal_0(A) & ~ v3_xxreal_0(B) & v1_xreal_0(B) ) => ~ v1_xboole_0(k4_xxreal_1(A,B)) ) )).
fof(fc13_toprealb,axiom,( ! [A] : ( ( 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) ) ) )).
fof(fc13_toprealc,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k2_toprealc(A)) & v1_valued_2(k2_toprealc(A)) ) ) )).
fof(fc13_tops_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc13_trees_3,axiom,( ! [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) ) => v5_trees_3(k10_finseq_1(A,B)) ) )).
fof(fc13_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_valued_0(A) & v1_relat_1(B) ) => v1_valued_0(k3_xboole_0(A,B)) ) )).
fof(fc13_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc13_waybel10,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc13_waybel18,axiom,( ! [A] : ! [B] : ( ( ~ 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(k4_yellow_1(A,k7_funcop_1(A,B))) & v2_waybel_8(k4_yellow_1(A,k7_funcop_1(A,B))) ) ) )).
fof(fc13_waybel23,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc13_waybel24,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc13_waybel25,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc13_waybel34,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc13_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc13_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc13_waybel_8,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k2_yellow_1(A))) => ( v1_waybel_0(k2_waybel_8(k2_yellow_1(A),B),k2_yellow_1(A)) & v12_waybel_0(k2_waybel_8(k2_yellow_1(A),B),k2_yellow_1(A)) ) ) )).
fof(fc13_waybel_9,axiom,( ! [A] : ( ( v1_lattice3(A) & l1_orders_2(A) ) => ( v6_waybel_0(k2_waybel_9(A),A) & v7_waybel_0(k2_waybel_9(A)) ) ) )).
fof(fc13_xreal_0,axiom,( ! [A] : ! [B] : ( ( v3_xxreal_0(A) & v1_xreal_0(A) & ~ v2_xxreal_0(B) & v1_xreal_0(B) ) => v3_xxreal_0(k2_xcmplx_0(A,B)) ) )).
fof(fc13_xxreal_2,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => v6_xxreal_2(k1_xxreal_1(A,B)) ) )).
fof(fc13_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc13_yellow_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v13_struct_0(k5_yellow_1(k1_xboole_0,A),1) & v1_orders_2(k5_yellow_1(k1_xboole_0,A)) ) ) )).
fof(fc13_yellow_7,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc14_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc14_abian,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) & ~ v1_abian(B) ) => ~ v1_abian(k6_xcmplx_0(B,A)) ) )).
fof(fc14_afinsq_1,axiom,( ! [A] : ! [B] : v3_card_1(k6_afinsq_1(A,B),2) )).
fof(fc14_algstr_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc14_algstr_4,axiom,( ! [A] : v15_algstr_0(k14_algstr_4(A)) )).
fof(fc14_ami_6,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) & v7_ordinal1(B) ) => v3_card_1(k2_amistd_1(k7_card_1(2),k1_ami_3,k9_ami_3(B,A)),1) ) )).
fof(fc14_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc14_aofa_a00,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(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_funct_1(B,1)) ) )).
fof(fc14_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k1_funct_7(B,C,D)) & v5_relat_1(k1_funct_7(B,C,D),A) & v1_funct_1(k1_funct_7(B,C,D)) ) ) )).
fof(fc14_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) ) )).
fof(fc14_binop_2,axiom,( v1_funct_1(k20_binop_2) & v1_funct_2(k20_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & v1_setwiseo(k20_binop_2,k4_numbers) )).
fof(fc14_borsuk_5,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc14_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ~ v2_struct_0(k9_c0sp2(A)) & v1_normsp_1(k9_c0sp2(A)) ) ) )).
fof(fc14_card_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_finset_1(A) & ~ v1_xboole_0(B) ) => ~ v1_finset_1(k2_zfmisc_1(A,B)) ) )).
fof(fc14_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_finset_1(A) ) => ~ v1_finset_1(k1_relat_1(A)) ) )).
fof(fc14_cayldick,axiom,( v30_algstr_0(k3_cayldick) & v33_algstr_0(k3_cayldick) & v4_rlvect_1(k3_cayldick) & v5_rlvect_1(k3_cayldick) & v6_rlvect_1(k3_cayldick) & v7_rlvect_1(k3_cayldick) & v8_rlvect_1(k3_cayldick) & v2_funcsdom(k3_cayldick) & v3_normsp_0(k3_cayldick) & v4_normsp_0(k3_cayldick) & v2_normsp_1(k3_cayldick) & v1_vectsp_1(k3_cayldick) & v4_vectsp_1(k3_cayldick) & v2_lopban_2(k3_cayldick) & v3_lopban_2(k3_cayldick) & v4_lopban_2(k3_cayldick) & v1_cayldick(k3_cayldick) & v3_cayldick(k3_cayldick) & v4_cayldick(k3_cayldick) & v5_cayldick(k3_cayldick) & v6_cayldick(k3_cayldick) )).
fof(fc14_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ~ v2_struct_0(k9_cc0sp2(A)) & v7_clvect_1(k9_cc0sp2(A)) ) ) )).
fof(fc14_circcomb,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(fc14_closure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc14_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc14_cohsp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc14_compos_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc14_compos_1,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) & 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)) ) ) )).
fof(fc14_comput_1,axiom,( v1_relat_1(k4_comput_1(3,3)) & v4_relat_1(k4_comput_1(3,3),k3_finseq_2(k4_ordinal1)) & 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)) )).
fof(fc14_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_3(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_funct_1(k2_series_1(k55_valued_1(k4_ordinal1,k2_numbers,A))) & v1_funct_2(k2_series_1(k55_valued_1(k4_ordinal1,k2_numbers,A)),k4_ordinal1,k1_numbers) & v1_seq_2(k2_series_1(k55_valued_1(k4_ordinal1,k2_numbers,A))) ) ) )).
fof(fc14_dickson,axiom,( ~ v2_struct_0(k11_dickson) & v4_orders_2(k11_dickson) )).
fof(fc14_euclid_7,axiom,( ! [A] : ( 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))) ) ) )).
fof(fc14_euclid_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xcmplx_0(A) & v7_ordinal1(B) & v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,B) & v1_finseq_1(C) & v1_valued_0(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) ) ) )).
fof(fc14_exchsort,axiom,( ! [A] : ! [B] : ( ( l1_orders_2(A) & v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & v1_xboole_0(B) & v1_funct_1(B) & v1_exchsort(B) ) => v1_xboole_0(k6_exchsort(A,B)) ) )).
fof(fc14_facirc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_facirc_1(A) ) => ~ v1_facirc_1(k10_xtuple_0(A)) ) )).
fof(fc14_fcont_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_funct_1(k4_relat_1(A)) & v2_fcont_1(k4_relat_1(A)) ) ) )).
fof(fc14_filter_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc14_finseq_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc14_finset_1,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_zfmisc_1(A,B)) ) )).
fof(fc14_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) ) => v12_fomodel1(k1_funct_1(k28_fomodel1(A),B),A) ) )).
fof(fc14_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k14_fomodel2(A,B)) ) )).
fof(fc14_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc14_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ 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(B),A) ) )).
fof(fc14_funcop_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => v1_funcop_1(k2_funcop_1(A,B)) ) )).
fof(fc14_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v4_funct_1(k1_tarski(A)) ) )).
fof(fc14_funct_9,axiom,( v1_funct_1(k18_sin_cos) & v1_funct_2(k18_sin_cos,k1_numbers,k1_numbers) & v2_funct_9(k18_sin_cos) )).
fof(fc14_functor0,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc14_gate_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => v1_xboole_0(k6_gate_1(A,B)) ) )).
fof(fc14_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => v4_glib_001(k8_glib_001(A,B,C,D),A) ) )).
fof(fc14_grcat_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc14_group_7,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc14_hermitan,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc14_hilbert3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)))) ) )).
fof(fc14_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc14_index_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_index_1(C,A,B) & m1_index_1(C,A,B) ) => v1_index_1(k1_xtuple_0(C)) ) )).
fof(fc14_jordan,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc14_kurato_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc14_lukasi_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc14_mazurulm,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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) ) ) )).
fof(fc14_member_1,axiom,( ! [A] : ( v3_membered(A) => ( v1_membered(k7_member_1(A)) & v3_membered(k7_member_1(A)) ) ) )).
fof(fc14_membered,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => v2_membered(k2_tarski(A,B)) ) )).
fof(fc14_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc14_mod_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc14_msafree4,axiom,( ! [A] : ! [B] : ( ( ~ 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(k1_msafree3(A,B),A) & v4_msualg_1(k1_msafree3(A,B),A) & v1_msafree1(k1_msafree3(A,B),A) ) ) )).
fof(fc14_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => v1_dilworth(k2_struct_0(k5_mycielsk(A)),k5_mycielsk(A)) ) )).
fof(fc14_nat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v8_ordinal1(A) & ~ v8_ordinal1(B) & ~ v8_ordinal1(C) & ~ v8_ordinal1(D) ) => v1_setfam_1(k2_enumset1(A,B,C,D)) ) )).
fof(fc14_nat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v4_valued_0(B) & v7_ordinal1(C) & ~ v8_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)) ) ) )).
fof(fc14_newton,axiom,( ~ v1_xboole_0(k8_newton) & ~ v1_finset_1(k8_newton) )).
fof(fc14_oposet_1,axiom,( v3_qmax_1(k1_oposet_1) & v10_oposet_1(k1_oposet_1) )).
fof(fc14_ordinal6,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc14_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc14_pcs_0,axiom,( ! [A] : ( ( v5_pcs_0(A) & l1_pcs_0(A) ) => v2_relat_2(u1_pcs_0(A)) ) )).
fof(fc14_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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(k14_polynom3(A)) & v36_algstr_0(k14_polynom3(A)) & v3_group_1(k14_polynom3(A)) ) ) )).
fof(fc14_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc14_prvect_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc14_quaterni,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_quaterni(B) ) => v1_quaterni(k20_quaterni(A,B)) ) )).
fof(fc14_ratfunc1,axiom,( ! [A] : ! [B] : ( ( ~ 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,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & ~ v1_ratfunc1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))),k4_ordinal1,u1_struct_0(A)) & v3_ratfunc1(k3_polynom5(A,B,k3_vectsp_1(A,k5_struct_0(A),k2_ratfunc1(A,B))),A) ) ) )).
fof(fc14_rcomp_3,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc14_relat_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k2_relat_1(A)) & v1_relat_1(k2_relat_1(A)) ) ) )).
fof(fc14_relat_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_relat_1(B) & v5_relat_2(B) ) => v5_relat_2(k3_xboole_0(A,B)) ) )).
fof(fc14_rfunct_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc14_rltopsp1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc14_robbins1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc14_rvsum_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc14_scm_halt,axiom,( ! [A] : ! [B] : ( ( 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc14_scmfsa10,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) & v7_ordinal1(B) ) => v3_card_1(k2_amistd_1(k7_card_1(3),k1_scmfsa_2,k13_scmfsa_2(B,A)),1) ) )).
fof(fc14_scmfsa6c,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc14_scmfsa_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc14_scmpds_4,axiom,( v1_relat_1(k4_compos_1(k1_scmpds_2)) & v4_relat_1(k4_compos_1(k1_scmpds_2),k4_ordinal1) & 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)) )).
fof(fc14_scmpds_5,axiom,( v1_scmpds_5(k2_compos_1(k1_scmpds_2)) )).
fof(fc14_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & 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_relat_1(k7_scmpds_6(B,C,A)) & v4_relat_1(k7_scmpds_6(B,C,A),k4_ordinal1) & v5_relat_1(k7_scmpds_6(B,C,A),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k7_scmpds_6(B,C,A)) & 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) ) ) )).
fof(fc14_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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),k7_card_1(2)) & v3_amistd_1(k1_scmring2(A),k7_card_1(2)) ) ) )).
fof(fc14_scmyciel,axiom,( ! [A] : v5_scmyciel(k5_scmyciel(A)) )).
fof(fc14_sfmastr1,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) & 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)) ) ) )).
fof(fc14_simplex0,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(fc14_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k16_sin_cos,k2_rcomp_1(k28_sin_cos,k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos)))) & v2_funct_1(k5_relat_1(k16_sin_cos,k2_rcomp_1(k28_sin_cos,k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos)))) )).
fof(fc14_sincos10,axiom,( v1_relat_1(k5_relat_1(k1_fdiff_9,k1_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos),k28_sin_cos))) & v2_funct_1(k5_relat_1(k1_fdiff_9,k1_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos),k28_sin_cos))) )).
fof(fc14_sppol_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(fc14_struct_0,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & l5_struct_0(A) ) => ~ v1_xboole_0(u4_struct_0(A)) ) )).
fof(fc14_subset_1,axiom,( ! [A] : ~ v1_subset_1(k2_subset_1(A),A) )).
fof(fc14_tex_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc14_topgrp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc14_topreala,axiom,( ! [A] : ! [B] : ( ( v3_xxreal_0(A) & v1_xreal_0(A) & ~ v3_xxreal_0(B) & v1_xreal_0(B) ) => ~ v1_xboole_0(k2_xxreal_1(A,B)) ) )).
fof(fc14_toprealb,axiom,( ! [A] : ( ( 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) ) ) )).
fof(fc14_toprealc,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_valued_2(A) ) => ( ~ v1_xboole_0(k2_toprealc(A)) & v1_valued_2(k2_toprealc(A)) ) ) )).
fof(fc14_tops_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ~ v2_tops_1(k2_struct_0(A),A) ) )).
fof(fc14_trees_3,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ 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)) ) ) )).
fof(fc14_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_valued_0(A) & v1_relat_1(B) ) => v1_valued_0(k4_xboole_0(A,B)) ) )).
fof(fc14_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc14_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(fc14_waybel10,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc14_waybel23,axiom,( ! [A] : ! [B] : ( ( ~ 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(k1_yellow_1(k7_waybel_0(B))),u1_struct_0(A)) & v5_orders_3(k3_waybel23(A,B),k1_yellow_1(k7_waybel_0(B)),A) ) ) )).
fof(fc14_waybel25,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(fc14_waybel34,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc14_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v12_waybel_0(k2_struct_0(A),A) & v13_waybel_0(k2_struct_0(A),A) ) ) )).
fof(fc14_waybel_4,axiom,( ! [A] : ! [B] : ( ( 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(k1_yellow_1(k7_waybel_0(A)))) & v5_orders_3(k7_waybel_4(A,B),A,k1_yellow_1(k7_waybel_0(A))) ) ) )).
fof(fc14_waybel_8,axiom,( ! [A] : ( v1_orders_2(k2_yellow_1(A)) & v2_waybel_8(k2_yellow_1(A)) ) )).
fof(fc14_waybel_9,axiom,( ! [A] : ( ( v7_waybel_0(A) & l1_orders_2(A) ) => ( v6_waybel_0(k2_waybel_9(A),A) & v7_waybel_0(k2_waybel_9(A)) ) ) )).
fof(fc14_xreal_0,axiom,( ! [A] : ! [B] : ( ( v3_xxreal_0(A) & v1_xreal_0(A) & ~ v2_xxreal_0(B) & v1_xreal_0(B) ) => v3_xxreal_0(k2_xcmplx_0(B,A)) ) )).
fof(fc14_xxreal_2,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => v6_xxreal_2(k3_xxreal_1(A,B)) ) )).
fof(fc14_xxreal_3,axiom,( ! [A] : ( ( v1_xxreal_0(A) & ~ v2_xxreal_0(A) ) => ( v1_xxreal_0(k2_xxreal_3(A)) & ~ v3_xxreal_0(k2_xxreal_3(A)) ) ) )).
fof(fc14_yellow_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ( v1_orders_2(k5_yellow_1(k1_xboole_0,A)) & v5_orders_2(k5_yellow_1(k1_xboole_0,A)) & v1_lattice3(k5_yellow_1(k1_xboole_0,A)) & v2_lattice3(k5_yellow_1(k1_xboole_0,A)) ) ) )).
fof(fc15_abcmiz_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc15_abian,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & ~ v1_abian(A) & v1_int_1(B) & ~ v1_abian(B) ) => v1_abian(k6_xcmplx_0(A,B)) ) )).
fof(fc15_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : v3_card_1(k7_afinsq_1(A,B,C),3) )).
fof(fc15_algstr_4,axiom,( ! [A] : ( v1_xboole_0(A) => v2_struct_0(k14_algstr_4(A)) ) )).
fof(fc15_ami_6,axiom,( v1_extpro_1(k1_ami_3,k7_card_1(2)) & v3_amistd_1(k1_ami_3,k7_card_1(2)) )).
fof(fc15_aofa_a00,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l6_aofa_a00(A) & ~ v2_struct_0(B) & l5_aofa_a00(B) ) => ( ~ v2_struct_0(k36_aofa_a00(A,B)) & v15_aofa_a00(k36_aofa_a00(A,B)) ) ) )).
fof(fc15_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) ) )).
fof(fc15_binop_2,axiom,( v1_funct_1(k23_binop_2) & v1_funct_2(k23_binop_2,k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1) & v1_setwiseo(k23_binop_2,k4_ordinal1) )).
fof(fc15_borsuk_5,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc15_c0sp2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc15_card_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_finset_1(A) & ~ v1_xboole_0(B) ) => ~ v1_finset_1(k2_zfmisc_1(B,A)) ) )).
fof(fc15_card_3,axiom,( ! [A] : ( ~ v1_finset_1(A) => ( v1_relat_1(k1_wellord2(A)) & ~ v1_finset_1(k1_wellord2(A)) ) ) )).
fof(fc15_cayldick,axiom,( ~ v23_algstr_0(k4_struct_0(k3_cayldick),k3_cayldick) & ~ v24_algstr_0(k4_struct_0(k3_cayldick),k3_cayldick) )).
fof(fc15_cc0sp2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc15_circcomb,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc15_closure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc15_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc15_cohsp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc15_compos_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc15_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ( v1_relat_1(k4_compos_1(A)) & v4_relat_1(k4_compos_1(A),k4_ordinal1) & 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) ) ) )).
fof(fc15_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v1_relat_1(k3_comput_1(k5_numbers,A)) & v4_relat_1(k3_comput_1(k5_numbers,A),k3_finseq_2(k4_ordinal1)) & v1_funct_1(k3_comput_1(k5_numbers,A)) & v4_valued_0(k3_comput_1(k5_numbers,A)) & v2_margrel1(k3_comput_1(k5_numbers,A)) & v8_comput_1(k3_comput_1(k5_numbers,A),k5_numbers) ) ) )).
fof(fc15_dickson,axiom,( ~ v2_struct_0(k11_dickson) & v1_wellfnd1(k11_dickson) )).
fof(fc15_euclid_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( ~ v2_struct_0(k7_real_ns1(A)) & v1_bhsp_1(k7_real_ns1(A)) & v1_rusub_4(k7_real_ns1(A)) ) ) )).
fof(fc15_euclid_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xcmplx_0(A) & v7_ordinal1(B) & v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,B) & v1_finseq_1(C) & v1_valued_0(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) ) ) )).
fof(fc15_exchsort,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc15_facirc_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc15_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc15_filter_2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(fc15_finseq_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc15_finset_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(A) & v1_finset_1(B) & v1_finset_1(C) ) => v1_finset_1(k3_zfmisc_1(A,B,C)) ) )).
fof(fc15_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & m1_subset_1(B,k3_fomodel0(k3_finseq_2(k15_fomodel1(A)),k29_fomodel1(A))) ) => v1_relat_1(k1_funct_1(k21_fomodel1(A),B)) ) )).
fof(fc15_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) ) => ~ v1_xboole_0(k24_fomodel2(A,B)) ) )).
fof(fc15_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc15_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v1_xboole_0(B) ) => v3_fomodel4(k13_fomodel0(A,B),A) ) )).
fof(fc15_funcop_1,axiom,( ! [A] : ! [B] : v3_funct_1(k2_funcop_1(A,B)) )).
fof(fc15_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => v4_funct_1(k2_tarski(A,B)) ) )).
fof(fc15_funct_9,axiom,( v1_funct_1(k2_fdiff_9) & v2_funct_9(k2_fdiff_9) )).
fof(fc15_functor0,axiom,( ! [A] : ( l1_altcat_1(A) => ( v9_functor0(k11_functor0(A),A,A) & v21_functor0(k11_functor0(A),A,A) ) ) )).
fof(fc15_gate_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_xboole_0(B) ) => ~ v1_xboole_0(k7_gate_1(A,B)) ) )).
fof(fc15_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => v5_glib_001(k8_glib_001(A,B,C,D),A) ) )).
fof(fc15_grcat_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc15_group_7,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc15_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc15_index_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_index_1(C,A,B) & m1_index_1(C,A,B) ) => v1_funcop_1(k2_xtuple_0(C)) ) )).
fof(fc15_kurato_1,axiom,( ~ v1_xboole_0(k6_kurato_1) )).
fof(fc15_lukasi_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc15_mazurulm,axiom,( ! [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) & 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) ) ) )).
fof(fc15_member_1,axiom,( ! [A] : ( v4_membered(A) => ( v1_membered(k7_member_1(A)) & v4_membered(k7_member_1(A)) ) ) )).
fof(fc15_membered,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => v3_membered(k2_tarski(A,B)) ) )).
fof(fc15_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc15_msafree4,axiom,( ! [A] : ! [B] : ( ( ~ 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(k1_msafree3(A,B),A) & v5_msafree4(k1_msafree3(A,B),A,B) ) ) )).
fof(fc15_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => v3_necklace(k7_mycielsk(A)) ) )).
fof(fc15_nat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v8_ordinal1(A) & ~ v8_ordinal1(B) & ~ v8_ordinal1(C) & ~ v8_ordinal1(D) & ~ v8_ordinal1(E) ) => v1_setfam_1(k3_enumset1(A,B,C,D,E)) ) )).
fof(fc15_nat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & ~ v8_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)) ) ) )).
fof(fc15_ordinal6,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc15_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc15_pcs_0,axiom,( ! [A] : ( ( v6_pcs_0(A) & l1_pcs_0(A) ) => v3_relat_2(u1_pcs_0(A)) ) )).
fof(fc15_polynom3,axiom,( ! [A] : ( ( ~ 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) ) => ( ~ v2_struct_0(k14_polynom3(A)) & v36_algstr_0(k14_polynom3(A)) & v4_vectsp_1(k14_polynom3(A)) ) ) )).
fof(fc15_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(B) & m1_finseq_1(B,k3_finseq_2(A)) ) => v1_xboole_0(k5_pre_poly(A,B)) ) )).
fof(fc15_prvect_3,axiom,( ! [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) ) => v1_prvect_2(k5_finseq_1(A)) ) )).
fof(fc15_relat_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc15_relat_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_relat_1(B) & v5_relat_2(B) ) => v5_relat_2(k3_xboole_0(B,A)) ) )).
fof(fc15_rfunct_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc15_rltopsp1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc15_scmfsa10,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc15_scmfsa6c,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc15_scmfsa_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc15_scmpds_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc15_scmpds_5,axiom,( ! [A] : ( ( v1_scmpds_5(A) & m1_subset_1(A,u1_compos_1(k1_scmpds_2)) ) => ( v1_relat_1(k3_afinsq_1(A)) & v4_relat_1(k3_afinsq_1(A),k4_ordinal1) & v5_relat_1(k3_afinsq_1(A),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k3_afinsq_1(A)) & 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)) ) ) )).
fof(fc15_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & 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_relat_1(k8_scmpds_6(B,C,A)) & v4_relat_1(k8_scmpds_6(B,C,A),k4_ordinal1) & v5_relat_1(k8_scmpds_6(B,C,A),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k8_scmpds_6(B,C,A)) & 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)) ) ) )).
fof(fc15_scmyciel,axiom,( ! [A] : ! [B] : ( ( v4_scmyciel(A) & v8_scmyciel(A) & m1_subset_1(B,k1_zfmisc_1(k3_tarski(A))) ) => v8_scmyciel(k7_scmyciel(A,B)) ) )).
fof(fc15_sfmastr1,axiom,( ! [A] : ! [B] : ( ( 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc15_simplex0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc15_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k16_sin_cos,k2_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(2,k28_sin_cos)))) & v2_funct_1(k5_relat_1(k16_sin_cos,k2_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(2,k28_sin_cos)))) )).
fof(fc15_sincos10,axiom,( v1_relat_1(k5_relat_1(k2_fdiff_9,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4))))) & v2_funct_1(k5_relat_1(k2_fdiff_9,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4))))) )).
fof(fc15_sppol_2,axiom,( v1_topreal4(k1_topreal1) )).
fof(fc15_struct_0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & l2_struct_0(A) ) => ~ v1_xboole_0(k8_struct_0(A)) ) )).
fof(fc15_tex_4,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc15_topgrp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc15_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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(k4_topreal9(A,B,C)) ) )).
fof(fc15_topreala,axiom,( ! [A] : ! [B] : ( ( v3_xxreal_0(A) & v1_xreal_0(A) & ~ v3_xxreal_0(B) & v1_xreal_0(B) ) => ~ v1_xboole_0(k3_xxreal_1(A,B)) ) )).
fof(fc15_toprealb,axiom,( ! [A] : ( ( 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))))) ) ) )).
fof(fc15_toprealc,axiom,( ! [A] : ( v3_valued_2(A) => ( v1_valued_2(k2_toprealc(A)) & v3_valued_2(k2_toprealc(A)) ) ) )).
fof(fc15_tops_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc15_trees_3,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc15_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v2_valued_0(A) & v1_relat_1(B) ) => v2_valued_0(k3_xboole_0(A,B)) ) )).
fof(fc15_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc15_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(fc15_waybel10,axiom,( ! [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) ) => ( 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)))) ) ) )).
fof(fc15_waybel23,axiom,( ! [A] : ! [B] : ( ( ~ 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(k1_yellow_1(k7_waybel_0(B))),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) & v5_orders_3(k4_waybel23(A,B),k1_yellow_1(k7_waybel_0(B)),k1_yellow_1(k7_waybel_0(A))) ) ) )).
fof(fc15_waybel25,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc15_waybel34,axiom,( ! [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) ) => ( v1_orders_2(k1_waybel_8(A)) & v4_yellow_0(k1_waybel_8(A),A) & v6_waybel34(k1_waybel_8(A),A) ) ) )).
fof(fc15_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc15_waybel_4,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc15_waybel_9,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc15_xreal_0,axiom,( ! [A] : ( ( ~ v2_xxreal_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & ~ v3_xxreal_0(k4_xcmplx_0(A)) ) ) )).
fof(fc15_xxreal_2,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => v6_xxreal_2(k2_xxreal_1(A,B)) ) )).
fof(fc15_xxreal_3,axiom,( ! [A] : ( ( v1_xxreal_0(A) & ~ v3_xxreal_0(A) ) => ( v1_xxreal_0(k2_xxreal_3(A)) & ~ v2_xxreal_0(k2_xxreal_3(A)) ) ) )).
fof(fc15_yellow_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( v1_orders_2(k5_yellow_1(A,B)) & v4_orders_2(k5_yellow_1(A,B)) ) ) )).
fof(fc15_yellow_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc16_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc16_abian,axiom,( ! [A] : ( ( v1_int_1(A) & v1_abian(A) ) => v1_abian(k2_xcmplx_0(A,2)) ) )).
fof(fc16_afinsq_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(A) => ( v5_ordinal1(k2_funcop_1(A,B)) & v1_finset_1(k2_funcop_1(A,B)) ) ) )).
fof(fc16_algstr_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v2_struct_0(k14_algstr_4(A)) ) )).
fof(fc16_ami_6,axiom,( v1_amistd_1(k4_xtuple_0(k2_compos_1(k1_ami_3)),k7_card_1(2),k1_ami_3) )).
fof(fc16_aofa_a00,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l6_aofa_a00(A) & ~ v2_struct_0(B) & l5_aofa_a00(B) ) => ( ~ v11_struct_0(k36_aofa_a00(A,B)) & v15_aofa_a00(k36_aofa_a00(A,B)) ) ) )).
fof(fc16_binop_2,axiom,( v1_funct_1(k5_binop_2) & v1_funct_2(k5_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & v1_setwiseo(k5_binop_2,k2_numbers) )).
fof(fc16_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => ~ v1_xboole_0(k4_xxreal_1(A,k1_xxreal_0)) ) )).
fof(fc16_card_1,axiom,( ! [A] : ( v1_finset_1(A) => ( v1_relat_1(k1_wellord2(A)) & v1_finset_1(k1_wellord2(A)) ) ) )).
fof(fc16_cayldick,axiom,( ! [A] : ! [B] : ( ( ~ v7_struct_0(A) & v3_normsp_0(A) & l1_cayldick(A) & ~ v9_struct_0(B,A) & m1_subset_1(B,u1_struct_0(A)) ) => ( ~ v8_ordinal1(k2_normsp_0(A,B)) & v1_xreal_0(k2_normsp_0(A,B)) ) ) )).
fof(fc16_circcomb,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc16_closure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc16_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc16_cohsp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc16_compos_0,axiom,( v1_compos_0(k2_tarski(k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0),k3_xtuple_0(1,k1_xboole_0,k1_xboole_0))) )).
fof(fc16_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_compos_1(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) ) )).
fof(fc16_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v1_relat_1(k3_comput_1(1,A)) & v4_relat_1(k3_comput_1(1,A),k3_finseq_2(k4_ordinal1)) & 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) ) ) )).
fof(fc16_dickson,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( ~ v2_struct_0(k4_yellow_1(A,k7_funcop_1(A,k11_dickson))) & v1_orders_2(k4_yellow_1(A,k7_funcop_1(A,k11_dickson))) ) ) )).
fof(fc16_euclid_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) ) => v3_valued_2(k1_tarski(A)) ) )).
fof(fc16_exchsort,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc16_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc16_finseq_1,axiom,( ! [A] : ~ v1_xboole_0(k5_finseq_1(A)) )).
fof(fc16_finset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc16_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & m1_subset_1(B,k3_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)) ) ) )).
fof(fc16_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ~ v1_xboole_0(k26_fomodel2(A)) ) )).
fof(fc16_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) ) )).
fof(fc16_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v3_fomodel4(B,A) ) => v3_fomodel4(k13_fomodel0(C,B),A) ) )).
fof(fc16_funcop_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc16_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc16_funct_9,axiom,( v1_funct_1(k1_fdiff_9) & v2_funct_9(k1_fdiff_9) )).
fof(fc16_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc16_gate_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(A) => v1_xboole_0(k7_gate_1(A,B)) ) )).
fof(fc16_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => v6_glib_001(k8_glib_001(A,B,C,D),A) ) )).
fof(fc16_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ~ v1_xboole_0(k26_grcat_1(A)) ) )).
fof(fc16_group_7,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc16_hermitan,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc16_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc16_index_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => v4_funct_1(k10_xtuple_0(A)) ) )).
fof(fc16_lukasi_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc16_mazurulm,axiom,( ! [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) & 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)) ) ) )).
fof(fc16_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v2_membered(B) ) => v1_xboole_0(k8_member_1(A,B)) ) )).
fof(fc16_membered,axiom,( ! [A] : ! [B] : ( ( v1_rat_1(A) & v1_rat_1(B) ) => v4_membered(k2_tarski(A,B)) ) )).
fof(fc16_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc16_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v9_msafree4(C,A,B) & m1_msualg_4(C,A,B,B) ) => ( v1_relat_1(k1_funct_1(C,D)) & v3_rewrite1(k1_funct_1(C,D)) ) ) )).
fof(fc16_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => v1_necklace(k7_mycielsk(A)) ) )).
fof(fc16_nat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v8_ordinal1(A) & ~ v8_ordinal1(B) & ~ v8_ordinal1(C) & ~ v8_ordinal1(D) & ~ v8_ordinal1(E) & ~ v8_ordinal1(F) ) => v1_setfam_1(k4_enumset1(A,B,C,D,E,F)) ) )).
fof(fc16_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_relat_1(k12_nat_3(A)) & v4_relat_1(k12_nat_3(A),k8_newton) & v1_funct_1(k12_nat_3(A)) & v1_partfun1(k12_nat_3(A),k8_newton) & v4_valued_0(k12_nat_3(A)) ) ) )).
fof(fc16_ordinal6,axiom,( ~ v1_zfmisc_1(k4_ordinal1) )).
fof(fc16_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc16_pcs_0,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(fc16_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ( ~ v2_struct_0(k14_polynom3(A)) & v36_algstr_0(k14_polynom3(A)) & v5_vectsp_1(k14_polynom3(A)) ) ) )).
fof(fc16_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v4_valued_0(A) & v7_ordinal1(C) ) => ( v1_relat_1(k1_funct_7(A,B,C)) & v1_funct_1(k1_funct_7(A,B,C)) & v4_valued_0(k1_funct_7(A,B,C)) ) ) )).
fof(fc16_prvect_3,axiom,( ! [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) & 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)) ) )).
fof(fc16_ratfunc1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc16_relat_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_xboole_0(B) ) => ( v1_xboole_0(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)) ) ) )).
fof(fc16_relat_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v5_relat_2(A) & v1_relat_1(B) ) => v5_relat_2(k4_xboole_0(A,B)) ) )).
fof(fc16_rfunct_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc16_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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(k5_rltopsp1(A,B,C)) ) )).
fof(fc16_scmfsa10,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(k7_card_1(3),k1_scmfsa_2,k14_scmfsa_2(A,B,C))) ) )).
fof(fc16_scmfsa6c,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc16_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc16_scmpds_4,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_relat_1(k3_afinsq_1(k3_scmpds_2(A))) & v4_relat_1(k3_afinsq_1(k3_scmpds_2(A)),k4_ordinal1) & v5_relat_1(k3_afinsq_1(k3_scmpds_2(A)),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k3_afinsq_1(k3_scmpds_2(A))) & 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))) ) ) )).
fof(fc16_scmpds_5,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc16_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & 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_relat_1(k8_scmpds_6(B,C,A)) & v4_relat_1(k8_scmpds_6(B,C,A),k4_ordinal1) & v5_relat_1(k8_scmpds_6(B,C,A),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k8_scmpds_6(B,C,A)) & 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) ) ) )).
fof(fc16_scmyciel,axiom,( ! [A] : ! [B] : ( ( v4_scmyciel(A) & v11_scmyciel(A) ) => v11_scmyciel(k7_scmyciel(A,B)) ) )).
fof(fc16_sfmastr1,axiom,( ! [A] : ! [B] : ( ( 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc16_simplex0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc16_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k18_sin_cos,k1_rcomp_1(k5_numbers,k28_sin_cos))) & v2_funct_1(k5_relat_1(k18_sin_cos,k1_rcomp_1(k5_numbers,k28_sin_cos))) )).
fof(fc16_sincos10,axiom,( v1_relat_1(k5_relat_1(k2_fdiff_9,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k7_xcmplx_0(k28_sin_cos,2)))) & v2_funct_1(k5_relat_1(k2_fdiff_9,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(fc16_struct_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v7_struct_0(A) & l2_struct_0(A) ) => v1_xboole_0(k8_struct_0(A)) ) )).
fof(fc16_tex_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc16_topgrp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc16_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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_convex1(k4_topreal9(A,B,C),A) ) )).
fof(fc16_topreala,axiom,( ! [A] : ! [B] : ( ( v3_xxreal_0(A) & v1_xreal_0(A) & ~ v3_xxreal_0(B) & v1_xreal_0(B) ) => ~ v1_xboole_0(k1_xxreal_1(A,B)) ) )).
fof(fc16_toprealb,axiom,( ! [A] : ( ( 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))))) ) ) )).
fof(fc16_toprealc,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc16_tops_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc16_trees_3,axiom,( ! [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) ) => ( ~ v1_xboole_0(k10_finseq_1(A,B)) & v6_trees_3(k10_finseq_1(A,B)) ) ) )).
fof(fc16_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v2_valued_0(A) & v1_relat_1(B) ) => v2_valued_0(k4_xboole_0(A,B)) ) )).
fof(fc16_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc16_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc16_waybel23,axiom,( ! [A] : ! [B] : ( ( 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(k1_yellow_1(k7_waybel_0(k5_yellow_0(A,B))))) & v5_orders_3(k5_waybel23(A,B),A,k1_yellow_1(k7_waybel_0(k5_yellow_0(A,B)))) ) ) )).
fof(fc16_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc16_waybel_4,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc16_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( ~ v2_struct_0(k3_waybel_9(A)) & v6_waybel_0(k3_waybel_9(A),A) ) ) )).
fof(fc16_xreal_0,axiom,( ! [A] : ( ( ~ v3_xxreal_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & ~ v2_xxreal_0(k4_xcmplx_0(A)) ) ) )).
fof(fc16_xxreal_2,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => v6_xxreal_2(k4_xxreal_1(A,B)) ) )).
fof(fc16_xxreal_3,axiom,( ! [A] : ( ( v1_xxreal_0(A) & v2_xxreal_0(A) ) => ( v1_xxreal_0(k2_xxreal_3(A)) & v3_xxreal_0(k2_xxreal_3(A)) ) ) )).
fof(fc16_yellow_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & l1_orders_2(B) ) => ( v1_orders_2(k5_yellow_1(A,B)) & v5_orders_2(k5_yellow_1(A,B)) ) ) )).
fof(fc16_yellow_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc17_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc17_abian,axiom,( ! [A] : ( ( v1_int_1(A) & ~ v1_abian(A) ) => ~ v1_abian(k2_xcmplx_0(A,2)) ) )).
fof(fc17_afinsq_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => v5_relat_1(k3_afinsq_1(B),A) ) )).
fof(fc17_algstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc17_algstr_4,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,u1_struct_0(k14_algstr_4(A))) ) => ( v7_ordinal1(k2_xtuple_0(B)) & ~ v8_ordinal1(k2_xtuple_0(B)) ) ) )).
fof(fc17_ami_6,axiom,( v2_amistd_1(k2_compos_1(k1_ami_3),k7_card_1(2),k1_ami_3) )).
fof(fc17_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & ~ v2_struct_0(C) & ~ v11_struct_0(C) & v14_aofa_a00(C,A) & l6_aofa_a00(C) & ~ v2_struct_0(D) & ~ v11_struct_0(D) & v14_aofa_a00(D,B) & l5_aofa_a00(D) ) => ( v14_aofa_a00(k36_aofa_a00(C,D),k2_xcmplx_0(A,B)) & v15_aofa_a00(k36_aofa_a00(C,D)) ) ) )).
fof(fc17_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(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) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) & v4_aofa_a01(D,A,B,C) & l4_aofa_a00(D,A,B,C) & v4_msualg_1(E,A) & v4_msafree4(E,A,C) & v17_aofa_a00(E,A) & v20_aofa_a00(E,4,1,A) & v22_aofa_a00(E,A,1,1,11) & l3_msualg_1(E,A) & m1_subset_1(F,k13_aofa_a00(A,C,E,u4_aofa_a00(A,B,C,D))) & v3_aofa_a01(G,A,B,C,u4_aofa_a00(A,B,C,D),k37_aofa_a00(A)) & m1_subset_1(G,k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),k37_aofa_a00(A))) ) => ( v1_relat_1(k1_funct_1(k1_msafree4(u1_struct_0(A),F,k37_aofa_a00(A)),G)) & v1_funct_1(k1_funct_1(k1_msafree4(u1_struct_0(A),F,k37_aofa_a00(A)),G)) ) ) )).
fof(fc17_binop_2,axiom,( v1_funct_1(k11_binop_2) & v1_funct_2(k11_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_setwiseo(k11_binop_2,k1_numbers) )).
fof(fc17_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => ~ v1_xboole_0(k3_xxreal_1(k2_xxreal_0,A)) ) )).
fof(fc17_card_1,axiom,( ! [A] : v3_card_1(k1_tarski(A),1) )).
fof(fc17_cayldick,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v3_cayldick(A) & l1_cayldick(A) & v9_struct_0(B,A) & m1_subset_1(B,u1_struct_0(A)) ) => v9_struct_0(k2_cayldick(A,B),A) ) )).
fof(fc17_circcomb,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(fc17_closure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc17_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc17_cohsp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc17_compos_0,axiom,( v2_compos_0(k2_tarski(k3_xtuple_0(k5_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(k5_numbers,k1_xboole_0,k1_xboole_0),k3_xtuple_0(1,k1_xboole_0,k1_xboole_0))) )).
fof(fc17_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_compos_1(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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),k4_ordinal1) & 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) ) ) )).
fof(fc17_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v1_relat_1(k3_comput_1(2,A)) & v4_relat_1(k3_comput_1(2,A),k3_finseq_2(k4_ordinal1)) & 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) ) ) )).
fof(fc17_dickson,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v1_orders_2(k4_yellow_1(A,k7_funcop_1(A,k11_dickson))) & v4_dickson(k4_yellow_1(A,k7_funcop_1(A,k11_dickson))) ) ) )).
fof(fc17_euclid_9,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc17_exchsort,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc17_finseq_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc17_finset_1,axiom,( ! [A] : ( v1_finset_1(A) => v1_finset_1(k1_zfmisc_1(A)) ) )).
fof(fc17_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc17_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v12_fomodel1(k31_fomodel1(A),A) ) )).
fof(fc17_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) )).
fof(fc17_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v3_fomodel4(B,A) & v3_fomodel4(C,A) ) => v3_fomodel4(k2_xboole_0(B,C),A) ) )).
fof(fc17_funcop_1,axiom,( ! [A] : ! [B] : v4_relat_1(k2_funcop_1(A,B),A) )).
fof(fc17_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc17_funct_9,axiom,( v1_funct_1(k26_sin_cos) & v2_funct_9(k26_sin_cos) )).
fof(fc17_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc17_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) ) => ~ v1_xboole_0(k8_gate_1(A,B,C)) ) )).
fof(fc17_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => v1_glib_001(k9_glib_001(A,B,C,D),A) ) )).
fof(fc17_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => v1_cat_1(k27_grcat_1(A)) ) )).
fof(fc17_group_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc17_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc17_index_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) ) )).
fof(fc17_lukasi_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc17_mazurulm,axiom,( ! [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) & 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) ) ) )).
fof(fc17_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v2_membered(B) ) => v1_xboole_0(k8_member_1(B,A)) ) )).
fof(fc17_membered,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_int_1(B) ) => v5_membered(k2_tarski(A,B)) ) )).
fof(fc17_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k5_numbers) ) ) )).
fof(fc17_mod_4,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc17_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v10_msafree4(C,A,B) & m1_msualg_4(C,A,B,B) ) => ( v1_relat_1(k1_funct_1(C,D)) & v4_rewrite1(k1_funct_1(C,D)) ) ) )).
fof(fc17_nat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ v8_ordinal1(A) & ~ v8_ordinal1(B) & ~ v8_ordinal1(C) & ~ v8_ordinal1(D) & ~ v8_ordinal1(E) & ~ v8_ordinal1(F) & ~ v8_ordinal1(G) ) => v1_setfam_1(k5_enumset1(A,B,C,D,E,F,G)) ) )).
fof(fc17_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( v1_relat_1(k12_nat_3(A)) & v4_relat_1(k12_nat_3(A),k8_newton) & v1_funct_1(k12_nat_3(A)) & v1_partfun1(k12_nat_3(A),k8_newton) & v2_pre_poly(k12_nat_3(A)) ) ) )).
fof(fc17_ordinal6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc17_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc17_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_xreal_0(C) ) => ( v1_relat_1(k1_funct_7(A,B,C)) & v1_funct_1(k1_funct_7(A,B,C)) & v3_valued_0(k1_funct_7(A,B,C)) ) ) )).
fof(fc17_prvect_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_prvect_2(A) & v1_relat_1(B) & ~ v1_xboole_0(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)) ) ) )).
fof(fc17_ratfunc1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc17_relat_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_relat_1(A) ) => ( v1_xboole_0(k5_relat_1(A,B)) & v1_relat_1(k5_relat_1(A,B)) ) ) )).
fof(fc17_relat_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_2(A) ) => ( v1_relat_1(k2_relat_1(A)) & v4_relat_2(k2_relat_1(A)) ) ) )).
fof(fc17_rfunct_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc17_scmfsa10,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc17_scmfsa6c,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc17_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc17_scmpds_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_int_1(A) & v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) & v7_ordinal1(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)),k4_ordinal1) & v5_relat_1(k3_afinsq_1(k7_scmpds_2(B,A,C)),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k3_afinsq_1(k7_scmpds_2(B,A,C))) & 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))) ) ) )).
fof(fc17_scmpds_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc17_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) & v2_scmpds_4(A) & v3_scmpds_4(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & 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_relat_1(k4_scmpds_6(C,D,A,B)) & v4_relat_1(k4_scmpds_6(C,D,A,B),k4_ordinal1) & v5_relat_1(k4_scmpds_6(C,D,A,B),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k4_scmpds_6(C,D,A,B)) & 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)) ) ) )).
fof(fc17_scmring3,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) & v7_ordinal1(B) ) => v1_amistd_1(k4_xtuple_0(k8_scmring2(A,B)),k7_card_1(2),k1_scmring2(A)) ) )).
fof(fc17_sfmastr1,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) & 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)) ) ) )).
fof(fc17_simplex0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc17_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k18_sin_cos,k1_rcomp_1(k28_sin_cos,k3_xcmplx_0(2,k28_sin_cos)))) & v2_funct_1(k5_relat_1(k18_sin_cos,k1_rcomp_1(k28_sin_cos,k3_xcmplx_0(2,k28_sin_cos)))) )).
fof(fc17_struct_0,axiom,( ! [A] : ( ( v8_struct_0(A) & l1_struct_0(A) ) => ( v7_ordinal1(k7_struct_0(A)) & v1_card_1(k7_struct_0(A)) ) ) )).
fof(fc17_tex_4,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc17_topgrp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc17_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc17_topreala,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_xxreal_0(A) & v1_xreal_0(A) & ~ v2_xxreal_0(B) & v1_xreal_0(B) & ~ v3_xxreal_0(C) & v1_xreal_0(C) & ~ v3_xxreal_0(D) & v1_xreal_0(D) ) => ~ v2_struct_0(k1_topreala(A,C,B,D)) ) )).
fof(fc17_toprealb,axiom,( ! [A] : ( ( 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)))) ) ) )).
fof(fc17_toprealc,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc17_tops_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc17_trees_3,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & 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)) ) ) )).
fof(fc17_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v3_valued_0(A) & v1_relat_1(B) ) => v3_valued_0(k3_xboole_0(A,B)) ) )).
fof(fc17_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc17_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc17_waybel23,axiom,( ! [A] : ! [B] : ( ( 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(k1_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)),k1_yellow_1(k7_waybel_0(k5_yellow_0(A,B))),A) & v18_waybel_0(k3_waybel23(A,k5_yellow_0(A,B)),k1_yellow_1(k7_waybel_0(k5_yellow_0(A,B))),A) ) ) )).
fof(fc17_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc17_waybel_4,axiom,( ! [A] : ( ( 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(k1_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A))) & v5_orders_3(k9_waybel_4(A),k1_yellow_1(k3_waybel_4(A)),k8_waybel_4(A)) ) ) )).
fof(fc17_waybel_9,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ( v3_orders_2(k3_waybel_9(A)) & v6_waybel_0(k3_waybel_9(A),A) ) ) )).
fof(fc17_xreal_0,axiom,( ! [A] : ! [B] : ( ( ~ v3_xxreal_0(A) & v1_xreal_0(A) & ~ v2_xxreal_0(B) & v1_xreal_0(B) ) => ~ v3_xxreal_0(k6_xcmplx_0(A,B)) ) )).
fof(fc17_xxreal_2,axiom,( v6_xxreal_2(k1_numbers) )).
fof(fc17_xxreal_3,axiom,( ! [A] : ( ( v1_xxreal_0(A) & v3_xxreal_0(A) ) => ( v1_xxreal_0(k2_xxreal_3(A)) & v2_xxreal_0(k2_xxreal_3(A)) ) ) )).
fof(fc17_yellow_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v2_struct_0(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) ) => ( v1_orders_2(k5_yellow_1(A,B)) & v2_lattice3(k5_yellow_1(A,B)) ) ) )).
fof(fc17_yellow_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc18_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc18_abian,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc18_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => v5_relat_1(k6_afinsq_1(B,C),A) ) )).
fof(fc18_algstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc18_algstr_4,axiom,( ! [A] : ! [B] : ( 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))) ) ) )).
fof(fc18_ami_6,axiom,( ! [A] : ( v7_ordinal1(A) => v1_amistd_1(k4_xtuple_0(k7_ami_3(A)),k7_card_1(2),k1_ami_3) ) )).
fof(fc18_aofa_a00,axiom,( ! [A] : ( ~ v1_xboole_0(A) => v2_relat_1(k5_finseq_1(A)) ) )).
fof(fc18_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(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) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) & v4_aofa_a01(D,A,B,C) & l4_aofa_a00(D,A,B,C) & v4_msualg_1(E,A) & v4_msafree4(E,A,C) & v17_aofa_a00(E,A) & v20_aofa_a00(E,4,1,A) & v22_aofa_a00(E,A,1,1,11) & l3_msualg_1(E,A) & m1_subset_1(F,k13_aofa_a00(A,C,E,u4_aofa_a00(A,B,C,D))) & v3_aofa_a01(G,A,B,C,u4_aofa_a00(A,B,C,D),k37_aofa_a00(A)) & m1_subset_1(G,k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),k37_aofa_a00(A))) ) => ( v5_relat_1(k1_funct_1(k1_msafree4(u1_struct_0(A),F,k37_aofa_a00(A)),G),k4_numbers) & v5_ordinal1(k1_funct_1(k1_msafree4(u1_struct_0(A),F,k37_aofa_a00(A)),G)) & v1_finset_1(k1_funct_1(k1_msafree4(u1_struct_0(A),F,k37_aofa_a00(A)),G)) ) ) )).
fof(fc18_binop_2,axiom,( v1_funct_1(k17_binop_2) & v1_funct_2(k17_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & v1_setwiseo(k17_binop_2,k3_numbers) )).
fof(fc18_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => ~ v1_xboole_0(k4_xxreal_1(k2_xxreal_0,A)) ) )).
fof(fc18_card_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc18_cayldick,axiom,( ! [A] : ! [B] : ( ( ~ v6_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) & v8_rlvect_1(A) & v3_normsp_0(A) & v2_vectsp_1(A) & v3_cayldick(A) & l1_cayldick(A) & ~ v9_struct_0(B,A) & m1_subset_1(B,u1_struct_0(A)) ) => ~ v9_struct_0(k2_cayldick(A,B),A) ) )).
fof(fc18_circcomb,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc18_closure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc18_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc18_compos_0,axiom,( v5_compos_0(k1_tarski(k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0))) )).
fof(fc18_compos_1,axiom,( ! [A] : ! [B] : ( ( l1_compos_1(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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),k4_ordinal1) & 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) ) ) )).
fof(fc18_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v1_relat_1(k3_comput_1(3,A)) & v4_relat_1(k3_comput_1(3,A),k3_finseq_2(k4_ordinal1)) & 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) ) ) )).
fof(fc18_dickson,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v1_orders_2(k4_yellow_1(A,k7_funcop_1(A,k11_dickson))) & v3_dickson(k4_yellow_1(A,k7_funcop_1(A,k11_dickson))) ) ) )).
fof(fc18_euclid_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & v1_relat_1(D) & v1_funct_1(D) & v3_card_1(D,A) & v1_finseq_1(D) ) => ( v1_relat_1(k1_funct_7(D,B,C)) & v1_funct_1(k1_funct_7(D,B,C)) & v3_card_1(k1_funct_7(D,B,C),A) ) ) )).
fof(fc18_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) )).
fof(fc18_finseq_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc18_finset_1,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k5_xboole_0(A,B)) ) )).
fof(fc18_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ~ v1_xboole_0(k31_fomodel1(A)) ) )).
fof(fc18_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v12_fomodel1(k24_fomodel2(A,k5_numbers),A) ) )).
fof(fc18_fomodel3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc18_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v3_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) ) )).
fof(fc18_funcop_1,axiom,( ! [A] : ! [B] : v4_relat_1(k16_funcop_1(A,B),k1_tarski(A)) )).
fof(fc18_funct_1,axiom,( ! [A] : ( ( ~ v1_zfmisc_1(A) & v1_relat_1(A) & v1_funct_1(A) ) => ~ v1_zfmisc_1(k9_xtuple_0(A)) ) )).
fof(fc18_funct_9,axiom,( v1_funct_1(k27_sin_cos) & v2_funct_9(k27_sin_cos) )).
fof(fc18_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc18_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_xboole_0(A) => v1_xboole_0(k8_gate_1(A,B,C)) ) )).
fof(fc18_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => v2_glib_001(k9_glib_001(A,B,C,D),A) ) )).
fof(fc18_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ~ v1_xboole_0(k28_grcat_1(A)) ) )).
fof(fc18_group_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc18_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc18_member_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v2_membered(A) & ~ v1_xboole_0(B) & v2_membered(B) ) => ~ v1_xboole_0(k8_member_1(A,B)) ) )).
fof(fc18_membered,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => v6_membered(k2_tarski(A,B)) ) )).
fof(fc18_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc18_nat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( ~ v8_ordinal1(A) & ~ v8_ordinal1(B) & ~ v8_ordinal1(C) & ~ v8_ordinal1(D) & ~ v8_ordinal1(E) & ~ v8_ordinal1(F) & ~ v8_ordinal1(G) & ~ v8_ordinal1(H) ) => v1_setfam_1(k6_enumset1(A,B,C,D,E,F,G,H)) ) )).
fof(fc18_nat_3,axiom,( v1_xboole_0(k13_pre_poly(k12_nat_3(1))) )).
fof(fc18_ordinal6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) ) => v3_ordinal6(k3_afinsq_1(A)) ) )).
fof(fc18_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc18_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc18_prvect_3,axiom,( ! [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) & 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)) ) ) )).
fof(fc18_ratfunc1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(fc18_relat_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_xboole_0(B) ) => ( v1_xboole_0(k6_relat_1(B,A)) & v1_relat_1(k6_relat_1(B,A)) ) ) )).
fof(fc18_relat_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_2(A) & v1_relat_1(B) ) => v4_relat_2(k3_xboole_0(A,B)) ) )).
fof(fc18_rfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc18_scmfsa10,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(k7_card_1(3),k1_scmfsa_2,k15_scmfsa_2(A,B,C))) ) )).
fof(fc18_scmfsa6c,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc18_scmfsa_2,axiom,( v1_extpro_1(k1_scmfsa_2,k7_card_1(3)) & v3_extpro_1(k1_scmfsa_2,k7_card_1(3)) )).
fof(fc18_scmpds_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_int_1(A) & v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) & v7_ordinal1(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)),k4_ordinal1) & v5_relat_1(k3_afinsq_1(k8_scmpds_2(B,A,C)),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k3_afinsq_1(k8_scmpds_2(B,A,C))) & 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))) ) ) )).
fof(fc18_scmpds_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc18_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) & v2_compos_1(A,k1_scmpds_2) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & 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_relat_1(k4_scmpds_6(C,D,A,B)) & v4_relat_1(k4_scmpds_6(C,D,A,B),k4_ordinal1) & v5_relat_1(k4_scmpds_6(C,D,A,B),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k4_scmpds_6(C,D,A,B)) & 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) ) ) )).
fof(fc18_scmring3,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) & v7_ordinal1(B) ) => v2_amistd_1(k8_scmring2(A,B),k7_card_1(2),k1_scmring2(A)) ) )).
fof(fc18_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v6_scmyciel(A) ) => ( v4_scmyciel(k6_scmyciel(A)) & v12_scmyciel(k6_scmyciel(A)) ) ) )).
fof(fc18_sfmastr1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc18_simplex0,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc18_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k18_sin_cos,k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) & v2_funct_1(k5_relat_1(k18_sin_cos,k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(fc18_struct_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & l1_struct_0(A) ) => ( v7_ordinal1(k7_struct_0(A)) & ~ v8_ordinal1(k7_struct_0(A)) ) ) )).
fof(fc18_tex_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc18_topgrp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc18_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v8_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)) ) )).
fof(fc18_toprealb,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(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))))) ) ) )).
fof(fc18_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc18_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v6_trees_3(A) ) => ( v1_relat_1(k1_funct_6(A)) & v1_funct_1(k1_funct_6(A)) & v1_finseq_1(k1_funct_6(A)) & v4_trees_3(k1_funct_6(A)) ) ) )).
fof(fc18_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v3_valued_0(A) & v1_relat_1(B) ) => v3_valued_0(k4_xboole_0(A,B)) ) )).
fof(fc18_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc18_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc18_waybel23,axiom,( ! [A] : ! [B] : ( ( 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(k1_yellow_1(k7_waybel_0(k5_yellow_0(A,B))))) & v18_waybel_0(k5_waybel23(A,B),A,k1_yellow_1(k7_waybel_0(k5_yellow_0(A,B)))) ) ) )).
fof(fc18_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc18_waybel_4,axiom,( ! [A] : ( ( 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(k1_yellow_1(k3_waybel_4(A)))) & v5_orders_3(k10_waybel_4(A),k8_waybel_4(A),k1_yellow_1(k3_waybel_4(A))) ) ) )).
fof(fc18_waybel_9,axiom,( ! [A] : ( ( v5_orders_2(A) & l1_orders_2(A) ) => ( v5_orders_2(k3_waybel_9(A)) & v6_waybel_0(k3_waybel_9(A),A) ) ) )).
fof(fc18_xreal_0,axiom,( ! [A] : ! [B] : ( ( ~ v3_xxreal_0(A) & v1_xreal_0(A) & ~ v2_xxreal_0(B) & v1_xreal_0(B) ) => ~ v2_xxreal_0(k6_xcmplx_0(B,A)) ) )).
fof(fc18_xxreal_2,axiom,( ! [A] : ! [B] : ( ( v2_membered(A) & v6_xxreal_2(A) & v2_membered(B) & v6_xxreal_2(B) ) => v6_xxreal_2(k3_xboole_0(A,B)) ) )).
fof(fc18_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc18_yellow_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v2_struct_0(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) ) => ( v1_orders_2(k5_yellow_1(A,B)) & v1_lattice3(k5_yellow_1(A,B)) ) ) )).
fof(fc18_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(k6_yellow_6(A)) ) )).
fof(fc19_abcmiz_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc19_abian,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v2_setfam_1(k1_zfmisc_1(A)) ) )).
fof(fc19_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(fc19_algstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc19_algstr_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc19_ami_6,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ v4_compos_0(k7_ami_3(A),u1_compos_1(k1_ami_3)) & v2_amistd_1(k7_ami_3(A),k7_card_1(2),k1_ami_3) & ~ v4_amistd_1(k7_ami_3(A),k7_card_1(2),k1_ami_3) ) ) )).
fof(fc19_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) ) => v2_relat_1(k11_finseq_1(A,B,C)) ) )).
fof(fc19_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(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) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) & v4_aofa_a01(D,A,B,C) & l4_aofa_a00(D,A,B,C) & v4_msualg_1(E,A) & v4_msafree4(E,A,C) & v17_aofa_a00(E,A) & v20_aofa_a00(E,4,1,A) & v22_aofa_a00(E,A,1,1,11) & l3_msualg_1(E,A) & m1_subset_1(F,k13_aofa_a00(A,C,E,u4_aofa_a00(A,B,C,D))) & v3_aofa_a01(G,A,B,C,u4_aofa_a00(A,B,C,D),k37_aofa_a00(A)) & m1_subset_1(G,k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),k37_aofa_a00(A))) ) => ( v1_finset_1(k10_xtuple_0(k1_funct_1(k1_msafree4(u1_struct_0(A),F,k37_aofa_a00(A)),G))) & v5_membered(k10_xtuple_0(k1_funct_1(k1_msafree4(u1_struct_0(A),F,k37_aofa_a00(A)),G))) ) ) )).
fof(fc19_binop_2,axiom,( v1_funct_1(k22_binop_2) & v1_funct_2(k22_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & v1_setwiseo(k22_binop_2,k4_numbers) )).
fof(fc19_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => ~ v1_xboole_0(k2_xxreal_1(A,k1_xxreal_0)) ) )).
fof(fc19_card_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc19_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ( ~ v2_struct_0(k4_cayldick(A)) & v1_cayldick(k4_cayldick(A)) ) ) )).
fof(fc19_circcomb,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(fc19_closure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc19_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc19_compos_0,axiom,( v5_compos_0(k2_tarski(k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0),k3_xtuple_0(1,k1_xboole_0,k1_xboole_0))) )).
fof(fc19_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_compos_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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) ) ) )).
fof(fc19_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v1_relat_1(k5_comput_1(1,A)) & v4_relat_1(k5_comput_1(1,A),k3_finseq_2(k4_ordinal1)) & 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) ) ) )).
fof(fc19_dickson,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v1_orders_2(k4_yellow_1(A,k7_funcop_1(A,k11_dickson))) & v5_orders_2(k4_yellow_1(A,k7_funcop_1(A,k11_dickson))) ) ) )).
fof(fc19_euclid_9,axiom,( v7_struct_0(k3_pcomps_1(k14_euclid(k5_numbers))) )).
fof(fc19_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v1_finset_1(k9_funct_7(A,B,C)) ) )).
fof(fc19_finseq_1,axiom,( ! [A] : ! [B] : ~ v1_xboole_0(k10_finseq_1(A,B)) )).
fof(fc19_finset_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k9_xtuple_0(A)) ) )).
fof(fc19_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc19_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v12_fomodel1(k27_fomodel1(A),A) ) )).
fof(fc19_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k42_fomodel1(A,k43_fomodel1(A,k1_fomodel2(A)),C),D),A,k1_nat_1(B,1)) ) )).
fof(fc19_fomodel3,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc19_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v6_fomodel4(B,A) & m1_subset_1(B,k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A)))) ) => v7_fomodel4(k1_tarski(B),A) ) )).
fof(fc19_funcop_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => v1_funcop_1(k16_funcop_1(A,B)) ) )).
fof(fc19_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v3_relat_1(A) & v1_funct_1(A) ) => v1_xboole_0(k1_funct_1(A,B)) ) )).
fof(fc19_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc19_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_xboole_0(A) => v1_xboole_0(k8_gate_1(B,A,C)) ) )).
fof(fc19_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => v3_glib_001(k9_glib_001(A,B,C,D),A) ) )).
fof(fc19_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => v1_cat_1(k29_grcat_1(A)) ) )).
fof(fc19_group_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc19_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ( ~ v2_struct_0(k10_hahnban1(A)) & v1_rlvect_1(k10_hahnban1(A)) ) ) )).
fof(fc19_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc19_member_1,axiom,( ! [A] : ! [B] : ( ( v2_membered(A) & v2_membered(B) ) => v2_membered(k8_member_1(A,B)) ) )).
fof(fc19_membered,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => v1_membered(k1_enumset1(A,B,C)) ) )).
fof(fc19_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc19_nat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ( ( ~ v8_ordinal1(A) & ~ v8_ordinal1(B) & ~ v8_ordinal1(C) & ~ v8_ordinal1(D) & ~ v8_ordinal1(E) & ~ v8_ordinal1(F) & ~ v8_ordinal1(G) & ~ v8_ordinal1(H) & ~ v8_ordinal1(I) ) => v1_setfam_1(k7_enumset1(A,B,C,D,E,F,G,H,I)) ) )).
fof(fc19_nat_3,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_int_2(A) & v7_ordinal1(B) & ~ v8_ordinal1(B) ) => v3_card_1(k13_pre_poly(k12_nat_3(k1_newton(A,B))),1) ) )).
fof(fc19_ordinal6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v2_card_3(k1_tarski(A)) ) )).
fof(fc19_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc19_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc19_prvect_3,axiom,( ! [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) & 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)) ) ) )).
fof(fc19_ratfunc1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & l5_algstr_0(A) ) => ~ v4_ratfunc1(k8_ratfunc1(A),A) ) )).
fof(fc19_relat_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_xboole_0(B) ) => v1_xboole_0(k7_relat_1(A,B)) ) )).
fof(fc19_relat_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_2(A) & v1_relat_1(B) ) => v4_relat_2(k3_xboole_0(B,A)) ) )).
fof(fc19_rfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc19_scmfsa10,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc19_scmfsa6c,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc19_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v4_memstr_0(k16_funcop_1(A,B),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(fc19_scmpds_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_int_1(A) & v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) & v7_ordinal1(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)),k4_ordinal1) & v5_relat_1(k3_afinsq_1(k9_scmpds_2(B,A,C)),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k3_afinsq_1(k9_scmpds_2(B,A,C))) & 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))) ) ) )).
fof(fc19_scmpds_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc19_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & 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_relat_1(k9_scmpds_6(B,C,A)) & v4_relat_1(k9_scmpds_6(B,C,A),k4_ordinal1) & v5_relat_1(k9_scmpds_6(B,C,A),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k9_scmpds_6(B,C,A)) & 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)) ) ) )).
fof(fc19_scmring3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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))) & v7_ordinal1(C) ) => v1_amistd_1(k4_xtuple_0(k9_scmring2(A,C,B)),k7_card_1(2),k1_scmring2(A)) ) )).
fof(fc19_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v12_scmyciel(A) ) => ( v4_scmyciel(k6_scmyciel(A)) & v6_scmyciel(k6_scmyciel(A)) ) ) )).
fof(fc19_simplex0,axiom,( ! [A] : ( ( v4_matroid0(A) & l1_pre_topc(A) ) => ( v1_xxreal_0(k6_simplex0(A)) & v1_int_1(k6_simplex0(A)) ) ) )).
fof(fc19_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k18_sin_cos,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos))) & v2_funct_1(k5_relat_1(k18_sin_cos,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos))) )).
fof(fc19_struct_0,axiom,( ! [A] : ! [B] : ( ( v1_card_1(A) & v13_struct_0(B,A) & l1_struct_0(B) ) => v3_card_1(u1_struct_0(B),A) ) )).
fof(fc19_tex_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc19_topgrp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc19_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc19_toprealb,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc19_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc19_trees_3,axiom,( ! [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) ) => ( v1_relat_1(k13_funct_3(A,B)) & v1_funct_1(k13_funct_3(A,B)) & v3_trees_2(k13_funct_3(A,B)) ) ) )).
fof(fc19_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v5_relat_1(A,k3_numbers) & v1_relat_1(B) ) => v5_relat_1(k3_xboole_0(A,B),k3_numbers) ) )).
fof(fc19_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc19_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(fc19_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc19_waybel_4,axiom,( ! [A] : ( ( 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(k1_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A))) ) ) )).
fof(fc19_waybel_9,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ( v4_orders_2(k3_waybel_9(A)) & v6_waybel_0(k3_waybel_9(A),A) ) ) )).
fof(fc19_xreal_0,axiom,( ! [A] : ! [B] : ( ( v2_xxreal_0(A) & v1_xreal_0(A) & ~ v2_xxreal_0(B) & v1_xreal_0(B) ) => v2_xxreal_0(k6_xcmplx_0(A,B)) ) )).
fof(fc19_xxreal_2,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => ~ v1_xxreal_2(k3_xxreal_1(A,B)) ) )).
fof(fc19_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc19_yellow_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k4_yellow_1(u1_struct_0(B),C)) & v4_orders_2(k4_yellow_1(u1_struct_0(B),C)) & v7_waybel_0(k4_yellow_1(u1_struct_0(B),C)) ) ) )).
fof(fc1_abcmiz_0,axiom,( ! [A] : ( ( v1_abcmiz_0(A) & l1_orders_2(A) ) => v1_rewrite1(u1_orders_2(A)) ) )).
fof(fc1_abcmiz_1,axiom,( ! [A] : ( v1_xboole_0(A) => v1_xboole_0(k1_abcmiz_1(A)) ) )).
fof(fc1_abcmiz_a,axiom,( v1_msualg_1(k27_abcmiz_1) & v1_instalg1(k27_abcmiz_1) & v1_abcmiz_1(k27_abcmiz_1) & v1_abcmiz_a(k27_abcmiz_1) )).
fof(fc1_abian,axiom,( ! [A] : ( v1_int_1(A) => v1_abian(k3_xcmplx_0(2,A)) ) )).
fof(fc1_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k9_complex1(A)) ) )).
fof(fc1_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v7_ordinal1(k9_xtuple_0(A)) ) )).
fof(fc1_afproj,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc1_afvect0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_afvect01,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_algspec1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc1_algstr_1,axiom,( v3_rlvect_1(k3_algstr_0) & v4_rlvect_1(k3_algstr_0) & v1_algstr_1(k3_algstr_0) & v4_algstr_1(k3_algstr_0) )).
fof(fc1_algstr_3,axiom,( ~ v2_struct_0(k3_algstr_3) & v1_algstr_3(k3_algstr_3) )).
fof(fc1_algstr_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) & v7_ordinal1(C) ) => ( v1_relat_1(k5_relat_1(B,C)) & v5_ordinal1(k5_relat_1(B,C)) ) ) )).
fof(fc1_altcat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc1_altcat_2,axiom,( ! [A] : ( 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)) ) )).
fof(fc1_altcat_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc1_altcat_5,axiom,( ! [A] : ( ~ 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)) & v1_altcat_5(k7_altcat_1(A)) ) ) )).
fof(fc1_ami_2,axiom,( ~ v1_xboole_0(k1_ami_2) )).
fof(fc1_ami_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ~ v1_setfam_1(k6_card_1(A)) ) )).
fof(fc1_ami_5,axiom,( ~ v1_finset_1(k8_struct_0(k1_ami_3)) )).
fof(fc1_ami_6,axiom,( v1_xboole_0(k2_amistd_1(k7_card_1(2),k1_ami_3,k2_compos_1(k1_ami_3))) )).
fof(fc1_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ( v1_extpro_1(k4_amistd_1(A),A) & v2_ami_wstd(k4_amistd_1(A),A) ) ) )).
fof(fc1_amistd_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc1_analmetr,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) ) )).
fof(fc1_analoaf,axiom,( ! [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) ) => ( ~ v2_struct_0(k2_analoaf(A)) & v1_analoaf(k2_analoaf(A)) ) ) )).
fof(fc1_analort,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) ) )).
fof(fc1_anproj_1,axiom,( ! [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) & l1_rlvect_1(A) ) => ~ v1_xboole_0(k3_anproj_1(A)) ) )).
fof(fc1_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => ( v1_collsp(k5_anproj_1(A)) & v2_collsp(k5_anproj_1(A)) & v3_collsp(k5_anproj_1(A)) ) ) )).
fof(fc1_aofa_000,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => v2_relat_1(k10_finseq_1(A,B)) ) )).
fof(fc1_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & ~ v1_xboole_0(D) ) => ( v1_relat_1(k1_funct_7(B,C,D)) & v2_relat_1(k1_funct_7(B,C,D)) & v1_funct_1(k1_funct_7(B,C,D)) ) ) )).
fof(fc1_aofa_i00,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_finset_1(B) ) => ~ v1_finset_1(k1_funct_2(A,B)) ) )).
fof(fc1_armstrng,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_pre_poly(A) ) => v1_finseq_1(k1_funct_1(A,B)) ) )).
fof(fc1_arrow,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_arrow(A)) ) )).
fof(fc1_arytm_0,axiom,( ! [A] : ! [B] : ~ v8_ordinal1(k4_tarski(A,B)) )).
fof(fc1_arytm_2,axiom,( ~ v1_xboole_0(k1_arytm_2) )).
fof(fc1_arytm_3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v7_ordinal1(A) & v3_ordinal1(B) & v7_ordinal1(B) ) => ( v3_ordinal1(k6_ordinal3(A,B)) & v7_ordinal1(k6_ordinal3(A,B)) ) ) )).
fof(fc1_asympt_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_funct_1(k5_asympt_0(A,B)) & v1_funct_2(k5_asympt_0(A,B),k4_ordinal1,k1_numbers) & v2_asympt_0(k5_asympt_0(A,B)) ) ) )).
fof(fc1_asympt_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) ) => ( v1_funct_1(k1_asympt_1(A,B,C)) & v1_funct_2(k1_asympt_1(A,B,C),k4_ordinal1,k1_numbers) & v4_asympt_0(k1_asympt_1(A,B,C)) ) ) )).
fof(fc1_autalg_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc1_bagorder,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_bcialg_2,axiom,( ! [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) ) => ( v10_bcialg_1(k4_struct_0(A),A) & v1_bcialg_2(k4_struct_0(A),A) ) ) )).
fof(fc1_bcialg_4,axiom,( v13_struct_0(k2_bcialg_4,1) & v1_bcialg_4(k2_bcialg_4) )).
fof(fc1_bcialg_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc1_bhsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) ) )).
fof(fc1_bhsp_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & v1_bhsp_3(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_bhsp_3(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k2_normsp_1(A,B,C)) & v1_funct_2(k2_normsp_1(A,B,C),k4_ordinal1,u1_struct_0(A)) & v1_bhsp_3(k2_normsp_1(A,B,C),A) ) ) )).
fof(fc1_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc1_binop_2,axiom,( v1_funct_1(k3_binop_2) & v1_funct_2(k3_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & v1_binop_1(k3_binop_2,k2_numbers) & v2_binop_1(k3_binop_2,k2_numbers) )).
fof(fc1_bintree1,axiom,( ~ v1_xboole_0(k2_trees_1(k5_numbers)) & v1_trees_1(k2_trees_1(k5_numbers)) & v1_bintree1(k2_trees_1(k5_numbers)) )).
fof(fc1_bintree2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree1(A) & v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( 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),k4_ordinal1) ) ) )).
fof(fc1_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc1_borsuk_2,axiom,( ! [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) & v1_t_0topsp(k3_struct_0(A),A,A) ) ) )).
fof(fc1_borsuk_3,axiom,( ! [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)) & v3_tops_2(k3_struct_0(A),A,A) ) ) )).
fof(fc1_borsuk_4,axiom,( ~ v2_struct_0(k1_borsuk_4) & v1_pre_topc(k1_borsuk_4) )).
fof(fc1_borsuk_5,axiom,( v2_pre_topc(k3_topmetr) & v1_borsuk_2(k3_topmetr) )).
fof(fc1_borsuk_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc1_borsuk_7,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_bspace,axiom,( ! [A] : ( ~ 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)) ) )).
fof(fc1_bvfunc26,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_c0sp2,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc1_calcul_2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => v1_finset_1(k1_calcul_2(A,B)) ) )).
fof(fc1_cantor_1,axiom,( ! [A] : ( l1_pre_topc(A) => v1_cantor_1(u1_pre_topc(A),A) ) )).
fof(fc1_card_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k1_card_1(A)) & v1_card_1(k1_card_1(A)) ) ) )).
fof(fc1_card_2,axiom,( ! [A] : ! [B] : ~ v7_ordinal1(k4_tarski(A,B)) )).
fof(fc1_card_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_card_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) ) => v3_ordinal1(k3_card_3(A)) ) )).
fof(fc1_card_fil,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc1_card_fin,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & ~ v1_xboole_0(A) ) => ~ v1_xboole_0(k4_classes1(A)) ) )).
fof(fc1_cardfin2,axiom,( ! [A] : ( v1_xreal_0(A) => v2_xxreal_0(k23_sin_cos(A)) ) )).
fof(fc1_cat_1,axiom,( ! [A] : ! [B] : ( ~ 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)) ) )).
fof(fc1_cat_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) )).
fof(fc1_cat_4,axiom,( ! [A] : ! [B] : ( ~ 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)) ) )).
fof(fc1_cat_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) )).
fof(fc1_catalan1,axiom,( ! [A] : ( v7_ordinal1(A) => ( v7_ordinal1(k1_catalan1(A)) & v1_xreal_0(k1_catalan1(A)) ) ) )).
fof(fc1_catalan2,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => v5_relat_1(k2_funcop_1(A,B),k4_ordinal1) ) )).
fof(fc1_catalg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_cayldick,axiom,( ! [A] : ! [B] : ( ( ~ 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) & ~ v9_struct_0(B,A) & m1_subset_1(B,u1_struct_0(A)) ) => ( v1_xreal_0(k2_normsp_0(A,B)) & v2_xxreal_0(k2_normsp_0(A,B)) ) ) )).
fof(fc1_cayley,axiom,( ! [A] : v2_funct_2(k1_partit_2(A,k1_xboole_0),k1_xboole_0) )).
fof(fc1_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v5_clvect_1(k8_cfuncdom(A)) & v1_cfuncdom(k8_cfuncdom(A)) ) ) )).
fof(fc1_cc0sp2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc1_cfdiff_1,axiom,( ! [A] : ( ( v2_xxreal_0(A) & v1_xreal_0(A) ) => ( v1_funct_1(k1_cfdiff_1(A)) & v1_funct_2(k1_cfdiff_1(A),k4_ordinal1,k2_numbers) & v2_comseq_2(k1_cfdiff_1(A)) ) ) )).
fof(fc1_cfuncdom,axiom,( ! [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)) & v7_valued_2(k1_cfuncdom(A)) ) )).
fof(fc1_cgames_1,axiom,( ! [A] : ( v3_ordinal1(A) => ~ v1_xboole_0(k2_cgames_1(A)) ) )).
fof(fc1_chain_1,axiom,( ! [A] : ! [B] : ( ~ v1_zfmisc_1(A) => ~ v1_zfmisc_1(k2_xboole_0(A,B)) ) )).
fof(fc1_circcmb2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc1_circcmb3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_circcomb,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(fc1_circtrm1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc1_circuit1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc1_ckspace1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) & ~ v1_xboole_0(C) & v1_pdiff_7(C,A) & m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) ) => ( ~ v1_xboole_0(k1_ckspace1(A,B,C)) & v3_c0sp1(k1_ckspace1(A,B,C),k12_funcsdom(C)) & v4_c0sp1(k1_ckspace1(A,B,C),k12_funcsdom(C)) ) ) )).
fof(fc1_classes1,axiom,( ! [A] : ~ v1_xboole_0(k1_classes1(A)) )).
fof(fc1_classes2,axiom,( ! [A] : v2_classes1(k1_classes1(A)) )).
fof(fc1_clopban1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => ( ~ v2_struct_0(k7_clopban2(A)) & v36_algstr_0(k7_clopban2(A)) ) ) )).
fof(fc1_clopban3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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,k4_ordinal1,u1_struct_0(A)) & v2_clopban3(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k3_normsp_0(A,B)) & v1_funct_2(k3_normsp_0(A,B),k4_ordinal1,k1_numbers) & v1_series_1(k3_normsp_0(A,B)) ) ) )).
fof(fc1_clopban4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & 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),k4_ordinal1,u1_struct_0(A)) & v2_clopban3(k1_clopban4(A,B),A) ) ) )).
fof(fc1_closure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc1_closure2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_clvect_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc1_coh_sp,axiom,( ! [A] : ~ v1_xboole_0(k3_coh_sp(A)) )).
fof(fc1_cohsp_1,axiom,( v1_classes1(k1_tarski(k1_xboole_0)) & v1_coh_sp(k1_tarski(k1_xboole_0)) )).
fof(fc1_compact1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc1_compl_sp,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ( v1_funct_1(k1_compl_sp(A,B)) & v1_funct_2(k1_compl_sp(A,B),k4_ordinal1,k1_numbers) & v3_valued_0(k1_compl_sp(A,B)) ) ) )).
fof(fc1_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xreal_0(k1_complex1(A)) ) )).
fof(fc1_complfld,axiom,( ~ v2_struct_0(k1_complfld) & v36_algstr_0(k1_complfld) )).
fof(fc1_complsp1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( ~ v2_struct_0(k1_complsp1(A)) & v1_pre_topc(k1_complsp1(A)) & v2_pre_topc(k1_complsp1(A)) ) ) )).
fof(fc1_compos_0,axiom,( v1_compos_0(k1_tarski(k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0))) )).
fof(fc1_compos_1,axiom,( ! [A] : ( 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),k4_ordinal1) & 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)) ) ) )).
fof(fc1_compos_2,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) & 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) ) ) )).
fof(fc1_comptrig,axiom,( v1_xreal_0(k28_sin_cos) & ~ v3_xxreal_0(k28_sin_cos) )).
fof(fc1_compts_1,axiom,( ! [A] : ( v1_pre_topc(k1_compts_1(A)) & v2_pre_topc(k1_compts_1(A)) ) )).
fof(fc1_comput_1,axiom,( ! [A] : ( ( v4_funct_1(A) & v1_comput_1(A) ) => ( v1_relat_1(k3_tarski(A)) & v1_funct_1(k3_tarski(A)) ) ) )).
fof(fc1_comseq_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_comseq_3,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc1_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l5_struct_0(A) ) => ~ v1_xboole_0(u4_struct_0(A)) ) )).
fof(fc1_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ( ~ v2_struct_0(k11_conlat_1(A)) & v3_lattices(k11_conlat_1(A)) & v15_lattices(k11_conlat_1(A)) ) ) )).
fof(fc1_connsp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc1_convex1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc1_convex4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & m1_convex4(B,A) ) => v1_finset_1(k13_pre_poly(B)) ) )).
fof(fc1_convfun1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) & ~ v2_struct_0(B) & l1_rlvect_1(B) ) => ~ v2_struct_0(k3_convfun1(A,B)) ) )).
fof(fc1_cqc_lang,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(A) & v7_ordinal1(B) & 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) ) )).
fof(fc1_cqc_sim1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k3_cqc_lang(A)) ) => ~ v1_xboole_0(k12_cqc_sim1(A,B)) ) )).
fof(fc1_cqc_the1,axiom,( ~ v1_xboole_0(k2_cqc_the1) )).
fof(fc1_csspace,axiom,( 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)) )).
fof(fc1_csspace3,axiom,( ~ v1_xboole_0(k1_csspace3) )).
fof(fc1_csspace4,axiom,( ~ v1_xboole_0(k1_csspace4) )).
fof(fc1_descip_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_dickson,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_relat_1(k3_dickson(A)) & v5_relat_2(k3_dickson(A)) ) ) )).
fof(fc1_diff_1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc1_dilworth,axiom,( ! [A] : ( ( v2_struct_0(A) & l1_orders_2(A) ) => ( v1_xboole_0(k1_dilworth(A)) & v7_ordinal1(k1_dilworth(A)) ) ) )).
fof(fc1_diraf,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ( ~ v2_struct_0(k2_diraf(A)) & v1_analoaf(k2_diraf(A)) ) ) )).
fof(fc1_dist_1,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & m1_finseq_1(B,A) ) => ~ v1_xboole_0(k5_dist_1(A,B)) ) )).
fof(fc1_dtconstr,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => v8_struct_0(k9_int_3(A)) ) )).
fof(fc1_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ~ v1_xboole_0(k1_ec_pf_2(A)) ) )).
fof(fc1_endalg,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc1_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v4_funct_1(k1_ens_1(A)) & ~ v1_xboole_0(k1_ens_1(A)) ) ) )).
fof(fc1_eqrel_1,axiom,( ! [A] : ( v1_relat_2(k1_eqrel_1(A)) & v1_partfun1(k1_eqrel_1(A),A) ) )).
fof(fc1_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ~ v1_xboole_0(k1_euclid(A)) ) )).
fof(fc1_euclid_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc1_euclid_7,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_euclid_9,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & ~ v2_xxreal_0(B) ) => v1_xboole_0(k4_xxreal_1(k6_xcmplx_0(A,B),k2_xcmplx_0(A,B))) ) )).
fof(fc1_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ v1_xboole_0(k1_euclidlp(A)) ) )).
fof(fc1_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_exchsort(A) ) => v1_ordinal6(k9_xtuple_0(A)) ) )).
fof(fc1_extpro_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ( v13_struct_0(k1_extpro_1(A),1) & v1_extpro_1(k1_extpro_1(A),A) ) ) )).
fof(fc1_extreal1,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ~ v3_xxreal_0(k3_extreal1(A)) ) )).
fof(fc1_facirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ~ v1_facirc_1(k1_tarski(A)) ) )).
fof(fc1_facirc_2,axiom,( ! [A] : ( ~ v2_struct_0(k1_facirc_2(A)) & v11_struct_0(k1_facirc_2(A)) & v1_msualg_1(k1_facirc_2(A)) ) )).
fof(fc1_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_fcont_3,axiom,( v2_rcomp_1(k2_subset_1(k1_numbers)) )).
fof(fc1_fdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v1_fdiff_1(A,k5_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_xboole_0(k1_seq_2(A)) & v1_xreal_0(k1_seq_2(A)) ) ) )).
fof(fc1_fdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v9_ordinal1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v1_fdiff_1(A,k5_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_relat_1(k30_valued_1(A)) & v1_funct_1(k30_valued_1(A)) & v9_ordinal1(k30_valued_1(A)) & v1_valued_0(k30_valued_1(A)) & v2_comseq_2(k30_valued_1(A)) ) ) )).
fof(fc1_fib_num2,axiom,( ! [A] : ( ( v1_int_1(A) & ~ v1_abian(A) ) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & ~ v1_abian(k4_xcmplx_0(A)) ) ) )).
fof(fc1_fib_num3,axiom,( v1_xreal_0(k1_fib_num) & v2_xxreal_0(k1_fib_num) )).
fof(fc1_filter_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc1_filter_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_filter_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc1_fin_topo,axiom,( ~ v2_struct_0(k4_fin_topo) & v1_orders_2(k4_fin_topo) )).
fof(fc1_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc1_finseq_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v8_ordinal1(A) ) => v1_xboole_0(k1_finseq_1(A)) ) )).
fof(fc1_finseq_2,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc1_finseq_3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(A) => v2_card_3(k4_finseq_2(A,B)) ) )).
fof(fc1_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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)) ) )).
fof(fc1_finseq_5,axiom,( ! [A] : v1_zfmisc_1(k5_finseq_1(A)) )).
fof(fc1_finseq_6,axiom,( ! [A] : ! [B] : ! [C] : ~ v1_zfmisc_1(k11_finseq_1(A,B,C)) )).
fof(fc1_finseq_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v7_ordinal1(B) & v7_ordinal1(C) ) => v1_finseq_1(k9_funct_7(A,B,C)) ) )).
fof(fc1_finset_1,axiom,( ! [A] : v1_finset_1(k1_tarski(A)) )).
fof(fc1_finsub_1,axiom,( ! [A] : v4_finsub_1(k1_zfmisc_1(A)) )).
fof(fc1_fintopo5,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ( ~ v2_struct_0(k3_fintopo5(A,B)) & v1_orders_2(k3_fintopo5(A,B)) ) ) )).
fof(fc1_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => v1_xboole_0(k9_fin_topo(A,k1_struct_0(A))) ) )).
fof(fc1_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ~ v1_xboole_0(k2_flang_2(A,B)) ) )).
fof(fc1_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_funct_1(k2_fomodel0(A)) & v1_funct_2(k2_fomodel0(A),k2_zfmisc_1(A,A),A) & v2_binop_1(k2_fomodel0(A),A) ) ) )).
fof(fc1_fomodel1,axiom,( ! [A] : ( ( v8_ordinal1(A) & v1_int_1(A) ) => ( v8_ordinal1(k9_complex1(A)) & v1_int_1(k9_complex1(A)) ) ) )).
fof(fc1_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc1_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ~ v1_xboole_0(k1_fomodel4(A)) ) )).
fof(fc1_fraenkel,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k1_funct_2(A,B)) ) )).
fof(fc1_frechet,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc1_freealg,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,k4_ordinal1) ) => ( ~ v2_struct_0(k3_freealg(A,B)) & v1_lang1(k3_freealg(A,B)) ) ) )).
fof(fc1_friends1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k9_relat_1(A,B)) ) )).
fof(fc1_fscirc_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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)) ) )).
fof(fc1_fsm_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc1_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k9_flang_1(A)) ) )).
fof(fc1_funcop_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(k2_funcop_1(A,B)) & v1_funct_1(k2_funcop_1(A,B)) ) )).
fof(fc1_funcsdom,axiom,( ! [A] : ( 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)) & v9_valued_2(k5_funcsdom(A)) ) )).
fof(fc1_funct_1,axiom,( ! [A] : ! [B] : v1_funct_1(k1_tarski(k4_tarski(A,B))) )).
fof(fc1_funct_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ~ v1_xboole_0(k1_funct_2(A,B)) ) )).
fof(fc1_funct_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v1_relat_1(k4_funct_4(A,B,C,D)) & v1_funct_1(k4_funct_4(A,B,C,D)) ) )).
fof(fc1_funct_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k1_funct_5(A)) & v1_funct_1(k1_funct_5(A)) & v1_funcop_1(k1_funct_5(A)) ) ) )).
fof(fc1_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ( v1_relat_1(k5_funct_6(A)) & v1_funct_1(k5_funct_6(A)) & v1_funcop_1(k5_funct_6(A)) ) ) )).
fof(fc1_funct_7,axiom,( ! [A] : ! [B] : ~ v1_xboole_0(k16_funcop_1(A,B)) )).
fof(fc1_funct_8,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_funct_8(A) ) => v1_funct_8(k9_xtuple_0(A)) ) )).
fof(fc1_funct_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & v1_xreal_0(A) ) => v1_funct_9(k2_funcop_1(k1_numbers,A),A) ) )).
fof(fc1_functor0,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc1_functor1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(fc1_functor3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc1_fuzzy_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(k4_funct_3(A,B)) & v5_relat_1(k4_funct_3(A,B),k1_rcomp_1(k5_numbers,1)) & v1_funct_1(k4_funct_3(A,B)) ) )).
fof(fc1_fuzzy_4,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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)) ) )).
fof(fc1_fvaluat1,axiom,( v1_fvaluat1(k1_xxreal_0) )).
fof(fc1_fvsum_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc1_gate_1,axiom,( ! [A] : ( v1_xboole_0(A) => ~ v1_xboole_0(k1_gate_1(A)) ) )).
fof(fc1_genealg1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => ~ v1_xboole_0(k3_card_3(A)) ) )).
fof(fc1_geomtrap,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) ) )).
fof(fc1_gfacirc2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc1_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ~ v1_xboole_0(k6_glib_000(A)) ) )).
fof(fc1_glib_001,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(fc1_glib_003,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc1_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(fc1_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(fc1_goboard1,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m1_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) & v7_ordinal1(B) ) => ( v1_matrix_0(k16_matrix_0(B,u1_struct_0(k15_euclid(2)),A)) & v1_goboard1(k16_matrix_0(B,u1_struct_0(k15_euclid(2)),A)) & v2_goboard1(k16_matrix_0(B,u1_struct_0(k15_euclid(2)),A)) & v3_goboard1(k16_matrix_0(B,u1_struct_0(k15_euclid(2)),A)) & v4_goboard1(k16_matrix_0(B,u1_struct_0(k15_euclid(2)),A)) ) ) )).
fof(fc1_goboard2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ~ v1_xboole_0(k1_goboard1(A)) ) )).
fof(fc1_goboard9,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc1_gobrd11,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(fc1_gobrd14,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(fc1_gr_cy_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ~ v1_xboole_0(k6_card_1(A)) ) )).
fof(fc1_gr_cy_3,axiom,( ! [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) ) => ( ~ 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)) ) ) )).
fof(fc1_graph_1,axiom,( ! [A] : ( ( v6_graph_1(A) & l1_graph_1(A) ) => v1_finset_1(u1_struct_0(A)) ) )).
fof(fc1_graph_3,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) & v1_abian(B) ) => v1_abian(k6_xcmplx_0(A,B)) ) )).
fof(fc1_graph_5,axiom,( ~ v1_xboole_0(k2_arytm_2) )).
fof(fc1_graphsp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) => v1_xreal_0(k11_graphsp(A,B,C,D)) ) )).
fof(fc1_grcat_1,axiom,( v2_midsp_2(k3_algstr_0) )).
fof(fc1_grfunc_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v1_funct_1(k3_xboole_0(A,B)) ) )).
fof(fc1_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ~ v1_xboole_0(k2_grnilp_1(A)) ) )).
fof(fc1_groeb_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( 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))) ) ) )).
fof(fc1_groeb_2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc1_groeb_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => v1_finset_1(k2_polynom1(B,C)) ) )).
fof(fc1_group_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc1_group_10,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc1_group_12,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc1_group_14,axiom,( ! [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) ) => ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) & ~ v1_xboole_0(k5_finseq_1(A)) & v1_finseq_1(k5_finseq_1(A)) & v1_prvect_1(k5_finseq_1(A)) ) ) )).
fof(fc1_group_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc1_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ~ v1_xboole_0(k1_group_3(A)) ) )).
fof(fc1_group_4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc1_group_6,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc1_group_7,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc1_group_9,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc1_groupp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc1_hahnban1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc1_hallmar1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(A) & m1_finseq_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k4_ordinal1) ) => v1_finset_1(k1_funct_1(B,C)) ) )).
fof(fc1_hausdorf,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(fc1_helly,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) ) )).
fof(fc1_hermitan,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc1_heyting1,axiom,( ! [A] : ( v3_lattices(k12_normform(A)) & v3_filter_0(k12_normform(A)) ) )).
fof(fc1_heyting2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(B) & m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) ) => v1_finset_1(k1_heyting2(A,B,C)) ) )).
fof(fc1_heyting3,axiom,( ! [A] : ! [B] : v1_funct_1(k2_zfmisc_1(A,k1_tarski(B))) )).
fof(fc1_hilbasis,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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),C) ) ) )).
fof(fc1_hilbert1,axiom,( v5_hilbert1(k1_hilbert1) )).
fof(fc1_hilbert3,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) & v7_ordinal1(B) & ~ v8_ordinal1(B) ) => v2_funct_1(k4_funct_4(k5_numbers,B,A,k5_numbers)) ) )).
fof(fc1_idea_1,axiom,( ~ v1_xboole_0(k14_idea_1) )).
fof(fc1_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => v1_ideal_1(k1_tarski(k4_struct_0(A)),A) ) )).
fof(fc1_incproj,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ~ v1_xboole_0(k1_incproj(A)) ) )).
fof(fc1_index_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & 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)) ) )).
fof(fc1_int_1,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_int_1(B) ) => v1_int_1(k2_xcmplx_0(A,B)) ) )).
fof(fc1_int_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( ~ v7_ordinal1(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)) ) ) )).
fof(fc1_int_3,axiom,( ~ v2_struct_0(k1_int_3) & v36_algstr_0(k1_int_3) )).
fof(fc1_int_4,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & v3_membered(A) & v1_xreal_0(B) ) => v1_finset_1(k17_member_1(A,B)) ) )).
fof(fc1_int_6,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_int_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( v1_relat_1(k13_nat_3(A)) & v4_relat_1(k13_nat_3(A),k8_newton) & v1_funct_1(k13_nat_3(A)) & v1_partfun1(k13_nat_3(A),k8_newton) & v1_int_7(k13_nat_3(A)) ) ) )).
fof(fc1_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => v1_finset_1(k1_int_8(A)) ) )).
fof(fc1_integr16,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc1_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ~ v1_xboole_0(k1_integra1(A)) ) )).
fof(fc1_interva1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc1_intpro_1,axiom,( v7_intpro_1(k1_intpro_1) )).
fof(fc1_isocat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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),k9_nattra_1(k6_cat_2(A,B),C),k9_nattra_1(A,k9_nattra_1(B,C))) ) )).
fof(fc1_jgraph_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v2_struct_0(k1_jgraph_1(A)) ) )).
fof(fc1_jgraph_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(fc1_jgraph_3,axiom,( 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))) )).
fof(fc1_jgraph_4,axiom,( ! [A] : ( 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) ) ) )).
fof(fc1_jgraph_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) ) => v2_compts_1(k5_jgraph_6(A,B,C),k15_euclid(2)) ) )).
fof(fc1_jgraph_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc1_jordan,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) => ( v1_xreal_0(k1_metric_1(A,B,C)) & ~ v3_xxreal_0(k1_metric_1(A,B,C)) ) ) )).
fof(fc1_jordan1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => v1_convex1(k4_topreal1(A),k15_euclid(2)) ) )).
fof(fc1_jordan10,axiom,( ! [A] : ! [B] : ( ( 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)))) & v7_ordinal1(B) ) => v2_compts_1(k2_pre_topc(k15_euclid(2),k3_goboard9(k2_jordan9(A,B))),k15_euclid(2)) ) )).
fof(fc1_jordan14,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(fc1_jordan18,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ~ v1_xboole_0(k7_relat_1(k5_pscomp_1,k4_topreal1(A))) ) )).
fof(fc1_jordan1d,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => v1_abian(k1_newton(2,A)) ) )).
fof(fc1_jordan1e,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc1_jordan1g,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_zfmisc_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(k3_finseq_5(A)) & ~ v1_zfmisc_1(k3_finseq_5(A)) & v1_funct_1(k3_finseq_5(A)) & v1_finseq_1(k3_finseq_5(A)) ) ) )).
fof(fc1_jordan1j,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & ~ v1_xboole_0(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_xboole_0(k3_graph_2(A,B)) & v1_funct_1(k3_graph_2(A,B)) & v1_finseq_1(k3_graph_2(A,B)) ) ) )).
fof(fc1_jordan21,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc1_jordan22,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc1_jordan23,axiom,( ! [A] : v2_funct_1(k5_finseq_1(A)) )).
fof(fc1_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ( v5_rltopsp1(k15_euclid(A)) & v6_rltopsp1(k15_euclid(A)) & v7_rltopsp1(k15_euclid(A)) ) ) )).
fof(fc1_jordan5a,axiom,( ! [A] : ( v7_ordinal1(A) => ( v5_rltopsp1(k15_euclid(A)) & v1_borsuk_2(k15_euclid(A)) ) ) )).
fof(fc1_jordan6,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc1_jordan8,axiom,( ! [A] : ! [B] : ( ( ~ 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_0(k1_jordan8(A,B)) & v1_goboard1(k1_jordan8(A,B)) & v2_goboard1(k1_jordan8(A,B)) ) ) )).
fof(fc1_kolmog01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc1_kurato_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc1_kurato_2,axiom,( ! [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) => v4_pre_topc(k3_topreal1(2,A),k15_euclid(2)) ) )).
fof(fc1_lang1,axiom,( ! [A] : ( ~ v2_struct_0(k6_lang1(A)) & v2_lang1(k6_lang1(A)) ) )).
fof(fc1_latsum_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( ~ v2_struct_0(k1_lattice2(A)) & v3_lattices(k1_lattice2(A)) ) ) )).
fof(fc1_lattice3,axiom,( ! [A] : ( ~ v2_struct_0(k1_lattice3(A)) & v3_lattices(k1_lattice3(A)) ) )).
fof(fc1_lattice5,axiom,( ! [A] : ( 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)) ) )).
fof(fc1_lattice6,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc1_lattice7,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_lattice7(A) ) => ( v1_orders_2(k1_yellow_1(A)) & v2_waybel_1(k1_yellow_1(A)) & v1_lattice3(k1_yellow_1(A)) & v2_lattice3(k1_yellow_1(A)) ) ) )).
fof(fc1_lattice8,axiom,( ! [A] : ~ v1_xboole_0(k1_lattice8(A)) )).
fof(fc1_lattices,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_lexbfs,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc1_lfuzzy_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_membered(A) ) => ( ~ v2_struct_0(k1_lfuzzy_0(A)) & v1_orders_2(k1_lfuzzy_0(A)) & v1_lfuzzy_0(k1_lfuzzy_0(A)) ) ) )).
fof(fc1_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v5_relat_1(k4_fuzzy_4(A,A),k1_rcomp_1(k5_numbers,1)) & v1_funct_1(k4_fuzzy_4(A,A)) & v1_funct_2(k4_fuzzy_4(A,A),k2_zfmisc_1(A,A),k1_numbers) & v1_lfuzzy_1(k4_fuzzy_4(A,A),A) & v2_lfuzzy_1(k4_fuzzy_4(A,A),A) & v3_lfuzzy_1(k4_fuzzy_4(A,A),A) & v4_lfuzzy_1(k4_fuzzy_4(A,A),A) ) ) )).
fof(fc1_lmod_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) ) )).
fof(fc1_lmod_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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)) ) )).
fof(fc1_lopban_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => ( ~ v2_struct_0(k7_lopban_2(A)) & v36_algstr_0(k7_lopban_2(A)) ) ) )).
fof(fc1_lopban_3,axiom,( ! [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) & 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,k4_ordinal1,u1_struct_0(A)) & v2_lopban_3(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k3_normsp_0(A,B)) & v1_funct_2(k3_normsp_0(A,B),k4_ordinal1,k1_numbers) & v1_series_1(k3_normsp_0(A,B)) ) ) )).
fof(fc1_lopban_4,axiom,( ! [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) & 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),k4_ordinal1,u1_struct_0(A)) & v2_lopban_3(k1_lopban_4(A,B),A) ) ) )).
fof(fc1_lopban_5,axiom,( ! [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) & 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)) ) ) )).
fof(fc1_lopban_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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(C) & v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ~ v1_xboole_0(k3_lopban_7(A,B,C)) ) )).
fof(fc1_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ~ v1_xboole_0(k1_lopclset(A)) ) )).
fof(fc1_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_funct_1(k9_lpspacc1(A)) & v1_funct_2(k9_lpspacc1(A),k2_zfmisc_1(k3_rfunct_3(A,k2_numbers),k3_rfunct_3(A,k2_numbers)),k3_rfunct_3(A,k2_numbers)) & v1_binop_1(k9_lpspacc1(A),k3_rfunct_3(A,k2_numbers)) & v2_binop_1(k9_lpspacc1(A),k3_rfunct_3(A,k2_numbers)) ) ) )).
fof(fc1_lpspace1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc1_lpspace2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_ltlaxio1,axiom,( v2_ltlaxio1(k13_ltlaxio1) )).
fof(fc1_ltlaxio2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_xboole_0(B) ) => v1_xboole_0(k1_funct_1(A,B)) ) )).
fof(fc1_ltlaxio3,axiom,( ! [A] : ~ v1_xboole_0(k1_ltlaxio3(A)) )).
fof(fc1_ltlaxio4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)))) ) => ~ v1_xboole_0(k3_ltlaxio4(A)) ) )).
fof(fc1_lukasi_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(fc1_margrel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k3_margrel1(A)) ) )).
fof(fc1_matrix11,axiom,( ! [A] : ( 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)))) ) ) )).
fof(fc1_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => v1_setfam_1(k1_finseq_1(A)) ) )).
fof(fc1_matrix15,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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_0(B) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(A))) & m1_subset_1(C,k4_ordinal1) ) => 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_0(B))) ) )).
fof(fc1_matrix17,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_matrix_0(k10_matrix_0(A,A,C)) & v2_matrix_0(k10_matrix_0(A,A,C),u1_struct_0(B),A,A) & v1_matrix17(k10_matrix_0(A,A,C),B,A) ) ) )).
fof(fc1_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v1_xboole_0(B) & v1_matrix_0(C) & v2_matrix_0(C,B,A,A) & m1_finseq_1(C,k3_finseq_2(B)) ) => ( v1_matrix_0(k4_matrix_0(B,C)) & v2_matrix_0(k4_matrix_0(B,C),B,A,A) ) ) )).
fof(fc1_matrix_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) & v7_ordinal1(B) ) => ~ v1_xboole_0(k1_matrix_1(A,B)) ) )).
fof(fc1_matrix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ v1_xboole_0(k3_matrix_2(A)) & v3_matrix_2(k3_matrix_2(A)) ) ) )).
fof(fc1_matrix_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v1_matrix_0(k2_matrix_3(B,C)) & v2_matrix_0(k2_matrix_3(B,C),u1_struct_0(B),A,A) ) ) )).
fof(fc1_matrix_8,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(k3_matrix_1(B,A)) & v2_matrix_0(k3_matrix_1(B,A),u1_struct_0(B),A,A) & v1_matrix_8(k3_matrix_1(B,A),A,B) & v3_matrix_8(k3_matrix_1(B,A),A,B) ) ) )).
fof(fc1_matrix_9,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_relat_1(k4_relat_1(k2_finseq_1(A))) & v1_finseq_1(k4_relat_1(k2_finseq_1(A))) ) ) )).
fof(fc1_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc1_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_matrix_0(k4_matrixr2(A)) & v2_matrix_0(k4_matrixr2(A),k1_numbers,A,A) & v1_matrixr2(k4_matrixr2(A),A) ) ) )).
fof(fc1_matrlin2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) & v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(A),k3_finseq_1(D),k3_finseq_1(E)) & m1_finseq_1(F,k3_finseq_2(u1_struct_0(A))) ) => ( 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) ) ) )).
fof(fc1_matroid0,axiom,( ! [A] : ( ( v1_matroid0(A) & l1_pre_topc(A) ) => v1_classes1(k1_matroid0(A)) ) )).
fof(fc1_matrprob,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v4_matrprob(A) & m1_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( ~ v1_xboole_0(k3_matrprob(A)) & v1_matrprob(k3_matrprob(A)) ) ) )).
fof(fc1_matrtop1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_partfun3(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( v1_relat_1(k5_relat_1(C,B)) & v1_partfun3(k5_relat_1(C,B)) ) ) )).
fof(fc1_matrtop2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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,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) ) ) )).
fof(fc1_matrtop3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(fc1_mazurulm,axiom,( v1_borsuk_1(k17_borsuk_1,k3_topmetr) )).
fof(fc1_mboolean,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc1_measure1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ~ v1_xboole_0(k7_setfam_1(A,B)) ) )).
fof(fc1_measure3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_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) ) ) )).
fof(fc1_measure4,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(fc1_measure6,axiom,( ~ v1_setfam_1(k1_numbers) )).
fof(fc1_measure7,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ~ v1_xboole_0(k8_measure7(A)) ) )).
fof(fc1_measure8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,k6_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,k6_numbers))) ) => ~ v1_xboole_0(k5_measure8(A,C,D,B)) ) )).
fof(fc1_member_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) & v1_xcmplx_0(D) ) => v1_membered(k2_enumset1(A,B,C,D)) ) )).
fof(fc1_membered,axiom,( v1_membered(k2_numbers) )).
fof(fc1_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ( v13_struct_0(k1_memstr_0(A),1) & v1_memstr_0(k1_memstr_0(A),A) ) ) )).
fof(fc1_mesfun6c,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc1_mesfun7c,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc1_mesfunc1,axiom,( ~ v1_xboole_0(k1_mesfunc1) )).
fof(fc1_mesfunc7,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( v1_funct_1(k10_mesfunc1(A,B)) & v6_supinf_2(k10_mesfunc1(A,B)) ) ) )).
fof(fc1_mesfunc8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,B)) & v1_mesfunc8(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,B)))) & v7_ordinal1(D) ) => ( v1_funct_1(k7_nat_1(C,D)) & v1_funct_2(k7_nat_1(C,D),k4_ordinal1,k4_partfun1(A,B)) & v1_mesfunc8(k7_nat_1(C,D),A,B) ) ) )).
fof(fc1_metric_1,axiom,( v1_relat_1(k7_funct_5) & v1_funct_1(k7_funct_5) & v4_valued_0(k7_funct_5) )).
fof(fc1_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ~ v1_xboole_0(k2_metric_2(A)) ) )).
fof(fc1_metric_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_metrizts,axiom,( ! [A] : ( ( 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)) ) )).
fof(fc1_mfold_1,axiom,( ! [A] : ! [B] : v2_funct_1(k1_tarski(k4_tarski(A,B))) )).
fof(fc1_mfold_2,axiom,( v5_relat_1(k1_xboole_0,k1_xboole_0) )).
fof(fc1_midsp_1,axiom,( ~ v2_struct_0(k2_midsp_1) & v1_midsp_1(k2_midsp_1) )).
fof(fc1_midsp_2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc1_midsp_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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) ) ) )).
fof(fc1_mmlquer2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_relat_2(A) & v1_relat_1(B) & v1_relat_2(B) ) => ( v1_relat_1(k1_mmlquer2(A,B)) & v1_relat_2(k1_mmlquer2(A,B)) ) ) )).
fof(fc1_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => v1_mmlquery(k18_mmlquery(A,B),A) ) )).
fof(fc1_mod_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) ) )).
fof(fc1_mod_4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc1_modal_1,axiom,( ~ v1_xboole_0(k3_modal_1) )).
fof(fc1_modcat_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc1_modelc_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => v1_modelc_1(k6_modelc_1(A)) ) )).
fof(fc1_modelc_2,axiom,( ! [A] : ( v7_ordinal1(A) => v1_modelc_2(k2_modelc_2(A)) ) )).
fof(fc1_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => v1_finset_1(k13_modelc_2(A)) ) )).
fof(fc1_moebius1,axiom,( v1_xboole_0(k19_finseq_1(k1_xboole_0)) )).
fof(fc1_monoid_0,axiom,( ~ 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) )).
fof(fc1_monoid_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ~ v2_struct_0(k9_monoid_1(A,B)) ) )).
fof(fc1_msafree,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_msafree1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc1_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_msafree2(A) & l1_msualg_1(A) ) => ~ v1_xboole_0(k2_msafree2(A)) ) )).
fof(fc1_msafree3,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(fc1_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) & v4_relat_1(C,k1_msaterm(A,B)) & v1_funct_1(C) & v1_partfun1(C,k1_msaterm(A,B)) & m1_subset_1(D,u4_struct_0(A)) & m1_msaterm(E,A,B,k2_msaterm(A,B,D)) ) => ( v1_relat_1(k3_relat_1(E,C)) & v1_finseq_1(k3_relat_1(E,C)) ) ) )).
fof(fc1_msaterm,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc1_msinst_1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc1_msscyc_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc1_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_funcop_1(B) ) => ( v1_relat_1(k1_funct_6(B)) & v4_relat_1(k1_funct_6(B),A) & v1_funct_1(k1_funct_6(B)) ) ) )).
fof(fc1_msualg_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_msualg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc1_msualg_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc1_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc1_msualg_5,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_msualg_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_relat_1(k4_relat_1(A)) & ~ v1_xboole_0(k4_relat_1(A)) ) ) )).
fof(fc1_msualg_7,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_msualg_8,axiom,( ! [A] : ( ~ 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)) ) )).
fof(fc1_msualg_9,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_mycielsk,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc1_nagata_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc1_nat_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => v7_ordinal1(k2_xcmplx_0(A,B)) ) )).
fof(fc1_nat_3,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) & v7_ordinal1(B) ) => ~ v8_ordinal1(k1_newton(A,B)) ) )).
fof(fc1_nat_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => v7_ordinal1(k2_uproots(C,k1_nat_5(A,B,C))) ) )).
fof(fc1_nat_lat,axiom,( v6_membered(u1_struct_0(k3_nat_lat)) )).
fof(fc1_ndiff_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & v1_ndiff_1(B,A,k4_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & m1_subset_1(C,k4_ordinal1) ) => ( v1_funct_1(k7_nat_1(B,C)) & v1_funct_2(k7_nat_1(B,C),k4_ordinal1,u1_struct_0(A)) & v1_ndiff_1(k7_nat_1(B,C),A,k4_struct_0(A)) ) ) )).
fof(fc1_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ( 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) ) ) )).
fof(fc1_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(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)) ) ) )).
fof(fc1_neckla_2,axiom,( ~ v1_xboole_0(k3_neckla_2) )).
fof(fc1_neckla_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_net_1,axiom,( ! [A] : ( l1_petri(A) => v1_relat_1(k1_net_1(A)) ) )).
fof(fc1_newton,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_nfcont_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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) ) ) )).
fof(fc1_nfcont_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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) ) ) )).
fof(fc1_normform,axiom,( ! [A] : ( 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))) ) )).
fof(fc1_normsp_0,axiom,( ! [A] : ! [B] : ( ( ~ 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(k3_normsp_0(A,B)) & v5_relat_1(k3_normsp_0(A,B),k1_numbers) & v1_funct_1(k3_normsp_0(A,B)) ) ) )).
fof(fc1_normsp_1,axiom,( ! [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) & 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(k2_normsp_0(A,B)) & v1_xreal_0(k2_normsp_0(A,B)) ) ) )).
fof(fc1_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ( ~ v2_struct_0(k3_normsp_2(A)) & v2_pre_topc(k3_normsp_2(A)) & v4_frechet(k3_normsp_2(A)) ) ) )).
fof(fc1_numbers,axiom,( ~ v1_xboole_0(k1_numbers) )).
fof(fc1_openlatt,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ~ v1_xboole_0(k1_openlatt(A)) ) )).
fof(fc1_oposet_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc1_oppcat_1,axiom,( ! [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) & 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)) ) ) )).
fof(fc1_orders_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k1_orders_1(A)) ) )).
fof(fc1_orders_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_ordinal1,axiom,( ! [A] : ~ v1_xboole_0(k1_ordinal1(A)) )).
fof(fc1_ordinal2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v5_ordinal1(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)) ) ) )).
fof(fc1_ordinal3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => v3_ordinal1(k2_xboole_0(A,B)) ) )).
fof(fc1_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => v3_ordinal1(k1_ordinal2(A)) ) )).
fof(fc1_ordinal5,axiom,( v4_ordinal1(k4_ordinal1) )).
fof(fc1_ordinal6,axiom,( ! [A] : v1_ordinal6(k2_ordinal1(A)) )).
fof(fc1_osafree,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_osalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc1_osalg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc1_osalg_3,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc1_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc1_papdesaf,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc1_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) ) )).
fof(fc1_partfun1,axiom,( ! [A] : ! [B] : ~ v1_xboole_0(k4_partfun1(A,B)) )).
fof(fc1_partfun3,axiom,( ! [A] : ( v1_xreal_0(A) => ~ v3_xxreal_0(k7_xcmplx_0(A,A)) ) )).
fof(fc1_partfun4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc1_partit1,axiom,( ! [A] : ~ v1_xboole_0(k1_partit1(A)) )).
fof(fc1_partit_2,axiom,( ! [A] : ! [B] : v1_xboole_0(k1_partit_2(A,B)) )).
fof(fc1_pboole,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc1_pcomps_1,axiom,( ! [A] : ( l1_metric_1(A) => ( v1_pre_topc(k3_pcomps_1(A)) & v2_pre_topc(k3_pcomps_1(A)) ) ) )).
fof(fc1_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc1_pdiff_1,axiom,( 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) )).
fof(fc1_pdiff_6,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc1_pdiff_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) & v7_ordinal1(B) & v1_xreal_0(C) ) => ( v1_relat_1(k1_funct_7(A,B,C)) & v1_funct_1(k1_funct_7(A,B,C)) & v3_valued_0(k1_funct_7(A,B,C)) ) ) )).
fof(fc1_pencil_1,axiom,( ! [A] : ( ( ~ v3_pencil_1(A) & l1_pre_topc(A) ) => ~ v1_xboole_0(u1_pre_topc(A)) ) )).
fof(fc1_pepin,axiom,( ! [A] : ( v1_int_1(A) => v7_ordinal1(k1_square_1(A)) ) )).
fof(fc1_pnproc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc1_polyalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & l6_algstr_0(A) ) => ( ~ v2_struct_0(k1_polyalg1(A)) & v2_rlvect_1(k1_polyalg1(A)) & v1_polyalg1(k1_polyalg1(A),A) ) ) )).
fof(fc1_polyeq_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => v1_xcmplx_0(k1_polyeq_1(A,B,C)) ) )).
fof(fc1_polyeq_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)) ) )).
fof(fc1_polyeq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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)) ) )).
fof(fc1_polyform,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(fc1_polynom1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,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,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)) & v1_polynom1(k5_polynom1(A,B,C,D),B) ) ) )).
fof(fc1_polynom2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,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,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ( v1_funct_1(k7_polynom1(A,B,C,D)) & v1_funct_2(k7_polynom1(A,B,C,D),k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(k7_polynom1(A,B,C,D),B) ) ) )).
fof(fc1_polynom3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v1_partfun1(k5_polynom3(A),k4_finseq_2(A,k4_ordinal1)) & v1_relat_2(k5_polynom3(A)) & v4_relat_2(k5_polynom3(A)) & v8_relat_2(k5_polynom3(A)) & v3_orders_1(k5_polynom3(A)) ) ) )).
fof(fc1_polynom4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k1_polynom4(A,B)) & v1_funct_2(k1_polynom4(A,B),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k1_polynom4(A,B),A) ) ) )).
fof(fc1_polynom5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v7_ordinal1(C) ) => ( v1_funct_1(k2_polynom5(A,B,C)) & v1_funct_2(k2_polynom5(A,B,C),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k2_polynom5(A,B,C),A) ) ) )).
fof(fc1_polynom6,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) & ~ v1_xboole_0(B) ) => ( v3_ordinal1(k10_ordinal2(A,B)) & ~ v1_xboole_0(k10_ordinal2(A,B)) ) ) )).
fof(fc1_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_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) ) ) )).
fof(fc1_polynom8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k2_polynom8(A,B,C)) & v1_funct_2(k2_polynom8(A,B,C),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k2_polynom8(A,B,C),A) ) ) )).
fof(fc1_polyred,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,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,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)) & v1_polynom7(k10_polynom1(A,B,C,D),A,B) ) ) )).
fof(fc1_poset_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc1_pralg_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc1_pralg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc1_pralg_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc1_pre_circ,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc1_pre_poly,axiom,( ! [A] : ( v7_ordinal1(A) => ~ v1_xboole_0(k1_finseq_1(k1_nat_1(A,1))) ) )).
fof(fc1_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ~ v1_xboole_0(u1_pre_topc(A)) ) )).
fof(fc1_prepower,axiom,( ! [A] : ( v1_int_1(A) => ( v7_ordinal1(k9_complex1(A)) & v1_xreal_0(k9_complex1(A)) ) ) )).
fof(fc1_prob_1,axiom,( ! [A] : v2_finsub_1(k1_zfmisc_1(A)) )).
fof(fc1_prob_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,k9_setfam_1(A)) ) ) )).
fof(fc1_prob_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_funct_1(k3_prob_3(A,B)) & v1_funct_2(k3_prob_3(A,B),k4_ordinal1,k9_setfam_1(A)) & v1_prob_2(k3_prob_3(A,B)) ) ) )).
fof(fc1_prob_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc1_prvect_2,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc1_prvect_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v2_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_relat_1(B) & v2_relat_1(B) & ~ v1_xboole_0(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)) ) ) )).
fof(fc1_pscomp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc1_pua2mss1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc1_pythtrip,axiom,( ! [A] : ( v7_ordinal1(A) => v1_pythtrip(k1_square_1(A)) ) )).
fof(fc1_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ~ v1_xboole_0(k1_qc_lang1(A)) ) )).
fof(fc1_qc_trans,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) ) => v1_finset_1(k6_goedelcp(A,B)) ) )).
fof(fc1_qmax_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc1_quatern2,axiom,( ! [A] : ! [B] : ( ( v1_quaterni(A) & v1_quaterni(B) ) => v1_quaterni(k4_quatern2(A,B)) ) )).
fof(fc1_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => v1_quaterni(k1_quatern3(A)) ) )).
fof(fc1_quaterni,axiom,( ~ v1_xboole_0(k1_quaterni) )).
fof(fc1_quin_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => v1_xcmplx_0(k1_quin_1(A,B,C)) ) )).
fof(fc1_quofield,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v6_struct_0(A) & l5_algstr_0(A) ) => ~ v1_xboole_0(k1_quofield(A)) ) )).
fof(fc1_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ v1_xboole_0(k2_radix_1(A)) ) )).
fof(fc1_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ~ v1_xboole_0(k1_radix_3(A)) ) )).
fof(fc1_ramsey_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v1_finset_1(B) ) => ~ v1_xboole_0(k3_group_10(B,A)) ) )).
fof(fc1_random_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc1_random_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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_funct_1(E) & v1_funct_2(E,C,k6_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,k6_numbers))) & v1_funct_1(F) & v1_funct_2(F,A,B) & v1_random_3(F,A,B,C,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( v1_funct_1(k1_random_3(A,B,C,D,E,F)) & v1_funct_2(k1_random_3(A,B,C,D,E,F),D,k6_numbers) & v10_valued_0(k1_random_3(A,B,C,D,E,F)) & v6_supinf_2(k1_random_3(A,B,C,D,E,F)) & v2_measure1(k1_random_3(A,B,C,D,E,F),B,D) & v4_measure1(k1_random_3(A,B,C,D,E,F),B,D) ) ) )).
fof(fc1_ranknull,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) )).
fof(fc1_rat_1,axiom,( ! [A] : ! [B] : ( ( v1_rat_1(A) & v1_rat_1(B) ) => v1_rat_1(k3_xcmplx_0(A,B)) ) )).
fof(fc1_ratfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc1_rcomp_1,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => v3_rcomp_1(k4_xxreal_1(A,B)) ) )).
fof(fc1_rcomp_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_subset_1(A)) ) )).
fof(fc1_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( v8_ordinal1(k4_int_1(A,k5_numbers)) & v1_int_1(k4_int_1(A,k5_numbers)) ) ) )).
fof(fc1_real_lat,axiom,( v3_membered(u1_struct_0(k3_real_lat)) )).
fof(fc1_real_ns1,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc1_realset1,axiom,( ! [A] : ! [B] : ( v1_relat_1(A) => v1_relat_1(k1_realset1(A,B)) ) )).
fof(fc1_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(A) => v1_relat_1(k3_xboole_0(A,B)) ) )).
fof(fc1_relat_2,axiom,( ! [A] : ( 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)) ) )).
fof(fc1_reloc,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc1_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc1_revrot_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc1_rfinseq,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => v1_finset_1(k10_relat_1(A,B)) ) )).
fof(fc1_rfunct_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_rfunct_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_rfunct_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v1_funct_1(k4_rinfsup2(A)) & v1_funct_2(k4_rinfsup2(A),k4_ordinal1,k6_numbers) & v8_valued_0(k4_rinfsup2(A)) ) ) )).
fof(fc1_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => v1_ideal_1(k2_struct_0(A),A) ) )).
fof(fc1_ringcat1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc1_rlaffin1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc1_rlaffin2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc1_rlaffin3,axiom,( ! [A] : ( v7_ordinal1(A) => ( v5_rltopsp1(k15_euclid(A)) & v6_rltopsp1(k15_euclid(A)) & v7_rltopsp1(k15_euclid(A)) ) ) )).
fof(fc1_rlsub_2,axiom,( ! [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) ) => ~ v1_xboole_0(k3_rlsub_2(A)) ) )).
fof(fc1_rltopsp1,axiom,( ! [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) & 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) ) ) )).
fof(fc1_rlvect_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc1_rlvect_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & m1_rlvect_2(B,A) ) => v1_finset_1(k13_pre_poly(B)) ) )).
fof(fc1_rmod_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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)) ) )).
fof(fc1_robbins3,axiom,( v13_struct_0(k1_robbins3,1) )).
fof(fc1_robbins4,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(fc1_rsspace,axiom,( v1_rlvect_1(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace)) & v2_rlvect_1(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace)) )).
fof(fc1_rsspace3,axiom,( ~ v1_xboole_0(k1_rsspace3) )).
fof(fc1_rsspace4,axiom,( ~ v1_xboole_0(k1_rsspace4) )).
fof(fc1_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ~ v1_xboole_0(k3_rusub_2(A)) ) )).
fof(fc1_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => v2_pre_topc(k5_rusub_5(A)) ) )).
fof(fc1_rvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc1_rvsum_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc1_scm_1,axiom,( ! [A] : ( v1_int_1(A) => v5_relat_1(k3_afinsq_1(A),k4_numbers) ) )).
fof(fc1_scm_comp,axiom,( ! [A] : ! [B] : ( ( 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(k7_card_1(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)) ) )).
fof(fc1_scm_halt,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc1_scm_inst,axiom,( ~ v1_xboole_0(k2_scm_inst) )).
fof(fc1_scmbsort,axiom,( v1_relat_1(k2_scmbsort) & v4_relat_1(k2_scmbsort,k4_ordinal1) & 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) )).
fof(fc1_scmfsa10,axiom,( v1_xboole_0(k2_amistd_1(k7_card_1(3),k1_scmfsa_2,k2_compos_1(k1_scmfsa_2))) )).
fof(fc1_scmfsa6a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc1_scmfsa6b,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ( v1_relat_1(k3_scmfsa6a(A,B)) & v4_relat_1(k3_scmfsa6a(A,B),k4_ordinal1) & 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),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(fc1_scmfsa6c,axiom,( v1_scmfsa6c(k2_compos_1(k1_scmfsa_2)) & v2_scmfsa6c(k2_compos_1(k1_scmfsa_2)) )).
fof(fc1_scmfsa7b,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) & v5_relat_1(k1_scmfsa_7(A,B),u1_compos_1(k1_scmfsa_2)) & ~ v1_xboole_0(k1_scmfsa_7(A,B)) & v1_funct_1(k1_scmfsa_7(A,B)) & v1_finset_1(k1_scmfsa_7(A,B)) & v1_afinsq_1(k1_scmfsa_7(A,B)) ) ) )).
fof(fc1_scmfsa8a,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) ) => ( v1_relat_1(k1_scmfsa6a(A,B)) & v4_relat_1(k1_scmfsa6a(A,B),k4_ordinal1) & 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)) ) ) )).
fof(fc1_scmfsa8b,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k7_card_1(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),k4_ordinal1) & 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),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(fc1_scmfsa8c,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc1_scmfsa_1,axiom,( ~ v1_xboole_0(k1_scmfsa_1) )).
fof(fc1_scmfsa_2,axiom,( ~ v2_struct_0(k1_scmfsa_2) & v2_memstr_0(k1_scmfsa_2,k7_card_1(3)) & v1_extpro_1(k1_scmfsa_2,k7_card_1(3)) )).
fof(fc1_scmfsa_3,axiom,( v1_extpro_1(k1_scmfsa_2,k7_card_1(3)) & v3_amistd_5(k1_scmfsa_2,k7_card_1(3)) )).
fof(fc1_scmfsa_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc1_scmfsa_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc1_scmfsa_i,axiom,( ~ v1_xboole_0(k1_scmfsa_i) )).
fof(fc1_scmfsa_m,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_int_1(B) ) => v5_funct_1(k16_funcop_1(k4_scmfsa_2(A),B),k2_memstr_0(k7_card_1(3),k1_scmfsa_2)) ) )).
fof(fc1_scmisort,axiom,( ~ v1_xboole_0(k3_scmisort) & v1_relat_1(k3_scmisort) & v4_relat_1(k3_scmisort,k4_ordinal1) & 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) )).
fof(fc1_scmpds_2,axiom,( ~ v2_struct_0(k1_scmpds_2) & v1_extpro_1(k1_scmpds_2,2) )).
fof(fc1_scmpds_3,axiom,( v1_extpro_1(k1_scmpds_2,2) & v3_amistd_5(k1_scmpds_2,2) )).
fof(fc1_scmpds_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc1_scmpds_5,axiom,( ! [A] : ( ( 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)) ) )).
fof(fc1_scmpds_6,axiom,( ! [A] : ( v7_ordinal1(A) => v6_compos_0(k3_scmpds_2(k1_nat_1(A,1)),u1_compos_1(k1_scmpds_2)) ) )).
fof(fc1_scmpds_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & 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) & v7_ordinal1(D) ) => ( v1_relat_1(k1_scmpds_7(B,C,D,A)) & v4_relat_1(k1_scmpds_7(B,C,D,A),k4_ordinal1) & v5_relat_1(k1_scmpds_7(B,C,D,A),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k1_scmpds_7(B,C,D,A)) & v1_funct_1(k1_scmpds_7(B,C,D,A)) & v1_finset_1(k1_scmpds_7(B,C,D,A)) & v1_afinsq_1(k1_scmpds_7(B,C,D,A)) & v3_scmpds_4(k1_scmpds_7(B,C,D,A)) ) ) )).
fof(fc1_scmpds_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc1_scmpds_9,axiom,( ! [A] : ( v1_int_1(A) => v1_xboole_0(k2_amistd_1(2,k1_scmpds_2,k3_scmpds_2(A))) ) )).
fof(fc1_scmpds_i,axiom,( ~ v1_xboole_0(k1_scmpds_i) )).
fof(fc1_scmring1,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(fc1_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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),k7_card_1(2)) ) ) )).
fof(fc1_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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(k7_card_1(2),k1_scmring2(A),k2_compos_1(k1_scmring2(A)))) ) )).
fof(fc1_scmring4,axiom,( ! [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) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ( v1_extpro_1(k1_scmring2(A),k7_card_1(2)) & v2_amistd_5(k1_scmring2(A),k7_card_1(2)) ) ) )).
fof(fc1_scmyciel,axiom,( v1_xboole_0(k3_tarski(k1_tarski(k1_xboole_0))) )).
fof(fc1_scpinvar,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc1_scpqsort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) & v3_scmpds_4(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & 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_relat_1(k3_scmpds_6(C,D,A,B)) & v4_relat_1(k3_scmpds_6(C,D,A,B),k4_ordinal1) & v5_relat_1(k3_scmpds_6(C,D,A,B),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k3_scmpds_6(C,D,A,B)) & 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)) ) ) )).
fof(fc1_seq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_funct_1(k1_seq_1(A)) & v3_funct_1(k1_seq_1(A)) & v1_funct_2(k1_seq_1(A),k4_ordinal1,k1_numbers) ) ) )).
fof(fc1_seq_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_comseq_2(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_funct_1(k1_valued_1(A,B)) & v1_funct_2(k1_valued_1(A,B),k4_ordinal1,k1_numbers) & v2_comseq_2(k1_valued_1(A,B)) ) ) )).
fof(fc1_seq_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_funct_1(k54_valued_1(A)) & v1_funct_2(k54_valued_1(A),k4_ordinal1,k1_numbers) & v2_comseq_2(k54_valued_1(A)) ) ) )).
fof(fc1_seqm_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_ordinal1) & v5_valued_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) & v7_ordinal1(B) ) => ( v1_relat_1(k7_nat_1(A,B)) & v1_funct_1(k7_nat_1(A,B)) & v2_valued_0(k7_nat_1(A,B)) & v4_valued_0(k7_nat_1(A,B)) & v5_valued_0(k7_nat_1(A,B)) ) ) )).
fof(fc1_series_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & v3_valued_0(A) ) => ( v1_relat_1(k2_series_1(A)) & v4_relat_1(k2_series_1(A),k4_ordinal1) & v1_funct_1(k2_series_1(A)) & v1_partfun1(k2_series_1(A),k4_ordinal1) & v1_valued_0(k2_series_1(A)) & v3_valued_0(k2_series_1(A)) ) ) )).
fof(fc1_series_3,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_xreal_0(k9_complex1(A)) & ~ v3_xxreal_0(k9_complex1(A)) ) ) )).
fof(fc1_setfam_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => v1_xboole_0(k7_setfam_1(A,B)) ) )).
fof(fc1_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_funct_1(k1_setlim_1(B)) & v1_funct_2(k1_setlim_1(B),k4_ordinal1,k9_setfam_1(A)) & v3_prob_1(k1_setlim_1(B)) ) ) )).
fof(fc1_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(fc1_sfmastr1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc1_sfmastr2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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_sfmastr2(B,A)) & v4_relat_1(k2_sfmastr2(B,A),k4_ordinal1) & v5_relat_1(k2_sfmastr2(B,A),u1_compos_1(k1_scmfsa_2)) & ~ v1_xboole_0(k2_sfmastr2(B,A)) & 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)) ) ) )).
fof(fc1_sfmastr3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc1_sgraph1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => v1_finset_1(k1_sgraph1(A,B)) ) )).
fof(fc1_simplex0,axiom,( ! [A] : v5_finset_1(k2_cohsp_1(A)) )).
fof(fc1_simplex1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc1_simplex2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(fc1_sin_cos2,axiom,( ! [A] : v1_xreal_0(k2_sin_cos2(A)) )).
fof(fc1_sin_cos6,axiom,( v1_xreal_0(k28_sin_cos) & v2_xxreal_0(k28_sin_cos) )).
fof(fc1_sin_cos9,axiom,( v1_relat_1(k5_relat_1(k26_sin_cos,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2)))) & v2_funct_1(k5_relat_1(k26_sin_cos,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(fc1_sincos10,axiom,( v1_relat_1(k5_relat_1(k1_fdiff_9,k3_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) & v2_funct_1(k5_relat_1(k1_fdiff_9,k3_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(fc1_sppol_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & 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)) ) )).
fof(fc1_sppol_2,axiom,( ! [A] : ! [B] : ( ( v2_topreal1(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & v7_ordinal1(B) ) => v2_topreal1(k16_finseq_1(B,A)) ) )).
fof(fc1_sprect_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v1_zfmisc_1(B) & m1_finseq_1(B,u1_struct_0(k15_euclid(A))) ) => ~ v1_xboole_0(k3_topreal1(A,B)) ) )).
fof(fc1_sprect_2,axiom,( v2_compts_1(k1_topreal1,k15_euclid(2)) )).
fof(fc1_sprect_3,axiom,( ! [A] : ( 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))) ) )).
fof(fc1_sprect_5,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc1_square_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xcmplx_0(k1_square_1(A)) ) )).
fof(fc1_stacks_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) ) )).
fof(fc1_stirl2_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => v7_ordinal1(k3_stirl2_1(A,B)) ) )).
fof(fc1_struct_0,axiom,( ! [A] : ( ( v2_struct_0(A) & l1_struct_0(A) ) => v1_xboole_0(u1_struct_0(A)) ) )).
fof(fc1_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(A) & v7_ordinal1(B) & 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) ) ) )).
fof(fc1_subset_1,axiom,( ! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)) )).
fof(fc1_substlat,axiom,( ! [A] : ! [B] : ~ v1_xboole_0(k1_substlat(A,B)) )).
fof(fc1_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ~ v1_xboole_0(k1_substut1(A)) ) )).
fof(fc1_supinf_1,axiom,( ! [A] : ( v2_membered(A) => ( ~ v1_xboole_0(k3_supinf_1(A)) & v2_membered(k3_supinf_1(A)) ) ) )).
fof(fc1_symsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) ) )).
fof(fc1_t_0topsp,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc1_t_1topsp,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc1_taxonom1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) & v1_xreal_0(k3_tbsp_1(A,B)) ) ) )).
fof(fc1_taylor_1,axiom,( v1_funct_1(k22_sin_cos) & v2_funct_1(k22_sin_cos) & v1_funct_2(k22_sin_cos,k1_numbers,k1_numbers) )).
fof(fc1_tbsp_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_metric_1(k5_metric_1(A)) & v5_tbsp_1(k5_metric_1(A)) ) ) )).
fof(fc1_tdgroup,axiom,( v8_algstr_0(k1_vectsp_1) & v12_vectsp_1(k1_vectsp_1) & v1_tdgroup(k1_vectsp_1) )).
fof(fc1_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ~ v1_xboole_0(k1_tdlat_1(A)) ) )).
fof(fc1_termord,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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(k10_polynom1(A,B,C,D)) & v1_funct_2(k10_polynom1(A,B,C,D),k15_pre_poly(A),u1_struct_0(B)) & v3_polynom7(k10_polynom1(A,B,C,D),A,B) ) ) )).
fof(fc1_tex_1,axiom,( ! [A] : ~ v1_xboole_0(k1_tex_1(A)) )).
fof(fc1_tex_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc1_tex_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc1_tietze,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc1_tmap_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc1_topalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc1_topalg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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)) ) ) )).
fof(fc1_topalg_3,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(fc1_topalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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))) ) ) )).
fof(fc1_topalg_5,axiom,( ~ v2_struct_0(k2_gr_cy_1) & ~ v8_struct_0(k2_gr_cy_1) & v15_algstr_0(k2_gr_cy_1) )).
fof(fc1_topalg_6,axiom,( ! [A] : ( ( v7_ordinal1(A) & v2_xxreal_0(A) ) => ( ~ v8_struct_0(k15_euclid(A)) & v5_rltopsp1(k15_euclid(A)) ) ) )).
fof(fc1_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_funct_1(k1_topdim_1(A)) & v1_funct_2(k1_topdim_1(A),k4_ordinal1,k9_setfam_1(k9_setfam_1(u1_struct_0(A)))) & v3_prob_1(k1_topdim_1(A)) ) ) )).
fof(fc1_topdim_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_topgen_1,axiom,( ! [A] : ( ( v8_struct_0(A) & l1_struct_0(A) ) => v1_finset_1(k2_struct_0(A)) ) )).
fof(fc1_topgen_2,axiom,( ! [A] : ! [B] : ( v1_pre_topc(k5_topgen_2(A,B)) & v2_pre_topc(k5_topgen_2(A,B)) ) )).
fof(fc1_topgen_3,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ( ~ v1_finset_1(k3_card_2(2,A)) & v1_card_1(k3_card_2(2,A)) ) ) )).
fof(fc1_topgen_4,axiom,( v4_card_3(k3_numbers) )).
fof(fc1_topgen_5,axiom,( ~ v1_xboole_0(k1_topgen_5) )).
fof(fc1_topgrp_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc1_topmetr,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_topreal1,axiom,( ! [A] : ( v7_ordinal1(A) => v4_funct_1(u1_struct_0(k15_euclid(A))) ) )).
fof(fc1_topreal2,axiom,( v1_topreal2(k1_topreal1) )).
fof(fc1_topreal6,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_topreal7,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc1_topreala,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v2_xxreal_0(B) & v1_xreal_0(B) ) => ~ v1_xboole_0(k4_xxreal_1(A,k2_xcmplx_0(A,B))) ) )).
fof(fc1_toprealb,axiom,( ~ v1_xboole_0(k4_xxreal_1(k5_numbers,1)) )).
fof(fc1_toprealc,axiom,( ! [A] : ( v1_xreal_0(A) => ~ v3_xxreal_0(k1_square_1(A)) ) )).
fof(fc1_tops_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc1_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => v1_tops_2(u1_pre_topc(A),A) ) )).
fof(fc1_trees_1,axiom,( v1_trees_1(k1_tarski(k1_xboole_0)) )).
fof(fc1_trees_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc1_trees_3,axiom,( ~ v1_xboole_0(k1_trees_3) )).
fof(fc1_trees_9,axiom,( ! [A] : ( 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)) ) )).
fof(fc1_unialg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_unialg_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(fc1_unialg_3,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc1_uniroots,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc1_uproots,axiom,( ! [A] : ! [B] : ( ( ~ 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)),k4_ordinal1,u1_struct_0(A)) & v1_uproots(k4_polynom5(A,B,k5_struct_0(A)),A) ) ) )).
fof(fc1_urysohn1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ v1_xboole_0(k1_urysohn1(A)) ) )).
fof(fc1_urysohn2,axiom,( ! [A] : ! [B] : ( ( v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & v1_xreal_0(B) ) => v6_xxreal_2(k23_member_1(A,B)) ) )).
fof(fc1_valuat_1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & ~ v1_xboole_0(B) ) => ( v4_funct_1(k1_valuat_1(A,B)) & ~ v1_xboole_0(k1_valuat_1(A,B)) ) ) )).
fof(fc1_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_valued_0(A) ) => v1_membered(k10_xtuple_0(A)) ) )).
fof(fc1_valued_1,axiom,( ! [A] : ( v1_rat_1(A) => ( v1_xreal_0(k9_complex1(A)) & v1_rat_1(k9_complex1(A)) ) ) )).
fof(fc1_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => v1_valued_2(k1_tarski(A)) ) )).
fof(fc1_vectmetr,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc1_vectsp11,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) ) )).
fof(fc1_vectsp_1,axiom,( ~ v2_struct_0(k1_vectsp_1) & v8_algstr_0(k1_vectsp_1) )).
fof(fc1_vectsp_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) ) )).
fof(fc1_vectsp_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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)) ) )).
fof(fc1_vfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc1_waybel10,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => v4_waybel_3(k2_funcop_1(A,B)) ) )).
fof(fc1_waybel11,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc1_waybel12,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc1_waybel14,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc1_waybel15,axiom,( ! [A] : ( v1_orders_2(k2_yellow_1(A)) & v3_waybel_8(k2_yellow_1(A)) ) )).
fof(fc1_waybel16,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(fc1_waybel17,axiom,( ! [A] : ! [B] : ( ( v3_orders_2(B) & l1_orders_2(B) ) => v5_waybel_3(k2_funcop_1(A,B)) ) )).
fof(fc1_waybel18,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_waybel21,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc1_waybel22,axiom,( ! [A] : ( ( ~ 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(k1_yellow_1(k8_waybel_0(A))) & v3_waybel_3(k1_yellow_1(k8_waybel_0(A))) ) ) )).
fof(fc1_waybel23,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_waybel24,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc1_waybel25,axiom,( v1_pre_topc(k9_waybel18) & ~ v7_pre_topc(k9_waybel18) )).
fof(fc1_waybel26,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_waybel28,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc1_waybel29,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_waybel30,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ( v1_orders_2(k1_yellow_1(k7_waybel_0(A))) & v24_waybel_0(k1_yellow_1(k7_waybel_0(A))) ) ) )).
fof(fc1_waybel31,axiom,( ! [A] : ! [B] : ( ( 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(k1_yellow_1(k7_waybel_0(k5_yellow_0(A,B)))) & v2_waybel_8(k1_yellow_1(k7_waybel_0(k5_yellow_0(A,B)))) ) ) )).
fof(fc1_waybel32,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc1_waybel34,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc1_waybel_0,axiom,( ! [A] : ( ( v1_lattice3(A) & l1_orders_2(A) ) => v1_waybel_0(k2_struct_0(A),A) ) )).
fof(fc1_waybel_1,axiom,( ! [A] : ( v1_orders_2(k2_yellow_1(A)) & v2_waybel_1(k2_yellow_1(A)) ) )).
fof(fc1_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc1_waybel_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc1_waybel_4,axiom,( ! [A] : ( l1_orders_2(A) => v1_waybel_4(k2_waybel_4(A),A) ) )).
fof(fc1_waybel_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))) ) )).
fof(fc1_waybel_7,axiom,( ! [A] : ( v1_orders_2(k2_yellow_1(A)) & v11_waybel_1(k2_yellow_1(A)) ) )).
fof(fc1_waybel_8,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc1_waybel_9,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc1_weddwitt,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc1_wellord2,axiom,( ! [A] : ( v1_relat_1(k1_wellord2(A)) & v1_relat_2(k1_wellord2(A)) ) )).
fof(fc1_wsierp_1,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v7_ordinal1(B) ) => v1_int_1(k1_newton(A,B)) ) )).
fof(fc1_xboole_0,axiom,( v1_xboole_0(k1_xboole_0) )).
fof(fc1_xboolean,axiom,( v1_xboolean(k1_xboolean) )).
fof(fc1_xcmplx_0,axiom,( v1_xcmplx_0(k1_xcmplx_0) )).
fof(fc1_xreal_0,axiom,( ~ v1_xreal_0(k2_xxreal_0) )).
fof(fc1_xtuple_0,axiom,( ! [A] : ! [B] : v1_xtuple_0(k4_tarski(A,B)) )).
fof(fc1_xxreal_0,axiom,( v1_xxreal_0(k1_xxreal_0) )).
fof(fc1_xxreal_1,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => v2_membered(k1_xxreal_1(A,B)) ) )).
fof(fc1_xxreal_2,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc1_xxreal_3,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_xxreal_0(k2_xxreal_3(A)) & v1_xreal_0(k2_xxreal_3(A)) ) ) )).
fof(fc1_yellow10,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc1_yellow11,axiom,( v1_orders_2(k1_yellow11) & v3_orders_2(k1_yellow11) & v4_orders_2(k1_yellow11) & v5_orders_2(k1_yellow11) )).
fof(fc1_yellow12,axiom,( ! [A] : ( v1_xboole_0(A) => v1_xboole_0(k3_tarski(A)) ) )).
fof(fc1_yellow13,axiom,( ! [A] : ( ( v1_compts_1(A) & l1_pre_topc(A) ) => v2_compts_1(k2_struct_0(A),A) ) )).
fof(fc1_yellow14,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc1_yellow15,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => v1_finset_1(k2_yellow15(A,B)) ) )).
fof(fc1_yellow16,axiom,( ! [A] : ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => v1_yellow16(k2_funcop_1(A,B)) ) )).
fof(fc1_yellow18,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(fc1_yellow19,axiom,( ! [A] : ! [B] : ( ( ~ 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(k2_yellow_1(k2_struct_0(A)))) & v2_waybel_0(k1_yellow19(A,B),k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(k1_yellow19(A,B),k2_yellow_1(k2_struct_0(A))) ) ) )).
fof(fc1_yellow20,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc1_yellow21,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_yellow21(A)) ) )).
fof(fc1_yellow_0,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(fc1_yellow_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc1_yellow_2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc1_yellow_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc1_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc1_yellow_6,axiom,( ! [A] : ( v1_ordinal1(k1_yellow_6(A)) & v2_classes1(k1_yellow_6(A)) ) )).
fof(fc1_yellow_7,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ( v1_orders_2(k7_lattice3(A)) & v3_orders_2(k7_lattice3(A)) ) ) )).
fof(fc1_yellow_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v2_struct_0(k1_yellow_8(A)) & v1_pre_topc(k1_yellow_8(A)) ) ) )).
fof(fc1_yellow_9,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc1_zf_fund1,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_zf_lang)) ) => v1_finset_1(k4_zf_fund1(A)) ) )).
fof(fc1_zf_lang,axiom,( ~ v1_xboole_0(k1_zf_lang) )).
fof(fc1_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) ) => v1_finset_1(k1_zf_model(A)) ) )).
fof(fc1_zf_model,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k3_zf_model(A)) ) )).
fof(fc1_zfmisc_1,axiom,( ! [A] : v1_zfmisc_1(k1_tarski(A)) )).
fof(fc1_zfmodel2,axiom,( ! [A] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) ) => v1_finset_1(k3_zf_lang1(A)) ) )).
fof(fc1_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc1_zmodul02,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_int_2(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) ) => ( ~ v2_struct_0(k12_zmodul02(A,B)) & v13_algstr_0(k12_zmodul02(A,B)) & v2_rlvect_1(k12_zmodul02(A,B)) & v3_rlvect_1(k12_zmodul02(A,B)) & v4_rlvect_1(k12_zmodul02(A,B)) & v7_vectsp_1(k12_zmodul02(A,B),k9_int_3(A)) & v8_vectsp_1(k12_zmodul02(A,B),k9_int_3(A)) & v9_vectsp_1(k12_zmodul02(A,B),k9_int_3(A)) & v10_vectsp_1(k12_zmodul02(A,B),k9_int_3(A)) & v11_vectsp_1(k12_zmodul02(A,B),k9_int_3(A)) ) ) )).
fof(fc20_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc20_afinsq_1,axiom,( ! [A] : ~ v1_xboole_0(k8_afinsq_1(A)) )).
fof(fc20_afinsq_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc20_algstr_0,axiom,( v13_struct_0(k8_algstr_0,1) & v22_algstr_0(k8_algstr_0) )).
fof(fc20_ami_6,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) & v7_ordinal1(B) ) => v1_amistd_1(k4_xtuple_0(k8_ami_3(B,A)),k7_card_1(2),k1_ami_3) ) )).
fof(fc20_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v4_funct_1(A) & ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & m1_subset_1(D,k4_card_3(k11_finseq_1(A,B,C))) ) => ( v1_relat_1(k1_funct_1(D,1)) & v1_funct_1(k1_funct_1(D,1)) ) ) )).
fof(fc20_aofa_a01,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v1_finset_1(k8_afinsq_1(A)) ) )).
fof(fc20_binop_2,axiom,( v1_funct_1(k24_binop_2) & v1_funct_2(k24_binop_2,k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1) & v1_setwiseo(k24_binop_2,k4_ordinal1) )).
fof(fc20_card_1,axiom,( ! [A] : ( v7_ordinal1(A) => v1_finset_1(k6_card_1(A)) ) )).
fof(fc20_cayldick,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_cayldick(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(k6_afinsq_1(B,C),k4_cayldick(A)) ) )).
fof(fc20_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc20_compos_0,axiom,( ! [A] : ( ( v1_compos_0(A) & v5_compos_0(A) ) => v4_compos_0(k6_compos_0(A),A) ) )).
fof(fc20_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v1_relat_1(k5_comput_1(2,A)) & v4_relat_1(k5_comput_1(2,A),k3_finseq_2(k4_ordinal1)) & 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) ) ) )).
fof(fc20_euclid_9,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc20_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc20_finseq_1,axiom,( ! [A] : ! [B] : ! [C] : ~ v1_xboole_0(k11_finseq_1(A,B,C)) )).
fof(fc20_finset_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc20_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) => v3_card_1(k3_relat_1(E,D),C) ) )).
fof(fc20_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(fc20_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k42_fomodel1(A,k43_fomodel1(A,k1_fomodel2(A)),B),C),A) ) )).
fof(fc20_fomodel3,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc20_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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(k5_fomodel4(B,C,A),D),B) ) )).
fof(fc20_funcop_1,axiom,( ! [A] : ! [B] : ( 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) ) )).
fof(fc20_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc20_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_xboole_0(A) => v1_xboole_0(k8_gate_1(B,C,A)) ) )).
fof(fc20_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => v4_glib_001(k9_glib_001(A,B,C,D),A) ) )).
fof(fc20_group_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc20_hahnban1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc20_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc20_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_membered(B) ) => v1_xboole_0(k9_member_1(A,B)) ) )).
fof(fc20_membered,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) & v1_xxreal_0(C) ) => v2_membered(k1_enumset1(A,B,C)) ) )).
fof(fc20_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc20_nat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ( ( ~ v8_ordinal1(A) & ~ v8_ordinal1(B) & ~ v8_ordinal1(C) & ~ v8_ordinal1(D) & ~ v8_ordinal1(E) & ~ v8_ordinal1(F) & ~ v8_ordinal1(G) & ~ v8_ordinal1(H) & ~ v8_ordinal1(I) & ~ v8_ordinal1(J) ) => v1_setfam_1(k8_enumset1(A,B,C,D,E,F,G,H,I,J)) ) )).
fof(fc20_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => v3_card_1(k13_pre_poly(k12_nat_3(A)),1) ) )).
fof(fc20_ordinal6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v4_ordinal6(k3_afinsq_1(A)) ) )).
fof(fc20_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc20_pre_poly,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_pre_poly(A) ) => v1_finset_1(k13_pre_poly(A)) ) )).
fof(fc20_prvect_3,axiom,( ! [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) & l1_normsp_1(A) ) => v2_prvect_2(k5_finseq_1(A)) ) )).
fof(fc20_ratfunc1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(fc20_relat_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_relat_1(A) ) => v1_xboole_0(k7_relat_1(A,B)) ) )).
fof(fc20_relat_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_2(A) & v1_relat_1(B) ) => v4_relat_2(k4_xboole_0(A,B)) ) )).
fof(fc20_rfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc20_scmfsa10,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) & m1_scmfsa_2(B) ) => v1_xboole_0(k2_amistd_1(k7_card_1(3),k1_scmfsa_2,k16_scmfsa_2(A,B))) ) )).
fof(fc20_scmfsa6c,axiom,( ! [A] : ! [B] : ( ( 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,k4_ordinal1) & 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,k7_card_1(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),k4_ordinal1) & 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),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(fc20_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v4_memstr_0(k16_funcop_1(A,B),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(fc20_scmpds_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc20_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & 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_relat_1(k9_scmpds_6(B,C,A)) & v4_relat_1(k9_scmpds_6(B,C,A),k4_ordinal1) & v5_relat_1(k9_scmpds_6(B,C,A),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k9_scmpds_6(B,C,A)) & 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) ) ) )).
fof(fc20_scmring3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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))) & v7_ordinal1(C) ) => v2_amistd_1(k9_scmring2(A,C,B),k7_card_1(2),k1_scmring2(A)) ) )).
fof(fc20_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v11_scmyciel(A) ) => ( v4_scmyciel(k6_scmyciel(A)) & v8_scmyciel(k6_scmyciel(A)) ) ) )).
fof(fc20_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => v4_simplex0(k8_simplex0(A,B,k2_xxreal_3(1))) ) )).
fof(fc20_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k18_sin_cos,k1_rcomp_1(k28_sin_cos,k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos)))) & v2_funct_1(k5_relat_1(k18_sin_cos,k1_rcomp_1(k28_sin_cos,k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos)))) )).
fof(fc20_struct_0,axiom,( ! [A] : ( ( v15_struct_0(A) & l5_struct_0(A) ) => v1_zfmisc_1(u4_struct_0(A)) ) )).
fof(fc20_tex_4,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc20_topgrp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc20_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc20_toprealb,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v8_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)) ) ) )).
fof(fc20_trees_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc20_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v5_relat_1(A,k3_numbers) & v1_relat_1(B) ) => v5_relat_1(k4_xboole_0(A,B),k3_numbers) ) )).
fof(fc20_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc20_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(fc20_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc20_waybel_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => v1_waybel_4(k1_waybel_4(A),A) ) )).
fof(fc20_waybel_9,axiom,( ! [A] : ( ( v2_lattice3(A) & l1_orders_2(A) ) => ( v6_waybel_0(k3_waybel_9(A),A) & v7_waybel_0(k3_waybel_9(A)) ) ) )).
fof(fc20_xreal_0,axiom,( ! [A] : ! [B] : ( ( v2_xxreal_0(A) & v1_xreal_0(A) & ~ v2_xxreal_0(B) & v1_xreal_0(B) ) => v3_xxreal_0(k6_xcmplx_0(B,A)) ) )).
fof(fc20_xxreal_2,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => ~ v2_xxreal_2(k2_xxreal_1(A,B)) ) )).
fof(fc20_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc20_yellow_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc21_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ~ v1_xboole_0(k39_abcmiz_1(A)) ) )).
fof(fc21_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ( v1_relat_1(k1_funct_7(A,B,C)) & v5_ordinal1(k1_funct_7(A,B,C)) & v1_funct_1(k1_funct_7(A,B,C)) & v1_finset_1(k1_funct_7(A,B,C)) ) ) )).
fof(fc21_algstr_0,axiom,( v21_algstr_0(k8_algstr_0) )).
fof(fc21_ami_6,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) & v7_ordinal1(B) ) => v1_amistd_1(k4_xtuple_0(k9_ami_3(B,A)),k7_card_1(2),k1_ami_3) ) )).
fof(fc21_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_membered(A) & ~ v1_xboole_0(B) & m1_subset_1(C,k4_card_3(k10_finseq_1(A,B))) ) => v1_int_1(k1_funct_1(C,1)) ) )).
fof(fc21_aofa_a01,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_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)) ) ) )).
fof(fc21_binop_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) ) => v1_xreal_0(k1_binop_1(A,B,C)) ) )).
fof(fc21_cayldick,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v6_struct_0(A) & l1_cayldick(A) & ~ v9_struct_0(B,A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => ~ v9_struct_0(k6_afinsq_1(B,C),k4_cayldick(A)) ) )).
fof(fc21_compos_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc21_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v1_relat_1(k5_comput_1(3,A)) & v4_relat_1(k5_comput_1(3,A),k3_finseq_2(k4_ordinal1)) & 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) ) ) )).
fof(fc21_euclid_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,u1_struct_0(k14_euclid(A))) & v1_xreal_0(C) & ~ v2_xxreal_0(C) ) => v1_xboole_0(k8_metric_1(k14_euclid(A),B,C)) ) )).
fof(fc21_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc21_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(k16_finseq_1(k5_numbers,A)) & v1_funct_1(k16_finseq_1(k5_numbers,A)) & v1_xboole_0(k16_finseq_1(k5_numbers,A)) & v1_finseq_1(k16_finseq_1(k5_numbers,A)) ) ) )).
fof(fc21_finset_1,axiom,( ! [A] : ! [B] : v1_finset_1(k16_funcop_1(A,B)) )).
fof(fc21_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v14_fomodel1(B,k5_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)) ) )).
fof(fc21_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k43_fomodel1(A,D),C),A,k1_nat_1(B,1)) ) )).
fof(fc21_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc21_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ 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_fomodel4(k1_tarski(k9_fomodel4(A,k1_xboole_0,k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k31_fomodel2(A)),B),B))),A,k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))),k26_fomodel4(A))) ) )).
fof(fc21_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(C,A) ) => v5_relat_1(k16_funcop_1(B,C),A) ) )).
fof(fc21_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc21_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xboole_0(A) & v1_xboole_0(B) & v1_xboole_0(C) ) => v1_xboole_0(k9_gate_1(A,B,C)) ) )).
fof(fc21_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => v5_glib_001(k9_glib_001(A,B,C,D),A) ) )).
fof(fc21_group_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc21_hahnban1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc21_hermitan,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc21_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc21_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ v1_xboole_0(k1_jordan2c(2,A)) ) )).
fof(fc21_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_membered(B) ) => v1_xboole_0(k9_member_1(B,A)) ) )).
fof(fc21_membered,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) ) => v3_membered(k1_enumset1(A,B,C)) ) )).
fof(fc21_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc21_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( v1_relat_1(k13_nat_3(A)) & v4_relat_1(k13_nat_3(A),k8_newton) & v1_funct_1(k13_nat_3(A)) & v1_partfun1(k13_nat_3(A),k8_newton) & v4_valued_0(k13_nat_3(A)) & v2_pre_poly(k13_nat_3(A)) ) ) )).
fof(fc21_ordinal6,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc21_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc21_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_pre_poly(A) ) => ( v1_relat_1(k1_funct_7(A,B,C)) & v1_funct_1(k1_funct_7(A,B,C)) & v2_pre_poly(k1_funct_7(A,B,C)) ) ) )).
fof(fc21_prvect_3,axiom,( ! [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) & 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)) ) )).
fof(fc21_ratfunc1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc21_relat_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_xboole_0(B) ) => v1_xboole_0(k8_relat_1(A,B)) ) )).
fof(fc21_relat_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v8_relat_2(A) ) => ( v1_relat_1(k2_relat_1(A)) & v8_relat_2(k2_relat_1(A)) ) ) )).
fof(fc21_rfunct_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc21_scmfsa10,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc21_scmfsa6c,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k7_card_1(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),k4_ordinal1) & 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),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(fc21_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc21_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & 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_relat_1(k10_scmpds_6(B,C,A)) & v4_relat_1(k10_scmpds_6(B,C,A),k4_ordinal1) & v5_relat_1(k10_scmpds_6(B,C,A),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k10_scmpds_6(B,C,A)) & 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)) ) ) )).
fof(fc21_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v8_scmyciel(A) ) => ( v4_scmyciel(k6_scmyciel(A)) & v11_scmyciel(k6_scmyciel(A)) ) ) )).
fof(fc21_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_simplex0(B,A) & v1_int_1(C) ) => v4_matroid0(k8_simplex0(A,B,C)) ) )).
fof(fc21_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k18_sin_cos,k1_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(2,k28_sin_cos)))) & v2_funct_1(k5_relat_1(k18_sin_cos,k1_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(2,k28_sin_cos)))) )).
fof(fc21_struct_0,axiom,( ! [A] : ( ( ~ v15_struct_0(A) & l5_struct_0(A) ) => ~ v1_zfmisc_1(u4_struct_0(A)) ) )).
fof(fc21_topgrp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc21_toprealb,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc21_trees_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc21_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_relat_1(B) ) => v5_relat_1(k3_xboole_0(A,B),k4_numbers) ) )).
fof(fc21_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc21_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc21_waybel_0,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc21_waybel_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => v2_waybel_4(k1_waybel_4(A),A) ) )).
fof(fc21_waybel_9,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc21_xreal_0,axiom,( ! [A] : ! [B] : ( ( v3_xxreal_0(A) & v1_xreal_0(A) & ~ v3_xxreal_0(B) & v1_xreal_0(B) ) => v3_xxreal_0(k6_xcmplx_0(A,B)) ) )).
fof(fc21_xxreal_2,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => ( ~ v1_xxreal_2(k4_xxreal_1(A,B)) & ~ v2_xxreal_2(k4_xxreal_1(A,B)) ) ) )).
fof(fc21_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc21_yellow_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc22_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc22_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k4_ordinal1) & m1_subset_1(D,A) ) => ( v1_relat_1(k1_funct_7(B,C,D)) & v5_relat_1(k1_funct_7(B,C,D),A) & v1_funct_1(k1_funct_7(B,C,D)) ) ) )).
fof(fc22_algstr_0,axiom,( v28_algstr_0(k8_algstr_0) )).
fof(fc22_ami_6,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) & v7_ordinal1(B) ) => ( ~ v4_compos_0(k8_ami_3(B,A),u1_compos_1(k1_ami_3)) & v2_amistd_1(k8_ami_3(B,A),k7_card_1(2),k1_ami_3) & ~ v4_amistd_1(k8_ami_3(B,A),k7_card_1(2),k1_ami_3) ) ) )).
fof(fc22_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_normsp_0(A) & l1_cayldick(A) ) => ( v4_normsp_0(k4_cayldick(A)) & v1_cayldick(k4_cayldick(A)) ) ) )).
fof(fc22_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v1_relat_1(k4_comput_1(1,A)) & v4_relat_1(k4_comput_1(1,A),k3_finseq_2(k4_ordinal1)) & 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) ) ) )).
fof(fc22_euclid_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,u1_struct_0(k14_euclid(A))) & v1_xreal_0(C) & v2_xxreal_0(C) ) => ~ v1_xboole_0(k8_metric_1(k14_euclid(A),B,C)) ) )).
fof(fc22_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc22_finseq_1,axiom,( ! [A] : v4_funct_1(k13_finseq_1(A)) )).
fof(fc22_finset_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k10_xtuple_0(A)) ) )).
fof(fc22_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : v1_xboole_0(k3_xboole_0(k6_subset_1(B,A),k3_xboole_0(A,C))) )).
fof(fc22_fomodel1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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(k4_ordinal1,k9_setfam_1(k3_finseq_2(k15_fomodel1(B))),k28_fomodel1(B),A)) ) )).
fof(fc22_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k43_fomodel1(A,B),C),A) ) )).
fof(fc22_fomodel3,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc22_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v6_fomodel4(k25_fomodel4(A),A) ) )).
fof(fc22_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,B) ) => v5_relat_1(k2_funcop_1(A,C),B) ) )).
fof(fc22_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k9_gate_1(A,B,C)) ) )).
fof(fc22_hahnban1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc22_hermitan,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc22_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc22_member_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_membered(A) & ~ v1_xboole_0(B) & v1_membered(B) ) => ~ v1_xboole_0(k9_member_1(A,B)) ) )).
fof(fc22_membered,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_rat_1(A) & v1_rat_1(B) & v1_rat_1(C) ) => v4_membered(k1_enumset1(A,B,C)) ) )).
fof(fc22_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc22_ordinal6,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc22_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc22_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc22_prvect_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) & v1_relat_1(B) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finseq_1(B) & v2_prvect_2(B) ) => ( v1_relat_1(k7_finseq_1(A,B)) & ~ v1_xboole_0(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)) ) ) )).
fof(fc22_ratfunc1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & l5_algstr_0(A) ) => v4_ratfunc1(k7_ratfunc1(A),A) ) )).
fof(fc22_relat_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_relat_1(A) ) => v1_xboole_0(k8_relat_1(A,B)) ) )).
fof(fc22_relat_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v8_relat_2(A) & v1_relat_1(B) & v8_relat_2(B) ) => v8_relat_2(k3_xboole_0(A,B)) ) )).
fof(fc22_rfunct_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc22_scmfsa10,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) & m1_scmfsa_2(B) ) => v1_xboole_0(k2_amistd_1(k7_card_1(3),k1_scmfsa_2,k17_scmfsa_2(A,B))) ) )).
fof(fc22_scmfsa6c,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) & 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),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(fc22_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc22_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & 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_relat_1(k10_scmpds_6(B,C,A)) & v4_relat_1(k10_scmpds_6(B,C,A),k4_ordinal1) & v5_relat_1(k10_scmpds_6(B,C,A),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k10_scmpds_6(B,C,A)) & 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) ) ) )).
fof(fc22_scmring3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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),k7_card_1(2),k1_scmring2(A)) ) )).
fof(fc22_scmyciel,axiom,( ! [A] : ( ( v1_finset_1(A) & v4_scmyciel(A) ) => ( v1_finset_1(k12_scmyciel(A)) & v4_scmyciel(k12_scmyciel(A)) ) ) )).
fof(fc22_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v4_simplex0(B) & m1_simplex0(B,A) & v1_int_1(C) ) => v4_simplex0(k8_simplex0(A,B,C)) ) )).
fof(fc22_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k18_sin_cos,k2_rcomp_1(k5_numbers,k28_sin_cos))) & v2_funct_1(k5_relat_1(k18_sin_cos,k2_rcomp_1(k5_numbers,k28_sin_cos))) )).
fof(fc22_topgrp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc22_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) ) => v1_convex1(k7_jgraph_6(A,B,C),k15_euclid(2)) ) )).
fof(fc22_toprealb,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc22_trees_3,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc22_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_relat_1(B) ) => v5_relat_1(k4_xboole_0(A,B),k4_numbers) ) )).
fof(fc22_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc22_valued_2,axiom,( ! [A] : ! [B] : ( v1_membered(B) => v1_valued_2(k4_partfun1(A,B)) ) )).
fof(fc22_waybel_0,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc22_waybel_4,axiom,( ! [A] : ( ( 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) ) )).
fof(fc22_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc22_xreal_0,axiom,( ! [A] : ! [B] : ( ( v3_xxreal_0(A) & v1_xreal_0(A) & ~ v3_xxreal_0(B) & v1_xreal_0(B) ) => v2_xxreal_0(k6_xcmplx_0(B,A)) ) )).
fof(fc22_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc22_yellow_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc23_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc23_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(fc23_afinsq_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc23_algstr_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc23_ami_6,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) & v7_ordinal1(B) ) => ( ~ v4_compos_0(k9_ami_3(B,A),u1_compos_1(k1_ami_3)) & v2_amistd_1(k9_ami_3(B,A),k7_card_1(2),k1_ami_3) & ~ v4_amistd_1(k9_ami_3(B,A),k7_card_1(2),k1_ami_3) ) ) )).
fof(fc23_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_normsp_0(A) & l1_cayldick(A) ) => ( v3_normsp_0(k4_cayldick(A)) & v1_cayldick(k4_cayldick(A)) ) ) )).
fof(fc23_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v1_relat_1(k4_comput_1(2,A)) & v4_relat_1(k4_comput_1(2,A),k3_finseq_2(k4_ordinal1)) & 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) ) ) )).
fof(fc23_euclid_9,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc23_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc23_finseq_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ~ v1_xboole_0(k1_finseq_1(A)) ) )).
fof(fc23_finset_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => v1_finset_1(k8_relat_1(A,B)) ) )).
fof(fc23_fomodel0,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_relat_1(k18_finseq_1(A)) & v8_relat_2(k18_finseq_1(A)) ) ) )).
fof(fc23_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc23_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k43_fomodel1(A,C),B),A) ) )).
fof(fc23_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc23_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v6_fomodel4(k26_fomodel4(A),A) ) )).
fof(fc23_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => v4_relat_1(k16_funcop_1(B,C),A) ) )).
fof(fc23_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k9_gate_1(B,A,C)) ) )).
fof(fc23_hahnban1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc23_hermitan,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc23_member_1,axiom,( ! [A] : ! [B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k9_member_1(A,B)) ) )).
fof(fc23_membered,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_int_1(A) & v1_int_1(B) & v1_int_1(C) ) => v5_membered(k1_enumset1(A,B,C)) ) )).
fof(fc23_memstr_0,axiom,( ! [A] : ! [B] : ( ( ~ v1_setfam_1(A) & v2_memstr_0(B,A) & l1_memstr_0(B,A) ) => ~ v1_xboole_0(k11_memstr_0(A,B)) ) )).
fof(fc23_ordinal6,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc23_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc23_pcs_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc23_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc23_prvect_3,axiom,( ! [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) & 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(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & 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(k7_prvect_3(A,B)) & v1_normsp_1(k7_prvect_3(A,B)) & v3_lopban_1(k7_prvect_3(A,B)) ) ) )).
fof(fc23_ratfunc1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(fc23_relat_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v3_relat_1(A) ) => ( v1_relat_1(k5_relat_1(A,B)) & v3_relat_1(k5_relat_1(A,B)) ) ) )).
fof(fc23_rfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc23_scmfsa10,axiom,( v1_extpro_1(k1_scmfsa_2,k7_card_1(3)) & v3_amistd_1(k1_scmfsa_2,k7_card_1(3)) )).
fof(fc23_scmfsa6c,axiom,( ! [A] : ! [B] : ( ( 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc23_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc23_scmpds_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc23_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v6_scmyciel(A) ) => ( v4_scmyciel(k12_scmyciel(A)) & v6_scmyciel(k12_scmyciel(A)) ) ) )).
fof(fc23_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc23_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k18_sin_cos,k2_rcomp_1(k28_sin_cos,k3_xcmplx_0(2,k28_sin_cos)))) & v2_funct_1(k5_relat_1(k18_sin_cos,k2_rcomp_1(k28_sin_cos,k3_xcmplx_0(2,k28_sin_cos)))) )).
fof(fc23_topgrp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc23_toprealb,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ~ v2_struct_0(k8_toprealb(A)) ) )).
fof(fc23_trees_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc23_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_valued_0(A) & v1_relat_1(B) ) => v4_valued_0(k3_xboole_0(A,B)) ) )).
fof(fc23_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc23_valued_2,axiom,( ! [A] : ! [B] : ( v2_membered(B) => v2_valued_2(k4_partfun1(A,B)) ) )).
fof(fc23_waybel_0,axiom,( ! [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) ) => ( v1_orders_2(k7_lattice3(A)) & v16_waybel_0(k7_lattice3(A)) ) ) )).
fof(fc23_waybel_4,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(fc23_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc23_xreal_0,axiom,( ! [A] : ! [B] : ( ( ~ v2_xxreal_0(A) & v1_xreal_0(A) & ~ v3_xxreal_0(B) & v1_xreal_0(B) ) => ~ v2_xxreal_0(k3_xcmplx_0(A,B)) ) )).
fof(fc23_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc23_yellow_6,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc24_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc24_afinsq_1,axiom,( ! [A] : v4_funct_1(k8_afinsq_1(A)) )).
fof(fc24_afinsq_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc24_algstr_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(fc24_ami_6,axiom,( ! [A] : ! [B] : ( ( 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)),k7_card_1(2),k1_ami_3) ) )).
fof(fc24_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_rlvect_1(A) & l1_cayldick(A) ) => ( v3_rlvect_1(k4_cayldick(A)) & v1_cayldick(k4_cayldick(A)) ) ) )).
fof(fc24_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v1_relat_1(k4_comput_1(3,A)) & v4_relat_1(k4_comput_1(3,A),k3_finseq_2(k4_ordinal1)) & 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) ) ) )).
fof(fc24_euclid_9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_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)) & v1_finseq_1(k3_euclid_9(A,B)) ) ) )).
fof(fc24_finseq_1,axiom,( ! [A] : v3_card_1(k5_finseq_1(A),1) )).
fof(fc24_finset_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc24_fomodel0,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_relat_1(k18_finseq_1(A)) & v1_relat_2(k18_finseq_1(A)) ) ) )).
fof(fc24_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ~ v5_fomodel1(k8_fomodel1(A),A) ) )).
fof(fc24_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k42_fomodel1(A,k43_fomodel1(A,D),B),C),A) ) )).
fof(fc24_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(fc24_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v6_fomodel4(k28_fomodel4(A),A) ) )).
fof(fc24_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc24_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k9_gate_1(B,C,A)) ) )).
fof(fc24_hahnban1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc24_hermitan,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc24_member_1,axiom,( ! [A] : ! [B] : ( ( v3_membered(A) & v3_membered(B) ) => v3_membered(k9_member_1(A,B)) ) )).
fof(fc24_membered,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) ) => v6_membered(k1_enumset1(A,B,C)) ) )).
fof(fc24_ordinal6,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc24_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc24_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc24_pre_poly,axiom,( ! [A] : ~ v1_xboole_0(k14_pre_poly(A)) )).
fof(fc24_ratfunc1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc24_relat_1,axiom,( ! [A] : ( ( v1_zfmisc_1(A) & v1_relat_1(A) ) => v1_zfmisc_1(k9_xtuple_0(A)) ) )).
fof(fc24_scmfsa10,axiom,( v1_amistd_1(k4_xtuple_0(k2_compos_1(k1_scmfsa_2)),k7_card_1(3),k1_scmfsa_2) )).
fof(fc24_scmfsa6c,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc24_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc24_scmpds_5,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) & v2_compos_1(A,k1_scmpds_2) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) & v2_compos_1(B,k1_scmpds_2) ) => ( v1_relat_1(k1_ordinal4(A,B)) & v5_ordinal1(k1_ordinal4(A,B)) & v1_funct_1(k1_ordinal4(A,B)) & v2_compos_1(k1_ordinal4(A,B),k1_scmpds_2) ) ) )).
fof(fc24_scmring3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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),k7_card_1(2),k1_scmring2(A)) ) )).
fof(fc24_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v11_scmyciel(A) ) => ( v4_scmyciel(k12_scmyciel(A)) & v11_scmyciel(k12_scmyciel(A)) ) ) )).
fof(fc24_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc24_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k18_sin_cos,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) & v2_funct_1(k5_relat_1(k18_sin_cos,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(fc24_topgrp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc24_toprealb,axiom,( v1_toprealb(k8_toprealb(2)) )).
fof(fc24_toprealc,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc24_trees_3,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc24_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_valued_0(A) & v1_relat_1(B) ) => v4_valued_0(k4_xboole_0(A,B)) ) )).
fof(fc24_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc24_valued_2,axiom,( ! [A] : ! [B] : ( v3_membered(B) => v3_valued_2(k4_partfun1(A,B)) ) )).
fof(fc24_waybel_4,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(fc24_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc24_xreal_0,axiom,( ! [A] : ! [B] : ( ( ~ v2_xxreal_0(A) & v1_xreal_0(A) & ~ v3_xxreal_0(B) & v1_xreal_0(B) ) => ~ v2_xxreal_0(k3_xcmplx_0(B,A)) ) )).
fof(fc24_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc24_yellow_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc25_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc25_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(fc25_afinsq_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc25_algstr_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc25_ami_6,axiom,( ! [A] : ! [B] : ( ( 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)),k7_card_1(2),k1_ami_3) ) )).
fof(fc25_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_rlvect_1(A) & l1_cayldick(A) ) => ( v4_rlvect_1(k4_cayldick(A)) & v1_cayldick(k4_cayldick(A)) ) ) )).
fof(fc25_comput_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => ( v1_relat_1(k3_comput_1(A,B)) & v4_relat_1(k3_comput_1(A,B),k3_finseq_2(k4_ordinal1)) & 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)) ) ) )).
fof(fc25_euclid_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) & m1_subset_1(B,u1_struct_0(k14_euclid(A))) & v1_xreal_0(C) & ~ v2_xxreal_0(C) ) => v1_xboole_0(k4_euclid_9(A,B,C)) ) )).
fof(fc25_finseq_1,axiom,( ! [A] : ! [B] : v3_card_1(k10_finseq_1(A,B),2) )).
fof(fc25_finset_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_finset_1(B) ) => ( v1_relat_1(k6_relat_1(A,B)) & v1_finset_1(k6_relat_1(A,B)) ) ) )).
fof(fc25_fomodel0,axiom,( ! [A] : ( v4_funct_1(A) => v1_relat_1(k3_tarski(A)) ) )).
fof(fc25_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ~ v9_fomodel1(k8_fomodel1(A),A) ) )).
fof(fc25_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ~ v7_fomodel1(k8_fomodel1(A),A) ) )).
fof(fc25_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(fc25_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k30_fomodel2(A))) ) => v5_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))),k24_fomodel4(A)),k1_xboole_0) ) )).
fof(fc25_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xboole_0(A) & v1_xboole_0(B) & v1_xboole_0(C) ) => v1_xboole_0(k10_gate_1(A,B,C)) ) )).
fof(fc25_hahnban1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc25_hermitan,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc25_member_1,axiom,( ! [A] : ! [B] : ( ( v4_membered(A) & v4_membered(B) ) => v4_membered(k9_member_1(A,B)) ) )).
fof(fc25_membered,axiom,( ! [A] : ! [B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k2_xboole_0(A,B)) ) )).
fof(fc25_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ~ v4_card_3(k1_classes1(k2_xboole_0(A,k4_ordinal1))) ) )).
fof(fc25_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc25_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc25_pre_poly,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc25_ratfunc1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc25_relat_1,axiom,( ! [A] : ( ( v1_zfmisc_1(A) & v1_relat_1(A) ) => v1_zfmisc_1(k10_xtuple_0(A)) ) )).
fof(fc25_scmfsa10,axiom,( v2_amistd_1(k2_compos_1(k1_scmfsa_2),k7_card_1(3),k1_scmfsa_2) )).
fof(fc25_scmfsa6c,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) & 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)) ) ) )).
fof(fc25_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc25_scmpds_5,axiom,( ! [A] : ( ( 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) ) )).
fof(fc25_scmyciel,axiom,( ! [A] : ! [B] : ( ( v4_scmyciel(A) & v7_ordinal1(B) ) => v4_scmyciel(k1_funct_1(k13_scmyciel(A),B)) ) )).
fof(fc25_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc25_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k18_sin_cos,k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos))) & v2_funct_1(k5_relat_1(k18_sin_cos,k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos))) )).
fof(fc25_toprealb,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc25_toprealc,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc25_trees_3,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc25_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_valued_0(A) & v1_relat_1(B) & v1_valued_0(B) ) => v1_valued_0(k5_xboole_0(A,B)) ) )).
fof(fc25_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc25_valued_2,axiom,( ! [A] : ! [B] : ( v4_membered(B) => v4_valued_2(k4_partfun1(A,B)) ) )).
fof(fc25_waybel_4,axiom,( ! [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) & l1_orders_2(A) ) => v6_waybel_4(k1_waybel_4(A),A) ) )).
fof(fc25_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc25_xreal_0,axiom,( ! [A] : ! [B] : ( ( ~ v2_xxreal_0(A) & v1_xreal_0(A) & ~ v2_xxreal_0(B) & v1_xreal_0(B) ) => ~ v3_xxreal_0(k3_xcmplx_0(A,B)) ) )).
fof(fc25_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc25_yellow_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc26_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc26_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v1_relat_1(k16_afinsq_1(A,B,C,D)) & v1_funct_1(k16_afinsq_1(A,B,C,D)) ) )).
fof(fc26_afinsq_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc26_ami_6,axiom,( ! [A] : ! [B] : ( ( 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)),k7_card_1(2),k1_ami_3) ) )).
fof(fc26_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_algstr_1(A) & l1_cayldick(A) ) => ( v1_algstr_1(k4_cayldick(A)) & v1_cayldick(k4_cayldick(A)) ) ) )).
fof(fc26_comput_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v7_comput_1(A) & v8_comput_1(A,k5_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) ) ) )).
fof(fc26_euclid_9,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,u1_struct_0(k14_euclid(k5_numbers))) & v1_xreal_0(B) ) => ~ v1_xboole_0(k4_euclid_9(k5_numbers,A,B)) ) )).
fof(fc26_finseq_1,axiom,( ! [A] : ! [B] : ! [C] : v3_card_1(k11_finseq_1(A,B,C),3) )).
fof(fc26_finset_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_finset_1(B) ) => ( v1_relat_1(k5_relat_1(B,A)) & v1_finset_1(k5_relat_1(B,A)) ) ) )).
fof(fc26_fomodel0,axiom,( ! [A] : v1_xboole_0(k4_xboole_0(A,A)) )).
fof(fc26_fomodel1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v8_ordinal1(B) & v14_fomodel1(C,B,A) & m1_subset_1(C,k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) ) => v8_ordinal1(k38_fomodel1(A,C)) ) )).
fof(fc26_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ 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(k43_fomodel1(A,k1_fomodel2(A)),B),A) ) )).
fof(fc26_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v7_ordinal1(C) & v8_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)))) ) )).
fof(fc26_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) => v5_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))),k24_fomodel4(A)),k1_xboole_0) ) )).
fof(fc26_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xboole_0(A) & v1_xboole_0(B) & ~ v1_xboole_0(C) ) => ~ v1_xboole_0(k10_gate_1(A,B,C)) ) )).
fof(fc26_member_1,axiom,( ! [A] : ! [B] : ( ( v5_membered(A) & v5_membered(B) ) => v5_membered(k9_member_1(A,B)) ) )).
fof(fc26_membered,axiom,( ! [A] : ! [B] : ( ( v2_membered(A) & v2_membered(B) ) => v2_membered(k2_xboole_0(A,B)) ) )).
fof(fc26_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc26_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc26_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ( v4_funct_1(k18_pre_poly(A,B)) & ~ v1_xboole_0(k18_pre_poly(A,B)) ) ) )).
fof(fc26_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc26_scmfsa10,axiom,( ! [A] : ( v7_ordinal1(A) => v1_amistd_1(k4_xtuple_0(k11_scmfsa_2(A)),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc26_scmfsa6c,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) & 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),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(fc26_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => v6_compos_0(k11_scmfsa_2(A),u1_compos_1(k1_scmfsa_2)) ) )).
fof(fc26_scmpds_5,axiom,( ! [A] : ! [B] : ( ( v6_compos_0(A,u1_compos_1(k1_scmpds_2)) & m1_subset_1(A,u1_compos_1(k1_scmpds_2)) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) & v2_compos_1(B,k1_scmpds_2) ) => ( v1_relat_1(k2_scmpds_4(A,B)) & v4_relat_1(k2_scmpds_4(A,B),k4_ordinal1) & v5_relat_1(k2_scmpds_4(A,B),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k2_scmpds_4(A,B)) & 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) ) ) )).
fof(fc26_scmring3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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),k7_card_1(2),k1_scmring2(A)) ) )).
fof(fc26_scmyciel,axiom,( ! [A] : ! [B] : ( ( v4_scmyciel(A) & v6_scmyciel(A) & v7_ordinal1(B) ) => v6_scmyciel(k1_funct_1(k13_scmyciel(A),B)) ) )).
fof(fc26_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc26_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k18_sin_cos,k2_rcomp_1(k28_sin_cos,k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos)))) & v2_funct_1(k5_relat_1(k18_sin_cos,k2_rcomp_1(k28_sin_cos,k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos)))) )).
fof(fc26_toprealb,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k8_toprealb(2))) => ( ~ v2_struct_0(k11_toprealb(A)) & v1_pre_topc(k11_toprealb(A)) ) ) )).
fof(fc26_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc26_trees_3,axiom,( ! [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) ) => ( ~ v1_xboole_0(k13_trees_3(A,B)) & v1_finset_1(k13_trees_3(A,B)) & v1_trees_1(k13_trees_3(A,B)) ) ) )).
fof(fc26_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v2_valued_0(A) & v1_relat_1(B) & v2_valued_0(B) ) => v2_valued_0(k5_xboole_0(A,B)) ) )).
fof(fc26_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc26_valued_2,axiom,( ! [A] : ! [B] : ( v5_membered(B) => v5_valued_2(k4_partfun1(A,B)) ) )).
fof(fc26_waybel_4,axiom,( ! [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) ) => ~ v1_xboole_0(k12_waybel_4(A)) ) )).
fof(fc26_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc26_xreal_0,axiom,( ! [A] : ! [B] : ( ( ~ v3_xxreal_0(A) & v1_xreal_0(A) & ~ v3_xxreal_0(B) & v1_xreal_0(B) ) => ~ v3_xxreal_0(k3_xcmplx_0(A,B)) ) )).
fof(fc26_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc27_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v5_ordinal1(k16_afinsq_1(A,B,C,D)) & v1_finset_1(k16_afinsq_1(A,B,C,D)) ) )).
fof(fc27_ami_6,axiom,( ! [A] : ! [B] : ( ( 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)),k7_card_1(2),k1_ami_3) ) )).
fof(fc27_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & l1_cayldick(A) ) => ( v13_algstr_0(k4_cayldick(A)) & v1_cayldick(k4_cayldick(A)) ) ) )).
fof(fc27_comput_1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc27_euclid_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,u1_struct_0(k14_euclid(A))) & v1_xreal_0(C) & v2_xxreal_0(C) ) => ~ v1_xboole_0(k4_euclid_9(A,B,C)) ) )).
fof(fc27_finseq_1,axiom,( ! [A] : v3_finseq_1(k13_finseq_1(A)) )).
fof(fc27_finset_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc27_fomodel0,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(fc27_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v5_fomodel1(B,A) & m1_subset_1(B,k1_fomodel1(A)) ) => ~ v8_ordinal1(k19_fomodel1(A,B)) ) )).
fof(fc27_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k43_fomodel1(A,B),C),A) ) )).
fof(fc27_fomodel3,axiom,( ! [A] : ! [B] : ( v4_funct_1(B) => v4_funct_1(k3_xboole_0(A,B)) ) )).
fof(fc27_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) => v5_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))),k24_fomodel4(A)),k1_xboole_0) ) )).
fof(fc27_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xboole_0(A) & v1_xboole_0(B) & ~ v1_xboole_0(C) ) => ~ v1_xboole_0(k10_gate_1(A,C,B)) ) )).
fof(fc27_hahnban1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc27_ideal_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc27_member_1,axiom,( ! [A] : ! [B] : ( ( v6_membered(A) & v6_membered(B) ) => v6_membered(k9_member_1(A,B)) ) )).
fof(fc27_membered,axiom,( ! [A] : ! [B] : ( ( v3_membered(A) & v3_membered(B) ) => v3_membered(k2_xboole_0(A,B)) ) )).
fof(fc27_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc27_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & v2_pre_poly(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => v1_finset_1(k18_pre_poly(A,B)) ) )).
fof(fc27_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc27_scmfsa10,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ v4_compos_0(k11_scmfsa_2(A),u1_compos_1(k1_scmfsa_2)) & v2_amistd_1(k11_scmfsa_2(A),k7_card_1(3),k1_scmfsa_2) & ~ v4_amistd_1(k11_scmfsa_2(A),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(fc27_scmfsa6c,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) & 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)) ) ) )).
fof(fc27_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & 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)) ) )).
fof(fc27_scmpds_5,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & 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_relat_1(k3_scmpds_4(A,B)) & v4_relat_1(k3_scmpds_4(A,B),k4_ordinal1) & v5_relat_1(k3_scmpds_4(A,B),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k3_scmpds_4(A,B)) & 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) ) ) )).
fof(fc27_scmyciel,axiom,( ! [A] : ! [B] : ( ( v4_scmyciel(A) & v11_scmyciel(A) & v7_ordinal1(B) ) => v11_scmyciel(k1_funct_1(k13_scmyciel(A),B)) ) )).
fof(fc27_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc27_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k18_sin_cos,k2_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(2,k28_sin_cos)))) & v2_funct_1(k5_relat_1(k18_sin_cos,k2_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(2,k28_sin_cos)))) )).
fof(fc27_toprealb,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc27_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc27_trees_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k5_trees_3(A)) ) => v1_finset_1(k9_xtuple_0(B)) ) )).
fof(fc27_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v3_valued_0(A) & v1_relat_1(B) & v3_valued_0(B) ) => v3_valued_0(k5_xboole_0(A,B)) ) )).
fof(fc27_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc27_valued_2,axiom,( ! [A] : ! [B] : ( v6_membered(B) => v6_valued_2(k4_partfun1(A,B)) ) )).
fof(fc27_waybel_4,axiom,( ! [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) & l1_orders_2(A) ) => v8_waybel_4(k1_waybel_4(A),A) ) )).
fof(fc27_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc27_xreal_0,axiom,( ! [A] : ( ( v2_xxreal_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(k5_xcmplx_0(A)) & v2_xxreal_0(k5_xcmplx_0(A)) ) ) )).
fof(fc27_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc28_afinsq_2,axiom,( ! [A] : ( ( v1_finset_1(A) & v6_membered(A) ) => ( v1_relat_1(k4_afinsq_2(A)) & v5_relat_1(k4_afinsq_2(A),k4_ordinal1) & 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)) ) ) )).
fof(fc28_ami_6,axiom,( ! [A] : ! [B] : ( ( 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)),k7_card_1(2),k1_ami_3) ) )).
fof(fc28_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v12_algstr_0(A) & l1_cayldick(A) ) => ( v12_algstr_0(k4_cayldick(A)) & v1_cayldick(k4_cayldick(A)) ) ) )).
fof(fc28_comput_1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc28_euclid_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(fc28_finseq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(fc28_finset_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_finset_1(A) ) => v1_finset_1(k1_relat_1(A)) ) )).
fof(fc28_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc28_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc28_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k43_fomodel1(A,C),B),A) ) )).
fof(fc28_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc28_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ 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(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))),k24_fomodel4(A)),k1_xboole_0) ) )).
fof(fc28_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xboole_0(A) & v1_xboole_0(B) & ~ v1_xboole_0(C) ) => ~ v1_xboole_0(k10_gate_1(C,A,B)) ) )).
fof(fc28_glib_003,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc28_hermitan,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc28_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v2_membered(B) ) => v1_xboole_0(k10_member_1(A,B)) ) )).
fof(fc28_membered,axiom,( ! [A] : ! [B] : ( ( v4_membered(A) & v4_membered(B) ) => v4_membered(k2_xboole_0(A,B)) ) )).
fof(fc28_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc28_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc28_relat_1,axiom,( ! [A] : ( v1_relat_1(k4_relat_1(A)) & v4_relat_1(k4_relat_1(A),A) & v5_relat_1(k4_relat_1(A),A) ) )).
fof(fc28_scmfsa10,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) & v7_ordinal1(B) ) => v1_amistd_1(k4_xtuple_0(k12_scmfsa_2(B,A)),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc28_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & 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)) ) )).
fof(fc28_scmpds_5,axiom,( ! [A] : ! [B] : ( ( 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_relat_1(k4_scmpds_4(A,B)) & v4_relat_1(k4_scmpds_4(A,B),k4_ordinal1) & v5_relat_1(k4_scmpds_4(A,B),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k4_scmpds_4(A,B)) & 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) ) ) )).
fof(fc28_scmring3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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),k7_card_1(2),k1_scmring2(A)) ) )).
fof(fc28_scmyciel,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & v4_scmyciel(A) & v7_ordinal1(B) ) => v1_finset_1(k1_funct_1(k13_scmyciel(A),B)) ) )).
fof(fc28_sin_cos6,axiom,( ! [A] : v1_xreal_0(k2_sin_cos6(A)) )).
fof(fc28_toprealb,axiom,( 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)) )).
fof(fc28_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc28_valued_0,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc28_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc28_valued_2,axiom,( ! [A] : ! [B] : ( v1_membered(B) => v1_valued_2(k1_funct_2(A,B)) ) )).
fof(fc28_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc28_xreal_0,axiom,( ! [A] : ( ( ~ v2_xxreal_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(k5_xcmplx_0(A)) & ~ v2_xxreal_0(k5_xcmplx_0(A)) ) ) )).
fof(fc28_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc29_abcmiz_1,axiom,( ~ 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) )).
fof(fc29_afinsq_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc29_algstr_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) ) )).
fof(fc29_ami_6,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(2),k1_ami_3) ) )).
fof(fc29_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & l1_cayldick(A) ) => ( v2_rlvect_1(k4_cayldick(A)) & v1_cayldick(k4_cayldick(A)) ) ) )).
fof(fc29_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & 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(k4_ordinal1)) & v1_funct_1(k14_comput_1(A)) & v4_valued_0(k14_comput_1(A)) ) ) )).
fof(fc29_finseq_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc29_finset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : v1_finset_1(k4_funct_4(A,B,C,D)) )).
fof(fc29_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & v3_fomodel0(C,A) ) => v3_fomodel0(k7_relat_1(k9_fomodel0(A),k4_finseq_2(B,C)),A) ) )).
fof(fc29_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc29_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ 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_ordinal1(k29_fomodel2(A,B)) & ~ v8_ordinal1(k29_fomodel2(A,B)) ) ) )).
fof(fc29_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(fc29_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v6_fomodel4(k24_fomodel4(A),A) ) )).
fof(fc29_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_xboole_0(C) ) => v1_xboole_0(k10_gate_1(A,B,C)) ) )).
fof(fc29_glib_003,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc29_hermitan,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc29_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v2_membered(B) ) => v1_xboole_0(k10_member_1(B,A)) ) )).
fof(fc29_membered,axiom,( ! [A] : ! [B] : ( ( v5_membered(A) & v5_membered(B) ) => v5_membered(k2_xboole_0(A,B)) ) )).
fof(fc29_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc29_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc29_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc29_scmfsa10,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) & v7_ordinal1(B) ) => v1_amistd_1(k4_xtuple_0(k13_scmfsa_2(B,A)),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc29_scmfsa_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc29_scmpds_5,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) & v2_scmpds_4(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) & v2_scmpds_4(B) & v3_scmpds_4(B) ) => ( v1_relat_1(k1_ordinal4(A,B)) & v4_relat_1(k1_ordinal4(A,B),k4_ordinal1) & v5_relat_1(k1_ordinal4(A,B),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k1_ordinal4(A,B)) & 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)) ) ) )).
fof(fc29_sin_cos6,axiom,( v1_funct_1(k1_sin_cos6) & v2_funct_1(k1_sin_cos6) )).
fof(fc29_toprealb,axiom,( 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))) )).
fof(fc29_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc29_valued_0,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc29_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc29_valued_2,axiom,( ! [A] : ! [B] : ( v2_membered(B) => v2_valued_2(k1_funct_2(A,B)) ) )).
fof(fc29_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc29_xreal_0,axiom,( ! [A] : ( ( v3_xxreal_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(k5_xcmplx_0(A)) & v3_xxreal_0(k5_xcmplx_0(A)) ) ) )).
fof(fc29_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_abcmiz_0,axiom,( ! [A] : ( ( ~ v4_abcmiz_0(A) & l1_abcmiz_0(A) ) => ~ v1_xboole_0(u1_abcmiz_0(A)) ) )).
fof(fc2_abcmiz_1,axiom,( ~ v1_xboole_0(k2_abcmiz_1) )).
fof(fc2_abcmiz_a,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc2_abian,axiom,( ! [A] : ( ( v1_int_1(A) & v1_abian(A) ) => ~ v1_abian(k2_xcmplx_0(A,1)) ) )).
fof(fc2_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_xreal_0(k1_absvalue(A)) & v1_int_1(k1_absvalue(A)) ) ) )).
fof(fc2_afinsq_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v1_incsp_1(k13_afproj(A)) & v5_incproj(k13_afproj(A)) ) ) )).
fof(fc2_afvect0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc2_algstr_1,axiom,( v2_rlvect_1(k3_algstr_0) )).
fof(fc2_altcat_1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc2_altcat_2,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc2_altcat_4,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc2_ami_2,axiom,( v1_relat_1(k3_relat_1(k3_ami_2,k4_ami_2)) & v2_relat_1(k3_relat_1(k3_ami_2,k4_ami_2)) )).
fof(fc2_ami_3,axiom,( ~ v2_struct_0(k1_ami_3) & v1_extpro_1(k1_ami_3,k7_card_1(2)) )).
fof(fc2_ami_5,axiom,( v1_extpro_1(k1_ami_3,k7_card_1(2)) & v3_amistd_5(k1_ami_3,k7_card_1(2)) )).
fof(fc2_ami_6,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(2),k1_ami_3) ) )).
fof(fc2_amistd_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) & v7_ordinal1(D) ) => ~ v1_xboole_0(k1_amistd_1(A,B,D,C)) ) )).
fof(fc2_amistd_2,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ( v1_extpro_1(k4_amistd_1(A),A) & v2_amistd_2(k4_amistd_1(A),A) ) ) )).
fof(fc2_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analmetr(A) ) => ( ~ v2_struct_0(k3_analmetr(A)) & v1_analoaf(k3_analmetr(A)) ) ) )).
fof(fc2_analort,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) ) )).
fof(fc2_anproj_1,axiom,( ! [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) & l1_rlvect_1(A) ) => ( ~ v2_struct_0(k5_anproj_1(A)) & v1_collsp(k5_anproj_1(A)) ) ) )).
fof(fc2_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => ( v1_collsp(k5_anproj_1(A)) & v2_anproj_2(k5_anproj_1(A)) ) ) )).
fof(fc2_aofa_000,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_msafree4(B,u1_struct_0(A)) & v4_msualg_1(C,A) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ( v2_relat_1(k1_aofa_a01(A,B,C)) & v7_msafree4(k1_aofa_a01(A,B,C),A,C,k5_msafree4(A,C)) ) ) )).
fof(fc2_armstrng,axiom,( ! [A] : ~ v1_xboole_0(k4_armstrng(A)) )).
fof(fc2_arrow,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k3_arrow(A)) ) )).
fof(fc2_arytm_2,axiom,( ~ v1_xboole_0(k2_arytm_2) )).
fof(fc2_arytm_3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v7_ordinal1(A) & v3_ordinal1(B) & v7_ordinal1(B) ) => ( v3_ordinal1(k7_ordinal3(A,B)) & v7_ordinal1(k7_ordinal3(A,B)) ) ) )).
fof(fc2_asympt_1,axiom,( v1_funct_1(k2_asympt_1) & v1_funct_2(k2_asympt_1,k4_ordinal1,k1_numbers) & v4_asympt_0(k2_asympt_1) )).
fof(fc2_bagorder,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(fc2_bcialg_2,axiom,( ! [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_2(k4_struct_0(A),A) ) )).
fof(fc2_bcialg_4,axiom,( 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) )).
fof(fc2_bcialg_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc2_bhsp_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & v1_bhsp_3(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_bhsp_3(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k3_normsp_1(A,B,C)) & v1_funct_2(k3_normsp_1(A,B,C),k4_ordinal1,u1_struct_0(A)) & v1_bhsp_3(k3_normsp_1(A,B,C),A) ) ) )).
fof(fc2_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc2_binop_2,axiom,( v1_funct_1(k5_binop_2) & v1_funct_2(k5_binop_2,k2_zfmisc_1(k2_numbers,k2_numbers),k2_numbers) & v1_binop_1(k5_binop_2,k2_numbers) & v2_binop_1(k5_binop_2,k2_numbers) )).
fof(fc2_bintree1,axiom,( ~ v1_xboole_0(k2_trees_1(2)) & v1_trees_1(k2_trees_1(2)) & v1_bintree1(k2_trees_1(2)) )).
fof(fc2_bintree2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree1(A) & v7_ordinal1(B) ) => v1_finset_1(k2_trees_2(A,B)) ) )).
fof(fc2_borsuk_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc2_borsuk_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc2_borsuk_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_borsuk_4,axiom,( v1_pre_topc(k1_borsuk_4) & v1_tsep_1(k1_borsuk_4,k5_topmetr) )).
fof(fc2_borsuk_5,axiom,( v1_xreal_0(k4_power) & ~ v1_rat_1(k4_power) )).
fof(fc2_borsuk_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc2_borsuk_7,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_bspace,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k8_bspace(A)) ) )).
fof(fc2_bvfunc26,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_c0sp1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc2_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ~ v1_xboole_0(k2_c0sp2(A)) ) )).
fof(fc2_calcul_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_cantor_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ~ v1_xboole_0(k2_cantor_1(A,B)) ) )).
fof(fc2_card_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v8_ordinal1(k1_card_1(A)) & v1_card_1(k1_card_1(A)) ) ) )).
fof(fc2_card_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc2_card_3,axiom,( ! [A] : ! [B] : ( v1_card_1(B) => v1_card_3(k2_funcop_1(A,B)) ) )).
fof(fc2_card_5,axiom,( ! [A] : ( v3_ordinal1(A) => ~ v1_finset_1(k3_card_1(A)) ) )).
fof(fc2_card_fil,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ( v1_card_1(k2_card_1(A)) & ~ v2_card_1(k2_card_1(A)) ) ) )).
fof(fc2_card_fin,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_cardfin2,axiom,( v2_xxreal_0(k4_power) & v1_xreal_0(k4_power) )).
fof(fc2_cat_1,axiom,( ! [A] : ! [B] : ( v1_cat_1(k3_cat_1(A,B)) & v2_cat_1(k3_cat_1(A,B)) ) )).
fof(fc2_cat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) ) )).
fof(fc2_cat_4,axiom,( ! [A] : ! [B] : ( ~ 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)) ) )).
fof(fc2_cat_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) )).
fof(fc2_catalan1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( ~ v8_ordinal1(k1_catalan1(A)) & v1_xreal_0(k1_catalan1(A)) ) ) )).
fof(fc2_catalan2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => v1_finset_1(k2_catalan2(A,B)) ) )).
fof(fc2_catalg_1,axiom,( ! [A] : ( v1_msualg_1(k2_catalg_1(A)) & v1_instalg1(k2_catalg_1(A)) ) )).
fof(fc2_cayldick,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & v1_xcmplx_0(A) ) => ~ v8_ordinal1(k1_square_1(A)) ) )).
fof(fc2_cayley,axiom,( ! [A] : ( ~ v1_xboole_0(k1_cayley(A)) & v4_funct_1(k1_cayley(A)) ) )).
fof(fc2_cc0sp1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc2_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ~ v1_xboole_0(k2_cc0sp2(A)) ) )).
fof(fc2_cfuncdom,axiom,( ! [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)) & v7_valued_2(k2_cfuncdom(A)) ) )).
fof(fc2_cgames_1,axiom,( v2_cgames_1(k1_cgames_1) )).
fof(fc2_chain_1,axiom,( ! [A] : ! [B] : ( ~ v1_zfmisc_1(A) => ~ v1_zfmisc_1(k2_xboole_0(B,A)) ) )).
fof(fc2_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & m1_subset_1(B,k4_ordinal1) & 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)) ) ) )).
fof(fc2_circcomb,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(fc2_circled1,axiom,( ! [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) & 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)) ) )).
fof(fc2_circtrm1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc2_ckspace1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) & ~ v1_xboole_0(C) & v1_pdiff_7(C,A) & m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) ) => ( v13_algstr_0(k2_ckspace1(A,B,C)) & v2_rlvect_1(k2_ckspace1(A,B,C)) & v3_rlvect_1(k2_ckspace1(A,B,C)) & v4_rlvect_1(k2_ckspace1(A,B,C)) & v5_rlvect_1(k2_ckspace1(A,B,C)) & v6_rlvect_1(k2_ckspace1(A,B,C)) & v7_rlvect_1(k2_ckspace1(A,B,C)) & v8_rlvect_1(k2_ckspace1(A,B,C)) & v3_group_1(k2_ckspace1(A,B,C)) & v5_group_1(k2_ckspace1(A,B,C)) & v1_vectsp_1(k2_ckspace1(A,B,C)) & v3_vectsp_1(k2_ckspace1(A,B,C)) & v2_funcsdom(k2_ckspace1(A,B,C)) ) ) )).
fof(fc2_classes1,axiom,( ! [A] : ( v3_ordinal1(A) => v1_ordinal1(k4_classes1(A)) ) )).
fof(fc2_classes2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => v3_ordinal1(k2_ordinal1(A)) ) )).
fof(fc2_clopban1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc2_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => v1_group_1(k7_clopban2(A)) ) )).
fof(fc2_closure2,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc2_closure3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc2_coh_sp,axiom,( ! [A] : ( v4_funct_1(k4_coh_sp(A)) & ~ v1_xboole_0(k4_coh_sp(A)) ) )).
fof(fc2_cohsp_1,axiom,( ! [A] : ( v1_classes1(k1_zfmisc_1(A)) & v1_coh_sp(k1_zfmisc_1(A)) ) )).
fof(fc2_compact1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc2_compl_sp,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc2_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_xreal_0(k2_complex1(A)) ) )).
fof(fc2_complfld,axiom,( v36_algstr_0(k1_complfld) & v4_vectsp_1(k1_complfld) )).
fof(fc2_compos_0,axiom,( v1_compos_0(k1_tarski(k3_xtuple_0(1,k1_xboole_0,k1_xboole_0))) )).
fof(fc2_compos_1,axiom,( ! [A] : ( 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),k4_ordinal1) & 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)) ) ) )).
fof(fc2_compos_2,axiom,( ! [A] : ! [B] : ( ( v1_amistd_4(A) & l1_compos_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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) ) ) )).
fof(fc2_compts_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v2_struct_0(k1_compts_1(A)) ) )).
fof(fc2_comput_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_comseq_2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc2_comseq_3,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc2_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l5_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) )).
fof(fc2_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ( v3_lattices(k1_lattice2(A)) & v4_lattice3(k1_lattice2(A)) ) ) )).
fof(fc2_connsp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc2_convex1,axiom,( ! [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) & 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)) ) )).
fof(fc2_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => v1_xboole_0(k13_pre_poly(k2_convex4(A))) ) )).
fof(fc2_convfun1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc2_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ~ v1_xboole_0(k3_cqc_lang(A)) ) )).
fof(fc2_csspace,axiom,( ~ 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) )).
fof(fc2_csspace3,axiom,( v6_clvect_1(k1_csspace3,k7_csspace) )).
fof(fc2_csspace4,axiom,( v6_clvect_1(k1_csspace4,k7_csspace) )).
fof(fc2_descip_1,axiom,( 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)) )).
fof(fc2_dickson,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( ~ v2_struct_0(k5_dickson(A)) & v1_orders_2(k5_dickson(A)) ) ) )).
fof(fc2_diff_1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc2_dilworth,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_dilworth(A) & l1_orders_2(A) ) => ( v2_xxreal_0(k1_dilworth(A)) & v7_ordinal1(k1_dilworth(A)) ) ) )).
fof(fc2_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ~ v1_xboole_0(k6_dist_1(A)) ) )).
fof(fc2_dtconstr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dtconstr(A) & l1_lang1(A) ) => ~ v1_xboole_0(k4_dtconstr(A)) ) )).
fof(fc2_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => v1_ec_pf_1(k9_int_3(A)) ) )).
fof(fc2_endalg,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc2_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_ens_1(A)) ) )).
fof(fc2_eqrel_1,axiom,( ! [A] : ( v3_relat_2(k1_eqrel_1(A)) & v8_relat_2(k1_eqrel_1(A)) & v1_partfun1(k1_eqrel_1(A),A) ) )).
fof(fc2_equation,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc2_euclid,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => ( v1_xreal_0(k12_euclid(A)) & ~ v3_xxreal_0(k12_euclid(A)) ) ) )).
fof(fc2_euclid_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc2_euclid_7,axiom,( ! [A] : ! [B] : ( ( v2_euclid_7(A) & v2_euclid_7(B) ) => v2_euclid_7(k2_xboole_0(A,B)) ) )).
fof(fc2_euclidlp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & 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)) ) )).
fof(fc2_exchsort,axiom,( ! [A] : ! [B] : ( v3_ordinal1(A) => v1_exchsort(k1_tarski(k4_tarski(A,B))) ) )).
fof(fc2_extpro_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ( v2_memstr_0(k1_extpro_1(A),A) & v1_extpro_1(k1_extpro_1(A),A) ) ) )).
fof(fc2_facirc_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xtuple_0(A) & ~ v1_xtuple_0(B) ) => ~ v1_facirc_1(k2_tarski(A,B)) ) )).
fof(fc2_facirc_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_facirc_1(A) ) => ~ v1_xtuple_0(k1_funct_1(A,B)) ) )).
fof(fc2_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_fcont_3,axiom,( v3_rcomp_1(k2_subset_1(k1_numbers)) )).
fof(fc2_fdiff_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v9_ordinal1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v7_ordinal1(B) ) => ( v1_funct_1(k7_nat_1(A,B)) & v9_ordinal1(k7_nat_1(A,B)) & v1_funct_2(k7_nat_1(A,B),k4_ordinal1,k1_numbers) ) ) )).
fof(fc2_fib_num2,axiom,( ! [A] : ( ( v1_int_1(A) & v1_abian(A) ) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_abian(k4_xcmplx_0(A)) ) ) )).
fof(fc2_fib_num3,axiom,( v1_xreal_0(k2_fib_num) & v3_xxreal_0(k2_fib_num) )).
fof(fc2_filter_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc2_filter_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc2_filter_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc2_finseq_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ~ v1_xboole_0(k1_finseq_1(A)) ) )).
fof(fc2_finseq_2,axiom,( v1_relat_1(k1_finseq_2(k5_numbers)) & v1_funct_1(k1_finseq_2(k5_numbers)) & v1_xboole_0(k1_finseq_2(k5_numbers)) & v1_finseq_1(k1_finseq_2(k5_numbers)) )).
fof(fc2_finseq_3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(A) => v3_card_3(k4_finseq_2(A,B)) ) )).
fof(fc2_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( 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)) ) )).
fof(fc2_finseq_5,axiom,( ! [A] : ! [B] : ~ v1_zfmisc_1(k10_finseq_1(A,B)) )).
fof(fc2_finseq_6,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(k3_finseq_5(A)) & ~ v1_xboole_0(k3_finseq_5(A)) & v1_funct_1(k3_finseq_5(A)) & v1_finseq_1(k3_finseq_5(A)) ) ) )).
fof(fc2_finset_1,axiom,( ! [A] : ! [B] : v1_finset_1(k2_tarski(A,B)) )).
fof(fc2_finsub_1,axiom,( ! [A] : ( ~ v1_xboole_0(k5_finsub_1(A)) & v4_finsub_1(k5_finsub_1(A)) ) )).
fof(fc2_fintopo5,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ( ~ v2_struct_0(k5_fintopo5(A,B)) & v1_orders_2(k5_fintopo5(A,B)) ) ) )).
fof(fc2_fintopo6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => v4_fin_topo(k1_tarski(B),A) ) )).
fof(fc2_fomodel0,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc2_fomodel1,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(fc2_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc2_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k3_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) ) )).
fof(fc2_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v1_relat_1(k1_fomodel4(A)) ) )).
fof(fc2_frechet,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc2_freealg,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,k4_ordinal1) ) => ( v1_lang1(k3_freealg(A,B)) & v2_dtconstr(k3_freealg(A,B)) ) ) )).
fof(fc2_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) ) )).
fof(fc2_fsm_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc2_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc2_funcop_1,axiom,( ! [A] : v1_xboole_0(k2_funcop_1(k1_xboole_0,A)) )).
fof(fc2_funcsdom,axiom,( ! [A] : ( 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)) & v9_valued_2(k6_funcsdom(A)) ) )).
fof(fc2_funct_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_funct_2,axiom,( ! [A] : ~ v1_xboole_0(k1_funct_2(A,A)) )).
fof(fc2_funct_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc2_funct_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k3_funct_5(A)) & v1_funct_1(k3_funct_5(A)) & v1_funcop_1(k3_funct_5(A)) ) ) )).
fof(fc2_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ~ v1_xboole_0(k4_funct_4(A,B,C,D)) )).
fof(fc2_funct_8,axiom,( 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) )).
fof(fc2_funct_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(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) ) ) )).
fof(fc2_functor0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_functor1,axiom,( ! [A] : ( v1_relat_1(k4_relat_1(A)) & v2_funct_2(k4_relat_1(A),A) ) )).
fof(fc2_fvaluat1,axiom,( ~ v1_fvaluat1(k2_xxreal_0) )).
fof(fc2_fvsum_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc2_gate_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => v1_xboole_0(k1_gate_1(A)) ) )).
fof(fc2_gcd_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc2_geomtrap,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_geomtrap(A) ) => ( ~ v2_struct_0(k8_geomtrap(A)) & v1_analoaf(k8_geomtrap(A)) ) ) )).
fof(fc2_gfacirc2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc2_glib_001,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) ) )).
fof(fc2_glib_003,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc2_glib_005,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(fc2_goboard2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ~ v1_xboole_0(k2_goboard1(A)) ) )).
fof(fc2_gr_cy_1,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(fc2_graph_1,axiom,( ! [A] : ( ( v6_graph_1(A) & l1_graph_1(A) ) => v1_finset_1(u4_struct_0(A)) ) )).
fof(fc2_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc2_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => v1_finset_1(k7_graph_5(A)) ) )).
fof(fc2_graphsp,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k3_finseq_2(k1_numbers)) & m1_subset_1(B,k4_ordinal1) ) => v1_finset_1(k12_graphsp(A,B)) ) )).
fof(fc2_grcat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) )).
fof(fc2_grfunc_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v1_funct_1(k4_xboole_0(A,B)) ) )).
fof(fc2_groeb_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc2_groeb_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,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),B) ) ) )).
fof(fc2_group_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc2_group_10,axiom,( ! [A] : ! [B] : ( v1_finset_1(A) => v1_finset_1(k3_group_10(A,B)) ) )).
fof(fc2_group_12,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc2_group_14,axiom,( ! [A] : ! [B] : ( ( ~ 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(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ( v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) & ~ v1_xboole_0(k10_finseq_1(A,B)) & v1_finseq_1(k10_finseq_1(A,B)) & v1_prvect_1(k10_finseq_1(A,B)) ) ) )).
fof(fc2_group_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc2_group_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc2_group_6,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc2_group_7,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_group_9,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc2_hahnban1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc2_hallmar1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(A) & m1_finseq_1(B,k1_zfmisc_1(A)) ) => v1_finset_1(k1_hallmar1(A,B,C)) ) )).
fof(fc2_hausdorf,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc2_helly,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) ) )).
fof(fc2_hermitan,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(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)))) ) => ( v1_funct_1(k3_hahnban1(k1_complfld,A,B,C)) & v1_funct_2(k3_hahnban1(k1_complfld,A,B,C),u1_struct_0(A),u1_struct_0(k1_complfld)) & v1_hermitan(k3_hahnban1(k1_complfld,A,B,C),A) ) ) )).
fof(fc2_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ( v3_lattices(k5_substlat(A,B)) & v3_filter_0(k5_substlat(A,B)) ) ) )).
fof(fc2_heyting3,axiom,( ! [A] : ! [B] : ( v1_lattice3(k1_heyting3(A,B)) & v2_lattice3(k1_heyting3(A,B)) ) )).
fof(fc2_hilbasis,axiom,( ! [A] : ! [B] : ( ( ~ 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,k4_ordinal1) ) => ( v1_funct_1(k6_hilbasis(A,B)) & v1_funct_2(k6_hilbasis(A,B),u1_struct_0(k14_polynom3(k12_polynom1(B,A))),u1_struct_0(k12_polynom1(k1_nat_1(B,1),A))) & v13_vectsp_1(k6_hilbasis(A,B),k14_polynom3(k12_polynom1(B,A)),k12_polynom1(k1_nat_1(B,1),A)) ) ) )).
fof(fc2_hilbert1,axiom,( v4_funct_1(k1_hilbert1) )).
fof(fc2_hilbert3,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) & v7_ordinal1(B) & ~ v8_ordinal1(B) ) => v2_funct_1(k4_funct_4(B,k5_numbers,k5_numbers,A)) ) )).
fof(fc2_idea_1,axiom,( v4_funct_1(k14_idea_1) )).
fof(fc2_ideal_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(fc2_incproj,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => v1_incsp_1(k3_incproj(A)) ) )).
fof(fc2_index_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_index_1(A) ) => v2_cat_5(k10_xtuple_0(A)) ) )).
fof(fc2_instalg1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc2_int_1,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_int_1(B) ) => v1_int_1(k3_xcmplx_0(A,B)) ) )).
fof(fc2_int_3,axiom,( v5_membered(u1_struct_0(k1_int_3)) )).
fof(fc2_int_4,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & v3_membered(A) & v1_xreal_0(B) ) => v1_finset_1(k23_member_1(A,B)) ) )).
fof(fc2_int_6,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_int_7,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc2_integr16,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc2_integra1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc2_interva1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc2_intpro_1,axiom,( v4_funct_1(k1_intpro_1) )).
fof(fc2_isocat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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),k9_nattra_1(A,k6_cat_2(B,C)),k6_cat_2(k9_nattra_1(A,B),k9_nattra_1(A,C))) ) )).
fof(fc2_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v5_tops_1(k2_struct_0(A),A) & v6_tops_1(k2_struct_0(A),A) ) ) )).
fof(fc2_jgraph_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc2_jgraph_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(fc2_jordan,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,u1_struct_0(k15_euclid(A))) ) => ( v1_xreal_0(k1_topreal6(A,B,C)) & ~ v3_xxreal_0(k1_topreal6(A,B,C)) ) ) )).
fof(fc2_jordan1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => v1_convex1(k5_topreal1(A),k15_euclid(2)) ) )).
fof(fc2_jordan10,axiom,( ! [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_xboole_0(k1_jordan10(A)) ) )).
fof(fc2_jordan14,axiom,( ! [A] : ! [B] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & v7_ordinal1(B) ) => v2_compts_1(k2_pre_topc(k15_euclid(2),k3_goboard9(k1_jordan13(A,B))),k15_euclid(2)) ) )).
fof(fc2_jordan18,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ~ v1_xboole_0(k7_relat_1(k5_pscomp_1,k6_topreal1(A))) ) )).
fof(fc2_jordan1d,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_abian(A) & v7_ordinal1(B) & ~ v8_ordinal1(B) ) => v1_abian(k1_newton(A,B)) ) )).
fof(fc2_jordan1e,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc2_jordan1g,axiom,( ! [A] : ! [B] : ( ( 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)))) & v7_ordinal1(B) ) => v2_goboard5(k1_jordan1e(A,B)) ) )).
fof(fc2_jordan1h,axiom,( 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) )).
fof(fc2_jordan21,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc2_jordan22,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc2_jordan23,axiom,( ! [A] : v2_jordan23(k5_finseq_1(A)) )).
fof(fc2_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => v1_convex1(k2_struct_0(k15_euclid(A)),k15_euclid(A)) ) )).
fof(fc2_jordan5a,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => v1_rcomp_1(k1_xxreal_1(A,B)) ) )).
fof(fc2_jordan6,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc2_jordan8,axiom,( ! [A] : ! [B] : ( ( ~ 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_0(k1_jordan8(A,B)) & v3_goboard1(k1_jordan8(A,B)) & v4_goboard1(k1_jordan8(A,B)) ) ) )).
fof(fc2_jordan_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_jordan_a(B,A) & v7_ordinal1(C) ) => ( ~ v1_xboole_0(k2_jordan_a(A,C,B)) & v2_compts_1(k2_jordan_a(A,C,B),k15_euclid(2)) ) ) )).
fof(fc2_kolmog01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc2_kurato_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc2_kurato_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(fc2_lang1,axiom,( ! [A] : ! [B] : ( ~ v2_struct_0(k7_lang1(A,B)) & v2_lang1(k7_lang1(A,B)) ) )).
fof(fc2_latsum_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc2_lattice2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc2_lattice3,axiom,( ! [A] : ( v3_lattices(k1_lattice3(A)) & v10_lattices(k1_lattice3(A)) ) )).
fof(fc2_lattice4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc2_lattice5,axiom,( ! [A] : ( v3_orders_2(k1_lattice5(A)) & v4_orders_2(k1_lattice5(A)) & v5_orders_2(k1_lattice5(A)) & v3_lattice3(k1_lattice5(A)) ) )).
fof(fc2_lattice8,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v3_ordinal1(B) ) => ~ v1_xboole_0(k3_lattice8(A,B)) ) )).
fof(fc2_lattices,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc2_lexbfs,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1),k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)))) ) => v1_finset_1(k1_xtuple_0(B)) ) )).
fof(fc2_lfuzzy_0,axiom,( ~ v1_xboole_0(k1_xxreal_1(k5_numbers,1)) )).
fof(fc2_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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(k5_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) ) ) )).
fof(fc2_lmod_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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)) ) ) )).
fof(fc2_lopban_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc2_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => v1_group_1(k7_lopban_2(A)) ) )).
fof(fc2_lopban_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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_rlsub_1(k3_lopban_7(A,B,C),k7_prvect_3(A,B)) ) )).
fof(fc2_lopclset,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc2_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_funct_1(k7_lpspacc1(A)) & v1_funct_2(k7_lpspacc1(A),k2_zfmisc_1(k3_rfunct_3(A,k2_numbers),k3_rfunct_3(A,k2_numbers)),k3_rfunct_3(A,k2_numbers)) & v1_binop_1(k7_lpspacc1(A),k3_rfunct_3(A,k2_numbers)) & v2_binop_1(k7_lpspacc1(A),k3_rfunct_3(A,k2_numbers)) ) ) )).
fof(fc2_lpspace1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_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)) ) ) )).
fof(fc2_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v2_xxreal_0(D) & v1_xreal_0(D) ) => ( ~ 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)) ) ) )).
fof(fc2_ltlaxio1,axiom,( ~ v1_xboole_0(k13_ltlaxio1) )).
fof(fc2_ltlaxio3,axiom,( ! [A] : ( v1_finset_1(A) => v1_finset_1(k1_ltlaxio3(A)) ) )).
fof(fc2_ltlaxio4,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)))) ) => v1_finset_1(k3_ltlaxio4(A)) ) )).
fof(fc2_lukasi_1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k3_cqc_lang(A)) ) => v2_cqc_the1(k2_qc_lang2(A,B,B),A) ) )).
fof(fc2_margrel1,axiom,( ~ v1_xboole_0(k6_margrel1) )).
fof(fc2_matrix11,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(C,k3_matrix_2(A)) ) => v7_ordinal1(k1_funct_1(C,B)) ) )).
fof(fc2_matrix13,axiom,( ! [A] : ! [B] : ( v1_setfam_1(A) => v1_setfam_1(k4_xboole_0(A,B)) ) )).
fof(fc2_matrix_0,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,k3_finseq_2(A)) ) => v1_finset_1(k9_matrix_0(B)) ) )).
fof(fc2_matrix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ v2_struct_0(k4_matrix_2(A)) & v15_algstr_0(k4_matrix_2(A)) ) ) )).
fof(fc2_matrix_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( v1_matrix_0(k3_matrix_3(B,C,D)) & v2_matrix_0(k3_matrix_3(B,C,D),u1_struct_0(B),A,A) ) ) )).
fof(fc2_matrix_8,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(k2_matrix_1(B,A)) & v2_matrix_0(k2_matrix_1(B,A),u1_struct_0(B),A,A) & v1_matrix_8(k2_matrix_1(B,A),A,B) & v2_matrix_8(k2_matrix_1(B,A),A,B) ) ) )).
fof(fc2_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc2_matrlin2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) ) )).
fof(fc2_matroid0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc2_matrtop1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v2_partfun3(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( v1_relat_1(k5_relat_1(C,B)) & v2_partfun3(k5_relat_1(C,B)) ) ) )).
fof(fc2_matrtop3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,B) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( 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)) ) ) )).
fof(fc2_mazurulm,axiom,( ! [A] : ! [B] : ( ( v3_membered(A) & v4_xxreal_2(A) & ~ v3_xxreal_0(B) & v1_xreal_0(B) ) => v4_xxreal_2(k23_member_1(A,B)) ) )).
fof(fc2_mboolean,axiom,( ! [A] : ( 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) ) )).
fof(fc2_measure4,axiom,( ! [A] : ! [B] : ( m1_measure4(B,A) => ( v1_funct_1(k3_measure4(A,B)) & v1_funct_2(k3_measure4(A,B),k1_measure4(A,B),k6_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)) ) ) )).
fof(fc2_measure6,axiom,( ~ v1_setfam_1(k4_ordinal1) )).
fof(fc2_member_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) & v1_xxreal_0(C) & v1_xxreal_0(D) ) => v2_membered(k2_enumset1(A,B,C,D)) ) )).
fof(fc2_membered,axiom,( v2_membered(k6_numbers) )).
fof(fc2_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ( v1_memstr_0(k1_memstr_0(A),A) & v2_memstr_0(k1_memstr_0(A),A) ) ) )).
fof(fc2_mesfun7c,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & v1_mesfunc8(B,A,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( v1_funct_1(k1_mesfun7c(A,B)) & v1_funct_2(k1_mesfun7c(A,B),k4_ordinal1,k4_partfun1(A,k6_numbers)) & v1_mesfunc8(k1_mesfun7c(A,B),A,k6_numbers) ) ) )).
fof(fc2_mesfunc7,axiom,( v1_funct_1(k1_mesfunc7) & v1_funct_2(k1_mesfunc7,k2_zfmisc_1(k6_numbers,k6_numbers),k6_numbers) & v1_binop_1(k1_mesfunc7,k6_numbers) & v2_binop_1(k1_mesfunc7,k6_numbers) )).
fof(fc2_metric_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v4_valued_0(A) ) => v7_ordinal1(k1_binop_1(A,B,C)) ) )).
fof(fc2_metrizts,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ v2_struct_0(k2_mfold_1(A)) ) )).
fof(fc2_mfold_2,axiom,( v2_funct_2(k1_xboole_0,k1_xboole_0) )).
fof(fc2_midsp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc2_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => v2_midsp_2(k15_midsp_1(A)) ) )).
fof(fc2_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc2_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ( ~ v2_struct_0(k2_mod_4(A)) & v36_algstr_0(k2_mod_4(A)) ) ) )).
fof(fc2_modal_1,axiom,( ~ v1_xboole_0(k4_modal_1) )).
fof(fc2_modcat_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc2_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m1_finseq_1(A,k4_ordinal1) ) => v1_modelc_1(k7_modelc_1(A)) ) )).
fof(fc2_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => v1_modelc_2(k3_modelc_2(A)) ) )).
fof(fc2_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => ( ~ v1_xboole_0(k22_modelc_3(A)) & v1_finset_1(k22_modelc_3(A)) ) ) )).
fof(fc2_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v1_moebius1(A) ) => ( ~ v8_ordinal1(k2_moebius1(A)) & v1_xreal_0(k2_moebius1(A)) ) ) )).
fof(fc2_monoid_0,axiom,( ! [A] : ( ~ 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)) ) )).
fof(fc2_monoid_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => v1_monoid_0(k9_monoid_1(A,B)) ) )).
fof(fc2_msafree,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc2_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ~ v1_xboole_0(k3_msafree2(A)) ) )).
fof(fc2_msafree3,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc2_msafree4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v6_trees_3(A) ) => v3_trees_3(k10_xtuple_0(A)) ) )).
fof(fc2_msalimit,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc2_msinst_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_msinst_1(A,B)) ) )).
fof(fc2_msscyc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc2_mssubfam,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_msualg_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc2_msualg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc2_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc2_msualg_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc2_msualg_7,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc2_msualg_8,axiom,( ! [A] : ( ~ 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)) ) )).
fof(fc2_msualg_9,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc2_mycielsk,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_nat_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => v7_ordinal1(k3_xcmplx_0(A,B)) ) )).
fof(fc2_nat_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_nat_lat,axiom,( ~ v2_struct_0(k3_nat_lat) & v3_lattices(k3_nat_lat) & v10_lattices(k3_nat_lat) )).
fof(fc2_nattra_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_cat_1(A) & v3_cat_1(A) & v4_cat_1(A) & v5_cat_1(A) & v6_cat_1(A) & v4_nattra_1(A) & l1_cat_1(A) & m1_subset_1(B,u1_struct_0(A)) ) => v1_zfmisc_1(k2_cat_1(A,B,B)) ) )).
fof(fc2_ndiff_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,u1_struct_0(A)) & v12_struct_0(B,k4_ordinal1,A) & v1_ndiff_1(B,A,k4_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & m1_subset_1(C,k4_ordinal1) ) => ( v1_funct_1(k7_nat_1(B,C)) & v1_funct_2(k7_nat_1(B,C),k4_ordinal1,u1_struct_0(A)) & v12_struct_0(k7_nat_1(B,C),k4_ordinal1,A) & v1_ndiff_1(k7_nat_1(B,C),A,k4_struct_0(A)) ) ) )).
fof(fc2_neckla_2,axiom,( ~ v1_xboole_0(k4_neckla_2) )).
fof(fc2_neckla_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc2_necklace,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_orders_2(k2_necklace(A)) & v1_necklace(k2_necklace(A)) ) ) )).
fof(fc2_net_1,axiom,( 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))) )).
fof(fc2_newton,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v7_ordinal1(B) ) => v1_xreal_0(k1_newton(A,B)) ) )).
fof(fc2_nfcont_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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) ) ) )).
fof(fc2_nfcont_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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) ) ) )).
fof(fc2_normform,axiom,( ! [A] : ~ v1_xboole_0(k7_normform(A)) )).
fof(fc2_normsp_0,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v4_normsp_0(A) & l2_normsp_0(A) & v9_struct_0(B,A) & m1_subset_1(B,u1_struct_0(A)) ) => ( v8_ordinal1(k2_normsp_0(A,B)) & v1_xreal_0(k2_normsp_0(A,B)) ) ) )).
fof(fc2_normsp_2,axiom,( ! [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) & 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)) ) ) )).
fof(fc2_numbers,axiom,( ~ v1_xboole_0(k2_numbers) )).
fof(fc2_openlatt,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc2_oposet_1,axiom,( v13_struct_0(k1_oposet_1,1) & v3_qmax_1(k1_oposet_1) )).
fof(fc2_ordeq_01,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_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) & l1_normsp_1(B) ) => ~ v1_xboole_0(k1_ordeq_01(A,B)) ) )).
fof(fc2_orders_1,axiom,( ! [A] : ( ( v1_xboole_0(A) & v1_relat_1(A) ) => v1_xboole_0(k1_relat_1(A)) ) )).
fof(fc2_orders_2,axiom,( ! [A] : ( ( v2_orders_2(A) & l1_orders_2(A) ) => v1_partfun1(u1_orders_2(A),u1_struct_0(A)) ) )).
fof(fc2_orders_3,axiom,( ! [A] : ( ( v2_struct_0(A) & l1_orders_2(A) ) => v1_xboole_0(u1_orders_2(A)) ) )).
fof(fc2_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => ( ~ v1_xboole_0(k1_ordinal1(A)) & v3_ordinal1(k1_ordinal1(A)) ) ) )).
fof(fc2_ordinal2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => v3_ordinal1(k1_funct_1(A,B)) ) )).
fof(fc2_ordinal3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => v3_ordinal1(k3_xboole_0(A,B)) ) )).
fof(fc2_ordinal4,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_ordinal5,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_ordinal6,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => v1_ordinal6(k4_xboole_0(A,B)) ) )).
fof(fc2_osafree,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc2_osalg_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) ) )).
fof(fc2_osalg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc2_osalg_3,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc2_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc2_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) ) )).
fof(fc2_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc2_partfun3,axiom,( ! [A] : ( v1_xreal_0(A) => ~ v3_xxreal_0(k3_xcmplx_0(A,A)) ) )).
fof(fc2_partit_2,axiom,( v1_relat_1(k6_funct_5) & v1_funct_1(k6_funct_5) & v1_partit_2(k6_funct_5) )).
fof(fc2_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc2_pcomps_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ~ v2_struct_0(k3_pcomps_1(A)) ) )).
fof(fc2_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc2_pencil_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_petri,axiom,( ! [A] : ( ( v2_petri(A) & l1_petri(A) ) => ~ v1_xboole_0(u1_petri(A)) ) )).
fof(fc2_pnproc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc2_polyalg1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc2_polyeq_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) ) => v1_xreal_0(k1_polyeq_1(A,B,C)) ) )).
fof(fc2_polyeq_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)) ) )).
fof(fc2_polyeq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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)) ) )).
fof(fc2_polyform,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(fc2_polynom1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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,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),B) ) ) )).
fof(fc2_polynom2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => v1_finset_1(k2_polynom1(B,C)) ) )).
fof(fc2_polynom3,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => ( v2_funct_1(k6_polynom3(A,B)) & ~ v1_xboole_0(k6_polynom3(A,B)) & v1_pre_poly(k6_polynom3(A,B)) ) ) )).
fof(fc2_polynom5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k3_polynom5(A,B,C),A) ) ) )).
fof(fc2_polynom6,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) & ~ v1_xboole_0(B) ) => ( v3_ordinal1(k10_ordinal2(B,A)) & ~ v1_xboole_0(k10_ordinal2(B,A)) ) ) )).
fof(fc2_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v4_vectsp_1(B) & l6_algstr_0(B) ) => ( v1_funct_1(k9_polynom1(A,B)) & v1_funct_2(k9_polynom1(A,B),k15_pre_poly(A),u1_struct_0(B)) & v4_polynom7(k9_polynom1(A,B),A,B) ) ) )).
fof(fc2_polyred,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,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),C) ) ) )).
fof(fc2_poset_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc2_pralg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc2_pralg_3,axiom,( ! [A] : ( v1_setfam_1(A) => ( v1_relat_1(k4_relat_1(A)) & v2_relat_1(k4_relat_1(A)) ) ) )).
fof(fc2_pre_circ,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc2_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ( v1_relat_1(k1_funct_7(B,C,D)) & v4_relat_1(k1_funct_7(B,C,D),A) & v1_funct_1(k1_funct_7(B,C,D)) ) ) )).
fof(fc2_pre_topc,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc2_prepower,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_xreal_0(B) ) => v1_xreal_0(k2_prepower(A,B)) ) )).
fof(fc2_prob_1,axiom,( ! [A] : v1_prob_1(k1_zfmisc_1(A),A) )).
fof(fc2_prob_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,k9_setfam_1(A)) ) ) )).
fof(fc2_prvect_1,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) ) )).
fof(fc2_prvect_2,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc2_prvect_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & l2_algstr_0(A) & ~ v2_struct_0(B) & v2_rlvect_1(B) & l2_algstr_0(B) ) => ( ~ v2_struct_0(k4_prvect_3(A,B)) & v8_algstr_0(k4_prvect_3(A,B)) & v2_rlvect_1(k4_prvect_3(A,B)) ) ) )).
fof(fc2_pscomp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc2_pua2mss1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc2_pythtrip,axiom,( ! [A] : ! [B] : ( ( v1_pythtrip(A) & v1_pythtrip(B) ) => v1_pythtrip(k3_xcmplx_0(A,B)) ) )).
fof(fc2_pzfmisc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc2_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ~ v1_xboole_0(k2_qc_lang1(A)) ) )).
fof(fc2_qmax_1,axiom,( ! [A] : ( l1_qmax_1(A) => ~ v1_xboole_0(k2_qmax_1(A)) ) )).
fof(fc2_quatern2,axiom,( ~ v2_struct_0(k14_quatern2) & v8_algstr_0(k14_quatern2) )).
fof(fc2_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => v1_quaterni(k3_quatern3(A)) ) )).
fof(fc2_quaterni,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( 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)) ) )).
fof(fc2_quin_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) ) => v1_xreal_0(k1_quin_1(A,B,C)) ) )).
fof(fc2_quofield,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc2_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ~ v1_xboole_0(k2_radix_3(A)) ) )).
fof(fc2_ramsey_1,axiom,( ! [A] : ! [B] : ( ~ v1_finset_1(A) => ~ v1_finset_1(k2_xboole_0(A,B)) ) )).
fof(fc2_random_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & v7_ordinal1(B) ) => ~ v1_xboole_0(k1_funct_1(A,B)) ) )).
fof(fc2_rat_1,axiom,( ! [A] : ! [B] : ( ( v1_rat_1(A) & v1_rat_1(B) ) => v1_rat_1(k2_xcmplx_0(A,B)) ) )).
fof(fc2_ratfunc1,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_int_1(B) ) => v1_int_1(k4_xxreal_0(A,B)) ) )).
fof(fc2_rcomp_1,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => v2_rcomp_1(k1_xxreal_1(A,B)) ) )).
fof(fc2_rcomp_3,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xxreal_0(B) ) => v3_xxreal_2(k2_xxreal_1(A,B)) ) )).
fof(fc2_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( v8_ordinal1(k5_int_1(A,k5_numbers)) & v1_int_1(k5_int_1(A,k5_numbers)) ) ) )).
fof(fc2_real_lat,axiom,( ~ v2_struct_0(k3_real_lat) & v3_lattices(k3_real_lat) )).
fof(fc2_real_ns1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( ~ v2_struct_0(k4_real_ns1(A)) & ~ v7_struct_0(k4_real_ns1(A)) & v1_normsp_1(k4_real_ns1(A)) ) ) )).
fof(fc2_realset1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v1_funct_1(k1_realset1(A,B)) ) )).
fof(fc2_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(A) => v1_relat_1(k4_xboole_0(A,B)) ) )).
fof(fc2_relat_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_relat_2(A) ) => ( v1_relat_1(k2_relat_1(A)) & v1_relat_2(k2_relat_1(A)) ) ) )).
fof(fc2_reloc,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc2_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_relat_1(C) ) => v4_relat_1(k3_xboole_0(B,C),A) ) )).
fof(fc2_revrot_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( ~ v7_struct_0(k15_euclid(A)) & v5_rltopsp1(k15_euclid(A)) ) ) )).
fof(fc2_rewrite2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_rfunct_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_rfunct_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_rfunct_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc2_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v1_funct_1(k3_rinfsup2(A)) & v1_funct_2(k3_rinfsup2(A),k4_ordinal1,k6_numbers) & v7_valued_0(k3_rinfsup2(A)) ) ) )).
fof(fc2_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v2_ideal_1(k2_struct_0(A),A) & v3_ideal_1(k2_struct_0(A),A) ) ) )).
fof(fc2_ringcat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) ) ) )).
fof(fc2_rlaffin1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc2_rlaffin3,axiom,( ! [A] : ( v7_ordinal1(A) => ( v5_rltopsp1(k15_euclid(A)) & v1_rlvect_5(k15_euclid(A)) ) ) )).
fof(fc2_rlsub_2,axiom,( ! [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) ) => ( 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))) ) ) )).
fof(fc2_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) ) )).
fof(fc2_rlvect_2,axiom,( ! [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) ) => ~ v1_xboole_0(k11_rlvect_2(A)) ) )).
fof(fc2_robbins3,axiom,( v3_orders_2(k1_robbins3) )).
fof(fc2_robbins4,axiom,( ~ v2_struct_0(k1_robbins4) )).
fof(fc2_rsspace,axiom,( ~ v2_struct_0(k6_rsspace) & v1_rlvect_1(k6_rsspace) )).
fof(fc2_rsspace3,axiom,( v1_rlsub_1(k1_rsspace3,k6_rsspace) )).
fof(fc2_rsspace4,axiom,( v1_rlsub_1(k1_rsspace4,k6_rsspace) )).
fof(fc2_rusub_2,axiom,( ! [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_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))) ) ) )).
fof(fc2_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ~ v2_struct_0(k5_rusub_5(A)) ) )).
fof(fc2_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => v3_valued_0(k5_finseq_1(A)) ) )).
fof(fc2_scm_1,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_int_1(B) ) => v5_relat_1(k6_afinsq_1(A,B),k4_numbers) ) )).
fof(fc2_scm_halt,axiom,( ! [A] : ( ( 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),k4_ordinal1) & 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)) ) ) )).
fof(fc2_scm_inst,axiom,( ~ v1_xboole_0(k3_scm_inst) )).
fof(fc2_scmfsa10,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc2_scmfsa6a,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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) ) ) )).
fof(fc2_scmfsa6b,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc2_scmfsa6c,axiom,( ! [A] : ( ( 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),k4_ordinal1) & 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),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(fc2_scmfsa7b,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) & 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),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(fc2_scmfsa8a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc2_scmfsa8b,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k7_card_1(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),k4_ordinal1) & 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),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(fc2_scmfsa8c,axiom,( ! [A] : ! [B] : ( ( 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,k4_ordinal1) & 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),k4_ordinal1) & 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) ) ) )).
fof(fc2_scmfsa_1,axiom,( ~ v1_xboole_0(k1_scmfsa_i) )).
fof(fc2_scmfsa_2,axiom,( v1_extpro_1(k1_scmfsa_2,k7_card_1(3)) & v1_amistd_4(k1_scmfsa_2) )).
fof(fc2_scmfsa_3,axiom,( v1_extpro_1(k1_scmfsa_2,k7_card_1(3)) & v4_amistd_5(k1_scmfsa_2,k7_card_1(3)) )).
fof(fc2_scmfsa_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc2_scmfsa_9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc2_scmfsa_i,axiom,( v3_finseq_1(k10_xtuple_0(k2_scmfsa_i)) )).
fof(fc2_scmfsa_m,axiom,( ! [A] : ( ( 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(k7_card_1(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(k7_card_1(3),k1_scmfsa_2)) & v5_memstr_0(k1_scmfsa_m(A),k7_card_1(3),k1_scmfsa_2,k5_numbers) ) ) )).
fof(fc2_scmpds_2,axiom,( v2_memstr_0(k1_scmpds_2,2) & v3_memstr_0(k1_scmpds_2,2) & v1_extpro_1(k1_scmpds_2,2) )).
fof(fc2_scmpds_3,axiom,( v1_extpro_1(k1_scmpds_2,2) & v4_amistd_5(k1_scmpds_2,2) )).
fof(fc2_scmpds_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc2_scmpds_5,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc2_scmpds_6,axiom,( ! [A] : ( v7_ordinal1(A) => v6_compos_0(k3_scmpds_2(k4_xcmplx_0(k1_nat_1(A,1))),u1_compos_1(k1_scmpds_2)) ) )).
fof(fc2_scmpds_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & 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) & v7_ordinal1(D) ) => ( v1_relat_1(k1_scmpds_7(B,C,D,A)) & v4_relat_1(k1_scmpds_7(B,C,D,A),k4_ordinal1) & v5_relat_1(k1_scmpds_7(B,C,D,A),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k1_scmpds_7(B,C,D,A)) & v1_funct_1(k1_scmpds_7(B,C,D,A)) & v1_finset_1(k1_scmpds_7(B,C,D,A)) & v1_afinsq_1(k1_scmpds_7(B,C,D,A)) & v2_compos_1(k1_scmpds_7(B,C,D,A),k1_scmpds_2) ) ) )).
fof(fc2_scmpds_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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) ) ) )).
fof(fc2_scmpds_i,axiom,( v3_finseq_1(k10_xtuple_0(k1_scmpds_i)) )).
fof(fc2_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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),k7_card_1(2)) & v1_extpro_1(k1_scmring2(A),k7_card_1(2)) ) ) )).
fof(fc2_scmring3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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),k7_card_1(2),k1_scmring2(A)) ) )).
fof(fc2_scmring4,axiom,( ! [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) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ( v1_extpro_1(k1_scmring2(A),k7_card_1(2)) & v3_amistd_5(k1_scmring2(A),k7_card_1(2)) ) ) )).
fof(fc2_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ( ~ v1_xboole_0(k1_scmringi(A)) & ~ v1_zfmisc_1(k1_scmringi(A)) ) ) )).
fof(fc2_scmyciel,axiom,( ! [A] : ( v1_finset_1(A) => v1_finset_1(k1_scmyciel(A)) ) )).
fof(fc2_scpinvar,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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) ) ) )).
fof(fc2_seq_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & v1_xreal_0(A) ) => ( v1_funct_1(k1_seq_1(A)) & v1_funct_2(k1_seq_1(A),k4_ordinal1,k1_numbers) & v9_ordinal1(k1_seq_1(A)) ) ) )).
fof(fc2_seq_2,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_comseq_2(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_funct_1(k24_valued_1(B,A)) & v1_funct_2(k24_valued_1(B,A),k4_ordinal1,k1_numbers) & v2_comseq_2(k24_valued_1(B,A)) ) ) )).
fof(fc2_seq_4,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v7_ordinal1(B) ) => ( v1_funct_1(k7_nat_1(A,B)) & v1_funct_2(k7_nat_1(A,B),k4_ordinal1,k1_numbers) & v2_comseq_2(k7_nat_1(A,B)) ) ) )).
fof(fc2_seqm_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v7_ordinal1(B) ) => ( v1_relat_1(k7_nat_1(A,B)) & v4_relat_1(k7_nat_1(A,B),k4_ordinal1) & v1_funct_1(k7_nat_1(A,B)) & v1_partfun1(k7_nat_1(A,B),k4_ordinal1) & v3_valued_0(k7_nat_1(A,B)) ) ) )).
fof(fc2_series_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => ( v7_ordinal1(k2_power(A,B)) & v1_xreal_0(k2_power(A,B)) ) ) )).
fof(fc2_setfam_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => v1_setfam_1(k1_tarski(A)) ) )).
fof(fc2_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_funct_1(k3_setlim_1(B)) & v1_funct_2(k3_setlim_1(B),k4_ordinal1,k9_setfam_1(A)) & v2_prob_1(k3_setlim_1(B)) ) ) )).
fof(fc2_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(fc2_sfmastr1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc2_sfmastr3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc2_sgraph1,axiom,( ! [A] : ~ v1_xboole_0(k3_sgraph1(A)) )).
fof(fc2_simplex0,axiom,( ! [A] : ( v1_classes1(A) => v1_classes1(k2_cohsp_1(A)) ) )).
fof(fc2_simplex1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc2_simplex2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( v1_funct_1(k3_sin_cos(A)) & v1_funct_2(k3_sin_cos(A),k4_ordinal1,k2_numbers) & v2_comseq_3(k3_sin_cos(A)) ) ) )).
fof(fc2_sin_cos2,axiom,( ! [A] : v1_xreal_0(k4_sin_cos2(A)) )).
fof(fc2_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k16_sin_cos,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2)))) & v2_funct_1(k5_relat_1(k16_sin_cos,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(fc2_sin_cos9,axiom,( v1_relat_1(k5_relat_1(k27_sin_cos,k2_rcomp_1(k5_numbers,k28_sin_cos))) & v2_funct_1(k5_relat_1(k27_sin_cos,k2_rcomp_1(k5_numbers,k28_sin_cos))) )).
fof(fc2_sincos10,axiom,( v1_relat_1(k5_relat_1(k1_fdiff_9,k4_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos))) & v2_funct_1(k5_relat_1(k1_fdiff_9,k4_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos))) )).
fof(fc2_sppol_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(k1_rltopsp1(k15_euclid(A),B,C),k15_euclid(A)) ) )).
fof(fc2_sppol_2,axiom,( ! [A] : ! [B] : ( ( v2_topreal1(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & v7_ordinal1(B) ) => v2_topreal1(k1_rfinseq(B,A)) ) )).
fof(fc2_sprect_1,axiom,( ! [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) => v2_compts_1(k3_topreal1(2,A),k15_euclid(2)) ) )).
fof(fc2_sprect_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(fc2_sprect_3,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc2_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k1_square_1(A)) ) )).
fof(fc2_stacks_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) ) )).
fof(fc2_struct_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(u1_struct_0(A)) ) )).
fof(fc2_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ~ v1_xboole_0(k1_enumset1(A,B,C)) )).
fof(fc2_substlat,axiom,( ! [A] : ! [B] : ( ~ v2_struct_0(k5_substlat(A,B)) & v3_lattices(k5_substlat(A,B)) ) )).
fof(fc2_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => v4_funct_1(k1_substut1(A)) ) )).
fof(fc2_supinf_1,axiom,( ! [A] : ( v2_membered(A) => ( ~ v1_xboole_0(k4_supinf_1(A)) & v2_membered(k4_supinf_1(A)) ) ) )).
fof(fc2_t_1topsp,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc2_taylor_1,axiom,( ~ v1_xboole_0(k3_limfunc1(k5_numbers)) )).
fof(fc2_tbsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k8_metric_1(A,B,C),A) ) )).
fof(fc2_tdgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ( ~ v2_struct_0(k2_tdgroup(A)) & v1_analoaf(k2_tdgroup(A)) ) ) )).
fof(fc2_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ~ v1_xboole_0(k5_tdlat_1(A)) ) )).
fof(fc2_termord,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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(k10_polynom1(A,B,C,D)) & v1_funct_2(k10_polynom1(A,B,C,D),k15_pre_poly(A),u1_struct_0(B)) & v4_polynom7(k10_polynom1(A,B,C,D),A,B) ) ) )).
fof(fc2_tex_1,axiom,( ! [A] : ( v1_pre_topc(k2_tex_1(A)) & v2_pre_topc(k2_tex_1(A)) & v2_tdlat_3(k2_tex_1(A)) ) )).
fof(fc2_tex_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc2_tex_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc2_tmap_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc2_topalg_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ~ v1_xboole_0(k2_topalg_1(A,B)) ) )).
fof(fc2_topalg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc2_topalg_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_topalg_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc2_topalg_5,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc2_topalg_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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) ) ) )).
fof(fc2_topdim_1,axiom,( ! [A] : v3_topdim_1(k1_compts_1(A)) )).
fof(fc2_topdim_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_topgen_1,axiom,( ! [A] : ( ( v1_orders_4(A) & l1_struct_0(A) ) => v4_card_3(k2_struct_0(A)) ) )).
fof(fc2_topgen_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(A) => ( ~ v2_struct_0(k5_topgen_2(A,B)) & v1_pre_topc(k5_topgen_2(A,B)) ) ) )).
fof(fc2_topgen_3,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc2_topgen_4,axiom,( ~ v4_card_3(k1_numbers) )).
fof(fc2_topgen_5,axiom,( ~ v1_xboole_0(k2_topgen_5) )).
fof(fc2_topgrp_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc2_topmetr,axiom,( ~ v2_struct_0(k3_topmetr) & v1_pre_topc(k3_topmetr) & v2_pre_topc(k3_topmetr) )).
fof(fc2_topreal1,axiom,( ! [A] : ( v7_ordinal1(A) => ( v8_pre_topc(k15_euclid(A)) & v5_rltopsp1(k15_euclid(A)) ) ) )).
fof(fc2_topreal6,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc2_topreal7,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc2_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc2_topreala,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v2_xxreal_0(B) & v1_xreal_0(B) ) => ~ v1_xboole_0(k2_xxreal_1(A,k2_xcmplx_0(A,B))) ) )).
fof(fc2_toprealb,axiom,( ~ v1_xboole_0(k1_xxreal_1(k4_xcmplx_0(1),1)) )).
fof(fc2_toprealc,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => v2_xxreal_0(k1_square_1(A)) ) )).
fof(fc2_tops_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc2_trees_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & ~ v1_xboole_0(B) & v1_trees_1(B) ) => v1_trees_1(k2_xboole_0(A,B)) ) )).
fof(fc2_trees_2,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc2_trees_3,axiom,( ~ v1_xboole_0(k2_trees_3) )).
fof(fc2_trees_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc2_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v2_trees_9(A) ) => v1_trees_2(k9_xtuple_0(A)) ) )).
fof(fc2_unialg_1,axiom,( ! [A] : ( ( v2_unialg_1(A) & l1_unialg_1(A) ) => v4_margrel1(u1_unialg_1(A),u1_struct_0(A)) ) )).
fof(fc2_unialg_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(fc2_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ~ v1_xboole_0(k2_uniroots(A)) ) )).
fof(fc2_uproots,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc2_urysohn1,axiom,( ~ v1_xboole_0(k2_urysohn1) )).
fof(fc2_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_valued_0(A) ) => v2_membered(k10_xtuple_0(A)) ) )).
fof(fc2_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_valued_2,axiom,( ! [A] : v1_valued_2(k2_valued_2(A)) )).
fof(fc2_vectmetr,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc2_vectsp_1,axiom,( v3_membered(u1_struct_0(k1_vectsp_1)) )).
fof(fc2_vectsp_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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) ) ) )).
fof(fc2_vfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc2_waybel10,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc2_waybel11,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc2_waybel12,axiom,( ! [A] : ( ( 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) ) )).
fof(fc2_waybel14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_orders_2(k1_yellow_1(u1_pre_topc(A))) & v2_waybel_1(k1_yellow_1(u1_pre_topc(A))) ) ) )).
fof(fc2_waybel16,axiom,( ! [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(k1_yellow_1(k8_waybel_0(A))) & v3_lattice3(k1_yellow_1(k8_waybel_0(A))) ) ) )).
fof(fc2_waybel17,axiom,( ! [A] : ! [B] : ( ( ~ 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,B)) & v3_lattice3(k5_yellow_1(A,B)) ) ) )).
fof(fc2_waybel18,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_waybel21,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc2_waybel22,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k1_yellow_1(k8_waybel_0(k2_yellow_1(A)))),u1_struct_0(B)) & v22_waybel_0(k2_waybel22(A,B,C),k1_yellow_1(k8_waybel_0(k2_yellow_1(A))),B) ) ) )).
fof(fc2_waybel23,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc2_waybel24,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc2_waybel25,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(fc2_waybel26,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc2_waybel28,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc2_waybel29,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & l1_orders_2(B) ) => ( v1_orders_2(k5_yellow_1(A,B)) & v1_yellow_0(k5_yellow_1(A,B)) ) ) )).
fof(fc2_waybel30,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ( v1_orders_2(k1_yellow_1(k7_waybel_0(A))) & v1_waybel_2(k1_yellow_1(k7_waybel_0(A))) ) ) )).
fof(fc2_waybel31,axiom,( ! [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) ) => ( v1_orders_2(k1_yellow_1(k5_waybel11(A))) & v1_lattice3(k1_yellow_1(k5_waybel11(A))) & v3_waybel_3(k1_yellow_1(k5_waybel11(A))) ) ) )).
fof(fc2_waybel32,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc2_waybel34,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc2_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_yellow_0(A) & l1_orders_2(A) ) => v1_waybel_0(k2_struct_0(A),A) ) )).
fof(fc2_waybel_1,axiom,( ! [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)) & v23_waybel_0(k3_struct_0(A),A,A) ) ) )).
fof(fc2_waybel_2,axiom,( ! [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) ) => v1_waybel_0(k2_struct_0(A),A) ) )).
fof(fc2_waybel_3,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc2_waybel_4,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => v2_waybel_4(k2_waybel_4(A),A) ) )).
fof(fc2_waybel_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ( v1_relat_1(k1_funct_6(A)) & v2_relat_1(k1_funct_6(A)) & v1_funct_1(k1_funct_6(A)) ) ) )).
fof(fc2_waybel_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v7_struct_0(k2_yellow_1(A)) & v1_orders_2(k2_yellow_1(A)) ) ) )).
fof(fc2_waybel_8,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc2_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc2_weddwitt,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc2_wellfnd1,axiom,( ! [A] : ( l1_orders_2(A) => ( v12_waybel_0(k1_wellfnd1(A),A) & v2_wellfnd1(k1_wellfnd1(A),A) ) ) )).
fof(fc2_wellord2,axiom,( ! [A] : ( v1_relat_1(k1_wellord2(A)) & v8_relat_2(k1_wellord2(A)) ) )).
fof(fc2_wsierp_1,axiom,( ! [A] : ( m1_finseq_1(A,k4_numbers) => ( v1_xcmplx_0(k19_rvsum_1(A)) & v1_int_1(k19_rvsum_1(A)) ) ) )).
fof(fc2_xboole_0,axiom,( ! [A] : ~ v1_xboole_0(k1_tarski(A)) )).
fof(fc2_xboolean,axiom,( v1_xboolean(k2_xboolean) )).
fof(fc2_xcmplx_0,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_xcmplx_0(k2_xcmplx_0(A,B)) ) )).
fof(fc2_xreal_0,axiom,( ~ v1_xreal_0(k1_xxreal_0) )).
fof(fc2_xtuple_0,axiom,( ! [A] : ! [B] : ! [C] : v2_xtuple_0(k3_xtuple_0(A,B,C)) )).
fof(fc2_xxreal_0,axiom,( v1_xxreal_0(k2_xxreal_0) )).
fof(fc2_xxreal_1,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => v2_membered(k2_xxreal_1(A,B)) ) )).
fof(fc2_xxreal_2,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc2_xxreal_3,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xxreal_0(k1_xxreal_3(A,B)) & v1_xreal_0(k1_xxreal_3(A,B)) ) ) )).
fof(fc2_yellow10,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc2_yellow11,axiom,( v1_lattice3(k1_yellow11) & v2_lattice3(k1_yellow11) )).
fof(fc2_yellow12,axiom,( ! [A] : ! [B] : ( 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))) ) )).
fof(fc2_yellow13,axiom,( ! [A] : ( ( ~ 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(k1_yellow_1(k7_waybel_0(A)))) ) ) )).
fof(fc2_yellow14,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(fc2_yellow15,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc2_yellow16,axiom,( ! [A] : ! [B] : ( ( ~ 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(k4_yellow_1(A,B)) & v4_orders_2(k4_yellow_1(A,B)) & v5_orders_2(k4_yellow_1(A,B)) ) ) )).
fof(fc2_yellow18,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc2_yellow19,axiom,( ! [A] : ! [B] : ( ( ~ 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),k2_yellow_1(k2_struct_0(A))) ) ) )).
fof(fc2_yellow20,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc2_yellow21,axiom,( ! [A] : ( v1_setfam_1(A) => v4_orders_3(k2_yellow21(A)) ) )).
fof(fc2_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ~ v1_xboole_0(k2_struct_0(A)) ) )).
fof(fc2_yellow_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc2_yellow_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc2_yellow_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc2_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc2_yellow_6,axiom,( ! [A] : ( ~ v1_xboole_0(k1_yellow_6(A)) & v1_classes2(k1_yellow_6(A)) ) )).
fof(fc2_yellow_7,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ( v1_orders_2(k7_lattice3(A)) & v4_orders_2(k7_lattice3(A)) ) ) )).
fof(fc2_yellow_8,axiom,( ! [A] : ( v1_pre_topc(k1_yellow_8(A)) & v2_pre_topc(k1_yellow_8(A)) ) )).
fof(fc2_yellow_9,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc2_zf_lang,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_zf_lang) & m1_subset_1(B,k1_zf_lang) ) => v1_zf_lang(k4_zf_lang(A,B)) ) )).
fof(fc2_zfmisc_1,axiom,( ! [A] : ! [B] : ( v1_xboole_0(B) => v1_xboole_0(k2_zfmisc_1(A,B)) ) )).
fof(fc2_zmodul02,axiom,( ! [A] : ( ( ~ 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(k15_zmodul02(A)) & v13_algstr_0(k15_zmodul02(A)) & v2_rlvect_1(k15_zmodul02(A)) & v3_rlvect_1(k15_zmodul02(A)) & v4_rlvect_1(k15_zmodul02(A)) & v7_vectsp_1(k15_zmodul02(A),k1_int_3) & v8_vectsp_1(k15_zmodul02(A),k1_int_3) & v9_vectsp_1(k15_zmodul02(A),k1_int_3) & v10_vectsp_1(k15_zmodul02(A),k1_int_3) & v11_vectsp_1(k15_zmodul02(A),k1_int_3) ) ) )).
fof(fc2_zmodul03,axiom,( ! [A] : ! [B] : ( ( ~ 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_zmodul02(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_zmodul01(k33_zmodul02(A,B)) & v1_zmodul03(k33_zmodul02(A,B)) ) ) )).
fof(fc30_abcmiz_1,axiom,( ~ 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) )).
fof(fc30_afinsq_2,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc30_algstr_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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)) ) ) )).
fof(fc30_ami_6,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(2),k1_ami_3) ) )).
fof(fc30_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v31_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v8_rlvect_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v3_lopban_2(A) & v3_cayldick(A) & l1_cayldick(A) ) => ( v4_vectsp_1(k4_cayldick(A)) & v1_cayldick(k4_cayldick(A)) ) ) )).
fof(fc30_comput_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc30_finseq_1,axiom,( ! [A] : ( v1_finset_1(A) => ( v2_funct_1(k19_finseq_1(A)) & v2_funct_2(k19_finseq_1(A),A) ) ) )).
fof(fc30_finset_1,axiom,( ! [A] : ( v1_finset_1(A) => v5_finset_1(k1_tarski(A)) ) )).
fof(fc30_fomodel0,axiom,( ! [A] : ( v1_relat_1(A) => v1_xboole_0(k4_xboole_0(A,k2_zfmisc_1(k9_xtuple_0(A),k10_xtuple_0(A)))) ) )).
fof(fc30_fomodel1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc30_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc30_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc30_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v6_fomodel4(k27_fomodel4(A),A) ) )).
fof(fc30_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_xboole_0(C) ) => v1_xboole_0(k10_gate_1(A,C,B)) ) )).
fof(fc30_glib_003,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc30_hermitan,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(fc30_member_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v2_membered(A) & ~ v1_xboole_0(B) & v2_membered(B) ) => ~ v1_xboole_0(k10_member_1(A,B)) ) )).
fof(fc30_membered,axiom,( ! [A] : ! [B] : ( ( v6_membered(A) & v6_membered(B) ) => v6_membered(k2_xboole_0(A,B)) ) )).
fof(fc30_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc30_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc30_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc30_scmfsa10,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) & v7_ordinal1(B) ) => ( ~ v4_compos_0(k12_scmfsa_2(B,A),u1_compos_1(k1_scmfsa_2)) & v2_amistd_1(k12_scmfsa_2(B,A),k7_card_1(3),k1_scmfsa_2) & ~ v4_amistd_1(k12_scmfsa_2(B,A),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(fc30_scmfsa_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc30_scmpds_5,axiom,( ! [A] : ! [B] : ( ( v1_scmpds_5(A) & m1_subset_1(A,u1_compos_1(k1_scmpds_2)) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) & v2_scmpds_4(B) & v3_scmpds_4(B) ) => ( v1_relat_1(k2_scmpds_4(A,B)) & v4_relat_1(k2_scmpds_4(A,B),k4_ordinal1) & v5_relat_1(k2_scmpds_4(A,B),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k2_scmpds_4(A,B)) & 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)) ) ) )).
fof(fc30_sin_cos6,axiom,( ! [A] : v1_xreal_0(k4_sin_cos6(A)) )).
fof(fc30_toprealb,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_relat_1(k5_relat_1(k12_toprealb,k3_rcomp_1(A,k2_xcmplx_0(A,1)))) & v2_funct_1(k5_relat_1(k12_toprealb,k3_rcomp_1(A,k2_xcmplx_0(A,1)))) ) ) )).
fof(fc30_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc30_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_valued_0(A) & v1_relat_1(B) & v4_valued_0(B) ) => v4_valued_0(k5_xboole_0(A,B)) ) )).
fof(fc30_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc30_valued_2,axiom,( ! [A] : ! [B] : ( v3_membered(B) => v3_valued_2(k1_funct_2(A,B)) ) )).
fof(fc30_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc30_xreal_0,axiom,( ! [A] : ( ( ~ v3_xxreal_0(A) & v1_xreal_0(A) ) => ( v1_xcmplx_0(k5_xcmplx_0(A)) & ~ v3_xxreal_0(k5_xcmplx_0(A)) ) ) )).
fof(fc30_xxreal_3,axiom,( ! [A] : ( ( v1_xxreal_0(A) & ~ v2_xxreal_0(A) ) => ( v1_xxreal_0(k5_xxreal_3(A)) & ~ v2_xxreal_0(k5_xxreal_3(A)) ) ) )).
fof(fc31_afinsq_2,axiom,( ! [A] : ( 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)) ) )).
fof(fc31_algstr_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) ) )).
fof(fc31_ami_6,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(2),k1_ami_3) ) )).
fof(fc31_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v6_struct_0(A) & l1_cayldick(A) ) => ( ~ v6_struct_0(k4_cayldick(A)) & v1_cayldick(k4_cayldick(A)) ) ) )).
fof(fc31_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & 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) ) ) )).
fof(fc31_finseq_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ~ v1_xboole_0(k19_finseq_1(A)) ) )).
fof(fc31_finset_1,axiom,( ! [A] : ( v1_finset_1(A) => v5_finset_1(k1_zfmisc_1(A)) ) )).
fof(fc31_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : v1_xboole_0(k5_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),k2_xboole_0(A,k2_xboole_0(B,C)))) )).
fof(fc31_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v1_relat_1(B) & v5_relat_1(B,k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ v1_xboole_0(k1_funct_1(k21_fomodel1(A),B)) ) )).
fof(fc31_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) ) => v12_fomodel1(k24_fomodel2(A,B),A) ) )).
fof(fc31_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(fc31_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v6_fomodel4(k29_fomodel4(A),A) ) )).
fof(fc31_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_xboole_0(C) ) => v1_xboole_0(k10_gate_1(C,A,B)) ) )).
fof(fc31_glib_003,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc31_hermitan,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(fc31_ideal_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc31_member_1,axiom,( ! [A] : ! [B] : ( ( v2_membered(A) & v2_membered(B) ) => v2_membered(k10_member_1(A,B)) ) )).
fof(fc31_membered,axiom,( ! [A] : ! [B] : ( v1_membered(A) => v1_membered(k3_xboole_0(A,B)) ) )).
fof(fc31_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc31_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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)) ) ) )).
fof(fc31_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc31_scmfsa10,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) & v7_ordinal1(B) ) => ( ~ v4_compos_0(k13_scmfsa_2(B,A),u1_compos_1(k1_scmfsa_2)) & v2_amistd_1(k13_scmfsa_2(B,A),k7_card_1(3),k1_scmfsa_2) & ~ v4_amistd_1(k13_scmfsa_2(B,A),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(fc31_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc31_scmpds_5,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & 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_relat_1(k3_scmpds_4(A,B)) & v4_relat_1(k3_scmpds_4(A,B),k4_ordinal1) & v5_relat_1(k3_scmpds_4(A,B),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k3_scmpds_4(A,B)) & 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)) ) ) )).
fof(fc31_scmring3,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) & v7_ordinal1(B) ) => ~ v4_amistd_1(k8_scmring2(A,B),k7_card_1(2),k1_scmring2(A)) ) )).
fof(fc31_sin_cos6,axiom,( v1_funct_1(k3_sin_cos6) & v2_funct_1(k3_sin_cos6) )).
fof(fc31_toprealb,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_relat_1(k5_relat_1(k12_toprealb,k2_rcomp_1(A,k2_xcmplx_0(A,1)))) & v2_funct_1(k5_relat_1(k12_toprealb,k2_rcomp_1(A,k2_xcmplx_0(A,1)))) ) ) )).
fof(fc31_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc31_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_valued_0(A) ) => v1_membered(k7_relat_1(A,B)) ) )).
fof(fc31_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc31_valued_2,axiom,( ! [A] : ! [B] : ( v4_membered(B) => v4_valued_2(k1_funct_2(A,B)) ) )).
fof(fc31_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc31_xreal_0,axiom,( ! [A] : ! [B] : ( ( ~ v3_xxreal_0(A) & v1_xreal_0(A) & ~ v2_xxreal_0(B) & v1_xreal_0(B) ) => ~ v2_xxreal_0(k7_xcmplx_0(A,B)) ) )).
fof(fc31_xxreal_3,axiom,( ! [A] : ( ( v1_xxreal_0(A) & ~ v3_xxreal_0(A) ) => ( v1_xxreal_0(k5_xxreal_3(A)) & ~ v3_xxreal_0(k5_xxreal_3(A)) ) ) )).
fof(fc32_abcmiz_1,axiom,( v1_msualg_1(k27_abcmiz_1) & v1_instalg1(k27_abcmiz_1) & v1_abcmiz_1(k27_abcmiz_1) & v12_abcmiz_1(k27_abcmiz_1) )).
fof(fc32_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(A) & v5_ordinal1(A) & v1_valued_0(A) & v1_finset_1(A) ) => v8_ordinal1(k7_afinsq_2(A)) ) )).
fof(fc32_ami_6,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(2),k1_ami_3) ) )).
fof(fc32_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc32_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v4_cayldick(A) & l1_cayldick(A) ) => ( v1_cayldick(k4_cayldick(A)) & v4_cayldick(k4_cayldick(A)) ) ) )).
fof(fc32_comput_1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(fc32_finset_1,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v5_finset_1(k2_tarski(A,B)) ) )).
fof(fc32_fomodel0,axiom,( ! [A] : v1_xboole_0(k5_xboole_0(k6_partfun1(k1_tarski(A)),k1_tarski(k4_tarski(A,A)))) )).
fof(fc32_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ 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),k5_numbers,A) ) )).
fof(fc32_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v12_fomodel1(k26_fomodel2(A),A) ) )).
fof(fc32_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(fc32_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v6_fomodel4(k30_fomodel4(A),A) ) )).
fof(fc32_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) ) => ~ v1_xboole_0(k10_gate_1(A,B,C)) ) )).
fof(fc32_glib_003,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc32_hermitan,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(fc32_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_membered(B) ) => v1_xboole_0(k11_member_1(A,B)) ) )).
fof(fc32_membered,axiom,( ! [A] : ! [B] : ( v1_membered(A) => v1_membered(k3_xboole_0(B,A)) ) )).
fof(fc32_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc32_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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)) ) ) )).
fof(fc32_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc32_scmfsa10,axiom,( ! [A] : ! [B] : ( ( 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)),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc32_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc32_scmpds_5,axiom,( ! [A] : ! [B] : ( ( 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_relat_1(k4_scmpds_4(A,B)) & v4_relat_1(k4_scmpds_4(A,B),k4_ordinal1) & v5_relat_1(k4_scmpds_4(A,B),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k4_scmpds_4(A,B)) & 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)) ) ) )).
fof(fc32_scmring3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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))) & v7_ordinal1(C) ) => ~ v4_amistd_1(k9_scmring2(A,C,B),k7_card_1(2),k1_scmring2(A)) ) )).
fof(fc32_toprealb,axiom,( ! [A] : ( 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,k2_xcmplx_0(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,k2_xcmplx_0(A,1)))),k11_toprealb(k3_funct_2(u1_struct_0(k2_topalg_2),u1_struct_0(k8_toprealb(2)),k12_toprealb,A))) ) ) )).
fof(fc32_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc32_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v2_valued_0(A) ) => v2_membered(k7_relat_1(A,B)) ) )).
fof(fc32_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc32_valued_2,axiom,( ! [A] : ! [B] : ( v5_membered(B) => v5_valued_2(k1_funct_2(A,B)) ) )).
fof(fc32_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc32_xreal_0,axiom,( ! [A] : ! [B] : ( ( ~ v3_xxreal_0(A) & v1_xreal_0(A) & ~ v2_xxreal_0(B) & v1_xreal_0(B) ) => ~ v2_xxreal_0(k7_xcmplx_0(B,A)) ) )).
fof(fc32_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc33_abcmiz_1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(fc33_afinsq_2,axiom,( ! [A] : ( ( 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)) ) )).
fof(fc33_ami_6,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(2),k1_ami_3) ) )).
fof(fc33_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc33_cayldick,axiom,( ! [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) & v5_cayldick(A) & l1_cayldick(A) ) => ( v1_cayldick(k4_cayldick(A)) & v5_cayldick(k4_cayldick(A)) ) ) )).
fof(fc33_comput_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc33_finset_1,axiom,( ! [A] : ! [B] : ( ( v5_finset_1(A) & v5_finset_1(B) ) => v5_finset_1(k2_xboole_0(A,B)) ) )).
fof(fc33_fomodel0,axiom,( ! [A] : ! [B] : v1_xboole_0(k5_xboole_0(k16_funcop_1(A,B),k1_tarski(k4_tarski(A,B)))) )).
fof(fc33_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(fc33_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v8_ordinal1(k2_xcmplx_0(k19_fomodel1(A,k31_fomodel2(A)),2)) ) )).
fof(fc33_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(fc33_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_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))))) & v7_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))))) ) => v7_fomodel4(k2_xboole_0(B,C),A) ) )).
fof(fc33_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k11_gate_1(A,B,C)) ) )).
fof(fc33_glib_003,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc33_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc33_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_membered(B) ) => v1_xboole_0(k11_member_1(B,A)) ) )).
fof(fc33_membered,axiom,( ! [A] : ! [B] : ( v2_membered(A) => v2_membered(k3_xboole_0(A,B)) ) )).
fof(fc33_partfun3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc33_pre_poly,axiom,( ! [A] : v1_xboole_0(k13_pre_poly(k16_pre_poly(A))) )).
fof(fc33_scmfsa10,axiom,( ! [A] : ! [B] : ( ( 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)),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc33_scmring3,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) & v7_ordinal1(B) ) => ~ v4_compos_0(k8_scmring2(A,B),u1_compos_1(k1_scmring2(A))) ) )).
fof(fc33_toprealb,axiom,( 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(k5_numbers,1))))) & v2_funct_2(k14_toprealb,u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k5_numbers,1))))) & v5_pre_topc(k14_toprealb,k11_toprealb(k9_toprealb),k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k5_numbers,1)))) )).
fof(fc33_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v3_valued_0(A) ) => v3_membered(k7_relat_1(A,B)) ) )).
fof(fc33_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc33_valued_2,axiom,( ! [A] : ! [B] : ( v6_membered(B) => v6_valued_2(k1_funct_2(A,B)) ) )).
fof(fc33_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc33_xreal_0,axiom,( ! [A] : ! [B] : ( ( ~ v3_xxreal_0(A) & v1_xreal_0(A) & ~ v3_xxreal_0(B) & v1_xreal_0(B) ) => ~ v3_xxreal_0(k7_xcmplx_0(A,B)) ) )).
fof(fc33_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc34_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc34_afinsq_2,axiom,( ! [A] : ( ( 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)) ) )).
fof(fc34_ami_6,axiom,( v1_extpro_1(k1_ami_3,k7_card_1(2)) & v2_amistd_2(k1_ami_3,k7_card_1(2)) )).
fof(fc34_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc34_cayldick,axiom,( ! [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) & v6_cayldick(A) & l1_cayldick(A) ) => ( v1_cayldick(k4_cayldick(A)) & v6_cayldick(k4_cayldick(A)) ) ) )).
fof(fc34_comput_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(k5_funct_6(k10_finseq_1(B,C)),A)) & v7_comput_1(k3_relat_1(k5_funct_6(k10_finseq_1(B,C)),A)) ) ) )).
fof(fc34_finset_1,axiom,( ! [A] : ( ( v1_finset_1(A) & v5_finset_1(A) ) => v1_finset_1(k3_tarski(A)) ) )).
fof(fc34_fomodel0,axiom,( ! [A] : v1_xboole_0(k5_xboole_0(k6_partfun1(k1_tarski(A)),k16_funcop_1(A,A))) )).
fof(fc34_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(fc34_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v8_ordinal1(k6_xcmplx_0(k1_int_2(k19_fomodel1(A,k31_fomodel2(A))),2)) ) )).
fof(fc34_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v8_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))) ) => v8_ordinal1(k29_fomodel2(A,C)) ) )).
fof(fc34_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v6_fomodel4(k33_fomodel4(A),A) ) )).
fof(fc34_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k11_gate_1(A,C,B)) ) )).
fof(fc34_glib_003,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc34_member_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_membered(A) & ~ v1_xboole_0(B) & v1_membered(B) ) => ~ v1_xboole_0(k11_member_1(A,B)) ) )).
fof(fc34_membered,axiom,( ! [A] : ! [B] : ( v2_membered(A) => v2_membered(k3_xboole_0(B,A)) ) )).
fof(fc34_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc34_scmfsa10,axiom,( ! [A] : ! [B] : ( ( 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)),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc34_scmring3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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))) & v7_ordinal1(C) ) => ~ v4_compos_0(k9_scmring2(A,C,B),u1_compos_1(k1_scmring2(A))) ) )).
fof(fc34_toprealb,axiom,( 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(k7_xcmplx_0(1,2),k7_xcmplx_0(3,2)))))) & v2_funct_2(k15_toprealb,u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k7_xcmplx_0(1,2),k7_xcmplx_0(3,2)))))) & v5_pre_topc(k15_toprealb,k11_toprealb(k10_toprealb),k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k7_xcmplx_0(1,2),k7_xcmplx_0(3,2))))) )).
fof(fc34_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v5_relat_1(A,k3_numbers) ) => v4_membered(k7_relat_1(A,B)) ) )).
fof(fc34_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc34_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v7_valued_2(A) ) => v1_valued_2(k10_xtuple_0(A)) ) )).
fof(fc34_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc34_xreal_0,axiom,( ! [A] : ! [B] : ( ( ~ v2_xxreal_0(A) & v1_xreal_0(A) & ~ v2_xxreal_0(B) & v1_xreal_0(B) ) => ~ v3_xxreal_0(k7_xcmplx_0(A,B)) ) )).
fof(fc34_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc35_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc35_afinsq_2,axiom,( ! [A] : ( ( 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)) ) )).
fof(fc35_ami_6,axiom,( v1_extpro_1(k1_ami_3,k7_card_1(2)) & v4_amistd_2(k1_ami_3,k7_card_1(2)) )).
fof(fc35_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc35_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_vectsp_1(A) & l1_cayldick(A) ) => ( v2_vectsp_1(k4_cayldick(A)) & v1_cayldick(k4_cayldick(A)) ) ) )).
fof(fc35_comput_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(k5_funct_6(k10_finseq_1(B,C)),A)) & v8_comput_1(k3_relat_1(k5_funct_6(k10_finseq_1(B,C)),A),2) ) ) )).
fof(fc35_finset_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_finset_1(A) ) => v1_finset_1(k1_funct_1(A,B)) ) )).
fof(fc35_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => v1_finseq_1(k6_funct_4(A,B,C)) ) )).
fof(fc35_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & m1_subset_1(B,k4_ordinal1) ) => v1_setfam_1(k1_funct_1(k39_fomodel1(A),B)) ) )).
fof(fc35_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) ) => ~ v1_xboole_0(k27_fomodel2(A,B)) ) )).
fof(fc35_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k29_fomodel2(A,B),C)) ) )).
fof(fc35_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v6_fomodel4(k35_fomodel4(A),A) ) )).
fof(fc35_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k11_gate_1(C,A,B)) ) )).
fof(fc35_glib_003,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc35_hermitan,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(fc35_member_1,axiom,( ! [A] : ! [B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k11_member_1(A,B)) ) )).
fof(fc35_membered,axiom,( ! [A] : ! [B] : ( v3_membered(A) => v3_membered(k3_xboole_0(A,B)) ) )).
fof(fc35_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc35_scmfsa10,axiom,( ! [A] : ! [B] : ( ( 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)),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc35_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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),k7_card_1(2)) & v2_amistd_2(k1_scmring2(A),k7_card_1(2)) ) ) )).
fof(fc35_toprealb,axiom,( ! [A] : ( 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),k2_xcmplx_0(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),k2_xcmplx_0(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)))) ) ) )).
fof(fc35_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(fc35_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) ) => v5_membered(k7_relat_1(A,B)) ) )).
fof(fc35_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc35_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v8_valued_2(A) ) => v2_valued_2(k10_xtuple_0(A)) ) )).
fof(fc35_xreal_0,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => v1_xreal_0(k3_xxreal_0(A,B)) ) )).
fof(fc35_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc36_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc36_afinsq_2,axiom,( ! [A] : ( ( 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)) ) )).
fof(fc36_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc36_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_vectsp_1(A) & v4_cayldick(A) & l1_cayldick(A) ) => ( v1_vectsp_1(k4_cayldick(A)) & v1_cayldick(k4_cayldick(A)) ) ) )).
fof(fc36_comput_1,axiom,( ! [A] : ! [B] : ( ( 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(k5_funct_6(k9_finseq_1(B)),A)) & v7_comput_1(k3_relat_1(k5_funct_6(k9_finseq_1(B)),A)) ) ) )).
fof(fc36_finset_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_finset_1(A) ) => v5_finset_1(k10_xtuple_0(A)) ) )).
fof(fc36_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(fc36_fomodel1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc36_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) ) => ~ v1_xboole_0(k28_fomodel2(A,B)) ) )).
fof(fc36_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k29_fomodel2(A,C))) & ~ v3_xxreal_0(k6_xcmplx_0(B,k29_fomodel2(A,C))) ) ) )).
fof(fc36_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v6_fomodel4(k34_fomodel4(A),A) ) )).
fof(fc36_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xboole_0(A) & v1_xboole_0(B) ) => v1_xboole_0(k11_gate_1(A,B,C)) ) )).
fof(fc36_glib_003,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc36_member_1,axiom,( ! [A] : ! [B] : ( ( v3_membered(A) & v3_membered(B) ) => v3_membered(k11_member_1(A,B)) ) )).
fof(fc36_membered,axiom,( ! [A] : ! [B] : ( v3_membered(A) => v3_membered(k3_xboole_0(B,A)) ) )).
fof(fc36_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc36_scmfsa10,axiom,( ! [A] : ! [B] : ( ( 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)),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc36_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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),k7_card_1(2)) & v4_amistd_2(k1_scmring2(A),k7_card_1(2)) ) ) )).
fof(fc36_toprealb,axiom,( ! [A] : ( v1_int_1(A) => ( v1_funct_1(k13_toprealb(k4_toprealb(k2_xcmplx_0(k7_xcmplx_0(1,2),A)))) & v1_funct_2(k13_toprealb(k4_toprealb(k2_xcmplx_0(k7_xcmplx_0(1,2),A))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k4_toprealb(k2_xcmplx_0(k7_xcmplx_0(1,2),A)),k2_xcmplx_0(k4_toprealb(k2_xcmplx_0(k7_xcmplx_0(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(k2_xcmplx_0(k7_xcmplx_0(1,2),A)))))) & v1_t_0topsp(k13_toprealb(k4_toprealb(k2_xcmplx_0(k7_xcmplx_0(1,2),A))),k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k4_toprealb(k2_xcmplx_0(k7_xcmplx_0(1,2),A)),k2_xcmplx_0(k4_toprealb(k2_xcmplx_0(k7_xcmplx_0(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(k2_xcmplx_0(k7_xcmplx_0(1,2),A))))) ) ) )).
fof(fc36_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_valued_0(A) ) => v6_membered(k7_relat_1(A,B)) ) )).
fof(fc36_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc36_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v9_valued_2(A) ) => v3_valued_2(k10_xtuple_0(A)) ) )).
fof(fc36_xreal_0,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => v1_xreal_0(k4_xxreal_0(A,B)) ) )).
fof(fc36_xxreal_3,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(A) & v1_xxreal_0(A) & ~ v8_ordinal1(B) & v1_xxreal_0(B) ) => ( ~ v8_ordinal1(k4_xxreal_3(A,B)) & v1_xxreal_0(k4_xxreal_3(A,B)) ) ) )).
fof(fc37_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc37_afinsq_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc37_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc37_cayldick,axiom,( ! [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) & l1_cayldick(A) ) => ( v2_normsp_1(k4_cayldick(A)) & v1_cayldick(k4_cayldick(A)) ) ) )).
fof(fc37_comput_1,axiom,( ! [A] : ! [B] : ( ( 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(k5_funct_6(k9_finseq_1(B)),A)) & v8_comput_1(k3_relat_1(k5_funct_6(k9_finseq_1(B)),A),2) ) ) )).
fof(fc37_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc37_fomodel1,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(fc37_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc37_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(fc37_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) => v5_fomodel4(k4_tarski(k7_domain_1(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k31_fomodel2(A)),B),C),k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k31_fomodel2(A)),C),D)),k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(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))),k27_fomodel4(A)),k1_xboole_0) ) )).
fof(fc37_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xboole_0(A) & v1_xboole_0(B) ) => v1_xboole_0(k11_gate_1(A,C,B)) ) )).
fof(fc37_glib_003,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc37_member_1,axiom,( ! [A] : ! [B] : ( ( v4_membered(A) & v4_membered(B) ) => v4_membered(k11_member_1(A,B)) ) )).
fof(fc37_membered,axiom,( ! [A] : ! [B] : ( v4_membered(A) => v4_membered(k3_xboole_0(A,B)) ) )).
fof(fc37_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc37_scmfsa10,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc37_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_valued_0(A) ) => v1_membered(k9_relat_1(A,B)) ) )).
fof(fc37_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc37_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v10_valued_2(A) ) => v4_valued_2(k10_xtuple_0(A)) ) )).
fof(fc37_xreal_0,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => v1_xreal_0(k1_xreal_0(A,B)) ) )).
fof(fc37_xxreal_3,axiom,( ! [A] : ! [B] : ( ( v8_ordinal1(A) & v1_xxreal_0(A) & v1_xxreal_0(B) ) => ( v8_ordinal1(k4_xxreal_3(A,B)) & v1_xxreal_0(k4_xxreal_3(A,B)) ) ) )).
fof(fc38_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc38_afinsq_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc38_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc38_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_rlvect_1(A) & l1_cayldick(A) ) => ( v5_rlvect_1(k4_cayldick(A)) & v1_cayldick(k4_cayldick(A)) ) ) )).
fof(fc38_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc38_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(fc38_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k43_fomodel1(A,C),B),A) ) )).
fof(fc38_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(fc38_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v3_fomodel4(B,A) & v3_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))) ) => v5_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))),k25_fomodel4(A)),k1_tarski(k4_tarski(B,D))) ) )).
fof(fc38_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xboole_0(A) & v1_xboole_0(B) ) => v1_xboole_0(k11_gate_1(C,A,B)) ) )).
fof(fc38_glib_003,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc38_member_1,axiom,( ! [A] : ! [B] : ( ( v5_membered(A) & v5_membered(B) ) => v5_membered(k11_member_1(A,B)) ) )).
fof(fc38_membered,axiom,( ! [A] : ! [B] : ( v4_membered(A) => v4_membered(k3_xboole_0(B,A)) ) )).
fof(fc38_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc38_scmfsa10,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc38_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v2_valued_0(A) ) => v2_membered(k9_relat_1(A,B)) ) )).
fof(fc38_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc38_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v11_valued_2(A) ) => v5_valued_2(k10_xtuple_0(A)) ) )).
fof(fc38_xreal_0,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( ~ v3_xxreal_0(k1_xreal_0(A,B)) & v1_xreal_0(k1_xreal_0(A,B)) ) ) )).
fof(fc38_xxreal_3,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_xxreal_0(k5_xxreal_3(A)) & v1_xreal_0(k5_xxreal_3(A)) ) ) )).
fof(fc39_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc39_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc39_cayldick,axiom,( ! [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) & v4_lopban_2(A) & l1_cayldick(A) ) => ( v2_funcsdom(k4_cayldick(A)) & v1_cayldick(k4_cayldick(A)) ) ) )).
fof(fc39_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_pre_poly(A) ) => v1_finseq_1(k1_funct_1(A,B)) ) )).
fof(fc39_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ~ v1_xboole_0(k9_fomodel1(A)) ) )).
fof(fc39_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k42_fomodel1(A,k43_fomodel1(A,D),B),C),A) ) )).
fof(fc39_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k29_fomodel2(A,k24_fomodel3(A,B,C,D)),k29_fomodel2(A,D))) ) )).
fof(fc39_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v3_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))) ) => v5_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))),k24_fomodel4(A)),k1_xboole_0) ) )).
fof(fc39_glib_003,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc39_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v2_membered(B) ) => v1_xboole_0(k12_member_1(A,B)) ) )).
fof(fc39_membered,axiom,( ! [A] : ! [B] : ( v5_membered(A) => v5_membered(k3_xboole_0(A,B)) ) )).
fof(fc39_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc39_pcs_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc39_scmfsa10,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc39_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(fc39_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v3_valued_0(A) ) => v3_membered(k9_relat_1(A,B)) ) )).
fof(fc39_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc39_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v12_valued_2(A) ) => v6_valued_2(k10_xtuple_0(A)) ) )).
fof(fc39_xxreal_3,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xxreal_0(k4_xxreal_3(A,B)) & v1_xreal_0(k4_xxreal_3(A,B)) ) ) )).
fof(fc3_abcmiz_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) ) )).
fof(fc3_abcmiz_1,axiom,( ! [A] : ( m1_subset_1(A,k2_abcmiz_1) => v1_finset_1(k1_xtuple_0(A)) ) )).
fof(fc3_abian,axiom,( ! [A] : ( ( v1_int_1(A) & ~ v1_abian(A) ) => v1_abian(k2_xcmplx_0(A,1)) ) )).
fof(fc3_afinsq_1,axiom,( ! [A] : ~ v1_xboole_0(k3_afinsq_1(A)) )).
fof(fc3_afvect0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc3_algstr_1,axiom,( ~ v2_struct_0(k8_algstr_0) )).
fof(fc3_algstr_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc3_altcat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v2_struct_0(k9_altcat_1(A)) & v6_altcat_1(k9_altcat_1(A)) & v10_altcat_1(k9_altcat_1(A)) & v11_altcat_1(k9_altcat_1(A)) & v12_altcat_1(k9_altcat_1(A)) & v13_altcat_1(k9_altcat_1(A)) & v14_altcat_1(k9_altcat_1(A)) ) ) )).
fof(fc3_altcat_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_altcat_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(fc3_altcat_4,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc3_altcat_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_altcat_5(A) & l1_altcat_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => v4_funct_1(k1_altcat_1(A,B,C)) ) )).
fof(fc3_ami_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc3_ami_3,axiom,( v2_memstr_0(k1_ami_3,k7_card_1(2)) & v1_extpro_1(k1_ami_3,k7_card_1(2)) )).
fof(fc3_ami_5,axiom,( v1_extpro_1(k1_ami_3,k7_card_1(2)) & v4_amistd_5(k1_ami_3,k7_card_1(2)) )).
fof(fc3_ami_6,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(2),k1_ami_3) ) )).
fof(fc3_amistd_1,axiom,( ! [A] : ( ~ 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) ) ) )).
fof(fc3_amistd_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc3_analmetr,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc3_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => ( v1_collsp(k5_anproj_1(A)) & v4_collsp(k5_anproj_1(A)) ) ) )).
fof(fc3_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc3_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( v1_relat_1(k4_aofa_a00(A,B,C,D,E,F,G,H)) & v1_funct_1(k4_aofa_a00(A,B,C,D,E,F,G,H)) ) )).
fof(fc3_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ( v2_relat_1(k1_aofa_a01(A,B,C)) & v2_aofa_a01(k1_aofa_a01(A,B,C),A,B,C) ) ) )).
fof(fc3_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(fc3_armstrng,axiom,( ! [A] : ~ v1_xboole_0(k7_armstrng(A)) )).
fof(fc3_arytm_3,axiom,( ~ v1_xboole_0(k5_arytm_3) )).
fof(fc3_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_funct_1(k3_asympt_1(A)) & v1_funct_2(k3_asympt_1(A),k4_ordinal1,k1_numbers) & v4_asympt_0(k3_asympt_1(A)) ) ) )).
fof(fc3_autalg_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc3_bagorder,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & 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)) ) ) )).
fof(fc3_bcialg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc3_bcialg_4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc3_bcialg_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc3_bhsp_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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_xreal_0(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_bhsp_3(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k5_normsp_1(A,C,B)) & v1_funct_2(k5_normsp_1(A,C,B),k4_ordinal1,u1_struct_0(A)) & v1_bhsp_3(k5_normsp_1(A,C,B),A) ) ) )).
fof(fc3_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc3_binop_2,axiom,( v1_funct_1(k9_binop_2) & v1_funct_2(k9_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_binop_1(k9_binop_2,k1_numbers) & v2_binop_1(k9_binop_2,k1_numbers) )).
fof(fc3_bintree1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc3_bintree2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree2(A) & v7_ordinal1(B) & ~ v8_ordinal1(B) ) => v2_funct_1(k2_bintree2(A,B)) ) )).
fof(fc3_borsuk_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_borsuk_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc3_borsuk_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) )).
fof(fc3_borsuk_5,axiom,( ~ v1_xboole_0(k1_borsuk_5) )).
fof(fc3_borsuk_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc3_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( v1_relat_1(k1_borsuk_7(A,B,C,D,E,F)) & v1_funct_1(k1_borsuk_7(A,B,C,D,E,F)) ) )).
fof(fc3_brouwer,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) & ~ v3_xxreal_0(C) ) => ~ v2_struct_0(k2_brouwer(A,B,C)) ) )).
fof(fc3_bspace,axiom,( ! [A] : ( v1_xboole_0(A) => v1_xboole_0(k8_bspace(A)) ) )).
fof(fc3_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_c0sp1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc3_c0sp2,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(fc3_cantor_1,axiom,( ! [A] : ( l1_pre_topc(A) => v2_cantor_1(u1_pre_topc(A),A) ) )).
fof(fc3_card_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v1_xboole_0(k1_card_1(A)) & v1_card_1(k1_card_1(A)) ) ) )).
fof(fc3_card_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v2_finset_1(A) ) => v1_finset_1(k4_card_3(A)) ) )).
fof(fc3_card_3,axiom,( ! [A] : ! [B] : ( v1_card_1(B) => v1_card_3(k16_funcop_1(A,B)) ) )).
fof(fc3_card_5,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc3_card_fin,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_cardfin2,axiom,( ! [A] : ( v1_finset_1(A) => v1_finset_1(k2_cardfin2(A)) ) )).
fof(fc3_cat_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc3_cat_4,axiom,( ! [A] : ! [B] : ( ~ 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)) ) )).
fof(fc3_catalg_1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc3_cayldick,axiom,( ! [A] : ( ~ v1_xboole_0(A) => v2_relat_1(k3_afinsq_1(A)) ) )).
fof(fc3_cayley,axiom,( ! [A] : ( v1_finset_1(A) => v1_finset_1(k1_cayley(A)) ) )).
fof(fc3_cc0sp1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc3_cc0sp2,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(fc3_cfdiff_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_cfuncdom,axiom,( ! [A] : ( ~ 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)) & v7_valued_2(k3_cfuncdom(A)) ) ) )).
fof(fc3_cgames_1,axiom,( v1_xboole_0(k6_cgames_1(k3_cgames_1)) )).
fof(fc3_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & m1_subset_1(B,k4_ordinal1) & 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)) ) ) )).
fof(fc3_circtrm1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc3_classes1,axiom,( ! [A] : v1_ordinal1(k5_classes1(A)) )).
fof(fc3_classes2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => v1_classes2(k1_classes1(A)) ) )).
fof(fc3_clopban1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) ) ) )).
fof(fc3_clopban2,axiom,( ! [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) & 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)) ) ) )).
fof(fc3_clopban3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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,k4_ordinal1,u1_struct_0(A)) & v1_clopban3(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_clopban3(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k3_normsp_1(A,B,C)) & v1_funct_2(k3_normsp_1(A,B,C),k4_ordinal1,u1_struct_0(A)) & v1_clopban3(k3_normsp_1(A,B,C),A) ) ) )).
fof(fc3_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc3_coh_sp,axiom,( ! [A] : ~ v1_xboole_0(k5_coh_sp(A)) )).
fof(fc3_cohsp_1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_cohsp_1(A)) & v1_classes1(k1_cohsp_1(A)) & v1_coh_sp(k1_cohsp_1(A)) ) )).
fof(fc3_compact1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc3_compl_sp,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc3_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => v8_ordinal1(k2_complex1(A)) ) )).
fof(fc3_complfld,axiom,( ~ 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) )).
fof(fc3_compos_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc3_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ( v1_relat_1(k4_compos_1(A)) & v4_relat_1(k4_compos_1(A),k4_ordinal1) & 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) ) ) )).
fof(fc3_compts_1,axiom,( ! [A] : v8_pre_topc(k1_compts_1(k1_tarski(A))) )).
fof(fc3_comput_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_funct_1(k1_comseq_2(A)) & v1_funct_2(k1_comseq_2(A),k4_ordinal1,k2_numbers) & v2_comseq_2(k1_comseq_2(A)) ) ) )).
fof(fc3_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_funct_1(k2_series_1(k55_valued_1(k4_ordinal1,k2_numbers,A))) & v1_funct_2(k2_series_1(k55_valued_1(k4_ordinal1,k2_numbers,A)),k4_ordinal1,k1_numbers) & v7_valued_0(k2_series_1(k55_valued_1(k4_ordinal1,k2_numbers,A))) ) ) )).
fof(fc3_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ~ v1_xboole_0(k7_conlat_1(A)) ) )).
fof(fc3_conlat_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) & ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) & l2_conlat_1(B,A) ) => ( v3_conlat_1(k8_conlat_2(A,B),k7_conlat_2(A)) & ~ v4_conlat_1(k8_conlat_2(A,B),k7_conlat_2(A)) & v6_conlat_1(k8_conlat_2(A,B),k7_conlat_2(A)) ) ) )).
fof(fc3_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ~ v1_xboole_0(k10_convex4(A)) ) )).
fof(fc3_convfun1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc3_csspace,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) ) )).
fof(fc3_csspace3,axiom,( 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))) )).
fof(fc3_csspace4,axiom,( 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))) )).
fof(fc3_descip_1,axiom,( 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)) )).
fof(fc3_dickson,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ( v1_orders_2(k5_dickson(A)) & v4_orders_2(k5_dickson(A)) ) ) )).
fof(fc3_diff_1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc3_dilworth,axiom,( ! [A] : ( ( v2_struct_0(A) & l1_orders_2(A) ) => ( v1_xboole_0(k2_dilworth(A)) & v7_ordinal1(k2_dilworth(A)) ) ) )).
fof(fc3_dist_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc3_dtconstr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_dtconstr(A) & l1_lang1(A) ) => ~ v1_xboole_0(k4_dtconstr(A)) ) )).
fof(fc3_ec_pf_1,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(fc3_endalg,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc3_ens_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc3_eqrel_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc3_equation,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc3_euclid,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k1_euclid(A)) ) => ( v8_ordinal1(k12_euclid(k8_euclid(A,B,B))) & v1_xreal_0(k12_euclid(k8_euclid(A,B,B))) ) ) )).
fof(fc3_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ v1_xboole_0(k5_euclidlp(A)) ) )).
fof(fc3_exchsort,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(fc3_extpro_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ( v1_extpro_1(k1_extpro_1(A),A) & v3_extpro_1(k1_extpro_1(A),A) ) ) )).
fof(fc3_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xtuple_0(A) & ~ v1_xtuple_0(B) & ~ v1_xtuple_0(C) ) => ~ v1_facirc_1(k1_enumset1(A,B,C)) ) )).
fof(fc3_facirc_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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)) ) )).
fof(fc3_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_fcont_3,axiom,( ! [A] : ( v1_xreal_0(A) => v2_rcomp_1(k2_limfunc1(A)) ) )).
fof(fc3_fdiff_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v9_ordinal1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v1_fdiff_1(A,k5_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v7_ordinal1(B) ) => ( v1_funct_1(k7_nat_1(A,B)) & v9_ordinal1(k7_nat_1(A,B)) & v1_funct_2(k7_nat_1(A,B),k4_ordinal1,k1_numbers) & v1_fdiff_1(k7_nat_1(A,B),k5_numbers) ) ) )).
fof(fc3_fib_num2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) & 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)) ) ) )).
fof(fc3_fib_num3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => v2_xxreal_0(k1_fib_num3(A)) ) )).
fof(fc3_filter_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc3_filter_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc3_filter_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc3_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => v1_finset_1(k1_finseq_1(A)) ) )).
fof(fc3_finseq_2,axiom,( ! [A] : ! [B] : ( v7_ordinal1(A) => v1_finseq_1(k2_funcop_1(k2_finseq_1(A),B)) ) )).
fof(fc3_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v1_funcop_1(k5_finseq_1(A)) ) )).
fof(fc3_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : v1_finseq_1(k7_finseq_4(A,B,C,D)) )).
fof(fc3_finseq_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc3_finseq_6,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(fc3_finset_1,axiom,( ! [A] : ! [B] : ! [C] : v1_finset_1(k1_enumset1(A,B,C)) )).
fof(fc3_fintopo6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => v2_fintopo6(k5_finseq_1(B),A) ) )).
fof(fc3_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k4_xboole_0(k3_finseq_2(A),k1_tarski(k1_xboole_0))) ) )).
fof(fc3_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & ~ v8_struct_0(A) & l4_struct_0(A) ) => ~ v1_finset_1(k8_relat_1(k14_fomodel1(A),k6_domain_1(k4_ordinal1,k5_numbers))) ) )).
fof(fc3_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ~ v1_xboole_0(k1_fomodel1(A)) ) )).
fof(fc3_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k3_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) ) )).
fof(fc3_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v1_fomodel4(B,A) ) => v2_fomodel4(k1_tarski(B),A) ) )).
fof(fc3_frechet,axiom,( v2_pre_topc(k3_topmetr) & v1_frechet(k3_topmetr) )).
fof(fc3_freealg,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v2_relat_1(A) & m1_finseq_1(A,k4_ordinal1) ) => ( v1_lang1(k3_freealg(A,B)) & v2_dtconstr(k3_freealg(A,B)) & v3_dtconstr(k3_freealg(A,B)) ) ) )).
fof(fc3_fsm_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc3_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc3_funcop_1,axiom,( ! [A] : ! [B] : ( v1_xboole_0(B) => v1_xboole_0(k2_funcop_1(B,A)) ) )).
fof(fc3_funcsdom,axiom,( ! [A] : ( 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)) & v9_valued_2(k7_funcsdom(A)) ) )).
fof(fc3_funct_1,axiom,( ! [A] : ( v1_relat_1(k4_relat_1(A)) & v1_funct_1(k4_relat_1(A)) ) )).
fof(fc3_funct_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_xboole_0(B) ) => v1_xboole_0(k1_funct_2(A,B)) ) )).
fof(fc3_funct_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_funct_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_funct_7,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & 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)) ) ) )).
fof(fc3_funct_8,axiom,( v1_funct_1(k18_sin_cos) & v1_funct_2(k18_sin_cos,k1_numbers,k1_numbers) & v4_funct_8(k18_sin_cos,k1_numbers,k1_numbers) )).
fof(fc3_functor0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_fvaluat1,axiom,( v2_xxreal_0(k8_mesfunc1) & v1_xreal_0(k8_mesfunc1) & v1_fvaluat1(k8_mesfunc1) )).
fof(fc3_fvsum_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc3_gate_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k2_gate_1(A,B)) ) )).
fof(fc3_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ~ v1_xboole_0(k3_gcd_1(A)) ) )).
fof(fc3_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => v1_finset_1(k6_glib_000(A)) ) )).
fof(fc3_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => v5_glib_001(k2_glib_001(A,B,D,C),A) ) )).
fof(fc3_glib_003,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc3_glib_004,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(fc3_glib_005,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(fc3_goboard2,axiom,( ! [A] : ! [B] : ( ( ~ 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_0(k1_goboard2(A,B)) & v1_goboard1(k1_goboard2(A,B)) & v2_goboard1(k1_goboard2(A,B)) ) ) )).
fof(fc3_gr_cy_1,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(fc3_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc3_graph_5,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc3_graphsp,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k3_finseq_2(k1_numbers)) & m1_subset_1(B,k4_ordinal1) ) => v1_finset_1(k7_graphsp(A,B)) ) )).
fof(fc3_grcat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) )).
fof(fc3_grnilp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc3_groeb_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,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) ) ) )).
fof(fc3_group_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc3_group_10,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc3_group_12,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc3_group_14,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v1_prvect_1(A) & v1_relat_1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_finseq_1(B) & v1_prvect_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)) & v1_prvect_1(k7_finseq_1(A,B)) ) ) )).
fof(fc3_group_2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc3_group_6,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc3_group_7,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_group_9,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc3_groupp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(fc3_hahnban1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc3_hausdorf,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc3_hermitan,axiom,( ! [A] : ! [B] : ( ( ~ 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(k4_hahnban1(k1_complfld,A,B)) & v1_funct_2(k4_hahnban1(k1_complfld,A,B),u1_struct_0(A),u1_struct_0(k1_complfld)) & v1_hermitan(k4_hahnban1(k1_complfld,A,B),A) ) ) )).
fof(fc3_heyting3,axiom,( ! [A] : ! [B] : ( v3_orders_2(k1_heyting3(A,B)) & v4_orders_2(k1_heyting3(A,B)) & v5_orders_2(k1_heyting3(A,B)) ) )).
fof(fc3_hilbasis,axiom,( ! [A] : ! [B] : ( ( ~ 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,k4_ordinal1) ) => ( v1_funct_1(k6_hilbasis(A,B)) & v1_funct_2(k6_hilbasis(A,B),u1_struct_0(k14_polynom3(k12_polynom1(B,A))),u1_struct_0(k12_polynom1(k1_nat_1(B,1),A))) & v1_group_6(k6_hilbasis(A,B),k14_polynom3(k12_polynom1(B,A)),k12_polynom1(k1_nat_1(B,1),A)) ) ) )).
fof(fc3_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => v6_hilbert1(k5_hilbert1(A)) ) )).
fof(fc3_hilbert2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc3_hilbert3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_idea_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) & ~ v8_ordinal1(C) & v1_matrix_0(D) & v2_matrix_0(D,k4_ordinal1,B,6) & m1_finseq_1(D,k3_finseq_2(k4_ordinal1)) ) => ( 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)) ) ) )).
fof(fc3_ideal_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(fc3_index_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_int_1(k4_xcmplx_0(A)) ) ) )).
fof(fc3_int_3,axiom,( v4_vectsp_1(k1_int_3) )).
fof(fc3_int_4,axiom,( ! [A] : ( v1_int_1(A) => v1_partfun1(k1_int_4(A),k4_numbers) ) )).
fof(fc3_int_6,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_integr16,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc3_integra1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc3_interva1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc3_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => v8_intpro_1(k7_intpro_1(A)) ) )).
fof(fc3_isomichi,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc3_jordan,axiom,( ! [A] : ( 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))) ) )).
fof(fc3_jordan1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => v1_convex1(k6_topreal1(A),k15_euclid(2)) ) )).
fof(fc3_jordan10,axiom,( ! [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_xboole_0(k2_jordan10(A)) ) )).
fof(fc3_jordan18,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ~ v1_xboole_0(k7_relat_1(k4_pscomp_1,k7_topreal1(A))) ) )).
fof(fc3_jordan1e,axiom,( ! [A] : ! [B] : ( ( 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) ) => ( 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)) ) ) )).
fof(fc3_jordan1g,axiom,( ! [A] : ! [B] : ( ( 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)))) & v7_ordinal1(B) ) => v2_goboard5(k2_jordan1e(A,B)) ) )).
fof(fc3_jordan1h,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => v5_valued_0(k7_pre_poly(k1_numbers,A,k1_jordan1h)) ) )).
fof(fc3_jordan22,axiom,( ! [A] : ( ( 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)) ) )).
fof(fc3_jordan23,axiom,( ! [A] : ! [B] : v3_jordan23(k10_finseq_1(A,B)) )).
fof(fc3_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => v3_connsp_1(k2_struct_0(k15_euclid(A)),k15_euclid(A)) ) )).
fof(fc3_kolmog01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) )).
fof(fc3_kurato_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc3_kurato_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( v5_rltopsp1(k15_euclid(A)) & v1_frechet(k15_euclid(A)) ) ) )).
fof(fc3_lang1,axiom,( ! [A] : ! [B] : ( ~ v2_struct_0(k8_lang1(A,B)) & v2_lang1(k8_lang1(A,B)) ) )).
fof(fc3_lattice2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc3_lattice3,axiom,( ! [A] : ( v3_lattices(k1_lattice3(A)) & v17_lattices(k1_lattice3(A)) ) )).
fof(fc3_lattice5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc3_lattice8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc3_lattices,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc3_lexbfs,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1),k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)))) ) => v1_finset_1(k2_xtuple_0(B)) ) )).
fof(fc3_lfuzzy_0,axiom,( v1_orders_2(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1))) & v1_lfuzzy_0(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1))) & v2_lfuzzy_0(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1))) )).
fof(fc3_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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(k5_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) ) ) )).
fof(fc3_lmod_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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)) ) ) )).
fof(fc3_lopban_1,axiom,( ! [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) & 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)) ) ) )).
fof(fc3_lopban_2,axiom,( ! [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) & 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)) & v4_vectsp_1(k7_lopban_2(A)) & v5_vectsp_1(k7_lopban_2(A)) & v6_vectsp_1(k7_lopban_2(A)) ) ) )).
fof(fc3_lopban_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & v1_lopban_3(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_lopban_3(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k3_normsp_1(A,B,C)) & v1_funct_2(k3_normsp_1(A,B,C),k4_ordinal1,u1_struct_0(A)) & v1_lopban_3(k3_normsp_1(A,B,C),A) ) ) )).
fof(fc3_lopban_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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)))) ) => ( ~ v2_struct_0(k5_lopban_7(A,B,C)) & v13_algstr_0(k5_lopban_7(A,B,C)) & v2_rlvect_1(k5_lopban_7(A,B,C)) & v3_rlvect_1(k5_lopban_7(A,B,C)) & v4_rlvect_1(k5_lopban_7(A,B,C)) & v5_rlvect_1(k5_lopban_7(A,B,C)) & v6_rlvect_1(k5_lopban_7(A,B,C)) & v7_rlvect_1(k5_lopban_7(A,B,C)) & v8_rlvect_1(k5_lopban_7(A,B,C)) ) ) )).
fof(fc3_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ~ v1_xboole_0(k7_lopclset(A)) ) )).
fof(fc3_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v2_struct_0(k12_lpspacc1(A)) & v2_rlvect_1(k12_lpspacc1(A)) & v3_rlvect_1(k12_lpspacc1(A)) & v4_rlvect_1(k12_lpspacc1(A)) & v1_clvect_1(k12_lpspacc1(A)) & v2_clvect_1(k12_lpspacc1(A)) & v3_clvect_1(k12_lpspacc1(A)) & v4_clvect_1(k12_lpspacc1(A)) & v5_clvect_1(k12_lpspacc1(A)) ) ) )).
fof(fc3_lpspace1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_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)) ) ) )).
fof(fc3_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v2_xxreal_0(D) & v1_xreal_0(D) ) => ( v1_rlvect_1(g1_rlvect_1(k1_lpspace2(A,B,C,D),k10_subset_1(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),k10_subset_1(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),k10_subset_1(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),k10_subset_1(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),k10_subset_1(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),k10_subset_1(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),k10_subset_1(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),k10_subset_1(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)))) ) ) )).
fof(fc3_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( ~ v1_xboole_0(k1_funct_1(k4_ltlaxio3,A)) & v1_finset_1(k1_funct_1(k4_ltlaxio3,A)) ) ) )).
fof(fc3_ltlaxio4,axiom,( ! [A] : ( ( ~ v2_ltlaxio3(A) & m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) ) => ( ~ v1_xboole_0(k5_ltlaxio4(A)) & v1_finset_1(k5_ltlaxio4(A)) ) ) )).
fof(fc3_lukasi_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc3_margrel1,axiom,( ! [A] : v1_xboolean(k11_margrel1(A)) )).
fof(fc3_matrix11,axiom,( ! [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)) ) ) )).
fof(fc3_matrix13,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc3_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & v1_matrix_0(C) & m1_finseq_1(C,k3_finseq_2(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_0(k2_finseq_3(B,C)) ) ) )).
fof(fc3_matrix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( v15_algstr_0(k4_matrix_2(A)) & v2_group_1(k4_matrix_2(A)) & v3_group_1(k4_matrix_2(A)) ) ) )).
fof(fc3_matrix_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( v1_matrix_0(k1_matrix_4(B,C,D)) & v2_matrix_0(k1_matrix_4(B,C,D),u1_struct_0(B),A,A) ) ) )).
fof(fc3_matrlin2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) ) )).
fof(fc3_matroid0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc3_matrprob,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( ~ v3_relat_1(k4_matrix_0(k1_numbers,A)) & v1_matrix_0(k4_matrix_0(k1_numbers,A)) ) ) )).
fof(fc3_matrtop1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v3_partfun3(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( v1_relat_1(k5_relat_1(C,B)) & v3_partfun3(k5_relat_1(C,B)) ) ) )).
fof(fc3_matrtop3,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_matrix_0(B) & v2_matrix_0(B,u1_struct_0(k2_vectsp_1),A,A) & m1_finseq_1(B,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( 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) ) ) )).
fof(fc3_mazurulm,axiom,( ! [A] : ! [B] : ( ( v3_membered(A) & v4_xxreal_2(A) & ~ v2_xxreal_0(B) & v1_xreal_0(B) ) => v3_xxreal_2(k23_member_1(A,B)) ) )).
fof(fc3_measure6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc3_member_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k4_member_1(A)) & v2_membered(k4_member_1(A)) ) ) )).
fof(fc3_membered,axiom,( v3_membered(k1_numbers) )).
fof(fc3_memstr_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc3_mesfun7c,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k2_numbers)) & v1_mesfunc8(B,A,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ( v1_funct_1(k11_mesfun7c(A,B)) & v1_funct_2(k11_mesfun7c(A,B),k4_ordinal1,k4_partfun1(A,k1_numbers)) & v1_mesfunc8(k11_mesfun7c(A,B),A,k1_numbers) ) ) )).
fof(fc3_mesfunc7,axiom,( v1_funct_1(k1_mesfunc7) & v1_funct_2(k1_mesfunc7,k2_zfmisc_1(k6_numbers,k6_numbers),k6_numbers) & v1_setwiseo(k1_mesfunc7,k6_numbers) )).
fof(fc3_metric_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v2_struct_0(k5_metric_1(A)) & v1_metric_1(k5_metric_1(A)) ) ) )).
fof(fc3_metrizts,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_mfold_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc3_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ~ v1_xboole_0(k10_midsp_1(A)) ) )).
fof(fc3_midsp_2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc3_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc3_mod_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) ) )).
fof(fc3_mod_4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc3_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m1_finseq_1(A,k4_ordinal1) ) => v1_modelc_1(k9_modelc_1(A)) ) )).
fof(fc3_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => v1_modelc_2(k6_modelc_2(A)) ) )).
fof(fc3_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => ( ~ v1_xboole_0(k23_modelc_3(A)) & v1_finset_1(k23_modelc_3(A)) ) ) )).
fof(fc3_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( v1_finset_1(k3_moebius1(A)) & v1_setfam_1(k3_moebius1(A)) ) ) )).
fof(fc3_monoid_0,axiom,( ! [A] : ( ~ v2_struct_0(k15_monoid_0(A)) & v15_algstr_0(k15_monoid_0(A)) & v1_group_1(k15_monoid_0(A)) ) )).
fof(fc3_monoid_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc3_msafree,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc3_msafree1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc3_msafree3,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc3_msafree4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_finset_1(A) & v1_funcop_1(A) ) => ( v1_relat_1(k1_funct_6(A)) & v1_funct_1(k1_funct_6(A)) & v2_finset_1(k1_funct_6(A)) ) ) )).
fof(fc3_msalimit,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(fc3_msinst_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc3_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_funcop_1(B) ) => ( v1_relat_1(k1_funct_6(B)) & v4_relat_1(k1_funct_6(B),A) & v1_funct_1(k1_funct_6(B)) & v1_partfun1(k1_funct_6(B),A) ) ) )).
fof(fc3_msualg_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc3_msualg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc3_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc3_msualg_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc3_mycielsk,axiom,( ! [A] : ( ( v2_struct_0(A) & l1_orders_2(A) ) => ( v1_xboole_0(k2_mycielsk(A)) & v7_ordinal1(k2_mycielsk(A)) ) ) )).
fof(fc3_nat_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ~ v8_ordinal1(k2_xcmplx_0(A,B)) ) )).
fof(fc3_nat_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_nat_lat,axiom,( ~ v2_struct_0(k3_nat_lat) & v3_lattices(k3_nat_lat) )).
fof(fc3_nattra_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_cat_1(A) & v3_cat_1(A) & v4_cat_1(A) & v5_cat_1(A) & v6_cat_1(A) & v4_nattra_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) & v4_nattra_1(B) & l1_cat_1(B) ) => ( ~ v2_struct_0(k6_cat_2(A,B)) & ~ v11_struct_0(k6_cat_2(A,B)) & v2_cat_1(k6_cat_2(A,B)) & v3_cat_1(k6_cat_2(A,B)) & v4_cat_1(k6_cat_2(A,B)) & v5_cat_1(k6_cat_2(A,B)) & v6_cat_1(k6_cat_2(A,B)) & v4_nattra_1(k6_cat_2(A,B)) ) ) )).
fof(fc3_neckla_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_necklace,axiom,( ! [A] : ( ( v1_necklace(A) & l1_orders_2(A) ) => v3_relat_2(u1_orders_2(A)) ) )).
fof(fc3_newton,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v7_ordinal1(B) ) => v1_xcmplx_0(k1_newton(A,B)) ) )).
fof(fc3_nfcont_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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) ) ) )).
fof(fc3_nfcont_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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) ) ) )).
fof(fc3_normform,axiom,( ! [A] : ~ v1_xboole_0(k8_normform(A)) )).
fof(fc3_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ( ~ v2_struct_0(k4_normsp_2(A)) & v8_pre_topc(k4_normsp_2(A)) & v5_rltopsp1(k4_normsp_2(A)) ) ) )).
fof(fc3_numbers,axiom,( ~ v1_xboole_0(k3_numbers) )).
fof(fc3_openlatt,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc3_oposet_1,axiom,( ~ v2_struct_0(k2_oposet_1) & v3_qmax_1(k2_oposet_1) )).
fof(fc3_ordeq_01,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_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) & l1_normsp_1(B) ) => v1_rlsub_1(k1_ordeq_01(A,B),k5_rsspace4(A,B)) ) )).
fof(fc3_orders_1,axiom,( ! [A] : ( v1_relat_1(k4_relat_1(A)) & v1_orders_1(k4_relat_1(A)) & v2_orders_1(k4_relat_1(A)) ) )).
fof(fc3_orders_2,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => v1_relat_2(u1_orders_2(A)) ) )).
fof(fc3_orders_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ~ v1_xboole_0(k1_orders_3(A,A)) ) )).
fof(fc3_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => v3_ordinal1(k3_tarski(A)) ) )).
fof(fc3_ordinal2,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => v1_ordinal2(k2_funcop_1(A,B)) ) )).
fof(fc3_ordinal3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v7_ordinal1(A) & v3_ordinal1(B) & v7_ordinal1(B) ) => ( v3_ordinal1(k5_ordinal3(A,B)) & v7_ordinal1(k5_ordinal3(A,B)) ) ) )).
fof(fc3_ordinal4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ~ v1_xboole_0(k2_ordinal1(A)) ) )).
fof(fc3_ordinal5,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_ordinal6,axiom,( ! [A] : ( v1_ordinal6(A) => v3_ordinal1(k3_tarski(A)) ) )).
fof(fc3_osafree,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc3_osalg_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc3_osalg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc3_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc3_papdesaf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ( v1_analoaf(k2_diraf(A)) & v1_translac(k2_diraf(A)) ) ) )).
fof(fc3_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) ) ) )).
fof(fc3_partfun1,axiom,( ! [A] : ( 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)) ) )).
fof(fc3_partfun3,axiom,( ! [A] : ( v1_xreal_0(A) => ~ v3_xxreal_0(k3_xcmplx_0(A,k5_xcmplx_0(A))) ) )).
fof(fc3_partit_2,axiom,( ! [A] : ( v1_relat_1(k4_relat_1(A)) & v1_partit_2(k4_relat_1(A)) ) )).
fof(fc3_pboole,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc3_pencil_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc3_petri,axiom,( ! [A] : ( ( v3_petri(A) & l1_petri(A) ) => ~ v1_xboole_0(u2_petri(A)) ) )).
fof(fc3_polyalg1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc3_polyeq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => v1_xreal_0(k2_polyeq_1(A,B,C,D)) ) )).
fof(fc3_polyeq_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)) ) )).
fof(fc3_polynom1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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,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,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ( v1_funct_1(k7_polynom1(A,B,C,D)) & v1_funct_2(k7_polynom1(A,B,C,D),k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(k7_polynom1(A,B,C,D),B) ) ) )).
fof(fc3_polynom2,axiom,( ! [A] : ! [B] : ( ( 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(k12_polynom1(A,B)) & v36_algstr_0(k12_polynom1(A,B)) & v4_vectsp_1(k12_polynom1(A,B)) ) ) )).
fof(fc3_polynom3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v4_rlvect_1(A) & l2_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k2_normsp_1(A,B,C)) & v1_funct_2(k2_normsp_1(A,B,C),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k2_normsp_1(A,B,C),A) ) ) )).
fof(fc3_polynom5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k4_polynom5(A,B,C),A) ) ) )).
fof(fc3_polynom7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc3_polyred,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_poset_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc3_pralg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc3_pralg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc3_pralg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc3_pre_circ,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ( v1_relat_1(k1_funct_7(B,C,D)) & v4_relat_1(k1_funct_7(B,C,D),A) & v1_funct_1(k1_funct_7(B,C,D)) & v1_partfun1(k1_funct_7(B,C,D),A) ) ) )).
fof(fc3_pre_topc,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_prepower,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_int_1(B) ) => v1_xreal_0(k3_prepower(A,B)) ) )).
fof(fc3_prob_1,axiom,( ! [A] : v2_finsub_1(k2_tarski(k1_xboole_0,A)) )).
fof(fc3_prob_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,k9_setfam_1(A)) ) ) )).
fof(fc3_prvect_1,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) ) )).
fof(fc3_prvect_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc3_pscomp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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)) ) )).
fof(fc3_pythtrip,axiom,( ! [A] : ( v1_int_1(A) => v1_int_1(k1_square_1(A)) ) )).
fof(fc3_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ~ v1_xboole_0(k3_qc_lang1(A)) ) )).
fof(fc3_qmax_1,axiom,( ! [A] : ( l1_qmax_1(A) => ~ v1_xboole_0(k3_qmax_1(A)) ) )).
fof(fc3_quatern2,axiom,( v8_algstr_0(k14_quatern2) & v13_algstr_0(k14_quatern2) & v2_rlvect_1(k14_quatern2) & v3_rlvect_1(k14_quatern2) & v4_rlvect_1(k14_quatern2) )).
fof(fc3_quaterni,axiom,( v1_quaterni(k1_xcmplx_0) )).
fof(fc3_quofield,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v6_struct_0(A) & l5_algstr_0(A) ) => ~ v1_xboole_0(k7_quofield(A)) ) )).
fof(fc3_ramsey_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_finset_1(A) & v1_finset_1(B) ) => ~ v1_finset_1(k4_xboole_0(A,B)) ) )).
fof(fc3_random_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( v1_relat_1(k5_random_3(A)) & v2_relat_1(k5_random_3(A)) & v4_relat_1(k5_random_3(A),k4_ordinal1) & v1_funct_1(k5_random_3(A)) & v1_partfun1(k5_random_3(A),k4_ordinal1) ) ) )).
fof(fc3_rat_1,axiom,( ! [A] : ! [B] : ( ( v1_rat_1(A) & v1_rat_1(B) ) => v1_rat_1(k6_xcmplx_0(A,B)) ) )).
fof(fc3_rcomp_3,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xxreal_0(B) ) => v4_xxreal_2(k3_xxreal_1(B,A)) ) )).
fof(fc3_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( v8_ordinal1(k4_int_1(k5_numbers,A)) & v1_int_1(k4_int_1(k5_numbers,A)) ) ) )).
fof(fc3_real_lat,axiom,( v3_lattices(k3_real_lat) & v10_lattices(k3_real_lat) )).
fof(fc3_real_ns1,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc3_relat_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k2_xboole_0(A,B)) ) )).
fof(fc3_relat_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_2(A) ) => ( v1_relat_1(k2_relat_1(A)) & v2_relat_2(k2_relat_1(A)) ) ) )).
fof(fc3_reloc,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc3_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_relat_1(C) ) => v4_relat_1(k4_xboole_0(B,C),A) ) )).
fof(fc3_revrot_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc3_rewrite2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_rewrite2(A) ) => v5_ordinal1(k1_funct_1(A,B)) ) )).
fof(fc3_rfunct_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc3_rfunct_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_ring_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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)) ) ) )).
fof(fc3_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ~ v1_xboole_0(k9_ringcat1(A)) ) )).
fof(fc3_rlaffin1,axiom,( ! [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) & v8_rlvect_1(A) & l1_rlvect_1(A) & m1_subset_1(B,u1_struct_0(A)) ) => v1_rlaffin1(k1_tarski(B),A) ) )).
fof(fc3_rlaffin3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc3_rlsub_2,axiom,( ! [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) ) => ( 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))) ) ) )).
fof(fc3_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) )).
fof(fc3_rlvect_2,axiom,( ! [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) ) => ( ~ v2_struct_0(k16_rlvect_2(A)) & v1_rlvect_1(k16_rlvect_2(A)) ) ) )).
fof(fc3_robbins3,axiom,( v3_robbins3(k1_robbins3) )).
fof(fc3_robbins4,axiom,( v3_orders_2(k1_robbins4) & v4_orders_2(k1_robbins4) & v5_orders_2(k1_robbins4) )).
fof(fc3_rsspace,axiom,( v13_algstr_0(k6_rsspace) & v2_rlvect_1(k6_rsspace) & v3_rlvect_1(k6_rsspace) & v4_rlvect_1(k6_rsspace) & v5_rlvect_1(k6_rsspace) & v6_rlvect_1(k6_rsspace) & v7_rlvect_1(k6_rsspace) & v8_rlvect_1(k6_rsspace) )).
fof(fc3_rsspace3,axiom,( v13_algstr_0(g1_rlvect_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3))) & v1_rlvect_1(g1_rlvect_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3))) & v2_rlvect_1(g1_rlvect_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3))) & v3_rlvect_1(g1_rlvect_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3))) & v4_rlvect_1(g1_rlvect_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3))) & v5_rlvect_1(g1_rlvect_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3))) & v6_rlvect_1(g1_rlvect_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3))) & v7_rlvect_1(g1_rlvect_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3))) & v8_rlvect_1(g1_rlvect_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3))) )).
fof(fc3_rsspace4,axiom,( v13_algstr_0(g1_rlvect_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4))) & v1_rlvect_1(g1_rlvect_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4))) & v2_rlvect_1(g1_rlvect_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4))) & v3_rlvect_1(g1_rlvect_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4))) & v4_rlvect_1(g1_rlvect_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4))) & v5_rlvect_1(g1_rlvect_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4))) & v6_rlvect_1(g1_rlvect_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4))) & v7_rlvect_1(g1_rlvect_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4))) & v8_rlvect_1(g1_rlvect_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4))) )).
fof(fc3_rusub_2,axiom,( ! [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_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))) ) ) )).
fof(fc3_rvsum_1,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => v3_valued_0(k10_finseq_1(A,B)) ) )).
fof(fc3_scm_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_int_1(A) & v1_int_1(B) & v1_int_1(C) ) => v5_relat_1(k7_afinsq_1(A,B,C),k4_numbers) ) )).
fof(fc3_scm_halt,axiom,( ! [A] : ! [B] : ( ( 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,k4_ordinal1) & 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,k7_card_1(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),k4_ordinal1) & 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)) ) ) )).
fof(fc3_scm_inst,axiom,( v3_finseq_1(k10_xtuple_0(k3_scm_inst)) )).
fof(fc3_scmfsa10,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc3_scmfsa6a,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & m1_subset_1(B,k4_ordinal1) ) => ( v1_relat_1(k1_scmfsa6a(A,B)) & v4_relat_1(k1_scmfsa6a(A,B),k4_ordinal1) & 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) ) ) )).
fof(fc3_scmfsa6c,axiom,( ! [A] : ( ( 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),k4_ordinal1) & 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)) ) ) )).
fof(fc3_scmfsa7b,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) & v5_relat_1(k4_scmfsa_7(A,B),u1_compos_1(k1_scmfsa_2)) & ~ v1_xboole_0(k4_scmfsa_7(A,B)) & v1_funct_1(k4_scmfsa_7(A,B)) & v1_finset_1(k4_scmfsa_7(A,B)) & v1_afinsq_1(k4_scmfsa_7(A,B)) ) ) )).
fof(fc3_scmfsa8a,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) ) => ( v1_relat_1(k1_scmfsa6a(A,B)) & v4_relat_1(k1_scmfsa6a(A,B),k4_ordinal1) & 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)) ) ) )).
fof(fc3_scmfsa8b,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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) ) ) )).
fof(fc3_scmfsa_1,axiom,( v1_relat_1(k3_relat_1(k4_scmfsa_1,k5_scmfsa_1)) & v2_relat_1(k3_relat_1(k4_scmfsa_1,k5_scmfsa_1)) )).
fof(fc3_scmfsa_2,axiom,( ~ v1_finset_1(k3_scmfsa_2) )).
fof(fc3_scmfsa_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc3_scmfsa_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc3_scmfsa_i,axiom,( ~ v1_xboole_0(k2_scmfsa_i) & v1_compos_0(k2_scmfsa_i) )).
fof(fc3_scmfsa_m,axiom,( ! [A] : ( ( 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(k7_card_1(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(k7_card_1(3),k1_scmfsa_2)) & v1_finset_1(k1_scmfsa_m(A)) ) ) )).
fof(fc3_scmpds_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc3_scmpds_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc3_scmpds_5,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) & v1_int_1(B) ) => v6_compos_0(k6_scmpds_2(A,B),u1_compos_1(k1_scmpds_2)) ) )).
fof(fc3_scmpds_6,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_relat_1(k1_scmpds_6(k1_nat_1(A,1))) & v4_relat_1(k1_scmpds_6(k1_nat_1(A,1)),k4_ordinal1) & v5_relat_1(k1_scmpds_6(k1_nat_1(A,1)),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k1_scmpds_6(k1_nat_1(A,1))) & v1_funct_1(k1_scmpds_6(k1_nat_1(A,1))) & v1_finset_1(k1_scmpds_6(k1_nat_1(A,1))) & v1_afinsq_1(k1_scmpds_6(k1_nat_1(A,1))) & v2_compos_1(k1_scmpds_6(k1_nat_1(A,1)),k1_scmpds_2) ) ) )).
fof(fc3_scmpds_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & 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) & v7_ordinal1(D) ) => ( v1_relat_1(k2_scmpds_7(B,C,D,A)) & v4_relat_1(k2_scmpds_7(B,C,D,A),k4_ordinal1) & v5_relat_1(k2_scmpds_7(B,C,D,A),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k2_scmpds_7(B,C,D,A)) & 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)) ) ) )).
fof(fc3_scmpds_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc3_scmpds_i,axiom,( v1_compos_0(k1_scmpds_i) )).
fof(fc3_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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),k7_card_1(2)) & v1_extpro_1(k1_scmring2(A),k7_card_1(2)) ) ) )).
fof(fc3_scmring3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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),k7_card_1(2),k1_scmring2(A)) ) )).
fof(fc3_scmring4,axiom,( ! [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) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ( v1_extpro_1(k1_scmring2(A),k7_card_1(2)) & v4_amistd_5(k1_scmring2(A),k7_card_1(2)) ) ) )).
fof(fc3_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => v3_finseq_1(k10_xtuple_0(k1_scmringi(A))) ) )).
fof(fc3_scmyciel,axiom,( ! [A] : ( v1_scmyciel(A) => v1_xboole_0(k3_tarski(A)) ) )).
fof(fc3_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_funct_1(k30_valued_1(A)) & v1_funct_2(k30_valued_1(A),k4_ordinal1,k1_numbers) & v2_comseq_2(k30_valued_1(A)) ) ) )).
fof(fc3_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ~ v1_xboole_0(k12_seq_4(A)) ) )).
fof(fc3_setfam_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => v1_setfam_1(k2_tarski(A,B)) ) )).
fof(fc3_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(fc3_sfmastr1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc3_sfmastr3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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),k4_ordinal1) & 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)) ) ) )).
fof(fc3_simplex0,axiom,( ! [A] : ! [B] : ( ( v1_classes1(A) & v1_classes1(B) ) => v1_classes1(k2_xboole_0(A,B)) ) )).
fof(fc3_simplex1,axiom,( ! [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) & 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) ) ) )).
fof(fc3_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k17_sin_cos(A)) ) )).
fof(fc3_sin_cos2,axiom,( ! [A] : v1_xreal_0(k6_sin_cos2(A)) )).
fof(fc3_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k16_sin_cos,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos)))) & v2_funct_1(k5_relat_1(k16_sin_cos,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos)))) )).
fof(fc3_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k3_sin_cos9(A)) ) )).
fof(fc3_sincos10,axiom,( v1_relat_1(k5_relat_1(k2_fdiff_9,k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers))) & v2_funct_1(k5_relat_1(k2_fdiff_9,k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers))) )).
fof(fc3_sppol_1,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & v7_ordinal1(B) ) => v4_pre_topc(k2_topreal1(2,A,B),k15_euclid(2)) ) )).
fof(fc3_sppol_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc3_sprect_1,axiom,( v1_topreal4(k1_topreal1) & ~ v1_sppol_1(k1_topreal1) & ~ v2_sppol_1(k1_topreal1) )).
fof(fc3_sprect_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(fc3_sprect_3,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(fc3_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k3_square_1(A)) ) )).
fof(fc3_stacks_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => v4_funct_1(u4_struct_0(k8_stacks_1(A))) ) )).
fof(fc3_struct_0,axiom,( ! [A] : ( l1_struct_0(A) => v1_xboole_0(k1_struct_0(A)) ) )).
fof(fc3_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ~ v1_xboole_0(k2_enumset1(A,B,C,D)) )).
fof(fc3_substlat,axiom,( ! [A] : ! [B] : ( v3_lattices(k5_substlat(A,B)) & v10_lattices(k5_substlat(A,B)) ) )).
fof(fc3_substut1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k9_qc_lang1(A)) ) => v1_finset_1(k9_substut1(A,B)) ) )).
fof(fc3_supinf_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_setfam_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k6_numbers))) ) => ( ~ v1_xboole_0(k5_supinf_1(A)) & v2_membered(k5_supinf_1(A)) ) ) )).
fof(fc3_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_tbsp_1(A) & l1_metric_1(A) ) => v6_tbsp_1(k2_struct_0(A),A) ) )).
fof(fc3_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ~ v1_xboole_0(k9_tdlat_1(A)) ) )).
fof(fc3_termord,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,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) ) ) )).
fof(fc3_tex_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v2_struct_0(k2_tex_1(A)) ) )).
fof(fc3_tex_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc3_tex_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc3_tmap_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc3_topalg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc3_topalg_2,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc3_topalg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(fc3_topalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))))) ) ) )).
fof(fc3_topalg_5,axiom,( v1_connsp_2(k17_borsuk_1) )).
fof(fc3_topalg_6,axiom,( ! [A] : ( v7_ordinal1(A) => ( v5_rltopsp1(k15_euclid(A)) & v1_topalg_6(k15_euclid(A)) ) ) )).
fof(fc3_topdim_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc3_topdim_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc3_topgen_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc3_topgen_3,axiom,( ! [A] : ! [B] : ( ~ 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)) ) ) )).
fof(fc3_topgen_4,axiom,( ! [A] : ! [B] : ( ( v4_card_3(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => v4_card_3(k7_setfam_1(A,B)) ) )).
fof(fc3_topgen_5,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc3_topgrp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc3_topmetr,axiom,( v3_topmetr(k17_borsuk_1) )).
fof(fc3_topreal1,axiom,( ~ v1_xboole_0(k1_topreal1) )).
fof(fc3_topreal6,axiom,( v2_connsp_1(k1_topreal1,k15_euclid(2)) )).
fof(fc3_topreal7,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc3_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc3_topreala,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v2_xxreal_0(B) & v1_xreal_0(B) ) => ~ v1_xboole_0(k3_xxreal_1(A,k2_xcmplx_0(A,B))) ) )).
fof(fc3_toprealb,axiom,( ~ v1_xboole_0(k4_xxreal_1(k7_xcmplx_0(1,2),k7_xcmplx_0(3,2))) )).
fof(fc3_toprealc,axiom,( v8_ordinal1(k3_square_1(k5_numbers)) & v1_xreal_0(k3_square_1(k5_numbers)) )).
fof(fc3_tops_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc3_trees_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc3_trees_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc3_trees_3,axiom,( v1_trees_3(k1_trees_3) )).
fof(fc3_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v3_trees_9(A) ) => v1_trees_9(k9_xtuple_0(A)) ) )).
fof(fc3_triang_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(fc3_unialg_1,axiom,( ! [A] : ( ( v3_unialg_1(A) & l1_unialg_1(A) ) => v5_margrel1(u1_unialg_1(A),u1_struct_0(A)) ) )).
fof(fc3_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => v1_finset_1(k2_uniroots(A)) ) )).
fof(fc3_uproots,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & v1_uproots(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & v1_uproots(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k11_polynom3(A,B,C)) & v1_funct_2(k11_polynom3(A,B,C),k4_ordinal1,u1_struct_0(A)) & v1_uproots(k11_polynom3(A,B,C),A) ) ) )).
fof(fc3_urysohn1,axiom,( ~ v1_xboole_0(k3_urysohn1) )).
fof(fc3_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_valued_0(A) ) => v3_membered(k10_xtuple_0(A)) ) )).
fof(fc3_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc3_vectmetr,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc3_vectsp_1,axiom,( 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) )).
fof(fc3_vfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc3_waybel10,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc3_waybel11,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc3_waybel14,axiom,( ! [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) ) => ~ v1_xboole_0(k5_waybel11(A)) ) )).
fof(fc3_waybel17,axiom,( ! [A] : ! [B] : ( ( 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),k6_yellow_1(A,B)) ) ) )).
fof(fc3_waybel18,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc3_waybel21,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc3_waybel22,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k1_yellow_1(k8_waybel_0(k2_yellow_1(A)))),u1_struct_0(B)) & v17_waybel_0(k2_waybel22(A,B,C),k1_yellow_1(k8_waybel_0(k2_yellow_1(A))),B) ) ) )).
fof(fc3_waybel23,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc3_waybel24,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc3_waybel25,axiom,( ! [A] : ( ( v2_struct_0(A) & l1_pre_topc(A) ) => ( v2_struct_0(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) ) ) )).
fof(fc3_waybel26,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc3_waybel27,axiom,( ! [A] : ( ( v1_monoid_0(A) & l1_struct_0(A) ) => v4_funct_1(u1_struct_0(A)) ) )).
fof(fc3_waybel29,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc3_waybel30,axiom,( ! [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) ) => ~ v1_xboole_0(k2_waybel19(A)) ) )).
fof(fc3_waybel32,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc3_waybel34,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc3_waybel_0,axiom,( ! [A] : ( ( v2_lattice3(A) & l1_orders_2(A) ) => v2_waybel_0(k2_struct_0(A),A) ) )).
fof(fc3_waybel_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc3_waybel_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc3_waybel_3,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc3_waybel_4,axiom,( ! [A] : ( ( v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => v3_waybel_4(k2_waybel_4(A),A) ) )).
fof(fc3_waybel_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(fc3_waybel_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc3_waybel_8,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc3_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc3_weddwitt,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc3_wellord2,axiom,( ! [A] : ( v1_relat_1(k1_wellord2(A)) & v4_relat_2(k1_wellord2(A)) ) )).
fof(fc3_xboole_0,axiom,( ! [A] : ! [B] : ~ v1_xboole_0(k2_tarski(A,B)) )).
fof(fc3_xboolean,axiom,( ! [A] : ! [B] : ( ( v1_xboolean(A) & v1_xboolean(B) ) => v1_xboolean(k4_xboolean(A,B)) ) )).
fof(fc3_xcmplx_0,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_xcmplx_0(k3_xcmplx_0(A,B)) ) )).
fof(fc3_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_xreal_0(k4_xcmplx_0(A)) ) ) )).
fof(fc3_xtuple_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : v3_xtuple_0(k6_xtuple_0(A,B,C,D)) )).
fof(fc3_xxreal_0,axiom,( v2_xxreal_0(k1_xxreal_0) )).
fof(fc3_xxreal_1,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => v2_membered(k3_xxreal_1(A,B)) ) )).
fof(fc3_xxreal_2,axiom,( ! [A] : ( ( v3_membered(A) & v1_xxreal_2(A) ) => ( v1_xxreal_0(k2_xxreal_2(A)) & v1_xreal_0(k2_xxreal_2(A)) ) ) )).
fof(fc3_xxreal_3,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xxreal_0(k3_xxreal_3(A,B)) & v1_xreal_0(k3_xxreal_3(A,B)) ) ) )).
fof(fc3_yellow10,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(fc3_yellow11,axiom,( v1_orders_2(k2_yellow11) & v3_orders_2(k2_yellow11) & v4_orders_2(k2_yellow11) & v5_orders_2(k2_yellow11) )).
fof(fc3_yellow12,axiom,( ! [A] : ( ( 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) ) ) )).
fof(fc3_yellow13,axiom,( ! [A] : ( ( 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(k1_yellow_1(k7_waybel_0(A))),u1_struct_0(A)) ) ) )).
fof(fc3_yellow14,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(fc3_yellow16,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(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)) ) )).
fof(fc3_yellow18,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc3_yellow19,axiom,( ! [A] : ! [B] : ( ( ~ 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(k2_yellow_1(k2_struct_0(A)))) & v2_waybel_0(k2_yellow19(A,B),k2_yellow_1(k2_struct_0(A))) ) ) )).
fof(fc3_yellow20,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc3_yellow21,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(fc3_yellow_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc3_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ~ v1_xboole_0(k7_waybel_0(A)) ) )).
fof(fc3_yellow_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc3_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc3_yellow_6,axiom,( ! [A] : ! [B] : ( l1_struct_0(B) => v2_pralg_1(k2_funcop_1(A,B)) ) )).
fof(fc3_yellow_7,axiom,( ! [A] : ( ( v5_orders_2(A) & l1_orders_2(A) ) => ( v1_orders_2(k7_lattice3(A)) & v5_orders_2(k7_lattice3(A)) ) ) )).
fof(fc3_yellow_9,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc3_zf_lang,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_zf_lang) & m1_subset_1(B,k1_zf_lang) ) => v1_zf_lang(k5_zf_lang(A,B)) ) )).
fof(fc3_zfmisc_1,axiom,( ! [A] : ! [B] : ( v1_xboole_0(A) => v1_xboole_0(k2_zfmisc_1(A,B)) ) )).
fof(fc3_zmodul01,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(fc3_zmodul02,axiom,( ! [A] : ( ( ~ 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_int_3) & v9_vectsp_1(A,k1_int_3) & v10_vectsp_1(A,k1_int_3) & v11_vectsp_1(A,k1_int_3) & l1_vectsp_1(A,k1_int_3) ) => ( ~ v2_struct_0(k17_zmodul02(A)) & v13_algstr_0(k17_zmodul02(A)) & v2_rlvect_1(k17_zmodul02(A)) & v3_rlvect_1(k17_zmodul02(A)) & v4_rlvect_1(k17_zmodul02(A)) & v1_zmodul01(k17_zmodul02(A)) & v2_zmodul01(k17_zmodul02(A)) & v3_zmodul01(k17_zmodul02(A)) & v4_zmodul01(k17_zmodul02(A)) & v5_zmodul01(k17_zmodul02(A)) ) ) )).
fof(fc40_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc40_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) ) )).
fof(fc40_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_rlvect_1(A) & l1_cayldick(A) ) => ( v6_rlvect_1(k4_cayldick(A)) & v1_cayldick(k4_cayldick(A)) ) ) )).
fof(fc40_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) ) )).
fof(fc40_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v16_fomodel1(k22_fomodel0(A),A) ) )).
fof(fc40_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ~ v4_fomodel1(k8_fomodel1(A),A) ) )).
fof(fc40_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(fc40_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v3_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))) ) => v5_fomodel4(k4_tarski(B,k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(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))),k34_fomodel4(A)),k1_tarski(k4_tarski(B,k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k1_fomodel2(A)),C),D)))) ) )).
fof(fc40_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc40_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v2_membered(B) ) => v1_xboole_0(k12_member_1(B,A)) ) )).
fof(fc40_membered,axiom,( ! [A] : ! [B] : ( v5_membered(A) => v5_membered(k3_xboole_0(B,A)) ) )).
fof(fc40_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc40_pcs_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc40_scmfsa10,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc40_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(fc40_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v5_relat_1(A,k3_numbers) ) => v4_membered(k9_relat_1(A,B)) ) )).
fof(fc40_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc40_valued_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc40_xxreal_3,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ( v1_xxreal_0(k6_xxreal_3(A,B)) & v1_xreal_0(k6_xxreal_3(A,B)) ) ) )).
fof(fc41_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc41_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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))) ) ) )).
fof(fc41_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v7_rlvect_1(A) & l1_cayldick(A) ) => ( v7_rlvect_1(k4_cayldick(A)) & v1_cayldick(k4_cayldick(A)) ) ) )).
fof(fc41_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc41_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(fc41_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k42_fomodel1(A,k43_fomodel1(A,k1_fomodel2(A)),B),C),A,k4_xxreal_0(k29_fomodel2(A,B),k29_fomodel2(A,C))) ) )).
fof(fc41_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v1_fomodel4(B,A) ) => v3_fomodel4(k1_xtuple_0(B),A) ) )).
fof(fc41_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc41_member_1,axiom,( ! [A] : ! [B] : ( ( v2_membered(A) & v2_membered(B) ) => v2_membered(k12_member_1(A,B)) ) )).
fof(fc41_membered,axiom,( ! [A] : ! [B] : ( v6_membered(A) => v6_membered(k3_xboole_0(A,B)) ) )).
fof(fc41_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc41_pcs_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc41_scmfsa10,axiom,( ! [A] : ! [B] : ( ( 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)),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc41_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) ) => v5_membered(k9_relat_1(A,B)) ) )).
fof(fc41_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc41_valued_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc41_xxreal_3,axiom,( v8_ordinal1(k5_xxreal_3(k2_xxreal_0)) & v1_xxreal_0(k5_xxreal_3(k2_xxreal_0)) )).
fof(fc42_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) ) )).
fof(fc42_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_rlvect_1(A) & l1_cayldick(A) ) => ( v8_rlvect_1(k4_cayldick(A)) & v1_cayldick(k4_cayldick(A)) ) ) )).
fof(fc42_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_relat_1(k8_fomodel0(A)) & v1_funct_1(k8_fomodel0(A)) & v1_pre_poly(k8_fomodel0(A)) ) ) )).
fof(fc42_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc42_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k43_fomodel1(A,C),B),A,k29_fomodel2(A,B)) ) )).
fof(fc42_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc42_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) & v3_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)) ) => v5_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)),k42_fomodel1(A,k43_fomodel1(A,D),B)))),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(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))) ) )).
fof(fc42_member_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v2_membered(A) & ~ v1_xboole_0(B) & v2_membered(B) ) => ~ v1_xboole_0(k12_member_1(A,B)) ) )).
fof(fc42_membered,axiom,( ! [A] : ! [B] : ( v6_membered(A) => v6_membered(k3_xboole_0(B,A)) ) )).
fof(fc42_partfun3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(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)) ) ) )).
fof(fc42_scmfsa10,axiom,( ! [A] : ! [B] : ( ( 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)),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc42_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_valued_0(A) ) => v6_membered(k9_relat_1(A,B)) ) )).
fof(fc42_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc42_valued_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v7_valued_2(A) ) => v1_valued_0(k1_funct_1(A,B)) ) )).
fof(fc42_xxreal_3,axiom,( v8_ordinal1(k5_xxreal_3(k1_xxreal_0)) & v1_xxreal_0(k5_xxreal_3(k1_xxreal_0)) )).
fof(fc43_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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))) ) ) )).
fof(fc43_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_normsp_0(A) & v3_lopban_2(A) & l1_cayldick(A) ) => ( v3_lopban_2(k4_cayldick(A)) & v1_cayldick(k4_cayldick(A)) ) ) )).
fof(fc43_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & ~ v8_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)) ) )).
fof(fc43_fomodel1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_xboole_0(A) ) => ( v1_relat_1(k6_relat_1(B,A)) & v1_xboole_0(k6_relat_1(B,A)) ) ) )).
fof(fc43_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k43_fomodel1(A,C),B),A,k2_xcmplx_0(1,k29_fomodel2(A,B))) ) )).
fof(fc43_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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(k30_fomodel2(A),k30_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) ) )).
fof(fc43_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) & ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) & v3_fomodel4(C,B) & v3_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))) ) => v5_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))),k25_fomodel4(B)),k1_tarski(k4_tarski(C,E))) ) )).
fof(fc43_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_membered(B) ) => v1_xboole_0(k13_member_1(A,B)) ) )).
fof(fc43_membered,axiom,( ! [A] : ! [B] : ( v1_membered(A) => v1_membered(k4_xboole_0(A,B)) ) )).
fof(fc43_pcs_0,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & l1_struct_0(B) ) => ( v1_relat_1(k18_pcs_0(A,B)) & v4_relat_1(k18_pcs_0(A,B),k7_domain_1(k4_ordinal1,k5_numbers,1)) & v1_funct_1(k18_pcs_0(A,B)) & v1_partfun1(k18_pcs_0(A,B),k7_domain_1(k4_ordinal1,k5_numbers,1)) & v2_pralg_1(k18_pcs_0(A,B)) ) ) )).
fof(fc43_scmfsa10,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc43_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_valued_0(A) ) => ( v1_relat_1(k5_relat_1(A,B)) & v1_valued_0(k5_relat_1(A,B)) ) ) )).
fof(fc43_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc43_valued_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v8_valued_2(A) ) => v2_valued_0(k1_funct_1(A,B)) ) )).
fof(fc43_xxreal_3,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => ( v7_ordinal1(k1_xxreal_3(A,B)) & v1_xxreal_0(k1_xxreal_3(A,B)) ) ) )).
fof(fc44_cayldick,axiom,( ! [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) & v4_lopban_2(A) & v6_cayldick(A) & l1_cayldick(A) ) => ( v4_lopban_2(k4_cayldick(A)) & v1_cayldick(k4_cayldick(A)) ) ) )).
fof(fc44_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc44_fomodel1,axiom,( ! [A] : ! [B] : ( v1_int_1(B) => ( v1_relat_1(k2_funcop_1(A,B)) & v5_relat_1(k2_funcop_1(A,B),k4_numbers) & v1_funct_1(k2_funcop_1(A,B)) ) ) )).
fof(fc44_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k35_fomodel2(A,C),A,k1_nat_1(B,1)) ) )).
fof(fc44_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(fc44_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v6_fomodel4(k32_fomodel4(A),A) ) )).
fof(fc44_glib_003,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc44_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_membered(B) ) => v1_xboole_0(k13_member_1(B,A)) ) )).
fof(fc44_membered,axiom,( ! [A] : ! [B] : ( v2_membered(A) => v2_membered(k4_xboole_0(A,B)) ) )).
fof(fc44_pcs_0,axiom,( ! [A] : ! [B] : ( ( l1_orders_2(A) & l1_orders_2(B) ) => ( v1_relat_1(k18_pcs_0(A,B)) & v4_relat_1(k18_pcs_0(A,B),k7_domain_1(k4_ordinal1,k5_numbers,1)) & v1_funct_1(k18_pcs_0(A,B)) & v1_partfun1(k18_pcs_0(A,B),k7_domain_1(k4_ordinal1,k5_numbers,1)) & v1_yellow_1(k18_pcs_0(A,B)) ) ) )).
fof(fc44_scmfsa10,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc44_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v2_valued_0(A) ) => ( v1_relat_1(k5_relat_1(A,B)) & v2_valued_0(k5_relat_1(A,B)) ) ) )).
fof(fc44_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc44_valued_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v9_valued_2(A) ) => v3_valued_0(k1_funct_1(A,B)) ) )).
fof(fc44_xxreal_3,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => ( v7_ordinal1(k4_xxreal_3(A,B)) & v1_xxreal_0(k4_xxreal_3(A,B)) ) ) )).
fof(fc45_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)))) ) ) )).
fof(fc45_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v8_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & v5_vectsp_1(A) & v3_cayldick(A) & l1_cayldick(A) ) => ( v1_cayldick(k4_cayldick(A)) & v3_cayldick(k4_cayldick(A)) ) ) )).
fof(fc45_fomodel0,axiom,( ! [A] : v1_xboole_0(k5_xboole_0(k9_finseq_1(A),k1_tarski(k4_tarski(1,A)))) )).
fof(fc45_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(fc45_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ 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(k35_fomodel2(A,B),A) ) )).
fof(fc45_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(fc45_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) => v5_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)),k42_fomodel1(A,k43_fomodel1(A,B),D)),1,A,k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))),k31_fomodel4(A)),k1_xboole_0) ) )).
fof(fc45_member_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_membered(A) & ~ v1_xboole_0(B) & v1_membered(B) ) => ~ v1_xboole_0(k13_member_1(A,B)) ) )).
fof(fc45_membered,axiom,( ! [A] : ! [B] : ( v3_membered(A) => v3_membered(k4_xboole_0(A,B)) ) )).
fof(fc45_pcs_0,axiom,( ! [A] : ! [B] : ( ( l1_pcs_0(A) & l1_pcs_0(B) ) => ( v1_relat_1(k18_pcs_0(A,B)) & v4_relat_1(k18_pcs_0(A,B),k7_domain_1(k4_ordinal1,k5_numbers,1)) & v1_funct_1(k18_pcs_0(A,B)) & v1_partfun1(k18_pcs_0(A,B),k7_domain_1(k4_ordinal1,k5_numbers,1)) & v7_pcs_0(k18_pcs_0(A,B)) ) ) )).
fof(fc45_scmfsa10,axiom,( v1_extpro_1(k1_scmfsa_2,k7_card_1(3)) & v2_amistd_2(k1_scmfsa_2,k7_card_1(3)) )).
fof(fc45_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_xreal_0(B) & ~ v3_xxreal_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)) ) )).
fof(fc45_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v3_valued_0(A) ) => ( v1_relat_1(k5_relat_1(A,B)) & v3_valued_0(k5_relat_1(A,B)) ) ) )).
fof(fc45_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc45_valued_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v10_valued_2(A) ) => v5_relat_1(k1_funct_1(A,B),k3_numbers) ) )).
fof(fc46_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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))) ) ) )).
fof(fc46_cayldick,axiom,( v3_group_1(k4_cayldick(k3_cayldick)) & v5_group_1(k4_cayldick(k3_cayldick)) & v1_cayldick(k4_cayldick(k3_cayldick)) )).
fof(fc46_fomodel0,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc46_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v1_orders_4(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v4_card_3(k1_fomodel1(A)) ) )).
fof(fc46_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ~ v9_fomodel1(k7_fomodel1(A),A) ) )).
fof(fc46_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v3_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))) ) => v5_fomodel4(k4_tarski(k13_fomodel0(k42_fomodel1(A,D,E),B),k35_fomodel2(A,C)),1,A,k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))),k35_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)),k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k1_fomodel2(A)),D),E)))) ) )).
fof(fc46_glib_003,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc46_member_1,axiom,( ! [A] : ! [B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k13_member_1(A,B)) ) )).
fof(fc46_membered,axiom,( ! [A] : ! [B] : ( v4_membered(A) => v4_membered(k4_xboole_0(A,B)) ) )).
fof(fc46_pcs_0,axiom,( ! [A] : ! [B] : ( ( l2_pcs_0(A) & l2_pcs_0(B) ) => ( v1_relat_1(k18_pcs_0(A,B)) & v4_relat_1(k18_pcs_0(A,B),k7_domain_1(k4_ordinal1,k5_numbers,1)) & v1_funct_1(k18_pcs_0(A,B)) & v1_partfun1(k18_pcs_0(A,B),k7_domain_1(k4_ordinal1,k5_numbers,1)) & v16_pcs_0(k18_pcs_0(A,B)) ) ) )).
fof(fc46_scmfsa10,axiom,( v1_extpro_1(k1_scmfsa_2,k7_card_1(3)) & v4_amistd_2(k1_scmfsa_2,k7_card_1(3)) )).
fof(fc46_valued_0,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc46_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc46_valued_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v11_valued_2(A) ) => v5_relat_1(k1_funct_1(A,B),k4_numbers) ) )).
fof(fc47_cayldick,axiom,( v3_group_1(k4_cayldick(k4_cayldick(k3_cayldick))) & ~ v5_group_1(k4_cayldick(k4_cayldick(k3_cayldick))) & v1_cayldick(k4_cayldick(k4_cayldick(k3_cayldick))) )).
fof(fc47_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(fc47_fomodel1,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(fc47_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v6_fomodel4(k31_fomodel4(A),A) ) )).
fof(fc47_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc47_member_1,axiom,( ! [A] : ! [B] : ( ( v3_membered(A) & v3_membered(B) ) => v3_membered(k13_member_1(A,B)) ) )).
fof(fc47_membered,axiom,( ! [A] : ! [B] : ( v5_membered(A) => v5_membered(k4_xboole_0(A,B)) ) )).
fof(fc47_pcs_0,axiom,( ! [A] : ! [B] : ( ( v3_orders_2(A) & l2_pcs_0(A) & v3_orders_2(B) & l2_pcs_0(B) ) => ( v1_relat_1(k18_pcs_0(A,B)) & v4_relat_1(k18_pcs_0(A,B),k7_domain_1(k4_ordinal1,k5_numbers,1)) & v1_funct_1(k18_pcs_0(A,B)) & v1_partfun1(k18_pcs_0(A,B),k7_domain_1(k4_ordinal1,k5_numbers,1)) & v5_waybel_3(k18_pcs_0(A,B)) ) ) )).
fof(fc47_valued_0,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc47_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc47_valued_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v12_valued_2(A) ) => v4_valued_0(k1_funct_1(A,B)) ) )).
fof(fc48_bilinear,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc48_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc48_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v1_xboole_0(k4_xboole_0(k32_fomodel1(A),k30_fomodel2(A))) ) )).
fof(fc48_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) & ~ v8_ordinal1(B) & v3_card_1(C,B) & m1_subset_1(C,k3_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,k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k35_fomodel1(A))) ) => v1_finset_1(k37_fomodel4(A,B,C,D)) ) )).
fof(fc48_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc48_member_1,axiom,( ! [A] : ! [B] : ( ( v4_membered(A) & v4_membered(B) ) => v4_membered(k13_member_1(A,B)) ) )).
fof(fc48_membered,axiom,( ! [A] : ! [B] : ( v6_membered(A) => v6_membered(k4_xboole_0(A,B)) ) )).
fof(fc48_pcs_0,axiom,( ! [A] : ! [B] : ( ( v4_orders_2(A) & l2_pcs_0(A) & v4_orders_2(B) & l2_pcs_0(B) ) => ( v1_relat_1(k18_pcs_0(A,B)) & v4_relat_1(k18_pcs_0(A,B),k7_domain_1(k4_ordinal1,k5_numbers,1)) & v1_funct_1(k18_pcs_0(A,B)) & v1_partfun1(k18_pcs_0(A,B),k7_domain_1(k4_ordinal1,k5_numbers,1)) & v1_pcs_0(k18_pcs_0(A,B)) ) ) )).
fof(fc48_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_valued_0(A) ) => ( v1_relat_1(k5_relat_1(A,B)) & v4_valued_0(k5_relat_1(A,B)) ) ) )).
fof(fc48_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc48_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v9_valued_2(A) ) => ( v1_relat_1(k1_binop_1(A,B,C)) & v1_funct_1(k1_binop_1(A,B,C)) & v3_valued_0(k1_binop_1(A,B,C)) ) ) )).
fof(fc49_bilinear,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc49_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(fc49_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc49_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ 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(k38_fomodel2(A,B)) ) )).
fof(fc49_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k3_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,k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k35_fomodel1(A))) ) => v4_fomodel4(k1_tarski(k4_tarski(k2_xboole_0(k38_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))),k30_fomodel4(A)),k1_xboole_0) ) )).
fof(fc49_glib_003,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)),k4_ordinal1) & 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))) ) ) )).
fof(fc49_member_1,axiom,( ! [A] : ! [B] : ( ( v5_membered(A) & v5_membered(B) ) => v5_membered(k13_member_1(A,B)) ) )).
fof(fc49_membered,axiom,( ! [A] : ! [B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k5_xboole_0(A,B)) ) )).
fof(fc49_pcs_0,axiom,( ! [A] : ! [B] : ( ( v4_pcs_0(A) & l2_pcs_0(A) & v4_pcs_0(B) & l2_pcs_0(B) ) => ( v1_relat_1(k18_pcs_0(A,B)) & v4_relat_1(k18_pcs_0(A,B),k7_domain_1(k4_ordinal1,k5_numbers,1)) & v1_funct_1(k18_pcs_0(A,B)) & v1_partfun1(k18_pcs_0(A,B),k7_domain_1(k4_ordinal1,k5_numbers,1)) & v9_pcs_0(k18_pcs_0(A,B)) ) ) )).
fof(fc49_valued_0,axiom,( ! [A] : ( v1_membered(A) => ( v1_relat_1(k4_relat_1(A)) & v1_valued_0(k4_relat_1(A)) ) ) )).
fof(fc49_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc49_valued_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc4_abcmiz_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) ) )).
fof(fc4_abcmiz_1,axiom,( ~ v1_xboole_0(k4_abcmiz_1) )).
fof(fc4_abian,axiom,( ! [A] : ( ( v1_int_1(A) & v1_abian(A) ) => ~ v1_abian(k6_xcmplx_0(A,1)) ) )).
fof(fc4_afinsq_1,axiom,( ! [A] : ( 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)) ) )).
fof(fc4_afvect0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc4_algstr_1,axiom,( v21_algstr_0(k8_algstr_0) & v4_vectsp_1(k8_algstr_0) & v5_algstr_1(k8_algstr_0) )).
fof(fc4_algstr_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc4_altcat_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc4_altcat_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(fc4_altcat_4,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc4_altcat_5,axiom,( ~ v2_struct_0(k7_altcat_1(k1_tarski(k1_xboole_0))) & v6_altcat_1(k7_altcat_1(k1_tarski(k1_xboole_0))) & v10_altcat_1(k7_altcat_1(k1_tarski(k1_xboole_0))) & v4_altcat_5(k7_altcat_1(k1_tarski(k1_xboole_0))) )).
fof(fc4_ami_3,axiom,( v3_memstr_0(k1_ami_3,k7_card_1(2)) & v1_extpro_1(k1_ami_3,k7_card_1(2)) )).
fof(fc4_ami_6,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(2),k1_ami_3) ) )).
fof(fc4_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ( v2_memstr_0(k4_amistd_1(A),A) & v1_extpro_1(k4_amistd_1(A),A) ) ) )).
fof(fc4_amistd_2,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ( v1_extpro_1(k1_extpro_1(A),A) & v2_amistd_2(k1_extpro_1(A),A) ) ) )).
fof(fc4_analmetr,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc4_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => ( v1_collsp(k5_anproj_1(A)) & v3_anproj_2(k5_anproj_1(A)) ) ) )).
fof(fc4_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( v1_relat_1(k5_aofa_a00(A,B,C,D,E,F)) & v1_funct_1(k5_aofa_a00(A,B,C,D,E,F)) & v3_card_1(k5_aofa_a00(A,B,C,D,E,F),6) & v1_finseq_1(k5_aofa_a00(A,B,C,D,E,F)) ) )).
fof(fc4_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) & v4_aofa_a01(D,A,B,C) & l4_aofa_a00(D,A,B,C) ) => ( v2_relat_1(u4_aofa_a00(A,B,C,D)) & v2_aofa_a01(u4_aofa_a00(A,B,C,D),A,B,C) ) ) )).
fof(fc4_armstrng,axiom,( ! [A] : ( 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)) ) )).
fof(fc4_asympt_1,axiom,( v1_funct_1(k1_seq_1(1)) & v1_funct_2(k1_seq_1(1),k4_ordinal1,k1_numbers) & v2_asympt_0(k1_seq_1(1)) )).
fof(fc4_autalg_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc4_bcialg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc4_bcialg_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc4_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc4_binop_2,axiom,( v1_funct_1(k11_binop_2) & v1_funct_2(k11_binop_2,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) & v1_binop_1(k11_binop_2,k1_numbers) & v2_binop_1(k11_binop_2,k1_numbers) )).
fof(fc4_bor_cant,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) & v7_ordinal1(C) & v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_relat_1(k7_nat_1(D,C)) & v4_relat_1(k7_nat_1(D,C),k4_ordinal1) & v5_relat_1(k7_nat_1(D,C),B) & v1_funct_1(k7_nat_1(D,C)) & v1_partfun1(k7_nat_1(D,C),k4_ordinal1) ) ) )).
fof(fc4_borsuk_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc4_borsuk_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) ) )).
fof(fc4_borsuk_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc4_borsuk_5,axiom,( ! [A] : ! [B] : ( ( v1_rat_1(A) & v1_xreal_0(B) & ~ v1_rat_1(B) ) => ~ v1_rat_1(k2_xcmplx_0(A,B)) ) )).
fof(fc4_borsuk_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc4_borsuk_7,axiom,( v1_borsuk_7(k1_xboole_0) )).
fof(fc4_brouwer,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => v1_topalg_2(k2_brouwer(A,B,C),A) ) )).
fof(fc4_bspace,axiom,( ! [A] : ( v1_finset_1(A) => v1_finset_1(k8_bspace(A)) ) )).
fof(fc4_bvfunc_1,axiom,( ! [A] : ( ~ 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) ) ) )).
fof(fc4_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v2_struct_0(k11_c0sp1(A)) ) )).
fof(fc4_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ~ v2_struct_0(k3_c0sp2(A)) & v1_funcsdom(k3_c0sp2(A)) ) ) )).
fof(fc4_card_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v8_ordinal1(k1_card_1(A)) & v1_card_1(k1_card_1(A)) ) ) )).
fof(fc4_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v4_funct_1(k4_card_3(A)) ) )).
fof(fc4_card_5,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc4_cardfin2,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_relat_1(B) & v5_relat_1(B,k4_numbers) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ( v1_relat_1(k24_valued_1(B,A)) & v5_relat_1(k24_valued_1(B,A),k4_numbers) & v5_ordinal1(k24_valued_1(B,A)) & v1_funct_1(k24_valued_1(B,A)) & v1_finset_1(k24_valued_1(B,A)) ) ) )).
fof(fc4_cat_4,axiom,( ! [A] : ! [B] : ( ~ 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)) ) )).
fof(fc4_catalg_1,axiom,( ! [A] : ( v1_msualg_1(k2_catalg_1(A)) & v3_catalg_1(k2_catalg_1(A)) ) )).
fof(fc4_cayldick,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ( v1_relat_1(k1_ordinal4(A,B)) & v2_relat_1(k1_ordinal4(A,B)) & v1_funct_1(k1_ordinal4(A,B)) & v5_ordinal1(k1_ordinal4(A,B)) ) ) )).
fof(fc4_cayley,axiom,( ! [A] : ( ~ 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)) ) )).
fof(fc4_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v2_struct_0(k7_cc0sp1(A)) ) )).
fof(fc4_cc0sp2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc4_cfdiff_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc4_cfuncdom,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc4_cgames_1,axiom,( v1_xboole_0(k7_cgames_1(k3_cgames_1)) )).
fof(fc4_circcmb3,axiom,( ! [A] : ( ( v4_circcmb3(A) & l1_msualg_1(A) ) => v1_xtuple_0(k3_circcmb3(A)) ) )).
fof(fc4_circtrm1,axiom,( ! [A] : ! [B] : ( ( v3_trees_3(A) & v3_trees_3(B) ) => v3_trees_3(k2_xboole_0(A,B)) ) )).
fof(fc4_classes2,axiom,( ! [A] : ( v3_ordinal1(A) => v1_classes2(k1_classes1(A)) ) )).
fof(fc4_clopban1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)))) ) ) )).
fof(fc4_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => ( ~ v2_struct_0(k8_clopban2(A)) & v1_cfuncdom(k8_clopban2(A)) ) ) )).
fof(fc4_closure1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc4_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc4_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_coh_sp(A)) => ( v1_relat_1(k2_xtuple_0(B)) & v1_funct_1(k2_xtuple_0(B)) ) ) )).
fof(fc4_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) ) => ( ~ v1_xboole_0(k2_cohsp_1(A)) & v1_classes1(k2_cohsp_1(A)) ) ) )).
fof(fc4_compact1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ~ v2_struct_0(k1_compact1(A)) & v1_pre_topc(k1_compact1(A)) ) ) )).
fof(fc4_compl_sp,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc4_complex1,axiom,( v8_ordinal1(k9_complex1(k5_numbers)) & v1_xreal_0(k9_complex1(k5_numbers)) )).
fof(fc4_compos_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc4_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_compos_1(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc4_compts_1,axiom,( ! [A] : ( v1_finset_1(A) => v8_struct_0(k1_compts_1(A)) ) )).
fof(fc4_comput_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => ( ~ 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(k4_ordinal1)) & 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)) ) ) )).
fof(fc4_comseq_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & v2_comseq_2(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_funct_1(k1_valued_1(A,B)) & v1_funct_2(k1_valued_1(A,B),k4_ordinal1,k2_numbers) & v2_comseq_2(k1_valued_1(A,B)) ) ) )).
fof(fc4_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_funct_1(k3_comseq_3(A)) & v1_funct_2(k3_comseq_3(A),k4_ordinal1,k1_numbers) & v2_comseq_2(k3_comseq_3(A)) ) ) )).
fof(fc4_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ( ~ v2_struct_0(k11_conlat_1(A)) & v3_lattices(k11_conlat_1(A)) & v10_lattices(k11_conlat_1(A)) ) ) )).
fof(fc4_convex4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc4_convfun1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc4_csspace,axiom,( ~ 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)) )).
fof(fc4_csspace3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) ) )).
fof(fc4_csspace4,axiom,( 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)) )).
fof(fc4_dickson,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_orders_2(k5_dickson(A)) & v5_orders_2(k5_dickson(A)) ) ) )).
fof(fc4_dilworth,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_dilworth(A) & l1_orders_2(A) ) => ( v2_xxreal_0(k2_dilworth(A)) & v7_ordinal1(k2_dilworth(A)) ) ) )).
fof(fc4_dist_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & ~ v1_xboole_0(B) & m1_finseq_1(B,A) ) => v1_matrprob(k4_dist_1(A,B)) ) )).
fof(fc4_dtconstr,axiom,( ~ v2_struct_0(k5_dtconstr) & v1_lang1(k5_dtconstr) & v1_dtconstr(k5_dtconstr) & v2_dtconstr(k5_dtconstr) & v3_dtconstr(k5_dtconstr) )).
fof(fc4_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => v2_ec_pf_1(k5_struct_0(k9_int_3(A)),A) ) )).
fof(fc4_endalg,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc4_ens_1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc4_eqrel_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc4_equation,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc4_euclid,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc4_exchsort,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(fc4_extpro_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc4_facirc_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_facirc_1(A) & ~ v1_facirc_1(B) ) => ~ v1_facirc_1(k2_xboole_0(A,B)) ) )).
fof(fc4_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc4_fcont_3,axiom,( ! [A] : ( v1_xreal_0(A) => v2_rcomp_1(k1_limfunc1(A)) ) )).
fof(fc4_fib_num2,axiom,( v3_xxreal_2(k4_ordinal1) )).
fof(fc4_filter_0,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(fc4_filter_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc4_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => v3_card_1(k1_finseq_1(A),A) ) )).
fof(fc4_finseq_2,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(fc4_finseq_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => v1_funcop_1(k10_finseq_1(A,B)) ) )).
fof(fc4_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : v1_finseq_1(k8_finseq_4(A,B,C,D,E)) )).
fof(fc4_finseq_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc4_finseq_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc4_finset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : v1_finset_1(k2_enumset1(A,B,C,D)) )).
fof(fc4_fintopo6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & m1_subset_1(B,u1_struct_0(A)) ) => v3_fintopo6(k1_tarski(B),A) ) )).
fof(fc4_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k5_relat_1(A,k1_tarski(B))) & v1_funct_1(k5_relat_1(A,k1_tarski(B))) & v2_funct_1(k5_relat_1(A,k1_tarski(B))) ) ) )).
fof(fc4_fomodel1,axiom,( ! [A] : ( ( v11_fomodel1(A) & l1_fomodel1(A) ) => ~ v1_finset_1(k2_fomodel1(A)) ) )).
fof(fc4_fomodel2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc4_fomodel3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc4_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc4_freealg,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,k4_ordinal1) & ~ 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)) ) ) )).
fof(fc4_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc4_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc4_funcop_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ~ v1_xboole_0(k2_funcop_1(B,A)) ) )).
fof(fc4_funcsdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v2_struct_0(k11_funcsdom(A)) & v36_algstr_0(k11_funcsdom(A)) ) ) )).
fof(fc4_funct_1,axiom,( ! [A] : ( v1_relat_1(k4_relat_1(A)) & v2_funct_1(k4_relat_1(A)) ) )).
fof(fc4_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(fc4_funct_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc4_funct_7,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc4_funct_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(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) ) ) )).
fof(fc4_functor0,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc4_fvaluat1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_fvaluat1(A) ) => v1_fvaluat1(k1_funct_1(A,B)) ) )).
fof(fc4_gate_1,axiom,( ! [A] : ! [B] : ( v1_xboole_0(A) => v1_xboole_0(k2_gate_1(A,B)) ) )).
fof(fc4_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => v1_finset_1(k7_glib_000(A)) ) )).
fof(fc4_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => v1_glib_001(k2_glib_001(A,B,B,C),A) ) )).
fof(fc4_glib_004,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(fc4_glib_005,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(fc4_goboard2,axiom,( ! [A] : ! [B] : ( ( ~ 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_0(k1_goboard2(A,B)) & v3_goboard1(k1_goboard2(A,B)) & v4_goboard1(k1_goboard2(A,B)) ) ) )).
fof(fc4_gr_cy_1,axiom,( ~ 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) )).
fof(fc4_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc4_graph_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc4_grcat_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc4_groeb_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,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),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) ) ) )).
fof(fc4_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ~ v4_group_1(k1_group_1(A),A) ) )).
fof(fc4_group_10,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(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) ) ) )).
fof(fc4_group_12,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc4_group_14,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( ~ v2_struct_0(k2_group_14(A)) & v8_algstr_0(k2_group_14(A)) ) ) )).
fof(fc4_group_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc4_group_7,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc4_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc4_hahnban1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & ~ 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)) & v13_vectsp_1(C,B,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)) & 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(k3_hahnban1(A,B,C,D)) & v1_funct_2(k3_hahnban1(A,B,C,D),u1_struct_0(B),u1_struct_0(A)) & v13_vectsp_1(k3_hahnban1(A,B,C,D),B,A) ) ) )).
fof(fc4_hausdorf,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc4_heyting3,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => v1_finset_1(k2_heyting3(A,B)) ) )).
fof(fc4_hilbasis,axiom,( ! [A] : ! [B] : ( ( ~ 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,k4_ordinal1) ) => ( v1_funct_1(k6_hilbasis(A,B)) & v1_funct_2(k6_hilbasis(A,B),u1_struct_0(k14_polynom3(k12_polynom1(B,A))),u1_struct_0(k12_polynom1(k1_nat_1(B,1),A))) & v6_group_1(k6_hilbasis(A,B),k14_polynom3(k12_polynom1(B,A)),k12_polynom1(k1_nat_1(B,1),A)) ) ) )).
fof(fc4_hilbert1,axiom,( v6_hilbert1(k6_hilbert1) )).
fof(fc4_hilbert3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(fc4_idea_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) & ~ v8_ordinal1(C) & v1_matrix_0(D) & v2_matrix_0(D,k4_ordinal1,B,6) & m1_finseq_1(D,k3_finseq_2(k4_ordinal1)) ) => ( 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)) ) ) )).
fof(fc4_index_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc4_int_1,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_int_1(B) ) => v1_int_1(k6_xcmplx_0(A,B)) ) )).
fof(fc4_int_3,axiom,( ~ 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) )).
fof(fc4_int_4,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc4_int_6,axiom,( ! [A] : ( v1_int_1(A) => v5_relat_1(k5_finseq_1(A),k4_numbers) ) )).
fof(fc4_integr16,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc4_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k1_interva1(A,k2_subset_1(A),k2_subset_1(A))) ) )).
fof(fc4_intpro_1,axiom,( v8_intpro_1(k8_intpro_1) )).
fof(fc4_isomichi,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc4_jordan,axiom,( ! [A] : ( 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))) ) )).
fof(fc4_jordan1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => v1_convex1(k7_topreal1(A),k15_euclid(2)) ) )).
fof(fc4_jordan18,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ~ v1_xboole_0(k7_relat_1(k4_pscomp_1,k5_topreal1(A))) ) )).
fof(fc4_jordan1e,axiom,( ! [A] : ! [B] : ( ( 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) ) => ( 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)) ) ) )).
fof(fc4_jordan1h,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_setfam_1(A) & v2_relat_1(B) & ~ v1_xboole_0(B) & m1_finseq_1(B,k3_finseq_2(A)) ) => ~ v1_xboole_0(k9_matrix_0(B)) ) )).
fof(fc4_jordan22,axiom,( ! [A] : ( ( 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)) ) )).
fof(fc4_jordan23,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc4_jordan2c,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc4_kurato_1,axiom,( ~ v3_pre_topc(k6_kurato_1,k3_topmetr) & ~ v4_pre_topc(k6_kurato_1,k3_topmetr) )).
fof(fc4_kurato_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => v4_pre_topc(k1_kurato_2(A,B),A) ) )).
fof(fc4_lang1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v2_struct_0(k9_lang1(A)) & v2_lang1(k9_lang1(A)) ) ) )).
fof(fc4_lattice2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc4_lattice3,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc4_lattice5,axiom,( ! [A] : ~ v1_xboole_0(k5_lattice5(A)) )).
fof(fc4_lattices,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc4_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => v2_lexbfs(k16_lexbfs(A)) ) )).
fof(fc4_lfuzzy_0,axiom,( ! [A] : ! [B] : ( ( ~ 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(k5_yellow_1(A,B)) & v9_waybel_1(k5_yellow_1(A,B)) ) ) )).
fof(fc4_lmod_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) ) )).
fof(fc4_lopban_1,axiom,( ! [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) & 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),k9_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k7_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)))) & v1_rlvect_1(g1_rlvect_1(k7_lopban_1(A,B),k9_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k7_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)))) & v2_rlvect_1(g1_rlvect_1(k7_lopban_1(A,B),k9_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k7_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)))) & v3_rlvect_1(g1_rlvect_1(k7_lopban_1(A,B),k9_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k7_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)))) & v4_rlvect_1(g1_rlvect_1(k7_lopban_1(A,B),k9_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k7_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)))) & v5_rlvect_1(g1_rlvect_1(k7_lopban_1(A,B),k9_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k7_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)))) & v6_rlvect_1(g1_rlvect_1(k7_lopban_1(A,B),k9_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k7_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)))) & v7_rlvect_1(g1_rlvect_1(k7_lopban_1(A,B),k9_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k7_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)))) & v8_rlvect_1(g1_rlvect_1(k7_lopban_1(A,B),k9_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k7_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)))) ) ) )).
fof(fc4_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => ( ~ v2_struct_0(k8_lopban_2(A)) & v1_funcsdom(k8_lopban_2(A)) ) ) )).
fof(fc4_lopban_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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)))) ) => ( ~ v2_struct_0(k5_lopban_7(A,B,C)) & v3_normsp_0(k5_lopban_7(A,B,C)) & v4_normsp_0(k5_lopban_7(A,B,C)) & v2_normsp_1(k5_lopban_7(A,B,C)) ) ) )).
fof(fc4_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ~ v1_xboole_0(k10_lopclset(A)) ) )).
fof(fc4_lpspacc1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_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)) ) ) )).
fof(fc4_lpspace1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_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)) ) ) )).
fof(fc4_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v2_xxreal_0(D) & v1_xreal_0(D) ) => ( ~ 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)) ) ) )).
fof(fc4_ltlaxio3,axiom,( ! [A] : ( ( v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) ) => v1_xboole_0(k5_ltlaxio3(A)) ) )).
fof(fc4_ltlaxio4,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)))) ) => v1_finset_1(k6_ltlaxio4(A)) ) )).
fof(fc4_lukasi_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(fc4_margrel1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_margrel1(A) ) => v1_xboolean(k1_funct_1(A,B)) ) )).
fof(fc4_matrix11,axiom,( ! [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)) ) ) )).
fof(fc4_matrix13,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc4_matrix_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( v1_matrix_0(k4_matrix_3(B,C,D)) & v2_matrix_0(k4_matrix_3(B,C,D),u1_struct_0(B),A,A) ) ) )).
fof(fc4_matroid0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc4_matrtop1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc4_matrtop3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc4_mazurulm,axiom,( ! [A] : ! [B] : ( ( v3_membered(A) & v3_xxreal_2(A) & ~ v3_xxreal_0(B) & v1_xreal_0(B) ) => v3_xxreal_2(k23_member_1(A,B)) ) )).
fof(fc4_measure6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ~ v1_xboole_0(k4_measure6(A)) ) )).
fof(fc4_member_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_membered(A) ) => ( ~ v1_xboole_0(k4_member_1(A)) & v2_membered(k4_member_1(A)) ) ) )).
fof(fc4_membered,axiom,( v4_membered(k3_numbers) )).
fof(fc4_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ( v1_memstr_0(k1_memstr_0(A),A) & v3_memstr_0(k1_memstr_0(A),A) ) ) )).
fof(fc4_mesfun7c,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k2_numbers)) & v1_mesfunc8(B,A,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ( v1_funct_1(k12_mesfun7c(A,B)) & v1_funct_2(k12_mesfun7c(A,B),k4_ordinal1,k4_partfun1(A,k1_numbers)) & v1_mesfunc8(k12_mesfun7c(A,B),A,k1_numbers) ) ) )).
fof(fc4_mesfunc7,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_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)) ) ) )).
fof(fc4_metric_1,axiom,( ! [A] : ( v1_metric_1(k5_metric_1(A)) & v6_metric_1(k5_metric_1(A)) & v7_metric_1(k5_metric_1(A)) & v8_metric_1(k5_metric_1(A)) & v9_metric_1(k5_metric_1(A)) ) )).
fof(fc4_metrizts,axiom,( ! [A] : ( ( v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_xboole_0(k2_waybel23(A)) & v1_card_1(k2_waybel23(A)) ) ) )).
fof(fc4_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( v5_rltopsp1(k15_euclid(A)) & v2_mfold_1(k15_euclid(A),A) ) ) )).
fof(fc4_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ v2_struct_0(k4_mfold_2(A)) & v2_pre_topc(k4_mfold_2(A)) ) ) )).
fof(fc4_midsp_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc4_midsp_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc4_mmlquer2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) & v1_relat_2(C) & v1_partfun1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( v1_relat_2(k1_mmlquer2(B,C)) & v1_partfun1(k1_mmlquer2(B,C),A) ) ) )).
fof(fc4_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc4_mod_2,axiom,( ~ v2_struct_0(k18_mod_2) & v36_algstr_0(k18_mod_2) )).
fof(fc4_mod_4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc4_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m1_finseq_1(A,k4_ordinal1) ) => v1_modelc_1(k10_modelc_1(A)) ) )).
fof(fc4_modelc_2,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & v1_modelc_2(B) & m1_finseq_1(B,k4_ordinal1) ) => v1_modelc_2(k4_modelc_2(A,B)) ) )).
fof(fc4_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => ~ v1_xboole_0(k3_tarski(k1_orders_1(k1_modelc_3(A)))) ) )).
fof(fc4_moebius1,axiom,( ! [A] : ( v1_relat_1(k4_moebius1(A)) & v4_relat_1(k4_moebius1(A),k4_ordinal1) & v1_funct_1(k4_moebius1(A)) & v1_partfun1(k4_moebius1(A),k4_ordinal1) & v3_valued_0(k4_moebius1(A)) ) )).
fof(fc4_monoid_0,axiom,( ! [A] : ( ~ 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)) ) )).
fof(fc4_monoid_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ~ v2_struct_0(k22_monoid_1(A)) ) )).
fof(fc4_msafree,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc4_msafree1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc4_msafree4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_finset_1(A) & v1_finseq_1(A) & v4_trees_3(A) ) => ( ~ v1_xboole_0(k11_trees_3(A)) & v1_finset_1(k11_trees_3(A)) & v1_trees_1(k11_trees_3(A)) ) ) )).
fof(fc4_msalimit,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v1_xboole_0(k4_msalimit(A)) & v2_msalimit(k4_msalimit(A)) ) ) )).
fof(fc4_mssubfam,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc4_msualg_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc4_msualg_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc4_msualg_9,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(fc4_mycielsk,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_mycielsk(A) & l1_orders_2(A) ) => ( v7_ordinal1(k2_mycielsk(A)) & v2_xxreal_0(k2_mycielsk(A)) ) ) )).
fof(fc4_nat_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ~ v8_ordinal1(k2_xcmplx_0(B,A)) ) )).
fof(fc4_nat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc4_nat_lat,axiom,( ~ v2_struct_0(k3_nat_lat) & v3_lattices(k3_nat_lat) & v13_lattices(k3_nat_lat) )).
fof(fc4_neckla_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc4_necklace,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( ~ v2_struct_0(k3_necklace(A)) & v1_orders_2(k3_necklace(A)) ) ) )).
fof(fc4_newton,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => v7_ordinal1(k1_newton(A,B)) ) )).
fof(fc4_nfcont_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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) ) ) )).
fof(fc4_nfcont_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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_xreal_0(C) ) => ( v1_funct_1(k9_integr15(A,C,k1_numbers,B)) & v1_nfcont_4(k9_integr15(A,C,k1_numbers,B),A) ) ) )).
fof(fc4_normform,axiom,( ! [A] : ( ~ v2_struct_0(k12_normform(A)) & v3_lattices(k12_normform(A)) ) )).
fof(fc4_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ( ~ v2_struct_0(k4_normsp_2(A)) & v4_yellow_8(k4_normsp_2(A)) & v5_rltopsp1(k4_normsp_2(A)) ) ) )).
fof(fc4_numbers,axiom,( ~ v1_xboole_0(k4_numbers) )).
fof(fc4_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ~ v1_xboole_0(k9_openlatt(A)) ) )).
fof(fc4_oposet_1,axiom,( v3_qmax_1(k1_oposet_1) & v1_oposet_1(k1_oposet_1) )).
fof(fc4_ordeq_01,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_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) & l1_normsp_1(B) ) => ( ~ v2_struct_0(k2_ordeq_01(A,B)) & v13_algstr_0(k2_ordeq_01(A,B)) & v1_rlvect_1(k2_ordeq_01(A,B)) & v2_rlvect_1(k2_ordeq_01(A,B)) & v3_rlvect_1(k2_ordeq_01(A,B)) & v4_rlvect_1(k2_ordeq_01(A,B)) & v5_rlvect_1(k2_ordeq_01(A,B)) & v6_rlvect_1(k2_ordeq_01(A,B)) & v7_rlvect_1(k2_ordeq_01(A,B)) & v8_rlvect_1(k2_ordeq_01(A,B)) ) ) )).
fof(fc4_orders_2,axiom,( ! [A] : ( ( v2_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => v4_relat_2(u1_orders_2(A)) ) )).
fof(fc4_orders_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_orders_3(A) ) => ~ v1_xboole_0(k2_orders_3(A)) ) )).
fof(fc4_ordinal1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) ) => v3_ordinal1(k9_xtuple_0(A)) ) )).
fof(fc4_ordinal2,axiom,( ! [A] : ! [B] : ( v3_ordinal1(A) => v5_ordinal1(k2_funcop_1(A,B)) ) )).
fof(fc4_ordinal3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v7_ordinal1(A) & v3_ordinal1(B) & v7_ordinal1(B) ) => ( v3_ordinal1(k11_ordinal2(A,B)) & v7_ordinal1(k11_ordinal2(A,B)) ) ) )).
fof(fc4_ordinal4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc4_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => v1_ordinal2(k3_afinsq_1(A)) ) )).
fof(fc4_ordinal6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => v1_ordinal6(k10_xtuple_0(A)) ) )).
fof(fc4_osafree,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc4_osalg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc4_osalg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc4_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc4_partfun1,axiom,( ! [A] : ! [B] : v4_funct_1(k4_partfun1(A,B)) )).
fof(fc4_partfun3,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xxreal_0(A) ) => ( v1_xreal_0(k3_square_1(A)) & ~ v3_xxreal_0(k3_square_1(A)) ) ) )).
fof(fc4_pboole,axiom,( ! [A] : ( 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) ) )).
fof(fc4_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc4_pencil_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc4_petri,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc4_polyalg1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc4_polyeq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) & v1_xcmplx_0(D) ) => v1_xcmplx_0(k2_polyeq_1(A,B,C,D)) ) )).
fof(fc4_polynom1,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & ~ v2_struct_0(B) & l2_struct_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),B) ) ) )).
fof(fc4_polynom3,axiom,( ! [A] : ! [B] : ( ( ~ 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,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k5_vfunct_1(k4_ordinal1,A,B)) & v1_polynom1(k5_vfunct_1(k4_ordinal1,A,B),A) ) ) )).
fof(fc4_polynom5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l6_algstr_0(A) ) => ( v1_funct_1(k9_polynom3(A)) & v1_funct_2(k9_polynom3(A),k4_ordinal1,u1_struct_0(A)) & v1_polynom5(k9_polynom3(A),A) ) ) )).
fof(fc4_polynom7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,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),B) ) ) )).
fof(fc4_polyred,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc4_poset_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc4_pralg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc4_pre_circ,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc4_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc4_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => v4_pre_topc(k2_struct_0(A),A) ) )).
fof(fc4_prepower,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_rat_1(B) ) => v1_xreal_0(k4_prepower(A,B)) ) )).
fof(fc4_prob_1,axiom,( ! [A] : v4_prob_1(k1_zfmisc_1(A),A) )).
fof(fc4_prob_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,k9_setfam_1(A)) ) ) )).
fof(fc4_prvect_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc4_pscomp_1,axiom,( 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)) )).
fof(fc4_pythtrip,axiom,( ! [A] : ( ( v1_int_1(A) & v1_abian(A) ) => v1_abian(k1_square_1(A)) ) )).
fof(fc4_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ~ v1_xboole_0(k4_qc_lang1(A)) ) )).
fof(fc4_qmax_1,axiom,( ! [A] : ( ( v2_qmax_1(A) & l1_qmax_1(A) ) => ~ v1_xboole_0(k5_qmax_1(A)) ) )).
fof(fc4_quatern2,axiom,( ~ v2_struct_0(k15_quatern2) & v36_algstr_0(k15_quatern2) )).
fof(fc4_quaterni,axiom,( v1_quaterni(k4_quaterni) )).
fof(fc4_quofield,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc4_random_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v2_finset_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( v1_relat_1(k5_random_3(A)) & v4_relat_1(k5_random_3(A),k4_ordinal1) & v1_funct_1(k5_random_3(A)) & v2_finset_1(k5_random_3(A)) & v1_partfun1(k5_random_3(A),k4_ordinal1) ) ) )).
fof(fc4_rat_1,axiom,( ! [A] : ! [B] : ( ( v1_rat_1(A) & v1_rat_1(B) ) => v1_rat_1(k7_xcmplx_0(A,B)) ) )).
fof(fc4_ratfunc1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ( v1_funct_1(k9_polynom3(A)) & v1_funct_2(k9_polynom3(A),k4_ordinal1,u1_struct_0(A)) & v1_ratfunc1(k9_polynom3(A),A) & v2_ratfunc1(k9_polynom3(A),A) ) ) )).
fof(fc4_rcomp_3,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => v5_xxreal_2(k2_xxreal_1(A,B)) ) )).
fof(fc4_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( v8_ordinal1(k5_int_1(k5_numbers,A)) & v1_int_1(k5_int_1(k5_numbers,A)) ) ) )).
fof(fc4_real_lat,axiom,( v3_lattices(k3_real_lat) & v11_lattices(k3_real_lat) )).
fof(fc4_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ v2_struct_0(k4_real_ns1(A)) & v1_normsp_1(k4_real_ns1(A)) & v3_lopban_1(k4_real_ns1(A)) ) ) )).
fof(fc4_realset2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) ) )).
fof(fc4_relat_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => v1_relat_1(k5_xboole_0(A,B)) ) )).
fof(fc4_relat_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_relat_2(A) & v1_relat_1(B) & v1_relat_2(B) ) => v1_relat_2(k2_xboole_0(A,B)) ) )).
fof(fc4_reloc,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc4_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc4_revrot_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc4_rewrite2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc4_rfunct_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc4_rfunct_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc4_ring_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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)) ) ) )).
fof(fc4_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => v4_ringcat1(k9_ringcat1(A)) ) )).
fof(fc4_rlaffin1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) )).
fof(fc4_rlaffin3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xreal_0(C) ) => v1_finset_1(k1_convex1(A,B,C)) ) )).
fof(fc4_rltopsp1,axiom,( ! [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) & 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) ) ) )).
fof(fc4_rlvect_2,axiom,( ! [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) ) => ( 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)) ) ) )).
fof(fc4_robbins4,axiom,( v1_lattice3(k1_robbins4) & v2_lattice3(k1_robbins4) )).
fof(fc4_rsspace,axiom,( ~ v1_xboole_0(k10_rsspace) & v1_rlsub_1(k10_rsspace,k6_rsspace) )).
fof(fc4_rsspace3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) ) )).
fof(fc4_rsspace4,axiom,( v13_algstr_0(g1_normsp_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4),k2_rsspace4)) & v2_rlvect_1(g1_normsp_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4),k2_rsspace4)) & v3_rlvect_1(g1_normsp_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4),k2_rsspace4)) & v4_rlvect_1(g1_normsp_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4),k2_rsspace4)) & v5_rlvect_1(g1_normsp_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4),k2_rsspace4)) & v6_rlvect_1(g1_normsp_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4),k2_rsspace4)) & v7_rlvect_1(g1_normsp_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4),k2_rsspace4)) & v8_rlvect_1(g1_normsp_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4),k2_rsspace4)) & v1_normsp_1(g1_normsp_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4),k2_rsspace4)) )).
fof(fc4_rvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) ) => v3_valued_0(k11_finseq_1(A,B,C)) ) )).
fof(fc4_scm_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(fc4_scm_halt,axiom,( ! [A] : ! [B] : ( ( 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc4_scm_inst,axiom,( ~ v1_xboole_0(k3_scm_inst) & v1_compos_0(k3_scm_inst) )).
fof(fc4_scmfsa10,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc4_scmfsa6a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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) ) ) )).
fof(fc4_scmfsa6c,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc4_scmfsa7b,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) & 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),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(fc4_scmfsa8a,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc4_scmfsa8b,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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) ) ) )).
fof(fc4_scmfsa_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc4_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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(k7_card_1(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)) ) )).
fof(fc4_scmfsa_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc4_scmfsa_9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc4_scmfsa_i,axiom,( ~ v1_xboole_0(k2_scmfsa_i) & v2_compos_0(k2_scmfsa_i) )).
fof(fc4_scmfsa_m,axiom,( ! [A] : ( ( 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(k7_card_1(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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(k1_scmfsa_m(A),u1_struct_0(k1_scmfsa_2)) ) ) )).
fof(fc4_scmpds_2,axiom,( v1_extpro_1(k1_scmpds_2,2) & v3_extpro_1(k1_scmpds_2,2) )).
fof(fc4_scmpds_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc4_scmpds_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc4_scmpds_6,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_relat_1(k1_scmpds_6(k4_xcmplx_0(k1_nat_1(A,1)))) & v4_relat_1(k1_scmpds_6(k4_xcmplx_0(k1_nat_1(A,1))),k4_ordinal1) & v5_relat_1(k1_scmpds_6(k4_xcmplx_0(k1_nat_1(A,1))),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k1_scmpds_6(k4_xcmplx_0(k1_nat_1(A,1)))) & v1_funct_1(k1_scmpds_6(k4_xcmplx_0(k1_nat_1(A,1)))) & v1_finset_1(k1_scmpds_6(k4_xcmplx_0(k1_nat_1(A,1)))) & v1_afinsq_1(k1_scmpds_6(k4_xcmplx_0(k1_nat_1(A,1)))) & v2_compos_1(k1_scmpds_6(k4_xcmplx_0(k1_nat_1(A,1))),k1_scmpds_2) ) ) )).
fof(fc4_scmpds_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & 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) & v7_ordinal1(D) ) => ( v1_relat_1(k2_scmpds_7(B,C,D,A)) & v4_relat_1(k2_scmpds_7(B,C,D,A),k4_ordinal1) & v5_relat_1(k2_scmpds_7(B,C,D,A),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k2_scmpds_7(B,C,D,A)) & 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) ) ) )).
fof(fc4_scmpds_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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) ) ) )).
fof(fc4_scmpds_i,axiom,( v2_compos_0(k1_scmpds_i) )).
fof(fc4_scmring2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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),k7_card_1(2),k1_scmring2(A)) ) )).
fof(fc4_scmring3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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),k7_card_1(2),k1_scmring2(A)) ) )).
fof(fc4_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) ) ) )).
fof(fc4_scmyciel,axiom,( ! [A] : ! [B] : ( v5_finset_1(A) => v5_finset_1(k3_xboole_0(A,B)) ) )).
fof(fc4_seq_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_comseq_2(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_funct_1(k45_valued_1(A,B)) & v1_funct_2(k45_valued_1(A,B),k4_ordinal1,k1_numbers) & v2_comseq_2(k45_valued_1(A,B)) ) ) )).
fof(fc4_seq_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,k1_numbers) ) => ( ~ v1_xboole_0(k26_seq_4(A)) & v5_valued_0(k26_seq_4(A)) ) ) )).
fof(fc4_setfam_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) ) => v1_setfam_1(k1_enumset1(A,B,C)) ) )).
fof(fc4_sfmastr1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc4_sfmastr3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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),k4_ordinal1) & 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),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(fc4_simplex0,axiom,( ! [A] : ! [B] : ( ( v1_classes1(A) & v1_classes1(B) ) => v1_classes1(k3_xboole_0(A,B)) ) )).
fof(fc4_simplex1,axiom,( ! [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) & 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) ) ) )).
fof(fc4_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k19_sin_cos(A)) ) )).
fof(fc4_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k16_sin_cos,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers))) & v2_funct_1(k5_relat_1(k16_sin_cos,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers))) )).
fof(fc4_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k4_sin_cos9(A)) ) )).
fof(fc4_sincos10,axiom,( v1_relat_1(k5_relat_1(k2_fdiff_9,k4_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) & v2_funct_1(k5_relat_1(k2_fdiff_9,k4_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(fc4_sppol_1,axiom,( ! [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) => v4_pre_topc(k3_topreal1(2,A),k15_euclid(2)) ) )).
fof(fc4_sppol_2,axiom,( ! [A] : ! [B] : ( ( v3_topreal1(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & v7_ordinal1(B) ) => v3_topreal1(k16_finseq_1(B,A)) ) )).
fof(fc4_sprect_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(fc4_sprect_3,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(fc4_stacks_1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc4_struct_0,axiom,( ! [A] : ( ( v2_struct_0(A) & l1_struct_0(A) ) => v1_xboole_0(k2_struct_0(A)) ) )).
fof(fc4_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ~ v1_xboole_0(k3_enumset1(A,B,C,D,E)) )).
fof(fc4_substlat,axiom,( ! [A] : ! [B] : ( v3_lattices(k5_substlat(A,B)) & v11_lattices(k5_substlat(A,B)) & v15_lattices(k5_substlat(A,B)) ) )).
fof(fc4_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ( ~ v1_xboole_0(k16_substut1(A)) & v1_substut1(k16_substut1(A),A) ) ) )).
fof(fc4_supinf_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_setfam_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k6_numbers))) ) => ( ~ v1_xboole_0(k6_supinf_1(A)) & v2_membered(k6_supinf_1(A)) ) ) )).
fof(fc4_termord,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,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) ) )).
fof(fc4_tex_1,axiom,( ! [A] : v1_tdlat_3(k1_compts_1(A)) )).
fof(fc4_tex_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc4_tex_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc4_tmap_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc4_topalg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc4_topalg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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) ) ) )).
fof(fc4_topalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) ) )).
fof(fc4_topalg_5,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc4_topalg_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc4_topdim_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc4_topdim_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc4_topgen_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc4_topgen_3,axiom,( ! [A] : ! [B] : ( ~ 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)) ) ) )).
fof(fc4_topgen_4,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc4_topgrp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc4_topmetr,axiom,( ! [A] : ( ( v3_topmetr(A) & l1_struct_0(A) ) => v3_membered(u1_struct_0(A)) ) )).
fof(fc4_topreal1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ~ v1_xboole_0(k4_topreal1(A)) ) )).
fof(fc4_topreal6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ~ v1_xboole_0(k5_measure6(A)) ) )).
fof(fc4_topreal7,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc4_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc4_topreala,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v2_xxreal_0(B) & v1_xreal_0(B) ) => ~ v1_xboole_0(k1_xxreal_1(A,k2_xcmplx_0(A,B))) ) )).
fof(fc4_toprealb,axiom,( v1_funct_1(k16_sin_cos) & v1_funct_2(k16_sin_cos,k1_numbers,k1_numbers) & v1_fcont_1(k16_sin_cos) )).
fof(fc4_toprealc,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc4_tops_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc4_trees_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ v1_xboole_0(k2_trees_1(A)) & v1_finset_1(k2_trees_1(A)) & v1_trees_1(k2_trees_1(A)) ) ) )).
fof(fc4_trees_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => v3_trees_2(k2_funcop_1(A,B)) ) )).
fof(fc4_trees_3,axiom,( v2_trees_3(k2_trees_3) )).
fof(fc4_trees_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc4_trees_9,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc4_unialg_1,axiom,( ! [A] : ( ( v4_unialg_1(A) & l1_unialg_1(A) ) => ( v2_relat_1(u1_unialg_1(A)) & ~ v1_xboole_0(u1_unialg_1(A)) ) ) )).
fof(fc4_uniroots,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v6_struct_0(A) & v4_vectsp_1(A) & l6_algstr_0(A) & ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ( v1_funct_1(k4_uniroots(B,A)) & v1_funct_2(k4_uniroots(B,A),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k4_uniroots(B,A),A) & v1_uproots(k4_uniroots(B,A),A) ) ) )).
fof(fc4_uproots,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1) ) => ( 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),k4_ordinal1,u1_struct_0(A)) & v1_uproots(k2_polynom5(A,k4_polynom5(A,B,k5_struct_0(A)),C),A) ) ) )).
fof(fc4_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k3_numbers) ) => v4_membered(k10_xtuple_0(A)) ) )).
fof(fc4_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc4_vectmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ~ v1_xboole_0(k1_vectmetr(A)) ) )).
fof(fc4_vectsp_1,axiom,( ~ v2_struct_0(k2_vectsp_1) & v36_algstr_0(k2_vectsp_1) )).
fof(fc4_vectsp_2,axiom,( ! [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) & 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) ) ) )).
fof(fc4_vfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) & v1_xreal_0(D) ) => ( v1_funct_1(k4_vfunct_1(A,B,C,D)) & v1_partfun1(k4_vfunct_1(A,B,C,D),A) ) ) )).
fof(fc4_waybel10,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc4_waybel11,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc4_waybel17,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc4_waybel18,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(fc4_waybel23,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc4_waybel24,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc4_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ( ~ v2_struct_0(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) ) ) )).
fof(fc4_waybel26,axiom,( ~ v7_struct_0(k9_waybel18) & v1_pre_topc(k9_waybel18) & v1_waybel25(k9_waybel18) )).
fof(fc4_waybel27,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc4_waybel30,axiom,( ! [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) ) => ( ~ v7_struct_0(k1_yellow_1(k5_waybel11(A))) & v1_orders_2(k1_yellow_1(k5_waybel11(A))) & v3_lattice3(k1_yellow_1(k5_waybel11(A))) ) ) )).
fof(fc4_waybel32,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc4_waybel34,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc4_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_yellow_0(A) & l1_orders_2(A) ) => v2_waybel_0(k2_struct_0(A),A) ) )).
fof(fc4_waybel_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc4_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc4_waybel_3,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc4_waybel_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => v4_waybel_4(k2_waybel_4(A),A) ) )).
fof(fc4_waybel_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) )).
fof(fc4_waybel_8,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(fc4_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc4_weddwitt,axiom,( ! [A] : ( ( ~ 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) ) => ( ~ 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)) ) ) )).
fof(fc4_wellord2,axiom,( ! [A] : ( v3_ordinal1(A) => ( v1_relat_1(k1_wellord2(A)) & v6_relat_2(k1_wellord2(A)) ) ) )).
fof(fc4_xboole_0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(A,B)) ) )).
fof(fc4_xboolean,axiom,( ! [A] : ! [B] : ( ( v1_xboolean(A) & v1_xboolean(B) ) => v1_xboolean(k5_xboolean(A,B)) ) )).
fof(fc4_xcmplx_0,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_xcmplx_0(k6_xcmplx_0(A,B)) ) )).
fof(fc4_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_xcmplx_0(k5_xcmplx_0(A)) & v1_xreal_0(k5_xcmplx_0(A)) ) ) )).
fof(fc4_xtuple_0,axiom,( ! [A] : ( v1_xboole_0(A) => v1_xboole_0(k9_xtuple_0(A)) ) )).
fof(fc4_xxreal_0,axiom,( v3_xxreal_0(k2_xxreal_0) )).
fof(fc4_xxreal_1,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => v2_membered(k4_xxreal_1(A,B)) ) )).
fof(fc4_xxreal_2,axiom,( ! [A] : ( ( v4_membered(A) & v1_xxreal_2(A) ) => ( v1_xxreal_0(k2_xxreal_2(A)) & v1_rat_1(k2_xxreal_2(A)) ) ) )).
fof(fc4_xxreal_3,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xxreal_0(B) & ~ v1_xreal_0(B) ) => ~ v1_xreal_0(k1_xxreal_3(A,B)) ) )).
fof(fc4_yellow10,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc4_yellow11,axiom,( v1_lattice3(k2_yellow11) & v2_lattice3(k2_yellow11) )).
fof(fc4_yellow13,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc4_yellow14,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc4_yellow16,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k4_yellow_1(A,B)))) ) => ~ v1_xboole_0(k5_card_3(D,C)) ) )).
fof(fc4_yellow18,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc4_yellow19,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k2_yellow_1(B)) & v13_waybel_0(C,k2_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_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) ) ) )).
fof(fc4_yellow21,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(fc4_yellow_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc4_yellow_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ( v1_orders_2(k1_yellow_1(k7_waybel_0(A))) & v2_lattice3(k1_yellow_1(k7_waybel_0(A))) ) ) )).
fof(fc4_yellow_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc4_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc4_yellow_6,axiom,( ! [A] : ! [B] : ( ( ~ 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(k4_yellow_1(A,B))) ) )).
fof(fc4_yellow_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v16_waybel_0(A) & l1_orders_2(A) ) => ( v1_orders_2(k7_lattice3(A)) & v16_waybel_0(k7_lattice3(A)) ) ) )).
fof(fc4_yellow_9,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc4_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) ) => v1_zf_lang(k6_zf_lang(A)) ) )).
fof(fc4_zfmisc_1,axiom,( ! [A] : ! [B] : ( ( v1_zfmisc_1(A) & v1_zfmisc_1(B) ) => v1_zfmisc_1(k2_zfmisc_1(A,B)) ) )).
fof(fc4_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc4_zmodul02,axiom,( ! [A] : ( ( ~ 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(k26_zmodul02(A)) ) )).
fof(fc50_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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)))) ) )).
fof(fc50_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ~ v1_finset_1(k11_fomodel1(A)) ) )).
fof(fc50_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ 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(k38_fomodel2(A,B),A) ) )).
fof(fc50_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v13_fomodel4(k39_fomodel4(A),2,A) ) )).
fof(fc50_glib_003,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)),k4_ordinal1) & 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))) ) ) )).
fof(fc50_member_1,axiom,( ! [A] : ! [B] : ( ( v6_membered(A) & v6_membered(B) ) => v6_membered(k13_member_1(A,B)) ) )).
fof(fc50_membered,axiom,( ! [A] : ! [B] : ( ( v2_membered(A) & v2_membered(B) ) => v2_membered(k5_xboole_0(A,B)) ) )).
fof(fc50_pcs_0,axiom,( ! [A] : ! [B] : ( ( v6_pcs_0(A) & l2_pcs_0(A) & v6_pcs_0(B) & l2_pcs_0(B) ) => ( v1_relat_1(k18_pcs_0(A,B)) & v4_relat_1(k18_pcs_0(A,B),k7_domain_1(k4_ordinal1,k5_numbers,1)) & v1_funct_1(k18_pcs_0(A,B)) & v1_partfun1(k18_pcs_0(A,B),k7_domain_1(k4_ordinal1,k5_numbers,1)) & v11_pcs_0(k18_pcs_0(A,B)) ) ) )).
fof(fc50_valued_0,axiom,( ! [A] : ( v2_membered(A) => ( v1_relat_1(k4_relat_1(A)) & v2_valued_0(k4_relat_1(A)) ) ) )).
fof(fc50_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc50_valued_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc51_fomodel0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc51_fomodel1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) => v15_fomodel1(k7_finseq_1(k42_fomodel1(A,k43_fomodel1(A,k18_fomodel1(A)),B),C),A) ) )).
fof(fc51_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(fc51_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v13_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))))) & v11_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,k8_fomodel4(A,B,C)) ) )).
fof(fc51_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(fc51_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v2_membered(B) ) => v1_xboole_0(k14_member_1(A,B)) ) )).
fof(fc51_membered,axiom,( ! [A] : ! [B] : ( ( v3_membered(A) & v3_membered(B) ) => v3_membered(k5_xboole_0(A,B)) ) )).
fof(fc51_pcs_0,axiom,( ! [A] : ! [B] : ( ( v14_pcs_0(A) & l2_pcs_0(A) & v14_pcs_0(B) & l2_pcs_0(B) ) => ( v1_relat_1(k18_pcs_0(A,B)) & v4_relat_1(k18_pcs_0(A,B),k7_domain_1(k4_ordinal1,k5_numbers,1)) & v1_funct_1(k18_pcs_0(A,B)) & v1_partfun1(k18_pcs_0(A,B),k7_domain_1(k4_ordinal1,k5_numbers,1)) & v17_pcs_0(k18_pcs_0(A,B)) ) ) )).
fof(fc51_valued_0,axiom,( ! [A] : ( v3_membered(A) => ( v1_relat_1(k4_relat_1(A)) & v3_valued_0(k4_relat_1(A)) ) ) )).
fof(fc51_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc51_valued_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc52_fomodel0,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v1_xboole_0(k4_xboole_0(B,A)) ) )).
fof(fc52_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(k37_fomodel2(B,C),B,A) ) )).
fof(fc52_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v13_fomodel4(B,k5_numbers,A) & m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) & v11_fomodel4(C,A,B) ) => ( v1_partfun1(k7_fomodel4(A,B,C),k35_fomodel1(A)) & v3_relat_2(k7_fomodel4(A,B,C)) & v8_relat_2(k7_fomodel4(A,B,C)) ) ) )).
fof(fc52_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(fc52_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v2_membered(B) ) => v1_xboole_0(k14_member_1(B,A)) ) )).
fof(fc52_membered,axiom,( ! [A] : ! [B] : ( ( v4_membered(A) & v4_membered(B) ) => v4_membered(k5_xboole_0(A,B)) ) )).
fof(fc52_pcs_0,axiom,( ! [A] : ! [B] : ( ( v3_orders_2(A) & l2_pcs_0(A) & v3_orders_2(B) & l2_pcs_0(B) ) => v3_orders_2(k19_pcs_0(A,B)) ) )).
fof(fc52_valued_0,axiom,( ! [A] : ( v4_membered(A) => ( v1_relat_1(k4_relat_1(A)) & v5_relat_1(k4_relat_1(A),k3_numbers) ) ) )).
fof(fc52_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc52_valued_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc53_fomodel0,axiom,( ! [A] : ! [B] : v1_xboole_0(k4_xboole_0(k1_tarski(A),k2_tarski(A,B))) )).
fof(fc53_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(k38_fomodel2(B,C),B,A) ) )).
fof(fc53_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v3_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))) ) => v5_fomodel4(k4_tarski(k13_fomodel0(D,B),k35_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))),k24_fomodel4(A)),k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))),k25_fomodel4(A))),k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))),k35_fomodel4(A))),k1_tarski(k4_tarski(B,k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k1_fomodel2(A)),C),D)))) ) )).
fof(fc53_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(fc53_member_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v2_membered(A) & ~ v1_xboole_0(B) & v2_membered(B) ) => ~ v1_xboole_0(k14_member_1(A,B)) ) )).
fof(fc53_membered,axiom,( ! [A] : ! [B] : ( ( v5_membered(A) & v5_membered(B) ) => v5_membered(k5_xboole_0(A,B)) ) )).
fof(fc53_partfun3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc53_pcs_0,axiom,( ! [A] : ! [B] : ( ( v4_pcs_0(A) & l2_pcs_0(A) & v4_pcs_0(B) & l2_pcs_0(B) ) => v4_pcs_0(k19_pcs_0(A,B)) ) )).
fof(fc53_valued_0,axiom,( ! [A] : ( v5_membered(A) => ( v1_relat_1(k4_relat_1(A)) & v5_relat_1(k4_relat_1(A),k4_numbers) ) ) )).
fof(fc53_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc53_valued_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc54_fomodel0,axiom,( ! [A] : ! [B] : v1_xboole_0(k5_xboole_0(k1_xtuple_0(k4_tarski(A,B)),A)) )).
fof(fc54_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v3_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))) ) => v5_fomodel4(k4_tarski(k13_fomodel0(C,B),k35_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))),k24_fomodel4(A)),k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))),k25_fomodel4(A))),k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))),k35_fomodel4(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,k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k1_fomodel2(A)),C),D)))) ) )).
fof(fc54_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(fc54_member_1,axiom,( ! [A] : ! [B] : ( ( v2_membered(A) & v2_membered(B) ) => v2_membered(k14_member_1(A,B)) ) )).
fof(fc54_membered,axiom,( ! [A] : ! [B] : ( ( v6_membered(A) & v6_membered(B) ) => v6_membered(k5_xboole_0(A,B)) ) )).
fof(fc54_partfun3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc54_pcs_0,axiom,( ! [A] : ! [B] : ( ( v6_pcs_0(A) & l2_pcs_0(A) & v6_pcs_0(B) & l2_pcs_0(B) ) => v6_pcs_0(k19_pcs_0(A,B)) ) )).
fof(fc54_valued_0,axiom,( ! [A] : ( v6_membered(A) => ( v1_relat_1(k4_relat_1(A)) & v4_valued_0(k4_relat_1(A)) ) ) )).
fof(fc54_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc55_fomodel0,axiom,( ! [A] : ! [B] : v1_xboole_0(k5_xboole_0(k2_xtuple_0(k4_tarski(A,B)),B)) )).
fof(fc55_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(fc55_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) => v5_fomodel4(k4_tarski(k7_domain_1(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k35_fomodel2(A,B),k35_fomodel2(A,C)),k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(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))),k33_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)),k35_fomodel2(A,B),k35_fomodel2(A,C)),k35_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)),k35_fomodel2(A,B),k35_fomodel2(A,C)),k35_fomodel2(A,C)))) ) )).
fof(fc55_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(fc55_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_membered(B) ) => v1_xboole_0(k15_member_1(A,B)) ) )).
fof(fc55_membered,axiom,( v7_membered(k2_numbers) )).
fof(fc55_pcs_0,axiom,( ! [A] : ! [B] : ( l2_pcs_0(A) => ( ~ v2_struct_0(k20_pcs_0(A,B)) & v12_pcs_0(k20_pcs_0(A,B)) ) ) )).
fof(fc55_valued_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc55_valued_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc56_fomodel0,axiom,( ! [A] : ! [B] : ( v1_relat_1(A) => v1_relat_1(k13_fomodel0(B,A)) ) )).
fof(fc56_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(fc56_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) => v5_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))),k24_fomodel4(A)),k1_xboole_0) ) )).
fof(fc56_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(fc56_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_membered(B) ) => v1_xboole_0(k15_member_1(B,A)) ) )).
fof(fc56_membered,axiom,( v7_membered(k1_numbers) )).
fof(fc56_pcs_0,axiom,( ! [A] : ! [B] : ( ( v3_orders_2(A) & l2_pcs_0(A) ) => ( v3_orders_2(k20_pcs_0(A,B)) & v12_pcs_0(k20_pcs_0(A,B)) ) ) )).
fof(fc56_valued_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc56_valued_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc57_fomodel0,axiom,( ! [A] : ! [B] : ( v1_funct_1(A) => v1_funct_1(k13_fomodel0(B,A)) ) )).
fof(fc57_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v13_fomodel4(B,k5_numbers,A) & v13_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))))) & v11_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),k8_fomodel4(A,B,C)) ) ) )).
fof(fc57_member_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_membered(A) & ~ v1_xboole_0(B) & v1_membered(B) ) => ~ v1_xboole_0(k15_member_1(A,B)) ) )).
fof(fc57_membered,axiom,( v7_membered(k3_numbers) )).
fof(fc57_partfun3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc57_pcs_0,axiom,( ! [A] : ! [B] : ( ( v4_pcs_0(A) & l2_pcs_0(A) ) => ( v4_pcs_0(k20_pcs_0(A,B)) & v12_pcs_0(k20_pcs_0(A,B)) ) ) )).
fof(fc57_valued_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc57_valued_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc58_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(k13_fomodel0(B,A)) & v1_finseq_1(k13_fomodel0(B,A)) ) ) )).
fof(fc58_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ~ v1_xboole_0(k40_fomodel2(A)) ) )).
fof(fc58_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v13_fomodel4(B,k5_numbers,A) & m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) & v11_fomodel4(C,A,B) ) => ( v1_relat_1(k40_fomodel4(A,B,C)) & v4_relat_1(k40_fomodel4(A,B,C),k37_fomodel1(A)) & v1_funct_1(k40_fomodel4(A,B,C)) ) ) )).
fof(fc58_member_1,axiom,( ! [A] : ! [B] : ( ( v1_membered(A) & v1_membered(B) ) => v1_membered(k15_member_1(A,B)) ) )).
fof(fc58_membered,axiom,( v7_membered(k4_numbers) )).
fof(fc58_partfun3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc58_pcs_0,axiom,( ! [A] : ! [B] : ( ( v6_pcs_0(A) & l2_pcs_0(A) ) => ( v6_pcs_0(k20_pcs_0(A,B)) & v12_pcs_0(k20_pcs_0(A,B)) ) ) )).
fof(fc58_valued_0,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc58_valued_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc59_fomodel0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc59_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v1_xboole_0(k4_xboole_0(k40_fomodel2(A),k30_fomodel2(A))) ) )).
fof(fc59_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v13_fomodel4(B,k5_numbers,A) & v13_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))))) & v11_fomodel4(C,A,B) ) => ( v1_relat_1(k40_fomodel4(A,B,C)) & v1_funct_1(k40_fomodel4(A,B,C)) & v1_fomodel2(k40_fomodel4(A,B,C),A,k8_eqrel_1(k35_fomodel1(A),k8_fomodel4(A,B,C))) ) ) )).
fof(fc59_member_1,axiom,( ! [A] : ! [B] : ( ( v3_membered(A) & v3_membered(B) ) => v3_membered(k15_member_1(A,B)) ) )).
fof(fc59_membered,axiom,( v7_membered(k4_ordinal1) )).
fof(fc59_partfun3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc59_pcs_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_pcs_0(A) ) => ( ~ v2_struct_0(k21_pcs_0(A)) & v12_pcs_0(k21_pcs_0(A)) ) ) )).
fof(fc59_valued_0,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc59_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc5_abcmiz_0,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc5_abcmiz_a,axiom,( ~ v1_xboole_0(k4_abcmiz_a) )).
fof(fc5_abian,axiom,( ! [A] : ( ( v1_int_1(A) & ~ v1_abian(A) ) => v1_abian(k6_xcmplx_0(A,1)) ) )).
fof(fc5_afinsq_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc5_afinsq_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc5_afvect0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc5_algstr_1,axiom,( v3_group_1(k8_algstr_0) )).
fof(fc5_algstr_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc5_altcat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc5_altcat_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(fc5_altcat_4,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc5_ami_3,axiom,( ! [A] : ! [B] : ( ( 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(k7_card_1(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)) ) )).
fof(fc5_ami_6,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(2),k1_ami_3) ) )).
fof(fc5_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ( v3_memstr_0(k4_amistd_1(A),A) & v1_extpro_1(k4_amistd_1(A),A) ) ) )).
fof(fc5_amistd_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc5_amistd_4,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(fc5_anproj_2,axiom,( ! [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) & 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)) ) ) )).
fof(fc5_aofa_000,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(fc5_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( v1_relat_1(k7_aofa_a00(A,B,C,D,E,F,G)) & v1_funct_1(k7_aofa_a00(A,B,C,D,E,F,G)) & v3_card_1(k7_aofa_a00(A,B,C,D,E,F,G),7) & v1_finseq_1(k7_aofa_a00(A,B,C,D,E,F,G)) ) )).
fof(fc5_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(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) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) & v4_aofa_a01(D,A,B,C) & l4_aofa_a00(D,A,B,C) & v4_msualg_1(E,A) & v4_msafree4(E,A,C) & v17_aofa_a00(E,A) & v20_aofa_a00(E,4,1,A) & l3_msualg_1(E,A) & v19_aofa_a00(F,A) & m1_subset_1(F,u1_struct_0(A)) & m1_subset_1(G,k13_aofa_a00(A,C,E,u4_aofa_a00(A,B,C,D))) & m1_subset_1(H,k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),F)) ) => v1_int_1(k1_funct_1(k1_msafree4(u1_struct_0(A),G,F),H)) ) )).
fof(fc5_armstrng,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc5_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v1_funct_1(k4_asympt_1(A)) & v1_funct_2(k4_asympt_1(A),k4_ordinal1,k1_numbers) & v4_asympt_0(k4_asympt_1(A)) ) ) )).
fof(fc5_autalg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc5_bagorder,axiom,( ! [A] : ( 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) ) ) )).
fof(fc5_bcialg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc5_bcialg_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc5_binop_2,axiom,( v1_funct_1(k15_binop_2) & v1_funct_2(k15_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & v1_binop_1(k15_binop_2,k3_numbers) & v2_binop_1(k15_binop_2,k3_numbers) )).
fof(fc5_bor_cant,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,k9_setfam_1(A)) ) ) )).
fof(fc5_borsuk_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc5_borsuk_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc5_borsuk_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc5_borsuk_5,axiom,( ! [A] : ! [B] : ( ( v1_rat_1(A) & v1_xreal_0(B) & ~ v1_rat_1(B) ) => ~ v1_rat_1(k2_xcmplx_0(B,A)) ) )).
fof(fc5_borsuk_6,axiom,( 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) )).
fof(fc5_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc5_bspace,axiom,( ! [A] : ( v1_finset_1(A) => ( ~ v2_struct_0(k7_bspace(A)) & v1_matrlin(k7_bspace(A),k2_bspace) ) ) )).
fof(fc5_bvfunc_1,axiom,( ! [A] : ( ~ 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) ) ) )).
fof(fc5_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => v1_group_1(k11_c0sp1(A)) ) )).
fof(fc5_c0sp2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc5_card_1,axiom,( ! [A] : ( v3_ordinal1(A) => v1_card_1(k3_card_1(A)) ) )).
fof(fc5_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => ~ v1_xboole_0(k4_card_3(A)) ) )).
fof(fc5_card_5,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc5_cardfin2,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v1_relat_1(B) & v1_xboole_0(B) & v1_funct_1(B) ) => ( v1_relat_1(k24_valued_1(B,A)) & v1_xboole_0(k24_valued_1(B,A)) & v1_funct_1(k24_valued_1(B,A)) ) ) )).
fof(fc5_catalg_1,axiom,( ! [A] : ( v1_msualg_1(k2_catalg_1(A)) & v3_catalg_1(k2_catalg_1(A)) ) )).
fof(fc5_cayldick,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => v2_relat_1(k6_afinsq_1(A,B)) ) )).
fof(fc5_cayley,axiom,( ! [A] : ( v7_ordinal1(A) => ( v15_algstr_0(k4_matrix_2(A)) & v1_monoid_0(k4_matrix_2(A)) ) ) )).
fof(fc5_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => v1_group_1(k7_cc0sp1(A)) ) )).
fof(fc5_cc0sp2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc5_cfdiff_1,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & 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)) ) ) )).
fof(fc5_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v2_struct_0(k7_cfuncdom(A)) & v36_algstr_0(k7_cfuncdom(A)) ) ) )).
fof(fc5_circcmb3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc5_circtrm1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) )).
fof(fc5_classes2,axiom,( ! [A] : v1_ordinal1(k5_classes1(A)) )).
fof(fc5_clopban1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) ) ) )).
fof(fc5_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => v1_group_1(k8_clopban2(A)) ) )).
fof(fc5_closure1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc5_coh_sp,axiom,( ! [A] : ( ~ 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)) ) )).
fof(fc5_cohsp_1,axiom,( ! [A] : ( v4_finsub_1(k5_finsub_1(A)) & v1_cohsp_1(k5_finsub_1(A)) & v2_cohsp_1(k5_finsub_1(A)) ) )).
fof(fc5_compact1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_pre_topc(k1_compact1(A)) & v2_pre_topc(k1_compact1(A)) ) ) )).
fof(fc5_compl_sp,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc5_complex1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & v1_xcmplx_0(A) ) => ( ~ v8_ordinal1(k9_complex1(A)) & v1_xreal_0(k9_complex1(A)) ) ) )).
fof(fc5_compos_0,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_compos_0(A) & m1_subset_1(B,A) ) => v1_finseq_1(k2_xtuple_0(B)) ) )).
fof(fc5_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_compos_1(A) & v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc5_compts_1,axiom,( ! [A] : ( l1_pre_topc(A) => v1_tops_2(u1_pre_topc(A),A) ) )).
fof(fc5_comput_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => ( ~ 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(k4_ordinal1)) & 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)) ) ) )).
fof(fc5_comseq_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & v1_xcmplx_0(B) ) => ( v1_funct_1(k24_valued_1(A,B)) & v1_funct_2(k24_valued_1(A,B),k4_ordinal1,k2_numbers) & v2_comseq_2(k24_valued_1(A,B)) ) ) )).
fof(fc5_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_funct_1(k4_comseq_3(A)) & v1_funct_2(k4_comseq_3(A),k4_ordinal1,k1_numbers) & v2_comseq_2(k4_comseq_3(A)) ) ) )).
fof(fc5_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ( ~ v2_struct_0(k11_conlat_1(A)) & v3_lattices(k11_conlat_1(A)) & v4_lattice3(k11_conlat_1(A)) ) ) )).
fof(fc5_convex4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) ) )).
fof(fc5_convfun1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc5_csspace,axiom,( ~ 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) )).
fof(fc5_csspace4,axiom,( ~ 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) )).
fof(fc5_dilworth,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(fc5_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => v1_dist_1(k19_finseq_1(A),A) ) )).
fof(fc5_ec_pf_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc5_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => ~ v1_xboole_0(k16_ens_1(A)) ) )).
fof(fc5_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ v2_struct_0(k15_euclid(A)) & v5_rltopsp1(k15_euclid(A)) ) ) )).
fof(fc5_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => v6_euclid_7(k1_tarski(k5_euclid(A)),A) ) )).
fof(fc5_euclid_9,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) & v1_valued_0(B) ) => ( v1_relat_1(k30_valued_1(B)) & v1_funct_1(k30_valued_1(B)) & v3_card_1(k30_valued_1(B),A) & v1_valued_0(k30_valued_1(B)) ) ) )).
fof(fc5_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(fc5_extpro_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ( v3_memstr_0(k1_extpro_1(A),A) & v1_extpro_1(k1_extpro_1(A),A) ) ) )).
fof(fc5_facirc_1,axiom,( ! [A] : ! [B] : ( ~ v1_facirc_1(A) => ~ v1_facirc_1(k4_xboole_0(A,B)) ) )).
fof(fc5_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc5_fcont_3,axiom,( ! [A] : ( v1_xreal_0(A) => v3_rcomp_1(k3_limfunc1(A)) ) )).
fof(fc5_fib_num2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => v1_setfam_1(k1_finseq_1(A)) ) )).
fof(fc5_filter_2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc5_finseq_1,axiom,( ! [A] : v1_xboole_0(k6_finseq_1(A)) )).
fof(fc5_finseq_2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k4_finseq_2(A,B)) ) )).
fof(fc5_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc5_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : v3_card_1(k7_finseq_4(A,B,C,D),4) )).
fof(fc5_finseq_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc5_finseq_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc5_finset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : v1_finset_1(k3_enumset1(A,B,C,D,E)) )).
fof(fc5_fomodel0,axiom,( ! [A] : ( v1_xboole_0(A) => v2_setfam_1(k1_tarski(A)) ) )).
fof(fc5_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v7_fomodel1(k7_fomodel1(A),A) ) )).
fof(fc5_fomodel2,axiom,( ! [A] : ! [B] : ( ( 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(k6_fomodel2(B,A)) & v1_relat_1(k6_fomodel2(B,A)) & v1_funct_1(k6_fomodel2(B,A)) ) ) )).
fof(fc5_fomodel3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc5_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc5_freealg,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,k4_ordinal1) & ~ 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)) ) ) )).
fof(fc5_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc5_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc5_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc5_funcsdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v36_algstr_0(k11_funcsdom(A)) & v1_group_1(k11_funcsdom(A)) ) ) )).
fof(fc5_funct_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc5_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(fc5_funct_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc5_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(k1_funct_7(A,B,C)) & v1_funct_1(k1_funct_7(A,B,C)) & v1_finseq_1(k1_funct_7(A,B,C)) ) ) )).
fof(fc5_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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)) ) ) )).
fof(fc5_gate_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ~ v1_xboole_0(k3_gate_1(A,B)) ) )).
fof(fc5_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v4_glib_000(A) ) => v1_finset_1(k6_glib_000(A)) ) )).
fof(fc5_glib_001,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(fc5_glib_004,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(fc5_goboard2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ( ~ v3_relat_1(k2_goboard2(A)) & v1_matrix_0(k2_goboard2(A)) & v1_goboard1(k2_goboard2(A)) & v2_goboard1(k2_goboard2(A)) & v3_goboard1(k2_goboard2(A)) & v4_goboard1(k2_goboard2(A)) ) ) )).
fof(fc5_gr_cy_1,axiom,( v5_membered(u1_struct_0(k2_gr_cy_1)) )).
fof(fc5_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc5_graph_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc5_grcat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc5_groeb_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,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(k3_polynom1(k15_pre_poly(A),C,D)))) & v1_funct_2(k6_groeb_3(A,B,C,D,k5_card_1(k3_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(k3_polynom1(k15_pre_poly(A),C,D))),C) & v3_polynom7(k6_groeb_3(A,B,C,D,k5_card_1(k3_polynom1(k15_pre_poly(A),C,D))),A,C) ) ) )).
fof(fc5_group_14,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( v13_algstr_0(k2_group_14(A)) & v2_rlvect_1(k2_group_14(A)) & v3_rlvect_1(k2_group_14(A)) & v4_rlvect_1(k2_group_14(A)) ) ) )).
fof(fc5_group_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc5_group_7,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc5_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc5_hahnban1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & ~ 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)) & v13_vectsp_1(C,B,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)) & v13_vectsp_1(k4_hahnban1(A,B,C),B,A) ) ) )).
fof(fc5_hermitan,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(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)))) ) => ( v1_funct_1(k5_hahnban1(k1_complfld,A,B,C)) & v1_funct_2(k5_hahnban1(k1_complfld,A,B,C),u1_struct_0(A),u1_struct_0(k1_complfld)) & v1_hermitan(k5_hahnban1(k1_complfld,A,B,C),A) ) ) )).
fof(fc5_heyting3,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => v1_finset_1(k3_heyting3(A,B)) ) )).
fof(fc5_hilbasis,axiom,( ! [A] : ! [B] : ( ( ~ 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,k4_ordinal1) ) => ( 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(k12_polynom1(B,A))),u1_struct_0(k12_polynom1(k1_nat_1(B,1),A))) ) ) )).
fof(fc5_hilbert3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc5_index_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc5_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k3_int_1(A)) ) )).
fof(fc5_int_3,axiom,( v1_int_3(k1_int_3) )).
fof(fc5_int_6,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc5_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k1_interva1(A,k1_subset_1(A),k1_subset_1(A))) ) )).
fof(fc5_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => v9_intpro_1(k11_intpro_1(A)) ) )).
fof(fc5_isomichi,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc5_jordan,axiom,( ! [A] : ( 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))) ) )).
fof(fc5_jordan18,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => v4_pre_topc(k4_topreal1(A),k15_euclid(2)) ) )).
fof(fc5_jordan1e,axiom,( ! [A] : ! [B] : ( ( 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) ) => v4_topreal1(k1_jordan1e(A,B)) ) )).
fof(fc5_jordan1h,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m1_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ~ v1_xboole_0(k9_matrix_0(A)) ) )).
fof(fc5_jordan23,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc5_jordan2c,axiom,( ! [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) => v2_tops_1(k3_topreal1(2,A),k15_euclid(2)) ) )).
fof(fc5_kurato_1,axiom,( v3_setfam_1(k3_kurato_1(k3_topmetr,k6_kurato_1),u1_struct_0(k3_topmetr)) )).
fof(fc5_lattice2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc5_lattice3,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc5_lattice5,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v3_ordinal1(B) ) => ~ v1_xboole_0(k8_lattice5(A,B)) ) )).
fof(fc5_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => v3_lexbfs(k16_lexbfs(A)) ) )).
fof(fc5_lfuzzy_0,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc5_lfuzzy_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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) ) ) )).
fof(fc5_lopban_1,axiom,( ! [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) & 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)) ) ) )).
fof(fc5_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => v1_group_1(k8_lopban_2(A)) ) )).
fof(fc5_lopclset,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc5_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( ~ v1_xboole_0(k13_lpspacc1(A,B,C)) & v1_ideal_1(k13_lpspacc1(A,B,C),k12_lpspacc1(A)) & v1_lpspacc1(k13_lpspacc1(A,B,C),k12_lpspacc1(A)) ) ) )).
fof(fc5_lpspace1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_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)) ) ) )).
fof(fc5_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v2_xxreal_0(D) & v1_xreal_0(D) ) => ( ~ 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)) ) ) )).
fof(fc5_ltlaxio3,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) ) => v1_finset_1(k5_ltlaxio3(A)) ) )).
fof(fc5_ltlaxio4,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) ) => v1_finset_1(k7_ltlaxio4(A)) ) )).
fof(fc5_lukasi_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc5_margrel1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v2_card_3(B) ) => ( v1_relat_1(k5_relat_1(A,B)) & v2_margrel1(k5_relat_1(A,B)) ) ) )).
fof(fc5_matrix_6,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(k3_matrix_1(B,A)) & v2_matrix_0(k3_matrix_1(B,A),u1_struct_0(B),A,A) & v2_matrix_6(k3_matrix_1(B,A),A,B) ) ) )).
fof(fc5_matroid0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) => ( ~ v2_struct_0(k2_matroid0(A)) & v1_pre_topc(k2_matroid0(A)) ) ) )).
fof(fc5_matrtop1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc5_matrtop3,axiom,( ! [A] : ( 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) ) ) )).
fof(fc5_mazurulm,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v3_membered(A) & v3_xxreal_2(A) & ~ v2_xxreal_0(B) & v1_xreal_0(B) ) => v4_xxreal_2(k23_member_1(A,B)) ) )).
fof(fc5_measure6,axiom,( ! [A] : ( ( v1_setfam_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => v1_setfam_1(k4_measure6(A)) ) )).
fof(fc5_member_1,axiom,( ! [A] : ( v1_xboole_0(A) => ( v1_xboole_0(k5_member_1(A)) & v1_membered(k5_member_1(A)) ) ) )).
fof(fc5_membered,axiom,( v5_membered(k4_numbers) )).
fof(fc5_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc5_mesfunc7,axiom,( v2_valued_0(k6_finseq_1(k6_numbers)) )).
fof(fc5_metric_1,axiom,( ~ v2_struct_0(k7_metric_1) & v1_metric_1(k7_metric_1) )).
fof(fc5_metrizts,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc5_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( v5_rltopsp1(k15_euclid(A)) & v5_waybel23(k15_euclid(A)) ) ) )).
fof(fc5_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( v2_pre_topc(k4_mfold_2(A)) & v5_waybel23(k4_mfold_2(A)) ) ) )).
fof(fc5_mmlquer2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) & v1_relat_2(C) & v6_relat_2(C) & v1_partfun1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( v1_relat_1(k1_mmlquer2(B,C)) & v6_relat_2(k1_mmlquer2(B,C)) ) ) )).
fof(fc5_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc5_mod_2,axiom,( v36_algstr_0(k18_mod_2) & v4_vectsp_1(k18_mod_2) )).
fof(fc5_mod_4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc5_modelc_1,axiom,( ! [A] : ! [B] : ( ( v1_modelc_1(A) & m1_finseq_1(A,k4_ordinal1) & v1_modelc_1(B) & m1_finseq_1(B,k4_ordinal1) ) => v1_modelc_1(k8_modelc_1(A,B)) ) )).
fof(fc5_modelc_2,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & v1_modelc_2(B) & m1_finseq_1(B,k4_ordinal1) ) => v1_modelc_2(k5_modelc_2(A,B)) ) )).
fof(fc5_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => ~ v1_xboole_0(k1_orders_1(k1_modelc_3(A))) ) )).
fof(fc5_moebius1,axiom,( ! [A] : ( v1_finset_1(A) => ( v1_relat_1(k4_moebius1(A)) & v4_relat_1(k4_moebius1(A),k4_ordinal1) & v1_funct_1(k4_moebius1(A)) & v1_partfun1(k4_moebius1(A),k4_ordinal1) & v2_pre_poly(k4_moebius1(A)) ) ) )).
fof(fc5_msafree,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc5_msafree1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc5_msafree4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) ) => v5_finset_1(k3_trees_9(A)) ) )).
fof(fc5_mssubfam,axiom,( ! [A] : ( 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)) ) )).
fof(fc5_msualg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc5_msualg_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc5_msualg_9,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc5_mycielsk,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc5_nat_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => v7_ordinal1(k3_xxreal_0(A,B)) ) )).
fof(fc5_nat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc5_nat_lat,axiom,( ~ v1_xboole_0(k6_nat_lat) )).
fof(fc5_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ( v1_cat_1(k10_nattra_1(A)) & v4_nattra_1(k10_nattra_1(A)) ) ) )).
fof(fc5_neckla_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc5_necklace,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_orders_2(k4_necklace(A)) & v1_necklace(k4_necklace(A)) ) ) )).
fof(fc5_newton,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc5_nfcont_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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_xreal_0(C) ) => ( v1_funct_1(k4_vfunct_1(k1_numbers,A,B,C)) & v1_nfcont_3(k4_vfunct_1(k1_numbers,A,B,C),A) ) ) )).
fof(fc5_nfcont_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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) ) ) )).
fof(fc5_normform,axiom,( ! [A] : ( v3_lattices(k12_normform(A)) & v10_lattices(k12_normform(A)) ) )).
fof(fc5_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ( ~ v2_struct_0(k4_normsp_2(A)) & v1_frechet(k4_normsp_2(A)) & v5_rltopsp1(k4_normsp_2(A)) ) ) )).
fof(fc5_numbers,axiom,( ~ v1_xboole_0(k6_numbers) )).
fof(fc5_openlatt,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc5_oposet_1,axiom,( v3_orders_2(k1_oposet_1) & v3_qmax_1(k1_oposet_1) )).
fof(fc5_ordeq_01,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_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) & l1_normsp_1(B) ) => ( ~ v2_struct_0(k5_ordeq_01(A,B)) & v13_algstr_0(k5_ordeq_01(A,B)) & v2_rlvect_1(k5_ordeq_01(A,B)) & v3_rlvect_1(k5_ordeq_01(A,B)) & v4_rlvect_1(k5_ordeq_01(A,B)) & v5_rlvect_1(k5_ordeq_01(A,B)) & v6_rlvect_1(k5_ordeq_01(A,B)) & v7_rlvect_1(k5_ordeq_01(A,B)) & v8_rlvect_1(k5_ordeq_01(A,B)) & v3_normsp_0(k5_ordeq_01(A,B)) & v4_normsp_0(k5_ordeq_01(A,B)) & v1_normsp_1(k5_ordeq_01(A,B)) & v2_normsp_1(k5_ordeq_01(A,B)) ) ) )).
fof(fc5_orders_2,axiom,( ! [A] : ( ( v2_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => v8_relat_2(u1_orders_2(A)) ) )).
fof(fc5_orders_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc5_ordinal1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc5_ordinal2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => ( v3_ordinal1(k10_ordinal2(A,B)) & v7_ordinal1(k10_ordinal2(A,B)) ) ) )).
fof(fc5_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ( v2_ordinal2(k3_afinsq_1(A)) & v1_ordinal5(k3_afinsq_1(A)) ) ) )).
fof(fc5_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ( v1_relat_1(k4_relat_1(A)) & v5_ordinal1(k4_relat_1(A)) & v1_ordinal2(k4_relat_1(A)) ) ) )).
fof(fc5_osafree,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc5_osalg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc5_partfun3,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ( v1_xreal_0(k3_square_1(A)) & v2_xxreal_0(k3_square_1(A)) ) ) )).
fof(fc5_pboole,axiom,( ! [A] : ( v1_setfam_1(A) => ( v1_relat_1(k4_relat_1(A)) & v2_relat_1(k4_relat_1(A)) ) ) )).
fof(fc5_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc5_pencil_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc5_polyalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_group_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ( ~ v2_struct_0(k1_polyalg1(A)) & v5_group_1(k1_polyalg1(A)) & v1_polyalg1(k1_polyalg1(A),A) ) ) )).
fof(fc5_polyeq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc5_polynom1,axiom,( ! [A] : ! [B] : ( ( 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(k9_polynom1(A,B)) & v1_funct_2(k9_polynom1(A,B),k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(k9_polynom1(A,B),B) ) ) )).
fof(fc5_polynom3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k3_normsp_1(A,B,C)) & v1_funct_2(k3_normsp_1(A,B,C),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k3_normsp_1(A,B,C),A) ) ) )).
fof(fc5_polynom5,axiom,( ! [A] : ! [B] : ( ( ~ 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,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k7_polynom5(A,B)) & v1_funct_2(k7_polynom5(A,B),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k7_polynom5(A,B),A) ) ) )).
fof(fc5_polynom7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,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),B) ) ) )).
fof(fc5_polyred,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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(k12_polynom1(A,C)))) ) => v3_rewrite1(k3_polyred(A,B,C,D)) ) )).
fof(fc5_poset_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc5_pralg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc5_pralg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc5_pre_circ,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc5_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc5_pre_topc,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc5_prob_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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) ) )).
fof(fc5_prvect_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc5_pscomp_1,axiom,( 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)) )).
fof(fc5_pythtrip,axiom,( ! [A] : ( ( v1_int_1(A) & ~ v1_abian(A) ) => ~ v1_abian(k1_square_1(A)) ) )).
fof(fc5_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ~ v1_xboole_0(k5_qc_lang1(A)) ) )).
fof(fc5_quatern2,axiom,( v36_algstr_0(k15_quatern2) & v4_vectsp_1(k15_quatern2) )).
fof(fc5_quaterni,axiom,( v1_quaterni(k5_quaterni) )).
fof(fc5_quofield,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc5_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & v1_rat_1(k4_xcmplx_0(A)) ) ) )).
fof(fc5_ratfunc1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & l5_algstr_0(A) ) => ( v1_funct_1(k10_polynom3(A)) & v1_funct_2(k10_polynom3(A),k4_ordinal1,u1_struct_0(A)) & ~ v1_ratfunc1(k10_polynom3(A),A) ) ) )).
fof(fc5_rcomp_3,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => v5_xxreal_2(k3_xxreal_1(A,B)) ) )).
fof(fc5_real_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => v8_ordinal1(k6_xcmplx_0(A,A)) ) )).
fof(fc5_real_lat,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc5_real_ns1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( ~ v2_struct_0(k7_real_ns1(A)) & ~ v7_struct_0(k7_real_ns1(A)) & v1_bhsp_1(k7_real_ns1(A)) ) ) )).
fof(fc5_relat_1,axiom,( ! [A] : ! [B] : v1_relat_1(k1_tarski(k4_tarski(A,B))) )).
fof(fc5_relat_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_relat_2(A) & v1_relat_1(B) & v1_relat_2(B) ) => v1_relat_2(k3_xboole_0(A,B)) ) )).
fof(fc5_reloc,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc5_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_relat_1(C) ) => v5_relat_1(k3_xboole_0(B,C),A) ) )).
fof(fc5_revrot_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc5_rewrite2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v5_ordinal1(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)) ) ) )).
fof(fc5_rfunct_1,axiom,( ! [A] : ! [B] : ( v1_funct_1(k4_funct_3(A,B)) & v1_partfun1(k4_funct_3(A,B),B) ) )).
fof(fc5_ring_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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)) ) ) )).
fof(fc5_ringcat1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc5_rlaffin1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) )).
fof(fc5_rlaffin3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) & m1_finseq_1(B,u1_struct_0(A)) & v1_xreal_0(C) ) => ( v1_funct_1(k4_vfunct_1(k4_ordinal1,A,B,C)) & v1_finseq_1(k4_vfunct_1(k4_ordinal1,A,B,C)) ) ) )).
fof(fc5_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) ) )).
fof(fc5_robbins4,axiom,( ~ v2_struct_0(k2_robbins4) & v4_robbins1(k2_robbins4) )).
fof(fc5_roughs_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc5_rvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc5_scm_halt,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc5_scm_inst,axiom,( ~ v1_xboole_0(k3_scm_inst) & v2_compos_0(k3_scm_inst) )).
fof(fc5_scmfsa10,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc5_scmfsa6c,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc5_scmfsa7b,axiom,( v1_relat_1(k4_compos_1(k1_scmfsa_2)) & v4_relat_1(k4_compos_1(k1_scmfsa_2),k4_ordinal1) & 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),k7_card_1(3),k1_scmfsa_2) & v1_scmfsa7b(k4_compos_1(k1_scmfsa_2)) )).
fof(fc5_scmfsa8a,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( ~ v1_xboole_0(k1_scmfsa8a(A)) & v1_relat_1(k1_scmfsa8a(A)) & v4_relat_1(k1_scmfsa8a(A),k4_ordinal1) & 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)) ) ) )).
fof(fc5_scmfsa8b,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) & ~ v2_compos_1(k3_scmfsa8b(A,B,C),k1_scmfsa_2) ) ) )).
fof(fc5_scmfsa_2,axiom,( v3_memstr_0(k1_scmfsa_2,k7_card_1(3)) & v1_extpro_1(k1_scmfsa_2,k7_card_1(3)) )).
fof(fc5_scmfsa_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc5_scmfsa_i,axiom,( ~ v1_xboole_0(k2_scmfsa_i) & v3_compos_0(k2_scmfsa_i) )).
fof(fc5_scmfsa_m,axiom,( ~ v1_xboole_0(k2_scm_inst) )).
fof(fc5_scmpds_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc5_scmpds_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc5_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) & v2_scmpds_4(A) & v3_scmpds_4(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & 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_relat_1(k2_scmpds_6(C,D,A,B)) & v4_relat_1(k2_scmpds_6(C,D,A,B),k4_ordinal1) & v5_relat_1(k2_scmpds_6(C,D,A,B),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k2_scmpds_6(C,D,A,B)) & 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)) ) ) )).
fof(fc5_scmpds_i,axiom,( v3_compos_0(k1_scmpds_i) )).
fof(fc5_scmring2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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),k7_card_1(2),k1_scmring2(A)) ) )).
fof(fc5_scmring3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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),k7_card_1(2),k1_scmring2(A)) ) )).
fof(fc5_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) ) ) )).
fof(fc5_scmyciel,axiom,( ! [A] : ! [B] : ( v5_finset_1(A) => v5_finset_1(k4_xboole_0(A,B)) ) )).
fof(fc5_seq_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_comseq_2(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_funct_1(k18_valued_1(A,B)) & v1_funct_2(k18_valued_1(A,B),k4_ordinal1,k1_numbers) & v2_comseq_2(k18_valued_1(A,B)) ) ) )).
fof(fc5_setfam_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc5_sfmastr1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc5_simplex0,axiom,( v1_xboole_0(k1_simplex0(k1_xboole_0)) & v1_classes1(k1_simplex0(k1_xboole_0)) )).
fof(fc5_simplex1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) )).
fof(fc5_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k23_sin_cos(A)) ) )).
fof(fc5_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k16_sin_cos,k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) & v2_funct_1(k5_relat_1(k16_sin_cos,k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(fc5_sin_cos9,axiom,( v1_funct_1(k1_sin_cos9) & v2_funct_1(k1_sin_cos9) )).
fof(fc5_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k5_sincos10(A)) ) )).
fof(fc5_sppol_2,axiom,( ! [A] : ! [B] : ( ( v3_topreal1(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & v7_ordinal1(B) ) => v3_topreal1(k1_rfinseq(B,A)) ) )).
fof(fc5_sprect_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(fc5_stacks_1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc5_struct_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(k2_struct_0(A)) ) )).
fof(fc5_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ~ v1_xboole_0(k4_enumset1(A,B,C,D,E,F)) )).
fof(fc5_substut1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_qc_lang1(A) & v7_ordinal1(B) & 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) ) )).
fof(fc5_tex_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ( v1_pre_topc(k3_tex_1(A,B)) & v2_pre_topc(k3_tex_1(A,B)) ) ) )).
fof(fc5_tex_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc5_tmap_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc5_topalg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc5_topalg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc5_topalg_5,axiom,( ! [A] : ( 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) ) ) )).
fof(fc5_topalg_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) )).
fof(fc5_topdim_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc5_topdim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( v5_rltopsp1(k15_euclid(A)) & v3_topdim_1(k15_euclid(A)) ) ) )).
fof(fc5_topgrp_1,axiom,( ! [A] : ( 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) ) ) )).
fof(fc5_topmetr,axiom,( v2_pre_topc(k3_topmetr) & v3_topmetr(k3_topmetr) )).
fof(fc5_topreal1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ~ v1_xboole_0(k5_topreal1(A)) ) )).
fof(fc5_topreal6,axiom,( ! [A] : ( ( v3_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => v3_xxreal_2(k5_measure6(A)) ) )).
fof(fc5_topreal7,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc5_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc5_topreala,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v2_xxreal_0(B) & v1_xreal_0(B) ) => ~ v1_xboole_0(k4_xxreal_1(k6_xcmplx_0(A,B),A)) ) )).
fof(fc5_toprealb,axiom,( v1_funct_1(k18_sin_cos) & v1_funct_2(k18_sin_cos,k1_numbers,k1_numbers) & v1_fcont_1(k18_sin_cos) )).
fof(fc5_toprealc,axiom,( ! [A] : ( v1_xboole_0(A) => ( v8_ordinal1(k12_euclid(A)) & v1_xreal_0(k12_euclid(A)) ) ) )).
fof(fc5_tops_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc5_trees_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc5_trees_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc5_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k4_trees_3(A)) ) )).
fof(fc5_trees_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc5_trees_9,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc5_unialg_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(fc5_uproots,axiom,( ! [A] : ! [B] : ( ( ~ 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,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & v1_uproots(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => v1_finset_1(k6_polynom5(A,B)) ) )).
fof(fc5_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) ) => v5_membered(k10_xtuple_0(A)) ) )).
fof(fc5_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc5_vectmetr,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) ) )).
fof(fc5_vectsp_1,axiom,( v3_membered(u1_struct_0(k2_vectsp_1)) )).
fof(fc5_vfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc5_waybel10,axiom,( ! [A] : ! [B] : ( ( l1_orders_2(A) & ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ( ~ v2_struct_0(k6_yellow_1(A,B)) & v1_orders_2(k6_yellow_1(A,B)) & v4_yellow_0(k6_yellow_1(A,B),k5_yellow_1(u1_struct_0(A),B)) ) ) )).
fof(fc5_waybel11,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc5_waybel17,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc5_waybel18,axiom,( ~ v2_struct_0(k9_waybel18) & v1_pre_topc(k9_waybel18) & v2_pre_topc(k9_waybel18) )).
fof(fc5_waybel23,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc5_waybel24,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc5_waybel25,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v2_pre_topc(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) ) ) )).
fof(fc5_waybel26,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v1_relat_1(k3_card_3(k2_card_3(A))) ) )).
fof(fc5_waybel27,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc5_waybel30,axiom,( ! [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) & l1_waybel_9(A) ) => ( ~ v7_struct_0(k1_yellow_1(k5_waybel11(A))) & v1_orders_2(k1_yellow_1(k5_waybel11(A))) & v3_lattice3(k1_yellow_1(k5_waybel11(A))) ) ) )).
fof(fc5_waybel32,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc5_waybel34,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc5_waybel_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(fc5_waybel_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc5_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc5_waybel_3,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc5_waybel_4,axiom,( ! [A] : ( ( 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)) ) )).
fof(fc5_waybel_5,axiom,( ! [A] : ! [B] : ( 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) ) )).
fof(fc5_waybel_8,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(fc5_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc5_weddwitt,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc5_wellord2,axiom,( ! [A] : ( v3_ordinal1(A) => ( v1_relat_1(k1_wellord2(A)) & v1_wellord1(k1_wellord2(A)) ) ) )).
fof(fc5_xboole_0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k2_xboole_0(B,A)) ) )).
fof(fc5_xboolean,axiom,( ! [A] : ! [B] : ( ( v1_xboolean(A) & v1_xboolean(B) ) => v1_xboolean(k6_xboolean(A,B)) ) )).
fof(fc5_xcmplx_0,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => v1_xcmplx_0(k7_xcmplx_0(A,B)) ) )).
fof(fc5_xreal_0,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => v1_xreal_0(k2_xcmplx_0(A,B)) ) )).
fof(fc5_xtuple_0,axiom,( ! [A] : ( v1_xboole_0(A) => v1_xboole_0(k10_xtuple_0(A)) ) )).
fof(fc5_xxreal_0,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => v1_xxreal_0(k3_xxreal_0(A,B)) ) )).
fof(fc5_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ~ v1_xboole_0(k1_xxreal_1(A,A)) ) )).
fof(fc5_xxreal_2,axiom,( ! [A] : ( ( v5_membered(A) & v1_xxreal_2(A) ) => ( v1_xxreal_0(k2_xxreal_2(A)) & v1_int_1(k2_xxreal_2(A)) ) ) )).
fof(fc5_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc5_yellow10,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc5_yellow11,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc5_yellow13,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc5_yellow14,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(fc5_yellow16,axiom,( ! [A] : ! [B] : ( ( ~ 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(k5_yellow_1(B,A)) & v24_waybel_0(k5_yellow_1(B,A)) ) ) )).
fof(fc5_yellow18,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc5_yellow19,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k2_yellow_1(B))) & v2_waybel_0(C,k2_yellow_1(B)) & v13_waybel_0(C,k2_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_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)) ) ) )).
fof(fc5_yellow21,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(fc5_yellow_1,axiom,( ! [A] : ( v1_orders_2(k1_yellow_1(A)) & v3_orders_2(k1_yellow_1(A)) & v4_orders_2(k1_yellow_1(A)) & v5_orders_2(k1_yellow_1(A)) ) )).
fof(fc5_yellow_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ( v1_orders_2(k1_yellow_1(k7_waybel_0(A))) & v1_lattice3(k1_yellow_1(k7_waybel_0(A))) ) ) )).
fof(fc5_yellow_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc5_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc5_yellow_6,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc5_yellow_7,axiom,( ! [A] : ( ( v2_lattice3(A) & l1_orders_2(A) ) => ( v1_orders_2(k7_lattice3(A)) & v1_lattice3(k7_lattice3(A)) ) ) )).
fof(fc5_yellow_9,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc5_zf_lang,axiom,( ! [A] : ! [B] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) & v1_zf_lang(B) & m1_finseq_1(B,k4_ordinal1) ) => v1_zf_lang(k7_zf_lang(A,B)) ) )).
fof(fc5_zmodul01,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(fc5_zmodul02,axiom,( ! [A] : ( ( ~ 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(k31_zmodul02(A)) & v1_zmodul01(k31_zmodul02(A)) ) ) )).
fof(fc5_zmodul03,axiom,( ! [A] : ! [B] : ( ( ~ 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_finset_1(B) & v1_zmodul02(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_zmodul01(k33_zmodul02(A,B)) & v2_zmodul03(k33_zmodul02(A,B)) ) ) )).
fof(fc60_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) ) => ~ v8_ordinal1(k1_card_1(A)) ) )).
fof(fc60_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc60_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) => v9_fomodel4(k7_finseq_1(k42_fomodel1(A,k43_fomodel1(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))),k24_fomodel4(A)),k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))),k33_fomodel4(A))),k7_domain_1(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k35_fomodel2(A,B),k35_fomodel2(A,C))) ) )).
fof(fc60_member_1,axiom,( ! [A] : ! [B] : ( ( v4_membered(A) & v4_membered(B) ) => v4_membered(k15_member_1(A,B)) ) )).
fof(fc60_partfun3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc60_pcs_0,axiom,( ! [A] : ( ( v3_orders_2(A) & l2_pcs_0(A) ) => ( v3_orders_2(k21_pcs_0(A)) & v12_pcs_0(k21_pcs_0(A)) ) ) )).
fof(fc60_valued_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc60_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc61_fomodel0,axiom,( ! [A] : ! [B] : ( v1_relat_1(A) => ( v1_relat_1(k5_relat_1(A,B)) & v4_relat_1(k5_relat_1(A,B),B) ) ) )).
fof(fc61_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k15_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) ) ) )).
fof(fc61_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k40_fomodel2(A)) ) => v1_xboole_0(k4_xboole_0(C,k42_fomodel4(A,B,C,D))) ) )).
fof(fc61_glib_003,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc61_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_xxreal_0(B) ) => v1_xboole_0(k16_member_1(A,B)) ) )).
fof(fc61_partfun3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc61_pcs_0,axiom,( ! [A] : ( ( v4_orders_2(A) & l2_pcs_0(A) ) => ( v4_orders_2(k21_pcs_0(A)) & v12_pcs_0(k21_pcs_0(A)) ) ) )).
fof(fc61_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => v1_xcmplx_0(k1_funct_1(A,B)) ) )).
fof(fc61_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc62_fomodel0,axiom,( ! [A] : ! [B] : ( v1_xboole_0(B) => v1_xboole_0(k13_fomodel0(A,B)) ) )).
fof(fc62_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) & v1_xboole_0(C) & m1_subset_1(D,k15_fomodel2(B,A)) ) => v10_fomodel2(k13_fomodel0(D,C),A,B,D) ) )).
fof(fc62_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k40_fomodel2(A)) ) => v1_zfmisc_1(k4_xboole_0(k42_fomodel4(A,B,C,D),C)) ) )).
fof(fc62_glib_003,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc62_member_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v2_membered(A) & v1_xxreal_0(B) ) => ~ v1_xboole_0(k16_member_1(A,B)) ) )).
fof(fc62_partfun3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc62_pcs_0,axiom,( ! [A] : ( ( v4_pcs_0(A) & l2_pcs_0(A) ) => ( v5_pcs_0(k21_pcs_0(A)) & v12_pcs_0(k21_pcs_0(A)) ) ) )).
fof(fc62_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_valued_0(A) ) => v1_xxreal_0(k1_funct_1(A,B)) ) )).
fof(fc62_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc63_fomodel0,axiom,( ! [A] : ! [B] : ( v1_xboole_0(B) => ( v1_relat_1(k13_fomodel0(A,B)) & v5_relat_1(k13_fomodel0(A,B),A) ) ) )).
fof(fc63_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(A) & ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) & m1_subset_1(C,k15_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) ) )).
fof(fc63_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k31_fomodel2(A)),B),C)),k10_finseq_1(B,C))) ) )).
fof(fc63_glib_003,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc63_member_1,axiom,( ! [A] : ! [B] : ( ( v2_membered(A) & v1_xxreal_0(B) ) => v2_membered(k16_member_1(A,B)) ) )).
fof(fc63_partfun3,axiom,( ! [A] : ! [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)) & v4_partfun3(k54_valued_1(B)) ) ) )).
fof(fc63_pcs_0,axiom,( ! [A] : ( ( v5_pcs_0(A) & l2_pcs_0(A) ) => ( v4_pcs_0(k21_pcs_0(A)) & v12_pcs_0(k21_pcs_0(A)) ) ) )).
fof(fc63_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) ) => v1_xreal_0(k1_funct_1(A,B)) ) )).
fof(fc63_valued_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc64_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(fc64_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) & m1_subset_1(C,k15_fomodel2(B,A)) & v10_fomodel2(D,A,B,C) ) => v11_fomodel2(k13_fomodel0(D,C),B,A,D) ) )).
fof(fc64_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v16_fomodel4(k24_fomodel4(A),A) ) )).
fof(fc64_glib_003,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc64_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_xcmplx_0(B) ) => v1_xboole_0(k17_member_1(A,B)) ) )).
fof(fc64_partfun3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc64_pcs_0,axiom,( ! [A] : ( ( v6_pcs_0(A) & l2_pcs_0(A) ) => ( v6_pcs_0(k21_pcs_0(A)) & v12_pcs_0(k21_pcs_0(A)) ) ) )).
fof(fc64_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v5_relat_1(A,k3_numbers) & v1_funct_1(A) ) => v1_rat_1(k1_funct_1(A,B)) ) )).
fof(fc64_valued_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc65_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(fc65_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v12_fomodel2(k13_fomodel0(A,k1_xboole_0),A) ) )).
fof(fc65_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v16_fomodel4(k25_fomodel4(A),A) ) )).
fof(fc65_glib_003,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc65_member_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_membered(A) & v1_xcmplx_0(B) ) => ~ v1_xboole_0(k17_member_1(A,B)) ) )).
fof(fc65_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) ) => v1_int_1(k1_funct_1(A,B)) ) )).
fof(fc65_valued_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc66_fomodel0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc66_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v16_fomodel4(k26_fomodel4(A),A) ) )).
fof(fc66_member_1,axiom,( ! [A] : ! [B] : ( ( v1_membered(A) & v1_xcmplx_0(B) ) => v1_membered(k17_member_1(A,B)) ) )).
fof(fc66_pcs_0,axiom,( ! [A] : ! [B] : ( ( l2_pcs_0(A) & l2_pcs_0(B) ) => v12_pcs_0(k22_pcs_0(A,B)) ) )).
fof(fc66_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v4_valued_0(A) ) => v7_ordinal1(k1_funct_1(A,B)) ) )).
fof(fc66_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc67_fomodel0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc67_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v16_fomodel4(k27_fomodel4(A),A) ) )).
fof(fc67_member_1,axiom,( ! [A] : ! [B] : ( ( v3_membered(A) & v1_xreal_0(B) ) => v3_membered(k17_member_1(A,B)) ) )).
fof(fc67_pcs_0,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_pcs_0(A) & ~ v2_struct_0(B) & l2_pcs_0(B) ) => ~ v2_struct_0(k22_pcs_0(A,B)) ) )).
fof(fc67_valued_0,axiom,( ! [A] : ! [B] : ( v1_xcmplx_0(B) => v1_valued_0(k2_funcop_1(A,B)) ) )).
fof(fc67_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc68_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc68_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) => v1_xboole_0(k5_xboole_0(k37_fomodel2(A,k42_fomodel1(A,k43_fomodel1(A,B),C)),C)) ) )).
fof(fc68_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v16_fomodel4(k28_fomodel4(A),A) ) )).
fof(fc68_member_1,axiom,( ! [A] : ! [B] : ( ( v4_membered(A) & v1_rat_1(B) ) => v4_membered(k17_member_1(A,B)) ) )).
fof(fc68_pcs_0,axiom,( ! [A] : ! [B] : ( ( v3_orders_2(A) & l2_pcs_0(A) & v3_orders_2(B) & l2_pcs_0(B) ) => v3_orders_2(k22_pcs_0(A,B)) ) )).
fof(fc68_valued_0,axiom,( ! [A] : ! [B] : ( v1_xxreal_0(B) => v2_valued_0(k2_funcop_1(A,B)) ) )).
fof(fc68_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc69_fomodel0,axiom,( ! [A] : ! [B] : ( 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))) ) ) )).
fof(fc69_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v16_fomodel4(k29_fomodel4(A),A) ) )).
fof(fc69_member_1,axiom,( ! [A] : ! [B] : ( ( v5_membered(A) & v1_int_1(B) ) => v5_membered(k17_member_1(A,B)) ) )).
fof(fc69_pcs_0,axiom,( ! [A] : ! [B] : ( ( v4_orders_2(A) & l2_pcs_0(A) & v4_orders_2(B) & l2_pcs_0(B) ) => v4_orders_2(k22_pcs_0(A,B)) ) )).
fof(fc69_valued_0,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => v3_valued_0(k2_funcop_1(A,B)) ) )).
fof(fc69_valued_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc6_abcmiz_0,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc6_abcmiz_1,axiom,( ~ v1_xboole_0(k17_abcmiz_1) )).
fof(fc6_abcmiz_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc6_abian,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) ) => v1_abian(k3_xcmplx_0(A,B)) ) )).
fof(fc6_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc6_afvect0,axiom,( ! [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) & 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)) ) ) )).
fof(fc6_algstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc6_algstr_1,axiom,( ~ v2_struct_0(k3_algstr_1) & v29_algstr_0(k3_algstr_1) )).
fof(fc6_algstr_4,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(fc6_altcat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc6_altcat_4,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc6_ami_3,axiom,( v1_extpro_1(k1_ami_3,k7_card_1(2)) & v3_extpro_1(k1_ami_3,k7_card_1(2)) )).
fof(fc6_ami_6,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(2),k1_ami_3) ) )).
fof(fc6_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ( v1_extpro_1(k4_amistd_1(A),A) & v3_amistd_1(k4_amistd_1(A),A) ) ) )).
fof(fc6_amistd_2,axiom,( ! [A] : ! [B] : ( ( ~ 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),k4_ordinal1) & 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) ) ) )).
fof(fc6_aofa_000,axiom,( ! [A] : ! [B] : v1_freealg(k2_zfmisc_1(A,B)) )).
fof(fc6_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( v1_relat_1(k9_aofa_a00(A,B,C,D,E,F,G,H)) & v1_funct_1(k9_aofa_a00(A,B,C,D,E,F,G,H)) & v3_card_1(k9_aofa_a00(A,B,C,D,E,F,G,H),8) & v1_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H)) ) )).
fof(fc6_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(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) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) & v4_aofa_a01(D,A,B,C) & l4_aofa_a00(D,A,B,C) & v4_msualg_1(E,A) & v4_msafree4(E,A,C) & v17_aofa_a00(E,A) & v20_aofa_a00(E,4,1,A) & l3_msualg_1(E,A) & v19_aofa_a00(F,A) & m1_subset_1(F,u1_struct_0(A)) & m1_subset_1(G,k13_aofa_a00(A,C,E,u4_aofa_a00(A,B,C,D))) & m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),F)) ) => v1_int_1(k15_aofa_a00(A,B,C,E,F,H,G)) ) )).
fof(fc6_armstrng,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc6_bagorder,axiom,( ! [A] : ( 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) ) ) )).
fof(fc6_binop_2,axiom,( v1_funct_1(k17_binop_2) & v1_funct_2(k17_binop_2,k2_zfmisc_1(k3_numbers,k3_numbers),k3_numbers) & v1_binop_1(k17_binop_2,k3_numbers) & v2_binop_1(k17_binop_2,k3_numbers) )).
fof(fc6_bor_cant,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k4_ordinal1,k9_setfam_1(A)) ) ) )).
fof(fc6_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc6_borsuk_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc6_borsuk_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v1_rat_1(A) ) => ( v1_xcmplx_0(k4_xcmplx_0(A)) & ~ v1_rat_1(k4_xcmplx_0(A)) ) ) )).
fof(fc6_borsuk_6,axiom,( 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) )).
fof(fc6_borsuk_7,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & ~ v3_xxreal_0(A) & v1_xreal_0(B) ) => ( 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)) ) ) )).
fof(fc6_c0sp1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc6_c0sp2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc6_card_1,axiom,( v1_card_1(k4_ordinal1) )).
fof(fc6_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ~ v1_xboole_0(k8_card_3(A)) & v4_funct_1(k8_card_3(A)) ) ) )).
fof(fc6_card_5,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc6_cardfin2,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k4_cardfin2(A,B)) ) )).
fof(fc6_catalg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc6_cayley,axiom,( ! [A] : ( v1_finset_1(A) => ( v8_struct_0(k2_cayley(A)) & v15_algstr_0(k2_cayley(A)) & v1_monoid_0(k2_cayley(A)) ) ) )).
fof(fc6_cc0sp1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc6_cc0sp2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc6_cfdiff_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc6_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => v1_group_1(k7_cfuncdom(A)) ) )).
fof(fc6_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => v3_cgames_1(k5_finseq_1(A)) ) )).
fof(fc6_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc6_circcomb,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc6_circtrm1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(fc6_classes2,axiom,( ! [A] : ( v1_ordinal1(A) => v1_ordinal1(k1_classes1(A)) ) )).
fof(fc6_clopban1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) ) ) )).
fof(fc6_clopban2,axiom,( ! [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) & 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)) ) ) )).
fof(fc6_clopban3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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,k4_ordinal1,u1_struct_0(A)) & v2_clopban3(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k2_series_1(k5_normsp_0(A,B))) & v1_funct_2(k2_series_1(k5_normsp_0(A,B)),k4_ordinal1,k1_numbers) & v1_seq_2(k2_series_1(k5_normsp_0(A,B))) ) ) )).
fof(fc6_closure1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc6_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v8_cohsp_1(A) ) => v3_cohsp_1(k9_xtuple_0(A)) ) )).
fof(fc6_compact1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_pre_topc(k1_compact1(A)) & v1_compts_1(k1_compact1(A)) ) ) )).
fof(fc6_compl_sp,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc6_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( v1_xreal_0(k9_complex1(A)) & ~ v3_xxreal_0(k9_complex1(A)) ) ) )).
fof(fc6_compos_0,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_compos_0(A) & m1_subset_1(B,A) ) => v1_finseq_1(k5_xtuple_0(B)) ) )).
fof(fc6_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_compos_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc6_comput_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => ( ~ 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(k4_ordinal1)) & 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)) ) ) )).
fof(fc6_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_funct_1(k30_valued_1(A)) & v1_funct_2(k30_valued_1(A),k4_ordinal1,k2_numbers) & v2_comseq_2(k30_valued_1(A)) ) ) )).
fof(fc6_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v1_comseq_3(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_funct_1(k2_series_1(A)) & v1_funct_2(k2_series_1(A),k4_ordinal1,k2_numbers) & v2_comseq_2(k2_series_1(A)) ) ) )).
fof(fc6_convfun1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc6_csspace4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc6_dickson,axiom,( ! [A] : ( ( 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(k4_yellow_1(k1_xboole_0,A)) & v1_orders_2(k4_yellow_1(k1_xboole_0,A)) ) ) )).
fof(fc6_dilworth,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(fc6_dist_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => v3_funct_1(k11_dist_1(A)) ) )).
fof(fc6_euclid,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc6_euclid_9,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) & v1_valued_0(B) ) => ( v1_relat_1(k35_valued_1(B)) & v1_funct_1(k35_valued_1(B)) & v3_card_1(k35_valued_1(B),A) & v1_valued_0(k35_valued_1(B)) ) ) )).
fof(fc6_exchsort,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(fc6_facirc_1,axiom,( ! [A] : ! [B] : ( ~ v1_facirc_1(A) => ~ v1_facirc_1(k3_xboole_0(A,B)) ) )).
fof(fc6_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc6_fcont_3,axiom,( ! [A] : ( v1_xreal_0(A) => v3_rcomp_1(k10_prob_1(A)) ) )).
fof(fc6_fib_num2,axiom,( ! [A] : ! [B] : ( v1_setfam_1(A) => v1_setfam_1(k3_xboole_0(A,B)) ) )).
fof(fc6_filter_2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc6_finseq_1,axiom,( ! [A] : ( v1_relat_1(k5_finseq_1(A)) & v1_funct_1(k5_finseq_1(A)) ) )).
fof(fc6_finseq_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc6_finseq_3,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_finset_1(B) ) => v1_finset_1(k4_finseq_2(A,B)) ) )).
fof(fc6_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : v3_card_1(k8_finseq_4(A,B,C,D,E),5) )).
fof(fc6_finseq_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_finseq_1(C,A) ) => ~ v1_xboole_0(k2_finseq_5(A,C,B)) ) )).
fof(fc6_finset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : v1_finset_1(k4_enumset1(A,B,C,D,E,F)) )).
fof(fc6_fomodel0,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & ~ v8_ordinal1(B) ) => v1_setfam_1(k4_finseq_2(B,A)) ) )).
fof(fc6_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ~ v1_xboole_0(k5_fomodel1(A)) ) )).
fof(fc6_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc6_fomodel3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc6_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k30_fomodel2(A))) & v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(k30_fomodel2(A))) ) => v1_fomodel4(k4_tarski(k4_subset_1(k30_fomodel2(A),C,D),B),A) ) )).
fof(fc6_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc6_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc6_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc6_funcsdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v2_struct_0(k12_funcsdom(A)) & v1_funcsdom(k12_funcsdom(A)) ) ) )).
fof(fc6_funct_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc6_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc6_funct_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc6_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v1_funct_7(k5_finseq_1(A)) ) )).
fof(fc6_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc6_gate_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_xboole_0(B) ) => v1_xboole_0(k3_gate_1(A,B)) ) )).
fof(fc6_glib_000,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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),k4_ordinal1) & 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)) ) ) )).
fof(fc6_glib_001,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(fc6_glib_004,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(fc6_gr_cy_1,axiom,( ! [A] : ( v7_ordinal1(A) => v6_membered(k6_card_1(A)) ) )).
fof(fc6_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc6_group_12,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc6_group_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc6_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc6_groupp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc6_hermitan,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc6_heyting3,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => ~ v1_xboole_0(k2_heyting3(A,B)) ) )).
fof(fc6_hilbert3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & m1_subset_1(B,k1_hilbert1) ) => ~ v1_xboole_0(k3_hilbert3(A,B)) ) )).
fof(fc6_index_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc6_int_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( ~ v2_struct_0(k9_int_3(A)) & v36_algstr_0(k9_int_3(A)) ) ) )).
fof(fc6_int_6,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc6_intpro_1,axiom,( v9_intpro_1(k12_intpro_1) )).
fof(fc6_isomichi,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc6_jordan,axiom,( ! [A] : ( 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))) ) )).
fof(fc6_jordan18,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => v4_pre_topc(k6_topreal1(A),k15_euclid(2)) ) )).
fof(fc6_jordan1e,axiom,( ! [A] : ! [B] : ( ( 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) ) => v4_topreal1(k2_jordan1e(A,B)) ) )).
fof(fc6_jordan23,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc6_jordan2c,axiom,( ! [A] : ( ( 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)) ) )).
fof(fc6_kurato_1,axiom,( v3_setfam_1(k4_kurato_1(k3_topmetr,k6_kurato_1),u1_struct_0(k3_topmetr)) )).
fof(fc6_lattice2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc6_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( ~ v2_struct_0(k7_lattice3(A)) & v1_orders_2(k7_lattice3(A)) ) ) )).
fof(fc6_lattice5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc6_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(fc6_lopban_1,axiom,( ! [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) & 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)) ) ) )).
fof(fc6_lopban_2,axiom,( ! [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) & 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)) ) ) )).
fof(fc6_lopban_3,axiom,( ! [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) & 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,k4_ordinal1,u1_struct_0(A)) & v2_lopban_3(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k2_series_1(k5_normsp_0(A,B))) & v1_funct_2(k2_series_1(k5_normsp_0(A,B)),k4_ordinal1,k1_numbers) & v1_seq_2(k2_series_1(k5_normsp_0(A,B))) ) ) )).
fof(fc6_lopclset,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc6_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( ~ v2_struct_0(k14_lpspacc1(A,B,C)) & v2_rlvect_1(k14_lpspacc1(A,B,C)) & v3_rlvect_1(k14_lpspacc1(A,B,C)) & v4_rlvect_1(k14_lpspacc1(A,B,C)) & v1_clvect_1(k14_lpspacc1(A,B,C)) & v2_clvect_1(k14_lpspacc1(A,B,C)) & v3_clvect_1(k14_lpspacc1(A,B,C)) & v4_clvect_1(k14_lpspacc1(A,B,C)) & v5_clvect_1(k14_lpspacc1(A,B,C)) ) ) )).
fof(fc6_lpspace1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_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)) ) ) )).
fof(fc6_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v2_xxreal_0(D) & v1_xreal_0(D) ) => ( ~ v2_struct_0(k10_lpspace2(A,B,C,D)) & v1_rlvect_1(k10_lpspace2(A,B,C,D)) ) ) )).
fof(fc6_ltlaxio3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) ) => ~ v1_xboole_0(k5_ltlaxio3(A)) ) )).
fof(fc6_ltlaxio4,axiom,( ! [A] : ( ( ~ v2_ltlaxio3(A) & m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) ) => ( ~ v1_xboole_0(k9_ltlaxio4(A)) & v1_finset_1(k9_ltlaxio4(A)) ) ) )).
fof(fc6_lukasi_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc6_margrel1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc6_matroid0,axiom,( ! [A] : ( v1_pre_topc(k2_matroid0(A)) & ~ v3_pencil_1(k2_matroid0(A)) & v1_matroid0(k2_matroid0(A)) ) )).
fof(fc6_matrtop1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc6_matrtop3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc6_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => v2_rcomp_1(k5_measure6(A)) ) )).
fof(fc6_member_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_membered(A) ) => ( ~ v1_xboole_0(k5_member_1(A)) & v1_membered(k5_member_1(A)) ) ) )).
fof(fc6_membered,axiom,( v6_membered(k4_ordinal1) )).
fof(fc6_mesfunc7,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => v2_valued_0(k5_finseq_1(A)) ) )).
fof(fc6_metric_1,axiom,( v1_metric_1(k7_metric_1) & v6_metric_1(k7_metric_1) & v7_metric_1(k7_metric_1) & v8_metric_1(k7_metric_1) & v9_metric_1(k7_metric_1) )).
fof(fc6_metrizts,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc6_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( v2_pre_topc(k4_mfold_2(A)) & v2_mfold_1(k4_mfold_2(A),A) ) ) )).
fof(fc6_mmlquer2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ( v4_relat_2(k3_mmlquer2(A,B)) & v8_relat_2(k3_mmlquer2(A,B)) & v1_mmlquer2(k3_mmlquer2(A,B),A) ) ) )).
fof(fc6_mmlquery,axiom,( ! [A] : ! [B] : ( ( v3_mmlquery(A) & l1_mmlquery(A) & m1_subset_1(B,u1_struct_0(A)) ) => v1_finset_1(k30_mmlquery(A,B)) ) )).
fof(fc6_mod_2,axiom,( v13_algstr_0(k18_mod_2) & v36_algstr_0(k18_mod_2) & v3_rlvect_1(k18_mod_2) & v4_rlvect_1(k18_mod_2) )).
fof(fc6_mod_4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc6_modelc_1,axiom,( ! [A] : ! [B] : ( ( v1_modelc_1(A) & m1_finseq_1(A,k4_ordinal1) & v1_modelc_1(B) & m1_finseq_1(B,k4_ordinal1) ) => v1_modelc_1(k11_modelc_1(A,B)) ) )).
fof(fc6_modelc_2,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & v1_modelc_2(B) & m1_finseq_1(B,k4_ordinal1) ) => v1_modelc_2(k7_modelc_2(A,B)) ) )).
fof(fc6_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( v1_relat_1(k5_moebius1(A)) & v4_relat_1(k5_moebius1(A),k8_newton) & v1_funct_1(k5_moebius1(A)) & v1_partfun1(k5_moebius1(A),k8_newton) & v4_valued_0(k5_moebius1(A)) & v2_pre_poly(k5_moebius1(A)) ) ) )).
fof(fc6_msafree,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc6_msafree1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) => ~ v1_xboole_0(k3_msualg_1(A,B,C)) ) )).
fof(fc6_msafree4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_finset_1(A) & v1_finseq_1(A) & v6_trees_3(A) ) => ( v1_relat_1(k4_trees_4(B,A)) & v1_funct_1(k4_trees_4(B,A)) & v1_finset_1(k4_trees_4(B,A)) & v3_trees_2(k4_trees_4(B,A)) ) ) )).
fof(fc6_mssubfam,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc6_msualg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc6_msualg_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc6_mycielsk,axiom,( ! [A] : ( ( v2_struct_0(A) & l1_orders_2(A) ) => ( v1_xboole_0(k3_mycielsk(A)) & v7_ordinal1(k3_mycielsk(A)) ) ) )).
fof(fc6_nat_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => v7_ordinal1(k4_xxreal_0(A,B)) ) )).
fof(fc6_nat_3,axiom,( ! [A] : ! [B] : ( ( 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,k5_numbers))) ) )).
fof(fc6_nat_lat,axiom,( ~ v2_struct_0(k10_nat_lat) & v3_lattices(k10_nat_lat) )).
fof(fc6_neckla_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc6_necklace,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_orders_2(k4_necklace(A)) & v3_necklace(k4_necklace(A)) ) ) )).
fof(fc6_newton,axiom,( ! [A] : ( v7_ordinal1(A) => v1_xreal_0(k2_newton(A)) ) )).
fof(fc6_nfcont_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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) ) ) )).
fof(fc6_nfcont_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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) ) ) )).
fof(fc6_normform,axiom,( ! [A] : ( v3_lattices(k12_normform(A)) & v11_lattices(k12_normform(A)) & v13_lattices(k12_normform(A)) ) )).
fof(fc6_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ( ~ v2_struct_0(k4_normsp_2(A)) & v3_frechet(k4_normsp_2(A)) & v5_rltopsp1(k4_normsp_2(A)) ) ) )).
fof(fc6_numbers,axiom,( ~ v1_finset_1(k4_numbers) )).
fof(fc6_openlatt,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc6_oposet_1,axiom,( v3_necklace(k2_oposet_1) & v3_qmax_1(k2_oposet_1) )).
fof(fc6_ordeq_01,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_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) & v3_lopban_1(B) & l1_normsp_1(B) ) => ( ~ v2_struct_0(k5_ordeq_01(A,B)) & v1_normsp_1(k5_ordeq_01(A,B)) & v3_lopban_1(k5_ordeq_01(A,B)) ) ) )).
fof(fc6_orders_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc6_orders_3,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc6_ordinal1,axiom,( ~ v1_xboole_0(k4_ordinal1) & v3_ordinal1(k4_ordinal1) )).
fof(fc6_ordinal5,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => ( v3_ordinal1(k12_ordinal2(A,B)) & v7_ordinal1(k12_ordinal2(A,B)) ) ) )).
fof(fc6_ordinal6,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc6_osafree,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) )).
fof(fc6_osalg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc6_partfun3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => v1_xboole_0(k8_relat_1(A,k1_tarski(k5_numbers))) ) )).
fof(fc6_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc6_polyeq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) & v1_xcmplx_0(D) & v1_xcmplx_0(E) ) => v1_xcmplx_0(k4_polyeq_1(A,B,C,D,E)) ) )).
fof(fc6_polynom1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,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,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)) & v1_polynom1(k10_polynom1(A,B,C,D),B) ) ) )).
fof(fc6_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ( v1_funct_1(k9_polynom3(A)) & v1_funct_2(k9_polynom3(A),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k9_polynom3(A),A) ) ) )).
fof(fc6_polynom5,axiom,( v36_algstr_0(k1_complfld) & v2_polynom5(k1_complfld) )).
fof(fc6_poset_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc6_pralg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc6_pre_circ,axiom,( ! [A] : ( 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)) ) )).
fof(fc6_pre_poly,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & 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)) ) ) )).
fof(fc6_pre_topc,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(fc6_prvect_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v8_algstr_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(B) & v8_algstr_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(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)) & v13_algstr_0(k4_prvect_3(A,B)) & v2_rlvect_1(k4_prvect_3(A,B)) & v3_rlvect_1(k4_prvect_3(A,B)) & v4_rlvect_1(k4_prvect_3(A,B)) ) ) )).
fof(fc6_pscomp_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc6_pythtrip,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc6_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ~ v1_xboole_0(k6_qc_lang1(A)) ) )).
fof(fc6_quatern2,axiom,( ~ v6_struct_0(k15_quatern2) & v13_algstr_0(k15_quatern2) & v34_algstr_0(k15_quatern2) & v36_algstr_0(k15_quatern2) & v2_rlvect_1(k15_quatern2) & v3_rlvect_1(k15_quatern2) & v4_rlvect_1(k15_quatern2) & v3_group_1(k15_quatern2) & v3_vectsp_1(k15_quatern2) & v5_vectsp_1(k15_quatern2) & v6_vectsp_1(k15_quatern2) )).
fof(fc6_quaterni,axiom,( ! [A] : ! [B] : ( ( v1_quaterni(A) & v1_quaterni(B) ) => v1_quaterni(k7_quaterni(A,B)) ) )).
fof(fc6_quofield,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc6_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ( v1_xcmplx_0(k5_xcmplx_0(A)) & v1_rat_1(k5_xcmplx_0(A)) ) ) )).
fof(fc6_ratfunc1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l5_algstr_0(A) ) => ( v1_funct_1(k10_polynom3(A)) & v1_funct_2(k10_polynom3(A),k4_ordinal1,u1_struct_0(A)) & v2_ratfunc1(k10_polynom3(A),A) ) ) )).
fof(fc6_rcomp_3,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => v5_xxreal_2(k4_xxreal_1(A,B)) ) )).
fof(fc6_real_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => v8_ordinal1(k7_xcmplx_0(A,k5_numbers)) ) )).
fof(fc6_real_ns1,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc6_relat_1,axiom,( ! [A] : ! [B] : v1_relat_1(k2_zfmisc_1(A,B)) )).
fof(fc6_relat_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v2_relat_2(A) & v1_relat_1(B) & v2_relat_2(B) ) => v2_relat_2(k2_xboole_0(A,B)) ) )).
fof(fc6_reloc,axiom,( v1_extpro_1(k1_ami_3,k7_card_1(2)) & v2_amistd_5(k1_ami_3,k7_card_1(2)) )).
fof(fc6_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_relat_1(C) ) => v5_relat_1(k4_xboole_0(B,C),A) ) )).
fof(fc6_revrot_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc6_rewrite2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v5_ordinal1(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)) ) ) )).
fof(fc6_rfunct_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc6_ring_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc6_ringcat1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc6_rlaffin1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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_xreal_0(C) ) => v1_rlaffin1(k1_convex1(A,B,C),A) ) )).
fof(fc6_rlaffin3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(k15_euclid(A),B,C),k15_euclid(A)) ) )).
fof(fc6_rltopsp1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc6_robbins4,axiom,( v10_lattices(k2_robbins4) & v4_robbins1(k2_robbins4) )).
fof(fc6_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_roughs_1(A) & l1_orders_2(A) ) => v8_relat_2(u1_orders_2(A)) ) )).
fof(fc6_rsspace4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc6_rvsum_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc6_scm_halt,axiom,( ! [A] : ! [B] : ( ( 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc6_scm_inst,axiom,( ~ v1_xboole_0(k3_scm_inst) & v3_compos_0(k3_scm_inst) )).
fof(fc6_scmfsa10,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc6_scmfsa6c,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc6_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc6_scmfsa_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc6_scmfsa_i,axiom,( ~ v1_xboole_0(k2_scmfsa_i) & v5_compos_0(k2_scmfsa_i) )).
fof(fc6_scmfsa_m,axiom,( v1_ami_2(k4_scmfsa_2(k5_numbers)) & v1_scmfsa_m(k4_scmfsa_2(k5_numbers)) )).
fof(fc6_scmpds_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc6_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) & v2_compos_1(A,k1_scmpds_2) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & 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_relat_1(k2_scmpds_6(C,D,A,B)) & v4_relat_1(k2_scmpds_6(C,D,A,B),k4_ordinal1) & v5_relat_1(k2_scmpds_6(C,D,A,B),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k2_scmpds_6(C,D,A,B)) & 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) ) ) )).
fof(fc6_scmpds_i,axiom,( v5_compos_0(k1_scmpds_i) )).
fof(fc6_scmring2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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),k7_card_1(2),k1_scmring2(A)) ) )).
fof(fc6_scmring3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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),k7_card_1(2),k1_scmring2(A)) ) )).
fof(fc6_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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)) ) ) )).
fof(fc6_scmyciel,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v3_scmyciel(B,A) & v3_scmyciel(C,A) ) => v3_scmyciel(k2_xboole_0(B,C),A) ) )).
fof(fc6_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_funct_1(k54_valued_1(A)) & v1_funct_2(k54_valued_1(A),k4_ordinal1,k1_numbers) & v2_comseq_2(k54_valued_1(A)) ) ) )).
fof(fc6_setfam_1,axiom,( ! [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_setfam_1(k3_enumset1(A,B,C,D,E)) ) )).
fof(fc6_sfmastr1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => v1_sfmastr1(k11_scmfsa_2(A)) ) )).
fof(fc6_simplex0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v1_xboole_0(k1_simplex0(A)) & v1_classes1(k1_simplex0(A)) ) ) )).
fof(fc6_simplex1,axiom,( ! [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) & 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) ) ) )).
fof(fc6_sin_cos,axiom,( v1_funct_1(k16_sin_cos) & v1_funct_2(k16_sin_cos,k1_numbers,k1_numbers) & v1_fcont_1(k16_sin_cos) )).
fof(fc6_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k16_sin_cos,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos))) & v2_funct_1(k5_relat_1(k16_sin_cos,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos))) )).
fof(fc6_sin_cos9,axiom,( v1_funct_1(k2_sin_cos9) & v2_funct_1(k2_sin_cos9) )).
fof(fc6_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k6_sincos10(A)) ) )).
fof(fc6_sppol_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc6_sprect_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc6_stacks_1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc6_struct_0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & l1_struct_0(A) ) => ~ v1_zfmisc_1(u1_struct_0(A)) ) )).
fof(fc6_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ~ v1_xboole_0(k5_enumset1(A,B,C,D,E,F,G)) )).
fof(fc6_substut1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k16_substut1(A)) ) => v5_substut1(k20_substut1(A,B),A) ) )).
fof(fc6_tex_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => ~ v2_struct_0(k3_tex_1(A,B)) ) )).
fof(fc6_tex_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc6_topalg_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc6_topalg_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc6_topalg_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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)) ) ) )).
fof(fc6_topdim_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc6_topgen_4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc6_topgrp_1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc6_topmetr,axiom,( v1_metric_1(k7_metric_1) & v3_topmetr(k7_metric_1) )).
fof(fc6_topreal1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ~ v1_xboole_0(k6_topreal1(A)) ) )).
fof(fc6_topreal6,axiom,( ! [A] : ( ( v4_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => v4_xxreal_2(k5_measure6(A)) ) )).
fof(fc6_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc6_topreala,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v2_xxreal_0(B) & v1_xreal_0(B) ) => ~ v1_xboole_0(k2_xxreal_1(k6_xcmplx_0(A,B),A)) ) )).
fof(fc6_toprealb,axiom,( v1_funct_1(k1_sin_cos6) & v1_fcont_1(k1_sin_cos6) )).
fof(fc6_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) & v1_xcmplx_0(C) ) => ( v1_relat_1(k1_funct_7(A,B,C)) & v1_funct_1(k1_funct_7(A,B,C)) & v1_valued_0(k1_funct_7(A,B,C)) ) ) )).
fof(fc6_tops_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc6_trees_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc6_trees_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc6_trees_9,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc6_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_valued_0(A) ) => v6_membered(k10_xtuple_0(A)) ) )).
fof(fc6_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc6_valued_2,axiom,( ! [A] : v3_valued_2(k6_valued_2(A)) )).
fof(fc6_vectmetr,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( ~ v2_struct_0(k5_vectmetr(A)) & v15_algstr_0(k5_vectmetr(A)) ) ) )).
fof(fc6_vectsp_1,axiom,( v36_algstr_0(k2_vectsp_1) & v4_vectsp_1(k2_vectsp_1) )).
fof(fc6_waybel10,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc6_waybel11,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc6_waybel17,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc6_waybel18,axiom,( v1_pre_topc(k9_waybel18) & v6_pre_topc(k9_waybel18) )).
fof(fc6_waybel23,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc6_waybel24,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc6_waybel25,axiom,( ! [A] : ( l1_pre_topc(A) => ( v3_orders_2(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) ) ) )).
fof(fc6_waybel27,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc6_waybel30,axiom,( ! [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) & l1_waybel_9(A) ) => ( ~ v7_struct_0(k1_yellow_1(k2_waybel19(A))) & v1_orders_2(k1_yellow_1(k2_waybel19(A))) & v3_lattice3(k1_yellow_1(k2_waybel19(A))) ) ) )).
fof(fc6_waybel32,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc6_waybel34,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc6_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc6_waybel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(fc6_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc6_waybel_3,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc6_waybel_4,axiom,( ! [A] : ( ( 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(k1_yellow_1(k3_waybel_4(A))) & v2_yellow_0(k1_yellow_1(k3_waybel_4(A))) ) ) )).
fof(fc6_waybel_8,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(fc6_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc6_wellord2,axiom,( v1_relat_1(k1_wellord2(k1_xboole_0)) & v1_xboole_0(k1_wellord2(k1_xboole_0)) )).
fof(fc6_xboolean,axiom,( ! [A] : ! [B] : ( ( v1_xboolean(A) & v1_xboolean(B) ) => v1_xboolean(k7_xboolean(A,B)) ) )).
fof(fc6_xcmplx_0,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & v1_xcmplx_0(A) ) => ( ~ v8_ordinal1(k4_xcmplx_0(A)) & v1_xcmplx_0(k4_xcmplx_0(A)) ) ) )).
fof(fc6_xreal_0,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => v1_xreal_0(k3_xcmplx_0(A,B)) ) )).
fof(fc6_xtuple_0,axiom,( ! [A] : ( v1_xboole_0(A) => v1_xboole_0(k11_xtuple_0(A)) ) )).
fof(fc6_xxreal_0,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => v1_xxreal_0(k4_xxreal_0(A,B)) ) )).
fof(fc6_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => v1_xboole_0(k2_xxreal_1(A,A)) ) )).
fof(fc6_xxreal_2,axiom,( ! [A] : ( ( v6_membered(A) & v1_xxreal_2(A) ) => ( v1_xxreal_0(k2_xxreal_2(A)) & v7_ordinal1(k2_xxreal_2(A)) ) ) )).
fof(fc6_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc6_yellow10,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc6_yellow14,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(fc6_yellow19,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) & ~ v1_xboole_0(B) & v2_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v3_waybel_7(B,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_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) ) ) )).
fof(fc6_yellow_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v2_struct_0(k1_yellow_1(A)) & v1_orders_2(k1_yellow_1(A)) ) ) )).
fof(fc6_yellow_2,axiom,( ! [A] : ( ( 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(k1_yellow_1(k7_waybel_0(A))) & v3_lattice3(k1_yellow_1(k7_waybel_0(A))) ) ) )).
fof(fc6_yellow_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc6_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc6_yellow_6,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc6_yellow_7,axiom,( ! [A] : ( ( v1_lattice3(A) & l1_orders_2(A) ) => ( v1_orders_2(k7_lattice3(A)) & v2_lattice3(k7_lattice3(A)) ) ) )).
fof(fc6_yellow_9,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc6_zf_lang,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_zf_lang) & v1_zf_lang(B) & m1_finseq_1(B,k4_ordinal1) ) => v1_zf_lang(k8_zf_lang(A,B)) ) )).
fof(fc6_zmodul01,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(fc6_zmodul02,axiom,( ! [A] : ( ( ~ 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_algstr_0(k31_zmodul02(A)) & v2_rlvect_1(k31_zmodul02(A)) & v3_rlvect_1(k31_zmodul02(A)) & v4_rlvect_1(k31_zmodul02(A)) & v2_zmodul01(k31_zmodul02(A)) & v3_zmodul01(k31_zmodul02(A)) & v4_zmodul01(k31_zmodul02(A)) & v5_zmodul01(k31_zmodul02(A)) ) ) )).
fof(fc70_fomodel0,axiom,( ! [A] : ! [B] : ( ( v4_funct_1(A) & v4_funct_1(B) ) => v4_funct_1(k2_xboole_0(A,B)) ) )).
fof(fc70_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v16_fomodel4(k30_fomodel4(A),A) ) )).
fof(fc70_member_1,axiom,( ! [A] : ! [B] : ( ( v6_membered(A) & v7_ordinal1(B) ) => v6_membered(k17_member_1(A,B)) ) )).
fof(fc70_partfun3,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc70_pcs_0,axiom,( ! [A] : ! [B] : ( ( l2_pcs_0(A) & v4_pcs_0(B) & l2_pcs_0(B) ) => v4_pcs_0(k22_pcs_0(A,B)) ) )).
fof(fc70_valued_0,axiom,( ! [A] : ! [B] : ( v1_rat_1(B) => v5_relat_1(k2_funcop_1(A,B),k3_numbers) ) )).
fof(fc70_valued_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc71_fomodel0,axiom,( ! [A] : ( ( v4_funct_1(A) & v1_finset_1(A) & v5_finset_1(A) ) => v1_finset_1(k21_fomodel0(A)) ) )).
fof(fc71_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v16_fomodel4(k31_fomodel4(A),A) ) )).
fof(fc71_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_xxreal_0(B) ) => v1_xboole_0(k18_member_1(A,B)) ) )).
fof(fc71_partfun3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc71_pcs_0,axiom,( ! [A] : ! [B] : ( ( v4_pcs_0(A) & l2_pcs_0(A) & l2_pcs_0(B) ) => v4_pcs_0(k22_pcs_0(A,B)) ) )).
fof(fc71_valued_0,axiom,( ! [A] : ! [B] : ( v1_int_1(B) => v5_relat_1(k2_funcop_1(A,B),k4_numbers) ) )).
fof(fc71_valued_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc72_fomodel0,axiom,( ! [A] : ( ( v1_finset_1(A) & v3_finseq_1(A) ) => v1_finset_1(k21_fomodel0(A)) ) )).
fof(fc72_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v16_fomodel4(k32_fomodel4(A),A) ) )).
fof(fc72_member_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v2_membered(A) & v1_xxreal_0(B) ) => ~ v1_xboole_0(k18_member_1(A,B)) ) )).
fof(fc72_partfun3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc72_pcs_0,axiom,( ! [A] : ! [B] : ( ( v6_pcs_0(A) & l2_pcs_0(A) & v6_pcs_0(B) & l2_pcs_0(B) ) => v6_pcs_0(k22_pcs_0(A,B)) ) )).
fof(fc72_valued_0,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => v4_valued_0(k2_funcop_1(A,B)) ) )).
fof(fc72_valued_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc73_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v1_xboole_0(k5_xboole_0(k21_fomodel0(k1_tarski(A)),k10_xtuple_0(A))) ) )).
fof(fc73_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v16_fomodel4(k33_fomodel4(A),A) ) )).
fof(fc73_glib_003,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc73_member_1,axiom,( ! [A] : ! [B] : ( ( v2_membered(A) & v1_xxreal_0(B) ) => v2_membered(k18_member_1(A,B)) ) )).
fof(fc73_valued_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc73_valued_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc74_fomodel0,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & v1_xcmplx_0(A) ) => ( v1_xxreal_0(k9_complex1(A)) & v2_xxreal_0(k9_complex1(A)) ) ) )).
fof(fc74_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v16_fomodel4(k34_fomodel4(A),A) ) )).
fof(fc74_glib_003,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc74_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_xcmplx_0(B) ) => v1_xboole_0(k19_member_1(A,B)) ) )).
fof(fc74_pcs_0,axiom,( ! [A] : ! [B] : ( ( l2_pcs_0(A) & l2_pcs_0(B) ) => v12_pcs_0(k23_pcs_0(A,B)) ) )).
fof(fc74_valued_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc74_valued_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc75_fomodel0,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_setfam_1(A))) => v1_xboole_0(k4_xboole_0(k5_setfam_1(A,B),A)) ) )).
fof(fc75_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v16_fomodel4(k35_fomodel4(A),A) ) )).
fof(fc75_member_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_membered(A) & v1_xcmplx_0(B) ) => ~ v1_xboole_0(k19_member_1(A,B)) ) )).
fof(fc75_pcs_0,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_pcs_0(A) & ~ v2_struct_0(B) & l2_pcs_0(B) ) => ~ v2_struct_0(k23_pcs_0(A,B)) ) )).
fof(fc75_valued_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc75_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc76_fomodel0,axiom,( ! [A] : ! [B] : v1_xboole_0(k5_xboole_0(k2_xboole_0(k6_subset_1(A,B),k3_xboole_0(A,B)),A)) )).
fof(fc76_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v16_fomodel4(B,A) & m1_subset_1(B,k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A)))) ) => v15_fomodel4(k1_tarski(B),A) ) )).
fof(fc76_member_1,axiom,( ! [A] : ! [B] : ( ( v1_membered(A) & v1_xcmplx_0(B) ) => v1_membered(k19_member_1(A,B)) ) )).
fof(fc76_valued_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc76_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc77_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : v1_xboole_0(k5_xboole_0(k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)),k3_xboole_0(A,k2_xboole_0(B,C)))) )).
fof(fc77_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v15_fomodel4(k39_fomodel4(A),A) ) )).
fof(fc77_glib_003,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_003(A) & v9_glib_003(A) & v1_xreal_0(C) ) => ( v1_relat_1(k12_glib_003(A,B,C)) & v4_relat_1(k12_glib_003(A,B,C),k4_ordinal1) & 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)) ) ) )).
fof(fc77_member_1,axiom,( ! [A] : ! [B] : ( ( v3_membered(A) & v1_xreal_0(B) ) => v3_membered(k19_member_1(A,B)) ) )).
fof(fc77_valued_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc77_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc78_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : v1_xboole_0(k5_xboole_0(k7_subset_1(A,k6_subset_1(A,B),C),k6_subset_1(A,k2_xboole_0(B,C)))) )).
fof(fc78_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v6_fomodel4(k36_fomodel4(A),A) ) )).
fof(fc78_glib_003,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc78_member_1,axiom,( ! [A] : ! [B] : ( ( v4_membered(A) & v1_rat_1(B) ) => v4_membered(k19_member_1(A,B)) ) )).
fof(fc78_valued_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc78_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc79_fomodel0,axiom,( ! [A] : ! [B] : ( ( v4_funct_1(A) & v4_funct_1(B) ) => v1_xboole_0(k5_xboole_0(k2_xboole_0(k21_fomodel0(A),k21_fomodel0(B)),k21_fomodel0(k2_xboole_0(A,B)))) ) )).
fof(fc79_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v3_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))) ) => v5_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))),k36_fomodel4(A)),k1_tarski(k4_tarski(B,k35_fomodel2(A,k35_fomodel2(A,C))))) ) )).
fof(fc79_glib_003,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc79_member_1,axiom,( ! [A] : ! [B] : ( ( v5_membered(A) & v1_int_1(B) ) => v5_membered(k19_member_1(A,B)) ) )).
fof(fc79_valued_0,axiom,( ! [A] : ! [B] : ( v1_xcmplx_0(B) => v1_valued_0(k16_funcop_1(A,B)) ) )).
fof(fc79_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc7_abcmiz_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc7_abcmiz_1,axiom,( ~ v1_xboole_0(k18_abcmiz_1) )).
fof(fc7_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => v5_abcmiz_a(k15_abcmiz_1(A),A) ) )).
fof(fc7_abian,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) ) => v1_abian(k3_xcmplx_0(B,A)) ) )).
fof(fc7_afinsq_1,axiom,( ! [A] : ( v1_relat_1(k3_afinsq_1(A)) & v1_funct_1(k3_afinsq_1(A)) ) )).
fof(fc7_algstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc7_algstr_1,axiom,( v29_algstr_0(k3_algstr_1) & v4_vectsp_1(k3_algstr_1) )).
fof(fc7_algstr_4,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc7_altcat_4,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc7_ami_6,axiom,( ! [A] : ! [B] : ( ( 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(k7_card_1(2),k1_ami_3,k2_ami_3(A,B))) ) )).
fof(fc7_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ( v1_extpro_1(k4_amistd_1(A),A) & v3_extpro_1(k4_amistd_1(A),A) ) ) )).
fof(fc7_amistd_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(fc7_aofa_000,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc7_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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_aofa_a00(D,A,A,B,C) ) => ( v1_relat_1(k1_funct_1(k1_funct_1(D,E),F)) & v1_funct_1(k1_funct_1(k1_funct_1(D,E),F)) ) ) )).
fof(fc7_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(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) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) & v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) & v19_aofa_a00(E,A) & m1_subset_1(E,u1_struct_0(A)) & m2_pboole(F,u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,D)) & m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),E)) ) => v1_int_1(k15_aofa_a00(A,B,C,D,E,G,F)) ) )).
fof(fc7_bhsp_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & v2_bhsp_3(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v2_bhsp_3(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k2_normsp_1(A,B,C)) & v1_funct_2(k2_normsp_1(A,B,C),k4_ordinal1,u1_struct_0(A)) & v2_bhsp_3(k2_normsp_1(A,B,C),A) ) ) )).
fof(fc7_binop_2,axiom,( v1_funct_1(k20_binop_2) & v1_funct_2(k20_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & v1_binop_1(k20_binop_2,k4_numbers) & v2_binop_1(k20_binop_2,k4_numbers) )).
fof(fc7_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ~ v1_xboole_0(k10_borsuk_1(A)) ) )).
fof(fc7_borsuk_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc7_borsuk_5,axiom,( ! [A] : ! [B] : ( ( v1_rat_1(A) & v1_xreal_0(B) & ~ v1_rat_1(B) ) => ~ v1_rat_1(k6_xcmplx_0(A,B)) ) )).
fof(fc7_borsuk_6,axiom,( 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) )).
fof(fc7_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ v8_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)) ) ) )).
fof(fc7_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => v3_lopban_1(k11_c0sp1(A)) ) )).
fof(fc7_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => v1_group_1(k5_c0sp2(A)) ) )).
fof(fc7_card_1,axiom,( v2_card_1(k4_ordinal1) )).
fof(fc7_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v2_card_3(k1_tarski(A)) ) )).
fof(fc7_card_5,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ( ~ v1_finset_1(k2_card_1(A)) & v1_card_1(k2_card_1(A)) ) ) )).
fof(fc7_catalg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc7_cayldick,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( v3_membered(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))) & 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_funct_1(H) & v1_funct_2(H,A,A) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( v3_topmetr(g1_cayldick(A,C,B,D,E,F,G,H)) & v1_cayldick(g1_cayldick(A,C,B,D,E,F,G,H)) ) ) )).
fof(fc7_cayley,axiom,( v7_struct_0(k2_cayley(k1_xboole_0)) & v15_algstr_0(k2_cayley(k1_xboole_0)) & v1_monoid_0(k2_cayley(k1_xboole_0)) )).
fof(fc7_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => v3_clopban1(k7_cc0sp1(A)) ) )).
fof(fc7_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => v1_group_1(k5_cc0sp2(A)) ) )).
fof(fc7_cfdiff_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc7_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v2_struct_0(k8_cfuncdom(A)) & v1_cfuncdom(k8_cfuncdom(A)) ) ) )).
fof(fc7_cgames_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc7_circcmb3,axiom,( ~ v1_facirc_1(k4_ordinal1) )).
fof(fc7_circcomb,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc7_circtrm1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc7_classes2,axiom,( ! [A] : ( v3_ordinal1(A) => ( ~ v1_xboole_0(k16_classes2(A)) & v1_classes2(k16_classes2(A)) ) ) )).
fof(fc7_clopban1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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)) ) )).
fof(fc7_clopban2,axiom,( ~ v2_struct_0(k3_csspace3) & v3_clopban1(k3_csspace3) )).
fof(fc7_closure1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc7_closure2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc7_coh_sp,axiom,( ! [A] : ~ v1_xboole_0(k14_coh_sp(A)) )).
fof(fc7_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v9_cohsp_1(A) ) => v2_finsub_1(k9_xtuple_0(A)) ) )).
fof(fc7_compos_0,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_compos_0(A) & m1_subset_1(B,A) ) => v7_ordinal1(k4_xtuple_0(B)) ) )).
fof(fc7_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_compos_1(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc7_comput_1,axiom,( ! [A] : ( ~ v1_xboole_0(k2_comput_1(A)) & v4_funct_1(k2_comput_1(A)) ) )).
fof(fc7_comseq_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & v2_comseq_2(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_funct_1(k45_valued_1(A,B)) & v1_funct_2(k45_valued_1(A,B),k4_ordinal1,k2_numbers) & v2_comseq_2(k45_valued_1(A,B)) ) ) )).
fof(fc7_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_3(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_funct_1(k54_valued_1(A)) & v1_funct_2(k54_valued_1(A),k4_ordinal1,k1_numbers) & v1_series_1(k54_valued_1(A)) ) ) )).
fof(fc7_convfun1,axiom,( ~ 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) )).
fof(fc7_csspace4,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) )).
fof(fc7_dickson,axiom,( ! [A] : ( ( 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(k4_yellow_1(k1_xboole_0,A)) & v5_orders_2(k4_yellow_1(k1_xboole_0,A)) ) ) )).
fof(fc7_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => v2_dilworth(k5_dilworth(A),A) ) )).
fof(fc7_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ( v2_monoid_0(k15_euclid(A)) & v5_rltopsp1(k15_euclid(A)) ) ) )).
fof(fc7_euclid_7,axiom,( v1_xboole_0(k8_euclid_7(k5_numbers)) )).
fof(fc7_euclid_9,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) & v1_valued_0(B) ) => ( v1_relat_1(k39_valued_1(B)) & v1_funct_1(k39_valued_1(B)) & v3_card_1(k39_valued_1(B),A) ) ) )).
fof(fc7_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) ) => v4_relat_1(k9_funct_7(B,C,D),A) ) )).
fof(fc7_facirc_1,axiom,( ! [A] : ! [B] : ( ~ v1_facirc_1(A) => ~ v1_facirc_1(k3_xboole_0(B,A)) ) )).
fof(fc7_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc7_fib_num2,axiom,( ! [A] : ! [B] : ( v1_setfam_1(A) => v1_setfam_1(k3_xboole_0(B,A)) ) )).
fof(fc7_filter_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc7_finseq_1,axiom,( ! [A] : v1_finseq_1(k5_finseq_1(A)) )).
fof(fc7_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_relat_1(k2_finseq_2(A,k5_numbers)) & v3_relat_1(k2_finseq_2(A,k5_numbers)) & v1_funct_1(k2_finseq_2(A,k5_numbers)) & v1_finseq_1(k2_finseq_2(A,k5_numbers)) ) ) )).
fof(fc7_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc7_finseq_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_relat_1(k3_finseq_5(A)) & v1_xboole_0(k3_finseq_5(A)) & v1_funct_1(k3_finseq_5(A)) & v1_finseq_1(k3_finseq_5(A)) ) ) )).
fof(fc7_finset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : v1_finset_1(k5_enumset1(A,B,C,D,E,F,G)) )).
fof(fc7_fomodel0,axiom,( ! [A] : ! [B] : ( v8_ordinal1(B) => v2_setfam_1(k4_finseq_2(B,A)) ) )).
fof(fc7_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v4_fomodel1(B,A) & m1_subset_1(B,k1_fomodel1(A)) ) => v8_ordinal1(k19_fomodel1(A,B)) ) )).
fof(fc7_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) )).
fof(fc7_fomodel3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc7_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v2_fomodel4(k3_xboole_0(k1_xboole_0,A),A) ) )).
fof(fc7_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc7_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc7_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc7_funcsdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_group_1(k12_funcsdom(A)) & v1_funcsdom(k12_funcsdom(A)) ) ) )).
fof(fc7_funct_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc7_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc7_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc7_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(k2_zfmisc_1(A,A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k2_zfmisc_1(A,A))))) & v7_ordinal1(C) ) => v1_relat_1(k1_funct_1(B,C)) ) )).
fof(fc7_funct_9,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc7_functor0,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_altcat_1(A) & l1_altcat_1(B) & l2_functor0(C,A,B) ) => v1_funcop_1(u2_functor0(A,B,C)) ) )).
fof(fc7_gate_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ v1_xboole_0(k4_gate_1(A,B)) ) )).
fof(fc7_glib_000,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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),k4_ordinal1) & 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)) ) ) )).
fof(fc7_glib_001,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(fc7_glib_004,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(fc7_gr_cy_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(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)) ) ) )).
fof(fc7_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc7_group_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc7_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => v4_relat_1(k5_finseq_1(A),k1_tarski(1)) ) )).
fof(fc7_hahnban1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(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(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(k3_hahnban1(A,B,C,D)) & v1_funct_2(k3_hahnban1(A,B,C,D),u1_struct_0(B),u1_struct_0(A)) & v1_hahnban1(k3_hahnban1(A,B,C,D),A,B) ) ) )).
fof(fc7_hermitan,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc7_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ v1_xboole_0(k4_heyting3(1,A)) ) )).
fof(fc7_hilbert3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & m1_subset_1(B,k1_hilbert1) & m1_subset_1(C,k1_hilbert1) ) => v4_funct_1(k3_hilbert3(A,k3_hilbert1(B,C))) ) )).
fof(fc7_index_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc7_int_3,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc7_int_6,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc7_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ~ v1_xboole_0(k18_interva1(A)) ) )).
fof(fc7_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => v10_intpro_1(k13_intpro_1(A)) ) )).
fof(fc7_isomichi,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc7_jordan,axiom,( ! [A] : ( 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))) ) )).
fof(fc7_jordan18,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => v4_pre_topc(k5_topreal1(A),k15_euclid(2)) ) )).
fof(fc7_jordan2c,axiom,( ! [A] : ( ( 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)) ) )).
fof(fc7_kurato_1,axiom,( v3_setfam_1(k2_kurato_1(k3_topmetr,k6_kurato_1),u1_struct_0(k3_topmetr)) )).
fof(fc7_lattice2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc7_lattice3,axiom,( ! [A] : ( v3_lattices(k1_lattice3(A)) & v4_lattice3(k1_lattice3(A)) ) )).
fof(fc7_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => v2_lexbfs(k26_lexbfs(A)) ) )).
fof(fc7_lopban_1,axiom,( ! [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) & 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)) ) )).
fof(fc7_lopclset,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(fc7_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( ~ v1_xboole_0(k15_lpspacc1(A,B,C)) & v1_ideal_1(k15_lpspacc1(A,B,C),k14_lpspacc1(A,B,C)) & v1_lpspacc1(k15_lpspacc1(A,B,C),k14_lpspacc1(A,B,C)) ) ) )).
fof(fc7_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v2_xxreal_0(D) & v1_xreal_0(D) ) => ( 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)) ) ) )).
fof(fc7_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( ~ v1_xboole_0(k1_funct_1(k6_ltlaxio3,A)) & v1_finset_1(k1_funct_1(k6_ltlaxio3,A)) ) ) )).
fof(fc7_ltlaxio4,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) & m3_ltlaxio4(B,A) ) => ( ~ v1_xboole_0(k10_xtuple_0(B)) & v1_finset_1(k10_xtuple_0(B)) ) ) )).
fof(fc7_lukasi_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(fc7_margrel1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_margrel1(A) ) => v2_card_3(k9_xtuple_0(A)) ) )).
fof(fc7_matrtop1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc7_member_1,axiom,( ! [A] : ( v3_membered(A) => ( v1_membered(k5_member_1(A)) & v3_membered(k5_member_1(A)) ) ) )).
fof(fc7_membered,axiom,( ! [A] : ( v1_xcmplx_0(A) => v1_membered(k1_tarski(A)) ) )).
fof(fc7_mesfunc7,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc7_metrizts,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc7_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( v2_pre_topc(k4_mfold_2(A)) & v3_mfold_1(k4_mfold_2(A),A) ) ) )).
fof(fc7_mod_2,axiom,( 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) )).
fof(fc7_mod_4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc7_modelc_2,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & v1_modelc_2(B) & m1_finseq_1(B,k4_ordinal1) ) => v1_modelc_2(k8_modelc_2(A,B)) ) )).
fof(fc7_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ~ v8_ordinal1(k6_moebius1(A)) ) )).
fof(fc7_msafree,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc7_msafree1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) => ~ v1_xboole_0(k4_msualg_1(A,B,C)) ) )).
fof(fc7_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) => ( v1_relat_1(k2_funct_6(D)) & v2_relat_1(k2_funct_6(D)) & v1_funct_1(k2_funct_6(D)) ) ) )).
fof(fc7_mssubfam,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc7_msualg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc7_mycielsk,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_mycielsk(A) & l1_orders_2(A) ) => ( v7_ordinal1(k3_mycielsk(A)) & v2_xxreal_0(k3_mycielsk(A)) ) ) )).
fof(fc7_nat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v7_ordinal1(C) ) => ( v1_relat_1(k7_nat_1(B,C)) & v4_relat_1(k7_nat_1(B,C),k4_ordinal1) & v5_relat_1(k7_nat_1(B,C),A) & v1_funct_1(k7_nat_1(B,C)) & v1_partfun1(k7_nat_1(B,C),k4_ordinal1) ) ) )).
fof(fc7_nat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc7_nat_lat,axiom,( 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) )).
fof(fc7_neckla_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc7_necklace,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( ~ v2_struct_0(k4_necklace(A)) & v1_orders_2(k4_necklace(A)) ) ) )).
fof(fc7_newton,axiom,( ! [A] : ( v7_ordinal1(A) => v7_ordinal1(k2_newton(A)) ) )).
fof(fc7_nfcont_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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) ) ) )).
fof(fc7_nfcont_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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) ) ) )).
fof(fc7_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ( ~ v2_struct_0(k4_normsp_2(A)) & v4_frechet(k4_normsp_2(A)) & v5_rltopsp1(k4_normsp_2(A)) ) ) )).
fof(fc7_numbers,axiom,( ~ v1_finset_1(k3_numbers) )).
fof(fc7_openlatt,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(fc7_oposet_1,axiom,( v1_necklace(k1_oposet_1) & v3_qmax_1(k1_oposet_1) )).
fof(fc7_orders_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc7_orders_3,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc7_ordinal1,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => v7_ordinal1(k1_ordinal1(A)) ) )).
fof(fc7_ordinal5,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => ( v3_ordinal1(k1_ordinal5(A,B)) & v7_ordinal1(k1_ordinal5(A,B)) ) ) )).
fof(fc7_ordinal6,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc7_osafree,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc7_osalg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc7_partfun3,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => v1_partfun3(k2_funcop_1(A,B)) ) )).
fof(fc7_partfun4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc7_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc7_polyalg1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc7_polyeq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) & v1_xreal_0(E) ) => v1_xreal_0(k4_polyeq_1(A,B,C,D,E)) ) )).
fof(fc7_polynom1,axiom,( ! [A] : ! [B] : ( ( 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(k12_polynom1(A,B)) & v36_algstr_0(k12_polynom1(A,B)) & v2_rlvect_1(k12_polynom1(A,B)) ) ) )).
fof(fc7_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l5_algstr_0(A) ) => ( v1_funct_1(k10_polynom3(A)) & v1_funct_2(k10_polynom3(A),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k10_polynom3(A),A) ) ) )).
fof(fc7_pralg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc7_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_pre_poly(A) ) => v1_finseq_1(k1_funct_1(A,B)) ) )).
fof(fc7_pre_topc,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(fc7_prvect_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc7_pscomp_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc7_qc_lang1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_qc_lang1(B) ) => ~ v1_xboole_0(k8_qc_lang1(B,A)) ) )).
fof(fc7_quaterni,axiom,( ! [A] : ! [B] : ( ( v1_quaterni(A) & v1_quaterni(B) ) => v1_quaterni(k10_quaterni(A,B)) ) )).
fof(fc7_quofield,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc7_ratfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1) ) => ( v1_funct_1(k3_hurwitz(A,B,C)) & v1_funct_2(k3_hurwitz(A,B,C),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k3_hurwitz(A,B,C),A) & ~ v1_ratfunc1(k3_hurwitz(A,B,C),A) ) ) )).
fof(fc7_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ v3_xxreal_2(k1_limfunc1(A)) & v4_xxreal_2(k1_limfunc1(A)) & v6_xxreal_2(k1_limfunc1(A)) ) ) )).
fof(fc7_real_3,axiom,( v8_ordinal1(k1_int_1(k5_numbers)) & v1_int_1(k1_int_1(k5_numbers)) )).
fof(fc7_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ v2_struct_0(k7_real_ns1(A)) & v1_bhsp_1(k7_real_ns1(A)) & v3_bhsp_3(k7_real_ns1(A)) ) ) )).
fof(fc7_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : v1_relat_1(k2_tarski(k4_tarski(A,B),k4_tarski(C,D))) )).
fof(fc7_relat_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v2_relat_2(A) & v1_relat_1(B) & v2_relat_2(B) ) => v2_relat_2(k3_xboole_0(A,B)) ) )).
fof(fc7_reloc,axiom,( v1_extpro_1(k1_ami_3,k7_card_1(2)) & v5_amistd_5(k1_ami_3,k7_card_1(2)) & v6_amistd_5(k1_ami_3,k7_card_1(2)) )).
fof(fc7_relset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v1_xboole_0(k4_relat_1(A)) & v1_relat_1(k4_relat_1(A)) ) ) )).
fof(fc7_revrot_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc7_rfunct_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc7_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => v6_cat_1(k17_ringcat1(A)) ) )).
fof(fc7_rlaffin1,axiom,( ! [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) & 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) ) )).
fof(fc7_rlaffin3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc7_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc7_robbins4,axiom,( v13_lattices(k2_robbins4) & v4_robbins1(k2_robbins4) )).
fof(fc7_roughs_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc7_rsspace4,axiom,( ! [A] : ! [B] : ( ( ~ 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),k9_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k7_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)))) & v1_rlvect_1(g1_rlvect_1(k4_rsspace4(A,B),k9_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k7_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)))) & v2_rlvect_1(g1_rlvect_1(k4_rsspace4(A,B),k9_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k7_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)))) & v3_rlvect_1(g1_rlvect_1(k4_rsspace4(A,B),k9_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k7_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)))) & v4_rlvect_1(g1_rlvect_1(k4_rsspace4(A,B),k9_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k7_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)))) & v5_rlvect_1(g1_rlvect_1(k4_rsspace4(A,B),k9_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k7_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)))) & v6_rlvect_1(g1_rlvect_1(k4_rsspace4(A,B),k9_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k7_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)))) & v7_rlvect_1(g1_rlvect_1(k4_rsspace4(A,B),k9_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k7_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)))) & v8_rlvect_1(g1_rlvect_1(k4_rsspace4(A,B),k9_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k7_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)))) ) ) )).
fof(fc7_rvsum_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc7_scm_halt,axiom,( ! [A] : ! [B] : ( ( 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc7_scm_inst,axiom,( ~ v1_xboole_0(k3_scm_inst) & v5_compos_0(k3_scm_inst) )).
fof(fc7_scmfsa10,axiom,( ! [A] : ! [B] : ( ( 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(k7_card_1(3),k1_scmfsa_2,k6_scmfsa_2(A,B))) ) )).
fof(fc7_scmfsa6c,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc7_scmfsa8b,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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) ) ) )).
fof(fc7_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc7_scmfsa_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc7_scmfsa_m,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(k7_card_1(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(k1_funct_7(A,B,C)) & v1_funct_1(k1_funct_7(A,B,C)) & v5_funct_1(k1_funct_7(A,B,C),k2_memstr_0(k7_card_1(3),k1_scmfsa_2)) ) ) )).
fof(fc7_scmpds_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc7_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & 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_relat_1(k5_scmpds_6(B,C,A)) & v4_relat_1(k5_scmpds_6(B,C,A),k4_ordinal1) & v5_relat_1(k5_scmpds_6(B,C,A),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k5_scmpds_6(B,C,A)) & 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)) ) ) )).
fof(fc7_scmring2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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),k7_card_1(2),k1_scmring2(A)) ) )).
fof(fc7_scmring3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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(k7_card_1(2),k1_scmring2(A),k3_scmring2(A,B,C))) ) )).
fof(fc7_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ( ~ v1_xboole_0(k1_scmringi(A)) & v5_compos_0(k1_scmringi(A)) ) ) )).
fof(fc7_scmyciel,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v3_scmyciel(B,A) ) => v3_scmyciel(k3_xboole_0(B,C),A) ) )).
fof(fc7_setfam_1,axiom,( ! [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_setfam_1(k4_enumset1(A,B,C,D,E,F)) ) )).
fof(fc7_sfmastr1,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) & m1_subset_1(B,k4_ordinal1) ) => v1_sfmastr1(k12_scmfsa_2(B,A)) ) )).
fof(fc7_simplex0,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ( ~ v2_setfam_1(k1_simplex0(A)) & v1_classes1(k1_simplex0(A)) ) ) )).
fof(fc7_simplex1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) ) )).
fof(fc7_sin_cos,axiom,( v1_funct_1(k18_sin_cos) & v1_funct_2(k18_sin_cos,k1_numbers,k1_numbers) & v1_fcont_1(k18_sin_cos) )).
fof(fc7_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k16_sin_cos,k1_rcomp_1(k28_sin_cos,k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos)))) & v2_funct_1(k5_relat_1(k16_sin_cos,k1_rcomp_1(k28_sin_cos,k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos)))) )).
fof(fc7_sin_cos9,axiom,( v1_relat_1(k5_relat_1(k26_sin_cos,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)),k7_xcmplx_0(k28_sin_cos,4)))) & v2_funct_1(k5_relat_1(k26_sin_cos,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)),k7_xcmplx_0(k28_sin_cos,4)))) )).
fof(fc7_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k7_sincos10(A)) ) )).
fof(fc7_sppol_2,axiom,( v1_topreal1(k6_finseq_1(u1_struct_0(k15_euclid(2)))) )).
fof(fc7_sprect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc7_stacks_1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc7_struct_0,axiom,( ! [A] : ( ( v7_struct_0(A) & l1_struct_0(A) ) => v1_zfmisc_1(u1_struct_0(A)) ) )).
fof(fc7_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ~ v1_xboole_0(k6_enumset1(A,B,C,D,E,F,G,H)) )).
fof(fc7_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ~ v1_xboole_0(k38_substut1(A)) ) )).
fof(fc7_tex_4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc7_topalg_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) ) )).
fof(fc7_topalg_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc7_topalg_6,axiom,( ! [A] : ( l1_pre_topc(A) => ~ v1_xboole_0(k1_topalg_6(A)) ) )).
fof(fc7_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( ~ v2_struct_0(k5_topgrp_1(A)) & v15_algstr_0(k5_topgrp_1(A)) ) ) )).
fof(fc7_topreal1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ~ v1_xboole_0(k7_topreal1(A)) ) )).
fof(fc7_topreal6,axiom,( v2_pre_topc(k3_topmetr) & v8_pre_topc(k3_topmetr) )).
fof(fc7_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc7_toprealb,axiom,( v1_funct_1(k3_sin_cos6) & v1_fcont_1(k3_sin_cos6) )).
fof(fc7_tops_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc7_trees_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => v1_finset_1(k1_trees_1(A)) ) )).
fof(fc7_trees_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc7_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ~ v1_xboole_0(k6_trees_9(A)) ) )).
fof(fc7_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_valued_0(A) & v1_relat_1(B) & v1_valued_0(B) ) => v1_valued_0(k2_xboole_0(A,B)) ) )).
fof(fc7_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc7_vectmetr,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v15_algstr_0(k5_vectmetr(A)) & v2_group_1(k5_vectmetr(A)) & v3_group_1(k5_vectmetr(A)) ) ) )).
fof(fc7_vectsp_1,axiom,( v36_algstr_0(k2_vectsp_1) & v1_group_1(k2_vectsp_1) )).
fof(fc7_waybel10,axiom,( ! [A] : ( l1_orders_2(A) => ( ~ v2_struct_0(k3_waybel10(A)) & v1_orders_2(k3_waybel10(A)) & v3_lattice3(k3_waybel10(A)) ) ) )).
fof(fc7_waybel11,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc7_waybel17,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc7_waybel18,axiom,( v1_pre_topc(k9_waybel18) & v2_waybel18(k9_waybel18) )).
fof(fc7_waybel23,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc7_waybel24,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc7_waybel25,axiom,( ! [A] : ( l1_pre_topc(A) => ( v4_orders_2(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) ) ) )).
fof(fc7_waybel29,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc7_waybel30,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc7_waybel34,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc7_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc7_waybel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc7_waybel_2,axiom,( ! [A] : ( ( 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) ) ) )).
fof(fc7_waybel_3,axiom,( ! [A] : ! [B] : ( ( 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(k4_yellow_1(A,B)) & v1_orders_2(k4_yellow_1(A,B)) ) ) )).
fof(fc7_waybel_4,axiom,( ! [A] : ( ( 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) ) )).
fof(fc7_waybel_8,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(fc7_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc7_wellord2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_relat_1(k1_wellord2(A)) & ~ v1_xboole_0(k1_wellord2(A)) ) ) )).
fof(fc7_xboolean,axiom,( ! [A] : ! [B] : ( ( v1_xboolean(A) & v1_xboolean(B) ) => v1_xboolean(k8_xboolean(A,B)) ) )).
fof(fc7_xcmplx_0,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & v1_xcmplx_0(A) ) => ( ~ v8_ordinal1(k5_xcmplx_0(A)) & v1_xcmplx_0(k5_xcmplx_0(A)) ) ) )).
fof(fc7_xreal_0,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => v1_xreal_0(k6_xcmplx_0(A,B)) ) )).
fof(fc7_xtuple_0,axiom,( ! [A] : ( v1_xboole_0(A) => v1_xboole_0(k12_xtuple_0(A)) ) )).
fof(fc7_xxreal_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) & v7_ordinal1(C) & v7_ordinal1(D) ) => v7_ordinal1(k5_xxreal_0(A,B,C,D)) ) )).
fof(fc7_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => v1_xboole_0(k3_xxreal_1(A,A)) ) )).
fof(fc7_xxreal_2,axiom,( ! [A] : ( ( v3_membered(A) & v2_xxreal_2(A) ) => ( v1_xxreal_0(k1_xxreal_2(A)) & v1_xreal_0(k1_xxreal_2(A)) ) ) )).
fof(fc7_xxreal_3,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v3_xxreal_0(A) & ~ v1_xreal_0(A) & v1_xxreal_0(B) & v2_xxreal_0(B) & ~ v1_xreal_0(B) ) => ( v8_ordinal1(k1_xxreal_3(A,B)) & v1_xxreal_0(k1_xxreal_3(A,B)) ) ) )).
fof(fc7_yellow10,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc7_yellow18,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc7_yellow21,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc7_yellow_1,axiom,( ! [A] : ( ~ v2_struct_0(k2_yellow_1(A)) & 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)) ) )).
fof(fc7_yellow_2,axiom,( ! [A] : ( ( ~ 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(k1_yellow_1(k7_waybel_0(A))),u1_struct_0(A)) & v5_orders_3(k2_yellow_2(A),k1_yellow_1(k7_waybel_0(A)),A) ) ) )).
fof(fc7_yellow_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc7_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc7_yellow_6,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc7_yellow_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_lattice3(A) & l1_orders_2(A) ) => ( v1_orders_2(k7_lattice3(A)) & v3_lattice3(k7_lattice3(A)) ) ) )).
fof(fc7_yellow_9,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc7_zmodul02,axiom,( ! [A] : ( ( ~ 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_zmodul02(k1_tarski(k4_struct_0(A)),A) ) )).
fof(fc7_zmodul03,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_int_2(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) & v1_zmodul03(B) & v2_zmodul03(B) & l1_zmodul01(B) ) => ( ~ v2_struct_0(k12_zmodul02(A,B)) & v7_vectsp_1(k12_zmodul02(A,B),k9_int_3(A)) & v1_matrlin(k12_zmodul02(A,B),k9_int_3(A)) ) ) )).
fof(fc80_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(A) => v5_relat_1(k1_funct_1(k9_fomodel0(A),B),A) ) )).
fof(fc80_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k35_fomodel2(A,k35_fomodel2(A,C)),A) & v13_fomodel2(k35_fomodel2(A,k35_fomodel2(A,C)),B,A) ) ) )).
fof(fc80_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_xxreal_0(B) ) => v1_xboole_0(k20_member_1(A,B)) ) )).
fof(fc80_valued_0,axiom,( ! [A] : ! [B] : ( v1_xxreal_0(B) => v2_valued_0(k16_funcop_1(A,B)) ) )).
fof(fc80_valued_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc81_fomodel0,axiom,( ! [A] : v1_setfam_1(k4_xboole_0(A,k1_tarski(k1_xboole_0))) )).
fof(fc81_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v6_fomodel4(B,A) & m1_subset_1(B,k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A)))) & v6_fomodel4(C,A) & m1_subset_1(C,k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A)))) ) => v7_fomodel4(k2_tarski(B,C),A) ) )).
fof(fc81_member_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v2_membered(A) & v1_xxreal_0(B) ) => ~ v1_xboole_0(k20_member_1(A,B)) ) )).
fof(fc81_valued_0,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => v3_valued_0(k16_funcop_1(A,B)) ) )).
fof(fc81_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc82_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v1_finset_1(k13_finseq_1(A)) ) )).
fof(fc82_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v6_fomodel4(B,A) & m1_subset_1(B,k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A)))) & v6_fomodel4(C,A) & m1_subset_1(C,k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A)))) & v6_fomodel4(D,A) & m1_subset_1(D,k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A)))) & v6_fomodel4(E,A) & m1_subset_1(E,k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A)))) ) => v7_fomodel4(k2_enumset1(B,C,D,E),A) ) )).
fof(fc82_member_1,axiom,( ! [A] : ! [B] : ( ( v2_membered(A) & v1_xxreal_0(B) ) => v2_membered(k20_member_1(A,B)) ) )).
fof(fc82_valued_0,axiom,( ! [A] : ! [B] : ( v1_rat_1(B) => v5_relat_1(k16_funcop_1(A,B),k3_numbers) ) )).
fof(fc82_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc83_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v2_setfam_1(k13_finseq_1(A)) ) )).
fof(fc83_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v7_fomodel4(k39_fomodel4(A),A) ) )).
fof(fc83_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_xcmplx_0(B) ) => v1_xboole_0(k21_member_1(A,B)) ) )).
fof(fc83_pcs_0,axiom,( ! [A] : ! [B] : ( ( l2_pcs_0(A) & ~ v1_xboole_0(B) ) => ~ v2_struct_0(k26_pcs_0(A,B)) ) )).
fof(fc83_valued_0,axiom,( ! [A] : ! [B] : ( v1_int_1(B) => v5_relat_1(k16_funcop_1(A,B),k4_numbers) ) )).
fof(fc83_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc84_fomodel0,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => v1_xboole_0(k4_xboole_0(k4_finseq_2(B,A),k3_finseq_2(A))) ) )).
fof(fc84_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,k4_ordinal1,k40_fomodel2(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k40_fomodel2(B)))) ) => v1_xboole_0(k4_xboole_0(A,k45_fomodel4(A,B,C,D))) ) )).
fof(fc84_member_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_membered(A) & v1_xcmplx_0(B) ) => ~ v1_xboole_0(k21_member_1(A,B)) ) )).
fof(fc84_valued_0,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => v4_valued_0(k16_funcop_1(A,B)) ) )).
fof(fc84_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc85_fomodel0,axiom,( ! [A] : ~ v1_xboole_0(k4_xboole_0(k9_setfam_1(A),A)) )).
fof(fc85_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k30_fomodel2(B)) ) => v1_xboole_0(k4_xboole_0(A,k47_fomodel4(A,B,C,D))) ) )).
fof(fc85_member_1,axiom,( ! [A] : ! [B] : ( ( v1_membered(A) & v1_xcmplx_0(B) ) => v1_membered(k21_member_1(A,B)) ) )).
fof(fc85_valued_0,axiom,( ! [A] : ! [B] : ( v1_membered(B) => v1_valued_0(k2_zfmisc_1(A,B)) ) )).
fof(fc85_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc86_fomodel0,axiom,( ! [A] : ! [B] : ( 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))) ) ) )).
fof(fc86_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k4_ordinal1,k30_fomodel2(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k30_fomodel2(B)))) ) => v1_xboole_0(k4_xboole_0(A,k49_fomodel4(A,B,C,D))) ) )).
fof(fc86_member_1,axiom,( ! [A] : ! [B] : ( ( v3_membered(A) & v1_xreal_0(B) ) => v3_membered(k21_member_1(A,B)) ) )).
fof(fc86_valued_0,axiom,( ! [A] : ! [B] : ( v2_membered(B) => v2_valued_0(k2_zfmisc_1(A,B)) ) )).
fof(fc86_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc87_fomodel0,axiom,( ! [A] : ~ v1_finset_1(k23_fomodel0(A)) )).
fof(fc87_glib_003,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc87_member_1,axiom,( ! [A] : ! [B] : ( ( v4_membered(A) & v1_rat_1(B) ) => v4_membered(k21_member_1(A,B)) ) )).
fof(fc87_valued_0,axiom,( ! [A] : ! [B] : ( v3_membered(B) => v3_valued_0(k2_zfmisc_1(A,B)) ) )).
fof(fc87_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc88_fomodel0,axiom,( ! [A] : v1_xboole_0(k3_xboole_0(k23_fomodel0(A),A)) )).
fof(fc88_glib_003,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc88_member_1,axiom,( ! [A] : ! [B] : ( ( v5_membered(A) & v1_int_1(B) ) => v5_membered(k21_member_1(A,B)) ) )).
fof(fc88_valued_0,axiom,( ! [A] : ! [B] : ( v4_membered(B) => v5_relat_1(k2_zfmisc_1(A,B),k3_numbers) ) )).
fof(fc88_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc89_fomodel0,axiom,( ! [A] : v4_card_3(k23_fomodel0(A)) )).
fof(fc89_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_xxreal_0(B) ) => v1_xboole_0(k22_member_1(A,B)) ) )).
fof(fc89_valued_0,axiom,( ! [A] : ! [B] : ( v5_membered(B) => v5_relat_1(k2_zfmisc_1(A,B),k4_numbers) ) )).
fof(fc89_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc8_abcmiz_1,axiom,( ~ v1_xboole_0(k19_abcmiz_1) )).
fof(fc8_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => v6_abcmiz_a(k16_abcmiz_1(A),A) ) )).
fof(fc8_abian,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & ~ v1_abian(A) & v1_int_1(B) & ~ v1_abian(B) ) => ~ v1_abian(k3_xcmplx_0(A,B)) ) )).
fof(fc8_afinsq_1,axiom,( ! [A] : ( v5_ordinal1(k3_afinsq_1(A)) & v1_finset_1(k3_afinsq_1(A)) ) )).
fof(fc8_algstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc8_algstr_1,axiom,( v29_algstr_0(k3_algstr_1) & v4_vectsp_1(k3_algstr_1) & v7_algstr_1(k3_algstr_1) )).
fof(fc8_algstr_4,axiom,( ! [A] : ! [B] : ( ( l3_algstr_0(A) & m1_algstr_4(B,A) ) => v2_algstr_4(u1_struct_0(B),A) ) )).
fof(fc8_altcat_2,axiom,( v2_struct_0(k5_altcat_2) & v6_altcat_1(k5_altcat_2) )).
fof(fc8_altcat_4,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc8_ami_6,axiom,( ! [A] : ! [B] : ( ( 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(k7_card_1(2),k1_ami_3,k3_ami_3(A,B))) ) )).
fof(fc8_amistd_2,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ( v1_extpro_1(k4_amistd_1(A),A) & v4_amistd_2(k4_amistd_1(A),A) ) ) )).
fof(fc8_aofa_000,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc8_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(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) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) & v4_aofa_a01(D,A,B,C) & l4_aofa_a00(D,A,B,C) & v4_msualg_1(E,A) & v4_msafree4(E,A,C) & v17_aofa_a00(E,A) & v20_aofa_a00(E,4,1,A) & l3_msualg_1(E,A) & m1_subset_1(F,k13_aofa_a00(A,C,E,u4_aofa_a00(A,B,C,D))) & m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),u8_aofa_a00(A))) ) => v1_xboolean(k15_aofa_a00(A,B,C,E,u8_aofa_a00(A),G,F)) ) )).
fof(fc8_bagorder,axiom,( ! [A] : ( 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) ) ) )).
fof(fc8_binop_2,axiom,( v1_funct_1(k22_binop_2) & v1_funct_2(k22_binop_2,k2_zfmisc_1(k4_numbers,k4_numbers),k4_numbers) & v1_binop_1(k22_binop_2,k4_numbers) & v2_binop_1(k22_binop_2,k4_numbers) )).
fof(fc8_borsuk_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc8_borsuk_2,axiom,( v8_pre_topc(k17_borsuk_1) & v1_compts_1(k17_borsuk_1) )).
fof(fc8_borsuk_5,axiom,( ! [A] : ! [B] : ( ( v1_rat_1(A) & v1_xreal_0(B) & ~ v1_rat_1(B) ) => ~ v1_rat_1(k6_xcmplx_0(B,A)) ) )).
fof(fc8_borsuk_6,axiom,( ~ v1_xboole_0(k6_borsuk_6) & v4_pre_topc(k6_borsuk_6,k2_borsuk_1(k5_topmetr,k5_topmetr)) )).
fof(fc8_borsuk_7,axiom,( 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)) )).
fof(fc8_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v2_vectsp_1(k11_c0sp1(A)) & v6_vectsp_1(k11_c0sp1(A)) & v2_lopban_2(k11_c0sp1(A)) & v3_lopban_2(k11_c0sp1(A)) & v4_lopban_2(k11_c0sp1(A)) ) ) )).
fof(fc8_c0sp2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc8_card_1,axiom,( ! [A] : ( v1_finset_1(A) => ( v1_finset_1(k1_card_1(A)) & v1_card_1(k1_card_1(A)) ) ) )).
fof(fc8_card_3,axiom,( ! [A] : ( v1_xboole_0(A) => v1_xboole_0(k9_card_3(A)) ) )).
fof(fc8_card_5,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ( ~ v1_finset_1(k1_card_5(A)) & v1_card_1(k1_card_5(A)) ) ) )).
fof(fc8_catalg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc8_cayldick,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v2_binop_1(B,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_funct_1(H) & v1_funct_2(H,A,A) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( v3_rlvect_1(g1_cayldick(A,C,B,D,E,F,G,H)) & v1_cayldick(g1_cayldick(A,C,B,D,E,F,G,H)) ) ) )).
fof(fc8_cayley,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(fc8_cc0sp2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc8_cfdiff_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc8_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_group_1(k8_cfuncdom(A)) & v1_cfuncdom(k8_cfuncdom(A)) ) ) )).
fof(fc8_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => v4_cgames_1(k5_finseq_1(A)) ) )).
fof(fc8_circcmb3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc8_circcomb,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc8_clopban1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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)))) ) ) )).
fof(fc8_clopban2,axiom,( ~ v2_struct_0(k3_csspace3) & ~ v7_struct_0(k3_csspace3) )).
fof(fc8_closure1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc8_closure2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc8_coh_sp,axiom,( ! [A] : ~ v1_xboole_0(k15_coh_sp(A)) )).
fof(fc8_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v1_relat_1(k5_cohsp_1(A)) ) )).
fof(fc8_compos_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_compos_0(A) ) => ~ v1_xboole_0(k1_compos_0(A)) ) )).
fof(fc8_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_compos_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc8_comput_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v3_comput_1(B) & m1_finseq_1(B,k2_comput_1(A)) ) => ( v1_relat_1(k5_funct_6(B)) & v1_funct_1(k5_funct_6(B)) & v2_margrel1(k5_funct_6(B)) ) ) )).
fof(fc8_comseq_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & v2_comseq_2(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_funct_1(k18_valued_1(A,B)) & v1_funct_2(k18_valued_1(A,B),k4_ordinal1,k2_numbers) & v2_comseq_2(k18_valued_1(A,B)) ) ) )).
fof(fc8_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v1_comseq_3(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_funct_1(k3_comseq_3(A)) & v1_funct_2(k3_comseq_3(A),k4_ordinal1,k1_numbers) & v1_series_1(k3_comseq_3(A)) ) ) )).
fof(fc8_csspace4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc8_dickson,axiom,( ! [A] : ( ( 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(k4_yellow_1(k1_xboole_0,A)) & v3_dickson(k4_yellow_1(k1_xboole_0,A)) ) ) )).
fof(fc8_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => v2_dilworth(k6_dilworth(A),A) ) )).
fof(fc8_euclid,axiom,( ! [A] : ! [B] : ( v7_ordinal1(A) => v3_finseq_1(k4_finseq_2(A,B)) ) )).
fof(fc8_euclid_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ~ v1_xboole_0(k8_euclid_7(A)) ) )).
fof(fc8_euclid_9,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) & v1_valued_0(B) ) => ( v1_relat_1(k54_valued_1(B)) & v1_funct_1(k54_valued_1(B)) & v3_card_1(k54_valued_1(B),A) & v3_valued_0(k54_valued_1(B)) ) ) )).
fof(fc8_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) ) => v5_relat_1(k9_funct_7(B,C,D),A) ) )).
fof(fc8_facirc_1,axiom,( ! [A] : ( v1_xtuple_0(A) => v1_relat_1(k1_tarski(A)) ) )).
fof(fc8_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc8_filter_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc8_finseq_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(k10_finseq_1(A,B)) & v1_funct_1(k10_finseq_1(A,B)) ) )).
fof(fc8_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc8_finseq_5,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc8_finset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : v1_finset_1(k6_enumset1(A,B,C,D,E,F,G,H)) )).
fof(fc8_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v7_ordinal1(B) & ~ v8_ordinal1(B) ) => v1_xboole_0(k4_finseq_2(B,A)) ) )).
fof(fc8_fomodel1,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(fc8_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(fc8_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & ~ v8_ordinal1(D) ) => v1_partfun1(k8_fomodel3(A,B,C,D),k4_finseq_2(D,A)) ) )).
fof(fc8_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v2_fomodel4(k13_fomodel0(A,k1_xboole_0),A) ) )).
fof(fc8_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc8_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc8_funcop_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc8_funcsdom,axiom,( ! [A] : ( ~ v2_struct_0(k12_funcsdom(A)) & v1_funcsdom(k12_funcsdom(A)) ) )).
fof(fc8_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k5_relat_1(A,B)) & v1_funct_1(k5_relat_1(A,B)) ) ) )).
fof(fc8_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc8_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc8_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v7_ordinal1(B) ) => ( v1_relat_1(k8_funct_7(A,B)) & v1_funct_1(k8_funct_7(A,B)) ) ) )).
fof(fc8_funct_9,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc8_gate_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_xboole_0(B) ) => v1_xboole_0(k4_gate_1(A,B)) ) )).
fof(fc8_glib_001,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(fc8_gr_cy_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc8_graph_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc8_grcat_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc8_group_6,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc8_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v1_partfun1(k5_finseq_1(A),k1_tarski(1)) & v1_group_7(k5_finseq_1(A)) ) ) )).
fof(fc8_hahnban1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & ~ 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)) & 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(k4_hahnban1(A,B,C)) & v1_funct_2(k4_hahnban1(A,B,C),u1_struct_0(B),u1_struct_0(A)) & v1_hahnban1(k4_hahnban1(A,B,C),A,B) ) ) )).
fof(fc8_hermitan,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc8_hilbert3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & 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)) ) ) )).
fof(fc8_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc8_index_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_index_1(C,A,B) => ( v1_relat_1(k1_xtuple_0(C)) & v1_funct_1(k1_xtuple_0(C)) ) ) )).
fof(fc8_int_3,axiom,( ~ v8_struct_0(k1_int_3) )).
fof(fc8_int_6,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc8_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ( ~ v2_struct_0(k21_interva1(A)) & v3_lattices(k21_interva1(A)) ) ) )).
fof(fc8_intpro_1,axiom,( v10_intpro_1(k14_intpro_1) )).
fof(fc8_isomichi,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(fc8_jordan,axiom,( ! [A] : ( 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))) ) )).
fof(fc8_jordan18,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => v4_pre_topc(k7_topreal1(A),k15_euclid(2)) ) )).
fof(fc8_jordan2c,axiom,( ! [A] : ( ( 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)) ) )).
fof(fc8_kurato_1,axiom,( v1_setfam_1(k2_kurato_1(k3_topmetr,k6_kurato_1)) )).
fof(fc8_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( v3_lattices(k1_lattice2(A)) & v10_lattices(k1_lattice2(A)) ) ) )).
fof(fc8_lattice3,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc8_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => v3_lexbfs(k26_lexbfs(A)) ) )).
fof(fc8_lopban_1,axiom,( ! [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) & 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),k9_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k7_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k8_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)))) & v1_rlvect_1(g1_rlvect_1(k10_lopban_1(A,B),k9_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k7_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k8_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)))) & v2_rlvect_1(g1_rlvect_1(k10_lopban_1(A,B),k9_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k7_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k8_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)))) & v3_rlvect_1(g1_rlvect_1(k10_lopban_1(A,B),k9_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k7_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k8_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)))) & v4_rlvect_1(g1_rlvect_1(k10_lopban_1(A,B),k9_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k7_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k8_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)))) & v5_rlvect_1(g1_rlvect_1(k10_lopban_1(A,B),k9_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k7_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k8_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)))) & v6_rlvect_1(g1_rlvect_1(k10_lopban_1(A,B),k9_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k7_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k8_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)))) & v7_rlvect_1(g1_rlvect_1(k10_lopban_1(A,B),k9_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k7_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k8_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)))) & v8_rlvect_1(g1_rlvect_1(k10_lopban_1(A,B),k9_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k7_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k8_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)))) ) ) )).
fof(fc8_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( ~ v2_struct_0(k14_lpspacc1(A,B,C)) & v2_rlvect_1(k14_lpspacc1(A,B,C)) & v3_rlvect_1(k14_lpspacc1(A,B,C)) & v4_rlvect_1(k14_lpspacc1(A,B,C)) & v1_clvect_1(k14_lpspacc1(A,B,C)) & v2_clvect_1(k14_lpspacc1(A,B,C)) & v3_clvect_1(k14_lpspacc1(A,B,C)) & v4_clvect_1(k14_lpspacc1(A,B,C)) & v5_clvect_1(k14_lpspacc1(A,B,C)) ) ) )).
fof(fc8_ltlaxio3,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) ) => ( v1_finset_1(k7_ltlaxio3(A)) & v5_finset_1(k7_ltlaxio3(A)) ) ) )).
fof(fc8_ltlaxio4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_ltlaxio3(A) & v3_ltlaxio3(A) & m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) & m3_ltlaxio4(B,A) & m1_subset_1(C,k9_xtuple_0(B)) ) => ( ~ v2_ltlaxio3(k1_funct_1(B,C)) & v3_ltlaxio3(k1_funct_1(B,C)) ) ) )).
fof(fc8_lukasi_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(fc8_margrel1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc8_matrtop1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc8_matrtop3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc8_mazurulm,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc8_member_1,axiom,( ! [A] : ( v4_membered(A) => ( v1_membered(k5_member_1(A)) & v4_membered(k5_member_1(A)) ) ) )).
fof(fc8_membered,axiom,( ! [A] : ( v1_xxreal_0(A) => v2_membered(k1_tarski(A)) ) )).
fof(fc8_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc8_metrizts,axiom,( ! [A] : ( 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)))) ) ) )).
fof(fc8_mmlquer2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => v7_ordinal1(k6_mmlquer2(A,B)) ) )).
fof(fc8_mod_4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc8_modelc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_modelc_1(A) & l2_modelc_1(A) ) => ~ v1_xboole_0(u3_modelc_1(A)) ) )).
fof(fc8_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => ~ v1_xboole_0(k13_modelc_2(A)) ) )).
fof(fc8_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ~ v1_moebius1(k6_moebius1(A)) ) )).
fof(fc8_msafree,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc8_msafree1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(fc8_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) & v4_relat_1(k3_relat_1(C,B),k4_finseq_1(C)) ) ) )).
fof(fc8_mssubfam,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc8_msualg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc8_mycielsk,axiom,( ! [A] : ( ( v8_struct_0(A) & l1_orders_2(A) ) => ( v8_struct_0(k3_necklace(A)) & v1_orders_2(k3_necklace(A)) ) ) )).
fof(fc8_nat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) & ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ( v1_relat_1(k3_relat_1(A,C)) & v4_relat_1(k3_relat_1(A,C),k4_ordinal1) & v5_relat_1(k3_relat_1(A,C),B) & v1_funct_1(k3_relat_1(A,C)) ) ) )).
fof(fc8_nat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc8_neckla_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc8_necklace,axiom,( ! [A] : ( v7_ordinal1(A) => v1_finset_1(u1_struct_0(k4_necklace(A))) ) )).
fof(fc8_newton,axiom,( ! [A] : ( v7_ordinal1(A) => v2_xxreal_0(k2_newton(A)) ) )).
fof(fc8_nfcont_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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) ) ) )).
fof(fc8_nfcont_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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_xreal_0(C) ) => ( v1_funct_1(k9_integr15(A,C,k1_numbers,B)) & v2_nfcont_4(k9_integr15(A,C,k1_numbers,B),A) ) ) )).
fof(fc8_numbers,axiom,( ~ v1_finset_1(k1_numbers) )).
fof(fc8_openlatt,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc8_oposet_1,axiom,( v2_necklace(k2_oposet_1) & v3_qmax_1(k2_oposet_1) )).
fof(fc8_orders_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc8_ordinal1,axiom,( v7_ordinal1(k5_ordinal1) )).
fof(fc8_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ( v3_ordinal1(k3_ordinal5(A)) & v4_ordinal5(k3_ordinal5(A)) ) ) )).
fof(fc8_ordinal6,axiom,( ! [A] : ( v1_ordinal6(A) => ( v1_relat_1(k1_wellord2(A)) & v2_wellord1(k1_wellord2(A)) ) ) )).
fof(fc8_osafree,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc8_osalg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc8_partfun3,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(B) & v3_xxreal_0(B) ) => v2_partfun3(k2_funcop_1(A,B)) ) )).
fof(fc8_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc8_polynom1,axiom,( ! [A] : ! [B] : ( ( 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(k12_polynom1(A,B)) & v36_algstr_0(k12_polynom1(A,B)) & v3_rlvect_1(k12_polynom1(A,B)) ) ) )).
fof(fc8_polynom3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k11_polynom3(A,B,C)) & v1_funct_2(k11_polynom3(A,B,C),k4_ordinal1,u1_struct_0(A)) & v1_polynom1(k11_polynom3(A,B,C),A) ) ) )).
fof(fc8_pralg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc8_pre_poly,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc8_pre_topc,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc8_prvect_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc8_pscomp_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc8_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => v1_xreal_0(k13_quaterni(A)) ) )).
fof(fc8_quofield,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc8_ratfunc1,axiom,( ! [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) ) => ( ~ v2_struct_0(k14_polynom3(A)) & ~ v6_struct_0(k14_polynom3(A)) & v36_algstr_0(k14_polynom3(A)) ) ) )).
fof(fc8_rcomp_3,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc8_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k9_xtuple_0(A)) ) )).
fof(fc8_relat_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v2_relat_2(A) & v1_relat_1(B) ) => v2_relat_2(k4_xboole_0(A,B)) ) )).
fof(fc8_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C))) => v1_relat_1(k9_xtuple_0(D)) ) )).
fof(fc8_rewrite2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc8_rfunct_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc8_rlaffin1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc8_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc8_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_robbins1(A) ) => ( ~ v2_struct_0(k8_robbins1(A)) & v4_robbins1(k8_robbins1(A)) ) ) )).
fof(fc8_robbins4,axiom,( v14_lattices(k2_robbins4) & v4_robbins1(k2_robbins4) )).
fof(fc8_roughs_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc8_rsspace4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc8_rvsum_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc8_scm_halt,axiom,( ! [A] : ! [B] : ( ( 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,k4_ordinal1) & 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,k7_card_1(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),k4_ordinal1) & 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)) ) ) )).
fof(fc8_scmfsa10,axiom,( ! [A] : ! [B] : ( ( 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(k7_card_1(3),k1_scmfsa_2,k7_scmfsa_2(A,B))) ) )).
fof(fc8_scmfsa6c,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc8_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc8_scmfsa_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc8_scmfsa_m,axiom,( ! [A] : ! [B] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v4_memstr_0(k16_funcop_1(A,B),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(fc8_scmpds_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc8_scmpds_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc8_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & 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_relat_1(k5_scmpds_6(B,C,A)) & v4_relat_1(k5_scmpds_6(B,C,A),k4_ordinal1) & v5_relat_1(k5_scmpds_6(B,C,A),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k5_scmpds_6(B,C,A)) & 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) ) ) )).
fof(fc8_scmring2,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) & v7_ordinal1(B) ) => ~ v2_extpro_1(k8_scmring2(A,B),k7_card_1(2),k1_scmring2(A)) ) )).
fof(fc8_scmring3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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(k7_card_1(2),k1_scmring2(A),k4_scmring2(A,B,C))) ) )).
fof(fc8_scmyciel,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v3_scmyciel(B,A) ) => v3_scmyciel(k4_xboole_0(B,C),A) ) )).
fof(fc8_setfam_1,axiom,( ! [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_setfam_1(k5_enumset1(A,B,C,D,E,F,G)) ) )).
fof(fc8_sfmastr1,axiom,( ! [A] : ! [B] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) & m1_subset_1(B,k4_ordinal1) ) => v1_sfmastr1(k13_scmfsa_2(B,A)) ) )).
fof(fc8_simplex0,axiom,( ! [A] : ( v5_finset_1(A) => ( v5_finset_1(k1_simplex0(A)) & v1_classes1(k1_simplex0(A)) ) ) )).
fof(fc8_simplex1,axiom,( ! [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) & 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))) ) ) )).
fof(fc8_sin_cos,axiom,( v1_funct_1(k22_sin_cos) & v1_funct_2(k22_sin_cos,k1_numbers,k1_numbers) & v1_fcont_1(k22_sin_cos) )).
fof(fc8_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k16_sin_cos,k1_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(2,k28_sin_cos)))) & v2_funct_1(k5_relat_1(k16_sin_cos,k1_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(2,k28_sin_cos)))) )).
fof(fc8_sin_cos9,axiom,( v1_relat_1(k5_relat_1(k27_sin_cos,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos)))) & v2_funct_1(k5_relat_1(k27_sin_cos,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos)))) )).
fof(fc8_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => v1_xreal_0(k8_sincos10(A)) ) )).
fof(fc8_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => v1_topreal1(k5_finseq_1(A)) ) )).
fof(fc8_sprect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc8_stacks_1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc8_struct_0,axiom,( ! [A] : ( ( v8_struct_0(A) & l1_struct_0(A) ) => v1_finset_1(u1_struct_0(A)) ) )).
fof(fc8_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ~ v1_xboole_0(k7_enumset1(A,B,C,D,E,F,G,H,I)) )).
fof(fc8_tex_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ~ v1_xboole_0(k1_tex_4(A,B)) ) )).
fof(fc8_topalg_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc8_topalg_5,axiom,( 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)) )).
fof(fc8_topalg_6,axiom,( ! [A] : ! [B] : ( ( l1_pre_topc(A) & m1_subset_1(B,k1_topalg_6(A)) ) => v3_membered(k9_xtuple_0(B)) ) )).
fof(fc8_topgen_4,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc8_topgrp_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc8_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => v9_rltopsp1(k1_topreal9(A,B,C),k15_euclid(A)) ) )).
fof(fc8_topreala,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v2_xxreal_0(B) & v1_xreal_0(B) ) => ~ v1_xboole_0(k1_xxreal_1(k6_xcmplx_0(A,B),A)) ) )).
fof(fc8_toprealb,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(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) ) ) )).
fof(fc8_toprealc,axiom,( ! [A] : ( v7_ordinal1(A) => ( v5_rltopsp1(k15_euclid(A)) & v2_toprealc(k15_euclid(A)) ) ) )).
fof(fc8_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => v1_xboole_0(k1_tops_1(A,k1_struct_0(A))) ) )).
fof(fc8_trees_1,axiom,( ~ v1_xboole_0(k8_trees_1) & v1_trees_1(k8_trees_1) )).
fof(fc8_trees_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc8_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) ) => ( ~ v1_xboole_0(k9_trees_9(A)) & v3_trees_3(k9_trees_9(A)) ) ) )).
fof(fc8_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v2_valued_0(A) & v1_relat_1(B) & v2_valued_0(B) ) => v2_valued_0(k2_xboole_0(A,B)) ) )).
fof(fc8_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc8_vectsp10,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc8_vectsp_1,axiom,( ~ 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) )).
fof(fc8_waybel10,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc8_waybel11,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc8_waybel17,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(fc8_waybel18,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => v4_waybel_3(k2_funcop_1(A,B)) ) )).
fof(fc8_waybel23,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc8_waybel24,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc8_waybel25,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc8_waybel34,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc8_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc8_waybel_1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc8_waybel_2,axiom,( ! [A] : ( ( 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) ) ) )).
fof(fc8_waybel_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc8_waybel_4,axiom,( ! [A] : ( ( 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(k1_yellow_1(k3_waybel_4(A))) & v1_yellow_0(k1_yellow_1(k3_waybel_4(A))) ) ) )).
fof(fc8_waybel_8,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(fc8_xboolean,axiom,( ! [A] : ! [B] : ( ( v1_xboolean(A) & v1_xboolean(B) ) => v1_xboolean(k9_xboolean(A,B)) ) )).
fof(fc8_xcmplx_0,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(A) & v1_xcmplx_0(A) & ~ v8_ordinal1(B) & v1_xcmplx_0(B) ) => ~ v8_ordinal1(k3_xcmplx_0(A,B)) ) )).
fof(fc8_xreal_0,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => v1_xreal_0(k7_xcmplx_0(A,B)) ) )).
fof(fc8_xtuple_0,axiom,( ! [A] : ( v1_xboole_0(A) => v1_xboole_0(k13_xtuple_0(A)) ) )).
fof(fc8_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => v1_xboole_0(k4_xxreal_1(A,A)) ) )).
fof(fc8_xxreal_2,axiom,( ! [A] : ( ( v4_membered(A) & v2_xxreal_2(A) ) => ( v1_xxreal_0(k1_xxreal_2(A)) & v1_rat_1(k1_xxreal_2(A)) ) ) )).
fof(fc8_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc8_yellow10,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc8_yellow18,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc8_yellow21,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc8_yellow_1,axiom,( ! [A] : ( v1_orders_2(k2_yellow_1(A)) & v3_lattice3(k2_yellow_1(A)) ) )).
fof(fc8_yellow_2,axiom,( ! [A] : ( ( ~ 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(k1_yellow_1(k7_waybel_0(A)))) & v5_orders_3(k3_yellow_2(A),A,k1_yellow_1(k7_waybel_0(A))) ) ) )).
fof(fc8_yellow_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc8_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(fc8_yellow_6,axiom,( ! [A] : ( v1_orders_2(k2_yellow_1(A)) & v7_waybel_0(k2_yellow_1(A)) ) )).
fof(fc8_yellow_7,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc8_yellow_9,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(fc90_fomodel0,axiom,( v1_xboole_0(k4_xboole_0(k4_ordinal1,k4_numbers)) )).
fof(fc90_member_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v2_membered(A) & v1_xxreal_0(B) ) => ~ v1_xboole_0(k22_member_1(A,B)) ) )).
fof(fc90_valued_0,axiom,( ! [A] : ! [B] : ( v6_membered(B) => v4_valued_0(k2_zfmisc_1(A,B)) ) )).
fof(fc90_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc91_fomodel0,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc91_glib_003,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc91_member_1,axiom,( ! [A] : ! [B] : ( ( v2_membered(A) & v1_xxreal_0(B) ) => v2_membered(k22_member_1(A,B)) ) )).
fof(fc91_valued_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc91_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc92_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v8_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))) & v1_partfun1(k13_fomodel0(B,C),k2_finseq_1(k2_xcmplx_0(A,B))) ) ) )).
fof(fc92_glib_003,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_003(A) & v10_glib_003(A) & v1_xreal_0(C) ) => ( v1_relat_1(k13_glib_003(A,B,C)) & v4_relat_1(k13_glib_003(A,B,C),k4_ordinal1) & 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)) ) ) )).
fof(fc92_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_xcmplx_0(B) ) => v1_xboole_0(k23_member_1(A,B)) ) )).
fof(fc92_valued_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc92_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc93_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k9_fomodel0(A),k10_finseq_1(B,C)),k7_finseq_1(B,C))) ) )).
fof(fc93_member_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_membered(A) & v1_xcmplx_0(B) ) => ~ v1_xboole_0(k23_member_1(A,B)) ) )).
fof(fc93_valued_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc93_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc94_fomodel0,axiom,( ! [A] : ( ( v5_finset_1(A) & v4_card_3(A) ) => v4_card_3(k3_tarski(A)) ) )).
fof(fc94_member_1,axiom,( ! [A] : ! [B] : ( ( v1_membered(A) & v1_xcmplx_0(B) ) => v1_membered(k23_member_1(A,B)) ) )).
fof(fc94_valued_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc94_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc95_fomodel0,axiom,( ! [A] : ( ( v4_funct_1(A) & v5_finset_1(A) & v4_card_3(A) ) => v4_card_3(k21_fomodel0(A)) ) )).
fof(fc95_member_1,axiom,( ! [A] : ! [B] : ( ( v3_membered(A) & v1_xreal_0(B) ) => v3_membered(k23_member_1(A,B)) ) )).
fof(fc95_valued_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc95_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc96_fomodel0,axiom,( ! [A] : ! [B] : ( ( v4_card_3(A) & v4_card_3(B) ) => v4_card_3(k2_xboole_0(A,B)) ) )).
fof(fc96_member_1,axiom,( ! [A] : ! [B] : ( ( v4_membered(A) & v1_rat_1(B) ) => v4_membered(k23_member_1(A,B)) ) )).
fof(fc96_valued_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc96_valued_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc97_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : v1_xboole_0(k5_xboole_0(k6_subset_1(A,k6_subset_1(k2_xboole_0(A,B),C)),k3_xboole_0(A,C))) )).
fof(fc97_member_1,axiom,( ! [A] : ! [B] : ( ( v5_membered(A) & v1_int_1(B) ) => v5_membered(k23_member_1(A,B)) ) )).
fof(fc97_valued_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc97_valued_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc98_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & 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(k7_fomodel0(A),k7_finseq_1(k12_finseq_1(A,B),C)),B)) ) )).
fof(fc98_member_1,axiom,( ! [A] : ! [B] : ( ( v6_membered(A) & v7_ordinal1(B) ) => v6_membered(k23_member_1(A,B)) ) )).
fof(fc98_valued_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc98_valued_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc99_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(C,k1_zfmisc_1(A)) & m1_subset_1(D,k1_zfmisc_1(B)) ) => v1_xboole_0(k4_xboole_0(k7_subset_1(A,C,B),k6_subset_1(A,D))) ) )).
fof(fc99_member_1,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(A) & v1_xxreal_0(B) ) => v1_xboole_0(k24_member_1(A,B)) ) )).
fof(fc99_valued_0,axiom,( ! [A] : ( 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)) ) ) )).
fof(fc99_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(fc9_abcmiz_a,axiom,( v1_msualg_1(k27_abcmiz_1) & v1_instalg1(k27_abcmiz_1) & v1_abcmiz_1(k27_abcmiz_1) & v3_abcmiz_a(k27_abcmiz_1) )).
fof(fc9_abian,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_abian(A) & v1_int_1(B) & v1_abian(B) ) => v1_abian(k2_xcmplx_0(A,B)) ) )).
fof(fc9_afinsq_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(k6_afinsq_1(A,B)) & v1_funct_1(k6_afinsq_1(A,B)) ) )).
fof(fc9_algstr_0,axiom,( v13_struct_0(k3_algstr_0,1) & v8_algstr_0(k3_algstr_0) )).
fof(fc9_algstr_1,axiom,( v29_algstr_0(k3_algstr_1) & v3_group_1(k3_algstr_1) )).
fof(fc9_algstr_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc9_ami_6,axiom,( ! [A] : ! [B] : ( ( 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(k7_card_1(2),k1_ami_3,k4_ami_3(A,B))) ) )).
fof(fc9_aofa_000,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc9_aofa_a00,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => v1_funcop_1(u4_msualg_1(A,B)) ) )).
fof(fc9_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(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) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) & v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) & m2_pboole(E,u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,D)) & m1_subset_1(F,k1_funct_1(u3_msualg_1(A,C),u8_aofa_a00(A))) ) => v1_xboolean(k15_aofa_a00(A,B,C,D,u8_aofa_a00(A),F,E)) ) )).
fof(fc9_bagorder,axiom,( ! [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(k14_bagorder(A)) & v3_orders_2(k14_bagorder(A)) & v4_orders_2(k14_bagorder(A)) & v5_orders_2(k14_bagorder(A)) ) ) )).
fof(fc9_bhsp_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & v2_bhsp_3(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v2_bhsp_3(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k3_normsp_1(A,B,C)) & v1_funct_2(k3_normsp_1(A,B,C),k4_ordinal1,u1_struct_0(A)) & v2_bhsp_3(k3_normsp_1(A,B,C),A) ) ) )).
fof(fc9_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc9_binop_2,axiom,( v1_funct_1(k23_binop_2) & v1_funct_2(k23_binop_2,k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1) & v1_binop_1(k23_binop_2,k4_ordinal1) & v2_binop_1(k23_binop_2,k4_ordinal1) )).
fof(fc9_borsuk_1,axiom,( ~ v2_struct_0(k17_borsuk_1) & v1_pre_topc(k17_borsuk_1) & v2_pre_topc(k17_borsuk_1) )).
fof(fc9_borsuk_2,axiom,( v1_borsuk_2(k17_borsuk_1) )).
fof(fc9_borsuk_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v1_rat_1(A) ) => ~ v1_rat_1(k3_int_1(A)) ) )).
fof(fc9_borsuk_6,axiom,( ~ v1_xboole_0(k7_borsuk_6) & v4_pre_topc(k7_borsuk_6,k2_borsuk_1(k5_topmetr,k5_topmetr)) )).
fof(fc9_borsuk_7,axiom,( ! [A] : ( v1_int_1(A) => v3_topalg_6(k13_borsuk_7(A),k8_toprealb(3),k8_borsuk_7) ) )).
fof(fc9_c0sp2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc9_card_1,axiom,( ~ v1_finset_1(k4_ordinal1) )).
fof(fc9_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v3_card_3(k4_card_3(A)) ) )).
fof(fc9_card_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc9_catalg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc9_cayldick,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_binop_1(B,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_funct_1(H) & v1_funct_2(H,A,A) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( v2_rlvect_1(g1_cayldick(A,C,B,D,E,F,G,H)) & v1_cayldick(g1_cayldick(A,C,B,D,E,F,G,H)) ) ) )).
fof(fc9_cayley,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(fc9_cc0sp2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc9_cfdiff_1,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & 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)) ) ) )).
fof(fc9_cfuncdom,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(fc9_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ~ v1_xboole_0(k10_cgames_1(A)) ) )).
fof(fc9_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_circcmb3(A) & l1_msualg_1(A) ) => ~ v1_facirc_1(k2_msafree2(A)) ) )).
fof(fc9_circcomb,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc9_clopban1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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)) ) ) )).
fof(fc9_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => ( ~ v2_struct_0(k9_clopban2(A)) & v1_clopban2(k9_clopban2(A)) ) ) )).
fof(fc9_closure1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc9_closure2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc9_coh_sp,axiom,( ! [A] : ~ v1_xboole_0(k16_coh_sp(A)) )).
fof(fc9_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v1_relat_1(k7_cohsp_1(A)) ) )).
fof(fc9_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_compos_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k4_ordinal1) & 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),k4_ordinal1) & 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)) ) ) )).
fof(fc9_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v2_margrel1(A) ) => v3_comput_1(k5_finseq_1(A)) ) )).
fof(fc9_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v1_comseq_3(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_funct_1(k4_comseq_3(A)) & v1_funct_2(k4_comseq_3(A),k4_ordinal1,k1_numbers) & v1_series_1(k4_comseq_3(A)) ) ) )).
fof(fc9_csspace4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc9_dickson,axiom,( ! [A] : ( ( 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(k4_yellow_1(k1_xboole_0,A)) & v4_dickson(k4_yellow_1(k1_xboole_0,A)) ) ) )).
fof(fc9_dilworth,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc9_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => v3_finseq_1(k1_euclid(A)) ) )).
fof(fc9_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => v5_euclid_7(k8_euclid_7(A),A) ) )).
fof(fc9_euclid_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) & v1_valued_0(B) & v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & v1_valued_0(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) ) ) )).
fof(fc9_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v1_relat_1(B) & v5_relat_1(B,A) & ~ v1_xboole_0(B) & 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(k9_funct_7(B,C,D),A) ) )).
fof(fc9_facirc_1,axiom,( ! [A] : ! [B] : ( ( v1_xtuple_0(A) & v1_xtuple_0(B) ) => v1_relat_1(k2_tarski(A,B)) ) )).
fof(fc9_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc9_filter_2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc9_finseq_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(k11_finseq_1(A,B,C)) & v1_funct_1(k11_finseq_1(A,B,C)) ) )).
fof(fc9_finseq_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc9_finset_1,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_xboole_0(A,B)) ) )).
fof(fc9_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc9_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ~ v1_finset_1(k1_fomodel1(A)) ) )).
fof(fc9_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(k10_fomodel2(A,B,C)) & v1_funct_1(k10_fomodel2(A,B,C)) & v2_fomodel2(k10_fomodel2(A,B,C),A,B,C) ) ) )).
fof(fc9_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc9_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v2_fomodel4(C,A) ) => v2_fomodel4(k3_xboole_0(C,B),A) ) )).
fof(fc9_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) )).
fof(fc9_funcop_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc9_funcsdom,axiom,( ! [A] : ( 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)) ) )).
fof(fc9_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( v1_relat_1(k6_relat_1(A,B)) & v1_funct_1(k6_relat_1(A,B)) ) ) )).
fof(fc9_funct_2,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(fc9_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(fc9_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_relat_1(k9_funct_7(A,B,C)) & v1_funct_1(k9_funct_7(A,B,C)) ) ) )).
fof(fc9_funct_9,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc9_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(fc9_gate_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => v1_xboole_0(k4_gate_1(A,B)) ) )).
fof(fc9_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(fc9_gr_cy_1,axiom,( ~ v2_struct_0(k2_gr_cy_1) & v15_algstr_0(k2_gr_cy_1) & v1_gr_cy_1(k2_gr_cy_1) )).
fof(fc9_graph_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc9_grcat_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(fc9_group_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc9_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & l3_algstr_0(A) ) => v2_group_7(k5_finseq_1(A),k1_tarski(1)) ) )).
fof(fc9_hermitan,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc9_hilbert3,axiom,( v1_hilbert3(k2_hilbert1) )).
fof(fc9_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc9_index_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_index_1(C,A,B) => ( v1_relat_1(k2_xtuple_0(C)) & v1_funct_1(k2_xtuple_0(C)) ) ) )).
fof(fc9_int_6,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc9_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ( v3_lattices(k21_interva1(A)) & v10_lattices(k21_interva1(A)) ) ) )).
fof(fc9_jordan,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) & ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & 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))) ) )).
fof(fc9_jordan2c,axiom,( ! [A] : ( ( 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)) ) )).
fof(fc9_kurato_1,axiom,( v1_setfam_1(k3_kurato_1(k3_topmetr,k6_kurato_1)) )).
fof(fc9_lattice2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc9_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(fc9_lopban_1,axiom,( ! [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) & 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)) ) ) )).
fof(fc9_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => ( ~ v2_struct_0(k9_lopban_2(A)) & v1_lopban_2(k9_lopban_2(A)) ) ) )).
fof(fc9_ltlaxio3,axiom,( ~ v2_ltlaxio3(k4_tarski(k6_finseq_1(k1_hilbert1),k6_finseq_1(k1_hilbert1))) )).
fof(fc9_ltlaxio4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_ltlaxio3(A) & m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) & m3_ltlaxio4(B,A) & m1_subset_1(C,k9_xtuple_0(B)) ) => ~ v1_xboole_0(k1_trees_2(k9_xtuple_0(B),C)) ) )).
fof(fc9_lukasi_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(fc9_matroid0,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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)) ) ) )).
fof(fc9_matrtop1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc9_matrtop3,axiom,( ! [A] : ! [B] : ( ( 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))))) ) => ( v1_matrix_0(k3_matrtop3(A,B)) & v2_matrix_0(k3_matrtop3(A,B),u1_struct_0(k2_vectsp_1),A,A) & v4_matrix_6(k3_matrtop3(A,B),A,k2_vectsp_1) ) ) )).
fof(fc9_mazurulm,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc9_member_1,axiom,( ! [A] : ( v5_membered(A) => ( v1_membered(k5_member_1(A)) & v5_membered(k5_member_1(A)) ) ) )).
fof(fc9_membered,axiom,( ! [A] : ( v1_xreal_0(A) => v3_membered(k1_tarski(A)) ) )).
fof(fc9_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_partfun1(D,u1_struct_0(B)) ) => ( v1_relat_1(k1_funct_7(D,k4_struct_0(B),C)) & v1_funct_1(k1_funct_7(D,k4_struct_0(B),C)) & v5_funct_1(k1_funct_7(D,k4_struct_0(B),C),k2_memstr_0(A,B)) ) ) )).
fof(fc9_metrizts,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc9_mod_4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc9_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ v1_xboole_0(k30_modelc_1(A)) ) )).
fof(fc9_msafree,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc9_msafree1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(fc9_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) & v4_relat_1(k3_relat_1(C,B),k4_finseq_1(C)) & v1_partfun1(k3_relat_1(C,B),k4_finseq_1(C)) ) ) )).
fof(fc9_msualg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) )).
fof(fc9_mycielsk,axiom,( ! [A] : ( ( v3_dilworth(A) & l1_orders_2(A) ) => ( v1_orders_2(k3_necklace(A)) & v4_dilworth(k3_necklace(A)) ) ) )).
fof(fc9_nat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) & ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ( v1_relat_1(k3_relat_1(A,C)) & v1_partfun1(k3_relat_1(A,C),k4_ordinal1) ) ) )).
fof(fc9_nat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc9_neckla_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc9_newton,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => v1_xreal_0(k3_newton(A,B)) ) )).
fof(fc9_nfcont_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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_xreal_0(C) ) => ( v1_funct_1(k4_vfunct_1(k1_numbers,A,B,C)) & v2_nfcont_3(k4_vfunct_1(k1_numbers,A,B,C),A) ) ) )).
fof(fc9_nfcont_4,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & 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)) ) ) )).
fof(fc9_numbers,axiom,( ~ v1_finset_1(k2_numbers) )).
fof(fc9_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v1_lattice2(A) & l3_lattices(A) ) => ~ v1_xboole_0(k7_openlatt(A)) ) )).
fof(fc9_orders_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) & m1_orders_1(B,k6_partfun1(k1_orders_1(u1_struct_0(A)))) ) => ~ v1_xboole_0(k4_orders_2(A,B)) ) )).
fof(fc9_ordinal1,axiom,( v8_ordinal1(k5_ordinal1) )).
fof(fc9_ordinal6,axiom,( ! [A] : ( v1_xboole_0(A) => v1_xboole_0(k2_ordinal1(A)) ) )).
fof(fc9_osafree,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) )).
fof(fc9_partfun3,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(B) & ~ v2_xxreal_0(B) ) => v3_partfun3(k2_funcop_1(A,B)) ) )).
fof(fc9_pcs_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc9_polynom1,axiom,( ! [A] : ! [B] : ( ( 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(k12_polynom1(A,B)) & v36_algstr_0(k12_polynom1(A,B)) & v4_rlvect_1(k12_polynom1(A,B)) ) ) )).
fof(fc9_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ( ~ v2_struct_0(k14_polynom3(A)) & v36_algstr_0(k14_polynom3(A)) & v2_rlvect_1(k14_polynom3(A)) ) ) )).
fof(fc9_pralg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc9_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc9_pre_topc,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc9_prvect_3,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc9_pscomp_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc9_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => v1_xreal_0(k14_quaterni(A)) ) )).
fof(fc9_quofield,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(fc9_ratfunc1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(fc9_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ( v3_xxreal_2(k2_limfunc1(A)) & ~ v4_xxreal_2(k2_limfunc1(A)) & v6_xxreal_2(k2_limfunc1(A)) ) ) )).
fof(fc9_relat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ~ v1_xboole_0(k10_xtuple_0(A)) ) )).
fof(fc9_relat_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_relat_2(A) ) => ( v1_relat_1(k2_relat_1(A)) & v3_relat_2(k2_relat_1(A)) ) ) )).
fof(fc9_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_zfmisc_1(B,C)))) => v1_relat_1(k10_xtuple_0(D)) ) )).
fof(fc9_rfunct_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc9_rlaffin1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc9_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(fc9_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & l2_robbins1(A) ) => ( v4_lattices(k8_robbins1(A)) & v4_robbins1(k8_robbins1(A)) ) ) )).
fof(fc9_roughs_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(fc9_rsspace4,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc9_rvsum_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(fc9_scm_halt,axiom,( ! [A] : ! [B] : ( ( 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),k4_ordinal1) & 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)) ) ) )).
fof(fc9_scmfsa10,axiom,( ! [A] : ! [B] : ( ( 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(k7_card_1(3),k1_scmfsa_2,k8_scmfsa_2(A,B))) ) )).
fof(fc9_scmfsa6c,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc9_scmfsa8b,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k7_card_1(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),k4_ordinal1) & 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),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(fc9_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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),k7_card_1(3),k1_scmfsa_2) ) )).
fof(fc9_scmfsa_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(fc9_scmfsa_m,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) & v7_ordinal1(B) ) => ~ v1_xboole_0(k1_funct_1(k8_scmfsa_m(A),B)) ) )).
fof(fc9_scmpds_4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) & v3_scmpds_4(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) & v3_scmpds_4(B) ) => ( v1_relat_1(k1_ordinal4(A,B)) & v4_relat_1(k1_ordinal4(A,B),k4_ordinal1) & v5_relat_1(k1_ordinal4(A,B),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k1_ordinal4(A,B)) & 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)) ) ) )).
fof(fc9_scmpds_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(fc9_scmpds_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & 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_relat_1(k6_scmpds_6(B,C,A)) & v4_relat_1(k6_scmpds_6(B,C,A),k4_ordinal1) & v5_relat_1(k6_scmpds_6(B,C,A),u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(k6_scmpds_6(B,C,A)) & 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)) ) ) )).
fof(fc9_scmring2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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))) & v7_ordinal1(C) ) => ~ v2_extpro_1(k9_scmring2(A,C,B),k7_card_1(2),k1_scmring2(A)) ) )).
fof(fc9_scmring3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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(k7_card_1(2),k1_scmring2(A),k5_scmring2(A,B,C))) ) )).
fof(fc9_scmyciel,axiom,( v4_scmyciel(k1_tarski(k1_xboole_0)) )).
fof(fc9_setfam_1,axiom,( ! [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_setfam_1(k6_enumset1(A,B,C,D,E,F,G,H)) ) )).
fof(fc9_sfmastr1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(fc9_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ( v1_finset_1(C) => v5_finset_1(k3_simplex0(A,B,C)) ) )).
fof(fc9_simplex1,axiom,( ! [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) & 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) ) ) )).
fof(fc9_sin_cos6,axiom,( v1_relat_1(k5_relat_1(k16_sin_cos,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2)))) & v2_funct_1(k5_relat_1(k16_sin_cos,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(fc9_sincos10,axiom,( v1_funct_1(k1_sincos10) & v2_funct_1(k1_sincos10) )).
fof(fc9_sppol_2,axiom,( ! [A] : ! [B] : ( ( v1_topreal1(A) & m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & v7_ordinal1(B) ) => v1_topreal1(k16_finseq_1(B,A)) ) )).
fof(fc9_sprect_1,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => v5_xxreal_2(k1_xxreal_1(A,B)) ) )).
fof(fc9_stacks_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_stacks_1(A) & l1_stacks_1(A) ) => ~ v1_xboole_0(u1_stacks_1(A)) ) )).
fof(fc9_struct_0,axiom,( ! [A] : ( ( ~ v8_struct_0(A) & l1_struct_0(A) ) => ~ v1_finset_1(u1_struct_0(A)) ) )).
fof(fc9_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ~ v1_xboole_0(k8_enumset1(A,B,C,D,E,F,G,H,I,J)) )).
fof(fc9_tex_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ~ v1_xboole_0(k2_tex_4(A,B)) ) )).
fof(fc9_topalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc9_topalg_5,axiom,( 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))) )).
fof(fc9_topalg_6,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc9_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => v9_rltopsp1(k2_topreal9(A,B,C),k15_euclid(A)) ) )).
fof(fc9_topreala,axiom,( ! [A] : ! [B] : ( ( ~ v2_xxreal_0(A) & v1_xreal_0(A) & v2_xxreal_0(B) & v1_xreal_0(B) ) => ~ v1_xboole_0(k4_xxreal_1(A,B)) ) )).
fof(fc9_toprealb,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => ~ v1_xboole_0(k1_toprealb(A,B)) ) )).
fof(fc9_toprealc,axiom,( v5_rltopsp1(k15_euclid(k5_numbers)) & v3_topmetr(k15_euclid(k5_numbers)) )).
fof(fc9_tops_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc9_trees_1,axiom,( ~ v1_finset_1(k8_trees_1) )).
fof(fc9_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ( ~ v1_xboole_0(k5_finseq_1(A)) & v4_trees_3(k5_finseq_1(A)) ) ) )).
fof(fc9_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => v3_trees_3(k1_tarski(A)) ) )).
fof(fc9_valued_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v3_valued_0(A) & v1_relat_1(B) & v3_valued_0(B) ) => v3_valued_0(k2_xboole_0(A,B)) ) )).
fof(fc9_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(fc9_vectsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) ) )).
fof(fc9_waybel10,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc9_waybel11,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc9_waybel18,axiom,( ! [A] : ! [B] : ( l1_pre_topc(B) => v1_waybel18(k2_funcop_1(A,B)) ) )).
fof(fc9_waybel23,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(fc9_waybel24,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc9_waybel25,axiom,( ! [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) ) => ( v3_lattice3(k1_waybel25(A)) & v1_waybel_9(k1_waybel25(A)) ) ) )).
fof(fc9_waybel29,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(fc9_waybel30,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) )).
fof(fc9_waybel34,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(fc9_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(fc9_waybel_1,axiom,( ! [A] : ( v1_orders_2(k2_yellow_1(A)) & v10_waybel_1(k2_yellow_1(A)) ) )).
fof(fc9_waybel_2,axiom,( ! [A] : ( ( 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(k1_yellow_1(k7_waybel_0(A))),u1_struct_0(A)) & v20_waybel_0(k2_yellow_2(A),k1_yellow_1(k7_waybel_0(A)),A) ) ) )).
fof(fc9_waybel_3,axiom,( ! [A] : ! [B] : ( ( 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(k4_yellow_1(A,B)) & v1_orders_2(k4_yellow_1(A,B)) ) ) )).
fof(fc9_waybel_4,axiom,( ! [A] : ( ( 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(k1_yellow_1(k3_waybel_4(A))) & v2_lattice3(k1_yellow_1(k3_waybel_4(A))) ) ) )).
fof(fc9_waybel_8,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(fc9_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( ~ v2_struct_0(k2_waybel_9(A)) & v6_waybel_0(k2_waybel_9(A),A) ) ) )).
fof(fc9_xboolean,axiom,( ! [A] : ! [B] : ( ( v1_xboolean(A) & v1_xboolean(B) ) => v1_xboolean(k10_xboolean(A,B)) ) )).
fof(fc9_xcmplx_0,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(A) & v1_xcmplx_0(A) & ~ v8_ordinal1(B) & v1_xcmplx_0(B) ) => ~ v8_ordinal1(k7_xcmplx_0(A,B)) ) )).
fof(fc9_xreal_0,axiom,( ! [A] : ! [B] : ( ( ~ v3_xxreal_0(A) & v1_xreal_0(A) & ~ v3_xxreal_0(B) & v1_xreal_0(B) ) => ~ v3_xxreal_0(k2_xcmplx_0(A,B)) ) )).
fof(fc9_xtuple_0,axiom,( ! [A] : ( v1_xboole_0(A) => v1_xboole_0(k14_xtuple_0(A)) ) )).
fof(fc9_xxreal_1,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => v3_membered(k4_xxreal_1(A,B)) ) )).
fof(fc9_xxreal_2,axiom,( ! [A] : ( ( v5_membered(A) & v2_xxreal_2(A) ) => ( v1_xxreal_0(k1_xxreal_2(A)) & v1_int_1(k1_xxreal_2(A)) ) ) )).
fof(fc9_xxreal_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(fc9_yellow10,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fc9_yellow_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ~ v7_struct_0(k1_yellow_1(u1_pre_topc(A))) & v1_orders_2(k1_yellow_1(u1_pre_topc(A))) & v3_lattice3(k1_yellow_1(u1_pre_topc(A))) ) ) )).
fof(fc9_yellow_3,axiom,( ! [A] : ( ( ~ v1_yellow_3(A) & l1_orders_2(A) ) => ~ v1_xboole_0(u1_orders_2(A)) ) )).
fof(fc9_yellow_6,axiom,( ! [A] : ! [B] : ( ( ~ 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(k4_yellow_1(A,B)) & v1_orders_2(k4_yellow_1(A,B)) ) ) )).
fof(fc9_yellow_7,axiom,( ! [A] : ( ( v1_yellow_0(A) & l1_orders_2(A) ) => ( v1_orders_2(k7_lattice3(A)) & v2_yellow_0(k7_lattice3(A)) ) ) )).
fof(fc9_yellow_9,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(fraenkel_a_0_0_abcmiz_1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_abcmiz_1) <=> ? [B] : ( m1_subset_1(B,k4_ordinal1) & A = k4_tarski(k1_xboole_0,B) ) ) )).
fof(fraenkel_a_0_0_ami_5,axiom,( ! [A] : ( r2_hidden(A,a_0_0_ami_5) <=> ? [B] : ? [C] : ( m2_subset_1(B,k4_ordinal1,k7_card_1(9)) & v7_ordinal1(C) & A = k3_xtuple_0(B,k9_finseq_1(C),k1_xboole_0) & B = 6 ) ) )).
fof(fraenkel_a_0_0_arytm_0,axiom,( ! [A] : ( r2_hidden(A,a_0_0_arytm_0) <=> ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k5_arytm_3)) & A = B & ! [C] : ( m1_subset_1(C,k5_arytm_3) => ( r2_hidden(C,B) => ( ! [D] : ( m1_subset_1(D,k5_arytm_3) => ( r3_arytm_3(D,C) => r2_hidden(D,B) ) ) & ? [D] : ( m1_subset_1(D,k5_arytm_3) & r2_hidden(D,B) & ~ r3_arytm_3(D,C) ) ) ) ) ) ) )).
fof(fraenkel_a_0_0_arytm_2,axiom,( ! [A] : ( r2_hidden(A,a_0_0_arytm_2) <=> ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k5_arytm_3)) & A = B & ! [C] : ( m1_subset_1(C,k5_arytm_3) => ( r2_hidden(C,B) => ( ! [D] : ( m1_subset_1(D,k5_arytm_3) => ( r3_arytm_3(D,C) => r2_hidden(D,B) ) ) & ? [D] : ( m1_subset_1(D,k5_arytm_3) & r2_hidden(D,B) & ~ r3_arytm_3(D,C) ) ) ) ) ) ) )).
fof(fraenkel_a_0_0_arytm_3,axiom,( ! [A] : ( r2_hidden(A,a_0_0_arytm_3) <=> ? [B] : ? [C] : ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & A = k4_tarski(B,C) & r1_arytm_3(B,C) & C != k1_xboole_0 ) ) )).
fof(fraenkel_a_0_0_asympt_1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_asympt_1) <=> ? [B] : ( m1_subset_1(B,k4_ordinal1) & A = k5_series_1(2,B) ) ) )).
fof(fraenkel_a_0_0_borsuk_1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_borsuk_1) <=> ? [B] : ( v1_xreal_0(B) & A = B & r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(B,1) ) ) )).
fof(fraenkel_a_0_0_calcul_1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_calcul_1) <=> ? [B] : ( v7_ordinal1(B) & A = B & r1_xxreal_0(B,9) ) ) )).
fof(fraenkel_a_0_0_complex1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_complex1) <=> ? [B] : ( m2_funct_2(B,2,k1_numbers,k9_funct_2(2,k1_numbers)) & A = B & k1_funct_1(B,1) = k5_numbers ) ) )).
fof(fraenkel_a_0_0_comput_1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_comput_1) <=> ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_comput_1(k4_ordinal1))) & A = B & v6_comput_1(B) ) ) )).
fof(fraenkel_a_0_0_cqc_the1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_cqc_the1) <=> ? [B] : ( v7_ordinal1(B) & A = B & r1_xxreal_0(B,9) ) ) )).
fof(fraenkel_a_0_0_dickson,axiom,( ! [A] : ( r2_hidden(A,a_0_0_dickson) <=> ? [B] : ? [C] : ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & A = k1_domain_1(k4_ordinal1,k4_ordinal1,B,C) & r1_xxreal_0(B,C) ) ) )).
fof(fraenkel_a_0_0_diff_4,axiom,( ! [A] : ( r2_hidden(A,a_0_0_diff_4) <=> ? [B] : ( v1_xreal_0(B) & A = B & ~ r1_xxreal_0(B,k5_numbers) ) ) )).
fof(fraenkel_a_0_0_entropy1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_entropy1) <=> ? [B] : ( v1_xreal_0(B) & A = B & ~ r1_xxreal_0(B,k5_numbers) ) ) )).
fof(fraenkel_a_0_0_euler_1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_euler_1) <=> ? [B] : ( m1_subset_1(B,k4_ordinal1) & A = B & r1_int_2(1,B) & r1_xxreal_0(1,B) & r1_xxreal_0(B,1) ) ) )).
fof(fraenkel_a_0_0_fdiff_10,axiom,( ! [A] : ( r2_hidden(A,a_0_0_fdiff_10) <=> ? [B] : ( v1_xreal_0(B) & A = B & ~ r1_xxreal_0(B,k5_numbers) ) ) )).
fof(fraenkel_a_0_0_fdiff_7,axiom,( ! [A] : ( r2_hidden(A,a_0_0_fdiff_7) <=> ? [B] : ( v1_xreal_0(B) & A = B & ~ r1_xxreal_0(B,k5_numbers) ) ) )).
fof(fraenkel_a_0_0_fdiff_8,axiom,( ! [A] : ( r2_hidden(A,a_0_0_fdiff_8) <=> ? [B] : ( v1_xreal_0(B) & A = B & ~ r1_xxreal_0(B,k5_numbers) ) ) )).
fof(fraenkel_a_0_0_fdiff_9,axiom,( ! [A] : ( r2_hidden(A,a_0_0_fdiff_9) <=> ? [B] : ( v1_xreal_0(B) & A = B & ~ r1_xxreal_0(B,k5_numbers) ) ) )).
fof(fraenkel_a_0_0_fib_num2,axiom,( ! [A] : ( r2_hidden(A,a_0_0_fib_num2) <=> ? [B] : ( v7_ordinal1(B) & A = k3_xcmplx_0(2,B) ) ) )).
fof(fraenkel_a_0_0_graph_5,axiom,( ! [A] : ( r2_hidden(A,a_0_0_graph_5) <=> ? [B] : ( v1_xreal_0(B) & A = B & r1_xxreal_0(k5_numbers,B) ) ) )).
fof(fraenkel_a_0_0_groeb_1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_groeb_1) <=> ? [B] : ( m1_subset_1(B,k4_ordinal1) & A = B & ~ r1_xxreal_0(k5_numbers,B) ) ) )).
fof(fraenkel_a_0_0_hilbert3,axiom,( ! [A] : ( r2_hidden(A,a_0_0_hilbert3) <=> ? [B] : ( m1_subset_1(B,k1_hilbert1) & A = B & v1_hilbert3(B) ) ) )).
fof(fraenkel_a_0_0_integr12,axiom,( ! [A] : ( r2_hidden(A,a_0_0_integr12) <=> ? [B] : ( v1_xreal_0(B) & A = B & ~ r1_xxreal_0(B,k5_numbers) ) ) )).
fof(fraenkel_a_0_0_integr13,axiom,( ! [A] : ( r2_hidden(A,a_0_0_integr13) <=> ? [B] : ( v1_xreal_0(B) & A = B & ~ r1_xxreal_0(B,k5_numbers) ) ) )).
fof(fraenkel_a_0_0_jgraph_2,axiom,( ! [A] : ( r2_hidden(A,a_0_0_jgraph_2) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & ( ( r1_xxreal_0(k18_euclid(B),k17_euclid(B)) & r1_xxreal_0(k4_xcmplx_0(k17_euclid(B)),k18_euclid(B)) ) | ( r1_xxreal_0(k17_euclid(B),k18_euclid(B)) & r1_xxreal_0(k18_euclid(B),k4_xcmplx_0(k17_euclid(B))) ) ) & B != k4_struct_0(k15_euclid(2)) ) ) )).
fof(fraenkel_a_0_0_jgraph_4,axiom,( ! [A] : ( r2_hidden(A,a_0_0_jgraph_4) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & r1_xxreal_0(k17_euclid(B),k5_numbers) & B != k4_struct_0(k15_euclid(2)) ) ) )).
fof(fraenkel_a_0_0_jgraph_5,axiom,( ! [A] : ( r2_hidden(A,a_0_0_jgraph_5) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & r1_xxreal_0(k12_euclid(B),1) ) ) )).
fof(fraenkel_a_0_0_jgraph_6,axiom,( ! [A] : ( r2_hidden(A,a_0_0_jgraph_6) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & k12_euclid(B) = 1 ) ) )).
fof(fraenkel_a_0_0_jordan,axiom,( ! [A] : ( r2_hidden(A,a_0_0_jordan) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & ~ ( ~ ( k17_euclid(B) = k4_xcmplx_0(1) & r1_xxreal_0(k18_euclid(B),3) & r1_xxreal_0(k4_xcmplx_0(3),k18_euclid(B)) ) & ~ ( r1_xxreal_0(k17_euclid(B),1) & r1_xxreal_0(k4_xcmplx_0(1),k17_euclid(B)) & k18_euclid(B) = 3 ) & ~ ( r1_xxreal_0(k17_euclid(B),1) & r1_xxreal_0(k4_xcmplx_0(1),k17_euclid(B)) & k18_euclid(B) = k4_xcmplx_0(3) ) & ~ ( k17_euclid(B) = 1 & r1_xxreal_0(k18_euclid(B),3) & r1_xxreal_0(k4_xcmplx_0(3),k18_euclid(B)) ) ) ) ) )).
fof(fraenkel_a_0_0_jordan1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_jordan1) <=> ? [B] : ( v1_xreal_0(B) & A = B & r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(B,1) ) ) )).
fof(fraenkel_a_0_0_jordan1h,axiom,( ! [A] : ( r2_hidden(A,a_0_0_jordan1h) <=> ? [B] : ? [C] : ( v1_xreal_0(B) & v1_xreal_0(C) & A = k4_tarski(B,C) & r1_xxreal_0(B,C) ) ) )).
fof(fraenkel_a_0_0_jordan1k,axiom,( ! [A] : ( r2_hidden(A,a_0_0_jordan1k) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & ~ r1_xxreal_0(1,k12_euclid(B)) ) ) )).
fof(fraenkel_a_0_0_jordan2c,axiom,( ! [A] : ( r2_hidden(A,a_0_0_jordan2c) <=> ? [B] : ( v1_xreal_0(B) & A = B & r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(B,1) ) ) )).
fof(fraenkel_a_0_0_jordan5c,axiom,( ! [A] : ( r2_hidden(A,a_0_0_jordan5c) <=> ? [B] : ( v1_xreal_0(B) & A = B & r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(B,1) ) ) )).
fof(fraenkel_a_0_0_jordan6,axiom,( ! [A] : ( r2_hidden(A,a_0_0_jordan6) <=> ? [B] : ( v1_xreal_0(B) & A = B & ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(1,B) ) ) )).
fof(fraenkel_a_0_0_ltlaxio1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_ltlaxio1) <=> ? [B] : ( m2_subset_1(B,k1_hilbert1,k13_ltlaxio1) & A = B & ~ ( ~ v1_ltlaxio1(B) & ~ v3_ltlaxio1(B) & ~ v4_ltlaxio1(B) & ~ v5_ltlaxio1(B) & ~ v6_ltlaxio1(B) & ~ v7_ltlaxio1(B) & ~ v8_ltlaxio1(B) & ~ v9_ltlaxio1(B) ) ) ) )).
fof(fraenkel_a_0_0_modelc_1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_modelc_1) <=> ? [B] : ( v1_modelc_1(B) & m2_finseq_1(B,k4_ordinal1) & A = B & v2_modelc_1(B) ) ) )).
fof(fraenkel_a_0_0_modelc_2,axiom,( ! [A] : ( r2_hidden(A,a_0_0_modelc_2) <=> ? [B] : ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) & A = B & v2_modelc_2(B) ) ) )).
fof(fraenkel_a_0_0_msualg_7,axiom,( ! [A] : ( r2_hidden(A,a_0_0_msualg_7) <=> ? [B] : ( v1_xreal_0(B) & A = B & ~ r1_xxreal_0(B,k7_xcmplx_0(1,2)) & r1_xxreal_0(B,1) ) ) )).
fof(fraenkel_a_0_0_neckla_2,axiom,( ! [A] : ( r2_hidden(A,a_0_0_neckla_2) <=> ? [B] : ( m1_subset_1(B,k4_ordinal1) & A = k4_tarski(k1_nat_1(B,1),B) & ~ r1_xxreal_0(4,k1_nat_1(B,1)) ) ) )).
fof(fraenkel_a_0_0_numbers,axiom,( ! [A] : ( r2_hidden(A,a_0_0_numbers) <=> ? [B] : ( m2_funct_2(B,k2_tarski(k5_ordinal1,1),k1_numbers,k9_funct_2(k2_tarski(k5_ordinal1,1),k1_numbers)) & A = B & k1_funct_1(B,1) = k5_ordinal1 ) ) )).
fof(fraenkel_a_0_0_pre_ff,axiom,( ! [A] : ( r2_hidden(A,a_0_0_pre_ff) <=> ? [B] : ( v7_ordinal1(B) & A = B & ~ r1_xxreal_0(2,B) ) ) )).
fof(fraenkel_a_0_0_prob_1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_prob_1) <=> ? [B] : ( m1_subset_1(B,k1_numbers) & A = k10_prob_1(B) ) ) )).
fof(fraenkel_a_0_0_pythtrip,axiom,( ! [A] : ( r2_hidden(A,a_0_0_pythtrip) <=> ? [B] : ( m1_pythtrip(B) & A = B & ~ v2_pythtrip(B) & v3_pythtrip(B) ) ) )).
fof(fraenkel_a_0_0_quaterni,axiom,( ! [A] : ( r2_hidden(A,a_0_0_quaterni) <=> ? [B] : ( m2_funct_2(B,4,k1_numbers,k9_funct_2(4,k1_numbers)) & A = B & k1_funct_1(B,2) = k5_numbers & k1_funct_1(B,3) = k5_numbers ) ) )).
fof(fraenkel_a_0_0_rat_1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_rat_1) <=> ? [B] : ? [C] : ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & A = k4_tarski(B,C) & r1_arytm_3(B,C) & C != k11_arytm_3 ) ) )).
fof(fraenkel_a_0_0_real_1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_real_1) <=> ? [B] : ( v1_xreal_0(B) & A = B & r1_xxreal_0(k5_numbers,B) ) ) )).
fof(fraenkel_a_0_0_rfunct_3,axiom,( ! [A] : ( r2_hidden(A,a_0_0_rfunct_3) <=> ? [B] : ( v1_xreal_0(B) & A = B & r1_xxreal_0(B,k5_numbers) ) ) )).
fof(fraenkel_a_0_0_scm_comp,axiom,( ! [A] : ( r2_hidden(A,a_0_0_scm_comp) <=> ? [B] : ( v7_ordinal1(B) & A = B & ~ r1_xxreal_0(1,B) ) ) )).
fof(fraenkel_a_0_0_scm_inst,axiom,( ! [A] : ( r2_hidden(A,a_0_0_scm_inst) <=> ? [B] : ? [C] : ( m2_subset_1(B,k4_ordinal1,k7_card_1(9)) & v7_ordinal1(C) & A = k3_xtuple_0(B,k9_finseq_1(C),k1_xboole_0) & B = 6 ) ) )).
fof(fraenkel_a_0_0_scmfsa_i,axiom,( ! [A] : ( r2_hidden(A,a_0_0_scmfsa_i) <=> ? [B] : ? [C] : ? [D] : ? [E] : ( m2_subset_1(B,k4_ordinal1,k7_card_1(13)) & m1_subset_1(C,k2_scm_inst) & m1_subset_1(D,k2_scm_inst) & m1_subset_1(E,k1_scmfsa_i) & A = k3_xtuple_0(B,k1_xboole_0,k11_finseq_1(D,E,C)) & r2_hidden(B,k2_tarski(9,10)) ) ) )).
fof(fraenkel_a_0_0_scmpds_i,axiom,( ! [A] : ( r2_hidden(A,a_0_0_scmpds_i) <=> ? [B] : ( m1_subset_1(B,k4_numbers) & A = k3_xtuple_0(14,k1_xboole_0,k12_finseq_1(k4_numbers,B)) ) ) )).
fof(fraenkel_a_0_0_scmring3,axiom,( ! [A] : ( r2_hidden(A,a_0_0_scmring3) <=> ? [B] : ? [C] : ? [D] : ( m2_subset_1(B,k4_ordinal1,k7_card_1(8)) & m1_subset_1(C,k8_struct_0(k1_ami_3)) & m1_subset_1(D,k8_struct_0(k1_ami_3)) & A = k3_xtuple_0(B,k1_xboole_0,k10_finseq_1(C,D)) & r2_hidden(B,k2_enumset1(1,2,3,4)) ) ) )).
fof(fraenkel_a_0_0_scmringi,axiom,( ! [A] : ( r2_hidden(A,a_0_0_scmringi) <=> ? [B] : ? [C] : ? [D] : ( m2_subset_1(B,k4_ordinal1,k7_card_1(8)) & m1_subset_1(C,k2_scm_inst) & m1_subset_1(D,k2_scm_inst) & A = k3_xtuple_0(B,k1_xboole_0,k2_finseq_4(k2_scm_inst,C,D)) & r2_hidden(B,k2_enumset1(1,2,3,4)) ) ) )).
fof(fraenkel_a_0_0_sgraph1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_sgraph1) <=> ? [B] : ? [C] : ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & A = k2_tarski(B,C) & r2_hidden(B,k2_finseq_1(3)) & r2_hidden(C,k2_finseq_1(3)) & B != C ) ) )).
fof(fraenkel_a_0_0_sin_cos9,axiom,( ! [A] : ( r2_hidden(A,a_0_0_sin_cos9) <=> ? [B] : ( v1_xreal_0(B) & A = B & ~ r1_xxreal_0(B,k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2))) & ~ r1_xxreal_0(k7_xcmplx_0(k28_sin_cos,2),B) ) ) )).
fof(fraenkel_a_0_0_taylor_1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_taylor_1) <=> ? [B] : ( v1_xreal_0(B) & A = B & ~ r1_xxreal_0(B,k5_numbers) ) ) )).
fof(fraenkel_a_0_0_topalg_1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_topalg_1) <=> ? [B] : ( v1_xreal_0(B) & A = B & r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(B,1) ) ) )).
fof(fraenkel_a_0_0_topdim_2,axiom,( ! [A] : ( r2_hidden(A,a_0_0_topdim_2) <=> ? [B] : ( v1_xreal_0(B) & A = k9_finseq_1(B) & ~ r1_xxreal_0(B,k3_xxreal_3(k5_numbers,1)) & ~ r1_xxreal_0(k1_nat_1(k5_numbers,1),B) ) ) )).
fof(fraenkel_a_0_0_topgen_3,axiom,( ! [A] : ( r2_hidden(A,a_0_0_topgen_3) <=> ? [B] : ? [C] : ( v1_xreal_0(B) & v1_xreal_0(C) & A = k3_rcomp_1(B,C) & ~ r1_xxreal_0(C,B) & v1_rat_1(C) ) ) )).
fof(fraenkel_a_0_0_topgen_5,axiom,( ! [A] : ( r2_hidden(A,a_0_0_topgen_5) <=> ? [B] : ( v1_xreal_0(B) & A = k19_euclid(B,k5_numbers) ) ) )).
fof(fraenkel_a_0_0_topreal1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_topreal1) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & k17_euclid(B) = k5_numbers & r1_xxreal_0(k18_euclid(B),1) & r1_xxreal_0(k5_numbers,k18_euclid(B)) ) ) )).
fof(fraenkel_a_0_0_topreal2,axiom,( ! [A] : ( r2_hidden(A,a_0_0_topreal2) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & ~ ( ~ ( k17_euclid(B) = k5_numbers & r1_xxreal_0(k18_euclid(B),1) & r1_xxreal_0(k5_numbers,k18_euclid(B)) ) & ~ ( r1_xxreal_0(k17_euclid(B),1) & r1_xxreal_0(k5_numbers,k17_euclid(B)) & k18_euclid(B) = 1 ) & ~ ( r1_xxreal_0(k17_euclid(B),1) & r1_xxreal_0(k5_numbers,k17_euclid(B)) & k18_euclid(B) = k5_numbers ) & ~ ( k17_euclid(B) = 1 & r1_xxreal_0(k18_euclid(B),1) & r1_xxreal_0(k5_numbers,k18_euclid(B)) ) ) ) ) )).
fof(fraenkel_a_0_0_treal_1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_treal_1) <=> ? [B] : ( v1_xreal_0(B) & A = B & r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(B,1) ) ) )).
fof(fraenkel_a_0_0_trees_1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_trees_1) <=> ? [B] : ( v7_ordinal1(B) & A = k5_finseq_2(k4_ordinal1,B,k5_numbers) ) ) )).
fof(fraenkel_a_0_0_uniroots,axiom,( ! [A] : ( r2_hidden(A,a_0_0_uniroots) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k1_uniroots(k1_complfld))) & A = B & k6_group_1(k1_uniroots(k1_complfld),B) = 1 ) ) )).
fof(fraenkel_a_0_0_urysohn2,axiom,( ! [A] : ( r2_hidden(A,a_0_0_urysohn2) <=> ? [B] : ( v1_xreal_0(B) & A = B & ~ r1_xxreal_0(k5_numbers,B) ) ) )).
fof(fraenkel_a_0_0_zf_lang,axiom,( ! [A] : ( r2_hidden(A,a_0_0_zf_lang) <=> ? [B] : ( m1_subset_1(B,k4_ordinal1) & A = B & r1_xxreal_0(5,B) ) ) )).
fof(fraenkel_a_0_10_borsuk_6,axiom,( ! [A] : ( r2_hidden(A,a_0_10_borsuk_6) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k2_borsuk_1(k3_topmetr,k3_topmetr))) & A = B & r1_xxreal_0(k2_xtuple_0(B),k6_xcmplx_0(k3_xcmplx_0(2,k1_xtuple_0(B)),1)) ) ) )).
fof(fraenkel_a_0_10_dtconstr,axiom,( ! [A] : ( r2_hidden(A,a_0_10_dtconstr) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k5_dtconstr)) & A = B & ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ~ r1_lang1(k5_dtconstr,B,C) ) ) ) )).
fof(fraenkel_a_0_11_borsuk_6,axiom,( ! [A] : ( r2_hidden(A,a_0_11_borsuk_6) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k2_borsuk_1(k3_topmetr,k3_topmetr))) & A = B & r1_xxreal_0(k6_xcmplx_0(1,k3_xcmplx_0(2,k1_xtuple_0(B))),k2_xtuple_0(B)) & r1_xxreal_0(k6_xcmplx_0(k3_xcmplx_0(2,k1_xtuple_0(B)),1),k2_xtuple_0(B)) ) ) )).
fof(fraenkel_a_0_11_dtconstr,axiom,( ! [A] : ( r2_hidden(A,a_0_11_dtconstr) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k5_dtconstr)) & A = B & ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & r1_lang1(k5_dtconstr,B,C) ) ) ) )).
fof(fraenkel_a_0_12_borsuk_6,axiom,( ! [A] : ( r2_hidden(A,a_0_12_borsuk_6) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))) & A = B & r1_xxreal_0(k2_xtuple_0(B),k6_xcmplx_0(1,k3_xcmplx_0(2,k1_xtuple_0(B)))) ) ) )).
fof(fraenkel_a_0_13_borsuk_6,axiom,( ! [A] : ( r2_hidden(A,a_0_13_borsuk_6) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))) & A = B & r1_xxreal_0(k6_xcmplx_0(1,k3_xcmplx_0(2,k1_xtuple_0(B))),k2_xtuple_0(B)) & r1_xxreal_0(k6_xcmplx_0(k3_xcmplx_0(2,k1_xtuple_0(B)),1),k2_xtuple_0(B)) ) ) )).
fof(fraenkel_a_0_13_jgraph_6,axiom,( ! [A] : ( r2_hidden(A,a_0_13_jgraph_6) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & ~ ( ~ ( k4_xcmplx_0(1) = k17_euclid(B) & r1_xxreal_0(k4_xcmplx_0(1),k18_euclid(B)) & r1_xxreal_0(k18_euclid(B),1) ) & ~ ( k17_euclid(B) = 1 & r1_xxreal_0(k4_xcmplx_0(1),k18_euclid(B)) & r1_xxreal_0(k18_euclid(B),1) ) & ~ ( k4_xcmplx_0(1) = k18_euclid(B) & r1_xxreal_0(k4_xcmplx_0(1),k17_euclid(B)) & r1_xxreal_0(k17_euclid(B),1) ) & ~ ( 1 = k18_euclid(B) & r1_xxreal_0(k4_xcmplx_0(1),k17_euclid(B)) & r1_xxreal_0(k17_euclid(B),1) ) ) ) ) )).
fof(fraenkel_a_0_14_borsuk_6,axiom,( ! [A] : ( r2_hidden(A,a_0_14_borsuk_6) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))) & A = B & r1_xxreal_0(k2_xtuple_0(B),k6_xcmplx_0(k3_xcmplx_0(2,k1_xtuple_0(B)),1)) ) ) )).
fof(fraenkel_a_0_14_jgraph_6,axiom,( ! [A] : ( r2_hidden(A,a_0_14_jgraph_6) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & ~ ( ~ ( k17_euclid(B) = k4_xcmplx_0(1) & r1_xxreal_0(k4_xcmplx_0(1),k18_euclid(B)) & r1_xxreal_0(k18_euclid(B),1) ) & ~ ( k18_euclid(B) = 1 & r1_xxreal_0(k4_xcmplx_0(1),k17_euclid(B)) & r1_xxreal_0(k17_euclid(B),1) ) & ~ ( k17_euclid(B) = 1 & r1_xxreal_0(k4_xcmplx_0(1),k18_euclid(B)) & r1_xxreal_0(k18_euclid(B),1) ) & ~ ( k18_euclid(B) = k4_xcmplx_0(1) & r1_xxreal_0(k4_xcmplx_0(1),k17_euclid(B)) & r1_xxreal_0(k17_euclid(B),1) ) ) ) ) )).
fof(fraenkel_a_0_15_borsuk_6,axiom,( ! [A] : ( r2_hidden(A,a_0_15_borsuk_6) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))) & A = B & k2_xtuple_0(B) = k6_xcmplx_0(1,k3_xcmplx_0(2,k1_xtuple_0(B))) ) ) )).
fof(fraenkel_a_0_16_borsuk_6,axiom,( ! [A] : ( r2_hidden(A,a_0_16_borsuk_6) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))) & A = B & k2_xtuple_0(B) = k6_xcmplx_0(k3_xcmplx_0(2,k1_xtuple_0(B)),1) ) ) )).
fof(fraenkel_a_0_17_borsuk_6,axiom,( ! [A] : ( r2_hidden(A,a_0_17_borsuk_6) <=> ? [B] : ( v1_xreal_0(B) & A = B & r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(B,1) ) ) )).
fof(fraenkel_a_0_1_abcmiz_1,axiom,( ! [A] : ( r2_hidden(A,a_0_1_abcmiz_1) <=> ? [B] : ? [C] : ( m1_subset_1(B,k1_zfmisc_1(k2_abcmiz_1)) & m1_subset_1(C,k4_ordinal1) & A = k4_tarski(k1_abcmiz_1(B),C) & v1_finset_1(B) ) ) )).
fof(fraenkel_a_0_1_ami_5,axiom,( ! [A] : ( r2_hidden(A,a_0_1_ami_5) <=> ? [B] : ? [C] : ? [D] : ( m2_subset_1(B,k4_ordinal1,k7_card_1(9)) & v7_ordinal1(C) & m1_subset_1(D,k8_struct_0(k1_ami_3)) & A = k3_xtuple_0(B,k9_finseq_1(C),k12_finseq_1(k8_struct_0(k1_ami_3),D)) & r2_hidden(B,k7_domain_1(k4_ordinal1,7,8)) ) ) )).
fof(fraenkel_a_0_1_arytm_0,axiom,( ! [A] : ( r2_hidden(A,a_0_1_arytm_0) <=> ? [B] : ? [C] : ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & A = k4_tarski(B,C) & r1_arytm_3(B,C) & C != k11_arytm_3 ) ) )).
fof(fraenkel_a_0_1_arytm_2,axiom,( ! [A] : ( r2_hidden(A,a_0_1_arytm_2) <=> ? [B] : ( m1_subset_1(B,k5_arytm_3) & A = a_1_0_arytm_2(B) & B != k11_arytm_3 ) ) )).
fof(fraenkel_a_0_1_arytm_3,axiom,( ! [A] : ( r2_hidden(A,a_0_1_arytm_3) <=> ? [B] : ( m1_subset_1(B,k4_ordinal1) & A = k4_tarski(B,1) ) ) )).
fof(fraenkel_a_0_1_asympt_1,axiom,( ! [A] : ( r2_hidden(A,a_0_1_asympt_1) <=> ? [B] : ( m2_funct_2(B,k4_ordinal1,k1_numbers,k9_funct_2(k4_ordinal1,k1_numbers)) & A = B & ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( m1_subset_1(E,k4_ordinal1) & ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(D,k5_numbers) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(E,F) => ( r1_xxreal_0(k3_xcmplx_0(D,k9_nat_1(k1_numbers,k4_asympt_1(1),F)),k9_nat_1(k1_numbers,B,F)) & r1_xxreal_0(k9_nat_1(k1_numbers,B,F),k3_xcmplx_0(C,k9_nat_1(k1_numbers,k4_asympt_1(1),F))) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_0_1_borsuk_2,axiom,( ! [A] : ( r2_hidden(A,a_0_1_borsuk_2) <=> ? [B] : ( v1_xreal_0(B) & A = B & r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(B,1) ) ) )).
fof(fraenkel_a_0_1_euler_1,axiom,( ! [A] : ( r2_hidden(A,a_0_1_euler_1) <=> ? [B] : ( m1_subset_1(B,k4_ordinal1) & A = B & r1_int_2(2,B) & r1_xxreal_0(1,B) & r1_xxreal_0(B,2) ) ) )).
fof(fraenkel_a_0_1_fib_num2,axiom,( ! [A] : ( r2_hidden(A,a_0_1_fib_num2) <=> ? [B] : ( m1_subset_1(B,k4_ordinal1) & A = k1_nat_1(k2_nat_1(2,B),1) ) ) )).
fof(fraenkel_a_0_1_jgraph_2,axiom,( ! [A] : ( r2_hidden(A,a_0_1_jgraph_2) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & ( ( r1_xxreal_0(k17_euclid(B),k18_euclid(B)) & r1_xxreal_0(k4_xcmplx_0(k18_euclid(B)),k17_euclid(B)) ) | ( r1_xxreal_0(k18_euclid(B),k17_euclid(B)) & r1_xxreal_0(k17_euclid(B),k4_xcmplx_0(k18_euclid(B))) ) ) & B != k4_struct_0(k15_euclid(2)) ) ) )).
fof(fraenkel_a_0_1_jgraph_4,axiom,( ! [A] : ( r2_hidden(A,a_0_1_jgraph_4) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & r1_xxreal_0(k5_numbers,k17_euclid(B)) & B != k4_struct_0(k15_euclid(2)) ) ) )).
fof(fraenkel_a_0_1_jgraph_5,axiom,( ! [A] : ( r2_hidden(A,a_0_1_jgraph_5) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & k12_euclid(B) = 1 & r1_xxreal_0(k18_euclid(B),k17_euclid(B)) & r1_xxreal_0(k4_xcmplx_0(k17_euclid(B)),k18_euclid(B)) ) ) )).
fof(fraenkel_a_0_1_jgraph_6,axiom,( ! [A] : ( r2_hidden(A,a_0_1_jgraph_6) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & r1_xxreal_0(k12_euclid(B),1) ) ) )).
fof(fraenkel_a_0_1_jordan2c,axiom,( ! [A] : ( r2_hidden(A,a_0_1_jordan2c) <=> ? [B] : ( v1_xreal_0(B) & A = B & r1_xxreal_0(k7_xcmplx_0(1,2),B) & r1_xxreal_0(B,1) ) ) )).
fof(fraenkel_a_0_1_modelc_2,axiom,( ! [A] : ( r2_hidden(A,a_0_1_modelc_2) <=> ? [B] : ( m1_subset_1(B,k30_modelc_1(k25_modelc_2(k43_modelc_2))) & A = B & ? [C] : B = k45_modelc_2(C) ) ) )).
fof(fraenkel_a_0_1_msualg_7,axiom,( ! [A] : ( r2_hidden(A,a_0_1_msualg_7) <=> ? [B] : ( v1_xreal_0(B) & A = B & ~ r1_xxreal_0(B,k7_xcmplx_0(1,2)) & ~ r1_xxreal_0(1,B) ) ) )).
fof(fraenkel_a_0_1_neckla_2,axiom,( ! [A] : ( r2_hidden(A,a_0_1_neckla_2) <=> ? [B] : ( m1_subset_1(B,k4_ordinal1) & A = k4_tarski(B,k1_nat_1(B,1)) & ~ r1_xxreal_0(4,k1_nat_1(B,1)) ) ) )).
fof(fraenkel_a_0_1_numbers,axiom,( ! [A] : ( r2_hidden(A,a_0_1_numbers) <=> ? [B] : ? [C] : ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & A = k4_tarski(B,C) & r1_arytm_3(B,C) & C != k11_arytm_3 ) ) )).
fof(fraenkel_a_0_1_quaterni,axiom,( ! [A] : ( r2_hidden(A,a_0_1_quaterni) <=> ? [B] : ? [C] : ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & A = k4_tarski(B,C) & r1_arytm_3(B,C) & C != k11_arytm_3 ) ) )).
fof(fraenkel_a_0_1_rat_1,axiom,( ! [A] : ( r2_hidden(A,a_0_1_rat_1) <=> ? [B] : ( m1_subset_1(B,k4_ordinal1) & A = k4_tarski(B,1) ) ) )).
fof(fraenkel_a_0_1_rfunct_3,axiom,( ! [A] : ( r2_hidden(A,a_0_1_rfunct_3) <=> ? [B] : ( v1_xreal_0(B) & A = B & r1_xxreal_0(k5_numbers,B) ) ) )).
fof(fraenkel_a_0_1_scm_comp,axiom,( ! [A] : ( r2_hidden(A,a_0_1_scm_comp) <=> ? [B] : ( v7_ordinal1(B) & A = B & ~ r1_xxreal_0(5,B) ) ) )).
fof(fraenkel_a_0_1_scm_inst,axiom,( ! [A] : ( r2_hidden(A,a_0_1_scm_inst) <=> ? [B] : ? [C] : ? [D] : ( m2_subset_1(B,k4_ordinal1,k7_card_1(9)) & v7_ordinal1(C) & m1_subset_1(D,k2_scm_inst) & A = k3_xtuple_0(B,k9_finseq_1(C),k12_finseq_1(k2_scm_inst,D)) & r2_hidden(B,k7_domain_1(k4_ordinal1,7,8)) ) ) )).
fof(fraenkel_a_0_1_scmfsa_i,axiom,( ! [A] : ( r2_hidden(A,a_0_1_scmfsa_i) <=> ? [B] : ? [C] : ? [D] : ( m2_subset_1(B,k4_ordinal1,k7_card_1(13)) & m1_subset_1(C,k2_scm_inst) & m1_subset_1(D,k1_scmfsa_i) & A = k3_xtuple_0(B,k1_xboole_0,k10_finseq_1(C,D)) & r2_hidden(B,k2_tarski(11,12)) ) ) )).
fof(fraenkel_a_0_1_scmpds_2,axiom,( ! [A] : ( r2_hidden(A,a_0_1_scmpds_2) <=> ? [B] : ( m1_subset_1(B,k4_numbers) & A = k3_xtuple_0(14,k1_xboole_0,k9_finseq_1(B)) ) ) )).
fof(fraenkel_a_0_1_scmpds_i,axiom,( ! [A] : ( r2_hidden(A,a_0_1_scmpds_i) <=> ? [B] : ( m1_subset_1(B,k2_scm_inst) & A = k3_xtuple_0(1,k1_xboole_0,k12_finseq_1(k2_scm_inst,B)) ) ) )).
fof(fraenkel_a_0_1_scmring2,axiom,( ! [A] : ( r2_hidden(A,a_0_1_scmring2) <=> ? [B] : ? [C] : ? [D] : ( m1_subset_1(B,k7_card_1(8)) & m1_subset_1(C,k8_struct_0(k1_ami_3)) & m1_subset_1(D,k8_struct_0(k1_ami_3)) & A = k3_xtuple_0(B,k1_xboole_0,k10_finseq_1(C,D)) & r2_hidden(B,k9_domain_1(k4_ordinal1,1,2,3,4)) ) ) )).
fof(fraenkel_a_0_1_scmring3,axiom,( ! [A] : ( r2_hidden(A,a_0_1_scmring3) <=> ? [B] : ( v7_ordinal1(B) & A = k3_xtuple_0(6,k9_finseq_1(B),k1_xboole_0) ) ) )).
fof(fraenkel_a_0_1_scmringi,axiom,( ! [A] : ( r2_hidden(A,a_0_1_scmringi) <=> ? [B] : ( v7_ordinal1(B) & A = k3_xtuple_0(6,k9_finseq_1(B),k1_xboole_0) ) ) )).
fof(fraenkel_a_0_1_sin_cos9,axiom,( ! [A] : ( r2_hidden(A,a_0_1_sin_cos9) <=> ? [B] : ( v1_xreal_0(B) & A = B & ~ r1_xxreal_0(B,k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4))) & ~ r1_xxreal_0(k7_xcmplx_0(k28_sin_cos,4),B) ) ) )).
fof(fraenkel_a_0_1_topgen_5,axiom,( ! [A] : ( r2_hidden(A,a_0_1_topgen_5) <=> ? [B] : ? [C] : ( v1_xreal_0(B) & v1_xreal_0(C) & A = k19_euclid(B,C) & r1_xxreal_0(k5_numbers,C) ) ) )).
fof(fraenkel_a_0_1_topreal1,axiom,( ! [A] : ( r2_hidden(A,a_0_1_topreal1) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & r1_xxreal_0(k17_euclid(B),1) & r1_xxreal_0(k5_numbers,k17_euclid(B)) & k18_euclid(B) = 1 ) ) )).
fof(fraenkel_a_0_1_uniroots,axiom,( ! [A] : ( r2_hidden(A,a_0_1_uniroots) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k1_uniroots(k1_complfld))) & A = B & r1_nat_d(k6_group_1(k1_uniroots(k1_complfld),B),1) ) ) )).
fof(fraenkel_a_0_1_urysohn2,axiom,( ! [A] : ( r2_hidden(A,a_0_1_urysohn2) <=> ? [B] : ( v1_xreal_0(B) & A = B & ~ r1_xxreal_0(B,1) ) ) )).
fof(fraenkel_a_0_2_abcmiz_1,axiom,( ! [A] : ( r2_hidden(A,a_0_2_abcmiz_1) <=> ? [B] : ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_abcmiz_1)) & A = k1_abcmiz_1(B) ) ) )).
fof(fraenkel_a_0_2_ami_5,axiom,( ! [A] : ( r2_hidden(A,a_0_2_ami_5) <=> ? [B] : ? [C] : ? [D] : ( m2_subset_1(B,k4_ordinal1,k7_card_1(9)) & m1_subset_1(C,k8_struct_0(k1_ami_3)) & m1_subset_1(D,k8_struct_0(k1_ami_3)) & A = k3_xtuple_0(B,k1_xboole_0,k10_finseq_1(C,D)) & r2_hidden(B,k10_domain_1(k4_ordinal1,1,2,3,4,5)) ) ) )).
fof(fraenkel_a_0_2_arytm_0,axiom,( ! [A] : ( r2_hidden(A,a_0_2_arytm_0) <=> ? [B] : ( m1_subset_1(B,k4_ordinal1) & A = k4_tarski(B,1) ) ) )).
fof(fraenkel_a_0_2_arytm_2,axiom,( ! [A] : ( r2_hidden(A,a_0_2_arytm_2) <=> ? [B] : ( m1_subset_1(B,k5_arytm_3) & A = B & ~ r3_arytm_3(k12_arytm_3,B) ) ) )).
fof(fraenkel_a_0_2_asympt_1,axiom,( ! [A] : ( r2_hidden(A,a_0_2_asympt_1) <=> ? [B] : ( m2_funct_2(B,k4_ordinal1,k1_numbers,k9_funct_2(k4_ordinal1,k1_numbers)) & A = B & ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( m1_subset_1(E,k4_ordinal1) & ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(D,k5_numbers) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(E,F) => ( r1_xxreal_0(k3_xcmplx_0(D,k9_nat_1(k1_numbers,k3_asympt_1(1),F)),k9_nat_1(k1_numbers,B,F)) & r1_xxreal_0(k9_nat_1(k1_numbers,B,F),k3_xcmplx_0(C,k9_nat_1(k1_numbers,k3_asympt_1(1),F))) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_0_2_borsuk_2,axiom,( ! [A] : ( r2_hidden(A,a_0_2_borsuk_2) <=> ? [B] : ( v1_xreal_0(B) & A = B & r1_xxreal_0(k7_xcmplx_0(1,2),B) & r1_xxreal_0(B,1) ) ) )).
fof(fraenkel_a_0_2_collsp,axiom,( ! [A] : ( r2_hidden(A,a_0_2_collsp) <=> ? [B] : ? [C] : ? [D] : ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) & A = k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,B,C,D) & ~ ( B != C & C != D & D != B ) & r2_hidden(B,k8_domain_1(k4_ordinal1,1,2,3)) & r2_hidden(C,k8_domain_1(k4_ordinal1,1,2,3)) & r2_hidden(D,k8_domain_1(k4_ordinal1,1,2,3)) ) ) )).
fof(fraenkel_a_0_2_jgraph_3,axiom,( ! [A] : ( r2_hidden(A,a_0_2_jgraph_3) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & ~ ( ~ ( k4_xcmplx_0(1) = k17_euclid(B) & r1_xxreal_0(k4_xcmplx_0(1),k18_euclid(B)) & r1_xxreal_0(k18_euclid(B),1) ) & ~ ( k17_euclid(B) = 1 & r1_xxreal_0(k4_xcmplx_0(1),k18_euclid(B)) & r1_xxreal_0(k18_euclid(B),1) ) & ~ ( k4_xcmplx_0(1) = k18_euclid(B) & r1_xxreal_0(k4_xcmplx_0(1),k17_euclid(B)) & r1_xxreal_0(k17_euclid(B),1) ) & ~ ( 1 = k18_euclid(B) & r1_xxreal_0(k4_xcmplx_0(1),k17_euclid(B)) & r1_xxreal_0(k17_euclid(B),1) ) ) ) ) )).
fof(fraenkel_a_0_2_jgraph_4,axiom,( ! [A] : ( r2_hidden(A,a_0_2_jgraph_4) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & r1_xxreal_0(k5_numbers,k18_euclid(B)) & B != k4_struct_0(k15_euclid(2)) ) ) )).
fof(fraenkel_a_0_2_jgraph_5,axiom,( ! [A] : ( r2_hidden(A,a_0_2_jgraph_5) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & k12_euclid(B) = 1 & r1_xxreal_0(k17_euclid(B),k18_euclid(B)) & r1_xxreal_0(k18_euclid(B),k4_xcmplx_0(k17_euclid(B))) ) ) )).
fof(fraenkel_a_0_2_jgraph_6,axiom,( ! [A] : ( r2_hidden(A,a_0_2_jgraph_6) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & k12_euclid(B) = 1 & r1_xxreal_0(k18_euclid(B),k17_euclid(B)) & r1_xxreal_0(k4_xcmplx_0(k17_euclid(B)),k18_euclid(B)) ) ) )).
fof(fraenkel_a_0_2_jordan2c,axiom,( ! [A] : ( r2_hidden(A,a_0_2_jordan2c) <=> ? [B] : ( v1_xreal_0(B) & A = B & r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(B,k7_xcmplx_0(1,2)) ) ) )).
fof(fraenkel_a_0_2_msualg_7,axiom,( ! [A] : ( r2_hidden(A,a_0_2_msualg_7) <=> ? [B] : ( v1_xreal_0(B) & A = B & r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(B,1) ) ) )).
fof(fraenkel_a_0_2_numbers,axiom,( ! [A] : ( r2_hidden(A,a_0_2_numbers) <=> ? [B] : ( m1_subset_1(B,k4_ordinal1) & A = k4_tarski(B,1) ) ) )).
fof(fraenkel_a_0_2_quaterni,axiom,( ! [A] : ( r2_hidden(A,a_0_2_quaterni) <=> ? [B] : ( m1_subset_1(B,k4_ordinal1) & A = k4_tarski(B,1) ) ) )).
fof(fraenkel_a_0_2_scm_inst,axiom,( ! [A] : ( r2_hidden(A,a_0_2_scm_inst) <=> ? [B] : ? [C] : ? [D] : ( m2_subset_1(B,k4_ordinal1,k7_card_1(9)) & m1_subset_1(C,k2_scm_inst) & m1_subset_1(D,k2_scm_inst) & A = k3_xtuple_0(B,k1_xboole_0,k2_finseq_4(k2_scm_inst,C,D)) & r2_hidden(B,k10_domain_1(k4_ordinal1,1,2,3,4,5)) ) ) )).
fof(fraenkel_a_0_2_scmfsa_2,axiom,( ! [A] : ( r2_hidden(A,a_0_2_scmfsa_2) <=> ? [B] : ? [C] : ? [D] : ( m2_subset_1(B,k4_ordinal1,k7_card_1(13)) & m2_subset_1(C,k1_scmfsa_1,k2_scmfsa_1) & m2_subset_1(D,k1_scmfsa_1,k3_scmfsa_1) & A = k3_xtuple_0(B,k1_xboole_0,k10_finseq_1(C,D)) & r2_hidden(B,k2_tarski(11,12)) ) ) )).
fof(fraenkel_a_0_2_scmfsa_i,axiom,( ! [A] : ( r2_hidden(A,a_0_2_scmfsa_i) <=> ? [B] : ( m1_subset_1(B,k2_scm_inst) & A = k3_xtuple_0(13,k1_xboole_0,k12_finseq_1(k2_scm_inst,B)) ) ) )).
fof(fraenkel_a_0_2_scmpds_2,axiom,( ! [A] : ( r2_hidden(A,a_0_2_scmpds_2) <=> ? [B] : ( m2_subset_1(B,k1_ami_2,k2_ami_2) & A = k3_xtuple_0(1,k1_xboole_0,k12_finseq_1(k2_ami_2,B)) ) ) )).
fof(fraenkel_a_0_2_scmpds_i,axiom,( ! [A] : ( r2_hidden(A,a_0_2_scmpds_i) <=> ? [B] : ? [C] : ? [D] : ( m2_subset_1(B,k4_ordinal1,k7_card_1(15)) & m1_subset_1(C,k2_scm_inst) & m1_subset_1(D,k4_numbers) & A = k3_xtuple_0(B,k1_xboole_0,k10_finseq_1(C,D)) & r2_hidden(B,k2_tarski(2,3)) ) ) )).
fof(fraenkel_a_0_2_scmring2,axiom,( ! [A] : ( r2_hidden(A,a_0_2_scmring2) <=> ? [B] : ( v7_ordinal1(B) & A = k3_xtuple_0(6,k9_finseq_1(B),k1_xboole_0) ) ) )).
fof(fraenkel_a_0_2_scmring3,axiom,( ! [A] : ( r2_hidden(A,a_0_2_scmring3) <=> ? [B] : ? [C] : ( v7_ordinal1(B) & m1_subset_1(C,k8_struct_0(k1_ami_3)) & A = k3_xtuple_0(7,k9_finseq_1(B),k9_finseq_1(C)) ) ) )).
fof(fraenkel_a_0_2_scmringi,axiom,( ! [A] : ( r2_hidden(A,a_0_2_scmringi) <=> ? [B] : ? [C] : ( v7_ordinal1(B) & m1_subset_1(C,k2_scm_inst) & A = k3_xtuple_0(7,k9_finseq_1(B),k12_finseq_1(k2_scm_inst,C)) ) ) )).
fof(fraenkel_a_0_2_sin_cos9,axiom,( ! [A] : ( r2_hidden(A,a_0_2_sin_cos9) <=> ? [B] : ( v1_xreal_0(B) & A = B & r1_xxreal_0(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)),B) & r1_xxreal_0(B,k7_xcmplx_0(k28_sin_cos,4)) ) ) )).
fof(fraenkel_a_0_2_topgen_5,axiom,( ! [A] : ( r2_hidden(A,a_0_2_topgen_5) <=> ? [B] : ? [C] : ( v1_xreal_0(B) & v1_xreal_0(C) & A = k2_rcomp_1(B,C) & ~ r1_xxreal_0(C,B) ) ) )).
fof(fraenkel_a_0_2_topreal1,axiom,( ! [A] : ( r2_hidden(A,a_0_2_topreal1) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & r1_xxreal_0(k17_euclid(B),1) & r1_xxreal_0(k5_numbers,k17_euclid(B)) & k18_euclid(B) = k5_numbers ) ) )).
fof(fraenkel_a_0_2_trees_1,axiom,( ! [A] : ( r2_hidden(A,a_0_2_trees_1) <=> ? [B] : ( v7_ordinal1(B) & A = k9_finseq_1(B) & ~ r1_xxreal_0(k5_numbers,B) ) ) )).
fof(fraenkel_a_0_3_abcmiz_a,axiom,( ! [A] : ( r2_hidden(A,a_0_3_abcmiz_a) <=> ? [B] : ? [C] : ( m1_subset_1(B,k1_zfmisc_1(k2_abcmiz_1)) & m1_subset_1(C,k4_ordinal1) & A = k4_tarski(k1_abcmiz_1(B),C) & v1_finset_1(B) ) ) )).
fof(fraenkel_a_0_3_arytm_0,axiom,( ! [A] : ( r2_hidden(A,a_0_3_arytm_0) <=> ? [B] : ( m2_funct_2(B,k2_tarski(k5_numbers,1),k1_numbers,k9_funct_2(k2_tarski(k5_numbers,1),k1_numbers)) & A = B & k1_funct_1(B,1) = k5_numbers ) ) )).
fof(fraenkel_a_0_3_arytm_2,axiom,( ! [A] : ( r2_hidden(A,a_0_3_arytm_2) <=> ? [B] : ? [C] : ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & A = k4_tarski(B,C) & r1_arytm_3(B,C) & C != k11_arytm_3 ) ) )).
fof(fraenkel_a_0_3_asympt_1,axiom,( ! [A] : ( r2_hidden(A,a_0_3_asympt_1) <=> ? [B] : ( m2_funct_2(B,k4_ordinal1,k1_numbers,k9_funct_2(k4_ordinal1,k1_numbers)) & A = B & ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( m1_subset_1(E,k4_ordinal1) & ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(D,k5_numbers) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(E,F) => ( r1_xxreal_0(k3_xcmplx_0(D,k9_nat_1(k1_numbers,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k3_asympt_1(1),k1_seq_1(1)),F)),k9_nat_1(k1_numbers,B,F)) & r1_xxreal_0(k9_nat_1(k1_numbers,B,F),k3_xcmplx_0(C,k9_nat_1(k1_numbers,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k3_asympt_1(1),k1_seq_1(1)),F))) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_0_3_borsuk_2,axiom,( ! [A] : ( r2_hidden(A,a_0_3_borsuk_2) <=> ? [B] : ( v1_xreal_0(B) & A = B & r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(B,k7_xcmplx_0(1,2)) ) ) )).
fof(fraenkel_a_0_3_jgraph_3,axiom,( ! [A] : ( r2_hidden(A,a_0_3_jgraph_3) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & k12_euclid(B) = 1 ) ) )).
fof(fraenkel_a_0_3_jgraph_4,axiom,( ! [A] : ( r2_hidden(A,a_0_3_jgraph_4) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & r1_xxreal_0(k18_euclid(B),k5_numbers) & B != k4_struct_0(k15_euclid(2)) ) ) )).
fof(fraenkel_a_0_3_jgraph_5,axiom,( ! [A] : ( r2_hidden(A,a_0_3_jgraph_5) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & k12_euclid(B) = 1 & r1_xxreal_0(k17_euclid(B),k18_euclid(B)) & r1_xxreal_0(k4_xcmplx_0(k17_euclid(B)),k18_euclid(B)) ) ) )).
fof(fraenkel_a_0_3_jgraph_6,axiom,( ! [A] : ( r2_hidden(A,a_0_3_jgraph_6) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & k12_euclid(B) = 1 & r1_xxreal_0(k17_euclid(B),k18_euclid(B)) & r1_xxreal_0(k18_euclid(B),k4_xcmplx_0(k17_euclid(B))) ) ) )).
fof(fraenkel_a_0_3_msualg_7,axiom,( ! [A] : ( r2_hidden(A,a_0_3_msualg_7) <=> ? [B] : ( v1_xreal_0(B) & A = B & r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(k7_xcmplx_0(1,2),B) ) ) )).
fof(fraenkel_a_0_3_numbers,axiom,( ! [A] : ( r2_hidden(A,a_0_3_numbers) <=> ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k5_arytm_3)) & A = B & ! [C] : ( m1_subset_1(C,k5_arytm_3) => ( r2_hidden(C,B) => ( ! [D] : ( m1_subset_1(D,k5_arytm_3) => ( r3_arytm_3(D,C) => r2_hidden(D,B) ) ) & ? [D] : ( m1_subset_1(D,k5_arytm_3) & r2_hidden(D,B) & ~ r3_arytm_3(D,C) ) ) ) ) ) ) )).
fof(fraenkel_a_0_3_quaterni,axiom,( ! [A] : ( r2_hidden(A,a_0_3_quaterni) <=> ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k5_arytm_3)) & A = B & ! [C] : ( m1_subset_1(C,k5_arytm_3) => ( r2_hidden(C,B) => ( ! [D] : ( m1_subset_1(D,k5_arytm_3) => ( r3_arytm_3(D,C) => r2_hidden(D,B) ) ) & ? [D] : ( m1_subset_1(D,k5_arytm_3) & r2_hidden(D,B) & ~ r3_arytm_3(D,C) ) ) ) ) ) ) )).
fof(fraenkel_a_0_3_scmfsa_2,axiom,( ! [A] : ( r2_hidden(A,a_0_3_scmfsa_2) <=> ? [B] : ? [C] : ? [D] : ? [E] : ( m2_subset_1(B,k4_ordinal1,k7_card_1(13)) & m2_subset_1(C,k1_scmfsa_1,k2_scmfsa_1) & m2_subset_1(D,k1_scmfsa_1,k2_scmfsa_1) & m2_subset_1(E,k1_scmfsa_1,k3_scmfsa_1) & A = k3_xtuple_0(B,k1_xboole_0,k11_finseq_1(D,E,C)) & r2_hidden(B,k2_tarski(9,10)) ) ) )).
fof(fraenkel_a_0_3_scmpds_2,axiom,( ! [A] : ( r2_hidden(A,a_0_3_scmpds_2) <=> ? [B] : ? [C] : ? [D] : ( m1_subset_1(B,k7_card_1(15)) & m2_subset_1(C,k1_ami_2,k2_ami_2) & m1_subset_1(D,k4_numbers) & A = k3_xtuple_0(B,k1_xboole_0,k3_scmpds_1(C,D)) & r2_hidden(B,k2_tarski(2,3)) ) ) )).
fof(fraenkel_a_0_3_scmpds_i,axiom,( ! [A] : ( r2_hidden(A,a_0_3_scmpds_i) <=> ? [B] : ? [C] : ? [D] : ? [E] : ( m2_subset_1(B,k4_ordinal1,k7_card_1(15)) & m1_subset_1(C,k2_scm_inst) & m1_subset_1(D,k4_numbers) & m1_subset_1(E,k4_numbers) & A = k3_xtuple_0(B,k1_xboole_0,k11_finseq_1(C,D,E)) & r2_hidden(B,k3_enumset1(4,5,6,7,8)) ) ) )).
fof(fraenkel_a_0_3_scmring2,axiom,( ! [A] : ( r2_hidden(A,a_0_3_scmring2) <=> ? [B] : ? [C] : ( v7_ordinal1(B) & m1_subset_1(C,k8_struct_0(k1_ami_3)) & A = k3_xtuple_0(7,k9_finseq_1(B),k9_finseq_1(C)) ) ) )).
fof(fraenkel_a_0_3_sin_cos9,axiom,( ! [A] : ( r2_hidden(A,a_0_3_sin_cos9) <=> ? [B] : ( v1_xreal_0(B) & A = B & ~ r1_xxreal_0(B,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,B) ) ) )).
fof(fraenkel_a_0_3_topgen_5,axiom,( ! [A] : ( r2_hidden(A,a_0_3_topgen_5) <=> ? [B] : ( v1_xreal_0(B) & A = k3_rcomp_1(k5_numbers,B) & ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(B,1) ) ) )).
fof(fraenkel_a_0_3_topreal1,axiom,( ! [A] : ( r2_hidden(A,a_0_3_topreal1) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & k17_euclid(B) = 1 & r1_xxreal_0(k18_euclid(B),1) & r1_xxreal_0(k5_numbers,k18_euclid(B)) ) ) )).
fof(fraenkel_a_0_4_arytm_2,axiom,( ! [A] : ( r2_hidden(A,a_0_4_arytm_2) <=> ? [B] : ( m1_subset_1(B,k4_ordinal1) & A = k4_tarski(B,1) ) ) )).
fof(fraenkel_a_0_4_comput_1,axiom,( ! [A] : ( r2_hidden(A,a_0_4_comput_1) <=> ? [B] : ( m2_rfunct_3(B,k3_finseq_2(k4_ordinal1),k4_ordinal1,k3_rfunct_3(k3_finseq_2(k4_ordinal1),k4_ordinal1)) & A = B & v2_margrel1(B) ) ) )).
fof(fraenkel_a_0_4_jgraph_5,axiom,( ! [A] : ( r2_hidden(A,a_0_4_jgraph_5) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & k12_euclid(B) = 1 & r1_xxreal_0(k18_euclid(B),k17_euclid(B)) & r1_xxreal_0(k18_euclid(B),k4_xcmplx_0(k17_euclid(B))) ) ) )).
fof(fraenkel_a_0_4_jgraph_6,axiom,( ! [A] : ( r2_hidden(A,a_0_4_jgraph_6) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & k12_euclid(B) = 1 & r1_xxreal_0(k17_euclid(B),k18_euclid(B)) & r1_xxreal_0(k4_xcmplx_0(k17_euclid(B)),k18_euclid(B)) ) ) )).
fof(fraenkel_a_0_4_msualg_7,axiom,( ! [A] : ( r2_hidden(A,a_0_4_msualg_7) <=> ? [B] : ( v1_xreal_0(B) & A = B & ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(k7_xcmplx_0(1,2),B) ) ) )).
fof(fraenkel_a_0_4_numbers,axiom,( ! [A] : ( r2_hidden(A,a_0_4_numbers) <=> ? [B] : ( m1_subset_1(B,k4_ordinal1) & A = k4_tarski(B,k12_arytm_3) ) ) )).
fof(fraenkel_a_0_4_quaterni,axiom,( ! [A] : ( r2_hidden(A,a_0_4_quaterni) <=> ? [B] : ( m2_funct_2(B,k2_tarski(k5_numbers,1),k1_numbers,k9_funct_2(k2_tarski(k5_numbers,1),k1_numbers)) & A = B & k1_funct_1(B,1) = k5_numbers ) ) )).
fof(fraenkel_a_0_4_scmpds_2,axiom,( ! [A] : ( r2_hidden(A,a_0_4_scmpds_2) <=> ? [B] : ? [C] : ? [D] : ? [E] : ( m1_subset_1(B,k7_card_1(15)) & m2_subset_1(C,k1_ami_2,k2_ami_2) & m1_subset_1(D,k4_numbers) & m1_subset_1(E,k4_numbers) & A = k3_xtuple_0(B,k1_xboole_0,k11_finseq_1(C,D,E)) & r2_hidden(B,k3_enumset1(4,5,6,7,8)) ) ) )).
fof(fraenkel_a_0_4_scmpds_i,axiom,( ! [A] : ( r2_hidden(A,a_0_4_scmpds_i) <=> ? [B] : ? [C] : ? [D] : ? [E] : ? [F] : ( m2_subset_1(B,k4_ordinal1,k7_card_1(15)) & m1_subset_1(C,k2_scm_inst) & m1_subset_1(D,k2_scm_inst) & m1_subset_1(E,k4_numbers) & m1_subset_1(F,k4_numbers) & A = k3_xtuple_0(B,k1_xboole_0,k7_finseq_4(C,D,E,F)) & r2_hidden(B,k3_enumset1(9,10,11,12,13)) ) ) )).
fof(fraenkel_a_0_4_sin_cos9,axiom,( ! [A] : ( r2_hidden(A,a_0_4_sin_cos9) <=> ? [B] : ( v1_xreal_0(B) & A = B & r1_xxreal_0(k4_xcmplx_0(1),B) & r1_xxreal_0(B,1) ) ) )).
fof(fraenkel_a_0_4_topgen_5,axiom,( ! [A] : ( r2_hidden(A,a_0_4_topgen_5) <=> ? [B] : ( v1_xreal_0(B) & A = k4_rcomp_1(B,1) & r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(1,B) ) ) )).
fof(fraenkel_a_0_4_topreal1,axiom,( ! [A] : ( r2_hidden(A,a_0_4_topreal1) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & ~ ( ~ ( k17_euclid(B) = k5_numbers & r1_xxreal_0(k18_euclid(B),1) & r1_xxreal_0(k5_numbers,k18_euclid(B)) ) & ~ ( r1_xxreal_0(k17_euclid(B),1) & r1_xxreal_0(k5_numbers,k17_euclid(B)) & k18_euclid(B) = 1 ) & ~ ( r1_xxreal_0(k17_euclid(B),1) & r1_xxreal_0(k5_numbers,k17_euclid(B)) & k18_euclid(B) = k5_numbers ) & ~ ( k17_euclid(B) = 1 & r1_xxreal_0(k18_euclid(B),1) & r1_xxreal_0(k5_numbers,k18_euclid(B)) ) ) ) ) )).
fof(fraenkel_a_0_4_trees_1,axiom,( ! [A] : ( r2_hidden(A,a_0_4_trees_1) <=> ? [B] : ( v7_ordinal1(B) & A = k9_finseq_1(B) & ~ r1_xxreal_0(1,B) ) ) )).
fof(fraenkel_a_0_5_arytm_2,axiom,( ! [A] : ( r2_hidden(A,a_0_5_arytm_2) <=> ? [B] : ( m1_subset_1(B,k5_arytm_3) & A = B & ~ r3_arytm_3(k11_arytm_3,B) ) ) )).
fof(fraenkel_a_0_5_jgraph_3,axiom,( ! [A] : ( r2_hidden(A,a_0_5_jgraph_3) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & r1_xxreal_0(k12_euclid(B),1) ) ) )).
fof(fraenkel_a_0_5_jgraph_5,axiom,( ! [A] : ( r2_hidden(A,a_0_5_jgraph_5) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & r1_xxreal_0(1,k12_euclid(B)) ) ) )).
fof(fraenkel_a_0_5_jgraph_6,axiom,( ! [A] : ( r2_hidden(A,a_0_5_jgraph_6) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & k12_euclid(B) = 1 & r1_xxreal_0(k18_euclid(B),k17_euclid(B)) & r1_xxreal_0(k18_euclid(B),k4_xcmplx_0(k17_euclid(B))) ) ) )).
fof(fraenkel_a_0_5_numbers,axiom,( ! [A] : ( r2_hidden(A,a_0_5_numbers) <=> ? [B] : ( m2_funct_2(B,k2_tarski(k5_numbers,k12_arytm_3),k1_numbers,k9_funct_2(k2_tarski(k5_numbers,k12_arytm_3),k1_numbers)) & A = B & k1_funct_1(B,k12_arytm_3) = k5_numbers ) ) )).
fof(fraenkel_a_0_5_quaterni,axiom,( ! [A] : ( r2_hidden(A,a_0_5_quaterni) <=> ? [B] : ( m2_funct_2(B,2,k1_numbers,k9_funct_2(2,k1_numbers)) & A = B & k1_funct_1(B,1) = k5_numbers ) ) )).
fof(fraenkel_a_0_5_scmpds_2,axiom,( ! [A] : ( r2_hidden(A,a_0_5_scmpds_2) <=> ? [B] : ? [C] : ? [D] : ? [E] : ? [F] : ( m1_subset_1(B,k7_card_1(15)) & m2_subset_1(C,k1_ami_2,k2_ami_2) & m2_subset_1(D,k1_ami_2,k2_ami_2) & m1_subset_1(E,k4_numbers) & m1_subset_1(F,k4_numbers) & A = k3_xtuple_0(B,k1_xboole_0,k7_finseq_4(C,D,E,F)) & r2_hidden(B,k3_enumset1(9,10,11,12,13)) ) ) )).
fof(fraenkel_a_0_5_scmpds_i,axiom,( ! [A] : ( r2_hidden(A,a_0_5_scmpds_i) <=> ? [B] : ? [C] : ? [D] : ( m2_subset_1(B,k4_ordinal1,k7_card_1(15)) & m1_subset_1(C,k2_scm_inst) & m1_subset_1(D,k4_numbers) & A = k3_xtuple_0(B,k1_xboole_0,k2_scmpds_i(C,D)) & r2_hidden(B,k2_tarski(2,3)) ) ) )).
fof(fraenkel_a_0_5_sin_cos9,axiom,( ! [A] : ( r2_hidden(A,a_0_5_sin_cos9) <=> ? [B] : ( v1_xreal_0(B) & A = B & ~ r1_xxreal_0(B,k7_xcmplx_0(k28_sin_cos,4)) & ~ r1_xxreal_0(k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos),B) ) ) )).
fof(fraenkel_a_0_5_topgen_5,axiom,( ! [A] : ( r2_hidden(A,a_0_5_topgen_5) <=> ? [B] : ? [C] : ( v1_xreal_0(B) & v1_xreal_0(C) & A = k2_rcomp_1(B,C) & r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(C,B) & r1_xxreal_0(C,1) ) ) )).
fof(fraenkel_a_0_5_trees_1,axiom,( ! [A] : ( r2_hidden(A,a_0_5_trees_1) <=> ? [B] : ( v7_ordinal1(B) & A = k9_finseq_1(B) & ~ r1_xxreal_0(2,B) ) ) )).
fof(fraenkel_a_0_6_jgraph_3,axiom,( ! [A] : ( r2_hidden(A,a_0_6_jgraph_3) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & k12_euclid(B) = 1 & r1_xxreal_0(k18_euclid(B),k17_euclid(B)) & r1_xxreal_0(k4_xcmplx_0(k17_euclid(B)),k18_euclid(B)) ) ) )).
fof(fraenkel_a_0_6_jgraph_5,axiom,( ! [A] : ( r2_hidden(A,a_0_6_jgraph_5) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & k12_euclid(B) = 1 ) ) )).
fof(fraenkel_a_0_6_scmfsa_2,axiom,( ! [A] : ( r2_hidden(A,a_0_6_scmfsa_2) <=> ? [B] : ? [C] : ? [D] : ( m2_subset_1(B,k4_ordinal1,k7_card_1(9)) & m1_subset_1(C,k2_ami_2) & m1_subset_1(D,k2_ami_2) & A = k3_xtuple_0(B,k1_xboole_0,k10_finseq_1(C,D)) & r2_hidden(B,k3_enumset1(1,2,3,4,5)) ) ) )).
fof(fraenkel_a_0_6_sin_cos9,axiom,( ! [A] : ( r2_hidden(A,a_0_6_sin_cos9) <=> ? [B] : ( v1_xreal_0(B) & A = B & r1_xxreal_0(k7_xcmplx_0(k28_sin_cos,4),B) & r1_xxreal_0(B,k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos)) ) ) )).
fof(fraenkel_a_0_7_jgraph_3,axiom,( ! [A] : ( r2_hidden(A,a_0_7_jgraph_3) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & k12_euclid(B) = 1 & r1_xxreal_0(k17_euclid(B),k18_euclid(B)) & r1_xxreal_0(k18_euclid(B),k4_xcmplx_0(k17_euclid(B))) ) ) )).
fof(fraenkel_a_0_7_scmfsa_2,axiom,( ! [A] : ( r2_hidden(A,a_0_7_scmfsa_2) <=> ? [B] : ? [C] : ( m2_subset_1(B,k4_ordinal1,k7_card_1(9)) & v7_ordinal1(C) & A = k3_xtuple_0(B,k9_finseq_1(C),k1_xboole_0) & B = 6 ) ) )).
fof(fraenkel_a_0_7_sin_cos9,axiom,( ! [A] : ( r2_hidden(A,a_0_7_sin_cos9) <=> ? [B] : ( v1_xreal_0(B) & A = B & ~ r1_xxreal_0(B,k5_numbers) ) ) )).
fof(fraenkel_a_0_8_jgraph_3,axiom,( ! [A] : ( r2_hidden(A,a_0_8_jgraph_3) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & k12_euclid(B) = 1 & r1_xxreal_0(k17_euclid(B),k18_euclid(B)) & r1_xxreal_0(k4_xcmplx_0(k17_euclid(B)),k18_euclid(B)) ) ) )).
fof(fraenkel_a_0_8_scmfsa_2,axiom,( ! [A] : ( r2_hidden(A,a_0_8_scmfsa_2) <=> ? [B] : ? [C] : ? [D] : ( m2_subset_1(B,k4_ordinal1,k7_card_1(9)) & v7_ordinal1(C) & m1_subset_1(D,k2_ami_2) & A = k3_xtuple_0(B,k9_finseq_1(C),k12_finseq_1(k2_ami_2,D)) & r2_hidden(B,k2_tarski(7,8)) ) ) )).
fof(fraenkel_a_0_8_topgen_5,axiom,( ! [A] : ( r2_hidden(A,a_0_8_topgen_5) <=> ? [B] : ? [C] : ( v1_xreal_0(B) & v1_xreal_0(C) & A = k3_rcomp_1(B,C) & ~ r1_xxreal_0(C,B) & v1_rat_1(C) ) ) )).
fof(fraenkel_a_0_9_borsuk_6,axiom,( ! [A] : ( r2_hidden(A,a_0_9_borsuk_6) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k2_borsuk_1(k3_topmetr,k3_topmetr))) & A = B & r1_xxreal_0(k2_xtuple_0(B),k6_xcmplx_0(1,k3_xcmplx_0(2,k1_xtuple_0(B)))) ) ) )).
fof(fraenkel_a_0_9_jgraph_3,axiom,( ! [A] : ( r2_hidden(A,a_0_9_jgraph_3) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & A = B & k12_euclid(B) = 1 & r1_xxreal_0(k18_euclid(B),k17_euclid(B)) & r1_xxreal_0(k18_euclid(B),k4_xcmplx_0(k17_euclid(B))) ) ) )).
fof(fraenkel_a_1_0_abcmiz_1,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_0_abcmiz_1(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k1_abcmiz_1(C) ) ) )).
fof(fraenkel_a_1_0_abcmiz_a,axiom,( ! [A] : ! [B] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & l1_msualg_1(B) ) => ( r2_hidden(A,a_1_0_abcmiz_a(B)) <=> ? [C] : ( v2_abcmiz_1(C,B) & m1_subset_1(C,u4_struct_0(B)) & A = C ) ) ) )).
fof(fraenkel_a_1_0_afinsq_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ( r2_hidden(A,a_1_0_afinsq_1(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = C & ~ r1_xxreal_0(k5_card_1(B),C) ) ) ) )).
fof(fraenkel_a_1_0_afproj,axiom,( ! [A] : ! [B] : ( ( ~ v7_struct_0(B) & v1_diraf(B) & l1_analoaf(B) ) => ( r2_hidden(A,a_1_0_afproj(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v1_aff_1(C,B) ) ) ) )).
fof(fraenkel_a_1_0_algstr_4,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_0_algstr_4(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k14_algstr_4(B))) & A = k1_xtuple_0(C) & k15_algstr_4(B,C) = 1 ) ) )).
fof(fraenkel_a_1_0_ami_6,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_compos_1(k1_ami_3)) => ( r2_hidden(A,a_1_0_ami_6(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k1_amistd_1(k7_card_1(2),k1_ami_3,C,B) ) ) ) )).
fof(fraenkel_a_1_0_aofa_000,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ( r2_hidden(A,a_1_0_aofa_000(B)) <=> ? [C] : ( m5_margrel1(C,u1_struct_0(B),k1_unialg_2(B)) & A = k2_relset_1(u1_struct_0(B),C) ) ) ) )).
fof(fraenkel_a_1_0_armstrng,axiom,( ! [A] : ! [B] : ( l1_armstrng(B) => ( r2_hidden(A,a_1_0_armstrng(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,k1_zfmisc_1(u1_armstrng(B))) & m1_subset_1(D,k1_zfmisc_1(u1_armstrng(B))) & A = k4_tarski(C,D) & r2_armstrng(B,C,D) ) ) ) )).
fof(fraenkel_a_1_0_arytm_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_arytm_3) => ( r2_hidden(A,a_1_0_arytm_2(B)) <=> ? [C] : ( m1_subset_1(C,k5_arytm_3) & A = C & ~ r3_arytm_3(B,C) ) ) ) )).
fof(fraenkel_a_1_0_arytm_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_arytm_3) => ( r2_hidden(A,a_1_0_arytm_3(B)) <=> ? [C] : ( m1_subset_1(C,k5_arytm_3) & A = C & ~ r3_arytm_3(B,C) ) ) ) )).
fof(fraenkel_a_1_0_asympt_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(A,a_1_0_asympt_0(B)) <=> ? [C] : ( m2_funct_2(C,k4_ordinal1,k1_numbers,k9_funct_2(k4_ordinal1,k1_numbers)) & A = C & ? [D] : ( v1_xreal_0(D) & ? [E] : ( m1_subset_1(E,k4_ordinal1) & ~ r1_xxreal_0(D,k5_numbers) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(E,F) => ( r1_xxreal_0(k9_nat_1(k1_numbers,C,F),k3_xcmplx_0(D,k9_nat_1(k1_numbers,B,F))) & r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,C,F)) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_1_0_asympt_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v4_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(A,a_1_0_asympt_1(B)) <=> ? [C] : ( m2_funct_2(C,k4_ordinal1,k1_numbers,k9_funct_2(k4_ordinal1,k1_numbers)) & A = C & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & ? [F] : ( m1_subset_1(F,k4_ordinal1) & ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(E,k5_numbers) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( r1_xxreal_0(F,G) => ( r1_xxreal_0(k3_xcmplx_0(E,k9_nat_1(k1_numbers,B,G)),k9_nat_1(k1_numbers,C,G)) & r1_xxreal_0(k9_nat_1(k1_numbers,C,G),k3_xcmplx_0(D,k9_nat_1(k1_numbers,B,G))) ) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_1_0_axioms,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_0_axioms(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_0_bagorder,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v16_waybel_0(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_1_0_bagorder(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,k5_finsub_1(u1_struct_0(B))) & m1_subset_1(D,k5_finsub_1(u1_struct_0(B))) & A = k1_domain_1(k5_finsub_1(u1_struct_0(B)),k5_finsub_1(u1_struct_0(B)),C,D) & ( C = k1_xboole_0 | ( C != k1_xboole_0 & D != k1_xboole_0 & k11_bagorder(B,C) != k11_bagorder(B,D) & r2_hidden(k1_domain_1(u1_struct_0(B),u1_struct_0(B),k11_bagorder(B,C),k11_bagorder(B,D)),u1_orders_2(B)) ) ) ) ) ) )).
fof(fraenkel_a_1_0_bcialg_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_bcialg_1(B) & v4_bcialg_1(B) & v5_bcialg_1(B) & v7_bcialg_1(B) & l2_bcialg_1(B) ) => ( r2_hidden(A,a_1_0_bcialg_1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & r1_bcialg_1(B,k4_struct_0(B),C) ) ) ) )).
fof(fraenkel_a_1_0_bcialg_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_bcialg_1(B) & v4_bcialg_1(B) & v5_bcialg_1(B) & v7_bcialg_1(B) & l2_bcialg_1(B) ) => ( r2_hidden(A,a_1_0_bcialg_2(B)) <=> ? [C] : ( m1_bcialg_2(C,B) & A = C ) ) ) )).
fof(fraenkel_a_1_0_bciideal,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_bcialg_1(B) & v4_bcialg_1(B) & v5_bcialg_1(B) & v7_bcialg_1(B) & l2_bcialg_1(B) ) => ( r2_hidden(A,a_1_0_bciideal(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & v10_bcialg_1(C,B) ) ) ) )).
fof(fraenkel_a_1_0_bintree2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( r2_hidden(A,a_1_0_bintree2(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & r1_xxreal_0(1,C) & r1_xxreal_0(C,k5_series_1(2,B)) ) ) ) )).
fof(fraenkel_a_1_0_bspace,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_0_bspace(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) & A = C & v3_card_1(C,1) ) ) )).
fof(fraenkel_a_1_0_bvfunc_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_0_bvfunc_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) & A = C & ? [D] : ( C = k1_tarski(D) & r2_hidden(D,B) ) ) ) ) )).
fof(fraenkel_a_1_0_c0sp1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_0_c0sp1(B)) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,B,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) & A = C & v1_comseq_2(k2_partfun1(B,k1_numbers,C,B)) ) ) ) )).
fof(fraenkel_a_1_0_c0sp2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_0_c0sp2(B)) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),k1_numbers) & v1_pscomp_1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),k1_numbers))) & A = C ) ) ) )).
fof(fraenkel_a_1_0_card_3,axiom,( ! [A] : ! [B] : ( v4_funct_1(B) => ( r2_hidden(A,a_1_0_card_3(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k9_xtuple_0(C) ) ) ) )).
fof(fraenkel_a_1_0_card_5,axiom,( ! [A] : ! [B] : ( ( ~ v1_finset_1(B) & v1_card_1(B) ) => ( r2_hidden(A,a_1_0_card_5(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = C & v1_card_1(C) ) ) ) )).
fof(fraenkel_a_1_0_card_fil,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_0_card_fil(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) & A = C & m1_card_fil(C,B) ) ) ) )).
fof(fraenkel_a_1_0_card_fin,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ( r2_hidden(A,a_1_0_card_fin(B)) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,B,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) & A = C & 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))) ) ) ) )).
fof(fraenkel_a_1_0_card_lar,axiom,( ! [A] : ! [B] : ( ( ~ v1_finset_1(B) & v1_card_1(B) & ~ v4_card_3(B) ) => ( r2_hidden(A,a_1_0_card_lar(B)) <=> ? [C] : ( ~ v1_finset_1(C) & v1_card_1(C) & m1_subset_1(C,B) & A = C & v1_card_5(C) ) ) ) )).
fof(fraenkel_a_1_0_cardfin2,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_0_cardfin2(B)) <=> ? [C] : ( 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))) & A = C & ~ v2_abian(C) ) ) )).
fof(fraenkel_a_1_0_cat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & 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_hidden(A,a_1_0_cat_1(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & A = k2_cat_1(B,C,D) ) ) ) )).
fof(fraenkel_a_1_0_catalan2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ( r2_hidden(A,a_1_0_catalan2(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & k3_xcmplx_0(2,k7_afinsq_2(k5_relat_1(B,C))) = C & ~ r1_xxreal_0(C,k5_numbers) ) ) ) )).
fof(fraenkel_a_1_0_cayley,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_0_cayley(B)) <=> ? [C] : ( 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))) & A = C ) ) )).
fof(fraenkel_a_1_0_cc0sp1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_0_cc0sp1(B)) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,B,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) & A = C & v1_comseq_2(k2_partfun1(B,k2_numbers,C,B)) ) ) ) )).
fof(fraenkel_a_1_0_cc0sp2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_0_cc0sp2(B)) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),k2_numbers) & v1_cc0sp2(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),k2_numbers))) & A = C ) ) ) )).
fof(fraenkel_a_1_0_circuit2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & v5_msafree2(B) & l1_msualg_1(B) ) => ( r2_hidden(A,a_1_0_circuit2(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & v1_msualg_2(C,B) ) ) ) )).
fof(fraenkel_a_1_0_closure2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v4_funct_1(B) ) => ( r2_hidden(A,a_1_0_closure2(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k9_xtuple_0(C) ) ) ) )).
fof(fraenkel_a_1_0_coh_sp,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_0_coh_sp(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) & A = C & ~ v1_xboole_0(C) & v1_classes1(C) & v1_coh_sp(C) ) ) )).
fof(fraenkel_a_1_0_cohsp_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ( r2_hidden(A,a_1_0_cohsp_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_tarski(B))) & A = C & ! [D] : ( m1_subset_1(D,B) => ? [E] : r1_tarski(k8_subset_1(k3_tarski(B),C,D),k1_tarski(E)) ) ) ) ) )).
fof(fraenkel_a_1_0_compact1,axiom,( ! [A] : ! [B] : ( l1_pre_topc(B) => ( r2_hidden(A,a_1_0_compact1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = k2_xboole_0(C,k6_domain_1(k1_zfmisc_1(u1_struct_0(B)),k2_struct_0(B))) & v3_pre_topc(C,B) & v2_compts_1(k3_subset_1(u1_struct_0(B),C),B) ) ) ) )).
fof(fraenkel_a_1_0_complsp2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_valued_0(B) ) => ( r2_hidden(A,a_1_0_complsp2(B)) <=> ? [C] : ( m2_finseq_2(C,k2_numbers,k3_finseq_2(k2_numbers)) & A = C & k3_finseq_1(C) = k3_finseq_1(B) ) ) ) )).
fof(fraenkel_a_1_0_comput_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v4_funct_1(B) & v1_comput_1(B) ) => ( r2_hidden(A,a_1_0_comput_1(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k9_xtuple_0(C) ) ) ) )).
fof(fraenkel_a_1_0_conlat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_conlat_1(B) ) => ( r2_hidden(A,a_1_0_conlat_1(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u4_struct_0(B))) & A = g2_conlat_1(B,C,D) & ~ v4_conlat_1(g2_conlat_1(B,C,D),B) & k3_funct_2(k1_zfmisc_1(u1_struct_0(B)),k9_setfam_1(u4_struct_0(B)),k1_conlat_1(B),C) = D & k3_funct_2(k1_zfmisc_1(u4_struct_0(B)),k9_setfam_1(u1_struct_0(B)),k2_conlat_1(B),D) = C ) ) ) )).
fof(fraenkel_a_1_0_connsp_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_0_connsp_3(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v3_connsp_1(C,B) ) ) ) )).
fof(fraenkel_a_1_0_cqc_lang,axiom,( ! [A] : ! [B] : ( m1_qc_lang1(B) => ( r2_hidden(A,a_1_0_cqc_lang(B)) <=> ? [C] : ( m1_subset_1(C,k9_qc_lang1(B)) & A = C & k6_qc_lang3(B,C) = k1_xboole_0 & k5_qc_lang3(B,C) = k1_xboole_0 ) ) ) )).
fof(fraenkel_a_1_0_cqc_sim1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( r2_hidden(A,a_1_0_cqc_sim1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k1_funct_1(B,C) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(B)) ) ) ) )).
fof(fraenkel_a_1_0_decomp_1,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_0_decomp_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & m1_decomp_1(C,B) ) ) ) )).
fof(fraenkel_a_1_0_ec_pf_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ( r2_hidden(A,a_1_0_ec_pf_1(B)) <=> ? [C] : ? [D] : ( m2_subset_1(C,k3_zfmisc_1(u1_struct_0(k9_int_3(B)),u1_struct_0(k9_int_3(B)),u1_struct_0(k9_int_3(B))),k3_ec_pf_1(k9_int_3(B))) & m2_subset_1(D,k3_zfmisc_1(u1_struct_0(k9_int_3(B)),u1_struct_0(k9_int_3(B)),u1_struct_0(k9_int_3(B))),k3_ec_pf_1(k9_int_3(B))) & A = k1_domain_1(k3_ec_pf_1(k9_int_3(B)),k3_ec_pf_1(k9_int_3(B)),C,D) & r1_ec_pf_1(B,C,D) ) ) ) )).
fof(fraenkel_a_1_0_ec_pf_2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) & v1_ec_pf_2(B,5) ) => ( r2_hidden(A,a_1_0_ec_pf_2(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,u1_struct_0(k9_int_3(B))) & m1_subset_1(D,u1_struct_0(k9_int_3(B))) & A = k1_domain_1(u1_struct_0(k9_int_3(B)),u1_struct_0(k9_int_3(B)),C,D) & k4_ec_pf_1(B,C,D) != k4_struct_0(k9_int_3(B)) ) ) ) )).
fof(fraenkel_a_1_0_ens_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_0_ens_1(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,B) & m1_subset_1(D,B) & A = k1_funct_2(C,D) ) ) ) )).
fof(fraenkel_a_1_0_eqrel_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_0_eqrel_1(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k6_domain_1(B,C) ) ) ) )).
fof(fraenkel_a_1_0_euclid_7,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_0_euclid_7(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = k6_euclid_7(B,C) & r1_xxreal_0(1,C) & r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_0_euclidlp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(A,a_1_0_euclidlp(B)) <=> ? [C] : ? [D] : ( m2_finseq_2(C,k1_numbers,k1_euclid(B)) & m2_finseq_2(D,k1_numbers,k1_euclid(B)) & A = k2_euclid_4(B,C,D) ) ) ) )).
fof(fraenkel_a_1_0_euler_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_0_euler_1(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = C & r1_int_2(B,C) & r1_xxreal_0(1,C) & r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_0_fcont_3,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_0_fcont_3(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_0_fdiff_2,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_0_fdiff_2(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(C,k4_xcmplx_0(B)) & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_0_filter_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ( r2_hidden(A,a_1_0_filter_1(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & A = k1_domain_1(u1_struct_0(B),u1_struct_0(B),C,D) & r3_lattices(B,C,D) ) ) ) )).
fof(fraenkel_a_1_0_fin_topo,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_1_0_fin_topo(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k1_fin_topo(B,C) ) ) ) )).
fof(fraenkel_a_1_0_finance1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_0_finance1(B)) <=> ? [C] : ( m1_subset_1(C,k6_numbers) & A = C & ~ r1_xxreal_0(C,k2_xxreal_0) & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_0_finseq_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_0_finseq_1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & r1_xxreal_0(1,C) & r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_0_finseq_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_0_finseq_2(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k12_finseq_1(B,C) ) ) ) )).
fof(fraenkel_a_1_0_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(A,a_1_0_fomodel0(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = k8_funct_7(B,C) ) ) ) )).
fof(fraenkel_a_1_0_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ( r2_hidden(A,a_1_0_fomodel1(B)) <=> ? [C] : ( m2_subset_1(C,k3_finseq_2(k15_fomodel1(B)),k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0))) & A = C & v15_fomodel1(C,B) ) ) ) )).
fof(fraenkel_a_1_0_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ( r2_hidden(A,a_1_0_fomodel2(B)) <=> ? [C] : ( m2_subset_1(C,k3_finseq_2(k15_fomodel1(B)),k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0))) & A = C & ? [D] : ( v7_ordinal1(D) & v3_fomodel2(C,B,D) ) ) ) ) )).
fof(fraenkel_a_1_0_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ( r2_hidden(A,a_1_0_fomodel4(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,k1_zfmisc_1(k30_fomodel2(B))) & 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))) & A = k1_domain_1(k1_zfmisc_1(k30_fomodel2(B)),k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0)),C,D) & v1_finset_1(C) ) ) ) )).
fof(fraenkel_a_1_0_frechet,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(A,a_1_0_frechet(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(C,k6_xcmplx_0(B,k7_xcmplx_0(1,4))) & ~ r1_xxreal_0(k2_xcmplx_0(B,k7_xcmplx_0(1,4)),C) ) ) ) )).
fof(fraenkel_a_1_0_funct_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v4_funct_1(B) ) => ( r2_hidden(A,a_1_0_funct_1(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k9_xtuple_0(C) ) ) ) )).
fof(fraenkel_a_1_0_goboard2,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,a_1_0_goboard2(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k2_topreal1(2,B,C) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(B)) ) ) ) )).
fof(fraenkel_a_1_0_goboard5,axiom,( ! [A] : ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_0_goboard5(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & r1_xxreal_0(D,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,k1_nat_1(1,k5_numbers)))) ) ) ) )).
fof(fraenkel_a_1_0_goboard6,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_0_goboard6(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & ~ r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,1)),C) ) ) ) )).
fof(fraenkel_a_1_0_goboard7,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_1_0_goboard7(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k2_topreal1(2,B,C) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(B)) ) ) ) )).
fof(fraenkel_a_1_0_goboard9,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_0_goboard9(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & ~ r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,1)),D) ) ) ) )).
fof(fraenkel_a_1_0_gobrd11,axiom,( ! [A] : ! [B] : ( ( ~ 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,a_1_0_gobrd11(B)) <=> ? [C] : ? [D] : ( v7_ordinal1(C) & v7_ordinal1(D) & A = k3_goboard5(k2_goboard2(B),C,D) & r1_xxreal_0(C,k3_finseq_1(k2_goboard2(B))) & r1_xxreal_0(D,k1_matrix_0(k2_goboard2(B))) ) ) ) )).
fof(fraenkel_a_1_0_gobrd12,axiom,( ! [A] : ! [B] : ( ( ~ 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,a_1_0_gobrd12(B)) <=> ? [C] : ? [D] : ( v7_ordinal1(C) & v7_ordinal1(D) & A = k2_pre_topc(k1_pre_topc(k15_euclid(2),k3_subset_1(u1_struct_0(k15_euclid(2)),k3_topreal1(2,B))),k4_connsp_3(k15_euclid(2),k1_tops_1(k15_euclid(2),k3_goboard5(k2_goboard2(B),C,D)),k3_subset_1(u1_struct_0(k15_euclid(2)),k3_topreal1(2,B)))) & r1_xxreal_0(C,k3_finseq_1(k2_goboard2(B))) & r1_xxreal_0(D,k1_matrix_0(k2_goboard2(B))) ) ) ) )).
fof(fraenkel_a_1_0_goedcpuc,axiom,( ! [A] : ! [B] : ( m1_qc_lang1(B) => ( r2_hidden(A,a_1_0_goedcpuc(B)) <=> ? [C] : ? [D] : ( m2_subset_1(C,k9_qc_lang1(B),k3_cqc_lang(B)) & m2_subset_1(D,k2_qc_lang1(B),k3_qc_lang1(B)) & A = k4_tarski(o_1_1_goedcpuc(B),k1_domain_1(k3_qc_lang1(B),k3_cqc_lang(B),D,C)) ) ) ) )).
fof(fraenkel_a_1_0_graph_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ( r2_hidden(A,a_1_0_graph_5(B)) <=> ? [C] : ( v7_graph_1(C,B) & v1_graph_4(C,B) & m2_graph_1(C,B) & A = C ) ) ) )).
fof(fraenkel_a_1_0_graphsp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(A,a_1_0_graphsp(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & r1_xxreal_0(1,C) & r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_0_grcat_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) ) => ( r2_hidden(A,a_1_0_grcat_1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k25_grcat_1(B))) & A = C & ? [D] : ( ~ v2_struct_0(D) & v13_algstr_0(D) & v2_rlvect_1(D) & v3_rlvect_1(D) & v4_rlvect_1(D) & l2_algstr_0(D) & C = D ) ) ) ) )).
fof(fraenkel_a_1_0_group_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ( r2_hidden(A,a_1_0_group_2(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k6_domain_1(u1_struct_0(B),C) ) ) ) )).
fof(fraenkel_a_1_0_group_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ( r2_hidden(A,a_1_0_group_4(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & ? [D] : ( v15_algstr_0(D) & m1_group_2(D,B) & C = u1_struct_0(D) & v2_group_4(D,B) ) ) ) ) )).
fof(fraenkel_a_1_0_group_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ( r2_hidden(A,a_1_0_group_5(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k6_algstr_0(B,C,D) = k6_algstr_0(B,D,C) ) ) ) ) )).
fof(fraenkel_a_1_0_group_6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ( r2_hidden(A,a_1_0_group_6(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & A = k2_group_5(B,C,D) ) ) ) )).
fof(fraenkel_a_1_0_henmodel,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_0_henmodel(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_0_heyting3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(A,a_1_0_heyting3(B)) <=> ? [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(k4_ordinal1,k6_domain_1(k4_ordinal1,B)))) & A = C & ! [D] : ( r2_hidden(D,C) => v1_finset_1(D) ) & ! [D] : ( m1_subset_1(D,k4_partfun1(k4_ordinal1,k6_domain_1(k4_ordinal1,B))) => ! [E] : ( m1_subset_1(E,k4_partfun1(k4_ordinal1,k6_domain_1(k4_ordinal1,B))) => ( ( r2_hidden(D,C) & r2_hidden(E,C) & r1_tarski(D,E) ) => D = E ) ) ) ) ) ) )).
fof(fraenkel_a_1_0_hilbasis,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_0_hilbasis(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_0_incproj,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_collsp(B) & v3_collsp(B) & v4_collsp(B) & l1_collsp(B) ) => ( r2_hidden(A,a_1_0_incproj(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & m1_incproj(C,B) ) ) ) )).
fof(fraenkel_a_1_0_int_8,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_0_int_8(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = C & r1_int_2(B,C) & r1_xxreal_0(1,C) & r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_0_integra2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(A,a_1_0_integra2(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & r1_xxreal_0(k3_seq_4(B),C) & r1_xxreal_0(C,k2_seq_4(B)) ) ) ) )).
fof(fraenkel_a_1_0_jct_misc,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_0_jct_misc(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_0_jgraph_1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,a_1_0_jgraph_1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k2_topreal1(2,B,C) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(B)) ) ) ) )).
fof(fraenkel_a_1_0_jgraph_5,axiom,( ! [A] : ! [B] : ( ( ~ 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,a_1_0_jgraph_5(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & r2_hidden(C,B) & r1_xxreal_0(k5_numbers,k18_euclid(C)) ) ) ) )).
fof(fraenkel_a_1_0_jgraph_6,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_0_jgraph_6(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & ~ r1_xxreal_0(B,k12_euclid(C)) ) ) ) )).
fof(fraenkel_a_1_0_jordan,axiom,( ! [A] : ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_0_jordan(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & A = C & r1_jordan2c(2,B,C) ) ) ) )).
fof(fraenkel_a_1_0_jordan1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_0_jordan1(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & ~ r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_0_jordan10,axiom,( ! [A] : ! [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)))) ) => ( r2_hidden(A,a_1_0_jordan10(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k2_jordan2c(2,k3_topreal1(2,k2_jordan9(B,C))) ) ) ) )).
fof(fraenkel_a_1_0_jordan12,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,a_1_0_jordan12(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k2_topreal1(2,B,C) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(B)) ) ) ) )).
fof(fraenkel_a_1_0_jordan1a,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,a_1_0_jordan1a(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & k17_euclid(B) = k17_euclid(C) ) ) ) )).
fof(fraenkel_a_1_0_jordan1k,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_0_jordan1k(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & ~ r1_xxreal_0(B,k12_euclid(C)) ) ) ) )).
fof(fraenkel_a_1_0_jordan20,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_0_jordan20(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & k17_euclid(C) = B ) ) ) )).
fof(fraenkel_a_1_0_jordan2b,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_0_jordan2b(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_0_jordan2c,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_0_jordan2c(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(1))) & A = C & ? [D] : ( v1_xreal_0(D) & C = k9_finseq_1(D) & ~ r1_xxreal_0(D,B) ) ) ) ) )).
fof(fraenkel_a_1_0_jordan3,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,a_1_0_jordan3(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k2_topreal1(2,B,C) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(B)) ) ) ) )).
fof(fraenkel_a_1_0_jordan4,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,a_1_0_jordan4(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k2_topreal1(2,B,C) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(B)) ) ) ) )).
fof(fraenkel_a_1_0_jordan5d,axiom,( ! [A] : ! [B] : ( ( ~ 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,a_1_0_jordan5d(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = k18_euclid(C) & k17_euclid(C) = k6_pscomp_1(k3_topreal1(2,B)) & r2_hidden(C,k3_topreal1(2,B)) ) ) ) )).
fof(fraenkel_a_1_0_jordan6,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_0_jordan6(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & r1_xxreal_0(B,k17_euclid(C)) ) ) ) )).
fof(fraenkel_a_1_0_jordan7,axiom,( ! [A] : ! [B] : ( ( ~ 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,a_1_0_jordan7(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & ( r1_jordan6(B,k22_pscomp_1(B),C) | ( r2_hidden(k22_pscomp_1(B),B) & C = k18_pscomp_1(B) ) ) ) ) ) )).
fof(fraenkel_a_1_0_jordan9,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,a_1_0_jordan9(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k2_topreal1(2,B,C) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(B)) ) ) ) )).
fof(fraenkel_a_1_0_lang1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_lang1(B) ) => ( r2_hidden(A,a_1_0_lang1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ~ r1_lang1(B,C,D) ) ) ) ) )).
fof(fraenkel_a_1_0_laplace,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(A,a_1_0_laplace(B)) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k2_setwop_2(B),k2_setwop_2(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_setwop_2(B),k2_setwop_2(B)))) & A = C & v1_funct_1(C) & v1_funct_2(C,k2_setwop_2(B),k2_setwop_2(B)) & v3_funct_2(C,k2_setwop_2(B),k2_setwop_2(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_setwop_2(B),k2_setwop_2(B)))) ) ) ) )).
fof(fraenkel_a_1_0_lattice3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ( r2_hidden(A,a_1_0_lattice3(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & A = k9_filter_1(B,B,C,D) & r3_lattices(B,C,D) ) ) ) )).
fof(fraenkel_a_1_0_lattice5,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_0_lattice5(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k2_zfmisc_1(C,C) & r2_hidden(C,B) ) ) ) )).
fof(fraenkel_a_1_0_lattice6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) ) => ( r2_hidden(A,a_1_0_lattice6(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & v3_lattice6(C,B) ) ) ) )).
fof(fraenkel_a_1_0_lattice7,axiom,( ! [A] : ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_1_0_lattice7(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & C != k3_yellow_0(B) & ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ~ ( C = k13_lattice3(B,D,E) & C != D & C != E ) ) ) ) ) ) )).
fof(fraenkel_a_1_0_limfunc1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_0_limfunc1(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_0_limfunc2,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_0_limfunc2(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_0_limfunc3,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_0_limfunc3(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_0_limfunc4,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_0_limfunc4(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_0_lopclset,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_0_lopclset(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v3_pre_topc(C,B) & v4_pre_topc(C,B) ) ) ) )).
fof(fraenkel_a_1_0_ltlaxio3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_hilbert1)) => ( r2_hidden(A,a_1_0_ltlaxio3(B)) <=> ? [C] : ( m1_subset_1(C,k1_hilbert1) & A = k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,C) & r2_hidden(C,B) ) ) ) )).
fof(fraenkel_a_1_0_ltlaxio4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)))) => ( r2_hidden(A,a_1_0_ltlaxio4(B)) <=> ? [C] : ( m1_subset_1(C,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) & A = k12_ltlaxio3(C) & r2_hidden(C,B) ) ) ) )).
fof(fraenkel_a_1_0_matrix11,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_0_matrix11(B)) <=> ? [C] : ( m1_matrix_2(C,k3_matrix_2(B)) & A = C & v5_matrix_2(C,k2_matrix_2(k3_matrix_2(B))) ) ) ) )).
fof(fraenkel_a_1_0_matrix13,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_0_matrix13(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_finseq_1(B))) & A = C & k5_card_1(C) = 2 ) ) ) )).
fof(fraenkel_a_1_0_matrixc1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_0_matrixc1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_nat_1(B,1)) ) ) ) )).
fof(fraenkel_a_1_0_matroid0,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_0_matroid0(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_tarski(B))) & A = C & ! [D] : ~ ( r2_hidden(D,B) & ! [E] : ~ r1_tarski(k8_subset_1(k3_tarski(B),C,D),k1_tarski(E)) ) ) ) )).
fof(fraenkel_a_1_0_matrprob,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k1_numbers) => ( r2_hidden(A,a_1_0_matrprob(B)) <=> ? [C] : ( m2_finseq_2(C,u1_struct_0(k2_vectsp_1),k3_finseq_2(u1_struct_0(k2_vectsp_1))) & A = C & k3_finseq_1(C) = k3_finseq_1(B) ) ) ) )).
fof(fraenkel_a_1_0_measure6,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( r2_hidden(A,a_1_0_measure6(B)) <=> ? [C] : ( v1_xreal_0(C) & A = k7_xcmplx_0(1,C) & r2_hidden(C,B) ) ) ) )).
fof(fraenkel_a_1_0_member_1,axiom,( ! [A] : ! [B] : ( v2_membered(B) => ( r2_hidden(A,a_1_0_member_1(B)) <=> ? [C] : ( m1_subset_1(C,k6_numbers) & A = k1_member_1(C) & r2_hidden(C,B) ) ) ) )).
fof(fraenkel_a_1_0_mesfunc9,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( r2_hidden(A,a_1_0_mesfunc9(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k12_supinf_2(B,C) & r1_xxreal_0(k5_numbers,C) ) ) ) )).
fof(fraenkel_a_1_0_metric_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_metric_1(B) ) => ( r2_hidden(A,a_1_0_metric_2(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & k1_metric_2(B,D) = C ) ) ) ) )).
fof(fraenkel_a_1_0_midsp_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_1(B) ) => ( r2_hidden(A,a_1_0_midsp_1(B)) <=> ? [C] : ( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) & A = C & k2_domain_1(u1_struct_0(B),u1_struct_0(B),C) = k3_domain_1(u1_struct_0(B),u1_struct_0(B),C) ) ) ) )).
fof(fraenkel_a_1_0_modal_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) ) => ( r2_hidden(A,a_1_0_modal_1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k8_finseq_1(k4_ordinal1,k1_modal_1(B),k14_trees_3(C)) & r2_hidden(k8_finseq_1(k4_ordinal1,k1_modal_1(B),k14_trees_3(C)),B) ) ) ) )).
fof(fraenkel_a_1_0_modelc_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_modelc_2)) => ( r2_hidden(A,a_1_0_modelc_2(B)) <=> ? [C] : ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) & A = C & ? [D] : ( v1_modelc_2(D) & m2_finseq_1(D,k4_ordinal1) & r2_hidden(D,B) & C = k6_modelc_2(D) ) ) ) ) )).
fof(fraenkel_a_1_0_modelc_3,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r2_hidden(A,a_1_0_modelc_3(B)) <=> ? [C] : ( m1_subset_1(C,k22_modelc_3(B)) & A = C & v1_modelc_3(C,B) & v3_modelc_3(C,B) & l1_modelc_3(C,B) ) ) ) )).
fof(fraenkel_a_1_0_moebius1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_0_moebius1(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = C & C != k5_numbers & r1_nat_d(C,B) ) ) ) )).
fof(fraenkel_a_1_0_msafree2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ( r2_hidden(A,a_1_0_msafree2(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & v1_msualg_2(C,B) ) ) ) )).
fof(fraenkel_a_1_0_msualg_5,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_0_msualg_5(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) & A = C & v1_partfun1(C,B) & v3_relat_2(C) & v8_relat_2(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) ) )).
fof(fraenkel_a_1_0_nat_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_0_nat_1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_0_nat_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(A,a_1_0_nat_4(B)) <=> ? [C] : ( v1_int_2(C) & m1_subset_1(C,k4_ordinal1) & A = C & r1_xxreal_0(C,k1_nat_1(B,1)) ) ) ) )).
fof(fraenkel_a_1_0_nattra_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & 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_hidden(A,a_1_0_nattra_1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k4_cat_1(B,C) ) ) ) )).
fof(fraenkel_a_1_0_necklace,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_0_necklace(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = k4_tarski(C,k1_nat_1(C,1)) & ~ r1_xxreal_0(B,k1_nat_1(C,1)) ) ) ) )).
fof(fraenkel_a_1_0_newton,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_0_newton(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = C & ~ r1_xxreal_0(C,1) & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_0_normform,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_0_normform(B)) <=> ? [C] : ( m1_subset_1(C,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B))) & A = C & r1_xboole_0(k2_domain_1(k5_finsub_1(B),k5_finsub_1(B),C),k3_domain_1(k5_finsub_1(B),k5_finsub_1(B),C)) ) ) )).
fof(fraenkel_a_1_0_ntalgo_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ( r2_hidden(A,a_1_0_ntalgo_1(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = C & k9_nat_1(k4_ordinal1,B,C) = k5_numbers ) ) ) )).
fof(fraenkel_a_1_0_openlatt,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v11_lattices(B) & l3_lattices(B) ) => ( r2_hidden(A,a_1_0_openlatt(B)) <=> ? [C] : ( ~ v1_xboole_0(C) & v19_lattices(C,B) & v20_lattices(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & C != u1_struct_0(B) & v2_filter_0(C,B) ) ) ) )).
fof(fraenkel_a_1_0_ordinal6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) ) => ( r2_hidden(A,a_1_0_ordinal6(B)) <=> ? [C] : ( m1_subset_1(C,k9_xtuple_0(B)) & A = C & r1_abian(C,B) ) ) ) )).
fof(fraenkel_a_1_0_partit1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_0_partit1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) & A = C & ? [D] : ( C = k1_tarski(D) & r2_hidden(D,B) ) ) ) ) )).
fof(fraenkel_a_1_0_pcs_0,axiom,( ! [A] : ! [B] : ( l2_pcs_0(B) => ( r2_hidden(A,a_1_0_pcs_0(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v21_pcs_0(C,B) ) ) ) )).
fof(fraenkel_a_1_0_pepin,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_0_pepin(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = C & r1_int_2(B,C) & r1_xxreal_0(1,C) & r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_0_petri_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_petri(B) & v3_petri(B) & l1_petri_2(B) ) => ( r2_hidden(A,a_1_0_petri_2(B)) <=> ? [C] : ( m1_subset_1(C,u4_struct_0(B)) & A = C & v2_petri_2(C,B) ) ) ) )).
fof(fraenkel_a_1_0_pre_circ,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_0_pre_circ(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & ~ r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_0_pscomp_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( r2_hidden(A,a_1_0_pscomp_1(B)) <=> ? [C] : ( v1_xcmplx_0(C) & A = k4_xcmplx_0(C) & r2_hidden(C,B) ) ) ) )).
fof(fraenkel_a_1_0_qc_lang1,axiom,( ! [A] : ! [B] : ( m1_qc_lang1(B) => ( r2_hidden(A,a_1_0_qc_lang1(B)) <=> ? [C] : ? [D] : ( v7_ordinal1(C) & m1_subset_1(D,k1_qc_lang1(B)) & A = k4_tarski(C,D) & r1_xxreal_0(7,C) ) ) ) )).
fof(fraenkel_a_1_0_qc_trans,axiom,( ! [A] : ! [B] : ( m1_qc_lang1(B) => ( r2_hidden(A,a_1_0_qc_trans(B)) <=> ? [C] : ? [D] : ( v7_ordinal1(C) & m1_subset_1(D,k1_qc_lang1(B)) & A = k4_tarski(C,D) & r1_xxreal_0(7,C) ) ) ) )).
fof(fraenkel_a_1_0_radix_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_0_radix_1(B)) <=> ? [C] : ( m1_subset_1(C,k4_numbers) & A = C & r1_xxreal_0(C,k6_xcmplx_0(k1_radix_1(B),1)) & r1_xxreal_0(k2_xcmplx_0(k4_xcmplx_0(k1_radix_1(B)),1),C) ) ) ) )).
fof(fraenkel_a_1_0_radix_3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_0_radix_3(B)) <=> ? [C] : ( m1_subset_1(C,k4_numbers) & A = C & r1_xxreal_0(k4_xcmplx_0(k1_radix_1(k7_nat_d(B,1))),C) & r1_xxreal_0(C,k6_xcmplx_0(k1_radix_1(k7_nat_d(B,1)),1)) ) ) ) )).
fof(fraenkel_a_1_0_radix_4,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_0_radix_4(B)) <=> ? [C] : ( m1_subset_1(C,k4_numbers) & A = C & r1_xxreal_0(k4_xcmplx_0(k1_radix_1(k7_nat_d(B,1))),C) & r1_xxreal_0(C,k6_xcmplx_0(k1_radix_1(k7_nat_d(B,1)),1)) ) ) ) )).
fof(fraenkel_a_1_0_radix_5,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_0_radix_5(B)) <=> ? [C] : ( m1_subset_1(C,k4_numbers) & A = C & r1_xxreal_0(C,k6_xcmplx_0(k1_radix_1(B),1)) & r1_xxreal_0(k2_xcmplx_0(k4_xcmplx_0(k1_radix_1(B)),1),C) ) ) ) )).
fof(fraenkel_a_1_0_random_3,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_0_random_3(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(C,k2_xxreal_0) & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_0_relset_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_0_relset_2(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k1_tarski(C) ) ) ) )).
fof(fraenkel_a_1_0_revrot_1,axiom,( ! [A] : ! [B] : ( ( v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_1_0_revrot_1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k2_topreal1(2,B,C) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(B)) ) ) ) )).
fof(fraenkel_a_1_0_rinfsup1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(A,a_1_0_rinfsup1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k1_funct_1(B,C) & r1_xxreal_0(k5_numbers,C) ) ) ) )).
fof(fraenkel_a_1_0_rlvect_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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) ) => ( r2_hidden(A,a_1_0_rlvect_3(B)) <=> ? [C] : ( m2_rlvect_2(C,B,k1_subset_1(u1_struct_0(B))) & A = k6_rlvect_2(B,C) ) ) ) )).
fof(fraenkel_a_1_0_rusub_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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) ) => ( r2_hidden(A,a_1_0_rusub_3(B)) <=> ? [C] : ( m2_rlvect_2(C,B,k1_subset_1(u1_struct_0(B))) & A = k6_rlvect_2(B,C) ) ) ) )).
fof(fraenkel_a_1_0_rusub_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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) ) => ( r2_hidden(A,a_1_0_rusub_5(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r1_struct_0(k1_rusub_1(B),D) => r1_bhsp_1(B,D,C) ) ) ) ) ) )).
fof(fraenkel_a_1_0_scmfsa10,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => ( r2_hidden(A,a_1_0_scmfsa10(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k1_amistd_1(k7_card_1(3),k1_scmfsa_2,C,B) ) ) ) )).
fof(fraenkel_a_1_0_scmfsa8a,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,a_1_0_scmfsa8a(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k1_nat_1(C,k5_card_1(B)) & r2_hidden(C,k2_afinsq_1(k4_compos_1(k1_scmfsa_2))) ) ) ) )).
fof(fraenkel_a_1_0_scmfsa_m,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_scmfsa_2)) ) => ( r2_hidden(A,a_1_0_scmfsa_m(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = C & ~ r2_hidden(k4_scmfsa_2(C),B) ) ) ) )).
fof(fraenkel_a_1_0_scmring2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) => ( r2_hidden(A,a_1_0_scmring2(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,k8_struct_0(k1_ami_3)) & m1_subset_1(D,u1_struct_0(B)) & A = k3_xtuple_0(5,k1_xboole_0,k10_finseq_1(C,D)) ) ) ) )).
fof(fraenkel_a_1_0_scmring3,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) => ( r2_hidden(A,a_1_0_scmring3(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,k8_struct_0(k1_ami_3)) & m1_subset_1(D,u1_struct_0(B)) & A = k3_xtuple_0(5,k1_xboole_0,k10_finseq_1(C,D)) ) ) ) )).
fof(fraenkel_a_1_0_scmringi,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ( r2_hidden(A,a_1_0_scmringi(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,k2_scm_inst) & m1_subset_1(D,u1_struct_0(B)) & A = k3_xtuple_0(5,k1_xboole_0,k10_finseq_1(C,D)) ) ) ) )).
fof(fraenkel_a_1_0_seq_4,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_0_seq_4(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k12_seq_4(B))) & A = C & v1_seq_4(C,B) ) ) ) )).
fof(fraenkel_a_1_0_sgraph1,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_0_sgraph1(B)) <=> ? [C] : ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(B)) & A = C & k5_card_1(C) = 2 ) ) )).
fof(fraenkel_a_1_0_simplex0,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_0_simplex0(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k9_setfam_1(C) & r2_hidden(C,B) ) ) )).
fof(fraenkel_a_1_0_sppol_1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,a_1_0_sppol_1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k2_topreal1(2,B,C) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(B)) ) ) ) )).
fof(fraenkel_a_1_0_sppol_2,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,a_1_0_sppol_2(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k2_topreal1(2,B,C) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(B)) ) ) ) )).
fof(fraenkel_a_1_0_sprect_1,axiom,( ! [A] : ! [B] : ( ( ~ 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,a_1_0_sprect_1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & k17_euclid(C) = k8_pscomp_1(B) & r1_xxreal_0(k18_euclid(C),k7_pscomp_1(B)) & r1_xxreal_0(k9_pscomp_1(B),k18_euclid(C)) ) ) ) )).
fof(fraenkel_a_1_0_sprect_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & v1_topreal1(B) & v2_topreal1(B) & v1_goboard5(B) & v1_sprect_1(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_1_0_sprect_3(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & ~ ( ~ ( k17_euclid(C) = k6_pscomp_1(k3_topreal1(2,B)) & r1_xxreal_0(k18_euclid(C),k7_pscomp_1(k3_topreal1(2,B))) & r1_xxreal_0(k9_pscomp_1(k3_topreal1(2,B)),k18_euclid(C)) ) & ~ ( r1_xxreal_0(k17_euclid(C),k8_pscomp_1(k3_topreal1(2,B))) & r1_xxreal_0(k6_pscomp_1(k3_topreal1(2,B)),k17_euclid(C)) & k18_euclid(C) = k7_pscomp_1(k3_topreal1(2,B)) ) & ~ ( r1_xxreal_0(k17_euclid(C),k8_pscomp_1(k3_topreal1(2,B))) & r1_xxreal_0(k6_pscomp_1(k3_topreal1(2,B)),k17_euclid(C)) & k18_euclid(C) = k9_pscomp_1(k3_topreal1(2,B)) ) & ~ ( k17_euclid(C) = k8_pscomp_1(k3_topreal1(2,B)) & r1_xxreal_0(k18_euclid(C),k7_pscomp_1(k3_topreal1(2,B))) & r1_xxreal_0(k9_pscomp_1(k3_topreal1(2,B)),k18_euclid(C)) ) ) ) ) ) )).
fof(fraenkel_a_1_0_substut1,axiom,( ! [A] : ! [B] : ( m1_qc_lang1(B) => ( r2_hidden(A,a_1_0_substut1(B)) <=> ? [C] : ( m1_subset_1(C,k16_substut1(B)) & A = C & m2_subset_1(k18_substut1(B,C),k9_qc_lang1(B),k3_cqc_lang(B)) ) ) ) )).
fof(fraenkel_a_1_0_substut2,axiom,( ! [A] : ! [B] : ( m1_qc_lang1(B) => ( r2_hidden(A,a_1_0_substut2(B)) <=> ? [C] : ( m1_subset_1(C,k16_substut1(B)) & A = C & m2_subset_1(k18_substut1(B,C),k9_qc_lang1(B),k3_cqc_lang(B)) ) ) ) )).
fof(fraenkel_a_1_0_t_1topsp,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_0_t_1topsp(B)) <=> ? [C] : ( m1_eqrel_1(C,u1_struct_0(B)) & A = C & v2_tops_2(C,B) ) ) ) )).
fof(fraenkel_a_1_0_tdlat_1,axiom,( ! [A] : ! [B] : ( l1_pre_topc(B) => ( r2_hidden(A,a_1_0_tdlat_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v4_tops_1(C,B) ) ) ) )).
fof(fraenkel_a_1_0_tdlat_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_0_tdlat_2(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v4_tops_1(C,B) ) ) ) )).
fof(fraenkel_a_1_0_topalg_6,axiom,( ! [A] : ! [B] : ( l1_pre_topc(B) => ( r2_hidden(A,a_1_0_topalg_6(B)) <=> ? [C] : ( m1_subset_1(C,k4_partfun1(k1_numbers,k2_struct_0(B))) & A = C & v1_funct_1(C) & v4_topalg_6(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_topalg_2),u1_struct_0(B)))) ) ) ) )).
fof(fraenkel_a_1_0_topgen_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_0_topgen_2(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k1_topgen_2(B,C) ) ) ) )).
fof(fraenkel_a_1_0_topgen_5,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_0_topgen_5(B)) <=> ? [C] : ( v1_xreal_0(C) & A = k4_subset_1(u1_struct_0(k15_euclid(2)),k1_topreal9(2,k19_euclid(B,C),C),k6_domain_1(u1_struct_0(k15_euclid(2)),k19_euclid(B,k5_numbers))) & ~ r1_xxreal_0(C,k5_numbers) ) ) ) )).
fof(fraenkel_a_1_0_topreal1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,a_1_0_topreal1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & k17_euclid(C) = k17_euclid(B) & r1_xxreal_0(k18_euclid(B),k18_euclid(C)) ) ) ) )).
fof(fraenkel_a_1_0_topreal3,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,a_1_0_topreal3(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k2_topreal1(2,B,C) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(B)) ) ) ) )).
fof(fraenkel_a_1_0_topreal4,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,a_1_0_topreal4(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(B)) ) ) ) )).
fof(fraenkel_a_1_0_topreal5,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_0_topreal5(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_0_topreal8,axiom,( ! [A] : ! [B] : ( ( v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & v2_topreal1(B) & v1_goboard5(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_1_0_topreal8(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k2_topreal1(2,k2_rfinseq(u1_struct_0(k15_euclid(2)),1,B),C) & ~ r1_xxreal_0(C,1) & ~ r1_xxreal_0(k3_finseq_1(k2_rfinseq(u1_struct_0(k15_euclid(2)),1,B)),k1_nat_1(C,1)) ) ) ) )).
fof(fraenkel_a_1_0_toprealb,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_0_toprealb(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & r1_xxreal_0(k4_xcmplx_0(B),k17_euclid(C)) & r1_xxreal_0(k17_euclid(C),B) & r1_xxreal_0(k4_xcmplx_0(B),k18_euclid(C)) & r1_xxreal_0(k18_euclid(C),B) ) ) ) )).
fof(fraenkel_a_1_0_trees_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_0_trees_1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k9_finseq_1(C) & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_0_trees_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ( r2_hidden(A,a_1_0_trees_2(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k2_trees_2(B,C) ) ) ) )).
fof(fraenkel_a_1_0_trees_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( r2_hidden(A,a_1_0_trees_3(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k9_finseq_1(C) & ~ r1_xxreal_0(k3_finseq_1(B),C) ) ) ) )).
fof(fraenkel_a_1_0_trees_9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ( r2_hidden(A,a_1_0_trees_9(B)) <=> ? [C] : ( m1_trees_1(C,k9_xtuple_0(B)) & A = k5_trees_2(B,C) ) ) ) )).
fof(fraenkel_a_1_0_triang_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_1_0_triang_1(B)) <=> ? [C] : ( m1_subset_1(C,k5_finsub_1(u1_struct_0(B))) & A = C & r3_orders_1(u1_orders_2(B),C) ) ) ) )).
fof(fraenkel_a_1_0_turing_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_0_turing_1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_0_unialg_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ( r2_hidden(A,a_1_0_unialg_2(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & ? [D] : ( m5_margrel1(D,u1_struct_0(B),k1_unialg_2(B)) & k19_margrel1(D) = k5_numbers & r2_hidden(C,k10_xtuple_0(D)) ) ) ) ) )).
fof(fraenkel_a_1_0_uniroots,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ( r2_hidden(A,a_1_0_uniroots(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k1_complfld)) & A = C & m1_comptrig(C,k1_group_1(k1_complfld),B) ) ) ) )).
fof(fraenkel_a_1_0_valued_2,axiom,( ! [A] : ! [B] : ( v4_funct_1(B) => ( r2_hidden(A,a_1_0_valued_2(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k9_xtuple_0(C) ) ) ) )).
fof(fraenkel_a_1_0_waybel11,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & l1_waybel_9(B) ) => ( r2_hidden(A,a_1_0_waybel11(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v3_waybel11(C,B) ) ) ) )).
fof(fraenkel_a_1_0_waybel13,axiom,( ! [A] : ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v1_yellow_0(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_1_0_waybel13(B)) <=> ? [C] : ( ~ 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))) & A = C ) ) ) )).
fof(fraenkel_a_1_0_waybel14,axiom,( ! [A] : ! [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) ) => ( r2_hidden(A,a_1_0_waybel14(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k6_waybel_0(B,C) & r2_hidden(C,u1_struct_0(k1_waybel_8(B))) ) ) ) )).
fof(fraenkel_a_1_0_waybel16,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_1_0_waybel16(B)) <=> ? [C] : ( ~ v1_xboole_0(C) & v1_waybel_0(C,k7_lattice3(B)) & v12_waybel_0(C,k7_lattice3(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k7_lattice3(B)))) & A = C ) ) ) )).
fof(fraenkel_a_1_0_waybel17,axiom,( ! [A] : ! [B] : ( ( 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) ) => ( r2_hidden(A,a_1_0_waybel17(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k2_waybel_3(B,C) ) ) ) )).
fof(fraenkel_a_1_0_waybel18,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_0_waybel18(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k4_card_3(k1_funct_7(k12_pralg_1(B,k7_funcop_1(B,k9_waybel18)),C,k1_tarski(1))) ) ) ) )).
fof(fraenkel_a_1_0_waybel19,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_9(B) ) => ( r2_hidden(A,a_1_0_waybel19(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k3_subset_1(u1_struct_0(B),k6_waybel_0(B,C)) ) ) ) )).
fof(fraenkel_a_1_0_waybel22,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_0_waybel22(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k2_yellow_1(B))) & A = k6_waybel_0(k2_yellow_1(B),C) & ? [D] : ( m1_subset_1(D,B) & C = k1_tarski(D) ) ) ) )).
fof(fraenkel_a_1_0_waybel23,axiom,( ! [A] : ! [B] : ( l1_pre_topc(B) => ( r2_hidden(A,a_1_0_waybel23(B)) <=> ? [C] : ( v1_cantor_1(C,B) & v1_tops_2(C,B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & A = k1_card_1(C) ) ) ) )).
fof(fraenkel_a_1_0_waybel28,axiom,( ! [A] : ! [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) ) => ( r2_hidden(A,a_1_0_waybel28(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r2_hidden(D,C) => ! [E] : ( ( ~ v2_struct_0(E) & v4_orders_2(E) & v7_waybel_0(E) & l1_waybel_0(E,B) ) => ( r2_hidden(k4_tarski(E,D),k3_waybel28(B)) => r1_waybel_0(B,E,C) ) ) ) ) ) ) ) )).
fof(fraenkel_a_1_0_waybel29,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v6_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_0_waybel29(B)) <=> ? [C] : ? [D] : ( v3_pre_topc(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) & A = k4_tarski(C,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_1_0_waybel30,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_1_0_waybel30(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k7_subset_1(u1_struct_0(B),C,k4_waybel_0(B,D)) & r2_hidden(C,k5_waybel11(B)) & v1_finset_1(D) ) ) ) )).
fof(fraenkel_a_1_0_waybel31,axiom,( ! [A] : ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v3_waybel_3(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_1_0_waybel31(B)) <=> ? [C] : ( v6_waybel23(C,B) & m1_waybel23(C,B) & A = k1_card_1(C) ) ) ) )).
fof(fraenkel_a_1_0_waybel32,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_9(B) ) => ( r2_hidden(A,a_1_0_waybel32(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k3_subset_1(u1_struct_0(B),k5_waybel_0(B,C)) ) ) ) )).
fof(fraenkel_a_1_0_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_1_0_waybel_0(B)) <=> ? [C] : ( ~ 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))) & A = C ) ) ) )).
fof(fraenkel_a_1_0_waybel_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_1_0_waybel_4(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & r3_orders_2(B,C,D) & r2_hidden(D,k6_domain_1(u1_struct_0(B),k3_yellow_0(B))) ) ) ) ) )).
fof(fraenkel_a_1_0_weddwitt,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ( r2_hidden(A,a_1_0_weddwitt(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k7_group_3(B,C) ) ) ) )).
fof(fraenkel_a_1_0_wellfnd1,axiom,( ! [A] : ! [B] : ( l1_orders_2(B) => ( r2_hidden(A,a_1_0_wellfnd1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v2_wellfnd1(C,B) & v12_waybel_0(C,B) ) ) ) )).
fof(fraenkel_a_1_0_xxreal_1,axiom,( ! [A] : ! [B] : ( v1_xxreal_0(B) => ( r2_hidden(A,a_1_0_xxreal_1(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_0_yellow12,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_0_yellow12(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k2_borsuk_1(B,B))) & A = C & k1_funct_1(k9_funct_3(u1_struct_0(B),u1_struct_0(B)),C) = k1_funct_1(k10_funct_3(u1_struct_0(B),u1_struct_0(B)),C) ) ) ) )).
fof(fraenkel_a_1_0_zf_colla,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_0_zf_colla(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = C & ! [D] : ( m1_subset_1(D,B) => ~ ( r2_hidden(D,C) & ! [E] : ( v3_ordinal1(E) => ~ ( r2_hidden(E,k1_xboole_0) & r2_hidden(D,k1_zf_colla(B,E)) ) ) ) ) ) ) ) )).
fof(fraenkel_a_1_0_zf_lang,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(A,a_1_0_zf_lang(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_nat_1(1,B)) ) ) ) )).
fof(fraenkel_a_1_10_decomp_1,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_10_decomp_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & k3_decomp_1(B,C) = k1_decomp_1(B,C) ) ) ) )).
fof(fraenkel_a_1_10_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_10_fomodel0(B)) <=> ? [C] : ( m2_finseq_2(C,B,k4_finseq_2(1,B)) & A = k1_domain_1(k4_finseq_2(1,B),k4_finseq_2(1,B),C,k3_funct_2(k4_finseq_2(1,B),k4_finseq_2(1,B),k6_partfun1(k4_finseq_2(1,B)),C)) & r2_hidden(C,k4_finseq_2(1,B)) ) ) ) )).
fof(fraenkel_a_1_10_fomodel2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_10_fomodel2(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,B) & m1_subset_1(D,B) & A = k10_finseq_1(C,D) ) ) ) )).
fof(fraenkel_a_1_10_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ( r2_hidden(A,a_1_10_fomodel4(B)) <=> ? [C] : ? [D] : ( m2_subset_1(C,k3_finseq_2(k1_fomodel1(B)),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0))) & m2_subset_1(D,k3_finseq_2(k1_fomodel1(B)),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0))) & A = k10_finseq_1(C,D) ) ) ) )).
fof(fraenkel_a_1_10_gobrd11,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_10_gobrd11(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B),1)),C) ) ) ) )).
fof(fraenkel_a_1_10_jordan5d,axiom,( ! [A] : ! [B] : ( ( ~ 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,a_1_10_jordan5d(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = C & r2_hidden(k4_tarski(C,1),k2_matrix_0(k2_goboard2(B))) & ? [D] : ( v7_ordinal1(D) & r2_hidden(D,k4_finseq_1(B)) & k7_partfun1(u1_struct_0(k15_euclid(2)),B,D) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(B),C,1) ) ) ) ) )).
fof(fraenkel_a_1_10_jordan6,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_10_jordan6(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & ~ r1_xxreal_0(B,k18_euclid(C)) ) ) ) )).
fof(fraenkel_a_1_10_member_1,axiom,( ! [A] : ! [B] : ( v1_membered(B) => ( r2_hidden(A,a_1_10_member_1(B)) <=> ? [C] : ( v1_xcmplx_0(C) & A = k2_xcmplx_0(k5_numbers,C) & r2_hidden(C,B) ) ) ) )).
fof(fraenkel_a_1_10_nat_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(A,a_1_10_nat_4(B)) <=> ? [C] : ( v1_int_2(C) & m1_subset_1(C,k4_ordinal1) & A = C & r1_xxreal_0(C,k7_xcmplx_0(k2_nat_1(2,B),3)) ) ) ) )).
fof(fraenkel_a_1_10_scmyciel,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ( r2_hidden(A,a_1_10_scmyciel(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k1_tarski(C) ) ) ) )).
fof(fraenkel_a_1_10_tdlat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_10_tdlat_3(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v5_tops_1(C,B) ) ) ) )).
fof(fraenkel_a_1_10_topgen_2,axiom,( ! [A] : ! [B] : ( ~ v1_finset_1(B) => ( r2_hidden(A,a_1_10_topgen_2(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k6_domain_1(B,C) ) ) ) )).
fof(fraenkel_a_1_10_topgen_5,axiom,( ! [A] : ! [B] : ( ( v1_tops_2(B,k3_topmetr) & v1_cantor_1(B,k3_topmetr) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_topmetr)))) ) => ( r2_hidden(A,a_1_10_topgen_5(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_topmetr))) & A = k9_subset_1(u1_struct_0(k5_topmetr),C,k2_struct_0(k5_topmetr)) & r2_hidden(C,B) & ~ r1_xboole_0(C,k2_struct_0(k5_topmetr)) ) ) ) )).
fof(fraenkel_a_1_10_trees_2,axiom,( ! [A] : ! [B] : ( ( v4_funct_1(B) & ~ v1_xboole_0(B) ) => ( r2_hidden(A,a_1_10_trees_2(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k9_xtuple_0(C) ) ) ) )).
fof(fraenkel_a_1_10_trees_9,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_10_trees_9(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & r1_xxreal_0(1,C) & r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_11_decomp_1,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_11_decomp_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & k3_decomp_1(B,C) = k4_decomp_1(B,C) ) ) ) )).
fof(fraenkel_a_1_11_gobrd11,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_11_gobrd11(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & r1_xxreal_0(D,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,1))) ) ) ) )).
fof(fraenkel_a_1_11_jordan2c,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( r2_hidden(A,a_1_11_jordan2c(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & A = C & r1_jordan2c(2,B,C) ) ) ) )).
fof(fraenkel_a_1_11_jordan5d,axiom,( ! [A] : ! [B] : ( ( ~ 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,a_1_11_jordan5d(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = C & r2_hidden(k4_tarski(C,k1_matrix_0(k2_goboard2(B))),k2_matrix_0(k2_goboard2(B))) & ? [D] : ( v7_ordinal1(D) & r2_hidden(D,k4_finseq_1(B)) & k7_partfun1(u1_struct_0(k15_euclid(2)),B,D) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(B),C,k1_matrix_0(k2_goboard2(B))) ) ) ) ) )).
fof(fraenkel_a_1_11_jordan6,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_11_jordan6(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & ~ r1_xxreal_0(B,k7_partfun1(k1_numbers,C,2)) ) ) ) )).
fof(fraenkel_a_1_11_scmyciel,axiom,( ! [A] : ! [B] : ( ( v1_scmyciel(B) & v4_scmyciel(B) ) => ( r2_hidden(A,a_1_11_scmyciel(B)) <=> ? [C] : ( m1_subset_1(C,k3_tarski(B)) & A = k2_tarski(k3_tarski(B),k4_tarski(C,k3_tarski(B))) & r2_hidden(C,k3_tarski(B)) ) ) ) )).
fof(fraenkel_a_1_11_topgen_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_11_topgen_2(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) & A = k3_subset_1(B,C) & v1_finset_1(C) ) ) ) )).
fof(fraenkel_a_1_11_trees_2,axiom,( ! [A] : ! [B] : ( ( v4_funct_1(B) & ~ v1_xboole_0(B) ) => ( r2_hidden(A,a_1_11_trees_2(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k10_xtuple_0(C) ) ) ) )).
fof(fraenkel_a_1_11_waybel19,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v1_waybel19(B) & l1_waybel_9(B) ) => ( r2_hidden(A,a_1_11_waybel19(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k3_subset_1(u1_struct_0(B),k6_waybel_0(B,C)) ) ) ) )).
fof(fraenkel_a_1_12_decomp_1,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_12_decomp_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & k2_decomp_1(B,C) = k5_decomp_1(B,C) ) ) ) )).
fof(fraenkel_a_1_12_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(A,a_1_12_fomodel0(B)) <=> ? [C] : ( m1_subset_1(C,k2_xboole_0(k1_tarski(B),k1_tarski(k1_xboole_0))) & A = k10_xtuple_0(C) & r2_hidden(C,k1_tarski(B)) ) ) ) )).
fof(fraenkel_a_1_12_gobrd11,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_12_gobrd11(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,k1_matrix_0(B))),D) ) ) ) )).
fof(fraenkel_a_1_12_jordan6,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_12_jordan6(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & ~ r1_xxreal_0(k18_euclid(C),B) ) ) ) )).
fof(fraenkel_a_1_12_ltlaxio4,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)))) ) => ( r2_hidden(A,a_1_12_ltlaxio4(B)) <=> ? [C] : ( m1_subset_1(C,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) & A = k5_ltlaxio4(C) & r2_hidden(C,B) ) ) ) )).
fof(fraenkel_a_1_12_member_1,axiom,( ! [A] : ! [B] : ( v1_membered(B) => ( r2_hidden(A,a_1_12_member_1(B)) <=> ? [C] : ( v1_xcmplx_0(C) & A = k3_xcmplx_0(k5_numbers,C) & r2_hidden(C,B) ) ) ) )).
fof(fraenkel_a_1_12_scmyciel,axiom,( ! [A] : ! [B] : ( ( v1_scmyciel(B) & v4_scmyciel(B) ) => ( r2_hidden(A,a_1_12_scmyciel(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,k3_tarski(B)) & m1_subset_1(D,k3_tarski(B)) & A = k2_tarski(C,k4_tarski(D,k3_tarski(B))) & r2_hidden(k2_tarski(C,D),k1_scmyciel(B)) ) ) ) )).
fof(fraenkel_a_1_12_trees_9,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ( r2_hidden(A,a_1_12_trees_9(B)) <=> ? [C] : ( m1_trees_1(C,B) & A = C & k3_finseq_1(C) = k5_numbers ) ) ) )).
fof(fraenkel_a_1_12_waybel19,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v1_waybel19(B) & l1_waybel_9(B) ) => ( r2_hidden(A,a_1_12_waybel19(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k3_subset_1(u1_struct_0(B),k6_waybel_0(B,C)) ) ) ) )).
fof(fraenkel_a_1_13_abcmiz_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_13_abcmiz_1(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k1_abcmiz_1(C) ) ) ) )).
fof(fraenkel_a_1_13_decomp_1,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_13_decomp_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & k2_decomp_1(B,C) = k4_decomp_1(B,C) ) ) ) )).
fof(fraenkel_a_1_13_gobrd11,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_13_gobrd11(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & r1_xxreal_0(C,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,1))) & r1_xxreal_0(D,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,1))) ) ) ) )).
fof(fraenkel_a_1_13_jordan6,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_13_jordan6(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & ~ r1_xxreal_0(k7_partfun1(k1_numbers,C,2),B) ) ) ) )).
fof(fraenkel_a_1_13_ltlaxio4,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_hilbert1)) ) => ( r2_hidden(A,a_1_13_ltlaxio4(B)) <=> ? [C] : ( m1_subset_1(C,k1_hilbert1) & A = C & r2_hidden(C,k5_ltlaxio3(B)) & v2_hilbert2(C) ) ) ) )).
fof(fraenkel_a_1_13_member_1,axiom,( ! [A] : ! [B] : ( v1_membered(B) => ( r2_hidden(A,a_1_13_member_1(B)) <=> ? [C] : ( v1_xcmplx_0(C) & A = k3_xcmplx_0(1,C) & r2_hidden(C,B) ) ) ) )).
fof(fraenkel_a_1_13_scmyciel,axiom,( ! [A] : ! [B] : ( ( v1_scmyciel(B) & v4_scmyciel(B) ) => ( r2_hidden(A,a_1_13_scmyciel(B)) <=> ? [C] : ( m1_subset_1(C,k2_xboole_0(k2_xboole_0(k3_tarski(B),k2_zfmisc_1(k3_tarski(B),k1_tarski(k3_tarski(B)))),k1_tarski(k3_tarski(B)))) & A = k1_tarski(C) ) ) ) )).
fof(fraenkel_a_1_14_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & l1_msualg_1(B) ) => ( r2_hidden(A,a_1_14_abcmiz_1(B)) <=> ? [C] : ( v8_abcmiz_1(C,B) & m1_abcmiz_1(C,B,k13_abcmiz_1(B)) & A = k45_abcmiz_1(B,C) & r2_hidden(C,k1_subset_1(k38_abcmiz_1(B))) ) ) ) )).
fof(fraenkel_a_1_14_decomp_1,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_14_decomp_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & k5_decomp_1(B,C) = k4_decomp_1(B,C) ) ) ) )).
fof(fraenkel_a_1_14_gobrd11,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_14_gobrd11(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & r1_xxreal_0(C,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,1))) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,k1_matrix_0(B))),D) ) ) ) )).
fof(fraenkel_a_1_14_waybel19,axiom,( ! [A] : ! [B] : ( ( ~ 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) & v1_waybel19(B) & l1_waybel_9(B) ) => ( r2_hidden(A,a_1_14_waybel19(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k3_subset_1(u1_struct_0(B),k6_waybel_0(B,C)) ) ) ) )).
fof(fraenkel_a_1_15_gobrd11,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_15_gobrd11(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B),1)),C) & r1_xxreal_0(D,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,1))) ) ) ) )).
fof(fraenkel_a_1_15_jordan6,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_15_jordan6(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_15_waybel19,axiom,( ! [A] : ! [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) & v1_waybel19(B) & l1_waybel_9(B) ) => ( r2_hidden(A,a_1_15_waybel19(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k3_subset_1(u1_struct_0(B),k6_waybel_0(B,C)) ) ) ) )).
fof(fraenkel_a_1_16_abcmiz_a,axiom,( ! [A] : ! [B] : ( m2_finseq_2(B,k2_abcmiz_1,k4_abcmiz_1) => ( r2_hidden(A,a_1_16_abcmiz_a(B)) <=> ? [C] : ( m1_abcmiz_1(C,k27_abcmiz_1,k14_abcmiz_1(k27_abcmiz_1)) & A = k45_abcmiz_1(k27_abcmiz_1,C) & r2_hidden(C,k2_relset_1(k3_card_3(u3_msualg_1(k27_abcmiz_1,k1_msafree3(k27_abcmiz_1,k28_abcmiz_1(k27_abcmiz_1)))),k16_abcmiz_a(B))) ) ) ) )).
fof(fraenkel_a_1_16_gobrd11,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_16_gobrd11(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B),1)),C) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,k1_matrix_0(B))),D) ) ) ) )).
fof(fraenkel_a_1_16_jgraph_4,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_16_jgraph_4(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_16_jordan6,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_16_jordan6(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_17_jgraph_4,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_17_jgraph_4(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_17_waybel30,axiom,( ! [A] : ! [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) & v2_waybel19(B) & v2_waybel_2(B) & l1_waybel_9(B) ) => ( r2_hidden(A,a_1_17_waybel30(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(o_1_14_waybel30(B))) & A = k6_waybel_0(o_1_14_waybel30(B),C) & r2_hidden(C,u1_struct_0(k1_waybel_8(o_1_14_waybel30(B)))) ) ) ) )).
fof(fraenkel_a_1_18_ltlaxio4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ( r2_hidden(A,a_1_18_ltlaxio4(B)) <=> ? [C] : ( m1_subset_1(C,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) & A = k5_ltlaxio4(C) & r2_hidden(C,k8_ltlaxio4(B)) ) ) ) )).
fof(fraenkel_a_1_1_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & l1_msualg_1(B) ) => ( r2_hidden(A,a_1_1_abcmiz_1(B)) <=> ? [C] : ( m1_abcmiz_1(C,B,k13_abcmiz_1(B)) & A = C & v8_abcmiz_1(C,B) ) ) ) )).
fof(fraenkel_a_1_1_abcmiz_a,axiom,( ! [A] : ! [B] : ( m3_abcmiz_1(B,k27_abcmiz_1) => ( r2_hidden(A,a_1_1_abcmiz_a(B)) <=> ? [C] : ( v8_abcmiz_1(C,k27_abcmiz_1) & m1_abcmiz_1(C,k27_abcmiz_1,k13_abcmiz_1(k27_abcmiz_1)) & A = k9_abcmiz_a(k27_abcmiz_1,C) & r2_hidden(C,k41_abcmiz_1(k27_abcmiz_1,B)) ) ) ) )).
fof(fraenkel_a_1_1_afinsq_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_1_afinsq_1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & ~ r1_xxreal_0(k1_nat_1(B,1),C) ) ) ) )).
fof(fraenkel_a_1_1_afproj,axiom,( ! [A] : ! [B] : ( ( ~ v7_struct_0(B) & v1_diraf(B) & l1_analoaf(B) ) => ( r2_hidden(A,a_1_1_afproj(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v1_aff_4(C,B) ) ) ) )).
fof(fraenkel_a_1_1_ami_6,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_1_ami_6(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k1_amistd_1(k7_card_1(2),k1_ami_3,C,k7_ami_3(B)) ) ) ) )).
fof(fraenkel_a_1_1_aofa_000,axiom,( ! [A] : ! [B] : ( ( ~ 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) & l1_unialg_1(B) ) => ( r2_hidden(A,a_1_1_aofa_000(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & A = k13_aofa_000(B,C,D) & C != k13_aofa_000(B,C,D) & D != k13_aofa_000(B,C,D) ) ) ) )).
fof(fraenkel_a_1_1_armstrng,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_1_armstrng(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,k4_armstrng(B)) & m1_subset_1(D,k4_armstrng(B)) & A = k4_tarski(C,D) & r3_armstrng(B,D,C) ) ) )).
fof(fraenkel_a_1_1_arytm_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_arytm_2)) => ( r2_hidden(A,a_1_1_arytm_2(B)) <=> ? [C] : ( m1_subset_1(C,k5_arytm_3) & A = C & ? [D] : ( m1_subset_1(D,k2_arytm_2) & ? [E] : ( m1_subset_1(E,k2_arytm_2) & E = C & r2_hidden(D,B) & ~ r1_arytm_2(D,E) ) ) ) ) ) )).
fof(fraenkel_a_1_1_asympt_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(A,a_1_1_asympt_0(B)) <=> ? [C] : ( m2_funct_2(C,k4_ordinal1,k1_numbers,k9_funct_2(k4_ordinal1,k1_numbers)) & A = C & ? [D] : ( v1_xreal_0(D) & ? [E] : ( m1_subset_1(E,k4_ordinal1) & ~ r1_xxreal_0(D,k5_numbers) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(E,F) => ( r1_xxreal_0(k3_xcmplx_0(D,k9_nat_1(k1_numbers,B,F)),k9_nat_1(k1_numbers,C,F)) & r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,C,F)) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_1_1_asympt_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(A,a_1_1_asympt_1(B)) <=> ? [C] : ( m2_funct_2(C,k4_ordinal1,k1_numbers,k9_funct_2(k4_ordinal1,k1_numbers)) & A = C & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & ? [F] : ( m1_subset_1(F,k4_ordinal1) & ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(E,k5_numbers) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( r1_xxreal_0(F,G) => ( r1_xxreal_0(k3_xcmplx_0(E,k9_nat_1(k1_numbers,B,G)),k9_nat_1(k1_numbers,C,G)) & r1_xxreal_0(k9_nat_1(k1_numbers,C,G),k3_xcmplx_0(D,k9_nat_1(k1_numbers,B,G))) ) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_1_1_axioms,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( r2_hidden(A,a_1_1_axioms(B)) <=> ? [C] : ( m1_subset_1(C,k2_arytm_2) & A = C & r2_hidden(k4_tarski(k5_numbers,C),B) ) ) ) )).
fof(fraenkel_a_1_1_bagorder,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(A,a_1_1_bagorder(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & r1_xxreal_0(1,C) & r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_1_bcialg_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_bcialg_1(B) & v4_bcialg_1(B) & v5_bcialg_1(B) & v7_bcialg_1(B) & l2_bcialg_1(B) ) => ( r2_hidden(A,a_1_1_bcialg_1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & v10_bcialg_1(C,B) ) ) ) )).
fof(fraenkel_a_1_1_bcialg_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_bcialg_1(B) & v4_bcialg_1(B) & v5_bcialg_1(B) & v7_bcialg_1(B) & l2_bcialg_1(B) ) => ( r2_hidden(A,a_1_1_bcialg_2(B)) <=> ? [C] : ( m2_bcialg_2(C,B) & A = C ) ) ) )).
fof(fraenkel_a_1_1_c0sp2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_1_c0sp2(B)) <=> ? [C] : ( 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))) & A = C & v1_pscomp_1(C,B) & ? [D] : ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v2_compts_1(D,B) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ( E = k13_pre_poly(C) => m1_subset_1(k2_pre_topc(B,E),k1_zfmisc_1(D)) ) ) ) ) ) ) )).
fof(fraenkel_a_1_1_card_fil,axiom,( ! [A] : ! [B] : ( ~ v1_finset_1(B) => ( r2_hidden(A,a_1_1_card_fil(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) & A = C & r2_hidden(k1_card_1(k6_subset_1(B,C)),k1_card_1(B)) ) ) ) )).
fof(fraenkel_a_1_1_card_fin,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ( r2_hidden(A,a_1_1_card_fin(B)) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,B,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) & A = C & v2_funct_1(C) & ! [D] : ~ ( r2_hidden(D,B) & k1_funct_1(C,D) = D ) ) ) ) )).
fof(fraenkel_a_1_1_card_lar,axiom,( ! [A] : ! [B] : ( ( ~ v1_finset_1(B) & v1_card_1(B) & ~ v4_card_3(B) ) => ( r2_hidden(A,a_1_1_card_lar(B)) <=> ? [C] : ( ~ v1_finset_1(C) & v1_card_1(C) & m1_subset_1(C,B) & A = C & v6_card_fil(C) ) ) ) )).
fof(fraenkel_a_1_1_cardfin2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ( r2_hidden(A,a_1_1_cardfin2(B)) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,B,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) & A = C & v2_funct_1(C) & ! [D] : ~ ( r2_hidden(D,B) & k1_funct_1(C,D) = D ) ) ) ) )).
fof(fraenkel_a_1_1_catalan2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ( r2_hidden(A,a_1_1_catalan2(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & ~ r1_xxreal_0(k3_xcmplx_0(2,k7_afinsq_2(k5_relat_1(B,C))),C) ) ) ) )).
fof(fraenkel_a_1_1_cc0sp2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_1_cc0sp2(B)) <=> ? [C] : ( 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))) & A = C & v1_cc0sp2(C,B) & ? [D] : ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v2_compts_1(D,B) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ( E = k13_pre_poly(C) => m1_subset_1(k2_pre_topc(B,E),k1_zfmisc_1(D)) ) ) ) ) ) ) )).
fof(fraenkel_a_1_1_cgames_1,axiom,( ! [A] : ! [B] : ( ( v1_cgames_1(B) & l1_cgames_1(B) ) => ( r2_hidden(A,a_1_1_cgames_1(B)) <=> ? [C] : ( m1_subset_1(C,k2_xboole_0(u1_cgames_1(B),u2_cgames_1(B))) & A = k9_cgames_1(C) ) ) ) )).
fof(fraenkel_a_1_1_circuit1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & v5_msafree2(B) & l1_msualg_1(B) ) => ( r2_hidden(A,a_1_1_circuit1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & v1_msualg_2(C,B) ) ) ) )).
fof(fraenkel_a_1_1_coh_sp,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_1_coh_sp(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,k3_coh_sp(B)) & m1_subset_1(D,k3_coh_sp(B)) & A = k1_funct_2(k3_tarski(C),k3_tarski(D)) ) ) )).
fof(fraenkel_a_1_1_cohsp_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ( r2_hidden(A,a_1_1_cohsp_1(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k14_cohsp_1(C,k1_xboole_0) ) ) ) )).
fof(fraenkel_a_1_1_comput_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v4_funct_1(B) & v1_comput_1(B) ) => ( r2_hidden(A,a_1_1_comput_1(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k10_xtuple_0(C) ) ) ) )).
fof(fraenkel_a_1_1_decomp_1,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_1_decomp_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v1_decomp_1(C,B) ) ) ) )).
fof(fraenkel_a_1_1_domain_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_1_domain_1(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = C & ~ $true ) ) ) )).
fof(fraenkel_a_1_1_ens_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_1_ens_1(B)) <=> ? [C] : ? [D] : ? [E] : ( m1_subset_1(C,B) & m1_subset_1(D,B) & m1_subset_1(E,k1_ens_1(B)) & A = k1_domain_1(k2_zfmisc_1(B,B),k1_ens_1(B),k1_domain_1(B,B,C,D),E) & ( D = k1_xboole_0 => C = k1_xboole_0 ) & v1_funct_1(E) & v1_funct_2(E,C,D) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,D))) ) ) ) )).
fof(fraenkel_a_1_1_euclidlp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(A,a_1_1_euclidlp(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(B))) & A = C & ? [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(B)) & ? [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(B)) & ? [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(B)) & C = k4_euclidlp(B,D,E,F) ) ) ) ) ) ) )).
fof(fraenkel_a_1_1_euler_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_1_euler_1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_1_fcont_3,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_1_fcont_3(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_1_fdiff_2,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_1_fdiff_2(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_1_finance1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_1_finance1(B)) <=> ? [C] : ( m1_subset_1(C,k6_numbers) & A = C & r1_xxreal_0(B,C) & ~ r1_xxreal_0(k1_xxreal_0,C) ) ) ) )).
fof(fraenkel_a_1_1_finseq_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_1_finseq_2(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,B) & m1_subset_1(D,B) & A = k10_finseq_1(C,D) ) ) ) )).
fof(fraenkel_a_1_1_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(A,a_1_1_fomodel0(B)) <=> ? [C] : ( m1_subset_1(C,k9_xtuple_0(B)) & A = k4_tarski(C,k1_funct_1(B,C)) & r2_hidden(C,k9_xtuple_0(B)) ) ) ) )).
fof(fraenkel_a_1_1_fomodel2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_1_fomodel2(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k10_finseq_1(C,C) ) ) ) )).
fof(fraenkel_a_1_1_fomodel3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_1_fomodel3(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k6_domain_1(B,C) ) ) ) )).
fof(fraenkel_a_1_1_frechet,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_1_frechet(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(C,k6_xcmplx_0(B,k7_xcmplx_0(1,4))) & ~ r1_xxreal_0(k2_xcmplx_0(B,k7_xcmplx_0(1,4)),C) ) ) ) )).
fof(fraenkel_a_1_1_funct_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v4_funct_1(B) ) => ( r2_hidden(A,a_1_1_funct_1(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k10_xtuple_0(C) ) ) ) )).
fof(fraenkel_a_1_1_goboard5,axiom,( ! [A] : ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_1_goboard5(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & r1_xxreal_0(C,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,k1_nat_1(1,k5_numbers)))) ) ) ) )).
fof(fraenkel_a_1_1_goboard6,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_1_goboard6(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & ~ r1_xxreal_0(C,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B),1))) ) ) ) )).
fof(fraenkel_a_1_1_goboard9,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_1_goboard9(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & ~ r1_xxreal_0(D,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,k1_matrix_0(B)))) ) ) ) )).
fof(fraenkel_a_1_1_gobrd11,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_1_gobrd11(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & r1_xxreal_0(D,B) ) ) ) )).
fof(fraenkel_a_1_1_gobrd12,axiom,( ! [A] : ! [B] : ( ( ~ 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,a_1_1_gobrd12(B)) <=> ? [C] : ? [D] : ( v7_ordinal1(C) & v7_ordinal1(D) & A = k3_goboard5(k2_goboard2(B),C,D) & r1_xxreal_0(C,k3_finseq_1(k2_goboard2(B))) & r1_xxreal_0(D,k1_matrix_0(k2_goboard2(B))) ) ) ) )).
fof(fraenkel_a_1_1_gobrd13,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_1_gobrd13(B)) <=> ? [C] : ? [D] : ( v7_ordinal1(C) & v7_ordinal1(D) & A = k3_matrix_0(u1_struct_0(k15_euclid(2)),B,C,D) & r2_hidden(k4_tarski(C,D),k2_matrix_0(B)) ) ) ) )).
fof(fraenkel_a_1_1_grcat_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) ) => ( r2_hidden(A,a_1_1_grcat_1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k27_grcat_1(B))) & A = C & ? [D] : ( ~ v2_struct_0(D) & v13_algstr_0(D) & v2_rlvect_1(D) & v3_rlvect_1(D) & v4_rlvect_1(D) & v2_midsp_2(D) & l2_algstr_0(D) & C = D ) ) ) ) )).
fof(fraenkel_a_1_1_group_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v15_algstr_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ( r2_hidden(A,a_1_1_group_4(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & ~ v1_group_4(C,B) ) ) ) )).
fof(fraenkel_a_1_1_int_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(A,a_1_1_int_4(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = C & r1_int_2(B,C) & r1_xxreal_0(1,C) & r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_1_integra1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(A,a_1_1_integra1(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & r1_xxreal_0(k3_seq_4(B),C) & r1_xxreal_0(C,k2_seq_4(B)) ) ) ) )).
fof(fraenkel_a_1_1_jct_misc,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_1_jct_misc(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_1_jgraph_6,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_1_jgraph_6(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & k12_euclid(C) = B ) ) ) )).
fof(fraenkel_a_1_1_jordan1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_1_jordan1(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_1_jordan10,axiom,( ! [A] : ! [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)))) ) => ( r2_hidden(A,a_1_1_jordan10(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k2_pre_topc(k15_euclid(2),k1_jordan2c(2,k3_topreal1(2,k2_jordan9(B,C)))) ) ) ) )).
fof(fraenkel_a_1_1_jordan1a,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_1_jordan1a(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & k17_euclid(C) = B ) ) ) )).
fof(fraenkel_a_1_1_jordan1k,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_1_jordan1k(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) & A = C & r1_jordan2c(B,k1_struct_0(k15_euclid(B)),C) ) ) ) )).
fof(fraenkel_a_1_1_jordan2b,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_1_jordan2b(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_1_jordan2c,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_1_jordan2c(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(1))) & A = C & ? [D] : ( v1_xreal_0(D) & C = k9_finseq_1(D) & ~ r1_xxreal_0(k4_xcmplx_0(B),D) ) ) ) ) )).
fof(fraenkel_a_1_1_jordan5d,axiom,( ! [A] : ! [B] : ( ( ~ 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,a_1_1_jordan5d(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = k18_euclid(C) & k17_euclid(C) = k8_pscomp_1(k3_topreal1(2,B)) & r2_hidden(C,k3_topreal1(2,B)) ) ) ) )).
fof(fraenkel_a_1_1_jordan6,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_1_jordan6(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & r1_xxreal_0(k17_euclid(C),B) ) ) ) )).
fof(fraenkel_a_1_1_jordan7,axiom,( ! [A] : ! [B] : ( ( ~ 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,a_1_1_jordan7(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & r1_jordan6(B,k18_pscomp_1(B),C) & r1_jordan6(B,C,k22_pscomp_1(B)) ) ) ) )).
fof(fraenkel_a_1_1_jordan9,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_1_jordan9(B)) <=> ? [C] : ? [D] : ( v7_ordinal1(C) & v7_ordinal1(D) & A = k3_matrix_0(u1_struct_0(k15_euclid(2)),B,C,D) & r2_hidden(k4_tarski(C,D),k2_matrix_0(B)) ) ) ) )).
fof(fraenkel_a_1_1_jordan_a,axiom,( ! [A] : ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_1_jordan_a(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & ( r1_jordan6(B,k18_pscomp_1(B),C) | ( r2_hidden(k18_pscomp_1(B),B) & C = k18_pscomp_1(B) ) ) ) ) ) )).
fof(fraenkel_a_1_1_lang1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_lang1(B) ) => ( r2_hidden(A,a_1_1_lang1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) & r1_lang1(B,C,D) ) ) ) ) )).
fof(fraenkel_a_1_1_lattice5,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_1_lattice5(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,B) & m1_subset_1(D,B) & A = k2_zfmisc_1(C,D) & r2_hidden(C,B) & r2_hidden(D,B) ) ) ) )).
fof(fraenkel_a_1_1_lattice6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) ) => ( r2_hidden(A,a_1_1_lattice6(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & v4_lattice6(C,B) ) ) ) )).
fof(fraenkel_a_1_1_lattice7,axiom,( ! [A] : ! [B] : ( l1_orders_2(B) => ( r2_hidden(A,a_1_1_lattice7(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v12_waybel_0(C,B) ) ) ) )).
fof(fraenkel_a_1_1_limfunc1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_1_limfunc1(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_1_limfunc2,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_1_limfunc2(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_1_limfunc3,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_1_limfunc3(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_1_limfunc4,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_1_limfunc4(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_1_lopclset,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v7_struct_0(B) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B) ) => ( r2_hidden(A,a_1_1_lopclset(B)) <=> ? [C] : ( ~ v1_xboole_0(C) & v19_lattices(C,B) & v20_lattices(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v1_filter_0(C,B) ) ) ) )).
fof(fraenkel_a_1_1_ltlaxio3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_hilbert1)) => ( r2_hidden(A,a_1_1_ltlaxio3(B)) <=> ? [C] : ( m1_subset_1(C,k1_hilbert1) & A = k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k6_ltlaxio3,C) & r2_hidden(C,B) ) ) ) )).
fof(fraenkel_a_1_1_ltlaxio4,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_hilbert1)) ) => ( r2_hidden(A,a_1_1_ltlaxio4(B)) <=> ? [C] : ( m1_subset_1(C,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) & A = C & k10_ltlaxio3(C) = k5_ltlaxio3(B) & r1_xboole_0(k2_relset_1(k1_hilbert1,k8_ltlaxio3(C)),k2_relset_1(k1_hilbert1,k9_ltlaxio3(C))) ) ) ) )).
fof(fraenkel_a_1_1_matrix11,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_1_matrix11(B)) <=> ? [C] : ( m1_matrix_2(C,k3_matrix_2(B)) & A = C & ~ v5_matrix_2(C,k2_matrix_2(k3_matrix_2(B))) ) ) ) )).
fof(fraenkel_a_1_1_matrixc1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_1_matrixc1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & r1_xxreal_0(1,C) & r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_1_matrprob,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k1_numbers) => ( r2_hidden(A,a_1_1_matrprob(B)) <=> ? [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) & A = C & k3_finseq_1(C) = k3_finseq_1(B) ) ) ) )).
fof(fraenkel_a_1_1_measure6,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( r2_hidden(A,a_1_1_measure6(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_numbers)) & A = C & r1_tarski(B,C) & v2_rcomp_1(C) ) ) ) )).
fof(fraenkel_a_1_1_member_1,axiom,( ! [A] : ! [B] : ( v1_membered(B) => ( r2_hidden(A,a_1_1_member_1(B)) <=> ? [C] : ( v1_xcmplx_0(C) & A = k4_xcmplx_0(C) & r2_hidden(C,B) ) ) ) )).
fof(fraenkel_a_1_1_metric_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_metric_1(B) ) => ( r2_hidden(A,a_1_1_metric_2(B)) <=> ? [C] : ( m1_subset_1(C,k1_numbers) & A = C & ? [D] : ( m1_subset_1(D,k2_metric_2(B)) & ? [E] : ( m1_subset_1(E,k2_metric_2(B)) & r4_metric_2(B,D,E,C) ) ) ) ) ) )).
fof(fraenkel_a_1_1_midsp_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_1(B) ) => ( r2_hidden(A,a_1_1_midsp_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) & A = C & m1_midsp_1(C,B) ) ) ) )).
fof(fraenkel_a_1_1_modal_1,axiom,( ! [A] : ! [B] : ( m2_trees_3(B,k2_trees_1(1),k1_relset_1(k2_trees_1(1),k8_funcop_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k2_trees_1(1),k1_domain_1(k4_ordinal1,k4_ordinal1,1,k5_numbers)))) => ( r2_hidden(A,a_1_1_modal_1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k8_finseq_1(k4_ordinal1,B,k14_trees_3(C)) & r2_hidden(k8_finseq_1(k4_ordinal1,B,k14_trees_3(C)),k1_relset_1(k2_trees_1(1),k8_funcop_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k2_trees_1(1),k1_domain_1(k4_ordinal1,k4_ordinal1,1,k5_numbers)))) ) ) ) )).
fof(fraenkel_a_1_1_modelc_2,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_1_modelc_2(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & r1_xxreal_0(1,C) & r1_xxreal_0(C,k2_xcmplx_0(1,B)) ) ) ) )).
fof(fraenkel_a_1_1_modelc_3,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(B) & v5_modelc_3(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r2_hidden(A,a_1_1_modelc_3(B)) <=> ? [C] : ( m1_subset_1(C,k3_zfmisc_1(k23_modelc_3(B),k43_modelc_2,k23_modelc_3(B))) & A = C & ? [D] : ( v1_modelc_3(D,B) & v3_modelc_3(D,B) & l1_modelc_3(D,B) & ? [E] : ( v1_modelc_3(E,B) & v3_modelc_3(E,B) & l1_modelc_3(E,B) & ? [F] : ( C = k4_tarski(k4_tarski(D,F),E) & r6_modelc_3(B,D,E) & r2_hidden(F,k29_modelc_3(B,E)) ) ) ) ) ) ) )).
fof(fraenkel_a_1_1_moebius1,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ( r2_hidden(A,a_1_1_moebius1(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = C & ~ r1_xxreal_0(C,k5_numbers) & r1_nat_d(C,B) & v1_moebius1(C) ) ) ) )).
fof(fraenkel_a_1_1_msualg_7,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_1_msualg_7(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(C,k7_xcmplx_0(1,2)) & r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_1_nat_4,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_1_nat_4(B)) <=> ? [C] : ( v1_int_2(C) & m1_subset_1(C,k4_ordinal1) & A = C & r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_1_nattra_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & 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_hidden(A,a_1_1_nattra_1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k2_cat_1(B,C,C) ) ) ) )).
fof(fraenkel_a_1_1_necklace,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_1_necklace(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = k4_tarski(k1_nat_1(C,1),C) & ~ r1_xxreal_0(B,k1_nat_1(C,1)) ) ) ) )).
fof(fraenkel_a_1_1_newton,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_1_newton(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = C & ~ r1_xxreal_0(B,C) & v1_int_2(C) ) ) ) )).
fof(fraenkel_a_1_1_normform,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_1_normform(B)) <=> ? [C] : ( m1_subset_1(C,k5_finsub_1(k7_normform(B))) & A = C & ! [D] : ( m2_subset_1(D,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B)) => ! [E] : ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B)) => ( ( r2_hidden(D,C) & r2_hidden(E,C) & r1_normform(k5_finsub_1(B),k5_finsub_1(B),D,E) ) => D = E ) ) ) ) ) )).
fof(fraenkel_a_1_1_ntalgo_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_numbers))) ) => ( r2_hidden(A,a_1_1_ntalgo_1(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = C & k9_nat_1(k4_numbers,B,C) = k5_numbers ) ) ) )).
fof(fraenkel_a_1_1_openlatt,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v7_struct_0(B) & v10_lattices(B) & v1_lattice2(B) & l3_lattices(B) ) => ( r2_hidden(A,a_1_1_openlatt(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_openlatt(B))) & A = k3_tarski(C) ) ) ) )).
fof(fraenkel_a_1_1_ordinal6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v3_ordinal6(B) ) => ( r2_hidden(A,a_1_1_ordinal6(B)) <=> ? [C] : ( m1_subset_1(C,k9_xtuple_0(k1_funct_1(B,k5_numbers))) & A = C & r2_hidden(C,k9_xtuple_0(k1_funct_1(B,k5_numbers))) & ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v5_ordinal1(D) & v1_ordinal2(D) ) => ( r2_hidden(D,k10_xtuple_0(B)) => r1_abian(C,D) ) ) ) ) ) )).
fof(fraenkel_a_1_1_polynom2,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_1_polynom2(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & r1_xxreal_0(1,C) & r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_1_polyred,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_1_polyred(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & r1_xxreal_0(1,C) & r1_xxreal_0(C,k2_xcmplx_0(B,1)) ) ) ) )).
fof(fraenkel_a_1_1_radix_3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_1_radix_3(B)) <=> ? [C] : ( m1_subset_1(C,k4_numbers) & A = C & r1_xxreal_0(k6_xcmplx_0(k4_xcmplx_0(k1_radix_1(k7_nat_d(B,1))),1),C) & r1_xxreal_0(C,k1_radix_1(k7_nat_d(B,1))) ) ) ) )).
fof(fraenkel_a_1_1_rltopsp1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v6_rltopsp1(B) & v7_rltopsp1(B) & l1_rltopsp1(B) ) => ( r2_hidden(A,a_1_1_rltopsp1(B)) <=> ? [C] : ( m1_connsp_2(C,B,k4_struct_0(B)) & A = C ) ) ) )).
fof(fraenkel_a_1_1_rusub_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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) ) => ( r2_hidden(A,a_1_1_rusub_5(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r1_struct_0(k2_rusub_1(B),D) => r1_bhsp_1(B,D,C) ) ) ) ) ) )).
fof(fraenkel_a_1_1_scmfsa10,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_1_scmfsa10(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k1_amistd_1(k7_card_1(3),k1_scmfsa_2,C,k11_scmfsa_2(B)) ) ) ) )).
fof(fraenkel_a_1_1_scmfsa8a,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,a_1_1_scmfsa8a(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k1_nat_1(C,k1_nat_1(k5_card_1(B),1)) & r2_hidden(C,k2_afinsq_1(k4_compos_1(k1_scmfsa_2))) ) ) ) )).
fof(fraenkel_a_1_1_scmfsa_m,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k3_scmfsa_2)) ) => ( r2_hidden(A,a_1_1_scmfsa_m(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = C & ~ r2_hidden(k5_scmfsa_2(C),B) ) ) ) )).
fof(fraenkel_a_1_1_scmringi,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ( r2_hidden(A,a_1_1_scmringi(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,k2_scm_inst) & m1_subset_1(D,u1_struct_0(B)) & A = k3_xtuple_0(5,k1_xboole_0,k7_scmringi(B,C,D)) ) ) ) )).
fof(fraenkel_a_1_1_sgraph1,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_1_sgraph1(B)) <=> ? [C] : ? [D] : ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(B)) & v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_sgraph1(C))) & A = g1_sgraph1(C,D) ) ) )).
fof(fraenkel_a_1_1_sppol_1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,a_1_1_sppol_1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k2_topreal1(2,B,C) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(B)) ) ) ) )).
fof(fraenkel_a_1_1_sprect_1,axiom,( ! [A] : ! [B] : ( ( ~ 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,a_1_1_sprect_1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & r1_xxreal_0(k17_euclid(C),k8_pscomp_1(B)) & r1_xxreal_0(k6_pscomp_1(B),k17_euclid(C)) & k18_euclid(C) = k9_pscomp_1(B) ) ) ) )).
fof(fraenkel_a_1_1_sprect_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & v1_topreal1(B) & v2_topreal1(B) & v1_goboard5(B) & v1_sprect_1(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_1_1_sprect_3(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & ~ ( r1_xxreal_0(k6_pscomp_1(k3_topreal1(2,B)),k17_euclid(C)) & r1_xxreal_0(k17_euclid(C),k8_pscomp_1(k3_topreal1(2,B))) & r1_xxreal_0(k9_pscomp_1(k3_topreal1(2,B)),k18_euclid(C)) & r1_xxreal_0(k18_euclid(C),k7_pscomp_1(k3_topreal1(2,B))) ) ) ) ) )).
fof(fraenkel_a_1_1_stirl2_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_1_stirl2_1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_1_t_1topsp,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_1_t_1topsp(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k12_eqrel_1(u1_struct_0(B),k1_t_1topsp(B)))) & A = C & r2_hidden(k3_tarski(C),u1_pre_topc(B)) ) ) ) )).
fof(fraenkel_a_1_1_tdlat_1,axiom,( ! [A] : ! [B] : ( l1_pre_topc(B) => ( r2_hidden(A,a_1_1_tdlat_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v5_tops_1(C,B) ) ) ) )).
fof(fraenkel_a_1_1_tdlat_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_1_tdlat_2(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v5_tops_1(C,B) ) ) ) )).
fof(fraenkel_a_1_1_topgen_2,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_1_topgen_2(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) & A = k3_subset_1(B,C) & v1_finset_1(C) ) ) )).
fof(fraenkel_a_1_1_topgen_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(k1_numbers))) => ( r2_hidden(A,a_1_1_topgen_3(B)) <=> ? [C] : ( m1_subset_1(C,k1_numbers) & A = C & ? [D] : ( r2_hidden(D,k1_cantor_1(k1_numbers,B)) & r1_topgen_3(D,C) ) ) ) ) )).
fof(fraenkel_a_1_1_topreal3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_1_topreal3(B)) <=> ? [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) & A = C & k3_finseq_1(C) = B ) ) ) )).
fof(fraenkel_a_1_1_topreal4,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,a_1_1_topreal4(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k2_topreal1(2,B,C) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(B)) ) ) ) )).
fof(fraenkel_a_1_1_topreal5,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_1_topreal5(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_1_topreal8,axiom,( ! [A] : ! [B] : ( ( v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & v2_topreal1(B) & v1_goboard5(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_1_1_topreal8(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k2_topreal1(2,k2_rfinseq(u1_struct_0(k15_euclid(2)),1,B),C) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(k2_rfinseq(u1_struct_0(k15_euclid(2)),1,B))) ) ) ) )).
fof(fraenkel_a_1_1_treal_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( r2_hidden(A,a_1_1_treal_1(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & r1_xxreal_0(k5_numbers,C) & ~ r1_xxreal_0(k3_seq_4(B),C) ) ) ) )).
fof(fraenkel_a_1_1_trees_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) ) => ( r2_hidden(A,a_1_1_trees_2(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k2_trees_2(B,C) & r1_xxreal_0(C,k6_trees_1(B)) ) ) ) )).
fof(fraenkel_a_1_1_trees_9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ( r2_hidden(A,a_1_1_trees_9(B)) <=> ? [C] : ( m1_trees_1(C,k9_xtuple_0(B)) & A = k4_tarski(C,k5_trees_2(B,C)) ) ) ) )).
fof(fraenkel_a_1_1_turing_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(A,a_1_1_turing_1(B)) <=> ? [C] : ( m2_finseq_2(C,k4_ordinal1,k3_finseq_2(k4_ordinal1)) & A = C & k3_finseq_1(C) = B ) ) ) )).
fof(fraenkel_a_1_1_uniroots,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ( r2_hidden(A,a_1_1_uniroots(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = k1_hahnban1(k19_sin_cos(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C),B)),k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C),B))) & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_1_waybel11,axiom,( ! [A] : ! [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) & v3_waybel_3(B) & v4_waybel11(B) & l1_waybel_9(B) ) => ( r2_hidden(A,a_1_1_waybel11(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k2_waybel_3(B,C) ) ) ) )).
fof(fraenkel_a_1_1_waybel16,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_1_1_waybel16(B)) <=> ? [C] : ( ~ v1_xboole_0(C) & v2_waybel_0(C,B) & v13_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C ) ) ) )).
fof(fraenkel_a_1_1_waybel19,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_waybel_9(B) ) => ( r2_hidden(A,a_1_1_waybel19(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = k3_subset_1(u1_struct_0(B),k4_waybel_0(B,C)) & v1_finset_1(C) ) ) ) )).
fof(fraenkel_a_1_1_waybel23,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_1_1_waybel23(B)) <=> ? [C] : ( ~ 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))) & A = C ) ) ) )).
fof(fraenkel_a_1_1_waybel31,axiom,( ! [A] : ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & v2_waybel_8(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_1_1_waybel31(B)) <=> ? [C] : ( v6_waybel23(C,B) & m1_waybel23(C,B) & A = k1_card_1(C) ) ) ) )).
fof(fraenkel_a_1_1_waybel33,axiom,( ! [A] : ! [B] : ( ( 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) ) => ( r2_hidden(A,a_1_1_waybel33(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r2_hidden(D,C) => ! [E] : ( ( ~ v2_struct_0(E) & v4_orders_2(E) & v7_waybel_0(E) & l1_waybel_0(E,B) ) => ( r2_hidden(k4_tarski(E,D),k3_waybel28(B)) => r1_waybel_0(B,E,C) ) ) ) ) ) ) ) )).
fof(fraenkel_a_1_1_waybel_0,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_1_1_waybel_0(B)) <=> ? [C] : ( ~ v1_xboole_0(C) & v2_waybel_0(C,B) & v13_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C ) ) ) )).
fof(fraenkel_a_1_1_waybel_4,axiom,( ! [A] : ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_1_1_waybel_4(B)) <=> ? [C] : ( ~ 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))) & A = C ) ) ) )).
fof(fraenkel_a_1_1_weddwitt,axiom,( ! [A] : ! [B] : ( ( ~ 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) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ( r2_hidden(A,a_1_1_weddwitt(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k6_algstr_0(B,C,D) = k6_algstr_0(B,D,C) ) ) ) ) )).
fof(fraenkel_a_1_1_wellfnd1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_1_1_wellfnd1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v2_wellfnd1(C,B) & v12_waybel_0(C,B) ) ) ) )).
fof(fraenkel_a_1_1_xxreal_1,axiom,( ! [A] : ! [B] : ( v1_xxreal_0(B) => ( r2_hidden(A,a_1_1_xxreal_1(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_1_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) => ( r2_hidden(A,a_1_1_zmodul02(B)) <=> ? [C] : ( m2_zmodul02(C,B,k1_subset_1(u1_struct_0(B))) & A = k21_zmodul02(B,C) ) ) ) )).
fof(fraenkel_a_1_21_waybel19,axiom,( ! [A] : ! [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) & v2_waybel19(B) & l1_waybel_9(B) ) => ( r2_hidden(A,a_1_21_waybel19(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(o_1_19_waybel19(B))) & A = k3_subset_1(u1_struct_0(o_1_19_waybel19(B)),k6_waybel_0(o_1_19_waybel19(B),C)) ) ) ) )).
fof(fraenkel_a_1_22_waybel19,axiom,( ! [A] : ! [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) & v2_waybel19(B) & l1_waybel_9(B) ) => ( r2_hidden(A,a_1_22_waybel19(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(o_1_19_waybel19(B)))) & A = k3_subset_1(u1_struct_0(o_1_19_waybel19(B)),k4_waybel_0(o_1_19_waybel19(B),C)) & v1_finset_1(C) ) ) ) )).
fof(fraenkel_a_1_23_gobrd11,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_23_gobrd11(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & r1_xxreal_0(D,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,1))) ) ) ) )).
fof(fraenkel_a_1_24_gobrd11,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_24_gobrd11(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & r1_xxreal_0(C,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,1))) ) ) ) )).
fof(fraenkel_a_1_25_gobrd11,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_25_gobrd11(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,k1_matrix_0(B))),D) ) ) ) )).
fof(fraenkel_a_1_26_gobrd11,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_26_gobrd11(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B),1)),C) ) ) ) )).
fof(fraenkel_a_1_2_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & l1_msualg_1(B) ) => ( r2_hidden(A,a_1_2_abcmiz_1(B)) <=> ? [C] : ? [D] : ( m1_abcmiz_1(C,B,k12_abcmiz_1(B)) & v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(k38_abcmiz_1(B))) & A = k1_domain_1(k1_zfmisc_1(k38_abcmiz_1(B)),k3_card_3(u3_msualg_1(B,k1_msafree3(B,k28_abcmiz_1(B)))),D,C) & v9_abcmiz_1(C,B) ) ) ) )).
fof(fraenkel_a_1_2_abcmiz_a,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k38_abcmiz_1(k27_abcmiz_1))) ) => ( r2_hidden(A,a_1_2_abcmiz_a(B)) <=> ? [C] : ( v8_abcmiz_1(C,k27_abcmiz_1) & m1_abcmiz_1(C,k27_abcmiz_1,k13_abcmiz_1(k27_abcmiz_1)) & A = k9_abcmiz_a(k27_abcmiz_1,C) & r2_hidden(C,B) ) ) ) )).
fof(fraenkel_a_1_2_afproj,axiom,( ! [A] : ! [B] : ( ( ~ v7_struct_0(B) & v1_diraf(B) & l1_analoaf(B) ) => ( r2_hidden(A,a_1_2_afproj(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k1_domain_1(k1_zfmisc_1(u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)),C,D) & v1_aff_1(C,B) & v1_aff_1(D,B) & r1_aff_4(B,C,D) ) ) ) )).
fof(fraenkel_a_1_2_ami_6,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_2_ami_6(B)) <=> ? [C] : ( m1_subset_1(C,u1_compos_1(k1_ami_3)) & A = k7_subset_1(k4_ordinal1,k1_amistd_1(k7_card_1(2),k1_ami_3,B,C),k2_amistd_1(k7_card_1(2),k1_ami_3,C)) ) ) ) )).
fof(fraenkel_a_1_2_asympt_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(A,a_1_2_asympt_0(B)) <=> ? [C] : ( m2_funct_2(C,k4_ordinal1,k1_numbers,k9_funct_2(k4_ordinal1,k1_numbers)) & A = C & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & ? [F] : ( m1_subset_1(F,k4_ordinal1) & ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(E,k5_numbers) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( r1_xxreal_0(F,G) => ( r1_xxreal_0(k3_xcmplx_0(E,k9_nat_1(k1_numbers,B,G)),k9_nat_1(k1_numbers,C,G)) & r1_xxreal_0(k9_nat_1(k1_numbers,C,G),k3_xcmplx_0(D,k9_nat_1(k1_numbers,B,G))) ) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_1_2_asympt_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & v6_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(A,a_1_2_asympt_1(B)) <=> ? [C] : ( m2_funct_2(C,k4_ordinal1,k1_numbers,k9_funct_2(k4_ordinal1,k1_numbers)) & A = C & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & ? [F] : ( m1_subset_1(F,k4_ordinal1) & ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(E,k5_numbers) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( r1_xxreal_0(F,G) => ( r1_xxreal_0(k3_xcmplx_0(E,k9_nat_1(k1_numbers,B,G)),k9_nat_1(k1_numbers,C,G)) & r1_xxreal_0(k9_nat_1(k1_numbers,C,G),k3_xcmplx_0(D,k9_nat_1(k1_numbers,B,G))) ) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_1_2_bagorder,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_2_bagorder(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_2_bcialg_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_bcialg_1(B) & v4_bcialg_1(B) & v5_bcialg_1(B) & v7_bcialg_1(B) & l2_bcialg_1(B) ) => ( r2_hidden(A,a_1_2_bcialg_2(B)) <=> ? [C] : ( m3_bcialg_2(C,B) & A = C ) ) ) )).
fof(fraenkel_a_1_2_card_fin,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ( r2_hidden(A,a_1_2_card_fin(B)) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,B,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) & A = C & v2_funct_1(C) ) ) ) )).
fof(fraenkel_a_1_2_catalan2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ( r2_hidden(A,a_1_2_catalan2(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & k3_xcmplx_0(2,k7_afinsq_2(k5_relat_1(k1_catalan2(k5_afinsq_1(k5_numbers),B),C))) = C & ~ r1_xxreal_0(C,k5_numbers) ) ) ) )).
fof(fraenkel_a_1_2_cgames_1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => ( r2_hidden(A,a_1_2_cgames_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_cgames_1(B))) & A = C & ! [D] : ( v2_cgames_1(D) => ( r2_hidden(D,C) => ! [E] : ( v2_cgames_1(E) => ~ ( r2_hidden(E,k7_cgames_1(D)) & ! [F] : ( v2_cgames_1(F) => ~ ( r2_hidden(F,k6_cgames_1(E)) & r2_hidden(F,C) ) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_1_2_coh_sp,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_2_coh_sp(B)) <=> ? [C] : ? [D] : ? [E] : ( m1_subset_1(C,k3_coh_sp(B)) & m1_subset_1(D,k3_coh_sp(B)) & m1_subset_1(E,k4_coh_sp(B)) & A = k4_tarski(k4_tarski(C,D),E) & ( k3_tarski(D) = k1_xboole_0 => k3_tarski(C) = k1_xboole_0 ) & v1_funct_1(E) & v1_funct_2(E,k3_tarski(C),k3_tarski(D)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k3_tarski(C),k3_tarski(D)))) & ! [F] : ! [G] : ( r2_hidden(k2_tarski(F,G),C) => r2_hidden(k2_tarski(k1_funct_1(E,F),k1_funct_1(E,G)),D) ) ) ) )).
fof(fraenkel_a_1_2_cohsp_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ( r2_hidden(A,a_1_2_cohsp_1(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k14_cohsp_1(k1_xboole_0,C) ) ) ) )).
fof(fraenkel_a_1_2_compact1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_2_compact1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = k2_xboole_0(C,k6_domain_1(k1_zfmisc_1(u1_struct_0(B)),k2_struct_0(B))) & v3_pre_topc(C,B) & v2_compts_1(k3_subset_1(u1_struct_0(B),C),B) ) ) ) )).
fof(fraenkel_a_1_2_comput_1,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_2_comput_1(B)) <=> ? [C] : ( m2_rfunct_3(C,k3_finseq_2(B),B,k3_rfunct_3(k3_finseq_2(B),B)) & A = C & v2_margrel1(C) ) ) )).
fof(fraenkel_a_1_2_decomp_1,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_2_decomp_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v2_decomp_1(C,B) ) ) ) )).
fof(fraenkel_a_1_2_ens_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_2_ens_1(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,B) & m1_subset_1(D,B) & A = k7_ens_1(B,C,D) ) ) ) )).
fof(fraenkel_a_1_2_euclid_7,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( r2_hidden(A,a_1_2_euclid_7(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = k6_euclid_7(B,C) & r1_xxreal_0(1,C) & r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_2_fcont_3,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_2_fcont_3(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_2_fdiff_2,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_2_fdiff_2(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_2_finseq_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_2_finseq_2(B)) <=> ? [C] : ? [D] : ? [E] : ( m1_subset_1(C,B) & m1_subset_1(D,B) & m1_subset_1(E,B) & A = k11_finseq_1(C,D,E) ) ) ) )).
fof(fraenkel_a_1_2_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_2_fomodel0(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k10_finseq_1(C,C) ) ) ) )).
fof(fraenkel_a_1_2_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ( r2_hidden(A,a_1_2_fomodel2(B)) <=> ? [C] : ( m2_subset_1(C,k3_finseq_2(k15_fomodel1(B)),k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0))) & A = C & v4_fomodel2(C,B) & v5_fomodel2(C,B) ) ) ) )).
fof(fraenkel_a_1_2_goboard6,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_2_goboard6(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & ~ r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,1)),D) ) ) ) )).
fof(fraenkel_a_1_2_goboard9,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_2_goboard9(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & ~ r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,1)),C) ) ) ) )).
fof(fraenkel_a_1_2_gobrd11,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_2_gobrd11(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & ~ r1_xxreal_0(D,B) ) ) ) )).
fof(fraenkel_a_1_2_gobrd13,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_2_gobrd13(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & r1_xxreal_0(C,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,1))) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,k1_matrix_0(B))),D) ) ) ) )).
fof(fraenkel_a_1_2_graph_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v6_graph_1(B) & l1_graph_1(B) ) => ( r2_hidden(A,a_1_2_graph_5(B)) <=> ? [C] : ( m2_finseq_2(C,u4_struct_0(B),k3_finseq_2(u4_struct_0(B))) & A = C & r1_xxreal_0(k3_finseq_1(C),k7_graph_1(B)) ) ) ) )).
fof(fraenkel_a_1_2_integra1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v5_valued_0(B) & m2_finseq_1(B,k1_numbers) ) => ( r2_hidden(A,a_1_2_integra1(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & r1_xxreal_0(k1_funct_1(B,1),C) & r1_xxreal_0(C,k1_funct_1(B,k3_finseq_1(B))) ) ) ) )).
fof(fraenkel_a_1_2_jgraph_6,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_2_jgraph_6(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & ~ r1_xxreal_0(k12_euclid(C),B) ) ) ) )).
fof(fraenkel_a_1_2_jordan1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_2_jordan1(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & ~ r1_xxreal_0(D,B) ) ) ) )).
fof(fraenkel_a_1_2_jordan2b,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_2_jordan2b(B)) <=> ? [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) & A = C & k3_finseq_1(C) = B ) ) ) )).
fof(fraenkel_a_1_2_jordan2c,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_2_jordan2c(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) & A = C & r2_jordan2c(B,k1_struct_0(k15_euclid(B)),C) ) ) ) )).
fof(fraenkel_a_1_2_jordan5d,axiom,( ! [A] : ! [B] : ( ( ~ 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,a_1_2_jordan5d(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = k17_euclid(C) & k18_euclid(C) = k7_pscomp_1(k3_topreal1(2,B)) & r2_hidden(C,k3_topreal1(2,B)) ) ) ) )).
fof(fraenkel_a_1_2_jordan6,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_2_jordan6(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & k17_euclid(C) = B ) ) ) )).
fof(fraenkel_a_1_2_lang1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_lang1(B) ) => ( r2_hidden(A,a_1_2_lang1(B)) <=> ? [C] : ( m2_finseq_2(C,u1_struct_0(B),k3_finseq_2(u1_struct_0(B))) & A = C & r1_tarski(k2_relset_1(u1_struct_0(B),C),k1_lang1(B)) & r3_lang1(B,k3_pre_poly(u1_struct_0(B),u2_lang1(B)),C) ) ) ) )).
fof(fraenkel_a_1_2_lattice5,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_2_lattice5(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) & A = C & v1_partfun1(C,B) & v3_relat_2(C) & v8_relat_2(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) ) )).
fof(fraenkel_a_1_2_lattice6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) ) => ( r2_hidden(A,a_1_2_lattice6(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & r3_lattices(B,k6_lattices(B),C) & C != k6_lattices(B) ) ) ) )).
fof(fraenkel_a_1_2_limfunc4,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r2_hidden(A,a_1_2_limfunc4(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(k4_limfunc1(B),C) ) ) ) )).
fof(fraenkel_a_1_2_lopclset,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v7_struct_0(B) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B) ) => ( r2_hidden(A,a_1_2_lopclset(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(k7_lopclset(B)))) & A = k5_setfam_1(k7_lopclset(B),C) & r1_tarski(C,k10_lopclset(B)) ) ) ) )).
fof(fraenkel_a_1_2_ltlaxio4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ( r2_hidden(A,a_1_2_ltlaxio4(B)) <=> ? [C] : ( ~ v2_ltlaxio3(C) & m1_subset_1(C,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) & A = C & r1_ltlaxio4(B,C) ) ) ) )).
fof(fraenkel_a_1_2_member_1,axiom,( ! [A] : ! [B] : ( v2_membered(B) => ( r2_hidden(A,a_1_2_member_1(B)) <=> ? [C] : ( m1_subset_1(C,k6_numbers) & A = k2_member_1(C) & r2_hidden(C,B) ) ) ) )).
fof(fraenkel_a_1_2_metric_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_metric_1(B) ) => ( r2_hidden(A,a_1_2_metric_2(B)) <=> ? [C] : ( m1_subset_1(C,k2_metric_2(B)) & A = C & ? [D] : ( m1_subset_1(D,k2_metric_2(B)) & ? [E] : ( m1_subset_1(E,k1_numbers) & r4_metric_2(B,C,D,E) ) ) ) ) ) )).
fof(fraenkel_a_1_2_modal_1,axiom,( ! [A] : ! [B] : ( m2_trees_3(B,k2_trees_1(1),k1_relset_1(k2_trees_1(1),k8_funcop_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k2_trees_1(1),k1_domain_1(k4_ordinal1,k4_ordinal1,1,1)))) => ( r2_hidden(A,a_1_2_modal_1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k8_finseq_1(k4_ordinal1,B,k14_trees_3(C)) & r2_hidden(k8_finseq_1(k4_ordinal1,B,k14_trees_3(C)),k1_relset_1(k2_trees_1(1),k8_funcop_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k2_trees_1(1),k1_domain_1(k4_ordinal1,k4_ordinal1,1,1)))) ) ) ) )).
fof(fraenkel_a_1_2_modelc_3,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(B) & v5_modelc_3(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r2_hidden(A,a_1_2_modelc_3(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k23_modelc_3(B))) & A = C & ? [D] : ( v1_modelc_2(D) & m2_finseq_1(D,k4_ordinal1) & r2_modelc_2(D,B) & v7_modelc_2(D) & C = k32_modelc_3(B,D) ) ) ) ) )).
fof(fraenkel_a_1_2_moebius1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( r2_hidden(A,a_1_2_moebius1(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = C & ~ r1_xxreal_0(C,k5_numbers) & r1_nat_d(C,B) & ~ v1_moebius1(C) ) ) ) )).
fof(fraenkel_a_1_2_nat_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_2_nat_1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & ~ r1_xxreal_0(k1_nat_1(B,1),C) ) ) ) )).
fof(fraenkel_a_1_2_necklace,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(A,a_1_2_necklace(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_2_partit1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_2_partit1(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k1_tarski(C) ) ) ) )).
fof(fraenkel_a_1_2_polyred,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_2_polyred(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & r1_xxreal_0(1,C) & r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_2_scmfsa10,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_2_scmfsa10(B)) <=> ? [C] : ( m1_subset_1(C,u1_compos_1(k1_scmfsa_2)) & A = k7_subset_1(k4_ordinal1,k1_amistd_1(k7_card_1(3),k1_scmfsa_2,B,C),k2_amistd_1(k7_card_1(3),k1_scmfsa_2,C)) ) ) ) )).
fof(fraenkel_a_1_2_scmfsa_m,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_scmfsa_2)) ) => ( r2_hidden(A,a_1_2_scmfsa_m(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = C & ~ r2_hidden(k4_scmfsa_2(C),B) & C != k5_numbers ) ) ) )).
fof(fraenkel_a_1_2_scmpds_9,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmpds_2)) => ( r2_hidden(A,a_1_2_scmpds_9(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k1_amistd_1(2,k1_scmpds_2,C,B) ) ) ) )).
fof(fraenkel_a_1_2_sgraph1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(A,a_1_2_sgraph1(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) & A = k2_tarski(C,D) & r2_hidden(C,k2_finseq_1(B)) & r2_hidden(D,k2_finseq_1(B)) & C != D ) ) ) )).
fof(fraenkel_a_1_2_sprect_1,axiom,( ! [A] : ! [B] : ( ( ~ 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,a_1_2_sprect_1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & r1_xxreal_0(k17_euclid(C),k8_pscomp_1(B)) & r1_xxreal_0(k6_pscomp_1(B),k17_euclid(C)) & k18_euclid(C) = k7_pscomp_1(B) ) ) ) )).
fof(fraenkel_a_1_2_sprect_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & v1_topreal1(B) & v2_topreal1(B) & v1_goboard5(B) & v1_sprect_1(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_1_2_sprect_3(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & ~ r1_xxreal_0(k17_euclid(C),k6_pscomp_1(k3_topreal1(2,B))) & ~ r1_xxreal_0(k8_pscomp_1(k3_topreal1(2,B)),k17_euclid(C)) & ~ r1_xxreal_0(k18_euclid(C),k9_pscomp_1(k3_topreal1(2,B))) & ~ r1_xxreal_0(k7_pscomp_1(k3_topreal1(2,B)),k18_euclid(C)) ) ) ) )).
fof(fraenkel_a_1_2_stirl2_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_2_stirl2_1(B)) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k7_card_1(B),k7_card_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(B),k7_card_1(B)))) & A = C & v2_funct_2(C,k7_card_1(B)) & v1_stirl2_1(C,B,B) ) ) ) )).
fof(fraenkel_a_1_2_tdlat_1,axiom,( ! [A] : ! [B] : ( l1_pre_topc(B) => ( r2_hidden(A,a_1_2_tdlat_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v6_tops_1(C,B) ) ) ) )).
fof(fraenkel_a_1_2_tdlat_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_2_tdlat_2(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v6_tops_1(C,B) ) ) ) )).
fof(fraenkel_a_1_2_topgen_2,axiom,( ! [A] : ! [B] : ( ~ v1_finset_1(B) => ( r2_hidden(A,a_1_2_topgen_2(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) & A = k3_subset_1(B,C) & v1_finset_1(C) ) ) ) )).
fof(fraenkel_a_1_2_topreal1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,a_1_2_topreal1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & r1_xxreal_0(k17_euclid(B),k17_euclid(C)) & k18_euclid(C) = k18_euclid(B) ) ) ) )).
fof(fraenkel_a_1_2_topreal4,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,a_1_2_topreal4(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k2_topreal1(2,k17_finseq_1(u1_struct_0(k15_euclid(2)),2,B),C) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(k17_finseq_1(u1_struct_0(k15_euclid(2)),2,B))) ) ) ) )).
fof(fraenkel_a_1_2_treal_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k1_rcomp_1(k5_numbers,1),k1_rcomp_1(k5_numbers,1)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_rcomp_1(k5_numbers,1),k1_rcomp_1(k5_numbers,1)))) ) => ( r2_hidden(A,a_1_2_treal_1(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & r2_hidden(C,k1_rcomp_1(k5_numbers,1)) & r2_hidden(k1_funct_1(B,C),k1_rcomp_1(k5_numbers,C)) ) ) ) )).
fof(fraenkel_a_1_2_trees_9,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v3_trees_3(B) ) => ( r2_hidden(A,a_1_2_trees_9(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,B) & m1_trees_1(D,k9_xtuple_0(C)) & A = k5_trees_2(C,D) ) ) ) )).
fof(fraenkel_a_1_2_uniroots,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ( r2_hidden(A,a_1_2_uniroots(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k1_uniroots(k1_complfld))) & A = C & r1_nat_d(k6_group_1(k1_uniroots(k1_complfld),C),B) ) ) ) )).
fof(fraenkel_a_1_2_valued_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( r2_hidden(A,a_1_2_valued_1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(B)) ) ) ) )).
fof(fraenkel_a_1_2_waybel13,axiom,( ! [A] : ! [B] : ( ( 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) ) => ( r2_hidden(A,a_1_2_waybel13(B)) <=> ? [C] : ( ~ 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))) & A = C ) ) ) )).
fof(fraenkel_a_1_2_waybel16,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_1_2_waybel16(B)) <=> ? [C] : ( ~ v1_xboole_0(C) & v2_waybel_0(C,k7_lattice3(B)) & v13_waybel_0(C,k7_lattice3(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k7_lattice3(B)))) & A = C ) ) ) )).
fof(fraenkel_a_1_2_waybel19,axiom,( ! [A] : ! [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) & v2_waybel19(B) & l1_waybel_9(B) ) => ( r2_hidden(A,a_1_2_waybel19(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k3_subset_1(u1_struct_0(B),k6_waybel_0(B,C)) ) ) ) )).
fof(fraenkel_a_1_2_xxreal_1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_2_xxreal_1(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_2_yellow_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_1_2_yellow_2(B)) <=> ? [C] : ( ~ 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))) & A = C ) ) ) )).
fof(fraenkel_a_1_3_afproj,axiom,( ! [A] : ! [B] : ( ( ~ v7_struct_0(B) & v1_diraf(B) & l1_analoaf(B) ) => ( r2_hidden(A,a_1_3_afproj(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k1_domain_1(k1_zfmisc_1(u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)),C,D) & v1_aff_4(C,B) & v1_aff_4(D,B) & r1_aff_4(B,C,D) ) ) ) )).
fof(fraenkel_a_1_3_aofa_a00,axiom,( ! [A] : ! [B] : ( ( ~ 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) & l1_unialg_1(B) ) => ( r2_hidden(A,a_1_3_aofa_a00(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & A = k13_aofa_000(B,C,D) & C != k13_aofa_000(B,C,D) & D != k13_aofa_000(B,C,D) ) ) ) )).
fof(fraenkel_a_1_3_asympt_0,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_3_asympt_0(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = k1_newton(B,C) ) ) ) )).
fof(fraenkel_a_1_3_asympt_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(A,a_1_3_asympt_1(B)) <=> ? [C] : ( m2_funct_2(C,k4_ordinal1,k1_numbers,k9_funct_2(k4_ordinal1,k1_numbers)) & A = C & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & ? [F] : ( m1_subset_1(F,k4_ordinal1) & ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(E,k5_numbers) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( r1_xxreal_0(F,G) => ( r1_xxreal_0(k3_xcmplx_0(E,k9_nat_1(k1_numbers,B,G)),k9_nat_1(k1_numbers,C,G)) & r1_xxreal_0(k9_nat_1(k1_numbers,C,G),k3_xcmplx_0(D,k9_nat_1(k1_numbers,B,G))) ) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_1_3_coh_sp,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_3_coh_sp(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) & A = k14_coh_sp(C) ) ) )).
fof(fraenkel_a_1_3_decomp_1,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_3_decomp_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v4_decomp_1(C,B) ) ) ) )).
fof(fraenkel_a_1_3_ens_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & 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_hidden(A,a_1_3_ens_1(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & A = k2_cat_1(B,C,D) ) ) ) )).
fof(fraenkel_a_1_3_fcont_3,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_3_fcont_3(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_3_finance1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_3_finance1(B)) <=> ? [C] : ( m1_subset_1(C,k6_numbers) & A = C & r1_xxreal_0(B,C) & r1_xxreal_0(C,k1_xxreal_0) ) ) ) )).
fof(fraenkel_a_1_3_finseq_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_3_finseq_2(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k4_finseq_2(C,B) ) ) ) )).
fof(fraenkel_a_1_3_fomodel0,axiom,( ! [A] : ! [B] : ( v4_funct_1(B) => ( r2_hidden(A,a_1_3_fomodel0(B)) <=> ? [C] : ( m1_subset_1(C,k2_xboole_0(B,k1_tarski(k1_xboole_0))) & A = k10_xtuple_0(C) & r2_hidden(C,B) ) ) ) )).
fof(fraenkel_a_1_3_goboard6,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_3_goboard6(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & ~ r1_xxreal_0(D,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,k1_matrix_0(B)))) ) ) ) )).
fof(fraenkel_a_1_3_goboard9,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_3_goboard9(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & ~ r1_xxreal_0(C,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B),1))) ) ) ) )).
fof(fraenkel_a_1_3_gobrd11,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_3_gobrd11(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & r1_xxreal_0(B,D) ) ) ) )).
fof(fraenkel_a_1_3_gobrd13,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_3_gobrd13(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B),1)),C) & r1_xxreal_0(D,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,1))) ) ) ) )).
fof(fraenkel_a_1_3_jgraph_6,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_3_jgraph_6(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & r1_xxreal_0(k12_euclid(C),B) ) ) ) )).
fof(fraenkel_a_1_3_jordan1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_3_jordan1(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & ~ r1_xxreal_0(B,D) ) ) ) )).
fof(fraenkel_a_1_3_jordan10,axiom,( ! [A] : ! [B] : ( ( 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_hidden(A,a_1_3_jordan10(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k2_jordan2c(2,k3_topreal1(2,k2_jordan9(B,C))) ) ) ) )).
fof(fraenkel_a_1_3_jordan11,axiom,( ! [A] : ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_3_jordan11(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & A = C & r1_jordan2c(2,B,C) ) ) ) )).
fof(fraenkel_a_1_3_jordan5d,axiom,( ! [A] : ! [B] : ( ( ~ 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,a_1_3_jordan5d(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = k17_euclid(C) & k18_euclid(C) = k9_pscomp_1(k3_topreal1(2,B)) & r2_hidden(C,k3_topreal1(2,B)) ) ) ) )).
fof(fraenkel_a_1_3_jordan6,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_3_jordan6(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & r1_xxreal_0(B,k18_euclid(C)) ) ) ) )).
fof(fraenkel_a_1_3_lang1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_3_lang1(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k4_tarski(B,k10_finseq_1(C,B)) & C = C ) ) ) )).
fof(fraenkel_a_1_3_lattice3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ( r2_hidden(A,a_1_3_lattice3(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,u1_struct_0(k1_lattice2(B))) & m1_subset_1(D,u1_struct_0(k1_lattice2(B))) & A = k9_filter_1(k1_lattice2(B),k1_lattice2(B),C,D) & r3_lattices(k1_lattice2(B),C,D) ) ) ) )).
fof(fraenkel_a_1_3_limfunc4,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r2_hidden(A,a_1_3_limfunc4(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(C,k4_limfunc1(B)) ) ) ) )).
fof(fraenkel_a_1_3_ltlaxio4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)))) => ( r2_hidden(A,a_1_3_ltlaxio4(B)) <=> ? [C] : ( m1_subset_1(C,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) & A = k5_ltlaxio4(C) & r2_hidden(C,B) ) ) ) )).
fof(fraenkel_a_1_3_measure6,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( r2_hidden(A,a_1_3_measure6(B)) <=> ? [C] : ( v1_xcmplx_0(C) & A = k4_xcmplx_0(C) & r2_hidden(C,B) ) ) ) )).
fof(fraenkel_a_1_3_member_1,axiom,( ! [A] : ! [B] : ( v1_membered(B) => ( r2_hidden(A,a_1_3_member_1(B)) <=> ? [C] : ( v1_xcmplx_0(C) & A = k5_xcmplx_0(C) & r2_hidden(C,B) ) ) ) )).
fof(fraenkel_a_1_3_metric_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_metric_1(B) ) => ( r2_hidden(A,a_1_3_metric_2(B)) <=> ? [C] : ( m1_subset_1(C,k2_metric_2(B)) & A = C & ? [D] : ( m1_subset_1(D,k2_metric_2(B)) & ? [E] : ( m1_subset_1(E,k1_numbers) & r4_metric_2(B,D,C,E) ) ) ) ) ) )).
fof(fraenkel_a_1_3_modal_1,axiom,( ! [A] : ! [B] : ( m2_trees_3(B,k2_trees_1(2),k1_relset_1(k2_trees_1(2),k8_funcop_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k2_trees_1(2),k1_domain_1(k4_ordinal1,k4_ordinal1,2,k5_numbers)))) => ( r2_hidden(A,a_1_3_modal_1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k8_finseq_1(k4_ordinal1,B,k14_trees_3(C)) & r2_hidden(k8_finseq_1(k4_ordinal1,B,k14_trees_3(C)),k1_relset_1(k2_trees_1(2),k8_funcop_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k2_trees_1(2),k1_domain_1(k4_ordinal1,k4_ordinal1,2,k5_numbers)))) ) ) ) )).
fof(fraenkel_a_1_3_modelc_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( r2_hidden(A,a_1_3_modelc_3(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(B)) ) ) ) )).
fof(fraenkel_a_1_3_moebius1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( r2_hidden(A,a_1_3_moebius1(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = C & ~ r1_xxreal_0(C,k5_numbers) & r1_nat_d(C,k6_moebius1(B)) ) ) ) )).
fof(fraenkel_a_1_3_nat_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_3_nat_1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_3_pua2mss1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_3_pua2mss1(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k1_tarski(C) ) ) ) )).
fof(fraenkel_a_1_3_scmyciel,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_3_scmyciel(B)) <=> ? [C] : ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(B)) & A = C & r1_xxreal_0(k5_card_1(C),2) ) ) )).
fof(fraenkel_a_1_3_sprect_1,axiom,( ! [A] : ! [B] : ( ( ~ 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,a_1_3_sprect_1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & k17_euclid(C) = k6_pscomp_1(B) & r1_xxreal_0(k18_euclid(C),k7_pscomp_1(B)) & r1_xxreal_0(k9_pscomp_1(B),k18_euclid(C)) ) ) ) )).
fof(fraenkel_a_1_3_sprect_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & v1_topreal1(B) & v2_topreal1(B) & v1_goboard5(B) & v1_sprect_1(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_1_3_sprect_3(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & k17_euclid(C) = k8_pscomp_1(k3_topreal1(2,B)) & r1_xxreal_0(k18_euclid(C),k7_pscomp_1(k3_topreal1(2,B))) & r1_xxreal_0(k9_pscomp_1(k3_topreal1(2,B)),k18_euclid(C)) ) ) ) )).
fof(fraenkel_a_1_3_stirl2_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_3_stirl2_1(B)) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k7_card_1(k5_numbers),k7_card_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(k5_numbers),k7_card_1(B)))) & A = C & v2_funct_2(C,k7_card_1(B)) & v1_stirl2_1(C,k5_numbers,B) ) ) ) )).
fof(fraenkel_a_1_3_tdlat_1,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_3_tdlat_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v4_tops_1(C,B) ) ) ) )).
fof(fraenkel_a_1_3_topgen_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_3_topgen_2(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k3_subset_1(B,k6_domain_1(B,C)) ) ) ) )).
fof(fraenkel_a_1_3_treal_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k1_rcomp_1(k5_numbers,1),k1_rcomp_1(k5_numbers,1)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_rcomp_1(k5_numbers,1),k1_rcomp_1(k5_numbers,1)))) ) => ( r2_hidden(A,a_1_3_treal_1(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & r2_hidden(C,k1_rcomp_1(k5_numbers,1)) & r2_hidden(k1_funct_1(B,C),k1_rcomp_1(C,1)) ) ) ) )).
fof(fraenkel_a_1_3_trees_9,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v3_trees_3(B) ) => ( r2_hidden(A,a_1_3_trees_9(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k3_trees_9(C) ) ) ) )).
fof(fraenkel_a_1_3_uniroots,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( r2_hidden(A,a_1_3_uniroots(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k1_uniroots(k1_complfld))) & A = C & k6_group_1(k1_uniroots(k1_complfld),C) = B ) ) ) )).
fof(fraenkel_a_1_3_valued_1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ( r2_hidden(A,a_1_3_valued_1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(B)) ) ) ) )).
fof(fraenkel_a_1_3_waybel11,axiom,( ! [A] : ! [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) ) => ( r2_hidden(A,a_1_3_waybel11(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r2_hidden(D,C) => ! [E] : ( ( ~ v2_struct_0(E) & v4_orders_2(E) & v7_waybel_0(E) & l1_waybel_0(E,B) ) => ( r2_hidden(k4_tarski(E,D),k2_waybel11(B)) => r1_waybel_0(B,E,C) ) ) ) ) ) ) ) )).
fof(fraenkel_a_1_3_waybel16,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_1_3_waybel16(B)) <=> ? [C] : ( ~ 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))) & A = C ) ) ) )).
fof(fraenkel_a_1_3_waybel19,axiom,( ! [A] : ! [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) & v2_waybel19(B) & l1_waybel_9(B) ) => ( r2_hidden(A,a_1_3_waybel19(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) & A = k7_subset_1(u1_struct_0(B),C,k6_waybel_0(B,D)) & r2_hidden(C,k5_waybel11(B)) ) ) ) )).
fof(fraenkel_a_1_3_waybel21,axiom,( ! [A] : ! [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) & v2_waybel19(B) & l1_waybel_9(B) ) => ( r2_hidden(A,a_1_3_waybel21(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k3_subset_1(u1_struct_0(B),k6_waybel_0(B,C)) ) ) ) )).
fof(fraenkel_a_1_3_waybel27,axiom,( ! [A] : ! [B] : ( ( 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) ) => ( r2_hidden(A,a_1_3_waybel27(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(o_1_2_waybel27(B))) & A = k6_waybel_0(o_1_2_waybel27(B),C) & r2_hidden(C,u1_struct_0(k1_waybel_8(o_1_2_waybel27(B)))) ) ) ) )).
fof(fraenkel_a_1_3_waybel32,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & v1_waybel32(B) & l1_waybel_9(B) ) => ( r2_hidden(A,a_1_3_waybel32(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k3_subset_1(u1_struct_0(B),k5_waybel_0(B,C)) ) ) ) )).
fof(fraenkel_a_1_3_xxreal_1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_3_xxreal_1(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_3_yellow_2,axiom,( ! [A] : ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_1_3_yellow_2(B)) <=> ? [C] : ( ~ 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))) & A = C ) ) ) )).
fof(fraenkel_a_1_4_abcmiz_a,axiom,( ! [A] : ! [B] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & v1_abcmiz_a(B) & l1_msualg_1(B) ) => ( r2_hidden(A,a_1_4_abcmiz_a(B)) <=> ? [C] : ( m1_dtconstr(C,u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))),k5_trees_3(u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers)))))),k1_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))) & A = C & k7_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),C) = k13_abcmiz_1(B) & r2_pboole(u1_struct_0(B),k4_msafree3(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),C),k28_abcmiz_1(B)) ) ) ) )).
fof(fraenkel_a_1_4_asympt_0,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(A,a_1_4_asympt_0(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = k11_newton(B,C) ) ) ) )).
fof(fraenkel_a_1_4_bintree1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v1_dtconstr(B) & v2_dtconstr(B) & v3_bintree1(B) & l1_lang1(B) ) => ( r2_hidden(A,a_1_4_bintree1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) & r1_lang1(B,C,D) ) ) ) ) )).
fof(fraenkel_a_1_4_card_fin,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ( r2_hidden(A,a_1_4_card_fin(B)) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,B,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) & A = C & v2_funct_1(C) & ! [D] : ~ ( r2_hidden(D,B) & k1_funct_1(C,D) = k1_funct_1(k6_partfun1(B),D) ) ) ) ) )).
fof(fraenkel_a_1_4_catalan2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k3_catalan2(k4_ordinal1)) => ( r2_hidden(A,a_1_4_catalan2(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & k3_xcmplx_0(2,k7_afinsq_2(k5_relat_1(B,C))) = C & ~ r1_xxreal_0(C,k5_numbers) ) ) ) )).
fof(fraenkel_a_1_4_coh_sp,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_4_coh_sp(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,k15_coh_sp(B)) & m1_subset_1(D,k1_zfmisc_1(B)) & A = k4_tarski(C,D) & v1_partfun1(C,D) & v1_relat_2(C) & v3_relat_2(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(D,D))) ) ) )).
fof(fraenkel_a_1_4_decomp_1,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_4_decomp_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v3_decomp_1(C,B) ) ) ) )).
fof(fraenkel_a_1_4_dtconstr,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_lang1(B) ) => ( r2_hidden(A,a_1_4_dtconstr(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ~ r1_lang1(B,C,D) ) ) ) ) )).
fof(fraenkel_a_1_4_finance1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_4_finance1(B)) <=> ? [C] : ( m1_subset_1(C,k6_numbers) & A = C & r1_xxreal_0(k2_xxreal_0,C) & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_4_fomodel0,axiom,( ! [A] : ! [B] : ( v4_funct_1(B) => ( r2_hidden(A,a_1_4_fomodel0(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k10_xtuple_0(C) & r2_hidden(C,B) ) ) ) )).
fof(fraenkel_a_1_4_goboard6,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_4_goboard6(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & ~ r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,1)),C) & ~ r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,1)),D) ) ) ) )).
fof(fraenkel_a_1_4_gobrd11,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_4_gobrd11(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & ~ r1_xxreal_0(B,D) ) ) ) )).
fof(fraenkel_a_1_4_jgraph_6,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_4_jgraph_6(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & r1_xxreal_0(B,k12_euclid(C)) ) ) ) )).
fof(fraenkel_a_1_4_jordan10,axiom,( ! [A] : ! [B] : ( ( 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_hidden(A,a_1_4_jordan10(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & A = C & r1_jordan2c(2,B,C) ) ) ) )).
fof(fraenkel_a_1_4_jordan5d,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,a_1_4_jordan5d(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = k17_euclid(C) & r2_hidden(C,k3_topreal1(2,B)) ) ) ) )).
fof(fraenkel_a_1_4_jordan6,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_4_jordan6(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & r1_xxreal_0(k18_euclid(C),B) ) ) ) )).
fof(fraenkel_a_1_4_lattice6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) ) => ( r2_hidden(A,a_1_4_lattice6(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & r3_lattices(B,C,k5_lattices(B)) & C != k5_lattices(B) ) ) ) )).
fof(fraenkel_a_1_4_limfunc4,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r2_hidden(A,a_1_4_limfunc4(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(k5_limfunc1(B),C) ) ) ) )).
fof(fraenkel_a_1_4_ltlaxio4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_hilbert1)) => ( r2_hidden(A,a_1_4_ltlaxio4(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,k1_hilbert1) & m1_subset_1(D,k1_hilbert1) & A = k1_ltlaxio2(C,D) & r2_hidden(k4_hilbert1(C,D),B) ) ) ) )).
fof(fraenkel_a_1_4_metric_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_metric_1(B) ) => ( r2_hidden(A,a_1_4_metric_2(B)) <=> ? [C] : ( m1_subset_1(C,k2_zfmisc_1(k2_metric_2(B),k2_metric_2(B))) & A = C & ? [D] : ( m1_subset_1(D,k2_metric_2(B)) & ? [E] : ( m1_subset_1(E,k2_metric_2(B)) & ? [F] : ( m1_subset_1(F,k1_numbers) & C = k1_domain_1(k2_metric_2(B),k2_metric_2(B),D,E) & r4_metric_2(B,D,E,F) ) ) ) ) ) ) )).
fof(fraenkel_a_1_4_scmpds_9,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(A,a_1_4_scmpds_9(B)) <=> ? [C] : ( m1_subset_1(C,u1_compos_1(k1_scmpds_2)) & A = k7_subset_1(k4_ordinal1,k1_amistd_1(2,k1_scmpds_2,B,C),k2_amistd_1(2,k1_scmpds_2,C)) ) ) ) )).
fof(fraenkel_a_1_4_scmyciel,axiom,( ! [A] : ! [B] : ( v4_scmyciel(B) => ( r2_hidden(A,a_1_4_scmyciel(B)) <=> ? [C] : ( m1_subset_1(C,k2_xboole_0(k2_xboole_0(k3_tarski(B),k2_zfmisc_1(k3_tarski(B),k1_tarski(k3_tarski(B)))),k1_tarski(k3_tarski(B)))) & A = k1_tarski(C) ) ) ) )).
fof(fraenkel_a_1_4_sprect_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v2_compts_1(B,k15_euclid(2)) & ~ v2_sppol_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_4_sprect_1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & k17_euclid(C) = k8_pscomp_1(B) & r1_xxreal_0(k18_euclid(C),k7_pscomp_1(B)) & r1_xxreal_0(k9_pscomp_1(B),k18_euclid(C)) ) ) ) )).
fof(fraenkel_a_1_4_sprect_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & v1_topreal1(B) & v2_topreal1(B) & v1_goboard5(B) & v1_sprect_1(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_1_4_sprect_3(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & r1_xxreal_0(k17_euclid(C),k8_pscomp_1(k3_topreal1(2,B))) & r1_xxreal_0(k6_pscomp_1(k3_topreal1(2,B)),k17_euclid(C)) & k18_euclid(C) = k9_pscomp_1(k3_topreal1(2,B)) ) ) ) )).
fof(fraenkel_a_1_4_stirl2_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_4_stirl2_1(B)) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k7_card_1(B),k7_card_1(k5_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(B),k7_card_1(k5_numbers)))) & A = C & v2_funct_2(C,k7_card_1(k5_numbers)) & v1_stirl2_1(C,B,k5_numbers) ) ) ) )).
fof(fraenkel_a_1_4_tdlat_1,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_4_tdlat_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v5_tops_1(C,B) ) ) ) )).
fof(fraenkel_a_1_4_topgen_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_4_topgen_2(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k1_topgen_2(B,C) ) ) ) )).
fof(fraenkel_a_1_4_topreal1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,a_1_4_topreal1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & k17_euclid(C) = k17_euclid(B) & r1_xxreal_0(k18_euclid(C),k18_euclid(B)) ) ) ) )).
fof(fraenkel_a_1_4_treal_1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_4_treal_1(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & r1_xxreal_0(B,C) & r1_xxreal_0(C,1) ) ) ) )).
fof(fraenkel_a_1_4_trees_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_4_trees_1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k9_finseq_1(C) & ~ r1_xxreal_0(k1_nat_1(B,1),C) ) ) ) )).
fof(fraenkel_a_1_4_waybel19,axiom,( ! [A] : ! [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) & v2_waybel19(B) & l1_waybel_9(B) ) => ( r2_hidden(A,a_1_4_waybel19(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k7_subset_1(u1_struct_0(B),C,k4_waybel_0(B,D)) & r2_hidden(C,k5_waybel11(B)) & v1_finset_1(D) ) ) ) )).
fof(fraenkel_a_1_4_waybel31,axiom,( ! [A] : ! [B] : ( ( 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) ) => ( r2_hidden(A,a_1_4_waybel31(B)) <=> ? [C] : ( v6_waybel23(C,B) & m1_waybel23(C,B) & A = k1_card_1(C) ) ) ) )).
fof(fraenkel_a_1_4_yellow_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_1_4_yellow_2(B)) <=> ? [C] : ( ~ 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))) & A = C ) ) ) )).
fof(fraenkel_a_1_5_abcmiz_a,axiom,( ! [A] : ! [B] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & v1_abcmiz_a(B) & l1_msualg_1(B) ) => ( r2_hidden(A,a_1_5_abcmiz_a(B)) <=> ? [C] : ( m1_dtconstr(C,u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))),k5_trees_3(u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers)))))),k1_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))) & A = C & k7_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),C) = k12_abcmiz_1(B) & r2_pboole(u1_struct_0(B),k4_msafree3(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),C),k28_abcmiz_1(B)) ) ) ) )).
fof(fraenkel_a_1_5_cat_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ 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) ) => ( r2_hidden(A,a_1_5_cat_5(B)) <=> ? [C] : ( m1_subset_1(C,u4_struct_0(B)) & A = k8_cat_5(B,C) ) ) ) )).
fof(fraenkel_a_1_5_catalan2,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_5_catalan2(B)) <=> ? [C] : ( m1_subset_1(C,k3_catalan2(k4_ordinal1)) & A = C & r2_hidden(C,k2_catalan2(k3_xcmplx_0(2,B),B)) & a_1_4_catalan2(C) != k1_xboole_0 ) ) ) )).
fof(fraenkel_a_1_5_coh_sp,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_5_coh_sp(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,k16_coh_sp(B)) & m1_subset_1(D,k16_coh_sp(B)) & A = k1_funct_2(k17_coh_sp(B,C),k17_coh_sp(B,D)) ) ) )).
fof(fraenkel_a_1_5_comput_1,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_5_comput_1(B)) <=> ? [C] : ( m2_finseq_2(C,B,k3_finseq_2(B)) & A = C & k3_finseq_1(C) = k5_numbers ) ) )).
fof(fraenkel_a_1_5_decomp_1,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_5_decomp_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & k1_tops_1(B,C) = k3_decomp_1(B,C) ) ) ) )).
fof(fraenkel_a_1_5_dtconstr,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_lang1(B) ) => ( r2_hidden(A,a_1_5_dtconstr(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = C & ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) & r1_lang1(B,C,D) ) ) ) ) )).
fof(fraenkel_a_1_5_goboard6,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_5_goboard6(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & ~ r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,1)),C) & ~ r1_xxreal_0(D,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,k1_matrix_0(B)))) ) ) ) )).
fof(fraenkel_a_1_5_gobrd11,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_5_gobrd11(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_5_jordan2c,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) => ( r2_hidden(A,a_1_5_jordan2c(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & A = C & r2_jordan2c(2,k3_topreal1(2,k1_sprect_1(B)),C) ) ) ) )).
fof(fraenkel_a_1_5_jordan5d,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,a_1_5_jordan5d(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = k18_euclid(C) & r2_hidden(C,k3_topreal1(2,B)) ) ) ) )).
fof(fraenkel_a_1_5_jordan6,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_5_jordan6(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & k18_euclid(C) = B ) ) ) )).
fof(fraenkel_a_1_5_limfunc4,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r2_hidden(A,a_1_5_limfunc4(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & ~ r1_xxreal_0(C,k5_limfunc1(B)) ) ) ) )).
fof(fraenkel_a_1_5_ltlaxio4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ( r2_hidden(A,a_1_5_ltlaxio4(B)) <=> ? [C] : ( m1_subset_1(C,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) & A = C & k2_relset_1(k1_hilbert1,k8_ltlaxio3(C)) = k7_ltlaxio4(k2_relset_1(k1_hilbert1,k8_ltlaxio3(B))) & k2_relset_1(k1_hilbert1,k9_ltlaxio3(C)) = k7_ltlaxio4(k2_relset_1(k1_hilbert1,k9_ltlaxio3(B))) ) ) ) )).
fof(fraenkel_a_1_5_metric_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_metric_1(B) ) => ( r2_hidden(A,a_1_5_metric_2(B)) <=> ? [C] : ( m1_subset_1(C,k3_zfmisc_1(k2_metric_2(B),k2_metric_2(B),k1_numbers)) & A = C & ? [D] : ( m1_subset_1(D,k2_metric_2(B)) & ? [E] : ( m1_subset_1(E,k2_metric_2(B)) & ? [F] : ( m1_subset_1(F,k1_numbers) & C = k4_domain_1(k2_metric_2(B),k2_metric_2(B),k1_numbers,D,E,F) & r4_metric_2(B,D,E,F) ) ) ) ) ) ) )).
fof(fraenkel_a_1_5_scmyciel,axiom,( ! [A] : ! [B] : ( v4_scmyciel(B) => ( r2_hidden(A,a_1_5_scmyciel(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,k3_tarski(B)) & m1_subset_1(D,k3_tarski(B)) & A = k2_tarski(C,k4_tarski(D,k3_tarski(B))) & r2_hidden(k2_tarski(C,D),k1_scmyciel(B)) ) ) ) )).
fof(fraenkel_a_1_5_sprect_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v2_compts_1(B,k15_euclid(2)) & ~ v2_sppol_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_5_sprect_1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & k17_euclid(C) = k6_pscomp_1(B) & r1_xxreal_0(k18_euclid(C),k7_pscomp_1(B)) & r1_xxreal_0(k9_pscomp_1(B),k18_euclid(C)) ) ) ) )).
fof(fraenkel_a_1_5_sprect_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & v1_topreal1(B) & v2_topreal1(B) & v1_goboard5(B) & v1_sprect_1(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_1_5_sprect_3(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & r1_xxreal_0(k17_euclid(C),k8_pscomp_1(k3_topreal1(2,B))) & r1_xxreal_0(k6_pscomp_1(k3_topreal1(2,B)),k17_euclid(C)) & k18_euclid(C) = k7_pscomp_1(k3_topreal1(2,B)) ) ) ) )).
fof(fraenkel_a_1_5_stirl2_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_5_stirl2_1(B)) <=> ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k7_card_1(B),k7_card_1(1)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(B),k7_card_1(1)))) & A = C & v2_funct_2(C,k7_card_1(1)) & v1_stirl2_1(C,B,1) ) ) ) )).
fof(fraenkel_a_1_5_tdlat_1,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_5_tdlat_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v6_tops_1(C,B) ) ) ) )).
fof(fraenkel_a_1_5_tdlat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v4_tdlat_3(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_5_tdlat_3(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v4_tops_1(C,B) ) ) ) )).
fof(fraenkel_a_1_5_treal_1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_5_treal_1(B)) <=> ? [C] : ( v1_xreal_0(C) & A = C & r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_5_trees_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v4_trees_3(B) ) => ( r2_hidden(A,a_1_5_trees_3(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k9_finseq_1(C) & ~ r1_xxreal_0(k3_finseq_1(B),C) ) ) ) )).
fof(fraenkel_a_1_5_waybel16,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_5_waybel16(B)) <=> ? [C] : ( ~ v1_xboole_0(C) & v2_waybel_0(C,k2_yellow_1(B)) & v13_waybel_0(C,k2_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(B)))) & A = C ) ) )).
fof(fraenkel_a_1_5_waybel19,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_1_5_waybel19(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k3_subset_1(u1_struct_0(B),k6_waybel_0(B,C)) ) ) ) )).
fof(fraenkel_a_1_5_waybel29,axiom,( ! [A] : ! [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) ) => ( r2_hidden(A,a_1_5_waybel29(B)) <=> ? [C] : ? [D] : ( v3_pre_topc(C,o_1_4_waybel29(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(o_1_4_waybel29(B)))) & m1_subset_1(D,u1_struct_0(o_1_4_waybel29(B))) & A = k4_tarski(C,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_1_5_waybel30,axiom,( ! [A] : ! [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) & v2_waybel19(B) & l1_waybel_9(B) ) => ( r2_hidden(A,a_1_5_waybel30(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k7_subset_1(u1_struct_0(B),C,k4_waybel_0(B,D)) & r2_hidden(C,k5_waybel11(B)) & v1_finset_1(D) ) ) ) )).
fof(fraenkel_a_1_5_waybel33,axiom,( ! [A] : ! [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) ) => ( r2_hidden(A,a_1_5_waybel33(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(o_1_3_waybel33(B))) & A = k3_subset_1(u1_struct_0(o_1_3_waybel33(B)),k6_waybel_0(o_1_3_waybel33(B),C)) ) ) ) )).
fof(fraenkel_a_1_6_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & l1_msualg_1(B) ) => ( r2_hidden(A,a_1_6_abcmiz_1(B)) <=> ? [C] : ( m1_dtconstr(C,u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))),k5_trees_3(u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers)))))),k1_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))) & A = C & k7_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),C) = k14_abcmiz_1(B) & r2_pboole(u1_struct_0(B),k4_msafree3(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),C),k28_abcmiz_1(B)) ) ) ) )).
fof(fraenkel_a_1_6_card_3,axiom,( ! [A] : ! [B] : ( ( v4_funct_1(B) & v2_card_3(B) ) => ( r2_hidden(A,a_1_6_card_3(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k9_xtuple_0(C) ) ) ) )).
fof(fraenkel_a_1_6_catalg_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_6_catalg_1(B)) <=> ? [C] : ( m2_finseq_2(C,B,k3_finseq_2(B)) & A = C & k3_finseq_1(C) = 2 ) ) ) )).
fof(fraenkel_a_1_6_coh_sp,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_6_coh_sp(B)) <=> ? [C] : ? [D] : ? [E] : ( m1_subset_1(C,k16_coh_sp(B)) & m1_subset_1(D,k16_coh_sp(B)) & m1_subset_1(E,k19_coh_sp(B)) & A = k4_tarski(k4_tarski(C,D),E) & ( k17_coh_sp(B,D) = k1_xboole_0 => k17_coh_sp(B,C) = k1_xboole_0 ) & v1_funct_1(E) & v1_funct_2(E,k17_coh_sp(B,C),k17_coh_sp(B,D)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k17_coh_sp(B,C),k17_coh_sp(B,D)))) & ! [F] : ! [G] : ( r2_hidden(k4_tarski(F,G),k18_coh_sp(B,C)) => r2_hidden(k4_tarski(k1_funct_1(E,F),k1_funct_1(E,G)),k18_coh_sp(B,D)) ) ) ) )).
fof(fraenkel_a_1_6_decomp_1,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_6_decomp_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & k1_tops_1(B,C) = k2_decomp_1(B,C) ) ) ) )).
fof(fraenkel_a_1_6_finseq_3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_6_finseq_3(B)) <=> ? [C] : ? [D] : ( m1_subset_1(C,B) & m1_subset_1(D,B) & A = k10_finseq_1(C,D) ) ) ) )).
fof(fraenkel_a_1_6_fomodel0,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_6_fomodel0(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = C ) ) )).
fof(fraenkel_a_1_6_goboard6,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_6_goboard6(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & ~ r1_xxreal_0(C,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B),1))) & ~ r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,1)),D) ) ) ) )).
fof(fraenkel_a_1_6_gobrd11,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_6_gobrd11(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_6_gobrd14,axiom,( ! [A] : ! [B] : ( ( ~ 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,a_1_6_gobrd14(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & ~ r1_xxreal_0(k17_euclid(C),k6_pscomp_1(k3_topreal1(2,k1_sprect_1(k3_topreal1(2,B))))) & ~ r1_xxreal_0(k8_pscomp_1(k3_topreal1(2,k1_sprect_1(k3_topreal1(2,B)))),k17_euclid(C)) & ~ r1_xxreal_0(k18_euclid(C),k9_pscomp_1(k3_topreal1(2,k1_sprect_1(k3_topreal1(2,B))))) & ~ r1_xxreal_0(k7_pscomp_1(k3_topreal1(2,k1_sprect_1(k3_topreal1(2,B)))),k18_euclid(C)) ) ) ) )).
fof(fraenkel_a_1_6_jordan2c,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_6_jordan2c(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & ~ r1_xxreal_0(B,k12_euclid(C)) ) ) ) )).
fof(fraenkel_a_1_6_jordan5d,axiom,( ! [A] : ! [B] : ( ( ~ 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,a_1_6_jordan5d(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = k17_euclid(C) & r2_hidden(C,k3_topreal1(2,B)) ) ) ) )).
fof(fraenkel_a_1_6_jordan6,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_6_jordan6(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & ~ r1_xxreal_0(B,k17_euclid(C)) ) ) ) )).
fof(fraenkel_a_1_6_ltlaxio4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ( r2_hidden(A,a_1_6_ltlaxio4(B)) <=> ? [C] : ( m1_subset_1(C,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) & A = C & r2_hidden(C,k6_ltlaxio4(k8_ltlaxio4(B))) ) ) ) )).
fof(fraenkel_a_1_6_nat_4,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ( r2_hidden(A,a_1_6_nat_4(B)) <=> ? [C] : ( v1_int_2(C) & m1_subset_1(C,k4_ordinal1) & A = C & r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_6_pua2mss1,axiom,( ! [A] : ! [B] : ( ( v2_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ( r2_hidden(A,a_1_6_pua2mss1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k1_tarski(C) ) ) ) )).
fof(fraenkel_a_1_6_scmyciel,axiom,( ! [A] : ! [B] : ( v4_scmyciel(B) => ( r2_hidden(A,a_1_6_scmyciel(B)) <=> ? [C] : ( m1_subset_1(C,k3_tarski(B)) & A = k2_tarski(k3_tarski(B),k4_tarski(C,k3_tarski(B))) & r2_hidden(C,k3_tarski(B)) ) ) ) )).
fof(fraenkel_a_1_6_sprect_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v2_compts_1(B,k15_euclid(2)) & ~ v1_sppol_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_6_sprect_1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & r1_xxreal_0(k17_euclid(C),k8_pscomp_1(B)) & r1_xxreal_0(k6_pscomp_1(B),k17_euclid(C)) & k18_euclid(C) = k7_pscomp_1(B) ) ) ) )).
fof(fraenkel_a_1_6_sprect_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & v1_topreal1(B) & v2_topreal1(B) & v1_goboard5(B) & v1_sprect_1(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_1_6_sprect_3(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & k17_euclid(C) = k6_pscomp_1(k3_topreal1(2,B)) & r1_xxreal_0(k18_euclid(C),k7_pscomp_1(k3_topreal1(2,B))) & r1_xxreal_0(k9_pscomp_1(k3_topreal1(2,B)),k18_euclid(C)) ) ) ) )).
fof(fraenkel_a_1_6_tdlat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v4_tdlat_3(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_6_tdlat_3(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v5_tops_1(C,B) ) ) ) )).
fof(fraenkel_a_1_6_topgen_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_6_topgen_2(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k6_domain_1(B,C) ) ) ) )).
fof(fraenkel_a_1_6_topreal1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,a_1_6_topreal1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & r1_xxreal_0(k17_euclid(C),k17_euclid(B)) & k18_euclid(C) = k18_euclid(B) ) ) ) )).
fof(fraenkel_a_1_6_trees_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(A,a_1_6_trees_3(B)) <=> ? [C] : ( v7_ordinal1(C) & A = k9_finseq_1(C) & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(fraenkel_a_1_7_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & l1_msualg_1(B) ) => ( r2_hidden(A,a_1_7_abcmiz_1(B)) <=> ? [C] : ( m1_dtconstr(C,u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))),k5_trees_3(u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers)))))),k1_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))) & A = C & k7_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),C) = k13_abcmiz_1(B) & r2_pboole(u1_struct_0(B),k4_msafree3(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),C),k28_abcmiz_1(B)) ) ) ) )).
fof(fraenkel_a_1_7_cat_5,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v2_cat_5(B) ) => ( r2_hidden(A,a_1_7_cat_5(B)) <=> ? [C] : ? [D] : ( m1_cat_5(C,B) & m1_cat_5(D,B) & A = k4_cat_2(C,D) ) ) ) )).
fof(fraenkel_a_1_7_cohsp_1,axiom,( ! [A] : ! [B] : ( r2_hidden(A,a_1_7_cohsp_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) & A = C & v1_finset_1(C) ) ) )).
fof(fraenkel_a_1_7_decomp_1,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_7_decomp_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & k1_tops_1(B,C) = k1_decomp_1(B,C) ) ) ) )).
fof(fraenkel_a_1_7_finseq_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_7_finseq_1(B)) <=> ? [C] : ( v7_ordinal1(C) & A = C & ~ r1_xxreal_0(k1_nat_1(B,1),C) ) ) ) )).
fof(fraenkel_a_1_7_finseq_3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_7_finseq_3(B)) <=> ? [C] : ? [D] : ? [E] : ( m1_subset_1(C,B) & m1_subset_1(D,B) & m1_subset_1(E,B) & A = k11_finseq_1(C,D,E) ) ) ) )).
fof(fraenkel_a_1_7_goboard6,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_7_goboard6(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & ~ r1_xxreal_0(C,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B),1))) & ~ r1_xxreal_0(D,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,k1_matrix_0(B)))) ) ) ) )).
fof(fraenkel_a_1_7_gobrd11,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_7_gobrd11(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_7_jordan2c,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) => ( r2_hidden(A,a_1_7_jordan2c(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & A = C & r1_jordan2c(2,k3_topreal1(2,k1_sprect_1(B)),C) ) ) ) )).
fof(fraenkel_a_1_7_jordan5d,axiom,( ! [A] : ! [B] : ( ( ~ 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,a_1_7_jordan5d(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = k18_euclid(C) & r2_hidden(C,k3_topreal1(2,B)) ) ) ) )).
fof(fraenkel_a_1_7_jordan6,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_7_jordan6(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & ~ r1_xxreal_0(B,k7_partfun1(k1_numbers,C,1)) ) ) ) )).
fof(fraenkel_a_1_7_nat_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(A,a_1_7_nat_4(B)) <=> ? [C] : ( v1_int_2(C) & m1_subset_1(C,k4_ordinal1) & A = k11_newton(C,k11_nat_3(k4_newton(B,k2_nat_1(2,B)),C)) & r1_xxreal_0(C,k3_square_1(k2_nat_1(2,B))) & ~ r1_xxreal_0(k11_nat_3(k4_newton(B,k2_nat_1(2,B)),C),k5_numbers) ) ) ) )).
fof(fraenkel_a_1_7_scmyciel,axiom,( ! [A] : ! [B] : ( v4_scmyciel(B) => ( r2_hidden(A,a_1_7_scmyciel(B)) <=> ? [C] : ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k3_tarski(B))) & A = C & r1_xxreal_0(k5_card_1(C),2) ) ) ) )).
fof(fraenkel_a_1_7_sprect_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v2_compts_1(B,k15_euclid(2)) & ~ v1_sppol_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_7_sprect_1(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & r1_xxreal_0(k17_euclid(C),k8_pscomp_1(B)) & r1_xxreal_0(k6_pscomp_1(B),k17_euclid(C)) & k18_euclid(C) = k9_pscomp_1(B) ) ) ) )).
fof(fraenkel_a_1_7_tdlat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v4_tdlat_3(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_7_tdlat_3(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v6_tops_1(C,B) ) ) ) )).
fof(fraenkel_a_1_7_topgen_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v1_tdlat_3(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_7_topgen_2(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k6_domain_1(u1_struct_0(B),C) ) ) ) )).
fof(fraenkel_a_1_8_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & l1_msualg_1(B) ) => ( r2_hidden(A,a_1_8_abcmiz_1(B)) <=> ? [C] : ( m1_dtconstr(C,u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))),k5_trees_3(u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers)))))),k1_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))) & A = C & k7_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),C) = k12_abcmiz_1(B) & r2_pboole(u1_struct_0(B),k4_msafree3(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),C),k28_abcmiz_1(B)) ) ) ) )).
fof(fraenkel_a_1_8_aofa_000,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_freealg(B) ) => ( r2_hidden(A,a_1_8_aofa_000(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k3_freealg(k19_aofa_000,B))) & A = C & ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) & r1_lang1(k3_freealg(k19_aofa_000,B),C,D) ) ) ) ) )).
fof(fraenkel_a_1_8_cohsp_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_8_cohsp_1(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k1_tarski(C) ) ) ) )).
fof(fraenkel_a_1_8_comput_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_8_comput_1(B)) <=> ? [C] : ( m2_rfunct_3(C,k3_finseq_2(B),B,k3_rfunct_3(k3_finseq_2(B),B)) & A = C & v2_margrel1(C) ) ) ) )).
fof(fraenkel_a_1_8_decomp_1,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_8_decomp_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & k1_tops_1(B,C) = k4_decomp_1(B,C) ) ) ) )).
fof(fraenkel_a_1_8_finseq_1,axiom,( ! [A] : ! [B] : ( v3_finseq_1(B) => ( r2_hidden(A,a_1_8_finseq_1(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k10_xtuple_0(C) & r2_hidden(C,B) ) ) ) )).
fof(fraenkel_a_1_8_gobrd11,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_8_gobrd11(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & ~ r1_xxreal_0(C,B) ) ) ) )).
fof(fraenkel_a_1_8_jordan5d,axiom,( ! [A] : ! [B] : ( ( ~ 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,a_1_8_jordan5d(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = C & r2_hidden(k4_tarski(1,C),k2_matrix_0(k2_goboard2(B))) & ? [D] : ( v7_ordinal1(D) & r2_hidden(D,k4_finseq_1(B)) & k7_partfun1(u1_struct_0(k15_euclid(2)),B,D) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(B),1,C) ) ) ) ) )).
fof(fraenkel_a_1_8_jordan6,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_8_jordan6(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & ~ r1_xxreal_0(k17_euclid(C),B) ) ) ) )).
fof(fraenkel_a_1_8_nat_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(A,a_1_8_nat_4(B)) <=> ? [C] : ( v1_int_2(C) & m1_subset_1(C,k4_ordinal1) & A = k11_newton(C,k11_nat_3(k4_newton(B,k2_nat_1(2,B)),C)) & ~ r1_xxreal_0(C,k3_square_1(k2_nat_1(2,B))) & r1_xxreal_0(C,k7_xcmplx_0(k2_nat_1(2,B),3)) & ~ r1_xxreal_0(k11_nat_3(k4_newton(B,k2_nat_1(2,B)),C),k5_numbers) ) ) ) )).
fof(fraenkel_a_1_8_tdlat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_8_tdlat_3(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v4_tops_1(C,B) ) ) ) )).
fof(fraenkel_a_1_8_topgen_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v1_tdlat_3(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_8_topgen_2(B)) <=> ? [C] : ( v1_tops_2(C,B) & v1_cantor_1(C,B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & A = k1_card_1(C) ) ) ) )).
fof(fraenkel_a_1_8_waybel19,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v1_waybel_9(B) & l1_waybel_9(B) ) => ( r2_hidden(A,a_1_8_waybel19(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k3_subset_1(u1_struct_0(B),k6_waybel_0(B,C)) ) ) ) )).
fof(fraenkel_a_1_9_card_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v4_funct_1(B) ) => ( r2_hidden(A,a_1_9_card_3(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k9_xtuple_0(C) ) ) ) )).
fof(fraenkel_a_1_9_decomp_1,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_9_decomp_1(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & k3_decomp_1(B,C) = k2_decomp_1(B,C) ) ) ) )).
fof(fraenkel_a_1_9_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_1_9_fomodel0(B)) <=> ? [C] : ( m1_subset_1(C,B) & A = k12_finseq_1(B,C) ) ) ) )).
fof(fraenkel_a_1_9_gobrd11,axiom,( ! [A] : ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_1_9_gobrd11(B)) <=> ? [C] : ? [D] : ( v1_xreal_0(C) & v1_xreal_0(D) & A = k19_euclid(C,D) & r1_xxreal_0(C,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,1))) ) ) ) )).
fof(fraenkel_a_1_9_jordan5d,axiom,( ! [A] : ! [B] : ( ( ~ 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,a_1_9_jordan5d(B)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & A = C & r2_hidden(k4_tarski(k3_finseq_1(k2_goboard2(B)),C),k2_matrix_0(k2_goboard2(B))) & ? [D] : ( v7_ordinal1(D) & r2_hidden(D,k4_finseq_1(B)) & k7_partfun1(u1_struct_0(k15_euclid(2)),B,D) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(B),k3_finseq_1(k2_goboard2(B)),C) ) ) ) ) )).
fof(fraenkel_a_1_9_jordan6,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ( r2_hidden(A,a_1_9_jordan6(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & A = C & ~ r1_xxreal_0(k7_partfun1(k1_numbers,C,1),B) ) ) ) )).
fof(fraenkel_a_1_9_nat_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(A,a_1_9_nat_4(B)) <=> ? [C] : ( v1_int_2(C) & m1_subset_1(C,k4_ordinal1) & A = k11_newton(C,k11_nat_3(k4_newton(B,k2_nat_1(2,B)),C)) & ~ r1_xxreal_0(C,B) & r1_xxreal_0(C,k2_nat_1(2,B)) & ~ r1_xxreal_0(k11_nat_3(k4_newton(B,k2_nat_1(2,B)),C),k5_numbers) ) ) ) )).
fof(fraenkel_a_1_9_tdlat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_9_tdlat_3(B)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & A = C & v6_tops_1(C,B) ) ) ) )).
fof(fraenkel_a_1_9_topgen_2,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_1_9_topgen_2(B)) <=> ? [C] : ( v1_tops_2(C,B) & v1_cantor_1(C,B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & A = k1_card_1(C) ) ) ) )).
fof(fraenkel_a_1_9_trees_2,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,a_1_9_trees_2(B)) <=> ? [C] : ( m1_trees_1(C,k8_trees_1) & A = C & k3_finseq_1(C) = B ) ) ) )).
fof(fraenkel_a_1_9_waybel19,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v1_waybel19(B) & l1_waybel_9(B) ) => ( r2_hidden(A,a_1_9_waybel19(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k3_subset_1(u1_struct_0(B),k6_waybel_0(B,C)) ) ) ) )).
fof(fraenkel_a_2_0_abcmiz_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l2_abcmiz_0(B) & m1_subset_1(C,u1_abcmiz_0(B)) ) => ( r2_hidden(A,a_2_0_abcmiz_0(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r2_hidden(C,k2_abcmiz_0(B,D)) ) ) ) )).
fof(fraenkel_a_2_0_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_0_abcmiz_1(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(k1_funct_1(B,C))) & m1_subset_1(E,k4_ordinal1) & A = k4_tarski(k1_abcmiz_1(D),E) & v1_finset_1(D) ) ) ) )).
fof(fraenkel_a_2_0_abcmiz_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & l1_msualg_1(B) & m1_dtconstr(C,u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))),k5_trees_3(u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers)))))),k1_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))) ) => ( r2_hidden(A,a_2_0_abcmiz_a(B,C)) <=> ? [D] : ( m1_dtconstr(D,u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))),k5_trees_3(u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers)))))),k1_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))) & A = D & k7_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),D) = k7_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),C) & r2_pboole(u1_struct_0(B),k4_msafree3(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),D),k28_abcmiz_1(B)) ) ) ) )).
fof(fraenkel_a_2_0_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) & v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,a_2_0_afinsq_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_nat_1(D,k5_card_1(B)) & r2_hidden(D,k9_xtuple_0(C)) ) ) ) )).
fof(fraenkel_a_2_0_algstr_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( l3_algstr_0(B) & v1_relat_1(C) & v5_relat_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) & v1_funct_1(C) ) => ( r2_hidden(A,a_2_0_algstr_4(B,C)) <=> ? [D] : ( v1_partfun1(D,u1_struct_0(B)) & v3_relat_2(D) & v8_relat_2(D) & v1_algstr_4(D,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) & A = D & ! [E] : ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ( ( r2_hidden(E,k9_xtuple_0(C)) & k1_funct_1(C,E) = k4_tarski(F,G) ) => r2_hidden(F,k6_eqrel_1(u1_struct_0(B),u1_struct_0(B),D,G)) ) ) ) ) ) ) )).
fof(fraenkel_a_2_0_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(A,a_2_0_aofa_000(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = k1_funct_1(k8_funct_7(B,D),C) & r2_hidden(C,k9_xtuple_0(k8_funct_7(B,D))) ) ) ) )).
fof(fraenkel_a_2_0_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ( r2_hidden(A,a_2_0_armstrng(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(B)) & A = k6_armstrng(B,D,E) & ( r1_tarski(C,D) | r1_tarski(E,D) ) ) ) ) )).
fof(fraenkel_a_2_0_arytm_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m2_subset_1(B,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) & m2_subset_1(C,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) ) => ( r2_hidden(A,a_2_0_arytm_2(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k5_arytm_3) & m1_subset_1(E,k5_arytm_3) & A = k9_arytm_3(D,E) & r2_hidden(D,B) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_0_asympt_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(A,a_2_0_asympt_0(B,C)) <=> ? [D] : ( m2_funct_2(D,k4_ordinal1,k1_numbers,k9_funct_2(k4_ordinal1,k1_numbers)) & A = D & ? [E] : ( v1_xreal_0(E) & ? [F] : ( m1_subset_1(F,k4_ordinal1) & ~ r1_xxreal_0(E,k5_numbers) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( ( r1_xxreal_0(F,G) & r2_hidden(G,C) ) => ( r1_xxreal_0(k9_nat_1(k1_numbers,D,G),k3_xcmplx_0(E,k9_nat_1(k1_numbers,B,G))) & r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,D,G)) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_2_0_bcialg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_bcialg_1(B) & v4_bcialg_1(B) & v5_bcialg_1(B) & v7_bcialg_1(B) & l2_bcialg_1(B) & m2_subset_1(C,u1_struct_0(B),k5_bcialg_1(B)) ) => ( r2_hidden(A,a_2_0_bcialg_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_bcialg_1(B,C,D) ) ) ) )).
fof(fraenkel_a_2_0_bcialg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_bcialg_4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_bcialg_1(B,D,C) ) ) ) )).
fof(fraenkel_a_2_0_bciideal,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_bciideal(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_bcialg_1(B,D,C) ) ) ) )).
fof(fraenkel_a_2_0_bintree1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) & m1_trees_1(C,B) ) => ( r2_hidden(A,a_2_0_bintree1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k8_finseq_1(k4_ordinal1,C,k14_trees_3(D)) & r2_hidden(k8_finseq_1(k4_ordinal1,C,k14_trees_3(D)),B) ) ) ) )).
fof(fraenkel_a_2_0_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & v2_pre_topc(C) & l1_pre_topc(C) ) => ( r2_hidden(A,a_2_0_borsuk_1(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) & A = k8_mcart_1(u1_struct_0(B),u1_struct_0(C),D,E) & r2_hidden(D,u1_pre_topc(B)) & r2_hidden(E,u1_pre_topc(C)) ) ) ) )).
fof(fraenkel_a_2_0_borsuk_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v1_compts_1(B) & l1_pre_topc(B) & ~ v2_struct_0(C) & v2_pre_topc(C) & v1_compts_1(C) & l1_pre_topc(C) ) => ( r2_hidden(A,a_2_0_borsuk_3(B,C)) <=> ? [D] : ( v3_pre_topc(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & r1_tarski(k3_borsuk_1(C,B,k2_struct_0(C),D),k5_setfam_1(u1_struct_0(k2_borsuk_1(C,B)),k7_borsuk_1(C,B,k2_struct_0(k2_borsuk_1(C,B))))) ) ) ) )).
fof(fraenkel_a_2_0_borsuk_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_borsuk_4(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & r1_xxreal_0(B,D) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_0_borsuk_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_borsuk_5(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & r1_xxreal_0(B,D) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_0_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & m1_subset_1(C,u1_struct_0(k15_euclid(3))) ) => ( r2_hidden(A,a_2_0_borsuk_7(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(k1_euclid_5(C),k7_xcmplx_0(B,k3_square_1(2)))) & ~ r1_xxreal_0(k2_xcmplx_0(k1_euclid_5(C),k7_xcmplx_0(B,k3_square_1(2))),D) ) ) ) )).
fof(fraenkel_a_2_0_brouwer,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ( r2_hidden(A,a_2_0_brouwer(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(C)) & A = k4_borsuk_1(B,C,D,E) & D != E ) ) ) )).
fof(fraenkel_a_2_0_c0sp1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(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))) ) => ( r2_hidden(A,a_2_0_c0sp1(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = k9_complex1(k3_funct_2(B,k1_numbers,C,D)) ) ) ) )).
fof(fraenkel_a_2_0_calcul_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(B) & m2_finseq_1(C,k3_cqc_lang(B)) ) => ( r2_hidden(A,a_2_0_calcul_1(B,C)) <=> ? [D] : ( m2_subset_1(D,k9_qc_lang1(B),k3_cqc_lang(B)) & A = k24_qc_lang1(B,D) & ? [E] : ( m1_subset_1(E,k4_ordinal1) & r2_hidden(E,k1_relset_1(k4_ordinal1,C)) & D = k1_funct_1(C,E) ) ) ) ) )).
fof(fraenkel_a_2_0_calcul_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_0_calcul_2(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = D & r1_xxreal_0(k2_xcmplx_0(1,B),D) & r1_xxreal_0(D,k2_xcmplx_0(C,B)) ) ) ) )).
fof(fraenkel_a_2_0_cantor_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(k9_setfam_1(B)))) ) => ( r2_hidden(A,a_2_0_cantor_1(B,C)) <=> ? [D] : ( m2_subset_1(D,k1_zfmisc_1(k9_setfam_1(B)),C) & A = k8_setfam_1(B,D) ) ) ) )).
fof(fraenkel_a_2_0_card_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v4_funct_1(B) ) => ( r2_hidden(A,a_2_0_card_3(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = k1_funct_1(D,C) ) ) ) )).
fof(fraenkel_a_2_0_card_fil,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) ) => ( r2_hidden(A,a_2_0_card_fil(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = D & r2_hidden(k3_subset_1(B,D),C) ) ) ) )).
fof(fraenkel_a_2_0_card_fin,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(B) & v1_finset_1(C) ) => ( r2_hidden(A,a_2_0_card_fin(B,C)) <=> ? [D] : ( v1_funct_1(D) & v1_funct_2(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) & A = D & v2_funct_1(D) ) ) ) )).
fof(fraenkel_a_2_0_card_lar,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_ordinal1(B) & v4_ordinal1(B) & ~ v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_2_0_card_lar(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = D & ~ v1_finset_1(D) & v4_ordinal1(D) & k3_ordinal2(k8_subset_1(B,C,D)) = D ) ) ) )).
fof(fraenkel_a_2_0_cardfin2,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(A,a_2_0_cardfin2(B,C)) <=> ? [D] : ( v1_funct_1(D) & v1_funct_2(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) & A = D & ~ v2_funct_1(D) ) ) )).
fof(fraenkel_a_2_0_cat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & 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(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_cat_2(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) & A = k2_cat_1(B,D,E) & r2_hidden(D,C) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_0_catalan2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_0_catalan2(B,C)) <=> ? [D] : ( m1_subset_1(D,k3_catalan2(k4_ordinal1)) & A = D & r2_hidden(D,k2_catalan2(B,C)) & a_1_4_catalan2(D) != k1_xboole_0 ) ) ) )).
fof(fraenkel_a_2_0_cc0sp1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,B,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => ( r2_hidden(A,a_2_0_cc0sp1(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = k9_complex1(k3_funct_2(B,k2_numbers,C,D)) ) ) ) )).
fof(fraenkel_a_2_0_cc0sp2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xcmplx_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_cc0sp2(B,C)) <=> ? [D] : ( v1_xcmplx_0(D) & A = D & ~ r1_xxreal_0(C,k9_complex1(k6_xcmplx_0(D,B))) ) ) ) )).
fof(fraenkel_a_2_0_cfdiff_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xcmplx_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_cfdiff_1(B,C)) <=> ? [D] : ( v1_xcmplx_0(D) & A = D & ~ r1_xxreal_0(C,k9_complex1(k6_xcmplx_0(D,B))) ) ) ) )).
fof(fraenkel_a_2_0_cgames_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v3_ordinal1(C) ) => ( r2_hidden(A,a_2_0_cgames_1(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(k3_tarski(k10_xtuple_0(k5_relat_1(B,C))))) & m1_subset_1(E,k1_zfmisc_1(k3_tarski(k10_xtuple_0(k5_relat_1(B,C))))) & A = g1_cgames_1(D,E) ) ) ) )).
fof(fraenkel_a_2_0_chord,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ( r2_hidden(A,a_2_0_chord(B,C)) <=> ? [D] : ( m1_subset_1(D,k6_glib_000(B)) & A = D & ~ r2_hidden(D,C) & ? [E] : ( m1_subset_1(E,k6_glib_000(B)) & r2_hidden(E,C) & r1_chord(B,D,E) ) ) ) ) )).
fof(fraenkel_a_2_0_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,k4_ordinal1) ) => ( r2_hidden(A,a_2_0_circcmb3(B,C)) <=> ? [D] : ( m2_finseq_2(D,B,k3_finseq_2(B)) & A = D & k3_finseq_1(D) = C ) ) ) )).
fof(fraenkel_a_2_0_circuit1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v8_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & v5_msafree2(B) & l1_msualg_1(B) & v4_msualg_1(C,B) & v4_msafree2(C,B) & l3_msualg_1(C,B) ) => ( r2_hidden(A,a_2_0_circuit1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k6_circuit1(B,C,D) & r2_hidden(D,u1_struct_0(B)) ) ) ) )).
fof(fraenkel_a_2_0_classes1,axiom,( ! [A] : ! [B] : ! [C] : ( v3_ordinal1(C) => ( r2_hidden(A,a_2_0_classes1(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_classes1(B)) & A = D & ? [E] : ( m1_subset_1(E,k1_classes1(B)) & r2_hidden(E,k3_classes1(B,C)) & r1_tarski(D,E) ) ) ) ) )).
fof(fraenkel_a_2_0_clopban2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_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(B),u1_struct_0(B)) & v13_vectsp_1(C,B,B) & v1_clopban1(C,B,B) & v2_clopban1(C,B,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) ) => ( r2_hidden(A,a_2_0_clopban2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k2_normsp_0(B,k3_funct_2(u1_struct_0(B),u1_struct_0(B),C,D)) & r1_xxreal_0(k2_normsp_0(B,D),1) ) ) ) )).
fof(fraenkel_a_2_0_closure1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_2_0_closure1(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = D & r1_tarski(C,D) ) ) ) )).
fof(fraenkel_a_2_0_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v4_funct_1(B) ) => ( r2_hidden(A,a_2_0_closure2(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = k1_funct_1(D,C) ) ) ) )).
fof(fraenkel_a_2_0_closure3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) ) => ( r2_hidden(A,a_2_0_closure3(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = D & k1_funct_1(C,D) != k1_xboole_0 ) ) ) )).
fof(fraenkel_a_2_0_cohsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) & ~ v1_xboole_0(C) & v1_classes1(C) & v1_coh_sp(C) ) => ( r2_hidden(A,a_2_0_cohsp_1(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,B) & m1_subset_1(E,C) & A = k14_cohsp_1(D,E) ) ) ) )).
fof(fraenkel_a_2_0_combgras,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v1_xboole_0(C) ) => ( r2_hidden(A,a_2_0_combgras(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(C)) & A = D & k1_card_1(D) = B ) ) ) )).
fof(fraenkel_a_2_0_compos_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_compos_0(B) & m1_subset_1(C,k1_compos_0(B)) ) => ( r2_hidden(A,a_2_0_compos_0(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = k5_xtuple_0(D) & k2_compos_0(B,D) = C ) ) ) )).
fof(fraenkel_a_2_0_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_compos_1(B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ( r2_hidden(A,a_2_0_compos_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = D & ~ r1_xxreal_0(k5_card_1(k63_valued_1(C)),D) ) ) ) )).
fof(fraenkel_a_2_0_conlat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_conlat_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_conlat_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u4_struct_0(B)) & A = D & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r2_hidden(E,C) => r1_conlat_1(B,E,D) ) ) ) ) ) )).
fof(fraenkel_a_2_0_conlat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_conlat_1(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) => ( r2_hidden(A,a_2_0_conlat_2(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k3_funct_2(k1_zfmisc_1(u1_struct_0(B)),k9_setfam_1(u4_struct_0(B)),k1_conlat_1(B),D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_0_connsp_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) => ( r2_hidden(A,a_2_0_connsp_3(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(E,C) & r1_tarski(D,E) & v3_connsp_1(D,B) ) ) ) ) )).
fof(fraenkel_a_2_0_convex1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_convex1(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) & A = k1_algstr_0(B,D,E) & r2_hidden(D,k1_xboole_0) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_0_convex3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_convex3(B,C)) <=> ? [D] : ( v2_convex1(D,B) & m2_rlvect_2(D,B,C) & A = k6_rlvect_2(B,D) & r2_hidden(D,k1_convex3(B)) ) ) ) )).
fof(fraenkel_a_2_0_convex4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) & m2_funct_2(C,u1_struct_0(B),k2_numbers,k9_funct_2(u1_struct_0(B),k2_numbers)) ) => ( r2_hidden(A,a_2_0_convex4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & k3_funct_2(u1_struct_0(B),k2_numbers,C,D) != k5_complex1 ) ) ) )).
fof(fraenkel_a_2_0_convfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_rlvect_1(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),k6_numbers))) ) => ( r2_hidden(A,a_2_0_convfun1(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,k1_numbers) & A = k1_domain_1(u1_struct_0(B),k1_numbers,D,E) & r1_xxreal_0(k12_supinf_2(C,D),E) ) ) ) )).
fof(fraenkel_a_2_0_cqc_sim1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(B) & m2_subset_1(C,k9_qc_lang1(B),k3_cqc_lang(B)) ) => ( r2_hidden(A,a_2_0_cqc_sim1(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_qc_lang1(B)) & A = D & ! [E] : ( m1_subset_1(E,k1_qc_lang1(B)) => ~ ( r1_qc_lang1(B,D,E) & r2_hidden(k2_qc_lang3(B,E),k24_qc_lang1(B,C)) ) ) ) ) ) )).
fof(fraenkel_a_2_0_cqc_the1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(B) & m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(B))) ) => ( r2_hidden(A,a_2_0_cqc_the1(B,C)) <=> ? [D] : ( m2_subset_1(D,k9_qc_lang1(B),k3_cqc_lang(B)) & A = D & ? [E] : ( m2_finseq_1(E,k2_zfmisc_1(k3_cqc_lang(B),k2_cqc_the1)) & r2_cqc_the1(B,C,E) & k3_cqc_the1(B,E) = D ) ) ) ) )).
fof(fraenkel_a_2_0_dist_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(B) & m2_finseq_1(C,B) ) => ( r2_hidden(A,a_2_0_dist_1(B,C)) <=> ? [D] : ( m2_finseq_1(D,B) & A = D & r1_dist_1(B,C,D) ) ) ) )).
fof(fraenkel_a_2_0_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) ) => ( r2_hidden(A,a_2_0_domain_1(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,B) & m1_subset_1(E,C) & A = k1_domain_1(B,C,D,E) ) ) ) )).
fof(fraenkel_a_2_0_dtconstr,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_dtconstr(B) & l1_lang1(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_dtconstr(B,C)) <=> ? [D] : ( m1_subset_1(D,k5_trees_3(u1_struct_0(B))) & A = k15_dtconstr(B,D) & r2_hidden(D,k4_dtconstr(B)) & k1_funct_1(D,k1_xboole_0) = C ) ) ) )).
fof(fraenkel_a_2_0_ec_pf_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_int_2(B) & m1_subset_1(C,u1_struct_0(k9_int_3(B))) ) => ( r2_hidden(A,a_2_0_ec_pf_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(B))) & A = D & k2_binom(k9_int_3(B),D,2) = C ) ) ) )).
fof(fraenkel_a_2_0_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) => ( r2_hidden(A,a_2_0_eqrel_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = k3_tarski(D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_0_euclid_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & m1_subset_1(C,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_2_0_euclid_3(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),B,k6_xcmplx_0(1,D)),k1_rlvect_1(k15_euclid(2),C,D)) & r1_xxreal_0(k5_numbers,D) & r1_xxreal_0(D,1) ) ) ) )).
fof(fraenkel_a_2_0_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_orders_2(B) & v1_relat_1(C) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & v1_exchsort(C) ) => ( r2_hidden(A,a_2_0_exchsort(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k9_xtuple_0(C)) & m1_subset_1(E,k9_xtuple_0(C)) & A = k4_tarski(D,E) & r2_hidden(D,E) & ~ r1_orders_2(B,k7_partfun1(u1_struct_0(B),C,D),k7_partfun1(u1_struct_0(B),C,E)) ) ) ) )).
fof(fraenkel_a_2_0_fcont_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_fcont_1(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(B,C)) & ~ r1_xxreal_0(k2_xcmplx_0(B,C),D) ) ) ) )).
fof(fraenkel_a_2_0_fcont_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_fcont_2(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & r1_xxreal_0(C,D) & r1_xxreal_0(D,B) ) ) ) )).
fof(fraenkel_a_2_0_fdiff_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_fdiff_2(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(B,C)) & ~ r1_xxreal_0(k2_xcmplx_0(B,C),D) ) ) ) )).
fof(fraenkel_a_2_0_fdiff_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_fdiff_3(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & r1_xxreal_0(k6_xcmplx_0(B,C),D) & r1_xxreal_0(D,B) ) ) ) )).
fof(fraenkel_a_2_0_fib_num2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k4_ordinal1) & v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) ) => ( r2_hidden(A,a_2_0_fib_num2(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_nat_1(D,B) & r2_hidden(D,k9_xtuple_0(C)) ) ) ) )).
fof(fraenkel_a_2_0_filter_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_filter_0(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r3_lattices(B,C,D) ) ) ) )).
fof(fraenkel_a_2_0_filter_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_filter_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r3_lattices(B,D,C) ) ) ) )).
fof(fraenkel_a_2_0_fin_topo,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_fin_topo(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ~ r1_xboole_0(k1_fin_topo(B,D),C) & ~ r1_xboole_0(k1_fin_topo(B,D),k3_subset_1(u1_struct_0(B),C)) ) ) ) )).
fof(fraenkel_a_2_0_finance1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_finance1(B,C)) <=> ? [D] : ( m1_subset_1(D,k6_numbers) & A = D & r1_xxreal_0(B,D) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_0_finseq_2,axiom,( ! [A] : ! [B] : ! [C] : ( v7_ordinal1(B) => ( r2_hidden(A,a_2_0_finseq_2(B,C)) <=> ? [D] : ( m2_finseq_2(D,C,k3_finseq_2(C)) & A = D & k3_finseq_1(D) = B ) ) ) )).
fof(fraenkel_a_2_0_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) ) => ( r2_hidden(A,a_2_0_finseq_3(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,B) & m1_subset_1(E,C) & A = k10_finseq_1(D,E) ) ) ) )).
fof(fraenkel_a_2_0_fintopo2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_fintopo2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_fintopo2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ( r2_hidden(E,k6_fintopo2(B,D)) => ( ~ r1_xboole_0(E,C) & ~ r1_xboole_0(E,k3_subset_1(u1_struct_0(B),C)) ) ) ) ) ) ) )).
fof(fraenkel_a_2_0_fintopo3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_fintopo3(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ~ ( r2_hidden(E,k3_subset_1(u1_struct_0(B),C)) & r2_hidden(D,k1_fin_topo(B,E)) ) ) ) ) ) )).
fof(fraenkel_a_2_0_fintopo6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_fintopo6(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_tarski(k1_fin_topo(B,D),C) ) ) ) )).
fof(fraenkel_a_2_0_flang_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_catalan2(B))) => ( r2_hidden(A,a_2_0_flang_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_catalan2(B))) & A = D & ? [E] : ( v7_ordinal1(E) & D = k7_flang_1(B,C,E) ) ) ) ) )).
fof(fraenkel_a_2_0_flang_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(B))) => ( r2_hidden(A,a_2_0_flang_2(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k8_afinsq_1(B))) & A = D & ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(E,1) & D = k7_flang_1(B,C,E) ) ) ) ) )).
fof(fraenkel_a_2_0_flang_3,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(B))) => ( r2_hidden(A,a_2_0_flang_3(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k8_afinsq_1(B))) & A = D & ? [E] : ( v7_ordinal1(E) & ~ r1_xxreal_0(E,k5_numbers) & D = k7_flang_1(B,C,E) ) ) ) ) )).
fof(fraenkel_a_2_0_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) & ~ v1_xboole_0(C) ) => ( r2_hidden(A,a_2_0_fomodel2(B,C)) <=> ? [D] : ( m2_funct_2(D,k37_fomodel1(B),k3_rfunct_3(k3_finseq_2(C),k2_xboole_0(C,k6_margrel1)),k9_funct_2(k37_fomodel1(B),k3_rfunct_3(k3_finseq_2(C),k2_xboole_0(C,k6_margrel1)))) & A = D & v1_fomodel2(D,B,C) ) ) ) )).
fof(fraenkel_a_2_0_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))))) ) => ( r2_hidden(A,a_2_0_fomodel4(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = k8_funct_7(k4_fomodel4(B,C),D) ) ) ) )).
fof(fraenkel_a_2_0_frechet2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_frechet2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r2_hidden(C,k2_pre_topc(B,k6_domain_1(u1_struct_0(B),D))) ) ) ) )).
fof(fraenkel_a_2_0_freealg,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,k4_ordinal1) & ~ v1_xboole_0(C) & v1_freealg(C) ) => ( r2_hidden(A,a_2_0_freealg(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k3_freealg(B,C))) & A = k2_trees_4(u1_struct_0(k3_freealg(B,C)),D) & r2_hidden(D,k6_dtconstr(k3_freealg(B,C))) ) ) ) )).
fof(fraenkel_a_2_0_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & ~ 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,a_2_0_fsm_3(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k4_fsm_3(B,k4_subset_1(k3_catalan2(B),k9_flang_1(B),k4_flang_1(B,k2_flang_1(B))),C))) & A = D & ~ r1_xboole_0(D,u2_fsm_3(B,k4_subset_1(k3_catalan2(B),k9_flang_1(B),k4_flang_1(B,k2_flang_1(B))),C)) ) ) ) )).
fof(fraenkel_a_2_0_goboard2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_0_goboard2(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_topreal1(2,k17_finseq_1(u1_struct_0(k15_euclid(2)),C,B),D) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(k17_finseq_1(u1_struct_0(k15_euclid(2)),C,B))) ) ) ) )).
fof(fraenkel_a_2_0_goboard5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_0_goboard5(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,C,1)),D) & r1_xxreal_0(D,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k1_nat_1(C,1),1))) ) ) ) )).
fof(fraenkel_a_2_0_goboard6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_0_goboard6(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & ~ r1_xxreal_0(D,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,B,1))) & ~ r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(B,1),1)),D) ) ) ) )).
fof(fraenkel_a_2_0_goboard9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_0_goboard9(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & ~ r1_xxreal_0(E,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,B))) & ~ r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,k1_nat_1(B,1))),E) ) ) ) )).
fof(fraenkel_a_2_0_gobrd11,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_0_gobrd11(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,B,1)),D) & r1_xxreal_0(D,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(B,1),1))) ) ) ) )).
fof(fraenkel_a_2_0_gobrd13,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_0_gobrd13(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(D,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,1))) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,B)),E) & r1_xxreal_0(E,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,k1_nat_1(B,1)))) ) ) ) )).
fof(fraenkel_a_2_0_goedelcp,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(B) & m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(B))) ) => ( r2_hidden(A,a_2_0_goedelcp(B,C)) <=> ? [D] : ( m2_subset_1(D,k9_qc_lang1(B),k3_cqc_lang(B)) & A = k24_qc_lang1(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_0_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v5_graph_1(B) & v6_graph_1(B) & l1_graph_1(B) & m2_finseq_2(C,u4_struct_0(B),k9_graph_3(B)) ) => ( r2_hidden(A,a_2_0_graph_3(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r2_hidden(D,k1_graph_3(B,k10_xtuple_0(C))) & k10_graph_1(B,D) != k7_graph_3(B,D,k10_xtuple_0(C)) ) ) ) )).
fof(fraenkel_a_2_0_graph_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ( r2_hidden(A,a_2_0_graph_4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u4_struct_0(B)) & r2_hidden(E,C) & D = k1_funct_1(u1_graph_1(B),E) ) ) ) ) )).
fof(fraenkel_a_2_0_graph_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(B) & m1_subset_1(C,k4_ordinal1) ) => ( r2_hidden(A,a_2_0_graph_5(B,C)) <=> ? [D] : ( m2_finseq_2(D,B,k3_finseq_2(B)) & A = D & r1_xxreal_0(1,k3_finseq_1(D)) & r1_xxreal_0(k3_finseq_1(D),C) ) ) ) )).
fof(fraenkel_a_2_0_graphsp,axiom,( ! [A] : ! [B] : ! [C] : ( ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_0_graphsp(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = D & r2_hidden(D,k4_finseq_1(B)) & r1_xxreal_0(1,D) & r1_xxreal_0(D,C) & k1_funct_1(B,D) != k4_xcmplx_0(1) & k1_funct_1(B,k1_nat_1(C,D)) != k4_xcmplx_0(1) ) ) ) )).
fof(fraenkel_a_2_0_grcat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & 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(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_grcat_1(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) & A = k2_cat_1(B,D,E) & r2_hidden(D,C) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_0_groeb_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_ordinal1(B) & m1_subset_1(C,k1_zfmisc_1(k15_pre_poly(B))) ) => ( r2_hidden(A,a_2_0_groeb_1(B,C)) <=> ? [D] : ( m2_subset_1(D,k14_pre_poly(B),k15_pre_poly(B)) & A = D & ? [E] : ( v1_relat_1(E) & v4_relat_1(E,B) & v1_funct_1(E) & v1_partfun1(E,B) & v4_valued_0(E) & v2_pre_poly(E) & r2_hidden(E,C) & r3_pre_poly(B,E,D) ) ) ) ) )).
fof(fraenkel_a_2_0_group_10,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(A,a_2_0_group_10(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = D & k1_card_1(D) = C ) ) )).
fof(fraenkel_a_2_0_group_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_group_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k2_group_1(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_0_group_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_group_3(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r2_group_3(B,C,D) ) ) ) )).
fof(fraenkel_a_2_0_group_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_group_4(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & ? [E] : ( v15_algstr_0(E) & m1_group_2(E,B) & D = u1_struct_0(E) & r1_tarski(C,k8_group_2(B,E)) ) ) ) ) )).
fof(fraenkel_a_2_0_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( v7_ordinal1(C) => ( r2_hidden(A,a_2_0_group_9(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = D & r2_hidden(D,B) & ~ r1_xxreal_0(C,D) ) ) ) )).
fof(fraenkel_a_2_0_groupp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_int_2(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_0_groupp_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = k1_newton(B,D) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_0_hermitan,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(B),u1_struct_0(B)),u1_struct_0(k1_complfld)) & v2_bilinear(C,k1_complfld,B,B) & v4_bilinear(C,k1_complfld,B,B) & v3_hermitan(C,B) & v5_hermitan(C,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(k1_complfld)))) ) => ( r2_hidden(A,a_2_0_hermitan(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & k2_binop_1(u1_struct_0(B),u1_struct_0(B),u1_struct_0(k1_complfld),C,D,D) = k4_struct_0(k1_complfld) ) ) ) )).
fof(fraenkel_a_2_0_heyting1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k7_normform(B))) => ( r2_hidden(A,a_2_0_heyting1(B,C)) <=> ? [D] : ( m2_funct_2(D,k7_normform(B),k1_heyting1(B),k9_funct_2(k7_normform(B),k1_heyting1(B))) & A = k4_tarski(a_3_0_heyting1(B,C,D),a_3_1_heyting1(B,C,D)) & ! [E] : ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B)) => ( r2_hidden(E,C) => r2_hidden(k3_funct_2(k7_normform(B),k1_heyting1(B),D,E),k5_setwiseo(B,k2_domain_1(k5_finsub_1(B),k5_finsub_1(B),E),k3_domain_1(k5_finsub_1(B),k5_finsub_1(B),E))) ) ) ) ) ) )).
fof(fraenkel_a_2_0_heyting2,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(A,a_2_0_heyting2(B,C)) <=> ? [D] : ( m1_subset_1(D,k5_finsub_1(k4_partfun1(B,C))) & A = D & ! [E] : ( r2_hidden(E,D) => v1_finset_1(E) ) & ! [E] : ( m1_subset_1(E,k4_partfun1(B,C)) => ! [F] : ( m1_subset_1(F,k4_partfun1(B,C)) => ( ( r2_hidden(E,D) & r2_hidden(F,D) & r1_tarski(E,F) ) => E = F ) ) ) ) ) )).
fof(fraenkel_a_2_0_heyting3,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(A,a_2_0_heyting3(B,C)) <=> ? [D] : ( m1_subset_1(D,k5_finsub_1(k4_partfun1(B,C))) & A = D & ! [E] : ( r2_hidden(E,D) => v1_finset_1(E) ) & ! [E] : ( m1_subset_1(E,k4_partfun1(B,C)) => ! [F] : ( m1_subset_1(F,k4_partfun1(B,C)) => ( ( r2_hidden(E,D) & r2_hidden(F,D) & r1_tarski(E,F) ) => E = F ) ) ) ) ) )).
fof(fraenkel_a_2_0_hilbasis,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_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_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k14_polynom3(B)))) ) => ( r2_hidden(A,a_2_0_hilbasis(B,C)) <=> ? [D] : ( m2_subset_1(D,u1_struct_0(k14_polynom3(B)),C) & A = D & ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(E,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(F,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( ( E = D & r2_hidden(F,C) ) => r1_xxreal_0(k1_algseq_1(B,E),k1_algseq_1(B,F)) ) ) ) ) ) ) )).
fof(fraenkel_a_2_0_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v7_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_algstr_1(B) & l6_algstr_0(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_ideal_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k8_group_1(B,C,D) ) ) ) )).
fof(fraenkel_a_2_0_int_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) & v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ( r2_hidden(A,a_2_0_int_7(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = D & r2_hidden(D,k22_pre_poly(k8_newton,k13_nat_3(B))) & k1_recdef_1(k12_nat_3(C),D) = k1_recdef_1(k12_nat_3(B),D) ) ) ) )).
fof(fraenkel_a_2_0_integr15,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_integr15(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(k1_seq_2(B),C)) & ~ r1_xxreal_0(k2_xcmplx_0(k1_seq_2(B),C),D) ) ) ) )).
fof(fraenkel_a_2_0_integr1c,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_integr1c(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & r1_xxreal_0(B,D) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_0_integra1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_integra1(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & r1_xxreal_0(B,D) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_0_integra2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(A,a_2_0_integra2(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = k3_xcmplx_0(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_0_jct_misc,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(A,a_2_0_jct_misc(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k9_complex1(k6_xcmplx_0(D,E)) & r2_hidden(D,B) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_0_jgraph_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_jgraph_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) & A = D & ~ r1_xxreal_0(k17_euclid(D),k6_xcmplx_0(k17_euclid(B),C)) & ~ r1_xxreal_0(k2_xcmplx_0(k17_euclid(B),C),k17_euclid(D)) & ~ r1_xxreal_0(k18_euclid(D),k6_xcmplx_0(k18_euclid(B),C)) & ~ r1_xxreal_0(k2_xcmplx_0(k18_euclid(B),C),k18_euclid(D)) ) ) ) )).
fof(fraenkel_a_2_0_jordan10,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & 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)))) ) => ( r2_hidden(A,a_2_0_jordan10(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_topreal1(2,k2_jordan9(C,B),D) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(k2_jordan9(C,B))) ) ) ) )).
fof(fraenkel_a_2_0_jordan12,axiom,( ! [A] : ! [B] : ! [C] : ( ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) & m2_finseq_1(C,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_2_0_jordan12(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_topreal1(2,k4_graph_2(u1_struct_0(k15_euclid(2)),B,C),D) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(k4_graph_2(u1_struct_0(k15_euclid(2)),B,C))) ) ) ) )).
fof(fraenkel_a_2_0_jordan14,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_0_jordan14(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_topreal1(2,k1_jordan13(B,C),D) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(k1_jordan13(B,C))) ) ) ) )).
fof(fraenkel_a_2_0_jordan16,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(C,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_2_0_jordan16(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) & A = D & ( r1_jordan6(B,C,D) | ( r2_hidden(C,B) & D = k18_pscomp_1(B) ) ) ) ) ) )).
fof(fraenkel_a_2_0_jordan2b,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_jordan2b(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(C,D) ) ) ) )).
fof(fraenkel_a_2_0_jordan2c,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) ) => ( r2_hidden(A,a_2_0_jordan2c(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) & A = D & r1_jordan2c(B,C,D) ) ) ) )).
fof(fraenkel_a_2_0_jordan3,axiom,( ! [A] : ! [B] : ! [C] : ( ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) & m1_subset_1(C,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_2_0_jordan3(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = D & r2_hidden(C,k2_topreal1(2,B,D)) ) ) ) )).
fof(fraenkel_a_2_0_jordan4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_0_jordan4(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_topreal1(2,k17_finseq_1(u1_struct_0(k15_euclid(2)),C,B),D) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(k17_finseq_1(u1_struct_0(k15_euclid(2)),C,B))) ) ) ) )).
fof(fraenkel_a_2_0_jordan5a,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k7_metric_1)) & m1_subset_1(C,k1_numbers) ) => ( r2_hidden(A,a_2_0_jordan5a(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k7_metric_1)) & A = D & ~ r1_xxreal_0(C,k3_metric_1(k7_metric_1,B,D)) ) ) ) )).
fof(fraenkel_a_2_0_jordan5b,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & m1_subset_1(C,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_2_0_jordan5b(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) & A = D & r2_jordan3(B,C,B,D) & r2_jordan3(B,C,D,C) ) ) ) )).
fof(fraenkel_a_2_0_jordan5c,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_jordan5c(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & r1_xxreal_0(B,D) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_0_jordan5d,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_0_jordan5d(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = D & r2_hidden(k4_tarski(C,D),k2_matrix_0(k2_goboard2(B))) & ? [E] : ( v7_ordinal1(E) & r2_hidden(E,k4_finseq_1(B)) & k7_partfun1(u1_struct_0(k15_euclid(2)),B,E) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(B),C,D) ) ) ) ) )).
fof(fraenkel_a_2_0_jordan6,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & m1_subset_1(C,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_2_0_jordan6(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) & A = D & k17_euclid(D) = k7_xcmplx_0(k2_xcmplx_0(k17_euclid(B),k17_euclid(C)),2) ) ) ) )).
fof(fraenkel_a_2_0_jordan7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v2_compts_1(B,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))) ) => ( r2_hidden(A,a_2_0_jordan7(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) & A = D & ( r1_jordan6(B,C,D) | ( r2_hidden(C,B) & D = k18_pscomp_1(B) ) ) ) ) ) )).
fof(fraenkel_a_2_0_jordan_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_jordan_a(C,B) ) => ( r2_hidden(A,a_2_0_jordan_a(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = k3_jordan_a(2,k2_jordan_a(B,D,C)) & r2_hidden(D,k4_finseq_1(C)) ) ) ) )).
fof(fraenkel_a_2_0_knaster,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k9_setfam_1(B),k9_setfam_1(B)) & v6_cohsp_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(B),k9_setfam_1(B)))) ) => ( r2_hidden(A,a_2_0_knaster(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = D & r1_tarski(k3_funct_2(k1_zfmisc_1(B),k9_setfam_1(B),C,D),D) ) ) ) )).
fof(fraenkel_a_2_0_lattice4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_lattice4(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) & A = k4_filter_0(B,D,E) & r2_hidden(D,C) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_0_lattice5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) ) => ( r2_hidden(A,a_2_0_lattice5(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,B) & m1_subset_1(E,C) & A = k2_zfmisc_1(D,E) & r2_hidden(D,B) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_0_lattice6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_lattice6(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k4_lattice3(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_0_lattice8,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_lattice8(C,u1_struct_0(B),B,k16_lattice5(B)) ) => ( r2_hidden(A,a_2_0_lattice8(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = k1_xtuple_0(k1_funct_1(C,D)) ) ) ) )).
fof(fraenkel_a_2_0_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v5_relat_1(C,k1_rcomp_1(k5_numbers,1)) & 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))) ) => ( r2_hidden(A,a_2_0_lfuzzy_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = k4_lfuzzy_1(B,C,D) & ~ r1_xxreal_0(D,k5_numbers) ) ) ) )).
fof(fraenkel_a_2_0_limfunc2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_limfunc2(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(B,C)) & ~ r1_xxreal_0(B,D) ) ) ) )).
fof(fraenkel_a_2_0_limfunc3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_limfunc3(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(C,B)) & ~ r1_xxreal_0(k2_xcmplx_0(C,B),D) ) ) ) )).
fof(fraenkel_a_2_0_limfunc4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_limfunc4(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(B,C)) & ~ r1_xxreal_0(B,D) ) ) ) )).
fof(fraenkel_a_2_0_lmod_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v6_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) & v1_vectsp_2(B) & l6_algstr_0(B) & ~ 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) ) => ( r2_hidden(A,a_2_0_lmod_5(B,C)) <=> ? [D] : ( m2_vectsp_6(D,B,C,k1_subset_1(u1_struct_0(C))) & A = k4_vectsp_6(B,C,D) ) ) ) )).
fof(fraenkel_a_2_0_lopban_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & v13_vectsp_1(C,B,B) & v1_lopban_1(C,B,B) & v2_lopban_1(C,B,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) ) => ( r2_hidden(A,a_2_0_lopban_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k2_normsp_0(B,k3_funct_2(u1_struct_0(B),u1_struct_0(B),C,D)) & r1_xxreal_0(k2_normsp_0(B,D),1) ) ) ) )).
fof(fraenkel_a_2_0_lopclset,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v7_struct_0(B) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_lopclset(B,C)) <=> ? [D] : ( ~ v1_xboole_0(D) & v19_lattices(D,B) & v20_lattices(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & v1_filter_0(D,B) & r2_hidden(C,D) ) ) ) )).
fof(fraenkel_a_2_0_ltlaxio4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) & m3_ltlaxio4(C,B) ) => ( r2_hidden(A,a_2_0_ltlaxio4(B,C)) <=> ? [D] : ( m1_trees_1(D,k9_xtuple_0(C)) & A = k3_trees_2(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)),C,D) & D != k1_xboole_0 ) ) ) )).
fof(fraenkel_a_2_0_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_mathmorp(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k4_algstr_0(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_0_matrix13,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_0_matrix13(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = D & k5_card_1(D) = C ) ) ) )).
fof(fraenkel_a_2_0_matrix14,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) & m2_finseq_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_matrix14(B,C)) <=> ? [D] : ( m2_finseq_2(D,u1_struct_0(B),k3_finseq_2(u1_struct_0(B))) & A = D & k3_finseq_1(D) = k3_finseq_1(C) ) ) ) )).
fof(fraenkel_a_2_0_matrix15,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & m1_subset_1(C,k4_ordinal1) ) => ( r2_hidden(A,a_2_0_matrix15(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_nat_1(D,C) & r2_hidden(D,k4_finseq_1(k1_finseq_2(B))) ) ) ) )).
fof(fraenkel_a_2_0_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(C,k3_finseq_2(B)) ) => ( r2_hidden(A,a_2_0_matrix_0(B,C)) <=> ? [D] : ( m2_finseq_2(D,B,k3_finseq_2(B)) & A = k10_xtuple_0(D) & r2_hidden(D,k10_xtuple_0(C)) ) ) ) )).
fof(fraenkel_a_2_0_matrixr1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) & m2_finseq_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_matrixr1(B,C)) <=> ? [D] : ( m2_finseq_2(D,u1_struct_0(B),k3_finseq_2(u1_struct_0(B))) & A = D & k3_finseq_1(D) = k3_finseq_1(C) ) ) ) )).
fof(fraenkel_a_2_0_matroid0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & ~ 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) ) => ( r2_hidden(A,a_2_0_matroid0(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) & A = D & v1_vectsp_7(D,B,C) ) ) ) )).
fof(fraenkel_a_2_0_matrtop1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_finseq_1(B) & m1_subset_1(C,k4_ordinal1) ) => ( r2_hidden(A,a_2_0_matrtop1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_xcmplx_0(D,C) & r2_hidden(D,k9_xtuple_0(B)) ) ) ) )).
fof(fraenkel_a_2_0_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) ) => ( r2_hidden(A,a_2_0_mcart_1(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = k2_xtuple_0(D) & k1_xtuple_0(D) = C ) ) ) )).
fof(fraenkel_a_2_0_measure6,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_measure6(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = k2_xcmplx_0(C,D) & r2_hidden(D,B) ) ) ) )).
fof(fraenkel_a_2_0_member_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_membered(B) & v2_membered(C) ) => ( r2_hidden(A,a_2_0_member_1(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k6_numbers) & m1_subset_1(E,k6_numbers) & A = k1_xxreal_3(D,E) & r2_hidden(D,B) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_0_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_setfam_1(B) & v2_memstr_0(C,B) & l1_memstr_0(C,B) ) => ( r2_hidden(A,a_2_0_memstr_0(B,C)) <=> ? [D] : ( m1_subset_1(D,k8_card_3(k2_memstr_0(B,C))) & A = D & v1_finset_1(D) ) ) ) )).
fof(fraenkel_a_2_0_mesfun10,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) & m1_subset_1(C,k4_ordinal1) ) => ( r2_hidden(A,a_2_0_mesfun10(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k12_supinf_2(B,D) & r1_xxreal_0(C,D) ) ) ) )).
fof(fraenkel_a_2_0_metric_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_metric_1(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_metric_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_metric_2(B,C,D) ) ) ) )).
fof(fraenkel_a_2_0_mfold_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) ) => ( r2_hidden(A,a_2_0_mfold_2(B,C)) <=> ? [D] : ( m2_rlvect_2(D,k15_euclid(B),C) & A = k6_rlvect_2(k15_euclid(B),D) ) ) ) )).
fof(fraenkel_a_2_0_midsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_1(B) & m1_subset_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_midsp_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) & A = D & r2_midsp_1(B,D,C) ) ) ) )).
fof(fraenkel_a_2_0_mmlquer2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v1_relat_1(C) ) => ( r2_hidden(A,a_2_0_mmlquer2(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_relat_1(C)) & m1_subset_1(E,k1_relat_1(C)) & A = k4_tarski(D,E) & ~ r1_mmlquery(E,D,B) & r1_mmlquery(D,E,C) ) ) ) )).
fof(fraenkel_a_2_0_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( r2_hidden(A,a_2_0_mmlquery(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = D & r2_hidden(D,k4_finseq_1(B)) & r2_hidden(C,k1_funct_1(B,D)) ) ) ) )).
fof(fraenkel_a_2_0_mod_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(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) ) => ( r2_hidden(A,a_2_0_mod_3(B,C)) <=> ? [D] : ( m2_vectsp_6(D,B,C,k1_subset_1(u1_struct_0(C))) & A = k4_vectsp_6(B,C,D) ) ) ) )).
fof(fraenkel_a_2_0_modal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) & m1_trees_1(C,B) ) => ( r2_hidden(A,a_2_0_modal_1(B,C)) <=> ? [D] : ( m2_finseq_2(D,k4_ordinal1,k3_finseq_2(k4_ordinal1)) & A = k8_finseq_1(k4_ordinal1,C,D) & r2_hidden(k8_finseq_1(k4_ordinal1,C,D),B) ) ) ) )).
fof(fraenkel_a_2_0_modcat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(C) & v1_classes2(C) ) => ( r2_hidden(A,a_2_0_modcat_1(B,C)) <=> ? [D] : ? [E] : ( m2_grcat_1(D,k17_grcat_1(C)) & m2_funct_2(E,k2_zfmisc_1(u1_struct_0(B),k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0),k9_funct_2(k2_zfmisc_1(u1_struct_0(B),k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0))) & A = k4_tarski(D,E) ) ) ) )).
fof(fraenkel_a_2_0_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,B,k6_margrel1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_margrel1))) ) => ( r2_hidden(A,a_2_0_modelc_1(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = D & k3_funct_2(B,k6_margrel1,C,D) = k8_margrel1 ) ) ) )).
fof(fraenkel_a_2_0_modelc_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_modelc_2(B) & v5_modelc_3(B) & m2_finseq_1(B,k4_ordinal1) & v1_modelc_3(C,B) & l1_modelc_3(C,B) ) => ( r2_hidden(A,a_2_0_modelc_3(B,C)) <=> ? [D] : ( v1_modelc_2(D) & m2_finseq_1(D,k4_ordinal1) & A = D & v2_modelc_2(D) & r2_hidden(D,u1_modelc_3(B,C)) ) ) ) )).
fof(fraenkel_a_2_0_moebius1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & v1_int_2(C) ) => ( r2_hidden(A,a_2_0_moebius1(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = D & ~ r1_xxreal_0(D,k5_numbers) & r1_nat_d(D,B) & r1_nat_d(C,D) ) ) ) )).
fof(fraenkel_a_2_0_msafree,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) => ( r2_hidden(A,a_2_0_msafree(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k5_msafree(B,C))) & A = k2_trees_4(u1_struct_0(k5_msafree(B,C)),D) & r2_hidden(D,k6_dtconstr(k5_msafree(B,C))) ) ) ) )).
fof(fraenkel_a_2_0_msafree3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) ) => ( r2_hidden(A,a_2_0_msafree3(B,C)) <=> ? [D] : ( m1_subset_1(D,k10_xtuple_0(B)) & A = k1_xtuple_0(D) & k2_xtuple_0(D) = C ) ) ) )).
fof(fraenkel_a_2_0_msscyc_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v5_msafree2(B) & l1_msualg_1(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_msscyc_2(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_funct_1(u3_msualg_1(B,k5_msafree2(B,o_1_0_msscyc_2(B))),C)) & A = k5_circuit1(B,o_1_0_msscyc_2(B),C,D) ) ) ) )).
fof(fraenkel_a_2_0_mycielsk,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & m1_mycielsk(C,B) ) => ( r2_hidden(A,a_2_0_mycielsk(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k4_ordinal1) & m1_subset_1(E,k4_ordinal1) & A = k4_tarski(D,k2_xcmplx_0(E,B)) & r2_hidden(k4_tarski(D,E),u1_orders_2(C)) ) ) ) )).
fof(fraenkel_a_2_0_nat_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_0_nat_5(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = k1_newton(C,D) & r1_xxreal_0(D,B) ) ) ) )).
fof(fraenkel_a_2_0_ndiff_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m2_finseq_2(B,k1_numbers,k1_euclid(1)) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_ndiff_4(B,C)) <=> ? [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(1)) & A = D & ~ r1_xxreal_0(C,k12_euclid(k8_euclid(1,D,B))) ) ) ) )).
fof(fraenkel_a_2_0_normform,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k7_normform(B))) => ( r2_hidden(A,a_2_0_normform(B,C)) <=> ? [D] : ( m2_subset_1(D,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B)) & A = D & ! [E] : ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B)) => ( ( r2_hidden(E,C) & r1_normform(k5_finsub_1(B),k5_finsub_1(B),E,D) ) <=> E = D ) ) ) ) ) )).
fof(fraenkel_a_2_0_openlatt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v11_lattices(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_openlatt(B,C)) <=> ? [D] : ( ~ v1_xboole_0(D) & v19_lattices(D,B) & v20_lattices(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & r2_hidden(D,k7_openlatt(B)) & r2_hidden(C,D) ) ) ) )).
fof(fraenkel_a_2_0_orders_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_orders_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r2_hidden(E,C) => r2_orders_2(B,E,D) ) ) ) ) ) )).
fof(fraenkel_a_2_0_ordinal6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v3_ordinal6(B) & v3_ordinal1(C) ) => ( r2_hidden(A,a_2_0_ordinal6(B,C)) <=> ? [D] : ( m1_subset_1(D,k9_xtuple_0(B)) & A = k1_funct_1(k1_funct_1(B,D),C) & r2_hidden(D,k9_xtuple_0(B)) ) ) ) )).
fof(fraenkel_a_2_0_osafree,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v4_osalg_1(B) & v5_osalg_1(B) & l3_osalg_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)) ) => ( r2_hidden(A,a_2_0_osafree(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k2_osafree(B,C))) & A = D & ? [E] : ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) & r1_lang1(k2_osafree(B,C),D,E) ) ) ) ) )).
fof(fraenkel_a_2_0_osalg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v4_osalg_1(B) & v5_osalg_1(B) & l3_osalg_1(B) & v12_osalg_1(C,B) & l3_msualg_1(C,B) ) => ( r2_hidden(A,a_2_0_osalg_2(B,C)) <=> ? [D] : ( m1_subset_1(D,k6_msualg_2(B,C)) & A = D & v1_relat_1(D) & v4_relat_1(D,u1_struct_0(B)) & v1_funct_1(D) & v1_partfun1(D,u1_struct_0(B)) & v11_osalg_1(D,B) ) ) ) )).
fof(fraenkel_a_2_0_pdiff_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k4_real_ns1(1))) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_pdiff_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k4_real_ns1(1))) & A = D & ~ r1_xxreal_0(C,k2_normsp_0(k4_real_ns1(1),k5_algstr_0(k4_real_ns1(1),D,B))) ) ) ) )).
fof(fraenkel_a_2_0_pdiff_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & m1_subset_1(C,u1_struct_0(k4_real_ns1(1))) ) => ( r2_hidden(A,a_2_0_pdiff_7(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k4_real_ns1(1))) & A = D & ~ r1_xxreal_0(B,k2_normsp_0(k4_real_ns1(1),k5_algstr_0(k4_real_ns1(1),D,C))) ) ) ) )).
fof(fraenkel_a_2_0_petri,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_petri(B) & v3_petri(B) & l1_petri(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_petri(B,C)) <=> ? [D] : ( m1_subset_1(D,u4_struct_0(B)) & A = D & ? [E] : ( m1_petri(E,u4_struct_0(B),u1_struct_0(B),u2_petri(B)) & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r2_hidden(F,C) & E = k1_domain_1(u4_struct_0(B),u1_struct_0(B),D,F) ) ) ) ) ) )).
fof(fraenkel_a_2_0_petri_2,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,a_2_0_petri_2(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(C,B))) & A = D & m1_petri_2(D,B,C) ) ) ) )).
fof(fraenkel_a_2_0_pnproc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(A,a_2_0_pnproc_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_nat_1(D,k3_finseq_1(B)) & r2_hidden(D,k4_finseq_1(C)) ) ) ) )).
fof(fraenkel_a_2_0_poset_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(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) ) => ( r2_hidden(A,a_2_0_poset_1(B,C)) <=> ? [D] : ( m2_funct_2(D,u1_struct_0(B),u1_struct_0(C),k9_funct_2(u1_struct_0(B),u1_struct_0(C))) & A = D & ? [E] : ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & v2_poset_1(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(B),u1_struct_0(C),E,D) ) ) ) ) )).
fof(fraenkel_a_2_0_projred2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v6_incsp_1(B) & v1_incproj(B) & v2_incproj(B) & v3_incproj(B) & v4_incproj(B) & l1_incsp_1(B) & m1_subset_1(C,u2_incsp_1(B)) ) => ( r2_hidden(A,a_2_0_projred2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_incsp_1(B)) & A = D & r1_incsp_1(B,D,C) ) ) ) )).
fof(fraenkel_a_2_0_pua2mss1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & m1_eqrel_1(C,B) ) => ( r2_hidden(A,a_2_0_pua2mss1(B,C)) <=> ? [D] : ( m2_finseq_2(D,C,k3_finseq_2(C)) & A = k4_card_3(D) ) ) ) )).
fof(fraenkel_a_2_0_qc_lang1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_0_qc_lang1(B,C)) <=> ? [D] : ( m1_subset_1(D,k6_qc_lang1(B)) & A = D & k7_qc_lang1(B,D) = C ) ) ) )).
fof(fraenkel_a_2_0_qc_lang3,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(B) & m1_subset_1(C,k6_qc_lang1(B)) ) => ( r2_hidden(A,a_2_0_qc_lang3(B,C)) <=> ? [D] : ( m1_subset_1(D,k6_qc_lang1(B)) & A = D & k7_qc_lang1(B,D) = k7_qc_lang1(B,C) ) ) ) )).
fof(fraenkel_a_2_0_qc_lang4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(B) & m1_subset_1(C,k9_qc_lang1(B)) ) => ( r2_hidden(A,a_2_0_qc_lang4(B,C)) <=> ? [D] : ( m1_subset_1(D,k9_qc_lang1(B)) & A = D & r1_qc_lang2(B,D,C) ) ) ) )).
fof(fraenkel_a_2_0_qc_trans,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(B) & v1_qc_trans(C,B) & m1_qc_lang1(C) ) => ( r2_hidden(A,a_2_0_qc_trans(B,C)) <=> ? [D] : ? [E] : ( v7_ordinal1(D) & m1_subset_1(E,k1_qc_lang1(C)) & A = k4_tarski(D,E) & r1_xxreal_0(7,D) ) ) ) )).
fof(fraenkel_a_2_0_quantal1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v1_group_1(B) & v3_group_1(B) & v10_lattices(B) & v4_lattice3(B) & v7_quantal1(B) & v8_quantal1(B) & v20_quantal1(B) & v21_quantal1(B) & l3_quantal1(B) ) => ( r2_hidden(A,a_2_0_quantal1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k5_quantal1(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_0_random_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) => ( r2_hidden(A,a_2_0_random_2(B,C)) <=> ? [D] : ( m1_random_1(D,B,C) & A = D ) ) ) )).
fof(fraenkel_a_2_0_random_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,a_2_0_random_3(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = k8_relat_1(C,D) ) ) ) )).
fof(fraenkel_a_2_0_rcomp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_rcomp_1(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & r1_xxreal_0(B,D) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_0_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_2_0_relset_2(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = k1_tarski(D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_0_revrot_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & v1_finseq_6(C,u1_struct_0(k15_euclid(2))) & m2_finseq_1(C,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_2_0_revrot_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_topreal1(2,k1_finseq_6(u1_struct_0(k15_euclid(2)),C,B),D) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(C)) ) ) ) )).
fof(fraenkel_a_2_0_rfunct_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_rfunct_4(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & r1_xxreal_0(B,D) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_0_rinfsup1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_0_rinfsup1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_funct_1(B,D) & r1_xxreal_0(C,D) ) ) ) )).
fof(fraenkel_a_2_0_rinfsup2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_0_rinfsup2(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k12_supinf_2(B,D) & r1_xxreal_0(C,D) ) ) ) )).
fof(fraenkel_a_2_0_rlaffin1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_rlvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_rlaffin1(B,C)) <=> ? [D] : ( v2_rusub_4(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & r1_tarski(C,D) ) ) ) )).
fof(fraenkel_a_2_0_rlaffin2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_rlaffin2(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k1_rlaffin2(B,D) & r1_tarski(D,C) ) ) ) )).
fof(fraenkel_a_2_0_rlaffin3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_0_rlaffin3(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(C))) & A = k7_finseq_1(D,k5_finseq_2(k4_ordinal1,B,k5_numbers)) ) ) ) )).
fof(fraenkel_a_2_0_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v6_rltopsp1(B) & v7_rltopsp1(B) & l1_rltopsp1(B) & m1_yellow13(C,B,k4_struct_0(B)) ) => ( r2_hidden(A,a_2_0_rltopsp1(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k5_rusub_4(B,E,D) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_0_rlvect_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) & m2_funct_2(C,u1_struct_0(B),k1_numbers,k9_funct_2(u1_struct_0(B),k1_numbers)) ) => ( r2_hidden(A,a_2_0_rlvect_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & k3_funct_2(u1_struct_0(B),k1_numbers,C,D) != k5_numbers ) ) ) )).
fof(fraenkel_a_2_0_rlvect_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_rlvect_3(B,C)) <=> ? [D] : ( m2_rlvect_2(D,B,C) & A = k6_rlvect_2(B,D) ) ) ) )).
fof(fraenkel_a_2_0_rlvect_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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_rlvect_2(C,B) ) => ( r2_hidden(A,a_2_0_rlvect_5(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & k3_funct_2(u1_struct_0(B),k1_numbers,C,D) != k5_numbers ) ) ) )).
fof(fraenkel_a_2_0_rlvect_x,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_rlvect_x(B,C)) <=> ? [D] : ( m2_rlvect_2(D,B,C) & A = k6_rlvect_2(B,D) & r1_tarski(k2_relset_1(k1_numbers,D),k4_numbers) ) ) ) )).
fof(fraenkel_a_2_0_rmod_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & ~ 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) ) => ( r2_hidden(A,a_2_0_rmod_4(B,C)) <=> ? [D] : ( m2_rmod_4(D,B,C,k1_subset_1(u1_struct_0(C))) & A = k5_rmod_4(B,C,D) ) ) ) )).
fof(fraenkel_a_2_0_roughs_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_roughs_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_tarski(k6_eqrel_1(u1_struct_0(B),u1_struct_0(B),u1_orders_2(B),D),C) ) ) ) )).
fof(fraenkel_a_2_0_rusub_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) ) => ( r2_hidden(A,a_2_0_rusub_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k3_rlvect_1(B,k4_struct_0(B),D) & r1_struct_0(C,D) ) ) ) )).
fof(fraenkel_a_2_0_rusub_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_rusub_3(B,C)) <=> ? [D] : ( m2_rlvect_2(D,B,C) & A = k6_rlvect_2(B,D) ) ) ) )).
fof(fraenkel_a_2_0_rusub_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C) & v2_rusub_4(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_rusub_5(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k1_rusub_5(B,C,k6_domain_1(u1_struct_0(B),D)) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_0_scmfsa8c,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ( r2_hidden(A,a_2_0_scmfsa8c(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_nat_1(D,k5_card_1(B)) & r2_hidden(D,k2_afinsq_1(C)) ) ) ) )).
fof(fraenkel_a_2_0_scmring3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_subset_1(C,u1_compos_1(k1_scmring2(B))) ) => ( r2_hidden(A,a_2_0_scmring3(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_amistd_1(k7_card_1(2),k1_scmring2(B),D,C) ) ) ) )).
fof(fraenkel_a_2_0_seq_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(A,a_2_0_seq_4(B,C)) <=> ? [D] : ? [E] : ( v1_xcmplx_0(D) & v1_xcmplx_0(E) & A = k2_xcmplx_0(D,E) & r2_hidden(D,B) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_0_setlim_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ( r2_hidden(A,a_2_0_setlim_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_funct_1(C,D) & r1_xxreal_0(k5_numbers,D) ) ) ) )).
fof(fraenkel_a_2_0_sf_mastr,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_0_sf_mastr(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_xcmplx_0(D,C) & r2_hidden(D,k1_relset_1(k4_ordinal1,B)) ) ) ) )).
fof(fraenkel_a_2_0_sfmastr1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ( r2_hidden(A,a_2_0_sfmastr1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_nat_1(D,k5_card_1(B)) & r2_hidden(D,k9_xtuple_0(C)) ) ) ) )).
fof(fraenkel_a_2_0_sgraph1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_0_sgraph1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = D & r1_xxreal_0(B,D) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_0_simplex1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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) & v6_ordinal1(C) & v1_finset_1(C) & v5_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) => ( r2_hidden(A,a_2_0_simplex1(B,C)) <=> ? [D] : ( m3_simplex0(D,k4_simplex1(B,k5_simplex0(u1_struct_0(B),k6_domain_1(k1_zfmisc_1(u1_struct_0(B)),k5_setfam_1(u1_struct_0(B),C)))),k5_card_1(C)) & A = D & r1_tarski(k7_relset_1(k1_orders_1(u1_struct_0(B)),u1_struct_0(B),k2_rlaffin2(B),C),D) ) ) ) )).
fof(fraenkel_a_2_0_sppol_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_0_sppol_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_topreal1(2,B,D) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(B)) & D != C & D != k1_nat_1(C,1) ) ) ) )).
fof(fraenkel_a_2_0_stacks_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & m1_subset_1(C,u4_struct_0(B)) ) => ( r2_hidden(A,a_2_0_stacks_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u4_struct_0(B)) & A = D & r1_rewrite1(k12_stacks_1(B),C,D) ) ) ) )).
fof(fraenkel_a_2_0_stirl2_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_0_stirl2_1(B,C)) <=> ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k7_card_1(B),k7_card_1(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(B),k7_card_1(C)))) & A = D & v2_funct_2(D,k7_card_1(C)) & v1_stirl2_1(D,B,C) ) ) ) )).
fof(fraenkel_a_2_0_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(B) & m2_finseq_1(C,k2_qc_lang1(B)) ) => ( r2_hidden(A,a_2_0_sublemma(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_funct_1(C,D) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(C)) & r2_hidden(k1_funct_1(C,D),k3_qc_lang1(B)) ) ) ) )).
fof(fraenkel_a_2_0_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(A,a_2_0_substlat(B,C)) <=> ? [D] : ( m1_subset_1(D,k5_finsub_1(k4_partfun1(B,C))) & A = D & ! [E] : ( r2_hidden(E,D) => v1_finset_1(E) ) & ! [E] : ( m1_subset_1(E,k4_partfun1(B,C)) => ! [F] : ( m1_subset_1(F,k4_partfun1(B,C)) => ( ( r2_hidden(E,D) & r2_hidden(F,D) & r1_tarski(E,F) ) => E = F ) ) ) ) ) )).
fof(fraenkel_a_2_0_substut1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(B) & m2_finseq_1(C,k2_qc_lang1(B)) ) => ( r2_hidden(A,a_2_0_substut1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_funct_1(C,D) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(C)) & r2_hidden(k1_funct_1(C,D),k3_qc_lang1(B)) ) ) ) )).
fof(fraenkel_a_2_0_substut2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_0_substut2(B,C)) <=> ? [D] : ( m1_subset_1(D,k6_qc_lang1(B)) & A = D & k7_qc_lang1(B,D) = C ) ) ) )).
fof(fraenkel_a_2_0_t_1topsp,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_t_1topsp(B,C)) <=> ? [D] : ( m1_eqrel_1(D,u1_struct_0(B)) & A = k11_eqrel_1(u1_struct_0(B),C,D) & r2_hidden(D,k1_t_1topsp(B)) ) ) ) )).
fof(fraenkel_a_2_0_taylor_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_taylor_1(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(C,D) ) ) ) )).
fof(fraenkel_a_2_0_tdlat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) => ( r2_hidden(A,a_2_0_tdlat_2(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & D = k2_pre_topc(B,E) & r2_hidden(E,C) ) ) ) ) )).
fof(fraenkel_a_2_0_tdlat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_tdlat_3(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,C) & D = k1_tarski(E) ) ) ) ) )).
fof(fraenkel_a_2_0_tex_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,B) => ( r2_hidden(A,a_2_0_tex_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = D & r2_hidden(C,D) & D != B ) ) ) )).
fof(fraenkel_a_2_0_tex_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v3_tdlat_3(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_tex_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k2_pre_topc(B,k6_domain_1(u1_struct_0(B),D)) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_0_tex_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_tex_4(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & v4_pre_topc(D,B) & r1_tarski(C,D) ) ) ) )).
fof(fraenkel_a_2_0_tmap_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_tmap_1(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k4_subset_1(u1_struct_0(B),D,k9_subset_1(u1_struct_0(B),E,C)) & r2_hidden(D,u1_pre_topc(B)) & r2_hidden(E,u1_pre_topc(B)) ) ) ) )).
fof(fraenkel_a_2_0_topalg_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_topalg_2(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(1,D),B),k3_xcmplx_0(D,C)) & r1_xxreal_0(k5_numbers,D) & r1_xxreal_0(D,1) ) ) ) )).
fof(fraenkel_a_2_0_topdim_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_topdim_2(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = k9_finseq_1(D) & r1_xxreal_0(k3_xxreal_3(C,B),D) & r1_xxreal_0(D,k1_xxreal_3(C,B)) ) ) ) )).
fof(fraenkel_a_2_0_topgen_2,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(A,a_2_0_topgen_2(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = D & ~ r2_hidden(C,D) ) ) )).
fof(fraenkel_a_2_0_topgen_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_topgen_4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r2_hidden(D,k2_pre_topc(B,k7_subset_1(u1_struct_0(B),C,k6_domain_1(u1_struct_0(B),D)))) ) ) ) )).
fof(fraenkel_a_2_0_topgen_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_topgen_5(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = k9_subset_1(u1_struct_0(k15_euclid(2)),k1_topreal9(2,k19_euclid(B,C),D),k2_topgen_5) & ~ r1_xxreal_0(D,k5_numbers) ) ) ) )).
fof(fraenkel_a_2_0_topreal1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & m2_finseq_1(C,u1_struct_0(k15_euclid(B))) ) => ( r2_hidden(A,a_2_0_topreal1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_topreal1(B,C,D) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(C)) ) ) ) )).
fof(fraenkel_a_2_0_topreal4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(C,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_2_0_topreal4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) & A = D & D != C & r2_hidden(D,B) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ~ ( r1_topreal4(E,C,D) & r1_tarski(E,B) ) ) ) ) ) )).
fof(fraenkel_a_2_0_topreal6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_topreal6(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & r1_xxreal_0(B,D) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_0_topreal7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) => ( r2_hidden(A,a_2_0_topreal7(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k3_pcomps_1(B),k3_pcomps_1(C)))))) & A = k3_tarski(D) & r1_tarski(D,a_2_1_topreal7(B,C)) ) ) ) )).
fof(fraenkel_a_2_0_toprealb,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_toprealb(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_numbers) & A = k2_rcomp_1(k2_xcmplx_0(B,D),k2_xcmplx_0(C,D)) ) ) ) )).
fof(fraenkel_a_2_0_treal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_treal_1(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & r1_xxreal_0(B,D) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_0_trees_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m2_finseq_1(B,k4_ordinal1) & ~ v1_xboole_0(C) & v1_trees_1(C) ) => ( r2_hidden(A,a_2_0_trees_1(B,C)) <=> ? [D] : ( m1_trees_1(D,C) & A = D & ~ r2_xboole_0(B,D) ) ) ) )).
fof(fraenkel_a_2_0_trees_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_0_trees_2(B,C)) <=> ? [D] : ( m1_trees_1(D,B) & A = D & k3_finseq_1(D) = C ) ) ) )).
fof(fraenkel_a_2_0_trees_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ( r2_hidden(A,a_2_0_trees_9(B,C)) <=> ? [D] : ( 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) ) ) ) ) )).
fof(fraenkel_a_2_0_trees_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) & m4_trees_1(C,B) ) => ( r2_hidden(A,a_2_0_trees_a(B,C)) <=> ? [D] : ( m1_trees_1(D,B) & A = D & ! [E] : ( m2_finseq_1(E,k4_ordinal1) => ~ ( r2_hidden(E,C) & r2_xboole_0(E,D) ) ) ) ) ) )).
fof(fraenkel_a_2_0_tsp_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_tsp_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k4_tex_4(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_0_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v1_funct_1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_0_valued_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_xcmplx_0(D,C) & r2_hidden(D,k9_xtuple_0(B)) ) ) ) )).
fof(fraenkel_a_2_0_vectsp_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & ~ 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) ) => ( r2_hidden(A,a_2_0_vectsp_7(B,C)) <=> ? [D] : ( m2_vectsp_6(D,B,C,k1_subset_1(u1_struct_0(C))) & A = k4_vectsp_6(B,C,D) ) ) ) )).
fof(fraenkel_a_2_0_waybel11,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_0_waybel11(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k2_yellow_0(B,a_3_0_waybel11(B,C,D)) ) ) ) )).
fof(fraenkel_a_2_0_waybel12,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_yellow_0(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_waybel12(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_tarski(k4_yellow_4(B,C,k6_domain_1(u1_struct_0(B),D)),C) ) ) ) )).
fof(fraenkel_a_2_0_waybel13,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_waybel13(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_orders_2(B,D,C) & v1_waybel_3(D,B) ) ) ) )).
fof(fraenkel_a_2_0_waybel14,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v3_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_waybel14(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k5_waybel_0(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_0_waybel15,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k2_yellow_1(B))) => ( r2_hidden(A,a_2_0_waybel15(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = D & r1_tarski(C,D) ) ) ) )).
fof(fraenkel_a_2_0_waybel16,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_waybel16(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r2_hidden(D,k6_waybel_0(B,C)) & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,u1_struct_0(k1_waybel_8(B))) & r3_waybel_4(B,k6_subset_1(u1_struct_0(B),k6_waybel_0(B,E)),D) ) ) ) ) )).
fof(fraenkel_a_2_0_waybel21,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_0_waybel21(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k2_yellow_0(B,a_3_0_waybel21(B,C,D)) ) ) ) )).
fof(fraenkel_a_2_0_waybel22,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(C) & v2_waybel_0(C,k2_yellow_1(B)) & v13_waybel_0(C,k2_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(B)))) ) => ( r2_hidden(A,a_2_0_waybel22(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = k2_yellow_0(k1_yellow_1(k8_waybel_0(k2_yellow_1(B))),a_2_1_waybel22(B,D)) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_0_waybel23,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & v3_waybel_3(B) & l1_orders_2(B) & v6_waybel23(C,B) & m1_waybel23(C,B) ) => ( r2_hidden(A,a_2_0_waybel23(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k5_yellow_0(B,C))) & A = k5_waybel_0(k5_yellow_0(B,C),D) ) ) ) )).
fof(fraenkel_a_2_0_waybel28,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_0_waybel28(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k2_yellow_0(B,a_3_0_waybel28(B,C,D)) ) ) ) )).
fof(fraenkel_a_2_0_waybel29,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & v2_pre_topc(C) & l1_pre_topc(C) ) => ( r2_hidden(A,a_2_0_waybel29(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k2_borsuk_1(B,C))))) & A = k5_setfam_1(u1_struct_0(k2_borsuk_1(B,C)),D) & r1_tarski(D,a_2_1_waybel29(B,C)) ) ) ) )).
fof(fraenkel_a_2_0_waybel30,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ( r2_hidden(A,a_2_0_waybel30(B,C)) <=> ? [D] : ( m1_subset_1(D,C) & A = k3_xboole_0(B,D) ) ) ) )).
fof(fraenkel_a_2_0_waybel31,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & v3_waybel_3(B) & l1_orders_2(B) & v6_waybel23(C,B) & m1_waybel23(C,B) ) => ( r2_hidden(A,a_2_0_waybel31(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,u1_struct_0(B)) & v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k2_waybel31(B,E,D) & r2_hidden(D,C) & r1_tarski(E,C) ) ) ) )).
fof(fraenkel_a_2_0_waybel32,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & v25_waybel_0(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_0_waybel32(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k2_yellow_0(B,a_3_0_waybel32(B,C,D)) ) ) ) )).
fof(fraenkel_a_2_0_waybel33,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_0_waybel33(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k1_waybel_9(B,k5_waybel_9(B,C,D)) ) ) ) )).
fof(fraenkel_a_2_0_waybel_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_waybel_0(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r1_orders_2(B,D,E) & r2_hidden(E,C) ) ) ) ) )).
fof(fraenkel_a_2_0_waybel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) & 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(A,a_2_0_waybel_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r3_orders_2(B,D,k3_funct_2(u1_struct_0(B),u1_struct_0(B),C,D)) ) ) ) )).
fof(fraenkel_a_2_0_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & v2_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & v1_waybel_0(C,k3_yellow_3(B,B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) ) => ( r2_hidden(A,a_2_0_waybel_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k1_yellow_0(B,k4_yellow_4(B,k6_domain_1(u1_struct_0(B),D),k5_yellow_3(B,B,C))) & r2_hidden(D,k4_yellow_3(B,B,C)) ) ) ) )).
fof(fraenkel_a_2_0_waybel_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_waybel_3(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_waybel_3(B,D,C) ) ) ) )).
fof(fraenkel_a_2_0_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) => ( r2_hidden(A,a_2_0_waybel_4(B,C)) <=> ? [D] : ( ~ 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))) & A = D & r3_orders_2(B,C,k1_yellow_0(B,D)) ) ) ) )).
fof(fraenkel_a_2_0_waybel_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & v3_waybel_3(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_waybel_5(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_waybel_3(B,D,C) ) ) ) )).
fof(fraenkel_a_2_0_waybel_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & v13_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_0_waybel_6(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k2_waybel_3(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_0_waybel_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_waybel_8(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_orders_2(B,D,C) & v1_waybel_3(D,B) ) ) ) )).
fof(fraenkel_a_2_0_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_waybel_9(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & k12_lattice3(B,D,C) = C ) ) ) )).
fof(fraenkel_a_2_0_weddwitt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_weddwitt(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & k6_algstr_0(B,C,D) = k6_algstr_0(B,D,C) ) ) ) )).
fof(fraenkel_a_2_0_weierstr,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k7_metric_1)) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_0_weierstr(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k7_metric_1)) & A = D & ~ r1_xxreal_0(C,k3_metric_1(k7_metric_1,B,D)) ) ) ) )).
fof(fraenkel_a_2_0_xxreal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xxreal_0(B) & v1_xxreal_0(C) ) => ( r2_hidden(A,a_2_0_xxreal_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k6_numbers) & A = D & r1_xxreal_0(B,D) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_0_yellow11,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_yellow11(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r3_orders_2(B,D,E) & r2_hidden(E,k6_domain_1(u1_struct_0(B),C)) ) ) ) ) )).
fof(fraenkel_a_2_0_yellow13,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_yellow13(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & r2_hidden(C,k1_tops_1(B,D)) ) ) ) )).
fof(fraenkel_a_2_0_yellow15,axiom,( ! [A] : ! [B] : ! [C] : ( m2_finseq_1(C,k9_setfam_1(B)) => ( r2_hidden(A,a_2_0_yellow15(B,C)) <=> ? [D] : ( m2_finseq_1(D,k6_margrel1) & A = k8_setfam_1(B,k2_relset_1(k9_setfam_1(B),k1_yellow15(B,C,D))) & k3_finseq_1(D) = k3_finseq_1(C) ) ) ) )).
fof(fraenkel_a_2_0_yellow19,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_yellow19(B,C)) <=> ? [D] : ( m1_connsp_2(D,B,C) & A = D ) ) ) )).
fof(fraenkel_a_2_0_yellow_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & v3_lattice3(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_2_0_yellow_0(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_lattice3(B,C,D) ) ) ) )).
fof(fraenkel_a_2_0_yellow_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) & 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(A,a_2_0_yellow_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & D = k3_funct_2(u1_struct_0(B),u1_struct_0(B),C,D) ) ) ) )).
fof(fraenkel_a_2_0_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) ) => ( r2_hidden(A,a_2_0_yellow_4(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & D = k1_yellow_4(B,k6_domain_1(u1_struct_0(B),E),k5_yellow_3(B,B,C)) & r2_hidden(E,k4_yellow_3(B,B,C)) ) ) ) ) )).
fof(fraenkel_a_2_0_yellow_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_0_yellow_6(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & r2_hidden(C,D) & v3_pre_topc(D,B) ) ) ) )).
fof(fraenkel_a_2_0_yellow_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_2_0_yellow_7(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_lattice3(B,C,D) ) ) ) )).
fof(fraenkel_a_2_0_yellow_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_struct_0(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) => ( r2_hidden(A,a_2_0_yellow_9(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k3_subset_1(u1_struct_0(B),D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_0_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) ) => ( r2_hidden(A,a_2_0_zf_fund1(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,B) & m1_subset_1(E,B) & A = k5_classes2(B,k6_classes2(B,k2_ordinal4(B),D),k6_classes2(B,k3_ordinal4(B),E)) & r2_hidden(D,E) & r2_hidden(D,C) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_0_zmodul02,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & v1_int_1(C) ) => ( r2_hidden(A,a_2_0_zmodul02(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k1_zmodul01(B,D,C) ) ) ) )).
fof(fraenkel_a_2_0_zmodul03,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_int_2(B) & ~ 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) ) => ( r2_hidden(A,a_2_0_zmodul03(B,C)) <=> ? [D] : ( m2_zmodul01(D,C,k5_zmodul02(C,B)) & A = D ) ) ) )).
fof(fraenkel_a_2_10_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) ) => ( r2_hidden(A,a_2_10_abcmiz_1(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(k1_funct_1(B,C))) & m1_subset_1(E,k4_ordinal1) & A = k4_tarski(k1_abcmiz_1(D),E) & v1_finset_1(D) ) ) ) )).
fof(fraenkel_a_2_10_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_2_10_armstrng(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = D & ~ r1_tarski(C,D) ) ) ) )).
fof(fraenkel_a_2_10_bintree2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) & v1_bintree2(B) & v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ( r2_hidden(A,a_2_10_bintree2(B,C)) <=> ? [D] : ( m1_bintree2(D,B) & A = D & k3_finseq_1(D) = C ) ) ) )).
fof(fraenkel_a_2_10_conlat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_conlat_1(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u4_struct_0(B)))) ) => ( r2_hidden(A,a_2_10_conlat_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ! [E] : ( m1_subset_1(E,u4_struct_0(B)) => ( r2_hidden(E,k5_setfam_1(u4_struct_0(B),C)) => r1_conlat_1(B,D,E) ) ) ) ) ) )).
fof(fraenkel_a_2_10_gobrd11,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_10_gobrd11(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,B)),E) ) ) ) )).
fof(fraenkel_a_2_10_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) ) => ( r2_hidden(A,a_2_10_lattice3(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r3_lattices(B,D,E) & r2_hidden(E,a_2_7_lattice3(B,C)) ) ) ) ) )).
fof(fraenkel_a_2_10_member_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_membered(B) & v1_xxreal_0(C) ) => ( r2_hidden(A,a_2_10_member_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k6_numbers) & A = k3_xxreal_3(C,D) & r2_hidden(D,B) ) ) ) )).
fof(fraenkel_a_2_10_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_mmlquery(B) & l1_mmlquery(B) & m2_finseq_1(C,u1_mmlquery(B)) ) => ( r2_hidden(A,a_2_10_mmlquery(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_tarski(k30_mmlquery(B,D),k2_relset_1(u1_mmlquery(B),C)) ) ) ) )).
fof(fraenkel_a_2_10_stirl2_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_10_stirl2_1(B,C)) <=> ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k7_card_1(k1_nat_1(C,1)),k7_card_1(k1_nat_1(B,1))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(k1_nat_1(C,1)),k7_card_1(k1_nat_1(B,1))))) & A = D & v2_funct_2(D,k7_card_1(k1_nat_1(B,1))) & v1_stirl2_1(D,k1_nat_1(C,1),k1_nat_1(B,1)) & k1_stirl2_1(k1_nat_1(C,1),k7_card_1(k1_nat_1(B,1)),D,k6_domain_1(k7_card_1(k1_nat_1(B,1)),k2_stirl2_1(k7_card_1(k1_nat_1(C,1)),k1_nat_1(B,1),D,C))) != k1_seq_4(C) ) ) ) )).
fof(fraenkel_a_2_10_tdlat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_2_10_tdlat_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k8_tdlat_1(B))) & A = D & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_10_tex_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_10_tex_4(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & v3_pre_topc(D,B) & r1_tarski(C,D) ) ) ) )).
fof(fraenkel_a_2_10_topreal4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_10_topreal4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) & A = D & D != B & r2_hidden(D,C) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ~ ( r1_topreal4(E,B,D) & r1_tarski(E,C) ) ) ) ) ) )).
fof(fraenkel_a_2_10_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) ) => ( r2_hidden(A,a_2_10_valued_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_xcmplx_0(D,B) & r2_hidden(D,k1_relset_1(k4_ordinal1,C)) ) ) ) )).
fof(fraenkel_a_2_10_waybel11,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & v1_yellow_6(C,B) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_10_waybel11(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k2_waybel_0(B,C,D) & r1_orders_2(C,o_2_9_waybel11(B,C),D) ) ) ) )).
fof(fraenkel_a_2_10_waybel12,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_10_waybel12(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k13_lattice3(B,k3_yellow_0(B),D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_10_waybel14,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_10_waybel14(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k5_waybel_0(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_10_waybel31,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & v3_waybel_3(B) & l1_orders_2(B) & v4_waybel11(C) & m1_yellow_9(C,B) ) => ( r2_hidden(A,a_2_10_waybel31(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k2_waybel_3(C,D) ) ) ) )).
fof(fraenkel_a_2_10_waybel33,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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_xboole_0(C) & v2_waybel_0(C,k2_yellow_1(k2_struct_0(B))) & v13_waybel_0(C,k2_yellow_1(k2_struct_0(B))) & v3_waybel_7(C,k2_yellow_1(k2_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(B))))) ) => ( r2_hidden(A,a_2_10_waybel33(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,u1_struct_0(B)) & m2_subset_1(E,u1_struct_0(k2_yellow_1(k2_struct_0(B))),C) & A = k1_domain_1(u1_struct_0(B),C,D,E) & r2_hidden(D,E) ) ) ) )).
fof(fraenkel_a_2_10_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_10_waybel_4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r3_orders_2(B,D,C) ) ) ) )).
fof(fraenkel_a_2_11_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(A,a_2_11_armstrng(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(B))) & A = k8_setfam_1(B,D) & r1_tarski(D,C) ) ) )).
fof(fraenkel_a_2_11_conlat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_conlat_1(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k11_conlat_1(B)))) ) => ( r2_hidden(A,a_2_11_conlat_1(B,C)) <=> ? [D] : ( m2_conlat_1(D,B,k8_conlat_1(B)) & A = u2_conlat_1(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_11_conlat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_conlat_1(B) & m1_subset_1(C,k1_zfmisc_1(u4_struct_0(B))) ) => ( r2_hidden(A,a_2_11_conlat_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ! [E] : ( m1_subset_1(E,u4_struct_0(B)) => ( r2_hidden(E,C) => r1_conlat_1(B,D,E) ) ) ) ) ) )).
fof(fraenkel_a_2_11_gobrd11,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_11_gobrd11(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(E,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,k1_nat_1(B,1)))) ) ) ) )).
fof(fraenkel_a_2_11_jordan2c,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_11_jordan2c(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(B))) & A = D & ? [E] : ( v1_xreal_0(E) & D = k9_finseq_1(E) & ~ r1_xxreal_0(E,C) ) ) ) ) )).
fof(fraenkel_a_2_11_member_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_membered(B) & v1_xcmplx_0(C) ) => ( r2_hidden(A,a_2_11_member_1(B,C)) <=> ? [D] : ( v1_xcmplx_0(D) & A = k6_xcmplx_0(C,D) & r2_hidden(D,B) ) ) ) )).
fof(fraenkel_a_2_11_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_mmlquery(B) & l1_mmlquery(B) & m2_finseq_1(C,u1_mmlquery(B)) ) => ( r2_hidden(A,a_2_11_mmlquery(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_xxreal_0(k5_card_1(k7_subset_1(u1_struct_0(B),k30_mmlquery(B,D),k2_relset_1(u1_mmlquery(B),C))),k5_numbers) & r1_xxreal_0(k5_card_1(k7_subset_1(u1_mmlquery(B),k2_relset_1(u1_mmlquery(B),C),k30_mmlquery(B,D))),k5_numbers) ) ) ) )).
fof(fraenkel_a_2_11_tdlat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_2_11_tdlat_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k12_tdlat_1(B))) & A = D & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_11_tex_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_11_tex_4(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & v4_pre_topc(D,B) & r1_tarski(k6_domain_1(u1_struct_0(B),C),D) ) ) ) )).
fof(fraenkel_a_2_11_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(A,a_2_11_valued_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = D & r1_xxreal_0(k1_nat_1(k3_finseq_1(B),1),D) & r1_xxreal_0(D,k1_nat_1(k3_finseq_1(B),k3_finseq_1(C))) ) ) ) )).
fof(fraenkel_a_2_11_waybel11,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_11_waybel11(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k4_waybel11(B,C))) & A = k2_yellow_0(B,a_3_5_waybel11(B,C,D)) ) ) ) )).
fof(fraenkel_a_2_11_waybel12,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_11_waybel12(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_tarski(k3_yellow_4(B,C,k6_domain_1(u1_struct_0(B),D)),C) ) ) ) )).
fof(fraenkel_a_2_11_waybel14,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_subset_1(C,u1_struct_0(k1_yellow_1(k5_waybel11(B)))) ) => ( r2_hidden(A,a_2_11_waybel14(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & r1_tarski(D,C) & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & ? [F] : ( v1_tops_2(F,B) & v1_yellow_8(F,B,E) & m1_subset_1(F,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & r2_hidden(E,C) & r2_hidden(D,F) & ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(B))) => ( r2_hidden(G,F) => ( v3_pre_topc(G,B) & v2_waybel_0(G,B) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_2_11_waybel33,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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_xboole_0(C) & v2_waybel_0(C,k2_yellow_1(k2_struct_0(B))) & v13_waybel_0(C,k2_yellow_1(k2_struct_0(B))) & v3_waybel_7(C,k2_yellow_1(k2_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(B))))) ) => ( r2_hidden(A,a_2_11_waybel33(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k2_yellow_0(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_11_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) => ( r2_hidden(A,a_2_11_waybel_4(B,C)) <=> ? [D] : ( ~ 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))) & A = k3_funct_2(u1_struct_0(B),u1_struct_0(k1_yellow_1(k7_waybel_0(B))),k11_waybel_4(B,D),C) & r3_orders_2(B,C,k1_yellow_0(B,D)) ) ) ) )).
fof(fraenkel_a_2_11_yellow19,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & ~ v1_xboole_0(C) & v2_waybel_0(C,k2_yellow_1(k2_struct_0(B))) & v13_waybel_0(C,k2_yellow_1(k2_struct_0(B))) & v3_waybel_7(C,k2_yellow_1(k2_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(B))))) ) => ( r2_hidden(A,a_2_11_yellow19(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k2_pre_topc(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_12_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & l1_msualg_1(B) & m1_subset_1(C,u4_struct_0(B)) ) => ( r2_hidden(A,a_2_12_abcmiz_1(B,C)) <=> ? [D] : ( m1_dtconstr(D,u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))),k5_trees_3(u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers)))))),k1_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))) & A = D & k7_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),D) = k2_msualg_1(B,C) & r2_pboole(u1_struct_0(B),k4_msafree3(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),D),k28_abcmiz_1(B)) ) ) ) )).
fof(fraenkel_a_2_12_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(B),k9_setfam_1(B)))) => ( r2_hidden(A,a_2_12_armstrng(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = D & r2_hidden(k4_tarski(D,B),k8_armstrng(B,C)) ) ) ) )).
fof(fraenkel_a_2_12_conlat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_conlat_1(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k11_conlat_1(B)))) ) => ( r2_hidden(A,a_2_12_conlat_1(B,C)) <=> ? [D] : ( m2_conlat_1(D,B,k8_conlat_1(B)) & A = u3_conlat_1(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_12_gobrd11,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_12_gobrd11(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,B)),E) & r1_xxreal_0(E,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,k1_nat_1(B,1)))) ) ) ) )).
fof(fraenkel_a_2_12_jordan2c,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_12_jordan2c(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(B))) & A = D & ? [E] : ( v1_xreal_0(E) & D = k9_finseq_1(E) & ~ r1_xxreal_0(k4_xcmplx_0(C),E) ) ) ) ) )).
fof(fraenkel_a_2_12_member_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_membered(B) & v1_xxreal_0(C) ) => ( r2_hidden(A,a_2_12_member_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k6_numbers) & A = k3_xxreal_3(D,C) & r2_hidden(D,B) ) ) ) )).
fof(fraenkel_a_2_12_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_mmlquery(B) & l1_mmlquery(B) & m2_finseq_1(C,u1_mmlquery(B)) ) => ( r2_hidden(A,a_2_12_mmlquery(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & k30_mmlquery(B,D) = k2_relset_1(u1_mmlquery(B),C) ) ) ) )).
fof(fraenkel_a_2_12_tex_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_12_tex_4(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & v1_tex_4(D,B) & r2_hidden(C,D) ) ) ) )).
fof(fraenkel_a_2_12_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(A,a_2_12_valued_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_nat_1(D,k3_finseq_1(B)) & r2_hidden(D,k4_finseq_1(C)) ) ) ) )).
fof(fraenkel_a_2_12_waybel12,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & v13_waybel_0(C,B) & v1_waybel_6(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_12_waybel12(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_tarski(k4_yellow_4(B,C,k6_domain_1(u1_struct_0(B),D)),C) ) ) ) )).
fof(fraenkel_a_2_12_waybel14,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_12_waybel14(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k1_yellow_1(k5_waybel11(B)))) & A = D & r2_hidden(C,D) & v6_waybel_6(D,k1_yellow_1(k5_waybel11(B))) ) ) ) )).
fof(fraenkel_a_2_12_waybel_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_12_waybel_0(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r1_orders_2(B,E,D) & r2_hidden(E,C) ) ) ) ) )).
fof(fraenkel_a_2_12_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) => ( r2_hidden(A,a_2_12_waybel_4(B,C)) <=> ? [D] : ( ~ 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))) & A = k9_subset_1(u1_struct_0(B),k5_waybel_0(B,C),D) & r3_orders_2(B,C,k1_yellow_0(B,D)) ) ) ) )).
fof(fraenkel_a_2_13_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & l1_msualg_1(B) & v2_abcmiz_1(C,B) & m1_subset_1(C,u4_struct_0(B)) ) => ( r2_hidden(A,a_2_13_abcmiz_1(B,C)) <=> ? [D] : ( m1_dtconstr(D,u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))),k5_trees_3(u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers)))))),k1_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))) & A = D & k7_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),D) = k2_msualg_1(B,C) & r2_pboole(u1_struct_0(B),k4_msafree3(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),D),k28_abcmiz_1(B)) ) ) ) )).
fof(fraenkel_a_2_13_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) ) => ( r2_hidden(A,a_2_13_armstrng(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = D & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(B)) => ~ ( r2_hidden(E,C) & r1_tarski(E,D) ) ) ) ) ) )).
fof(fraenkel_a_2_13_gobrd11,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_13_gobrd11(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,B,1)),D) ) ) ) )).
fof(fraenkel_a_2_13_member_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_membered(B) & v1_xcmplx_0(C) ) => ( r2_hidden(A,a_2_13_member_1(B,C)) <=> ? [D] : ( v1_xcmplx_0(D) & A = k6_xcmplx_0(D,C) & r2_hidden(D,B) ) ) ) )).
fof(fraenkel_a_2_13_tex_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_13_tex_4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k2_tex_4(B,D) & r2_hidden(D,k6_domain_1(u1_struct_0(B),C)) ) ) ) )).
fof(fraenkel_a_2_13_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(A,a_2_13_valued_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = D & r1_xxreal_0(1,D) & r1_xxreal_0(D,k1_nat_1(k3_finseq_1(B),k3_finseq_1(C))) ) ) ) )).
fof(fraenkel_a_2_13_waybel11,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_13_waybel11(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k4_waybel11(B,C))) & A = k2_waybel_0(B,k4_waybel11(B,C),D) & r1_orders_2(k4_waybel11(B,C),o_2_12_waybel11(B,C),D) ) ) ) )).
fof(fraenkel_a_2_13_waybel14,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_13_waybel14(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k3_subset_1(u1_struct_0(B),k5_waybel_0(B,D)) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_13_waybel_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_13_waybel_0(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r3_orders_2(B,D,E) & r2_hidden(E,C) ) ) ) ) )).
fof(fraenkel_a_2_13_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) => ( r2_hidden(A,a_2_13_waybel_4(B,C)) <=> ? [D] : ( ~ 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))) & A = k3_funct_2(u1_struct_0(B),u1_struct_0(k1_yellow_1(k7_waybel_0(B))),k11_waybel_4(B,D),C) & ~ r3_orders_2(B,C,k1_yellow_0(B,D)) ) ) ) )).
fof(fraenkel_a_2_14_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(B),k9_setfam_1(B)))) => ( r2_hidden(A,a_2_14_armstrng(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = D & ? [E] : ( m1_subset_1(E,k1_zfmisc_1(B)) & ? [F] : ( m1_subset_1(F,k1_zfmisc_1(B)) & r2_hidden(k6_armstrng(B,E,F),C) & r1_tarski(E,D) & ~ r1_tarski(F,D) ) ) ) ) ) )).
fof(fraenkel_a_2_14_gobrd11,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_14_gobrd11(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(D,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(B,1),1))) ) ) ) )).
fof(fraenkel_a_2_14_member_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_membered(B) & v1_xxreal_0(C) ) => ( r2_hidden(A,a_2_14_member_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k6_numbers) & A = k4_xxreal_3(C,D) & r2_hidden(D,B) ) ) ) )).
fof(fraenkel_a_2_14_tex_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_14_tex_4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k2_tex_4(B,D) & r2_hidden(D,k3_tex_4(B,C)) ) ) ) )).
fof(fraenkel_a_2_14_waybel30,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(o_1_12_waybel30(B)))) ) => ( r2_hidden(A,a_2_14_waybel30(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(o_1_12_waybel30(B))) & A = k2_waybel_3(o_1_12_waybel30(B),D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_14_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) => ( r2_hidden(A,a_2_14_waybel_4(B,C)) <=> ? [D] : ( ~ 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))) & A = k5_waybel_0(B,C) & ~ r3_orders_2(B,C,k1_yellow_0(B,D)) ) ) ) )).
fof(fraenkel_a_2_15_gobrd11,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_15_gobrd11(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,B,1)),D) & r1_xxreal_0(D,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(B,1),1))) ) ) ) )).
fof(fraenkel_a_2_15_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & v4_vectsp_1(B) & v5_vectsp_1(B) & v1_algstr_1(B) & l6_algstr_0(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_15_ideal_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k8_group_1(B,C,D) ) ) ) )).
fof(fraenkel_a_2_15_jordan_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_jordan_a(C,B) ) => ( r2_hidden(A,a_2_15_jordan_a(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) & A = D & ( r1_jordan6(B,k7_partfun1(u1_struct_0(k15_euclid(2)),C,k3_finseq_1(C)),D) | ( r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),C,k3_finseq_1(C)),B) & D = k18_pscomp_1(B) ) ) ) ) ) )).
fof(fraenkel_a_2_15_member_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_membered(B) & v1_xcmplx_0(C) ) => ( r2_hidden(A,a_2_15_member_1(B,C)) <=> ? [D] : ( v1_xcmplx_0(D) & A = k3_xcmplx_0(C,D) & r2_hidden(D,B) ) ) ) )).
fof(fraenkel_a_2_15_topreal3,axiom,( ! [A] : ! [B] : ! [C] : ( ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_15_topreal3(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_topreal1(2,k17_finseq_1(u1_struct_0(k15_euclid(2)),k1_nat_1(C,1),B),D) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(k17_finseq_1(u1_struct_0(k15_euclid(2)),k1_nat_1(C,1),B))) ) ) ) )).
fof(fraenkel_a_2_15_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_finseq_1(B) & v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) ) => ( r2_hidden(A,a_2_15_valued_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_nat_1(D,k3_finseq_1(k15_finseq_1(B))) & r2_hidden(D,k4_finseq_1(k15_finseq_1(C))) ) ) ) )).
fof(fraenkel_a_2_15_waybel11,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_15_waybel11(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k2_waybel_0(B,C,D) & r1_orders_2(C,o_2_14_waybel11(B,C),D) ) ) ) )).
fof(fraenkel_a_2_15_waybel30,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & v2_waybel_2(B) & l1_waybel_9(B) & m1_subset_1(C,u1_struct_0(o_1_14_waybel30(B))) ) => ( r2_hidden(A,a_2_15_waybel30(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(o_1_14_waybel30(B)))) & A = k2_yellow_0(o_1_14_waybel30(B),D) & r2_hidden(C,D) & r2_hidden(D,k5_waybel11(o_1_14_waybel30(B))) ) ) ) )).
fof(fraenkel_a_2_15_waybel33,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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_xboole_0(C) & v2_waybel_0(C,k2_yellow_1(k2_struct_0(o_1_4_waybel33(B)))) & v13_waybel_0(C,k2_yellow_1(k2_struct_0(o_1_4_waybel33(B)))) & v3_waybel_7(C,k2_yellow_1(k2_struct_0(o_1_4_waybel33(B)))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(o_1_4_waybel33(B)))))) ) => ( r2_hidden(A,a_2_15_waybel33(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(o_1_4_waybel33(B)))) & A = k2_yellow_0(o_1_4_waybel33(B),D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_15_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & v2_lattice3(B) & v2_waybel_2(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_15_waybel_4(B,C)) <=> ? [D] : ( ~ 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))) & A = D & r3_orders_2(B,C,k1_yellow_0(B,D)) ) ) ) )).
fof(fraenkel_a_2_16_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(B),k9_setfam_1(B)))) ) => ( r2_hidden(A,a_2_16_armstrng(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(B)) & A = k6_armstrng(B,D,E) & ! [F] : ( ( r2_hidden(F,k9_armstrng(B,C)) & r1_tarski(D,F) ) => r1_tarski(E,F) ) ) ) ) )).
fof(fraenkel_a_2_16_gobrd11,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_16_gobrd11(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,B)),E) & r1_xxreal_0(E,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,k1_nat_1(B,1)))) ) ) ) )).
fof(fraenkel_a_2_16_member_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_membered(B) & v1_xxreal_0(C) ) => ( r2_hidden(A,a_2_16_member_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k6_numbers) & A = k6_xxreal_3(C,D) & r2_hidden(D,B) ) ) ) )).
fof(fraenkel_a_2_16_tex_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_16_tex_4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k4_tex_4(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_16_waybel30,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & v8_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) & v2_waybel_2(B) & l1_waybel_9(B) & m1_subset_1(C,u1_struct_0(o_1_15_waybel30(B))) ) => ( r2_hidden(A,a_2_16_waybel30(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(o_1_15_waybel30(B)))) & A = k2_yellow_0(o_1_15_waybel30(B),D) & r2_hidden(C,D) & r2_hidden(D,k5_waybel11(o_1_15_waybel30(B))) ) ) ) )).
fof(fraenkel_a_2_16_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & v2_lattice3(B) & v2_waybel_2(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_16_waybel_4(B,C)) <=> ? [D] : ( ~ 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))) & A = k3_funct_2(u1_struct_0(B),u1_struct_0(k1_yellow_1(k7_waybel_0(B))),k11_waybel_4(B,D),C) ) ) ) )).
fof(fraenkel_a_2_17_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(B),k9_setfam_1(B)))) ) => ( r2_hidden(A,a_2_17_armstrng(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = D & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(B)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(B)) => ( ( r2_hidden(k6_armstrng(B,E,F),C) & r1_tarski(E,D) ) => r1_tarski(F,D) ) ) ) ) ) ) )).
fof(fraenkel_a_2_17_gobrd11,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_17_gobrd11(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,B,1)),D) & r1_xxreal_0(D,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(B,1),1))) ) ) ) )).
fof(fraenkel_a_2_17_member_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_membered(B) & v1_xcmplx_0(C) ) => ( r2_hidden(A,a_2_17_member_1(B,C)) <=> ? [D] : ( v1_xcmplx_0(D) & A = k7_xcmplx_0(C,D) & r2_hidden(D,B) ) ) ) )).
fof(fraenkel_a_2_17_waybel30,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & v8_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) & v2_waybel_2(B) & l1_waybel_9(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_17_waybel30(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(o_1_15_waybel30(B)))) & A = k2_yellow_0(o_1_15_waybel30(B),D) & r2_hidden(C,D) & r2_hidden(D,k5_waybel11(o_1_15_waybel30(B))) ) ) ) )).
fof(fraenkel_a_2_17_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) => ( r2_hidden(A,a_2_17_waybel_4(B,C)) <=> ? [D] : ( v5_waybel_4(D,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) & A = k5_waybel_4(B,C,D) & r2_hidden(D,k12_waybel_4(B)) ) ) ) )).
fof(fraenkel_a_2_18_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) ) => ( r2_hidden(A,a_2_18_armstrng(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(B)) & A = k6_armstrng(B,D,E) & ! [F] : ( ( r2_hidden(F,C) & r1_tarski(D,F) ) => r1_tarski(E,F) ) ) ) ) )).
fof(fraenkel_a_2_18_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v7_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) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_18_ideal_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k8_group_1(B,C,D) ) ) ) )).
fof(fraenkel_a_2_18_member_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_membered(B) & v1_xxreal_0(C) ) => ( r2_hidden(A,a_2_18_member_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k6_numbers) & A = k6_xxreal_3(D,C) & r2_hidden(D,B) ) ) ) )).
fof(fraenkel_a_2_18_waybel30,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & v2_waybel_2(B) & l1_waybel_9(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_18_waybel30(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(o_1_16_waybel30(B)))) & A = k2_yellow_0(o_1_16_waybel30(B),D) & r2_hidden(C,D) & r2_hidden(D,k5_waybel11(o_1_16_waybel30(B))) ) ) ) )).
fof(fraenkel_a_2_19_member_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_membered(B) & v1_xcmplx_0(C) ) => ( r2_hidden(A,a_2_19_member_1(B,C)) <=> ? [D] : ( v1_xcmplx_0(D) & A = k7_xcmplx_0(D,C) & r2_hidden(D,B) ) ) ) )).
fof(fraenkel_a_2_19_waybel30,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & v2_waybel_2(B) & l1_waybel_9(B) & m1_subset_1(C,u1_struct_0(o_1_16_waybel30(B))) ) => ( r2_hidden(A,a_2_19_waybel30(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(o_1_16_waybel30(B)))) & A = k2_yellow_0(o_1_16_waybel30(B),D) & r2_hidden(C,D) & r2_hidden(D,k5_waybel11(o_1_16_waybel30(B))) ) ) ) )).
fof(fraenkel_a_2_1_abcmiz_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v4_abcmiz_0(B) & l2_abcmiz_0(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_1_abcmiz_0(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_abcmiz_0(B)) & A = D & r2_hidden(C,k3_abcmiz_0(B,D)) ) ) ) )).
fof(fraenkel_a_2_1_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & l1_msualg_1(B) & v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v6_trees_3(C) ) => ( r2_hidden(A,a_2_1_abcmiz_1(B,C)) <=> ? [D] : ( m1_abcmiz_1(D,B,k14_abcmiz_1(B)) & A = k45_abcmiz_1(B,D) & r2_hidden(D,k10_xtuple_0(C)) ) ) ) )).
fof(fraenkel_a_2_1_abcmiz_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & v1_abcmiz_a(B) & l1_msualg_1(B) & m1_dtconstr(C,u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))),k5_trees_3(u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers)))))),k1_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))) ) => ( r2_hidden(A,a_2_1_abcmiz_a(B,C)) <=> ? [D] : ( m1_dtconstr(D,u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))),k5_trees_3(u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers)))))),k1_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))) & A = D & k7_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),D) = k7_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),C) & r2_pboole(u1_struct_0(B),k4_msafree3(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),D),k28_abcmiz_1(B)) ) ) ) )).
fof(fraenkel_a_2_1_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ( r2_hidden(A,a_2_1_afinsq_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_nat_1(D,k5_card_1(B)) & r2_hidden(D,k2_afinsq_1(C)) ) ) ) )).
fof(fraenkel_a_2_1_ami_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_1_ami_6(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_amistd_1(k7_card_1(2),k1_ami_3,D,k8_ami_3(C,B)) ) ) ) )).
fof(fraenkel_a_2_1_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_aofa_000(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = k9_aofa_000(B,C,D) ) ) ) )).
fof(fraenkel_a_2_1_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(B),k9_setfam_1(B)))) ) => ( r2_hidden(A,a_2_1_armstrng(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(B)) & A = k6_armstrng(B,D,E) & ? [F] : ( m1_subset_1(F,k1_zfmisc_1(B)) & ? [G] : ( m1_subset_1(G,k1_zfmisc_1(B)) & r3_armstrng(B,k6_armstrng(B,F,G),k6_armstrng(B,D,E)) & r2_hidden(k6_armstrng(B,F,G),C) ) ) ) ) ) )).
fof(fraenkel_a_2_1_arytm_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m2_subset_1(B,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) & m2_subset_1(C,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) ) => ( r2_hidden(A,a_2_1_arytm_2(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k5_arytm_3) & m1_subset_1(E,k5_arytm_3) & A = k10_arytm_3(D,E) & r2_hidden(D,B) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_1_asympt_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(A,a_2_1_asympt_0(B,C)) <=> ? [D] : ( m2_funct_2(D,k4_ordinal1,k1_numbers,k9_funct_2(k4_ordinal1,k1_numbers)) & A = D & ? [E] : ( v1_xreal_0(E) & ? [F] : ( m1_subset_1(F,k4_ordinal1) & ~ r1_xxreal_0(E,k5_numbers) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( ( r1_xxreal_0(F,G) & r2_hidden(G,C) ) => ( r1_xxreal_0(k3_xcmplx_0(E,k9_nat_1(k1_numbers,B,G)),k9_nat_1(k1_numbers,D,G)) & r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,D,G)) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_2_1_bagorder,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_1_bagorder(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = D & ~ r1_xxreal_0(k7_nat_d(C,B),D) ) ) ) )).
fof(fraenkel_a_2_1_bcialg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_1_bcialg_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_bcialg_1(B,k1_bcialg_1(B,D,k4_struct_0(B)),C) ) ) ) )).
fof(fraenkel_a_2_1_bcialg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & m2_subset_1(C,u1_struct_0(B),k5_bcialg_1(B)) ) => ( r2_hidden(A,a_2_1_bcialg_4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_bcialg_1(B,C,D) ) ) ) )).
fof(fraenkel_a_2_1_bintree2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) & m1_trees_1(C,B) ) => ( r2_hidden(A,a_2_1_bintree2(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k7_finseq_1(C,k9_finseq_1(D)) & r2_hidden(k7_finseq_1(C,k9_finseq_1(D)),B) ) ) ) )).
fof(fraenkel_a_2_1_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & m1_eqrel_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_1_borsuk_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(C)) & A = D & r2_hidden(k3_tarski(D),u1_pre_topc(B)) ) ) ) )).
fof(fraenkel_a_2_1_borsuk_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & v2_pre_topc(C) & l1_pre_topc(C) ) => ( r2_hidden(A,a_2_1_borsuk_3(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k3_borsuk_1(C,B,D,E) & r2_hidden(D,u1_pre_topc(C)) & r2_hidden(E,u1_pre_topc(B)) ) ) ) )).
fof(fraenkel_a_2_1_borsuk_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k5_topmetr)) & m1_subset_1(C,u1_struct_0(k5_topmetr)) ) => ( r2_hidden(A,a_2_1_borsuk_4(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,B) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_1_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & m1_subset_1(C,u1_struct_0(k15_euclid(3))) ) => ( r2_hidden(A,a_2_1_borsuk_7(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(k2_euclid_5(C),k7_xcmplx_0(B,k3_square_1(2)))) & ~ r1_xxreal_0(k2_xcmplx_0(k2_euclid_5(C),k7_xcmplx_0(B,k3_square_1(2))),D) ) ) ) )).
fof(fraenkel_a_2_1_card_fil,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) ) => ( r2_hidden(A,a_2_1_card_fil(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = k3_subset_1(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_1_card_fin,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(B) & v1_finset_1(C) ) => ( r2_hidden(A,a_2_1_card_fin(B,C)) <=> ? [D] : ( v1_funct_1(D) & v1_funct_2(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) & A = D & v2_funct_2(D,C) ) ) ) )).
fof(fraenkel_a_2_1_catalan2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_1_catalan2(B,C)) <=> ? [D] : ( m1_subset_1(D,k3_catalan2(k4_ordinal1)) & A = D & r2_hidden(D,k2_catalan2(k1_nat_1(C,1),B)) & a_1_4_catalan2(D) = k1_xboole_0 ) ) ) )).
fof(fraenkel_a_2_1_cc0sp2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xcmplx_0(C) ) => ( r2_hidden(A,a_2_1_cc0sp2(B,C)) <=> ? [D] : ( v1_xcmplx_0(D) & A = D & ~ r1_xxreal_0(k7_xcmplx_0(B,2),k9_complex1(k6_xcmplx_0(D,C))) ) ) ) )).
fof(fraenkel_a_2_1_cfdiff_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k2_numbers) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_1_cfdiff_1(B,C)) <=> ? [D] : ( v1_xcmplx_0(D) & A = D & ~ r1_xxreal_0(C,k9_complex1(k6_xcmplx_0(D,B))) ) ) ) )).
fof(fraenkel_a_2_1_cgames_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_cgames_1(C) ) => ( r2_hidden(A,a_2_1_cgames_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k7_cgames_1(C)) & A = k1_funct_1(B,D) & k7_cgames_1(C) != k1_xboole_0 ) ) ) )).
fof(fraenkel_a_2_1_classes1,axiom,( ! [A] : ! [B] : ! [C] : ( v3_ordinal1(C) => ( r2_hidden(A,a_2_1_classes1(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_classes1(B)) & A = k9_setfam_1(D) & r2_hidden(D,k3_classes1(B,C)) ) ) ) )).
fof(fraenkel_a_2_1_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(C) & v4_funct_1(C) ) => ( r2_hidden(A,a_2_1_closure2(B,C)) <=> ? [D] : ( m1_subset_1(D,C) & A = k1_funct_1(D,B) ) ) ) )).
fof(fraenkel_a_2_1_clvect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(C,B) ) => ( r2_hidden(A,a_2_1_clvect_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k3_rlvect_1(B,k4_struct_0(B),D) & r1_struct_0(C,D) ) ) ) )).
fof(fraenkel_a_2_1_cohsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) & ~ v1_xboole_0(C) & v1_classes1(C) & v1_coh_sp(C) ) => ( r2_hidden(A,a_2_1_cohsp_1(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,B) & m1_subset_1(E,C) & A = k1_zfmisc_1(k2_zfmisc_1(D,E)) ) ) ) )).
fof(fraenkel_a_2_1_combgras,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v1_xboole_0(C) ) => ( r2_hidden(A,a_2_1_combgras(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(C)) & A = D & k1_card_1(D) = k1_nat_1(B,1) ) ) ) )).
fof(fraenkel_a_2_1_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & l1_compos_1(C) ) => ( r2_hidden(A,a_2_1_compos_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_xcmplx_0(D,B) & r2_hidden(D,k2_afinsq_1(k4_compos_1(C))) ) ) ) )).
fof(fraenkel_a_2_1_conlat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_conlat_1(B) & m1_subset_1(C,k1_zfmisc_1(u4_struct_0(B))) ) => ( r2_hidden(A,a_2_1_conlat_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ! [E] : ( m1_subset_1(E,u4_struct_0(B)) => ( r2_hidden(E,C) => r1_conlat_1(B,D,E) ) ) ) ) ) )).
fof(fraenkel_a_2_1_conlat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_conlat_1(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u4_struct_0(B)))) ) => ( r2_hidden(A,a_2_1_conlat_2(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u4_struct_0(B))) & A = k3_funct_2(k1_zfmisc_1(u4_struct_0(B)),k9_setfam_1(u1_struct_0(B)),k2_conlat_1(B),D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_1_connsp_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) => ( r2_hidden(A,a_2_1_connsp_3(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & v3_connsp_1(D,B) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ( r2_hidden(E,C) => r1_tarski(D,E) ) ) ) ) ) )).
fof(fraenkel_a_2_1_convex1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v4_rlvect_1(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_convex1(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) & A = k1_algstr_0(B,D,E) & r2_hidden(D,C) & r2_hidden(E,k6_domain_1(u1_struct_0(B),k4_struct_0(B))) ) ) ) )).
fof(fraenkel_a_2_1_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_2_1_domain_1(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = D & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_1_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v16_waybel_0(B) & l1_orders_2(B) & v1_relat_1(C) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & v1_exchsort(C) ) => ( r2_hidden(A,a_2_1_exchsort(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k9_xtuple_0(C)) & m1_subset_1(E,k9_xtuple_0(C)) & A = k4_tarski(D,E) & r2_hidden(D,E) & r2_orders_2(B,k7_partfun1(u1_struct_0(B),C,E),k7_partfun1(u1_struct_0(B),C,D)) ) ) ) )).
fof(fraenkel_a_2_1_fcont_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_1_fcont_1(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(C,D) ) ) ) )).
fof(fraenkel_a_2_1_fcont_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_1_fcont_2(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & r1_xxreal_0(B,D) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_1_fdiff_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k1_numbers) & m1_subset_1(C,k1_numbers) ) => ( r2_hidden(A,a_2_1_fdiff_2(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(k3_xxreal_0(B,C),1)) & ~ r1_xxreal_0(k2_xcmplx_0(k4_xxreal_0(B,C),1),D) ) ) ) )).
fof(fraenkel_a_2_1_fdiff_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_1_fdiff_3(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & r1_xxreal_0(B,D) & r1_xxreal_0(D,k2_xcmplx_0(B,C)) ) ) ) )).
fof(fraenkel_a_2_1_filter_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) & ~ v1_xboole_0(C) & v19_lattices(C,B) & v20_lattices(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_filter_0(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & r1_tarski(C,D) & ~ v1_xboole_0(D) & v19_lattices(D,B) & v20_lattices(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & D != u1_struct_0(B) ) ) ) )).
fof(fraenkel_a_2_1_fin_topo,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_fin_topo(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_tarski(k1_fin_topo(B,D),C) ) ) ) )).
fof(fraenkel_a_2_1_finance1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_1_finance1(B,C)) <=> ? [D] : ( m1_subset_1(D,k6_numbers) & A = D & r1_xxreal_0(B,D) & ~ r1_xxreal_0(k2_xcmplx_0(C,1),D) ) ) ) )).
fof(fraenkel_a_2_1_fintopo2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_fintopo2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_fintopo2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ~ ( r2_hidden(E,k6_fintopo2(B,D)) & r1_xboole_0(E,C) ) ) ) ) ) )).
fof(fraenkel_a_2_1_fintopo3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_fintopo3(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,k3_subset_1(u1_struct_0(B),C)) & r2_hidden(D,k1_fin_topo(B,E)) ) ) ) ) )).
fof(fraenkel_a_2_1_fintopo6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_fintopo6(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ~ r1_xboole_0(k1_fin_topo(B,D),C) ) ) ) )).
fof(fraenkel_a_2_1_fomodel1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k4_ordinal1) & ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ( r2_hidden(A,a_2_1_fomodel1(B,C)) <=> ? [D] : ( v10_fomodel1(D,C) & m1_subset_1(D,k1_fomodel1(C)) & A = k24_fomodel1(C,D,k3_funct_2(k4_ordinal1,k9_setfam_1(k3_finseq_2(k15_fomodel1(C))),k28_fomodel1(C),B)) & v6_fomodel1(D,C) ) ) ) )).
fof(fraenkel_a_2_1_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_1_fomodel2(B,C)) <=> ? [D] : ? [E] : ( m2_subset_1(D,k15_fomodel1(B),k16_fomodel1(B)) & m2_subset_1(E,k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0)),k24_fomodel2(B,C)) & A = k42_fomodel1(B,k43_fomodel1(B,D),E) ) ) ) )).
fof(fraenkel_a_2_1_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ( r2_hidden(A,a_2_1_fomodel3(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = D & ~ r2_hidden(B,k9_nat_1(k9_setfam_1(k6_subset_1(k3_finseq_2(k15_fomodel1(C)),k1_tarski(k1_xboole_0))),k39_fomodel1(C),D)) ) ) ) )).
fof(fraenkel_a_2_1_fvaluat1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) & m1_fvaluat1(C,B) ) => ( r2_hidden(A,a_2_1_fvaluat1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_xxreal_0(k5_numbers,k3_funct_2(u1_struct_0(B),k6_numbers,C,D)) ) ) ) )).
fof(fraenkel_a_2_1_goboard2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) & m2_finseq_1(C,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_2_1_goboard2(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_topreal1(2,k8_finseq_1(u1_struct_0(k15_euclid(2)),B,C),D) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(2)),B,C))) ) ) ) )).
fof(fraenkel_a_2_1_goboard5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_1_goboard5(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,C,1)),D) ) ) ) )).
fof(fraenkel_a_2_1_goboard6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_1_goboard6(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & ~ r1_xxreal_0(E,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,B))) & ~ r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,k1_nat_1(B,1))),E) ) ) ) )).
fof(fraenkel_a_2_1_goboard9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_1_goboard9(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & ~ r1_xxreal_0(E,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,B))) ) ) ) )).
fof(fraenkel_a_2_1_gobrd11,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_1_gobrd11(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,B)),E) & r1_xxreal_0(E,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,k1_nat_1(B,1)))) ) ) ) )).
fof(fraenkel_a_2_1_gobrd13,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_1_gobrd13(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(D,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,1))) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,B)),E) ) ) ) )).
fof(fraenkel_a_2_1_goedelcp,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(B) & m2_subset_1(C,k9_qc_lang1(B),k3_cqc_lang(B)) ) => ( r2_hidden(A,a_2_1_goedelcp(B,C)) <=> ? [D] : ( m2_subset_1(D,k9_qc_lang1(B),k3_cqc_lang(B)) & A = k24_qc_lang1(B,D) & r2_hidden(D,k6_domain_1(k3_cqc_lang(B),C)) ) ) ) )).
fof(fraenkel_a_2_1_graph_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ( r2_hidden(A,a_2_1_graph_4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u4_struct_0(B)) & r2_hidden(E,C) & D = k1_funct_1(u2_graph_1(B),E) ) ) ) ) )).
fof(fraenkel_a_2_1_graph_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(B) & m1_subset_1(C,k4_ordinal1) ) => ( r2_hidden(A,a_2_1_graph_5(B,C)) <=> ? [D] : ( m2_finseq_2(D,B,k3_finseq_2(B)) & A = D & r1_xxreal_0(k3_finseq_1(D),C) ) ) ) )).
fof(fraenkel_a_2_1_graphsp,axiom,( ! [A] : ! [B] : ! [C] : ( ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) & m1_subset_1(C,k4_ordinal1) ) => ( r2_hidden(A,a_2_1_graphsp(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = D & r2_hidden(D,k4_finseq_1(B)) & r1_xxreal_0(1,D) & r1_xxreal_0(D,C) & k1_funct_1(B,D) != k4_xcmplx_0(1) ) ) ) )).
fof(fraenkel_a_2_1_group_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_group_3(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & r4_group_3(B,C,D) ) ) ) )).
fof(fraenkel_a_2_1_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( v7_ordinal1(C) => ( r2_hidden(A,a_2_1_group_9(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = k6_xcmplx_0(D,1) & r2_hidden(D,B) & ~ r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_1_heyting2,axiom,( ! [A] : ! [B] : ! [C] : ( v1_finset_1(C) => ( r2_hidden(A,a_2_1_heyting2(B,C)) <=> ? [D] : ( m1_subset_1(D,k5_finsub_1(k4_partfun1(B,C))) & A = D & ! [E] : ( r2_hidden(E,D) => v1_finset_1(E) ) & ! [E] : ( m1_subset_1(E,k4_partfun1(B,C)) => ! [F] : ( m1_subset_1(F,k4_partfun1(B,C)) => ( ( r2_hidden(E,D) & r2_hidden(F,D) & r1_tarski(E,F) ) => E = F ) ) ) ) ) ) )).
fof(fraenkel_a_2_1_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v4_vectsp_1(B) & l6_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_ideal_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,k4_ordinal1) & r2_hidden(k2_binom(B,D,E),C) ) ) ) ) )).
fof(fraenkel_a_2_1_integr1c,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_1_integr1c(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(C,D) ) ) ) )).
fof(fraenkel_a_2_1_integra2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(A,a_2_1_integra2(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = k3_xcmplx_0(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_1_interva1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_roughs_1(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k21_interva1(B)))) ) => ( r2_hidden(A,a_2_1_interva1(B,C)) <=> ? [D] : ( m2_interva1(D,B) & A = k14_interva1(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_1_jgraph_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_1_jgraph_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) & A = D & ~ r1_xxreal_0(C,k12_euclid(k5_algstr_0(k15_euclid(2),B,D))) ) ) ) )).
fof(fraenkel_a_2_1_jordan14,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_1_jordan14(B,C)) <=> ? [D] : ? [E] : ( v7_ordinal1(D) & v7_ordinal1(E) & A = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,C),D,E) & r2_hidden(k4_tarski(D,E),k2_matrix_0(k1_jordan8(B,C))) ) ) ) )).
fof(fraenkel_a_2_1_jordan1h,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(B)) ) => ( r2_hidden(A,a_2_1_jordan1h(B,C)) <=> ? [D] : ? [E] : ( v7_ordinal1(D) & v7_ordinal1(E) & A = k3_matrix_0(B,C,D,E) & r2_hidden(k4_tarski(D,E),k2_matrix_0(C)) ) ) ) )).
fof(fraenkel_a_2_1_jordan20,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_1_jordan20(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(k17_euclid(B),C)) & ~ r1_xxreal_0(k2_xcmplx_0(k17_euclid(B),C),D) ) ) ) )).
fof(fraenkel_a_2_1_jordan2b,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_1_jordan2b(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(C,B)) & ~ r1_xxreal_0(k2_xcmplx_0(C,B),D) ) ) ) )).
fof(fraenkel_a_2_1_jordan2c,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) ) => ( r2_hidden(A,a_2_1_jordan2c(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) & A = D & r2_jordan2c(B,C,D) ) ) ) )).
fof(fraenkel_a_2_1_jordan3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & m2_finseq_1(C,u1_struct_0(k15_euclid(B))) ) => ( r2_hidden(A,a_2_1_jordan3(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_topreal1(B,C,D) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(C)) ) ) ) )).
fof(fraenkel_a_2_1_jordan4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_1_jordan4(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_topreal1(2,k2_rfinseq(u1_struct_0(k15_euclid(2)),k7_nat_d(C,1),B),D) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(k2_rfinseq(u1_struct_0(k15_euclid(2)),k7_nat_d(C,1),B))) ) ) ) )).
fof(fraenkel_a_2_1_jordan5a,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k7_metric_1)) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_1_jordan5a(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k7_metric_1)) & A = D & ~ r1_xxreal_0(C,k3_metric_1(k7_metric_1,B,D)) ) ) ) )).
fof(fraenkel_a_2_1_jordan5d,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_1_jordan5d(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = D & r2_hidden(k4_tarski(D,C),k2_matrix_0(k2_goboard2(B))) & ? [E] : ( v7_ordinal1(E) & r2_hidden(E,k4_finseq_1(B)) & k7_partfun1(u1_struct_0(k15_euclid(2)),B,E) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(B),D,C) ) ) ) ) )).
fof(fraenkel_a_2_1_jordan6,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & m1_subset_1(C,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_2_1_jordan6(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) & A = D & k18_euclid(D) = k7_xcmplx_0(k2_xcmplx_0(k18_euclid(B),k18_euclid(C)),2) ) ) ) )).
fof(fraenkel_a_2_1_jordan7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v2_compts_1(B,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))) ) => ( r2_hidden(A,a_2_1_jordan7(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) & A = D & r1_jordan6(B,C,D) & r1_jordan6(B,D,C) ) ) ) )).
fof(fraenkel_a_2_1_jordan_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_jordan_a(C,B) ) => ( r2_hidden(A,a_2_1_jordan_a(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k4_ordinal1) & m1_subset_1(E,k4_ordinal1) & A = k4_jordan1k(2,k2_jordan_a(B,D,C),k2_jordan_a(B,E,C)) & r1_xxreal_0(1,D) & ~ r1_xxreal_0(E,D) & ~ r1_xxreal_0(k3_finseq_1(C),E) & ~ r1_gobrd10(D,E) ) ) ) )).
fof(fraenkel_a_2_1_knaster,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k9_setfam_1(B),k9_setfam_1(B)) & v6_cohsp_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(B),k9_setfam_1(B)))) ) => ( r2_hidden(A,a_2_1_knaster(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = D & r1_tarski(D,k3_funct_2(k1_zfmisc_1(B),k9_setfam_1(B),C,D)) ) ) ) )).
fof(fraenkel_a_2_1_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l3_lattices(B) ) => ( r2_hidden(A,a_2_1_lattice3(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r3_lattice3(B,D,C) ) ) ) )).
fof(fraenkel_a_2_1_lattice4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B) & ~ v1_xboole_0(C) & v20_lattices(C,B) & v21_lattices(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_lattice4(B,C)) <=> ? [D] : ( m1_subset_1(D,k5_finsub_1(u1_struct_0(B))) & A = k2_lattice4(B,D) & r1_tarski(D,k4_lattice4(B,C)) ) ) ) )).
fof(fraenkel_a_2_1_lattice5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m2_lattice5(C,u1_struct_0(B),B,k16_lattice5(B)) ) => ( r2_hidden(A,a_2_1_lattice5(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = k1_xtuple_0(k1_funct_1(C,D)) ) ) ) )).
fof(fraenkel_a_2_1_lattice6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_lattice3(B)))) ) => ( r2_hidden(A,a_2_1_lattice6(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k3_lattice3(B))) & A = k5_lattice3(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_1_lattice8,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_lattice8(C,u1_struct_0(B),B,k16_lattice5(B)) ) => ( r2_hidden(A,a_2_1_lattice8(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = k2_xtuple_0(k1_funct_1(C,D)) ) ) ) )).
fof(fraenkel_a_2_1_limfunc2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_1_limfunc2(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(k2_xcmplx_0(B,C),D) ) ) ) )).
fof(fraenkel_a_2_1_limfunc3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_1_limfunc3(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(C,B)) & ~ r1_xxreal_0(C,D) ) ) ) )).
fof(fraenkel_a_2_1_limfunc4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r2_hidden(A,a_2_1_limfunc4(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(k1_limfunc2(C,B),D) ) ) ) )).
fof(fraenkel_a_2_1_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_rlvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_mathmorp(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k4_algstr_0(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_1_matrix13,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(C) & v1_matrix_1(C,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_matrix13(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = D & r2_hidden(k1_domain_1(k4_ordinal1,k4_ordinal1,D,D),k2_matrix_0(C)) & k3_matrix_0(u1_struct_0(B),C,D,D) != k4_struct_0(B) ) ) ) )).
fof(fraenkel_a_2_1_matrix15,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_matrix15(B,C)) <=> ? [D] : ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),k1_matrix_0(C),1) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) & A = D ) ) ) )).
fof(fraenkel_a_2_1_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(B)) ) => ( r2_hidden(A,a_2_1_matrix_0(B,C)) <=> ? [D] : ? [E] : ( v7_ordinal1(D) & v7_ordinal1(E) & A = k3_matrix_0(B,C,D,E) & r2_hidden(k4_tarski(D,E),k2_matrix_0(C)) ) ) ) )).
fof(fraenkel_a_2_1_matroid0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v3_pencil_1(B) & v1_matroid0(B) & v2_matroid0(B) & v4_matroid0(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_matroid0(B,C)) <=> ? [D] : ( v3_pre_topc(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k5_card_1(D) & r1_tarski(D,C) ) ) ) )).
fof(fraenkel_a_2_1_matrtop1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(A,a_2_1_matrtop1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_xcmplx_0(D,k3_finseq_1(B)) & r2_hidden(D,k4_finseq_1(C)) ) ) ) )).
fof(fraenkel_a_2_1_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(B) => ( r2_hidden(A,a_2_1_mcart_1(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = k2_xtuple_0(D) & k1_xtuple_0(D) = k1_xtuple_0(C) ) ) ) )).
fof(fraenkel_a_2_1_measure6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(A,a_2_1_measure6(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = k2_xcmplx_0(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_1_member_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_membered(B) & v1_membered(C) ) => ( r2_hidden(A,a_2_1_member_1(B,C)) <=> ? [D] : ? [E] : ( v1_xcmplx_0(D) & v1_xcmplx_0(E) & A = k2_xcmplx_0(D,E) & r2_hidden(D,B) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_1_metric_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_metric_1(B) & m1_subset_1(C,k1_numbers) ) => ( r2_hidden(A,a_2_1_metric_2(B,C)) <=> ? [D] : ( m1_subset_1(D,k2_zfmisc_1(k2_metric_2(B),k2_metric_2(B))) & A = D & ? [E] : ( m1_subset_1(E,k2_metric_2(B)) & ? [F] : ( m1_subset_1(F,k2_metric_2(B)) & D = k1_domain_1(k2_metric_2(B),k2_metric_2(B),E,F) & r4_metric_2(B,E,F,C) ) ) ) ) ) )).
fof(fraenkel_a_2_1_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_mmlquery(B) & m2_finseq_1(C,u1_mmlquery(B)) ) => ( r2_hidden(A,a_2_1_mmlquery(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_tarski(k2_relset_1(u1_mmlquery(B),C),k30_mmlquery(B,D)) ) ) ) )).
fof(fraenkel_a_2_1_modal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) & m1_trees_1(C,B) ) => ( r2_hidden(A,a_2_1_modal_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k8_finseq_1(k4_ordinal1,C,k14_trees_3(D)) & r2_hidden(k8_finseq_1(k4_ordinal1,C,k14_trees_3(D)),B) ) ) ) )).
fof(fraenkel_a_2_1_modcat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_classes2(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) ) => ( r2_hidden(A,a_2_1_modcat_1(B,C)) <=> ? [D] : ? [E] : ( m2_grcat_1(D,k17_grcat_1(B)) & m2_funct_2(E,k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)),u1_struct_0(D),k9_funct_2(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)),u1_struct_0(D))) & A = k4_tarski(D,E) ) ) ) )).
fof(fraenkel_a_2_1_modelc_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_modelc_2(B) & v5_modelc_3(B) & m2_finseq_1(B,k4_ordinal1) & v1_modelc_3(C,B) & l1_modelc_3(C,B) ) => ( r2_hidden(A,a_2_1_modelc_3(B,C)) <=> ? [D] : ( v1_modelc_2(D) & m2_finseq_1(D,k4_ordinal1) & A = D & v2_modelc_2(D) & r2_hidden(k3_modelc_2(D),u1_modelc_3(B,C)) ) ) ) )).
fof(fraenkel_a_2_1_moebius1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & v1_int_2(C) ) => ( r2_hidden(A,a_2_1_moebius1(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = k2_nat_1(C,D) & ~ r1_xxreal_0(D,k5_numbers) & r1_nat_d(D,k3_nat_d(B,C)) ) ) ) )).
fof(fraenkel_a_2_1_msafree3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) ) => ( r2_hidden(A,a_2_1_msafree3(B,C)) <=> ? [D] : ( m1_subset_1(D,k10_xtuple_0(C)) & A = k1_xtuple_0(D) & k2_xtuple_0(D) = B ) ) ) )).
fof(fraenkel_a_2_1_msualg_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_1_msualg_7(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & r1_xxreal_0(B,D) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_1_mycielsk,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & m1_mycielsk(C,B) ) => ( r2_hidden(A,a_2_1_mycielsk(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k4_ordinal1) & m1_subset_1(E,k4_ordinal1) & A = k4_tarski(k2_xcmplx_0(D,B),E) & r2_hidden(k4_tarski(D,E),u1_orders_2(C)) ) ) ) )).
fof(fraenkel_a_2_1_ndiff_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k4_real_ns1(1))) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_1_ndiff_4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k4_real_ns1(1))) & A = D & ~ r1_xxreal_0(C,k2_normsp_0(k4_real_ns1(1),k5_algstr_0(k4_real_ns1(1),D,B))) ) ) ) )).
fof(fraenkel_a_2_1_openlatt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v11_lattices(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_1_openlatt(B,C)) <=> ? [D] : ( ~ v1_xboole_0(D) & v19_lattices(D,B) & v20_lattices(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & r2_hidden(C,D) ) ) ) )).
fof(fraenkel_a_2_1_orders_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_orders_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r2_hidden(E,C) => r2_orders_2(B,D,E) ) ) ) ) ) )).
fof(fraenkel_a_2_1_pcomps_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) => ( r2_hidden(A,a_2_1_pcomps_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & r2_hidden(D,C) & ~ r1_xboole_0(D,k2_struct_0(B)) ) ) ) )).
fof(fraenkel_a_2_1_pdiff_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_1_pdiff_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_numbers) & A = D & ~ r1_xxreal_0(C,k9_complex1(k6_xcmplx_0(D,B))) ) ) ) )).
fof(fraenkel_a_2_1_pdiff_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_1_pdiff_7(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & r1_xxreal_0(B,D) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_1_petri,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_petri(B) & v3_petri(B) & l1_petri(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_petri(B,C)) <=> ? [D] : ( m1_subset_1(D,u4_struct_0(B)) & A = D & ? [E] : ( m1_petri(E,u1_struct_0(B),u4_struct_0(B),u1_petri(B)) & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r2_hidden(F,C) & E = k1_domain_1(u1_struct_0(B),u4_struct_0(B),F,D) ) ) ) ) ) )).
fof(fraenkel_a_2_1_pnproc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) ) => ( r2_hidden(A,a_2_1_pnproc_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_nat_1(D,k3_finseq_1(B)) & r2_hidden(D,k9_xtuple_0(C)) ) ) ) )).
fof(fraenkel_a_2_1_polyred,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_ordinal1(B) & v1_partfun1(C,k15_pre_poly(B)) & v1_relat_2(C) & v4_relat_2(C) & v6_relat_2(C) & v8_relat_2(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),k15_pre_poly(B)))) ) => ( r2_hidden(A,a_2_1_polyred(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k5_finsub_1(u1_struct_0(g1_orders_2(k15_pre_poly(B),C)))) & m1_subset_1(E,k5_finsub_1(u1_struct_0(g1_orders_2(k15_pre_poly(B),C)))) & A = k4_tarski(D,E) & ( D = k1_xboole_0 | ( D != k1_xboole_0 & E != k1_xboole_0 & k11_bagorder(g1_orders_2(k15_pre_poly(B),C),D) != k11_bagorder(g1_orders_2(k15_pre_poly(B),C),E) & r2_hidden(k4_tarski(k11_bagorder(g1_orders_2(k15_pre_poly(B),C),D),k11_bagorder(g1_orders_2(k15_pre_poly(B),C),E)),u1_orders_2(g1_orders_2(k15_pre_poly(B),C))) ) ) ) ) ) )).
fof(fraenkel_a_2_1_pre_circ,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) & m1_trees_1(C,B) ) => ( r2_hidden(A,a_2_1_pre_circ(B,C)) <=> ? [D] : ( m1_trees_1(D,B) & A = D & ~ r1_tarski(C,D) ) ) ) )).
fof(fraenkel_a_2_1_pua2mss1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & ~ v1_xboole_0(B) & v1_funct_1(B) & m1_eqrel_1(C,k9_xtuple_0(B)) ) => ( r2_hidden(A,a_2_1_pua2mss1(B,C)) <=> ? [D] : ( m2_subset_1(D,k1_zfmisc_1(k9_xtuple_0(B)),C) & A = k5_relat_1(B,D) ) ) ) )).
fof(fraenkel_a_2_1_qc_lang1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(B) & m2_finseq_1(C,k2_qc_lang1(B)) ) => ( r2_hidden(A,a_2_1_qc_lang1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_funct_1(C,D) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(C)) & r2_hidden(k1_funct_1(C,D),k3_qc_lang1(B)) ) ) ) )).
fof(fraenkel_a_2_1_qc_lang3,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(B) & m1_subset_1(C,k9_qc_lang1(B)) ) => ( r2_hidden(A,a_2_1_qc_lang3(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_funct_1(k17_qc_lang1(B,C),D) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(k17_qc_lang1(B,C))) & r2_hidden(k1_funct_1(k17_qc_lang1(B,C),D),k3_qc_lang1(B)) ) ) ) )).
fof(fraenkel_a_2_1_quantal1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_group_1(B) & v10_lattices(B) & v4_lattice3(B) & v7_quantal1(B) & v8_quantal1(B) & l1_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_1_quantal1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r3_lattices(B,D,C) ) ) ) )).
fof(fraenkel_a_2_1_rcomp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xxreal_0(B) & v1_xxreal_0(C) ) => ( r2_hidden(A,a_2_1_rcomp_1(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(C,D) ) ) ) )).
fof(fraenkel_a_2_1_rfunct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_1_rfunct_3(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & r1_xxreal_0(B,D) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_1_rinfsup1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(A,a_2_1_rinfsup1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_funct_1(C,D) & r1_xxreal_0(B,D) ) ) ) )).
fof(fraenkel_a_2_1_rinfsup2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) & m1_subset_1(C,k4_ordinal1) ) => ( r2_hidden(A,a_2_1_rinfsup2(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k12_supinf_2(B,D) & r1_xxreal_0(C,D) ) ) ) )).
fof(fraenkel_a_2_1_rlaffin1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_rlaffin1(B,C)) <=> ? [D] : ( m2_rlvect_2(D,B,C) & A = k6_rlvect_2(B,D) & k3_rlaffin1(B,D) = 1 ) ) ) )).
fof(fraenkel_a_2_1_rlaffin2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_rlaffin2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k3_convex1(B,k7_subset_1(u1_struct_0(B),C,k6_domain_1(u1_struct_0(B),D))) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_1_rlsub_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) ) => ( r2_hidden(A,a_2_1_rlsub_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k3_rlvect_1(B,k4_struct_0(B),D) & r1_struct_0(C,D) ) ) ) )).
fof(fraenkel_a_2_1_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v6_rltopsp1(B) & v7_rltopsp1(B) & l1_rltopsp1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_rltopsp1(B,C)) <=> ? [D] : ( m1_connsp_2(D,B,k4_struct_0(B)) & A = k7_rusub_4(B,C,D) ) ) ) )).
fof(fraenkel_a_2_1_rlvect_x,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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) & m2_finseq_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_1_rlvect_x(B,C)) <=> ? [D] : ( v3_card_1(D,k3_finseq_1(C)) & m2_finseq_1(D,u1_struct_0(B)) & A = k4_rlvect_1(B,D) & ? [E] : ( v1_relat_1(E) & v5_relat_1(E,k4_numbers) & v1_funct_1(E) & v3_card_1(E,k3_finseq_1(C)) & v1_finseq_1(E) & ! [F] : ( v7_ordinal1(F) => ( r2_hidden(F,k2_finseq_1(k3_finseq_1(C))) => k7_partfun1(u1_struct_0(B),D,F) = k1_rlvect_1(B,k7_partfun1(u1_struct_0(B),C,F),k1_funct_1(E,F)) ) ) ) ) ) ) )).
fof(fraenkel_a_2_1_roughs_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_roughs_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ~ r1_xboole_0(k6_eqrel_1(u1_struct_0(B),u1_struct_0(B),u1_orders_2(B),D),C) ) ) ) )).
fof(fraenkel_a_2_1_rusub_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) ) => ( r2_hidden(A,a_2_1_rusub_5(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r1_struct_0(C,E) => r1_bhsp_1(B,E,D) ) ) ) ) ) )).
fof(fraenkel_a_2_1_scmfsa10,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ( r2_hidden(A,a_2_1_scmfsa10(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_amistd_1(k7_card_1(3),k1_scmfsa_2,D,k12_scmfsa_2(B,C)) ) ) ) )).
fof(fraenkel_a_2_1_scmfsa8a,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ( r2_hidden(A,a_2_1_scmfsa8a(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_nat_1(D,k5_card_1(B)) & r2_hidden(D,k2_afinsq_1(k3_scmfsa6a(k1_scmfsa8a(k1_nat_1(k5_card_1(C),1)),k3_scmfsa6a(C,k4_compos_1(k1_scmfsa_2))))) ) ) ) )).
fof(fraenkel_a_2_1_scmpds_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) & v3_scmpds_4(B) & v1_int_1(C) ) => ( r2_hidden(A,a_2_1_scmpds_4(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_nat_1(D,k5_card_1(B)) & r2_hidden(D,k2_afinsq_1(k9_compos_1(k1_scmpds_2,k3_scmpds_2(C)))) ) ) ) )).
fof(fraenkel_a_2_1_scmring3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_1_scmring3(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_amistd_1(k7_card_1(2),k1_scmring2(B),D,k8_scmring2(B,C)) ) ) ) )).
fof(fraenkel_a_2_1_setlim_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v1_funct_1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_1_setlim_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_funct_1(B,D) & r1_xxreal_0(C,D) ) ) ) )).
fof(fraenkel_a_2_1_sppol_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & m1_subset_1(C,u1_struct_0(k14_euclid(2))) ) => ( r2_hidden(A,a_2_1_sppol_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(2))) & A = D & ~ r1_xxreal_0(B,k3_metric_1(k14_euclid(2),C,D)) ) ) ) )).
fof(fraenkel_a_2_1_stirl2_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_1_stirl2_1(B,C)) <=> ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k7_card_1(k1_nat_1(C,1)),k7_card_1(k1_nat_1(B,1))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(k1_nat_1(C,1)),k7_card_1(k1_nat_1(B,1))))) & A = D & v2_funct_2(D,k7_card_1(k1_nat_1(B,1))) & v1_stirl2_1(D,k1_nat_1(C,1),k1_nat_1(B,1)) & k1_stirl2_1(k1_nat_1(C,1),k7_card_1(k1_nat_1(B,1)),D,k6_domain_1(k7_card_1(k1_nat_1(B,1)),k2_stirl2_1(k7_card_1(k1_nat_1(C,1)),k1_nat_1(B,1),D,C))) = k1_seq_4(C) ) ) ) )).
fof(fraenkel_a_2_1_substut1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(B) & m1_subset_1(C,k9_qc_lang1(B)) ) => ( r2_hidden(A,a_2_1_substut1(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_qc_lang1(B)) & A = D & r2_hidden(k2_qc_lang3(B,D),k9_substut1(B,C)) ) ) ) )).
fof(fraenkel_a_2_1_taylor_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_1_taylor_1(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(B,k6_xcmplx_0(B,C))) & ~ r1_xxreal_0(B,D) ) ) ) )).
fof(fraenkel_a_2_1_tdlat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) => ( r2_hidden(A,a_2_1_tdlat_2(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & D = k1_tops_1(B,E) & r2_hidden(E,C) ) ) ) ) )).
fof(fraenkel_a_2_1_tex_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_tex_1(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k4_subset_1(u1_struct_0(B),D,k9_subset_1(u1_struct_0(B),E,C)) & r2_hidden(D,u1_pre_topc(B)) & r2_hidden(E,u1_pre_topc(B)) ) ) ) )).
fof(fraenkel_a_2_1_tex_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_1_tex_4(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & v4_pre_topc(D,B) & r2_hidden(C,D) ) ) ) )).
fof(fraenkel_a_2_1_tmap_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_tmap_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k9_subset_1(u1_struct_0(B),D,C) & r2_hidden(D,u1_pre_topc(B)) ) ) ) )).
fof(fraenkel_a_2_1_topgen_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) => ( r2_hidden(A,a_2_1_topgen_2(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & A = k2_pre_topc(B,k5_setfam_1(u1_struct_0(B),D)) & r1_tarski(D,C) & v1_finset_1(k7_subset_1(k1_zfmisc_1(u1_struct_0(B)),C,D)) ) ) ) )).
fof(fraenkel_a_2_1_topgen_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v2_xxreal_0(C) ) => ( r2_hidden(A,a_2_1_topgen_5(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = k9_subset_1(u1_struct_0(k15_euclid(2)),k1_topreal9(2,k19_euclid(B,C),D),k2_topgen_5) & ~ r1_xxreal_0(D,k5_numbers) ) ) ) )).
fof(fraenkel_a_2_1_topreal4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_1_topreal4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) & A = D & ~ ( D != B & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ~ ( r1_topreal4(E,B,D) & r1_tarski(E,C) ) ) ) ) ) ) )).
fof(fraenkel_a_2_1_topreal6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_1_topreal6(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(C,D) ) ) ) )).
fof(fraenkel_a_2_1_topreal7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) => ( r2_hidden(A,a_2_1_topreal7(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(B)))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(C)))) & A = k3_borsuk_1(k3_pcomps_1(B),k3_pcomps_1(C),D,E) & r2_hidden(D,u1_pre_topc(k3_pcomps_1(B))) & r2_hidden(E,u1_pre_topc(k3_pcomps_1(C))) ) ) ) )).
fof(fraenkel_a_2_1_treal_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(B,u1_struct_0(k7_metric_1)) => ( r2_hidden(A,a_2_1_treal_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k7_metric_1)) & A = D & ~ r1_xxreal_0(C,k3_metric_1(k7_metric_1,B,D)) ) ) ) )).
fof(fraenkel_a_2_1_trees_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m2_finseq_1(B,k4_ordinal1) & ~ v1_xboole_0(C) & v1_trees_1(C) ) => ( r2_hidden(A,a_2_1_trees_1(B,C)) <=> ? [D] : ( m1_trees_1(D,C) & A = k8_finseq_1(k4_ordinal1,B,D) & D = D ) ) ) )).
fof(fraenkel_a_2_1_trees_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) & m1_trees_1(C,B) ) => ( r2_hidden(A,a_2_1_trees_2(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k7_finseq_1(C,k9_finseq_1(D)) & r2_hidden(k7_finseq_1(C,k9_finseq_1(D)),B) ) ) ) )).
fof(fraenkel_a_2_1_trees_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v3_trees_3(B) ) => ( r2_hidden(A,a_2_1_trees_9(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,B) & 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),C) ) ) ) ) )).
fof(fraenkel_a_2_1_trees_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) & m4_trees_1(C,B) ) => ( r2_hidden(A,a_2_1_trees_a(B,C)) <=> ? [D] : ( m1_trees_1(D,B) & A = D & ! [E] : ( m2_finseq_1(E,k4_ordinal1) => ~ ( r2_hidden(E,C) & r1_tarski(E,D) ) ) ) ) ) )).
fof(fraenkel_a_2_1_uniform1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_1_uniform1(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & r1_xxreal_0(B,D) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_1_uproots,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v6_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) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_1_uproots(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = D & ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(E,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) & r2_funct_2(k4_ordinal1,u1_struct_0(B),k4_polynom5(B,k4_algstr_0(B,C),k5_struct_0(B)),k13_polynom3(B,k2_polynom5(B,k4_polynom5(B,k4_algstr_0(B,C),k5_struct_0(B)),D),E)) ) ) ) ) )).
fof(fraenkel_a_2_1_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(A,a_2_1_valued_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = D & r1_xxreal_0(k1_nat_1(B,1),D) & r1_xxreal_0(D,k1_nat_1(B,k3_finseq_1(C))) ) ) ) )).
fof(fraenkel_a_2_1_waybel10,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & v4_yellow_0(C,B) & v7_yellow_0(C,B) & m1_yellow_0(C,B) ) => ( r2_hidden(A,a_2_1_waybel10(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r3_orders_2(B,k3_funct_2(u1_struct_0(B),u1_struct_0(B),k6_waybel10(B,C),D),D) ) ) ) )).
fof(fraenkel_a_2_1_waybel11,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) & ~ v2_struct_0(C) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_1_waybel11(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k2_waybel_0(B,C,D) ) ) ) )).
fof(fraenkel_a_2_1_waybel12,axiom,( ! [A] : ! [B] : ! [C] : ( ( v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_waybel12(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_tarski(k4_yellow_4(B,C,k6_domain_1(u1_struct_0(B),D)),C) ) ) ) )).
fof(fraenkel_a_2_1_waybel13,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_1_waybel13(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_orders_2(B,D,C) & v1_waybel_3(D,B) ) ) ) )).
fof(fraenkel_a_2_1_waybel14,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v3_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_waybel14(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k6_waybel_0(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_1_waybel15,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_1_waybel15(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_waybel_3(B,D,C) ) ) ) )).
fof(fraenkel_a_2_1_waybel16,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_1_waybel16(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_orders_2(B,D,C) & v1_waybel_3(D,B) ) ) ) )).
fof(fraenkel_a_2_1_waybel20,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & v22_waybel_0(C,B,B) & v8_waybel_1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) ) => ( r2_hidden(A,a_2_1_waybel20(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) & A = k1_domain_1(k1_zfmisc_1(u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)),k6_eqrel_1(u1_struct_0(B),u1_struct_0(B),k2_waybel20(B,k4_waybel20(B,C)),D),k6_eqrel_1(u1_struct_0(B),u1_struct_0(B),k2_waybel20(B,k4_waybel20(B,C)),E)) & r3_orders_2(B,k3_funct_2(u1_struct_0(B),u1_struct_0(B),C,D),k3_funct_2(u1_struct_0(B),u1_struct_0(B),C,E)) ) ) ) )).
fof(fraenkel_a_2_1_waybel21,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v7_waybel_0(C) & v8_waybel_0(C,B) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_1_waybel21(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k2_yellow_0(B,a_3_1_waybel21(B,C,D)) ) ) ) )).
fof(fraenkel_a_2_1_waybel22,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ( r2_hidden(A,a_2_1_waybel22(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k2_yellow_1(B))) & A = k6_waybel_0(k2_yellow_1(B),D) & ? [E] : ( m1_subset_1(E,B) & D = k1_tarski(E) & r2_hidden(E,C) ) ) ) ) )).
fof(fraenkel_a_2_1_waybel23,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_waybel23(B,C)) <=> ? [D] : ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(C)) & A = k1_yellow_0(B,D) & r1_yellow_0(B,D) ) ) ) )).
fof(fraenkel_a_2_1_waybel29,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & v2_pre_topc(C) & l1_pre_topc(C) ) => ( r2_hidden(A,a_2_1_waybel29(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) & A = k3_borsuk_1(B,C,D,E) & r2_hidden(D,u1_pre_topc(B)) & r2_hidden(E,u1_pre_topc(C)) ) ) ) )).
fof(fraenkel_a_2_1_waybel30,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_waybel30(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ! [E] : ( ( ~ v1_xboole_0(E) & v1_waybel_0(E,B) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) ) => ~ ( r3_orders_2(B,D,k1_yellow_0(B,E)) & r1_xboole_0(C,E) ) ) ) ) ) )).
fof(fraenkel_a_2_1_waybel31,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_waybel31(B,C)) <=> ? [D] : ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(C)) & A = k1_yellow_0(B,D) & r1_yellow_0(B,D) ) ) ) )).
fof(fraenkel_a_2_1_waybel32,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v16_waybel_0(B) & l1_orders_2(B) & v4_waybel11(C) & m1_yellow_9(C,B) ) => ( r2_hidden(A,a_2_1_waybel32(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k3_subset_1(u1_struct_0(C),k5_waybel_0(C,D)) ) ) ) )).
fof(fraenkel_a_2_1_waybel33,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v25_waybel_0(B) & v2_lattice3(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_1_waybel33(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k2_yellow_0(B,a_3_3_waybel33(B,C,D)) ) ) ) )).
fof(fraenkel_a_2_1_waybel_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_waybel_0(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r1_orders_2(B,E,D) & r2_hidden(E,C) ) ) ) ) )).
fof(fraenkel_a_2_1_waybel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) & 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(A,a_2_1_waybel_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r3_orders_2(B,k3_funct_2(u1_struct_0(B),u1_struct_0(B),C,D),D) ) ) ) )).
fof(fraenkel_a_2_1_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & v2_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & v1_waybel_0(C,k3_yellow_3(B,B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) ) => ( r2_hidden(A,a_2_1_waybel_2(B,C)) <=> ? [D] : ( ~ v1_xboole_0(D) & v1_waybel_0(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k1_yellow_0(B,D) & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & D = k4_yellow_4(B,k6_domain_1(u1_struct_0(B),E),k5_yellow_3(B,B,C)) & r2_hidden(E,k4_yellow_3(B,B,C)) ) ) ) ) )).
fof(fraenkel_a_2_1_waybel_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_1_waybel_3(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_waybel_3(B,C,D) ) ) ) )).
fof(fraenkel_a_2_1_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) => ( r2_hidden(A,a_2_1_waybel_4(B,C)) <=> ? [D] : ( ~ 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))) & A = k3_funct_2(u1_struct_0(B),u1_struct_0(k1_yellow_1(k7_waybel_0(B))),k11_waybel_4(B,D),C) ) ) ) )).
fof(fraenkel_a_2_1_waybel_8,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k2_yellow_1(B))) => ( r2_hidden(A,a_2_1_waybel_8(B,C)) <=> ? [D] : ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(C)) & A = D ) ) ) )).
fof(fraenkel_a_2_1_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_1_waybel_9(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k13_lattice3(B,C,D) & r2_hidden(D,k2_struct_0(B)) ) ) ) )).
fof(fraenkel_a_2_1_weddwitt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_1_weddwitt(B,C)) <=> ? [D] : ( m2_subset_1(D,u1_struct_0(B),k7_group_3(B,C)) & A = k8_relset_1(u1_struct_0(B),k7_group_3(B,C),k2_weddwitt(B,C),k1_tarski(D)) ) ) ) )).
fof(fraenkel_a_2_1_xxreal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xxreal_0(B) & v1_xxreal_0(C) ) => ( r2_hidden(A,a_2_1_xxreal_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k6_numbers) & A = D & r1_xxreal_0(B,D) & ~ r1_xxreal_0(C,D) ) ) ) )).
fof(fraenkel_a_2_1_yellow11,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_1_yellow11(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r1_orders_2(B,E,D) & r2_hidden(E,k6_domain_1(u1_struct_0(B),C)) ) ) ) ) )).
fof(fraenkel_a_2_1_yellow15,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_1_yellow15(B,C)) <=> ? [D] : ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(B)),u1_pre_topc(B)) & A = D & r2_hidden(C,D) ) ) ) )).
fof(fraenkel_a_2_1_yellow19,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) & ~ v2_struct_0(C) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_1_yellow19(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & r1_waybel_0(B,C,D) ) ) ) )).
fof(fraenkel_a_2_1_yellow_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) ) => ( r2_hidden(A,a_2_1_yellow_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & D = k3_funct_2(u1_struct_0(B),u1_struct_0(B),C,D) ) ) ) )).
fof(fraenkel_a_2_1_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) ) => ( r2_hidden(A,a_2_1_yellow_4(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & D = k3_yellow_4(B,k6_domain_1(u1_struct_0(B),E),k5_yellow_3(B,B,C)) & r2_hidden(E,k4_yellow_3(B,B,C)) ) ) ) ) )).
fof(fraenkel_a_2_1_yellow_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) & m4_yellow_6(C,B) ) => ( r2_hidden(A,a_2_1_yellow_6(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r2_hidden(E,D) => ! [F] : ( ( ~ v2_struct_0(F) & v4_orders_2(F) & v7_waybel_0(F) & l1_waybel_0(F,B) ) => ( r2_hidden(k4_tarski(F,E),C) => r1_waybel_0(B,F,D) ) ) ) ) ) ) ) )).
fof(fraenkel_a_2_1_yellow_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_1_yellow_9(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k6_waybel_0(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_1_zf_colla,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v3_ordinal1(C) ) => ( r2_hidden(A,a_2_1_zf_colla(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = D & ! [E] : ( m1_subset_1(E,B) => ~ ( r2_hidden(E,D) & ! [F] : ( v3_ordinal1(F) => ~ ( r2_hidden(F,C) & r2_hidden(E,k1_zf_colla(B,F)) ) ) ) ) ) ) ) )).
fof(fraenkel_a_2_1_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) ) => ( r2_hidden(A,a_2_1_zf_fund1(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = k5_classes2(B,k6_classes2(B,k2_ordinal4(B),D),k6_classes2(B,k3_ordinal4(B),D)) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_1_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(C,B) ) => ( r2_hidden(A,a_2_1_zmodul01(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k3_rlvect_1(B,k4_struct_0(B),D) & r1_struct_0(C,D) ) ) ) )).
fof(fraenkel_a_2_1_zmodul02,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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(C,B) ) => ( r2_hidden(A,a_2_1_zmodul02(B,C)) <=> ? [D] : ( m2_zmodul01(D,B,C) & A = D ) ) ) )).
fof(fraenkel_a_2_20_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) ) => ( r2_hidden(A,a_2_20_armstrng(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(B))) & A = k8_setfam_1(B,D) & r1_tarski(D,C) ) ) ) )).
fof(fraenkel_a_2_20_waybel30,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & v2_waybel_2(B) & l1_waybel_9(B) & m1_subset_1(C,u1_struct_0(o_1_16_waybel30(B))) ) => ( r2_hidden(A,a_2_20_waybel30(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k2_yellow_0(B,D) & r2_hidden(C,D) & r2_hidden(D,k2_waybel19(B)) ) ) ) )).
fof(fraenkel_a_2_21_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & v6_armstrng(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(B),k9_setfam_1(B)))) ) => ( r2_hidden(A,a_2_21_armstrng(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(B))) & A = k8_setfam_1(B,D) & r1_tarski(D,k9_armstrng(B,C)) ) ) ) )).
fof(fraenkel_a_2_22_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) ) => ( r2_hidden(A,a_2_22_armstrng(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(B))) & A = k8_setfam_1(B,D) & r1_tarski(D,k2_armstrng(C)) ) ) ) )).
fof(fraenkel_a_2_22_waybel11,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_22_waybel11(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & r2_hidden(D,a_1_1_waybel11(B)) & r1_tarski(D,C) ) ) ) )).
fof(fraenkel_a_2_23_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) ) => ( r2_hidden(A,a_2_23_armstrng(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(B)) & A = k6_armstrng(B,D,E) & ! [F] : ( ( r2_hidden(F,C) & r1_tarski(D,F) ) => r1_tarski(E,F) ) ) ) ) )).
fof(fraenkel_a_2_24_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) ) => ( r2_hidden(A,a_2_24_armstrng(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = D & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(B)) => ~ ( r2_hidden(E,C) & k9_subset_1(B,D,E) = k1_xboole_0 ) ) ) ) ) )).
fof(fraenkel_a_2_24_conlat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_conlat_1(B) & m1_subset_1(C,k1_zfmisc_1(u4_struct_0(k7_conlat_2(B)))) ) => ( r2_hidden(A,a_2_24_conlat_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k7_conlat_2(B))) & A = D & ! [E] : ( m1_subset_1(E,u4_struct_0(k7_conlat_2(B))) => ( r2_hidden(E,C) => r1_conlat_1(k7_conlat_2(B),D,E) ) ) ) ) ) )).
fof(fraenkel_a_2_25_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & ~ v1_xboole_0(C) ) => ( r2_hidden(A,a_2_25_armstrng(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = k1_funct_4(k1_margrel1(k4_ordinal1,B,k5_numbers),k1_margrel1(k1_zfmisc_1(B),D,D)) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_25_conlat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_conlat_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k7_conlat_2(B)))) ) => ( r2_hidden(A,a_2_25_conlat_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u4_struct_0(k7_conlat_2(B))) & A = D & ! [E] : ( m1_subset_1(E,u1_struct_0(k7_conlat_2(B))) => ( r2_hidden(E,C) => r1_conlat_1(k7_conlat_2(B),E,D) ) ) ) ) ) )).
fof(fraenkel_a_2_25_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & v1_algstr_1(B) & v1_int_3(B) & l6_algstr_0(B) & ~ v1_xboole_0(C) & v1_ideal_1(C,B) & v2_ideal_1(C,B) & v3_ideal_1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_25_ideal_1(B,C)) <=> ? [D] : ( m2_subset_1(D,u1_struct_0(B),C) & A = D & D != k4_struct_0(B) ) ) ) )).
fof(fraenkel_a_2_26_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & v2_armstrng(C) & l1_armstrng(C) ) => ( r2_hidden(A,a_2_26_armstrng(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = D & r2_hidden(k4_tarski(D,B),k8_armstrng(u1_armstrng(C),k5_armstrng(C))) ) ) ) )).
fof(fraenkel_a_2_27_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) ) => ( r2_hidden(A,a_2_27_armstrng(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(B)) & A = k6_armstrng(B,D,E) & ! [F] : ( ( r2_hidden(F,C) & r1_tarski(D,F) ) => r1_tarski(E,F) ) ) ) ) )).
fof(fraenkel_a_2_28_member_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_membered(B) & v1_xcmplx_0(C) ) => ( r2_hidden(A,a_2_28_member_1(B,C)) <=> ? [D] : ? [E] : ( v1_xcmplx_0(D) & v1_xcmplx_0(E) & A = k6_xcmplx_0(D,E) & r2_hidden(D,k1_tarski(C)) & r2_hidden(E,B) ) ) ) )).
fof(fraenkel_a_2_29_member_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_membered(B) & v1_xcmplx_0(C) ) => ( r2_hidden(A,a_2_29_member_1(B,C)) <=> ? [D] : ? [E] : ( v1_xcmplx_0(D) & v1_xcmplx_0(E) & A = k6_xcmplx_0(D,E) & r2_hidden(D,B) & r2_hidden(E,k1_tarski(C)) ) ) ) )).
fof(fraenkel_a_2_2_abcmiz_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v1_abcmiz_0(B) & ~ v4_abcmiz_0(B) & v9_abcmiz_0(B) & v14_abcmiz_0(B) & l3_abcmiz_0(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_2_abcmiz_0(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(u1_abcmiz_0(B))) & r6_abcmiz_0(B,D,E) & k6_abcmiz_0(B,D,E) = C ) ) ) ) )).
fof(fraenkel_a_2_2_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & l1_msualg_1(B) & v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v6_trees_3(C) ) => ( r2_hidden(A,a_2_2_abcmiz_1(B,C)) <=> ? [D] : ( m1_abcmiz_1(D,B,k14_abcmiz_1(B)) & A = k46_abcmiz_1(B,D) & r2_hidden(D,k10_xtuple_0(C)) ) ) ) )).
fof(fraenkel_a_2_2_abcmiz_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & v1_abcmiz_a(B) & l1_msualg_1(B) & m1_subset_1(C,u4_struct_0(B)) ) => ( r2_hidden(A,a_2_2_abcmiz_a(B,C)) <=> ? [D] : ( m1_dtconstr(D,u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))),k5_trees_3(u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers)))))),k1_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))) & A = D & k7_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),D) = k2_msualg_1(B,C) & r2_pboole(u1_struct_0(B),k4_msafree3(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),D),k28_abcmiz_1(B)) ) ) ) )).
fof(fraenkel_a_2_2_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ( r2_hidden(A,a_2_2_afinsq_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_xcmplx_0(D,B) & r2_hidden(D,k2_afinsq_1(C)) ) ) ) )).
fof(fraenkel_a_2_2_algstr_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) & v1_relat_1(C) & v5_relat_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) & v1_funct_1(C) ) => ( r2_hidden(A,a_2_2_algstr_4(B,C)) <=> ? [D] : ( v1_partfun1(D,u1_struct_0(B)) & v3_relat_2(D) & v8_relat_2(D) & v1_algstr_4(D,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) & A = D & ! [E] : ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ( ( r2_hidden(E,k9_xtuple_0(C)) & k1_funct_1(C,E) = k4_tarski(F,G) ) => r2_hidden(F,k6_eqrel_1(u1_struct_0(B),u1_struct_0(B),D,G)) ) ) ) ) ) ) )).
fof(fraenkel_a_2_2_ami_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_2_ami_6(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_amistd_1(k7_card_1(2),k1_ami_3,D,k9_ami_3(C,B)) ) ) ) )).
fof(fraenkel_a_2_2_amistd_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_setfam_1(B) & m1_subset_1(C,u1_compos_1(k4_amistd_1(B))) ) => ( r2_hidden(A,a_2_2_amistd_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_amistd_1(B,k4_amistd_1(B),D,C) ) ) ) )).
fof(fraenkel_a_2_2_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_2_2_armstrng(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(B)) & A = k6_armstrng(B,D,E) & ( r1_tarski(C,D) | r1_tarski(E,D) ) ) ) ) )).
fof(fraenkel_a_2_2_asympt_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(A,a_2_2_asympt_0(B,C)) <=> ? [D] : ( m2_funct_2(D,k4_ordinal1,k1_numbers,k9_funct_2(k4_ordinal1,k1_numbers)) & A = D & ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & ? [G] : ( m1_subset_1(G,k4_ordinal1) & ~ r1_xxreal_0(E,k5_numbers) & ~ r1_xxreal_0(F,k5_numbers) & ! [H] : ( m1_subset_1(H,k4_ordinal1) => ( ( r1_xxreal_0(G,H) & r2_hidden(H,C) ) => ( r1_xxreal_0(k3_xcmplx_0(F,k9_nat_1(k1_numbers,B,H)),k9_nat_1(k1_numbers,D,H)) & r1_xxreal_0(k9_nat_1(k1_numbers,D,H),k3_xcmplx_0(E,k9_nat_1(k1_numbers,B,H))) ) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_2_2_bagorder,axiom,( ! [A] : ! [B] : ! [C] : ( v3_ordinal1(B) => ( r2_hidden(A,a_2_2_bagorder(B,C)) <=> ? [D] : ( m2_subset_1(D,k14_pre_poly(B),k15_pre_poly(B)) & A = k3_bagorder(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_2_bcialg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & m2_subset_1(C,u1_struct_0(B),k5_bcialg_1(B)) ) => ( r2_hidden(A,a_2_2_bcialg_4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_bcialg_1(B,k6_bcialg_1(B,C,C),D) ) ) ) )).
fof(fraenkel_a_2_2_bintree2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) & v1_bintree1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_2_bintree2(B,C)) <=> ? [D] : ( m1_bintree2(D,B) & A = D & k3_finseq_1(D) = C ) ) ) )).
fof(fraenkel_a_2_2_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & ~ v2_struct_0(C) & m1_pre_topc(C,B) ) => ( r2_hidden(A,a_2_2_borsuk_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k6_domain_1(u1_struct_0(B),D) & ~ r2_hidden(D,u1_struct_0(C)) ) ) ) )).
fof(fraenkel_a_2_2_borsuk_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & v2_pre_topc(C) & l1_pre_topc(C) ) => ( r2_hidden(A,a_2_2_borsuk_3(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k2_borsuk_1(C,B))))) & A = k5_setfam_1(u1_struct_0(k2_borsuk_1(C,B)),D) & r1_tarski(D,a_2_1_borsuk_3(B,C)) ) ) ) )).
fof(fraenkel_a_2_2_borsuk_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k5_topmetr)) & m1_subset_1(C,u1_struct_0(k5_topmetr)) ) => ( r2_hidden(A,a_2_2_borsuk_4(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & r1_xxreal_0(B,D) & ~ r1_xxreal_0(C,D) ) ) ) )).
fof(fraenkel_a_2_2_card_3,axiom,( ! [A] : ! [B] : ! [C] : ( v4_funct_1(B) => ( r2_hidden(A,a_2_2_card_3(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = k1_funct_1(D,C) ) ) ) )).
fof(fraenkel_a_2_2_card_fin,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(B) & v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,a_2_2_card_fin(B,C)) <=> ? [D] : ( v1_funct_1(D) & v1_funct_2(D,B,k10_xtuple_0(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k10_xtuple_0(C)))) & A = D & v2_funct_1(D) & ! [E] : ~ ( r2_hidden(E,B) & k1_funct_1(D,E) = k1_funct_1(C,E) ) ) ) ) )).
fof(fraenkel_a_2_2_cc0sp2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xcmplx_0(C) ) => ( r2_hidden(A,a_2_2_cc0sp2(B,C)) <=> ? [D] : ( v1_xcmplx_0(D) & A = D & ~ r1_xxreal_0(B,k9_complex1(k6_xcmplx_0(D,C))) ) ) ) )).
fof(fraenkel_a_2_2_cgames_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_cgames_1(C) ) => ( r2_hidden(A,a_2_2_cgames_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k6_cgames_1(C)) & A = k1_funct_1(B,D) & k6_cgames_1(C) != k1_xboole_0 ) ) ) )).
fof(fraenkel_a_2_2_chord,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) & m3_glib_001(C,B) ) => ( r2_hidden(A,a_2_2_chord(B,C)) <=> ? [D] : ( v5_glib_001(D,B) & m3_glib_001(D,B) & A = k3_finseq_1(D) & r1_glib_001(B,k3_glib_001(B,C),k4_glib_001(B,C),D) ) ) ) )).
fof(fraenkel_a_2_2_classes1,axiom,( ! [A] : ! [B] : ! [C] : ( v3_ordinal1(C) => ( r2_hidden(A,a_2_2_classes1(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_classes1(B)) & A = D & ? [E] : ( v3_ordinal1(E) & r2_hidden(E,C) & r2_hidden(D,k3_classes1(B,E)) ) ) ) ) )).
fof(fraenkel_a_2_2_combgras,axiom,( ! [A] : ! [B] : ! [C] : ( v1_finset_1(C) => ( r2_hidden(A,a_2_2_combgras(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = D & k1_card_1(D) = k1_nat_1(k5_card_1(C),1) & r1_tarski(C,D) ) ) ) )).
fof(fraenkel_a_2_2_compl_sp,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v6_metric_1(B) & v8_metric_1(B) & v9_metric_1(B) & l1_metric_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_compl_sp(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k3_pcomps_1(B))) & A = k6_domain_1(u1_struct_0(k3_pcomps_1(B)),D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_2_compos_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_compos_0(B) & v2_compos_0(B) & v3_compos_0(B) & m1_subset_1(C,B) ) => ( r2_hidden(A,a_2_2_compos_0(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = k5_xtuple_0(D) & k2_compos_0(B,C) = k2_compos_0(B,D) ) ) ) )).
fof(fraenkel_a_2_2_conlat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_conlat_1(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_2_conlat_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u4_struct_0(B)) & A = D & r1_conlat_1(B,C,D) ) ) ) )).
fof(fraenkel_a_2_2_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_2_2_domain_1(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = D & ~ r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_2_fcont_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & m1_subset_1(C,k1_numbers) ) => ( r2_hidden(A,a_2_2_fcont_1(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(B,k6_xcmplx_0(C,B))) & ~ r1_xxreal_0(k2_xcmplx_0(B,k6_xcmplx_0(C,B)),D) ) ) ) )).
fof(fraenkel_a_2_2_fdiff_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_2_fdiff_2(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(k3_xxreal_0(B,C),1)) & ~ r1_xxreal_0(k2_xcmplx_0(k4_xxreal_0(B,C),1),D) ) ) ) )).
fof(fraenkel_a_2_2_fin_topo,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_fin_topo(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ~ r1_xboole_0(k1_fin_topo(B,D),C) ) ) ) )).
fof(fraenkel_a_2_2_finance1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_2_finance1(B,C)) <=> ? [D] : ( m1_subset_1(D,k6_numbers) & A = D & r1_xxreal_0(B,D) & ~ r1_xxreal_0(C,D) ) ) ) )).
fof(fraenkel_a_2_2_fintopo2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_fintopo2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_fintopo2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(E,k6_fintopo2(B,D)) & r1_tarski(E,C) ) ) ) ) )).
fof(fraenkel_a_2_2_fomodel1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_2_fomodel1(B,C)) <=> ? [D] : ( v10_fomodel1(D,B) & m1_subset_1(D,k1_fomodel1(B)) & A = k24_fomodel1(B,D,k1_funct_1(k28_fomodel1(B),C)) & v6_fomodel1(D,B) ) ) ) )).
fof(fraenkel_a_2_2_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_2_fomodel2(B,C)) <=> ? [D] : ? [E] : ( m2_subset_1(D,k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0)),k24_fomodel2(B,C)) & m2_subset_1(E,k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0)),k24_fomodel2(B,C)) & A = k42_fomodel1(B,k42_fomodel1(B,k43_fomodel1(B,k1_fomodel2(B)),D),E) ) ) ) )).
fof(fraenkel_a_2_2_freealg,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r2_hidden(A,a_2_2_freealg(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k3_freealg(B,C))) & A = D & ? [E] : ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) & r1_lang1(k3_freealg(B,C),D,E) ) ) ) ) )).
fof(fraenkel_a_2_2_fvaluat1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & m1_fvaluat1(C,B) ) => ( r2_hidden(A,a_2_2_fvaluat1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ~ r1_xxreal_0(k3_funct_2(u1_struct_0(B),k6_numbers,C,D),k5_numbers) ) ) ) )).
fof(fraenkel_a_2_2_goboard5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_2_goboard5(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(D,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k1_nat_1(C,1),1))) ) ) ) )).
fof(fraenkel_a_2_2_goboard6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_2_goboard6(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & ~ r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,1)),D) & ~ r1_xxreal_0(E,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,B))) & ~ r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,k1_nat_1(B,1))),E) ) ) ) )).
fof(fraenkel_a_2_2_goboard9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_2_goboard9(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & ~ r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,k1_nat_1(B,1))),E) ) ) ) )).
fof(fraenkel_a_2_2_gobrd11,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_2_gobrd11(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(D,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,1))) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,B)),E) & r1_xxreal_0(E,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,k1_nat_1(B,1)))) ) ) ) )).
fof(fraenkel_a_2_2_gobrd13,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_2_gobrd13(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,B,1)),D) & r1_xxreal_0(D,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(B,1),1))) & r1_xxreal_0(E,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,1))) ) ) ) )).
fof(fraenkel_a_2_2_goedelcp,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(B) & m2_finseq_1(C,k3_cqc_lang(B)) ) => ( r2_hidden(A,a_2_2_goedelcp(B,C)) <=> ? [D] : ( m2_subset_1(D,k9_qc_lang1(B),k3_cqc_lang(B)) & A = k24_qc_lang1(B,D) & r2_hidden(D,k2_relset_1(k3_cqc_lang(B),C)) ) ) ) )).
fof(fraenkel_a_2_2_graph_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ( r2_hidden(A,a_2_2_graph_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u4_struct_0(B)) & r2_hidden(E,C) & ( D = k1_funct_1(u1_graph_1(B),E) | D = k1_funct_1(u2_graph_1(B),E) ) ) ) ) ) )).
fof(fraenkel_a_2_2_graph_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) & m2_finseq_1(C,u4_struct_0(B)) ) => ( r2_hidden(A,a_2_2_graph_5(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,k4_ordinal1) & r2_hidden(E,k4_finseq_1(C)) & r2_hidden(D,k1_graph_5(B,k7_partfun1(u4_struct_0(B),C,E))) ) ) ) ) )).
fof(fraenkel_a_2_2_graphsp,axiom,( ! [A] : ! [B] : ! [C] : ( ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) & m1_subset_1(C,k4_ordinal1) ) => ( r2_hidden(A,a_2_2_graphsp(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = D & r2_hidden(D,k4_finseq_1(B)) & r1_xxreal_0(1,D) & r1_xxreal_0(D,C) & k1_funct_1(B,D) = k4_xcmplx_0(1) ) ) ) )).
fof(fraenkel_a_2_2_group_10,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) ) => ( r2_hidden(A,a_2_2_group_10(B,C)) <=> ? [D] : ( m1_subset_1(D,C) & A = k2_zfmisc_1(B,k6_domain_1(C,D)) ) ) ) )).
fof(fraenkel_a_2_2_group_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_2_group_3(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k6_domain_1(u1_struct_0(B),D) & r2_hidden(D,k7_group_3(B,C)) ) ) ) )).
fof(fraenkel_a_2_2_group_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_group_4(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & ? [E] : ( v15_algstr_0(E) & m1_group_2(E,B) & D = u1_struct_0(E) & r1_tarski(k7_subset_1(u1_struct_0(B),C,k6_domain_1(u1_struct_0(B),k1_group_1(B))),k8_group_2(B,E)) ) ) ) ) )).
fof(fraenkel_a_2_2_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_finset_1(C) ) => ( r2_hidden(A,a_2_2_group_9(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = k4_tarski(k6_xcmplx_0(D,1),D) & r2_hidden(D,C) & ~ r1_xxreal_0(D,B) ) ) ) )).
fof(fraenkel_a_2_2_integra2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_2_integra2(B,C)) <=> ? [D] : ( m1_subset_1(D,k6_numbers) & A = k4_xxreal_3(C,D) & r2_hidden(D,B) ) ) ) )).
fof(fraenkel_a_2_2_interva1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_roughs_1(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k21_interva1(B)))) ) => ( r2_hidden(A,a_2_2_interva1(B,C)) <=> ? [D] : ( m2_interva1(D,B) & A = k15_interva1(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_2_jct_misc,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(A,a_2_2_jct_misc(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k9_complex1(k6_xcmplx_0(D,E)) & r2_hidden(D,B) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_2_jgraph_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_2_jgraph_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) & A = D & ~ r1_xxreal_0(k17_euclid(D),k6_xcmplx_0(k17_euclid(B),k7_xcmplx_0(C,k3_square_1(2)))) & ~ r1_xxreal_0(k2_xcmplx_0(k17_euclid(B),k7_xcmplx_0(C,k3_square_1(2))),k17_euclid(D)) & ~ r1_xxreal_0(k18_euclid(D),k6_xcmplx_0(k18_euclid(B),k7_xcmplx_0(C,k3_square_1(2)))) & ~ r1_xxreal_0(k2_xcmplx_0(k18_euclid(B),k7_xcmplx_0(C,k3_square_1(2))),k18_euclid(D)) ) ) ) )).
fof(fraenkel_a_2_2_jordan2b,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_2_jordan2b(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = k9_finseq_1(D) & ~ r1_xxreal_0(D,k6_xcmplx_0(C,B)) & ~ r1_xxreal_0(k2_xcmplx_0(C,B),D) ) ) ) )).
fof(fraenkel_a_2_2_jordan2c,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_2_jordan2c(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(B))) & A = D & ~ r1_xxreal_0(k12_euclid(D),C) ) ) ) )).
fof(fraenkel_a_2_2_jordan3,axiom,( ! [A] : ! [B] : ! [C] : ( ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) & m1_subset_1(C,k4_ordinal1) ) => ( r2_hidden(A,a_2_2_jordan3(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_topreal1(2,k2_rfinseq(u1_struct_0(k15_euclid(2)),C,B),D) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(k2_rfinseq(u1_struct_0(k15_euclid(2)),C,B))) ) ) ) )).
fof(fraenkel_a_2_2_jordan5a,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_2_jordan5a(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & r1_xxreal_0(B,D) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_2_jordan5b,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_2_jordan5b(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & r1_xxreal_0(B,D) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_2_jordan6,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k7_metric_1)) & m1_subset_1(C,k1_numbers) ) => ( r2_hidden(A,a_2_2_jordan6(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k7_metric_1)) & A = D & ~ r1_xxreal_0(C,k3_metric_1(k7_metric_1,B,D)) ) ) ) )).
fof(fraenkel_a_2_2_jordan7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v2_compts_1(B,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))) ) => ( r2_hidden(A,a_2_2_jordan7(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) & A = D & r1_jordan6(B,k18_pscomp_1(B),D) & r1_jordan6(B,D,C) ) ) ) )).
fof(fraenkel_a_2_2_jordan_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_jordan_a(C,B) ) => ( r2_hidden(A,a_2_2_jordan_a(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = k4_jordan1k(2,k2_jordan_a(B,k3_finseq_1(C),C),k2_jordan_a(B,D,C)) & ~ r1_xxreal_0(D,1) & ~ r1_xxreal_0(k7_nat_d(k3_finseq_1(C),1),D) ) ) ) )).
fof(fraenkel_a_2_2_knaster,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & 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(A,a_2_2_knaster(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r2_abian(u1_struct_0(B),D,C) ) ) ) )).
fof(fraenkel_a_2_2_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) ) => ( r2_hidden(A,a_2_2_lattice3(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r4_lattice3(B,D,C) ) ) ) )).
fof(fraenkel_a_2_2_lattice5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m2_lattice5(C,u1_struct_0(B),B,k16_lattice5(B)) ) => ( r2_hidden(A,a_2_2_lattice5(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = k2_xtuple_0(k1_funct_1(C,D)) ) ) ) )).
fof(fraenkel_a_2_2_lattice6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_2_lattice6(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r3_lattices(B,C,D) & D != C ) ) ) )).
fof(fraenkel_a_2_2_limfunc3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_2_limfunc3(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,C) & ~ r1_xxreal_0(k2_xcmplx_0(C,B),D) ) ) ) )).
fof(fraenkel_a_2_2_limfunc4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r2_hidden(A,a_2_2_limfunc4(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k1_limfunc2(C,B)) ) ) ) )).
fof(fraenkel_a_2_2_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_rlvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_mathmorp(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k4_algstr_0(B,D) & r2_hidden(D,k2_mathmorp(B,C)) ) ) ) )).
fof(fraenkel_a_2_2_matroid0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v3_pencil_1(B) & v1_matroid0(B) & v2_matroid0(B) & v4_matroid0(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_matroid0(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r2_matroid0(B,D,C) ) ) ) )).
fof(fraenkel_a_2_2_member_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_membered(B) & v2_membered(C) ) => ( r2_hidden(A,a_2_2_member_1(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k6_numbers) & m1_subset_1(E,k6_numbers) & A = k3_xxreal_3(D,E) & r2_hidden(D,B) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_2_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_mmlquery(B) & m2_finseq_1(C,u1_mmlquery(B)) ) => ( r2_hidden(A,a_2_2_mmlquery(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_tarski(k30_mmlquery(B,D),k2_relset_1(u1_mmlquery(B),C)) ) ) ) )).
fof(fraenkel_a_2_2_modal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) & m1_trees_1(C,B) ) => ( r2_hidden(A,a_2_2_modal_1(B,C)) <=> ? [D] : ( m2_finseq_2(D,k4_ordinal1,k3_finseq_2(k4_ordinal1)) & A = k8_finseq_1(k4_ordinal1,C,D) & r2_hidden(k8_finseq_1(k4_ordinal1,C,D),B) ) ) ) )).
fof(fraenkel_a_2_2_modelc_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_modelc_2(B) & v5_modelc_3(B) & m2_finseq_1(B,k4_ordinal1) & v1_modelc_3(C,B) & l1_modelc_3(C,B) ) => ( r2_hidden(A,a_2_2_modelc_3(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k15_modelc_2)) & A = D & r1_tarski(k27_modelc_3(B,C),D) & r1_xboole_0(k28_modelc_3(B,C),D) ) ) ) )).
fof(fraenkel_a_2_2_moebius1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_int_2(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_2_moebius1(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = D & ~ r1_xxreal_0(D,k5_numbers) & r1_nat_d(D,C) & ~ r1_nat_d(B,D) ) ) ) )).
fof(fraenkel_a_2_2_msafree3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ( r2_hidden(A,a_2_2_msafree3(B,C)) <=> ? [D] : ( m1_subset_1(D,k10_xtuple_0(B)) & A = k1_xtuple_0(D) & k2_xtuple_0(D) = C ) ) ) )).
fof(fraenkel_a_2_2_nattra_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & 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) ) => ( r2_hidden(A,a_2_2_nattra_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k6_cat_2(B,C))) & A = k4_cat_1(k6_cat_2(B,C),D) ) ) ) )).
fof(fraenkel_a_2_2_ndiff_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k1_numbers) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_2_ndiff_4(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_numbers) & A = D & ~ r1_xxreal_0(C,k9_complex1(k5_real_1(D,B))) ) ) ) )).
fof(fraenkel_a_2_2_petri,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_petri(B) & v3_petri(B) & l1_petri(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_petri(B,C)) <=> ? [D] : ( m1_petri(D,u4_struct_0(B),u1_struct_0(B),u2_petri(B)) & A = k4_petri(B,D) & r2_hidden(k5_petri(B,D),C) ) ) ) )).
fof(fraenkel_a_2_2_polyred,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_ordinal1(B) & v1_partfun1(C,k15_pre_poly(B)) & v1_relat_2(C) & v4_relat_2(C) & v6_relat_2(C) & v8_relat_2(C) & v2_bagorder(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),k15_pre_poly(B)))) ) => ( r2_hidden(A,a_2_2_polyred(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k5_finsub_1(u1_struct_0(g1_orders_2(k15_pre_poly(B),C)))) & m1_subset_1(E,k5_finsub_1(u1_struct_0(g1_orders_2(k15_pre_poly(B),C)))) & A = k4_tarski(D,E) & ( D = k1_xboole_0 | ( D != k1_xboole_0 & E != k1_xboole_0 & k11_bagorder(g1_orders_2(k15_pre_poly(B),C),D) != k11_bagorder(g1_orders_2(k15_pre_poly(B),C),E) & r2_hidden(k4_tarski(k11_bagorder(g1_orders_2(k15_pre_poly(B),C),D),k11_bagorder(g1_orders_2(k15_pre_poly(B),C),E)),u1_orders_2(g1_orders_2(k15_pre_poly(B),C))) ) ) ) ) ) )).
fof(fraenkel_a_2_2_qc_lang1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(B) & m1_subset_1(C,k9_qc_lang1(B)) ) => ( r2_hidden(A,a_2_2_qc_lang1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_funct_1(k17_qc_lang1(B,C),D) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(k17_qc_lang1(B,C))) & r2_hidden(k1_funct_1(k17_qc_lang1(B,C),D),k3_qc_lang1(B)) ) ) ) )).
fof(fraenkel_a_2_2_quantal1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v1_group_1(B) & v3_group_1(B) & v10_lattices(B) & v4_lattice3(B) & v7_quantal1(B) & v8_quantal1(B) & v20_quantal1(B) & v21_quantal1(B) & l3_quantal1(B) ) => ( r2_hidden(A,a_2_2_quantal1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k6_algstr_0(B,k16_lattice3(B,a_2_0_quantal1(B,C)),D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_2_rcomp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xxreal_0(C) ) => ( r2_hidden(A,a_2_2_rcomp_1(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & r1_xxreal_0(B,D) & ~ r1_xxreal_0(C,D) ) ) ) )).
fof(fraenkel_a_2_2_rinfsup2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( r2_hidden(A,a_2_2_rinfsup2(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k12_supinf_2(C,D) & r1_xxreal_0(B,D) ) ) ) )).
fof(fraenkel_a_2_2_rlaffin1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_rlvect_1(B) & v2_rusub_4(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_rlaffin1(B,C)) <=> ? [D] : ( v2_rusub_4(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & r1_tarski(C,D) ) ) ) )).
fof(fraenkel_a_2_2_rlaffin2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_rlaffin2(B,C)) <=> ? [D] : ( v2_convex1(D,B) & m2_rlvect_2(D,B,C) & A = k6_rlvect_2(B,D) & r2_hidden(D,k1_convex3(B)) ) ) ) )).
fof(fraenkel_a_2_2_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_rltopsp1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k1_algstr_0(B,k4_struct_0(B),D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_2_roughs_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v8_struct_0(B) & v2_roughs_1(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_roughs_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & k3_funct_2(u1_struct_0(B),k1_numbers,k6_roughs_1(B,C),D) = 1 ) ) ) )).
fof(fraenkel_a_2_2_rusub_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_rusub_5(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r2_hidden(E,C) => r1_bhsp_1(B,E,D) ) ) ) ) ) )).
fof(fraenkel_a_2_2_scmfsa10,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ( r2_hidden(A,a_2_2_scmfsa10(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_amistd_1(k7_card_1(3),k1_scmfsa_2,D,k13_scmfsa_2(B,C)) ) ) ) )).
fof(fraenkel_a_2_2_scmring3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_2_scmring3(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_compos_1(k1_scmring2(B))) & A = k7_subset_1(k4_ordinal1,k1_amistd_1(k7_card_1(2),k1_scmring2(B),C,D),k2_amistd_1(k7_card_1(2),k1_scmring2(B),D)) ) ) ) )).
fof(fraenkel_a_2_2_simplex1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_simplex1(B,C)) <=> ? [D] : ( v2_convex1(D,B) & m2_rlvect_2(D,B,C) & A = k6_rlvect_2(B,D) & r2_hidden(D,k1_convex3(B)) ) ) ) )).
fof(fraenkel_a_2_2_sppol_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) & m1_subset_1(C,k4_ordinal1) ) => ( r2_hidden(A,a_2_2_sppol_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_topreal1(2,B,D) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(B)) & D != C & D != k1_nat_1(C,1) ) ) ) )).
fof(fraenkel_a_2_2_stirl2_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_2_stirl2_1(B,C)) <=> ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k7_card_1(C),k7_card_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(C),k7_card_1(B)))) & A = D & v2_funct_2(D,k7_card_1(B)) & v1_stirl2_1(D,C,B) ) ) ) )).
fof(fraenkel_a_2_2_substut1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(B) & v1_finset_1(C) & m1_subset_1(C,k1_substut1(B)) ) => ( r2_hidden(A,a_2_2_substut1(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_qc_lang1(B)) & A = D & r2_hidden(k2_qc_lang3(B,D),k10_xtuple_0(C)) ) ) ) )).
fof(fraenkel_a_2_2_taylor_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_2_taylor_1(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(k2_xcmplx_0(B,k6_xcmplx_0(C,B)),D) ) ) ) )).
fof(fraenkel_a_2_2_tdlat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) => ( r2_hidden(A,a_2_2_tdlat_2(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & D = k2_pre_topc(B,k1_tops_1(B,E)) & r2_hidden(E,C) ) ) ) ) )).
fof(fraenkel_a_2_2_tdlat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_tdlat_3(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r2_hidden(F,C) & E = k1_tarski(F) & D = k2_pre_topc(B,E) ) ) ) ) ) )).
fof(fraenkel_a_2_2_tex_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_tex_4(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & v3_pre_topc(D,B) & r1_tarski(D,C) ) ) ) )).
fof(fraenkel_a_2_2_topdim_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k14_euclid(1))) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_2_topdim_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(1))) & A = D & r1_xxreal_0(k3_metric_1(k14_euclid(1),B,D),C) ) ) ) )).
fof(fraenkel_a_2_2_topreal6,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_2_topreal6(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(k17_euclid(B),k7_xcmplx_0(C,k3_square_1(2)))) & ~ r1_xxreal_0(k2_xcmplx_0(k17_euclid(B),k7_xcmplx_0(C,k3_square_1(2))),D) ) ) ) )).
fof(fraenkel_a_2_2_treal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k7_metric_1)) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_2_treal_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k7_metric_1)) & A = D & ~ r1_xxreal_0(C,k3_metric_1(k7_metric_1,B,D)) ) ) ) )).
fof(fraenkel_a_2_2_trees_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) & m1_trees_2(C,B) ) => ( r2_hidden(A,a_2_2_trees_2(B,C)) <=> ? [D] : ( m1_trees_1(D,B) & A = D & ? [E] : ( m2_finseq_1(E,k4_ordinal1) & r2_hidden(E,C) & r1_tarski(D,E) ) ) ) ) )).
fof(fraenkel_a_2_2_trees_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(C) & v3_trees_3(C) ) => ( r2_hidden(A,a_2_2_trees_9(B,C)) <=> ? [D] : ( m1_subset_1(D,C) & A = k7_trees_9(D,B) ) ) ) )).
fof(fraenkel_a_2_2_trees_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) & m4_trees_1(C,k9_xtuple_0(B)) ) => ( r2_hidden(A,a_2_2_trees_a(B,C)) <=> ? [D] : ( m1_trees_1(D,k9_xtuple_0(B)) & A = D & ! [E] : ( m2_finseq_1(E,k4_ordinal1) => ~ ( r2_hidden(E,C) & r1_tarski(E,D) ) ) ) ) ) )).
fof(fraenkel_a_2_2_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,a_2_2_valued_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_xcmplx_0(D,B) & r2_hidden(D,k9_xtuple_0(C)) ) ) ) )).
fof(fraenkel_a_2_2_waybel11,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_2_waybel11(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k2_yellow_0(B,a_3_1_waybel11(B,C,D)) ) ) ) )).
fof(fraenkel_a_2_2_waybel12,axiom,( ! [A] : ! [B] : ! [C] : ( ( v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & v13_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_waybel12(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_tarski(k4_yellow_4(B,C,k6_domain_1(u1_struct_0(B),D)),C) ) ) ) )).
fof(fraenkel_a_2_2_waybel13,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v1_yellow_0(B) & v2_waybel_8(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & v1_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_waybel13(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_orders_2(B,D,k1_yellow_0(B,C)) & v1_waybel_3(D,B) ) ) ) )).
fof(fraenkel_a_2_2_waybel14,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & v2_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_waybel14(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k3_subset_1(u1_struct_0(B),k5_waybel_0(B,D)) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_2_waybel15,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_2_waybel15(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_waybel_3(B,D,C) ) ) ) )).
fof(fraenkel_a_2_2_waybel19,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_yellow_0(C) & l1_orders_2(C) ) => ( r2_hidden(A,a_2_2_waybel19(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(o_2_1_waybel19(B,C))) & A = k3_subset_1(u1_struct_0(o_2_1_waybel19(B,C)),k6_waybel_0(o_2_1_waybel19(B,C),D)) ) ) ) )).
fof(fraenkel_a_2_2_waybel23,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_waybel23(B,C)) <=> ? [D] : ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(C)) & A = k1_yellow_0(B,D) & r1_yellow_0(B,D) ) ) ) )).
fof(fraenkel_a_2_2_waybel24,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_waybel24(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_2_waybel28,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_2_waybel28(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k2_waybel_0(B,C,D) & r1_orders_2(C,o_2_1_waybel28(B,C),D) ) ) ) )).
fof(fraenkel_a_2_2_waybel29,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v6_pre_topc(B) & l1_pre_topc(B) & v4_waybel11(C) & m1_yellow_9(C,k1_yellow_1(u1_pre_topc(B))) ) => ( r2_hidden(A,a_2_2_waybel29(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k3_borsuk_1(C,B,D,E) & r2_hidden(D,u1_pre_topc(C)) & r2_hidden(E,u1_pre_topc(B)) ) ) ) )).
fof(fraenkel_a_2_2_waybel30,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v4_waybel11(B) & v2_waybel_2(B) & l1_waybel_9(B) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_waybel30(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k2_waybel_3(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_2_waybel32,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_2_waybel32(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k2_yellow_0(B,a_3_2_waybel32(B,C,D)) ) ) ) )).
fof(fraenkel_a_2_2_waybel33,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_2_waybel33(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k2_yellow_0(B,a_3_4_waybel33(B,C,D)) ) ) ) )).
fof(fraenkel_a_2_2_waybel_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_waybel_0(B,C)) <=> ? [D] : ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(C)) & A = k1_yellow_0(B,D) & r1_yellow_0(B,D) ) ) ) )).
fof(fraenkel_a_2_2_waybel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_2_waybel_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & k11_lattice3(B,C,D) = k3_yellow_0(B) ) ) ) )).
fof(fraenkel_a_2_2_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & v1_waybel_0(C,k3_yellow_3(B,B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) ) => ( r2_hidden(A,a_2_2_waybel_2(B,C)) <=> ? [D] : ( ~ v1_xboole_0(D) & v1_waybel_0(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & D = k4_yellow_4(B,k6_domain_1(u1_struct_0(B),E),k5_yellow_3(B,B,C)) & r2_hidden(E,k4_yellow_3(B,B,C)) ) ) ) ) )).
fof(fraenkel_a_2_2_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & v2_lattice3(B) & v2_waybel_2(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_2_waybel_4(B,C)) <=> ? [D] : ( v5_waybel_4(D,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) & A = k5_waybel_4(B,C,D) & r2_hidden(D,k12_waybel_4(B)) ) ) ) )).
fof(fraenkel_a_2_2_waybel_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_2_waybel_6(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_waybel_3(B,D,C) ) ) ) )).
fof(fraenkel_a_2_2_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_2_waybel_9(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & k13_lattice3(B,D,C) = C ) ) ) )).
fof(fraenkel_a_2_2_weddwitt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v8_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_2_weddwitt(B,C)) <=> ? [D] : ( m2_subset_1(D,u1_struct_0(B),k7_group_3(B,C)) & A = k8_relset_1(u1_struct_0(B),k7_group_3(B,C),k2_weddwitt(B,C),k1_tarski(D)) ) ) ) )).
fof(fraenkel_a_2_2_xxreal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xxreal_0(B) & v1_xxreal_0(C) ) => ( r2_hidden(A,a_2_2_xxreal_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k6_numbers) & A = D & ~ r1_xxreal_0(D,B) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_2_yellow_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_2_2_yellow_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_lattice3(B,C,D) ) ) ) )).
fof(fraenkel_a_2_2_yellow_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_2_yellow_9(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k5_waybel_0(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_2_zf_colla,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v3_ordinal1(C) ) => ( r2_hidden(A,a_2_2_zf_colla(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = D & ! [E] : ( m1_subset_1(E,B) => ~ ( r2_hidden(E,D) & ! [F] : ( v3_ordinal1(F) => ~ ( r2_hidden(F,k1_ordinal1(C)) & r2_hidden(E,k1_zf_colla(B,F)) ) ) ) ) ) ) ) )).
fof(fraenkel_a_2_2_zf_model,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) & ~ v1_xboole_0(C) ) => ( r2_hidden(A,a_2_2_zf_model(B,C)) <=> ? [D] : ( m1_subset_1(D,k3_zf_model(C)) & A = D & ! [E] : ( ( 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))) ) => ( E = D => k3_funct_2(k1_zf_lang,C,E,k18_zf_lang(B)) = k3_funct_2(k1_zf_lang,C,E,k19_zf_lang(B)) ) ) ) ) ) )).
fof(fraenkel_a_2_2_zmodul02,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) & m1_zmodul02(C,B) ) => ( r2_hidden(A,a_2_2_zmodul02(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & k3_funct_2(u1_struct_0(B),k4_numbers,C,D) != k5_numbers ) ) ) )).
fof(fraenkel_a_2_3_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & l1_msualg_1(B) & m1_trees_4(C,k3_card_3(u3_msualg_1(B,k1_msafree3(B,k28_abcmiz_1(B)))),k34_abcmiz_1(B)) ) => ( r2_hidden(A,a_2_3_abcmiz_1(B,C)) <=> ? [D] : ( m1_abcmiz_1(D,B,k14_abcmiz_1(B)) & A = k45_abcmiz_1(B,D) & r2_hidden(D,k2_relset_1(k3_card_3(u3_msualg_1(B,k1_msafree3(B,k28_abcmiz_1(B)))),C)) ) ) ) )).
fof(fraenkel_a_2_3_amistd_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_setfam_1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_3_amistd_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_compos_1(k4_amistd_1(B))) & A = k7_subset_1(k4_ordinal1,k1_amistd_1(B,k4_amistd_1(B),C,D),k2_amistd_1(B,k4_amistd_1(B),D)) ) ) ) )).
fof(fraenkel_a_2_3_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_2_3_armstrng(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = k6_armstrng(B,D,D) & ~ r1_tarski(C,D) ) ) ) )).
fof(fraenkel_a_2_3_asympt_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_funct_2(B,k4_ordinal1,k1_numbers) & m1_funct_2(C,k4_ordinal1,k1_numbers) ) => ( r2_hidden(A,a_2_3_asympt_0(B,C)) <=> ? [D] : ( m2_funct_2(D,k4_ordinal1,k1_numbers,k9_funct_2(k4_ordinal1,k1_numbers)) & A = D & ? [E] : ( m2_funct_2(E,k4_ordinal1,k1_numbers,k9_funct_2(k4_ordinal1,k1_numbers)) & ? [F] : ( m2_funct_2(F,k4_ordinal1,k1_numbers,k9_funct_2(k4_ordinal1,k1_numbers)) & ? [G] : ( m1_subset_1(G,k4_ordinal1) & r2_hidden(E,B) & r2_hidden(F,C) & ! [H] : ( m1_subset_1(H,k4_ordinal1) => ( r1_xxreal_0(G,H) => k9_nat_1(k1_numbers,D,H) = k2_power(k9_nat_1(k1_numbers,E,H),k9_nat_1(k1_numbers,F,H)) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_2_3_bcialg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_bcialg_1(B) & v4_bcialg_1(B) & v5_bcialg_1(B) & v7_bcialg_1(B) & v8_bcialg_1(B) & v2_bcialg_4(B) & v3_bcialg_4(B) & l1_bcialg_4(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_3_bcialg_4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_bcialg_1(B,D,C) ) ) ) )).
fof(fraenkel_a_2_3_borsuk_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & v2_pre_topc(C) & l1_pre_topc(C) ) => ( r2_hidden(A,a_2_3_borsuk_3(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) & A = k3_borsuk_1(B,C,D,E) & r2_hidden(D,u1_pre_topc(B)) & r2_hidden(E,u1_pre_topc(C)) ) ) ) )).
fof(fraenkel_a_2_3_cgames_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_ordinal1(B) & v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) ) => ( r2_hidden(A,a_2_3_cgames_1(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(k3_tarski(k10_xtuple_0(k5_relat_1(C,B))))) & m1_subset_1(E,k1_zfmisc_1(k3_tarski(k10_xtuple_0(k5_relat_1(C,B))))) & A = g1_cgames_1(D,E) ) ) ) )).
fof(fraenkel_a_2_3_classes1,axiom,( ! [A] : ! [B] : ! [C] : ( v3_ordinal1(C) => ( r2_hidden(A,a_2_3_classes1(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_classes1(B)) & A = D & ? [E] : ( m1_subset_1(E,k1_classes1(B)) & r2_hidden(E,k2_classes1(B,C)) & r1_tarski(D,E) ) ) ) ) )).
fof(fraenkel_a_2_3_combgras,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k4_ordinal1) & ~ v1_xboole_0(C) ) => ( r2_hidden(A,a_2_3_combgras(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(C)) & A = D & k1_card_1(D) = B ) ) ) )).
fof(fraenkel_a_2_3_compact1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v8_pre_topc(B) & l1_pre_topc(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_3_compact1(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & v3_pre_topc(D,B) & r1_tarski(D,C) ) ) ) )).
fof(fraenkel_a_2_3_conlat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_conlat_1(B) & m1_subset_1(C,u4_struct_0(B)) ) => ( r2_hidden(A,a_2_3_conlat_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_conlat_1(B,D,C) ) ) ) )).
fof(fraenkel_a_2_3_fcont_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_3_fcont_1(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & r1_xxreal_0(B,D) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_3_fin_topo,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_3_fin_topo(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r2_hidden(D,C) & r1_xboole_0(k7_subset_1(u1_struct_0(B),k1_fin_topo(B,D),k6_domain_1(u1_struct_0(B),D)),C) ) ) ) )).
fof(fraenkel_a_2_3_finance1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) => ( r2_hidden(A,a_2_3_finance1(B,C)) <=> ? [D] : ( m1_random_1(D,B,C) & A = D ) ) ) )).
fof(fraenkel_a_2_3_finseq_2,axiom,( ! [A] : ! [B] : ! [C] : ( m2_finseq_1(C,B) => ( r2_hidden(A,a_2_3_finseq_2(B,C)) <=> ? [D] : ( m2_finseq_2(D,B,k3_finseq_2(B)) & A = D & k3_finseq_1(D) = k3_finseq_1(C) ) ) ) )).
fof(fraenkel_a_2_3_fintopo2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_fintopo2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_3_fintopo2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r2_hidden(D,C) & ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(E,k6_fintopo2(B,D)) & r1_xboole_0(k7_subset_1(u1_struct_0(B),E,k6_domain_1(u1_struct_0(B),D)),C) ) ) ) ) )).
fof(fraenkel_a_2_3_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v4_funct_1(B) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_2_3_fomodel0(B,C)) <=> ? [D] : ( m1_subset_1(D,C) & A = k10_xtuple_0(D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_3_goboard5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_3_goboard5(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,C)),E) & r1_xxreal_0(E,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,k1_nat_1(C,1)))) ) ) ) )).
fof(fraenkel_a_2_3_goboard6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_3_goboard6(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & ~ r1_xxreal_0(D,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k3_finseq_1(C),1))) & ~ r1_xxreal_0(E,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,B))) & ~ r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,k1_nat_1(B,1))),E) ) ) ) )).
fof(fraenkel_a_2_3_goboard9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_3_goboard9(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & ~ r1_xxreal_0(D,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,B,1))) & ~ r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(B,1),1)),D) ) ) ) )).
fof(fraenkel_a_2_3_gobrd11,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_3_gobrd11(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k3_finseq_1(C),1)),D) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,B)),E) & r1_xxreal_0(E,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,k1_nat_1(B,1)))) ) ) ) )).
fof(fraenkel_a_2_3_gobrd13,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_3_gobrd13(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,B,1)),D) & r1_xxreal_0(E,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,1))) ) ) ) )).
fof(fraenkel_a_2_3_graph_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) & v7_graph_1(C,B) & m2_graph_1(C,B) ) => ( r2_hidden(A,a_2_3_graph_5(B,C)) <=> ? [D] : ( v7_graph_1(D,B) & v1_graph_4(D,B) & m2_graph_1(D,B) & A = D & D != k1_xboole_0 & k1_funct_1(u1_graph_1(B),k1_funct_1(D,1)) = k1_funct_1(u1_graph_1(B),k1_funct_1(C,1)) & k1_funct_1(u2_graph_1(B),k1_funct_1(D,k3_finseq_1(D))) = k1_funct_1(u2_graph_1(B),k1_funct_1(C,k3_finseq_1(C))) & r1_tarski(k10_xtuple_0(D),k10_xtuple_0(C)) ) ) ) )).
fof(fraenkel_a_2_3_graphsp,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k4_ordinal1) & m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) ) => ( r2_hidden(A,a_2_3_graphsp(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = D & r2_hidden(D,k4_finseq_1(C)) & r1_xxreal_0(1,D) & r1_xxreal_0(D,B) & k1_funct_1(C,D) != k4_xcmplx_0(1) & k1_funct_1(C,k1_nat_1(B,D)) != k4_xcmplx_0(1) ) ) ) )).
fof(fraenkel_a_2_3_group_10,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v1_xboole_0(C) ) => ( r2_hidden(A,a_2_3_group_10(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(C)) & A = D & k1_card_1(D) = B ) ) ) )).
fof(fraenkel_a_2_3_group_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_3_group_3(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & k4_group_3(B,C,D) = C ) ) ) )).
fof(fraenkel_a_2_3_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_finset_1(C) ) => ( r2_hidden(A,a_2_3_group_9(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = D & r2_hidden(D,C) & ~ r1_xxreal_0(D,k1_nat_1(B,1)) ) ) ) )).
fof(fraenkel_a_2_3_heyting1,axiom,( ! [A] : ! [B] : ! [C] : ( m2_subset_1(C,k5_finsub_1(k7_normform(B)),k8_normform(B)) => ( r2_hidden(A,a_2_3_heyting1(B,C)) <=> ? [D] : ( m2_funct_2(D,k7_normform(B),k1_heyting1(B),k9_funct_2(k7_normform(B),k1_heyting1(B))) & A = k4_tarski(a_3_3_heyting1(B,C,D),a_3_4_heyting1(B,C,D)) & ! [E] : ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B)) => ( r2_hidden(E,C) => r2_hidden(k3_funct_2(k7_normform(B),k1_heyting1(B),D,E),k5_setwiseo(B,k2_domain_1(k5_finsub_1(B),k5_finsub_1(B),E),k3_domain_1(k5_finsub_1(B),k5_finsub_1(B),E))) ) ) ) ) ) )).
fof(fraenkel_a_2_3_jct_misc,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(C) & v1_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(A,a_2_3_jct_misc(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k9_complex1(k6_xcmplx_0(D,E)) & r2_hidden(D,B) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_3_jordan2b,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k7_metric_1)) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_3_jordan2b(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k7_metric_1)) & A = D & ~ r1_xxreal_0(C,k3_metric_1(k7_metric_1,B,D)) ) ) ) )).
fof(fraenkel_a_2_3_jordan2c,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_3_jordan2c(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(B))) & A = D & ~ r1_xxreal_0(C,k12_euclid(D)) ) ) ) )).
fof(fraenkel_a_2_3_jordan5a,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_3_jordan5a(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(B,C)) & ~ r1_xxreal_0(k2_xcmplx_0(B,C),D) ) ) ) )).
fof(fraenkel_a_2_3_jordan6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_3_jordan6(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & r2_hidden(D,B) & ~ r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_3_jordan_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_jordan_a(C,B) ) => ( r2_hidden(A,a_2_3_jordan_a(B,C)) <=> ? [D] : ? [E] : ( v7_ordinal1(D) & v7_ordinal1(E) & A = k4_jordan1k(2,k2_jordan_a(B,D,C),k2_jordan_a(B,E,C)) & r1_xxreal_0(1,D) & ~ r1_xxreal_0(E,D) & r1_xxreal_0(E,k3_finseq_1(C)) & r1_subset_1(k2_jordan_a(B,D,C),k2_jordan_a(B,E,C)) ) ) ) )).
fof(fraenkel_a_2_3_knaster,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & 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)))) ) => ( r2_hidden(A,a_2_3_knaster(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r2_abian(u1_struct_0(B),D,C) ) ) ) )).
fof(fraenkel_a_2_3_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_3_lattice3(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r3_lattices(B,D,C) ) ) ) )).
fof(fraenkel_a_2_3_lattice6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_3_lattice6(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r3_lattices(B,D,C) & D != C ) ) ) )).
fof(fraenkel_a_2_3_limfunc3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_3_limfunc3(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(B,C)) & ~ r1_xxreal_0(k2_xcmplx_0(B,C),D) ) ) ) )).
fof(fraenkel_a_2_3_limfunc4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_3_limfunc4(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(k2_xcmplx_0(B,C),D) ) ) ) )).
fof(fraenkel_a_2_3_lopclset,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v7_struct_0(B) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_3_lopclset(B,C)) <=> ? [D] : ( m1_subset_1(D,k5_finsub_1(u1_struct_0(B))) & A = k2_lattice4(B,D) & r1_tarski(D,C) & D != k1_xboole_0 ) ) ) )).
fof(fraenkel_a_2_3_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_rlvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_3_mathmorp(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,D,E) & r2_hidden(D,C) & r2_hidden(E,k6_domain_1(u1_struct_0(B),k4_struct_0(B))) ) ) ) )).
fof(fraenkel_a_2_3_measure6,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_3_measure6(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = k2_xcmplx_0(k4_xcmplx_0(C),D) & r2_hidden(D,B) ) ) ) )).
fof(fraenkel_a_2_3_member_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_membered(B) & v1_membered(C) ) => ( r2_hidden(A,a_2_3_member_1(B,C)) <=> ? [D] : ? [E] : ( v1_xcmplx_0(D) & v1_xcmplx_0(E) & A = k6_xcmplx_0(D,E) & r2_hidden(D,B) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_3_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_mmlquery(B) & m2_finseq_1(C,u1_mmlquery(B)) ) => ( r2_hidden(A,a_2_3_mmlquery(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & k30_mmlquery(B,D) = k2_relset_1(u1_mmlquery(B),C) ) ) ) )).
fof(fraenkel_a_2_3_modelc_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_modelc_2(B) & v5_modelc_3(B) & m2_finseq_1(B,k4_ordinal1) & v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ( r2_hidden(A,a_2_3_modelc_3(B,C)) <=> ? [D] : ( m1_subset_1(D,k23_modelc_3(B)) & A = D & ~ ( r2_hidden(C,u1_modelc_3(B,k10_modelc_3(D,B))) & ~ r2_hidden(k12_modelc_2(C),u1_modelc_3(B,k10_modelc_3(D,B))) ) ) ) ) )).
fof(fraenkel_a_2_3_moebius1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_int_2(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_3_moebius1(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = D & ~ r1_xxreal_0(D,k5_numbers) & r1_nat_d(D,k3_nat_d(C,B)) ) ) ) )).
fof(fraenkel_a_2_3_ndiff_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k4_real_ns1(1))) & m1_subset_1(C,k1_numbers) ) => ( r2_hidden(A,a_2_3_ndiff_4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k4_real_ns1(1))) & A = D & ~ r1_xxreal_0(C,k2_normsp_0(k4_real_ns1(1),k5_algstr_0(k4_real_ns1(1),D,B))) ) ) ) )).
fof(fraenkel_a_2_3_orders_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_3_orders_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r2_hidden(E,k6_domain_1(u1_struct_0(B),C)) => r2_orders_2(B,D,E) ) ) ) ) ) )).
fof(fraenkel_a_2_3_ordinal6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_ordinal1(B) & v4_ordinal1(B) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & v1_classes2(C) ) => ( r2_hidden(A,a_2_3_ordinal6(B,C)) <=> ? [D] : ( m1_subset_1(D,k9_xtuple_0(k1_funct_1(k5_relat_1(k11_ordinal6(C),B),k5_numbers))) & A = D & r2_hidden(D,k9_xtuple_0(k1_funct_1(k5_relat_1(k11_ordinal6(C),B),k5_numbers))) & ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v5_ordinal1(E) & v1_ordinal2(E) ) => ( r2_hidden(E,k10_xtuple_0(k5_relat_1(k11_ordinal6(C),B))) => r1_abian(D,E) ) ) ) ) ) )).
fof(fraenkel_a_2_3_petri,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_petri(B) & v3_petri(B) & l1_petri(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_3_petri(B,C)) <=> ? [D] : ( m1_petri(D,u1_struct_0(B),u4_struct_0(B),u1_petri(B)) & A = k3_petri(B,D) & r2_hidden(k2_petri(B,D),C) ) ) ) )).
fof(fraenkel_a_2_3_qc_lang1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(B) & m1_subset_1(C,k1_qc_lang1(B)) ) => ( r2_hidden(A,a_2_3_qc_lang1(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_qc_lang1(B)) & A = D & r2_qc_lang1(B,C,D) ) ) ) )).
fof(fraenkel_a_2_3_quantal1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v1_group_1(B) & v3_group_1(B) & v10_lattices(B) & v4_lattice3(B) & v7_quantal1(B) & v8_quantal1(B) & v20_quantal1(B) & v21_quantal1(B) & l3_quantal1(B) ) => ( r2_hidden(A,a_2_3_quantal1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k5_quantal1(B,D) & r2_hidden(D,a_2_0_quantal1(B,C)) ) ) ) )).
fof(fraenkel_a_2_3_rcomp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xxreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_3_rcomp_1(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,B) & r1_xxreal_0(D,C) ) ) ) )).
fof(fraenkel_a_2_3_rcomp_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_2_3_rcomp_3(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & A = D & m1_setfam_1(D,u1_struct_0(B)) & r1_tarski(D,C) ) ) ) )).
fof(fraenkel_a_2_3_rinfsup1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(A,a_2_3_rinfsup1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_funct_1(C,D) & r1_xxreal_0(k1_nat_1(B,1),D) ) ) ) )).
fof(fraenkel_a_2_3_rinfsup2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & m1_subset_1(C,k4_ordinal1) ) => ( r2_hidden(A,a_2_3_rinfsup2(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k12_supinf_2(B,D) & r1_xxreal_0(C,D) ) ) ) )).
fof(fraenkel_a_2_3_rlaffin1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_3_rlaffin1(B,C)) <=> ? [D] : ( v2_convex1(D,B) & m2_rlvect_2(D,B,C) & A = k6_rlvect_2(B,D) & r2_hidden(D,k1_convex3(B)) ) ) ) )).
fof(fraenkel_a_2_3_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v6_rltopsp1(B) & v7_rltopsp1(B) & l1_rltopsp1(B) & v3_pre_topc(C,B) & m1_connsp_2(C,B,k4_struct_0(B)) ) => ( r2_hidden(A,a_2_3_rltopsp1(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,D,E) & r2_hidden(D,C) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_3_rolle,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_3_rolle(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(k2_xcmplx_0(B,C),D) ) ) ) )).
fof(fraenkel_a_2_3_roughs_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v8_struct_0(B) & v2_roughs_1(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_3_roughs_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ~ r1_xxreal_0(k3_funct_2(u1_struct_0(B),k1_numbers,k6_roughs_1(B,C),D),k5_numbers) ) ) ) )).
fof(fraenkel_a_2_3_rusub_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_3_rusub_5(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & k2_bhsp_1(B,D,C) = k5_numbers ) ) ) )).
fof(fraenkel_a_2_3_setlim_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ( r2_hidden(A,a_2_3_setlim_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_funct_1(C,D) & r1_xxreal_0(k5_numbers,D) ) ) ) )).
fof(fraenkel_a_2_3_stirl2_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_3_stirl2_1(B,C)) <=> ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k7_card_1(k1_nat_1(C,1)),k7_card_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(k1_nat_1(C,1)),k7_card_1(B)))) & A = D & v2_funct_2(D,k7_card_1(B)) & v1_stirl2_1(D,k1_nat_1(C,1),B) & k1_stirl2_1(k1_nat_1(C,1),k7_card_1(B),D,k1_seq_4(k2_stirl2_1(k7_card_1(k1_nat_1(C,1)),B,D,C))) != k1_seq_4(C) ) ) ) )).
fof(fraenkel_a_2_3_tdlat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) => ( r2_hidden(A,a_2_3_tdlat_2(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & D = k1_tops_1(B,k2_pre_topc(B,E)) & r2_hidden(E,C) ) ) ) ) )).
fof(fraenkel_a_2_3_tex_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,B) ) => ( r2_hidden(A,a_2_3_tex_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = D & r2_hidden(C,D) & D != B ) ) ) )).
fof(fraenkel_a_2_3_tex_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_3_tex_4(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & v1_tex_4(D,B) & r2_hidden(C,D) ) ) ) )).
fof(fraenkel_a_2_3_topdim_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & m1_subset_1(C,k1_numbers) ) => ( r2_hidden(A,a_2_3_topdim_2(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = k9_finseq_1(D) & r1_xxreal_0(k3_xxreal_3(C,B),D) & r1_xxreal_0(D,k1_xxreal_3(C,B)) ) ) ) )).
fof(fraenkel_a_2_3_topreal6,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_3_topreal6(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(k18_euclid(B),k7_xcmplx_0(C,k3_square_1(2)))) & ~ r1_xxreal_0(k2_xcmplx_0(k18_euclid(B),k7_xcmplx_0(C,k3_square_1(2))),D) ) ) ) )).
fof(fraenkel_a_2_3_treal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k7_metric_1)) & m1_subset_1(C,k1_numbers) ) => ( r2_hidden(A,a_2_3_treal_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k7_metric_1)) & A = D & ~ r1_xxreal_0(C,k3_metric_1(k7_metric_1,B,D)) ) ) ) )).
fof(fraenkel_a_2_3_trees_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v1_xboole_0(C) & v1_trees_1(C) ) => ( r2_hidden(A,a_2_3_trees_9(B,C)) <=> ? [D] : ( m1_trees_1(D,C) & A = k1_trees_2(C,D) & k3_finseq_1(D) = B ) ) ) )).
fof(fraenkel_a_2_3_trees_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( m2_finseq_1(B,k4_ordinal1) & v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) ) => ( r2_hidden(A,a_2_3_trees_a(B,C)) <=> ? [D] : ( m1_trees_1(D,k9_xtuple_0(C)) & A = D & ~ r1_tarski(B,D) ) ) ) )).
fof(fraenkel_a_2_3_waybel11,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_3_waybel11(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k2_waybel_3(B,D) & r1_waybel_3(B,D,C) ) ) ) )).
fof(fraenkel_a_2_3_waybel12,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & v1_yellow_0(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_3_waybel12(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r1_orders_2(B,D,E) & r2_hidden(E,C) ) ) ) ) )).
fof(fraenkel_a_2_3_waybel13,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_3_waybel13(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_orders_2(B,D,C) & v1_waybel_3(D,B) ) ) ) )).
fof(fraenkel_a_2_3_waybel14,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_3_waybel14(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k2_waybel_3(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_3_waybel15,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & v6_waybel_1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) ) => ( r2_hidden(A,a_2_3_waybel15(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r3_orders_2(B,k3_funct_2(u1_struct_0(B),u1_struct_0(B),C,D),D) ) ) ) )).
fof(fraenkel_a_2_3_waybel17,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_3_waybel17(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k2_yellow_0(B,a_3_3_waybel17(B,C,D)) ) ) ) )).
fof(fraenkel_a_2_3_waybel19,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & l1_orders_2(B) & v2_pre_topc(C) & v1_waybel19(C) & m1_yellow_9(C,B) ) => ( r2_hidden(A,a_2_3_waybel19(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k3_subset_1(u1_struct_0(C),k6_waybel_0(C,D)) ) ) ) )).
fof(fraenkel_a_2_3_waybel20,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & v6_waybel_1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) ) => ( r2_hidden(A,a_2_3_waybel20(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r3_orders_2(B,D,k3_funct_2(u1_struct_0(B),u1_struct_0(B),C,D)) ) ) ) )).
fof(fraenkel_a_2_3_waybel23,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v5_orders_2(B) & v3_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_3_waybel23(B,C)) <=> ? [D] : ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(C)) & A = k1_yellow_0(B,D) & r1_yellow_0(B,D) ) ) ) )).
fof(fraenkel_a_2_3_waybel28,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) & m4_yellow_6(C,B) ) => ( r2_hidden(A,a_2_3_waybel28(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r2_hidden(E,D) => ! [F] : ( ( ~ v2_struct_0(F) & v4_orders_2(F) & v7_waybel_0(F) & l1_waybel_0(F,B) ) => ( r2_hidden(k4_tarski(F,E),C) => r1_waybel_0(B,F,D) ) ) ) ) ) ) ) )).
fof(fraenkel_a_2_3_waybel29,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v6_pre_topc(B) & l1_pre_topc(B) & ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ( r2_hidden(A,a_2_3_waybel29(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k3_borsuk_1(C,B,D,E) & r2_hidden(D,u1_pre_topc(C)) & r2_hidden(E,u1_pre_topc(B)) ) ) ) )).
fof(fraenkel_a_2_3_waybel30,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_3_waybel30(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k2_yellow_0(B,D) & r2_hidden(C,D) & r2_hidden(D,k2_waybel19(B)) ) ) ) )).
fof(fraenkel_a_2_3_waybel33,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_3_waybel33(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k2_yellow_0(B,a_3_5_waybel33(B,C,D)) ) ) ) )).
fof(fraenkel_a_2_3_waybel_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_3_waybel_0(B,C)) <=> ? [D] : ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(C)) & A = k2_yellow_0(B,D) & r2_yellow_0(B,D) ) ) ) )).
fof(fraenkel_a_2_3_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & v2_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & v1_waybel_0(C,k3_yellow_3(B,B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) ) => ( r2_hidden(A,a_2_3_waybel_2(B,C)) <=> ? [D] : ( ~ v1_xboole_0(D) & v1_waybel_0(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & D = k4_yellow_4(B,k6_domain_1(u1_struct_0(B),E),k5_yellow_3(B,B,C)) & r2_hidden(E,k4_yellow_3(B,B,C)) ) ) ) ) )).
fof(fraenkel_a_2_3_waybel_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_3_waybel_6(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_waybel_3(B,C,D) ) ) ) )).
fof(fraenkel_a_2_3_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_3_waybel_9(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k12_lattice3(B,C,D) & r2_hidden(D,k2_struct_0(B)) ) ) ) )).
fof(fraenkel_a_2_3_weddwitt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_3_weddwitt(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & k6_algstr_0(B,D,C) = k6_algstr_0(B,C,D) ) ) ) )).
fof(fraenkel_a_2_3_xxreal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xxreal_0(B) & v1_xxreal_0(C) ) => ( r2_hidden(A,a_2_3_xxreal_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k6_numbers) & A = D & ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(C,D) ) ) ) )).
fof(fraenkel_a_2_3_yellow12,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ( r2_hidden(A,a_2_3_yellow12(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k2_borsuk_1(B,C))))) & A = k5_setfam_1(u1_struct_0(k2_borsuk_1(B,C)),D) & r1_tarski(D,a_2_4_yellow12(B,C)) ) ) ) )).
fof(fraenkel_a_2_3_yellow_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ( r2_hidden(A,a_2_3_yellow_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r2_lattice3(B,C,D) ) ) ) )).
fof(fraenkel_a_2_3_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) ) => ( r2_hidden(A,a_2_3_zf_fund1(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,B) & m1_subset_1(E,B) & A = k5_classes2(B,k6_classes2(B,k2_ordinal4(B),D),k6_classes2(B,k3_ordinal4(B),E)) & r2_hidden(D,E) & r2_hidden(D,k1_classes2(B,C)) & r2_hidden(E,k1_classes2(B,C)) ) ) ) )).
fof(fraenkel_a_2_3_zf_model,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) & ~ v1_xboole_0(C) ) => ( r2_hidden(A,a_2_3_zf_model(B,C)) <=> ? [D] : ( m1_subset_1(D,k3_zf_model(C)) & A = D & ! [E] : ( ( 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))) ) => ( E = D => r2_hidden(k3_funct_2(k1_zf_lang,C,E,k18_zf_lang(B)),k3_funct_2(k1_zf_lang,C,E,k19_zf_lang(B))) ) ) ) ) ) )).
fof(fraenkel_a_2_3_zmodul03,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_int_2(B) & ~ 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) & v1_zmodul03(C) & l1_zmodul01(C) ) => ( r2_hidden(A,a_2_3_zmodul03(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k1_zmodul01(C,D,B) ) ) ) )).
fof(fraenkel_a_2_4_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & l1_msualg_1(B) & m1_trees_4(C,k3_card_3(u3_msualg_1(B,k1_msafree3(B,k28_abcmiz_1(B)))),k34_abcmiz_1(B)) ) => ( r2_hidden(A,a_2_4_abcmiz_1(B,C)) <=> ? [D] : ( m1_abcmiz_1(D,B,k14_abcmiz_1(B)) & A = k46_abcmiz_1(B,D) & r2_hidden(D,k2_relset_1(k3_card_3(u3_msualg_1(B,k1_msafree3(B,k28_abcmiz_1(B)))),C)) ) ) ) )).
fof(fraenkel_a_2_4_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(B),k9_setfam_1(B)))) => ( r2_hidden(A,a_2_4_armstrng(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = D & ? [E] : ( m1_subset_1(E,k1_zfmisc_1(B)) & r4_armstrng(B,C,E,D) ) ) ) ) )).
fof(fraenkel_a_2_4_arytm_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k2_arytm_2) & m1_subset_1(C,k2_arytm_2) ) => ( r2_hidden(A,a_2_4_arytm_2(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k5_arytm_3) & m1_subset_1(E,k5_arytm_3) & A = k10_arytm_3(D,E) & r2_hidden(D,k3_arytm_2(B)) & r2_hidden(E,k3_arytm_2(C)) ) ) ) )).
fof(fraenkel_a_2_4_asympt_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & v2_asympt_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(A,a_2_4_asympt_0(B,C)) <=> ? [D] : ( m2_funct_2(D,k4_ordinal1,k1_numbers,k9_funct_2(k4_ordinal1,k1_numbers)) & A = D & ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & ? [G] : ( m1_subset_1(G,k4_ordinal1) & ~ r1_xxreal_0(E,k5_numbers) & ~ r1_xxreal_0(F,k5_numbers) & ! [H] : ( m1_subset_1(H,k4_ordinal1) => ( r1_xxreal_0(G,H) => ( r1_xxreal_0(k3_xcmplx_0(F,k9_nat_1(k1_numbers,k5_asympt_0(B,C),H)),k9_nat_1(k1_numbers,D,H)) & r1_xxreal_0(k9_nat_1(k1_numbers,D,H),k3_xcmplx_0(E,k9_nat_1(k1_numbers,k5_asympt_0(B,C),H))) ) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_2_4_bagorder,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v16_waybel_0(B) & l1_orders_2(B) & m1_subset_1(C,k4_ordinal1) ) => ( r2_hidden(A,a_2_4_bagorder(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k5_finsub_1(u1_struct_0(B))) & m1_subset_1(E,k5_finsub_1(u1_struct_0(B))) & A = k1_domain_1(k5_finsub_1(u1_struct_0(B)),k5_finsub_1(u1_struct_0(B)),D,E) & D != k1_xboole_0 & E != k1_xboole_0 & k11_bagorder(B,D) = k11_bagorder(B,E) & r2_hidden(k1_domain_1(k1_zfmisc_1(D),k1_zfmisc_1(E),k6_subset_1(D,k6_domain_1(u1_struct_0(B),k11_bagorder(B,D))),k6_subset_1(E,k6_domain_1(u1_struct_0(B),k11_bagorder(B,E)))),k1_funct_1(k12_bagorder(B),k6_xcmplx_0(C,1))) ) ) ) )).
fof(fraenkel_a_2_4_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & v2_pre_topc(C) & l1_pre_topc(C) ) => ( r2_hidden(A,a_2_4_borsuk_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k2_borsuk_1(B,C))))) & A = k5_setfam_1(u1_struct_0(k2_borsuk_1(B,C)),D) & r1_tarski(D,a_2_0_borsuk_1(B,C)) ) ) ) )).
fof(fraenkel_a_2_4_borsuk_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & v2_pre_topc(C) & l1_pre_topc(C) ) => ( r2_hidden(A,a_2_4_borsuk_3(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k2_borsuk_1(B,C))))) & A = k5_setfam_1(u1_struct_0(k2_borsuk_1(B,C)),D) & r1_tarski(D,a_2_3_borsuk_3(B,C)) ) ) ) )).
fof(fraenkel_a_2_4_catalan2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_4_catalan2(B,C)) <=> ? [D] : ( m1_subset_1(D,k3_catalan2(k4_ordinal1)) & A = D & r2_hidden(D,k2_catalan2(B,C)) & a_1_4_catalan2(D) = k1_xboole_0 ) ) ) )).
fof(fraenkel_a_2_4_classes1,axiom,( ! [A] : ! [B] : ! [C] : ( v3_ordinal1(C) => ( r2_hidden(A,a_2_4_classes1(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_classes1(B)) & A = k9_setfam_1(D) & r2_hidden(D,k2_classes1(B,C)) ) ) ) )).
fof(fraenkel_a_2_4_combgras,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k4_ordinal1) & ~ v1_xboole_0(C) ) => ( r2_hidden(A,a_2_4_combgras(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(C)) & A = D & k1_card_1(D) = k1_nat_1(B,1) ) ) ) )).
fof(fraenkel_a_2_4_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_compos_1(B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ( r2_hidden(A,a_2_4_compos_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_nat_1(D,k5_card_1(C)) & r2_hidden(D,k2_afinsq_1(k4_compos_1(B))) ) ) ) )).
fof(fraenkel_a_2_4_fcont_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & m1_subset_1(C,k1_numbers) ) => ( r2_hidden(A,a_2_4_fcont_1(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(B,k6_xcmplx_0(B,C))) & ~ r1_xxreal_0(k2_xcmplx_0(B,k6_xcmplx_0(B,C)),D) ) ) ) )).
fof(fraenkel_a_2_4_fin_topo,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_4_fin_topo(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,C) & r2_hidden(D,k1_fin_topo(B,E)) ) ) ) ) )).
fof(fraenkel_a_2_4_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v4_funct_1(B) & v4_funct_1(C) ) => ( r2_hidden(A,a_2_4_fomodel0(B,C)) <=> ? [D] : ( m1_subset_1(D,k2_xboole_0(B,C)) & A = k10_xtuple_0(D) & r2_hidden(D,k2_xboole_0(B,C)) ) ) ) )).
fof(fraenkel_a_2_4_goboard5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_4_goboard5(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,C)),E) ) ) ) )).
fof(fraenkel_a_2_4_goboard6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_4_goboard6(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & ~ r1_xxreal_0(D,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,B,1))) & ~ r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(B,1),1)),D) & ~ r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,1)),E) ) ) ) )).
fof(fraenkel_a_2_4_goboard9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_4_goboard9(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & ~ r1_xxreal_0(D,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,B,1))) ) ) ) )).
fof(fraenkel_a_2_4_gobrd11,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_4_gobrd11(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,B,1)),D) & r1_xxreal_0(D,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(B,1),1))) & r1_xxreal_0(E,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,1))) ) ) ) )).
fof(fraenkel_a_2_4_group_10,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v8_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) & ~ v1_xboole_0(C) ) => ( r2_hidden(A,a_2_4_group_10(B,C)) <=> ? [D] : ( m1_subset_1(D,C) & A = k2_zfmisc_1(u1_struct_0(B),k6_domain_1(C,D)) ) ) ) )).
fof(fraenkel_a_2_4_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_finset_1(C) ) => ( r2_hidden(A,a_2_4_group_9(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = D & r2_hidden(D,C) & ~ r1_xxreal_0(B,D) ) ) ) )).
fof(fraenkel_a_2_4_heyting1,axiom,( ! [A] : ! [B] : ! [C] : ( m2_subset_1(C,k5_finsub_1(k7_normform(B)),k8_normform(B)) => ( r2_hidden(A,a_2_4_heyting1(B,C)) <=> ? [D] : ( m2_subset_1(D,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B)) & A = k3_funct_2(k7_normform(B),k1_heyting1(B),o_1_3_heyting1(B),D) & r2_hidden(k3_funct_2(k7_normform(B),k1_heyting1(B),o_1_3_heyting1(B),D),k3_domain_1(k5_finsub_1(B),k5_finsub_1(B),D)) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_4_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_4_ideal_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k8_group_1(B,C,D) ) ) ) )).
fof(fraenkel_a_2_4_jordan2b,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k7_metric_1)) & m1_subset_1(C,k1_numbers) ) => ( r2_hidden(A,a_2_4_jordan2b(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k7_metric_1)) & A = D & ~ r1_xxreal_0(C,k3_metric_1(k7_metric_1,B,D)) ) ) ) )).
fof(fraenkel_a_2_4_jordan5a,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_4_jordan5a(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(C,D) ) ) ) )).
fof(fraenkel_a_2_4_jordan6,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k7_metric_1)) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_4_jordan6(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k7_metric_1)) & A = D & ~ r1_xxreal_0(C,k3_metric_1(k7_metric_1,B,D)) ) ) ) )).
fof(fraenkel_a_2_4_jordan_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & v2_pre_topc(C) & l1_pre_topc(C) ) => ( r2_hidden(A,a_2_4_jordan_a(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k2_borsuk_1(g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)),g1_pre_topc(u1_struct_0(C),u1_pre_topc(C))))))) & A = k3_tarski(D) & r1_tarski(D,a_2_5_jordan_a(B,C)) ) ) ) )).
fof(fraenkel_a_2_4_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_4_lattice3(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r3_lattices(B,C,D) ) ) ) )).
fof(fraenkel_a_2_4_lattice6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & v1_lattice6(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_4_lattice6(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r3_lattices(B,C,D) & D != C ) ) ) )).
fof(fraenkel_a_2_4_limfunc4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r2_hidden(A,a_2_4_limfunc4(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k2_limfunc2(C,B)) ) ) ) )).
fof(fraenkel_a_2_4_lopclset,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v7_struct_0(B) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_4_lopclset(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r2_hidden(E,a_2_3_lopclset(B,C)) & r3_lattices(B,E,D) ) ) ) ) )).
fof(fraenkel_a_2_4_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(B)) ) => ( r2_hidden(A,a_2_4_matrix_0(B,C)) <=> ? [D] : ( m2_finseq_2(D,B,k3_finseq_2(B)) & A = k10_xtuple_0(D) & r2_hidden(D,k10_xtuple_0(C)) ) ) ) )).
fof(fraenkel_a_2_4_measure6,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_4_measure6(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = k2_xcmplx_0(C,D) & r2_hidden(D,k1_measure6(B,k4_xcmplx_0(C))) ) ) ) )).
fof(fraenkel_a_2_4_member_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_membered(B) & v2_membered(C) ) => ( r2_hidden(A,a_2_4_member_1(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k6_numbers) & m1_subset_1(E,k6_numbers) & A = k3_member_1(D,E) & r2_hidden(D,B) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_4_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_mmlquery(B) & m2_finseq_1(C,u1_mmlquery(B)) ) => ( r2_hidden(A,a_2_4_mmlquery(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k31_mmlquery(B,D) & r2_hidden(D,k2_relset_1(u1_mmlquery(B),C)) ) ) ) )).
fof(fraenkel_a_2_4_modal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v5_relat_1(B,k2_zfmisc_1(k4_ordinal1,k4_ordinal1)) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) & m1_trees_1(C,k9_xtuple_0(B)) ) => ( r2_hidden(A,a_2_4_modal_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k8_finseq_1(k4_ordinal1,C,k14_trees_3(D)) & r2_hidden(k8_finseq_1(k4_ordinal1,C,k14_trees_3(D)),k9_xtuple_0(B)) ) ) ) )).
fof(fraenkel_a_2_4_moebius1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & v7_ordinal1(C) & v1_int_2(C) ) => ( r2_hidden(A,a_2_4_moebius1(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = D & ~ r1_xxreal_0(D,k5_numbers) & r1_nat_d(D,k6_moebius1(B)) & r1_nat_d(C,D) ) ) ) )).
fof(fraenkel_a_2_4_nat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) ) => ( r2_hidden(A,a_2_4_nat_4(B,C)) <=> ? [D] : ( v1_int_2(D) & m1_subset_1(D,k4_ordinal1) & A = k11_newton(D,k11_nat_3(C,D)) & r1_xxreal_0(D,k3_square_1(k2_nat_1(2,B))) & ~ r1_xxreal_0(k11_nat_3(C,D),k5_numbers) ) ) ) )).
fof(fraenkel_a_2_4_openlatt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v7_struct_0(B) & v10_lattices(B) & v1_lattice2(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_4_openlatt(B,C)) <=> ? [D] : ( ~ v1_xboole_0(D) & v19_lattices(D,B) & v20_lattices(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & r2_hidden(D,k7_openlatt(B)) & r2_hidden(C,D) ) ) ) )).
fof(fraenkel_a_2_4_petri,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_petri(B) & v3_petri(B) & l1_petri(B) & m1_subset_1(C,k1_zfmisc_1(u4_struct_0(B))) ) => ( r2_hidden(A,a_2_4_petri(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_petri(E,u1_struct_0(B),u4_struct_0(B),u1_petri(B)) & ? [F] : ( m1_subset_1(F,u4_struct_0(B)) & r2_hidden(F,C) & E = k1_domain_1(u1_struct_0(B),u4_struct_0(B),D,F) ) ) ) ) ) )).
fof(fraenkel_a_2_4_rcomp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_4_rcomp_1(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(k1_seq_2(B),C)) & ~ r1_xxreal_0(k2_xcmplx_0(k1_seq_2(B),C),D) ) ) ) )).
fof(fraenkel_a_2_4_rlaffin1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_4_rlaffin1(B,C)) <=> ? [D] : ( m2_rlvect_2(D,B,k3_convex1(B,C)) & A = k6_rlvect_2(B,D) & k3_rlaffin1(B,D) = 1 ) ) ) )).
fof(fraenkel_a_2_4_rlvect_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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_rlvect_2(C,B) ) => ( r2_hidden(A,a_2_4_rlvect_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & k3_funct_2(u1_struct_0(B),k1_numbers,C,D) != k5_numbers ) ) ) )).
fof(fraenkel_a_2_4_roughs_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v8_struct_0(B) & v2_roughs_1(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_4_roughs_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ~ r1_xxreal_0(k3_funct_2(u1_struct_0(B),k1_numbers,k6_roughs_1(B,C),D),k5_numbers) & ~ r1_xxreal_0(1,k3_funct_2(u1_struct_0(B),k1_numbers,k6_roughs_1(B,C),D)) ) ) ) )).
fof(fraenkel_a_2_4_rusub_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v4_rlvect_1(B) & l1_rlvect_1(B) & v2_rusub_4(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_4_rusub_5(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) & A = k1_algstr_0(B,D,E) & r2_hidden(D,C) & r2_hidden(E,k6_domain_1(u1_struct_0(B),k4_struct_0(B))) ) ) ) )).
fof(fraenkel_a_2_4_tdlat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) => ( r2_hidden(A,a_2_4_tdlat_2(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & D = k2_pre_topc(B,k1_tops_1(B,k2_pre_topc(B,E))) & r2_hidden(E,C) ) ) ) ) )).
fof(fraenkel_a_2_4_tex_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_4_tex_4(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & v4_pre_topc(D,B) & r2_hidden(C,D) ) ) ) )).
fof(fraenkel_a_2_4_topdim_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_4_topdim_2(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = k9_finseq_1(D) & ~ r1_xxreal_0(D,k3_xxreal_3(C,B)) & ~ r1_xxreal_0(k1_xxreal_3(C,B),D) ) ) ) )).
fof(fraenkel_a_2_4_topreal3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & m2_finseq_1(C,u1_struct_0(k15_euclid(B))) ) => ( r2_hidden(A,a_2_4_topreal3(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_topreal1(B,C,D) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(C)) ) ) ) )).
fof(fraenkel_a_2_4_topreal6,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_4_topreal6(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(k3_funct_2(u1_struct_0(k15_euclid(2)),k1_numbers,k4_pscomp_1,B),C)) & ~ r1_xxreal_0(k2_xcmplx_0(k3_funct_2(u1_struct_0(k15_euclid(2)),k1_numbers,k4_pscomp_1,B),C),D) ) ) ) )).
fof(fraenkel_a_2_4_trees_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( m2_finseq_1(B,k4_ordinal1) & v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) ) => ( r2_hidden(A,a_2_4_trees_a(B,C)) <=> ? [D] : ( m1_trees_1(D,k9_xtuple_0(C)) & A = k8_finseq_1(k4_ordinal1,B,D) & D = D ) ) ) )).
fof(fraenkel_a_2_4_waybel11,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_4_waybel11(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k2_waybel_3(B,D) & r1_tarski(k2_waybel_3(B,D),C) ) ) ) )).
fof(fraenkel_a_2_4_waybel12,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & v2_yellow_0(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_4_waybel12(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r1_orders_2(B,E,D) & r2_hidden(E,C) ) ) ) ) )).
fof(fraenkel_a_2_4_waybel14,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_4_waybel14(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k2_yellow_0(B,D) & r2_hidden(C,D) & r2_hidden(D,k5_waybel11(B)) ) ) ) )).
fof(fraenkel_a_2_4_waybel17,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_4_waybel17(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k2_waybel_3(B,D) & r1_waybel_3(B,D,C) ) ) ) )).
fof(fraenkel_a_2_4_waybel21,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v7_waybel_0(C) & v8_waybel_0(C,B) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_4_waybel21(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k2_waybel_0(B,C,D) & r1_orders_2(C,o_2_3_waybel21(B,C),D) ) ) ) )).
fof(fraenkel_a_2_4_waybel23,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_4_waybel23(B,C)) <=> ? [D] : ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(C)) & A = k1_yellow_0(B,D) & r1_yellow_0(B,D) ) ) ) )).
fof(fraenkel_a_2_4_waybel30,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & v2_waybel_2(B) & l1_waybel_9(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_4_waybel30(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k2_yellow_0(B,D) & r2_hidden(C,D) & r2_hidden(D,k2_waybel19(B)) ) ) ) )).
fof(fraenkel_a_2_4_waybel33,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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_xboole_0(C) & v1_subset_1(C,u1_struct_0(k2_yellow_1(k2_struct_0(B)))) & v2_waybel_0(C,k2_yellow_1(k2_struct_0(B))) & v13_waybel_0(C,k2_yellow_1(k2_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(B))))) ) => ( r2_hidden(A,a_2_4_waybel33(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,u1_struct_0(B)) & m2_subset_1(E,u1_struct_0(k2_yellow_1(k2_struct_0(B))),C) & A = k1_domain_1(u1_struct_0(B),C,D,E) & r2_hidden(D,E) ) ) ) )).
fof(fraenkel_a_2_4_waybel_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v2_waybel_8(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & v7_waybel_1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) ) => ( r2_hidden(A,a_2_4_waybel_8(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & D = k3_funct_2(u1_struct_0(B),u1_struct_0(B),C,D) ) ) ) )).
fof(fraenkel_a_2_4_yellow12,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ( r2_hidden(A,a_2_4_yellow12(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) & A = k3_borsuk_1(B,C,D,E) & r2_hidden(D,u1_pre_topc(B)) & r2_hidden(E,u1_pre_topc(C)) ) ) ) )).
fof(fraenkel_a_2_4_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_4_yellow_4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r1_orders_2(B,D,E) & r2_hidden(E,C) ) ) ) ) )).
fof(fraenkel_a_2_4_yellow_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_4_yellow_9(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r1_orders_2(B,E,D) & r2_hidden(E,C) ) ) ) ) )).
fof(fraenkel_a_2_4_zf_model,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) & ~ v1_xboole_0(C) ) => ( r2_hidden(A,a_2_4_zf_model(B,C)) <=> ? [D] : ( m1_subset_1(D,k3_zf_model(C)) & A = D & ! [E] : ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k1_zf_lang,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang,C))) ) => ( ( E = k4_zf_model(k24_zf_lang(B),C) & F = D ) => ( r2_hidden(F,E) & ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k1_zf_lang,C) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang,C))) ) => ( ! [H] : ( m2_subset_1(H,k4_ordinal1,k1_zf_lang) => ( k3_funct_2(k1_zf_lang,C,G,H) != k3_funct_2(k1_zf_lang,C,F,H) => k23_zf_lang(B) = H ) ) => r2_hidden(G,E) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_2_4_zmodul02,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_4_zmodul02(B,C)) <=> ? [D] : ( m2_zmodul02(D,B,C) & A = k21_zmodul02(B,D) ) ) ) )).
fof(fraenkel_a_2_4_zmodul03,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_int_2(B) & ~ 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) & v1_zmodul03(C) & v2_zmodul03(C) & l1_zmodul01(C) ) => ( r2_hidden(A,a_2_4_zmodul03(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k13_zmodul02(B,C,D) & r2_hidden(D,o_1_3_zmodul03(C)) ) ) ) )).
fof(fraenkel_a_2_5_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & l1_msualg_1(B) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k38_abcmiz_1(B))) ) => ( r2_hidden(A,a_2_5_abcmiz_1(B,C)) <=> ? [D] : ( v8_abcmiz_1(D,B) & m1_abcmiz_1(D,B,k13_abcmiz_1(B)) & A = k45_abcmiz_1(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_5_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(A,a_2_5_armstrng(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(B)) & A = k6_armstrng(B,D,E) & ! [F] : ( ( r2_hidden(F,C) & r1_tarski(D,F) ) => r1_tarski(E,F) ) ) ) )).
fof(fraenkel_a_2_5_arytm_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k2_arytm_2) & m1_subset_1(C,k2_arytm_2) ) => ( r2_hidden(A,a_2_5_arytm_2(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k5_arytm_3) & m1_subset_1(E,k5_arytm_3) & A = k9_arytm_3(D,E) & r2_hidden(D,k3_arytm_2(B)) & r2_hidden(E,k3_arytm_2(C)) ) ) ) )).
fof(fraenkel_a_2_5_asympt_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & v2_asympt_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(A,a_2_5_asympt_0(B,C)) <=> ? [D] : ( m2_funct_2(D,k4_ordinal1,k1_numbers,k9_funct_2(k4_ordinal1,k1_numbers)) & A = D & ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & ? [G] : ( m1_subset_1(G,k4_ordinal1) & ~ r1_xxreal_0(E,k5_numbers) & ~ r1_xxreal_0(F,k5_numbers) & ! [H] : ( m1_subset_1(H,k4_ordinal1) => ( r1_xxreal_0(G,H) => ( r1_xxreal_0(k3_xcmplx_0(F,k9_nat_1(k1_numbers,k1_asympt_0(B,C),H)),k9_nat_1(k1_numbers,D,H)) & r1_xxreal_0(k9_nat_1(k1_numbers,D,H),k3_xcmplx_0(E,k9_nat_1(k1_numbers,k1_asympt_0(B,C),H))) ) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_2_5_bagorder,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v16_waybel_0(B) & l1_orders_2(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_5_bagorder(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k5_finsub_1(u1_struct_0(B))) & m1_subset_1(E,k5_finsub_1(u1_struct_0(B))) & A = k1_domain_1(k5_finsub_1(u1_struct_0(B)),k5_finsub_1(u1_struct_0(B)),D,E) & D != k1_xboole_0 & E != k1_xboole_0 & k11_bagorder(B,D) = k11_bagorder(B,E) & r2_hidden(k1_domain_1(k1_zfmisc_1(D),k1_zfmisc_1(E),k6_subset_1(D,k6_domain_1(u1_struct_0(B),k11_bagorder(B,D))),k6_subset_1(E,k6_domain_1(u1_struct_0(B),k11_bagorder(B,E)))),k9_nat_1(k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(B)),k5_finsub_1(u1_struct_0(B)))),k12_bagorder(B),C)) ) ) ) )).
fof(fraenkel_a_2_5_cfdiff_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_5_cfdiff_1(B,C)) <=> ? [D] : ( v1_xcmplx_0(D) & A = D & ~ r1_xxreal_0(C,k9_complex1(k6_xcmplx_0(D,k3_comseq_2(B)))) ) ) ) )).
fof(fraenkel_a_2_5_cgames_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_cgames_1(B) & v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,a_2_5_cgames_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k7_cgames_1(B)) & A = k1_funct_1(k5_relat_1(C,k11_cgames_1(B)),D) & k7_cgames_1(B) != k1_xboole_0 ) ) ) )).
fof(fraenkel_a_2_5_convex4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_clvect_1(B) & m1_convex4(C,B) ) => ( r2_hidden(A,a_2_5_convex4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & k3_funct_2(u1_struct_0(B),k2_numbers,C,D) != k5_complex1 ) ) ) )).
fof(fraenkel_a_2_5_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : ( v7_ordinal1(C) => ( r2_hidden(A,a_2_5_finseq_3(B,C)) <=> ? [D] : ( m2_finseq_2(D,B,k3_finseq_2(B)) & A = D & k3_finseq_1(D) = C ) ) ) )).
fof(fraenkel_a_2_5_goboard5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_5_goboard5(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(E,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,k1_nat_1(C,1)))) ) ) ) )).
fof(fraenkel_a_2_5_goboard6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_5_goboard6(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & ~ r1_xxreal_0(D,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,B,1))) & ~ r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(B,1),1)),D) & ~ r1_xxreal_0(E,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,k1_matrix_0(C)))) ) ) ) )).
fof(fraenkel_a_2_5_goboard9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_5_goboard9(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & ~ r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(B,1),1)),D) ) ) ) )).
fof(fraenkel_a_2_5_gobrd11,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_5_gobrd11(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,B,1)),D) & r1_xxreal_0(D,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(B,1),1))) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,k1_matrix_0(C))),E) ) ) ) )).
fof(fraenkel_a_2_5_graph_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) & v7_graph_1(C,B) & m2_graph_1(C,B) ) => ( r2_hidden(A,a_2_5_graph_5(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,k4_ordinal1) & r2_hidden(E,k4_finseq_1(C)) & r2_hidden(D,k1_graph_5(B,k7_partfun1(u4_struct_0(B),C,E))) ) ) ) ) )).
fof(fraenkel_a_2_5_group_10,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & ~ v1_xboole_0(C) & v1_finset_1(C) ) => ( r2_hidden(A,a_2_5_group_10(B,C)) <=> ? [D] : ( m1_subset_1(D,C) & A = k2_zfmisc_1(u1_struct_0(k4_gr_cy_1(B)),k6_domain_1(C,D)) ) ) ) )).
fof(fraenkel_a_2_5_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & l6_algstr_0(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_5_ideal_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k8_group_1(B,C,D) ) ) ) )).
fof(fraenkel_a_2_5_jordan2b,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & m1_subset_1(C,k1_numbers) ) => ( r2_hidden(A,a_2_5_jordan2b(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = k9_finseq_1(D) & ~ r1_xxreal_0(D,k6_xcmplx_0(C,B)) & ~ r1_xxreal_0(k2_xcmplx_0(C,B),D) ) ) ) )).
fof(fraenkel_a_2_5_jordan2c,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_5_jordan2c(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(B))) & A = D & k12_euclid(D) = C ) ) ) )).
fof(fraenkel_a_2_5_jordan_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & v2_pre_topc(C) & l1_pre_topc(C) ) => ( r2_hidden(A,a_2_5_jordan_a(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(g1_pre_topc(u1_struct_0(C),u1_pre_topc(C))))) & A = k3_borsuk_1(g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)),g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)),D,E) & r2_hidden(D,u1_pre_topc(g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)))) & r2_hidden(E,u1_pre_topc(g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)))) ) ) ) )).
fof(fraenkel_a_2_5_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) ) => ( r2_hidden(A,a_2_5_lattice3(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r3_lattices(B,D,E) & r2_hidden(E,C) ) ) ) ) )).
fof(fraenkel_a_2_5_lattice6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & v2_lattice6(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_5_lattice6(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r3_lattices(B,D,C) & D != C ) ) ) )).
fof(fraenkel_a_2_5_limfunc4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r2_hidden(A,a_2_5_limfunc4(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(k2_limfunc2(C,B),D) ) ) ) )).
fof(fraenkel_a_2_5_member_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_membered(B) & v1_membered(C) ) => ( r2_hidden(A,a_2_5_member_1(B,C)) <=> ? [D] : ? [E] : ( v1_xcmplx_0(D) & v1_xcmplx_0(E) & A = k3_xcmplx_0(D,E) & r2_hidden(D,B) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_5_moebius1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & v7_ordinal1(C) & v1_int_2(C) ) => ( r2_hidden(A,a_2_5_moebius1(B,C)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & A = D & ~ r1_xxreal_0(D,k5_numbers) & r1_nat_d(D,k6_moebius1(B)) & ~ r1_nat_d(C,D) ) ) ) )).
fof(fraenkel_a_2_5_nat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) ) => ( r2_hidden(A,a_2_5_nat_4(B,C)) <=> ? [D] : ( v1_int_2(D) & m1_subset_1(D,k4_ordinal1) & A = k11_newton(D,k11_nat_3(C,D)) & ~ r1_xxreal_0(D,k3_square_1(k2_nat_1(2,B))) & r1_xxreal_0(D,k7_xcmplx_0(k2_nat_1(2,B),3)) & ~ r1_xxreal_0(k11_nat_3(C,D),k5_numbers) ) ) ) )).
fof(fraenkel_a_2_5_orders_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) & m2_orders_2(C,B,o_1_1_orders_2(B)) ) => ( r2_hidden(A,a_2_5_orders_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r2_hidden(E,C) => r2_orders_2(B,E,D) ) ) ) ) ) )).
fof(fraenkel_a_2_5_petri,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_petri(B) & v3_petri(B) & l1_petri(B) & m1_subset_1(C,k1_zfmisc_1(u4_struct_0(B))) ) => ( r2_hidden(A,a_2_5_petri(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_petri(E,u4_struct_0(B),u1_struct_0(B),u2_petri(B)) & ? [F] : ( m1_subset_1(F,u4_struct_0(B)) & r2_hidden(F,C) & E = k1_domain_1(u4_struct_0(B),u1_struct_0(B),F,D) ) ) ) ) ) )).
fof(fraenkel_a_2_5_rcomp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_5_rcomp_1(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(k2_seq_4(B),C)) & ~ r1_xxreal_0(k2_xcmplx_0(k2_seq_4(B),C),D) ) ) ) )).
fof(fraenkel_a_2_5_rlaffin1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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_rlaffin1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_5_rlaffin1(B,C)) <=> ? [D] : ( m2_rlvect_2(D,B,C) & A = k6_rlvect_2(B,D) & k3_rlaffin1(B,D) = 1 ) ) ) )).
fof(fraenkel_a_2_5_rusub_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_5_rusub_5(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) & A = k5_algstr_0(B,D,E) & r2_hidden(D,C) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_5_tdlat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) => ( r2_hidden(A,a_2_5_tdlat_2(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & D = k1_tops_1(B,k2_pre_topc(B,k1_tops_1(B,E))) & r2_hidden(E,C) ) ) ) ) )).
fof(fraenkel_a_2_5_tex_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_5_tex_4(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & v3_pre_topc(D,B) & r2_hidden(C,D) ) ) ) )).
fof(fraenkel_a_2_5_topreal3,axiom,( ! [A] : ! [B] : ! [C] : ( ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_5_topreal3(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_topreal1(2,k17_finseq_1(u1_struct_0(k15_euclid(2)),C,B),D) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(k17_finseq_1(u1_struct_0(k15_euclid(2)),C,B))) ) ) ) )).
fof(fraenkel_a_2_5_topreal6,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_5_topreal6(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(k3_funct_2(u1_struct_0(k15_euclid(2)),k1_numbers,k5_pscomp_1,B),C)) & ~ r1_xxreal_0(k2_xcmplx_0(k3_funct_2(u1_struct_0(k15_euclid(2)),k1_numbers,k5_pscomp_1,B),C),D) ) ) ) )).
fof(fraenkel_a_2_5_trees_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) & m1_trees_1(C,k9_xtuple_0(B)) ) => ( r2_hidden(A,a_2_5_trees_a(B,C)) <=> ? [D] : ( m1_trees_1(D,k9_xtuple_0(B)) & A = D & ! [E] : ( m2_finseq_1(E,k4_ordinal1) => ~ ( r2_hidden(E,k2_trees_a(k9_xtuple_0(B),C)) & r1_tarski(E,D) ) ) ) ) ) )).
fof(fraenkel_a_2_5_waybel12,axiom,( ! [A] : ! [B] : ! [C] : ( ( v5_orders_2(B) & v1_yellow_0(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_5_waybel12(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k12_lattice3(B,k3_yellow_0(B),D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_5_waybel14,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & v2_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_5_waybel14(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k5_waybel_0(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_5_waybel17,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_5_waybel17(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k2_waybel_3(B,D) & r1_tarski(k2_waybel_3(B,D),C) ) ) ) )).
fof(fraenkel_a_2_5_waybel22,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(A,a_2_5_waybel22(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k2_yellow_1(B))) & A = k6_waybel_0(k2_yellow_1(B),D) & ? [E] : ( m1_subset_1(E,B) & D = k1_tarski(E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_5_waybel23,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v4_yellow_0(C,B) & m1_yellow_0(C,B) ) => ( r2_hidden(A,a_2_5_waybel23(B,C)) <=> ? [D] : ( ~ v1_xboole_0(D) & v1_waybel_0(D,C) & v12_waybel_0(D,C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) & A = D ) ) ) )).
fof(fraenkel_a_2_5_waybel30,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & v8_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) & v2_waybel_2(B) & l1_waybel_9(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_5_waybel30(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k2_yellow_0(B,D) & r2_hidden(C,D) & r2_hidden(D,k2_waybel19(B)) ) ) ) )).
fof(fraenkel_a_2_5_waybel33,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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_xboole_0(C) & v1_subset_1(C,u1_struct_0(k2_yellow_1(k2_struct_0(B)))) & v2_waybel_0(C,k2_yellow_1(k2_struct_0(B))) & v13_waybel_0(C,k2_yellow_1(k2_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(B))))) ) => ( r2_hidden(A,a_2_5_waybel33(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k3_yellow19(B,k2_struct_0(B),C))) & A = k1_waybel_9(B,k5_waybel_9(B,k3_yellow19(B,k2_struct_0(B),C),D)) ) ) ) )).
fof(fraenkel_a_2_5_waybel_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_5_waybel_0(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r1_orders_2(B,D,E) & r2_hidden(E,k6_domain_1(u1_struct_0(B),C)) ) ) ) ) )).
fof(fraenkel_a_2_5_waybel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v3_lattice3(B) & l1_orders_2(B) & 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(A,a_2_5_waybel_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r3_orders_2(B,D,k3_funct_2(u1_struct_0(B),u1_struct_0(B),C,D)) ) ) ) )).
fof(fraenkel_a_2_5_waybel_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & v7_waybel_1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) ) => ( r2_hidden(A,a_2_5_waybel_8(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & D = k3_funct_2(u1_struct_0(B),u1_struct_0(B),C,D) ) ) ) )).
fof(fraenkel_a_2_5_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & v8_pre_topc(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v1_compts_1(B) & l1_waybel_9(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_5_waybel_9(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k12_lattice3(B,C,D) & r2_hidden(D,k2_struct_0(B)) ) ) ) )).
fof(fraenkel_a_2_5_weddwitt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) & m1_subset_1(C,u1_struct_0(k1_uniroots(B))) ) => ( r2_hidden(A,a_2_5_weddwitt(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k1_uniroots(B))) & A = D & k6_algstr_0(k1_uniroots(B),C,D) = k6_algstr_0(k1_uniroots(B),D,C) ) ) ) )).
fof(fraenkel_a_2_5_yellow15,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_pre_topc(B) & m2_finseq_1(C,k9_setfam_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_5_yellow15(B,C)) <=> ? [D] : ( m2_finseq_1(D,k6_margrel1) & A = k8_setfam_1(u1_struct_0(B),k2_relset_1(k9_setfam_1(u1_struct_0(B)),k1_yellow15(u1_struct_0(B),C,D))) & k3_finseq_1(D) = k3_finseq_1(C) ) ) ) )).
fof(fraenkel_a_2_5_yellow19,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) & ~ v1_xboole_0(C) & v2_waybel_0(C,k2_yellow_1(k2_struct_0(B))) & v13_waybel_0(C,k2_yellow_1(k2_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(B))))) ) => ( r2_hidden(A,a_2_5_yellow19(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,u1_struct_0(B)) & m2_subset_1(E,u1_struct_0(k2_yellow_1(k2_struct_0(B))),C) & A = k4_tarski(D,E) & r2_hidden(D,E) ) ) ) )).
fof(fraenkel_a_2_5_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_5_yellow_4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r1_orders_2(B,E,D) & r2_hidden(E,C) ) ) ) ) )).
fof(fraenkel_a_2_5_yellow_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_5_yellow_9(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r1_orders_2(B,D,E) & r2_hidden(E,C) ) ) ) ) )).
fof(fraenkel_a_2_5_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) ) => ( r2_hidden(A,a_2_5_zf_fund1(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = k1_classes2(B,k6_classes2(B,k3_ordinal4(B),D)) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_5_zmodul03,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & v1_zmodul03(B) & v2_zmodul03(B) & l1_zmodul01(B) & m1_zmodul03(C,B) ) => ( r2_hidden(A,a_2_5_zmodul03(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k13_zmodul02(o_0_1_zmodul03,B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_6_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & l1_msualg_1(B) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k38_abcmiz_1(B))) ) => ( r2_hidden(A,a_2_6_abcmiz_1(B,C)) <=> ? [D] : ( v8_abcmiz_1(D,B) & m1_abcmiz_1(D,B,k13_abcmiz_1(B)) & A = k46_abcmiz_1(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_6_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(B),k9_setfam_1(B)))) => ( r2_hidden(A,a_2_6_armstrng(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = D & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(B)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(B)) => ( ( r2_hidden(k6_armstrng(B,E,F),C) & r1_tarski(E,D) ) => r1_tarski(F,D) ) ) ) ) ) ) )).
fof(fraenkel_a_2_6_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & ~ v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_6_borsuk_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(C)) & A = D & r2_hidden(k3_tarski(D),u1_pre_topc(B)) ) ) ) )).
fof(fraenkel_a_2_6_cgames_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_cgames_1(B) & v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,a_2_6_cgames_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k7_cgames_1(B)) & A = k1_funct_1(C,D) & k7_cgames_1(B) != k1_xboole_0 ) ) ) )).
fof(fraenkel_a_2_6_conlat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_conlat_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_6_conlat_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ! [E] : ( m1_subset_1(E,u4_struct_0(B)) => ( r2_hidden(E,a_2_0_conlat_1(B,C)) => r1_conlat_1(B,D,E) ) ) ) ) ) )).
fof(fraenkel_a_2_6_conlat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_conlat_1(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) => ( r2_hidden(A,a_2_6_conlat_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u4_struct_0(B)) & A = D & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r2_hidden(E,k5_setfam_1(u1_struct_0(B),C)) => r1_conlat_1(B,E,D) ) ) ) ) ) )).
fof(fraenkel_a_2_6_dickson,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_6_dickson(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k5_dickson(B))) & A = D & r4_waybel_4(C,D,u1_orders_2(k5_dickson(B))) ) ) ) )).
fof(fraenkel_a_2_6_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ( r2_hidden(A,a_2_6_fomodel2(B,C)) <=> ? [D] : ? [E] : ( m2_subset_1(D,k6_subset_1(k3_finseq_2(k1_fomodel1(C)),k1_tarski(k1_xboole_0)),k24_fomodel2(C,B)) & m2_subset_1(E,k6_subset_1(k3_finseq_2(k1_fomodel1(C)),k1_tarski(k1_xboole_0)),k24_fomodel2(C,B)) & A = k7_finseq_1(k7_finseq_1(k43_fomodel1(C,k1_fomodel2(C)),D),E) ) ) ) )).
fof(fraenkel_a_2_6_goboard5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_6_goboard5(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,B,k1_matrix_0(C))),E) ) ) ) )).
fof(fraenkel_a_2_6_heyting1,axiom,( ! [A] : ! [B] : ! [C] : ( m2_subset_1(C,k5_finsub_1(k7_normform(B)),k8_normform(B)) => ( r2_hidden(A,a_2_6_heyting1(B,C)) <=> ? [D] : ( m2_subset_1(D,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B)) & A = k3_funct_2(k7_normform(B),k1_heyting1(B),o_1_3_heyting1(B),D) & r2_hidden(k3_funct_2(k7_normform(B),k1_heyting1(B),o_1_3_heyting1(B),D),k2_domain_1(k5_finsub_1(B),k5_finsub_1(B),D)) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_6_jordan2b,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,u1_struct_0(k14_euclid(1))) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_6_jordan2b(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(1))) & A = D & ~ r1_xxreal_0(C,k3_metric_1(k14_euclid(1),B,D)) ) ) ) )).
fof(fraenkel_a_2_6_jordan_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & v2_pre_topc(C) & l1_pre_topc(C) ) => ( r2_hidden(A,a_2_6_jordan_a(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k2_borsuk_1(g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)),g1_pre_topc(u1_struct_0(C),u1_pre_topc(C))))))) & A = k3_tarski(D) & r1_tarski(D,a_2_7_jordan_a(B,C)) ) ) ) )).
fof(fraenkel_a_2_6_knaster,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & 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)))) ) => ( r2_hidden(A,a_2_6_knaster(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r3_lattices(B,D,k3_funct_2(u1_struct_0(B),u1_struct_0(B),C,D)) ) ) ) )).
fof(fraenkel_a_2_6_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) ) => ( r2_hidden(A,a_2_6_lattice3(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r3_lattices(B,E,D) & r2_hidden(E,C) ) ) ) ) )).
fof(fraenkel_a_2_6_lattice6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_lattice3(B)))) ) => ( r2_hidden(A,a_2_6_lattice6(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k3_lattice3(B))) & A = k5_lattice3(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_6_limfunc4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_6_limfunc4(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(B,C)) & ~ r1_xxreal_0(k2_xcmplx_0(B,C),D) ) ) ) )).
fof(fraenkel_a_2_6_member_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_membered(B) & v2_membered(C) ) => ( r2_hidden(A,a_2_6_member_1(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k6_numbers) & m1_subset_1(E,k6_numbers) & A = k6_xxreal_3(D,E) & r2_hidden(D,B) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_6_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( m2_finseq_1(C,k9_setfam_1(B)) => ( r2_hidden(A,a_2_6_mmlquery(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = D & r1_xxreal_0(k3_finseq_1(C),k24_mmlquery(C,D)) ) ) ) )).
fof(fraenkel_a_2_6_modal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k6_modal_1) & m1_trees_1(C,k9_xtuple_0(B)) ) => ( r2_hidden(A,a_2_6_modal_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k8_finseq_1(k4_ordinal1,C,k14_trees_3(D)) & r2_hidden(k8_finseq_1(k4_ordinal1,C,k14_trees_3(D)),k9_xtuple_0(B)) ) ) ) )).
fof(fraenkel_a_2_6_nat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) ) => ( r2_hidden(A,a_2_6_nat_4(B,C)) <=> ? [D] : ( v1_int_2(D) & m1_subset_1(D,k4_ordinal1) & A = k11_newton(D,k11_nat_3(C,D)) & ~ r1_xxreal_0(D,B) & r1_xxreal_0(D,k2_nat_1(2,B)) & ~ r1_xxreal_0(k11_nat_3(C,D),k5_numbers) ) ) ) )).
fof(fraenkel_a_2_6_petri,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_petri(B) & v3_petri(B) & l1_petri(B) & m1_subset_1(C,k1_zfmisc_1(u4_struct_0(B))) ) => ( r2_hidden(A,a_2_6_petri(B,C)) <=> ? [D] : ( m1_petri(D,u1_struct_0(B),u4_struct_0(B),u1_petri(B)) & A = k2_petri(B,D) & r2_hidden(k3_petri(B,D),C) ) ) ) )).
fof(fraenkel_a_2_6_rcomp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) & v1_xreal_0(C) ) => ( r2_hidden(A,a_2_6_rcomp_1(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(k3_seq_4(B),C)) & ~ r1_xxreal_0(k2_xcmplx_0(k3_seq_4(B),C),D) ) ) ) )).
fof(fraenkel_a_2_6_rlaffin2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_6_rlaffin2(B,C)) <=> ? [D] : ( v2_convex1(D,B) & m2_rlvect_2(D,B,C) & A = k6_rlvect_2(B,D) & r2_hidden(D,k1_convex3(B)) ) ) ) )).
fof(fraenkel_a_2_6_rusub_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_6_rusub_5(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r1_struct_0(k3_rusub_5(B,C),E) => r1_bhsp_1(B,E,D) ) ) ) ) ) )).
fof(fraenkel_a_2_6_substut1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_6_substut1(B,C)) <=> ? [D] : ( m1_subset_1(D,k6_qc_lang1(B)) & A = D & k7_qc_lang1(B,D) = C ) ) ) )).
fof(fraenkel_a_2_6_tdlat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) => ( r2_hidden(A,a_2_6_tdlat_2(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & D = k2_pre_topc(B,E) & r2_hidden(E,k1_pcomps_1(B,C)) ) ) ) ) )).
fof(fraenkel_a_2_6_tex_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_6_tex_4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k2_tex_4(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_6_trees_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) & m2_finseq_1(C,k4_ordinal1) ) => ( r2_hidden(A,a_2_6_trees_a(B,C)) <=> ? [D] : ( m1_trees_1(D,k9_xtuple_0(B)) & A = D & ~ r1_tarski(C,D) ) ) ) )).
fof(fraenkel_a_2_6_waybel12,axiom,( ! [A] : ! [B] : ! [C] : ( ( v5_orders_2(B) & v1_yellow_0(B) & v2_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_6_waybel12(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k12_lattice3(B,k3_yellow_0(B),D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_6_waybel14,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_6_waybel14(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k2_waybel_3(B,D) & r1_waybel_3(B,D,C) ) ) ) )).
fof(fraenkel_a_2_6_waybel17,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_6_waybel17(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & r2_hidden(D,a_1_0_waybel17(B)) & r1_tarski(D,C) ) ) ) )).
fof(fraenkel_a_2_6_waybel23,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & v3_waybel_3(B) & l1_orders_2(B) & v6_waybel23(C,B) & m1_waybel23(C,B) ) => ( r2_hidden(A,a_2_6_waybel23(B,C)) <=> ? [D] : ( ~ v1_xboole_0(D) & v1_waybel_0(D,k5_yellow_0(B,C)) & v12_waybel_0(D,k5_yellow_0(B,C)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_yellow_0(B,C)))) & A = D ) ) ) )).
fof(fraenkel_a_2_6_waybel33,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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_xboole_0(C) & v1_subset_1(C,u1_struct_0(k2_yellow_1(k2_struct_0(B)))) & v2_waybel_0(C,k2_yellow_1(k2_struct_0(B))) & v13_waybel_0(C,k2_yellow_1(k2_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(B))))) ) => ( r2_hidden(A,a_2_6_waybel33(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k2_yellow_0(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_6_waybel_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_6_waybel_0(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r1_orders_2(B,E,D) & r2_hidden(E,k6_domain_1(u1_struct_0(B),C)) ) ) ) ) )).
fof(fraenkel_a_2_6_waybel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v3_lattice3(B) & l1_orders_2(B) & 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(A,a_2_6_waybel_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r3_orders_2(B,k3_funct_2(u1_struct_0(B),u1_struct_0(B),C,D),D) ) ) ) )).
fof(fraenkel_a_2_6_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & v1_waybel_0(C,k3_yellow_3(B,B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) ) => ( r2_hidden(A,a_2_6_waybel_2(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,D,E) & r2_hidden(D,k4_yellow_3(B,B,C)) & r2_hidden(E,k5_yellow_3(B,B,C)) ) ) ) )).
fof(fraenkel_a_2_6_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) => ( r2_hidden(A,a_2_6_waybel_4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_waybel_3(B,D,C) ) ) ) )).
fof(fraenkel_a_2_6_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_6_yellow_4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r1_orders_2(B,D,E) & r2_hidden(E,C) ) ) ) ) )).
fof(fraenkel_a_2_6_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) ) => ( r2_hidden(A,a_2_6_zf_fund1(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,B) & m1_subset_1(E,B) & A = k1_zf_fund1(B,D,E) & r2_hidden(D,k1_classes2(B,k5_classes2(B,k6_classes2(B,k2_ordinal4(B),k3_ordinal4(B)),k6_classes2(B,k3_ordinal4(B),k3_ordinal4(B))))) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_7_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & l1_msualg_1(B) & m1_subset_1(C,k1_zfmisc_1(k2_abcmiz_1)) ) => ( r2_hidden(A,a_2_7_abcmiz_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k2_abcmiz_1) & A = k1_domain_1(k2_abcmiz_1,k3_card_3(u3_msualg_1(B,k1_msafree3(B,k28_abcmiz_1(B)))),D,k35_abcmiz_1(D,B)) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_7_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ( r2_hidden(A,a_2_7_armstrng(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = D & ~ r1_tarski(C,D) ) ) ) )).
fof(fraenkel_a_2_7_cgames_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_cgames_1(B) & v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,a_2_7_cgames_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k6_cgames_1(B)) & A = k1_funct_1(k5_relat_1(C,k11_cgames_1(B)),D) & k6_cgames_1(B) != k1_xboole_0 ) ) ) )).
fof(fraenkel_a_2_7_conlat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_conlat_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_7_conlat_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u4_struct_0(B)) & A = D & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r2_hidden(E,a_2_6_conlat_1(B,C)) => r1_conlat_1(B,E,D) ) ) ) ) ) )).
fof(fraenkel_a_2_7_conlat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_conlat_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_7_conlat_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u4_struct_0(B)) & A = D & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r2_hidden(E,C) => r1_conlat_1(B,E,D) ) ) ) ) ) )).
fof(fraenkel_a_2_7_euclid_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k10_funcsdom(k2_finseq_1(B))))) ) => ( r2_hidden(A,a_2_7_euclid_7(B,C)) <=> ? [D] : ( m2_rlvect_2(D,k10_funcsdom(k2_finseq_1(B)),C) & A = k6_rlvect_2(k10_funcsdom(k2_finseq_1(B)),D) ) ) ) )).
fof(fraenkel_a_2_7_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) & ~ v1_xboole_0(C) ) => ( r2_hidden(A,a_2_7_fomodel2(B,C)) <=> ? [D] : ? [E] : ( m2_subset_1(D,k9_funct_2(k37_fomodel1(B),k3_rfunct_3(k3_finseq_2(C),k2_xboole_0(C,k6_margrel1))),k15_fomodel2(B,C)) & m2_subset_1(E,k3_finseq_2(k1_fomodel1(B)),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0))) & A = k1_domain_1(k15_fomodel2(B,C),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0)),D,E) ) ) ) )).
fof(fraenkel_a_2_7_goboard5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_7_goboard5(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(E,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,B,1))) ) ) ) )).
fof(fraenkel_a_2_7_jordan2b,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & m1_subset_1(C,k1_numbers) ) => ( r2_hidden(A,a_2_7_jordan2b(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k6_xcmplx_0(C,B)) & ~ r1_xxreal_0(k2_xcmplx_0(C,B),D) ) ) ) )).
fof(fraenkel_a_2_7_jordan_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & v2_pre_topc(C) & l1_pre_topc(C) ) => ( r2_hidden(A,a_2_7_jordan_a(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) & A = k3_borsuk_1(B,C,D,E) & r2_hidden(D,u1_pre_topc(B)) & r2_hidden(E,u1_pre_topc(C)) ) ) ) )).
fof(fraenkel_a_2_7_knaster,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & 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)))) ) => ( r2_hidden(A,a_2_7_knaster(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k3_funct_2(u1_struct_0(B),u1_struct_0(B),C,D) & r3_lattices(B,D,k3_funct_2(u1_struct_0(B),u1_struct_0(B),C,D)) ) ) ) )).
fof(fraenkel_a_2_7_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) ) => ( r2_hidden(A,a_2_7_lattice3(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = k15_lattice3(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_7_lattice6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_7_lattice6(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k4_lattice3(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_7_limfunc4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r2_hidden(A,a_2_7_limfunc4(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(D,k1_limfunc3(C,B)) ) ) ) )).
fof(fraenkel_a_2_7_member_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_membered(B) & v1_membered(C) ) => ( r2_hidden(A,a_2_7_member_1(B,C)) <=> ? [D] : ? [E] : ( v1_xcmplx_0(D) & v1_xcmplx_0(E) & A = k7_xcmplx_0(D,E) & r2_hidden(D,B) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_2_7_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( m2_finseq_1(C,k9_setfam_1(B)) => ( r2_hidden(A,a_2_7_mmlquery(B,C)) <=> ? [D] : ( m1_subset_1(D,B) & A = D & r1_xxreal_0(1,k24_mmlquery(C,D)) ) ) ) )).
fof(fraenkel_a_2_7_petri,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_petri(B) & v3_petri(B) & l1_petri(B) & m1_subset_1(C,k1_zfmisc_1(u4_struct_0(B))) ) => ( r2_hidden(A,a_2_7_petri(B,C)) <=> ? [D] : ( m1_petri(D,u4_struct_0(B),u1_struct_0(B),u2_petri(B)) & A = k5_petri(B,D) & r2_hidden(k4_petri(B,D),C) ) ) ) )).
fof(fraenkel_a_2_7_pua2mss1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) & m4_pua2mss1(C,B) ) => ( r2_hidden(A,a_2_7_pua2mss1(B,C)) <=> ? [D] : ( m2_finseq_2(D,k10_pua2mss1(B,C),k3_finseq_2(k10_pua2mss1(B,C))) & A = k4_card_3(D) ) ) ) )).
fof(fraenkel_a_2_7_tex_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_7_tex_4(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & v3_pre_topc(D,B) & r1_tarski(C,D) ) ) ) )).
fof(fraenkel_a_2_7_waybel12,axiom,( ! [A] : ! [B] : ! [C] : ( ( v5_orders_2(B) & v2_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_7_waybel12(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k13_lattice3(B,k4_yellow_0(B),D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_7_waybel14,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_7_waybel14(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k2_waybel_3(B,D) & r2_hidden(D,k3_subset_1(u1_struct_0(B),k5_waybel_0(B,k1_yellow_0(B,k1_waybel_3(B,C))))) ) ) ) )).
fof(fraenkel_a_2_7_waybel33,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(B))))) ) => ( r2_hidden(A,a_2_7_waybel33(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,u1_struct_0(B)) & m2_subset_1(E,u1_struct_0(k2_yellow_1(k2_struct_0(B))),C) & A = k1_domain_1(u1_struct_0(B),C,D,E) & r2_hidden(D,E) ) ) ) )).
fof(fraenkel_a_2_7_waybel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_7_waybel_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_orders_2(B,k11_lattice3(B,C,D),k3_yellow_0(B)) ) ) ) )).
fof(fraenkel_a_2_7_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_7_waybel_4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_waybel_3(B,D,C) ) ) ) )).
fof(fraenkel_a_2_7_yellow19,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & ~ v1_xboole_0(C) & v1_subset_1(C,u1_struct_0(k2_yellow_1(k2_struct_0(B)))) & v2_waybel_0(C,k2_yellow_1(k2_struct_0(B))) & v13_waybel_0(C,k2_yellow_1(k2_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(B))))) ) => ( r2_hidden(A,a_2_7_yellow19(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,u1_struct_0(B)) & m2_subset_1(E,u1_struct_0(k2_yellow_1(k2_struct_0(B))),C) & A = k4_tarski(D,E) & r2_hidden(D,E) ) ) ) )).
fof(fraenkel_a_2_7_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_7_yellow_4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r1_orders_2(B,E,D) & r2_hidden(E,C) ) ) ) ) )).
fof(fraenkel_a_2_7_yellow_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) & v8_yellow_6(C,B) & m4_yellow_6(C,B) ) => ( r2_hidden(A,a_2_7_yellow_6(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r2_hidden(E,D) => ! [F] : ( ( ~ v2_struct_0(F) & v4_orders_2(F) & v7_waybel_0(F) & l1_waybel_0(F,B) ) => ( r2_hidden(k4_tarski(F,E),C) => r1_waybel_0(B,F,D) ) ) ) ) ) ) ) )).
fof(fraenkel_a_2_7_zmodul02,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_zmodul02(C,B) ) => ( r2_hidden(A,a_2_7_zmodul02(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & k3_funct_2(u1_struct_0(B),k4_numbers,C,D) != k5_numbers ) ) ) )).
fof(fraenkel_a_2_8_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(A,a_2_8_abcmiz_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k2_tarski(B,C)) & A = k1_abcmiz_1(D) ) ) )).
fof(fraenkel_a_2_8_abcmiz_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & l1_msualg_1(B) & v4_abcmiz_a(C,B) & m1_subset_1(C,u4_struct_0(B)) ) => ( r2_hidden(A,a_2_8_abcmiz_a(B,C)) <=> ? [D] : ( m1_dtconstr(D,u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))),k5_trees_3(u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers)))))),k1_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))) & A = D & k7_msaterm(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),D) = k2_msualg_1(B,C) & r2_pboole(u1_struct_0(B),k4_msafree3(B,k2_pboole(u1_struct_0(B),k28_abcmiz_1(B),k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),D),k28_abcmiz_1(B)) ) ) ) )).
fof(fraenkel_a_2_8_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_2_8_armstrng(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(B)) & A = k6_armstrng(B,D,E) & ( r1_tarski(C,D) | r1_tarski(E,D) ) ) ) ) )).
fof(fraenkel_a_2_8_arytm_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k2_arytm_2) & m2_subset_1(C,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) ) => ( r2_hidden(A,a_2_8_arytm_2(B,C)) <=> ? [D] : ? [E] : ( m1_subset_1(D,k5_arytm_3) & m1_subset_1(E,k5_arytm_3) & A = k9_arytm_3(D,E) & r2_hidden(D,C) & r2_hidden(E,k3_arytm_2(B)) ) ) ) )).
fof(fraenkel_a_2_8_bintree2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_8_bintree2(B,C)) <=> ? [D] : ( m1_trees_1(D,B) & A = D & k3_finseq_1(D) = C ) ) ) )).
fof(fraenkel_a_2_8_cgames_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_cgames_1(B) & v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,a_2_8_cgames_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k6_cgames_1(B)) & A = k1_funct_1(C,D) & k6_cgames_1(B) != k1_xboole_0 ) ) ) )).
fof(fraenkel_a_2_8_conlat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_conlat_1(B) & m1_subset_1(C,k1_zfmisc_1(u4_struct_0(B))) ) => ( r2_hidden(A,a_2_8_conlat_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u4_struct_0(B)) & A = D & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r2_hidden(E,a_2_1_conlat_1(B,C)) => r1_conlat_1(B,E,D) ) ) ) ) ) )).
fof(fraenkel_a_2_8_euclid_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k7_real_ns1(B)))) ) => ( r2_hidden(A,a_2_8_euclid_7(B,C)) <=> ? [D] : ( m2_rlvect_2(D,k7_real_ns1(B),C) & A = k6_rlvect_2(k7_real_ns1(B),D) ) ) ) )).
fof(fraenkel_a_2_8_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ( r2_hidden(A,a_2_8_fomodel2(B,C)) <=> ? [D] : ? [E] : ( m2_subset_1(D,k15_fomodel1(C),k16_fomodel1(C)) & m2_subset_1(E,k6_subset_1(k3_finseq_2(k1_fomodel1(C)),k1_tarski(k1_xboole_0)),k24_fomodel2(C,B)) & A = k7_finseq_1(k9_finseq_1(D),E) ) ) ) )).
fof(fraenkel_a_2_8_goboard5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_8_goboard5(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k3_finseq_1(C),B)),D) ) ) ) )).
fof(fraenkel_a_2_8_limfunc4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(B) & v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r2_hidden(A,a_2_8_limfunc4(B,C)) <=> ? [D] : ( v1_xreal_0(D) & A = D & ~ r1_xxreal_0(k1_limfunc3(C,B),D) ) ) ) )).
fof(fraenkel_a_2_8_member_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_membered(B) & v1_xxreal_0(C) ) => ( r2_hidden(A,a_2_8_member_1(B,C)) <=> ? [D] : ( m1_subset_1(D,k6_numbers) & A = k1_xxreal_3(C,D) & r2_hidden(D,B) ) ) ) )).
fof(fraenkel_a_2_8_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_mmlquery(B) & m2_finseq_1(C,u1_mmlquery(B)) ) => ( r2_hidden(A,a_2_8_mmlquery(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_xxreal_0(k5_card_1(k7_subset_1(u1_mmlquery(B),k2_relset_1(u1_mmlquery(B),C),k30_mmlquery(B,D))),k5_numbers) ) ) ) )).
fof(fraenkel_a_2_8_tex_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_8_tex_4(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & v4_pre_topc(D,B) & r1_tarski(C,D) ) ) ) )).
fof(fraenkel_a_2_8_waybel11,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & v1_yellow_6(C,B) & l1_waybel_0(C,B) ) => ( r2_hidden(A,a_2_8_waybel11(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(C)) & A = k2_yellow_0(B,a_3_4_waybel11(B,C,D)) ) ) ) )).
fof(fraenkel_a_2_8_waybel12,axiom,( ! [A] : ! [B] : ! [C] : ( ( v5_orders_2(B) & v2_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_8_waybel12(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k13_lattice3(B,k4_yellow_0(B),D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_8_waybel14,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_8_waybel14(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r1_tarski(D,k2_waybel_3(B,E)) & r1_waybel_3(B,E,C) & r2_hidden(C,D) & v3_pre_topc(D,B) & v2_waybel_0(D,B) ) ) ) ) )).
fof(fraenkel_a_2_8_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) => ( r2_hidden(A,a_2_8_waybel_4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r2_hidden(k1_domain_1(u1_struct_0(B),u1_struct_0(B),D,C),k1_waybel_4(B)) ) ) ) )).
fof(fraenkel_a_2_8_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_pre_topc(B) & v8_pre_topc(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v1_compts_1(B) & l1_waybel_9(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_8_waybel_9(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k13_lattice3(B,C,D) & r2_hidden(D,k2_struct_0(B)) ) ) ) )).
fof(fraenkel_a_2_9_abcmiz_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( v8_abcmiz_1(B,k27_abcmiz_1) & m1_abcmiz_1(B,k27_abcmiz_1,k13_abcmiz_1(k27_abcmiz_1)) & m3_abcmiz_1(C,k27_abcmiz_1) ) => ( r2_hidden(A,a_2_9_abcmiz_a(B,C)) <=> ? [D] : ( v8_abcmiz_1(D,k27_abcmiz_1) & m1_abcmiz_1(D,k27_abcmiz_1,k13_abcmiz_1(k27_abcmiz_1)) & A = k9_abcmiz_a(k27_abcmiz_1,D) & r2_hidden(D,k2_xboole_0(k6_domain_1(k3_card_3(u3_msualg_1(k27_abcmiz_1,k1_msafree3(k27_abcmiz_1,k28_abcmiz_1(k27_abcmiz_1)))),B),k41_abcmiz_1(k27_abcmiz_1,C))) ) ) ) )).
fof(fraenkel_a_2_9_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_2_9_armstrng(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & A = D & ~ r1_tarski(C,D) ) ) ) )).
fof(fraenkel_a_2_9_bintree2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) & v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ( r2_hidden(A,a_2_9_bintree2(B,C)) <=> ? [D] : ( m1_trees_1(D,B) & A = D & k3_finseq_1(D) = C ) ) ) )).
fof(fraenkel_a_2_9_conlat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_conlat_1(B) & m1_subset_1(C,k1_zfmisc_1(u4_struct_0(B))) ) => ( r2_hidden(A,a_2_9_conlat_1(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & ! [E] : ( m1_subset_1(E,u4_struct_0(B)) => ( r2_hidden(E,a_2_8_conlat_1(B,C)) => r1_conlat_1(B,D,E) ) ) ) ) ) )).
fof(fraenkel_a_2_9_goboard5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_2_9_goboard5(B,C)) <=> ? [D] : ? [E] : ( v1_xreal_0(D) & v1_xreal_0(E) & A = k19_euclid(D,E) & r1_xxreal_0(D,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,B))) ) ) ) )).
fof(fraenkel_a_2_9_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) ) => ( r2_hidden(A,a_2_9_lattice3(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r3_lattice3(B,D,C) ) ) ) )).
fof(fraenkel_a_2_9_member_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_membered(B) & v1_xcmplx_0(C) ) => ( r2_hidden(A,a_2_9_member_1(B,C)) <=> ? [D] : ( v1_xcmplx_0(D) & A = k2_xcmplx_0(C,D) & r2_hidden(D,B) ) ) ) )).
fof(fraenkel_a_2_9_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_mmlquery(B) & l1_mmlquery(B) & m2_finseq_1(C,u1_mmlquery(B)) ) => ( r2_hidden(A,a_2_9_mmlquery(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_xxreal_0(k5_card_1(k7_subset_1(u1_struct_0(B),k30_mmlquery(B,D),k2_relset_1(u1_mmlquery(B),C))),k5_numbers) ) ) ) )).
fof(fraenkel_a_2_9_stirl2_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_2_9_stirl2_1(B,C)) <=> ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k7_card_1(k1_nat_1(C,1)),k7_card_1(k1_nat_1(B,1))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(k1_nat_1(C,1)),k7_card_1(k1_nat_1(B,1))))) & A = D & v2_funct_2(D,k7_card_1(k1_nat_1(B,1))) & v1_stirl2_1(D,k1_nat_1(C,1),k1_nat_1(B,1)) ) ) ) )).
fof(fraenkel_a_2_9_tdlat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( r2_hidden(A,a_2_9_tdlat_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k4_tdlat_1(B))) & A = D & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_9_tex_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_9_tex_4(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & v3_pre_topc(D,B) & r2_hidden(C,D) ) ) ) )).
fof(fraenkel_a_2_9_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(A,a_2_9_valued_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k2_xcmplx_0(D,B) & r2_hidden(D,k4_finseq_1(C)) ) ) ) )).
fof(fraenkel_a_2_9_waybel12,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_yellow_0(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_2_9_waybel12(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k12_lattice3(B,k4_yellow_0(B),D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_9_waybel14,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) & m1_subset_1(C,u1_struct_0(k1_yellow_1(u1_pre_topc(B)))) ) => ( r2_hidden(A,a_2_9_waybel14(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k2_waybel_3(B,D) & r2_hidden(D,C) ) ) ) )).
fof(fraenkel_a_2_9_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_2_9_waybel_4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r2_hidden(k1_domain_1(u1_struct_0(B),u1_struct_0(B),D,C),k2_waybel_4(B)) ) ) ) )).
fof(fraenkel_a_3_0_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & l1_msualg_1(B) & v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_abcmiz_1,k34_abcmiz_1(B)))) & m1_subset_1(D,k1_zfmisc_1(k38_abcmiz_1(B))) ) => ( r2_hidden(A,a_3_0_abcmiz_1(B,C,D)) <=> ? [E] : ( v8_abcmiz_1(E,B) & m1_abcmiz_1(E,B,k13_abcmiz_1(B)) & A = k61_abcmiz_1(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_0_aff_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v7_struct_0(B) & v1_diraf(B) & l1_analoaf(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_aff_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r2_aff_1(B,E,F,C) & r2_hidden(F,D) ) ) ) ) )).
fof(fraenkel_a_3_0_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v1_relat_1(D) & v1_funct_1(D) ) => ( r2_hidden(A,a_3_0_afinsq_1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_nat_1(E,k1_nat_1(B,k5_card_1(C))) & r2_hidden(E,k9_xtuple_0(D)) ) ) ) )).
fof(fraenkel_a_3_0_algstr_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) & ~ v2_struct_0(C) & l3_algstr_0(C) & 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(A,a_3_0_algstr_4(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k4_tarski(E,F) & 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) ) ) ) )).
fof(fraenkel_a_3_0_ami_wstd,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_setfam_1(B) & ~ v2_struct_0(C) & v2_memstr_0(C,B) & v3_memstr_0(C,B) & v2_ami_wstd(C,B) & l1_extpro_1(C,B) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(C)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) ) => ( r2_hidden(A,a_3_0_ami_wstd(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = k3_ami_wstd(B,C,E) & r2_hidden(E,k1_relset_1(k4_ordinal1,D)) ) ) ) )).
fof(fraenkel_a_3_0_amistd_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_setfam_1(B) & ~ v2_struct_0(C) & v2_memstr_0(C,B) & v3_memstr_0(C,B) & l1_extpro_1(C,B) & m1_subset_1(D,u1_compos_1(C)) ) => ( r2_hidden(A,a_3_0_amistd_1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_amistd_1(B,C,E,D) ) ) ) )).
fof(fraenkel_a_3_0_amistd_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_setfam_1(B) & ~ v2_struct_0(C) & v2_memstr_0(C,B) & v3_memstr_0(C,B) & v3_amistd_1(C,B) & l1_extpro_1(C,B) & m1_subset_1(D,u1_compos_1(C)) ) => ( r2_hidden(A,a_3_0_amistd_2(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_amistd_1(B,C,E,D) ) ) ) )).
fof(fraenkel_a_3_0_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v4_unialg_1(B) & l1_unialg_1(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(u1_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(B))))) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_0_aofa_000(B,C,D)) <=> ? [E] : ? [F] : ( m2_subset_1(E,k4_ordinal1,k4_finseq_1(u1_unialg_1(B))) & m2_finseq_2(F,u1_struct_0(B),k3_finseq_2(u1_struct_0(B))) & A = k1_funct_1(k2_pua2mss1(B,E),F) & r2_hidden(F,k1_relset_1(k3_finseq_2(u1_struct_0(B)),k2_pua2mss1(B,E))) & r1_tarski(k2_relset_1(u1_struct_0(B),F),k9_nat_1(k9_setfam_1(u1_struct_0(B)),C,D)) ) ) ) )).
fof(fraenkel_a_3_0_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v4_funct_1(B) ) => ( r2_hidden(A,a_3_0_aofa_i00(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & k1_funct_1(E,C) != D ) ) ) )).
fof(fraenkel_a_3_0_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_finset_1(B) & m1_subset_1(C,k4_armstrng(B)) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(B),k9_setfam_1(B)))) ) => ( r2_hidden(A,a_3_0_armstrng(B,C,D)) <=> ? [E] : ( m1_armstrng(E,B,D) & A = E & r3_armstrng(B,E,C) ) ) ) )).
fof(fraenkel_a_3_0_asympt_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m1_funct_2(C,B,k1_numbers) & m1_funct_2(D,B,k1_numbers) ) => ( r2_hidden(A,a_3_0_asympt_0(B,C,D)) <=> ? [E] : ( m2_funct_2(E,B,k1_numbers,k9_funct_2(B,k1_numbers)) & A = E & ? [F] : ( m2_funct_2(F,B,k1_numbers,k9_funct_2(B,k1_numbers)) & ? [G] : ( m2_funct_2(G,B,k1_numbers,k9_funct_2(B,k1_numbers)) & r2_hidden(F,C) & r2_hidden(G,D) & ! [H] : ( m1_subset_1(H,B) => k3_funct_2(B,k1_numbers,E,H) = k3_real_1(k3_funct_2(B,k1_numbers,F,H),k3_funct_2(B,k1_numbers,G,H)) ) ) ) ) ) ) )).
fof(fraenkel_a_3_0_bagorder,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v16_waybel_0(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(B)),k5_finsub_1(u1_struct_0(B))))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(B)),k5_finsub_1(u1_struct_0(B))))))) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_0_bagorder(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,k5_finsub_1(u1_struct_0(B))) & m1_subset_1(F,k5_finsub_1(u1_struct_0(B))) & A = k1_domain_1(k5_finsub_1(u1_struct_0(B)),k5_finsub_1(u1_struct_0(B)),E,F) & E != k1_xboole_0 & F != k1_xboole_0 & k11_bagorder(B,E) = k11_bagorder(B,F) & r2_hidden(k1_domain_1(k1_zfmisc_1(E),k1_zfmisc_1(F),k6_subset_1(E,k6_domain_1(u1_struct_0(B),k11_bagorder(B,E))),k6_subset_1(F,k6_domain_1(u1_struct_0(B),k11_bagorder(B,F)))),k9_nat_1(k1_zfmisc_1(k2_zfmisc_1(k5_finsub_1(u1_struct_0(B)),k5_finsub_1(u1_struct_0(B)))),C,D)) ) ) ) )).
fof(fraenkel_a_3_0_bcialg_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_bcialg_1(B) & v4_bcialg_1(B) & v5_bcialg_1(B) & v7_bcialg_1(B) & l2_bcialg_1(B) & m2_subset_1(C,u1_struct_0(B),k5_bcialg_1(B)) & m2_subset_1(D,u1_struct_0(B),k5_bcialg_1(B)) ) => ( r2_hidden(A,a_3_0_bcialg_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_bcialg_1(B,k6_bcialg_1(B,C,D),E) ) ) ) )).
fof(fraenkel_a_3_0_bcialg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_bcialg_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_bcialg_1(B,k1_bcialg_1(B,E,C),D) ) ) ) )).
fof(fraenkel_a_3_0_bcialg_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_bcialg_1(B) & v4_bcialg_1(B) & v5_bcialg_1(B) & v7_bcialg_1(B) & l2_bcialg_1(B) & ~ v2_struct_0(C) & v3_bcialg_1(C) & v4_bcialg_1(C) & v5_bcialg_1(C) & v7_bcialg_1(C) & l2_bcialg_1(C) & 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)))) ) => ( r2_hidden(A,a_3_0_bcialg_6(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,E) = k4_struct_0(C) ) ) ) )).
fof(fraenkel_a_3_0_bhsp_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_bhsp_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(D,k3_bhsp_1(B,k5_algstr_0(B,C,E))) ) ) ) )).
fof(fraenkel_a_3_0_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( l2_struct_0(B) & ~ v2_struct_0(C) & l1_vectsp_1(C,B) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(u1_struct_0(C),u1_struct_0(C)),u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(C)),u1_struct_0(B)))) ) => ( r2_hidden(A,a_3_0_bilinear(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = E & k2_binop_1(u1_struct_0(C),u1_struct_0(C),u1_struct_0(B),D,E,E) = k4_struct_0(B) ) ) ) )).
fof(fraenkel_a_3_0_bintree1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) & ~ v1_xboole_0(C) & v1_trees_1(C) & m1_trees_1(D,k13_trees_3(B,C)) ) => ( r2_hidden(A,a_3_0_bintree1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k8_finseq_1(k4_ordinal1,D,k14_trees_3(E)) & r2_hidden(k8_finseq_1(k4_ordinal1,D,k14_trees_3(E)),k13_trees_3(B,C)) ) ) ) )).
fof(fraenkel_a_3_0_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & v2_pre_topc(C) & l1_pre_topc(C) & v1_pre_topc(D) & v2_pre_topc(D) & l1_pre_topc(D) ) => ( r2_hidden(A,a_3_0_borsuk_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(D)))) & A = k5_setfam_1(u1_struct_0(D),E) & r1_tarski(E,a_2_0_borsuk_1(B,C)) ) ) ) )).
fof(fraenkel_a_3_0_borsuk_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & ~ v2_struct_0(C) & v2_pre_topc(C) & v1_compts_1(C) & l1_pre_topc(C) & v3_pre_topc(D,k2_borsuk_1(C,B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(C,B)))) ) => ( r2_hidden(A,a_3_0_borsuk_3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_tarski(k3_borsuk_1(C,B,k2_struct_0(C),k6_domain_1(u1_struct_0(B),E)),D) ) ) ) )).
fof(fraenkel_a_3_0_card_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & 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,a_3_0_card_3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & k3_funct_2(B,C,D,E) != k1_xboole_0 ) ) ) )).
fof(fraenkel_a_3_0_card_fil,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m1_card_fil(C,B) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_3_0_card_fil(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(B)) & A = E & ? [F] : ( m1_subset_1(F,k1_zfmisc_1(B)) & r2_hidden(F,a_3_1_card_fil(B,C,D)) & r1_tarski(F,E) ) ) ) ) )).
fof(fraenkel_a_3_0_card_lar,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_ordinal1(B) & v4_ordinal1(B) & ~ v1_finset_1(B) & v3_ordinal1(C) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_3_0_card_lar(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & r2_hidden(E,D) & r2_hidden(C,E) ) ) ) )).
fof(fraenkel_a_3_0_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_cat_1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_cat_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u4_struct_0(B)) & A = E & k3_graph_1(B,E) = C & k4_graph_1(B,E) = D ) ) ) )).
fof(fraenkel_a_3_0_cc0sp2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xcmplx_0(B) & v1_xreal_0(C) & v1_xcmplx_0(D) ) => ( r2_hidden(A,a_3_0_cc0sp2(B,C,D)) <=> ? [E] : ( v1_xcmplx_0(E) & A = E & ~ r1_xxreal_0(k7_xcmplx_0(C,k9_complex1(B)),k9_complex1(k6_xcmplx_0(E,D))) ) ) ) )).
fof(fraenkel_a_3_0_cfdiff_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xcmplx_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_cfdiff_1(B,C,D)) <=> ? [E] : ( v1_xcmplx_0(E) & A = E & ~ r1_xxreal_0(k3_xxreal_0(C,D),k9_complex1(k6_xcmplx_0(E,B))) ) ) ) )).
fof(fraenkel_a_3_0_cgames_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v3_ordinal1(C) & v3_ordinal1(D) ) => ( r2_hidden(A,a_3_0_cgames_1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,k1_zfmisc_1(k3_tarski(k10_xtuple_0(k5_relat_1(k5_relat_1(B,C),D))))) & m1_subset_1(F,k1_zfmisc_1(k3_tarski(k10_xtuple_0(k5_relat_1(k5_relat_1(B,C),D))))) & A = g1_cgames_1(E,F) ) ) ) )).
fof(fraenkel_a_3_0_chain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & m2_finseq_2(C,k1_numbers,k1_euclid(B)) & m2_finseq_2(D,k1_numbers,k1_euclid(B)) ) => ( r2_hidden(A,a_3_0_chain_1(B,C,D)) <=> ? [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(B)) & A = E & ~ ( ~ ! [F] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(B)) => ( r1_xxreal_0(k1_funct_1(C,F),k1_funct_1(E,F)) & r1_xxreal_0(k1_funct_1(E,F),k1_funct_1(D,F)) ) ) & ! [F] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(B)) => ~ ( ~ r1_xxreal_0(k1_funct_1(C,F),k1_funct_1(D,F)) & ( r1_xxreal_0(k1_funct_1(E,F),k1_funct_1(D,F)) | r1_xxreal_0(k1_funct_1(C,F),k1_funct_1(E,F)) ) ) ) ) ) ) ) )).
fof(fraenkel_a_3_0_chord,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k6_glib_000(B))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k6_glib_000(B))) ) => ( r2_hidden(A,a_3_0_chord(B,C,D)) <=> ? [E] : ( v5_glib_001(E,B) & m3_glib_001(E,B) & A = k3_finseq_1(E) & r2_hidden(k3_glib_001(B,E),C) & r2_hidden(k4_glib_001(B,E),D) ) ) ) )).
fof(fraenkel_a_3_0_circled1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_rlvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_circled1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k5_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_0_circuit1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & v5_msafree2(B) & l1_msualg_1(B) & v4_msualg_1(C,B) & v4_msafree2(C,B) & l3_msualg_1(C,B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_circuit1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(B,k5_msafree2(B,C)),D)) & A = k5_card_1(E) ) ) ) )).
fof(fraenkel_a_3_0_circuit2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & v5_msafree2(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_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_circuit2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_dtconstr(k5_msafree(B,C))) & A = E & ~ ( ! [F] : ~ ( r2_hidden(F,k1_funct_1(C,D)) & E = k1_trees_4(k4_tarski(F,D)) ) & ! [F] : ( m1_subset_1(F,u4_struct_0(B)) => ~ ( k4_tarski(F,u1_struct_0(B)) = k1_funct_1(E,k1_xboole_0) & k2_msualg_1(B,F) = D ) ) ) ) ) ) )).
fof(fraenkel_a_3_0_ckspace1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & ~ v1_xboole_0(D) & v1_pdiff_7(D,B) & m1_subset_1(D,k1_zfmisc_1(k1_euclid(B))) ) => ( r2_hidden(A,a_3_0_ckspace1(B,C,D)) <=> ? [E] : ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(B),k1_numbers))) & A = E & r1_ckspace1(B,E,C,D) & k1_relset_1(k1_euclid(B),E) = D ) ) ) )).
fof(fraenkel_a_3_0_clopban1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(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) & v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C)) & v13_vectsp_1(D,B,C) & v1_clopban1(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)))) ) => ( r2_hidden(A,a_3_0_clopban1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k2_normsp_0(C,k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,E)) & r1_xxreal_0(k2_normsp_0(B,E),1) ) ) ) )).
fof(fraenkel_a_3_0_closure2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( l1_struct_0(B) & v1_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,k6_closure2(u1_struct_0(B),C),k6_closure2(u1_struct_0(B),C)) & v7_closure2(D,u1_struct_0(B),C) & v8_closure2(D,u1_struct_0(B),C) & v9_closure2(D,u1_struct_0(B),C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k6_closure2(u1_struct_0(B),C),k6_closure2(u1_struct_0(B),C)))) ) => ( r2_hidden(A,a_3_0_closure2(B,C,D)) <=> ? [E] : ( m1_closure2(E,u1_struct_0(B),C,k6_closure2(u1_struct_0(B),C)) & A = E & r6_pboole(u1_struct_0(B),k7_closure2(u1_struct_0(B),C,D,E),E) ) ) ) )).
fof(fraenkel_a_3_0_closure3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) ) => ( r2_hidden(A,a_3_0_closure3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(k1_closure2(B,C))) & A = k2_closure3(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_0_clvect_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_clvect_1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,F,E) & r2_hidden(F,C) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_0_clvect_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & m1_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_clvect_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(D,k13_csspace(B,k5_algstr_0(B,C,E))) ) ) ) )).
fof(fraenkel_a_3_0_collsp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_collsp(B) & v3_collsp(B) & l1_collsp(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_collsp(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_collsp(B,C,D,E) ) ) ) )).
fof(fraenkel_a_3_0_combgras,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(B,k4_ordinal1) & ~ v1_xboole_0(C) & m1_subset_1(D,k1_zfmisc_1(C)) ) => ( r2_hidden(A,a_3_0_combgras(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(C)) & A = E & k1_card_1(E) = B & r1_tarski(D,E) ) ) ) )).
fof(fraenkel_a_3_0_compos_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_compos_0(B) & v2_compos_0(B) & m1_subset_1(C,B) ) => ( r2_hidden(A,a_3_0_compos_0(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k3_compos_0(B,k2_compos_0(B,C))) & A = k1_funct_1(E,D) ) ) ) )).
fof(fraenkel_a_3_0_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( l1_compos_1(B) & v7_ordinal1(C) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(B)) & v1_funct_1(D) & v1_finset_1(D) ) => ( r2_hidden(A,a_3_0_compos_1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k2_xcmplx_0(E,C) & r2_hidden(E,k9_xtuple_0(D)) ) ) ) )).
fof(fraenkel_a_3_0_conlat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_conlat_1(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k11_conlat_1(B)))) & m3_conlat_1(D,B,C) ) => ( r2_hidden(A,a_3_0_conlat_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ! [F] : ( m1_subset_1(F,u4_struct_0(B)) => ( r2_hidden(F,u3_conlat_1(B,D)) => r1_conlat_1(B,E,F) ) ) ) ) ) )).
fof(fraenkel_a_3_0_convex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_rlvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_convex1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_rlvect_1(B,E,D) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_0_convex2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_bhsp_1(B) & l1_bhsp_1(B) & m2_finseq_1(C,u1_struct_0(B)) & m2_finseq_1(D,k1_numbers) ) => ( r2_hidden(A,a_3_0_convex2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( r2_hidden(F,k9_subset_1(k4_ordinal1,k4_finseq_1(C),k4_finseq_1(D))) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ~ ( G = k1_funct_1(C,F) & r1_xxreal_0(k1_bhsp_1(B,E,G),k1_funct_1(D,F)) ) ) ) ) ) ) ) )).
fof(fraenkel_a_3_0_convex4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_clvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v1_xcmplx_0(D) ) => ( r2_hidden(A,a_3_0_convex4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_clvect_1(B,E,D) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_0_cqc_lang,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(B) & v7_ordinal1(C) & v3_card_1(D,C) & m2_finseq_1(D,k2_qc_lang1(B)) ) => ( r2_hidden(A,a_3_0_cqc_lang(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_funct_1(D,E) & r1_xxreal_0(1,E) & r1_xxreal_0(E,k3_finseq_1(D)) & r2_hidden(k1_funct_1(D,E),k5_qc_lang1(B)) ) ) ) )).
fof(fraenkel_a_3_0_cqc_sim1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(B) & m1_subset_1(C,k4_ordinal1) & v3_card_1(D,C) & m2_finseq_1(D,k2_qc_lang1(B)) ) => ( r2_hidden(A,a_3_0_cqc_sim1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_funct_1(D,E) & r1_xxreal_0(1,E) & r1_xxreal_0(E,k3_finseq_1(D)) & r2_hidden(k1_funct_1(D,E),k4_qc_lang1(B)) ) ) ) )).
fof(fraenkel_a_3_0_cqc_the3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(B) & v7_ordinal1(C) & v3_card_1(D,C) & m2_finseq_1(D,k2_qc_lang1(B)) ) => ( r2_hidden(A,a_3_0_cqc_the3(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_funct_1(D,E) & r1_xxreal_0(1,E) & r1_xxreal_0(E,k3_finseq_1(D)) & r2_hidden(k1_funct_1(D,E),k3_qc_lang1(B)) ) ) ) )).
fof(fraenkel_a_3_0_csspace4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & ~ 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) & 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)))) ) => ( r2_hidden(A,a_3_0_csspace4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = k2_normsp_0(C,k3_funct_2(B,u1_struct_0(C),D,E)) ) ) ) )).
fof(fraenkel_a_3_0_ec_pf_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v1_int_2(B) & m1_subset_1(C,u1_struct_0(k9_int_3(B))) & m1_subset_1(D,u1_struct_0(k9_int_3(B))) ) => ( r2_hidden(A,a_3_0_ec_pf_1(B,C,D)) <=> ? [E] : ( m2_subset_1(E,k3_zfmisc_1(u1_struct_0(k9_int_3(B)),u1_struct_0(k9_int_3(B)),u1_struct_0(k9_int_3(B))),k3_ec_pf_1(k9_int_3(B))) & A = E & k3_funct_2(k3_zfmisc_1(u1_struct_0(k9_int_3(B)),u1_struct_0(k9_int_3(B)),u1_struct_0(k9_int_3(B))),u1_struct_0(k9_int_3(B)),k5_ec_pf_1(B,C,D),E) = k4_struct_0(k9_int_3(B)) ) ) ) )).
fof(fraenkel_a_3_0_ec_pf_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v1_int_2(B) & m1_subset_1(C,u1_struct_0(k9_int_3(B))) & m1_subset_1(D,u1_struct_0(k9_int_3(B))) ) => ( r2_hidden(A,a_3_0_ec_pf_2(B,C,D)) <=> ? [E] : ( m2_subset_1(E,k3_zfmisc_1(u1_struct_0(k9_int_3(B)),u1_struct_0(k9_int_3(B)),u1_struct_0(k9_int_3(B))),k3_ec_pf_1(k9_int_3(B))) & A = E & k3_funct_2(k3_zfmisc_1(u1_struct_0(k9_int_3(B)),u1_struct_0(k9_int_3(B)),u1_struct_0(k9_int_3(B))),u1_struct_0(k9_int_3(B)),k5_ec_pf_1(B,C,D),E) = k4_struct_0(k9_int_3(B)) ) ) ) )).
fof(fraenkel_a_3_0_ens_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,B) & m1_subset_1(D,B) ) => ( r2_hidden(A,a_3_0_ens_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_ens_1(B)) & A = k1_domain_1(k2_zfmisc_1(B,B),k1_ens_1(B),k1_domain_1(B,B,C,D),E) & r2_hidden(k1_domain_1(k2_zfmisc_1(B,B),k1_ens_1(B),k1_domain_1(B,B,C,D),E),k2_ens_1(B)) ) ) ) )).
fof(fraenkel_a_3_0_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & v1_eqrel_1(C,B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(k9_setfam_1(B)))) & m1_subset_1(D,B) ) => ( r2_hidden(A,a_3_0_eqrel_1(B,C,D)) <=> ? [E] : ( m1_eqrel_1(E,B) & A = k11_eqrel_1(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_0_euclid_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) => ( r2_hidden(A,a_3_0_euclid_3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) & A = E & ? [F] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & ~ r1_xxreal_0(F,k5_numbers) & ~ r1_xxreal_0(G,k5_numbers) & ~ r1_xxreal_0(H,k5_numbers) & k2_xcmplx_0(k2_xcmplx_0(F,G),H) = 1 & E = k3_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),B,F),k1_rlvect_1(k15_euclid(2),C,G)),k1_rlvect_1(k15_euclid(2),D,H)) ) ) ) ) ) ) )).
fof(fraenkel_a_3_0_euclid_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & m2_finseq_2(C,k1_numbers,k1_euclid(B)) & m2_finseq_2(D,k1_numbers,k1_euclid(B)) ) => ( r2_hidden(A,a_3_0_euclid_4(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = k7_euclid(B,k9_euclid(B,C,k6_xcmplx_0(1,E)),k9_euclid(B,D,E)) ) ) ) )).
fof(fraenkel_a_3_0_euclidlp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(B,k4_ordinal1) & m2_finseq_2(C,k1_numbers,k1_euclid(B)) & m2_subset_1(D,k1_zfmisc_1(k1_euclid(B)),k1_euclidlp(B)) ) => ( r2_hidden(A,a_3_0_euclidlp(B,C,D)) <=> ? [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(B)) & A = k12_euclid(k8_euclid(B,C,E)) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_0_fcont_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & m1_subset_1(C,k1_numbers) & m1_subset_1(D,k1_numbers) ) => ( r2_hidden(A,a_3_0_fcont_1(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = E & ~ r1_xxreal_0(E,k6_xcmplx_0(B,k3_xxreal_0(k6_xcmplx_0(B,D),k6_xcmplx_0(C,B)))) & ~ r1_xxreal_0(k2_xcmplx_0(B,k3_xxreal_0(k6_xcmplx_0(B,D),k6_xcmplx_0(C,B))),E) ) ) ) )).
fof(fraenkel_a_3_0_fdiff_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & m1_subset_1(C,k1_numbers) & m1_subset_1(D,k1_numbers) ) => ( r2_hidden(A,a_3_0_fdiff_2(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = E & ~ r1_xxreal_0(E,k6_xcmplx_0(k3_xxreal_0(C,D),1)) & ~ r1_xxreal_0(B,E) ) ) ) )).
fof(fraenkel_a_3_0_filter_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_filter_0(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k4_lattices(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_0_filter_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_filter_2(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_lattices(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_0_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(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))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_finance1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & r1_xxreal_0(D,k3_funct_2(B,k1_numbers,C,E)) ) ) ) )).
fof(fraenkel_a_3_0_finseq_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & ~ v1_xboole_0(D) ) => ( r2_hidden(A,a_3_0_finseq_2(B,C,D)) <=> ? [E] : ? [F] : ( v3_card_1(E,B) & m2_finseq_1(E,D) & v3_card_1(F,C) & m2_finseq_1(F,D) & A = k8_finseq_1(D,E,F) ) ) ) )).
fof(fraenkel_a_3_0_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_0_finseq_3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = E & r2_hidden(E,k1_relset_1(k4_ordinal1,B)) & r1_xxreal_0(E,D) & r2_hidden(k1_funct_1(B,E),C) ) ) ) )).
fof(fraenkel_a_3_0_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_0_finseq_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = E & r2_hidden(E,k4_finseq_1(B)) & r1_xxreal_0(E,D) & r2_hidden(k1_funct_1(B,E),k1_tarski(C)) ) ) ) )).
fof(fraenkel_a_3_0_flang_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(B))) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_0_flang_3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_afinsq_1(B))) & A = E & ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(D,F) & E = k7_flang_1(B,C,F) ) ) ) ) )).
fof(fraenkel_a_3_0_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => ( r2_hidden(A,a_3_0_fomodel0(B,C,D)) <=> ? [E] : ? [F] : ( v3_card_1(E,C) & m2_finseq_1(E,B) & v3_card_1(F,D) & m2_finseq_1(F,B) & A = k1_monoid_0(B,E,F) ) ) ) )).
fof(fraenkel_a_3_0_fomodel1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) & v10_fomodel1(C,B) & m1_subset_1(C,k1_fomodel1(B)) ) => ( r2_hidden(A,a_3_0_fomodel1(B,C,D)) <=> ? [E] : ( m2_finseq_2(E,k3_finseq_2(k15_fomodel1(B)),k3_finseq_2(k3_finseq_2(k15_fomodel1(B)))) & A = k7_finseq_1(k12_finseq_1(k1_fomodel1(B),C),k3_funct_2(k3_finseq_2(k3_finseq_2(k15_fomodel1(B))),k3_finseq_2(k15_fomodel1(B)),k21_fomodel1(B),E)) & r1_tarski(k2_relset_1(k3_finseq_2(k15_fomodel1(B)),E),D) & v3_card_1(E,k1_int_2(k19_fomodel1(B,C))) ) ) ) )).
fof(fraenkel_a_3_0_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))))) ) => ( r2_hidden(A,a_3_0_fomodel4(B,C,D)) <=> ? [E] : ? [F] : ( 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))) & 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))) & A = 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)),E,F) & v9_fomodel4(k42_fomodel1(B,k42_fomodel1(B,k43_fomodel1(B,k31_fomodel2(B)),E),F),B,C,D) ) ) ) )).
fof(fraenkel_a_3_0_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & ~ v2_struct_0(D) & l2_fsm_1(D,B,C) ) => ( r2_hidden(A,a_3_0_fsm_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(D)) & A = E & v6_fsm_1(E,B,C,D) ) ) ) )).
fof(fraenkel_a_3_0_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(B))) & ~ v2_struct_0(D) & l2_fsm_3(D,B,C) ) => ( r2_hidden(A,a_3_0_fsm_3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k8_afinsq_1(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(D)) & ? [G] : ( m1_subset_1(G,u1_struct_0(D)) & r2_hidden(F,u1_fsm_3(B,C,D)) & r2_hidden(G,u2_fsm_3(B,C,D)) & r4_rewrite3(B,C,D,F,E,G) ) ) ) ) ) )).
fof(fraenkel_a_3_0_fvaluat1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & m1_fvaluat1(C,B) & m1_subset_1(D,u1_struct_0(k7_fvaluat1(B,C))) ) => ( r2_hidden(A,a_3_0_fvaluat1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k7_fvaluat1(B,C))) & A = k8_group_1(k7_fvaluat1(B,C),D,E) ) ) ) )).
fof(fraenkel_a_3_0_goboard2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) & v7_ordinal1(C) & m1_subset_1(D,k4_ordinal1) ) => ( r2_hidden(A,a_3_0_goboard2(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k2_topreal1(2,k17_finseq_1(u1_struct_0(k15_euclid(2)),D,k17_finseq_1(u1_struct_0(k15_euclid(2)),C,B)),E) & r1_xxreal_0(1,E) & r1_xxreal_0(k1_nat_1(E,1),k3_finseq_1(k17_finseq_1(u1_struct_0(k15_euclid(2)),D,k17_finseq_1(u1_struct_0(k15_euclid(2)),C,B)))) ) ) ) )).
fof(fraenkel_a_3_0_goboard5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_3_0_goboard5(B,C,D)) <=> ? [E] : ? [F] : ( v1_xreal_0(E) & v1_xreal_0(F) & A = k19_euclid(E,F) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,B,C)),F) & r1_xxreal_0(F,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,B,k1_nat_1(C,1)))) ) ) ) )).
fof(fraenkel_a_3_0_goboard6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_3_0_goboard6(B,C,D)) <=> ? [E] : ? [F] : ( v1_xreal_0(E) & v1_xreal_0(F) & A = k19_euclid(E,F) & ~ r1_xxreal_0(E,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,B,1))) & ~ r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,k1_nat_1(B,1),1)),E) & ~ r1_xxreal_0(F,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,1,C))) & ~ r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,1,k1_nat_1(C,1))),F) ) ) ) )).
fof(fraenkel_a_3_0_gobrd11,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_3_0_gobrd11(B,C,D)) <=> ? [E] : ? [F] : ( v1_xreal_0(E) & v1_xreal_0(F) & A = k19_euclid(E,F) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,B,1)),E) & r1_xxreal_0(E,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,k1_nat_1(B,1),1))) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,1,C)),F) & r1_xxreal_0(F,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,1,k1_nat_1(C,1)))) ) ) ) )).
fof(fraenkel_a_3_0_gobrd13,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_3_0_gobrd13(B,C,D)) <=> ? [E] : ? [F] : ( v1_xreal_0(E) & v1_xreal_0(F) & A = k19_euclid(E,F) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,B,C)),E) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,B,C)),F) ) ) ) )).
fof(fraenkel_a_3_0_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) & m1_subset_1(C,u1_struct_0(B)) & m2_finseq_2(D,u4_struct_0(B),k9_graph_3(B)) ) => ( r2_hidden(A,a_3_0_graph_3(B,C,D)) <=> ? [E] : ( m2_finseq_2(E,u4_struct_0(B),k9_graph_3(B)) & A = E & k10_xtuple_0(E) = k10_xtuple_0(D) & ? [F] : ( m2_finseq_1(F,u1_struct_0(B)) & r1_graph_2(B,F,E) & k1_funct_1(F,1) = C ) ) ) ) )).
fof(fraenkel_a_3_0_graph_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_graph_5(B,C,D)) <=> ? [E] : ( v7_graph_1(E,B) & m2_graph_1(E,B) & A = E & r1_graph_5(B,E,C,D) ) ) ) )).
fof(fraenkel_a_3_0_graphsp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & m2_finseq_2(D,k1_numbers,k3_finseq_2(k1_numbers)) ) => ( r2_hidden(A,a_3_0_graphsp(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = E & r2_hidden(E,k4_finseq_1(k6_graphsp(k9_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),k15_graphsp(C),k18_graphsp(C))),B),D))) & r1_xxreal_0(1,E) & r1_xxreal_0(E,C) & k1_funct_1(k6_graphsp(k9_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),k15_graphsp(C),k18_graphsp(C))),B),D),E) = k4_xcmplx_0(1) ) ) ) )).
fof(fraenkel_a_3_0_group_11,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_group_2(D,B) ) => ( r2_hidden(A,a_3_0_group_11(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_tarski(k13_group_2(B,D,E),C) ) ) ) )).
fof(fraenkel_a_3_0_group_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_group_2(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k6_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_0_group_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_group_3(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k2_group_3(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_0_group_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_group_5(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k2_group_5(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_0_group_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(B),u1_struct_0(C)) & v1_group_6(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)))) ) => ( r2_hidden(A,a_3_0_group_6(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,E) = k1_group_1(C) ) ) ) )).
fof(fraenkel_a_3_0_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,B) & l1_group_9(C,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) ) => ( r2_hidden(A,a_3_0_group_9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) & A = E & ? [F] : ( v2_group_9(F,B) & m1_group_9(F,B,C) & E = u1_struct_0(F) & r1_tarski(D,k15_group_9(B,C,F)) ) ) ) ) )).
fof(fraenkel_a_3_0_hahnban,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_rlsub_1(D,B) ) => ( r2_hidden(A,a_3_0_hahnban(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,F,E) & r1_struct_0(C,F) & r1_struct_0(D,E) ) ) ) )).
fof(fraenkel_a_3_0_heyting1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(C,k5_finsub_1(k7_normform(B))) & m2_funct_2(D,k7_normform(B),k1_heyting1(B),k9_funct_2(k7_normform(B),k1_heyting1(B))) ) => ( r2_hidden(A,a_3_0_heyting1(B,C,D)) <=> ? [E] : ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B)) & A = k3_funct_2(k7_normform(B),k1_heyting1(B),D,E) & r2_hidden(k3_funct_2(k7_normform(B),k1_heyting1(B),D,E),k3_domain_1(k5_finsub_1(B),k5_finsub_1(B),E)) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_0_heyting2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_finset_1(C) & m1_subset_1(D,k5_finsub_1(k4_partfun1(B,C))) ) => ( r2_hidden(A,a_3_0_heyting2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_partfun1(k1_heyting2(B,C,D),C)) & A = E & ! [F] : ( m1_subset_1(F,k4_partfun1(B,C)) => ~ ( r2_hidden(F,D) & r1_partfun1(E,F) ) ) ) ) ) )).
fof(fraenkel_a_3_0_heyting3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k5_finsub_1(k4_partfun1(B,C))) => ( r2_hidden(A,a_3_0_heyting3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_partfun1(B,C)) & A = E & v1_finset_1(E) & ! [F] : ( m1_subset_1(F,k4_partfun1(B,C)) => ( ( r2_hidden(F,D) & r1_tarski(F,E) ) <=> F = E ) ) ) ) ) )).
fof(fraenkel_a_3_0_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v7_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) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_ideal_1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,k8_group_1(B,C,E),k8_group_1(B,D,F)) ) ) ) )).
fof(fraenkel_a_3_0_integra2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & ~ v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,C,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,k1_numbers))) ) => ( r2_hidden(A,a_3_0_integra2(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = k3_xcmplx_0(B,E) & r2_hidden(E,k1_rvsum_1(D)) ) ) ) )).
fof(fraenkel_a_3_0_interva1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_3_0_interva1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(B)) & A = E & r1_tarski(C,E) & r1_tarski(E,D) ) ) ) )).
fof(fraenkel_a_3_0_jct_misc,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(B,C)))) ) => ( r2_hidden(A,a_3_0_jct_misc(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(C))) & A = k3_borsuk_1(B,C,E,F) & v3_pre_topc(E,B) & v3_pre_topc(F,C) & r1_tarski(k3_borsuk_1(B,C,E,F),D) ) ) ) )).
fof(fraenkel_a_3_0_jgraph_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & m1_subset_1(C,u1_struct_0(k15_euclid(B))) & m1_subset_1(D,u1_struct_0(k15_euclid(B))) ) => ( r2_hidden(A,a_3_0_jgraph_1(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = k3_rlvect_1(k15_euclid(B),k1_rlvect_1(k15_euclid(B),C,k6_xcmplx_0(1,E)),k1_rlvect_1(k15_euclid(B),D,E)) & r1_xxreal_0(k5_numbers,E) & r1_xxreal_0(E,1) ) ) ) )).
fof(fraenkel_a_3_0_jgraph_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,u1_struct_0(k15_euclid(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_jgraph_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(B))) & A = E & ~ r1_xxreal_0(D,k12_euclid(k5_algstr_0(k15_euclid(B),C,E))) ) ) ) )).
fof(fraenkel_a_3_0_jgraph_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) & 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)))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_jgraph_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(k7_partfun1(u1_struct_0(k3_topmetr),C,E),D) ) ) ) )).
fof(fraenkel_a_3_0_jgraph_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & ~ v2_struct_0(C) & l1_metric_1(C) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_0_jgraph_5(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = E & ~ r1_xxreal_0(B,k1_metric_1(C,D,E)) ) ) ) )).
fof(fraenkel_a_3_0_jgraph_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_jgraph_6(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) & A = E & k12_euclid(k5_algstr_0(k15_euclid(2),E,k19_euclid(B,C))) = D ) ) ) )).
fof(fraenkel_a_3_0_jordan16,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_topreal2(B) & 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))) ) => ( r2_hidden(A,a_3_0_jordan16(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) & A = E & r1_jordan6(B,C,E) & r1_jordan6(B,E,D) ) ) ) )).
fof(fraenkel_a_3_0_jordan20,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(2),B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(2),B))))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_jordan20(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) & A = E & ? [F] : ( v1_xreal_0(F) & r1_xxreal_0(k5_numbers,F) & ~ r1_xxreal_0(D,F) & E = k1_funct_1(C,F) ) ) ) ) )).
fof(fraenkel_a_3_0_jordan2b,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(B,k4_ordinal1) & v1_xreal_0(C) & m1_subset_1(D,k4_ordinal1) ) => ( r2_hidden(A,a_3_0_jordan2b(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(B))) & A = E & ~ r1_xxreal_0(C,k7_partfun1(k1_numbers,E,D)) ) ) ) )).
fof(fraenkel_a_3_0_jordan2c,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) & m1_subset_1(D,u1_struct_0(k15_euclid(B))) ) => ( r2_hidden(A,a_3_0_jordan2c(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(B))) & A = E & E != D & r2_hidden(E,C) & ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B))) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B))))) ) => ~ ( v5_pre_topc(F,k5_topmetr,k15_euclid(B)) & r1_tarski(k2_relset_1(u1_struct_0(k15_euclid(B)),F),C) & k1_funct_1(F,k5_numbers) = D & k1_funct_1(F,1) = E ) ) ) ) ) )).
fof(fraenkel_a_3_0_jordan3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) & v7_ordinal1(C) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_0_jordan3(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k2_topreal1(2,k3_finseq_6(u1_struct_0(k15_euclid(2)),B,C,D),E) & r1_xxreal_0(1,E) & r1_xxreal_0(k1_nat_1(E,1),k3_finseq_1(k3_finseq_6(u1_struct_0(k15_euclid(2)),B,C,D))) ) ) ) )).
fof(fraenkel_a_3_0_jordan4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) & v7_ordinal1(C) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_0_jordan4(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k2_topreal1(2,k3_finseq_6(u1_struct_0(k15_euclid(2)),B,C,D),E) & r1_xxreal_0(1,E) & r1_xxreal_0(k1_nat_1(E,1),k3_finseq_1(k3_finseq_6(u1_struct_0(k15_euclid(2)),B,C,D))) ) ) ) )).
fof(fraenkel_a_3_0_jordan7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v2_compts_1(B,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))) ) => ( r2_hidden(A,a_3_0_jordan7(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) & A = E & r1_jordan6(B,C,E) & r1_jordan6(B,E,D) ) ) ) )).
fof(fraenkel_a_3_0_laplace,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_0_laplace(B,C,D)) <=> ? [E] : ( m1_matrix_2(E,k3_matrix_2(k1_nat_1(B,1))) & A = E & k1_funct_1(E,C) = D ) ) ) )).
fof(fraenkel_a_3_0_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l3_lattices(B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_lattice3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k2_lattices(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_0_lattice4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) & ~ v1_xboole_0(C) & v19_lattices(C,B) & v20_lattices(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_lattice4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & ? [G] : ( m1_subset_1(G,u1_struct_0(B)) & r3_lattices(B,k4_lattices(B,F,G),E) & r2_hidden(F,k2_filter_0(B,D)) & r2_hidden(G,C) ) ) ) ) ) )).
fof(fraenkel_a_3_0_lattice5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_lattice3(C) & v2_lattice3(C) & v1_yellow_0(C) & l1_orders_2(C) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(B,B),u1_struct_0(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B,B),u1_struct_0(C)))) ) => ( r2_hidden(A,a_3_0_lattice5(B,C,D)) <=> ? [E] : ? [F] : ? [G] : ? [H] : ( m1_subset_1(E,B) & m1_subset_1(F,B) & m1_subset_1(G,u1_struct_0(C)) & m1_subset_1(H,u1_struct_0(C)) & A = k5_domain_1(B,B,u1_struct_0(C),u1_struct_0(C),E,F,G,H) & r3_orders_2(C,k3_lattice5(B,C,D,E,F),k13_lattice3(C,G,H)) ) ) ) )).
fof(fraenkel_a_3_0_lattice6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_lattice6(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r2_hidden(E,C) & r3_lattices(B,E,D) ) ) ) )).
fof(fraenkel_a_3_0_lattice7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v8_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_waybel_1(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_lattice7(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r2_orders_2(B,E,C) & ~ r3_orders_2(B,E,D) ) ) ) )).
fof(fraenkel_a_3_0_lfuzzy_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_lfuzzy_0(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,E,D) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_0_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_lfuzzy_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_0_lmod_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v6_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) & v1_vectsp_2(B) & l6_algstr_0(B) & ~ 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) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) ) => ( r2_hidden(A,a_3_0_lmod_5(B,C,D)) <=> ? [E] : ( m2_vectsp_6(E,B,C,D) & A = k4_vectsp_6(B,C,E) ) ) ) )).
fof(fraenkel_a_3_0_lopban_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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) & v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C)) & v13_vectsp_1(D,B,C) & v1_lopban_1(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)))) ) => ( r2_hidden(A,a_3_0_lopban_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k2_normsp_0(C,k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,E)) & r1_xxreal_0(k2_normsp_0(B,E),1) ) ) ) )).
fof(fraenkel_a_3_0_lopban_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_lopban_5(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(D,k2_normsp_0(B,k5_algstr_0(B,C,E))) ) ) ) )).
fof(fraenkel_a_3_0_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_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,k6_numbers))) ) => ( r2_hidden(A,a_3_0_lpspacc1(B,C,D)) <=> ? [E] : ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) & A = E & ? [F] : ( m2_subset_1(F,k1_zfmisc_1(B),C) & k12_supinf_2(D,F) = k5_numbers & k1_relset_1(B,E) = k3_subset_1(B,F) & r2_mesfun6c(B,C,D,E) ) ) ) ) )).
fof(fraenkel_a_3_0_lpspace1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_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,k6_numbers))) ) => ( r2_hidden(A,a_3_0_lpspace1(B,C,D)) <=> ? [E] : ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) & A = E & ? [F] : ( m2_subset_1(F,k1_zfmisc_1(B),C) & k3_funct_2(C,k6_numbers,D,F) = k5_numbers & k1_relset_1(B,E) = k3_subset_1(B,F) & r3_mesfunc6(B,C,D,E) ) ) ) ) )).
fof(fraenkel_a_3_0_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_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,k6_numbers))) ) => ( r2_hidden(A,a_3_0_lpspace2(B,C,D)) <=> ? [E] : ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) & A = E & ? [F] : ( m2_subset_1(F,k1_zfmisc_1(B),C) & k1_funct_1(D,k3_subset_1(B,F)) = k5_numbers & k1_relset_1(B,E) = F & r1_mesfunc6(B,C,E,F) & r3_mesfunc6(B,C,D,k2_mesfun6c(1,B,k56_valued_1(B,k1_numbers,E))) ) ) ) ) )).
fof(fraenkel_a_3_0_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_algstr_0(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_mathmorp(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_algstr_0(B,E,C) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_0_matrix15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_matrix15(B,C,D)) <=> ? [E] : ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) & A = E & k3_finseq_1(E) = k1_matrix_0(C) & k1_matrix_0(E) = k1_matrix_0(D) & k4_matrix_3(B,C,E) = D ) ) ) )).
fof(fraenkel_a_3_0_matroid0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & ~ 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) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) ) => ( r2_hidden(A,a_3_0_matroid0(B,C,D)) <=> ? [E] : ( m2_vectsp_6(E,B,C,D) & A = k4_vectsp_6(B,C,E) ) ) ) )).
fof(fraenkel_a_3_0_matrtop1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) & m1_subset_1(D,k4_ordinal1) ) => ( r2_hidden(A,a_3_0_matrtop1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k2_xcmplx_0(E,D) & r2_hidden(E,k9_xtuple_0(k5_relat_1(C,B))) ) ) ) )).
fof(fraenkel_a_3_0_mazurulm,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_mazurulm(B,C,D)) <=> ? [E] : ( 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)))) & A = k2_normsp_0(B,k5_algstr_0(B,k3_funct_2(u1_struct_0(B),u1_struct_0(B),E,k1_rlvect_1(B,k3_rlvect_1(B,C,D),k6_xxreal_3(1,2))),k1_rlvect_1(B,k3_rlvect_1(B,C,D),k6_xxreal_3(1,2)))) & r2_hidden(E,a_3_1_mazurulm(B,C,D)) ) ) ) )).
fof(fraenkel_a_3_0_mesfun9c,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(B,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(B,k1_numbers)))) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_0_mesfun9c(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = k1_relset_1(B,k4_mesfunc5(B,k1_numbers,C,E)) & r1_xxreal_0(E,D) ) ) ) )).
fof(fraenkel_a_3_0_mesfunc8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) & m1_subset_1(D,k4_ordinal1) ) => ( r2_hidden(A,a_3_0_mesfunc8(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k9_nat_1(k9_setfam_1(B),C,E) & r1_xxreal_0(D,E) ) ) ) )).
fof(fraenkel_a_3_0_mesfunc9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(B,k6_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(B,k6_numbers)))) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_0_mesfunc9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = k1_relset_1(B,k4_mesfunc5(B,k6_numbers,C,E)) & r1_xxreal_0(E,D) ) ) ) )).
fof(fraenkel_a_3_0_metric_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( l1_metric_1(B) & m1_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_metric_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(D,k1_metric_1(B,C,E)) ) ) ) )).
fof(fraenkel_a_3_0_metric_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_metric_1(B) & m1_subset_1(C,k2_metric_2(B)) & m1_subset_1(D,k2_metric_2(B)) ) => ( r2_hidden(A,a_3_0_metric_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_numbers) & A = E & r4_metric_2(B,C,D,E) ) ) ) )).
fof(fraenkel_a_3_0_metrizts,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(B)))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_metrizts(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k3_pcomps_1(B))) & A = E & ~ r1_xxreal_0(D,k3_funct_2(u1_struct_0(k3_pcomps_1(B)),u1_struct_0(k3_topmetr),k6_weierstr(B,C),E)) ) ) ) )).
fof(fraenkel_a_3_0_mfold_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & m1_subset_1(C,u1_struct_0(k15_euclid(B))) & m1_subset_1(D,u1_struct_0(k15_euclid(B))) ) => ( r2_hidden(A,a_3_0_mfold_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(B))) & A = E & k22_rvsum_1(C,k5_algstr_0(k15_euclid(B),E,D)) = k5_numbers ) ) ) )).
fof(fraenkel_a_3_0_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_3_0_mmlquery(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = k1_mmlquery(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_0_mod_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(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) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) ) => ( r2_hidden(A,a_3_0_mod_3(B,C,D)) <=> ? [E] : ( m2_vectsp_6(E,B,C,D) & A = k4_vectsp_6(B,C,E) ) ) ) )).
fof(fraenkel_a_3_0_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v10_modelc_1(B) & l2_modelc_1(B) & 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)))) & m1_subset_1(D,k4_ordinal1) ) => ( r2_hidden(A,a_3_0_modelc_1(B,C,D)) <=> ? [E] : ( 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)))) & A = E & r2_modelc_1(B,C,E,D) ) ) ) )).
fof(fraenkel_a_3_0_modelc_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v10_modelc_2(B) & l1_modelc_2(B) & 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)))) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_0_modelc_2(B,C,D)) <=> ? [E] : ( 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)))) & A = E & r5_modelc_2(B,C,E,D) ) ) ) )).
fof(fraenkel_a_3_0_morph_01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_morph_01(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( r2_hidden(F,D) => r2_hidden(k5_algstr_0(B,E,F),C) ) ) ) ) ) )).
fof(fraenkel_a_3_0_msafree,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_msafree(B,C,D)) <=> ? [E] : ( m1_dtconstr(E,u1_struct_0(k5_msafree(B,C)),k5_trees_3(u1_struct_0(k5_msafree(B,C))),k4_dtconstr(k5_msafree(B,C))) & A = E & ~ ( ! [F] : ~ ( r2_hidden(F,k1_funct_1(C,D)) & E = k1_trees_4(k4_tarski(F,D)) ) & ! [F] : ( m1_subset_1(F,u4_struct_0(B)) => ~ ( k4_tarski(F,u1_struct_0(B)) = k1_funct_1(E,k1_xboole_0) & k2_msualg_1(B,F) = D ) ) ) ) ) ) )).
fof(fraenkel_a_3_0_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) & l3_msualg_1(C,B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_msafree4(B,C,D)) <=> ? [E] : ( m1_msafree4(E,u1_struct_0(B),k4_equation(B),k1_msafree4(u1_struct_0(B),k4_equation(B),D)) & A = E & r1_equation(B,C,D,E) ) ) ) )).
fof(fraenkel_a_3_0_msscyc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_msscyc_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(B,k11_msafree(B,C)),D)) & A = E & k8_msafree2(B,C,D,E) = k5_numbers ) ) ) )).
fof(fraenkel_a_3_0_msualg_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) & v4_msualg_1(C,B) & l3_msualg_1(C,B) & m1_subset_1(D,u1_struct_0(k5_msualg_5(u1_struct_0(B),u3_msualg_1(B,C)))) ) => ( r2_hidden(A,a_3_0_msualg_8(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k5_msualg_5(u1_struct_0(B),u3_msualg_1(B,C)))) & A = E & v2_msualg_4(E,B,C) & v3_msualg_4(E,B,C) & m1_msualg_4(E,u1_struct_0(B),u3_msualg_1(B,C),u3_msualg_1(B,C)) & r3_lattices(k5_msualg_5(u1_struct_0(B),u3_msualg_1(B,C)),D,E) ) ) ) )).
fof(fraenkel_a_3_0_mycielsk,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_eqrel_1(C,B) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_3_0_mycielsk(B,C,D)) <=> ? [E] : ( m1_subset_1(E,C) & A = k9_subset_1(B,E,D) & ~ r1_xboole_0(E,D) ) ) ) )).
fof(fraenkel_a_3_0_nagata_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_nagata_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & r2_hidden(E,C) & ~ r1_xboole_0(E,D) ) ) ) )).
fof(fraenkel_a_3_0_nagata_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),k1_numbers))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_nagata_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & k3_funct_2(u1_struct_0(B),k1_numbers,k3_nagata_2(u1_struct_0(B),C,D),E) = k5_numbers ) ) ) )).
fof(fraenkel_a_3_0_ncfcont1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_ncfcont1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(D,k2_normsp_0(B,k5_algstr_0(B,E,C))) ) ) ) )).
fof(fraenkel_a_3_0_ndiff_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_ndiff_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(D,k2_normsp_0(B,k5_algstr_0(B,E,C))) ) ) ) )).
fof(fraenkel_a_3_0_ndiff_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_ndiff_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(D,k2_normsp_0(B,k5_algstr_0(B,E,C))) ) ) ) )).
fof(fraenkel_a_3_0_ndiff_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_ndiff_5(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = k3_rlvect_1(B,C,k1_rlvect_1(B,k5_algstr_0(B,D,C),E)) & ~ r1_xxreal_0(E,k5_numbers) & ~ r1_xxreal_0(1,E) ) ) ) )).
fof(fraenkel_a_3_0_nfcont_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_nfcont_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(D,k2_normsp_0(B,k5_algstr_0(B,E,C))) ) ) ) )).
fof(fraenkel_a_3_0_nfcont_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(B,k4_ordinal1) & v1_xreal_0(C) & m1_subset_1(D,k1_euclid(B)) ) => ( r2_hidden(A,a_3_0_nfcont_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_euclid(B)) & A = E & ~ r1_xxreal_0(C,k12_euclid(k8_euclid(B,E,D))) ) ) ) )).
fof(fraenkel_a_3_0_normform,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(C,k5_finsub_1(k7_normform(B))) & m1_subset_1(D,k5_finsub_1(k7_normform(B))) ) => ( r2_hidden(A,a_3_0_normform(B,C,D)) <=> ? [E] : ? [F] : ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B)) & m2_subset_1(F,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B)) & A = k1_normform(k5_finsub_1(B),k5_finsub_1(B),E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_0_normsp_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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_xreal_0(C) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_normsp_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(C,k2_normsp_0(B,k5_algstr_0(B,D,E))) ) ) ) )).
fof(fraenkel_a_3_0_ordinal6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_ordinal1(B) & v3_ordinal1(C) & v4_ordinal1(C) & ~ v1_xboole_0(C) & ~ v1_xboole_0(D) & v1_classes2(D) ) => ( r2_hidden(A,a_3_0_ordinal6(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k9_xtuple_0(k5_relat_1(k11_ordinal6(D),C))) & A = k1_funct_1(k1_funct_1(k5_relat_1(k11_ordinal6(D),C),E),B) & r2_hidden(E,k9_xtuple_0(k5_relat_1(k11_ordinal6(D),C))) ) ) ) )).
fof(fraenkel_a_3_0_osafree,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v4_osalg_1(B) & v5_osalg_1(B) & l3_osalg_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_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_osafree(B,C,D)) <=> ? [E] : ( m1_dtconstr(E,u1_struct_0(k2_osafree(B,C)),k5_trees_3(u1_struct_0(k2_osafree(B,C))),k4_dtconstr(k2_osafree(B,C))) & A = E & ~ ( ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ~ ( r3_orders_2(B,F,D) & r2_hidden(G,k1_funct_1(C,F)) & E = k1_trees_4(k4_tarski(G,F)) ) ) & ! [F] : ( m1_subset_1(F,u4_struct_0(B)) => ~ ( k4_tarski(F,u1_struct_0(B)) = k1_funct_1(E,k1_xboole_0) & r3_orders_2(B,k2_msualg_1(B,F),D) ) ) ) ) ) ) )).
fof(fraenkel_a_3_0_osalg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v4_osalg_1(B) & v5_osalg_1(B) & l3_osalg_1(B) & v12_osalg_1(C,B) & l3_msualg_1(C,B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_osalg_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_msualg_2(B,C,E) & r3_orders_2(B,E,D) ) ) ) )).
fof(fraenkel_a_3_0_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(B)) & m2_subset_1(D,k1_zfmisc_1(u1_struct_0(B)),k2_osalg_4(B)) ) => ( r2_hidden(A,a_3_0_osalg_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_funct_1(C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_0_partit1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m1_eqrel_1(C,B) ) => ( r2_hidden(A,a_3_0_partit1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(B)) & A = E & r2_hidden(E,C) & r1_tarski(E,D) ) ) ) )).
fof(fraenkel_a_3_0_pcomps_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_pcomps_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & r2_hidden(E,C) & ~ r1_xboole_0(E,D) ) ) ) )).
fof(fraenkel_a_3_0_pdiff_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(B,k4_ordinal1) & m2_finseq_2(C,k1_numbers,k1_euclid(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_pdiff_6(B,C,D)) <=> ? [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(B)) & A = E & ~ r1_xxreal_0(D,k12_euclid(k8_euclid(B,E,C))) ) ) ) )).
fof(fraenkel_a_3_0_pdiff_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & m2_finseq_2(C,k1_numbers,k1_euclid(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_pdiff_7(B,C,D)) <=> ? [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(B)) & A = E & ~ r1_xxreal_0(D,k12_euclid(k8_euclid(B,E,C))) ) ) ) )).
fof(fraenkel_a_3_0_pdiff_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & m2_finseq_2(C,k1_numbers,k1_euclid(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_pdiff_9(B,C,D)) <=> ? [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(B)) & A = E & ~ r1_xxreal_0(D,k12_euclid(k8_euclid(B,E,C))) ) ) ) )).
fof(fraenkel_a_3_0_pencil_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) & v15_pencil_1(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_pencil_1(B,C)))) ) => ( r2_hidden(A,a_3_0_pencil_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k5_pencil_1(B,C)))) & A = E & ~ v1_zfmisc_1(E) & v2_pencil_1(E,k5_pencil_1(B,C)) & v1_pencil_1(E,k5_pencil_1(B,C)) & r1_pencil_2(k5_pencil_1(B,C),D,E) ) ) ) )).
fof(fraenkel_a_3_0_pencil_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) & v1_relat_1(D) & v4_relat_1(D,B) & v1_funct_1(D) & v1_partfun1(D,B) ) => ( r2_hidden(A,a_3_0_pencil_3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & k1_funct_1(C,E) != k1_funct_1(D,E) ) ) ) )).
fof(fraenkel_a_3_0_poset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & v5_orders_3(C,B,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(B)) ) => ( r2_hidden(A,a_3_0_poset_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( v7_ordinal1(F) & E = k3_funct_2(u1_struct_0(B),u1_struct_0(B),k1_abian(u1_struct_0(B),C,F),D) ) ) ) ) )).
fof(fraenkel_a_3_0_pralg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & ~ v2_struct_0(C) & l1_msualg_1(C) & m1_pralg_2(D,B,C) ) => ( r2_hidden(A,a_3_0_pralg_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = k6_pralg_2(C,k5_pralg_2(B,C,D,E)) ) ) ) )).
fof(fraenkel_a_3_0_pralg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) & l3_msualg_1(C,B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_pralg_3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u4_struct_0(B)) & A = k1_pralg_3(B,C,E) & k2_msualg_1(B,E) = D & k1_msualg_1(B,E) = k1_xboole_0 ) ) ) )).
fof(fraenkel_a_3_0_pre_circ,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) & ~ v1_xboole_0(C) & v1_finset_1(C) & v1_trees_1(C) & m1_trees_1(D,B) ) => ( r2_hidden(A,a_3_0_pre_circ(B,C,D)) <=> ? [E] : ( m1_trees_1(E,C) & A = k8_finseq_1(k4_ordinal1,D,E) ) ) ) )).
fof(fraenkel_a_3_0_pua2mss1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,k4_ordinal1) & m1_eqrel_1(D,B) ) => ( r2_hidden(A,a_3_0_pua2mss1(B,C,D)) <=> ? [E] : ( m2_finseq_2(E,D,k4_finseq_2(C,D)) & A = k4_card_3(E) ) ) ) )).
fof(fraenkel_a_3_0_qc_lang3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(B) & m2_finseq_1(C,k2_qc_lang1(B)) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k2_qc_lang1(B))) ) => ( r2_hidden(A,a_3_0_qc_lang3(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_funct_1(C,E) & r1_xxreal_0(1,E) & r1_xxreal_0(E,k3_finseq_1(C)) & r2_hidden(k1_funct_1(C,E),D) ) ) ) )).
fof(fraenkel_a_3_0_qc_lang4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(B) & m1_subset_1(C,k9_qc_lang1(B)) & m1_subset_1(D,k9_qc_lang1(B)) ) => ( r2_hidden(A,a_3_0_qc_lang4(B,C,D)) <=> ? [E] : ( m1_trees_1(E,k9_xtuple_0(k2_qc_lang4(B,C))) & A = E & k3_trees_2(k9_qc_lang1(B),k2_qc_lang4(B,C),E) = D ) ) ) )).
fof(fraenkel_a_3_0_quantal1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_quantal1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k6_algstr_0(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_0_quofield,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & ~ 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) & 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(A,a_3_0_quofield(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k1_domain_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(C),k1_domain_1(u1_struct_0(B),u1_struct_0(B),E,F),k8_group_1(C,k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,E),k11_algstr_0(C,k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,F)))) & F != k4_struct_0(B) ) ) ) )).
fof(fraenkel_a_3_0_random_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,B,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ( r2_hidden(A,a_3_0_random_3(B,C,D)) <=> ? [E] : ( m2_subset_1(E,k1_zfmisc_1(k1_numbers),k12_prob_1) & A = E & m2_subset_1(k8_relset_1(B,k1_numbers,D,E),k1_zfmisc_1(B),C) ) ) ) )).
fof(fraenkel_a_3_0_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) & v1_relat_1(D) ) => ( r2_hidden(A,a_3_0_relset_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(B)) & A = k7_relat_1(D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_0_rewrite2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(B),k8_afinsq_1(B)))) & m1_subset_1(D,k8_afinsq_1(B)) ) => ( r2_hidden(A,a_3_0_rewrite2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k8_afinsq_1(B)) & A = E & r3_rewrite2(B,C,D,E) ) ) ) )).
fof(fraenkel_a_3_0_rinfsup2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) & m1_subset_1(C,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => ( r2_hidden(A,a_3_0_rinfsup2(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k12_supinf_2(k1_valued_0(k6_numbers,B,C),E) & r1_xxreal_0(D,E) ) ) ) )).
fof(fraenkel_a_3_0_ring_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_xboole_0(C) & v1_ideal_1(C,B) & v2_ideal_1(C,B) & v3_ideal_1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_ring_1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,k6_algstr_0(B,D,E),F) & r2_hidden(F,C) ) ) ) )).
fof(fraenkel_a_3_0_rlaffin3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(C)))) ) => ( r2_hidden(A,a_3_0_rlaffin3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(B))) & A = E & r2_hidden(k16_finseq_1(C,E),D) ) ) ) )).
fof(fraenkel_a_3_0_rlsub_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_rlsub_1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,F,E) & r2_hidden(F,C) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_0_rlsub_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_rlsub_1(D,B) ) => ( r2_hidden(A,a_3_0_rlsub_2(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,F,E) & r1_struct_0(C,F) & r1_struct_0(D,E) ) ) ) )).
fof(fraenkel_a_3_0_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_rltopsp1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k5_rusub_4(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_0_rlvect_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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_xreal_0(C) & m1_rlvect_2(D,B) ) => ( r2_hidden(A,a_3_0_rlvect_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & k3_funct_2(u1_struct_0(B),k1_numbers,k8_rlvect_2(B,C,D),E) != k5_numbers ) ) ) )).
fof(fraenkel_a_3_0_rmod_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & v4_vectsp_2(C,B) & l1_vectsp_2(C,B) & m1_rmod_4(D,B,C) ) => ( r2_hidden(A,a_3_0_rmod_4(B,C,D)) <=> ? [E] : ( 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) ) ) ) )).
fof(fraenkel_a_3_0_rsspace4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(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) & 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)))) ) => ( r2_hidden(A,a_3_0_rsspace4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = k2_normsp_0(C,k3_funct_2(B,u1_struct_0(C),D,E)) ) ) ) )).
fof(fraenkel_a_3_0_rusub_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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_subset_1(C,u1_struct_0(B)) & m1_rusub_1(D,B) ) => ( r2_hidden(A,a_3_0_rusub_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,C,E) & r1_struct_0(D,E) ) ) ) )).
fof(fraenkel_a_3_0_rusub_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_rusub_1(D,B) ) => ( r2_hidden(A,a_3_0_rusub_2(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,E,F) & r1_struct_0(C,E) & r1_struct_0(D,F) ) ) ) )).
fof(fraenkel_a_3_0_rusub_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_rusub_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_algstr_0(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_0_rusub_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_rusub_5(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k5_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_0_seq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & m2_finseq_2(C,k2_numbers,k12_seq_4(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_seq_4(B,C,D)) <=> ? [E] : ( m2_finseq_2(E,k2_numbers,k12_seq_4(B)) & A = E & ~ r1_xxreal_0(D,k20_seq_4(k17_seq_4(B,E,C))) ) ) ) )).
fof(fraenkel_a_3_0_setlim_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,C))) ) => ( r2_hidden(A,a_3_0_setlim_1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_funct_1(D,E) & r1_xxreal_0(B,E) ) ) ) )).
fof(fraenkel_a_3_0_setlim_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(C)))) ) => ( r2_hidden(A,a_3_0_setlim_2(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k9_nat_1(k9_setfam_1(C),D,E) & r1_xxreal_0(B,E) ) ) ) )).
fof(fraenkel_a_3_0_sgraph1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m1_sgraph1(C,B) ) => ( r2_hidden(A,a_3_0_sgraph1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & r2_hidden(E,u1_struct_0(C)) & r2_hidden(k2_tarski(D,E),u1_sgraph1(C)) ) ) ) )).
fof(fraenkel_a_3_0_simplex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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) & v6_ordinal1(C) & v1_finset_1(C) & v5_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_simplex1(B,C,D)) <=> ? [E] : ( m3_simplex0(E,k4_simplex1(B,k5_simplex0(u1_struct_0(B),k6_domain_1(k1_zfmisc_1(u1_struct_0(B)),k4_subset_1(u1_struct_0(B),k5_setfam_1(u1_struct_0(B),C),k6_domain_1(u1_struct_0(B),D))))),k5_card_1(C)) & A = E & r1_tarski(k7_relset_1(k1_orders_1(u1_struct_0(B)),u1_struct_0(B),k2_rlaffin2(B),C),E) ) ) ) )).
fof(fraenkel_a_3_0_sppol_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & m1_subset_1(C,u1_struct_0(k14_euclid(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_sppol_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(B))) & A = E & ~ r1_xxreal_0(D,k3_metric_1(k14_euclid(B),C,E)) ) ) ) )).
fof(fraenkel_a_3_0_sppol_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_sppol_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) & A = E & k18_euclid(E) = D & r1_xxreal_0(B,k17_euclid(E)) & r1_xxreal_0(k17_euclid(E),C) ) ) ) )).
fof(fraenkel_a_3_0_sprect_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & m2_finseq_1(D,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_3_0_sprect_2(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k2_topreal1(2,D,E) & r1_xxreal_0(B,E) & ~ r1_xxreal_0(C,E) ) ) ) )).
fof(fraenkel_a_3_0_sprect_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & m2_finseq_1(D,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_3_0_sprect_3(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k2_topreal1(2,D,E) & r1_xxreal_0(B,E) & ~ r1_xxreal_0(C,E) ) ) ) )).
fof(fraenkel_a_3_0_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(B) & v7_ordinal1(C) & v5_relat_1(D,k3_qc_lang1(B)) & v3_card_1(D,C) & m2_finseq_1(D,k2_qc_lang1(B)) ) => ( r2_hidden(A,a_3_0_sublemma(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_funct_1(D,E) & r1_xxreal_0(1,E) & r1_xxreal_0(E,k3_finseq_1(D)) & r2_hidden(k1_funct_1(D,E),k3_qc_lang1(B)) ) ) ) )).
fof(fraenkel_a_3_0_substlat,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k5_finsub_1(k4_partfun1(B,C))) => ( r2_hidden(A,a_3_0_substlat(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_partfun1(B,C)) & A = E & v1_finset_1(E) & ! [F] : ( m1_subset_1(F,k4_partfun1(B,C)) => ( ( r2_hidden(F,D) & r1_tarski(F,E) ) <=> F = E ) ) ) ) ) )).
fof(fraenkel_a_3_0_substut2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(B) & v7_ordinal1(C) & v3_card_1(D,C) & m2_finseq_1(D,k2_qc_lang1(B)) ) => ( r2_hidden(A,a_3_0_substut2(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_funct_1(D,E) & r1_xxreal_0(1,E) & r1_xxreal_0(E,k3_finseq_1(D)) & r2_hidden(k1_funct_1(D,E),k4_qc_lang1(B)) ) ) ) )).
fof(fraenkel_a_3_0_t_1topsp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) => ( r2_hidden(A,a_3_0_t_1topsp(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k8_relset_1(u1_struct_0(B),u1_struct_0(C),D,k6_domain_1(u1_struct_0(C),E)) & r2_hidden(E,k2_relset_1(u1_struct_0(C),D)) ) ) ) )).
fof(fraenkel_a_3_0_tex_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_tex_1(B,C)))) ) => ( r2_hidden(A,a_3_0_tex_1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_tex_1(B,C)))) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k3_tex_1(B,C)))) & A = k4_subset_1(u1_struct_0(k3_tex_1(B,C)),E,k9_subset_1(u1_struct_0(k3_tex_1(B,C)),F,D)) & r2_hidden(E,k7_subset_1(k1_zfmisc_1(B),k9_setfam_1(B),a_2_3_tex_1(B,C))) & r2_hidden(F,k7_subset_1(k1_zfmisc_1(B),k9_setfam_1(B),a_2_3_tex_1(B,C))) ) ) ) )).
fof(fraenkel_a_3_0_tex_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_tex_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k2_tex_4(B,E) & r2_hidden(E,k4_subset_1(u1_struct_0(B),C,D)) ) ) ) )).
fof(fraenkel_a_3_0_topalg_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & m1_subset_1(D,u1_struct_0(k2_topmetr(B,C))) ) => ( r2_hidden(A,a_3_0_topalg_5(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k8_metric_1(k2_topmetr(B,C),D,k7_xcmplx_0(1,E)) & E != k5_numbers ) ) ) )).
fof(fraenkel_a_3_0_topgen_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_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)))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_topgen_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & r2_hidden(D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_0_topgen_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_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)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_topgen_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & r2_hidden(E,C) & r1_tarski(E,D) ) ) ) )).
fof(fraenkel_a_3_0_topgen_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_pre_topc(C,B) & v1_tops_2(D,B) & v1_cantor_1(D,B) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) => ( r2_hidden(A,a_3_0_topgen_5(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k9_subset_1(u1_struct_0(C),E,k2_struct_0(C)) & r2_hidden(E,D) & ~ r1_xboole_0(E,k2_struct_0(C)) ) ) ) )).
fof(fraenkel_a_3_0_topgrp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v2_group_1(B) & v3_group_1(B) & v3_topgrp_1(B) & v4_topgrp_1(B) & l1_topgrp_1(B) & v1_tops_2(C,B) & v1_yellow_8(C,B,k1_group_1(B)) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & v1_tops_1(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_topgrp_1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(F,u1_struct_0(B)) & A = k5_group_2(B,F,E) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_0_topmetr,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & m1_topmetr(C,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(C)))) ) => ( r2_hidden(A,a_3_0_topmetr(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & v1_xreal_0(F) & A = k8_metric_1(B,E,F) & r2_hidden(E,D) & ~ r1_xxreal_0(F,k5_numbers) & r1_tarski(k8_subset_1(u1_struct_0(B),k8_metric_1(B,E,F),u1_struct_0(C)),D) ) ) ) )).
fof(fraenkel_a_3_0_topreal1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & m1_subset_1(C,u1_struct_0(k15_euclid(B))) & m1_subset_1(D,u1_struct_0(k15_euclid(B))) ) => ( r2_hidden(A,a_3_0_topreal1(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = k3_rlvect_1(k15_euclid(B),k1_rlvect_1(k15_euclid(B),D,k6_xcmplx_0(1,E)),k1_rlvect_1(k15_euclid(B),C,E)) & r1_xxreal_0(k5_numbers,E) & r1_xxreal_0(E,1) ) ) ) )).
fof(fraenkel_a_3_0_topreal3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_topreal3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) & A = E & k17_euclid(E) = B & r1_xxreal_0(C,k18_euclid(E)) & r1_xxreal_0(k18_euclid(E),D) ) ) ) )).
fof(fraenkel_a_3_0_topreal7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k3_pcomps_1(B),k3_pcomps_1(C))))) ) => ( r2_hidden(A,a_3_0_topreal7(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(B)))) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(C)))) & A = k3_borsuk_1(k3_pcomps_1(B),k3_pcomps_1(C),E,F) & r1_tarski(k3_borsuk_1(k3_pcomps_1(B),k3_pcomps_1(C),E,F),D) & v3_pre_topc(E,k3_pcomps_1(B)) & v3_pre_topc(F,k3_pcomps_1(C)) ) ) ) )).
fof(fraenkel_a_3_0_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & m1_subset_1(C,u1_struct_0(k15_euclid(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_0_topreal9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(B))) & A = E & ~ r1_xxreal_0(D,k12_euclid(k5_algstr_0(k15_euclid(B),E,C))) ) ) ) )).
fof(fraenkel_a_3_0_treal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & m1_subset_1(D,u1_struct_0(k2_topmetr(k5_numbers,1))) ) => ( r2_hidden(A,a_3_0_treal_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k2_topmetr(k5_numbers,1))) & A = E & ~ r1_xxreal_0(k3_xcmplx_0(k6_xcmplx_0(C,B),k5_xcmplx_0(2)),k3_metric_1(k2_topmetr(k5_numbers,1),D,E)) ) ) ) )).
fof(fraenkel_a_3_0_trees_a,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) & ~ v1_xboole_0(C) & v1_trees_1(C) & m4_trees_1(D,B) ) => ( r2_hidden(A,a_3_0_trees_a(B,C,D)) <=> ? [E] : ? [F] : ( m1_trees_1(E,B) & m1_trees_1(F,C) & A = k8_finseq_1(k4_ordinal1,E,F) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_0_unialg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m5_margrel1(D,u1_struct_0(B),k1_unialg_2(B)) ) => ( r2_hidden(A,a_3_0_unialg_2(B,C,D)) <=> ? [E] : ( m2_finseq_2(E,C,k3_finseq_2(C)) & A = E & k3_finseq_1(E) = k19_margrel1(D) ) ) ) )).
fof(fraenkel_a_3_0_uproots,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v6_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) & m1_subset_1(C,u1_struct_0(B)) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(D,B) & v1_uproots(D,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( r2_hidden(A,a_3_0_uproots(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = E & ? [F] : ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(F,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) & r2_funct_2(k4_ordinal1,u1_struct_0(B),D,k13_polynom3(B,k2_polynom5(B,k4_polynom5(B,k4_algstr_0(B,C),k5_struct_0(B)),E),F)) ) ) ) ) )).
fof(fraenkel_a_3_0_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & v1_relat_1(D) & v1_funct_1(D) ) => ( r2_hidden(A,a_3_0_valued_1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k2_xcmplx_0(E,B) & r2_hidden(E,a_2_2_valued_1(C,D)) ) ) ) )).
fof(fraenkel_a_3_0_vectsp10,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & 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) & m1_vectsp_4(D,B,C) ) => ( r2_hidden(A,a_3_0_vectsp10(B,C,D)) <=> ? [E] : ( m2_vectsp_4(E,B,C,D) & A = E ) ) ) )).
fof(fraenkel_a_3_0_vectsp11,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & ~ 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) & 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)))) ) => ( r2_hidden(A,a_3_0_vectsp11(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = E & ? [F] : ( v7_ordinal1(F) & k3_funct_2(u1_struct_0(C),u1_struct_0(C),k1_vectsp11(C,D,F),E) = k4_struct_0(C) ) ) ) ) )).
fof(fraenkel_a_3_0_vectsp_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(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) & m1_vectsp_4(D,B,C) ) => ( r2_hidden(A,a_3_0_vectsp_5(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(C)) & m1_subset_1(F,u1_struct_0(C)) & A = k3_rlvect_1(C,F,E) & r1_struct_0(D,F) & r1_struct_0(D,E) ) ) ) )).
fof(fraenkel_a_3_0_vectsp_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) & ~ v2_struct_0(C) & l1_vectsp_1(C,B) & m1_vectsp_6(D,B,C) ) => ( r2_hidden(A,a_3_0_vectsp_6(B,C,D)) <=> ? [E] : ( 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) ) ) ) )).
fof(fraenkel_a_3_0_vectsp_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & ~ 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) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) ) => ( r2_hidden(A,a_3_0_vectsp_7(B,C,D)) <=> ? [E] : ( m2_vectsp_6(E,B,C,D) & A = k4_vectsp_6(B,C,E) ) ) ) )).
fof(fraenkel_a_3_0_waybel11,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_0_waybel11(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k2_waybel_0(B,C,E) & r1_orders_2(C,D,E) ) ) ) )).
fof(fraenkel_a_3_0_waybel12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) & m1_subset_1(D,k4_ordinal1) ) => ( r2_hidden(A,a_3_0_waybel12(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = k3_funct_2(k4_ordinal1,u1_struct_0(B),C,E) & r1_xxreal_0(E,D) ) ) ) )).
fof(fraenkel_a_3_0_waybel13,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(C) & v4_yellow_0(C,k2_yellow_1(B)) & v7_yellow_0(C,k2_yellow_1(B)) & v4_waybel_0(C,k2_yellow_1(B)) & m1_yellow_0(C,k2_yellow_1(B)) & m1_subset_1(D,u1_struct_0(k2_yellow_1(B))) ) => ( r2_hidden(A,a_3_0_waybel13(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = E & r1_tarski(D,E) ) ) ) )).
fof(fraenkel_a_3_0_waybel14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_waybel14(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k13_lattice3(B,E,F) & r2_hidden(E,k1_waybel_3(B,C)) & r2_hidden(F,k1_waybel_3(B,D)) ) ) ) )).
fof(fraenkel_a_3_0_waybel15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v11_waybel_1(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_waybel15(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_0_waybel16,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_waybel16(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k13_lattice3(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_0_waybel17,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_0_waybel17(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k2_waybel_0(B,C,E) & r1_orders_2(C,D,E) ) ) ) )).
fof(fraenkel_a_3_0_waybel20,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) & v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(B)) & v8_waybel_1(D,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) ) => ( r2_hidden(A,a_3_0_waybel20(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k1_domain_1(k1_zfmisc_1(u1_struct_0(B)),k1_zfmisc_1(u1_struct_0(B)),k6_eqrel_1(u1_struct_0(B),u1_struct_0(B),k2_waybel20(B,C),E),k6_eqrel_1(u1_struct_0(B),u1_struct_0(B),k2_waybel20(B,C),F)) & r3_orders_2(B,k3_funct_2(u1_struct_0(B),u1_struct_0(B),D,E),k3_funct_2(u1_struct_0(B),u1_struct_0(B),D,F)) ) ) ) )).
fof(fraenkel_a_3_0_waybel21,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_0_waybel21(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k2_waybel_0(B,C,E) & r1_orders_2(C,D,E) ) ) ) )).
fof(fraenkel_a_3_0_waybel22,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(C) & v2_waybel_0(C,k2_yellow_1(B)) & v13_waybel_0(C,k2_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(B)))) & m2_subset_1(D,u1_struct_0(k2_yellow_1(B)),C) ) => ( r2_hidden(A,a_3_0_waybel22(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k2_yellow_1(B))) & A = k6_waybel_0(k2_yellow_1(B),E) & ? [F] : ( m1_subset_1(F,B) & E = k1_tarski(F) & r2_hidden(F,D) ) ) ) ) )).
fof(fraenkel_a_3_0_waybel23,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v4_yellow_0(C,B) & v8_yellow_0(C,B) & m1_yellow_0(C,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) ) => ( r2_hidden(A,a_3_0_waybel23(B,C,D)) <=> ? [E] : ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(D)) & A = k1_yellow_0(C,E) & r1_yellow_0(C,E) ) ) ) )).
fof(fraenkel_a_3_0_waybel28,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_0_waybel28(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k2_waybel_0(B,C,E) & r1_orders_2(C,D,E) ) ) ) )).
fof(fraenkel_a_3_0_waybel30,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & v1_waybel_0(C,k1_yellow_1(k7_waybel_0(B))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_yellow_1(k7_waybel_0(B))))) & m1_subset_1(D,u1_struct_0(k1_yellow_1(k7_waybel_0(B)))) ) => ( r2_hidden(A,a_3_0_waybel30(B,C,D)) <=> ? [E] : ( m2_subset_1(E,u1_struct_0(k1_yellow_1(k7_waybel_0(B))),C) & A = k3_xboole_0(D,E) ) ) ) )).
fof(fraenkel_a_3_0_waybel32,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & v25_waybel_0(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_0_waybel32(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k2_waybel_0(B,C,E) & r1_orders_2(C,D,E) ) ) ) )).
fof(fraenkel_a_3_0_waybel33,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & v2_waybel_0(D,k2_yellow_1(C)) & v13_waybel_0(D,k2_yellow_1(C)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k2_yellow_1(C)))) ) => ( r2_hidden(A,a_3_0_waybel33(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k2_yellow_0(B,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_0_waybel_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_waybel_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_orders_2(B,k11_lattice3(B,C,E),D) ) ) ) )).
fof(fraenkel_a_3_0_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_waybel_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k11_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_0_waybel_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_waybel_3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_orders_2(B,C,E) & r1_orders_2(B,D,E) ) ) ) )).
fof(fraenkel_a_3_0_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) ) => ( r2_hidden(A,a_3_0_waybel_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r2_hidden(k1_domain_1(u1_struct_0(B),u1_struct_0(B),E,C),D) ) ) ) )).
fof(fraenkel_a_3_0_waybel_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_waybel_5(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_0_waybel_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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_xboole_0(D) & v1_waybel_0(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_waybel_6(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_0_waybel_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_waybel_1(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(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))) & ~ v1_xboole_0(D) & v2_waybel_0(D,B) & v13_waybel_0(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_waybel_7(B,C,D)) <=> ? [E] : ( ~ v1_xboole_0(E) & v1_waybel_0(E,B) & v12_waybel_0(E,B) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & r1_tarski(C,E) & r1_subset_1(E,D) ) ) ) )).
fof(fraenkel_a_3_0_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) & ~ v2_struct_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_0_waybel_9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = E & r1_orders_2(C,D,E) ) ) ) )).
fof(fraenkel_a_3_0_yellow12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_yellow12(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k12_lattice3(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_0_yellow13,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & v1_cantor_1(C,B) & v1_tops_2(C,B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_0_yellow13(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & r2_hidden(E,C) & r2_hidden(D,E) ) ) ) )).
fof(fraenkel_a_3_0_yellow19,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & v2_waybel_0(D,k2_yellow_1(C)) & v13_waybel_0(D,k2_yellow_1(C)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k2_yellow_1(C)))) ) => ( r2_hidden(A,a_3_0_yellow19(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m2_subset_1(F,u1_struct_0(k2_yellow_1(C)),D) & A = k4_tarski(E,F) & r2_hidden(E,F) ) ) ) )).
fof(fraenkel_a_3_0_yellow_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(k1_yellow_1(k7_waybel_0(B)))) & m1_subset_1(D,u1_struct_0(k1_yellow_1(k7_waybel_0(B)))) ) => ( r2_hidden(A,a_3_0_yellow_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ ( ~ r2_hidden(E,C) & ~ r2_hidden(E,D) & ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ~ ( r2_hidden(F,C) & r2_hidden(G,D) & E = k13_lattice3(B,F,G) ) ) ) ) ) ) ) )).
fof(fraenkel_a_3_0_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_xboole_0(D) & v1_waybel_0(D,k3_yellow_3(B,C)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,C)))) ) => ( r2_hidden(A,a_3_0_yellow_3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k3_yellow_3(B,C))) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(k3_yellow_3(B,C))) & r3_orders_2(k3_yellow_3(B,C),E,F) & r2_hidden(F,D) ) ) ) ) )).
fof(fraenkel_a_3_0_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_yellow_4(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k10_lattice3(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_0_yellow_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) & ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m3_yellow_6(D,u1_struct_0(C),B) ) => ( r2_hidden(A,a_3_0_yellow_6(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k2_relset_1(u1_struct_0(B),u1_waybel_0(B,k7_yellow_6(u1_struct_0(C),B,D,E))) ) ) ) )).
fof(fraenkel_a_3_0_yellow_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( l1_pre_topc(B) & v1_cantor_1(C,B) & v1_tops_2(C,B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_yellow_8(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & r2_hidden(E,C) & r1_tarski(E,D) ) ) ) )).
fof(fraenkel_a_3_0_yellow_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_tops_2(D,C) & v2_cantor_1(D,C) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C)))) ) => ( r2_hidden(A,a_3_0_yellow_9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) & A = k2_zfmisc_1(u1_struct_0(B),E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_0_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) & m1_subset_1(D,B) ) => ( r2_hidden(A,a_3_0_zf_fund1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,B) & m1_subset_1(F,B) & A = k1_classes2(B,k6_classes2(B,E,F)) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_0_zf_fund2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) & ~ v1_xboole_0(C) & 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(A,a_3_0_zf_fund2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,C) & A = E & r1_zf_model(C,k2_zf_lang1(C,D,k2_zf_lang(k5_numbers),E),B) ) ) ) )).
fof(fraenkel_a_3_0_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_0_zmodul01(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,F,E) & r2_hidden(F,C) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_0_zmodul02,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_zmodul02(C,B) & v1_int_1(D) ) => ( r2_hidden(A,a_3_0_zmodul02(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & k3_funct_2(u1_struct_0(B),k4_numbers,k23_zmodul02(B,D,C),E) != k5_numbers ) ) ) )).
fof(fraenkel_a_3_0_zmodul03,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v1_int_2(B) & ~ 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) & v1_zmodul03(C) & l1_zmodul01(C) & m1_zmodul03(D,C) ) => ( r2_hidden(A,a_3_0_zmodul03(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k13_zmodul02(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_10_convex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_rlvect_1(B) & v3_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,k1_zfmisc_1(u1_struct_0(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_10_convex1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_rlvect_1(B,E,D) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_10_convex4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_csspace(B) & l1_csspace(B) & m1_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_10_convex4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(D,k9_complex1(k12_csspace(B,E,C))) ) ) ) )).
fof(fraenkel_a_3_10_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(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))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_10_finance1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & r1_xxreal_0(D,k3_funct_2(B,k1_numbers,C,E)) & r1_xxreal_0(k3_funct_2(B,k1_numbers,C,E),D) ) ) ) )).
fof(fraenkel_a_3_10_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) ) => ( r2_hidden(A,a_3_10_mathmorp(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(k15_euclid(B))) & m1_subset_1(F,u1_struct_0(k15_euclid(B))) & A = k3_rlvect_1(k15_euclid(B),E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_10_morph_01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_10_morph_01(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k3_funct_2(k1_zfmisc_1(u1_struct_0(B)),k9_setfam_1(u1_struct_0(B)),k4_morph_01(B,D),E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_10_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_10_rltopsp1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,E,F) & r2_hidden(E,D) & r2_hidden(F,k1_convex1(B,C,k4_xcmplx_0(1))) ) ) ) )).
fof(fraenkel_a_3_10_rusub_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C) & v2_rusub_4(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_10_rusub_5(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,E,F) & r2_hidden(E,C) & r2_hidden(F,k6_domain_1(u1_struct_0(B),D)) ) ) ) )).
fof(fraenkel_a_3_10_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_10_waybel_2(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k10_lattice3(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_10_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(k1_yellow_1(k7_waybel_0(B)))) & m1_subset_1(D,u1_struct_0(k1_yellow_1(k7_waybel_0(B)))) ) => ( r2_hidden(A,a_3_10_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ ( ~ r2_hidden(E,C) & ~ r2_hidden(E,D) & ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ~ ( r2_hidden(F,C) & r2_hidden(G,D) & E = k13_lattice3(B,F,G) ) ) ) ) ) ) ) )).
fof(fraenkel_a_3_10_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) & m1_subset_1(D,k4_ordinal1) ) => ( r2_hidden(A,a_3_10_zf_fund1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = k1_domain_1(k4_ordinal1,B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_11_convex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_rlvect_1(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_11_convex1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k1_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_11_convex4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_clvect_1(B) & v1_xcmplx_0(C) & m1_convex4(D,B) ) => ( r2_hidden(A,a_3_11_convex4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & k3_funct_2(u1_struct_0(B),k2_numbers,k7_convex4(B,C,D),E) != k5_complex1 ) ) ) )).
fof(fraenkel_a_3_11_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_xreal_0(C) ) => ( r2_hidden(A,a_3_11_finance1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & m1_subset_1(k3_funct_2(B,k1_tarski(C),k7_funcop_1(B,C),E),D) ) ) ) )).
fof(fraenkel_a_3_11_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_11_lattice3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_orders_2(B,E,C) & r1_orders_2(B,E,D) ) ) ) )).
fof(fraenkel_a_3_11_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(C) & m2_finseq_1(D,k9_setfam_1(B)) ) => ( r2_hidden(A,a_3_11_mmlquery(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & r1_xxreal_0(C,k24_mmlquery(D,E)) & r1_xxreal_0(k24_mmlquery(D,E),k3_finseq_1(D)) ) ) ) )).
fof(fraenkel_a_3_11_morph_01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_11_morph_01(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & k9_subset_1(u1_struct_0(B),k5_rusub_4(B,k6_mathmorp(k4_xcmplx_0(1),B,D),E),k6_subset_1(u1_struct_0(B),C)) != k1_xboole_0 ) ) ) )).
fof(fraenkel_a_3_11_osafree,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v4_osalg_1(B) & v5_osalg_1(B) & v2_osalg_4(B) & l3_osalg_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_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_11_osafree(B,C,D)) <=> ? [E] : ? [F] : ( m1_dtconstr(E,u1_struct_0(k2_osafree(B,C)),k5_trees_3(u1_struct_0(k2_osafree(B,C))),k4_dtconstr(k2_osafree(B,C))) & m1_dtconstr(F,u1_struct_0(k2_osafree(B,C)),k5_trees_3(u1_struct_0(k2_osafree(B,C))),k4_dtconstr(k2_osafree(B,C))) & A = k4_tarski(E,F) & r2_hidden(k4_tarski(E,D),k3_funct_2(k4_dtconstr(k2_osafree(B,C)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(B,C)),u1_struct_0(B))),k19_osafree(B,C),F)) ) ) ) )).
fof(fraenkel_a_3_11_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_11_rltopsp1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_11_rusub_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C) & v2_rusub_4(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_11_rusub_5(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k5_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,k6_domain_1(u1_struct_0(B),D)) ) ) ) )).
fof(fraenkel_a_3_11_waybel30,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v2_pre_topc(B) & v8_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) & v2_yellow13(B) & v3_waybel30(B) & l1_waybel_9(B) & m1_subset_1(C,u1_struct_0(B)) & 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)))) ) => ( r2_hidden(A,a_3_11_waybel30(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k2_pre_topc(B,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_11_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & ~ v1_xboole_0(D) & v1_waybel_0(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_11_waybel_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k11_lattice3(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_11_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_11_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k10_lattice3(B,D,E) & r2_hidden(E,k5_yellow_3(B,B,C)) ) ) ) )).
fof(fraenkel_a_3_11_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) & m1_subset_1(D,B) ) => ( r2_hidden(A,a_3_11_zf_fund1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,B) & m1_subset_1(F,B) & A = k7_classes2(B,E,F) & r2_hidden(E,D) & r2_hidden(F,C) ) ) ) )).
fof(fraenkel_a_3_12_convex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(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,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_12_convex1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k1_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_12_convex4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_12_convex4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_12_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(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))) & m1_subset_1(D,k1_numbers) ) => ( r2_hidden(A,a_3_12_finance1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & ~ r1_xxreal_0(D,k3_funct_2(B,k1_numbers,C,E)) ) ) ) )).
fof(fraenkel_a_3_12_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,u1_struct_0(k1_lattice3(B))) => ( r2_hidden(A,a_3_12_lattice3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k1_lattice3(B))) & A = k2_lattices(k1_lattice3(B),D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_12_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(C) & m2_finseq_1(D,k9_setfam_1(B)) ) => ( r2_hidden(A,a_3_12_mmlquery(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & r1_xxreal_0(C,k24_mmlquery(D,E)) ) ) ) )).
fof(fraenkel_a_3_12_morph_01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_12_morph_01(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_tarski(k5_rusub_4(B,k6_mathmorp(k4_xcmplx_0(1),B,D),E),k6_subset_1(u1_struct_0(B),C)) ) ) ) )).
fof(fraenkel_a_3_12_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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_rltopsp1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v3_rltopsp1(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_12_rltopsp1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_12_rusub_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_12_rusub_5(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & k3_bhsp_1(B,k5_algstr_0(B,C,E)) = D ) ) ) )).
fof(fraenkel_a_3_12_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & v2_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & v1_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & v1_waybel_0(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_12_waybel_2(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k12_lattice3(B,E,F) & r2_hidden(E,C) & r2_hidden(F,k6_domain_1(u1_struct_0(B),k1_yellow_0(B,D))) ) ) ) )).
fof(fraenkel_a_3_12_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_12_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r1_orders_2(B,E,F) & r2_hidden(F,k2_yellow_4(B,k3_waybel_0(B,C),k3_waybel_0(B,D))) ) ) ) ) )).
fof(fraenkel_a_3_12_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) & m1_subset_1(D,B) ) => ( r2_hidden(A,a_3_12_zf_fund1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,B) & m1_subset_1(F,B) & A = k9_classes2(B,E,F) & r2_hidden(E,D) & r2_hidden(F,k1_classes2(B,C)) ) ) ) )).
fof(fraenkel_a_3_13_convex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(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,k1_zfmisc_1(u1_struct_0(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_13_convex1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_rlvect_1(B,E,D) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_13_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(C) & v6_graph_1(C) & l1_graph_1(C) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_13_graph_3(B,C,D)) <=> ? [E] : ( m2_finseq_2(E,u4_struct_0(C),k9_graph_3(C)) & A = E & r1_tarski(k10_xtuple_0(E),B) & ~ v1_xboole_0(E) & ? [F] : ( m2_finseq_1(F,u1_struct_0(C)) & r1_graph_2(C,F,E) & k1_funct_1(F,1) = D ) ) ) ) )).
fof(fraenkel_a_3_13_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,u1_struct_0(k1_lattice3(B))) => ( r2_hidden(A,a_3_13_lattice3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k1_lattice3(B))) & A = k4_lattices(k1_lattice3(B),D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_13_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m2_finseq_1(C,k9_setfam_1(B)) & m1_subset_1(D,B) ) => ( r2_hidden(A,a_3_13_mmlquery(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = E & r2_hidden(E,k4_finseq_1(C)) & r2_hidden(D,k4_prob_3(B,C,E)) ) ) ) )).
fof(fraenkel_a_3_13_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_rltopsp1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_13_rltopsp1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_algstr_0(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_13_rusub_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_13_rusub_5(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(D,k3_bhsp_1(B,k5_algstr_0(B,C,E))) ) ) ) )).
fof(fraenkel_a_3_13_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & v2_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & v1_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & v1_waybel_0(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_13_waybel_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_yellow_0(B,k4_yellow_4(B,k6_domain_1(u1_struct_0(B),E),D)) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_13_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_13_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r1_orders_2(B,E,F) & r2_hidden(F,k2_yellow_4(B,C,D)) ) ) ) ) )).
fof(fraenkel_a_3_13_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) & m1_subset_1(D,B) ) => ( r2_hidden(A,a_3_13_zf_fund1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,B) & m1_subset_1(F,B) & A = k1_classes2(B,k6_classes2(B,E,F)) & r2_hidden(E,D) & r2_hidden(F,C) ) ) ) )).
fof(fraenkel_a_3_14_convex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_14_convex1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_14_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m2_finseq_1(C,k9_setfam_1(B)) => ( r2_hidden(A,a_3_14_mmlquery(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = E & r2_hidden(E,k4_finseq_1(C)) & r2_hidden(D,k4_prob_3(B,C,E)) ) ) ) )).
fof(fraenkel_a_3_14_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v6_rltopsp1(B) & v7_rltopsp1(B) & l1_rltopsp1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_14_rltopsp1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_14_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & ~ v2_struct_0(D) & v7_waybel_0(D) & l1_waybel_0(D,B) ) => ( r2_hidden(A,a_3_14_waybel_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,C,E) & r2_hidden(E,k2_relset_1(u1_struct_0(B),u1_waybel_0(B,k2_waybel_2(B,u1_struct_0(D),u1_waybel_0(B,D))))) ) ) ) )).
fof(fraenkel_a_3_14_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_14_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r3_orders_2(B,E,F) & r2_hidden(F,k2_yellow_4(B,C,D)) ) ) ) ) )).
fof(fraenkel_a_3_15_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & l1_mmlquery(C) & m2_finseq_1(D,u1_mmlquery(C)) ) => ( r2_hidden(A,a_3_15_mmlquery(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = E & r1_xxreal_0(k5_card_1(k7_subset_1(u1_mmlquery(C),k2_relset_1(u1_mmlquery(C),D),k30_mmlquery(C,E))),B) ) ) ) )).
fof(fraenkel_a_3_15_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v6_rltopsp1(B) & v7_rltopsp1(B) & l1_rltopsp1(B) & v3_pre_topc(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_15_rltopsp1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k5_rusub_4(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_15_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & v2_waybel_2(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_15_waybel_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_15_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_15_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r3_orders_2(B,E,F) & r2_hidden(F,k2_yellow_4(B,k3_waybel_0(B,C),k3_waybel_0(B,D))) ) ) ) ) )).
fof(fraenkel_a_3_16_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_rlvect_1(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_16_ideal_1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k1_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_16_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v3_mmlquery(C) & l1_mmlquery(C) & m2_finseq_1(D,u1_mmlquery(C)) ) => ( r2_hidden(A,a_3_16_mmlquery(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = E & r1_xxreal_0(k5_card_1(k7_subset_1(u1_struct_0(C),k30_mmlquery(C,E),k2_relset_1(u1_mmlquery(C),D))),B) ) ) ) )).
fof(fraenkel_a_3_16_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v6_rltopsp1(B) & v7_rltopsp1(B) & l1_rltopsp1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_16_rltopsp1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,C,E) & r2_hidden(E,k1_tops_1(B,D)) ) ) ) )).
fof(fraenkel_a_3_16_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v3_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_16_waybel_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_16_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_16_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r1_orders_2(B,F,E) & r2_hidden(F,k2_yellow_4(B,k4_waybel_0(B,C),k4_waybel_0(B,D))) ) ) ) ) )).
fof(fraenkel_a_3_17_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v6_algstr_0(B) & v4_rlvect_1(B) & v1_vectsp_1(B) & v1_algstr_1(B) & l6_algstr_0(B) & ~ v1_xboole_0(C) & v3_ideal_1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & v3_ideal_1(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_17_ideal_1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k1_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_17_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v3_mmlquery(C) & l1_mmlquery(C) & m2_finseq_1(D,u1_mmlquery(C)) ) => ( r2_hidden(A,a_3_17_mmlquery(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = E & r1_xxreal_0(k5_card_1(k7_subset_1(u1_mmlquery(C),k2_relset_1(u1_mmlquery(C),D),k30_mmlquery(C,E))),B) ) ) ) )).
fof(fraenkel_a_3_17_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v6_rltopsp1(B) & v7_rltopsp1(B) & l1_rltopsp1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_17_rltopsp1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,C,E) & r2_hidden(E,k2_pre_topc(B,D)) ) ) ) )).
fof(fraenkel_a_3_17_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_17_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r1_orders_2(B,F,E) & r2_hidden(F,k2_yellow_4(B,C,D)) ) ) ) ) )).
fof(fraenkel_a_3_18_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v6_algstr_0(B) & v1_vectsp_1(B) & v1_algstr_1(B) & l6_algstr_0(B) & ~ v1_xboole_0(C) & v3_ideal_1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & v3_ideal_1(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_18_ideal_1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k1_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_18_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_18_lattice3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k2_lattices(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_18_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v6_rltopsp1(B) & v7_rltopsp1(B) & l1_rltopsp1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_18_rltopsp1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,k4_algstr_0(B,C),E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_18_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_18_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r1_orders_2(B,F,E) & r2_hidden(F,k2_yellow_4(B,C,D)) ) ) ) ) )).
fof(fraenkel_a_3_19_compl_sp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v6_metric_1(B) & v8_metric_1(B) & v9_metric_1(B) & l1_metric_1(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_pcomps_1(B))))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(B)))) ) => ( r2_hidden(A,a_3_19_compl_sp(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(B)))) & A = E & r2_hidden(E,C) & ~ r1_xboole_0(E,D) ) ) ) )).
fof(fraenkel_a_3_19_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v7_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) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_19_ideal_1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,E,F) & r2_hidden(E,k7_ideal_1(B,k6_domain_1(u1_struct_0(B),C))) & r2_hidden(F,k7_ideal_1(B,k6_domain_1(u1_struct_0(B),D))) ) ) ) )).
fof(fraenkel_a_3_19_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_19_lattice3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_lattices(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_19_quantal1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_group_1(B) & v10_lattices(B) & v4_lattice3(B) & v7_quantal1(B) & v8_quantal1(B) & l1_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_19_quantal1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r3_lattices(B,k6_algstr_0(B,E,D),C) ) ) ) )).
fof(fraenkel_a_3_19_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v6_rltopsp1(B) & v7_rltopsp1(B) & l1_rltopsp1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_connsp_2(D,B,C) ) => ( r2_hidden(A,a_3_19_rltopsp1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,k4_algstr_0(B,C),E) & r2_hidden(E,k1_tops_1(B,D)) ) ) ) )).
fof(fraenkel_a_3_19_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_19_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r1_orders_2(B,F,E) & r2_hidden(F,k2_yellow_4(B,k4_waybel_0(B,C),k4_waybel_0(B,D))) ) ) ) ) )).
fof(fraenkel_a_3_1_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v11_struct_0(B) & v1_instalg1(B) & l1_msualg_1(B) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(B)) & v13_abcmiz_1(C,B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_abcmiz_1(B,C,D)) <=> ? [E] : ( m1_dtconstr(E,u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),C,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))),k5_trees_3(u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),C,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers)))))),k1_msaterm(B,k2_pboole(u1_struct_0(B),C,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))) & A = E & k7_msaterm(B,k2_pboole(u1_struct_0(B),C,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),E) = D & r2_pboole(u1_struct_0(B),k4_msafree3(B,k2_pboole(u1_struct_0(B),C,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),E),C) ) ) ) )).
fof(fraenkel_a_3_1_amistd_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_setfam_1(B) & ~ v2_struct_0(C) & v2_memstr_0(C,B) & v3_memstr_0(C,B) & l1_extpro_1(C,B) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_1_amistd_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_compos_1(C)) & A = k7_subset_1(k4_ordinal1,k1_amistd_1(B,C,D,E),k2_amistd_1(B,C,E)) ) ) ) )).
fof(fraenkel_a_3_1_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_1_aofa_000(B,C,D)) <=> ? [E] : ? [F] : ( m2_subset_1(E,k4_ordinal1,k4_finseq_1(u1_unialg_1(B))) & m2_finseq_2(F,u1_struct_0(B),k3_finseq_2(u1_struct_0(B))) & A = k1_funct_1(k2_pua2mss1(B,E),F) & r2_hidden(F,k1_relset_1(k3_finseq_2(u1_struct_0(B)),k2_pua2mss1(B,E))) & r1_tarski(k2_relset_1(u1_struct_0(B),F),k9_aofa_000(B,C,D)) ) ) ) )).
fof(fraenkel_a_3_1_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & ~ v1_xboole_0(C) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_3_1_armstrng(B,C,D)) <=> ? [E] : ( m1_subset_1(E,C) & A = E & r1_tarski(D,E) ) ) ) )).
fof(fraenkel_a_3_1_bagorder,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_ordinal1(B) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ( r2_hidden(A,a_3_1_bagorder(B,C,D)) <=> ? [E] : ( m2_subset_1(E,k14_pre_poly(B),k15_pre_poly(B)) & A = E & r2_hidden(E,C) & k3_bagorder(B,E) = k4_seq_4(D) ) ) ) )).
fof(fraenkel_a_3_1_bcialg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_bcialg_1(B) & v4_bcialg_1(B) & v5_bcialg_1(B) & v7_bcialg_1(B) & v8_bcialg_1(B) & v2_bcialg_4(B) & v3_bcialg_4(B) & l1_bcialg_4(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_bcialg_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_bcialg_1(B,k1_bcialg_1(B,E,C),D) ) ) ) )).
fof(fraenkel_a_3_1_bhsp_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_1_bhsp_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_xxreal_0(k3_bhsp_1(B,k5_algstr_0(B,C,E)),D) ) ) ) )).
fof(fraenkel_a_3_1_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) & ~ v2_struct_0(C) & l1_vectsp_1(C,B) & 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_hidden(A,a_3_1_bilinear(B,C,D)) <=> ? [E] : ( 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) ) ) ) )).
fof(fraenkel_a_3_1_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & v2_pre_topc(C) & l1_pre_topc(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(B,C)))) ) => ( r2_hidden(A,a_3_1_borsuk_1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(C))) & A = k3_borsuk_1(B,C,E,F) & r1_tarski(k3_borsuk_1(B,C,E,F),D) & v3_pre_topc(E,B) & v3_pre_topc(F,C) ) ) ) )).
fof(fraenkel_a_3_1_borsuk_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v1_compts_1(B) & l1_pre_topc(B) & ~ v2_struct_0(C) & v2_pre_topc(C) & v1_compts_1(C) & l1_pre_topc(C) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k2_borsuk_1(C,B))))) ) => ( r2_hidden(A,a_3_1_borsuk_3(B,C,D)) <=> ? [E] : ( v3_pre_topc(E,B) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & ? [F] : ( m1_subset_1(F,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k2_borsuk_1(C,B))))) & r1_tarski(F,D) & v1_finset_1(F) & r1_tarski(k3_borsuk_1(C,B,k2_struct_0(C),E),k5_setfam_1(u1_struct_0(k2_borsuk_1(C,B)),F)) ) ) ) ) )).
fof(fraenkel_a_3_1_card_fil,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m1_card_fil(C,B) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_3_1_card_fil(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(B)) & A = k9_subset_1(B,E,D) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_1_cc0sp2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xcmplx_0(C) & v1_xcmplx_0(D) ) => ( r2_hidden(A,a_3_1_cc0sp2(B,C,D)) <=> ? [E] : ( v1_xcmplx_0(E) & A = E & ~ r1_xxreal_0(k7_xcmplx_0(B,k2_xcmplx_0(k2_xcmplx_0(k9_complex1(C),k9_complex1(D)),1)),k9_complex1(k6_xcmplx_0(E,C))) ) ) ) )).
fof(fraenkel_a_3_1_cgames_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_cgames_1(C) & v2_cgames_1(D) ) => ( r2_hidden(A,a_3_1_cgames_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k7_cgames_1(D)) & A = k1_funct_1(k5_relat_1(B,k10_cgames_1(C)),E) & k7_cgames_1(D) != k1_xboole_0 ) ) ) )).
fof(fraenkel_a_3_1_chain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & m1_chain_1(C,B) & m1_subset_1(D,k4_ordinal1) ) => ( r2_hidden(A,a_3_1_chain_1(B,C,D)) <=> ? [E] : ? [F] : ( m2_finseq_2(E,k1_numbers,k1_euclid(B)) & m2_finseq_2(F,k1_numbers,k1_euclid(B)) & A = k3_chain_1(B,E,F) & ~ ( ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k2_finseq_1(B))) => ~ ( k5_card_1(G) = D & ! [H] : ( m2_subset_1(H,k4_ordinal1,k2_finseq_1(B)) => ( ( r2_hidden(H,G) & ~ r1_xxreal_0(k1_funct_1(F,H),k1_funct_1(E,H)) & m2_chain_1(k4_tarski(k1_funct_1(E,H),k1_funct_1(F,H)),k2_chain_1(B,C,H)) ) | ( ~ r2_hidden(H,G) & k1_funct_1(E,H) = k1_funct_1(F,H) & r2_hidden(k1_funct_1(E,H),k2_chain_1(B,C,H)) ) ) ) ) ) & ~ ( D = B & ! [G] : ( m2_subset_1(G,k4_ordinal1,k2_finseq_1(B)) => ( ~ r1_xxreal_0(k1_funct_1(E,G),k1_funct_1(F,G)) & m2_chain_1(k4_tarski(k1_funct_1(E,G),k1_funct_1(F,G)),k2_chain_1(B,C,G)) ) ) ) ) ) ) ) )).
fof(fraenkel_a_3_1_circled1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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_rltopsp1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v3_rltopsp1(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_1_circled1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k5_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_1_circuit1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v5_msafree2(B) & l1_msualg_1(B) & v4_msualg_1(C,B) & v4_msafree2(C,B) & l3_msualg_1(C,B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_circuit1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(B,k5_msafree2(B,C)),D)) & A = k5_circuit1(B,C,D,E) ) ) ) )).
fof(fraenkel_a_3_1_circuit2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & v5_msafree2(B) & l1_msualg_1(B) & v4_msualg_1(C,B) & v4_msafree2(C,B) & l3_msualg_1(C,B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_circuit2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_dtconstr(k5_msafree(B,u3_msualg_1(B,C)))) & A = E & ~ ( ! [F] : ~ ( r2_hidden(F,k1_funct_1(u3_msualg_1(B,C),D)) & E = k1_trees_4(k4_tarski(F,D)) ) & ! [F] : ( m1_subset_1(F,u4_struct_0(B)) => ~ ( k4_tarski(F,u1_struct_0(B)) = k1_funct_1(E,k1_xboole_0) & k2_msualg_1(B,F) = D ) ) ) ) ) ) )).
fof(fraenkel_a_3_1_closure2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( l1_struct_0(B) & v15_closure2(C,B) & l1_closure2(C,B) & m3_pboole(D,u1_struct_0(B),u3_msualg_1(B,C)) ) => ( r2_hidden(A,a_3_1_closure2(B,C,D)) <=> ? [E] : ( m1_closure2(E,u1_struct_0(B),u3_msualg_1(B,C),k6_closure2(u1_struct_0(B),u3_msualg_1(B,C))) & A = E & r2_pboole(u1_struct_0(B),D,E) & r2_hidden(E,u1_closure2(B,C)) ) ) ) )).
fof(fraenkel_a_3_1_clvect_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(B)) & m1_clvect_1(D,B) ) => ( r2_hidden(A,a_3_1_clvect_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,C,E) & r1_struct_0(D,E) ) ) ) )).
fof(fraenkel_a_3_1_clvect_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & m1_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_1_clvect_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_xxreal_0(k13_csspace(B,k5_algstr_0(B,C,E)),D) ) ) ) )).
fof(fraenkel_a_3_1_combgras,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(B,k4_ordinal1) & ~ v1_xboole_0(C) & m1_subset_1(D,k1_zfmisc_1(C)) ) => ( r2_hidden(A,a_3_1_combgras(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(C)) & A = E & k1_card_1(E) = B & r1_tarski(E,D) ) ) ) )).
fof(fraenkel_a_3_1_compl_sp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(u1_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(B))))) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_1_compl_sp(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = k3_funct_2(k4_ordinal1,k9_setfam_1(u1_struct_0(B)),C,E) & r1_xxreal_0(E,D) ) ) ) )).
fof(fraenkel_a_3_1_compos_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & ~ v1_xboole_0(C) & v1_compos_0(C) & v2_compos_0(C) & v3_compos_0(C) & m1_subset_1(D,C) ) => ( r2_hidden(A,a_3_1_compos_0(B,C,D)) <=> ? [E] : ( m1_subset_1(E,C) & A = k5_xtuple_0(E) & k2_compos_0(C,k5_compos_0(C,D,B)) = k2_compos_0(C,E) ) ) ) )).
fof(fraenkel_a_3_1_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( l1_compos_1(B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(B)) & v1_funct_1(D) & v1_finset_1(D) ) => ( r2_hidden(A,a_3_1_compos_1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_nat_1(E,k7_nat_d(k5_card_1(C),1)) & r2_hidden(E,k9_xtuple_0(k5_compos_1(B,D,k7_nat_d(k5_card_1(C),1)))) ) ) ) )).
fof(fraenkel_a_3_1_convex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_bhsp_1(B) & l1_bhsp_1(B) & m1_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_1_convex1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_xxreal_0(D,k1_bhsp_1(B,E,C)) ) ) ) )).
fof(fraenkel_a_3_1_convex2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_bhsp_1(B) & l1_bhsp_1(B) & m2_finseq_1(C,u1_struct_0(B)) & m2_finseq_1(D,k1_numbers) ) => ( r2_hidden(A,a_3_1_convex2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( r2_hidden(F,k9_subset_1(k4_ordinal1,k4_finseq_1(C),k4_finseq_1(D))) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ~ ( G = k1_funct_1(C,F) & ~ r1_xxreal_0(k1_funct_1(D,F),k1_bhsp_1(B,E,G)) ) ) ) ) ) ) ) )).
fof(fraenkel_a_3_1_convex4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_csspace(B) & l1_csspace(B) & m1_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_1_convex4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_xxreal_0(D,k3_complex1(k12_csspace(B,E,C))) ) ) ) )).
fof(fraenkel_a_3_1_cqc_lang,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(B) & v7_ordinal1(C) & v3_card_1(D,C) & m2_finseq_1(D,k2_qc_lang1(B)) ) => ( r2_hidden(A,a_3_1_cqc_lang(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_funct_1(D,E) & r1_xxreal_0(1,E) & r1_xxreal_0(E,k3_finseq_1(D)) & r2_hidden(k1_funct_1(D,E),k4_qc_lang1(B)) ) ) ) )).
fof(fraenkel_a_3_1_cqc_sim1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(B) & m1_subset_1(C,k4_ordinal1) & v3_card_1(D,C) & m2_finseq_1(D,k2_qc_lang1(B)) ) => ( r2_hidden(A,a_3_1_cqc_sim1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_funct_1(D,E) & r1_xxreal_0(1,E) & r1_xxreal_0(E,k3_finseq_1(D)) & r2_hidden(k1_funct_1(D,E),k5_qc_lang1(B)) ) ) ) )).
fof(fraenkel_a_3_1_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_3_1_domain_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & r2_hidden(E,C) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_1_ec_pf_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v1_int_2(B) & m1_subset_1(C,u1_struct_0(k9_int_3(B))) & m1_subset_1(D,u1_struct_0(k9_int_3(B))) ) => ( r2_hidden(A,a_3_1_ec_pf_1(B,C,D)) <=> ? [E] : ( m2_subset_1(E,k3_zfmisc_1(u1_struct_0(k9_int_3(B)),u1_struct_0(k9_int_3(B)),u1_struct_0(k9_int_3(B))),k3_ec_pf_1(k9_int_3(B))) & A = k6_eqrel_1(k6_ec_pf_1(B,C,D),k6_ec_pf_1(B,C,D),k8_ec_pf_1(B,C,D),E) & r2_hidden(E,k6_ec_pf_1(B,C,D)) & ? [F] : ( m1_subset_1(F,u1_struct_0(k9_int_3(B))) & ? [G] : ( m1_subset_1(G,u1_struct_0(k9_int_3(B))) & E = k4_domain_1(u1_struct_0(k9_int_3(B)),u1_struct_0(k9_int_3(B)),k4_ordinal1,F,G,1) ) ) ) ) ) )).
fof(fraenkel_a_3_1_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,B) & v1_eqrel_1(D,B) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(k9_setfam_1(B)))) ) => ( r2_hidden(A,a_3_1_eqrel_1(B,C,D)) <=> ? [E] : ( m1_eqrel_1(E,B) & A = k11_eqrel_1(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_1_euclid_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & m1_subset_1(C,u1_struct_0(k15_euclid(B))) & m1_subset_1(D,u1_struct_0(k15_euclid(B))) ) => ( r2_hidden(A,a_3_1_euclid_4(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = k3_rlvect_1(k15_euclid(B),k1_rlvect_1(k15_euclid(B),C,k6_xcmplx_0(1,E)),k1_rlvect_1(k15_euclid(B),D,E)) ) ) ) )).
fof(fraenkel_a_3_1_fcont_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_1_fcont_1(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = E & r1_xxreal_0(k6_xcmplx_0(B,k7_xcmplx_0(k3_xxreal_0(D,k6_xcmplx_0(C,B)),2)),E) & r1_xxreal_0(E,k2_xcmplx_0(B,k7_xcmplx_0(k3_xxreal_0(D,k6_xcmplx_0(C,B)),2))) ) ) ) )).
fof(fraenkel_a_3_1_fdiff_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & m1_subset_1(C,k1_numbers) & m1_subset_1(D,k1_numbers) ) => ( r2_hidden(A,a_3_1_fdiff_2(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = E & ~ r1_xxreal_0(E,B) & ~ r1_xxreal_0(k2_xcmplx_0(k4_xxreal_0(C,D),1),E) ) ) ) )).
fof(fraenkel_a_3_1_filter_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) & ~ v1_xboole_0(C) & v19_lattices(C,B) & v20_lattices(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & v19_lattices(D,B) & v20_lattices(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_1_filter_0(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & ? [G] : ( m1_subset_1(G,u1_struct_0(B)) & r3_lattices(B,k4_lattices(B,F,G),E) & r2_hidden(F,D) & r2_hidden(G,C) ) ) ) ) ) )).
fof(fraenkel_a_3_1_filter_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) & ~ v1_xboole_0(C) & v18_lattices(C,B) & v21_lattices(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & v18_lattices(D,B) & v21_lattices(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_1_filter_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & ? [G] : ( m1_subset_1(G,u1_struct_0(B)) & r3_lattices(B,E,k3_lattices(B,F,G)) & r2_hidden(F,C) & r2_hidden(G,D) ) ) ) ) ) )).
fof(fraenkel_a_3_1_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(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))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_1_finance1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & ~ r1_xxreal_0(D,k3_funct_2(B,k1_numbers,C,E)) ) ) ) )).
fof(fraenkel_a_3_1_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & ~ v1_xboole_0(D) ) => ( r2_hidden(A,a_3_1_finseq_3(B,C,D)) <=> ? [E] : ? [F] : ? [G] : ( m1_subset_1(E,B) & m1_subset_1(F,C) & m1_subset_1(G,D) & A = k11_finseq_1(E,F,G) ) ) ) )).
fof(fraenkel_a_3_1_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_1_finseq_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = E & r2_hidden(E,k4_finseq_1(B)) & r1_xxreal_0(E,k1_nat_1(D,1)) & r2_hidden(k1_funct_1(B,E),k1_tarski(C)) ) ) ) )).
fof(fraenkel_a_3_1_fomodel1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) & v1_relat_1(C) & v1_funct_1(C) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_1_fomodel1(B,C,D)) <=> ? [E] : ( v10_fomodel1(E,B) & m1_subset_1(E,k1_fomodel1(B)) & A = k24_fomodel1(B,E,k1_funct_1(C,D)) & v6_fomodel1(E,B) ) ) ) )).
fof(fraenkel_a_3_1_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(k1_fomodel4(B)),k1_fomodel4(B)))) ) => ( r2_hidden(A,a_3_1_fomodel4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_fomodel4(B)) & A = E & r2_hidden(k4_tarski(D,E),C) ) ) ) )).
fof(fraenkel_a_3_1_goboard5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_3_1_goboard5(B,C,D)) <=> ? [E] : ? [F] : ( v1_xreal_0(E) & v1_xreal_0(F) & A = k19_euclid(E,F) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,B,C)),E) & r1_xxreal_0(E,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,k1_nat_1(B,1),C))) ) ) ) )).
fof(fraenkel_a_3_1_goboard6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v6_metric_1(B) & l1_metric_1(B) & m1_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_1_goboard6(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(D,k1_metric_1(B,C,E)) ) ) ) )).
fof(fraenkel_a_3_1_gobrd13,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_3_1_gobrd13(B,C,D)) <=> ? [E] : ? [F] : ( v1_xreal_0(E) & v1_xreal_0(F) & A = k19_euclid(E,F) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,B,C)),E) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,B,C)),F) & r1_xxreal_0(F,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,1,k1_nat_1(C,1)))) ) ) ) )).
fof(fraenkel_a_3_1_goedelcp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(B) & m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(B))) & m1_subset_1(D,k1_zfmisc_1(k3_cqc_lang(B))) ) => ( r2_hidden(A,a_3_1_goedelcp(B,C,D)) <=> ? [E] : ( m2_subset_1(E,k9_qc_lang1(B),k3_cqc_lang(B)) & A = k24_qc_lang1(B,E) & r2_hidden(E,k4_subset_1(k3_cqc_lang(B),C,D)) ) ) ) )).
fof(fraenkel_a_3_1_graph_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_graph_5(B,C,D)) <=> ? [E] : ( v7_graph_1(E,B) & v1_graph_4(E,B) & m2_graph_1(E,B) & A = E & r3_graph_5(B,E,C,D) ) ) ) )).
fof(fraenkel_a_3_1_group_11,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_group_2(D,B) ) => ( r2_hidden(A,a_3_1_group_11(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xboole_0(k13_group_2(B,D,E),C) ) ) ) )).
fof(fraenkel_a_3_1_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_1_group_9(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k6_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_1_heyting1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(C,k5_finsub_1(k7_normform(B))) & m2_funct_2(D,k7_normform(B),k1_heyting1(B),k9_funct_2(k7_normform(B),k1_heyting1(B))) ) => ( r2_hidden(A,a_3_1_heyting1(B,C,D)) <=> ? [E] : ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B)) & A = k3_funct_2(k7_normform(B),k1_heyting1(B),D,E) & r2_hidden(k3_funct_2(k7_normform(B),k1_heyting1(B),D,E),k2_domain_1(k5_finsub_1(B),k5_finsub_1(B),E)) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_1_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_ideal_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k6_algstr_0(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_1_interva1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & v1_interva1(C,B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) & ~ v1_xboole_0(D) & v1_interva1(D,B) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(B))) ) => ( r2_hidden(A,a_3_1_interva1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(B)) & A = E & r1_tarski(k7_subset_1(B,k7_interva1(B,C),k8_interva1(B,D)),E) & r1_tarski(E,k7_subset_1(B,k8_interva1(B,C),k7_interva1(B,D))) ) ) ) )).
fof(fraenkel_a_3_1_jgraph_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & m1_subset_1(C,u1_struct_0(k15_euclid(B))) & m1_subset_1(D,u1_struct_0(k15_euclid(B))) ) => ( r2_hidden(A,a_3_1_jgraph_1(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = k3_rlvect_1(k15_euclid(B),k1_rlvect_1(k15_euclid(B),D,k6_xcmplx_0(1,E)),k1_rlvect_1(k15_euclid(B),C,E)) & r1_xxreal_0(k5_numbers,E) & r1_xxreal_0(E,1) ) ) ) )).
fof(fraenkel_a_3_1_jgraph_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,u1_struct_0(k14_euclid(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_1_jgraph_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(B))) & A = E & ~ r1_xxreal_0(D,k3_metric_1(k14_euclid(B),C,E)) ) ) ) )).
fof(fraenkel_a_3_1_jgraph_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) & 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)))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_1_jgraph_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(D,k7_partfun1(u1_struct_0(k3_topmetr),C,E)) ) ) ) )).
fof(fraenkel_a_3_1_jgraph_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_1_jgraph_6(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) & A = E & ~ r1_xxreal_0(D,k12_euclid(k5_algstr_0(k15_euclid(2),E,k19_euclid(B,C)))) ) ) ) )).
fof(fraenkel_a_3_1_jordan20,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(2),B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(2),B))))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_1_jordan20(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) & A = E & ? [F] : ( v1_xreal_0(F) & ~ r1_xxreal_0(F,D) & r1_xxreal_0(F,1) & E = k1_funct_1(C,F) ) ) ) ) )).
fof(fraenkel_a_3_1_jordan2b,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(B,k4_ordinal1) & v1_xreal_0(C) & m1_subset_1(D,k4_ordinal1) ) => ( r2_hidden(A,a_3_1_jordan2b(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(B))) & A = E & ~ r1_xxreal_0(k7_partfun1(k1_numbers,E,D),C) ) ) ) )).
fof(fraenkel_a_3_1_jordan2c,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & m1_subset_1(C,u1_struct_0(k15_euclid(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) ) => ( r2_hidden(A,a_3_1_jordan2c(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(B))) & A = E & ~ ( E != C & ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B))) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B))))) ) => ~ ( v5_pre_topc(F,k5_topmetr,k15_euclid(B)) & r1_tarski(k2_relset_1(u1_struct_0(k15_euclid(B)),F),D) & k1_funct_1(F,k5_numbers) = C & k1_funct_1(F,1) = E ) ) ) ) ) ) )).
fof(fraenkel_a_3_1_jordan3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) & v7_ordinal1(C) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_1_jordan3(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k2_topreal1(2,k3_finseq_6(u1_struct_0(k15_euclid(2)),B,D,C),E) & r1_xxreal_0(1,E) & r1_xxreal_0(k1_nat_1(E,1),k3_finseq_1(k3_finseq_6(u1_struct_0(k15_euclid(2)),B,D,C))) ) ) ) )).
fof(fraenkel_a_3_1_jordan4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) & v7_ordinal1(C) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_1_jordan4(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k2_topreal1(2,k3_finseq_6(u1_struct_0(k15_euclid(2)),B,D,C),E) & r1_xxreal_0(1,E) & r1_xxreal_0(k1_nat_1(E,1),k3_finseq_1(k3_finseq_6(u1_struct_0(k15_euclid(2)),B,D,C))) ) ) ) )).
fof(fraenkel_a_3_1_jordan5a,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_1_jordan5a(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = E & ~ r1_xxreal_0(E,k6_xcmplx_0(C,k3_xxreal_0(k6_xcmplx_0(C,B),D))) & ~ r1_xxreal_0(k2_xcmplx_0(C,k3_xxreal_0(k6_xcmplx_0(C,B),D)),E) ) ) ) )).
fof(fraenkel_a_3_1_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l3_lattices(B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_lattice3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_lattices(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_1_lattice5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_lattice3(C) & v2_lattice3(C) & v1_yellow_0(C) & l1_orders_2(C) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(B,B),u1_struct_0(C)) & v1_lattice5(D,B,C) & v2_lattice5(D,B,C) & v3_lattice5(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B,B),u1_struct_0(C)))) ) => ( r2_hidden(A,a_3_1_lattice5(B,C,D)) <=> ? [E] : ? [F] : ? [G] : ? [H] : ( m1_subset_1(E,B) & m1_subset_1(F,B) & m1_subset_1(G,u1_struct_0(C)) & m1_subset_1(H,u1_struct_0(C)) & A = k5_domain_1(B,B,u1_struct_0(C),u1_struct_0(C),E,F,G,H) & r3_orders_2(C,k3_lattice5(B,C,D,E,F),k13_lattice3(C,G,H)) ) ) ) )).
fof(fraenkel_a_3_1_lattice6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_lattice6(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r2_hidden(E,C) & r3_lattices(B,D,E) ) ) ) )).
fof(fraenkel_a_3_1_lattice8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_yellow_0(C) & v1_lattice3(C) & v2_lattice3(C) & l1_orders_2(C) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(B,B),u1_struct_0(C)) & v1_lattice5(D,B,C) & v2_lattice5(D,B,C) & v3_lattice5(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B,B),u1_struct_0(C)))) ) => ( r2_hidden(A,a_3_1_lattice8(B,C,D)) <=> ? [E] : ? [F] : ? [G] : ? [H] : ( m1_subset_1(E,B) & m1_subset_1(F,B) & m1_subset_1(G,u1_struct_0(C)) & m1_subset_1(H,u1_struct_0(C)) & A = k5_domain_1(B,B,u1_struct_0(C),u1_struct_0(C),E,F,G,H) & r3_orders_2(C,k3_lattice5(B,C,D,E,F),k13_lattice3(C,G,H)) ) ) ) )).
fof(fraenkel_a_3_1_lfuzzy_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_lfuzzy_0(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_1_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v5_relat_1(C,k1_rcomp_1(k5_numbers,1)) & 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))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(B,B))))) ) => ( r2_hidden(A,a_3_1_lfuzzy_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(B,B)))) & A = k3_fuzzy_4(B,B,B,C,k5_lfuzzy_0(k2_zfmisc_1(B,B),E)) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_1_lmod_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v6_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) & v1_vectsp_2(B) & l6_algstr_0(B) & ~ 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) & m1_vectsp_6(D,B,C) ) => ( r2_hidden(A,a_3_1_lmod_5(B,C,D)) <=> ? [E] : ( 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) ) ) ) )).
fof(fraenkel_a_3_1_lopban_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & 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) & v1_xreal_0(C) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_lopban_5(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(C,k2_normsp_0(B,k5_algstr_0(B,D,E))) ) ) ) )).
fof(fraenkel_a_3_1_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_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,k6_numbers))) ) => ( r2_hidden(A,a_3_1_lpspacc1(B,C,D)) <=> ? [E] : ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) & A = E & r2_hidden(E,k13_lpspacc1(B,C,D)) & r1_lpspacc1(B,C,D,E,k8_funcop_1(k2_numbers,B,k5_complex1)) ) ) ) )).
fof(fraenkel_a_3_1_lpspace1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_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,k6_numbers))) ) => ( r2_hidden(A,a_3_1_lpspace1(B,C,D)) <=> ? [E] : ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) & A = E & r2_hidden(E,k9_lpspace1(B,C,D)) & r1_lpspace1(B,C,D,E,k8_lpspace1(B,k5_numbers)) ) ) ) )).
fof(fraenkel_a_3_1_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_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,k6_numbers))) ) => ( r2_hidden(A,a_3_1_lpspace2(B,C,D)) <=> ? [E] : ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) & A = k13_lpspace1(B,C,D,E) & r2_hidden(E,k9_lpspace1(B,C,D)) ) ) ) )).
fof(fraenkel_a_3_1_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_1_mathmorp(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_tarski(k1_mathmorp(B,E,D),C) ) ) ) )).
fof(fraenkel_a_3_1_matrix15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & ~ 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) ) => ( r2_hidden(A,a_3_1_matrix15(B,C,D)) <=> ? [E] : ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(D),B,C) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(D))) & A = E ) ) ) )).
fof(fraenkel_a_3_1_matrtop1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ( r2_hidden(A,a_3_1_matrtop1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = E & r2_hidden(k2_xcmplx_0(E,k3_finseq_1(C)),k7_subset_1(k4_ordinal1,k9_subset_1(k4_ordinal1,B,k4_finseq_1(k7_finseq_1(C,D))),k2_finseq_1(k3_finseq_1(C)))) ) ) ) )).
fof(fraenkel_a_3_1_mazurulm,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_mazurulm(B,C,D)) <=> ? [E] : ( 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)))) & A = E & v3_funct_2(E,u1_struct_0(B),u1_struct_0(B)) & v1_mazurulm(E,B,B) & k3_funct_2(u1_struct_0(B),u1_struct_0(B),E,C) = C & k3_funct_2(u1_struct_0(B),u1_struct_0(B),E,D) = D ) ) ) )).
fof(fraenkel_a_3_1_mesfun9c,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v7_ordinal1(C) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(B,k2_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(B,k2_numbers)))) ) => ( r2_hidden(A,a_3_1_mesfun9c(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = k1_relset_1(B,k4_mesfunc5(B,k2_numbers,D,E)) & r1_xxreal_0(E,C) ) ) ) )).
fof(fraenkel_a_3_1_mesfunc8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) & v5_relat_1(D,C) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ( r2_hidden(A,a_3_1_mesfunc8(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k9_nat_1(k9_setfam_1(B),D,E) & r1_xxreal_0(k5_numbers,E) ) ) ) )).
fof(fraenkel_a_3_1_metric_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( l1_metric_1(B) & m1_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_1_metric_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_xxreal_0(k1_metric_1(B,C,E),D) ) ) ) )).
fof(fraenkel_a_3_1_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_3_1_mmlquery(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & ? [F] : ( m1_subset_1(F,B) & r1_mmlquery(E,F,C) & r2_hidden(E,D) ) ) ) ) )).
fof(fraenkel_a_3_1_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_partfun1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_3_1_modelc_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & ? [F] : ( m1_subset_1(F,B) & r2_hidden(F,D) & r2_hidden(k4_tarski(E,F),C) ) ) ) ) )).
fof(fraenkel_a_3_1_morph_01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_1_morph_01(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k5_rusub_4(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_1_msafree,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_msafree(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k5_msafree(B,C))) & A = k2_trees_4(u1_struct_0(k5_msafree(B,C)),E) & r2_hidden(E,k6_dtconstr(k5_msafree(B,C))) & k2_xtuple_0(E) = D ) ) ) )).
fof(fraenkel_a_3_1_msafree2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) & v4_msualg_1(C,B) & l3_msualg_1(C,B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_msafree2(B,C,D)) <=> ? [E] : ( m1_dtconstr(E,u1_struct_0(k5_msafree(B,u3_msualg_1(B,C))),k5_trees_3(u1_struct_0(k5_msafree(B,u3_msualg_1(B,C)))),k4_dtconstr(k5_msafree(B,u3_msualg_1(B,C)))) & A = E & ~ ( ! [F] : ~ ( r2_hidden(F,k1_funct_1(u3_msualg_1(B,C),D)) & E = k1_trees_4(k4_tarski(F,D)) ) & ! [F] : ( m1_subset_1(F,u4_struct_0(B)) => ~ ( k4_tarski(F,u1_struct_0(B)) = k1_funct_1(E,k1_xboole_0) & k2_msualg_1(B,F) = D ) ) ) ) ) ) )).
fof(fraenkel_a_3_1_msaterm,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_msaterm(B,C,D)) <=> ? [E] : ( m1_dtconstr(E,u1_struct_0(k5_msafree(B,C)),k5_trees_3(u1_struct_0(k5_msafree(B,C))),k4_dtconstr(k5_msafree(B,C))) & A = E & ~ ( ! [F] : ~ ( r2_hidden(F,k1_funct_1(C,D)) & E = k1_trees_4(k4_tarski(F,D)) ) & ! [F] : ( m1_subset_1(F,u4_struct_0(B)) => ~ ( k4_tarski(F,u1_struct_0(B)) = k1_funct_1(E,k1_xboole_0) & k2_msualg_1(B,F) = D ) ) ) ) ) ) )).
fof(fraenkel_a_3_1_msualg_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) & v4_msualg_1(C,B) & l3_msualg_1(C,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_msualg_5(u1_struct_0(B),u3_msualg_1(B,C))))) ) => ( r2_hidden(A,a_3_1_msualg_8(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k5_msualg_5(u1_struct_0(B),u3_msualg_1(B,C)))) & A = E & v2_msualg_4(E,B,C) & v3_msualg_4(E,B,C) & m1_msualg_4(E,u1_struct_0(B),u3_msualg_1(B,C),u3_msualg_1(B,C)) & r4_lattice3(k5_msualg_5(u1_struct_0(B),u3_msualg_1(B,C)),E,D) ) ) ) )).
fof(fraenkel_a_3_1_msualg_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_msualg_9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k5_msafree(B,C))) & A = k2_trees_4(u1_struct_0(k5_msafree(B,C)),E) & r2_hidden(E,k6_dtconstr(k5_msafree(B,C))) & k2_xtuple_0(E) = D ) ) ) )).
fof(fraenkel_a_3_1_nagata_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & v3_pre_topc(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_1_nagata_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & r2_hidden(E,C) & ~ r1_xboole_0(E,D) ) ) ) )).
fof(fraenkel_a_3_1_nagata_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),k1_numbers))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_1_nagata_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & k3_funct_2(u1_struct_0(B),k1_numbers,k3_nagata_2(u1_struct_0(B),C,k3_subset_1(u1_struct_0(B),D)),E) = k5_numbers ) ) ) )).
fof(fraenkel_a_3_1_ncfcont1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_1_ncfcont1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(D,k2_normsp_0(B,k5_algstr_0(B,E,C))) ) ) ) )).
fof(fraenkel_a_3_1_ndiff_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_1_ndiff_5(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(D,k2_normsp_0(B,k5_algstr_0(B,E,C))) ) ) ) )).
fof(fraenkel_a_3_1_nfcont_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(B,k4_ordinal1) & v1_xreal_0(C) & m1_subset_1(D,u1_struct_0(k4_real_ns1(B))) ) => ( r2_hidden(A,a_3_1_nfcont_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(B))) & A = E & ~ r1_xxreal_0(C,k2_normsp_0(k4_real_ns1(B),k5_algstr_0(k4_real_ns1(B),E,D))) ) ) ) )).
fof(fraenkel_a_3_1_normsp_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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_xreal_0(C) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_normsp_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_xxreal_0(k2_normsp_0(B,k5_algstr_0(B,D,E)),C) ) ) ) )).
fof(fraenkel_a_3_1_ordinal6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_ordinal1(B) & v4_ordinal1(B) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & v1_classes2(C) & v3_ordinal1(D) ) => ( r2_hidden(A,a_3_1_ordinal6(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k9_xtuple_0(k5_relat_1(k11_ordinal6(C),B))) & A = k1_funct_1(k1_funct_1(k5_relat_1(k11_ordinal6(C),B),E),k1_ordinal1(D)) & r2_hidden(E,k9_xtuple_0(k5_relat_1(k11_ordinal6(C),B))) ) ) ) )).
fof(fraenkel_a_3_1_osafree,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v4_osalg_1(B) & v5_osalg_1(B) & l3_osalg_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_subset_1(D,u1_struct_0(k2_osafree(B,C))) ) => ( r2_hidden(A,a_3_1_osafree(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k4_tarski(k2_trees_4(u1_struct_0(k2_osafree(B,C)),D),E) & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & ? [G] : ( r2_hidden(G,k1_funct_1(C,F)) & D = k4_tarski(G,F) & r3_orders_2(B,F,E) ) ) ) ) ) )).
fof(fraenkel_a_3_1_osalg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v4_osalg_1(B) & v5_osalg_1(B) & l3_osalg_1(B) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_osalg_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_funct_1(C,E) & r3_orders_2(B,E,D) ) ) ) )).
fof(fraenkel_a_3_1_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_osalg_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_funct_1(C,E) & r2_hidden(E,k3_osalg_4(B,D)) ) ) ) )).
fof(fraenkel_a_3_1_partit1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m1_eqrel_1(C,B) ) => ( r2_hidden(A,a_3_1_partit1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & r2_hidden(k4_tarski(o_1_1_partit1(D),E),k4_partit1(B,C)) ) ) ) )).
fof(fraenkel_a_3_1_pcomps_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_1_pcomps_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & r2_hidden(E,C) & ~ r1_xboole_0(E,D) ) ) ) )).
fof(fraenkel_a_3_1_pdiff_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,u1_struct_0(k4_real_ns1(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_1_pdiff_6(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(B))) & A = E & ~ r1_xxreal_0(D,k2_normsp_0(k4_real_ns1(B),k5_algstr_0(k4_real_ns1(B),E,C))) ) ) ) )).
fof(fraenkel_a_3_1_pdiff_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_1_pdiff_7(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(D,k2_normsp_0(B,k5_algstr_0(B,E,C))) ) ) ) )).
fof(fraenkel_a_3_1_poset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(B,B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_poset_1(B,B)))) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_1_poset_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(k6_poset_1(B,B))) & ? [G] : ( v1_funct_1(G) & v1_funct_2(G,u1_struct_0(B),u1_struct_0(B)) & v2_poset_1(G,B,B) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) & G = F & r2_hidden(F,C) & E = k3_funct_2(u1_struct_0(B),u1_struct_0(B),k1_abian(u1_struct_0(B),G,D),k3_yellow_0(B)) ) ) ) ) ) )).
fof(fraenkel_a_3_1_pralg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & ~ v2_struct_0(C) & ~ v11_struct_0(C) & l1_msualg_1(C) & m1_pralg_2(D,B,C) ) => ( r2_hidden(A,a_3_1_pralg_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = k6_pralg_2(C,k5_pralg_2(B,C,D,E)) ) ) ) )).
fof(fraenkel_a_3_1_pralg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & ~ v2_struct_0(C) & ~ v11_struct_0(C) & l1_msualg_1(C) & m1_pralg_2(D,B,C) ) => ( r2_hidden(A,a_3_1_pralg_3(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,B) & m1_subset_1(F,u1_struct_0(C)) & A = k1_funct_1(u3_msualg_1(C,k5_pralg_2(B,C,D,E)),F) ) ) ) )).
fof(fraenkel_a_3_1_prelamb,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_prelamb(B) & m1_prelamb(C,B) & m1_trees_1(D,k9_xtuple_0(C)) ) => ( r2_hidden(A,a_3_1_prelamb(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k7_finseq_1(D,k9_finseq_1(E)) & r2_hidden(k7_finseq_1(D,k9_finseq_1(E)),k9_xtuple_0(C)) ) ) ) )).
fof(fraenkel_a_3_1_pua2mss1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m1_eqrel_1(D,B) ) => ( r2_hidden(A,a_3_1_pua2mss1(B,C,D)) <=> ? [E] : ( m2_subset_1(E,k1_zfmisc_1(B),D) & A = k8_subset_1(B,E,C) & ~ r1_xboole_0(E,C) ) ) ) )).
fof(fraenkel_a_3_1_qc_lang3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(B) & m1_subset_1(C,k9_qc_lang1(B)) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k2_qc_lang1(B))) ) => ( r2_hidden(A,a_3_1_qc_lang3(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_funct_1(k17_qc_lang1(B,C),E) & r1_xxreal_0(1,E) & r1_xxreal_0(E,k3_finseq_1(k17_qc_lang1(B,C))) & r2_hidden(k1_funct_1(k17_qc_lang1(B,C),E),D) ) ) ) )).
fof(fraenkel_a_3_1_qc_lang4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(B) & m1_subset_1(C,k9_qc_lang1(B)) & m1_subset_1(D,k9_qc_lang1(B)) ) => ( r2_hidden(A,a_3_1_qc_lang4(B,C,D)) <=> ? [E] : ( m1_trees_1(E,k9_xtuple_0(k2_qc_lang4(B,C))) & A = E & k5_trees_2(k2_qc_lang4(B,C),E) = k2_qc_lang4(B,D) ) ) ) )).
fof(fraenkel_a_3_1_quantal1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_quantal1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k6_algstr_0(B,E,C) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_1_quofield,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & ~ 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) & v1_funct_1(D) & v1_funct_2(D,k1_quofield(B),u1_struct_0(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_quofield(B),u1_struct_0(C)))) ) => ( r2_hidden(A,a_3_1_quofield(B,C,D)) <=> ? [E] : ( m2_subset_1(E,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),k1_quofield(B)) & A = k1_domain_1(k7_quofield(B),u1_struct_0(C),k10_quofield(B,E),k3_funct_2(k1_quofield(B),u1_struct_0(C),D,E)) & k5_struct_0(B) = k5_struct_0(B) ) ) ) )).
fof(fraenkel_a_3_1_rinfsup2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) & m1_subset_1(C,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => ( r2_hidden(A,a_3_1_rinfsup2(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k12_supinf_2(B,E) & r1_xxreal_0(k1_nat_1(C,D),E) ) ) ) )).
fof(fraenkel_a_3_1_rlsub_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(B)) & m1_rlsub_1(D,B) ) => ( r2_hidden(A,a_3_1_rlsub_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,C,E) & r1_struct_0(D,E) ) ) ) )).
fof(fraenkel_a_3_1_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_rltopsp1(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = k3_rlvect_1(B,k1_rlvect_1(B,C,k6_xcmplx_0(1,E)),k1_rlvect_1(B,D,E)) & r1_xxreal_0(k5_numbers,E) & r1_xxreal_0(E,1) ) ) ) )).
fof(fraenkel_a_3_1_rmod_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(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) & m1_rmod_2(D,B,C) ) => ( r2_hidden(A,a_3_1_rmod_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k3_rlvect_1(C,k4_struct_0(C),E) & r1_struct_0(D,E) ) ) ) )).
fof(fraenkel_a_3_1_rmod_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & ~ 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) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) ) => ( r2_hidden(A,a_3_1_rmod_4(B,C,D)) <=> ? [E] : ( m2_rmod_4(E,B,C,D) & A = k5_rmod_4(B,C,E) ) ) ) )).
fof(fraenkel_a_3_1_rusub_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_rusub_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,D,E) & r1_struct_0(C,E) ) ) ) )).
fof(fraenkel_a_3_1_rusub_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_1_rusub_4(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k1_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_1_rusub_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_rlvect_1(B) & v2_rusub_4(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_rusub_5(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k1_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,k6_domain_1(u1_struct_0(B),D)) ) ) ) )).
fof(fraenkel_a_3_1_scmring3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(B))) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_1_scmring3(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_amistd_1(k7_card_1(2),k1_scmring2(B),E,k9_scmring2(B,D,C)) ) ) ) )).
fof(fraenkel_a_3_1_setlim_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,C))) ) => ( r2_hidden(A,a_3_1_setlim_1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_funct_1(D,E) & r1_xxreal_0(k1_nat_1(B,1),E) ) ) ) )).
fof(fraenkel_a_3_1_simplex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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)) & v1_simplex1(C,B) & v2_simplex1(C,B) & m1_simplex0(C,u1_struct_0(B)) & v1_finset_1(D) & v1_tops_2(D,C) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C)))) ) => ( r2_hidden(A,a_3_1_simplex1(B,C,D)) <=> ? [E] : ( m3_simplex0(E,k4_simplex1(B,C),k5_card_1(D)) & A = E & r1_tarski(k7_relset_1(k1_orders_1(u1_struct_0(B)),u1_struct_0(B),k2_rlaffin2(B),D),E) & r1_tarski(k3_convex1(B,k1_simplex1(B,k4_simplex1(B,C),E)),k3_convex1(B,k1_simplex1(B,C,k5_setfam_1(u1_struct_0(C),D)))) ) ) ) )).
fof(fraenkel_a_3_1_sppol_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_1_sppol_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) & A = E & k17_euclid(E) = B & r1_xxreal_0(C,k18_euclid(E)) & r1_xxreal_0(k18_euclid(E),D) ) ) ) )).
fof(fraenkel_a_3_1_sprect_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & m2_finseq_1(D,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_3_1_sprect_2(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k2_topreal1(2,k3_finseq_6(u1_struct_0(k15_euclid(2)),D,B,C),E) & r1_xxreal_0(1,E) & r1_xxreal_0(k1_nat_1(E,1),k3_finseq_1(k3_finseq_6(u1_struct_0(k15_euclid(2)),D,B,C))) ) ) ) )).
fof(fraenkel_a_3_1_sprect_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & m2_finseq_1(D,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_3_1_sprect_3(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k2_topreal1(2,D,E) & r1_xxreal_0(k1_nat_1(B,1),E) & ~ r1_xxreal_0(C,E) ) ) ) )).
fof(fraenkel_a_3_1_substlat,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k5_finsub_1(k4_partfun1(B,C))) => ( r2_hidden(A,a_3_1_substlat(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,k4_partfun1(B,C)) & m1_subset_1(F,k4_partfun1(B,C)) & A = k2_xboole_0(E,F) & r2_hidden(E,D) & r2_hidden(F,k1_tarski(k1_xboole_0)) & r1_partfun1(E,F) ) ) ) )).
fof(fraenkel_a_3_1_substut2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(B) & v7_ordinal1(C) & v3_card_1(D,C) & m2_finseq_1(D,k2_qc_lang1(B)) ) => ( r2_hidden(A,a_3_1_substut2(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_funct_1(D,E) & r1_xxreal_0(1,E) & r1_xxreal_0(E,k3_finseq_1(D)) & r2_hidden(k1_funct_1(D,E),k5_qc_lang1(B)) ) ) ) )).
fof(fraenkel_a_3_1_topgen_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(C))) ) => ( r2_hidden(A,a_3_1_topgen_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & A = k2_pre_topc(B,k5_setfam_1(u1_struct_0(B),E)) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_1_topreal3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_1_topreal3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) & A = E & k18_euclid(E) = B & r1_xxreal_0(C,k17_euclid(E)) & r1_xxreal_0(k17_euclid(E),D) ) ) ) )).
fof(fraenkel_a_3_1_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & m1_subset_1(C,u1_struct_0(k15_euclid(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_1_topreal9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(B))) & A = E & r1_xxreal_0(k12_euclid(k5_algstr_0(k15_euclid(B),E,C)),D) ) ) ) )).
fof(fraenkel_a_3_1_treal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & m1_subset_1(D,u1_struct_0(k2_topmetr(k5_numbers,1))) ) => ( r2_hidden(A,a_3_1_treal_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k2_topmetr(k5_numbers,1))) & A = E & ~ r1_xxreal_0(k3_xcmplx_0(k6_xcmplx_0(B,C),k5_xcmplx_0(2)),k3_metric_1(k2_topmetr(k5_numbers,1),D,E)) ) ) ) )).
fof(fraenkel_a_3_1_trees_a,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) & v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) & m4_trees_1(D,k9_xtuple_0(B)) ) => ( r2_hidden(A,a_3_1_trees_a(B,C,D)) <=> ? [E] : ? [F] : ( m1_trees_1(E,k9_xtuple_0(B)) & m1_trees_1(F,k9_xtuple_0(C)) & A = k8_finseq_1(k4_ordinal1,E,F) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_1_uproots,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v6_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) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(C,B) & v1_uproots(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_uproots(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = E & ? [F] : ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(F,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) & r2_funct_2(k4_ordinal1,u1_struct_0(B),C,k13_polynom3(B,k2_polynom5(B,k4_polynom5(B,k4_algstr_0(B,D),k5_struct_0(B)),E),F)) ) ) ) ) )).
fof(fraenkel_a_3_1_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & v1_relat_1(D) & v1_funct_1(D) ) => ( r2_hidden(A,a_3_1_valued_1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k2_xcmplx_0(E,k2_xcmplx_0(C,B)) & r2_hidden(E,k9_xtuple_0(D)) ) ) ) )).
fof(fraenkel_a_3_1_vectsp10,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) & ~ v2_struct_0(C) & l1_vectsp_1(C,B) & 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_hidden(A,a_3_1_vectsp10(B,C,D)) <=> ? [E] : ( 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) ) ) ) )).
fof(fraenkel_a_3_1_vectsp_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(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) & m1_vectsp_4(D,B,C) ) => ( r2_hidden(A,a_3_1_vectsp_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k3_rlvect_1(C,k4_struct_0(C),E) & r1_struct_0(D,E) ) ) ) )).
fof(fraenkel_a_3_1_waybel11,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_1_waybel11(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k2_waybel_0(B,C,E) & r1_orders_2(C,D,E) ) ) ) )).
fof(fraenkel_a_3_1_waybel12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) & m1_subset_1(D,k4_ordinal1) ) => ( r2_hidden(A,a_3_1_waybel12(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = k3_funct_2(k4_ordinal1,u1_struct_0(B),C,E) & r1_xxreal_0(E,D) ) ) ) )).
fof(fraenkel_a_3_1_waybel13,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v1_yellow_0(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v4_yellow_0(C,k2_yellow_1(u1_struct_0(B))) & v7_yellow_0(C,k2_yellow_1(u1_struct_0(B))) & v4_waybel_0(C,k2_yellow_1(u1_struct_0(B))) & m1_yellow_0(C,k2_yellow_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(k2_yellow_1(u1_struct_0(B)))) ) => ( r2_hidden(A,a_3_1_waybel13(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = E & r1_tarski(D,E) ) ) ) )).
fof(fraenkel_a_3_1_waybel14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_waybel14(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k6_waybel_0(B,E) & r2_hidden(k6_waybel_0(B,E),C) & r2_hidden(D,k6_waybel_0(B,E)) ) ) ) )).
fof(fraenkel_a_3_1_waybel15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & v11_waybel_1(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_1_waybel15(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_1_waybel16,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k7_lattice3(B)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k7_lattice3(B)))) ) => ( r2_hidden(A,a_3_1_waybel16(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(k7_lattice3(B))) & m1_subset_1(F,u1_struct_0(k7_lattice3(B))) & A = k12_lattice3(k7_lattice3(B),E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_1_waybel20,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_1_waybel20(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k7_yellow_3(B,B,k3_funct_2(u1_struct_0(B),u1_struct_0(B),k3_waybel20(B,C),E),E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_1_waybel21,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v7_waybel_0(C) & v8_waybel_0(C,B) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_1_waybel21(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k2_waybel_0(B,C,E) & r1_orders_2(C,D,E) ) ) ) )).
fof(fraenkel_a_3_1_waybel23,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v5_orders_2(B) & v3_lattice3(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v4_yellow_0(C,B) & v8_yellow_0(C,B) & m1_yellow_0(C,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) ) => ( r2_hidden(A,a_3_1_waybel23(B,C,D)) <=> ? [E] : ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(D)) & A = k1_yellow_0(C,E) & r1_yellow_0(C,E) ) ) ) )).
fof(fraenkel_a_3_1_waybel30,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) & v2_waybel_2(B) & l1_waybel_9(B) & m1_subset_1(C,u1_struct_0(B)) & 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)))) ) => ( r2_hidden(A,a_3_1_waybel30(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k4_waybel_0(B,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_1_waybel31,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & v3_waybel_3(B) & l1_orders_2(B) & v4_waybel11(C) & m1_yellow_9(C,B) & v1_tops_2(D,C) & v1_cantor_1(D,C) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C)))) ) => ( r2_hidden(A,a_3_1_waybel31(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) & A = k2_waybel_3(C,k2_yellow_0(C,E)) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_1_waybel32,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_1_waybel32(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k2_waybel_0(B,C,E) & r1_orders_2(C,D,E) ) ) ) )).
fof(fraenkel_a_3_1_waybel33,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & v2_waybel_0(D,k2_yellow_1(C)) & v13_waybel_0(D,k2_yellow_1(C)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k2_yellow_1(C)))) ) => ( r2_hidden(A,a_3_1_waybel33(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k2_yellow_0(B,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_1_waybel_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_1_waybel_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k11_lattice3(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_1_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & v1_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & v1_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & v1_waybel_0(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_1_waybel_2(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k13_lattice3(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_1_waybel_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) & m1_subset_1(C,u1_struct_0(B)) & ~ 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))) ) => ( r2_hidden(A,a_3_1_waybel_3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_1_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) ) => ( r2_hidden(A,a_3_1_waybel_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r2_hidden(k1_domain_1(u1_struct_0(B),u1_struct_0(B),C,E),D) ) ) ) )).
fof(fraenkel_a_3_1_waybel_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v1_waybel_5(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_waybel_5(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_1_waybel_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) & v13_waybel_0(C,B) & v1_waybel_6(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_waybel_6(B,C,D)) <=> ? [E] : ( v6_orders_2(E,B) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & r1_tarski(E,k3_subset_1(u1_struct_0(B),C)) & r2_hidden(D,E) ) ) ) )).
fof(fraenkel_a_3_1_yellow12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_1_yellow12(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k11_lattice3(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_1_yellow13,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v3_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_1_yellow13(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_1_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_xboole_0(D) & v2_waybel_0(D,k3_yellow_3(B,C)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,C)))) ) => ( r2_hidden(A,a_3_1_yellow_3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k3_yellow_3(B,C))) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(k3_yellow_3(B,C))) & r1_orders_2(k3_yellow_3(B,C),F,E) & r2_hidden(F,D) ) ) ) ) )).
fof(fraenkel_a_3_1_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_1_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k10_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_1_yellow_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_1_yellow_6(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k2_waybel_0(B,C,E) & r1_orders_2(C,D,E) ) ) ) )).
fof(fraenkel_a_3_1_yellow_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & v1_cantor_1(C,B) & v1_tops_2(C,B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_1_yellow_8(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & r2_hidden(E,C) & r1_tarski(E,D) ) ) ) )).
fof(fraenkel_a_3_1_yellow_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_tops_2(D,B) & v2_cantor_1(D,B) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) => ( r2_hidden(A,a_3_1_yellow_9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k2_zfmisc_1(E,u1_struct_0(C)) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_1_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) & m1_subset_1(D,B) ) => ( r2_hidden(A,a_3_1_zf_fund1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,B) & m1_subset_1(F,B) & A = k7_classes2(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_1_zf_fund2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) & ~ v1_xboole_0(C) & 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(A,a_3_1_zf_fund2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,C) & A = E & r2_hidden(k2_xboole_0(k1_tarski(k4_tarski(k1_xboole_0,E)),k2_partfun1(k4_ordinal1,C,k1_partfun1(k4_ordinal1,k1_zf_lang,k1_zf_lang,C,k2_zf_fund1,D),k7_subset_1(k4_ordinal1,k4_zf_fund1(k2_zf_model(B)),k1_tarski(k1_xboole_0)))),k5_zf_fund1(B,C)) ) ) ) )).
fof(fraenkel_a_3_1_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_subset_1(C,u1_struct_0(B)) & m1_zmodul01(D,B) ) => ( r2_hidden(A,a_3_1_zmodul01(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,C,E) & r1_struct_0(D,E) ) ) ) )).
fof(fraenkel_a_3_1_zmodul03,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v1_int_2(B) & ~ 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) & v1_zmodul03(C) & l1_zmodul01(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) ) => ( r2_hidden(A,a_3_1_zmodul03(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k13_zmodul02(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_20_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_20_lattice3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r3_lattice3(B,E,k7_domain_1(u1_struct_0(B),C,D)) ) ) ) )).
fof(fraenkel_a_3_20_quantal1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_group_1(B) & v10_lattices(B) & v4_lattice3(B) & v7_quantal1(B) & v8_quantal1(B) & l1_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_20_quantal1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r3_lattices(B,k6_algstr_0(B,D,E),C) ) ) ) )).
fof(fraenkel_a_3_20_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v6_rltopsp1(B) & v7_rltopsp1(B) & l1_rltopsp1(B) & m1_connsp_2(C,B,k4_struct_0(B)) & m1_connsp_2(D,B,k4_struct_0(B)) ) => ( r2_hidden(A,a_3_20_rltopsp1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,E,F) & r2_hidden(E,k1_tops_1(B,C)) & r2_hidden(F,k1_tops_1(B,D)) ) ) ) )).
fof(fraenkel_a_3_21_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_21_lattice3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r3_lattices(B,k4_lattices(B,D,E),k15_lattice3(B,a_3_3_lattice3(B,C,D))) ) ) ) )).
fof(fraenkel_a_3_21_quantal1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_group_1(B) & v10_lattices(B) & v4_lattice3(B) & v7_quantal1(B) & v8_quantal1(B) & l1_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_21_quantal1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r3_lattices(B,k6_algstr_0(B,E,k1_quantal1(B,D,C)),C) ) ) ) )).
fof(fraenkel_a_3_21_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_21_yellow_4(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k11_lattice3(B,E,F) & r2_hidden(E,k6_domain_1(u1_struct_0(B),C)) & r2_hidden(F,k6_domain_1(u1_struct_0(B),D)) ) ) ) )).
fof(fraenkel_a_3_22_quantal1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_group_1(B) & v10_lattices(B) & v4_lattice3(B) & v7_quantal1(B) & v8_quantal1(B) & l1_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_22_quantal1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r3_lattices(B,k6_algstr_0(B,k2_quantal1(B,D,C),E),C) ) ) ) )).
fof(fraenkel_a_3_22_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_22_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_23_quantal1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v1_group_1(B) & v3_group_1(B) & v10_lattices(B) & v4_lattice3(B) & v7_quantal1(B) & v8_quantal1(B) & v20_quantal1(B) & v21_quantal1(B) & l3_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_23_quantal1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k5_quantal1(B,E) & r2_hidden(E,k7_domain_1(u1_struct_0(B),C,D)) ) ) ) )).
fof(fraenkel_a_3_23_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_23_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_24_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_24_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_25_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_25_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r1_orders_2(B,F,E) & r2_hidden(F,k4_yellow_4(B,C,D)) ) ) ) ) )).
fof(fraenkel_a_3_26_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_26_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k11_lattice3(B,D,E) & r2_hidden(E,k5_yellow_3(B,B,C)) ) ) ) )).
fof(fraenkel_a_3_27_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v6_rltopsp1(B) & v7_rltopsp1(B) & l1_rltopsp1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_connsp_2(D,B,k4_struct_0(B)) ) => ( r2_hidden(A,a_3_27_rltopsp1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,E,F) & r2_hidden(E,C) & r2_hidden(F,k1_convex1(B,k1_tops_1(B,D),k4_xcmplx_0(1))) ) ) ) )).
fof(fraenkel_a_3_27_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_27_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r1_orders_2(B,E,F) & r2_hidden(F,k4_yellow_4(B,k3_waybel_0(B,C),k3_waybel_0(B,D))) ) ) ) ) )).
fof(fraenkel_a_3_28_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v6_rltopsp1(B) & v7_rltopsp1(B) & l1_rltopsp1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_connsp_2(D,B,k4_struct_0(B)) ) => ( r2_hidden(A,a_3_28_rltopsp1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,C,E) & r2_hidden(E,k1_tops_1(B,D)) ) ) ) )).
fof(fraenkel_a_3_28_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_28_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r1_orders_2(B,E,F) & r2_hidden(F,k4_yellow_4(B,C,D)) ) ) ) ) )).
fof(fraenkel_a_3_29_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v7_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v3_group_1(B) & v5_group_1(B) & v5_vectsp_1(B) & v1_algstr_1(B) & l6_algstr_0(B) & ~ v1_xboole_0(C) & v3_ideal_1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & v3_ideal_1(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_29_ideal_1(B,C,D)) <=> ? [E] : ( m2_finseq_1(E,u1_struct_0(B)) & A = k4_rlvect_1(B,E) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( r1_xxreal_0(1,F) & r1_xxreal_0(F,k3_finseq_1(E)) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ~ ( k1_funct_1(E,F) = k8_group_1(B,G,H) & r2_hidden(G,C) & r2_hidden(H,D) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_3_29_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v6_rltopsp1(B) & v7_rltopsp1(B) & l1_rltopsp1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_connsp_2(D,B,k4_struct_0(B)) ) => ( r2_hidden(A,a_3_29_rltopsp1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_29_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_29_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r3_orders_2(B,E,F) & r2_hidden(F,k4_yellow_4(B,C,D)) ) ) ) ) )).
fof(fraenkel_a_3_2_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k4_ordinal1,k9_setfam_1(u1_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(B))))) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_2_aofa_000(B,C,D)) <=> ? [E] : ? [F] : ( m2_subset_1(E,k4_ordinal1,k4_finseq_1(u1_unialg_1(B))) & m2_finseq_2(F,u1_struct_0(B),k3_finseq_2(u1_struct_0(B))) & A = k1_funct_1(k2_pua2mss1(B,E),F) & r2_hidden(F,k1_relset_1(k3_finseq_2(u1_struct_0(B)),k2_pua2mss1(B,E))) & r1_tarski(k2_relset_1(u1_struct_0(B),F),k9_nat_1(k9_setfam_1(u1_struct_0(B)),C,D)) ) ) ) )).
fof(fraenkel_a_3_2_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_3_2_armstrng(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(B)) & A = E & r2_hidden(E,C) & r1_tarski(D,E) ) ) ) )).
fof(fraenkel_a_3_2_bhsp_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_2_bhsp_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & k3_bhsp_1(B,k5_algstr_0(B,C,E)) = D ) ) ) )).
fof(fraenkel_a_3_2_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v33_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) & l6_algstr_0(B) & ~ v2_struct_0(C) & l1_vectsp_1(C,B) & 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_hidden(A,a_3_2_bilinear(B,C,D)) <=> ? [E] : ( 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) ) ) ) )).
fof(fraenkel_a_3_2_card_lar,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_ordinal1(B) & v4_ordinal1(B) & ~ v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(B)) & v3_ordinal1(D) ) => ( r2_hidden(A,a_3_2_card_lar(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = k1_ordinal1(E) & r2_hidden(E,C) & r2_hidden(D,k1_ordinal1(E)) ) ) ) )).
fof(fraenkel_a_3_2_cc0sp2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xcmplx_0(C) & v1_xcmplx_0(D) ) => ( r2_hidden(A,a_3_2_cc0sp2(B,C,D)) <=> ? [E] : ( v1_xcmplx_0(E) & A = E & ~ r1_xxreal_0(k7_xcmplx_0(B,k2_xcmplx_0(k2_xcmplx_0(k9_complex1(C),k9_complex1(D)),1)),k9_complex1(k6_xcmplx_0(E,D))) ) ) ) )).
fof(fraenkel_a_3_2_cgames_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_cgames_1(C) & v2_cgames_1(D) ) => ( r2_hidden(A,a_3_2_cgames_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k6_cgames_1(D)) & A = k1_funct_1(k5_relat_1(B,k10_cgames_1(C)),E) & k6_cgames_1(D) != k1_xboole_0 ) ) ) )).
fof(fraenkel_a_3_2_clvect_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & m1_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_2_clvect_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & k13_csspace(B,k5_algstr_0(B,C,E)) = D ) ) ) )).
fof(fraenkel_a_3_2_compl_sp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(u1_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(B))))) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_2_compl_sp(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = k3_funct_2(k4_ordinal1,k9_setfam_1(u1_struct_0(B)),C,E) & r1_xxreal_0(D,E) ) ) ) )).
fof(fraenkel_a_3_2_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( l1_compos_1(B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(B)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ( r2_hidden(A,a_3_2_compos_1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_nat_1(E,k7_nat_d(k5_card_1(C),1)) & r2_hidden(E,k2_afinsq_1(k5_compos_1(B,D,k7_nat_d(k5_card_1(C),1)))) ) ) ) )).
fof(fraenkel_a_3_2_convex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_bhsp_1(B) & l1_bhsp_1(B) & m1_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_2_convex1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(k1_bhsp_1(B,E,C),D) ) ) ) )).
fof(fraenkel_a_3_2_convex2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_bhsp_1(B) & l1_bhsp_1(B) & m2_finseq_1(C,u1_struct_0(B)) & m2_finseq_1(D,k1_numbers) ) => ( r2_hidden(A,a_3_2_convex2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( r2_hidden(F,k9_subset_1(k4_ordinal1,k4_finseq_1(C),k4_finseq_1(D))) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ~ ( G = k1_funct_1(C,F) & r1_xxreal_0(k1_funct_1(D,F),k1_bhsp_1(B,E,G)) ) ) ) ) ) ) ) )).
fof(fraenkel_a_3_2_convex4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_csspace(B) & l1_csspace(B) & m1_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_2_convex4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(k3_complex1(k12_csspace(B,E,C)),D) ) ) ) )).
fof(fraenkel_a_3_2_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_3_2_domain_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & ( r2_hidden(E,C) | r2_hidden(E,D) ) ) ) ) )).
fof(fraenkel_a_3_2_fcont_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_2_fcont_1(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = E & r1_xxreal_0(k6_xcmplx_0(C,k7_xcmplx_0(k3_xxreal_0(D,k6_xcmplx_0(C,B)),2)),E) & r1_xxreal_0(E,k2_xcmplx_0(C,k7_xcmplx_0(k3_xxreal_0(D,k6_xcmplx_0(C,B)),2))) ) ) ) )).
fof(fraenkel_a_3_2_fcont_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_2_fcont_2(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = E & r1_xxreal_0(k1_funct_1(C,D),E) & r1_xxreal_0(E,k1_funct_1(C,B)) ) ) ) )).
fof(fraenkel_a_3_2_fdiff_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_2_fdiff_2(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = E & ~ r1_xxreal_0(E,k6_xcmplx_0(k3_xxreal_0(C,D),1)) & ~ r1_xxreal_0(B,E) ) ) ) )).
fof(fraenkel_a_3_2_filter_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_2_filter_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r3_lattices(B,C,E) & r3_lattices(B,E,D) ) ) ) )).
fof(fraenkel_a_3_2_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(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))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_2_finance1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & k3_funct_2(B,k1_numbers,C,E) = D ) ) ) )).
fof(fraenkel_a_3_2_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & ~ v2_struct_0(D) & v8_struct_0(D) & l2_fsm_1(D,B,C) ) => ( r2_hidden(A,a_3_2_fsm_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(D)) & A = E & v6_fsm_1(E,B,C,D) ) ) ) )).
fof(fraenkel_a_3_2_gobrd13,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_3_2_gobrd13(B,C,D)) <=> ? [E] : ? [F] : ( v1_xreal_0(E) & v1_xreal_0(F) & A = k19_euclid(E,F) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,B,C)),E) & r1_xxreal_0(E,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,k1_nat_1(B,1),1))) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,B,C)),F) ) ) ) )).
fof(fraenkel_a_3_2_group_11,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) & m1_group_2(C,B) & m1_group_2(D,B) ) => ( r2_hidden(A,a_3_2_group_11(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_tarski(k13_group_2(B,D,E),k8_group_2(B,C)) ) ) ) )).
fof(fraenkel_a_3_2_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,B) & l1_group_9(C,B) & v15_algstr_0(D) & m1_group_2(D,C) ) => ( r2_hidden(A,a_3_2_group_9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = k4_tarski(E,k2_partfun1(u1_struct_0(C),u1_struct_0(C),k3_group_9(B,C,E),u1_struct_0(D))) ) ) ) )).
fof(fraenkel_a_3_2_heyting1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(C,k5_finsub_1(k7_normform(B))) & m1_subset_1(D,k5_finsub_1(k7_normform(B))) ) => ( r2_hidden(A,a_3_2_heyting1(B,C,D)) <=> ? [E] : ( m2_funct_2(E,k7_normform(B),k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k9_funct_2(k7_normform(B),k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)))) & A = k6_normform(k7_normform(B),B,C,k6_funcop_1(k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B),k5_heyting1(B),E,k6_funct_3(k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B)))) & r1_tarski(k8_setwiseo(k7_normform(B),k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),E,C),D) ) ) ) )).
fof(fraenkel_a_3_2_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_2_ideal_1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k1_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_2_jgraph_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_2_jgraph_6(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) & A = E & r1_xxreal_0(k12_euclid(k5_algstr_0(k15_euclid(2),E,k19_euclid(B,C))),D) ) ) ) )).
fof(fraenkel_a_3_2_jordan2c,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) & m1_subset_1(D,u1_struct_0(k15_euclid(B))) ) => ( r2_hidden(A,a_3_2_jordan2c(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(B))) & A = E & ~ ( E != D & ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B))) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(B))))) ) => ~ ( v5_pre_topc(F,k5_topmetr,k15_euclid(B)) & r1_tarski(k2_relset_1(u1_struct_0(k15_euclid(B)),F),C) & k1_funct_1(F,k5_numbers) = D & k1_funct_1(F,1) = E ) ) ) ) ) ) )).
fof(fraenkel_a_3_2_jordan5a,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_2_jordan5a(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = E & ~ r1_xxreal_0(E,k6_xcmplx_0(C,k3_xxreal_0(k6_xcmplx_0(B,C),D))) & ~ r1_xxreal_0(k2_xcmplx_0(C,k3_xxreal_0(k6_xcmplx_0(B,C),D)),E) ) ) ) )).
fof(fraenkel_a_3_2_laplace,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & m1_subset_1(D,k4_ordinal1) ) => ( r2_hidden(A,a_3_2_laplace(B,C,D)) <=> ? [E] : ( m1_matrix_2(E,k3_matrix_2(k1_nat_1(D,1))) & A = E & k1_funct_1(E,B) = C ) ) ) )).
fof(fraenkel_a_3_2_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_2_lattice3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k4_lattices(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_2_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_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,k6_numbers))) ) => ( r2_hidden(A,a_3_2_lpspacc1(B,C,D)) <=> ? [E] : ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) & A = k17_lpspacc1(B,C,D,E) & r2_hidden(E,k13_lpspacc1(B,C,D)) ) ) ) )).
fof(fraenkel_a_3_2_lpspace1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_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,k6_numbers))) ) => ( r2_hidden(A,a_3_2_lpspace1(B,C,D)) <=> ? [E] : ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) & A = k13_lpspace1(B,C,D,E) & r2_hidden(E,k9_lpspace1(B,C,D)) ) ) ) )).
fof(fraenkel_a_3_2_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & ~ v2_struct_0(C) & l1_rlvect_1(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) ) => ( r2_hidden(A,a_3_2_mathmorp(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k1_rlvect_1(C,E,B) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_2_matrix15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & m2_finseq_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_2_matrix15(B,C,D)) <=> ? [E] : ( m2_finseq_1(E,u1_struct_0(B)) & A = E & r2_hidden(k3_matrix15(u1_struct_0(B),E),k4_matrix15(B,C,k3_matrix15(u1_struct_0(B),D))) ) ) ) )).
fof(fraenkel_a_3_2_mesfun9c,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(B,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(B,k1_numbers)))) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_2_mesfun9c(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = k1_relset_1(B,k4_mesfunc5(B,k6_numbers,k1_mesfun7c(B,C),E)) & r1_xxreal_0(E,D) ) ) ) )).
fof(fraenkel_a_3_2_metric_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( l1_metric_1(B) & m1_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_2_metric_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & k1_metric_1(B,C,E) = D ) ) ) )).
fof(fraenkel_a_3_2_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_3_2_mmlquery(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = k14_funcop_1(k1_mmlquery(B,C,E),k1_xboole_0,k1_tarski(E),k1_xboole_0) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_2_morph_01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_2_morph_01(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k5_rusub_4(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_2_msafree2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_subset_1(D,u4_struct_0(B)) ) => ( r2_hidden(A,a_3_2_msafree2(B,C,D)) <=> ? [E] : ( m1_dtconstr(E,u1_struct_0(k5_msafree(B,C)),k5_trees_3(u1_struct_0(k5_msafree(B,C))),k4_dtconstr(k5_msafree(B,C))) & A = E & ~ ( ! [F] : ~ ( r2_hidden(F,k1_funct_1(C,k2_msualg_1(B,D))) & E = k1_trees_4(k4_tarski(F,k2_msualg_1(B,D))) ) & ! [F] : ( m1_subset_1(F,u4_struct_0(B)) => ~ ( k4_tarski(F,u1_struct_0(B)) = k1_funct_1(E,k1_xboole_0) & k2_msualg_1(B,F) = k2_msualg_1(B,D) ) ) ) ) ) ) )).
fof(fraenkel_a_3_2_msaterm,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_dtconstr(D,u1_struct_0(k5_msafree(B,C)),k5_trees_3(u1_struct_0(k5_msafree(B,C))),k1_msaterm(B,C)) ) => ( r2_hidden(A,a_3_2_msaterm(B,C,D)) <=> ? [E] : ( m1_dtconstr(E,u1_struct_0(k5_msafree(B,C)),k5_trees_3(u1_struct_0(k5_msafree(B,C))),k4_dtconstr(k5_msafree(B,C))) & A = E & ~ ( ! [F] : ~ ( r2_hidden(F,k1_funct_1(C,k7_msaterm(B,C,D))) & E = k1_trees_4(k4_tarski(F,k7_msaterm(B,C,D))) ) & ! [F] : ( m1_subset_1(F,u4_struct_0(B)) => ~ ( k4_tarski(F,u1_struct_0(B)) = k1_funct_1(E,k1_xboole_0) & k2_msualg_1(B,F) = k7_msaterm(B,C,D) ) ) ) ) ) ) )).
fof(fraenkel_a_3_2_msualg_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) & v4_msualg_1(C,B) & l3_msualg_1(C,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_msualg_5(B,C)))) ) => ( r2_hidden(A,a_3_2_msualg_8(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k5_msualg_5(u1_struct_0(B),u3_msualg_1(B,C))))) & A = k15_lattice3(k5_msualg_5(u1_struct_0(B),u3_msualg_1(B,C)),E) & v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(D)) ) ) ) )).
fof(fraenkel_a_3_2_ndiff_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_2_ndiff_5(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = k3_rlvect_1(B,k1_rlvect_1(B,C,k6_xcmplx_0(1,E)),k1_rlvect_1(B,D,E)) & r1_xxreal_0(k5_numbers,E) & r1_xxreal_0(E,1) ) ) ) )).
fof(fraenkel_a_3_2_normsp_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_2_normsp_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(D,k2_normsp_0(B,k5_algstr_0(B,C,E))) ) ) ) )).
fof(fraenkel_a_3_2_ordinal6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_ordinal1(B) & v4_ordinal1(B) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & v1_classes2(C) & v3_ordinal1(D) ) => ( r2_hidden(A,a_3_2_ordinal6(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k9_xtuple_0(k5_relat_1(k11_ordinal6(C),B))) & A = k1_funct_1(k1_funct_1(k5_relat_1(k11_ordinal6(C),B),E),D) & r2_hidden(E,k9_xtuple_0(k5_relat_1(k11_ordinal6(C),B))) ) ) ) )).
fof(fraenkel_a_3_2_osafree,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v4_osalg_1(B) & v5_osalg_1(B) & v2_osalg_4(B) & l3_osalg_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)) ) => ( r2_hidden(A,a_3_2_osafree(B,C,D)) <=> ? [E] : ? [F] : ( m1_dtconstr(E,u1_struct_0(k2_osafree(B,C)),k5_trees_3(u1_struct_0(k2_osafree(B,C))),k4_dtconstr(k2_osafree(B,C))) & m1_dtconstr(F,u1_struct_0(k2_osafree(B,C)),k5_trees_3(u1_struct_0(k2_osafree(B,C))),k4_dtconstr(k2_osafree(B,C))) & A = k4_tarski(E,F) & r2_hidden(k4_tarski(E,D),k3_funct_2(k4_dtconstr(k2_osafree(B,C)),k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(B,C)),u1_struct_0(B))),k19_osafree(B,C),F)) ) ) ) )).
fof(fraenkel_a_3_2_osalg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v4_osalg_1(B) & v5_osalg_1(B) & l3_osalg_1(B) & v12_osalg_1(C,B) & l3_msualg_1(C,B) & m2_osalg_2(D,B,C) ) => ( r2_hidden(A,a_3_2_osalg_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k5_msualg_2(B,C,D)) & A = E & v1_relat_1(E) & v4_relat_1(E,u1_struct_0(B)) & v1_funct_1(E) & v1_partfun1(E,u1_struct_0(B)) & v11_osalg_1(E,B) ) ) ) )).
fof(fraenkel_a_3_2_partit1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m1_eqrel_1(C,B) ) => ( r2_hidden(A,a_3_2_partit1(B,C,D)) <=> ? [E] : ( m2_subset_1(E,k1_zfmisc_1(B),C) & A = E & ? [F] : ( r2_hidden(F,D) & k8_subset_1(B,E,F) != k1_xboole_0 ) ) ) ) )).
fof(fraenkel_a_3_2_pdiff_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & m2_finseq_2(C,k1_numbers,k1_euclid(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_2_pdiff_6(B,C,D)) <=> ? [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(B)) & A = E & ~ r1_xxreal_0(D,k12_euclid(k8_euclid(B,E,C))) ) ) ) )).
fof(fraenkel_a_3_2_pdiff_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,u1_struct_0(k4_real_ns1(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_2_pdiff_7(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(B))) & A = E & ~ r1_xxreal_0(D,k2_normsp_0(k4_real_ns1(B),k5_algstr_0(k4_real_ns1(B),E,C))) ) ) ) )).
fof(fraenkel_a_3_2_pralg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & ~ v2_struct_0(C) & ~ v11_struct_0(C) & l1_msualg_1(C) & v1_relat_1(D) & v4_relat_1(D,B) & v1_funct_1(D) & v1_partfun1(D,B) & v1_funcop_1(D) ) => ( r2_hidden(A,a_3_2_pralg_3(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(C)) & m1_subset_1(F,B) & A = k1_funct_1(k1_funct_1(D,F),E) ) ) ) )).
fof(fraenkel_a_3_2_qc_lang3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & m1_qc_lang1(C) & v3_card_1(D,B) & m2_finseq_1(D,k2_qc_lang1(C)) ) => ( r2_hidden(A,a_3_2_qc_lang3(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_funct_1(D,E) & r1_xxreal_0(1,E) & r1_xxreal_0(E,k3_finseq_1(D)) & r2_hidden(k1_funct_1(D,E),k5_qc_lang1(C)) ) ) ) )).
fof(fraenkel_a_3_2_qc_lang4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(B) & m1_subset_1(C,k9_qc_lang1(B)) & m1_trees_2(D,k9_xtuple_0(k2_qc_lang4(B,C))) ) => ( r2_hidden(A,a_3_2_qc_lang4(B,C,D)) <=> ? [E] : ( m1_trees_1(E,k9_xtuple_0(k2_qc_lang4(B,C))) & A = k3_trees_2(k9_qc_lang1(B),k2_qc_lang4(B,C),E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_2_rinfsup2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) & m1_subset_1(C,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => ( r2_hidden(A,a_3_2_rinfsup2(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k12_supinf_2(B,k2_xcmplx_0(C,E)) & r1_xxreal_0(D,E) ) ) ) )).
fof(fraenkel_a_3_2_rlaffin1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_2_rlaffin1(B,C,D)) <=> ? [E] : ( v2_rusub_4(E,B) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & r1_tarski(k5_rusub_4(B,D,k4_algstr_0(B,C)),E) ) ) ) )).
fof(fraenkel_a_3_2_rlsub_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_rlsub_1(D,B) ) => ( r2_hidden(A,a_3_2_rlsub_2(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,F,E) & r1_struct_0(D,F) & r1_struct_0(C,E) ) ) ) )).
fof(fraenkel_a_3_2_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_2_rltopsp1(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = k3_rlvect_1(B,k1_rlvect_1(B,C,k6_xcmplx_0(1,E)),k1_rlvect_1(B,D,E)) ) ) ) )).
fof(fraenkel_a_3_2_rusub_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_rusub_1(D,B) ) => ( r2_hidden(A,a_3_2_rusub_2(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,E,F) & r1_struct_0(D,E) & r1_struct_0(C,F) ) ) ) )).
fof(fraenkel_a_3_2_rusub_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_rlvect_1(B) & v2_rusub_4(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_2_rusub_5(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k1_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,k6_domain_1(u1_struct_0(B),k4_algstr_0(B,D))) ) ) ) )).
fof(fraenkel_a_3_2_seq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & m1_subset_1(C,k1_zfmisc_1(k12_seq_4(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_2_seq_4(B,C,D)) <=> ? [E] : ( m2_finseq_2(E,k2_numbers,k12_seq_4(B)) & A = E & ~ r1_xxreal_0(D,k22_seq_4(B,E,C)) ) ) ) )).
fof(fraenkel_a_3_2_setlim_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & ~ v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,C))) ) => ( r2_hidden(A,a_3_2_setlim_1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_funct_1(D,E) & r1_xxreal_0(B,E) ) ) ) )).
fof(fraenkel_a_3_2_simplex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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_matroid0(C) & m1_simplex0(C,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) ) => ( r2_hidden(A,a_3_2_simplex1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k1_rlaffin2(B,E) & r1_tarski(E,k1_simplex1(B,C,D)) ) ) ) )).
fof(fraenkel_a_3_2_sprect_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & ~ 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))) ) => ( r2_hidden(A,a_3_2_sprect_2(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k2_topreal1(2,D,E) & r1_xxreal_0(B,E) & ~ r1_xxreal_0(C,E) ) ) ) )).
fof(fraenkel_a_3_2_sprect_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & m2_finseq_1(D,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_3_2_sprect_3(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k2_topreal1(2,D,E) & r1_xxreal_0(B,E) & ~ r1_xxreal_0(k7_nat_d(C,1),E) ) ) ) )).
fof(fraenkel_a_3_2_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & m1_subset_1(C,u1_struct_0(k15_euclid(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_2_topreal9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(B))) & A = E & k12_euclid(k5_algstr_0(k15_euclid(B),E,C)) = D ) ) ) )).
fof(fraenkel_a_3_2_uproots,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v6_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) & v1_vectsp_2(B) & l6_algstr_0(B) & m1_subset_1(C,u1_struct_0(B)) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(D,B) & v1_uproots(D,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( r2_hidden(A,a_3_2_uproots(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = E & ? [F] : ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(F,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) & r2_funct_2(k4_ordinal1,u1_struct_0(B),D,k13_polynom3(B,k2_polynom5(B,k4_polynom5(B,k4_algstr_0(B,C),k5_struct_0(B)),E),F)) ) ) ) ) )).
fof(fraenkel_a_3_2_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_relat_1(C) & v1_funct_1(C) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_2_valued_1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k2_xcmplx_0(E,D) & r2_hidden(E,k9_xtuple_0(k3_relat_1(B,C))) ) ) ) )).
fof(fraenkel_a_3_2_vectsp_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(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) & m1_vectsp_6(D,B,C) ) => ( r2_hidden(A,a_3_2_vectsp_6(B,C,D)) <=> ? [E] : ( 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) ) ) ) )).
fof(fraenkel_a_3_2_waybel11,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,C,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,u1_struct_0(B)))) ) => ( r2_hidden(A,a_3_2_waybel11(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k3_waybel11(B,C,D))) & A = k2_waybel_0(B,k3_waybel11(B,C,D),E) ) ) ) )).
fof(fraenkel_a_3_2_waybel14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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_tops_2(C,B) & v1_cantor_1(C,B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & m1_subset_1(D,u1_struct_0(k1_yellow_1(k5_waybel11(B)))) ) => ( r2_hidden(A,a_3_2_waybel14(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & r2_hidden(E,C) & r1_tarski(E,D) ) ) ) )).
fof(fraenkel_a_3_2_waybel16,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_2_waybel16(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k12_lattice3(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_2_waybel23,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v4_yellow_0(C,B) & v6_yellow_0(C,B) & m1_yellow_0(C,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) ) => ( r2_hidden(A,a_3_2_waybel23(B,C,D)) <=> ? [E] : ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(D)) & A = k1_yellow_0(C,E) & r1_yellow_0(C,E) ) ) ) )).
fof(fraenkel_a_3_2_waybel30,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) & v4_waybel11(C) & m1_yellow_9(C,B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_2_waybel30(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) & A = k2_yellow_0(C,E) & r2_hidden(D,E) & r2_hidden(E,k5_waybel11(C)) ) ) ) )).
fof(fraenkel_a_3_2_waybel32,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_2_waybel32(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k2_waybel_0(B,C,E) & r1_orders_2(C,D,E) ) ) ) )).
fof(fraenkel_a_3_2_waybel33,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_2_waybel33(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k2_waybel_0(B,C,E) & r1_orders_2(C,D,E) ) ) ) )).
fof(fraenkel_a_3_2_waybel_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_2_waybel_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r3_orders_2(B,k12_lattice3(B,C,E),D) ) ) ) )).
fof(fraenkel_a_3_2_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & v1_waybel_0(C,k3_yellow_3(B,B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,B)))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_2_waybel_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,D,E) & r2_hidden(E,k5_yellow_3(B,B,C)) ) ) ) )).
fof(fraenkel_a_3_2_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & ~ v1_xboole_0(D) & v12_waybel_0(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_2_waybel_4(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k12_lattice3(B,E,F) & r2_hidden(E,k6_domain_1(u1_struct_0(B),C)) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_2_yellow12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_2_yellow12(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k13_lattice3(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_2_yellow13,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m2_yellow13(C,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_2_yellow13(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & r2_hidden(E,k1_tdlat_2(B,C)) & r1_tarski(k1_tops_1(B,E),D) ) ) ) )).
fof(fraenkel_a_3_2_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_2_yellow_4(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k11_lattice3(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_2_yellow_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & v1_cantor_1(C,B) & v1_tops_2(C,B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_2_yellow_8(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & r2_hidden(E,C) & r1_tarski(E,k1_tops_1(B,D)) ) ) ) )).
fof(fraenkel_a_3_2_yellow_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) => ( r2_hidden(A,a_3_2_yellow_9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(B)) & A = E & r2_hidden(E,C) & r1_tarski(E,D) ) ) ) )).
fof(fraenkel_a_3_2_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) & m1_subset_1(D,B) ) => ( r2_hidden(A,a_3_2_zf_fund1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,B) & m1_subset_1(F,B) & A = k9_classes2(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_2_zf_fund2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,B) & 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,a_3_2_zf_fund2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & r1_zf_model(B,k2_zf_lang1(B,k2_zf_lang1(B,D,k2_zf_lang(1),C),k2_zf_lang(k5_numbers),E),k8_zf_lang(k2_zf_lang(2),k11_zf_lang(k5_zf_lang(k2_zf_lang(2),k2_zf_lang(k5_numbers)),k5_zf_lang(k2_zf_lang(2),k2_zf_lang(1))))) ) ) ) )).
fof(fraenkel_a_3_2_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(C,B) & m1_zmodul01(D,B) ) => ( r2_hidden(A,a_3_2_zmodul01(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,F,E) & r1_struct_0(C,F) & r1_struct_0(D,E) ) ) ) )).
fof(fraenkel_a_3_30_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v6_rltopsp1(B) & v7_rltopsp1(B) & l1_rltopsp1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_connsp_2(D,B,k4_struct_0(B)) ) => ( r2_hidden(A,a_3_30_rltopsp1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,E,F) & r2_hidden(E,C) & r2_hidden(F,k1_convex1(B,k1_tops_1(B,k1_convex1(B,D,k4_xcmplx_0(1))),k4_xcmplx_0(1))) ) ) ) )).
fof(fraenkel_a_3_30_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_30_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r3_orders_2(B,E,F) & r2_hidden(F,k4_yellow_4(B,k3_waybel_0(B,C),k3_waybel_0(B,D))) ) ) ) ) )).
fof(fraenkel_a_3_31_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v6_rltopsp1(B) & v7_rltopsp1(B) & l1_rltopsp1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_31_rltopsp1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,E,F) & r2_hidden(E,k2_pre_topc(B,C)) & r2_hidden(F,k2_pre_topc(B,D)) ) ) ) )).
fof(fraenkel_a_3_31_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_31_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r1_orders_2(B,F,E) & r2_hidden(F,k4_yellow_4(B,k4_waybel_0(B,C),k4_waybel_0(B,D))) ) ) ) ) )).
fof(fraenkel_a_3_32_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v6_rltopsp1(B) & v7_rltopsp1(B) & l1_rltopsp1(B) & m1_connsp_2(C,B,k4_struct_0(B)) & v2_xxreal_0(D) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_32_rltopsp1(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = k1_convex1(B,C,E) & ~ r1_xxreal_0(D,k9_complex1(E)) ) ) ) )).
fof(fraenkel_a_3_32_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_32_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r1_orders_2(B,F,E) & r2_hidden(F,k4_yellow_4(B,C,D)) ) ) ) ) )).
fof(fraenkel_a_3_33_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v6_rltopsp1(B) & v7_rltopsp1(B) & l1_rltopsp1(B) & m1_connsp_2(C,B,k4_struct_0(B)) & v2_xxreal_0(D) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_33_rltopsp1(B,C,D)) <=> ? [E] : ( ~ v8_ordinal1(E) & v1_xreal_0(E) & A = k1_convex1(B,k1_tops_1(B,C),E) & ~ r1_xxreal_0(D,k9_complex1(E)) ) ) ) )).
fof(fraenkel_a_3_33_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_33_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r1_orders_2(B,F,E) & r2_hidden(F,k4_yellow_4(B,C,D)) ) ) ) ) )).
fof(fraenkel_a_3_34_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v6_rltopsp1(B) & v7_rltopsp1(B) & l1_rltopsp1(B) & v2_xxreal_0(C) & v1_xreal_0(C) & m1_connsp_2(D,B,k4_struct_0(B)) ) => ( r2_hidden(A,a_3_34_rltopsp1(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = k1_convex1(B,D,E) & ~ r1_xxreal_0(C,k9_complex1(E)) ) ) ) )).
fof(fraenkel_a_3_34_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_34_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r1_orders_2(B,F,E) & r2_hidden(F,k4_yellow_4(B,k4_waybel_0(B,C),k4_waybel_0(B,D))) ) ) ) ) )).
fof(fraenkel_a_3_37_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v6_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v1_vectsp_1(B) & v1_algstr_1(B) & l6_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_37_ideal_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k8_group_1(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_38_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v6_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v1_vectsp_1(B) & v1_algstr_1(B) & l6_algstr_0(B) & ~ v1_xboole_0(C) & v1_ideal_1(C,B) & v3_ideal_1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_38_ideal_1(B,C,D)) <=> ? [E] : ( m2_finseq_1(E,u1_struct_0(B)) & A = k4_rlvect_1(B,E) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( r1_xxreal_0(1,F) & r1_xxreal_0(F,k3_finseq_1(E)) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ~ ( k1_funct_1(E,F) = k8_group_1(B,G,H) & r2_hidden(G,k16_ideal_1(B,C,D)) & r2_hidden(H,D) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_3_39_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v6_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v1_vectsp_1(B) & v1_algstr_1(B) & l6_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_39_ideal_1(B,C,D)) <=> ? [E] : ( m2_finseq_1(E,u1_struct_0(B)) & A = k4_rlvect_1(B,E) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( r1_xxreal_0(1,F) & r1_xxreal_0(F,k3_finseq_1(E)) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ~ ( k1_funct_1(E,F) = k8_group_1(B,G,H) & r2_hidden(G,C) & r2_hidden(H,D) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_3_3_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_3_3_armstrng(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & ~ r2_hidden(E,D) & ? [F] : ( r2_hidden(F,C) & r2_hidden(E,F) ) ) ) ) )).
fof(fraenkel_a_3_3_borsuk_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v1_compts_1(B) & l1_pre_topc(B) & ~ v2_struct_0(C) & v2_pre_topc(C) & v1_compts_1(C) & l1_pre_topc(C) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k2_borsuk_1(C,B))))) ) => ( r2_hidden(A,a_3_3_borsuk_3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_tarski(k3_borsuk_1(C,B,k2_struct_0(C),k6_domain_1(u1_struct_0(B),E)),k5_setfam_1(u1_struct_0(k2_borsuk_1(C,B)),D)) ) ) ) )).
fof(fraenkel_a_3_3_card_fin,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_finset_1(B) & v1_finset_1(C) & 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,a_3_3_card_fin(B,C,D)) <=> ? [E] : ( v1_funct_1(E) & v1_funct_2(E,B,k2_relset_1(C,D)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k2_relset_1(C,D)))) & A = E & v2_funct_1(E) & ! [F] : ~ ( r2_hidden(F,B) & k1_funct_1(E,F) = k1_funct_1(D,F) ) ) ) ) )).
fof(fraenkel_a_3_3_chain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(B,k4_ordinal1) & ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) & m1_chain_1(D,C) ) => ( r2_hidden(A,a_3_3_chain_1(B,C,D)) <=> ? [E] : ? [F] : ( m2_finseq_2(E,k1_numbers,k1_euclid(C)) & m2_finseq_2(F,k1_numbers,k1_euclid(C)) & A = k3_chain_1(C,E,F) & ~ ( ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k2_finseq_1(C))) => ~ ( k5_card_1(G) = B & ! [H] : ( m2_subset_1(H,k4_ordinal1,k2_finseq_1(C)) => ( ( r2_hidden(H,G) & ~ r1_xxreal_0(k1_funct_1(F,H),k1_funct_1(E,H)) & m2_chain_1(k4_tarski(k1_funct_1(E,H),k1_funct_1(F,H)),k2_chain_1(C,D,H)) ) | ( ~ r2_hidden(H,G) & k1_funct_1(E,H) = k1_funct_1(F,H) & r2_hidden(k1_funct_1(E,H),k2_chain_1(C,D,H)) ) ) ) ) ) & ~ ( B = C & ! [G] : ( m2_subset_1(G,k4_ordinal1,k2_finseq_1(C)) => ( ~ r1_xxreal_0(k1_funct_1(E,G),k1_funct_1(F,G)) & m2_chain_1(k4_tarski(k1_funct_1(E,G),k1_funct_1(F,G)),k2_chain_1(C,D,G)) ) ) ) ) ) ) ) )).
fof(fraenkel_a_3_3_circled1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(u1_struct_0(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_3_circled1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_rlvect_1(B,E,D) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_3_circuit1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & v5_msafree2(B) & l1_msualg_1(B) & v4_msualg_1(C,B) & v4_msafree2(C,B) & l3_msualg_1(C,B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_3_circuit1(B,C,D)) <=> ? [E] : ( m1_dtconstr(E,u1_struct_0(k5_msafree(B,u3_msualg_1(B,C))),k5_trees_3(u1_struct_0(k5_msafree(B,u3_msualg_1(B,C)))),k4_dtconstr(k5_msafree(B,u3_msualg_1(B,C)))) & A = E & ~ ( ! [F] : ~ ( r2_hidden(F,k1_funct_1(u3_msualg_1(B,C),D)) & E = k1_trees_4(k4_tarski(F,D)) ) & ! [F] : ( m1_subset_1(F,u4_struct_0(B)) => ~ ( k4_tarski(F,u1_struct_0(B)) = k1_funct_1(E,k1_xboole_0) & k2_msualg_1(B,F) = D ) ) ) ) ) ) )).
fof(fraenkel_a_3_3_combgras,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( l1_incsp_1(B) & l1_combgras(C,B,B) & m1_subset_1(D,k1_zfmisc_1(u1_incsp_1(B))) ) => ( r2_hidden(A,a_3_3_combgras(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_incsp_1(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_incsp_1(B)) & r2_hidden(F,D) & k2_combgras(B,B,C,F) = E ) ) ) ) )).
fof(fraenkel_a_3_3_convex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_bhsp_1(B) & l1_bhsp_1(B) & m1_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_3_convex1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_xxreal_0(k1_bhsp_1(B,E,C),D) ) ) ) )).
fof(fraenkel_a_3_3_convex2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_bhsp_1(B) & l1_bhsp_1(B) & m2_finseq_1(C,u1_struct_0(B)) & m2_finseq_1(D,k1_numbers) ) => ( r2_hidden(A,a_3_3_convex2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( r2_hidden(F,k9_subset_1(k4_ordinal1,k4_finseq_1(C),k4_finseq_1(D))) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ~ ( G = k1_funct_1(C,F) & ~ r1_xxreal_0(k1_bhsp_1(B,E,G),k1_funct_1(D,F)) ) ) ) ) ) ) ) )).
fof(fraenkel_a_3_3_convex4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_csspace(B) & l1_csspace(B) & m1_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_3_convex4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_xxreal_0(k3_complex1(k12_csspace(B,E,C)),D) ) ) ) )).
fof(fraenkel_a_3_3_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_3_3_domain_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & r2_hidden(E,C) & ~ r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_3_fcont_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & m1_subset_1(C,k1_numbers) & m1_subset_1(D,k1_numbers) ) => ( r2_hidden(A,a_3_3_fcont_1(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = E & ~ r1_xxreal_0(E,k6_xcmplx_0(B,k3_xxreal_0(k6_xcmplx_0(D,B),k6_xcmplx_0(B,C)))) & ~ r1_xxreal_0(k2_xcmplx_0(B,k3_xxreal_0(k6_xcmplx_0(D,B),k6_xcmplx_0(B,C))),E) ) ) ) )).
fof(fraenkel_a_3_3_fcont_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_3_fcont_2(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = E & r1_xxreal_0(k1_funct_1(C,B),E) & r1_xxreal_0(E,k1_funct_1(C,D)) ) ) ) )).
fof(fraenkel_a_3_3_fdiff_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_3_fdiff_2(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = E & ~ r1_xxreal_0(E,B) & ~ r1_xxreal_0(k2_xcmplx_0(k4_xxreal_0(C,D),1),E) ) ) ) )).
fof(fraenkel_a_3_3_filter_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) & ~ v1_xboole_0(C) & v18_lattices(C,B) & v21_lattices(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & v18_lattices(D,B) & v21_lattices(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_3_filter_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k1_lattice2(B))) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(k1_lattice2(B))) & ? [G] : ( m1_subset_1(G,u1_struct_0(k1_lattice2(B))) & r3_lattices(k1_lattice2(B),k4_lattices(k1_lattice2(B),F,G),E) & r2_hidden(F,C) & r2_hidden(G,D) ) ) ) ) ) )).
fof(fraenkel_a_3_3_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_3_finance1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k6_numbers) & A = E & r1_xxreal_0(B,E) & ~ r1_xxreal_0(k2_xcmplx_0(C,k7_xcmplx_0(1,k1_nat_1(D,1))),E) ) ) ) )).
fof(fraenkel_a_3_3_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) & m1_subset_1(D,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C))))) ) => ( r2_hidden(A,a_3_3_fomodel4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_mcart_1(k1_zfmisc_1(k1_fomodel4(C)),k1_zfmisc_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C))))) & A = k7_relset_1(k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C)),E,k1_tarski(B)) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_3_gobrd13,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_3_3_gobrd13(B,C,D)) <=> ? [E] : ? [F] : ( v1_xreal_0(E) & v1_xreal_0(F) & A = k19_euclid(E,F) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,B,C)),E) & r1_xxreal_0(E,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,k1_nat_1(B,1),C))) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,B,C)),F) & r1_xxreal_0(F,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,B,k1_nat_1(C,1)))) ) ) ) )).
fof(fraenkel_a_3_3_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v6_graph_1(B) & l1_graph_1(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_3_graph_3(B,C,D)) <=> ? [E] : ( m2_finseq_2(E,D,k3_finseq_2(D)) & A = E & v2_funct_1(E) & m2_graph_1(E,B) & ~ v1_xboole_0(E) & ? [F] : ( m2_finseq_1(F,u1_struct_0(B)) & r1_graph_2(B,F,E) & k1_funct_1(F,1) = C ) ) ) ) )).
fof(fraenkel_a_3_3_group_11,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) & m1_group_2(C,B) & m1_group_2(D,B) ) => ( r2_hidden(A,a_3_3_group_11(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xboole_0(k13_group_2(B,D,E),k8_group_2(B,C)) ) ) ) )).
fof(fraenkel_a_3_3_heyting1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m2_subset_1(C,k5_finsub_1(k7_normform(B)),k8_normform(B)) & m2_funct_2(D,k7_normform(B),k1_heyting1(B),k9_funct_2(k7_normform(B),k1_heyting1(B))) ) => ( r2_hidden(A,a_3_3_heyting1(B,C,D)) <=> ? [E] : ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B)) & A = k3_funct_2(k7_normform(B),k1_heyting1(B),D,E) & r2_hidden(k3_funct_2(k7_normform(B),k1_heyting1(B),D,E),k3_domain_1(k5_finsub_1(B),k5_finsub_1(B),E)) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_3_heyting2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_finset_1(C) & m2_subset_1(D,k5_finsub_1(k4_partfun1(B,C)),k1_substlat(B,C)) ) => ( r2_hidden(A,a_3_3_heyting2(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,k4_partfun1(B,C)) & m1_subset_1(F,k4_partfun1(B,C)) & A = k2_xboole_0(E,F) & r2_hidden(E,D) & r2_hidden(F,k2_heyting2(B,C,D)) & r1_partfun1(E,F) ) ) ) )).
fof(fraenkel_a_3_3_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_3_ideal_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r2_hidden(E,C) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_3_jgraph_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_3_jgraph_6(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) & A = E & ~ r1_xxreal_0(k12_euclid(k5_algstr_0(k15_euclid(2),E,k19_euclid(B,C))),D) ) ) ) )).
fof(fraenkel_a_3_3_laplace,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & m1_subset_1(D,k4_ordinal1) ) => ( r2_hidden(A,a_3_3_laplace(B,C,D)) <=> ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k2_xboole_0(k6_subset_1(k2_setwop_2(k1_nat_1(D,1)),k1_tarski(B)),k1_tarski(B)),k2_xboole_0(k6_subset_1(k2_setwop_2(k1_nat_1(D,1)),k1_tarski(C)),k1_tarski(C))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k2_xboole_0(k6_subset_1(k2_setwop_2(k1_nat_1(D,1)),k1_tarski(B)),k1_tarski(B)),k2_xboole_0(k6_subset_1(k2_setwop_2(k1_nat_1(D,1)),k1_tarski(C)),k1_tarski(C))))) & A = E & v2_funct_1(E) & k1_funct_1(E,B) = C ) ) ) )).
fof(fraenkel_a_3_3_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_3_lattice3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k4_lattices(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_3_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_rlvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_3_mathmorp(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_tarski(k1_mathmorp(B,E,D),C) ) ) ) )).
fof(fraenkel_a_3_3_matrtop1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & m1_subset_1(C,u1_struct_0(k15_euclid(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) ) => ( r2_hidden(A,a_3_3_matrtop1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(B))) & A = k1_algstr_0(k15_euclid(B),C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_3_mesfun9c,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v7_ordinal1(C) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(B,k2_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(B,k2_numbers)))) ) => ( r2_hidden(A,a_3_3_mesfun9c(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = k1_relset_1(B,k4_mesfunc5(B,k1_numbers,k11_mesfun7c(B,D),E)) & r1_xxreal_0(E,C) ) ) ) )).
fof(fraenkel_a_3_3_metric_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & ~ v2_struct_0(C) & l1_metric_1(C) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_3_metric_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = E & ~ r1_xxreal_0(B,k1_metric_1(C,D,E)) ) ) ) )).
fof(fraenkel_a_3_3_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m2_finseq_1(C,k9_setfam_1(B)) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_3_mmlquery(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & r1_xxreal_0(D,k24_mmlquery(C,E)) ) ) ) )).
fof(fraenkel_a_3_3_morph_01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_3_morph_01(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & k9_subset_1(u1_struct_0(B),k5_rusub_4(B,k6_mathmorp(k4_xcmplx_0(1),B,D),E),C) != k1_xboole_0 ) ) ) )).
fof(fraenkel_a_3_3_msafree3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v11_struct_0(B) & v1_instalg1(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)) ) => ( r2_hidden(A,a_3_3_msafree3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k5_msafree(B,C))) & A = k2_trees_4(u1_struct_0(k5_msafree(B,C)),E) & r2_hidden(E,k1_lang1(k5_msafree(B,C))) & k2_xtuple_0(E) = D ) ) ) )).
fof(fraenkel_a_3_3_msualg_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) & v4_msualg_1(C,B) & l3_msualg_1(C,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_msualg_5(u1_struct_0(B),u3_msualg_1(B,C))))) ) => ( r2_hidden(A,a_3_3_msualg_8(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k5_msualg_5(u1_struct_0(B),u3_msualg_1(B,C)))) & A = E & v2_msualg_4(E,B,C) & v3_msualg_4(E,B,C) & m1_msualg_4(E,u1_struct_0(B),u3_msualg_1(B,C),u3_msualg_1(B,C)) & r3_lattices(k5_msualg_5(u1_struct_0(B),u3_msualg_1(B,C)),k15_lattice3(k5_msualg_5(u1_struct_0(B),u3_msualg_1(B,C)),D),E) ) ) ) )).
fof(fraenkel_a_3_3_ndiff_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_3_ndiff_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(D,k2_normsp_0(B,k5_algstr_0(B,E,k6_normsp_1(B,C)))) ) ) ) )).
fof(fraenkel_a_3_3_normsp_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_3_normsp_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_xxreal_0(k2_normsp_0(B,k5_algstr_0(B,C,E)),D) ) ) ) )).
fof(fraenkel_a_3_3_ordinal6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_ordinal1(B) & v4_ordinal1(B) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & v1_classes2(C) ) => ( r2_hidden(A,a_3_3_ordinal6(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k9_xtuple_0(k5_relat_1(k11_ordinal6(C),B))) & A = k1_funct_1(k1_funct_1(k5_relat_1(k11_ordinal6(C),B),E),D) & r2_hidden(E,k9_xtuple_0(k5_relat_1(k11_ordinal6(C),B))) ) ) ) )).
fof(fraenkel_a_3_3_osafree,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v4_osalg_1(B) & v5_osalg_1(B) & v2_osalg_4(B) & l3_osalg_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_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_3_osafree(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k2_osafree(B,C))) & A = k2_trees_4(u1_struct_0(k2_osafree(B,C)),E) & r2_hidden(E,k6_dtconstr(k2_osafree(B,C))) & k2_xtuple_0(E) = D ) ) ) )).
fof(fraenkel_a_3_3_osalg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v4_osalg_1(B) & v5_osalg_1(B) & l3_osalg_1(B) & v12_osalg_1(C,B) & l3_msualg_1(C,B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_3_osalg_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_funct_1(k2_msualg_2(B,C),E) & r3_orders_2(B,E,D) ) ) ) )).
fof(fraenkel_a_3_3_pdiff_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,u1_struct_0(k4_real_ns1(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_3_pdiff_6(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(B))) & A = E & ~ r1_xxreal_0(D,k2_normsp_0(k4_real_ns1(B),k5_algstr_0(k4_real_ns1(B),E,C))) ) ) ) )).
fof(fraenkel_a_3_3_pdiff_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,u1_struct_0(k4_real_ns1(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_3_pdiff_7(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(B))) & A = E & ~ r1_xxreal_0(D,k2_normsp_0(k4_real_ns1(B),k5_algstr_0(k4_real_ns1(B),E,C))) ) ) ) )).
fof(fraenkel_a_3_3_qc_lang3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & m1_qc_lang1(C) & v3_card_1(D,B) & m2_finseq_1(D,k2_qc_lang1(C)) ) => ( r2_hidden(A,a_3_3_qc_lang3(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_funct_1(D,E) & r1_xxreal_0(1,E) & r1_xxreal_0(E,k3_finseq_1(D)) & r2_hidden(k1_funct_1(D,E),k4_qc_lang1(C)) ) ) ) )).
fof(fraenkel_a_3_3_qc_lang4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(B) & m1_subset_1(C,k9_qc_lang1(B)) & m1_qc_lang4(D,B,C) ) => ( r2_hidden(A,a_3_3_qc_lang4(B,C,D)) <=> ? [E] : ( m2_qc_lang4(E,B,C,D) & A = E & E = E ) ) ) )).
fof(fraenkel_a_3_3_rlaffin1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_3_rlaffin1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,k4_algstr_0(B,D),E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_3_rlaffin3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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) & v1_rlaffin1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_3_rlaffin3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_algstr_0(B,k4_algstr_0(B,D),E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_3_rlsub_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & v1_rlvect_1(D) & m1_rlsub_1(D,B) ) => ( r2_hidden(A,a_3_3_rlsub_2(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,F,E) & r1_struct_0(C,F) & r1_struct_0(D,E) ) ) ) )).
fof(fraenkel_a_3_3_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_3_rltopsp1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k1_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_3_rmod_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & ~ 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) & m1_rmod_4(D,B,C) ) => ( r2_hidden(A,a_3_3_rmod_4(B,C,D)) <=> ? [E] : ( 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) ) ) ) )).
fof(fraenkel_a_3_3_rusub_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & v1_bhsp_1(D) & m1_rusub_1(D,B) ) => ( r2_hidden(A,a_3_3_rusub_2(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,E,F) & r1_struct_0(C,E) & r1_struct_0(D,F) ) ) ) )).
fof(fraenkel_a_3_3_rusub_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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_rlvect_1(C) & m1_rlsub_1(C,B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_3_rusub_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,D,E) & r1_struct_0(C,E) ) ) ) )).
fof(fraenkel_a_3_3_rusub_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_rlvect_1(B) & v2_rusub_4(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_3_rusub_5(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,E,F) & r2_hidden(E,C) & r2_hidden(F,k6_domain_1(u1_struct_0(B),D)) ) ) ) )).
fof(fraenkel_a_3_3_setlim_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_3_setlim_1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_funct_1(C,E) & r1_xxreal_0(D,E) ) ) ) )).
fof(fraenkel_a_3_3_simplex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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_matroid0(C) & v3_matroid0(C) & v2_simplex1(C,B) & m1_simplex0(C,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) ) => ( r2_hidden(A,a_3_3_simplex1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k1_rlaffin2(B,E) & r1_tarski(E,k1_simplex1(B,C,D)) ) ) ) )).
fof(fraenkel_a_3_3_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_3_topreal9(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = k3_rlvect_1(B,k1_rlvect_1(B,C,k6_xcmplx_0(1,E)),k1_rlvect_1(B,D,E)) & r1_xxreal_0(k5_numbers,E) ) ) ) )).
fof(fraenkel_a_3_3_trees_a,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) & v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) & m1_trees_1(D,k9_xtuple_0(B)) ) => ( r2_hidden(A,a_3_3_trees_a(B,C,D)) <=> ? [E] : ? [F] : ( m1_trees_1(E,k9_xtuple_0(B)) & m1_trees_1(F,k9_xtuple_0(C)) & A = k8_finseq_1(k4_ordinal1,E,F) & r2_hidden(E,k2_trees_a(k9_xtuple_0(B),D)) ) ) ) )).
fof(fraenkel_a_3_3_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_relat_1(C) & v1_funct_1(C) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_3_valued_1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k2_xcmplx_0(E,D) & r2_hidden(E,k2_xboole_0(k9_xtuple_0(B),k9_xtuple_0(C))) ) ) ) )).
fof(fraenkel_a_3_3_vectsp_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & ~ 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) & m1_vectsp_6(D,B,C) ) => ( r2_hidden(A,a_3_3_vectsp_6(B,C,D)) <=> ? [E] : ( 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) ) ) ) )).
fof(fraenkel_a_3_3_waybel12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_3_waybel12(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_3_waybel14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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_tops_2(C,B) & v1_cantor_1(C,B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_3_waybel14(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & r2_hidden(E,C) & r1_tarski(E,k3_subset_1(u1_struct_0(B),k5_waybel_0(B,k1_yellow_0(B,k2_waybel_8(B,D))))) ) ) ) )).
fof(fraenkel_a_3_3_waybel16,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k7_lattice3(B)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k7_lattice3(B)))) ) => ( r2_hidden(A,a_3_3_waybel16(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(k7_lattice3(B))) & m1_subset_1(F,u1_struct_0(k7_lattice3(B))) & A = k13_lattice3(k7_lattice3(B),E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_3_waybel17,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) & ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_3_waybel17(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k2_waybel_0(B,C,E) & r1_orders_2(C,D,E) ) ) ) )).
fof(fraenkel_a_3_3_waybel21,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m2_yellow_6(D,B,C) ) => ( r2_hidden(A,a_3_3_waybel21(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(D)) & A = k2_yellow_0(B,a_4_3_waybel21(B,C,D,E)) ) ) ) )).
fof(fraenkel_a_3_3_waybel30,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) & v2_waybel_2(B) & l1_waybel_9(B) & v4_waybel11(C) & m1_yellow_9(C,B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_3_waybel30(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) & A = k2_yellow_0(C,E) & r2_hidden(D,E) & r2_hidden(E,k5_waybel11(C)) ) ) ) )).
fof(fraenkel_a_3_3_waybel33,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v25_waybel_0(B) & v2_lattice3(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_3_waybel33(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k2_waybel_0(B,C,E) & r1_orders_2(C,D,E) ) ) ) )).
fof(fraenkel_a_3_3_waybel_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_3_waybel_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_3_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & v2_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & v1_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & v1_waybel_0(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_3_waybel_2(B,C,D)) <=> ? [E] : ( ~ v1_xboole_0(E) & v1_waybel_0(E,B) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & E = k4_yellow_4(B,k6_domain_1(u1_struct_0(B),F),D) & r2_hidden(F,C) ) ) ) ) )).
fof(fraenkel_a_3_3_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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_waybel_0(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_3_waybel_4(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k12_lattice3(B,E,F) & r2_hidden(E,k6_domain_1(u1_struct_0(B),C)) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_3_waybel_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v1_waybel_5(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_3_waybel_5(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_3_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v2_pre_topc(B) & v8_pre_topc(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v1_compts_1(B) & l1_waybel_9(B) & ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_3_waybel_9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & k12_lattice3(B,E,k2_waybel_0(B,C,D)) = k2_waybel_0(B,C,D) ) ) ) )).
fof(fraenkel_a_3_3_yellow12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_3_yellow12(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k10_lattice3(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_3_yellow19,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_3_yellow19(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = E & r1_orders_2(C,D,E) ) ) ) )).
fof(fraenkel_a_3_3_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_3_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k11_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_3_yellow_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_3_yellow_8(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & r2_hidden(E,C) & r1_tarski(E,D) ) ) ) )).
fof(fraenkel_a_3_3_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) & m1_subset_1(D,B) ) => ( r2_hidden(A,a_3_3_zf_fund1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,B) & m1_subset_1(F,B) & A = k1_zf_fund1(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_40_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v6_algstr_0(B) & v4_rlvect_1(B) & v1_vectsp_1(B) & v1_algstr_1(B) & l6_algstr_0(B) & ~ v1_xboole_0(C) & v3_ideal_1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_40_ideal_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k6_algstr_0(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_41_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & v1_algstr_1(B) & v1_int_3(B) & l6_algstr_0(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),k4_ordinal1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),k4_ordinal1))) ) => ( r2_hidden(A,a_3_41_ideal_1(B,C,D)) <=> ? [E] : ( m2_subset_1(E,u1_struct_0(B),C) & A = k3_funct_2(u1_struct_0(B),k4_ordinal1,D,E) ) ) ) )).
fof(fraenkel_a_3_4_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & l1_unialg_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_4_aofa_000(B,C,D)) <=> ? [E] : ? [F] : ( m2_subset_1(E,k4_ordinal1,k4_finseq_1(u1_unialg_1(B))) & m2_finseq_2(F,u1_struct_0(B),k3_finseq_2(u1_struct_0(B))) & A = k1_funct_1(k2_pua2mss1(B,E),F) & r2_hidden(F,k1_relset_1(k3_finseq_2(u1_struct_0(B)),k2_pua2mss1(B,E))) & r1_tarski(k2_relset_1(u1_struct_0(B),F),k9_aofa_000(B,C,D)) ) ) ) )).
fof(fraenkel_a_3_4_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(B),k9_setfam_1(B)))) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_3_4_armstrng(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(B)) & A = E & r2_hidden(k6_armstrng(B,D,E),k12_armstrng(B,C)) ) ) ) )).
fof(fraenkel_a_3_4_circled1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(u1_struct_0(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_4_circled1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_rlvect_1(B,E,D) & r2_hidden(E,k2_circled1(B,C)) ) ) ) )).
fof(fraenkel_a_3_4_closure2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( l1_struct_0(B) & v15_closure2(C,B) & l1_closure2(C,B) & m1_closure2(D,u1_struct_0(B),u3_msualg_1(B,C),k6_closure2(u1_struct_0(B),u3_msualg_1(B,C))) ) => ( r2_hidden(A,a_3_4_closure2(B,C,D)) <=> ? [E] : ( m1_closure2(E,u1_struct_0(B),u3_msualg_1(B,C),k6_closure2(u1_struct_0(B),u3_msualg_1(B,C))) & A = E & r2_pboole(u1_struct_0(B),D,E) & r2_hidden(E,u1_closure2(B,C)) ) ) ) )).
fof(fraenkel_a_3_4_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( l1_compos_1(B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v3_compos_1(C,B) & v4_compos_1(C,B) & ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(B)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v3_compos_1(D,B) & v4_compos_1(D,B) ) => ( r2_hidden(A,a_3_4_compos_1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_nat_1(E,k7_nat_d(k5_card_1(C),1)) & r2_hidden(E,k2_afinsq_1(k5_compos_1(B,D,k7_nat_d(k5_card_1(C),1)))) ) ) ) )).
fof(fraenkel_a_3_4_convex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_bhsp_1(B) & l1_bhsp_1(B) & m1_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_4_convex1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(D,k1_bhsp_1(B,E,C)) ) ) ) )).
fof(fraenkel_a_3_4_convex2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(u1_struct_0(B))) & m2_rlvect_2(D,B,C) ) => ( r2_hidden(A,a_3_4_convex2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & k3_funct_2(u1_struct_0(B),k1_numbers,D,E) != k5_numbers ) ) ) )).
fof(fraenkel_a_3_4_convex4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_csspace(B) & l1_csspace(B) & m1_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_4_convex4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(D,k3_complex1(k12_csspace(B,E,C))) ) ) ) )).
fof(fraenkel_a_3_4_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_3_4_domain_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & ( ( r2_hidden(E,C) & ~ r2_hidden(E,D) ) | ( ~ r2_hidden(E,C) & r2_hidden(E,D) ) ) ) ) ) )).
fof(fraenkel_a_3_4_fcont_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r2_hidden(A,a_3_4_fcont_2(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = E & r1_xxreal_0(k3_seq_4(k7_relset_1(k1_numbers,k1_numbers,D,k1_rcomp_1(C,B))),E) & r1_xxreal_0(E,k2_seq_4(k7_relset_1(k1_numbers,k1_numbers,D,k1_rcomp_1(C,B)))) ) ) ) )).
fof(fraenkel_a_3_4_fdiff_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_4_fdiff_3(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = E & r1_xxreal_0(k6_xcmplx_0(B,k3_xxreal_0(C,D)),E) & r1_xxreal_0(E,B) ) ) ) )).
fof(fraenkel_a_3_4_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(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))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_4_finance1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & r2_hidden(k3_funct_2(B,k1_numbers,C,E),k3_rcomp_1(D,k1_xxreal_0)) ) ) ) )).
fof(fraenkel_a_3_4_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_4_finseq_3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = E & r2_hidden(E,k1_relset_1(k4_ordinal1,C)) & r1_xxreal_0(E,D) & r2_hidden(k1_funct_1(C,E),B) ) ) ) )).
fof(fraenkel_a_3_4_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k1_zfmisc_1(k1_fomodel4(B))) ) => ( r2_hidden(A,a_3_4_fomodel4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_mcart_1(k1_zfmisc_1(k1_fomodel4(B)),k1_zfmisc_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) & A = k7_relset_1(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B)),E,k6_domain_1(k1_zfmisc_1(k1_fomodel4(B)),D)) & r2_hidden(E,k6_fomodel4(B,C)) ) ) ) )).
fof(fraenkel_a_3_4_gobrd13,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_3_4_gobrd13(B,C,D)) <=> ? [E] : ? [F] : ( v1_xreal_0(E) & v1_xreal_0(F) & A = k19_euclid(E,F) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,B,1)),E) & r1_xxreal_0(E,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,k1_nat_1(B,1),1))) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,1,C)),F) & r1_xxreal_0(F,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,1,k1_nat_1(C,1)))) ) ) ) )).
fof(fraenkel_a_3_4_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v6_graph_1(B) & l1_graph_1(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_4_graph_3(B,C,D)) <=> ? [E] : ( m2_finseq_2(E,u4_struct_0(B),k9_graph_3(B)) & A = E & r1_tarski(k10_xtuple_0(E),D) & ~ v1_xboole_0(E) & ? [F] : ( m2_finseq_1(F,u1_struct_0(B)) & r1_graph_2(B,F,E) & k1_funct_1(F,1) = C ) ) ) ) )).
fof(fraenkel_a_3_4_heyting1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m2_subset_1(C,k5_finsub_1(k7_normform(B)),k8_normform(B)) & m2_funct_2(D,k7_normform(B),k1_heyting1(B),k9_funct_2(k7_normform(B),k1_heyting1(B))) ) => ( r2_hidden(A,a_3_4_heyting1(B,C,D)) <=> ? [E] : ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B)) & A = k3_funct_2(k7_normform(B),k1_heyting1(B),D,E) & r2_hidden(k3_funct_2(k7_normform(B),k1_heyting1(B),D,E),k2_domain_1(k5_finsub_1(B),k5_finsub_1(B),E)) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_4_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_4_ideal_1(B,C,D)) <=> ? [E] : ( m2_finseq_1(E,u1_struct_0(B)) & A = k4_rlvect_1(B,E) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( r1_xxreal_0(1,F) & r1_xxreal_0(F,k3_finseq_1(E)) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ~ ( k1_funct_1(E,F) = k6_algstr_0(B,G,H) & r2_hidden(G,C) & r2_hidden(H,D) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_3_4_jgraph_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_4_jgraph_6(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) & A = E & r1_xxreal_0(D,k12_euclid(k5_algstr_0(k15_euclid(2),E,k19_euclid(B,C)))) ) ) ) )).
fof(fraenkel_a_3_4_jordan_a,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_jordan_a(C,B) & m1_subset_1(D,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_3_4_jordan_a(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = E & r2_hidden(E,k4_finseq_1(C)) & r1_jordan6(B,k7_partfun1(u1_struct_0(k15_euclid(2)),C,E),D) ) ) ) )).
fof(fraenkel_a_3_4_laplace,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & m1_subset_1(D,k4_ordinal1) ) => ( r2_hidden(A,a_3_4_laplace(B,C,D)) <=> ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k6_subset_1(k2_setwop_2(k1_nat_1(D,1)),k1_tarski(B)),k6_subset_1(k2_setwop_2(k1_nat_1(D,1)),k1_tarski(C))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k6_subset_1(k2_setwop_2(k1_nat_1(D,1)),k1_tarski(B)),k6_subset_1(k2_setwop_2(k1_nat_1(D,1)),k1_tarski(C))))) & A = E & v2_funct_1(E) ) ) ) )).
fof(fraenkel_a_3_4_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_4_lattice3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_lattices(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_4_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_rlvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_4_mathmorp(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,E,D) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_4_metric_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & ~ v2_struct_0(C) & l1_metric_1(C) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_4_metric_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = E & r1_xxreal_0(k1_metric_1(C,D,E),B) ) ) ) )).
fof(fraenkel_a_3_4_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( l1_mmlquery(B) & m2_finseq_1(C,u1_mmlquery(B)) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_4_mmlquery(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_xxreal_0(k5_card_1(k7_subset_1(u1_mmlquery(B),k2_relset_1(u1_mmlquery(B),C),k30_mmlquery(B,E))),D) ) ) ) )).
fof(fraenkel_a_3_4_morph_01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_4_morph_01(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_tarski(k5_rusub_4(B,k6_mathmorp(k4_xcmplx_0(1),B,D),E),C) ) ) ) )).
fof(fraenkel_a_3_4_msafree2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_4_msafree2(B,C,D)) <=> ? [E] : ( m1_dtconstr(E,u1_struct_0(k5_msafree(B,C)),k5_trees_3(u1_struct_0(k5_msafree(B,C))),k4_dtconstr(k5_msafree(B,C))) & A = E & ~ ( ! [F] : ~ ( r2_hidden(F,k1_funct_1(C,D)) & E = k1_trees_4(k4_tarski(F,D)) ) & ! [F] : ( m1_subset_1(F,u4_struct_0(B)) => ~ ( k4_tarski(F,u1_struct_0(B)) = k1_funct_1(E,k1_xboole_0) & k2_msualg_1(B,F) = D ) ) ) ) ) ) )).
fof(fraenkel_a_3_4_msafree3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v11_struct_0(B) & v1_instalg1(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_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_4_msafree3(B,C,D)) <=> ? [E] : ( m1_dtconstr(E,u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),C,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))),k5_trees_3(u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),C,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers)))))),k1_msaterm(B,k2_pboole(u1_struct_0(B),C,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))) & A = E & k7_msaterm(B,k2_pboole(u1_struct_0(B),C,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),E) = D & r2_pboole(u1_struct_0(B),k4_msafree3(B,k2_pboole(u1_struct_0(B),C,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),E),C) ) ) ) )).
fof(fraenkel_a_3_4_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_4_msafree4(B,C,D)) <=> ? [E] : ( m1_dtconstr(E,u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),C,k7_funcop_1(u1_struct_0(B),k1_tarski(k5_numbers))))),k5_trees_3(u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),C,k7_funcop_1(u1_struct_0(B),k1_tarski(k5_numbers)))))),k1_msaterm(B,k2_pboole(u1_struct_0(B),C,k7_funcop_1(u1_struct_0(B),k1_tarski(k5_numbers))))) & A = E & k7_msaterm(B,k2_pboole(u1_struct_0(B),C,k7_funcop_1(u1_struct_0(B),k1_tarski(k5_numbers))),E) = D & r2_pboole(u1_struct_0(B),k4_msafree3(B,k2_pboole(u1_struct_0(B),C,k7_funcop_1(u1_struct_0(B),k1_tarski(k5_numbers))),E),C) ) ) ) )).
fof(fraenkel_a_3_4_msualg_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) & v4_msualg_1(C,B) & l3_msualg_1(C,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_msualg_5(B,C)))) ) => ( r2_hidden(A,a_3_4_msualg_8(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k5_msualg_5(u1_struct_0(B),u3_msualg_1(B,C))))) & A = E & v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(D)) ) ) ) )).
fof(fraenkel_a_3_4_ndiff_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(B) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finseq_1(B) & v2_prvect_2(B) & m1_subset_1(C,u1_struct_0(k14_prvect_2(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_4_ndiff_5(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k14_prvect_2(B))) & A = E & ~ r1_xxreal_0(D,k2_normsp_0(k14_prvect_2(B),k5_algstr_0(k14_prvect_2(B),E,C))) ) ) ) )).
fof(fraenkel_a_3_4_normsp_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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(k2_normsp_2(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_4_normsp_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k2_normsp_2(B))) & A = E & ~ r1_xxreal_0(D,k3_metric_1(k2_normsp_2(B),C,E)) ) ) ) )).
fof(fraenkel_a_3_4_osafree,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v4_osalg_1(B) & v5_osalg_1(B) & v2_osalg_4(B) & l3_osalg_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_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_4_osafree(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k2_osafree(B,C))) & A = k1_funct_1(k1_msualg_3(u1_struct_0(B),u3_msualg_1(B,k8_osafree(B,C)),u3_msualg_1(B,k16_osalg_4(B,k8_osafree(B,C),k15_osafree(B,C))),k18_osalg_4(B,k8_osafree(B,C),k15_osafree(B,C)),D),k2_trees_4(u1_struct_0(k2_osafree(B,C)),E)) & r2_hidden(E,k6_dtconstr(k2_osafree(B,C))) & k2_xtuple_0(E) = D ) ) ) )).
fof(fraenkel_a_3_4_pdiff_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,u1_struct_0(k4_real_ns1(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_4_pdiff_7(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(B))) & A = E & ~ r1_xxreal_0(D,k2_normsp_0(k4_real_ns1(B),k5_algstr_0(k4_real_ns1(B),C,E))) ) ) ) )).
fof(fraenkel_a_3_4_qc_lang4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(B) & m1_subset_1(C,k9_qc_lang1(B)) & m1_trees_1(D,k9_xtuple_0(k2_qc_lang4(B,C))) ) => ( r2_hidden(A,a_3_4_qc_lang4(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k7_finseq_1(D,k9_finseq_1(E)) & r2_hidden(k7_finseq_1(D,k9_finseq_1(E)),k9_xtuple_0(k2_qc_lang4(B,C))) ) ) ) )).
fof(fraenkel_a_3_4_quantal1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l3_lattices(B) & 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,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_4_quantal1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_funct_2(u1_struct_0(B),u1_struct_0(B),C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_4_rlaffin1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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_rlaffin1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_4_rlaffin1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,k4_algstr_0(B,D),E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_4_rlaffin3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(C)))) ) => ( r2_hidden(A,a_3_4_rlaffin3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(k2_xcmplx_0(C,B)))) & A = E & r2_hidden(k16_finseq_1(C,E),D) ) ) ) )).
fof(fraenkel_a_3_4_rlsub_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_rlsub_1(D,B) ) => ( r2_hidden(A,a_3_4_rlsub_2(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,F,E) & r1_struct_0(k2_rlsub_2(B,C,D),F) & r1_struct_0(D,E) ) ) ) )).
fof(fraenkel_a_3_4_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_4_rltopsp1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_algstr_0(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_4_rmod_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & v4_vectsp_2(C,B) & l1_vectsp_2(C,B) & m1_rmod_4(D,B,C) ) => ( r2_hidden(A,a_3_4_rmod_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = E & k3_funct_2(u1_struct_0(C),u1_struct_0(B),k7_rmod_4(B,C,k4_algstr_0(B,k1_group_1(B)),D),E) != k4_struct_0(B) ) ) ) )).
fof(fraenkel_a_3_4_rusub_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_rusub_1(D,B) ) => ( r2_hidden(A,a_3_4_rusub_2(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,E,F) & r1_struct_0(k2_rusub_2(B,C,D),E) & r1_struct_0(D,F) ) ) ) )).
fof(fraenkel_a_3_4_rusub_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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) & v1_bhsp_1(C) & m1_rusub_1(C,B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_4_rusub_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,D,E) & r1_struct_0(C,E) ) ) ) )).
fof(fraenkel_a_3_4_rusub_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_4_rusub_5(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k1_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_4_seq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v1_xreal_0(C) & m2_finseq_2(D,k2_numbers,k12_seq_4(B)) ) => ( r2_hidden(A,a_3_4_seq_4(B,C,D)) <=> ? [E] : ( m2_finseq_2(E,k2_numbers,k12_seq_4(B)) & A = E & ~ r1_xxreal_0(C,k20_seq_4(k17_seq_4(B,E,D))) ) ) ) )).
fof(fraenkel_a_3_4_setlim_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) & m1_subset_1(D,k4_ordinal1) ) => ( r2_hidden(A,a_3_4_setlim_1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_funct_1(C,E) & r1_xxreal_0(D,E) ) ) ) )).
fof(fraenkel_a_3_4_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v1_xreal_0(C) & m1_subset_1(D,u1_struct_0(k15_euclid(B))) ) => ( r2_hidden(A,a_3_4_topreal9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(B))) & A = E & r1_xxreal_0(k12_euclid(k5_algstr_0(k15_euclid(B),E,D)),C) ) ) ) )).
fof(fraenkel_a_3_4_trees_a,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) & v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) & m1_trees_1(D,k9_xtuple_0(B)) ) => ( r2_hidden(A,a_3_4_trees_a(B,C,D)) <=> ? [E] : ( m1_trees_1(E,k9_xtuple_0(C)) & A = k8_finseq_1(k4_ordinal1,D,E) & E = E ) ) ) )).
fof(fraenkel_a_3_4_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_relat_1(C) & v1_funct_1(C) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_4_valued_1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k2_xcmplx_0(E,D) & r2_hidden(E,k9_xtuple_0(k1_funct_4(B,C))) ) ) ) )).
fof(fraenkel_a_3_4_waybel11,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & v1_yellow_6(C,B) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_4_waybel11(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k2_waybel_0(B,C,E) & r1_orders_2(C,D,E) ) ) ) )).
fof(fraenkel_a_3_4_waybel12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_4_waybel12(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k13_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_4_waybel30,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & v1_waybel_0(C,k1_yellow_1(k7_waybel_0(B))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_yellow_1(k7_waybel_0(B))))) & m1_subset_1(D,u1_struct_0(k1_yellow_1(k7_waybel_0(B)))) ) => ( r2_hidden(A,a_3_4_waybel30(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k1_yellow_1(k7_waybel_0(B)))) & A = k12_lattice3(k1_yellow_1(k7_waybel_0(B)),D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_4_waybel33,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) & ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_4_waybel33(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k2_waybel_0(B,C,E) & r1_orders_2(C,D,E) ) ) ) )).
fof(fraenkel_a_3_4_waybel_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v3_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_4_waybel_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_4_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & v2_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & v1_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & v1_waybel_0(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_4_waybel_2(B,C,D)) <=> ? [E] : ( ~ v1_xboole_0(E) & v1_waybel_0(E,B) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k1_yellow_0(B,E) & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & E = k4_yellow_4(B,k6_domain_1(u1_struct_0(B),F),D) & r2_hidden(F,C) ) ) ) ) )).
fof(fraenkel_a_3_4_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) & ~ v1_xboole_0(C) & v1_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_4_waybel_4(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k12_lattice3(B,E,F) & r2_hidden(E,k6_domain_1(u1_struct_0(B),D)) & r2_hidden(F,C) ) ) ) )).
fof(fraenkel_a_3_4_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v2_pre_topc(B) & v8_pre_topc(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v1_compts_1(B) & l1_waybel_9(B) & ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_4_waybel_9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & k13_lattice3(B,E,k2_waybel_0(B,C,D)) = k2_waybel_0(B,C,D) ) ) ) )).
fof(fraenkel_a_3_4_yellow12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_4_yellow12(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k12_lattice3(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_4_yellow_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v2_pre_topc(B) & l1_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)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_4_yellow_9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & r2_hidden(E,C) & r1_tarski(E,D) ) ) ) )).
fof(fraenkel_a_3_4_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) & m1_subset_1(D,B) ) => ( r2_hidden(A,a_3_4_zf_fund1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = k1_zf_fund1(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_4_zf_model,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m2_subset_1(C,k4_ordinal1,k1_zf_lang) & m2_subset_1(D,k4_ordinal1,k1_zf_lang) ) => ( r2_hidden(A,a_3_4_zf_model(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k3_zf_model(B)) & A = E & ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k1_zf_lang,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang,B))) ) => ( F = E => k3_funct_2(k1_zf_lang,B,F,k18_zf_lang(k4_zf_lang(C,D))) = k3_funct_2(k1_zf_lang,B,F,k19_zf_lang(k4_zf_lang(C,D))) ) ) ) ) ) )).
fof(fraenkel_a_3_5_circled1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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_xreal_0(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_5_circled1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_rlvect_1(B,E,k5_xcmplx_0(C)) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_5_compl_sp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(u1_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(B))))) & m1_subset_1(D,k4_ordinal1) ) => ( r2_hidden(A,a_3_5_compl_sp(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = k3_funct_2(k4_ordinal1,k9_setfam_1(u1_struct_0(B)),C,E) & r1_xxreal_0(E,D) ) ) ) )).
fof(fraenkel_a_3_5_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( l1_compos_1(B) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_5_compos_1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k2_xcmplx_0(E,D) & r2_hidden(E,k9_xtuple_0(C)) ) ) ) )).
fof(fraenkel_a_3_5_convex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_rlvect_1(B) & v3_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,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_5_convex1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_5_convex4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_csspace(B) & l1_csspace(B) & m1_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_5_convex4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_xxreal_0(D,k4_complex1(k12_csspace(B,E,C))) ) ) ) )).
fof(fraenkel_a_3_5_fdiff_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_5_fdiff_3(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = E & r1_xxreal_0(B,E) & r1_xxreal_0(E,k2_xcmplx_0(B,k3_xxreal_0(D,C))) ) ) ) )).
fof(fraenkel_a_3_5_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(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))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_5_finance1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & r2_hidden(k3_funct_2(B,k1_numbers,C,E),k1_xxreal_1(D,k1_xxreal_0)) ) ) ) )).
fof(fraenkel_a_3_5_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) & m1_subset_1(D,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C))))) ) => ( r2_hidden(A,a_3_5_fomodel4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = k1_funct_1(k5_fomodel4(C,D,E),B) ) ) ) )).
fof(fraenkel_a_3_5_gobrd13,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_3_5_gobrd13(B,C,D)) <=> ? [E] : ? [F] : ( v1_xreal_0(E) & v1_xreal_0(F) & A = k19_euclid(E,F) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,k7_nat_d(B,1),1)),E) & r1_xxreal_0(E,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,B,1))) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,1,C)),F) ) ) ) )).
fof(fraenkel_a_3_5_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,B) & l1_group_9(C,B) & v2_group_9(D,B) & v4_group_9(D,B,C) & m1_group_9(D,B,C) ) => ( r2_hidden(A,a_3_5_group_9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = E & k3_funct_2(u1_struct_0(C),u1_struct_0(k10_group_9(B,C,D)),k12_group_9(B,C,D),E) = k1_group_1(k10_group_9(B,C,D)) ) ) ) )).
fof(fraenkel_a_3_5_heyting1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m2_subset_1(C,k5_finsub_1(k7_normform(B)),k8_normform(B)) & m2_subset_1(D,k5_finsub_1(k7_normform(B)),k8_normform(B)) ) => ( r2_hidden(A,a_3_5_heyting1(B,C,D)) <=> ? [E] : ( m2_funct_2(E,k7_normform(B),k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k9_funct_2(k7_normform(B),k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)))) & A = k6_normform(k7_normform(B),B,C,k6_funcop_1(k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B),k5_heyting1(B),E,k6_funct_3(k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),k7_normform(B)))) & r1_tarski(k8_setwiseo(k7_normform(B),k2_zfmisc_1(k5_finsub_1(B),k5_finsub_1(B)),E,C),D) ) ) ) )).
fof(fraenkel_a_3_5_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_5_ideal_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_tarski(k10_ideal_1(B,D,E),C) ) ) ) )).
fof(fraenkel_a_3_5_jordan_a,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & m1_jordan_a(C,B) & ~ v1_xboole_0(D) & v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ( r2_hidden(A,a_3_5_jordan_a(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) & A = E & r1_jordan6(B,k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_xxreal_2(D)),E) & r1_jordan6(B,E,k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_nat_1(k1_xxreal_2(D),1))) ) ) ) )).
fof(fraenkel_a_3_5_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_5_lattice3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_lattices(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_5_lopban_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & 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(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) & 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(A,a_3_5_lopban_5(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k2_normsp_0(C,k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,E)) & r1_xxreal_0(k2_normsp_0(B,E),1) ) ) ) )).
fof(fraenkel_a_3_5_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_rlvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_5_mathmorp(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_5_metric_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & ~ v2_struct_0(C) & l1_metric_1(C) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_5_metric_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = E & k1_metric_1(C,D,E) = B ) ) ) )).
fof(fraenkel_a_3_5_metrizts,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(B)))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(B)))) ) => ( r2_hidden(A,a_3_5_metrizts(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k3_pcomps_1(B))) & A = E & ~ r1_xxreal_0(k5_numbers,k6_xcmplx_0(k3_funct_2(u1_struct_0(k3_pcomps_1(B)),u1_struct_0(k3_topmetr),k6_weierstr(B,C),E),k3_funct_2(u1_struct_0(k3_pcomps_1(B)),u1_struct_0(k3_topmetr),k6_weierstr(B,D),E))) ) ) ) )).
fof(fraenkel_a_3_5_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_mmlquery(B) & l1_mmlquery(B) & m2_finseq_1(C,u1_mmlquery(B)) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_5_mmlquery(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_xxreal_0(k5_card_1(k7_subset_1(u1_struct_0(B),k30_mmlquery(B,E),k2_relset_1(u1_mmlquery(B),C))),D) ) ) ) )).
fof(fraenkel_a_3_5_morph_01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_5_morph_01(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k2_morph_01(B,E,D) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_5_msualg_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) & v4_msualg_1(C,B) & l3_msualg_1(C,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_msualg_5(B,C)))) ) => ( r2_hidden(A,a_3_5_msualg_8(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k5_msualg_5(u1_struct_0(B),u3_msualg_1(B,C))))) & A = k15_lattice3(k5_msualg_5(u1_struct_0(B),u3_msualg_1(B,C)),E) & r2_hidden(E,a_3_4_msualg_8(B,C,D)) ) ) ) )).
fof(fraenkel_a_3_5_normsp_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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(k2_normsp_2(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_5_normsp_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k2_normsp_2(B))) & A = E & r1_xxreal_0(k3_metric_1(k2_normsp_2(B),C,E),D) ) ) ) )).
fof(fraenkel_a_3_5_osafree,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v4_osalg_1(B) & v5_osalg_1(B) & l3_osalg_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_subset_1(D,u4_struct_0(B)) ) => ( r2_hidden(A,a_3_5_osafree(B,C,D)) <=> ? [E] : ( m1_dtconstr(E,u1_struct_0(k2_osafree(B,C)),k5_trees_3(u1_struct_0(k2_osafree(B,C))),k4_dtconstr(k2_osafree(B,C))) & A = E & ~ ( ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ~ ( r3_orders_2(B,F,k2_msualg_1(B,D)) & r2_hidden(G,k1_funct_1(C,F)) & E = k1_trees_4(k4_tarski(G,F)) ) ) & ! [F] : ( m1_subset_1(F,u4_struct_0(B)) => ~ ( k4_tarski(F,u1_struct_0(B)) = k1_funct_1(E,k1_xboole_0) & r3_orders_2(B,k2_msualg_1(B,F),k2_msualg_1(B,D)) ) ) ) ) ) ) )).
fof(fraenkel_a_3_5_qc_lang4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(B) & m1_subset_1(C,k9_qc_lang1(B)) & m1_trees_1(D,k9_xtuple_0(k2_qc_lang4(B,C))) ) => ( r2_hidden(A,a_3_5_qc_lang4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k9_qc_lang1(B)) & A = E & r1_qc_lang2(B,E,k3_trees_2(k9_qc_lang1(B),k2_qc_lang4(B,C),D)) ) ) ) )).
fof(fraenkel_a_3_5_quantal1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & 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,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_5_quantal1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_funct_2(u1_struct_0(B),u1_struct_0(B),C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_5_rlaffin1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_rlvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_5_rlaffin1(B,C,D)) <=> ? [E] : ( v2_rusub_4(E,B) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & r1_tarski(k4_subset_1(u1_struct_0(B),C,D),E) ) ) ) )).
fof(fraenkel_a_3_5_rlaffin3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(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) & l1_rlvect_1(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) ) => ( r2_hidden(A,a_3_5_rlaffin3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k1_rlvect_1(C,E,B) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_5_rlsub_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_5_rlsub_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,D,E) & r1_struct_0(C,E) ) ) ) )).
fof(fraenkel_a_3_5_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_rlvect_1(B) & l2_algstr_0(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_5_rltopsp1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_algstr_0(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_5_rusub_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_5_rusub_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,D,E) & r1_struct_0(C,E) ) ) ) )).
fof(fraenkel_a_3_5_rusub_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_5_rusub_5(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k1_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_5_setlim_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) & v7_ordinal1(D) ) => ( r2_hidden(A,a_3_5_setlim_1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_funct_1(C,E) & r1_xxreal_0(k1_nat_1(D,1),E) ) ) ) )).
fof(fraenkel_a_3_5_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v1_xreal_0(C) & m1_subset_1(D,u1_struct_0(k15_euclid(B))) ) => ( r2_hidden(A,a_3_5_topreal9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(B))) & A = E & ~ r1_xxreal_0(C,k12_euclid(k5_algstr_0(k15_euclid(B),E,D))) ) ) ) )).
fof(fraenkel_a_3_5_waybel11,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(k4_waybel11(B,C))) ) => ( r2_hidden(A,a_3_5_waybel11(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k4_waybel11(B,C))) & A = k2_waybel_0(B,k4_waybel11(B,C),E) & r1_orders_2(k4_waybel11(B,C),D,E) ) ) ) )).
fof(fraenkel_a_3_5_waybel21,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_5_waybel21(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = E & r1_orders_2(C,D,E) ) ) ) )).
fof(fraenkel_a_3_5_waybel33,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_5_waybel33(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k2_waybel_0(B,C,E) & r1_orders_2(C,D,E) ) ) ) )).
fof(fraenkel_a_3_5_waybel_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_5_waybel_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_5_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & v2_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & v1_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_5_waybel_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_5_waybel_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) & v5_waybel_4(D,B) & v6_waybel_4(D,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) ) => ( r2_hidden(A,a_3_5_waybel_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r2_hidden(k1_domain_1(u1_struct_0(B),u1_struct_0(B),E,F),D) & r2_hidden(k1_domain_1(u1_struct_0(B),u1_struct_0(B),F,C),D) ) ) ) ) )).
fof(fraenkel_a_3_5_yellow12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k2_borsuk_1(B,B)),u1_struct_0(B)) & v5_pre_topc(C,k2_borsuk_1(B,B),B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_borsuk_1(B,B)),u1_struct_0(B)))) & v1_funct_1(D) & v1_funct_2(D,u1_struct_0(k2_borsuk_1(B,B)),u1_struct_0(B)) & v5_pre_topc(D,k2_borsuk_1(B,B),B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_borsuk_1(B,B)),u1_struct_0(B)))) ) => ( r2_hidden(A,a_3_5_yellow12(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k2_borsuk_1(B,B))) & A = E & k3_funct_2(u1_struct_0(k2_borsuk_1(B,B)),u1_struct_0(B),C,E) = k3_funct_2(u1_struct_0(k2_borsuk_1(B,B)),u1_struct_0(B),D,E) ) ) ) )).
fof(fraenkel_a_3_5_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_5_yellow_4(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k10_lattice3(B,E,F) & r2_hidden(E,k6_domain_1(u1_struct_0(B),C)) & r2_hidden(F,k6_domain_1(u1_struct_0(B),D)) ) ) ) )).
fof(fraenkel_a_3_5_yellow_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_5_yellow_9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & r2_hidden(E,C) & r1_tarski(E,D) ) ) ) )).
fof(fraenkel_a_3_5_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) & m1_subset_1(D,B) ) => ( r2_hidden(A,a_3_5_zf_fund1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,B) & m1_subset_1(F,B) & A = k7_classes2(B,E,F) & r2_hidden(E,k1_classes2(B,D)) & r2_hidden(F,k1_classes2(B,C)) ) ) ) )).
fof(fraenkel_a_3_5_zf_model,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m2_subset_1(C,k4_ordinal1,k1_zf_lang) & m2_subset_1(D,k4_ordinal1,k1_zf_lang) ) => ( r2_hidden(A,a_3_5_zf_model(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k3_zf_model(B)) & A = E & ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k1_zf_lang,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang,B))) ) => ( F = E => r2_hidden(k3_funct_2(k1_zf_lang,B,F,k18_zf_lang(k5_zf_lang(C,D))),k3_funct_2(k1_zf_lang,B,F,k19_zf_lang(k5_zf_lang(C,D)))) ) ) ) ) ) )).
fof(fraenkel_a_3_6_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( l1_compos_1(B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(B)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ( r2_hidden(A,a_3_6_compos_1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_nat_1(E,k5_card_1(C)) & r2_hidden(E,k2_afinsq_1(D)) ) ) ) )).
fof(fraenkel_a_3_6_convex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_6_convex1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k5_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_6_convex2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_rlsub_1(D,B) ) => ( r2_hidden(A,a_3_6_convex2(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,F,E) & r1_struct_0(C,F) & r1_struct_0(D,E) ) ) ) )).
fof(fraenkel_a_3_6_convex4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_csspace(B) & l1_csspace(B) & m1_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_6_convex4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(k4_complex1(k12_csspace(B,E,C)),D) ) ) ) )).
fof(fraenkel_a_3_6_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(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))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_6_finance1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & m1_subset_1(k3_funct_2(B,k1_numbers,C,E),k3_rcomp_1(D,k1_xxreal_0)) ) ) ) )).
fof(fraenkel_a_3_6_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k1_zfmisc_1(k1_fomodel4(B))) ) => ( r2_hidden(A,a_3_6_fomodel4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_mcart_1(k1_zfmisc_1(k1_fomodel4(B)),k1_zfmisc_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) & A = k7_relset_1(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B)),E,k6_domain_1(k1_zfmisc_1(k1_fomodel4(B)),D)) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_6_gobrd13,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_3_6_gobrd13(B,C,D)) <=> ? [E] : ? [F] : ( v1_xreal_0(E) & v1_xreal_0(F) & A = k19_euclid(E,F) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,k7_nat_d(B,1),1)),E) & r1_xxreal_0(E,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,B,1))) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,1,C)),F) & r1_xxreal_0(F,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,1,k1_nat_1(C,1)))) ) ) ) )).
fof(fraenkel_a_3_6_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,B) & l1_group_9(C,B) & v15_algstr_0(D) & v1_group_3(D,C) & m1_group_2(D,C) ) => ( r2_hidden(A,a_3_6_group_9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = E & k3_funct_2(u1_struct_0(C),u1_struct_0(k5_group_6(C,D)),k8_group_6(C,D),E) = k1_group_1(k5_group_6(C,D)) ) ) ) )).
fof(fraenkel_a_3_6_jordan2c,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & m1_subset_1(C,u1_struct_0(k14_euclid(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_6_jordan2c(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(B))) & A = E & ~ r1_xxreal_0(D,k3_metric_1(k14_euclid(B),C,E)) ) ) ) )).
fof(fraenkel_a_3_6_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_6_lattice3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r3_lattices(B,k4_lattices(B,C,E),D) ) ) ) )).
fof(fraenkel_a_3_6_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_rlvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_6_mathmorp(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_tarski(k1_mathmorp(B,E,D),k4_mathmorp(B,C,D)) ) ) ) )).
fof(fraenkel_a_3_6_metric_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_metric_1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_6_metric_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_metric_1(B,C,E,D) ) ) ) )).
fof(fraenkel_a_3_6_metrizts,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v6_metric_1(B) & v7_metric_1(B) & v8_metric_1(B) & v9_metric_1(B) & l1_metric_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(B)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(B)))) ) => ( r2_hidden(A,a_3_6_metrizts(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(k5_numbers,k6_xcmplx_0(k1_funct_1(k6_weierstr(B,C),E),k1_funct_1(k6_weierstr(B,D),E))) ) ) ) )).
fof(fraenkel_a_3_6_morph_01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_6_morph_01(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k2_morph_01(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_6_normsp_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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_xreal_0(C) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_6_normsp_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(C,k2_normsp_0(B,k5_algstr_0(B,E,D))) ) ) ) )).
fof(fraenkel_a_3_6_qc_lang4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_qc_lang1(B) & m1_subset_1(C,k9_qc_lang1(B)) & m1_qc_lang4(D,B,C) ) => ( r2_hidden(A,a_3_6_qc_lang4(B,C,D)) <=> ? [E] : ( m1_trees_1(E,k9_xtuple_0(k2_qc_lang4(B,C))) & A = E & k3_trees_2(k9_qc_lang1(B),k2_qc_lang4(B,C),E) = D ) ) ) )).
fof(fraenkel_a_3_6_quantal1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_6_quantal1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_lattices(B,k6_algstr_0(B,E,C),D) ) ) ) )).
fof(fraenkel_a_3_6_rlaffin1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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_rlaffin1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_6_rlaffin1(B,C,D)) <=> ? [E] : ( m2_rlvect_2(E,B,k7_subset_1(u1_struct_0(B),C,D)) & A = k6_rlvect_2(B,E) & k3_rlaffin1(B,E) = 1 ) ) ) )).
fof(fraenkel_a_3_6_rlaffin3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_6_rlaffin3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_algstr_0(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_6_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_rlvect_1(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_6_rltopsp1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k1_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_6_rusub_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_6_rusub_5(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k5_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_6_seq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v1_xreal_0(C) & m1_subset_1(D,k1_zfmisc_1(k12_seq_4(B))) ) => ( r2_hidden(A,a_3_6_seq_4(B,C,D)) <=> ? [E] : ( m2_finseq_2(E,k2_numbers,k12_seq_4(B)) & A = E & ~ r1_xxreal_0(C,k22_seq_4(B,E,D)) ) ) ) )).
fof(fraenkel_a_3_6_setlim_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) & m1_subset_1(D,k4_ordinal1) ) => ( r2_hidden(A,a_3_6_setlim_1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_funct_1(k2_prob_1(B,C),E) & r1_xxreal_0(D,E) ) ) ) )).
fof(fraenkel_a_3_6_topgen_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_topgen_2(B,C)))) ) => ( r2_hidden(A,a_3_6_topgen_2(B,C,D)) <=> ? [E] : ( m2_subset_1(E,u1_struct_0(k5_topgen_2(B,C)),D) & A = k6_domain_1(D,E) ) ) ) )).
fof(fraenkel_a_3_6_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_6_topreal9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) & A = E & k12_euclid(k5_algstr_0(k15_euclid(2),E,k19_euclid(B,C))) = D ) ) ) )).
fof(fraenkel_a_3_6_waybel12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) & v13_waybel_0(C,B) & v1_waybel_6(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_6_waybel12(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_6_waybel16,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_waybel_1(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & ~ v1_xboole_0(D) & v2_waybel_0(D,B) & v13_waybel_0(D,B) & v1_waybel_6(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_6_waybel16(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k13_lattice3(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_6_waybel30,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & v2_waybel_2(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & v1_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_6_waybel30(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_6_waybel33,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_6_waybel33(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k5_waybel_9(B,C,D))) & A = k2_waybel_0(B,k5_waybel_9(B,C,D),E) ) ) ) )).
fof(fraenkel_a_3_6_waybel_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v3_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_6_waybel_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_6_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_waybel_1(B) & v1_lattice3(B) & v2_lattice3(B) & v3_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_6_waybel_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,C,E) & r2_hidden(E,D) ) ) ) )).
fof(fraenkel_a_3_6_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_6_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k13_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_6_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) & m1_subset_1(D,B) ) => ( r2_hidden(A,a_3_6_zf_fund1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,B) & m1_subset_1(F,B) & A = k9_classes2(B,E,F) & r2_hidden(E,k1_classes2(B,D)) & r2_hidden(F,k1_classes2(B,C)) ) ) ) )).
fof(fraenkel_a_3_6_zf_model,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & m2_subset_1(C,k4_ordinal1,k1_zf_lang) & v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ( r2_hidden(A,a_3_6_zf_model(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k3_zf_model(B)) & A = E & ! [F] : ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k1_zf_lang,B) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang,B))) ) => ( ( F = k5_zf_model(k24_zf_lang(k8_zf_lang(C,D)),B) & G = E ) => ( r2_hidden(G,F) & ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,k1_zf_lang,B) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang,B))) ) => ( ! [I] : ( m2_subset_1(I,k4_ordinal1,k1_zf_lang) => ( k3_funct_2(k1_zf_lang,B,H,I) != k3_funct_2(k1_zf_lang,B,G,I) => k23_zf_lang(k8_zf_lang(C,D)) = I ) ) => r2_hidden(H,F) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_3_6_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(C,B) & v1_zmodul01(D) & m1_zmodul01(D,B) ) => ( r2_hidden(A,a_3_6_zmodul01(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,F,E) & r1_struct_0(C,F) & r1_struct_0(D,E) ) ) ) )).
fof(fraenkel_a_3_7_circled1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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_circled1(C,B) & m1_rlvect_2(C,B) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_7_circled1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & k3_funct_2(u1_struct_0(B),k1_numbers,k8_rlvect_2(B,D,C),E) != k5_numbers ) ) ) )).
fof(fraenkel_a_3_7_circuit1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & v5_msafree2(B) & l1_msualg_1(B) & v4_msualg_1(C,B) & v4_msafree2(C,B) & l3_msualg_1(C,B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_7_circuit1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(B,k5_msafree2(B,C)),D)) & A = k5_circuit1(B,C,D,E) ) ) ) )).
fof(fraenkel_a_3_7_convex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_rlvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_7_convex1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k1_algstr_0(B,E,F) & r2_hidden(E,k1_convex1(B,C,D)) & r2_hidden(F,k1_convex1(B,C,k6_xcmplx_0(1,D))) ) ) ) )).
fof(fraenkel_a_3_7_convex2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_rlsub_1(D,B) ) => ( r2_hidden(A,a_3_7_convex2(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,E,F) & r2_hidden(E,k3_rusub_4(B,C)) & r2_hidden(F,k3_rusub_4(B,D)) ) ) ) )).
fof(fraenkel_a_3_7_convex4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_csspace(B) & l1_csspace(B) & m1_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_7_convex4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_xxreal_0(k4_complex1(k12_csspace(B,E,C)),D) ) ) ) )).
fof(fraenkel_a_3_7_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(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))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_7_finance1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & r2_hidden(k3_funct_2(B,k1_numbers,C,E),k2_rcomp_1(k2_xxreal_0,D)) ) ) ) )).
fof(fraenkel_a_3_7_gobrd13,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_3_7_gobrd13(B,C,D)) <=> ? [E] : ? [F] : ( v1_xreal_0(E) & v1_xreal_0(F) & A = k19_euclid(E,F) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,B,1)),E) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,1,k7_nat_d(C,1))),F) & r1_xxreal_0(F,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,1,C))) ) ) ) )).
fof(fraenkel_a_3_7_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) & m2_finseq_2(C,u4_struct_0(B),k9_graph_3(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_7_graph_3(B,C,D)) <=> ? [E] : ( m2_finseq_2(E,u4_struct_0(B),k9_graph_3(B)) & A = E & k10_xtuple_0(E) = k10_xtuple_0(C) & ? [F] : ( m2_finseq_1(F,u1_struct_0(B)) & r1_graph_2(B,F,E) & k1_funct_1(F,1) = D ) ) ) ) )).
fof(fraenkel_a_3_7_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(B),u1_struct_0(C)) & v1_group_6(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)))) ) => ( r2_hidden(A,a_3_7_group_9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,E) = k1_group_1(C) ) ) ) )).
fof(fraenkel_a_3_7_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) ) => ( r2_hidden(A,a_3_7_mathmorp(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(B))) & A = E & r1_tarski(k1_mathmorp(k15_euclid(B),E,D),C) ) ) ) )).
fof(fraenkel_a_3_7_metric_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & l1_metric_1(C) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_7_metric_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = E & r1_xxreal_0(k1_metric_1(C,D,E),B) ) ) ) )).
fof(fraenkel_a_3_7_metrizts,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v6_metric_1(B) & v7_metric_1(B) & v8_metric_1(B) & v9_metric_1(B) & l1_metric_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(B)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(B)))) ) => ( r2_hidden(A,a_3_7_metrizts(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(k5_numbers,k6_xcmplx_0(k1_funct_1(k6_weierstr(B,D),E),k1_funct_1(k6_weierstr(B,C),E))) ) ) ) )).
fof(fraenkel_a_3_7_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) => ( r2_hidden(A,a_3_7_mmlquery(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = k1_mmlquery(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_7_morph_01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_7_morph_01(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k1_morph_01(B,E,D) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_7_normsp_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_7_normsp_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(D,k2_normsp_0(B,k5_algstr_0(B,E,C))) ) ) ) )).
fof(fraenkel_a_3_7_quantal1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_7_quantal1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_lattices(B,k6_algstr_0(B,C,E),D) ) ) ) )).
fof(fraenkel_a_3_7_rlaffin3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(B)) & v1_finset_1(D) & v1_rlaffin1(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_7_rlaffin3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_algstr_0(B,C,E) & r2_hidden(E,k4_rlaffin1(B,D)) ) ) ) )).
fof(fraenkel_a_3_7_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_7_rltopsp1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k1_algstr_0(B,E,F) & r2_hidden(E,D) & r2_hidden(F,C) ) ) ) )).
fof(fraenkel_a_3_7_rusub_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_7_rusub_5(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,E,F) & r2_hidden(E,C) & r2_hidden(F,k6_domain_1(u1_struct_0(B),D)) ) ) ) )).
fof(fraenkel_a_3_7_setlim_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) & m1_subset_1(D,k4_ordinal1) ) => ( r2_hidden(A,a_3_7_setlim_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & A = k3_subset_1(B,k3_funct_2(k4_ordinal1,k9_setfam_1(B),C,E)) & r1_xxreal_0(D,E) ) ) ) )).
fof(fraenkel_a_3_7_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_7_topreal9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) & A = E & r1_xxreal_0(k12_euclid(k5_algstr_0(k15_euclid(2),E,k19_euclid(B,C))),D) ) ) ) )).
fof(fraenkel_a_3_7_waybel21,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v2_pre_topc(B) & 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) & v2_waybel19(B) & l1_waybel_9(B) & ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_7_waybel21(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k5_waybel_9(B,C,D))) & A = k2_yellow_0(B,a_4_5_waybel21(B,C,D,E)) ) ) ) )).
fof(fraenkel_a_3_7_waybel33,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_7_waybel33(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = E & r1_orders_2(C,D,E) ) ) ) )).
fof(fraenkel_a_3_7_waybel_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_7_waybel_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k11_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_7_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & ~ v2_struct_0(D) & l1_waybel_0(D,B) ) => ( r2_hidden(A,a_3_7_waybel_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k11_lattice3(B,C,E) & r2_hidden(E,k2_relset_1(u1_struct_0(B),u1_waybel_0(B,D))) ) ) ) )).
fof(fraenkel_a_3_7_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_7_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k13_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_7_yellow_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(B,C)))) ) => ( r2_hidden(A,a_3_7_yellow_9(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(C))) & A = k3_borsuk_1(B,C,E,F) & r1_tarski(k3_borsuk_1(B,C,E,F),D) & v3_pre_topc(E,B) & v3_pre_topc(F,C) ) ) ) )).
fof(fraenkel_a_3_7_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) & m1_subset_1(D,B) ) => ( r2_hidden(A,a_3_7_zf_fund1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,B) & m1_subset_1(F,B) & A = k1_zf_fund1(B,E,F) & r2_hidden(E,k1_classes2(B,D)) & r2_hidden(F,k1_classes2(B,C)) ) ) ) )).
fof(fraenkel_a_3_7_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(C,B) & m1_zmodul01(D,B) ) => ( r2_hidden(A,a_3_7_zmodul01(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,F,E) & r1_struct_0(k7_zmodul01(B,C,D),F) & r1_struct_0(D,E) ) ) ) )).
fof(fraenkel_a_3_8_convex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_rlvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_8_convex1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_rlvect_1(B,E,k6_xcmplx_0(1,D)) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_8_convex2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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_convex1(C,B) & m1_rlvect_2(C,B) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_8_convex2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & k3_funct_2(u1_struct_0(B),k1_numbers,k8_rlvect_2(B,D,C),E) != k5_numbers ) ) ) )).
fof(fraenkel_a_3_8_convex4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_csspace(B) & l1_csspace(B) & m1_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_8_convex4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ~ r1_xxreal_0(D,k4_complex1(k12_csspace(B,E,C))) ) ) ) )).
fof(fraenkel_a_3_8_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(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))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_8_finance1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & r2_hidden(k3_funct_2(B,k1_numbers,C,E),k2_xxreal_1(k2_xxreal_0,D)) ) ) ) )).
fof(fraenkel_a_3_8_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) & m1_subset_1(C,k1_zfmisc_1(k1_fomodel4(B))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(k1_fomodel4(B)),k1_fomodel4(B)))) ) => ( r2_hidden(A,a_3_8_fomodel4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_fomodel4(B)) & A = E & r2_hidden(k1_domain_1(k1_zfmisc_1(k1_fomodel4(B)),k1_fomodel4(B),C,E),D) ) ) ) )).
fof(fraenkel_a_3_8_gobrd13,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_3_8_gobrd13(B,C,D)) <=> ? [E] : ? [F] : ( v1_xreal_0(E) & v1_xreal_0(F) & A = k19_euclid(E,F) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,B,1)),E) & r1_xxreal_0(E,k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,k1_nat_1(B,1),1))) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,1,k7_nat_d(C,1))),F) & r1_xxreal_0(F,k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,1,C))) ) ) ) )).
fof(fraenkel_a_3_8_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) & m1_subset_1(D,u1_struct_0(k15_euclid(B))) ) => ( r2_hidden(A,a_3_8_mathmorp(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(B))) & A = k3_rlvect_1(k15_euclid(B),E,D) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_8_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) => ( r2_hidden(A,a_3_8_mmlquery(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = k14_funcop_1(k1_mmlquery(B,C,E),k1_xboole_0,k1_tarski(E),k1_xboole_0) & r2_hidden(E,k1_tarski(D)) ) ) ) )).
fof(fraenkel_a_3_8_morph_01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_8_morph_01(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k1_morph_01(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_8_rlaffin3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(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) & l1_rlvect_1(C) & v1_finset_1(D) & v1_rlaffin1(D,C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) ) => ( r2_hidden(A,a_3_8_rlaffin3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = k1_rlvect_1(C,E,B) & r2_hidden(E,k4_rlaffin1(C,D)) ) ) ) )).
fof(fraenkel_a_3_8_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v4_rlvect_1(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_8_rltopsp1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k1_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_8_rusub_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_8_rusub_5(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k5_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,k6_domain_1(u1_struct_0(B),D)) ) ) ) )).
fof(fraenkel_a_3_8_setlim_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(C)))) ) => ( r2_hidden(A,a_3_8_setlim_1(B,C,D)) <=> ? [E] : ( v7_ordinal1(E) & A = k1_funct_1(D,E) & r1_xxreal_0(k1_nat_1(B,1),E) ) ) ) )).
fof(fraenkel_a_3_8_topreal9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_8_topreal9(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) & A = E & ~ r1_xxreal_0(D,k12_euclid(k5_algstr_0(k15_euclid(2),E,k19_euclid(B,C)))) ) ) ) )).
fof(fraenkel_a_3_8_waybel12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) & ~ v1_xboole_0(C) & v4_card_3(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_8_waybel12(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_8_waybel33,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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_xboole_0(C) & v1_subset_1(C,u1_struct_0(k2_yellow_1(k2_struct_0(B)))) & v2_waybel_0(C,k2_yellow_1(k2_struct_0(B))) & v13_waybel_0(C,k2_yellow_1(k2_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(B))))) & m1_subset_1(D,u1_struct_0(k3_yellow19(B,k2_struct_0(B),C))) ) => ( r2_hidden(A,a_3_8_waybel33(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k3_yellow19(B,k2_struct_0(B),C))) & A = E & r3_orders_2(k3_yellow19(B,k2_struct_0(B),C),D,E) ) ) ) )).
fof(fraenkel_a_3_8_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & ~ v1_xboole_0(C) & v1_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_8_waybel_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k12_lattice3(B,D,E) & r2_hidden(E,k11_waybel_0(B,C)) ) ) ) )).
fof(fraenkel_a_3_8_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_8_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k13_lattice3(B,D,E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_8_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(C,B) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_8_zmodul01(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k3_rlvect_1(B,D,E) & r1_struct_0(C,E) ) ) ) )).
fof(fraenkel_a_3_9_convex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_rlvect_1(B) & l1_rlvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_9_convex1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,E,F) & r2_hidden(E,k1_convex1(B,C,k6_xcmplx_0(1,D))) & r2_hidden(F,k1_convex1(B,C,D)) ) ) ) )).
fof(fraenkel_a_3_9_convex4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_csspace(B) & l1_csspace(B) & m1_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_9_convex4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & r1_xxreal_0(k9_complex1(k12_csspace(B,E,C)),D) ) ) ) )).
fof(fraenkel_a_3_9_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(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))) & v1_xreal_0(D) ) => ( r2_hidden(A,a_3_9_finance1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = E & m1_subset_1(k3_funct_2(B,k1_numbers,C,E),k2_rcomp_1(k2_xxreal_0,D)) ) ) ) )).
fof(fraenkel_a_3_9_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(k1_fomodel4(B)),k1_fomodel4(B)))) & m2_subset_1(D,k1_zfmisc_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))) ) => ( r2_hidden(A,a_3_9_fomodel4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_fomodel4(B)) & A = E & r2_hidden(k1_domain_1(k9_setfam_1(k1_fomodel4(B)),k1_fomodel4(B),D,E),C) ) ) ) )).
fof(fraenkel_a_3_9_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(C) & v6_graph_1(C) & l1_graph_1(C) & m1_subset_1(D,u1_struct_0(C)) ) => ( r2_hidden(A,a_3_9_graph_3(B,C,D)) <=> ? [E] : ( m2_finseq_2(E,B,k3_finseq_2(B)) & A = E & v2_funct_1(E) & m2_graph_1(E,C) & ~ v1_xboole_0(E) & ? [F] : ( m2_finseq_1(F,u1_struct_0(C)) & r1_graph_2(C,F,E) & k1_funct_1(F,1) = D ) ) ) ) )).
fof(fraenkel_a_3_9_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_9_mathmorp(B,C,D)) <=> ? [E] : ( v1_xreal_0(E) & A = k3_rlvect_1(B,k1_rlvect_1(B,D,k6_xcmplx_0(1,E)),k1_rlvect_1(B,C,E)) & r1_xxreal_0(k5_numbers,E) & r1_xxreal_0(E,1) ) ) ) )).
fof(fraenkel_a_3_9_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) & m1_subset_1(D,B) ) => ( r2_hidden(A,a_3_9_mmlquery(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & A = k14_funcop_1(k1_mmlquery(B,C,E),k1_xboole_0,k1_tarski(E),k1_xboole_0) & r2_hidden(E,k1_tarski(D)) ) ) ) )).
fof(fraenkel_a_3_9_morph_01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_9_morph_01(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = k3_funct_2(k1_zfmisc_1(u1_struct_0(B)),k9_setfam_1(u1_struct_0(B)),k3_morph_01(B,D),E) & r2_hidden(E,C) ) ) ) )).
fof(fraenkel_a_3_9_osafree,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v4_osalg_1(B) & v5_osalg_1(B) & v2_osalg_4(B) & l3_osalg_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_subset_1(D,u1_struct_0(k2_osafree(B,C))) ) => ( r2_hidden(A,a_3_9_osafree(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k4_tarski(k2_trees_4(u1_struct_0(k2_osafree(B,C)),D),E) & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & ? [G] : ( r2_hidden(G,k1_funct_1(C,F)) & D = k4_tarski(G,F) & r3_orders_2(B,F,E) ) ) ) ) ) )).
fof(fraenkel_a_3_9_rlaffin3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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) & v1_finset_1(C) & v1_rlaffin1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_3_9_rlaffin3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k1_algstr_0(B,D,E) & r2_hidden(E,k4_rlaffin1(B,C)) ) ) ) )).
fof(fraenkel_a_3_9_rusub_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_9_rusub_5(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_9_waybel12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v3_yellow_0(C) & v1_lattice3(C) & v2_lattice3(C) & v3_waybel_3(C) & l1_orders_2(C) & v4_card_3(D) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) => ( r2_hidden(A,a_3_9_waybel12(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & A = E & ? [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B))) & r2_hidden(F,D) & F = E & v2_waybel12(E,C) ) ) ) ) )).
fof(fraenkel_a_3_9_waybel30,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) & v1_tops_2(C,B) & v1_cantor_1(C,B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_9_waybel30(B,C,D)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & A = E & r2_hidden(E,C) & r1_tarski(E,D) ) ) ) )).
fof(fraenkel_a_3_9_waybel33,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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_xboole_0(C) & v1_subset_1(C,u1_struct_0(k2_yellow_1(k2_struct_0(B)))) & v2_waybel_0(C,k2_yellow_1(k2_struct_0(B))) & v13_waybel_0(C,k2_yellow_1(k2_struct_0(B))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(B))))) & m1_subset_1(D,u1_struct_0(k3_yellow19(B,k2_struct_0(B),C))) ) => ( r2_hidden(A,a_3_9_waybel33(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(k5_waybel_9(B,k3_yellow19(B,k2_struct_0(B),C),D))) & A = k2_waybel_0(B,k5_waybel_9(B,k3_yellow19(B,k2_struct_0(B),C),D),E) ) ) ) )).
fof(fraenkel_a_3_9_waybel_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_9_waybel_2(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & A = k11_lattice3(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_3_9_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_3_9_yellow_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = E & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r1_orders_2(B,E,F) & r2_hidden(F,k2_yellow_4(B,C,D)) ) ) ) ) )).
fof(fraenkel_a_3_9_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) & m1_subset_1(D,B) ) => ( r2_hidden(A,a_3_9_zf_fund1(B,C,D)) <=> ? [E] : ? [F] : ( m1_subset_1(E,B) & m1_subset_1(F,B) & A = k1_zf_fund1(B,E,F) & r2_hidden(E,k1_classes2(B,C)) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_4_0_afproj,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v7_struct_0(B) & v1_diraf(B) & l1_analoaf(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_0_afproj(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = F & ? [G] : ( m1_subset_1(G,u1_struct_0(B)) & r2_aff_1(B,F,G,k2_aff_1(B,C,E)) & r2_hidden(G,k2_aff_1(B,C,D)) ) ) ) ) )).
fof(fraenkel_a_4_0_algstr_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) & ~ v2_struct_0(C) & l3_algstr_0(C) & 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)))) ) => ( r2_hidden(A,a_4_0_algstr_4(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = F & k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,F) = k3_funct_2(u1_struct_0(B),u1_struct_0(C),E,F) ) ) ) )).
fof(fraenkel_a_4_0_amistd_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_setfam_1(B) & ~ v2_struct_0(C) & v2_memstr_0(C,B) & v3_memstr_0(C,B) & l1_extpro_1(C,B) & v7_ordinal1(D) & m1_subset_1(E,u1_compos_1(C)) ) => ( r2_hidden(A,a_4_0_amistd_1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k4_card_3(k2_memstr_0(B,C))) & A = k5_memstr_0(B,C,k2_extpro_1(B,C,E,F)) & k5_memstr_0(B,C,F) = D ) ) ) )).
fof(fraenkel_a_4_0_bcialg_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m2_subset_1(D,u1_struct_0(B),C) & m2_subset_1(E,u1_struct_0(B),C) ) => ( r2_hidden(A,a_4_0_bcialg_1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = F & r1_bcialg_1(B,k1_bcialg_1(B,F,D),E) ) ) ) )).
fof(fraenkel_a_4_0_bcialg_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(C,B) & v12_bcialg_1(D,B) & m2_bcialg_1(D,B) & m5_bcialg_2(E,B,D) ) => ( r2_hidden(A,a_4_0_bcialg_6(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(C)) & A = k6_eqrel_1(u1_struct_0(B),u1_struct_0(B),E,F) & r2_hidden(k6_eqrel_1(u1_struct_0(B),u1_struct_0(B),E,F),u1_struct_0(k9_bcialg_2(B,E))) ) ) ) )).
fof(fraenkel_a_4_0_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( l2_struct_0(B) & ~ v2_struct_0(C) & l1_vectsp_1(C,B) & ~ v2_struct_0(D) & l1_vectsp_1(D,B) & v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)),u1_struct_0(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)),u1_struct_0(B)))) ) => ( r2_hidden(A,a_4_0_bilinear(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(C)) & A = F & ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => k2_binop_1(u1_struct_0(C),u1_struct_0(D),u1_struct_0(B),E,F,G) = k4_struct_0(B) ) ) ) ) )).
fof(fraenkel_a_4_0_borsuk_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & v2_pre_topc(C) & l1_pre_topc(C) & m1_pre_topc(D,B) & m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k2_borsuk_1(C,D))))) ) => ( r2_hidden(A,a_4_0_borsuk_3(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(C))) & m1_subset_1(G,k1_zfmisc_1(u1_struct_0(B))) & A = k3_borsuk_1(C,B,F,G) & ? [H] : ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(D))) & H = k9_subset_1(u1_struct_0(D),G,k2_struct_0(D)) & v3_pre_topc(F,C) & v3_pre_topc(G,B) & r2_hidden(k3_borsuk_1(C,D,F,H),E) ) ) ) ) )).
fof(fraenkel_a_4_0_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) & ~ v2_struct_0(C) & v2_pre_topc(C) & v1_connsp_1(C) & l1_pre_topc(C) & v1_funct_1(D) & v1_funct_2(D,u1_struct_0(C),u1_struct_0(k1_pre_topc(k3_topmetr,k5_toprealb(B)))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(k1_pre_topc(k3_topmetr,k5_toprealb(B)))))) & v1_xreal_0(E) & ~ v1_rat_1(E) ) => ( r2_hidden(A,a_4_0_borsuk_7(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k3_numbers) & A = F & r2_hidden(F,k2_relset_1(u1_struct_0(k1_pre_topc(k3_topmetr,k5_toprealb(B))),D)) & ~ r1_xxreal_0(E,F) ) ) ) )).
fof(fraenkel_a_4_0_card_fin,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_finset_1(B) & v1_finset_1(C) ) => ( r2_hidden(A,a_4_0_card_fin(B,C,D,E)) <=> ? [F] : ( v1_funct_1(F) & v1_funct_2(F,k2_xboole_0(B,k1_tarski(D)),k2_xboole_0(C,k1_tarski(E))) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k2_xboole_0(B,k1_tarski(D)),k2_xboole_0(C,k1_tarski(E))))) & A = F & r1_tarski(k2_relset_1(k2_xboole_0(C,k1_tarski(E)),k2_partfun1(k2_xboole_0(B,k1_tarski(D)),k2_xboole_0(C,k1_tarski(E)),F,B)),C) & k1_funct_1(F,D) = E ) ) ) )).
fof(fraenkel_a_4_0_cc0sp2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v1_compts_1(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) & v1_xreal_0(D) & v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),k2_numbers) & v1_cc0sp2(E,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),k2_numbers))) ) => ( r2_hidden(A,a_4_0_cc0sp2(B,C,D,E)) <=> ? [F] : ( v1_xcmplx_0(F) & A = F & ~ r1_xxreal_0(k7_xcmplx_0(D,3),k9_complex1(k6_xcmplx_0(F,k3_funct_2(u1_struct_0(B),k2_numbers,E,C)))) ) ) ) )).
fof(fraenkel_a_4_0_chain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & m1_chain_1(C,B) & m1_subset_1(D,k4_ordinal1) & m2_subset_1(E,k1_zfmisc_1(k1_euclid(B)),k4_chain_1(B,C,D)) ) => ( r2_hidden(A,a_4_0_chain_1(B,C,D,E)) <=> ? [F] : ( m2_subset_1(F,k1_zfmisc_1(k1_euclid(B)),k4_chain_1(B,C,k1_nat_1(D,1))) & A = F & r1_tarski(E,F) ) ) ) )).
fof(fraenkel_a_4_0_circled1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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_rltopsp1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v3_rltopsp1(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_0_circled1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k1_rlvect_1(B,F,E) & r2_hidden(F,k1_rusub_5(B,C,D)) ) ) ) )).
fof(fraenkel_a_4_0_circuit1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) & v4_msualg_1(C,B) & v4_msafree2(C,B) & l3_msualg_1(C,B) & m1_subset_1(D,u1_struct_0(B)) & ~ v1_xboole_0(E) ) => ( r2_hidden(A,a_4_0_circuit1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,E) & A = F & ? [G] : ( m1_subset_1(G,u4_struct_0(B)) & k1_funct_1(u1_msualg_1(B),G) = k1_xboole_0 & k1_funct_1(u2_msualg_1(B),G) = D & r2_hidden(F,k2_relset_1(k4_msualg_1(B,G,C),k5_msualg_1(B,G,C))) ) ) ) ) )).
fof(fraenkel_a_4_0_circuit2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & v5_msafree2(B) & l1_msualg_1(B) & v4_msualg_1(C,B) & v4_msafree2(C,B) & l3_msualg_1(C,B) & m1_subset_1(D,u1_struct_0(B)) & ~ v1_xboole_0(E) ) => ( r2_hidden(A,a_4_0_circuit2(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,E) & A = F & ? [G] : ( m1_subset_1(G,u4_struct_0(B)) & k3_funct_2(u4_struct_0(B),k3_finseq_2(u1_struct_0(B)),u1_msualg_1(B),G) = k1_xboole_0 & k3_funct_2(u4_struct_0(B),u1_struct_0(B),u2_msualg_1(B),G) = D & r2_hidden(F,k10_xtuple_0(k5_msualg_1(B,G,C))) ) ) ) ) )).
fof(fraenkel_a_4_0_closure2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) & m1_subset_1(D,k1_zfmisc_1(k1_closure2(B,C))) ) => ( r2_hidden(A,a_4_0_closure2(B,C,D,E)) <=> ? [F] : ( m1_closure2(F,B,C,k2_closure2(B,C)) & A = k1_funct_1(F,E) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_4_0_closure3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) & m1_subset_1(D,k1_zfmisc_1(k1_closure2(B,C))) ) => ( r2_hidden(A,a_4_0_closure3(B,C,D,E)) <=> ? [F] : ( m1_closure2(F,B,C,k6_closure2(B,C)) & A = k1_funct_1(F,E) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_4_0_clvect_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(B)) & v1_xcmplx_0(D) & m1_clvect_1(E,B) ) => ( r2_hidden(A,a_4_0_clvect_1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,k1_clvect_1(B,C,D),F) & r1_struct_0(E,F) ) ) ) )).
fof(fraenkel_a_4_0_combgras,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( l1_incsp_1(B) & l1_incsp_1(C) & l1_combgras(D,B,C) & m1_subset_1(E,k1_zfmisc_1(u1_incsp_1(B))) ) => ( r2_hidden(A,a_4_0_combgras(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_incsp_1(C)) & A = F & ? [G] : ( m1_subset_1(G,u1_incsp_1(B)) & r2_hidden(G,E) & k2_combgras(B,C,D,G) = F ) ) ) ) )).
fof(fraenkel_a_4_0_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( l1_compos_1(B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v3_compos_1(C,B) & v4_compos_1(C,B) & ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(B)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v3_compos_1(D,B) & v4_compos_1(D,B) & ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(B)) & v1_funct_1(E) & v1_finset_1(E) & v1_afinsq_1(E) & v3_compos_1(E,B) & v4_compos_1(E,B) ) => ( r2_hidden(A,a_4_0_compos_1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k4_ordinal1) & A = F & ~ r1_xxreal_0(k6_xcmplx_0(k6_xcmplx_0(k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),k5_card_1(E)),1),1),F) ) ) ) )).
fof(fraenkel_a_4_0_convex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v2_rlvect_1(B) & v3_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,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_0_convex1(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k3_rlvect_1(B,F,G) & r2_hidden(F,k1_convex1(B,C,E)) & r2_hidden(G,k1_convex1(B,D,k6_xcmplx_0(1,E))) ) ) ) )).
fof(fraenkel_a_4_0_ec_pf_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(B) & v1_int_2(B) & m1_subset_1(C,u1_struct_0(k9_int_3(B))) & m1_subset_1(D,u1_struct_0(k9_int_3(B))) & m1_subset_1(E,u1_struct_0(k9_int_3(B))) ) => ( r2_hidden(A,a_4_0_ec_pf_1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k9_int_3(B))) & A = F & k2_binom(k9_int_3(B),F,2) = k3_rlvect_1(k9_int_3(B),k3_rlvect_1(k9_int_3(B),k2_binom(k9_int_3(B),E,3),k8_group_1(k9_int_3(B),C,E)),D) ) ) ) )).
fof(fraenkel_a_4_0_euclid_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,u1_struct_0(k15_euclid(B))) & m1_subset_1(D,u1_struct_0(k15_euclid(B))) & m1_subset_1(E,u1_struct_0(k15_euclid(B))) ) => ( r2_hidden(A,a_4_0_euclid_3(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(B))) & A = F & ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & ? [I] : ( v1_xreal_0(I) & r1_xxreal_0(k5_numbers,G) & r1_xxreal_0(k5_numbers,H) & r1_xxreal_0(k5_numbers,I) & k2_xcmplx_0(k2_xcmplx_0(G,H),I) = 1 & F = k3_rlvect_1(k15_euclid(B),k3_rlvect_1(k15_euclid(B),k1_rlvect_1(k15_euclid(B),C,G),k1_rlvect_1(k15_euclid(B),D,H)),k1_rlvect_1(k15_euclid(B),E,I)) ) ) ) ) ) ) )).
fof(fraenkel_a_4_0_euclid_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(B) & m2_finseq_2(C,k1_numbers,k1_euclid(B)) & m2_finseq_2(D,k1_numbers,k1_euclid(B)) & m2_finseq_2(E,k1_numbers,k1_euclid(B)) ) => ( r2_hidden(A,a_4_0_euclid_4(B,C,D,E)) <=> ? [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(B)) & A = k12_euclid(k8_euclid(B,E,F)) & r2_hidden(F,k2_euclid_4(B,C,D)) ) ) ) )).
fof(fraenkel_a_4_0_euclidlp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(B,k4_ordinal1) & m2_finseq_2(C,k1_numbers,k1_euclid(B)) & m2_finseq_2(D,k1_numbers,k1_euclid(B)) & m2_finseq_2(E,k1_numbers,k1_euclid(B)) ) => ( r2_hidden(A,a_4_0_euclidlp(B,C,D,E)) <=> ? [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(B)) & A = k12_euclid(k8_euclid(B,C,F)) & r2_hidden(F,k2_euclid_4(B,D,E)) ) ) ) )).
fof(fraenkel_a_4_0_fcont_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_0_fcont_1(B,C,D,E)) <=> ? [F] : ( v1_xreal_0(F) & A = F & ~ r1_xxreal_0(F,k6_xcmplx_0(k1_funct_1(k2_partfun1(k1_numbers,k1_numbers,C,B),D),E)) & ~ r1_xxreal_0(k2_xcmplx_0(k1_funct_1(k2_partfun1(k1_numbers,k1_numbers,C,B),D),E),F) ) ) ) )).
fof(fraenkel_a_4_0_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))) ) => ( r2_hidden(A,a_4_0_finance1(B,C,D,E)) <=> ? [F] : ( v1_funct_1(F) & v1_funct_2(F,B,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,C))) & A = F & r1_finance1(B,C,D,E,F) ) ) ) )).
fof(fraenkel_a_4_0_flang_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(B))) & v7_ordinal1(D) & v7_ordinal1(E) ) => ( r2_hidden(A,a_4_0_flang_2(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(B))) & A = F & ? [G] : ( v7_ordinal1(G) & r1_xxreal_0(D,G) & r1_xxreal_0(G,E) & F = k7_flang_1(B,C,G) ) ) ) ) )).
fof(fraenkel_a_4_0_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) & v7_ordinal1(E) ) => ( r2_hidden(A,a_4_0_fomodel3(B,C,D,E)) <=> ? [F] : ? [G] : ( m2_finseq_2(F,B,k4_finseq_2(E,B)) & m2_finseq_2(G,C,k4_finseq_2(E,C)) & A = k1_domain_1(k4_finseq_2(E,B),k4_finseq_2(E,C),F,G) & ! [H] : ( r2_hidden(H,k2_finseq_1(E)) => r2_hidden(k4_tarski(k1_funct_1(F,H),k1_funct_1(G,H)),D) ) ) ) ) )).
fof(fraenkel_a_4_0_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) & v5_fomodel1(C,B) & m1_subset_1(C,k1_fomodel1(B)) & v3_card_1(D,k1_int_2(k19_fomodel1(B,C))) & m2_subset_1(D,k3_finseq_2(k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0))),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0)),k35_fomodel1(B))) & v3_card_1(E,k1_int_2(k19_fomodel1(B,C))) & m2_subset_1(E,k3_finseq_2(k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0))),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0)),k35_fomodel1(B))) ) => ( r2_hidden(A,a_4_0_fomodel4(B,C,D,E)) <=> ? [F] : ? [G] : ? [H] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(k1_int_2(k19_fomodel1(B,C)))) & v1_funct_1(G) & v1_funct_2(G,k2_finseq_1(k1_int_2(k19_fomodel1(B,C))),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0))) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(k1_int_2(k19_fomodel1(B,C))),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0))))) & v1_funct_1(H) & v1_funct_2(H,k2_finseq_1(k1_int_2(k19_fomodel1(B,C))),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0))) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(k1_int_2(k19_fomodel1(B,C))),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0))))) & A = k42_fomodel1(B,k42_fomodel1(B,k43_fomodel1(B,k31_fomodel2(B)),k3_funct_2(k2_finseq_1(k1_int_2(k19_fomodel1(B,C))),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0)),G,F)),k3_funct_2(k2_finseq_1(k1_int_2(k19_fomodel1(B,C))),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0)),H,F)) & G = D & H = E ) ) ) )).
fof(fraenkel_a_4_0_frechet,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & ~ v2_struct_0(C) & l1_pre_topc(C) & 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,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C)))) ) => ( r2_hidden(A,a_4_0_frechet(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(C))) & A = k8_relset_1(u1_struct_0(B),u1_struct_0(C),D,F) & r2_hidden(F,E) ) ) ) )).
fof(fraenkel_a_4_0_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(B))) & ~ v2_struct_0(D) & l1_fsm_3(D,B,C) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(D))) ) => ( r2_hidden(A,a_4_0_fsm_3(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k8_afinsq_1(B)) & A = F & ~ r1_xboole_0(E,k3_rewrite3(B,C,D,F,u1_fsm_3(B,C,D))) ) ) ) )).
fof(fraenkel_a_4_0_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & l1_altcat_1(B) & ~ v2_struct_0(C) & l1_altcat_1(C) & m1_subset_1(D,u1_struct_0(C)) & m1_subset_1(E,k1_altcat_1(C,D,D)) ) => ( r2_hidden(A,a_4_0_functor0(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k4_tarski(k4_tarski(F,G),k7_funcop_1(k1_altcat_1(B,F,G),E)) ) ) ) )).
fof(fraenkel_a_4_0_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v6_graph_1(B) & l1_graph_1(B) & v2_funct_1(C) & v1_msscyc_1(C,B) & m2_graph_1(C,B) & m2_finseq_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_0_graph_3(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k4_ordinal1) & A = F & r1_xxreal_0(1,F) & r1_xxreal_0(F,k3_finseq_1(C)) & k1_funct_1(D,F) = E ) ) ) )).
fof(fraenkel_a_4_0_graph_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_0_graph_5(B,C,D,E)) <=> ? [F] : ( v7_graph_1(F,B) & v1_graph_4(F,B) & m2_graph_1(F,B) & A = F & r4_graph_5(B,F,C,D,E) ) ) ) )).
fof(fraenkel_a_4_0_groeb_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v3_ordinal1(B) & v1_partfun1(C,k15_pre_poly(B)) & v1_relat_2(C) & v4_relat_2(C) & v6_relat_2(C) & v8_relat_2(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),k15_pre_poly(B)))) & ~ v2_struct_0(D) & ~ v7_struct_0(D) & v13_algstr_0(D) & v4_vectsp_1(D) & v5_vectsp_1(D) & v3_rlvect_1(D) & v4_rlvect_1(D) & l6_algstr_0(D) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(B,D)))) ) => ( r2_hidden(A,a_4_0_groeb_1(B,C,D,E)) <=> ? [F] : ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(B),u1_struct_0(D)) & v1_polynom1(F,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(D)))) & A = k3_termord(B,C,D,F) & r2_hidden(F,E) & F != k8_polynom1(B,D) ) ) ) )).
fof(fraenkel_a_4_0_groeb_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v3_ordinal1(B) & ~ 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) & v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(B),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(C)))) & v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(B),u1_struct_0(C)) & v1_polynom7(E,B,C) & v3_polynom7(E,B,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(C)))) ) => ( r2_hidden(A,a_4_0_groeb_3(B,C,D,E)) <=> ? [F] : ( m2_subset_1(F,k14_pre_poly(B),k15_pre_poly(B)) & A = k11_pre_poly(B,k2_polynom7(B,C,E),F) & r2_hidden(F,k3_polynom1(k15_pre_poly(B),C,D)) ) ) ) )).
fof(fraenkel_a_4_0_group_10,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) & ~ v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),k1_funct_2(C,C)) & v1_group_10(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),k1_funct_2(C,C)))) & m1_subset_1(E,k1_zfmisc_1(C)) ) => ( r2_hidden(A,a_4_0_group_10(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = F & k7_relset_1(C,C,k1_group_10(B,C,D,F),E) = E ) ) ) )).
fof(fraenkel_a_4_0_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,B) & l1_group_9(C,B) & v4_group_9(D,B,C) & m1_group_9(D,B,C) & m1_subset_1(E,B) ) => ( r2_hidden(A,a_4_0_group_9(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,k7_group_9(B,C,D)) & m1_subset_1(G,k7_group_9(B,C,D)) & A = k4_tarski(F,G) & ? [H] : ( m1_subset_1(H,u1_struct_0(C)) & ? [I] : ( m1_subset_1(I,u1_struct_0(C)) & r2_hidden(H,F) & r2_hidden(I,G) & I = k3_funct_2(u1_struct_0(C),u1_struct_0(C),k3_group_9(B,C,E),H) ) ) ) ) ) )).
fof(fraenkel_a_4_0_heyting2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_finset_1(C) & m1_subset_1(D,k5_finsub_1(k4_partfun1(B,C))) & m1_subset_1(E,k5_finsub_1(k4_partfun1(B,C))) ) => ( r2_hidden(A,a_4_0_heyting2(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k4_partfun1(D,E)) & A = k3_tarski(a_5_0_heyting2(B,C,D,E,F)) & k9_xtuple_0(F) = D ) ) ) )).
fof(fraenkel_a_4_0_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v3_rlvect_1(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_4_0_ideal_1(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k1_algstr_0(B,F,G) & r2_hidden(F,C) & r2_hidden(G,k11_ideal_1(B,D,E)) ) ) ) )).
fof(fraenkel_a_4_0_integra2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & ~ v1_xboole_0(C) & ~ v1_xboole_0(D) & v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,k1_numbers))) ) => ( r2_hidden(A,a_4_0_integra2(B,C,D,E)) <=> ? [F] : ( v1_xreal_0(F) & A = k3_xcmplx_0(B,F) & r2_hidden(F,k1_rvsum_1(k2_partfun1(C,k1_numbers,E,D))) ) ) ) )).
fof(fraenkel_a_4_0_jgraph_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_0_jgraph_6(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & ~ r1_xxreal_0(k17_euclid(F),B) & ~ r1_xxreal_0(C,k17_euclid(F)) & ~ r1_xxreal_0(k18_euclid(F),D) & ~ r1_xxreal_0(E,k18_euclid(F)) ) ) ) )).
fof(fraenkel_a_4_0_jgraph_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_0_jgraph_8(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & r1_xxreal_0(B,k17_euclid(F)) & r1_xxreal_0(k17_euclid(F),C) & r1_xxreal_0(D,k18_euclid(F)) & r1_xxreal_0(k18_euclid(F),E) ) ) ) )).
fof(fraenkel_a_4_0_jordan,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_0_jordan(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & ~ ( ~ ( k17_euclid(F) = B & r1_xxreal_0(k18_euclid(F),E) & r1_xxreal_0(D,k18_euclid(F)) ) & ~ ( r1_xxreal_0(k17_euclid(F),C) & r1_xxreal_0(B,k17_euclid(F)) & k18_euclid(F) = E ) & ~ ( r1_xxreal_0(k17_euclid(F),C) & r1_xxreal_0(B,k17_euclid(F)) & k18_euclid(F) = D ) & ~ ( k17_euclid(F) = C & r1_xxreal_0(k18_euclid(F),E) & r1_xxreal_0(D,k18_euclid(F)) ) ) ) ) ) )).
fof(fraenkel_a_4_0_jordan1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_0_jordan1(B,C,D,E)) <=> ? [F] : ? [G] : ( v1_xreal_0(F) & v1_xreal_0(G) & A = k19_euclid(F,G) & ~ r1_xxreal_0(F,B) & ~ r1_xxreal_0(D,F) & ~ r1_xxreal_0(G,C) & ~ r1_xxreal_0(E,G) ) ) ) )).
fof(fraenkel_a_4_0_jordan16,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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(E,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_4_0_jordan16(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & r1_jordan5c(B,C,D,F,E) ) ) ) )).
fof(fraenkel_a_4_0_jordan18,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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))) & ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_4_0_jordan18(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & r1_jordan5c(E,B,C,B,F) & r1_jordan5c(E,B,C,F,D) ) ) ) )).
fof(fraenkel_a_4_0_jordan20,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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(E,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_4_0_jordan20(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & r1_jordan5c(B,C,D,E,F) & r1_jordan5c(B,C,D,F,E) ) ) ) )).
fof(fraenkel_a_4_0_jordan2b,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(B,k4_ordinal1) & v1_xreal_0(C) & v1_xreal_0(D) & m1_subset_1(E,k4_ordinal1) ) => ( r2_hidden(A,a_4_0_jordan2b(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(B))) & A = F & ~ r1_xxreal_0(k7_partfun1(k1_numbers,F,E),C) & ~ r1_xxreal_0(D,k7_partfun1(k1_numbers,F,E)) ) ) ) )).
fof(fraenkel_a_4_0_jordan5a,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & m1_subset_1(D,u1_struct_0(k2_topmetr(B,C))) & m1_subset_1(E,k1_numbers) ) => ( r2_hidden(A,a_4_0_jordan5a(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k2_topmetr(B,C))) & A = F & ~ r1_xxreal_0(E,k3_metric_1(k2_topmetr(B,C),D,F)) ) ) ) )).
fof(fraenkel_a_4_0_jordan6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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(E,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_4_0_jordan6(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & r1_jordan5c(B,C,D,F,E) ) ) ) )).
fof(fraenkel_a_4_0_jordan_a,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(B) & ~ v1_xboole_0(C) & v2_compts_1(C,k15_euclid(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) & v1_funct_1(D) & v1_funct_2(D,u1_struct_0(k2_borsuk_1(k15_euclid(B),k15_euclid(B))),k1_numbers) & v1_pscomp_1(D,k2_borsuk_1(k15_euclid(B),k15_euclid(B))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_borsuk_1(k15_euclid(B),k15_euclid(B))),k1_numbers))) & m1_subset_1(E,u1_struct_0(k15_euclid(B))) ) => ( r2_hidden(A,a_4_0_jordan_a(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(B))) & A = k1_binop_1(D,E,F) & r2_hidden(F,C) ) ) ) )).
fof(fraenkel_a_4_0_laplace,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(B) & ~ 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) & m1_matrix_2(D,k3_matrix_2(k1_nat_1(B,2))) & m1_subset_1(E,k5_finsub_1(k2_sgraph1(k2_finseq_1(k1_nat_1(B,2))))) ) => ( r2_hidden(A,a_4_0_laplace(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k2_sgraph1(k2_finseq_1(k1_nat_1(B,2)))) & A = F & r2_hidden(F,E) & k3_funct_2(k2_sgraph1(k2_finseq_1(k1_nat_1(B,2))),u1_struct_0(C),k1_matrix11(B,C,D),F) = k4_algstr_0(C,k1_group_1(C)) ) ) ) )).
fof(fraenkel_a_4_0_lmod_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & ~ v6_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) & v1_vectsp_2(B) & l6_algstr_0(B) & ~ 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) & m1_vectsp_6(D,B,C) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_0_lmod_5(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(C)) & A = F & k3_funct_2(u1_struct_0(C),u1_struct_0(B),k6_vectsp_6(B,C,E,D),F) != k4_struct_0(B) ) ) ) )).
fof(fraenkel_a_4_0_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k6_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,k6_numbers))) & v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => ( r2_hidden(A,a_4_0_lpspacc1(B,C,D,E)) <=> ? [F] : ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) & A = F & r2_hidden(F,k13_lpspacc1(B,C,D)) & r2_hidden(E,k13_lpspacc1(B,C,D)) & r1_lpspacc1(B,C,D,E,F) ) ) ) )).
fof(fraenkel_a_4_0_lpspace1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k6_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,k6_numbers))) & v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ( r2_hidden(A,a_4_0_lpspace1(B,C,D,E)) <=> ? [F] : ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) & A = F & r2_hidden(F,k9_lpspace1(B,C,D)) & r2_hidden(E,k9_lpspace1(B,C,D)) & r1_lpspace1(B,C,D,E,F) ) ) ) )).
fof(fraenkel_a_4_0_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k6_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,k6_numbers))) & v2_xxreal_0(E) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_0_lpspace2(B,C,D,E)) <=> ? [F] : ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) & A = F & ? [G] : ( m2_subset_1(G,k1_zfmisc_1(B),C) & k1_funct_1(D,k3_subset_1(B,G)) = k5_numbers & k1_relset_1(B,F) = G & r1_mesfunc6(B,C,F,G) & r3_mesfunc6(B,C,D,k2_mesfun6c(E,B,k56_valued_1(B,k1_numbers,F))) ) ) ) ) )).
fof(fraenkel_a_4_0_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_rlvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_0_mathmorp(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,F,k5_algstr_0(B,E,D)) & r2_hidden(F,C) ) ) ) )).
fof(fraenkel_a_4_0_measure6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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_xreal_0(E) ) => ( r2_hidden(A,a_4_0_measure6(B,C,D,E)) <=> ? [F] : ( v1_xreal_0(F) & A = k2_xcmplx_0(E,F) & r2_hidden(F,k7_relset_1(B,k1_numbers,D,C)) ) ) ) )).
fof(fraenkel_a_4_0_modal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) & ~ v1_xboole_0(C) & v1_trees_1(C) & m2_finseq_1(D,k4_ordinal1) & m1_trees_1(E,k5_trees_1(B,D,C)) ) => ( r2_hidden(A,a_4_0_modal_1(B,C,D,E)) <=> ? [F] : ( v7_ordinal1(F) & A = k8_finseq_1(k4_ordinal1,E,k14_trees_3(F)) & r2_hidden(k8_finseq_1(k4_ordinal1,E,k14_trees_3(F)),k5_trees_1(B,D,C)) ) ) ) )).
fof(fraenkel_a_4_0_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & v1_partfun1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k30_modelc_1(B))) & m1_subset_1(E,u1_struct_0(k48_modelc_1(B,C,D))) ) => ( r2_hidden(A,a_4_0_modelc_1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & r3_modelc_1(B,C,D,F,E) ) ) ) )).
fof(fraenkel_a_4_0_msafree,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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_subset_1(D,u4_struct_0(B)) & v7_ordinal1(E) ) => ( r2_hidden(A,a_4_0_msafree(B,C,D,E)) <=> ? [F] : ( m1_dtconstr(F,u1_struct_0(k5_msafree(B,C)),k5_trees_3(u1_struct_0(k5_msafree(B,C))),k4_dtconstr(k5_msafree(B,C))) & A = F & ~ ( ! [G] : ~ ( r2_hidden(G,k1_funct_1(C,k7_partfun1(u1_struct_0(B),k1_msualg_1(B,D),E))) & F = k1_trees_4(k4_tarski(G,k7_partfun1(u1_struct_0(B),k1_msualg_1(B,D),E))) ) & ! [G] : ( m1_subset_1(G,u4_struct_0(B)) => ~ ( k4_tarski(G,u1_struct_0(B)) = k1_funct_1(F,k1_xboole_0) & k2_msualg_1(B,G) = k7_partfun1(u1_struct_0(B),k1_msualg_1(B,D),E) ) ) ) ) ) ) )).
fof(fraenkel_a_4_0_msafree3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v11_struct_0(B) & v1_instalg1(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_relat_1(D) & v4_relat_1(D,u1_struct_0(B)) & v1_funct_1(D) & v1_partfun1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_0_msafree3(B,C,D,E)) <=> ? [F] : ( m1_dtconstr(F,u1_struct_0(k5_msafree(B,C)),k5_trees_3(u1_struct_0(k5_msafree(B,C))),k1_msaterm(B,C)) & A = F & k7_msaterm(B,C,F) = E & r2_pboole(u1_struct_0(B),k4_msafree3(B,C,F),D) ) ) ) )).
fof(fraenkel_a_4_0_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) & v9_msafree4(D,B,C) & v10_msafree4(D,B,C) & m1_msualg_4(D,B,C,C) & m1_subset_1(E,B) ) => ( r2_hidden(A,a_4_0_msafree4(B,C,D,E)) <=> ? [F] : ( m1_msafree4(F,B,C,k1_msafree4(B,C,E)) & A = k8_msafree4(k1_msafree4(B,C,E),k7_msafree4(B,C,C,D,E),F) ) ) ) )).
fof(fraenkel_a_4_0_msscyc_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) & v2_finset_1(C) & v7_ordinal1(D) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_0_msscyc_2(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(B,k11_msafree(B,C)),E)) & A = F & r1_xxreal_0(k8_msafree2(B,C,E,F),D) ) ) ) )).
fof(fraenkel_a_4_0_msualg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) & l3_msualg_1(C,B) & m1_subset_1(D,u1_struct_0(B)) & ~ v1_xboole_0(E) ) => ( r2_hidden(A,a_4_0_msualg_2(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,E) & A = F & ? [G] : ( m1_subset_1(G,u4_struct_0(B)) & k3_funct_2(u4_struct_0(B),k3_finseq_2(u1_struct_0(B)),u1_msualg_1(B),G) = k1_xboole_0 & k3_funct_2(u4_struct_0(B),u1_struct_0(B),u2_msualg_1(B),G) = D & r2_hidden(F,k10_xtuple_0(k5_msualg_1(B,G,C))) ) ) ) ) )).
fof(fraenkel_a_4_0_msualg_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) & m1_subset_1(D,k1_zfmisc_1(k1_closure2(B,k6_pboole(B,C,C)))) ) => ( r2_hidden(A,a_4_0_msualg_7(B,C,D,E)) <=> ? [F] : ( m1_closure2(F,B,k6_pboole(B,C,C),k6_closure2(B,k6_pboole(B,C,C))) & A = k1_funct_1(F,E) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_4_0_msualg_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) & v4_msualg_1(C,B) & l3_msualg_1(C,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_msualg_5(B,C)))) & m1_subset_1(E,u4_struct_0(B)) ) => ( r2_hidden(A,a_4_0_msualg_8(B,C,D,E)) <=> ? [F] : ( m1_closure2(F,u1_struct_0(B),k6_pboole(u1_struct_0(B),u3_msualg_1(B,C),u3_msualg_1(B,C)),k6_closure2(u1_struct_0(B),k6_pboole(u1_struct_0(B),u3_msualg_1(B,C),u3_msualg_1(B,C)))) & A = k1_funct_1(F,k2_msualg_1(B,E)) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_4_0_msualg_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) & v4_msualg_1(C,B) & l3_msualg_1(C,B) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k1_closure2(u1_struct_0(B),k6_pboole(u1_struct_0(B),u3_msualg_1(B,C),u3_msualg_1(B,C))))) & m1_subset_1(E,u4_struct_0(B)) ) => ( r2_hidden(A,a_4_0_msualg_9(B,C,D,E)) <=> ? [F] : ( m1_closure2(F,u1_struct_0(B),k6_pboole(u1_struct_0(B),u3_msualg_1(B,C),u3_msualg_1(B,C)),k6_closure2(u1_struct_0(B),k6_pboole(u1_struct_0(B),u3_msualg_1(B,C),u3_msualg_1(B,C)))) & A = k1_funct_1(F,k2_msualg_1(B,E)) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_4_0_ndiff_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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(B)) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_0_ndiff_1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = F & ~ r1_xxreal_0(k3_xxreal_0(D,E),k2_normsp_0(B,k5_algstr_0(B,F,C))) ) ) ) )).
fof(fraenkel_a_4_0_nfcont_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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(k1_numbers,u1_struct_0(B)))) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_0_nfcont_3(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = F & ~ r1_xxreal_0(E,k2_normsp_0(B,k5_algstr_0(B,F,k7_partfun1(u1_struct_0(B),C,D)))) ) ) ) )).
fof(fraenkel_a_4_0_nfcont_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(B,k4_ordinal1) & v1_xreal_0(C) & v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(B)))) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_0_nfcont_4(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_euclid(B)) & A = F & ~ r1_xxreal_0(E,k12_euclid(k8_euclid(B,F,k7_partfun1(k1_euclid(B),D,C)))) ) ) ) )).
fof(fraenkel_a_4_0_osafree,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v4_osalg_1(B) & v5_osalg_1(B) & l3_osalg_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_subset_1(D,u1_struct_0(k2_osafree(B,C))) & m2_finseq_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k2_osafree(B,C)),u1_struct_0(B)))) ) => ( r2_hidden(A,a_4_0_osafree(B,C,D,E)) <=> ? [F] : ? [G] : ? [H] : ( m1_subset_1(F,u4_struct_0(B)) & m1_subset_1(G,k3_msualg_1(B,F,k8_osafree(B,C))) & m1_subset_1(H,u1_struct_0(B)) & A = k4_tarski(k3_funct_2(k3_msualg_1(B,F,k8_osafree(B,C)),k4_msualg_1(B,F,k8_osafree(B,C)),k5_msualg_1(B,F,k8_osafree(B,C)),G),H) & ? [I] : ( m1_subset_1(I,u4_struct_0(B)) & D = k4_tarski(I,u1_struct_0(B)) & r1_osalg_1(B,I,F) & k3_finseq_1(k1_msualg_1(B,I)) = k3_finseq_1(k1_msualg_1(B,F)) & r3_orders_2(B,k2_msualg_1(B,I),H) & r3_orders_2(B,k2_msualg_1(B,F),H) ) & ? [I] : ( m2_finseq_2(I,u1_struct_0(B),k3_finseq_2(u1_struct_0(B))) & k4_finseq_1(I) = k4_finseq_1(E) & ! [J] : ( v7_ordinal1(J) => ( r2_hidden(J,k4_finseq_1(E)) => r2_hidden(k4_tarski(k1_funct_1(G,J),k7_partfun1(u1_struct_0(B),I,J)),k1_funct_1(E,J)) ) ) ) ) ) ) )).
fof(fraenkel_a_4_0_pdiff_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,u1_struct_0(k4_real_ns1(B))) & m1_subset_1(D,k4_ordinal1) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_0_pdiff_7(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k4_real_ns1(1))) & A = F & ~ r1_xxreal_0(E,k2_normsp_0(k4_real_ns1(1),k5_algstr_0(k4_real_ns1(1),F,k3_funct_2(u1_struct_0(k4_real_ns1(B)),u1_struct_0(k4_real_ns1(1)),k4_pdiff_1(D,B),C)))) ) ) ) )).
fof(fraenkel_a_4_0_pencil_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) & v15_pencil_1(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_pencil_1(B,C)))) & v1_funct_1(E) & v1_funct_2(E,u1_struct_0(k5_pencil_1(B,C)),u1_struct_0(k5_pencil_1(B,C))) & v1_pencil_2(E,k5_pencil_1(B,C),k5_pencil_1(B,C)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_pencil_1(B,C)),u1_struct_0(k5_pencil_1(B,C))))) ) => ( r2_hidden(A,a_4_0_pencil_2(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k5_pencil_1(B,C)))) & A = F & ~ v1_zfmisc_1(F) & v2_pencil_1(F,k5_pencil_1(B,C)) & v1_pencil_1(F,k5_pencil_1(B,C)) & r1_pencil_2(k5_pencil_1(B,C),k7_relset_1(u1_struct_0(k5_pencil_1(B,C)),u1_struct_0(k5_pencil_1(B,C)),E,D),F) ) ) ) )).
fof(fraenkel_a_4_0_pencil_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) & v1_relat_1(D) & v4_relat_1(D,B) & v1_funct_1(D) & v1_partfun1(D,B) & m1_subset_1(E,B) ) => ( r2_hidden(A,a_4_0_pencil_3(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & k1_funct_1(C,F) != k1_funct_1(k1_funct_7(D,E,k1_funct_1(C,E)),F) ) ) ) )).
fof(fraenkel_a_4_0_petri_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & v1_funct_1(E) & v1_funct_2(E,D,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(D,B))) ) => ( r2_hidden(A,a_4_0_petri_2(B,C,D,E)) <=> ? [F] : ( v1_funct_1(F) & v1_funct_2(F,C,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(C,B))) & A = F & k2_partfun1(C,B,F,D) = E ) ) ) )).
fof(fraenkel_a_4_0_pnproc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m2_pnproc_1(C,B) & m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(C))) & m1_subset_1(E,k1_zfmisc_1(k3_finseq_2(C))) ) => ( r2_hidden(A,a_4_0_pnproc_1(B,C,D,E)) <=> ? [F] : ? [G] : ( m2_finseq_2(F,C,k3_finseq_2(C)) & m2_finseq_2(G,C,k3_finseq_2(C)) & A = k1_pre_poly(C,F,G) & r2_hidden(F,D) & r2_hidden(G,E) ) ) ) )).
fof(fraenkel_a_4_0_polyred,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v3_ordinal1(B) & ~ v2_struct_0(C) & l2_struct_0(C) & v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(B),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(C)))) & v1_relat_1(E) & v4_relat_1(E,B) & v1_funct_1(E) & v1_partfun1(E,B) & v4_valued_0(E) & v2_pre_poly(E) ) => ( r2_hidden(A,a_4_0_polyred(B,C,D,E)) <=> ? [F] : ( m2_subset_1(F,k14_pre_poly(B),k15_pre_poly(B)) & A = k11_pre_poly(B,E,F) & r2_hidden(F,k3_polynom1(k15_pre_poly(B),C,D)) ) ) ) )).
fof(fraenkel_a_4_0_poset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(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) & ~ v1_xboole_0(D) & v6_orders_2(D,k6_poset_1(B,C)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_poset_1(B,C)))) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_0_poset_1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(C)) & A = F & ? [G] : ( v1_funct_1(G) & v1_funct_2(G,u1_struct_0(B),u1_struct_0(C)) & v2_poset_1(G,B,C) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)))) & r2_hidden(G,D) & F = k3_funct_2(u1_struct_0(B),u1_struct_0(C),G,E) ) ) ) ) )).
fof(fraenkel_a_4_0_pralg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & ~ v2_struct_0(C) & ~ v11_struct_0(C) & l1_msualg_1(C) & m1_pralg_2(D,B,C) & m1_subset_1(E,u4_struct_0(C)) ) => ( r2_hidden(A,a_4_0_pralg_3(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = k4_msualg_1(C,E,k5_pralg_2(B,C,D,F)) ) ) ) )).
fof(fraenkel_a_4_0_pua2mss1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & m1_eqrel_1(D,B) & m1_eqrel_1(E,C) ) => ( r2_hidden(A,a_4_0_pua2mss1(B,C,D,E)) <=> ? [F] : ? [G] : ( m2_subset_1(F,k1_zfmisc_1(B),D) & m2_subset_1(G,k1_zfmisc_1(C),E) & A = k8_mcart_1(B,C,F,G) ) ) ) )).
fof(fraenkel_a_4_0_qc_lang3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(B) & m1_qc_lang1(C) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k2_qc_lang1(C))) & v3_card_1(E,B) & m2_finseq_1(E,k2_qc_lang1(C)) ) => ( r2_hidden(A,a_4_0_qc_lang3(B,C,D,E)) <=> ? [F] : ( v7_ordinal1(F) & A = k1_funct_1(E,F) & r1_xxreal_0(1,F) & r1_xxreal_0(F,k3_finseq_1(E)) & r2_hidden(k1_funct_1(E,F),D) ) ) ) )).
fof(fraenkel_a_4_0_qc_lang4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_qc_lang1(B) & m1_subset_1(C,k9_qc_lang1(B)) & m1_subset_1(D,k9_qc_lang1(B)) & m1_subset_1(E,k9_qc_lang1(B)) ) => ( r2_hidden(A,a_4_0_qc_lang4(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_trees_1(F,k9_xtuple_0(k2_qc_lang4(B,C))) & m1_trees_1(G,k9_xtuple_0(k2_qc_lang4(B,D))) & A = k8_finseq_1(k4_ordinal1,F,G) & r2_hidden(F,k3_qc_lang4(B,C,D)) & r2_hidden(G,k3_qc_lang4(B,D,E)) ) ) ) )).
fof(fraenkel_a_4_0_quantal1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & v7_quantal1(B) & v8_quantal1(B) & l1_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_0_quantal1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k6_algstr_0(B,F,E) & r2_hidden(F,k7_domain_1(u1_struct_0(B),C,D)) ) ) ) )).
fof(fraenkel_a_4_0_random_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & v1_xreal_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))) & m1_random_1(E,B,D) ) => ( r2_hidden(A,a_4_0_random_1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & r1_xxreal_0(C,k3_funct_2(B,k1_numbers,E,F)) ) ) ) )).
fof(fraenkel_a_4_0_random_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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_xreal_0(D) & m1_random_1(E,B,C) ) => ( r2_hidden(A,a_4_0_random_2(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & r1_xxreal_0(k2_power(D,2),k12_supinf_2(E,F)) ) ) ) )).
fof(fraenkel_a_4_0_random_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(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(E) & v1_funct_2(E,k4_ordinal1,k9_setfam_1(C)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(C)))) ) => ( r2_hidden(A,a_4_0_random_3(B,C,D,E)) <=> ? [F] : ( m2_subset_1(F,k1_zfmisc_1(C),k4_measure1(C,k9_setfam_1(C),E)) & A = k8_relset_1(B,C,D,F) ) ) ) )).
fof(fraenkel_a_4_0_ranknull,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) & ~ 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) & ~ 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) & v1_funct_1(E) & v1_funct_2(E,u1_struct_0(C),u1_struct_0(D)) & v13_vectsp_1(E,C,D) & v1_mod_2(E,B,C,D) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)))) ) => ( r2_hidden(A,a_4_0_ranknull(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(C)) & A = F & k3_funct_2(u1_struct_0(C),u1_struct_0(D),E,F) = k4_struct_0(D) ) ) ) )).
fof(fraenkel_a_4_0_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ( r2_hidden(A,a_4_0_relset_2(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = k6_eqrel_1(B,C,E,F) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_4_0_rlaffin3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(C)))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(k2_xcmplx_0(C,B))))) ) => ( r2_hidden(A,a_4_0_rlaffin3(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(k2_xcmplx_0(C,B)))) & A = F & r2_hidden(k16_finseq_1(C,F),D) & r2_hidden(F,E) ) ) ) )).
fof(fraenkel_a_4_0_rlsub_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(B)) & v1_xreal_0(D) & m1_rlsub_1(E,B) ) => ( r2_hidden(A,a_4_0_rlsub_1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,k1_rlvect_1(B,C,D),F) & r1_struct_0(E,F) ) ) ) )).
fof(fraenkel_a_4_0_rlsub_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_rlsub_1(D,B) & m1_rlsub_1(E,B) ) => ( r2_hidden(A,a_4_0_rlsub_2(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k3_rlvect_1(B,G,F) & r1_struct_0(k1_rlsub_2(B,C,D),G) & r1_struct_0(E,F) ) ) ) )).
fof(fraenkel_a_4_0_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v3_rlvect_1(B) & l2_algstr_0(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_4_0_rltopsp1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k1_algstr_0(B,C,F) & r2_hidden(F,k5_rusub_4(B,E,D)) ) ) ) )).
fof(fraenkel_a_4_0_rmod_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(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) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) ) => ( r2_hidden(A,a_4_0_rmod_2(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(C)) & m1_subset_1(G,u1_struct_0(C)) & A = k3_rlvect_1(C,G,F) & r2_hidden(G,D) & r2_hidden(F,E) ) ) ) )).
fof(fraenkel_a_4_0_rmod_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(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) & m1_rmod_2(D,B,C) & m1_rmod_2(E,B,C) ) => ( r2_hidden(A,a_4_0_rmod_3(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(C)) & m1_subset_1(G,u1_struct_0(C)) & A = k3_rlvect_1(C,G,F) & r1_struct_0(D,G) & r1_struct_0(E,F) ) ) ) )).
fof(fraenkel_a_4_0_rmod_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) & v4_vectsp_2(C,B) & l1_vectsp_2(C,B) & m1_subset_1(D,u1_struct_0(B)) & m1_rmod_4(E,B,C) ) => ( r2_hidden(A,a_4_0_rmod_4(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(C)) & A = F & k3_funct_2(u1_struct_0(C),u1_struct_0(B),k7_rmod_4(B,C,D,E),F) != k4_struct_0(B) ) ) ) )).
fof(fraenkel_a_4_0_rusub_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_subset_1(D,u1_struct_0(B)) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_0_rusub_1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,k1_rlvect_1(B,D,E),F) & r1_struct_0(C,F) ) ) ) )).
fof(fraenkel_a_4_0_rusub_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_rusub_1(D,B) & m1_rusub_1(E,B) ) => ( r2_hidden(A,a_4_0_rusub_2(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k3_rlvect_1(B,F,G) & r1_struct_0(k1_rusub_2(B,C,D),F) & r1_struct_0(E,G) ) ) ) )).
fof(fraenkel_a_4_0_rusub_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_rlvect_1(B) & v2_rusub_4(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_0_rusub_5(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k3_rlvect_1(B,F,G) & r2_hidden(F,C) & r2_hidden(G,k6_domain_1(u1_struct_0(B),k3_rlvect_1(B,E,D))) ) ) ) )).
fof(fraenkel_a_4_0_scmpds_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) & v3_scmpds_4(B) & v1_int_1(C) & v1_int_1(D) & v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ( r2_hidden(A,a_4_0_scmpds_4(B,C,D,E)) <=> ? [F] : ( v7_ordinal1(F) & A = k1_nat_1(F,k5_card_1(B)) & r2_hidden(F,k2_afinsq_1(k9_compos_1(k1_scmpds_2,k7_scmpds_2(E,C,D)))) ) ) ) )).
fof(fraenkel_a_4_0_sgraph1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_sgraph1(C,B) & m1_subset_1(D,u1_struct_0(C)) & m1_subset_1(E,u1_struct_0(C)) ) => ( r2_hidden(A,a_4_0_sgraph1(B,C,D,E)) <=> ? [F] : ( m2_finseq_2(F,u1_struct_0(C),k3_finseq_2(u1_struct_0(C))) & A = F & r3_sgraph1(B,C,D,E,F) ) ) ) )).
fof(fraenkel_a_4_0_simplex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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)) & v1_simplex1(C,B) & v2_simplex1(C,B) & m1_simplex0(C,u1_struct_0(B)) & v1_finset_1(D) & v1_tops_2(D,C) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C)))) & v3_pre_topc(E,C) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) ) => ( r2_hidden(A,a_4_0_simplex1(B,C,D,E)) <=> ? [F] : ( m3_simplex0(F,k4_simplex1(B,C),k5_card_1(D)) & A = F & r1_tarski(k7_relset_1(k1_orders_1(u1_struct_0(B)),u1_struct_0(B),k2_rlaffin2(B),D),F) & r1_tarski(k3_convex1(B,k1_simplex1(B,k4_simplex1(B,C),F)),k3_convex1(B,k1_simplex1(B,C,E))) ) ) ) )).
fof(fraenkel_a_4_0_sppol_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(B) & m1_subset_1(C,u1_struct_0(k15_euclid(B))) & m1_subset_1(D,u1_struct_0(k15_euclid(B))) & ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) ) => ( r2_hidden(A,a_4_0_sppol_1(B,C,D,E)) <=> ? [F] : ( v1_xreal_0(F) & A = F & r1_xxreal_0(k5_numbers,F) & r1_xxreal_0(F,1) & r2_hidden(k3_rlvect_1(k15_euclid(B),k1_rlvect_1(k15_euclid(B),C,k6_xcmplx_0(1,F)),k1_rlvect_1(k15_euclid(B),D,F)),E) ) ) ) )).
fof(fraenkel_a_4_0_sppol_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_0_sppol_2(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & ~ ( ~ ( k17_euclid(F) = B & r1_xxreal_0(k18_euclid(F),E) & r1_xxreal_0(D,k18_euclid(F)) ) & ~ ( r1_xxreal_0(k17_euclid(F),C) & r1_xxreal_0(B,k17_euclid(F)) & k18_euclid(F) = E ) & ~ ( r1_xxreal_0(k17_euclid(F),C) & r1_xxreal_0(B,k17_euclid(F)) & k18_euclid(F) = D ) & ~ ( k17_euclid(F) = C & r1_xxreal_0(k18_euclid(F),E) & r1_xxreal_0(D,k18_euclid(F)) ) ) ) ) ) )).
fof(fraenkel_a_4_0_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_qc_lang1(B) & m2_subset_1(C,k2_qc_lang1(B),k3_qc_lang1(B)) & m2_subset_1(D,k16_substut1(B),k38_substut1(B)) & m1_substut1(E,B,k7_sublemma(B,D,C)) ) => ( r2_hidden(A,a_4_0_sublemma(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_qc_lang1(B)) & A = F & r2_hidden(k2_qc_lang3(B,F),k9_substut1(B,k22_qc_lang1(B,k2_sublemma(B,k9_sublemma(B,k7_sublemma(B,D,C),E))))) ) ) ) )).
fof(fraenkel_a_4_0_substlat,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(D,k5_finsub_1(k4_partfun1(B,C))) & m1_subset_1(E,k5_finsub_1(k4_partfun1(B,C))) ) => ( r2_hidden(A,a_4_0_substlat(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,k4_partfun1(B,C)) & m1_subset_1(G,k4_partfun1(B,C)) & A = k2_xboole_0(F,G) & r2_hidden(F,D) & r2_hidden(G,E) & r1_partfun1(F,G) ) ) ) )).
fof(fraenkel_a_4_0_substut1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_qc_lang1(B) & m2_subset_1(C,k2_qc_lang1(B),k3_qc_lang1(B)) & m1_subset_1(D,k9_qc_lang1(B)) & m1_subset_1(E,k1_substut1(B)) ) => ( r2_hidden(A,a_4_0_substut1(B,C,D,E)) <=> ? [F] : ( m2_subset_1(F,k2_qc_lang1(B),k3_qc_lang1(B)) & A = F & r2_hidden(F,k24_qc_lang1(B,D)) & m1_subset_1(F,k9_xtuple_0(E)) & F != C & F != k1_funct_1(E,F) ) ) ) )).
fof(fraenkel_a_4_0_substut2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_qc_lang1(B) & m2_subset_1(C,k9_qc_lang1(B),k3_cqc_lang(B)) & m2_subset_1(D,k2_qc_lang1(B),k3_qc_lang1(B)) & m1_subset_1(E,k1_substut1(B)) ) => ( r2_hidden(A,a_4_0_substut2(B,C,D,E)) <=> ? [F] : ( m2_subset_1(F,k2_qc_lang1(B),k3_qc_lang1(B)) & A = F & r2_hidden(F,k24_qc_lang1(B,k11_cqc_lang(B,D,C))) & m1_subset_1(F,k9_xtuple_0(E)) & F != D & F != k1_funct_1(E,F) ) ) ) )).
fof(fraenkel_a_4_0_termord,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v3_ordinal1(B) & ~ v2_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) & v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(B),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(C)))) & v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(B),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(C)))) ) => ( r2_hidden(A,a_4_0_termord(B,C,D,E)) <=> ? [F] : ? [G] : ( m2_subset_1(F,k14_pre_poly(B),k15_pre_poly(B)) & m2_subset_1(G,k14_pre_poly(B),k15_pre_poly(B)) & A = k11_pre_poly(B,F,G) & r2_hidden(F,k3_polynom1(k15_pre_poly(B),C,D)) & r2_hidden(G,k3_polynom1(k15_pre_poly(B),C,E)) ) ) ) )).
fof(fraenkel_a_4_0_topalg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & v1_tops_2(C,B) & v4_taxonom2(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_4_0_topalg_3(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B))) & A = k9_subset_1(u1_struct_0(B),F,D) & r2_hidden(F,C) & ~ r2_hidden(E,F) ) ) ) )).
fof(fraenkel_a_4_0_topalg_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(B) & m1_subset_1(C,u1_struct_0(k15_euclid(B))) & m1_subset_1(D,u1_struct_0(k15_euclid(B))) & m1_subset_1(E,u1_struct_0(k15_euclid(B))) ) => ( r2_hidden(A,a_4_0_topalg_6(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(B))) & A = F & k22_rvsum_1(k5_algstr_0(k15_euclid(B),E,D),k5_algstr_0(k15_euclid(B),F,C)) = k5_numbers ) ) ) )).
fof(fraenkel_a_4_0_topreala,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_0_topreala(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & r1_xxreal_0(B,k17_euclid(F)) & r1_xxreal_0(k17_euclid(F),C) & r1_xxreal_0(D,k18_euclid(F)) & r1_xxreal_0(k18_euclid(F),E) ) ) ) )).
fof(fraenkel_a_4_0_treal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & m1_subset_1(D,u1_struct_0(k2_topmetr(k5_numbers,1))) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_0_treal_1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k2_topmetr(k5_numbers,1))) & A = F & ~ r1_xxreal_0(k3_xxreal_0(E,k3_xcmplx_0(k6_xcmplx_0(C,B),k5_xcmplx_0(2))),k3_metric_1(k2_topmetr(k5_numbers,1),D,F)) ) ) ) )).
fof(fraenkel_a_4_0_uniform1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(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_xreal_0(E) ) => ( r2_hidden(A,a_4_0_uniform1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(B)))) & A = F & ? [G] : ( m1_subset_1(G,u1_struct_0(B)) & ? [H] : ( v1_xreal_0(H) & F = k8_metric_1(B,G,H) & ! [I] : ( m1_subset_1(I,u1_struct_0(B)) => ! [J] : ( m1_subset_1(J,u1_struct_0(C)) => ! [K] : ( m1_subset_1(K,u1_struct_0(C)) => ~ ( J = k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,G) & K = k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,I) & ~ r1_xxreal_0(H,k3_metric_1(B,G,I)) & r1_xxreal_0(k7_xcmplx_0(E,2),k3_metric_1(C,J,K)) ) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_4_0_uproots,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & ~ v6_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) & v1_vectsp_2(B) & l6_algstr_0(B) & m1_subset_1(C,u1_struct_0(B)) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(D,B) & v1_uproots(D,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) & v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(E,B) & v1_uproots(E,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( r2_hidden(A,a_4_0_uproots(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k4_ordinal1) & A = F & ? [G] : ( v1_funct_1(G) & v1_funct_2(G,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(G,B) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) & r2_funct_2(k4_ordinal1,u1_struct_0(B),k13_polynom3(B,D,E),k13_polynom3(B,k2_polynom5(B,k4_polynom5(B,k4_algstr_0(B,C),k5_struct_0(B)),F),G)) ) ) ) ) )).
fof(fraenkel_a_4_0_vectsp_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(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) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) ) => ( r2_hidden(A,a_4_0_vectsp_4(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(C)) & m1_subset_1(G,u1_struct_0(C)) & A = k3_rlvect_1(C,F,G) & r2_hidden(F,D) & r2_hidden(G,E) ) ) ) )).
fof(fraenkel_a_4_0_vectsp_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(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) & m1_vectsp_4(D,B,C) & m1_vectsp_4(E,B,C) ) => ( r2_hidden(A,a_4_0_vectsp_5(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(C)) & m1_subset_1(G,u1_struct_0(C)) & A = k3_rlvect_1(C,G,F) & r1_struct_0(D,G) & r1_struct_0(E,F) ) ) ) )).
fof(fraenkel_a_4_0_vectsp_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(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) & m1_subset_1(D,u1_struct_0(B)) & m1_vectsp_6(E,B,C) ) => ( r2_hidden(A,a_4_0_vectsp_6(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(C)) & A = F & k3_funct_2(u1_struct_0(C),u1_struct_0(B),k6_vectsp_6(B,C,D,E),F) != k4_struct_0(B) ) ) ) )).
fof(fraenkel_a_4_0_waybel15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v24_waybel_0(C) & l1_orders_2(C) & 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(B)) ) => ( r2_hidden(A,a_4_0_waybel15(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(C)) & A = F & r1_waybel_3(C,F,k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,E)) ) ) ) )).
fof(fraenkel_a_4_0_waybel17,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_lattice3(C) & v2_lattice3(C) & v1_yellow_0(C) & v3_waybel_3(C) & l1_orders_2(C) & 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(B)) ) => ( r2_hidden(A,a_4_0_waybel17(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,F) & r1_waybel_3(B,F,E) ) ) ) )).
fof(fraenkel_a_4_0_waybel22,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) & v1_funct_1(D) & v1_funct_2(D,k1_waybel22(B),u1_struct_0(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_waybel22(B),u1_struct_0(C)))) & m1_subset_1(E,u1_struct_0(k1_yellow_1(k8_waybel_0(k2_yellow_1(B))))) ) => ( r2_hidden(A,a_4_0_waybel22(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_zfmisc_1(B)) & A = k2_yellow_0(C,a_4_1_waybel22(B,C,D,F)) & r2_hidden(F,E) ) ) ) )).
fof(fraenkel_a_4_0_waybel35,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v3_lattice3(B) & l1_orders_2(B) & v1_waybel35(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) & v3_waybel35(D,B,C) & m1_waybel35(D,B,C) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_0_waybel35(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = F & r2_hidden(F,k6_waybel35(B,C,D)) & r2_hidden(k1_domain_1(u1_struct_0(B),u1_struct_0(B),F,E),C) ) ) ) )).
fof(fraenkel_a_4_0_waybel_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_0_waybel_1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k12_lattice3(B,C,F) & r2_hidden(F,k7_domain_1(u1_struct_0(B),D,E)) ) ) ) )).
fof(fraenkel_a_4_0_waybel_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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_xboole_0(C) & ~ v1_xboole_0(D) & v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(C,D),u1_struct_0(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(C,D),u1_struct_0(B)))) ) => ( r2_hidden(A,a_4_0_waybel_5(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = F & ? [G] : ( v1_relat_1(G) & v2_relat_1(G) & v4_relat_1(G,C) & v1_funct_1(G) & v1_partfun1(G,C) & r2_hidden(G,k1_funct_2(C,k5_finsub_1(D))) & ? [H] : ( m2_pboole(H,C,G,k7_funcop_1(C,u1_struct_0(B))) & ! [I] : ( m1_subset_1(I,C) => ! [J] : ( r2_hidden(J,k1_funct_1(G,I)) => k1_funct_1(k1_waybel_5(C,u1_struct_0(B),G,H,I),J) = k1_binop_1(E,I,J) ) ) & F = k5_yellow_2(B,k4_waybel_5(B,H)) ) ) ) ) ) )).
fof(fraenkel_a_4_0_yellow10,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & v5_orders_2(C) & v2_lattice3(C) & l1_orders_2(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,C)))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,C)))) ) => ( r2_hidden(A,a_4_0_yellow10(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(k3_yellow_3(B,C))) & m1_subset_1(G,u1_struct_0(k3_yellow_3(B,C))) & A = k12_lattice3(k3_yellow_3(B,C),F,G) & r2_hidden(F,D) & r2_hidden(G,E) ) ) ) )).
fof(fraenkel_a_4_0_yellow12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & ~ v2_struct_0(C) & v2_pre_topc(C) & v8_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(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)))) ) => ( r2_hidden(A,a_4_0_yellow12(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = F & k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,F) != k3_funct_2(u1_struct_0(B),u1_struct_0(C),E,F) ) ) ) )).
fof(fraenkel_a_4_0_yellow17,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) & v4_waybel_3(C) & v1_waybel18(C) & m1_subset_1(D,B) & ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k4_waybel18(B,C,D))))) ) => ( r2_hidden(A,a_4_0_yellow17(B,C,D,E)) <=> ? [F] : ( m2_subset_1(F,k1_zfmisc_1(u1_struct_0(k4_waybel18(B,C,D))),E) & A = k8_relset_1(u1_struct_0(k3_waybel18(B,C)),u1_struct_0(k4_waybel18(B,C,D)),k6_waybel18(B,C,D),F) ) ) ) )).
fof(fraenkel_a_4_0_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_0_yellow_4(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k10_lattice3(B,F,G) & r2_hidden(F,k6_domain_1(u1_struct_0(B),C)) & r2_hidden(G,k7_domain_1(u1_struct_0(B),D,E)) ) ) ) )).
fof(fraenkel_a_4_0_yellow_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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_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(E,C) & v1_cantor_1(E,C) & m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C)))) ) => ( r2_hidden(A,a_4_0_yellow_9(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(G,k1_zfmisc_1(u1_struct_0(C))) & A = k3_borsuk_1(B,C,F,G) & r2_hidden(F,D) & r2_hidden(G,E) ) ) ) )).
fof(fraenkel_a_4_0_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) & m1_subset_1(D,B) & m1_subset_1(E,k4_ordinal1) ) => ( r2_hidden(A,a_4_0_zf_fund1(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,B) & m1_subset_1(G,B) & A = k2_xboole_0(k1_tarski(k1_domain_1(k4_ordinal1,B,E,F)),G) & r2_hidden(F,C) & r2_hidden(G,D) ) ) ) )).
fof(fraenkel_a_4_0_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(C,B) & m1_zmodul01(D,B) & m1_zmodul01(E,B) ) => ( r2_hidden(A,a_4_0_zmodul01(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k3_rlvect_1(B,G,F) & r1_struct_0(k6_zmodul01(B,C,D),G) & r1_struct_0(E,F) ) ) ) )).
fof(fraenkel_a_4_0_zmodul03,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(B) & v1_int_2(B) & ~ 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) & v1_zmodul03(C) & l1_zmodul01(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_zmodul02(B,C)))) & m2_vectsp_6(E,k9_int_3(B),k12_zmodul02(B,C),D) ) => ( r2_hidden(A,a_4_0_zmodul03(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k12_zmodul02(B,C))) & A = F & k1_zmodul03(k9_int_3(B),k12_zmodul02(B,C),E,F) != k4_struct_0(k9_int_3(B)) ) ) ) )).
fof(fraenkel_a_4_10_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,B) & l1_group_9(C,B) & v8_group_9(D,B,C) & m2_finseq_1(D,k6_group_9(B,C)) & v8_group_9(E,B,C) & m2_finseq_1(E,k6_group_9(B,C)) ) => ( r2_hidden(A,a_4_10_group_9(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k4_ordinal1) & A = k4_tarski(F,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(F,1),k6_xcmplx_0(k3_finseq_1(E),1)),1)) & r1_xxreal_0(1,F) & r1_xxreal_0(F,k3_finseq_1(D)) ) ) ) )).
fof(fraenkel_a_4_11_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,B) & l1_group_9(C,B) & v8_group_9(D,B,C) & m2_finseq_1(D,k6_group_9(B,C)) & v8_group_9(E,B,C) & m2_finseq_1(E,k6_group_9(B,C)) ) => ( r2_hidden(A,a_4_11_group_9(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,k4_ordinal1) & m1_subset_1(G,k4_ordinal1) & A = k4_tarski(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(G,1),k6_xcmplx_0(k3_finseq_1(D),1)),F),k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(F,1),k6_xcmplx_0(k3_finseq_1(E),1)),G)) & r1_xxreal_0(1,F) & r1_xxreal_0(F,k6_xcmplx_0(k3_finseq_1(D),1)) & r1_xxreal_0(1,G) & r1_xxreal_0(G,k6_xcmplx_0(k3_finseq_1(E),1)) ) ) ) )).
fof(fraenkel_a_4_12_conlat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) & ~ v2_struct_0(C) & ~ v11_struct_0(C) & l1_conlat_1(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_lattice4(E,B,k11_conlat_1(C)) ) => ( r2_hidden(A,a_4_12_conlat_2(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k3_funct_2(u1_struct_0(B),u1_struct_0(k11_conlat_1(C)),E,F) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_4_13_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,B))) & m1_subset_1(E,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_4_13_mmlquery(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = k3_mmlquery(B,D,k1_mmlquery(B,C,F)) & r2_hidden(F,E) ) ) ) )).
fof(fraenkel_a_4_14_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m2_finseq_1(C,k9_setfam_1(B)) & v7_ordinal1(D) & v7_ordinal1(E) ) => ( r2_hidden(A,a_4_14_mmlquery(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & r1_xxreal_0(D,k24_mmlquery(C,F)) & r1_xxreal_0(k24_mmlquery(C,F),E) ) ) ) )).
fof(fraenkel_a_4_15_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v3_mmlquery(B) & l1_mmlquery(B) & m2_finseq_1(C,u1_mmlquery(B)) & v7_ordinal1(D) & v7_ordinal1(E) ) => ( r2_hidden(A,a_4_15_mmlquery(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = F & r1_xxreal_0(k5_card_1(k7_subset_1(u1_struct_0(B),k30_mmlquery(B,F),k2_relset_1(u1_mmlquery(B),C))),D) & r1_xxreal_0(k5_card_1(k7_subset_1(u1_mmlquery(B),k2_relset_1(u1_mmlquery(B),C),k30_mmlquery(B,F))),E) ) ) ) )).
fof(fraenkel_a_4_16_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) => ( r2_hidden(A,a_4_16_mmlquery(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = k1_mmlquery(B,E,F) & r2_hidden(F,k16_mmlquery(B,C,D)) ) ) ) )).
fof(fraenkel_a_4_17_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,B))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) => ( r2_hidden(A,a_4_17_mmlquery(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = k1_mmlquery(B,k15_mmlquery(k2_zfmisc_1(B,B),D,E),F) & r2_hidden(F,C) ) ) ) )).
fof(fraenkel_a_4_18_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m2_finseq_1(C,k9_setfam_1(B)) & v7_ordinal1(D) & v7_ordinal1(E) ) => ( r2_hidden(A,a_4_18_mmlquery(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & r1_xxreal_0(E,k24_mmlquery(C,F)) & r1_xxreal_0(k24_mmlquery(C,F),D) ) ) ) )).
fof(fraenkel_a_4_19_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(C) & v7_ordinal1(D) & m2_finseq_1(E,k9_setfam_1(B)) ) => ( r2_hidden(A,a_4_19_mmlquery(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & r1_xxreal_0(C,k24_mmlquery(E,F)) & r1_xxreal_0(k24_mmlquery(E,F),D) ) ) ) )).
fof(fraenkel_a_4_1_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( l2_struct_0(B) & ~ v2_struct_0(C) & l1_vectsp_1(C,B) & ~ v2_struct_0(D) & l1_vectsp_1(D,B) & v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)),u1_struct_0(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)),u1_struct_0(B)))) ) => ( r2_hidden(A,a_4_1_bilinear(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(D)) & A = F & ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => k2_binop_1(u1_struct_0(C),u1_struct_0(D),u1_struct_0(B),E,G,F) = k4_struct_0(B) ) ) ) ) )).
fof(fraenkel_a_4_1_borsuk_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & v2_pre_topc(C) & l1_pre_topc(C) & m1_pre_topc(D,B) & m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k2_borsuk_1(D,C))))) ) => ( r2_hidden(A,a_4_1_borsuk_3(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(G,k1_zfmisc_1(u1_struct_0(C))) & A = k3_borsuk_1(B,C,F,G) & ? [H] : ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(D))) & H = k9_subset_1(u1_struct_0(D),F,k2_struct_0(D)) & v3_pre_topc(F,B) & v3_pre_topc(G,C) & r2_hidden(k3_borsuk_1(D,C,H,G),E) ) ) ) ) )).
fof(fraenkel_a_4_1_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) & ~ v2_struct_0(C) & v2_pre_topc(C) & v1_connsp_1(C) & l1_pre_topc(C) & v1_funct_1(D) & v1_funct_2(D,u1_struct_0(C),u1_struct_0(k1_pre_topc(k3_topmetr,k5_toprealb(B)))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(k1_pre_topc(k3_topmetr,k5_toprealb(B)))))) & v1_xreal_0(E) & ~ v1_rat_1(E) ) => ( r2_hidden(A,a_4_1_borsuk_7(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k3_numbers) & A = F & r2_hidden(F,k2_relset_1(u1_struct_0(k1_pre_topc(k3_topmetr,k5_toprealb(B))),D)) & ~ r1_xxreal_0(F,E) ) ) ) )).
fof(fraenkel_a_4_1_card_fin,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_finset_1(B) & v1_finset_1(C) ) => ( r2_hidden(A,a_4_1_card_fin(B,C,D,E)) <=> ? [F] : ( v1_funct_1(F) & v1_funct_2(F,k2_xboole_0(B,k1_tarski(D)),C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k2_xboole_0(B,k1_tarski(D)),C))) & A = F & k1_funct_1(F,D) = E ) ) ) )).
fof(fraenkel_a_4_1_chain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & m1_chain_1(C,B) & m1_subset_1(D,k4_ordinal1) & m1_subset_1(E,k1_zfmisc_1(k4_chain_1(B,C,k1_nat_1(D,1)))) ) => ( r2_hidden(A,a_4_1_chain_1(B,C,D,E)) <=> ? [F] : ( m2_subset_1(F,k1_zfmisc_1(k1_euclid(B)),k4_chain_1(B,C,D)) & A = F & r1_xxreal_0(k1_nat_1(D,1),B) & ~ v1_abian(k5_card_1(k9_subset_1(k4_chain_1(B,C,k1_nat_1(D,1)),k9_chain_1(B,C,D,F),E))) ) ) ) )).
fof(fraenkel_a_4_1_circled1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(B)) & m1_subset_1(D,u1_struct_0(B)) & m2_rlvect_2(E,B,k7_domain_1(u1_struct_0(B),C,D)) ) => ( r2_hidden(A,a_4_1_circled1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = F & k3_funct_2(u1_struct_0(B),k1_numbers,E,F) != k5_numbers ) ) ) )).
fof(fraenkel_a_4_1_closure1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( l1_struct_0(B) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(B)) & ~ v1_xboole_0(E) ) => ( r2_hidden(A,a_4_1_closure1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,E) & A = F & r1_tarski(k1_funct_1(C,D),F) ) ) ) )).
fof(fraenkel_a_4_1_combgras,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( l1_incsp_1(B) & l1_incsp_1(C) & l1_combgras(D,B,C) & m1_subset_1(E,k1_zfmisc_1(u1_incsp_1(C))) ) => ( r2_hidden(A,a_4_1_combgras(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_incsp_1(B)) & A = F & ? [G] : ( m1_subset_1(G,u1_incsp_1(C)) & r2_hidden(G,E) & k2_combgras(B,C,D,F) = G ) ) ) ) )).
fof(fraenkel_a_4_1_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( l1_compos_1(B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v3_compos_1(C,B) & v4_compos_1(C,B) & ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(B)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v3_compos_1(D,B) & v4_compos_1(D,B) & ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(B)) & v1_funct_1(E) & v1_finset_1(E) & v1_afinsq_1(E) & v3_compos_1(E,B) & v4_compos_1(E,B) ) => ( r2_hidden(A,a_4_1_compos_1(B,C,D,E)) <=> ? [F] : ( v7_ordinal1(F) & A = k1_nat_1(F,k7_nat_d(k5_card_1(C),1)) & r2_hidden(F,k2_afinsq_1(k5_compos_1(B,k8_compos_1(B,D,E),k7_nat_d(k5_card_1(C),1)))) ) ) ) )).
fof(fraenkel_a_4_1_convex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v3_rlvect_1(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_4_1_convex1(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k1_algstr_0(B,F,G) & r2_hidden(F,C) & r2_hidden(G,k6_rusub_4(B,D,E)) ) ) ) )).
fof(fraenkel_a_4_1_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(C)) ) => ( r2_hidden(A,a_4_1_domain_1(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,B) & m1_subset_1(G,C) & A = k1_domain_1(B,C,F,G) & r2_hidden(F,D) & r2_hidden(G,E) ) ) ) )).
fof(fraenkel_a_4_1_ec_pf_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(B) & v1_int_2(B) & m1_subset_1(C,u1_struct_0(k9_int_3(B))) & m1_subset_1(D,u1_struct_0(k9_int_3(B))) & m1_subset_1(E,u1_struct_0(k9_int_3(B))) ) => ( r2_hidden(A,a_4_1_ec_pf_1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k9_int_3(B))) & A = k6_eqrel_1(k6_ec_pf_1(B,C,D),k6_ec_pf_1(B,C,D),k8_ec_pf_1(B,C,D),k4_domain_1(u1_struct_0(k9_int_3(B)),u1_struct_0(k9_int_3(B)),k4_ordinal1,E,F,1)) & r2_hidden(k4_domain_1(u1_struct_0(k9_int_3(B)),u1_struct_0(k9_int_3(B)),k4_ordinal1,E,F,1),k6_ec_pf_1(B,C,D)) ) ) ) )).
fof(fraenkel_a_4_1_euclid_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,u1_struct_0(k15_euclid(B))) & m1_subset_1(D,u1_struct_0(k15_euclid(B))) & m1_subset_1(E,u1_struct_0(k15_euclid(B))) ) => ( r2_hidden(A,a_4_1_euclid_3(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(B))) & A = F & ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & ? [I] : ( v1_xreal_0(I) & ~ ( r1_xxreal_0(k5_numbers,G) & r1_xxreal_0(k5_numbers,H) & r1_xxreal_0(k5_numbers,I) ) & k2_xcmplx_0(k2_xcmplx_0(G,H),I) = 1 & F = k3_rlvect_1(k15_euclid(B),k3_rlvect_1(k15_euclid(B),k1_rlvect_1(k15_euclid(B),C,G),k1_rlvect_1(k15_euclid(B),D,H)),k1_rlvect_1(k15_euclid(B),E,I)) ) ) ) ) ) ) )).
fof(fraenkel_a_4_1_euclidlp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(B,k4_ordinal1) & m2_finseq_2(C,k1_numbers,k1_euclid(B)) & m2_finseq_2(D,k1_numbers,k1_euclid(B)) & m2_finseq_2(E,k1_numbers,k1_euclid(B)) ) => ( r2_hidden(A,a_4_1_euclidlp(B,C,D,E)) <=> ? [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(B)) & A = F & ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & ? [I] : ( v1_xreal_0(I) & k2_xcmplx_0(k2_xcmplx_0(G,H),I) = 1 & F = k7_euclid(B,k7_euclid(B,k9_euclid(B,C,G),k9_euclid(B,D,H)),k9_euclid(B,E,I)) ) ) ) ) ) ) )).
fof(fraenkel_a_4_1_fcont_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_1_fcont_1(B,C,D,E)) <=> ? [F] : ( v1_xreal_0(F) & A = F & r1_xxreal_0(k6_xcmplx_0(k1_funct_1(k2_partfun1(k1_numbers,k1_numbers,C,B),D),k7_xcmplx_0(E,2)),F) & r1_xxreal_0(F,k2_xcmplx_0(k1_funct_1(k2_partfun1(k1_numbers,k1_numbers,C,B),D),k7_xcmplx_0(E,2))) ) ) ) )).
fof(fraenkel_a_4_1_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(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))) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_1_finance1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & r1_xxreal_0(D,k3_funct_2(B,k1_numbers,C,F)) & ~ r1_xxreal_0(E,k3_funct_2(B,k1_numbers,C,F)) ) ) ) )).
fof(fraenkel_a_4_1_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) & v7_fomodel1(C,B) & m1_subset_1(C,k1_fomodel1(B)) & v3_card_1(D,k1_int_2(k19_fomodel1(B,C))) & m2_subset_1(D,k3_finseq_2(k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0))),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0)),k35_fomodel1(B))) & v3_card_1(E,k1_int_2(k19_fomodel1(B,C))) & m2_subset_1(E,k3_finseq_2(k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0))),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0)),k35_fomodel1(B))) ) => ( r2_hidden(A,a_4_1_fomodel4(B,C,D,E)) <=> ? [F] : ? [G] : ? [H] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(k1_int_2(k19_fomodel1(B,C)))) & v1_funct_1(G) & v1_funct_2(G,k2_finseq_1(k1_int_2(k19_fomodel1(B,C))),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0))) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(k1_int_2(k19_fomodel1(B,C))),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0))))) & v1_funct_1(H) & v1_funct_2(H,k2_finseq_1(k1_int_2(k19_fomodel1(B,C))),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0))) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(k1_int_2(k19_fomodel1(B,C))),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0))))) & A = k42_fomodel1(B,k42_fomodel1(B,k43_fomodel1(B,k31_fomodel2(B)),k3_funct_2(k2_finseq_1(k1_int_2(k19_fomodel1(B,C))),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0)),G,F)),k3_funct_2(k2_finseq_1(k1_int_2(k19_fomodel1(B,C))),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0)),H,F)) & G = D & H = E ) ) ) )).
fof(fraenkel_a_4_1_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(B))) & ~ v2_struct_0(D) & l2_fsm_3(D,B,C) & v3_fsm_3(E,B,k9_flang_1(B)) & l2_fsm_3(E,B,k9_flang_1(B)) ) => ( r2_hidden(A,a_4_1_fsm_3(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(E)) & A = F & ~ r1_xboole_0(F,u2_fsm_3(B,C,D)) ) ) ) )).
fof(fraenkel_a_4_1_groeb_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(B,k4_ordinal1) & v1_partfun1(C,k15_pre_poly(B)) & v1_relat_2(C) & v4_relat_2(C) & v6_relat_2(C) & v8_relat_2(C) & v2_bagorder(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),k15_pre_poly(B)))) & ~ 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) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(B,D)))) ) => ( r2_hidden(A,a_4_1_groeb_1(B,C,D,E)) <=> ? [F] : ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(B),u1_struct_0(D)) & v1_polynom7(F,B,D) & v1_polynom1(F,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(D)))) & A = F & r2_hidden(F,k7_ideal_1(k12_polynom1(B,D),E)) & ~ r10_polyred(B,C,D,F,E) ) ) ) )).
fof(fraenkel_a_4_1_groeb_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v3_ordinal1(B) & ~ 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) & v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(B),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(C)))) & v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(B),u1_struct_0(C)) & v1_polynom7(E,B,C) & v3_polynom7(E,B,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(C)))) ) => ( r2_hidden(A,a_4_1_groeb_3(B,C,D,E)) <=> ? [F] : ? [G] : ( m2_subset_1(F,k14_pre_poly(B),k15_pre_poly(B)) & m2_subset_1(G,k14_pre_poly(B),k15_pre_poly(B)) & A = k11_pre_poly(B,F,G) & r2_hidden(F,k3_polynom1(k15_pre_poly(B),C,E)) & r2_hidden(G,k3_polynom1(k15_pre_poly(B),C,D)) ) ) ) )).
fof(fraenkel_a_4_1_group_10,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v1_group_1(B) & l3_algstr_0(B) & ~ v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),k1_funct_2(C,C)) & v1_group_10(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),k1_funct_2(C,C)))) & m1_subset_1(E,C) ) => ( r2_hidden(A,a_4_1_group_10(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,C) & A = F & r2_group_10(B,C,D,E,F) ) ) ) )).
fof(fraenkel_a_4_1_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,B) & l1_group_9(C,B) & ~ v2_struct_0(D) & v2_group_1(D) & v3_group_1(D) & v3_group_9(D,B) & l1_group_9(D,B) & v1_funct_1(E) & v1_funct_2(E,u1_struct_0(C),u1_struct_0(D)) & v1_group_6(E,C,D) & v7_group_9(E,B,C,D) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)))) ) => ( r2_hidden(A,a_4_1_group_9(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(C)) & A = F & k3_funct_2(u1_struct_0(C),u1_struct_0(D),E,F) = k1_group_1(D) ) ) ) )).
fof(fraenkel_a_4_1_heyting2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_finset_1(C) & m2_subset_1(D,k5_finsub_1(k4_partfun1(B,C)),k1_substlat(B,C)) & m2_subset_1(E,k5_finsub_1(k4_partfun1(B,C)),k1_substlat(B,C)) ) => ( r2_hidden(A,a_4_1_heyting2(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,k4_partfun1(B,C)) & m1_subset_1(G,k4_partfun1(B,C)) & A = k2_xboole_0(F,G) & r2_hidden(F,D) & r2_hidden(G,E) & r1_partfun1(F,G) ) ) ) )).
fof(fraenkel_a_4_1_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v3_rlvect_1(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_4_1_ideal_1(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k1_algstr_0(B,F,G) & r2_hidden(F,k11_ideal_1(B,C,D)) & r2_hidden(G,E) ) ) ) )).
fof(fraenkel_a_4_1_jgraph_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_1_jgraph_6(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & r1_xxreal_0(B,k17_euclid(F)) & r1_xxreal_0(k17_euclid(F),C) & r1_xxreal_0(D,k18_euclid(F)) & r1_xxreal_0(k18_euclid(F),E) ) ) ) )).
fof(fraenkel_a_4_1_jordan,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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))) & ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_4_1_jordan(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & r1_jordan5c(E,B,C,B,F) & r1_jordan5c(E,B,C,F,D) ) ) ) )).
fof(fraenkel_a_4_1_jordan1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_1_jordan1(B,C,D,E)) <=> ? [F] : ? [G] : ( v1_xreal_0(F) & v1_xreal_0(G) & A = k19_euclid(F,G) & ~ ( r1_xxreal_0(B,F) & r1_xxreal_0(F,D) & r1_xxreal_0(C,G) & r1_xxreal_0(G,E) ) ) ) ) )).
fof(fraenkel_a_4_1_jordan16,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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(E,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_4_1_jordan16(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & r1_jordan5c(B,C,D,E,F) ) ) ) )).
fof(fraenkel_a_4_1_jordan20,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & v1_xreal_0(C) & v1_funct_1(D) & v1_funct_2(D,u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(2),B))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(2),B))))) & m1_subset_1(E,k1_numbers) ) => ( r2_hidden(A,a_4_1_jordan20(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_numbers) & A = F & r1_xxreal_0(k5_numbers,F) & r1_xxreal_0(F,E) & ! [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(2))) => ~ ( G = k1_funct_1(D,F) & k17_euclid(G) = C ) ) ) ) ) )).
fof(fraenkel_a_4_1_jordan2b,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_1_jordan2b(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(B))) & A = F & ~ r1_xxreal_0(k7_partfun1(k1_numbers,F,C),k6_xcmplx_0(E,D)) & ~ r1_xxreal_0(k2_xcmplx_0(E,D),k7_partfun1(k1_numbers,F,C)) ) ) ) )).
fof(fraenkel_a_4_1_jordan5a,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_1_jordan5a(B,C,D,E)) <=> ? [F] : ( v1_xreal_0(F) & A = F & ~ r1_xxreal_0(F,k6_xcmplx_0(k1_funct_1(D,E),k3_xxreal_0(k6_xcmplx_0(k1_funct_1(D,E),B),k6_xcmplx_0(C,k1_funct_1(D,E))))) & ~ r1_xxreal_0(k2_xcmplx_0(k1_funct_1(D,E),k3_xxreal_0(k6_xcmplx_0(k1_funct_1(D,E),B),k6_xcmplx_0(C,k1_funct_1(D,E)))),F) ) ) ) )).
fof(fraenkel_a_4_1_jordan6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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(E,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_4_1_jordan6(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & r1_jordan5c(B,C,D,E,F) ) ) ) )).
fof(fraenkel_a_4_1_jordan_a,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(B) & ~ v1_xboole_0(C) & v2_compts_1(C,k15_euclid(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) & v1_funct_1(D) & v1_funct_2(D,u1_struct_0(k2_borsuk_1(k15_euclid(B),k15_euclid(B))),k1_numbers) & v1_pscomp_1(D,k2_borsuk_1(k15_euclid(B),k15_euclid(B))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_borsuk_1(k15_euclid(B),k15_euclid(B))),k1_numbers))) & m1_subset_1(E,u1_struct_0(k15_euclid(B))) ) => ( r2_hidden(A,a_4_1_jordan_a(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(B))) & A = k1_binop_1(D,F,E) & r2_hidden(F,C) ) ) ) )).
fof(fraenkel_a_4_1_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k6_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,k6_numbers))) & v2_xxreal_0(E) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_1_lpspace2(B,C,D,E)) <=> ? [F] : ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) & A = F & r2_hidden(F,k1_lpspace2(B,C,D,E)) & r1_lpspace1(B,C,D,F,k8_lpspace1(B,k5_numbers)) ) ) ) )).
fof(fraenkel_a_4_1_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_rlvect_1(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_1_mathmorp(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,F,E) & r2_hidden(F,k3_mathmorp(B,C,D)) ) ) ) )).
fof(fraenkel_a_4_1_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) => ( r2_hidden(A,a_4_1_mmlquery(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & r1_ordinal1(k1_card_1(k1_mmlquery(B,C,F)),k1_card_1(k1_mmlquery(B,E,F))) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_4_1_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & v1_partfun1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k30_modelc_1(B))) & m1_subset_1(E,u1_struct_0(k48_modelc_1(B,C,D))) ) => ( r2_hidden(A,a_4_1_modelc_1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & k3_funct_2(B,k6_margrel1,k31_modelc_1(B,E),F) = k8_margrel1 ) ) ) )).
fof(fraenkel_a_4_1_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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_msafree4(C,u1_struct_0(B)) & v5_msafree4(D,B,C) & l3_msualg_1(D,B) & m1_subset_1(E,u4_struct_0(B)) ) => ( r2_hidden(A,a_4_1_msafree4(B,C,D,E)) <=> ? [F] : ( m1_msafree4(F,u1_struct_0(B),k4_equation(B),k1_msafree4(u1_struct_0(B),k4_equation(B),k2_msualg_1(B,E))) & A = F & r1_equation(B,D,k2_msualg_1(B,E),F) ) ) ) )).
fof(fraenkel_a_4_1_msscyc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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_subset_1(D,u1_struct_0(B)) & ~ v1_xboole_0(E) ) => ( r2_hidden(A,a_4_1_msscyc_1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,E) & A = F & ? [G] : ( m1_subset_1(G,u4_struct_0(B)) & k3_funct_2(u4_struct_0(B),k3_finseq_2(u1_struct_0(B)),u1_msualg_1(B),G) = k1_xboole_0 & k3_funct_2(u4_struct_0(B),u1_struct_0(B),u2_msualg_1(B),G) = D & r2_hidden(F,k10_xtuple_0(k5_msualg_1(B,G,k11_msafree(B,C)))) ) ) ) ) )).
fof(fraenkel_a_4_1_msualg_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) & v4_msualg_1(C,B) & l3_msualg_1(C,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_msualg_5(B,C)))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k6_msualg_5(B,C)))) ) => ( r2_hidden(A,a_4_1_msualg_8(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k5_msualg_5(u1_struct_0(B),u3_msualg_1(B,C))))) & A = k15_lattice3(k5_msualg_5(u1_struct_0(B),u3_msualg_1(B,C)),F) & r2_hidden(F,k7_domain_1(k1_zfmisc_1(u1_struct_0(k6_msualg_5(B,C))),D,E)) ) ) ) )).
fof(fraenkel_a_4_1_ndiff_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(B) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finseq_1(B) & v2_prvect_2(B) & m2_subset_1(C,k4_ordinal1,k4_finseq_1(B)) & m1_subset_1(D,u1_struct_0(k14_prvect_2(B))) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_1_ndiff_5(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k11_prvect_2(B,C))) & A = F & ~ r1_xxreal_0(E,k2_normsp_0(k11_prvect_2(B,C),k5_algstr_0(k11_prvect_2(B,C),F,k3_funct_2(u1_struct_0(k14_prvect_2(B)),u1_struct_0(k11_prvect_2(B,C)),k3_ndiff_5(B,C),D)))) ) ) ) )).
fof(fraenkel_a_4_1_nfcont_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(B,k4_ordinal1) & v1_xreal_0(C) & v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(B))))) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_1_nfcont_4(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k4_real_ns1(B))) & A = F & ~ r1_xxreal_0(E,k2_normsp_0(k4_real_ns1(B),k5_algstr_0(k4_real_ns1(B),F,k7_partfun1(u1_struct_0(k4_real_ns1(B)),D,C)))) ) ) ) )).
fof(fraenkel_a_4_1_osafree,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v4_osalg_1(B) & v5_osalg_1(B) & l3_osalg_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_subset_1(D,u4_struct_0(B)) & v7_ordinal1(E) ) => ( r2_hidden(A,a_4_1_osafree(B,C,D,E)) <=> ? [F] : ( m1_dtconstr(F,u1_struct_0(k2_osafree(B,C)),k5_trees_3(u1_struct_0(k2_osafree(B,C))),k4_dtconstr(k2_osafree(B,C))) & A = F & ~ ( ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ~ ( r3_orders_2(B,G,k7_partfun1(u1_struct_0(B),k1_msualg_1(B,D),E)) & r2_hidden(H,k1_funct_1(C,G)) & F = k1_trees_4(k4_tarski(H,G)) ) ) & ! [G] : ( m1_subset_1(G,u4_struct_0(B)) => ~ ( k4_tarski(G,u1_struct_0(B)) = k1_funct_1(F,k1_xboole_0) & r3_orders_2(B,k2_msualg_1(B,G),k7_partfun1(u1_struct_0(B),k1_msualg_1(B,D),E)) ) ) ) ) ) ) )).
fof(fraenkel_a_4_1_petri_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & m1_subset_1(D,k1_zfmisc_1(C)) & v1_funct_1(E) & v1_funct_2(E,D,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(D,B))) ) => ( r2_hidden(A,a_4_1_petri_2(B,C,D,E)) <=> ? [F] : ( v1_funct_1(F) & v1_funct_2(F,C,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(C,B))) & A = F & k2_partfun1(C,B,F,D) = E ) ) ) )).
fof(fraenkel_a_4_1_pnproc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m2_pnproc_1(C,B) & m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(C))) & m1_subset_1(E,k1_zfmisc_1(k3_finseq_2(C))) ) => ( r2_hidden(A,a_4_1_pnproc_1(B,C,D,E)) <=> ? [F] : ( m2_finseq_2(F,C,k3_finseq_2(C)) & A = F & ? [G] : ( v1_relat_1(G) & v1_funct_1(G) & v2_finseq_1(G) & ? [H] : ( v1_relat_1(H) & v1_funct_1(H) & v2_finseq_1(H) & F = k2_xboole_0(G,H) & r1_xboole_0(G,H) & r2_hidden(k15_finseq_1(G),D) & r2_hidden(k15_finseq_1(H),E) ) ) ) ) ) )).
fof(fraenkel_a_4_1_pralg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) & l3_msualg_1(C,B) & m1_subset_1(D,u1_struct_0(B)) & ~ v1_xboole_0(E) ) => ( r2_hidden(A,a_4_1_pralg_3(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,E) & A = F & ? [G] : ( m1_subset_1(G,u4_struct_0(B)) & k3_funct_2(u4_struct_0(B),k3_finseq_2(u1_struct_0(B)),u1_msualg_1(B),G) = k1_xboole_0 & k3_funct_2(u4_struct_0(B),u1_struct_0(B),u2_msualg_1(B),G) = D & r2_hidden(F,k2_relset_1(k4_msualg_1(B,G,C),k5_msualg_1(B,G,C))) ) ) ) ) )).
fof(fraenkel_a_4_1_qc_lang4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_qc_lang1(B) & m1_subset_1(C,k9_qc_lang1(B)) & m1_qc_lang4(D,B,C) & m1_qc_lang4(E,B,C) ) => ( r2_hidden(A,a_4_1_qc_lang4(B,C,D,E)) <=> ? [F] : ? [G] : ( m2_qc_lang4(F,B,C,D) & m1_trees_1(G,k9_xtuple_0(k2_qc_lang4(B,D))) & A = k8_finseq_1(k4_ordinal1,F,G) & r2_hidden(G,k3_qc_lang4(B,D,E)) ) ) ) )).
fof(fraenkel_a_4_1_qc_trans,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_qc_lang1(B) & m1_subset_1(C,k1_substut1(B)) & m2_subset_1(D,k2_qc_lang1(B),k3_qc_lang1(B)) & m2_subset_1(E,k9_qc_lang1(B),k3_cqc_lang(B)) ) => ( r2_hidden(A,a_4_1_qc_trans(B,C,D,E)) <=> ? [F] : ( m2_subset_1(F,k2_qc_lang1(B),k3_qc_lang1(B)) & A = F & r2_hidden(F,k24_qc_lang1(B,E)) & m1_subset_1(F,k9_xtuple_0(C)) & F != D & F != k1_funct_1(C,F) ) ) ) )).
fof(fraenkel_a_4_1_quantal1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & v7_quantal1(B) & v8_quantal1(B) & l1_quantal1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_1_quantal1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k6_algstr_0(B,E,F) & r2_hidden(F,k7_domain_1(u1_struct_0(B),C,D)) ) ) ) )).
fof(fraenkel_a_4_1_random_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(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(E) & v1_funct_2(E,k4_ordinal1,k9_setfam_1(C)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(C)))) ) => ( r2_hidden(A,a_4_1_random_3(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k4_ordinal1) & A = k8_relset_1(B,C,D,k1_prob_4(C,k9_setfam_1(C),E,F)) ) ) ) )).
fof(fraenkel_a_4_1_rlsub_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_rlsub_1(D,B) & m1_rlsub_1(E,B) ) => ( r2_hidden(A,a_4_1_rlsub_2(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k3_rlvect_1(B,G,F) & r1_struct_0(C,G) & r1_struct_0(k1_rlsub_2(B,D,E),F) ) ) ) )).
fof(fraenkel_a_4_1_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v3_rlvect_1(B) & l2_algstr_0(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_4_1_rltopsp1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k1_algstr_0(B,k1_algstr_0(B,C,D),F) & r2_hidden(F,E) ) ) ) )).
fof(fraenkel_a_4_1_rmod_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(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) & m1_subset_1(D,u1_struct_0(C)) & m1_rmod_2(E,B,C) ) => ( r2_hidden(A,a_4_1_rmod_2(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(C)) & A = k3_rlvect_1(C,D,F) & r1_struct_0(E,F) ) ) ) )).
fof(fraenkel_a_4_1_rmod_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) & ~ 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) & m1_rmod_4(D,B,C) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_1_rmod_4(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(C)) & A = F & k3_funct_2(u1_struct_0(C),u1_struct_0(B),k7_rmod_4(B,C,E,D),F) != k4_struct_0(B) ) ) ) )).
fof(fraenkel_a_4_1_rusub_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_rusub_1(D,B) & m1_rusub_1(E,B) ) => ( r2_hidden(A,a_4_1_rusub_2(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k3_rlvect_1(B,F,G) & r1_struct_0(C,F) & r1_struct_0(k1_rusub_2(B,D,E),G) ) ) ) )).
fof(fraenkel_a_4_1_scmpds_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) & v3_scmpds_4(B) & v1_int_1(C) & v1_int_1(D) & v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ( r2_hidden(A,a_4_1_scmpds_4(B,C,D,E)) <=> ? [F] : ( v7_ordinal1(F) & A = k1_nat_1(F,k5_card_1(B)) & r2_hidden(F,k2_afinsq_1(k9_compos_1(k1_scmpds_2,k8_scmpds_2(E,C,D)))) ) ) ) )).
fof(fraenkel_a_4_1_sgraph1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & v1_finset_1(D) & v1_finset_1(E) ) => ( r2_hidden(A,a_4_1_sgraph1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = k4_tarski(F,k2_tarski(C,F)) & r2_hidden(F,E) & r2_hidden(k2_tarski(C,F),D) ) ) ) )).
fof(fraenkel_a_4_1_topalg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v2_pre_topc(B) & l1_pre_topc(B) & v1_tops_2(C,B) & v4_taxonom2(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_4_1_topalg_3(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B))) & A = k9_subset_1(u1_struct_0(B),F,D) & r2_hidden(F,C) & r2_hidden(E,F) ) ) ) )).
fof(fraenkel_a_4_1_treal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & m1_subset_1(D,u1_struct_0(k2_topmetr(k5_numbers,1))) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_1_treal_1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k2_topmetr(k5_numbers,1))) & A = F & ~ r1_xxreal_0(k3_xxreal_0(E,k3_xcmplx_0(k6_xcmplx_0(B,C),k5_xcmplx_0(2))),k3_metric_1(k2_topmetr(k5_numbers,1),D,F)) ) ) ) )).
fof(fraenkel_a_4_1_vectsp_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(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) & m1_subset_1(D,u1_struct_0(C)) & m1_vectsp_4(E,B,C) ) => ( r2_hidden(A,a_4_1_vectsp_4(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(C)) & A = k3_rlvect_1(C,D,F) & r1_struct_0(E,F) ) ) ) )).
fof(fraenkel_a_4_1_vectsp_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) & ~ 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) & m1_subset_1(D,u1_struct_0(B)) & m1_vectsp_6(E,B,C) ) => ( r2_hidden(A,a_4_1_vectsp_6(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(C)) & A = F & k3_funct_2(u1_struct_0(C),u1_struct_0(B),k6_vectsp_6(B,C,D,E),F) != k4_struct_0(B) ) ) ) )).
fof(fraenkel_a_4_1_waybel13,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v24_waybel_0(C) & l1_orders_2(C) & 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(B)) ) => ( r2_hidden(A,a_4_1_waybel13(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(C)) & A = F & r1_orders_2(C,F,k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,E)) & v1_waybel_3(F,C) ) ) ) )).
fof(fraenkel_a_4_1_waybel22,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) & v1_funct_1(D) & v1_funct_2(D,k1_waybel22(B),u1_struct_0(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_waybel22(B),u1_struct_0(C)))) & m1_subset_1(E,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_4_1_waybel22(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k2_yellow_1(B))) & A = k1_funct_1(D,k6_waybel_0(k2_yellow_1(B),F)) & ? [G] : ( m1_subset_1(G,B) & F = k1_tarski(G) & r2_hidden(G,E) ) ) ) ) )).
fof(fraenkel_a_4_1_waybel24,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & 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) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_yellow_1(u1_struct_0(B),C)))) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_1_waybel24(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k5_yellow_1(u1_struct_0(B),C))) & A = k1_funct_1(F,E) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_4_1_waybel_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) & v5_waybel_4(C,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(B)) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_1_waybel_7(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = F & r2_hidden(k7_yellow_3(B,B,F,k12_lattice3(B,D,E)),C) ) ) ) )).
fof(fraenkel_a_4_1_yellow10,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & v5_orders_2(C) & v2_lattice3(C) & l1_orders_2(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,C)))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,C)))) ) => ( r2_hidden(A,a_4_1_yellow10(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k12_lattice3(B,F,G) & r2_hidden(F,k4_yellow_3(B,C,D)) & r2_hidden(G,k4_yellow_3(B,C,E)) ) ) ) )).
fof(fraenkel_a_4_1_yellow12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & ~ v2_struct_0(C) & v2_pre_topc(C) & v8_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(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)))) ) => ( r2_hidden(A,a_4_1_yellow12(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = F & k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,F) = k3_funct_2(u1_struct_0(B),u1_struct_0(C),E,F) ) ) ) )).
fof(fraenkel_a_4_1_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_1_yellow_4(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k11_lattice3(B,F,G) & r2_hidden(F,k6_domain_1(u1_struct_0(B),C)) & r2_hidden(G,k7_domain_1(u1_struct_0(B),D,E)) ) ) ) )).
fof(fraenkel_a_4_1_yellow_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(B))) & ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(C))) ) => ( r2_hidden(A,a_4_1_yellow_9(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,k1_zfmisc_1(B)) & m1_subset_1(G,k1_zfmisc_1(C)) & A = k8_mcart_1(B,C,F,G) & r2_hidden(F,D) & r2_hidden(G,E) ) ) ) )).
fof(fraenkel_a_4_1_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) & m1_subset_1(D,B) & m1_subset_1(E,k4_ordinal1) ) => ( r2_hidden(A,a_4_1_zf_fund1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = k2_xboole_0(k1_tarski(k1_domain_1(k4_ordinal1,B,E,F)),D) & r2_hidden(F,C) ) ) ) )).
fof(fraenkel_a_4_1_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(C,B) & m1_zmodul01(D,B) & m1_zmodul01(E,B) ) => ( r2_hidden(A,a_4_1_zmodul01(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k3_rlvect_1(B,G,F) & r1_struct_0(C,G) & r1_struct_0(k6_zmodul01(B,D,E),F) ) ) ) )).
fof(fraenkel_a_4_20_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & v3_mmlquery(D) & l1_mmlquery(D) & m2_finseq_1(E,u1_mmlquery(D)) ) => ( r2_hidden(A,a_4_20_mmlquery(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(D)) & A = F & r1_xxreal_0(k5_card_1(k7_subset_1(u1_struct_0(D),k30_mmlquery(D,F),k2_relset_1(u1_mmlquery(D),E))),B) & r1_xxreal_0(k5_card_1(k7_subset_1(u1_mmlquery(D),k2_relset_1(u1_mmlquery(D),E),k30_mmlquery(D,F))),C) ) ) ) )).
fof(fraenkel_a_4_2_card_fin,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_finset_1(B) & v1_finset_1(C) ) => ( r2_hidden(A,a_4_2_card_fin(B,C,D,E)) <=> ? [F] : ( v1_funct_1(F) & v1_funct_2(F,k2_xboole_0(B,k1_tarski(D)),k2_xboole_0(C,k1_tarski(E))) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k2_xboole_0(B,k1_tarski(D)),k2_xboole_0(C,k1_tarski(E))))) & A = F & v2_funct_1(F) & k1_funct_1(F,D) = E ) ) ) )).
fof(fraenkel_a_4_2_closure2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( l1_struct_0(B) & v15_closure2(C,B) & l1_closure2(C,B) & m1_subset_1(D,k1_zfmisc_1(k1_closure2(u1_struct_0(B),u3_msualg_1(B,C)))) ) => ( r2_hidden(A,a_4_2_closure2(B,C,D,E)) <=> ? [F] : ( m1_closure2(F,u1_struct_0(B),u3_msualg_1(B,C),k6_closure2(u1_struct_0(B),u3_msualg_1(B,C))) & A = k1_funct_1(F,E) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_4_2_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( l1_compos_1(B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v3_compos_1(C,B) & v4_compos_1(C,B) & ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(B)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v3_compos_1(D,B) & v4_compos_1(D,B) & ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(B)) & v1_funct_1(E) & v1_finset_1(E) & v1_afinsq_1(E) & v3_compos_1(E,B) & v4_compos_1(E,B) ) => ( r2_hidden(A,a_4_2_compos_1(B,C,D,E)) <=> ? [F] : ( v7_ordinal1(F) & A = k1_nat_1(F,k7_nat_d(k5_card_1(k8_compos_1(B,C,D)),1)) & r2_hidden(F,k2_afinsq_1(k5_compos_1(B,E,k7_nat_d(k5_card_1(k8_compos_1(B,C,D)),1)))) ) ) ) )).
fof(fraenkel_a_4_2_convex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v3_rlvect_1(B) & l2_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_4_2_convex1(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k1_algstr_0(B,F,G) & r2_hidden(F,k6_rusub_4(B,C,D)) & r2_hidden(G,E) ) ) ) )).
fof(fraenkel_a_4_2_euclid_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,u1_struct_0(k15_euclid(B))) & m1_subset_1(D,u1_struct_0(k15_euclid(B))) & m1_subset_1(E,u1_struct_0(k15_euclid(B))) ) => ( r2_hidden(A,a_4_2_euclid_3(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(B))) & A = F & ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & ? [I] : ( v1_xreal_0(I) & k2_xcmplx_0(k2_xcmplx_0(G,H),I) = 1 & F = k3_rlvect_1(k15_euclid(B),k3_rlvect_1(k15_euclid(B),k1_rlvect_1(k15_euclid(B),C,G),k1_rlvect_1(k15_euclid(B),D,H)),k1_rlvect_1(k15_euclid(B),E,I)) ) ) ) ) ) ) )).
fof(fraenkel_a_4_2_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(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))) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_2_finance1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & r1_xxreal_0(D,k3_funct_2(B,k1_numbers,C,F)) & r1_xxreal_0(k3_funct_2(B,k1_numbers,C,F),E) ) ) ) )).
fof(fraenkel_a_4_2_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) & v7_ordinal1(C) & ~ v8_ordinal1(C) & v3_card_1(D,C) & m2_subset_1(D,k3_finseq_2(k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0))),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0)),k35_fomodel1(B))) & v3_card_1(E,C) & m2_subset_1(E,k3_finseq_2(k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0))),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0)),k35_fomodel1(B))) ) => ( r2_hidden(A,a_4_2_fomodel4(B,C,D,E)) <=> ? [F] : ? [G] : ? [H] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(C)) & v1_funct_1(G) & v1_funct_2(G,k2_finseq_1(C),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0))) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(C),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0))))) & v1_funct_1(H) & v1_funct_2(H,k2_finseq_1(C),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0))) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(C),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0))))) & A = k42_fomodel1(B,k42_fomodel1(B,k43_fomodel1(B,k31_fomodel2(B)),k3_funct_2(k2_finseq_1(C),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0)),G,F)),k3_funct_2(k2_finseq_1(C),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0)),H,F)) & G = D & H = E ) ) ) )).
fof(fraenkel_a_4_2_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(B))) & ~ v2_struct_0(D) & l2_fsm_3(D,B,C) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(D))) ) => ( r2_hidden(A,a_4_2_fsm_3(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k8_afinsq_1(B)) & A = F & ~ r1_xboole_0(k3_rewrite3(B,C,D,F,E),u2_fsm_3(B,C,D)) ) ) ) )).
fof(fraenkel_a_4_2_groeb_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v3_ordinal1(B) & v1_partfun1(C,k15_pre_poly(B)) & v1_relat_2(C) & v4_relat_2(C) & v6_relat_2(C) & v8_relat_2(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),k15_pre_poly(B)))) & ~ v7_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) & v3_rlvect_1(D) & v4_rlvect_1(D) & l6_algstr_0(D) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(B,D)))) ) => ( r2_hidden(A,a_4_2_groeb_1(B,C,D,E)) <=> ? [F] : ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(B),u1_struct_0(D)) & v1_polynom1(F,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(D)))) & A = k3_termord(B,C,D,F) & r2_hidden(F,E) & F != k8_polynom1(B,D) ) ) ) )).
fof(fraenkel_a_4_2_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v6_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v1_vectsp_1(B) & v1_algstr_1(B) & l6_algstr_0(B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_2_ideal_1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k8_group_1(B,E,F) & r2_hidden(F,k15_ideal_1(B,C,D)) ) ) ) )).
fof(fraenkel_a_4_2_jgraph_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_2_jgraph_6(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & ~ ( r1_xxreal_0(B,k17_euclid(F)) & r1_xxreal_0(k17_euclid(F),C) & r1_xxreal_0(D,k18_euclid(F)) & r1_xxreal_0(k18_euclid(F),E) ) ) ) ) )).
fof(fraenkel_a_4_2_jordan1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_2_jordan1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & ~ r1_xxreal_0(k17_euclid(F),B) & ~ r1_xxreal_0(C,k17_euclid(F)) & ~ r1_xxreal_0(k18_euclid(F),D) & ~ r1_xxreal_0(E,k18_euclid(F)) ) ) ) )).
fof(fraenkel_a_4_2_jordan20,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & v1_xreal_0(C) & v1_funct_1(D) & v1_funct_2(D,u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(2),B))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(2),B))))) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_2_jordan20(B,C,D,E)) <=> ? [F] : ( v1_xreal_0(F) & A = F & r1_xxreal_0(F,1) & r1_xxreal_0(E,F) & ! [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(2))) => ~ ( G = k1_funct_1(D,F) & k17_euclid(G) = C ) ) ) ) ) )).
fof(fraenkel_a_4_2_jordan6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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(E,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_4_2_jordan6(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & r1_jordan5c(B,D,C,F,E) ) ) ) )).
fof(fraenkel_a_4_2_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & v5_relat_1(C,k1_rcomp_1(k5_numbers,1)) & 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))) & m1_subset_1(D,B) & m1_subset_1(E,B) ) => ( r2_hidden(A,a_4_2_lfuzzy_1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = k12_lattice3(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),k8_lfuzzy_0(B,B,k4_fuzzy_4(B,B),D,F),k8_lfuzzy_0(B,B,C,F,E)) ) ) ) )).
fof(fraenkel_a_4_2_lopban_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & 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) & v1_xreal_0(C) & m1_subset_1(D,u1_struct_0(B)) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_2_lopban_5(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = F & ~ r1_xxreal_0(k7_xcmplx_0(E,k3_xcmplx_0(3,k2_xcmplx_0(1,C))),k2_normsp_0(B,k5_algstr_0(B,D,F))) ) ) ) )).
fof(fraenkel_a_4_2_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k6_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,k6_numbers))) & v2_xxreal_0(E) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_2_lpspace2(B,C,D,E)) <=> ? [F] : ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) & A = k5_lpspace2(B,C,D,F,E) & r2_hidden(F,k1_lpspace2(B,C,D,E)) ) ) ) )).
fof(fraenkel_a_4_2_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & m1_subset_1(C,k4_ordinal1) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(C)))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(C)))) ) => ( r2_hidden(A,a_4_2_mathmorp(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(C))) & A = k1_rlvect_1(k15_euclid(C),F,B) & r2_hidden(F,k3_mathmorp(k15_euclid(C),D,E)) ) ) ) )).
fof(fraenkel_a_4_2_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) => ( r2_hidden(A,a_4_2_mmlquery(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & r1_ordinal1(k1_card_1(k1_mmlquery(B,E,F)),k1_card_1(k1_mmlquery(B,C,F))) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_4_2_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & v1_partfun1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k30_modelc_1(B))) & m1_subset_1(E,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_4_2_modelc_1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & k3_funct_2(B,k6_margrel1,k31_modelc_1(B,k52_modelc_1(B,C,D,E)),F) = k8_margrel1 ) ) ) )).
fof(fraenkel_a_4_2_modelc_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) & v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k23_modelc_3(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k23_modelc_3(C)))) & v7_ordinal1(E) ) => ( r2_hidden(A,a_4_2_modelc_3(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k4_ordinal1) & A = F & r1_xxreal_0(1,F) & r1_xxreal_0(F,E) & r2_hidden(B,u1_modelc_3(C,k10_modelc_3(k1_funct_1(D,F),C))) ) ) ) )).
fof(fraenkel_a_4_2_msafree3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v11_struct_0(B) & v1_instalg1(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_relat_1(D) & v4_relat_1(D,u1_struct_0(B)) & v1_funct_1(D) & v1_partfun1(D,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_2_msafree3(B,C,D,E)) <=> ? [F] : ( m1_dtconstr(F,u1_struct_0(k5_msafree(B,C)),k5_trees_3(u1_struct_0(k5_msafree(B,C))),k1_msaterm(B,C)) & A = F & k7_msaterm(B,C,F) = E & r2_pboole(u1_struct_0(B),k4_msafree3(B,C,F),D) ) ) ) )).
fof(fraenkel_a_4_2_ndiff_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(B) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finseq_1(B) & v2_prvect_2(B) & v1_xreal_0(D) & m1_subset_1(E,u1_struct_0(k11_prvect_2(B,k5_ndiff_5(B,C)))) ) => ( r2_hidden(A,a_4_2_ndiff_5(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k11_prvect_2(B,k5_ndiff_5(B,C)))) & A = F & ~ r1_xxreal_0(D,k2_normsp_0(k11_prvect_2(B,k5_ndiff_5(B,C)),k5_algstr_0(k11_prvect_2(B,k5_ndiff_5(B,C)),F,E))) ) ) ) )).
fof(fraenkel_a_4_2_orders_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) & m2_orders_1(C,k1_orders_1(u1_struct_0(B)),k6_partfun1(k1_orders_1(u1_struct_0(B)))) & m2_orders_2(D,B,C) & m2_orders_2(E,B,C) ) => ( r2_hidden(A,a_4_2_orders_2(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = F & r2_hidden(F,k9_subset_1(u1_struct_0(B),D,E)) & k3_orders_2(B,D,F) = k3_orders_2(B,E,F) ) ) ) )).
fof(fraenkel_a_4_2_partit1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & m1_eqrel_1(C,B) & m1_eqrel_1(D,B) ) => ( r2_hidden(A,a_4_2_partit1(B,C,D,E)) <=> ? [F] : ( m2_subset_1(F,k1_zfmisc_1(B),C) & A = F & ? [G] : ( m2_finseq_1(G,B) & r1_xxreal_0(1,k3_finseq_1(G)) & k1_funct_1(G,1) = E & r2_hidden(k1_funct_1(G,k3_finseq_1(G)),F) & ! [H] : ( m1_subset_1(H,k4_ordinal1) => ~ ( r1_xxreal_0(1,H) & ~ r1_xxreal_0(k3_finseq_1(G),H) & ! [I] : ! [J] : ! [K] : ~ ( r2_hidden(I,C) & r2_hidden(J,D) & r2_hidden(k1_funct_1(G,H),I) & r2_hidden(K,k3_xboole_0(I,J)) & r2_hidden(k1_funct_1(G,k1_nat_1(H,1)),J) ) ) ) ) ) ) ) )).
fof(fraenkel_a_4_2_petri_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_zfmisc_1(B) & m1_subset_1(D,k1_zfmisc_1(C)) & v1_funct_1(E) & v1_funct_2(E,D,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(D,B))) ) => ( r2_hidden(A,a_4_2_petri_2(B,C,D,E)) <=> ? [F] : ( v1_funct_1(F) & v1_funct_2(F,C,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(C,B))) & A = F & k2_partfun1(C,B,F,D) = E ) ) ) )).
fof(fraenkel_a_4_2_pnproc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m2_pnproc_1(C,B) & m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(C))) & m1_subset_1(E,k1_zfmisc_1(k3_finseq_2(C))) ) => ( r2_hidden(A,a_4_2_pnproc_1(B,C,D,E)) <=> ? [F] : ? [G] : ( m2_finseq_2(F,C,k3_finseq_2(C)) & m2_finseq_2(G,C,k3_finseq_2(C)) & A = k1_pre_poly(C,F,G) & r2_hidden(F,E) & r2_hidden(G,D) ) ) ) )).
fof(fraenkel_a_4_2_qc_lang4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_qc_lang1(B) & m1_subset_1(C,k9_qc_lang1(B)) & m1_qc_lang4(D,B,C) & m1_qc_lang4(E,B,C) ) => ( r2_hidden(A,a_4_2_qc_lang4(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_trees_1(F,k9_xtuple_0(k2_qc_lang4(B,C))) & m1_trees_1(G,k9_xtuple_0(k2_qc_lang4(B,D))) & A = k8_finseq_1(k4_ordinal1,F,G) & r2_hidden(F,k3_qc_lang4(B,C,D)) & r2_hidden(G,k3_qc_lang4(B,D,E)) ) ) ) )).
fof(fraenkel_a_4_2_rlsub_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_rlsub_1(D,B) & m1_rlsub_1(E,B) ) => ( r2_hidden(A,a_4_2_rlsub_2(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k3_rlvect_1(B,G,F) & r1_struct_0(k2_rlsub_2(B,C,D),G) & r1_struct_0(k2_rlsub_2(B,D,E),F) ) ) ) )).
fof(fraenkel_a_4_2_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v3_rlvect_1(B) & l2_algstr_0(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_4_2_rltopsp1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k1_algstr_0(B,C,F) & r2_hidden(F,k6_rusub_4(B,D,E)) ) ) ) )).
fof(fraenkel_a_4_2_rmod_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(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) & m1_rmod_2(D,B,C) & m1_rmod_2(E,B,C) ) => ( r2_hidden(A,a_4_2_rmod_3(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(C)) & m1_subset_1(G,u1_struct_0(C)) & A = k3_rlvect_1(C,G,F) & r1_struct_0(E,G) & r1_struct_0(D,F) ) ) ) )).
fof(fraenkel_a_4_2_rusub_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_rusub_1(D,B) & m1_rusub_1(E,B) ) => ( r2_hidden(A,a_4_2_rusub_2(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k3_rlvect_1(B,F,G) & r1_struct_0(k2_rusub_2(B,C,D),F) & r1_struct_0(k2_rusub_2(B,D,E),G) ) ) ) )).
fof(fraenkel_a_4_2_scmpds_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) & v3_scmpds_4(B) & v1_int_1(C) & v1_int_1(D) & v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ( r2_hidden(A,a_4_2_scmpds_4(B,C,D,E)) <=> ? [F] : ( v7_ordinal1(F) & A = k1_nat_1(F,k5_card_1(B)) & r2_hidden(F,k2_afinsq_1(k9_compos_1(k1_scmpds_2,k9_scmpds_2(E,C,D)))) ) ) ) )).
fof(fraenkel_a_4_2_sgraph1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & m1_sgraph1(C,B) & v1_finset_1(E) ) => ( r2_hidden(A,a_4_2_sgraph1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & r2_hidden(F,E) & r2_hidden(k2_tarski(D,F),u1_sgraph1(C)) ) ) ) )).
fof(fraenkel_a_4_2_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_qc_lang1(B) & m2_subset_1(C,k2_qc_lang1(B),k3_qc_lang1(B)) & m2_subset_1(D,k16_substut1(B),k38_substut1(B)) & m1_substut1(E,B,k7_sublemma(B,D,C)) ) => ( r2_hidden(A,a_4_2_sublemma(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_qc_lang1(B)) & A = F & r2_hidden(k2_qc_lang3(B,F),k10_xtuple_0(k7_substut1(B,k21_qc_lang1(B,k2_sublemma(B,k9_sublemma(B,k7_sublemma(B,D,C),E))),k2_sublemma(B,k9_sublemma(B,k7_sublemma(B,D,C),E)),k19_substut1(B,k9_sublemma(B,k7_sublemma(B,D,C),E))))) ) ) ) )).
fof(fraenkel_a_4_2_vectsp_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(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) & m1_vectsp_4(D,B,C) & m1_vectsp_4(E,B,C) ) => ( r2_hidden(A,a_4_2_vectsp_5(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(C)) & m1_subset_1(G,u1_struct_0(C)) & A = k3_rlvect_1(C,G,F) & r1_struct_0(E,G) & r1_struct_0(D,F) ) ) ) )).
fof(fraenkel_a_4_2_waybel17,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_lattice3(C) & v2_lattice3(C) & v1_yellow_0(C) & v3_waybel_3(C) & l1_orders_2(C) & 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(B)) ) => ( r2_hidden(A,a_4_2_waybel17(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,F) & r1_waybel_3(B,F,E) ) ) ) )).
fof(fraenkel_a_4_2_waybel21,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v24_waybel_0(C) & l1_orders_2(C) & v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C)) & v5_orders_3(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)))) & ~ v1_xboole_0(E) & v1_waybel_0(E,B) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_4_2_waybel21(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k6_waybel_9(B,C,D,k4_waybel17(B,E)))) & A = k2_yellow_0(C,a_5_1_waybel21(B,C,D,E,F)) ) ) ) )).
fof(fraenkel_a_4_2_waybel24,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) & v2_pre_topc(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_lattice3(C) & v2_lattice3(C) & v3_lattice3(C) & l1_waybel_9(C) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_waybel24(B,C)))) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_2_waybel24(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k5_yellow_1(u1_struct_0(B),C))) & A = k1_funct_1(F,E) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_4_2_waybel29,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) & 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) & m1_subset_1(D,u1_struct_0(k1_yellow_1(k5_waybel11(k3_yellow_3(C,B))))) & m1_subset_1(E,u1_struct_0(C)) ) => ( r2_hidden(A,a_4_2_waybel29(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = F & r2_hidden(k7_yellow_3(C,B,E,F),D) ) ) ) )).
fof(fraenkel_a_4_2_yellow10,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) & v5_orders_2(C) & v2_lattice3(C) & l1_orders_2(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,C)))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,C)))) ) => ( r2_hidden(A,a_4_2_yellow10(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(C)) & m1_subset_1(G,u1_struct_0(C)) & A = k12_lattice3(C,F,G) & r2_hidden(F,k5_yellow_3(B,C,D)) & r2_hidden(G,k5_yellow_3(B,C,E)) ) ) ) )).
fof(fraenkel_a_4_2_yellow12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) & ~ v2_struct_0(E) & v2_pre_topc(E) & l1_pre_topc(E) ) => ( r2_hidden(A,a_4_2_yellow12(B,C,D,E)) <=> ? [F] : ? [G] : ? [H] : ? [I] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(G,k1_zfmisc_1(u1_struct_0(C))) & m1_subset_1(H,k1_zfmisc_1(u1_struct_0(D))) & m1_subset_1(I,k1_zfmisc_1(u1_struct_0(E))) & A = k9_subset_1(u1_struct_0(k2_borsuk_1(C,E)),k3_borsuk_1(B,D,F,H),k3_borsuk_1(C,E,G,I)) & v3_pre_topc(F,B) & v3_pre_topc(G,C) & v3_pre_topc(H,D) & v3_pre_topc(I,E) ) ) ) )).
fof(fraenkel_a_4_2_yellow_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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_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(E,C) & v2_cantor_1(E,C) & m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C)))) ) => ( r2_hidden(A,a_4_2_yellow_9(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(G,k1_zfmisc_1(u1_struct_0(C))) & A = k3_borsuk_1(B,C,F,G) & r2_hidden(F,D) & r2_hidden(G,E) ) ) ) )).
fof(fraenkel_a_4_2_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) & m1_subset_1(D,B) & m1_subset_1(E,k4_ordinal1) ) => ( r2_hidden(A,a_4_2_zf_fund1(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,B) & m1_subset_1(G,B) & A = k2_xboole_0(k1_tarski(k1_domain_1(k4_ordinal1,B,E,F)),G) & r2_hidden(F,C) & r2_hidden(G,k1_classes2(B,D)) ) ) ) )).
fof(fraenkel_a_4_2_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(C,B) & m1_zmodul01(D,B) & m1_zmodul01(E,B) ) => ( r2_hidden(A,a_4_2_zmodul01(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k3_rlvect_1(B,G,F) & r1_struct_0(k7_zmodul01(B,C,D),G) & r1_struct_0(k7_zmodul01(B,D,E),F) ) ) ) )).
fof(fraenkel_a_4_3_closure2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( l1_struct_0(B) & v1_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,k6_closure2(u1_struct_0(B),C),k6_closure2(u1_struct_0(B),C)) & v7_closure2(D,u1_struct_0(B),C) & v8_closure2(D,u1_struct_0(B),C) & v9_closure2(D,u1_struct_0(B),C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k6_closure2(u1_struct_0(B),C),k6_closure2(u1_struct_0(B),C)))) & m1_closure2(E,u1_struct_0(B),u3_msualg_1(B,k10_closure2(B,C,D)),k6_closure2(u1_struct_0(B),u3_msualg_1(B,k10_closure2(B,C,D)))) ) => ( r2_hidden(A,a_4_3_closure2(B,C,D,E)) <=> ? [F] : ( m1_closure2(F,u1_struct_0(B),u3_msualg_1(B,k10_closure2(B,C,D)),k6_closure2(u1_struct_0(B),u3_msualg_1(B,k10_closure2(B,C,D)))) & A = F & r2_pboole(u1_struct_0(B),E,F) & r2_hidden(F,u1_closure2(B,k10_closure2(B,C,D))) ) ) ) )).
fof(fraenkel_a_4_3_convex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(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,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_3_convex1(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k1_algstr_0(B,F,G) & r2_hidden(F,k1_convex1(B,C,E)) & r2_hidden(G,k1_convex1(B,D,E)) ) ) ) )).
fof(fraenkel_a_4_3_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & v1_funct_1(D) & v1_funct_2(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) & ~ v1_xboole_0(E) ) => ( r2_hidden(A,a_4_3_finance1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & m1_subset_1(k3_funct_2(B,C,D,F),E) ) ) ) )).
fof(fraenkel_a_4_3_groeb_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(B,k4_ordinal1) & v1_partfun1(C,k15_pre_poly(B)) & v1_relat_2(C) & v4_relat_2(C) & v6_relat_2(C) & v8_relat_2(C) & v2_bagorder(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),k15_pre_poly(B)))) & ~ 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) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(B,D)))) ) => ( r2_hidden(A,a_4_3_groeb_1(B,C,D,E)) <=> ? [F] : ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(B),u1_struct_0(D)) & v1_polynom1(F,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(D)))) & A = k3_termord(B,C,D,F) & r2_hidden(F,k7_ideal_1(k12_polynom1(B,D),E)) & F != k8_polynom1(B,D) ) ) ) )).
fof(fraenkel_a_4_3_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v6_algstr_0(B) & v4_rlvect_1(B) & v1_vectsp_1(B) & v1_algstr_1(B) & l6_algstr_0(B) & ~ v1_xboole_0(C) & v3_ideal_1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_xboole_0(D) & v3_ideal_1(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_3_ideal_1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k6_algstr_0(B,E,F) & r2_hidden(F,k11_ideal_1(B,C,D)) ) ) ) )).
fof(fraenkel_a_4_3_jordan1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_3_jordan1(B,C,D,E)) <=> ? [F] : ? [G] : ( v1_xreal_0(F) & v1_xreal_0(G) & A = k19_euclid(F,G) & ~ r1_xxreal_0(F,B) & ~ r1_xxreal_0(C,F) & ~ r1_xxreal_0(G,D) & ~ r1_xxreal_0(E,G) ) ) ) )).
fof(fraenkel_a_4_3_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & v5_relat_1(C,k1_rcomp_1(k5_numbers,1)) & 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))) & m1_subset_1(D,B) & m1_subset_1(E,B) ) => ( r2_hidden(A,a_4_3_lfuzzy_1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = k12_lattice3(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),k8_lfuzzy_0(B,B,C,D,F),k8_lfuzzy_0(B,B,k4_fuzzy_4(B,B),F,E)) ) ) ) )).
fof(fraenkel_a_4_3_mathmorp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & m1_subset_1(D,k4_ordinal1) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(D)))) ) => ( r2_hidden(A,a_4_3_mathmorp(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(D))) & A = k1_rlvect_1(k15_euclid(D),F,k2_xcmplx_0(C,B)) & r2_hidden(F,E) ) ) ) )).
fof(fraenkel_a_4_3_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) => ( r2_hidden(A,a_4_3_mmlquery(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & r2_hidden(k1_card_1(k1_mmlquery(B,C,F)),k1_card_1(k1_mmlquery(B,E,F))) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_4_3_msafree3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v11_struct_0(B) & v1_instalg1(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_relat_1(D) & v4_relat_1(D,u1_struct_0(B)) & v1_funct_1(D) & v1_partfun1(D,u1_struct_0(B)) & m1_subset_1(E,u4_struct_0(B)) ) => ( r2_hidden(A,a_4_3_msafree3(B,C,D,E)) <=> ? [F] : ( m1_dtconstr(F,u1_struct_0(k5_msafree(B,C)),k5_trees_3(u1_struct_0(k5_msafree(B,C))),k1_msaterm(B,C)) & A = F & k7_msaterm(B,C,F) = k2_msualg_1(B,E) & r2_pboole(u1_struct_0(B),k4_msafree3(B,C,F),D) ) ) ) )).
fof(fraenkel_a_4_3_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) & v3_msualg_6(D,B,k1_msafree3(B,C)) & v4_msualg_6(D,B,k1_msafree3(B,C)) & v9_msafree4(D,u1_struct_0(B),u3_msualg_1(B,k1_msafree3(B,C))) & v10_msafree4(D,u1_struct_0(B),u3_msualg_1(B,k1_msafree3(B,C))) & m1_msualg_4(D,u1_struct_0(B),u3_msualg_1(B,k1_msafree3(B,C)),u3_msualg_1(B,k1_msafree3(B,C))) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_3_msafree4(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(B,k1_msafree3(B,C)),E)) & A = k8_msafree4(k1_funct_1(u3_msualg_1(B,k1_msafree3(B,C)),E),k7_msafree4(u1_struct_0(B),u3_msualg_1(B,k1_msafree3(B,C)),u3_msualg_1(B,k1_msafree3(B,C)),D,E),F) ) ) ) )).
fof(fraenkel_a_4_3_ndiff_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(B) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finseq_1(B) & v2_prvect_2(B) & m1_subset_1(D,u1_struct_0(k11_prvect_2(B,k5_ndiff_5(B,C)))) & m1_subset_1(E,u1_struct_0(k11_prvect_2(B,k5_ndiff_5(B,C)))) ) => ( r2_hidden(A,a_4_3_ndiff_5(B,C,D,E)) <=> ? [F] : ( v1_xreal_0(F) & A = k3_rlvect_1(k11_prvect_2(B,k5_ndiff_5(B,C)),k1_rlvect_1(k11_prvect_2(B,k5_ndiff_5(B,C)),D,k6_xcmplx_0(1,F)),k1_rlvect_1(k11_prvect_2(B,k5_ndiff_5(B,C)),E,F)) & r1_xxreal_0(k5_numbers,F) & r1_xxreal_0(F,1) ) ) ) )).
fof(fraenkel_a_4_3_petri_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_zfmisc_1(B) & v1_funct_1(E) & v1_funct_2(E,D,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(D,B))) ) => ( r2_hidden(A,a_4_3_petri_2(B,C,D,E)) <=> ? [F] : ( v1_funct_1(F) & v1_funct_2(F,C,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(C,B))) & A = F & k2_partfun1(C,B,F,D) = E ) ) ) )).
fof(fraenkel_a_4_3_pnproc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m2_pnproc_1(C,B) & m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(C))) & m1_subset_1(E,k1_zfmisc_1(k3_finseq_2(C))) ) => ( r2_hidden(A,a_4_3_pnproc_1(B,C,D,E)) <=> ? [F] : ( m2_finseq_2(F,C,k3_finseq_2(C)) & A = F & ? [G] : ( v1_relat_1(G) & v1_funct_1(G) & v2_finseq_1(G) & ? [H] : ( v1_relat_1(H) & v1_funct_1(H) & v2_finseq_1(H) & F = k2_xboole_0(G,H) & r1_xboole_0(G,H) & r2_hidden(k15_finseq_1(G),E) & r2_hidden(k15_finseq_1(H),D) ) ) ) ) ) )).
fof(fraenkel_a_4_3_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) & m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(B))) ) => ( r2_hidden(A,a_4_3_relset_2(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_zfmisc_1(B)) & A = k6_relset_2(B,C,F,D) & r2_hidden(F,E) ) ) ) )).
fof(fraenkel_a_4_3_rlsub_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_rlsub_1(D,B) & m1_rlsub_1(E,B) ) => ( r2_hidden(A,a_4_3_rlsub_2(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k3_rlvect_1(B,G,F) & r1_struct_0(D,G) & r1_struct_0(k2_rlsub_2(B,C,E),F) ) ) ) )).
fof(fraenkel_a_4_3_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v3_rlvect_1(B) & l2_algstr_0(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_4_3_rltopsp1(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k1_algstr_0(B,F,G) & r2_hidden(F,k5_rusub_4(B,D,C)) & r2_hidden(G,E) ) ) ) )).
fof(fraenkel_a_4_3_rmod_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(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) & m1_rmod_2(D,B,C) & v2_vectsp_2(E,B) & m1_rmod_2(E,B,C) ) => ( r2_hidden(A,a_4_3_rmod_3(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(C)) & m1_subset_1(G,u1_struct_0(C)) & A = k3_rlvect_1(C,G,F) & r1_struct_0(D,G) & r1_struct_0(E,F) ) ) ) )).
fof(fraenkel_a_4_3_rusub_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_rusub_1(D,B) & m1_rusub_1(E,B) ) => ( r2_hidden(A,a_4_3_rusub_2(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k3_rlvect_1(B,F,G) & r1_struct_0(D,F) & r1_struct_0(k2_rusub_2(B,C,E),G) ) ) ) )).
fof(fraenkel_a_4_3_simplex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(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) & l1_rlvect_1(C) & v1_finset_1(D) & v1_rlaffin1(D,C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) & v1_funct_1(E) & v1_funct_2(E,k4_simplex0(k5_simplex1(B,C,k5_simplex0(u1_struct_0(C),k6_domain_1(k1_zfmisc_1(u1_struct_0(C)),D)))),D) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_simplex0(k5_simplex1(B,C,k5_simplex0(u1_struct_0(C),k6_domain_1(k1_zfmisc_1(u1_struct_0(C)),D)))),D))) ) => ( r2_hidden(A,a_4_3_simplex1(B,C,D,E)) <=> ? [F] : ( m3_simplex0(F,k5_simplex1(B,C,k5_simplex0(u1_struct_0(C),k6_domain_1(k1_zfmisc_1(u1_struct_0(C)),D))),k6_xcmplx_0(k5_card_1(D),1)) & A = F & k7_relset_1(k4_simplex0(k5_simplex1(B,C,k5_simplex0(u1_struct_0(C),k6_domain_1(k1_zfmisc_1(u1_struct_0(C)),D)))),D,E,F) = D ) ) ) )).
fof(fraenkel_a_4_3_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_qc_lang1(B) & v7_ordinal1(C) & m2_subset_1(D,k6_qc_lang1(B),k8_qc_lang1(B,C)) & v5_relat_1(E,k3_qc_lang1(B)) & v3_card_1(E,C) & m2_finseq_1(E,k2_qc_lang1(B)) ) => ( r2_hidden(A,a_4_3_sublemma(B,C,D,E)) <=> ? [F] : ( v7_ordinal1(F) & A = k1_funct_1(k17_qc_lang1(B,k4_cqc_lang(C,B,D,E)),F) & r1_xxreal_0(1,F) & r1_xxreal_0(F,k3_finseq_1(k17_qc_lang1(B,k4_cqc_lang(C,B,D,E)))) & r2_hidden(k1_funct_1(k17_qc_lang1(B,k4_cqc_lang(C,B,D,E)),F),k3_qc_lang1(B)) ) ) ) )).
fof(fraenkel_a_4_3_termord,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v3_ordinal1(B) & ~ 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) & v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(B),u1_struct_0(C)) & v1_polynom7(D,B,C) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(C)))) & v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(B),u1_struct_0(C)) & v1_polynom7(E,B,C) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(C)))) ) => ( r2_hidden(A,a_4_3_termord(B,C,D,E)) <=> ? [F] : ? [G] : ( m2_subset_1(F,k14_pre_poly(B),k15_pre_poly(B)) & m2_subset_1(G,k14_pre_poly(B),k15_pre_poly(B)) & A = k11_pre_poly(B,F,G) & r2_hidden(F,k3_polynom1(k15_pre_poly(B),C,D)) & r2_hidden(G,k3_polynom1(k15_pre_poly(B),C,E)) ) ) ) )).
fof(fraenkel_a_4_3_vectsp_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(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) & m1_vectsp_4(D,B,C) & v7_vectsp_1(E,B) & m1_vectsp_4(E,B,C) ) => ( r2_hidden(A,a_4_3_vectsp_5(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(C)) & m1_subset_1(G,u1_struct_0(C)) & A = k3_rlvect_1(C,G,F) & r1_struct_0(D,G) & r1_struct_0(E,F) ) ) ) )).
fof(fraenkel_a_4_3_waybel17,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) & v2_pre_topc(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) & v4_waybel11(C) & l1_waybel_9(C) & 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(B)) ) => ( r2_hidden(A,a_4_3_waybel17(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,F) & r1_waybel_3(B,F,E) ) ) ) )).
fof(fraenkel_a_4_3_waybel21,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m2_yellow_6(D,B,C) & m1_subset_1(E,u1_struct_0(D)) ) => ( r2_hidden(A,a_4_3_waybel21(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(D)) & A = k2_waybel_0(B,D,F) & r1_orders_2(D,E,F) ) ) ) )).
fof(fraenkel_a_4_3_waybel24,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) & 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) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_yellow_1(u1_struct_0(B),C)))) & ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_4_3_waybel24(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k1_yellow_0(C,a_4_1_waybel24(B,C,D,F)) & r2_hidden(F,E) ) ) ) )).
fof(fraenkel_a_4_3_yellow10,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & v5_orders_2(C) & v1_lattice3(C) & l1_orders_2(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,C)))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,C)))) ) => ( r2_hidden(A,a_4_3_yellow10(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(k3_yellow_3(B,C))) & m1_subset_1(G,u1_struct_0(k3_yellow_3(B,C))) & A = k13_lattice3(k3_yellow_3(B,C),F,G) & r2_hidden(F,D) & r2_hidden(G,E) ) ) ) )).
fof(fraenkel_a_4_3_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) & m1_subset_1(D,B) & m1_subset_1(E,k4_ordinal1) ) => ( r2_hidden(A,a_4_3_zf_fund1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = k1_tarski(k1_domain_1(k4_ordinal1,B,E,F)) & r2_hidden(k2_xboole_0(k1_tarski(k1_domain_1(k4_ordinal1,B,E,F)),D),C) ) ) ) )).
fof(fraenkel_a_4_3_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(C,B) & m1_zmodul01(D,B) & m1_zmodul01(E,B) ) => ( r2_hidden(A,a_4_3_zmodul01(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k3_rlvect_1(B,G,F) & r1_struct_0(D,G) & r1_struct_0(k7_zmodul01(B,C,E),F) ) ) ) )).
fof(fraenkel_a_4_4_closure2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( l1_struct_0(B) & v1_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,k6_closure2(u1_struct_0(B),C),k6_closure2(u1_struct_0(B),C)) & v7_closure2(D,u1_struct_0(B),C) & v8_closure2(D,u1_struct_0(B),C) & v9_closure2(D,u1_struct_0(B),C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k6_closure2(u1_struct_0(B),C),k6_closure2(u1_struct_0(B),C)))) & v1_funct_1(E) & v1_funct_2(E,k6_closure2(u1_struct_0(B),u3_msualg_1(B,k10_closure2(B,C,D))),k6_closure2(u1_struct_0(B),u3_msualg_1(B,k10_closure2(B,C,D)))) & v7_closure2(E,u1_struct_0(B),u3_msualg_1(B,k10_closure2(B,C,D))) & v8_closure2(E,u1_struct_0(B),u3_msualg_1(B,k10_closure2(B,C,D))) & v9_closure2(E,u1_struct_0(B),u3_msualg_1(B,k10_closure2(B,C,D))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k6_closure2(u1_struct_0(B),u3_msualg_1(B,k10_closure2(B,C,D))),k6_closure2(u1_struct_0(B),u3_msualg_1(B,k10_closure2(B,C,D)))))) ) => ( r2_hidden(A,a_4_4_closure2(B,C,D,E)) <=> ? [F] : ( m1_closure2(F,u1_struct_0(B),u3_msualg_1(B,k10_closure2(B,C,D)),k6_closure2(u1_struct_0(B),u3_msualg_1(B,k10_closure2(B,C,D)))) & A = F & r6_pboole(u1_struct_0(B),k7_closure2(u1_struct_0(B),u3_msualg_1(B,k10_closure2(B,C,D)),E,F),F) ) ) ) )).
fof(fraenkel_a_4_4_closure3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) & m1_subset_1(E,k1_zfmisc_1(k1_closure2(B,C))) ) => ( r2_hidden(A,a_4_4_closure3(B,C,D,E)) <=> ? [F] : ( m1_closure2(F,B,C,k6_closure2(B,C)) & A = k1_funct_1(F,D) & r2_hidden(F,E) ) ) ) )).
fof(fraenkel_a_4_4_convex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(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,k1_zfmisc_1(u1_struct_0(B))) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_4_convex1(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k1_algstr_0(B,F,G) & r2_hidden(F,k1_convex1(B,C,D)) & r2_hidden(G,k1_convex1(B,C,E)) ) ) ) )).
fof(fraenkel_a_4_4_groeb_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(B,k4_ordinal1) & v1_partfun1(C,k15_pre_poly(B)) & v1_relat_2(C) & v4_relat_2(C) & v6_relat_2(C) & v8_relat_2(C) & v2_bagorder(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),k15_pre_poly(B)))) & ~ 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) & ~ v1_xboole_0(E) & v1_ideal_1(E,k12_polynom1(B,D)) & v2_ideal_1(E,k12_polynom1(B,D)) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(B,D)))) ) => ( r2_hidden(A,a_4_4_groeb_1(B,C,D,E)) <=> ? [F] : ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(B),u1_struct_0(D)) & v1_polynom1(F,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(D)))) & A = k3_termord(B,C,D,F) & r2_hidden(F,E) & F != k8_polynom1(B,D) ) ) ) )).
fof(fraenkel_a_4_4_jgraph_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_4_jgraph_6(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & ~ ( ~ ( k17_euclid(F) = B & r1_xxreal_0(D,k18_euclid(F)) & r1_xxreal_0(k18_euclid(F),E) ) & ~ ( k18_euclid(F) = E & r1_xxreal_0(B,k17_euclid(F)) & r1_xxreal_0(k17_euclid(F),C) ) & ~ ( k17_euclid(F) = C & r1_xxreal_0(D,k18_euclid(F)) & r1_xxreal_0(k18_euclid(F),E) ) & ~ ( k18_euclid(F) = D & r1_xxreal_0(B,k17_euclid(F)) & r1_xxreal_0(k17_euclid(F),C) ) ) ) ) ) )).
fof(fraenkel_a_4_4_jordan1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_4_jordan1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & ~ ( r1_xxreal_0(B,k17_euclid(F)) & r1_xxreal_0(k17_euclid(F),C) & r1_xxreal_0(D,k18_euclid(F)) & r1_xxreal_0(k18_euclid(F),E) ) ) ) ) )).
fof(fraenkel_a_4_4_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) => ( r2_hidden(A,a_4_4_mmlquery(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & r2_hidden(k1_card_1(k1_mmlquery(B,E,F)),k1_card_1(k1_mmlquery(B,C,F))) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_4_4_msafree3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v11_struct_0(B) & v1_instalg1(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_relat_1(D) & v4_relat_1(D,u1_struct_0(B)) & v1_funct_1(D) & v1_partfun1(D,u1_struct_0(B)) & m1_dtconstr(E,u1_struct_0(k5_msafree(B,C)),k5_trees_3(u1_struct_0(k5_msafree(B,C))),k1_msaterm(B,C)) ) => ( r2_hidden(A,a_4_4_msafree3(B,C,D,E)) <=> ? [F] : ( m1_dtconstr(F,u1_struct_0(k5_msafree(B,C)),k5_trees_3(u1_struct_0(k5_msafree(B,C))),k1_msaterm(B,C)) & A = F & k7_msaterm(B,C,F) = k7_msaterm(B,C,E) & r2_pboole(u1_struct_0(B),k4_msafree3(B,C,F),D) ) ) ) )).
fof(fraenkel_a_4_4_msscyc_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) & v2_finset_1(C) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,k4_ordinal1) ) => ( r2_hidden(A,a_4_4_msscyc_2(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(B,k11_msafree(B,C)),D)) & A = F & r1_xxreal_0(k8_msafree2(B,C,D,F),E) ) ) ) )).
fof(fraenkel_a_4_4_ndiff_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(B) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finseq_1(B) & v2_prvect_2(B) & m2_subset_1(C,k4_ordinal1,k4_finseq_1(B)) & m1_subset_1(D,u1_struct_0(k11_prvect_2(B,C))) & m1_subset_1(E,u1_struct_0(k11_prvect_2(B,C))) ) => ( r2_hidden(A,a_4_4_ndiff_5(B,C,D,E)) <=> ? [F] : ( v1_xreal_0(F) & A = k3_rlvect_1(k11_prvect_2(B,C),k1_rlvect_1(k11_prvect_2(B,C),D,k6_xcmplx_0(1,F)),k1_rlvect_1(k11_prvect_2(B,C),E,F)) & r1_xxreal_0(k5_numbers,F) & r1_xxreal_0(F,1) ) ) ) )).
fof(fraenkel_a_4_4_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(B,C)))) ) => ( r2_hidden(A,a_4_4_relset_2(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,C))) & A = k7_relset_1(B,C,F,D) & r2_hidden(F,E) ) ) ) )).
fof(fraenkel_a_4_4_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v6_rltopsp1(B) & v7_rltopsp1(B) & l1_rltopsp1(B) & m1_subset_1(C,u1_struct_0(B)) & m1_subset_1(D,u1_struct_0(B)) & m1_connsp_2(E,B,C) ) => ( r2_hidden(A,a_4_4_rltopsp1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,D,F) & r2_hidden(F,k1_tops_1(B,E)) ) ) ) )).
fof(fraenkel_a_4_4_rmod_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(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) & m1_rmod_2(D,B,C) & m1_rmod_2(E,B,C) ) => ( r2_hidden(A,a_4_4_rmod_3(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(C)) & m1_subset_1(G,u1_struct_0(C)) & A = k3_rlvect_1(C,G,F) & r1_struct_0(k2_rmod_3(B,C,D,E),G) & r1_struct_0(E,F) ) ) ) )).
fof(fraenkel_a_4_4_rusub_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_rusub_1(D,B) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_4_rusub_2(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k3_rlvect_1(B,E,F) & r1_struct_0(k2_rusub_2(B,C,D),F) ) ) ) )).
fof(fraenkel_a_4_4_simplex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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)) & v1_simplex1(C,B) & v2_simplex1(C,B) & m1_simplex0(C,u1_struct_0(B)) & v1_finset_1(D) & v1_tops_2(D,C) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C)))) & v1_finset_1(E) & v1_rlaffin1(E,B) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_4_4_simplex1(B,C,D,E)) <=> ? [F] : ( m3_simplex0(F,k4_simplex1(B,k5_simplex0(u1_struct_0(B),k6_domain_1(k1_zfmisc_1(u1_struct_0(B)),E))),k5_card_1(D)) & A = F & r1_tarski(k7_relset_1(k1_orders_1(u1_struct_0(B)),u1_struct_0(B),k2_rlaffin2(B),D),F) ) ) ) )).
fof(fraenkel_a_4_4_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_qc_lang1(B) & m2_subset_1(C,k2_qc_lang1(B),k3_qc_lang1(B)) & m2_subset_1(D,k16_substut1(B),k38_substut1(B)) & m1_substut1(E,B,k7_sublemma(B,D,C)) ) => ( r2_hidden(A,a_4_4_sublemma(B,C,D,E)) <=> ? [F] : ( m2_subset_1(F,k2_qc_lang1(B),k3_qc_lang1(B)) & A = F & r2_hidden(F,k24_qc_lang1(B,k11_cqc_lang(B,C,k2_sublemma(B,D)))) & m1_subset_1(F,k9_xtuple_0(E)) & F != C & F != k1_funct_1(E,F) ) ) ) )).
fof(fraenkel_a_4_4_vectsp_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(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) & m1_vectsp_4(D,B,C) & m1_vectsp_4(E,B,C) ) => ( r2_hidden(A,a_4_4_vectsp_5(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(C)) & m1_subset_1(G,u1_struct_0(C)) & A = k3_rlvect_1(C,G,F) & r1_struct_0(k2_vectsp_5(B,C,D,E),G) & r1_struct_0(E,F) ) ) ) )).
fof(fraenkel_a_4_4_waybel17,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) & 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) & 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(B)) ) => ( r2_hidden(A,a_4_4_waybel17(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,F) & r3_orders_2(B,F,E) & v1_waybel_3(F,B) ) ) ) )).
fof(fraenkel_a_4_4_waybel24,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) & v2_pre_topc(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_lattice3(C) & v2_lattice3(C) & v3_lattice3(C) & v4_waybel11(C) & l1_waybel_9(C) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_waybel24(B,C)))) & ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_4_4_waybel24(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k1_yellow_0(C,a_4_5_waybel24(B,C,D,F)) & r2_hidden(F,E) ) ) ) )).
fof(fraenkel_a_4_4_yellow10,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & v5_orders_2(C) & v1_lattice3(C) & l1_orders_2(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,C)))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,C)))) ) => ( r2_hidden(A,a_4_4_yellow10(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,u1_struct_0(B)) & A = k13_lattice3(B,F,G) & r2_hidden(F,k4_yellow_3(B,C,D)) & r2_hidden(G,k4_yellow_3(B,C,E)) ) ) ) )).
fof(fraenkel_a_4_4_yellow_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & m1_subset_1(C,u1_struct_0(B)) & v1_tops_2(D,B) & v1_cantor_1(D,B) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & m1_connsp_2(E,B,C) ) => ( r2_hidden(A,a_4_4_yellow_9(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B))) & A = F & r2_hidden(F,D) & r1_tarski(F,E) ) ) ) )).
fof(fraenkel_a_4_5_closure3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) ) => ( r2_hidden(A,a_4_5_closure3(B,C,D,E)) <=> ? [F] : ( m1_closure2(F,B,C,k6_closure2(B,C)) & A = k1_funct_1(F,E) & r2_hidden(F,k3_tarski(D)) ) ) ) )).
fof(fraenkel_a_4_5_convex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(B)) & m1_subset_1(D,u1_struct_0(B)) & m2_rlvect_2(E,B,k7_domain_1(u1_struct_0(B),C,D)) ) => ( r2_hidden(A,a_4_5_convex1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = F & k1_funct_1(E,F) != k5_numbers ) ) ) )).
fof(fraenkel_a_4_5_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(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))) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_5_finance1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & m1_subset_1(k3_funct_2(B,k1_numbers,C,F),k3_rcomp_1(D,E)) ) ) ) )).
fof(fraenkel_a_4_5_group_10,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) & ~ v1_xboole_0(C) & m1_subset_1(D,C) & v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),k1_funct_2(C,C)) & v1_group_10(E,B,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),k1_funct_2(C,C)))) ) => ( r2_hidden(A,a_4_5_group_10(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,C) & m1_subset_1(G,k1_zfmisc_1(u1_struct_0(B))) & A = k1_domain_1(C,k1_zfmisc_1(u1_struct_0(B)),F,G) & ? [H] : ( m1_subset_1(H,u1_struct_0(B)) & F = k3_funct_2(C,C,k1_group_10(B,C,E,H),D) & G = k13_group_2(B,k11_group_10(B,C,E,D),H) ) ) ) ) )).
fof(fraenkel_a_4_5_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,B) & l1_group_9(C,B) & m1_group_9(D,B,C) & m1_group_9(E,B,C) ) => ( r2_hidden(A,a_4_5_group_9(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(C))) & A = F & ? [G] : ( v2_group_9(G,B) & m1_group_9(G,B,C) & F = u1_struct_0(G) & r1_tarski(k4_subset_1(u1_struct_0(C),k15_group_9(B,C,D),k15_group_9(B,C,E)),k15_group_9(B,C,G)) ) ) ) ) )).
fof(fraenkel_a_4_5_jgraph_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_5_jgraph_6(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & ~ ( ~ ( k17_euclid(F) = B & r1_xxreal_0(k18_euclid(F),E) & r1_xxreal_0(D,k18_euclid(F)) ) & ~ ( r1_xxreal_0(k17_euclid(F),C) & r1_xxreal_0(B,k17_euclid(F)) & k18_euclid(F) = E ) & ~ ( r1_xxreal_0(k17_euclid(F),C) & r1_xxreal_0(B,k17_euclid(F)) & k18_euclid(F) = D ) & ~ ( k17_euclid(F) = C & r1_xxreal_0(k18_euclid(F),E) & r1_xxreal_0(D,k18_euclid(F)) ) ) ) ) ) )).
fof(fraenkel_a_4_5_jordan1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_5_jordan1(B,C,D,E)) <=> ? [F] : ? [G] : ( v1_xreal_0(F) & v1_xreal_0(G) & A = k19_euclid(F,G) & ~ ( r1_xxreal_0(B,F) & r1_xxreal_0(F,C) & r1_xxreal_0(D,G) & r1_xxreal_0(G,E) ) ) ) ) )).
fof(fraenkel_a_4_5_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,B))) & v7_ordinal1(E) ) => ( r2_hidden(A,a_4_5_mmlquery(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & k1_card_1(k1_mmlquery(B,D,F)) = E & r2_hidden(F,C) ) ) ) )).
fof(fraenkel_a_4_5_msafree3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v11_struct_0(B) & v1_instalg1(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_dtconstr(D,u1_struct_0(k5_msafree(B,C)),k5_trees_3(u1_struct_0(k5_msafree(B,C))),k1_msaterm(B,C)) ) => ( r2_hidden(A,a_4_5_msafree3(B,C,D,E)) <=> ? [F] : ( m2_subset_1(F,u1_struct_0(k5_msafree(B,C)),k2_relset_1(u1_struct_0(k5_msafree(B,C)),D)) & A = k1_xtuple_0(F) & k2_xtuple_0(F) = E ) ) ) )).
fof(fraenkel_a_4_5_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(B,C)))) ) => ( r2_hidden(A,a_4_5_relset_2(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,C))) & A = k6_relset_2(B,C,D,F) & r2_hidden(F,E) ) ) ) )).
fof(fraenkel_a_4_5_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_qc_lang1(B) & m2_subset_1(C,k9_qc_lang1(B),k3_cqc_lang(B)) & m2_subset_1(D,k2_qc_lang1(B),k3_qc_lang1(B)) & m1_subset_1(E,k1_substut1(B)) ) => ( r2_hidden(A,a_4_5_sublemma(B,C,D,E)) <=> ? [F] : ( m2_subset_1(F,k2_qc_lang1(B),k3_qc_lang1(B)) & A = F & r2_hidden(F,k24_qc_lang1(B,k11_cqc_lang(B,D,C))) & m1_subset_1(F,k9_xtuple_0(E)) & F != D & F != k1_funct_1(E,F) ) ) ) )).
fof(fraenkel_a_4_5_vectsp_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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(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) & m1_vectsp_4(D,B,C) & m1_subset_1(E,u1_struct_0(C)) ) => ( r2_hidden(A,a_4_5_vectsp_5(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(C)) & A = k3_rlvect_1(C,E,F) & r1_struct_0(D,F) ) ) ) )).
fof(fraenkel_a_4_5_waybel17,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) & v2_pre_topc(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_lattice3(C) & v2_lattice3(C) & v3_lattice3(C) & v4_waybel11(C) & l1_waybel_9(C) & 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(B)) ) => ( r2_hidden(A,a_4_5_waybel17(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,F) & r3_orders_2(B,F,E) & v1_waybel_3(F,B) ) ) ) )).
fof(fraenkel_a_4_5_waybel21,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v2_pre_topc(B) & 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) & v2_waybel19(B) & l1_waybel_9(B) & ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m1_subset_1(D,u1_struct_0(C)) & m1_subset_1(E,u1_struct_0(k5_waybel_9(B,C,D))) ) => ( r2_hidden(A,a_4_5_waybel21(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k5_waybel_9(B,C,D))) & A = k2_waybel_0(B,k5_waybel_9(B,C,D),F) & r1_orders_2(k5_waybel_9(B,C,D),E,F) ) ) ) )).
fof(fraenkel_a_4_5_waybel24,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) & v2_pre_topc(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_lattice3(C) & v2_lattice3(C) & v3_lattice3(C) & v4_waybel11(C) & l1_waybel_9(C) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_waybel24(B,C)))) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_5_waybel24(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k5_yellow_1(u1_struct_0(B),C))) & A = k1_funct_1(F,E) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_4_5_yellow10,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) & v5_orders_2(C) & v1_lattice3(C) & l1_orders_2(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,C)))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k3_yellow_3(B,C)))) ) => ( r2_hidden(A,a_4_5_yellow10(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(C)) & m1_subset_1(G,u1_struct_0(C)) & A = k13_lattice3(C,F,G) & r2_hidden(F,k5_yellow_3(B,C,D)) & r2_hidden(G,k5_yellow_3(B,C,E)) ) ) ) )).
fof(fraenkel_a_4_6_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(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))) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_6_finance1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & m1_subset_1(k3_funct_2(B,k1_numbers,C,F),k1_rcomp_1(D,E)) ) ) ) )).
fof(fraenkel_a_4_6_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & v7_ordinal1(D) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ( r2_hidden(A,a_4_6_fomodel3(B,C,D,E)) <=> ? [F] : ? [G] : ( m2_finseq_2(F,B,k4_finseq_2(D,B)) & m2_finseq_2(G,C,k4_finseq_2(D,C)) & A = k1_domain_1(k4_finseq_2(D,B),k4_finseq_2(D,C),F,G) & r1_relset_1(k4_ordinal1,C,G,k4_relset_1(k4_ordinal1,B,B,C,F,E)) ) ) ) )).
fof(fraenkel_a_4_6_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,B) & l1_group_9(C,B) & v2_group_9(D,B) & v4_group_9(D,B,C) & m1_group_9(D,B,C) & m1_subset_1(E,B) ) => ( r2_hidden(A,a_4_6_group_9(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,k7_group_9(B,C,D)) & m1_subset_1(G,k7_group_9(B,C,D)) & A = k4_tarski(F,G) & ? [H] : ( m1_subset_1(H,u1_struct_0(C)) & ? [I] : ( m1_subset_1(I,u1_struct_0(C)) & r2_hidden(H,F) & r2_hidden(I,G) & I = k3_funct_2(u1_struct_0(C),u1_struct_0(C),k3_group_9(B,C,E),H) ) ) ) ) ) )).
fof(fraenkel_a_4_6_jordan1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_6_jordan1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & ~ r1_xxreal_0(k17_euclid(F),B) & ~ r1_xxreal_0(D,k17_euclid(F)) & ~ r1_xxreal_0(k18_euclid(F),C) & ~ r1_xxreal_0(E,k18_euclid(F)) ) ) ) )).
fof(fraenkel_a_4_6_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,B))) & v7_ordinal1(E) ) => ( r2_hidden(A,a_4_6_mmlquery(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & r1_ordinal1(k1_card_1(k1_mmlquery(B,D,F)),E) & r2_hidden(F,C) ) ) ) )).
fof(fraenkel_a_4_6_msafree3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v11_struct_0(B) & v1_instalg1(B) & l1_msualg_1(B) & 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)) & m1_dtconstr(D,u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),C,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))),k5_trees_3(u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),C,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers)))))),k1_msaterm(B,k2_pboole(u1_struct_0(B),C,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))) & m1_trees_1(E,k9_xtuple_0(D)) ) => ( r2_hidden(A,a_4_6_msafree3(B,C,D,E)) <=> ? [F] : ( m1_dtconstr(F,u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),C,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))),k5_trees_3(u1_struct_0(k5_msafree(B,k2_pboole(u1_struct_0(B),C,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers)))))),k1_msaterm(B,k2_pboole(u1_struct_0(B),C,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))))) & A = F & k7_msaterm(B,k2_pboole(u1_struct_0(B),C,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),F) = k7_msaterm(B,k2_pboole(u1_struct_0(B),C,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),k8_msaterm(B,k2_pboole(u1_struct_0(B),C,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),D,E)) & r2_pboole(u1_struct_0(B),k4_msafree3(B,k2_pboole(u1_struct_0(B),C,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(B),k6_domain_1(k4_ordinal1,k5_numbers))),F),C) ) ) ) )).
fof(fraenkel_a_4_6_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_qc_lang1(B) & m2_subset_1(C,k9_qc_lang1(B),k3_cqc_lang(B)) & m2_subset_1(D,k2_qc_lang1(B),k3_qc_lang1(B)) & m1_subset_1(E,k1_substut1(B)) ) => ( r2_hidden(A,a_4_6_sublemma(B,C,D,E)) <=> ? [F] : ( m2_subset_1(F,k2_qc_lang1(B),k3_qc_lang1(B)) & A = F & r2_hidden(F,k24_qc_lang1(B,C)) & m1_subset_1(F,k9_xtuple_0(E)) & F != D & F != k1_funct_1(E,F) ) ) ) )).
fof(fraenkel_a_4_6_waybel17,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) & v2_pre_topc(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_lattice3(C) & v2_lattice3(C) & v3_lattice3(C) & v4_waybel11(C) & l1_waybel_9(C) & 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(B)) ) => ( r2_hidden(A,a_4_6_waybel17(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,F) & r1_waybel_3(B,F,E) ) ) ) )).
fof(fraenkel_a_4_7_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,B) & l1_group_9(C,B) & v2_group_9(D,B) & m1_group_9(D,B,C) & v2_group_9(E,B) & m1_group_9(E,B,C) ) => ( r2_hidden(A,a_4_7_group_9(B,C,D,E)) <=> ? [F] : ? [G] : ( m1_subset_1(F,u1_struct_0(C)) & m1_subset_1(G,u1_struct_0(C)) & A = k6_algstr_0(C,F,G) & r2_hidden(F,k15_group_9(B,C,D)) & r2_hidden(G,k15_group_9(B,C,E)) ) ) ) )).
fof(fraenkel_a_4_7_jordan1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_7_jordan1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & ~ ( r1_xxreal_0(B,k17_euclid(F)) & r1_xxreal_0(k17_euclid(F),D) & r1_xxreal_0(C,k18_euclid(F)) & r1_xxreal_0(k18_euclid(F),E) ) ) ) ) )).
fof(fraenkel_a_4_7_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,B))) & v7_ordinal1(E) ) => ( r2_hidden(A,a_4_7_mmlquery(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & r1_ordinal1(E,k1_card_1(k1_mmlquery(B,D,F))) & r2_hidden(F,C) ) ) ) )).
fof(fraenkel_a_4_7_msafree3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v11_struct_0(B) & v1_instalg1(B) & l1_msualg_1(B) & 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)) & m1_subset_1(D,k3_card_3(u3_msualg_1(B,k1_msafree3(B,C)))) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_7_msafree3(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k10_xtuple_0(D)) & A = k1_xtuple_0(F) & k2_xtuple_0(F) = E ) ) ) )).
fof(fraenkel_a_4_7_waybel22,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) & v1_funct_1(D) & v1_funct_2(D,k1_waybel22(B),u1_struct_0(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_waybel22(B),u1_struct_0(C)))) & ~ v1_xboole_0(E) & v2_waybel_0(E,k2_yellow_1(B)) & v13_waybel_0(E,k2_yellow_1(B)) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k2_yellow_1(B)))) ) => ( r2_hidden(A,a_4_7_waybel22(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_zfmisc_1(B)) & A = k2_yellow_0(C,a_4_1_waybel22(B,C,D,F)) & r2_hidden(F,E) ) ) ) )).
fof(fraenkel_a_4_7_yellow_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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_tops_2(D,B) & v2_cantor_1(D,B) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) ) => ( r2_hidden(A,a_4_7_yellow_9(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B))) & A = k3_borsuk_1(B,C,F,E) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_4_8_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,B) & l1_group_9(C,B) & v2_group_9(D,B) & m1_group_9(D,B,C) & v2_group_9(E,B) & m1_group_9(E,B,C) ) => ( r2_hidden(A,a_4_8_group_9(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(C))) & A = F & ? [G] : ( v2_group_9(G,B) & m1_group_9(G,B,C) & F = u1_struct_0(G) & r1_tarski(k16_group_9(B,C,D,E),k15_group_9(B,C,G)) ) ) ) ) )).
fof(fraenkel_a_4_8_jordan1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_8_jordan1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & ~ ( ~ ( k17_euclid(F) = B & r1_xxreal_0(k18_euclid(F),E) & r1_xxreal_0(C,k18_euclid(F)) ) & ~ ( r1_xxreal_0(k17_euclid(F),D) & r1_xxreal_0(B,k17_euclid(F)) & k18_euclid(F) = E ) & ~ ( r1_xxreal_0(k17_euclid(F),D) & r1_xxreal_0(B,k17_euclid(F)) & k18_euclid(F) = C ) & ~ ( k17_euclid(F) = D & r1_xxreal_0(k18_euclid(F),E) & r1_xxreal_0(C,k18_euclid(F)) ) ) ) ) ) )).
fof(fraenkel_a_4_8_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,B))) & v7_ordinal1(E) ) => ( r2_hidden(A,a_4_8_mmlquery(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & r2_hidden(k1_card_1(k1_mmlquery(B,D,F)),E) & r2_hidden(F,C) ) ) ) )).
fof(fraenkel_a_4_8_waybel17,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) & v2_pre_topc(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_lattice3(C) & v2_lattice3(C) & v3_lattice3(C) & v4_waybel11(C) & l1_waybel_9(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)))) & ~ v2_struct_0(E) & v4_orders_2(E) & v7_waybel_0(E) & l1_waybel_0(E,B) ) => ( r2_hidden(A,a_4_8_waybel17(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k6_waybel_9(B,C,D,E))) & A = k2_yellow_0(C,a_5_2_waybel17(B,C,D,E,F)) ) ) ) )).
fof(fraenkel_a_4_8_yellow_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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_tops_2(D,C) & v2_cantor_1(D,C) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C)))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_4_8_yellow_9(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(C))) & A = k3_borsuk_1(B,C,E,F) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_4_9_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & v7_ordinal1(D) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ( r2_hidden(A,a_4_9_fomodel3(B,C,D,E)) <=> ? [F] : ? [G] : ( m2_finseq_2(F,B,k4_finseq_2(D,B)) & m2_finseq_2(G,C,k4_finseq_2(D,C)) & A = k1_domain_1(k4_finseq_2(D,C),k4_finseq_2(D,B),G,F) & ! [H] : ( r2_hidden(H,k2_finseq_1(D)) => r2_hidden(k4_tarski(k1_funct_1(F,H),k1_funct_1(G,H)),E) ) ) ) ) )).
fof(fraenkel_a_4_9_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,B) & l1_group_9(C,B) & v8_group_9(D,B,C) & m2_finseq_1(D,k6_group_9(B,C)) & v8_group_9(E,B,C) & m2_finseq_1(E,k6_group_9(B,C)) ) => ( r2_hidden(A,a_4_9_group_9(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,k4_ordinal1) & A = F & r2_hidden(F,k4_finseq_1(D)) & k1_funct_1(D,F) = k1_funct_1(E,F) ) ) ) )).
fof(fraenkel_a_4_9_jordan1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) & v1_xreal_0(E) ) => ( r2_hidden(A,a_4_9_jordan1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) & A = F & ~ ( ~ ( k17_euclid(F) = B & r1_xxreal_0(k18_euclid(F),E) & r1_xxreal_0(D,k18_euclid(F)) ) & ~ ( r1_xxreal_0(k17_euclid(F),C) & r1_xxreal_0(B,k17_euclid(F)) & k18_euclid(F) = E ) & ~ ( r1_xxreal_0(k17_euclid(F),C) & r1_xxreal_0(B,k17_euclid(F)) & k18_euclid(F) = D ) & ~ ( k17_euclid(F) = C & r1_xxreal_0(k18_euclid(F),E) & r1_xxreal_0(D,k18_euclid(F)) ) ) ) ) ) )).
fof(fraenkel_a_4_9_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,B))) & v7_ordinal1(E) ) => ( r2_hidden(A,a_4_9_mmlquery(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & A = F & r2_hidden(E,k1_card_1(k1_mmlquery(B,D,F))) & r2_hidden(F,C) ) ) ) )).
fof(fraenkel_a_4_9_waybel24,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) & v2_pre_topc(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_lattice3(C) & v2_lattice3(C) & v3_lattice3(C) & v4_waybel11(C) & l1_waybel_9(C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_yellow_1(u1_struct_0(B),C)))) & m1_subset_1(E,u1_struct_0(B)) ) => ( r2_hidden(A,a_4_9_waybel24(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(k5_yellow_1(u1_struct_0(B),C))) & A = k1_funct_1(F,E) & r2_hidden(F,D) ) ) ) )).
fof(fraenkel_a_5_0_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v13_aofa_a00(B) & v16_aofa_a00(B) & v18_aofa_a00(B,4,1) & v21_aofa_a00(B,1,1,11) & v23_aofa_a00(B,11) & l6_aofa_a00(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)) & v4_msualg_1(D,B) & v5_msafree4(D,B,C) & v3_aofa_a00(D,B,C) & v6_aofa_a01(D,B) & l1_aofa_a00(D,B) & v4_aofa_a01(E,B,C,D) & l4_aofa_a00(E,B,C,D) & v19_aofa_a00(F,B) & m1_subset_1(F,u1_struct_0(B)) ) => ( r2_hidden(A,a_5_0_aofa_a01(B,C,D,E,F)) <=> ? [G] : ? [H] : ( v3_aofa_a01(G,B,C,D,u4_aofa_a00(B,C,D,E),k37_aofa_a00(B)) & m1_msafree4(G,u1_struct_0(B),u4_aofa_a00(B,C,D,E),k1_msafree4(u1_struct_0(B),u4_aofa_a00(B,C,D,E),k37_aofa_a00(B))) & m1_subset_1(H,k1_funct_1(u3_msualg_1(B,D),F)) & A = k39_aofa_a00(B,D,k4_aofa_a01(B,D,u4_aofa_a00(B,C,D,E),k37_aofa_a00(B),G),F,H) ) ) ) )).
fof(fraenkel_a_5_0_card_fin,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v1_finset_1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_5_0_card_fin(B,C,D,E,F)) <=> ? [G] : ( v1_funct_1(G) & v1_funct_2(G,k2_xboole_0(B,k1_tarski(D)),k2_tarski(E,F)) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k2_xboole_0(B,k1_tarski(D)),k2_tarski(E,F)))) & A = G & k5_card_1(k8_relset_1(k2_xboole_0(B,k1_tarski(D)),k2_tarski(E,F),G,k1_tarski(E))) = k1_nat_1(C,1) & k1_funct_1(G,D) = E ) ) ) )).
fof(fraenkel_a_5_0_circled1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v1_xreal_0(E) & v1_xreal_0(F) ) => ( r2_hidden(A,a_5_0_circled1(B,C,D,E,F)) <=> ? [G] : ? [H] : ( m1_subset_1(G,u1_struct_0(B)) & m1_subset_1(H,u1_struct_0(B)) & A = k3_rlvect_1(B,G,H) & r2_hidden(G,k1_convex1(B,C,E)) & r2_hidden(H,k1_convex1(B,D,F)) ) ) ) )).
fof(fraenkel_a_5_0_closure1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) & m1_pboole(D,B,k5_mssubfam(B,C)) & ~ v1_xboole_0(F) ) => ( r2_hidden(A,a_5_0_closure1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,F) & A = G & r1_tarski(k1_funct_1(D,E),G) ) ) ) )).
fof(fraenkel_a_5_0_closure2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( l1_struct_0(B) & v1_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,k6_closure2(u1_struct_0(B),C),k6_closure2(u1_struct_0(B),C)) & v7_closure2(D,u1_struct_0(B),C) & v8_closure2(D,u1_struct_0(B),C) & v9_closure2(D,u1_struct_0(B),C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k6_closure2(u1_struct_0(B),C),k6_closure2(u1_struct_0(B),C)))) & ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(k1_closure2(u1_struct_0(B),u3_msualg_1(B,k10_closure2(B,C,D))))) ) => ( r2_hidden(A,a_5_0_closure2(B,C,D,E,F)) <=> ? [G] : ( m1_closure2(G,u1_struct_0(B),u3_msualg_1(B,k10_closure2(B,C,D)),k6_closure2(u1_struct_0(B),u3_msualg_1(B,k10_closure2(B,C,D)))) & A = k1_funct_1(G,F) & r2_hidden(G,E) ) ) ) )).
fof(fraenkel_a_5_0_closure3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) & m1_subset_1(D,k1_zfmisc_1(k1_closure2(B,C))) & m1_subset_1(E,k1_zfmisc_1(k1_closure2(B,C))) ) => ( r2_hidden(A,a_5_0_closure3(B,C,D,E,F)) <=> ? [G] : ( m1_closure2(G,B,C,k6_closure2(B,C)) & A = k1_funct_1(G,F) & r2_hidden(G,k3_closure3(B,C,D,E)) ) ) ) )).
fof(fraenkel_a_5_0_convex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(B) & v2_rlvect_1(B) & v3_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,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & v1_xreal_0(E) & v1_xreal_0(F) ) => ( r2_hidden(A,a_5_0_convex1(B,C,D,E,F)) <=> ? [G] : ? [H] : ( m1_subset_1(G,u1_struct_0(B)) & m1_subset_1(H,u1_struct_0(B)) & A = k3_rlvect_1(B,G,H) & r2_hidden(G,k1_convex1(B,C,E)) & r2_hidden(H,k1_convex1(B,D,F)) ) ) ) )).
fof(fraenkel_a_5_0_convex4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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(B)) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) & m2_convex4(F,B,k8_domain_1(u1_struct_0(B),C,D,E)) ) => ( r2_hidden(A,a_5_0_convex4(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(B)) & A = G & k3_funct_2(u1_struct_0(B),k2_numbers,F,G) != k5_numbers ) ) ) )).
fof(fraenkel_a_5_0_cqc_the3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( m1_qc_lang1(B) & v7_ordinal1(C) & v3_card_1(D,C) & m2_finseq_1(D,k2_qc_lang1(B)) & m2_subset_1(E,k2_qc_lang1(B),k5_qc_lang1(B)) & m2_subset_1(F,k2_qc_lang1(B),k3_qc_lang1(B)) ) => ( r2_hidden(A,a_5_0_cqc_the3(B,C,D,E,F)) <=> ? [G] : ( v7_ordinal1(G) & A = k1_funct_1(k1_cqc_lang(B,D,k2_cqc_lang(B,E,F)),G) & r1_xxreal_0(1,G) & r1_xxreal_0(G,k3_finseq_1(k1_cqc_lang(B,D,k2_cqc_lang(B,E,F)))) & r2_hidden(k1_funct_1(k1_cqc_lang(B,D,k2_cqc_lang(B,E,F)),G),k3_qc_lang1(B)) ) ) ) )).
fof(fraenkel_a_5_0_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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))) & v7_ordinal1(D) & v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k6_finance1(B,k1_numbers,C,k12_prob_1)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_finance1(B,k1_numbers,C,k12_prob_1)))) ) => ( r2_hidden(A,a_5_0_finance1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,B) & A = G & r1_xxreal_0(k5_numbers,k11_finance1(D,E,B,C,k6_finance1(B,k1_numbers,C,k12_prob_1),F,G)) ) ) ) )).
fof(fraenkel_a_5_0_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & 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,C) & v3_relat_2(E) & v8_relat_2(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,C))) & v1_relat_1(F) ) => ( r2_hidden(A,a_5_0_fomodel3(B,C,D,E,F)) <=> ? [G] : ? [H] : ( m2_subset_1(G,k1_zfmisc_1(B),k8_eqrel_1(B,D)) & m2_subset_1(H,k1_zfmisc_1(C),k8_eqrel_1(C,E)) & A = k1_domain_1(k8_eqrel_1(B,D),k8_eqrel_1(C,E),G,H) & ? [I] : ? [J] : ( r2_hidden(I,G) & r2_hidden(J,H) & r2_hidden(k4_tarski(I,J),F) ) ) ) ) )).
fof(fraenkel_a_5_0_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(B) & v6_graph_1(B) & l1_graph_1(B) & v2_funct_1(C) & v1_msscyc_1(C,B) & m2_graph_1(C,B) & m2_finseq_1(D,u1_struct_0(B)) & ~ v1_xboole_0(E) & ~ v1_xboole_0(F) & v1_finset_1(F) ) => ( r2_hidden(A,a_5_0_graph_3(B,C,D,E,F)) <=> ? [G] : ? [H] : ( m1_subset_1(G,k2_zfmisc_1(2,F)) & m1_subset_1(H,E) & A = k4_tarski(G,H) & ? [I] : ( m1_subset_1(I,k4_ordinal1) & r1_xxreal_0(1,I) & r1_xxreal_0(I,k3_finseq_1(C)) & ( ( G = k4_tarski(k5_numbers,I) & ~ ( ! [J] : ( m1_subset_1(J,k4_ordinal1) => ~ ( r1_xxreal_0(1,J) & I = k1_nat_1(J,1) & ( ( k1_funct_1(D,I) = k1_funct_1(u2_graph_1(B),k1_funct_1(C,J)) & H = k4_tarski(k5_numbers,k1_funct_1(C,J)) ) | ( k1_funct_1(D,I) = k1_funct_1(u1_graph_1(B),k1_funct_1(C,J)) & H = k4_tarski(1,k1_funct_1(C,J)) & k1_funct_1(u2_graph_1(B),k1_funct_1(C,J)) != k1_funct_1(u1_graph_1(B),k1_funct_1(C,J)) ) ) ) ) & ~ ( I = 1 & ( ( k1_funct_1(D,1) = k1_funct_1(u2_graph_1(B),k1_funct_1(C,k3_finseq_1(C))) & H = k4_tarski(k5_numbers,k1_funct_1(C,k3_finseq_1(C))) ) | ( k1_funct_1(D,1) = k1_funct_1(u1_graph_1(B),k1_funct_1(C,k3_finseq_1(C))) & H = k4_tarski(1,k1_funct_1(C,k3_finseq_1(C))) & k1_funct_1(u2_graph_1(B),k1_funct_1(C,k3_finseq_1(C))) != k1_funct_1(u1_graph_1(B),k1_funct_1(C,k3_finseq_1(C))) ) ) ) ) ) | ( G = k4_tarski(1,I) & ( ( k1_funct_1(D,I) = k1_funct_1(u1_graph_1(B),k1_funct_1(C,I)) & H = k4_tarski(1,k1_funct_1(C,I)) ) | ( k1_funct_1(D,I) = k1_funct_1(u2_graph_1(B),k1_funct_1(C,I)) & H = k4_tarski(k5_numbers,k1_funct_1(C,I)) & k1_funct_1(u2_graph_1(B),k1_funct_1(C,I)) != k1_funct_1(u1_graph_1(B),k1_funct_1(C,I)) ) ) ) ) ) ) ) ) )).
fof(fraenkel_a_5_0_groeb_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( m1_subset_1(B,k4_ordinal1) & v1_partfun1(C,k15_pre_poly(B)) & v1_relat_2(C) & v4_relat_2(C) & v6_relat_2(C) & v8_relat_2(C) & v2_bagorder(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),k15_pre_poly(B)))) & ~ 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) & v1_ideal_1(E,k12_polynom1(B,D)) & v2_ideal_1(E,k12_polynom1(B,D)) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(B,D)))) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k12_polynom1(B,D)))) ) => ( r2_hidden(A,a_5_0_groeb_1(B,C,D,E,F)) <=> ? [G] : ( v1_funct_1(G) & v1_funct_2(G,k15_pre_poly(B),u1_struct_0(D)) & v1_polynom7(G,B,D) & v1_polynom1(G,D) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(D)))) & A = G & r2_hidden(G,E) & ~ r10_polyred(B,C,D,G,F) ) ) ) )).
fof(fraenkel_a_5_0_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,B) & l1_group_9(C,B) & ~ v2_struct_0(D) & v2_group_1(D) & v3_group_1(D) & v3_group_9(D,B) & l1_group_9(D,B) & v15_algstr_0(E) & m1_group_2(E,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,B,C,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)))) ) => ( r2_hidden(A,a_5_0_group_9(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(C)) & A = k3_funct_2(u1_struct_0(C),u1_struct_0(D),F,G) & r1_struct_0(E,G) ) ) ) )).
fof(fraenkel_a_5_0_hahnban,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_subset_1(D,u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),k1_numbers) & v1_hahnban(E,B) & v4_hahnban(E,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),k1_numbers))) & v1_funct_1(F) & v1_funct_2(F,u1_struct_0(C),k1_numbers) & v2_hahnban(F,C) & v3_hahnban(F,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),k1_numbers))) ) => ( r2_hidden(A,a_5_0_hahnban(B,C,D,E,F)) <=> ? [G] : ? [H] : ( m1_subset_1(G,u1_struct_0(C)) & m1_subset_1(H,u1_struct_0(B)) & A = k5_real_1(k3_funct_2(u1_struct_0(C),k1_numbers,F,G),k3_funct_2(u1_struct_0(B),k1_numbers,E,k5_algstr_0(B,H,D))) & G = H ) ) ) )).
fof(fraenkel_a_5_0_heyting2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v1_finset_1(C) & m1_subset_1(D,k5_finsub_1(k4_partfun1(B,C))) & m1_subset_1(E,k5_finsub_1(k4_partfun1(B,C))) & m1_subset_1(F,k4_partfun1(D,E)) ) => ( r2_hidden(A,a_5_0_heyting2(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,k4_partfun1(B,C)) & A = k6_subset_1(k1_funct_1(F,G),G) & r2_hidden(G,D) ) ) ) )).
fof(fraenkel_a_5_0_heyting3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v1_finset_1(C) & m1_subset_1(D,k5_finsub_1(k4_partfun1(B,C))) & m1_subset_1(E,k5_finsub_1(k4_partfun1(B,C))) & v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(E,D))) ) => ( r2_hidden(A,a_5_0_heyting3(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,k4_partfun1(B,C)) & A = k6_subset_1(k1_funct_1(F,G),G) & r2_hidden(G,E) ) ) ) )).
fof(fraenkel_a_5_0_interva1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(B)) & m1_subset_1(F,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_5_0_interva1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,k1_zfmisc_1(B)) & A = G & r1_tarski(k9_subset_1(B,C,E),G) & r1_tarski(G,k9_subset_1(B,D,F)) ) ) ) )).
fof(fraenkel_a_5_0_jordan16,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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(E,u1_struct_0(k15_euclid(2))) & m1_subset_1(F,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_5_0_jordan16(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(2))) & A = G & r1_jordan5c(B,C,D,E,G) & r1_jordan5c(B,C,D,G,F) ) ) ) )).
fof(fraenkel_a_5_0_jordan20,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(B) & 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(E,u1_struct_0(k15_euclid(2))) & m1_subset_1(F,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_5_0_jordan20(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(2))) & A = G & r1_jordan5c(B,C,D,E,G) & r1_jordan5c(B,C,D,G,F) ) ) ) )).
fof(fraenkel_a_5_0_jordan2b,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & v1_xreal_0(D) & m1_subset_1(E,u1_struct_0(k14_euclid(B))) & m1_subset_1(F,u1_struct_0(k15_euclid(B))) ) => ( r2_hidden(A,a_5_0_jordan2b(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k14_euclid(B))) & A = G & ~ r1_xxreal_0(k7_xcmplx_0(k6_xcmplx_0(D,k7_partfun1(k1_numbers,F,C)),2),k3_metric_1(k14_euclid(B),E,G)) ) ) ) )).
fof(fraenkel_a_5_0_jordan6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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(E,u1_struct_0(k15_euclid(2))) & m1_subset_1(F,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_5_0_jordan6(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(2))) & A = G & r1_jordan5c(B,C,D,E,G) & r1_jordan5c(B,C,D,G,F) ) ) ) )).
fof(fraenkel_a_5_0_laplace,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v7_ordinal1(B) & ~ 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) & m1_matrix_2(D,k3_matrix_2(k1_nat_1(B,2))) & m1_subset_1(E,k5_finsub_1(k2_sgraph1(k2_finseq_1(k1_nat_1(B,2))))) & m1_matrix_2(F,k3_matrix_2(k1_nat_1(B,2))) ) => ( r2_hidden(A,a_5_0_laplace(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,k2_sgraph1(k2_finseq_1(k1_nat_1(B,2)))) & A = G & r2_hidden(G,E) & k3_funct_2(k2_sgraph1(k2_finseq_1(k1_nat_1(B,2))),u1_struct_0(C),k1_matrix11(B,C,D),G) != k3_funct_2(k2_sgraph1(k2_finseq_1(k1_nat_1(B,2))),u1_struct_0(C),k1_matrix11(B,C,F),G) ) ) ) )).
fof(fraenkel_a_5_0_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(B) & v5_relat_1(C,k1_rcomp_1(k5_numbers,1)) & 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))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(B,B))))) & m1_subset_1(E,B) & m1_subset_1(F,B) ) => ( r2_hidden(A,a_5_0_lfuzzy_1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,B) & A = k12_lattice3(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),k8_lfuzzy_0(B,B,C,E,G),k8_lfuzzy_0(B,B,k5_lfuzzy_0(k2_zfmisc_1(B,B),k1_yellow_0(k4_lfuzzy_0(k2_zfmisc_1(B,B)),D)),G,F)) ) ) ) )).
fof(fraenkel_a_5_0_lpspace2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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,k6_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,k6_numbers))) & v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) & v2_xxreal_0(F) & v1_xreal_0(F) ) => ( r2_hidden(A,a_5_0_lpspace2(B,C,D,E,F)) <=> ? [G] : ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) & A = G & r2_hidden(G,k1_lpspace2(B,C,D,F)) & r1_lpspace1(B,C,D,E,G) ) ) ) )).
fof(fraenkel_a_5_0_matrix11,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v7_ordinal1(B) & ~ 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_subset_1(D,k5_finsub_1(k2_sgraph1(k2_finseq_1(k1_nat_1(B,2))))) & m1_matrix_2(E,k3_matrix_2(k1_nat_1(B,2))) & m1_matrix_2(F,k3_matrix_2(k1_nat_1(B,2))) ) => ( r2_hidden(A,a_5_0_matrix11(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,k2_sgraph1(k2_finseq_1(k1_nat_1(B,2)))) & A = G & r2_hidden(G,D) & k3_funct_2(k2_sgraph1(k2_finseq_1(k1_nat_1(B,2))),u1_struct_0(C),k1_matrix11(B,C,E),G) != k3_funct_2(k2_sgraph1(k2_finseq_1(k1_nat_1(B,2))),u1_struct_0(C),k1_matrix11(B,C,F),G) ) ) ) )).
fof(fraenkel_a_5_0_matrtop1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & m1_subset_1(D,u1_struct_0(k15_euclid(B))) & v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(k2_vectsp_1),B,C) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k2_vectsp_1))) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) ) => ( r2_hidden(A,a_5_0_matrtop1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(C))) & A = k1_algstr_0(k15_euclid(C),k3_funct_2(u1_struct_0(k15_euclid(B)),u1_struct_0(k15_euclid(C)),k3_matrtop1(B,C,E),D),G) & r2_hidden(G,k2_ranknull(k15_euclid(B),k15_euclid(C),k3_matrtop1(B,C,E),F)) ) ) ) )).
fof(fraenkel_a_5_0_msualg_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) & v4_msualg_1(C,B) & l3_msualg_1(C,B) & ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k1_closure2(u1_struct_0(B),k6_pboole(u1_struct_0(B),u3_msualg_1(B,C),u3_msualg_1(B,C))))) & m1_subset_1(E,u4_struct_0(B)) & v7_ordinal1(F) ) => ( r2_hidden(A,a_5_0_msualg_9(B,C,D,E,F)) <=> ? [G] : ( m1_closure2(G,u1_struct_0(B),k6_pboole(u1_struct_0(B),u3_msualg_1(B,C),u3_msualg_1(B,C)),k6_closure2(u1_struct_0(B),k6_pboole(u1_struct_0(B),u3_msualg_1(B,C),u3_msualg_1(B,C)))) & A = k1_funct_1(G,k7_partfun1(u1_struct_0(B),k1_msualg_1(B,E),F)) & r2_hidden(G,D) ) ) ) )).
fof(fraenkel_a_5_0_ncfcont1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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(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) & v1_funct_1(D) & 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(B)) & v1_xreal_0(F) ) => ( r2_hidden(A,a_5_0_ncfcont1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(C)) & A = G & ~ r1_xxreal_0(F,k2_normsp_0(C,k5_algstr_0(C,G,k7_partfun1(u1_struct_0(C),D,E)))) ) ) ) )).
fof(fraenkel_a_5_0_nfcont_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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) & v1_funct_1(D) & 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(B)) & v1_xreal_0(F) ) => ( r2_hidden(A,a_5_0_nfcont_1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(C)) & A = G & ~ r1_xxreal_0(F,k2_normsp_0(C,k5_algstr_0(C,G,k7_partfun1(u1_struct_0(C),D,E)))) ) ) ) )).
fof(fraenkel_a_5_0_polyred,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v7_ordinal1(B) & v1_partfun1(C,k15_pre_poly(B)) & v1_relat_2(C) & v4_relat_2(C) & v6_relat_2(C) & v8_relat_2(C) & v2_bagorder(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),k15_pre_poly(B)))) & ~ v7_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) & v1_algstr_1(D) & l6_algstr_0(D) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(B,D)))) & v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(B),u1_struct_0(D)) & v1_polynom1(F,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(D)))) ) => ( r2_hidden(A,a_5_0_polyred(B,C,D,E,F)) <=> ? [G] : ( v1_funct_1(G) & v1_funct_2(G,k15_pre_poly(B),u1_struct_0(D)) & v1_polynom1(G,D) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(D)))) & A = G & ~ r1_rewrite1(k3_polyred(B,C,D,E),k11_polynom1(B,D,G,F),k8_polynom1(B,D)) ) ) ) )).
fof(fraenkel_a_5_0_qc_trans,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( m1_qc_lang1(B) & v1_qc_trans(C,B) & m1_qc_lang1(C) & m2_subset_1(D,k9_qc_lang1(C),k3_cqc_lang(C)) & m1_subset_1(E,k1_substut1(C)) & m2_subset_1(F,k2_qc_lang1(C),k3_qc_lang1(C)) ) => ( r2_hidden(A,a_5_0_qc_trans(B,C,D,E,F)) <=> ? [G] : ( m2_subset_1(G,k2_qc_lang1(C),k3_qc_lang1(C)) & A = G & r2_hidden(G,k24_qc_lang1(C,D)) & m1_subset_1(G,k9_xtuple_0(E)) & G != F & G != k1_funct_1(E,G) ) ) ) )).
fof(fraenkel_a_5_0_random_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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))) & m2_prob_1(D,B,C) & v1_xreal_0(E) & m1_random_1(F,B,C) ) => ( r2_hidden(A,a_5_0_random_2(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,B) & A = G & r1_xxreal_0(E,k9_complex1(k6_xcmplx_0(k12_supinf_2(F,G),k8_random_1(B,C,D,F)))) ) ) ) )).
fof(fraenkel_a_5_0_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(B))) & ~ v2_struct_0(D) & l1_rewrite3(D,C) ) => ( r2_hidden(A,a_5_0_rewrite3(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(D)) & A = G & ? [H] : ( m1_subset_1(H,u1_struct_0(D)) & r2_hidden(H,F) & r4_rewrite3(B,C,D,H,E,G) ) ) ) ) )).
fof(fraenkel_a_5_0_rlaffin3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & v1_rlaffin1(D,k15_euclid(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(C)))) & m2_rlaffin3(F,k15_euclid(B),D) ) => ( r2_hidden(A,a_5_0_rlaffin3(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(B))) & A = G & r2_hidden(k17_finseq_1(k1_numbers,C,k1_rlaffin3(k15_euclid(B),D,F,G)),E) ) ) ) )).
fof(fraenkel_a_5_0_rmod_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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(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) & m1_rmod_2(D,B,C) & m1_rmod_2(E,B,C) & m1_rmod_2(F,B,C) ) => ( r2_hidden(A,a_5_0_rmod_3(B,C,D,E,F)) <=> ? [G] : ? [H] : ( m1_subset_1(G,u1_struct_0(C)) & m1_subset_1(H,u1_struct_0(C)) & A = k3_rlvect_1(C,H,G) & r1_struct_0(k1_rmod_3(B,C,D,E),H) & r1_struct_0(F,G) ) ) ) )).
fof(fraenkel_a_5_0_sgraph1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( m1_sgraph1(C,B) & v1_finset_1(E) & ~ v1_xboole_0(F) ) => ( r2_hidden(A,a_5_0_sgraph1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,F) & A = G & r2_hidden(G,E) & r2_hidden(k2_tarski(D,G),u1_sgraph1(C)) ) ) ) )).
fof(fraenkel_a_5_0_topgen_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) & l1_pre_topc(D) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(D))) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(D))) ) => ( r2_hidden(A,a_5_0_topgen_3(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(D))) & A = G & r2_hidden(G,C) & r1_tarski(G,k9_subset_1(u1_struct_0(D),E,F)) ) ) ) )).
fof(fraenkel_a_5_0_valuat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( m1_qc_lang1(B) & ~ v1_xboole_0(C) & m2_subset_1(D,k2_qc_lang1(B),k3_qc_lang1(B)) & m2_funct_2(E,k2_valuat_1(B,C),k6_margrel1,k9_funct_2(k2_valuat_1(B,C),k6_margrel1)) & m2_funct_2(F,k3_qc_lang1(B),C,k2_valuat_1(B,C)) ) => ( r2_hidden(A,a_5_0_valuat_1(B,C,D,E,F)) <=> ? [G] : ( m2_funct_2(G,k3_qc_lang1(B),C,k2_valuat_1(B,C)) & A = k3_funct_2(k2_valuat_1(B,C),k6_margrel1,E,G) & ! [H] : ( m2_subset_1(H,k2_qc_lang1(B),k3_qc_lang1(B)) => ( D != H => k3_funct_2(k3_qc_lang1(B),C,G,H) = k3_funct_2(k3_qc_lang1(B),C,F,H) ) ) ) ) ) )).
fof(fraenkel_a_5_0_vectsp_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) & ~ 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) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(C)) & m1_vectsp_4(F,B,C) ) => ( r2_hidden(A,a_5_0_vectsp_4(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(C)) & A = k3_rlvect_1(C,k4_vectsp_1(B,C,D,E),G) & r1_struct_0(F,G) ) ) ) )).
fof(fraenkel_a_5_0_vectsp_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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(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) & m1_vectsp_4(D,B,C) & m1_vectsp_4(E,B,C) & m1_vectsp_4(F,B,C) ) => ( r2_hidden(A,a_5_0_vectsp_5(B,C,D,E,F)) <=> ? [G] : ? [H] : ( m1_subset_1(G,u1_struct_0(C)) & m1_subset_1(H,u1_struct_0(C)) & A = k3_rlvect_1(C,H,G) & r1_struct_0(k1_vectsp_5(B,C,D,E),H) & r1_struct_0(F,G) ) ) ) )).
fof(fraenkel_a_5_0_waybel17,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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) & 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) & 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_struct_0(E) & v4_orders_2(E) & v7_waybel_0(E) & l1_waybel_0(E,B) & m1_subset_1(F,u1_struct_0(k6_waybel_9(B,C,D,E))) ) => ( r2_hidden(A,a_5_0_waybel17(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k6_waybel_9(B,C,D,E))) & A = k2_waybel_0(C,k6_waybel_9(B,C,D,E),G) & r1_orders_2(k6_waybel_9(B,C,D,E),F,G) ) ) ) )).
fof(fraenkel_a_5_0_waybel19,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_yellow_0(C) & l1_orders_2(C) & v2_pre_topc(D) & v1_waybel19(D) & m1_yellow_9(D,B) & v1_tops_2(E,D) & v2_cantor_1(E,D) & m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(D)))) & v2_pre_topc(F) & v1_waybel19(F) & m1_yellow_9(F,C) ) => ( r2_hidden(A,a_5_0_waybel19(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(D))) & A = k2_zfmisc_1(G,u1_struct_0(F)) & r2_hidden(G,E) ) ) ) )).
fof(fraenkel_a_5_0_waybel_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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) & 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) & v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C)) & v18_waybel_0(D,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(B)) & ~ v1_xboole_0(F) & v1_waybel_0(F,B) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,a_5_0_waybel_6(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(C)) & A = k12_lattice3(C,k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,E),G) & r2_hidden(G,k7_relset_1(u1_struct_0(B),u1_struct_0(C),D,F)) ) ) ) )).
fof(fraenkel_a_5_0_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) & m1_subset_1(D,B) & m1_subset_1(E,k4_ordinal1) & v1_finset_1(F) & m1_subset_1(F,k1_zfmisc_1(k4_ordinal1)) ) => ( r2_hidden(A,a_5_0_zf_fund1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,B) & A = G & r2_hidden(G,k1_funct_2(k7_subset_1(k4_ordinal1,F,k6_domain_1(k4_ordinal1,E)),C)) & ? [H] : r2_hidden(k2_xboole_0(k1_tarski(k4_tarski(E,H)),G),D) ) ) ) )).
fof(fraenkel_a_5_0_zf_fund2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & ~ v1_xboole_0(C) & m1_subset_1(D,k4_ordinal1) & m1_subset_1(E,B) & m1_subset_1(F,B) ) => ( r2_hidden(A,a_5_0_zf_fund2(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,C) & A = G & r2_hidden(k2_xboole_0(k1_tarski(k4_tarski(D,G)),F),E) ) ) ) )).
fof(fraenkel_a_5_10_rlaffin3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & v1_rlaffin1(D,k15_euclid(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(C)))) & m2_rlaffin3(F,k15_euclid(B),D) ) => ( r2_hidden(A,a_5_10_rlaffin3(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k1_pre_topc(k15_euclid(B),k4_rlaffin1(k15_euclid(B),D)))) & A = G & r2_hidden(k17_finseq_1(k1_numbers,C,k1_rlaffin3(k15_euclid(B),D,F,G)),k3_subset_1(u1_struct_0(k15_euclid(C)),E)) ) ) ) )).
fof(fraenkel_a_5_1_card_fin,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v1_finset_1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_5_1_card_fin(B,C,D,E,F)) <=> ? [G] : ( v1_funct_1(G) & v1_funct_2(G,k2_xboole_0(B,k1_tarski(D)),k2_tarski(E,F)) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k2_xboole_0(B,k1_tarski(D)),k2_tarski(E,F)))) & A = G & k5_card_1(k8_relset_1(k2_xboole_0(B,k1_tarski(D)),k2_tarski(E,F),G,k1_tarski(E))) = C & k1_funct_1(G,D) = F ) ) ) )).
fof(fraenkel_a_5_1_closure3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) & m1_subset_1(D,k1_zfmisc_1(k1_closure2(B,C))) & m1_subset_1(E,k1_zfmisc_1(k1_closure2(B,C))) ) => ( r2_hidden(A,a_5_1_closure3(B,C,D,E,F)) <=> ? [G] : ( m1_closure2(G,B,C,k6_closure2(B,C)) & A = k1_funct_1(G,F) & r2_hidden(G,k4_closure3(B,C,D,E)) ) ) ) )).
fof(fraenkel_a_5_1_convex1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(B)) & m1_subset_1(D,u1_struct_0(B)) & m1_subset_1(E,u1_struct_0(B)) & m2_rlvect_2(F,B,k8_domain_1(u1_struct_0(B),C,D,E)) ) => ( r2_hidden(A,a_5_1_convex1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(B)) & A = G & k1_funct_1(F,G) != k5_numbers ) ) ) )).
fof(fraenkel_a_5_1_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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))) & v7_ordinal1(D) & v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k6_finance1(B,k1_numbers,C,k12_prob_1)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_finance1(B,k1_numbers,C,k12_prob_1)))) ) => ( r2_hidden(A,a_5_1_finance1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,B) & A = G & ~ r1_xxreal_0(k11_finance1(D,E,B,C,k6_finance1(B,k1_numbers,C,k12_prob_1),F,G),k5_numbers) ) ) ) )).
fof(fraenkel_a_5_1_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & v7_ordinal1(D) & ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(C)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,E))) ) => ( r2_hidden(A,a_5_1_fomodel3(B,C,D,E,F)) <=> ? [G] : ? [H] : ( m2_finseq_2(G,B,k4_finseq_2(D,B)) & m2_finseq_2(H,E,k4_finseq_2(D,E)) & A = k1_domain_1(k4_finseq_2(D,B),k4_finseq_2(D,E),G,H) & r1_relset_1(k4_ordinal1,E,H,k4_relset_1(k4_ordinal1,B,B,E,G,F)) ) ) ) )).
fof(fraenkel_a_5_1_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,B) & l1_group_9(C,B) & v2_group_9(D,B) & v4_group_9(D,B,C) & m1_group_9(D,B,C) & v1_group_3(E,D) & m1_group_2(E,D) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(D))) ) => ( r2_hidden(A,a_5_1_group_9(B,C,D,E,F)) <=> ? [G] : ? [H] : ( m1_subset_1(G,u1_struct_0(D)) & m1_subset_1(H,u1_struct_0(D)) & A = k6_algstr_0(D,G,H) & r2_hidden(G,F) & r2_hidden(H,k8_group_2(D,E)) ) ) ) )).
fof(fraenkel_a_5_1_hahnban,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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(C,B) & m1_subset_1(D,u1_struct_0(B)) & v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),k1_numbers) & v1_hahnban(E,B) & v4_hahnban(E,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),k1_numbers))) & v1_funct_1(F) & v1_funct_2(F,u1_struct_0(C),k1_numbers) & v2_hahnban(F,C) & v3_hahnban(F,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),k1_numbers))) ) => ( r2_hidden(A,a_5_1_hahnban(B,C,D,E,F)) <=> ? [G] : ? [H] : ( m1_subset_1(G,u1_struct_0(C)) & m1_subset_1(H,u1_struct_0(B)) & A = k3_real_1(k3_funct_2(u1_struct_0(C),k1_numbers,F,G),k3_funct_2(u1_struct_0(B),k1_numbers,E,k5_algstr_0(B,D,H))) & G = H ) ) ) )).
fof(fraenkel_a_5_1_heyting2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v1_finset_1(C) & m1_subset_1(D,k5_finsub_1(k4_partfun1(B,C))) & m1_subset_1(E,k5_finsub_1(k4_partfun1(B,C))) & v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(D,E))) ) => ( r2_hidden(A,a_5_1_heyting2(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,k4_partfun1(B,C)) & A = k6_subset_1(k1_funct_1(F,G),G) & r2_hidden(G,D) ) ) ) )).
fof(fraenkel_a_5_1_interva1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(B)) & m1_subset_1(F,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_5_1_interva1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,k1_zfmisc_1(B)) & A = G & r1_tarski(k4_subset_1(B,C,E),G) & r1_tarski(G,k4_subset_1(B,D,F)) ) ) ) )).
fof(fraenkel_a_5_1_jordan16,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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(E,u1_struct_0(k15_euclid(2))) & m1_subset_1(F,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_5_1_jordan16(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(2))) & A = G & r1_jordan5c(B,C,D,F,G) & r1_jordan5c(B,C,D,G,E) ) ) ) )).
fof(fraenkel_a_5_1_jordan20,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(B) & 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(E,u1_struct_0(k15_euclid(2))) & m1_subset_1(F,u1_struct_0(k15_euclid(2))) ) => ( r2_hidden(A,a_5_1_jordan20(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(2))) & A = G & r1_jordan5c(B,C,D,F,G) & r1_jordan5c(B,C,D,G,E) ) ) ) )).
fof(fraenkel_a_5_1_jordan2b,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & v1_xreal_0(D) & m1_subset_1(E,u1_struct_0(k14_euclid(B))) & m1_subset_1(F,u1_struct_0(k15_euclid(B))) ) => ( r2_hidden(A,a_5_1_jordan2b(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k14_euclid(B))) & A = G & ~ r1_xxreal_0(k7_xcmplx_0(k6_xcmplx_0(k7_partfun1(k1_numbers,F,C),D),2),k3_metric_1(k14_euclid(B),E,G)) ) ) ) )).
fof(fraenkel_a_5_1_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(B) & v5_relat_1(C,k1_rcomp_1(k5_numbers,1)) & 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))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(B,B))))) & m1_subset_1(E,B) & m1_subset_1(F,B) ) => ( r2_hidden(A,a_5_1_lfuzzy_1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,B) & A = k12_lattice3(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),k7_lfuzzy_0(k2_zfmisc_1(B,B),C,k1_domain_1(B,B,E,G)),k1_yellow_0(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),k5_card_3(k1_domain_1(B,B,G,F),D))) ) ) ) )).
fof(fraenkel_a_5_1_matrtop1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & m1_subset_1(D,u1_struct_0(k15_euclid(B))) & v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(k2_vectsp_1),B,C) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k2_vectsp_1))) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(C)))) ) => ( r2_hidden(A,a_5_1_matrtop1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(B))) & A = k1_algstr_0(k15_euclid(B),D,G) & r2_hidden(G,k7_ranknull(k15_euclid(B),k15_euclid(C),k3_matrtop1(B,C,E),F)) ) ) ) )).
fof(fraenkel_a_5_1_ncfcont1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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(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) & v1_funct_1(D) & 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(B)) & v1_xreal_0(F) ) => ( r2_hidden(A,a_5_1_ncfcont1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(C)) & A = G & ~ r1_xxreal_0(F,k2_normsp_0(C,k5_algstr_0(C,G,k7_partfun1(u1_struct_0(C),D,E)))) ) ) ) )).
fof(fraenkel_a_5_1_random_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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))) & m2_prob_1(D,B,C) & v1_xreal_0(E) & m1_random_1(F,B,C) ) => ( r2_hidden(A,a_5_1_random_2(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,B) & A = G & r1_xxreal_0(k2_power(E,2),k2_power(k9_complex1(k6_xcmplx_0(k12_supinf_2(F,G),k8_random_1(B,C,D,F))),2)) ) ) ) )).
fof(fraenkel_a_5_1_rlaffin3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & v1_rlaffin1(D,k15_euclid(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(C)))) & m2_rlaffin3(F,k15_euclid(B),D) ) => ( r2_hidden(A,a_5_1_rlaffin3(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k1_pre_topc(k15_euclid(B),k4_rlaffin1(k15_euclid(B),D)))) & A = G & r2_hidden(k17_finseq_1(k1_numbers,C,k1_rlaffin3(k15_euclid(B),D,F,G)),E) ) ) ) )).
fof(fraenkel_a_5_1_rmod_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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(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) & m1_rmod_2(D,B,C) & m1_rmod_2(E,B,C) & m1_rmod_2(F,B,C) ) => ( r2_hidden(A,a_5_1_rmod_3(B,C,D,E,F)) <=> ? [G] : ? [H] : ( m1_subset_1(G,u1_struct_0(C)) & m1_subset_1(H,u1_struct_0(C)) & A = k3_rlvect_1(C,H,G) & r1_struct_0(D,H) & r1_struct_0(k1_rmod_3(B,C,E,F),G) ) ) ) )).
fof(fraenkel_a_5_1_vectsp_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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(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) & m1_vectsp_4(D,B,C) & m1_vectsp_4(E,B,C) & m1_vectsp_4(F,B,C) ) => ( r2_hidden(A,a_5_1_vectsp_5(B,C,D,E,F)) <=> ? [G] : ? [H] : ( m1_subset_1(G,u1_struct_0(C)) & m1_subset_1(H,u1_struct_0(C)) & A = k3_rlvect_1(C,H,G) & r1_struct_0(D,H) & r1_struct_0(k1_vectsp_5(B,C,E,F),G) ) ) ) )).
fof(fraenkel_a_5_1_waybel19,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_yellow_0(C) & l1_orders_2(C) & v2_pre_topc(D) & v1_waybel19(D) & m1_yellow_9(D,B) & v2_pre_topc(E) & v1_waybel19(E) & m1_yellow_9(E,C) & v1_tops_2(F,E) & v2_cantor_1(F,E) & m1_subset_1(F,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(E)))) ) => ( r2_hidden(A,a_5_1_waybel19(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(E))) & A = k2_zfmisc_1(u1_struct_0(D),G) & r2_hidden(G,F) ) ) ) )).
fof(fraenkel_a_5_1_waybel21,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & l1_orders_2(B) & ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v24_waybel_0(C) & l1_orders_2(C) & v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(C)) & v5_orders_3(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)))) & ~ v1_xboole_0(E) & v1_waybel_0(E,B) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) & m1_subset_1(F,u1_struct_0(k6_waybel_9(B,C,D,k4_waybel17(B,E)))) ) => ( r2_hidden(A,a_5_1_waybel21(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k6_waybel_9(B,C,D,k4_waybel17(B,E)))) & A = k2_waybel_0(C,k6_waybel_9(B,C,D,k4_waybel17(B,E)),G) & r1_orders_2(k6_waybel_9(B,C,D,k4_waybel17(B,E)),F,G) ) ) ) )).
fof(fraenkel_a_5_1_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) & m1_subset_1(D,B) & m1_subset_1(E,B) & m1_subset_1(F,k4_ordinal1) ) => ( r2_hidden(A,a_5_1_zf_fund1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,B) & A = G & r2_hidden(G,C) & r2_hidden(k2_xboole_0(k1_tarski(k1_domain_1(k4_ordinal1,B,F,G)),E),D) ) ) ) )).
fof(fraenkel_a_5_1_zf_fund2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & m1_subset_1(C,B) & m1_subset_1(D,k4_ordinal1) & m1_subset_1(E,B) & m1_subset_1(F,B) ) => ( r2_hidden(A,a_5_1_zf_fund2(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,B) & A = G & r2_hidden(G,C) & r2_hidden(k2_xboole_0(k1_tarski(k4_tarski(D,G)),F),E) ) ) ) )).
fof(fraenkel_a_5_2_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,B) & l1_group_9(C,B) & v1_group_3(D,C) & m1_group_2(D,C) & v1_group_3(E,D) & m1_group_6(E,C,D) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(D))) ) => ( r2_hidden(A,a_5_2_group_9(B,C,D,E,F)) <=> ? [G] : ? [H] : ( m1_subset_1(G,u1_struct_0(D)) & m1_subset_1(H,u1_struct_0(D)) & A = k6_algstr_0(D,G,H) & r2_hidden(G,F) & r2_hidden(H,k8_group_2(D,E)) ) ) ) )).
fof(fraenkel_a_5_2_heyting2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v1_finset_1(C) & m1_subset_1(D,k5_finsub_1(k4_partfun1(B,C))) & m2_subset_1(E,k5_finsub_1(k4_partfun1(B,C)),k1_substlat(B,C)) & v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(D,E))) ) => ( r2_hidden(A,a_5_2_heyting2(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,k4_partfun1(B,C)) & A = k6_subset_1(k1_funct_1(F,G),G) & r2_hidden(G,D) ) ) ) )).
fof(fraenkel_a_5_2_interva1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(B)) & m1_subset_1(D,k1_zfmisc_1(B)) & m1_subset_1(E,k1_zfmisc_1(B)) & m1_subset_1(F,k1_zfmisc_1(B)) ) => ( r2_hidden(A,a_5_2_interva1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,k1_zfmisc_1(B)) & A = G & r1_tarski(k7_subset_1(B,C,F),G) & r1_tarski(G,k7_subset_1(B,D,E)) ) ) ) )).
fof(fraenkel_a_5_2_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(B) & v5_relat_1(C,k1_rcomp_1(k5_numbers,1)) & 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))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(B,B))))) & m1_subset_1(E,B) & m1_subset_1(F,B) ) => ( r2_hidden(A,a_5_2_lfuzzy_1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,B) & A = k1_yellow_0(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),a_6_0_lfuzzy_1(B,C,D,E,F,G)) ) ) ) )).
fof(fraenkel_a_5_2_matrtop1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & m1_subset_1(D,u1_struct_0(k15_euclid(B))) & v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(k2_vectsp_1),B,C) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k2_vectsp_1))) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(C)))) ) => ( r2_hidden(A,a_5_2_matrtop1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(C))) & A = k1_algstr_0(k15_euclid(C),k3_funct_2(u1_struct_0(k15_euclid(B)),u1_struct_0(k15_euclid(C)),k3_matrtop1(B,C,E),D),G) & r2_hidden(G,F) ) ) ) )).
fof(fraenkel_a_5_2_ncfcont1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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(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) & v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(B)))) & m1_subset_1(E,u1_struct_0(C)) & v1_xreal_0(F) ) => ( r2_hidden(A,a_5_2_ncfcont1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(B)) & A = G & ~ r1_xxreal_0(F,k2_normsp_0(B,k5_algstr_0(B,G,k7_partfun1(u1_struct_0(B),D,E)))) ) ) ) )).
fof(fraenkel_a_5_2_rlaffin3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v1_xreal_0(B) & ~ v2_struct_0(C) & l1_rlvect_1(C) & ~ v1_xboole_0(D) & v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(D,u1_struct_0(C)))) ) => ( r2_hidden(A,a_5_2_rlaffin3(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(C)) & A = k1_rlvect_1(C,G,B) & r2_hidden(G,k7_relset_1(D,u1_struct_0(C),E,F)) ) ) ) )).
fof(fraenkel_a_5_2_rmod_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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(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) & m1_rmod_2(D,B,C) & m1_rmod_2(E,B,C) & m1_rmod_2(F,B,C) ) => ( r2_hidden(A,a_5_2_rmod_3(B,C,D,E,F)) <=> ? [G] : ? [H] : ( m1_subset_1(G,u1_struct_0(C)) & m1_subset_1(H,u1_struct_0(C)) & A = k3_rlvect_1(C,H,G) & r1_struct_0(k2_rmod_3(B,C,D,E),H) & r1_struct_0(k2_rmod_3(B,C,E,F),G) ) ) ) )).
fof(fraenkel_a_5_2_valuat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( m1_qc_lang1(B) & ~ v1_xboole_0(C) & m2_subset_1(D,k2_qc_lang1(B),k3_qc_lang1(B)) & m2_funct_2(E,k3_qc_lang1(B),C,k2_valuat_1(B,C)) & m2_funct_2(F,k2_valuat_1(B,C),k6_margrel1,k9_funct_2(k2_valuat_1(B,C),k6_margrel1)) ) => ( r2_hidden(A,a_5_2_valuat_1(B,C,D,E,F)) <=> ? [G] : ( m2_funct_2(G,k3_qc_lang1(B),C,k2_valuat_1(B,C)) & A = k3_funct_2(k2_valuat_1(B,C),k6_margrel1,F,G) & ! [H] : ( m2_subset_1(H,k2_qc_lang1(B),k3_qc_lang1(B)) => ( D != H => k3_funct_2(k3_qc_lang1(B),C,G,H) = k3_funct_2(k3_qc_lang1(B),C,E,H) ) ) ) ) ) )).
fof(fraenkel_a_5_2_vectsp_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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(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) & m1_vectsp_4(D,B,C) & m1_vectsp_4(E,B,C) & m1_vectsp_4(F,B,C) ) => ( r2_hidden(A,a_5_2_vectsp_5(B,C,D,E,F)) <=> ? [G] : ? [H] : ( m1_subset_1(G,u1_struct_0(C)) & m1_subset_1(H,u1_struct_0(C)) & A = k3_rlvect_1(C,H,G) & r1_struct_0(k2_vectsp_5(B,C,D,E),H) & r1_struct_0(k2_vectsp_5(B,C,E,F),G) ) ) ) )).
fof(fraenkel_a_5_2_waybel17,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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) & v2_pre_topc(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_lattice3(C) & v2_lattice3(C) & v3_lattice3(C) & v4_waybel11(C) & l1_waybel_9(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)))) & ~ v2_struct_0(E) & v4_orders_2(E) & v7_waybel_0(E) & l1_waybel_0(E,B) & m1_subset_1(F,u1_struct_0(k6_waybel_9(B,C,D,E))) ) => ( r2_hidden(A,a_5_2_waybel17(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k6_waybel_9(B,C,D,E))) & A = k2_waybel_0(C,k6_waybel_9(B,C,D,E),G) & r1_orders_2(k6_waybel_9(B,C,D,E),F,G) ) ) ) )).
fof(fraenkel_a_5_2_waybel21,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,B) & m2_yellow_6(D,B,C) & m2_waybel21(E,B,C,D) & m1_subset_1(F,u1_struct_0(D)) ) => ( r2_hidden(A,a_5_2_waybel21(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(C)) & A = k2_waybel_0(B,C,G) & r1_orders_2(C,k2_yellow_6(u1_struct_0(D),C,E,F),G) ) ) ) )).
fof(fraenkel_a_5_2_waybel22,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) & v1_funct_1(D) & v1_funct_2(D,k1_waybel22(B),u1_struct_0(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_waybel22(B),u1_struct_0(C)))) & m1_subset_1(E,u1_struct_0(k1_yellow_1(k8_waybel_0(k2_yellow_1(B))))) & m1_subset_1(F,E) ) => ( r2_hidden(A,a_5_2_waybel22(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k2_yellow_1(B))) & A = k1_funct_1(D,k6_waybel_0(k2_yellow_1(B),G)) & ? [H] : ( m1_subset_1(H,B) & G = k1_tarski(H) & r2_hidden(H,F) ) ) ) ) )).
fof(fraenkel_a_5_2_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) & v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & m2_subset_1(D,k4_ordinal1,k1_zf_lang) & m1_subset_1(E,B) & m1_subset_1(F,B) ) => ( r2_hidden(A,a_5_2_zf_fund1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,B) & A = G & r2_hidden(G,k1_funct_2(k7_subset_1(k4_ordinal1,k4_zf_fund1(k2_zf_model(C)),k6_domain_1(k4_ordinal1,k3_zf_fund1(D))),E)) & ? [H] : r2_hidden(k2_xboole_0(k1_tarski(k4_tarski(k3_zf_fund1(D),H)),G),F) ) ) ) )).
fof(fraenkel_a_5_3_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,B) & l1_group_9(C,B) & v2_group_9(D,B) & v4_group_9(D,B,C) & m1_group_9(D,B,C) & v4_group_9(E,B,D) & m1_group_9(E,B,D) & m1_subset_1(F,B) ) => ( r2_hidden(A,a_5_3_group_9(B,C,D,E,F)) <=> ? [G] : ? [H] : ( m1_subset_1(G,k7_group_9(B,D,E)) & m1_subset_1(H,k7_group_9(B,D,E)) & A = k4_tarski(G,H) & ? [I] : ( m1_subset_1(I,u1_struct_0(D)) & ? [J] : ( m1_subset_1(J,u1_struct_0(D)) & r2_hidden(I,G) & r2_hidden(J,H) & J = k3_funct_2(u1_struct_0(D),u1_struct_0(D),k3_group_9(B,D,F),I) ) ) ) ) ) )).
fof(fraenkel_a_5_3_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(B) & v5_relat_1(C,k1_rcomp_1(k5_numbers,1)) & 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))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(B,B))))) & m1_subset_1(E,B) & m1_subset_1(F,B) ) => ( r2_hidden(A,a_5_3_lfuzzy_1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,B) & A = k1_yellow_0(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),a_6_1_lfuzzy_1(B,C,D,E,F,G)) ) ) ) )).
fof(fraenkel_a_5_3_rlaffin3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v7_ordinal1(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) & v2_pre_topc(C) & v6_rltopsp1(C) & v7_rltopsp1(C) & l1_rltopsp1(C) & v1_finset_1(D) & v1_rlaffin1(D,C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) & m2_rlaffin3(E,C,D) ) => ( r2_hidden(A,a_5_3_rlaffin3(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(C)) & A = G & r2_hidden(G,k4_rlaffin1(C,D)) & r2_hidden(k17_finseq_1(k1_numbers,B,k1_rlaffin3(C,D,E,G)),F) ) ) ) )).
fof(fraenkel_a_5_3_rmod_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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(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) & m1_rmod_2(D,B,C) & m1_rmod_2(E,B,C) & m1_rmod_2(F,B,C) ) => ( r2_hidden(A,a_5_3_rmod_3(B,C,D,E,F)) <=> ? [G] : ? [H] : ( m1_subset_1(G,u1_struct_0(C)) & m1_subset_1(H,u1_struct_0(C)) & A = k3_rlvect_1(C,H,G) & r1_struct_0(E,H) & r1_struct_0(k2_rmod_3(B,C,D,F),G) ) ) ) )).
fof(fraenkel_a_5_3_vectsp_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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(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) & m1_vectsp_4(D,B,C) & m1_vectsp_4(E,B,C) & m1_vectsp_4(F,B,C) ) => ( r2_hidden(A,a_5_3_vectsp_5(B,C,D,E,F)) <=> ? [G] : ? [H] : ( m1_subset_1(G,u1_struct_0(C)) & m1_subset_1(H,u1_struct_0(C)) & A = k3_rlvect_1(C,H,G) & r1_struct_0(E,H) & r1_struct_0(k2_vectsp_5(B,C,D,F),G) ) ) ) )).
fof(fraenkel_a_5_4_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,B) & l1_group_9(C,B) & ~ v2_struct_0(D) & v2_group_1(D) & v3_group_1(D) & v3_group_9(D,B) & l1_group_9(D,B) & v1_funct_1(E) & v1_funct_2(E,u1_struct_0(C),u1_struct_0(D)) & v1_group_6(E,C,D) & v7_group_9(E,B,C,D) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)))) & m1_subset_1(F,B) ) => ( r2_hidden(A,a_5_4_group_9(B,C,D,E,F)) <=> ? [G] : ? [H] : ( m1_subset_1(G,k7_group_9(B,C,k13_group_9(B,C,D,E))) & m1_subset_1(H,k7_group_9(B,C,k13_group_9(B,C,D,E))) & A = k4_tarski(G,H) & ? [I] : ( m1_subset_1(I,u1_struct_0(C)) & ? [J] : ( m1_subset_1(J,u1_struct_0(C)) & r2_hidden(I,G) & r2_hidden(J,H) & J = k3_funct_2(u1_struct_0(C),u1_struct_0(C),k3_group_9(B,C,F),I) ) ) ) ) ) )).
fof(fraenkel_a_5_4_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(B) & v5_relat_1(C,k1_rcomp_1(k5_numbers,1)) & 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))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(B,B))))) & m1_subset_1(E,B) & m1_subset_1(F,B) ) => ( r2_hidden(A,a_5_4_lfuzzy_1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(B,B)))) & A = k1_yellow_0(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),a_5_5_lfuzzy_1(B,C,E,F,G)) & r2_hidden(G,D) ) ) ) )).
fof(fraenkel_a_5_5_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,B) & l1_group_9(C,B) & ~ v2_struct_0(D) & v2_group_1(D) & v3_group_1(D) & v3_group_9(D,B) & l1_group_9(D,B) & v15_algstr_0(E) & m1_group_2(E,D) & 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,B,C,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)))) ) => ( r2_hidden(A,a_5_5_group_9(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(C)) & A = G & r1_struct_0(E,k3_funct_2(u1_struct_0(C),u1_struct_0(D),F,G)) ) ) ) )).
fof(fraenkel_a_5_5_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(B) & v5_relat_1(C,k1_rcomp_1(k5_numbers,1)) & 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))) & m1_subset_1(D,B) & m1_subset_1(E,B) & m1_subset_1(F,u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(B,B)))) ) => ( r2_hidden(A,a_5_5_lfuzzy_1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,B) & A = k12_lattice3(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),k7_lfuzzy_0(k2_zfmisc_1(B,B),C,k1_domain_1(B,B,D,G)),k9_lfuzzy_0(k2_zfmisc_1(B,B),F,k1_domain_1(B,B,G,E))) ) ) ) )).
fof(fraenkel_a_5_6_groeb_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( m1_subset_1(B,k4_ordinal1) & v1_partfun1(C,k15_pre_poly(B)) & v1_relat_2(C) & v4_relat_2(C) & v6_relat_2(C) & v8_relat_2(C) & v2_bagorder(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),k15_pre_poly(B)))) & ~ 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) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(B,D)))) & v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(B),u1_struct_0(D)) & v1_polynom1(F,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(D)))) ) => ( r2_hidden(A,a_5_6_groeb_1(B,C,D,E,F)) <=> ? [G] : ( v1_funct_1(G) & v1_funct_2(G,k15_pre_poly(B),u1_struct_0(D)) & v1_polynom1(G,D) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(D)))) & A = k3_termord(B,C,D,G) & r2_hidden(G,k7_subset_1(u1_struct_0(k12_polynom1(B,D)),E,k1_groeb_1(B,D,F))) & G != k8_polynom1(B,D) ) ) ) )).
fof(fraenkel_a_5_6_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v2_group_9(C,B) & v3_group_9(C,B) & l1_group_9(C,B) & ~ v2_struct_0(D) & v2_group_1(D) & v3_group_1(D) & v2_group_9(D,B) & v3_group_9(D,B) & l1_group_9(D,B) & v1_funct_1(E) & v1_funct_2(E,u1_struct_0(C),u1_struct_0(D)) & v1_group_6(E,C,D) & v7_group_9(E,B,C,D) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)))) & v15_algstr_0(F) & v1_group_3(F,D) & m1_group_2(F,D) ) => ( r2_hidden(A,a_5_6_group_9(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(C)) & A = G & r1_struct_0(F,k3_funct_2(u1_struct_0(C),u1_struct_0(D),E,G)) ) ) ) )).
fof(fraenkel_a_5_6_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(B) & v5_relat_1(C,k1_rcomp_1(k5_numbers,1)) & 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))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(B,B))))) & m1_subset_1(E,B) & m1_subset_1(F,B) ) => ( r2_hidden(A,a_5_6_lfuzzy_1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(B,B)))) & A = k1_yellow_0(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),a_5_7_lfuzzy_1(B,C,E,F,G)) & r2_hidden(G,D) ) ) ) )).
fof(fraenkel_a_5_7_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,B) & l1_group_9(C,B) & m1_group_9(D,B,C) & v2_group_9(E,B) & m1_group_9(E,B,D) & v2_group_9(F,B) & m1_group_9(F,B,D) ) => ( r2_hidden(A,a_5_7_group_9(B,C,D,E,F)) <=> ? [G] : ? [H] : ( m1_subset_1(G,u1_struct_0(D)) & m1_subset_1(H,u1_struct_0(D)) & A = k6_algstr_0(D,G,H) & r2_hidden(G,k15_group_9(B,D,E)) & r2_hidden(H,k15_group_9(B,D,F)) ) ) ) )).
fof(fraenkel_a_5_7_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(B) & v5_relat_1(C,k1_rcomp_1(k5_numbers,1)) & 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))) & m1_subset_1(D,B) & m1_subset_1(E,B) & m1_subset_1(F,u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(B,B)))) ) => ( r2_hidden(A,a_5_7_lfuzzy_1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,B) & A = k12_lattice3(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),k7_lfuzzy_0(k2_zfmisc_1(B,B),C,k1_domain_1(B,B,D,G)),k7_lfuzzy_0(k2_zfmisc_1(B,B),k5_lfuzzy_0(k2_zfmisc_1(B,B),F),k1_domain_1(B,B,G,E))) ) ) ) )).
fof(fraenkel_a_5_8_card_fin,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v1_finset_1(B) & v7_ordinal1(C) ) => ( r2_hidden(A,a_5_8_card_fin(B,C,D,E,F)) <=> ? [G] : ( v1_funct_1(G) & v1_funct_2(G,k2_xboole_0(B,k1_tarski(D)),k2_tarski(E,F)) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k2_xboole_0(B,k1_tarski(D)),k2_tarski(E,F)))) & A = G & k5_card_1(k8_relset_1(k2_xboole_0(B,k1_tarski(D)),k2_tarski(E,F),G,k1_tarski(E))) = k1_nat_1(C,1) & k1_funct_1(G,D) = F ) ) ) )).
fof(fraenkel_a_5_8_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,B) & l1_group_9(C,B) & m1_group_9(D,B,C) & v2_group_9(E,B) & m1_group_9(E,B,D) & v2_group_9(F,B) & m1_group_9(F,B,D) ) => ( r2_hidden(A,a_5_8_group_9(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(D))) & A = G & ? [H] : ( v2_group_9(H,B) & m1_group_9(H,B,D) & G = u1_struct_0(H) & r1_tarski(k16_group_9(B,D,E,F),k15_group_9(B,D,H)) ) ) ) ) )).
fof(fraenkel_a_5_8_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(B) & v5_relat_1(C,k1_rcomp_1(k5_numbers,1)) & 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))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(B,B))))) & m1_subset_1(E,B) & m1_subset_1(F,B) ) => ( r2_hidden(A,a_5_8_lfuzzy_1(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(B,B)))) & A = k7_lfuzzy_0(k2_zfmisc_1(B,B),k3_fuzzy_4(B,B,B,C,k5_lfuzzy_0(k2_zfmisc_1(B,B),G)),k1_domain_1(B,B,E,F)) & r2_hidden(G,D) ) ) ) )).
fof(fraenkel_a_5_8_rlaffin3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v7_ordinal1(B) & v7_ordinal1(C) & v1_rlaffin1(D,k15_euclid(B)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(C)))) & m2_rlaffin3(F,k15_euclid(B),D) ) => ( r2_hidden(A,a_5_8_rlaffin3(B,C,D,E,F)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(B))) & A = G & r2_hidden(k17_finseq_1(k1_numbers,C,k1_rlaffin3(k15_euclid(B),D,F,G)),k3_subset_1(u1_struct_0(k15_euclid(C)),E)) ) ) ) )).
fof(fraenkel_a_6_0_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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)) & v5_msafree4(D,B,C) & l1_aofa_a00(D,B) & m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,u1_struct_0(B)) & m1_subset_1(G,k1_funct_1(u3_msualg_1(B,D),E)) ) => ( r2_hidden(A,a_6_0_aofa_a00(B,C,D,E,F,G)) <=> ? [H] : ( m1_trees_1(H,k9_xtuple_0(G)) & A = k5_trees_2(G,H) & k2_xtuple_0(k1_funct_1(k5_trees_2(G,H),k1_xboole_0)) = F ) ) ) )).
fof(fraenkel_a_6_0_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v13_aofa_a00(B) & v16_aofa_a00(B) & v18_aofa_a00(B,4,1) & v21_aofa_a00(B,1,1,11) & v23_aofa_a00(B,11) & l6_aofa_a00(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)) & v4_msualg_1(D,B) & v5_msafree4(D,B,C) & v3_aofa_a00(D,B,C) & v6_aofa_a01(D,B) & l1_aofa_a00(D,B) & v4_msualg_1(E,B) & v4_msafree4(E,B,D) & v17_aofa_a00(E,B) & v20_aofa_a00(E,4,1,B) & v22_aofa_a00(E,B,1,1,11) & l3_msualg_1(E,B) & v4_aofa_a01(F,B,C,D) & l4_aofa_a00(F,B,C,D) & v3_aofa_a01(G,B,C,D,u4_aofa_a00(B,C,D,F),k37_aofa_a00(B)) & m1_msafree4(G,u1_struct_0(B),u4_aofa_a00(B,C,D,F),k1_msafree4(u1_struct_0(B),u4_aofa_a00(B,C,D,F),k37_aofa_a00(B))) ) => ( r2_hidden(A,a_6_0_aofa_a01(B,C,D,E,F,G)) <=> ? [H] : ( m2_subset_1(H,k4_autalg_1(u1_struct_0(B),u4_aofa_a00(B,C,D,F),u3_msualg_1(B,E)),k13_aofa_a00(B,D,E,u4_aofa_a00(B,C,D,F))) & A = H & k1_funct_1(k1_msafree4(u1_struct_0(B),H,k37_aofa_a00(B)),G) != k1_xboole_0 ) ) ) )).
fof(fraenkel_a_6_0_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & ~ v1_xboole_0(D) & m1_subset_1(E,k1_zfmisc_1(B)) & m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(G,k1_zfmisc_1(D)) ) => ( r2_hidden(A,a_6_0_domain_1(B,C,D,E,F,G)) <=> ? [H] : ? [I] : ? [J] : ( m1_subset_1(H,B) & m1_subset_1(I,C) & m1_subset_1(J,D) & A = k4_domain_1(B,C,D,H,I,J) & r2_hidden(H,E) & r2_hidden(I,F) & r2_hidden(J,G) ) ) ) )).
fof(fraenkel_a_6_0_groeb_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( v3_ordinal1(B) & v1_partfun1(C,k15_pre_poly(B)) & v1_relat_2(C) & v4_relat_2(C) & v6_relat_2(C) & v8_relat_2(C) & v2_bagorder(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),k15_pre_poly(B)))) & ~ v7_struct_0(D) & v13_algstr_0(D) & v4_vectsp_1(D) & v5_vectsp_1(D) & v3_rlvect_1(D) & v4_rlvect_1(D) & v1_vectsp_2(D) & l6_algstr_0(D) & v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(B),u1_struct_0(D)) & v1_polynom1(E,D) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(D)))) & v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(B),u1_struct_0(D)) & v1_polynom7(F,B,D) & v3_polynom7(F,B,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(D)))) & m1_subset_1(G,k4_ordinal1) ) => ( r2_hidden(A,a_6_0_groeb_3(B,C,D,E,F,G)) <=> ? [H] : ? [I] : ( m2_subset_1(H,k14_pre_poly(B),k15_pre_poly(B)) & m2_subset_1(I,k14_pre_poly(B),k15_pre_poly(B)) & A = k11_pre_poly(B,H,I) & r2_hidden(H,k3_polynom1(k15_pre_poly(B),D,F)) & r2_hidden(I,k3_polynom1(k15_pre_poly(B),D,k6_groeb_3(B,C,D,E,G))) ) ) ) )).
fof(fraenkel_a_6_0_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,B) & l1_group_9(C,B) & ~ v2_struct_0(D) & v2_group_1(D) & v3_group_1(D) & v3_group_9(D,B) & l1_group_9(D,B) & ~ v2_struct_0(E) & v2_group_1(E) & v3_group_1(E) & v3_group_9(E,B) & l1_group_9(E,B) & 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,B,C,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)))) & v1_funct_1(G) & v1_funct_2(G,u1_struct_0(D),u1_struct_0(E)) & v1_group_6(G,D,E) & v7_group_9(G,B,D,E) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(D),u1_struct_0(E)))) ) => ( r2_hidden(A,a_6_0_group_9(B,C,D,E,F,G)) <=> ? [H] : ( m1_subset_1(H,u1_struct_0(C)) & A = H & k3_funct_2(u1_struct_0(C),u1_struct_0(E),k11_group_9(B,C,D,E,F,G),H) = k1_group_1(E) ) ) ) )).
fof(fraenkel_a_6_0_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ v1_xboole_0(B) & v5_relat_1(C,k1_rcomp_1(k5_numbers,1)) & 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))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(B,B))))) & m1_subset_1(E,B) & m1_subset_1(F,B) & m1_subset_1(G,B) ) => ( r2_hidden(A,a_6_0_lfuzzy_1(B,C,D,E,F,G)) <=> ? [H] : ( m1_subset_1(H,u1_struct_0(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)))) & A = k12_lattice3(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),k7_lfuzzy_0(k2_zfmisc_1(B,B),C,k1_domain_1(B,B,E,G)),H) & r2_hidden(H,k5_card_3(k1_domain_1(B,B,G,F),D)) ) ) ) )).
fof(fraenkel_a_6_0_matrlin,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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) & ~ 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) & m1_matrlin(D,B,C) & m1_vectsp_7(E,B,C) & ~ v1_xboole_0(F) & m2_vectsp_6(G,B,C,E) ) => ( r2_hidden(A,a_6_0_matrlin(B,C,D,E,F,G)) <=> ? [H] : ( m1_subset_1(H,F) & A = k4_vectsp_1(B,C,k3_funct_2(u1_struct_0(C),u1_struct_0(B),G,k7_partfun1(u1_struct_0(C),D,H)),k7_partfun1(u1_struct_0(C),D,H)) ) ) ) )).
fof(fraenkel_a_6_0_monoid_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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,k1_zfmisc_1(B)) & m1_subset_1(G,k1_zfmisc_1(C)) ) => ( r2_hidden(A,a_6_0_monoid_1(B,C,D,E,F,G)) <=> ? [H] : ? [I] : ( m1_subset_1(H,B) & m1_subset_1(I,C) & A = k2_binop_1(B,C,D,E,H,I) & r2_hidden(H,F) & r2_hidden(I,G) ) ) ) )).
fof(fraenkel_a_6_0_random_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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(F) & v1_funct_2(F,B,C) & v1_random_3(F,B,C,D,E) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,C))) & m2_subset_1(G,k1_zfmisc_1(C),E) ) => ( r2_hidden(A,a_6_0_random_3(B,C,D,E,F,G)) <=> ? [H] : ( m1_subset_1(H,B) & A = H & m1_subset_1(k3_funct_2(B,C,F,H),G) ) ) ) )).
fof(fraenkel_a_6_0_rlaffin3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( v7_ordinal1(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) & v2_pre_topc(C) & v6_rltopsp1(C) & v7_rltopsp1(C) & l1_rltopsp1(C) & v1_finset_1(D) & v1_rlaffin1(D,C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) & m1_subset_1(E,u1_struct_0(C)) & m2_rlaffin3(F,C,k5_rusub_4(C,D,E)) ) => ( r2_hidden(A,a_6_0_rlaffin3(B,C,D,E,F,G)) <=> ? [H] : ( m1_subset_1(H,u1_struct_0(C)) & A = H & r2_hidden(H,k4_rlaffin1(C,k5_rusub_4(C,D,E))) & r2_hidden(k17_finseq_1(k1_numbers,B,k1_rlaffin3(C,k5_rusub_4(C,D,E),F,H)),G) ) ) ) )).
fof(fraenkel_a_6_1_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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) & ~ v1_xboole_0(C) & v4_card_3(C) & m1_subset_1(D,k1_zfmisc_1(k9_funct_2(C,k4_numbers))) & v1_aofa_i00(E,B,C,D) & m1_aofa_000(E,B,k9_funct_2(C,k4_numbers),D) & m2_aofa_i00(F,B,C,D,E) & m3_aofa_i00(G,B,C,D,E) ) => ( r2_hidden(A,a_6_1_aofa_i00(B,C,D,E,F,G)) <=> ? [H] : ( m1_subset_1(H,u1_struct_0(B)) & A = H & r2_hidden(H,k18_aofa_000(B)) & ! [I] : ( m2_funct_2(I,C,k4_numbers,k9_funct_2(C,k4_numbers)) => k2_binop_1(k9_funct_2(C,k4_numbers),u1_struct_0(B),k9_funct_2(C,k4_numbers),E,I,H) = k14_funct_7(C,k4_numbers,I,k3_funct_2(k9_funct_2(C,k4_numbers),C,F,I),k3_funct_2(k9_funct_2(C,k4_numbers),k4_numbers,G,I)) ) ) ) ) )).
fof(fraenkel_a_6_1_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v2_group_9(C,B) & v3_group_9(C,B) & l1_group_9(C,B) & ~ v2_struct_0(D) & v2_group_1(D) & v3_group_1(D) & v2_group_9(D,B) & v3_group_9(D,B) & l1_group_9(D,B) & v2_group_9(E,B) & m1_group_9(E,B,C) & v2_group_9(F,B) & m1_group_9(F,B,D) & v1_funct_1(G) & v1_funct_2(G,u1_struct_0(E),u1_struct_0(F)) & v1_group_6(G,E,F) & v7_group_9(G,B,E,F) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(E),u1_struct_0(F)))) ) => ( r2_hidden(A,a_6_1_group_9(B,C,D,E,F,G)) <=> ? [H] : ( m1_subset_1(H,u1_struct_0(E)) & A = H & k3_funct_2(u1_struct_0(E),u1_struct_0(F),G,H) = k1_group_1(F) ) ) ) )).
fof(fraenkel_a_6_1_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ v1_xboole_0(B) & v5_relat_1(C,k1_rcomp_1(k5_numbers,1)) & 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))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(B,B))))) & m1_subset_1(E,B) & m1_subset_1(F,B) & m1_subset_1(G,B) ) => ( r2_hidden(A,a_6_1_lfuzzy_1(B,C,D,E,F,G)) <=> ? [H] : ( m1_subset_1(H,u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(B,B)))) & A = k12_lattice3(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),k7_lfuzzy_0(k2_zfmisc_1(B,B),C,k1_domain_1(B,B,E,G)),k9_lfuzzy_0(k2_zfmisc_1(B,B),H,k1_domain_1(B,B,G,F))) & r2_hidden(H,D) ) ) ) )).
fof(fraenkel_a_6_2_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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) & ~ v1_xboole_0(C) & v4_card_3(C) & m1_subset_1(D,C) & v1_aofa_i00(E,B,C,k1_aofa_i00(k9_funct_2(C,k4_numbers),D,k5_numbers)) & m1_aofa_000(E,B,k9_funct_2(C,k4_numbers),k1_aofa_i00(k9_funct_2(C,k4_numbers),D,k5_numbers)) & m1_aofa_i00(F,C,u1_struct_0(B),k9_funct_2(C,k4_numbers),E) & m1_aofa_i00(G,C,u1_struct_0(B),k9_funct_2(C,k4_numbers),E) ) => ( r2_hidden(A,a_6_2_aofa_i00(B,C,D,E,F,G)) <=> ? [H] : ( m2_funct_2(H,C,k4_numbers,k9_funct_2(C,k4_numbers)) & A = H & ~ r1_xxreal_0(k21_aofa_i00(C,k4_numbers,H,F),k21_aofa_i00(C,k4_numbers,H,G)) & r1_xxreal_0(k5_numbers,k21_aofa_i00(C,k4_numbers,H,G)) ) ) ) )).
fof(fraenkel_a_6_3_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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) & ~ v1_xboole_0(C) & v4_card_3(C) & m1_subset_1(D,C) & v1_aofa_i00(E,B,C,k1_aofa_i00(k9_funct_2(C,k4_numbers),D,k5_numbers)) & m1_aofa_000(E,B,k9_funct_2(C,k4_numbers),k1_aofa_i00(k9_funct_2(C,k4_numbers),D,k5_numbers)) & m1_aofa_i00(F,C,u1_struct_0(B),k9_funct_2(C,k4_numbers),E) & m1_aofa_i00(G,C,u1_struct_0(B),k9_funct_2(C,k4_numbers),E) ) => ( r2_hidden(A,a_6_3_aofa_i00(B,C,D,E,F,G)) <=> ? [H] : ( m2_funct_2(H,C,k4_numbers,k9_funct_2(C,k4_numbers)) & A = H & r1_xxreal_0(k5_numbers,k21_aofa_i00(C,k4_numbers,H,F)) & r1_xxreal_0(k5_numbers,k21_aofa_i00(C,k4_numbers,H,G)) ) ) ) )).
fof(fraenkel_a_6_5_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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)) & v5_msafree4(D,B,C) & v3_aofa_a00(D,B,C) & l1_aofa_a00(D,B) & m1_subset_1(E,u1_struct_0(B)) & m1_subset_1(F,k1_funct_1(u3_msualg_1(B,D),E)) & m1_subset_1(G,u1_struct_0(B)) ) => ( r2_hidden(A,a_6_5_aofa_a00(B,C,D,E,F,G)) <=> ? [H] : ( m1_trees_1(H,k9_xtuple_0(F)) & A = k5_trees_2(F,H) & k2_xtuple_0(k1_funct_1(k5_trees_2(F,H),k1_xboole_0)) = G ) ) ) )).
fof(fraenkel_a_7_0_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( ~ 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))) & v7_ordinal1(D) & v1_xreal_0(E) & v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k1_numbers) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & m1_finance1(G) & v1_funct_1(H) & v1_funct_2(H,k4_ordinal1,k6_finance1(B,k1_numbers,C,k12_prob_1)) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_finance1(B,k1_numbers,C,k12_prob_1)))) ) => ( r2_hidden(A,a_7_0_finance1(B,C,D,E,F,G,H)) <=> ? [I] : ( m1_subset_1(I,B) & A = I & r1_xxreal_0(k3_xcmplx_0(k2_xcmplx_0(1,E),k5_finance1(D,F,G)),k12_finance1(D,F,B,C,k6_finance1(B,k1_numbers,C,k12_prob_1),H,I)) ) ) ) )).
fof(fraenkel_a_7_0_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & ~ v1_xboole_0(D) & v7_ordinal1(E) & ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(C)) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(B,F))) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(C,D))) ) => ( r2_hidden(A,a_7_0_fomodel3(B,C,D,E,F,G,H)) <=> ? [I] : ? [J] : ( m2_finseq_2(I,B,k4_finseq_2(E,B)) & m2_finseq_2(J,D,k4_finseq_2(E,D)) & A = k1_domain_1(k4_finseq_2(E,B),k4_finseq_2(E,D),I,J) & r1_relset_1(k4_ordinal1,D,J,k4_relset_1(k4_ordinal1,B,B,D,I,k4_relset_1(B,F,C,D,G,H))) ) ) ) )).
fof(fraenkel_a_7_0_lfuzzy_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & ~ v1_xboole_0(D) & v5_relat_1(E,k1_rcomp_1(k5_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(F,k1_rcomp_1(k5_numbers,1)) & v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(C,D),k1_numbers) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(C,D),k1_numbers))) & m1_subset_1(G,B) & m1_subset_1(H,D) ) => ( r2_hidden(A,a_7_0_lfuzzy_0(B,C,D,E,F,G,H)) <=> ? [I] : ( m1_subset_1(I,C) & A = k12_lattice3(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),k8_lfuzzy_0(B,C,E,G,I),k8_lfuzzy_0(C,D,F,I,H)) ) ) ) )).
fof(fraenkel_a_7_0_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & ~ v1_xboole_0(D) & v5_relat_1(E,k1_rcomp_1(k5_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(F,k1_rcomp_1(k5_numbers,1)) & v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(C,D),k1_numbers) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(C,D),k1_numbers))) & m1_subset_1(G,B) & m1_subset_1(H,D) ) => ( r2_hidden(A,a_7_0_lfuzzy_1(B,C,D,E,F,G,H)) <=> ? [I] : ( m1_subset_1(I,C) & A = k12_lattice3(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),k7_lfuzzy_0(k2_zfmisc_1(B,C),E,k1_domain_1(B,C,G,I)),k7_lfuzzy_0(k2_zfmisc_1(C,D),F,k1_domain_1(C,D,I,H))) ) ) ) )).
fof(fraenkel_a_7_1_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v13_aofa_a00(B) & v16_aofa_a00(B) & v18_aofa_a00(B,4,1) & v21_aofa_a00(B,1,1,11) & v23_aofa_a00(B,11) & l6_aofa_a00(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)) & v4_msualg_1(D,B) & v5_msafree4(D,B,C) & v3_aofa_a00(D,B,C) & v6_aofa_a01(D,B) & l1_aofa_a00(D,B) & v4_aofa_a01(E,B,C,D) & l4_aofa_a00(E,B,C,D) & v19_aofa_a00(F,B) & m1_subset_1(F,u1_struct_0(B)) & v3_aofa_a01(G,B,C,D,u4_aofa_a00(B,C,D,E),F) & m1_msafree4(G,u1_struct_0(B),u4_aofa_a00(B,C,D,E),k1_msafree4(u1_struct_0(B),u4_aofa_a00(B,C,D,E),F)) & v3_aofa_a01(H,B,C,D,u4_aofa_a00(B,C,D,E),k37_aofa_a00(B)) & m1_msafree4(H,u1_struct_0(B),u4_aofa_a00(B,C,D,E),k1_msafree4(u1_struct_0(B),u4_aofa_a00(B,C,D,E),k37_aofa_a00(B))) ) => ( r2_hidden(A,a_7_1_aofa_a01(B,C,D,E,F,G,H)) <=> ? [I] : ( m1_trees_1(I,k9_xtuple_0(k39_aofa_a00(B,D,k4_aofa_a01(B,D,u4_aofa_a00(B,C,D,E),k37_aofa_a00(B),H),F,k4_aofa_a01(B,D,u4_aofa_a00(B,C,D,E),F,G)))) & A = k5_trees_2(k39_aofa_a00(B,D,k4_aofa_a01(B,D,u4_aofa_a00(B,C,D,E),k37_aofa_a00(B),H),F,k4_aofa_a01(B,D,u4_aofa_a00(B,C,D,E),F,G)),I) & k2_xtuple_0(k1_funct_1(k5_trees_2(k39_aofa_a00(B,D,k4_aofa_a01(B,D,u4_aofa_a00(B,C,D,E),k37_aofa_a00(B),H),F,k4_aofa_a01(B,D,u4_aofa_a00(B,C,D,E),F,G)),I),k1_xboole_0)) = k37_aofa_a00(B) ) ) ) )).
fof(fraenkel_a_7_1_finance1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( ~ 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))) & v7_ordinal1(D) & v1_xreal_0(E) & v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k1_numbers) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & m1_finance1(G) & v1_funct_1(H) & v1_funct_2(H,k4_ordinal1,k6_finance1(B,k1_numbers,C,k12_prob_1)) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_finance1(B,k1_numbers,C,k12_prob_1)))) ) => ( r2_hidden(A,a_7_1_finance1(B,C,D,E,F,G,H)) <=> ? [I] : ( m1_subset_1(I,B) & A = I & ~ r1_xxreal_0(k12_finance1(D,F,B,C,k6_finance1(B,k1_numbers,C,k12_prob_1),H,I),k3_xcmplx_0(k2_xcmplx_0(1,E),k5_finance1(D,F,G))) ) ) ) )).
fof(fraenkel_a_7_2_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v13_aofa_a00(B) & v16_aofa_a00(B) & v18_aofa_a00(B,4,1) & v21_aofa_a00(B,1,1,11) & v23_aofa_a00(B,11) & l6_aofa_a00(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)) & v4_msualg_1(D,B) & v5_msafree4(D,B,C) & v3_aofa_a00(D,B,C) & v6_aofa_a01(D,B) & l1_aofa_a00(D,B) & v4_aofa_a01(E,B,C,D) & l4_aofa_a00(E,B,C,D) & v19_aofa_a00(F,B) & m1_subset_1(F,u1_struct_0(B)) & v3_aofa_a01(G,B,C,D,u4_aofa_a00(B,C,D,E),F) & m1_msafree4(G,u1_struct_0(B),u4_aofa_a00(B,C,D,E),k1_msafree4(u1_struct_0(B),u4_aofa_a00(B,C,D,E),F)) & v3_aofa_a01(H,B,C,D,u4_aofa_a00(B,C,D,E),k37_aofa_a00(B)) & m1_msafree4(H,u1_struct_0(B),u4_aofa_a00(B,C,D,E),k1_msafree4(u1_struct_0(B),u4_aofa_a00(B,C,D,E),k37_aofa_a00(B))) ) => ( r2_hidden(A,a_7_2_aofa_a01(B,C,D,E,F,G,H)) <=> ? [I] : ( m1_trees_1(I,k9_xtuple_0(k39_aofa_a00(B,D,k4_aofa_a01(B,D,u4_aofa_a00(B,C,D,E),k37_aofa_a00(B),H),F,k4_aofa_a01(B,D,u4_aofa_a00(B,C,D,E),F,G)))) & A = k5_trees_2(k39_aofa_a00(B,D,k4_aofa_a01(B,D,u4_aofa_a00(B,C,D,E),k37_aofa_a00(B),H),F,k4_aofa_a01(B,D,u4_aofa_a00(B,C,D,E),F,G)),I) & k2_xtuple_0(k1_funct_1(k5_trees_2(k39_aofa_a00(B,D,k4_aofa_a01(B,D,u4_aofa_a00(B,C,D,E),k37_aofa_a00(B),H),F,k4_aofa_a01(B,D,u4_aofa_a00(B,C,D,E),F,G)),I),k1_xboole_0)) = F ) ) ) )).
fof(fraenkel_a_8_0_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v13_aofa_a00(B) & v16_aofa_a00(B) & v18_aofa_a00(B,4,1) & v21_aofa_a00(B,1,1,11) & v23_aofa_a00(B,11) & l6_aofa_a00(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)) & v4_msualg_1(D,B) & v5_msafree4(D,B,C) & v3_aofa_a00(D,B,C) & v6_aofa_a01(D,B) & l1_aofa_a00(D,B) & v4_aofa_a01(E,B,C,D) & l4_aofa_a00(E,B,C,D) & v19_aofa_a00(F,B) & m1_subset_1(F,u1_struct_0(B)) & v3_aofa_a01(G,B,C,D,u4_aofa_a00(B,C,D,E),F) & m1_msafree4(G,u1_struct_0(B),u4_aofa_a00(B,C,D,E),k1_msafree4(u1_struct_0(B),u4_aofa_a00(B,C,D,E),F)) & v3_aofa_a01(H,B,C,D,u4_aofa_a00(B,C,D,E),k37_aofa_a00(B)) & m1_msafree4(H,u1_struct_0(B),u4_aofa_a00(B,C,D,E),k1_msafree4(u1_struct_0(B),u4_aofa_a00(B,C,D,E),k37_aofa_a00(B))) & m1_subset_1(I,u1_struct_0(B)) ) => ( r2_hidden(A,a_8_0_aofa_a01(B,C,D,E,F,G,H,I)) <=> ? [J] : ( m1_trees_1(J,k9_xtuple_0(k39_aofa_a00(B,D,k4_aofa_a01(B,D,u4_aofa_a00(B,C,D,E),k37_aofa_a00(B),H),F,k4_aofa_a01(B,D,u4_aofa_a00(B,C,D,E),F,G)))) & A = k5_trees_2(k39_aofa_a00(B,D,k4_aofa_a01(B,D,u4_aofa_a00(B,C,D,E),k37_aofa_a00(B),H),F,k4_aofa_a01(B,D,u4_aofa_a00(B,C,D,E),F,G)),J) & k2_xtuple_0(k1_funct_1(k5_trees_2(k39_aofa_a00(B,D,k4_aofa_a01(B,D,u4_aofa_a00(B,C,D,E),k37_aofa_a00(B),H),F,k4_aofa_a01(B,D,u4_aofa_a00(B,C,D,E),F,G)),J),k1_xboole_0)) = I ) ) ) )).
fof(fraenkel_a_8_0_jordan,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ( ( v1_xreal_0(B) & v1_xreal_0(C) & v1_xreal_0(D) & v1_xreal_0(E) & m1_subset_1(F,u1_struct_0(k15_euclid(2))) & m1_subset_1(G,u1_struct_0(k15_euclid(2))) & m1_subset_1(H,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(I) & m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r2_hidden(A,a_8_0_jordan(B,C,D,E,F,G,H,I)) <=> ? [J] : ( m1_subset_1(J,u1_struct_0(k15_euclid(2))) & A = J & r1_jordan5c(I,F,G,F,J) & r1_jordan5c(I,F,G,J,k1_jordan5c(H,k1_sppol_2(B,C,D,E),F,G)) ) ) ) )).
fof(fraenkel_a_8_0_lfuzzy_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & ~ v1_xboole_0(D) & v5_relat_1(E,k1_rcomp_1(k5_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(F,k1_rcomp_1(k5_numbers,1)) & v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(C,D),k1_numbers) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(C,D),k1_numbers))) & m1_subset_1(G,B) & m1_subset_1(H,D) & m1_subset_1(I,u1_struct_0(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)))) ) => ( r2_hidden(A,a_8_0_lfuzzy_0(B,C,D,E,F,G,H,I)) <=> ? [J] : ( m1_subset_1(J,C) & A = k12_lattice3(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),k12_lattice3(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),k8_lfuzzy_0(B,C,E,G,J),k8_lfuzzy_0(C,D,F,J,H)),I) ) ) ) )).
fof(fraenkel_a_8_0_yellow12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ( ( ~ 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) & ~ v2_struct_0(E) & v2_pre_topc(E) & l1_pre_topc(E) & m3_yellow_9(F,B,C) & m3_yellow_9(G,D,E) & v1_tops_2(H,G) & v1_cantor_1(H,G) & m1_subset_1(H,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(G)))) & v1_tops_2(I,F) & v1_cantor_1(I,F) & m1_subset_1(I,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(F)))) ) => ( r2_hidden(A,a_8_0_yellow12(B,C,D,E,F,G,H,I)) <=> ? [J] : ? [K] : ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(F))) & m1_subset_1(K,k1_zfmisc_1(u1_struct_0(G))) & A = k3_borsuk_1(F,G,J,K) & r2_hidden(J,I) & r2_hidden(K,H) ) ) ) )).
fof(fraenkel_a_8_1_lfuzzy_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & ~ v1_xboole_0(D) & v5_relat_1(E,k1_rcomp_1(k5_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(F,k1_rcomp_1(k5_numbers,1)) & v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(C,D),k1_numbers) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(C,D),k1_numbers))) & m1_subset_1(G,B) & m1_subset_1(H,D) & m1_subset_1(I,u1_struct_0(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)))) ) => ( r2_hidden(A,a_8_1_lfuzzy_0(B,C,D,E,F,G,H,I)) <=> ? [J] : ( m1_subset_1(J,u1_struct_0(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)))) & A = k12_lattice3(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),J,I) & r2_hidden(J,a_7_0_lfuzzy_0(B,C,D,E,F,G,H)) ) ) ) )).
fof(fraenkel_a_8_2_lfuzzy_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ( ( ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & ~ v1_xboole_0(D) & v5_relat_1(E,k1_rcomp_1(k5_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(F,k1_rcomp_1(k5_numbers,1)) & v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(C,D),k1_numbers) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(C,D),k1_numbers))) & m1_subset_1(G,B) & m1_subset_1(H,D) & m1_subset_1(I,u1_struct_0(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)))) ) => ( r2_hidden(A,a_8_2_lfuzzy_0(B,C,D,E,F,G,H,I)) <=> ? [J] : ( m1_subset_1(J,C) & A = k12_lattice3(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),k12_lattice3(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),I,k8_lfuzzy_0(B,C,E,G,J)),k8_lfuzzy_0(C,D,F,J,H)) ) ) ) )).
fof(free_g1_abcmiz_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ! [D] : ( g1_abcmiz_0(A,B) = g1_abcmiz_0(C,D) => ( A = C & B = D ) ) ) )).
fof(free_g1_algstr_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ! [F] : ! [G] : ! [H] : ( g1_algstr_3(A,B,C,D) = g1_algstr_3(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) )).
fof(free_g1_analmetr,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ! [E] : ! [F] : ( g1_analmetr(A,B,C) = g1_analmetr(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g1_analoaf,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),k2_zfmisc_1(A,A)))) => ! [C] : ! [D] : ( g1_analoaf(A,B) = g1_analoaf(C,D) => ( A = C & B = D ) ) ) )).
fof(free_g1_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ! [E] : ! [F] : ( g1_armstrng(A,B,C) = g1_armstrng(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g1_bcialg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ! [F] : ! [G] : ! [H] : ( g1_bcialg_4(A,B,C,D) = g1_bcialg_4(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) )).
fof(free_g1_bhsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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] : ! [G] : ! [H] : ! [I] : ! [J] : ( 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 ) ) ) )).
fof(free_g1_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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] : ! [G] : ! [H] : ! [I] : ! [J] : ( 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 ) ) ) )).
fof(free_g1_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [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] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ! [Q] : ! [R] : ( 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 ) ) ) )).
fof(free_g1_cayldick,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( 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_funct_1(H) & v1_funct_2(H,A,A) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ( g1_cayldick(A,B,C,D,E,F,G,H) = g1_cayldick(I,J,K,L,M,N,O,P) => ( A = I & B = J & C = K & D = L & E = M & F = N & G = O & H = P ) ) ) )).
fof(free_g1_cfuncdom,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ( 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 ) ) ) )).
fof(free_g1_cgames_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( g1_cgames_1(A,B) = g1_cgames_1(C,D) => ( A = C & B = D ) ) )).
fof(free_g1_clopban2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ( 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 ) ) ) )).
fof(free_g1_closure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ! [E] : ! [F] : ( g1_closure1(A,B,C) = g1_closure1(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g1_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ! [E] : ! [F] : ( g1_closure2(A,B,C) = g1_closure2(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g1_clvect_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ! [F] : ! [G] : ! [H] : ( g1_clvect_1(A,B,C,D) = g1_clvect_1(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) )).
fof(free_g1_collsp,axiom,( ! [A] : ! [B] : ( m1_collsp(B,A) => ! [C] : ! [D] : ( g1_collsp(A,B) = g1_collsp(C,D) => ( A = C & B = D ) ) ) )).
fof(free_g1_combgras,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ! [F] : ! [G] : ! [H] : ( g1_combgras(A,B,C,D) = g1_combgras(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) )).
fof(free_g1_compos_1,axiom,( ! [A] : ( ( v1_compos_0(A) & v2_compos_0(A) & v3_compos_0(A) & v5_compos_0(A) ) => ! [B] : ( g1_compos_1(A) = g1_compos_1(B) => A = B ) ) )).
fof(free_g1_conlat_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ! [D] : ! [E] : ! [F] : ( g1_conlat_1(A,B,C) = g1_conlat_1(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g1_csspace,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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] : ! [G] : ! [H] : ! [I] : ! [J] : ( g1_csspace(A,B,C,D,E) = g1_csspace(F,G,H,I,J) => ( A = F & B = G & C = H & D = I & E = J ) ) ) )).
fof(free_g1_e_siec,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v1_relat_1(C) ) => ! [D] : ! [E] : ! [F] : ( g1_e_siec(A,B,C) = g1_e_siec(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g1_extpro_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ( 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 ) ) ) )).
fof(free_g1_fomodel1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ! [F] : ! [G] : ! [H] : ( g1_fomodel1(A,B,C,D) = g1_fomodel1(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) )).
fof(free_g1_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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] : ! [G] : ! [H] : ! [I] : ! [J] : ( 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 ) ) ) )).
fof(free_g1_funcsdom,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ( 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 ) ) ) )).
fof(free_g1_geomtrap,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ! [E] : ! [F] : ( g1_geomtrap(A,B,C) = g1_geomtrap(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g1_graph_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ! [F] : ! [G] : ! [H] : ( g1_graph_1(A,B,C,D) = g1_graph_1(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) )).
fof(free_g1_grcat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ! [E] : ! [F] : ( g1_grcat_1(A,B,C) = g1_grcat_1(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g1_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ! [F] : ! [G] : ! [H] : ( g1_group_9(A,B,C,D) = g1_group_9(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) )).
fof(free_g1_incsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ! [E] : ! [F] : ( g1_incsp_1(A,B,C) = g1_incsp_1(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g1_lang1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k3_finseq_2(A)))) => ! [C] : ! [D] : ( g1_lang1(A,B) = g1_lang1(C,D) => ( A = C & B = D ) ) ) )).
fof(free_g1_lattices,axiom,( ! [A] : ! [B] : ( ( 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] : ! [D] : ( g1_lattices(A,B) = g1_lattices(C,D) => ( A = C & B = D ) ) ) )).
fof(free_g1_lopban_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ( 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 ) ) ) )).
fof(free_g1_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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] : ! [G] : ! [H] : ! [I] : ! [J] : ( 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 ) ) ) )).
fof(free_g1_metric_1,axiom,( ! [A] : ! [B] : ( ( 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] : ! [D] : ( g1_metric_1(A,B) = g1_metric_1(C,D) => ( A = C & B = D ) ) ) )).
fof(free_g1_midsp_1,axiom,( ! [A] : ! [B] : ( ( 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] : ! [D] : ( g1_midsp_1(A,B) = g1_midsp_1(C,D) => ( A = C & B = D ) ) ) )).
fof(free_g1_midsp_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & 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] : ! [F] : ! [G] : ! [H] : ( g1_midsp_3(A,B,C,D) = g1_midsp_3(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) )).
fof(free_g1_mod_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : ! [F] : ! [G] : ! [H] : ( g1_mod_2(A,B,C,D) = g1_mod_2(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) )).
fof(free_g1_modelc_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( 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] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ( 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 ) ) ) )).
fof(free_g1_modelc_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & 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] : ! [F] : ! [G] : ! [H] : ( g1_modelc_3(A,B,C,D) = g1_modelc_3(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) )).
fof(free_g1_msualg_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ! [F] : ! [G] : ! [H] : ( g1_msualg_1(A,B,C,D) = g1_msualg_1(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) )).
fof(free_g1_normsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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] : ! [G] : ! [H] : ! [I] : ! [J] : ( 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 ) ) ) )).
fof(free_g1_orders_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ! [D] : ( g1_orders_2(A,B) = g1_orders_2(C,D) => ( A = C & B = D ) ) ) )).
fof(free_g1_parsp_1,axiom,( ! [A] : ! [B] : ( m1_parsp_1(B,A) => ! [C] : ! [D] : ( g1_parsp_1(A,B) = g1_parsp_1(C,D) => ( A = C & B = D ) ) ) )).
fof(free_g1_pcs_0,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ! [D] : ( g1_pcs_0(A,B) = g1_pcs_0(C,D) => ( A = C & B = D ) ) ) )).
fof(free_g1_petri,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ! [F] : ! [G] : ! [H] : ( g1_petri(A,B,C,D) = g1_petri(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) )).
fof(free_g1_polyalg1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ( 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 ) ) ) )).
fof(free_g1_pre_topc,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ! [D] : ( g1_pre_topc(A,B) = g1_pre_topc(C,D) => ( A = C & B = D ) ) ) )).
fof(free_g1_qmax_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ! [E] : ! [F] : ( g1_qmax_1(A,B,C) = g1_qmax_1(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g1_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B,A),B))) => ! [D] : ! [E] : ! [F] : ( g1_rewrite3(A,B,C) = g1_rewrite3(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g1_ringcat1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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] : ! [E] : ! [F] : ( g1_ringcat1(A,B,C) = g1_ringcat1(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g1_rltopsp1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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] : ! [G] : ! [H] : ! [I] : ! [J] : ( g1_rltopsp1(A,B,C,D,E) = g1_rltopsp1(F,G,H,I,J) => ( A = F & B = G & C = H & D = I & E = J ) ) ) )).
fof(free_g1_rlvect_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ! [F] : ! [G] : ! [H] : ( g1_rlvect_1(A,B,C,D) = g1_rlvect_1(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) )).
fof(free_g1_sgraph1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_sgraph1(A))) => ! [C] : ! [D] : ( g1_sgraph1(A,B) = g1_sgraph1(C,D) => ( A = C & B = D ) ) ) )).
fof(free_g1_stacks_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ( 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 ) ) ) )).
fof(free_g1_symsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ( 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 ) ) ) )).
fof(free_g1_turing_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k1_enumset1(k4_xcmplx_0(1),k5_numbers,1))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B,A),k3_zfmisc_1(B,A,k1_enumset1(k4_xcmplx_0(1),k5_numbers,1))))) & m1_subset_1(D,B) & m1_subset_1(E,B) ) => ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ( 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 ) ) ) )).
fof(free_g1_unialg_1,axiom,( ! [A] : ! [B] : ( m1_finseq_1(B,k4_partfun1(k3_finseq_2(A),A)) => ! [C] : ! [D] : ( g1_unialg_1(A,B) = g1_unialg_1(C,D) => ( A = C & B = D ) ) ) )).
fof(free_g1_vectmetr,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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] : ! [G] : ! [H] : ! [I] : ! [J] : ( g1_vectmetr(A,B,C,D,E) = g1_vectmetr(F,G,H,I,J) => ( A = F & B = G & C = H & D = I & E = J ) ) ) )).
fof(free_g1_vectsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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] : ! [G] : ! [H] : ! [I] : ! [J] : ( 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 ) ) ) )).
fof(free_g1_vectsp_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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] : ! [G] : ! [H] : ! [I] : ! [J] : ( 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 ) ) ) )).
fof(free_g1_waybel_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ! [F] : ! [G] : ! [H] : ( g1_waybel_0(A,B,C,D) = g1_waybel_0(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) )).
fof(free_g1_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ! [D] : ! [E] : ! [F] : ( g1_waybel_9(A,B,C) = g1_waybel_9(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g1_zmodul01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ! [F] : ! [G] : ! [H] : ( g1_zmodul01(A,B,C,D) = g1_zmodul01(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) )).
fof(free_g2_abcmiz_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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] : ! [G] : ! [H] : ! [I] : ! [J] : ( 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 ) ) ) )).
fof(free_g2_algstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ! [E] : ! [F] : ( g2_algstr_0(A,B,C) = g2_algstr_0(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g2_altcat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ! [E] : ! [F] : ( g2_altcat_1(A,B,C) = g2_altcat_1(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g2_bcialg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ! [E] : ! [F] : ( g2_bcialg_1(A,B,C) = g2_bcialg_1(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g2_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [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] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ! [Q] : ! [R] : ( 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 ) ) ) )).
fof(free_g2_clvect_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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] : ! [G] : ! [H] : ! [I] : ! [J] : ( 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 ) ) ) )).
fof(free_g2_conlat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ! [E] : ! [F] : ( g2_conlat_1(A,B,C) = g2_conlat_1(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g2_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ( 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 ) ) ) )).
fof(free_g2_fsm_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ( 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 ) ) ) )).
fof(free_g2_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ( 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 ) ) ) )).
fof(free_g2_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ! [F] : ! [G] : ! [H] : ( g2_functor0(A,B,C,D) = g2_functor0(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) )).
fof(free_g2_lang1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k3_finseq_2(A)))) ) => ! [D] : ! [E] : ! [F] : ( g2_lang1(A,B,C) = g2_lang1(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g2_lattices,axiom,( ! [A] : ! [B] : ( ( 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] : ! [D] : ( g2_lattices(A,B) = g2_lattices(C,D) => ( A = C & B = D ) ) ) )).
fof(free_g2_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ( 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 ) ) ) )).
fof(free_g2_modelc_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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] : ! [G] : ! [H] : ! [I] : ! [J] : ( 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 ) ) ) )).
fof(free_g2_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ! [E] : ! [F] : ( g2_pcs_0(A,B,C) = g2_pcs_0(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g2_qmax_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ! [E] : ! [F] : ( g2_qmax_1(A,B,C) = g2_qmax_1(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g2_robbins1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ! [E] : ! [F] : ( g2_robbins1(A,B,C) = g2_robbins1(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g2_vectsp_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ( 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 ) ) ) )).
fof(free_g3_algstr_0,axiom,( ! [A] : ! [B] : ( ( 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] : ! [D] : ( g3_algstr_0(A,B) = g3_algstr_0(C,D) => ( A = C & B = D ) ) ) )).
fof(free_g3_lattices,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ! [E] : ! [F] : ( g3_lattices(A,B,C) = g3_lattices(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g3_msualg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ! [E] : ! [F] : ( g3_msualg_1(A,B,C) = g3_msualg_1(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g3_osalg_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ( 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 ) ) ) )).
fof(free_g3_robbins3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ! [F] : ! [G] : ! [H] : ( g3_robbins3(A,B,C,D) = g3_robbins3(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) )).
fof(free_g4_algstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ! [E] : ! [F] : ( g4_algstr_0(A,B,C) = g4_algstr_0(D,E,F) => ( A = D & B = E & C = F ) ) ) )).
fof(free_g4_robbins1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ! [F] : ! [G] : ! [H] : ( g4_robbins1(A,B,C,D) = g4_robbins1(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) )).
fof(free_g5_algstr_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ! [F] : ! [G] : ! [H] : ( g5_algstr_0(A,B,C,D) = g5_algstr_0(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) )).
fof(free_g5_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k13_finseq_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k13_finseq_1(A)))) & v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) & m1_finseq_1(E,B) ) => ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ( g5_aofa_a00(A,B,C,D,E) = g5_aofa_a00(F,G,H,I,J) => ( A = F & B = G & C = H & D = I & E = J ) ) ) )).
fof(free_g6_algstr_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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] : ! [G] : ! [H] : ! [I] : ! [J] : ( 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 ) ) ) )).
fof(free_g6_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k13_finseq_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k13_finseq_1(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) & m1_finseq_1(F,B) ) => ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ( g6_aofa_a00(A,B,C,D,E,F) = g6_aofa_a00(G,H,I,J,K,L) => ( A = G & B = H & C = I & D = J & E = K & F = L ) ) ) )).
fof(idempotence_k10_margrel1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => k10_margrel1(A,A) = A ) )).
fof(idempotence_k11_openlatt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) )).
fof(idempotence_k12_fomodel0,axiom,( ! [A] : ! [B] : k12_fomodel0(A,A) = A )).
fof(idempotence_k12_openlatt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) )).
fof(idempotence_k13_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) )).
fof(idempotence_k14_margrel1,axiom,( ! [A] : ! [B] : ( ( 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 ) )).
fof(idempotence_k14_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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 ) )).
fof(idempotence_k15_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k15_mmlquery(A,B,B) = B ) )).
fof(idempotence_k16_margrel1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) )).
fof(idempotence_k16_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k16_mmlquery(A,B,B) = B ) )).
fof(idempotence_k19_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) )).
fof(idempotence_k1_binarith,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => k1_binarith(A,A) = A ) )).
fof(idempotence_k1_circcomb,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( 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 ) )).
fof(idempotence_k1_circuit2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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 ) )).
fof(idempotence_k1_extreal2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_numbers) & m1_subset_1(B,k6_numbers) ) => k1_extreal2(A,A) = A ) )).
fof(idempotence_k1_finsub_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) )).
fof(idempotence_k1_funct_4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => k1_funct_4(A,A) = A ) )).
fof(idempotence_k1_fuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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 ) )).
fof(idempotence_k1_geomtrap,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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 ) )).
fof(idempotence_k1_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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 ) )).
fof(idempotence_k1_measure1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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 ) )).
fof(idempotence_k1_normform,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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 ) )).
fof(idempotence_k1_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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 ) )).
fof(idempotence_k20_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) )).
fof(idempotence_k2_bvfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) )).
fof(idempotence_k2_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) )).
fof(idempotence_k2_finsop_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) & m1_finseq_1(C,A) ) => k2_finsop_1(A,B,B) = B ) )).
fof(idempotence_k2_fuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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 ) )).
fof(idempotence_k2_groeb_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) )).
fof(idempotence_k2_lfuzzy_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) )).
fof(idempotence_k2_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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 ) )).
fof(idempotence_k2_lopclset,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) )).
fof(idempotence_k2_measure1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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 ) )).
fof(idempotence_k2_normform,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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 ) )).
fof(idempotence_k2_openlatt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) )).
fof(idempotence_k2_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) )).
fof(idempotence_k2_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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 ) )).
fof(idempotence_k2_substlat,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(C,k1_substlat(A,B)) & m1_subset_1(D,k1_substlat(A,B)) ) => k2_substlat(A,B,C,C) = C ) )).
fof(idempotence_k2_xboole_0,axiom,( ! [A] : ! [B] : k2_xboole_0(A,A) = A )).
fof(idempotence_k3_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( 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 ) )).
fof(idempotence_k3_closure3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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 ) )).
fof(idempotence_k3_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) )).
fof(idempotence_k3_finsub_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) )).
fof(idempotence_k3_lfuzzy_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) )).
fof(idempotence_k3_lopclset,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) )).
fof(idempotence_k3_openlatt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) )).
fof(idempotence_k3_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) )).
fof(idempotence_k3_xboole_0,axiom,( ! [A] : ! [B] : k3_xboole_0(A,A) = A )).
fof(idempotence_k3_xxreal_0,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => k3_xxreal_0(A,A) = A ) )).
fof(idempotence_k4_closure3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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 ) )).
fof(idempotence_k4_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) )).
fof(idempotence_k4_nat_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => k4_nat_1(A,A) = A ) )).
fof(idempotence_k4_stacks_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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 ) )).
fof(idempotence_k4_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k1_zfmisc_1(A)) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k4_subset_1(A,B,B) = B ) )).
fof(idempotence_k4_xboolean,axiom,( ! [A] : ! [B] : ( ( v1_xboolean(A) & v1_xboolean(B) ) => k4_xboolean(A,A) = A ) )).
fof(idempotence_k4_xxreal_0,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => k4_xxreal_0(A,A) = A ) )).
fof(idempotence_k5_bvfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) )).
fof(idempotence_k5_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) )).
fof(idempotence_k5_nat_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => k5_nat_1(A,A) = A ) )).
fof(idempotence_k5_prob_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_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 ) )).
fof(idempotence_k5_setwiseo,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k5_finsub_1(A)) & m1_subset_1(C,k5_finsub_1(A)) ) => k5_setwiseo(A,B,B) = B ) )).
fof(idempotence_k5_xboolean,axiom,( ! [A] : ! [B] : ( ( v1_xboolean(A) & v1_xboolean(B) ) => k5_xboolean(A,A) = A ) )).
fof(idempotence_k6_prob_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_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 ) )).
fof(idempotence_k7_classes2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => k7_classes2(A,B,B) = B ) )).
fof(idempotence_k7_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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 ) )).
fof(idempotence_k8_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k8_subset_1(A,B,B) = B ) )).
fof(idempotence_k9_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k9_subset_1(A,B,B) = B ) )).
fof(ie10_fomodel0,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k2_xboole_0(A,B) = k13_fomodel0(B,A) ) )).
fof(ie10_member_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(ie11_fomodel0,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k13_fomodel0(B,A) = k2_xboole_0(A,B) ) )).
fof(ie11_member_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(ie12_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) ) => k6_relat_1(A,B) = k13_fomodel0(A,B) ) )).
fof(ie12_member_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(ie13_fomodel0,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(ie14_fomodel0,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(ie15_fomodel0,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(ie16_fomodel0,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(ie17_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) ) => k5_relat_1(B,A) = k13_fomodel0(A,B) ) )).
fof(ie18_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) ) => k13_fomodel0(A,B) = k5_relat_1(B,A) ) )).
fof(ie19_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(ie1_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => k1_card_1(A) = k9_xtuple_0(A) ) )).
fof(ie1_cayldick,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,u1_struct_0(k3_cayldick)) & m1_subset_1(B,u1_struct_0(k3_cayldick)) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( ( A = C & B = D ) => k3_rlvect_1(k3_cayldick,A,B) = k2_xcmplx_0(C,D) ) ) )).
fof(ie1_cfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_xcmplx_0(C) ) => k10_funct_2(k2_numbers,A,B,C) = k1_funct_1(B,C) ) )).
fof(ie1_complfld,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) = k2_xcmplx_0(A,B) ) ) )).
fof(ie1_euclid,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) ) )).
fof(ie1_extreal1,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xcmplx_0(B) ) => ( A = B => k3_extreal1(A) = k9_complex1(B) ) ) )).
fof(ie1_fomodel0,axiom,( ! [A] : ( v1_xboole_0(A) => k3_finseq_2(A) = k1_tarski(A) ) )).
fof(ie1_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) => k37_fomodel2(A,B) = k22_fomodel0(B) ) )).
fof(ie1_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(ie1_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(ie1_gr_cy_1,axiom,( ! [A] : ! [B] : ( ( 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) = k2_xcmplx_0(A,B) ) )).
fof(ie1_int_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) = k3_xcmplx_0(C,D) ) ) )).
fof(ie1_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) ) )).
fof(ie1_lfuzzy_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(ie1_member_1,axiom,( ! [A] : ! [B] : ( ( v3_membered(A) & v2_membered(B) ) => ( A = B => k5_member_1(A) = k4_member_1(B) ) ) )).
fof(ie1_nat_lat,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(ie1_pdiff_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) ) )).
fof(ie1_power,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v7_ordinal1(B) ) => k2_power(A,B) = k1_newton(A,B) ) )).
fof(ie1_quatern2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,u1_struct_0(k14_quatern2)) & m1_subset_1(B,u1_struct_0(k14_quatern2)) & v1_quaterni(C) & v1_quaterni(D) ) => ( ( A = C & B = D ) => k1_algstr_0(k14_quatern2,A,B) = k22_quaterni(C,D) ) ) )).
fof(ie1_real_lat,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(ie1_seq_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_membered(A) & v3_xxreal_2(A) ) => k3_seq_4(A) = k2_xxreal_2(A) ) )).
fof(ie1_sin_cos3,axiom,( ! [A] : ! [B] : ( ( 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))) & v1_xcmplx_0(B) ) => k10_funct_2(k2_numbers,k2_numbers,A,B) = k1_funct_1(A,B) ) )).
fof(ie1_vectsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) = k2_xcmplx_0(C,D) ) ) )).
fof(ie1_xxreal_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(ie20_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(ie21_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(B) ) => k1_funct_4(A,B) = k13_fomodel0(B,A) ) )).
fof(ie22_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(B) ) => k13_fomodel0(B,A) = k1_funct_4(A,B) ) )).
fof(ie23_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(B) ) => k1_funct_4(B,A) = k13_fomodel0(B,A) ) )).
fof(ie24_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(B) ) => k13_fomodel0(B,A) = k1_funct_4(B,A) ) )).
fof(ie25_fomodel0,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k24_fomodel0(A,B) = k5_relat_1(B,A) ) )).
fof(ie26_fomodel0,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k5_relat_1(B,A) = k24_fomodel0(A,B) ) )).
fof(ie27_fomodel0,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k25_fomodel0(A,B) = k5_relat_1(B,A) ) )).
fof(ie28_fomodel0,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k5_relat_1(B,A) = k25_fomodel0(A,B) ) )).
fof(ie29_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => k26_fomodel0(A,B) = k27_fomodel0(A,B) ) )).
fof(ie2_cayldick,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,u1_struct_0(k3_cayldick)) & m1_subset_1(B,u1_struct_0(k3_cayldick)) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( ( A = C & B = D ) => k8_group_1(k3_cayldick,A,B) = k3_xcmplx_0(C,D) ) ) )).
fof(ie2_complfld,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) = k3_xcmplx_0(A,B) ) ) )).
fof(ie2_euclid,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) ) )).
fof(ie2_fomodel0,axiom,( ! [A] : ( v1_xboole_0(A) => k1_tarski(A) = k3_finseq_2(A) ) )).
fof(ie2_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & ~ v1_xboole_0(B) & m1_subset_1(C,k15_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))) ) => k25_fomodel2(A,B,C,D) = k13_fomodel2(A,B,C,D) ) )).
fof(ie2_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(ie2_int_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) = k2_xcmplx_0(C,D) ) ) )).
fof(ie2_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) ) )).
fof(ie2_lfuzzy_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(ie2_member_1,axiom,( ! [A] : ! [B] : ( ( v3_membered(A) & v2_membered(B) ) => ( A = B => k7_member_1(A) = k6_member_1(B) ) ) )).
fof(ie2_nat_lat,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(ie2_real_lat,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(ie2_seq_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_membered(A) & v4_xxreal_2(A) ) => k2_seq_4(A) = k1_xxreal_2(A) ) )).
fof(ie2_xxreal_3,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xcmplx_0(B) ) => ( A = B => k2_xxreal_3(A) = k4_xcmplx_0(B) ) ) )).
fof(ie30_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => k27_fomodel0(A,B) = k28_fomodel0(A,B) ) )).
fof(ie31_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => k1_funct_4(A,B) = k26_fomodel0(A,B) ) )).
fof(ie32_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => k26_fomodel0(A,B) = k1_funct_4(A,B) ) )).
fof(ie33_fomodel0,axiom,( ! [A] : ! [B] : k2_tarski(A,B) = k29_fomodel0(A,B) )).
fof(ie34_fomodel0,axiom,( ! [A] : ! [B] : k29_fomodel0(A,B) = k2_tarski(A,B) )).
fof(ie35_fomodel0,axiom,( ! [A] : ! [B] : k29_fomodel0(A,B) = k29_fomodel0(B,A) )).
fof(ie36_fomodel0,axiom,( ! [A] : ! [B] : ( v1_relat_1(A) => k7_relat_1(A,B) = k30_fomodel0(A,B) ) )).
fof(ie37_fomodel0,axiom,( ! [A] : ! [B] : ( v1_relat_1(A) => k30_fomodel0(A,B) = k7_relat_1(A,B) ) )).
fof(ie38_fomodel0,axiom,( ! [A] : k32_fomodel0(A) = k33_fomodel0(A) )).
fof(ie39_fomodel0,axiom,( ! [A] : k33_fomodel0(A) = k32_fomodel0(A) )).
fof(ie3_cayldick,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,u1_struct_0(k3_cayldick)) & v1_xreal_0(B) ) => ( A = B => k4_algstr_0(k3_cayldick,A) = k4_xcmplx_0(B) ) ) )).
fof(ie3_euclid,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(ie3_fomodel0,axiom,( ! [A] : ! [B] : k12_fomodel0(A,B) = k12_fomodel0(B,A) )).
fof(ie3_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & ~ v1_xboole_0(B) & m1_subset_1(C,k15_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))) ) => k13_fomodel2(A,B,C,D) = k25_fomodel2(A,B,C,D) ) )).
fof(ie3_int_3,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,u1_struct_0(k1_int_3)) & v1_int_1(B) ) => ( A = B => k4_algstr_0(k1_int_3,A) = k4_xcmplx_0(B) ) ) )).
fof(ie3_member_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(ie3_nat_lat,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(ie3_pdiff_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) = k30_valued_1(C) ) ) )).
fof(ie3_vectsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) = k2_xcmplx_0(C,D) ) ) )).
fof(ie3_xxreal_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(ie4_cayldick,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,u1_struct_0(k3_cayldick)) & m1_subset_1(B,u1_struct_0(k3_cayldick)) & v1_xreal_0(C) & v1_xreal_0(D) ) => ( ( A = C & B = D ) => k5_algstr_0(k3_cayldick,A,B) = k6_xcmplx_0(C,D) ) ) )).
fof(ie4_euclid,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) ) )).
fof(ie4_fomodel0,axiom,( ! [A] : ! [B] : k3_xboole_0(A,B) = k12_fomodel0(A,B) )).
fof(ie4_member_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(ie4_nat_lat,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(ie4_pdiff_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) ) )).
fof(ie4_vectsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) = k3_xcmplx_0(C,D) ) ) )).
fof(ie4_xxreal_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(ie5_cayldick,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,u1_struct_0(k3_cayldick)) & v1_xreal_0(B) & v1_xreal_0(C) ) => ( A = C => k1_rlvect_1(k3_cayldick,A,B) = k3_xcmplx_0(B,C) ) ) )).
fof(ie5_euclid_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) ) )).
fof(ie5_fomodel0,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k9_subset_1(A,A,B) = k13_fomodel0(A,B) ) )).
fof(ie5_member_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(ie5_quatern2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_quaterni(A) & v1_quaterni(B) & m1_subset_1(C,u1_struct_0(k15_quatern2)) & m1_subset_1(D,u1_struct_0(k15_quatern2)) ) => ( ( C = A & D = B ) => k6_algstr_0(k15_quatern2,C,D) = k23_quaterni(A,B) ) ) )).
fof(ie5_vectsp_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,u1_struct_0(k2_vectsp_1)) & v1_xreal_0(B) ) => ( A = B => k4_algstr_0(k2_vectsp_1,A) = k4_xcmplx_0(B) ) ) )).
fof(ie5_xxreal_3,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xcmplx_0(B) ) => ( A = B => k5_xxreal_3(A) = k5_xcmplx_0(B) ) ) )).
fof(ie6_cayldick,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_cayldick)) => k2_normsp_0(k3_cayldick,A) = k9_complex1(A) ) )).
fof(ie6_euclid_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) ) )).
fof(ie6_fomodel0,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k13_fomodel0(A,B) = k9_subset_1(A,A,B) ) )).
fof(ie6_member_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(ie6_quatern2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,u1_struct_0(k15_quatern2)) & v1_quaterni(B) ) => ( A = B => k4_algstr_0(k15_quatern2,A) = k24_quaterni(B) ) ) )).
fof(ie6_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_vectsp_1(A) & l4_algstr_0(A) ) => k1_group_1(A) = k5_struct_0(A) ) )).
fof(ie6_xxreal_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(ie7_fomodel0,axiom,( ! [A] : ! [B] : k6_subset_1(A,B) = k14_fomodel0(A,B) )).
fof(ie7_member_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(ie8_fomodel0,axiom,( ! [A] : ! [B] : k15_fomodel0(A,B) = k13_fomodel0(B,A) )).
fof(ie8_member_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(ie9_fomodel0,axiom,( ! [A] : ! [B] : k13_fomodel0(B,A) = k15_fomodel0(A,B) )).
fof(ie9_member_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(involutiveness_k10_petri,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) )).
fof(involutiveness_k12_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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 ) )).
fof(involutiveness_k13_margrel1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_margrel1(A) ) => k13_margrel1(k13_margrel1(A)) = A ) )).
fof(involutiveness_k15_margrel1,axiom,( ! [A] : ! [B] : ( ( ~ 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 ) )).
fof(involutiveness_k16_seq_4,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k12_seq_4(A)) ) => k16_seq_4(A,k16_seq_4(A,B)) = B ) )).
fof(involutiveness_k17_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_xreal_0(B) & ~ v3_xxreal_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)))) ) => k17_toprealc(A,B,k17_toprealc(A,B,C)) = C ) )).
fof(involutiveness_k1_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( ~ 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 ) )).
fof(involutiveness_k1_card_fil,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_card_fil(B,A) ) => k1_card_fil(A,k1_card_fil(A,B)) = B ) )).
fof(involutiveness_k1_comseq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => k1_comseq_2(k1_comseq_2(A)) = A ) )).
fof(involutiveness_k1_descip_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) )).
fof(involutiveness_k1_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k1_funcop_1(k1_funcop_1(A)) = A ) )).
fof(involutiveness_k1_goboard9,axiom,( ! [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))) ) => k1_goboard9(k1_goboard9(A)) = A ) )).
fof(involutiveness_k1_group_2,axiom,( ! [A] : ! [B] : ( ( ~ 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 ) )).
fof(involutiveness_k1_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m1_finseq_1(A,k3_finseq_2(k2_numbers)) ) => k1_matrixc1(k1_matrixc1(A)) = A ) )).
fof(involutiveness_k1_member_1,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => k1_member_1(k1_member_1(A)) = A ) )).
fof(involutiveness_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k1_real_1(k1_real_1(A)) = A ) )).
fof(involutiveness_k24_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => k24_quaterni(k24_quaterni(A)) = A ) )).
fof(involutiveness_k24_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ 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_zmodul02(B,A) ) => k24_zmodul02(A,k24_zmodul02(A,B)) = B ) )).
fof(involutiveness_k2_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => k2_complfld(k2_complfld(A)) = A ) )).
fof(involutiveness_k2_comseq_2,axiom,( ! [A] : ! [B] : ( ( ~ 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 ) )).
fof(involutiveness_k2_group_1,axiom,( ! [A] : ! [B] : ( ( ~ 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 ) )).
fof(involutiveness_k2_prob_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k2_prob_1(A,k2_prob_1(A,B)) = B ) )).
fof(involutiveness_k2_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k2_real_1(k2_real_1(A)) = A ) )).
fof(involutiveness_k2_rearran1,axiom,( ! [A] : ! [B] : ( ( ~ 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 ) )).
fof(involutiveness_k2_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => k2_relat_1(k2_relat_1(A)) = A ) )).
fof(involutiveness_k2_supinf_2,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => k2_supinf_2(k2_supinf_2(A)) = A ) )).
fof(involutiveness_k2_toprealc,axiom,( ! [A] : ( v1_valued_2(A) => k2_toprealc(k2_toprealc(A)) = A ) )).
fof(involutiveness_k2_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => k2_xxreal_3(k2_xxreal_3(A)) = A ) )).
fof(involutiveness_k30_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => k30_valued_1(k30_valued_1(A)) = A ) )).
fof(involutiveness_k31_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) )).
fof(involutiveness_k32_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) )).
fof(involutiveness_k34_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) )).
fof(involutiveness_k35_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => k35_valued_1(k35_valued_1(A)) = A ) )).
fof(involutiveness_k36_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) )).
fof(involutiveness_k37_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) )).
fof(involutiveness_k3_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k3_arytm_0(k3_arytm_0(A)) = A ) )).
fof(involutiveness_k3_finseq_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_5(k3_finseq_5(A)) = A ) )).
fof(involutiveness_k3_fuzzy_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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 ) )).
fof(involutiveness_k3_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => k3_measure6(k3_measure6(A)) = A ) )).
fof(involutiveness_k3_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => k3_relset_1(A,B,k3_relset_1(A,B,C)) = C ) )).
fof(involutiveness_k3_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k3_subset_1(A,k3_subset_1(A,B)) = B ) )).
fof(involutiveness_k3_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => k3_xboolean(k3_xboolean(A)) = A ) )).
fof(involutiveness_k4_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k4_arytm_0(k4_arytm_0(A)) = A ) )).
fof(involutiveness_k4_finseq_5,axiom,( ! [A] : ! [B] : ( m1_finseq_1(B,A) => k4_finseq_5(A,k4_finseq_5(A,B)) = B ) )).
fof(involutiveness_k4_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => k4_measure6(k4_measure6(A)) = A ) )).
fof(involutiveness_k4_member_1,axiom,( ! [A] : ( v2_membered(A) => k4_member_1(k4_member_1(A)) = A ) )).
fof(involutiveness_k4_seqfunc,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => k4_seqfunc(A,k4_seqfunc(A,B)) = B ) )).
fof(involutiveness_k4_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => k4_xcmplx_0(k4_xcmplx_0(A)) = A ) )).
fof(involutiveness_k5_complsp2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_finseq_2(A,k2_numbers)) ) => k5_complsp2(A,k5_complsp2(A,B)) = B ) )).
fof(involutiveness_k5_member_1,axiom,( ! [A] : ( v1_membered(A) => k5_member_1(k5_member_1(A)) = A ) )).
fof(involutiveness_k5_rvsum_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => k5_rvsum_2(k5_rvsum_2(A)) = A ) )).
fof(involutiveness_k5_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => k5_xcmplx_0(k5_xcmplx_0(A)) = A ) )).
fof(involutiveness_k6_euclid,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k1_euclid(A)) ) => k6_euclid(A,k6_euclid(A,B)) = B ) )).
fof(involutiveness_k6_glib_001,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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 ) )).
fof(involutiveness_k6_lattice3,axiom,( ! [A] : ! [B] : ( ( 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 ) )).
fof(involutiveness_k6_measure6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_membered(B) & v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => k6_measure6(A,B,k6_measure6(A,B,C)) = C ) )).
fof(involutiveness_k6_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => k6_rvsum_1(k6_rvsum_1(A)) = A ) )).
fof(involutiveness_k6_rvsum_2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v3_card_1(B,A) & m1_finseq_1(B,k2_numbers) ) => k6_rvsum_2(A,k6_rvsum_2(A,B)) = B ) )).
fof(involutiveness_k6_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => k6_scmyciel(k6_scmyciel(A)) = A ) )).
fof(involutiveness_k6_supinf_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k6_numbers)) => k6_supinf_2(k6_supinf_2(A)) = A ) )).
fof(involutiveness_k7_hurwitz,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(A,k1_complfld) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => k7_hurwitz(k7_hurwitz(A)) = A ) )).
fof(involutiveness_k7_member_1,axiom,( ! [A] : ( v1_membered(A) => k7_member_1(k7_member_1(A)) = A ) )).
fof(involutiveness_k7_rvsum_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k4_finseq_2(A,k1_numbers)) ) => k7_rvsum_1(A,k7_rvsum_1(A,B)) = B ) )).
fof(involutiveness_k7_setfam_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => k7_setfam_1(A,k7_setfam_1(A,B)) = B ) )).
fof(involutiveness_k7_vectsp_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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 ) )).
fof(involutiveness_k8_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k8_complex1(k8_complex1(A)) = A ) )).
fof(involutiveness_k8_qmax_1,axiom,( ! [A] : ! [B] : ( ( 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 ) )).
fof(involutiveness_k8_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => k8_quaterni(k8_quaterni(A)) = A ) )).
fof(involutiveness_k8_rmod_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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 ) )).
fof(involutiveness_k9_margrel1,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => k9_margrel1(k9_margrel1(A)) = A ) )).
fof(involutiveness_k9_seq_4,axiom,( ! [A] : ( m1_finseq_1(A,k2_numbers) => k9_seq_4(k9_seq_4(A)) = A ) )).
fof(irreflexivity_r10_analmetr,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(irreflexivity_r1_afvect0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(irreflexivity_r1_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(irreflexivity_r1_gobrd10,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => ~ r1_gobrd10(A,A) ) )).
fof(irreflexivity_r1_subset_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ r1_subset_1(A,A) ) )).
fof(irreflexivity_r2_orders_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(irreflexivity_r2_subset_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ~ r2_subset_1(A,A) ) )).
fof(irreflexivity_r2_tsep_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(irreflexivity_r2_xboole_0,axiom,( ! [A] : ! [B] : ~ r2_xboole_0(A,A) )).
fof(irreflexivity_r3_modelc_2,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & v1_modelc_2(B) & m1_finseq_1(B,k4_ordinal1) ) => ~ r3_modelc_2(A,A) ) )).
fof(irreflexivity_r3_qc_lang2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(irreflexivity_r4_tsep_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(irreflexivity_r7_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ~ r7_glib_000(A,A) ) )).
fof(l100_asympt_1,axiom,( v4_asympt_0(k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k3_asympt_1(1),k1_seq_1(1))) )).
fof(l100_borsuk_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(l100_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k4_xcmplx_0(B),A) & r1_xxreal_0(A,B) ) <=> r1_xxreal_0(k9_complex1(A),B) ) ) ) )).
fof(l100_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(l100_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m2_subset_1(D,k9_funct_2(k37_fomodel1(A),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_fomodel2(A,B)) => k25_fomodel2(A,B,D,C) = k13_fomodel2(A,B,D,C) ) ) ) ) )).
fof(l100_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v7_fomodel1(B,A) & m1_subset_1(B,k1_fomodel1(A)) ) => ! [C] : ( ( 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))),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k35_fomodel1(A))) ) => ! [D] : ( ( 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))),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k35_fomodel1(A))) ) => v4_fomodel4(k1_tarski(k4_tarski(k2_xboole_0(k38_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))),k30_fomodel4(A)),k1_xboole_0) ) ) ) ) )).
fof(l100_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ! [F] : ( 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] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l100_geomtrap,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_geomtrap(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_diraf(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_diraf(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_diraf(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_diraf(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_diraf(A))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k2_diraf(A))) => ( ( r2_analoaf(k2_diraf(A),F,G,B,C) & r2_analoaf(k2_diraf(A),F,G,D,E) ) => ( F = G | r2_analoaf(k2_diraf(A),B,C,D,E) ) ) ) ) ) ) ) ) ) )).
fof(l100_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( v5_glib_001(B,A) => v5_glib_001(k8_glib_001(A,B,C,D),A) ) ) ) ) ) )).
fof(l100_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k21_interva1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k21_interva1(A))) => k1_lattices(k21_interva1(A),k2_lattices(k21_interva1(A),B,C),C) = C ) ) ) )).
fof(l100_jordan,axiom,( k18_euclid(k19_euclid(k5_numbers,k4_xcmplx_0(3))) = k4_xcmplx_0(3) )).
fof(l100_modelc_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_modelc_2(A) & l1_modelc_2(A) ) => ! [B] : ( ( 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] : ( ( 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,k5_numbers) ) ) ) )).
fof(l100_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( k2_nat_1(k1_newton(2,A),k1_nat_1(k3_xcmplx_0(2,C),1)) = k2_nat_1(k1_newton(2,B),k1_nat_1(k3_xcmplx_0(2,D),1)) => r1_xxreal_0(A,B) ) ) ) ) ) )).
fof(l100_pepin,axiom,( k4_nat_d(k11_newton(3,128),k4_pepin(4)) = k2_nat_1(52,289) )).
fof(l100_sincos10,axiom,( v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k7_xcmplx_0(k28_sin_cos,2))),k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(l100_toprealb,axiom,( v1_funct_1(k2_partfun1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_relset_1(k1_numbers,k1_fcont_1(k4_xcmplx_0(1),1))))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_relset_1(k1_numbers,k1_fcont_1(k4_xcmplx_0(1),1))))),k6_toprealb(k1_fcont_1(k4_xcmplx_0(1),1)),k5_toprealb(k2_rcomp_1(k5_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(k4_xcmplx_0(1),1))))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_relset_1(k1_numbers,k1_fcont_1(k4_xcmplx_0(1),1))))),k6_toprealb(k1_fcont_1(k4_xcmplx_0(1),1)),k5_toprealb(k2_rcomp_1(k5_numbers,1))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k5_numbers,1)))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k5_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(k4_xcmplx_0(1),1))))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_relset_1(k1_numbers,k1_fcont_1(k4_xcmplx_0(1),1))))),k6_toprealb(k1_fcont_1(k4_xcmplx_0(1),1)),k5_toprealb(k2_rcomp_1(k5_numbers,1))),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k5_numbers,1)))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k5_numbers,1))))))) )).
fof(l100_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v9_waybel_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_orders_2(A,k11_lattice3(A,B,k6_waybel_1(A,B,C)),C) ) ) ) ) )).
fof(l100_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) != k5_numbers ) ) ) )).
fof(l101_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v19_aofa_a00(D,A) & m1_subset_1(D,u1_struct_0(A)) ) => ! [E] : ( v1_int_1(E) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_numbers,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,C),D)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_numbers,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,C),D)))) ) => ( ( k1_funct_1(F,k5_numbers) = k27_aofa_a00(A,C,D) & ! [G] : ( v7_ordinal1(G) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),D)) => ( k1_funct_1(F,G) = H => ( k1_funct_1(F,k2_xcmplx_0(G,1)) = k30_aofa_a00(A,C,D,H,k28_aofa_a00(A,C,D)) & k1_funct_1(F,k4_xcmplx_0(k2_xcmplx_0(G,1))) = k29_aofa_a00(A,C,D,k30_aofa_a00(A,C,D,H,k28_aofa_a00(A,C,D))) ) ) ) ) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k4_numbers,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,C),D)) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_numbers,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,C),D)))) ) => ( ( k1_funct_1(G,k5_numbers) = k27_aofa_a00(A,C,D) & ! [H] : ( v7_ordinal1(H) => ! [I] : ( m1_subset_1(I,k1_funct_1(u3_msualg_1(A,C),D)) => ( k1_funct_1(G,H) = I => ( k1_funct_1(G,k2_xcmplx_0(H,1)) = k30_aofa_a00(A,C,D,I,k28_aofa_a00(A,C,D)) & k1_funct_1(G,k4_xcmplx_0(k2_xcmplx_0(H,1))) = k29_aofa_a00(A,C,D,k30_aofa_a00(A,C,D,I,k28_aofa_a00(A,C,D))) ) ) ) ) ) => r2_funct_2(k4_numbers,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,C),D),F,G) ) ) ) ) ) ) ) ) ) )).
fof(l101_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k7_toprealb(k1_nat_1(2,1),k4_struct_0(k15_euclid(k1_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(k1_nat_1(2,1),k4_struct_0(k15_euclid(k1_nat_1(2,1))),1)),u1_struct_0(k15_euclid(2))))) ) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,k7_xcmplx_0(1,2)) ) => ( v2_borsuk_7(B,k1_nat_1(2,1),2,k4_struct_0(k15_euclid(k1_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,k7_xcmplx_0(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)) ) ) ) ) )).
fof(l101_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_relat_1(D) & v5_relat_1(D,B) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( 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)) ) ) ) ) )).
fof(l101_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_fomodel2(D,B,C) ) => ! [E] : ( ( 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,k9_fomodel2(B,C,D),k3_finseq_2(A)),k5_relset_1(k35_fomodel1(B),C,k9_fomodel2(B,C,E),k3_finseq_2(A))) ) ) ) ) ) )).
fof(l101_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(D) & v11_fomodel1(D) & l1_fomodel1(D) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(D)),k9_setfam_1(k1_fomodel4(D))))) => ! [F] : ( ( v5_fomodel1(F,D) & m1_subset_1(F,k1_fomodel1(D)) ) => ~ ( v11_fomodel4(A,D,E) & r2_hidden(k4_tarski(B,C),k9_fomodel3(k35_fomodel1(D),k8_fomodel4(D,E,A),k1_int_2(k19_fomodel1(D,F)))) & ! [G] : ( ( 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))),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(D)),k1_tarski(k1_xboole_0)),k35_fomodel1(D))) ) => ! [H] : ( ( 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))),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(D)),k1_tarski(k1_xboole_0)),k35_fomodel1(D))) ) => ~ ( G = B & H = C & r1_tarski(k38_fomodel4(D,k1_int_2(k19_fomodel1(D,F)),G,H),A) ) ) ) ) ) ) ) )).
fof(l101_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l101_geomtrap,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_geomtrap(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_diraf(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_diraf(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_diraf(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_diraf(A))) => ! [F] : ( 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 ) ) ) ) ) ) ) )).
fof(l101_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( ( v5_glib_001(B,A) & r1_glib_000(A,k4_glib_001(A,B),D,C) & ! [E] : ( ( ~ v1_abian(E) & m1_subset_1(E,k4_ordinal1) ) => ~ ( ~ 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) ) ) ) ) )).
fof(l101_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => m1_group_2(k10_group_2(A,B,C),B) ) ) ) )).
fof(l101_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( m1_group_9(D,A,B) => m1_group_9(k17_group_9(A,B,C,D),A,C) ) ) ) )).
fof(l101_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k21_interva1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k21_interva1(A))) => k2_lattices(k21_interva1(A),B,C) = k2_lattices(k21_interva1(A),C,B) ) ) ) )).
fof(l101_jordan,axiom,( k17_euclid(k19_euclid(k4_xcmplx_0(1),3)) = k4_xcmplx_0(1) )).
fof(l101_modelc_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v10_modelc_2(B) & l1_modelc_2(B) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(l101_pepin,axiom,( k4_nat_d(k11_newton(3,256),k4_pepin(4)) = 282 )).
fof(l101_sincos10,axiom,( v2_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,4)))) )).
fof(l101_toprealb,axiom,( k2_relset_1(k1_numbers,k1_fcont_1(k4_xcmplx_0(1),1)) = k1_numbers )).
fof(l101_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(k5_numbers,C) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(k7_xcmplx_0(A,C),k7_xcmplx_0(B,C)) ) ) ) ) )).
fof(l102_borsuk_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_topmetr)) => ! [B] : ( 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] : ( ( v1_int_1(C) & ~ v1_abian(C) ) => A != k2_borsuk_7(B,k7_xcmplx_0(C,2)) ) ) ) ) )).
fof(l102_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v5_chord(B,A) => v5_chord(k6_glib_001(A,B),A) ) ) ) )).
fof(l102_facirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k15_facirc_1(A,B,C),k18_facirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(l102_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ! [D] : ( ( 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))),k29_fomodel4(B)),C) & v11_fomodel4(A,B,C) & v8_fomodel1(D,B) ) => v2_fomodel3(k4_fomodel3(B,D,A),B,k35_fomodel1(B),D,k8_fomodel4(B,C,A)) ) ) ) ) )).
fof(l102_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l102_geomtrap,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_geomtrap(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_analoaf(A,B,C,B,C) ) ) ) )).
fof(l102_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( ( 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) ) ) ) )).
fof(l102_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k21_interva1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k21_interva1(A))) => ! [D] : ( 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) ) ) ) ) )).
fof(l102_jordan,axiom,( k18_euclid(k19_euclid(k4_xcmplx_0(1),3)) = 3 )).
fof(l102_modelc_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v10_modelc_2(B) & l1_modelc_2(B) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(l102_pepin,axiom,( k4_nat_d(k11_newton(3,k2_nat_1(256,2)),k4_pepin(4)) = k2_nat_1(71,197) )).
fof(l102_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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,k4_ordinal1))) ) ) )).
fof(l102_sincos10,axiom,( v2_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos),k28_sin_cos))) )).
fof(l102_toprealb,axiom,( k1_pre_topc(k2_topalg_2,k2_struct_0(k2_topalg_2)) = k2_topalg_2 )).
fof(l102_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(k7_xcmplx_0(A,C),k7_xcmplx_0(B,C)) & r1_xxreal_0(B,A) ) ) ) ) )).
fof(l103_borsuk_7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(k7_toprealb(k1_nat_1(2,1),k4_struct_0(k15_euclid(k1_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(k1_nat_1(2,1),k4_struct_0(k15_euclid(k1_nat_1(2,1))),1)),u1_struct_0(k15_euclid(2))))) ) => ( v5_pre_topc(A,k7_toprealb(k1_nat_1(2,1),k4_struct_0(k15_euclid(k1_nat_1(2,1))),1),k15_euclid(2)) => ( v2_borsuk_7(A,k1_nat_1(2,1),2,k4_struct_0(k15_euclid(k1_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(k1_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(k1_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(k1_nat_1(2,1))),u1_struct_0(k8_toprealb(2)),k16_borsuk_7(2,A),c18__borsuk_7)) ) ) ) ) )).
fof(l103_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(D) & v11_fomodel1(D) & l1_fomodel1(D) ) => ! [E] : ( ( v7_fomodel1(E,D) & m1_subset_1(E,k1_fomodel1(D)) ) => ! [F] : ( 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))),k30_fomodel4(D)),F) & v11_fomodel4(A,D,F) & r2_hidden(k4_tarski(B,C),k9_fomodel3(k35_fomodel1(D),k8_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) ) ) ) ) )).
fof(l103_geomtrap,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_geomtrap(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_diraf(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_diraf(A))) => r2_analoaf(k2_diraf(A),B,C,C,B) ) ) ) )).
fof(l103_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( r1_xxreal_0(C,k3_finseq_1(B)) => k19_glib_001(A,B,C) = C ) ) => v5_glib_001(B,A) ) ) ) )).
fof(l103_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k18_interva1(A)) => ! [C] : ( m1_subset_1(C,k18_interva1(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(l103_jordan,axiom,( k17_euclid(k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3))) = k4_xcmplx_0(1) )).
fof(l103_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( v6_supinf_2(D) & v6_supinf_2(E) ) => ( ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(l103_modelc_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v10_modelc_2(B) & l1_modelc_2(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( v1_modelc_2(F) & m2_finseq_1(F,k4_ordinal1) ) => ( r1_xxreal_0(k3_finseq_1(F),A) => k1_funct_1(D,F) = k1_funct_1(E,F) ) ) ) ) ) ) ) ) )).
fof(l103_pepin,axiom,( k4_nat_d(k11_newton(3,k2_nat_1(256,4)),k4_pepin(4)) = k2_nat_1(32,257) )).
fof(l103_sincos10,axiom,( v2_funct_1(k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4))))) )).
fof(l103_toprealb,axiom,( v1_funct_1(c31__toprealb) & v1_funct_2(c31__toprealb,u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k5_numbers,1)))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k5_numbers,1))))) & v5_pre_topc(c31__toprealb,k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k5_numbers,1))),k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k5_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(k5_numbers,1)))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k5_numbers,1))))))) )).
fof(l104_borsuk_7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(k7_toprealb(k1_nat_1(2,1),k4_struct_0(k15_euclid(k1_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(k1_nat_1(2,1),k4_struct_0(k15_euclid(k1_nat_1(2,1))),1)),u1_struct_0(k15_euclid(2))))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ~ ( ~ v2_borsuk_7(A,k1_nat_1(2,1),2,k4_struct_0(k15_euclid(k1_nat_1(2,1))),1) & v5_pre_topc(A,k7_toprealb(k1_nat_1(2,1),k4_struct_0(k15_euclid(k1_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(k5_numbers,B) & r1_xxreal_0(B,k7_xcmplx_0(1,2)) & ! [D] : ( ( v1_int_1(D) & ~ v1_abian(D) ) => ? [E] : ( m1_borsuk_2(E,k8_toprealb(2),k3_funct_2(u1_struct_0(k8_toprealb(k1_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(k1_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(k1_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(k1_nat_1(2,1))),u1_struct_0(k8_toprealb(2)),k16_borsuk_7(2,A),c18__borsuk_7),C,E),k2_xcmplx_0(B,k7_xcmplx_0(1,2))) != k2_xcmplx_0(k1_funct_1(k17_borsuk_7(k3_funct_2(u1_struct_0(k8_toprealb(k1_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(k1_nat_1(2,1))),u1_struct_0(k8_toprealb(2)),k16_borsuk_7(2,A),c18__borsuk_7),C,E),B),k7_xcmplx_0(D,2)) ) ) ) ) ) )).
fof(l104_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,B) ) => r2_hidden(C,k4_finseq_2(A,B)) ) ) ) )).
fof(l104_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(D) & v11_fomodel1(D) & l1_fomodel1(D) ) => ! [E] : ( ( v7_fomodel1(E,D) & m1_subset_1(E,k1_fomodel1(D)) ) => ! [F] : ( 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))),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))),k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(D)),k9_setfam_1(k1_fomodel4(D))),k28_fomodel4(D)),F) = k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(D)),k9_setfam_1(k1_fomodel4(D))),k28_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))),k30_fomodel4(D))) = k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(D)),k9_setfam_1(k1_fomodel4(D))),k30_fomodel4(D)) & v11_fomodel4(A,D,F) & r2_hidden(k4_tarski(B,C),k9_fomodel3(k35_fomodel1(D),k8_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) ) ) ) ) ) )).
fof(l104_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( ( 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) ) ) ) ) )).
fof(l104_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v4_group_9(C,A,B) & m1_group_9(C,A,B) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(l104_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k21_interva1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k21_interva1(A))) => k2_lattices(k21_interva1(A),B,k1_lattices(k21_interva1(A),B,C)) = B ) ) ) )).
fof(l104_jordan,axiom,( k18_euclid(k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3))) = k4_xcmplx_0(3) )).
fof(l104_pepin,axiom,( k4_nat_d(k11_newton(3,k2_nat_1(256,8)),k4_pepin(4)) = k2_nat_1(81,809) )).
fof(l104_pre_poly,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( 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) ) ) ) )).
fof(l104_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ( v2_extpro_1(A,k7_card_1(3),k1_scmfsa_2) => A = k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0) ) ) )).
fof(l104_sin_cos6,axiom,( k2_funct_1(k3_sin_cos6) = k5_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k5_numbers,k28_sin_cos)) )).
fof(l104_sincos10,axiom,( v2_funct_1(k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(l104_toprealb,axiom,( v1_funct_1(k6_toprealb(k3_sin_cos6)) & v1_funct_2(k6_toprealb(k3_sin_cos6),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k4_xcmplx_0(1),1)))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k5_numbers,k28_sin_cos))))) & v5_pre_topc(k6_toprealb(k3_sin_cos6),k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k4_xcmplx_0(1),1))),k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k5_numbers,k28_sin_cos)))) & m1_subset_1(k6_toprealb(k3_sin_cos6),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k4_xcmplx_0(1),1)))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k5_numbers,k28_sin_cos))))))) )).
fof(l105_borsuk_7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(k7_toprealb(k1_nat_1(2,1),k4_struct_0(k15_euclid(k1_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(k1_nat_1(2,1),k4_struct_0(k15_euclid(k1_nat_1(2,1))),1)),u1_struct_0(k15_euclid(2))))) ) => ! [B] : ~ ( ~ v2_borsuk_7(A,k1_nat_1(2,1),2,k4_struct_0(k15_euclid(k1_nat_1(2,1))),1) & v5_pre_topc(A,k7_toprealb(k1_nat_1(2,1),k4_struct_0(k15_euclid(k1_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] : ( ( v1_int_1(C) & ~ v1_abian(C) ) => ~ ! [D] : ( m1_borsuk_2(D,k8_toprealb(2),k3_funct_2(u1_struct_0(k8_toprealb(k1_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(k1_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] : ( v1_xreal_0(E) => ( ( r1_xxreal_0(k5_numbers,E) & r1_xxreal_0(E,k7_xcmplx_0(1,2)) ) => k1_funct_1(k17_borsuk_7(k3_funct_2(u1_struct_0(k8_toprealb(k1_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(k1_nat_1(2,1))),u1_struct_0(k8_toprealb(2)),k16_borsuk_7(2,A),c18__borsuk_7),B,D),k2_xcmplx_0(E,k7_xcmplx_0(1,2))) = k2_xcmplx_0(k1_funct_1(k17_borsuk_7(k3_funct_2(u1_struct_0(k8_toprealb(k1_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(k1_nat_1(2,1))),u1_struct_0(k8_toprealb(2)),k16_borsuk_7(2,A),c18__borsuk_7),B,D),E),k7_xcmplx_0(C,2)) ) ) ) ) ) ) ) )).
fof(l105_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( 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(k9_fomodel0(B),D)) = k1_funct_1(k9_fomodel0(B),k3_relat_1(D,k20_fomodel0(B,A,C))) ) ) ) ) )).
fof(l105_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( v7_fomodel1(C,B) & m1_subset_1(C,k1_fomodel1(B)) ) => ! [D] : ( 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))),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))),k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))),k28_fomodel4(B)),D) = k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))),k28_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))),k30_fomodel4(B))) = k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))),k30_fomodel4(B)) & v11_fomodel4(A,B,D) ) => v2_fomodel3(k4_fomodel3(B,C,A),B,k35_fomodel1(B),C,k8_fomodel4(B,D,A)) ) ) ) ) )).
fof(l105_geomtrap,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_geomtrap(A) & l1_analoaf(A) ) => v4_geomtrap(k2_diraf(A)) ) )).
fof(l105_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( r1_xxreal_0(k3_finseq_1(B),3) => v5_glib_001(B,A) ) ) ) )).
fof(l105_jordan,axiom,( k17_euclid(k19_euclid(1,3)) = 1 )).
fof(l105_modelc_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_modelc_2(A) & l1_modelc_2(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( v7_ordinal1(D) => r5_modelc_2(A,B,C,D) ) => r4_modelc_2(A,B,C) ) ) ) ) )).
fof(l105_pepin,axiom,( k4_nat_d(k11_newton(3,k2_nat_1(256,16)),k4_pepin(4)) = 64 )).
fof(l105_toprealb,axiom,( k1_relset_1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k4_xcmplx_0(1),1)))),k2_partfun1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k4_xcmplx_0(1),1)))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k5_numbers,k28_sin_cos)))),c33__toprealb,k5_toprealb(c25__toprealb))) = c25__toprealb )).
fof(l106_borsuk_7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(k7_toprealb(k1_nat_1(2,1),k4_struct_0(k15_euclid(k1_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(k1_nat_1(2,1),k4_struct_0(k15_euclid(k1_nat_1(2,1))),1)),u1_struct_0(k15_euclid(2))))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_topmetr)) => ! [C] : ( m1_borsuk_2(C,k8_toprealb(2),k3_funct_2(u1_struct_0(k8_toprealb(k1_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(k1_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] : ( v1_int_1(D) => ( ! [E] : ( m1_borsuk_2(E,k8_toprealb(2),k3_funct_2(u1_struct_0(k8_toprealb(k1_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(k1_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] : ( v1_xreal_0(F) => ( ( r1_xxreal_0(k5_numbers,F) & r1_xxreal_0(F,k7_xcmplx_0(1,2)) ) => k1_funct_1(k17_borsuk_7(k3_funct_2(u1_struct_0(k8_toprealb(k1_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(k1_nat_1(2,1))),u1_struct_0(k8_toprealb(2)),k16_borsuk_7(2,A),c18__borsuk_7),B,E),k2_xcmplx_0(F,k7_xcmplx_0(1,2))) = k2_xcmplx_0(k1_funct_1(k17_borsuk_7(k3_funct_2(u1_struct_0(k8_toprealb(k1_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(k1_nat_1(2,1))),u1_struct_0(k8_toprealb(2)),k16_borsuk_7(2,A),c18__borsuk_7),B,E),F),k7_xcmplx_0(D,2)) ) ) ) ) => k1_funct_1(k17_borsuk_7(k3_funct_2(u1_struct_0(k8_toprealb(k1_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(k1_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(k1_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(k1_nat_1(2,1))),u1_struct_0(k8_toprealb(2)),k16_borsuk_7(2,A),c18__borsuk_7),B,C),k5_numbers),D) ) ) ) ) ) ) )).
fof(l106_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( v4_fomodel1(C,B) & m1_subset_1(C,k1_fomodel1(B)) ) => ! [D] : ( m1_subset_1(D,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))),k27_fomodel4(B)),D) & r1_tarski(k7_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))),k26_fomodel4(B),k28_fomodel4(B)),D) & v11_fomodel4(A,B,D) ) => v2_fomodel3(k4_fomodel3(B,C,A),B,k35_fomodel1(B),C,k8_fomodel4(B,D,A)) ) ) ) ) )).
fof(l106_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => r2_hidden(k22_interva1(A),k18_interva1(A)) ) )).
fof(l106_jordan,axiom,( k18_euclid(k19_euclid(1,3)) = 3 )).
fof(l106_modelc_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ~ ( B != k1_xboole_0 & r1_tarski(B,k2_finseq_1(A)) & ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(C,A) & r2_hidden(C,B) & ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(1,D) & ~ r1_xxreal_0(C,D) & r2_hidden(D,B) ) ) ) ) ) ) )).
fof(l106_pepin,axiom,( k4_nat_d(k11_newton(3,k2_nat_1(256,32)),k4_pepin(4)) = k2_nat_1(256,16) )).
fof(l106_toprealb,axiom,( r1_tarski(k2_relset_1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k5_numbers,k28_sin_cos)))),k2_partfun1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k4_xcmplx_0(1),1)))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k5_numbers,k28_sin_cos)))),c33__toprealb,k5_toprealb(c25__toprealb))),c26__toprealb) )).
fof(l107_borsuk_7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(k7_toprealb(k1_nat_1(2,1),k4_struct_0(k15_euclid(k1_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(k1_nat_1(2,1),k4_struct_0(k15_euclid(k1_nat_1(2,1))),1)),u1_struct_0(k15_euclid(2))))) ) => ~ ( ~ v2_borsuk_7(A,k1_nat_1(2,1),2,k4_struct_0(k15_euclid(k1_nat_1(2,1))),1) & v5_pre_topc(A,k7_toprealb(k1_nat_1(2,1),k4_struct_0(k15_euclid(k1_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(k1_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(k1_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(k1_nat_1(2,1))),u1_struct_0(k8_toprealb(2)),k16_borsuk_7(2,A),c18__borsuk_7)) ) ) )).
fof(l107_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( v10_fomodel1(C,B) & m1_subset_1(C,k1_fomodel1(B)) ) => ! [D] : ( m1_subset_1(D,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))),k27_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))),k29_fomodel4(B))) = k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))),k29_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))),k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))),k28_fomodel4(B)),D) = k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))),k28_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))),k30_fomodel4(B))) = k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))),k30_fomodel4(B)) & v11_fomodel4(A,B,D) ) => v2_fomodel3(k4_fomodel3(B,C,A),B,k35_fomodel1(B),C,k8_fomodel4(B,D,A)) ) ) ) ) )).
fof(l107_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => m4_glib_001(B,A,B) ) ) )).
fof(l107_jordan,axiom,( k17_euclid(k19_euclid(1,k4_xcmplx_0(3))) = 1 )).
fof(l107_pepin,axiom,( k4_nat_d(k11_newton(3,k2_nat_1(256,64)),k4_pepin(4)) = k2_nat_1(673,97) )).
fof(l107_toprealb,axiom,( v1_funct_1(k2_partfun1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k4_xcmplx_0(1),1)))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k5_numbers,k28_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(k4_xcmplx_0(1),1)))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k5_numbers,k28_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(k4_xcmplx_0(1),1)))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k5_numbers,k28_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)))))) )).
fof(l108_borsuk_7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(k7_toprealb(k1_nat_1(2,1),k4_struct_0(k15_euclid(k1_nat_1(2,1))),1)),u1_struct_0(k15_euclid(2))) & v5_pre_topc(A,k7_toprealb(k1_nat_1(2,1),k4_struct_0(k15_euclid(k1_nat_1(2,1))),1),k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k7_toprealb(k1_nat_1(2,1),k4_struct_0(k15_euclid(k1_nat_1(2,1))),1)),u1_struct_0(k15_euclid(2))))) ) => v2_borsuk_7(A,k1_nat_1(2,1),2,k4_struct_0(k15_euclid(k1_nat_1(2,1))),1) ) )).
fof(l108_card_3,axiom,( ! [A] : ! [B] : ( ( r1_tarski(B,A) & v4_card_3(A) ) => v4_card_3(B) ) )).
fof(l108_convex4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(l108_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m4_glib_001(C,A,B) => ! [D] : ( m4_glib_001(D,A,C) => m4_glib_001(D,A,B) ) ) ) ) )).
fof(l108_jordan,axiom,( k18_euclid(k19_euclid(1,k4_xcmplx_0(3))) = k4_xcmplx_0(3) )).
fof(l108_pepin,axiom,( k4_nat_d(k11_newton(3,k2_nat_1(256,128)),k4_pepin(4)) = k2_nat_1(256,256) )).
fof(l108_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_rat_1(C) => ( ~ r1_xxreal_0(A,k5_numbers) => k4_prepower(k6_prepower(A,B),C) = k6_prepower(A,k3_xcmplx_0(B,C)) ) ) ) ) )).
fof(l108_toprealb,axiom,( u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k4_xcmplx_0(1),1)))) = k1_rcomp_1(k4_xcmplx_0(1),1) )).
fof(l108_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) ) ) ) )).
fof(l109_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ( m4_glib_001(B,A,C) => r1_xxreal_0(k3_finseq_1(B),k3_finseq_1(C)) ) ) ) ) )).
fof(l109_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => r2_hidden(k23_interva1(A),k18_interva1(A)) ) )).
fof(l109_modelc_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v10_modelc_2(B) & l1_modelc_2(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(l109_pepin,axiom,( r1_nat_d(k4_pepin(3),k1_nat_1(k11_newton(3,k1_nat_1(k2_nat_1(32,k5_numbers),128)),1)) )).
fof(l109_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( r1_xxreal_0(1,A) & v2_comseq_2(B) & v2_comseq_2(C) & ! [D] : ( v7_ordinal1(D) => k1_funct_1(C,D) = k6_prepower(A,k1_funct_1(B,D)) ) ) => k1_seq_2(C) = k6_prepower(A,k1_seq_2(B)) ) ) ) ) )).
fof(l109_toprealb,axiom,( m1_subset_1(k5_toprealb(c25__toprealb),k1_zfmisc_1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k4_xcmplx_0(1),1)))))) )).
fof(l109_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( r1_tarski(A,k2_zfmisc_1(C,E)) & r1_tarski(B,k2_zfmisc_1(D,F)) & ! [G] : ! [H] : ( r2_hidden(k4_tarski(G,H),A) <=> r2_hidden(k4_tarski(G,H),B) ) ) => A = B ) )).
fof(l109_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( m1_zmodul01(D,A) => ( ( m1_zmodul01(B,C) & m1_zmodul01(B,D) ) => m1_zmodul01(B,k7_zmodul01(A,C,D)) ) ) ) ) ) )).
fof(l10_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l10_algstr_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_0)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_algstr_0)) => ! [C] : ( 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] : ( m1_subset_1(A,u1_struct_0(k3_algstr_0)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_algstr_0)) => ! [C] : ( 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 ) ) ) ) )).
fof(l10_algstr_3,axiom,( ! [A] : ( 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 ) )).
fof(l10_ami_2,axiom,( k1_afinsq_1(k6_afinsq_1(k4_ordinal1,k4_numbers)) = 2 )).
fof(l10_ami_wstd,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_setfam_1(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( 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(k4_ordinal1,k1_nat_1(A,1)) ) ) ) ) ) )).
fof(l10_amistd_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_setfam_1(B) => ! [C] : ( ( ~ v2_struct_0(C) & v2_memstr_0(C,B) & v3_memstr_0(C,B) & l1_extpro_1(C,B) ) => ? [D] : ( ~ v1_xboole_0(D) & m2_finseq_1(D,k4_ordinal1) & k7_partfun1(k4_ordinal1,D,1) = A & k7_partfun1(k4_ordinal1,D,k3_finseq_1(D)) = A & ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(1,E) => ( r1_xxreal_0(k3_finseq_1(D),E) | r2_hidden(k7_partfun1(k4_ordinal1,D,k1_nat_1(E,1)),k3_amistd_1(B,C,k7_partfun1(k4_ordinal1,D,E))) ) ) ) ) ) ) ) )).
fof(l10_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ! [K] : ( v1_xreal_0(K) => ( ( F = k3_rlvect_1(A,k1_rlvect_1(A,B,J),k1_rlvect_1(A,E,K)) & E = 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)) ) => F = k3_rlvect_1(A,k3_rlvect_1(A,k1_rlvect_1(A,B,k2_xcmplx_0(J,k3_xcmplx_0(K,G))),k1_rlvect_1(A,C,k3_xcmplx_0(K,H))),k1_rlvect_1(A,D,k3_xcmplx_0(K,I))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l10_arytm_0,axiom,( r2_hidden(k5_numbers,k4_ordinal1) )).
fof(l10_arytm_2,axiom,( r1_tarski(k4_ordinal1,k2_xboole_0(k6_subset_1(a_0_3_arytm_2,a_0_4_arytm_2),k4_ordinal1)) )).
fof(l10_borsuk_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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] : ( ( 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,k5_numbers) & C = k1_funct_1(E,1) & v5_pre_topc(F,k5_topmetr,A) & C = k1_funct_1(F,k5_numbers) & D = k1_funct_1(F,1) & ! [G] : ( ( 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,k5_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))) ) ) ) ) ) ) ) ) ) )).
fof(l10_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( 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] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(l10_cat_4,axiom,( ! [A] : ! [B] : v2_cat_1(k5_cat_4(A,B)) )).
fof(l10_cfdiff_1,axiom,( 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))) )).
fof(l10_cfdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(2)) => ( D = k10_finseq_1(A,B) => k9_euclid(2,D,C) = k10_finseq_1(k3_xcmplx_0(C,A),k3_xcmplx_0(C,B)) ) ) ) ) ) )).
fof(l10_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ( k2_afinsq_1(k4_compos_1(A)) = k6_domain_1(k4_ordinal1,k5_numbers) & r2_hidden(k5_numbers,k2_afinsq_1(k4_compos_1(A))) ) ) )).
fof(l10_comptrig,axiom,( ~ r1_xxreal_0(k2_xcmplx_0(k28_sin_cos,k7_xcmplx_0(k28_sin_cos,2)),k2_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),k7_xcmplx_0(k28_sin_cos,2))) )).
fof(l10_convex1,axiom,( ! [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) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => k1_convex1(A,B,k5_numbers) = k6_domain_1(u1_struct_0(A),k4_struct_0(A)) ) ) )).
fof(l10_convex3,axiom,( ! [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) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(l10_convfun1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k4_convfun1)) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k4_finseq_1(A)) => k1_funct_1(A,C) = k12_supinf_2(B,C) ) ) ) => k4_rlvect_1(k4_convfun1,A) = k18_rvsum_1(B) ) ) ) )).
fof(l10_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l10_csspace2,axiom,( k4_struct_0(k18_csspace) = k6_csspace )).
fof(l10_csspace4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => k1_funct_1(A,B) = k5_complex1 ) => ( v1_comseq_2(A) & k2_seq_4(k2_relset_1(k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,A))) = k5_numbers ) ) ) )).
fof(l10_ens_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( k4_tarski(k4_tarski(A,C),E) = k4_tarski(k4_tarski(B,D),F) => ( A = B & C = D ) ) )).
fof(l10_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => r1_tarski(k1_euclid_4(A,B,C),k1_euclid_4(A,C,B)) ) ) ) )).
fof(l10_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,k2_numbers) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l10_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => k7_euclid(3,k1_euclid_8(A,B,C),k1_euclid_8(D,E,F)) = k1_euclid_8(k2_xcmplx_0(A,D),k2_xcmplx_0(B,E),k2_xcmplx_0(C,F)) ) ) ) ) ) ) )).
fof(l10_fib_fusc,axiom,( k10_ami_3(1) != k10_ami_3(2) )).
fof(l10_fib_num,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k1_pre_ff(k1_nat_1(A,1)) != k5_numbers ) )).
fof(l10_fib_num4,axiom,( k2_power(k1_fib_num,2) = k7_xcmplx_0(k2_xcmplx_0(3,k3_square_1(5)),2) )).
fof(l10_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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 ) ) ) ) ) )).
fof(l10_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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] : ( ( v3_card_1(F,D) & m2_finseq_1(F,B) ) => ! [G] : ( ( v3_card_1(G,k5_numbers) & m2_finseq_1(G,A) ) => r2_relset_1(k4_ordinal1,C,k1_finseqop(A,B,C,E,G,F),k6_finseq_1(C)) ) ) ) ) ) ) ) )).
fof(l10_finset_1,axiom,( ! [A] : ( ( v1_finset_1(A) & ! [B] : ( r2_hidden(B,A) => v1_finset_1(B) ) ) => v1_finset_1(k3_tarski(A)) ) )).
fof(l10_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( 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) = k5_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) ) ) ) ) ) )).
fof(l10_flang_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( ( v1_relat_1(D) & v5_ordinal1(D) & v1_funct_1(D) & v1_finset_1(D) ) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(l10_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ~ r1_xboole_0(k4_finseq_2(C,A),k4_finseq_2(D,B)) => C = D ) ) ) )).
fof(l10_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(l10_gobrd11,axiom,( ! [A] : ( v1_xreal_0(A) => m1_subset_1(a_1_3_gobrd11(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) )).
fof(l10_gobrd12,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(B,k3_finseq_1(k2_goboard2(A))) & r1_xxreal_0(C,k1_matrix_0(k2_goboard2(A))) & r1_xxreal_0(D,k3_finseq_1(k2_goboard2(A))) & r1_xxreal_0(E,k1_matrix_0(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 != k1_nat_1(B,1) & B != k1_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))) ) ) ) ) ) ) ) )).
fof(l10_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( B != C & r1_aff_1(A,B,C,D) & ! [F] : ( 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] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l10_int_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_int_1(A,B) <=> ? [C] : ( v7_ordinal1(C) & B = k3_xcmplx_0(A,C) ) ) ) ) )).
fof(l10_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( r1_int_1(C,A) & r1_int_1(C,k6_xcmplx_0(A,B)) ) => r1_int_1(C,B) ) ) ) ) )).
fof(l10_int_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k8_newton) & v1_funct_1(B) & v1_partfun1(B,k8_newton) & v4_valued_0(B) & v2_pre_poly(B) ) => ( ( v1_int_7(B) & r2_hidden(A,k22_pre_poly(k8_newton,B)) ) => ( r1_int_1(A,k8_nat_3(k8_newton,B)) & ? [C] : ( v7_ordinal1(C) & r1_int_1(k1_newton(A,C),k8_nat_3(k8_newton,B)) ) ) ) ) ) )).
fof(l10_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(C,B) => r1_nat_d(k1_newton(A,C),k1_newton(A,B)) ) ) ) ) )).
fof(l10_integr16,axiom,( k17_rvsum_1(k6_finseq_1(k2_numbers)) = k5_numbers )).
fof(l10_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => m1_subset_1(a_1_3_jordan1(A),k1_zfmisc_1(k1_euclid(2))) ) )).
fof(l10_jordan1d,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => r1_xxreal_0(k5_numbers,k6_xcmplx_0(k3_xcmplx_0(2,A),1)) ) ) )).
fof(l10_kurato_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))))))))) ) ) )).
fof(l10_lopban_1,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l10_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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),D),E),k8_cqc_lang(A,k8_cqc_lang(A,C,D),E))),k4_cqc_the1(A)) ) ) ) ) ) )).
fof(l10_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) ) ) ) ) )).
fof(l10_mesfunc2,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l10_modelc_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => k3_finseq_1(k7_finseq_1(k7_finseq_1(k9_finseq_1(A),B),C)) = k1_nat_1(k1_nat_1(1,k3_finseq_1(B)),k3_finseq_1(C)) ) ) ) )).
fof(l10_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ( ( r2_modelc_2(A,C) & r2_modelc_2(B,C) ) => m1_subset_1(k2_tarski(A,B),k1_zfmisc_1(k13_modelc_2(C))) ) ) ) ) )).
fof(l10_nat_lat,axiom,( ! [A] : ( 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 ) ) )).
fof(l10_numbers,axiom,( ! [A] : ! [B] : ! [C] : ( k4_tarski(A,B) = k1_tarski(C) => ( C = k1_tarski(A) & A = B ) ) )).
fof(l10_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(l10_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(l10_parsp_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( k5_algstr_0(A,k8_group_1(A,B,k5_algstr_0(A,E,D)),k8_group_1(A,C,k5_algstr_0(A,E,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,E,D)) = k8_group_1(A,k3_rlvect_1(A,C,k4_algstr_0(A,k1_group_1(A))),k5_algstr_0(A,E,F)) ) ) ) ) ) ) ) )).
fof(l10_polyform,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( ~ r1_xxreal_0(A,k5_numbers) => r1_xxreal_0(k2_xcmplx_0(k5_numbers,1),A) ) ) )).
fof(l10_poset_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ! [H] : ( ( 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) & F = k3_funct_2(u1_struct_0(C),u1_struct_0(C),H,D) & r3_orders_2(C,D,F) & E = k3_funct_2(u1_struct_0(C),u1_struct_0(C),k1_abian(u1_struct_0(C),H,A),D) & G = k3_funct_2(u1_struct_0(C),u1_struct_0(C),k1_abian(u1_struct_0(C),H,B),D) ) => r3_orders_2(C,E,G) ) ) ) ) ) ) ) ) ) )).
fof(l10_prob_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(B) <=> v2_prob_1(k2_prob_1(A,B)) ) ) )).
fof(l10_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_projdes1(A,B,C,D,E) => r1_projdes1(A,C,D,E,B) ) ) ) ) ) ) )).
fof(l10_prvect_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) ) )).
fof(l10_qmax_1,axiom,( ! [A] : ( ( v5_relat_1(A,k12_prob_1) & v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k9_setfam_1(k1_numbers)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k1_numbers)))) ) => ( v2_prob_1(A) => ( v2_comseq_2(k8_prob_1(k1_numbers,k12_prob_1,A,c2__qmax_1)) & k1_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)) ) ) ) )).
fof(l10_ramsey_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ( ( 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 != k5_numbers & ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(l10_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ? [C] : ( 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(k19_finseq_1(k1_relset_1(A,B))) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(C)) => k1_funct_1(C,D) = k1_tarski(k1_funct_1(k19_finseq_1(k1_relset_1(A,B)),D)) ) ) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( 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)) ) => k12_supinf_2(B,E) = k12_supinf_2(B,F) ) ) ) ) ) ) ) )).
fof(l10_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ~ v4_xxreal_2(k3_limfunc1(A)) ) )).
fof(l10_real_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_real_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_real_lat)) => ! [C] : ( 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)) ) ) ) )).
fof(l10_realset2,axiom,( k9_xtuple_0(k13_funcop_1(1,k5_numbers,1)) = k6_domain_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,1,k5_numbers)) )).
fof(l10_ringcat1,axiom,( ! [A] : ( ( v3_ringcat1(A) & l1_ringcat1(A) ) => v3_ringcat1(g1_ringcat1(u1_ringcat1(A),u2_ringcat1(A),u3_ringcat1(A))) ) )).
fof(l10_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_ordinal1(k1_card_1(k5_rusub_4(A,B,C)),k1_card_1(B)) ) ) ) )).
fof(l10_rlaffin3,axiom,( ! [A] : ( v7_ordinal1(A) => u1_struct_0(k6_prvect_1(k2_vectsp_1,A)) = u1_struct_0(k15_euclid(A)) ) )).
fof(l10_rlvect_4,axiom,( m1_subset_1(k5_numbers,k1_numbers) )).
fof(l10_robbins4,axiom,( r1_xboole_0(k6_subset_1(3,2),2) )).
fof(l10_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( m1_rusub_1(D,A) => ( m1_rusub_1(B,D) => m1_rusub_1(k2_rusub_2(A,B,C),D) ) ) ) ) ) )).
fof(l10_scmfsa_1,axiom,( k1_funct_1(k4_scmfsa_1,k4_ordinal1) = k5_numbers )).
fof(l10_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v5_valued_0(A) <=> ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,A,k1_nat_1(B,1)),k9_nat_1(k1_numbers,A,B)) ) ) ) )).
fof(l10_series_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k6_xcmplx_0(k7_xcmplx_0(1,k1_nat_1(A,1)),k7_xcmplx_0(2,k2_nat_1(k1_nat_1(A,1),k1_nat_1(A,3)))) = k7_xcmplx_0(1,k1_nat_1(A,3)) ) )).
fof(l10_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => k3_square_1(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k3_xcmplx_0(A,B)),k1_square_1(B))) = k3_xcmplx_0(k7_xcmplx_0(1,2),k3_square_1(k2_xcmplx_0(k3_xcmplx_0(4,k2_xcmplx_0(k1_square_1(A),k1_square_1(B))),k3_xcmplx_0(k3_xcmplx_0(4,A),B)))) ) ) )).
fof(l10_sin_cos6,axiom,( k1_rcomp_1(k2_xcmplx_0(k28_sin_cos,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k5_numbers)),k2_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k5_numbers))) = k1_rcomp_1(k28_sin_cos,k3_xcmplx_0(2,k28_sin_cos)) )).
fof(l10_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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))) ) ) ) ) )).
fof(l10_taylor_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => k6_prepower(k23_sin_cos(A),B) = k23_sin_cos(k3_xcmplx_0(B,A)) ) ) )).
fof(l10_tex_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => m1_subset_1(u1_struct_0(B),k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(l10_topalg_4,axiom,( m1_subset_1(k5_numbers,u1_struct_0(k17_borsuk_1)) & m1_subset_1(1,u1_struct_0(k17_borsuk_1)) )).
fof(l10_topalg_5,axiom,( r1_xxreal_0(k6_xcmplx_0(k7_xcmplx_0(3,2),k7_xcmplx_0(1,2)),1) )).
fof(l10_topdim_1,axiom,( ! [A] : r2_hidden(A,k13_prob_1(u1_struct_0(k1_compts_1(A)),k4_ordinal1,k9_setfam_1(u1_struct_0(k1_compts_1(A))),k1_topdim_1(k1_compts_1(A)),1)) )).
fof(l10_topreal2,axiom,( k17_euclid(k19_euclid(1,1)) = 1 )).
fof(l10_toprealb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => m1_subset_1(D,u1_struct_0(A)) ) ) ) ) )).
fof(l10_uniform1,axiom,( k5_topmetr = k3_pcomps_1(k2_topmetr(k5_numbers,1)) )).
fof(l10_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( 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] : ( v7_ordinal1(E) => ! [F] : ( ( v5_relat_1(F,k3_qc_lang1(A)) & v3_card_1(F,E) & m2_finseq_1(F,k2_qc_lang1(A)) ) => ! [G] : ( 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] : ( 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] : ( 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] : ( 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))) ) ) ) ) ) ) )).
fof(l10_xcmplx_0,axiom,( r2_hidden(k5_numbers,k4_ordinal1) )).
fof(l10_xreal_0,axiom,( m1_subset_1(1,k2_arytm_2) )).
fof(l10_xxreal_0,axiom,( ~ r2_hidden(k2_xxreal_0,k2_arytm_2) )).
fof(l10_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => k2_xxreal_2(k1_tarski(A)) = A ) )).
fof(l10_zf_fund2,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( 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] : ( m1_subset_1(E,k4_ordinal1) => ( 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))) ) ) ) ) ) ) )).
fof(l10_zfmodel1,axiom,( ! [A] : ( v7_ordinal1(A) => ( ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(A,B) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_zf_lang(E) & m2_finseq_1(E,k4_ordinal1) ) => ! [F] : ( ( 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] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(l110_comput_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_funct_1(A) & v2_margrel1(A) & v3_margrel1(A,k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(k4_ordinal1),k4_ordinal1))) ) => ( k19_margrel1(A) = 2 => ( k9_xtuple_0(k5_funct_6(k10_finseq_1(k5_comput_1(3,1),k5_comput_1(3,3)))) = k9_subset_1(k3_finseq_2(k4_ordinal1),k1_relset_1(k3_finseq_2(k4_ordinal1),k5_comput_1(3,1)),k1_relset_1(k3_finseq_2(k4_ordinal1),k5_comput_1(3,3))) & k9_xtuple_0(k5_funct_6(k10_finseq_1(k5_comput_1(3,1),k5_comput_1(3,3)))) = k4_finseq_2(3,k4_ordinal1) & k9_xtuple_0(k3_relat_1(k5_funct_6(k10_finseq_1(k5_comput_1(3,1),k5_comput_1(3,3))),A)) = k4_finseq_2(3,k4_ordinal1) & ? [B] : ( v1_funct_1(B) & v2_margrel1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(k4_ordinal1),k4_ordinal1))) & B = k3_relat_1(k5_funct_6(k10_finseq_1(k5_comput_1(3,1),k5_comput_1(3,3))),A) & m2_rfunct_3(B,k3_finseq_2(k4_ordinal1),k4_ordinal1,k2_comput_1(k4_ordinal1)) & k19_margrel1(B) = 3 & v3_margrel1(B,k4_ordinal1) & ~ v1_xboole_0(B) ) ) ) ) )).
fof(l110_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( v10_fomodel1(C,B) & m1_subset_1(C,k1_fomodel1(B)) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ( ( v13_fomodel4(D,1,B) & v11_fomodel4(A,B,D) ) => v2_fomodel3(k4_fomodel3(B,C,A),B,k35_fomodel1(B),C,k8_fomodel4(B,D,A)) ) ) ) ) )).
fof(l110_pepin,axiom,( r1_nat_d(k4_pepin(4),k1_nat_1(k11_newton(3,k1_nat_1(k2_nat_1(64,k5_numbers),k2_nat_1(256,128))),1)) )).
fof(l110_toprealb,axiom,( u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k5_numbers,k28_sin_cos)))) = k1_rcomp_1(k5_numbers,k28_sin_cos) )).
fof(l110_zfmisc_1,axiom,( ! [A] : ! [B] : ( ( ! [C] : ~ ( r2_hidden(C,A) & ! [D] : ! [E] : C != k4_tarski(D,E) ) & ! [C] : ~ ( r2_hidden(C,B) & ! [D] : ! [E] : C != k4_tarski(D,E) ) & ! [C] : ! [D] : ( r2_hidden(k4_tarski(C,D),A) <=> r2_hidden(k4_tarski(C,D),B) ) ) => A = B ) )).
fof(l110_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( m1_zmodul01(D,A) => ( ( m1_zmodul01(B,D) & m1_zmodul01(C,D) ) => m1_zmodul01(k6_zmodul01(A,B,C),D) ) ) ) ) ) )).
fof(l111_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ( ( v13_fomodel4(C,k5_numbers,B) & v11_fomodel4(A,B,C) ) => ( v1_partfun1(k8_fomodel4(B,C,A),k35_fomodel1(B)) & v3_relat_2(k8_fomodel4(B,C,A)) & v8_relat_2(k8_fomodel4(B,C,A)) & m1_subset_1(k8_fomodel4(B,C,A),k1_zfmisc_1(k2_zfmisc_1(k35_fomodel1(B),k35_fomodel1(B)))) ) ) ) ) )).
fof(l111_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(A) & v1_finseq_1(A) ) => k19_rvsum_1(A) = 1 ) )).
fof(l111_toprealb,axiom,( m1_subset_1(k5_toprealb(c26__toprealb),k1_zfmisc_1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k5_numbers,k28_sin_cos)))))) )).
fof(l112_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => v4_lattice3(k21_interva1(A)) ) )).
fof(l112_toprealb,axiom,( k1_pre_topc(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k4_xcmplx_0(1),1))),c36__toprealb) = k1_pre_topc(k2_topalg_2,k5_toprealb(c25__toprealb)) )).
fof(l113_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => r1_bcialg_1(A,k2_bcialg_1(A,B),B) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(l113_fomodel0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( 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 ) ) ) ) ) ) ) )).
fof(l113_fomodel4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C))))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C))))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C))))) => ! [G] : ( v2_fomodel4(G,C) => ! [H] : ( v2_fomodel4(H,C) => ! [I] : ! [J] : ! [K] : ( ( v7_fomodel4(k4_subset_1(k9_funct_2(k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C))),D,E),C) & v7_fomodel4(k4_subset_1(k9_funct_2(k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C))),k4_subset_1(k9_funct_2(k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C))),D,E),F),C) & v5_fomodel4(I,A,C,D,G) & v5_fomodel4(J,A,C,E,H) & v5_fomodel4(K,B,C,F,k2_tarski(I,J)) ) => v5_fomodel4(K,k2_xcmplx_0(A,B),C,k4_subset_1(k9_funct_2(k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C))),k4_subset_1(k9_funct_2(k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C))),D,E),F),k2_xboole_0(G,H)) ) ) ) ) ) ) ) ) ) )).
fof(l113_jordan,axiom,( k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(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(k4_xcmplx_0(1),k4_xcmplx_0(3)),k19_euclid(k4_xcmplx_0(1),3)),k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(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,k4_xcmplx_0(3))),k1_rltopsp1(k15_euclid(2),k19_euclid(1,k4_xcmplx_0(3)),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3))))) )).
fof(l113_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => m1_subset_1(k10_xtuple_0(D),k1_zfmisc_1(u1_struct_0(k6_prvect_1(C,B)))) ) ) ) ) )).
fof(l113_toprealb,axiom,( k1_pre_topc(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k5_numbers,k28_sin_cos))),c37__toprealb) = k1_pre_topc(k2_topalg_2,k5_toprealb(c26__toprealb)) )).
fof(l114_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(l114_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ( ( v7_fomodel4(D,B) & r2_hidden(k25_fomodel4(B),D) & r2_hidden(k35_fomodel4(B),D) & v10_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) ) => v9_fomodel4(k35_fomodel2(B,C),B,D,A) ) ) ) ) )).
fof(l114_jordan,axiom,( r1_tarski(k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3)),k19_euclid(k4_xcmplx_0(1),3)),k4_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3)),k19_euclid(k4_xcmplx_0(1),3)),k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),3),k19_euclid(1,3)))) )).
fof(l114_toprealb,axiom,( 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))) )).
fof(l114_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( r2_hidden(A,k2_zfmisc_1(B,C)) & ! [D] : ! [E] : k4_tarski(D,E) != A ) )).
fof(l115_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(l115_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ( ( v10_fomodel4(A,B,D) & v7_fomodel4(D,B) & r2_hidden(k25_fomodel4(B),D) & r2_hidden(k35_fomodel4(B),D) ) => v9_fomodel4(k35_fomodel2(B,C),B,D,A) ) ) ) ) )).
fof(l115_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => r1_tarski(k11_intpro_1(k11_intpro_1(A)),k11_intpro_1(A)) ) )).
fof(l115_jordan,axiom,( r1_tarski(k4_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3)),k19_euclid(k4_xcmplx_0(1),3)),k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),3),k19_euclid(1,3))),k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(3),3)) )).
fof(l115_sin_cos,axiom,( k1_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k26_sin_cos,k1_rcomp_1(k5_numbers,1))) = k1_rcomp_1(k5_numbers,1) & ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k1_rcomp_1(k5_numbers,1)) => k1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k26_sin_cos,k1_rcomp_1(k5_numbers,1)),A) = k1_funct_1(k26_sin_cos,A) ) ) )).
fof(l115_toprealb,axiom,( 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)))) )).
fof(l115_waybel_1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(l115_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(1,k5_xcmplx_0(A)) = A ) )).
fof(l115_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => r1_tarski(u1_struct_0(B),u1_struct_0(k6_zmodul01(A,B,C))) ) ) ) )).
fof(l116_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) )).
fof(l116_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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] : ( ( v4_fomodel1(D,B) & m1_subset_1(D,k1_fomodel1(B)) ) => ! [E] : ( ( v4_fomodel1(E,B) & m1_subset_1(E,k1_fomodel1(B)) ) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ( ( v7_fomodel4(F,B) & r2_hidden(k25_fomodel4(B),F) & r2_hidden(k35_fomodel4(B),F) & r2_hidden(k26_fomodel4(B),F) & r2_hidden(k32_fomodel4(B),F) & v10_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) | v10_fomodel4(k2_xboole_0(A,k6_domain_1(k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0)),k42_fomodel1(B,k43_fomodel1(B,D),C))),B,F) ) ) ) ) ) ) ) )).
fof(l116_jordan,axiom,( r1_tarski(k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3)),k19_euclid(k4_xcmplx_0(1),3)),k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(3),3)) )).
fof(l116_modelc_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_modelc_2(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k23_modelc_3(D)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k23_modelc_3(D)))) ) => ( ( r2_hidden(k7_modelc_2(B,C),u1_modelc_3(D,k10_modelc_3(k3_funct_2(k4_ordinal1,k23_modelc_3(D),E,1),D))) & ! [F] : ( v7_ordinal1(F) => r6_modelc_3(D,k10_modelc_3(k1_funct_1(E,F),D),k10_modelc_3(k3_funct_2(k4_ordinal1,k23_modelc_3(D),E,k1_nat_1(F,1)),D)) ) & ! [F] : ( 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] : ( 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))) ) ) ) ) ) ) ) ) ) ) )).
fof(l116_sin_cos,axiom,( r2_fdiff_1(k26_sin_cos,k2_rcomp_1(k5_numbers,1)) & ! [A] : ( v1_xreal_0(A) => ~ ( r2_hidden(A,k2_rcomp_1(k5_numbers,1)) & r1_xxreal_0(k1_fdiff_1(k26_sin_cos,A),k5_numbers) ) ) )).
fof(l116_toprealb,axiom,( k1_relset_1(u1_struct_0(k15_euclid(2)),c38__toprealb) = u1_struct_0(k15_euclid(2)) )).
fof(l116_waybel_1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ! [D] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => k7_waybel_1(A,k7_waybel_1(A,B)) = B ) ) ) ) )).
fof(l116_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( ( v1_zmodul01(C) & m1_zmodul01(C,A) ) => ( r1_tarski(u1_struct_0(B),u1_struct_0(C)) => k6_zmodul01(A,B,C) = C ) ) ) ) )).
fof(l117_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => r1_bcialg_1(A,k2_bcialg_1(A,B),B) ) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(l117_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => v9_intpro_1(k11_intpro_1(A)) ) )).
fof(l117_jordan,axiom,( r1_tarski(k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),3),k19_euclid(1,3)),k4_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3)),k19_euclid(k4_xcmplx_0(1),3)),k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),3),k19_euclid(1,3)))) )).
fof(l117_toprealb,axiom,( v5_pre_topc(c38__toprealb,k15_euclid(2),k2_topalg_2) )).
fof(l117_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A)) ) ) ) ) )).
fof(l118_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( r2_hidden(C,k4_finseq_2(A,B)) => ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) ) ) ) )).
fof(l118_jordan,axiom,( r1_tarski(k4_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3)),k19_euclid(k4_xcmplx_0(1),3)),k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),3),k19_euclid(1,3))),k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(3),3)) )).
fof(l118_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k23_modelc_3(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k23_modelc_3(C)))) ) => ~ ( r2_hidden(k7_modelc_2(A,B),u1_modelc_3(C,k10_modelc_3(k3_funct_2(k4_ordinal1,k23_modelc_3(C),D,1),C))) & ! [E] : ( v7_ordinal1(E) => r6_modelc_3(C,k10_modelc_3(k1_funct_1(D,E),C),k10_modelc_3(k3_funct_2(k4_ordinal1,k23_modelc_3(C),D,k1_nat_1(E,1)),C)) ) & ? [E] : ( 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] : ( 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] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l118_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => ( r1_xxreal_0(k5_numbers,B) | r1_xxreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A)) ) ) ) ) )).
fof(l119_integra8,axiom,( ! [A] : ( ( ~ 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,k18_sin_cos,k18_sin_cos)) & v1_comseq_2(k2_partfun1(k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k18_sin_cos),A)) ) ) )).
fof(l119_jordan,axiom,( r1_tarski(k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),3),k19_euclid(1,3)),k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(3),3)) )).
fof(l119_sin_cos,axiom,( k1_funct_1(k26_sin_cos,k5_numbers) = k5_numbers & ~ r1_xxreal_0(k1_funct_1(k26_sin_cos,1),1) )).
fof(l11_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(l11_algseq_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r2_funct_2(k4_ordinal1,u1_struct_0(A),B,k2_algseq_1(A,k4_struct_0(A))) => k1_algseq_1(A,B) = k5_numbers ) ) ) )).
fof(l11_algstr_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_3)) => ! [B] : ( 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 ) ) )).
fof(l11_ami_2,axiom,( r1_tarski(k10_xtuple_0(k3_ami_2),k9_xtuple_0(k4_ami_2)) )).
fof(l11_ami_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(B,u1_struct_0(k1_ami_3)) & v5_memstr_0(B,k7_card_1(2),k1_ami_3,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_ami_3)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( r1_tarski(k1_ami_4,C) => ( r1_xxreal_0(k1_funct_1(B,k10_ami_3(k5_numbers)),k5_numbers) | r1_xxreal_0(k1_funct_1(B,k10_ami_3(1)),k5_numbers) | ( ~ r1_xxreal_0(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,C,B,k3_xcmplx_0(4,A)),k10_ami_3(k5_numbers)),k5_numbers) & ( ( ~ r1_xxreal_0(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,C,B,k3_xcmplx_0(4,A)),k10_ami_3(1)),k5_numbers) & k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,C,B,k3_xcmplx_0(4,A))) = k5_numbers ) | ( k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,C,B,k3_xcmplx_0(4,A)),k10_ami_3(1)) = k5_numbers & k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,C,B,k3_xcmplx_0(4,A))) = 4 ) ) ) ) ) ) ) ) )).
fof(l11_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => k1_rlvect_1(A,B,k2_xcmplx_0(k2_xcmplx_0(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)) ) ) ) ) ) )).
fof(l11_arytm_0,axiom,( r2_hidden(k5_numbers,k1_numbers) )).
fof(l11_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( 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) ) ) ) ) ) )).
fof(l11_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B),C) = k6_real_1(k9_nat_1(k1_numbers,A,C),k9_nat_1(k1_numbers,B,C)) ) ) ) )).
fof(l11_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(l11_bhsp_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & r1_xxreal_0(C,k9_complex1(k6_xcmplx_0(A,B))) ) ) => A = B ) ) ) )).
fof(l11_bintree2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => m2_finseq_1(k4_finseq_5(A,B),A) ) ) )).
fof(l11_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_boolealg(A,B,C) => r2_boolealg(A,C,B) ) ) ) ) )).
fof(l11_boolmark,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ! [C] : ( 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] : ( 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) ) ) ) )).
fof(l11_card_2,axiom,( ! [A] : ! [B] : r2_wellord2(k2_zfmisc_1(A,B),k2_zfmisc_1(k1_card_1(A),B)) )).
fof(l11_cfdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => m1_subset_1(k10_finseq_1(A,B),u1_struct_0(k4_real_ns1(2))) ) ) )).
fof(l11_clopban1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m2_funct_2(C,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => ! [D] : ( m2_funct_2(D,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(l11_complex1,axiom,( m1_subset_1(k5_numbers,k1_numbers) & m1_subset_1(1,k1_numbers) )).
fof(l11_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => k7_nat_d(k5_card_1(k4_compos_1(A)),1) = k5_numbers ) )).
fof(l11_comptrig,axiom,( k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k7_xcmplx_0(k28_sin_cos,2)) = k3_xcmplx_0(2,k28_sin_cos) )).
fof(l11_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(l11_convfun1,axiom,( ! [A] : ( m2_finseq_1(A,k6_numbers) => ! [B] : ( m1_subset_1(B,k6_numbers) => k4_extreal1(k8_finseq_1(k6_numbers,A,k12_finseq_1(k6_numbers,B))) = k3_supinf_2(k4_extreal1(A),B) ) ) )).
fof(l11_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l11_csspace2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k18_csspace)) => A = k2_csspace(A) ) )).
fof(l11_csspace4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_comseq_2(A) => v1_comseq_2(k55_valued_1(k4_ordinal1,k2_numbers,A)) ) ) )).
fof(l11_euclid,axiom,( ! [A] : ( ( 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) ) )).
fof(l11_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m1_subset_1(B,k2_numbers) => ( B = k5_numbers => k1_comptrig(k2_complex2(B,k4_xcmplx_0(k1_comptrig(A)))) = k5_numbers ) ) ) )).
fof(l11_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => ! [D] : ( 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)) ) ) ) ) )).
fof(l11_extreal1,axiom,( ! [A] : ( m2_finseq_1(A,k6_numbers) => ~ ( ~ r2_hidden(k2_supinf_1,k2_relset_1(k6_numbers,A)) & k4_extreal1(A) = k2_supinf_1 ) ) )).
fof(l11_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [C] : ( ( v1_funct_1(C) & v9_ordinal1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & v1_fdiff_1(C,k5_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v3_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,D) = k1_tarski(A) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,D)),k1_relset_1(k1_numbers,B)) ) => v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,C),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,D),B),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,D,B)))) ) ) ) => ( ! [C] : ( m1_rcomp_1(C,A) => ~ r1_tarski(C,k1_relset_1(k1_numbers,B)) ) | ( r1_fdiff_1(B,A) & ! [C] : ( ( v1_funct_1(C) & v9_ordinal1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & v1_fdiff_1(C,k5_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v3_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,D) = k1_tarski(A) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,D)),k1_relset_1(k1_numbers,B)) ) => k1_fdiff_1(B,A) = k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,C),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,D),B),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,D,B)))) ) ) ) ) ) ) ) ) )).
fof(l11_fib_fusc,axiom,( k10_ami_3(1) != k10_ami_3(3) )).
fof(l11_fib_num4,axiom,( k2_power(k2_fib_num,2) = k7_xcmplx_0(k6_xcmplx_0(3,k3_square_1(5)),2) )).
fof(l11_finseq_2,axiom,( ! [A] : ! [B] : k10_xtuple_0(k10_finseq_1(A,B)) = k2_tarski(A,B) )).
fof(l11_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( ( 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] : ( ( v3_card_1(F,k5_numbers) & m2_finseq_1(F,B) ) => r2_relset_1(k4_ordinal1,C,k3_finseqop(A,B,C,E,D,F),k6_finseq_1(C)) ) ) ) ) ) ) )).
fof(l11_fomodel0,axiom,( ! [A] : k4_finseq_2(k5_numbers,A) = k1_tarski(k1_xboole_0) )).
fof(l11_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_fomodel2(C,A,B) ) => ! [D] : ( ( 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(k1_fomodel0(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))) ) ) ) ) ) )).
fof(l11_gobrd11,axiom,( ! [A] : ( v1_xreal_0(A) => m1_subset_1(a_1_2_gobrd11(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) )).
fof(l11_gobrd12,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(B,k3_finseq_1(k2_goboard2(A))) & r1_xxreal_0(C,k1_matrix_0(k2_goboard2(A))) & r1_xxreal_0(D,k3_finseq_1(k2_goboard2(A))) & r1_xxreal_0(E,k1_matrix_0(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 != k1_nat_1(C,1) & C != k1_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))) ) ) ) ) ) ) ) )).
fof(l11_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => m1_group_6(k5_group_4(A,k8_group_2(A,B)),A,B) ) ) )).
fof(l11_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k12_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,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) ) ) ) ) ) ) )).
fof(l11_group_9,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(l11_henmodel,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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(k4_ordinal1,k2_finseq_1(k3_finseq_1(A)),k2_calcul_2(k3_finseq_1(A),k3_finseq_1(B))) ) ) )).
fof(l11_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( B != C & B != D & r1_aff_1(A,B,C,D) & ! [F] : ( 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] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l11_hurwitz,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k5_vfunct_1(k4_ordinal1,A,k5_vfunct_1(k4_ordinal1,A,B)),B) ) ) )).
fof(l11_int_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_int_1(A,B) & r1_int_1(B,A) ) => A = B ) ) ) )).
fof(l11_int_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( v1_int_2(A) & r1_int_2(A,B) & r1_nat_d(A,B) ) ) ) )).
fof(l11_integr16,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m1_subset_1(B,k2_numbers) => k17_rvsum_1(k8_finseq_1(k2_numbers,A,k12_finseq_1(k2_numbers,B))) = k2_xcmplx_0(k17_rvsum_1(A),B) ) ) )).
fof(l11_integr18,axiom,( v1_xreal_0(1) )).
fof(l11_integr19,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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] : ( v1_xreal_0(G) => ( r2_hidden(G,k3_integra5(k3_xxreal_0(C,D),k4_xxreal_0(C,D))) => r1_xxreal_0(k9_complex1(k1_funct_1(F,G)),E) ) ) ) => r1_xxreal_0(k9_complex1(k4_integra5(C,D,F)),k3_xcmplx_0(E,k9_complex1(k6_xcmplx_0(D,C)))) ) ) ) ) ) ) ) )).
fof(l11_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => m1_subset_1(a_1_0_jordan1(A),k1_zfmisc_1(k1_euclid(2))) ) )).
fof(l11_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(2,A) => k6_xcmplx_0(k3_xcmplx_0(2,A),2) = k7_nat_d(k3_xcmplx_0(2,A),2) ) ) )).
fof(l11_lpspace1,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l11_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => r2_hidden(k8_cqc_lang(A,k8_cqc_lang(A,C,k8_cqc_lang(A,k8_cqc_lang(A,k6_cqc_lang(A,B),B),B)),k8_cqc_lang(A,k8_cqc_lang(A,k6_cqc_lang(A,B),B),B)),k4_cqc_the1(A)) ) ) ) )).
fof(l11_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_matrix_2(C,k3_matrix_2(k1_nat_1(A,2))) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(l11_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( r2_hidden(k4_tarski(A,B),k2_matrix_0(C)) => k3_matrix_0(k1_numbers,k4_matrixr1(C),A,B) = k1_real_1(k3_matrix_0(k1_numbers,C,A,B)) ) ) ) ) )).
fof(l11_mesfunc9,axiom,( v1_xxreal_0(k5_numbers) )).
fof(l11_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_group_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k8_group_1(A,B,C) = k8_group_1(A,C,B) ) ) ) )).
fof(l11_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ~ ( ~ 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))) ) ) )).
fof(l11_morph_01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => k6_rusub_4(A,B,C) = k6_rusub_4(A,C,B) ) ) ) )).
fof(l11_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_prvect_2(A) ) => k4_finseq_1(k4_prvect_2(A)) = k4_finseq_1(A) ) )).
fof(l11_numbers,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ~ r2_hidden(k5_funct_4(k1_numbers,k5_ordinal1,k12_arytm_3,A,B),k1_numbers) ) ) )).
fof(l11_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_o_ring_1(B,A) => v3_o_ring_1(B,A) ) ) ) )).
fof(l11_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(l11_parsp_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k5_algstr_0(A,B,C) = k5_algstr_0(A,E,D) => D = k5_algstr_0(A,k3_rlvect_1(A,C,E),B) ) ) ) ) ) ) )).
fof(l11_poset_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( 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) => k3_funct_2(u1_struct_0(B),u1_struct_0(B),k1_abian(u1_struct_0(B),D,A),C) = C ) ) ) ) ) )).
fof(l11_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => m1_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)),A) ) )).
fof(l11_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_newton(B,C),k1_newton(A,C)) ) ) ) ) )).
fof(l11_qmax_1,axiom,( m2_prob_1(c2__qmax_1,k1_numbers,k12_prob_1) )).
fof(l11_random_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( m2_prob_1(C,A,k1_random_1(A)) => ! [D] : ( m2_prob_1(D,B,k1_random_1(B)) => ! [E] : ( ( 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] : ( ( 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] : ! [H] : ( ( r2_hidden(G,A) & r2_hidden(H,B) ) => k1_binop_1(E,G,H) = k1_extreal1(k12_supinf_2(C,k1_tarski(G)),k12_supinf_2(D,k1_tarski(H))) ) & ! [G] : ! [H] : ( ( r2_hidden(G,A) & r2_hidden(H,B) ) => k1_binop_1(F,G,H) = k1_extreal1(k12_supinf_2(C,k1_tarski(G)),k12_supinf_2(D,k1_tarski(H))) ) ) => r8_binop_1(A,B,k1_numbers,E,F) ) ) ) ) ) ) ) )).
fof(l11_realset2,axiom,( k9_xtuple_0(k13_funcop_1(k5_numbers,1,1)) = k6_domain_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,1)) )).
fof(l11_robbins4,axiom,( r1_ordinal1(1,2) )).
fof(l11_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l11_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ! [F] : ( v1_int_1(F) => ! [G] : ( m2_finseq_1(G,k4_numbers) => ! [H] : ( m2_finseq_1(H,k4_numbers) => ! [I] : ( v7_ordinal1(I) => ! [J] : ( v7_ordinal1(J) => ! [K] : ( v7_ordinal1(K) => ( ( 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 = k1_nat_1(k2_xcmplx_0(I,J),1) & k1_nat_1(I,1) = k1_funct_1(B,k1_scmp_gcd(K)) & k2_xcmplx_0(I,J) = k1_funct_1(B,k1_scmp_gcd(k1_nat_1(K,1))) & ! [L] : ( ( 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,k5_numbers) ) => ! [M] : ( ( v1_relat_1(M) & v4_relat_1(M,k4_ordinal1) & v5_relat_1(M,u1_compos_1(k1_scmpds_2)) & v1_funct_1(M) & v1_partfun1(M,k4_ordinal1) ) => ! [N] : ( m2_finseq_1(N,k4_numbers) => ! [O] : ( m2_finseq_1(O,k4_numbers) => ! [P] : ( v7_ordinal1(P) => ! [Q] : ( v7_ordinal1(Q) => ! [R] : ( v7_ordinal1(R) => ! [S] : ( v7_ordinal1(S) => ( ( k1_funct_1(L,D) = F & k1_nat_1(k3_xcmplx_0(2,P),1) = k1_funct_1(L,k2_scmpds_2(F,E)) & Q = k1_nat_1(k2_xcmplx_0(k2_xcmplx_0(I,J),k3_xcmplx_0(2,P)),1) & k2_xcmplx_0(I,R) = k1_funct_1(L,k1_scmp_gcd(Q)) & k2_xcmplx_0(I,S) = k1_funct_1(L,k1_scmp_gcd(k1_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] : ( v7_ordinal1(T) => ( r1_xxreal_0(1,T) => ( r1_xxreal_0(k1_nat_1(k3_xcmplx_0(2,P),1),T) | k1_funct_1(k6_scmpds_4(C,L,M),k1_scmp_gcd(k2_xcmplx_0(k2_xcmplx_0(I,J),T))) = k1_funct_1(L,k1_scmp_gcd(k2_xcmplx_0(k2_xcmplx_0(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(k3_xcmplx_0(2,P),1) & ! [T] : ( v7_ordinal1(T) => ( ( r1_xxreal_0(1,T) & r1_xxreal_0(T,J) ) => k1_funct_1(k6_scmpds_4(C,L,M),k1_scmp_gcd(k2_xcmplx_0(I,T))) = k1_funct_1(L,k1_scmp_gcd(k2_xcmplx_0(I,T))) ) ) ) ) & ( ~ r1_xxreal_0(S,R) => ( k1_funct_1(k6_scmpds_4(C,L,M),k2_scmpds_2(F,E)) = k1_nat_1(k3_xcmplx_0(2,P),3) & ! [T] : ( v7_ordinal1(T) => ( ( ( 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_xcmplx_0(I,T))) = k1_funct_1(L,k1_scmp_gcd(k2_xcmplx_0(I,T))) ) ) & ? [T] : ( v7_ordinal1(T) & r1_xxreal_0(R,T) & r1_xxreal_0(T,S) & k2_xcmplx_0(I,R) = k1_funct_1(k6_scmpds_4(C,L,M),k1_scmp_gcd(Q)) & k6_xcmplx_0(k2_xcmplx_0(I,T),1) = k1_funct_1(k6_scmpds_4(C,L,M),k1_scmp_gcd(k1_nat_1(Q,1))) & k1_nat_1(k2_xcmplx_0(I,T),1) = k1_funct_1(k6_scmpds_4(C,L,M),k1_scmp_gcd(k1_nat_1(Q,2))) & k2_xcmplx_0(I,S) = k1_funct_1(k6_scmpds_4(C,L,M),k1_scmp_gcd(k1_nat_1(Q,3))) & ! [U] : ( v7_ordinal1(U) => ( 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_xcmplx_0(I,U))),k1_funct_1(k6_scmpds_4(C,L,M),k1_scmp_gcd(k2_xcmplx_0(I,T)))) ) ) ) & ! [U] : ( v7_ordinal1(U) => ( 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_xcmplx_0(I,T))),k1_funct_1(k6_scmpds_4(C,L,M),k1_scmp_gcd(k2_xcmplx_0(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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l11_seq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v3_membered(B) ) => ( ( ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => r1_xxreal_0(A,C) ) ) & ! [C] : ( v1_xreal_0(C) => ( ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => r1_xxreal_0(C,D) ) ) => r1_xxreal_0(C,A) ) ) ) => A = k3_seq_4(B) ) ) ) )).
fof(l11_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v6_valued_0(A) <=> ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,A,k1_nat_1(B,1))) ) ) ) )).
fof(l11_series_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k6_xcmplx_0(k7_xcmplx_0(1,k1_nat_1(A,1)),k7_xcmplx_0(3,k2_nat_1(k1_nat_1(A,1),k1_nat_1(A,4)))) = k7_xcmplx_0(1,k1_nat_1(A,4)) ) )).
fof(l11_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => r1_xxreal_0(k3_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,2),k3_square_1(3)),k2_xcmplx_0(A,B)),k3_square_1(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k3_xcmplx_0(A,B)),k1_square_1(B)))) ) ) )).
fof(l11_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k2_xcmplx_0(k1_square_1(A),k1_square_1(B)) = 1 => ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) ) ) ) )).
fof(l11_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => r1_xxreal_0(2,k2_xcmplx_0(k23_sin_cos(A),k23_sin_cos(k4_xcmplx_0(A)))) ) )).
fof(l11_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( m1_subset_1(D,k5_finsub_1(k4_partfun1(A,B))) => ( ! [E] : ( r2_hidden(E,C) => r2_hidden(E,D) ) => r1_tarski(C,D) ) ) ) )).
fof(l11_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(l11_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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) ) ) ) )).
fof(l11_topreal2,axiom,( k18_euclid(k19_euclid(1,1)) = 1 )).
fof(l11_toprealb,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_pre_topc(C,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) => m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) )).
fof(l11_uniform1,axiom,( u1_struct_0(k5_topmetr) = u1_struct_0(k2_topmetr(k5_numbers,1)) )).
fof(l11_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(l11_waybel_4,axiom,( ! [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] : ( ( v1_waybel_4(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ! [D] : ( r2_hidden(k4_tarski(C,D),B) => r2_hidden(k4_tarski(C,D),k2_waybel_4(A)) ) ) ) )).
fof(l11_xcmplx_0,axiom,( m1_subset_1(k5_numbers,k1_numbers) )).
fof(l11_xreal_0,axiom,( r1_arytm_2(c1__xreal_0,c2__xreal_0) )).
fof(l11_xxreal_0,axiom,( ~ r2_hidden(k1_xxreal_0,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) )).
fof(l11_xxreal_3,axiom,( k1_xxreal_3(k1_xxreal_0,k1_xxreal_0) = k1_xxreal_0 )).
fof(l11_zfmodel2,axiom,( k2_zf_lang(k5_numbers) != k2_zf_lang(3) )).
fof(l120_clvect_1,axiom,( 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)) )).
fof(l120_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) ) => ( k15_finseq_1(A) = k1_xboole_0 => A = k1_xboole_0 ) ) )).
fof(l120_jordan,axiom,( r1_tarski(k1_rltopsp1(k15_euclid(2),k19_euclid(1,3),k19_euclid(1,k4_xcmplx_0(3))),k4_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k19_euclid(1,3),k19_euclid(1,k4_xcmplx_0(3))),k1_rltopsp1(k15_euclid(2),k19_euclid(1,k4_xcmplx_0(3)),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3))))) )).
fof(l121_card_3,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_finset_1(k1_relat_1(A)) => v1_finset_1(A) ) ) )).
fof(l121_clvect_1,axiom,( v1_funct_1(k8_funcop_1(k1_numbers,u1_struct_0(k3_clvect_1(o_0_5_clvect_1)),k10_subset_1(k5_numbers,k1_numbers))) & v1_funct_2(k8_funcop_1(k1_numbers,u1_struct_0(k3_clvect_1(o_0_5_clvect_1)),k10_subset_1(k5_numbers,k1_numbers)),u1_struct_0(k3_clvect_1(o_0_5_clvect_1)),k1_numbers) & m1_subset_1(k8_funcop_1(k1_numbers,u1_struct_0(k3_clvect_1(o_0_5_clvect_1)),k10_subset_1(k5_numbers,k1_numbers)),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k3_clvect_1(o_0_5_clvect_1)),k1_numbers))) )).
fof(l121_jordan,axiom,( r1_tarski(k4_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k19_euclid(1,3),k19_euclid(1,k4_xcmplx_0(3))),k1_rltopsp1(k15_euclid(2),k19_euclid(1,k4_xcmplx_0(3)),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3)))),k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(3),3)) )).
fof(l121_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) & v1_finseq_1(A) ) => ~ ( k3_finseq_1(A) != k5_numbers & ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) & v1_finseq_1(B) ) => ! [C] : ( v1_xcmplx_0(C) => A != k7_finseq_1(B,k9_finseq_1(C)) ) ) ) ) )).
fof(l121_toprealb,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l122_clvect_1,axiom,( m1_subset_1(k4_struct_0(o_0_5_clvect_1),u1_struct_0(k3_clvect_1(o_0_5_clvect_1))) )).
fof(l122_fomodel0,axiom,( ! [A] : ( v4_funct_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => r1_tarski(a_2_3_fomodel0(A,B),a_1_4_fomodel0(A)) ) ) )).
fof(l122_jordan,axiom,( r1_tarski(k1_rltopsp1(k15_euclid(2),k19_euclid(1,3),k19_euclid(1,k4_xcmplx_0(3))),k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(3),3)) )).
fof(l122_toprealb,axiom,( v1_funct_1(k8_funcop_1(k1_numbers,k1_numbers,c39__toprealb)) & m1_subset_1(k8_funcop_1(k1_numbers,k1_numbers,c39__toprealb),k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) )).
fof(l122_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) ) ) ) )).
fof(l123_clvect_1,axiom,( k1_funct_1(c2__clvect_1,k4_struct_0(o_0_5_clvect_1)) = k5_numbers )).
fof(l123_jordan,axiom,( r1_tarski(k1_rltopsp1(k15_euclid(2),k19_euclid(1,k4_xcmplx_0(3)),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3))),k4_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k19_euclid(1,3),k19_euclid(1,k4_xcmplx_0(3))),k1_rltopsp1(k15_euclid(2),k19_euclid(1,k4_xcmplx_0(3)),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3))))) )).
fof(l124_clvect_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_clvect_1(o_0_5_clvect_1))) => ! [B] : ( 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)) = k3_xcmplx_0(k9_complex1(B),k3_funct_2(u1_struct_0(k3_clvect_1(o_0_5_clvect_1)),k1_numbers,c2__clvect_1,A)) ) ) )).
fof(l124_integra8,axiom,( ! [A] : ( ( ~ 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,k22_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos))) & v1_comseq_2(k2_partfun1(k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)),A)) ) ) )).
fof(l124_jordan,axiom,( r1_tarski(k4_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k19_euclid(1,3),k19_euclid(1,k4_xcmplx_0(3))),k1_rltopsp1(k15_euclid(2),k19_euclid(1,k4_xcmplx_0(3)),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3)))),k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(3),3)) )).
fof(l124_toprealb,axiom,( ~ v1_xboole_0(k4_rcomp_1(k4_xcmplx_0(1),1)) & m1_subset_1(k4_rcomp_1(k4_xcmplx_0(1),1),k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(k3_rcomp_1(k5_numbers,k28_sin_cos)) & m1_subset_1(k3_rcomp_1(k5_numbers,k28_sin_cos),k1_zfmisc_1(k1_numbers)) )).
fof(l125_clvect_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_clvect_1(o_0_5_clvect_1))) => ! [B] : ( 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)),k3_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))) ) ) )).
fof(l125_integra8,axiom,( ! [A] : ( ( ~ 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,k22_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k16_sin_cos))) & v1_comseq_2(k2_partfun1(k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k16_sin_cos)),A)) ) ) )).
fof(l125_jordan,axiom,( r1_tarski(k1_rltopsp1(k15_euclid(2),k19_euclid(1,k4_xcmplx_0(3)),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3))),k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(3),3)) )).
fof(l125_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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,k3_matrix_1(B,A)),B,k6_prvect_1(B,A)) & k8_matrix13(B,k3_matrix_1(B,A)) = A ) ) ) )).
fof(l125_quaterni,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => r1_xxreal_0(k1_square_1(A),k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(C)),k1_square_1(D))) ) ) ) ) )).
fof(l125_toprealb,axiom,( u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(c45__toprealb))) = k5_toprealb(c45__toprealb) )).
fof(l125_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(l126_clvect_1,axiom,( ~ 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)) )).
fof(l126_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v13_fomodel4(B,k5_numbers,A) & v13_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] : ( v11_fomodel4(C,A,B) => ! [D] : ( ( 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,k8_eqrel_1(k35_fomodel1(A),k8_fomodel4(A,B,C)),k41_fomodel4(A,B,C),D) = 1 <=> r2_hidden(D,C) ) ) ) ) ) )).
fof(l126_jordan,axiom,( v2_sppol_1(k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3)),k19_euclid(k4_xcmplx_0(1),3))) )).
fof(l126_quaterni,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => r1_xxreal_0(k1_square_1(C),k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(C)),k1_square_1(D))) ) ) ) ) )).
fof(l126_toprealb,axiom,( u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(c46__toprealb))) = k5_toprealb(c46__toprealb) )).
fof(l126_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k4_xxreal_3(A,k1_xxreal_3(k5_numbers,B)) = k1_xxreal_3(k4_xxreal_3(A,k5_numbers),k4_xxreal_3(A,B)) ) ) )).
fof(l127_clvect_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(c3__clvect_1)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c3__clvect_1)) => ! [C] : ( v1_xcmplx_0(C) => ( ( k2_normsp_0(c3__clvect_1,A) = k5_numbers => A = k4_struct_0(c3__clvect_1) ) & ( A = k4_struct_0(c3__clvect_1) => k2_normsp_0(c3__clvect_1,A) = k5_numbers ) & k2_normsp_0(c3__clvect_1,k1_clvect_1(c3__clvect_1,A,C)) = k3_xcmplx_0(k9_complex1(C),k2_normsp_0(c3__clvect_1,A)) & r1_xxreal_0(k2_normsp_0(c3__clvect_1,k1_algstr_0(c3__clvect_1,A,B)),k2_xcmplx_0(k2_normsp_0(c3__clvect_1,A),k2_normsp_0(c3__clvect_1,B))) ) ) ) ) )).
fof(l127_jordan,axiom,( v2_sppol_1(k1_rltopsp1(k15_euclid(2),k19_euclid(1,k4_xcmplx_0(3)),k19_euclid(1,3))) )).
fof(l127_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k25_modelc_2(A)) => k29_modelc_2(A,B,k5_numbers) = B ) ) )).
fof(l127_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l127_quaterni,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => r1_xxreal_0(k1_square_1(D),k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(C)),k1_square_1(D))) ) ) ) ) )).
fof(l127_toprealb,axiom,( u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k7_xcmplx_0(1,2),k2_xcmplx_0(k7_xcmplx_0(1,2),c5__toprealb))))) = k5_toprealb(k2_rcomp_1(k7_xcmplx_0(1,2),k2_xcmplx_0(k7_xcmplx_0(1,2),c5__toprealb))) )).
fof(l127_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k4_xxreal_3(k5_numbers,k1_xxreal_3(A,B)) = k1_xxreal_3(k4_xxreal_3(k5_numbers,A),k4_xxreal_3(k5_numbers,B)) ) ) )).
fof(l127_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => r1_tarski(u1_struct_0(k7_zmodul01(A,B,C)),u1_struct_0(B)) ) ) ) )).
fof(l128_bcialg_1,axiom,( ! [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) ) => ( v20_bcialg_1(A) <=> v13_bcialg_1(A) ) ) )).
fof(l128_jordan,axiom,( v2_sppol_1(k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(k4_xcmplx_0(1),3))) )).
fof(l128_modelc_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(l128_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l128_quaterni,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k1_square_1(B),A) => r1_xxreal_0(B,k3_square_1(A)) ) ) ) )).
fof(l128_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k1_rcomp_1(k5_numbers,1)) => r1_xxreal_0(k5_numbers,k1_funct_1(k16_sin_cos,A)) ) ) )).
fof(l128_toprealb,axiom,( k1_relset_1(k1_numbers,k1_fcont_1(k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos))),1)) = u1_struct_0(k2_topalg_2) )).
fof(l128_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_xxreal_0(B) & ~ v3_xxreal_0(B) & v1_xreal_0(B) ) => k5_numbers = k3_xcmplx_0(B,A) ) ) )).
fof(l128_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(l129_bcialg_1,axiom,( ! [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) ) => ( v20_bcialg_1(A) => v17_bcialg_1(A) ) ) )).
fof(l129_jordan,axiom,( v2_sppol_1(k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3)))) )).
fof(l129_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l129_quaterni,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ! [K] : ( v1_xreal_0(K) => ! [L] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l129_toprealb,axiom,( k1_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fcont_1(k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos))),1),k5_toprealb(c46__toprealb))) = k5_toprealb(c46__toprealb) )).
fof(l129_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(l12_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l12_algstr_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_3)) => ! [B] : ( 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 ) ) )).
fof(l12_ami_2,axiom,( k9_xtuple_0(k3_relat_1(k3_ami_2,k4_ami_2)) = k1_ami_2 )).
fof(l12_ami_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(B,u1_struct_0(k1_ami_3)) & v5_memstr_0(B,k7_card_1(2),k1_ami_3,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_ami_3)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( r1_tarski(k1_ami_4,C) => ( r1_xxreal_0(k1_funct_1(B,k10_ami_3(k5_numbers)),k5_numbers) | r1_xxreal_0(k1_funct_1(B,k10_ami_3(1)),k5_numbers) | r1_xxreal_0(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,C,B,k3_xcmplx_0(4,A)),k10_ami_3(1)),k5_numbers) | ( k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,C,B,k2_nat_1(4,k1_nat_1(A,1))),k10_ami_3(k5_numbers)) = k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,C,B,k3_xcmplx_0(4,A)),k10_ami_3(1)) & k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,C,B,k2_nat_1(4,k1_nat_1(A,1))),k10_ami_3(1)) = k5_int_1(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,C,B,k3_xcmplx_0(4,A)),k10_ami_3(k5_numbers)),k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,C,B,k3_xcmplx_0(4,A)),k10_ami_3(1))) ) ) ) ) ) ) )).
fof(l12_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(l12_arithm,axiom,( k5_xcmplx_0(1) = 1 )).
fof(l12_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( r2_hidden(A,k6_asympt_0(B)) & r2_hidden(B,k6_asympt_0(A)) ) <=> k6_asympt_0(A) = k6_asympt_0(B) ) ) ) )).
fof(l12_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( r2_hidden(B,k2_c0sp2(A)) => r2_hidden(B,k6_c0sp1(u1_struct_0(A))) ) ) )).
fof(l12_card_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) ) => ! [B] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(l12_cfdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(2))) => ! [F] : ( 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(k2_xcmplx_0(A,C),k2_xcmplx_0(B,D)) & k5_algstr_0(k4_real_ns1(2),E,F) = k10_finseq_1(k6_xcmplx_0(A,C),k6_xcmplx_0(B,D)) ) ) ) ) ) ) ) ) )).
fof(l12_classes1,axiom,( ! [A] : ( k2_classes1(A,k5_ordinal1) = k1_tarski(A) & ! [B] : ( 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] : ( v3_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) ) => ( ( v4_ordinal1(B) & k9_xtuple_0(C) = B & ! [D] : ( v3_ordinal1(D) => ( r2_hidden(D,B) => k1_funct_1(C,D) = k2_classes1(A,D) ) ) ) => ( B = k5_ordinal1 | k2_classes1(A,B) = k3_xboole_0(k3_tarski(k10_xtuple_0(C)),k1_classes1(A)) ) ) ) ) ) )).
fof(l12_complex1,axiom,( k5_numbers = k5_arytm_0(c1__complex1,c1__complex1) )).
fof(l12_complex2,axiom,( k1_comptrig(k5_numbers) = k5_numbers )).
fof(l12_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => k62_valued_1(k4_compos_1(A)) = k5_numbers ) )).
fof(l12_comptrig,axiom,( ~ r1_xxreal_0(k3_xcmplx_0(2,k28_sin_cos),k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos)) )).
fof(l12_comseq_2,axiom,( v1_funct_1(k8_funcop_1(k2_numbers,k4_ordinal1,k5_complex1)) & v1_funct_2(k8_funcop_1(k2_numbers,k4_ordinal1,k5_complex1),k4_ordinal1,k2_numbers) & m1_subset_1(k8_funcop_1(k2_numbers,k4_ordinal1,k5_complex1),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) )).
fof(l12_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l12_convex1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k1_convex1(A,k1_convex1(A,B,D),C) = k1_convex1(A,B,k3_xcmplx_0(C,D)) ) ) ) ) )).
fof(l12_convex2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(l12_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l12_csspace2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k18_csspace)) => ! [B] : ( 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)) ) ) )).
fof(l12_csspace3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(B) & v2_comseq_2(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [E] : ( v7_ordinal1(E) => k1_funct_1(D,E) = k2_xcmplx_0(k9_complex1(k6_xcmplx_0(k1_funct_1(B,E),A)),k1_funct_1(C,E)) ) => ( v2_comseq_2(D) & k1_seq_2(D) = k2_xcmplx_0(k9_complex1(k6_xcmplx_0(k3_comseq_2(B),A)),k1_seq_2(C)) ) ) ) ) ) ) ) )).
fof(l12_csspace4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_comseq_2(k55_valued_1(k4_ordinal1,k2_numbers,A)) => v1_comseq_2(A) ) ) )).
fof(l12_dtconstr,axiom,( u1_struct_0(k5_dtconstr) = k7_domain_1(k4_ordinal1,k5_numbers,1) )).
fof(l12_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(l12_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m1_subset_1(B,k2_numbers) => ( ( B = k5_numbers & k1_comptrig(A) = k5_numbers ) => k3_complex2(A,B) = k5_numbers ) ) ) )).
fof(l12_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => ! [D] : ( 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)) ) ) ) ) )).
fof(l12_fib_fusc,axiom,( k10_ami_3(2) != k10_ami_3(3) )).
fof(l12_fib_num4,axiom,( k2_power(k2_fib_num,3) = k6_xcmplx_0(2,k3_square_1(5)) )).
fof(l12_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( 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] : ( ( v3_card_1(F,k5_numbers) & m2_finseq_1(F,A) ) => r2_relset_1(k4_ordinal1,C,k2_finseqop(A,B,C,E,F,D),k6_finseq_1(C)) ) ) ) ) ) ) )).
fof(l12_fomodel0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : k4_finseq_2(A,B) = k1_funct_2(k2_finseq_1(A),B) ) )).
fof(l12_fomodel3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_funct_2(C,k2_finseq_1(A),B,k9_funct_2(k2_finseq_1(A),B)) => ! [D] : ( m2_funct_2(D,k2_finseq_1(A),B,k9_funct_2(k2_finseq_1(A),B)) => ! [E] : ( 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] : ( m2_subset_1(F,k4_ordinal1,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) ) ) ) ) ) ) ) )).
fof(l12_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( 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)))) => v6_fomodel4(B,A) ) ) ) ) )).
fof(l12_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(l12_gobrd11,axiom,( ! [A] : ( v1_xreal_0(A) => m1_subset_1(a_1_1_gobrd11(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) )).
fof(l12_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v2_group_9(C,A) & m1_group_9(C,A,B) ) => ! [D] : ( ( v2_group_9(D,A) & m1_group_9(D,A,B) ) => ( u1_struct_0(C) = u1_struct_0(D) => C = D ) ) ) ) )).
fof(l12_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( B = C => ( D = B | ( ~ ( ~ r1_aff_1(A,D,B,E) & r1_aff_1(A,D,E,F) & r2_analoaf(A,B,E,C,F) ) & ~ ( r1_aff_1(A,D,B,E) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & ~ r1_aff_1(A,D,B,G) & r1_aff_1(A,D,G,H) & r2_analoaf(A,B,G,C,H) & r2_analoaf(A,G,E,H,F) & r1_aff_1(A,D,B,F) ) ) ) ) | E = F ) ) ) ) ) ) ) ) )).
fof(l12_int_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( ~ r1_xxreal_0(1,A) => A = k5_numbers ) ) )).
fof(l12_int_4,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => r1_xxreal_0(k2_xcmplx_0(1,k5_numbers),A) ) ) )).
fof(l12_int_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k8_newton) & v1_funct_1(C) & v1_partfun1(C,k8_newton) & v4_valued_0(C) & v2_pre_poly(C) ) => ! [D] : ( ( v7_ordinal1(D) & v1_int_2(D) ) => ( ( k3_finseq_1(B) = A & v1_int_7(C) & r1_int_1(D,k8_nat_3(k8_newton,C)) & k8_nat_3(k8_newton,C) = k3_wsierp_1(B) & B = k3_relat_1(k19_finseq_1(k22_pre_poly(k8_newton,C)),C) ) => ( k8_nat_3(k8_newton,C) = 1 | r2_hidden(D,k22_pre_poly(k8_newton,C)) ) ) ) ) ) ) )).
fof(l12_integr12,axiom,( k3_limfunc1(k5_numbers) = a_0_0_integr12 )).
fof(l12_integr19,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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))) ) ) ) ) )).
fof(l12_jgraph_5,axiom,( r2_hidden(k5_numbers,k1_rcomp_1(k5_numbers,1)) )).
fof(l12_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => m1_subset_1(a_1_2_jordan1(A),k1_zfmisc_1(k1_euclid(2))) ) )).
fof(l12_jordan1c,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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))) ) ) ) ) )).
fof(l12_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => k6_xcmplx_0(k3_xcmplx_0(2,A),1) = k7_nat_d(k3_xcmplx_0(2,A),1) ) ) )).
fof(l12_jordan5a,axiom,( ! [A] : ( ( 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] : ( ( 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(k5_numbers,1))) & ~ v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,B,k1_rcomp_1(k5_numbers,1))) ) ) ) )).
fof(l12_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( v1_lattice6(A) & v2_lattice6(A) ) ) )).
fof(l12_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => r2_hidden(k8_cqc_lang(A,C,k8_cqc_lang(A,k8_cqc_lang(A,k6_cqc_lang(A,B),B),B)),k4_cqc_the1(A)) ) ) ) )).
fof(l12_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ( r2_hidden(A,k4_finseq_1(B)) => k2_wsierp_1(k17_finseq_1(k4_ordinal1,A,B)) = k2_xcmplx_0(k2_wsierp_1(k17_finseq_1(k4_ordinal1,k7_nat_d(A,1),B)),k1_funct_1(B,A)) ) ) ) )).
fof(l12_mesfun10,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l12_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ~ ( ~ 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))) ) ) ) )).
fof(l12_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( m2_pboole(E,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [F] : ( m1_subset_1(F,k3_msualg_1(A,D,B)) => ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) ) => ! [H] : ( ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l12_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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) ) ) ) ) )).
fof(l12_neckla_2,axiom,( u1_struct_0(k4_necklace(4)) = k2_enumset1(k5_numbers,1,2,3) )).
fof(l12_ntalgo_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => ! [B] : ( m1_subset_1(B,k4_numbers) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_numbers))) ) => ( ( k9_nat_1(k4_numbers,C,k5_numbers) = A & k9_nat_1(k4_numbers,D,k5_numbers) = B & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( k9_nat_1(k4_numbers,C,k1_nat_1(E,1)) = k9_nat_1(k4_numbers,D,E) & k9_nat_1(k4_numbers,D,k1_nat_1(E,1)) = k5_int_1(k9_nat_1(k4_numbers,C,E),k9_nat_1(k4_numbers,D,E)) ) ) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( k9_nat_1(k4_numbers,D,E) != k5_numbers => k3_int_2(k9_nat_1(k4_numbers,C,E),k9_nat_1(k4_numbers,D,E)) = k3_int_2(k9_nat_1(k4_numbers,C,k1_nat_1(E,1)),k9_nat_1(k4_numbers,D,k1_nat_1(E,1))) ) ) ) ) ) ) ) )).
fof(l12_orders_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(l12_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(l12_pdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(2)) => ! [E] : ( ( 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] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & D = k10_finseq_1(F,G) & ? [H] : ( m1_rcomp_1(H,F) & r1_tarski(H,k1_relset_1(k1_numbers,k1_pdiff_2(2,1,E,D))) & ? [I] : ( v1_funct_1(I) & v3_fdiff_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [J] : ( v1_funct_1(J) & v2_fdiff_1(J) & m1_subset_1(J,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & C = k1_funct_1(I,1) & ! [K] : ( v1_xreal_0(K) => ( r2_hidden(K,H) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(2,1,E,D),K),k1_funct_1(k1_pdiff_2(2,1,E,D),F)) = k2_xcmplx_0(k1_funct_1(I,k6_xcmplx_0(K,F)),k1_funct_1(J,k6_xcmplx_0(K,F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l12_pdiff_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_real_ns1(A)))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( v3_nfcont_1(C,k4_real_ns1(A)) & r2_hidden(B,C) & r1_xxreal_0(1,D) & r1_xxreal_0(D,A) & ! [E] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(l12_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k12_polynom1(A,B))) => ( C = D => k5_vfunct_1(k15_pre_poly(A),B,C) = k4_algstr_0(k12_polynom1(A,B),D) ) ) ) ) ) )).
fof(l12_poset_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( ( 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] : ( ( 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) & D = k3_funct_2(u1_struct_0(B),u1_struct_0(B),k1_abian(u1_struct_0(B),F,A),C) & E = k3_funct_2(u1_struct_0(B),u1_struct_0(B),k1_abian(u1_struct_0(B),G,A),C) ) => r3_orders_2(B,D,E) ) ) ) ) ) ) ) ) )).
fof(l12_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l12_qmax_1,axiom,( k9_xtuple_0(k6_domain_1(k2_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_zfmisc_1(k2_zfmisc_1(k12_prob_1,k1_numbers))),k1_domain_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_zfmisc_1(k2_zfmisc_1(k12_prob_1,k1_numbers)),k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers),c3__qmax_1))) = k6_domain_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers)) )).
fof(l12_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(2,A) => k11_radix_1(k6_xcmplx_0(k1_radix_1(A),1)) = 1 ) ) )).
fof(l12_realset2,axiom,( k5_binop_1(2,k1_realset2,k10_subset_1(k5_numbers,2),k10_subset_1(k5_numbers,2)) = k10_subset_1(k5_numbers,2) )).
fof(l12_rfunct_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( r1_rfunct_4(B,C) => r1_rfunct_4(k15_valued_1(k1_numbers,k1_numbers,B,A),C) ) ) ) )).
fof(l12_ringcat1,axiom,( ! [A] : ( ( v3_ringcat1(A) & l1_ringcat1(A) ) => v1_ringcat1(u3_ringcat1(A),u1_ringcat1(A),u2_ringcat1(A)) ) )).
fof(l12_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l12_robbins4,axiom,( r1_xboole_0(k6_subset_1(3,2),1) )).
fof(l12_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( m1_rusub_1(D,A) => ( m1_rusub_1(B,C) => m1_rusub_1(B,k1_rusub_2(A,C,D)) ) ) ) ) ) )).
fof(l12_scmfsa9a,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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_sf_mastr(k1_scmfsa8b(A,k3_scmfsa6a(B,k1_scmfsa8a(k5_numbers)),k4_compos_1(k1_scmfsa_2))) = k2_sf_mastr(k1_funct_4(k1_scmfsa8b(A,k3_scmfsa6a(B,k1_scmfsa8a(k5_numbers)),k4_compos_1(k1_scmfsa_2)),k16_funcop_1(k1_nat_1(k5_card_1(B),4),k11_scmfsa_2(k5_numbers)))) ) ) )).
fof(l12_scmfsa_1,axiom,( ! [A] : ( m2_subset_1(A,k1_scmfsa_1,k2_scmfsa_1) => k3_funct_2(k1_scmfsa_1,k7_card_1(3),k4_scmfsa_1,A) = 1 ) )).
fof(l12_scpinvar,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ( k1_funct_1(B,k2_scmp_gcd) = k5_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) = k5_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) ) ) ) ) )).
fof(l12_scpisort,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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))) = k1_nat_1(k5_card_1(D),4) ) ) ) ) )).
fof(l12_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ! [F] : ( v1_int_1(F) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ! [I] : ( v7_ordinal1(I) => ( ( k1_funct_1(B,D) = F & 1 = k1_funct_1(B,k2_scmpds_2(F,E)) & I = k1_nat_1(k2_xcmplx_0(G,H),1) & k1_nat_1(G,1) = k1_funct_1(B,k1_scmp_gcd(I)) & k2_xcmplx_0(G,H) = k1_funct_1(B,k1_scmp_gcd(k1_nat_1(I,1))) & ! [J] : ( ( 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,k5_numbers) ) => ! [K] : ( ( v1_relat_1(K) & v4_relat_1(K,k4_ordinal1) & v5_relat_1(K,u1_compos_1(k1_scmpds_2)) & v1_funct_1(K) & v1_partfun1(K,k4_ordinal1) ) => ! [L] : ( m2_finseq_1(L,k4_numbers) => ! [M] : ( m2_finseq_1(M,k4_numbers) => ! [N] : ( v7_ordinal1(N) => ! [O] : ( v7_ordinal1(O) => ! [P] : ( v7_ordinal1(P) => ! [Q] : ( v7_ordinal1(Q) => ( ( k1_funct_1(J,D) = F & k1_nat_1(k3_xcmplx_0(2,N),1) = k1_funct_1(J,k2_scmpds_2(F,E)) & O = k1_nat_1(k2_xcmplx_0(k2_xcmplx_0(G,H),k3_xcmplx_0(2,N)),1) & k2_xcmplx_0(G,P) = k1_funct_1(J,k1_scmp_gcd(O)) & k2_xcmplx_0(G,Q) = k1_funct_1(J,k1_scmp_gcd(k1_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] : ( v7_ordinal1(R) => ( r1_xxreal_0(1,R) => ( r1_xxreal_0(k1_nat_1(k3_xcmplx_0(2,N),1),R) | k1_funct_1(k6_scmpds_4(C,J,K),k1_scmp_gcd(k2_xcmplx_0(k2_xcmplx_0(G,H),R))) = k1_funct_1(J,k1_scmp_gcd(k2_xcmplx_0(k2_xcmplx_0(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(k3_xcmplx_0(2,N),1) & ! [R] : ( v7_ordinal1(R) => ( ( r1_xxreal_0(1,R) & r1_xxreal_0(R,H) ) => k1_funct_1(k6_scmpds_4(C,J,K),k1_scmp_gcd(k2_xcmplx_0(G,R))) = k1_funct_1(J,k1_scmp_gcd(k2_xcmplx_0(G,R))) ) ) ) ) & ( ~ r1_xxreal_0(Q,P) => ( k1_funct_1(k6_scmpds_4(C,J,K),k2_scmpds_2(F,E)) = k1_nat_1(k3_xcmplx_0(2,N),3) & ! [R] : ( v7_ordinal1(R) => ( ( ( 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_xcmplx_0(G,R))) = k1_funct_1(J,k1_scmp_gcd(k2_xcmplx_0(G,R))) ) ) & ? [R] : ( v7_ordinal1(R) & r1_xxreal_0(P,R) & r1_xxreal_0(R,Q) & k2_xcmplx_0(G,P) = k1_funct_1(k6_scmpds_4(C,J,K),k1_scmp_gcd(O)) & k6_xcmplx_0(k2_xcmplx_0(G,R),1) = k1_funct_1(k6_scmpds_4(C,J,K),k1_scmp_gcd(k1_nat_1(O,1))) & k1_nat_1(k2_xcmplx_0(G,R),1) = k1_funct_1(k6_scmpds_4(C,J,K),k1_scmp_gcd(k1_nat_1(O,2))) & k2_xcmplx_0(G,Q) = k1_funct_1(k6_scmpds_4(C,J,K),k1_scmp_gcd(k1_nat_1(O,3))) & ! [S] : ( v7_ordinal1(S) => ( 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_xcmplx_0(G,S))),k1_funct_1(k6_scmpds_4(C,J,K),k1_scmp_gcd(k2_xcmplx_0(G,R)))) ) ) ) & ! [S] : ( v7_ordinal1(S) => ( 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_xcmplx_0(G,R))),k1_funct_1(k6_scmpds_4(C,J,K),k1_scmp_gcd(k2_xcmplx_0(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) ) ) ) ) ) ) ) ) ) ) )).
fof(l12_seq_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_membered(A) ) => ! [B] : ( v1_xreal_0(B) => ( ( ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => r1_xxreal_0(C,B) ) ) & ! [C] : ( v1_xreal_0(C) => ( ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => r1_xxreal_0(D,C) ) ) => r1_xxreal_0(B,C) ) ) ) => B = k2_seq_4(A) ) ) ) )).
fof(l12_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v7_valued_0(A) <=> ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,A,k1_nat_1(B,1))) ) ) ) )).
fof(l12_series_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k1_nat_1(k1_nat_1(k11_newton(A,2),k2_nat_1(3,A)),2) = k2_nat_1(k1_nat_1(A,1),k1_nat_1(A,2)) ) )).
fof(l12_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => r1_xxreal_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k3_xcmplx_0(A,B)),k1_square_1(B)),3)),k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),2))) ) ) )).
fof(l12_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(l12_sin_cos6,axiom,( ~ r1_xxreal_0(k7_xcmplx_0(k28_sin_cos,1),k7_xcmplx_0(k28_sin_cos,2)) )).
fof(l12_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(l12_topreal1,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(l12_topreal2,axiom,( ~ r2_hidden(k19_euclid(k5_numbers,k5_numbers),k1_rltopsp1(k15_euclid(2),k19_euclid(1,k5_numbers),k19_euclid(1,1))) )).
fof(l12_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( B != C & ! [E] : ( 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] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(l12_vectsp_1,axiom,( v1_xreal_0(1) )).
fof(l12_waybel15,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(l12_waybel31,axiom,( ! [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] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => ! [C] : ( ( v2_pre_topc(C) & v2_waybel19(C) & m1_yellow_9(C,A) ) => r1_ordinal1(k2_waybel23(B),k2_waybel23(C)) ) ) ) )).
fof(l12_waybel33,axiom,( ! [A] : ( ( 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] : ( ( 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)))) ) ) ) )).
fof(l12_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(l12_xcmplx_0,axiom,( k5_numbers = k5_arytm_0(c1__xcmplx_0,c1__xcmplx_0) )).
fof(l12_xreal_0,axiom,( r1_xxreal_0(k5_numbers,1) )).
fof(l12_xxreal_0,axiom,( ~ r2_hidden(k2_xxreal_0,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) )).
fof(l12_xxreal_3,axiom,( k1_xxreal_3(k2_xxreal_0,k2_xxreal_0) = k2_xxreal_0 )).
fof(l12_zfmodel1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r2_relset_1(k4_ordinal1,k4_ordinal1,k24_zf_lang(k8_zf_lang(A,B)),B) & k23_zf_lang(k8_zf_lang(A,B)) = A ) ) ) )).
fof(l12_zfmodel2,axiom,( k2_zf_lang(k5_numbers) != k2_zf_lang(4) )).
fof(l130_jordan,axiom,( v2_sppol_1(k1_rltopsp1(k15_euclid(2),k19_euclid(1,k5_numbers),k19_euclid(1,3))) )).
fof(l130_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l130_quaterni,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k1_square_1(B),k1_square_1(A)) ) => r1_xxreal_0(B,A) ) ) ) )).
fof(l130_toprealb,axiom,( r1_tarski(k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fcont_1(k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos))),1),k5_toprealb(c46__toprealb))),k2_rcomp_1(k7_xcmplx_0(1,2),k2_xcmplx_0(k7_xcmplx_0(1,2),c5__toprealb))) )).
fof(l131_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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(k9_fomodel0(B),C) = k1_xboole_0 ) ) ) )).
fof(l131_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ( ~ v10_fomodel4(A,B,C) <=> ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ~ v10_fomodel4(D,B,C) ) ) ) ) )).
fof(l131_jordan,axiom,( v2_sppol_1(k1_rltopsp1(k15_euclid(2),k19_euclid(1,k5_numbers),k19_euclid(1,k4_xcmplx_0(3)))) )).
fof(l131_quaterni,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => k1_square_1(k2_xcmplx_0(k3_square_1(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(D)),k1_square_1(C))),k3_square_1(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(E),k1_square_1(F)),k1_square_1(G)),k1_square_1(H))))) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(D)),k1_square_1(C)),k1_square_1(E)),k1_square_1(F)),k1_square_1(G)),k1_square_1(H)),k3_xcmplx_0(2,k3_square_1(k3_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(D)),k1_square_1(C)),k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(E),k1_square_1(F)),k1_square_1(G)),k1_square_1(H)))))) ) ) ) ) ) ) ) ) )).
fof(l131_toprealb,axiom,( v1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fcont_1(k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos))),1),k5_toprealb(c46__toprealb))) & v1_funct_2(k2_partfun1(k1_numbers,k1_numbers,k1_fcont_1(k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos))),1),k5_toprealb(c46__toprealb)),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(c46__toprealb))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k7_xcmplx_0(1,2),k2_xcmplx_0(k7_xcmplx_0(1,2),c5__toprealb)))))) & m1_subset_1(k2_partfun1(k1_numbers,k1_numbers,k1_fcont_1(k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos))),1),k5_toprealb(c46__toprealb)),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(c46__toprealb))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k7_xcmplx_0(1,2),k2_xcmplx_0(k7_xcmplx_0(1,2),c5__toprealb)))))))) )).
fof(l132_bcialg_1,axiom,( ! [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) ) => ( v13_bcialg_1(A) => v16_bcialg_1(A) ) ) )).
fof(l132_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ( ( r2_hidden(k24_fomodel4(B),C) & v9_fomodel2(A,B) ) => ( v10_fomodel4(A,B,C) | ( v6_fomodel2(A,B) & v11_fomodel4(A,B,C) ) ) ) ) ) )).
fof(l132_jordan,axiom,( v1_sppol_1(k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3)),k19_euclid(k5_numbers,k4_xcmplx_0(3)))) )).
fof(l132_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( 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) ) ) ) ) )).
fof(l132_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l132_quaterni,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => k1_square_1(k3_square_1(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k2_xcmplx_0(A,E)),k1_square_1(k2_xcmplx_0(B,F))),k1_square_1(k2_xcmplx_0(C,G))),k1_square_1(k2_xcmplx_0(D,H))))) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k2_xcmplx_0(A,E)),k1_square_1(k2_xcmplx_0(B,F))),k1_square_1(k2_xcmplx_0(C,G))),k1_square_1(k2_xcmplx_0(D,H))) ) ) ) ) ) ) ) ) )).
fof(l132_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) & v1_finseq_1(A) ) => m2_finseq_1(A,k2_numbers) ) )).
fof(l132_toprealb,axiom,( k6_toprealb(k1_fcont_1(k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos))),1)) = k1_fcont_1(k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos))),1) )).
fof(l133_bcialg_1,axiom,( ! [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) ) => ( ( ~ 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) ) ) ) )).
fof(l133_fomodel4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C))))) => ! [E] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(C),k3_rfunct_3(k3_finseq_2(A),k2_xboole_0(A,k6_margrel1))),k15_fomodel2(C,A)) => ~ ( v15_fomodel4(D,C) & v10_fomodel2(B,A,C,E) & v10_fomodel4(B,C,D) ) ) ) ) ) )).
fof(l133_jordan,axiom,( v1_sppol_1(k1_rltopsp1(k15_euclid(2),k19_euclid(1,k4_xcmplx_0(3)),k19_euclid(k5_numbers,k4_xcmplx_0(3)))) )).
fof(l133_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(l133_o_ring_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v2_struct_0(C) & l6_algstr_0(C) ) => ! [D] : ( 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 = k5_numbers | B = k5_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) ) ) ) ) ) ) )).
fof(l133_toprealb,axiom,( k1_relset_1(k1_numbers,k1_fcont_1(k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos))),1)) = k1_numbers )).
fof(l134_fomodel4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_fomodel2(E,B,A) ) => ( k13_fomodel2(B,A,E,k42_fomodel1(B,k42_fomodel1(B,k43_fomodel1(B,k31_fomodel2(B)),C),D)) = 1 <=> k1_funct_1(k9_fomodel2(B,A,E),C) = k1_funct_1(k9_fomodel2(B,A,E),D) ) ) ) ) ) ) )).
fof(l134_jordan,axiom,( v1_sppol_1(k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),3),k19_euclid(k5_numbers,3))) )).
fof(l134_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(l134_o_ring_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v2_struct_0(C) & l6_algstr_0(C) ) => ! [D] : ( 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 = k5_numbers | B = k5_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) ) ) ) ) ) ) )).
fof(l134_toprealb,axiom,( k2_relset_1(k1_numbers,k1_fcont_1(k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos))),1)) = k1_numbers )).
fof(l134_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => r1_tarski(u1_struct_0(k7_zmodul01(A,B,C)),u1_struct_0(k6_zmodul01(A,B,C))) ) ) ) )).
fof(l135_jordan,axiom,( v1_sppol_1(k1_rltopsp1(k15_euclid(2),k19_euclid(1,3),k19_euclid(k5_numbers,3))) )).
fof(l135_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l135_toprealb,axiom,( v1_funct_1(c48__toprealb) & v1_funct_2(c48__toprealb,u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(c46__toprealb))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k7_xcmplx_0(1,2),k2_xcmplx_0(k7_xcmplx_0(1,2),c5__toprealb)))))) & v5_pre_topc(c48__toprealb,k1_pre_topc(k2_topalg_2,k5_toprealb(c46__toprealb)),k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k7_xcmplx_0(1,2),k2_xcmplx_0(k7_xcmplx_0(1,2),c5__toprealb))))) & m1_subset_1(c48__toprealb,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(c46__toprealb))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k7_xcmplx_0(1,2),k2_xcmplx_0(k7_xcmplx_0(1,2),c5__toprealb)))))))) )).
fof(l136_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(l136_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v16_fomodel4(k24_fomodel4(A),A) ) )).
fof(l136_jordan,axiom,( v1_sppol_1(k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),3),k19_euclid(1,3))) )).
fof(l136_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( r1_mesfunc5(A,B,C,D) & r1_mesfunc5(A,B,C,E) ) => ( ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(l136_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l136_toprealb,axiom,( k1_relset_1(k1_numbers,k1_fcont_1(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos)),1)) = u1_struct_0(k2_topalg_2) )).
fof(l136_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k4_xcmplx_0(k7_xcmplx_0(A,B)) = k7_xcmplx_0(k4_xcmplx_0(A),B) ) ) )).
fof(l136_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => u1_struct_0(k6_zmodul01(A,k7_zmodul01(A,B,C),C)) = u1_struct_0(C) ) ) ) )).
fof(l137_bcialg_1,axiom,( ! [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) ) => ( v15_bcialg_1(A) <=> v16_bcialg_1(A) ) ) )).
fof(l137_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v16_fomodel4(k25_fomodel4(A),A) ) )).
fof(l137_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => r1_tarski(k13_intpro_1(k13_intpro_1(A)),k13_intpro_1(A)) ) )).
fof(l137_jordan,axiom,( v1_sppol_1(k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3)),k19_euclid(1,k4_xcmplx_0(3)))) )).
fof(l137_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l137_toprealb,axiom,( k1_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos)),1),k5_toprealb(c46__toprealb))) = k5_toprealb(c46__toprealb) )).
fof(l138_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v16_fomodel4(k26_fomodel4(A),A) ) )).
fof(l138_jordan,axiom,( r1_tarski(k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(k4_xcmplx_0(1),3)),k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3)),k19_euclid(k4_xcmplx_0(1),3))) )).
fof(l138_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ~ ( r1_mesfunc5(A,B,C,D) & r1_mesfunc5(A,B,C,E) & k1_relset_1(A,D) = k1_relset_1(A,E) & ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ! [G] : ( m2_subset_1(G,k1_zfmisc_1(A),B) => ! [H] : ( 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,k6_numbers,D,F)) & F = k1_relset_1(A,k2_partfun1(A,k6_numbers,D,F)) & r1_mesfunc1(A,B,k2_partfun1(A,k6_numbers,D,F),F) & r1_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,F)) & k7_mesfunc5(A,B,C,D) = k7_mesfunc5(A,B,C,k2_partfun1(A,k6_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,k6_numbers,E,F)) & F = k1_relset_1(A,k2_partfun1(A,k6_numbers,E,F)) & r1_mesfunc1(A,B,k2_partfun1(A,k6_numbers,E,F),F) & r1_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,E,F)) & k7_mesfunc5(A,B,C,E) = k7_mesfunc5(A,B,C,k2_partfun1(A,k6_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) = k5_numbers & k12_supinf_2(C,H) = k5_numbers & F = k1_relset_1(A,k2_partfun1(A,k6_numbers,k3_mesfunc1(A,D,E),F)) & r1_mesfunc1(A,B,k2_partfun1(A,k6_numbers,k3_mesfunc1(A,D,E),F),F) & r1_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,k3_mesfunc1(A,D,E),F)) & r2_relset_1(A,k6_numbers,k2_partfun1(A,k6_numbers,k3_mesfunc1(A,D,E),F),k3_mesfunc1(A,k2_partfun1(A,k6_numbers,D,F),k2_partfun1(A,k6_numbers,E,F))) & k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,k3_mesfunc1(A,D,E),F)) = k3_supinf_2(k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,F)),k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,E,F))) ) ) ) ) ) ) ) ) ) ) )).
fof(l138_toprealb,axiom,( r1_tarski(k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos)),1),k5_toprealb(c46__toprealb))),k2_rcomp_1(k7_xcmplx_0(1,2),k2_xcmplx_0(k7_xcmplx_0(1,2),c5__toprealb))) )).
fof(l138_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => u1_struct_0(k7_zmodul01(A,B,k6_zmodul01(A,B,C))) = u1_struct_0(B) ) ) ) )).
fof(l139_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v16_fomodel4(k27_fomodel4(A),A) ) )).
fof(l139_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => v10_intpro_1(k13_intpro_1(A)) ) )).
fof(l139_jordan,axiom,( r1_tarski(k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3))),k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3)),k19_euclid(k4_xcmplx_0(1),3))) )).
fof(l139_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_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)) ) ) ) ) ) ) ) )).
fof(l139_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => A = k25_quaterni(k22_quaterni(A,B),B) ) ) )).
fof(l139_toprealb,axiom,( v1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos)),1),k5_toprealb(c46__toprealb))) & v1_funct_2(k2_partfun1(k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos)),1),k5_toprealb(c46__toprealb)),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(c46__toprealb))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k7_xcmplx_0(1,2),k2_xcmplx_0(k7_xcmplx_0(1,2),c5__toprealb)))))) & m1_subset_1(k2_partfun1(k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos)),1),k5_toprealb(c46__toprealb)),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(c46__toprealb))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k7_xcmplx_0(1,2),k2_xcmplx_0(k7_xcmplx_0(1,2),c5__toprealb)))))))) )).
fof(l13_algstr_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_3)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_algstr_3)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_algstr_3)) => ? [D] : ( m1_subset_1(D,u1_struct_0(k3_algstr_3)) & k1_algstr_3(k3_algstr_3,A,B,D) = C ) ) ) ) )).
fof(l13_ami_4,axiom,( ! [A] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(A,u1_struct_0(k1_ami_3)) & v5_memstr_0(A,k7_card_1(2),k1_ami_3,k5_numbers) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_ami_3)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ( r1_tarski(k1_ami_4,B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ( ( k1_funct_1(A,k10_ami_3(k5_numbers)) = C & k1_funct_1(A,k10_ami_3(1)) = D ) => ( r1_xxreal_0(C,D) | r1_xxreal_0(D,k5_numbers) | ( k1_funct_1(k6_extpro_1(k7_card_1(2),k1_ami_3,B,A),k10_ami_3(k5_numbers)) = k3_int_2(C,D) & ? [E] : ( v7_ordinal1(E) & r1_compos_1(k1_ami_3,B,k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,E))) ) ) ) ) ) ) ) ) ) )).
fof(l13_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(k4_amistd_1(A))) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(l13_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => k3_rlvect_1(A,k1_rlvect_1(A,B,k3_xcmplx_0(D,E)),k1_rlvect_1(A,C,k3_xcmplx_0(D,F))) = k1_rlvect_1(A,k3_rlvect_1(A,k1_rlvect_1(A,B,E),k1_rlvect_1(A,C,F)),D) ) ) ) ) ) ) )).
fof(l13_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => k1_arytm_1(A,A) = k11_arytm_3 ) )).
fof(l13_bcialg_1,axiom,( ! [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] : ( 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) ) ) ) )).
fof(l13_brouwer2,axiom,( ! [A] : ( v7_ordinal1(A) => ~ v2_tops_1(k2_topreal9(A,k4_struct_0(k15_euclid(A)),1),k15_euclid(A)) ) )).
fof(l13_catalg_1,axiom,( ! [A] : ! [B] : ( r2_hidden(B,k10_xtuple_0(k2_xboole_0(u1_struct_0(k3_catalg_1(A)),u4_struct_0(k3_catalg_1(A))))) => ( v1_relat_1(B) & v1_funct_1(B) ) ) )).
fof(l13_cfdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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(k3_xcmplx_0(C,A),k3_xcmplx_0(C,B)) ) ) ) ) ) )).
fof(l13_compl_sp,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) )).
fof(l13_complex1,axiom,( k6_complex1 = k5_arytm_0(c2__complex1,c1__complex1) )).
fof(l13_comptrig,axiom,( ~ r1_xxreal_0(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k5_numbers) )).
fof(l13_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( v7_ordinal1(B) => ( k9_complex1(k9_nat_1(k2_numbers,A,B)) = k9_nat_1(k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,A),B) & r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,A),B)) ) ) ) )).
fof(l13_convex1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( v1_xreal_0(D) => k1_convex1(A,k6_rusub_4(A,B,C),D) = k6_rusub_4(A,k1_convex1(A,B,D),k1_convex1(A,C,D)) ) ) ) ) )).
fof(l13_convex2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(l13_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l13_csspace2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k18_csspace)) => k1_clvect_1(k18_csspace,B,A) = k25_valued_1(k4_ordinal1,k2_numbers,k2_csspace(B),A) ) ) )).
fof(l13_csspace4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v1_comseq_2(A) & k2_seq_4(k2_relset_1(k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,A))) = k5_numbers ) => ! [B] : ( v7_ordinal1(B) => k1_funct_1(A,B) = k5_complex1 ) ) ) )).
fof(l13_dtconstr,axiom,( m1_subset_1(k5_numbers,u1_struct_0(k5_dtconstr)) & m1_subset_1(1,u1_struct_0(k5_dtconstr)) )).
fof(l13_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_enumset1(A,B,C,D) = k2_xboole_0(k2_tarski(A,B),k2_tarski(C,D)) )).
fof(l13_euclid_6,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( r1_xxreal_0(k5_numbers,k6_xcmplx_0(k1_comptrig(B),k1_comptrig(A))) => ( B = k5_numbers | k1_comptrig(k2_complex2(B,k4_xcmplx_0(k1_comptrig(A)))) = k6_xcmplx_0(k1_comptrig(B),k1_comptrig(A)) ) ) ) ) )).
fof(l13_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => k8_euclid(3,k1_euclid_8(A,B,C),k1_euclid_8(D,E,F)) = k1_euclid_8(k6_xcmplx_0(A,D),k6_xcmplx_0(B,E),k6_xcmplx_0(C,F)) ) ) ) ) ) ) )).
fof(l13_fib_fusc,axiom,( k10_ami_3(k5_numbers) != k10_ami_3(4) )).
fof(l13_fib_num4,axiom,( k2_power(k2_fib_num,6) = k6_xcmplx_0(9,k3_xcmplx_0(4,k3_square_1(5))) )).
fof(l13_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => r2_wellord2(k2_finseq_1(A),A) ) )).
fof(l13_finseq_2,axiom,( ! [A] : ! [B] : ! [C] : k10_xtuple_0(k11_finseq_1(A,B,C)) = k1_enumset1(A,B,C) )).
fof(l13_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( v7_ordinal1(C) => r1_tarski(k3_xboole_0(k4_finseq_2(C,A),k3_finseq_2(B)),k4_finseq_2(C,B)) ) )).
fof(l13_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_fomodel2(D,A,B) ) => ! [E] : ( ( 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] : ( m1_subset_1(F,k4_ordinal1) => ( k1_funct_1(k10_funct_5(k4_ordinal1,k35_fomodel1(A),B,k9_funct_2(k35_fomodel1(A),B),k7_fomodel2(A,B,C,D),k1_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(k4_ordinal1,k35_fomodel1(A),B,k9_funct_2(k35_fomodel1(A),B),k7_fomodel2(A,B,C,D),F))) & ( v14_fomodel1(E,k5_numbers,A) => k1_funct_1(k10_funct_5(k4_ordinal1,k35_fomodel1(A),B,k9_funct_2(k35_fomodel1(A),B),k7_fomodel2(A,B,C,D),k1_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) ) ) ) ) ) ) ) ) )).
fof(l13_fomodel3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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)))) ) ) ) ) )).
fof(l13_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) ) => ( v1_glib_000(A) <=> ( r1_tarski(k5_glib_000,k1_relset_1(k4_ordinal1,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)))) ) ) ) )).
fof(l13_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(l13_gobrd11,axiom,( ! [A] : ( v1_xreal_0(A) => m1_subset_1(a_1_4_gobrd11(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) )).
fof(l13_gr_cy_3,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( ~ r1_xxreal_0(A,2) & r1_xxreal_0(k1_nat_1(k3_xcmplx_0(2,A),1),5) ) ) )).
fof(l13_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(l13_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_aff_1(A,D,B,C) & v4_aff_2(A) & r1_aff_1(A,D,B,F) ) => ( D = B | ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ~ ( ~ r1_aff_1(A,D,B,H) & r1_aff_1(A,D,H,I) & r2_analoaf(A,B,H,C,I) & r2_analoaf(A,H,F,I,G) & r1_aff_1(A,D,B,G) ) ) ) | ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ~ ( ~ r1_aff_1(A,D,B,H) & r1_aff_1(A,D,H,I) & r2_analoaf(A,B,H,C,I) & r2_analoaf(A,H,F,I,E) & r1_aff_1(A,D,B,E) ) ) ) | G = E ) ) ) ) ) ) ) ) ) )).
fof(l13_hurwitz,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_polynom3(A))) => ( C = B => k4_algstr_0(k14_polynom3(A),C) = k5_vfunct_1(k4_ordinal1,A,B) ) ) ) ) )).
fof(l13_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => r1_xxreal_0(1,A) ) ) )).
fof(l13_integra7,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r1_integra7(A,C,B) <=> ( r2_fdiff_1(C,A) & r2_relset_1(k1_numbers,k1_numbers,k2_fdiff_1(C,A),k2_partfun1(k1_numbers,k1_numbers,B,A)) ) ) ) ) )).
fof(l13_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ( 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) = k4_xcmplx_0(k1_funct_1(k18_sin_cos,A)) ) ) )).
fof(l13_jgraph_5,axiom,( r2_hidden(1,k1_rcomp_1(k5_numbers,1)) )).
fof(l13_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => m1_subset_1(a_4_3_jordan1(A,B,C,D),k1_zfmisc_1(k1_euclid(2))) ) ) ) ) )).
fof(l13_jordan18,axiom,( g1_pre_topc(u1_struct_0(k15_euclid(2)),u1_pre_topc(k15_euclid(2))) = k3_pcomps_1(k14_euclid(2)) )).
fof(l13_jordan1c,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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))) ) ) ) ) )).
fof(l13_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => k1_nat_1(k7_nat_d(k3_xcmplx_0(2,A),2),1) = k7_nat_d(k3_xcmplx_0(2,A),1) ) ) )).
fof(l13_jordan24,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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) ) ) ) ) ) )).
fof(l13_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(l13_matrixj2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)))) ) ) )).
fof(l13_measure7,axiom,( r2_hidden(k1_numbers,k9_setfam_1(k1_numbers)) )).
fof(l13_modelc_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => k3_finseq_1(k8_finseq_1(k4_ordinal1,k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,A),B),C)) = k1_nat_1(k1_nat_1(1,k3_finseq_1(B)),k3_finseq_1(C)) ) ) ) )).
fof(l13_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => m1_subset_1(k1_tarski(A),k1_zfmisc_1(k13_modelc_2(A))) ) )).
fof(l13_msalimit,axiom,( ! [A] : ( ( 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))) ) )).
fof(l13_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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))) ) ) ) ) )).
fof(l13_ntalgo_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => ! [B] : ( m1_subset_1(B,k4_numbers) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_numbers))) ) => ( ( k9_nat_1(k4_numbers,C,k5_numbers) = A & k9_nat_1(k4_numbers,D,k5_numbers) = B & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( k9_nat_1(k4_numbers,C,k1_nat_1(E,1)) = k9_nat_1(k4_numbers,D,E) & k9_nat_1(k4_numbers,D,k1_nat_1(E,1)) = k5_int_1(k9_nat_1(k4_numbers,C,E),k9_nat_1(k4_numbers,D,E)) ) ) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( k9_nat_1(k4_numbers,D,E) != k5_numbers => k3_int_2(k9_nat_1(k4_numbers,C,k5_numbers),k9_nat_1(k4_numbers,D,k5_numbers)) = k3_int_2(k9_nat_1(k4_numbers,C,E),k9_nat_1(k4_numbers,D,E)) ) ) ) ) ) ) ) )).
fof(l13_numbers,axiom,( r1_tarski(k3_numbers,k1_numbers) )).
fof(l13_orders_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => v5_orders_3(k3_struct_0(A),A,A) ) )).
fof(l13_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l13_parsp_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k5_algstr_0(A,k8_group_1(A,C,B),k8_group_1(A,C,D)) = k3_rlvect_1(A,D,B) => k8_group_1(A,k5_algstr_0(A,C,k1_group_1(A)),B) = k8_group_1(A,k3_rlvect_1(A,C,k1_group_1(A)),D) ) ) ) ) ) )).
fof(l13_pdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(2)) => ! [E] : ( ( 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] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & D = k10_finseq_1(F,G) & ? [H] : ( m1_rcomp_1(H,G) & r1_tarski(H,k1_relset_1(k1_numbers,k1_pdiff_2(2,2,E,D))) & ? [I] : ( v1_funct_1(I) & v3_fdiff_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [J] : ( v1_funct_1(J) & v2_fdiff_1(J) & m1_subset_1(J,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & C = k1_funct_1(I,1) & ! [K] : ( v1_xreal_0(K) => ( r2_hidden(K,H) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(2,2,E,D),K),k1_funct_1(k1_pdiff_2(2,2,E,D),G)) = k2_xcmplx_0(k1_funct_1(I,k6_xcmplx_0(K,G)),k1_funct_1(J,k6_xcmplx_0(K,G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l13_pdiff_8,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k16_lopban_1(k4_real_ns1(A),k4_real_ns1(B)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k16_lopban_1(k4_real_ns1(A),k4_real_ns1(B)))) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,u1_struct_0(k16_lopban_1(k4_real_ns1(A),k4_real_ns1(1)))) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(l13_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( 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] : ( m1_rcomp_1(E,k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_1(B,A),C)) => ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(l13_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(D) => ( v2_comseq_2(k8_prob_1(A,B,D,C)) & k1_seq_2(k8_prob_1(A,B,D,C)) = k1_funct_1(C,k1_prob_1(A,D)) ) ) ) ) ) ) )).
fof(l13_projred1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u2_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u2_incsp_1(A)) => ~ ( ? [H] : ( 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] : ( m1_subset_1(H,u1_incsp_1(A)) => ! [I] : ( m1_subset_1(I,u1_incsp_1(A)) => ! [J] : ( m1_subset_1(J,u1_incsp_1(A)) => ! [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l13_qmax_1,axiom,( k9_xtuple_0(k6_domain_1(k2_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_zfmisc_1(k2_zfmisc_1(k12_prob_1,k1_numbers))),k1_domain_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_zfmisc_1(k2_zfmisc_1(k12_prob_1,k1_numbers)),k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers),c3__qmax_1))) = k8_mcart_1(k4_ordinal1,k4_ordinal1,k6_domain_1(k4_ordinal1,k5_numbers),k6_domain_1(k4_ordinal1,k5_numbers)) )).
fof(l13_quaterni,axiom,( m1_subset_1(1,k1_numbers) & m1_subset_1(k5_numbers,k1_numbers) )).
fof(l13_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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))) = k5_numbers ) ) ) ) )).
fof(l13_random_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( m2_prob_1(C,A,k1_random_1(A)) => ! [D] : ( m2_prob_1(D,B,k1_random_1(B)) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( v1_finset_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => k12_supinf_2(F,H) = k5_bhsp_5(k1_numbers,k2_zfmisc_1(A,B),k9_binop_2,H,E) ) & ! [H] : ( ( v1_finset_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => k12_supinf_2(G,H) = k5_bhsp_5(k1_numbers,k2_zfmisc_1(A,B),k9_binop_2,H,E) ) ) => r2_funct_2(k1_zfmisc_1(k2_zfmisc_1(A,B)),k1_numbers,F,G) ) ) ) ) ) ) ) ) )).
fof(l13_realset2,axiom,( k5_binop_1(2,k1_realset2,k10_subset_1(k5_numbers,2),k10_subset_1(1,2)) = k10_subset_1(1,2) )).
fof(l13_ringcat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(l13_robbins3,axiom,( v10_lattices(k1_robbins3) )).
fof(l13_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l13_scmfsa9a,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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_sf_mastr(k1_scmfsa8b(A,k3_scmfsa6a(B,k1_scmfsa8a(k5_numbers)),k4_compos_1(k1_scmfsa_2))) = k4_sf_mastr(k1_funct_4(k1_scmfsa8b(A,k3_scmfsa6a(B,k1_scmfsa8a(k5_numbers)),k4_compos_1(k1_scmfsa_2)),k16_funcop_1(k1_nat_1(k5_card_1(B),4),k11_scmfsa_2(k5_numbers)))) ) ) )).
fof(l13_scmpds_8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ! [C] : ( v1_int_1(C) => r1_tarski(k61_valued_1(A,1),k1_scmpds_8(B,C,A)) ) ) ) )).
fof(l13_scpinvar,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( k1_funct_1(B,k2_scmp_gcd) = k5_numbers & k1_funct_1(B,k1_scmp_gcd(1)) = k5_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(k1_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) ) ) ) ) ) )).
fof(l13_scpisort,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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,k1_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(k1_nat_1(k5_card_1(D),2))))) ) ) ) ) )).
fof(l13_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ! [F] : ( v1_int_1(F) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ! [I] : ( v7_ordinal1(I) => ( ( k1_funct_1(B,D) = F & 1 = k1_funct_1(B,k2_scmpds_2(F,E)) & I = k1_nat_1(k2_xcmplx_0(G,H),1) & k1_nat_1(G,1) = k1_funct_1(B,k1_scmp_gcd(I)) & k2_xcmplx_0(G,H) = k1_funct_1(B,k1_scmp_gcd(k1_nat_1(I,1))) & ! [J] : ( ( 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,k5_numbers) ) => ! [K] : ( ( v1_relat_1(K) & v4_relat_1(K,k4_ordinal1) & v5_relat_1(K,u1_compos_1(k1_scmpds_2)) & v1_funct_1(K) & v1_partfun1(K,k4_ordinal1) ) => ! [L] : ( m2_finseq_1(L,k4_numbers) => ! [M] : ( m2_finseq_1(M,k4_numbers) => ! [N] : ( v7_ordinal1(N) => ! [O] : ( v7_ordinal1(O) => ! [P] : ( v7_ordinal1(P) => ! [Q] : ( v7_ordinal1(Q) => ( ( k1_funct_1(J,D) = F & k1_nat_1(k3_xcmplx_0(2,N),1) = k1_funct_1(J,k2_scmpds_2(F,E)) & O = k1_nat_1(k2_xcmplx_0(k2_xcmplx_0(G,H),k3_xcmplx_0(2,N)),1) & k2_xcmplx_0(G,P) = k1_funct_1(J,k1_scmp_gcd(O)) & k2_xcmplx_0(G,Q) = k1_funct_1(J,k1_scmp_gcd(k1_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] : ( v7_ordinal1(R) => ( r1_xxreal_0(1,R) => ( r1_xxreal_0(k1_nat_1(k3_xcmplx_0(2,N),1),R) | k1_funct_1(k6_scmpds_4(C,J,K),k1_scmp_gcd(k2_xcmplx_0(k2_xcmplx_0(G,H),R))) = k1_funct_1(J,k1_scmp_gcd(k2_xcmplx_0(k2_xcmplx_0(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(k3_xcmplx_0(2,N),1) & ! [R] : ( v7_ordinal1(R) => ( ( r1_xxreal_0(1,R) & r1_xxreal_0(R,H) ) => k1_funct_1(k6_scmpds_4(C,J,K),k1_scmp_gcd(k2_xcmplx_0(G,R))) = k1_funct_1(J,k1_scmp_gcd(k2_xcmplx_0(G,R))) ) ) ) ) & ( ~ r1_xxreal_0(Q,P) => ( k1_funct_1(k6_scmpds_4(C,J,K),k2_scmpds_2(F,E)) = k1_nat_1(k3_xcmplx_0(2,N),3) & ! [R] : ( v7_ordinal1(R) => ( ( ( 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_xcmplx_0(G,R))) = k1_funct_1(J,k1_scmp_gcd(k2_xcmplx_0(G,R))) ) ) & ? [R] : ( v7_ordinal1(R) & r1_xxreal_0(P,R) & r1_xxreal_0(R,Q) & k2_xcmplx_0(G,P) = k1_funct_1(k6_scmpds_4(C,J,K),k1_scmp_gcd(O)) & k6_xcmplx_0(k2_xcmplx_0(G,R),1) = k1_funct_1(k6_scmpds_4(C,J,K),k1_scmp_gcd(k1_nat_1(O,1))) & k1_nat_1(k2_xcmplx_0(G,R),1) = k1_funct_1(k6_scmpds_4(C,J,K),k1_scmp_gcd(k1_nat_1(O,2))) & k2_xcmplx_0(G,Q) = k1_funct_1(k6_scmpds_4(C,J,K),k1_scmp_gcd(k1_nat_1(O,3))) & ! [S] : ( v7_ordinal1(S) => ( 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_xcmplx_0(G,S))),k1_funct_1(k6_scmpds_4(C,J,K),k1_scmp_gcd(k2_xcmplx_0(G,R)))) ) ) ) & ! [S] : ( v7_ordinal1(S) => ( 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_xcmplx_0(G,R))),k1_funct_1(k6_scmpds_4(C,J,K),k1_scmp_gcd(k2_xcmplx_0(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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l13_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v8_valued_0(A) <=> ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_nat_1(k1_numbers,A,k1_nat_1(B,1)),k9_nat_1(k1_numbers,A,B)) ) ) ) )).
fof(l13_series_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k1_nat_1(k1_nat_1(k1_nat_1(k2_nat_1(A,k2_nat_1(4,k11_newton(A,2))),k2_nat_1(11,A)),k2_nat_1(12,k11_newton(A,2))),3) = k3_xcmplx_0(k1_nat_1(A,1),k6_xcmplx_0(k2_nat_1(4,k11_newton(k1_nat_1(A,1),2)),1)) ) )).
fof(l13_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => r1_xxreal_0(k3_xcmplx_0(2,k1_square_1(C)),k2_xcmplx_0(k1_square_1(k7_xcmplx_0(k3_xcmplx_0(B,C),A)),k1_square_1(k7_xcmplx_0(k3_xcmplx_0(C,A),B)))) ) ) ) )).
fof(l13_sin_cos6,axiom,( ~ r1_xxreal_0(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(1,k28_sin_cos)) )).
fof(l13_sysrel,axiom,( ! [A] : r1_tarski(k4_relat_1(A),k2_zfmisc_1(A,A)) )).
fof(l13_taxonom2,axiom,( ! [A] : ! [B] : ( ( r2_hidden(A,k1_tarski(k1_xboole_0)) & r2_hidden(B,k1_tarski(k1_xboole_0)) ) => ( A = B | r1_xboole_0(A,B) ) ) )).
fof(l13_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(l13_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_pre_topc(A,B)) => ! [D] : ( ( 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] : ~ ( r2_hidden(E,D) & r1_xboole_0(E,B) ) ) ) ) ) ) )).
fof(l13_topreal2,axiom,( ~ r2_hidden(k19_euclid(k5_numbers,k5_numbers),k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,1),k19_euclid(1,1))) )).
fof(l13_topreal8,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(B,k1_nat_1(C,1)) & r1_xxreal_0(C,k3_finseq_1(A)) ) => ( k2_xcmplx_0(k3_finseq_1(k1_graph_2(A,B,C)),B) = k1_nat_1(C,1) & ! [D] : ( v7_ordinal1(D) => ( ~ r1_xxreal_0(k3_finseq_1(k1_graph_2(A,B,C)),D) => k1_funct_1(k1_graph_2(A,B,C),k1_nat_1(D,1)) = k1_funct_1(A,k2_xcmplx_0(B,D)) ) ) ) ) ) ) ) )).
fof(l13_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( B != C & ! [E] : ( 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] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(l13_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ( v5_vectsp_1(A) => ( v1_vectsp_1(A) & v2_vectsp_1(A) ) ) ) )).
fof(l13_xboole_0,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) )).
fof(l13_xcmplx_0,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l13_xreal_0,axiom,( k2_xcmplx_0(1,k4_xcmplx_0(1)) = k5_numbers )).
fof(l13_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C)) => r1_xxreal_0(A,B) ) ) ) ) )).
fof(l13_xxreal_0,axiom,( ~ r1_xxreal_0(k1_xxreal_0,k2_xxreal_0) )).
fof(l13_zfmodel2,axiom,( k2_zf_lang(3) != k2_zf_lang(4) )).
fof(l140_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v16_fomodel4(k28_fomodel4(A),A) ) )).
fof(l140_jordan,axiom,( r1_tarski(k1_rltopsp1(k15_euclid(2),k19_euclid(1,k5_numbers),k19_euclid(1,3)),k1_rltopsp1(k15_euclid(2),k19_euclid(1,k4_xcmplx_0(3)),k19_euclid(1,3))) )).
fof(l140_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l140_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => A = k22_quaterni(k25_quaterni(A,B),B) ) ) )).
fof(l140_toprealb,axiom,( k6_toprealb(k1_fcont_1(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos)),1)) = k1_fcont_1(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos)),1) )).
fof(l140_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( 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)))) ) ) ) ) )).
fof(l141_jordan,axiom,( r1_tarski(k1_rltopsp1(k15_euclid(2),k19_euclid(1,k5_numbers),k19_euclid(1,k4_xcmplx_0(3))),k1_rltopsp1(k15_euclid(2),k19_euclid(1,k4_xcmplx_0(3)),k19_euclid(1,3))) )).
fof(l141_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k25_quaterni(A,B) = k6_quaterni(k6_xcmplx_0(k13_quaterni(A),k13_quaterni(B)),k6_xcmplx_0(k14_quaterni(A),k14_quaterni(B)),k6_xcmplx_0(k15_quaterni(A),k15_quaterni(B)),k6_xcmplx_0(k16_quaterni(A),k16_quaterni(B))) ) ) )).
fof(l141_toprealb,axiom,( k1_relset_1(k1_numbers,k1_fcont_1(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos)),1)) = k1_numbers )).
fof(l142_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(l142_jordan,axiom,( k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(3),3) = a_0_0_jordan )).
fof(l142_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k25_quaterni(A,B) = k24_quaterni(k25_quaterni(B,A)) ) ) )).
fof(l142_toprealb,axiom,( k2_relset_1(k1_numbers,k1_fcont_1(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos)),1)) = k1_numbers )).
fof(l142_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( ~ r2_hidden(A,C) & ~ r2_hidden(B,C) & ~ r1_xboole_0(k2_tarski(A,B),C) ) )).
fof(l142_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(l143_aofa_000,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( ~ 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] : ( m1_aofa_000(D,C,A,B) => ! [E] : ( 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] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(l143_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v16_fomodel4(k31_fomodel4(A),A) ) )).
fof(l143_jordan,axiom,( r2_hidden(k19_euclid(k5_numbers,3),k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(3),3)) )).
fof(l143_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ( k25_quaterni(A,B) = k5_numbers => A = B ) ) ) )).
fof(l143_toprealb,axiom,( v1_funct_1(c51__toprealb) & v1_funct_2(c51__toprealb,u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(c46__toprealb))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k7_xcmplx_0(1,2),k2_xcmplx_0(k7_xcmplx_0(1,2),c5__toprealb)))))) & v5_pre_topc(c51__toprealb,k1_pre_topc(k2_topalg_2,k5_toprealb(c46__toprealb)),k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k7_xcmplx_0(1,2),k2_xcmplx_0(k7_xcmplx_0(1,2),c5__toprealb))))) & m1_subset_1(c51__toprealb,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(c46__toprealb))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k7_xcmplx_0(1,2),k2_xcmplx_0(k7_xcmplx_0(1,2),c5__toprealb)))))))) )).
fof(l144_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_aofa_i00(D,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [G] : ( m1_aofa_i00(G,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ( ? [H] : ( v1_relat_1(H) & v1_funct_1(H) & k1_funct_1(H,C) = k5_numbers & k1_funct_1(H,E) = 1 & k1_funct_1(H,F) = 2 & k1_funct_1(H,G) = 3 ) => ! [H] : ( 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,k5_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,k5_numbers),D,G,E),k83_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,G,F)),k48_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,E,F)),k48_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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,k5_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,k5_numbers),D,G,E),k83_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,G,F)),k48_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,E,F)),k48_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,F,G))),F) = k5_int_1(k21_aofa_i00(B,k4_numbers,H,E),k21_aofa_i00(B,k4_numbers,H,F)) & ! [I] : ( m1_subset_1(I,k4_ordinal1) => ! [J] : ( m1_subset_1(J,k4_ordinal1) => ~ ( J = k21_aofa_i00(B,k4_numbers,H,F) & ~ ( r2_hidden(H,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & r1_xxreal_0(J,k5_numbers) ) & ( ~ r1_xxreal_0(J,k5_numbers) => r2_hidden(H,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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,k5_numbers),D,G,E),k83_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,G,F)),k48_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,E,F)),k48_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,F,G)),k78_aofa_i00(A,B,C,D,F,k5_numbers)),k9_funct_2(B,k4_numbers),H,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l144_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v16_fomodel4(k32_fomodel4(A),A) ) )).
fof(l144_jordan,axiom,( r2_hidden(k19_euclid(k5_numbers,k4_xcmplx_0(3)),k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(3),3)) )).
fof(l144_toprealb,axiom,( k1_relset_1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k4_xcmplx_0(1),1)))),k2_partfun1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k4_xcmplx_0(1),1)))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k5_numbers,k28_sin_cos)))),c33__toprealb,k5_toprealb(c45__toprealb))) = c45__toprealb )).
fof(l144_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( m1_zmodul01(D,A) => r1_tarski(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)))) ) ) ) ) )).
fof(l145_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v16_fomodel4(k33_fomodel4(A),A) ) )).
fof(l145_jordan,axiom,( k1_square_1(k2_xcmplx_0(2,1)) = k2_xcmplx_0(k2_xcmplx_0(4,4),1) )).
fof(l145_toprealb,axiom,( r1_tarski(k2_relset_1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k5_numbers,k28_sin_cos)))),k2_partfun1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k4_xcmplx_0(1),1)))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k5_numbers,k28_sin_cos)))),c33__toprealb,k5_toprealb(c45__toprealb))),c46__toprealb) )).
fof(l146_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_funct_2(A,B))) => m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,B)))) ) )).
fof(l146_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v16_fomodel4(k34_fomodel4(A),A) ) )).
fof(l146_jordan,axiom,( k3_square_1(9) = 3 )).
fof(l146_toprealb,axiom,( v1_funct_1(k2_partfun1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k4_xcmplx_0(1),1)))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k5_numbers,k28_sin_cos)))),c33__toprealb,k5_toprealb(c45__toprealb))) & v1_funct_2(k2_partfun1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k4_xcmplx_0(1),1)))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k5_numbers,k28_sin_cos)))),c33__toprealb,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(c46__toprealb)))) & m1_subset_1(k2_partfun1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k4_xcmplx_0(1),1)))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k5_numbers,k28_sin_cos)))),c33__toprealb,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(c46__toprealb)))))) )).
fof(l146_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(l147_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_aofa_i00(D,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [G] : ( m1_aofa_i00(G,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ( ? [H] : ( v1_relat_1(H) & v1_funct_1(H) & k1_funct_1(H,C) = k5_numbers & k1_funct_1(H,E) = 1 & k1_funct_1(H,F) = 2 & k1_funct_1(H,G) = 3 ) => ! [H] : ( 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,k5_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,k5_numbers),D,G,k32_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,k42_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,E),k42_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,F))),k15_aofa_000(A,k79_aofa_i00(A,B,C,D,G,k5_numbers),k58_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,G,k4_xcmplx_0(1)))),k48_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,E,F)),k48_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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,k5_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,k5_numbers),D,G,k32_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,k42_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,E),k42_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,F))),k15_aofa_000(A,k79_aofa_i00(A,B,C,D,G,k5_numbers),k58_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,G,k4_xcmplx_0(1)))),k48_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,E,F)),k48_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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] : ( m1_subset_1(I,k4_ordinal1) => ! [J] : ( m1_subset_1(J,k4_ordinal1) => ( ( 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,k5_numbers)) & r1_xxreal_0(J,k5_numbers) ) | ( ~ r1_xxreal_0(J,k5_numbers) & ~ r2_hidden(H,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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,k5_numbers),D,G,k32_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,k42_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,E),k42_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,F))),k15_aofa_000(A,k79_aofa_i00(A,B,C,D,G,k5_numbers),k58_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,G,k4_xcmplx_0(1)))),k48_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,E,F)),k48_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,F,G)),k78_aofa_i00(A,B,C,D,F,k5_numbers)),k9_funct_2(B,k4_numbers),H,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l147_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v16_fomodel4(k35_fomodel4(A),A) ) )).
fof(l147_toprealb,axiom,( u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k4_xcmplx_0(1),1)))) = k1_rcomp_1(k4_xcmplx_0(1),1) )).
fof(l148_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m1_subset_1(D,B) => ~ ( ( r2_hidden(C,A) => r2_hidden(D,A) ) & ( r2_hidden(D,A) => r2_hidden(C,A) ) & ~ r2_hidden(k4_tarski(k3_funct_2(B,k6_margrel1,k10_fomodel0(A,B),C),k3_funct_2(B,k6_margrel1,k10_fomodel0(A,B),D)),k6_partfun1(k6_margrel1)) ) ) ) ) )).
fof(l148_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l148_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k25_quaterni(B,C) = k22_quaterni(k25_quaterni(B,A),k25_quaterni(A,C)) ) ) ) )).
fof(l148_toprealb,axiom,( m1_subset_1(k5_toprealb(c45__toprealb),k1_zfmisc_1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k4_xcmplx_0(1),1)))))) )).
fof(l149_toprealb,axiom,( u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k5_numbers,k28_sin_cos)))) = k1_rcomp_1(k5_numbers,k28_sin_cos) )).
fof(l14_afvect01,axiom,( ! [A] : ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(o_0_0_afvect01)) & ? [D] : ( m1_subset_1(D,u1_struct_0(o_0_0_afvect01)) & ? [E] : ( m1_subset_1(E,u1_struct_0(o_0_0_afvect01)) & ? [F] : ( 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) ) ) ) ) ) ) )).
fof(l14_algstr_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_3)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_algstr_3)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_algstr_3)) => ! [D] : ( 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 ) ) ) ) ) )).
fof(l14_arytm_0,axiom,( r2_hidden(1,k4_ordinal1) )).
fof(l14_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ( ! [C] : ( 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 ) ) ) )).
fof(l14_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(k5_numbers,C) ) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(k2_power(A,C),k2_power(B,C)) ) ) ) ) ) )).
fof(l14_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k2_binom(A,B,k1_nat_1(C,D)) = k6_algstr_0(A,k2_binom(A,B,C),k2_binom(A,B,D)) ) ) ) ) )).
fof(l14_brouwer2,axiom,( v1_xreal_0(1) )).
fof(l14_cfdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( 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) = k9_finseq_1(k1_funct_1(A,B)) ) ) ) )).
fof(l14_convfun1,axiom,( ! [A] : ( m2_finseq_1(A,k6_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k4_finseq_1(A)) => k12_supinf_2(A,C) = k12_supinf_2(B,C) ) ) ) => k4_extreal1(A) = k18_rvsum_1(B) ) ) ) )).
fof(l14_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l14_csspace2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k18_csspace)) => ( k4_algstr_0(k18_csspace,A) = k31_valued_1(k4_ordinal1,k2_numbers,k2_csspace(A)) & r2_funct_2(k4_ordinal1,k2_numbers,k2_csspace(k4_algstr_0(k18_csspace,A)),k31_valued_1(k4_ordinal1,k2_numbers,k2_csspace(A))) ) ) )).
fof(l14_dtconstr,axiom,( r1_lang1(k5_dtconstr,c3__dtconstr,k3_pre_poly(u1_struct_0(k5_dtconstr),c2__dtconstr)) )).
fof(l14_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k2_ens_1(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(l14_euclid_6,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( r1_xxreal_0(k5_numbers,k6_xcmplx_0(k1_comptrig(B),k1_comptrig(A))) => ( B = k5_numbers | k3_complex2(A,B) = k6_xcmplx_0(k1_comptrig(B),k1_comptrig(A)) ) ) ) ) )).
fof(l14_extreal1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( ( 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] : ( m2_finseq_1(E,k2_finseq_1(k1_nat_1(A,1))) => ( ( E = C & B = k1_funct_1(C,k1_nat_1(A,1)) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r2_hidden(F,k2_finseq_1(k1_nat_1(A,1))) => ( ( ~ r1_xxreal_0(B,F) => k1_funct_1(D,F) = F ) & ( F = B => k1_funct_1(D,F) = k1_nat_1(A,1) ) & ( ~ r1_xxreal_0(F,B) => k1_funct_1(D,F) = k6_xcmplx_0(F,1) ) ) ) ) ) => ( v1_funct_1(k1_partfun1(k4_ordinal1,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(k4_ordinal1,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(k4_ordinal1,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(k4_ordinal1,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)))) ) ) ) ) ) ) ) )).
fof(l14_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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_funct_1(B,A)) ) => ( ! [D] : ( m1_rcomp_1(D,A) => ~ r1_tarski(D,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) ) | ( 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) = k3_xcmplx_0(k1_fdiff_1(C,k1_funct_1(B,A)),k1_fdiff_1(B,A)) ) ) ) ) ) ) )).
fof(l14_fib_fusc,axiom,( k10_ami_3(1) != k10_ami_3(4) )).
fof(l14_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)) & v3_funct_2(E,k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)))) ) => ( ( r1_xxreal_0(1,k3_finseq_1(B)) & k3_finseq_1(B) = k3_finseq_1(C) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r2_hidden(F,k1_relset_1(k4_ordinal1,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) ) ) ) ) ) ) ) )).
fof(l14_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_fomodel2(C,A,B) ) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( ( 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] : ( v7_ordinal1(H) => k1_funct_1(k10_funct_5(k4_ordinal1,k35_fomodel1(A),B,k9_funct_2(k35_fomodel1(A),B),k7_fomodel2(A,B,D,C),k1_nat_1(F,1)),G) = k1_funct_1(k9_nat_1(k9_funct_2(k35_fomodel1(A),B),k7_fomodel2(A,B,E,C),k2_xcmplx_0(k1_nat_1(F,1),H)),G) ) ) ) ) ) ) ) ) )).
fof(l14_fomodel3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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)))) ) ) ) ) )).
fof(l14_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(l14_gfacirc1,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( ( 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] : ! [E] : ! [F] : ~ ( 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)) ) ) ) ) ) )).
fof(l14_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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) ) ) )).
fof(l14_gobrd11,axiom,( ! [A] : ( v1_xreal_0(A) => m1_subset_1(a_1_7_gobrd11(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) )).
fof(l14_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => m1_group_6(B,A,k7_group_2(A)) ) ) )).
fof(l14_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_group_4(A,k5_finseq_2(u1_struct_0(A),k5_numbers,B)) = k5_group_1(A,k5_numbers,B) ) ) )).
fof(l14_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_aff_1(A,D,B,C) & v4_aff_2(A) ) => ( D = B | D = C | ( ~ ( ~ r1_aff_1(A,D,B,F) & r1_aff_1(A,D,F,G) & r2_analoaf(A,B,F,C,G) ) & ~ ( r1_aff_1(A,D,B,F) & ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & ? [I] : ( m1_subset_1(I,u1_struct_0(A)) & ~ r1_aff_1(A,D,B,H) & r1_aff_1(A,D,H,I) & r2_analoaf(A,B,H,C,I) & r2_analoaf(A,H,F,I,G) & r1_aff_1(A,D,B,G) ) ) ) ) | ( ~ ( ~ r1_aff_1(A,D,B,E) & r1_aff_1(A,D,E,G) & r2_analoaf(A,B,E,C,G) ) & ~ ( r1_aff_1(A,D,B,E) & ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & ? [I] : ( m1_subset_1(I,u1_struct_0(A)) & ~ r1_aff_1(A,D,B,H) & r1_aff_1(A,D,H,I) & r2_analoaf(A,B,H,C,I) & r2_analoaf(A,H,E,I,G) & r1_aff_1(A,D,B,G) ) ) ) ) | F = E ) ) ) ) ) ) ) ) ) )).
fof(l14_index_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( m3_index_1(E,A,B,C,D) => ? [F] : ( ~ 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] : ( m1_subset_1(G,A) => m1_subset_1(k2_index_1(A,k1_xtuple_0(E),G),u1_struct_0(F)) ) & ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(l14_int_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_int_1(A,B) => ( r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(A,B) ) ) ) ) )).
fof(l14_int_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k8_newton) & v1_funct_1(B) & v1_partfun1(B,k8_newton) & v4_valued_0(B) & v2_pre_poly(B) ) => ( ( v1_int_7(B) & r1_int_1(A,k8_nat_3(k8_newton,B)) ) => r2_hidden(A,k22_pre_poly(k8_newton,B)) ) ) ) )).
fof(l14_integra3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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_comseq_2(k2_partfun1(A,k1_numbers,B,A)) => r1_xxreal_0(k3_seq_4(k1_rvsum_1(B)),k2_seq_4(k1_rvsum_1(B))) ) ) ) )).
fof(l14_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => m1_subset_1(a_4_5_jordan1(A,B,C,D),k1_zfmisc_1(k1_euclid(2))) ) ) ) ) )).
fof(l14_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(2,B) => k3_xcmplx_0(k7_xcmplx_0(C,k1_newton(2,A)),k6_xcmplx_0(B,2)) = k3_xcmplx_0(k7_xcmplx_0(C,k11_newton(2,k1_nat_1(A,1))),k6_xcmplx_0(k7_nat_d(k3_xcmplx_0(2,B),2),2)) ) ) ) ) )).
fof(l14_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( r1_glib_000(A,k4_glib_001(A,B),D,C) => k15_glib_001(A,k10_glib_001(A,B,C)) = k1_nat_1(k15_glib_001(A,B),1) ) ) ) )).
fof(l14_lopban_7,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(k5_lopban_7(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_lopban_7(A,B,C))) => ! [F] : ( v1_xreal_0(F) => ( ( k2_normsp_0(k5_lopban_7(A,B,C),D) = k5_numbers => D = k4_struct_0(k5_lopban_7(A,B,C)) ) & ( D = k4_struct_0(k5_lopban_7(A,B,C)) => k2_normsp_0(k5_lopban_7(A,B,C),D) = k5_numbers ) & r1_xxreal_0(k5_numbers,k2_normsp_0(k5_lopban_7(A,B,C),D)) & r1_xxreal_0(k2_normsp_0(k5_lopban_7(A,B,C),k3_rlvect_1(k5_lopban_7(A,B,C),D,E)),k2_xcmplx_0(k2_normsp_0(k5_lopban_7(A,B,C),D),k2_normsp_0(k5_lopban_7(A,B,C),E))) & k2_normsp_0(k5_lopban_7(A,B,C),k1_rlvect_1(k5_lopban_7(A,B,C),D,F)) = k3_xcmplx_0(k9_complex1(F),k2_normsp_0(k5_lopban_7(A,B,C),D)) ) ) ) ) ) ) ) )).
fof(l14_lpspace2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_complex1(k9_nat_1(k1_numbers,k3_series_1(A),B)),k9_nat_1(k1_numbers,k3_series_1(k56_valued_1(k4_ordinal1,k1_numbers,A)),B)) ) ) )).
fof(l14_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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,E,k8_cqc_lang(A,k8_cqc_lang(A,C,B),B)),D),k8_cqc_lang(A,k8_cqc_lang(A,k6_cqc_lang(A,B),C),D)),k4_cqc_the1(A)) ) ) ) ) ) )).
fof(l14_measure7,axiom,( v1_funct_1(k7_funcop_1(k4_ordinal1,k1_numbers)) & v1_funct_2(k7_funcop_1(k4_ordinal1,k1_numbers),k4_ordinal1,k9_setfam_1(k1_numbers)) & m1_subset_1(k7_funcop_1(k4_ordinal1,k1_numbers),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k1_numbers)))) )).
fof(l14_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_metric_2(B,A) => ~ v1_xboole_0(B) ) ) )).
fof(l14_metrizts,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( 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)))) ) ) ) ) )).
fof(l14_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ( v3_modelc_2(A) | v6_modelc_2(A) ) => m1_subset_1(k1_tarski(k10_modelc_2(A)),k1_zfmisc_1(k13_modelc_2(A))) ) ) )).
fof(l14_msalimit,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(l14_msualg_1,axiom,( m1_subset_1(k5_numbers,k1_tarski(k5_numbers)) )).
fof(l14_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => m1_msualg_2(g3_msualg_1(A,u3_msualg_1(A,B),u4_msualg_1(A,B)),A,B) ) ) )).
fof(l14_nat_4,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ ( ~ v1_int_2(A) & ~ r1_xxreal_0(A,1) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( r1_nat_d(B,A) & ~ r1_xxreal_0(B,1) & r1_xxreal_0(k2_nat_1(B,B),A) & v1_int_2(B) ) ) ) & ~ ( ~ ( ~ r1_xxreal_0(A,1) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( r1_nat_d(B,A) & ~ r1_xxreal_0(B,1) & r1_xxreal_0(k2_nat_1(B,B),A) & v1_int_2(B) ) ) ) & v1_int_2(A) ) ) ) )).
fof(l14_numbers,axiom,( ! [A] : ( ( v3_ordinal1(A) & m1_subset_1(A,k5_arytm_3) ) => ! [B] : ( ( v3_ordinal1(B) & m1_subset_1(B,k5_arytm_3) ) => ~ ( r2_hidden(A,B) & r3_arytm_3(B,A) ) ) ) )).
fof(l14_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(l14_oposet_1,axiom,( v5_orders_2(k1_oposet_1) )).
fof(l14_ordinal3,axiom,( 1 = k1_ordinal1(k5_ordinal1) )).
fof(l14_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(l14_parsp_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( k8_group_1(A,C,k5_algstr_0(A,B,D)) = k5_algstr_0(A,E,F) & F = k5_algstr_0(A,k3_rlvect_1(A,B,D),E) ) => k8_group_1(A,k5_algstr_0(A,C,k1_group_1(A)),k5_algstr_0(A,E,D)) = k8_group_1(A,k3_rlvect_1(A,C,k1_group_1(A)),k5_algstr_0(A,E,B)) ) ) ) ) ) ) ) )).
fof(l14_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ( v2_bvfunc_2(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( 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)))) ) ) ) ) ) ) )).
fof(l14_pdiff_1,axiom,( 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)))) )).
fof(l14_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k3_finseq_1(k1_funct_7(B,D,C)) = A ) ) ) ) )).
fof(l14_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( ( 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] : ( ( 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) => k4_polynom1(A,B,D,E) = k4_struct_0(B) ) ) ) ) ) ) )).
fof(l14_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(l14_qmax_1,axiom,( k10_xtuple_0(k6_domain_1(k2_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_zfmisc_1(k2_zfmisc_1(k12_prob_1,k1_numbers))),k1_domain_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_zfmisc_1(k2_zfmisc_1(k12_prob_1,k1_numbers)),k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_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)) )).
fof(l14_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ( k28_quaterni(A) = k5_numbers => A = k5_numbers ) ) )).
fof(l14_quaterni,axiom,( k1_xcmplx_0 = k5_arytm_0(c2__quaterni,c1__quaterni) )).
fof(l14_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ! [E] : ( ( 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) ) ) ) ) ) )).
fof(l14_random_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [D] : ( m2_finseq_1(D,B) => ! [E] : ( m2_finseq_1(E,B) => ! [F] : ( m2_finseq_1(F,A) => ! [G] : ( m2_finseq_1(G,A) => ( ( r2_relset_1(k4_ordinal1,A,F,k1_partfun1(k4_ordinal1,B,B,A,D,C)) & r2_relset_1(k4_ordinal1,A,G,k1_partfun1(k4_ordinal1,B,B,A,E,C)) ) => r2_relset_1(k4_ordinal1,A,k1_partfun1(k4_ordinal1,B,B,A,k8_finseq_1(B,D,E),C),k8_finseq_1(A,F,G)) ) ) ) ) ) ) ) ) )).
fof(l14_random_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( m2_prob_1(D,B,C) => v4_random_3(k8_funcop_1(k1_zfmisc_1(k2_zfmisc_1(C,k1_numbers)),A,D),B,C) ) ) ) ) )).
fof(l14_realset2,axiom,( k5_binop_1(2,k1_realset2,k10_subset_1(1,2),k10_subset_1(k5_numbers,2)) = k10_subset_1(1,2) )).
fof(l14_rearran1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( m2_finseq_1(C,k1_zfmisc_1(B)) => ( r2_hidden(A,k4_finseq_1(C)) => r1_tarski(k1_funct_1(C,A),B) ) ) ) ) )).
fof(l14_rfunct_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( r1_rfunct_4(B,C) => ( r1_xxreal_0(A,k5_numbers) | r1_rfunct_4(k26_valued_1(k1_numbers,k1_numbers,B,A),C) ) ) ) ) )).
fof(l14_ringcat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(l14_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l14_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ~ r1_xxreal_0(k5_card_1(A),k5_numbers) ) )).
fof(l14_scmfsa_1,axiom,( ! [A] : ( m2_subset_1(A,k1_scmfsa_1,k3_scmfsa_1) => k3_funct_2(k1_scmfsa_1,k7_card_1(3),k4_scmfsa_1,A) = 2 ) )).
fof(l14_scpisort,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ! [C] : ( v1_int_1(C) => ! [D] : ( v7_ordinal1(D) => 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)) ) ) ) ) )).
fof(l14_seq_2,axiom,( v7_ordinal1(k5_numbers) )).
fof(l14_series_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k3_xcmplx_0(k11_newton(k1_nat_1(A,1),2),k6_xcmplx_0(k2_nat_1(2,k11_newton(k1_nat_1(A,1),2)),1)) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_nat_1(k2_nat_1(k11_newton(A,2),k11_newton(A,2)),2),k3_xcmplx_0(k6_xcmplx_0(12,1),k11_newton(A,2))),k2_nat_1(8,k11_newton(A,3))),k2_nat_1(6,A)),1) ) )).
fof(l14_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => k3_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(B,C),A),k7_xcmplx_0(k3_xcmplx_0(C,A),B)) = k1_square_1(C) ) ) ) )).
fof(l14_setlim_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ( v3_funct_1(C) & k3_funct_1(C) = B ) => ! [D] : ( v7_ordinal1(D) => ( k1_funct_1(C,D) = B & k1_kurato_0(A,C) = B & k3_prob_1(A,C) = B ) ) ) ) ) )).
fof(l14_sin_cos6,axiom,( ~ r1_xxreal_0(k2_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),1)),k2_xcmplx_0(k5_numbers,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),1))) )).
fof(l14_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_topdim_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v7_ordinal1(k2_xcmplx_0(k2_topdim_1(A,B),1)) ) ) )).
fof(l14_topdim_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(l14_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ? [D] : ( 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] : ~ ( r2_hidden(E,D) & r1_xboole_0(E,B) ) ) => r2_hidden(C,k2_pre_topc(A,B)) ) ) ) ) )).
fof(l14_topreal2,axiom,( ~ r2_hidden(k19_euclid(k5_numbers,1),k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,k5_numbers),k19_euclid(1,k5_numbers))) )).
fof(l14_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ( ( v11_aff_2(A) & r1_aff_1(A,B,C,H) & 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) & r2_analoaf(A,D,F,H,I) & r2_analoaf(A,E,G,H,J) & r2_analoaf(A,D,H,F,I) & r2_analoaf(A,E,H,G,J) ) => ( B = C | r1_aff_1(A,B,C,D) | r1_aff_1(A,B,C,E) | r1_aff_1(A,D,F,E) | I = J ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l14_waybel35,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & m1_waybel35(C,A,B) ) => ! [D] : ( 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] : ( 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] : ( m1_subset_1(F,u1_struct_0(k5_yellow_0(A,C))) & E = F & r2_lattice3(k5_yellow_0(A,C),D,F) & ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(l14_xcmplx_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ( ( k1_arytm_0(A,B) = k5_numbers & k1_arytm_0(A,C) = k5_numbers ) => B = C ) ) ) ) )).
fof(l14_xreal_0,axiom,( ? [A] : ( m1_subset_1(A,k1_numbers) & ? [B] : ( m1_subset_1(B,k1_numbers) & ? [C] : ( m1_subset_1(C,k1_numbers) & ? [D] : ( m1_subset_1(D,k1_numbers) & 1 = k5_arytm_0(A,B) & k4_xcmplx_0(1) = k5_arytm_0(C,D) & k5_numbers = k5_arytm_0(k1_arytm_0(A,C),k1_arytm_0(B,D)) ) ) ) ) )).
fof(l14_zf_fund1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => A = k3_zf_fund1(k2_zf_lang(k5_card_1(A))) ) )).
fof(l150_jordan,axiom,( r1_tarski(k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(3),3),k2_jgraph_6(k4_xcmplx_0(1),1,k4_xcmplx_0(3),3)) )).
fof(l150_toprealb,axiom,( m1_subset_1(k5_toprealb(c46__toprealb),k1_zfmisc_1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k5_numbers,k28_sin_cos)))))) )).
fof(l151_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => k5_relat_1(C,k6_subset_1(A,B)) = k6_subset_1(k5_relat_1(C,A),k2_zfmisc_1(B,k10_xtuple_0(C))) ) )).
fof(l151_jordan,axiom,( k18_euclid(k19_euclid(k4_xcmplx_0(1),3)) = k18_euclid(k19_euclid(k4_xcmplx_0(1),3)) )).
fof(l151_toprealb,axiom,( k1_pre_topc(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k4_xcmplx_0(1),1))),c55__toprealb) = k1_pre_topc(k2_topalg_2,k5_toprealb(c45__toprealb)) )).
fof(l152_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => k1_funct_4(A,B) = k2_xboole_0(k6_subset_1(A,k2_zfmisc_1(k9_xtuple_0(B),k10_xtuple_0(A))),B) ) ) )).
fof(l152_jordan,axiom,( r1_xxreal_0(k17_euclid(k19_euclid(k4_xcmplx_0(1),3)),k17_euclid(k19_euclid(k5_numbers,3))) )).
fof(l152_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & v5_modelc_3(A) & m2_finseq_1(A,k4_ordinal1) ) => k48_modelc_2(k13_modelc_3(A,k7_modelc_3(A))) = k1_xboole_0 ) )).
fof(l152_toprealb,axiom,( k1_pre_topc(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_rcomp_1(k5_numbers,k28_sin_cos))),c56__toprealb) = k1_pre_topc(k2_topalg_2,k5_toprealb(c46__toprealb)) )).
fof(l153_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : k3_xboole_0(A,C) = k6_subset_1(A,k6_subset_1(k2_xboole_0(A,B),C)) )).
fof(l153_jordan,axiom,( r1_xxreal_0(k17_euclid(k19_euclid(k5_numbers,3)),k17_euclid(k19_euclid(1,3))) )).
fof(l153_toprealb,axiom,( v5_pre_topc(c54__toprealb,k1_pre_topc(k2_topalg_2,k5_toprealb(c45__toprealb)),k1_pre_topc(k2_topalg_2,k5_toprealb(c46__toprealb))) )).
fof(l154_jordan,axiom,( r1_tarski(k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),3),k19_euclid(k5_numbers,3)),k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),3),k19_euclid(1,3))) )).
fof(l155_fomodel0,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k5_relat_1(B,k6_subset_1(k9_xtuple_0(B),A)) = k6_subset_1(B,k2_zfmisc_1(A,k10_xtuple_0(B))) ) )).
fof(l155_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) => ! [C] : ( v4_funct_1(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k40_fomodel2(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k40_fomodel2(A)))) ) => ( ( v7_fomodel4(B,A) & r2_hidden(k25_fomodel4(A),B) & r2_hidden(k35_fomodel4(A),B) & r2_hidden(k26_fomodel4(A),B) & r2_hidden(k32_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)))))) | v10_fomodel4(C,A,B) | v1_cohsp_1(k10_xtuple_0(k44_fomodel4(C,A,B,D))) ) ) ) ) ) ) )).
fof(l155_jordan,axiom,( r1_tarski(k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),3),k19_euclid(k5_numbers,3)),k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(3),3)) )).
fof(l155_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_zmodul01(B) & m1_zmodul01(B,A) ) => ( ! [C] : ( 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)) ) ) ) )).
fof(l156_jordan,axiom,( r1_tarski(k1_rltopsp1(k15_euclid(2),k19_euclid(1,3),k19_euclid(k5_numbers,3)),k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),3),k19_euclid(1,3))) )).
fof(l156_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(l157_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) => ! [C] : ( v4_funct_1(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k40_fomodel2(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k40_fomodel2(A)))) ) => ~ ( v7_fomodel4(B,A) & r2_hidden(k25_fomodel4(A),B) & r2_hidden(k26_fomodel4(A),B) & r2_hidden(k32_fomodel4(A),B) & r2_hidden(k35_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)))))) & ~ v10_fomodel4(C,A,B) & v10_fomodel4(k45_fomodel4(C,A,B,D),A,B) ) ) ) ) ) )).
fof(l157_jordan,axiom,( r1_tarski(k1_rltopsp1(k15_euclid(2),k19_euclid(1,3),k19_euclid(k5_numbers,3)),k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(3),3)) )).
fof(l158_jordan,axiom,( k18_euclid(k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3))) = k18_euclid(k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3))) )).
fof(l158_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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 ) ) )).
fof(l158_toprealb,axiom,( v1_t_0topsp(k13_toprealb(k4_toprealb(k5_numbers)),k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k4_toprealb(k5_numbers),k2_xcmplx_0(k4_toprealb(k5_numbers),1)))),k11_toprealb(k3_funct_2(u1_struct_0(k2_topalg_2),u1_struct_0(k8_toprealb(2)),k12_toprealb,k4_toprealb(k5_numbers)))) )).
fof(l159_jordan,axiom,( r1_xxreal_0(k17_euclid(k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3))),k17_euclid(k19_euclid(k5_numbers,k4_xcmplx_0(3)))) )).
fof(l159_seq_4,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( k5_card_1(A) = k5_numbers => ( A = k1_xboole_0 | ( v4_xxreal_2(A) & r2_hidden(k2_seq_4(A),A) & v3_xxreal_2(A) & r2_hidden(k3_seq_4(A),A) ) ) ) ) )).
fof(l159_toprealb,axiom,( v1_t_0topsp(k13_toprealb(k4_toprealb(k7_xcmplx_0(1,2))),k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k4_toprealb(k7_xcmplx_0(1,2)),k2_xcmplx_0(k4_toprealb(k7_xcmplx_0(1,2)),1)))),k11_toprealb(k3_funct_2(u1_struct_0(k2_topalg_2),u1_struct_0(k8_toprealb(2)),k12_toprealb,k4_toprealb(k7_xcmplx_0(1,2))))) )).
fof(l159_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ( r1_zmodul01(A,B,C) => r1_zmodul01(A,C,B) ) ) ) ) )).
fof(l15_afvect01,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(o_0_0_afvect01)) => ! [B] : ( m1_subset_1(B,u1_struct_0(o_0_0_afvect01)) => ! [C] : ( m1_subset_1(C,u1_struct_0(o_0_0_afvect01)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l15_algstr_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_3)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_algstr_3)) => ( A != B => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_algstr_3)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_algstr_3)) => ? [E] : ( m1_subset_1(E,u1_struct_0(k3_algstr_3)) & ? [F] : ( 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 ) ) ) ) ) ) ) )).
fof(l15_ami_6,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => k1_amistd_1(k7_card_1(2),k1_ami_3,B,A) = k1_tarski(k1_ordinal1(B)) ) => v1_xboole_0(k2_amistd_1(k7_card_1(2),k1_ami_3,A)) ) ) )).
fof(l15_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( k3_rlvect_1(A,B,k1_rlvect_1(A,D,E)) = k3_rlvect_1(A,C,k1_rlvect_1(A,D,F)) => k3_rlvect_1(A,k1_rlvect_1(A,D,k6_xcmplx_0(E,F)),B) = C ) ) ) ) ) ) ) )).
fof(l15_arytm_0,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l15_asympt_1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( r1_xxreal_0(4,A) & r1_xxreal_0(k5_series_1(2,A),k1_nat_1(k3_xcmplx_0(2,A),3)) ) ) )).
fof(l15_borsuk_2,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,1) ) => ( r1_xxreal_0(k5_numbers,k6_xcmplx_0(1,A)) & r1_xxreal_0(k6_xcmplx_0(1,A),1) ) ) ) )).
fof(l15_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( k17_sin_cos(k7_xcmplx_0(k6_xcmplx_0(A,B),2)) = k5_numbers & ! [C] : ( v1_int_1(C) => A != k2_xcmplx_0(B,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)) ) ) ) ) )).
fof(l15_brouwer2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(l15_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( 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] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(l15_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ! [E] : ( D != E => ( k2_xboole_0(a_5_0_card_fin(A,B,C,D,E),a_5_8_card_fin(A,B,C,D,E)) = k1_card_fin(k2_xboole_0(A,k1_tarski(C)),k1_nat_1(B,1),D,E) & r1_xboole_0(a_5_0_card_fin(A,B,C,D,E),a_5_8_card_fin(A,B,C,D,E)) ) ) ) ) )).
fof(l15_cardfin2,axiom,( m1_subset_1(1,k4_numbers) & m1_subset_1(k5_numbers,k4_numbers) )).
fof(l15_cfdiff_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( m1_cfdiff_1(B,A) => ! [C] : ( m1_cfdiff_1(C,A) => ? [D] : ( m1_cfdiff_1(D,A) & r1_tarski(D,B) & r1_tarski(D,C) ) ) ) ) )).
fof(l15_cfdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( 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))) ) ) ) ) )).
fof(l15_chord,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v1_abian(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v1_abian(B) ) => ~ ( r1_xxreal_0(A,B) & ! [C] : ( v7_ordinal1(C) => k2_xcmplx_0(A,k3_xcmplx_0(2,C)) != B ) ) ) ) )).
fof(l15_compos_1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ r1_xxreal_0(A,k4_xcmplx_0(1)) ) )).
fof(l15_convex2,axiom,( ! [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) ) => ! [B] : ( ( v2_convex1(B,A) & m1_rlvect_2(B,A) ) => ! [C] : ( ( v2_convex1(C,A) & m1_rlvect_2(C,A) ) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ~ r1_xxreal_0(k3_xcmplx_0(D,E),k5_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))) ) ) ) ) ) ) )).
fof(l15_convfun1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k6_numbers) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k4_convfun1)) => ( ( k3_finseq_1(B) = A & k3_finseq_1(C) = A & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( 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) ) ) ) ) )).
fof(l15_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) )).
fof(l15_csspace2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k18_csspace)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k18_csspace)) => k5_algstr_0(k18_csspace,A,B) = k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k2_csspace(A),k2_csspace(B)) ) ) )).
fof(l15_dtconstr,axiom,( r1_lang1(k5_dtconstr,c3__dtconstr,k3_pre_poly(u1_struct_0(k5_dtconstr),c3__dtconstr)) )).
fof(l15_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m1_subset_1(B,k2_numbers) => ~ ( B != k5_numbers & ~ r1_xxreal_0(k5_numbers,k6_xcmplx_0(k1_comptrig(B),k1_comptrig(A))) & k1_comptrig(k2_complex2(B,k4_xcmplx_0(k1_comptrig(A)))) != k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k1_comptrig(A)),k1_comptrig(B)) ) ) ) )).
fof(l15_extreal1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( m2_finseq_1(D,k6_numbers) => ! [E] : ( m2_finseq_1(E,k6_numbers) => ( ( D = k1_partfun1(k2_finseq_1(k1_nat_1(A,1)),k2_finseq_1(k1_nat_1(A,1)),k4_ordinal1,k6_numbers,C,E) & r2_hidden(B,k2_finseq_1(k1_nat_1(A,1))) & k3_finseq_1(E) = k1_nat_1(A,1) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r2_hidden(F,k2_finseq_1(k1_nat_1(A,1))) => ( ( ~ r1_xxreal_0(B,F) => k1_funct_1(C,F) = F ) & ( F = B => k1_funct_1(C,F) = k1_nat_1(A,1) ) & ( ~ r1_xxreal_0(F,B) => k1_funct_1(C,F) = k6_xcmplx_0(F,1) ) ) ) ) ) => ( r2_hidden(k2_supinf_1,k2_relset_1(k6_numbers,E)) | k4_extreal1(D) = k4_extreal1(E) ) ) ) ) ) ) ) )).
fof(l15_fib_fusc,axiom,( k10_ami_3(2) != k10_ami_3(4) )).
fof(l15_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ~ r1_xxreal_0(k3_xcmplx_0(k2_power(k9_complex1(k2_fib_num),A),k7_xcmplx_0(1,k3_square_1(5))),k5_numbers) ) )).
fof(l15_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)) & v3_funct_2(E,k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)))) ) => ( ( v1_setwiseo(D,A) & k3_finseq_1(B) = k5_numbers & C = k3_relat_1(E,B) ) => k1_finsop_1(A,B,D) = k1_finsop_1(A,C,D) ) ) ) ) ) ) )).
fof(l15_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : k3_xboole_0(k1_funct_2(A,B),k1_funct_2(A,C)) = k1_funct_2(A,k3_xboole_0(B,C)) )).
fof(l15_fomodel3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v8_ordinal1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(l15_friends1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(D) & v1_finset_1(D) ) => ! [E] : ( ( v3_friends1(D) & r2_hidden(k4_tarski(A,C),D) & r2_hidden(k4_tarski(C,B),D) & r2_hidden(k4_tarski(A,E),D) & r2_hidden(k4_tarski(E,B),D) ) => ( A = B | C = E ) ) ) )).
fof(l15_functor2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ( ( r1_functor2(A,B,C,D) & r1_functor2(A,B,D,E) ) => ! [F] : ( m1_functor2(F,A,B,C,D) => ( ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( k1_altcat_1(A,G,H) != k1_xboole_0 => ! [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] : ( m1_functor2(G,A,B,D,E) => ( ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ( k1_altcat_1(A,H,I) != k1_xboole_0 => ! [J] : ( 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] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ( k1_altcat_1(A,H,I) != k1_xboole_0 => ! [J] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l15_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_analoaf(A,B,D,D,C) => ( r1_analoaf(A,C,D,D,B) & r1_analoaf(A,B,D,B,C) & r1_analoaf(A,D,C,B,C) ) ) ) ) ) ) )).
fof(l15_gfacirc1,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ! [F] : ! [G] : 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) ) ) ) ) )).
fof(l15_gobrd11,axiom,( ! [A] : ( v1_xreal_0(A) => m1_subset_1(a_1_6_gobrd11(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) )).
fof(l15_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => m1_graph_1(k1_xboole_0,A) ) )).
fof(l15_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m2_finseq_1(C,u4_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(l15_group_14,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v1_int_1(B) => r2_hidden(k5_int_1(B,A),k7_card_1(A)) ) ) )).
fof(l15_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( 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),k1_nat_1(C,1),B)) = k5_group_1(A,k1_nat_1(C,1),B) ) ) ) ) )).
fof(l15_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( v4_aff_2(A) & B != C & B != D & r1_aff_1(A,B,C,D) & ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(H,u1_struct_0(A)) & ? [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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l15_int_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_ordinal1))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( D != k4_struct_0(A) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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),k4_ordinal1,B,D),k3_funct_2(u1_struct_0(A),k4_ordinal1,B,F)) ) ) ) ) ) ) ) ) ) )).
fof(l15_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ( r1_int_2(A,B) | r1_int_1(B,A) ) ) ) )).
fof(l15_integra3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [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_comseq_2(k2_partfun1(A,k1_numbers,C,A)) & r1_tarski(B,A) ) => ( r1_xxreal_0(k3_seq_4(k1_rvsum_1(C)),k3_seq_4(k1_rvsum_1(k2_partfun1(A,k1_numbers,C,B)))) & r1_xxreal_0(k3_seq_4(k1_rvsum_1(C)),k2_seq_4(k1_rvsum_1(k2_partfun1(A,k1_numbers,C,B)))) & r1_xxreal_0(k2_seq_4(k1_rvsum_1(k2_partfun1(A,k1_numbers,C,B))),k2_seq_4(k1_rvsum_1(C))) & r1_xxreal_0(k3_seq_4(k1_rvsum_1(k2_partfun1(A,k1_numbers,C,B))),k2_seq_4(k1_rvsum_1(C))) ) ) ) ) ) )).
fof(l15_integra8,axiom,( ~ r1_xxreal_0(k19_sin_cos(k7_xcmplx_0(k28_sin_cos,4)),k5_numbers) )).
fof(l15_jgraph_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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) ) ) )).
fof(l15_jordan1c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v9_rltopsp1(A,k15_euclid(2)) => ! [B] : ( v1_xreal_0(B) => ~ ( k1_jordan2c(2,A) != k1_xboole_0 & ~ r1_xxreal_0(B,k6_pscomp_1(k1_jordan2c(2,A))) & ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( r2_hidden(C,k1_jordan2c(2,A)) => r1_xxreal_0(B,k17_euclid(C)) ) ) ) ) ) ) )).
fof(l15_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(2,A) => r1_xxreal_0(1,k7_nat_d(k3_xcmplx_0(2,A),2)) ) ) )).
fof(l15_lattice5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r1_xxreal_0(1,A) & ~ r1_xxreal_0(k1_nat_1(B,C),A) & ~ ( r1_xxreal_0(1,A) & ~ r1_xxreal_0(B,A) ) & ~ ( B = A & ~ r1_xxreal_0(k1_nat_1(B,C),A) ) & ~ ( r1_xxreal_0(k1_nat_1(B,1),A) & ~ r1_xxreal_0(k1_nat_1(B,C),A) ) ) ) ) ) )).
fof(l15_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => k15_glib_001(A,B) = k15_glib_001(A,k6_glib_001(A,B)) ) ) )).
fof(l15_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,C) => ( k2_relset_1(k1_numbers,k2_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,k2_fuzzy_4(A,B,C,D,E,F,G)) != k1_xboole_0 ) ) ) ) ) ) ) ) )).
fof(l15_lopban_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m2_funct_2(C,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => ! [D] : ( m2_funct_2(D,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => ! [E] : ( v1_xreal_0(E) => k1_binop_1(k2_lopban_1(A,B),k1_funct_1(k3_lopban_1(A,B),k4_tarski(E,C)),k1_funct_1(k3_lopban_1(A,B),k4_tarski(E,D))) = k1_funct_1(k3_lopban_1(A,B),k4_tarski(E,k1_funcsdom(A,u1_struct_0(B),k2_lopban_1(A,B),C,D))) ) ) ) ) ) )).
fof(l15_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(l15_measure7,axiom,( k2_relset_1(k9_setfam_1(k1_numbers),c1__measure7) = k1_tarski(k1_numbers) )).
fof(l15_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( ( D = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),B,k6_xcmplx_0(1,G)),k1_rlvect_1(k15_euclid(2),C,G)) & E = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),C,k6_xcmplx_0(1,H)),k1_rlvect_1(k15_euclid(2),A,H)) & F = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),A,k6_xcmplx_0(1,I)),k1_rlvect_1(k15_euclid(2),D,I)) ) => k1_euclid_6(B,E,F) = k3_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(1,H),k3_xcmplx_0(I,k2_xcmplx_0(k6_xcmplx_0(1,H),k3_xcmplx_0(G,H)))),k1_euclid_6(A,B,C)) ) ) ) ) ) ) ) ) ) ) )).
fof(l15_mesfunc3,axiom,( ! [A] : ( m2_finseq_1(A,k6_numbers) => ! [B] : ( m1_subset_1(B,k6_numbers) => ! [C] : ( m1_subset_1(C,k6_numbers) => ( ( C = k3_finseq_1(A) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(A)) => k12_supinf_2(A,D) = B ) ) ) => k4_extreal1(A) = k1_extreal1(C,B) ) ) ) ) )).
fof(l15_mesfunc9,axiom,( v1_xreal_0(1) )).
fof(l15_msualg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_finseq_1(k1_unialg_1(A)),k3_finseq_2(k1_tarski(k5_numbers))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_1(k1_unialg_1(A)),k3_finseq_2(k1_tarski(k5_numbers))))) ) => ( v5_msualg_1(g1_msualg_1(k1_tarski(k5_numbers),k4_finseq_1(k1_unialg_1(A)),B,k1_margrel1(k1_tarski(k5_numbers),k4_finseq_1(k1_unialg_1(A)),c1__msualg_1))) & v13_struct_0(g1_msualg_1(k1_tarski(k5_numbers),k4_finseq_1(k1_unialg_1(A)),B,k1_margrel1(k1_tarski(k5_numbers),k4_finseq_1(k1_unialg_1(A)),c1__msualg_1)),1) & ~ v11_struct_0(g1_msualg_1(k1_tarski(k5_numbers),k4_finseq_1(k1_unialg_1(A)),B,k1_margrel1(k1_tarski(k5_numbers),k4_finseq_1(k1_unialg_1(A)),c1__msualg_1))) & v1_msualg_1(g1_msualg_1(k1_tarski(k5_numbers),k4_finseq_1(k1_unialg_1(A)),B,k1_margrel1(k1_tarski(k5_numbers),k4_finseq_1(k1_unialg_1(A)),c1__msualg_1))) ) ) ) )).
fof(l15_numbers,axiom,( ! [A] : ( ( v3_ordinal1(A) & m1_subset_1(A,k5_arytm_3) ) => ! [B] : ( ( v3_ordinal1(B) & m1_subset_1(B,k5_arytm_3) ) => ( r1_ordinal1(A,B) => r3_arytm_3(A,B) ) ) ) )).
fof(l15_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_o_ring_1(B,A) => v5_o_ring_1(B,A) ) ) ) )).
fof(l15_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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,G),k4_algstr_0(A,F)))),k8_group_1(A,k5_algstr_0(A,E,k3_rlvect_1(A,k3_rlvect_1(A,E,C),k4_algstr_0(A,B))),k5_algstr_0(A,F,G))) = k4_struct_0(A) ) ) ) ) ) ) ) )).
fof(l15_parsp_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l15_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,A) ) => ( ( C = D => k1_funct_1(k1_funct_7(k5_euclid(A),C,B),D) = B ) & ( C != D => k1_funct_1(k1_funct_7(k5_euclid(A),C,B),D) = k5_numbers ) ) ) ) ) ) ) )).
fof(l15_projred1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & v8_incproj(A) & l1_incsp_1(A) ) => ? [B] : ( m1_subset_1(B,u1_incsp_1(A)) & ? [C] : ( m1_subset_1(C,u1_incsp_1(A)) & ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & ? [E] : ( m1_subset_1(E,u1_incsp_1(A)) & ? [F] : ( m1_subset_1(F,u1_incsp_1(A)) & ? [G] : ( m1_subset_1(G,u1_incsp_1(A)) & ? [H] : ( m1_subset_1(H,u1_incsp_1(A)) & ? [I] : ( m1_subset_1(I,u2_incsp_1(A)) & ? [J] : ( m1_subset_1(J,u2_incsp_1(A)) & ? [K] : ( m1_subset_1(K,u2_incsp_1(A)) & ? [L] : ( m1_subset_1(L,u2_incsp_1(A)) & ? [M] : ( m1_subset_1(M,u2_incsp_1(A)) & ? [N] : ( m1_subset_1(N,u2_incsp_1(A)) & ? [O] : ( m1_subset_1(O,u2_incsp_1(A)) & ? [P] : ( m1_subset_1(P,u2_incsp_1(A)) & ? [Q] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l15_prvect_2,axiom,( ! [A] : ( ( ~ 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) ) ) ) )).
fof(l15_qmax_1,axiom,( r1_tarski(k10_xtuple_0(k6_domain_1(k2_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_zfmisc_1(k2_zfmisc_1(k12_prob_1,k1_numbers))),k1_domain_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_zfmisc_1(k2_zfmisc_1(k12_prob_1,k1_numbers)),k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers),c3__qmax_1))),k1_qmax_1(k1_numbers,k12_prob_1)) )).
fof(l15_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => m2_finseq_1(k1_partfun1(k4_ordinal1,k1_relset_1(A,B),A,k1_numbers,k19_finseq_1(k1_relset_1(A,B)),B),k1_numbers) ) ) )).
fof(l15_realset2,axiom,( k5_binop_1(2,k1_realset2,k10_subset_1(1,2),k10_subset_1(1,2)) = k10_subset_1(k5_numbers,2) )).
fof(l15_ringcat1,axiom,( ! [A] : ( ( v3_ringcat1(A) & l1_ringcat1(A) ) => ? [B] : ( ~ 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] : ( ~ 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) ) ) ) )).
fof(l15_rlaffin3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v1_xreal_0(C) => r1_ordinal1(k1_card_1(k1_convex1(A,B,C)),k1_card_1(B)) ) ) ) )).
fof(l15_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(l15_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( u1_struct_0(B) = C => v1_rlsub_1(C,A) ) ) ) ) ) )).
fof(l15_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => m2_finseq_1(A,k1_numbers) ) )).
fof(l15_scmp_gcd,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( r1_tarski(k4_scmp_gcd,A) => ( k3_compos_1(k1_scmpds_2,A,k5_numbers) = k5_scmpds_2(k2_scmp_gcd,k5_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,k1_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) ) ) ) )).
fof(l15_series_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k3_xcmplx_0(k1_nat_1(A,2),k6_xcmplx_0(k1_nat_1(k11_newton(k1_nat_1(A,1),2),k1_nat_1(A,1)),1)) = k1_nat_1(k1_nat_1(k1_nat_1(k11_newton(A,3),k2_nat_1(5,k11_newton(A,2))),k2_nat_1(7,A)),2) ) )).
fof(l15_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k7_xcmplx_0(k3_xcmplx_0(B,C),A)),k7_xcmplx_0(k3_xcmplx_0(C,A),B)),k3_xcmplx_0(k3_xcmplx_0(2,k7_xcmplx_0(k3_xcmplx_0(B,C),A)),k7_xcmplx_0(k3_xcmplx_0(A,B),C))),k3_xcmplx_0(k3_xcmplx_0(2,k7_xcmplx_0(k3_xcmplx_0(C,A),B)),k7_xcmplx_0(k3_xcmplx_0(A,B),C))) = k3_xcmplx_0(2,k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(C))) ) ) ) )).
fof(l15_sin_cos6,axiom,( ~ r1_xxreal_0(k3_xcmplx_0(2,k28_sin_cos),k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos)) )).
fof(l15_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(1,k1_square_1(A)) & r1_xxreal_0(k7_xcmplx_0(k2_xcmplx_0(A,1),k6_xcmplx_0(1,A)),k5_numbers) ) ) )).
fof(l15_t_0topsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_t_0topsp(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_t_0topsp(A))) => ~ ( B != C & ! [D] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l15_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(l15_topalg_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(l15_topgen_3,axiom,( u1_struct_0(k2_topgen_3) = k1_numbers )).
fof(l15_topreal2,axiom,( ~ r2_hidden(k19_euclid(k5_numbers,1),k1_rltopsp1(k15_euclid(2),k19_euclid(1,k5_numbers),k19_euclid(1,1))) )).
fof(l15_uniform1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( k3_finseq_1(k7_finseq_1(B,k9_finseq_1(A))) = k1_nat_1(k3_finseq_1(B),1) & k3_finseq_1(k7_finseq_1(k9_finseq_1(A),B)) = k1_nat_1(k3_finseq_1(B),1) & k1_funct_1(k7_finseq_1(B,k9_finseq_1(A)),k1_nat_1(k3_finseq_1(B),1)) = A & k1_funct_1(k7_finseq_1(k9_finseq_1(A),B),1) = A ) ) )).
fof(l15_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ? [D] : ( v7_vectsp_1(D,A) & m1_vectsp_4(D,A,B) & u1_struct_0(C) = u1_struct_0(D) ) ) ) ) )).
fof(l15_waybel17,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_orders_2(A,B,C) => k1_waybel11(A,k3_waybel17(A,B,C)) = B ) ) ) ) )).
fof(l15_waybel25,axiom,( ! [A] : ( l1_pre_topc(A) => u1_struct_0(A) = u1_struct_0(k1_waybel25(A)) ) )).
fof(l15_waybel_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,C,k7_funcop_1(A,B)) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r2_hidden(E,k1_relset_1(k4_card_3(k1_funct_6(D)),k2_pralg_2(D))) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(l15_weierstr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) = k2_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) = k3_seq_4(k1_weierstr(k7_relset_1(u1_struct_0(A),u1_struct_0(k3_topmetr),B,C))) ) ) ) ) ) ) ) )).
fof(l15_xreal_0,axiom,( 1 = k5_arytm_0(c3__xreal_0,c4__xreal_0) )).
fof(l15_xreal_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( A = C & B = D ) => k2_arytm_0(A,B) = k3_xcmplx_0(C,D) ) ) ) ) ) )).
fof(l15_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ( r1_xxreal_0(A,k2_xxreal_0) => A = k2_xxreal_0 ) ) )).
fof(l15_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ( r2_hidden(k2_xxreal_3(A),k1_numbers) <=> r2_hidden(A,k1_numbers) ) ) )).
fof(l15_yellow11,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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 ) ) ) ) ) ) ) ) )).
fof(l15_yellow21,axiom,( ! [A] : ! [B] : ( r2_hidden(A,B) <=> B = k2_xboole_0(k6_subset_1(B,k1_tarski(A)),k1_tarski(A)) ) )).
fof(l15_zf_fund1,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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 ) ) ) ) )).
fof(l15_zfmisc_1,axiom,( ! [A] : ! [B] : ( r1_tarski(k2_xboole_0(k1_tarski(A),B),B) => r2_hidden(A,B) ) )).
fof(l160_jordan,axiom,( r1_xxreal_0(k17_euclid(k19_euclid(k5_numbers,k4_xcmplx_0(3))),k17_euclid(k19_euclid(1,k4_xcmplx_0(3)))) )).
fof(l160_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ( ! [B] : ( ( 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(k2_seq_4(B),B) & v3_xxreal_2(B) & r2_hidden(k3_seq_4(B),B) ) ) ) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( k5_card_1(B) = k1_nat_1(A,1) => ( B = k1_xboole_0 | ( v4_xxreal_2(B) & r2_hidden(k2_seq_4(B),B) & v3_xxreal_2(B) & r2_hidden(k3_seq_4(B),B) ) ) ) ) ) ) )).
fof(l160_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( m2_subset_1(E,k4_ordinal1,k1_zf_lang) => ! [F] : ( m2_subset_1(F,k4_ordinal1,k1_zf_lang) => ( ( A = k5_zf_lang1(C,E,F) & B = k5_zf_lang1(D,E,F) ) => k7_zf_lang(A,B) = k5_zf_lang1(k7_zf_lang(C,D),E,F) ) ) ) ) ) ) ) )).
fof(l161_jordan,axiom,( r1_tarski(k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3)),k19_euclid(k5_numbers,k4_xcmplx_0(3))),k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3)),k19_euclid(1,k4_xcmplx_0(3)))) )).
fof(l161_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ! [E] : ( m2_subset_1(E,k4_ordinal1,k1_zf_lang) => ! [F] : ( m2_subset_1(F,k4_ordinal1,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) ) ) ) ) ) ) ) ) )).
fof(l162_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( m1_subset_1(C,k15_funct_3(A,B)) => ~ ( A != k1_xboole_0 & B != k1_xboole_0 & ~ ( v1_xtuple_0(k1_xtuple_0(C)) & v1_xtuple_0(k2_xtuple_0(C)) ) ) ) ) ) )).
fof(l162_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k30_fomodel2(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k30_fomodel2(B)))) ) => ( k10_xtuple_0(D) = k30_fomodel2(B) => v9_fomodel2(k49_fomodel4(A,B,C,D),B) ) ) ) ) )).
fof(l162_jordan,axiom,( r1_tarski(k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3)),k19_euclid(k5_numbers,k4_xcmplx_0(3))),k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(3),3)) )).
fof(l163_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => r1_tarski(k3_relat_1(C,k2_zfmisc_1(A,B)),k2_zfmisc_1(k8_relat_1(C,A),B)) ) )).
fof(l163_jordan,axiom,( r1_tarski(k1_rltopsp1(k15_euclid(2),k19_euclid(1,k4_xcmplx_0(3)),k19_euclid(k5_numbers,k4_xcmplx_0(3))),k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3)),k19_euclid(1,k4_xcmplx_0(3)))) )).
fof(l164_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => k3_relat_1(C,k2_zfmisc_1(A,B)) = k2_zfmisc_1(k8_relat_1(C,A),B) ) )).
fof(l164_jordan,axiom,( r1_tarski(k1_rltopsp1(k15_euclid(2),k19_euclid(1,k4_xcmplx_0(3)),k19_euclid(k5_numbers,k4_xcmplx_0(3))),k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(3),3)) )).
fof(l165_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r1_tarski(D,B) => ( D = k1_xboole_0 | k3_relat_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,C)) = k2_zfmisc_1(A,C) ) ) )).
fof(l165_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ~ ( v7_fomodel4(D,B) & r2_hidden(k25_fomodel4(B),D) & r2_hidden(k35_fomodel4(B),D) & v9_fomodel4(C,B,D,A) & ~ v10_fomodel4(A,B,D) & v10_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) ) ) ) ) )).
fof(l165_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ~ ( r1_xxreal_0(k5_numbers,k18_euclid(A)) & r2_hidden(A,k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(3),3)) & ~ r2_hidden(A,k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(k4_xcmplx_0(1),3))) & ~ r2_hidden(A,k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),3),k19_euclid(k5_numbers,3))) & ~ r2_hidden(A,k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,3),k19_euclid(1,3))) & ~ r2_hidden(A,k1_rltopsp1(k15_euclid(2),k19_euclid(1,3),k19_euclid(1,k5_numbers))) ) ) )).
fof(l166_fomodel0,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k3_relat_1(B,k2_zfmisc_1(k10_xtuple_0(B),A)) = k2_zfmisc_1(k9_xtuple_0(B),A) ) )).
fof(l166_fomodel4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ( ( ~ v6_struct_0(D) & v11_fomodel1(D) & l1_fomodel1(D) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(D)),k9_setfam_1(k1_fomodel4(D))))) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k30_fomodel2(D)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k30_fomodel2(D)))) ) => ( ( v7_fomodel4(E,D) & r2_hidden(k25_fomodel4(D),E) & r2_hidden(k35_fomodel4(D),E) ) => ( v10_fomodel4(C,D,E) | ( r1_tarski(k9_nat_1(k9_setfam_1(k2_xboole_0(C,k30_fomodel2(D))),k48_fomodel4(C,D,E,F),A),k9_nat_1(k9_setfam_1(k2_xboole_0(C,k30_fomodel2(D))),k48_fomodel4(C,D,E,F),k2_xcmplx_0(A,B))) & ~ v10_fomodel4(k9_nat_1(k9_setfam_1(k2_xboole_0(C,k30_fomodel2(D))),k48_fomodel4(C,D,E,F),B),D,E) ) ) ) ) ) ) ) ) )).
fof(l166_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ~ ( r1_xxreal_0(k18_euclid(A),k5_numbers) & r2_hidden(A,k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(3),3)) & ~ r2_hidden(A,k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3)))) & ~ r2_hidden(A,k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3)),k19_euclid(k5_numbers,k4_xcmplx_0(3)))) & ~ r2_hidden(A,k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,k4_xcmplx_0(3)),k19_euclid(1,k4_xcmplx_0(3)))) & ~ r2_hidden(A,k1_rltopsp1(k15_euclid(2),k19_euclid(1,k4_xcmplx_0(3)),k19_euclid(1,k5_numbers))) ) ) )).
fof(l167_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( k10_xtuple_0(A) = k9_xtuple_0(A) => ( v1_funct_1(A) & v1_funct_2(A,k9_xtuple_0(A),k9_xtuple_0(A)) & v2_funct_2(A,k9_xtuple_0(A)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k9_xtuple_0(A),k9_xtuple_0(A)))) ) ) ) )).
fof(l167_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k30_fomodel2(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k30_fomodel2(B)))) ) => ( ( v7_fomodel4(C,B) & r2_hidden(k25_fomodel4(B),C) & r2_hidden(k35_fomodel4(B),C) ) => ( v10_fomodel4(A,B,C) | v1_cohsp_1(k10_xtuple_0(k48_fomodel4(A,B,C,D))) ) ) ) ) ) )).
fof(l168_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_partit_2(A) => r1_tarski(k3_relat_1(A,A),k6_partfun1(k9_xtuple_0(A))) ) ) )).
fof(l168_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k30_fomodel2(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k30_fomodel2(B)))) ) => ~ ( v7_fomodel4(C,B) & r2_hidden(k25_fomodel4(B),C) & r2_hidden(k35_fomodel4(B),C) & ~ v10_fomodel4(A,B,C) & v10_fomodel4(k49_fomodel4(A,B,C,D),B,C) ) ) ) ) )).
fof(l168_group_9,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( 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))) ) ) ) )).
fof(l169_fomodel0,axiom,( ! [A] : k9_subset_1(k2_zfmisc_1(k3_xboole_0(k9_xtuple_0(A),k10_xtuple_0(A)),k3_xboole_0(k9_xtuple_0(A),k10_xtuple_0(A))),A,k6_partfun1(k3_xboole_0(k9_xtuple_0(A),k10_xtuple_0(A)))) = k9_subset_1(k2_zfmisc_1(k9_xtuple_0(A),k9_xtuple_0(A)),A,k6_partfun1(k9_xtuple_0(A))) )).
fof(l169_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v13_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] : ( v4_funct_1(C) => ~ ( v4_card_3(k30_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)))))) & ~ v10_fomodel4(C,A,B) & v7_fomodel4(B,A) & ! [D] : ( ( ~ v1_xboole_0(D) & v4_card_3(D) ) => ! [E] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(A),k3_rfunct_3(k3_finseq_2(D),k2_xboole_0(D,k6_margrel1))),k15_fomodel2(A,D)) => ~ v10_fomodel2(C,D,A,E) ) ) ) ) ) ) )).
fof(l169_group_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_finset_1(B) => ~ ( ! [C] : ~ ( r2_hidden(C,B) & ! [D] : ( v1_finset_1(D) => ~ ( D = C & k5_card_1(D) = A & ! [E] : ( r2_hidden(E,B) => ( C = E | ( r2_wellord2(C,E) & r1_xboole_0(C,E) ) ) ) ) ) ) & ! [C] : ( v1_finset_1(C) => ~ ( C = k3_tarski(B) & k5_card_1(C) = k2_nat_1(A,k5_card_1(B)) ) ) ) ) ) )).
fof(l169_group_9,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => k3_relat_1(B,k5_relat_1(C,A)) = k3_relat_1(k6_relat_1(A,B),C) ) ) )).
fof(l169_seq_4,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ~ ( k5_card_1(k1_rvsum_1(A)) = k5_numbers & ! [B] : ( 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) ) ) ) ) )).
fof(l169_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m2_zmodul01(D,A,B) & r2_hidden(C,D) ) ) ) ) )).
fof(l16_afvect01,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(o_0_0_afvect01)) => ! [B] : ( m1_subset_1(B,u1_struct_0(o_0_0_afvect01)) => ! [C] : ( m1_subset_1(C,u1_struct_0(o_0_0_afvect01)) => ! [D] : ( m1_subset_1(D,u1_struct_0(o_0_0_afvect01)) => ! [E] : ( m1_subset_1(E,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [F] : ( m1_subset_1(F,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [G] : ( m1_subset_1(G,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(l16_algstr_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_0)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_algstr_0)) => ! [C] : ( 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)) ) ) ) )).
fof(l16_algstr_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_3)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_algstr_3)) => ( A != B => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_algstr_3)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_algstr_3)) => ? [E] : ( 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) ) ) ) ) ) ) )).
fof(l16_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => k4_algstr_0(A,k1_rlvect_1(A,B,C)) = k1_rlvect_1(A,B,k4_xcmplx_0(C)) ) ) ) )).
fof(l16_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ~ ( r2_hidden(B,k1_arytm_2) & r2_hidden(A,B) & ! [C] : ( m1_subset_1(C,k5_arytm_3) => ~ ( r2_hidden(C,B) & ~ r3_arytm_3(C,A) ) ) ) ) )).
fof(l16_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(6,A) & r1_xxreal_0(k5_series_1(2,A),k1_square_1(k1_nat_1(A,1))) ) ) )).
fof(l16_borsuk_2,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,u1_struct_0(k5_topmetr)) => r2_hidden(k6_xcmplx_0(1,A),u1_struct_0(k5_topmetr)) ) ) )).
fof(l16_borsuk_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(l16_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_c0sp2(A))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(l16_catalg_1,axiom,( ! [A] : ( ( v3_catalg_1(A) & l1_msualg_1(A) ) => ! [B] : ( r2_hidden(B,k10_xtuple_0(k2_xboole_0(u1_struct_0(A),u4_struct_0(A)))) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) )).
fof(l16_cfdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_real_ns1(2))) => ( ( C = k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1)) & D = k10_finseq_1(A,B) ) => k9_complex1(C) = k2_normsp_0(k4_real_ns1(2),D) ) ) ) ) ) )).
fof(l16_cohsp_1,axiom,( ! [A] : ! [B] : k3_tarski(k1_enumset1(A,B,k2_xboole_0(A,B))) = k2_xboole_0(A,B) )).
fof(l16_compos_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( 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(k1_nat_1(B,C),3)) ) & A != k6_xcmplx_0(k1_nat_1(B,C),2) & r1_xxreal_0(A,k6_xcmplx_0(k1_nat_1(B,C),2)) & A != k6_xcmplx_0(B,1) ) ) ) ) ) )).
fof(l16_comseq_2,axiom,( v7_ordinal1(k5_numbers) )).
fof(l16_convex2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_classes1(A,B) => ! [C] : ! [D] : ~ ( r2_hidden(C,k9_xtuple_0(A)) & r2_hidden(D,k9_xtuple_0(A)) & C != D & ! [E] : ! [F] : ~ ( 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) ) ) ) ) ) )).
fof(l16_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) )).
fof(l16_csspace2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k18_csspace)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k18_csspace)) => v1_series_1(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,k2_csspace(A)),k55_valued_1(k4_ordinal1,k2_numbers,k2_csspace(B)))) ) ) )).
fof(l16_dtconstr,axiom,( r1_lang1(k5_dtconstr,c3__dtconstr,k3_pre_poly(u1_struct_0(k5_dtconstr),c2__dtconstr)) )).
fof(l16_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(l16_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(l16_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m1_subset_1(B,k2_numbers) => ~ ( B != k5_numbers & ~ r1_xxreal_0(k5_numbers,k6_xcmplx_0(k1_comptrig(B),k1_comptrig(A))) & k3_complex2(A,B) != k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k1_comptrig(A)),k1_comptrig(B)) ) ) ) )).
fof(l16_fdiff_9,axiom,( k3_limfunc1(k5_numbers) = a_0_0_fdiff_9 )).
fof(l16_fib_fusc,axiom,( k10_ami_3(3) != k10_ami_3(4) )).
fof(l16_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ~ r1_xxreal_0(k7_xcmplx_0(1,2),k3_xcmplx_0(k2_power(k9_complex1(k2_fib_num),A),k7_xcmplx_0(1,k3_square_1(5)))) ) )).
fof(l16_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) <=> r2_hidden(k3_lattices(A,C,D),B) ) ) ) ) ) ) )).
fof(l16_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l16_gfacirc1,axiom,( ! [A] : ( ( 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] : ! [C] : ! [D] : ( D != k4_tarski(k10_finseq_1(B,C),A) => ! [E] : ( 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) ) ) ) ) )).
fof(l16_gfacirc2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( 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(k5_numbers,k6_margrel1),k7_margrel1) & k9_xtuple_0(k2_xtuple_0(k3_gfacirc2(C,A,B))) = k4_finseq_2(k5_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) ) ) ) ) ) )).
fof(l16_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & ~ v4_glib_000(A) & v1_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l16_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) ) => r1_tarski(k2_glib_004,k1_relset_1(k4_ordinal1,A)) ) )).
fof(l16_goboard5,axiom,( m1_subset_1(1,k1_numbers) & m1_subset_1(k5_numbers,k1_numbers) )).
fof(l16_gobrd11,axiom,( ! [A] : ( v1_xreal_0(A) => m1_subset_1(a_1_5_gobrd11(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) )).
fof(l16_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( r1_graph_2(A,C,B) => ! [D] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(l16_heyting1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k12_normform(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k12_normform(A))) => ( r3_lattices(k12_normform(A),B,C) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))) => ~ ( r2_hidden(D,B) & ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(l16_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( ( v4_aff_2(A) & r1_aff_1(A,D,B,C) & r1_aff_1(A,D,F,G) & r2_analoaf(A,B,F,C,G) & r1_aff_1(A,D,B,H) ) => ( D = B | r1_aff_1(A,D,B,F) | ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ~ ( ~ r1_aff_1(A,D,B,I) & r1_aff_1(A,D,I,J) & r2_analoaf(A,B,I,C,J) & r2_analoaf(A,I,H,J,E) & r1_aff_1(A,D,B,E) ) ) ) | r2_analoaf(A,F,H,G,E) ) ) ) ) ) ) ) ) ) ) )).
fof(l16_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(B,k4_finseq_1(A)) & r2_hidden(C,k4_finseq_1(A)) & C != B & k1_funct_1(A,C) != k5_numbers & ! [D] : ( 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)) ) ) ) ) ) )).
fof(l16_integra3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(l16_integra4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ~ ( ~ r1_xxreal_0(k3_integra1(A),k5_numbers) & ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_integra1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) ) => ~ ( v2_comseq_2(k2_integra3(A,B)) & k1_seq_2(k2_integra3(A,B)) = k5_numbers ) ) ) ) )).
fof(l16_jgraph_3,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l16_jordan1b,axiom,( ! [A] : ( ( ~ 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,k5_numbers)),1) = 3 ) )).
fof(l16_jordan1c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v9_rltopsp1(A,k15_euclid(2)) => ! [B] : ( v1_xreal_0(B) => ~ ( k1_jordan2c(2,A) != k1_xboole_0 & ~ r1_xxreal_0(k8_pscomp_1(k1_jordan2c(2,A)),B) & ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( r2_hidden(C,k1_jordan2c(2,A)) => r1_xxreal_0(k17_euclid(C),B) ) ) ) ) ) ) )).
fof(l16_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => r1_xxreal_0(1,k7_nat_d(k3_xcmplx_0(2,A),1)) ) ) )).
fof(l16_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( r1_glib_000(A,k4_glib_001(A,B),D,C) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k1_relset_1(k4_ordinal1,B)) => ( k1_funct_1(k10_glib_001(A,B,C),E) = k1_funct_1(B,E) & r2_hidden(E,k1_relset_1(k4_ordinal1,k10_glib_001(A,B,C))) ) ) ) ) ) ) )).
fof(l16_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(l16_matrix11,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r2_hidden(A,k2_sgraph1(k2_finseq_1(C))) & r2_hidden(B,A) ) => ( r2_hidden(B,k2_finseq_1(C)) & ? [D] : ( v7_ordinal1(D) & r2_hidden(D,k2_finseq_1(C)) & B != D & A = k2_tarski(B,D) ) ) ) ) ) )).
fof(l16_matrtop2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => 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)))) ) ) ) )).
fof(l16_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,A) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(B,C) & ! [D] : ( ( 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_funct_1(D,1) = A & k1_funct_1(D,2) = B & ! [E] : ( 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_funct_1(D,E) = k6_xcmplx_0(E,2) ) & ( r1_xxreal_0(E,B) => ( r1_xxreal_0(E,k1_nat_1(A,1)) | k1_funct_1(D,E) = k6_xcmplx_0(E,1) ) ) & ( ~ r1_xxreal_0(E,B) => k1_funct_1(D,E) = E ) ) ) ) ) ) ) ) ) ) ) )).
fof(l16_measure7,axiom,( r1_tarski(k1_numbers,k5_setfam_1(k1_numbers,k2_relset_1(k9_setfam_1(k1_numbers),c1__measure7))) )).
fof(l16_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ( r1_tarski(A,B) => r1_tarski(k5_member_1(A),k5_member_1(B)) ) ) ) )).
fof(l16_mesfunc3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ~ ( r1_mesfunc2(A,B,C) & ! [D] : ( r2_hidden(D,k1_relset_1(A,C)) => r1_xxreal_0(k1_supinf_2,k1_funct_1(C,D)) ) & ! [D] : ~ ( r2_hidden(D,k1_relset_1(A,C)) & k1_supinf_2 = k1_funct_1(C,D) ) & ! [D] : ( ( v1_prob_2(D) & m2_finseq_1(D,B) ) => ! [E] : ( m2_finseq_1(E,k6_numbers) => ~ ( r1_mesfunc3(A,B,C,D,E) & k12_supinf_2(E,1) = k1_supinf_2 & ! [F] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(l16_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( v2_mfold_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ? [D] : ( m1_connsp_2(D,B,C) & ? [E] : ( ~ 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) ) ) ) ) ) ) )).
fof(l16_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => u1_struct_0(k10_funcsdom(k2_finseq_1(A))) = u1_struct_0(k15_euclid(A)) ) )).
fof(l16_msuhom_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(l16_numbers,axiom,( 2 = k2_tarski(k5_numbers,1) )).
fof(l16_pdiff_1,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l16_pdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(3)) => ! [F] : ( ( 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] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & ? [I] : ( v1_xreal_0(I) & E = k11_finseq_1(G,H,I) & ? [J] : ( m1_rcomp_1(J,G) & r1_tarski(J,k1_relset_1(k1_numbers,k1_pdiff_2(3,1,F,E))) & ? [K] : ( v1_funct_1(K) & v3_fdiff_1(K) & m1_subset_1(K,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [L] : ( v1_funct_1(L) & v2_fdiff_1(L) & m1_subset_1(L,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & D = k1_funct_1(K,1) & ! [M] : ( v1_xreal_0(M) => ( r2_hidden(M,J) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,1,F,E),M),k1_funct_1(k1_pdiff_2(3,1,F,E),G)) = k2_xcmplx_0(k1_funct_1(K,k6_xcmplx_0(M,G)),k1_funct_1(L,k6_xcmplx_0(M,G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l16_polyeq_1,axiom,( 3 = k1_nat_1(k2_nat_1(2,1),1) )).
fof(l16_pre_ff,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k4_ordinal1,k3_finseq_2(k4_ordinal1)) => ? [C] : ( m2_finseq_2(C,k4_ordinal1,k3_finseq_2(k4_ordinal1)) & ! [D] : ( v7_ordinal1(D) => ( k1_nat_1(A,2) = k3_xcmplx_0(2,D) => C = k8_finseq_1(k4_ordinal1,B,k12_finseq_1(k4_ordinal1,k7_partfun1(k4_ordinal1,B,D))) ) ) & ! [D] : ( v7_ordinal1(D) => ( k1_nat_1(A,2) = k1_nat_1(k3_xcmplx_0(2,D),1) => C = k8_finseq_1(k4_ordinal1,B,k12_finseq_1(k4_ordinal1,k1_nat_1(k7_partfun1(k4_ordinal1,B,D),k7_partfun1(k4_ordinal1,B,k1_nat_1(D,1))))) ) ) ) ) ) )).
fof(l16_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(l16_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r1_collsp(A,D,E,F) & r1_projdes1(A,B,C,D,E) ) => ( D = E | r1_projdes1(A,B,C,D,F) ) ) ) ) ) ) ) ) )).
fof(l16_prvect_2,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(l16_qmax_1,axiom,( v1_funct_1(k6_domain_1(k2_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_zfmisc_1(k2_zfmisc_1(k12_prob_1,k1_numbers))),k1_domain_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_zfmisc_1(k2_zfmisc_1(k12_prob_1,k1_numbers)),k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers),c3__qmax_1))) & v1_funct_2(k6_domain_1(k2_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_zfmisc_1(k2_zfmisc_1(k12_prob_1,k1_numbers))),k1_domain_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_zfmisc_1(k2_zfmisc_1(k12_prob_1,k1_numbers)),k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers),c3__qmax_1)),k8_mcart_1(k4_ordinal1,k4_ordinal1,k6_domain_1(k4_ordinal1,k5_numbers),k6_domain_1(k4_ordinal1,k5_numbers)),k1_qmax_1(k1_numbers,k12_prob_1)) & m1_subset_1(k6_domain_1(k2_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_zfmisc_1(k2_zfmisc_1(k12_prob_1,k1_numbers))),k1_domain_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_zfmisc_1(k2_zfmisc_1(k12_prob_1,k1_numbers)),k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers),c3__qmax_1)),k1_zfmisc_1(k2_zfmisc_1(k8_mcart_1(k4_ordinal1,k4_ordinal1,k6_domain_1(k4_ordinal1,k5_numbers),k6_domain_1(k4_ordinal1,k5_numbers)),k1_qmax_1(k1_numbers,k12_prob_1)))) )).
fof(l16_quaterni,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => k6_quaterni(A,B,k5_numbers,k5_numbers) = k5_arytm_0(A,B) ) ) )).
fof(l16_quin_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( k1_square_1(A) = k1_square_1(B) & A != B & A != k4_xcmplx_0(B) ) ) ) )).
fof(l16_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => k1_relset_1(k4_ordinal1,k1_partfun1(k4_ordinal1,k1_relset_1(A,B),A,k1_numbers,k19_finseq_1(k1_relset_1(A,B)),B)) = k4_finseq_1(k19_finseq_1(k1_relset_1(A,B))) ) ) )).
fof(l16_realset2,axiom,( k9_xtuple_0(k13_funcop_1(1,1,1)) = k6_domain_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,1,1)) )).
fof(l16_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => v8_valued_0(k4_rinfsup2(A)) ) )).
fof(l16_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & k1_algstr_0(A,B,D) = C ) ) ) ) )).
fof(l16_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => m1_rmod_2(C,A,k2_rmod_2(A,B)) ) ) ) )).
fof(l16_scmfsa_1,axiom,( k9_xtuple_0(k4_scmfsa_1) = k1_scmfsa_1 )).
fof(l16_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_scmringi(A)) => r1_xxreal_0(k2_compos_0(k1_scmringi(A),B),7) ) ) )).
fof(l16_scpqsort,axiom,( 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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_numbers))))) = 9 )).
fof(l16_series_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [D] : ( m1_subset_1(D,k4_ordinal1) => k9_nat_1(k1_numbers,C,D) = k2_xcmplx_0(k3_xcmplx_0(A,D),B) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k9_nat_1(k1_numbers,k3_series_1(C),D) = k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(A,k1_nat_1(D,1)),D),2),k3_xcmplx_0(D,B)),B) ) ) ) ) ) )).
fof(l16_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => k1_square_1(k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(B,C),A),k7_xcmplx_0(k3_xcmplx_0(C,A),B)),k7_xcmplx_0(k3_xcmplx_0(A,B),C))) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k7_xcmplx_0(k3_xcmplx_0(C,A),B)),k1_square_1(k7_xcmplx_0(k3_xcmplx_0(A,B),C))),k1_square_1(k7_xcmplx_0(k3_xcmplx_0(B,C),A))),k3_xcmplx_0(2,k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(C)))) ) ) ) )).
fof(l16_sin_cos6,axiom,( ~ r1_xxreal_0(k3_xcmplx_0(2,k28_sin_cos),k3_xcmplx_0(1,k28_sin_cos)) )).
fof(l16_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(A,k1_square_1(B)) ) ) ) ) )).
fof(l16_taylor_1,axiom,( ~ r1_xxreal_0(k4_power,1) )).
fof(l16_topgen_3,axiom,( ? [A] : ( 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 ) )).
fof(l16_topreal2,axiom,( ~ r2_hidden(k19_euclid(1,k5_numbers),k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,k5_numbers),k19_euclid(k5_numbers,1))) )).
fof(l16_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ( ( v11_aff_2(A) & r1_aff_1(A,B,C,H) & 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) & r2_analoaf(A,D,F,H,I) & r2_analoaf(A,E,G,H,J) & r2_analoaf(A,D,H,F,I) & r2_analoaf(A,E,H,G,J) ) => ( B = C | r1_aff_1(A,B,C,D) | r1_aff_1(A,B,C,E) | I = J ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l16_uniform1,axiom,( ! [A] : ! [B] : ( ( 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),k1_nat_1(k3_finseq_1(B),1)) = k1_funct_1(B,k3_finseq_1(B)) ) ) ) )).
fof(l16_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(l16_waybel15,axiom,( ! [A] : ( ( 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] : ( 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] : ( 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] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k2_yellow_1(B)),u1_struct_0(k2_yellow_1(B))) & v6_waybel_1(C,k2_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_yellow_1(B)),u1_struct_0(k2_yellow_1(B))))) ) => ~ ( v22_waybel_0(C,k2_yellow_1(B),k2_yellow_1(B)) & r5_waybel_1(A,k1_yellow_2(k2_yellow_1(B),k2_yellow_1(B),C)) ) ) ) ) ) )).
fof(l16_waybel25,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(l16_waybel_5,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_pboole(D,A,B,k7_funcop_1(A,C)) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r2_hidden(E,k1_relset_1(k4_card_3(k1_funct_6(D)),k2_pralg_2(D))) => ! [F] : ( r2_hidden(F,A) => r2_hidden(k1_funct_1(E,F),k1_funct_1(B,F)) ) ) ) ) ) ) )).
fof(l16_xreal_0,axiom,( k4_xcmplx_0(1) = k5_arytm_0(c5__xreal_0,c6__xreal_0) & k5_numbers = k5_arytm_0(k1_arytm_0(c3__xreal_0,c5__xreal_0),k1_arytm_0(c4__xreal_0,c6__xreal_0)) )).
fof(l16_xreal_1,axiom,( m1_subset_1(k5_numbers,k2_arytm_2) )).
fof(l16_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ( r1_xxreal_0(k1_xxreal_0,A) => A = k1_xxreal_0 ) ) )).
fof(l16_xxreal_3,axiom,( k2_xxreal_3(k1_xxreal_3(k1_xxreal_0,k2_xxreal_0)) = k3_xxreal_3(k2_xxreal_3(k2_xxreal_0),k1_xxreal_0) )).
fof(l16_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_pre_topc(A,B)) => ! [D] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(E,D) & r1_xboole_0(B,E) ) ) ) ) ) ) ) )).
fof(l16_zf_fund1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ( k3_funct_2(k4_ordinal1,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(k4_ordinal1,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) ) ) ) ) )).
fof(l170_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( v4_funct_1(B) => ! [C] : ( ( v13_fomodel4(C,2,A) & m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) ) => ~ ( v1_finset_1(B) & v4_card_3(k30_fomodel2(A)) & ~ v10_fomodel4(B,A,C) & v7_fomodel4(C,A) & ! [D] : ( ( ~ v1_xboole_0(D) & v4_card_3(D) ) => ! [E] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(A),k3_rfunct_3(k3_finseq_2(D),k2_xboole_0(D,k6_margrel1))),k15_fomodel2(A,D)) => ~ v10_fomodel2(B,D,A,E) ) ) ) ) ) ) )).
fof(l170_group_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( 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),k6_subset_1(k4_ordinal1,k1_tarski(k5_numbers))) ) => k14_finseq_1(k7_relset_1(k1_numbers,k1_numbers,C,B)) = k1_partfun1(k4_ordinal1,k4_ordinal1,k1_numbers,k1_numbers,k14_finseq_1(B),C) ) ) ) )).
fof(l170_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_jordan24(2,A,k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) => r1_xboole_0(k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),3),k19_euclid(k5_numbers,3)),A) ) ) )).
fof(l170_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ( ! [B] : ( m2_finseq_1(B,k1_numbers) => ~ ( k5_card_1(k1_rvsum_1(B)) = A & ! [C] : ( 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] : ( m2_finseq_1(B,k1_numbers) => ~ ( k5_card_1(k1_rvsum_1(B)) = k1_nat_1(A,1) & ! [C] : ( 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) ) ) ) ) ) ) )).
fof(l171_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( ( k3_xboole_0(k10_xtuple_0(C),k10_xtuple_0(D)) = k1_xboole_0 & r1_tarski(k10_xtuple_0(C),k9_xtuple_0(D)) & r1_tarski(k10_xtuple_0(D),k9_xtuple_0(C)) ) => ( A = B | r1_tarski(k2_xboole_0(k2_zfmisc_1(k10_xtuple_0(C),k1_tarski(B)),k2_zfmisc_1(k10_xtuple_0(D),k1_tarski(A))),k3_relat_1(k3_relat_1(k2_xboole_0(C,D),k2_xboole_0(k2_zfmisc_1(k10_xtuple_0(C),k1_tarski(B)),k2_zfmisc_1(k10_xtuple_0(D),k1_tarski(A)))),k4_funct_4(A,B,B,A))) ) ) ) ) )).
fof(l171_group_9,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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] : ~ ( k14_finseq_1(D) = k3_relat_1(k14_finseq_1(A),k2_funct_1(k14_finseq_1(k7_subset_1(k4_ordinal1,k2_finseq_1(k1_nat_1(C,1)),k1_tarski(B))))) & r1_tarski(D,k2_finseq_1(C)) ) ) ) ) )).
fof(l171_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_jordan24(2,A,k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) => r1_xboole_0(k1_rltopsp1(k15_euclid(2),k19_euclid(1,3),k19_euclid(k5_numbers,3)),A) ) ) )).
fof(l172_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r2_hidden(A,k2_tarski(B,k1_funct_1(C,B))) & v1_partit_2(C) & r2_hidden(B,k9_xtuple_0(C)) ) => k2_tarski(A,k1_funct_1(C,A)) = k2_tarski(B,k1_funct_1(C,B)) ) ) )).
fof(l172_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v1_orders_4(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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,k30_fomodel2(B)) & v13_fomodel2(k35_fomodel2(B,C),A,B) ) => v9_fomodel4(k35_fomodel2(B,C),B,k39_fomodel4(B),A) ) ) ) )).
fof(l172_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_jordan24(2,A,k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) => r1_xboole_0(k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(3)),k19_euclid(k5_numbers,k4_xcmplx_0(3))),A) ) ) )).
fof(l173_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( v1_partit_2(C) & r2_hidden(A,k9_xtuple_0(C)) & r2_hidden(B,k9_xtuple_0(C)) ) => ( ( ~ r2_hidden(A,k2_tarski(B,k1_funct_1(C,B))) & ~ r2_hidden(k1_funct_1(C,A),k2_tarski(B,k1_funct_1(C,B))) ) | k2_tarski(A,k1_funct_1(C,A)) = k2_tarski(B,k1_funct_1(C,B)) ) ) ) )).
fof(l173_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_jordan24(2,A,k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) => r1_xboole_0(k1_rltopsp1(k15_euclid(2),k19_euclid(1,k4_xcmplx_0(3)),k19_euclid(k5_numbers,k4_xcmplx_0(3))),A) ) ) )).
fof(l173_seq_4,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( ( k3_finseq_1(A) = k5_numbers & k3_finseq_1(B) = k5_numbers & k1_rvsum_1(A) = k1_rvsum_1(B) & v5_valued_0(A) & v5_valued_0(B) ) => A = B ) ) ) )).
fof(l174_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(A,B) => k9_xtuple_0(k6_subset_1(B,A)) = k6_subset_1(k9_xtuple_0(B),k9_xtuple_0(A)) ) ) )).
fof(l174_relat_1,axiom,( ! [A] : ! [B] : ( v4_relat_1(k1_xboole_0,A) & v5_relat_1(k1_xboole_0,B) ) )).
fof(l174_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ( ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( 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] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ( ( k3_finseq_1(B) = k1_nat_1(A,1) & k3_finseq_1(C) = k1_nat_1(A,1) & k1_rvsum_1(B) = k1_rvsum_1(C) & v5_valued_0(B) & v5_valued_0(C) ) => B = C ) ) ) ) ) )).
fof(l175_fomodel0,axiom,( ! [A] : ( A != k1_xboole_0 => a_1_6_fomodel0(A) = A ) )).
fof(l176_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ( r2_hidden(k4_tarski(k4_tarski(A,B),k4_tarski(C,D)),k15_funct_3(E,F)) <=> ( r2_hidden(k4_tarski(A,C),E) & r2_hidden(k4_tarski(B,D),F) ) ) ) ) )).
fof(l177_fomodel0,axiom,( ! [A] : ! [B] : ( A = B <=> ! [C] : ( r2_hidden(C,k2_xboole_0(A,B)) => ( r2_hidden(C,A) <=> r2_hidden(C,B) ) ) ) )).
fof(l178_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,k15_funct_3(B,C)) => A = k4_tarski(k4_tarski(k1_xtuple_0(k1_xtuple_0(A)),k2_xtuple_0(k1_xtuple_0(A))),k4_tarski(k1_xtuple_0(k2_xtuple_0(A)),k2_xtuple_0(k2_xtuple_0(A)))) ) ) ) )).
fof(l179_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => k3_xboole_0(k15_funct_3(A,B),k15_funct_3(C,D)) = k15_funct_3(k3_xboole_0(A,C),k3_xboole_0(B,D)) ) ) ) ) )).
fof(l17_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,k1_aff_4(A,B,C)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_aff_1(A,D,E,B) & r2_hidden(E,C) ) ) ) ) ) ) )).
fof(l17_afvect01,axiom,( ~ ! [A] : ( m1_subset_1(A,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [B] : ( m1_subset_1(B,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => A = B ) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [B] : ( 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] : ( m1_subset_1(A,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [B] : ( 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] : ( m1_subset_1(A,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [B] : ( m1_subset_1(B,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [C] : ( m1_subset_1(C,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [D] : ( m1_subset_1(D,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [E] : ( m1_subset_1(E,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [F] : ( 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] : ( m1_subset_1(A,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [B] : ( m1_subset_1(B,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ? [C] : ( 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] : ( m1_subset_1(A,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [B] : ( m1_subset_1(B,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [C] : ( m1_subset_1(C,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [D] : ( m1_subset_1(D,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [E] : ( 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] : ( m1_subset_1(A,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [B] : ( m1_subset_1(B,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ~ ( A != B & ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [E] : ( 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] : ( m1_subset_1(A,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [B] : ( m1_subset_1(B,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [C] : ( m1_subset_1(C,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [D] : ( m1_subset_1(D,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [E] : ( m1_subset_1(E,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [F] : ( 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] : ( m1_subset_1(A,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [B] : ( m1_subset_1(B,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [C] : ( m1_subset_1(C,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [F] : ( 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] : ( m1_subset_1(A,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [B] : ( m1_subset_1(B,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [C] : ( m1_subset_1(C,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [D] : ( m1_subset_1(D,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [E] : ( m1_subset_1(E,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [F] : ( m1_subset_1(F,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [G] : ( 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] : ( m1_subset_1(H,u1_struct_0(g1_analoaf(u1_struct_0(o_0_0_afvect01),c4__afvect01))) => ! [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l17_algstr_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_0)) => ! [B] : ( 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) ) ) )).
fof(l17_algstr_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_3)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_algstr_3)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_algstr_3)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_algstr_3)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k3_algstr_3)) => ! [F] : ( 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 ) ) ) ) ) ) ) )).
fof(l17_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ( A = k11_arytm_3 => k1_arytm_1(B,A) = B ) ) ) )).
fof(l17_arytm_2,axiom,( r2_hidden(k11_arytm_3,k1_arytm_2) )).
fof(l17_arytm_3,axiom,( 1 = k1_ordinal1(k5_ordinal1) )).
fof(l17_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,6) & r1_xxreal_0(k2_power(2,A),k1_square_1(A)) ) ) )).
fof(l17_cfdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( C = k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1)) => r1_xxreal_0(k9_complex1(C),k2_xcmplx_0(k9_complex1(A),k9_complex1(B))) ) ) ) ) )).
fof(l17_complex1,axiom,( k7_complex1 = k5_arytm_0(c1__complex1,c2__complex1) )).
fof(l17_convex2,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r1_tarski(C,k3_rlvect_2(A,B)) & ! [D] : ( m1_rlvect_2(D,A) => k3_rlvect_2(A,D) != C ) ) ) ) ) )).
fof(l17_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) )).
fof(l17_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => v2_cqc_the1(k10_cqc_lang(A,B,B),A) ) ) )).
fof(l17_csspace2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k18_csspace)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k18_csspace)) => k12_csspace(k18_csspace,A,B) = k11_comseq_3(k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k2_csspace(A),k2_comseq_2(k4_ordinal1,k2_csspace(B)))) ) ) )).
fof(l17_dtconstr,axiom,( r1_lang1(k5_dtconstr,c3__dtconstr,k3_pre_poly(u1_struct_0(k5_dtconstr),c3__dtconstr)) )).
fof(l17_endalg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k6_endalg(A,B))) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(l17_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k3_enumset1(A,B,C,D,E) = k2_xboole_0(k1_enumset1(A,B,C),k2_tarski(D,E)) )).
fof(l17_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m1_subset_1(B,k2_numbers) => ! [C] : ( m1_subset_1(C,k2_numbers) => ( k2_xcmplx_0(k3_complex2(A,B),k3_complex2(B,C)) = k3_complex2(A,C) | k2_xcmplx_0(k3_complex2(A,B),k3_complex2(B,C)) = k2_xcmplx_0(k3_complex2(A,C),k3_xcmplx_0(2,k28_sin_cos)) ) ) ) ) )).
fof(l17_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ( D = k1_euclid_8(A,B,C) => k22_rvsum_1(D,D) = k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(C)) ) ) ) ) ) )).
fof(l17_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v2_conmetr(A) <=> v2_aff_2(k3_analmetr(A)) ) ) )).
fof(l17_fdiff_2,axiom,( r2_hidden(1,k4_ordinal1) )).
fof(l17_fib_num,axiom,( k1_square_1(k1_fib_num) = k2_xcmplx_0(k1_fib_num,1) & k1_square_1(k2_fib_num) = k2_xcmplx_0(k2_fib_num,1) )).
fof(l17_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(l17_fscirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(l17_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ! [F] : ( 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] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( m1_subset_1(H,k6_margrel1) => ! [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) ) ) ) ) ) ) ) ) ) ) )).
fof(l17_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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] : ( ( v5_relat_1(F,k1_rcomp_1(k5_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] : ! [H] : ( ( r2_hidden(G,A) & r2_hidden(H,C) ) => k2_seq_4(k2_relset_1(k1_numbers,k2_fuzzy_4(A,B,C,D,k2_fuzzy_1(k2_zfmisc_1(B,C),E,F),G,H))) = k4_xxreal_0(k2_seq_4(k2_relset_1(k1_numbers,k2_fuzzy_4(A,B,C,D,E,G,H))),k2_seq_4(k2_relset_1(k1_numbers,k2_fuzzy_4(A,B,C,D,F,G,H)))) ) ) ) ) ) ) ) )).
fof(l17_gfacirc2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ! [E] : ( ( 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) ) ) ) ) )).
fof(l17_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ( ? [B] : ( m1_subset_1(B,k6_glib_000(A)) & ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ? [D] : ( m3_glib_001(D,A) & r1_glib_001(A,B,C,D) ) ) ) => v1_glib_002(A) ) ) )).
fof(l17_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(l17_goboard5,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => k4_finseq_1(k1_goboard1(A)) = k4_finseq_1(A) ) )).
fof(l17_goboard6,axiom,( 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))) )).
fof(l17_gobrd11,axiom,( ! [A] : ( v1_xreal_0(A) => m1_subset_1(a_1_8_gobrd11(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) )).
fof(l17_grfunc_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( D = k2_xboole_0(B,C) => ( r2_hidden(A,k9_xtuple_0(D)) <=> ( r2_hidden(A,k9_xtuple_0(B)) | r2_hidden(A,k9_xtuple_0(C)) ) ) ) ) ) ) )).
fof(l17_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( v1_group_3(C,A) & m1_group_2(C,A) ) => m1_group_6(k1_grnilp_1(A,C,B),A,C) ) ) ) )).
fof(l17_hessenbe,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ( ( r1_collsp(A,B,C,J) & r1_collsp(A,E,F,J) & r1_collsp(A,C,D,H) & r1_collsp(A,F,G,H) & r1_collsp(A,B,D,I) & r1_collsp(A,E,G,I) & r1_collsp(A,K,B,E) & r1_collsp(A,K,C,F) & r1_collsp(A,K,D,G) ) => ( K = E | K = F | r1_collsp(A,K,B,C) | r1_collsp(A,K,B,D) | r1_collsp(A,K,C,D) | ( ~ r1_collsp(A,B,C,D) & ~ r1_collsp(A,E,F,G) ) | r1_collsp(A,H,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l17_heyting1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k12_normform(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k12_normform(A))) => ( ! [D] : ( m2_subset_1(D,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ~ ( r2_hidden(D,B) & ! [E] : ( 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) ) ) ) )).
fof(l17_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( ( v4_aff_2(A) & r1_aff_1(A,D,B,C) & r1_aff_1(A,D,B,F) & r1_aff_1(A,D,H,E) & r2_analoaf(A,B,H,C,E) ) => ( D = B | ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ~ ( ~ r1_aff_1(A,D,B,I) & r1_aff_1(A,D,I,J) & r2_analoaf(A,B,I,C,J) & r2_analoaf(A,I,F,J,G) & r1_aff_1(A,D,B,G) ) ) ) | r1_aff_1(A,D,B,H) | r2_analoaf(A,F,H,G,E) ) ) ) ) ) ) ) ) ) ) )).
fof(l17_integr11,axiom,( k9_xtuple_0(k1_fcont_1(2,k5_numbers)) = k2_subset_1(k1_numbers) )).
fof(l17_integr15,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(A) & v2_comseq_2(C) & k1_seq_2(A) = k1_seq_2(C) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => r1_xxreal_0(k3_funct_2(k4_ordinal1,k1_numbers,A,D),k3_funct_2(k4_ordinal1,k1_numbers,B,D)) ) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => r1_xxreal_0(k3_funct_2(k4_ordinal1,k1_numbers,B,D),k3_funct_2(k4_ordinal1,k1_numbers,C,D)) ) ) => ( v2_comseq_2(B) & k1_seq_2(A) = k1_seq_2(B) & k1_seq_2(C) = k1_seq_2(B) ) ) ) ) ) )).
fof(l17_integra3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( m1_integra1(C,B) => ! [D] : ( m1_integra1(D,B) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( E = k6_xcmplx_0(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)) ) ) ) ) ) ) )).
fof(l17_integra4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ~ ( k3_integra1(A) = k5_numbers & ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_integra1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) ) => ~ ( v2_comseq_2(k2_integra3(A,B)) & k1_seq_2(k2_integra3(A,B)) = k5_numbers ) ) ) ) )).
fof(l17_jgraph_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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) ) ) )).
fof(l17_jgraph_6,axiom,( k17_euclid(k19_euclid(k4_xcmplx_0(1),k5_numbers)) = k4_xcmplx_0(1) )).
fof(l17_jordan1c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v9_rltopsp1(A,k15_euclid(2)) => ! [B] : ( v1_xreal_0(B) => ~ ( k1_jordan2c(2,A) != k1_xboole_0 & ~ r1_xxreal_0(k7_pscomp_1(k1_jordan2c(2,A)),B) & ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( r2_hidden(C,k1_jordan2c(2,A)) => r1_xxreal_0(k18_euclid(C),B) ) ) ) ) ) ) )).
fof(l17_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(k1_nat_1(k1_newton(2,A),3),B) & r1_xxreal_0(k1_nat_1(k11_newton(2,k1_nat_1(A,1)),3),k7_nat_d(k3_xcmplx_0(2,B),2)) ) ) ) )).
fof(l17_lpspacc1,axiom,( m1_subset_1(k4_xcmplx_0(k6_complex1),k2_numbers) )).
fof(l17_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k3_rlvect_1(A,k5_algstr_0(A,C,B),B) = C & k5_algstr_0(A,k3_rlvect_1(A,C,B),B) = C ) ) ) ) )).
fof(l17_matrix_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( 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) ) ) ) )).
fof(l17_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => v1_matrixj1(k10_laplace(k3_finseq_2(A),B),A) ) ) )).
fof(l17_matrtop3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(1,B) & ~ r1_xxreal_0(C,B) & r1_xxreal_0(C,D) & ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(k2_vectsp_1),D,D) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ~ ( k12_matrix_3(D,k2_vectsp_1,E) = k5_struct_0(k2_vectsp_1) & k3_matrix_0(u1_struct_0(k2_vectsp_1),E,B,B) = k19_sin_cos(A) & k3_matrix_0(u1_struct_0(k2_vectsp_1),E,C,C) = k19_sin_cos(A) & k3_matrix_0(u1_struct_0(k2_vectsp_1),E,B,C) = k17_sin_cos(A) & k3_matrix_0(u1_struct_0(k2_vectsp_1),E,C,B) = k4_xcmplx_0(k17_sin_cos(A)) & ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ( r2_hidden(k4_tarski(F,G),k2_matrix_0(E)) => ( ( F = G => ( F = B | F = C | k3_matrix_0(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_0(u1_struct_0(k2_vectsp_1),E,F,G) != k4_struct_0(k2_vectsp_1) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l17_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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 ) ) ) ) ) )).
fof(l17_mcart_1,axiom,( ! [A] : ! [B] : ~ ( A != k1_xboole_0 & B != k1_xboole_0 & ? [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) & ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,B) => C != k4_tarski(D,E) ) ) ) ) )).
fof(l17_measure5,axiom,( ! [A] : ( ( v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => r1_xxreal_0(k5_numbers,k2_measure5(A)) ) )).
fof(l17_measure7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v6_xxreal_2(k9_nat_1(k9_setfam_1(k1_numbers),c1__measure7,A)) & m1_subset_1(k9_nat_1(k9_setfam_1(k1_numbers),c1__measure7,A),k1_zfmisc_1(k1_numbers)) ) ) )).
fof(l17_mesfunc3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ~ ( r1_mesfunc2(A,B,C) & ! [D] : ( r2_hidden(D,k1_relset_1(A,C)) => r1_xxreal_0(k1_supinf_2,k1_funct_1(C,D)) ) & ? [D] : ( r2_hidden(D,k1_relset_1(A,C)) & k1_supinf_2 = k12_supinf_2(C,D) ) & ! [D] : ( ( v1_prob_2(D) & m2_finseq_1(D,B) ) => ! [E] : ( m2_finseq_1(E,k6_numbers) => ~ ( r1_mesfunc3(A,B,C,D,E) & k12_supinf_2(E,1) = k1_supinf_2 & ! [F] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(l17_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => k4_struct_0(k10_funcsdom(k2_finseq_1(A))) = k4_struct_0(k15_euclid(A)) ) )).
fof(l17_nfcont_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_normsp_0(A,k5_algstr_0(A,B,C)) = k5_numbers <=> B = C ) ) ) ) & ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ~ ( k2_normsp_0(A,k5_algstr_0(A,B,C)) != k5_numbers & B = C ) & ~ ( B != C & k2_normsp_0(A,k5_algstr_0(A,B,C)) = k5_numbers ) ) ) ) ) & ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ~ ( ~ r1_xxreal_0(k2_normsp_0(A,k5_algstr_0(A,B,C)),k5_numbers) & B = C ) & ~ ( B != C & r1_xxreal_0(k2_normsp_0(A,k5_algstr_0(A,B,C)),k5_numbers) ) ) ) ) ) & ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_normsp_0(A,k5_algstr_0(A,B,C)) = k2_normsp_0(A,k5_algstr_0(A,C,B)) ) ) ) & ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ~ r1_xxreal_0(k7_xcmplx_0(E,2),k2_normsp_0(A,k5_algstr_0(A,B,D))) & ~ r1_xxreal_0(k7_xcmplx_0(E,2),k2_normsp_0(A,k5_algstr_0(A,D,C))) & r1_xxreal_0(E,k2_normsp_0(A,k5_algstr_0(A,B,C))) ) ) ) ) ) ) & ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ~ r1_xxreal_0(k7_xcmplx_0(E,2),k2_normsp_0(A,k5_algstr_0(A,B,D))) & ~ r1_xxreal_0(k7_xcmplx_0(E,2),k2_normsp_0(A,k5_algstr_0(A,C,D))) & r1_xxreal_0(E,k2_normsp_0(A,k5_algstr_0(A,B,C))) ) ) ) ) ) ) & ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & r1_xxreal_0(C,k2_normsp_0(A,B)) ) ) => B = k4_struct_0(A) ) ) ) & ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_xxreal_0(D,k2_normsp_0(A,k5_algstr_0(A,B,C))) ) ) => B = C ) ) ) ) )).
fof(l17_ntalgo_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => ! [B] : ( m1_subset_1(B,k4_numbers) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_numbers))) ) => ( ( k9_nat_1(k4_numbers,C,k5_numbers) = A & k9_nat_1(k4_numbers,D,k5_numbers) = B & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( k9_nat_1(k4_numbers,C,k1_nat_1(E,1)) = k9_nat_1(k4_numbers,D,E) & k9_nat_1(k4_numbers,D,k1_nat_1(E,1)) = k5_int_1(k9_nat_1(k4_numbers,C,E),k9_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(k4_ordinal1)) ) ) ) ) ) ) )).
fof(l17_numbers,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ~ ( k9_ordinal3(A,A) = k9_ordinal3(2,B) & ! [C] : ( ( v3_ordinal1(C) & v7_ordinal1(C) ) => A != k9_ordinal3(2,C) ) ) ) ) )).
fof(l17_pdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(3)) => ! [F] : ( ( 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] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & ? [I] : ( v1_xreal_0(I) & E = k11_finseq_1(G,H,I) & ? [J] : ( m1_rcomp_1(J,H) & r1_tarski(J,k1_relset_1(k1_numbers,k1_pdiff_2(3,2,F,E))) & ? [K] : ( v1_funct_1(K) & v3_fdiff_1(K) & m1_subset_1(K,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [L] : ( v1_funct_1(L) & v2_fdiff_1(L) & m1_subset_1(L,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & D = k1_funct_1(K,1) & ! [M] : ( v1_xreal_0(M) => ( r2_hidden(M,J) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,2,F,E),M),k1_funct_1(k1_pdiff_2(3,2,F,E),H)) = k2_xcmplx_0(k1_funct_1(K,k6_xcmplx_0(M,H)),k1_funct_1(L,k6_xcmplx_0(M,H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l17_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k3_nat_d(k2_nat_1(A,k11_newton(2,k1_nat_1(B,1))),2) = k3_xcmplx_0(A,k1_newton(2,B)) ) ) )).
fof(l17_polyeq_1,axiom,( ~ v1_abian(3) )).
fof(l17_pre_ff,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k4_ordinal1,k3_finseq_2(k4_ordinal1)) => ! [C] : ( m2_finseq_2(C,k4_ordinal1,k3_finseq_2(k4_ordinal1)) => ! [D] : ( m2_finseq_2(D,k4_ordinal1,k3_finseq_2(k4_ordinal1)) => ( ( ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( k1_nat_1(A,2) = k2_nat_1(2,E) => C = k8_finseq_1(k4_ordinal1,B,k12_finseq_1(k4_ordinal1,k7_partfun1(k4_ordinal1,B,E))) ) ) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( k1_nat_1(A,2) = k1_nat_1(k2_nat_1(2,E),1) => C = k8_finseq_1(k4_ordinal1,B,k12_finseq_1(k4_ordinal1,k1_nat_1(k7_partfun1(k4_ordinal1,B,E),k7_partfun1(k4_ordinal1,B,k1_nat_1(E,1))))) ) ) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( k1_nat_1(A,2) = k2_nat_1(2,E) => D = k8_finseq_1(k4_ordinal1,B,k12_finseq_1(k4_ordinal1,k7_partfun1(k4_ordinal1,B,E))) ) ) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( k1_nat_1(A,2) = k1_nat_1(k2_nat_1(2,E),1) => D = k8_finseq_1(k4_ordinal1,B,k12_finseq_1(k4_ordinal1,k1_nat_1(k7_partfun1(k4_ordinal1,B,E),k7_partfun1(k4_ordinal1,B,k1_nat_1(E,1))))) ) ) ) => C = D ) ) ) ) ) )).
fof(l17_prob_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => r2_funct_2(k4_ordinal1,k1_zfmisc_1(A),k2_prob_1(A,k11_funct_7(k1_zfmisc_1(A),B,C)),k11_funct_7(k1_zfmisc_1(A),k3_subset_1(A,B),k3_subset_1(A,C))) ) ) )).
fof(l17_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(l17_prvect_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v1_prvect_2(A) ) => ! [B] : ( m1_subset_1(B,k4_card_3(k4_prvect_2(A))) => ! [C] : ( m1_subset_1(C,k4_card_3(k4_prvect_2(A))) => ! [D] : ( m2_subset_1(D,k4_ordinal1,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] : ( m1_subset_1(E,u1_struct_0(k5_prvect_2(A,D))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l17_qmax_1,axiom,( ! [A] : ( m1_subset_1(A,k2_qmax_1(g1_qmax_1(k6_domain_1(k4_ordinal1,k5_numbers),k6_domain_1(k4_ordinal1,k5_numbers),c5__qmax_1))) => ! [B] : ( m1_subset_1(B,k2_qmax_1(g1_qmax_1(k6_domain_1(k4_ordinal1,k5_numbers),k6_domain_1(k4_ordinal1,k5_numbers),c5__qmax_1))) => ( ! [C] : ( m1_subset_1(C,k3_qmax_1(g1_qmax_1(k6_domain_1(k4_ordinal1,k5_numbers),k6_domain_1(k4_ordinal1,k5_numbers),c5__qmax_1))) => r2_funct_2(k12_prob_1,k1_numbers,k4_qmax_1(g1_qmax_1(k6_domain_1(k4_ordinal1,k5_numbers),k6_domain_1(k4_ordinal1,k5_numbers),c5__qmax_1),A,C),k4_qmax_1(g1_qmax_1(k6_domain_1(k4_ordinal1,k5_numbers),k6_domain_1(k4_ordinal1,k5_numbers),c5__qmax_1),B,C)) ) => A = B ) ) ) & ! [A] : ( m1_subset_1(A,k3_qmax_1(g1_qmax_1(k6_domain_1(k4_ordinal1,k5_numbers),k6_domain_1(k4_ordinal1,k5_numbers),c5__qmax_1))) => ! [B] : ( m1_subset_1(B,k3_qmax_1(g1_qmax_1(k6_domain_1(k4_ordinal1,k5_numbers),k6_domain_1(k4_ordinal1,k5_numbers),c5__qmax_1))) => ( ! [C] : ( m1_subset_1(C,k2_qmax_1(g1_qmax_1(k6_domain_1(k4_ordinal1,k5_numbers),k6_domain_1(k4_ordinal1,k5_numbers),c5__qmax_1))) => r2_funct_2(k12_prob_1,k1_numbers,k4_qmax_1(g1_qmax_1(k6_domain_1(k4_ordinal1,k5_numbers),k6_domain_1(k4_ordinal1,k5_numbers),c5__qmax_1),C,A),k4_qmax_1(g1_qmax_1(k6_domain_1(k4_ordinal1,k5_numbers),k6_domain_1(k4_ordinal1,k5_numbers),c5__qmax_1),C,B)) ) => A = B ) ) ) & ! [A] : ( m1_subset_1(A,k3_qmax_1(g1_qmax_1(k6_domain_1(k4_ordinal1,k5_numbers),k6_domain_1(k4_ordinal1,k5_numbers),c5__qmax_1))) => ! [B] : ( m1_subset_1(B,k3_qmax_1(g1_qmax_1(k6_domain_1(k4_ordinal1,k5_numbers),k6_domain_1(k4_ordinal1,k5_numbers),c5__qmax_1))) => ! [C] : ( v1_xreal_0(C) => ~ ( r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(C,1) & ! [D] : ( m1_subset_1(D,k3_qmax_1(g1_qmax_1(k6_domain_1(k4_ordinal1,k5_numbers),k6_domain_1(k4_ordinal1,k5_numbers),c5__qmax_1))) => ~ ! [E] : ( m1_subset_1(E,k2_qmax_1(g1_qmax_1(k6_domain_1(k4_ordinal1,k5_numbers),k6_domain_1(k4_ordinal1,k5_numbers),c5__qmax_1))) => ! [F] : ( 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(k4_ordinal1,k5_numbers),k6_domain_1(k4_ordinal1,k5_numbers),c5__qmax_1),E,D),F) = k2_xcmplx_0(k3_xcmplx_0(C,k3_funct_2(k12_prob_1,k1_numbers,k4_qmax_1(g1_qmax_1(k6_domain_1(k4_ordinal1,k5_numbers),k6_domain_1(k4_ordinal1,k5_numbers),c5__qmax_1),E,A),F)),k3_xcmplx_0(k6_xcmplx_0(1,C),k3_funct_2(k12_prob_1,k1_numbers,k4_qmax_1(g1_qmax_1(k6_domain_1(k4_ordinal1,k5_numbers),k6_domain_1(k4_ordinal1,k5_numbers),c5__qmax_1),E,B),F))) ) ) ) ) ) ) ) )).
fof(l17_random_2,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(l17_realset2,axiom,( k9_xtuple_0(k13_funcop_1(1,k5_numbers,k5_numbers)) = k6_domain_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,1,k5_numbers)) )).
fof(l17_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => v7_valued_0(k3_rinfsup2(A)) ) )).
fof(l17_scmfsa_1,axiom,( k1_afinsq_1(k7_afinsq_1(k4_ordinal1,k4_numbers,k3_finseq_2(k4_numbers))) = 3 )).
fof(l17_scmfsa_i,axiom,( ! [A] : ( m1_subset_1(A,k2_scmfsa_i) => r1_xxreal_0(k2_compos_0(k2_scmfsa_i,A),12) ) )).
fof(l17_scmp_gcd,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & k2_scmp_gcd = k1_scmp_gcd(k2_xcmplx_0(A,B)) ) ) ) )).
fof(l17_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_scmringi(A)) => ( ~ ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(C,4) & k4_xtuple_0(B) = C ) ) => k5_xtuple_0(B) = k1_xboole_0 ) ) ) )).
fof(l17_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( 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) = k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_numbers)))),B,A),k2_scmp_gcd) = k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_numbers)))),B,A),k1_scmp_gcd(3)) = k1_funct_1(B,k1_scmp_gcd(3)) & ! [E] : ( v7_ordinal1(E) => ( 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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_numbers)))),B,A),k1_scmp_gcd(5)) = k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_numbers)))),B,A),k1_scmp_gcd(7)) = k1_funct_1(B,k1_scmp_gcd(5)) ) ) ) ) ) ) ) ) )).
fof(l17_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => ( k2_xcmplx_0(k2_xcmplx_0(A,B),C) = 1 => k6_xcmplx_0(k7_xcmplx_0(1,A),1) = k7_xcmplx_0(k2_xcmplx_0(B,C),A) ) ) ) ) )).
fof(l17_sincos10,axiom,( r2_hidden(k5_numbers,k3_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) & r2_hidden(k7_xcmplx_0(k28_sin_cos,4),k3_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) )).
fof(l17_taxonom2,axiom,( ! [A] : ! [B] : ( m1_taxonom2(B,A) => ( v3_abian(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( ( v4_taxonom2(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ( ( r1_tarski(C,B) & ! [D] : ( ( 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 ) ) ) ) )).
fof(l17_topalg_2,axiom,( ! [A] : ( m1_pre_topc(A,k3_topmetr) => ( A = k3_topmetr => v2_topalg_2(A) ) ) )).
fof(l17_topdim_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & v5_waybel23(A) & v3_topdim_1(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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))) ) ) ) ) )).
fof(l17_topgen_3,axiom,( u1_pre_topc(k2_topgen_3) = k1_cantor_1(k1_numbers,c1__topgen_3) )).
fof(l17_topgen_4,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(l17_topreal2,axiom,( ~ r2_hidden(k19_euclid(1,k5_numbers),k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,1),k19_euclid(1,1))) )).
fof(l17_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_aff_1(A,B,C,F) & r2_analoaf(A,B,C,D,E) & r2_analoaf(A,B,D,C,E) & r2_analoaf(A,D,E,F,G) ) => ( B = C | r1_aff_1(A,B,C,D) | ( D != E & r1_aff_1(A,B,C,G) ) ) ) ) ) ) ) ) ) ) )).
fof(l17_uniroots,axiom,( v8_struct_0(k18_mod_2) )).
fof(l17_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => m1_vectsp_4(C,A,k2_vectsp_4(A,B)) ) ) ) )).
fof(l17_xreal_0,axiom,( c3__xreal_0 = 1 )).
fof(l17_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(k5_numbers,C) ) => r1_xxreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) ) ) ) )).
fof(l17_xxreal_3,axiom,( k2_xxreal_3(k1_xxreal_0) = k2_xxreal_0 )).
fof(l17_yellow11,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(l17_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( ! [D] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(E,D) & r1_xboole_0(B,E) ) ) ) & ! [D] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(E,D) & r1_xboole_0(B,E) ) ) ) ) ) ) )).
fof(l17_zf_fund1,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_zf_lang)) ) => ( r2_hidden(A,k4_zf_fund1(B)) <=> ? [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) & r2_hidden(C,B) & A = k3_zf_fund1(C) ) ) ) )).
fof(l183_fomodel0,axiom,( ! [A] : ( v1_relat_1(A) => k33_fomodel0(A) = k33_fomodel0(k2_relat_1(A)) ) )).
fof(l183_group_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(B,A) <=> r1_xxreal_0(A,k6_xcmplx_0(B,1)) ) ) ) )).
fof(l184_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r2_hidden(B,k32_fomodel0(A)) <=> r1_abian(B,A) ) ) )).
fof(l184_group_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ ( r2_hidden(A,k4_finseq_1(B)) & ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(l185_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => k32_fomodel0(k15_funct_3(A,B)) = k2_zfmisc_1(k32_fomodel0(A),k32_fomodel0(B)) ) ) )).
fof(l185_group_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(l186_group_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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(k1_nat_1(k3_finseq_1(B),A),k7_finseq_1(B,C)) = k7_finseq_1(B,k2_finseq_3(A,C)) ) ) ) ) ) )).
fof(l187_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v3_funct_1(A) <=> v5_fomodel0(A) ) ) )).
fof(l187_group_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l18_algstr_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k6_algstr_0(A,D,k5_struct_0(A)) = D ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( D != k4_struct_0(A) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k6_algstr_0(A,D,E) != k5_struct_0(A) ) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( 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) ) ) ) ) ) )).
fof(l18_amistd_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_setfam_1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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(k4_ordinal1,k1_nat_1(A,1)) ) ) ) ) ) )).
fof(l18_arytm_0,axiom,( ! [A] : ! [B] : ! [C] : ( k4_tarski(A,B) = k1_tarski(C) => ( C = k1_tarski(A) & A = B ) ) )).
fof(l18_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => k1_arytm_1(k7_arytm_2(A,B),B) = A ) ) )).
fof(l18_arytm_2,axiom,( k8_subset_1(k1_zfmisc_1(k5_arytm_3),k1_arytm_2,k5_arytm_3) = k1_tarski(k11_arytm_3) )).
fof(l18_asympt_1,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ r1_xxreal_0(C,k5_numbers) => k9_nat_1(k1_numbers,B,C) = k3_power(2,k2_power(C,A)) ) ) => ( v2_comseq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,k3_asympt_1(A))) & k1_seq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,k3_asympt_1(A))) = k5_numbers ) ) ) ) )).
fof(l18_bcialg_6,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k3_bcialg_6(A,k2_xcmplx_0(D,C),B) = k1_bcialg_1(A,k3_bcialg_6(A,C,B),k2_bcialg_1(A,k3_bcialg_6(A,D,B))) ) ) ) ) )).
fof(l18_brouwer,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => v1_pscomp_1(k8_funcop_1(k1_numbers,u1_struct_0(A),B),A) ) ) )).
fof(l18_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_c0sp2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k11_c0sp1(u1_struct_0(A)))) => ( B = C => k2_normsp_0(k5_c0sp2(A),B) = k2_normsp_0(k11_c0sp1(u1_struct_0(A)),C) ) ) ) ) )).
fof(l18_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ( ( v3_lopban_2(A) & v31_algstr_0(A) & v3_cayldick(A) & v8_rlvect_1(A) ) => ( ( ~ v6_vectsp_1(A) & ~ v3_vectsp_1(A) ) | k2_cayldick(A,k5_struct_0(A)) = k5_struct_0(A) ) ) ) )).
fof(l18_cfdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k9_complex1(A),k9_complex1(k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1)))) & r1_xxreal_0(k9_complex1(B),k9_complex1(k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1)))) ) ) ) )).
fof(l18_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r1_tarski(k2_relset_1(k4_ordinal1,B),k2_finseq_1(A)) & r1_xxreal_0(C,k6_xcmplx_0(k3_finseq_1(B),1)) ) => ( r1_xxreal_0(1,k7_partfun1(k4_ordinal1,B,k1_nat_1(C,1))) & r1_xxreal_0(k7_partfun1(k4_ordinal1,B,k1_nat_1(C,1)),A) ) ) ) ) ) )).
fof(l18_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( ( 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] : ( ( 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] : ( 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,k5_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] : ( 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,k5_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) ) ) ) ) ) )).
fof(l18_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l18_csspace2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,A),k55_valued_1(k4_ordinal1,k2_numbers,k2_comseq_2(k4_ordinal1,A))) ) )).
fof(l18_csspace4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( r2_funct_2(k4_ordinal1,k2_numbers,A,k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,C)) <=> ! [D] : ( v7_ordinal1(D) => k1_funct_1(A,D) = k6_xcmplx_0(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) ) )).
fof(l18_dtconstr,axiom,( k1_lang1(k5_dtconstr) = a_0_10_dtconstr )).
fof(l18_fdiff_2,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l18_fib_fusc,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_ami_3)) => ! [C] : ( m1_subset_1(C,u1_compos_1(k1_ami_3)) => ! [D] : ( m1_subset_1(D,u1_compos_1(k1_ami_3)) => ! [E] : ( m1_subset_1(E,u1_compos_1(k1_ami_3)) => ! [F] : ( m1_subset_1(F,u1_compos_1(k1_ami_3)) => ! [G] : ( m1_subset_1(G,u1_compos_1(k1_ami_3)) => ! [H] : ( m1_subset_1(H,u1_compos_1(k1_ami_3)) => ! [I] : ( m1_subset_1(I,u1_compos_1(k1_ami_3)) => ! [J] : ( 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,k5_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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l18_fib_num,axiom,( ~ r1_xxreal_0(k3_square_1(5),2) )).
fof(l18_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( 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) = k5_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) ) ) ) ) ) )).
fof(l18_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => k1_binop_1(k11_monoid_0(A),B,C) = k1_monoid_0(A,B,C) ) ) ) )).
fof(l18_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(D) & v11_fomodel1(D) & l1_fomodel1(D) ) => ! [E] : ( 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) & v9_fomodel4(C,D,E,A) ) => v9_fomodel4(C,D,E,B) ) ) ) )).
fof(l18_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ! [F] : ( 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] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l18_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_analoaf(A,B,D,C,E) => r1_geomtrap(A,B,D,k1_geomtrap(A,B,E),k1_geomtrap(A,D,C)) ) ) ) ) ) ) )).
fof(l18_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ( r1_glib_000(A,C,D,B) <=> ( r2_glib_000(A,C,D,B) | r2_glib_000(A,D,C,B) ) ) ) )).
fof(l18_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ( ? [B] : ( m1_subset_1(B,k6_glib_000(A)) & k1_glib_002(A,B) = k6_glib_000(A) ) => v1_glib_002(A) ) ) )).
fof(l18_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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 ) )).
fof(l18_goboard5,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => k4_finseq_1(k2_goboard1(A)) = k4_finseq_1(A) ) )).
fof(l18_groeb_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k15_pre_poly(A))) => r1_tarski(k3_polynom1(k15_pre_poly(A),B,k2_groeb_3(A,B,C,D)),k3_polynom1(k15_pre_poly(A),B,C)) ) ) ) )).
fof(l18_group_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(B,k4_finseq_1(A)) => ( m1_subset_1(k2_xcmplx_0(k6_xcmplx_0(k3_finseq_1(A),B),1),k4_ordinal1) & 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)) ) ) ) ) )).
fof(l18_hessenbe,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ! [L] : ( m1_subset_1(L,u1_struct_0(A)) => ( ( r1_collsp(A,B,C,J) & r1_collsp(A,E,F,J) & r1_collsp(A,C,D,H) & r1_collsp(A,F,G,H) & r1_collsp(A,B,D,I) & r1_collsp(A,E,G,I) & r1_collsp(A,K,B,E) & r1_collsp(A,K,C,F) & r1_collsp(A,K,D,G) & r1_collsp(A,K,C,L) & r1_collsp(A,B,D,L) ) => ( K = E | B = E | K = F | C = F | K = G | D = G | r1_collsp(A,K,B,C) | r1_collsp(A,K,B,D) | r1_collsp(A,K,C,D) | r1_collsp(A,K,H,J) | r1_collsp(A,H,J,L) | r1_collsp(A,H,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l18_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( ( r1_aff_1(A,D,B,F) & r1_aff_1(A,D,B,H) ) => ( D = B | ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ~ ( ~ r1_aff_1(A,D,B,I) & r1_aff_1(A,D,I,J) & r2_analoaf(A,B,I,C,J) & r2_analoaf(A,I,F,J,G) & r1_aff_1(A,D,B,G) ) ) ) | ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ~ ( ~ r1_aff_1(A,D,B,I) & r1_aff_1(A,D,I,J) & r2_analoaf(A,B,I,C,J) & r2_analoaf(A,I,H,J,E) & r1_aff_1(A,D,B,E) ) ) ) | r2_analoaf(A,F,H,G,E) ) ) ) ) ) ) ) ) ) ) )).
fof(l18_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ~ ( r1_xxreal_0(A,B) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => k2_xcmplx_0(A,C) != B ) ) ) ) )).
fof(l18_integr11,axiom,( k9_xtuple_0(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,2),k5_numbers),k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(2,k5_numbers),k16_sin_cos),k7_xcmplx_0(1,4)))) = k1_numbers )).
fof(l18_integra5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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) ) ) ) )).
fof(l18_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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) = k2_xcmplx_0(k4_integra5(A,C,D),k4_integra5(C,B,D)) & r1_integra5(k3_integra5(A,C),D) & r1_integra5(k3_integra5(C,B),D) ) ) ) ) ) ) ) )).
fof(l18_jgraph_2,axiom,( k4_struct_0(k15_euclid(2)) = k16_euclid(2) )).
fof(l18_jgraph_3,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l18_jgraph_6,axiom,( k18_euclid(k19_euclid(k4_xcmplx_0(1),k5_numbers)) = k5_numbers )).
fof(l18_jordan1c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v9_rltopsp1(A,k15_euclid(2)) => ! [B] : ( v1_xreal_0(B) => ~ ( k1_jordan2c(2,A) != k1_xboole_0 & ~ r1_xxreal_0(B,k9_pscomp_1(k1_jordan2c(2,A))) & ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( r2_hidden(C,k1_jordan2c(2,A)) => r1_xxreal_0(B,k18_euclid(C)) ) ) ) ) ) ) )).
fof(l18_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(2,A) => k6_xcmplx_0(k1_nat_1(k7_nat_d(k3_xcmplx_0(2,A),2),1),2) = k6_xcmplx_0(k3_xcmplx_0(2,A),3) ) ) )).
fof(l18_jordan5a,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) ) ) )).
fof(l18_lattice7,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( ! [C] : ( 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 ) ) ) )).
fof(l18_lattices,axiom,( ! [A] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(l18_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ~ ( ( A = k5_numbers => B = k5_numbers ) & k8_matrix13(C,D) = A & ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(C),k7_nat_d(B,A),B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(C))) ) => k8_matrix13(C,k8_matrlin(u1_struct_0(C),A,k7_nat_d(B,A),B,D,E)) != B ) ) ) ) ) ) )).
fof(l18_measure5,axiom,( ! [A] : ( ( v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(l18_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ( ( D = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),B,k6_xcmplx_0(1,G)),k1_rlvect_1(k15_euclid(2),C,G)) & E = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),C,k6_xcmplx_0(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 | ( k2_xcmplx_0(k6_xcmplx_0(1,H),k3_xcmplx_0(G,H)) != k5_numbers & ? [I] : ( v1_xreal_0(I) & F = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),A,k6_xcmplx_0(1,I)),k1_rlvect_1(k15_euclid(2),D,I)) & I = k7_xcmplx_0(k6_xcmplx_0(1,H),k2_xcmplx_0(k6_xcmplx_0(1,H),k3_xcmplx_0(G,H))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l18_metrizts,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => k2_card_2(k4_ordinal1,A) = A ) )).
fof(l18_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(l18_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) & v2_nagata_1(B,A) ) ) )).
fof(l18_ndiff_3,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l18_nfcont_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) & ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(C,k9_complex1(k3_xcmplx_0(B,k2_power(A,D)))) ) ) ) ) ) )).
fof(l18_ntalgo_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => k3_int_2(A,k5_numbers) = k1_int_2(A) ) )).
fof(l18_numbers,axiom,( r2_hidden(1,k4_ordinal1) )).
fof(l18_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(l18_orders_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_orders_3(A) ) => ! [B] : ( m1_orders_3(B,A) => r2_hidden(u1_struct_0(B),k2_orders_3(A)) ) ) )).
fof(l18_papdesaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( B != C & D != C & r1_analoaf(A,B,C,C,D) & ! [E] : ( v1_xreal_0(E) => ~ ( k5_algstr_0(A,C,B) = k1_rlvect_1(A,k5_algstr_0(A,D,C),E) & ~ r1_xxreal_0(E,k5_numbers) ) ) ) ) ) ) ) )).
fof(l18_pdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(3)) => ! [F] : ( ( 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] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & ? [I] : ( v1_xreal_0(I) & E = k11_finseq_1(G,H,I) & ? [J] : ( m1_rcomp_1(J,I) & r1_tarski(J,k1_relset_1(k1_numbers,k1_pdiff_2(3,3,F,E))) & ? [K] : ( v1_funct_1(K) & v3_fdiff_1(K) & m1_subset_1(K,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [L] : ( v1_funct_1(L) & v2_fdiff_1(L) & m1_subset_1(L,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & D = k1_funct_1(K,1) & ! [M] : ( v1_xreal_0(M) => ( r2_hidden(M,J) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,3,F,E),M),k1_funct_1(k1_pdiff_2(3,3,F,E),I)) = k2_xcmplx_0(k1_funct_1(K,k6_xcmplx_0(M,I)),k1_funct_1(L,k6_xcmplx_0(M,I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l18_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(A,C) => r1_nat_d(k1_newton(B,A),k1_newton(B,C)) ) ) ) ) )).
fof(l18_pre_ff,axiom,( m2_finseq_2(k12_finseq_1(k4_ordinal1,1),k4_ordinal1,k3_finseq_2(k4_ordinal1)) )).
fof(l18_prob_4,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k1_prob_4(A,k9_setfam_1(A),k2_prob_3(A,B),C) = k1_prob_4(A,k9_setfam_1(A),B,C) ) ) ) )).
fof(l18_prvect_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v1_prvect_2(A) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k4_card_3(k4_prvect_2(A))) => ! [D] : ( m2_subset_1(D,k4_ordinal1,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] : ( 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) ) ) ) ) ) ) ) )).
fof(l18_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k1_qc_lang1(A)) => m2_finseq_1(k9_finseq_1(k4_tarski(B,C)),k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))) ) ) ) )).
fof(l18_random_1,axiom,( v1_xreal_0(1) )).
fof(l18_real_ns1,axiom,( ! [A] : ( 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)) ) ) )).
fof(l18_realset2,axiom,( k9_xtuple_0(k13_funcop_1(k5_numbers,1,k5_numbers)) = k6_domain_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,1)) )).
fof(l18_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( r2_classes1(A,B) => r1_xxreal_0(k3_rfinseq2(A),k3_rfinseq2(B)) ) ) ) )).
fof(l18_ringcat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_ringcat1(C,A,B) => ~ ( r1_ringcat1(A,B) & ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(l18_scm_inst,axiom,( ! [A] : ( 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 ) ) )).
fof(l18_scmfsa6b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) & v1_scmfsa6b(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [D] : ( ( 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(k7_card_1(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(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)),D) ) => ( k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D,k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),D),1))) = k5_card_1(B) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D,k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),D),1))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_funct_4(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),D,k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),D)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))) & r1_tarski(k6_compos_1(k1_scmfsa_2,C,k5_card_1(B)),A) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D,k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),D),1)),k4_scmfsa_2(k5_numbers)) = 1 & r1_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D) & k8_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D) = k2_xcmplx_0(k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),D),1),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(k1_funct_4(A,B),C),k1_funct_4(k6_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),D),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))))) & ( v1_scmfsa6b(C) => k1_funct_1(k6_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D),k4_scmfsa_2(k5_numbers)) = 1 ) ) ) ) ) ) ) )).
fof(l18_scmfsa_1,axiom,( r1_tarski(k10_xtuple_0(k4_scmfsa_1),k9_xtuple_0(k5_scmfsa_1)) )).
fof(l18_scmfsa_i,axiom,( ! [A] : ( 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 ) ) )).
fof(l18_scmp_gcd,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(B,1) & k3_scmp_gcd = k1_scmp_gcd(k2_xcmplx_0(A,B)) ) ) ) )).
fof(l18_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_scmringi(A)) => ( k4_xtuple_0(B) = 5 => k5_xtuple_0(B) = k1_xboole_0 ) ) ) )).
fof(l18_scpinvar,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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))) = k1_nat_1(k5_card_1(C),4) ) ) ) )).
fof(l18_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( k1_funct_1(B,k2_scmp_gcd) = k5_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)),k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_numbers))))),B,A),k2_scmp_gcd) = k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_numbers))))),B,A),k1_scmp_gcd(5)) = k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_numbers))))),B,A),k1_scmp_gcd(3)) = k1_funct_1(B,k1_scmp_gcd(3)) & ! [E] : ( v7_ordinal1(E) => ( 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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_numbers))))),B,A),k1_scmp_gcd(E)) = k1_funct_1(B,k1_scmp_gcd(E)) ) ) & ? [E] : ( v7_ordinal1(E) & 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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_numbers))))),B,A),k1_scmp_gcd(4)) = k2_xcmplx_0(C,E) & r1_xxreal_0(E,k1_funct_1(B,k1_scmp_gcd(5))) & ! [F] : ( v7_ordinal1(F) => ~ ( ~ r1_xxreal_0(F,k2_xcmplx_0(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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_numbers))))),B,A),k1_scmp_gcd(D))) ) ) & ( E = k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_numbers))))),B,A),k1_scmp_gcd(k2_xcmplx_0(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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_numbers))))),B,A),k1_scmp_gcd(D))) ) ) ) ) ) ) ) ) ) )).
fof(l18_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => k3_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(2,k3_square_1(k3_xcmplx_0(B,C))),A),k7_xcmplx_0(k3_xcmplx_0(2,k3_square_1(k3_xcmplx_0(A,C))),B)),k7_xcmplx_0(k3_xcmplx_0(2,k3_square_1(k3_xcmplx_0(A,B))),C)) = 8 ) ) ) )).
fof(l18_simplex2,axiom,( ! [A] : ( v7_ordinal1(A) => k2_struct_0(k15_euclid(A)) = k2_struct_0(k14_euclid(A)) ) )).
fof(l18_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( 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(k6_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(C,D)),k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,C)),k7_complex1)) & k8_complex1(k2_xcmplx_0(B,k3_xcmplx_0(D,k7_complex1))) = k2_xcmplx_0(B,k3_xcmplx_0(k4_xcmplx_0(D),k7_complex1)) ) ) ) ) ) )).
fof(l18_sincos10,axiom,( r2_hidden(k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos),k4_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos)) & r2_hidden(k28_sin_cos,k4_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos)) )).
fof(l18_sppol_1,axiom,( ! [A] : ( 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) ) ) )).
fof(l18_substut1,axiom,( ! [A] : ! [B] : ~ ( r2_hidden(k1_card_1(A),k1_card_1(B)) & k6_subset_1(B,A) = k1_xboole_0 ) )).
fof(l18_taxonom2,axiom,( ! [A] : ! [B] : ( m1_taxonom2(B,A) => ! [C] : ( ( v4_taxonom2(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ( ( r1_tarski(C,B) & ! [D] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ~ ( r2_hidden(D,C) & D = k1_xboole_0 ) ) ) ) ) )).
fof(l18_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v13_struct_0(k1_tex_2(A,B),1) ) ) )).
fof(l18_topgen_3,axiom,( c1__topgen_3 = a_0_0_topgen_3 )).
fof(l18_topreal2,axiom,( ~ r2_hidden(k19_euclid(1,1),k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,k5_numbers),k19_euclid(k5_numbers,1))) )).
fof(l18_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ( ( v11_aff_2(A) & r1_aff_1(A,B,C,H) & 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) & r2_analoaf(A,D,F,H,J) & r2_analoaf(A,D,H,F,J) & r2_analoaf(A,E,G,I,J) & r2_analoaf(A,E,I,G,J) ) => ( B = C | r1_aff_1(A,B,C,D) | r1_aff_1(A,B,C,E) | H = I ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l18_uniform1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r2_hidden(A,k1_rcomp_1(B,C)) <=> ( r1_xxreal_0(B,A) & r1_xxreal_0(A,C) ) ) ) ) ) )).
fof(l18_urysohn2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ( v4_xxreal_2(k1_integra2(A,B)) => ( r1_xxreal_0(B,k5_numbers) | v4_xxreal_2(A) ) ) ) ) )).
fof(l18_xreal_0,axiom,( c5__xreal_0 = k4_xcmplx_0(1) & k1_arytm_0(c3__xreal_0,c5__xreal_0) = k5_numbers )).
fof(l18_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(k3_xcmplx_0(B,C),k3_xcmplx_0(A,C)) ) ) ) ) )).
fof(l18_xxreal_3,axiom,( ! [A] : ( 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)) ) ) )).
fof(l18_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ? [D] : ( 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] : ( 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)) ) ) ) ) )).
fof(l18_zf_fund1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => k4_zf_fund1(k6_domain_1(k1_zf_lang,A)) = k6_domain_1(k4_ordinal1,k3_zf_fund1(A)) ) )).
fof(l18_zfmisc_1,axiom,( ! [A] : ! [B] : ~ ( r1_xboole_0(k1_tarski(A),B) & r2_hidden(A,B) ) )).
fof(l194_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v8_group_9(C,A,B) & m2_finseq_1(C,k6_group_9(A,B)) ) => ! [D] : ( ( v8_group_9(D,A,B) & m2_finseq_1(D,k6_group_9(A,B)) ) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( 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] : ( v7_ordinal1(G) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(l195_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( ( v8_group_9(G,A,B) & m2_finseq_1(G,k6_group_9(A,B)) ) => ! [H] : ( ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(l196_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( v1_int_1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( ( v8_group_9(F,A,B) & m2_finseq_1(F,k6_group_9(A,B)) ) => ! [G] : ( ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(l19_algstr_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_algstr_0(A,C,k5_struct_0(A)) = C ) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( C != k4_struct_0(A) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k6_algstr_0(A,C,D) != k5_struct_0(A) ) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( 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)) ) ) ) ) )).
fof(l19_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(k4_amistd_1(A))) => v1_xboole_0(k2_amistd_1(A,k4_amistd_1(A),B)) ) ) )).
fof(l19_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( k1_rlvect_1(A,B,D) = C => ( D = k5_numbers | r1_anproj_1(A,B,C) ) ) ) ) ) ) )).
fof(l19_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ( r1_arytm_2(A,B) => k1_arytm_1(B,k1_arytm_1(B,A)) = A ) ) ) )).
fof(l19_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ( k3_arytm_2(A) = k11_arytm_3 <=> A = k11_arytm_3 ) ) )).
fof(l19_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ( v2_comseq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k2_asympt_1,k3_asympt_1(A))) & k1_seq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k2_asympt_1,k3_asympt_1(A))) = k5_numbers ) ) ) )).
fof(l19_bcialg_6,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k3_bcialg_6(A,D,k3_bcialg_6(A,C,B)) = k3_bcialg_6(A,k3_xcmplx_0(C,D),B) ) ) ) ) )).
fof(l19_borsuk_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(B,A)))) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(l19_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(l19_c0sp1,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l19_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_c0sp2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_c0sp2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k11_c0sp1(u1_struct_0(A)))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l19_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(l19_cfdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(2))) => ( C = k10_finseq_1(A,B) => r1_xxreal_0(k2_normsp_0(k4_real_ns1(2),C),k2_xcmplx_0(k9_complex1(A),k9_complex1(B))) ) ) ) ) )).
fof(l19_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r1_tarski(k2_relset_1(k4_ordinal1,B),k2_finseq_1(A)) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(B)) ) => ( r1_xxreal_0(1,k7_partfun1(k4_ordinal1,B,C)) & r1_xxreal_0(k7_partfun1(k4_ordinal1,B,C),A) ) ) ) ) ) )).
fof(l19_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_clopban2(A))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(l19_clvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => k4_rlvect_1(A,k6_finseq_1(u1_struct_0(A))) = k4_struct_0(A) ) )).
fof(l19_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ( A = k5_arytm_0(B,C) => ( C = k5_numbers & A = B ) ) ) ) ) )).
fof(l19_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) )).
fof(l19_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(l19_csspace2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k18_csspace)) <=> ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & v2_comseq_3(k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k2_csspace(A),k2_comseq_2(k4_ordinal1,k2_csspace(A)))) ) ) )).
fof(l19_dtconstr,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ~ r1_lang1(k5_dtconstr,c2__dtconstr,A) ) )).
fof(l19_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( k17_euclid(k5_algstr_0(k15_euclid(2),A,B)) = k6_xcmplx_0(k17_euclid(A),k17_euclid(B)) & k18_euclid(k5_algstr_0(k15_euclid(2),A,B)) = k6_xcmplx_0(k18_euclid(A),k18_euclid(B)) ) ) ) )).
fof(l19_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => k5_euclid_8(k1_euclid_8(A,B,C),k1_euclid_8(D,E,F)) = k1_euclid_8(k6_xcmplx_0(k3_xcmplx_0(B,F),k3_xcmplx_0(C,E)),k6_xcmplx_0(k3_xcmplx_0(C,D),k3_xcmplx_0(A,F)),k6_xcmplx_0(k3_xcmplx_0(A,E),k3_xcmplx_0(B,D))) ) ) ) ) ) ) )).
fof(l19_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v1_conaffm(A) <=> v4_aff_2(k3_analmetr(A)) ) ) )).
fof(l19_fdiff_1,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l19_fdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( r4_fdiff_3(A,C) & r4_fdiff_3(B,C) ) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k1_relset_1(k1_numbers,B)) & r2_hidden(E,k1_rcomp_1(k6_xcmplx_0(C,D),C)) & k1_funct_1(B,E) = k5_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)) = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_3(C,A),k1_funct_1(B,C)),k3_xcmplx_0(k1_fdiff_3(C,B),k1_funct_1(A,C))),k1_square_1(k1_funct_1(B,C))) ) ) ) ) ) ) )).
fof(l19_fib_num,axiom,( k3_square_1(5) != k5_numbers )).
fof(l19_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( v10_fomodel4(D,B,C) => v10_fomodel4(A,B,C) ) ) ) ) )).
fof(l19_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l19_functor1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r1_pzfmisc1(A,B,C) => ! [D] : ( m2_pboole(D,A,B,C) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(l19_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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] : ( ( v5_relat_1(F,k1_rcomp_1(k5_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] : ! [H] : ( ( r2_hidden(G,A) & r2_hidden(H,C) ) => k2_seq_4(k2_relset_1(k1_numbers,k2_fuzzy_4(A,B,C,k2_fuzzy_1(k2_zfmisc_1(A,B),D,E),F,G,H))) = k4_xxreal_0(k2_seq_4(k2_relset_1(k1_numbers,k2_fuzzy_4(A,B,C,D,F,G,H))),k2_seq_4(k2_relset_1(k1_numbers,k2_fuzzy_4(A,B,C,E,F,G,H)))) ) ) ) ) ) ) ) )).
fof(l19_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(l19_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ( v1_glib_002(A) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => k1_glib_002(A,B) = k6_glib_000(A) ) ) ) )).
fof(l19_hessenbe,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ( ( r1_collsp(A,B,C,J) & r1_collsp(A,E,F,J) & r1_collsp(A,C,D,H) & r1_collsp(A,F,G,H) & r1_collsp(A,B,D,I) & r1_collsp(A,E,G,I) & r1_collsp(A,K,B,E) & r1_collsp(A,K,C,F) & r1_collsp(A,K,D,G) ) => ( K = E | B = E | K = F | C = F | K = G | D = G | r1_collsp(A,K,B,C) | r1_collsp(A,K,B,D) | r1_collsp(A,K,C,D) | r1_collsp(A,K,H,J) | r1_collsp(A,H,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l19_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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,D,B,C) & v4_aff_2(A) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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,D,B,F) & r1_aff_1(A,D,F,G) & r2_analoaf(A,B,F,C,G) ) | ( r1_aff_1(A,D,B,F) & ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & ? [I] : ( m1_subset_1(I,u1_struct_0(A)) & ~ r1_aff_1(A,D,B,H) & r1_aff_1(A,D,H,I) & r2_analoaf(A,B,H,C,I) & r2_analoaf(A,H,F,I,G) & r1_aff_1(A,D,B,G) ) ) ) ) ) ) ) ) => ( D = B | ( v6_transgeo(E,A) & k3_funct_2(u1_struct_0(A),u1_struct_0(A),E,D) = D & k3_funct_2(u1_struct_0(A),u1_struct_0(A),E,B) = C ) ) ) ) ) ) ) ) )).
fof(l19_hurwitz,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_polynom3(A))) => ( D = C => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(l19_index_1,axiom,( ! [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) & 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))) ) )).
fof(l19_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ~ ( r1_xxreal_0(A,B) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => k6_xcmplx_0(B,C) != A ) ) ) ) )).
fof(l19_integr11,axiom,( m1_subset_1(k28_sin_cos,k1_numbers) )).
fof(l19_jgraph_6,axiom,( k17_euclid(k19_euclid(1,k5_numbers)) = 1 )).
fof(l19_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( 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) ) ) ) ) )).
fof(l19_jordan1c,axiom,( ! [A] : ( 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)) ) ) )).
fof(l19_jordan5a,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k4_topmetr(A,B))) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [H] : ( v1_xreal_0(H) => ( ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(l19_lattices,axiom,( ! [A] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(l19_lfuzzy_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => v1_monoid_0(k4_lfuzzy_0(A)) ) )).
fof(l19_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_lopban_2(A))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(l19_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ( ( r2_hidden(k4_tarski(C,D),k2_matrix_0(k3_matrix_1(B,A))) & r2_hidden(E,k4_finseq_1(k3_matrix_1(B,A))) & r2_hidden(F,k4_finseq_1(k3_matrix_1(B,A))) ) => ( F = E | k3_matrix_0(u1_struct_0(B),k3_matrix_1(B,A),C,D) = k3_matrix_0(u1_struct_0(B),k3_matrix12(A,A,B,k3_matrix12(A,A,B,k3_matrix_1(B,A),E,F,k4_algstr_0(B,G)),E,F,G),C,D) ) ) ) ) ) ) ) ) ) )).
fof(l19_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ r1_euclid_6(A,B,C) & D = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),B,k6_xcmplx_0(1,F)),k1_rlvect_1(k15_euclid(2),C,F)) & E = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),C,k6_xcmplx_0(1,G)),k1_rlvect_1(k15_euclid(2),A,G)) & k2_xcmplx_0(k6_xcmplx_0(1,G),k3_xcmplx_0(F,G)) != k5_numbers & ! [H] : ( m1_subset_1(H,u1_struct_0(k15_euclid(2))) => ~ ( r1_euclid_6(A,D,H) & r1_euclid_6(B,E,H) ) ) ) ) ) ) ) ) ) ) )).
fof(l19_mfold_1,axiom,( k1_pre_topc(k15_euclid(k5_numbers),k2_struct_0(k15_euclid(k5_numbers))) = g1_pre_topc(u1_struct_0(k15_euclid(k5_numbers)),u1_pre_topc(k15_euclid(k5_numbers))) )).
fof(l19_mod_3,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( 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) ) ) ) ) ) ) )).
fof(l19_ntalgo_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => ! [B] : ( m1_subset_1(B,k4_numbers) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k4_numbers) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_numbers))) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k4_ordinal1,k4_numbers) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_numbers))) ) => ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,k4_ordinal1,k4_numbers) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_numbers))) ) => ! [I] : ( ( v1_funct_1(I) & v1_funct_2(I,k4_ordinal1,k4_numbers) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_numbers))) ) => ! [J] : ( ( v1_funct_1(J) & v1_funct_2(J,k4_ordinal1,k4_numbers) & m1_subset_1(J,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_numbers))) ) => ( ( k9_nat_1(k4_numbers,G,k5_numbers) = 1 & k9_nat_1(k4_numbers,H,k5_numbers) = k5_numbers & k9_nat_1(k4_numbers,C,k5_numbers) = A & k9_nat_1(k4_numbers,E,k5_numbers) = k5_numbers & k9_nat_1(k4_numbers,J,k5_numbers) = k5_numbers & k9_nat_1(k4_numbers,I,k5_numbers) = 1 & k9_nat_1(k4_numbers,D,k5_numbers) = B & k9_nat_1(k4_numbers,F,k5_numbers) = k5_numbers & ! [K] : ( m1_subset_1(K,k4_ordinal1) => ( k9_nat_1(k4_numbers,E,k1_nat_1(K,1)) = k4_int_1(k9_nat_1(k4_numbers,C,K),k9_nat_1(k4_numbers,D,K)) & k9_nat_1(k4_numbers,F,k1_nat_1(K,1)) = k5_int_1(k9_nat_1(k4_numbers,C,K),k9_nat_1(k4_numbers,D,K)) & k9_nat_1(k4_numbers,G,k1_nat_1(K,1)) = k9_nat_1(k4_numbers,J,K) & k9_nat_1(k4_numbers,H,k1_nat_1(K,1)) = k9_nat_1(k4_numbers,I,K) & k9_nat_1(k4_numbers,C,k1_nat_1(K,1)) = k9_nat_1(k4_numbers,D,K) & k9_nat_1(k4_numbers,J,k1_nat_1(K,1)) = k6_xcmplx_0(k9_nat_1(k4_numbers,G,K),k3_xcmplx_0(k9_nat_1(k4_numbers,E,k1_nat_1(K,1)),k9_nat_1(k4_numbers,J,K))) & k9_nat_1(k4_numbers,I,k1_nat_1(K,1)) = k6_xcmplx_0(k9_nat_1(k4_numbers,H,K),k3_xcmplx_0(k9_nat_1(k4_numbers,E,k1_nat_1(K,1)),k9_nat_1(k4_numbers,I,K))) & k9_nat_1(k4_numbers,D,k1_nat_1(K,1)) = k9_nat_1(k4_numbers,F,k1_nat_1(K,1)) ) ) ) => ! [K] : ( m1_subset_1(K,k4_ordinal1) => ( k9_nat_1(k4_numbers,D,K) != k5_numbers => k2_xcmplx_0(k3_xcmplx_0(k9_nat_1(k4_numbers,G,k1_nat_1(K,1)),A),k3_xcmplx_0(k9_nat_1(k4_numbers,H,k1_nat_1(K,1)),B)) = k9_nat_1(k4_numbers,C,k1_nat_1(K,1)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l19_numbers,axiom,( m1_subset_1(1,k5_arytm_3) )).
fof(l19_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_o_ring_1(B,A) => v7_o_ring_1(B,A) ) ) ) )).
fof(l19_pepin,axiom,( k11_newton(2,8) = 256 )).
fof(l19_polynom8,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_int_1(C) => ( ~ r1_xxreal_0(k5_numbers,C) => k3_polynom8(A,B,C) = k11_algstr_0(A,k3_polynom8(A,B,k1_int_2(C))) ) ) ) ) )).
fof(l19_prvect_2,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l19_prvect_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_hidden(B,k4_card_3(A)) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ) )).
fof(l19_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [D] : ( ( 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(k4_ordinal1,k1_qc_lang1(A))) ) ) ) ) )).
fof(l19_quantal1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(l19_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k1_random_1(A),k6_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),k6_numbers))) ) => ! [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))) ) => ~ ( ~ r1_xxreal_0(k1_xxreal_0,k12_supinf_2(B,A)) & ! [D] : ( m2_finseq_1(D,k6_numbers) => ~ ( k3_finseq_1(D) = k5_card_1(A) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(D)) => k12_supinf_2(D,E) = k1_extreal1(k12_supinf_2(C,k1_funct_1(k19_finseq_1(A),E)),k12_supinf_2(B,k1_tarski(k1_funct_1(k19_finseq_1(A),E)))) ) ) & k1_mesfunc6(A,k1_random_1(A),B,C) = k4_extreal1(D) ) ) ) ) ) ) )).
fof(l19_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(k9_nat_1(k4_ordinal1,k1_real_3(C,B),A),k9_nat_1(k4_ordinal1,k1_real_3(C,B),k1_nat_1(A,1))) & k9_nat_1(k4_ordinal1,k1_real_3(C,B),A) != k5_numbers ) ) ) ) )).
fof(l19_realset2,axiom,( k5_binop_1(2,k2_realset2,k10_subset_1(k5_numbers,2),k10_subset_1(k5_numbers,2)) = k10_subset_1(k5_numbers,2) )).
fof(l19_ringcat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_ringcat1(C,A,B) => ~ ( r1_ringcat1(A,B) & ! [D] : ( ( 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) ) ) ) ) ) )).
fof(l19_rlaffin2,axiom,( v1_xreal_0(1) )).
fof(l19_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_rmod_2(D,A,B) => ( u1_struct_0(D) = C => v1_rmod_2(C,A,B) ) ) ) ) ) )).
fof(l19_scm_inst,axiom,( ! [A] : ( 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) ) ) )).
fof(l19_scmfsa_1,axiom,( k9_xtuple_0(k3_relat_1(k4_scmfsa_1,k5_scmfsa_1)) = k1_scmfsa_1 )).
fof(l19_scmfsa_i,axiom,( ! [A] : ( 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 ) ) )).
fof(l19_scmp_gcd,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( ( 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) = k5_numbers ) => ( r1_xxreal_0(k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,k3_scmp_gcd),3)),k5_numbers) | ( k5_memstr_0(2,k1_scmpds_2,k5_extpro_1(2,k1_scmpds_2,C,B,7)) = k1_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) = k1_nat_1(A,4) & k1_funct_1(k5_extpro_1(2,k1_scmpds_2,C,B,7),k2_scmp_gcd) = k5_numbers & k1_funct_1(k5_extpro_1(2,k1_scmpds_2,C,B,7),k1_scmp_gcd(k1_nat_1(A,7))) = k5_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(k1_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(k1_nat_1(A,4))) = A & k1_funct_1(k5_extpro_1(2,k1_scmpds_2,C,B,7),k1_scmp_gcd(k1_nat_1(A,5))) = 11 ) ) ) ) ) ) )).
fof(l19_scmring3,axiom,( ! [A] : ! [B] : ( r2_hidden(A,k4_finseq_1(k9_finseq_1(B))) => A = 1 ) )).
fof(l19_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(l19_scpisort,axiom,( 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,k5_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),k5_numbers)),k16_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,k5_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,k5_numbers))))) = 10 )).
fof(l19_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( k1_funct_1(B,k2_scmp_gcd) = k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_numbers))))),B,A) ) ) ) ) ) ) )).
fof(l19_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => ( k2_xcmplx_0(k2_xcmplx_0(A,B),C) = 1 => k2_xcmplx_0(1,k7_xcmplx_0(1,A)) = k2_xcmplx_0(2,k7_xcmplx_0(k2_xcmplx_0(B,C),A)) ) ) ) ) )).
fof(l19_simplex2,axiom,( ! [A] : v6_ordinal1(k1_tarski(A)) )).
fof(l19_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k4_sin_cos2(k2_xcmplx_0(A,B)) = k2_xcmplx_0(k3_xcmplx_0(k4_sin_cos2(A),k4_sin_cos2(B)),k3_xcmplx_0(k2_sin_cos2(A),k2_sin_cos2(B))) & k4_sin_cos2(k6_xcmplx_0(A,B)) = k6_xcmplx_0(k3_xcmplx_0(k4_sin_cos2(A),k4_sin_cos2(B)),k3_xcmplx_0(k2_sin_cos2(A),k2_sin_cos2(B))) & k2_sin_cos2(k2_xcmplx_0(A,B)) = k2_xcmplx_0(k3_xcmplx_0(k2_sin_cos2(A),k4_sin_cos2(B)),k3_xcmplx_0(k4_sin_cos2(A),k2_sin_cos2(B))) & k2_sin_cos2(k6_xcmplx_0(A,B)) = k6_xcmplx_0(k3_xcmplx_0(k2_sin_cos2(A),k4_sin_cos2(B)),k3_xcmplx_0(k4_sin_cos2(A),k2_sin_cos2(B))) & k6_sin_cos2(k2_xcmplx_0(A,B)) = k7_xcmplx_0(k2_xcmplx_0(k6_sin_cos2(A),k6_sin_cos2(B)),k2_xcmplx_0(1,k3_xcmplx_0(k6_sin_cos2(A),k6_sin_cos2(B)))) & k6_sin_cos2(k6_xcmplx_0(A,B)) = k7_xcmplx_0(k6_xcmplx_0(k6_sin_cos2(A),k6_sin_cos2(B)),k6_xcmplx_0(1,k3_xcmplx_0(k6_sin_cos2(A),k6_sin_cos2(B)))) ) ) ) )).
fof(l19_sin_cos9,axiom,( k2_funct_1(k1_sin_cos9) = k2_partfun1(k1_numbers,k1_numbers,k26_sin_cos,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))) )).
fof(l19_sincos10,axiom,( r2_hidden(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers)) & r2_hidden(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)),k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers)) )).
fof(l19_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) & k1_square_1(A) = k1_square_1(B) ) => A = B ) ) ) )).
fof(l19_topgen_3,axiom,( r1_tarski(c1__topgen_3,u1_pre_topc(k2_topgen_3)) )).
fof(l19_topreal2,axiom,( ~ r2_hidden(k19_euclid(1,1),k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,k5_numbers),k19_euclid(1,k5_numbers))) )).
fof(l19_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( v11_aff_2(A) & B != C & ! [D] : ( ( 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 ) ) ) ) ) ) )).
fof(l19_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => m1_subset_1(u1_struct_0(B),k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(l19_waybel15,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ( ? [B] : ? [C] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k2_yellow_1(B)),u1_struct_0(k2_yellow_1(B))) & v6_waybel_1(C,k2_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_yellow_1(B)),u1_struct_0(k2_yellow_1(B))))) & v22_waybel_0(C,k2_yellow_1(B),k2_yellow_1(B)) & r5_waybel_1(A,k1_yellow_2(k2_yellow_1(B),k2_yellow_1(B),C)) ) => v3_waybel_3(A) ) ) )).
fof(l19_waybel17,axiom,( ! [A] : ( ( 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] : ( ( ~ 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) ) ) )).
fof(l19_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_lattice3(C) & v2_lattice3(C) & l1_orders_2(C) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(l19_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k3_xcmplx_0(A,k3_xcmplx_0(B,C)) = k3_xcmplx_0(k3_xcmplx_0(A,B),C) ) ) ) )).
fof(l19_xreal_0,axiom,( ~ r2_hidden(k4_xcmplx_0(1),k2_arytm_2) )).
fof(l19_xxreal_3,axiom,( ! [A] : ( 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)) ) ) )).
fof(l19_yellow_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k2_yellow_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_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)) ) ) ) )).
fof(l19_yellow_6,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( 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) ) ) )).
fof(l19_zf_fund1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => k4_zf_fund1(k7_domain_1(k1_zf_lang,A,B)) = k7_domain_1(k4_ordinal1,k3_zf_fund1(A),k3_zf_fund1(B)) ) ) )).
fof(l19_zmodul01,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(l1_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( r2_hidden(C,B) => m1_subset_1(C,u1_struct_0(A)) ) ) ) )).
fof(l1_afinsq_2,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(l1_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_diraf(A,B,C,C,D) => ( B = D | r2_analoaf(A,B,C,C,D) ) ) ) ) ) ) )).
fof(l1_algstr_2,axiom,( k5_numbers = k4_struct_0(k2_vectsp_1) )).
fof(l1_ami_4,axiom,( k10_ami_3(k5_numbers) != k10_ami_3(1) & k10_ami_3(1) != k10_ami_3(2) )).
fof(l1_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( ( 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)) ) => ( k3_rlvect_1(A,B,C) = k3_rlvect_1(A,k1_rlvect_1(A,D,k2_xcmplx_0(F,H)),k1_rlvect_1(A,E,k2_xcmplx_0(G,I))) & k5_algstr_0(A,B,C) = k3_rlvect_1(A,k1_rlvect_1(A,D,k6_xcmplx_0(F,H)),k1_rlvect_1(A,E,k6_xcmplx_0(G,I))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l1_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( ( 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)) ) => ( k3_rlvect_1(A,B,C) = k3_rlvect_1(A,k1_rlvect_1(A,D,k2_xcmplx_0(F,H)),k1_rlvect_1(A,E,k2_xcmplx_0(G,I))) & k5_algstr_0(A,B,C) = k3_rlvect_1(A,k1_rlvect_1(A,D,k6_xcmplx_0(F,H)),k1_rlvect_1(A,E,k6_xcmplx_0(G,I))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l1_arithm,axiom,( r2_hidden(k5_numbers,k4_ordinal1) )).
fof(l1_armstrng,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,B) ) => k4_finseq_1(C) = k2_finseq_1(A) ) ) ) )).
fof(l1_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => r2_hidden(k4_tarski(k5_numbers,A),k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) ) )).
fof(l1_arytm_3,axiom,( r2_hidden(k1_xboole_0,k4_ordinal1) )).
fof(l1_asympt_1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( r1_xxreal_0(2,A) & r1_xxreal_0(k5_series_1(2,A),k1_nat_1(A,1)) ) ) )).
fof(l1_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) )).
fof(l1_axioms,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ ( ~ ( r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_arytm_2) & ? [C] : ( m1_subset_1(C,k2_arytm_2) & ? [D] : ( m1_subset_1(D,k2_arytm_2) & A = C & B = D & r1_arytm_2(C,D) ) ) ) & ~ ( r2_hidden(A,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) & r2_hidden(B,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) & ? [C] : ( m1_subset_1(C,k2_arytm_2) & ? [D] : ( m1_subset_1(D,k2_arytm_2) & A = k4_tarski(k5_numbers,C) & B = k4_tarski(k5_numbers,D) & r1_arytm_2(D,C) ) ) ) & ~ ( r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) ) ) => r1_xxreal_0(A,B) ) ) ) )).
fof(l1_bhsp_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(k7_xcmplx_0(D,2),k9_complex1(k6_xcmplx_0(A,B))) & ~ r1_xxreal_0(k7_xcmplx_0(D,2),k9_complex1(k6_xcmplx_0(B,C))) & r1_xxreal_0(D,k9_complex1(k6_xcmplx_0(A,C))) ) ) ) ) ) )).
fof(l1_binari_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k6_margrel1) ) => ( ( k3_finseq_1(B) = A & k3_finseq_1(C) = A & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k2_finseq_1(A)) => k7_partfun1(k6_margrel1,B,D) = k7_partfun1(k6_margrel1,C,D) ) ) ) => B = C ) ) ) ) )).
fof(l1_bintree2,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => m2_finseq_1(k8_finseq_1(A,B,C),A) ) ) )).
fof(l1_borsuk_2,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,1) ) <=> r2_hidden(A,u1_struct_0(k5_topmetr)) ) ) )).
fof(l1_borsuk_7,axiom,( v7_ordinal1(k5_numbers) )).
fof(l1_brouwer2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( v1_xreal_0(D) => k5_algstr_0(k15_euclid(A),k3_rlvect_1(k15_euclid(A),k1_rlvect_1(k15_euclid(A),B,k6_xcmplx_0(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) ) ) ) ) )).
fof(l1_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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) ) ) ) )).
fof(l1_card_5,axiom,( 1 = k5_card_1(1) )).
fof(l1_cfdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( r1_funct_2(k4_ordinal1,k1_numbers,k4_ordinal1,k2_numbers,A,B) & v2_comseq_2(A) & k1_seq_2(A) = C ) => k3_comseq_2(B) = C ) ) ) ) )).
fof(l1_circcomb,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => k4_card_3(k7_funcop_1(k2_finseq_1(A),B)) = k4_finseq_2(A,B) ) ) )).
fof(l1_circled1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(l1_circuit2,axiom,( ! [A] : ~ r2_hidden(A,A) )).
fof(l1_classes2,axiom,( ! [A] : v2_classes1(k1_classes1(A)) )).
fof(l1_cohsp_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( r2_hidden(E,k3_funct_2(A,B,C,D)) => r2_hidden(E,k3_tarski(B)) ) ) ) ) ) )).
fof(l1_comseq_3,axiom,( k5_complex1 = k2_xcmplx_0(k5_numbers,k3_xcmplx_0(k5_numbers,k7_complex1)) )).
fof(l1_convex2,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l1_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ~ r2_hidden(B,k4_qc_lang1(A)) ) ) )).
fof(l1_csspace2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_funct_2(k4_ordinal1,k2_numbers,k10_comseq_3(k2_comseq_2(k4_ordinal1,A)),k2_comseq_2(k4_ordinal1,k10_comseq_3(A))) ) )).
fof(l1_csspace4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k1_funct_1(A,C),B) ) => r1_xxreal_0(k2_seq_4(k2_relset_1(k1_numbers,A)),B) ) ) ) )).
fof(l1_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(A,k3_tarski(k2_tarski(C,k1_tarski(B)))) <=> ( r2_hidden(A,C) | A = B ) ) )).
fof(l1_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( k12_euclid(k5_algstr_0(k15_euclid(2),A,B)) = k5_numbers <=> A = B ) ) ) )).
fof(l1_euler_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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 = k5_numbers | r1_xxreal_0(k6_xcmplx_0(B,k3_xcmplx_0(k1_int_1(k7_xcmplx_0(B,A)),A)),A) ) ) ) ) )).
fof(l1_euler_2,axiom,( ! [A] : ( v1_int_1(A) => ( ~ r1_xxreal_0(1,A) <=> r1_xxreal_0(A,k5_numbers) ) ) )).
fof(l1_fdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_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] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_1(k2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,C,D),B),E) = k3_xcmplx_0(2,E) ) ) ) ) ) ) ) ) )).
fof(l1_fdiff_6,axiom,( ! [A] : ( v1_xreal_0(A) => k6_xcmplx_0(1,k19_sin_cos(k3_xcmplx_0(2,A))) = k3_xcmplx_0(2,k1_square_1(k17_sin_cos(A))) ) )).
fof(l1_fib_fusc,axiom,( k5_numbers = k1_int_1(k3_power(2,1)) )).
fof(l1_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k4_xcmplx_0(A),k3_xcmplx_0(A,k2_power(k4_xcmplx_0(1),B))) ) ) )).
fof(l1_finseq_6,axiom,( ! [A] : ! [B] : k10_xtuple_0(k10_finseq_1(A,B)) = k2_tarski(A,B) )).
fof(l1_frechet,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(A,k7_xcmplx_0(1,B)) & ~ r1_xxreal_0(B,k5_numbers) ) ) ) ) )).
fof(l1_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( 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) ) ) )).
fof(l1_friends1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k3_xcmplx_0(B,A) = k2_card_2(B,A) & k2_xcmplx_0(B,A) = k1_card_2(B,A) ) ) ) )).
fof(l1_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( k4_tarski(k4_tarski(A,E),k4_tarski(B,F)) = k4_tarski(k4_tarski(C,G),k4_tarski(D,H)) => ( A = C & B = D & E = G & F = H ) ) )).
fof(l1_fuzzy_4,axiom,( v1_xreal_0(1) )).
fof(l1_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : k9_xtuple_0(k1_funct_4(A,k16_funcop_1(B,C))) = k2_xboole_0(k9_xtuple_0(A),k1_tarski(B)) ) )).
fof(l1_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : k9_xtuple_0(k1_funct_4(A,k16_funcop_1(B,C))) = k2_xboole_0(k9_xtuple_0(A),k1_tarski(B)) ) )).
fof(l1_goboard3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ( ( k3_finseq_1(A) = k1_nat_1(B,1) & v2_topreal1(A) ) => ( B = k5_numbers | v2_topreal1(k17_finseq_1(u1_struct_0(k15_euclid(2)),B,A)) ) ) ) ) )).
fof(l1_gobrd11,axiom,( ~ r1_xxreal_0(k3_square_1(2),k5_numbers) )).
fof(l1_gobrd12,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(l1_gobrd14,axiom,( u1_struct_0(k15_euclid(2)) = k1_euclid(2) )).
fof(l1_gr_cy_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,k7_card_1(B)) => m1_subset_1(A,k4_ordinal1) ) ) )).
fof(l1_group_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(g3_algstr_0(k1_numbers,k9_binop_2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(g3_algstr_0(k1_numbers,k9_binop_2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(g3_algstr_0(k1_numbers,k9_binop_2))) => k6_algstr_0(g3_algstr_0(k1_numbers,k9_binop_2),k6_algstr_0(g3_algstr_0(k1_numbers,k9_binop_2),A,B),C) = k6_algstr_0(g3_algstr_0(k1_numbers,k9_binop_2),A,k6_algstr_0(g3_algstr_0(k1_numbers,k9_binop_2),B,C)) ) ) ) & ? [A] : ( m1_subset_1(A,u1_struct_0(g3_algstr_0(k1_numbers,k9_binop_2))) & ! [B] : ( m1_subset_1(B,u1_struct_0(g3_algstr_0(k1_numbers,k9_binop_2))) => ( k6_algstr_0(g3_algstr_0(k1_numbers,k9_binop_2),B,A) = B & k6_algstr_0(g3_algstr_0(k1_numbers,k9_binop_2),A,B) = B & ? [C] : ( m1_subset_1(C,u1_struct_0(g3_algstr_0(k1_numbers,k9_binop_2))) & k6_algstr_0(g3_algstr_0(k1_numbers,k9_binop_2),B,C) = A & k6_algstr_0(g3_algstr_0(k1_numbers,k9_binop_2),C,B) = A ) ) ) ) )).
fof(l1_group_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( r2_hidden(A,C) => m1_subset_1(A,u1_struct_0(B)) ) ) ) )).
fof(l1_hahnban1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(l1_hermitan,axiom,( k5_numbers = k2_xcmplx_0(k5_numbers,k3_xcmplx_0(k5_numbers,k7_complex1)) )).
fof(l1_heyting3,axiom,( ! [A] : ! [B] : ( v1_relat_1(k2_zfmisc_1(A,k1_tarski(B))) & v1_funct_1(k2_zfmisc_1(A,k1_tarski(B))) ) )).
fof(l1_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v4_aff_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l1_hurwitz,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( v7_ordinal1(D) => ( ( C = k2_partfun1(k4_ordinal1,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)))) ) ) ) ) ) ) )).
fof(l1_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( v1_int_2(B) => ( A = k5_numbers | r1_xxreal_0(B,A) | r1_int_2(A,B) ) ) ) ) )).
fof(l1_int_1,axiom,( ! [A] : ~ ( r2_hidden(A,k6_subset_1(k2_zfmisc_1(k1_tarski(k5_numbers),k4_ordinal1),k1_tarski(k4_tarski(k5_numbers,k5_numbers)))) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => A != k4_xcmplx_0(B) ) ) )).
fof(l1_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_finseq_1(A,k4_numbers) ) )).
fof(l1_int_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( D != A => k1_funct_1(k1_funct_7(k8_funcop_1(k4_ordinal1,C,k5_numbers),A,B),D) = k5_numbers ) )).
fof(l1_integr11,axiom,( k2_subset_1(k1_numbers) = k9_xtuple_0(k1_fcont_1(k7_xcmplx_0(1,2),k5_numbers)) )).
fof(l1_integr13,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(k5_numbers,A) => k8_relset_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k1_seq_4(k5_numbers)) = k1_seq_4(k5_numbers) ) ) )).
fof(l1_integr14,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(k5_numbers,A) => k8_relset_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k1_seq_4(k5_numbers)) = k1_seq_4(k5_numbers) ) ) )).
fof(l1_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(l1_integra3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k1_nat_1(k7_nat_d(A,A),1) = 1 ) )).
fof(l1_integra8,axiom,( ~ r1_xxreal_0(k17_sin_cos(k7_xcmplx_0(k28_sin_cos,4)),k5_numbers) )).
fof(l1_integra9,axiom,( 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(k4_xcmplx_0(1),k5_numbers),k22_sin_cos))) = k2_subset_1(k1_numbers) )).
fof(l1_jgraph_3,axiom,( ! [A] : ( v1_xreal_0(A) => ~ r1_xxreal_0(k2_xcmplx_0(k1_square_1(A),1),k5_numbers) ) )).
fof(l1_jgraph_4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ~ ( A != k4_struct_0(k15_euclid(2)) & r1_xxreal_0(k12_euclid(A),k5_numbers) ) ) )).
fof(l1_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(A,B) ) => r1_xxreal_0(k3_xcmplx_0(A,k3_square_1(k2_xcmplx_0(1,k1_square_1(B)))),k3_xcmplx_0(B,k3_square_1(k2_xcmplx_0(1,k1_square_1(A))))) ) ) ) )).
fof(l1_jgraph_8,axiom,( k17_borsuk_1 = k3_pcomps_1(k2_topmetr(k5_numbers,1)) )).
fof(l1_jordan,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( r1_tarski(A,D) & r1_tarski(B,D) & r1_tarski(C,D) ) => r1_tarski(k2_xboole_0(k2_xboole_0(A,B),C),D) ) )).
fof(l1_jordan1,axiom,( r2_hidden(k5_numbers,k1_rcomp_1(k5_numbers,1)) & r2_hidden(1,k1_rcomp_1(k5_numbers,1)) )).
fof(l1_jordan12,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(l1_jordan18,axiom,( k1_relset_1(u1_struct_0(k15_euclid(2)),k4_pscomp_1) = u1_struct_0(k15_euclid(2)) )).
fof(l1_jordan1a,axiom,( 3 = k1_nat_1(k2_nat_1(2,1),1) )).
fof(l1_jordan1c,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => k6_xcmplx_0(k1_int_1(k2_xcmplx_0(A,B)),B) = k1_int_1(A) ) ) )).
fof(l1_jordan1d,axiom,( 1 = k1_nat_1(k2_nat_1(2,k5_numbers),1) )).
fof(l1_jordan21,axiom,( k1_relset_1(u1_struct_0(k15_euclid(2)),k5_pscomp_1) = u1_struct_0(k15_euclid(2)) )).
fof(l1_jordan22,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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] : ( 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 ) ) ) ) ) )).
fof(l1_jordan2b,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ? [D] : ( v1_xreal_0(D) & ? [E] : ( m2_finseq_1(E,k1_numbers) & E = C & D = k7_partfun1(k1_numbers,E,B) ) ) ) ) ) )).
fof(l1_jordan7,axiom,( k7_nat_d(2,1) = 1 )).
fof(l1_jordan9,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => k1_nat_1(k7_nat_d(A,1),2) = k1_nat_1(A,1) ) ) )).
fof(l1_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : k9_xtuple_0(k1_funct_4(A,k16_funcop_1(B,C))) = k2_xboole_0(k9_xtuple_0(A),k1_tarski(B)) ) )).
fof(l1_limfunc1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(A,B) => ( r1_xxreal_0(C,k5_numbers) | ( ~ r1_xxreal_0(B,k6_xcmplx_0(A,C)) & ~ r1_xxreal_0(k2_xcmplx_0(B,C),A) ) ) ) ) ) ) )).
fof(l1_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(A,C) => ( r1_xxreal_0(B,k5_numbers) | ( ~ r1_xxreal_0(C,k6_xcmplx_0(A,B)) & ~ r1_xxreal_0(k2_xcmplx_0(C,B),A) ) ) ) ) ) ) )).
fof(l1_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(B,C) => ( r1_xxreal_0(A,k5_numbers) | ( ~ r1_xxreal_0(C,k6_xcmplx_0(B,A)) & ~ r1_xxreal_0(k2_xcmplx_0(C,A),B) ) ) ) ) ) ) )).
fof(l1_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,k5_numbers) => ( ~ r1_xxreal_0(A,k6_xcmplx_0(A,B)) & ~ r1_xxreal_0(k2_xcmplx_0(A,B),A) ) ) ) ) )).
fof(l1_lmod_7,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l1_ltlaxio1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( 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) ) ) ) )).
fof(l1_ltlaxio2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k1_funct_1(A,k5_numbers) = k5_numbers ) )).
fof(l1_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(C),A,B) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(C))) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(C),A,B) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(C))) ) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(C),A,B) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(C))) ) => ! [I] : ( m2_finseq_1(I,u1_struct_0(C)) => ! [J] : ( m2_finseq_1(J,u1_struct_0(C)) => ! [K] : ( v7_ordinal1(K) => ! [L] : ( v7_ordinal1(L) => ( ( r2_hidden(K,k2_finseq_1(A)) & r2_hidden(L,k2_finseq_1(k1_matrix_0(F))) & I = k7_matrix_0(u1_struct_0(C),F,E) & J = k7_matrix_0(u1_struct_0(C),F,D) & G = k3_matrix11(D,A,B,u1_struct_0(C),F,I) & H = k3_matrix11(E,A,B,u1_struct_0(C),G,J) ) => ( ( K = E => k3_matrix_0(u1_struct_0(C),H,K,L) = k3_matrix_0(u1_struct_0(C),F,D,L) ) & ( K = D => k3_matrix_0(u1_struct_0(C),H,K,L) = k3_matrix_0(u1_struct_0(C),F,E,L) ) & ~ ( K != E & K != D & k3_matrix_0(u1_struct_0(C),H,K,L) != k3_matrix_0(u1_struct_0(C),F,K,L) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l1_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(B,A) & r1_xxreal_0(1,B) ) => k5_int_1(k6_xcmplx_0(B,1),A) = k6_xcmplx_0(B,1) ) ) ) )).
fof(l1_matrix17,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) ) )).
fof(l1_matrixj1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => k4_finseq_1(k3_fvsum_1(A,B,C)) = k9_subset_1(k4_ordinal1,k4_finseq_1(B),k4_finseq_1(C)) ) ) ) )).
fof(l1_matrixj2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( v2_funct_1(C) & r2_hidden(A,k9_xtuple_0(C)) ) => k10_xtuple_0(k1_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)) ) ) )).
fof(l1_matrixr2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( v7_ordinal1(C) => ( 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)) ) ) ) ) )).
fof(l1_matrtop2,axiom,( ! [A] : ( v7_ordinal1(A) => u1_struct_0(k6_prvect_1(k2_vectsp_1,A)) = u1_struct_0(k15_euclid(A)) ) )).
fof(l1_mazurulm,axiom,( m1_subset_1(k2_urysohn1,k1_zfmisc_1(u1_struct_0(k5_topmetr))) )).
fof(l1_mesfunc5,axiom,( v1_xreal_0(1) )).
fof(l1_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ( ~ v2_struct_0(g1_vectsp_1(A,k1_tarski(k5_numbers),k9_funct_5,k5_funct_5,k10_funct_3(u1_struct_0(A),k1_tarski(k5_numbers)))) & v13_algstr_0(g1_vectsp_1(A,k1_tarski(k5_numbers),k9_funct_5,k5_funct_5,k10_funct_3(u1_struct_0(A),k1_tarski(k5_numbers)))) & v7_vectsp_1(g1_vectsp_1(A,k1_tarski(k5_numbers),k9_funct_5,k5_funct_5,k10_funct_3(u1_struct_0(A),k1_tarski(k5_numbers))),A) & v8_vectsp_1(g1_vectsp_1(A,k1_tarski(k5_numbers),k9_funct_5,k5_funct_5,k10_funct_3(u1_struct_0(A),k1_tarski(k5_numbers))),A) & v9_vectsp_1(g1_vectsp_1(A,k1_tarski(k5_numbers),k9_funct_5,k5_funct_5,k10_funct_3(u1_struct_0(A),k1_tarski(k5_numbers))),A) & v10_vectsp_1(g1_vectsp_1(A,k1_tarski(k5_numbers),k9_funct_5,k5_funct_5,k10_funct_3(u1_struct_0(A),k1_tarski(k5_numbers))),A) & v11_vectsp_1(g1_vectsp_1(A,k1_tarski(k5_numbers),k9_funct_5,k5_funct_5,k10_funct_3(u1_struct_0(A),k1_tarski(k5_numbers))),A) & v2_rlvect_1(g1_vectsp_1(A,k1_tarski(k5_numbers),k9_funct_5,k5_funct_5,k10_funct_3(u1_struct_0(A),k1_tarski(k5_numbers)))) & v3_rlvect_1(g1_vectsp_1(A,k1_tarski(k5_numbers),k9_funct_5,k5_funct_5,k10_funct_3(u1_struct_0(A),k1_tarski(k5_numbers)))) & v4_rlvect_1(g1_vectsp_1(A,k1_tarski(k5_numbers),k9_funct_5,k5_funct_5,k10_funct_3(u1_struct_0(A),k1_tarski(k5_numbers)))) & l1_vectsp_1(g1_vectsp_1(A,k1_tarski(k5_numbers),k9_funct_5,k5_funct_5,k10_funct_3(u1_struct_0(A),k1_tarski(k5_numbers))),A) ) ) )).
fof(l1_mod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( k4_algstr_0(A,B) = k4_struct_0(A) => B = k4_struct_0(A) ) ) ) )).
fof(l1_modal_1,axiom,( ! [A] : ( v7_ordinal1(A) => r2_xboole_0(k1_xboole_0,k14_trees_3(A)) ) )).
fof(l1_modelc_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,k1_nat_1(C,1)) => ( r1_xxreal_0(B,A) | r1_xxreal_0(A,C) ) ) ) ) ) )).
fof(l1_modelc_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r2_hidden(A,k2_xboole_0(k2_xboole_0(B,C),D)) <=> ~ ( ~ r2_hidden(A,B) & ~ r2_hidden(A,C) & ~ r2_hidden(A,D) ) ) )).
fof(l1_moebius1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ~ ( r1_xboole_0(A,B) & r2_hidden(D,k3_xboole_0(A,C)) & r2_hidden(D,k3_xboole_0(B,C)) ) )).
fof(l1_msaterm,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ ( r2_hidden(A,k4_finseq_1(B)) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( A = k1_nat_1(C,1) & ~ r1_xxreal_0(k3_finseq_1(B),C) ) ) ) ) )).
fof(l1_nagata_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => ( r1_xxreal_0(C,k2_xcmplx_0(A,B)) | ( ~ r1_xxreal_0(C,A) & ~ r1_xxreal_0(C,B) ) ) ) ) ) ) )).
fof(l1_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(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)) ) ) ) ) )).
fof(l1_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => v7_ordinal1(k4_int_1(A,B)) ) ) )).
fof(l1_ndiff_4,axiom,( u1_struct_0(k4_real_ns1(1)) = k1_euclid(1) )).
fof(l1_normsp_0,axiom,( r2_hidden(k5_numbers,k1_numbers) )).
fof(l1_normsp_1,axiom,( 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)) )).
fof(l1_numbers,axiom,( r1_tarski(k4_ordinal1,k2_xboole_0(k6_subset_1(a_0_1_numbers,a_0_2_numbers),k4_ordinal1)) )).
fof(l1_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ( D = k8_finseq_1(u1_struct_0(A),B,C) <=> ( k4_finseq_1(D) = k2_finseq_1(k1_nat_1(k3_finseq_1(B),k3_finseq_1(C))) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(B)) => k7_partfun1(u1_struct_0(A),D,E) = k7_partfun1(u1_struct_0(A),B,E) ) ) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(C)) => k7_partfun1(u1_struct_0(A),D,k2_xcmplx_0(k3_finseq_1(B),E)) = k7_partfun1(u1_struct_0(A),C,E) ) ) ) ) ) ) ) ) )).
fof(l1_orders_1,axiom,( ! [A] : ( ~ ( ? [B] : ( B != k1_xboole_0 & r2_hidden(B,A) ) & k3_tarski(A) = k1_xboole_0 ) & ~ ( k3_tarski(A) != k1_xboole_0 & ! [B] : ~ ( B != k1_xboole_0 & r2_hidden(B,A) ) ) ) )).
fof(l1_ordinal4,axiom,( r2_hidden(k1_xboole_0,k4_ordinal1) )).
fof(l1_ortsp_1,axiom,( ~ v1_xboole_0(k1_tarski(k5_numbers)) )).
fof(l1_osalg_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(l1_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k4_algstr_0(A,k5_algstr_0(A,B,C)) = k5_algstr_0(A,C,B) ) ) ) )).
fof(l1_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k5_algstr_0(A,B,C) = k4_struct_0(A) => B = C ) ) ) ) )).
fof(l1_partfun4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => v1_pscomp_1(k8_funcop_1(k1_numbers,u1_struct_0(A),B),A) ) ) )).
fof(l1_pcs_0,axiom,( m2_subset_1(k5_numbers,k4_ordinal1,k7_domain_1(k4_ordinal1,k5_numbers,1)) & m2_subset_1(1,k4_ordinal1,k7_domain_1(k4_ordinal1,k5_numbers,1)) )).
fof(l1_pdiff_7,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_nfcont_1(C,A,B) => ! [D] : ( m1_nfcont_1(D,A,B) => m1_nfcont_1(k9_subset_1(u1_struct_0(A),C,D),A,B) ) ) ) ) )).
fof(l1_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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 = k5_numbers ) ) ) ) ) ) )).
fof(l1_polyeq_2,axiom,( 4 = k3_xcmplx_0(2,2) )).
fof(l1_polynom2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( 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) ) ) ) )).
fof(l1_polynom8,axiom,( ! [A] : ( v1_int_1(A) => ~ ( ~ r1_xxreal_0(k5_numbers,A) & A != k4_xcmplx_0(1) & r1_xxreal_0(k4_xcmplx_0(1),A) ) ) )).
fof(l1_polyred,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( 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) ) ) ) )).
fof(l1_poset_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r1_lattice3(A,u1_struct_0(A),B) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_orders_2(A,B,C) ) ) ) ) )).
fof(l1_prob_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(A,B) => ( r1_xxreal_0(C,k5_numbers) | ( ~ r1_xxreal_0(k2_xcmplx_0(B,C),A) & ~ r1_xxreal_0(B,k6_xcmplx_0(A,C)) ) ) ) ) ) ) )).
fof(l1_prob_4,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(l1_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v3_xxreal_2(A) => v4_xxreal_2(k3_measure6(A)) ) ) )).
fof(l1_pua2mss1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(l1_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ? [B] : ( m1_subset_1(B,k1_numbers) & ? [C] : ( m1_subset_1(C,k1_numbers) & ? [D] : ( m1_subset_1(D,k1_numbers) & ? [E] : ( m1_subset_1(E,k1_numbers) & A = k6_quaterni(B,C,D,E) ) ) ) ) ) )).
fof(l1_radix_3,axiom,( ! [A] : ( 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))) ) ) )).
fof(l1_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( r1_xxreal_0(1,A) & r1_xxreal_0(k2_xcmplx_0(A,2),1) ) ) )).
fof(l1_rat_1,axiom,( r1_tarski(k4_ordinal1,k2_xboole_0(k6_subset_1(a_0_0_rat_1,a_0_1_rat_1),k4_ordinal1)) )).
fof(l1_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(B,A) ) => A = B ) ) ) )).
fof(l1_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,1) => v7_ordinal1(k6_xcmplx_0(A,1)) ) ) )).
fof(l1_rearran1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ~ r2_hidden(B,k10_xtuple_0(A)) => k8_relat_1(A,k1_tarski(B)) = k1_xboole_0 ) ) )).
fof(l1_recdef_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(l1_rfunct_1,axiom,( k5_xcmplx_0(k4_xcmplx_0(1)) = k4_xcmplx_0(1) )).
fof(l1_rinfsup1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(A,B) => ( r1_xxreal_0(C,k5_numbers) | ( ~ r1_xxreal_0(k2_xcmplx_0(B,C),A) & ~ r1_xxreal_0(B,k6_xcmplx_0(A,C)) ) ) ) ) ) ) )).
fof(l1_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(B,k3_convex1(A,B)) ) ) )).
fof(l1_rlaffin2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( k3_rlvect_1(B,k1_rlvect_1(B,D,A),k1_rlvect_1(B,E,k6_xcmplx_0(1,A))) = C => ( A = 1 | E = k3_rlvect_1(B,k1_rlvect_1(B,C,k7_xcmplx_0(1,k6_xcmplx_0(1,A))),k1_rlvect_1(B,D,k6_xcmplx_0(1,k7_xcmplx_0(1,k6_xcmplx_0(1,A))))) ) ) ) ) ) ) ) )).
fof(l1_rlaffin3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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))) ) ) )).
fof(l1_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(l1_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ? [D] : ( 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 ) ) ) ) )).
fof(l1_rlvect_x,axiom,( v1_xreal_0(k5_numbers) )).
fof(l1_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(B)) => ( ( k3_finseq_1(D) = k1_nat_1(k3_finseq_1(E),1) & E = k2_partfun1(k4_ordinal1,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) ) ) ) ) ) ) )).
fof(l1_rsspace4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k1_funct_1(A,C),B) ) => r1_xxreal_0(k2_seq_4(k2_relset_1(k1_numbers,A)),B) ) ) ) )).
fof(l1_scm_comp,axiom,( 1 = a_0_0_scm_comp )).
fof(l1_scm_halt,axiom,( 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(k7_card_1(3),k1_scmfsa_2)) )).
fof(l1_scmfsa8b,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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)) ) ) )).
fof(l1_scmfsa_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v5_ordinal1(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) ) ) ) ) ) )).
fof(l1_scmfsa_9,axiom,( k5_card_1(k4_compos_1(k1_scmfsa_2)) = 1 )).
fof(l1_scmpds_5,axiom,( k5_card_1(k4_compos_1(k1_scmpds_2)) = 1 )).
fof(l1_scmpds_6,axiom,( k1_funct_1(k4_compos_1(k1_scmpds_2),k5_numbers) = k2_compos_1(k1_scmpds_2) )).
fof(l1_seqfunc,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,B)))) ) <=> ( k9_xtuple_0(C) = k4_ordinal1 & ! [D] : ( r2_hidden(D,k4_ordinal1) => ( v1_funct_1(k1_funct_1(C,D)) & m1_subset_1(k1_funct_1(C,D),k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ) ) ) ) )).
fof(l1_seqm_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(B,A) & ! [C] : ( v7_ordinal1(C) => B != k2_xcmplx_0(k1_nat_1(A,1),C) ) ) ) ) )).
fof(l1_series_3,axiom,( ! [A] : ( v1_xreal_0(A) => k1_square_1(A) = k1_newton(A,2) ) )).
fof(l1_series_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( 4 = k11_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)) ) ) ) )).
fof(l1_series_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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(k1_square_1(A),k3_xcmplx_0(A,B)),k1_square_1(B))) ) ) )).
fof(l1_setlim_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(A,B) & A != B & ~ r1_xxreal_0(k1_nat_1(A,1),B) ) ) ) )).
fof(l1_setwop_2,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k2_finseq_1(A),k5_finsub_1(k4_ordinal1)) ) )).
fof(l1_simplex2,axiom,( v1_xreal_0(1) & v2_xxreal_0(1) )).
fof(l1_sin_cos7,axiom,( k4_power != 1 )).
fof(l1_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,k4_sin_cos2(A)) & k4_sin_cos2(k5_numbers) = 1 & k2_sin_cos2(k5_numbers) = k5_numbers ) ) )).
fof(l1_sincos10,axiom,( r1_tarski(k3_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)),k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))) )).
fof(l1_symsp_1,axiom,( m1_subset_1(k5_numbers,k1_tarski(k5_numbers)) )).
fof(l1_sysrel,axiom,( ! [A] : ! [B] : ~ ( 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 ) ) )).
fof(l1_topalg_3,axiom,( 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)) )).
fof(l1_topalg_4,axiom,( r2_hidden(1,k2_tarski(1,2)) )).
fof(l1_topalg_5,axiom,( r2_hidden(k5_numbers,k4_numbers) )).
fof(l1_topreal2,axiom,( ! [A] : ! [B] : ( ~ r2_hidden(A,B) => k3_xboole_0(k1_tarski(A),B) = k1_xboole_0 ) )).
fof(l1_topreal5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) )).
fof(l1_topreala,axiom,( u1_struct_0(k2_borsuk_1(k3_topmetr,k3_topmetr)) = k2_zfmisc_1(u1_struct_0(k3_topmetr),u1_struct_0(k3_topmetr)) )).
fof(l1_toprealb,axiom,( r2_hidden(k5_numbers,k4_numbers) )).
fof(l1_treal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( r2_hidden(C,k1_rcomp_1(A,B)) => m1_subset_1(C,k1_numbers) ) ) ) )).
fof(l1_trees_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(l1_trees_4,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) ) )).
fof(l1_trees_9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ ( r2_hidden(A,k4_finseq_1(B)) & ! [C] : ( v7_ordinal1(C) => ~ ( A = k1_nat_1(C,1) & ~ r1_xxreal_0(k3_finseq_1(B),C) ) ) ) ) )).
fof(l1_tsep_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(l1_uniroots,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( ~ v8_ordinal1(A) <=> r1_xxreal_0(1,A) ) ) )).
fof(l1_uproots,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l1_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(l1_valued_2,axiom,( ! [A] : ! [B] : ! [C] : k3_xboole_0(A,k3_xboole_0(B,C)) = k3_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)) )).
fof(l1_vectsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ( v4_vectsp_1(A) => k5_struct_0(A) = k1_group_1(A) ) ) )).
fof(l1_vectsp_4,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(l1_vectsp_9,axiom,( ! [A] : ! [B] : ( r2_hidden(B,A) => k2_xboole_0(k6_subset_1(A,k1_tarski(B)),k1_tarski(B)) = A ) )).
fof(l1_waybel11,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(l1_waybel12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ 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))) ) ) ) ) )).
fof(l1_waybel35,axiom,( ! [A] : ! [B] : ! [C] : ~ ( r2_hidden(B,k2_xboole_0(k1_tarski(A),C)) & B != A & ~ r2_hidden(B,C) ) )).
fof(l1_waybel_5,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & v3_waybel_3(A) & l1_orders_2(A) ) => ! [B] : ( 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] : ( ( ~ 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) ) ) ) ) ) )).
fof(l1_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_relat_2(A) <=> ! [B] : ( r2_hidden(B,k1_relat_1(A)) => r2_hidden(k4_tarski(B,B),A) ) ) ) )).
fof(l1_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ ( ~ ( r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_arytm_2) & ? [C] : ( m1_subset_1(C,k2_arytm_2) & ? [D] : ( m1_subset_1(D,k2_arytm_2) & A = C & B = D & r1_arytm_2(C,D) ) ) ) & ~ ( r2_hidden(A,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) & r2_hidden(B,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) & ? [C] : ( m1_subset_1(C,k2_arytm_2) & ? [D] : ( m1_subset_1(D,k2_arytm_2) & A = k4_tarski(k5_numbers,C) & B = k4_tarski(k5_numbers,D) & r1_arytm_2(D,C) ) ) ) & ~ ( r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) ) ) => r1_xxreal_0(A,B) ) ) ) )).
fof(l1_yellow12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(l1_zfmisc_1,axiom,( ! [A] : ! [B] : ( r1_tarski(k1_tarski(A),B) <=> r2_hidden(A,B) ) )).
fof(l1_zfrefle1,axiom,( r2_hidden(k1_xboole_0,k4_ordinal1) )).
fof(l202_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ ( r1_jordan24(2,A,k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) & ! [B] : ( ( v2_compts_1(B,k15_euclid(2)) & v1_jordan21(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( 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(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers),B) & r1_topreal1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_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(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_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) ) ) ) ) ) )).
fof(l204_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,1) & r1_xxreal_0(1,k5_xcmplx_0(A)) ) ) )).
fof(l205_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_jordan24(2,A,k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) => v1_jordan1(A) ) ) )).
fof(l205_zmodul01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_numbers) => ! [D] : ( m1_subset_1(D,k4_numbers) => ~ ( C != k5_numbers & D != k5_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)) ) ) ) ) ) )).
fof(l206_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => v1_jordan1(A) ) )).
fof(l206_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(k5_numbers,A) ) => r1_xxreal_0(k7_xcmplx_0(A,B),1) ) ) ) )).
fof(l206_zmodul01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_numbers) => ! [D] : ( m1_subset_1(D,k4_numbers) => ( ( C = k5_numbers | D = k5_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)) ) ) ) ) ) )).
fof(l207_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(B,A) & r1_xxreal_0(k5_numbers,A) ) => r1_xxreal_0(k7_xcmplx_0(B,A),1) ) ) ) )).
fof(l20_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_tarski(k1_aff_1(A,B,C),k1_aff_1(A,C,B)) ) ) ) )).
fof(l20_algstr_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ( ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_algstr_0(A,B,k5_struct_0(A)) = B ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ( B != k4_struct_0(A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_algstr_0(A,B,C) != k5_struct_0(A) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ( B != k4_struct_0(A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_algstr_0(A,C,B) != k5_struct_0(A) ) ) ) ) ) ) )).
fof(l20_ami_3,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => ~ ( ? [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(B,u1_struct_0(k1_ami_3)) & k1_funct_1(k2_extpro_1(k7_card_1(2),k1_ami_3,A,B),k4_struct_0(k1_ami_3)) = k4_card_1(k5_memstr_0(k7_card_1(2),k1_ami_3,B)) ) & v2_extpro_1(A,k7_card_1(2),k1_ami_3) ) ) )).
fof(l20_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ( ( D = k3_rlvect_1(A,B,k1_rlvect_1(A,C,G)) & E = k3_rlvect_1(A,B,k1_rlvect_1(A,F,H)) & r1_anproj_1(A,D,E) ) => ( G = k5_numbers | r2_anproj_1(A,B,C,F) ) ) ) ) ) ) ) ) ) ) )).
fof(l20_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( r1_arytm_2(k1_arytm_1(C,B),A) <=> r1_arytm_2(C,k7_arytm_2(A,B)) ) ) ) ) )).
fof(l20_arytm_2,axiom,( ! [A] : ( m2_subset_1(A,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) => ( k4_arytm_2(A) = k11_arytm_3 <=> A = k11_arytm_3 ) ) )).
fof(l20_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_c0sp2(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l20_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( r2_hidden(B,k2_cc0sp2(A)) => r2_hidden(B,k2_cc0sp1(u1_struct_0(A))) ) ) )).
fof(l20_clvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ( k3_finseq_1(B) = k5_numbers => k4_rlvect_1(A,B) = k4_struct_0(A) ) ) ) )).
fof(l20_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) ) => ! [B] : ( m1_subset_1(B,A) => r1_tarski(k5_finsub_1(B),A) ) ) )).
fof(l20_complex1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( A = C & B = D ) => k1_arytm_0(A,B) = k2_xcmplx_0(C,D) ) ) ) ) ) )).
fof(l20_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) )).
fof(l20_connsp_3,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & ! [C] : ( 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) ) ) )).
fof(l20_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( v1_xreal_0(D) => ( r1_tarski(B,C) => r1_tarski(k1_convex1(A,B,D),k1_convex1(A,C,D)) ) ) ) ) ) )).
fof(l20_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l20_dtconstr,axiom,( r2_hidden(c2__dtconstr,k1_lang1(k5_dtconstr)) )).
fof(l20_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,k2_numbers) => ! [E] : ( 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)) = k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(k17_euclid(A),k17_euclid(B)),k6_xcmplx_0(k17_euclid(C),k17_euclid(B))),k3_xcmplx_0(k6_xcmplx_0(k18_euclid(A),k18_euclid(B)),k6_xcmplx_0(k18_euclid(C),k18_euclid(B)))) & k4_complex1(k1_complex2(D,E)) = k2_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(k17_euclid(A),k17_euclid(B)),k6_xcmplx_0(k18_euclid(C),k18_euclid(B)))),k3_xcmplx_0(k6_xcmplx_0(k18_euclid(A),k18_euclid(B)),k6_xcmplx_0(k17_euclid(C),k17_euclid(B)))) & k9_complex1(D) = k3_square_1(k2_xcmplx_0(k1_square_1(k6_xcmplx_0(k17_euclid(A),k17_euclid(B))),k1_square_1(k6_xcmplx_0(k18_euclid(A),k18_euclid(B))))) & k12_euclid(k5_algstr_0(k15_euclid(2),A,B)) = k9_complex1(D) ) ) ) ) ) ) ) )).
fof(l20_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( 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)) ) ) ) ) )).
fof(l20_euler_1,axiom,( ! [A] : ( r2_hidden(A,a_0_0_euler_1) <=> A = 1 ) )).
fof(l20_fib_num,axiom,( ~ r1_xxreal_0(3,k3_square_1(5)) )).
fof(l20_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( 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) ) ) ) ) )).
fof(l20_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l20_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( r3_analmetr(A,B,D,C,E,F,G) => r3_analmetr(A,B,D,E,C,F,G) ) ) ) ) ) ) ) ) )).
fof(l20_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l20_gr_cy_3,axiom,( k11_newton(2,2) = 4 )).
fof(l20_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k12_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,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) ) ) ) ) ) ) )).
fof(l20_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k12_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,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) ) ) ) ) ) ) )).
fof(l20_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(l20_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l20_integr11,axiom,( r2_hidden(k5_numbers,k1_numbers) )).
fof(l20_integra3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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) != k5_numbers & r2_hidden(A,k1_rvsum_1(k9_integra1(B,C))) & ! [D] : ( m1_integra1(D,B) => ~ ( r2_hidden(D,k9_xtuple_0(k9_integra1(B,C))) & A = k1_funct_1(k9_integra1(B,C),D) & ~ r1_xxreal_0(k1_funct_1(D,1),k3_seq_4(B)) ) ) ) ) ) ) )).
fof(l20_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(l20_jgraph_6,axiom,( k18_euclid(k19_euclid(1,k5_numbers)) = k5_numbers )).
fof(l20_jordan,axiom,( 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))) )).
fof(l20_lattices,axiom,( ! [A] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(l20_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_normsp_1(B) ) => ( B = g1_normsp_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)),k3_lp_space(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( v1_xreal_0(D) => r2_funct_2(k4_ordinal1,k1_numbers,k1_lp_space(k2_rsspace(k1_rlvect_1(B,C,D)),A),k26_valued_1(k4_ordinal1,k1_numbers,k1_lp_space(k2_rsspace(C),A),k2_power(k9_complex1(D),A))) ) ) ) ) ) ) )).
fof(l20_matrprob,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k4_tarski(C,D),k2_matrix_0(B)) => r1_xxreal_0(A,k3_matrix_0(k1_numbers,B,C,D)) ) ) ) <=> ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(D,k4_finseq_1(k1_matrprob(k1_numbers,B,C))) ) => r1_xxreal_0(A,k1_funct_1(k1_matrprob(k1_numbers,B,C),D)) ) ) ) ) ) ) )).
fof(l20_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(l20_menelaus,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( A != 1 & B != 1 & C != 1 & ~ ( k5_numbers = k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(A,B),C),k3_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(1,A),k6_xcmplx_0(1,B)),k6_xcmplx_0(1,C))) <=> k3_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(A,k6_xcmplx_0(1,A)),k7_xcmplx_0(B,k6_xcmplx_0(1,B))),k7_xcmplx_0(C,k6_xcmplx_0(1,C))) = 1 ) ) ) ) ) )).
fof(l20_metric_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => ( k3_square_1(k2_xcmplx_0(A,B)) = k5_numbers <=> ( A = k5_numbers & B = k5_numbers ) ) ) ) ) )).
fof(l20_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(k15_midsp_1(A))) => ? [C] : ( m1_subset_1(C,u1_struct_0(k15_midsp_1(A))) & k1_midsp_2(k15_midsp_1(A),C) = B ) ) & ! [B] : ( 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)) ) ) ) ) )).
fof(l20_ndiff_5,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => 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,k6_xcmplx_0(1,D)),k1_rlvect_1(A,C,D)) ) ) ) ) )).
fof(l20_nfcont_1,axiom,( v1_xreal_0(1) )).
fof(l20_numbers,axiom,( r2_hidden(2,k4_ordinal1) )).
fof(l20_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(l20_polynom8,axiom,( ! [A] : ( ( ~ 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] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_xxreal_0(B,k5_numbers) => k3_polynom8(A,C,B) = k11_algstr_0(A,k3_polynom8(A,C,k1_int_2(B))) ) ) ) ) )).
fof(l20_prepower,axiom,( r2_hidden(1,k4_ordinal1) )).
fof(l20_prvect_2,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(l20_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_finseq_1(C,k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))) => m2_finseq_1(k7_finseq_1(k7_finseq_1(k9_finseq_1(k4_tarski(3,k5_numbers)),k12_finseq_1(k3_qc_lang1(A),B)),C),k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))) ) ) ) )).
fof(l20_quaterni,axiom,( ! [A] : ! [B] : ! [C] : ( k4_tarski(A,B) = k1_tarski(C) => ( C = k1_tarski(A) & A = B ) ) )).
fof(l20_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(l20_realset2,axiom,( k5_binop_1(2,k2_realset2,k10_subset_1(k5_numbers,2),k10_subset_1(1,2)) = k10_subset_1(k5_numbers,2) )).
fof(l20_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( r2_classes1(A,B) => r1_xxreal_0(k4_rfinseq2(B),k4_rfinseq2(A)) ) ) ) )).
fof(l20_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_rlsub_1(C,A) => ( u1_struct_0(C) = B => v1_rlsub_1(B,A) ) ) ) ) )).
fof(l20_rlvect_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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) ) ) )).
fof(l20_rusub_1,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l20_scm_inst,axiom,( ! [A] : ( 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) ) ) )).
fof(l20_scmfsa_i,axiom,( ! [A] : ( m1_subset_1(A,k2_scmfsa_i) => ! [B] : ( 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)) ) ) ) )).
fof(l20_scmp_gcd,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ( ( r1_tarski(k4_scmp_gcd,D) & k5_memstr_0(2,k1_scmpds_2,C) = 5 & B = k1_funct_1(C,k3_scmp_gcd) & k1_funct_1(C,k2_scmp_gcd) = k5_numbers & r1_xxreal_0(A,k1_nat_1(B,1)) ) => ( r1_xxreal_0(k1_funct_1(C,k2_scmpds_2(k1_funct_1(C,k3_scmp_gcd),3)),k5_numbers) | r1_xxreal_0(A,1) | k1_funct_1(k5_extpro_1(2,k1_scmpds_2,D,C,7),k1_scmp_gcd(A)) = k1_funct_1(C,k1_scmp_gcd(A)) ) ) ) ) ) ) )).
fof(l20_scmpds_8,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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))) = k1_nat_1(k5_card_1(C),3) ) ) ) )).
fof(l20_scmpds_9,axiom,( ~ v1_int_1(k7_xcmplx_0(5,3)) )).
fof(l20_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_compos_0(u1_compos_1(k1_scmring2(A)))) => ~ ( B != k5_numbers & B != 1 & B != 2 & B != 3 & B != 4 & B != 5 & B != 6 & B != 7 ) ) ) )).
fof(l20_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(l20_scpisort,axiom,( 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,k5_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),k5_numbers)),k16_scmpds_2(k1_scmp_gcd(4),k2_scmp_gcd,k5_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,k5_numbers))))))) = 16 )).
fof(l20_scpqsort,axiom,( 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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_numbers)))))) = 11 )).
fof(l20_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => k3_xcmplx_0(k2_xcmplx_0(1,k7_xcmplx_0(k3_square_1(k3_xcmplx_0(A,C)),B)),k7_xcmplx_0(k3_square_1(k3_xcmplx_0(A,B)),C)) = k2_xcmplx_0(k7_xcmplx_0(k3_square_1(k3_xcmplx_0(A,B)),C),k7_xcmplx_0(A,k3_square_1(k3_xcmplx_0(B,C)))) ) ) ) )).
fof(l20_sin_cos9,axiom,( k2_funct_1(k2_sin_cos9) = k2_partfun1(k1_numbers,k1_numbers,k27_sin_cos,k2_rcomp_1(k5_numbers,k28_sin_cos)) )).
fof(l20_sincos10,axiom,( r2_hidden(k7_xcmplx_0(k28_sin_cos,4),k4_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) & r2_hidden(k7_xcmplx_0(k28_sin_cos,2),k4_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) )).
fof(l20_topgen_3,axiom,( 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)))) )).
fof(l20_topreal2,axiom,( r2_hidden(k19_euclid(k5_numbers,k5_numbers),k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,k5_numbers),k19_euclid(k5_numbers,1))) )).
fof(l20_tsep_1,axiom,( ! [A] : ( l1_pre_topc(A) => m1_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)),A) ) )).
fof(l20_urysohn2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ( v3_xxreal_2(k1_integra2(A,B)) => ( r1_xxreal_0(B,k5_numbers) | v3_xxreal_2(A) ) ) ) ) )).
fof(l20_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( u1_struct_0(C) = D => v1_vectsp_4(D,A,B) ) ) ) ) ) )).
fof(l20_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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) ) ) )).
fof(l20_waybel33,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_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)))) ) ) )).
fof(l20_xcmplx_0,axiom,( r1_tarski(k1_numbers,k2_numbers) )).
fof(l20_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(k2_xcmplx_0(A,B),k5_numbers) ) ) ) )).
fof(l20_zf_fund1,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_zf_lang)) ) => r2_tarski(A,k4_zf_fund1(A)) ) )).
fof(l20_zfmisc_1,axiom,( ! [A] : ! [B] : ( ~ r2_hidden(A,B) => r1_xboole_0(k1_tarski(A),B) ) )).
fof(l20_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(A)) => ( k3_finseq_1(B) = k5_numbers => k4_rlvect_1(A,B) = k4_struct_0(A) ) ) ) )).
fof(l216_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ~ ( A != k5_numbers & A = k5_xcmplx_0(A) & A != 1 & A != k4_xcmplx_0(1) ) ) )).
fof(l21_ami_3,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => ( A = k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0) => v2_extpro_1(A,k7_card_1(2),k1_ami_3) ) ) )).
fof(l21_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ~ ( k1_rlvect_1(A,B,D) = C & D != k5_numbers & ~ v9_struct_0(B,A) & v9_struct_0(C,A) ) ) ) ) ) )).
fof(l21_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( r1_arytm_2(B,A) => ( r1_arytm_2(k7_arytm_2(C,B),A) <=> r1_arytm_2(C,k1_arytm_1(A,B)) ) ) ) ) ) )).
fof(l21_arytm_2,axiom,( ! [A] : ( m2_subset_1(A,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) => k3_arytm_2(k4_arytm_2(A)) = A ) )).
fof(l21_c0sp1,axiom,( ! [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) & v2_funcsdom(A) & l1_funcsdom(A) ) => ( ! [B] : ( 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) ) ) ) )).
fof(l21_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_c0sp2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_c0sp2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k11_c0sp1(u1_struct_0(A)))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l21_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ! [C] : ( m2_funct_2(C,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ! [D] : ( 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))) ) ) ) ) )).
fof(l21_complex1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k3_arytm_0(A) = k1_real_1(A) ) )).
fof(l21_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( 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) & v4_conlat_1(B,A) ) ) ) )).
fof(l21_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( v1_xreal_0(C) => k1_convex1(A,B,C) = k1_xboole_0 ) ) ) )).
fof(l21_convfun1,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ! [B] : ( m1_subset_1(B,k6_numbers) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( ( A = C & B = D ) => k2_xcmplx_0(k3_xcmplx_0(E,C),k3_xcmplx_0(F,D)) = k1_xxreal_3(k4_xxreal_3(E,A),k4_xxreal_3(F,B)) ) ) ) ) ) ) ) )).
fof(l21_dtconstr,axiom,( r1_tarski(k1_lang1(k5_dtconstr),k6_domain_1(u1_struct_0(k5_dtconstr),c2__dtconstr)) )).
fof(l21_endalg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( k9_xtuple_0(B) = k1_endalg(A) & ! [C] : ( r2_hidden(C,k1_endalg(A)) => k1_funct_1(B,C) = k16_funcop_1(k5_numbers,C) ) ) => k10_xtuple_0(B) = k4_endalg(k6_msualg_1(A),k9_msualg_1(A)) ) ) ) )).
fof(l21_euler_1,axiom,( k5_card_1(k1_tarski(1)) = k1_euler_1(1) )).
fof(l21_fdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r4_fdiff_3(A,B) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,k1_relset_1(k1_numbers,A)) & r2_hidden(D,k1_rcomp_1(k6_xcmplx_0(B,C),B)) & k1_funct_1(A,D) = k5_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)) = k4_xcmplx_0(k7_xcmplx_0(k1_fdiff_3(B,A),k1_square_1(k1_funct_1(A,B)))) ) ) ) ) ) )).
fof(l21_fib_num,axiom,( ~ r1_xxreal_0(k1_fib_num,1) )).
fof(l21_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( ( 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] : ( m1_subset_1(F,k4_ordinal1) => ( r2_hidden(F,k1_relset_1(k4_ordinal1,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)) ) ) ) ) ) ) )).
fof(l21_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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))) ) => ( ( v2_fomodel0(B,C,D) & r1_tarski(A,B) ) => v2_fomodel0(A,C,D) ) ) ) )).
fof(l21_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ! [D] : ! [E] : ( 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) ) ) ) ) )).
fof(l21_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ! [F] : ( 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] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( m1_subset_1(H,k6_margrel1) => ! [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) ) ) ) ) ) ) ) ) ) )).
fof(l21_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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] : ( ( v5_relat_1(F,k1_rcomp_1(k5_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] : ! [H] : ( ( r2_hidden(G,A) & r2_hidden(H,C) ) => r1_xxreal_0(k2_seq_4(k2_relset_1(k1_numbers,k2_fuzzy_4(A,B,C,D,k1_fuzzy_1(k2_zfmisc_1(B,C),E,F),G,H))),k3_xxreal_0(k2_seq_4(k2_relset_1(k1_numbers,k2_fuzzy_4(A,B,C,D,E,G,H))),k2_seq_4(k2_relset_1(k1_numbers,k2_fuzzy_4(A,B,C,D,F,G,H))))) ) ) ) ) ) ) ) )).
fof(l21_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( r3_analmetr(A,B,D,C,E,F,G) => r3_analmetr(A,C,E,B,D,F,G) ) ) ) ) ) ) ) ) )).
fof(l21_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_glib_002(B) & m1_glib_000(B,A) ) => ( v9_glib_000(B,A) => v1_glib_002(A) ) ) ) )).
fof(l21_gr_cy_3,axiom,( k11_newton(2,3) = 8 )).
fof(l21_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ~ ( r1_rewrite1(k3_polyred(A,B,C,F),D,E) & E != D & ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(G,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) ) ) ) ) ) ) ) ) ) )).
fof(l21_group_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( ( v15_algstr_0(E) & m1_group_2(E,A) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(l21_heyting2,axiom,( ! [A] : ! [B] : ! [C] : ( v1_finset_1(C) => ! [D] : ( m1_subset_1(D,k5_finsub_1(k4_partfun1(B,C))) => ! [E] : ( 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] : ~ ( r2_hidden(F,E) & r1_tarski(F,A) ) ) ) ) ) )).
fof(l21_int_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( B != k5_numbers & ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k8_newton) & v1_funct_1(C) & v1_partfun1(C,k8_newton) & v4_valued_0(C) & v2_pre_poly(C) ) => ~ ( r8_pboole(k8_newton,C,k14_funct_7(k8_newton,k4_ordinal1,k8_funcop_1(k4_ordinal1,k8_newton,k5_numbers),A,B)) & k22_pre_poly(k8_newton,C) = k1_tarski(A) & k8_nat_3(k8_newton,C) = B ) ) ) ) ) )).
fof(l21_jgraph_6,axiom,( k17_euclid(k19_euclid(k5_numbers,k4_xcmplx_0(1))) = k5_numbers )).
fof(l21_jordan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => v1_pscomp_1(k8_funcop_1(k1_numbers,u1_struct_0(A),B),A) ) ) )).
fof(l21_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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,A)),k1_nat_1(B,1)) & r1_xxreal_0(k3_finseq_1(k1_jordan8(C,k1_nat_1(A,1))),k7_nat_d(k3_xcmplx_0(2,B),1)) ) ) ) ) )).
fof(l21_jordan20,axiom,( k2_struct_0(k5_topmetr) != k1_xboole_0 )).
fof(l21_jordan7,axiom,( ! [A] : ( v7_ordinal1(A) => ~ r1_xxreal_0(A,k6_xcmplx_0(k6_xcmplx_0(A,1),1)) ) )).
fof(l21_lfuzzy_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_lfuzzy_0(A))) => ( v5_relat_1(B,k1_rcomp_1(k5_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))) ) ) ) )).
fof(l21_limfunc1,axiom,( r2_hidden(k5_numbers,k1_numbers) )).
fof(l21_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_normsp_1(B) ) => ( B = g1_normsp_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)),k3_lp_space(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( v1_xreal_0(D) => k4_series_1(k1_lp_space(k2_rsspace(k1_rlvect_1(B,C,D)),A)) = k3_xcmplx_0(k2_power(k9_complex1(D),A),k4_series_1(k1_lp_space(k2_rsspace(C),A))) ) ) ) ) ) ) )).
fof(l21_matrixc1,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => k10_seq_4(B,A) = k4_finseqop(k2_numbers,k2_numbers,B,k10_funcop_1(k2_numbers,k2_numbers,k5_binop_2,A,k6_partfun1(k2_numbers))) ) ) )).
fof(l21_matrprob,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k4_tarski(C,D),k2_matrix_0(B)) => r1_xxreal_0(A,k3_matrix_0(k1_numbers,B,C,D)) ) ) ) <=> ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(D,k4_finseq_1(k7_matrix_0(k1_numbers,B,C))) ) => r1_xxreal_0(A,k1_funct_1(k7_matrix_0(k1_numbers,B,C),D)) ) ) ) ) ) ) )).
fof(l21_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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))) ) ) )).
fof(l21_menelaus,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( k5_numbers = k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(A,B),C),k3_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(1,A),k6_xcmplx_0(1,B)),k6_xcmplx_0(1,C))) & k2_xcmplx_0(k6_xcmplx_0(1,B),k3_xcmplx_0(B,A)) = k5_numbers ) => ( B = 1 | k2_xcmplx_0(k6_xcmplx_0(1,A),k3_xcmplx_0(A,C)) = k5_numbers ) ) ) ) ) )).
fof(l21_modal_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_finset_1(k9_xtuple_0(A)) => v1_finset_1(A) ) ) )).
fof(l21_numbers,axiom,( v3_ordinal1(2) & m1_subset_1(2,k5_arytm_3) )).
fof(l21_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v5_o_ring_1(B,A) => v7_o_ring_1(B,A) ) ) ) )).
fof(l21_papdesaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r1_geomtrap(A,B,C,B,D) & B != C & B != D & ! [E] : ( v1_xreal_0(E) => ~ ( k5_algstr_0(A,C,B) = k1_rlvect_1(A,k5_algstr_0(A,D,B),E) & E != k5_numbers ) ) ) ) ) ) ) )).
fof(l21_pdiff_9,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l21_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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) ) ) ) ) )).
fof(l21_pre_ff,axiom,( ! [A] : ( v7_ordinal1(A) => ( ! [B] : ( v7_ordinal1(B) => ( k1_nat_1(A,2) = k3_xcmplx_0(2,B) => k2_pre_ff(c2__pre_ff,k1_nat_1(A,1)) = k8_finseq_1(k4_ordinal1,k2_pre_ff(c2__pre_ff,A),k12_finseq_1(k4_ordinal1,k7_partfun1(k4_ordinal1,k2_pre_ff(c2__pre_ff,A),B))) ) ) & ! [B] : ( v7_ordinal1(B) => ( k1_nat_1(A,2) = k1_nat_1(k3_xcmplx_0(2,B),1) => k2_pre_ff(c2__pre_ff,k1_nat_1(A,1)) = k8_finseq_1(k4_ordinal1,k2_pre_ff(c2__pre_ff,A),k12_finseq_1(k4_ordinal1,k1_nat_1(k7_partfun1(k4_ordinal1,k2_pre_ff(c2__pre_ff,A),B),k7_partfun1(k4_ordinal1,k2_pre_ff(c2__pre_ff,A),k1_nat_1(B,1))))) ) ) ) ) )).
fof(l21_prepower,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l21_realset2,axiom,( k5_binop_1(2,k2_realset2,k10_subset_1(1,2),k10_subset_1(k5_numbers,2)) = k10_subset_1(k5_numbers,2) )).
fof(l21_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => r1_tarski(u1_struct_0(k2_rlsub_2(A,B,C)),u1_struct_0(B)) ) ) ) )).
fof(l21_rlvect_2,axiom,( m1_subset_1(k5_numbers,k1_numbers) )).
fof(l21_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => r1_tarski(u1_struct_0(k2_rusub_2(A,B,C)),u1_struct_0(B)) ) ) ) )).
fof(l21_rusub_4,axiom,( ! [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_bhsp_1(A) & v1_rusub_4(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( r1_xxreal_0(B,k1_rusub_4(A)) & ! [C] : ( ( v1_bhsp_1(C) & m1_rusub_1(C,A) ) => k1_rusub_4(C) != B ) ) ) ) )).
fof(l21_scmfsa8a,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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)) = k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A)),1) ) ) ) ) ) )).
fof(l21_scmpds_9,axiom,( ! [A] : ( v1_xreal_0(A) => k2_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k9_complex1(A),k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),k9_complex1(A)),4)),2),2),A) != k4_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k9_complex1(A),k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),k9_complex1(A)),4)),k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),k9_complex1(A)),4)),2),2),A)) ) )).
fof(l21_scpqsort,axiom,( 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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_numbers))))) = 9 )).
fof(l21_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => k3_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(k3_square_1(k3_xcmplx_0(B,C)),A),k7_xcmplx_0(C,k3_square_1(k3_xcmplx_0(B,A)))),k7_xcmplx_0(k3_square_1(k3_xcmplx_0(A,B)),C)) = k2_xcmplx_0(k7_xcmplx_0(B,k3_square_1(k3_xcmplx_0(A,C))),1) ) ) ) )).
fof(l21_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) & r1_xxreal_0(k6_xcmplx_0(1,k1_square_1(A)),k5_numbers) ) ) )).
fof(l21_sincos10,axiom,( r1_tarski(k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)),k3_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) )).
fof(l21_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l21_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_numbers) => v6_tbsp_1(k8_metric_1(A,B,C),A) ) ) ) ) )).
fof(l21_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_borsuk_2(G,k2_borsuk_1(A,B),k4_borsuk_1(A,B,C,E),k4_borsuk_1(A,B,D,F)) => ! [H] : ( m1_borsuk_2(H,k2_borsuk_1(A,B),k4_borsuk_1(A,B,C,E),k4_borsuk_1(A,B,D,F)) => ! [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] : ( 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,k5_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] : ( 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),k5_numbers,K) = C & k1_binop_1(k3_topalg_4(A,B,k2_borsuk_1(k5_topmetr,k5_topmetr),I),1,K) = D ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l21_topreal2,axiom,( r2_hidden(k19_euclid(k5_numbers,k5_numbers),k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,k5_numbers),k19_euclid(1,k5_numbers))) )).
fof(l21_waybel18,axiom,( v6_pre_topc(k9_waybel18) )).
fof(l21_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & v1_waybel25(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(l21_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_lattice3(C) & v2_lattice3(C) & l1_orders_2(C) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(l21_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( A != k5_numbers => ( r1_nat_d(A,B) <=> m1_subset_1(k7_xcmplx_0(B,A),k4_ordinal1) ) ) ) ) )).
fof(l21_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k5_numbers,k2_xcmplx_0(A,B)) ) ) ) )).
fof(l21_yellow_6,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( 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) ) ) ) )).
fof(l21_zf_fund1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ( 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) ) ) ) ) ) )).
fof(l22_algstr_1,axiom,( ! [A] : ( 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] : ( m1_subset_1(A,u1_struct_0(k8_algstr_0)) => k6_algstr_0(k8_algstr_0,k5_struct_0(k8_algstr_0),A) = A ) )).
fof(l22_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ~ v2_extpro_1(k2_ami_3(A,B),k7_card_1(2),k1_ami_3) ) ) )).
fof(l22_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ! [K] : ( v1_xreal_0(K) => ( ( C = k3_rlvect_1(A,k1_rlvect_1(A,F,J),k1_rlvect_1(A,G,K)) & F = k3_rlvect_1(A,B,k1_rlvect_1(A,D,H)) & G = k3_rlvect_1(A,B,k1_rlvect_1(A,E,I)) ) => C = k3_rlvect_1(A,k3_rlvect_1(A,k1_rlvect_1(A,B,k2_xcmplx_0(J,K)),k1_rlvect_1(A,D,k3_xcmplx_0(J,H))),k1_rlvect_1(A,E,k3_xcmplx_0(K,I))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l22_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => k1_arytm_1(k1_arytm_1(C,B),A) = k1_arytm_1(C,k7_arytm_2(A,B)) ) ) ) )).
fof(l22_arytm_2,axiom,( ! [A] : ! [B] : ~ ( r2_hidden(A,a_0_0_arytm_2) & r2_hidden(B,a_0_0_arytm_2) & ~ r1_tarski(A,B) & ~ r1_tarski(B,A) ) )).
fof(l22_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_xxreal_0(C,B) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,A,C)) ) ) => r1_xxreal_0(k5_numbers,k6_series_1(A,B)) ) ) ) )).
fof(l22_c0sp2,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l22_cardfin2,axiom,( ~ r1_xxreal_0(k3_xcmplx_0(2,k6_xcmplx_0(k11_newton(365,23),k7_xcmplx_0(k2_newton(365),k2_newton(k7_nat_d(365,23))))),k11_newton(365,23)) )).
fof(l22_cfdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(2))) => ( B = k10_finseq_1(A,k5_numbers) => k2_normsp_0(k4_real_ns1(2),B) = k9_complex1(A) ) ) ) )).
fof(l22_complex1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( A = C & B = D ) => k2_arytm_0(A,B) = k3_xcmplx_0(C,D) ) ) ) ) ) )).
fof(l22_compos_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(A,B) => ! [C] : ! [D] : ( ~ r2_hidden(C,k10_xtuple_0(A)) => r1_tarski(A,k6_subset_1(B,k16_funcop_1(D,C))) ) ) ) ) )).
fof(l22_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => k6_rusub_4(A,B,C) = k1_xboole_0 ) ) ) )).
fof(l22_csspace2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => r1_xxreal_0(k3_xcmplx_0(2,k9_complex1(k3_xcmplx_0(A,B))),k2_xcmplx_0(k1_square_1(k9_complex1(A)),k1_square_1(k9_complex1(B)))) ) ) )).
fof(l22_dtconstr,axiom,( k2_lang1(k5_dtconstr) = a_0_11_dtconstr )).
fof(l22_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k1_enumset1(A,B,C),k1_enumset1(D,E,F)) )).
fof(l22_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v8_conmetr(A) <=> v11_aff_2(k3_analmetr(A)) ) ) )).
fof(l22_facirc_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,k1_nat_1(A,1)) & v1_finseq_1(B) ) => ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & ? [D] : B = k7_finseq_1(C,k9_finseq_1(D)) ) ) ) )).
fof(l22_fib_num,axiom,( ~ r1_xxreal_0(k1_fib_num,k5_numbers) )).
fof(l22_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( ( 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) = k5_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)) ) ) ) ) ) ) )).
fof(l22_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) )).
fof(l22_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m2_subset_1(C,k1_zfmisc_1(A),k8_eqrel_1(A,B)) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),k8_eqrel_1(A,B)) => ! [E] : ! [F] : ( ( r2_hidden(E,C) & r2_hidden(F,D) & r2_hidden(k4_tarski(E,F),B) ) => C = D ) ) ) ) ) )).
fof(l22_fscirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(l22_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ! [F] : ( 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] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l22_funcsdom,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ! [C] : ( m2_funct_2(C,B,k1_numbers,k9_funct_2(B,k1_numbers)) => ! [D] : ( m2_funct_2(D,B,k1_numbers,k9_funct_2(B,k1_numbers)) => k1_binop_1(k5_funcsdom(B),k1_binop_1(k7_funcsdom(B),A,C),k1_binop_1(k7_funcsdom(B),A,D)) = k1_binop_1(k7_funcsdom(B),A,k1_funcsdom(B,k1_numbers,k5_funcsdom(B),C,D)) ) ) ) )).
fof(l22_fvaluat1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => k3_fvaluat1(B,C,k2_xcmplx_0(A,1)) = k8_group_1(B,k3_fvaluat1(B,C,A),C) ) ) ) )).
fof(l22_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( r1_analmetr(A,E,F) => r3_analmetr(A,B,D,C,C,E,F) ) ) ) ) ) ) ) )).
fof(l22_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(l22_goboard1,axiom,( ! [A] : ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => r1_goboard1(A,k6_finseq_1(A),B) ) )).
fof(l22_gr_cy_3,axiom,( k11_newton(2,4) = 16 )).
fof(l22_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r3_graph_4(A,k12_finseq_1(u1_struct_0(A),B),k1_xboole_0) ) ) )).
fof(l22_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => r1_xxreal_0(k1_nat_1(k2_nat_1(2,A),1),k1_nat_1(k2_nat_1(2,k1_nat_1(A,1)),1)) ) )).
fof(l22_int_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k8_newton) & v1_funct_1(A) & v1_partfun1(A,k8_newton) & v4_valued_0(A) & v2_pre_poly(A) ) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ~ ( v1_int_7(A) & r2_hidden(B,k22_pre_poly(k8_newton,A)) & k1_recdef_1(A,B) = B & ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k8_newton) & v1_funct_1(C) & v1_partfun1(C,k8_newton) & v4_valued_0(C) & v2_pre_poly(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k8_newton) & v1_funct_1(D) & v1_partfun1(D,k8_newton) & v4_valued_0(D) & v2_pre_poly(D) ) => ~ ( v1_int_7(C) & k22_pre_poly(k8_newton,D) = k1_tarski(B) & k8_nat_3(k8_newton,D) = B & k22_pre_poly(k8_newton,C) = k7_subset_1(k8_newton,k22_pre_poly(k8_newton,A),k1_tarski(B)) & k5_relat_1(C,k22_pre_poly(k8_newton,C)) = k5_relat_1(A,k22_pre_poly(k8_newton,C)) & k8_nat_3(k8_newton,A) = k3_xcmplx_0(k8_nat_3(k8_newton,C),B) ) ) ) ) ) ) )).
fof(l22_integr11,axiom,( m1_subset_1(k3_xcmplx_0(2,k28_sin_cos),k1_numbers) & m1_subset_1(k2_xcmplx_0(k3_xcmplx_0(2,k3_xcmplx_0(2,k28_sin_cos)),k5_numbers),k1_numbers) )).
fof(l22_integr19,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(l22_integra3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ( k3_finseq_1(B) = 1 => ( k3_integra1(A) = k5_numbers | ( ~ v1_xboole_0(k7_finseq_1(k9_finseq_1(k3_seq_4(A)),B)) & v5_valued_0(k7_finseq_1(k9_finseq_1(k3_seq_4(A)),B)) & m2_finseq_1(k7_finseq_1(k9_finseq_1(k3_seq_4(A)),B),k1_numbers) ) ) ) ) ) )).
fof(l22_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ( r1_nattra_1(A,B,C,D) => ! [E] : ( m1_nattra_1(E,A,B,C,D) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => r2_hidden(k2_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))) ) ) ) ) ) ) ) )).
fof(l22_jgraph_6,axiom,( k18_euclid(k19_euclid(k5_numbers,k4_xcmplx_0(1))) = k4_xcmplx_0(1) )).
fof(l22_jordan12,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(B,k3_finseq_1(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(l22_jordan1b,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(A,B) & r1_xxreal_0(B,k1_nat_1(A,1)) & A != B & A != k7_nat_d(B,1) ) ) ) )).
fof(l22_jordan7,axiom,( r2_hidden(k5_numbers,k1_rcomp_1(k5_numbers,1)) )).
fof(l22_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_normsp_1(B) ) => ( B = g1_normsp_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)),k3_lp_space(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( v1_xreal_0(D) => k2_power(k4_series_1(k1_lp_space(k2_rsspace(k1_rlvect_1(B,C,D)),A)),k7_xcmplx_0(1,A)) = k3_xcmplx_0(k9_complex1(D),k2_power(k4_series_1(k1_lp_space(k2_rsspace(C),A)),k7_xcmplx_0(1,A))) ) ) ) ) ) ) )).
fof(l22_lpspacc1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_rfunct_3(C,B,k2_numbers,k3_rfunct_3(B,k2_numbers)) => ! [D] : ( m2_rfunct_3(D,B,k2_numbers,k3_rfunct_3(B,k2_numbers)) => k1_binop_1(k9_lpspacc1(B),k1_binop_1(k8_lpspacc1(B),A,C),k1_binop_1(k8_lpspacc1(B),A,D)) = k1_binop_1(k8_lpspacc1(B),A,k2_lpspace1(B,k2_numbers,k9_lpspacc1(B),C,D)) ) ) ) ) )).
fof(l22_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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,C,k8_cqc_lang(A,E,B)),D),k8_cqc_lang(A,k8_cqc_lang(A,E,k8_cqc_lang(A,C,B)),D)),k4_cqc_the1(A)) ) ) ) ) ) )).
fof(l22_matrprob,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k4_tarski(C,D),k2_matrix_0(B)) => r1_xxreal_0(A,k3_matrix_0(k1_numbers,B,C,D)) ) ) ) <=> ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(D,k2_finseq_1(k1_matrix_0(B))) & r2_hidden(C,k4_finseq_1(k8_matrix_0(k1_numbers,B,D))) ) => r1_xxreal_0(A,k1_funct_1(k8_matrix_0(k1_numbers,B,D),C)) ) ) ) ) ) ) )).
fof(l22_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( v6_supinf_2(k1_mesfunc2(A,D)) & v6_supinf_2(k2_mesfunc2(A,D)) ) ) ) ) ) )).
fof(l22_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v3_modelc_2(A) => k1_funct_1(A,1) = k5_numbers ) ) )).
fof(l22_monoid_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => v1_monoid_0(k9_monoid_1(B,A)) ) )).
fof(l22_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(u1_unialg_1(A))) => m1_subset_1(B,u4_struct_0(k6_msualg_1(A))) ) ) ) )).
fof(l22_ndiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ( ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,k5_numbers) => r1_xxreal_0(A,B) ) ) => r1_xxreal_0(A,k5_numbers) ) ) )).
fof(l22_ntalgo_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => ! [B] : ( m1_subset_1(B,k4_numbers) => ! [C] : ( m1_subset_1(C,k4_numbers) => ( ( B = k5_int_1(A,C) & k3_mcart_1(k4_numbers,k4_numbers,k4_numbers,k2_ntalgo_1(C,B)) = 1 ) => ( C = k5_numbers | k5_int_1(k3_xcmplx_0(k3_ntalgo_1(A,C),A),C) = k5_int_1(1,C) ) ) ) ) ) )).
fof(l22_numbers,axiom,( k9_arytm_3(k12_arytm_3,k12_arytm_3) = c2__numbers )).
fof(l22_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ( v2_o_ring_1(B,A) => v6_o_ring_1(B,A) ) ) ) )).
fof(l22_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( r1_tarski(k10_xtuple_0(A),C) => k3_relat_1(A,k5_relat_1(B,C)) = k3_relat_1(A,B) ) ) ) )).
fof(l22_papdesaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(l22_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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 ) ) ) )).
fof(l22_polynom2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(D,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [E] : ( ( 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] : ( ( 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(k15_pre_poly(A),B,D) = k2_xboole_0(k3_polynom1(k15_pre_poly(A),B,C),k1_tarski(F)) & ! [G] : ( ( 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 => k4_polynom1(A,B,D,G) = k4_polynom1(A,B,C,G) ) ) ) => ( r2_hidden(F,k3_polynom1(k15_pre_poly(A),B,C)) | k2_polynom2(A,B,D,E) = k3_rlvect_1(B,k2_polynom2(A,B,C,E),k6_algstr_0(B,k4_polynom1(A,B,D,F),k1_polynom2(A,F,B,E))) ) ) ) ) ) ) ) ) )).
fof(l22_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( ~ v2_struct_0(D) & l2_struct_0(D) ) => ! [E] : ( ( 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)))) ) => k4_polynom1(A,D,k1_polyred(A,B,D,E),k11_pre_poly(A,C,B)) = k4_polynom1(A,D,E,C) ) ) ) ) ) )).
fof(l22_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_abian(u1_struct_0(A),D,C) => r3_orders_2(A,B,D) ) ) ) ) ) ) )).
fof(l22_pre_ff,axiom,( ! [A] : ( v7_ordinal1(A) => ( ! [B] : ( v7_ordinal1(B) => ( k1_nat_1(A,2) = k3_xcmplx_0(2,B) => k2_pre_ff(c2__pre_ff,k1_nat_1(A,1)) = k8_finseq_1(k4_ordinal1,k2_pre_ff(c2__pre_ff,A),k12_finseq_1(k4_ordinal1,k7_partfun1(k4_ordinal1,k2_pre_ff(c2__pre_ff,A),B))) ) ) & ! [B] : ( v7_ordinal1(B) => ( k1_nat_1(A,2) = k1_nat_1(k3_xcmplx_0(2,B),1) => k2_pre_ff(c2__pre_ff,k1_nat_1(A,1)) = k8_finseq_1(k4_ordinal1,k2_pre_ff(c2__pre_ff,A),k12_finseq_1(k4_ordinal1,k1_nat_1(k7_partfun1(k4_ordinal1,k2_pre_ff(c2__pre_ff,A),B),k7_partfun1(k4_ordinal1,k2_pre_ff(c2__pre_ff,A),k1_nat_1(B,1))))) ) ) ) ) )).
fof(l22_prvect_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => v1_prvect_2(A) ) )).
fof(l22_quaterni,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ r2_hidden(k2_quaterni(k5_numbers,1,2,3,A,B,C,D),k1_numbers) ) ) ) ) )).
fof(l22_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( k9_nat_1(k4_ordinal1,k1_real_3(C,B),A) = k5_numbers => k9_nat_1(k4_ordinal1,k2_real_3(C,B),k1_nat_1(A,1)) = k5_numbers ) ) ) ) )).
fof(l22_realset2,axiom,( k5_binop_1(2,k2_realset2,k10_subset_1(1,2),k10_subset_1(1,2)) = k10_subset_1(1,2) )).
fof(l22_ring_1,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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] : ( 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 ) ) ) ) ) ) )).
fof(l22_rltopsp1,axiom,( ! [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) ) => k3_convex1(A,k1_struct_0(A)) = k1_xboole_0 ) )).
fof(l22_scm_inst,axiom,( ! [A] : ( m1_subset_1(A,k1_compos_0(k3_scm_inst)) => ( A = k5_numbers => k3_compos_0(k3_scm_inst,A) = k1_tarski(k1_xboole_0) ) ) )).
fof(l22_scmpds_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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),k9_complex1(B)),4),B)) ) ) )).
fof(l22_scpinvar,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k1_nat_1(k5_card_1(C),2)),C),k3_scmpds_2(k4_xcmplx_0(k1_nat_1(k5_card_1(C),2))))) ) ) ) )).
fof(l22_scpqsort,axiom,( 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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_numbers)))))) = 11 )).
fof(l22_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => k3_xcmplx_0(k3_xcmplx_0(k2_xcmplx_0(1,k7_xcmplx_0(k3_square_1(k3_xcmplx_0(B,C)),A)),k2_xcmplx_0(1,k7_xcmplx_0(k3_square_1(k3_xcmplx_0(A,C)),B))),k2_xcmplx_0(1,k7_xcmplx_0(k3_square_1(k3_xcmplx_0(A,B)),C))) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(2,k7_xcmplx_0(k3_square_1(k3_xcmplx_0(A,C)),B)),k7_xcmplx_0(B,k3_square_1(k3_xcmplx_0(A,C)))),k7_xcmplx_0(k3_square_1(k3_xcmplx_0(A,B)),C)),k7_xcmplx_0(C,k3_square_1(k3_xcmplx_0(B,A)))),k7_xcmplx_0(A,k3_square_1(k3_xcmplx_0(B,C)))),k7_xcmplx_0(k3_square_1(k3_xcmplx_0(B,C)),A)) ) ) ) )).
fof(l22_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k3_sin_cos2,k2_xcmplx_0(A,B)) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(k3_sin_cos2,A),k1_funct_1(k3_sin_cos2,B)),k3_xcmplx_0(k1_funct_1(k1_sin_cos2,A),k1_funct_1(k1_sin_cos2,B))) ) ) )).
fof(l22_sincos10,axiom,( r1_tarski(k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)),k1_relset_1(k1_numbers,k1_fdiff_9)) )).
fof(l22_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l22_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( m1_subset_1(D,k5_finsub_1(k4_partfun1(A,B))) => ! [E] : ( v1_finset_1(E) => ~ ( r2_hidden(E,k4_substlat(A,B,C,D)) & ! [F] : ( v1_finset_1(F) => ~ ( r1_tarski(F,E) & r2_hidden(F,k4_substlat(A,B,k3_substlat(A,B,C),D)) ) ) ) ) ) ) )).
fof(l22_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_borsuk_2(G,k2_borsuk_1(A,B),k4_borsuk_1(A,B,C,E),k4_borsuk_1(A,B,D,F)) => ! [H] : ( m1_borsuk_2(H,k2_borsuk_1(A,B),k4_borsuk_1(A,B,C,E),k4_borsuk_1(A,B,D,F)) => ! [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] : ( 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,k5_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] : ( 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),k5_numbers,K) = E & k1_binop_1(k4_topalg_4(A,B,k2_borsuk_1(k5_topmetr,k5_topmetr),I),1,K) = F ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l22_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(l22_topgen_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & ~ v1_topgen_2(A) & l1_pre_topc(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)))) ) => ? [C] : ( 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) ) ) ) )).
fof(l22_topreal2,axiom,( r2_hidden(k19_euclid(k5_numbers,1),k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,k5_numbers),k19_euclid(k5_numbers,1))) )).
fof(l22_topreal7,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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)) ) ) )).
fof(l22_toprealc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) & v3_valued_0(B) ) => m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) ) ) )).
fof(l22_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_waybel_9(A) ) => v3_waybel11(k2_struct_0(A),A) ) )).
fof(l22_waybel29,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( ( v4_waybel11(D) & m1_yellow_9(D,k3_waybel24(A,C)) ) => ? [E] : ( 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] : ( 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] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( ( v4_waybel11(D) & m1_yellow_9(D,k3_waybel24(A,C)) ) => ? [E] : ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(l22_wellord1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => r1_tarski(k9_xtuple_0(k6_relat_1(A,B)),k9_xtuple_0(B)) ) )).
fof(l22_xreal_0,axiom,( m1_subset_1(k5_numbers,k2_arytm_2) )).
fof(l22_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( r1_xxreal_0(A,B) => m1_xxreal_2(B,k2_tarski(A,B)) ) ) ) )).
fof(l22_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( k1_xxreal_3(A,B) = k1_xxreal_0 & A != k1_xxreal_0 & B != k1_xxreal_0 ) ) ) )).
fof(l22_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(l22_zf_fund1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(l22_zfmisc_1,axiom,( ! [A] : ! [B] : ( k3_xboole_0(B,k1_tarski(A)) = k1_tarski(A) => r2_hidden(A,B) ) )).
fof(l230_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k5_xcmplx_0(k4_xcmplx_0(A)) = k4_xcmplx_0(k5_xcmplx_0(A)) ) )).
fof(l23_algstr_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k8_algstr_0)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k8_algstr_0)) => ? [C] : ( m1_subset_1(C,u1_struct_0(k8_algstr_0)) & k6_algstr_0(k8_algstr_0,A,C) = B ) ) ) )).
fof(l23_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ~ v2_extpro_1(k3_ami_3(A,B),k7_card_1(2),k1_ami_3) ) ) )).
fof(l23_analoaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( k1_rlvect_1(A,k5_algstr_0(A,C,B),F) = k1_rlvect_1(A,k5_algstr_0(A,D,E),G) & ~ ( F = k5_numbers & G = k5_numbers ) & ~ r1_analoaf(A,B,C,D,E) & ~ r1_analoaf(A,B,C,E,D) ) ) ) ) ) ) ) ) )).
fof(l23_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => 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,k3_xcmplx_0(D,E)),k1_rlvect_1(A,C,k3_xcmplx_0(D,F))) ) ) ) ) ) ) )).
fof(l23_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( E = k3_rlvect_1(A,k1_rlvect_1(A,C,F),k1_rlvect_1(A,D,G)) => E = k3_rlvect_1(A,k3_rlvect_1(A,k1_rlvect_1(A,B,k5_numbers),k1_rlvect_1(A,C,F)),k1_rlvect_1(A,D,G)) ) ) ) ) ) ) ) ) )).
fof(l23_arytm_0,axiom,( m1_subset_1(k5_numbers,k1_numbers) )).
fof(l23_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => k1_arytm_1(k1_arytm_1(B,C),A) = k1_arytm_1(k1_arytm_1(B,A),C) ) ) ) )).
fof(l23_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r1_xxreal_0(D,C) => r1_xxreal_0(k9_nat_1(k1_numbers,A,D),k9_nat_1(k1_numbers,B,D)) ) ) => r1_xxreal_0(k6_series_1(A,C),k6_series_1(B,C)) ) ) ) ) )).
fof(l23_card_1,axiom,( k3_card_1(k5_ordinal1) = k1_card_1(k4_ordinal1) & ! [A] : ( v3_ordinal1(A) => k3_card_1(k1_ordinal1(A)) = k2_card_1(k3_tarski(k1_tarski(k3_card_1(A)))) ) & ! [A] : ( v3_ordinal1(A) => ( v4_ordinal1(A) => ( A = k5_ordinal1 | ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) ) => ( ( k9_xtuple_0(B) = A & ! [C] : ( 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)) ) ) ) ) ) )).
fof(l23_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,C,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,C,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,B))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(C,C),C))) ) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(l23_cfdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(2))) => ( B = k10_finseq_1(k5_numbers,A) => k2_normsp_0(k4_real_ns1(2),B) = k9_complex1(A) ) ) ) )).
fof(l23_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k8_clopban2(A))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(l23_collsp,axiom,( r1_tarski(a_0_2_collsp,k3_zfmisc_1(k8_domain_1(k4_ordinal1,1,2,3),k8_domain_1(k4_ordinal1,1,2,3),k8_domain_1(k4_ordinal1,1,2,3))) )).
fof(l23_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( C = k2_xcmplx_0(A,B) => k3_complex1(C) = k3_real_1(k3_complex1(A),k3_complex1(B)) ) ) ) ) )).
fof(l23_comput_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(l23_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( 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 ) ) )).
fof(l23_csspace2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( r1_xxreal_0(k3_xcmplx_0(k9_complex1(k2_xcmplx_0(A,B)),k9_complex1(k2_xcmplx_0(A,B))),k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k9_complex1(A)),k9_complex1(A)),k3_xcmplx_0(k3_xcmplx_0(2,k9_complex1(B)),k9_complex1(B)))) & r1_xxreal_0(k3_xcmplx_0(k9_complex1(A),k9_complex1(A)),k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k9_complex1(k6_xcmplx_0(A,B))),k9_complex1(k6_xcmplx_0(A,B))),k3_xcmplx_0(k3_xcmplx_0(2,k9_complex1(B)),k9_complex1(B)))) ) ) ) )).
fof(l23_dtconstr,axiom,( r2_hidden(c3__dtconstr,k2_lang1(k5_dtconstr)) )).
fof(l23_euler_1,axiom,( ! [A] : ( r2_hidden(A,a_0_1_euler_1) <=> A = 1 ) )).
fof(l23_facirc_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,k1_nat_1(A,1)) & v1_finseq_1(B) & v2_facirc_1(B) ) => ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & v2_facirc_1(C) & ? [D] : ( ~ v1_xtuple_0(D) & B = k7_finseq_1(C,k9_finseq_1(D)) ) ) ) ) )).
fof(l23_fdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( r2_hidden(A,k9_xtuple_0(k3_taylor_1)) & r1_xxreal_0(A,k5_numbers) ) ) )).
fof(l23_fib_num,axiom,( ~ r1_xxreal_0(k5_numbers,k2_fib_num) )).
fof(l23_finseq_1,axiom,( ! [A] : ! [B] : ( m1_finseq_1(B,A) => ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) ) )).
fof(l23_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ( v2_funct_1(C) => v2_funct_1(k17_finseq_1(B,A,C)) ) ) ) ) )).
fof(l23_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(l23_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(l23_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & l4_struct_0(A) ) => k1_funct_1(k14_fomodel1(A),u2_struct_0(A)) = k4_xcmplx_0(2) ) )).
fof(l23_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l23_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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] : ( ( v5_relat_1(F,k1_rcomp_1(k5_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] : ! [H] : ( ( r2_hidden(G,A) & r2_hidden(H,C) ) => r1_xxreal_0(k2_seq_4(k2_relset_1(k1_numbers,k2_fuzzy_4(A,B,C,k1_fuzzy_1(k2_zfmisc_1(A,B),D,E),F,G,H))),k3_xxreal_0(k2_seq_4(k2_relset_1(k1_numbers,k2_fuzzy_4(A,B,C,D,F,G,H))),k2_seq_4(k2_relset_1(k1_numbers,k2_fuzzy_4(A,B,C,E,F,G,H))))) ) ) ) ) ) ) ) )).
fof(l23_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( ( r1_analmetr(A,F,H) & r3_analmetr(A,B,C,G,D,F,H) & r3_analmetr(A,B,C,G,E,F,H) ) => r3_analmetr(A,B,C,D,E,F,H) ) ) ) ) ) ) ) ) ) )).
fof(l23_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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) ) ) ) )).
fof(l23_gr_cy_3,axiom,( k11_newton(2,8) = 256 )).
fof(l23_groeb_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => r2_hidden(C,k7_ideal_1(A,B)) ) ) ) ) )).
fof(l23_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m2_subset_1(C,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B)) => ! [D] : ( r1_tarski(D,C) => r2_hidden(D,k1_substlat(A,B)) ) ) ) )).
fof(l23_int_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( B != k5_numbers & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r1_xxreal_0(k3_xcmplx_0(C,B),A) & ~ r1_xxreal_0(k3_xcmplx_0(k2_xcmplx_0(C,1),B),A) ) ) ) ) ) )).
fof(l23_int_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k8_newton) & v1_funct_1(A) & v1_partfun1(A,k8_newton) & v4_valued_0(A) & v2_pre_poly(A) ) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ~ ( v1_int_7(A) & r2_hidden(B,k22_pre_poly(k8_newton,A)) & k1_recdef_1(A,B) != B & ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k8_newton) & v1_funct_1(C) & v1_partfun1(C,k8_newton) & v4_valued_0(C) & v2_pre_poly(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k8_newton) & v1_funct_1(D) & v1_partfun1(D,k8_newton) & v4_valued_0(D) & v2_pre_poly(D) ) => ~ ( v1_int_7(C) & k22_pre_poly(k8_newton,D) = k1_tarski(B) & k8_nat_3(k8_newton,D) = B & k22_pre_poly(k8_newton,C) = k22_pre_poly(k8_newton,A) & k5_relat_1(C,k7_subset_1(k8_newton,k22_pre_poly(k8_newton,C),k1_tarski(B))) = k5_relat_1(A,k7_subset_1(k8_newton,k22_pre_poly(k8_newton,C),k1_tarski(B))) & k1_recdef_1(A,B) = k3_xcmplx_0(k1_recdef_1(C,B),B) & k8_nat_3(k8_newton,A) = k3_xcmplx_0(k8_nat_3(k8_newton,C),B) ) ) ) ) ) ) )).
fof(l23_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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)))) ) ) ) ) ) )).
fof(l23_integra3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ( ~ r1_xxreal_0(k1_funct_1(B,1),k3_seq_4(A)) => ( ~ v1_xboole_0(k7_finseq_1(k9_finseq_1(k3_seq_4(A)),B)) & v5_valued_0(k7_finseq_1(k9_finseq_1(k3_seq_4(A)),B)) & m2_finseq_1(k7_finseq_1(k9_finseq_1(k3_seq_4(A)),B),k1_numbers) ) ) ) ) )).
fof(l23_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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) = k2_xcmplx_0(k4_integra5(A,C,E),k4_integra5(C,D,E)) ) ) ) ) ) ) )).
fof(l23_integra8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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) ) ) )).
fof(l23_jgraph_3,axiom,( k16_euclid(2) = k4_struct_0(k15_euclid(2)) )).
fof(l23_jgraph_4,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(l23_jgraph_6,axiom,( k17_euclid(k19_euclid(k5_numbers,1)) = k5_numbers )).
fof(l23_jordan1,axiom,( g1_pre_topc(u1_struct_0(k15_euclid(2)),u1_pre_topc(k15_euclid(2))) = k3_pcomps_1(k14_euclid(2)) )).
fof(l23_jordan7,axiom,( r2_hidden(1,k1_rcomp_1(k5_numbers,1)) )).
fof(l23_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k8_lopban_2(A))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(l23_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(l23_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => k2_wsierp_1(k10_matrixj1(A,k4_matrixj1(A,B))) = k3_finseq_1(B) ) ) )).
fof(l23_measure6,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,k1_measure6(A,B)) <=> ? [D] : ( v1_xreal_0(D) & r2_hidden(D,A) & C = k2_xcmplx_0(B,D) ) ) ) ) ) )).
fof(l23_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( ( D = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),B,k6_xcmplx_0(1,G)),k1_rlvect_1(k15_euclid(2),C,G)) & E = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),C,k6_xcmplx_0(1,H)),k1_rlvect_1(k15_euclid(2),A,H)) & F = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),A,k6_xcmplx_0(1,I)),k1_rlvect_1(k15_euclid(2),B,I)) ) => ( r1_euclid_6(A,B,C) | G = 1 | H = 1 | I = 1 | ( k2_xcmplx_0(k6_xcmplx_0(1,H),k3_xcmplx_0(G,H)) != k5_numbers & k2_xcmplx_0(k6_xcmplx_0(1,G),k3_xcmplx_0(I,G)) != k5_numbers & k2_xcmplx_0(k6_xcmplx_0(1,I),k3_xcmplx_0(H,I)) != k5_numbers ) | ( k3_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(G,k6_xcmplx_0(1,G)),k7_xcmplx_0(H,k6_xcmplx_0(1,H))),k7_xcmplx_0(I,k6_xcmplx_0(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)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l23_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(l23_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_finset_1(B) & v1_card_1(B) ) => ( ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ( v1_tops_2(C,A) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) )).
fof(l23_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v4_modelc_2(A) => k1_funct_1(A,1) = 1 ) ) )).
fof(l23_nagata_2,axiom,( k2_tops_2(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1,k1_nagata_2) = k2_funct_1(k1_nagata_2) )).
fof(l23_necklace,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(l23_normform,axiom,( ! [A] : v3_binop_1(k5_normform(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))) )).
fof(l23_numbers,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => k9_arytm_3(A,A) = k10_arytm_3(c2__numbers,A) ) )).
fof(l23_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v3_o_ring_1(B,A) => v7_o_ring_1(B,A) ) ) ) )).
fof(l23_petri_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( 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] : ( r2_hidden(F,k9_xtuple_0(A)) => k1_funct_1(E,F) = k1_funct_1(A,F) ) & ! [F] : ( r2_hidden(F,k9_xtuple_0(B)) => k1_funct_1(E,F) = k1_funct_1(B,F) ) & ! [F] : ( r2_hidden(F,k9_xtuple_0(C)) => k1_funct_1(E,F) = k1_funct_1(C,F) ) & ! [F] : ( r2_hidden(F,k9_xtuple_0(D)) => k1_funct_1(E,F) = k1_funct_1(D,F) ) ) ) ) ) ) ) ) )).
fof(l23_polynom2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ( ? [D] : ( 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(k15_pre_poly(A),B,C) = k1_tarski(D) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(D,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [E] : ( ( 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)))) ) => k2_polynom2(A,B,k6_polynom1(A,B,C,D),E) = k3_rlvect_1(B,k2_polynom2(A,B,C,E),k2_polynom2(A,B,D,E)) ) ) ) ) ) ) )).
fof(l23_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( 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) = k4_polynom1(A,B,C,k16_pre_poly(A)) ) ) ) )).
fof(l23_polynom8,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k4_ordinal1) => k3_polynom8(A,k5_struct_0(A),B) = k5_struct_0(A) ) ) )).
fof(l23_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( ( 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(k3_polynom1(k15_pre_poly(A),B,k1_polyred(A,D,B,C)),a_4_0_polyred(A,B,C,D)) ) ) ) ) )).
fof(l23_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u2_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u2_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u2_incsp_1(A)) => ! [H] : ( 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,H) & ~ r1_incsp_1(A,C,H) & D != H & B != C & r1_incsp_1(A,B,G) & r1_incsp_1(A,C,G) & ~ r1_projred2(A,E,F,G) & ! [I] : ( m1_subset_1(I,u1_incsp_1(A)) => ~ ( r1_incsp_1(A,I,G) & ~ r1_incsp_1(A,I,D) & ~ r1_incsp_1(A,I,H) & k3_relat_1(k1_projred1(A,D,F,B),k1_projred1(A,F,E,C)) = k3_relat_1(k1_projred1(A,D,H,I),k1_projred1(A,H,E,C)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l23_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m2_prob_1(B,A,k1_random_1(A)) => ! [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))) ) => ? [D] : ( m2_finseq_1(D,k1_numbers) & k3_finseq_1(D) = k5_card_1(A) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(D)) => k12_supinf_2(D,E) = k1_extreal1(k12_supinf_2(C,k1_funct_1(k19_finseq_1(A),E)),k12_supinf_2(B,k1_tarski(k1_funct_1(k19_finseq_1(A),E)))) ) ) & k1_mesfunc6(A,k1_random_1(A),k2_prob_4(A,k1_random_1(A),B),C) = k18_rvsum_1(D) ) ) ) ) )).
fof(l23_random_2,axiom,( m1_subset_1(1,k6_numbers) )).
fof(l23_realset2,axiom,( k6_subset_1(c4__realset2,k1_tarski(k10_subset_1(k5_numbers,2))) = k1_tarski(k10_subset_1(1,2)) )).
fof(l23_rlvect_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( 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)) ) ) )).
fof(l23_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => r1_tarski(u1_struct_0(k2_rmod_3(A,B,C,D)),u1_struct_0(C)) ) ) ) ) )).
fof(l23_scm_inst,axiom,( ! [A] : ( m1_subset_1(A,k1_compos_0(k3_scm_inst)) => ( ~ ! [B] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(1,B) & r1_xxreal_0(B,5) & A = B ) ) => k3_compos_0(k3_scm_inst,A) = k1_tarski(k1_xboole_0) ) ) )).
fof(l23_scmpds_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & k2_xcmplx_0(k2_xcmplx_0(k9_complex1(B),A),1) = k4_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k9_complex1(B),A),A),B)) ) ) ) )).
fof(l23_scmyciel,axiom,( ! [A] : k3_tarski(a_1_3_scmyciel(A)) = A )).
fof(l23_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( 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) = k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_numbers)))),B,A),k2_scmp_gcd) = k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_numbers)))),B,A),k1_scmp_gcd(4)) = k1_funct_1(B,k1_scmp_gcd(4)) & ! [E] : ( v7_ordinal1(E) => ( 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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_numbers)))),B,A),k1_scmp_gcd(7)) = k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_numbers)))),B,A),k1_scmp_gcd(5)) = k1_funct_1(B,k1_scmp_gcd(7)) ) ) ) ) ) ) ) ) )).
fof(l23_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => r1_xxreal_0(6,k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(k3_square_1(k3_xcmplx_0(A,C)),B),k7_xcmplx_0(B,k3_square_1(k3_xcmplx_0(A,C)))),k7_xcmplx_0(k3_square_1(k3_xcmplx_0(A,B)),C)),k7_xcmplx_0(C,k3_square_1(k3_xcmplx_0(B,A)))),k7_xcmplx_0(A,k3_square_1(k3_xcmplx_0(B,C)))),k7_xcmplx_0(k3_square_1(k3_xcmplx_0(B,C)),A))) ) ) ) )).
fof(l23_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k1_sin_cos2,k2_xcmplx_0(A,B)) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_sin_cos2,A),k1_funct_1(k3_sin_cos2,B)),k3_xcmplx_0(k1_funct_1(k3_sin_cos2,A),k1_funct_1(k1_sin_cos2,B))) ) ) )).
fof(l23_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k2_xcmplx_0(k2_sin_cos2(A),k2_sin_cos2(B)) = k3_xcmplx_0(k3_xcmplx_0(2,k2_sin_cos2(k2_xcmplx_0(k7_xcmplx_0(A,2),k7_xcmplx_0(B,2)))),k4_sin_cos2(k6_xcmplx_0(k7_xcmplx_0(A,2),k7_xcmplx_0(B,2)))) & k6_xcmplx_0(k2_sin_cos2(A),k2_sin_cos2(B)) = k3_xcmplx_0(k3_xcmplx_0(2,k2_sin_cos2(k6_xcmplx_0(k7_xcmplx_0(A,2),k7_xcmplx_0(B,2)))),k4_sin_cos2(k2_xcmplx_0(k7_xcmplx_0(A,2),k7_xcmplx_0(B,2)))) & k2_xcmplx_0(k4_sin_cos2(A),k4_sin_cos2(B)) = k3_xcmplx_0(k3_xcmplx_0(2,k4_sin_cos2(k2_xcmplx_0(k7_xcmplx_0(A,2),k7_xcmplx_0(B,2)))),k4_sin_cos2(k6_xcmplx_0(k7_xcmplx_0(A,2),k7_xcmplx_0(B,2)))) & k6_xcmplx_0(k4_sin_cos2(A),k4_sin_cos2(B)) = k3_xcmplx_0(k3_xcmplx_0(2,k2_sin_cos2(k6_xcmplx_0(k7_xcmplx_0(A,2),k7_xcmplx_0(B,2)))),k2_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)) = k7_xcmplx_0(k2_sin_cos2(k2_xcmplx_0(A,B)),k3_xcmplx_0(k4_sin_cos2(A),k4_sin_cos2(B))) & k6_xcmplx_0(k6_sin_cos2(A),k6_sin_cos2(B)) = k7_xcmplx_0(k2_sin_cos2(k6_xcmplx_0(A,B)),k3_xcmplx_0(k4_sin_cos2(A),k4_sin_cos2(B))) ) ) ) )).
fof(l23_sin_cos9,axiom,( r2_hidden(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)),k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))) )).
fof(l23_sincos10,axiom,( r1_tarski(k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos),k4_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos)) )).
fof(l23_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l23_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(k3_square_1(B),k3_square_1(A)) ) ) ) )).
fof(l23_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(l23_topalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_topalg_2(A) & m1_pre_topc(A,k2_topalg_2) ) => ! [B] : ( ( 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] : ( ( 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) ) ) ) )).
fof(l23_topalg_6,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( 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) ) ) ) )).
fof(l23_topreal2,axiom,( r2_hidden(k19_euclid(k5_numbers,1),k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,1),k19_euclid(1,1))) )).
fof(l23_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => r1_tarski(u1_struct_0(k2_vectsp_5(A,B,C,D)),u1_struct_0(C)) ) ) ) ) )).
fof(l23_waybel_5,axiom,( ! [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] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) ) => ! [D] : ( m2_pboole(D,B,C,k7_funcop_1(B,u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k4_card_3(k1_funct_6(D))) <=> r2_hidden(E,k1_relset_1(k4_card_3(k1_funct_6(D)),k2_waybel_5(B,u1_struct_0(A),C,D))) ) ) ) ) ) )).
fof(l23_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_int_1(C) => ( k3_xcmplx_0(A,C) = B => ( B = k5_numbers | m1_subset_1(C,k4_ordinal1) ) ) ) ) ) )).
fof(l23_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(k5_numbers,C) ) => r1_xxreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) ) ) ) )).
fof(l23_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => r1_xxreal_0(k4_xcmplx_0(B),k4_xcmplx_0(A)) ) ) ) )).
fof(l23_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( m1_xxreal_2(C,k2_tarski(A,B)) => r1_xxreal_0(B,C) ) ) ) )).
fof(l23_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( k1_xxreal_3(A,B) = k2_xxreal_0 & A != k2_xxreal_0 & B != k2_xxreal_0 ) ) ) )).
fof(l23_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(l23_zf_fund1,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k4_ordinal1)) ) => ! [C] : ( ~ v1_xboole_0(C) => ~ ( r2_hidden(A,k9_funct_2(B,C)) & ! [D] : ( ( 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) ) ) ) ) )).
fof(l23_zfmodel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_ordinal1(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ( ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,B) <=> r2_hidden(D,C) ) ) => B = C ) ) ) ) ) )).
fof(l24_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( ( r2_hidden(B,E) & r2_hidden(B,k1_aff_4(A,C,D)) & r5_aff_1(A,C,E) ) => r1_tarski(E,k1_aff_4(A,C,D)) ) ) ) ) ) ) )).
fof(l24_algstr_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k8_algstr_0)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k8_algstr_0)) => ? [C] : ( m1_subset_1(C,u1_struct_0(k8_algstr_0)) & k6_algstr_0(k8_algstr_0,C,A) = B ) ) ) )).
fof(l24_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ~ v2_extpro_1(k4_ami_3(A,B),k7_card_1(2),k1_ami_3) ) ) )).
fof(l24_ami_6,axiom,( k10_ami_3(k5_numbers) != k10_ami_3(1) )).
fof(l24_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_rlvect_1(A,k1_rlvect_1(A,B,k5_numbers),k1_rlvect_1(A,C,k5_numbers)) = k4_struct_0(A) ) ) ) )).
fof(l24_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ! [D] : ( m1_subset_1(D,k2_arytm_2) => ( ( C = A & D = B ) => ( r1_arytm_2(C,D) <=> r3_arytm_3(A,B) ) ) ) ) ) ) )).
fof(l24_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( r2_hidden(A,k6_asympt_0(B)) & r2_hidden(B,k6_asympt_0(A)) ) <=> k6_asympt_0(A) = k6_asympt_0(B) ) ) ) )).
fof(l24_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( ( k9_nat_1(k1_numbers,A,k5_numbers) = k5_numbers & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ r1_xxreal_0(C,k5_numbers) => k9_nat_1(k1_numbers,A,C) = B ) ) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k6_series_1(A,C) = k3_xcmplx_0(B,C) ) ) ) ) )).
fof(l24_bcialg_4,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(l24_borsuk_4,axiom,( v1_borsuk_1(k5_topmetr,k3_topmetr) & m1_pre_topc(k5_topmetr,k3_topmetr) )).
fof(l24_card_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( A != B => r1_xboole_0(k2_zfmisc_1(C,k1_tarski(A)),k2_zfmisc_1(D,k1_tarski(B))) ) )).
fof(l24_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,C,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,C,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,B))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(C,C),C))) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(l24_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_cc0sp2(A))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(l24_cfdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(1))) => ( B = k9_finseq_1(A) => k2_normsp_0(k4_real_ns1(1),B) = k9_complex1(A) ) ) ) )).
fof(l24_circled1,axiom,( m1_subset_1(1,k1_numbers) & m1_subset_1(k7_xcmplx_0(1,2),k1_numbers) )).
fof(l24_collsp,axiom,( ~ v1_xboole_0(k8_domain_1(k4_ordinal1,1,2,3)) )).
fof(l24_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( C = k2_xcmplx_0(A,B) => k4_complex1(C) = k3_real_1(k4_complex1(A),k4_complex1(B)) ) ) ) ) )).
fof(l24_convex1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(k5_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,k2_xcmplx_0(C,D))) ) ) ) ) ) )).
fof(l24_csspace2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v2_comseq_2(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [D] : ( v7_ordinal1(D) => k1_funct_1(C,D) = k3_xcmplx_0(k9_complex1(k6_xcmplx_0(k1_funct_1(B,D),A)),k9_complex1(k6_xcmplx_0(k1_funct_1(B,D),A))) ) => ( v2_comseq_2(C) & k1_seq_2(C) = k3_xcmplx_0(k9_complex1(k6_xcmplx_0(k3_comseq_2(B),A)),k9_complex1(k6_xcmplx_0(k3_comseq_2(B),A))) ) ) ) ) ) ) )).
fof(l24_dist_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( v1_prob_2(A) => v1_prob_2(k5_relat_1(A,B)) ) ) )).
fof(l24_dtconstr,axiom,( r1_tarski(k6_domain_1(u1_struct_0(k5_dtconstr),c3__dtconstr),k2_lang1(k5_dtconstr)) )).
fof(l24_euler_1,axiom,( k5_card_1(k1_tarski(1)) = k1_euler_1(2) )).
fof(l24_fib_num,axiom,( ~ r1_xxreal_0(1,k9_complex1(k2_fib_num)) )).
fof(l24_fib_num4,axiom,( k1_square_1(k2_fib_num) = k7_xcmplx_0(k6_xcmplx_0(3,k3_square_1(5)),2) )).
fof(l24_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( v7_ordinal1(C) & ~ v8_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)))) ) ) ) )).
fof(l24_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( 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(k4_fomodel4(B,C),A) = k3_tarski(k3_tarski(a_3_3_fomodel4(A,B,C))) ) ) ) )).
fof(l24_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l24_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(l24_funct_9,axiom,( v1_funct_9(k16_sin_cos,k3_xcmplx_0(2,k28_sin_cos)) )).
fof(l24_fvaluat1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ~ ( C != k4_struct_0(B) & k3_fvaluat1(B,C,A) = k4_struct_0(B) ) ) ) ) )).
fof(l24_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r1_analmetr(A,D,E) & r3_analmetr(A,B,C,B,C,D,E) ) => B = C ) ) ) ) ) ) )).
fof(l24_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( r2_hidden(B,k3_glib_002(A)) => ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) ) ) ) )).
fof(l24_goedelcp,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ ( v4_card_3(A) & ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ~ ( k9_xtuple_0(B) = k4_ordinal1 & A = k10_xtuple_0(B) ) ) ) ) )).
fof(l24_graph_2,axiom,( ~ r1_xxreal_0(k3_finseq_1(k2_finseq_4(k4_ordinal1,1,2)),1) & 1 != 2 & k10_xtuple_0(k2_finseq_4(k4_ordinal1,1,2)) = k2_tarski(1,2) )).
fof(l24_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(k12_polynom1(A,C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k12_polynom1(A,C))) => ( ( F = D & G = E ) => k5_algstr_0(k12_polynom1(A,C),F,G) = k7_polynom1(A,C,D,E) ) ) ) ) ) ) ) ) )).
fof(l24_group_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k15_group_2(A,B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,C) <=> C = k13_group_2(A,B,D) ) ) ) ) ) )).
fof(l24_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ r1_tarski(k3_heyting3(k1_nat_1(A,1),B),k3_heyting3(A,B)) ) ) )).
fof(l24_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => r1_tarski(k5_hilbert1(k5_hilbert1(A)),k5_hilbert1(A)) ) )).
fof(l24_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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] : ( 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) ) ) ) )).
fof(l24_integra3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [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))) ) => ! [D] : ( m1_integra1(D,A) => ( D = k7_finseq_1(k9_finseq_1(k3_seq_4(A)),B) => ( ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k2_finseq_1(k3_finseq_1(B))) => k2_integra1(A,D,k1_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)) ) ) ) ) ) ) )).
fof(l24_jgraph_3,axiom,( ( r1_xxreal_0(k18_euclid(k22_euclid(2)),k17_euclid(k22_euclid(2))) & r1_xxreal_0(k4_xcmplx_0(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)),k4_xcmplx_0(k17_euclid(k22_euclid(2)))) ) )).
fof(l24_jgraph_4,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(l24_jgraph_6,axiom,( k18_euclid(k19_euclid(k5_numbers,1)) = 1 )).
fof(l24_jordan12,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(B,k1_matrix_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(l24_jordan5b,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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))) ) ) ) ) )).
fof(l24_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( 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) ) ) )).
fof(l24_lattice7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(l24_limfunc1,axiom,( v1_xreal_0(1) )).
fof(l24_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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,D),E),k8_cqc_lang(A,k8_cqc_lang(A,B,C),k8_cqc_lang(A,k8_cqc_lang(A,C,D),E))),k4_cqc_the1(A)) ) ) ) ) ) )).
fof(l24_matrtop3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(C,D) ) => ( r1_xxreal_0(C,B) | k4_matrix_0(u1_struct_0(k2_vectsp_1),k2_matrtop3(D,A,B,C)) = k2_matrtop3(D,k4_xcmplx_0(A),B,C) ) ) ) ) ) ) )).
fof(l24_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ? [E] : ( v7_ordinal1(E) & k1_mesfunc9(k6_measure8(A,B,C),k9_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(k4_ordinal1,k9_setfam_1(A),k9_setfam_1(A),k6_numbers,D,k6_measure8(A,B,C)))) ) ) ) ) )).
fof(l24_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v5_modelc_2(A) => k1_funct_1(A,1) = 2 ) ) )).
fof(l24_msaterm,axiom,( ! [A] : ~ r2_hidden(A,A) )).
fof(l24_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(l24_nagata_2,axiom,( v1_xreal_0(1) )).
fof(l24_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k2_cat_1(A,D,E) != k1_xboole_0 => ! [F] : ( m1_cat_1(F,A,D,E) => k5_cat_1(B,k8_cat_1(A,B,C,D),k8_cat_1(A,B,C,E),k8_cat_1(A,B,C,E),k9_cat_3(A,D,E,B,C,F),k2_nattra_1(A,B,C,C,k1_nattra_1(A,B,C),E)) = k5_cat_1(B,k8_cat_1(A,B,C,D),k8_cat_1(A,B,C,D),k8_cat_1(A,B,C,E),k2_nattra_1(A,B,C,C,k1_nattra_1(A,B,C),D),k9_cat_3(A,D,E,B,C,F)) ) ) ) ) ) ) ) )).
fof(l24_normform,axiom,( ! [A] : v1_binop_1(k5_normform(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))) )).
fof(l24_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => a_3_0_normsp_2(A,B,C) = a_3_6_normsp_2(A,B,C) ) ) ) )).
fof(l24_petri_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( 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 ) ) )).
fof(l24_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(1,B) => ( r1_xxreal_0(A,k5_numbers) | ( k1_newton(k2_prepower(B,A),B) = A & k2_prepower(B,k1_newton(A,B)) = A ) ) ) ) ) )).
fof(l24_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u2_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u2_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u2_incsp_1(A)) => ! [H] : ( 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,H) & ~ r1_incsp_1(A,C,H) & D != H & B != C & r1_incsp_1(A,B,G) & r1_incsp_1(A,C,G) & r1_projred2(A,E,F,G) & ! [I] : ( m1_subset_1(I,u1_incsp_1(A)) => ~ ( r1_incsp_1(A,I,G) & ~ r1_incsp_1(A,I,D) & ~ r1_incsp_1(A,I,H) & k3_relat_1(k1_projred1(A,D,F,B),k1_projred1(A,F,E,C)) = k3_relat_1(k1_projred1(A,D,H,I),k1_projred1(A,H,E,C)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l24_random_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( m2_prob_1(C,A,k1_random_1(A)) => ! [D] : ( m2_prob_1(D,B,k1_random_1(B)) => ! [E] : ( ( 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] : ( ( 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] : ( ( ~ v1_xboole_0(G) & v1_finset_1(G) & m1_subset_1(G,k1_zfmisc_1(A)) ) => ! [H] : ( ( ~ v1_xboole_0(H) & v1_finset_1(H) & m1_subset_1(H,k1_zfmisc_1(B)) ) => ( ( ! [I] : ! [J] : ( ( r2_hidden(I,A) & r2_hidden(J,B) ) => k1_binop_1(E,I,J) = k1_extreal1(k12_supinf_2(C,k1_tarski(I)),k12_supinf_2(D,k1_tarski(J))) ) & ! [I] : ( ( v1_finset_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => k12_supinf_2(F,I) = k5_bhsp_5(k1_numbers,k2_zfmisc_1(A,B),k9_binop_2,I,E) ) ) => k12_supinf_2(F,k2_zfmisc_1(G,H)) = k1_extreal1(k12_supinf_2(C,G),k12_supinf_2(D,H)) ) ) ) ) ) ) ) ) ) )).
fof(l24_realset2,axiom,( k2_zfmisc_1(k6_subset_1(c4__realset2,k1_tarski(k10_subset_1(k5_numbers,2))),k6_subset_1(c4__realset2,k1_tarski(k10_subset_1(k5_numbers,2)))) = k1_tarski(k4_tarski(k10_subset_1(1,2),k10_subset_1(1,2))) )).
fof(l24_scmp_gcd,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmpds_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ( ( 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) = k5_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) = k5_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)),k5_numbers) | ( k5_memstr_0(2,k1_scmpds_2,k5_extpro_1(2,k1_scmpds_2,D,B,7)) = k1_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) = k1_nat_1(A,4) & k1_funct_1(k5_extpro_1(2,k1_scmpds_2,D,B,7),k2_scmp_gcd) = k5_numbers & k1_funct_1(k5_extpro_1(2,k1_scmpds_2,D,B,7),k1_scmp_gcd(k1_nat_1(A,7))) = k5_int_1(k1_funct_1(B,k1_scmp_gcd(k1_nat_1(A,2))),k1_funct_1(B,k1_scmp_gcd(k1_nat_1(A,3)))) & k1_funct_1(k5_extpro_1(2,k1_scmpds_2,D,B,7),k1_scmp_gcd(k1_nat_1(A,6))) = k1_funct_1(B,k1_scmp_gcd(k1_nat_1(A,3))) & k5_memstr_0(2,k1_scmpds_2,k5_extpro_1(2,k1_scmpds_2,E,C,7)) = k1_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) = k1_nat_1(A,4) & k1_funct_1(k5_extpro_1(2,k1_scmpds_2,E,C,7),k2_scmp_gcd) = k5_numbers & k1_funct_1(k5_extpro_1(2,k1_scmpds_2,E,C,7),k1_scmp_gcd(k1_nat_1(A,7))) = k5_int_1(k1_funct_1(B,k1_scmp_gcd(k1_nat_1(A,2))),k1_funct_1(B,k1_scmp_gcd(k1_nat_1(A,3)))) & k1_funct_1(k5_extpro_1(2,k1_scmpds_2,E,C,7),k1_scmp_gcd(k1_nat_1(A,6))) = k1_funct_1(B,k1_scmp_gcd(k1_nat_1(A,3))) & k1_funct_1(k5_extpro_1(2,k1_scmpds_2,D,B,7),k1_scmp_gcd(k1_nat_1(A,4))) = A & k1_funct_1(k5_extpro_1(2,k1_scmpds_2,D,B,7),k1_scmp_gcd(k1_nat_1(A,5))) = 11 & k1_funct_1(k5_extpro_1(2,k1_scmpds_2,E,C,7),k1_scmp_gcd(k1_nat_1(A,4))) = A & k1_funct_1(k5_extpro_1(2,k1_scmpds_2,E,C,7),k1_scmp_gcd(k1_nat_1(A,5))) = 11 ) ) ) ) ) ) ) ) )).
fof(l24_scmpds_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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) ) ) ) )).
fof(l24_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => r1_xxreal_0(k2_compos_0(k1_scmpds_i,A),14) ) )).
fof(l24_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( k1_funct_1(B,k2_scmp_gcd) = k5_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)),k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_numbers))))),B,A),k2_scmp_gcd) = k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_numbers))))),B,A),k1_scmp_gcd(7)) = k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_numbers))))),B,A),k1_scmp_gcd(4)) = k1_funct_1(B,k1_scmp_gcd(4)) & ! [E] : ( v7_ordinal1(E) => ( 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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_numbers))))),B,A),k1_scmp_gcd(E)) = k1_funct_1(B,k1_scmp_gcd(E)) ) ) & ? [E] : ( v7_ordinal1(E) & ? [F] : ( v7_ordinal1(F) & 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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_numbers))))),B,A),k1_scmp_gcd(3)) = F & k2_xcmplx_0(F,E) = C & r1_xxreal_0(E,k1_funct_1(B,k1_scmp_gcd(7))) & ! [G] : ( v7_ordinal1(G) => ~ ( 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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_numbers))))),B,A),k1_scmp_gcd(G))) ) ) & ( E = k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_numbers))))),B,A),k1_scmp_gcd(F))) ) ) ) ) ) ) ) ) ) ) )).
fof(l24_sin_cos9,axiom,( r2_hidden(k7_xcmplx_0(k28_sin_cos,4),k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))) )).
fof(l24_sincos10,axiom,( r1_tarski(k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos),k1_relset_1(k1_numbers,k1_fdiff_9)) )).
fof(l24_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => r1_tarski(k3_topreal1(2,k17_finseq_1(u1_struct_0(k15_euclid(2)),B,A)),k3_topreal1(2,A)) ) ) )).
fof(l24_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l24_topalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_topalg_2(A) & m1_pre_topc(A,k2_topalg_2) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( m1_subset_1(F,u1_struct_0(k5_topmetr)) => ( k1_binop_1(k3_topalg_2(A,D,E),F,k5_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] : ( m1_subset_1(G,u1_struct_0(k5_topmetr)) => ( k1_binop_1(k3_topalg_2(A,D,E),k5_numbers,G) = B & k1_binop_1(k3_topalg_2(A,D,E),1,G) = C ) ) ) ) ) ) ) ) ) )).
fof(l24_topalg_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(l24_topreal2,axiom,( r2_hidden(k19_euclid(1,k5_numbers),k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,k5_numbers),k19_euclid(1,k5_numbers))) )).
fof(l24_toprealb,axiom,( 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)))) )).
fof(l24_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(l24_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k2_xcmplx_0(A,B),C) => ( r1_xxreal_0(A,C) & r1_xxreal_0(B,C) ) ) ) ) ) )).
fof(l24_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(k3_xcmplx_0(A,B),k5_numbers) ) ) ) )).
fof(l24_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k4_xcmplx_0(B),k4_xcmplx_0(A)) => r1_xxreal_0(A,B) ) ) ) )).
fof(l24_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ~ ( ~ r2_hidden(A,k1_numbers) & A != k1_xxreal_0 & A != k2_xxreal_0 ) ) )).
fof(l24_zfmisc_1,axiom,( ! [A] : ! [B] : ( r2_hidden(A,B) => k3_xboole_0(B,k1_tarski(A)) = k1_tarski(A) ) )).
fof(l25_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(l25_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(l25_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ~ v2_extpro_1(k5_ami_3(A,B),k7_card_1(2),k1_ami_3) ) ) )).
fof(l25_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => k3_rlvect_1(A,k3_rlvect_1(A,k1_rlvect_1(A,B,k5_numbers),k1_rlvect_1(A,C,k3_xcmplx_0(E,F))),k1_rlvect_1(A,D,k3_xcmplx_0(k4_xcmplx_0(E),G))) = k1_rlvect_1(A,k5_algstr_0(A,k1_rlvect_1(A,C,F),k1_rlvect_1(A,D,G)),E) ) ) ) ) ) ) ) )).
fof(l25_arytm_2,axiom,( ! [A] : ~ ( r2_hidden(A,k1_arytm_2) & A != k11_arytm_3 & ! [B] : ( m1_subset_1(B,k5_arytm_3) => ~ ( r2_hidden(B,A) & B != k11_arytm_3 ) ) ) )).
fof(l25_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k2_xcmplx_0(k7_series_1(A,B,C),k9_nat_1(k1_numbers,A,k1_nat_1(B,1))) = k7_series_1(A,k1_nat_1(B,1),C) ) ) ) )).
fof(l25_bcialg_4,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(l25_binop_2,axiom,( r2_hidden(k5_numbers,k4_ordinal1) )).
fof(l25_borsuk_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v1_compts_1(B) & l1_pre_topc(B) ) => v1_compts_1(k2_borsuk_1(A,B)) ) ) )).
fof(l25_c0sp2,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(l25_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_cc0sp2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_cc0sp1(u1_struct_0(A)))) => ( B = C => k2_normsp_0(k5_cc0sp2(A),B) = k2_normsp_0(k7_cc0sp1(u1_struct_0(A)),C) ) ) ) ) )).
fof(l25_cfdiff_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k4_real_ns1(1))) => k9_complex1(k1_funct_1(k1_pdiff_1(1,1),A)) = k2_normsp_0(k4_real_ns1(1),A) ) )).
fof(l25_collsp,axiom,( m1_collsp(a_0_2_collsp,c7__collsp) )).
fof(l25_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( C = k3_xcmplx_0(A,B) => k3_complex1(C) = k5_real_1(k4_real_1(k3_complex1(A),k3_complex1(B)),k4_real_1(k4_complex1(A),k4_complex1(B))) ) ) ) ) )).
fof(l25_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( 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))) ) ) ) )).
fof(l25_csspace2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v2_comseq_2(C) & v2_comseq_2(B) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [E] : ( v7_ordinal1(E) => k1_funct_1(D,E) = k2_xcmplx_0(k3_xcmplx_0(k9_complex1(k6_xcmplx_0(k1_funct_1(C,E),A)),k9_complex1(k6_xcmplx_0(k1_funct_1(C,E),A))),k1_funct_1(B,E)) ) => ( v2_comseq_2(D) & k1_seq_2(D) = k2_xcmplx_0(k3_xcmplx_0(k9_complex1(k6_xcmplx_0(k3_comseq_2(C),A)),k9_complex1(k6_xcmplx_0(k3_comseq_2(C),A))),k1_seq_2(B)) ) ) ) ) ) ) ) )).
fof(l25_dist_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( ( v1_prob_2(B) & k9_xtuple_0(B) = k4_finseq_1(C) & A = k3_finseq_1(C) & ! [D] : ( 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) ) ) ) ) ) )).
fof(l25_dtconstr,axiom,( r1_tarski(k2_lang1(k5_dtconstr),k6_domain_1(u1_struct_0(k5_dtconstr),c3__dtconstr)) )).
fof(l25_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => k2_binop_1(u1_struct_0(k9_int_3(A)),k4_ordinal1,u1_struct_0(k9_int_3(A)),k4_group_1(k9_int_3(A)),B,1) = B ) ) )).
fof(l25_fdiff_2,axiom,( ! [A] : ( ( 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(k5_numbers)) = k8_relset_1(k1_numbers,k1_numbers,A,k1_tarski(k5_numbers)) ) )).
fof(l25_fib_num4,axiom,( ~ r1_xxreal_0(k3_square_1(5),k5_numbers) )).
fof(l25_fomodel1,axiom,( ? [A] : ( l1_fomodel1(A) & ~ v6_struct_0(A) & v11_fomodel1(A) ) )).
fof(l25_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( 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,k4_fomodel4(A,k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))),B))) ) ) )).
fof(l25_funct_9,axiom,( v1_funct_9(k18_sin_cos,k3_xcmplx_0(2,k28_sin_cos)) )).
fof(l25_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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] : ! [G] : ( ( r2_hidden(F,A) & r2_hidden(G,C) ) => k2_seq_4(k2_relset_1(k1_numbers,k2_fuzzy_4(C,B,A,k1_fuzzy_4(C,B,E),k1_fuzzy_4(B,A,D),G,F))) = k2_seq_4(k2_relset_1(k1_numbers,k2_fuzzy_4(A,B,C,D,E,F,G))) ) ) ) ) ) ) )).
fof(l25_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v1_algstr_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( 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 ) ) ) )).
fof(l25_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( r1_analmetr(A,E,F) => ( r3_analmetr(A,B,D,C,C,E,F) & r3_analmetr(A,C,C,B,D,E,F) ) ) ) ) ) ) ) ) )).
fof(l25_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v4_glib_002(B,A) & m1_glib_000(B,A) ) => k25_glib_000(A,B) = k21_glib_000(A,k24_glib_000(A,B)) ) ) )).
fof(l25_glib_003,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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))) ) ) ) )).
fof(l25_goboard7,axiom,( k6_xcmplx_0(1,k7_xcmplx_0(1,2)) = k7_xcmplx_0(1,2) )).
fof(l25_gr_cy_1,axiom,( ! [A] : ( v7_ordinal1(A) => k5_group_1(k2_gr_cy_1,A,k5_gr_cy_1(1)) = A ) )).
fof(l25_graph_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m2_graph_1(C,B) => m2_graph_1(k2_partfun1(k4_ordinal1,u4_struct_0(B),C,k2_finseq_1(A)),B) ) ) ) )).
fof(l25_group_9,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( m1_group_9(D,A,C) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(l25_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( 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] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l25_integra3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [C] : ( m1_integra1(C,A) => ( C = k7_finseq_1(k9_finseq_1(k3_seq_4(A)),B) => k3_integra1(k2_integra1(A,C,1)) = k5_numbers ) ) ) ) )).
fof(l25_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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(k9_complex1(k4_integra5(C,D,E)),k4_integra5(C,D,k56_valued_1(k1_numbers,k1_numbers,E))) ) ) ) ) ) ) ) )).
fof(l25_jgraph_3,axiom,( k22_euclid(2) != k4_struct_0(k15_euclid(2)) )).
fof(l25_jgraph_4,axiom,( k1_relset_1(u1_struct_0(k15_euclid(2)),k1_jgraph_4(2)) = u1_struct_0(k15_euclid(2)) )).
fof(l25_jgraph_6,axiom,( k12_euclid(k19_euclid(k4_xcmplx_0(1),k5_numbers)) = 1 & k12_euclid(k19_euclid(1,k5_numbers)) = 1 & k12_euclid(k19_euclid(k5_numbers,k4_xcmplx_0(1))) = 1 & k12_euclid(k19_euclid(k5_numbers,1)) = 1 )).
fof(l25_lattice7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(l25_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(l25_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_6(D,A,C) => ? [E] : ( 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 ) ) ) ) ) )).
fof(l25_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_finset_1(B) & v1_card_1(B) ) => ( r1_ordinal1(k4_topgen_1(A),B) => r1_ordinal1(k2_waybel23(A),B) ) ) ) )).
fof(l25_mod_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v1_mod_3(C,A,B) ) ) ) )).
fof(l25_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v3_modelc_1(A) => k1_funct_1(A,1) = k5_numbers ) ) )).
fof(l25_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v6_modelc_2(A) => k1_funct_1(A,1) = 3 ) ) )).
fof(l25_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l25_msualg_7,axiom,( v1_xreal_0(1) )).
fof(l25_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,A) <=> r1_xxreal_0(A,k6_xcmplx_0(B,1)) ) ) ) )).
fof(l25_ndiff_5,axiom,( v1_xreal_0(1) )).
fof(l25_normform,axiom,( ! [A] : v2_binop_1(k5_normform(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))) )).
fof(l25_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(B,k7_subset_1(k1_zfmisc_1(u1_struct_0(A)),k10_openlatt(A,D),k10_openlatt(A,C))) <=> ( r2_hidden(D,B) & ~ r2_hidden(C,B) ) ) ) ) ) ) )).
fof(l25_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( 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] : ( 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 ) ) ) ) ) ) )).
fof(l25_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => m1_subset_1(k9_qc_lang1(A),k1_zfmisc_1(k13_finseq_1(k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))))) ) )).
fof(l25_random_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( m2_prob_1(C,A,k1_random_1(A)) => ! [D] : ( m2_prob_1(D,B,k1_random_1(B)) => ! [E] : ( ( 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] : ( ( 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] : ! [H] : ( ( r2_hidden(G,A) & r2_hidden(H,B) ) => k1_binop_1(E,G,H) = k1_extreal1(k12_supinf_2(C,k1_tarski(G)),k12_supinf_2(D,k1_tarski(H))) ) & ! [G] : ( ( v1_finset_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => k12_supinf_2(F,G) = k5_bhsp_5(k1_numbers,k2_zfmisc_1(A,B),k9_binop_2,G,E) ) ) => k12_supinf_2(F,k2_zfmisc_1(A,B)) = 1 ) ) ) ) ) ) ) )).
fof(l25_realset2,axiom,( ! [A] : ( r2_hidden(A,k2_zfmisc_1(k6_subset_1(c4__realset2,k1_tarski(k10_subset_1(k5_numbers,2))),k6_subset_1(c4__realset2,k1_tarski(k10_subset_1(k5_numbers,2))))) => r2_hidden(k1_funct_1(k2_realset2,A),k6_subset_1(c4__realset2,k1_tarski(k10_subset_1(k5_numbers,2)))) ) )).
fof(l25_rfinseq2,axiom,( ! [A] : ( ( v1_integra2(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( ( v1_integra2(B) & m2_finseq_1(B,k1_numbers) ) => ! [C] : ( v7_ordinal1(C) => ( ( k3_finseq_1(A) = k1_nat_1(C,1) & k3_finseq_1(A) = k3_finseq_1(B) & r2_classes1(A,B) ) => ( k1_funct_1(A,k3_finseq_1(A)) = k1_funct_1(B,k3_finseq_1(B)) & r2_classes1(k17_finseq_1(k1_numbers,C,A),k17_finseq_1(k1_numbers,C,B)) ) ) ) ) ) )).
fof(l25_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( m1_rlsub_1(D,A) => ( m1_rlsub_1(B,D) => m1_rlsub_1(k2_rlsub_2(A,B,C),D) ) ) ) ) ) )).
fof(l25_scmp_gcd,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmpds_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ( ( 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) = k5_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) = k5_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)),k5_numbers) | ! [F] : ( v7_ordinal1(F) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l25_scmpds_4,axiom,( v2_scmpds_4(k9_compos_1(k1_scmpds_2,k2_compos_1(k1_scmpds_2))) )).
fof(l25_scmpds_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) & v2_scmpds_4(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v2_scmpds_4(D) & v3_scmpds_4(D) ) => ! [E] : ( ( 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,k5_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_xcmplx_0(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)))) ) ) ) ) ) ) ) )).
fof(l25_scmpds_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k9_complex1(B),A),A),1) = k4_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k9_complex1(B),A),B)) ) ) ) )).
fof(l25_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => ( k2_compos_0(k1_scmpds_i,A) = k5_numbers => k5_xtuple_0(A) = k1_xboole_0 ) ) )).
fof(l25_scmyciel,axiom,( ! [A] : ( v7_ordinal1(A) => v3_scmyciel(k1_tarski(k1_xboole_0),A) ) )).
fof(l25_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( v7_ordinal1(C) => ( ( k1_funct_1(B,k2_scmp_gcd) = k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_numbers))))),B,A) ) ) ) ) ) )).
fof(l25_sin_cos9,axiom,( r2_hidden(k7_xcmplx_0(k28_sin_cos,4),k2_rcomp_1(k5_numbers,k28_sin_cos)) )).
fof(l25_sincos10,axiom,( r1_tarski(k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,4)),k3_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) )).
fof(l25_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l25_square_1,axiom,( k1_square_1(2) = k3_xcmplx_0(2,2) )).
fof(l25_topdim_2,axiom,( g1_pre_topc(u1_struct_0(k15_euclid(1)),u1_pre_topc(k15_euclid(1))) = k3_pcomps_1(k14_euclid(1)) )).
fof(l25_topreal2,axiom,( r2_hidden(k19_euclid(1,k5_numbers),k1_rltopsp1(k15_euclid(2),k19_euclid(1,k5_numbers),k19_euclid(1,1))) )).
fof(l25_toprealb,axiom,( v1_funct_1(k18_sin_cos) & v1_funct_2(k18_sin_cos,u1_struct_0(k2_topalg_2),u1_struct_0(k2_topalg_2)) & m1_subset_1(k18_sin_cos,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_topalg_2),u1_struct_0(k2_topalg_2)))) )).
fof(l25_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(l25_waybel30,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(l25_waybel31,axiom,( ! [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] : ( ( v2_pre_topc(B) & v2_waybel19(B) & m1_yellow_9(B,A) ) => r1_ordinal1(k2_waybel23(B),k1_waybel31(A)) ) ) )).
fof(l25_waybel_7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(l25_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) = k5_xcmplx_0(k3_xcmplx_0(A,B)) ) ) )).
fof(l25_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k5_numbers,k3_xcmplx_0(A,B)) ) ) ) )).
fof(l25_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(B)) & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & E = C & F = D & ? [G] : ( m1_subset_1(G,k1_altcat_1(A,C,D)) & ? [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l26_algstr_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k8_algstr_0)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k8_algstr_0)) => ! [C] : ( 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)) ) ) ) )).
fof(l26_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ~ v2_extpro_1(k6_ami_3(A,B),k7_card_1(2),k1_ami_3) ) ) )).
fof(l26_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ~ r2_anproj_1(A,B,C,D) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(G,u1_struct_0(A)) => r2_anproj_1(A,E,F,G) ) ) ) ) ) ) ) ) ) )).
fof(l26_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( r1_arytm_2(B,C) => k1_arytm_1(A,k1_arytm_1(C,B)) = k1_arytm_1(k7_arytm_2(A,B),C) ) ) ) ) )).
fof(l26_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( ( r2_hidden(C,k1_arytm_2) & r2_hidden(A,C) & r3_arytm_3(B,A) ) => r2_hidden(B,C) ) ) ) )).
fof(l26_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(k1_nat_1(C,1),D) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(k1_nat_1(C,1),E) & r1_xxreal_0(E,D) ) => r1_xxreal_0(k9_nat_1(k1_numbers,A,E),k9_nat_1(k1_numbers,B,E)) ) ) ) => r1_xxreal_0(k7_series_1(A,D,C),k7_series_1(B,D,C)) ) ) ) ) ) )).
fof(l26_binop_2,axiom,( m1_subset_1(k5_numbers,k2_numbers) )).
fof(l26_borsuk_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_pre_topc(C,A) => m1_pre_topc(k2_borsuk_1(C,B),k2_borsuk_1(A,B)) ) ) ) )).
fof(l26_c0sp2,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(l26_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_cc0sp1(A))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(l26_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_cc0sp2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_cc0sp2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_cc0sp1(u1_struct_0(A)))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l26_classes2,axiom,( ! [A] : ( ( v2_classes1(A) & r2_hidden(k5_numbers,k2_ordinal1(A)) ) => ( r2_hidden(k1_card_1(k4_classes1(k5_numbers)),k1_card_1(A)) & r2_hidden(k4_classes1(k5_numbers),A) ) ) )).
fof(l26_collsp,axiom,( ~ v2_struct_0(g1_collsp(c7__collsp,c8__collsp)) & l1_collsp(g1_collsp(c7__collsp,c8__collsp)) )).
fof(l26_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( C = k3_xcmplx_0(A,B) => k4_complex1(C) = k3_real_1(k4_real_1(k3_complex1(A),k4_complex1(B)),k4_real_1(k4_complex1(A),k3_complex1(B))) ) ) ) ) )).
fof(l26_convfun1,axiom,( ! [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) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k6_numbers))) ) => ! [C] : ( ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ! [E] : ( m2_finseq_1(E,k6_numbers) => ! [F] : ( m2_finseq_1(F,u1_struct_0(A)) => ~ ( k3_finseq_1(E) = C & ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => k12_supinf_2(B,G) != k2_supinf_1 ) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( r2_hidden(G,k2_finseq_1(C)) => ( r1_xxreal_0(k5_numbers,k12_supinf_2(D,G)) & k12_supinf_2(E,G) = k1_extreal1(k12_supinf_2(D,G),k12_supinf_2(B,k7_partfun1(u1_struct_0(A),F,G))) ) ) ) & r2_hidden(k2_supinf_1,k2_relset_1(k6_numbers,E)) ) ) ) ) ) ) ) )).
fof(l26_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(l26_dtconstr,axiom,( k2_lang1(k5_dtconstr) = k6_domain_1(u1_struct_0(k5_dtconstr),c3__dtconstr) )).
fof(l26_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => k2_binop_1(u1_struct_0(k9_int_3(A)),k4_ordinal1,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) ) ) )).
fof(l26_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( 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) ) ) ) )).
fof(l26_fib_num,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k9_complex1(B),1) => r1_xxreal_0(k9_complex1(k1_newton(B,A)),1) ) ) ) )).
fof(l26_fib_num4,axiom,( ~ r1_xxreal_0(k2_xcmplx_0(k3_square_1(5),3),k2_xcmplx_0(k4_xcmplx_0(k3_square_1(5)),3)) )).
fof(l26_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( A = k1_xboole_0 <=> k3_finseq_1(A) = k5_numbers ) ) )).
fof(l26_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m2_finseq_1(C,A) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(k2_xcmplx_0(D,1),k3_finseq_1(C)) => r2_hidden(k1_funct_1(k4_fomodel0(A,B,C),D),A) ) & ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(k2_xcmplx_0(D,1),E) => k1_funct_1(k4_fomodel0(A,B,k17_finseq_1(A,E,C)),D) = k1_funct_1(k4_fomodel0(A,B,C),D) ) ) ) ) ) ) ) )).
fof(l26_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & l1_fomodel1(A) ) => r2_hidden(k7_fomodel1(A),k6_subset_1(k15_fomodel1(A),k1_tarski(k8_fomodel1(A)))) ) )).
fof(l26_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( 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(B,k1_funct_1(D,A)) => v5_fomodel4(B,1,C,k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C))),D),A) ) ) ) )).
fof(l26_fscirc_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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) ) ) ) ) ) ) )).
fof(l26_funct_9,axiom,( ! [A] : ( v7_ordinal1(A) => v1_funct_9(k16_sin_cos,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k2_xcmplx_0(A,1))) ) )).
fof(l26_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ( r1_analmetr(A,H,I) => ( ( ~ r1_geomtrap(A,C,F,B,E) & ~ r1_geomtrap(A,B,E,C,F) ) | ( ~ r3_analmetr(A,D,G,B,E,H,I) & ~ r3_analmetr(A,B,E,D,G,H,I) ) | B = E | ( r3_analmetr(A,C,F,D,G,H,I) & r3_analmetr(A,D,G,C,F,H,I) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l26_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ( k7_glib_000(A) = k1_xboole_0 => v7_glib_000(A) ) ) )).
fof(l26_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v4_glib_002(B,A) & m1_glib_000(B,A) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(l26_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v1_graph_1(B) & m3_graph_1(B,A) ) => ! [C] : ( ( 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 ) ) ) ) )).
fof(l26_graph_2,axiom,( v1_graph_2(k2_finseq_4(k4_ordinal1,1,2)) )).
fof(l26_group_10,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => k7_group_1(k4_gr_cy_1(A)) = A ) )).
fof(l26_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => v6_hilbert1(k5_hilbert1(A)) ) )).
fof(l26_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_aff_1(A,B,C,D) => ( r2_hidden(B,D) | ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ~ ( r2_hidden(E,D) & E = F ) & ~ ( ~ r2_hidden(E,D) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l26_ideal_1,axiom,( ! [A] : ( ( ~ 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] : ( 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))) ) ) ) )).
fof(l26_int_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k8_newton) & v1_funct_1(B) & v1_partfun1(B,k8_newton) & v4_valued_0(B) & v2_pre_poly(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k8_newton) & v1_funct_1(C) & v1_partfun1(C,k8_newton) & v4_valued_0(C) & v2_pre_poly(C) ) => ( ( v1_int_7(B) & v1_int_7(C) & r1_xxreal_0(k8_nat_3(k8_newton,B),k11_newton(2,A)) & k8_nat_3(k8_newton,B) = k8_nat_3(k8_newton,C) ) => r8_pboole(k8_newton,B,C) ) ) ) ) )).
fof(l26_integra3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [C] : ( m1_integra1(C,A) => ( C = k7_finseq_1(k9_finseq_1(k3_seq_4(A)),B) => k1_integra3(A,C) = k1_integra3(A,B) ) ) ) ) )).
fof(l26_integra8,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l26_jgraph_3,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(l26_jgraph_4,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(l26_jgraph_6,axiom,( r2_hidden(k5_numbers,k1_rcomp_1(k5_numbers,1)) )).
fof(l26_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l26_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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,D,B),B),E),k8_cqc_lang(A,k8_cqc_lang(A,k8_cqc_lang(A,B,C),D),E)),k4_cqc_the1(A)) ) ) ) ) ) )).
fof(l26_matrtop3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(C,D) ) => ( r1_xxreal_0(C,B) | k1_matrix_6(D,k2_vectsp_1,k2_matrtop3(D,A,B,C)) = k2_matrtop3(D,k4_xcmplx_0(A),B,C) ) ) ) ) ) ) )).
fof(l26_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( A != k1_xboole_0 & B != k1_xboole_0 & C != k1_xboole_0 & ? [D] : ( m1_subset_1(D,k3_zfmisc_1(A,B,C)) & ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,B) => ! [G] : ( m1_subset_1(G,C) => D != k3_xtuple_0(E,F,G) ) ) ) ) ) )).
fof(l26_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v4_modelc_1(A) => k1_funct_1(A,1) = 1 ) ) )).
fof(l26_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v7_modelc_2(A) => k1_funct_1(A,1) = 4 ) ) )).
fof(l26_msafree4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(k3_finseq_1(A),B) => r2_hidden(k2_xcmplx_0(B,1),k4_finseq_1(A)) ) ) ) )).
fof(l26_msualg_7,axiom,( v1_xreal_0(k7_xcmplx_0(1,2)) )).
fof(l26_nat_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ ( r2_hidden(A,k4_finseq_1(B)) & ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(l26_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ( ( r1_nattra_1(A,B,C,D) & r1_nattra_1(A,B,D,E) ) => ! [F] : ( m1_nattra_1(F,A,B,C,D) => ( ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( k2_cat_1(A,G,H) != k1_xboole_0 => ! [I] : ( m1_cat_1(I,A,G,H) => k5_cat_1(B,k8_cat_1(A,B,C,G),k8_cat_1(A,B,C,H),k8_cat_1(A,B,D,H),k9_cat_3(A,G,H,B,C,I),k2_nattra_1(A,B,C,D,F,H)) = k5_cat_1(B,k8_cat_1(A,B,C,G),k8_cat_1(A,B,D,G),k8_cat_1(A,B,D,H),k2_nattra_1(A,B,C,D,F,G),k9_cat_3(A,G,H,B,D,I)) ) ) ) ) => ! [G] : ( m1_nattra_1(G,A,B,D,E) => ( ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ( k2_cat_1(A,H,I) != k1_xboole_0 => ! [J] : ( m1_cat_1(J,A,H,I) => k5_cat_1(B,k8_cat_1(A,B,D,H),k8_cat_1(A,B,D,I),k8_cat_1(A,B,E,I),k9_cat_3(A,H,I,B,D,J),k2_nattra_1(A,B,D,E,G,I)) = k5_cat_1(B,k8_cat_1(A,B,D,H),k8_cat_1(A,B,E,H),k8_cat_1(A,B,E,I),k2_nattra_1(A,B,D,E,G,H),k9_cat_3(A,H,I,B,E,J)) ) ) ) ) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ( k2_cat_1(A,H,I) != k1_xboole_0 => ! [J] : ( m1_cat_1(J,A,H,I) => k5_cat_1(B,k8_cat_1(A,B,C,H),k8_cat_1(A,B,C,I),k8_cat_1(A,B,E,I),k9_cat_3(A,H,I,B,C,J),k2_nattra_1(A,B,C,E,k3_nattra_1(A,B,C,D,E,F,G),I)) = k5_cat_1(B,k8_cat_1(A,B,C,H),k8_cat_1(A,B,E,H),k8_cat_1(A,B,E,I),k2_nattra_1(A,B,C,E,k3_nattra_1(A,B,C,D,E,F,G),H),k9_cat_3(A,H,I,B,E,J)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l26_numbers,axiom,( r1_tarski(k4_numbers,k3_numbers) )).
fof(l26_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(l26_polynom2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(D,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [E] : ( ( 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] : ( ( 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(k15_pre_poly(A),B,C) = k1_tarski(E) & k3_polynom1(k15_pre_poly(A),B,D) = k1_tarski(F) ) => ! [G] : ( ( 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)))) ) => k2_polynom2(A,B,k11_polynom1(A,B,C,D),G) = k8_group_1(B,k2_polynom2(A,B,C,G),k2_polynom2(A,B,D,G)) ) ) ) ) ) ) ) ) )).
fof(l26_polynom4,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( ~ r1_xxreal_0(k1_algseq_1(A,B),k5_numbers) & ~ r1_xxreal_0(k1_algseq_1(A,C),k5_numbers) & ~ ! [D] : ( 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),k4_ordinal1,u1_struct_0(A),k4_group_1(A),D,k7_nat_d(k1_nat_1(k1_algseq_1(A,B),k1_algseq_1(A,C)),2))) ) ) ) ) ) )).
fof(l26_polynom8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k2_binom(A,k5_struct_0(A),B) = k5_struct_0(A) ) ) )).
fof(l26_prvect_3,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( 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)) ) ) )).
fof(l26_random_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( m2_prob_1(C,A,k1_random_1(A)) => ! [D] : ( m2_prob_1(D,B,k1_random_1(B)) => ! [E] : ( ( 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] : ( ( 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] : ! [H] : ( ( r2_hidden(G,A) & r2_hidden(H,B) ) => k1_binop_1(E,G,H) = k1_extreal1(k12_supinf_2(C,k1_tarski(G)),k12_supinf_2(D,k1_tarski(H))) ) & ! [G] : ( ( v1_finset_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => k12_supinf_2(F,G) = k5_bhsp_5(k1_numbers,k2_zfmisc_1(A,B),k9_binop_2,G,E) ) ) => ! [G] : ( r1_tarski(G,k2_zfmisc_1(A,B)) => ( r1_xxreal_0(k5_numbers,k12_supinf_2(F,G)) & r1_xxreal_0(k12_supinf_2(F,G),1) ) ) ) ) ) ) ) ) ) )).
fof(l26_realset2,axiom,( m2_subset_1(k10_subset_1(1,2),c4__realset2,k6_subset_1(c4__realset2,k6_domain_1(c4__realset2,c5__realset2))) )).
fof(l26_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l26_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) & v2_compos_1(B,k1_scmpds_2) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [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_partfun1(D,u1_struct_0(k1_scmpds_2)) & v5_memstr_0(D,2,k1_scmpds_2,k5_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(k1_nat_1(k5_card_1(C),1))),C))),D,k1_nat_1(k8_extpro_1(2,k1_scmpds_2,k1_funct_4(A,k10_compos_1(k1_scmpds_2,B)),D),1))) = k1_nat_1(k1_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(k1_nat_1(k5_card_1(C),1))),C))),D,k1_nat_1(k8_extpro_1(2,k1_scmpds_2,k1_funct_4(A,k10_compos_1(k1_scmpds_2,B)),D),1))) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( 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(k1_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(k1_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(k1_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(k1_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(k1_nat_1(k5_card_1(C),1))),C))),D) = k1_nat_1(k8_extpro_1(2,k1_scmpds_2,k1_funct_4(A,k10_compos_1(k1_scmpds_2,B)),D),1) ) ) ) ) ) ) )).
fof(l26_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v2_compos_1(D,k1_scmpds_2) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(E) & v1_funct_1(E) & v1_finset_1(E) & v1_afinsq_1(E) & v3_scmpds_4(E) ) => ! [F] : ( ( 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,k5_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) & C = k1_funct_4(A,k10_compos_1(k1_scmpds_2,k1_scmpds_4(D,E))) & B = 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,C,F,k8_extpro_1(2,k1_scmpds_2,B,F))) = k5_card_1(D) & k6_memstr_0(2,k1_scmpds_2,k5_extpro_1(2,k1_scmpds_2,C,F,k8_extpro_1(2,k1_scmpds_2,B,F))) = k6_memstr_0(2,k1_scmpds_2,k8_memstr_0(2,k1_scmpds_2,k5_extpro_1(2,k1_scmpds_2,B,F,k8_extpro_1(2,k1_scmpds_2,B,F)))) & r1_tarski(k61_valued_1(k10_compos_1(k1_scmpds_2,E),k5_card_1(D)),C) & k8_extpro_1(2,k1_scmpds_2,C,F) = k2_xcmplx_0(k8_extpro_1(2,k1_scmpds_2,B,F),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,k6_extpro_1(2,k1_scmpds_2,B,F)))) ) ) ) ) ) ) ) ) )).
fof(l26_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => ( k2_compos_0(k1_scmpds_i,A) = 14 => k5_xtuple_0(A) = k1_xboole_0 ) ) )).
fof(l26_scpqsort,axiom,( 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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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 )).
fof(l26_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_xboole_0(k4_simplex0(A)) <=> v4_simplex0(A) ) ) )).
fof(l26_sin_cos3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k15_sin_cos(k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1))) = k3_xcmplx_0(k23_sin_cos(A),k2_xcmplx_0(k19_sin_cos(B),k3_xcmplx_0(k17_sin_cos(B),k7_complex1))) ) ) )).
fof(l26_sin_cos9,axiom,( r2_hidden(k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos),k2_rcomp_1(k5_numbers,k28_sin_cos)) )).
fof(l26_sincos10,axiom,( r1_tarski(k1_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos),k28_sin_cos),k4_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos)) )).
fof(l26_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l26_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_finseq_1(C,k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))) => m2_finseq_1(k7_finseq_1(k7_finseq_1(k12_finseq_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,3,k5_numbers)),k12_finseq_1(k3_qc_lang1(A),B)),C),k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))) ) ) ) )).
fof(l26_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_topgen_2(A) & l1_pre_topc(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)))) ) => ? [C] : ( 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) ) ) ) )).
fof(l26_topreal2,axiom,( r2_hidden(k19_euclid(1,1),k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,1),k19_euclid(1,1))) )).
fof(l26_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ( C = a_3_4_topreal9(A,B,D) => v1_convex1(C,k15_euclid(A)) ) ) ) ) ) )).
fof(l26_toprealb,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & v1_xreal_0(A) ) => ! [B] : ( 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)))) ) ) ) )).
fof(l26_valued_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_membered(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_membered(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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 ) ) ) ) )).
fof(l26_waybel12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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))) ) ) )).
fof(l26_waybel13,axiom,( ! [A] : ( ( 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] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v4_yellow_0(C,k2_yellow_1(B)) & m1_yellow_0(C,k2_yellow_1(B)) ) => ~ ( v7_yellow_0(C,k2_yellow_1(B)) & v4_waybel_0(C,k2_yellow_1(B)) & r5_waybel_1(A,C) ) ) ) ) ) )).
fof(l26_waybel14,axiom,( ! [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] : ( ( v2_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k1_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,k1_yellow_1(k5_waybel11(A))) ) ) ) ) ) )).
fof(l26_wsierp_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( ~ r1_xxreal_0(B,A) <=> r1_xxreal_0(A,k6_xcmplx_0(B,1)) ) ) ) )).
fof(l26_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k7_xcmplx_0(A,k7_xcmplx_0(B,C)) = k7_xcmplx_0(k3_xcmplx_0(A,C),B) ) ) ) )).
fof(l26_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => r1_xxreal_0(k4_xcmplx_0(B),k4_xcmplx_0(A)) ) ) ) )).
fof(l26_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( r1_xxreal_0(B,A) => m2_xxreal_2(B,k2_tarski(A,B)) ) ) ) )).
fof(l26_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( C = a_2_0_yellow13(A,B) => m1_yellow13(C,A,B) ) ) ) )).
fof(l26_zfmisc_1,axiom,( ! [A] : ! [B] : ( k4_xboole_0(k1_tarski(A),B) = k1_tarski(A) <=> ~ r2_hidden(A,B) ) )).
fof(l27_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_1(B,A) & r1_tarski(D,k1_aff_4(A,B,C)) ) => r1_tarski(k1_aff_4(A,B,D),k1_aff_4(A,B,C)) ) ) ) ) ) )).
fof(l27_algstr_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k6_algstr_0(A,D,k5_struct_0(A)) = D ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & k6_algstr_0(A,D,E) = k5_struct_0(A) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) )).
fof(l27_ami_3,axiom,( ! [A] : ( v7_ordinal1(A) => ~ v2_extpro_1(k7_ami_3(A),k7_card_1(2),k1_ami_3) ) )).
fof(l27_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( ( r1_arytm_2(C,A) & r1_arytm_2(B,C) ) => k1_arytm_1(A,k1_arytm_1(C,B)) = k7_arytm_2(k1_arytm_1(A,C),B) ) ) ) ) )).
fof(l27_arytm_2,axiom,( ! [A] : ( r2_hidden(A,k1_arytm_2) => ( A = k11_arytm_3 | r2_hidden(k11_arytm_3,A) ) ) )).
fof(l27_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v4_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v4_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) => ( r1_xxreal_0(k1_seq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)),k5_numbers) | r2_hidden(A,k6_asympt_0(B)) ) ) ) ) )).
fof(l27_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => r1_xxreal_0(k2_int_1(k7_xcmplx_0(A,2)),A) ) )).
fof(l27_bcialg_6,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(D,k5_numbers) & k1_bcialg_1(A,k3_bcialg_6(A,C,B),k3_bcialg_6(A,D,B)) != k3_bcialg_6(A,k6_xcmplx_0(C,D),B) ) ) ) ) ) )).
fof(l27_binop_2,axiom,( r3_binop_1(k2_numbers,c1__binop_2,k3_binop_2) )).
fof(l27_borsuk_7,axiom,( r1_zfmisc_1(1,2,3) )).
fof(l27_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_cc0sp2(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l27_cfdiff_2,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l27_classes2,axiom,( ! [A] : ( v3_ordinal1(A) => ( ! [B] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(l27_collsp,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(c9__collsp)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c9__collsp)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(l27_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k2_xcmplx_0(A,B) = k5_arytm_0(k3_real_1(k3_complex1(A),k3_complex1(B)),k3_real_1(k4_complex1(A),k4_complex1(B))) ) ) )).
fof(l27_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( 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) & v4_conlat_1(B,A) ) ) ) )).
fof(l27_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(l27_dtconstr,axiom,( ~ 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)))) )).
fof(l27_fdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( r3_fdiff_3(A,C) & r3_fdiff_3(B,C) ) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k1_relset_1(k1_numbers,B)) & r2_hidden(E,k1_rcomp_1(C,k2_xcmplx_0(C,D))) & k1_funct_1(B,E) = k5_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)) = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k2_fdiff_3(C,A),k1_funct_1(B,C)),k3_xcmplx_0(k2_fdiff_3(C,B),k1_funct_1(A,C))),k1_square_1(k1_funct_1(B,C))) ) ) ) ) ) ) )).
fof(l27_fib_num,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ r1_xxreal_0(1,k9_complex1(k7_xcmplx_0(k2_power(k2_fib_num,A),k3_square_1(5)))) ) )).
fof(l27_fib_num4,axiom,( ~ r1_xxreal_0(k7_xcmplx_0(k2_xcmplx_0(k3_square_1(5),3),2),k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(k3_square_1(5)),3),2)) )).
fof(l27_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(l27_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_fomodel4(A))) => ! [D] : ~ ( v4_fomodel4(k1_tarski(D),A,B,C) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ v5_fomodel4(D,E,A,B,C) ) ) ) ) ) )).
fof(l27_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v4_glib_002(B,A) & m1_glib_000(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(l27_gr_cy_1,axiom,( 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))) )).
fof(l27_graph_2,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(k2_finseq_4(k4_ordinal1,1,2))) & k1_recdef_1(k2_finseq_4(k4_ordinal1,1,2),A) = k1_recdef_1(k2_finseq_4(k4_ordinal1,1,2),k1_nat_1(A,1)) ) ) )).
fof(l27_heyting1,axiom,( k5_finsub_1(k7_normform(k1_xboole_0)) = k2_tarski(k1_xboole_0,k1_tarski(k4_tarski(k1_xboole_0,k1_xboole_0))) )).
fof(l27_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => r1_tarski(k3_heyting3(A,B),k3_heyting3(k1_nat_1(A,1),B)) ) ) )).
fof(l27_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_aff_1(A,B,C,D) => ( r2_hidden(B,D) | ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ~ ( r2_hidden(F,D) & F = E ) & ~ ( ~ r2_hidden(F,D) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l27_hurwitz,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( ~ r1_xxreal_0(k1_algseq_1(A,B),k5_numbers) & k1_funct_1(B,k6_xcmplx_0(k1_algseq_1(A,B),1)) = k4_struct_0(A) ) ) ) )).
fof(l27_integr16,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k2_numbers))) ) => ! [B] : ( 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)) ) ) ) )).
fof(l27_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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(k9_complex1(k4_integra5(C,D,E)),k4_integra5(C,D,k56_valued_1(k1_numbers,k1_numbers,E))) ) ) ) ) ) ) ) )).
fof(l27_jgraph_3,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(l27_jgraph_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( 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] : ( 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] : ( 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) != k5_numbers ) ) ) ) )).
fof(l27_jgraph_6,axiom,( r2_hidden(1,k1_rcomp_1(k5_numbers,1)) )).
fof(l27_jordan5b,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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,k1_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)) ) ) ) ) ) )).
fof(l27_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( ( A = k1_relset_1(A,D) & ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,k1_relset_1(A,D)) => k5_numbers = k1_funct_1(D,E) ) ) ) => ( r2_mesfun6c(A,B,C,D) & k1_mesfun6c(A,B,C,D) = k5_numbers ) ) ) ) ) ) )).
fof(l27_lpspace1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_rfunct_3(C,B,k1_numbers,k3_rfunct_3(B,k1_numbers)) => ! [D] : ( m2_rfunct_3(D,B,k1_numbers,k3_rfunct_3(B,k1_numbers)) => k1_binop_1(k13_rfunct_3(B),k1_binop_1(k4_lpspace1(B),A,C),k1_binop_1(k4_lpspace1(B),A,D)) = k1_binop_1(k4_lpspace1(B),A,k2_lpspace1(B,k1_numbers,k13_rfunct_3(B),C,D)) ) ) ) ) )).
fof(l27_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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,C,D),B),k8_cqc_lang(A,k8_cqc_lang(A,C,B),B)),k4_cqc_the1(A)) ) ) ) ) )).
fof(l27_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( 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))) ) ) ) )).
fof(l27_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v5_modelc_1(A) => k1_funct_1(A,1) = 2 ) ) )).
fof(l27_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v8_modelc_2(A) => k1_funct_1(A,1) = 5 ) ) )).
fof(l27_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v5_group_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_algstr_0(A,B,C) = k6_algstr_0(A,C,B) ) ) ) ) )).
fof(l27_nat_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( ~ r1_xxreal_0(A,1) & ~ r1_xxreal_0(5,A) & v1_int_2(A) & A != 2 & A != 3 ) ) )).
fof(l27_nat_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(l27_nat_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k10_nat_lat)) => ! [B] : ( 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] : ( m1_subset_1(A,u1_struct_0(k10_nat_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k10_nat_lat)) => ! [C] : ( 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) ) ) ) )).
fof(l27_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_o_ring_1(B,A) => v9_o_ring_1(B,A) ) ) ) )).
fof(l27_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(l27_ordeq_01,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(k5_ordeq_01(B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_ordeq_01(B,C))) => ( ( k2_normsp_0(k5_ordeq_01(B,C),D) = k5_numbers => D = k4_struct_0(k5_ordeq_01(B,C)) ) & ( D = k4_struct_0(k5_ordeq_01(B,C)) => k2_normsp_0(k5_ordeq_01(B,C),D) = k5_numbers ) & k2_normsp_0(k5_ordeq_01(B,C),k1_rlvect_1(k5_ordeq_01(B,C),D,A)) = k3_xcmplx_0(k9_complex1(A),k2_normsp_0(k5_ordeq_01(B,C),D)) & r1_xxreal_0(k2_normsp_0(k5_ordeq_01(B,C),k1_algstr_0(k5_ordeq_01(B,C),D,E)),k2_xcmplx_0(k2_normsp_0(k5_ordeq_01(B,C),D),k2_normsp_0(k5_ordeq_01(B,C),E))) ) ) ) ) ) ) )).
fof(l27_ordinal4,axiom,( ! [A] : ( v3_ordinal1(A) => ( v4_ordinal1(A) => ( A = k1_xboole_0 | ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_ordinal2(B) ) => ( ( k9_xtuple_0(B) = A & ! [C] : ( v3_ordinal1(C) => ( r2_hidden(C,A) => k1_funct_1(B,C) = k12_ordinal2(k1_xboole_0,C) ) ) ) => r1_ordinal2(k5_ordinal1,B) ) ) ) ) ) )).
fof(l27_polynom4,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(l27_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ 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)),k8_polynom1(A,B)) ) )).
fof(l27_polynom8,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( 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) ) ) ) ) )).
fof(l27_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) )).
fof(l27_quaterni,axiom,( k5_numbers = k6_quaterni(k5_numbers,k5_numbers,k5_numbers,k5_numbers) )).
fof(l27_real_3,axiom,( k1_relset_1(k4_ordinal1,k8_funcop_1(k4_ordinal1,k4_ordinal1,k5_numbers)) = k4_ordinal1 )).
fof(l27_realset2,axiom,( 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))) )).
fof(l27_rfinseq2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_integra2(B) & m2_finseq_1(B,k1_numbers) ) => ! [C] : ( ( v1_integra2(C) & m2_finseq_1(C,k1_numbers) ) => ( ( A = k3_finseq_1(B) & r2_classes1(B,C) ) => B = C ) ) ) ) )).
fof(l27_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( m1_rlsub_1(D,A) => ( m1_rlsub_1(B,C) => m1_rlsub_1(B,k1_rlsub_2(A,C,D)) ) ) ) ) ) )).
fof(l27_scm_comp,axiom,( ? [A] : ( v1_funct_1(A) & v1_funct_2(A,k4_dtconstr(k1_scm_comp),k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_dtconstr(k1_scm_comp),k4_ordinal1))) & k17_scm_comp(o_0_2_scm_comp) = k3_funct_2(k4_dtconstr(k1_scm_comp),k4_ordinal1,A,o_0_2_scm_comp) & ! [B] : ( m2_subset_1(B,u1_struct_0(k1_scm_comp),k6_dtconstr(k1_scm_comp)) => k3_funct_2(k4_dtconstr(k1_scm_comp),k4_ordinal1,A,k3_scm_comp(B)) = k16_scm_comp(B) ) & ! [B] : ( m2_subset_1(B,u1_struct_0(k1_scm_comp),k7_dtconstr(k1_scm_comp)) => ! [C] : ( m1_dtconstr(C,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [D] : ( m1_dtconstr(D,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k1_scm_comp)) => ! [F] : ( 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] : ( m1_subset_1(G,k4_ordinal1) => ! [H] : ( m1_subset_1(H,k4_ordinal1) => ( ( G = k3_funct_2(k4_dtconstr(k1_scm_comp),k4_ordinal1,A,C) & H = k3_funct_2(k4_dtconstr(k1_scm_comp),k4_ordinal1,A,D) ) => k3_funct_2(k4_dtconstr(k1_scm_comp),k4_ordinal1,A,k2_scm_comp(B,C,D)) = k5_nat_1(G,H) ) ) ) ) ) ) ) ) ) ) )).
fof(l27_scmp_gcd,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v7_ordinal1(F) => ( ( r1_tarski(k7_memstr_0(2,k1_scmpds_2,k5_numbers),C) & r1_tarski(k7_memstr_0(2,k1_scmpds_2,k5_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) ) ) ) ) ) ) ) ) )).
fof(l27_scmpds_8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ! [C] : ( v1_int_1(C) => r1_tarski(k61_valued_1(A,1),k2_scmpds_8(B,C,A)) ) ) ) )).
fof(l27_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => ( k2_compos_0(k1_scmpds_i,A) = 1 => k5_xtuple_0(A) = k1_xboole_0 ) ) )).
fof(l27_scpinvar,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ! [C] : ( v1_int_1(C) => r1_tarski(k61_valued_1(A,2),k4_scpinvar(B,C,A)) ) ) ) )).
fof(l27_scpqsort,axiom,( 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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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 )).
fof(l27_seqm_3,axiom,( v5_valued_0(k6_partfun1(k4_ordinal1)) & v4_valued_0(k6_partfun1(k4_ordinal1)) )).
fof(l27_simplex0,axiom,( ! [A] : ! [B] : ( l1_pre_topc(B) => ! [C] : ( 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)) ) ) ) )).
fof(l27_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( C != k5_numbers & B != k5_numbers & k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(C,D)),k2_xcmplx_0(k3_xcmplx_0(C,B),k3_xcmplx_0(A,D))) != k7_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,C),k7_xcmplx_0(D,B)),k2_xcmplx_0(1,k3_xcmplx_0(k7_xcmplx_0(A,C),k7_xcmplx_0(D,B)))) ) ) ) ) ) )).
fof(l27_sin_cos9,axiom,( k1_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k26_sin_cos,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)),k7_xcmplx_0(k28_sin_cos,4)))) = k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)),k7_xcmplx_0(k28_sin_cos,4)) )).
fof(l27_sincos10,axiom,( r1_tarski(k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers),k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers)) )).
fof(l27_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l27_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k1_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k1_substut1(A)) => r2_hidden(k4_tarski(k9_finseq_1(k4_tarski(B,C)),D),k2_zfmisc_1(k13_finseq_1(k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))),k1_substut1(A))) ) ) ) ) )).
fof(l27_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_borsuk_2(G,k2_borsuk_1(A,B),k4_borsuk_1(A,B,C,E),k4_borsuk_1(A,B,D,F)) => ! [H] : ( m1_borsuk_2(H,k2_borsuk_1(A,B),k4_borsuk_1(A,B,C,E),k4_borsuk_1(A,B,D,F)) => ! [I] : ( m1_borsuk_2(I,A,C,D) => ! [J] : ( m1_borsuk_2(J,A,C,D) => ! [K] : ( m1_borsuk_2(K,B,E,F) => ! [L] : ( m1_borsuk_2(L,B,E,F) => ! [M] : ( m1_borsuk_6(M,A,C,D,I,J) => ! [N] : ( 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] : ( 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,k5_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] : ( 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),k5_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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l27_topreal2,axiom,( r2_hidden(k19_euclid(1,1),k1_rltopsp1(k15_euclid(2),k19_euclid(1,k5_numbers),k19_euclid(1,1))) )).
fof(l27_topreal4,axiom,( k3_pcomps_1(k14_euclid(2)) = g1_pre_topc(u1_struct_0(k15_euclid(2)),u1_pre_topc(k15_euclid(2))) )).
fof(l27_topreal7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ? [C] : ( 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(k1_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(k1_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(k1_nat_1(A,B)))) & ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(l27_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ( C = a_3_5_topreal9(A,B,D) => v1_convex1(C,k15_euclid(A)) ) ) ) ) ) )).
fof(l27_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => m1_subset_1(u1_struct_0(B),k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(l27_vectsp_1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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)) ) ) ) )).
fof(l27_waybel_5,axiom,( ! [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) ) => ( v3_waybel_3(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) ) => ! [D] : ( m2_pboole(D,B,C,k7_funcop_1(B,u1_struct_0(A))) => ( ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(l27_waybel_7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(l27_wsierp_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( ~ r1_xxreal_0(k2_xcmplx_0(B,1),A) <=> r1_xxreal_0(A,B) ) ) ) )).
fof(l27_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( B != k5_numbers => k3_xcmplx_0(k7_xcmplx_0(A,B),B) = A ) ) ) )).
fof(l27_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k5_numbers,B) ) => r1_xxreal_0(k3_xcmplx_0(A,B),k5_numbers) ) ) ) )).
fof(l27_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k2_xcmplx_0(A,B),C) => r1_xxreal_0(A,k6_xcmplx_0(C,B)) ) ) ) ) )).
fof(l27_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( m2_xxreal_2(C,k2_tarski(A,B)) => r1_xxreal_0(C,B) ) ) ) )).
fof(l27_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_yellow13(C,A,B) => ( C = a_2_0_yellow13(A,B) => v1_yellow13(C,A,B) ) ) ) ) )).
fof(l27_yellow_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => v1_yellow_0(k1_yellow_1(u1_pre_topc(A))) ) )).
fof(l28_algstr_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_algstr_0(A,C,k5_struct_0(A)) = C ) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & k6_algstr_0(A,C,D) = k5_struct_0(A) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) )).
fof(l28_altcat_2,axiom,( ! [A] : ( ( v6_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( v6_altcat_1(B) & l2_altcat_1(B) ) => ( ( v1_xboole_0(u1_struct_0(A)) & v1_xboole_0(u1_struct_0(B)) ) => A = B ) ) ) )).
fof(l28_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( v7_ordinal1(B) => ~ v2_extpro_1(k8_ami_3(B,A),k7_card_1(2),k1_ami_3) ) ) )).
fof(l28_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ! [K] : ( v1_xreal_0(K) => ! [L] : ( v1_xreal_0(L) => ! [M] : ( v1_xreal_0(M) => 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,k2_xcmplx_0(k3_xcmplx_0(K,E),k3_xcmplx_0(M,I))),k1_rlvect_1(A,C,k2_xcmplx_0(k3_xcmplx_0(K,F),k3_xcmplx_0(L,G)))),k1_rlvect_1(A,D,k2_xcmplx_0(k3_xcmplx_0(L,H),k3_xcmplx_0(M,J)))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l28_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( ( r1_arytm_2(A,C) & r1_arytm_2(B,C) ) => k1_arytm_1(A,k1_arytm_1(C,B)) = k1_arytm_1(B,k1_arytm_1(C,A)) ) ) ) ) )).
fof(l28_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ~ ( 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] : ( m1_subset_1(C,k5_arytm_3) => ~ ( ~ r2_hidden(C,B) & ~ r3_arytm_3(A,C) ) ) ) ) )).
fof(l28_arytm_3,axiom,( k5_ordinal1 = k1_xboole_0 )).
fof(l28_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( k9_nat_1(k1_numbers,A,k5_numbers) = k5_numbers & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ~ r1_xxreal_0(D,k5_numbers) => k9_nat_1(k1_numbers,A,D) = B ) ) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k7_series_1(A,C,D) = k3_xcmplx_0(B,k6_xcmplx_0(C,D)) ) ) ) ) ) )).
fof(l28_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v10_bcialg_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_bcialg_1(A,C,B) => C = B ) ) ) ) ) )).
fof(l28_binop_2,axiom,( r3_binop_1(k1_numbers,k10_subset_1(k5_numbers,k1_numbers),k9_binop_2) )).
fof(l28_bspace,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k7_bspace(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_bspace(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_bspace(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l28_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_cc0sp2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_cc0sp2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_cc0sp1(u1_struct_0(A)))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l28_collsp,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(c9__collsp)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c9__collsp)) => ! [C] : ( m1_subset_1(C,u1_struct_0(c9__collsp)) => ! [D] : ( m1_subset_1(D,u1_struct_0(c9__collsp)) => ! [E] : ( m1_subset_1(E,u1_struct_0(c9__collsp)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(l28_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k3_xcmplx_0(A,B) = k5_arytm_0(k5_real_1(k4_real_1(k3_complex1(A),k3_complex1(B)),k4_real_1(k4_complex1(A),k4_complex1(B))),k3_real_1(k4_real_1(k3_complex1(A),k4_complex1(B)),k4_real_1(k3_complex1(B),k4_complex1(A)))) ) ) )).
fof(l28_csspace,axiom,( 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)) )).
fof(l28_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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))) ) ) ) ) ) ) )).
fof(l28_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k2_enumset1(A,B,C,D),k1_enumset1(E,F,G)) )).
fof(l28_euclmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l28_fib_num4,axiom,( ~ r1_xxreal_0(k1_square_1(k1_fib_num),k1_square_1(k2_fib_num)) )).
fof(l28_fomodel4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( 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(k5_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)),k4_fomodel4(C,D)),k1_tarski(B)))) ) ) ) ) )).
fof(l28_fscirc_2,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C)))) & ? [E] : ( m1_subset_1(E,k6_margrel1) & ? [F] : ( m1_subset_1(F,k6_margrel1) & ? [G] : ( 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) ) ) ) ) ) ) )).
fof(l28_funct_9,axiom,( ! [A] : ( v7_ordinal1(A) => v1_funct_9(k18_sin_cos,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k2_xcmplx_0(A,1))) ) )).
fof(l28_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v4_glib_002(B,A) & m1_glib_000(B,A) ) => ! [C] : ( ( v4_glib_002(C,A) & m1_glib_000(C,A) ) => ! [D] : ( ( r2_hidden(D,k24_glib_000(A,B)) & r2_hidden(D,k24_glib_000(A,C)) ) => r5_glib_000(B,C) ) ) ) ) )).
fof(l28_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(l28_graph_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(B,k1_nat_1(C,1)) & r1_xxreal_0(C,k3_finseq_1(A)) ) => ( k1_nat_1(k3_finseq_1(k1_graph_2(A,B,C)),B) = k1_nat_1(C,1) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ~ r1_xxreal_0(k3_finseq_1(k1_graph_2(A,B,C)),D) => k1_funct_1(k1_graph_2(A,B,C),k1_nat_1(D,1)) = k1_funct_1(A,k1_nat_1(B,D)) ) ) ) ) ) ) ) )).
fof(l28_graphsp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_funct_2(A,A)) => k9_xtuple_0(B) = A ) )).
fof(l28_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => r1_group_2(B,k3_group_6(A,k7_group_2(A),B),k7_group_2(B)) ) ) )).
fof(l28_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & v5_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k8_group_1(A,B,C) = k8_group_1(A,C,B) ) ) ) )).
fof(l28_int_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,k7_card_1(B)) => ( r1_xxreal_0(A,k5_numbers) | r2_hidden(k6_xcmplx_0(B,A),k7_card_1(B)) ) ) ) ) )).
fof(l28_integr15,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(l28_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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(k9_complex1(k4_integra5(D,C,E)),k4_integra5(C,D,k56_valued_1(k1_numbers,k1_numbers,E))) ) ) ) ) ) ) )).
fof(l28_jgraph_3,axiom,( k8_struct_0(k15_euclid(2)) != k1_xboole_0 )).
fof(l28_jordan5c,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v7_ordinal1(D) => ( ( v4_topreal1(A) & v4_pre_topc(B,k15_euclid(2)) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_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,k1_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,k1_nat_1(D,1))),C) ) ) ) ) ) ) )).
fof(l28_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l28_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( 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) ) ) )).
fof(l28_lp_space,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,A,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k1_series_1(k1_numbers,A,B),B)) ) ) )).
fof(l28_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k6_rusub_4(A,k3_mathmorp(A,B,C),C),B) ) ) ) )).
fof(l28_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => k2_wsierp_1(k11_matrixj1(A,k4_matrixj1(A,B))) = k1_matrix_0(B) ) ) )).
fof(l28_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( 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))) ) ) ) )).
fof(l28_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(2))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k15_euclid(2))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k15_euclid(2))) => ! [J] : ( v1_xreal_0(J) => ! [K] : ( v1_xreal_0(K) => ! [L] : ( v1_xreal_0(L) => ( ( D = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),B,k6_xcmplx_0(1,J)),k1_rlvect_1(k15_euclid(2),C,J)) & E = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),C,k6_xcmplx_0(1,K)),k1_rlvect_1(k15_euclid(2),A,K)) & F = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),A,k6_xcmplx_0(1,L)),k1_rlvect_1(k15_euclid(2),B,L)) & r1_euclid_6(A,D,I) & r1_euclid_6(B,E,I) & r1_euclid_6(B,E,G) & r1_euclid_6(C,F,G) & r1_euclid_6(A,D,H) & r1_euclid_6(C,F,H) ) => ( r1_euclid_6(A,B,C) | J = 1 | K = 1 | L = 1 | ( k3_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(J,k6_xcmplx_0(1,J)),k7_xcmplx_0(K,k6_xcmplx_0(1,K))),k7_xcmplx_0(L,k6_xcmplx_0(1,L))) = 1 <=> r1_euclid_6(G,H,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l28_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v6_modelc_1(A) => k1_funct_1(A,1) = 3 ) ) )).
fof(l28_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v2_modelc_2(A) => ( k1_funct_1(A,1) != k5_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 ) ) ) )).
fof(l28_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v3_group_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l28_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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) ) ) ) ) )).
fof(l28_nat_1,axiom,( k5_numbers = k1_xboole_0 )).
fof(l28_nat_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( ~ r1_xxreal_0(25,A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( ~ r1_xxreal_0(B,1) & r1_xxreal_0(k2_nat_1(B,B),A) & v1_int_2(B) & B != 2 & B != 3 ) ) ) ) )).
fof(l28_nat_5,axiom,( ! [A] : ( ( 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)))) ) ) ) )).
fof(l28_nat_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k10_nat_lat)) => ! [B] : ( 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] : ( m1_subset_1(A,u1_struct_0(k10_nat_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k10_nat_lat)) => k2_lattices(k10_nat_lat,A,B) = k2_lattices(k10_nat_lat,B,A) ) ) )).
fof(l28_normsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => m1_subset_1(k1_normsp_0(A,B,C),u1_struct_0(A)) ) ) ) )).
fof(l28_ntalgo_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => ! [B] : ( m1_subset_1(B,k4_numbers) => ! [C] : ( m1_subset_1(C,k4_numbers) => ~ ( A = k5_int_1(B,C) & C != k5_numbers & ! [D] : ( m1_subset_1(D,k4_numbers) => A != k2_xcmplx_0(B,k3_xcmplx_0(D,C)) ) ) ) ) ) )).
fof(l28_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(l28_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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(k5_ordeq_01(A,B)) & v3_normsp_0(k5_ordeq_01(A,B)) & v2_normsp_1(k5_ordeq_01(A,B)) ) ) ) )).
fof(l28_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v6_relat_2(A) => v6_relat_2(k2_relat_1(A)) ) ) )).
fof(l28_ordinal4,axiom,( ! [A] : ( v3_ordinal1(A) => ( A != k1_xboole_0 => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_ordinal2(B) ) => ( ( k9_xtuple_0(B) = A & ! [C] : ( v3_ordinal1(C) => ( r2_hidden(C,A) => k1_funct_1(B,C) = k12_ordinal2(1,C) ) ) ) => r1_ordinal2(1,B) ) ) ) ) )).
fof(l28_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(l28_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u2_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u2_incsp_1(A)) => ! [H] : ( m1_subset_1(H,u2_incsp_1(A)) => ! [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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l28_qc_lang4,axiom,( ! [A] : ! [B] : k4_finseq_1(k10_finseq_1(A,B)) = k2_finseq_1(2) )).
fof(l28_realset2,axiom,( 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))) )).
fof(l28_rfinseq,axiom,( ! [A] : ( ( v8_valued_0(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( ( v8_valued_0(B) & m2_finseq_1(B,k1_numbers) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( k3_finseq_1(A) = k1_nat_1(C,1) & k3_finseq_1(A) = k3_finseq_1(B) & r2_classes1(A,B) ) => ( k1_funct_1(A,k3_finseq_1(A)) = k1_funct_1(B,k3_finseq_1(B)) & r2_classes1(k17_finseq_1(k1_numbers,C,A),k17_finseq_1(k1_numbers,C,B)) ) ) ) ) ) )).
fof(l28_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( 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))) ) ) ) )).
fof(l28_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( m1_rlsub_1(D,A) => ( ( m1_rlsub_1(B,D) & m1_rlsub_1(C,D) ) => m1_rlsub_1(k1_rlsub_2(A,B,C),D) ) ) ) ) ) )).
fof(l28_rlvect_x,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( ( 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] : ( 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_funct_1(E,F)) ) ) ) => r2_hidden(k4_rlvect_1(A,D),k2_rlvect_x(A,B)) ) ) ) ) ) ) )).
fof(l28_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( 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))) ) ) ) )).
fof(l28_scmbsort,axiom,( k4_scmfsa_2(k5_numbers) != k4_scmfsa_2(2) )).
fof(l28_scmpds_i,axiom,( ! [A] : ( 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 ) ) )).
fof(l28_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ( v5_valued_0(A) <=> ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k9_nat_1(k4_ordinal1,A,k1_nat_1(B,1)),k9_nat_1(k4_ordinal1,A,B)) ) ) ) )).
fof(l28_sfmastr3,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & ~ v1_scmfsa_m(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & 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(k5_numbers)) = 1 => ( ( ~ r1_sfmastr3(E,B,C,D,F,A) & ~ v7_amistd_1(F,k7_card_1(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(k5_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(k5_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(k5_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(k5_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(k5_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(k5_numbers)))) ) ) ) ) ) ) ) ) ) )).
fof(l28_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) => r1_tarski(B,k4_simplex0(A)) ) ) ) )).
fof(l28_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k5_sin_cos2,k2_xcmplx_0(A,B)) = k7_xcmplx_0(k2_xcmplx_0(k1_funct_1(k5_sin_cos2,A),k1_funct_1(k5_sin_cos2,B)),k2_xcmplx_0(1,k3_xcmplx_0(k1_funct_1(k5_sin_cos2,A),k1_funct_1(k5_sin_cos2,B)))) ) ) )).
fof(l28_sin_cos9,axiom,( k1_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k27_sin_cos,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos)))) = k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos)) )).
fof(l28_sincos10,axiom,( r1_tarski(k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers),k1_relset_1(k1_numbers,k2_fdiff_9)) )).
fof(l28_sppol_1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => v1_finset_1(a_2_0_sppol_1(A,B)) ) ) )).
fof(l28_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => v2_topreal1(k2_finseq_4(u1_struct_0(k15_euclid(2)),A,B)) ) ) )).
fof(l28_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l28_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [D] : ( ( v3_card_1(D,B) & m2_finseq_1(D,k2_qc_lang1(A)) ) => ! [E] : ( 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(k4_ordinal1,k1_qc_lang1(A))),k1_substut1(A))) ) ) ) ) ) )).
fof(l28_taxonom1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v3_xxreal_0(C) & v1_xreal_0(C) ) => ! [D] : ( ( ~ v3_xxreal_0(D) & v1_xreal_0(D) ) => ( r1_xxreal_0(C,D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B,B),k1_numbers))) ) => ! [F] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(l28_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(l28_topdim_2,axiom,( v3_topdim_1(k15_euclid(k5_numbers)) & k4_topdim_1(k15_euclid(k5_numbers)) = k5_numbers )).
fof(l28_topreal2,axiom,( r2_hidden(k19_euclid(k5_numbers,k5_numbers),a_0_0_topreal2) )).
fof(l28_vectsp_1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( 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 ) ) ) ) ) ) ) ) )).
fof(l28_waybel13,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ~ ( ? [B] : ( ~ v1_xboole_0(B) & ? [C] : ( v4_yellow_0(C,k2_yellow_1(B)) & m1_yellow_0(C,k2_yellow_1(B)) & v7_yellow_0(C,k2_yellow_1(B)) & v4_waybel_0(C,k2_yellow_1(B)) & r5_waybel_1(A,C) ) ) & ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k2_yellow_1(B)),u1_struct_0(k2_yellow_1(B))) & v7_waybel_1(C,k2_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_yellow_1(B)),u1_struct_0(k2_yellow_1(B))))) ) => ~ ( v22_waybel_0(C,k2_yellow_1(B),k2_yellow_1(B)) & r5_waybel_1(A,k1_yellow_2(k2_yellow_1(B),k2_yellow_1(B),C)) ) ) ) ) ) )).
fof(l28_waybel17,axiom,( ! [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] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(l28_waybel31,axiom,( ! [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] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => r1_ordinal1(k1_waybel31(A),k2_waybel23(B)) ) ) )).
fof(l28_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ ( r2_hidden(A,k4_finseq_1(B)) & ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(l28_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(1,A) = k5_xcmplx_0(A) ) )).
fof(l28_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(A,k6_xcmplx_0(B,C)) => r1_xxreal_0(k2_xcmplx_0(A,C),B) ) ) ) ) )).
fof(l28_zfmisc_1,axiom,( ! [A] : ! [B] : ( k4_xboole_0(k1_tarski(A),B) = k1_xboole_0 <=> r2_hidden(A,B) ) )).
fof(l28_zmodul03,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( k3_xboole_0(k13_zmodul02(A,B,D),k13_zmodul02(A,B,C)) != k1_xboole_0 => k13_zmodul02(A,B,D) = k13_zmodul02(A,B,C) ) ) ) ) ) )).
fof(l29_algstr_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ( ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_algstr_0(A,B,k5_struct_0(A)) = B ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & k6_algstr_0(A,B,C) = k5_struct_0(A) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & k6_algstr_0(A,C,B) = k5_struct_0(A) ) ) ) ) )).
fof(l29_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( v7_ordinal1(B) => ~ v2_extpro_1(k9_ami_3(B,A),k7_card_1(2),k1_ami_3) ) ) )).
fof(l29_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( k1_rlvect_1(A,B,D) = C => ( D = k5_numbers | r1_anproj_1(A,B,C) ) ) ) ) ) ) )).
fof(l29_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ( r2_hidden(k3_arytm_2(A),a_0_1_arytm_2) => r2_hidden(A,k5_arytm_3) ) ) )).
fof(l29_bcialg_2,axiom,( ! [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) ) => v1_bcialg_2(k4_struct_0(A),A) ) )).
fof(l29_binari_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_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)) ) )).
fof(l29_binop_2,axiom,( m1_subset_1(k5_numbers,k3_numbers) )).
fof(l29_bspace,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k2_bspace)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_bspace)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_bspace(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k7_bspace(A))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(A)) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(l29_card_5,axiom,( 1 = k5_card_1(1) )).
fof(l29_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_clopban2(A))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(l29_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( 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)) ) ) ) ) )).
fof(l29_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_coh_sp(A)) => ! [C] : ( 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 ) ) ) )).
fof(l29_collsp,axiom,( ~ ! [A] : ( m1_subset_1(A,u1_struct_0(c9__collsp)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c9__collsp)) => ! [C] : ( m1_subset_1(C,u1_struct_0(c9__collsp)) => r1_collsp(c9__collsp,A,B,C) ) ) ) )).
fof(l29_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k3_complex1(k3_xcmplx_0(A,B)) = k5_real_1(k4_real_1(k3_complex1(A),k3_complex1(B)),k4_real_1(k4_complex1(A),k4_complex1(B))) & k4_complex1(k3_xcmplx_0(A,B)) = k3_real_1(k4_real_1(k3_complex1(A),k4_complex1(B)),k4_real_1(k3_complex1(B),k4_complex1(A))) ) ) ) )).
fof(l29_csspace,axiom,( 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))) )).
fof(l29_dist_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_margrel1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_margrel1(B) ) => ! [C] : ( r2_hidden(C,k3_xboole_0(k9_xtuple_0(A),k9_xtuple_0(B))) => ( k1_funct_1(k3_bvfunc_1(A,B),C) = k8_margrel1 <=> ( k1_funct_1(A,C) = k8_margrel1 | k1_funct_1(B,C) = k8_margrel1 ) ) ) ) ) )).
fof(l29_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(A,k6_jgraph_6(C,D,E)) & r2_hidden(B,k8_jgraph_6(C,D,E)) & ! [F] : ( 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))) ) ) ) ) ) ) ) )).
fof(l29_euclmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( 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,k3_xcmplx_0(F,E)),k1_rlvect_1(A,C,k4_xcmplx_0(k3_xcmplx_0(F,D))))) = k5_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,k3_xcmplx_0(F,E)),k1_rlvect_1(A,C,k4_xcmplx_0(k3_xcmplx_0(F,D)))),B,C) ) ) ) ) ) ) ) ) )).
fof(l29_fdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r3_fdiff_3(A,B) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,k1_relset_1(k1_numbers,A)) & r2_hidden(D,k1_rcomp_1(B,k2_xcmplx_0(B,C))) & k1_funct_1(A,D) = k5_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)) = k4_xcmplx_0(k7_xcmplx_0(k2_fdiff_3(B,A),k1_square_1(k1_funct_1(A,B)))) ) ) ) ) ) )).
fof(l29_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => k1_pre_ff(k1_nat_1(k2_nat_1(2,k1_nat_1(A,2)),1)) = k1_nat_1(k1_pre_ff(k1_nat_1(k3_xcmplx_0(2,A),3)),k1_pre_ff(k1_nat_1(k3_xcmplx_0(2,A),4))) ) )).
fof(l29_fib_num4,axiom,( ~ r1_xxreal_0(k3_square_1(k1_pepin(3)),k3_square_1(5)) )).
fof(l29_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & m2_finseq_1(C,A) ) => ! [D] : ( m1_subset_1(D,A) => ( k1_funct_1(k6_fomodel0(A,B),k12_finseq_1(A,D)) = D & k1_funct_1(k6_fomodel0(A,B),k1_monoid_0(A,C,k12_finseq_1(A,D))) = k1_binop_1(B,k1_funct_1(k6_fomodel0(A,B),C),D) ) ) ) ) ) )).
fof(l29_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( 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)),k15_fomodel2(C,D),k6_subset_1(k3_finseq_2(k1_fomodel1(C)),k1_tarski(k1_xboole_0))),k22_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)),k15_fomodel2(C,D),k6_subset_1(k3_finseq_2(k1_fomodel1(C)),k1_tarski(k1_xboole_0))),k22_fomodel2(C,k2_xcmplx_0(A,E),D))) & k1_funct_1(k22_fomodel2(C,A,D),B) = k1_funct_1(k22_fomodel2(C,k2_xcmplx_0(A,E),D),B) ) ) ) ) ) ) )).
fof(l29_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( 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)),k4_fomodel4(B,C)),k1_tarski(A))) = k3_tarski(a_3_5_fomodel4(A,B,C)) ) ) )).
fof(l29_fuzzy_2,axiom,( v1_xreal_0(1) )).
fof(l29_fuzzy_4,axiom,( r2_hidden(1,k1_numbers) & r2_hidden(k5_numbers,k1_numbers) )).
fof(l29_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ( v1_glib_002(A) <=> k4_glib_002(A) = 1 ) ) )).
fof(l29_graph_2,axiom,( v2_graph_2(k2_finseq_4(k4_ordinal1,1,2)) )).
fof(l29_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(l29_group_10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ~ ( A != k5_numbers & ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( A = k3_xcmplx_0(k1_newton(B,D),C) & ~ r1_nat_d(B,C) ) ) ) ) ) ) )).
fof(l29_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & v2_group_1(D) & v3_group_1(D) & v3_group_9(D,A) & l1_group_9(D,A) ) => ! [E] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) )).
fof(l29_hahnban,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ~ r2_hidden(C,u1_struct_0(B)) => ! [D] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( 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] : ( ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l29_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_substlat(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_substlat(A,B))) => ( r2_hidden(D,k6_heyting2(A,B,C)) => k3_lattices(k5_substlat(A,B),D,k3_funct_2(u1_struct_0(k5_substlat(A,B)),u1_struct_0(k5_substlat(A,B)),k7_heyting2(A,B,C),D)) = C ) ) ) ) )).
fof(l29_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ r1_xxreal_0(C,A) => r1_tarski(k3_heyting3(A,B),k2_heyting3(C,B)) ) ) ) ) )).
fof(l29_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A))) => ( ( r2_aff_1(A,B,C,J) & v7_aff_2(A) & r2_hidden(D,J) & r2_hidden(E,J) & r2_analoaf(A,D,B,E,H) & r2_analoaf(A,D,C,E,I) & r2_aff_1(A,H,I,J) & r2_hidden(F,J) & r2_hidden(G,J) & r2_analoaf(A,F,B,G,H) ) => ( r2_hidden(B,J) | r2_hidden(H,J) | r2_analoaf(A,F,C,G,I) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l29_hurwitz,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( k2_hurwitz(A,B) != k4_xcmplx_0(1) & k1_funct_1(B,k2_hurwitz(A,B)) = k4_struct_0(A) ) ) ) )).
fof(l29_int_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,1) => k5_struct_0(k9_int_3(A)) = 1 ) ) )).
fof(l29_int_8,axiom,( ! [A] : ( v1_finset_1(A) => ( k5_card_1(A) = k5_numbers => A = k1_xboole_0 ) ) )).
fof(l29_jordan5c,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v7_ordinal1(D) => ( ( 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(k1_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,k1_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) ) ) ) ) ) ) )).
fof(l29_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_lopban_2(A))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(l29_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) ) )).
fof(l29_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => r2_hidden(k8_lpspace1(A,k5_numbers),k13_lpspacc1(A,B,C)) ) ) ) )).
fof(l29_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => r2_hidden(k8_cqc_lang(A,k8_cqc_lang(A,C,E),k8_cqc_lang(A,k8_cqc_lang(A,k8_cqc_lang(A,C,D),B),k8_cqc_lang(A,k8_cqc_lang(A,E,B),B))),k4_cqc_the1(A)) ) ) ) ) ) )).
fof(l29_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_matrix_2(B,k3_matrix_2(A)) => ( ~ r1_xxreal_0(2,A) => ( v5_matrix_2(B,k2_matrix_2(k3_matrix_2(A))) & B = k1_finseq_2(A) ) ) ) ) )).
fof(l29_matrtop1,axiom,( v1_xreal_0(k5_numbers) )).
fof(l29_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( r2_hidden(E,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,k4_mesfunc9(A,B),C))) & r1_xxreal_0(D,C) ) => r2_hidden(E,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,k4_mesfunc9(A,B),D))) ) ) ) ) ) )).
fof(l29_modcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u4_struct_0(k11_modcat_1(A,B))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(l29_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v7_modelc_1(A) => k1_funct_1(A,1) = 4 ) ) )).
fof(l29_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ~ ( ~ ( v2_modelc_2(A) & k1_funct_1(A,1) != k5_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) = k5_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 ) ) ) )).
fof(l29_nat_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k10_nat_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k10_nat_lat)) => ! [C] : ( 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] : ( m1_subset_1(A,u1_struct_0(k10_nat_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k10_nat_lat)) => k2_lattices(k10_nat_lat,A,k1_lattices(k10_nat_lat,A,B)) = A ) ) )).
fof(l29_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v5_o_ring_1(B,A) => v9_o_ring_1(B,A) ) ) ) )).
fof(l29_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_cat_1(E,A,B,C) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(l29_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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_ordeq_01(A,B)) & v13_algstr_0(k5_ordeq_01(A,B)) & v2_rlvect_1(k5_ordeq_01(A,B)) & v3_rlvect_1(k5_ordeq_01(A,B)) & v4_rlvect_1(k5_ordeq_01(A,B)) & v5_rlvect_1(k5_ordeq_01(A,B)) & v6_rlvect_1(k5_ordeq_01(A,B)) & v7_rlvect_1(k5_ordeq_01(A,B)) & v8_rlvect_1(k5_ordeq_01(A,B)) & v3_normsp_0(k5_ordeq_01(A,B)) & v4_normsp_0(k5_ordeq_01(A,B)) & v2_normsp_1(k5_ordeq_01(A,B)) & l1_normsp_1(k5_ordeq_01(A,B)) ) ) ) )).
fof(l29_ordinal4,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ~ ( B != k1_xboole_0 & v4_ordinal1(B) & ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_ordinal2(C) ) => ~ ( k9_xtuple_0(C) = B & ! [D] : ( v3_ordinal1(D) => ( r2_hidden(D,B) => k1_funct_1(C,D) = k12_ordinal2(A,D) ) ) & ? [D] : ( v3_ordinal1(D) & r1_ordinal2(D,C) ) ) ) ) ) ) )).
fof(l29_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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) ) ) ) ) ) )).
fof(l29_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ( ( r2_projdes1(A,H,B,D,F) & r1_collsp(A,H,B,C) & r1_collsp(A,H,D,E) & r1_collsp(A,H,F,G) & r1_collsp(A,B,D,I) & r1_collsp(A,C,E,I) & r1_collsp(A,D,F,J) & r1_collsp(A,E,G,J) & r1_collsp(A,B,F,K) & r1_collsp(A,C,G,K) ) => ( H = C | H = E | H = G | B = C | D = E | r1_collsp(A,I,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l29_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u2_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u2_incsp_1(A)) => ! [H] : ( m1_subset_1(H,u2_incsp_1(A)) => ! [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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l29_radix_1,axiom,( ! [A] : ( v1_int_1(A) => ( r1_xxreal_0(k4_xcmplx_0(1),k11_radix_1(A)) & r1_xxreal_0(k11_radix_1(A),1) ) ) )).
fof(l29_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_6(C,A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => v1_finset_1(k5_ranknull(A,B,C,D)) ) ) ) ) )).
fof(l29_realset2,axiom,( ! [A] : ( m1_subset_1(A,c4__realset2) => ! [B] : ( m1_subset_1(B,c4__realset2) => ! [C] : ( 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)) ) ) ) )).
fof(l29_rfinseq,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ~ ( k5_numbers = k3_finseq_1(A) & ! [B] : ( ( v8_valued_0(B) & m2_finseq_1(B,k1_numbers) ) => ~ r2_classes1(A,B) ) ) ) )).
fof(l29_rlvect_x,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ~ ( r2_hidden(C,k2_rlvect_x(A,B)) & ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(A)) => ! [F] : ( ( 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] : ( 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_funct_1(F,G)) ) ) ) ) ) ) ) ) ) )).
fof(l29_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => v4_lattices(A) ) )).
fof(l29_scm_comp,axiom,( ! [A] : ( m2_subset_1(A,u1_struct_0(k1_scm_comp),k6_dtconstr(k1_scm_comp)) => k3_funct_2(k4_dtconstr(k1_scm_comp),k4_ordinal1,c8__scm_comp,k3_scm_comp(A)) = k16_scm_comp(A) ) )).
fof(l29_scmbsort,axiom,( k4_scmfsa_2(k5_numbers) != k4_scmfsa_2(4) )).
fof(l29_scmfsa8a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [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(k7_card_1(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(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k3_scmfsa6a(A,k4_compos_1(k1_scmfsa_2))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,C),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,A),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,C)),1))) = k5_card_1(A) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,A),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,C),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,A),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,C)))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k3_scmfsa6a(A,k4_compos_1(k1_scmfsa_2))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,C),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,A),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,C)),1))) & r1_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k3_scmfsa6a(A,k4_compos_1(k1_scmfsa_2))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,C)) & k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k3_scmfsa6a(A,k4_compos_1(k1_scmfsa_2))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,C)) = k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,A),k8_memstr_0(k7_card_1(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) ) ) ) ) ) )).
fof(l29_scmpds_i,axiom,( ! [A] : ( 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 ) ) )).
fof(l29_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( k1_funct_1(B,k2_scmp_gcd) = k5_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)),k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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) = k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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] : ( v7_ordinal1(E) => ( 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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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)) ) ) ) ) ) ) ) ) ) ) )).
fof(l29_seq_4,axiom,( v7_ordinal1(k5_numbers) )).
fof(l29_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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] : ( m2_finseq_1(D,A) => ! [E] : ( m2_finseq_1(E,A) => ( ( k3_finseq_1(D) = k3_finseq_1(E) & k5_binop_1(A,C,B,B) = B ) => r2_funct_2(k4_ordinal1,A,k6_funcop_1(A,k4_ordinal1,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)) ) ) ) ) ) ) )).
fof(l29_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => k4_simplex0(A) = k5_setfam_1(u1_struct_0(A),u1_pre_topc(A)) ) )).
fof(l29_simplex2,axiom,( ! [A] : ( v7_ordinal1(A) => k2_struct_0(k15_euclid(A)) = k2_struct_0(k3_pcomps_1(k14_euclid(A))) ) )).
fof(l29_sincos10,axiom,( r1_tarski(k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)),k4_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) )).
fof(l29_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ( v2_topreal1(A) => v2_topreal1(k17_finseq_1(u1_struct_0(k15_euclid(2)),B,A)) ) ) ) )).
fof(l29_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l29_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( m1_subset_1(D,k5_finsub_1(k4_partfun1(A,B))) => ! [E] : ~ ( r2_hidden(E,k4_substlat(A,B,C,D)) & ! [F] : ~ ( r2_hidden(F,D) & r1_tarski(F,E) ) ) ) ) )).
fof(l29_taxonom2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ~ ( r1_tarski(A,B) & r1_xboole_0(A,B) ) ) )).
fof(l29_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_topdim_1(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(l29_topdim_2,axiom,( v3_topdim_1(k15_euclid(1)) & k4_topdim_1(k15_euclid(1)) = 1 )).
fof(l29_topgen_5,axiom,( u1_struct_0(k3_topgen_5) = k2_topgen_5 )).
fof(l29_topmetr,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(k2_xcmplx_0(A,C),B) ) => r1_xxreal_0(A,B) ) ) ) ) )).
fof(l29_topreal2,axiom,( r2_hidden(k19_euclid(1,1),a_0_0_topreal2) )).
fof(l29_waybel13,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ~ ( ? [B] : ? [C] : ( v4_yellow_0(C,k2_yellow_1(B)) & m1_yellow_0(C,k2_yellow_1(B)) & v7_yellow_0(C,k2_yellow_1(B)) & v4_waybel_0(C,k2_yellow_1(B)) & r5_waybel_1(A,C) ) & ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k2_yellow_1(B)),u1_struct_0(k2_yellow_1(B))) & v7_waybel_1(C,k2_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_yellow_1(B)),u1_struct_0(k2_yellow_1(B))))) ) => ~ ( v22_waybel_0(C,k2_yellow_1(B),k2_yellow_1(B)) & r5_waybel_1(A,k1_yellow_2(k2_yellow_1(B),k2_yellow_1(B),C)) ) ) ) ) )).
fof(l29_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ 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)))) ) ) ) )).
fof(l29_waybel29,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => v23_waybel_0(k3_waybel29(B,A),k1_yellow_1(u1_pre_topc(k2_borsuk_1(B,A))),k3_waybel24(B,k1_waybel29(k1_yellow_1(u1_pre_topc(A))))) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v4_waybel11(C) & m1_yellow_9(C,k1_yellow_1(u1_pre_topc(A))) ) => ! [D] : ( ( 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)))) ) ) ) ) ) ) )).
fof(l29_waybel_4,axiom,( ! [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] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ! [C] : ! [D] : ( 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)) ) ) ) ) )).
fof(l29_waybel_5,axiom,( ! [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] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) ) => ! [D] : ( m2_pboole(D,B,C,k7_funcop_1(B,u1_struct_0(A))) => ( ! [E] : ( 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) ) ) )).
fof(l29_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( A != k5_numbers => k7_xcmplx_0(A,A) = 1 ) ) )).
fof(l29_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(A,k2_xcmplx_0(B,C)) => r1_xxreal_0(k6_xcmplx_0(A,B),C) ) ) ) ) )).
fof(l29_yellow_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => v3_lattice3(k1_yellow_1(u1_pre_topc(A))) ) )).
fof(l2_abian,axiom,( ! [A] : ( v1_int_1(A) => ( v1_abian(A) <=> ? [B] : ( v1_int_1(B) & A = k3_xcmplx_0(2,B) ) ) ) )).
fof(l2_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_analoaf(A,B,C,C,B) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( 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) ) ) ) ) ) ) )).
fof(l2_algstr_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k2_vectsp_1)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_vectsp_1)) => ~ ( A != k4_struct_0(k2_vectsp_1) & ! [C] : ( m1_subset_1(C,u1_struct_0(k2_vectsp_1)) => k8_group_1(k2_vectsp_1,A,C) != B ) ) ) ) )).
fof(l2_altcat_5,axiom,( m1_subset_1(k5_numbers,2) & m1_subset_1(1,2) )).
fof(l2_ami_2,axiom,( ! [A] : ( m1_subset_1(A,k1_ami_2) => ( A = k4_ordinal1 | r2_hidden(A,k2_ami_2) ) ) )).
fof(l2_ami_3,axiom,( k2_memstr_0(k7_card_1(2),k1_ami_3) = k3_relat_1(k3_ami_2,k4_ami_2) )).
fof(l2_ami_4,axiom,( k10_ami_3(2) != k10_ami_3(k5_numbers) )).
fof(l2_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_rlvect_1(A,k1_rlvect_1(A,B,k5_numbers),k1_rlvect_1(A,C,k5_numbers)) = k4_struct_0(A) ) ) ) )).
fof(l2_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( B = k3_rlvect_1(A,k1_rlvect_1(A,C,F),k1_rlvect_1(A,D,G)) => k1_rlvect_1(A,B,E) = k3_rlvect_1(A,k1_rlvect_1(A,C,k3_xcmplx_0(E,F)),k1_rlvect_1(A,D,k3_xcmplx_0(E,G))) ) ) ) ) ) ) ) ) )).
fof(l2_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( k3_rlvect_1(A,k1_rlvect_1(A,B,D),k1_rlvect_1(A,C,E)) = k4_struct_0(A) => ( D = k5_numbers & E = k5_numbers ) ) ) ) => ( ~ v9_struct_0(B,A) & ~ v9_struct_0(C,A) & ~ r1_anproj_1(A,B,C) ) ) ) ) ) )).
fof(l2_arithm,axiom,( m1_subset_1(k5_numbers,k1_numbers) )).
fof(l2_armstrng,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_2(C,B,k4_finseq_2(A,B)) => k4_finseq_1(C) = k2_finseq_1(A) ) ) ) )).
fof(l2_arytm_1,axiom,( m1_subset_1(k12_arytm_3,k2_arytm_2) )).
fof(l2_arytm_3,axiom,( r2_hidden(1,k4_ordinal1) )).
fof(l2_asympt_0,axiom,( m1_subset_1(1,k1_numbers) & m1_subset_1(2,k1_numbers) )).
fof(l2_asympt_1,axiom,( m1_subset_1(k5_numbers,k1_numbers) )).
fof(l2_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ( v1_group_3(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(l2_axioms,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ( A = k5_arytm_0(B,C) => ( C = k5_numbers & A = B ) ) ) ) ) )).
fof(l2_bhsp_1,axiom,( 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)) )).
fof(l2_bhsp_7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(A,k7_xcmplx_0(1,k1_nat_1(B,1))) ) ) ) )).
fof(l2_bintree2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => m2_finseq_1(k10_binarith(A,B),A) ) ) )).
fof(l2_borsuk_7,axiom,( m1_subset_1(k5_numbers,u1_struct_0(k17_borsuk_1)) & m1_subset_1(1,u1_struct_0(k17_borsuk_1)) )).
fof(l2_brouwer2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k5_numbers,C) => r2_hidden(k1_rlvect_1(k15_euclid(A),B,C),k4_topreal9(k15_euclid(A),k4_struct_0(k15_euclid(A)),B)) ) ) ) ) )).
fof(l2_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(l2_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(l2_card_5,axiom,( 2 = k5_card_1(2) )).
fof(l2_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( C = D => k4_cat_1(A,C) = k4_cat_1(B,D) ) ) ) ) ) ) )).
fof(l2_cc0sp1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) ) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( m1_subset_1(F,B) => ! [G] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( ~ v2_struct_0(J) & l1_cfuncdom(J) ) => ( J = g1_cfuncdom(B,H,G,I,F,E) => ! [K] : ( m1_subset_1(K,u1_struct_0(J)) => ! [L] : ( m1_subset_1(L,u1_struct_0(C)) => ( K = L => k1_clvect_1(J,K,A) = k1_clvect_1(C,L,A) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l2_cfdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( r1_funct_2(k4_ordinal1,k1_numbers,k4_ordinal1,k2_numbers,A,B) & v2_comseq_2(B) & k3_comseq_2(B) = C ) => k1_seq_2(A) = C ) ) ) ) )).
fof(l2_cgames_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) ) => ( ! [B] : ( v3_ordinal1(B) => ( r2_hidden(B,k9_xtuple_0(A)) => k1_funct_1(A,B) = a_2_0_cgames_1(A,B) ) ) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(l2_clopban4,axiom,( ! [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) & 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] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(l2_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(k5_numbers,k2_xcmplx_0(k1_square_1(A),k1_square_1(B))) ) ) )).
fof(l2_complfld,axiom,( k1_group_1(k1_complfld) = k6_complex1 )).
fof(l2_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m1_subset_1(B,k2_numbers) => k10_seq_4(A,B) = k4_finseqop(k2_numbers,k2_numbers,A,k10_funcop_1(k2_numbers,k2_numbers,k5_binop_2,B,k6_partfun1(k2_numbers))) ) ) )).
fof(l2_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( 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)) ) ) )).
fof(l2_csspace2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(k5_numbers,k2_xcmplx_0(k1_square_1(A),k1_square_1(B))) ) ) )).
fof(l2_csspace4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_comseq_2(A) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k1_funct_1(A,B),k2_seq_4(k2_relset_1(k1_numbers,A))) ) ) ) )).
fof(l2_entropy1,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l2_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) )).
fof(l2_euclid_7,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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) ) ) ) )).
fof(l2_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( v1_xreal_0(B) => k9_euclid(3,A,B) = k1_euclid_8(k3_xcmplx_0(B,k1_funct_1(A,1)),k3_xcmplx_0(B,k1_funct_1(A,2)),k3_xcmplx_0(B,k1_funct_1(A,3))) ) ) )).
fof(l2_euler_1,axiom,( ~ v1_int_2(1) )).
fof(l2_euler_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( A != k5_numbers => r1_xxreal_0(k5_numbers,k6_xcmplx_0(A,1)) ) ) )).
fof(l2_fdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_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] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_1(k2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,C,D),B),E) = k4_xcmplx_0(k3_xcmplx_0(2,E)) ) ) ) ) ) ) ) ) )).
fof(l2_fdiff_6,axiom,( ! [A] : ( v1_xreal_0(A) => k2_xcmplx_0(1,k19_sin_cos(k3_xcmplx_0(2,A))) = k3_xcmplx_0(2,k1_square_1(k19_sin_cos(A))) ) )).
fof(l2_fib_fusc,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( ~ r1_xxreal_0(A,k5_numbers) => ( m1_subset_1(k1_int_1(k3_power(2,A)),k4_ordinal1) & ~ r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(6,k2_xcmplx_0(k1_int_1(k3_power(2,A)),1)),1),k5_numbers) ) ) ) )).
fof(l2_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k4_xcmplx_0(A),k4_xcmplx_0(k3_xcmplx_0(A,k2_power(k4_xcmplx_0(1),B)))) ) ) )).
fof(l2_finseq_6,axiom,( ! [A] : ! [B] : ! [C] : k10_xtuple_0(k11_finseq_1(A,B,C)) = k1_enumset1(A,B,C) )).
fof(l2_finset_1,axiom,( ! [A] : v1_finset_1(k1_tarski(A)) )).
fof(l2_fomodel3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v6_struct_0(D) & v11_fomodel1(D) & l1_fomodel1(D) ) => ~ ( ~ r2_hidden(A,k9_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,k9_nat_1(k9_setfam_1(k6_subset_1(k3_finseq_2(k15_fomodel1(D)),k1_tarski(k1_xboole_0))),k39_fomodel1(D),B)) ) ) ) ) )).
fof(l2_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ~ ( ~ v7_pre_topc(A) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(l2_freealg,axiom,( ~ r2_hidden(k5_numbers,k10_xtuple_0(k3_pre_poly(k4_ordinal1,1))) & r2_hidden(k5_numbers,k10_xtuple_0(k3_pre_poly(k4_ordinal1,k5_numbers))) )).
fof(l2_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ( r2_hidden(D,k9_xtuple_0(k1_funct_4(A,k16_funcop_1(B,C)))) => ( r2_hidden(D,k9_xtuple_0(A)) | B = D ) ) ) )).
fof(l2_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : r2_hidden(B,k9_xtuple_0(k1_funct_4(A,k16_funcop_1(B,C)))) ) )).
fof(l2_gobrd12,axiom,( u1_struct_0(k15_euclid(2)) = k1_euclid(2) )).
fof(l2_graph_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(B,k1_nat_1(C,1)) & r1_xxreal_0(C,k3_finseq_1(A)) ) => ( k1_nat_1(k3_finseq_1(k1_graph_2(A,B,C)),B) = k1_nat_1(C,1) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ~ r1_xxreal_0(k3_finseq_1(k1_graph_2(A,B,C)),D) => k1_funct_1(k1_graph_2(A,B,C),k1_nat_1(D,1)) = k1_funct_1(A,k1_nat_1(B,D)) ) ) ) ) ) ) ) )).
fof(l2_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & v5_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k8_group_1(A,B,C) = k8_group_1(A,C,B) ) ) ) )).
fof(l2_group_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v1_group_7(C) ) => ! [D] : ( 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))) ) ) ) ) )).
fof(l2_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(l2_heyting2,axiom,( ! [A] : ! [B] : ! [C] : ( ( A = k2_xboole_0(B,C) & r1_tarski(A,B) ) => A = B ) )).
fof(l2_heyting3,axiom,( k5_numbers = k2_nat_1(2,k5_numbers) )).
fof(l2_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v7_aff_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l2_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( v1_int_2(B) & ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(B,C) & A != k5_numbers & ! [D] : ( v7_ordinal1(D) => k4_nat_d(k3_xcmplx_0(D,A),B) != C ) ) ) ) ) )).
fof(l2_int_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( A = k4_xcmplx_0(B) => ( B = A | r2_hidden(A,k6_subset_1(k2_zfmisc_1(k1_tarski(k5_numbers),k4_ordinal1),k1_tarski(k4_tarski(k5_numbers,k5_numbers)))) ) ) ) )).
fof(l2_integr11,axiom,( k2_subset_1(k1_numbers) = k9_xtuple_0(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(2,k5_numbers),k16_sin_cos)) )).
fof(l2_integr13,axiom,( k3_limfunc1(k5_numbers) = a_0_0_integr13 )).
fof(l2_integr15,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => ! [C] : ( m1_integra1(C,A) => ! [D] : ( m1_integr15(D,A,B,C) => ! [E] : ( v7_ordinal1(E) => ( ( v2_seq_2(k2_partfun1(A,k1_numbers,B,A)) & r2_hidden(E,k4_finseq_1(C)) ) => r1_xxreal_0(k1_funct_1(k5_integra1(A,B,C),E),k1_funct_1(D,E)) ) ) ) ) ) ) )).
fof(l2_integr16,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(l2_integra3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(1,A) & r1_xxreal_0(A,2) & A != 1 & A != 2 ) ) )).
fof(l2_integra8,axiom,( ~ r1_xxreal_0(k5_numbers,k17_sin_cos(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)))) )).
fof(l2_integra9,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l2_jgraph_3,axiom,( k1_relset_1(u1_struct_0(k15_euclid(2)),k4_pscomp_1) = u1_struct_0(k15_euclid(2)) )).
fof(l2_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(A,B) ) => r1_xxreal_0(k3_xcmplx_0(A,k3_square_1(k2_xcmplx_0(1,k1_square_1(B)))),k3_xcmplx_0(B,k3_square_1(k2_xcmplx_0(1,k1_square_1(A))))) ) ) ) )).
fof(l2_jgraph_8,axiom,( ! [A] : ! [B] : ( ( 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),k1_nat_1(k3_finseq_1(B),1)) = k1_funct_1(B,k3_finseq_1(B)) ) ) ) )).
fof(l2_jordan,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(l2_jordan12,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_zfmisc_1(A) => v1_zfmisc_1(k3_finseq_1(A)) ) ) )).
fof(l2_jordan18,axiom,( k1_relset_1(u1_struct_0(k15_euclid(2)),k5_pscomp_1) = u1_struct_0(k15_euclid(2)) )).
fof(l2_jordan1a,axiom,( k3_nat_d(3,2) = 1 )).
fof(l2_jordan1c,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( A != k5_numbers & B != k5_numbers & k3_xcmplx_0(k7_xcmplx_0(A,B),k3_xcmplx_0(k7_xcmplx_0(C,A),B)) != C ) ) ) ) )).
fof(l2_jordan1d,axiom,( k3_nat_d(1,2) = k5_numbers )).
fof(l2_jordan21,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(C,B) & k1_funct_1(k5_pscomp_1,C) = A ) ) ) ) ) )).
fof(l2_jordan24,axiom,( g1_pre_topc(u1_struct_0(k15_euclid(2)),u1_pre_topc(k15_euclid(2))) = k3_pcomps_1(k14_euclid(2)) )).
fof(l2_jordan7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k7_nat_d(A,C),B) => r1_xxreal_0(A,k2_xcmplx_0(B,C)) ) ) ) ) )).
fof(l2_kurato_1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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)))) ) ) ) )).
fof(l2_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( ~ v1_xboole_0(B) & ! [C] : ( m1_subset_1(C,u1_struct_0(k3_lattice3(A))) => ~ ( r2_hidden(C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(k3_lattice3(A))) => ~ ( r2_hidden(D,B) & D != C & r3_orders_2(k3_lattice3(A),C,D) ) ) ) ) ) ) ) )).
fof(l2_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) => ! [B] : ! [C] : ( r1_tarski(B,C) => ! [D] : ( 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) ) ) ) )).
fof(l2_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r1_tarski(k10_xtuple_0(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(k10_xtuple_0(A),k1_relset_1(k1_numbers,B)) & r1_tarski(k10_xtuple_0(A),k1_relset_1(k1_numbers,C)) ) ) ) ) ) )).
fof(l2_limfunc2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(l2_limfunc3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l2_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r1_tarski(k10_xtuple_0(C),k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) => ( r1_tarski(k10_xtuple_0(C),k1_relset_1(k1_numbers,A)) & r1_tarski(k10_xtuple_0(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,C,A)),k1_relset_1(k1_numbers,B)) ) ) ) ) ) )).
fof(l2_matrix16,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r2_hidden(B,k2_finseq_1(A)) & r2_hidden(C,k2_finseq_1(A)) ) => r2_hidden(k2_xcmplx_0(k5_int_1(k6_xcmplx_0(C,B),A),1),k2_finseq_1(A)) ) ) ) ) )).
fof(l2_matrix17,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(l2_matrix_9,axiom,( k2_finseq_4(k4_ordinal1,1,2) != k2_finseq_4(k4_ordinal1,2,1) )).
fof(l2_matrtop2,axiom,( ! [A] : ( v7_ordinal1(A) => k4_struct_0(k6_prvect_1(k2_vectsp_1,A)) = k4_struct_0(k15_euclid(A)) ) )).
fof(l2_mazurulm,axiom,( k2_pre_topc(k5_topmetr,c1__mazurulm) = k2_struct_0(k5_topmetr) )).
fof(l2_mboolean,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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 ) ) )).
fof(l2_mesfunc1,axiom,( k5_numbers = k4_xcmplx_0(k5_numbers) )).
fof(l2_metric_1,axiom,( r2_hidden(k5_numbers,k1_numbers) )).
fof(l2_metrizts,axiom,( ! [A] : ( ( v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => r1_borsuk_3(A,B) ) ) )).
fof(l2_modelc_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,k1_nat_1(C,1)) => ( r1_xxreal_0(B,A) | r1_xxreal_0(A,C) ) ) ) ) ) )).
fof(l2_modelc_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( 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) ) ) ) )).
fof(l2_msafree4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,C) => ! [E] : ( 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)))) ) ) ) ) )).
fof(l2_msaterm,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ( m2_finseq_1(C,B) => ( ~ r1_xxreal_0(k3_finseq_1(C),A) => r2_hidden(k1_funct_1(C,k1_nat_1(A,1)),B) ) ) ) )).
fof(l2_nagata_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(A,D)),k2_xcmplx_0(k2_xcmplx_0(k9_complex1(k6_xcmplx_0(A,B)),k9_complex1(k6_xcmplx_0(B,C))),k9_complex1(k6_xcmplx_0(C,D)))) ) ) ) ) )).
fof(l2_nat_1,axiom,( r2_hidden(k5_numbers,k1_numbers) )).
fof(l2_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => v7_ordinal1(k5_int_1(A,B)) ) ) )).
fof(l2_normsp_0,axiom,( v1_funct_1(k8_funct_5) & v1_funct_2(k8_funct_5,k1_tarski(k5_numbers),k1_numbers) & m1_subset_1(k8_funct_5,k1_zfmisc_1(k2_zfmisc_1(k1_tarski(k5_numbers),k1_numbers))) )).
fof(l2_normsp_1,axiom,( v1_funct_1(k8_funcop_1(k1_numbers,u1_struct_0(k1_rlsub_1(o_0_5_normsp_1)),k10_subset_1(k5_numbers,k1_numbers))) & v1_funct_2(k8_funcop_1(k1_numbers,u1_struct_0(k1_rlsub_1(o_0_5_normsp_1)),k10_subset_1(k5_numbers,k1_numbers)),u1_struct_0(k1_rlsub_1(o_0_5_normsp_1)),k1_numbers) & m1_subset_1(k8_funcop_1(k1_numbers,u1_struct_0(k1_rlsub_1(o_0_5_normsp_1)),k10_subset_1(k5_numbers,k1_numbers)),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_rlsub_1(o_0_5_normsp_1)),k1_numbers))) )).
fof(l2_numbers,axiom,( 1 = k1_ordinal1(k5_ordinal1) )).
fof(l2_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) ) )).
fof(l2_orders_3,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_struct_0(A) => v1_orders_3(A) ) ) )).
fof(l2_ordinal4,axiom,( v4_ordinal1(k4_ordinal1) )).
fof(l2_ortsp_1,axiom,( m1_subset_1(k5_numbers,c1__ortsp_1) )).
fof(l2_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(l2_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(l2_partfun4,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l2_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,B))) => ( r1_xboole_0(A,B) => ! [E] : ! [F] : ( ( 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) ) ) ) ) ) )).
fof(l2_pdiff_1,axiom,( 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] : ( v1_xreal_0(A) => ( k1_funct_1(k1_pdiff_1(1,1),k9_finseq_1(A)) = A & k1_funct_1(k2_funct_1(k1_pdiff_1(1,1)),A) = k9_finseq_1(A) ) ) )).
fof(l2_pdiff_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r1_xxreal_0(A,B) => k2_xcmplx_0(A,k7_nat_d(B,A)) = k7_nat_d(k2_xcmplx_0(A,B),A) ) ) ) )).
fof(l2_pencil_4,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(B,k5_card_1(A)) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k5_card_1(C) != B ) ) ) ) )).
fof(l2_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ~ r1_xxreal_0(k1_newton(2,k1_newton(2,A)),1) ) )).
fof(l2_polyeq_2,axiom,( r1_int_1(2,4) )).
fof(l2_polynom2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( 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) ) ) ) )).
fof(l2_polynom4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_algstr_0(A) & v1_vectsp_1(A) & v1_algstr_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_algstr_0(A,B,k4_struct_0(A)) = k4_struct_0(A) ) ) )).
fof(l2_polynom8,axiom,( ! [A] : ( v1_int_1(A) => ~ ( ~ r1_xxreal_0(1,A) & A != k5_numbers & r1_xxreal_0(k5_numbers,A) ) ) )).
fof(l2_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(l2_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) )).
fof(l2_pscomp_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ( v6_measure6(B,A) => v5_measure6(k32_valued_1(A,k1_numbers,B),A) ) ) ) )).
fof(l2_pua2mss1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( 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(k4_ordinal1,A,A,B,C,D),B) ) ) ) )).
fof(l2_quatern2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => r1_xxreal_0(k5_numbers,k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(C)),k1_square_1(D))) ) ) ) ) )).
fof(l2_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ( v1_xreal_0(A) => ( A = k13_quaterni(A) & k14_quaterni(A) = k5_numbers & k15_quaterni(A) = k5_numbers & k16_quaterni(A) = k5_numbers ) ) ) )).
fof(l2_radix_3,axiom,( ! [A] : ( 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)) ) ) )).
fof(l2_radix_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) ) ) )).
fof(l2_rat_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k8_arytm_3(A,B) = k7_xcmplx_0(A,B) ) ) )).
fof(l2_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(B,C) ) => r1_xxreal_0(A,C) ) ) ) ) )).
fof(l2_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( A = k2_xcmplx_0(k3_xcmplx_0(B,C),D) => ( k6_xcmplx_0(k7_xcmplx_0(A,B),C) = k5_numbers | D = k5_numbers | B = k5_numbers | k7_xcmplx_0(1,k6_xcmplx_0(k7_xcmplx_0(A,B),C)) = k7_xcmplx_0(B,D) ) ) ) ) ) ) )).
fof(l2_recdef_1,axiom,( r2_hidden(1,k4_ordinal1) )).
fof(l2_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => ( r1_xxreal_0(B,k3_finseq_1(A)) & r1_xxreal_0(k1_nat_1(k5_numbers,1),B) & ~ r1_xxreal_0(B,k5_numbers) ) ) ) ) )).
fof(l2_rltopsp1,axiom,( v2_xxreal_0(1) & v1_xreal_0(1) )).
fof(l2_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( B != C & ! [F] : ( 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 ) ) ) ) ) ) ) ) )).
fof(l2_rsspace4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_comseq_2(A) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k1_funct_1(A,B),k2_seq_4(k2_relset_1(k1_numbers,A))) ) ) ) )).
fof(l2_rusub_4,axiom,( ! [A] : ! [B] : ( r2_hidden(B,A) => k2_xboole_0(k6_subset_1(A,k1_tarski(B)),k1_tarski(B)) = A ) )).
fof(l2_scm_comp,axiom,( 5 = a_0_1_scm_comp )).
fof(l2_scm_halt,axiom,( k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_3(k4_scmfsa_2(k5_numbers),1))) = k5_numbers )).
fof(l2_scmfsa_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v5_ordinal1(D) & v1_funct_1(D) & v1_finset_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v5_ordinal1(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)) ) ) ) ) ) ) )).
fof(l2_scmfsa_9,axiom,( k1_funct_1(k4_compos_1(k1_scmfsa_2),k5_numbers) = k2_compos_1(k1_scmfsa_2) )).
fof(l2_scmpds_6,axiom,( r2_hidden(k5_numbers,k9_xtuple_0(k4_compos_1(k1_scmpds_2))) )).
fof(l2_scmring1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => k9_xtuple_0(k3_relat_1(k3_ami_2,k1_scmring1(A))) = k1_ami_2 ) )).
fof(l2_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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(k7_card_1(2),k1_scmring2(A)) = k3_relat_1(k3_ami_2,k1_scmring1(A)) ) )).
fof(l2_scpqsort,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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,k1_nat_1(k5_card_1(C),2)),k3_scmpds_4(C,k3_scmpds_2(k4_xcmplx_0(k1_nat_1(k5_card_1(C),1))))) ) ) ) )).
fof(l2_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,A,k1_nat_1(B,1)),k9_nat_1(k1_numbers,A,B)) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,A,k2_xcmplx_0(k1_nat_1(B,1),C)),k9_nat_1(k1_numbers,A,B)) ) ) ) & ( ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,A,k2_xcmplx_0(k1_nat_1(B,1),C)),k9_nat_1(k1_numbers,A,B)) ) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(C,B) & r1_xxreal_0(k9_nat_1(k1_numbers,A,C),k9_nat_1(k1_numbers,A,B)) ) ) ) ) & ( ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(C,B) & r1_xxreal_0(k9_nat_1(k1_numbers,A,C),k9_nat_1(k1_numbers,A,B)) ) ) ) => ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,A,k1_nat_1(B,1)),k9_nat_1(k1_numbers,A,B)) ) ) ) ) )).
fof(l2_series_2,axiom,( ! [A] : ( v1_xreal_0(A) => k1_newton(A,3) = k3_xcmplx_0(k3_xcmplx_0(A,A),A) ) )).
fof(l2_series_3,axiom,( k11_newton(1,3) = 1 )).
fof(l2_series_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k1_newton(k2_xcmplx_0(k1_newton(k7_xcmplx_0(1,2),k1_nat_1(A,1)),k11_newton(2,k1_nat_1(A,1))),2) = k2_xcmplx_0(k2_xcmplx_0(k1_newton(k7_xcmplx_0(1,4),k1_nat_1(A,1)),k11_newton(4,k1_nat_1(A,1))),2) ) )).
fof(l2_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => k7_xcmplx_0(2,k2_xcmplx_0(k7_xcmplx_0(1,A),k7_xcmplx_0(1,B))) = k7_xcmplx_0(k3_xcmplx_0(2,k3_xcmplx_0(A,B)),k2_xcmplx_0(A,B)) ) ) )).
fof(l2_setwop_2,axiom,( ! [A] : ( v7_ordinal1(A) => ~ r2_hidden(k1_nat_1(A,1),k2_finseq_1(A)) ) )).
fof(l2_simplex0,axiom,( ! [A] : ? [B] : ( v1_classes1(B) & B = k3_tarski(a_1_0_simplex0(A)) & r1_tarski(A,B) & ! [C] : ( ( r1_tarski(A,C) & v1_classes1(C) ) => r1_tarski(B,C) ) ) )).
fof(l2_sin_cos,axiom,( r2_hidden(1,k4_ordinal1) )).
fof(l2_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(1,k1_square_1(A)) & ~ r1_xxreal_0(1,B) & r1_xxreal_0(1,k3_xcmplx_0(k1_square_1(A),B)) ) ) ) )).
fof(l2_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ( k2_sin_cos2(A) = k7_xcmplx_0(k6_xcmplx_0(k23_sin_cos(A),k23_sin_cos(k4_xcmplx_0(A))),2) & k4_sin_cos2(A) = k7_xcmplx_0(k2_xcmplx_0(k23_sin_cos(A),k23_sin_cos(k4_xcmplx_0(A))),2) & k6_sin_cos2(A) = k7_xcmplx_0(k6_xcmplx_0(k23_sin_cos(A),k23_sin_cos(k4_xcmplx_0(A))),k2_xcmplx_0(k23_sin_cos(A),k23_sin_cos(k4_xcmplx_0(A)))) ) ) )).
fof(l2_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( r2_hidden(C,B) => r2_hidden(C,A) ) ) )).
fof(l2_substlat,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( r2_hidden(D,k1_substlat(A,B)) & r2_hidden(C,D) ) => v1_finset_1(C) ) )).
fof(l2_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( 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 ) ) ) ) ) ) )).
fof(l2_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(l2_topalg_3,axiom,( m1_subset_1(k5_numbers,u1_struct_0(k17_borsuk_1)) & m1_subset_1(1,u1_struct_0(k17_borsuk_1)) )).
fof(l2_topalg_4,axiom,( r2_hidden(2,k2_tarski(1,2)) )).
fof(l2_topalg_5,axiom,( r2_hidden(k5_numbers,u1_struct_0(k5_topmetr)) )).
fof(l2_topmetr2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(l2_topreal2,axiom,( k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,k5_numbers),k19_euclid(1,k5_numbers)),k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,1),k19_euclid(1,1))) = k1_xboole_0 )).
fof(l2_toprealb,axiom,( v1_xreal_0(k4_xcmplx_0(1)) & v3_xxreal_0(k4_xcmplx_0(1)) )).
fof(l2_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_aff_1(A,E,B,F) & E != F & B != F ) ) ) ) ) ) ) ) )).
fof(l2_treal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_topmetr(A,B))) => ( r1_xxreal_0(A,B) => m1_subset_1(C,k1_numbers) ) ) ) ) )).
fof(l2_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(k3_finseq_1(A),C) => k1_funct_1(A,k1_nat_1(C,1)) = k1_funct_1(B,k1_nat_1(C,1)) ) ) ) => A = B ) ) ) )).
fof(l2_tsep_1,axiom,( ! [A] : ! [B] : ! [C] : k6_subset_1(k3_xboole_0(A,B),C) = k9_subset_1(B,k6_subset_1(A,C),k6_subset_1(B,C)) )).
fof(l2_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( k9_xtuple_0(C) = k9_subset_1(k4_ordinal1,k4_finseq_1(A),k4_finseq_1(B)) => ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) ) ) ) ) )).
fof(l2_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => k1_vectsp_5(A,B,C,D) = k1_vectsp_5(A,B,D,C) ) ) ) ) )).
fof(l2_waybel14,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(l2_waybel15,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(l2_waybel19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(l2_waybel23,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_yellow_1(A)))) => ( r1_yellow_0(k1_yellow_1(A),B) => r1_tarski(k3_tarski(B),k1_yellow_0(k1_yellow_1(A),B)) ) ) ) )).
fof(l2_waybel_5,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ( ! [B] : ( 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] : ( ( ~ 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) ) ) )).
fof(l2_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ( v8_relat_2(A) <=> ! [B] : ! [C] : ! [D] : ( ( r2_hidden(k4_tarski(B,C),A) & r2_hidden(k4_tarski(C,D),A) ) => r2_hidden(k4_tarski(B,D),A) ) ) ) )).
fof(l2_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ( A = k5_arytm_0(B,C) => ( C = k5_numbers & A = B ) ) ) ) ) )).
fof(l2_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ( A = k5_arytm_0(B,C) => ( C = k5_numbers & A = B ) ) ) ) ) )).
fof(l2_xtuple_0,axiom,( ! [A] : ! [B] : ! [C] : ( k1_tarski(A) = k2_tarski(B,C) => A = B ) )).
fof(l2_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( 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 ) ) )).
fof(l2_zf_model,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( B = k1_zf_model(A) <=> ? [C] : ( ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ! [E] : ( m2_subset_1(E,k4_ordinal1,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] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( 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] : ~ ( E = F & r2_hidden(k4_tarski(k20_zf_lang(D),F),C) ) ) & ~ ( v5_zf_lang(D) & ! [F] : ! [G] : ~ ( 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] : ~ ( 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) ) ) ) ) ) ) ) ) )).
fof(l2_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(C,B) => ( r2_hidden(A,C) | r1_tarski(C,k4_xboole_0(B,k1_tarski(A))) ) ) )).
fof(l2_zfrefle1,axiom,( v4_ordinal1(k4_ordinal1) )).
fof(l2_zmodul03,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_int_3)) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( v1_int_1(C) => ( C = B => k3_xcmplx_0(C,A) = k5_binom(k1_int_3,A,B) ) ) ) ) )).
fof(l30_ami_3,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) <=> ~ ( A != k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0) & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_ami_3)) ) => A != k2_ami_3(B,C) ) ) & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_ami_3)) ) => A != k3_ami_3(B,C) ) ) & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_ami_3)) ) => A != k4_ami_3(B,C) ) ) & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_ami_3)) ) => A != k5_ami_3(B,C) ) ) & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_ami_3)) ) => A != k6_ami_3(B,C) ) ) & ! [B] : ( v7_ordinal1(B) => A != k7_ami_3(B) ) & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [C] : ( v7_ordinal1(C) => A != k8_ami_3(C,B) ) ) & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [C] : ( v7_ordinal1(C) => A != k9_ami_3(C,B) ) ) ) ) )).
fof(l30_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_anproj_1(A,B,C) & D = k1_rlvect_1(A,C,E) & E != k5_numbers & r1_anproj_1(A,B,D) ) ) ) ) ) ) )).
fof(l30_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ( r1_tarski(k3_arytm_2(A),k3_arytm_2(B)) => r1_arytm_2(A,B) ) ) ) )).
fof(l30_bcialg_2,axiom,( ! [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) ) => v10_bcialg_1(k4_struct_0(A),A) ) )).
fof(l30_binari_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( 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 ) ) ) ) )).
fof(l30_binari_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( k4_nat_d(B,A) = k4_nat_d(C,A) & ~ r1_xxreal_0(B,C) & ! [D] : ( v1_int_1(D) => B != k2_xcmplx_0(C,k3_xcmplx_0(D,A)) ) ) ) ) ) )).
fof(l30_binop_2,axiom,( r3_binop_1(k3_numbers,c2__binop_2,k15_binop_2) )).
fof(l30_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(l30_collsp,axiom,( ~ v2_struct_0(c9__collsp) & v2_collsp(c9__collsp) & v3_collsp(c9__collsp) & l1_collsp(c9__collsp) )).
fof(l30_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k3_complex1(k2_xcmplx_0(A,B)) = k3_real_1(k3_complex1(A),k3_complex1(B)) & k4_complex1(k2_xcmplx_0(A,B)) = k3_real_1(k4_complex1(A),k4_complex1(B)) ) ) ) )).
fof(l30_csspace,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_clvect_1(o_0_6_csspace))) => ! [B] : ( 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 ) ) )).
fof(l30_dist_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_margrel1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_margrel1(B) ) => ! [C] : ( r2_hidden(C,k3_xboole_0(k9_xtuple_0(A),k9_xtuple_0(B))) => ( k1_funct_1(k14_margrel1(A,B),C) = k8_margrel1 <=> ( k1_funct_1(A,C) = k8_margrel1 & k1_funct_1(B,C) = k8_margrel1 ) ) ) ) ) )).
fof(l30_euclid_9,axiom,( k3_pcomps_1(k14_euclid(k5_numbers)) = k3_waybel18(k1_xboole_0,k7_funcop_1(k1_xboole_0,k3_topmetr)) )).
fof(l30_fib_num4,axiom,( ~ r1_xxreal_0(3,k3_square_1(5)) )).
fof(l30_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( v1_fomodel0(B,k2_zfmisc_1(C,A)) <=> ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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 ) ) ) ) ) )).
fof(l30_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r2_hidden(D,k2_xboole_0(k2_xboole_0(A,B),C)) <=> ~ ( ~ r2_hidden(D,A) & ~ r2_hidden(D,B) & ~ r2_hidden(D,C) ) ) )).
fof(l30_fomodel4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( 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(k5_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)),k4_fomodel4(C,D)),k1_tarski(B)))) ) ) ) )).
fof(l30_funct_9,axiom,( v1_funct_9(k2_fdiff_9,k3_xcmplx_0(2,k28_sin_cos)) )).
fof(l30_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ( ~ v5_glib_002(B,A) <=> ! [C] : ( 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)) ) ) ) ) )).
fof(l30_goboard7,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(l30_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [E] : ! [F] : ( 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,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,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) ) ) ) ) ) ) )).
fof(l30_group_10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => k1_card_1(a_2_2_group_10(A,B)) = k1_card_1(B) ) ) )).
fof(l30_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_group_3(A,k5_group_1(A,k5_ordinal1,B),C) = k5_group_1(A,k5_ordinal1,k2_group_3(A,B,C)) ) ) ) )).
fof(l30_hahnban,axiom,( ! [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) ) => ( ~ 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))) ) ) )).
fof(l30_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_substlat(A,B))) => ! [D] : ( m1_subset_1(D,k4_partfun1(A,B)) => ! [E] : ( m1_subset_1(E,k5_finsub_1(k4_partfun1(A,B))) => ~ ( E = k1_tarski(D) & ! [F] : ( 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] : ( m1_subset_1(G,k4_partfun1(A,B)) => ( r2_hidden(G,k1_funct_1(k7_heyting2(A,B,C),F)) => r1_partfun1(G,D) ) ) ) ) ) ) ) ) ) )).
fof(l30_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,k1_zfmisc_1(u1_struct_0(A))) => ( ( r2_aff_1(A,B,C,K) & v7_aff_2(A) & r2_hidden(D,K) & r2_hidden(E,K) & r2_analoaf(A,D,B,E,I) & r2_analoaf(A,D,C,E,J) & r2_aff_1(A,I,J,K) & r2_hidden(F,K) & r2_hidden(G,K) & r2_analoaf(A,F,B,G,I) & r2_aff_1(A,I,H,K) & r2_analoaf(A,F,C,G,H) ) => ( r2_hidden(B,K) | r2_hidden(I,K) | H = J ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l30_hurwitz,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( m1_subset_1(k2_hurwitz(A,B),k4_ordinal1) <=> B != k9_polynom3(A) ) ) ) )).
fof(l30_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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] : ( v1_xreal_0(G) => ( r2_hidden(G,k3_integra5(k3_xxreal_0(C,D),k4_xxreal_0(C,D))) => r1_xxreal_0(k9_complex1(k1_funct_1(F,G)),E) ) ) ) => r1_xxreal_0(k9_complex1(k4_integra5(C,D,F)),k3_xcmplx_0(E,k9_complex1(k6_xcmplx_0(D,C)))) ) ) ) ) ) ) ) )).
fof(l30_jgraph_3,axiom,( ( r1_xxreal_0(k17_euclid(k22_euclid(2)),k18_euclid(k22_euclid(2))) & r1_xxreal_0(k4_xcmplx_0(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)),k4_xcmplx_0(k18_euclid(k22_euclid(2)))) ) )).
fof(l30_jgraph_5,axiom,( ! [A] : ( ( ~ 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(k4_xcmplx_0(1),1) & k7_relset_1(u1_struct_0(k15_euclid(2)),k1_numbers,k5_pscomp_1,A) = k1_rcomp_1(k4_xcmplx_0(1),1) ) ) ) )).
fof(l30_jordan12,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(D,k1_rltopsp1(k15_euclid(2),A,B)) & ? [E] : 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] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(l30_jordan5a,axiom,( k3_topmetr = g1_pre_topc(u1_struct_0(k7_metric_1),k2_pcomps_1(k7_metric_1)) )).
fof(l30_jordan5c,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v7_ordinal1(D) => ( ( v4_topreal1(A) & v4_pre_topc(B,k15_euclid(2)) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_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,k1_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,k1_nat_1(D,1)))) ) ) ) ) ) ) )).
fof(l30_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( ( k12_supinf_2(C,D) = k5_numbers & k12_supinf_2(C,E) = k5_numbers ) => k12_supinf_2(C,k1_measure1(A,B,D,E)) = k5_numbers ) ) ) ) ) ) )).
fof(l30_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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,C,D),B),k8_cqc_lang(A,k8_cqc_lang(A,C,E),k8_cqc_lang(A,k8_cqc_lang(A,E,B),B))),k4_cqc_the1(A)) ) ) ) ) ) )).
fof(l30_matrprob,axiom,( r2_hidden(k5_numbers,k1_numbers) )).
fof(l30_measure7,axiom,( v1_funct_1(k8_funcop_1(k1_zfmisc_1(k1_numbers),k4_ordinal1,k1_subset_1(k1_numbers))) & v1_funct_2(k8_funcop_1(k1_zfmisc_1(k1_numbers),k4_ordinal1,k1_subset_1(k1_numbers)),k4_ordinal1,k9_setfam_1(k1_numbers)) & m1_subset_1(k8_funcop_1(k1_zfmisc_1(k1_numbers),k4_ordinal1,k1_subset_1(k1_numbers)),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k1_numbers)))) )).
fof(l30_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( v6_supinf_2(k1_mesfunc2(A,D)) & v6_supinf_2(k2_mesfunc2(A,D)) & v6_supinf_2(k10_mesfunc1(A,D)) ) ) ) ) ) )).
fof(l30_modcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u4_struct_0(k11_modcat_1(A,B))) => ! [D] : ( m1_subset_1(D,u4_struct_0(k11_modcat_1(A,B))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(l30_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v2_modelc_1(A) => ( k1_funct_1(A,1) != k5_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 ) ) ) )).
fof(l30_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_int_2(k1_nat_1(A,2)) => ! [B] : ( v7_ordinal1(B) => ~ ( r2_hidden(B,k2_finseq_1(A)) & B != 1 & ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(C,k2_finseq_1(A)) & C != 1 & C != B & k4_nat_d(k3_xcmplx_0(B,C),k1_nat_1(A,2)) = 1 ) ) ) ) ) ) )).
fof(l30_nat_lat,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(l30_ndiff_4,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l30_prvect_2,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(l30_realset2,axiom,( ~ 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)) )).
fof(l30_rlaffin2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_rlvect_2(E,C) => ! [F] : ( 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,k6_xcmplx_0(1,A),F)),D) = B <=> A = k7_xcmplx_0(k6_xcmplx_0(k3_funct_2(u1_struct_0(C),k1_numbers,F,D),B),k5_real_1(k3_funct_2(u1_struct_0(C),k1_numbers,F,D),k3_funct_2(u1_struct_0(C),k1_numbers,E,D))) ) ) ) ) ) ) ) ) )).
fof(l30_rlaffin3,axiom,( r2_hidden(k5_numbers,k1_numbers) )).
fof(l30_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => u1_struct_0(k1_rlsub_2(A,k2_rlsub_2(A,B,C),C)) = u1_struct_0(C) ) ) ) )).
fof(l30_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => u1_struct_0(k1_rusub_2(A,k2_rusub_2(A,B,C),C)) = u1_struct_0(C) ) ) ) )).
fof(l30_scm_comp,axiom,( ! [A] : ( m2_subset_1(A,u1_struct_0(k1_scm_comp),k7_dtconstr(k1_scm_comp)) => ! [B] : ( m1_dtconstr(B,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [C] : ( m1_dtconstr(C,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_scm_comp)) => ! [E] : ( 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] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( ( F = k3_funct_2(k4_dtconstr(k1_scm_comp),k4_ordinal1,c8__scm_comp,B) & G = k3_funct_2(k4_dtconstr(k1_scm_comp),k4_ordinal1,c8__scm_comp,C) ) => k3_funct_2(k4_dtconstr(k1_scm_comp),k4_ordinal1,c8__scm_comp,k2_scm_comp(A,B,C)) = k5_nat_1(F,G) ) ) ) ) ) ) ) ) ) )).
fof(l30_scmbsort,axiom,( k4_scmfsa_2(k5_numbers) != k4_scmfsa_2(5) )).
fof(l30_scmpds_i,axiom,( ! [A] : ( 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 ) ) )).
fof(l30_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => ~ v2_extpro_1(k3_scmring2(A,B,C),k7_card_1(2),k1_scmring2(A)) ) ) ) )).
fof(l30_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( k1_funct_1(B,k2_scmp_gcd) = k5_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)),k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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) = k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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] : ( v7_ordinal1(E) & ? [F] : ( v7_ordinal1(F) & 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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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] : ( v7_ordinal1(G) => ( 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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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] : ( v7_ordinal1(G) => ( ( 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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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] : ( v7_ordinal1(G) => ( ( 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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l30_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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] : ( m2_finseq_1(E,A) => ( k5_binop_1(A,D,C,B) = C => r2_funct_2(k4_ordinal1,A,k9_funcop_1(A,k4_ordinal1,D,k1_setwop_2(A,E,C),B),k1_setwop_2(A,k2_finseqop(A,A,A,D,E,B),C)) ) ) ) ) ) ) )).
fof(l30_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ( v2_simplex0(A) => v1_finset_1(u1_pre_topc(A)) ) ) )).
fof(l30_simplex1,axiom,( ! [A] : ( v7_ordinal1(A) => k5_card_1(A) = A ) )).
fof(l30_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_funct_1(k1_sin_cos2,k3_xcmplx_0(2,A)) = k3_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k1_sin_cos2,A)),k1_funct_1(k3_sin_cos2,A)) & k1_funct_1(k3_sin_cos2,k3_xcmplx_0(2,A)) = k6_xcmplx_0(k3_xcmplx_0(2,k1_square_1(k1_funct_1(k3_sin_cos2,A))),1) ) ) )).
fof(l30_sincos10,axiom,( r1_tarski(k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)),k1_relset_1(k1_numbers,k2_fdiff_9)) )).
fof(l30_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ( v2_topreal1(A) => v2_topreal1(k2_rfinseq(u1_struct_0(k15_euclid(2)),B,A)) ) ) ) )).
fof(l30_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l30_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( 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) ) ) )).
fof(l30_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_topdim_1(A) => v1_topdim_1(B,A) ) ) ) )).
fof(l30_topdim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( v3_topdim_1(k15_euclid(A)) & r1_xxreal_0(k4_topdim_1(k15_euclid(A)),A) ) ) )).
fof(l30_topreal2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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(k5_numbers,k5_numbers),k19_euclid(k5_numbers,1))) & ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(l30_transgeo,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(l30_vectsp_2,axiom,( ! [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) & 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))) ) ) )).
fof(l30_waybel13,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(l30_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(l30_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k6_xcmplx_0(A,B),C) => r1_xxreal_0(A,k2_xcmplx_0(B,C)) ) ) ) ) )).
fof(l30_yellow_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ~ v7_struct_0(k1_yellow_1(u1_pre_topc(A))) ) )).
fof(l31_algstr_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k8_algstr_0)) => ! [B] : ( 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) ) ) )).
fof(l31_ami_3,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => ( v2_extpro_1(A,k7_card_1(2),k1_ami_3) => A = k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0) ) ) )).
fof(l31_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) ) => ( v5_amistd_1(C,A,B) <=> ! [D] : ( ( 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(k4_ordinal1,C)) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(B)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ( r1_tarski(C,E) => ! [F] : ( v7_ordinal1(F) => r2_hidden(k5_memstr_0(A,B,k5_extpro_1(A,B,E,D,F)),k1_relset_1(k4_ordinal1,C)) ) ) ) ) ) ) ) ) ) )).
fof(l31_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( ( D = k3_rlvect_1(A,k1_rlvect_1(A,C,G),k1_rlvect_1(A,F,H)) & F = k3_rlvect_1(A,B,k1_rlvect_1(A,E,I)) ) => D = k3_rlvect_1(A,k3_rlvect_1(A,k1_rlvect_1(A,B,H),k1_rlvect_1(A,C,G)),k1_rlvect_1(A,E,k3_xcmplx_0(H,I))) ) ) ) ) ) ) ) ) ) ) )).
fof(l31_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ( ( r1_arytm_2(A,B) & r1_arytm_2(B,A) ) => A = B ) ) ) )).
fof(l31_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(1,C) ) => ( r1_xxreal_0(A,1) | r1_xxreal_0(k3_power(B,C),k3_power(A,C)) ) ) ) ) ) )).
fof(l31_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(l31_bciideal,axiom,( ! [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) ) => r1_tarski(u1_struct_0(A),k4_bcialg_1(A)) ) )).
fof(l31_binari_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(l31_binari_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( k4_nat_d(B,A) = k4_nat_d(C,A) & ! [D] : ( v1_int_1(D) => B != k2_xcmplx_0(C,k3_xcmplx_0(D,A)) ) ) ) ) ) )).
fof(l31_binop_2,axiom,( m1_subset_1(k5_numbers,k4_numbers) )).
fof(l31_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(l31_cfuncdom,axiom,( ? [A] : ( ~ v1_xboole_0(A) & ? [B] : ? [C] : ( A = k2_tarski(B,C) & B != C ) ) )).
fof(l31_coh_sp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( k4_tarski(k4_tarski(A,C),E) = k4_tarski(k4_tarski(B,D),F) => ( A = B & C = D ) ) )).
fof(l31_complex1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k3_complex1(k3_xcmplx_0(A,k7_complex1)) = k5_numbers ) )).
fof(l31_csspace,axiom,( r2_hidden(k4_struct_0(o_0_6_csspace),u1_struct_0(k3_clvect_1(o_0_6_csspace))) )).
fof(l31_descip_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( 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) ) ) )).
fof(l31_dist_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_margrel1(A) ) => ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => ( k1_funct_1(k13_margrel1(A),B) = k8_margrel1 <=> k1_funct_1(A,B) = k7_margrel1 ) ) ) )).
fof(l31_dtconstr,axiom,( v1_dtconstr(k5_dtconstr) & v2_dtconstr(k5_dtconstr) & v3_dtconstr(k5_dtconstr) )).
fof(l31_fib_num4,axiom,( ~ r1_xxreal_0(k6_xcmplx_0(3,3),k6_xcmplx_0(k3_square_1(5),3)) )).
fof(l31_fomodel4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C))))) => ! [E] : ( v5_fomodel4(E,A,C,D,B) => v4_fomodel4(k1_tarski(E),C,D,B) ) ) ) ) )).
fof(l31_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k24_gfacirc1(A,B,C) != k4_tarski(D,k3_gfacirc1) )).
fof(l31_funct_9,axiom,( v1_funct_9(k1_fdiff_9,k3_xcmplx_0(2,k28_sin_cos)) )).
fof(l31_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l31_group_10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(l31_group_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l31_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) )).
fof(l31_hahnban,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( ~ 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] : ( 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) ) ) ) ) ) ) )).
fof(l31_heyting1,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A)) => ! [C] : ( m2_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [D] : ( 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) ) ) ) )).
fof(l31_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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(E,G) & E = F ) & ~ ( ~ r2_hidden(E,G) & ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & ? [I] : ( m1_subset_1(I,u1_struct_0(A)) & r2_hidden(H,G) & r2_hidden(I,G) & r2_analoaf(A,H,B,I,E) & r2_analoaf(A,H,C,I,F) & r2_aff_1(A,E,F,G) ) ) ) ) | ( ~ ( r2_hidden(D,G) & D = F ) & ~ ( ~ r2_hidden(D,G) & ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & ? [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,F) & r2_aff_1(A,D,F,G) ) ) ) ) | E = D ) ) ) ) ) ) ) ) ) )).
fof(l31_integr19,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( ~ v8_ordinal1(E) & m1_subset_1(E,k4_ordinal1) ) => ! [F] : ( ( 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))) ) ) ) ) ) ) ) ) )).
fof(l31_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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] : ( v1_xreal_0(G) => ( r2_hidden(G,k3_integra5(C,D)) => r1_xxreal_0(k9_complex1(k1_funct_1(F,G)),E) ) ) ) => r1_xxreal_0(k9_complex1(k4_integra5(C,D,F)),k3_xcmplx_0(E,k6_xcmplx_0(D,C))) ) ) ) ) ) ) ) )).
fof(l31_jgraph_3,axiom,( k22_euclid(2) != k4_struct_0(k15_euclid(2)) )).
fof(l31_jgraph_5,axiom,( ! [A] : ( ( ~ 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) = k4_xcmplx_0(1) ) ) )).
fof(l31_jordan5c,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v7_ordinal1(D) => ( ( 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(k1_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,k1_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)))) ) ) ) ) ) ) )).
fof(l31_lfuzzy_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,C) => ( k2_relset_1(k1_numbers,k2_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,k2_fuzzy_4(A,B,C,D,E,F,G)) != k1_xboole_0 ) ) ) ) ) ) ) ) )).
fof(l31_limfunc1,axiom,( v1_funct_1(k6_partfun1(k4_ordinal1)) & v1_funct_2(k6_partfun1(k4_ordinal1),k4_ordinal1,k1_numbers) & m1_subset_1(k6_partfun1(k4_ordinal1),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) )).
fof(l31_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => r2_hidden(k8_cqc_lang(A,k8_cqc_lang(A,C,E),k8_cqc_lang(A,k8_cqc_lang(A,E,k8_cqc_lang(A,B,k8_cqc_lang(A,C,D))),k8_cqc_lang(A,B,k8_cqc_lang(A,C,D)))),k4_cqc_the1(A)) ) ) ) ) ) )).
fof(l31_matrix_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_matrix_2(B,k3_matrix_2(A)) => ( ( v5_matrix_2(B,k2_matrix_2(k3_matrix_2(A))) & r1_xxreal_0(1,A) ) => v5_matrix_2(k3_matrix_7(A,B),k2_matrix_2(k3_matrix_2(A))) ) ) ) )).
fof(l31_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ~ ( ~ ( v2_modelc_1(A) & k1_funct_1(A,1) != k5_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) = k5_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 ) ) ) )).
fof(l31_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( B = k7_finseq_1(A,C) => B = A ) ) ) ) )).
fof(l31_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ( ( v1_int_2(k1_nat_1(A,2)) & r1_tarski(k1_rvsum_1(B),k2_finseq_1(A)) & v2_funct_1(B) & ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(C,k1_rvsum_1(B)) & C != 1 & ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(D,k1_rvsum_1(B)) & D != 1 & D != C & k4_nat_d(k3_xcmplx_0(C,D),k1_nat_1(A,2)) = 1 ) ) ) ) ) => k4_nat_d(k3_wsierp_1(B),k1_nat_1(A,2)) = 1 ) ) ) )).
fof(l31_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_normsp_1(A,B,C),k2_normsp_1(A,B,k5_vfunct_1(k4_ordinal1,A,C))) ) ) ) )).
fof(l31_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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)) ) ) )).
fof(l31_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r2_prelamb(A,B,E) & r2_prelamb(A,k8_finseq_1(u1_struct_0(A),C,k12_finseq_1(u1_struct_0(A),D)),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,D,E))),B),F) ) ) ) ) ) ) ) )).
fof(l31_random_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ( v4_c0sp1(k3_random_2(A,B),k12_funcsdom(A)) & v3_c0sp1(k3_random_2(A,B),k12_funcsdom(A)) ) ) ) )).
fof(l31_rat_1,axiom,( k5_xcmplx_0(1) = 1 )).
fof(l31_realset2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(c10__realset2)) => k1_algstr_0(c10__realset2,A,k4_struct_0(c10__realset2)) = A ) )).
fof(l31_scmbsort,axiom,( k4_scmfsa_2(k5_numbers) != k4_scmfsa_2(6) )).
fof(l31_scmfsa9a,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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_sf_mastr(k2_scmfsa8b(A,k3_scmfsa6a(B,k1_scmfsa8a(k5_numbers)),k4_compos_1(k1_scmfsa_2))) = k2_sf_mastr(k1_funct_4(k2_scmfsa8b(A,k3_scmfsa6a(B,k1_scmfsa8a(k5_numbers)),k4_compos_1(k1_scmfsa_2)),k16_funcop_1(k1_nat_1(k5_card_1(B),4),k11_scmfsa_2(k5_numbers)))) ) ) )).
fof(l31_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => ~ v2_extpro_1(k4_scmring2(A,B,C),k7_card_1(2),k1_scmring2(A)) ) ) ) )).
fof(l31_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmring2(A))) => ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => k1_amistd_1(k7_card_1(2),k1_scmring2(A),C,B) = k1_tarski(k1_ordinal1(C)) ) => v1_xboole_0(k2_amistd_1(k7_card_1(2),k1_scmring2(A),B)) ) ) ) )).
fof(l31_scpinvar,axiom,( 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 )).
fof(l31_scpqsort,axiom,( ! [A] : ( v1_int_1(A) => ~ ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,k5_numbers) & A != k4_xcmplx_0(1) & A != k5_numbers ) ) )).
fof(l31_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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] : ( m2_finseq_1(E,A) => ( k5_binop_1(A,D,B,C) = C => r2_funct_2(k4_ordinal1,A,k10_funcop_1(A,k4_ordinal1,D,B,k1_setwop_2(A,E,C)),k1_setwop_2(A,k3_finseqop(A,A,A,D,B,E),C)) ) ) ) ) ) ) )).
fof(l31_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => k2_xcmplx_0(1,k2_xcmplx_0(k4_sin_cos2(A),k4_sin_cos2(A))) != k5_numbers ) )).
fof(l31_sincos10,axiom,( r1_tarski(k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4))),k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers)) )).
fof(l31_sppol_1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => m1_subset_1(a_2_0_sppol_1(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k15_euclid(2))))) ) ) )).
fof(l31_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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,k8_polynom1(A,C)) ) ) ) ) ) )).
fof(l31_topreal2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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(k5_numbers,1),k19_euclid(1,1))) & ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(l31_transgeo,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(l31_valued_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_membered(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_membered(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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 ) ) ) ) )).
fof(l31_waybel17,axiom,( ! [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] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ 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) ) ) ) ) )).
fof(l31_waybel29,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v4_waybel11(C) & m1_yellow_9(C,k1_yellow_1(u1_pre_topc(A))) ) => ! [D] : ( ( 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] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => v23_waybel_0(k3_waybel29(B,A),k1_yellow_1(u1_pre_topc(k2_borsuk_1(B,A))),k3_waybel24(B,k1_waybel29(k1_yellow_1(u1_pre_topc(A))))) ) ) ) )).
fof(l31_weierstr,axiom,( k2_struct_0(k3_topmetr) != k1_xboole_0 )).
fof(l31_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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)) ) ) )).
fof(l31_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( k4_xboole_0(k2_tarski(A,B),C) = k1_tarski(A) <=> ( ~ r2_hidden(A,C) & ( r2_hidden(B,C) | A = B ) ) ) )).
fof(l32_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( ( E = k3_rlvect_1(A,k1_rlvect_1(A,F,G),k1_rlvect_1(A,D,H)) & D = k3_rlvect_1(A,B,k1_rlvect_1(A,C,I)) ) => E = k3_rlvect_1(A,k3_rlvect_1(A,k1_rlvect_1(A,B,H),k1_rlvect_1(A,C,k3_xcmplx_0(H,I))),k1_rlvect_1(A,F,G)) ) ) ) ) ) ) ) ) ) ) )).
fof(l32_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ( k3_arytm_2(A) = k3_arytm_2(B) => A = B ) ) ) )).
fof(l32_binari_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(k5_series_1(2,A),B) => ! [C] : ( ( 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) ) ) ) ) ) ) )).
fof(l32_binari_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(l32_binop_2,axiom,( r3_binop_1(k4_numbers,c3__binop_2,k20_binop_2) )).
fof(l32_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(l32_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(l32_complex1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k4_complex1(k3_xcmplx_0(A,k7_complex1)) = A ) )).
fof(l32_csspace,axiom,( 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 )).
fof(l32_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) => ! [D] : ( m2_subset_1(D,A,B) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ( ( C = E & D = F ) => k7_ens_1(B,C,D) = k7_ens_1(A,E,F) ) ) ) ) ) ) ) )).
fof(l32_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_valued_0(D) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(l32_euclmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => 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,k6_xcmplx_0(D,F)),k1_rlvect_1(A,C,k6_xcmplx_0(E,G))) ) ) ) ) ) ) ) )).
fof(l32_fib_num4,axiom,( ~ r1_xxreal_0(k5_numbers,k7_xcmplx_0(k6_xcmplx_0(k3_square_1(5),3),2)) )).
fof(l32_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( m2_finseq_2(E,A,k4_finseq_2(k2_xcmplx_0(D,1),A)) => k1_funct_1(k6_fomodel0(A,B),k1_monoid_0(A,k12_finseq_1(A,C),E)) = k1_binop_1(B,C,k1_funct_1(k6_fomodel0(A,B),E)) ) ) ) ) ) ) )).
fof(l32_fomodel2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ~ v1_xboole_0(C) => ( v1_funct_1(k1_funct_5(k9_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)),k15_fomodel2(B,C),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0))),k6_margrel1),k21_fomodel2(B,C),A))) & v1_funct_2(k1_funct_5(k9_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)),k15_fomodel2(B,C),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0))),k6_margrel1),k21_fomodel2(B,C),A)),k15_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(k9_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)),k15_fomodel2(B,C),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0))),k6_margrel1),k21_fomodel2(B,C),A)),k1_zfmisc_1(k2_zfmisc_1(k15_fomodel2(B,C),k3_rfunct_3(k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0)),k6_margrel1)))) ) ) ) ) )).
fof(l32_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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) ) ) ) ) )).
fof(l32_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_fomodel4(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k1_fomodel4(A))) => ( ( r1_tarski(D,E) & r1_tarski(B,C) ) => ( ( ~ v7_fomodel4(C,A) & ~ v7_fomodel4(B,A) ) | r1_tarski(k3_funct_2(k1_zfmisc_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A)),k4_fomodel4(A,B),D),k3_funct_2(k1_zfmisc_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A)),k4_fomodel4(A,C),E)) ) ) ) ) ) ) ) )).
fof(l32_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ! [E] : ! [F] : r1_xboole_0(k2_msafree2(k25_gfacirc1(A,B,C)),k3_msafree2(k37_gfacirc1(D,E,F))) ) ) ) )).
fof(l32_funct_9,axiom,( ! [A] : ( v7_ordinal1(A) => v1_funct_9(k1_fdiff_9,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k2_xcmplx_0(A,1))) ) )).
fof(l32_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v11_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ! [F] : ( ( v15_functor0(F,B,C) & m2_functor0(F,B,C) ) => ! [G] : ( ( v15_functor0(G,B,C) & m2_functor0(G,B,C) ) => ! [H] : ( m2_functor2(H,B,C,F,G) => ! [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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l32_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(l32_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,k6_glib_000(A)) & ? [C] : ( m1_subset_1(C,k6_glib_000(A)) & B != C & ~ v5_glib_002(B,A) & ~ v5_glib_002(C,A) ) ) ) )).
fof(l32_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(E,k5_card_1(k3_polynom1(k15_pre_poly(A),C,D))) => ( k3_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) & k3_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) ) ) ) ) ) ) ) )).
fof(l32_group_10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v7_ordinal1(D) & v1_int_2(D) ) => ~ ( A = k3_xcmplx_0(k1_newton(D,C),B) & ~ r1_nat_d(D,B) & k4_nat_d(k4_newton(k1_newton(D,C),A),D) = k5_numbers ) ) ) ) ) )).
fof(l32_group_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) )).
fof(l32_hahnban,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( 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))) ) ) ) ) ) )).
fof(l32_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( 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) ) ) ) )).
fof(l32_hfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(A,1) => k3_xcmplx_0(k7_xcmplx_0(k2_newton(B),k2_newton(A)),A) = k7_xcmplx_0(k2_newton(B),k2_newton(k7_nat_d(A,1))) ) ) ) )).
fof(l32_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(H,u1_struct_0(A)) & ? [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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l32_hurwitz,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r1_xxreal_0(k4_xcmplx_0(1),k2_hurwitz(A,B)) ) ) )).
fof(l32_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(l32_integr11,axiom,( m1_subset_1(k7_xcmplx_0(k28_sin_cos,2),k1_numbers) & m1_subset_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k1_numbers) )).
fof(l32_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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] : ( v1_xreal_0(G) => ( r2_hidden(G,k3_integra5(C,D)) => r1_xxreal_0(k9_complex1(k1_funct_1(F,G)),E) ) ) ) => r1_xxreal_0(k9_complex1(k4_integra5(D,C,F)),k3_xcmplx_0(E,k6_xcmplx_0(D,C))) ) ) ) ) ) ) ) )).
fof(l32_interva1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [D] : ( 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))) ) ) ) )).
fof(l32_limfunc1,axiom,( ! [A] : ( v7_ordinal1(A) => k1_funct_1(c2__limfunc1,A) = A ) )).
fof(l32_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( ( A = k1_relset_1(A,D) & ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,k1_relset_1(A,D)) => k5_numbers = k1_funct_1(D,E) ) ) ) => ( r3_mesfunc6(A,B,C,D) & k1_mesfunc6(A,B,C,D) = k5_numbers ) ) ) ) ) ) )).
fof(l32_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => r2_hidden(k8_cqc_lang(A,k8_cqc_lang(A,E,k8_cqc_lang(A,B,k8_cqc_lang(A,C,D))),k8_cqc_lang(A,k8_cqc_lang(A,C,E),k8_cqc_lang(A,B,k8_cqc_lang(A,C,D)))),k4_cqc_the1(A)) ) ) ) ) ) )).
fof(l32_matrix_9,axiom,( k3_finseq_4(k4_ordinal1,1,2,3) != k3_finseq_4(k4_ordinal1,3,2,1) )).
fof(l32_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v3_membered(D) => ( D = a_3_0_mazurulm(A,B,C) => m1_xxreal_2(k4_xxreal_3(2,k2_normsp_0(A,k5_algstr_0(A,B,k1_rlvect_1(A,k3_rlvect_1(A,B,C),k6_xxreal_3(1,2))))),D) ) ) ) ) ) )).
fof(l32_metric_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(k5_numbers,D) & r1_xxreal_0(k5_numbers,E) & r1_xxreal_0(k5_numbers,F) ) => r1_xxreal_0(k3_square_1(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k2_xcmplx_0(A,C)),k1_square_1(k2_xcmplx_0(B,D))),k1_square_1(k2_xcmplx_0(E,F)))),k2_xcmplx_0(k3_square_1(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(E))),k3_square_1(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(C),k1_square_1(D)),k1_square_1(F))))) ) ) ) ) ) ) ) )).
fof(l32_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => r1_xxreal_0(1,k3_finseq_1(A)) ) )).
fof(l32_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_modelc_2(D) & m2_finseq_1(D,k4_ordinal1) ) => ( k4_modelc_2(C,A) = k4_modelc_2(D,B) => ( C = D & A = B ) ) ) ) ) ) )).
fof(l32_nat_4,axiom,( ~ 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) )).
fof(l32_ndiff_3,axiom,( v2_rcomp_1(k1_subset_1(k1_numbers)) )).
fof(l32_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(l32_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k9_rsspace4(A,B)))) => ( C = k1_ordeq_01(A,B) => v2_nfcont_1(C,k9_rsspace4(A,B)) ) ) ) ) )).
fof(l32_pdiff_7,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l32_polynom8,axiom,( ! [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) & v2_vectsp_1(A) & v4_vectsp_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( 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)) ) ) ) ) )).
fof(l32_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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)) ) ) )).
fof(l32_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r2_prelamb(A,B,E) & r2_prelamb(A,k8_finseq_1(u1_struct_0(A),k12_finseq_1(u1_struct_0(A),D),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,D,E)),B),C),F) ) ) ) ) ) ) ) )).
fof(l32_prvect_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( ( v3_normsp_1(B,A) & k6_normsp_1(A,B) = C ) => ( v2_comseq_2(k5_normsp_0(A,k4_normsp_1(A,B,C))) & k1_seq_2(k5_normsp_0(A,k4_normsp_1(A,B,C))) = k5_numbers ) ) & ( ( v2_comseq_2(k5_normsp_0(A,k4_normsp_1(A,B,C))) & k1_seq_2(k5_normsp_0(A,k4_normsp_1(A,B,C))) = k5_numbers ) => ( v3_normsp_1(B,A) & k6_normsp_1(A,B) = C ) ) ) ) ) ) )).
fof(l32_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ? [C] : ( v7_ordinal1(C) & k9_nat_1(k4_ordinal1,k1_real_3(B,A),C) = k5_numbers ) ) ) )).
fof(l32_realset2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(c10__realset2)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c10__realset2)) => ! [C] : ( 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)) ) ) ) )).
fof(l32_rfinseq,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v8_valued_0(B) & m2_finseq_1(B,k1_numbers) ) => ! [C] : ( ( v8_valued_0(C) & m2_finseq_1(C,k1_numbers) ) => ( ( A = k3_finseq_1(B) & r2_classes1(B,C) ) => B = C ) ) ) ) )).
fof(l32_rlaffin3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_finset_1(C) & v1_rlaffin1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( m2_rlaffin3(D,B,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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] : 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) ) ) ) ) ) ) ) )).
fof(l32_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => u1_struct_0(k2_rlsub_2(A,B,k1_rlsub_2(A,B,C))) = u1_struct_0(B) ) ) ) )).
fof(l32_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( 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))) ) ) ) ) )).
fof(l32_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => u1_struct_0(k2_rusub_2(A,B,k1_rusub_2(A,B,C))) = u1_struct_0(B) ) ) ) )).
fof(l32_scm_comp,axiom,( k7_dtconstr(k1_scm_comp) = k2_zfmisc_1(1,5) )).
fof(l32_scmbsort,axiom,( k4_scmfsa_2(1) != k4_scmfsa_2(2) )).
fof(l32_scmfsa8a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( ( r5_scmfsa7b(A,k1_scmfsa_m(B),C) & r6_scmfsa7b(A,k1_scmfsa_m(B),C) ) => ( k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_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(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(C,A),k1_funct_4(B,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))),1))) = k5_card_1(A) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(C,A),k1_funct_4(B,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(C,A),k1_funct_4(B,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_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(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(C,A),k1_funct_4(B,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))),1))) & r1_extpro_1(k7_card_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(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))) & k8_extpro_1(k7_card_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(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))) = k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(C,A),k1_funct_4(B,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))),1) ) ) ) ) ) )).
fof(l32_scmfsa9a,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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_sf_mastr(k2_scmfsa8b(A,k3_scmfsa6a(B,k1_scmfsa8a(k5_numbers)),k4_compos_1(k1_scmfsa_2))) = k4_sf_mastr(k1_funct_4(k2_scmfsa8b(A,k3_scmfsa6a(B,k1_scmfsa8a(k5_numbers)),k4_compos_1(k1_scmfsa_2)),k16_funcop_1(k1_nat_1(k5_card_1(B),4),k11_scmfsa_2(k5_numbers)))) ) ) )).
fof(l32_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => ~ v2_extpro_1(k5_scmring2(A,B,C),k7_card_1(2),k1_scmring2(A)) ) ) ) )).
fof(l32_scpinvar,axiom,( 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 )).
fof(l32_scpqsort,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,k5_numbers) & D = k2_xcmplx_0(B,1) & B = k2_xcmplx_0(C,A) ) => ( r1_xxreal_0(D,E) | r1_xxreal_0(E,C) ) ) ) ) ) ) ) )).
fof(l32_simplex2,axiom,( ! [A] : ( 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)) ) ) )).
fof(l32_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k3_sin_cos2,k6_xcmplx_0(A,B)) = k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(k3_sin_cos2,A),k1_funct_1(k3_sin_cos2,B)),k3_xcmplx_0(k1_funct_1(k1_sin_cos2,A),k1_funct_1(k1_sin_cos2,B))) ) ) )).
fof(l32_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(k2_xcmplx_0(k4_sin_cos2(A),1),k5_numbers) & r1_xxreal_0(k5_numbers,k6_xcmplx_0(k4_sin_cos2(A),1)) & k2_xcmplx_0(k2_xcmplx_0(k4_sin_cos2(A),2),k4_sin_cos2(A)) != k5_numbers ) ) )).
fof(l32_sincos10,axiom,( r1_tarski(k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k7_xcmplx_0(k28_sin_cos,2)),k4_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) )).
fof(l32_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(l32_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => k4_polynom1(A,C,k5_termord(A,B,C,D),k3_termord(A,B,C,D)) = k4_polynom1(A,C,D,k3_termord(A,B,C,D)) ) ) ) ) )).
fof(l32_topreal2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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(k5_numbers,k5_numbers),k19_euclid(1,k5_numbers))) & ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(l32_valued_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( m1_valued_0(C,B) => r1_tarski(k10_xtuple_0(C),k10_xtuple_0(B)) ) ) ) )).
fof(l32_vectsp_2,axiom,( ! [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) & 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))) ) ) )).
fof(l32_waybel24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => B = a_2_2_waybel24(A,B) ) ) )).
fof(l32_waybel29,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v4_waybel11(C) & m1_yellow_9(C,k1_yellow_1(u1_pre_topc(A))) ) => ! [D] : ( ( 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] : ( ( v4_waybel11(B) & m1_yellow_9(B,k1_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)))) ) ) ) ) )).
fof(l32_waybel_5,axiom,( ! [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] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( 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) ) ) )).
fof(l32_waybel_9,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k1_tarski(k5_numbers)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_tarski(k5_numbers),k1_tarski(k5_numbers)))) => ( ( A = k2_tarski(k1_xboole_0,k1_tarski(k5_numbers)) & B = k1_tarski(k4_tarski(k5_numbers,k5_numbers)) ) => ( v3_orders_2(g1_waybel_9(k1_tarski(k5_numbers),B,A)) & v1_tdlat_3(g1_waybel_9(k1_tarski(k5_numbers),B,A)) & v8_struct_0(g1_waybel_9(k1_tarski(k5_numbers),B,A)) & v13_struct_0(g1_waybel_9(k1_tarski(k5_numbers),B,A),1) ) ) ) ) )).
fof(l32_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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_xcmplx_0(k3_finseq_1(B),A),k7_finseq_1(B,C)) = k7_finseq_1(B,k2_finseq_3(A,C)) ) ) ) ) ) )).
fof(l32_xboole_1,axiom,( ! [A] : ! [B] : ( k4_xboole_0(A,B) = k1_xboole_0 <=> r1_tarski(A,B) ) )).
fof(l33_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r2_hidden(k4_tarski(A,B),k1_tarski(k4_tarski(C,D))) => ( A = C & B = D ) ) )).
fof(l33_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ~ ( k1_rlvect_1(A,B,D) = C & D != k5_numbers & ~ v9_struct_0(B,A) & v9_struct_0(C,A) ) ) ) ) ) )).
fof(l33_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( 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)) ) ) ) )).
fof(l33_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => k4_arytm_2(k3_arytm_2(A)) = A ) )).
fof(l33_binari_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( k5_int_1(B,k5_series_1(2,A)) = k5_int_1(C,k5_series_1(2,A)) => k5_int_1(k2_xcmplx_0(k5_series_1(2,k1_binari_4(A,k1_int_2(B))),B),k5_series_1(2,A)) = k5_int_1(k2_xcmplx_0(k5_series_1(2,k1_binari_4(A,k1_int_2(C))),C),k5_series_1(2,A)) ) ) ) ) )).
fof(l33_binop_2,axiom,( r3_binop_1(k4_ordinal1,k5_numbers,k23_binop_2) )).
fof(l33_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m2_connsp_2(C,A,B) => ? [D] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(l33_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(l33_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_c0sp2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_c0sp2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k11_c0sp1(u1_struct_0(A)))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l33_cc0sp2,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(l33_complex1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => k5_arytm_0(A,B) = k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1)) ) ) )).
fof(l33_csspace,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_clvect_1(o_0_6_csspace))) => ( r1_xxreal_0(k5_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))) = k5_numbers ) ) )).
fof(l33_descip_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,64,k2_finseq_1(64)) & v1_descip_1(A,64) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(64,k2_finseq_1(64)))) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( m1_subset_1(F,B) => ! [G] : ( m1_subset_1(G,B) => ! [H] : ( m1_subset_1(H,B) => ! [I] : ( m1_subset_1(I,B) => ! [J] : ( m1_subset_1(J,B) => ! [K] : ( m1_subset_1(K,B) => ! [L] : ( m1_subset_1(L,B) => ! [M] : ( m1_subset_1(M,B) => ! [N] : ( m1_subset_1(N,B) => ! [O] : ( m1_subset_1(O,B) => ! [P] : ( m1_subset_1(P,B) => ! [Q] : ( m1_subset_1(Q,B) => ! [R] : ( m1_subset_1(R,B) => ! [S] : ( m1_subset_1(S,B) => ! [T] : ( m1_subset_1(T,B) => ! [U] : ( m1_subset_1(U,B) => ! [V] : ( m1_subset_1(V,B) => ! [W] : ( m1_subset_1(W,B) => ! [X] : ( m1_subset_1(X,B) => ! [Y] : ( m1_subset_1(Y,B) => ! [Z] : ( m1_subset_1(Z,B) => ! [A1] : ( m1_subset_1(A1,B) => ! [B1] : ( m1_subset_1(B1,B) => ! [C1] : ( m1_subset_1(C1,B) => ! [D1] : ( m1_subset_1(D1,B) => ! [E1] : ( m1_subset_1(E1,B) => ! [F1] : ( m1_subset_1(F1,B) => ! [G1] : ( m1_subset_1(G1,B) => ! [H1] : ( m1_subset_1(H1,B) => ! [I1] : ( m1_subset_1(I1,B) => ! [J1] : ( m1_subset_1(J1,B) => ! [K1] : ( m1_subset_1(K1,B) => ! [L1] : ( m1_subset_1(L1,B) => ! [M1] : ( m1_subset_1(M1,B) => ! [N1] : ( m1_subset_1(N1,B) => ! [O1] : ( m1_subset_1(O1,B) => ! [P1] : ( m1_subset_1(P1,B) => ! [Q1] : ( m1_subset_1(Q1,B) => ! [R1] : ( m1_subset_1(R1,B) => ! [S1] : ( m1_subset_1(S1,B) => ! [T1] : ( m1_subset_1(T1,B) => ! [U1] : ( m1_subset_1(U1,B) => ! [V1] : ( m1_subset_1(V1,B) => ! [W1] : ( m1_subset_1(W1,B) => ! [X1] : ( m1_subset_1(X1,B) => ! [Y1] : ( m1_subset_1(Y1,B) => ! [Z1] : ( m1_subset_1(Z1,B) => ! [A2] : ( m1_subset_1(A2,B) => ! [B2] : ( m1_subset_1(B2,B) => ! [C2] : ( m1_subset_1(C2,B) => ! [D2] : ( m1_subset_1(D2,B) => ! [E2] : ( m1_subset_1(E2,B) => ! [F2] : ( m1_subset_1(F2,B) => ! [G2] : ( m1_subset_1(G2,B) => ! [H2] : ( m1_subset_1(H2,B) => ! [I2] : ( m1_subset_1(I2,B) => ! [J2] : ( m1_subset_1(J2,B) => ! [K2] : ( m1_subset_1(K2,B) => ! [L2] : ( m1_subset_1(L2,B) => ! [M2] : ( m1_subset_1(M2,B) => ! [N2] : ( m1_subset_1(N2,B) => ! [O2] : ( m2_finseq_2(O2,B,k4_finseq_2(64,B)) => ( ( k1_funct_1(O2,1) = C & k1_funct_1(O2,2) = D & k1_funct_1(O2,3) = E & k1_funct_1(O2,4) = F & k1_funct_1(O2,5) = G & k1_funct_1(O2,6) = H & k1_funct_1(O2,7) = I & k1_funct_1(O2,8) = J & k1_funct_1(O2,9) = K & k1_funct_1(O2,10) = L & k1_funct_1(O2,11) = M & k1_funct_1(O2,12) = N & k1_funct_1(O2,13) = O & k1_funct_1(O2,14) = P & k1_funct_1(O2,15) = Q & k1_funct_1(O2,16) = R & k1_funct_1(O2,17) = S & k1_funct_1(O2,18) = T & k1_funct_1(O2,19) = U & k1_funct_1(O2,20) = V & k1_funct_1(O2,21) = W & k1_funct_1(O2,22) = X & k1_funct_1(O2,23) = Y & k1_funct_1(O2,24) = Z & k1_funct_1(O2,25) = A1 & k1_funct_1(O2,26) = B1 & k1_funct_1(O2,27) = C1 & k1_funct_1(O2,28) = D1 & k1_funct_1(O2,29) = E1 & k1_funct_1(O2,30) = F1 & k1_funct_1(O2,31) = G1 & k1_funct_1(O2,32) = H1 & k1_funct_1(O2,33) = I1 & k1_funct_1(O2,34) = J1 & k1_funct_1(O2,35) = K1 & k1_funct_1(O2,36) = L1 & k1_funct_1(O2,37) = M1 & k1_funct_1(O2,38) = N1 & k1_funct_1(O2,39) = O1 & k1_funct_1(O2,40) = P1 & k1_funct_1(O2,41) = Q1 & k1_funct_1(O2,42) = R1 & k1_funct_1(O2,43) = S1 & k1_funct_1(O2,44) = T1 & k1_funct_1(O2,45) = U1 & k1_funct_1(O2,46) = V1 & k1_funct_1(O2,47) = W1 & k1_funct_1(O2,48) = X1 & k1_funct_1(O2,49) = Y1 & k1_funct_1(O2,50) = Z1 & k1_funct_1(O2,51) = A2 & k1_funct_1(O2,52) = B2 & k1_funct_1(O2,53) = C2 & k1_funct_1(O2,54) = D2 & k1_funct_1(O2,55) = E2 & k1_funct_1(O2,56) = F2 & k1_funct_1(O2,57) = G2 & k1_funct_1(O2,58) = H2 & k1_funct_1(O2,59) = I2 & k1_funct_1(O2,60) = J2 & k1_funct_1(O2,61) = K2 & k1_funct_1(O2,62) = L2 & k1_funct_1(O2,63) = M2 & k1_funct_1(O2,64) = N2 ) => ( k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),k5_numbers) = C & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),1) = D & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),2) = E & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),3) = F & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),4) = G & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),5) = H & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),6) = I & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),7) = J & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),8) = K & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),9) = L & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),10) = M & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),11) = N & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),12) = O & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),13) = P & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),14) = Q & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),15) = R & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),16) = S & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),17) = T & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),18) = U & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),19) = V & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),20) = W & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),21) = X & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),22) = Y & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),23) = Z & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),24) = A1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),25) = B1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),26) = C1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),27) = D1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),28) = E1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),29) = F1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),30) = G1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),31) = H1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),32) = I1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),33) = J1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),34) = K1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),35) = L1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),36) = M1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),37) = N1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),38) = O1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),39) = P1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),40) = Q1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),41) = R1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),42) = S1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),43) = T1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),44) = U1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),45) = V1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),46) = W1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),47) = X1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),48) = Y1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),49) = Z1 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),50) = A2 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),51) = B2 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),52) = C2 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),53) = D2 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),54) = E2 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),55) = F2 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),56) = G2 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),57) = H2 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),58) = I2 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),59) = J2 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),60) = K2 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),61) = L2 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),62) = M2 & k1_funct_1(k1_partfun1(64,k2_finseq_1(64),k4_ordinal1,B,A,O2),63) = N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l33_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(l33_euclmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(l33_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( 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] : ( 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,k6_fomodel0(A,C),k4_finseq_2(k2_xcmplx_0(D,1),B)),A,C) ) ) ) ) ) )).
fof(l33_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ~ v1_xboole_0(C) => ( v1_funct_1(k1_funct_5(k22_fomodel2(B,A,C))) & v1_funct_2(k1_funct_5(k22_fomodel2(B,A,C)),k15_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(k22_fomodel2(B,A,C)),k1_zfmisc_1(k2_zfmisc_1(k15_fomodel2(B,C),k3_rfunct_3(k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0)),k6_margrel1)))) ) ) ) ) )).
fof(l33_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(B)) ) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,E))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(B,C))) => r1_relset_1(k4_finseq_2(D,A),k4_finseq_2(D,C),k4_relset_1(k4_finseq_2(D,A),k4_finseq_2(D,E),k4_finseq_2(D,B),k4_finseq_2(D,C),k8_fomodel3(A,E,F,D),k8_fomodel3(B,C,G,D)),k8_fomodel3(A,C,k4_relset_1(A,E,B,C,F,G),D)) ) ) ) ) ) ) ) )).
fof(l33_fomodel4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k1_fomodel4(B))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k1_fomodel4(B))) => ( ( r1_tarski(E,F) & r1_tarski(C,D) ) => ( ( ~ v7_fomodel4(D,B) & ~ v7_fomodel4(C,B) ) | r1_tarski(k3_funct_2(k1_zfmisc_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B)),k5_fomodel4(B,C,A),E),k3_funct_2(k1_zfmisc_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B)),k5_fomodel4(B,D,A),F)) ) ) ) ) ) ) ) ) )).
fof(l33_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_numbers,1)) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(B,C),k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B,C),k1_numbers))) ) => ! [E] : ! [F] : ( ( r2_hidden(E,A) & r2_hidden(F,C) ) => k2_seq_4(k2_relset_1(k1_numbers,k2_fuzzy_4(A,B,C,k4_fuzzy_2(A,B),D,E,F))) = k1_funct_1(k4_fuzzy_2(A,C),k4_tarski(E,F)) ) ) ) ) ) )).
fof(l33_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_002(A) ) => ! [B] : ( ( v5_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(l33_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( ( 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) ) ) ) )).
fof(l33_hahnban,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( 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))) ) ) ) ) ) )).
fof(l33_heyting1,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k12_normform(A))) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(l33_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(H,u1_struct_0(A)) & ? [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 ) ) ) ) ) ) ) )).
fof(l33_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(l33_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ~ ( k3_int_2(A,B) = 1 & r1_int_1(B,A) ) ) ) )).
fof(l33_int_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(g3_algstr_0(k1_int_7(A),k2_int_7(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(g3_algstr_0(k1_int_7(A),k2_int_7(A)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l33_integr19,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( ~ v8_ordinal1(E) & m1_subset_1(E,k4_ordinal1) ) => ! [F] : ( ( 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))) ) ) ) ) ) ) ) ) )).
fof(l33_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => r1_tarski(k7_intpro_1(k7_intpro_1(A)),k7_intpro_1(A)) ) )).
fof(l33_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l33_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(l33_lfuzzy_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,C) => ! [H] : ( m1_subset_1(H,u1_struct_0(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)))) => k12_lattice3(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),k8_lfuzzy_0(A,C,k3_fuzzy_4(A,B,C,D,E),F,G),H) = k1_yellow_0(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),a_8_0_lfuzzy_0(A,B,C,D,E,F,G,H)) ) ) ) ) ) ) ) ) )).
fof(l33_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( v1_ideal_1(k13_lpspacc1(A,B,C),k12_lpspacc1(A)) & v1_lpspacc1(k13_lpspacc1(A,B,C),k12_lpspacc1(A)) ) ) ) ) )).
fof(l33_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v2_xxreal_0(D) & v1_xreal_0(D) ) => ( v1_ideal_1(k1_lpspace2(A,B,C,D),k7_lpspace1(A)) & v1_lpspace1(k1_lpspace2(A,B,C,D),k7_lpspace1(A)) ) ) ) ) ) )).
fof(l33_matrix_9,axiom,( k3_finseq_4(k4_ordinal1,1,2,3) != k3_finseq_4(k4_ordinal1,1,3,2) )).
fof(l33_matrtop3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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) | k2_xcmplx_0(k3_xcmplx_0(k1_funct_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_funct_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)),k3_xcmplx_0(k1_funct_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_funct_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))) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(E,B),k1_funct_1(E,B)),k3_xcmplx_0(k1_funct_1(E,C),k1_funct_1(E,C))) ) ) ) ) ) ) ) )).
fof(l33_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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),k6_xxreal_3(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),k6_xxreal_3(1,2)))))),a_3_1_mazurulm(A,B,C)) ) ) ) ) ) )).
fof(l33_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_metrizts(A) <=> ! [B] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(l33_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => v1_midsp_2(k5_midsp_2(A),A,k15_midsp_1(A)) ) )).
fof(l33_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_1(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( B = k7_finseq_1(A,C) => B = A ) ) ) ) )).
fof(l33_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_modelc_2(D) & m2_finseq_1(D,k4_ordinal1) ) => ( k5_modelc_2(C,A) = k5_modelc_2(D,B) => ( C = D & A = B ) ) ) ) ) ) )).
fof(l33_nagata_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_metric_1)) => ( ~ r1_xxreal_0(A,k5_numbers) => r2_hidden(B,k8_metric_1(k7_metric_1,B,A)) ) ) ) )).
fof(l33_ntalgo_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => ! [B] : ( m1_subset_1(B,k4_numbers) => ! [C] : ( m1_subset_1(C,k4_numbers) => ! [D] : ( m1_subset_1(D,k4_numbers) => ( ( k5_int_1(A,C) = k5_int_1(B,C) & k5_int_1(A,D) = k5_int_1(B,D) & r1_int_2(C,D) ) => k5_int_1(A,k3_xcmplx_0(C,D)) = k5_int_1(B,k3_xcmplx_0(C,D)) ) ) ) ) ) )).
fof(l33_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_o_ring_1(B,A) => v11_o_ring_1(B,A) ) ) ) )).
fof(l33_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => k1_square_1(k1_newton(2,k1_newton(2,A))) = k11_newton(2,k11_newton(2,k1_nat_1(A,1))) ) )).
fof(l33_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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)) ) ) )).
fof(l33_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r2_prelamb(A,B,D) & r2_prelamb(A,k12_finseq_1(u1_struct_0(A),C),E) ) => r2_prelamb(A,k8_finseq_1(u1_struct_0(A),k12_finseq_1(u1_struct_0(A),k2_prelamb(A,C,D)),B),E) ) ) ) ) ) ) )).
fof(l33_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(l33_realset2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(c10__realset2)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c10__realset2)) => k1_algstr_0(c10__realset2,A,B) = k1_algstr_0(c10__realset2,B,A) ) ) )).
fof(l33_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r2_rewrite1(A,B,C) => r2_rewrite1(A,C,B) ) ) )).
fof(l33_rlvect_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_orders_1(B,A,k6_partfun1(A)) => ( ~ r2_hidden(k1_xboole_0,A) => k9_xtuple_0(B) = A ) ) ) )).
fof(l33_scmbsort,axiom,( k4_scmfsa_2(1) != k4_scmfsa_2(3) )).
fof(l33_scmfsa10,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ( ! [B] : ( v7_ordinal1(B) => k1_amistd_1(k7_card_1(3),k1_scmfsa_2,B,A) = k1_tarski(k1_ordinal1(B)) ) => v1_xboole_0(k2_amistd_1(k7_card_1(3),k1_scmfsa_2,A)) ) ) )).
fof(l33_scmpds_7,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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))) = k1_nat_1(k5_card_1(D),4) ) ) ) ) )).
fof(l33_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => ~ v2_extpro_1(k6_scmring2(A,B,C),k7_card_1(2),k1_scmring2(A)) ) ) ) )).
fof(l33_scpqsort,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( 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) ) ) ) ) ) )).
fof(l33_series_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k2_xcmplx_0(k3_xcmplx_0(k11_newton(A,2),k6_xcmplx_0(k1_nat_1(k2_nat_1(2,k11_newton(A,2)),k2_nat_1(2,A)),1)),k2_nat_1(k11_newton(k1_nat_1(A,1),3),12)) = k3_xcmplx_0(k11_newton(k1_nat_1(A,2),2),k6_xcmplx_0(k1_nat_1(k2_nat_1(2,k11_newton(k1_nat_1(A,1),2)),k2_nat_1(2,k1_nat_1(A,1))),1)) ) )).
fof(l33_sincos10,axiom,( k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)) = k1_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(l33_sppol_1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( v7_ordinal1(C) => ( B = k3_tarski(a_2_0_sppol_1(A,C)) => v4_pre_topc(B,k15_euclid(2)) ) ) ) ) )).
fof(l33_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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),k3_polynom1(k15_pre_poly(A),C,k5_termord(A,B,C,D))) ) ) ) ) ) )).
fof(l33_tex_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( C = a_2_3_tex_1(A,B) & A = k6_domain_1(A,B) ) => C = k1_xboole_0 ) ) ) )).
fof(l33_topdim_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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)),k5_numbers) ) => ! [C] : ( ( v3_pre_topc(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( 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] : ( ( v3_pre_topc(E,A) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(l33_topreal2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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,k5_numbers),k19_euclid(1,1))) & ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(l33_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(l33_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( 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))) ) ) ) ) )).
fof(l33_waybel12,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(l33_waybel15,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(C,k1_waybel15(A)) & B = k1_yellow_0(A,C) ) ) ) ) ) )).
fof(l33_waybel17,axiom,( ! [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] : ( ( 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] : ( ( 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] : ( ( ~ 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))) ) ) ) ) )).
fof(l33_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) ) => ! [D] : ( 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)))) ) ) ) ) ) )).
fof(l33_waybel29,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( ( v4_waybel11(B) & m1_yellow_9(B,k1_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] : ( ( v4_waybel11(B) & m1_yellow_9(B,k1_yellow_1(u1_pre_topc(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v3_pre_topc(D,A) & m1_connsp_2(D,A,C) ) => ? [E] : ( 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) ) ) ) ) ) ) )).
fof(l33_wsierp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( k2_finseq_3(1,k7_finseq_1(k9_finseq_1(B),A)) = A & k2_finseq_3(k1_nat_1(k3_finseq_1(A),1),k7_finseq_1(A,k9_finseq_1(B))) = A ) ) )).
fof(l33_yellow16,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_yellow_1(A,B)))) => ~ ( ! [D] : ( m1_subset_1(D,A) => r1_yellow_0(k2_yellow16(A,B,D),k5_waybel_3(A,B,D,C)) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(k4_yellow_1(A,B))) => ~ ( ! [E] : ( 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(k4_yellow_1(A,B),C,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(k4_yellow_1(A,B))) => ( r2_lattice3(k4_yellow_1(A,B),C,E) => r3_orders_2(k4_yellow_1(A,B),D,E) ) ) ) ) ) ) ) ) )).
fof(l34_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l34_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) )).
fof(l34_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( 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))) ) ) ) ) ) )).
fof(l34_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ r1_anproj_1(A,B,C) & E = k1_rlvect_1(A,C,F) & F != k5_numbers & D = k1_rlvect_1(A,B,G) & G != k5_numbers & r1_anproj_1(A,D,E) ) ) ) ) ) ) ) ) )).
fof(l34_binari_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k5_numbers,C) & k5_int_1(B,k5_series_1(2,A)) = k5_int_1(C,k5_series_1(2,A)) ) => k2_binari_4(A,B) = k2_binari_4(A,C) ) ) ) ) )).
fof(l34_binop_2,axiom,( r2_hidden(1,k4_ordinal1) )).
fof(l34_cc0sp2,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(l34_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_cfuncdom(A))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(l34_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v8_compl_sp(A) => ! [B] : ( 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) ) ) ) ) )).
fof(l34_csspace,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_clvect_1(o_0_6_csspace))) => ! [B] : ( 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)) = 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)),B,A))) ) ) )).
fof(l34_ec_pf_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(l34_fdiff_7,axiom,( k3_limfunc1(k5_numbers) = a_0_0_fdiff_7 )).
fof(l34_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( v7_ordinal1(D) => ( ( v2_binop_1(C,B) & v2_fomodel0(A,B,C) ) => v2_fomodel0(k7_relset_1(k6_subset_1(k3_finseq_2(B),k1_tarski(k1_xboole_0)),B,k6_fomodel0(B,C),k4_finseq_2(k2_xcmplx_0(D,1),A)),B,C) ) ) ) ) )).
fof(l34_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(B)) ) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,E))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(B,C))) => r1_relset_1(k4_finseq_2(D,A),k4_finseq_2(D,C),k8_fomodel3(A,C,k4_relset_1(A,E,B,C,F,G),D),k4_relset_1(k4_finseq_2(D,A),k4_finseq_2(D,E),k4_finseq_2(D,B),k4_finseq_2(D,C),k8_fomodel3(A,E,F,D),k8_fomodel3(B,C,G,D))) ) ) ) ) ) ) ) )).
fof(l34_fomodel4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ! [E] : ( v2_fomodel4(E,B) => ! [F] : ( v2_fomodel4(F,B) => ( ( r1_tarski(E,F) & r1_tarski(C,D) ) => ( ( ~ v7_fomodel4(D,B) & ~ v7_fomodel4(C,B) ) | r1_tarski(k1_funct_1(k5_fomodel4(B,C,A),E),k1_funct_1(k5_fomodel4(B,D,A),F)) ) ) ) ) ) ) ) ) )).
fof(l34_funcsdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k11_funcsdom(A))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(l34_funct_9,axiom,( ! [A] : ( v7_ordinal1(A) => v1_funct_9(k2_fdiff_9,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k2_xcmplx_0(A,1))) ) )).
fof(l34_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(l34_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( ~ v1_xboole_0(D) & v1_ideal_1(D,k12_polynom1(A,C)) & v2_ideal_1(D,k12_polynom1(A,C)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ( ( r1_tarski(E,D) & ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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,k8_polynom1(A,C)) ) ) ) => k7_ideal_1(k12_polynom1(A,C),E) = D ) ) ) ) ) ) )).
fof(l34_group_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( 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) ) ) ) )).
fof(l34_group_10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_card_1(B) = k1_card_1(k5_group_2(A,C,B)) ) ) ) )).
fof(l34_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( 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)) ) ) ) ) )).
fof(l34_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( r2_hidden(C,k4_heyting3(A,B)) => v1_finset_1(C) ) ) ) )).
fof(l34_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(H,u1_struct_0(A)) & ? [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] : ( 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) ) ) ) ) ) ) ) )).
fof(l34_int_4,axiom,( ! [A] : ( 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))) ) ) )).
fof(l34_integr19,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( ~ v8_ordinal1(E) & m1_subset_1(E,k4_ordinal1) ) => ! [F] : ( ( 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))) ) ) ) ) ) ) ) )).
fof(l34_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( 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)) = k2_xcmplx_0(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)) = k6_xcmplx_0(k4_integra5(C,D,E),k4_integra5(C,D,F)) ) ) ) ) ) ) ) ) )).
fof(l34_lfuzzy_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,C) => ! [H] : ( m1_subset_1(H,u1_struct_0(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)))) => k12_lattice3(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),H,k8_lfuzzy_0(A,C,k3_fuzzy_4(A,B,C,D,E),F,G)) = k1_yellow_0(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),a_8_2_lfuzzy_0(A,B,C,D,E,F,G,H)) ) ) ) ) ) ) ) ) )).
fof(l34_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( v1_funct_1(k8_lpspace1(A,k5_numbers)) & m1_subset_1(k8_lpspace1(A,k5_numbers),k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) & r2_hidden(k8_lpspace1(A,k5_numbers),k9_lpspace1(A,B,C)) ) ) ) ) )).
fof(l34_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v2_xxreal_0(D) & v1_xreal_0(D) ) => ( v2_rlvect_1(g1_rlvect_1(k1_lpspace2(A,B,C,D),k10_subset_1(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),k10_subset_1(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),k10_subset_1(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),k10_subset_1(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),k10_subset_1(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),k10_subset_1(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),k10_subset_1(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)))) ) ) ) ) ) )).
fof(l34_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,C,A,B) & m2_finseq_1(E,k3_finseq_2(C)) ) => ! [F] : ( m2_finseq_1(F,C) => ( k2_matrix_0(E) = k2_matrix_0(k3_matrix11(D,A,B,C,E,F)) & k3_finseq_1(E) = k3_finseq_1(k3_matrix11(D,A,B,C,E,F)) & k1_matrix_0(E) = k1_matrix_0(k3_matrix11(D,A,B,C,E,F)) ) ) ) ) ) ) ) )).
fof(l34_matrix_9,axiom,( k3_finseq_4(k4_ordinal1,1,2,3) != k3_finseq_4(k4_ordinal1,2,1,3) )).
fof(l34_matrixc1,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m1_subset_1(B,k2_numbers) => k9_matrix_5(k10_funcop_1(k2_numbers,k2_numbers,k5_binop_2,A,k6_partfun1(k2_numbers)),B) = k3_xcmplx_0(A,B) ) ) )).
fof(l34_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ 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)) ) ) ) ) ) )).
fof(l34_mesfun6c,axiom,( v1_xreal_0(1) )).
fof(l34_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(k2_xcmplx_0(A,1)))) => ( B = k6_euclid_7(k2_xcmplx_0(A,1),k2_xcmplx_0(A,1)) => r1_mfold_2(k15_euclid(A),k3_mfold_2(k2_xcmplx_0(A,1),B,k4_struct_0(k15_euclid(k2_xcmplx_0(A,1))))) ) ) ) )).
fof(l34_mod_2,axiom,( ? [A] : ( m1_subset_1(A,k1_enumset1(k5_numbers,1,2)) & A = k5_numbers ) )).
fof(l34_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_1(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_1(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_modelc_1(D) & m2_finseq_1(D,k4_ordinal1) ) => ( k8_modelc_1(C,A) = k8_modelc_1(D,B) => ( C = D & A = B ) ) ) ) ) ) )).
fof(l34_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_modelc_2(D) & m2_finseq_1(D,k4_ordinal1) ) => ( k7_modelc_2(C,A) = k7_modelc_2(D,B) => ( C = D & A = B ) ) ) ) ) ) )).
fof(l34_modelc_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ~ ( r5_modelc_3(C,B) & r1_xxreal_0(1,A) & r1_xxreal_0(A,k3_finseq_1(B)) & ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( 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) = k6_xcmplx_0(k3_finseq_1(B),k6_xcmplx_0(A,1)) & k1_funct_1(E,k3_finseq_1(E)) = k1_funct_1(B,k3_finseq_1(B)) ) ) ) ) ) ) ) )).
fof(l34_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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] : ( v7_ordinal1(E) => ~ ( r2_hidden(E,k4_finseq_1(D)) & ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(l34_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(l34_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ( v2_o_ring_1(B,A) => v10_o_ring_1(B,A) ) ) ) )).
fof(l34_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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)) ) ) )).
fof(l34_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r2_prelamb(A,B,E) & r2_prelamb(A,k8_finseq_1(u1_struct_0(A),C,k12_finseq_1(u1_struct_0(A),D)),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,E,D))),F) ) ) ) ) ) ) ) )).
fof(l34_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(g3_lattices(k9_funct_2(A,k1_numbers),k4_real_lat(A),k5_real_lat(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(g3_lattices(k9_funct_2(A,k1_numbers),k4_real_lat(A),k5_real_lat(A)))) => ! [D] : ( 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) ) ) ) ) )).
fof(l34_realset2,axiom,( m3_realset1(k2_realset2,c4__realset2,c5__realset2) )).
fof(l34_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( 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)))) ) ) ) ) )).
fof(l34_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( 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) ) ) ) ) )).
fof(l34_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( 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)))) ) ) ) ) )).
fof(l34_rusub_3,axiom,( ! [A] : ! [B] : ( ~ r2_hidden(B,A) => k6_subset_1(A,k1_tarski(B)) = A ) )).
fof(l34_scm_comp,axiom,( ! [A] : ( m2_subset_1(A,u1_struct_0(k1_scm_comp),k6_dtconstr(k1_scm_comp)) => ! [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(B,u1_struct_0(k1_ami_3)) ) => ! [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(C,u1_struct_0(k1_ami_3)) ) => ( ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( 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)) ) ) ) ) )).
fof(l34_scmbsort,axiom,( k4_scmfsa_2(1) != k4_scmfsa_2(4) )).
fof(l34_scpinvar,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ( k1_funct_1(B,k2_scmp_gcd) = k5_numbers => ( ( ~ r1_xxreal_0(k1_funct_1(B,k1_scmp_gcd(3)),k5_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)),k5_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) = k5_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))) ) ) ) ) )).
fof(l34_scpqsort,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( m2_finseq_1(G,k4_numbers) => ! [H] : ( 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] : ( v7_ordinal1(I) => ( r1_xxreal_0(k1_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(k1_nat_1(C,1),D) & r1_xxreal_0(k1_nat_1(C,1),E) & r1_xxreal_0(D,k2_xcmplx_0(C,F)) & r1_xxreal_0(E,k2_xcmplx_0(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) ) ) ) ) ) ) ) ) ) ) )).
fof(l34_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k1_sin_cos2,k6_xcmplx_0(A,B)) = k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_sin_cos2,A),k1_funct_1(k3_sin_cos2,B)),k3_xcmplx_0(k1_funct_1(k3_sin_cos2,A),k1_funct_1(k1_sin_cos2,B))) ) ) )).
fof(l34_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k7_xcmplx_0(k3_xcmplx_0(k2_sin_cos2(A),k4_sin_cos2(B)),k3_xcmplx_0(k4_sin_cos2(A),k4_sin_cos2(B))) = k6_sin_cos2(A) & k3_xcmplx_0(k2_sin_cos2(A),k4_sin_cos2(B)) = k3_xcmplx_0(k6_sin_cos2(A),k3_xcmplx_0(k4_sin_cos2(A),k4_sin_cos2(B))) & k2_sin_cos2(A) = k3_xcmplx_0(k6_sin_cos2(A),k4_sin_cos2(A)) & k3_xcmplx_0(k2_sin_cos2(A),k2_sin_cos2(B)) = k3_xcmplx_0(k3_xcmplx_0(k6_sin_cos2(A),k6_sin_cos2(B)),k3_xcmplx_0(k4_sin_cos2(A),k4_sin_cos2(B))) ) ) ) )).
fof(l34_sincos10,axiom,( r1_tarski(k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_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(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))),k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))))) )).
fof(l34_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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) => k3_polynom1(k15_pre_poly(A),C,k5_termord(A,B,C,D)) = k1_xboole_0 ) ) ) ) ) )).
fof(l34_topreal8,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( ~ r1_xxreal_0(k3_finseq_1(A),C) & ~ r1_xxreal_0(C,1) & ? [E] : ( 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) ) ) ) ) ) ) )).
fof(l34_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ( k12_euclid(k5_algstr_0(k15_euclid(A),B,C)) = k5_numbers => B = C ) ) ) ) )).
fof(l34_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( D = u1_struct_0(B) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(l34_waybel15,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(C,k1_waybel15(A)) & B = k1_yellow_0(A,C) ) ) & ! [B] : ~ r5_waybel_1(A,k2_yellow_1(B)) ) ) )).
fof(l34_waybel17,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v3_pre_topc(C,A) & r2_hidden(B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r1_waybel_3(A,D,B) & r2_hidden(D,C) ) ) ) ) ) ) )).
fof(l34_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) ) => ! [D] : ( 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))) ) ) ) ) )).
fof(l34_waybel29,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( ( v4_waybel11(B) & m1_yellow_9(B,k1_yellow_1(u1_pre_topc(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v3_pre_topc(D,A) & m1_connsp_2(D,A,C) ) => ? [E] : ( 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] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v4_waybel11(C) & m1_yellow_9(C,k1_yellow_1(u1_pre_topc(A))) ) => ! [D] : ( ( 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)))) ) ) ) ) ) ) )).
fof(l34_waybel_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(C,k1_funct_2(A,k5_finsub_1(B))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(l34_yellow16,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_yellow_1(A,B)))) => ~ ( ! [D] : ( m1_subset_1(D,A) => r2_yellow_0(k2_yellow16(A,B,D),k5_waybel_3(A,B,D,C)) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(k4_yellow_1(A,B))) => ~ ( ! [E] : ( 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(k4_yellow_1(A,B),C,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(k4_yellow_1(A,B))) => ( r1_lattice3(k4_yellow_1(A,B),C,E) => r1_orders_2(k4_yellow_1(A,B),E,D) ) ) ) ) ) ) ) ) )).
fof(l34_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( v8_zf_fund1(B,A) => r2_hidden(C,B) ) ) ) ) )).
fof(l35_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ! [K] : ( v1_xreal_0(K) => ( ( C = k3_rlvect_1(A,k1_rlvect_1(A,F,J),k1_rlvect_1(A,G,K)) & F = k3_rlvect_1(A,B,k1_rlvect_1(A,D,H)) & G = k3_rlvect_1(A,B,k1_rlvect_1(A,E,I)) ) => C = k3_rlvect_1(A,k3_rlvect_1(A,k1_rlvect_1(A,B,k2_xcmplx_0(J,K)),k1_rlvect_1(A,D,k3_xcmplx_0(J,H))),k1_rlvect_1(A,E,k3_xcmplx_0(K,I))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l35_arytm_2,axiom,( ! [A] : ~ ( r2_hidden(A,k1_arytm_2) & ! [B] : ( m1_subset_1(B,k5_arytm_3) => r2_hidden(B,A) ) ) )).
fof(l35_binari_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( k5_int_1(B,k5_series_1(2,A)) = k5_int_1(C,k5_series_1(2,A)) => ( r1_xxreal_0(k5_numbers,B) | r1_xxreal_0(k5_numbers,C) | k2_binari_4(A,B) = k2_binari_4(A,C) ) ) ) ) ) )).
fof(l35_binop_2,axiom,( m1_subset_1(1,k2_numbers) )).
fof(l35_closure2,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(l35_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( 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] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ( v1_pcomps_1(B,A) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => k1_card_1(C) = 1 ) ) ) => v1_finset_1(B) ) ) ) ) )).
fof(l35_csspace,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_clvect_1(o_0_6_csspace))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_clvect_1(o_0_6_csspace))) => ! [C] : ( 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)) = k2_xcmplx_0(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))) ) ) ) )).
fof(l35_descip_1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,15) & ~ m1_subset_1(A,16) ) ) )).
fof(l35_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,A) => ( r2_hidden(B,k5_dist_1(A,k19_finseq_1(A))) => v1_dist_1(B,A) ) ) ) )).
fof(l35_dtconstr,axiom,( m2_subset_1(c2__dtconstr,u1_struct_0(k5_dtconstr),k6_dtconstr(k5_dtconstr)) )).
fof(l35_ec_pf_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(l35_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : 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)) )).
fof(l35_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( C != E & D != E & k1_funct_1(k2_finseq_7(A,B,C,D),E) != k1_funct_1(B,E) ) ) ) ) ) ) )).
fof(l35_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( 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] : ( v7_ordinal1(D) => ( ( v2_binop_1(C,A) & v2_fomodel0(B,A,C) ) => v1_fomodel0(k6_fomodel0(A,C),k4_finseq_2(k2_xcmplx_0(D,1),B)) ) ) ) ) ) )).
fof(l35_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(C),k3_rfunct_3(k3_finseq_2(D),k2_xboole_0(D,k6_margrel1))),k15_fomodel2(C,D)) => r1_relset_1(k6_subset_1(k3_finseq_2(k1_fomodel1(C)),k1_tarski(k1_xboole_0)),k6_margrel1,k23_fomodel2(C,D,A,E),k23_fomodel2(C,D,k2_xcmplx_0(A,B),E)) ) ) ) ) ) )).
fof(l35_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(B)) ) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,E))) => ! [G] : ( m1_subset_1(G,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,E,B,C,F,G),D),k4_relset_1(k4_finseq_2(D,A),k4_finseq_2(D,E),k4_finseq_2(D,B),k4_finseq_2(D,C),k8_fomodel3(A,E,F,D),k8_fomodel3(B,C,G,D))) ) ) ) ) ) ) ) )).
fof(l35_fomodel4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C))))) => ! [E] : ( 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) => ( ( ~ v7_fomodel4(E,C) & ~ v7_fomodel4(D,C) ) | r1_tarski(k1_funct_1(k5_fomodel4(C,D,A),B),k1_funct_1(k5_fomodel4(C,E,A),B)) ) ) ) ) ) ) )).
fof(l35_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ! [F] : ( ( r2_hidden(E,A) & r2_hidden(F,C) ) => k2_seq_4(k2_relset_1(k1_numbers,k2_fuzzy_4(A,B,C,D,k4_fuzzy_2(B,C),E,F))) = k1_funct_1(k4_fuzzy_2(A,C),k4_tarski(E,F)) ) ) ) ) ) )).
fof(l35_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,k6_glib_000(A)) & ? [C] : ( m1_subset_1(C,k6_glib_000(A)) & B != C & v11_glib_000(B,A) & v11_glib_000(C,A) ) ) ) )).
fof(l35_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_group_1(A,k5_numbers,B) = k1_group_1(A) ) ) )).
fof(l35_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ~ ( C != k1_xboole_0 & ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ( r2_hidden(D,C) => r2_hidden(k2_group_1(B,D),C) ) ) & ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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] : ( ( v2_group_9(D,A) & m1_group_9(D,A,B) ) => u1_struct_0(D) != C ) ) ) ) )).
fof(l35_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_substlat(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_substlat(A,B))) => ( ! [E] : ~ ( r2_hidden(E,C) & ! [F] : ~ ( r2_hidden(F,D) & r1_tarski(F,E) ) ) => r3_lattices(k5_substlat(A,B),C,D) ) ) ) ) )).
fof(l35_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(H,u1_struct_0(A)) & ? [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) ) ) ) ) ) ) ) )).
fof(l35_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ( ( r1_xxreal_0(k5_numbers,C) & ! [E] : ( 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(k5_numbers,D) & ! [E] : ( 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 ) ) ) ) ) ) )).
fof(l35_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => v8_intpro_1(k7_intpro_1(A)) ) )).
fof(l35_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & v14_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(l35_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(l35_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( ( k3_funct_2(B,k6_numbers,C,D) = k5_numbers & k3_funct_2(B,k6_numbers,C,E) = k5_numbers ) => k3_funct_2(B,k6_numbers,C,k1_measure1(A,B,D,E)) = k5_numbers ) ) ) ) ) ) )).
fof(l35_matrix_9,axiom,( k3_finseq_4(k4_ordinal1,1,2,3) != k3_finseq_4(k4_ordinal1,2,3,1) & k3_finseq_4(k4_ordinal1,1,2,3) != k3_finseq_4(k4_ordinal1,3,1,2) )).
fof(l35_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v3_membered(D) => ( D = a_3_0_mazurulm(A,B,C) => ! [E] : ( ( 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),k6_xxreal_3(1,2))) = k1_rlvect_1(A,k3_rlvect_1(A,B,C),k6_xxreal_3(1,2)) ) ) ) ) ) ) ) )).
fof(l35_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ( v1_metrizts(A) <=> v5_waybel23(A) ) ) )).
fof(l35_mod_2,axiom,( ? [A] : ( m1_subset_1(A,k1_enumset1(k5_numbers,1,2)) & A = 1 ) )).
fof(l35_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_1(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_1(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_modelc_1(D) & m2_finseq_1(D,k4_ordinal1) ) => ( k11_modelc_1(C,A) = k11_modelc_1(D,B) => ( C = D & A = B ) ) ) ) ) ) )).
fof(l35_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_modelc_2(D) & m2_finseq_1(D,k4_ordinal1) ) => ( k8_modelc_2(C,A) = k8_modelc_2(D,B) => ( C = D & A = B ) ) ) ) ) ) )).
fof(l35_nat_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( ~ 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 ) ) )).
fof(l35_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l35_ndiff_3,axiom,( v3_rcomp_1(k2_subset_1(k1_numbers)) )).
fof(l35_neckla_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ 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)) ) ) ) ) )).
fof(l35_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v3_o_ring_1(B,A) => v11_o_ring_1(B,A) ) ) ) )).
fof(l35_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & 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(k5_ordeq_01(A,B)) & v13_algstr_0(k5_ordeq_01(A,B)) & v2_rlvect_1(k5_ordeq_01(A,B)) & v3_rlvect_1(k5_ordeq_01(A,B)) & v4_rlvect_1(k5_ordeq_01(A,B)) & v5_rlvect_1(k5_ordeq_01(A,B)) & v6_rlvect_1(k5_ordeq_01(A,B)) & v7_rlvect_1(k5_ordeq_01(A,B)) & v8_rlvect_1(k5_ordeq_01(A,B)) & v3_normsp_0(k5_ordeq_01(A,B)) & v4_normsp_0(k5_ordeq_01(A,B)) & v2_normsp_1(k5_ordeq_01(A,B)) & v3_lopban_1(k5_ordeq_01(A,B)) & l1_normsp_1(k5_ordeq_01(A,B)) ) ) ) )).
fof(l35_polyeq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k1_newton(k5_numbers,A) = k5_numbers ) ) )).
fof(l35_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => r2_hidden(k3_polynom1(k15_pre_poly(A),C,D),k5_finsub_1(u1_struct_0(g1_orders_2(k15_pre_poly(A),B)))) ) ) ) ) )).
fof(l35_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r2_prelamb(A,B,E) & r2_prelamb(A,k8_finseq_1(u1_struct_0(A),k12_finseq_1(u1_struct_0(A),D),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,E,D))),C),F) ) ) ) ) ) ) ) )).
fof(l35_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(g3_lattices(k9_funct_2(A,k1_numbers),k4_real_lat(A),k5_real_lat(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(g3_lattices(k9_funct_2(A,k1_numbers),k4_real_lat(A),k5_real_lat(A)))) => ! [D] : ( 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) ) ) ) ) )).
fof(l35_realset2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(l35_scm_comp,axiom,( ! [A] : ( m2_subset_1(A,u1_struct_0(k1_scm_comp),k7_dtconstr(k1_scm_comp)) => ! [B] : ( m1_dtconstr(B,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [C] : ( 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] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ! [E] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(E,u1_struct_0(k1_ami_3)) ) => ( ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( 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] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ! [E] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(E,u1_struct_0(k1_ami_3)) ) => ( ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( 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] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ! [E] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(E,u1_struct_0(k1_ami_3)) ) => ( ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( 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)) ) ) ) ) ) ) ) )).
fof(l35_scmbsort,axiom,( k4_scmfsa_2(1) != k4_scmfsa_2(5) )).
fof(l35_scpinvar,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ( ( k1_funct_1(B,k2_scmp_gcd) = k5_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)),k5_numbers) | r1_xxreal_0(k1_funct_1(B,k1_scmp_gcd(2)),k5_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) ) ) ) ) ) )).
fof(l35_scpqsort,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v1_int_1(F) => ! [G] : ( v1_int_1(G) => ( ( ! [H] : ( v7_ordinal1(H) => ( 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] : ( v7_ordinal1(H) => ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l35_series_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k3_xcmplx_0(k2_nat_1(k1_nat_1(A,2),k1_nat_1(k2_nat_1(2,k1_nat_1(A,1)),1)),k2_xcmplx_0(k6_xcmplx_0(k1_nat_1(k2_nat_1(3,k11_newton(k1_nat_1(A,1),4)),k2_nat_1(6,k11_newton(k1_nat_1(A,1),3))),k2_nat_1(3,k1_nat_1(A,1))),1)) = k1_nat_1(k1_nat_1(k1_nat_1(k1_nat_1(k1_nat_1(k1_nat_1(k2_nat_1(6,k11_newton(A,6)),k2_nat_1(57,k11_newton(A,5))),k2_nat_1(216,k11_newton(A,4))),k2_nat_1(414,k11_newton(A,3))),k2_nat_1(419,k11_newton(A,2))),k2_nat_1(211,A)),42) ) )).
fof(l35_sincos10,axiom,( k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos) = k1_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos))) )).
fof(l35_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k5_substlat(A,B))) => ! [D] : ( 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) ) ) )).
fof(l35_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(l35_topalg_5,axiom,( k1_relset_1(u1_struct_0(k2_topalg_2),k12_toprealb) = k1_numbers )).
fof(l35_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( 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) ) ) ) )).
fof(l35_topreal8,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( ~ 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)),k1_nat_1(D,1)) & ? [E] : ( 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)) ) ) ) ) ) ) )).
fof(l35_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ( B = C => k12_euclid(k5_algstr_0(k15_euclid(A),B,C)) = k5_numbers ) ) ) ) )).
fof(l35_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) ) ) )).
fof(l35_valuat_1,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( 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 ) ) ) )).
fof(l35_vectsp_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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,k1_tarski(k5_ordinal1),k9_funct_5,k5_funct_5,k10_funct_3(u1_struct_0(A),k1_tarski(k5_ordinal1)),k9_funct_3(k1_tarski(k5_ordinal1),u1_struct_0(B)))) & v3_rlvect_1(g2_vectsp_2(A,B,k1_tarski(k5_ordinal1),k9_funct_5,k5_funct_5,k10_funct_3(u1_struct_0(A),k1_tarski(k5_ordinal1)),k9_funct_3(k1_tarski(k5_ordinal1),u1_struct_0(B)))) & v4_rlvect_1(g2_vectsp_2(A,B,k1_tarski(k5_ordinal1),k9_funct_5,k5_funct_5,k10_funct_3(u1_struct_0(A),k1_tarski(k5_ordinal1)),k9_funct_3(k1_tarski(k5_ordinal1),u1_struct_0(B)))) & v13_algstr_0(g2_vectsp_2(A,B,k1_tarski(k5_ordinal1),k9_funct_5,k5_funct_5,k10_funct_3(u1_struct_0(A),k1_tarski(k5_ordinal1)),k9_funct_3(k1_tarski(k5_ordinal1),u1_struct_0(B)))) ) ) ) )).
fof(l35_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( 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) ) ) ) ) )).
fof(l35_waybel12,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( m1_waybel12(C,A,B) => r1_tarski(C,B) ) ) ) )).
fof(l35_waybel17,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => v3_pre_topc(k2_waybel_3(A,B),A) ) ) )).
fof(l35_waybel29,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( ( v4_waybel11(B) & m1_yellow_9(B,k1_yellow_1(u1_pre_topc(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v3_pre_topc(D,A) & m1_connsp_2(D,A,C) ) => ? [E] : ( 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(k1_yellow_1(u1_pre_topc(A))) ) ) )).
fof(l35_waybel_5,axiom,( ! [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] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( ( 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] : ( ( 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] : ( m2_pboole(H,B,G,k7_funcop_1(B,u1_struct_0(A))) => ( ! [I] : ( m1_subset_1(I,B) => ! [J] : ( 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)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l35_wsierp_1,axiom,( ! [A] : ( ( 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)))) ) ) ) )).
fof(l35_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_compts_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r3_waybel_9(A,B,C) ) ) ) ) )).
fof(l35_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(l36_algstr_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_1)) => ! [B] : ( 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 ) ) ) ) )).
fof(l36_anproj_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( A != C & B != k5_numbers & k6_xcmplx_0(k3_xcmplx_0(C,B),k3_xcmplx_0(A,B)) = k5_numbers ) ) ) ) )).
fof(l36_binop_2,axiom,( r3_binop_1(k2_numbers,c4__binop_2,k5_binop_2) )).
fof(l36_catalg_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(l36_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ? [B] : ( 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 ) ) )).
fof(l36_classes1,axiom,( k4_classes1(k5_ordinal1) = k1_xboole_0 & ! [A] : ( v3_ordinal1(A) => k4_classes1(k1_ordinal1(A)) = k9_setfam_1(k4_classes1(A)) ) & ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) ) => ( ( v4_ordinal1(A) & k9_xtuple_0(B) = A & ! [C] : ( v3_ordinal1(C) => ( r2_hidden(C,A) => k1_funct_1(B,C) = k4_classes1(C) ) ) ) => ( A = k5_ordinal1 | k4_classes1(A) = k3_tarski(k10_xtuple_0(B)) ) ) ) ) )).
fof(l36_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ( v1_pcomps_1(B,A) & ! [C] : ( 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( ~ v1_finset_1(B) & v1_xboole_0(k2_topgen_1(A,B)) ) ) ) ) )).
fof(l36_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => r1_tarski(a_2_0_cqc_the1(A,B),k3_cqc_lang(A)) ) ) )).
fof(l36_csspace,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_clvect_1(o_0_6_csspace))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_clvect_1(o_0_6_csspace))) => ! [C] : ( 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))) ) ) ) )).
fof(l36_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,A) => ( v1_dist_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( v1_dist_1(C,A) => r2_hidden(C,k5_dist_1(A,B)) ) ) ) ) ) )).
fof(l36_dtconstr,axiom,( m2_subset_1(c3__dtconstr,u1_struct_0(k5_dtconstr),k7_dtconstr(k5_dtconstr)) )).
fof(l36_facirc_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k15_facirc_1(A,B,C),k18_facirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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) ) ) ) ) ) ) )).
fof(l36_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ( v2_funct_1(C) => v2_funct_1(k2_rfinseq(B,A,C)) ) ) ) ) )).
fof(l36_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( v7_ordinal1(D) => ( ( v2_binop_1(C,B) & v2_fomodel0(A,B,C) ) => v1_fomodel0(k6_fomodel0(B,C),k4_finseq_2(k2_xcmplx_0(D,1),A)) ) ) ) ) )).
fof(l36_fomodel1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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))) ) ) ) )).
fof(l36_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(B),k3_rfunct_3(k3_finseq_2(C),k2_xboole_0(C,k6_margrel1))),k15_fomodel2(B,C)) => ! [F] : ( m2_subset_1(F,k9_funct_2(k37_fomodel1(B),k3_rfunct_3(k3_finseq_2(D),k2_xboole_0(D,k6_margrel1))),k15_fomodel2(B,D)) => r1_tarski(k1_relset_1(k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0)),k23_fomodel2(B,C,A,E)),k1_relset_1(k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0)),k23_fomodel2(B,D,A,F))) ) ) ) ) ) ) )).
fof(l36_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(l36_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ! [D] : ( 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) => ( ( ~ v7_fomodel4(D,B) & ~ v7_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)),k4_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)),k4_fomodel4(B,D)),k1_tarski(A)))) ) ) ) ) ) )).
fof(l36_funct_9,axiom,( v1_funct_9(k26_sin_cos,k28_sin_cos) )).
fof(l36_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ( ( r1_analmetr(A,H,I) & r1_geomtrap(A,B,E,B,C) & r1_geomtrap(A,B,E,B,F) & r1_geomtrap(A,B,E,B,D) & r1_geomtrap(A,B,E,B,G) ) => ( B = E | r1_geomtrap(A,C,F,D,G) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l36_gfacirc2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( 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(k5_numbers,k6_margrel1),k8_margrel1) & k9_xtuple_0(k2_xtuple_0(k7_gfacirc2(C,A,B))) = k4_finseq_2(k5_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) ) ) ) ) ) )).
fof(l36_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => m1_glib_000(A,A) ) )).
fof(l36_gr_cy_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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) ) ) ) )).
fof(l36_group_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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) ) ) )).
fof(l36_group_10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(l36_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(l36_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(l36_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(H,u1_struct_0(A)) & ? [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) ) ) ) ) ) ) ) )).
fof(l36_hurwitz,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( C != k5_numbers => ( k1_funct_1(k1_funct_4(k9_polynom3(A),k5_funct_4(u1_struct_0(A),k5_numbers,C,k4_algstr_0(A,k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k4_group_1(A),B,C)),k1_group_1(A))),k5_numbers) = k4_algstr_0(A,k2_binop_1(u1_struct_0(A),k4_ordinal1,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),k5_numbers,C,k4_algstr_0(A,k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k4_group_1(A),B,C)),k1_group_1(A))),C) = k1_group_1(A) ) ) ) ) ) )).
fof(l36_integr19,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( ~ v8_ordinal1(F) & m1_subset_1(F,k4_ordinal1) ) => ! [G] : ( ( 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] : ( 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)),k3_xcmplx_0(E,k9_complex1(k6_xcmplx_0(D,C)))) ) ) ) ) ) ) ) ) )).
fof(l36_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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)) = k3_xcmplx_0(E,k4_integra5(C,D,F)) ) ) ) ) ) ) ) )).
fof(l36_interva1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_interva1(B,A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ! [C] : ( r2_hidden(C,B) => ( C = k7_interva1(A,B) <=> ! [D] : ( r2_hidden(D,B) => r1_tarski(C,D) ) ) ) ) )).
fof(l36_jordan22,axiom,( g1_pre_topc(u1_struct_0(k15_euclid(2)),u1_pre_topc(k15_euclid(2))) = k3_pcomps_1(k14_euclid(2)) )).
fof(l36_matrix_9,axiom,( k3_finseq_4(k4_ordinal1,3,2,1) != k3_finseq_4(k4_ordinal1,2,3,1) & k3_finseq_4(k4_ordinal1,3,2,1) != k3_finseq_4(k4_ordinal1,3,1,2) )).
fof(l36_matrixj2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( m1_vectsp_4(E,A,B) => ! [F] : ( m1_vectsp_4(F,A,C) => ! [G] : ( ( 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)))) ) ) ) ) ) ) ) ) ) )).
fof(l36_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ( r1_tarski(A,B) => r1_tarski(k7_member_1(A),k7_member_1(B)) ) ) ) )).
fof(l36_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ( v1_metrizts(A) <=> v7_topgen_1(A) ) ) )).
fof(l36_mod_2,axiom,( ? [A] : ( m1_subset_1(A,k1_enumset1(k5_numbers,1,2)) & A = 2 ) )).
fof(l36_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v2_modelc_1(A) => ( ~ v3_modelc_1(A) & ~ v4_modelc_1(A) & ~ v5_modelc_1(A) & ~ v6_modelc_1(A) & ~ v7_modelc_1(A) ) ) ) )).
fof(l36_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( 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) ) ) ) )).
fof(l36_msualg_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,k13_msualg_4(A,B,C)),F)) => ! [H] : ( 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))) ) ) ) ) ) ) )).
fof(l36_nat_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( ~ r1_xxreal_0(841,A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( ~ r1_xxreal_0(B,1) & r1_xxreal_0(k2_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 ) ) ) ) )).
fof(l36_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(l36_oposet_1,axiom,( k6_partfun1(k1_tarski(k1_xboole_0)) = k1_tarski(k4_tarski(k1_xboole_0,k1_xboole_0)) )).
fof(l36_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => r1_tarski(A,k2_zfmisc_1(k1_relat_1(A),k1_relat_1(A))) ) )).
fof(l36_polynom8,axiom,( ! [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) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B != k4_struct_0(A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k3_polynom8(A,k11_algstr_0(A,B),C) = k11_algstr_0(A,k3_polynom8(A,B,C)) ) ) ) ) )).
fof(l36_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r2_prelamb(A,B,D) & r2_prelamb(A,k12_finseq_1(u1_struct_0(A),C),E) ) => r2_prelamb(A,k8_finseq_1(u1_struct_0(A),B,k12_finseq_1(u1_struct_0(A),k1_prelamb(A,D,C))),E) ) ) ) ) ) ) )).
fof(l36_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ 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))) ) ) ) ) )).
fof(l36_realset2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(c10__realset2)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c10__realset2)) => ! [C] : ( 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)) ) ) ) ) )).
fof(l36_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(l36_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( 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) ) ) ) ) )).
fof(l36_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(l36_scmbsort,axiom,( k4_scmfsa_2(1) != k4_scmfsa_2(6) )).
fof(l36_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => ~ v2_extpro_1(k7_scmring2(A,C,B),k7_card_1(2),k1_scmring2(A)) ) ) ) )).
fof(l36_scpinvar,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ~ ( ~ r1_xxreal_0(k1_funct_1(B,k1_scmp_gcd(1)),k5_numbers) & ~ r1_xxreal_0(k1_funct_1(B,k1_scmp_gcd(2)),k5_numbers) & ~ ( k1_funct_1(k6_scmpds_4(k1_scmpds_4(k3_scmpds_4(k4_scmpds_4(k5_scmpds_2(k2_scmp_gcd,k5_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,k5_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,k5_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,k5_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) ) ) ) ) )).
fof(l36_scpqsort,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( 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,k5_numbers) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( m2_finseq_1(G,k4_numbers) => ! [H] : ( m2_finseq_1(H,k4_numbers) => ( ( k1_funct_1(C,k2_scmp_gcd) = k5_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(k1_nat_1(F,1),D) & r1_xxreal_0(D,E) & r1_xxreal_0(k1_nat_1(F,1),k1_funct_1(C,k1_scmp_gcd(3))) & r1_xxreal_0(k1_funct_1(C,k1_scmp_gcd(4)),k2_xcmplx_0(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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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)),k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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) = k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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] : ( v7_ordinal1(I) => ( ( 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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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] : ( v7_ordinal1(I) => ( 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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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] : ( v7_ordinal1(I) => ( r1_xxreal_0(k1_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l36_series_1,axiom,( v1_xreal_0(1) )).
fof(l36_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k5_sin_cos2,k6_xcmplx_0(A,B)) = k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(k5_sin_cos2,A),k1_funct_1(k5_sin_cos2,B)),k6_xcmplx_0(1,k3_xcmplx_0(k1_funct_1(k5_sin_cos2,A),k1_funct_1(k5_sin_cos2,B)))) ) ) )).
fof(l36_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ r1_xxreal_0(k2_xcmplx_0(k1_square_1(A),1),k5_numbers) ) )).
fof(l36_sincos10,axiom,( r1_tarski(k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_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(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos)),k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos)))) )).
fof(l36_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k5_substlat(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_substlat(A,B))) => ! [E] : ( 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) ) ) ) )).
fof(l36_taylor_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ? [D] : ( 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] : ( v1_xreal_0(E) => k1_funct_1(D,E) = k7_xcmplx_0(k3_xcmplx_0(B,k1_newton(k6_xcmplx_0(C,E),k1_nat_1(A,1))),k2_newton(k1_nat_1(A,1))) ) & ! [E] : ( v1_xreal_0(E) => ( r1_fdiff_1(D,E) & k1_fdiff_1(D,E) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(B,k1_newton(k6_xcmplx_0(C,E),A)),k2_newton(A))) ) ) ) ) ) ) )).
fof(l36_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(l36_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [F] : ( m2_funct_2(F,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ? [G] : ( m2_funct_2(G,k3_qc_lang1(A),B,k2_valuat_1(A,B)) & ! [H] : ( 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) ) ) ) ) ) ) ) )).
fof(l36_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(l36_waybel17,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_yellow_8(a_2_4_waybel17(A,B),A,B) & v1_tops_2(a_2_4_waybel17(A,B),A) & m1_subset_1(a_2_4_waybel17(A,B),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) ) )).
fof(l36_waybel29,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & l1_pre_topc(A) ) => ( v3_waybel_3(k1_yellow_1(u1_pre_topc(A))) => ! [B] : ( ( v4_waybel11(B) & m1_yellow_9(B,k1_yellow_1(u1_pre_topc(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v3_pre_topc(D,A) & m1_connsp_2(D,A,C) ) => ? [E] : ( 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) ) ) ) ) ) ) )).
fof(l36_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : k4_xboole_0(A,k3_xboole_0(B,C)) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C)) )).
fof(l36_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l36_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ~ r3_waybel_9(A,B,C) ) ) ) => v1_compts_1(A) ) ) )).
fof(l37_algstr_1,axiom,( k5_numbers = k4_struct_0(k3_algstr_1) )).
fof(l37_anproj_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ( ( k2_xcmplx_0(E,G) = k2_xcmplx_0(F,H) & k3_xcmplx_0(E,A) = k3_xcmplx_0(F,C) & k3_xcmplx_0(G,D) = k3_xcmplx_0(H,B) ) => ( A = C | B = k5_numbers | E = k3_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(C,D),k3_xcmplx_0(C,B)),k5_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(C,B),k3_xcmplx_0(A,B)))),G) ) ) ) ) ) ) ) ) ) ) )).
fof(l37_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_bhsp_2(D,A) & k1_bhsp_2(A,D) = C ) => ( v2_comseq_2(k2_bhsp_2(A,k5_bhsp_1(A,D,B))) & k1_seq_2(k2_bhsp_2(A,k5_bhsp_1(A,D,B))) = k3_bhsp_1(A,k3_rlvect_1(A,C,B)) ) ) ) ) ) ) )).
fof(l37_binop_2,axiom,( r2_hidden(1,k4_ordinal1) )).
fof(l37_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_clvect_2(D,A) & k1_clvect_2(A,D) = C ) => ( v2_comseq_2(k2_clvect_2(A,k5_bhsp_1(A,D,B))) & k1_seq_2(k2_clvect_2(A,k5_bhsp_1(A,D,B))) = k13_csspace(A,k3_rlvect_1(A,C,B)) ) ) ) ) ) ) )).
fof(l37_convex1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(l37_csspace,axiom,( ! [A] : ( 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] : ( 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] : ( 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] : ( 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(k5_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))) & k5_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) = k8_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)) ) ) ) ) ) )).
fof(l37_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(l37_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ~ ( r3_euclidlp(A,B,C) & B = k5_euclid(A) ) ) ) ) )).
fof(l37_finseq_3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r1_tarski(A,k2_finseq_1(B)) => v2_funct_1(k14_finseq_1(A)) ) ) )).
fof(l37_fomodel2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(B),k3_rfunct_3(k3_finseq_2(C),k2_xboole_0(C,k6_margrel1))),k15_fomodel2(B,C)) => ! [F] : ( m2_subset_1(F,k9_funct_2(k37_fomodel1(B),k3_rfunct_3(k3_finseq_2(D),k2_xboole_0(D,k6_margrel1))),k15_fomodel2(B,D)) => k1_relset_1(k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0)),k23_fomodel2(B,C,A,E)) = k1_relset_1(k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0)),k23_fomodel2(B,D,A,F)) ) ) ) ) ) ) )).
fof(l37_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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))) ) ) ) ) )).
fof(l37_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C))))) => ! [E] : ( 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) & v4_fomodel4(B,C,D,A) ) => ( ( ~ v7_fomodel4(E,C) & ~ v7_fomodel4(D,C) ) | v4_fomodel4(B,C,E,A) ) ) ) ) ) )).
fof(l37_frechet,axiom,( r1_tarski(k1_tarski(k1_numbers),u1_struct_0(k3_frechet)) )).
fof(l37_funct_9,axiom,( v1_funct_9(k27_sin_cos,k28_sin_cos) )).
fof(l37_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [D] : ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [E] : ( 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) => D = E ) ) ) ) ) ) )).
fof(l37_gfacirc2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ! [E] : ( ( 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) ) ) ) ) )).
fof(l37_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ! [D] : ! [E] : ( r1_glib_000(B,C,D,E) => r1_glib_000(A,C,D,E) ) ) ) )).
fof(l37_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( r1_xxreal_0(C,k3_finseq_1(B)) => r2_hidden(k1_funct_1(B,C),k6_glib_000(A)) ) ) ) ) )).
fof(l37_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(l37_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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) ) ) )).
fof(l37_hurwitz,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( v7_ordinal1(D) => ~ ( D != k5_numbers & D != C & k1_funct_1(k1_funct_4(k9_polynom3(A),k5_funct_4(u1_struct_0(A),k5_numbers,C,k4_algstr_0(A,k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k4_group_1(A),B,C)),k1_group_1(A))),D) != k4_struct_0(A) ) ) ) ) ) )).
fof(l37_integr19,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( ~ v8_ordinal1(F) & m1_subset_1(F,k4_ordinal1) ) => ! [G] : ( ( 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] : ( 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)),k3_xcmplx_0(E,k6_xcmplx_0(D,C))) ) ) ) ) ) ) ) ) )).
fof(l37_interva1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_interva1(B,A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ! [C] : ( r2_hidden(C,B) => ( C = k8_interva1(A,B) <=> ! [D] : ( r2_hidden(D,B) => r1_tarski(D,C) ) ) ) ) )).
fof(l37_jgraph_3,axiom,( g1_pre_topc(u1_struct_0(k15_euclid(2)),u1_pre_topc(k15_euclid(2))) = k3_pcomps_1(k14_euclid(2)) )).
fof(l37_jordan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(l37_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [C] : ( m2_finseq_2(C,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ( ( k10_xtuple_0(B) = k10_xtuple_0(C) & v2_funct_1(B) ) => v2_funct_1(C) ) ) ) ) )).
fof(l37_matrix_9,axiom,( k3_finseq_4(k4_ordinal1,3,2,1) != k3_finseq_4(k4_ordinal1,2,1,3) & k3_finseq_4(k4_ordinal1,1,3,2) != k3_finseq_4(k4_ordinal1,2,1,3) )).
fof(l37_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => k3_rlvect_1(A,k1_rlvect_1(A,B,k3_xxreal_3(1,D)),k1_rlvect_1(A,C,D)) = k3_rlvect_1(A,B,k1_rlvect_1(A,k5_algstr_0(A,C,B),D)) ) ) ) ) )).
fof(l37_metrizts,axiom,( v5_waybel23(g1_pre_topc(u1_struct_0(k15_euclid(1)),u1_pre_topc(k15_euclid(1)))) )).
fof(l37_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v3_modelc_1(A) => ( ~ v2_modelc_1(A) & ~ v4_modelc_1(A) & ~ v5_modelc_1(A) & ~ v6_modelc_1(A) & ~ v7_modelc_1(A) ) ) ) )).
fof(l37_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( 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) ) ) ) )).
fof(l37_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & m1_msualg_2(D,A,C) ) => ! [E] : ( m2_pboole(E,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(l37_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_nattra_1(E,A,B,C,D) => ( ( r2_nattra_1(A,B,C,D) & v1_nattra_1(E,A,B,C,D) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( k2_cat_1(A,F,G) != k1_xboole_0 => ! [H] : ( 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),k2_nattra_1(A,B,D,C,k6_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),k2_nattra_1(A,B,D,C,k6_nattra_1(A,B,C,D,E),F),k9_cat_3(A,F,G,B,C,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(l37_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v5_o_ring_1(B,A) => v11_o_ring_1(B,A) ) ) ) )).
fof(l37_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,k2_oppcat_1(B),A) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k3_funct_2(u4_struct_0(B),u4_struct_0(A),k9_oppcat_1(B,A,C),k4_cat_1(B,D)) = k4_cat_1(A,k3_funct_2(u1_struct_0(k2_oppcat_1(B)),u1_struct_0(A),k7_cat_1(k2_oppcat_1(B),A,C),k3_oppcat_1(B,D))) ) ) ) ) )).
fof(l37_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ( v1_relat_2(A) & r1_tarski(B,k1_relat_1(A)) ) => k1_relat_1(k2_wellord1(A,B)) = B ) ) )).
fof(l37_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l37_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k2_finseq_1(C)) => k4_radix_1(D,A,k2_xcmplx_0(C,1),k10_radix_1(A,k2_xcmplx_0(C,1),B)) = k4_radix_1(D,A,C,k10_radix_1(A,C,k4_nat_d(B,k1_newton(k1_radix_1(A),C)))) ) ) ) ) ) )).
fof(l37_ratfunc1,axiom,( ! [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) & v1_vectsp_2(A) & l6_algstr_0(A) ) => ! [B] : ( m1_ratfunc1(B,A) => ~ ( v5_ratfunc1(B,A) & ! [C] : ( m1_ratfunc1(C,A) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & ~ v1_ratfunc1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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] : ( m2_finseq_1(E,u1_struct_0(k14_polynom3(A))) & D = k3_group_4(k14_polynom3(A),E) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( r2_hidden(F,k4_finseq_1(E)) & ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l37_scmbsort,axiom,( k4_scmfsa_2(2) != k4_scmfsa_2(3) )).
fof(l37_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmring2(A))) => ( v2_extpro_1(B,k7_card_1(2),k1_scmring2(A)) => B = k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0) ) ) ) )).
fof(l37_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( k1_funct_1(B,k2_scmp_gcd) = k5_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(k1_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(2),6,k5_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,k5_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,k5_numbers)),k13_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),6,k5_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,k5_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,k5_numbers),k16_scmpds_2(k1_scmp_gcd(4),k1_scmp_gcd(3),k5_numbers,k5_numbers)),k16_scmpds_2(k1_scmp_gcd(3),k2_scmp_gcd,k5_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) ) ) ) ) ) ) ) )).
fof(l37_series_1,axiom,( r2_hidden(1,k1_numbers) )).
fof(l37_series_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k3_xcmplx_0(k11_newton(k1_nat_1(A,2),2),k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k1_nat_1(k2_nat_1(3,k11_newton(k1_nat_1(A,1),4)),k2_nat_1(6,k11_newton(k1_nat_1(A,1),3))),k11_newton(k1_nat_1(A,1),2)),k2_nat_1(4,k1_nat_1(A,1))),2)) = k2_xcmplx_0(k3_xcmplx_0(k11_newton(A,2),k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k1_nat_1(k2_nat_1(3,k11_newton(A,4)),k2_nat_1(6,k11_newton(A,3))),k11_newton(A,2)),k2_nat_1(4,A)),2)),k2_nat_1(k11_newton(k1_nat_1(A,1),5),24)) ) )).
fof(l37_sincos10,axiom,( k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers) = k1_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers))) )).
fof(l37_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m2_subset_1(C,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B)) => ! [D] : ( 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 ) ) )).
fof(l37_taylor_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_numbers)) => ! [D] : ( v1_xreal_0(D) => ? [E] : ( 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] : ( v1_xreal_0(F) => ( r2_hidden(F,C) => k1_funct_1(E,F) = k6_xcmplx_0(k1_funct_1(B,D),k9_nat_1(k1_numbers,k3_series_1(k6_taylor_1(B,C,F,D)),A)) ) ) ) ) ) ) ) )).
fof(l37_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(l37_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(l37_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(l37_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( 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) ) ) ) ) )).
fof(l37_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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] : ( ( v7_vectsp_1(D,A) & m1_vectsp_4(D,A,C) ) => k1_vectsp_9(A,D) != B ) ) ) ) ) )).
fof(l37_waybel13,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ( ? [B] : ? [C] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k2_yellow_1(B)),u1_struct_0(k2_yellow_1(B))) & v7_waybel_1(C,k2_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_yellow_1(B)),u1_struct_0(k2_yellow_1(B))))) & v22_waybel_0(C,k2_yellow_1(B),k2_yellow_1(B)) & r5_waybel_1(A,k1_yellow_2(k2_yellow_1(B),k2_yellow_1(B),C)) ) => v2_waybel_8(A) ) ) )).
fof(l37_waybel17,axiom,( ! [A] : ( ( 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)))) ) ) )).
fof(l37_waybel_5,axiom,( ! [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) ) => ( v3_waybel_3(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(l37_zfmisc_1,axiom,( ! [A] : ! [B] : ~ ( B != k1_tarski(A) & B != k1_xboole_0 & ! [C] : ~ ( r2_hidden(C,B) & C != A ) ) )).
fof(l38_algstr_1,axiom,( 1 = k1_group_1(k3_algstr_1) )).
fof(l38_anproj_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( B != k5_numbers & A != C & D != k5_numbers & k3_xcmplx_0(D,k5_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(C,B),k3_xcmplx_0(A,B)))) = k5_numbers ) ) ) ) ) )).
fof(l38_binop_2,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l38_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k8_cfuncdom(A))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(l38_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m2_collsp(B,A) => ! [C] : ( r2_hidden(C,B) => m1_subset_1(C,u1_struct_0(A)) ) ) ) )).
fof(l38_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v7_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( 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) ) ) )).
fof(l38_convex1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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(k5_numbers,k1_funct_1(D,B)) & r1_xxreal_0(k5_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))) ) ) ) ) ) ) ) )).
fof(l38_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => r2_hidden(k5_cqc_lang(A),a_2_0_cqc_the1(A,B)) ) ) )).
fof(l38_facirc_2,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k15_facirc_1(A,B,C),k18_facirc_1(A,B,C)))) & ? [E] : ( m1_subset_1(E,k6_margrel1) & ? [F] : ( m1_subset_1(F,k6_margrel1) & ? [G] : ( 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) ) ) ) ) ) ) )).
fof(l38_fdiff_1,axiom,( v2_rcomp_1(k1_subset_1(k1_numbers)) )).
fof(l38_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,A) ) => k1_funct_1(k7_fomodel0(A),B) = k1_funct_1(B,1) ) ) )).
fof(l38_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) )).
fof(l38_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C))))) => ! [E] : ( 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) & v9_fomodel4(B,C,D,A) ) => ( ( ~ v7_fomodel4(D,C) & ~ v7_fomodel4(E,C) ) | v9_fomodel4(B,C,E,A) ) ) ) ) ) )).
fof(l38_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => r1_tarski(k10_xtuple_0(k6_funct_6(A)),k4_card_3(k2_funct_6(A))) ) )).
fof(l38_funct_9,axiom,( ! [A] : ( v7_ordinal1(A) => v1_funct_9(k26_sin_cos,k3_xcmplx_0(k28_sin_cos,k2_xcmplx_0(A,1))) ) )).
fof(l38_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ~ ( r2_hidden(C,k1_relset_1(k4_ordinal1,B)) & ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ~ ( D = k6_xcmplx_0(C,1) & r2_hidden(k6_xcmplx_0(C,1),k1_relset_1(k4_ordinal1,B)) & r2_hidden(k1_nat_1(C,1),k1_relset_1(k4_ordinal1,B)) & r1_glib_000(A,k1_funct_1(B,D),k1_funct_1(B,k1_nat_1(C,1)),k1_funct_1(B,C)) ) ) ) ) ) ) )).
fof(l38_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( ( v2_group_9(D,A) & m1_group_9(D,A,B) ) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(l38_integr19,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( ~ v8_ordinal1(F) & m1_subset_1(F,k4_ordinal1) ) => ! [G] : ( ( 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] : ( 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)),k3_xcmplx_0(E,k6_xcmplx_0(D,C))) ) ) ) ) ) ) ) ) )).
fof(l38_isomichi,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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) ) ) ) )).
fof(l38_knaster,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ~ ( ~ r2_xboole_0(A,B) & A != B & ~ r2_xboole_0(B,A) ) ) ) )).
fof(l38_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( v1_ideal_1(k9_lpspace1(A,B,C),k7_lpspace1(A)) & v1_lpspace1(k9_lpspace1(A,B,C),k7_lpspace1(A)) ) ) ) ) )).
fof(l38_matrix11,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_finseq_1(B) = k3_finseq_1(k9_fvsum_1(A,B,C)) ) ) ) )).
fof(l38_matrix_9,axiom,( k3_finseq_4(k4_ordinal1,1,3,2) != k3_finseq_4(k4_ordinal1,2,3,1) & k3_finseq_4(k4_ordinal1,1,3,2) != k3_finseq_4(k4_ordinal1,3,1,2) )).
fof(l38_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ~ ( v3_mazurulm(C,A,B) & r1_xxreal_0(G,k1_newton(2,F)) & ! [H] : ( v7_ordinal1(H) => ~ ( H = k3_xxreal_3(k1_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),k6_xxreal_3(G,k1_newton(2,k2_xcmplx_0(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)),k6_xxreal_3(1,k1_newton(2,F))))),k6_xxreal_3(1,2)) ) ) ) ) ) ) ) ) ) ) )).
fof(l38_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_midsp_3(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(B))) => ! [E] : ( ( v4_midsp_2(E,B) & l1_midsp_2(E,B) ) => ! [F] : ( m2_finseq_2(F,u1_struct_0(u1_midsp_2(B,E)),k4_finseq_2(k1_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)) ) ) ) ) ) ) ) )).
fof(l38_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v4_modelc_1(A) => ( ~ v2_modelc_1(A) & ~ v3_modelc_1(A) & ~ v5_modelc_1(A) & ~ v6_modelc_1(A) & ~ v7_modelc_1(A) ) ) ) )).
fof(l38_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( 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) ) ) ) )).
fof(l38_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(l38_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v13_monoid_0(A) <=> ( v11_monoid_0(A) & v12_monoid_0(A) ) ) ) )).
fof(l38_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l38_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ( v6_o_ring_1(B,A) => v10_o_ring_1(B,A) ) ) ) )).
fof(l38_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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) ) ) ) )).
fof(l38_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l38_quatern2,axiom,( r2_hidden(k5_numbers,k1_numbers) )).
fof(l38_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(l38_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( m1_rlsub_1(D,A) => r1_tarski(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)))) ) ) ) ) )).
fof(l38_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( 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)))) ) ) ) ) ) )).
fof(l38_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(l38_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( 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)))) ) ) ) ) )).
fof(l38_scmbsort,axiom,( k4_scmfsa_2(2) != k4_scmfsa_2(4) )).
fof(l38_scmfsa8a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( 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(k7_card_1(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(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(k3_scmfsa6a(k3_scmfsa6a(B,k1_scmfsa8a(k1_nat_1(k5_card_1(C),1))),C),k4_compos_1(k1_scmfsa_2))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D)),2))) = k1_nat_1(k1_nat_1(k5_card_1(B),k5_card_1(C)),1) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D)))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(k3_scmfsa6a(k3_scmfsa6a(B,k1_scmfsa8a(k1_nat_1(k5_card_1(C),1))),C),k4_compos_1(k1_scmfsa_2))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D)),2))) & ! [E] : ( v7_ordinal1(E) => ~ ( ~ r1_xxreal_0(k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D)),2),E) & k3_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(k3_scmfsa6a(k3_scmfsa6a(B,k1_scmfsa8a(k1_nat_1(k5_card_1(C),1))),C),k4_compos_1(k1_scmfsa_2))),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(k3_scmfsa6a(k3_scmfsa6a(B,k1_scmfsa8a(k1_nat_1(k5_card_1(C),1))),C),k4_compos_1(k1_scmfsa_2))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D),E)) = k2_compos_1(k1_scmfsa_2) ) ) & ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(E,k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D))) => k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(k3_scmfsa6a(k3_scmfsa6a(B,k1_scmfsa8a(k1_nat_1(k5_card_1(C),1))),C),k4_compos_1(k1_scmfsa_2))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D),E)) = k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D),E)) ) ) & k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(k3_scmfsa6a(k3_scmfsa6a(B,k1_scmfsa8a(k1_nat_1(k5_card_1(C),1))),C),k4_compos_1(k1_scmfsa_2))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D)),1))) = k5_card_1(B) & r1_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(k3_scmfsa6a(k3_scmfsa6a(B,k1_scmfsa8a(k1_nat_1(k5_card_1(C),1))),C),k4_compos_1(k1_scmfsa_2))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D)) & k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(k3_scmfsa6a(k3_scmfsa6a(B,k1_scmfsa8a(k1_nat_1(k5_card_1(C),1))),C),k4_compos_1(k1_scmfsa_2))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D)) = k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D)),2) ) ) ) ) ) ) )).
fof(l38_scmisort,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(A,k7_card_1(3),k1_scmfsa_2,k5_numbers) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ( r1_tarski(k3_scmisort,B) => ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(12,C) & ~ ( k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,C),k4_struct_0(k1_scmfsa_2)) = C & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,C),k4_scmfsa_2(k5_numbers)) = k1_funct_1(A,k4_scmfsa_2(k5_numbers)) & k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,C),k5_scmfsa_2(k5_numbers)) = k18_scmfsa_2(A,k5_scmfsa_2(k5_numbers)) ) ) ) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,11),k4_scmfsa_2(1)) = k3_finseq_1(k18_scmfsa_2(A,k5_scmfsa_2(k5_numbers))) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,11),k4_scmfsa_2(2)) = k1_funct_1(A,k4_scmfsa_2(k5_numbers)) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,11),k4_scmfsa_2(3)) = k1_funct_1(A,k4_scmfsa_2(k5_numbers)) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,11),k4_scmfsa_2(4)) = k1_funct_1(A,k4_scmfsa_2(k5_numbers)) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,11),k4_scmfsa_2(5)) = k1_funct_1(A,k4_scmfsa_2(k5_numbers)) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,11),k4_scmfsa_2(6)) = k1_funct_1(A,k4_scmfsa_2(k5_numbers)) ) ) ) ) )).
fof(l38_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ( k1_funct_1(B,k2_scmp_gcd) = k5_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) = k5_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] : ( v7_ordinal1(C) => ( 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)) ) ) ) ) ) ) )).
fof(l38_series_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ r1_xxreal_0(k2_xcmplx_0(k11_newton(2,k1_nat_1(A,2)),k1_newton(k4_xcmplx_0(1),k1_nat_1(A,2))),k5_numbers) ) )).
fof(l38_sincos10,axiom,( r1_tarski(k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers),k1_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers)),k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers)))) )).
fof(l38_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k5_substlat(A,B))) => ! [D] : ( 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 ) ) )).
fof(l38_topalg_5,axiom,( ? [A] : ( 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k8_toprealb(2)))) => ~ ( r2_hidden(B,A) & ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k2_topalg_2))) => ( r2_hidden(D,C) => ! [E] : ( ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(l38_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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) ) ) ) ) ) )).
fof(l38_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)))) ) ) ) )).
fof(l38_turing_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( r1_xxreal_0(A,5) => m1_subset_1(A,u2_turing_1(k14_turing_1)) ) ) )).
fof(l38_vectsp_2,axiom,( ! [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) & 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) ) ) )).
fof(l38_waybel17,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k1_tops_1(A,B) = k3_tarski(a_2_5_waybel17(A,B)) ) ) )).
fof(l38_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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) ) ) ) ) )).
fof(l38_waybel_5,axiom,( ! [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] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( 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) ) ) )).
fof(l38_xxreal_3,axiom,( k2_xxreal_3(k1_xxreal_0) = k2_xxreal_0 )).
fof(l38_yellow_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_yellow_1(A,B))) => ( r2_hidden(C,u1_struct_0(k4_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)))) ) ) ) )).
fof(l38_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(C,k2_tarski(A,B)) <=> ~ ( C != k1_xboole_0 & C != k1_tarski(A) & C != k1_tarski(B) & C != k2_tarski(A,B) ) ) )).
fof(l39_algstr_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_1)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_algstr_1)) => ~ ( A != k4_struct_0(k3_algstr_1) & ! [C] : ( m1_subset_1(C,u1_struct_0(k3_algstr_1)) => k6_algstr_0(k3_algstr_1,A,C) != B ) ) ) ) )).
fof(l39_algstr_4,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,k5_numbers) => r1_tarski(k2_zfmisc_1(k11_algstr_4(A,B),k1_tarski(B)),k12_algstr_4(A)) ) ) )).
fof(l39_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ! [K] : ( v1_xreal_0(K) => ( ( J = k3_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(H,I),k3_xcmplx_0(H,G)),k5_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(H,G),k3_xcmplx_0(F,G)))),K) & D = k3_rlvect_1(A,k3_rlvect_1(A,k1_rlvect_1(A,B,k2_xcmplx_0(J,K)),k1_rlvect_1(A,C,k3_xcmplx_0(J,F))),k1_rlvect_1(A,E,k3_xcmplx_0(K,I))) ) => ( G = k5_numbers | F = H | D = k1_rlvect_1(A,k3_rlvect_1(A,k3_rlvect_1(A,k1_rlvect_1(A,B,k6_xcmplx_0(k3_xcmplx_0(H,I),k3_xcmplx_0(F,G))),k1_rlvect_1(A,C,k3_xcmplx_0(k3_xcmplx_0(F,H),k6_xcmplx_0(I,G)))),k1_rlvect_1(A,E,k3_xcmplx_0(k3_xcmplx_0(G,I),k6_xcmplx_0(H,F)))),k3_xcmplx_0(K,k5_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(H,G),k3_xcmplx_0(F,G))))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l39_arytm_3,axiom,( r1_arytm_3(1,1) )).
fof(l39_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(A,B) & r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(C,D) ) => r1_xxreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D)) ) ) ) ) ) )).
fof(l39_binop_2,axiom,( r3_binop_1(k1_numbers,c5__binop_2,k11_binop_2) )).
fof(l39_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v4_normsp_0(k7_cc0sp1(A)) & v3_normsp_0(k7_cc0sp1(A)) & v8_clvect_1(k7_cc0sp1(A)) ) ) )).
fof(l39_cfunct_1,axiom,( k5_xcmplx_0(k4_xcmplx_0(k6_complex1)) = k4_xcmplx_0(k6_complex1) )).
fof(l39_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ( v1_pcomps_1(B,A) & ! [C] : ( 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) ) ) )).
fof(l39_convex1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : ! [D] : ~ ( 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) ) ) )).
fof(l39_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(l39_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l39_euclid_7,axiom,( r2_hidden(k5_numbers,k1_numbers) )).
fof(l39_fdiff_1,axiom,( v3_rcomp_1(k2_subset_1(k1_numbers)) )).
fof(l39_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ~ ( r2_hidden(A,k27_fomodel1(B)) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ r2_hidden(A,k1_funct_1(k25_fomodel1(B),C)) ) ) ) )).
fof(l39_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => r1_tarski(k24_fomodel2(C,A),k24_fomodel2(C,k2_xcmplx_0(A,B))) ) ) ) )).
fof(l39_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v5_relat_1(D,A) & v1_funct_1(D) & v3_card_1(D,C) & v1_finseq_1(D) ) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(l39_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( 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] : ( 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)) => v4_fomodel4(A,B,k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))),C),D) ) ) ) ) )).
fof(l39_funcsdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k12_funcsdom(A))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(l39_gcd_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r2_gcd_1(A,D,B) & r2_gcd_1(A,D,C) & ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l39_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( ~ r1_xxreal_0(k3_finseq_1(B),C) => ( r2_hidden(C,k1_relset_1(k4_ordinal1,B)) & r2_hidden(k1_nat_1(C,1),k1_relset_1(k4_ordinal1,B)) & r2_hidden(k1_nat_1(C,2),k1_relset_1(k4_ordinal1,B)) ) ) ) ) ) )).
fof(l39_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & v5_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k8_group_1(A,B,C) = k8_group_1(A,C,B) ) ) ) )).
fof(l39_heyting1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k12_normform(A))) => ! [C] : ( 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 ) ) ) )).
fof(l39_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( m1_subset_1(D,k1_hilbert1) => r2_hidden(k3_hilbert1(k3_hilbert1(k3_hilbert1(k3_hilbert1(B,C),k3_hilbert1(A,C)),D),k3_hilbert1(k3_hilbert1(A,B),D)),k6_hilbert1) ) ) ) ) )).
fof(l39_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & B != D & r1_incsp_1(A,D,C) ) ) ) ) )).
fof(l39_jordan1b,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(C,k1_matrix_0(k1_jordan8(A,D))) & r1_tarski(k3_goboard5(k1_jordan8(A,D),B,C),k1_jordan2c(2,A)) & B = k5_numbers ) ) ) ) ) )).
fof(l39_matrix11,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(l39_matrix_9,axiom,( k3_finseq_4(k4_ordinal1,3,2,1) != k3_finseq_4(k4_ordinal1,1,3,2) & k3_finseq_4(k4_ordinal1,2,3,1) != k3_finseq_4(k4_ordinal1,3,1,2) )).
fof(l39_matrtop3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(l39_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ~ ( v3_mazurulm(C,A,B) & r1_xxreal_0(k1_newton(2,F),G) & ! [H] : ( v7_ordinal1(H) => ~ ( H = k3_xxreal_3(k1_xxreal_3(k1_newton(2,F),G),k1_newton(2,k2_xcmplx_0(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),k6_xxreal_3(G,k1_newton(2,k2_xcmplx_0(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,k3_xxreal_3(k1_newton(2,k2_xcmplx_0(F,1)),G)),k1_rlvect_1(A,E,H)),k6_xxreal_3(1,k1_newton(2,F))))),k6_xxreal_3(1,2)) ) ) ) ) ) ) ) ) ) ) )).
fof(l39_mesfunc8,axiom,( v1_xreal_0(1) )).
fof(l39_metrizts,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( ( ~ 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)))) ) ) ) ) )).
fof(l39_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_midsp_3(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(B))) => ! [E] : ( ( v4_midsp_2(E,B) & l1_midsp_2(E,B) ) => ! [F] : ( m2_finseq_2(F,u1_struct_0(u1_midsp_2(B,E)),k4_finseq_2(k1_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)) ) ) ) ) ) ) ) )).
fof(l39_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v5_modelc_1(A) => ( ~ v2_modelc_1(A) & ~ v4_modelc_1(A) & ~ v3_modelc_1(A) & ~ v6_modelc_1(A) & ~ v7_modelc_1(A) ) ) ) )).
fof(l39_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( 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) ) ) ) )).
fof(l39_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_3(C,B) & l1_modelc_3(C,B) ) => ! [D] : ( 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))) ) ) ) ) ) ) ) )).
fof(l39_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v16_monoid_0(A) <=> ( v14_monoid_0(A) & v15_monoid_0(A) ) ) ) )).
fof(l39_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v7_o_ring_1(B,A) => v11_o_ring_1(B,A) ) ) ) )).
fof(l39_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(A,B) & ~ r1_xxreal_0(C,1) & r1_xxreal_0(k1_newton(C,A),k1_newton(C,B)) ) ) ) ) )).
fof(l39_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & v6_orders_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => r3_orders_2(A,C,k1_yellow_0(A,B)) ) ) ) ) )).
fof(l39_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l39_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( m1_ratfunc1(B,A) => ( v5_ratfunc1(B,A) => ! [C] : ( m1_ratfunc1(C,A) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & ~ v1_ratfunc1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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] : ( m2_finseq_1(E,u1_struct_0(k14_polynom3(A))) => ~ ( D = k3_group_4(k14_polynom3(A),E) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( r2_hidden(F,k4_finseq_1(E)) & ! [G] : ( 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] : ( m1_ratfunc1(E,A) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(F,A) & ~ v1_ratfunc1(F,A) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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] : ( m2_finseq_1(G,u1_struct_0(k14_polynom3(A))) => ~ ( F = k3_group_4(k14_polynom3(A),G) & ! [H] : ( m1_subset_1(H,k4_ordinal1) => ~ ( r2_hidden(H,k4_finseq_1(G)) & ! [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(k4_ordinal1,u1_struct_0(A),D,k10_polynom3(A)) & r2_funct_2(k4_ordinal1,u1_struct_0(A),F,k10_polynom3(A)) & C = E ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l39_realset2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(l39_rltopsp1,axiom,( ! [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) ) => ! [B] : ( ( v3_rltopsp1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v3_rltopsp1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => v3_rltopsp1(k7_rusub_4(A,B,C),A) ) ) ) )).
fof(l39_rlvect_2,axiom,( ! [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) ) => k6_rlvect_2(A,k4_rlvect_2(A)) = k4_struct_0(A) ) )).
fof(l39_scmbsort,axiom,( k4_scmfsa_2(2) != k4_scmfsa_2(5) )).
fof(l39_series_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ r1_xxreal_0(k2_xcmplx_0(k11_newton(2,k1_nat_1(A,3)),k1_newton(k4_xcmplx_0(1),k1_nat_1(A,3))),k5_numbers) ) )).
fof(l39_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k3_xcmplx_0(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))) ) ) )).
fof(l39_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ ( r1_xxreal_0(A,1) & r1_xxreal_0(k4_xcmplx_0(1),A) ) & r1_xxreal_0(k7_xcmplx_0(k2_xcmplx_0(A,1),k6_xcmplx_0(A,1)),k5_numbers) ) ) )).
fof(l39_sincos10,axiom,( k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)) = k1_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(l39_sppol_1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ~ ( v3_sppol_1(A) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_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,k1_nat_1(B,2)) & ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(l39_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => v3_topreal1(k2_finseq_4(u1_struct_0(k15_euclid(2)),A,B)) ) ) )).
fof(l39_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k5_substlat(A,B))) => ! [D] : ( 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) ) ) )).
fof(l39_taylor_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( r1_tarski(B,k1_relset_1(k1_numbers,A)) => ! [C] : ( v7_ordinal1(C) => ( r1_taylor_1(A,C,B) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( 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,k1_nat_1(C,1),k2_rcomp_1(D,E)) ) => ( r1_xxreal_0(E,D) | ! [F] : ( ( 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] : ( v1_xreal_0(G) => ( r2_hidden(G,B) => k1_funct_1(F,G) = k6_xcmplx_0(k1_funct_1(A,E),k9_nat_1(k1_numbers,k3_series_1(k6_taylor_1(A,B,G,E)),C)) ) ) ) => ( k1_funct_1(F,E) = k5_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] : ( v1_xreal_0(G) => ( r2_hidden(G,k2_rcomp_1(D,E)) => k1_fdiff_1(F,G) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(A,k2_rcomp_1(D,E)),k1_nat_1(C,1)),G),k1_newton(k6_xcmplx_0(E,G),C)),k2_newton(C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l39_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ( k3_polynom1(k15_pre_poly(A),C,k5_termord(A,B,C,D)) = k1_xboole_0 | k3_polynom1(k15_pre_poly(A),C,k5_termord(A,B,C,D)) = k1_tarski(k3_termord(A,B,C,D)) ) ) ) ) ) )).
fof(l39_topalg_5,axiom,( k2_struct_0(k1_tex_2(k17_borsuk_1,k18_borsuk_1)) = k6_domain_1(k4_ordinal1,k5_numbers) )).
fof(l39_topreal2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [E] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(l39_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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)))) ) ) ) ) ) )).
fof(l39_waybel17,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( 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) ) ) ) ) )).
fof(l39_xxreal_3,axiom,( ! [A] : ( 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)) ) ) )).
fof(l39_zmodul03,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,k4_numbers) => m1_subset_1(k5_int_1(B,A),u1_struct_0(k9_int_3(A))) ) ) )).
fof(l3_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,E) => r2_analoaf(A,D,E,B,C) ) ) ) ) ) ) )).
fof(l3_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_diraf(A,B,C,D,E) => r2_diraf(A,C,B,D,E) ) ) ) ) ) ) )).
fof(l3_algseq_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ? [C] : ( v7_ordinal1(C) & r1_algseq_1(A,B,C) ) ) ) )).
fof(l3_algstr_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k2_vectsp_1)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_vectsp_1)) => ~ ( A != k4_struct_0(k2_vectsp_1) & ! [C] : ( m1_subset_1(C,u1_struct_0(k2_vectsp_1)) => k8_group_1(k2_vectsp_1,C,A) != B ) ) ) ) )).
fof(l3_altcat_5,axiom,( u1_struct_0(k7_altcat_1(k1_tarski(k1_xboole_0))) = k1_tarski(k5_numbers) )).
fof(l3_ami_2,axiom,( ~ r2_hidden(k4_ordinal1,k2_ami_2) )).
fof(l3_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( B = k3_rlvect_1(A,k1_rlvect_1(A,C,F),k1_rlvect_1(A,D,G)) => k1_rlvect_1(A,B,E) = k3_rlvect_1(A,k1_rlvect_1(A,C,k3_xcmplx_0(E,F)),k1_rlvect_1(A,D,k3_xcmplx_0(E,G))) ) ) ) ) ) ) ) ) )).
fof(l3_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( ( 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 ) ) ) ) ) ) ) ) ) )).
fof(l3_arithm,axiom,( r2_hidden(1,k4_ordinal1) )).
fof(l3_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( k8_arytm_2(A,B) = k8_arytm_2(A,C) => ( A = k11_arytm_3 | B = C ) ) ) ) ) )).
fof(l3_arytm_2,axiom,( ! [A] : ! [B] : ~ r2_hidden(k4_tarski(A,B),a_0_0_arytm_2) )).
fof(l3_axioms,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( A = C & B = D ) => k1_arytm_0(A,B) = k2_xcmplx_0(C,D) ) ) ) ) ) )).
fof(l3_bhsp_1,axiom,( v1_funct_1(k8_funcop_1(k1_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))),k10_subset_1(k5_numbers,k1_numbers))) & v1_funct_2(k8_funcop_1(k1_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))),k10_subset_1(k5_numbers,k1_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(k1_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))),k10_subset_1(k5_numbers,k1_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))) )).
fof(l3_bhsp_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(A,k7_xcmplx_0(1,k1_nat_1(C,1))) & r1_xxreal_0(B,C) ) ) ) ) ) )).
fof(l3_binom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( 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] : ( v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(k4_ordinal1,A),B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A),B))) & ! [F] : ( m1_subset_1(F,A) => ( k2_binop_1(k4_ordinal1,A,B,E,k5_numbers,F) = C & ! [G] : ( m1_subset_1(G,k4_ordinal1) => k2_binop_1(k4_ordinal1,A,B,E,k1_nat_1(G,1),F) = k2_binop_1(A,B,B,D,F,k2_binop_1(k4_ordinal1,A,B,E,G,F)) ) ) ) ) ) ) ) ) )).
fof(l3_borsuk_3,axiom,( ! [A] : ( l1_pre_topc(A) => r1_t_0topsp(A,A) ) )).
fof(l3_borsuk_7,axiom,( 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)) )).
fof(l3_bvfunc14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : 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) )).
fof(l3_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(l3_c0sp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => v1_ideal_1(k2_struct_0(A),A) ) )).
fof(l3_cfdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( r1_funct_2(k4_ordinal1,k1_numbers,k4_ordinal1,k2_numbers,A,B) => ( ( ( v1_fdiff_1(A,k5_numbers) & v9_ordinal1(A) ) => ( v1_cfdiff_1(B,k5_numbers) & v9_ordinal1(B) ) ) & ( ( v1_cfdiff_1(B,k5_numbers) & v9_ordinal1(B) ) => ( v1_fdiff_1(A,k5_numbers) & v9_ordinal1(A) ) ) ) ) ) ) )).
fof(l3_chord,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(l3_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,C) => ! [E] : ( m1_pboole(E,A,B) => m1_pboole(k16_pralg_1(A,D,E),A,C) ) ) ) ) )).
fof(l3_complfld,axiom,( k5_struct_0(k1_complfld) = k6_complex1 )).
fof(l3_convex3,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l3_csspace2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( ( k3_xcmplx_0(k3_complex1(A),k4_complex1(B)) = k3_xcmplx_0(k3_complex1(B),k4_complex1(A)) & r1_xxreal_0(k5_numbers,k2_xcmplx_0(k3_xcmplx_0(k3_complex1(A),k3_complex1(B)),k3_xcmplx_0(k4_complex1(A),k4_complex1(B)))) ) => k9_complex1(k2_xcmplx_0(A,B)) = k2_xcmplx_0(k9_complex1(A),k9_complex1(B)) ) ) ) )).
fof(l3_csspace3,axiom,( 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) )).
fof(l3_dtconstr,axiom,( k4_finseq_1(k15_trees_3(k1_xboole_0)) = k1_xboole_0 )).
fof(l3_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ( v1_funct_1(k13_funct_7(A,B,C,D)) & v1_funct_2(k13_funct_7(A,B,C,D),k4_ordinal1,A) & m1_subset_1(k13_funct_7(A,B,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) ) ) ) ) )).
fof(l3_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => k7_euclid(3,A,B) = k1_euclid_8(k2_xcmplx_0(k1_funct_1(A,1),k1_funct_1(B,1)),k2_xcmplx_0(k1_funct_1(A,2),k1_funct_1(B,2)),k2_xcmplx_0(k1_funct_1(A,3),k1_funct_1(B,3))) ) ) )).
fof(l3_euler_2,axiom,( ! [A] : ( v1_int_1(A) => k3_int_2(1,A) = 1 ) )).
fof(l3_fdiff_5,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k9_xtuple_0(k4_taylor_1(k7_xcmplx_0(1,2)))) => ( r2_fdiff_1(k4_taylor_1(k7_xcmplx_0(1,2)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k4_taylor_1(k7_xcmplx_0(1,2)),A),B) = k3_xcmplx_0(k7_xcmplx_0(1,2),k6_prepower(B,k4_xcmplx_0(k7_xcmplx_0(1,2)))) ) ) ) ) ) )).
fof(l3_fdiff_6,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(k1_funct_1(k16_sin_cos,A),k5_numbers) => k1_funct_1(k16_sin_cos,A) = k6_prepower(k3_xcmplx_0(k6_xcmplx_0(1,k1_funct_1(k18_sin_cos,A)),k2_xcmplx_0(1,k1_funct_1(k18_sin_cos,A))),k7_xcmplx_0(1,2)) ) ) )).
fof(l3_fib_fusc,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( A = k1_nat_1(k2_nat_1(2,B),1) => ( r1_xxreal_0(B,k5_numbers) | k2_xcmplx_0(6,k2_xcmplx_0(k3_xcmplx_0(6,k2_xcmplx_0(k1_int_1(k3_power(2,B)),1)),1)) = k2_xcmplx_0(k3_xcmplx_0(6,k2_xcmplx_0(k1_int_1(k3_power(2,A)),1)),1) ) ) ) ) )).
fof(l3_fomodel3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ( r2_hidden(A,k9_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) ) ) ) )).
fof(l3_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ~ ( ~ v7_pre_topc(A) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( r2_funct_2(k4_ordinal1,u1_struct_0(A),D,k8_funcop_1(u1_struct_0(A),k4_ordinal1,B)) & B != C & r1_frechet(A,D,C) ) ) ) ) ) ) )).
fof(l3_friends1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ~ ( v2_relat_2(B) & r2_hidden(k4_tarski(A,A),B) ) ) )).
fof(l3_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : k1_funct_1(k1_funct_4(A,k16_funcop_1(B,C)),B) = C ) )).
fof(l3_groeb_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => r2_hidden(C,k7_ideal_1(A,B)) ) ) ) ) )).
fof(l3_heyting3,axiom,( 1 = k1_nat_1(k5_numbers,1) )).
fof(l3_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v7_aff_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l3_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k4_numbers)) => r1_tarski(k1_measure6(B,A),k4_numbers) ) ) )).
fof(l3_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( ( r1_int_1(A,B) => k5_int_1(B,A) = k5_numbers ) & ( k5_int_1(B,A) = k5_numbers => ( A = k5_numbers | r1_int_1(A,B) ) ) ) ) ) )).
fof(l3_integr11,axiom,( k9_xtuple_0(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(2,k5_numbers),k16_sin_cos),k7_xcmplx_0(1,4))) = k2_subset_1(k1_numbers) )).
fof(l3_integr15,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => ! [C] : ( m1_integra1(C,A) => ! [D] : ( v1_xreal_0(D) => ~ ( v2_seq_2(k2_partfun1(A,k1_numbers,B,A)) & ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( m1_integr15(E,A,B,C) => ? [F] : ( v7_ordinal1(F) & r2_hidden(F,k4_finseq_1(C)) & ~ ( r1_xxreal_0(k1_funct_1(k5_integra1(A,B,C),F),k1_funct_1(E,F)) & ~ r1_xxreal_0(k2_xcmplx_0(k1_funct_1(k5_integra1(A,B,C),F),D),k1_funct_1(E,F)) ) ) ) ) ) ) ) ) )).
fof(l3_jgraph_3,axiom,( k1_relset_1(u1_struct_0(k15_euclid(2)),k5_pscomp_1) = u1_struct_0(k15_euclid(2)) )).
fof(l3_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(B,A) ) => r1_xxreal_0(k3_xcmplx_0(B,k3_square_1(k2_xcmplx_0(1,k1_square_1(A)))),k3_xcmplx_0(A,k3_square_1(k2_xcmplx_0(1,k1_square_1(B))))) ) ) ) )).
fof(l3_jordan,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(l3_jordan1a,axiom,( 1 = k1_nat_1(k2_nat_1(2,k5_numbers),1) )).
fof(l3_jordan1c,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => m1_subset_1(A,u1_struct_0(k14_euclid(2))) ) )).
fof(l3_jordan1d,axiom,( 2 = k1_nat_1(k2_nat_1(2,1),k5_numbers) )).
fof(l3_jordan21,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ~ ( r2_hidden(A,k2_xboole_0(k2_xboole_0(B,C),D)) & ~ r2_hidden(A,B) & ~ r2_hidden(A,C) & ~ r2_hidden(A,D) ) )).
fof(l3_jordan7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k2_xcmplx_0(B,C),A) => r1_xxreal_0(C,k7_nat_d(A,B)) ) ) ) ) )).
fof(l3_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( ~ v1_xboole_0(B) & ! [C] : ( m1_subset_1(C,u1_struct_0(k3_lattice3(A))) => ? [D] : ( m1_subset_1(D,u1_struct_0(k3_lattice3(A))) & r2_hidden(D,B) & ~ r3_orders_2(k3_lattice3(A),D,C) ) ) ) ) ) )).
fof(l3_lattice8,axiom,( ~ v1_abian(1) )).
fof(l3_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r1_tarski(k10_xtuple_0(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(k10_xtuple_0(A),k1_relset_1(k1_numbers,B)) & r1_tarski(k10_xtuple_0(A),k1_relset_1(k1_numbers,C)) ) ) ) ) ) )).
fof(l3_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(A,k6_xcmplx_0(A,k7_xcmplx_0(1,k1_nat_1(B,1)))) & ~ r1_xxreal_0(k2_xcmplx_0(A,k7_xcmplx_0(1,k1_nat_1(B,1))),A) ) ) ) )).
fof(l3_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(A,k6_xcmplx_0(A,k7_xcmplx_0(1,k1_nat_1(B,1)))) & ~ r1_xxreal_0(k2_xcmplx_0(A,k7_xcmplx_0(1,k1_nat_1(B,1))),A) ) ) ) )).
fof(l3_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(l3_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k5_numbers,A) => ( r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(k5_numbers,k2_power(A,B)) ) ) ) ) )).
fof(l3_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => k2_matrix_0(B) = k2_matrix_0(k2_matrix_3(A,B)) ) ) )).
fof(l3_matrix16,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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(k5_int_1(k6_xcmplx_0(C,B),A),1),k2_finseq_1(A)) ) ) ) ) )).
fof(l3_matrix_9,axiom,( r2_hidden(k2_finseq_4(k4_ordinal1,2,1),k3_matrix_2(2)) )).
fof(l3_matrixr2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(C)) ) => k7_matrix_0(A,C,B) = k1_funct_1(C,B) ) ) ) ) )).
fof(l3_matrtop2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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))) ) ) )).
fof(l3_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( 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))) ) ) ) )).
fof(l3_mesfunc7,axiom,( v1_xreal_0(1) )).
fof(l3_metric_1,axiom,( k1_binop_1(k9_funct_5,k5_numbers,k5_numbers) = k5_numbers )).
fof(l3_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_mod_4(A))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(l3_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( k1_funct_1(k12_finseq_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1)),A),1) = A & k2_relset_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1)),k12_finseq_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1)),A)) = k1_tarski(A) ) ) )).
fof(l3_nat_1,axiom,( m1_subset_1(k4_ordinal1,k1_zfmisc_1(k1_numbers)) )).
fof(l3_normsp_0,axiom,( m1_subset_1(k5_numbers,k1_tarski(k5_numbers)) )).
fof(l3_normsp_1,axiom,( m1_subset_1(k4_struct_0(o_0_5_normsp_1),u1_struct_0(k1_rlsub_1(o_0_5_normsp_1))) )).
fof(l3_normsp_2,axiom,( ! [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) & 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)))) ) )).
fof(l3_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)),k1_nat_1(k3_finseq_1(C),1)) = B ) ) ) )).
fof(l3_ordinal4,axiom,( 1 = k4_card_1(k1_xboole_0) )).
fof(l3_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(l3_partfun1,axiom,( ! [A] : ! [B] : ? [C] : ( r1_tarski(k9_xtuple_0(C),A) & r1_tarski(k10_xtuple_0(C),B) ) )).
fof(l3_pdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(A,k2_finseq_1(B)) => v2_funct_2(k1_pdiff_1(A,B),k1_numbers) ) ) ) )).
fof(l3_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ( A != k5_numbers => r1_xxreal_0(k5_numbers,k6_xcmplx_0(A,1)) ) ) )).
fof(l3_polyeq_2,axiom,( v1_abian(4) )).
fof(l3_polynom2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( 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) ) ) ) )).
fof(l3_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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 ) ) ) ) )).
fof(l3_prvect_1,axiom,( ! [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) ) => r1_finseqop(u1_struct_0(A),k5_vectsp_1(A),u1_algstr_0(A)) ) )).
fof(l3_quatern2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(C)),k1_square_1(D)) = k5_numbers => ( A = k5_numbers & B = k5_numbers & C = k5_numbers & D = k5_numbers ) ) ) ) ) ) )).
fof(l3_radix_3,axiom,( ! [A] : ( 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))) ) ) )).
fof(l3_radix_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l3_ramsey_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(A,B) => r1_tarski(k3_group_10(A,C),k3_group_10(B,C)) ) )).
fof(l3_rat_1,axiom,( r2_hidden(k5_numbers,k4_ordinal1) )).
fof(l3_realset2,axiom,( r2_hidden(1,2) )).
fof(l3_recdef_1,axiom,( r2_hidden(1,k1_numbers) )).
fof(l3_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ~ ( r2_hidden(k1_nat_1(B,1),k4_finseq_1(A)) & r1_xxreal_0(k3_finseq_1(A),B) ) ) ) )).
fof(l3_rlsub_1,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l3_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( B != C & B != D & C != D & ! [H] : ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(l3_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(B)) => ( ( k3_finseq_1(D) = k3_finseq_1(E) & ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(l3_rsspace2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,A,B)) ) => ( ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,k3_series_1(A),B)) ) & ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,k3_series_1(A),B)) ) & ( v1_series_1(A) => ( ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_nat_1(k1_numbers,k3_series_1(A),B),k4_series_1(A)) ) & ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k4_series_1(A)) ) ) ) ) ) ) )).
fof(l3_rsspace3,axiom,( m1_rlsub_1(g1_rlvect_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3)),k6_rsspace) )).
fof(l3_rusub_3,axiom,( m1_subset_1(1,k1_numbers) & m1_subset_1(k10_subset_1(k5_numbers,k1_numbers),k1_numbers) )).
fof(l3_rvsum_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k1_funct_1(k5_funcop_1(k5_binop_2,A,k6_partfun1(k2_numbers)),B) = k3_xcmplx_0(A,B) ) ) )).
fof(l3_scm_halt,axiom,( r1_tarski(k7_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_numbers),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_3(k4_scmfsa_2(k5_numbers),1))) )).
fof(l3_scmfsa_9,axiom,( r2_hidden(k5_numbers,k2_afinsq_1(k4_compos_1(k1_scmfsa_2))) )).
fof(l3_scmpds_i,axiom,( r2_hidden(k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0),k1_scmpds_i) )).
fof(l3_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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(k4_ordinal1)) = k2_ami_2 ) )).
fof(l3_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ! [C] : ( v1_int_1(C) => r1_tarski(k61_valued_1(A,1),k2_scmpds_8(B,C,A)) ) ) ) )).
fof(l3_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,A,k1_nat_1(B,1))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,A,k2_xcmplx_0(k1_nat_1(B,1),C))) ) ) ) & ( ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,A,k2_xcmplx_0(k1_nat_1(B,1),C))) ) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(C,B) & r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,A,C)) ) ) ) ) & ( ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(C,B) & r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,A,C)) ) ) ) => ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,A,k1_nat_1(B,1))) ) ) ) ) )).
fof(l3_series_2,axiom,( ! [A] : ( v1_xreal_0(A) => k1_newton(A,3) = k3_xcmplx_0(k1_newton(A,2),A) ) )).
fof(l3_series_3,axiom,( k11_newton(2,3) = 8 )).
fof(l3_series_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k1_newton(k2_xcmplx_0(k1_newton(k7_xcmplx_0(1,3),k1_nat_1(A,1)),k11_newton(3,k1_nat_1(A,1))),2) = k2_xcmplx_0(k2_xcmplx_0(k1_newton(k7_xcmplx_0(1,9),k1_nat_1(A,1)),k11_newton(9,k1_nat_1(A,1))),2) ) )).
fof(l3_series_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k3_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,A),k7_xcmplx_0(1,B)),k7_xcmplx_0(1,C)) = k7_xcmplx_0(1,k3_xcmplx_0(k3_xcmplx_0(A,B),C)) ) ) ) )).
fof(l3_sin_cos,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l3_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( r2_hidden(A,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) & r1_xxreal_0(k1_funct_1(k16_sin_cos,A),k5_numbers) ) ) )).
fof(l3_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ( k6_xcmplx_0(k1_square_1(k4_sin_cos2(A)),k1_square_1(k2_sin_cos2(A))) = 1 & k6_xcmplx_0(k3_xcmplx_0(k4_sin_cos2(A),k4_sin_cos2(A)),k3_xcmplx_0(k2_sin_cos2(A),k2_sin_cos2(A))) = 1 ) ) )).
fof(l3_sin_cos9,axiom,( r2_fdiff_1(k26_sin_cos,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))) )).
fof(l3_sincos10,axiom,( r1_tarski(k4_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos),k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos))) )).
fof(l3_symsp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_tarski(k5_numbers)) => ! [B] : ( m1_subset_1(B,k1_tarski(k5_numbers)) => k5_binop_1(k1_tarski(k5_numbers),c3__symsp_1,A,B) = c2__symsp_1 ) ) )).
fof(l3_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(l3_topalg_2,axiom,( u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)) = k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) )).
fof(l3_topalg_5,axiom,( r1_tarski(k6_domain_1(k4_ordinal1,k5_numbers),u1_struct_0(k5_topmetr)) )).
fof(l3_topgen_4,axiom,( ! [A] : ( v4_card_3(A) <=> ? [B] : ( v1_relat_1(B) & v1_funct_1(B) & k9_xtuple_0(B) = k3_numbers & r1_tarski(A,k10_xtuple_0(B)) ) ) )).
fof(l3_topreal2,axiom,( k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,k5_numbers),k19_euclid(k5_numbers,1)),k1_rltopsp1(k15_euclid(2),k19_euclid(1,k5_numbers),k19_euclid(1,1))) = k1_xboole_0 )).
fof(l3_toprealb,axiom,( v1_xreal_0(1) & v2_xxreal_0(1) )).
fof(l3_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( r1_aff_1(A,E,F,G) & E != G & F != G ) ) ) ) ) ) ) ) ) )).
fof(l3_trees_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ r1_xxreal_0(k3_finseq_1(B),A) => ( r2_hidden(k1_nat_1(A,1),k4_finseq_1(B)) & r2_hidden(k1_funct_1(B,k1_nat_1(A,1)),k10_xtuple_0(B)) ) ) ) ) )).
fof(l3_uniroots,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( 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)) ) ) ) ) )).
fof(l3_waybel30,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,k1_yellow_1(k7_waybel_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_yellow_1(k7_waybel_0(A))))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) => ( C = k3_tarski(B) => r2_lattice3(k1_yellow_1(k7_waybel_0(A)),B,C) ) ) ) ) )).
fof(l3_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ( v4_relat_2(A) <=> ! [B] : ! [C] : ( ( r2_hidden(k4_tarski(B,C),A) & r2_hidden(k4_tarski(C,B),A) ) => B = C ) ) ) )).
fof(l3_xcmplx_0,axiom,( r2_hidden(k5_numbers,k4_ordinal1) )).
fof(l3_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ ( ~ ( r2_hidden(A,k2_arytm_2) & r2_hidden(B,k2_arytm_2) & ? [C] : ( m1_subset_1(C,k2_arytm_2) & ? [D] : ( m1_subset_1(D,k2_arytm_2) & A = C & B = D & r1_arytm_2(C,D) ) ) ) & ~ ( r2_hidden(A,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) & r2_hidden(B,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) & ? [C] : ( m1_subset_1(C,k2_arytm_2) & ? [D] : ( m1_subset_1(D,k2_arytm_2) & A = k4_tarski(k5_numbers,C) & B = k4_tarski(k5_numbers,D) & r1_arytm_2(D,C) ) ) ) & ~ ( r2_hidden(B,k2_arytm_2) & r2_hidden(A,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) ) ) => r1_xxreal_0(A,B) ) ) ) )).
fof(l3_xreal_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( A = C & B = D ) => k1_arytm_0(A,B) = k2_xcmplx_0(C,D) ) ) ) ) ) )).
fof(l3_xtuple_0,axiom,( ! [A] : ! [B] : ! [C] : ( k1_tarski(A) = k2_tarski(B,C) => B = C ) )).
fof(l3_zf_fund1,axiom,( 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 )).
fof(l3_zf_model,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ( 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] : ! [C] : ( ( 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))) ) ) ) )).
fof(l3_zfmisc_1,axiom,( ! [A] : ! [B] : ( r1_tarski(B,k1_tarski(A)) <=> ( B = k1_xboole_0 | B = k1_tarski(A) ) ) )).
fof(l40_algstr_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_1)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_algstr_1)) => ~ ( A != k4_struct_0(k3_algstr_1) & ! [C] : ( m1_subset_1(C,u1_struct_0(k3_algstr_1)) => k6_algstr_0(k3_algstr_1,C,A) != B ) ) ) ) )).
fof(l40_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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,G),F)) = k3_rlvect_1(A,k3_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,G)),k3_rlvect_1(A,D,F)) ) ) ) ) ) ) ) )).
fof(l40_arytm_3,axiom,( r2_hidden(k4_tarski(1,1),a_0_0_arytm_3) )).
fof(l40_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_2(A,B,C,k5_numbers) = k1_bcialg_1(A,B,k6_bcialg_4(A,C,k5_numbers)) ) ) ) )).
fof(l40_binop_2,axiom,( m1_subset_1(1,k3_numbers) )).
fof(l40_cayldick,axiom,( k8_group_1(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k5_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k5_struct_0(k3_cayldick),k4_struct_0(k3_cayldick))) = k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k8_group_1(k3_cayldick,k2_cayldick(k3_cayldick,k5_struct_0(k3_cayldick)),k5_struct_0(k3_cayldick))) )).
fof(l40_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(l40_convex1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(l40_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(l40_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(l40_fib_num4,axiom,( ~ r1_xxreal_0(k3_square_1(5),1) )).
fof(l40_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k24_fomodel2(A,k5_numbers) = k32_fomodel1(A) ) )).
fof(l40_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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))) ) ) ) )).
fof(l40_fomodel4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ( ( ~ v6_struct_0(D) & v11_fomodel1(D) & l1_fomodel1(D) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(D)),k9_setfam_1(k1_fomodel4(D))))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(D)),k9_setfam_1(k1_fomodel4(D))))) => ! [G] : ( v2_fomodel4(G,D) => ! [H] : ( v2_fomodel4(H,D) => ( ( v7_fomodel4(E,D) & v7_fomodel4(k4_subset_1(k9_funct_2(k9_setfam_1(k1_fomodel4(D)),k9_setfam_1(k1_fomodel4(D))),E,F),D) & r1_tarski(H,k1_funct_1(k8_funct_7(k4_fomodel4(D,E),A),G)) & r1_tarski(C,k1_funct_1(k8_funct_7(k4_fomodel4(D,F),B),H)) ) => r1_tarski(C,k1_funct_1(k8_funct_7(k4_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)),G)) ) ) ) ) ) ) ) ) )).
fof(l40_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => r1_tarski(k4_card_3(k2_funct_6(A)),k10_xtuple_0(k6_funct_6(A))) ) )).
fof(l40_funct_9,axiom,( ! [A] : ( v7_ordinal1(A) => v1_funct_9(k27_sin_cos,k3_xcmplx_0(k28_sin_cos,k2_xcmplx_0(A,1))) ) )).
fof(l40_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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) ) ) ) )).
fof(l40_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_substlat(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_substlat(A,B))) => ( r3_lattices(k5_substlat(A,B),C,D) => ! [E] : ~ ( r2_hidden(E,C) & ! [F] : ~ ( r2_hidden(F,D) & r1_tarski(F,E) ) ) ) ) ) ) )).
fof(l40_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(l40_jgraph_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r1_xxreal_0(k6_xcmplx_0(k6_xcmplx_0(A,C),k6_xcmplx_0(B,D)),k6_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(A,B),4),k4_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(A,B),4)))) => r1_xxreal_0(k7_xcmplx_0(k6_xcmplx_0(A,B),2),k6_xcmplx_0(C,D)) ) ) ) ) ) )).
fof(l40_jordan1b,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(B,k3_finseq_1(k1_jordan8(A,D))) & r1_tarski(k3_goboard5(k1_jordan8(A,D),B,C),k1_jordan2c(2,A)) & C = k5_numbers ) ) ) ) ) )).
fof(l40_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v2_xxreal_0(D) & v1_xreal_0(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)) ) ) ) ) ) )).
fof(l40_matrix_9,axiom,( k3_finseq_4(k4_ordinal1,2,3,1) != k3_finseq_4(k4_ordinal1,2,1,3) & k3_finseq_4(k4_ordinal1,2,1,3) != k3_finseq_4(k4_ordinal1,3,1,2) )).
fof(l40_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r1_connsp_1(A,B,C) & ! [D] : ( ( v3_pre_topc(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(l40_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v6_modelc_1(A) => ( ~ v2_modelc_1(A) & ~ v4_modelc_1(A) & ~ v3_modelc_1(A) & ~ v5_modelc_1(A) & ~ v7_modelc_1(A) ) ) ) )).
fof(l40_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( 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) ) ) ) )).
fof(l40_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( ( v3_group_1(A) & v13_monoid_0(A) ) => v2_group_1(A) ) ) )).
fof(l40_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(l40_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,k2_oppcat_1(B),A) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k3_funct_2(u4_struct_0(B),u4_struct_0(A),k9_oppcat_1(B,A,C),k4_cat_1(B,D)) = k4_cat_1(A,k3_funct_2(u1_struct_0(B),u1_struct_0(A),k7_cat_1(B,A,k9_oppcat_1(B,A,C)),D)) ) ) ) ) )).
fof(l40_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_nat_d(k1_newton(2,A),k1_newton(2,B)) => r1_xxreal_0(A,B) ) ) ) )).
fof(l40_polynom8,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( 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) ) ) ) ) ) )).
fof(l40_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & v6_orders_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ! [D] : ( 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) ) ) ) ) )).
fof(l40_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( ~ 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] : ( 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] : ( 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] : ( 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] : ( 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)) ) ) ) ) ) )).
fof(l40_revrot_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(l40_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(l40_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(l40_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(l40_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(l40_scmbsort,axiom,( k4_scmfsa_2(2) != k4_scmfsa_2(6) )).
fof(l40_scmisort,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ~ ( r1_xxreal_0(k1_funct_1(A,k4_scmfsa_2(k1_nat_1(1,1))),k1_funct_1(k1_scmfsa6b(k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))),A,B),k4_scmfsa_2(k1_nat_1(1,1)))) & ~ r1_xxreal_0(k1_funct_1(k1_scmfsa6b(k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))),A,B),k4_scmfsa_2(k1_nat_1(1,1))),k5_numbers) ) ) ) )).
fof(l40_scmpds_2,axiom,( ! [A] : ( 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 ) ) )).
fof(l40_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ! [C] : ( v1_int_1(C) => ! [D] : ( v7_ordinal1(D) => r1_tarski(k61_valued_1(A,1),k1_scmpds_7(B,C,D,A)) ) ) ) ) )).
fof(l40_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ r1_xxreal_0(k3_square_1(k2_xcmplx_0(k1_square_1(A),1)),A) ) )).
fof(l40_sincos10,axiom,( r1_tarski(k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_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(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))),k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))))) )).
fof(l40_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ( v3_topreal1(A) => v3_topreal1(k17_finseq_1(u1_struct_0(k15_euclid(2)),B,A)) ) ) ) )).
fof(l40_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k5_substlat(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_substlat(A,B))) => ! [E] : ( 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) ) ) ) )).
fof(l40_taylor_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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,k1_nat_1(A,1),k2_rcomp_1(D,E)) & ! [F] : ( ( 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] : ( v1_xreal_0(G) => ( r2_hidden(G,C) => k1_funct_1(F,G) = k6_xcmplx_0(k1_funct_1(B,E),k9_nat_1(k1_numbers,k3_series_1(k6_taylor_1(B,C,G,E)),A)) ) ) & k1_funct_1(F,E) = k5_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] : ( v1_xreal_0(G) => ( r2_hidden(G,k2_rcomp_1(D,E)) => k1_fdiff_1(F,G) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(B,k2_rcomp_1(D,E)),k1_nat_1(A,1)),G),k1_newton(k6_xcmplx_0(E,G),A)),k2_newton(A))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l40_tex_2,axiom,( ! [A] : ! [B] : ~ ( r1_tarski(A,B) & A != B & k6_subset_1(B,A) = k1_xboole_0 ) )).
fof(l40_topalg_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B))))) => ! [D] : ( m1_rcomp_3(D,A,B,C) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l40_turing_1,axiom,( r2_hidden(k5_numbers,u1_turing_1(k14_turing_1)) & r2_hidden(1,u1_turing_1(k14_turing_1)) )).
fof(l40_waybel19,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ! [C] : ( 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) ) ) ) )).
fof(l40_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ( u1_struct_0(A) = u1_struct_0(B) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(l40_zmodul03,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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) & v1_zmodul03(B) & l1_zmodul01(B) ) => ! [C] : ( v1_int_1(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k13_zmodul02(A,B,k1_zmodul01(B,D,k5_int_1(C,A))) = k13_zmodul02(A,B,k1_zmodul01(B,D,C)) ) ) ) ) )).
fof(l41_algstr_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_1)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_algstr_1)) => ! [C] : ( 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 ) ) ) ) ) )).
fof(l41_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ! [K] : ( v1_xreal_0(K) => ! [L] : ( v1_xreal_0(L) => ! [M] : ( v1_xreal_0(M) => ( ( D = k3_rlvect_1(A,k3_rlvect_1(A,k1_rlvect_1(A,B,k6_xcmplx_0(k3_xcmplx_0(J,K),k3_xcmplx_0(H,I))),k1_rlvect_1(A,C,k3_xcmplx_0(k3_xcmplx_0(H,J),k6_xcmplx_0(K,I)))),k1_rlvect_1(A,F,k3_xcmplx_0(k3_xcmplx_0(I,K),k6_xcmplx_0(J,H)))) & E = k3_rlvect_1(A,k3_rlvect_1(A,B,k1_rlvect_1(A,C,J)),k1_rlvect_1(A,F,K)) & G = k3_rlvect_1(A,k3_rlvect_1(A,B,k1_rlvect_1(A,C,H)),k1_rlvect_1(A,F,I)) & k2_xcmplx_0(L,M) = k6_xcmplx_0(k3_xcmplx_0(H,I),k3_xcmplx_0(J,K)) & k2_xcmplx_0(k3_xcmplx_0(L,J),k3_xcmplx_0(M,H)) = k3_xcmplx_0(k3_xcmplx_0(H,J),k6_xcmplx_0(I,K)) & k2_xcmplx_0(k3_xcmplx_0(L,K),k3_xcmplx_0(M,I)) = k3_xcmplx_0(k3_xcmplx_0(I,K),k6_xcmplx_0(H,J)) ) => k3_rlvect_1(A,k3_rlvect_1(A,k1_rlvect_1(A,D,1),k1_rlvect_1(A,E,L)),k1_rlvect_1(A,G,M)) = k4_struct_0(A) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l41_arytm_2,axiom,( ! [A] : ( m2_subset_1(A,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) => ! [C] : ( 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)) ) ) ) )).
fof(l41_arytm_3,axiom,( ~ v1_xboole_0(a_0_0_arytm_3) )).
fof(l41_binop_2,axiom,( r3_binop_1(k3_numbers,c6__binop_2,k17_binop_2) )).
fof(l41_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_cat_1(G,A,D,E) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(l41_convex1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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(k5_numbers,k1_funct_1(E,B)) & r1_xxreal_0(k5_numbers,k1_funct_1(E,C)) & r1_xxreal_0(k5_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))) ) ) ) ) ) ) ) ) )).
fof(l41_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(l41_fib_num4,axiom,( k6_xcmplx_0(1,k3_square_1(5)) != k5_numbers )).
fof(l41_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => r2_funct_2(k6_subset_1(k3_finseq_2(k3_finseq_2(A)),k1_tarski(k1_xboole_0)),k3_finseq_2(A),k17_funct_3(k3_finseq_2(k3_finseq_2(A)),k3_finseq_2(A),k9_fomodel0(A),k6_subset_1(k3_finseq_2(k3_finseq_2(A)),k1_tarski(k1_xboole_0))),k6_fomodel0(k3_finseq_2(A),k11_monoid_0(A))) ) )).
fof(l41_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) )).
fof(l41_fomodel4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ( ( ~ v6_struct_0(D) & v11_fomodel1(D) & l1_fomodel1(D) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(D)),k9_setfam_1(k1_fomodel4(D))))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(D)),k9_setfam_1(k1_fomodel4(D))))) => ! [G] : ! [H] : ( ( v7_fomodel4(E,D) & v7_fomodel4(k4_subset_1(k9_funct_2(k9_setfam_1(k1_fomodel4(D)),k9_setfam_1(k1_fomodel4(D))),E,F),D) & v5_fomodel4(G,A,D,E,C) & v5_fomodel4(H,B,D,F,k1_tarski(G)) ) => v5_fomodel4(H,k2_xcmplx_0(A,B),D,k4_subset_1(k9_funct_2(k9_setfam_1(k1_fomodel4(D)),k9_setfam_1(k1_fomodel4(D))),E,F),C) ) ) ) ) ) ) )).
fof(l41_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ( r1_glib_000(A,B,D,C) => k3_finseq_1(k2_glib_001(A,B,D,C)) = 3 ) ) )).
fof(l41_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ! [F] : ( m2_ideal_1(F,k12_polynom1(A,C),E) => ( r2_groeb_2(A,C,D,E,F) => ! [G] : ( ( 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] : ( m1_subset_1(H,k4_ordinal1) => ( r2_hidden(H,k4_finseq_1(F)) => ! [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] : ( ( v1_funct_1(J) & v1_funct_2(J,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(J,C) & m1_subset_1(J,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ( ( k1_funct_1(F,H) = k10_polynom1(A,C,I,J) & r2_hidden(J,E) ) => k4_polynom1(A,C,k10_polynom1(A,C,I,J),G) = k4_struct_0(C) ) ) ) ) ) => k4_polynom1(A,C,D,G) = k4_struct_0(C) ) ) ) ) ) ) ) ) ) )).
fof(l41_heyting1,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k12_normform(A))) => ? [D] : ( 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] : ( 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)) ) ) ) ) ) )).
fof(l41_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( 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] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r3_pua2mss1(B,A,D,E) => ! [F] : ( ( v4_msualg_1(F,B) & l3_msualg_1(F,B) ) => ( F = k1_instalg1(B,A,C,D,E) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l41_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ? [D] : ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,k2_rcomp_1(A,B)) => k1_funct_1(D,E) = k4_integra5(A,E,C) ) ) ) ) ) ) )).
fof(l41_jgraph_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( k17_euclid(k5_algstr_0(k15_euclid(2),A,B)) = k6_xcmplx_0(k17_euclid(A),k17_euclid(B)) & k18_euclid(k5_algstr_0(k15_euclid(2),A,B)) = k6_xcmplx_0(k18_euclid(A),k18_euclid(B)) ) ) ) )).
fof(l41_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l41_jordan1a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( 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))) ) ) ) )).
fof(l41_jordan1b,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(C,k1_matrix_0(k1_jordan8(A,D))) & r1_tarski(k3_goboard5(k1_jordan8(A,D),B,C),k1_jordan2c(2,A)) & B = k3_finseq_1(k1_jordan8(A,D)) ) ) ) ) ) )).
fof(l41_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_matrlin(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k9_xtuple_0(k9_matrlin(A,B,C,D)) = k9_xtuple_0(C) ) ) ) ) )).
fof(l41_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( k1_matrix_0(B) = k1_matrix_0(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(B)) ) => k7_matrix_0(u1_struct_0(A),k3_matrix_3(A,B,C),D) = k3_fvsum_1(A,k7_matrix_0(u1_struct_0(A),B,D),k7_matrix_0(u1_struct_0(A),C,D)) ) ) ) ) ) ) )).
fof(l41_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(l41_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(l41_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( 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) ) ) ) )).
fof(l41_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_3(C,B) & l1_modelc_3(C,B) ) => ! [D] : ( 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))) ) ) ) ) ) ) ) )).
fof(l41_nat_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( v7_ordinal1(B) => r1_tarski(k10_xtuple_0(k7_nat_1(A,B)),k10_xtuple_0(A)) ) ) )).
fof(l41_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v9_o_ring_1(B,A) => v11_o_ring_1(B,A) ) ) ) )).
fof(l41_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,k2_oppcat_1(A),B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( 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) ) ) ) ) ) )).
fof(l41_polynom8,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( 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) ) ) ) ) ) )).
fof(l41_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => r1_polyred(A,B,C,k8_polynom1(A,C),D) ) ) ) ) )).
fof(l41_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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) ) ) ) )).
fof(l41_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_int_1(B) => ( ~ r1_xxreal_0(B,1) => ( k9_nat_1(k1_numbers,k3_real_3(k7_xcmplx_0(1,B)),1) = B & k9_nat_1(k1_numbers,k3_real_3(k7_xcmplx_0(1,B)),k1_nat_1(A,2)) = k5_numbers & k9_nat_1(k1_numbers,k4_real_3(k7_xcmplx_0(1,B)),k5_numbers) = k5_numbers & k9_nat_1(k1_numbers,k4_real_3(k7_xcmplx_0(1,B)),1) = B & k9_nat_1(k1_numbers,k4_real_3(k7_xcmplx_0(1,B)),k1_nat_1(A,2)) = k5_numbers ) ) ) ) )).
fof(l41_rltopsp1,axiom,( ! [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) ) => ! [B] : ( ( v3_rltopsp1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v2_rltopsp1(B,A) ) ) )).
fof(l41_rlvect_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_rlvect_1(C) & m1_rlsub_1(C,B) ) => k1_rlvect_5(C) != A ) ) ) ) )).
fof(l41_scmbsort,axiom,( k4_scmfsa_2(3) != k4_scmfsa_2(4) )).
fof(l41_scmfsa8a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( 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(k7_card_1(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(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(k3_scmfsa6a(k3_scmfsa6a(B,k1_scmfsa8a(k1_nat_1(k5_card_1(C),1))),C),k4_compos_1(k1_scmfsa_2))),k1_funct_4(D,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),k1_funct_4(D,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))),2))) = k1_nat_1(k1_nat_1(k5_card_1(B),k5_card_1(C)),1) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),k1_funct_4(D,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),k1_funct_4(D,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(k3_scmfsa6a(k3_scmfsa6a(B,k1_scmfsa8a(k1_nat_1(k5_card_1(C),1))),C),k4_compos_1(k1_scmfsa_2))),k1_funct_4(D,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),k1_funct_4(D,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))),2))) & ! [E] : ( v7_ordinal1(E) => ~ ( ~ r1_xxreal_0(k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),k1_funct_4(D,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))),2),E) & k3_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(k3_scmfsa6a(k3_scmfsa6a(B,k1_scmfsa8a(k1_nat_1(k5_card_1(C),1))),C),k4_compos_1(k1_scmfsa_2))),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(k3_scmfsa6a(k3_scmfsa6a(B,k1_scmfsa8a(k1_nat_1(k5_card_1(C),1))),C),k4_compos_1(k1_scmfsa_2))),k1_funct_4(D,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),E)) = k2_compos_1(k1_scmfsa_2) ) ) & ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(E,k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),k1_funct_4(D,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))))) => k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(k3_scmfsa6a(k3_scmfsa6a(B,k1_scmfsa8a(k1_nat_1(k5_card_1(C),1))),C),k4_compos_1(k1_scmfsa_2))),k1_funct_4(D,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),E)) = k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),k1_funct_4(D,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),E)) ) ) & k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(k3_scmfsa6a(k3_scmfsa6a(B,k1_scmfsa8a(k1_nat_1(k5_card_1(C),1))),C),k4_compos_1(k1_scmfsa_2))),k1_funct_4(D,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),k1_funct_4(D,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))),1))) = k5_card_1(B) & r1_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(k3_scmfsa6a(k3_scmfsa6a(B,k1_scmfsa8a(k1_nat_1(k5_card_1(C),1))),C),k4_compos_1(k1_scmfsa_2))),k1_funct_4(D,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))) & k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(k3_scmfsa6a(k3_scmfsa6a(B,k1_scmfsa8a(k1_nat_1(k5_card_1(C),1))),C),k4_compos_1(k1_scmfsa_2))),k1_funct_4(D,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))) = k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),k1_funct_4(D,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))),2) ) ) ) ) ) ) )).
fof(l41_scmisort,axiom,( ~ v1_xboole_0(k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))))) & v1_relat_1(k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))))) & v4_relat_1(k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers)))))),k4_ordinal1) & v5_relat_1(k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers)))))),u1_compos_1(k1_scmfsa_2)) & v1_funct_1(k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))))) & v1_finset_1(k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))))) & v1_afinsq_1(k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))))) & v2_scm_halt(k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))))) & v1_scmfsa7b(k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))))) )).
fof(l41_scmpds_2,axiom,( ! [A] : ( 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 ) ) )).
fof(l41_scmpds_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmpds_2)) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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)) = k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),2) ) ) ) ) )).
fof(l41_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ r1_xxreal_0(k6_xcmplx_0(k3_xcmplx_0(k3_square_1(k2_xcmplx_0(k1_square_1(A),1)),k3_square_1(k2_xcmplx_0(k1_square_1(B),1))),k3_xcmplx_0(A,B)),k5_numbers) ) ) )).
fof(l41_sin_cos9,axiom,( v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k26_sin_cos,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)),k7_xcmplx_0(k28_sin_cos,4))),k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)),k7_xcmplx_0(k28_sin_cos,4)))) )).
fof(l41_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ( v3_topreal1(A) => v3_topreal1(k2_rfinseq(u1_struct_0(k15_euclid(2)),B,A)) ) ) ) )).
fof(l41_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l41_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m2_subset_1(C,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B)) => ! [D] : ( m2_subset_1(D,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B)) => ! [E] : ( 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)) ) ) ) )).
fof(l41_vectsp_2,axiom,( ! [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) & l6_algstr_0(A) ) => v4_vectsp_2(k4_vectsp_2(A),A) ) )).
fof(l41_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(l41_waybel19,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(l41_waybel_4,axiom,( ! [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] : ( ( ~ 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) ) ) )).
fof(l41_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ( u1_struct_0(A) = u1_struct_0(B) => k6_yellow_6(A) = k6_yellow_6(B) ) ) ) )).
fof(l41_zmodul02,axiom,( ! [A] : ( ( ~ 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) ) => k21_zmodul02(A,k19_zmodul02(A)) = k4_struct_0(A) ) )).
fof(l42_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(l42_algstr_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_1)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_algstr_1)) => ! [C] : ( 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 ) ) ) ) ) )).
fof(l42_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ! [K] : ( v1_xreal_0(K) => ! [L] : ( v1_xreal_0(L) => ( ( F = k3_rlvect_1(A,k3_rlvect_1(A,B,k1_rlvect_1(A,C,G)),k1_rlvect_1(A,E,H)) & D = k3_rlvect_1(A,k3_rlvect_1(A,k1_rlvect_1(A,B,K),k1_rlvect_1(A,C,I)),k1_rlvect_1(A,E,k3_xcmplx_0(K,H))) & K = L & I = k3_xcmplx_0(L,G) ) => D = k1_rlvect_1(A,F,K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l42_arytm_2,axiom,( ! [A] : ( m2_subset_1(A,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) => ! [C] : ( 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) ) ) ) )).
fof(l42_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ( r2_hidden(k4_tarski(A,B),c2__arytm_3) => ( r1_arytm_3(A,B) & B != k1_xboole_0 ) ) ) ) )).
fof(l42_binop_2,axiom,( m1_subset_1(1,k4_numbers) )).
fof(l42_card_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_wellord2(B,A) => B = A ) ) ) )).
fof(l42_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(l42_catalg_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( l3_msualg_1(B,k3_catalg_1(u1_struct_0(A))) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(l42_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k13_coh_sp(A))) => ! [C] : ( m1_subset_1(C,k3_coh_sp(A)) => ( B = C => ! [D] : ( m1_cat_1(D,k13_coh_sp(A),B,B) => ( D = k8_coh_sp(A,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(k13_coh_sp(A))) => ( ( k2_cat_1(k13_coh_sp(A),B,E) != k1_xboole_0 => ! [F] : ( 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] : ( m1_cat_1(F,k13_coh_sp(A),E,B) => k1_cat_1(k13_coh_sp(A),F,D) = F ) ) ) ) ) ) ) ) ) )).
fof(l42_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(l42_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(l42_dtconstr,axiom,( k5_numbers = k3_funct_2(k4_dtconstr(k5_dtconstr),k4_ordinal1,k12_dtconstr,k9_nat_1(k4_dtconstr(k5_dtconstr),k14_dtconstr,k5_numbers)) )).
fof(l42_facirc_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ? [B] : ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) & k3_funct_2(k4_ordinal1,k4_ordinal1,B,k5_numbers) = 1 & k3_funct_2(k4_ordinal1,k4_ordinal1,B,1) = 2 & k3_funct_2(k4_ordinal1,k4_ordinal1,B,2) = A ) ) )).
fof(l42_fib_num4,axiom,( ~ r1_xxreal_0(k1_square_1(k6_xcmplx_0(1,k3_square_1(5))),k5_numbers) )).
fof(l42_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => k5_relset_1(k3_finseq_2(k3_finseq_2(B)),k3_finseq_2(B),k9_fomodel0(B),k6_subset_1(A,k1_tarski(k1_xboole_0))) = k5_relset_1(k6_subset_1(k3_finseq_2(k3_finseq_2(B)),k1_tarski(k1_xboole_0)),k3_finseq_2(B),k6_fomodel0(k3_finseq_2(B),k11_monoid_0(B)),A) ) )).
fof(l42_fomodel1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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] : ( ( v8_fomodel1(D,B) & m1_subset_1(D,k1_fomodel1(B)) ) => ! [E] : ( m2_subset_1(E,k3_finseq_2(k3_finseq_2(k15_fomodel1(B))),k3_fomodel0(k3_finseq_2(k15_fomodel1(B)),k3_funct_2(k4_ordinal1,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(k12_finseq_1(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)) ) ) ) ) ) ) ) )).
fof(l42_fomodel3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(l42_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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),k8_fomodel4(B,E,A)) <=> v9_fomodel4(k42_fomodel1(B,k42_fomodel1(B,k43_fomodel1(B,k31_fomodel2(B)),C),D),B,E,A) ) ) ) ) ) )).
fof(l42_funct_9,axiom,( v1_funct_9(k55_valued_1(k1_numbers,k1_numbers,k16_sin_cos),k28_sin_cos) )).
fof(l42_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ( 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)) ) ) ) )).
fof(l42_group_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & l3_algstr_0(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => k5_group_1(C,k2_xcmplx_0(B,A),D) = k6_algstr_0(C,k5_group_1(C,B,D),k5_group_1(C,A,D)) ) ) ) ) )).
fof(l42_group_10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v8_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => ! [D] : ( m1_group_2(D,A) => ! [E] : ( m1_group_2(E,B) => ( ( D = E & r3_group_10(C,A,D) & m1_group_2(B,A) ) => r3_group_10(C,B,E) ) ) ) ) ) ) )).
fof(l42_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => r1_struct_0(C,k1_group_1(B)) ) ) )).
fof(l42_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m3_cat_2(C,B) => ! [D] : ( m2_cat_1(D,A,C) => m2_cat_1(D,A,B) ) ) ) ) )).
fof(l42_int_7,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & v1_uproots(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( k2_hurwitz(A,C) = B & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( D = k5_card_1(k6_polynom5(A,C)) & r1_xxreal_0(D,B) ) ) ) ) ) ) )).
fof(l42_interva1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [D] : ( 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))) ) ) ) )).
fof(l42_jgraph_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => k1_square_1(k12_euclid(k5_algstr_0(k15_euclid(2),A,B))) = k2_xcmplx_0(k1_square_1(k17_euclid(k5_algstr_0(k15_euclid(2),A,B))),k1_square_1(k18_euclid(k5_algstr_0(k15_euclid(2),A,B)))) ) ) )).
fof(l42_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l42_jordan1a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( 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_0(k1_jordan8(A,B))) ) ) ) ) )).
fof(l42_jordan1b,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(B,k3_finseq_1(k1_jordan8(A,D))) & r1_tarski(k3_goboard5(k1_jordan8(A,D),B,C),k1_jordan2c(2,A)) & C = k1_matrix_0(k1_jordan8(A,D)) ) ) ) ) ) )).
fof(l42_matrix15,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k5_numbers & k1_matrix_0(C) = k5_numbers ) => B = C ) ) ) ) )).
fof(l42_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ( ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(l42_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_3(C,B) & l1_modelc_3(C,B) ) => ! [D] : ( 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))) ) ) ) ) ) ) ) )).
fof(l42_ndiff_4,axiom,( 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] : ( m1_subset_1(A,k1_numbers) => ( k1_funct_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) ) ) )).
fof(l42_normform,axiom,( ! [A] : r2_hidden(k1_xboole_0,a_1_1_normform(A)) )).
fof(l42_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,k2_oppcat_1(B),A) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ( k3_funct_2(u1_struct_0(B),u1_struct_0(A),k7_cat_1(B,A,k9_oppcat_1(B,A,C)),k3_graph_1(B,D)) = k4_graph_1(A,k3_funct_2(u4_struct_0(B),u4_struct_0(A),k9_oppcat_1(B,A,C),D)) & k3_funct_2(u1_struct_0(B),u1_struct_0(A),k7_cat_1(B,A,k9_oppcat_1(B,A,C)),k4_graph_1(B,D)) = k3_graph_1(A,k3_funct_2(u4_struct_0(B),u4_struct_0(A),k9_oppcat_1(B,A,C),D)) ) ) ) ) ) )).
fof(l42_ordinal4,axiom,( k5_ordinal1 = k1_xboole_0 )).
fof(l42_polynom1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k12_polynom1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k12_polynom1(A,B))) => ( D = k5_struct_0(k12_polynom1(A,B)) => ( k6_algstr_0(k12_polynom1(A,B),C,D) = C & k6_algstr_0(k12_polynom1(A,B),D,C) = C ) ) ) ) ) ) )).
fof(l42_polynom7,axiom,( ! [A] : ( v3_ordinal1(A) => ! [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) & v5_group_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & v1_algstr_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( 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)))) ) => k2_polynom2(A,B,k11_polynom1(A,B,k4_polynom7(A,B,D),C),E) = k8_group_1(B,D,k2_polynom2(A,B,C,E)) ) ) ) ) ) )).
fof(l42_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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))) ) ) ) )).
fof(l42_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v4_ratfunc1(B,A) & v5_ratfunc1(B,A) & m1_ratfunc1(B,A) ) => k11_ratfunc1(A,B) = k6_ratfunc1(A,B) ) ) )).
fof(l42_rltopsp1,axiom,( ! [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) ) => ! [B] : ( ( v3_rltopsp1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v3_rltopsp1(k3_convex1(A,B),A) ) ) )).
fof(l42_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( m1_rmod_2(E,A,B) => r1_tarski(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)))) ) ) ) ) ) )).
fof(l42_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => k3_rusub_1(A,k4_struct_0(A),B) = u1_struct_0(B) ) ) )).
fof(l42_scmbsort,axiom,( k4_scmfsa_2(3) != k4_scmfsa_2(5) )).
fof(l42_scmfsa10,axiom,( k4_scmfsa_2(k5_numbers) != k4_scmfsa_2(1) )).
fof(l42_scmisort,axiom,( ~ r4_scmfsa7b(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k4_scmfsa_2(k1_nat_1(3,1))) )).
fof(l42_scmpds_2,axiom,( ! [A] : ( 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 ) ) )).
fof(l42_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( k5_card_1(k2_scpqsort(D,C)) = 57 & ( r1_xxreal_0(7,C) => ( r2_scmpds_6(k2_scpqsort(D,C),B,A) & ? [E] : ( m2_finseq_1(E,k4_numbers) & ? [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(l42_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( r1_xxreal_0(1,A) & r1_xxreal_0(k2_xcmplx_0(A,k3_square_1(k6_xcmplx_0(k1_square_1(A),1))),k5_numbers) ) ) )).
fof(l42_sin_cos9,axiom,( v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k27_sin_cos,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos))),k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos)))) )).
fof(l42_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(l42_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l42_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) & A != B & k6_xcmplx_0(k1_square_1(k3_square_1(A)),k1_square_1(k3_square_1(B))) = k5_numbers ) ) ) )).
fof(l42_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k5_substlat(A,B))) => ! [D] : ( 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 ) ) )).
fof(l42_topreal2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(l42_toprealb,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => r2_borsuk_3(k8_toprealb(A),k7_toprealb(A,C,B)) ) ) ) )).
fof(l42_turing_1,axiom,( ! [A] : ( 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] : ! [C] : ! [D] : ( 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),k1_enumset1(k4_xcmplx_0(1),k5_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),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),k8_turing_1(k14_turing_1,A)))) ) ) ) )).
fof(l42_vectsp_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(k6_vectsp_2(A,B))) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(l42_waybel17,axiom,( ! [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) & v4_waybel11(A) & l1_waybel_9(A) ) => ! [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) & v3_waybel_3(B) & v4_waybel11(B) & l1_waybel_9(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) )).
fof(l42_waybel19,axiom,( ! [A] : ( ( 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) ) )).
fof(l42_waybel29,axiom,( ! [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] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => ! [C] : ( ( 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] : ( ( v4_waybel11(D) & m1_yellow_9(D,C) ) => k5_waybel11(k3_yellow_3(C,A)) = u1_pre_topc(k2_borsuk_1(D,B)) ) ) ) <=> ! [B] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => ! [C] : ( ( 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] : ( ( v4_waybel11(D) & m1_yellow_9(D,C) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(l42_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(l42_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(l42_zfmisc_1,axiom,( ! [A] : ! [B] : ( r2_hidden(B,A) => r1_tarski(B,k3_tarski(A)) ) )).
fof(l43_algstr_1,axiom,( ! [A] : ( 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) ) )).
fof(l43_arytm_2,axiom,( ! [A] : ( m2_subset_1(A,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) => ! [B] : ( 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 ) ) ) )).
fof(l43_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( k9_xtuple_0(B) = k1_autalg_1(A) & ! [C] : ( r2_hidden(C,k1_autalg_1(A)) => k1_funct_1(B,C) = k16_funcop_1(k5_numbers,C) ) ) => k10_xtuple_0(B) = k5_autalg_1(k6_msualg_1(A),k9_msualg_1(A)) ) ) ) )).
fof(l43_binop_2,axiom,( r3_binop_1(k4_numbers,c7__binop_2,k22_binop_2) )).
fof(l43_borsuk_7,axiom,( u1_struct_0(k8_toprealb(3)) = k3_topreal9(3,k4_euclid_5(k5_numbers,k5_numbers,k5_numbers),1) )).
fof(l43_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k11_c0sp1(A))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(l43_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k12_funcsdom(u1_struct_0(A)))) => ! [C] : ( 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)) ) ) ) ) )).
fof(l43_card_5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v1_finset_1(B) => ( r1_tarski(B,A) => v1_finset_1(k2_wellord2(k1_wellord2(B))) ) ) ) )).
fof(l43_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => ? [B] : ( 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) ) ) )).
fof(l43_cayldick,axiom,( k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)) = k4_struct_0(k4_cayldick(k3_cayldick)) )).
fof(l43_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_cc0sp2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_cc0sp2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_cc0sp1(u1_struct_0(A)))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l43_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k4_xcmplx_0(A) = k2_xcmplx_0(k1_real_1(k3_complex1(A)),k3_xcmplx_0(k1_real_1(k4_complex1(A)),k7_complex1)) ) )).
fof(l43_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l43_dtconstr,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( A = k3_funct_2(k4_dtconstr(k5_dtconstr),k4_ordinal1,k12_dtconstr,k9_nat_1(k4_dtconstr(k5_dtconstr),k14_dtconstr,A)) => k1_nat_1(A,1) = k3_funct_2(k4_dtconstr(k5_dtconstr),k4_ordinal1,k12_dtconstr,k9_nat_1(k4_dtconstr(k5_dtconstr),k14_dtconstr,k1_nat_1(A,1))) ) ) )).
fof(l43_equation,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_funct_1(k4_equation(A),B)) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_pralg_2(E,D,A) => ( ! [F] : ( 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) ) ) ) ) ) ) )).
fof(l43_fib_num4,axiom,( ~ r1_xxreal_0(k2_power(k6_xcmplx_0(1,k3_square_1(5)),2),k5_numbers) )).
fof(l43_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => r1_partfun1(k16_funcop_1(k1_xboole_0,k1_xboole_0),k6_fomodel0(k3_finseq_2(A),k11_monoid_0(A))) ) )).
fof(l43_fomodel1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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] : ( v8_fomodel1(D,B) & m1_subset_1(D,k1_fomodel1(B)) & ? [E] : ( m2_subset_1(E,k3_finseq_2(k3_finseq_2(k15_fomodel1(B))),k3_fomodel0(k3_finseq_2(k15_fomodel1(B)),k3_funct_2(k4_ordinal1,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(k12_finseq_1(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)) ) ) ) ) ) )).
fof(l43_fomodel3,axiom,( ! [A] : ( ~ 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) ) )).
fof(l43_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(l43_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ! [F] : ( 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] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( m1_subset_1(H,k6_margrel1) => ! [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)) ) ) ) ) ) ) ) ) ) ) )).
fof(l43_funct_9,axiom,( v1_funct_9(k55_valued_1(k1_numbers,k1_numbers,k18_sin_cos),k28_sin_cos) )).
fof(l43_fvaluat1,axiom,( ! [A] : ( v1_fvaluat1(A) => ! [B] : ( v1_fvaluat1(B) => ( r1_xxreal_0(A,B) => r1_xxreal_0(k5_numbers,k3_xxreal_3(B,A)) ) ) ) )).
fof(l43_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( ( 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)) ) => ( k3_rlvect_1(A,B,C) = k3_rlvect_1(A,k1_rlvect_1(A,D,k2_xcmplx_0(F,H)),k1_rlvect_1(A,E,k2_xcmplx_0(G,I))) & k5_algstr_0(A,B,C) = k3_rlvect_1(A,k1_rlvect_1(A,D,k6_xcmplx_0(F,H)),k1_rlvect_1(A,E,k6_xcmplx_0(G,I))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l43_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(l43_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(l43_gr_cy_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_int_1(B) => ( A != k5_numbers => r2_int_1(k5_int_1(B,A),B,A) ) ) ) )).
fof(l43_group_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(l43_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(l43_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l43_idea_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( v7_ordinal1(B) => ( ( B = 2 & r2_hidden(B,k4_finseq_1(A)) ) => k1_recdef_1(k13_idea_1(A),B) = k1_recdef_1(A,3) ) ) ) )).
fof(l43_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,A,C) => ! [G] : ( m2_cat_1(G,A,C) => ( ( r1_nattra_1(A,B,D,E) & r1_nattra_1(A,C,F,G) ) => ! [H] : ( m1_nattra_1(H,A,B,D,E) => ! [I] : ( m1_nattra_1(I,A,C,F,G) => ! [J] : ( 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) = k8_cat_2(B,C,k2_nattra_1(A,B,D,E,H,J),k2_nattra_1(A,C,F,G,I,J)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l43_jordan1a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( 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_0(k1_jordan8(A,B))) ) ) ) ) )).
fof(l43_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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,k1_nat_1(k1_jordan3(A,B),1)),B,C) ) ) | r1_jordan3(k4_jordan3(A,B,C),B,C) ) ) ) ) ) )).
fof(l43_lopclset,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(l43_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) )).
fof(l43_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_3(C,B) & l1_modelc_3(C,B) ) => ! [D] : ( 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))) ) ) ) ) ) ) ) )).
fof(l43_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,k2_oppcat_1(A),B) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(l43_pdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => k7_euclid(3,k1_euclid_8(A,C,E),k1_euclid_8(B,D,F)) = k1_euclid_8(k2_xcmplx_0(A,B),k2_xcmplx_0(C,D),k2_xcmplx_0(E,F)) ) ) ) ) ) ) )).
fof(l43_polynom7,axiom,( ! [A] : ( v3_ordinal1(A) => ! [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) & v5_group_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & v1_algstr_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( 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)))) ) => k2_polynom2(A,B,k11_polynom1(A,B,C,k4_polynom7(A,B,D)),E) = k8_group_1(B,k2_polynom2(A,B,C,E),D) ) ) ) ) ) )).
fof(l43_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ~ ( r2_hidden(D,C) & ! [E] : ( ( 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 ) ) ) ) ) )).
fof(l43_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ( v3_rinfsup2(A) & v8_valued_0(A) ) => ( v7_mesfunc5(A) & v10_mesfunc5(A) & k2_mesfunc5(A) = k2_rinfsup2(A) ) ) ) )).
fof(l43_scmbsort,axiom,( k4_scmfsa_2(3) != k4_scmfsa_2(6) )).
fof(l43_scmpds_2,axiom,( ! [A] : ( 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 ) ) )).
fof(l43_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => k1_sin_cos5(k4_xcmplx_0(A)) = k4_xcmplx_0(k1_sin_cos5(A)) ) )).
fof(l43_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k7_xcmplx_0(k6_xcmplx_0(k1_square_1(A),1),k2_xcmplx_0(k1_square_1(A),1)),k4_xcmplx_0(1)) ) ) )).
fof(l43_sin_cos9,axiom,( v2_funct_1(k2_partfun1(k1_numbers,k1_numbers,k26_sin_cos,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)),k7_xcmplx_0(k28_sin_cos,4)))) )).
fof(l43_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l43_topreal2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(l43_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m1_vectsp_4(E,A,B) => r1_tarski(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)))) ) ) ) ) ) )).
fof(l43_waybel27,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(k5_yellow_1(A,C))) & v22_waybel_0(D,B,k5_yellow_1(A,C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(k5_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(k9_funct_6(D)),k9_funct_2(u1_struct_0(B),u1_struct_0(C))) & k9_xtuple_0(k9_funct_6(D)) = A ) ) ) ) ) )).
fof(l43_waybel_4,axiom,( ! [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] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))))) ) => ( r1_funct_2(u1_struct_0(A),u1_struct_0(k1_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,k1_yellow_1(k7_waybel_0(A))) ) ) ) )).
fof(l43_waybel_5,axiom,( ! [A] : ( ( 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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)) ) ) ) )).
fof(l43_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_zmodul01(C,A) => ( u1_struct_0(C) = B => v7_zmodul01(B,A) ) ) ) ) )).
fof(l44_algstr_1,axiom,( ! [A] : ( 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) ) )).
fof(l44_arytm_3,axiom,( r1_tarski(k4_ordinal1,k5_arytm_3) )).
fof(l44_binop_2,axiom,( r3_binop_1(k4_ordinal1,1,k24_binop_2) )).
fof(l44_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(l44_cayldick,axiom,( k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick))) = k4_struct_0(k4_cayldick(k4_cayldick(k3_cayldick))) )).
fof(l44_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(l44_euclid_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(B)) => ( k6_euclid(B,k9_euclid(B,C,A)) = k9_euclid(B,C,k4_xcmplx_0(A)) & k6_euclid(B,k9_euclid(B,C,A)) = k9_euclid(B,k6_euclid(B,C),A) ) ) ) ) )).
fof(l44_fib_num4,axiom,( ~ r1_xxreal_0(k3_square_1(5),k5_numbers) )).
fof(l44_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ( ( v3_fomodel0(B,C) & r1_tarski(A,B) ) => v3_fomodel0(A,C) ) ) )).
fof(l44_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v6_struct_0(D) & v11_fomodel1(D) & l1_fomodel1(D) ) => ! [E] : ( ( 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] : ( ( v1_relat_1(F) & v1_funct_1(F) & v1_fomodel2(F,D,A) & v3_fomodel3(F,D,A,E) ) => k9_nat_1(k9_funct_2(k35_fomodel1(D),k8_eqrel_1(A,E)),k7_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(k9_nat_1(k9_funct_2(k35_fomodel1(D),A),k7_fomodel2(D,A,B,F),C),k17_fomodel3(A,E)) ) ) ) ) ) ) )).
fof(l44_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C))))) => ( v9_fomodel4(B,C,D,A) => ( v4_fomodel2(B,C) & m2_subset_1(B,k3_finseq_2(k15_fomodel1(C)),k6_subset_1(k3_finseq_2(k15_fomodel1(C)),k1_tarski(k1_xboole_0))) ) ) ) ) )).
fof(l44_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ! [F] : ( 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] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(l44_funct_9,axiom,( ! [A] : ( v7_ordinal1(A) => v1_funct_9(k55_valued_1(k1_numbers,k1_numbers,k16_sin_cos),k3_xcmplx_0(k28_sin_cos,k2_xcmplx_0(A,1))) ) )).
fof(l44_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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)) ) ) ) ) )).
fof(l44_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( B = k3_rlvect_1(A,k1_rlvect_1(A,C,F),k1_rlvect_1(A,D,G)) => k1_rlvect_1(A,B,E) = k3_rlvect_1(A,k1_rlvect_1(A,C,k3_xcmplx_0(E,F)),k1_rlvect_1(A,D,k3_xcmplx_0(E,G))) ) ) ) ) ) ) ) ) )).
fof(l44_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => k7_glib_000(A) = k21_glib_000(A,k6_glib_000(A)) ) )).
fof(l44_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k1_relset_1(k4_ordinal1,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(k4_ordinal1,B)) ) ) ) ) ) )).
fof(l44_gr_cy_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_int_1(B) => ~ ( A != k5_numbers & ! [C] : ( v7_ordinal1(C) => ~ r2_int_1(C,B,A) ) ) ) ) )).
fof(l44_group_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & l3_algstr_0(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => k5_group_1(C,k3_xcmplx_0(B,A),D) = k5_group_1(C,A,k5_group_1(C,B,D)) ) ) ) ) )).
fof(l44_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r1_struct_0(C,D) => r1_struct_0(C,k2_group_1(B,D)) ) ) ) ) )).
fof(l44_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => ! [E] : ( ( v5_glib_001(E,A) & m3_glib_001(E,A) ) => ! [F] : ( ( 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)))) ) ) ) ) ) ) ) ) )).
fof(l44_idea_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( v7_ordinal1(B) => ( ( B = 3 & r2_hidden(B,k4_finseq_1(A)) ) => k1_recdef_1(k13_idea_1(A),B) = k1_recdef_1(A,2) ) ) ) )).
fof(l44_jgraph_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( k18_euclid(k5_algstr_0(k15_euclid(2),A,B)) = k6_xcmplx_0(k18_euclid(A),k18_euclid(B)) & k17_euclid(k5_algstr_0(k15_euclid(2),A,B)) = k6_xcmplx_0(k17_euclid(A),k17_euclid(B)) ) ) ) )).
fof(l44_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(A,k5_numbers) => k3_xcmplx_0(k7_xcmplx_0(C,k1_newton(2,A)),k6_xcmplx_0(k1_jordan1a(k1_jordan8(B,A)),2)) = k7_xcmplx_0(C,2) ) ) ) ) )).
fof(l44_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(A,A))))) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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) ) ) ) ) ) )).
fof(l44_matrixr2,axiom,( v1_funct_1(k1_finseq_2(k5_numbers)) & v1_funct_2(k1_finseq_2(k5_numbers),k2_finseq_1(k5_numbers),k2_finseq_1(k5_numbers)) & v3_funct_2(k1_finseq_2(k5_numbers),k2_finseq_1(k5_numbers),k2_finseq_1(k5_numbers)) & m1_subset_1(k1_finseq_2(k5_numbers),k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(k5_numbers),k2_finseq_1(k5_numbers)))) )).
fof(l44_mod_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(l44_modal_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => r2_hidden(k14_trees_3(k5_numbers),k1_relset_1(k2_trees_1(1),k7_funcop_1(k2_trees_1(1),k4_tarski(A,B)))) ) ) )).
fof(l44_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v6_modelc_1(A) => A = k10_modelc_1(k14_modelc_1(A)) ) ) )).
fof(l44_msaterm,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ r1_xxreal_0(k3_finseq_1(B),A) => ( r2_hidden(k1_nat_1(A,1),k4_finseq_1(B)) & r2_hidden(k1_funct_1(B,k1_nat_1(A,1)),k10_xtuple_0(B)) ) ) ) ) )).
fof(l44_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(l44_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,k2_oppcat_1(B),A) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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] : ( m1_cat_1(G,B,D,E) => ! [H] : ( m1_cat_1(H,B,E,F) => k3_funct_2(u4_struct_0(B),u4_struct_0(A),k9_oppcat_1(B,A,C),k1_cat_1(B,G,H)) = k1_cat_1(A,k3_funct_2(u4_struct_0(B),u4_struct_0(A),k9_oppcat_1(B,A,C),H),k3_funct_2(u4_struct_0(B),u4_struct_0(A),k9_oppcat_1(B,A,C),G)) ) ) ) ) ) ) ) ) ) )).
fof(l44_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ( v3_rinfsup2(A) & v7_valued_0(A) ) => ( v7_mesfunc5(A) & v10_mesfunc5(A) & k2_mesfunc5(A) = k1_rinfsup2(A) ) ) ) )).
fof(l44_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(l44_scmbsort,axiom,( k4_scmfsa_2(4) != k4_scmfsa_2(5) )).
fof(l44_scmpds_2,axiom,( ! [A] : ( 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 ) ) )).
fof(l44_scmpds_6,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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),k5_numbers) = A ) ) ) ) )).
fof(l44_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & A != 1 & r1_xxreal_0(k7_xcmplx_0(k2_xcmplx_0(k1_square_1(A),1),k6_xcmplx_0(k1_square_1(A),1)),1) & r1_xxreal_0(k4_xcmplx_0(1),k7_xcmplx_0(k2_xcmplx_0(k1_square_1(A),1),k6_xcmplx_0(k1_square_1(A),1))) ) ) )).
fof(l44_sin_cos9,axiom,( v2_funct_1(k2_partfun1(k1_numbers,k1_numbers,k27_sin_cos,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos)))) )).
fof(l44_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l44_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,A) => k2_xboole_0(B,k1_seq_4(A)) = B ) ) ) )).
fof(l44_taylor_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( r1_tarski(B,k1_relset_1(k1_numbers,A)) => ! [C] : ( v7_ordinal1(C) => ( r1_taylor_1(A,C,B) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( 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,k1_nat_1(C,1),k2_rcomp_1(D,E)) ) => ( r1_xxreal_0(E,D) | ! [F] : ( ( 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] : ( v1_xreal_0(G) => ( r2_hidden(G,B) => k1_funct_1(F,G) = k6_xcmplx_0(k1_funct_1(A,D),k9_nat_1(k1_numbers,k3_series_1(k6_taylor_1(A,B,G,D)),C)) ) ) ) => ( k1_funct_1(F,D) = k5_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] : ( v1_xreal_0(G) => ( r2_hidden(G,k2_rcomp_1(D,E)) => k1_fdiff_1(F,G) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(A,k2_rcomp_1(D,E)),k1_nat_1(C,1)),G),k1_newton(k6_xcmplx_0(D,G),C)),k2_newton(C))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l44_topreal2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ( ? [C] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(l44_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)) ) ) )).
fof(l44_waybel29,axiom,( ! [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) ) => ( v3_waybel_3(k1_yellow_1(k5_waybel11(A))) => ! [B] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => ! [C] : ( ( 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] : ( ( v4_waybel11(D) & m1_yellow_9(D,C) ) => k5_waybel11(k3_yellow_3(C,A)) = u1_pre_topc(k2_borsuk_1(D,B)) ) ) ) ) ) )).
fof(l44_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( 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] : ( r2_hidden(C,k2_relset_1(u1_struct_0(A),B)) => k1_funct_1(B,C) = C ) ) ) ) )).
fof(l44_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( B != D => k3_relat_1(k2_tarski(k4_tarski(A,B),k4_tarski(C,D)),k2_tarski(k4_tarski(B,E),k4_tarski(D,F))) = k2_tarski(k4_tarski(A,E),k4_tarski(C,F)) ) )).
fof(l44_zfmisc_1,axiom,( ! [A] : ! [B] : k3_tarski(k2_tarski(A,B)) = k2_xboole_0(A,B) )).
fof(l45_analmetr,axiom,( ? [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) & ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r1_analmetr(A,B,C) ) ) ) )).
fof(l45_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => v2_rcomp_1(k4_rcomp_1(k2_xxreal_0,A)) ) )).
fof(l45_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(l45_cayldick,axiom,( k2_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k5_struct_0(k3_cayldick))) = k5_cayldick(k3_cayldick,k2_cayldick(k3_cayldick,k4_struct_0(k3_cayldick)),k4_algstr_0(k3_cayldick,k5_struct_0(k3_cayldick))) )).
fof(l45_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(l45_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ~ ( B != C & k12_euclid(k8_euclid(A,B,C)) = k5_numbers ) ) ) ) )).
fof(l45_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ~ ( r2_euclidlp(A,B,C) & r3_euclidlp(A,B,C) ) ) ) ) )).
fof(l45_fib_num4,axiom,( ~ r1_xxreal_0(k3_xcmplx_0(2,k3_square_1(5)),k3_xcmplx_0(2,1)) )).
fof(l45_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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] : ( ( 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),k9_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),k9_fomodel2(B,A,D),k17_fomodel3(A,C))) ) ) ) ) )).
fof(l45_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))))) => v11_fomodel4(k30_fomodel2(A),A,B) ) ) )).
fof(l45_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l45_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( ( k10_xtuple_0(D) = A & k3_relat_1(D,B) = k4_relat_1(k9_xtuple_0(C)) & k3_relat_1(B,C) = k4_relat_1(A) ) => C = D ) ) ) ) )).
fof(l45_fuzzy_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k5_numbers,C) => k3_xcmplx_0(C,k3_xxreal_0(A,B)) = k3_xxreal_0(k3_xcmplx_0(C,A),k3_xcmplx_0(C,B)) ) ) ) ) )).
fof(l45_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( ( 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 ) ) ) ) ) ) ) ) ) )).
fof(l45_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ( k4_glib_001(A,B) = k3_glib_001(A,C) => k1_nat_1(k3_finseq_1(k7_glib_001(A,B,C)),1) = k1_nat_1(k3_finseq_1(B),k3_finseq_1(C)) ) ) ) ) )).
fof(l45_gr_cy_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_int_1(A,B,C) => ( C = k5_numbers | r2_int_1(k1_newton(A,D),k1_newton(B,D),C) ) ) ) ) ) ) )).
fof(l45_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(l45_group_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(l45_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_substlat(A,B))) => ! [D] : ( 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] : ( 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)))) ) ) ) ) ) ) )).
fof(l45_heyting3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ ( A != k1_tarski(k1_xboole_0) & r2_hidden(k1_xboole_0,A) & ! [B] : ~ ( r2_hidden(B,A) & B != k1_xboole_0 ) ) ) )).
fof(l45_idea_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => ( B = 2 | B = 3 | k1_recdef_1(k13_idea_1(A),B) = k1_recdef_1(A,B) ) ) ) ) )).
fof(l45_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ( k5_int_1(A,C) = k5_numbers => ( r1_xxreal_0(C,k5_numbers) | k5_int_1(k3_xcmplx_0(A,B),C) = k5_numbers ) ) ) ) ) )).
fof(l45_integra8,axiom,( k9_xtuple_0(k16_sin_cos) = k1_numbers )).
fof(l45_jgraph_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => k1_square_1(k12_euclid(k5_algstr_0(k15_euclid(2),A,B))) = k2_xcmplx_0(k1_square_1(k18_euclid(k5_algstr_0(k15_euclid(2),A,B))),k1_square_1(k17_euclid(k5_algstr_0(k15_euclid(2),A,B)))) ) ) )).
fof(l45_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(A,B) ) => r1_xxreal_0(k7_xcmplx_0(C,k1_newton(2,B)),k7_xcmplx_0(C,k1_newton(2,A))) ) ) ) ) ) )).
fof(l45_jordan5d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( ~ 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 = k4_seq_4(C) ) => r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),1,A)),k18_euclid(B)) ) ) ) ) ) )).
fof(l45_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(l45_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [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] : ( m1_subset_1(F,u1_struct_0(E)) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(E),C,D) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(E))) ) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(E),C,B) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(E))) ) => ( F != k4_struct_0(E) => k4_matrix15(E,G,H) = k4_matrix15(E,k3_matrix11(A,C,D,u1_struct_0(E),G,k10_fvsum_1(k1_matrix_0(G),E,k7_matrix_0(u1_struct_0(E),G,A),F)),k3_matrix11(A,C,B,u1_struct_0(E),H,k10_fvsum_1(k1_matrix_0(H),E,k7_matrix_0(u1_struct_0(E),H,A),F))) ) ) ) ) ) ) ) ) ) )).
fof(l45_matrlin,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ~ ( r2_hidden(B,k9_xtuple_0(A)) & r1_xxreal_0(k3_finseq_1(A),k5_numbers) ) ) )).
fof(l45_mod_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ( v1_ringcat1(C,A,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)) ) ) ) ) ) )).
fof(l45_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v4_modelc_1(A) => A = k8_modelc_1(k15_modelc_1(A),k16_modelc_1(A)) ) ) )).
fof(l45_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ( 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)) ) ) )).
fof(l45_nagata_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ( k1_binop_1(B,C,C) = k5_numbers & k1_binop_1(B,C,D) = k1_binop_1(B,D,C) & r1_xxreal_0(k1_binop_1(B,C,E),k2_xcmplx_0(k1_binop_1(B,C,D),k1_binop_1(B,D,E))) ) ) ) ) ) ) )).
fof(l45_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_o_ring_1(B,A) => v13_o_ring_1(B,A) ) ) ) )).
fof(l45_pdiff_4,axiom,( v1_xreal_0(1) )).
fof(l45_pdiff_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(A)),k1_numbers))) ) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( 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] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,u1_struct_0(k4_real_ns1(A))) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,k1_numbers,u1_struct_0(k4_real_ns1(A)),F,C)) & k7_partfun1(k1_numbers,C,E) = k1_seq_2(k8_funct_2(k4_ordinal1,k1_numbers,u1_struct_0(k4_real_ns1(A)),F,C)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l45_prepower,axiom,( k5_xcmplx_0(1) = 1 )).
fof(l45_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l45_scmbsort,axiom,( k4_scmfsa_2(4) != k4_scmfsa_2(6) )).
fof(l45_scmisort,axiom,( ~ r4_scmfsa7b(k3_scmfsa6a(k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k16_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1)))),k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(3,1)))),k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))))),k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))))),k4_scmfsa_2(k1_nat_1(k5_numbers,1))) )).
fof(l45_scmpds_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ( r2_hidden(A,k1_tarski(k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0))) => k2_compos_0(u1_compos_1(k1_scmpds_2),A) = k5_numbers ) ) )).
fof(l45_scmpds_7,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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))) = k1_nat_1(k5_card_1(D),4) ) ) ) ) )).
fof(l45_seq_1,axiom,( k5_xcmplx_0(k4_xcmplx_0(1)) = k4_xcmplx_0(1) )).
fof(l45_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k7_xcmplx_0(k3_xcmplx_0(2,A),k2_xcmplx_0(1,k1_square_1(A))),k5_numbers) ) ) )).
fof(l45_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l45_taylor_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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,k1_nat_1(A,1),k2_rcomp_1(D,E)) & ! [F] : ( ( 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] : ( v1_xreal_0(G) => ( r2_hidden(G,C) => k1_funct_1(F,G) = k6_xcmplx_0(k1_funct_1(B,D),k9_nat_1(k1_numbers,k3_series_1(k6_taylor_1(B,C,G,D)),A)) ) ) & k1_funct_1(F,D) = k5_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] : ( v1_xreal_0(G) => ( r2_hidden(G,k2_rcomp_1(D,E)) => k1_fdiff_1(F,G) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(B,k2_rcomp_1(D,E)),k1_nat_1(A,1)),G),k1_newton(k6_xcmplx_0(D,G),A)),k2_newton(A))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l45_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) )).
fof(l45_uniroots,axiom,( r2_funct_2(k4_ordinal1,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))) )).
fof(l45_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(l45_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(l45_waybel17,axiom,( ! [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] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(l45_waybel29,axiom,( ! [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] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => ! [C] : ( ( 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] : ( ( 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(k1_yellow_1(k5_waybel11(A))) ) ) )).
fof(l45_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(l46_analmetr,axiom,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1__analmetr)) & ? [B] : ( m1_subset_1(B,u1_struct_0(c1__analmetr)) & r1_analmetr(c1__analmetr,A,B) ) ) )).
fof(l46_arytm_2,axiom,( ! [A] : ~ ( r2_hidden(A,k2_arytm_2) & A = k5_arytm_3 ) )).
fof(l46_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ r1_xxreal_0(k2_xcmplx_0(k6_xcmplx_0(k1_square_1(A),A),1),k5_numbers) ) )).
fof(l46_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => v2_rcomp_1(k3_rcomp_1(A,k1_xxreal_0)) ) )).
fof(l46_borsuk_7,axiom,( m1_subset_1(k3_numbers,k1_zfmisc_1(k1_numbers)) )).
fof(l46_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_clvect_1(C,A) => ( u1_struct_0(C) = B => v6_clvect_1(B,A) ) ) ) ) )).
fof(l46_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r2_hidden(D,C) & r2_hidden(E,C) ) => ( D = E | r1_xxreal_0(B,k3_metric_1(A,D,E)) ) ) ) ) => ( r1_xxreal_0(B,k5_numbers) | ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(l46_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k6_xcmplx_0(A,B) = k2_xcmplx_0(k5_real_1(k3_complex1(A),k3_complex1(B)),k3_xcmplx_0(k5_real_1(k4_complex1(A),k4_complex1(B)),k7_complex1)) ) ) )).
fof(l46_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(l46_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( 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] : ( v1_xreal_0(F) => k8_euclid(A,B,C) != k9_euclid(A,k8_euclid(A,D,E),F) ) ) ) ) ) ) ) )).
fof(l46_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_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] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_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) = k3_xcmplx_0(2,k1_funct_1(k18_sin_cos,C)) ) ) ) ) ) ) )).
fof(l46_fib_num4,axiom,( ~ r1_xxreal_0(k4_xcmplx_0(2),k4_xcmplx_0(k3_xcmplx_0(2,k3_square_1(5)))) )).
fof(l46_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(l46_finseq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r2_hidden(k4_tarski(A,B),k1_tarski(k4_tarski(C,D))) => ( A = C & B = D ) ) )).
fof(l46_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => r2_relset_1(k4_ordinal1,k4_ordinal1,k2_partfun1(k4_ordinal1,k4_ordinal1,k14_finseq_1(k2_finseq_1(k1_nat_1(A,k5_numbers))),k2_finseq_1(A)),k14_finseq_1(k2_finseq_1(A))) ) )).
fof(l46_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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) != k31_fomodel2(B) => k13_fomodel2(B,k8_eqrel_1(A,C),k23_fomodel3(B,A,C,E),D) = k13_fomodel2(B,A,E,D) ) ) ) ) ) ) )).
fof(l46_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l46_funct_9,axiom,( ! [A] : ( v7_ordinal1(A) => v1_funct_9(k55_valued_1(k1_numbers,k1_numbers,k18_sin_cos),k3_xcmplx_0(k28_sin_cos,k2_xcmplx_0(A,1))) ) )).
fof(l46_fuzzy_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k5_numbers,C) => k3_xcmplx_0(C,k4_xxreal_0(A,B)) = k4_xxreal_0(k3_xcmplx_0(C,A),k3_xcmplx_0(C,B)) ) ) ) ) )).
fof(l46_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => r2_hidden(k1_fvaluat1(k2_relset_1(k6_numbers,B)),k2_relset_1(k6_numbers,B)) ) ) ) )).
fof(l46_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(l46_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( m1_group_9(D,A,B) => ( r1_tarski(u1_struct_0(C),u1_struct_0(D)) => m1_group_9(C,A,D) ) ) ) ) )).
fof(l46_heyting1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k12_normform(A))) => ! [C] : ( 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] : ( 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)))) ) ) ) ) ) )).
fof(l46_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => v3_filter_0(k5_substlat(A,B)) ) )).
fof(l46_hfdiff_1,axiom,( r2_relset_1(k1_numbers,k1_numbers,k1_taylor_1(1),k6_partfun1(k1_numbers)) )).
fof(l46_int_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [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] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & B = k9_int_3(A) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(D,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ~ ( k2_hurwitz(B,D) = C & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(k3_int_7(A))) => ! [G] : ( 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))) ) ) ) ) ) ) ) ) ) ) )).
fof(l46_integra8,axiom,( k9_xtuple_0(k18_sin_cos) = k1_numbers )).
fof(l46_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,A,C) => ! [G] : ( m2_cat_1(G,A,C) => ( ( r1_nattra_1(A,B,D,E) & r1_nattra_1(A,C,F,G) ) => ! [H] : ( m1_nattra_1(H,A,B,D,E) => ! [I] : ( m1_nattra_1(I,A,C,F,G) => ! [J] : ( 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(k6_cat_2(B,C),k8_cat_1(A,k6_cat_2(B,C),k8_isocat_2(A,B,C,D,F),J),k8_cat_1(A,k6_cat_2(B,C),k8_isocat_2(A,B,C,E,G),J))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l46_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(A,B) ) => r1_xxreal_0(k2_xcmplx_0(D,k7_xcmplx_0(C,k1_newton(2,B))),k2_xcmplx_0(D,k7_xcmplx_0(C,k1_newton(2,A)))) ) ) ) ) ) )).
fof(l46_jordan23,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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,k1_nat_1(k1_jordan3(A,B),1)),B,C) ) ) | r1_jordan3(k4_jordan3(A,B,C),B,C) ) ) ) ) ) )).
fof(l46_jordan5d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( ~ 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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),1,A))) ) ) ) ) ) )).
fof(l46_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(A,A))))) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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) ) ) ) ) ) )).
fof(l46_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( v1_ideal_1(k15_lpspacc1(A,B,C),k14_lpspacc1(A,B,C)) & v1_lpspacc1(k15_lpspacc1(A,B,C),k14_lpspacc1(A,B,C)) ) ) ) ) )).
fof(l46_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) )).
fof(l46_mod_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k18_mod_2)) => ! [B] : ( 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 ) ) ) ) )).
fof(l46_mod_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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,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)) ) ) ) ) ) ) )).
fof(l46_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v7_modelc_1(A) => A = k11_modelc_1(k15_modelc_1(A),k16_modelc_1(A)) ) ) )).
fof(l46_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ~ ( ~ 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)) ) ) )).
fof(l46_o_ring_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v2_struct_0(C) & l6_algstr_0(C) ) => ! [D] : ( 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 = k5_numbers | B = k5_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) ) ) ) ) ) ) )).
fof(l46_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ( l2_pcs_0(B) => ! [C] : ( ( r2_hidden(C,u1_struct_0(A)) & r3_pcs_0(A,B) ) => m1_subset_1(C,u1_struct_0(B)) ) ) ) )).
fof(l46_polynom3,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k14_polynom3(A))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(l46_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( 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) | k4_polynom1(A,C,D,E) = k4_struct_0(C) ) ) ) ) ) ) ) )).
fof(l46_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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))) ) ) )).
fof(l46_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l46_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ( k9_nat_1(k1_numbers,k3_real_3(k7_xcmplx_0(1,k6_xcmplx_0(B,k9_nat_1(k1_numbers,k4_real_3(B),k5_numbers)))),A) = k9_nat_1(k1_numbers,k3_real_3(B),k1_nat_1(A,1)) & k9_nat_1(k1_numbers,k4_real_3(k7_xcmplx_0(1,k6_xcmplx_0(B,k9_nat_1(k1_numbers,k4_real_3(B),k5_numbers)))),A) = k9_nat_1(k1_numbers,k4_real_3(B),k1_nat_1(A,1)) ) ) ) )).
fof(l46_scmbsort,axiom,( k4_scmfsa_2(5) != k4_scmfsa_2(6) )).
fof(l46_scmisort,axiom,( v1_scmfsa7b(k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))))) & v2_scm_halt(k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))))) )).
fof(l46_scmpds_6,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => 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)))) ) ) ) )).
fof(l46_simplex1,axiom,( ! [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) ) => ! [B] : ( ( 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] : ( ( ~ 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)) ) ) ) ) ) )).
fof(l46_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => k1_funct_1(k7_binop_2,A) = k3_xcmplx_0(k4_xcmplx_0(1),A) ) )).
fof(l46_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => r1_xxreal_0(k7_xcmplx_0(k3_xcmplx_0(2,A),k2_xcmplx_0(1,k1_square_1(A))),1) ) ) )).
fof(l46_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l46_toprealb,axiom,( k9_toprealb != k10_toprealb )).
fof(l46_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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 ) ) )).
fof(l46_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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] : ( ( 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))) ) ) ) ) ) )).
fof(l46_waybel17,axiom,( ! [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] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(l46_waybel_4,axiom,( ! [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] : ( 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) ) ) )).
fof(l46_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,A) & r1_xxreal_0(k6_xcmplx_0(B,A),k5_numbers) ) ) ) )).
fof(l46_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) <=> ( r2_hidden(A,C) & r2_hidden(B,D) ) ) )).
fof(l47_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_aff_4(C,A) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & r2_hidden(E,C) & ~ r1_aff_1(A,B,D,E) ) ) ) ) ) ) ) )).
fof(l47_afinsq_2,axiom,( v7_ordinal1(k5_numbers) )).
fof(l47_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k1_afvect0(A,D,B) = C <=> r2_analoaf(A,B,D,D,C) ) ) ) ) ) )).
fof(l47_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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,k5_numbers),k2_compos_1(B)),k6_ami_wstd(A,B,k16_funcop_1(k1_ami_wstd(A,B,k5_numbers),k2_compos_1(B)))) = k2_compos_1(B) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( k1_funct_1(k16_funcop_1(k1_ami_wstd(A,B,k5_numbers),k2_compos_1(B)),C) = k2_compos_1(B) & r2_hidden(C,k1_relset_1(k1_tarski(k1_ami_wstd(A,B,k5_numbers)),k16_funcop_1(k1_ami_wstd(A,B,k5_numbers),k2_compos_1(B)))) ) => C = k6_ami_wstd(A,B,k16_funcop_1(k1_ami_wstd(A,B,k5_numbers),k2_compos_1(B))) ) ) ) ) ) )).
fof(l47_analmetr,axiom,( ? [A] : ( m1_subset_1(A,u1_struct_0(c1__analmetr)) & ? [B] : ( m1_subset_1(B,u1_struct_0(c1__analmetr)) & r1_analmetr(c1__analmetr,A,B) ) ) )).
fof(l47_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( ( r2_hidden(C,a_0_0_arytm_2) & r2_hidden(A,C) & r3_arytm_3(B,A) ) => r2_hidden(B,C) ) ) ) )).
fof(l47_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( v1_xreal_0(D) => ( ( v2_comseq_2(A) & k1_seq_2(A) = D & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(C,E) => k9_nat_1(k1_numbers,A,E) = k9_nat_1(k1_numbers,B,E) ) ) ) => ( v2_comseq_2(B) & k1_seq_2(B) = D ) ) ) ) ) ) )).
fof(l47_borsuk_5,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => v3_rcomp_1(k2_rcomp_1(A,B)) ) ) )).
fof(l47_borsuk_7,axiom,( u1_struct_0(k1_pre_topc(k3_topmetr,k5_toprealb(c15__borsuk_7))) = c15__borsuk_7 )).
fof(l47_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( 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))) ) ) ) )).
fof(l47_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ? [E] : ( 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(l47_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( ( 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] : ( 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) ) ) ) ) )).
fof(l47_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l47_fib_num4,axiom,( ~ r1_xxreal_0(k2_xcmplx_0(k4_xcmplx_0(2),6),k2_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(2,k3_square_1(5))),6)) )).
fof(l47_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( ! [B] : ( v7_ordinal1(B) => r2_relset_1(k4_ordinal1,k4_ordinal1,k2_partfun1(k4_ordinal1,k4_ordinal1,k14_finseq_1(k2_finseq_1(k2_xcmplx_0(B,A))),k2_finseq_1(B)),k14_finseq_1(k2_finseq_1(B))) ) => ! [B] : ( v7_ordinal1(B) => r2_relset_1(k4_ordinal1,k4_ordinal1,k2_partfun1(k4_ordinal1,k4_ordinal1,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))) ) ) ) )).
fof(l47_fomodel3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( m2_subset_1(D,k6_subset_1(k3_finseq_2(k15_fomodel1(C)),k1_tarski(k1_xboole_0)),k35_fomodel1(C)) => ! [E] : ( ( v14_fomodel1(E,k5_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(k9_nat_1(k9_funct_2(k35_fomodel1(C),k35_fomodel1(C)),k7_fomodel2(C,k35_fomodel1(C),D,k7_fomodel3(C,A)),k1_nat_1(B,1)),E) = E ) ) ) ) )).
fof(l47_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ! [F] : ( 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] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( m1_subset_1(H,k6_margrel1) => ! [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)) ) ) ) ) ) ) ) ) ) )).
fof(l47_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(l47_graphsp,axiom,( v1_xreal_0(1) )).
fof(l47_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(k12_polynom1(A,C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k12_polynom1(A,C))) => ( ( D = F & E = G ) => ! [H] : ( ( ~ v1_xboole_0(H) & m1_subset_1(H,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ~ ( r1_rewrite1(k3_polyred(A,B,C,H),D,E) & ! [I] : ( m2_ideal_1(I,k12_polynom1(A,C),H) => ~ ( F = k3_rlvect_1(k12_polynom1(A,C),G,k4_rlvect_1(k12_polynom1(A,C),I)) & ! [J] : ( m1_subset_1(J,k4_ordinal1) => ~ ( r2_hidden(J,k4_finseq_1(I)) & ! [K] : ( ( 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] : ( ( v1_funct_1(L) & v1_funct_2(L,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(L,A,C) & v1_polynom1(L,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) = k11_polynom1(A,C,K,L) & r1_termord(A,B,k3_termord(A,B,C,k11_polynom1(A,C,K,L)),k3_termord(A,B,C,D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l47_group_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & l3_algstr_0(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( 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,B,D),k5_group_1(C,A,E)) = k6_algstr_0(C,k5_group_1(C,A,E),k5_group_1(C,B,D)) ) ) ) ) ) ) )).
fof(l47_heyting1,axiom,( ! [A] : v3_filter_0(k12_normform(A)) )).
fof(l47_int_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(l47_integra8,axiom,( k9_xtuple_0(k32_valued_1(k1_numbers,k1_numbers,k16_sin_cos)) = k1_numbers )).
fof(l47_jgraph_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( k4_xcmplx_0(k17_euclid(k5_algstr_0(k15_euclid(2),A,B))) = k6_xcmplx_0(k4_xcmplx_0(k17_euclid(A)),k4_xcmplx_0(k17_euclid(B))) & k18_euclid(k5_algstr_0(k15_euclid(2),A,B)) = k6_xcmplx_0(k18_euclid(A),k18_euclid(B)) ) ) ) )).
fof(l47_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(A,B) ) => r1_xxreal_0(k6_xcmplx_0(D,k7_xcmplx_0(C,k1_newton(2,A))),k6_xcmplx_0(D,k7_xcmplx_0(C,k1_newton(2,B)))) ) ) ) ) ) )).
fof(l47_jordan5d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( ~ 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 = k4_seq_4(C) ) => r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k3_finseq_1(k2_goboard2(D)),A)),k18_euclid(B)) ) ) ) ) ) )).
fof(l47_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(A,A))))) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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) ) ) ) ) ) )).
fof(l47_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(l47_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) )).
fof(l47_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [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] : ( m1_subset_1(G,u1_struct_0(F)) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(F),D,E) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(F))) ) => ! [I] : ( ( v1_matrix_0(I) & v2_matrix_0(I,u1_struct_0(F),D,C) & m2_finseq_1(I,k3_finseq_2(u1_struct_0(F))) ) => ( r2_hidden(B,k2_finseq_1(D)) => ( A = B | k4_matrix15(F,H,I) = k4_matrix15(F,k3_matrix11(A,D,E,u1_struct_0(F),H,k4_fvsum_1(k1_matrix_0(H),F,k7_matrix_0(u1_struct_0(F),H,A),k10_fvsum_1(k1_matrix_0(H),F,k7_matrix_0(u1_struct_0(F),H,B),G))),k3_matrix11(A,D,C,u1_struct_0(F),I,k4_fvsum_1(k1_matrix_0(I),F,k7_matrix_0(u1_struct_0(F),I,A),k10_fvsum_1(k1_matrix_0(I),F,k7_matrix_0(u1_struct_0(F),I,B),G)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l47_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( 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) = k5_numbers ) => ( ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ~ ( E = k1_relset_1(A,D) & r1_mesfun6c(A,B,D,E) ) ) | r1_xxreal_0(k9_complex1(k1_mesfun6c(A,B,C,D)),k1_mesfunc6(A,B,C,k55_valued_1(A,k2_numbers,D))) ) ) ) ) ) ) )).
fof(l47_mesfunc5,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k1_relset_1(k4_ordinal1,B)) => r2_hidden(k1_funct_1(B,C),A) ) ) => m2_finseq_1(B,A) ) ) )).
fof(l47_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_midsp_3(B,A) => ! [C] : ( m2_midsp_3(C,A) => ! [D] : ( ( v4_midsp_2(D,C) & l1_midsp_2(D,C) ) => ( r2_midsp_3(A,B,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ! [H] : ( m2_finseq_2(H,u1_struct_0(C),k4_finseq_2(k1_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)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l47_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ~ ( ~ ( ~ 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))) ) ) )).
fof(l47_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v2_modelc_2(A) => k1_modelc_3(A) = k1_tarski(A) ) ) )).
fof(l47_nagata_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,B) => ! [E] : ( m1_subset_1(E,B) => k2_binop_1(B,B,k1_numbers,k5_nagata_1(k2_zfmisc_1(B,B),A,C),D,E) = k3_xxreal_0(A,k2_binop_1(B,B,k1_numbers,C,D,E)) ) ) ) ) ) )).
fof(l47_nat_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(1,A) & ~ r1_xxreal_0(4001,A) & ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ~ ( ~ r1_xxreal_0(B,A) & r1_xxreal_0(B,k2_nat_1(2,A)) ) ) ) ) )).
fof(l47_ncfcont2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(k7_xcmplx_0(E,2),k2_normsp_0(A,k5_algstr_0(A,B,D))) & ~ r1_xxreal_0(k7_xcmplx_0(E,2),k2_normsp_0(A,k5_algstr_0(A,D,C))) & r1_xxreal_0(E,k2_normsp_0(A,k5_algstr_0(A,B,C))) ) ) ) ) ) ) )).
fof(l47_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l47_ordinal2,axiom,( 1 = k1_ordinal1(k5_ordinal1) )).
fof(l47_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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),k8_polynom1(A,C)) ) ) ) ) ) )).
fof(l47_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l47_quaterni,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ( k3_complex1(k5_arytm_0(A,B)) = A & k4_complex1(k5_arytm_0(A,B)) = B ) ) ) )).
fof(l47_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( r2_funct_2(k4_ordinal1,u1_struct_0(A),k11_polynom3(A,B,C),k9_polynom3(A)) & ~ r2_funct_2(k4_ordinal1,u1_struct_0(A),B,k9_polynom3(A)) & ~ r2_funct_2(k4_ordinal1,u1_struct_0(A),C,k9_polynom3(A)) ) ) ) ) )).
fof(l47_scmisort,axiom,( ~ v1_xboole_0(k3_scmfsa6a(k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k16_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1)))),k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(3,1)))),k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))))),k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers)))))) & v1_relat_1(k3_scmfsa6a(k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k16_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1)))),k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(3,1)))),k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))))),k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers)))))) & v4_relat_1(k3_scmfsa6a(k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k16_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1)))),k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(3,1)))),k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))))),k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))))),k4_ordinal1) & v5_relat_1(k3_scmfsa6a(k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k16_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1)))),k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(3,1)))),k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))))),k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_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(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1)))),k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(3,1)))),k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))))),k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers)))))) & v1_finset_1(k3_scmfsa6a(k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k16_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1)))),k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(3,1)))),k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))))),k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers)))))) & v1_afinsq_1(k3_scmfsa6a(k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k16_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1)))),k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(3,1)))),k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))))),k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers)))))) & v2_scm_halt(k3_scmfsa6a(k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k16_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1)))),k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(3,1)))),k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))))),k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers)))))) & v1_scmfsa7b(k3_scmfsa6a(k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k16_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1)))),k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(3,1)))),k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))))),k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers)))))) )).
fof(l47_scmpds_6,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmpds_2)) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => 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)))) ) ) ) ) )).
fof(l47_sin_cos2,axiom,( k1_relset_1(k1_numbers,k7_binop_2) = k1_numbers )).
fof(l47_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => k1_square_1(k1_funct_1(k3_sin_cos2,A)) = k2_xcmplx_0(1,k1_square_1(k1_funct_1(k1_sin_cos2,A))) ) )).
fof(l47_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k5_numbers,k7_xcmplx_0(k6_xcmplx_0(1,k3_square_1(k2_xcmplx_0(1,k1_square_1(A)))),A)) ) ) )).
fof(l47_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l47_subset_1,axiom,( ! [A] : ! [B] : ( ! [C] : ( r2_hidden(C,A) => r2_hidden(C,B) ) => m1_subset_1(A,k1_zfmisc_1(B)) ) )).
fof(l47_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(l47_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) )).
fof(l47_waybel17,axiom,( ! [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] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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] : ( 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)) ) ) ) ) ) )).
fof(l47_waybel_6,axiom,( ! [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) & l1_orders_2(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & B = k1_yellow_0(A,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,C) => v6_waybel_6(D,A) ) ) ) ) => v1_waybel_5(A) ) ) )).
fof(l48_algstr_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_1)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_algstr_1)) => ! [C] : ( 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)) ) ) ) )).
fof(l48_analmetr,axiom,( r1_analmetr(c1__analmetr,c2__analmetr,c3__analmetr) )).
fof(l48_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ~ ( ~ r1_arytm_2(A,B) & ! [C] : ( m1_subset_1(C,k2_arytm_2) => ~ ( r2_hidden(C,k5_arytm_3) & ~ r1_arytm_2(A,C) & ~ r1_arytm_2(C,B) ) ) ) ) ) )).
fof(l48_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( r1_xxreal_0(1,A) => r1_xxreal_0(k2_xcmplx_0(k6_xcmplx_0(k1_square_1(A),A),1),k1_square_1(A)) ) ) )).
fof(l48_catalan2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k1_numbers) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ( ( k1_relset_1(k4_ordinal1,A) = 1 | k1_afinsq_1(A) = 1 ) => k7_afinsq_2(A) = k1_funct_1(A,k5_numbers) ) ) )).
fof(l48_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k3_tarski(B)))) => ~ ( ! [D] : ( r2_hidden(D,C) => v1_finset_1(k1_xtuple_0(D)) ) & ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,A) ) => ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,A) ) => ( r1_tarski(D,E) => ! [F] : ( r2_hidden(k4_tarski(D,F),C) => r2_hidden(k4_tarski(E,F),C) ) ) ) ) & ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,A) ) => ! [E] : ! [F] : ( ( r2_hidden(k4_tarski(D,E),C) & r2_hidden(k4_tarski(D,F),C) ) => r2_hidden(k2_tarski(E,F),B) ) ) & ! [D] : ( ( 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] : ( m1_subset_1(E,A) => k3_funct_2(A,B,D,E) = k7_relat_1(C,k3_cohsp_1(A,E)) ) ) ) ) ) ) ) )).
fof(l48_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k5_xcmplx_0(A) = k2_xcmplx_0(k7_xcmplx_0(k3_complex1(A),k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A)))),k3_xcmplx_0(k7_xcmplx_0(k1_real_1(k4_complex1(A)),k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A)))),k7_complex1)) ) )).
fof(l48_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) )).
fof(l48_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k11_ens_1(A))) => ! [C] : ( 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 ) ) ) ) )).
fof(l48_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ? [C] : ( 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] : ( 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) ) ) ) )).
fof(l48_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k18_sin_cos,2)))) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(B,C) = 1 ) ) ) => ( r2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,B,k26_valued_1(k1_numbers,k1_numbers,k18_sin_cos,2)),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(k2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,B,k26_valued_1(k1_numbers,k1_numbers,k18_sin_cos,2)),A),C) = k4_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k16_sin_cos,C))) ) ) ) ) ) ) )).
fof(l48_fib_num4,axiom,( ~ r1_xxreal_0(4,k2_xcmplx_0(k6_xcmplx_0(1,k3_xcmplx_0(2,k3_square_1(5))),5)) )).
fof(l48_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => r2_relset_1(k4_ordinal1,k4_ordinal1,k2_partfun1(k4_ordinal1,k4_ordinal1,k14_finseq_1(k2_finseq_1(k2_xcmplx_0(B,A))),k2_finseq_1(B)),k14_finseq_1(k2_finseq_1(B))) ) ) )).
fof(l48_fomodel3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( m2_subset_1(D,k6_subset_1(k3_finseq_2(k15_fomodel1(C)),k1_tarski(k1_xboole_0)),k35_fomodel1(C)) => k5_relat_1(k9_nat_1(k9_funct_2(k35_fomodel1(C),k35_fomodel1(C)),k7_fomodel2(C,k35_fomodel1(C),D,k7_fomodel3(C,A)),k1_nat_1(B,1)),k9_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(k9_nat_1(k9_setfam_1(k6_subset_1(k3_finseq_2(k15_fomodel1(C)),k1_tarski(k1_xboole_0))),k39_fomodel1(C),B)) ) ) ) )).
fof(l48_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ! [F] : ( 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] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(l48_funct_9,axiom,( 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,k18_sin_cos)),k7_xcmplx_0(k28_sin_cos,2)) )).
fof(l48_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_analmetr(A,C,D) => B = k3_rlvect_1(A,k1_rlvect_1(A,C,k2_geomtrap(A,C,D,B)),k1_rlvect_1(A,D,k3_geomtrap(A,C,D,B))) ) ) ) ) ) )).
fof(l48_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( r2_hidden(C,k26_glib_000(A,B)) <=> ( r2_hidden(C,k7_glib_000(A)) & k1_funct_1(k11_glib_000(A),C) = B ) ) ) ) )).
fof(l48_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,B)) => ( k1_funct_1(k7_glib_001(A,B,C),D) = k1_funct_1(B,D) & r2_hidden(D,k1_relset_1(k4_ordinal1,k7_glib_001(A,B,C))) ) ) ) ) ) ) )).
fof(l48_group_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l48_integra8,axiom,( k9_xtuple_0(k22_sin_cos) = k1_numbers )).
fof(l48_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => ! [D] : ( m1_subset_1(D,k1_intpro_1) => r2_hidden(k3_intpro_1(k3_intpro_1(k3_intpro_1(k3_intpro_1(B,C),k3_intpro_1(A,C)),D),k3_intpro_1(k3_intpro_1(A,B),D)),k8_intpro_1) ) ) ) ) )).
fof(l48_jgraph_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => k1_square_1(k12_euclid(k5_algstr_0(k15_euclid(2),A,B))) = k2_xcmplx_0(k1_square_1(k4_xcmplx_0(k17_euclid(k5_algstr_0(k15_euclid(2),A,B)))),k1_square_1(k18_euclid(k5_algstr_0(k15_euclid(2),A,B)))) ) ) )).
fof(l48_jordan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_borsuk_2(G,A,B,C) => ! [H] : ( m1_borsuk_2(H,A,C,D) => ! [I] : ( m1_borsuk_2(I,A,D,E) => ! [J] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l48_jordan5d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( ~ 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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k3_finseq_1(k2_goboard2(D)),A))) ) ) ) ) ) )).
fof(l48_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,C) => ( k2_relset_1(k1_numbers,k2_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,k2_fuzzy_4(A,B,C,D,E,F,G)) != k1_xboole_0 ) ) ) ) ) ) ) ) )).
fof(l48_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( ( 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] : ( m1_matrlin(E,A,B) => ! [F] : ( m1_matrlin(F,A,C) => k9_xtuple_0(k10_matrlin(A,B,C,D,E,F)) = k9_xtuple_0(E) ) ) ) ) ) ) )).
fof(l48_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ~ ( A != k1_xboole_0 & B != k1_xboole_0 & C != k1_xboole_0 & D != k1_xboole_0 & ? [E] : ( m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) & ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,B) => ! [H] : ( m1_subset_1(H,C) => ! [I] : ( m1_subset_1(I,D) => E != k6_xtuple_0(F,G,H,I) ) ) ) ) ) ) )).
fof(l48_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v4_xxreal_2(A) => v3_xxreal_2(k3_measure6(A)) ) ) )).
fof(l48_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_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 ) ) ) ) ) ) ) ) )).
fof(l48_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_midsp_3(B,A) => ! [C] : ( m2_midsp_3(C,A) => ! [D] : ( ( v4_midsp_2(D,C) & l1_midsp_2(D,C) ) => ( ! [E] : ( m2_finseq_2(E,u1_struct_0(u1_midsp_2(C,D)),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(u1_midsp_2(C,D)))) => ! [F] : ( 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)),k1_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)),k1_nat_1(A,1),E,B,F))) ) ) => r2_midsp_3(A,B,C) ) ) ) ) ) )).
fof(l48_mod_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k18_mod_2)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k18_mod_2)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k18_mod_2)) => ! [D] : ( m1_subset_1(D,k1_enumset1(k5_numbers,1,2)) => ! [E] : ( m1_subset_1(E,k1_enumset1(k5_numbers,1,2)) => ! [F] : ( m1_subset_1(F,k1_enumset1(k5_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)) ) ) ) ) ) ) ) ) )).
fof(l48_mod_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(l48_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ( 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))) ) ) ) )).
fof(l48_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k13_modelc_2(A))) => ~ r2_hidden(k1_xboole_0,B) ) ) )).
fof(l48_ncfcont2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(k7_xcmplx_0(E,2),k2_normsp_0(A,k5_algstr_0(A,B,D))) & ~ r1_xxreal_0(k7_xcmplx_0(E,2),k2_normsp_0(A,k5_algstr_0(A,C,D))) & r1_xxreal_0(E,k2_normsp_0(A,k5_algstr_0(A,B,C))) ) ) ) ) ) ) )).
fof(l48_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l48_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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,k8_polynom1(A,C)) & E != k8_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)) ) ) ) ) ) ) ) ) )).
fof(l48_poset_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) ) )).
fof(l48_quaterni,axiom,( ! [A] : ( v1_xcmplx_0(A) => k5_arytm_0(k3_complex1(A),k4_complex1(A)) = A ) )).
fof(l48_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => k3_rmod_2(A,B,k4_struct_0(B),C) = u1_struct_0(C) ) ) ) )).
fof(l48_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_struct_0(B,C) <=> k3_rusub_1(A,C,B) = u1_struct_0(B) ) ) ) ) )).
fof(l48_scmisort,axiom,( v1_scmfsa7b(k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(k5_numbers,1)),k3_scmfsa6a(k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k16_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1)))),k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(3,1)))),k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))))),k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))))))) & v2_scm_halt(k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(k5_numbers,1)),k3_scmfsa6a(k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k16_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1)))),k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(3,1)))),k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))))),k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))))))) )).
fof(l48_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => k11_comseq_3(k3_sin_cos(k3_xcmplx_0(A,k7_complex1))) = k2_xcmplx_0(k1_funct_1(k18_sin_cos,A),k3_xcmplx_0(k1_funct_1(k16_sin_cos,A),k7_complex1)) ) )).
fof(l48_sin_cos2,axiom,( ! [A] : ( ( 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,k7_binop_2) => ! [B] : ( v1_xreal_0(B) => ( r1_fdiff_1(A,B) & k1_fdiff_1(A,B) = k4_xcmplx_0(1) ) ) ) ) )).
fof(l48_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => k6_xcmplx_0(k1_square_1(k1_funct_1(k3_sin_cos2,A)),1) = k1_square_1(k1_funct_1(k1_sin_cos2,A)) ) )).
fof(l48_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(A,1) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(k5_numbers,k6_xcmplx_0(1,k1_square_1(A))) ) ) ) )).
fof(l48_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ( v1_topreal1(A) => v1_topreal1(k17_finseq_1(u1_struct_0(k15_euclid(2)),B,A)) ) ) ) )).
fof(l48_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l48_stirl2_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ~ ( ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k2_afinsq_1(B)) => v1_finset_1(k1_funct_1(B,C)) ) ) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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] : ( ( v1_relat_1(C) & v5_relat_1(C,k4_ordinal1) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ~ ( k2_afinsq_1(C) = k2_afinsq_1(B) & ! [D] : ( 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) ) ) ) ) ) )).
fof(l48_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( r2_hidden(C,B) => m1_subset_1(C,A) ) ) )).
fof(l48_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r1_borsuk_6(A,B,C) & ! [D] : ( ( 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] : ! [F] : ( 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] : ( m1_borsuk_2(G,A,B,C) & ? [H] : ( m1_borsuk_2(H,A,B,C) & G = E & H = F & r3_borsuk_2(A,B,C,G,H) ) ) ) ) ) ) ) ) ) )).
fof(l48_topalg_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) )).
fof(l48_tops_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r1_tarski(A,C) & B = k6_subset_1(C,A) ) => r1_tarski(A,k6_subset_1(C,B)) ) )).
fof(l48_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) )).
fof(l48_waybel_6,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(l48_waybel_9,axiom,( ! [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) & v1_compts_1(A) & l1_waybel_9(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( C = D & ! [E] : ( 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) ) ) ) ) ) )).
fof(l48_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => r1_xxreal_0(k5_numbers,k6_xcmplx_0(B,A)) ) ) ) )).
fof(l49_algstr_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_1)) => ! [B] : ( 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) ) ) )).
fof(l49_analmetr,axiom,( ~ 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] : ( m1_subset_1(A,u1_struct_0(k2_analmetr(c1__analmetr,c2__analmetr,c3__analmetr))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_analmetr(c1__analmetr,c2__analmetr,c3__analmetr))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_analmetr(c1__analmetr,c2__analmetr,c3__analmetr))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_analmetr(c1__analmetr,c2__analmetr,c3__analmetr))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_analmetr(c1__analmetr,c2__analmetr,c3__analmetr))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_analmetr(c1__analmetr,c2__analmetr,c3__analmetr))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k2_analmetr(c1__analmetr,c2__analmetr,c3__analmetr))) => ! [H] : ( 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] : ( m1_subset_1(A,u1_struct_0(k2_analmetr(c1__analmetr,c2__analmetr,c3__analmetr))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_analmetr(c1__analmetr,c2__analmetr,c3__analmetr))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_analmetr(c1__analmetr,c2__analmetr,c3__analmetr))) => ~ ( A != B & ! [D] : ( 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] : ( m1_subset_1(A,u1_struct_0(k2_analmetr(c1__analmetr,c2__analmetr,c3__analmetr))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_analmetr(c1__analmetr,c2__analmetr,c3__analmetr))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_analmetr(c1__analmetr,c2__analmetr,c3__analmetr))) => ? [D] : ( 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 ) ) ) ) )).
fof(l49_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( ( r1_arytm_2(A,B) & r1_arytm_2(B,C) ) => r1_arytm_2(A,C) ) ) ) ) )).
fof(l49_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( r1_xxreal_0(1,A) => r1_xxreal_0(k1_square_1(A),k3_xcmplx_0(2,k2_xcmplx_0(k6_xcmplx_0(k1_square_1(A),A),1))) ) ) )).
fof(l49_bagorder,axiom,( ! [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) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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 ) ) ) ) )).
fof(l49_bcialg_3,axiom,( ! [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) & v6_bcialg_3(A) & l2_bcialg_1(A) ) => ( v11_bcialg_3(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v2_bcialg_3(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_1(A,B,k1_bcialg_1(A,B,C)) = C ) ) ) ) ) )).
fof(l49_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( 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)) ) ) ) ) )).
fof(l49_card_1,axiom,( ! [A] : ~ ( v1_finset_1(A) & ! [B] : ( v7_ordinal1(B) => ~ r2_wellord2(A,B) ) ) )).
fof(l49_catalan2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k1_numbers) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k1_numbers) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ( ( k1_relset_1(k4_ordinal1,A) = k1_relset_1(k4_ordinal1,B) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k1_afinsq_1(A)) => k1_funct_1(A,C) = k1_funct_1(B,k7_nat_d(k1_afinsq_1(A),k2_xcmplx_0(1,C))) ) ) ) => k7_afinsq_2(A) = k7_afinsq_2(B) ) ) ) )).
fof(l49_descip_1,axiom,( ! [A] : ( m2_finseq_2(A,k6_margrel1,k4_finseq_2(64,k6_margrel1)) => k27_descip_1(k25_descip_1(A)) = A ) )).
fof(l49_diff_1,axiom,( ? [A] : ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)))) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( v1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,A,B)) & v1_funct_2(k1_seqfunc(k1_numbers,k1_numbers,A,B),k4_ordinal1,k1_numbers) & m1_subset_1(k1_seqfunc(k1_numbers,k1_numbers,A,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) ) )).
fof(l49_fib_num4,axiom,( ~ r1_xxreal_0(4,k2_xcmplx_0(k6_xcmplx_0(k1_pepin(1),k3_xcmplx_0(k3_xcmplx_0(2,1),k3_square_1(5))),k1_square_1(k3_square_1(5)))) )).
fof(l49_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v12_fomodel1(k29_fomodel1(A),A) ) )).
fof(l49_fomodel3,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => r2_funct_2(k35_fomodel1(B),k35_fomodel1(B),k9_fomodel2(B,k35_fomodel1(B),k7_fomodel3(B,A)),k3_fomodel2(k35_fomodel1(B))) ) )).
fof(l49_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l49_funct_9,axiom,( ! [A] : ( 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,k18_sin_cos)),k3_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),k2_xcmplx_0(A,1))) ) )).
fof(l49_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => r2_hidden(k1_fvaluat1(k2_relset_1(k6_numbers,B)),k1_numbers) ) ) ) )).
fof(l49_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( ( r1_analmetr(A,C,D) & B = k3_rlvect_1(A,k1_rlvect_1(A,C,E),k1_rlvect_1(A,D,F)) ) => ( E = k2_geomtrap(A,C,D,B) & F = k3_geomtrap(A,C,D,B) ) ) ) ) ) ) ) ) )).
fof(l49_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( r2_hidden(C,k27_glib_000(A,B)) <=> ( r2_hidden(C,k7_glib_000(A)) & k1_funct_1(k10_glib_000(A),C) = B ) ) ) ) )).
fof(l49_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ( k4_glib_001(A,B) = k3_glib_001(A,C) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ~ r1_xxreal_0(k3_finseq_1(C),D) => ( k1_funct_1(k7_glib_001(A,B,C),k1_nat_1(k3_finseq_1(B),D)) = k1_funct_1(C,k1_nat_1(D,1)) & r2_hidden(k1_nat_1(k3_finseq_1(B),D),k1_relset_1(k4_ordinal1,k7_glib_001(A,B,C))) ) ) ) ) ) ) ) )).
fof(l49_groeb_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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] : ( m1_ideal_1(D,A,B) => ! [E] : ~ ( E = k4_rlvect_1(A,D) & ! [F] : ( m1_ideal_1(F,A,C) => E != k4_rlvect_1(A,F) ) ) ) ) ) ) ) )).
fof(l49_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k4_real_ns1(A))) => ( ( B = D & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( r2_hidden(E,k2_finseq_1(A)) & ! [F] : ( m2_finseq_1(F,k1_numbers) => ~ ( F = k4_finseqop(k1_euclid(A),k1_numbers,B,k1_pdiff_1(E,A)) & k1_funct_1(C,E) = k18_rvsum_1(F) ) ) ) ) ) => C = k4_rlvect_1(k4_real_ns1(A),D) ) ) ) ) ) )).
fof(l49_integra8,axiom,( k9_xtuple_0(k1_sin_cos2) = k1_numbers )).
fof(l49_jordan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_borsuk_2(G,A,B,C) => ! [H] : ( m1_borsuk_2(H,A,C,D) => ! [I] : ( m1_borsuk_2(I,A,D,E) => ! [J] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(l49_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( 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)) ) ) ) ) ) ) )).
fof(l49_jordan5d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( ~ 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 = k4_seq_4(C) ) => r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,1)),k17_euclid(B)) ) ) ) ) ) )).
fof(l49_matrtop3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(k15_euclid(C)),u1_struct_0(k15_euclid(C))) & v13_vectsp_1(D,k15_euclid(C),k15_euclid(C)) & v1_topreal9(D,C) & v2_matrtop3(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(C)),u1_struct_0(k15_euclid(C))))) ) => ( v1_matrtop3(D,A) => ( r2_hidden(B,A) | k1_funct_1(D,k6_matrixr2(C,B)) = k6_matrixr2(C,B) ) ) ) ) ) )).
fof(l49_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v3_xxreal_2(A) => v4_xxreal_2(k3_measure6(A)) ) ) )).
fof(l49_mod_2,axiom,( ! [A] : ( m1_subset_1(A,k1_enumset1(k5_numbers,1,2)) => ! [B] : ( m1_subset_1(B,k1_enumset1(k5_numbers,1,2)) => ! [C] : ( m1_subset_1(C,k1_enumset1(k5_numbers,1,2)) => ! [D] : ( m1_subset_1(D,k1_enumset1(k5_numbers,1,2)) => ( D = k5_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)) ) ) ) ) ) ) )).
fof(l49_mod_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ( v2_mod_4(C,A,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)) ) ) ) ) ) )).
fof(l49_ncfcont2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & r1_xxreal_0(C,k2_normsp_0(A,B)) ) ) => B = k4_struct_0(A) ) ) ) )).
fof(l49_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l49_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r1_relat_2(A,B) => v1_relat_2(k2_wellord1(A,B)) ) ) )).
fof(l49_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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))) ) ) ) )).
fof(l49_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_rlaffin1(B,A) => ! [C] : ( m2_rlvect_2(C,A,B) => ( ( k6_rlvect_2(A,C) = k4_struct_0(A) & k3_rlaffin1(A,C) = k5_numbers ) => k3_rlvect_2(A,C) = k1_xboole_0 ) ) ) ) ) )).
fof(l49_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => k3_rlsub_1(A,k4_struct_0(A),B) = u1_struct_0(B) ) ) )).
fof(l49_rlsub_2,axiom,( ! [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) ) => ! [B] : ( ( v1_rlvect_1(B) & m1_rlsub_1(B,A) ) => ( ! [C] : ( 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)) ) ) ) )).
fof(l49_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_bhsp_1(B) & m1_rusub_1(B,A) ) => ( ! [C] : ( 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)) ) ) ) )).
fof(l49_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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,k7_binop_2) => ( r1_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k22_sin_cos),A) & k1_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k22_sin_cos),A) = k3_xcmplx_0(k4_xcmplx_0(1),k1_funct_1(k22_sin_cos,k1_funct_1(B,A))) ) ) ) ) )).
fof(l49_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(A,1) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(k5_numbers,k6_xcmplx_0(4,k3_xcmplx_0(4,k1_square_1(A)))) ) ) ) )).
fof(l49_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ( v1_topreal1(A) => v1_topreal1(k2_rfinseq(u1_struct_0(k15_euclid(2)),B,A)) ) ) ) )).
fof(l49_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l49_termord,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( 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) ) ) ) )).
fof(l49_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) ) )).
fof(l49_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => k3_vectsp_4(A,B,k4_struct_0(B),C) = u1_struct_0(C) ) ) ) )).
fof(l49_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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))) ) ) ) )).
fof(l49_waybel_6,axiom,( ! [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) ) => ( ( v2_waybel_1(A) & v3_waybel_3(A) & v3_waybel_3(k7_lattice3(A)) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & B = k1_yellow_0(A,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,C) => v6_waybel_6(D,A) ) ) ) ) ) ) )).
fof(l49_waybel_9,axiom,( ! [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) & v1_compts_1(A) & l1_waybel_9(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( C = D & ! [E] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(l4_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_diraf(A,B,C,C,B) ) ) ) )).
fof(l4_algstr_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k2_vectsp_1)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_vectsp_1)) => ! [C] : ( 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] : ( m1_subset_1(A,u1_struct_0(k2_vectsp_1)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_vectsp_1)) => ! [C] : ( 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 ) ) ) ) ) )).
fof(l4_altcat_5,axiom,( m1_subset_1(k1_xboole_0,u1_struct_0(k7_altcat_1(k1_tarski(k1_xboole_0)))) )).
fof(l4_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(B)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => r2_hidden(k5_memstr_0(A,B,k4_extpro_1(A,B,k1_funct_7(E,k4_struct_0(B),D),k1_funct_7(F,D,C))),k1_amistd_1(A,B,D,C)) ) ) ) ) ) ) )).
fof(l4_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ( B != k4_struct_0(A) & C != k4_struct_0(A) ) ) ) ) ) )).
fof(l4_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => k1_rlvect_1(A,k3_rlvect_1(A,k3_rlvect_1(A,k1_rlvect_1(A,C,F),k1_rlvect_1(A,D,G)),k1_rlvect_1(A,B,H)),E) = k3_rlvect_1(A,k3_rlvect_1(A,k1_rlvect_1(A,C,k3_xcmplx_0(E,F)),k1_rlvect_1(A,D,k3_xcmplx_0(E,G))),k1_rlvect_1(A,B,k3_xcmplx_0(E,H))) ) ) ) ) ) ) ) ) )).
fof(l4_arithm,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l4_arytm_2,axiom,( r1_xboole_0(k5_arytm_3,a_0_1_arytm_2) )).
fof(l4_asympt_1,axiom,( ! [A] : ( ( v1_xreal_0(A) & v1_asympt_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ r1_xxreal_0(C,k5_numbers) => k9_nat_1(k1_numbers,B,C) = k3_power(A,C) ) ) => ( r1_xxreal_0(A,1) | v4_asympt_0(B) ) ) ) ) )).
fof(l4_axioms,axiom,( r2_hidden(k1_xboole_0,k1_tarski(k1_xboole_0)) )).
fof(l4_bcialg_4,axiom,( 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) )).
fof(l4_bhsp_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_rlsub_1(o_0_5_bhsp_1))) => ! [B] : ( 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)) = k5_numbers ) ) & r2_hidden(k4_struct_0(o_0_5_bhsp_1),u1_struct_0(k1_rlsub_1(o_0_5_bhsp_1))) )).
fof(l4_binom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( 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] : ( v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(A,k4_ordinal1),B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1),B))) & ! [F] : ( m1_subset_1(F,A) => ( k2_binop_1(A,k4_ordinal1,B,E,F,k5_numbers) = C & ! [G] : ( m1_subset_1(G,k4_ordinal1) => k2_binop_1(A,k4_ordinal1,B,E,F,k1_nat_1(G,1)) = k2_binop_1(B,A,B,D,k2_binop_1(A,k4_ordinal1,B,E,F,G),F) ) ) ) ) ) ) ) ) )).
fof(l4_borsuk_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) ) => ( r1_t_0topsp(A,B) => r1_t_0topsp(B,A) ) ) ) )).
fof(l4_borsuk_7,axiom,( r2_hidden(k5_numbers,k1_tarski(k5_numbers)) )).
fof(l4_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(l4_bvfunc14,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ( B != C => k1_funct_1(k1_funct_4(k1_funct_4(A,k16_funcop_1(B,D)),k16_funcop_1(C,E)),B) = D ) ) )).
fof(l4_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(l4_c0sp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => v1_c0sp1(k2_struct_0(A),A) ) )).
fof(l4_calcul_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ~ ( r1_calcul_1(A,B) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r2_hidden(C,k1_relset_1(k4_ordinal1,A)) & k1_funct_1(A,C) = B ) ) ) ) )).
fof(l4_card_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ! [D] : ( 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)))) ) ) ) ) )).
fof(l4_card_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( k2_nat_1(k1_newton(2,A),k1_nat_1(k3_xcmplx_0(2,D),1)) = k2_nat_1(k1_newton(2,B),k1_nat_1(k3_xcmplx_0(2,C),1)) => r1_xxreal_0(A,B) ) ) ) ) ) )).
fof(l4_collsp,axiom,( r2_hidden(1,k6_domain_1(k4_ordinal1,1)) )).
fof(l4_csspace2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( v7_ordinal1(B) => ( ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k5_numbers,k1_funct_1(k7_comseq_3(A),C)) & k1_funct_1(k8_comseq_3(A),C) = k5_numbers ) ) => k1_funct_1(k55_valued_1(k4_ordinal1,k2_numbers,k10_comseq_3(A)),B) = k1_funct_1(k3_series_1(k55_valued_1(k4_ordinal1,k2_numbers,A)),B) ) ) ) )).
fof(l4_csspace4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v1_comseq_2(A) & v1_comseq_2(B) ) => v1_comseq_2(k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)) ) ) ) )).
fof(l4_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,E) => r2_analoaf(A,D,E,B,C) ) ) ) ) ) ) )).
fof(l4_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) => ~ v1_xboole_0(B) ) ) )).
fof(l4_euclid_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => m2_finseq_1(A,k1_numbers) ) )).
fof(l4_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ( k1_funct_1(k6_euclid(3,A),1) = k4_xcmplx_0(k1_funct_1(A,1)) & k1_funct_1(k6_euclid(3,A),2) = k4_xcmplx_0(k1_funct_1(A,2)) & k1_funct_1(k6_euclid(3,A),3) = k4_xcmplx_0(k1_funct_1(A,3)) ) ) )).
fof(l4_fdiff_1,axiom,( v1_funct_1(k8_funcop_1(k1_numbers,k1_numbers,k10_subset_1(k5_numbers,k1_numbers))) & v1_funct_2(k8_funcop_1(k1_numbers,k1_numbers,k10_subset_1(k5_numbers,k1_numbers)),k1_numbers,k1_numbers) & m1_subset_1(k8_funcop_1(k1_numbers,k1_numbers,k10_subset_1(k5_numbers,k1_numbers)),k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) )).
fof(l4_fdiff_6,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(k1_funct_1(k16_sin_cos,A),k5_numbers) & ~ r1_xxreal_0(1,k1_funct_1(k18_sin_cos,A)) & ~ r1_xxreal_0(k1_funct_1(k18_sin_cos,A),k4_xcmplx_0(1)) & k7_xcmplx_0(k1_funct_1(k16_sin_cos,A),k6_prepower(k6_xcmplx_0(1,k1_funct_1(k18_sin_cos,A)),k7_xcmplx_0(1,2))) != k6_prepower(k2_xcmplx_0(1,k1_funct_1(k18_sin_cos,A)),k7_xcmplx_0(1,2)) ) ) )).
fof(l4_fdiff_7,axiom,( ! [A] : ( v1_xreal_0(A) => k3_xcmplx_0(2,k1_square_1(k1_funct_1(k18_sin_cos,k7_xcmplx_0(A,2)))) = k2_xcmplx_0(1,k1_funct_1(k18_sin_cos,A)) ) )).
fof(l4_fib_fusc,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( ~ r1_xxreal_0(A,k5_numbers) => ( k3_power(2,k2_nat_1(2,A)) = k2_xcmplx_0(1,k3_power(2,A)) & k3_power(2,k2_nat_1(2,A)) = k2_xcmplx_0(k3_power(2,A),1) ) ) ) )).
fof(l4_fib_num,axiom,( k1_nat_1(k1_nat_1(k5_numbers,1),1) = 2 )).
fof(l4_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( 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(k4_ordinal1,A,C,k3_finsop_1(B),k2_finsop_1(A,k8_funcop_1(A,k4_ordinal1,k4_binop_1(A,C)),B)) ) ) ) ) )).
fof(l4_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m2_subset_1(B,k3_finseq_2(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k35_fomodel1(A))) => ? [C] : ( m1_subset_1(C,k4_ordinal1) & m2_subset_1(B,k3_finseq_2(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k9_nat_1(k9_setfam_1(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))),k39_fomodel1(A),C))) ) ) ) )).
fof(l4_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v8_pre_topc(A) => v7_pre_topc(A) ) ) )).
fof(l4_friends1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( ( v3_relat_2(C) & r2_hidden(k4_tarski(A,B),C) ) => r2_hidden(k4_tarski(B,A),C) ) ) )).
fof(l4_functor3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,B) & v1_funct_1(E) & v1_partfun1(E,B) ) => ! [F] : ( 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) ) ) ) ) ) )).
fof(l4_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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) ) ) ) ) )).
fof(l4_fvaluat1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( A = C & B = D ) => k6_xcmplx_0(A,B) = k3_xxreal_3(C,D) ) ) ) ) ) )).
fof(l4_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ( B != D => k1_funct_1(k1_funct_4(A,k16_funcop_1(B,C)),D) = k1_funct_1(A,D) ) ) )).
fof(l4_graph_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(l4_grfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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) ) ) ) )).
fof(l4_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(k12_polynom1(A,C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k12_polynom1(A,C))) => ( ( F = D & G = E ) => k5_algstr_0(k12_polynom1(A,C),F,G) = k7_polynom1(A,C,D,E) ) ) ) ) ) ) ) ) )).
fof(l4_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v7_aff_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l4_int_2,axiom,( ! [A] : ( v1_int_1(A) => ( r1_int_1(A,k4_xcmplx_0(A)) & r1_int_1(k4_xcmplx_0(A),A) ) ) )).
fof(l4_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k4_numbers)) => r1_tarski(k1_integra2(B,A),k4_numbers) ) ) )).
fof(l4_integr15,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => ! [C] : ( m1_integra1(C,A) => ! [D] : ( v1_xreal_0(D) => ~ ( v1_seq_2(k2_partfun1(A,k1_numbers,B,A)) & ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( m1_integr15(E,A,B,C) => ? [F] : ( v7_ordinal1(F) & r2_hidden(F,k4_finseq_1(C)) & ~ ( r1_xxreal_0(k1_funct_1(E,F),k1_funct_1(k4_integra1(A,B,C),F)) & ~ r1_xxreal_0(k1_funct_1(E,F),k6_xcmplx_0(k1_funct_1(k4_integra1(A,B,C),F),D)) ) ) ) ) ) ) ) ) )).
fof(l4_integr19,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l4_integr1c,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k1_numbers)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k1_numbers)) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(l4_jordan1a,axiom,( k3_nat_d(1,2) = k5_numbers )).
fof(l4_jordan1c,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(A,k3_xcmplx_0(2,k7_xcmplx_0(A,4))) ) ) )).
fof(l4_jordan1d,axiom,( k3_nat_d(2,2) = 1 )).
fof(l4_jordan21,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(l4_jordan5b,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,1) ) => ( r1_xxreal_0(k5_numbers,k6_xcmplx_0(1,A)) & r1_xxreal_0(k6_xcmplx_0(1,A),1) ) ) ) )).
fof(l4_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ? [B] : ( m1_subset_1(B,u1_struct_0(k3_lattice3(A))) & ! [C] : ( m1_subset_1(C,u1_struct_0(k3_lattice3(A))) => r3_orders_2(k3_lattice3(A),C,B) ) ) ) )).
fof(l4_lattice8,axiom,( v1_abian(2) )).
fof(l4_lattices,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(g3_lattices(k1_zfmisc_1(k1_xboole_0),A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(g3_lattices(k1_zfmisc_1(k1_xboole_0),A,B))) => C = D ) ) ) ) )).
fof(l4_lexbfs,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(l4_limfunc2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(l4_limfunc3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l4_lopban_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(l4_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => ( r1_xxreal_0(C,k5_numbers) | k2_power(k3_xcmplx_0(A,B),C) = k3_xcmplx_0(k2_power(A,C),k2_power(B,C)) ) ) ) ) ) )).
fof(l4_lpspace2,axiom,( v1_xreal_0(1) )).
fof(l4_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( 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) ) ) ) ) )).
fof(l4_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( 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))) ) ) ) )).
fof(l4_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ( r1_tarski(A,B) => r1_tarski(k4_member_1(A),k4_member_1(B)) ) ) ) )).
fof(l4_metric_1,axiom,( ! [A] : ( m1_subset_1(A,1) => ! [B] : ( m1_subset_1(B,1) => ( k1_binop_1(k9_funct_5,A,B) = k5_numbers <=> A = B ) ) ) )).
fof(l4_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_metric_2(A,B,B) ) ) )).
fof(l4_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_mod_4(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_mod_4(A))) => ! [D] : ( 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 ) ) ) ) ) )).
fof(l4_modelc_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => r1_xxreal_0(k1_int_1(A),k1_int_1(B)) ) ) ) )).
fof(l4_normsp_1,axiom,( k1_funct_1(c2__normsp_1,k4_struct_0(o_0_5_normsp_1)) = k5_numbers )).
fof(l4_normsp_2,axiom,( ! [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) & 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)))) ) )).
fof(l4_numbers,axiom,( r1_tarski(k2_arytm_2,k1_numbers) )).
fof(l4_o_ring_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ( r1_xxreal_0(A,k3_finseq_1(C)) => ( A = k5_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) ) ) ) ) ) ) )).
fof(l4_orders_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ r2_hidden(k1_xboole_0,A) => ! [B] : ( m2_orders_1(B,A,k6_partfun1(A)) => ! [C] : ( r2_hidden(C,A) => r2_hidden(k1_funct_1(B,C),C) ) ) ) ) )).
fof(l4_ortsp_1,axiom,( ! [A] : ( m1_subset_1(A,c1__ortsp_1) => ! [B] : ( m1_subset_1(B,c1__ortsp_1) => k5_binop_1(c1__ortsp_1,c3__ortsp_1,A,B) = c2__ortsp_1 ) ) )).
fof(l4_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( k5_algstr_0(A,k8_group_1(A,B,F),k8_group_1(A,E,C)) = k4_struct_0(A) & k5_algstr_0(A,k8_group_1(A,B,D),k8_group_1(A,G,C)) = k4_struct_0(A) ) => ( B = k4_struct_0(A) | k5_algstr_0(A,k8_group_1(A,E,D),k8_group_1(A,G,F)) = k4_struct_0(A) ) ) ) ) ) ) ) ) ) )).
fof(l4_parsp_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) => ! [E] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l4_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ( A != k5_numbers => k1_nat_1(k7_nat_d(A,1),1) = k7_nat_d(k1_nat_1(A,1),1) ) ) )).
fof(l4_pnproc_1,axiom,( ! [A] : ! [B] : ( r2_hidden(B,A) => k1_funct_1(k1_pnproc_1(A),B) = k5_numbers ) )).
fof(l4_polyeq_2,axiom,( 3 = k2_xcmplx_0(k3_xcmplx_0(2,1),1) )).
fof(l4_polynom5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(1,C) & ~ r1_xxreal_0(B,k3_xcmplx_0(C,A)) ) ) => r1_xxreal_0(B,k5_numbers) ) ) ) )).
fof(l4_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(l4_pralg_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r2_hidden(B,k4_card_3(A)) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) )).
fof(l4_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_qc_lang1(A))) => ( C = k24_qc_lang1(A,B) <=> ? [D] : ( 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] : ( m1_subset_1(E,k9_qc_lang1(A)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k3_qc_lang1(A))) => ! [G] : ( 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))) ) ) ) ) ) ) ) ) ) ) )).
fof(l4_quatern2,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l4_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => r1_xxreal_0(2,k1_radix_1(A)) ) ) )).
fof(l4_radix_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(l4_rat_1,axiom,( m1_subset_1(k5_numbers,k2_arytm_2) )).
fof(l4_real_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_real_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_real_lat)) => k1_lattices(k3_real_lat,A,B) = k1_lattices(k3_real_lat,B,A) ) ) )).
fof(l4_realset2,axiom,( r2_hidden(k5_numbers,2) )).
fof(l4_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(B)) ) => v1_finset_1(k1_funct_1(B,C)) ) ) ) ) )).
fof(l4_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( 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,k5_numbers) ) & ~ r2_hidden(B,k4_finseq_1(A)) ) ) ) )).
fof(l4_rlaffin3,axiom,( ! [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) ) => ! [B] : ( 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)))) ) ) )).
fof(l4_rlvect_3,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l4_rlvect_5,axiom,( ! [A] : ! [B] : ( r2_hidden(B,A) => k2_xboole_0(k6_subset_1(A,k1_tarski(B)),k1_tarski(B)) = A ) )).
fof(l4_roughs_1,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v3_orders_2(A) & v7_struct_0(A) ) => v1_orders_3(A) ) ) )).
fof(l4_rsspace2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(k3_xcmplx_0(k2_xcmplx_0(A,B),k2_xcmplx_0(A,B)),k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,A),A),k3_xcmplx_0(k3_xcmplx_0(2,B),B))) ) ) & ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(k3_xcmplx_0(A,A),k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k6_xcmplx_0(A,B)),k6_xcmplx_0(A,B)),k3_xcmplx_0(k3_xcmplx_0(2,B),B))) ) ) )).
fof(l4_rsspace3,axiom,( ~ v2_struct_0(g1_rlvect_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3))) & v13_algstr_0(g1_rlvect_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3))) & v2_rlvect_1(g1_rlvect_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3))) & v3_rlvect_1(g1_rlvect_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3))) & v4_rlvect_1(g1_rlvect_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3))) & v5_rlvect_1(g1_rlvect_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3))) & v6_rlvect_1(g1_rlvect_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3))) & v7_rlvect_1(g1_rlvect_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3))) & v8_rlvect_1(g1_rlvect_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3))) & l1_rlvect_1(g1_rlvect_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3))) )).
fof(l4_rsspace4,axiom,( m1_rlsub_1(g1_rlvect_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4)),k6_rsspace) )).
fof(l4_scm_comp,axiom,( k7_dtconstr(k1_scm_comp) = k2_zfmisc_1(1,5) )).
fof(l4_scm_halt,axiom,( k9_xtuple_0(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_3(k4_scmfsa_2(k5_numbers),1))) = k2_xboole_0(k4_scmfsa_m(k4_scmfsa_2(k5_numbers)),k1_tarski(k4_struct_0(k1_scmfsa_2))) )).
fof(l4_scmfsa_i,axiom,( r1_tarski(k2_scmfsa_i,k3_zfmisc_1(k4_ordinal1,k13_finseq_1(k4_ordinal1),k10_xtuple_0(k2_scmfsa_i))) )).
fof(l4_scmpds_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ~ ( ~ r2_hidden(A,k1_tarski(k3_xtuple_0(k5_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) ) ) )).
fof(l4_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,A,k1_nat_1(B,1))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,A,k2_xcmplx_0(B,C))) ) ) ) & ( ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,A,k2_xcmplx_0(B,C))) ) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,A,C)) ) ) ) ) & ( ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,A,C)) ) ) ) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,A,k1_nat_1(B,1))) ) ) ) ) )).
fof(l4_series_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( 4 = k11_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)) ) ) ) )).
fof(l4_series_3,axiom,( k11_newton(3,3) = 27 )).
fof(l4_series_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(l4_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( v1_xreal_0(C) => k2_power(k7_xcmplx_0(A,B),k4_xcmplx_0(C)) = k2_power(k7_xcmplx_0(B,A),C) ) ) ) )).
fof(l4_sin_cos9,axiom,( r2_fdiff_1(k27_sin_cos,k2_rcomp_1(k5_numbers,k28_sin_cos)) )).
fof(l4_tdgroup,axiom,( v12_vectsp_1(k1_vectsp_1) )).
fof(l4_topalg_2,axiom,( 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)) )).
fof(l4_topalg_5,axiom,( r2_hidden(k5_numbers,k6_domain_1(k4_ordinal1,k5_numbers)) )).
fof(l4_topmetr2,axiom,( v1_xreal_0(2) )).
fof(l4_topreal2,axiom,( k17_euclid(k19_euclid(k5_numbers,k5_numbers)) = k5_numbers )).
fof(l4_toprealb,axiom,( u1_struct_0(k4_topmetr(k4_xcmplx_0(1),1)) = k1_rcomp_1(k4_xcmplx_0(1),1) )).
fof(l4_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( r1_aff_1(A,E,F,G) & E != G & F != G ) ) ) ) ) ) ) ) ) )).
fof(l4_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ~ ( r2_hidden(B,k10_xtuple_0(A)) & ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(k3_finseq_1(A),C) & B = k1_funct_1(A,k1_nat_1(C,1)) ) ) ) ) )).
fof(l4_vectsp_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k3_rlvect_1(A,B,C) = D => B = k5_algstr_0(A,D,C) ) ) ) ) ) )).
fof(l4_waybel17,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => v2_waybel11(k5_waybel_0(A,B),A) ) ) )).
fof(l4_waybel30,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,k1_yellow_1(k7_waybel_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_yellow_1(k7_waybel_0(A))))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) => ( C = k3_tarski(B) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) => ( r2_lattice3(k1_yellow_1(k7_waybel_0(A)),B,D) => r3_orders_2(k1_yellow_1(k7_waybel_0(A)),C,D) ) ) ) ) ) ) )).
fof(l4_waybel34,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) ) )).
fof(l4_waybel_5,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( ~ 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] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(l4_waybel_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(l4_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ( v6_relat_2(A) <=> ! [B] : ! [C] : ~ ( 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) ) ) ) )).
fof(l4_wsierp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) => r1_xxreal_0(B,k2_xcmplx_0(A,B)) ) & ( r1_xxreal_0(B,k2_xcmplx_0(A,B)) => r1_xxreal_0(k5_numbers,A) ) & ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k2_xcmplx_0(A,B),B) ) & ~ ( ~ r1_xxreal_0(k2_xcmplx_0(A,B),B) & r1_xxreal_0(A,k5_numbers) ) & ( r1_xxreal_0(k5_numbers,A) => r1_xxreal_0(k6_xcmplx_0(B,A),B) ) & ( r1_xxreal_0(k6_xcmplx_0(B,A),B) => r1_xxreal_0(k5_numbers,A) ) & ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(B,k6_xcmplx_0(B,A)) ) & ~ ( ~ r1_xxreal_0(B,k6_xcmplx_0(B,A)) & r1_xxreal_0(A,k5_numbers) ) ) ) ) )).
fof(l4_xcmplx_0,axiom,( r2_hidden(k5_numbers,k1_numbers) )).
fof(l4_xreal_0,axiom,( r2_hidden(k1_xboole_0,k1_tarski(k1_xboole_0)) )).
fof(l4_xreal_1,axiom,( r2_hidden(k1_xboole_0,k1_tarski(k1_xboole_0)) )).
fof(l4_xtuple_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ~ ( k2_tarski(A,B) = k2_tarski(C,D) & A != C & A != D ) )).
fof(l4_zf_fund2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ~ ( r2_hidden(B,k3_card_3(A)) & ! [C] : ~ ( r2_hidden(C,k9_xtuple_0(A)) & r2_hidden(B,k1_funct_1(A,C)) ) ) ) )).
fof(l50_anproj_2,axiom,( ? [A] : ( ~ v1_xboole_0(A) & ? [B] : ( m1_subset_1(B,A) & ? [C] : ( m1_subset_1(C,A) & ? [D] : ( m1_subset_1(D,A) & A = k8_domain_1(A,B,C,D) & B != C & B != D & C != D ) ) ) ) )).
fof(l50_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ? [C] : ( m1_subset_1(C,k4_ordinal1) & r1_xxreal_0(B,C) & r1_xxreal_0(k6_xcmplx_0(k3_xcmplx_0(C,k3_power(2,k2_xcmplx_0(1,A))),k3_xcmplx_0(8,k3_power(2,C))),k3_xcmplx_0(8,k3_power(2,C))) ) ) ) ) )).
fof(l50_borsuk_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_connsp_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ! [D] : ~ ( 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] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(l50_card_3,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ~ ( r2_hidden(A,k1_relat_1(B)) & ! [C] : ( ~ r2_hidden(k4_tarski(A,C),B) & ~ r2_hidden(k4_tarski(C,A),B) ) ) ) )).
fof(l50_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & r1_xxreal_0(C,k2_normsp_0(A,B)) ) ) => B = k4_struct_0(A) ) ) ) )).
fof(l50_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => k1_square_1(k9_complex1(A)) = k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A))) ) )).
fof(l50_descip_1,axiom,( ! [A] : ( m2_finseq_2(A,k6_margrel1,k4_finseq_2(64,k6_margrel1)) => k25_descip_1(k27_descip_1(A)) = A ) )).
fof(l50_diff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( ( 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_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,C,D),A),1),B) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(C,B),k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(D,A),1),B)),k3_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(C,A),1),B),k1_funct_1(D,k2_xcmplx_0(B,A)))) ) ) ) ) )).
fof(l50_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ? [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) & ? [E] : ( 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) ) ) ) ) ) )).
fof(l50_fib_num4,axiom,( ~ r1_xxreal_0(k1_pepin(2),k1_square_1(k6_xcmplx_0(1,k3_square_1(5)))) )).
fof(l50_finseq_3,axiom,( ! [A] : ( 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)) ) ) )).
fof(l50_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v2_fintopo6(k12_finseq_1(u1_struct_0(A),B),A) ) ) )).
fof(l50_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => k8_fomodel3(A,B,C,k5_numbers) = k3_fomodel2(k1_tarski(k1_xboole_0)) ) ) ) )).
fof(l50_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l50_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ( r1_analmetr(A,D,E) => ( k2_geomtrap(A,D,E,k3_rlvect_1(A,B,C)) = k2_xcmplx_0(k2_geomtrap(A,D,E,B),k2_geomtrap(A,D,E,C)) & k3_geomtrap(A,D,E,k3_rlvect_1(A,B,C)) = k2_xcmplx_0(k3_geomtrap(A,D,E,B),k3_geomtrap(A,D,E,C)) & k2_geomtrap(A,D,E,k5_algstr_0(A,B,C)) = k6_xcmplx_0(k2_geomtrap(A,D,E,B),k2_geomtrap(A,D,E,C)) & k3_geomtrap(A,D,E,k5_algstr_0(A,B,C)) = k6_xcmplx_0(k3_geomtrap(A,D,E,B),k3_geomtrap(A,D,E,C)) & k2_geomtrap(A,D,E,k1_rlvect_1(A,B,F)) = k3_xcmplx_0(F,k2_geomtrap(A,D,E,B)) & k3_geomtrap(A,D,E,k1_rlvect_1(A,B,F)) = k3_xcmplx_0(F,k3_geomtrap(A,D,E,B)) ) ) ) ) ) ) ) ) )).
fof(l50_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( r2_hidden(D,k1_relset_1(k4_ordinal1,k7_glib_001(A,B,C))) & ~ r2_hidden(D,k1_relset_1(k4_ordinal1,B)) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( ~ r1_xxreal_0(k3_finseq_1(C),E) & D = k1_nat_1(k3_finseq_1(B),E) ) ) ) ) ) ) ) )).
fof(l50_gr_cy_3,axiom,( ! [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] : ( m1_group_2(B,k1_uniroots(A)) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( k2_hurwitz(A,D) = C & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(l50_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( ( r1_int_1(A,B) => k5_int_1(B,A) = k5_numbers ) & ( k5_int_1(B,A) = k5_numbers => ( A = k5_numbers | r1_int_1(A,B) ) ) ) ) ) )).
fof(l50_integra8,axiom,( k9_xtuple_0(k3_sin_cos2) = k1_numbers )).
fof(l50_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,A,C) => ! [G] : ( m2_cat_1(G,A,C) => ( ( r2_nattra_1(A,B,D,E) & r2_nattra_1(A,C,F,G) ) => ! [H] : ( m2_nattra_1(H,A,B,D,E) => ! [I] : ( m2_nattra_1(I,A,C,F,G) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ( k2_cat_1(A,J,K) != k1_xboole_0 => ! [L] : ( m1_cat_1(L,A,J,K) => k5_cat_1(k6_cat_2(B,C),k8_cat_1(A,k6_cat_2(B,C),k8_isocat_2(A,B,C,D,F),J),k8_cat_1(A,k6_cat_2(B,C),k8_isocat_2(A,B,C,D,F),K),k8_cat_1(A,k6_cat_2(B,C),k8_isocat_2(A,B,C,E,G),K),k9_cat_3(A,J,K,k6_cat_2(B,C),k8_isocat_2(A,B,C,D,F),L),k2_nattra_1(A,k6_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(k6_cat_2(B,C),k8_cat_1(A,k6_cat_2(B,C),k8_isocat_2(A,B,C,D,F),J),k8_cat_1(A,k6_cat_2(B,C),k8_isocat_2(A,B,C,E,G),J),k8_cat_1(A,k6_cat_2(B,C),k8_isocat_2(A,B,C,E,G),K),k2_nattra_1(A,k6_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,k6_cat_2(B,C),k8_isocat_2(A,B,C,E,G),L)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l50_jgraph_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( k18_euclid(k5_algstr_0(k15_euclid(2),A,B)) = k6_xcmplx_0(k18_euclid(A),k18_euclid(B)) & k4_xcmplx_0(k17_euclid(k5_algstr_0(k15_euclid(2),A,B))) = k6_xcmplx_0(k4_xcmplx_0(k17_euclid(A)),k4_xcmplx_0(k17_euclid(B))) ) ) ) )).
fof(l50_jgraph_4,axiom,( g1_pre_topc(u1_struct_0(k15_euclid(2)),u1_pre_topc(k15_euclid(2))) = k3_pcomps_1(k14_euclid(2)) )).
fof(l50_jordan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_borsuk_2(H,A,B,C) => ! [I] : ( m1_borsuk_2(I,A,C,D) => ! [J] : ( m1_borsuk_2(J,A,D,E) => ! [K] : ( m1_borsuk_2(K,A,E,F) => ! [L] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l50_jordan1a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k2_xcmplx_0(D,k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(C,D),k1_newton(2,B)),k6_xcmplx_0(k3_finseq_1(k1_jordan8(A,B)),2))) = k2_xcmplx_0(C,k7_xcmplx_0(k6_xcmplx_0(C,D),k1_newton(2,B))) ) ) ) ) )).
fof(l50_jordan3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => k17_finseq_1(B,A,k6_finseq_1(B)) = k6_finseq_1(B) ) ) )).
fof(l50_jordan5d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( ~ 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 = k4_seq_4(C) ) => r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_matrix_0(k2_goboard2(D)))),k17_euclid(B)) ) ) ) ) ) )).
fof(l50_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(A,A))))) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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) ) ) ) ) ) )).
fof(l50_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) )).
fof(l50_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(B,k4_ordinal1)) => ( r2_hidden(A,k2_finseq_1(B)) => k7_matrix_0(u1_struct_0(C),k1_matrix13(u1_struct_0(C),D,B,k5_card_1(k2_finseq_1(k1_matrix_0(D))),E,k5_matrix13(k2_finseq_1(k1_matrix_0(D)))),A) = k7_matrix_0(u1_struct_0(C),D,k1_funct_1(E,A)) ) ) ) ) ) ) )).
fof(l50_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( r2_mesfun6c(A,B,C,D) => ( ! [E] : ( 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) = k5_numbers | r1_xxreal_0(k9_complex1(k1_mesfun6c(A,B,C,D)),k1_mesfunc6(A,B,C,k55_valued_1(A,k2_numbers,D))) ) ) ) ) ) ) )).
fof(l50_mod_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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,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)) ) ) ) ) ) ) )).
fof(l50_ncfcont2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_xxreal_0(D,k2_normsp_0(A,k5_algstr_0(A,B,C))) ) ) => B = C ) ) ) ) )).
fof(l50_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l50_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r8_relat_2(A,B) => v8_relat_2(k2_wellord1(A,B)) ) ) )).
fof(l50_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_int_1(A,1,B) => ( r1_xxreal_0(B,1) | r1_xxreal_0(A,1) | k4_nat_d(A,B) = 1 ) ) ) ) )).
fof(l50_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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 = k8_polynom1(A,C) | r1_polyred(A,B,C,D,E) ) ) ) ) ) ) ) )).
fof(l50_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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] : ( 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(k3_seq_4(k7_partfun1(k1_zfmisc_1(k1_numbers),k12_finseq_1(k1_zfmisc_1(k1_numbers),k1_rcomp_1(A,B)),D)),k3_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(k2_seq_4(k7_partfun1(k1_zfmisc_1(k1_numbers),k12_finseq_1(k1_zfmisc_1(k1_numbers),k1_rcomp_1(A,B)),D)),k2_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(k2_seq_4(k7_partfun1(k1_zfmisc_1(k1_numbers),k12_finseq_1(k1_zfmisc_1(k1_numbers),k1_rcomp_1(A,B)),D)),k3_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(k2_seq_4(k7_partfun1(k1_zfmisc_1(k1_numbers),k12_finseq_1(k1_zfmisc_1(k1_numbers),k1_rcomp_1(A,B)),D)),k3_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)))) ) ) ) ) ) ) ) ) ) )).
fof(l50_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ! [C] : ( m2_rlvect_2(C,A,B) => ( ( k6_rlvect_2(A,C) = k4_struct_0(A) & k3_rlaffin1(A,C) = k5_numbers ) => k3_rlvect_2(A,C) = k1_xboole_0 ) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(l50_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(l50_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(l50_rvsum_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(A) & v1_finseq_1(A) ) => k19_rvsum_1(A) = 1 ) )).
fof(l50_scmisort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => k18_scmfsa_2(k1_scmfsa6b(k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers)))),B,A),k5_scmfsa_2(k5_numbers)) = k18_scmfsa_2(B,k5_scmfsa_2(k5_numbers)) ) ) )).
fof(l50_scmpds_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ~ ( ~ ( ~ r2_hidden(A,k1_tarski(k3_xtuple_0(k5_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) != k5_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 ) ) )).
fof(l50_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => k8_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)))) ) )).
fof(l50_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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,k7_binop_2) => k1_funct_1(k22_sin_cos,k3_xcmplx_0(k4_xcmplx_0(1),A)) = k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k22_sin_cos),A) ) ) ) )).
fof(l50_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(A,1) & r1_xxreal_0(k2_xcmplx_0(1,k3_square_1(k6_xcmplx_0(1,k1_square_1(A)))),k5_numbers) ) ) )).
fof(l50_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(D,A,C) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(E,A,C) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => k4_polynom1(A,C,k10_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,k4_polynom1(A,C,D,k3_termord(A,B,C,D)),k4_polynom1(A,C,E,k3_termord(A,B,C,E))) ) ) ) ) ) )).
fof(l50_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(l50_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) )).
fof(l50_vectsp_6,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) )).
fof(l50_waybel_4,axiom,( ! [A] : ( ( 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),k1_yellow_1(k3_waybel_4(A)),k8_waybel_4(A)) ) )).
fof(l50_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(A,B) => r1_xxreal_0(k1_xxreal_3(A,C),k1_xxreal_3(B,C)) ) ) ) ) )).
fof(l51_arytm_2,axiom,( k12_arytm_3 = 1 )).
fof(l51_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_xxreal_0(D,k2_normsp_0(A,k5_algstr_0(A,B,C))) ) ) => B = C ) ) ) ) )).
fof(l51_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => k16_seq_4(k3_finseq_1(A),k15_seq_4(k3_finseq_1(A))) = k15_seq_4(k3_finseq_1(A)) ) )).
fof(l51_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( v3_conlat_1(B,A) & ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) & l2_conlat_1(B,A) ) => ! [C] : ( ( v3_conlat_1(C,A) & ~ v4_conlat_1(C,A) & v6_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))) ) ) ) )).
fof(l51_descip_1,axiom,( r2_relset_1(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))) )).
fof(l51_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_eqrel_1(C,A) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(k9_setfam_1(A)))) ) => ! [D] : ~ ( r2_hidden(D,a_3_1_eqrel_1(A,B,C)) & ! [E] : ( m1_eqrel_1(E,A) => ~ ( r2_hidden(E,C) & D = k11_eqrel_1(A,B,E) ) ) ) ) ) ) )).
fof(l51_fib_num4,axiom,( ~ r1_xxreal_0(k2_power(2,2),k1_square_1(k6_xcmplx_0(1,k3_square_1(5)))) )).
fof(l51_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ~ v1_xboole_0(C) => ( v1_funct_1(k1_funct_5(k22_fomodel2(B,A,C))) & v1_funct_2(k1_funct_5(k22_fomodel2(B,A,C)),k15_fomodel2(B,C),k9_funct_2(k24_fomodel2(B,A),k6_margrel1)) & m1_subset_1(k1_funct_5(k22_fomodel2(B,A,C)),k1_zfmisc_1(k2_zfmisc_1(k15_fomodel2(B,C),k9_funct_2(k24_fomodel2(B,A),k6_margrel1)))) ) ) ) ) )).
fof(l51_funct_9,axiom,( v1_funct_9(k41_valued_1(k1_numbers,k1_numbers,k16_sin_cos),k28_sin_cos) )).
fof(l51_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_analmetr(A,D,E) => ( k3_xcmplx_0(2,k2_geomtrap(A,D,E,k1_geomtrap(A,B,C))) = k2_xcmplx_0(k2_geomtrap(A,D,E,B),k2_geomtrap(A,D,E,C)) & k3_xcmplx_0(2,k3_geomtrap(A,D,E,k1_geomtrap(A,B,C))) = k2_xcmplx_0(k3_geomtrap(A,D,E,B),k3_geomtrap(A,D,E,C)) ) ) ) ) ) ) ) )).
fof(l51_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( ( r1_xxreal_0(C,D) & r1_xxreal_0(D,k3_finseq_1(B)) ) => ( k1_nat_1(k3_finseq_1(k8_glib_001(A,B,C,D)),C) = k1_nat_1(D,1) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ~ r1_xxreal_0(k3_finseq_1(k8_glib_001(A,B,C,D)),E) => ( k1_funct_1(k8_glib_001(A,B,C,D),k1_nat_1(E,1)) = k1_funct_1(B,k1_nat_1(C,E)) & r2_hidden(k1_nat_1(C,E),k1_relset_1(k4_ordinal1,B)) ) ) ) ) ) ) ) ) ) )).
fof(l51_gr_cy_3,axiom,( ! [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] : ( m1_group_2(B,k1_uniroots(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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,k5_numbers) | m1_subset_1(D,u1_struct_0(k5_group_4(B,k6_domain_1(u1_struct_0(B),C)))) ) ) ) ) ) ) ) )).
fof(l51_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r1_xxreal_0(1,A) => r1_xxreal_0(B,k2_nat_1(A,B)) ) ) ) )).
fof(l51_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r1_int_1(A,B) => B = k3_xcmplx_0(k4_int_1(B,A),A) ) ) ) )).
fof(l51_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_integra5(A,k18_sin_cos) & v1_comseq_2(k2_partfun1(k1_numbers,k1_numbers,k18_sin_cos,A)) ) ) )).
fof(l51_jgraph_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => k1_square_1(k12_euclid(k5_algstr_0(k15_euclid(2),A,B))) = k2_xcmplx_0(k1_square_1(k18_euclid(k5_algstr_0(k15_euclid(2),A,B))),k1_square_1(k4_xcmplx_0(k17_euclid(k5_algstr_0(k15_euclid(2),A,B))))) ) ) )).
fof(l51_jordan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_borsuk_2(H,A,B,C) => ! [I] : ( m1_borsuk_2(I,A,C,D) => ! [J] : ( m1_borsuk_2(J,A,D,E) => ! [K] : ( m1_borsuk_2(K,A,E,F) => ! [L] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l51_jordan1a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k4_tarski(C,1),k2_matrix_0(k1_jordan8(A,B))) => k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),C,1)) = k6_xcmplx_0(k9_pscomp_1(A),k7_xcmplx_0(k6_xcmplx_0(k7_pscomp_1(A),k9_pscomp_1(A)),k1_newton(2,B))) ) ) ) ) )).
fof(l51_jordan3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ( ( 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 ) ) ) ) ) )).
fof(l51_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ( ( 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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),B,1))) ) ) ) ) ) )).
fof(l51_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( k1_relset_1(k6_glib_000(A),k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),k9_lexbfs(A))) = k6_glib_000(A) & k1_funct_1(k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),k9_lexbfs(A)),B) = k1_xboole_0 ) ) )).
fof(l51_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(A,A))))) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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) ) ) ) ) ) )).
fof(l51_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_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)) ) ) ) ) )).
fof(l51_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_card_1(D,A) & v1_finseq_1(D) & v3_valued_0(D) ) => ? [E] : ( 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)),k3_xcmplx_0(k18_rvsum_1(E),k12_euclid(D))) & ! [F] : ( v7_ordinal1(F) => ( r2_hidden(F,k4_finseq_1(E)) => k1_funct_1(E,F) = k12_euclid(k2_matrtop1(k8_matrix_0(u1_struct_0(k2_vectsp_1),C,F))) ) ) ) ) ) ) ) )).
fof(l51_o_ring_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(B)) => ( ( v2_o_ring_1(C,B) & r1_xxreal_0(A,k3_finseq_1(C)) ) => ( k5_numbers = A | v13_o_ring_1(k7_partfun1(u1_struct_0(B),C,A),B) ) ) ) ) ) )).
fof(l51_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r4_relat_2(A,B) => v4_relat_2(k2_wellord1(A,B)) ) ) )).
fof(l51_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k6_poset_1(A,A))) => ! [C] : ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(l51_rlsub_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( B = k1_algstr_0(A,C,D) <=> C = k5_algstr_0(A,B,D) ) ) ) ) ) )).
fof(l51_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) => ( k1_funct_1(B,k4_scmfsa_2(k5_numbers)) = 1 => ( r5_scmfsa7b(C,B,A) <=> r5_scmfsa7b(C,k1_scmfsa_m(B),A) ) ) ) ) ) )).
fof(l51_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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,k7_binop_2) => ( r1_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k22_sin_cos)),A) & r1_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k22_sin_cos)),A) & k1_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k22_sin_cos)),A) = k2_xcmplx_0(k1_funct_1(k22_sin_cos,A),k1_funct_1(k22_sin_cos,k4_xcmplx_0(A))) & k1_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k22_sin_cos)),A) = k6_xcmplx_0(k1_funct_1(k22_sin_cos,A),k1_funct_1(k22_sin_cos,k4_xcmplx_0(A))) ) ) ) ) )).
fof(l51_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(A,1) & r1_xxreal_0(k7_xcmplx_0(k2_xcmplx_0(1,k3_square_1(k6_xcmplx_0(1,k1_square_1(A)))),A),k5_numbers) ) ) )).
fof(l51_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(l51_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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 ) ) ) )).
fof(l51_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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))) ) ) ) )).
fof(l51_waybel_9,axiom,( ! [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) & v1_compts_1(A) & l1_waybel_9(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( C = D & ! [E] : ( 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) ) ) ) ) ) )).
fof(l51_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(k1_xxreal_3(A,B),k5_numbers) ) ) ) )).
fof(l52_analmetr,axiom,( ? [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) & ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r1_analmetr(A,B,C) ) ) ) )).
fof(l52_arytm_2,axiom,( k11_arytm_3 = k11_arytm_3 )).
fof(l52_borsuk_1,axiom,( ! [A] : ( l1_pre_topc(A) => m1_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)),A) ) )).
fof(l52_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(D) & k1_seq_2(D) = k5_numbers & ! [E] : ( v7_ordinal1(E) => r1_xxreal_0(k2_normsp_0(A,k5_algstr_0(A,B,C)),k9_nat_1(k1_numbers,D,E)) ) ) => B = C ) ) ) ) ) )).
fof(l52_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( v3_conlat_1(B,A) & ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) & l2_conlat_1(B,A) ) => ! [C] : ( ( v3_conlat_1(C,A) & ~ v4_conlat_1(C,A) & v6_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))) ) ) ) )).
fof(l52_descip_1,axiom,( r2_relset_1(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))) )).
fof(l52_fib_num4,axiom,( ~ r1_xxreal_0(k2_power(2,2),k2_power(k6_xcmplx_0(1,k3_square_1(5)),2)) )).
fof(l52_funct_9,axiom,( v1_funct_9(k41_valued_1(k1_numbers,k1_numbers,k18_sin_cos),k28_sin_cos) )).
fof(l52_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(l52_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( ( 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)) ) ) ) ) ) ) )).
fof(l52_graph_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ! [B] : ! [C] : ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => B = C ) => k1_card_1(A) = 1 ) ) )).
fof(l52_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( ~ r1_xxreal_0(k1_nat_1(k1_nat_1(k2_nat_1(A,A),k2_nat_1(3,A)),1),k2_nat_1(3,A)) & ~ r1_xxreal_0(k1_nat_1(k1_nat_1(k2_nat_1(A,A),k2_nat_1(3,A)),1),A) & ~ r1_xxreal_0(k1_nat_1(k1_nat_1(k2_nat_1(A,A),k2_nat_1(3,A)),1),k2_nat_1(2,A)) ) ) )).
fof(l52_group_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k5_group_1(B,k4_xcmplx_0(A),C) = k2_group_1(B,k5_group_1(B,A,C)) ) ) ) )).
fof(l52_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( ~ ( A = k5_numbers & B = k5_numbers ) => r1_int_2(k4_int_1(A,k3_int_2(A,B)),k4_int_1(B,k3_int_2(A,B))) ) ) ) )).
fof(l52_integra1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( 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)) = k2_xcmplx_0(k6_xcmplx_0(B,A),1) ) ) ) ) )).
fof(l52_jordan1a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k4_tarski(1,C),k2_matrix_0(k1_jordan8(A,B))) => k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),1,C)) = k6_xcmplx_0(k6_pscomp_1(A),k7_xcmplx_0(k6_xcmplx_0(k8_pscomp_1(A),k6_pscomp_1(A)),k1_newton(2,B))) ) ) ) ) )).
fof(l52_jordan3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => k3_finseq_6(A,B,k5_numbers,k5_numbers) = k17_finseq_1(A,1,B) ) ) )).
fof(l52_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ( ( 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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),B,k1_matrix_0(k2_goboard2(A))))) ) ) ) ) ) )).
fof(l52_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(A,A))))) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(l52_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & r1_xxreal_0(C,k2_normsp_0(A,B)) ) ) => B = k4_struct_0(A) ) ) ) )).
fof(l52_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v3_o_ring_1(B,A) => v13_o_ring_1(B,A) ) ) ) )).
fof(l52_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_oppcat_1(C,k2_oppcat_1(B),A) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k3_funct_2(u4_struct_0(B),u4_struct_0(A),k9_oppcat_1(B,A,C),k4_cat_1(B,D)) = k4_cat_1(A,k3_funct_2(u1_struct_0(k2_oppcat_1(B)),u1_struct_0(A),k7_cat_1(k2_oppcat_1(B),A,C),k3_oppcat_1(B,D))) ) ) ) ) )).
fof(l52_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v7_ordinal1(B) => k1_funct_1(k1_pdiff_1(B,A),k4_struct_0(k4_real_ns1(A))) = k5_numbers ) ) )).
fof(l52_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r6_relat_2(A,B) => v6_relat_2(k2_wellord1(A,B)) ) ) )).
fof(l52_poset_1,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l52_quofield,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(l52_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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))) ) ) ) )).
fof(l52_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) => ( k1_funct_1(B,k4_scmfsa_2(k5_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) ) ) ) ) ) ) ) )).
fof(l52_scmisort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_ami_2(B) & ~ v1_scmfsa_m(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ~ ( B != k4_scmfsa_2(k1_nat_1(3,1)) & B != k4_scmfsa_2(k1_nat_1(1,1)) & k1_funct_1(k1_scmfsa6b(k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers)))),C,A),B) != k1_funct_1(C,B) ) ) ) ) )).
fof(l52_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ! [C] : ( v1_int_1(C) => ! [D] : ( v7_ordinal1(D) => r1_tarski(k61_valued_1(A,1),k2_scmpds_7(B,C,D,A)) ) ) ) ) )).
fof(l52_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => v4_scmyciel(k6_subset_1(k5_scmyciel(k3_tarski(A)),k1_scmyciel(A))) ) )).
fof(l52_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( A = B => ( k9_complex1(k11_comseq_3(k3_sin_cos(k3_xcmplx_0(A,k7_complex1)))) = 1 & r1_xxreal_0(k9_complex1(k1_funct_1(k16_sin_cos,B)),1) & r1_xxreal_0(k9_complex1(k1_funct_1(k18_sin_cos,B)),1) ) ) ) ) )).
fof(l52_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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,k7_binop_2) => ( r1_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k22_sin_cos)),k7_xcmplx_0(1,2)),A) & k1_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k22_sin_cos)),k7_xcmplx_0(1,2)),A) = k3_xcmplx_0(k7_xcmplx_0(1,2),k1_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k22_sin_cos)),A)) ) ) ) ) )).
fof(l52_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => r1_xxreal_0(k5_numbers,k2_sin_cos2(A)) ) ) )).
fof(l52_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & A != 1 & k7_xcmplx_0(k3_xcmplx_0(2,A),k6_xcmplx_0(k1_square_1(A),1)) = k5_numbers ) ) )).
fof(l52_turing_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( r1_xxreal_0(A,4) => m1_subset_1(A,u2_turing_1(k16_turing_1)) ) ) )).
fof(l52_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(l52_waybel11,axiom,( ! [A] : ( l1_pre_topc(A) => ! [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)) & v2_pre_topc(A) ) => v2_pre_topc(B) ) ) ) )).
fof(l52_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) )).
fof(l52_waybel_4,axiom,( ! [A] : ( ( 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),k1_yellow_1(k3_waybel_4(A))) ) )).
fof(l52_waybel_9,axiom,( ! [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) & v1_compts_1(A) & l1_waybel_9(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( C = D & ! [E] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(l52_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k5_numbers,k1_xxreal_3(A,B)) ) ) ) )).
fof(l52_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(l53_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_afvect0(A,B))) => ! [D] : ( 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) ) ) ) ) )).
fof(l53_analmetr,axiom,( ? [A] : ( m1_subset_1(A,u1_struct_0(c4__analmetr)) & ? [B] : ( m1_subset_1(B,u1_struct_0(c4__analmetr)) & r1_analmetr(c4__analmetr,A,B) ) ) )).
fof(l53_arytm_2,axiom,( ! [A] : ( m2_subset_1(A,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) => ! [B] : ( 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 ) ) ) ) )).
fof(l53_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k8_cfuncdom(u1_struct_0(A)))) => ! [C] : ( 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)) ) ) ) ) )).
fof(l53_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k7_xcmplx_0(A,B) = k2_xcmplx_0(k7_xcmplx_0(k3_real_1(k4_real_1(k3_complex1(A),k3_complex1(B)),k4_real_1(k4_complex1(A),k4_complex1(B))),k2_xcmplx_0(k1_square_1(k3_complex1(B)),k1_square_1(k4_complex1(B)))),k3_xcmplx_0(k7_xcmplx_0(k5_real_1(k4_real_1(k3_complex1(B),k4_complex1(A)),k4_real_1(k3_complex1(A),k4_complex1(B))),k2_xcmplx_0(k1_square_1(k3_complex1(B)),k1_square_1(k4_complex1(B)))),k7_complex1)) ) ) )).
fof(l53_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_rlsub_1(B,k10_funcsdom(k2_finseq_1(A))) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( v1_xreal_0(E) => ( ( 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)) ) ) ) ) ) ) )).
fof(l53_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ! [E] : ( ( r2_hidden(k4_tarski(C,D),k9_xtuple_0(A)) & B = k1_funct_1(k1_funct_5(A),C) & r2_hidden(E,k9_xtuple_0(B)) ) => r2_hidden(k4_tarski(C,E),k9_xtuple_0(A)) ) ) ) )).
fof(l53_funct_9,axiom,( ! [A] : ( v7_ordinal1(A) => v1_funct_9(k41_valued_1(k1_numbers,k1_numbers,k16_sin_cos),k3_xcmplx_0(k28_sin_cos,k2_xcmplx_0(A,1))) ) )).
fof(l53_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => k5_algstr_0(A,k3_rlvect_1(A,C,k1_rlvect_1(A,D,F)),k3_rlvect_1(A,B,k1_rlvect_1(A,D,E))) = k3_rlvect_1(A,k5_algstr_0(A,C,B),k1_rlvect_1(A,D,k6_xcmplx_0(F,E))) ) ) ) ) ) ) )).
fof(l53_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ! [E] : ( ( ~ v1_abian(E) & m1_subset_1(E,k4_ordinal1) ) => ( ( r1_xxreal_0(C,D) & r1_xxreal_0(D,E) & r1_xxreal_0(E,k3_finseq_1(B)) ) => r2_relset_1(k4_ordinal1,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)) ) ) ) ) ) ) )).
fof(l53_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( r1_xxreal_0(A,k2_nat_1(2,B)) => ( r1_xxreal_0(A,B) | ( ~ ( ~ r1_xxreal_0(A,k2_nat_1(2,B)) & r1_xxreal_0(A,k2_nat_1(3,B)) ) & ~ r1_xxreal_0(A,B) & r1_xxreal_0(A,k2_nat_1(3,B)) ) ) ) & ( ~ ( ~ r1_xxreal_0(A,B) & r1_xxreal_0(A,k2_nat_1(3,B)) ) => ( ~ ( ~ r1_xxreal_0(A,k2_nat_1(2,B)) & r1_xxreal_0(A,k2_nat_1(3,B)) ) & ~ ( ~ r1_xxreal_0(A,B) & r1_xxreal_0(A,k2_nat_1(2,B)) ) ) ) & ( r1_xxreal_0(A,k2_nat_1(3,B)) => ( r1_xxreal_0(A,k2_nat_1(2,B)) | ( ~ ( ~ r1_xxreal_0(A,B) & r1_xxreal_0(A,k2_nat_1(2,B)) ) & ~ r1_xxreal_0(A,B) & r1_xxreal_0(A,k2_nat_1(3,B)) ) ) ) ) ) ) )).
fof(l53_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [E] : ( m1_rewrite1(E,k3_polyred(A,B,C,D)) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ( 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),C) & m1_subset_1(k1_funct_1(E,F),k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) ) ) ) ) ) ) ) ) )).
fof(l53_group_1,axiom,( ! [A] : ( v1_int_1(A) => ~ ( ~ r1_xxreal_0(1,A) & A != k5_numbers & r1_xxreal_0(k5_numbers,A) ) ) )).
fof(l53_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( r1_int_1(B,A) & r1_int_1(C,A) & r1_int_2(B,C) ) => r1_int_1(k3_xcmplx_0(B,C),A) ) ) ) ) )).
fof(l53_jgraph_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( k4_xcmplx_0(k18_euclid(k5_algstr_0(k15_euclid(2),A,B))) = k6_xcmplx_0(k4_xcmplx_0(k18_euclid(A)),k4_xcmplx_0(k18_euclid(B))) & k17_euclid(k5_algstr_0(k15_euclid(2),A,B)) = k6_xcmplx_0(k17_euclid(A),k17_euclid(B)) ) ) ) )).
fof(l53_jordan1a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k4_tarski(C,k3_finseq_1(k1_jordan8(A,B))),k2_matrix_0(k1_jordan8(A,B))) => k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),C,k3_finseq_1(k1_jordan8(A,B)))) = k2_xcmplx_0(k7_pscomp_1(A),k7_xcmplx_0(k6_xcmplx_0(k7_pscomp_1(A),k9_pscomp_1(A)),k1_newton(2,B))) ) ) ) ) )).
fof(l53_jordan3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(C,k3_finseq_1(B)) => k3_finseq_6(A,B,C,C) = k6_finseq_1(A) ) ) ) ) )).
fof(l53_jordan5d,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(l53_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(A,A))))) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => k1_yellow_0(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),a_5_3_lfuzzy_1(A,B,C,D,E)) = k1_yellow_0(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),a_5_4_lfuzzy_1(A,B,C,D,E)) ) ) ) ) ) )).
fof(l53_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_xxreal_0(D,k2_normsp_0(A,k5_algstr_0(A,B,C))) ) ) => B = C ) ) ) ) )).
fof(l53_matrix_9,axiom,( v1_funct_1(k3_finseq_4(k4_ordinal1,1,2,3)) & v1_funct_2(k3_finseq_4(k4_ordinal1,1,2,3),k2_finseq_1(3),k2_finseq_1(3)) & v3_funct_2(k3_finseq_4(k4_ordinal1,1,2,3),k2_finseq_1(3),k2_finseq_1(3)) & v5_matrix_2(k3_finseq_4(k4_ordinal1,1,2,3),3) & m1_subset_1(k3_finseq_4(k4_ordinal1,1,2,3),k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(3),k2_finseq_1(3)))) )).
fof(l53_matrlin2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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,k3_matrix_1(B,A)) = A ) ) )).
fof(l53_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ( v8_o_ring_1(B,A) => v12_o_ring_1(B,A) ) ) ) )).
fof(l53_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( v7_ordinal1(C) => ! [D] : ! [E] : ~ ( D = a_3_1_poset_1(A,B,C) & r2_hidden(E,D) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( ( 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 = k3_funct_2(u1_struct_0(A),u1_struct_0(A),k1_abian(u1_struct_0(A),G,C),k3_yellow_0(A)) ) ) ) ) ) ) ) )).
fof(l53_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_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) ) ) ) )).
fof(l53_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => v2_funct_1(k3_rltopsp1(A,B)) ) ) )).
fof(l53_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => k4_rlvect_1(A,k6_finseq_1(u1_struct_0(A))) = k4_struct_0(A) ) )).
fof(l53_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ( r1_rusub_2(A,B,C) => r1_rusub_2(A,C,B) ) ) ) ) )).
fof(l53_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( r1_tarski(k2_scmbsort,A) => ( k3_compos_1(k1_scmfsa_2,A,k5_numbers) = k6_scmfsa_2(k4_scmfsa_2(2),k4_scmfsa_2(k5_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(k5_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(k5_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(k5_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(k5_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(k5_numbers)) & k3_compos_1(k1_scmfsa_2,A,11) = k11_scmfsa_2(12) ) ) ) )).
fof(l53_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => k3_tarski(A) = k3_tarski(k6_subset_1(k5_scmyciel(k3_tarski(A)),k1_scmyciel(A))) ) )).
fof(l53_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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,k7_binop_2) => k1_funct_1(k1_sin_cos2,A) = k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k22_sin_cos)),k7_xcmplx_0(1,2)),A) ) ) ) )).
fof(l53_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,k7_xcmplx_0(k2_xcmplx_0(1,k3_square_1(k2_xcmplx_0(1,k1_square_1(A)))),A)) ) ) )).
fof(l53_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) ) )).
fof(l53_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => k1_newton(A,3) = k3_xcmplx_0(k3_xcmplx_0(A,A),A) ) )).
fof(l53_toprealb,axiom,( u1_struct_0(k11_toprealb(k9_toprealb)) = k2_struct_0(k11_toprealb(k9_toprealb)) )).
fof(l53_turing_1,axiom,( r2_hidden(k5_numbers,u1_turing_1(k16_turing_1)) & r2_hidden(1,u1_turing_1(k16_turing_1)) )).
fof(l53_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ( u1_struct_0(A) = u1_struct_0(B) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(l53_waybel_7,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ( v5_waybel_7(k1_waybel_4(A),A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) )).
fof(l53_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( r1_xxreal_0(A,B) => r1_xxreal_0(k2_xxreal_3(B),k2_xxreal_3(A)) ) ) ) )).
fof(l53_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(l54_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l54_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_afvect0(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_afvect0(A,B))) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(l54_analmetr,axiom,( ? [A] : ( m1_subset_1(A,u1_struct_0(c4__analmetr)) & ? [B] : ( m1_subset_1(B,u1_struct_0(c4__analmetr)) & r1_analmetr(c4__analmetr,A,B) ) ) )).
fof(l54_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ( k7_arytm_2(A,B) = A => B = k11_arytm_3 ) ) ) )).
fof(l54_borsuk_1,axiom,( k3_pcomps_1(k7_metric_1) = g1_pre_topc(u1_struct_0(k7_metric_1),k2_pcomps_1(k7_metric_1)) )).
fof(l54_borsuk_7,axiom,( m1_subset_1(k8_borsuk_7,u1_struct_0(k15_euclid(3))) )).
fof(l54_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(l54_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ! [B] : ( ( 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) ) ) ) )).
fof(l54_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( ( 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] : ( ( 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] : ( v1_xcmplx_0(G) => ! [H] : ( m1_subset_1(H,u1_struct_0(g1_clvect_1(C,D,E,F))) => ! [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) ) ) ) ) ) ) ) ) ) ) )).
fof(l54_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v3_fintopo6(k6_domain_1(u1_struct_0(A),B),A) ) ) )).
fof(l54_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => r2_relset_1(k4_ordinal1,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),k8_glib_001(A,B,1,k3_finseq_1(B)),B) ) ) )).
fof(l54_groeb_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_ideal_1(E,k12_polynom1(A,C)) & v2_ideal_1(E,k12_polynom1(A,C)) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ~ ( r2_hidden(D,E) & D != k8_polynom1(A,C) & ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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 != k8_polynom1(A,C) ) ) ) ) ) ) ) ) )).
fof(l54_group_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k5_group_1(B,k6_xcmplx_0(A,1),C) = k6_algstr_0(B,k5_group_1(B,A,C),k5_group_1(B,k4_xcmplx_0(1),C)) ) ) ) )).
fof(l54_jgraph_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => k1_square_1(k12_euclid(k5_algstr_0(k15_euclid(2),A,B))) = k2_xcmplx_0(k1_square_1(k4_xcmplx_0(k18_euclid(k5_algstr_0(k15_euclid(2),A,B)))),k1_square_1(k17_euclid(k5_algstr_0(k15_euclid(2),A,B)))) ) ) )).
fof(l54_jgraph_4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k14_euclid(2))) => ( ( r2_hidden(E,k9_metric_1(k14_euclid(2),D,k2_xcmplx_0(k12_euclid(C),1))) & B = F & A = E & D = k4_struct_0(k15_euclid(2)) & k12_euclid(A) = k12_euclid(B) ) => r2_hidden(B,k9_metric_1(k14_euclid(2),D,k2_xcmplx_0(k12_euclid(C),1))) ) ) ) ) ) ) ) )).
fof(l54_jordan1a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k4_tarski(k3_finseq_1(k1_jordan8(A,B)),C),k2_matrix_0(k1_jordan8(A,B))) => k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k3_finseq_1(k1_jordan8(A,B)),C)) = k2_xcmplx_0(k8_pscomp_1(A),k7_xcmplx_0(k6_xcmplx_0(k8_pscomp_1(A),k6_pscomp_1(A)),k1_newton(2,B))) ) ) ) ) )).
fof(l54_jordan3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k3_finseq_6(A,B,C,D) = k4_finseq_5(A,k3_finseq_6(A,B,D,C)) ) ) ) ) )).
fof(l54_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(D) & k1_seq_2(D) = k5_numbers & ! [E] : ( v7_ordinal1(E) => r1_xxreal_0(k2_normsp_0(A,k5_algstr_0(A,B,C)),k9_nat_1(k1_numbers,D,E)) ) ) => B = C ) ) ) ) ) )).
fof(l54_matrix_9,axiom,( v1_funct_1(k3_finseq_4(k4_ordinal1,2,3,1)) & v1_funct_2(k3_finseq_4(k4_ordinal1,2,3,1),k2_finseq_1(3),k2_finseq_1(3)) & v3_funct_2(k3_finseq_4(k4_ordinal1,2,3,1),k2_finseq_1(3),k2_finseq_1(3)) & v5_matrix_2(k3_finseq_4(k4_ordinal1,2,3,1),3) & m1_subset_1(k3_finseq_4(k4_ordinal1,2,3,1),k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(3),k2_finseq_1(3)))) )).
fof(l54_matrtop1,axiom,( v1_xreal_0(1) )).
fof(l54_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v2_rcomp_1(A) => v2_rcomp_1(k3_measure6(A)) ) ) )).
fof(l54_modelc_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(E,A) => ( E = B | k1_funct_1(C,E) = k1_funct_1(D,E) ) ) ) & r1_xxreal_0(B,A) ) => k6_xcmplx_0(k6_series_1(C,A),k1_funct_1(C,B)) = k6_xcmplx_0(k6_series_1(D,A),k1_funct_1(D,B)) ) ) ) ) ) )).
fof(l54_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v9_o_ring_1(B,A) => v13_o_ring_1(B,A) ) ) ) )).
fof(l54_pcs_0,axiom,( ! [A] : ! [B] : k10_xtuple_0(k6_afinsq_1(A,B)) = k2_tarski(A,B) )).
fof(l54_poset_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( v7_ordinal1(D) => ! [E] : ( ( E = a_3_1_poset_1(B,C,D) & r2_hidden(A,E) ) => m1_subset_1(A,u1_struct_0(B)) ) ) ) ) )).
fof(l54_quaterni,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(C)),k1_square_1(D)) = k5_numbers => ( A = k5_numbers & B = k5_numbers & C = k5_numbers & D = k5_numbers ) ) ) ) ) ) )).
fof(l54_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_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) ) ) ) )).
fof(l54_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(k17_ringcat1(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(l54_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ( r1_rlsub_2(A,B,C) => r1_rlsub_2(A,C,B) ) ) ) ) )).
fof(l54_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_finseq_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( k3_finseq_1(B) = k5_numbers => k4_rlvect_1(A,B) = k4_struct_0(A) ) ) ) )).
fof(l54_scmbsort,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(A,k7_card_1(3),k1_scmfsa_2,k5_numbers) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ( r1_tarski(k2_scmbsort,B) => ( k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,1),k4_struct_0(k1_scmfsa_2)) = 1 & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,1),k4_scmfsa_2(k5_numbers)) = k1_funct_1(A,k4_scmfsa_2(k5_numbers)) & k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,1),k5_scmfsa_2(k5_numbers)) = k18_scmfsa_2(A,k5_scmfsa_2(k5_numbers)) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,2),k4_struct_0(k1_scmfsa_2)) = 2 & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,2),k4_scmfsa_2(k5_numbers)) = k1_funct_1(A,k4_scmfsa_2(k5_numbers)) & k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,2),k5_scmfsa_2(k5_numbers)) = k18_scmfsa_2(A,k5_scmfsa_2(k5_numbers)) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,3),k4_struct_0(k1_scmfsa_2)) = 3 & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,3),k4_scmfsa_2(k5_numbers)) = k1_funct_1(A,k4_scmfsa_2(k5_numbers)) & k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,3),k5_scmfsa_2(k5_numbers)) = k18_scmfsa_2(A,k5_scmfsa_2(k5_numbers)) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,4),k4_struct_0(k1_scmfsa_2)) = 4 & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,4),k4_scmfsa_2(k5_numbers)) = k1_funct_1(A,k4_scmfsa_2(k5_numbers)) & k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,4),k5_scmfsa_2(k5_numbers)) = k18_scmfsa_2(A,k5_scmfsa_2(k5_numbers)) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,5),k4_struct_0(k1_scmfsa_2)) = 5 & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,5),k4_scmfsa_2(k5_numbers)) = k1_funct_1(A,k4_scmfsa_2(k5_numbers)) & k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,5),k5_scmfsa_2(k5_numbers)) = k18_scmfsa_2(A,k5_scmfsa_2(k5_numbers)) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,6),k4_struct_0(k1_scmfsa_2)) = 6 & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,6),k4_scmfsa_2(k5_numbers)) = k1_funct_1(A,k4_scmfsa_2(k5_numbers)) & k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,6),k5_scmfsa_2(k5_numbers)) = k18_scmfsa_2(A,k5_scmfsa_2(k5_numbers)) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,7),k4_struct_0(k1_scmfsa_2)) = 7 & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,7),k4_scmfsa_2(k5_numbers)) = k1_funct_1(A,k4_scmfsa_2(k5_numbers)) & k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,7),k5_scmfsa_2(k5_numbers)) = k18_scmfsa_2(A,k5_scmfsa_2(k5_numbers)) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,8),k4_struct_0(k1_scmfsa_2)) = 8 & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,8),k4_scmfsa_2(k5_numbers)) = k1_funct_1(A,k4_scmfsa_2(k5_numbers)) & k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,8),k5_scmfsa_2(k5_numbers)) = k18_scmfsa_2(A,k5_scmfsa_2(k5_numbers)) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,9),k4_struct_0(k1_scmfsa_2)) = 9 & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,9),k4_scmfsa_2(k5_numbers)) = k1_funct_1(A,k4_scmfsa_2(k5_numbers)) & k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,9),k5_scmfsa_2(k5_numbers)) = k18_scmfsa_2(A,k5_scmfsa_2(k5_numbers)) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,10),k4_struct_0(k1_scmfsa_2)) = 10 & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,10),k4_scmfsa_2(k5_numbers)) = k1_funct_1(A,k4_scmfsa_2(k5_numbers)) & k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,10),k5_scmfsa_2(k5_numbers)) = k18_scmfsa_2(A,k5_scmfsa_2(k5_numbers)) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,11),k4_struct_0(k1_scmfsa_2)) = 11 & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,11),k4_scmfsa_2(k5_numbers)) = k1_funct_1(A,k4_scmfsa_2(k5_numbers)) & k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,11),k5_scmfsa_2(k5_numbers)) = k18_scmfsa_2(A,k5_scmfsa_2(k5_numbers)) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,11),k4_scmfsa_2(1)) = k3_finseq_1(k18_scmfsa_2(A,k5_scmfsa_2(k5_numbers))) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,11),k4_scmfsa_2(2)) = k1_funct_1(A,k4_scmfsa_2(k5_numbers)) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,11),k4_scmfsa_2(3)) = k1_funct_1(A,k4_scmfsa_2(k5_numbers)) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,11),k4_scmfsa_2(4)) = k1_funct_1(A,k4_scmfsa_2(k5_numbers)) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,11),k4_scmfsa_2(5)) = k1_funct_1(A,k4_scmfsa_2(k5_numbers)) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,11),k4_scmfsa_2(6)) = k1_funct_1(A,k4_scmfsa_2(k5_numbers)) ) ) ) ) )).
fof(l54_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ! [C] : ( ( 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)))) ) ) ) ) )).
fof(l54_sin_cos2,axiom,( ! [A] : ( ( 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,k7_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,k22_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,k22_sin_cos)),k7_xcmplx_0(1,2))) ) ) )).
fof(l54_toprealb,axiom,( u1_struct_0(k11_toprealb(k10_toprealb)) = k2_struct_0(k11_toprealb(k10_toprealb)) )).
fof(l54_turing_1,axiom,( ! [A] : ( 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] : ! [C] : ! [D] : ( 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),k1_enumset1(k4_xcmplx_0(1),k5_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),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),k8_turing_1(k16_turing_1,A)))) ) ) ) )).
fof(l54_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ( u1_struct_0(A) = u1_struct_0(B) => k6_yellow_6(A) = k6_yellow_6(B) ) ) ) )).
fof(l54_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,A) & r1_xxreal_0(k5_numbers,k6_xcmplx_0(A,B)) ) ) ) )).
fof(l55_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ~ ( ~ ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) & ! [B] : ( m1_subset_1(B,u1_incsp_1(k14_afproj(A))) => ! [C] : ( m1_subset_1(C,u2_incsp_1(k14_afproj(A))) => r1_incsp_1(k14_afproj(A),B,C) ) ) ) ) )).
fof(l55_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) )).
fof(l55_analmetr,axiom,( r1_analmetr(c4__analmetr,c5__analmetr,c6__analmetr) )).
fof(l55_arytm_2,axiom,( ! [A] : ( m2_subset_1(A,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) => ~ ( A != k11_arytm_3 & r1_tarski(A,B) & A != B & ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) => k5_arytm_2(A,C) != B ) ) ) ) )).
fof(l55_borsuk_7,axiom,( m1_subset_1(k8_borsuk_7,u1_struct_0(k8_toprealb(k1_nat_1(2,1)))) )).
fof(l55_card_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_wellord2(A,B) => A = B ) ) ) )).
fof(l55_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(l55_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ( m2_subset_1(k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k5_numbers,1,k5_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(k4_ordinal1,k4_ordinal1,k4_ordinal1,k5_numbers,1,k5_numbers)) = k4_struct_0(k9_int_3(A)) ) ) ) ) )).
fof(l55_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(l55_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ~ 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)),k15_fomodel2(B,C),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0))),k20_fomodel2(B,C,k22_fomodel2(B,A,C))) = k2_zfmisc_1(k15_fomodel2(B,C),k28_fomodel2(B,A)) ) ) ) )).
fof(l55_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v4_fomodel1(B,A) & m1_subset_1(B,k1_fomodel1(A)) ) => ! [C] : ( ( 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)))) ) ) ) ) )).
fof(l55_funct_9,axiom,( ! [A] : ( v7_ordinal1(A) => v1_funct_9(k41_valued_1(k1_numbers,k1_numbers,k18_sin_cos),k3_xcmplx_0(k28_sin_cos,k2_xcmplx_0(A,1))) ) )).
fof(l55_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( 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)) ) ) ) ) )).
fof(l55_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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] : ( ( 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] : ( ( 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_polynom1(k15_pre_poly(A),C,D)) & r2_hidden(G,k3_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) ) ) ) ) ) ) ) ) ) )).
fof(l55_group_1,axiom,( ! [A] : ( v1_int_1(A) => ~ ( ~ r1_xxreal_0(k5_numbers,A) & A != k4_xcmplx_0(1) & r1_xxreal_0(k4_xcmplx_0(1),A) ) ) )).
fof(l55_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ v3_lattice3(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A))) ) )).
fof(l55_int_5,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => m1_subset_1(k2_wsierp_1(A),k4_ordinal1) ) )).
fof(l55_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( 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)) ) ) ) ) )).
fof(l55_matrix_9,axiom,( v1_funct_1(k3_finseq_4(k4_ordinal1,3,1,2)) & v1_funct_2(k3_finseq_4(k4_ordinal1,3,1,2),k2_finseq_1(3),k2_finseq_1(3)) & v3_funct_2(k3_finseq_4(k4_ordinal1,3,1,2),k2_finseq_1(3),k2_finseq_1(3)) & v5_matrix_2(k3_finseq_4(k4_ordinal1,3,1,2),3) & m1_subset_1(k3_finseq_4(k4_ordinal1,3,1,2),k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(3),k2_finseq_1(3)))) )).
fof(l55_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ~ ( r1_tarski(D,k1_relset_1(A,F)) & r1_mesfunc1(A,B,F,D) & D = k1_xboole_0 & ! [G] : ( v7_ordinal1(G) => r1_mesfunc2(A,B,k4_mesfunc5(A,k6_numbers,E,G)) ) & ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k4_ordinal1,k6_numbers) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ~ ( ! [H] : ( v7_ordinal1(H) => k1_mesfunc9(G,H) = k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,E,H),D)) ) & v1_mesfunc9(G) & k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,F,D)) = k3_mesfunc9(G) ) ) ) ) ) ) ) ) ) )).
fof(l55_mod_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => r2_hidden(u1_struct_0(k18_mod_2),A) ) )).
fof(l55_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(l55_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(k7_normform(A))) => ! [C] : ( m1_subset_1(C,k5_finsub_1(k7_normform(A))) => ( ! [D] : ( 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) ) ) ) )).
fof(l55_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(l55_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_oppcat_1(C,k2_oppcat_1(B),A) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k3_funct_2(u4_struct_0(B),u4_struct_0(A),k9_oppcat_1(B,A,C),k4_cat_1(B,D)) = k4_cat_1(A,k3_funct_2(u1_struct_0(B),u1_struct_0(A),k7_cat_1(B,A,k9_oppcat_1(B,A,C)),D)) ) ) ) ) )).
fof(l55_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( v7_ordinal1(C) => ! [D] : ( D = a_3_1_poset_1(A,B,C) => ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) )).
fof(l55_quofield,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(l55_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_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) ) ) ) )).
fof(l55_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(k17_ringcat1(A))) => ! [C] : ( m1_subset_1(C,u4_struct_0(k17_ringcat1(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l55_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rlsub_1(C,A) => ( r1_struct_0(C,B) <=> k3_rlsub_1(A,B,C) = u1_struct_0(C) ) ) ) ) )).
fof(l55_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_rmod_2(D,A,B) => ( r1_struct_0(D,C) <=> k3_rmod_2(A,B,C,D) = u1_struct_0(D) ) ) ) ) ) )).
fof(l55_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & ? [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l55_scmbsort,axiom,( ~ r4_scmfsa7b(k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(4,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(5,1)),k5_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers)),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k4_compos_1(k1_scmfsa_2))),k4_scmfsa_2(k1_nat_1(1,1))) )).
fof(l55_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( 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 ) ) ) )).
fof(l55_tmap_1,axiom,( ! [A] : ( 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))) ) )).
fof(l55_topreal6,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ( D = k9_metric_1(A,B,C) => v3_pre_topc(k3_subset_1(u1_struct_0(k3_pcomps_1(A)),D),k3_pcomps_1(A)) ) ) ) ) ) )).
fof(l55_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ! [D] : ( ( ~ v2_struct_0(D) & v4_orders_2(D) & v7_waybel_0(D) & l1_waybel_0(D,A) ) => ! [E] : ( ( ~ 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) ) ) ) ) ) )).
fof(l55_wsierp_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r1_int_1(A,B) <=> r1_int_1(A,k1_int_2(B)) ) ) ) )).
fof(l56_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k13_afproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) => ! [D] : ( m1_subset_1(D,u2_incsp_1(k13_afproj(A))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(l56_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(l56_algstr_4,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => v2_funct_1(k16_algstr_4(A,B)) ) )).
fof(l56_analmetr,axiom,( ~ 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] : ( m1_subset_1(A,u1_struct_0(k2_analmetr(c4__analmetr,c5__analmetr,c6__analmetr))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_analmetr(c4__analmetr,c5__analmetr,c6__analmetr))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_analmetr(c4__analmetr,c5__analmetr,c6__analmetr))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_analmetr(c4__analmetr,c5__analmetr,c6__analmetr))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_analmetr(c4__analmetr,c5__analmetr,c6__analmetr))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_analmetr(c4__analmetr,c5__analmetr,c6__analmetr))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k2_analmetr(c4__analmetr,c5__analmetr,c6__analmetr))) => ! [H] : ( 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] : ( m1_subset_1(A,u1_struct_0(k2_analmetr(c4__analmetr,c5__analmetr,c6__analmetr))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_analmetr(c4__analmetr,c5__analmetr,c6__analmetr))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_analmetr(c4__analmetr,c5__analmetr,c6__analmetr))) => ? [D] : ( 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 ) ) ) ) )).
fof(l56_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ( r1_arytm_2(A,B) => r1_tarski(k3_arytm_2(A),k3_arytm_2(B)) ) ) ) )).
fof(l56_asympt_1,axiom,( k5_series_1(2,12) = 4096 )).
fof(l56_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_c0sp2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_c0sp2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k11_c0sp1(u1_struct_0(A)))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l56_card_1,axiom,( ! [A] : ( v3_ordinal1(A) => ( v1_finset_1(A) <=> r2_hidden(A,k4_ordinal1) ) ) )).
fof(l56_catalan2,axiom,( v7_ordinal1(k5_numbers) )).
fof(l56_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( k9_xtuple_0(B) = k10_cgames_1(A) & ! [C] : ( 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] : ( v2_cgames_1(C) => ( r2_hidden(C,k9_xtuple_0(B)) => k1_funct_1(B,C) = k13_cgames_1(C) ) ) ) ) ) )).
fof(l56_dickson,axiom,( ! [A] : ( ( 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(k4_yellow_1(k1_xboole_0,A)) & v3_dickson(k4_yellow_1(k1_xboole_0,A)) & v4_dickson(k4_yellow_1(k1_xboole_0,A)) & v5_orders_2(k4_yellow_1(k1_xboole_0,A)) ) ) )).
fof(l56_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ~ 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)),k15_fomodel2(B,C),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0))),k18_fomodel2(B,C,k22_fomodel2(B,A,C))) = k2_zfmisc_1(k15_fomodel2(B,C),k27_fomodel2(B,A)) ) ) ) )).
fof(l56_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v4_fomodel1(B,A) & m1_subset_1(B,k1_fomodel1(A)) ) => ! [C] : ( ( v4_fomodel1(C,A) & m1_subset_1(C,k1_fomodel1(A)) ) => ! [D] : ( ( 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] : ( 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))) & k29_fomodel2(A,D) = k29_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 ) ) ) ) ) )).
fof(l56_funct_6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ~ ( B != k1_xboole_0 & A != k1_xboole_0 & ~ r2_wellord2(k4_card_3(k8_funct_6(A,B)),k1_funct_2(A,k4_card_3(B))) ) ) )).
fof(l56_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r1_xxreal_0(C,D) => ( v1_abian(C) | r2_relset_1(k4_ordinal1,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)) ) ) ) ) ) ) )).
fof(l56_group_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k5_group_1(B,k2_xcmplx_0(A,1),C) = k6_algstr_0(B,k5_group_1(B,A,C),k5_group_1(B,1,C)) ) ) ) )).
fof(l56_jgraph_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( k17_euclid(k5_algstr_0(k15_euclid(2),A,B)) = k6_xcmplx_0(k17_euclid(A),k17_euclid(B)) & k4_xcmplx_0(k18_euclid(k5_algstr_0(k15_euclid(2),A,B))) = k6_xcmplx_0(k4_xcmplx_0(k18_euclid(A)),k4_xcmplx_0(k18_euclid(B))) ) ) ) )).
fof(l56_jordan3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(l56_jordan6,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ~ r1_xxreal_0(1,E) & k1_funct_1(A,E) = D ) ) ) ) ) ) ) )).
fof(l56_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( v1_xreal_0(B) => k1_measure6(A,B) = a_2_0_measure6(A,B) ) ) )).
fof(l56_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,k6_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,k6_numbers,E,D) & ! [G] : ( v7_ordinal1(G) => ( r1_mesfunc2(A,B,k4_mesfunc5(A,k6_numbers,E,G)) & v6_supinf_2(k4_mesfunc5(A,k6_numbers,E,G)) ) ) & ! [G] : ( 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] : ( ( v1_funct_1(G) & v1_funct_2(G,k4_ordinal1,k6_numbers) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ~ ( ! [H] : ( v7_ordinal1(H) => k1_mesfunc9(G,H) = k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,E,H),D)) ) & v1_mesfunc9(G) & k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,F,D)) = k3_mesfunc9(G) ) ) ) ) ) ) ) ) ) )).
fof(l56_modelc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_modelc_1(A) & l2_modelc_1(A) ) => ! [B] : ( ( 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] : ( ( 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,k5_numbers) ) ) ) )).
fof(l56_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ( v2_nattra_1(A) => u4_struct_0(A) = k3_tarski(a_1_1_nattra_1(A)) ) ) )).
fof(l56_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l56_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_oppcat_1(C,k2_oppcat_1(B),A) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ( k3_funct_2(u1_struct_0(B),u1_struct_0(A),k7_cat_1(B,A,k9_oppcat_1(B,A,C)),k3_graph_1(B,D)) = k3_graph_1(A,k3_funct_2(u4_struct_0(B),u4_struct_0(A),k9_oppcat_1(B,A,C),D)) & k3_funct_2(u1_struct_0(B),u1_struct_0(A),k7_cat_1(B,A,k9_oppcat_1(B,A,C)),k4_graph_1(B,D)) = k4_graph_1(A,k3_funct_2(u4_struct_0(B),u4_struct_0(A),k9_oppcat_1(B,A,C),D)) ) ) ) ) ) )).
fof(l56_pnproc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) ) => ! [D] : ( ( 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,k61_valued_1(D,k3_finseq_1(A)))),k4_finseq_1(k7_finseq_1(A,B))) ) ) ) ) ) )).
fof(l56_polynom8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(B,k5_numbers) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k6_matrix_3(A,k4_matrix_3(A,k3_matrix_1(A,k2_nat_1(2,B)),k4_polynom8(k2_nat_1(2,B),A,k13_polynom3(A,C,D))),k1_polynom8(A,k2_nat_1(2,B))) = k6_matrix_3(A,k4_polynom8(k2_nat_1(2,B),A,k13_polynom3(A,C,D)),k1_polynom8(A,k2_nat_1(2,B))) ) ) ) ) ) )).
fof(l56_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(l56_quofield,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(l56_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k17_ringcat1(A))) => ! [C] : ( m2_ringcat1(C,k9_ringcat1(A)) => ( B = C => ! [D] : ( m1_cat_1(D,k17_ringcat1(A),B,B) => ( D = k13_ringcat1(k9_ringcat1(A),C) => ! [E] : ( m1_subset_1(E,u1_struct_0(k17_ringcat1(A))) => ( ( k2_cat_1(k17_ringcat1(A),B,E) != k1_xboole_0 => ! [F] : ( 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] : ( m1_cat_1(F,k17_ringcat1(A),E,B) => k1_cat_1(k17_ringcat1(A),F,D) = F ) ) ) ) ) ) ) ) ) ) )).
fof(l56_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v3_pre_topc(B,A) => v3_pre_topc(k5_rusub_4(A,B,C),A) ) ) ) ) )).
fof(l56_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( C = k3_rlvect_1(B,D,E) <=> D = k5_algstr_0(B,C,E) ) ) ) ) ) ) )).
fof(l56_scmbsort,axiom,( v1_scmfsa7b(k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(4,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(5,1)),k5_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers)),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k4_compos_1(k1_scmfsa_2))))) & v2_scm_halt(k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(4,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(5,1)),k5_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers)),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k4_compos_1(k1_scmfsa_2))))) )).
fof(l56_scmpds_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ~ ( ~ ( ~ r2_hidden(A,k1_tarski(k3_xtuple_0(k5_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) != k5_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 ) ) )).
fof(l56_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ r2_semi_af1(A,B,C,D,E) ) ) ) ) ) ) )).
fof(l56_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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,k7_binop_2) => ( r1_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k22_sin_cos)),k7_xcmplx_0(1,2)),A) & k1_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k22_sin_cos)),k7_xcmplx_0(1,2)),A) = k3_xcmplx_0(k7_xcmplx_0(1,2),k1_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k22_sin_cos)),A)) ) ) ) ) )).
fof(l56_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_topalg_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_topalg_1(A,B))) => ! [E] : ( m1_borsuk_2(E,A,B,B) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(l56_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m2_finseq_1(B,k1_topalg_6(A)) => ! [C] : ( 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)) ) ) ) )).
fof(l56_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_vectsp_4(D,A,B) => ( r1_struct_0(D,C) <=> k3_vectsp_4(A,B,C,D) = u1_struct_0(D) ) ) ) ) ) )).
fof(l56_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & ? [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l56_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & v4_orders_2(D) & v7_waybel_0(D) & l1_waybel_0(D,B) ) => ( C = D => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(l56_wsierp_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => k5_int_1(k3_xcmplx_0(A,B),B) = k5_numbers ) ) )).
fof(l57_afinsq_2,axiom,( ! [A] : ( ( 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) ) )).
fof(l57_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(k13_afproj(A))) => ? [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) & ? [D] : ( m1_subset_1(D,u1_incsp_1(k13_afproj(A))) & ? [E] : ( 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 ) ) ) ) ) )).
fof(l57_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v13_algstr_0(k5_afvect0(A,B)) ) ) )).
fof(l57_algstr_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( k1_relset_1(k11_algstr_4(A,1),k16_algstr_4(A,1)) = A & ! [B] : ( r2_hidden(B,A) => k1_funct_1(k16_algstr_4(A,1),B) = k4_tarski(B,1) ) ) ) )).
fof(l57_anproj_2,axiom,( ? [A] : ( ~ v1_xboole_0(A) & ? [B] : ( m1_subset_1(B,A) & ? [C] : ( m1_subset_1(C,A) & ? [D] : ( m1_subset_1(D,A) & ? [E] : ( 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 ) ) ) ) ) )).
fof(l57_asympt_1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( r1_xxreal_0(3,A) & r1_xxreal_0(k1_square_1(A),k1_nat_1(k3_xcmplx_0(2,A),1)) ) ) )).
fof(l57_bcialg_1,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k7_bcialg_1(A,B)) => k1_bcialg_1(A,B,C) = k4_struct_0(A) ) ) ) )).
fof(l57_borsuk_7,axiom,( m1_subset_1(k9_borsuk_7,u1_struct_0(k15_euclid(3))) )).
fof(l57_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_c0sp2(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l57_compl_sp,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(l57_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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,k8_complex1(B)),k12_csspace(A,D,D)),k3_xcmplx_0(k3_xcmplx_0(B,k8_complex1(C)),k12_csspace(A,D,E))),k3_xcmplx_0(k3_xcmplx_0(k8_complex1(B),C),k12_csspace(A,E,D))),k3_xcmplx_0(k3_xcmplx_0(C,k8_complex1(C)),k12_csspace(A,E,E))) ) ) ) ) ) )).
fof(l57_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( 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)),k4_ordinal1,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))) ) ) ) )).
fof(l57_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_finset_1(k8_euclid_7(A)) & k1_card_1(k8_euclid_7(A)) = A ) ) )).
fof(l57_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) ) => ! [F] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(l57_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v4_fomodel1(B,A) & m1_subset_1(B,k1_fomodel1(A)) ) => ! [C] : ( ( v4_fomodel1(C,A) & m1_subset_1(C,k1_fomodel1(A)) ) => ! [D] : ( ( 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))) ) => k29_fomodel2(A,D) = k29_fomodel2(A,k24_fomodel3(A,B,C,D)) ) ) ) ) )).
fof(l57_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k36_gfacirc1(A,B,C) != k4_tarski(D,k3_twoscomp) )).
fof(l57_funct_9,axiom,( v1_funct_9(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),k28_sin_cos) )).
fof(l57_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ! [E] : ( ( ~ v1_abian(E) & m1_subset_1(E,k4_ordinal1) ) => ( ( 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(k4_ordinal1,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)) ) ) ) ) ) ) )).
fof(l57_jgraph_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => k1_square_1(k12_euclid(k5_algstr_0(k15_euclid(2),A,B))) = k2_xcmplx_0(k1_square_1(k17_euclid(k5_algstr_0(k15_euclid(2),A,B))),k1_square_1(k4_xcmplx_0(k18_euclid(k5_algstr_0(k15_euclid(2),A,B))))) ) ) )).
fof(l57_jgraph_4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(k1_square_1(1),k1_square_1(k7_xcmplx_0(k4_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(C,k12_euclid(A)),B)),k6_xcmplx_0(1,B)))) & r1_xxreal_0(k4_xcmplx_0(k5_numbers),k4_xcmplx_0(k3_square_1(k6_xcmplx_0(1,k1_square_1(k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(C,k12_euclid(A)),B),k6_xcmplx_0(1,B))))))) ) ) ) ) )).
fof(l57_jordan3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l57_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,B,A,A) & m2_finseq_1(C,k3_finseq_2(B)) ) => ( v2_matrixj1(k4_matrixj1(B,C),B) & m2_finseq_1(k4_matrixj1(B,C),k3_finseq_2(k3_finseq_2(B))) ) ) ) ) )).
fof(l57_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( m1_matrlin(D,A,B) => ! [E] : ( m1_matrlin(E,A,C) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(A),k3_finseq_1(D),k3_finseq_1(E)) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(A))) ) => ~ ( ~ r1_xxreal_0(k3_finseq_1(D),k5_numbers) & ~ r1_xxreal_0(k3_finseq_1(E),k5_numbers) & k11_ranknull(A,B,C,k4_matrlin2(A,B,C,D,E,F)) != k6_xcmplx_0(k3_finseq_1(D),k8_matrix13(A,F)) ) ) ) ) ) ) ) )).
fof(l57_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ( ( r2_hidden(k1_relset_1(A,D),B) & ! [F] : ( r2_hidden(F,k1_relset_1(A,D)) => k1_funct_1(D,F) = E ) ) => r1_mesfunc2(A,B,D) ) ) ) ) ) ) )).
fof(l57_mod_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) ) => ( ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(l57_modelc_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v10_modelc_1(B) & l2_modelc_1(B) ) => ! [C] : ( ( 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] : ( ( 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,k1_nat_1(A,1)) => r2_modelc_1(B,C,D,A) ) ) ) ) ) )).
fof(l57_nat_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ( ( r1_xxreal_0(k1_newton(C,B),k2_nat_1(2,A)) & k3_finseq_1(D) = k2_nat_1(2,A) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k4_finseq_1(D)) => k1_funct_1(D,E) = k6_xcmplx_0(k1_int_1(k7_xcmplx_0(k2_nat_1(2,A),k1_newton(C,E))),k3_xcmplx_0(2,k1_int_1(k7_xcmplx_0(A,k1_newton(C,E))))) ) ) ) => ( r1_xxreal_0(k1_newton(C,k1_nat_1(B,1)),k2_nat_1(2,A)) | r1_xxreal_0(k18_rvsum_1(D),B) ) ) ) ) ) ) )).
fof(l57_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v3_nattra_1(A) => k2_cat_1(A,B,B) = k1_tarski(k4_cat_1(A,B)) ) ) ) )).
fof(l57_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l57_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( ( r6_relat_2(A,B) & r1_tarski(C,B) ) => r6_relat_2(A,C) ) ) )).
fof(l57_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m2_orders_1(B,k1_orders_1(u1_struct_0(A)),k6_partfun1(k1_orders_1(u1_struct_0(A)))) => m1_subset_1(k3_tarski(k4_orders_2(A,B)),k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(l57_pnproc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) ) => ( r1_tarski(B,A) => r1_xboole_0(B,k61_valued_1(C,k3_finseq_1(A))) ) ) ) ) )).
fof(l57_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( v7_ordinal1(C) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(l57_real_3,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l57_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( ( v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => v3_pre_topc(k7_rusub_4(A,C,B),A) ) ) ) )).
fof(l57_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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,k7_binop_2) => k1_funct_1(k3_sin_cos2,A) = k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k22_sin_cos)),k7_xcmplx_0(1,2)),A) ) ) ) )).
fof(l57_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(l57_wsierp_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( k5_int_1(A,C) = k5_int_1(B,C) => k5_int_1(k6_xcmplx_0(A,B),C) = k5_numbers ) ) ) ) )).
fof(l57_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(l57_yellow_9,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : ( 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)))) ) ) )).
fof(l58_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k13_afproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) => ? [D] : ( 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) ) ) ) ) )).
fof(l58_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(10,A) & r1_xxreal_0(k2_power(2,k6_xcmplx_0(A,1)),k1_square_1(k2_nat_1(2,A))) ) ) )).
fof(l58_descip_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k6_margrel1) => r1_xxreal_0(k3_xcmplx_0(A,B),A) ) ) )).
fof(l58_euclid,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l58_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ! [E] : ! [F] : r1_xboole_0(k2_msafree2(k37_gfacirc1(A,B,C)),k3_msafree2(k25_gfacirc1(D,E,F))) ) ) ) )).
fof(l58_funct_9,axiom,( ! [A] : ( v7_ordinal1(A) => v1_funct_9(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),k3_xcmplx_0(k28_sin_cos,k2_xcmplx_0(A,1))) ) )).
fof(l58_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( r1_xxreal_0(C,k3_finseq_1(B)) => k3_finseq_1(k8_glib_001(A,B,1,C)) = C ) ) ) ) )).
fof(l58_jordan3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l58_matrix13,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & v1_setfam_1(B) & m1_subset_1(B,k1_zfmisc_1(k4_ordinal1)) ) => ( r1_tarski(A,B) => k1_card_1(A) = k5_card_1(k8_relat_1(k5_matrix13(B),A)) ) ) )).
fof(l58_modelc_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v10_modelc_1(B) & l2_modelc_1(B) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(l58_mycielsk,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( k9_xtuple_0(A) = k4_ordinal1 & k1_funct_1(A,k5_numbers) = k5_mycielsk(2) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_mycielsk(D,k7_nat_d(k3_xcmplx_0(3,k1_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,k1_newton(2,C)),1),D) ) ) ) & k9_xtuple_0(B) = k4_ordinal1 & k1_funct_1(B,k5_numbers) = k5_mycielsk(2) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_mycielsk(D,k7_nat_d(k3_xcmplx_0(3,k1_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,k1_newton(2,C)),1),D) ) ) ) ) => A = B ) ) ) )).
fof(l58_nat_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ( r1_xxreal_0(3,A) => ( ( ~ r1_xxreal_0(B,k2_nat_1(2,A)) => k11_nat_3(k4_newton(A,k2_nat_1(2,A)),B) = k5_numbers ) & ( r1_xxreal_0(B,k2_nat_1(2,A)) => ( r1_xxreal_0(B,A) | r1_xxreal_0(k11_nat_3(k4_newton(A,k2_nat_1(2,A)),B),1) ) ) & ( r1_xxreal_0(B,A) => ( r1_xxreal_0(B,k7_xcmplx_0(k2_nat_1(2,A),3)) | k11_nat_3(k4_newton(A,k2_nat_1(2,A)),B) = k5_numbers ) ) & ( r1_xxreal_0(B,k7_xcmplx_0(k2_nat_1(2,A),3)) => ( r1_xxreal_0(B,k3_square_1(k2_nat_1(2,A))) | r1_xxreal_0(k11_nat_3(k4_newton(A,k2_nat_1(2,A)),B),1) ) ) & ( r1_xxreal_0(B,k3_square_1(k2_nat_1(2,A))) => r1_xxreal_0(k1_newton(B,k11_nat_3(k4_newton(A,k2_nat_1(2,A)),B)),k2_nat_1(2,A)) ) ) ) ) ) )).
fof(l58_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ( v10_o_ring_1(B,A) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(C,k3_finseq_1(B)) => ( C = k5_numbers | v13_o_ring_1(k7_partfun1(u1_struct_0(A),B,C),A) ) ) ) ) ) ) )).
fof(l58_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m2_orders_1(B,k1_orders_1(u1_struct_0(A)),k6_partfun1(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))) ) ) ) )).
fof(l58_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(l58_quaterni,axiom,( k6_quaterni(c1__quaterni,c2__quaterni,c2__quaterni,c2__quaterni) = 1 )).
fof(l58_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => v4_pre_topc(k5_rusub_4(A,B,C),A) ) ) ) )).
fof(l58_scmbsort,axiom,( ~ r4_scmfsa7b(k3_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))),k16_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(4,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(5,1)),k5_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers)),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k4_compos_1(k1_scmfsa_2))))),k4_scmfsa_2(k1_nat_1(k5_numbers,1))) )).
fof(l58_scmisort,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ( k1_funct_1(A,k4_scmfsa_2(k1_nat_1(k5_numbers,1))) = k6_xcmplx_0(k3_finseq_1(k18_scmfsa_2(A,k5_scmfsa_2(k5_numbers))),1) => ( r2_classes1(k18_scmfsa_2(A,k5_scmfsa_2(k5_numbers)),k18_scmfsa_2(k1_scmfsa6b(k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(k5_numbers,1)),k3_scmfsa6a(k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k16_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1)))),k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(3,1)))),k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))))),k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers)))))),A,B),k5_scmfsa_2(k5_numbers))) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(D,k3_finseq_1(k18_scmfsa_2(A,k5_scmfsa_2(k5_numbers)))) ) => ( r1_xxreal_0(D,C) | ! [E] : ( v1_int_1(E) => ! [F] : ( v1_int_1(F) => ( ( E = k1_funct_1(k18_scmfsa_2(k1_scmfsa6b(k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(k5_numbers,1)),k3_scmfsa6a(k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k16_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1)))),k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(3,1)))),k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))))),k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers)))))),A,B),k5_scmfsa_2(k5_numbers)),C) & F = k1_funct_1(k18_scmfsa_2(k1_scmfsa6b(k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(k5_numbers,1)),k3_scmfsa6a(k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k16_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1)))),k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(3,1)))),k2_scmfsa_9(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(5,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(4,1)),k11_compos_1(k1_scmfsa_2,k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(1,1)))),k6_scmfsa6a(k7_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))))))),k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(1,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers)))))),A,B),k5_scmfsa_2(k5_numbers)),D) ) => r1_xxreal_0(F,E) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l58_sin_cos2,axiom,( ! [A] : ( ( 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,k7_binop_2) => r2_relset_1(k1_numbers,k1_numbers,k3_sin_cos2,k26_valued_1(k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,k22_sin_cos)),k7_xcmplx_0(1,2))) ) ) )).
fof(l58_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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),k3_polynom1(k15_pre_poly(A),C,k6_termord(A,B,C,D))) ) ) ) ) )).
fof(l58_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( r1_vectsp_5(A,B,C,D) => r1_vectsp_5(A,B,D,C) ) ) ) ) ) )).
fof(l58_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(l58_waybel23,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( v2_waybel23(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ( r2_hidden(k3_yellow_0(A),B) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r1_waybel_3(A,C,D) & ! [E] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( ~ r3_orders_2(A,D,C) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,B) & ~ r3_orders_2(A,E,C) & r3_orders_2(A,E,D) ) ) ) ) ) ) ) ) ) )).
fof(l58_wsierp_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( k5_int_1(A,B) = k5_numbers => ( B = k5_numbers | r1_int_1(B,A) ) ) ) ) )).
fof(l58_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r1_tarski(A,B) & r2_xboole_0(B,C) ) => r2_xboole_0(A,C) ) )).
fof(l58_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k5_xcmplx_0(k7_xcmplx_0(A,B)) = k7_xcmplx_0(B,A) ) ) )).
fof(l59_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(k13_afproj(A))) => ! [C] : ( m1_subset_1(C,u2_incsp_1(k13_afproj(A))) => ~ ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) & ! [D] : ( 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) ) ) ) ) ) ) )).
fof(l59_asympt_1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( r1_xxreal_0(9,A) & r1_xxreal_0(k2_nat_1(2,k5_series_1(A,6)),k5_series_1(k1_nat_1(A,1),6)) ) ) )).
fof(l59_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k3_tarski(B)))) => ~ ( ! [D] : ( r2_hidden(D,C) => v1_finset_1(k1_xtuple_0(D)) ) & ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(k2_xboole_0(D,E),A) => ! [F] : ! [G] : ( ( r2_hidden(k4_tarski(D,F),C) & r2_hidden(k4_tarski(E,G),C) ) => r2_hidden(k2_tarski(F,G),B) ) ) ) ) & ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(k2_xboole_0(D,E),A) => ! [F] : ( ( r2_hidden(k4_tarski(D,F),C) & r2_hidden(k4_tarski(E,F),C) ) => D = E ) ) ) ) & ! [D] : ( ( 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] : ( m1_subset_1(E,A) => k3_funct_2(A,B,D,E) = k7_relat_1(C,k3_cohsp_1(A,E)) ) ) ) ) ) ) ) )).
fof(l59_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r2_hidden(D,k1_relset_1(k4_ordinal1,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) ) ) ) ) ) )).
fof(l59_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( ( v2_funct_1(B) & v1_msscyc_1(B,A) & m2_graph_1(B,A) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(l59_group_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(l59_integra8,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(l59_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(B,k2_finseq_1(A)) & r2_hidden(C,k2_finseq_1(A)) & ~ r1_xxreal_0(C,B) & ! [D] : ( v1_finset_1(D) => ! [E] : ( 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) = k3_matrix_2(A) & ? [F] : ( v1_funct_1(F) & v1_funct_2(F,E,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(E,D))) & ? [G] : ( m1_matrix_2(G,k3_matrix_2(A)) & v4_matrix_2(G,k2_matrix_2(k3_matrix_2(A))) & k1_funct_1(G,B) = C & k9_xtuple_0(F) = E & v3_funct_2(F,E,D) & ! [H] : ( m1_matrix_2(H,k3_matrix_2(A)) => ( r2_hidden(H,E) => k1_funct_1(F,H) = k1_partfun1(k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),G,H) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l59_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(A),B) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( v1_xreal_0(E) => k9_subset_1(A,C,k15_mesfunc1(A,D,E)) = k15_mesfunc1(A,k2_partfun1(A,k6_numbers,D,C),E) ) ) ) ) ) )).
fof(l59_modelc_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v10_modelc_1(B) & l2_modelc_1(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( v1_modelc_1(F) & m2_finseq_1(F,k4_ordinal1) ) => ( r1_xxreal_0(k3_finseq_1(F),A) => k1_funct_1(D,F) = k1_funct_1(E,F) ) ) ) ) ) ) ) ) )).
fof(l59_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ( v4_nattra_1(A) => r1_tarski(u4_struct_0(A),a_1_0_nattra_1(A)) ) ) )).
fof(l59_ordeq_01,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => k1_funct_1(B,C) = k6_xcmplx_0(C,A) ) => ! [C] : ( v1_xreal_0(C) => ( r1_fdiff_1(B,C) & k1_fdiff_1(B,C) = 1 ) ) ) ) ) )).
fof(l59_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v7_ordinal1(E) => ( ( C = k1_funct_1(k10_poset_1(A),B) & D = k3_funct_2(u1_struct_0(A),u1_struct_0(A),k1_abian(u1_struct_0(A),B,E),k3_yellow_0(A)) ) => r3_orders_2(A,D,C) ) ) ) ) ) ) )).
fof(l59_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ( r1_xxreal_0(k5_numbers,A) => r1_xxreal_0(k5_numbers,k3_prepower(A,B)) ) ) ) )).
fof(l59_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k4_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)) = B ) ) )).
fof(l59_scmbsort,axiom,( v1_scmfsa7b(k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(k5_numbers,1)),k3_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))),k16_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(4,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(5,1)),k5_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers)),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k4_compos_1(k1_scmfsa_2))))))) & v2_scm_halt(k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(k5_numbers,1)),k3_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))),k16_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(4,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(5,1)),k5_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers)),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k4_compos_1(k1_scmfsa_2))))))) )).
fof(l59_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(l59_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( 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,k3_polynom1(k15_pre_poly(A),C,D)) => ( E = k3_termord(A,B,C,D) | r2_hidden(E,k3_polynom1(k15_pre_poly(A),C,k6_termord(A,B,C,D))) ) ) ) ) ) ) ) )).
fof(l59_trees_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ r1_xxreal_0(k3_finseq_1(B),A) => ( r2_hidden(k1_nat_1(A,1),k1_relset_1(k4_ordinal1,B)) & r2_hidden(k1_funct_1(B,k1_nat_1(A,1)),k10_xtuple_0(B)) ) ) ) ) )).
fof(l59_waybel11,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( ( D = E & r2_lattice3(A,C,D) ) => r2_lattice3(B,C,E) ) ) ) ) ) ) )).
fof(l59_waybel23,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( ~ r3_orders_2(A,D,C) & ! [E] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( ~ r3_orders_2(A,D,C) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,B) & ~ r3_orders_2(A,E,C) & r1_waybel_3(A,E,D) ) ) ) ) ) ) ) ) )).
fof(l59_waybel_4,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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,k1_yellow_1(k7_waybel_0(A))) ) ) )).
fof(l59_wsierp_1,axiom,( ! [A] : ( v1_int_1(A) => ( ( ~ r1_xxreal_0(A,1) => ( ~ r1_xxreal_0(k3_square_1(A),1) & ~ r1_xxreal_0(A,k3_square_1(A)) ) ) & ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) & ~ ( ~ r1_xxreal_0(k3_square_1(A),k5_numbers) & ~ r1_xxreal_0(1,k3_square_1(A)) & ~ r1_xxreal_0(k3_square_1(A),A) ) ) ) ) )).
fof(l59_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k3_xcmplx_0(A,k7_xcmplx_0(B,C)) = k7_xcmplx_0(k3_xcmplx_0(A,B),C) ) ) ) )).
fof(l5_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,E) => r2_analoaf(A,C,B,D,E) ) ) ) ) ) ) )).
fof(l5_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_diraf(A,B,C,D,D) => B = C ) ) ) ) ) )).
fof(l5_algstr_2,axiom,( ! [A] : ( 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] : ( 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) ) )).
fof(l5_altcat_5,axiom,( k1_funct_2(k1_xboole_0,k1_xboole_0) = k1_tarski(k1_xboole_0) )).
fof(l5_ami_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( r1_tarski(k1_ami_4,A) => ( k3_compos_1(k1_ami_3,A,k5_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(k5_numbers),k10_ami_3(1)) & k3_compos_1(k1_ami_3,A,2) = k2_ami_3(k10_ami_3(k5_numbers),k10_ami_3(2)) & k3_compos_1(k1_ami_3,A,3) = k9_ami_3(k5_numbers,k10_ami_3(1)) & r1_compos_1(k1_ami_3,A,4) ) ) ) )).
fof(l5_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_analmetr(A,C,D) => B = k3_rlvect_1(A,k1_rlvect_1(A,C,k2_geomtrap(A,C,D,B)),k1_rlvect_1(A,D,k3_geomtrap(A,C,D,B))) ) ) ) ) ) )).
fof(l5_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(l5_axioms,axiom,( m1_subset_1(k5_numbers,k2_arytm_2) )).
fof(l5_bhsp_1,axiom,( 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))) = k5_numbers )).
fof(l5_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(A,k7_xcmplx_0(1,2)) & r1_xxreal_0(k5_numbers,A) ) => r2_hidden(A,u1_struct_0(k17_borsuk_1)) ) ) )).
fof(l5_bvfunc14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ~ ( 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 ) )).
fof(l5_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(l5_calcul_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ? [C] : ( m1_subset_1(C,k4_ordinal1) & r2_hidden(C,k1_relset_1(k4_ordinal1,A)) & k1_funct_1(A,C) = B ) => r1_calcul_1(A,B) ) ) )).
fof(l5_card_2,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(l5_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(C,B) => k5_relset_1(B,k1_tarski(A),k7_funcop_1(B,A),C) = k7_funcop_1(C,A) ) ) ) ) )).
fof(l5_catalg_1,axiom,( ! [A] : ! [B] : ( k9_finseq_1(A) = k9_finseq_1(B) => A = B ) )).
fof(l5_cfdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( r2_relset_1(k4_ordinal1,k2_numbers,B,k25_valued_1(k4_ordinal1,k2_numbers,A,k7_complex1)) => ( v9_ordinal1(A) <=> v9_ordinal1(B) ) ) ) ) )).
fof(l5_closure3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) )).
fof(l5_collsp,axiom,( r1_tarski(k1_tarski(k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,1,1,1)),k3_zfmisc_1(k6_domain_1(k4_ordinal1,1),k6_domain_1(k4_ordinal1,1),k6_domain_1(k4_ordinal1,1))) )).
fof(l5_comptrig,axiom,( r2_hidden(k28_sin_cos,k2_rcomp_1(k5_numbers,4)) )).
fof(l5_convex3,axiom,( m1_subset_1(k7_xcmplx_0(1,2),k1_numbers) & m1_subset_1(k7_xcmplx_0(1,3),k1_numbers) )).
fof(l5_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l5_csspace2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_comseq_3(A) => k11_comseq_3(k2_comseq_2(k4_ordinal1,A)) = k8_complex1(k11_comseq_3(A)) ) ) )).
fof(l5_csspace4,axiom,( v1_xreal_0(1) )).
fof(l5_fdiff_7,axiom,( ! [A] : ( v1_xreal_0(A) => k3_xcmplx_0(2,k1_square_1(k1_funct_1(k16_sin_cos,k7_xcmplx_0(A,2)))) = k6_xcmplx_0(1,k1_funct_1(k18_sin_cos,A)) ) )).
fof(l5_fdiff_8,axiom,( k3_limfunc1(k5_numbers) = a_0_0_fdiff_8 )).
fof(l5_fib_fusc,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( A = k2_nat_1(2,B) => ( r1_xxreal_0(B,k5_numbers) | k2_xcmplx_0(6,k2_xcmplx_0(k3_xcmplx_0(6,k2_xcmplx_0(k1_int_1(k3_power(2,B)),1)),1)) = k2_xcmplx_0(k3_xcmplx_0(6,k2_xcmplx_0(k1_int_1(k3_power(2,A)),1)),1) ) ) ) ) )).
fof(l5_fib_num,axiom,( k1_pre_ff(2) = 1 )).
fof(l5_finseq_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k7_nat_d(k7_nat_d(B,A),1) = k7_nat_d(k7_nat_d(B,1),A) ) ) )).
fof(l5_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( 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) = k5_numbers & v1_setwiseo(C,A) & v2_binop_1(C,A) & v1_binop_1(C,A) ) => k1_finsop_1(A,B,C) = k7_setwiseo(k4_ordinal1,A,C,k3_finsop_1(B),k2_finsop_1(A,k8_funcop_1(A,k4_ordinal1,k4_binop_1(A,C)),B)) ) ) ) ) )).
fof(l5_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m3_fomodel2(C,A,B) => r1_tarski(k37_fomodel1(A),k9_xtuple_0(C)) ) ) ) )).
fof(l5_frechet,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) )).
fof(l5_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k12_gfacirc1(A,B,C) != k4_tarski(D,k2_twoscomp) )).
fof(l5_funcsdom,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l5_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( A != k5_numbers => v1_funct_9(k7_funcop_1(k1_numbers,B),A) ) ) ) )).
fof(l5_goboard6,axiom,( ! [A] : ( ( v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( B = k8_metric_1(A,D,C) => v3_pre_topc(B,k3_pcomps_1(A)) ) ) ) ) ) )).
fof(l5_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v2_funct_1(B) & m2_graph_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( 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) ) ) ) ) ) )).
fof(l5_graph_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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),k1_nat_1(k3_finseq_1(B),A)) ) ) ) ) )).
fof(l5_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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,k8_polynom1(A,C)) ) ) ) ) )).
fof(l5_heyting1,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(l5_hurwitz,axiom,( k4_complex1(k1_group_1(k1_complfld)) = k5_numbers & k4_complex1(k4_algstr_0(k1_complfld,k1_group_1(k1_complfld))) = k5_numbers & k4_complex1(k4_struct_0(k1_complfld)) = k5_numbers )).
fof(l5_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( r1_int_1(A,B) & r1_int_1(B,C) ) => r1_int_1(A,C) ) ) ) ) )).
fof(l5_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k4_numbers)) => ! [C] : ( v1_int_1(C) => ( r2_hidden(A,k1_integra2(B,C)) <=> ? [D] : ( v1_int_1(D) & r2_hidden(D,B) & A = k3_xcmplx_0(C,D) ) ) ) ) ) )).
fof(l5_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(l5_integr15,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => ! [C] : ( m1_integra1(C,A) => ! [D] : ( m1_integr15(D,A,B,C) => ! [E] : ( v7_ordinal1(E) => ( ( v1_seq_2(k2_partfun1(A,k1_numbers,B,A)) & r2_hidden(E,k4_finseq_1(C)) ) => r1_xxreal_0(k1_funct_1(D,E),k1_funct_1(k4_integra1(A,B,C),E)) ) ) ) ) ) ) )).
fof(l5_integr1c,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k1_numbers)) => ! [H] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(l5_jordan19,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(B,k1_matrix_0(A)) ) => r2_hidden(k4_tarski(k1_jordan1a(A),B),k2_matrix_0(A)) ) ) ) )).
fof(l5_jordan1d,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( 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) ) ) )).
fof(l5_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,k5_numbers) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(A))) => ( C = k5_euclid(A) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(A))) => ( ( F = D & k1_rlvect_1(k15_euclid(A),F,B) = E ) => k3_xcmplx_0(B,k3_metric_1(k14_euclid(A),C,D)) = k3_metric_1(k14_euclid(A),C,E) ) ) ) ) ) ) ) ) ) )).
fof(l5_jordan5a,axiom,( ! [A] : ( v7_ordinal1(A) => v1_borsuk_2(k15_euclid(A)) ) )).
fof(l5_kurato_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)))) => ! [D] : ( 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)))))) ) ) ) ) ) ) )).
fof(l5_lattices,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(g2_lattices(k1_zfmisc_1(k1_xboole_0),A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(g2_lattices(k1_zfmisc_1(k1_xboole_0),A))) => B = C ) ) ) )).
fof(l5_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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,C,D),k8_cqc_lang(A,B,D)),E),k8_cqc_lang(A,k8_cqc_lang(A,B,C),E)),k4_cqc_the1(A)) ) ) ) ) ) )).
fof(l5_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( r2_hidden(A,k2_finseq_1(B)) & ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),B,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ~ ( k12_matrix_3(B,k2_vectsp_1,C) = k4_algstr_0(k2_vectsp_1,k5_struct_0(k2_vectsp_1)) & k3_matrix_0(u1_struct_0(k2_vectsp_1),C,A,A) = k4_algstr_0(k2_vectsp_1,k5_struct_0(k2_vectsp_1)) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(D,E),k2_matrix_0(C)) => ( ( D = E => ( D = A | k3_matrix_0(u1_struct_0(k2_vectsp_1),C,D,D) = k5_struct_0(k2_vectsp_1) ) ) & ( D != E => k3_matrix_0(u1_struct_0(k2_vectsp_1),C,D,E) = k4_struct_0(k2_vectsp_1) ) ) ) ) ) ) ) ) ) ) )).
fof(l5_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( 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))) ) ) ) )).
fof(l5_metric_1,axiom,( ! [A] : ( m1_subset_1(A,1) => ! [B] : ( m1_subset_1(B,1) => k1_binop_1(k9_funct_5,A,B) = k1_binop_1(k9_funct_5,B,A) ) ) )).
fof(l5_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_mod_4(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(l5_modelc_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,k6_xcmplx_0(B,1)) => r1_xxreal_0(k1_int_1(A),k6_xcmplx_0(k1_int_1(B),1)) ) ) ) )).
fof(l5_moebius1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( A != 1 & ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ~ r1_nat_d(B,A) ) ) ) )).
fof(l5_normsp_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_rlsub_1(o_0_5_normsp_1))) => ! [B] : ( v1_xreal_0(B) => 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)) = k3_xcmplx_0(k9_complex1(B),k3_funct_2(u1_struct_0(k1_rlsub_1(o_0_5_normsp_1)),k1_numbers,c2__normsp_1,A)) ) ) )).
fof(l5_normsp_2,axiom,( ! [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) & 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)))) ) )).
fof(l5_ntalgo_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => ! [B] : ( m1_subset_1(B,k4_numbers) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_ordinal1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ( ( k9_nat_1(k4_ordinal1,C,k5_numbers) = k1_int_2(A) & k9_nat_1(k4_ordinal1,D,k5_numbers) = k1_int_2(B) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( k9_nat_1(k4_ordinal1,C,k1_nat_1(E,1)) = k9_nat_1(k4_ordinal1,D,E) & k9_nat_1(k4_ordinal1,D,k1_nat_1(E,1)) = k4_nat_d(k9_nat_1(k4_ordinal1,C,E),k9_nat_1(k4_ordinal1,D,E)) ) ) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( k9_nat_1(k4_ordinal1,D,E) != k5_numbers => k6_nat_d(k9_nat_1(k4_ordinal1,C,E),k9_nat_1(k4_ordinal1,D,E)) = k6_nat_d(k9_nat_1(k4_ordinal1,C,k1_nat_1(E,1)),k9_nat_1(k4_ordinal1,D,k1_nat_1(E,1))) ) ) ) ) ) ) ) )).
fof(l5_o_ring_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ( r1_xxreal_0(A,k3_finseq_1(D)) => ( A = k5_numbers | k7_partfun1(u1_struct_0(B),k8_finseq_1(u1_struct_0(B),C,D),k2_xcmplx_0(k3_finseq_1(C),A)) = k7_partfun1(u1_struct_0(B),D,A) ) ) ) ) ) ) )).
fof(l5_orders_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ r2_hidden(k1_xboole_0,A) => ! [B] : ( m2_orders_1(B,A,k6_partfun1(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)))) ) ) ) ) )).
fof(l5_orders_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( r2_hidden(A,C) => m1_subset_1(A,u1_struct_0(B)) ) ) ) )).
fof(l5_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l5_pdiff_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r1_xxreal_0(A,B) => k2_rfinseq(k1_numbers,A,k5_euclid(B)) = k5_euclid(k7_nat_d(B,A)) ) ) ) )).
fof(l5_polyeq_2,axiom,( ~ v1_abian(3) )).
fof(l5_poset_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( 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,k5_numbers),C) = C ) ) ) )).
fof(l5_prvect_1,axiom,( ! [A] : ( ( ~ 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) ) ) ) )).
fof(l5_qmax_1,axiom,( ? [A] : ( 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] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( r2_hidden(B,k12_prob_1) => ( ( r2_hidden(k5_numbers,B) => k1_funct_1(A,B) = 1 ) & ( ~ r2_hidden(k5_numbers,B) => k1_funct_1(A,B) = k5_numbers ) ) ) ) ) )).
fof(l5_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)))) ) ) ) ) ) )).
fof(l5_ramsey_1,axiom,( ! [A] : k3_group_10(A,k5_numbers) = k1_tarski(k5_numbers) )).
fof(l5_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,k6_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,k6_numbers))) ) => ! [E] : ( ( v1_prob_2(E) & m2_finseq_1(E,B) ) => ! [F] : ( m2_finseq_1(F,k1_numbers) => ! [G] : ( m2_finseq_1(G,k6_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] : ( v7_ordinal1(H) => ( r2_hidden(H,k4_finseq_1(E)) => ! [I] : ( r2_hidden(I,k1_funct_1(E,H)) => k1_funct_1(C,I) = k12_supinf_2(F,H) ) ) ) & k4_finseq_1(G) = k4_finseq_1(E) & ! [H] : ( v7_ordinal1(H) => ( r2_hidden(H,k4_finseq_1(G)) => k12_supinf_2(G,H) = k4_xxreal_3(k12_supinf_2(F,H),k12_supinf_2(k1_partfun1(k4_ordinal1,B,B,k6_numbers,E,D),H)) ) ) ) => ( k1_relset_1(A,C) = k1_xboole_0 | k1_mesfunc6(A,B,D,C) = k4_extreal1(G) ) ) ) ) ) ) ) ) ) )).
fof(l5_rat_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ( B = A => k2_arytm_1(c1__rat_1,B) = k4_xcmplx_0(A) ) ) ) )).
fof(l5_real_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_real_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_real_lat)) => ! [C] : ( 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) ) ) ) )).
fof(l5_realset2,axiom,( k10_subset_1(k5_numbers,2) = k5_numbers )).
fof(l5_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ( ( k3_finseq_1(B) = k5_card_1(A) & v1_rearran1(B) ) => ! [C] : ( v1_finset_1(C) => ( C = k1_funct_1(B,k3_finseq_1(B)) => C = A ) ) ) ) ) )).
fof(l5_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(k3_finseq_1(A),B) => r2_hidden(k1_nat_1(B,1),k4_finseq_1(A)) ) ) ) )).
fof(l5_rfinseq,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ~ ( k5_card_1(k9_xtuple_0(k5_relat_1(B,A))) = k5_numbers & ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ~ r2_classes1(k5_relat_1(B,A),C) ) ) ) ) )).
fof(l5_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l5_rsspace2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(B) => ( ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & ~ r1_xxreal_0(k9_nat_1(k1_numbers,B,D),A) ) ) | r1_xxreal_0(k1_seq_2(B),A) ) ) ) ) )).
fof(l5_rsspace4,axiom,( v2_rlvect_1(g1_rlvect_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4))) & v3_rlvect_1(g1_rlvect_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4))) & v4_rlvect_1(g1_rlvect_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4))) & v13_algstr_0(g1_rlvect_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4))) & v5_rlvect_1(g1_rlvect_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4))) & v6_rlvect_1(g1_rlvect_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4))) & v7_rlvect_1(g1_rlvect_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4))) & v8_rlvect_1(g1_rlvect_1(k1_rsspace4,k9_rsspace(k6_rsspace,k1_rsspace4),k7_rsspace(k6_rsspace,k1_rsspace4),k8_rsspace(k6_rsspace,k1_rsspace4))) )).
fof(l5_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( r1_struct_0(k1_rusub_1(A),B) <=> B = k4_struct_0(A) ) ) )).
fof(l5_rvsum_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => m2_finseq_1(A,k2_numbers) ) )).
fof(l5_scm_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(C,u1_struct_0(k1_ami_3)) ) => k5_extpro_1(k7_card_1(2),k1_ami_3,A,C,k1_nat_1(B,1)) = k2_extpro_1(k7_card_1(2),k1_ami_3,k3_extpro_1(k7_card_1(2),k1_ami_3,A,k5_extpro_1(k7_card_1(2),k1_ami_3,A,C,B)),k5_extpro_1(k7_card_1(2),k1_ami_3,A,C,B)) ) ) ) )).
fof(l5_scmfsa6b,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ~ r1_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_7(B,k5_memstr_0(k7_card_1(3),k1_scmfsa_2,A),k11_scmfsa_2(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,A))),A) ) ) )).
fof(l5_scmfsa7b,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v5_ordinal1(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)) ) ) ) ) )).
fof(l5_scmpds_9,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,1) => m1_subset_1(k6_xcmplx_0(A,2),k4_ordinal1) ) ) )).
fof(l5_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_nat_1(k1_numbers,A,k1_nat_1(B,1)),k9_nat_1(k1_numbers,A,B)) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k9_nat_1(k1_numbers,A,k2_xcmplx_0(B,C)),k9_nat_1(k1_numbers,A,B)) ) ) ) & ( ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k9_nat_1(k1_numbers,A,k2_xcmplx_0(B,C)),k9_nat_1(k1_numbers,A,B)) ) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => r1_xxreal_0(k9_nat_1(k1_numbers,A,C),k9_nat_1(k1_numbers,A,B)) ) ) ) ) & ( ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => r1_xxreal_0(k9_nat_1(k1_numbers,A,C),k9_nat_1(k1_numbers,A,B)) ) ) ) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_nat_1(k1_numbers,A,k1_nat_1(B,1)),k9_nat_1(k1_numbers,A,B)) ) ) ) ) )).
fof(l5_series_2,axiom,( ! [A] : ( 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) ) )).
fof(l5_series_3,axiom,( ! [A] : ( v1_xreal_0(A) => k1_newton(k4_xcmplx_0(A),3) = k4_xcmplx_0(k1_newton(A,3)) ) )).
fof(l5_series_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(l5_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => ! [D] : ( ( v1_xreal_0(D) & v2_xxreal_0(D) ) => r1_xxreal_0(k3_xcmplx_0(k3_xcmplx_0(B,C),k1_square_1(k2_xcmplx_0(A,D))),k3_xcmplx_0(k2_xcmplx_0(k1_square_1(k3_square_1(k3_xcmplx_0(A,B))),k1_square_1(k3_square_1(k3_xcmplx_0(C,D)))),k2_xcmplx_0(k1_square_1(k3_square_1(k3_xcmplx_0(A,C))),k1_square_1(k3_square_1(k3_xcmplx_0(B,D)))))) ) ) ) ) )).
fof(l5_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A) = k7_xcmplx_0(k6_xcmplx_0(k15_sin_cos(A),k15_sin_cos(k4_xcmplx_0(A))),2) ) )).
fof(l5_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ( A != k5_numbers => ( k2_sin_cos2(A) != k5_numbers & k6_sin_cos2(A) != k5_numbers ) ) ) )).
fof(l5_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))) => k1_fdiff_1(k26_sin_cos,A) = k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,A))) ) ) )).
fof(l5_sincos10,axiom,( r1_tarski(k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers),k2_rcomp_1(k4_xcmplx_0(k28_sin_cos),k5_numbers)) )).
fof(l5_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),k1_tarski(k5_numbers)),k1_tarski(k5_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_tarski(k5_numbers)),k1_tarski(k5_numbers)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_tarski(k5_numbers),k1_tarski(k5_numbers)))) => ( v2_rlvect_1(g1_symsp_1(A,k1_tarski(k5_numbers),c3__symsp_1,c2__symsp_1,B,C)) & v3_rlvect_1(g1_symsp_1(A,k1_tarski(k5_numbers),c3__symsp_1,c2__symsp_1,B,C)) & v4_rlvect_1(g1_symsp_1(A,k1_tarski(k5_numbers),c3__symsp_1,c2__symsp_1,B,C)) & v13_algstr_0(g1_symsp_1(A,k1_tarski(k5_numbers),c3__symsp_1,c2__symsp_1,B,C)) ) ) ) ) )).
fof(l5_taxonom2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ! [D] : ! [E] : ( ( r2_hidden(C,B) & r2_hidden(D,B) & r2_hidden(E,C) & r2_hidden(E,D) ) => C = D ) ) ) )).
fof(l5_taylor_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => k6_prepower(k23_sin_cos(B),A) = k23_sin_cos(k3_xcmplx_0(A,B)) ) ) )).
fof(l5_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) <=> ( k9_xtuple_0(B) = k4_ordinal1 & ! [C] : ( r2_hidden(C,k4_ordinal1) => m1_subset_1(k1_funct_1(B,C),u1_struct_0(A)) ) ) ) ) ) )).
fof(l5_topalg_2,axiom,( u1_struct_0(k2_borsuk_1(k3_topmetr,k5_topmetr)) = k2_zfmisc_1(u1_struct_0(k3_topmetr),u1_struct_0(k5_topmetr)) )).
fof(l5_topalg_5,axiom,( u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)) = k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k5_topmetr)) )).
fof(l5_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ( v1_card_1(k3_tarski(a_1_0_topgen_2(A))) & ! [B] : ( v1_card_1(B) => ( B = k3_tarski(a_1_0_topgen_2(A)) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_ordinal1(k1_topgen_2(A,C),B) ) & ! [C] : ( v1_card_1(C) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_ordinal1(k1_topgen_2(A,D),C) ) => r1_ordinal1(B,C) ) ) ) ) ) ) ) )).
fof(l5_topreal1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l5_topreal2,axiom,( k18_euclid(k19_euclid(k5_numbers,k5_numbers)) = k5_numbers )).
fof(l5_toprealb,axiom,( r1_xxreal_0(k6_xcmplx_0(1,k5_numbers),1) )).
fof(l5_trees_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ r1_xxreal_0(k3_finseq_1(B),A) => ( r2_hidden(k1_nat_1(A,1),k4_finseq_1(B)) & r2_hidden(k1_funct_1(B,k1_nat_1(A,1)),k10_xtuple_0(B)) ) ) ) ) )).
fof(l5_vectsp_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( B = k5_algstr_0(A,D,C) => k3_rlvect_1(A,B,C) = D ) ) ) ) ) )).
fof(l5_waybel17,axiom,( ! [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) & v4_waybel11(A) & l1_waybel_9(A) ) => ! [B] : ( 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) ) ) )).
fof(l5_waybel34,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) ) )).
fof(l5_waybel_5,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( ~ 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] : ( ( ~ 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) ) ) )).
fof(l5_waybel_9,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_waybel_0(A,B) = a_2_0_waybel_9(A,B) ) ) )).
fof(l5_wsierp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_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) ) ) ) ) ) )).
fof(l5_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(B,A) ) => A = B ) ) ) )).
fof(l5_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(A,B) => r1_xxreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C)) ) ) ) ) )).
fof(l5_yellow11,axiom,( r1_tarski(k6_subset_1(3,2),k6_subset_1(3,1)) )).
fof(l60_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ~ ! [B] : ( m1_subset_1(B,u1_incsp_1(k13_afproj(A))) => ! [C] : ( m1_subset_1(C,u2_incsp_1(k13_afproj(A))) => r1_incsp_1(k13_afproj(A),B,C) ) ) ) )).
fof(l60_arytm_2,axiom,( ! [A] : ( m2_subset_1(A,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) => ! [C] : ( 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)) ) ) ) )).
fof(l60_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(30,A) & r1_xxreal_0(k5_series_1(2,A),k5_series_1(A,6)) ) ) )).
fof(l60_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( 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)) ) => k3_xcmplx_0(k12_euclid(k5_algstr_0(k15_euclid(2),A,D)),k12_euclid(k5_algstr_0(k15_euclid(2),D,B))) = k3_xcmplx_0(k12_euclid(k5_algstr_0(k15_euclid(2),A,D)),k12_euclid(k5_algstr_0(k15_euclid(2),D,C))) ) ) ) ) ) ) ) ) )).
fof(l60_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(l60_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r1_tarski(C,A) => r1_tarski(k8_funct_7(C,B),k8_funct_7(A,B)) ) ) ) ) )).
fof(l60_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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)),k24_fomodel2(B,A),k24_fomodel2(B,k5_numbers))) & ! [D] : ( 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) ) ) ) ) ) ) )).
fof(l60_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => v1_funct_9(k9_valued_1(k1_numbers,k1_numbers,k26_valued_1(k1_numbers,k1_numbers,k16_sin_cos,A),B),k3_xcmplx_0(2,k28_sin_cos)) ) ) )).
fof(l60_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( ( r1_xxreal_0(C,D) & r1_xxreal_0(D,k3_finseq_1(B)) & k1_funct_1(B,C) = k1_funct_1(B,D) ) => k1_nat_1(k3_finseq_1(k9_glib_001(A,B,C,D)),D) = k1_nat_1(k3_finseq_1(B),C) ) ) ) ) ) )).
fof(l60_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_graph_2(A,k12_finseq_1(u1_struct_0(A),B),k1_xboole_0) ) ) )).
fof(l60_hurwitz,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(A,k1_complfld) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(B,k1_complfld) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(C,k1_complfld) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => ( r2_funct_2(k4_ordinal1,u1_struct_0(k1_complfld),A,k13_polynom3(k1_complfld,B,C)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(l60_matrix_9,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k4_matrix_2(3))) => ~ ( k4_nat_d(k3_finseq_1(A),2) = k5_numbers & ! [B] : ( v7_ordinal1(B) => ~ ( r2_hidden(B,k4_finseq_1(A)) & ! [C] : ( m1_matrix_2(C,k3_matrix_2(3)) => ~ ( k1_funct_1(A,B) = C & v4_matrix_2(C,k2_matrix_2(k3_matrix_2(3))) ) ) ) ) & k3_group_4(k4_matrix_2(3),A) != k3_finseq_4(k4_ordinal1,1,2,3) & k3_group_4(k4_matrix_2(3),A) != k3_finseq_4(k4_ordinal1,2,3,1) & k3_group_4(k4_matrix_2(3),A) != k3_finseq_4(k4_ordinal1,3,1,2) ) ) )).
fof(l60_matrprob,axiom,( m1_subset_1(1,k1_numbers) & m1_subset_1(k5_numbers,k1_numbers) )).
fof(l60_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( v1_xreal_0(B) => ( v4_xxreal_2(A) => v4_xxreal_2(k1_measure6(A,B)) ) ) ) )).
fof(l60_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( r1_mesfunc1(A,B,k2_partfun1(A,k6_numbers,E,D),D) <=> r1_mesfunc1(A,B,E,D) ) ) ) ) ) ) )).
fof(l60_o_ring_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v2_struct_0(C) & l6_algstr_0(C) ) => ! [D] : ( 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 = k5_numbers | B = k5_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) ) ) ) ) ) ) )).
fof(l60_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v1_xboole_0(E) & v6_orders_2(E,A) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) ) => ! [F] : ( ( 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] : ( ( 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 = k3_funct_2(u1_struct_0(A),u1_struct_0(A),F,k3_funct_2(u1_struct_0(A),u1_struct_0(A),k1_abian(u1_struct_0(A),G,D),k3_yellow_0(A))) ) ) ) ) ) ) ) ) )).
fof(l60_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => v5_lattices(A) ) )).
fof(l60_series_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,A,B)) ) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k5_numbers,k4_real_1(k9_nat_1(k1_numbers,k3_series_1(A),B),k3_funct_2(k4_ordinal1,k1_numbers,A,k1_nat_1(B,1)))) ) ) ) )).
fof(l60_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,k1_sin_cos2,k3_sin_cos2),A) & k1_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,k1_sin_cos2,k3_sin_cos2),A) = k7_xcmplx_0(1,k1_square_1(k1_funct_1(k3_sin_cos2,A))) ) ) )).
fof(l60_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(l60_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l60_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => k3_polynom1(k15_pre_poly(A),C,k6_termord(A,B,C,D)) = k7_subset_1(k15_pre_poly(A),k3_polynom1(k15_pre_poly(A),C,D),k1_tarski(k3_termord(A,B,C,D))) ) ) ) ) )).
fof(l60_turing_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( r1_xxreal_0(A,4) => m1_subset_1(A,u2_turing_1(k18_turing_1)) ) ) )).
fof(l60_waybel11,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( ( D = E & r1_lattice3(A,C,D) ) => r1_lattice3(B,C,E) ) ) ) ) ) ) )).
fof(l60_waybel_4,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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(k1_yellow_1(k7_waybel_0(A))),k11_waybel_4(A,C),B),k5_waybel_0(A,B)) ) ) ) )).
fof(l61_arytm_2,axiom,( ! [A] : ( m2_subset_1(A,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) => ! [C] : ( 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) ) ) ) )).
fof(l61_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,9) & r1_xxreal_0(k2_power(2,A),k1_square_1(k3_xcmplx_0(2,A))) ) ) )).
fof(l61_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => m3_cat_2(k11_ens_1(B),k11_ens_1(A)) ) ) )).
fof(l61_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( 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)) ) => k3_xcmplx_0(k12_euclid(k5_algstr_0(k15_euclid(2),A,D)),k12_euclid(k5_algstr_0(k15_euclid(2),D,A))) = k3_xcmplx_0(k12_euclid(k5_algstr_0(k15_euclid(2),B,D)),k12_euclid(k5_algstr_0(k15_euclid(2),D,C))) ) ) ) ) ) ) ) ) )).
fof(l61_fib_num4,axiom,( ~ r1_xxreal_0(k3_square_1(5),k5_numbers) )).
fof(l61_fomodel0,axiom,( ! [A] : ( v1_relat_1(A) => r8_relat_2(k18_finseq_1(A),k1_relat_1(A)) ) )).
fof(l61_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( 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] : ( ( v4_fomodel1(D,B) & m1_subset_1(D,k1_fomodel1(B)) ) => ! [E] : ( ( 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 != k42_fomodel1(B,k43_fomodel1(B,D),E) ) ) & ! [D] : ( ( 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] : ( ( 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 != k42_fomodel1(B,k42_fomodel1(B,k43_fomodel1(B,k1_fomodel2(B)),D),E) ) ) ) ) ) ) )).
fof(l61_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v4_fomodel1(B,A) & m1_subset_1(B,k1_fomodel1(A)) ) => ! [C] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(l61_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => v1_funct_9(k9_valued_1(k1_numbers,k1_numbers,k26_valued_1(k1_numbers,k1_numbers,k18_sin_cos,A),B),k3_xcmplx_0(2,k28_sin_cos)) ) ) )).
fof(l61_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ! [F] : ( r1_glib_001(A,E,F,B) => r1_glib_001(A,E,F,k9_glib_001(A,B,C,D)) ) ) ) ) ) )).
fof(l61_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(l61_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ~ ( ? [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) & F = k1_relset_1(A,D) & r1_mesfunc1(A,B,D,F) ) & ? [F] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l61_modelc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_modelc_1(A) & l2_modelc_1(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,k4_ordinal1) => r2_modelc_1(A,B,C,D) ) => r1_modelc_1(A,B,C) ) ) ) ) )).
fof(l61_mssubfam,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(l61_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l61_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,B,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_oppcat_1(B))) => k3_funct_2(u4_struct_0(k2_oppcat_1(B)),u4_struct_0(A),k10_oppcat_1(B,A,C),k4_cat_1(k2_oppcat_1(B),D)) = k4_cat_1(A,k3_funct_2(u1_struct_0(B),u1_struct_0(A),k7_cat_1(B,A,C),k4_oppcat_1(B,D))) ) ) ) ) )).
fof(l61_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r1_relat_2(A,B) => r1_relat_2(k2_relat_1(A),B) ) ) )).
fof(l61_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(B,k4_rlaffin1(A,B)) ) ) )).
fof(l61_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => v5_robbins1(A) ) )).
fof(l61_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ( ( ~ r1_xxreal_0(k1_funct_1(B,k4_scmfsa_2(k1_nat_1(5,1))),k5_numbers) => k18_scmfsa_2(k1_scmfsa6b(k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(5,1)),k5_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers)),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k4_compos_1(k1_scmfsa_2)),B,A),k5_scmfsa_2(k5_numbers)) = k1_funct_7(k1_funct_7(k18_scmfsa_2(B,k5_scmfsa_2(k5_numbers)),k9_complex1(k1_funct_1(B,k4_scmfsa_2(k1_nat_1(2,1)))),k7_partfun1(k4_numbers,k18_scmfsa_2(B,k5_scmfsa_2(k5_numbers)),k9_complex1(k1_funct_1(B,k4_scmfsa_2(k1_nat_1(3,1)))))),k9_complex1(k1_funct_1(B,k4_scmfsa_2(k1_nat_1(3,1)))),k1_funct_1(B,k4_scmfsa_2(k1_nat_1(4,1)))) ) & ( r1_xxreal_0(k1_funct_1(B,k4_scmfsa_2(k1_nat_1(5,1))),k5_numbers) => k18_scmfsa_2(k1_scmfsa6b(k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(5,1)),k5_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers)),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k4_compos_1(k1_scmfsa_2)),B,A),k5_scmfsa_2(k5_numbers)) = k18_scmfsa_2(B,k5_scmfsa_2(k5_numbers)) ) ) ) ) )).
fof(l61_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(l61_sin_cos2,axiom,( r2_relset_1(k1_numbers,k1_numbers,k5_sin_cos2,k3_rfunct_1(k1_numbers,k1_numbers,k1_sin_cos2,k3_sin_cos2)) )).
fof(l61_sincos10,axiom,( k2_funct_1(k1_sincos10) = k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k3_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) )).
fof(l61_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l61_toprealb,axiom,( k1_relset_1(u1_struct_0(k2_topalg_2),k12_toprealb) = k1_numbers )).
fof(l61_turing_1,axiom,( r2_hidden(k5_numbers,u1_turing_1(k18_turing_1)) & r2_hidden(1,u1_turing_1(k18_turing_1)) )).
fof(l61_waybel11,axiom,( ! [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] : ( ( 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] : k1_yellow_0(A,C) = k1_yellow_0(B,C) ) ) ) )).
fof(l62_asympt_1,axiom,( ? [A] : ( m1_subset_1(A,k4_ordinal1) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( r1_xxreal_0(A,B) & r1_xxreal_0(k6_xcmplx_0(k3_square_1(B),k3_power(2,B)),1) ) ) ) )).
fof(l62_fib_num4,axiom,( k7_xcmplx_0(k3_square_1(5),k3_xcmplx_0(k6_xcmplx_0(k3_square_1(5),5),k1_fib_num)) = k4_xcmplx_0(k7_xcmplx_0(1,2)) )).
fof(l62_fomodel0,axiom,( ! [A] : ( v1_relat_1(A) => r1_tarski(k1_relat_1(k18_finseq_1(A)),k1_relat_1(A)) ) )).
fof(l62_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v4_fomodel1(B,A) & m1_subset_1(B,k1_fomodel1(A)) ) => ! [C] : ( ( 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] : ( 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),k9_fomodel2(A,k35_fomodel1(A),k34_fomodel2(A,k35_fomodel1(A),k7_fomodel3(A,k1_xboole_0),B,D))) ) ) ) ) ) )).
fof(l62_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => v1_funct_9(k9_valued_1(k1_numbers,k1_numbers,k26_valued_1(k1_numbers,k1_numbers,k16_sin_cos,A),B),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k2_xcmplx_0(C,1))) ) ) ) )).
fof(l62_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => r1_xxreal_0(k3_finseq_1(k9_glib_001(A,B,C,D)),k3_finseq_1(B)) ) ) ) ) )).
fof(l62_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & v5_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k8_group_1(A,B,C) = k8_group_1(A,C,B) ) ) ) )).
fof(l62_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( v1_xreal_0(B) => ( v3_xxreal_2(A) => v3_xxreal_2(k1_measure6(A,B)) ) ) ) )).
fof(l62_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l62_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r8_relat_2(A,B) => r8_relat_2(k2_relat_1(A),B) ) ) )).
fof(l62_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => ! [D] : ( v1_quaterni(D) => ! [E] : ( v1_quaterni(E) => ( E = k7_quaterni(k7_quaterni(k7_quaterni(A,B),C),D) => ( k13_quaterni(E) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k13_quaterni(A),k13_quaterni(B)),k13_quaterni(C)),k13_quaterni(D)) & k14_quaterni(E) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k14_quaterni(A),k14_quaterni(B)),k14_quaterni(C)),k14_quaterni(D)) & k15_quaterni(E) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k15_quaterni(A),k15_quaterni(B)),k15_quaterni(C)),k15_quaterni(D)) & k16_quaterni(E) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k16_quaterni(A),k16_quaterni(B)),k16_quaterni(C)),k16_quaterni(D)) ) ) ) ) ) ) ) )).
fof(l62_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( v2_rusub_4(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => B = k4_rlaffin1(A,B) ) ) )).
fof(l62_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( r2_hidden(D,k3_rusub_1(A,C,B)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r1_struct_0(B,E) & D = k3_rlvect_1(A,C,E) ) ) ) ) ) )).
fof(l62_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => k1_funct_1(k1_scmfsa6b(k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(5,1)),k5_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers)),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k4_compos_1(k1_scmfsa_2)),B,A),k4_scmfsa_2(k1_nat_1(2,1))) = k1_funct_1(B,k4_scmfsa_2(k1_nat_1(2,1))) ) ) )).
fof(l62_seq_4,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m1_subset_1(B,k2_numbers) => k3_funct_2(k2_numbers,k2_numbers,k10_funcop_1(k2_numbers,k2_numbers,k5_binop_2,A,k6_partfun1(k2_numbers)),B) = k3_xcmplx_0(A,B) ) ) )).
fof(l62_sincos10,axiom,( k2_funct_1(k2_sincos10) = k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k4_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos)) )).
fof(l62_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l62_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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,k1_square_1(A)),k1_square_1(B)),k2_xcmplx_0(1,k1_square_1(B))) ) ) ) )).
fof(l62_topalg_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_mfold_2(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(l62_topgen_1,axiom,( k3_numbers = k6_subset_1(k1_numbers,k1_borsuk_5) )).
fof(l62_turing_1,axiom,( ! [A] : ( 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] : ! [C] : ! [D] : ( 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),k1_enumset1(k4_xcmplx_0(1),k5_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),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),k8_turing_1(k18_turing_1,A)))) ) ) ) )).
fof(l62_waybel11,axiom,( ! [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] : ( ( 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] : k2_yellow_0(A,C) = k2_yellow_0(B,C) ) ) ) )).
fof(l62_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( B != k5_numbers => A = k7_xcmplx_0(k3_xcmplx_0(A,B),B) ) ) ) )).
fof(l63_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(A))) => ! [J] : ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A))) => ! [K] : ( m1_subset_1(K,k1_zfmisc_1(u1_struct_0(A))) => ( ( r2_hidden(H,I) & r2_hidden(H,K) & r2_hidden(H,J) & r2_hidden(B,I) & r2_hidden(E,I) & r2_hidden(C,K) & r2_hidden(F,K) & r2_hidden(D,J) & r2_hidden(G,J) & v1_aff_1(I,A) & v1_aff_1(K,A) & v1_aff_1(J,A) & r2_analoaf(A,B,C,E,F) & r2_analoaf(A,B,D,E,G) ) => ( r2_aff_4(A,I,K,J) | H = B | H = C | H = D | I = K | I = J | r2_analoaf(A,C,D,F,G) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l63_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ! [F] : ( m1_subset_1(F,u1_incsp_1(k13_afproj(A))) => ! [G] : ( m1_subset_1(G,u1_incsp_1(k13_afproj(A))) => ! [H] : ( m1_subset_1(H,u2_incsp_1(k13_afproj(A))) => ! [I] : ( m1_subset_1(I,u2_incsp_1(k13_afproj(A))) => ! [J] : ( m1_subset_1(J,u2_incsp_1(k13_afproj(A))) => ( ( v1_aff_1(B,A) & v1_aff_1(D,A) & v1_aff_4(C,A) & r1_tarski(B,C) & r1_tarski(D,C) & H = k4_tarski(B,1) & I = k4_tarski(D,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,C) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l63_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ~ ( k8_arytm_2(A,B) = k11_arytm_3 & A != k11_arytm_3 & B != k11_arytm_3 ) ) ) )).
fof(l63_asympt_1,axiom,( k7_newton(5) = 120 )).
fof(l63_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ~ ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,k4_numbers) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ~ ( k1_relset_1(k4_ordinal1,C) = k5_card_1(B) & k6_xcmplx_0(k11_newton(k5_card_1(B),k5_card_1(A)),k7_afinsq_2(C)) = k1_card_1(a_2_1_card_fin(A,B)) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,C)) => k1_funct_1(C,D) = k3_xcmplx_0(k3_xcmplx_0(k1_newton(k4_xcmplx_0(1),D),k4_newton(k1_nat_1(D,1),k5_card_1(B))),k1_newton(k6_xcmplx_0(k6_xcmplx_0(k5_card_1(B),D),1),k5_card_1(A))) ) ) ) ) ) ) ) )).
fof(l63_dickson,axiom,( v16_waybel_0(k11_dickson) )).
fof(l63_fomodel0,axiom,( ! [A] : ( v1_relat_1(A) => r1_relat_2(k18_finseq_1(A),k1_relat_1(A)) ) )).
fof(l63_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( 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) & k29_fomodel2(A,B) = k5_numbers ) ) ) )).
fof(l63_fomodel3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( ( v4_fomodel1(D,C) & m1_subset_1(D,k1_fomodel1(C)) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_fomodel2(E,C,B) ) => ! [F] : ( 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,k9_fomodel2(C,k35_fomodel1(C),k34_fomodel2(C,k35_fomodel1(C),k7_fomodel3(C,A),D,F)),k9_fomodel2(C,B,E)),k9_fomodel2(C,B,k5_fomodel2(E,D,k3_funct_2(k35_fomodel1(C),B,k9_fomodel2(C,B,E),F)))) ) ) ) ) ) )).
fof(l63_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( v1_xreal_0(J) => ! [K] : ( v1_xreal_0(K) => ( ( J = k3_xcmplx_0(k6_xcmplx_0(k4_geomtrap(A,B,C,k5_algstr_0(A,D,E),k3_rlvect_1(A,D,E)),k3_xcmplx_0(2,k4_geomtrap(A,B,C,k5_algstr_0(A,D,E),F))),k5_xcmplx_0(k4_geomtrap(A,B,C,k5_algstr_0(A,D,E),k5_algstr_0(A,D,E)))) & K = k3_xcmplx_0(k6_xcmplx_0(k4_geomtrap(A,B,C,k5_algstr_0(A,D,E),k3_rlvect_1(A,D,E)),k3_xcmplx_0(2,k4_geomtrap(A,B,C,k5_algstr_0(A,D,E),G))),k5_xcmplx_0(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),k6_xcmplx_0(K,J))) & k6_xcmplx_0(K,J) = k3_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2),k4_geomtrap(A,B,C,k5_algstr_0(A,D,E),k5_algstr_0(A,G,F))),k5_xcmplx_0(k4_geomtrap(A,B,C,k5_algstr_0(A,D,E),k5_algstr_0(A,D,E)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l63_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => r2_relset_1(k4_ordinal1,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),k9_glib_001(A,B,C,C),B) ) ) ) )).
fof(l63_jgraph_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k3_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),1),k1_square_1(A)),k1_square_1(B)) => r1_xxreal_0(k3_xcmplx_0(k6_xcmplx_0(k1_square_1(A),1),k2_xcmplx_0(k1_square_1(A),k1_square_1(B))),k5_numbers) ) ) ) )).
fof(l63_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k6_modal_1) => ! [B] : ( 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) ) ) ) )).
fof(l63_normform,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [C] : ( m1_subset_1(C,k5_finsub_1(k7_normform(A))) => ! [D] : ( m1_subset_1(D,k5_finsub_1(k7_normform(A))) => ~ ( r2_hidden(B,k10_normform(A,C,D)) & ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(l63_o_ring_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(B)) => ( ( v4_o_ring_1(C,B) & r1_xxreal_0(A,k3_finseq_1(C)) ) => ( k5_numbers = A | v13_o_ring_1(k7_partfun1(u1_struct_0(B),C,A),B) ) ) ) ) ) )).
fof(l63_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r4_relat_2(A,B) => r4_relat_2(k2_relat_1(A),B) ) ) )).
fof(l63_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => ( C = k7_quaterni(A,B) => ( k13_quaterni(C) = k2_xcmplx_0(k13_quaterni(A),k13_quaterni(B)) & k14_quaterni(C) = k2_xcmplx_0(k14_quaterni(A),k14_quaterni(B)) & k15_quaterni(C) = k2_xcmplx_0(k15_quaterni(A),k15_quaterni(B)) & k16_quaterni(C) = k2_xcmplx_0(k16_quaterni(A),k16_quaterni(B)) ) ) ) ) ) )).
fof(l63_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ( ( r1_xxreal_0(k1_funct_1(B,k4_scmfsa_2(k1_nat_1(2,1))),k3_finseq_1(k18_scmfsa_2(B,k5_scmfsa_2(k5_numbers)))) & r1_xxreal_0(2,k1_funct_1(B,k4_scmfsa_2(k1_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(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(4,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(5,1)),k5_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers)),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k4_compos_1(k1_scmfsa_2))),B,A),k4_scmfsa_2(k1_nat_1(2,1))) = k6_xcmplx_0(k1_funct_1(B,k4_scmfsa_2(k1_nat_1(2,1))),1) & r2_classes1(k18_scmfsa_2(B,k5_scmfsa_2(k5_numbers)),k18_scmfsa_2(k1_scmfsa6b(k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(4,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(5,1)),k5_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers)),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k4_compos_1(k1_scmfsa_2))),B,A),k5_scmfsa_2(k5_numbers))) & ( k1_funct_1(k18_scmfsa_2(B,k5_scmfsa_2(k5_numbers)),k1_funct_1(B,k4_scmfsa_2(k1_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(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(4,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(5,1)),k5_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers)),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k4_compos_1(k1_scmfsa_2))),B,A),k5_scmfsa_2(k5_numbers)),k1_funct_1(B,k4_scmfsa_2(k1_nat_1(2,1)))) | k1_funct_1(k18_scmfsa_2(B,k5_scmfsa_2(k5_numbers)),k1_funct_1(B,k4_scmfsa_2(k1_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(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(4,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(5,1)),k5_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers)),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k4_compos_1(k1_scmfsa_2))),B,A),k5_scmfsa_2(k5_numbers)),k6_xcmplx_0(k1_funct_1(B,k4_scmfsa_2(k1_nat_1(2,1))),1)) ) & ( k1_funct_1(k18_scmfsa_2(B,k5_scmfsa_2(k5_numbers)),k1_funct_1(B,k4_scmfsa_2(k1_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(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(4,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(5,1)),k5_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers)),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k4_compos_1(k1_scmfsa_2))),B,A),k5_scmfsa_2(k5_numbers)),k1_funct_1(B,k4_scmfsa_2(k1_nat_1(2,1)))) | k1_funct_1(k18_scmfsa_2(B,k5_scmfsa_2(k5_numbers)),k6_xcmplx_0(k1_funct_1(B,k4_scmfsa_2(k1_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(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(4,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(5,1)),k5_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers)),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k4_compos_1(k1_scmfsa_2))),B,A),k5_scmfsa_2(k5_numbers)),k1_funct_1(B,k4_scmfsa_2(k1_nat_1(2,1)))) ) & ( k1_funct_1(k18_scmfsa_2(B,k5_scmfsa_2(k5_numbers)),k1_funct_1(B,k4_scmfsa_2(k1_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(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(4,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(5,1)),k5_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers)),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k4_compos_1(k1_scmfsa_2))),B,A),k5_scmfsa_2(k5_numbers)),k6_xcmplx_0(k1_funct_1(B,k4_scmfsa_2(k1_nat_1(2,1))),1)) | k1_funct_1(k18_scmfsa_2(B,k5_scmfsa_2(k5_numbers)),k6_xcmplx_0(k1_funct_1(B,k4_scmfsa_2(k1_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(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(4,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(5,1)),k5_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers)),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k4_compos_1(k1_scmfsa_2))),B,A),k5_scmfsa_2(k5_numbers)),k6_xcmplx_0(k1_funct_1(B,k4_scmfsa_2(k1_nat_1(2,1))),1)) ) & ! [C] : ( r2_hidden(C,k4_finseq_1(k18_scmfsa_2(B,k5_scmfsa_2(k5_numbers)))) => ( C = k6_xcmplx_0(k1_funct_1(B,k4_scmfsa_2(k1_nat_1(2,1))),1) | C = k1_funct_1(B,k4_scmfsa_2(k1_nat_1(2,1))) | k1_funct_1(k18_scmfsa_2(B,k5_scmfsa_2(k5_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(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(4,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(5,1)),k5_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers)),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k4_compos_1(k1_scmfsa_2))),B,A),k5_scmfsa_2(k5_numbers)),C) ) ) & ? [C] : ( v1_int_1(C) & ? [D] : ( 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(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(4,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(5,1)),k5_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers)),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k4_compos_1(k1_scmfsa_2))),B,A),k5_scmfsa_2(k5_numbers)),k6_xcmplx_0(k1_funct_1(B,k4_scmfsa_2(k1_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(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(4,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(5,1)),k5_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers)),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k4_compos_1(k1_scmfsa_2))),B,A),k5_scmfsa_2(k5_numbers)),k1_funct_1(B,k4_scmfsa_2(k1_nat_1(2,1)))) & r1_xxreal_0(D,C) ) ) ) ) ) ) )).
fof(l63_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ! [C] : ( r2_hidden(C,k3_tarski(k7_scmyciel(A,B))) => r2_hidden(C,B) ) ) )).
fof(l63_series_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [E] : ( v7_ordinal1(E) => k9_nat_1(k1_numbers,B,E) = k1_square_1(k3_real_1(k9_nat_1(k1_numbers,C,E),k9_nat_1(k1_numbers,D,E))) ) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,k3_series_1(B),A)) ) ) ) ) ) )).
fof(l63_sin_cos6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(B,k1_rcomp_1(k2_xcmplx_0(C,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A)),k2_xcmplx_0(D,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A)))) => r2_hidden(k2_xcmplx_0(B,k3_xcmplx_0(2,k28_sin_cos)),k1_rcomp_1(k2_xcmplx_0(C,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k2_xcmplx_0(A,1))),k2_xcmplx_0(D,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k2_xcmplx_0(A,1))))) ) ) ) ) ) )).
fof(l63_sincos10,axiom,( k2_funct_1(k3_sincos10) = k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers)) )).
fof(l63_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l63_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => k4_polynom1(A,C,k6_termord(A,B,C,D),k3_termord(A,B,C,D)) = k4_struct_0(C) ) ) ) ) )).
fof(l63_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(l63_topalg_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_mfold_2(A))) => ! [C] : ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(l63_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( ( C = D & v1_waybel_0(C,A) ) => v1_waybel_0(D,B) ) ) ) ) ) ) )).
fof(l63_waybel_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & v2_waybel_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v22_waybel_0(k4_waybel_1(A,B),A,A) ) ) )).
fof(l64_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ! [F] : ( m1_subset_1(F,u1_incsp_1(k13_afproj(A))) => ! [G] : ( m1_subset_1(G,u1_incsp_1(k13_afproj(A))) => ! [H] : ( m1_subset_1(H,u2_incsp_1(k13_afproj(A))) => ! [I] : ( m1_subset_1(I,u2_incsp_1(k13_afproj(A))) => ! [J] : ( m1_subset_1(J,u2_incsp_1(k13_afproj(A))) => ( ( v1_aff_1(B,A) & v1_aff_1(D,A) & v1_aff_4(C,A) & r1_tarski(B,C) & r1_tarski(D,C) & H = k4_tarski(B,1) & I = k4_tarski(D,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,C) & r1_aff_4(A,C,E) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l64_arytm_2,axiom,( ! [A] : ( m2_subset_1(A,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) => ! [C] : ( 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)) ) ) ) )).
fof(l64_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(10,A) & r1_xxreal_0(k7_xcmplx_0(1,k2_power(2,k6_xcmplx_0(A,9))),k7_xcmplx_0(k5_series_1(2,k2_nat_1(2,A)),k7_newton(A))) ) ) )).
fof(l64_bcialg_1,axiom,( ! [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) ) => m2_bcialg_1(k1_tarski(k4_struct_0(A)),A) ) )).
fof(l64_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(l64_dickson,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( ~ v2_struct_0(k4_yellow_1(A,k7_funcop_1(A,k11_dickson))) & v4_dickson(k4_yellow_1(A,k7_funcop_1(A,k11_dickson))) & v3_dickson(k4_yellow_1(A,k7_funcop_1(A,k11_dickson))) & v5_orders_2(k4_yellow_1(A,k7_funcop_1(A,k11_dickson))) ) ) )).
fof(l64_fib_num4,axiom,( ~ r1_xxreal_0(k3_square_1(5),1) )).
fof(l64_fomodel0,axiom,( ! [A] : ( v1_relat_1(A) => k1_relat_1(k18_finseq_1(A)) = k1_relat_1(A) ) )).
fof(l64_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(l64_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( ( 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))) ) ) ) ) ) )).
fof(l64_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(k25_grcat_1(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(l64_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u4_incsp_1(A)) => ? [C] : ( m1_subset_1(C,u1_incsp_1(A)) & ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & ? [E] : ( m1_subset_1(E,u1_incsp_1(A)) & ? [F] : ( 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) ) ) ) ) ) ) )).
fof(l64_jgraph_3,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( k6_xcmplx_0(k1_square_1(A),1) = k5_numbers & A != 1 & A != k4_xcmplx_0(1) ) ) )).
fof(l64_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k3_finseq_1(A)) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(A)) & k1_funct_1(A,B) = k1_funct_1(A,C) ) => B = C ) ) ) ) )).
fof(l64_modal_1,axiom,( m1_subset_1(k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers),k4_modal_1) )).
fof(l64_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v5_o_ring_1(B,A) => v13_o_ring_1(B,A) ) ) ) )).
fof(l64_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,B,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k3_funct_2(u4_struct_0(B),u4_struct_0(k2_oppcat_1(A)),k11_oppcat_1(B,A,C),k4_cat_1(B,D)) = k4_cat_1(k2_oppcat_1(A),k3_oppcat_1(A,k3_funct_2(u1_struct_0(B),u1_struct_0(A),k7_cat_1(B,A,C),D))) ) ) ) ) )).
fof(l64_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r6_relat_2(A,B) => r6_relat_2(k2_relat_1(A),B) ) ) )).
fof(l64_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k7_quaterni(A,B) = k6_quaterni(k2_xcmplx_0(k13_quaterni(A),k13_quaterni(B)),k2_xcmplx_0(k14_quaterni(A),k14_quaterni(B)),k2_xcmplx_0(k15_quaterni(A),k15_quaterni(B)),k2_xcmplx_0(k16_quaterni(A),k16_quaterni(B))) ) ) )).
fof(l64_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m2_rlsub_1(D,A,B) & r2_hidden(C,D) ) ) ) ) )).
fof(l64_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m2_rusub_1(D,A,B) & r2_hidden(C,D) ) ) ) ) )).
fof(l64_scmpds_2,axiom,( k8_struct_0(k1_scmpds_2) = k2_ami_2 )).
fof(l64_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ! [C] : ( ( r2_hidden(C,B) & r2_hidden(C,k3_tarski(A)) ) => r2_hidden(C,k3_tarski(k7_scmyciel(A,B))) ) ) )).
fof(l64_sin_cos6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(B,k8_subset_1(k1_numbers,k1_rcomp_1(k2_xcmplx_0(C,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A)),k2_xcmplx_0(D,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A))),k1_numbers)) => r2_hidden(k2_xcmplx_0(B,k3_xcmplx_0(2,k28_sin_cos)),k8_subset_1(k1_numbers,k1_rcomp_1(k2_xcmplx_0(C,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k2_xcmplx_0(A,1))),k2_xcmplx_0(D,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k2_xcmplx_0(A,1)))),k1_numbers)) ) ) ) ) ) )).
fof(l64_sincos10,axiom,( k2_funct_1(k4_sincos10) = k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k4_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) )).
fof(l64_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l64_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( 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) => k4_polynom1(A,C,k6_termord(A,B,C,D),E) = k4_polynom1(A,C,D,E) ) ) ) ) ) ) )).
fof(l64_uproots,axiom,( ! [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) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & v1_uproots(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & v1_uproots(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k3_uproots(u1_struct_0(A),k7_uproots(A,k13_polynom3(A,B,C))) = k1_nat_1(k3_uproots(u1_struct_0(A),k7_uproots(A,B)),k3_uproots(u1_struct_0(A),k7_uproots(A,C))) ) ) ) )).
fof(l64_waybel11,axiom,( ! [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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_waybel_3(A,C,D) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( C = E & D = F ) => r1_waybel_3(B,E,F) ) ) ) ) ) ) ) ) ) )).
fof(l64_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( C != k5_numbers => k7_xcmplx_0(A,B) = k7_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) ) ) ) )).
fof(l65_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => v2_collsp(k5_anproj_1(A)) ) )).
fof(l65_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( r1_xxreal_0(3,A) => r1_xxreal_0(k6_xcmplx_0(A,1),k3_xcmplx_0(2,k6_xcmplx_0(A,2))) ) ) )).
fof(l65_bcialg_1,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( B = k1_tarski(k4_struct_0(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),B) => r2_hidden(k2_bcialg_1(A,C),k1_tarski(k4_struct_0(A))) ) ) ) ) )).
fof(l65_bcialg_6,axiom,( ! [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] : ( ( ~ 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] : ( m1_bcialg_1(C,B) => ! [D] : ( ( 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)))) ) => ( u1_struct_0(C) = k2_relset_1(u1_struct_0(B),D) => ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(C)) & v2_bcialg_6(D,A,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(C)))) ) ) ) ) ) ) )).
fof(l65_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l65_fib_num4,axiom,( ~ r1_xxreal_0(k6_xcmplx_0(k3_square_1(5),1),k6_xcmplx_0(1,1)) & ~ r1_xxreal_0(k3_square_1(5),k5_numbers) )).
fof(l65_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(l65_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => r1_tarski(k8_funct_7(A,k5_numbers),k18_finseq_1(A)) ) )).
fof(l65_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => v1_funct_9(k9_valued_1(k1_numbers,k1_numbers,k26_valued_1(k1_numbers,k1_numbers,k18_sin_cos,A),B),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k2_xcmplx_0(C,1))) ) ) ) )).
fof(l65_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ! [E] : ( ( ~ v1_abian(E) & m1_subset_1(E,k4_ordinal1) ) => ! [F] : ( ( ~ v1_abian(F) & m1_subset_1(F,k4_ordinal1) ) => ( ( r1_xxreal_0(E,F) & r1_xxreal_0(F,k3_finseq_1(B)) & k1_funct_1(B,E) = k1_funct_1(B,F) ) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( r2_hidden(G,k2_finseq_1(E)) => k1_funct_1(k9_glib_001(A,B,E,F),G) = k1_funct_1(B,G) ) ) ) ) ) ) ) )).
fof(l65_graph_5,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,k1_rvsum_1(A)) => r1_xxreal_0(k5_numbers,B) ) ) <=> ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => r1_xxreal_0(k5_numbers,k1_funct_1(A,B)) ) ) ) ) )).
fof(l65_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => r1_xxreal_0(k6_xcmplx_0(B,A),B) ) ) )).
fof(l65_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k25_grcat_1(A))) => ! [C] : ( m2_grcat_1(C,k17_grcat_1(A)) => ( B = C => ! [D] : ( m1_cat_1(D,k25_grcat_1(A),B,B) => ( D = k21_grcat_1(k17_grcat_1(A),C) => ! [E] : ( m1_subset_1(E,u1_struct_0(k25_grcat_1(A))) => ( ( k2_cat_1(k25_grcat_1(A),B,E) != k1_xboole_0 => ! [F] : ( 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] : ( m1_cat_1(F,k25_grcat_1(A),E,B) => k1_cat_1(k25_grcat_1(A),F,D) = F ) ) ) ) ) ) ) ) ) ) )).
fof(l65_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => r2_hidden(k3_hilbert1(k4_hilbert1(k4_hilbert1(A,B),C),B),k6_hilbert1) ) ) ) )).
fof(l65_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(l65_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => k1_funct_1(B,C) = k7_matrix_0(A,B,C) ) ) ) ) )).
fof(l65_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k3_modal_1) => k17_modal_1 != k16_modal_1(A) ) )).
fof(l65_modelc_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v10_modelc_1(B) & l2_modelc_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(l65_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(l65_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [G] : ( ( 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,k3_polynom1(k15_pre_poly(A),C,F)) ) ) ) ) ) ) ) ) )).
fof(l65_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => ( C = k10_quaterni(A,B) => ( k13_quaterni(C) = k6_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k13_quaterni(B)),k3_xcmplx_0(k14_quaterni(A),k14_quaterni(B))),k3_xcmplx_0(k15_quaterni(A),k15_quaterni(B))),k3_xcmplx_0(k16_quaterni(A),k16_quaterni(B))) & k14_quaterni(C) = k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k14_quaterni(B)),k3_xcmplx_0(k14_quaterni(A),k13_quaterni(B))),k3_xcmplx_0(k15_quaterni(A),k16_quaterni(B))),k3_xcmplx_0(k16_quaterni(A),k15_quaterni(B))) & k15_quaterni(C) = k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k15_quaterni(B)),k3_xcmplx_0(k15_quaterni(A),k13_quaterni(B))),k3_xcmplx_0(k16_quaterni(A),k14_quaterni(B))),k3_xcmplx_0(k14_quaterni(A),k16_quaterni(B))) & k16_quaterni(C) = k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k16_quaterni(B)),k3_xcmplx_0(k16_quaterni(A),k13_quaterni(B))),k3_xcmplx_0(k14_quaterni(A),k15_quaterni(B))),k3_xcmplx_0(k15_quaterni(A),k14_quaterni(B))) ) ) ) ) ) )).
fof(l65_scmpds_6,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmpds_2)) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => k5_card_1(k1_scmpds_4(k4_scmpds_4(A,B),C)) = k1_nat_1(k5_card_1(C),2) ) ) ) )).
fof(l65_series_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [C] : ( v7_ordinal1(C) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,B,C),k5_numbers) ) & r1_xxreal_0(k1_power(k1_nat_1(A,1),k9_nat_1(k1_numbers,k1_series_3(B),A)),k5_numbers) ) ) ) )).
fof(l65_sin_cos6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(B,k1_rcomp_1(k2_xcmplx_0(C,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A)),k2_xcmplx_0(D,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A)))) => r2_hidden(k6_xcmplx_0(B,k3_xcmplx_0(2,k28_sin_cos)),k1_rcomp_1(k2_xcmplx_0(C,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k6_xcmplx_0(A,1))),k2_xcmplx_0(D,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k6_xcmplx_0(A,1))))) ) ) ) ) ) )).
fof(l65_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l65_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(A,B) ) => r1_xxreal_0(k3_xcmplx_0(A,k3_square_1(k2_xcmplx_0(1,k1_square_1(B)))),k3_xcmplx_0(B,k3_square_1(k2_xcmplx_0(1,k1_square_1(A))))) ) ) ) )).
fof(l65_stirl2_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ~ ( r2_hidden(B,A) & r1_xxreal_0(k5_card_1(A),k5_card_1(k6_subset_1(A,k1_tarski(B)))) ) ) )).
fof(l65_toprealb,axiom,( k1_funct_1(k12_toprealb,k7_xcmplx_0(1,2)) = k19_euclid(k4_xcmplx_0(1),k5_numbers) )).
fof(l65_valued_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & k4_finseq_1(C) = k4_finseq_1(B) & k10_xtuple_0(C) = k1_relset_1(k4_ordinal1,k61_valued_1(B,A)) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k4_finseq_1(B)) => k1_funct_1(C,D) = k1_nat_1(A,D) ) ) & v2_funct_1(C) ) ) ) )).
fof(l65_waybel11,axiom,( ! [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] : ( ( 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] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(l65_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(k5_numbers,C) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) ) ) ) )).
fof(l66_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(A))) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(A))) => ! [J] : ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A))) => ( ( r5_aff_1(A,H,J) & r5_aff_1(A,H,I) & r2_hidden(B,H) & r2_hidden(E,H) & r2_hidden(C,J) & r2_hidden(F,J) & r2_hidden(D,I) & r2_hidden(G,I) & v1_aff_1(H,A) & r2_analoaf(A,B,C,E,F) & r2_analoaf(A,B,D,E,G) ) => ( r2_aff_4(A,H,J,I) | H = J | H = I | r2_analoaf(A,C,D,F,G) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l66_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k13_afproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k13_afproj(A))) => ! [E] : ( m1_subset_1(E,u1_incsp_1(k13_afproj(A))) => ! [F] : ( m1_subset_1(F,u1_incsp_1(k13_afproj(A))) => ! [G] : ( m1_subset_1(G,u2_incsp_1(k13_afproj(A))) => ! [H] : ( m1_subset_1(H,u2_incsp_1(k13_afproj(A))) => ! [I] : ( m1_subset_1(I,u2_incsp_1(k13_afproj(A))) => ! [J] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l66_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => v3_collsp(k5_anproj_1(A)) ) )).
fof(l66_arytm_2,axiom,( r2_hidden(k12_arytm_3,k5_arytm_3) )).
fof(l66_asympt_1,axiom,( k5_series_1(5,5) = 3125 )).
fof(l66_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k20_coh_sp(A)) => ! [C] : ( 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 ) ) ) )).
fof(l66_fib_num4,axiom,( ~ r1_xxreal_0(k3_square_1(5),2) )).
fof(l66_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(l66_fomodel0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => r1_tarski(k8_funct_7(B,k2_xcmplx_0(A,1)),k18_finseq_1(B)) ) ) )).
fof(l66_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v12_fomodel1(k30_fomodel2(A),A) ) )).
fof(l66_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( ( r1_xxreal_0(C,D) & r1_xxreal_0(D,k3_finseq_1(B)) & k1_funct_1(B,C) = k1_funct_1(B,D) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( 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),k4_ordinal1) & r1_xxreal_0(k2_xcmplx_0(k6_xcmplx_0(E,C),D),k3_finseq_1(B)) ) ) ) ) ) ) ) ) )).
fof(l66_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_2(B,u4_struct_0(A),k9_graph_3(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l66_graph_5,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ( ( C = k8_finseq_1(k1_numbers,A,B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,k1_rvsum_1(C)) => r1_xxreal_0(k5_numbers,D) ) ) ) => ( ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k4_finseq_1(A)) => r1_xxreal_0(k5_numbers,k1_funct_1(A,D)) ) ) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k4_finseq_1(B)) => r1_xxreal_0(k5_numbers,k1_funct_1(B,D)) ) ) ) ) ) ) ) )).
fof(l66_graphsp,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(1,F) => ( r1_xxreal_0(k3_finseq_1(A),F) | k1_funct_1(A,k6_xcmplx_0(k3_finseq_1(A),F)) = k1_funct_1(C,k1_nat_1(k7_partfun1(k4_ordinal1,A,k2_xcmplx_0(k6_xcmplx_0(k3_finseq_1(A),F),1)),E)) ) ) ) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(1,F) => ( r1_xxreal_0(k3_finseq_1(B),F) | k1_funct_1(B,k6_xcmplx_0(k3_finseq_1(B),F)) = k1_funct_1(C,k1_nat_1(k7_partfun1(k4_ordinal1,B,k2_xcmplx_0(k6_xcmplx_0(k3_finseq_1(B),F),1)),E)) ) ) ) & r1_xxreal_0(k3_finseq_1(A),k3_finseq_1(B)) & k1_funct_1(A,k3_finseq_1(A)) = k1_funct_1(B,k3_finseq_1(B)) ) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(1,F) => ( r1_xxreal_0(k3_finseq_1(A),F) | k1_funct_1(A,k6_xcmplx_0(k3_finseq_1(A),F)) = k1_funct_1(B,k6_xcmplx_0(k3_finseq_1(B),F)) ) ) ) ) ) ) ) ) ) )).
fof(l66_hfdiff_1,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(l66_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(l66_measure6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( v2_rcomp_1(B) => v2_rcomp_1(k1_measure6(B,A)) ) ) ) )).
fof(l66_nat_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( B = k4_newton(A,k2_nat_1(2,A)) & r1_xxreal_0(3,A) ) => B = k2_nat_1(k2_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)))) ) ) ) )).
fof(l66_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l66_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_oppcat_1(C,B,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_oppcat_1(B))) => k3_funct_2(u4_struct_0(k2_oppcat_1(B)),u4_struct_0(A),k10_oppcat_1(B,A,C),k4_cat_1(k2_oppcat_1(B),D)) = k4_cat_1(A,k3_funct_2(u1_struct_0(B),u1_struct_0(A),k7_cat_1(B,A,C),k4_oppcat_1(B,D))) ) ) ) ) )).
fof(l66_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => ! [D] : ( v1_quaterni(D) => k7_quaterni(k7_quaterni(k7_quaterni(A,B),C),D) = k6_quaterni(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k13_quaterni(A),k13_quaterni(B)),k13_quaterni(C)),k13_quaterni(D)),k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k14_quaterni(A),k14_quaterni(B)),k14_quaterni(C)),k14_quaterni(D)),k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k15_quaterni(A),k15_quaterni(B)),k15_quaterni(C)),k15_quaterni(D)),k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k16_quaterni(A),k16_quaterni(B)),k16_quaterni(C)),k16_quaterni(D))) ) ) ) ) )).
fof(l66_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_robbins1(A) ) => ( ( v2_robbins2(A) & v3_robbins2(A) ) => ( v4_lattices(A) & v6_robbins1(A) & v5_lattices(A) ) ) ) )).
fof(l66_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(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(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))),k16_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),B,A),k4_scmfsa_2(k1_nat_1(1,1))) = k6_xcmplx_0(k1_funct_1(B,k4_scmfsa_2(k1_nat_1(k5_numbers,1))),1) & k1_funct_1(k1_scmfsa6b(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))),k16_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),B,A),k4_scmfsa_2(k1_nat_1(2,1))) = k3_finseq_1(k18_scmfsa_2(B,k5_scmfsa_2(k5_numbers))) & k18_scmfsa_2(k1_scmfsa6b(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))),k16_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),B,A),k5_scmfsa_2(k5_numbers)) = k18_scmfsa_2(B,k5_scmfsa_2(k5_numbers)) ) ) ) )).
fof(l66_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( r1_tarski(B,k3_tarski(A)) => k3_tarski(k7_scmyciel(A,B)) = B ) ) )).
fof(l66_series_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(k9_nat_1(k1_numbers,B,C),k5_numbers) & r1_xxreal_0(k1_funct_1(B,k6_xcmplx_0(C,1)),k9_nat_1(k1_numbers,B,C)) ) ) => r1_xxreal_0(k5_numbers,k7_xcmplx_0(k6_xcmplx_0(k3_funct_2(k4_ordinal1,k1_numbers,B,k1_nat_1(A,1)),k7_xcmplx_0(k9_nat_1(k1_numbers,k3_series_1(B),A),k1_nat_1(A,1))),k1_nat_1(A,2))) ) ) ) )).
fof(l66_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => r1_xxreal_0(2,k2_xcmplx_0(k1_funct_1(k22_sin_cos,A),k1_funct_1(k22_sin_cos,k4_xcmplx_0(A)))) ) )).
fof(l66_sin_cos6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(B,k8_subset_1(k1_numbers,k1_rcomp_1(k2_xcmplx_0(C,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A)),k2_xcmplx_0(D,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A))),k1_numbers)) => r2_hidden(k6_xcmplx_0(B,k3_xcmplx_0(2,k28_sin_cos)),k8_subset_1(k1_numbers,k1_rcomp_1(k2_xcmplx_0(C,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k6_xcmplx_0(A,1))),k2_xcmplx_0(D,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k6_xcmplx_0(A,1)))),k1_numbers)) ) ) ) ) ) )).
fof(l66_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l66_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(A,B) ) => r1_xxreal_0(k3_xcmplx_0(A,k3_square_1(k2_xcmplx_0(1,k1_square_1(B)))),k3_xcmplx_0(B,k3_square_1(k2_xcmplx_0(1,k1_square_1(A))))) ) ) ) )).
fof(l66_topgen_1,axiom,( m1_subset_1(k3_numbers,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )).
fof(l66_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ v2_struct_0(D) & v4_orders_2(D) & v7_waybel_0(D) & l1_waybel_0(D,A) ) => ! [E] : ( ( ~ v2_struct_0(E) & v4_orders_2(E) & v7_waybel_0(E) & l1_waybel_0(E,B) ) => ( D = E => ! [F] : ( m3_yellow_6(F,u1_struct_0(D),A) => ! [G] : ( m3_yellow_6(G,u1_struct_0(E),B) => ( F = G => k8_yellow_6(A,D,F) = k8_yellow_6(B,E,G) ) ) ) ) ) ) ) ) ) )).
fof(l66_waybel_4,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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) ) ) ) )).
fof(l66_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(B,A) ) => r1_xxreal_0(k7_xcmplx_0(B,C),k7_xcmplx_0(A,C)) ) ) ) ) )).
fof(l66_xxreal_3,axiom,( r2_hidden(k5_numbers,k1_numbers) )).
fof(l67_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k13_afproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k13_afproj(A))) => ! [E] : ( m1_subset_1(E,u1_incsp_1(k13_afproj(A))) => ! [F] : ( m1_subset_1(F,u1_incsp_1(k13_afproj(A))) => ! [G] : ( m1_subset_1(G,u2_incsp_1(k13_afproj(A))) => ! [H] : ( m1_subset_1(H,u2_incsp_1(k13_afproj(A))) => ! [I] : ( m1_subset_1(I,u2_incsp_1(k13_afproj(A))) => ! [J] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l67_arytm_2,axiom,( m1_subset_1(k12_arytm_3,k2_arytm_2) )).
fof(l67_asympt_1,axiom,( k5_series_1(4,4) = 256 )).
fof(l67_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(l67_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ! [C] : ( ( 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] : ( ( v1_relat_1(D) & v5_relat_1(D,k4_numbers) & v5_ordinal1(D) & v1_funct_1(D) & v1_finset_1(D) ) => ~ ( k1_relset_1(k4_ordinal1,D) = k5_card_1(A) & k6_xcmplx_0(k7_newton(k5_card_1(A)),k7_afinsq_2(D)) = k1_card_1(a_3_3_card_fin(A,B,C)) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k1_relset_1(k4_ordinal1,D)) => k1_funct_1(D,E) = k7_xcmplx_0(k3_xcmplx_0(k1_newton(k4_xcmplx_0(1),E),k7_newton(k5_card_1(A))),k7_newton(k1_nat_1(E,1))) ) ) ) ) ) ) ) ) )).
fof(l67_fib_num4,axiom,( ~ r1_xxreal_0(k4_xcmplx_0(2),k4_xcmplx_0(k3_square_1(5))) )).
fof(l67_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r2_hidden(k4_filter_0(A,C,E),B) & r2_hidden(k4_filter_0(A,D,E),B) ) => r2_hidden(k4_filter_0(A,k3_lattices(A,C,D),E),B) ) ) ) ) ) ) )).
fof(l67_fomodel0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => r1_tarski(k8_funct_7(B,A),k18_finseq_1(B)) ) ) )).
fof(l67_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( ( 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(k1_nat_1(k3_finseq_1(B),C),D) ) ) ) ) ) )).
fof(l67_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(l67_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_integra5(A,k22_sin_cos) & v1_comseq_2(k2_partfun1(k1_numbers,k1_numbers,k22_sin_cos,A)) ) ) )).
fof(l67_nat_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( B = k4_newton(A,k2_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))),k2_power(k2_nat_1(2,A),k3_square_1(k2_nat_1(2,A)))) ) ) ) )).
fof(l67_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l67_ordinal5,axiom,( r2_hidden(k5_numbers,1) )).
fof(l67_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k10_quaterni(A,B) = k6_quaterni(k6_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k13_quaterni(B)),k3_xcmplx_0(k14_quaterni(A),k14_quaterni(B))),k3_xcmplx_0(k15_quaterni(A),k15_quaterni(B))),k3_xcmplx_0(k16_quaterni(A),k16_quaterni(B))),k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k14_quaterni(B)),k3_xcmplx_0(k14_quaterni(A),k13_quaterni(B))),k3_xcmplx_0(k15_quaterni(A),k16_quaterni(B))),k3_xcmplx_0(k16_quaterni(A),k15_quaterni(B))),k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k15_quaterni(B)),k3_xcmplx_0(k15_quaterni(A),k13_quaterni(B))),k3_xcmplx_0(k16_quaterni(A),k14_quaterni(B))),k3_xcmplx_0(k14_quaterni(A),k16_quaterni(B))),k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k16_quaterni(B)),k3_xcmplx_0(k16_quaterni(A),k13_quaterni(B))),k3_xcmplx_0(k14_quaterni(A),k15_quaterni(B))),k3_xcmplx_0(k15_quaterni(A),k14_quaterni(B)))) ) ) )).
fof(l67_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ( k1_funct_1(B,k4_scmfsa_2(k1_nat_1(k5_numbers,1))) = k3_finseq_1(k18_scmfsa_2(B,k5_scmfsa_2(k5_numbers))) => ( r2_classes1(k18_scmfsa_2(B,k5_scmfsa_2(k5_numbers)),k18_scmfsa_2(k1_scmfsa6b(k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(k5_numbers,1)),k3_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))),k16_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(4,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(5,1)),k5_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers)),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k4_compos_1(k1_scmfsa_2)))))),B,A),k5_scmfsa_2(k5_numbers))) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(D,k3_finseq_1(k18_scmfsa_2(B,k5_scmfsa_2(k5_numbers)))) ) => ( r1_xxreal_0(D,C) | ! [E] : ( v1_int_1(E) => ! [F] : ( v1_int_1(F) => ( ( E = k1_funct_1(k18_scmfsa_2(k1_scmfsa6b(k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(k5_numbers,1)),k3_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))),k16_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(4,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(5,1)),k5_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers)),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k4_compos_1(k1_scmfsa_2)))))),B,A),k5_scmfsa_2(k5_numbers)),C) & F = k1_funct_1(k18_scmfsa_2(k1_scmfsa6b(k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(k5_numbers,1)),k3_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k1_nat_1(k5_numbers,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(1,1)),k4_scmfsa_2(k5_numbers))),k16_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k2_scmfsa8c(k4_scmfsa_2(k1_nat_1(1,1)),k3_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k5_scmfsa6a(k6_scmfsa6a(k6_scmfsa_2(k4_scmfsa_2(k1_nat_1(3,1)),k4_scmfsa_2(k1_nat_1(2,1))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(2,1)),k4_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k8_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(4,1)))),k2_scmfsa8b(k4_scmfsa_2(k1_nat_1(5,1)),k5_scmfsa6a(k6_scmfsa6a(k14_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers)),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(5,1)),k4_scmfsa_2(k1_nat_1(2,1)),k5_scmfsa_2(k5_numbers))),k15_scmfsa_2(k4_scmfsa_2(k1_nat_1(4,1)),k4_scmfsa_2(k1_nat_1(3,1)),k5_scmfsa_2(k5_numbers))),k4_compos_1(k1_scmfsa_2)))))),B,A),k5_scmfsa_2(k5_numbers)),D) ) => r1_xxreal_0(F,E) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l67_scmpds_6,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmpds_2)) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ( r2_hidden(k5_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))) ) ) ) ) )).
fof(l67_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(l67_sin_cos,axiom,( ! [A] : ( v7_ordinal1(A) => k9_nat_1(k1_numbers,c2__sin_cos,A) = k2_xcmplx_0(k3_xcmplx_0(2,A),1) ) )).
fof(l67_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( v4_topreal1(E) & m2_finseq_1(E,u1_struct_0(k15_euclid(2))) ) => ! [F] : ( ( 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] : ( ( v4_topreal1(G) & m2_finseq_1(G,u1_struct_0(k15_euclid(2))) ) => ! [H] : ( ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(l67_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(B,A) ) => r1_xxreal_0(k3_xcmplx_0(B,k3_square_1(k2_xcmplx_0(1,k1_square_1(A)))),k3_xcmplx_0(A,k3_square_1(k2_xcmplx_0(1,k1_square_1(B))))) ) ) ) )).
fof(l67_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ~ 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] : ( ( ~ v2_struct_0(D) & v4_orders_2(D) & v7_waybel_0(D) & l1_waybel_0(D,A) ) => ! [E] : ( ( ~ v2_struct_0(E) & v4_orders_2(E) & v7_waybel_0(E) & l1_waybel_0(E,B) ) => ( D = E => ! [F] : ( m3_yellow_6(F,u1_struct_0(D),A) => m3_yellow_6(F,u1_struct_0(E),B) ) ) ) ) ) ) ) ) )).
fof(l67_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k5_xcmplx_0(k3_xcmplx_0(A,k5_xcmplx_0(B))) = k3_xcmplx_0(k5_xcmplx_0(A),B) ) ) )).
fof(l67_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(k7_xcmplx_0(B,C),k7_xcmplx_0(A,C)) ) ) ) ) )).
fof(l68_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k13_afproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k13_afproj(A))) => ! [E] : ( m1_subset_1(E,u1_incsp_1(k13_afproj(A))) => ! [F] : ( m1_subset_1(F,u1_incsp_1(k13_afproj(A))) => ! [G] : ( m1_subset_1(G,u2_incsp_1(k13_afproj(A))) => ! [H] : ( m1_subset_1(H,u2_incsp_1(k13_afproj(A))) => ! [I] : ( m1_subset_1(I,u2_incsp_1(k13_afproj(A))) => ! [J] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l68_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_anproj_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_anproj_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_anproj_1(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_anproj_1(A))) => ! [F] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(l68_arytm_2,axiom,( ! [A] : ~ ( r2_hidden(A,a_0_0_arytm_2) & A != k11_arytm_3 & ! [B] : ( m1_subset_1(B,k5_arytm_3) => ~ ( r2_hidden(B,A) & B != k11_arytm_3 ) ) ) )).
fof(l68_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k7_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,D)) = k3_xcmplx_0(k7_xcmplx_0(A,C),k7_xcmplx_0(D,B)) ) ) ) ) )).
fof(l68_card_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( ! [B] : ( v1_finset_1(B) => ( ( k5_card_1(B) = A & ! [C] : ! [D] : ~ ( 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] : ( v1_finset_1(B) => ( ( k5_card_1(B) = k1_nat_1(A,1) & ! [C] : ! [D] : ~ ( 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) ) ) ) ) ) )).
fof(l68_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_cc0sp2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_cc0sp2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_cc0sp1(u1_struct_0(A)))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l68_classes2,axiom,( v4_ordinal1(k4_ordinal1) )).
fof(l68_fib_num4,axiom,( ~ r1_xxreal_0(k2_xcmplx_0(k4_xcmplx_0(2),5),k2_xcmplx_0(k4_xcmplx_0(k3_square_1(5)),5)) )).
fof(l68_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k7_lattices(k1_lattice2(A),k1_filter_2(A,B)) = k7_lattices(A,B) ) ) )).
fof(l68_finseq_4,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ! [C] : ( ( 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) ) ) ) ) )).
fof(l68_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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(B,k5_numbers) = A & ! [E] : ( v7_ordinal1(E) => ( ~ r1_xxreal_0(C,E) => k1_funct_1(B,k2_xcmplx_0(E,1)) = k1_funct_1(D,k1_funct_1(B,E)) ) ) ) => k1_funct_1(B,C) = k1_funct_1(k8_funct_7(D,C),A) ) ) ) ) )).
fof(l68_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( k3_glib_001(A,B) = k1_funct_1(B,C) => r2_relset_1(k4_ordinal1,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))) ) ) ) ) )).
fof(l68_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => r2_hidden(k3_hilbert1(k4_hilbert1(k4_hilbert1(A,B),C),k4_hilbert1(A,C)),k6_hilbert1) ) ) ) )).
fof(l68_hurwitz,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m1_subset_1(B,k2_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,k1_numbers) => ! [E] : ( m1_subset_1(E,k1_numbers) => ! [F] : ( 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(k1_square_1(k9_complex1(k2_xcmplx_0(A,k8_complex1(B)))),k1_square_1(k9_complex1(k6_xcmplx_0(A,B)))) = k3_xcmplx_0(k3_xcmplx_0(4,C),E) ) ) ) ) ) ) ) )).
fof(l68_matrix11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ! [C] : ( 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(k4_ordinal1),k4_finseq_1(B),k4_finseq_1(C)) ) ) ) )).
fof(l68_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(l68_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( ! [C] : ( m2_subset_1(C,u1_struct_0(A),B) => ! [D] : ( m2_subset_1(D,u1_struct_0(A),B) => r2_hidden(k6_algstr_0(A,C,D),B) ) ) & ! [C] : ( ( ~ v2_struct_0(C) & v15_algstr_0(C) & m2_monoid_0(C,A) ) => u1_struct_0(C) != B ) ) ) ) )).
fof(l68_o_ring_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(B)) => ( ( v6_o_ring_1(C,B) & r1_xxreal_0(A,k3_finseq_1(C)) ) => ( k5_numbers = A | v13_o_ring_1(k7_partfun1(u1_struct_0(B),C,A),B) ) ) ) ) ) )).
fof(l68_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ( k13_quaterni(k10_quaterni(A,B)) = k6_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k13_quaterni(B)),k3_xcmplx_0(k14_quaterni(A),k14_quaterni(B))),k3_xcmplx_0(k15_quaterni(A),k15_quaterni(B))),k3_xcmplx_0(k16_quaterni(A),k16_quaterni(B))) & k14_quaterni(k10_quaterni(A,B)) = k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k14_quaterni(B)),k3_xcmplx_0(k14_quaterni(A),k13_quaterni(B))),k3_xcmplx_0(k15_quaterni(A),k16_quaterni(B))),k3_xcmplx_0(k16_quaterni(A),k15_quaterni(B))) & k15_quaterni(k10_quaterni(A,B)) = k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k15_quaterni(B)),k3_xcmplx_0(k15_quaterni(A),k13_quaterni(B))),k3_xcmplx_0(k16_quaterni(A),k14_quaterni(B))),k3_xcmplx_0(k14_quaterni(A),k16_quaterni(B))) & k16_quaterni(k10_quaterni(A,B)) = k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k16_quaterni(B)),k3_xcmplx_0(k16_quaterni(A),k13_quaterni(B))),k3_xcmplx_0(k14_quaterni(A),k15_quaterni(B))),k3_xcmplx_0(k15_quaterni(A),k14_quaterni(B))) ) ) ) )).
fof(l68_sin_cos,axiom,( v1_funct_1(c2__sin_cos) & v1_funct_2(c2__sin_cos,k4_ordinal1,k4_ordinal1) & v5_valued_0(c2__sin_cos) & m1_subset_1(c2__sin_cos,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) )).
fof(l68_topgen_1,axiom,( m1_subset_1(k1_borsuk_5,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )).
fof(l68_turing_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( r1_xxreal_0(A,3) => m1_subset_1(A,u2_turing_1(k20_turing_1)) ) ) )).
fof(l68_waybel11,axiom,( ! [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] : ( ( 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)) ) ) ) )).
fof(l68_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(A,k7_xcmplx_0(A,2)) ) ) )).
fof(l69_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k13_afproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k13_afproj(A))) => ! [E] : ( m1_subset_1(E,u1_incsp_1(k13_afproj(A))) => ! [F] : ( m1_subset_1(F,u1_incsp_1(k13_afproj(A))) => ! [G] : ( m1_subset_1(G,u2_incsp_1(k13_afproj(A))) => ! [H] : ( m1_subset_1(H,u2_incsp_1(k13_afproj(A))) => ! [I] : ( m1_subset_1(I,u2_incsp_1(k13_afproj(A))) => ! [J] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l69_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_anproj_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_anproj_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_anproj_1(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_anproj_1(A))) => ! [F] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(l69_arytm_2,axiom,( ! [A] : ( m2_subset_1(A,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) => ~ ( A != k11_arytm_3 & ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) => k6_arytm_2(A,B) != k3_arytm_2(c3__arytm_2) ) ) ) )).
fof(l69_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k5_numbers,A) => k3_square_1(A) = k2_power(A,k7_xcmplx_0(1,2)) ) ) )).
fof(l69_bcialg_1,axiom,( ! [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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( m2_bcialg_1(B,A) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),B) => ! [D] : ( m2_subset_1(D,u1_struct_0(A),B) => r1_tarski(a_4_0_bcialg_1(A,B,C,D),B) ) ) ) ) ) )).
fof(l69_bcialg_6,axiom,( ! [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] : ( m1_bcialg_1(B,A) => ! [C] : ( ( v12_bcialg_1(C,A) & m2_bcialg_1(C,A) ) => ! [D] : ( m5_bcialg_2(D,A,C) => ! [E] : ( m2_subset_1(E,u1_struct_0(A),k7_bcialg_6(A,B,C,D)) => ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r2_hidden(E,k6_eqrel_1(u1_struct_0(A),u1_struct_0(A),D,F)) ) ) ) ) ) ) )).
fof(l69_card_2,axiom,( ! [A] : ( v1_finset_1(A) => ( ! [B] : ! [C] : ~ ( 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) ) ) ) )).
fof(l69_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_cc0sp2(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l69_comput_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v4_valued_0(A) & v2_margrel1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) ) => ! [C] : ( m2_finseq_2(C,k4_ordinal1,k4_finseq_2(k1_nat_1(k19_margrel1(A),1),k4_ordinal1)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k2_comput_1(k4_ordinal1)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_comput_1(k4_ordinal1)))) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k4_ordinal1,k2_comput_1(k4_ordinal1)) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_comput_1(k4_ordinal1)))) ) => ( ( ! [H] : ( m1_subset_1(H,k4_ordinal1) => ( ( ( r2_hidden(D,k4_finseq_1(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)))) & r2_hidden(k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)),D,H),k1_relset_1(k3_finseq_2(k4_ordinal1),k9_nat_1(k2_comput_1(k4_ordinal1),F,H))) & r2_hidden(k7_finseq_1(k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)),D,H),k12_finseq_1(k4_ordinal1,k1_recdef_1(k9_nat_1(k2_comput_1(k4_ordinal1),F,H),k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)),D,H)))),k9_xtuple_0(B)) ) => k9_nat_1(k2_comput_1(k4_ordinal1),F,k1_nat_1(H,1)) = k1_funct_4(k9_nat_1(k2_comput_1(k4_ordinal1),F,H),k16_funcop_1(k2_funct_7(k4_ordinal1,k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)),D,k1_nat_1(H,1)),k1_funct_1(B,k7_finseq_1(k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)),D,H),k12_finseq_1(k4_ordinal1,k1_recdef_1(k9_nat_1(k2_comput_1(k4_ordinal1),F,H),k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)),D,H))))))) ) & ( ~ ( r2_hidden(D,k4_finseq_1(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)))) & r2_hidden(k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)),D,H),k1_relset_1(k3_finseq_2(k4_ordinal1),k9_nat_1(k2_comput_1(k4_ordinal1),F,H))) & r2_hidden(k7_finseq_1(k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)),D,H),k12_finseq_1(k4_ordinal1,k1_recdef_1(k9_nat_1(k2_comput_1(k4_ordinal1),F,H),k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)),D,H)))),k9_xtuple_0(B)) ) => k9_nat_1(k2_comput_1(k4_ordinal1),F,k1_nat_1(H,1)) = k9_nat_1(k2_comput_1(k4_ordinal1),F,H) ) ) ) & ! [H] : ( m1_subset_1(H,k4_ordinal1) => ( ( ( r2_hidden(D,k4_finseq_1(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,E))) & r2_hidden(k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,E),D,H),k1_relset_1(k3_finseq_2(k4_ordinal1),k9_nat_1(k2_comput_1(k4_ordinal1),G,H))) & r2_hidden(k7_finseq_1(k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,E),D,H),k12_finseq_1(k4_ordinal1,k1_recdef_1(k9_nat_1(k2_comput_1(k4_ordinal1),G,H),k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,E),D,H)))),k9_xtuple_0(B)) ) => k9_nat_1(k2_comput_1(k4_ordinal1),G,k1_nat_1(H,1)) = k1_funct_4(k9_nat_1(k2_comput_1(k4_ordinal1),G,H),k16_funcop_1(k2_funct_7(k4_ordinal1,k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,E),D,k1_nat_1(H,1)),k1_funct_1(B,k7_finseq_1(k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,E),D,H),k12_finseq_1(k4_ordinal1,k1_recdef_1(k9_nat_1(k2_comput_1(k4_ordinal1),G,H),k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,E),D,H))))))) ) & ( ~ ( r2_hidden(D,k4_finseq_1(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,E))) & r2_hidden(k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,E),D,H),k1_relset_1(k3_finseq_2(k4_ordinal1),k9_nat_1(k2_comput_1(k4_ordinal1),G,H))) & r2_hidden(k7_finseq_1(k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,E),D,H),k12_finseq_1(k4_ordinal1,k1_recdef_1(k9_nat_1(k2_comput_1(k4_ordinal1),G,H),k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,E),D,H)))),k9_xtuple_0(B)) ) => k9_nat_1(k2_comput_1(k4_ordinal1),G,k1_nat_1(H,1)) = k9_nat_1(k2_comput_1(k4_ordinal1),G,H) ) ) ) ) => ( ( r2_hidden(D,k4_finseq_1(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)))) & r2_hidden(k2_finseq_3(D,k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1))),k1_relset_1(k3_finseq_2(k4_ordinal1),A)) & k9_nat_1(k2_comput_1(k4_ordinal1),F,k5_numbers) != k8_funcop_1(k4_ordinal1,k1_tarski(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)),D,k5_numbers)),k1_recdef_1(A,k2_finseq_3(D,k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1))))) ) | ( ~ ( r2_hidden(D,k4_finseq_1(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)))) & r2_hidden(k2_finseq_3(D,k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1))),k1_relset_1(k3_finseq_2(k4_ordinal1),A)) ) & k9_nat_1(k2_comput_1(k4_ordinal1),F,k5_numbers) != k1_xboole_0 ) | ( r2_hidden(D,k4_finseq_1(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,E))) & r2_hidden(k2_finseq_3(D,k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,E)),k1_relset_1(k3_finseq_2(k4_ordinal1),A)) & k9_nat_1(k2_comput_1(k4_ordinal1),G,k5_numbers) != k8_funcop_1(k4_ordinal1,k1_tarski(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,E),D,k5_numbers)),k1_recdef_1(A,k2_finseq_3(D,k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,E)))) ) | ( ~ ( r2_hidden(D,k4_finseq_1(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,E))) & r2_hidden(k2_finseq_3(D,k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,E)),k1_relset_1(k3_finseq_2(k4_ordinal1),A)) ) & k9_nat_1(k2_comput_1(k4_ordinal1),G,k5_numbers) != k1_xboole_0 ) | r2_funct_2(k4_ordinal1,k2_comput_1(k4_ordinal1),F,G) ) ) ) ) ) ) ) ) ) )).
fof(l69_fib_num4,axiom,( ~ r1_xxreal_0(3,k2_xcmplx_0(k4_xcmplx_0(k3_square_1(5)),k1_square_1(k3_square_1(5)))) )).
fof(l69_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l69_finseq_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(l69_fomodel2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k8_relset_1(k4_finseq_2(2,A),k6_margrel1,k2_fomodel2(A),k6_domain_1(k4_ordinal1,1)) = 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))) ) )).
fof(l69_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ! [F] : ( 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] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( m1_subset_1(H,k6_margrel1) => ! [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) ) ) ) ) ) ) ) ) ) ) )).
fof(l69_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( 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) ) ) ) ) ) )).
fof(l69_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => m1_group_2(B,k8_group_4(A,B,C)) ) ) ) )).
fof(l69_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( ( 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 ) ) ) ) )).
fof(l69_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(l69_hurwitz,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m1_subset_1(B,k2_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,k1_numbers) => ! [E] : ( m1_subset_1(E,k1_numbers) => ! [F] : ( 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(k5_numbers,E) | ( ~ ( ~ r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(k9_complex1(k2_xcmplx_0(A,k8_complex1(B))),k9_complex1(k6_xcmplx_0(A,B))) ) & ~ ( ~ r1_xxreal_0(C,k5_numbers) & r1_xxreal_0(k9_complex1(k6_xcmplx_0(A,B)),k9_complex1(k2_xcmplx_0(A,k8_complex1(B)))) ) & ( C = k5_numbers => k9_complex1(k6_xcmplx_0(A,B)) = k9_complex1(k2_xcmplx_0(A,k8_complex1(B))) ) ) ) ) ) ) ) ) ) ) )).
fof(l69_integra8,axiom,( v1_xreal_0(1) )).
fof(l69_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => k4_member_1(k8_member_1(A,B)) = k8_member_1(k4_member_1(A),k4_member_1(B)) ) ) )).
fof(l69_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => 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)) ) ) ) ) )).
fof(l69_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v7_o_ring_1(B,A) => v13_o_ring_1(B,A) ) ) ) )).
fof(l69_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_oppcat_1(C,B,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k3_funct_2(u4_struct_0(B),u4_struct_0(k2_oppcat_1(A)),k11_oppcat_1(B,A,C),k4_cat_1(B,D)) = k4_cat_1(k2_oppcat_1(A),k3_oppcat_1(A,k3_funct_2(u1_struct_0(B),u1_struct_0(A),k7_cat_1(B,A,C),D))) ) ) ) ) )).
fof(l69_scmpds_6,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmpds_2)) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ( k1_funct_1(k1_scmpds_4(k4_scmpds_4(A,B),C),k5_numbers) = A & k1_funct_1(k1_scmpds_4(k4_scmpds_4(A,B),C),1) = B ) ) ) ) )).
fof(l69_sin_cos,axiom,( v1_funct_1(c2__sin_cos) & v1_funct_2(c2__sin_cos,k4_ordinal1,k4_ordinal1) & v5_valued_0(c2__sin_cos) & m1_subset_1(c2__sin_cos,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) )).
fof(l69_toprealb,axiom,( ! [A] : ( 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(k3_xcmplx_0(2,k28_sin_cos),k5_numbers),k18_sin_cos),A),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k3_xcmplx_0(2,k28_sin_cos),k5_numbers),k16_sin_cos),A)) ) )).
fof(l69_turing_1,axiom,( r2_hidden(k5_numbers,u1_turing_1(k20_turing_1)) & r2_hidden(1,u1_turing_1(k20_turing_1)) )).
fof(l69_waybel11,axiom,( ! [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] : ( ( 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) ) ) ) )).
fof(l6_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,E) => r2_analoaf(A,B,C,E,D) ) ) ) ) ) ) )).
fof(l6_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l6_altcat_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k7_altcat_1(k1_tarski(k1_xboole_0)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_altcat_1(k1_tarski(k1_xboole_0)))) => ( m1_subset_1(k1_xboole_0,k1_altcat_1(k7_altcat_1(k1_tarski(k1_xboole_0)),A,B)) & r2_hidden(k1_xboole_0,k1_altcat_1(k7_altcat_1(k1_tarski(k1_xboole_0)),A,B)) ) ) ) )).
fof(l6_ami_2,axiom,( r2_hidden(k4_ordinal1,k1_ami_2) )).
fof(l6_ami_wstd,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_setfam_1(B) => ! [C] : ( ( ~ 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) ) ) ) )).
fof(l6_amistd_2,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_extpro_1(A))) => k5_xtuple_0(B) = k5_numbers ) ) )).
fof(l6_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( ( 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 ) ) ) ) ) ) ) ) ) )).
fof(l6_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( ( r1_analmetr(A,C,D) & B = k3_rlvect_1(A,k1_rlvect_1(A,C,E),k1_rlvect_1(A,D,F)) ) => ( E = k2_geomtrap(A,C,D,B) & F = k3_geomtrap(A,C,D,B) ) ) ) ) ) ) ) ) )).
fof(l6_aofa_000,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( v7_ordinal1(C) => v8_comput_1(k1_aofa_000(A,A,k4_finseq_2(C,A),B),C) ) ) ) )).
fof(l6_arithm,axiom,( k4_xcmplx_0(k5_numbers) = k5_numbers )).
fof(l6_arytm_2,axiom,( r1_tarski(k2_xboole_0(k5_arytm_3,k1_arytm_2),k2_xboole_0(k5_arytm_3,a_0_0_arytm_2)) )).
fof(l6_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( 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)))) ) ) ) ) )).
fof(l6_bhsp_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_rlsub_1(o_0_5_bhsp_1))) => ! [B] : ( 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)) ) ) )).
fof(l6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) )).
fof(l6_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,k7_xcmplx_0(1,2)) ) => r2_hidden(k2_xcmplx_0(A,k7_xcmplx_0(1,2)),u1_struct_0(k17_borsuk_1)) ) ) )).
fof(l6_bvfunc14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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)) ) ) )).
fof(l6_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(l6_card_4,axiom,( ! [A] : ~ ( r2_hidden(A,k2_zfmisc_1(k4_ordinal1,k4_ordinal1)) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => A != k1_domain_1(k4_ordinal1,k4_ordinal1,B,C) ) ) ) )).
fof(l6_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => v1_catalan2(k8_funcop_1(k4_ordinal1,A,k5_numbers)) ) )).
fof(l6_cfdiff_1,axiom,( v1_funct_1(k8_funcop_1(k2_numbers,k4_ordinal1,k5_complex1)) & v1_funct_2(k8_funcop_1(k2_numbers,k4_ordinal1,k5_complex1),k4_ordinal1,k2_numbers) & m1_subset_1(k8_funcop_1(k2_numbers,k4_ordinal1,k5_complex1),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) )).
fof(l6_cfdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( r2_relset_1(k4_ordinal1,k2_numbers,B,k25_valued_1(k4_ordinal1,k2_numbers,A,k7_complex1)) => ( ( ( v1_cfdiff_1(A,k5_numbers) & v9_ordinal1(A) ) => ( v1_cfdiff_1(B,k5_numbers) & v9_ordinal1(B) ) ) & ( ( v1_cfdiff_1(B,k5_numbers) & v9_ordinal1(B) ) => ( v1_cfdiff_1(A,k5_numbers) & v9_ordinal1(A) ) ) ) ) ) ) )).
fof(l6_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(l6_collsp,axiom,( ~ v1_xboole_0(k6_domain_1(k4_ordinal1,1)) )).
fof(l6_complex1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ( k3_complex1(k5_arytm_0(A,B)) = A & k4_complex1(k5_arytm_0(A,B)) = B ) ) ) )).
fof(l6_comptrig,axiom,( ~ r1_xxreal_0(k28_sin_cos,k5_numbers) )).
fof(l6_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(l6_csspace2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v2_comseq_3(A) => r1_xxreal_0(k9_complex1(k11_comseq_3(A)),k4_series_1(k55_valued_1(k4_ordinal1,k2_numbers,A))) ) ) )).
fof(l6_csspace4,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_comseq_2(B) => v1_comseq_2(k25_valued_1(k4_ordinal1,k2_numbers,B,A)) ) ) ) )).
fof(l6_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( r2_hidden(k4_tarski(B,C),D) => ( r2_hidden(B,A) & r2_hidden(C,A) ) ) ) )).
fof(l6_euclid,axiom,( ! [A] : ( ( 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))) ) )).
fof(l6_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => k4_euclid_3(A,B,C) != k2_xcmplx_0(k3_xcmplx_0(2,k4_euclid_3(D,E,F)),k3_xcmplx_0(2,k28_sin_cos)) ) ) ) ) ) ) )).
fof(l6_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(A,B) & ! [C] : ( v7_ordinal1(C) => A != k2_xcmplx_0(k1_nat_1(B,1),C) ) ) ) ) )).
fof(l6_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => k8_euclid(3,A,B) = k1_euclid_8(k6_xcmplx_0(k1_funct_1(A,1),k1_funct_1(B,1)),k6_xcmplx_0(k1_funct_1(A,2),k1_funct_1(B,2)),k6_xcmplx_0(k1_funct_1(A,3),k1_funct_1(B,3))) ) ) )).
fof(l6_euler_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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 = k5_numbers ) ) ) )).
fof(l6_fib_fusc,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( A != k5_numbers & r1_xxreal_0(k6_xcmplx_0(k2_nat_1(6,A),4),k5_numbers) ) ) )).
fof(l6_fib_num,axiom,( k1_nat_1(k1_nat_1(1,1),1) = 3 )).
fof(l6_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( v5_relat_1(B,A) & v1_finseq_1(B) ) => m2_finseq_1(B,A) ) ) )).
fof(l6_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( v1_fomodel2(C,A,B) => r1_tarski(k37_fomodel1(A),k9_xtuple_0(C)) ) ) ) ) )).
fof(l6_fomodel4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ! [D] : ( 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] : ( m1_subset_1(E,k1_zfmisc_1(k1_fomodel4(B))) => ! [F] : ( v2_fomodel4(F,B) => ( k1_relset_1(k9_setfam_1(k1_fomodel4(B)),k4_fomodel4(B,C)) = k9_setfam_1(k1_fomodel4(B)) & r1_tarski(k10_xtuple_0(k4_fomodel4(B,C)),k1_relset_1(k9_setfam_1(k1_fomodel4(B)),k4_fomodel4(B,C))) & v1_funct_1(k8_funct_7(k4_fomodel4(B,C),A)) & v1_funct_2(k8_funct_7(k4_fomodel4(B,C),A),k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))) & m1_subset_1(k8_funct_7(k4_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(k8_funct_7(k4_fomodel4(B,C),A)) = k9_setfam_1(k1_fomodel4(B)) & k2_xboole_0(k1_relset_1(k9_setfam_1(k1_fomodel4(B)),k4_fomodel4(B,C)),k10_xtuple_0(k4_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(k8_funct_7(D,A))) ) ) ) ) ) ) ) )).
fof(l6_freealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_unialg_2(B,A) => r1_tarski(k6_unialg_2(A),B) ) ) ) )).
fof(l6_friends1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ r2_hidden(A,k4_finseq_1(B)) => k7_finseq_1(k1_rfinseq(A,B),k16_finseq_1(A,B)) = B ) ) ) )).
fof(l6_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ! [E] : ! [F] : r1_xboole_0(k2_msafree2(k13_gfacirc1(A,B,C)),k3_msafree2(k13_gfacirc1(D,E,F))) ) ) ) )).
fof(l6_gobrd12,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l6_graphsp,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(l6_hilbert1,axiom,( ! [A] : ~ ( v5_hilbert1(A) & v1_xboole_0(A) ) )).
fof(l6_holder_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,A,B)) ) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,k3_series_1(A),B)) ) ) ) )).
fof(l6_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r1_int_1(A,B) <=> r1_int_1(A,k4_xcmplx_0(B)) ) ) ) )).
fof(l6_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(l6_int_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k8_newton) & v1_funct_1(A) & v1_partfun1(A,k8_newton) & v4_valued_0(A) & v2_pre_poly(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k8_newton) & v1_funct_1(B) & v1_partfun1(B,k8_newton) & v4_valued_0(B) & v2_pre_poly(B) ) => ~ ( r1_tarski(k22_pre_poly(k8_newton,A),k22_pre_poly(k8_newton,B)) & k5_relat_1(A,k22_pre_poly(k8_newton,A)) = k5_relat_1(B,k22_pre_poly(k8_newton,A)) & ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k8_newton) & v1_funct_1(C) & v1_partfun1(C,k8_newton) & v4_valued_0(C) & v2_pre_poly(C) ) => ~ ( k22_pre_poly(k8_newton,C) = k7_subset_1(k8_newton,k22_pre_poly(k8_newton,B),k22_pre_poly(k8_newton,A)) & r1_xboole_0(k22_pre_poly(k8_newton,A),k22_pre_poly(k8_newton,C)) & k5_relat_1(C,k22_pre_poly(k8_newton,C)) = k5_relat_1(B,k22_pre_poly(k8_newton,C)) & r8_pboole(k8_newton,k11_pre_poly(k8_newton,A,C),B) ) ) ) ) ) )).
fof(l6_integra4,axiom,( r2_hidden(k5_numbers,k1_numbers) )).
fof(l6_jordan1d,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k3_tarski(k2_enumset1(A,B,C,D)) = k2_xboole_0(k2_xboole_0(k2_xboole_0(A,B),C),D) )).
fof(l6_jordan1h,axiom,( r1_relat_2(k1_jordan1h,k1_numbers) )).
fof(l6_jordan22,axiom,( k1_relset_1(u1_struct_0(k15_euclid(2)),k5_pscomp_1) = u1_struct_0(k15_euclid(2)) )).
fof(l6_jordan24,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_int_1(C) => k2_complex2(B,A) = k2_complex2(B,k2_xcmplx_0(A,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C))) ) ) ) )).
fof(l6_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(B,k5_numbers) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => ( D = k5_euclid(A) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( E = k8_metric_1(k14_euclid(A),D,C) => k1_convex1(k15_euclid(A),E,B) = k8_metric_1(k14_euclid(A),D,k3_xcmplx_0(B,C)) ) ) ) ) ) ) ) ) )).
fof(l6_lattices,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(g1_lattices(k1_zfmisc_1(k1_xboole_0),A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(g1_lattices(k1_zfmisc_1(k1_xboole_0),A))) => B = C ) ) ) )).
fof(l6_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ( 1 = A => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k2_power(k9_nat_1(k1_numbers,k3_series_1(k1_lp_space(k1_series_1(k1_numbers,B,C),A)),D),k7_xcmplx_0(1,A)),k2_xcmplx_0(k2_power(k9_nat_1(k1_numbers,k3_series_1(k1_lp_space(B,A)),D),k7_xcmplx_0(1,A)),k2_power(k9_nat_1(k1_numbers,k3_series_1(k1_lp_space(C,A)),D),k7_xcmplx_0(1,A)))) ) ) ) ) ) )).
fof(l6_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(l6_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(C),A,B) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(C))) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(C),A,B) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(C))) ) => ! [H] : ( m2_finseq_1(H,u1_struct_0(C)) => ! [I] : ( v7_ordinal1(I) => ! [J] : ( v7_ordinal1(J) => ( ( r2_hidden(I,k2_finseq_1(A)) & r2_hidden(J,k2_finseq_1(k1_matrix_0(F))) & H = k7_matrix_0(u1_struct_0(C),F,E) & G = k3_matrix11(E,A,B,u1_struct_0(C),F,k9_fvsum_1(C,H,D)) ) => ( ( I = E => k3_matrix_0(u1_struct_0(C),G,I,J) = k8_group_1(C,D,k3_matrix_0(u1_struct_0(C),F,E,J)) ) & ( I != E => k3_matrix_0(u1_struct_0(C),G,I,J) = k3_matrix_0(u1_struct_0(C),F,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l6_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( 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))) ) ) ) )).
fof(l6_metric_1,axiom,( ! [A] : ( m1_subset_1(A,1) => ! [B] : ( m1_subset_1(B,1) => ! [C] : ( m1_subset_1(C,1) => r1_xxreal_0(k1_binop_1(k9_funct_5,A,C),k2_xcmplx_0(k1_binop_1(k9_funct_5,A,B),k1_binop_1(k9_funct_5,B,C))) ) ) ) )).
fof(l6_metrizts,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(l6_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(l6_modelc_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( A = k5_numbers | r1_xxreal_0(1,A) ) ) )).
fof(l6_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ~ ( r2_hidden(C,k6_dtconstr(k5_msafree(A,B))) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(B,D)) => C != k4_tarski(E,D) ) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(B,D)) => ( C = k4_tarski(E,D) => r2_hidden(C,k6_dtconstr(k5_msafree(A,B))) ) ) ) ) ) ) )).
fof(l6_ndiff_5,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l6_normsp_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_rlsub_1(o_0_5_normsp_1))) => ! [B] : ( 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)),k3_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))) ) ) )).
fof(l6_normsp_2,axiom,( ! [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) & 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)))) ) )).
fof(l6_ntalgo_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => ! [B] : ( m1_subset_1(B,k4_numbers) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_ordinal1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ( ( k9_nat_1(k4_ordinal1,C,k5_numbers) = k1_int_2(A) & k9_nat_1(k4_ordinal1,D,k5_numbers) = k1_int_2(B) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( k9_nat_1(k4_ordinal1,C,k1_nat_1(E,1)) = k9_nat_1(k4_ordinal1,D,E) & k9_nat_1(k4_ordinal1,D,k1_nat_1(E,1)) = k4_nat_d(k9_nat_1(k4_ordinal1,C,E),k9_nat_1(k4_ordinal1,D,E)) ) ) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( k9_nat_1(k4_ordinal1,D,E) != k5_numbers => k6_nat_d(k9_nat_1(k4_ordinal1,C,k5_numbers),k9_nat_1(k4_ordinal1,D,k5_numbers)) = k6_nat_d(k9_nat_1(k4_ordinal1,C,E),k9_nat_1(k4_ordinal1,D,E)) ) ) ) ) ) ) ) )).
fof(l6_ordeq_01,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(k7_xcmplx_0(E,2),k2_normsp_0(A,k5_algstr_0(A,B,D))) & ~ r1_xxreal_0(k7_xcmplx_0(E,2),k2_normsp_0(A,k5_algstr_0(A,C,D))) & r1_xxreal_0(E,k2_normsp_0(A,k5_algstr_0(A,B,C))) ) ) ) ) ) ) )).
fof(l6_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(l6_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( k5_algstr_0(A,k8_group_1(A,B,F),k8_group_1(A,E,C)) = k4_struct_0(A) & k5_algstr_0(A,k8_group_1(A,B,D),k8_group_1(A,G,C)) = k4_struct_0(A) ) => ( C = k4_struct_0(A) | k5_algstr_0(A,k8_group_1(A,E,D),k8_group_1(A,G,F)) = k4_struct_0(A) ) ) ) ) ) ) ) ) ) )).
fof(l6_partfun3,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l6_pdiff_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(A,B) => k2_rfinseq(k1_numbers,A,k5_euclid(B)) = k5_euclid(k7_nat_d(B,A)) ) ) ) )).
fof(l6_petri_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( r1_tarski(B,C) => r1_tarski(k2_petri_2(A,B),k9_setfam_1(k4_partfun1(C,A))) ) ) )).
fof(l6_polynom7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k15_pre_poly(k1_xboole_0),u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(k1_xboole_0),u1_struct_0(A)))) ) => ? [C] : ( 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)) ) ) ) )).
fof(l6_polyred,axiom,( ! [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) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( v7_ordinal1(D) => ( ( k3_finseq_1(B) = k2_xcmplx_0(D,1) & C = k2_partfun1(k4_ordinal1,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))) ) ) ) ) ) )).
fof(l6_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( ~ r1_collsp(A,B,C,E) & r1_collsp(A,B,C,D) & r1_collsp(A,B,E,F) & B != D & D = F ) ) ) ) ) ) ) )).
fof(l6_prvect_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(l6_pua2mss1,axiom,( ! [A] : ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ! [D] : ! [E] : ( ( r2_hidden(C,D) & r2_hidden(D,B) & r2_hidden(C,E) & r2_hidden(E,B) ) => D = E ) ) )).
fof(l6_qmax_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( r2_hidden(A,k12_prob_1) => ( ( r2_hidden(k5_numbers,A) => k1_funct_1(c2__qmax_1,A) = 1 ) & ( ~ r2_hidden(k5_numbers,A) => k1_funct_1(c2__qmax_1,A) = k5_numbers ) ) ) ) )).
fof(l6_quaterni,axiom,( r2_zfmisc_1(k5_numbers,1,2,3) )).
fof(l6_ramsey_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ( k5_card_1(B) = A => k3_group_10(B,A) = k1_tarski(B) ) ) ) )).
fof(l6_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ~ ( r2_mesfunc6(A,B,C) & ! [D] : ( ( v1_prob_2(D) & m2_finseq_1(D,B) ) => ! [E] : ( 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] : ( v7_ordinal1(F) => ( r2_hidden(F,k4_finseq_1(D)) => ! [G] : ( r2_hidden(G,k1_funct_1(D,F)) => k12_supinf_2(C,G) = k12_supinf_2(E,F) ) ) ) ) ) ) ) ) ) ) )).
fof(l6_rat_1,axiom,( ! [A] : ~ ( r2_hidden(A,k3_numbers) & ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => A != k7_xcmplx_0(B,C) ) ) ) )).
fof(l6_real_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_real_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_real_lat)) => k1_lattices(k3_real_lat,k2_lattices(k3_real_lat,A,B),B) = B ) ) )).
fof(l6_realset2,axiom,( k10_subset_1(1,2) = 1 )).
fof(l6_reloc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( ~ 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(k7_card_1(2),k1_ami_3)) & v1_finset_1(C) & v4_extpro_1(C,k7_card_1(2),k1_ami_3,B) ) => ! [D] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ! [E] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(E,u1_struct_0(k1_ami_3)) ) => ( ( r1_tarski(C,D) & r1_tarski(k9_memstr_0(k7_card_1(2),k1_ami_3,C,A),E) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_ami_3)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ! [G] : ( ( v1_relat_1(G) & v4_relat_1(G,k4_ordinal1) & v5_relat_1(G,u1_compos_1(k1_ami_3)) & v1_funct_1(G) & v1_partfun1(G,k4_ordinal1) ) => ( ( r1_tarski(B,F) & r1_tarski(k6_compos_1(k1_ami_3,B,A),G) ) => ! [H] : ( v7_ordinal1(H) => ( k2_xcmplx_0(k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,F,D,H)),A) = k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,G,E,H)) & k5_compos_0(u1_compos_1(k1_ami_3),k3_extpro_1(k7_card_1(2),k1_ami_3,F,k5_extpro_1(k7_card_1(2),k1_ami_3,F,D,H)),A) = k3_extpro_1(k7_card_1(2),k1_ami_3,G,k5_extpro_1(k7_card_1(2),k1_ami_3,G,E,H)) & k5_relat_1(k5_extpro_1(k7_card_1(2),k1_ami_3,F,D,H),k9_xtuple_0(k6_memstr_0(k7_card_1(2),k1_ami_3,C))) = k5_relat_1(k5_extpro_1(k7_card_1(2),k1_ami_3,G,E,H),k9_xtuple_0(k6_memstr_0(k7_card_1(2),k1_ami_3,C))) & k6_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,F,k1_funct_4(D,k6_memstr_0(k7_card_1(2),k1_ami_3,E)),H)) = k6_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,G,E,H)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l6_rfinseq,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( ! [B] : ( v1_finset_1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ~ ( k5_card_1(k9_xtuple_0(k5_relat_1(C,B))) = A & ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ~ r2_classes1(k5_relat_1(C,B),D) ) ) ) ) => ! [B] : ( v1_finset_1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ~ ( k5_card_1(k9_xtuple_0(k5_relat_1(C,B))) = k1_nat_1(A,1) & ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ~ r2_classes1(k5_relat_1(C,B),D) ) ) ) ) ) ) )).
fof(l6_ringcat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => v1_ringcat1(k3_struct_0(A),A,A) ) )).
fof(l6_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) )).
fof(l6_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => k1_rlsub_2(A,B,C) = k1_rlsub_2(A,C,B) ) ) ) )).
fof(l6_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)))) ) ) ) )).
fof(l6_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => k1_rmod_3(A,B,C,D) = k1_rmod_3(A,B,D,C) ) ) ) ) )).
fof(l6_roughs_1,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_orders_3(A) => v1_roughs_1(A) ) ) )).
fof(l6_rsspace2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k3_xcmplx_0(k6_xcmplx_0(k9_nat_1(k1_numbers,B,D),A),k6_xcmplx_0(k9_nat_1(k1_numbers,B,D),A)) ) => ( v2_comseq_2(C) & k1_seq_2(C) = k3_xcmplx_0(k6_xcmplx_0(k1_seq_2(B),A),k6_xcmplx_0(k1_seq_2(B),A)) ) ) ) ) ) ) )).
fof(l6_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => k1_rusub_2(A,B,C) = k1_rusub_2(A,C,B) ) ) ) )).
fof(l6_scm_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_ami_3)) ) => ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_ami_3)) ) => ( k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_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(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1)) = k2_extpro_1(k7_card_1(2),k1_ami_3,k3_compos_1(k1_ami_3,A,C),k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B)) & k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1))) = k1_nat_1(C,1) ) ) ) ) ) ) ) ) ) )).
fof(l6_scmfsa7b,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(B,k7_card_1(3),k1_scmfsa_2,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( v1_int_1(E) => ( ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ~ 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,k1_nat_1(A,F)) ) ) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(F,k1_afinsq_1(k2_scmfsa_7(D,E))) => k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,C,B,F)) = k1_nat_1(A,F) ) ) ) ) ) ) ) ) )).
fof(l6_scmpds_8,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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))) = k1_nat_1(k5_card_1(C),3) ) ) ) )).
fof(l6_scpinvar,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( k1_funct_1(B,k2_scmp_gcd) = k5_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,k5_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) = k5_numbers & k1_funct_1(k6_scmpds_4(k3_scmpds_4(k4_scmpds_4(k12_scmpds_2(k2_scmp_gcd,k1_scmp_gcd(3),1,k5_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,k5_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,k5_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)) = k1_nat_1(C,1) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ~ 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,k5_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)) ) ) ) ) ) ) ) )).
fof(l6_series_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k2_xcmplx_0(k3_xcmplx_0(k2_nat_1(A,k1_nat_1(k2_nat_1(2,A),1)),k6_xcmplx_0(k1_nat_1(k2_nat_1(3,k11_newton(A,2)),k2_nat_1(3,A)),1)),k2_nat_1(k11_newton(k1_nat_1(A,1),3),30)) = k3_xcmplx_0(k2_nat_1(k1_nat_1(A,2),k1_nat_1(k2_nat_1(2,k1_nat_1(A,1)),1)),k6_xcmplx_0(k1_nat_1(k2_nat_1(3,k11_newton(k1_nat_1(A,1),2)),k2_nat_1(3,k1_nat_1(A,1))),1)) ) )).
fof(l6_series_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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_square_1(A)),B)),k3_xcmplx_0(k3_xcmplx_0(3,A),k1_square_1(B))),k1_newton(B,3)) ) ) )).
fof(l6_series_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( 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,k1_nat_1(A,1))),k6_xcmplx_0(1,B))),k3_xcmplx_0(A,k1_newton(B,k1_nat_1(A,1)))),k1_newton(B,k1_nat_1(A,1))) = k6_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(B,k6_xcmplx_0(1,k1_newton(B,k1_nat_1(A,1)))),k1_newton(k6_xcmplx_0(1,B),2)),k7_xcmplx_0(k3_xcmplx_0(k1_nat_1(A,1),k1_newton(B,k1_nat_1(A,2))),k6_xcmplx_0(1,B))) ) ) ) )).
fof(l6_series_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k1_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(k1_square_1(A),k1_square_1(B)),k1_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)) ) ) ) )).
fof(l6_sfmastr1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ( ( k1_funct_1(D,k4_scmfsa_2(k5_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(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)),D) & r1_tarski(k3_scmfsa6a(B,C),A) ) => ( k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D,k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),D),1))) = k5_card_1(B) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D,k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),D),1))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_m(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),D,k8_extpro_1(k7_card_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(k7_card_1(3),k1_scmfsa_2,A,D,k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),D),1)),k4_scmfsa_2(k5_numbers)) = 1 & r1_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D) & k8_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D) = k2_xcmplx_0(k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),D),1),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(k1_funct_4(A,B),C),k1_scmfsa_m(k6_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),D)))) & ( v1_scmfsa7b(C) => k1_funct_1(k6_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D),k4_scmfsa_2(k5_numbers)) = 1 ) ) ) ) ) ) ) )).
fof(l6_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A) = k7_xcmplx_0(k2_xcmplx_0(k15_sin_cos(A),k15_sin_cos(k4_xcmplx_0(A))),2) ) )).
fof(l6_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( k6_xcmplx_0(A,B) != k5_numbers & k2_sin_cos2(k6_xcmplx_0(k7_xcmplx_0(A,2),k7_xcmplx_0(B,2))) = k5_numbers ) ) ) )).
fof(l6_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k2_rcomp_1(k5_numbers,k28_sin_cos)) => k1_fdiff_1(k27_sin_cos,A) = k4_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,A)))) ) ) )).
fof(l6_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),k1_tarski(k5_numbers)),k1_tarski(k5_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_tarski(k5_numbers)),k1_tarski(k5_numbers)))) ) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_tarski(k5_numbers)) => k2_binop_1(u1_struct_0(A),k1_tarski(k5_numbers),k1_tarski(k5_numbers),B,C,D) = c2__symsp_1 ) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_tarski(k5_numbers),k1_tarski(k5_numbers)))) => ! [D] : ( ( ~ 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(k5_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) ) ) ) ) ) ) ) )).
fof(l6_taylor_2,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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 ) ) )).
fof(l6_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(l6_topalg_2,axiom,( k9_xtuple_0(k3_struct_0(k5_topmetr)) = u1_struct_0(k5_topmetr) )).
fof(l6_topalg_5,axiom,( m1_subset_1(k5_numbers,u1_struct_0(k5_topmetr)) & m1_subset_1(1,u1_struct_0(k5_topmetr)) )).
fof(l6_topdim_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(l6_topgen_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( ! [C] : ( ( 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)) ) ) ) ) )).
fof(l6_topreal2,axiom,( k17_euclid(k19_euclid(k5_numbers,1)) = k5_numbers )).
fof(l6_toprealb,axiom,( r1_xxreal_0(k6_xcmplx_0(k7_xcmplx_0(3,2),k7_xcmplx_0(1,2)),1) )).
fof(l6_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(l6_trees_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m2_finseq_1(C,B) => ( ~ r1_xxreal_0(k3_finseq_1(C),A) => r2_hidden(k1_funct_1(C,k1_nat_1(A,1)),B) ) ) ) )).
fof(l6_waybel17,axiom,( ! [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) & v4_waybel11(A) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v4_pre_topc(k5_waybel_0(A,B),A) ) ) )).
fof(l6_waybel33,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ! [D] : ( ( ~ 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] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(l6_wellset1,axiom,( ! [A] : ! [B] : ( r2_tarski(B,A) <=> ? [C] : ( ! [D] : ~ ( r2_hidden(D,B) & ! [E] : ~ ( r2_hidden(E,A) & r2_hidden(k4_tarski(D,E),C) ) ) & ! [D] : ~ ( r2_hidden(D,A) & ! [E] : ~ ( r2_hidden(E,B) & r2_hidden(k4_tarski(E,D),C) ) ) & ! [D] : ! [E] : ! [F] : ! [G] : ( ( r2_hidden(k4_tarski(D,E),C) & r2_hidden(k4_tarski(F,G),C) ) => ( D = F <=> E = G ) ) ) ) )).
fof(l6_wsierp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,C) ) | ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(C,B) ) ) => ( ~ r1_xxreal_0(k2_xcmplx_0(A,B),C) & ~ r1_xxreal_0(B,k6_xcmplx_0(C,A)) ) ) ) ) ) )).
fof(l6_xcmplx_0,axiom,( r2_hidden(1,k4_ordinal1) )).
fof(l6_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(A,B) => r1_xxreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C)) ) ) ) ) )).
fof(l6_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l6_xxreal_0,axiom,( r2_hidden(k5_numbers,k4_ordinal1) )).
fof(l6_yellow17,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ! [E] : ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k1_funct_1(A,D))) => ( ( r2_hidden(B,k4_card_3(A)) & r2_hidden(k1_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)) ) ) ) ) ) )).
fof(l6_yellow_6,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(l6_zf_fund2,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ( ( r1_xboole_0(k1_enumset1(k2_zf_lang(k5_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(k5_numbers),k8_zf_lang(k2_zf_lang(4),k12_zf_lang(A,k4_zf_lang(k2_zf_lang(4),k2_zf_lang(k5_numbers))))))) ) => ( r2_hidden(D,k4_zf_lang1(A)) | ( r1_xboole_0(k1_enumset1(k2_zf_lang(k5_numbers),k2_zf_lang(1),k2_zf_lang(2)),k2_zf_model(k6_zf_lang1(A,k2_zf_lang(k5_numbers),D))) & r1_zf_model(B,C,k8_zf_lang(k2_zf_lang(3),k13_zf_lang(k2_zf_lang(k5_numbers),k8_zf_lang(k2_zf_lang(4),k12_zf_lang(k6_zf_lang1(A,k2_zf_lang(k5_numbers),D),k4_zf_lang(k2_zf_lang(4),k2_zf_lang(k5_numbers))))))) & r2_funct_2(B,B,k1_zfmodel1(A,B,C),k1_zfmodel1(k6_zf_lang1(A,k2_zf_lang(k5_numbers),D),B,C)) ) ) ) ) ) ) ) )).
fof(l70_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(H,u1_struct_0(A)) => ~ ( r2_analoaf(A,B,D,E,H) & r2_analoaf(A,C,D,F,H) ) ) ) ) ) ) ) ) ) ) )).
fof(l70_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => v2_anproj_2(k5_anproj_1(A)) ) )).
fof(l70_asympt_1,axiom,( ? [A] : ( m1_subset_1(A,k4_ordinal1) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( r1_xxreal_0(A,B) & r1_xxreal_0(k6_xcmplx_0(B,k3_xcmplx_0(k3_square_1(B),k3_power(2,B))),k7_xcmplx_0(B,2)) ) ) ) )).
fof(l70_bcialg_4,axiom,( 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) )).
fof(l70_borsuk_5,axiom,( 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)) )).
fof(l70_comput_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v4_valued_0(A) & v2_margrel1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) ) => ! [C] : ( m2_finseq_2(C,k4_ordinal1,k4_finseq_2(k1_nat_1(k19_margrel1(A),1),k4_ordinal1)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(D,k4_finseq_1(C)) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k2_comput_1(k4_ordinal1)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_comput_1(k4_ordinal1)))) ) => ( ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( ( ( r2_hidden(D,k4_finseq_1(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)))) & r2_hidden(k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)),D,G),k1_relset_1(k3_finseq_2(k4_ordinal1),k9_nat_1(k2_comput_1(k4_ordinal1),F,G))) & r2_hidden(k7_finseq_1(k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)),D,G),k12_finseq_1(k4_ordinal1,k1_recdef_1(k9_nat_1(k2_comput_1(k4_ordinal1),F,G),k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)),D,G)))),k9_xtuple_0(B)) ) => k9_nat_1(k2_comput_1(k4_ordinal1),F,k1_nat_1(G,1)) = k1_funct_4(k9_nat_1(k2_comput_1(k4_ordinal1),F,G),k16_funcop_1(k2_funct_7(k4_ordinal1,k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)),D,k1_nat_1(G,1)),k1_funct_1(B,k7_finseq_1(k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)),D,G),k12_finseq_1(k4_ordinal1,k1_recdef_1(k9_nat_1(k2_comput_1(k4_ordinal1),F,G),k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)),D,G))))))) ) & ( ~ ( r2_hidden(D,k4_finseq_1(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)))) & r2_hidden(k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)),D,G),k1_relset_1(k3_finseq_2(k4_ordinal1),k9_nat_1(k2_comput_1(k4_ordinal1),F,G))) & r2_hidden(k7_finseq_1(k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)),D,G),k12_finseq_1(k4_ordinal1,k1_recdef_1(k9_nat_1(k2_comput_1(k4_ordinal1),F,G),k1_funct_7(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)),D,G)))),k9_xtuple_0(B)) ) => k9_nat_1(k2_comput_1(k4_ordinal1),F,k1_nat_1(G,1)) = k9_nat_1(k2_comput_1(k4_ordinal1),F,G) ) ) ) => ( ( r2_hidden(D,k4_finseq_1(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)))) & r2_hidden(k2_finseq_3(D,k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1))),k1_relset_1(k3_finseq_2(k4_ordinal1),A)) & k9_nat_1(k2_comput_1(k4_ordinal1),F,k5_numbers) != k8_funcop_1(k4_ordinal1,k1_tarski(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)),D,k5_numbers)),k1_recdef_1(A,k2_finseq_3(D,k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1))))) ) | ( ~ ( r2_hidden(D,k4_finseq_1(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)))) & r2_hidden(k2_finseq_3(D,k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1))),k1_relset_1(k3_finseq_2(k4_ordinal1),A)) ) & k9_nat_1(k2_comput_1(k4_ordinal1),F,k5_numbers) != k1_xboole_0 ) | ( k1_recdef_1(k9_nat_1(k2_comput_1(k4_ordinal1),F,k1_nat_1(E,1)),k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,E)) = k1_recdef_1(k9_nat_1(k2_comput_1(k4_ordinal1),F,E),k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,E)) & ~ r2_hidden(k1_midsp_3(k4_ordinal1,k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(E,1)),k1_relset_1(k3_finseq_2(k4_ordinal1),k9_nat_1(k2_comput_1(k4_ordinal1),F,E))) ) ) ) ) ) ) ) ) ) ) )).
fof(l70_fib_num4,axiom,( ~ r1_xxreal_0(k7_xcmplx_0(3,5),k7_xcmplx_0(k3_xcmplx_0(k3_square_1(5),k6_xcmplx_0(k3_square_1(5),1)),5)) )).
fof(l70_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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(B,1) = A & ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(1,E) => ( r1_xxreal_0(k2_xcmplx_0(C,1),E) | k1_funct_1(B,k2_xcmplx_0(E,1)) = k1_funct_1(D,k1_funct_1(B,E)) ) ) ) ) => k1_funct_1(B,k2_xcmplx_0(C,1)) = k1_funct_1(k8_funct_7(D,C),A) ) ) ) ) )).
fof(l70_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ! [F] : ( 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] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(l70_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( r2_hidden(E,k1_relset_1(k4_ordinal1,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))) ) ) ) ) ) ) ) )).
fof(l70_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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))) ) ) ) ) )).
fof(l70_hfdiff_1,axiom,( ! [A] : ( ( 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(k4_ordinal1,k4_xboole_0(k1_relset_1(k1_numbers,A),k8_relset_1(k1_numbers,k1_numbers,A,k1_tarski(k5_numbers))),1) ) )).
fof(l70_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(l70_matrix13,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ! [E] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l70_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => 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)) ) ) ) ) ) )).
fof(l70_ordeq_01,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v7_ordinal1(F) => ( ( r1_xxreal_0(C,E) & r1_xxreal_0(E,D) & r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k5_numbers,A) ) => r1_xxreal_0(k3_xcmplx_0(k7_xcmplx_0(k1_newton(k3_xcmplx_0(A,k6_xcmplx_0(E,C)),k2_xcmplx_0(F,1)),k2_newton(k2_xcmplx_0(F,1))),B),k3_xcmplx_0(k7_xcmplx_0(k1_newton(k3_xcmplx_0(A,k6_xcmplx_0(D,C)),k2_xcmplx_0(F,1)),k2_newton(k2_xcmplx_0(F,1))),B)) ) ) ) ) ) ) ) )).
fof(l70_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ~ r1_xxreal_0(k4_pepin(A),1) ) )).
fof(l70_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_xreal_0(B) => ( A = B => ( k13_quaterni(A) = B & k14_quaterni(A) = k5_numbers & k15_quaterni(A) = k5_numbers & k16_quaterni(A) = k5_numbers ) ) ) ) )).
fof(l70_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v7_valued_0(B) => k1_funct_1(k3_rinfsup1(B),A) = k1_funct_1(B,A) ) ) ) )).
fof(l70_simplex0,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(l70_sin_cos,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( k1_newton(B,k3_xcmplx_0(2,A)) = k1_newton(k1_newton(B,A),2) & k1_newton(k4_xcmplx_0(1),k3_xcmplx_0(2,A)) = 1 & k1_newton(k4_xcmplx_0(1),k1_nat_1(k3_xcmplx_0(2,A),1)) = k4_xcmplx_0(1) ) ) ) ) ) ) )).
fof(l70_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A)) = k6_xcmplx_0(k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A)),1) ) )).
fof(l70_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( 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] : ( ( 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] : ( 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] : ( 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) ) ) ) ) )).
fof(l70_topalg_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(l70_turing_1,axiom,( ! [A] : ( 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] : ! [C] : ! [D] : ( 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),k1_enumset1(k4_xcmplx_0(1),k5_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),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),k8_turing_1(k20_turing_1,A)))) ) ) ) )).
fof(l70_waybel11,axiom,( ! [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] : ( ( 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) ) ) ) )).
fof(l70_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k5_xcmplx_0(A) = k5_xcmplx_0(B) => A = B ) ) ) )).
fof(l71_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => ( v1_anproj_2(A) => v4_collsp(k5_anproj_1(A)) ) ) )).
fof(l71_arytm_2,axiom,( ! [A] : ( m2_subset_1(A,k1_zfmisc_1(k5_arytm_3),k1_arytm_2) => ! [B] : ( 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 ) ) ) )).
fof(l71_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => k9_nat_1(k1_numbers,A,B) = k2_power(k2_xcmplx_0(1,k7_xcmplx_0(1,k1_nat_1(B,1))),k1_nat_1(B,1)) ) => v7_valued_0(A) ) ) )).
fof(l71_borsuk_5,axiom,( r1_tarski(k2_rcomp_1(1,k1_xxreal_0),k3_rcomp_1(1,k1_xxreal_0)) )).
fof(l71_bvfunc14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [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)) )).
fof(l71_cat_4,axiom,( ! [A] : ! [B] : v2_cat_1(k23_cat_4(A,B)) )).
fof(l71_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => v8_clvect_1(k9_cc0sp2(A)) ) )).
fof(l71_comput_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v4_valued_0(A) & v2_margrel1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) ) => ! [C] : ( m2_finseq_2(C,k4_ordinal1,k4_finseq_2(k1_nat_1(k19_margrel1(A),1),k4_ordinal1)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(D,k4_finseq_1(C)) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_finseq_2(k1_nat_1(k19_margrel1(A),1),k4_ordinal1),k2_comput_1(k4_ordinal1)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(k1_nat_1(k19_margrel1(A),1),k4_ordinal1),k2_comput_1(k4_ordinal1)))) ) => ( ! [G] : ( m2_finseq_2(G,k4_ordinal1,k4_finseq_2(k1_nat_1(k19_margrel1(A),1),k4_ordinal1)) => k3_funct_2(k4_finseq_2(k1_nat_1(k19_margrel1(A),1),k4_ordinal1),k2_comput_1(k4_ordinal1),F,G) = k6_comput_1(A,B,D,G) ) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ! [H] : ( m1_subset_1(H,k4_ordinal1) => r1_tarski(k1_relset_1(k3_finseq_2(k4_ordinal1),k3_funct_2(k4_finseq_2(k1_nat_1(k19_margrel1(A),1),k4_ordinal1),k2_comput_1(k4_ordinal1),F,k8_comput_1(k1_nat_1(k19_margrel1(A),1),C,D,G))),k1_relset_1(k3_finseq_2(k4_ordinal1),k3_funct_2(k4_finseq_2(k1_nat_1(k19_margrel1(A),1),k4_ordinal1),k2_comput_1(k4_ordinal1),F,k8_comput_1(k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(G,H))))) ) ) ) ) ) ) ) ) ) ) )).
fof(l71_fib_num4,axiom,( ~ r1_xxreal_0(k7_xcmplx_0(6,10),k3_xcmplx_0(k6_xcmplx_0(k3_square_1(5),1),k7_xcmplx_0(k3_square_1(5),5))) )).
fof(l71_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l71_fomodel0,axiom,( ! [A] : ! [B] : ( ( 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] : ( v7_ordinal1(C) => ~ r2_hidden(A,k8_funct_7(B,C)) ) ) ) )).
fof(l71_fomodel1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fomodel1(A) ) => ! [B] : ( ( 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(k4_ordinal1,k5_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)) ) ) ) )).
fof(l71_fomodel3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( v4_fomodel1(C,B) & m1_subset_1(C,k1_fomodel1(B)) ) => ! [D] : ( ( 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] : ( ( 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] : ( m2_funct_2(F,k30_fomodel2(B),k30_fomodel2(B),k9_funct_2(k30_fomodel2(B),k30_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))) ) ) ) ) ) ) ) )).
fof(l71_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l71_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( 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)) ) ) ) )).
fof(l71_hfdiff_1,axiom,( ! [A] : ( ( 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(k5_numbers)) = k8_relset_1(k1_numbers,k1_numbers,A,k1_tarski(k5_numbers)) ) )).
fof(l71_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => r2_hidden(k3_hilbert1(k4_hilbert1(k4_hilbert1(A,C),B),k4_hilbert1(k4_hilbert1(C,A),B)),k6_hilbert1) ) ) ) )).
fof(l71_integra8,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(l71_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ~ r1_nat_d(k1_newton(B,2),k6_moebius1(A)) ) ) )).
fof(l71_normform,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [C] : ( m1_subset_1(C,k5_finsub_1(k7_normform(A))) => ! [D] : ( m1_subset_1(D,k5_finsub_1(k7_normform(A))) => ~ ( r2_hidden(B,k10_normform(A,C,D)) & ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l71_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( 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] : ( 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))) ) ) ) ) )).
fof(l71_ordeq_01,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( ~ r1_xxreal_0(1,k7_xcmplx_0(k1_newton(k3_xcmplx_0(C,k6_xcmplx_0(B,A)),k2_xcmplx_0(D,1)),k2_newton(k2_xcmplx_0(D,1)))) & ~ r1_xxreal_0(k7_xcmplx_0(k1_newton(k3_xcmplx_0(C,k6_xcmplx_0(B,A)),k2_xcmplx_0(D,1)),k2_newton(k2_xcmplx_0(D,1))),k5_numbers) ) ) ) ) ) ) )).
fof(l71_orders_2,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( ( r6_relat_2(C,A) & r1_tarski(B,A) ) => r6_relat_2(C,B) ) ) )).
fof(l71_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => k4_nat_d(k7_nat_d(k4_pepin(A),1),2) = k5_numbers ) )).
fof(l71_topalg_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_borsuk_2(D,k15_euclid(A),B,C) => ! [E] : ( m1_borsuk_2(E,k15_euclid(A),B,C) => ! [F] : ( m1_subset_1(F,u1_struct_0(k17_borsuk_1)) => ( k1_binop_1(k7_topalg_1(A,D,E),F,k5_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] : ( m1_subset_1(G,u1_struct_0(k17_borsuk_1)) => ( k1_binop_1(k7_topalg_1(A,D,E),k5_numbers,G) = B & k1_binop_1(k7_topalg_1(A,D,E),1,G) = C ) ) ) ) ) ) ) ) ) )).
fof(l71_toprealb,axiom,( ! [A] : ( 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))))) ) ) )).
fof(l71_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(l71_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k9_funct_2(k4_numbers,u1_turing_1(A)))) => ! [C] : ( m1_subset_1(C,u2_turing_1(A)) => ! [D] : ( m1_subset_1(D,k4_numbers) => ! [E] : ( m2_funct_2(E,k4_numbers,u1_turing_1(A),k9_funct_2(k4_numbers,u1_turing_1(A))) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ~ ( G = D & m1_subset_1(k5_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),k4_ordinal1,C,1)) = k4_domain_1(u2_turing_1(A),k4_ordinal1,k4_ordinal1,C,k5_numbers,1) & C != u5_turing_1(A) & ! [H] : ( v1_int_1(H) => ( r1_xxreal_0(G,H) => ( r1_xxreal_0(k1_nat_1(G,F),H) | k1_funct_1(E,H) = 1 ) ) ) & ! [H] : ( m2_funct_2(H,k4_numbers,u1_turing_1(A),k9_funct_2(k4_numbers,u1_turing_1(A))) => ~ ( k9_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),k4_ordinal1,k9_funct_2(k4_numbers,u1_turing_1(A)),C,k1_nat_1(G,F),H) & ! [I] : ( v1_int_1(I) => ( r1_xxreal_0(G,I) => ( r1_xxreal_0(k1_nat_1(G,F),I) | k1_funct_1(H,I) = k5_numbers ) ) ) & ! [I] : ( v1_int_1(I) => ( ~ ( r1_xxreal_0(G,I) & ~ r1_xxreal_0(k1_nat_1(G,F),I) ) => k1_funct_1(H,I) = k1_funct_1(E,I) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l71_valued_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,C) ) | ( r1_xxreal_0(k1_nat_1(C,1),A) & r1_xxreal_0(A,k2_xcmplx_0(C,B)) ) ) => ( r1_xxreal_0(1,A) & r1_xxreal_0(A,k2_xcmplx_0(C,B)) ) ) ) ) ) )).
fof(l71_waybel11,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(l71_waybel_4,axiom,( ! [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) & l1_orders_2(A) ) => v6_waybel_4(k1_waybel_4(A),A) ) )).
fof(l72_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( r1_xxreal_0(1,A) => r1_xxreal_0(k2_power(k7_xcmplx_0(k1_nat_1(A,1),A),A),k2_power(k7_xcmplx_0(k1_nat_1(A,2),k1_nat_1(A,1)),k1_nat_1(A,1))) ) ) )).
fof(l72_borsuk_5,axiom,( 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) )).
fof(l72_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(l72_comput_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v4_valued_0(A) & v2_margrel1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) ) => ! [C] : ( m2_finseq_2(C,k4_ordinal1,k4_finseq_2(k1_nat_1(k19_margrel1(A),1),k4_ordinal1)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(D,k4_finseq_1(C)) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_finseq_2(k1_nat_1(k19_margrel1(A),1),k4_ordinal1),k2_comput_1(k4_ordinal1)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(k1_nat_1(k19_margrel1(A),1),k4_ordinal1),k2_comput_1(k4_ordinal1)))) ) => ( ! [G] : ( m2_finseq_2(G,k4_ordinal1,k4_finseq_2(k1_nat_1(k19_margrel1(A),1),k4_ordinal1)) => k3_funct_2(k4_finseq_2(k1_nat_1(k19_margrel1(A),1),k4_ordinal1),k2_comput_1(k4_ordinal1),F,G) = k6_comput_1(A,B,D,G) ) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ! [H] : ( m1_subset_1(H,k4_ordinal1) => ~ ( ~ r2_hidden(k8_comput_1(k1_nat_1(k19_margrel1(A),1),C,D,G),k1_relset_1(k3_finseq_2(k4_ordinal1),k3_funct_2(k4_finseq_2(k1_nat_1(k19_margrel1(A),1),k4_ordinal1),k2_comput_1(k4_ordinal1),F,k8_comput_1(k1_nat_1(k19_margrel1(A),1),C,D,G)))) & r2_hidden(k8_comput_1(k1_nat_1(k19_margrel1(A),1),C,D,G),k1_relset_1(k3_finseq_2(k4_ordinal1),k3_funct_2(k4_finseq_2(k1_nat_1(k19_margrel1(A),1),k4_ordinal1),k2_comput_1(k4_ordinal1),F,k8_comput_1(k1_nat_1(k19_margrel1(A),1),C,D,k1_nat_1(G,H))))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l72_fib_num4,axiom,( ~ r1_xxreal_0(k7_xcmplx_0(6,10),k3_xcmplx_0(k6_xcmplx_0(k3_square_1(5),1),k7_xcmplx_0(k3_square_1(5),k1_square_1(k3_square_1(5))))) )).
fof(l72_finseq_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(l72_fomodel0,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(l72_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l72_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( 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)) ) ) ) ) )).
fof(l72_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(l72_integr19,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k2_normsp_0(B,k1_rlvect_1(B,C,k5_xcmplx_0(A))) = k7_xcmplx_0(k2_normsp_0(B,C),k9_complex1(A)) ) ) ) )).
fof(l72_integra8,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(l72_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(k2_jordan9(B,A))) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k1_matrix_0(k1_jordan8(B,A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),k2_jordan9(B,A),C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),1,D) ) ) ) ) )).
fof(l72_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ! [E] : ( ( v1_finset_1(E) & v1_setfam_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ! [F] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(l72_matrix_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( ? [D] : ( m1_subset_1(D,k4_ordinal1) & r2_hidden(D,k2_finseq_1(A)) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k2_finseq_1(A)) => k1_funct_1(k8_matrix_0(u1_struct_0(B),C,D),E) = k4_struct_0(B) ) ) ) => k7_setwiseo(k3_matrix_2(A),u1_struct_0(B),u1_algstr_0(B),k6_matrix_2(k3_matrix_2(A)),k1_matrix_9(A,B,C)) = k4_struct_0(B) ) ) ) ) )).
fof(l72_mod_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(l72_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ~ v1_moebius1(k6_moebius1(A)) ) )).
fof(l72_normform,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A)) => ! [C] : ( 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) ) ) )).
fof(l72_orders_2,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( ( r2_wellord1(C,A) & r1_tarski(B,A) ) => r2_wellord1(C,B) ) ) )).
fof(l72_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ~ r1_xxreal_0(k7_nat_d(k4_pepin(A),1),k5_numbers) ) )).
fof(l72_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => r1_relat_2(k17_pre_poly(A),k15_pre_poly(A)) ) )).
fof(l72_rlaffin1,axiom,( ! [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) ) => ! [B] : ( 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) ) ) )).
fof(l72_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B)))) = k11_scmfsa_2(k5_numbers) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( r1_xxreal_0(D,k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B))) & k3_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),D)) = k2_compos_1(k1_scmfsa_2) ) ) ) ) ) ) ) )).
fof(l72_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => k4_finseq_1(B) = k2_finseq_1(A) ) ) )).
fof(l72_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ~ ( v1_topreal4(A) & ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( B != C & r2_hidden(B,A) & r2_hidden(C,A) ) ) ) ) ) )).
fof(l72_sprect_2,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( 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))) ) ) ) ) ) ) )).
fof(l72_toprealb,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) => ( r1_xxreal_0(k5_numbers,k7_xcmplx_0(k4_sin_cos6(A),k3_xcmplx_0(2,k28_sin_cos))) & r1_xxreal_0(k7_xcmplx_0(k4_sin_cos6(A),k3_xcmplx_0(2,k28_sin_cos)),k7_xcmplx_0(1,2)) ) ) ) )).
fof(l72_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(l72_waybel11,axiom,( ! [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] : ( ( 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) ) ) ) )).
fof(l72_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => k5_zmodul01(A,k4_struct_0(A),B) = u1_struct_0(B) ) ) )).
fof(l73_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => ( v1_anproj_2(A) => v3_anproj_2(k5_anproj_1(A)) ) ) )).
fof(l73_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k5_arytm_3) => ! [D] : ( m1_subset_1(D,k5_arytm_3) => ( ( A = C & B = D ) => k10_ordinal2(A,B) = k9_arytm_3(C,D) ) ) ) ) ) )).
fof(l73_borsuk_5,axiom,( 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)) )).
fof(l73_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k3_finseq_2(k4_ordinal1)) & v1_funct_1(C) & v4_valued_0(C) & v2_margrel1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k3_finseq_2(k4_ordinal1)) & v1_funct_1(D) & v4_valued_0(D) & v2_margrel1(D) ) => ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(k1_nat_1(k19_margrel1(C),1),k4_ordinal1)) => ( r2_hidden(A,k4_finseq_1(E)) => ( ( r2_hidden(k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,k5_numbers),k1_relset_1(k3_finseq_2(k4_ordinal1),k7_comput_1(C,D,A))) => r2_hidden(k2_finseq_3(A,E),k1_relset_1(k3_finseq_2(k4_ordinal1),C)) ) & ( r2_hidden(k2_finseq_3(A,E),k1_relset_1(k3_finseq_2(k4_ordinal1),C)) => r2_hidden(k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,k5_numbers),k1_relset_1(k3_finseq_2(k4_ordinal1),k7_comput_1(C,D,A))) ) & ( r2_hidden(k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,k5_numbers),k1_relset_1(k3_finseq_2(k4_ordinal1),k7_comput_1(C,D,A))) => k1_recdef_1(k7_comput_1(C,D,A),k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,k5_numbers)) = k1_recdef_1(C,k2_finseq_3(A,E)) ) & ( r2_hidden(k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,k1_nat_1(B,1)),k1_relset_1(k3_finseq_2(k4_ordinal1),k7_comput_1(C,D,A))) => ( r2_hidden(k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,B),k1_relset_1(k3_finseq_2(k4_ordinal1),k7_comput_1(C,D,A))) & r2_hidden(k8_finseq_1(k4_ordinal1,k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,B),k12_finseq_1(k4_ordinal1,k1_recdef_1(k7_comput_1(C,D,A),k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,B)))),k1_relset_1(k3_finseq_2(k4_ordinal1),D)) ) ) & ( ( r2_hidden(k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,B),k1_relset_1(k3_finseq_2(k4_ordinal1),k7_comput_1(C,D,A))) & r2_hidden(k8_finseq_1(k4_ordinal1,k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,B),k12_finseq_1(k4_ordinal1,k1_recdef_1(k7_comput_1(C,D,A),k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,B)))),k1_relset_1(k3_finseq_2(k4_ordinal1),D)) ) => r2_hidden(k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,k1_nat_1(B,1)),k1_relset_1(k3_finseq_2(k4_ordinal1),k7_comput_1(C,D,A))) ) & ( r2_hidden(k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,k1_nat_1(B,1)),k1_relset_1(k3_finseq_2(k4_ordinal1),k7_comput_1(C,D,A))) => k1_recdef_1(k7_comput_1(C,D,A),k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,k1_nat_1(B,1))) = k1_recdef_1(D,k8_finseq_1(k4_ordinal1,k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,B),k12_finseq_1(k4_ordinal1,k1_recdef_1(k7_comput_1(C,D,A),k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,B))))) ) ) ) ) ) ) ) ) )).
fof(l73_fib_num4,axiom,( ~ r1_xxreal_0(k7_xcmplx_0(6,10),k3_xcmplx_0(k6_xcmplx_0(k3_square_1(5),1),k7_xcmplx_0(k3_xcmplx_0(1,k3_square_1(5)),k3_xcmplx_0(k3_square_1(5),k3_square_1(5))))) & ~ r1_xxreal_0(k3_square_1(5),k5_numbers) )).
fof(l73_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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))) ) => ( ( k29_fomodel2(B,C) = k1_nat_1(A,1) & v5_fomodel2(C,B) ) => r2_hidden(C,k27_fomodel2(B,A)) ) ) ) ) )).
fof(l73_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ! [F] : ( 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] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( m1_subset_1(H,k6_margrel1) => ! [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) ) ) ) ) ) ) ) ) ) )).
fof(l73_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( r1_glib_000(A,k4_glib_001(A,B),D,C) => k3_finseq_1(k10_glib_001(A,B,C)) = k1_nat_1(k3_finseq_1(B),2) ) ) ) )).
fof(l73_group_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(B,k4_finseq_1(A)) => ( m1_subset_1(k2_xcmplx_0(k6_xcmplx_0(k3_finseq_1(A),B),1),k4_ordinal1) & 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)) ) ) ) ) )).
fof(l73_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(l73_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(k2_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)),k2_jordan9(B,A),C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,1) ) ) ) ) )).
fof(l73_mod_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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(A,D,F,G)) = k4_vectsp_1(B,E,k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,F),k3_funct_2(u1_struct_0(D),u1_struct_0(E),k6_grcat_1(D,E),G)) ) ) ) ) ) ) ) )).
fof(l73_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r2_hidden(A,k1_modelc_3(B)) => r1_xxreal_0(k18_modelc_3(B,k19_modelc_3(B,A)),k6_xcmplx_0(k3_finseq_1(A),1)) ) ) ) )).
fof(l73_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(1)))) ) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(A)) => ( r2_relset_1(k1_euclid(A),k1_euclid(1),k3_pdiff_1(A,B),C) => k9_complex1(k5_real_1(k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_7(A,B,D),F),k3_funct_2(k1_euclid(A),k1_numbers,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))) ) ) ) ) ) ) ) )).
fof(l73_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => k4_nat_d(k4_pepin(A),k1_newton(2,k1_newton(2,A))) = 1 ) )).
fof(l73_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => r4_relat_2(k17_pre_poly(A),k15_pre_poly(A)) ) )).
fof(l73_sprect_2,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(l73_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(l74_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( B = a_2_5_armstrng(A,C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ( r2_hidden(k6_armstrng(A,D,E),B) <=> ! [F] : ( ( r2_hidden(F,C) & r1_tarski(D,F) ) => r1_tarski(E,F) ) ) ) ) ) )).
fof(l74_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( m1_subset_1(C,k5_arytm_3) => ~ ( ~ r3_arytm_3(k9_arytm_3(A,B),C) & A != k11_arytm_3 & B != k11_arytm_3 & ! [D] : ( m1_subset_1(D,k5_arytm_3) => ! [E] : ( m1_subset_1(E,k5_arytm_3) => ~ ( C = k9_arytm_3(D,E) & ~ r3_arytm_3(A,D) & ~ r3_arytm_3(B,E) ) ) ) ) ) ) ) )).
fof(l74_fib_num4,axiom,( ~ r1_xxreal_0(k7_xcmplx_0(6,10),k3_xcmplx_0(k6_xcmplx_0(k3_square_1(5),1),k7_xcmplx_0(1,k3_square_1(5)))) )).
fof(l74_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v4_fomodel1(B,A) & m1_subset_1(B,k1_fomodel1(A)) ) => ! [C] : ( ( 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(k29_fomodel2(A,k42_fomodel1(A,k43_fomodel1(A,B),C)),k29_fomodel2(A,C)) ) ) ) )).
fof(l74_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ! [F] : ( 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] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(l74_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(l74_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( r1_glib_000(A,k4_glib_001(A,B),D,C) => ( k1_funct_1(k10_glib_001(A,B,C),k1_nat_1(k3_finseq_1(B),1)) = C & k1_funct_1(k10_glib_001(A,B,C),k1_nat_1(k3_finseq_1(B),2)) = D & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k1_relset_1(k4_ordinal1,B)) => k1_funct_1(k10_glib_001(A,B,C),E) = k1_funct_1(B,E) ) ) ) ) ) ) )).
fof(l74_group_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_1(E,k4_numbers) => ! [F] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(l74_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(l74_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ? [E] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(l74_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(l74_jgraph_5,axiom,( k17_euclid(k19_euclid(k4_xcmplx_0(1),k5_numbers)) = k4_xcmplx_0(1) )).
fof(l74_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(k2_jordan9(B,A))) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k1_matrix_0(k1_jordan8(B,A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),k2_jordan9(B,A),C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),k3_finseq_1(k1_jordan8(B,A)),D) ) ) ) ) )).
fof(l74_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( 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 ) ) ) ) ) ) ) ) )).
fof(l74_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r2_hidden(A,k1_modelc_3(B)) => r1_xxreal_0(k18_modelc_3(B,k20_modelc_3(B,A)),k6_xcmplx_0(k3_finseq_1(A),1)) ) ) ) )).
fof(l74_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ~ v1_abian(k4_pepin(A)) ) )).
fof(l74_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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 != k8_polynom1(A,C) & F != k8_polynom1(A,C) ) ) ) ) ) ) ) ) )).
fof(l74_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => r8_relat_2(k17_pre_poly(A),k15_pre_poly(A)) ) )).
fof(l74_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v8_ordinal1(B) & v1_xreal_0(B) ) => v2_funct_1(k4_rltopsp1(A,B)) ) ) )).
fof(l74_sprect_2,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( 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))) ) ) ) ) ) ) )).
fof(l74_toprealb,axiom,( v2_funct_1(k2_partfun1(u1_struct_0(k2_topalg_2),u1_struct_0(k8_toprealb(2)),k12_toprealb,k3_rcomp_1(k5_numbers,1))) )).
fof(l74_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l74_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(l75_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ~ ( r2_hidden(A,k5_arytm_3) & r2_hidden(B,k5_arytm_3) & ! [C] : ( m1_subset_1(C,k5_arytm_3) => ! [D] : ( m1_subset_1(D,k5_arytm_3) => ~ ( A = C & B = D & k7_arytm_2(A,B) = k9_arytm_3(C,D) ) ) ) ) ) ) )).
fof(l75_card_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_finset_1(k4_classes1(A)) => v1_finset_1(k4_classes1(k1_nat_1(A,1))) ) ) )).
fof(l75_classes2,axiom,( k16_classes2(k5_numbers) = k13_classes2 & ! [A] : ( v3_ordinal1(A) => k16_classes2(k1_ordinal1(A)) = k1_classes1(k16_classes2(A)) ) & ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) ) => ( ( v4_ordinal1(A) & k9_xtuple_0(B) = A & ! [C] : ( v3_ordinal1(C) => ( r2_hidden(C,A) => k1_funct_1(B,C) = k16_classes2(C) ) ) ) => ( A = k5_numbers | k16_classes2(A) = k15_classes2(k3_card_3(B)) ) ) ) ) )).
fof(l75_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ( m1_subset_1(E,k4_card_3(u3_msualg_1(k8_facirc_1(A,B,C,D),k10_facirc_1(A,B,C,D)))) => ( C != k4_tarski(k10_finseq_1(A,B),D) => ( k11_facirc_1(k8_facirc_1(A,B,C,D),k10_facirc_1(A,B,C,D),k6_circuit2(k8_facirc_1(A,B,C,D),k10_facirc_1(A,B,C,D),E),k9_facirc_1(A,B,C,D)) = k1_funct_1(D,k10_finseq_1(k1_funct_1(E,k4_tarski(k10_finseq_1(A,B),D)),k1_funct_1(E,C))) & k1_funct_1(k6_circuit2(k8_facirc_1(A,B,C,D),k10_facirc_1(A,B,C,D),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(k8_facirc_1(A,B,C,D),k10_facirc_1(A,B,C,D),E),A) = k1_funct_1(E,A) & k1_funct_1(k6_circuit2(k8_facirc_1(A,B,C,D),k10_facirc_1(A,B,C,D),E),B) = k1_funct_1(E,B) & k1_funct_1(k6_circuit2(k8_facirc_1(A,B,C,D),k10_facirc_1(A,B,C,D),E),C) = k1_funct_1(E,C) ) ) ) ) )).
fof(l75_fib_num4,axiom,( ~ r1_xxreal_0(k7_xcmplx_0(6,10),k7_xcmplx_0(k6_xcmplx_0(k3_square_1(5),1),k3_square_1(5))) )).
fof(l75_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( 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] : ( ( 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(k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k18_fomodel1(A)),B),C),A) & m2_subset_1(k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k18_fomodel1(A)),B),C),k3_finseq_2(k15_fomodel1(A)),k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) ) ) ) ) )).
fof(l75_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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))) ) => ( k29_fomodel2(B,C) = k1_nat_1(A,1) => ( v5_fomodel2(C,B) | r2_hidden(C,k32_fomodel2(B,A)) ) ) ) ) ) )).
fof(l75_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l75_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)) ) ) ) )).
fof(l75_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => r2_hidden(k3_hilbert1(k4_hilbert1(A,k4_hilbert1(C,B)),k4_hilbert1(A,k4_hilbert1(B,C))),k6_hilbert1) ) ) ) )).
fof(l75_integra8,axiom,( ! [A] : ( ( ~ 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,k3_sin_cos2,A)) ) )).
fof(l75_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(l75_jgraph_5,axiom,( k18_euclid(k19_euclid(k4_xcmplx_0(1),k5_numbers)) = k5_numbers )).
fof(l75_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l75_pdiff_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(l75_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => r3_orders_1(k17_pre_poly(A),k15_pre_poly(A)) ) )).
fof(l75_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(l76_card_2,axiom,( 1 = k5_card_1(1) )).
fof(l76_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_clvect_1(B,A) => k5_clvect_1(A,k4_struct_0(A),B) = u1_struct_0(B) ) ) )).
fof(l76_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v2_cqc_the1(B,A) <=> r2_hidden(B,k4_cqc_the1(A)) ) ) ) )).
fof(l76_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( 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))))) ) ) ) ) ) )).
fof(l76_fib_num4,axiom,( r1_xxreal_0(k3_square_1(k1_square_1(k7_xcmplx_0(3,2))),k3_square_1(5)) )).
fof(l76_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_fomodel4(A))) => ! [C] : ( m1_subset_1(C,k1_fomodel4(A)) => ! [D] : ( 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)),k23_fomodel4(A,D),B)) ) ) ) ) ) )).
fof(l76_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l76_funct_7,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(l76_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( v7_ordinal1(C) & v1_abian(C) ) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(B)) ) => ( r2_hidden(k3_nat_d(C,2),k1_relset_1(k4_ordinal1,k12_glib_001(A,B))) & k1_funct_1(B,C) = k1_funct_1(k12_glib_001(A,B),k3_nat_d(C,2)) ) ) ) ) ) )).
fof(l76_goboard6,axiom,( k2_xcmplx_0(k7_xcmplx_0(1,2),k7_xcmplx_0(1,2)) = 1 )).
fof(l76_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(l76_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_integra5(A,k3_sin_cos2) & v1_comseq_2(k2_partfun1(k1_numbers,k1_numbers,k3_sin_cos2,A)) ) ) )).
fof(l76_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(l76_jgraph_5,axiom,( k17_euclid(k19_euclid(1,k5_numbers)) = 1 & k18_euclid(k19_euclid(1,k5_numbers)) = k5_numbers )).
fof(l76_moebius1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ( r1_nat_d(A,B) => ( v1_moebius1(A) | r1_nat_d(A,k6_moebius1(B)) ) ) ) ) )).
fof(l76_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k12_normform(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k12_normform(A))) => k1_lattices(k12_normform(A),B,C) = k1_lattices(k12_normform(A),C,B) ) ) )).
fof(l76_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l76_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : k2_relat_1(k2_wellord1(A,B)) = k2_wellord1(k2_relat_1(A),B) ) )).
fof(l76_quatern3,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l77_card_2,axiom,( 2 = k5_card_1(2) )).
fof(l77_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r1_tarski(k16_ens_1(B),A) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(l77_fib_num4,axiom,( r1_xxreal_0(k7_xcmplx_0(3,2),k3_square_1(5)) )).
fof(l77_finseq_3,axiom,( ! [A] : ! [B] : ( k1_finseq_3(k9_finseq_1(A),B) = k9_finseq_1(A) <=> ~ r2_hidden(A,B) ) )).
fof(l77_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( 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] : ( ( 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(k29_fomodel2(A,k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k1_fomodel2(A)),B),C)),k29_fomodel2(A,B)) & ~ r1_xxreal_0(k29_fomodel2(A,k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k1_fomodel2(A)),B),C)),k29_fomodel2(A,C)) ) ) ) ) )).
fof(l77_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(l77_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k1_relset_1(k4_ordinal1,k12_glib_001(A,B))) <=> r2_hidden(k3_xcmplx_0(2,C),k1_relset_1(k4_ordinal1,B)) ) ) ) ) )).
fof(l77_group_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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,k12_finseq_1(A,C)) = k3_funct_2(A,k1_funct_2(B,B),D,C) ) ) ) )).
fof(l77_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(l77_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(l77_jgraph_5,axiom,( k17_euclid(k19_euclid(k5_numbers,k4_xcmplx_0(1))) = k5_numbers )).
fof(l77_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k12_normform(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k12_normform(A))) => ! [D] : ( 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) ) ) ) )).
fof(l77_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l77_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => k2_wellord1(A,k1_xboole_0) = k1_xboole_0 ) )).
fof(l77_ordinal6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ( r2_hidden(k4_ordinal1,A) => ( v1_funct_1(k1_funct_1(k11_ordinal6(A),k5_numbers)) & v1_funct_2(k1_funct_1(k11_ordinal6(A),k5_numbers),k2_ordinal1(A),k2_ordinal1(A)) & v2_ordinal6(k1_funct_1(k11_ordinal6(A),k5_numbers)) & m1_subset_1(k1_funct_1(k11_ordinal6(A),k5_numbers),k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A),k2_ordinal1(A)))) ) ) ) )).
fof(l77_quatern3,axiom,( k3_quatern2 = k5_arytm_0(k10_subset_1(k5_numbers,k1_numbers),c1__quatern3) )).
fof(l77_quaterni,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k6_quaterni(A,B,C,D) = k7_quaterni(k7_quaterni(k19_quaterni(A,k21_quaterni(B,k1_xcmplx_0)),k21_quaterni(C,k11_quaterni)),k21_quaterni(D,k12_quaterni)) ) ) ) ) )).
fof(l77_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v8_valued_0(B) => k1_funct_1(k4_rinfsup1(B),A) = k1_funct_1(B,A) ) ) ) )).
fof(l77_sincos10,axiom,( k1_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,4)))) = k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,4)) )).
fof(l78_classes2,axiom,( 1 = k1_ordinal1(k5_numbers) )).
fof(l78_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k28_coh_sp(A))) => ! [C] : ( m1_subset_1(C,k16_coh_sp(A)) => ( B = C => ! [D] : ( m1_cat_1(D,k28_coh_sp(A),B,B) => ( D = k23_coh_sp(A,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(k28_coh_sp(A))) => ( ( k2_cat_1(k28_coh_sp(A),B,E) != k1_xboole_0 => ! [F] : ( 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] : ( m1_cat_1(F,k28_coh_sp(A),E,B) => k1_cat_1(k28_coh_sp(A),F,D) = F ) ) ) ) ) ) ) ) ) )).
fof(l78_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r1_tarski(k16_ens_1(B),A) => ! [E] : ( m1_subset_1(E,u1_struct_0(k11_ens_1(A))) => ( E = k2_cat_1(B,D,C) => k3_funct_2(u4_struct_0(B),k2_ens_1(k16_ens_1(B)),k20_ens_1(B,C),k4_cat_1(B,D)) = k4_cat_1(k11_ens_1(A),E) ) ) ) ) ) ) ) )).
fof(l78_fib_num4,axiom,( r1_xxreal_0(k3_xcmplx_0(k7_xcmplx_0(3,2),2),k3_xcmplx_0(k3_square_1(5),2)) )).
fof(l78_finseq_3,axiom,( ! [A] : ! [B] : ( k1_finseq_3(k9_finseq_1(A),B) = k1_xboole_0 <=> r2_hidden(A,B) ) )).
fof(l78_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( 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] : ( ( 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))) ) => k29_fomodel2(A,k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k1_fomodel2(A)),B),C)) = k1_nat_1(k4_xxreal_0(k29_fomodel2(A,B),k29_fomodel2(A,C)),1) ) ) ) )).
fof(l78_fomodel3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( v4_fomodel1(C,B) & m1_subset_1(C,k1_fomodel1(B)) ) => ! [D] : ( ( 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] : ( ( 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] : ( m2_funct_2(F,k30_fomodel2(B),k30_fomodel2(B),k9_funct_2(k30_fomodel2(B),k30_fomodel2(B))) => k1_funct_1(k9_nat_1(k9_funct_2(k30_fomodel2(B),k30_fomodel2(B)),k32_fomodel3(B,C,D,F),k1_nat_1(A,1)),E) = k29_fomodel3(B,C,D,A,k9_nat_1(k9_funct_2(k30_fomodel2(B),k30_fomodel2(B)),k32_fomodel3(B,C,D,F),A),E) ) ) ) ) ) ) )).
fof(l78_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( v2_fomodel4(B,A) => ! [C] : ( v1_fomodel4(C,A) => ! [D] : ( 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) => v5_fomodel4(C,1,A,k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))),k23_fomodel4(A,D)),B) ) ) ) ) ) )).
fof(l78_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(l78_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C))) => ! [F] : ( 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 ) ) ) ) ) ) ) ) )).
fof(l78_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ? [C] : ( v1_abian(C) & m1_subset_1(C,k4_ordinal1) & C = k6_xcmplx_0(k3_finseq_1(B),1) & k3_finseq_1(k12_glib_001(A,B)) = k3_nat_d(C,2) ) ) ) )).
fof(l78_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(l78_group_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( ( 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,k12_finseq_1(A,C))),k1_partfun1(B,B,B,B,k2_group_9(A,B,E,k12_finseq_1(A,C)),k2_group_9(A,B,E,D))) ) ) ) ) )).
fof(l78_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => r2_hidden(k3_hilbert1(k4_hilbert1(k4_hilbert1(C,B),A),k4_hilbert1(k4_hilbert1(B,C),A)),k6_hilbert1) ) ) ) )).
fof(l78_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(l78_jgraph_5,axiom,( k18_euclid(k19_euclid(k5_numbers,k4_xcmplx_0(1))) = k4_xcmplx_0(1) )).
fof(l78_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ~ ( r1_tarski(C,k4_finseq_1(B)) & ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(A)) => ~ ( D = k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,u1_struct_0(A),k14_finseq_1(C),B) & E = k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,u1_struct_0(A),k14_finseq_1(k7_subset_1(k4_ordinal1,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)) ) ) ) ) ) ) )).
fof(l78_normform,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A)) => ! [C] : ( 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 ) ) )).
fof(l78_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l78_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,u4_struct_0(k2_oppcat_1(B)),u4_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(k2_oppcat_1(B)),u4_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u4_struct_0(A),u4_struct_0(C)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(A),u4_struct_0(C)))) ) => r2_funct_2(u4_struct_0(B),u4_struct_0(C),k9_oppcat_1(B,C,k1_partfun1(u4_struct_0(k2_oppcat_1(B)),u4_struct_0(A),u4_struct_0(A),u4_struct_0(C),D,E)),k1_partfun1(u4_struct_0(B),u4_struct_0(A),u4_struct_0(A),u4_struct_0(C),k9_oppcat_1(B,A,D),E)) ) ) ) ) ) )).
fof(l78_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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)))) ) ) ) ) )).
fof(l78_pepin,axiom,( k11_newton(3,2) = 9 )).
fof(l78_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k22_quaterni(A,B) = k22_quaterni(k22_quaterni(k19_quaterni(k2_xcmplx_0(k13_quaterni(A),k13_quaterni(B)),k21_quaterni(k2_xcmplx_0(k14_quaterni(A),k14_quaterni(B)),k1_xcmplx_0)),k21_quaterni(k2_xcmplx_0(k15_quaterni(A),k15_quaterni(B)),k11_quaterni)),k21_quaterni(k2_xcmplx_0(k16_quaterni(A),k16_quaterni(B)),k12_quaterni)) ) ) )).
fof(l78_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => k16_seq_4(A,k15_seq_4(A)) = k15_seq_4(A) ) )).
fof(l78_sin_cos,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xcmplx_0(B) => ( k9_nat_1(k2_numbers,k3_sin_cos(B),1) = B & k9_nat_1(k2_numbers,k3_sin_cos(B),k5_numbers) = k6_complex1 & k9_complex1(k1_newton(B,A)) = k1_newton(k9_complex1(B),A) ) ) ) )).
fof(l78_sin_cos6,axiom,( k2_funct_1(k1_sin_cos6) = k5_relset_1(k1_numbers,k1_numbers,k16_sin_cos,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))) )).
fof(l78_sincos10,axiom,( k1_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos),k28_sin_cos))) = k1_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos),k28_sin_cos) )).
fof(l78_toprealb,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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),k2_xcmplx_0(k2_xcmplx_0(B,A),1)))) = k2_rcomp_1(B,k2_xcmplx_0(B,1)) ) ) )).
fof(l78_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_zmodul01(C,A) => ( r1_struct_0(C,B) <=> k5_zmodul01(A,B,C) = u1_struct_0(C) ) ) ) ) )).
fof(l79_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,B) & r2_hidden(D,C) ) ) ) ) ) ) ) )).
fof(l79_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_1(A,C,B) = k1_bcialg_1(A,B,C) ) ) => v13_bcialg_1(A) ) ) )).
fof(l79_card_2,axiom,( k5_card_1(k5_numbers) = k5_numbers )).
fof(l79_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(l79_fib_num4,axiom,( r1_xxreal_0(k7_xcmplx_0(3,4),k7_xcmplx_0(k3_xcmplx_0(2,k3_square_1(5)),k3_xcmplx_0(2,2))) )).
fof(l79_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : 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)) ) )).
fof(l79_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( v1_relat_1(C) => ( r2_hidden(C,k15_fomodel2(A,B)) => k9_xtuple_0(C) = k37_fomodel1(A) ) ) ) ) )).
fof(l79_fomodel3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( v4_fomodel1(C,B) & m1_subset_1(C,k1_fomodel1(B)) ) => ! [D] : ( ( 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] : ( ( 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] : ( m2_funct_2(F,k30_fomodel2(B),k30_fomodel2(B),k9_funct_2(k30_fomodel2(B),k30_fomodel2(B))) => ( k1_funct_1(k9_nat_1(k9_funct_2(k30_fomodel2(B),k30_fomodel2(B)),k32_fomodel3(B,C,D,F),k2_xcmplx_0(k29_fomodel2(B,E),A)),E) = k1_funct_1(k9_nat_1(k9_funct_2(k30_fomodel2(B),k30_fomodel2(B)),k32_fomodel3(B,C,D,F),k29_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(k9_nat_1(k9_funct_2(k30_fomodel2(B),k30_fomodel2(B)),k32_fomodel3(B,C,D,k36_fomodel3(B,C,D)),k29_fomodel2(B,E)),E) = E ) ) ) ) ) ) ) ) )).
fof(l79_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( v2_fomodel4(C,B) => ! [D] : ( 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(k23_fomodel4(B,D),C)) <=> ( r2_hidden(A,k1_fomodel4(B)) & r2_hidden(k4_tarski(C,A),D) ) ) ) ) ) )).
fof(l79_funct_7,axiom,( ! [A] : ( 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 ) ) )).
fof(l79_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,B,C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k7_geomtrap(A,B,C))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k7_geomtrap(A,B,C))) => ! [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l79_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_relset_1(k4_ordinal1,k7_glib_000(A),k12_glib_001(A,k8_glib_001(A,B,1,C)),k12_glib_001(A,B)) ) ) ) )).
fof(l79_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => v1_finset_1(k7_graph_5(A)) ) )).
fof(l79_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(l79_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(l79_jgraph_5,axiom,( k17_euclid(k19_euclid(k5_numbers,1)) = k5_numbers )).
fof(l79_lattice3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => k3_funct_2(k1_zfmisc_1(A),A,B,k6_domain_1(A,C)) = C ) & ! [C] : ( 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] : ( ( ~ v2_struct_0(C) & v3_lattices(C) & v10_lattices(C) & l3_lattices(C) ) => ~ ( u1_struct_0(C) = A & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) => k15_lattice3(C,D) = k1_funct_1(B,D) ) ) ) ) ) ) )).
fof(l79_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( v2_xxreal_0(F) & v1_xreal_0(F) ) => ! [G] : ( ( v2_xxreal_0(G) & v1_xreal_0(G) ) => ~ ( k3_supinf_2(k2_extreal1(1,F),k2_extreal1(1,G)) = 1 & r2_hidden(D,k1_lpspace2(A,B,C,F)) & r2_hidden(E,k1_lpspace2(A,B,C,F)) & ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ~ ( 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(k2_power(J,k2_extreal1(1,F)),k2_xcmplx_0(k2_power(H,k2_extreal1(1,F)),k2_power(I,k2_extreal1(1,F)))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l79_modelc_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( v1_partfun1(B,A) => ! [C] : ~ ( r2_hidden(C,A) & ! [D] : ~ ( r2_hidden(D,A) & r2_hidden(k4_tarski(C,D),B) ) ) ) ) )).
fof(l79_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k12_normform(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k12_normform(A))) => k1_lattices(k12_normform(A),k2_lattices(k12_normform(A),B,C),C) = C ) ) )).
fof(l79_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l79_ordinal6,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_xboole_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) ) => ( ( r2_hidden(A,B) & ! [C] : ( 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)))) ) ) ) ) )).
fof(l79_pepin,axiom,( k11_newton(3,4) = 81 )).
fof(l79_rlaffin1,axiom,( v1_xreal_0(1) )).
fof(l79_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => k11_comseq_3(k3_sin_cos(A)) = k4_series_1(k4_sin_cos(A)) ) )).
fof(l79_sincos10,axiom,( k1_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4))))) = k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4))) )).
fof(l79_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [D] : ( ( 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 ) ) ) ) )).
fof(l79_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_tex_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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))) ) ) ) ) ) ) ) )).
fof(l7_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r2_diraf(A,B,D,D,C) ) ) ) ) )).
fof(l7_algstr_1,axiom,( ! [A] : ( 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] : ( m1_subset_1(A,u1_struct_0(k3_algstr_0)) => k1_algstr_0(k3_algstr_0,k4_struct_0(k3_algstr_0),A) = A ) )).
fof(l7_algstr_3,axiom,( v1_xreal_0(1) & v1_xreal_0(k5_numbers) )).
fof(l7_altcat_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k7_altcat_1(k1_tarski(k1_xboole_0)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_altcat_1(k1_tarski(k1_xboole_0)))) => ! [C] : ( m1_subset_1(C,k1_altcat_1(k7_altcat_1(k1_tarski(k1_xboole_0)),A,B)) => C = k1_xboole_0 ) ) ) )).
fof(l7_amistd_2,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( 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(k5_numbers) ) ) )).
fof(l7_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ( r1_analmetr(A,D,E) => ( k2_geomtrap(A,D,E,k3_rlvect_1(A,B,C)) = k2_xcmplx_0(k2_geomtrap(A,D,E,B),k2_geomtrap(A,D,E,C)) & k3_geomtrap(A,D,E,k3_rlvect_1(A,B,C)) = k2_xcmplx_0(k3_geomtrap(A,D,E,B),k3_geomtrap(A,D,E,C)) & k2_geomtrap(A,D,E,k5_algstr_0(A,B,C)) = k6_xcmplx_0(k2_geomtrap(A,D,E,B),k2_geomtrap(A,D,E,C)) & k3_geomtrap(A,D,E,k5_algstr_0(A,B,C)) = k6_xcmplx_0(k3_geomtrap(A,D,E,B),k3_geomtrap(A,D,E,C)) & k2_geomtrap(A,D,E,k1_rlvect_1(A,B,F)) = k3_xcmplx_0(F,k2_geomtrap(A,D,E,B)) & k3_geomtrap(A,D,E,k1_rlvect_1(A,B,F)) = k3_xcmplx_0(F,k3_geomtrap(A,D,E,B)) ) ) ) ) ) ) ) ) )).
fof(l7_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => k1_rlvect_1(A,k3_rlvect_1(A,k3_rlvect_1(A,k3_rlvect_1(A,k1_rlvect_1(A,C,G),k1_rlvect_1(A,D,H)),k1_rlvect_1(A,B,I)),k1_rlvect_1(A,E,J)),F) = k3_rlvect_1(A,k3_rlvect_1(A,k3_rlvect_1(A,k1_rlvect_1(A,C,k3_xcmplx_0(F,G)),k1_rlvect_1(A,D,k3_xcmplx_0(F,H))),k1_rlvect_1(A,B,k3_xcmplx_0(F,I))),k1_rlvect_1(A,E,k3_xcmplx_0(F,J))) ) ) ) ) ) ) ) ) ) ) )).
fof(l7_arithm,axiom,( k3_arytm_0(c1__arithm) = k5_numbers )).
fof(l7_arytm_2,axiom,( r1_tarski(k2_arytm_2,k2_xboole_0(k5_arytm_3,a_0_0_arytm_2)) )).
fof(l7_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(C,k5_numbers) & C != 1 & k2_power(A,B) != k2_power(C,k3_xcmplx_0(B,k3_power(C,A))) ) ) ) ) )).
fof(l7_bhsp_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_rlsub_1(o_0_5_bhsp_1))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_rlsub_1(o_0_5_bhsp_1))) => ! [C] : ( 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)) = k3_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))) ) ) ) )).
fof(l7_collsp,axiom,( m1_collsp(k1_tarski(k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,1,1,1)),c2__collsp) )).
fof(l7_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k5_arytm_0(k3_complex1(A),k4_complex1(A)) = A ) )).
fof(l7_comptrig,axiom,( ~ r1_xxreal_0(k2_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),k7_xcmplx_0(k28_sin_cos,2)),k2_xcmplx_0(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) )).
fof(l7_convex2,axiom,( ! [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) ) => ! [B] : ( ( v1_convex1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m2_rlvect_2(D,A,C) => ( ( v2_convex1(D,A) & r1_tarski(C,B) ) => r2_hidden(k6_rlvect_2(A,D),B) ) ) ) ) ) )).
fof(l7_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l7_csspace2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v1_comseq_3(A) & ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(k5_numbers,k1_funct_1(k7_comseq_3(A),B)) & k1_funct_1(k8_comseq_3(A),B) = k5_numbers ) ) ) => k9_complex1(k11_comseq_3(A)) = k4_series_1(k55_valued_1(k4_ordinal1,k2_numbers,A)) ) ) )).
fof(l7_csspace3,axiom,( ~ 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))) )).
fof(l7_csspace4,axiom,( 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) )).
fof(l7_endalg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_endalg(A))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(l7_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => k4_euclid_3(A,B,C) != k2_xcmplx_0(k3_xcmplx_0(2,k4_euclid_3(D,E,F)),k3_xcmplx_0(4,k28_sin_cos)) ) ) ) ) ) ) )).
fof(l7_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => k22_rvsum_1(A,B) = k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(A,1),k1_funct_1(B,1)),k3_xcmplx_0(k1_funct_1(A,2),k1_funct_1(B,2))),k3_xcmplx_0(k1_funct_1(A,3),k1_funct_1(B,3))) ) ) )).
fof(l7_fdiff_6,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(k1_funct_1(k16_sin_cos,A),k5_numbers) & ~ r1_xxreal_0(1,k1_funct_1(k18_sin_cos,A)) & ~ r1_xxreal_0(k1_funct_1(k18_sin_cos,A),k4_xcmplx_0(1)) & k7_xcmplx_0(k1_funct_1(k16_sin_cos,A),k6_prepower(k2_xcmplx_0(1,k1_funct_1(k18_sin_cos,A)),k7_xcmplx_0(1,2))) != k6_prepower(k6_xcmplx_0(1,k1_funct_1(k18_sin_cos,A)),k7_xcmplx_0(1,2)) ) ) )).
fof(l7_fib_fusc,axiom,( k10_ami_3(k5_numbers) != k10_ami_3(1) )).
fof(l7_fib_num,axiom,( ! [A] : ( v7_ordinal1(A) => r1_xxreal_0(A,k1_pre_ff(k1_nat_1(A,1))) ) )).
fof(l7_fib_num4,axiom,( k3_xcmplx_0(k1_fib_num,k2_fib_num) = k4_xcmplx_0(1) )).
fof(l7_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(l7_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(C,k1_funct_2(A,B)) => r1_tarski(k3_tarski(C),k2_zfmisc_1(A,B)) ) )).
fof(l7_freealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(l7_funcsdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(l7_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => r2_hidden(B,k1_glib_002(A,B)) ) ) )).
fof(l7_gobrd10,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,A) ) => k1_funct_1(k5_finseq_2(k4_ordinal1,A,B),C) = B ) ) ) ) )).
fof(l7_gobrd12,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l7_gr_cy_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) )).
fof(l7_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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),k1_nat_1(k3_finseq_1(B),A)) ) ) ) ) )).
fof(l7_grfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r2_hidden(k4_tarski(A,C),k1_tarski(k4_tarski(B,D))) => ( A = B & C = D ) ) )).
fof(l7_group_9,axiom,( ! [A] : ! [B] : ( 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)))) ) )).
fof(l7_holder_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,A,B)) ) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,k3_series_1(A),B)) ) ) ) )).
fof(l7_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r1_aff_1(A,D,B,C) & r1_aff_1(A,D,B,F) ) => ( D = B | D = C | ( ~ ( ~ r1_aff_1(A,D,B,E) & r1_aff_1(A,D,E,F) & r2_analoaf(A,B,E,C,F) ) & ~ ( r1_aff_1(A,D,B,E) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & ~ r1_aff_1(A,D,B,G) & r1_aff_1(A,D,G,H) & r2_analoaf(A,B,G,C,H) & r2_analoaf(A,G,E,H,F) & r1_aff_1(A,D,B,F) ) ) ) ) | r1_aff_1(A,D,B,E) ) ) ) ) ) ) ) ) )).
fof(l7_int_1,axiom,( ! [A] : ( r2_hidden(A,k4_numbers) => r2_hidden(A,k1_numbers) ) )).
fof(l7_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r1_int_1(A,B) <=> r1_int_1(k4_xcmplx_0(A),B) ) ) ) )).
fof(l7_int_3,axiom,( ! [A] : ( v1_int_1(A) => ( A = k5_numbers | r1_xxreal_0(1,k1_funct_1(k2_euclid,A)) ) ) )).
fof(l7_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(l7_int_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k8_newton) & v1_funct_1(A) & v1_partfun1(A,k8_newton) & v4_valued_0(A) & v2_pre_poly(A) ) => ! [B] : ~ ( r1_tarski(B,k22_pre_poly(k8_newton,A)) & ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k8_newton) & v1_funct_1(C) & v1_partfun1(C,k8_newton) & v4_valued_0(C) & v2_pre_poly(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k8_newton) & v1_funct_1(D) & v1_partfun1(D,k8_newton) & v4_valued_0(D) & v2_pre_poly(D) ) => ~ ( k22_pre_poly(k8_newton,C) = k7_subset_1(k8_newton,k22_pre_poly(k8_newton,A),B) & k22_pre_poly(k8_newton,D) = B & r1_xboole_0(k22_pre_poly(k8_newton,C),k22_pre_poly(k8_newton,D)) & k5_relat_1(C,k22_pre_poly(k8_newton,C)) = k5_relat_1(A,k22_pre_poly(k8_newton,C)) & k5_relat_1(D,k22_pre_poly(k8_newton,D)) = k5_relat_1(A,k22_pre_poly(k8_newton,D)) & r8_pboole(k8_newton,k11_pre_poly(k8_newton,C,D),A) ) ) ) ) ) )).
fof(l7_integra4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,k1_integra1(A)) => ( k3_integra1(A) = k5_numbers => ( v1_integra1(B,A) & k10_integra1(A,B) = k5_numbers ) ) ) ) ) )).
fof(l7_integra6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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))) ) ) ) ) )).
fof(l7_jordan1c,axiom,( k3_pcomps_1(k14_euclid(2)) = g1_pre_topc(u1_struct_0(k15_euclid(2)),u1_pre_topc(k15_euclid(2))) )).
fof(l7_jordan1h,axiom,( r4_relat_2(k1_jordan1h,k1_numbers) )).
fof(l7_jordan22,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(1,k3_finseq_1(k1_jordan8(A,B))) ) ) )).
fof(l7_jordan24,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => r2_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k1_jordan24(A),k1_jordan24(k2_xcmplx_0(A,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)))) ) ) )).
fof(l7_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r1_xxreal_0(C,D) => ( r1_xxreal_0(C,k5_numbers) | ! [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(A))) => ( E = k5_euclid(A) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( F = k8_metric_1(k14_euclid(A),E,B) => r1_tarski(k1_convex1(k15_euclid(A),F,C),k1_convex1(k15_euclid(A),F,D)) ) ) ) ) ) ) ) ) ) ) )).
fof(l7_jordan5a,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v3_rcomp_1(A) => r2_hidden(A,k2_pcomps_1(k7_metric_1)) ) ) )).
fof(l7_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( ! [D] : ( v1_xreal_0(D) => ? [E] : ( v1_xreal_0(E) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(E,F) & ~ r1_xxreal_0(F,A) & r2_hidden(F,k1_relset_1(k1_numbers,C)) & r1_xxreal_0(D,k1_funct_1(C,F)) ) ) ) ) & v2_comseq_2(B) & k1_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(k4_ordinal1,k1_numbers,k1_numbers,B,C)) ) ) ) ) )).
fof(l7_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(l7_matrix17,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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(k5_int_1(k6_xcmplx_0(k2_xcmplx_0(B,C),1),A),k2_finseq_1(A)) ) ) ) ) ) )).
fof(l7_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => k4_finseq_1(k5_matrlin(A,B,D,C)) = k9_subset_1(k4_ordinal1,k4_finseq_1(D),k4_finseq_1(C)) ) ) ) ) )).
fof(l7_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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(k4_ordinal1,A),A,B) ) )).
fof(l7_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => k2_memstr_0(A,k1_memstr_0(A)) = k16_funcop_1(k5_numbers,k4_ordinal1) ) )).
fof(l7_mesfunc7,axiom,( r3_binop_1(k6_numbers,k8_mesfunc1,k1_mesfunc7) )).
fof(l7_metrizts,axiom,( ! [A] : ( ( v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => v1_xboole_0(k2_waybel23(A)) ) )).
fof(l7_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( m2_finseq_2(E,C,k4_finseq_2(A,C)) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r2_hidden(F,k7_subset_1(k4_ordinal1,k4_finseq_1(E),k1_tarski(B))) => k1_funct_1(k1_midsp_3(C,A,E,B,D),F) = k1_funct_1(E,F) ) ) ) ) ) ) ) )).
fof(l7_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_mod_4(A))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k2_mod_4(A))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k2_mod_4(A))) => ! [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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l7_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ( v3_modelc_2(A) | v6_modelc_2(A) ) => r2_modelc_2(k10_modelc_2(A),A) ) ) )).
fof(l7_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( ( 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] : ( ~ ( r2_hidden(D,k6_dtconstr(k5_msafree(A,k2_pboole(u1_struct_0(A),u3_msualg_1(A,B),C)))) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ~ ( r2_hidden(F,k1_funct_1(u3_msualg_1(A,B),E)) & D = k4_tarski(F,E) ) ) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_funct_1(C,E)) => D != k4_tarski(F,E) ) ) ) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ! [F] : ( ( 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] : ( 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)))) ) ) ) ) ) ) ) ) )).
fof(l7_msscyc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(l7_mssublat,axiom,( m1_subset_1(k5_numbers,k1_tarski(k5_numbers)) )).
fof(l7_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( v1_finset_1(k1_enumset1(A,B,C)) & m1_subset_1(k1_enumset1(A,B,C),k1_zfmisc_1(k4_ordinal1)) ) ) ) ) )).
fof(l7_net_1,axiom,( 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))) )).
fof(l7_normsp_1,axiom,( ~ 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)) )).
fof(l7_ntalgo_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => ! [B] : ( m1_subset_1(B,k4_numbers) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_ordinal1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ( ( k9_nat_1(k4_ordinal1,C,k5_numbers) = k1_int_2(A) & k9_nat_1(k4_ordinal1,D,k5_numbers) = k1_int_2(B) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( k9_nat_1(k4_ordinal1,C,k1_nat_1(E,1)) = k9_nat_1(k4_ordinal1,D,E) & k9_nat_1(k4_ordinal1,D,k1_nat_1(E,1)) = k4_nat_d(k9_nat_1(k4_ordinal1,C,E),k9_nat_1(k4_ordinal1,D,E)) ) ) ) => ( ~ v1_xboole_0(a_1_0_ntalgo_1(D)) & m1_subset_1(a_1_0_ntalgo_1(D),k1_zfmisc_1(k4_ordinal1)) ) ) ) ) ) ) )).
fof(l7_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,c1__ortsp_1) => k1_funct_1(B,k4_tarski(C,D)) = c2__ortsp_1 ) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(c1__ortsp_1,c1__ortsp_1))) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(l7_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k8_group_1(A,k8_group_1(A,D,E),k8_group_1(A,B,C)) = k8_group_1(A,k8_group_1(A,k8_group_1(A,B,D),E),C) ) ) ) ) ) )).
fof(l7_petri_2,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,C,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,A))) ) => ! [F] : ( ( 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] : ( ( 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 ) ) ) ) ) ) ) ) )).
fof(l7_polyeq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k1_newton(A,2) = k3_xcmplx_0(A,A) ) )).
fof(l7_poset_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( 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(k1_partfun1(u1_struct_0(B),u1_struct_0(B),u1_struct_0(B),u1_struct_0(B),k1_abian(u1_struct_0(B),D,A),D),C) = k3_funct_2(u1_struct_0(B),u1_struct_0(B),D,k3_funct_2(u1_struct_0(B),u1_struct_0(B),k1_abian(u1_struct_0(B),D,A),C)) & k1_funct_1(k1_partfun1(u1_struct_0(B),u1_struct_0(B),u1_struct_0(B),u1_struct_0(B),D,k1_abian(u1_struct_0(B),D,A)),C) = k3_funct_2(u1_struct_0(B),u1_struct_0(B),k1_abian(u1_struct_0(B),D,A),k3_funct_2(u1_struct_0(B),u1_struct_0(B),D,C)) ) ) ) ) ) )).
fof(l7_prvect_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) ) )).
fof(l7_prvect_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ~ ( r2_hidden(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => C != k1_domain_1(u1_struct_0(A),u1_struct_0(B),D,E) ) ) ) ) ) )).
fof(l7_qc_lang1,axiom,( ! [A] : ( 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),k4_ordinal1),k2_qc_lang1(A)) ) ) )).
fof(l7_qmax_1,axiom,( ! [A] : ( m1_prob_1(A,k1_numbers,k12_prob_1) => r1_xxreal_0(k5_numbers,k3_funct_2(k12_prob_1,k1_numbers,c2__qmax_1,A)) ) )).
fof(l7_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(l7_rat_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_int_1(C) => ( A = k7_xcmplx_0(C,B) => r2_hidden(A,k3_numbers) ) ) ) )).
fof(l7_real_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_real_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_real_lat)) => k2_lattices(k3_real_lat,A,B) = k2_lattices(k3_real_lat,B,A) ) ) )).
fof(l7_realset2,axiom,( ~ v1_zfmisc_1(2) )).
fof(l7_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(l7_rlaffin2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k1_rlaffin2(A,B),k3_convex1(A,B)) ) ) )).
fof(l7_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => r1_tarski(u1_struct_0(B),u1_struct_0(k1_rlsub_2(A,B,C))) ) ) ) )).
fof(l7_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => r1_tarski(u1_struct_0(C),u1_struct_0(k1_rmod_3(A,B,C,D))) ) ) ) ) )).
fof(l7_rsspace2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(B) & v2_comseq_2(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [E] : ( v7_ordinal1(E) => k9_nat_1(k1_numbers,D,E) = k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(k9_nat_1(k1_numbers,B,E),A),k6_xcmplx_0(k9_nat_1(k1_numbers,B,E),A)),k9_nat_1(k1_numbers,C,E)) ) => ( v2_comseq_2(D) & k1_seq_2(D) = k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(k1_seq_2(B),A),k6_xcmplx_0(k1_seq_2(B),A)),k1_seq_2(C)) ) ) ) ) ) ) ) )).
fof(l7_rsspace4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => k1_funct_1(A,B) = k10_subset_1(k5_numbers,k1_numbers) ) => ( v1_comseq_2(A) & k2_seq_4(k2_relset_1(k1_numbers,k56_valued_1(k4_ordinal1,k1_numbers,A))) = k5_numbers ) ) ) )).
fof(l7_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => r1_tarski(u1_struct_0(B),u1_struct_0(k1_rusub_2(A,B,C))) ) ) ) )).
fof(l7_scmfsa7b,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(A,k7_card_1(3),k1_scmfsa_2,k5_numbers) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( v1_int_1(D) => ( r1_tarski(k2_scmfsa_7(C,D),B) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(E,k1_afinsq_1(k2_scmfsa_7(C,D))) => k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,E)) = E ) ) ) ) ) ) ) )).
fof(l7_scmfsa_1,axiom,( r1_subset_1(k3_scmfsa_1,k1_ami_2) )).
fof(l7_scpinvar,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( 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)) = k5_numbers & k1_funct_1(B,k2_scmp_gcd) = k5_numbers & k1_funct_1(B,k1_scmp_gcd(2)) = k4_xcmplx_0(C) & k1_funct_1(B,k1_scmp_gcd(3)) = k1_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,k5_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,k5_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,k5_numbers),k11_scmpds_2(k2_scmp_gcd,2,1)),k11_scmpds_2(k2_scmp_gcd,3,1))),B,A) ) ) ) ) ) ) ) )).
fof(l7_series_2,axiom,( ! [A] : ( 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) ) ) )).
fof(l7_series_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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(k1_square_1(A),k3_xcmplx_0(A,B)),k1_square_1(B))) ) ) )).
fof(l7_series_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k7_xcmplx_0(1,k2_xcmplx_0(k2_prepower(2,k1_nat_1(A,2)),k2_prepower(2,k1_nat_1(A,1)))) = k6_xcmplx_0(k2_prepower(2,k1_nat_1(A,2)),k2_prepower(2,k1_nat_1(A,1))) ) )).
fof(l7_series_5,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(1,k9_complex1(A)) & r1_xxreal_0(1,k1_square_1(A)) ) ) )).
fof(l7_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(k15_sin_cos(A),k15_sin_cos(k4_xcmplx_0(A))) = 1 ) )).
fof(l7_sin_cos6,axiom,( k1_rcomp_1(k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k5_numbers)),k2_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k5_numbers))) = k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2)) )).
fof(l7_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( k2_xcmplx_0(A,B) != k5_numbers & k2_sin_cos2(k2_xcmplx_0(k7_xcmplx_0(A,2),k7_xcmplx_0(B,2))) = k5_numbers ) ) ) )).
fof(l7_sincos10,axiom,( r1_tarski(k4_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)),k2_rcomp_1(k5_numbers,k28_sin_cos)) )).
fof(l7_sprect_4,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(l7_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),k1_tarski(k5_numbers)),k1_tarski(k5_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_tarski(k5_numbers)),k1_tarski(k5_numbers)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_tarski(k5_numbers),k1_tarski(k5_numbers)))) => ( ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,k2_zfmisc_1(k1_tarski(k5_numbers),k1_tarski(k5_numbers))) & ? [E] : ( m1_subset_1(E,k1_tarski(k5_numbers)) & ? [F] : ( m1_subset_1(F,k1_tarski(k5_numbers)) & D = k1_domain_1(k1_tarski(k5_numbers),k1_tarski(k5_numbers),E,F) & F = c2__symsp_1 ) ) ) ) => ! [D] : ( ( ~ 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(k5_numbers),c3__symsp_1,c2__symsp_1,B,C) => ( ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ~ ( E != k4_struct_0(D) & ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => r1_orders_2(D,F,E) ) ) ) & ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ! [G] : ( 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] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ! [G] : ( 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] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => ~ ( ~ r1_orders_2(D,F,E) & ! [H] : ( 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] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l7_taylor_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_xreal_0(B) => k6_prepower(k23_sin_cos(B),A) = k23_sin_cos(k3_xcmplx_0(A,B)) ) ) )).
fof(l7_topalg_5,axiom,( k2_struct_0(k5_topmetr) = u1_struct_0(k5_topmetr) )).
fof(l7_topreal2,axiom,( k18_euclid(k19_euclid(k5_numbers,1)) = 1 )).
fof(l7_toprealb,axiom,( ~ r1_xxreal_0(k7_xcmplx_0(k28_sin_cos,1),k7_xcmplx_0(k28_sin_cos,2)) )).
fof(l7_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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,B,C),k1_transgeo(A,B,D)) => r2_funct_2(A,A,C,D) ) ) ) ) ) )).
fof(l7_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l7_tsep_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) )).
fof(l7_tsp_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ~ v6_pre_topc(A) ) )).
fof(l7_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ( v4_vectsp_1(A) => v1_group_1(A) ) ) )).
fof(l7_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => r1_tarski(u1_struct_0(C),u1_struct_0(k1_vectsp_5(A,B,C,D))) ) ) ) ) )).
fof(l7_waybel33,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v25_waybel_0(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ! [D] : ( ( ~ 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)) ) ) ) ) ) ) )).
fof(l7_waybel_9,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_waybel_0(A,B) = a_2_2_waybel_9(A,B) ) ) )).
fof(l7_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ! [B] : ( v7_ordinal1(B) => ( A != k3_xcmplx_0(2,B) & A != k1_nat_1(k3_xcmplx_0(2,B),1) ) ) ) )).
fof(l7_xcmplx_0,axiom,( r2_hidden(1,k1_numbers) )).
fof(l7_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(B,C) ) => r1_xxreal_0(A,C) ) ) ) ) )).
fof(l7_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(A,B) => r1_xxreal_0(k6_xcmplx_0(A,C),k6_xcmplx_0(B,C)) ) ) ) ) )).
fof(l7_xxreal_0,axiom,( r2_hidden(k5_numbers,k1_numbers) )).
fof(l7_yellow_6,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(l7_zf_fund2,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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(k5_numbers),k8_zf_lang(k2_zf_lang(4),k12_zf_lang(A,k4_zf_lang(k2_zf_lang(4),k2_zf_lang(k5_numbers))))))) => ( r2_hidden(k2_zf_lang(4),k2_zf_model(A)) | ! [D] : ( m1_subset_1(D,B) => k7_relset_1(B,B,k1_zfmodel1(A,B,C),D) = k1_xboole_0 ) ) ) ) ) ) )).
fof(l7_zf_model,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ 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] : ! [D] : ( ( 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) ) ) ) ) )).
fof(l80_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => v4_anproj_2(k5_anproj_1(A)) ) )).
fof(l80_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r1_xxreal_0(A,B) => r1_xxreal_0(k7_xcmplx_0(k4_newton(A,k1_nat_1(B,1)),k1_nat_1(B,1)),k4_newton(A,B)) ) ) ) )).
fof(l80_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => k2_bcialg_1(A,B) = B ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_1(A,B,C) = k1_bcialg_1(A,C,B) ) ) ) ) )).
fof(l80_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_enumset1(A,B,C,D) = k2_enumset1(B,C,A,D) )).
fof(l80_fib_num4,axiom,( ~ r1_xxreal_0(k6_xcmplx_0(k3_square_1(5),1),k6_xcmplx_0(1,1)) & ~ r1_xxreal_0(k3_square_1(5),k5_numbers) )).
fof(l80_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : 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)) ) )).
fof(l80_fomodel0,axiom,( ! [A] : ! [B] : k10_fomodel0(A,B) = k1_funct_4(k1_margrel1(k4_ordinal1,B,k5_numbers),k1_margrel1(k4_ordinal1,k3_xboole_0(A,B),1)) )).
fof(l80_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( 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] : ( ~ v1_xboole_0(D) => ! [E] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(B),k3_rfunct_3(k3_finseq_2(D),k2_xboole_0(D,k6_margrel1))),k15_fomodel2(B,D)) => ( v3_fomodel2(C,B,A) => k1_funct_1(k23_fomodel2(B,D,A,E),C) = k1_funct_1(k22_fomodel2(B,A,D),k1_domain_1(k15_fomodel2(B,D),k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0)),E,C)) ) ) ) ) ) ) )).
fof(l80_fomodel3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( v4_fomodel1(C,B) & m1_subset_1(C,k1_fomodel1(B)) ) => ! [D] : ( ( 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] : ( ( 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(k9_nat_1(k9_funct_2(k30_fomodel2(B),k30_fomodel2(B)),k32_fomodel3(B,C,D,k36_fomodel3(B,C,D)),A),E) ) ) ) ) ) ) )).
fof(l80_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(k1_fomodel4(C)),k1_fomodel4(C)))) => ( r2_hidden(B,k1_funct_1(k23_fomodel4(C,D),A)) <=> ( r2_hidden(B,k1_fomodel4(C)) & r2_hidden(k4_tarski(A,B),D) ) ) ) ) )).
fof(l80_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(A,B) => k1_funct_4(B,A) = B ) ) ) )).
fof(l80_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,B,C))) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(l80_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( 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)) ) ) ) )).
fof(l80_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( ( v7_graph_1(B,A) & m2_graph_1(B,A) ) => v1_finset_1(k6_graph_5(A,B)) ) ) )).
fof(l80_group_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( ( 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))) ) ) ) ) )).
fof(l80_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(l80_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => r2_hidden(k3_intpro_1(k4_intpro_1(k4_intpro_1(A,C),B),k4_intpro_1(k4_intpro_1(C,A),B)),k8_intpro_1) ) ) ) )).
fof(l80_jgraph_5,axiom,( k18_euclid(k19_euclid(k5_numbers,1)) = 1 )).
fof(l80_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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,k3_matrix_1(B,A))) = k5_numbers ) ) )).
fof(l80_matrixj1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ! [E] : ( ( v1_matrix_0(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))) ) ) ) ) ) )).
fof(l80_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => k5_member_1(k9_member_1(A,B)) = k9_member_1(k5_member_1(A),k5_member_1(B)) ) ) )).
fof(l80_modelc_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( ! [C] : ~ ( r2_hidden(C,A) & ! [D] : ~ ( r2_hidden(D,A) & r2_hidden(k4_tarski(C,D),B) ) ) => v1_partfun1(B,A) ) ) )).
fof(l80_newton,axiom,( k9_newton(2) = k1_xboole_0 )).
fof(l80_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k12_normform(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k12_normform(A))) => k2_lattices(k12_normform(A),B,C) = k2_lattices(k12_normform(A),C,B) ) ) )).
fof(l80_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l80_pepin,axiom,( k11_newton(3,8) = 6561 )).
fof(l80_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k23_quaterni(A,B) = k22_quaterni(k22_quaterni(k19_quaterni(k6_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k13_quaterni(B)),k3_xcmplx_0(k14_quaterni(A),k14_quaterni(B))),k3_xcmplx_0(k15_quaterni(A),k15_quaterni(B))),k3_xcmplx_0(k16_quaterni(A),k16_quaterni(B))),k21_quaterni(k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k14_quaterni(B)),k3_xcmplx_0(k14_quaterni(A),k13_quaterni(B))),k3_xcmplx_0(k15_quaterni(A),k16_quaterni(B))),k3_xcmplx_0(k16_quaterni(A),k15_quaterni(B))),k1_xcmplx_0)),k21_quaterni(k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k15_quaterni(B)),k3_xcmplx_0(k15_quaterni(A),k13_quaterni(B))),k3_xcmplx_0(k16_quaterni(A),k14_quaterni(B))),k3_xcmplx_0(k14_quaterni(A),k16_quaterni(B))),k11_quaterni)),k21_quaterni(k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k16_quaterni(B)),k3_xcmplx_0(k16_quaterni(A),k13_quaterni(B))),k3_xcmplx_0(k14_quaterni(A),k15_quaterni(B))),k3_xcmplx_0(k15_quaterni(A),k14_quaterni(B))),k12_quaterni)) ) ) )).
fof(l80_sincos10,axiom,( k1_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k7_xcmplx_0(k28_sin_cos,2)))) = k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k7_xcmplx_0(k28_sin_cos,2)) )).
fof(l81_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => v5_anproj_2(k5_anproj_1(A)) ) )).
fof(l81_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k3_tarski(A),k3_tarski(B)))) => ~ ( ! [D] : ! [E] : ( r2_hidden(k2_tarski(D,E),A) => ! [F] : ! [G] : ( ( r2_hidden(k4_tarski(D,F),C) & r2_hidden(k4_tarski(E,G),C) ) => r2_hidden(k2_tarski(F,G),B) ) ) & ! [D] : ! [E] : ( r2_hidden(k2_tarski(D,E),A) => ! [F] : ( ( r2_hidden(k4_tarski(D,F),C) & r2_hidden(k4_tarski(E,F),C) ) => D = E ) ) & ! [D] : ( ( 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] : ( m1_subset_1(E,A) => k3_funct_2(A,B,D,E) = k7_relat_1(C,E) ) ) ) ) ) ) ) )).
fof(l81_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ~ ( A != B & C != B & ~ ( k3_complex1(k1_complex2(k6_xcmplx_0(A,B),k6_xcmplx_0(C,B))) = k5_numbers <=> ( k4_complex2(A,B,C) = k7_xcmplx_0(k28_sin_cos,2) | k4_complex2(A,B,C) = k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos) ) ) ) ) ) ) )).
fof(l81_fib_num4,axiom,( ~ r1_xxreal_0(k2_xcmplx_0(k5_numbers,k3_square_1(5)),k2_xcmplx_0(k4_xcmplx_0(1),k3_square_1(5))) & ~ r1_xxreal_0(k3_square_1(5),k5_numbers) )).
fof(l81_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : k1_finseq_3(k7_finseq_1(C,A),D) = k7_finseq_1(k1_finseq_3(C,D),k1_finseq_3(A,D)) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : 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)) ) ) ) )).
fof(l81_fomodel0,axiom,( ! [A] : ! [B] : k10_fomodel0(A,B) = k1_funct_4(k1_margrel1(k4_ordinal1,k6_subset_1(B,A),k5_numbers),k1_margrel1(k4_ordinal1,k3_xboole_0(A,B),1)) )).
fof(l81_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v4_fomodel1(D,B) & m1_subset_1(D,k1_fomodel1(B)) ) => ! [E] : ( ( 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] : ( m2_subset_1(F,k9_funct_2(k37_fomodel1(B),k3_rfunct_3(k3_finseq_2(C),k2_xboole_0(C,k6_margrel1))),k15_fomodel2(B,C)) => ! [G] : ( ( 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)),k15_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)),k15_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)),k15_fomodel2(B,C),k24_fomodel2(B,A)) & v3_fomodel2(E,B,A) ) => ( k17_fomodel2(B,C,F,G,k42_fomodel1(B,k43_fomodel1(B,D),E)) = 1 <=> ? [H] : ( m1_subset_1(H,C) & k1_binop_1(G,k34_fomodel2(B,C,F,D,H),E) = k8_margrel1 ) ) ) ) ) ) ) ) ) ) )).
fof(l81_funct_7,axiom,( ! [A] : ( v1_relat_1(A) => ( r1_tarski(k10_xtuple_0(A),k9_xtuple_0(A)) => k8_funct_7(A,k5_numbers) = k6_partfun1(k9_xtuple_0(A)) ) ) )).
fof(l81_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => r2_hidden(k4_struct_0(A),a_2_2_fvaluat1(A,B)) ) ) ) )).
fof(l81_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,B,C))) => ~ ( r1_analmetr(A,B,C) & ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(l81_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( r2_hidden(C,k13_glib_001(A,B)) <=> ? [D] : ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) & r1_xxreal_0(D,k3_finseq_1(B)) & k1_funct_1(B,D) = C ) ) ) ) )).
fof(l81_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => v1_finset_1(k4_graph_5(A,B,C)) ) ) ) )).
fof(l81_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) => ! [E] : ( ( 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) ) ) ) ) )).
fof(l81_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(l81_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(l81_jgraph_5,axiom,( k12_euclid(k19_euclid(k4_xcmplx_0(1),k5_numbers)) = 1 & k12_euclid(k19_euclid(1,k5_numbers)) = 1 & k12_euclid(k19_euclid(k5_numbers,k4_xcmplx_0(1))) = 1 & k12_euclid(k19_euclid(k5_numbers,1)) = 1 )).
fof(l81_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_xreal_0(D) & v1_lpspace2(D) ) => ( 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)) ) ) ) ) ) )).
fof(l81_mesfunc5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_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 ) ) )).
fof(l81_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m1_subset_1(C,A) => ~ v1_xboole_0(k7_relat_1(B,k1_tarski(C))) ) ) ) )).
fof(l81_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k12_normform(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k12_normform(A))) => ! [D] : ( 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) ) ) ) )).
fof(l81_o_ring_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v2_struct_0(C) & l6_algstr_0(C) ) => ! [D] : ( 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 = k5_numbers | B = k5_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) ) ) ) ) ) ) )).
fof(l81_pepin,axiom,( k11_newton(3,16) = k2_nat_1(6561,6561) )).
fof(l81_prepower,axiom,( ! [A] : ( ( v5_relat_1(A,k3_numbers) & v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( ( v2_comseq_2(A) & r1_xxreal_0(1,B) ) => v2_comseq_2(k5_prepower(B,A)) ) ) ) )).
fof(l81_sincos10,axiom,( k1_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k3_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) = k3_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)) & ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k3_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) => k1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k3_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))),A) = k1_funct_1(k1_fdiff_9,A) ) ) )).
fof(l81_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l82_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => v6_anproj_2(k5_anproj_1(A)) ) )).
fof(l82_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => k9_nat_1(k1_numbers,A,B) = k3_power(2,k7_newton(B)) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k9_nat_1(k1_numbers,A,B) = k6_series_1(k2_asympt_1,B) ) ) ) )).
fof(l82_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_clvect_1(C,A) => ( r1_struct_0(C,B) <=> k5_clvect_1(A,B,C) = u1_struct_0(C) ) ) ) ) )).
fof(l82_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k9_complex1(k4_xcmplx_0(A)) = k9_complex1(A) ) )).
fof(l82_ec_pf_1,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l82_fib_num4,axiom,( ~ r1_xxreal_0(k7_xcmplx_0(k3_square_1(5),k3_square_1(5)),k7_xcmplx_0(k6_xcmplx_0(k3_square_1(5),1),k3_square_1(5))) & ~ r1_xxreal_0(k3_square_1(5),k5_numbers) )).
fof(l82_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : k1_finseq_3(k7_finseq_1(B,A),C) = k7_finseq_1(k1_finseq_3(B,C),k1_finseq_3(A,C)) ) ) )).
fof(l82_finseq_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(l82_fomodel0,axiom,( ! [A] : ! [B] : k10_fomodel0(A,B) = k2_xboole_0(k1_margrel1(k4_ordinal1,k6_subset_1(B,A),k5_numbers),k1_margrel1(k4_ordinal1,k3_xboole_0(A,B),1)) )).
fof(l82_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v4_fomodel1(C,A) & m1_subset_1(C,k1_fomodel1(A)) ) => ! [D] : ( ( 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] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(A),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_fomodel2(A,B)) => ( k25_fomodel2(A,B,E,k42_fomodel1(A,k43_fomodel1(A,C),D)) = k8_margrel1 <=> ? [F] : ( m1_subset_1(F,B) & k25_fomodel2(A,B,k34_fomodel2(A,B,E,C,F),D) = 1 ) ) ) ) ) ) ) )).
fof(l82_fomodel3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( ( ~ v6_struct_0(D) & v11_fomodel1(D) & l1_fomodel1(D) ) => ! [E] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(C),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_fomodel2(C,B)) => ! [F] : ( m2_subset_1(F,k9_funct_2(k37_fomodel1(D),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_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,k9_fomodel2(C,B,E),k3_finseq_2(A)),k2_partfun1(k35_fomodel1(D),B,k9_fomodel2(D,B,F),k3_finseq_2(A))) ) ) ) ) ) ) )).
fof(l82_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,B,C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k7_geomtrap(A,B,C))) => ! [H] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(l82_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( r2_hidden(C,k14_glib_001(A,B)) <=> ? [D] : ( v1_abian(D) & m1_subset_1(D,k4_ordinal1) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(B)) & k1_funct_1(B,D) = C ) ) ) ) )).
fof(l82_graph_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v6_graph_1(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => v1_finset_1(k5_graph_5(B,C,D,A)) ) ) ) )).
fof(l82_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,B) ) => ( ~ r1_xxreal_0(k1_nat_1(k2_nat_1(2,B),A),1) & ~ r1_xxreal_0(k1_nat_1(k1_nat_1(k2_nat_1(B,B),k2_nat_1(3,B)),1),k1_nat_1(k2_nat_1(2,B),A)) & ~ r1_xxreal_0(k1_nat_1(k2_nat_1(2,B),A),A) ) ) ) ) )).
fof(l82_group_9,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(B)) => ! [E] : ( m1_subset_1(E,B) => ( ~ v1_xboole_0(D) => ( r2_hidden(E,k1_group_9(A,B,C,D)) <=> ? [F] : ( m2_finseq_1(F,A) & ? [G] : ( m1_subset_1(G,D) & k1_funct_1(k2_group_9(A,B,C,F),G) = E ) ) ) ) ) ) ) ) )).
fof(l82_integra8,axiom,( k9_xtuple_0(k2_fdiff_1(k1_sin_cos6,k2_rcomp_1(k4_xcmplx_0(1),1))) = k2_rcomp_1(k4_xcmplx_0(1),1) )).
fof(l82_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(l82_jgraph_5,axiom,( r2_hidden(k5_numbers,k1_rcomp_1(k5_numbers,1)) )).
fof(l82_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m1_subset_1(C,A) => ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) & k3_funct_2(k4_ordinal1,A,D,k5_numbers) = C & ! [E] : ( m1_subset_1(E,k4_ordinal1) => r2_hidden(k4_tarski(k3_funct_2(k4_ordinal1,A,D,E),k3_funct_2(k4_ordinal1,A,D,k1_nat_1(E,1))),B) ) ) ) ) ) )).
fof(l82_normform,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A)) => ! [C] : ( m2_subset_1(C,k5_finsub_1(k7_normform(A)),k8_normform(A)) => ! [D] : ( 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)) ) ) ) )).
fof(l82_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l82_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_oppcat_1(C,B,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_oppcat_1(B))) => k3_funct_2(u4_struct_0(k2_oppcat_1(B)),u4_struct_0(A),k10_oppcat_1(B,A,C),k4_cat_1(k2_oppcat_1(B),D)) = k4_cat_1(A,k3_funct_2(u1_struct_0(k2_oppcat_1(B)),u1_struct_0(A),k7_cat_1(k2_oppcat_1(B),A,k10_oppcat_1(B,A,C)),D)) ) ) ) ) )).
fof(l82_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => r1_nat_d(k4_pepin(1),k1_nat_1(k11_newton(3,k1_nat_1(k3_xcmplx_0(4,A),2)),1)) ) )).
fof(l82_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => k22_quaterni(A,k17_quaterni) = A ) )).
fof(l82_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => ! [D] : ( m2_finseq_2(D,k2_numbers,k12_seq_4(A)) => ( k13_seq_4(A,C,B) = k13_seq_4(A,D,B) => C = D ) ) ) ) ) )).
fof(l82_sincos10,axiom,( k1_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k4_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos))) = k4_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos) & ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k4_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos)) => k1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k4_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos)),A) = k1_funct_1(k1_fdiff_9,A) ) ) )).
fof(l82_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l83_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( r1_xxreal_0(4,A) => r1_xxreal_0(k2_nat_1(2,A),k3_xcmplx_0(A,k3_power(2,A))) ) ) )).
fof(l83_borsuk_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_topmetr)) => ! [B] : ( 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))) ) ) )).
fof(l83_borsuk_7,axiom,( 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)))) )).
fof(l83_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(A,k5_numbers) => k9_complex1(A) = k4_xcmplx_0(A) ) ) )).
fof(l83_fib_num4,axiom,( ~ r1_xxreal_0(1,k7_xcmplx_0(k6_xcmplx_0(k3_square_1(5),1),k3_square_1(5))) )).
fof(l83_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( 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] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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] : ( m2_subset_1(F,k9_funct_2(k37_fomodel1(B),k3_rfunct_3(k3_finseq_2(D),k2_xboole_0(D,k6_margrel1))),k15_fomodel2(B,D)) => ! [G] : ( ( 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)),k15_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)),k15_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)),k15_fomodel2(B,D),k24_fomodel2(B,A)) & v3_fomodel2(E,B,A) ) => ( k19_fomodel2(B,D,G,F,k42_fomodel1(B,k42_fomodel1(B,k43_fomodel1(B,k1_fomodel2(B)),E),C)) = 1 <=> ( k1_binop_1(G,F,E) = k5_numbers & k1_binop_1(G,F,C) = k5_numbers ) ) ) ) ) ) ) ) ) ) )).
fof(l83_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k48_gfacirc1(A,B,C) != k4_tarski(D,k4_twoscomp) )).
fof(l83_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C))) => ! [E] : ( 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) ) ) ) ) ) )).
fof(l83_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ~ ( r2_hidden(C,k14_glib_001(A,B)) & ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => ! [E] : ( m1_subset_1(E,k6_glib_000(A)) => ! [F] : ( ( ~ v1_abian(F) & m1_subset_1(F,k4_ordinal1) ) => ~ ( r1_xxreal_0(k1_nat_1(F,2),k3_finseq_1(B)) & D = k1_funct_1(B,F) & C = k1_funct_1(B,k1_nat_1(F,1)) & E = k1_funct_1(B,k1_nat_1(F,2)) & r1_glib_000(A,D,E,C) ) ) ) ) ) ) ) )).
fof(l83_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,B) ) => ( ~ r1_xxreal_0(k1_nat_1(B,A),1) & r1_xxreal_0(k1_nat_1(B,A),k2_nat_1(2,B)) & ~ r1_xxreal_0(k1_nat_1(k1_nat_1(k2_nat_1(B,B),k2_nat_1(3,B)),1),k1_nat_1(B,A)) ) ) ) ) )).
fof(l83_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(l83_jgraph_5,axiom,( r2_hidden(1,k1_rcomp_1(k5_numbers,1)) )).
fof(l83_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_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)) ) ) ) ) )).
fof(l83_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( m2_finseq_2(D,k4_ordinal1,k4_finseq_2(B,k4_ordinal1)) => ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [F] : ( ( v1_matrix_0(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_0(F)) & ( B = k5_numbers => A = k5_numbers ) & ( A = k5_numbers => B = k5_numbers ) & ! [G] : ( ( v1_finset_1(G) & v1_setfam_1(G) & m1_subset_1(G,k1_zfmisc_1(k4_ordinal1)) ) => ! [H] : ( ( v1_finset_1(H) & v1_setfam_1(H) & m1_subset_1(H,k1_zfmisc_1(k4_ordinal1)) ) => ~ ( G = k10_xtuple_0(D) & H = k10_xtuple_0(E) ) ) ) ) ) ) ) ) ) ) )).
fof(l83_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k12_normform(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k12_normform(A))) => k2_lattices(k12_normform(A),B,k1_lattices(k12_normform(A),B,C)) = B ) ) )).
fof(l83_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l83_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_oppcat_1(C,B,A) => ! [D] : ( m1_subset_1(D,u4_struct_0(k2_oppcat_1(B))) => ( k3_funct_2(u1_struct_0(k2_oppcat_1(B)),u1_struct_0(A),k7_cat_1(k2_oppcat_1(B),A,k10_oppcat_1(B,A,C)),k3_graph_1(k2_oppcat_1(B),D)) = k3_graph_1(A,k3_funct_2(u4_struct_0(k2_oppcat_1(B)),u4_struct_0(A),k10_oppcat_1(B,A,C),D)) & k3_funct_2(u1_struct_0(k2_oppcat_1(B)),u1_struct_0(A),k7_cat_1(k2_oppcat_1(B),A,k10_oppcat_1(B,A,C)),k4_graph_1(k2_oppcat_1(B),D)) = k4_graph_1(A,k3_funct_2(u4_struct_0(k2_oppcat_1(B)),u4_struct_0(A),k10_oppcat_1(B,A,C),D)) ) ) ) ) ) )).
fof(l83_partfun1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( B = k4_relat_1(A) => v1_partfun1(B,A) ) ) )).
fof(l83_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ( A = 1 => r2_int_1(k11_newton(3,k3_nat_d(k7_nat_d(k4_pepin(A),1),2)),k4_xcmplx_0(1),k4_pepin(A)) ) ) )).
fof(l83_prepower,axiom,( ! [A] : ( ( v5_relat_1(A,k3_numbers) & v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v5_relat_1(B,k3_numbers) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( v2_comseq_2(A) & v2_comseq_2(B) & k1_seq_2(A) = k1_seq_2(B) & r1_xxreal_0(1,C) ) => k1_seq_2(k5_prepower(C,A)) = k1_seq_2(k5_prepower(C,B)) ) ) ) ) )).
fof(l83_quaterni,axiom,( k21_quaterni(k5_numbers,k1_xcmplx_0) = k5_numbers & k21_quaterni(k5_numbers,k11_quaterni) = k5_numbers & k21_quaterni(k5_numbers,k12_quaterni) = k5_numbers )).
fof(l83_sincos10,axiom,( k1_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers))) = k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers) & ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers)) => k1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers)),A) = k1_funct_1(k2_fdiff_9,A) ) ) )).
fof(l83_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l84_borsuk_7,axiom,( v1_funct_1(k18_sin_cos) & v1_funct_2(k18_sin_cos,u1_struct_0(k3_topmetr),u1_struct_0(k3_topmetr)) & m1_subset_1(k18_sin_cos,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k3_topmetr),u1_struct_0(k3_topmetr)))) )).
fof(l84_card_3,axiom,( ! [A] : ( ( v4_funct_1(A) & v2_card_3(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(B,A) => k9_xtuple_0(B) = k9_card_3(A) ) ) ) )).
fof(l84_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => k3_square_1(k1_square_1(A)) = k9_complex1(A) ) )).
fof(l84_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v5_relat_1(C,u1_struct_0(B)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_exchsort(C) ) => ! [D] : ( m1_subset_1(D,k9_xtuple_0(C)) => ! [E] : ( m1_subset_1(E,k9_xtuple_0(C)) => ( ( r2_hidden(D,E) & A = k7_exchsort(B,C,D,E) ) => ! [F] : ( m1_subset_1(F,k9_xtuple_0(C)) => ! [G] : ( m1_subset_1(G,k9_xtuple_0(C)) => ! [H] : ( m1_subset_1(H,k9_xtuple_0(C)) => ! [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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l84_fib_num4,axiom,( ~ r1_xxreal_0(k3_square_1(k1_pepin(3)),k3_square_1(5)) )).
fof(l84_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(A),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_fomodel2(A,B)) => ( k25_fomodel2(A,B,E,k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k1_fomodel2(A)),C),D)) = k8_margrel1 <=> ( k25_fomodel2(A,B,E,C) = k7_margrel1 & k25_fomodel2(A,B,E,D) = k7_margrel1 ) ) ) ) ) ) ) )).
fof(l84_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ! [E] : ! [F] : r1_xboole_0(k2_msafree2(k49_gfacirc1(A,B,C)),k3_msafree2(k49_gfacirc1(D,E,F))) ) ) ) )).
fof(l84_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)))) ) )).
fof(l84_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C))) => k9_geomtrap(k7_geomtrap(A,B,C),D,D) = D ) ) ) ) )).
fof(l84_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ! [E] : ( ( 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)) ) ) ) ) )).
fof(l84_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,C) & r1_xxreal_0(B,C) ) => ( ~ r1_xxreal_0(k1_nat_1(k1_nat_1(k2_nat_1(2,C),k2_nat_1(C,A)),B),1) & ~ r1_xxreal_0(k1_nat_1(k1_nat_1(k2_nat_1(2,C),k2_nat_1(C,A)),B),A) & ~ r1_xxreal_0(k1_nat_1(k1_nat_1(k2_nat_1(C,C),k2_nat_1(3,C)),1),k1_nat_1(k1_nat_1(k2_nat_1(2,C),k2_nat_1(C,A)),B)) ) ) ) ) ) )).
fof(l84_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => r2_hidden(k3_intpro_1(k4_intpro_1(A,k4_intpro_1(C,B)),k4_intpro_1(A,k4_intpro_1(B,C))),k8_intpro_1) ) ) ) )).
fof(l84_lpspace2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_ordinal1) & v5_valued_0(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ( ( v1_rsspace3(B,A) & ! [F] : ( v7_ordinal1(F) => k9_nat_1(k1_numbers,D,F) = k2_normsp_0(A,k5_algstr_0(A,C,k5_rsspace3(A,B,k1_recdef_1(E,F)))) ) & v2_comseq_2(D) & k1_seq_2(D) = k5_numbers ) => ( v3_normsp_1(B,A) & k6_normsp_1(A,B) = C & v2_comseq_2(k5_normsp_0(A,k4_normsp_1(A,B,C))) & k1_seq_2(k5_normsp_0(A,k4_normsp_1(A,B,C))) = k5_numbers ) ) ) ) ) ) ) )).
fof(l84_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l84_partfun1,axiom,( ! [A] : ! [B] : ( 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) ) ) ) )).
fof(l84_pdiff_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,k3_finseq_1(B)) & r1_tarski(k1_rvsum_1(B),C) ) => r2_hidden(k7_partfun1(k4_ordinal1,B,A),C) ) ) ) )).
fof(l84_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => r1_nat_d(k4_pepin(2),k1_nat_1(k11_newton(3,k1_nat_1(k3_xcmplx_0(16,A),8)),1)) ) )).
fof(l84_rlsub_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(l84_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( ( v9_rltopsp1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( v1_xreal_0(C) => v9_rltopsp1(k1_convex1(A,B,C),A) ) ) ) )).
fof(l84_sincos10,axiom,( k1_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k4_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) = k4_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)) & ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k4_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) => k1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k4_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))),A) = k1_funct_1(k2_fdiff_9,A) ) ) )).
fof(l84_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l84_toprealb,axiom,( ~ v1_xboole_0(k3_rcomp_1(k4_xcmplx_0(1),1)) & m1_subset_1(k3_rcomp_1(k4_xcmplx_0(1),1),k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(k4_rcomp_1(k5_numbers,k28_sin_cos)) & m1_subset_1(k4_rcomp_1(k5_numbers,k28_sin_cos),k1_zfmisc_1(k1_numbers)) )).
fof(l85_borsuk_7,axiom,( ! [A] : ( 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(k3_xcmplx_0(2,k28_sin_cos),c1__borsuk_7),k18_sin_cos),A),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k3_xcmplx_0(2,k28_sin_cos),k5_numbers),k16_sin_cos),A),k5_numbers) ) )).
fof(l85_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( k4_complex2(A,B,C) != k5_numbers => k4_complex2(C,B,A) = k6_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k4_complex2(A,B,C)) ) ) ) ) )).
fof(l85_fib_num4,axiom,( ~ r1_xxreal_0(3,k3_square_1(5)) )).
fof(l85_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,B,C))) => ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(l85_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( r1_xxreal_0(C,k3_finseq_1(B)) => r1_xxreal_0(k17_glib_001(A,B,C),C) ) ) ) ) )).
fof(l85_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,C) & r1_xxreal_0(1,B) & r1_xxreal_0(B,C) ) => ( r1_xxreal_0(k1_nat_1(k2_nat_1(3,C),1),k1_nat_1(k1_nat_1(k2_nat_1(2,C),k2_nat_1(C,A)),B)) & r1_xxreal_0(k1_nat_1(k1_nat_1(k2_nat_1(2,C),k2_nat_1(C,A)),B),k1_nat_1(k2_nat_1(C,C),k2_nat_1(3,C))) ) ) ) ) ) )).
fof(l85_group_4,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(l85_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_oppcat_1(C,B,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k3_funct_2(u4_struct_0(B),u4_struct_0(k2_oppcat_1(A)),k11_oppcat_1(B,A,C),k4_cat_1(B,D)) = k4_cat_1(k2_oppcat_1(A),k3_funct_2(u1_struct_0(B),u1_struct_0(k2_oppcat_1(A)),k7_cat_1(B,k2_oppcat_1(A),k11_oppcat_1(B,A,C)),D)) ) ) ) ) )).
fof(l85_partfun1,axiom,( ! [A] : m1_subset_1(k4_relat_1(A),k1_zfmisc_1(k2_zfmisc_1(A,A))) )).
fof(l85_pepin,axiom,( k4_nat_d(k11_newton(3,1),k4_pepin(3)) = 3 )).
fof(l85_rlsub_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k4_lattices(A,C,B) = B ) => B = k5_lattices(A) ) ) ) )).
fof(l85_toprealb,axiom,( u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(c25__toprealb))) = k5_toprealb(c25__toprealb) )).
fof(l85_waybel23,axiom,( ! [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) & 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] : ( ( v6_waybel23(B,A) & m1_waybel23(B,A) ) => r1_tarski(u1_struct_0(k1_waybel_8(A)),B) ) ) ) ) )).
fof(l86_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( 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 = k5_numbers & G = k5_numbers & H = k5_numbers & I = k5_numbers ) ) ) ) ) ) ) ) ) ) => v1_anproj_2(A) ) ) )).
fof(l86_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(2,A) & r1_xxreal_0(A,k2_int_1(k7_xcmplx_0(A,2))) ) ) )).
fof(l86_card_2,axiom,( v4_ordinal1(k4_ordinal1) )).
fof(l86_comput_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,B) ) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(l86_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_enumset1(A,B,C,D) = k2_enumset1(C,B,A,D) )).
fof(l86_fib_num4,axiom,( ~ r1_xxreal_0(k4_xcmplx_0(k3_square_1(5)),k4_xcmplx_0(3)) )).
fof(l86_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ~ ( r2_hidden(B,k2_finseq_1(A)) & ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(C,A) & B = C ) ) ) ) )).
fof(l86_fomodel3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( ( ~ v6_struct_0(D) & v11_fomodel1(D) & l1_fomodel1(D) ) => ! [E] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(C),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_fomodel2(C,B)) => ! [F] : ( m2_subset_1(F,k9_funct_2(k37_fomodel1(D),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_fomodel2(D,B)) => ( ( v16_fomodel1(D,C) & r1_tarski(A,k30_fomodel2(C)) & k5_relat_1(E,k37_fomodel1(C)) = k5_relat_1(F,k37_fomodel1(C)) ) => ( v10_fomodel2(A,B,C,E) <=> v10_fomodel2(A,B,D,F) ) ) ) ) ) ) ) )).
fof(l86_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C))) => ? [F] : ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,B,C))) & k9_geomtrap(k7_geomtrap(A,B,C),F,D) = E ) ) ) ) ) ) )).
fof(l86_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( r1_xxreal_0(C,k3_finseq_1(B)) => r1_xxreal_0(C,k19_glib_001(A,B,C)) ) ) ) ) )).
fof(l86_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( D = u1_struct_0(k5_group_4(B,C)) => k18_group_9(A,B,C) = k18_group_9(A,B,D) ) ) ) ) )).
fof(l86_ideal_1,axiom,( ! [A] : ! [B] : r1_tarski(k1_tarski(A),k2_tarski(A,B)) )).
fof(l86_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(l86_measure6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ( v5_measure6(B,A) => v6_measure6(k32_valued_1(A,k1_numbers,B),A) ) ) ) )).
fof(l86_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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 ) ) ) )).
fof(l86_newton,axiom,( ! [A] : ( v7_ordinal1(A) => k9_newton(A) = a_1_1_newton(A) ) )).
fof(l86_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l86_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_oppcat_1(C,B,A) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ( k3_funct_2(u1_struct_0(B),u1_struct_0(k2_oppcat_1(A)),k7_cat_1(B,k2_oppcat_1(A),k11_oppcat_1(B,A,C)),k3_graph_1(B,D)) = k3_graph_1(k2_oppcat_1(A),k3_funct_2(u4_struct_0(B),u4_struct_0(k2_oppcat_1(A)),k11_oppcat_1(B,A,C),D)) & k3_funct_2(u1_struct_0(B),u1_struct_0(k2_oppcat_1(A)),k7_cat_1(B,k2_oppcat_1(A),k11_oppcat_1(B,A,C)),k4_graph_1(B,D)) = k4_graph_1(k2_oppcat_1(A),k3_funct_2(u4_struct_0(B),u4_struct_0(k2_oppcat_1(A)),k11_oppcat_1(B,A,C),D)) ) ) ) ) ) )).
fof(l86_pepin,axiom,( k4_nat_d(k11_newton(3,2),k4_pepin(3)) = 9 )).
fof(l86_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ! [D] : ! [E] : ( 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) & k5_numbers = k5_card_1(E) & ! [F] : ( m1_subset_1(F,A) => ! [G] : ( 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_funct_1(B,G),k1_funct_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))) ) ) ) ) )).
fof(l86_rlsub_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_lattices(A,C,B) = B ) => B = k6_lattices(A) ) ) ) )).
fof(l86_scmpds_2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_compos_1(k1_scmpds_2)) => ( k2_compos_0(u1_compos_1(k1_scmpds_2),B) = k5_numbers => k2_extpro_1(2,k1_scmpds_2,B,A) = A ) ) ) )).
fof(l86_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k22_sin_cos,k2_xcmplx_0(A,B)) = k3_xcmplx_0(k1_funct_1(k22_sin_cos,A),k1_funct_1(k22_sin_cos,B)) ) ) )).
fof(l86_sprect_2,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(l86_toprealb,axiom,( u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(c26__toprealb))) = k5_toprealb(c26__toprealb) )).
fof(l87_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( 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 = k5_numbers & G = k5_numbers & H = k5_numbers & I = k5_numbers ) ) ) ) ) ) ) ) ) ) => ( v4_collsp(k5_anproj_1(A)) & v3_anproj_2(k5_anproj_1(A)) ) ) ) )).
fof(l87_classes1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ~ r2_hidden(B,k10_xtuple_0(A)) => k10_relat_1(A,B) = k1_xboole_0 ) ) )).
fof(l87_convex4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( v2_convex4(B,A) => ( ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ~ ( C = E & D = F & r1_xxreal_0(k5_numbers,E) & r1_xxreal_0(k5_numbers,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))) ) ) ) ) ) ) )).
fof(l87_fib_num4,axiom,( ~ r1_xxreal_0(k2_xcmplx_0(k4_xcmplx_0(k3_square_1(5)),3),k2_xcmplx_0(k4_xcmplx_0(3),3)) )).
fof(l87_fomodel0,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( r1_tarski(k9_xtuple_0(B),k9_xtuple_0(A)) & r1_tarski(A,B) ) => A = B ) ) ) )).
fof(l87_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C))) => ! [F] : ( 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 ) ) ) ) ) ) ) )).
fof(l87_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v2_glib_001(B,A) <=> ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( ~ r1_xxreal_0(k3_finseq_1(B),C) => r2_glib_000(A,k1_funct_1(B,C),k1_funct_1(B,k1_nat_1(C,2)),k1_funct_1(B,k1_nat_1(C,1))) ) ) ) ) ) )).
fof(l87_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => r2_hidden(k3_intpro_1(k4_intpro_1(k4_intpro_1(C,B),A),k4_intpro_1(k4_intpro_1(B,C),A)),k8_intpro_1) ) ) ) )).
fof(l87_measure6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ( v6_measure6(B,A) => v5_measure6(k32_valued_1(A,k1_numbers,B),A) ) ) ) )).
fof(l87_pepin,axiom,( k4_nat_d(k11_newton(3,4),k4_pepin(3)) = 81 )).
fof(l87_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => k24_quaterni(A) = k22_quaterni(k22_quaterni(k19_quaterni(k4_xcmplx_0(k13_quaterni(A)),k21_quaterni(k4_xcmplx_0(k14_quaterni(A)),k1_xcmplx_0)),k21_quaterni(k4_xcmplx_0(k15_quaterni(A)),k11_quaterni)),k21_quaterni(k4_xcmplx_0(k16_quaterni(A)),k12_quaterni)) ) )).
fof(l87_rfunct_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [D] : ! [E] : ! [F] : ( 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] : ( m1_subset_1(G,B) => ! [H] : ( 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_funct_1(C,H),k1_funct_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] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [D] : ! [E] : ! [F] : ( 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) & k1_nat_1(A,1) = k5_card_1(F) & ! [G] : ( m1_subset_1(G,B) => ! [H] : ( 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_funct_1(C,H),k1_funct_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))) ) ) ) ) ) ) )).
fof(l87_toprealb,axiom,( u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k5_numbers,1)))) = k5_toprealb(k2_rcomp_1(k5_numbers,1)) )).
fof(l87_valued_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) ) => ( r1_tarski(C,B) => r1_tarski(k1_relset_1(k4_ordinal1,k61_valued_1(C,A)),k1_relset_1(k4_ordinal1,k61_valued_1(B,A))) ) ) ) ) )).
fof(l87_waybel23,axiom,( ! [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) & l1_orders_2(A) ) => ( ? [B] : ( v6_waybel23(B,A) & m1_waybel23(B,A) & ! [C] : ( ( v6_waybel23(C,A) & m1_waybel23(C,A) ) => r1_tarski(B,C) ) ) => v2_waybel_8(A) ) ) )).
fof(l87_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),k4_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_numbers))) ) => k20_zmodul02(A,k8_finseq_1(u1_struct_0(A),B,C),D) = k8_finseq_1(u1_struct_0(A),k20_zmodul02(A,B,D),k20_zmodul02(A,C,D)) ) ) ) ) )).
fof(l88_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(2,A) & r1_xxreal_0(k1_square_1(A),k1_nat_1(A,1)) ) ) )).
fof(l88_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => k2_bcialg_1(A,k2_bcialg_1(A,B)) = B ) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_1(A,C,k1_bcialg_1(A,C,B)) = B ) ) ) ) )).
fof(l88_fib_num4,axiom,( ~ r1_xxreal_0(k4_xcmplx_0(1),k4_xcmplx_0(k3_square_1(5))) )).
fof(l88_fomodel0,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) ) => ( ( v1_partfun1(D,A) & v4_relat_1(C,A) & v1_funct_1(k3_relat_1(k3_relat_1(k3_relat_1(B,D),k2_relat_1(D)),C)) & r1_tarski(k10_xtuple_0(B),k9_xtuple_0(C)) ) => k3_relat_1(k3_relat_1(k3_relat_1(B,D),k2_relat_1(D)),C) = k3_relat_1(B,C) ) ) ) ) )).
fof(l88_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,B,C))) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(l88_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)) ) ) ) ) )).
fof(l88_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => ! [D] : ( ( ~ v2_struct_0(D) & v2_graph_1(D) & v6_graph_1(D) & l1_graph_1(D) ) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(D)) => ( ( r6_graphsp(B,D,A,E) & F = 1 & r1_xxreal_0(1,A) & C = k6_graphsp(k9_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),k15_graphsp(A),k18_graphsp(A))),1),B) ) => ( ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => ! [H] : ( m1_subset_1(H,k4_ordinal1) => ~ ( G != F & G = H & k1_funct_1(C,k1_nat_1(A,H)) != k4_xcmplx_0(1) & ! [I] : ( m2_finseq_1(I,k4_ordinal1) => ! [J] : ( ( v7_graph_1(J,D) & m2_graph_1(J,D) ) => ~ ( r4_graphsp(I,C,H,A) & ! [K] : ( m1_subset_1(K,k4_ordinal1) => ( r1_xxreal_0(1,K) => ( r1_xxreal_0(k3_finseq_1(I),K) | r2_hidden(k1_funct_1(I,K),k13_graphsp(C,A)) ) ) ) & r5_graphsp(D,J,I) & r8_graph_5(D,F,G,J,k13_graphsp(C,A),E) & k10_graph_5(D,J,E) = k1_funct_1(C,k1_nat_1(k2_nat_1(2,A),H)) & ( ~ r2_hidden(G,k13_graphsp(C,A)) => r9_graph_5(D,J,k13_graphsp(C,A),F,E) ) ) ) ) ) ) ) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ! [H] : ( m1_subset_1(H,k4_ordinal1) => ( ( k1_funct_1(C,k1_nat_1(A,H)) = k4_xcmplx_0(1) & r1_xxreal_0(1,H) & r1_xxreal_0(H,A) & r2_hidden(G,k13_graphsp(C,A)) ) => k1_funct_1(B,k1_nat_1(k1_nat_1(k2_nat_1(2,A),k2_nat_1(A,G)),H)) = k4_xcmplx_0(1) ) ) ) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ~ ( r2_hidden(G,k13_graphsp(C,A)) & k1_funct_1(C,k1_nat_1(A,G)) = k4_xcmplx_0(1) ) ) ) ) ) ) ) ) ) ) )).
fof(l88_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(l88_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( k1_matrix_0(C) = k1_matrix_0(D) & r2_hidden(A,k4_finseq_1(C)) ) => k7_matrix_0(u1_struct_0(B),k3_matrix_3(B,C,D),A) = k3_fvsum_1(B,k7_matrix_0(u1_struct_0(B),C,A),k7_matrix_0(u1_struct_0(B),D,A)) ) ) ) ) ) )).
fof(l88_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l88_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,B,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_oppcat_1(B))) => k3_funct_2(u4_struct_0(k2_oppcat_1(B)),u4_struct_0(A),k10_oppcat_1(B,A,C),k4_cat_1(k2_oppcat_1(B),D)) = k4_cat_1(A,k3_funct_2(u1_struct_0(k2_oppcat_1(B)),u1_struct_0(A),k7_cat_1(k2_oppcat_1(B),A,k10_oppcat_1(B,A,C)),D)) ) ) ) ) )).
fof(l88_pepin,axiom,( k4_nat_d(k11_newton(3,8),k4_pepin(3)) = 136 )).
fof(l88_sin_cos,axiom,( k1_funct_1(k22_sin_cos,k5_numbers) = 1 )).
fof(l88_toprealb,axiom,( k1_relset_1(k1_numbers,k1_fcont_1(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos)),k5_numbers)) = u1_struct_0(k2_topalg_2) )).
fof(l88_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v2_finseq_1(D) ) => ( ( r1_tarski(C,A) & r1_tarski(D,B) ) => k14_finseq_1(k4_subset_1(k4_ordinal1,k1_relset_1(k4_ordinal1,C),k1_relset_1(k4_ordinal1,k61_valued_1(D,k3_finseq_1(A))))) = k8_finseq_1(k4_ordinal1,k14_finseq_1(k1_relset_1(k4_ordinal1,C)),k14_finseq_1(k1_relset_1(k4_ordinal1,k61_valued_1(D,k3_finseq_1(A))))) ) ) ) ) ) )).
fof(l89_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_anproj_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_anproj_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_anproj_1(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_anproj_1(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k5_anproj_1(A))) => ! [G] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(l89_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(1,A) & r1_xxreal_0(k6_xcmplx_0(k5_series_1(2,k1_nat_1(A,1)),k5_series_1(2,A)),1) ) ) )).
fof(l89_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_1(A,C,k1_bcialg_1(A,C,B)) = B ) ) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l89_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k4_xcmplx_0(k9_complex1(A)),A) & r1_xxreal_0(A,k9_complex1(A)) ) ) )).
fof(l89_fib_num4,axiom,( ~ r1_xxreal_0(k2_xcmplx_0(k4_xcmplx_0(1),3),k2_xcmplx_0(k4_xcmplx_0(k3_square_1(5)),3)) )).
fof(l89_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,B,C))) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(l89_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( v2_glib_001(B,A) => v2_glib_001(k8_glib_001(A,B,C,D),A) ) ) ) ) ) )).
fof(l89_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_2(D,k1_numbers,k3_finseq_2(k1_numbers)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k3_finseq_2(k1_numbers)) => ! [F] : ( m2_finseq_2(F,k1_numbers,k3_finseq_2(k1_numbers)) => ( ( E = k6_graphsp(k9_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),k15_graphsp(C),k18_graphsp(C))),B),D) & F = k6_graphsp(k9_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),k15_graphsp(C),k18_graphsp(C))),k1_nat_1(B,1)),D) & r2_hidden(A,k13_graphsp(E,C)) & k3_finseq_1(D) = k1_nat_1(k1_nat_1(k2_nat_1(C,C),k2_nat_1(3,C)),1) ) => ( k7_graphsp(E,C) = k1_xboole_0 | k1_funct_1(F,k1_nat_1(C,A)) = k1_funct_1(E,k1_nat_1(C,A)) ) ) ) ) ) ) ) ) )).
fof(l89_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(l89_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [E] : ( ( v1_xreal_0(E) & ~ v3_xxreal_0(E) ) => ~ ( r1_topreal1(k15_euclid(2),B,C,D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k2_brouwer(2,A,E)))) & ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(k2_brouwer(2,A,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,A,E)),u1_struct_0(k1_pre_topc(k15_euclid(2),D))))) ) => ~ ( v5_pre_topc(F,k2_brouwer(2,A,E),k1_pre_topc(k15_euclid(2),D)) & k2_partfun1(u1_struct_0(k2_brouwer(2,A,E)),u1_struct_0(k1_pre_topc(k15_euclid(2),D)),F,D) = k6_partfun1(D) ) ) ) ) ) ) ) ) )).
fof(l89_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l89_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,B,A) => ! [D] : ( m1_subset_1(D,u4_struct_0(k2_oppcat_1(B))) => ( k3_funct_2(u1_struct_0(k2_oppcat_1(B)),u1_struct_0(A),k7_cat_1(k2_oppcat_1(B),A,k10_oppcat_1(B,A,C)),k3_graph_1(k2_oppcat_1(B),D)) = k4_graph_1(A,k3_funct_2(u4_struct_0(k2_oppcat_1(B)),u4_struct_0(A),k10_oppcat_1(B,A,C),D)) & k3_funct_2(u1_struct_0(k2_oppcat_1(B)),u1_struct_0(A),k7_cat_1(k2_oppcat_1(B),A,k10_oppcat_1(B,A,C)),k4_graph_1(k2_oppcat_1(B),D)) = k3_graph_1(A,k3_funct_2(u4_struct_0(k2_oppcat_1(B)),u4_struct_0(A),k10_oppcat_1(B,A,C),D)) ) ) ) ) ) )).
fof(l89_pepin,axiom,( k4_nat_d(k11_newton(3,16),k4_pepin(3)) = k2_nat_1(83,3) )).
fof(l89_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(E,A,C) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [G] : ( m1_subset_1(G,u1_struct_0(k12_polynom1(A,C))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k12_polynom1(A,C))) => ( ( E = G & F = H & r5_polyred(A,B,C,E,F,D) ) => r11_polyred(k12_polynom1(A,C),k7_ideal_1(k12_polynom1(A,C),D),G,H) ) ) ) ) ) ) ) ) ) )).
fof(l89_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k25_quaterni(A,B) = k22_quaterni(k22_quaterni(k19_quaterni(k6_xcmplx_0(k13_quaterni(A),k13_quaterni(B)),k21_quaterni(k6_xcmplx_0(k14_quaterni(A),k14_quaterni(B)),k1_xcmplx_0)),k21_quaterni(k6_xcmplx_0(k15_quaterni(A),k15_quaterni(B)),k11_quaterni)),k21_quaterni(k6_xcmplx_0(k16_quaterni(A),k16_quaterni(B)),k12_quaterni)) ) ) )).
fof(l89_toprealb,axiom,( k1_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos)),k5_numbers),k5_toprealb(c26__toprealb))) = k5_toprealb(c26__toprealb) )).
fof(l89_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => k4_xxreal_3(A,k5_numbers) = k5_numbers ) )).
fof(l8_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l8_algstr_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_0)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_algstr_0)) => ? [C] : ( m1_subset_1(C,u1_struct_0(k3_algstr_0)) & k1_algstr_0(k3_algstr_0,A,C) = B ) ) ) )).
fof(l8_altcat_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k7_altcat_1(k1_tarski(k1_xboole_0)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_altcat_1(k1_tarski(k1_xboole_0)))) => A = B ) ) )).
fof(l8_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ( B != k4_struct_0(A) & C != k4_struct_0(A) ) ) ) ) ) )).
fof(l8_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( 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,k4_xcmplx_0(E)) ) ) ) ) ) ) )).
fof(l8_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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,G,H),I),F)) = k3_rlvect_1(A,k3_rlvect_1(A,k3_rlvect_1(A,k3_rlvect_1(A,B,G),k3_rlvect_1(A,C,H)),k3_rlvect_1(A,D,I)),k3_rlvect_1(A,E,F)) ) ) ) ) ) ) ) ) ) )).
fof(l8_arytm_0,axiom,( ! [A] : ! [B] : 1 != k4_tarski(A,B) )).
fof(l8_arytm_2,axiom,( 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)) )).
fof(l8_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(l8_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(l8_bhsp_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_rlsub_1(o_0_5_bhsp_1))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_rlsub_1(o_0_5_bhsp_1))) => ! [C] : ( v1_xreal_0(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)),k1_rlvect_1(k1_rlsub_1(o_0_5_bhsp_1),A,C),B)) = k3_xcmplx_0(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))) ) ) ) )).
fof(l8_cfdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(1))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_real_ns1(1))) => ( ( C = k9_finseq_1(A) & D = k9_finseq_1(B) ) => ( k3_rlvect_1(k4_real_ns1(1),C,D) = k9_finseq_1(k2_xcmplx_0(A,B)) & k5_algstr_0(k4_real_ns1(1),C,D) = k9_finseq_1(k6_xcmplx_0(A,B)) ) ) ) ) ) ) )).
fof(l8_cfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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) ) ) ) ) )).
fof(l8_collsp,axiom,( ~ v2_struct_0(g1_collsp(c2__collsp,c3__collsp)) & l1_collsp(g1_collsp(c2__collsp,c3__collsp)) )).
fof(l8_complsp2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => m2_finseq_1(A,k2_numbers) ) )).
fof(l8_compos_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_compos_0(A) & v2_compos_0(A) ) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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),k4_ordinal1) ) ) ) )).
fof(l8_comptrig,axiom,( ~ r1_xxreal_0(k2_xcmplx_0(k28_sin_cos,k28_sin_cos),k2_xcmplx_0(k5_numbers,k28_sin_cos)) )).
fof(l8_convex2,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l8_convex3,axiom,( ! [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) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(l8_convfun1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_convfun1(A,k4_convfun1))) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( C = k4_tarski(B,E) => k1_rlvect_1(k3_convfun1(A,k4_convfun1),C,D) = k4_tarski(k1_rlvect_1(A,B,D),k3_xcmplx_0(D,E)) ) ) ) ) ) ) )).
fof(l8_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l8_csspace2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(k5_numbers,k1_funct_1(k7_comseq_3(k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,k2_comseq_2(k4_ordinal1,A))),B)) & k1_funct_1(k8_comseq_3(k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,k2_comseq_2(k4_ordinal1,A))),B) = k5_numbers ) ) ) )).
fof(l8_csspace4,axiom,( 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))) )).
fof(l8_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => k4_euclid_3(A,B,C) != k6_xcmplx_0(k3_xcmplx_0(2,k4_euclid_3(D,E,F)),k3_xcmplx_0(4,k28_sin_cos)) ) ) ) ) ) ) )).
fof(l8_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k9_euclid(3,k1_euclid_8(B,C,D),A) = k1_euclid_8(k3_xcmplx_0(A,B),k3_xcmplx_0(A,C),k3_xcmplx_0(A,D)) ) ) ) ) )).
fof(l8_fib_fusc,axiom,( k10_ami_3(k5_numbers) != k10_ami_3(2) )).
fof(l8_fib_num4,axiom,( k7_xcmplx_0(k2_fib_num,k1_fib_num) = k7_xcmplx_0(k6_xcmplx_0(k3_square_1(5),3),2) )).
fof(l8_finance1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ~ v1_xboole_0(D) => a_4_3_finance1(A,B,C,D) = k8_relset_1(A,B,C,D) ) ) ) ) )).
fof(l8_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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 ) ) ) )).
fof(l8_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( v1_fomodel0(B,A) <=> ! [C] : ! [D] : ( ( 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 ) ) ) )).
fof(l8_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( 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)) ) ) ) ) )).
fof(l8_fuzzy_1,axiom,( m1_subset_1(1,k1_numbers) )).
fof(l8_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ! [D] : ! [E] : ( ( r2_hidden(D,k1_glib_002(A,B)) & r1_glib_000(A,D,E,C) ) => r2_hidden(E,k1_glib_002(A,B)) ) ) ) )).
fof(l8_goboard9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(l8_gobrd11,axiom,( u1_struct_0(k15_euclid(2)) = k1_euclid(2) )).
fof(l8_gr_cy_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,k4_numbers) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l8_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(B,k1_nat_1(C,1)) & r1_xxreal_0(C,k3_finseq_1(A)) ) => ( k1_nat_1(k3_finseq_1(k1_graph_2(A,B,C)),B) = k1_nat_1(C,1) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ~ r1_xxreal_0(k3_finseq_1(k1_graph_2(A,B,C)),D) => k1_funct_1(k1_graph_2(A,B,C),k1_nat_1(D,1)) = k1_funct_1(A,k1_nat_1(B,D)) ) ) ) ) ) ) ) )).
fof(l8_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v15_algstr_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ? [C] : ( ~ 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)) ) ) )).
fof(l8_holder_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,A,B)) ) => ! [B] : ( v7_ordinal1(B) => ( k9_nat_1(k1_numbers,k3_series_1(A),B) = k5_numbers => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(C,B) => k9_nat_1(k1_numbers,A,C) = k5_numbers ) ) ) ) ) ) )).
fof(l8_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( r1_aff_1(A,D,B,C) => ( D = B | D = C | ( ~ ( ~ r1_aff_1(A,D,B,E) & r1_aff_1(A,D,E,F) & r2_analoaf(A,B,E,C,F) ) & ~ ( r1_aff_1(A,D,B,E) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & ~ r1_aff_1(A,D,B,G) & r1_aff_1(A,D,G,H) & r2_analoaf(A,B,G,C,H) & r2_analoaf(A,G,E,H,F) & r1_aff_1(A,D,B,F) ) ) ) ) | ( D != C & D != B & r1_aff_1(A,D,C,B) & ( ( ~ r1_aff_1(A,D,C,F) & r1_aff_1(A,D,F,E) & r2_analoaf(A,C,F,B,E) ) | ( r1_aff_1(A,D,C,F) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & ~ r1_aff_1(A,D,C,G) & r1_aff_1(A,D,G,H) & r2_analoaf(A,C,G,B,H) & r2_analoaf(A,G,F,H,E) & r1_aff_1(A,D,C,E) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l8_int_2,axiom,( ! [A] : ( v1_int_1(A) => ( r1_int_1(A,k5_numbers) & r1_int_1(1,A) & r1_int_1(k4_xcmplx_0(1),A) ) ) )).
fof(l8_int_8,axiom,( ! [A] : ( v1_int_1(A) => r1_int_1(2,k3_xcmplx_0(A,k2_xcmplx_0(A,1))) ) )).
fof(l8_integr19,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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))) ) ) ) ) ) ) )).
fof(l8_integra4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,k1_integra1(A)) => ( k3_integra1(A) = k5_numbers => ( v2_integra1(B,A) & k11_integra1(A,B) = k5_numbers ) ) ) ) ) )).
fof(l8_intpro_1,axiom,( ! [A] : ~ ( v7_intpro_1(A) & v1_xboole_0(A) ) )).
fof(l8_jordan1,axiom,( u1_struct_0(k15_euclid(2)) = k1_euclid(2) )).
fof(l8_jordan1c,axiom,( 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))) )).
fof(l8_jordan1h,axiom,( r8_relat_2(k1_jordan1h,k1_numbers) )).
fof(l8_jordan5a,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( r2_hidden(A,k2_pcomps_1(k7_metric_1)) => v3_rcomp_1(A) ) ) )).
fof(l8_jordan5b,axiom,( v1_xreal_0(1) )).
fof(l8_jordan9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [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(C)) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( r2_hidden(k4_tarski(D,E),k2_matrix_0(B)) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,A) = k3_matrix_0(u1_struct_0(k15_euclid(2)),B,D,E) ) ) ) ) ) ) ) )).
fof(l8_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => v1_wellfnd1(k7_lattice3(k3_lattice3(A))) ) )).
fof(l8_lp_space,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( 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(k2_power(k4_series_1(k1_lp_space(k1_series_1(k1_numbers,A,B),C)),k7_xcmplx_0(1,C)),k2_xcmplx_0(k2_power(k4_series_1(k1_lp_space(A,C)),k7_xcmplx_0(1,C)),k2_power(k4_series_1(k1_lp_space(B,C)),k7_xcmplx_0(1,C)))) ) ) ) ) ) )).
fof(l8_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( m2_subset_1(F,k9_qc_lang1(A),k3_cqc_lang(A)) => r2_hidden(k8_cqc_lang(A,k8_cqc_lang(A,F,k8_cqc_lang(A,k8_cqc_lang(A,B,D),E)),k8_cqc_lang(A,k8_cqc_lang(A,B,C),k8_cqc_lang(A,F,k8_cqc_lang(A,k8_cqc_lang(A,C,D),E)))),k4_cqc_the1(A)) ) ) ) ) ) ) )).
fof(l8_matrix10,axiom,( r2_hidden(1,k1_numbers) )).
fof(l8_matrix17,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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(k5_int_1(k6_xcmplx_0(k2_xcmplx_0(B,C),1),A),k2_finseq_1(A)) ) ) ) ) ) )).
fof(l8_matrix_7,axiom,( k10_finseq_1(1,2) != k10_finseq_1(2,1) )).
fof(l8_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => k4_finseq_1(k3_fvsum_1(A,B,C)) = k9_subset_1(k4_ordinal1,k4_finseq_1(B),k4_finseq_1(C)) ) ) ) )).
fof(l8_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_finseq_2(k1_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(k1_nat_1(A,2),u1_struct_0(B)),u1_struct_0(B)))) ) => v2_midsp_1(g1_midsp_3(k1_nat_1(A,2),u1_struct_0(B),u1_midsp_1(B),C)) ) ) ) )).
fof(l8_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ~ ( ~ 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) ) ) ) )).
fof(l8_msafree1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ( v4_msualg_1(k2_msafree1(A),A) & v1_msafree1(k2_msafree1(A),A) ) ) )).
fof(l8_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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)))) ) ) ) )).
fof(l8_msualg_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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) ) ) )).
fof(l8_nagata_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(l8_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( v1_finset_1(k2_enumset1(B,C,D,A)) & m1_subset_1(k2_enumset1(B,C,D,A),k1_zfmisc_1(k4_ordinal1)) ) ) ) ) ) )).
fof(l8_normsp_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(c3__normsp_1)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c3__normsp_1)) => ! [C] : ( v1_xreal_0(C) => ( ( k2_normsp_0(c3__normsp_1,A) = k5_numbers => A = k4_struct_0(c3__normsp_1) ) & ( A = k4_struct_0(c3__normsp_1) => k2_normsp_0(c3__normsp_1,A) = k5_numbers ) & k2_normsp_0(c3__normsp_1,k1_rlvect_1(c3__normsp_1,A,C)) = k3_xcmplx_0(k9_complex1(C),k2_normsp_0(c3__normsp_1,A)) & r1_xxreal_0(k2_normsp_0(c3__normsp_1,k1_algstr_0(c3__normsp_1,A,B)),k2_xcmplx_0(k2_normsp_0(c3__normsp_1,A),k2_normsp_0(c3__normsp_1,B))) ) ) ) ) )).
fof(l8_numbers,axiom,( r1_tarski(k5_arytm_3,k3_numbers) )).
fof(l8_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(c1__ortsp_1,c1__ortsp_1))) => ( ! [D] : ( r2_hidden(D,C) <=> ( r2_hidden(D,k2_zfmisc_1(c1__ortsp_1,c1__ortsp_1)) & ? [E] : ( m1_subset_1(E,c1__ortsp_1) & ? [F] : ( m1_subset_1(F,c1__ortsp_1) & D = k1_domain_1(c1__ortsp_1,c1__ortsp_1,E,F) & F = c2__ortsp_1 ) ) ) ) => ! [D] : ( ( ~ 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] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => ! [H] : ( 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] : ( 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] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ! [G] : ( 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] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ! [G] : ( 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] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => ~ ( ~ r1_orders_2(D,F,E) & ! [H] : ( 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] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l8_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l8_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(l8_petri_2,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,C,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,A))) ) => ! [F] : ( ( 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] : ( ( 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 ) ) ) ) ) ) ) ) )).
fof(l8_polyalg1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k1_polyalg1(A))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(l8_poset_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( ( 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,E) & D = k3_funct_2(u1_struct_0(B),u1_struct_0(B),k1_abian(u1_struct_0(B),G,A),C) & F = k3_funct_2(u1_struct_0(B),u1_struct_0(B),k1_abian(u1_struct_0(B),G,A),E) ) => r3_orders_2(B,D,F) ) ) ) ) ) ) ) ) )).
fof(l8_qmax_1,axiom,( k1_funct_1(c2__qmax_1,k1_numbers) = 1 )).
fof(l8_quaterni,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( r2_zfmisc_1(E,F,G,H) => r1_tarski(k2_enumset1(A,B,C,D),k10_xtuple_0(k2_quaterni(E,F,G,H,A,B,C,D))) ) )).
fof(l8_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(l8_rat_1,axiom,( ! [A] : ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( A = k7_xcmplx_0(B,C) => r2_hidden(A,k3_numbers) ) ) ) )).
fof(l8_real_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_real_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_real_lat)) => ! [C] : ( 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) ) ) ) )).
fof(l8_realset2,axiom,( m1_subset_1(k10_subset_1(k5_numbers,2),c4__realset2) )).
fof(l8_rfunct_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ( r1_xxreal_0(k3_finseq_1(C),A) => k17_finseq_1(B,A,C) = C ) ) ) ) )).
fof(l8_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( ( 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 ) ) ) ) )).
fof(l8_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( ( 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 ) ) ) ) ) )).
fof(l8_rsspace4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_comseq_2(A) & k2_seq_4(k2_relset_1(k1_numbers,k56_valued_1(k4_ordinal1,k1_numbers,A))) = k5_numbers ) => ! [B] : ( v7_ordinal1(B) => k1_funct_1(A,B) = k5_numbers ) ) ) )).
fof(l8_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( ( 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 ) ) ) ) )).
fof(l8_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k5_funcop_1(k11_binop_2,A,k6_partfun1(k1_numbers)),B) = k3_xcmplx_0(A,B) ) ) )).
fof(l8_scm_comp,axiom,( m2_subset_1(k4_tarski(k5_numbers,k5_numbers),u1_struct_0(k1_scm_comp),k7_dtconstr(k1_scm_comp)) & m2_subset_1(k4_tarski(k5_numbers,1),u1_struct_0(k1_scm_comp),k7_dtconstr(k1_scm_comp)) & m2_subset_1(k4_tarski(k5_numbers,2),u1_struct_0(k1_scm_comp),k7_dtconstr(k1_scm_comp)) & m2_subset_1(k4_tarski(k5_numbers,3),u1_struct_0(k1_scm_comp),k7_dtconstr(k1_scm_comp)) & m2_subset_1(k4_tarski(k5_numbers,4),u1_struct_0(k1_scm_comp),k7_dtconstr(k1_scm_comp)) )).
fof(l8_scmfsa8a,axiom,( ! [A] : ( v7_ordinal1(A) => ( k9_xtuple_0(k16_funcop_1(k5_numbers,k11_scmfsa_2(A))) = k1_tarski(k5_numbers) & r2_hidden(k5_numbers,k9_xtuple_0(k16_funcop_1(k5_numbers,k11_scmfsa_2(A)))) & k1_funct_1(k16_funcop_1(k5_numbers,k11_scmfsa_2(A)),k5_numbers) = k11_scmfsa_2(A) & k1_card_1(k16_funcop_1(k5_numbers,k11_scmfsa_2(A))) = 1 & ~ r2_hidden(k2_compos_1(k1_scmfsa_2),k10_xtuple_0(k16_funcop_1(k5_numbers,k11_scmfsa_2(A)))) ) ) )).
fof(l8_scmfsa_1,axiom,( r1_tarski(k9_xtuple_0(k3_ami_2),k9_xtuple_0(k4_scmfsa_1)) )).
fof(l8_series_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v1_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) & v1_valued_0(C) ) => ( A = k1_valued_1(B,C) <=> ! [D] : ( v7_ordinal1(D) => k1_funct_1(A,D) = k2_xcmplx_0(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) ) )).
fof(l8_series_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k1_square_1(A),k3_xcmplx_0(B,C)) => r1_xxreal_0(k9_complex1(A),k3_square_1(k3_xcmplx_0(B,C))) ) ) ) ) )).
fof(l8_series_5,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(1,k1_square_1(A)) & r1_xxreal_0(1,k9_complex1(A)) ) ) )).
fof(l8_sgraph1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( r2_hidden(C,A) => m1_subset_1(k2_xboole_0(B,k1_tarski(C)),k1_zfmisc_1(A)) ) ) )).
fof(l8_sin_cos6,axiom,( k1_rcomp_1(k2_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k5_numbers)),k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k5_numbers))) = k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos)) )).
fof(l8_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => r1_xxreal_0(k5_numbers,k6_xcmplx_0(k1_square_1(A),1)) ) ) )).
fof(l8_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_square_1(k2_sin_cos2(A)) = k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k4_sin_cos2(k3_xcmplx_0(2,A)),1)) & k1_square_1(k4_sin_cos2(A)) = k3_xcmplx_0(k7_xcmplx_0(1,2),k2_xcmplx_0(k4_sin_cos2(k3_xcmplx_0(2,A)),1)) ) ) )).
fof(l8_tex_1,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) <=> m1_subset_1(A,k1_zfmisc_1(B)) ) )).
fof(l8_topalg_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v1_topalg_2(B,A) & m1_pre_topc(B,k15_euclid(A)) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(l8_topalg_5,axiom,( k1_pre_topc(k5_topmetr,k2_struct_0(k5_topmetr)) = k5_topmetr )).
fof(l8_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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),k4_ordinal1,k9_setfam_1(u1_struct_0(A)),k1_topdim_1(A),k5_card_1(B))) ) ) ) )).
fof(l8_topdim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v2_pre_topc(B) & v3_pcomps_1(B) & l1_pre_topc(B) ) => ( v5_waybel23(B) => ( ( ? [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) ) ) & ~ ( v3_topdim_1(B) & r1_xxreal_0(k4_topdim_1(B),A) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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),k5_numbers) ) ) ) ) ) ) ) ) )).
fof(l8_topgen_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( ! [C] : ( ( 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)) ) ) ) ) )).
fof(l8_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(l8_topmetr,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(l8_topreal2,axiom,( k17_euclid(k19_euclid(1,k5_numbers)) = 1 )).
fof(l8_toprealb,axiom,( ~ r1_xxreal_0(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(1,k28_sin_cos)) )).
fof(l8_tops_2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( 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) ) ) ) )).
fof(l8_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l8_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_hidden(B,k2_pre_topc(A,k6_domain_1(u1_struct_0(A),B))) ) ) )).
fof(l8_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ( v4_vectsp_1(A) => k5_struct_0(A) = k1_group_1(A) ) ) )).
fof(l8_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( ( 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 ) ) ) ) ) )).
fof(l8_xreal_0,axiom,( m1_subset_1(k5_numbers,k2_arytm_2) )).
fof(l8_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l8_xxreal_0,axiom,( k1_xxreal_0 != k4_tarski(k5_numbers,k5_numbers) )).
fof(l8_zf_fund2,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ~ ( ~ r2_hidden(C,k4_zf_lang1(A)) & B != k2_zf_lang(k5_numbers) & C != k2_zf_lang(k5_numbers) & C != k2_zf_lang(4) & ~ ( r2_hidden(k2_zf_lang(4),k2_zf_model(A)) <=> r2_hidden(k2_zf_lang(k5_numbers),k2_zf_model(k13_zf_lang(k2_zf_lang(3),k7_zf_lang(k5_zf_lang(k2_zf_lang(3),B),k6_zf_lang1(k6_zf_lang1(A,k2_zf_lang(k5_numbers),C),k2_zf_lang(4),k2_zf_lang(k5_numbers)))))) ) ) ) ) ) )).
fof(l90_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(2,A) & r2_hidden(k6_xcmplx_0(k5_series_1(2,A),1),k5_asympt_1) ) ) )).
fof(l90_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k4_complex1(A) = k5_numbers => ( r1_xxreal_0(k3_complex1(A),k5_numbers) | r1_xxreal_0(k1_comptrig(B),k5_numbers) | r1_xxreal_0(k28_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)) = k28_sin_cos & ~ r1_xxreal_0(k4_complex2(k5_complex1,B,A),k5_numbers) & ~ r1_xxreal_0(k4_complex2(B,A,k5_complex1),k5_numbers) ) ) ) ) ) )).
fof(l90_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l90_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r1_tarski(k16_ens_1(B),A) => ! [E] : ( m1_subset_1(E,u1_struct_0(k11_ens_1(A))) => ( E = k2_cat_1(B,C,D) => k3_funct_2(u4_struct_0(k6_cat_2(B,B)),k2_ens_1(k16_ens_1(B)),k22_ens_1(B),k8_cat_2(B,B,k4_cat_1(B,C),k4_cat_1(B,D))) = k4_cat_1(k11_ens_1(A),E) ) ) ) ) ) ) ) )).
fof(l90_fib_num4,axiom,( ~ r1_xxreal_0(k7_xcmplx_0(2,2),k7_xcmplx_0(k6_xcmplx_0(3,k3_square_1(5)),2)) )).
fof(l90_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,B,C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k7_geomtrap(A,B,C))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k7_geomtrap(A,B,C))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k7_geomtrap(A,B,C))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k7_geomtrap(A,B,C))) => ! [K] : ( m1_subset_1(K,u1_struct_0(k7_geomtrap(A,B,C))) => ! [L] : ( 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) = L & k9_geomtrap(k7_geomtrap(A,B,C),E,I) = L & k9_geomtrap(k7_geomtrap(A,B,C),F,J) = L & k9_geomtrap(k7_geomtrap(A,B,C),G,K) = L ) => r2_analoaf(k7_geomtrap(A,B,C),H,I,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l90_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( ~ v3_glib_001(B,A) <=> r1_xxreal_0(3,k3_finseq_1(B)) ) ) ) )).
fof(l90_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_2(D,k1_numbers,k3_finseq_2(k1_numbers)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k3_finseq_2(k1_numbers)) => ! [F] : ( m2_finseq_2(F,k1_numbers,k3_finseq_2(k1_numbers)) => ! [G] : ( m2_finseq_1(G,k4_ordinal1) => ( ( E = k6_graphsp(k9_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),k15_graphsp(C),k18_graphsp(C))),B),D) & F = k6_graphsp(k9_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),k15_graphsp(C),k18_graphsp(C))),k1_nat_1(B,1)),D) & k3_finseq_1(D) = k1_nat_1(k1_nat_1(k2_nat_1(C,C),k2_nat_1(3,C)),1) & r4_graphsp(G,E,A,C) & k1_funct_1(E,k1_nat_1(C,A)) = k1_funct_1(F,k1_nat_1(C,A)) & ! [H] : ( m1_subset_1(H,k4_ordinal1) => ( r1_xxreal_0(1,H) => ( r1_xxreal_0(k3_finseq_1(G),H) | r2_hidden(k1_funct_1(G,H),k13_graphsp(E,C)) ) ) ) ) => ( k7_graphsp(E,C) = k1_xboole_0 | r4_graphsp(G,F,A,C) ) ) ) ) ) ) ) ) ) )).
fof(l90_integra8,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(l90_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(l90_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( ( v1_topreal2(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [H] : ( 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] : ( ( v1_xreal_0(I) & v2_xxreal_0(I) ) => ( ( r1_topreal1(k15_euclid(2),B,C,E) & r1_tarski(E,D) & r1_tarski(D,k1_topreal9(2,A,I)) & r2_hidden(A,H) & r1_tarski(k9_subset_1(u1_struct_0(k15_euclid(2)),k2_pre_topc(k15_euclid(2),G),k3_subset_1(u1_struct_0(k15_euclid(2)),G)),E) & r1_tarski(G,k1_topreal9(2,A,I)) ) => ! [J] : ( ( v1_funct_1(J) & v1_funct_2(J,u1_struct_0(k2_brouwer(2,A,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,A,I)),u1_struct_0(k1_pre_topc(k15_euclid(2),E))))) ) => ~ ( v5_pre_topc(J,k2_brouwer(2,A,I),k1_pre_topc(k15_euclid(2),E)) & k2_partfun1(u1_struct_0(k2_brouwer(2,A,I)),u1_struct_0(k1_pre_topc(k15_euclid(2),E)),J,E) = k6_partfun1(E) & H = G & v3_connsp_1(H,k1_pre_topc(k15_euclid(2),k3_subset_1(u1_struct_0(k15_euclid(2)),D))) & F = k7_subset_1(u1_struct_0(k15_euclid(2)),k2_topreal9(2,A,I),k6_domain_1(u1_struct_0(k15_euclid(2)),A)) & ! [K] : ( ( v1_funct_1(K) & v1_funct_2(K,u1_struct_0(k2_brouwer(2,A,I)),u1_struct_0(k1_pre_topc(k15_euclid(2),F))) & m1_subset_1(K,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_brouwer(2,A,I)),u1_struct_0(k1_pre_topc(k15_euclid(2),F))))) ) => ~ ( v5_pre_topc(K,k2_brouwer(2,A,I),k1_pre_topc(k15_euclid(2),F)) & ! [L] : ( m1_subset_1(L,u1_struct_0(k2_brouwer(2,A,I))) => ( ( r2_hidden(L,k2_pre_topc(k15_euclid(2),G)) => k3_funct_2(u1_struct_0(k2_brouwer(2,A,I)),u1_struct_0(k1_pre_topc(k15_euclid(2),F)),K,L) = k3_funct_2(u1_struct_0(k2_brouwer(2,A,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)),G)) => k3_funct_2(u1_struct_0(k2_brouwer(2,A,I)),u1_struct_0(k1_pre_topc(k15_euclid(2),F)),K,L) = L ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l90_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l90_pepin,axiom,( k4_nat_d(k11_newton(3,32),k4_pepin(3)) = 64 )).
fof(l90_toprealb,axiom,( r1_tarski(k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos)),k5_numbers),k5_toprealb(c26__toprealb))),k2_rcomp_1(k5_numbers,1)) )).
fof(l90_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(l90_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( k4_xxreal_3(A,B) = k5_numbers => ( v1_xreal_0(A) | B = k5_numbers ) ) ) ) )).
fof(l91_funct_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_relat_1(C) => ( k8_funct_7(k8_funct_7(C,A),B) = k8_funct_7(C,k3_xcmplx_0(A,B)) => k8_funct_7(k8_funct_7(C,A),k1_nat_1(B,1)) = k8_funct_7(C,k2_nat_1(A,k1_nat_1(B,1))) ) ) ) ) )).
fof(l91_fvaluat1,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( v2_vectsp_2(C,A) & m1_rmod_2(C,A,k4_vectsp_2(A)) & u1_struct_0(C) = B ) ) ) )).
fof(l91_fvsum_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(l91_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k7_geomtrap(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,B,C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k7_geomtrap(A,B,C))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k7_geomtrap(A,B,C))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k7_geomtrap(A,B,C))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k7_geomtrap(A,B,C))) => ! [K] : ( m1_subset_1(K,u1_struct_0(k7_geomtrap(A,B,C))) => ! [L] : ( m1_subset_1(L,u1_struct_0(k7_geomtrap(A,B,C))) => ! [M] : ( m1_subset_1(M,u1_struct_0(k7_geomtrap(A,B,C))) => ( ( r1_analmetr(A,B,C) & r2_analoaf(k7_geomtrap(A,B,C),L,M,D,H) & r2_analoaf(k7_geomtrap(A,B,C),L,M,E,I) & r2_analoaf(k7_geomtrap(A,B,C),L,M,F,J) & r2_analoaf(k7_geomtrap(A,B,C),L,M,G,K) & r2_analoaf(k7_geomtrap(A,B,C),D,E,F,G) ) => ( L = M | r2_analoaf(k7_geomtrap(A,B,C),H,I,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l91_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(l91_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m2_finseq_2(E,k1_numbers,k3_finseq_2(k1_numbers)) => ! [F] : ( m2_finseq_2(F,k1_numbers,k3_finseq_2(k1_numbers)) => ! [G] : ( m2_finseq_2(G,k1_numbers,k3_finseq_2(k1_numbers)) => ! [H] : ( m2_finseq_1(H,k4_ordinal1) => ( ( F = k6_graphsp(k9_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),k15_graphsp(D),k18_graphsp(D))),B),E) & G = k6_graphsp(k9_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),k15_graphsp(D),k18_graphsp(D))),k1_nat_1(B,1)),E) & k3_finseq_1(E) = k1_nat_1(k1_nat_1(k2_nat_1(D,D),k2_nat_1(3,D)),1) & r4_graphsp(H,F,C,D) & C = k1_funct_1(G,k1_nat_1(D,A)) & k1_funct_1(F,k1_nat_1(D,C)) = k1_funct_1(G,k1_nat_1(D,C)) & ! [I] : ( m1_subset_1(I,k4_ordinal1) => ( r1_xxreal_0(1,I) => ( r1_xxreal_0(k3_finseq_1(H),I) | r2_hidden(k1_funct_1(H,I),k13_graphsp(F,D)) ) ) ) ) => ( k7_graphsp(F,D) = k1_xboole_0 | C = A | r2_hidden(A,k13_graphsp(F,D)) | r4_graphsp(k8_finseq_1(k4_ordinal1,H,k12_finseq_1(k4_ordinal1,A)),G,A,D) ) ) ) ) ) ) ) ) ) ) )).
fof(l91_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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)))) ) => ( r2_group_6(k5_group_6(A,k9_group_6(A,B,C)),k10_group_6(A,B,C)) & ? [D] : ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(k5_group_6(A,k9_group_6(A,B,C))),u1_struct_0(k10_group_6(A,B,C))) & v1_group_6(D,k5_group_6(A,k9_group_6(A,B,C)),k10_group_6(A,B,C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_group_6(A,k9_group_6(A,B,C))),u1_struct_0(k10_group_6(A,B,C))))) & v3_funct_2(D,u1_struct_0(k5_group_6(A,k9_group_6(A,B,C))),u1_struct_0(k10_group_6(A,B,C))) & r1_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),u1_struct_0(k10_group_6(A,B,C)),C,k1_partfun1(u1_struct_0(A),u1_struct_0(k5_group_6(A,k9_group_6(A,B,C))),u1_struct_0(k5_group_6(A,k9_group_6(A,B,C))),u1_struct_0(k10_group_6(A,B,C)),k8_group_6(A,k9_group_6(A,B,C)),D)) ) ) ) ) ) )).
fof(l91_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [E] : ( 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] : ( 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] : ( ( ~ v1_xboole_0(G) & m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( E != F => ! [H] : ( ( v1_xreal_0(H) & v2_xxreal_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),D),k3_subset_1(u1_struct_0(k15_euclid(2)),D)),G) ) => ( r1_xboole_0(k1_topreal9(2,A,H),D) | ! [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 = D & 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))) & C = 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] : ( ( 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),C))) & 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),C))))) ) => ~ ( v5_pre_topc(J,k2_brouwer(2,A,H),k1_pre_topc(k15_euclid(2),C)) & ! [K] : ( m1_subset_1(K,u1_struct_0(k2_brouwer(2,A,H))) => ( ( r2_hidden(K,k2_pre_topc(k15_euclid(2),D)) => k3_funct_2(u1_struct_0(k2_brouwer(2,A,H)),u1_struct_0(k1_pre_topc(k15_euclid(2),C)),J,K) = K ) & ( r2_hidden(K,k3_subset_1(u1_struct_0(k15_euclid(2)),D)) => k3_funct_2(u1_struct_0(k2_brouwer(2,A,H)),u1_struct_0(k1_pre_topc(k15_euclid(2),C)),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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l91_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l91_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,B,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k3_funct_2(u4_struct_0(B),u4_struct_0(k2_oppcat_1(A)),k11_oppcat_1(B,A,C),k4_cat_1(B,D)) = k4_cat_1(k2_oppcat_1(A),k3_funct_2(u1_struct_0(B),u1_struct_0(k2_oppcat_1(A)),k7_cat_1(B,k2_oppcat_1(A),k11_oppcat_1(B,A,C)),D)) ) ) ) ) )).
fof(l91_pepin,axiom,( k4_nat_d(k11_newton(3,64),k4_pepin(3)) = 241 )).
fof(l91_polyred,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k12_polynom1(A,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k12_polynom1(A,C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k12_polynom1(A,C))) => ( r2_hidden(F,D) => ( F = k8_polynom1(A,C) | G = k8_polynom1(A,C) | r2_rewrite1(k3_polyred(A,B,C,D),E,k3_rlvect_1(k12_polynom1(A,C),E,k8_group_1(k12_polynom1(A,C),G,F))) ) ) ) ) ) ) ) ) ) )).
fof(l91_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(A,k5_numbers) => r1_xxreal_0(k5_numbers,k6_prepower(A,B)) ) ) ) )).
fof(l91_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_pre_topc(C,A) => ( r1_tarski(u1_struct_0(B),u1_struct_0(C)) => m1_pre_topc(B,C) ) ) ) ) )).
fof(l91_toprealb,axiom,( v1_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos)),k5_numbers),k5_toprealb(c26__toprealb))) & v1_funct_2(k2_partfun1(k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos)),k5_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(k5_numbers,1))))) & m1_subset_1(k2_partfun1(k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos)),k5_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(k5_numbers,1))))))) )).
fof(l91_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(C,k5_numbers) ) => r1_xxreal_0(k3_xcmplx_0(B,C),k3_xcmplx_0(A,C)) ) ) ) ) )).
fof(l91_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( A = k5_numbers => k4_xxreal_3(A,k4_xxreal_3(B,C)) = k4_xxreal_3(k4_xxreal_3(A,B),C) ) ) ) ) )).
fof(l92_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_partfun1(D,C) & v1_relat_2(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,C))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ( r2_hidden(B,A) => v1_fomodel3(E,k1_tarski(k4_tarski(B,B)),D) ) ) ) ) )).
fof(l92_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v3_glib_001(B,A) <=> ? [C] : ( m1_subset_1(C,k6_glib_000(A)) & r2_relset_1(k4_ordinal1,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B,k1_glib_001(A,C)) ) ) ) ) )).
fof(l92_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ! [D] : ( m2_finseq_2(D,k1_numbers,k3_finseq_2(k1_numbers)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k3_finseq_2(k1_numbers)) => ! [F] : ( ( ~ v2_struct_0(F) & v2_graph_1(F) & v6_graph_1(F) & l1_graph_1(F) ) => ! [G] : ( ( v7_graph_1(G,F) & m2_graph_1(G,F) ) => ! [H] : ( ( 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] : ( m1_subset_1(I,u1_struct_0(F)) => ! [J] : ( m1_subset_1(J,u1_struct_0(F)) => ~ ( r6_graphsp(D,F,B,H) & r5_graph_5(F,H) & J = A & I != J & r1_xxreal_0(1,A) & r1_xxreal_0(A,B) & r8_graph_5(F,I,J,G,C,H) & ! [K] : ( m1_subset_1(K,k4_ordinal1) => ! [L] : ( m1_subset_1(L,k4_ordinal1) => ( ( k1_funct_1(E,k1_nat_1(B,L)) = k4_xcmplx_0(1) & r1_xxreal_0(1,L) & r1_xxreal_0(L,B) & r2_hidden(K,C) ) => k1_funct_1(D,k1_nat_1(k1_nat_1(k2_nat_1(2,B),k2_nat_1(B,K)),L)) = k4_xcmplx_0(1) ) ) ) & k1_funct_1(E,k1_nat_1(B,A)) = k4_xcmplx_0(1) ) ) ) ) ) ) ) ) ) ) )).
fof(l92_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(l92_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( 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] : ( m2_subset_1(E,k1_zfmisc_1(A),B) & k1_funct_1(C,k3_subset_1(A,E)) = k5_numbers & E = k1_relset_1(A,D) & r1_mesfunc6(A,B,D,E) ) ) ) ) ) ) ) )).
fof(l92_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(l92_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,B,A) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ( k3_funct_2(u1_struct_0(B),u1_struct_0(k2_oppcat_1(A)),k7_cat_1(B,k2_oppcat_1(A),k11_oppcat_1(B,A,C)),k3_graph_1(B,D)) = k4_graph_1(k2_oppcat_1(A),k3_funct_2(u4_struct_0(B),u4_struct_0(k2_oppcat_1(A)),k11_oppcat_1(B,A,C),D)) & k3_funct_2(u1_struct_0(B),u1_struct_0(k2_oppcat_1(A)),k7_cat_1(B,k2_oppcat_1(A),k11_oppcat_1(B,A,C)),k4_graph_1(B,D)) = k3_graph_1(k2_oppcat_1(A),k3_funct_2(u4_struct_0(B),u4_struct_0(k2_oppcat_1(A)),k11_oppcat_1(B,A,C),D)) ) ) ) ) ) )).
fof(l92_pepin,axiom,( k4_nat_d(k11_newton(3,128),k4_pepin(3)) = 256 )).
fof(l92_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & k6_prepower(A,B) = k5_numbers ) ) ) )).
fof(l92_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_convex1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v1_convex1(k2_pre_topc(A,B),A) ) ) )).
fof(l92_toprealb,axiom,( k6_toprealb(k1_fcont_1(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos)),k5_numbers)) = k1_fcont_1(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos)),k5_numbers) )).
fof(l92_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( B = k5_numbers => k4_xxreal_3(A,k4_xxreal_3(B,C)) = k4_xxreal_3(k4_xxreal_3(A,B),C) ) ) ) ) )).
fof(l93_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( ( k4_complex1(A) = k5_numbers & k1_comptrig(B) = k28_sin_cos ) => ( r1_xxreal_0(k3_complex1(A),k5_numbers) | ( k2_xcmplx_0(k2_xcmplx_0(k4_complex2(A,k5_numbers,B),k4_complex2(k5_numbers,B,A)),k4_complex2(B,A,k5_numbers)) = k28_sin_cos & k5_numbers = k4_complex2(k5_numbers,B,A) & k5_numbers = k4_complex2(B,A,k5_numbers) ) ) ) ) ) )).
fof(l93_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [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)) )).
fof(l93_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( v4_fomodel1(C,B) & m1_subset_1(C,k1_fomodel1(B)) ) => ! [D] : ( ( v1_partfun1(D,A) & v1_relat_2(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [E] : ( m2_fomodel2(E,B,A,C) => v2_fomodel3(E,B,A,C,D) ) ) ) ) ) )).
fof(l93_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v4_glib_001(B,A) <=> ! [C] : ( ( v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ~ ( 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) ) ) ) ) ) ) )).
fof(l93_jordan,axiom,( k17_euclid(k19_euclid(k4_xcmplx_0(1),k5_numbers)) = k4_xcmplx_0(1) )).
fof(l93_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v2_xxreal_0(E) & v1_xreal_0(E) ) => ( 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))) ) ) ) ) ) ) )).
fof(l93_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l93_pepin,axiom,( k4_nat_d(k11_newton(3,1),k4_pepin(4)) = 3 )).
fof(l93_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_convex1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v1_convex1(k1_tops_1(A,B),A) ) ) )).
fof(l93_toprealb,axiom,( k1_relset_1(k1_numbers,k1_fcont_1(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos)),k5_numbers)) = k1_numbers )).
fof(l93_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ~ v1_xreal_0(B) => k4_xxreal_3(A,k4_xxreal_3(B,C)) = k4_xxreal_3(k4_xxreal_3(A,B),C) ) ) ) ) )).
fof(l94_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(2,A) & r1_xxreal_0(k7_newton(A),1) ) ) )).
fof(l94_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(l94_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( 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) => v1_partfun1(k8_fomodel4(B,C,A),k35_fomodel1(B)) ) ) ) )).
fof(l94_geomtrap,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k8_geomtrap(o_0_3_geomtrap))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k8_geomtrap(o_0_3_geomtrap))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k8_geomtrap(o_0_3_geomtrap))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k8_geomtrap(o_0_3_geomtrap))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k8_geomtrap(o_0_3_geomtrap))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k8_geomtrap(o_0_3_geomtrap))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k8_geomtrap(o_0_3_geomtrap))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k8_geomtrap(o_0_3_geomtrap))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k8_geomtrap(o_0_3_geomtrap))) => ! [J] : ( 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] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l94_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v4_glib_001(B,A) <=> v4_glib_001(k6_glib_001(A,B),A) ) ) ) )).
fof(l94_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( m1_group_9(D,A,B) => m1_group_9(C,A,k19_group_9(A,B,C,D)) ) ) ) )).
fof(l94_jordan,axiom,( k17_euclid(k19_euclid(1,k5_numbers)) = 1 )).
fof(l94_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( ? [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) & k1_funct_1(C,k3_subset_1(A,E)) = k5_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)) ) ) ) ) ) )).
fof(l94_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(l94_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l94_pepin,axiom,( k4_nat_d(k11_newton(3,2),k4_pepin(4)) = 9 )).
fof(l94_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( ( v3_rltopsp1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v3_rltopsp1(k2_pre_topc(A,B),A) ) ) )).
fof(l94_toprealb,axiom,( k2_relset_1(k1_numbers,k1_fcont_1(k7_xcmplx_0(1,k3_xcmplx_0(2,k28_sin_cos)),k5_numbers)) = k1_numbers )).
fof(l94_turing_1,axiom,( ! [A] : ( 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] : ( m2_funct_2(B,k4_numbers,u1_turing_1(k18_turing_1),k9_funct_2(k4_numbers,u1_turing_1(k18_turing_1))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( A = k4_domain_1(k4_ordinal1,k4_ordinal1,k9_funct_2(k4_numbers,u1_turing_1(k18_turing_1)),k5_numbers,C,B) & r2_turing_1(k2_finseq_4(k4_ordinal1,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(k4_ordinal1,C,k5_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))) ) ) ) ) ) ) )).
fof(l94_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(l95_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r1_xxreal_0(B,A) => r1_xxreal_0(k7_newton(B),k7_newton(A)) ) ) ) )).
fof(l95_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l95_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( k3_finseq_1(B) = A => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,B)) => ! [E] : ( 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] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( k3_finseq_1(B) = k1_nat_1(A,1) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,B)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l95_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( 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))),k28_fomodel4(B)),C) & v11_fomodel4(A,B,C) ) => v3_relat_2(k8_fomodel4(B,C,A)) ) ) ) )).
fof(l95_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ! [F] : ( 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] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( m1_subset_1(H,k6_margrel1) => ! [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)) ) ) ) ) ) ) ) ) ) ) )).
fof(l95_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( v4_glib_001(B,A) => v4_glib_001(k8_glib_001(A,B,C,D),A) ) ) ) ) ) )).
fof(l95_jordan,axiom,( k18_euclid(k19_euclid(k4_xcmplx_0(1),k5_numbers)) = k5_numbers )).
fof(l95_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(l95_newton,axiom,( r1_xxreal_0(k1_nat_1(k5_numbers,1),k1_newton(2,k5_numbers)) )).
fof(l95_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l95_pepin,axiom,( k4_nat_d(k11_newton(3,4),k4_pepin(4)) = 81 )).
fof(l95_toprealb,axiom,( k1_pre_topc(k2_topalg_2,k2_struct_0(k2_topalg_2)) = k2_topalg_2 )).
fof(l96_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(1,A) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( r1_xxreal_0(k7_newton(B),A) & ~ r1_xxreal_0(k7_newton(k1_nat_1(B,1)),A) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_xxreal_0(k7_newton(C),A) => ( r1_xxreal_0(k7_newton(k1_nat_1(C,1)),A) | C = B ) ) ) ) ) ) ) )).
fof(l96_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l96_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( k3_finseq_1(B) = A => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,B)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(l96_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( 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))),k27_fomodel4(B)),C) & v11_fomodel4(A,B,C) ) => v8_relat_2(k8_fomodel4(B,C,A)) ) ) ) )).
fof(l96_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ! [F] : ( 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] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( 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) ) ) ) ) ) ) ) ) )).
fof(l96_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( 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) ) ) ) ) )).
fof(l96_jordan,axiom,( k18_euclid(k19_euclid(1,k5_numbers)) = k5_numbers )).
fof(l96_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( ? [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) & k1_funct_1(C,k3_subset_1(A,E)) = k5_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) ) ) ) ) ) )).
fof(l96_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(k1_nat_1(A,1),k1_newton(2,A)) => r1_xxreal_0(k1_nat_1(k1_nat_1(A,1),1),k1_newton(2,k1_nat_1(A,1))) ) ) )).
fof(l96_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l96_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( ( r2_wellord1(A,B) & r1_tarski(C,B) ) => r2_wellord1(A,C) ) ) )).
fof(l96_pepin,axiom,( k4_nat_d(k11_newton(3,8),k4_pepin(4)) = 6561 )).
fof(l96_pre_poly,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ( k4_finseq_1(B) != k1_xboole_0 => r2_hidden(1,k4_finseq_1(B)) ) ) )).
fof(l96_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( ( v9_rltopsp1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v9_rltopsp1(k2_pre_topc(A,B),A) ) ) )).
fof(l96_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k3_complex1(k3_xcmplx_0(k3_xcmplx_0(A,k7_complex1),B)) = k4_xcmplx_0(k3_xcmplx_0(A,k4_complex1(B))) & k4_complex1(k3_xcmplx_0(k3_xcmplx_0(A,k7_complex1),B)) = k3_xcmplx_0(A,k3_complex1(B)) & k3_complex1(k3_xcmplx_0(A,B)) = k3_xcmplx_0(A,k3_complex1(B)) & k4_complex1(k3_xcmplx_0(A,B)) = k3_xcmplx_0(A,k4_complex1(B)) ) ) ) )).
fof(l96_toprealb,axiom,( 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(k5_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(k5_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(k5_numbers,1))))))) )).
fof(l96_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k3_xcmplx_0(A,k7_xcmplx_0(1,B)) = k7_xcmplx_0(A,B) ) ) )).
fof(l97_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k1_bcialg_1(A,B,C) = k1_bcialg_1(A,B,D) => C = D ) ) ) ) ) ) )).
fof(l97_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => r1_tarski(k13_cohsp_1(k13_cohsp_1(A)),A) ) )).
fof(l97_facirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k15_facirc_1(A,B,C),k18_facirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(l97_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(l97_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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))) ) => ~ ( k29_fomodel2(B,C) = k1_nat_1(A,1) & ~ v5_fomodel2(C,B) & ! [D] : ( ( 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))) ) => k38_fomodel2(B,C) != D ) ) ) ) ) )).
fof(l97_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( 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))),k27_fomodel4(B)),C) & r1_tarski(k7_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))),k26_fomodel4(B),k28_fomodel4(B)),C) & v11_fomodel4(A,B,C) ) => ( v1_partfun1(k8_fomodel4(B,C,A),k35_fomodel1(B)) & v3_relat_2(k8_fomodel4(B,C,A)) & v8_relat_2(k8_fomodel4(B,C,A)) & m1_subset_1(k8_fomodel4(B,C,A),k1_zfmisc_1(k2_zfmisc_1(k35_fomodel1(B),k35_fomodel1(B)))) ) ) ) ) )).
fof(l97_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l97_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( r1_xxreal_0(k3_finseq_1(B),3) => v4_glib_001(B,A) ) ) ) )).
fof(l97_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(l97_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k21_interva1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k21_interva1(A))) => k1_lattices(k21_interva1(A),B,C) = k1_lattices(k21_interva1(A),C,B) ) ) ) )).
fof(l97_jordan,axiom,( k17_euclid(k19_euclid(k5_numbers,3)) = k5_numbers )).
fof(l97_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( m2_finseq_2(D,u1_struct_0(C),k4_finseq_2(A,u1_struct_0(C))) => ! [E] : ( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(A,u1_struct_0(C))) => ! [F] : ( m2_finseq_2(F,u1_struct_0(C),k4_finseq_2(B,u1_struct_0(C))) => ! [G] : ( 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,k12_fvsum_1(A,C,D,E)),k4_rlvect_1(C,k12_fvsum_1(B,C,F,G))) ) ) ) ) ) ) ) )).
fof(l97_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l97_ordinal6,axiom,( k13_ordinal6(1,k5_numbers) = k3_ordinal5(k5_numbers) )).
fof(l97_pepin,axiom,( k4_nat_d(k11_newton(3,16),k4_pepin(4)) = k1_nat_1(k2_nat_1(164,332),1) )).
fof(l97_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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) ) ) ) ) )).
fof(l97_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_connsp_2(B,A,k4_struct_0(A)) => ! [C] : ( m1_connsp_2(C,A,k4_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [E] : ( ( v2_xxreal_0(E) & v1_xreal_0(E) ) => ( ( ! [F] : ( v1_xreal_0(F) => ( ~ r1_xxreal_0(E,k9_complex1(F)) => r1_tarski(k1_convex1(A,C,F),B) ) ) & D = a_3_32_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) ) ) ) ) ) ) ) )).
fof(l97_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( ~ r1_xxreal_0(A,k5_numbers) => ( k3_complex1(k7_xcmplx_0(B,k3_xcmplx_0(A,k7_complex1))) = k7_xcmplx_0(k4_complex1(B),A) & k4_complex1(k7_xcmplx_0(B,k3_xcmplx_0(A,k7_complex1))) = k4_xcmplx_0(k7_xcmplx_0(k3_complex1(B),A)) & k9_complex1(k7_xcmplx_0(B,A)) = k7_xcmplx_0(k9_complex1(B),A) ) ) ) ) )).
fof(l97_sincos10,axiom,( v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,4))),k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,4)))) )).
fof(l97_toprealb,axiom,( k1_relset_1(k1_numbers,k1_fcont_1(k4_xcmplx_0(1),1)) = k1_numbers )).
fof(l97_xboole_1,axiom,( ! [A] : ! [B] : r1_xboole_0(k3_xboole_0(A,B),k5_xboole_0(A,B)) )).
fof(l97_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k3_xcmplx_0(k7_xcmplx_0(1,C),k7_xcmplx_0(A,B)) = k7_xcmplx_0(A,k3_xcmplx_0(B,C)) ) ) ) )).
fof(l98_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(3,A) & r1_xxreal_0(k7_newton(A),A) ) ) )).
fof(l98_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(l98_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_relat_1(D) & v5_relat_1(D,B) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( 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)) ) ) ) ) )).
fof(l98_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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(k37_fomodel2(B,C),B,A) & m2_subset_1(k37_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(k38_fomodel2(B,C),B,A) & m2_subset_1(k38_fomodel2(B,C),k3_finseq_2(k15_fomodel1(B)),k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0))) ) ) ) ) ) ) )).
fof(l98_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l98_geomtrap,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_geomtrap(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_diraf(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_diraf(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_diraf(A))) => ? [E] : ( m1_subset_1(E,u1_struct_0(k2_diraf(A))) & r2_analoaf(k2_diraf(A),B,C,D,E) ) ) ) ) ) )).
fof(l98_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ( r1_glib_000(A,B,D,C) => v5_glib_001(k2_glib_001(A,B,D,C),A) ) ) )).
fof(l98_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k21_interva1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k21_interva1(A))) => ! [D] : ( 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) ) ) ) ) )).
fof(l98_jordan,axiom,( k18_euclid(k19_euclid(k5_numbers,3)) = 3 )).
fof(l98_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v3_msualg_6(C,A,k1_msafree3(A,B)) & v4_msualg_6(C,A,k1_msafree3(A,B)) & v9_msafree4(C,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B))) & v10_msafree4(C,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B))) & m1_msualg_4(C,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,k1_msafree3(A,B))) ) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => r1_tarski(k3_msualg_1(A,D,k10_msafree4(A,B,C)),k3_msualg_1(A,D,k1_msafree3(A,B))) ) ) ) ) )).
fof(l98_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l98_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ( k13_ordinal6(1,A) = k3_ordinal5(A) => k13_ordinal6(1,k1_ordinal1(A)) = k3_ordinal5(k1_ordinal1(A)) ) ) )).
fof(l98_pepin,axiom,( k4_nat_d(k11_newton(3,32),k4_pepin(4)) = k2_nat_1(123,503) )).
fof(l98_sincos10,axiom,( v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos),k28_sin_cos)),k1_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos),k28_sin_cos))) )).
fof(l98_tex_4,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => u1_struct_0(k1_pre_topc(A,B)) = B ) ) )).
fof(l98_toprealb,axiom,( k1_relset_1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_relset_1(k1_numbers,k1_fcont_1(k4_xcmplx_0(1),1))))),k2_partfun1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_relset_1(k1_numbers,k1_fcont_1(k4_xcmplx_0(1),1))))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_relset_1(k1_numbers,k1_fcont_1(k4_xcmplx_0(1),1))))),k6_toprealb(k1_fcont_1(k4_xcmplx_0(1),1)),k5_toprealb(k2_rcomp_1(k5_numbers,1)))) = k2_rcomp_1(k5_numbers,1) )).
fof(l98_xboole_1,axiom,( ! [A] : ! [B] : k5_xboole_0(A,B) = k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B)) )).
fof(l99_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k1_bcialg_1(A,C,B) = k1_bcialg_1(A,D,B) => C = D ) ) ) ) ) ) )).
fof(l99_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v5_fomodel1(B,A) & m1_subset_1(B,k1_fomodel1(A)) ) => ! [C] : ( ( 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))),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k35_fomodel1(A))) ) => ! [D] : ( ( 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))),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k35_fomodel1(A))) ) => ( v8_fomodel1(B,A) => v4_fomodel4(k4_lang1(k1_zfmisc_1(k30_fomodel2(A)),k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k1_domain_1(k1_zfmisc_1(k30_fomodel2(A)),k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k38_fomodel4(A,k1_int_2(k19_fomodel1(A,B)),C,D),k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k31_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))),k29_fomodel4(A)),k1_xboole_0) ) ) ) ) ) )).
fof(l99_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ! [F] : ( 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] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( m1_subset_1(H,k6_margrel1) => ! [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)) ) ) ) ) ) ) ) ) ) )).
fof(l99_geomtrap,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_geomtrap(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_diraf(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_diraf(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_diraf(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l99_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v5_glib_001(B,A) <=> v5_glib_001(k6_glib_001(A,B),A) ) ) ) )).
fof(l99_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k18_interva1(A)) => ! [C] : ( 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 ) ) ) )).
fof(l99_jordan,axiom,( k17_euclid(k19_euclid(k5_numbers,k4_xcmplx_0(3))) = k5_numbers )).
fof(l99_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_modelc_3(D,C) & v3_modelc_3(D,C) & l1_modelc_3(D,C) ) => ! [E] : ( ( v1_modelc_3(E,C) & v3_modelc_3(E,C) & l1_modelc_3(E,C) ) => ! [F] : ( ( v1_modelc_3(F,C) & v3_modelc_3(F,C) & l1_modelc_3(F,C) ) => ~ ( r6_modelc_3(C,D,E) & r6_modelc_3(C,E,F) & r2_hidden(k7_modelc_2(A,B),u1_modelc_3(C,E)) & ~ r2_hidden(B,u1_modelc_3(C,E)) & ~ ( r2_hidden(A,u1_modelc_3(C,E)) & r2_hidden(k7_modelc_2(A,B),u1_modelc_3(C,F)) ) ) ) ) ) ) ) ) )).
fof(l99_ordinal6,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_xboole_0(A) ) => ( ! [B] : ( v3_ordinal1(B) => ( r2_hidden(B,A) => k13_ordinal6(1,B) = k3_ordinal5(B) ) ) => k13_ordinal6(1,A) = k3_ordinal5(A) ) ) )).
fof(l99_pepin,axiom,( k4_nat_d(k11_newton(3,64),k4_pepin(4)) = k1_nat_1(k2_nat_1(14,1367),1) )).
fof(l99_sincos10,axiom,( v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)))),k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4))))) )).
fof(l99_toprealb,axiom,( r1_tarski(k2_relset_1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_relset_1(k1_numbers,k1_fcont_1(k4_xcmplx_0(1),1))))),k2_partfun1(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k1_relset_1(k1_numbers,k1_fcont_1(k4_xcmplx_0(1),1))))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_relset_1(k1_numbers,k1_fcont_1(k4_xcmplx_0(1),1))))),k6_toprealb(k1_fcont_1(k4_xcmplx_0(1),1)),k5_toprealb(k2_rcomp_1(k5_numbers,1)))),k2_rcomp_1(k5_numbers,1)) )).
fof(l9_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(l9_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r5_aff_1(A,E,F) & r2_hidden(B,E) & r2_hidden(D,E) & r2_hidden(C,F) & ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( r2_hidden(G,F) & r2_analoaf(A,B,C,D,G) ) ) ) ) ) ) ) ) ) )).
fof(l9_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ~ ( B != D & r2_diraf(A,B,C,C,D) ) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(l9_algstr_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_0)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_algstr_0)) => ? [C] : ( m1_subset_1(C,u1_struct_0(k3_algstr_0)) & k1_algstr_0(k3_algstr_0,C,A) = B ) ) ) )).
fof(l9_algstr_3,axiom,( ! [A] : ( 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 ) )).
fof(l9_altcat_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k7_altcat_1(k1_tarski(k1_xboole_0)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_altcat_1(k1_tarski(k1_xboole_0)))) => ! [C] : ( m1_subset_1(C,k1_altcat_1(k7_altcat_1(k1_tarski(k1_xboole_0)),A,B)) => ! [D] : ( m1_subset_1(D,k1_altcat_1(k7_altcat_1(k1_tarski(k1_xboole_0)),A,B)) => C = D ) ) ) ) )).
fof(l9_ami_2,axiom,( k9_xtuple_0(k3_ami_2) = k1_ami_2 )).
fof(l9_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(k4_amistd_1(A))) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(l9_analoaf,axiom,( v1_xreal_0(1) )).
fof(l9_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( 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 = k5_numbers | B = k3_rlvect_1(A,k1_rlvect_1(A,C,k4_xcmplx_0(k3_xcmplx_0(k5_xcmplx_0(E),F))),k1_rlvect_1(A,D,k4_xcmplx_0(k3_xcmplx_0(k5_xcmplx_0(E),G)))) ) ) ) ) ) ) ) ) ) )).
fof(l9_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => k1_rlvect_1(A,k3_rlvect_1(A,k3_rlvect_1(A,k1_rlvect_1(A,C,F),k1_rlvect_1(A,D,G)),k1_rlvect_1(A,B,H)),E) = k3_rlvect_1(A,k3_rlvect_1(A,k1_rlvect_1(A,C,k3_xcmplx_0(E,F)),k1_rlvect_1(A,D,k3_xcmplx_0(E,G))),k1_rlvect_1(A,B,k3_xcmplx_0(E,H))) ) ) ) ) ) ) ) ) )).
fof(l9_arytm_2,axiom,( r1_tarski(k7_subset_1(k1_zfmisc_1(k5_arytm_3),k1_arytm_2,a_0_1_arytm_2),k2_arytm_2) )).
fof(l9_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( 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) ) ) ) )).
fof(l9_bhsp_1,axiom,( ! [A] : ( 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] : ( 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] : ( 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] : ( v1_xreal_0(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,A) = k10_subset_1(k5_numbers,k1_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) = k10_subset_1(k5_numbers,k1_numbers) ) & r1_xxreal_0(k5_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) = k2_xcmplx_0(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) = k3_xcmplx_0(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)) ) ) ) ) ) )).
fof(l9_borsuk_2,axiom,( r2_hidden(k5_numbers,k1_rcomp_1(k5_numbers,1)) & r2_hidden(1,k1_rcomp_1(k5_numbers,1)) )).
fof(l9_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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)))) ) ) ) ) ) )).
fof(l9_cfdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(2)) => ! [F] : ( 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(k2_xcmplx_0(A,C),k2_xcmplx_0(B,D)) & k8_euclid(2,E,F) = k10_finseq_1(k6_xcmplx_0(A,C),k6_xcmplx_0(B,D)) ) ) ) ) ) ) ) ) )).
fof(l9_collsp,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(c4__collsp)) => ! [B] : ( m1_subset_1(B,u1_struct_0(c4__collsp)) => ! [C] : ( m1_subset_1(C,u1_struct_0(c4__collsp)) => ! [D] : ( m1_subset_1(D,u1_struct_0(c4__collsp)) => ! [E] : ( m1_subset_1(E,u1_struct_0(c4__collsp)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(l9_compos_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_compos_0(A) & v2_compos_0(A) ) => ( v3_compos_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( r2_hidden(C,k4_finseq_1(k5_xtuple_0(B))) => r1_tarski(k4_ordinal1,k1_funct_1(k10_card_3(k3_compos_0(A,k2_compos_0(A,B))),C)) ) ) ) ) )).
fof(l9_comptrig,axiom,( ~ r1_xxreal_0(k2_xcmplx_0(k28_sin_cos,k7_xcmplx_0(k28_sin_cos,2)),k2_xcmplx_0(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) )).
fof(l9_convex1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k1_convex1(A,B,1) = B ) ) )).
fof(l9_convex2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) )).
fof(l9_convfun1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( m1_subset_1(F,u1_struct_0(k3_convfun1(A,k4_convfun1))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k3_convfun1(A,k4_convfun1))) => ( ( F = k4_tarski(B,D) & G = k4_tarski(C,E) ) => k1_algstr_0(k3_convfun1(A,k4_convfun1),F,G) = k4_tarski(k1_algstr_0(A,B,C),k2_xcmplx_0(D,E)) ) ) ) ) ) ) ) ) )).
fof(l9_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(l9_csspace2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k18_csspace)) <=> ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & v1_series_1(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,k2_csspace(A)),k55_valued_1(k4_ordinal1,k2_numbers,k2_csspace(A)))) ) ) )).
fof(l9_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => k4_euclid_3(A,B,C) != k6_xcmplx_0(k3_xcmplx_0(2,k4_euclid_3(D,E,F)),k3_xcmplx_0(6,k28_sin_cos)) ) ) ) ) ) ) )).
fof(l9_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => k7_euclid(3,A,k6_euclid(3,B)) = k1_euclid_8(k6_xcmplx_0(k1_funct_1(A,1),k1_funct_1(B,1)),k6_xcmplx_0(k1_funct_1(A,2),k1_funct_1(B,2)),k6_xcmplx_0(k1_funct_1(A,3),k1_funct_1(B,3))) ) ) )).
fof(l9_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ~ ( B != C & k12_euclid(k8_euclid(A,B,C)) = k5_numbers ) ) ) ) )).
fof(l9_extreal1,axiom,( ! [A] : ( m2_finseq_1(A,k6_numbers) => ! [B] : ( m1_subset_1(B,k6_numbers) => k4_extreal1(k8_finseq_1(k6_numbers,A,k12_finseq_1(k6_numbers,B))) = k3_supinf_2(k4_extreal1(A),B) ) ) )).
fof(l9_fib_fusc,axiom,( k10_ami_3(k5_numbers) != k10_ami_3(3) )).
fof(l9_fib_num4,axiom,( k7_xcmplx_0(k1_fib_num,k2_fib_num) = k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(3),k3_square_1(5)),2) )).
fof(l9_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(l9_fintopo6,axiom,( ! [A] : ( l1_orders_2(A) => m1_fintopo6(g1_orders_2(u1_struct_0(A),u1_orders_2(A)),A) ) )).
fof(l9_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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))) ) => ( ( r1_tarski(A,B) & v1_fomodel0(D,B) ) => v1_fomodel0(D,A) ) ) ) )).
fof(l9_fomodel2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_fomodel2(C,B,A) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(l9_fomodel3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v8_ordinal1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(l9_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_frechet(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( 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] : ( v1_relat_1(D) & v1_funct_1(D) & k9_xtuple_0(D) = k4_ordinal1 & k10_xtuple_0(D) = C & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(E,F) => r1_tarski(k1_funct_1(D,F),k1_funct_1(D,E)) ) ) ) ) ) ) ) ) )).
fof(l9_fsm_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(l9_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(l9_goboard6,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(l9_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( E = D => ( D = B | ( ~ ( ~ r1_aff_1(A,D,B,E) & r1_aff_1(A,D,E,F) & r2_analoaf(A,B,E,C,F) ) & ~ ( r1_aff_1(A,D,B,E) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & ~ r1_aff_1(A,D,B,G) & r1_aff_1(A,D,G,H) & r2_analoaf(A,B,G,C,H) & r2_analoaf(A,G,E,H,F) & r1_aff_1(A,D,B,F) ) ) ) ) | F = D ) ) ) ) ) ) ) ) )).
fof(l9_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( r1_int_1(A,B) & r1_int_1(A,C) ) => r1_int_1(A,k5_int_1(B,C)) ) ) ) ) )).
fof(l9_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( r1_int_1(A,B) & r1_int_1(A,C) ) => r1_int_1(A,k6_xcmplx_0(B,C)) ) ) ) ) )).
fof(l9_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & v1_finseq_1(A) ) => m2_finseq_1(A,k1_numbers) ) )).
fof(l9_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => m1_subset_1(a_1_1_jordan1(A),k1_zfmisc_1(k1_euclid(2))) ) )).
fof(l9_jordan1d,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(2,A) => r1_xxreal_0(k5_numbers,k6_xcmplx_0(k3_xcmplx_0(2,A),2)) ) ) )).
fof(l9_jordan1h,axiom,( r6_relat_2(k1_jordan1h,k1_numbers) )).
fof(l9_jordan_a,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(l9_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(l9_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(l9_matrix10,axiom,( r2_hidden(k4_xcmplx_0(1),k1_numbers) )).
fof(l9_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [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] : ( m1_subset_1(H,u1_struct_0(G)) => ! [I] : ( ( v1_matrix_0(I) & v2_matrix_0(I,u1_struct_0(G),D,E) & m2_finseq_1(I,k3_finseq_2(u1_struct_0(G))) ) => ! [J] : ( ( v1_matrix_0(J) & v2_matrix_0(J,u1_struct_0(G),D,E) & m2_finseq_1(J,k3_finseq_2(u1_struct_0(G))) ) => ! [K] : ( m2_finseq_1(K,u1_struct_0(G)) => ! [L] : ( m2_finseq_1(L,u1_struct_0(G)) => ( ( r2_hidden(F,k2_finseq_1(D)) & r2_hidden(A,k2_finseq_1(k1_matrix_0(I))) & r2_hidden(B,k4_finseq_1(I)) & K = k7_matrix_0(u1_struct_0(G),I,C) & L = k7_matrix_0(u1_struct_0(G),I,B) & J = k3_matrix11(C,D,E,u1_struct_0(G),I,k3_fvsum_1(G,k9_fvsum_1(G,L,H),K)) ) => ( ( F = C => k3_matrix_0(u1_struct_0(G),J,F,A) = k1_algstr_0(G,k8_group_1(G,H,k3_matrix_0(u1_struct_0(G),I,B,A)),k3_matrix_0(u1_struct_0(G),I,C,A)) ) & ( F != C => k3_matrix_0(u1_struct_0(G),J,F,A) = k3_matrix_0(u1_struct_0(G),I,F,A) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(l9_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => k4_finseq_1(k3_fvsum_1(B,C,D)) = k9_subset_1(k4_ordinal1,k4_finseq_1(C),k4_finseq_1(D)) ) ) ) ) )).
fof(l9_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r2_modelc_2(A,B) => m1_subset_1(k1_tarski(A),k1_zfmisc_1(k13_modelc_2(B))) ) ) ) )).
fof(l9_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dtconstr(A) & v2_dtconstr(A) & l1_lang1(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(l9_numbers,axiom,( r1_tarski(k4_ordinal1,k4_numbers) )).
fof(l9_orders_1,axiom,( ! [A] : ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => k1_relat_1(B) = A ) )).
fof(l9_ordinal1,axiom,( v1_ordinal1(k1_xboole_0) & v2_ordinal1(k1_xboole_0) )).
fof(l9_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( v3_ordinal1(B) => ~ ( r1_ordinal2(B,A) & k9_xtuple_0(A) = k1_xboole_0 ) ) ) )).
fof(l9_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))))) ) ) ) ) ) )).
fof(l9_parsp_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(l9_pcomps_2,axiom,( v1_xreal_0(k7_xcmplx_0(1,2)) )).
fof(l9_pdiff_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(1)) => ( k9_finseq_1(A) = B => k9_complex1(A) = k12_euclid(B) ) ) ) )).
fof(l9_petri_2,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,C,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,A))) ) => ! [F] : ( ( 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) ) ) ) ) ) ) )).
fof(l9_poset_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ! [H] : ( ( 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)))) ) => ( ( F = k3_funct_2(u1_struct_0(C),u1_struct_0(C),H,D) & r3_orders_2(C,D,F) & E = k3_funct_2(u1_struct_0(C),u1_struct_0(C),k1_abian(u1_struct_0(C),H,A),D) & G = k3_funct_2(u1_struct_0(C),u1_struct_0(C),k1_abian(u1_struct_0(C),H,k2_xcmplx_0(A,B)),D) ) => r3_orders_2(C,E,G) ) ) ) ) ) ) ) ) ) )).
fof(l9_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_projdes1(A,B,C,D,E) => r1_projdes1(A,C,B,D,E) ) ) ) ) ) ) )).
fof(l9_qmax_1,axiom,( ! [A] : ( m1_prob_1(A,k1_numbers,k12_prob_1) => ! [B] : ( 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)) = k2_xcmplx_0(k3_funct_2(k12_prob_1,k1_numbers,c2__qmax_1,A),k3_funct_2(k12_prob_1,k1_numbers,c2__qmax_1,B)) ) ) ) )).
fof(l9_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(2,A) => r1_xxreal_0(k2_xcmplx_0(2,2),k1_radix_1(A)) ) ) )).
fof(l9_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(l9_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ~ v3_xxreal_2(k10_prob_1(A)) ) )).
fof(l9_real_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_real_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_real_lat)) => k2_lattices(k3_real_lat,A,k1_lattices(k3_real_lat,A,B)) = A ) ) )).
fof(l9_realset2,axiom,( k9_xtuple_0(k13_funcop_1(1,1,k5_numbers)) = k6_domain_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,1,1)) )).
fof(l9_rfinseq,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ( r1_xxreal_0(k3_finseq_1(C),A) => k17_finseq_1(B,A,C) = C ) ) ) ) )).
fof(l9_rfunct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ~ r2_hidden(B,k10_xtuple_0(A)) => k8_relat_1(A,k1_tarski(B)) = k1_xboole_0 ) ) )).
fof(l9_scmfsa_1,axiom,( r2_hidden(k4_ordinal1,k9_xtuple_0(k4_scmfsa_1)) )).
fof(l9_series_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( k6_xcmplx_0(1,k7_xcmplx_0(1,k1_nat_1(A,2))) = k7_xcmplx_0(k1_nat_1(A,1),k1_nat_1(A,2)) & k7_xcmplx_0(1,k7_newton(k1_nat_1(A,1))) = k7_xcmplx_0(k1_nat_1(A,2),k2_nat_1(k7_newton(k1_nat_1(A,1)),k1_nat_1(A,2))) ) ) )).
fof(l9_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( 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,k1_square_1(A)),k3_square_1(k3_xcmplx_0(B,C))),2),k1_square_1(B)),k3_square_1(k3_xcmplx_0(A,C))),2),k1_square_1(C)),k3_square_1(k3_xcmplx_0(A,B))) = k1_newton(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,A),B),C),3) ) ) ) )).
fof(l9_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( m1_subset_1(D,k5_finsub_1(A)) => m1_subset_1(k7_relset_1(A,B,C,D),k5_finsub_1(B)) ) ) ) ) )).
fof(l9_sin_cos6,axiom,( k1_rcomp_1(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k5_numbers),k2_xcmplx_0(k28_sin_cos,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k5_numbers))) = k1_rcomp_1(k5_numbers,k28_sin_cos) )).
fof(l9_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ( k2_sin_cos2(k4_xcmplx_0(A)) = k4_xcmplx_0(k2_sin_cos2(A)) & k4_sin_cos2(k4_xcmplx_0(A)) = k4_sin_cos2(A) & k6_sin_cos2(k4_xcmplx_0(A)) = k4_xcmplx_0(k6_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)) ) ) )).
fof(l9_topalg_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v1_topalg_2(B,A) & m1_pre_topc(B,k15_euclid(A)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_borsuk_2(E,B,C,D) => ! [F] : ( m1_borsuk_2(F,B,C,D) => ! [G] : ( m1_subset_1(G,u1_struct_0(k5_topmetr)) => ( k1_binop_1(k1_topalg_2(A,B,E,F),G,k5_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] : ( m1_subset_1(H,u1_struct_0(k5_topmetr)) => ( k1_binop_1(k1_topalg_2(A,B,E,F),k5_numbers,H) = C & k1_binop_1(k1_topalg_2(A,B,E,F),1,H) = D ) ) ) ) ) ) ) ) ) ) )).
fof(l9_topalg_5,axiom,( r1_xxreal_0(k6_xcmplx_0(1,k5_numbers),1) )).
fof(l9_topreal2,axiom,( k18_euclid(k19_euclid(1,k5_numbers)) = k5_numbers )).
fof(l9_toprealb,axiom,( ~ r1_xxreal_0(k3_xcmplx_0(2,k28_sin_cos),k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos)) )).
fof(l9_uniform1,axiom,( k4_topmetr(k5_numbers,1) = k3_pcomps_1(k2_topmetr(k5_numbers,1)) )).
fof(l9_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( m1_vectsp_4(E,A,B) => ! [F] : ( m1_vectsp_4(F,A,C) => ! [G] : ( ( 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)))) ) ) ) ) ) ) ) ) ) )).
fof(l9_waybel17,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(l9_waybel_4,axiom,( ! [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] : ( ( 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) ) ) )).
fof(l9_xreal_0,axiom,( ~ r2_hidden(k5_numbers,k2_zfmisc_1(k1_tarski(k5_numbers),k2_arytm_2)) )).
fof(l9_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k2_xcmplx_0(B,A),B) ) ) ) )).
fof(l9_xxreal_0,axiom,( ~ r2_hidden(k1_xxreal_0,k2_arytm_2) )).
fof(l9_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => k1_xxreal_2(k1_tarski(A)) = A ) )).
fof(l9_yellow_6,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(projectivity_k10_euclid,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k1_euclid(A)) ) => k10_euclid(A,k10_euclid(A,B)) = k10_euclid(A,B) ) )).
fof(projectivity_k11_seq_4,axiom,( ! [A] : ( m1_finseq_1(A,k2_numbers) => k11_seq_4(k11_seq_4(A)) = k11_seq_4(A) ) )).
fof(projectivity_k19_seq_4,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k12_seq_4(A)) ) => k19_seq_4(A,k19_seq_4(A,B)) = k19_seq_4(A,B) ) )).
fof(projectivity_k1_abcmiz_1,axiom,( ! [A] : k1_abcmiz_1(k1_abcmiz_1(A)) = k1_abcmiz_1(A) )).
fof(projectivity_k1_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => k1_absvalue(k1_absvalue(A)) = k1_absvalue(A) ) )).
fof(projectivity_k1_afinsq_1,axiom,( ! [A] : ( ( 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) ) )).
fof(projectivity_k1_card_1,axiom,( ! [A] : k1_card_1(k1_card_1(A)) = k1_card_1(A) )).
fof(projectivity_k1_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => k1_int_1(k1_int_1(A)) = k1_int_1(A) ) )).
fof(projectivity_k1_int_2,axiom,( ! [A] : ( v1_int_1(A) => k1_int_2(k1_int_2(A)) = k1_int_2(A) ) )).
fof(projectivity_k1_scmfsa_m,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) ) => k1_scmfsa_m(k1_scmfsa_m(A)) = k1_scmfsa_m(A) ) )).
fof(projectivity_k1_tdlat_2,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(projectivity_k1_tops_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(projectivity_k2_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => k2_absvalue(k2_absvalue(A)) = k2_absvalue(A) ) )).
fof(projectivity_k2_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => k2_int_1(k2_int_1(A)) = k2_int_1(A) ) )).
fof(projectivity_k2_int_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_int_3)) => k2_int_3(k2_int_3(A)) = k2_int_3(A) ) )).
fof(projectivity_k2_pre_topc,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(projectivity_k3_euclid,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => k3_euclid(k3_euclid(A)) = k3_euclid(A) ) )).
fof(projectivity_k3_extreal1,axiom,( ! [A] : ( v1_xxreal_0(A) => k3_extreal1(k3_extreal1(A)) = k3_extreal1(A) ) )).
fof(projectivity_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(k3_finseq_1(A)) = k3_finseq_1(A) ) )).
fof(projectivity_k54_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => k54_valued_1(k54_valued_1(A)) = k54_valued_1(A) ) )).
fof(projectivity_k55_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(projectivity_k56_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(projectivity_k5_card_1,axiom,( ! [A] : ( v1_finset_1(A) => k5_card_1(k5_card_1(A)) = k5_card_1(A) ) )).
fof(projectivity_k5_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => k5_measure6(k5_measure6(A)) = k5_measure6(A) ) )).
fof(projectivity_k5_rfinseq2,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => k5_rfinseq2(k5_rfinseq2(A)) = k5_rfinseq2(A) ) )).
fof(projectivity_k5_seqfunc,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => k5_seqfunc(A,k5_seqfunc(A,B)) = k5_seqfunc(A,B) ) )).
fof(projectivity_k6_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(projectivity_k6_rfinseq2,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => k6_rfinseq2(k6_rfinseq2(A)) = k6_rfinseq2(A) ) )).
fof(projectivity_k7_group_2,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(projectivity_k7_random_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(projectivity_k8_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(projectivity_k9_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k9_complex1(k9_complex1(A)) = k9_complex1(A) ) )).
fof(rc10_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ? [B] : ( m1_abcmiz_1(B,A,k12_abcmiz_1(A)) & ~ v1_xtuple_0(B) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) & v9_abcmiz_1(B,A) ) ) )).
fof(rc10_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ? [B] : ( m1_subset_1(B,u4_struct_0(A)) & v2_abcmiz_1(B,A) & v4_abcmiz_a(B,A) ) ) )).
fof(rc10_algstr_0,axiom,( ? [A] : ( l4_algstr_0(A) & v22_algstr_0(A) ) )).
fof(rc10_altcat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ? [B] : ( m1_altcat_2(B,A) & ~ v2_struct_0(B) & v2_altcat_1(B) & v3_altcat_2(B,A) ) ) )).
fof(rc10_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ? [B] : ( l3_msualg_1(B,A) & v4_msualg_1(B,A) & v6_aofa_a01(B,A) ) ) )).
fof(rc10_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ? [B] : ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v10_cohsp_1(B) ) ) )).
fof(rc10_comput_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k3_finseq_2(A)) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,A) & v1_funct_1(B) & v1_finset_1(B) & v4_card_3(B) & v1_finseq_1(B) & v2_finseq_1(B) & v3_comput_1(B) ) )).
fof(rc10_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ? [B] : ( l2_conlat_1(B,A) & v3_conlat_1(B,A) & ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) ) ) )).
fof(rc10_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ? [B] : ( l1_extpro_1(B,A) & ~ v2_struct_0(B) & v3_memstr_0(B,A) ) ) )).
fof(rc10_finseq_1,axiom,( ! [A] : ( v1_finset_1(A) => ? [B] : ( m1_finseq_1(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,A) & v1_funct_1(B) & v2_funct_1(B) & v2_funct_2(B,A) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) ) ) )).
fof(rc10_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ? [C] : ( v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,A) ) ) )).
fof(rc10_fomodel1,axiom,( ? [A] : ( l1_fomodel1(A) & ~ v2_struct_0(A) & v1_fomodel1(A) ) )).
fof(rc10_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & ~ v1_xboole_0(B) ) => ? [C] : ( m1_subset_1(C,k15_fomodel2(A,B)) & v1_relat_1(C) & v4_relat_1(C,k37_fomodel1(A)) & v1_funct_1(C) & v1_funcop_1(C) & v2_funcop_1(C) & v1_fomodel2(C,A,B) ) ) )).
fof(rc10_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(k30_fomodel2(A))) & ~ v10_ordinal1(C) & v4_funct_1(C) & v5_finset_1(C) & v3_finseq_1(C) & v1_setfam_1(C) & v11_fomodel4(C,A,B) ) ) )).
fof(rc10_functor0,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) => ? [C] : ( m2_functor0(C,A,B) & v8_functor0(C,A,B) & v9_functor0(C,A,B) & v15_functor0(C,A,B) & v16_functor0(C,A,B) ) ) )).
fof(rc10_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ? [C] : ( m1_finseq_1(C,k6_group_9(A,B)) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,k6_group_9(A,B)) & v1_funct_1(C) & v1_finset_1(C) & v1_finseq_1(C) & v2_finseq_1(C) & v8_group_9(C,A,B) ) ) )).
fof(rc10_ideal_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : ( m1_ideal_1(C,A,B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & v1_finset_1(C) & v1_finseq_1(C) & v2_finseq_1(C) ) ) )).
fof(rc10_lattices,axiom,( ? [A] : ( l3_lattices(A) & ~ v2_struct_0(A) & v3_lattices(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v11_lattices(A) & v12_lattices(A) & v13_lattices(A) & v14_lattices(A) ) )).
fof(rc10_monoid_0,axiom,( ! [A] : ( l3_algstr_0(A) => ? [B] : ( m3_monoid_0(B,A) & v22_algstr_0(B) ) ) )).
fof(rc10_msafree4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_msafree(C,A,B) & ~ v1_xboole_0(C) & 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)) ) ) )).
fof(rc10_oposet_1,axiom,( ? [A] : ( l2_qmax_1(A) & ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_necklace(A) & v3_qmax_1(A) ) )).
fof(rc10_ordinal1,axiom,( ? [A] : ( v1_relat_1(A) & v9_ordinal1(A) ) )).
fof(rc10_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( ~ 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)) & v11_osalg_1(B,A) ) ) )).
fof(rc10_pcs_0,axiom,( ? [A] : ( l2_pcs_0(A) & v12_pcs_0(A) ) )).
fof(rc10_pre_poly,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_card_3(A) & v4_card_3(A) & v1_finseq_1(A) & v2_finseq_1(A) ) )).
fof(rc10_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A) ) ) )).
fof(rc10_robbins1,axiom,( ? [A] : ( l4_robbins1(A) & ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v17_lattices(A) & v4_robbins1(A) & v8_robbins1(A) ) )).
fof(rc10_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v10_ordinal1(B) & v5_finset_1(B) & v2_finsub_1(B) & ~ v1_setfam_1(B) & v1_classes1(B) & v3_scmyciel(B,1) & v4_scmyciel(B) & v5_scmyciel(B) ) ) )).
fof(rc10_simplex0,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v3_pencil_1(B) & v1_matroid0(B) & m1_simplex0(B,A) ) => ? [C] : ( m2_simplex0(C,A,B) & ~ v3_pencil_1(C) & v1_matroid0(C) & v3_matroid0(C) ) ) )).
fof(rc10_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v4_tdlat_3(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v4_tdlat_3(B) ) ) )).
fof(rc10_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v7_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) ) ) )).
fof(rc10_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v3_tdlat_3(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v4_tex_3(B,A) ) ) )).
fof(rc10_vectsp_1,axiom,( ? [A] : ( l6_algstr_0(A) & ~ v2_struct_0(A) & ~ v6_struct_0(A) & ~ v7_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v36_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v1_group_1(A) & v3_group_1(A) & v5_group_1(A) & v1_vectsp_1(A) & v2_vectsp_1(A) & v3_vectsp_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v12_vectsp_1(A) ) )).
fof(rc10_vectsp_2,axiom,( ! [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) & l6_algstr_0(A) ) => ? [B] : ( l1_vectsp_1(B,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) ) ) )).
fof(rc10_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( 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) ) ) )).
fof(rc10_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m4_yellow_6(B,A) & v1_relat_1(B) & ~ v1_xboole_0(B) & v8_yellow_6(B,A) ) ) )).
fof(rc11_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ? [B] : ( m1_abcmiz_1(B,A,k12_abcmiz_1(A)) & ~ v1_xtuple_0(B) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) & v4_abcmiz_1(B,A,k28_abcmiz_1(A)) & v9_abcmiz_1(B,A) ) ) )).
fof(rc11_abcmiz_a,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_struct_0(A) & v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & v3_abcmiz_a(A) ) )).
fof(rc11_algstr_0,axiom,( ? [A] : ( l4_algstr_0(A) & v13_struct_0(A,1) & v22_algstr_0(A) ) )).
fof(rc11_aofa_a00,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_prob_2(B) ) => ? [C] : ( m3_pboole(C,A,B) & v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v1_prob_2(C) ) ) )).
fof(rc11_aofa_a01,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) & v4_msualg_1(B,A) & v6_aofa_a01(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( l3_msualg_1(C,A) & v4_msualg_1(C,A) & v4_msafree4(C,A,B) & v6_msafree4(C,A,k5_msafree4(A,B)) & v17_aofa_a00(C,A) & v20_aofa_a00(C,4,1,A) & v22_aofa_a00(C,A,1,1,11) ) ) )).
fof(rc11_cohsp_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) & ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,A))) & v1_relat_1(C) & v4_relat_1(C,B) & v5_relat_1(C,A) & v1_funct_1(C) & v1_funct_2(C,B,A) & v10_cohsp_1(C) ) ) )).
fof(rc11_comput_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k2_comput_1(A)) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(A)) & v5_relat_1(B,A) & v1_funct_1(B) & v2_margrel1(B) & v3_margrel1(B,A) ) ) )).
fof(rc11_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ? [B] : ( l2_conlat_1(B,A) & v3_conlat_1(B,A) & ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) & v7_conlat_1(B,A) ) ) )).
fof(rc11_fomodel0,axiom,( ? [A] : ( v4_funct_1(A) & ~ v1_xboole_0(A) & v1_zfmisc_1(A) & v5_finset_1(A) & v3_finseq_1(A) ) )).
fof(rc11_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : ( l1_fomodel1(B) & ~ v2_struct_0(B) & ~ v6_struct_0(B) & ~ v7_struct_0(B) & ~ v8_struct_0(B) & v11_fomodel1(B) & v16_fomodel1(B,A) ) ) )).
fof(rc11_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ? [C] : ( m1_subset_1(C,k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & ~ v8_ordinal1(C) & v1_finset_1(C) & v1_finseq_1(C) & v2_finseq_1(C) & v2_pre_poly(C) & ~ v15_fomodel1(C,A) & v3_fomodel2(C,A,B) & v4_fomodel2(C,A) & ~ v5_fomodel2(C,A) ) ) )).
fof(rc11_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : v11_fomodel4(C,A,B) ) )).
fof(rc11_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ? [B] : ( l2_functor0(B,A,A) & v8_functor0(B,A,A) & v10_functor0(B,A,A) ) ) )).
fof(rc11_glib_003,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) ) => ? [D] : ( m2_glib_000(D,A,B,C) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v1_funct_1(D) & v1_finset_1(D) & v1_glib_000(D) & v1_glib_003(D) & v4_glib_003(D,A) ) ) )).
fof(rc11_ideal_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : ( m2_ideal_1(C,A,B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & v1_finset_1(C) & v1_finseq_1(C) & v2_finseq_1(C) ) ) )).
fof(rc11_lattices,axiom,( ? [A] : ( l3_lattices(A) & ~ v2_struct_0(A) & v3_lattices(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v15_lattices(A) ) )).
fof(rc11_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ? [B] : ( m3_monoid_0(B,A) & ~ v2_struct_0(B) & v22_algstr_0(B) ) ) )).
fof(rc11_msafree4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( l3_msualg_1(C,A) & v3_msualg_1(C,A) & v5_msafree4(C,A,B) ) ) )).
fof(rc11_ordinal1,axiom,( ? [A] : ( v1_relat_1(A) & ~ v9_ordinal1(A) ) )).
fof(rc11_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( ~ v1_xboole_0(B) & v1_relat_1(B) & v2_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) ) ) )).
fof(rc11_pcs_0,axiom,( ? [A] : ( l2_pcs_0(A) & ~ v2_struct_0(A) & v12_pcs_0(A) & v14_pcs_0(A) ) )).
fof(rc11_pre_poly,axiom,( ? [A] : ( m1_finseq_1(A,k4_ordinal1) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_card_3(A) & v4_card_3(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v4_valued_0(A) ) )).
fof(rc11_pre_topc,axiom,( ? [A] : ( l1_pre_topc(A) & v2_struct_0(A) & v1_pre_topc(A) ) )).
fof(rc11_quantal1,axiom,( ? [A] : ( l3_quantal1(A) & ~ v2_struct_0(A) ) )).
fof(rc11_robbins1,axiom,( ? [A] : ( l4_robbins1(A) & ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v17_lattices(A) & v4_robbins1(A) & v5_robbins1(A) & v6_robbins1(A) & v10_robbins1(A) ) )).
fof(rc11_robbins3,axiom,( ? [A] : ( l4_robbins1(A) & ~ v2_struct_0(A) & v7_struct_0(A) & v8_struct_0(A) & v13_struct_0(A,1) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v11_lattices(A) & v12_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A) & v17_lattices(A) & v10_robbins1(A) & v1_sheffer1(A) & v2_sheffer1(A) & v3_sheffer1(A) & v4_sheffer1(A) & v1_robbins3(A) & v2_robbins3(A) & v3_robbins3(A) & v8_robbins3(A) & v9_robbins3(A) ) )).
fof(rc11_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v10_ordinal1(B) & v1_finset_1(B) & v5_finset_1(B) & v2_finsub_1(B) & ~ v1_setfam_1(B) & v1_classes1(B) & v3_scmyciel(B,1) & v4_scmyciel(B) & v5_scmyciel(B) ) ) )).
fof(rc11_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ? [C] : ( m2_simplex0(C,A,B) & v1_pre_topc(C) & v1_matroid0(C) & v3_matroid0(C) & v7_simplex0(C,A,B) ) ) )).
fof(rc11_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v5_tdlat_3(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v4_tdlat_3(B) & v5_tdlat_3(B) ) ) )).
fof(rc11_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v1_tdlat_3(B) & v2_tdlat_3(B) ) ) )).
fof(rc11_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v3_tdlat_3(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v1_tex_2(B,A) & v2_tex_3(B,A) ) ) )).
fof(rc11_vectsp_1,axiom,( ? [A] : ( l4_algstr_0(A) & ~ v2_struct_0(A) & v4_vectsp_1(A) ) )).
fof(rc11_vectsp_2,axiom,( ! [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) & l6_algstr_0(A) ) => ? [B] : ( l1_vectsp_2(B,A) & ~ 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) ) ) )).
fof(rc11_waybel_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ? [B] : ( 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) & v12_waybel_0(B,A) & v13_waybel_0(B,A) ) ) )).
fof(rc12_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ? [B] : ( m1_abcmiz_1(B,A,k13_abcmiz_1(A)) & ~ v1_xtuple_0(B) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) & v4_abcmiz_1(B,A,k28_abcmiz_1(A)) & v8_abcmiz_1(B,A) ) ) )).
fof(rc12_abcmiz_a,axiom,( ! [A] : ! [B] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_a(A) & l1_msualg_1(A) & m1_subset_1(B,u1_struct_0(A)) ) => ? [C] : ( m2_abcmiz_1(C,A,B) & v2_abcmiz_1(C,A) & v4_abcmiz_a(C,A) ) ) )).
fof(rc12_algstr_0,axiom,( ? [A] : ( l4_algstr_0(A) & v13_struct_0(A,1) & v21_algstr_0(A) & v22_algstr_0(A) & v28_algstr_0(A) ) )).
fof(rc12_aofa_a01,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(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] : ( l3_msualg_1(C,A) & v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v1_msafree1(C,A) & ~ v8_aofa_a01(C,A,B) ) ) )).
fof(rc12_comput_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_comput_1(k4_ordinal1))) & ~ v1_xboole_0(A) & v4_funct_1(A) & v6_comput_1(A) ) )).
fof(rc12_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ? [B] : ( l2_conlat_1(B,A) & v3_conlat_1(B,A) & ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) & v8_conlat_1(B,A) ) ) )).
fof(rc12_fomodel0,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_setfam_1(B) ) ) )).
fof(rc12_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : ( m1_subset_1(B,k1_fomodel1(A)) & ~ v4_fomodel1(B,A) & v10_fomodel1(B,A) ) ) )).
fof(rc12_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : ( 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(B) & v4_funct_1(B) & v7_fomodel4(B,A) ) ) )).
fof(rc12_ideal_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : ( m3_ideal_1(C,A,B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & v1_finset_1(C) & v1_finseq_1(C) & v2_finseq_1(C) ) ) )).
fof(rc12_lattices,axiom,( ? [A] : ( l3_lattices(A) & ~ v2_struct_0(A) & v3_lattices(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) ) )).
fof(rc12_msafree4,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_prob_2(B) ) )).
fof(rc12_oposet_1,axiom,( ? [A] : ( l2_qmax_1(A) & ~ v2_struct_0(A) & v3_qmax_1(A) & v1_oposet_1(A) & v4_oposet_1(A) & v5_oposet_1(A) ) )).
fof(rc12_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v3_msualg_1(B,A) & v4_msualg_1(B,A) & v12_osalg_1(B,A) ) ) )).
fof(rc12_pcs_0,axiom,( ? [A] : ( l2_pcs_0(A) & ~ v2_struct_0(A) & v12_pcs_0(A) & v15_pcs_0(A) ) )).
fof(rc12_pre_poly,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v4_valued_0(A) & v2_pre_poly(A) ) )).
fof(rc12_pre_topc,axiom,( ? [A] : ( l1_pre_topc(A) & v2_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) ) )).
fof(rc12_scmyciel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v10_ordinal1(A) & v5_finset_1(A) & v2_finsub_1(A) & ~ v1_setfam_1(A) & v1_classes1(A) & v3_scmyciel(A,1) & v4_scmyciel(A) & v6_scmyciel(A) ) )).
fof(rc12_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) & v1_borsuk_1(B,A) & v1_tsep_1(B,A) ) ) )).
fof(rc12_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v3_tdlat_3(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v1_borsuk_1(B,A) & v3_tex_3(B,A) ) ) )).
fof(rc12_vectsp_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) => ? [C] : ( l2_vectsp_2(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) & v3_vectsp_2(C,A,B) & v4_vectsp_2(C,B) & v5_vectsp_2(C,A,B) ) ) )).
fof(rc12_waybel_0,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v16_waybel_0(A) ) )).
fof(rc13_algstr_0,axiom,( ? [A] : ( l5_algstr_0(A) & v29_algstr_0(A) ) )).
fof(rc13_aofa_a00,axiom,( ? [A] : ( l5_aofa_a00(A) & v12_aofa_a00(A) ) )).
fof(rc13_comput_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v7_comput_1(A) ) )).
fof(rc13_fomodel0,axiom,( ! [A] : ( ~ v1_finset_1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v5_card_3(B) ) ) )).
fof(rc13_fomodel2,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ? [C] : ( m1_subset_1(C,k1_fomodel1(B)) & v4_fomodel1(C,B) & ~ v6_fomodel1(C,B) & ~ v7_fomodel1(C,B) & v8_fomodel1(C,B) & v9_fomodel1(C,B) & v10_fomodel1(C,B) & ~ v7_fomodel2(C,A,B) ) ) )).
fof(rc13_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : ( 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(B) & v13_fomodel4(B,2,A) ) ) )).
fof(rc13_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ? [B] : ( 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) & v5_ideal_1(B,A) ) ) )).
fof(rc13_lattices,axiom,( ? [A] : ( l3_lattices(A) & ~ v2_struct_0(A) & v3_lattices(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v17_lattices(A) ) )).
fof(rc13_msafree4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( l3_msualg_1(C,A) & v3_msualg_1(C,A) & v5_msafree4(C,A,B) ) ) )).
fof(rc13_oposet_1,axiom,( ? [A] : ( l2_qmax_1(A) & ~ v2_struct_0(A) & v3_qmax_1(A) & v1_oposet_1(A) & v6_oposet_1(A) & v7_oposet_1(A) ) )).
fof(rc13_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v3_msualg_1(B,A) & v4_msualg_1(B,A) & v12_osalg_1(B,A) & v13_osalg_1(B,A) ) ) )).
fof(rc13_pcs_0,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v17_pcs_0(B) ) )).
fof(rc13_pre_poly,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,A) & v1_funct_2(B,A,k4_ordinal1) & v1_valued_0(B) & v2_valued_0(B) & v3_valued_0(B) & v4_valued_0(B) & v2_pre_poly(B) ) )).
fof(rc13_robbins3,axiom,( ? [A] : ( l3_robbins3(A) & v13_struct_0(A,1) & v3_orders_2(A) ) )).
fof(rc13_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ? [B] : ( m1_eqrel_1(B,k3_tarski(A)) & ~ v10_ordinal1(B) & v1_setfam_1(B) & v7_scmyciel(B,A) ) ) )).
fof(rc13_tex_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) & v1_borsuk_1(B,A) & v1_tsep_1(B,A) & v1_tdlat_3(B) & v3_tdlat_3(B) & v1_tex_2(B,A) ) ) )).
fof(rc13_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v3_tdlat_3(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v1_tsep_1(B,A) & v1_tex_2(B,A) & v1_tex_3(B,A) ) ) )).
fof(rc13_waybel_0,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) ) )).
fof(rc14_abcmiz_1,axiom,( ! [A] : ( l1_msualg_1(A) => ? [B] : ( 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) ) ) )).
fof(rc14_algstr_0,axiom,( ? [A] : ( l5_algstr_0(A) & v13_struct_0(A,1) & v29_algstr_0(A) ) )).
fof(rc14_aofa_a00,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( l5_aofa_a00(B) & ~ v2_struct_0(B) & ~ v11_struct_0(B) & v12_aofa_a00(B) & v14_aofa_a00(B,A) ) ) )).
fof(rc14_comput_1,axiom,( ? [A] : ( m1_subset_1(A,k2_comput_1(k4_ordinal1)) & v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v5_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v4_valued_0(A) & v2_margrel1(A) & v7_comput_1(A) ) )).
fof(rc14_fomodel0,axiom,( ? [A] : ( v1_xreal_0(A) & v1_int_1(A) & v1_xxreal_0(A) & v3_xxreal_0(A) & v1_xcmplx_0(A) ) )).
fof(rc14_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(B) & ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) & m1_subset_1(D,k15_fomodel2(C,B)) ) => ? [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) & v10_fomodel2(E,B,C,D) ) ) )).
fof(rc14_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : ( 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(B) & v13_fomodel4(B,1,A) ) ) )).
fof(rc14_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v18_lattices(B,A) & v19_lattices(B,A) ) ) )).
fof(rc14_pre_poly,axiom,( ! [A] : ? [B] : ( 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) ) )).
fof(rc14_robbins3,axiom,( ? [A] : ( l4_robbins3(A) & v13_struct_0(A,1) & v3_orders_2(A) ) )).
fof(rc14_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v8_scmyciel(A) ) => ? [B] : ( m1_eqrel_1(B,k3_tarski(A)) & ~ v10_ordinal1(B) & v1_finset_1(B) & v1_setfam_1(B) & v7_scmyciel(B,A) ) ) )).
fof(rc14_tex_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) & ~ v1_borsuk_1(B,A) & ~ v1_tsep_1(B,A) & v2_tdlat_3(B) & v3_tdlat_3(B) & v1_tex_2(B,A) ) ) )).
fof(rc15_abcmiz_1,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_struct_0(A) & v1_msualg_1(A) & v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & v12_abcmiz_1(A) ) )).
fof(rc15_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_a(A) & l1_msualg_1(A) ) => ? [B] : ( m1_subset_1(B,u4_struct_0(A)) & v2_abcmiz_1(B,A) & v5_abcmiz_a(B,A) ) ) )).
fof(rc15_algstr_0,axiom,( ? [A] : ( l5_algstr_0(A) & v13_struct_0(A,1) & v29_algstr_0(A) & v32_algstr_0(A) ) )).
fof(rc15_aofa_a00,axiom,( ? [A] : ( l6_aofa_a00(A) & v15_aofa_a00(A) ) )).
fof(rc15_comput_1,axiom,( ? [A] : ( m1_subset_1(A,k9_comput_1) & ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v5_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v4_valued_0(A) & v2_margrel1(A) & v3_margrel1(A,k4_ordinal1) & v7_comput_1(A) ) )).
fof(rc15_fomodel0,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_partit_2(A) ) )).
fof(rc15_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) & m1_subset_1(C,k15_fomodel2(B,A)) ) => ? [D] : v10_fomodel2(D,A,B,C) ) )).
fof(rc15_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : ( 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(B) & v13_fomodel4(B,k5_numbers,A) ) ) )).
fof(rc15_ideal_1,axiom,( ? [A] : ( l6_algstr_0(A) & ~ 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) & v6_ideal_1(A) ) )).
fof(rc15_msafree4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ? [C] : ( m1_msualg_4(C,A,B,B) & v1_relat_1(C) & v3_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v2_funcop_1(C) ) ) )).
fof(rc15_oposet_1,axiom,( ? [A] : ( l2_qmax_1(A) & ~ v2_struct_0(A) & v6_oposet_1(A) & v7_oposet_1(A) & v10_oposet_1(A) ) )).
fof(rc15_pre_poly,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( v1_relat_1(B) & ~ v3_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k3_numbers) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_partfun1(B,A) & v1_valued_0(B) & v2_valued_0(B) & v3_valued_0(B) & v4_valued_0(B) & v2_pre_poly(B) ) ) )).
fof(rc15_robbins3,axiom,( ? [A] : ( l2_qmax_1(A) & v13_struct_0(A,1) & v3_orders_2(A) ) )).
fof(rc15_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_tarski(A))) & v9_scmyciel(B,A) ) ) )).
fof(rc15_tex_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v3_tdlat_3(B) & v1_tex_2(B,A) ) ) )).
fof(rc16_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_abcmiz_1,k34_abcmiz_1(A)))) & v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k2_abcmiz_1) & v5_relat_1(B,k34_abcmiz_1(A)) & v1_funct_1(B) & v1_funcop_1(B) & v2_funcop_1(B) ) ) )).
fof(rc16_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_a(A) & l1_msualg_1(A) ) => ? [B] : ( m1_subset_1(B,u4_struct_0(A)) & v2_abcmiz_1(B,A) & v6_abcmiz_a(B,A) ) ) )).
fof(rc16_aofa_a00,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( l6_aofa_a00(B) & ~ v2_struct_0(B) & ~ v11_struct_0(B) & v14_aofa_a00(B,A) & v15_aofa_a00(B) ) ) )).
fof(rc16_comput_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_margrel1(A) & v7_comput_1(A) & v8_comput_1(A,k5_numbers) ) )).
fof(rc16_fomodel0,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v4_fomodel0(A) ) )).
fof(rc16_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) & v12_fomodel2(C,A) ) ) )).
fof(rc16_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : ( 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(B) & v13_fomodel4(B,k5_numbers,A) & v13_fomodel4(B,1,A) ) ) )).
fof(rc16_msafree4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_msualg_4(C,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,k1_msafree3(A,B))) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) & v2_funcop_1(C) & v3_msualg_6(C,A,k1_msafree3(A,B)) & v4_msualg_6(C,A,k1_msafree3(A,B)) & v9_msafree4(C,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B))) & v10_msafree4(C,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B))) & v11_msafree4(C,A,B) ) ) )).
fof(rc16_robbins3,axiom,( ? [A] : ( l4_robbins3(A) & ~ v2_struct_0(A) & v10_lattices(A) & v1_lattice3(A) & v2_lattice3(A) & v10_robbins1(A) & v6_oposet_1(A) & v7_oposet_1(A) & v10_oposet_1(A) & v10_robbins3(A) & v11_robbins3(A) ) )).
fof(rc16_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_tarski(A))) & v1_finset_1(B) & v9_scmyciel(B,A) ) ) )).
fof(rc16_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v4_tex_2(B,A) ) ) )).
fof(rc17_algstr_0,axiom,( ? [A] : ( l6_algstr_0(A) & v36_algstr_0(A) ) )).
fof(rc17_aofa_a00,axiom,( ? [A] : ( l6_aofa_a00(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v14_aofa_a00(A,3) & v15_aofa_a00(A) & v16_aofa_a00(A) ) )).
fof(rc17_comput_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_margrel1(A) & v7_comput_1(A) & v8_comput_1(A,1) ) )).
fof(rc17_fomodel0,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & ~ v1_xboole_0(A) ) )).
fof(rc17_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : ( m1_subset_1(B,k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A)))) & v1_relat_1(B) & v4_relat_1(B,k9_setfam_1(k1_fomodel4(A))) & v5_relat_1(B,k9_setfam_1(k1_fomodel4(A))) & v1_funct_1(B) & v1_partfun1(B,k9_setfam_1(k1_fomodel4(A))) & v1_funct_2(B,k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))) & v16_fomodel4(B,A) ) ) )).
fof(rc17_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v21_pcs_0(B,A) ) ) )).
fof(rc17_robbins3,axiom,( ? [A] : ( l3_robbins3(A) & ~ v2_struct_0(A) & v10_lattices(A) & v1_lattice3(A) & v2_lattice3(A) & v10_robbins3(A) & v11_robbins3(A) ) )).
fof(rc17_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ? [B] : ( m1_eqrel_1(B,k3_tarski(A)) & ~ v10_ordinal1(B) & v1_setfam_1(B) & v10_scmyciel(B,A) ) ) )).
fof(rc17_struct_0,axiom,( ! [A] : ( l2_struct_0(A) => ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & v9_struct_0(B,A) ) ) )).
fof(rc18_algstr_0,axiom,( ? [A] : ( l6_algstr_0(A) & v13_struct_0(A,1) & v36_algstr_0(A) ) )).
fof(rc18_aofa_a00,axiom,( ? [A] : ( l5_aofa_a00(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) ) )).
fof(rc18_comput_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_margrel1(A) & v7_comput_1(A) & v8_comput_1(A,2) ) )).
fof(rc18_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,A) & v1_funct_1(B) & v2_funct_1(B) & ~ v1_xboole_0(B) & v1_partfun1(B,A) & v1_funct_2(B,A,A) & v2_funct_2(B,A) & v3_funct_2(B,A,A) & v3_relat_2(B) & v2_abian(B) & v4_fomodel0(B) ) ) )).
fof(rc18_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ? [C] : ( m1_subset_1(C,k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0))) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,k17_fomodel1(B)) & ~ v1_xboole_0(C) & ~ v8_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_finseq_1(C) & v2_finseq_1(C) & v4_card_3(C) & v2_pre_poly(C) & v15_fomodel1(C,B) & v3_fomodel2(C,B,k5_numbers) & v4_fomodel2(C,B) & v13_fomodel2(C,A,B) ) ) )).
fof(rc18_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v10_robbins1(A) & v8_robbins3(A) & v9_robbins3(A) & l4_robbins1(A) ) => ? [B] : ( m3_robbins3(B,A) & ~ v2_struct_0(B) & v4_lattices(B) & v5_lattices(B) & v6_lattices(B) & v7_lattices(B) & v8_lattices(B) & v9_lattices(B) & v10_lattices(B) & v1_robbins3(B) & v2_robbins3(B) & v3_robbins3(B) & v9_robbins3(B) & v10_robbins3(B) & v11_robbins3(B) ) ) )).
fof(rc18_scmyciel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v10_ordinal1(A) & v5_finset_1(A) & v2_finsub_1(A) & ~ v1_setfam_1(A) & v1_classes1(A) & v3_scmyciel(A,1) & v4_scmyciel(A) & v11_scmyciel(A) ) )).
fof(rc19_comput_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_margrel1(A) & v7_comput_1(A) & v8_comput_1(A,3) ) )).
fof(rc19_fomodel0,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v3_relat_2(A) & v2_abian(A) ) )).
fof(rc19_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ? [C] : ( m1_subset_1(C,k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0))) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & ~ v1_xboole_0(C) & ~ v8_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_finseq_1(C) & v2_finseq_1(C) & v4_card_3(C) & v2_pre_poly(C) & v4_fomodel2(C,B) & v13_fomodel2(C,A,B) ) ) )).
fof(rc19_robbins3,axiom,( ? [A] : ( l4_robbins3(A) & ~ v2_struct_0(A) & v10_lattices(A) & v8_robbins1(A) & v10_robbins1(A) & v8_robbins3(A) & v9_robbins3(A) & v10_robbins3(A) ) )).
fof(rc19_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v11_scmyciel(A) ) => ? [B] : ( m1_eqrel_1(B,k3_tarski(A)) & ~ v10_ordinal1(B) & v1_finset_1(B) & v1_setfam_1(B) & v10_scmyciel(B,A) ) ) )).
fof(rc19_struct_0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & l2_struct_0(A) ) => ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ~ v9_struct_0(B,A) ) ) )).
fof(rc1_abcmiz_0,axiom,( ? [A] : ( 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_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & v2_abcmiz_0(A) ) )).
fof(rc1_abcmiz_1,axiom,( ? [A] : ( l1_msualg_1(A) & v1_msualg_1(A) & v1_instalg1(A) & v1_abcmiz_1(A) ) )).
fof(rc1_abcmiz_a,axiom,( ? [A] : ( m1_subset_1(A,k4_abcmiz_1) & v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k2_abcmiz_1) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) ) )).
fof(rc1_abian,axiom,( ? [A] : ( m1_subset_1(A,k4_ordinal1) & v1_xxreal_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v7_ordinal1(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & v1_rat_1(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) & v6_membered(A) & v3_xxreal_2(A) & v1_abian(A) ) )).
fof(rc1_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_aff_1(B,A) ) ) )).
fof(rc1_afinsq_1,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v5_relat_1(B,A) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) )).
fof(rc1_afinsq_2,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_xboole_0(A) & v5_ordinal1(A) & v4_valued_0(A) & v1_finset_1(A) & v1_afinsq_1(A) ) )).
fof(rc1_afproj,axiom,( ? [A] : ( l1_incsp_1(A) & v1_incsp_1(A) & v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & v5_incproj(A) ) )).
fof(rc1_afvect0,axiom,( ? [A] : ( l1_analoaf(A) & ~ v2_struct_0(A) & ~ v7_struct_0(A) & v1_analoaf(A) & v1_afvect0(A) ) )).
fof(rc1_algseq_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) ) ) )).
fof(rc1_algspec1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ? [B] : ( m2_algspec1(B,A) & ~ v2_struct_0(B) & ~ v11_struct_0(B) & v1_msualg_1(B) & v1_instalg1(B) ) ) )).
fof(rc1_algstr_1,axiom,( ? [A] : ( l2_algstr_0(A) & ~ v2_struct_0(A) & v8_algstr_0(A) & v4_rlvect_1(A) & v1_algstr_1(A) & v4_algstr_1(A) ) )).
fof(rc1_algstr_3,axiom,( ? [A] : ( l1_algstr_3(A) & v1_algstr_3(A) ) )).
fof(rc1_algstr_4,axiom,( ? [A] : ( l3_algstr_0(A) & v2_struct_0(A) ) )).
fof(rc1_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ? [B] : ( m1_altcat_2(B,A) & ~ v2_struct_0(B) & v2_altcat_1(B) & v6_altcat_1(B) & v2_altcat_2(B,A) & v3_altcat_2(B,A) ) ) )).
fof(rc1_altcat_5,axiom,( ? [A] : ( l2_altcat_1(A) & ~ v2_struct_0(A) & v2_altcat_1(A) & v6_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & v1_altcat_5(A) ) )).
fof(rc1_ami_3,axiom,( ? [A] : ( m1_subset_1(A,u1_struct_0(k1_ami_3)) & v1_ami_2(A) ) )).
fof(rc1_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ? [B] : ( l1_extpro_1(B,A) & ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & v3_extpro_1(B,A) & v2_ami_wstd(B,A) ) ) )).
fof(rc1_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ? [B] : ( l1_extpro_1(B,A) & ~ v2_struct_0(B) & v2_memstr_0(B,A) ) ) )).
fof(rc1_amistd_2,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ? [B] : ( l1_extpro_1(B,A) & ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & v3_amistd_1(B,A) ) ) )).
fof(rc1_analmetr,axiom,( ? [A] : ( l1_analmetr(A) & v1_analmetr(A) ) )).
fof(rc1_analoaf,axiom,( ? [A] : ( l1_analoaf(A) & v1_analoaf(A) ) )).
fof(rc1_anproj_2,axiom,( ? [A] : ( 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) ) )).
fof(rc1_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ? [B] : ( l3_msualg_1(B,A) & v4_msualg_1(B,A) & v1_aofa_a01(B,A) ) ) )).
fof(rc1_aofa_i00,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_card_1(A)))) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k1_card_1(A)) & 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)) ) )).
fof(rc1_armstrng,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_relat_2(A) & v4_relat_2(A) & v8_relat_2(A) ) )).
fof(rc1_arrow,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,A) & v1_partfun1(B,A) & v1_relat_2(B) & v4_relat_2(B) & v6_relat_2(B) & v8_relat_2(B) ) )).
fof(rc1_arytm_3,axiom,( ? [A] : ( m1_subset_1(A,k5_arytm_3) & ~ v1_xboole_0(A) & v3_ordinal1(A) ) )).
fof(rc1_asympt_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xxreal_0(A) & v2_xxreal_0(A) & v1_xreal_0(A) ) )).
fof(rc1_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),k15_pre_poly(A)))) & v1_relat_1(B) & v4_relat_1(B,k15_pre_poly(A)) & v5_relat_1(B,k15_pre_poly(A)) & v1_partfun1(B,k15_pre_poly(A)) & v1_funct_2(B,k15_pre_poly(A),k15_pre_poly(A)) & v1_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) & v2_bagorder(B,A) ) ) )).
fof(rc1_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) & v1_bcialg_2(B,A) ) ) )).
fof(rc1_bcialg_3,axiom,( ? [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) ) )).
fof(rc1_bcialg_4,axiom,( ? [A] : ( l1_bcialg_4(A) & v1_bcialg_4(A) ) )).
fof(rc1_bcialg_5,axiom,( ? [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) & v1_bcialg_5(A) ) )).
fof(rc1_bcialg_6,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v2_bcialg_6(C,A,B) ) ) )).
fof(rc1_bhsp_1,axiom,( ? [A] : ( l1_bhsp_1(A) & v1_bhsp_1(A) ) )).
fof(rc1_bhsp_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ? [B] : ( m1_bhsp_5(B,A) & v1_finset_1(B) ) ) )).
fof(rc1_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) => ? [D] : ( 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(D) & v1_relat_1(D) & v4_relat_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C))) & v5_relat_1(D,u1_struct_0(A)) & v1_funct_1(D) & v1_partfun1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C))) & 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) ) ) )).
fof(rc1_binom,axiom,( ? [A] : ( l6_algstr_0(A) & ~ 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) ) )).
fof(rc1_bintree1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) & v1_bintree1(A) ) )).
fof(rc1_bintree2,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree2(A) ) )).
fof(rc1_borsuk_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) & v1_borsuk_1(B,A) ) ) )).
fof(rc1_borsuk_2,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v2_funct_1(B) & v1_partfun1(B,u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v5_pre_topc(B,A,A) ) ) )).
fof(rc1_borsuk_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) ) ) )).
fof(rc1_borsuk_5,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v2_pre_topc(A) & v1_connsp_1(A) ) )).
fof(rc1_borsuk_6,axiom,( ? [A] : ( l1_struct_0(A) & ~ v2_struct_0(A) & v3_topmetr(A) ) )).
fof(rc1_borsuk_7,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) & v2_funcop_1(A) & v7_valued_2(A) & v1_borsuk_7(A) ) )).
fof(rc1_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k6_margrel1) & v1_funct_1(B) & v3_funct_1(B) & v1_partfun1(B,A) & v1_funct_2(B,A,k6_margrel1) & v1_margrel1(B) ) ) )).
fof(rc1_c0sp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_ideal_1(B,A) & v1_c0sp1(B,A) ) ) )).
fof(rc1_cantor_1,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & v1_tops_2(B,A) & v1_cantor_1(B,A) ) ) )).
fof(rc1_card_1,axiom,( ? [A] : v1_card_1(A) )).
fof(rc1_card_3,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) ) )).
fof(rc1_card_5,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & ~ v1_finset_1(A) & v1_card_1(A) ) )).
fof(rc1_card_fil,axiom,( ! [A] : ( ~ v1_finset_1(A) => ? [B] : ( m1_card_fil(B,A) & ~ v1_xboole_0(B) & ~ v2_card_fil(B,A) & v3_card_fil(B,A) ) ) )).
fof(rc1_card_lar,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_xboole_0(A) & ~ v1_finset_1(A) & v1_card_1(A) & ~ v4_card_3(A) & v1_card_5(A) ) )).
fof(rc1_cat_1,axiom,( ? [A] : ( l1_cat_1(A) & v1_cat_1(A) ) )).
fof(rc1_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ? [B] : ( m3_cat_2(B,A) & ~ v2_struct_0(B) & ~ v11_struct_0(B) & v14_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) ) ) )).
fof(rc1_cat_4,axiom,( ? [A] : ( l1_cat_4(A) & v2_cat_4(A) ) )).
fof(rc1_cat_5,axiom,( ? [A] : ( l1_cat_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_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) & v1_cat_5(A) ) )).
fof(rc1_catalan2,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_xboole_0(A) & v5_ordinal1(A) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v4_valued_0(A) & v1_finset_1(A) & v4_partfun3(A) & v1_afinsq_1(A) & v1_catalan2(A) ) )).
fof(rc1_catalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v3_msualg_1(B,A) & v4_msualg_1(B,A) & v1_msafree1(B,A) ) ) )).
fof(rc1_cayldick,axiom,( ? [A] : ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) & v4_card_3(A) & v1_afinsq_1(A) ) )).
fof(rc1_cc0sp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_cc0sp1(B,A) & ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v1_group_1(B) & v3_group_1(B) & v5_group_1(B) & v1_vectsp_1(B) & v3_vectsp_1(B) & v4_vectsp_1(B) & v6_vectsp_1(B) & v2_clvect_1(B) & v3_clvect_1(B) & v4_clvect_1(B) & v1_cfuncdom(B) & v2_cfuncdom(B) ) ) )).
fof(rc1_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k2_numbers))) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,k2_numbers) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_partfun1(B,u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),k2_numbers) & v1_valued_0(B) & v1_cc0sp2(B,A) ) ) )).
fof(rc1_cfdiff_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k2_numbers) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_partfun1(A,k4_ordinal1) & v9_ordinal1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v1_valued_0(A) & v1_cfdiff_1(A,k5_numbers) ) )).
fof(rc1_cfuncdom,axiom,( ? [A] : ( l1_cfuncdom(A) & v1_cfuncdom(A) ) )).
fof(rc1_cgames_1,axiom,( ? [A] : ( l1_cgames_1(A) & v1_cgames_1(A) ) )).
fof(rc1_chain_1,axiom,( ? [A] : ( ~ v1_zfmisc_1(A) & v1_finset_1(A) ) )).
fof(rc1_chord,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v4_glib_000(A) & v7_glib_000(A) & v2_chord(A) ) )).
fof(rc1_circcmb3,axiom,( ? [A] : ( l1_msualg_1(A) & v4_circcmb3(A) ) )).
fof(rc1_circcomb,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_msualg_1(A) & v1_circcomb(A) & v2_circcomb(A) ) )).
fof(rc1_circled1,axiom,( ! [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) ) => ? [B] : ( m1_rlvect_2(B,A) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,k1_numbers) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v1_valued_0(B) & v2_valued_0(B) & v3_valued_0(B) & v1_circled1(B,A) ) ) )).
fof(rc1_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) & ~ v1_xboole_0(B) & v4_funct_1(B) & v3_finseq_1(B) & v1_pdiff_7(B,A) ) ) )).
fof(rc1_classes2,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_classes2(A) ) )).
fof(rc1_clopban1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(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) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v13_vectsp_1(C,A,B) & v1_clopban1(C,A,B) ) ) )).
fof(rc1_clopban2,axiom,( ? [A] : ( l2_clvect_1(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) & v3_normsp_0(A) & 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) ) )).
fof(rc1_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_clopban3(B,A) ) ) )).
fof(rc1_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ? [C] : ( m1_pboole(C,A,k5_mssubfam(A,B)) & v1_relat_1(C) & v3_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v2_finset_1(C) ) ) )).
fof(rc1_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & ~ v1_xboole_0(C) & v4_funct_1(C) & v2_card_3(C) ) ) )).
fof(rc1_clvect_1,axiom,( ? [A] : ( l1_clvect_1(A) & v1_clvect_1(A) ) )).
fof(rc1_coh_sp,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) )).
fof(rc1_cohsp_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_classes1(A) & v1_coh_sp(A) ) )).
fof(rc1_collsp,axiom,( ? [A] : ( l1_collsp(A) & v1_collsp(A) ) )).
fof(rc1_compact1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_compact1(B,A) ) ) )).
fof(rc1_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) & v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k9_setfam_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & v1_compl_sp(B,A) ) ) )).
fof(rc1_compos_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_compos_0(A) ) )).
fof(rc1_compos_1,axiom,( ? [A] : ( l1_compos_1(A) & v1_compos_1(A) ) )).
fof(rc1_compos_2,axiom,( ? [A] : ( l1_compos_1(A) & v1_amistd_4(A) ) )).
fof(rc1_compts_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v2_pre_topc(A) & v8_pre_topc(A) ) )).
fof(rc1_comput_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v4_funct_1(A) & v1_comput_1(A) ) )).
fof(rc1_comseq_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k2_numbers) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_partfun1(A,k4_ordinal1) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v9_ordinal1(A) & v1_valued_0(A) ) )).
fof(rc1_comseq_2,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k2_numbers) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_partfun1(A,k4_ordinal1) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v1_valued_0(A) & v1_comseq_2(A) ) )).
fof(rc1_comseq_3,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k1_numbers) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_partfun1(A,k4_ordinal1) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v2_series_1(A) ) )).
fof(rc1_connsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) ) ) )).
fof(rc1_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_connsp_3(B,A) & ~ v1_xboole_0(B) ) ) )).
fof(rc1_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_convex1(B,A) ) ) )).
fof(rc1_convex2,axiom,( ! [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) ) => ? [B] : ( m1_rlvect_2(B,A) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,k1_numbers) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v1_valued_0(B) & v2_valued_0(B) & v3_valued_0(B) & v2_convex1(B,A) ) ) )).
fof(rc1_convex3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_convex3(B,A) ) ) )).
fof(rc1_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_convex4(B,A) ) ) )).
fof(rc1_cqc_lang,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & v7_ordinal1(B) ) => ? [C] : ( m1_finseq_1(C,k2_qc_lang1(A)) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,k2_qc_lang1(A)) & v5_relat_1(C,k3_qc_lang1(A)) & v1_funct_1(C) & v3_card_1(C,B) & v1_finseq_1(C) ) ) )).
fof(rc1_csspace,axiom,( ? [A] : ( l1_csspace(A) & v1_csspace(A) ) )).
fof(rc1_csspace4,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,u1_struct_0(B)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_partfun1(C,A) & v1_funct_2(C,A,u1_struct_0(B)) & v1_csspace4(C,A,B) ) ) )).
fof(rc1_descip_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_finseq_1(A)))) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k2_finseq_1(A)) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_partfun1(B,A) & v1_funct_2(B,A,k2_finseq_1(A)) & v1_valued_0(B) & v2_valued_0(B) & v3_valued_0(B) & v4_valued_0(B) & v1_descip_1(B,A) ) ) )).
fof(rc1_diff_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k4_partfun1(k1_numbers,k1_numbers)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & v1_funct_2(A,k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)) & v1_diff_1(A) ) )).
fof(rc1_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_dilworth(B,A) ) ) )).
fof(rc1_diraf,axiom,( ? [A] : ( l1_analoaf(A) & ~ v2_struct_0(A) & ~ v7_struct_0(A) & v1_analoaf(A) & v1_diraf(A) ) )).
fof(rc1_dirort,axiom,( ? [A] : ( l1_analoaf(A) & ~ v2_struct_0(A) & v1_dirort(A) ) )).
fof(rc1_dist_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ? [B] : ( m1_dist_1(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k1_numbers) & ~ v1_xboole_0(B) & v1_funct_1(B) & v3_funct_1(B) & v1_finset_1(B) & v1_valued_0(B) & v2_valued_0(B) & v3_valued_0(B) & v1_finseq_1(B) & v2_finseq_1(B) & v4_partfun3(B) & v1_matrprob(B) ) ) )).
fof(rc1_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ? [B] : ( m1_subset_1(B,k6_dist_1(A)) & ~ v1_xboole_0(B) & v1_setfam_1(B) ) ) )).
fof(rc1_dtconstr,axiom,( ? [A] : ( l1_lang1(A) & ~ v2_struct_0(A) & v1_lang1(A) & v1_dtconstr(A) & v2_dtconstr(A) & v3_dtconstr(A) ) )).
fof(rc1_e_siec,axiom,( ? [A] : ( l1_e_siec(A) & v1_e_siec(A) ) )).
fof(rc1_ec_pf_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ? [B] : ( m1_ec_pf_1(B,A) & ~ v2_struct_0(B) & ~ v6_struct_0(B) & ~ v7_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v36_algstr_0(B) & v1_group_1(B) & v3_group_1(B) & v5_group_1(B) & v1_int_3(B) & v1_vectsp_1(B) & v2_vectsp_1(B) & v3_vectsp_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & v6_vectsp_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) ) ) )).
fof(rc1_ec_pf_2,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v7_ordinal1(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & v1_int_2(A) & v1_xxreal_0(A) & v1_ec_pf_2(A,5) ) )).
fof(rc1_endalg,axiom,( ? [A] : ( l4_algstr_0(A) & ~ v2_struct_0(A) & v6_vectsp_1(A) ) )).
fof(rc1_entropy1,axiom,( ? [A] : ( m1_finseq_1(A,k1_numbers) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k1_numbers) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v4_partfun3(A) ) )).
fof(rc1_eqrel_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(k9_setfam_1(A)))) & v1_eqrel_1(B,A) ) )).
fof(rc1_equation,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v3_msualg_1(B,A) & v4_msualg_1(B,A) & v2_msafree(B,A) ) ) )).
fof(rc1_euclid_7,axiom,( ? [A] : v2_euclid_7(A) )).
fof(rc1_euclmetr,axiom,( ? [A] : ( l1_analmetr(A) & ~ v2_struct_0(A) & v2_analmetr(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) ) )).
fof(rc1_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( v3_ordinal1(A) => ? [D] : ( v1_relat_1(D) & v4_relat_1(D,C) & v5_relat_1(D,B) & v1_xboole_0(D) & v5_ordinal1(D) & v1_funct_1(D) & v1_finset_1(D) & v1_exchsort(D) & v2_exchsort(D,A) & v2_exchsort(D,k5_numbers) ) ) )).
fof(rc1_extens_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_msafree(C,A,B) & v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,u1_struct_0(A)) ) ) )).
fof(rc1_extpro_1,axiom,( ! [A] : ? [B] : ( l1_extpro_1(B,A) & v1_extpro_1(B,A) ) )).
fof(rc1_facirc_1,axiom,( ? [A] : ~ v1_xtuple_0(A) )).
fof(rc1_facirc_2,axiom,( ? [A] : ( l1_msualg_1(A) & v11_struct_0(A) & v1_msualg_1(A) ) )).
fof(rc1_fcont_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & v1_relat_1(A) & v4_relat_1(A,k1_numbers) & v5_relat_1(A,k1_numbers) & v1_funct_1(A) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v1_fcont_1(A) ) )).
fof(rc1_fdiff_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k1_numbers) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_partfun1(A,k4_ordinal1) & v9_ordinal1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v1_fdiff_1(A,k5_numbers) ) )).
fof(rc1_fib_num2,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_setfam_1(A) & v6_membered(A) ) )).
fof(rc1_filter_0,axiom,( ? [A] : ( l3_lattices(A) & ~ v2_struct_0(A) & v3_lattices(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v3_filter_0(A) ) )).
fof(rc1_fin_topo,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v1_orders_2(A) ) )).
fof(rc1_finance1,axiom,( ? [A] : ( m1_subset_1(A,k12_prob_1) & ~ v1_xboole_0(A) ) )).
fof(rc1_finseq_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) )).
fof(rc1_finseq_2,axiom,( ! [A] : ? [B] : ( m1_finseq_2(B,A) & ~ v1_xboole_0(B) ) )).
fof(rc1_finseq_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ? [B] : ( m1_eqrel_1(B,A) & ~ v10_ordinal1(B) & ~ v1_xboole_0(B) & v1_finset_1(B) & v5_finset_1(B) & v1_setfam_1(B) ) ) )).
fof(rc1_finseq_5,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & ~ v1_xboole_0(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) ) )).
fof(rc1_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_finseq_1(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,A) & v1_funct_1(B) & v1_finset_1(B) & v3_card_1(B,1) & v1_finseq_1(B) & v2_finseq_1(B) & v1_finseq_6(B,A) ) ) )).
fof(rc1_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) ) )).
fof(rc1_finsub_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finsub_1(A) & v2_finsub_1(A) & v3_finsub_1(A) ) )).
fof(rc1_fintopo6,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_fintopo6(B,A) & v1_orders_2(B) ) ) )).
fof(rc1_fomodel0,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),A))) & v1_relat_1(B) & v4_relat_1(B,k2_zfmisc_1(A,A)) & v5_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,k2_zfmisc_1(A,A)) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v2_binop_1(B,A) ) )).
fof(rc1_fomodel1,axiom,( ? [A] : ( l1_fomodel1(A) & v1_fomodel1(A) ) )).
fof(rc1_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & ~ v1_xboole_0(B) ) => ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & v1_fomodel2(C,A,B) ) ) )).
fof(rc1_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) => ? [E] : ( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) & ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,A) & v5_relat_1(E,B) & v1_funct_1(E) & v1_partfun1(E,A) & v1_funct_2(E,A,B) & v1_fomodel3(E,C,D) ) ) )).
fof(rc1_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : ( m1_subset_1(B,k1_fomodel4(A)) & v1_xtuple_0(B) & v1_fomodel4(B,A) ) ) )).
fof(rc1_freealg,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_freealg(A) ) )).
fof(rc1_friends1,axiom,( ? [A] : ( v1_relat_1(A) & v2_relat_2(A) & v3_relat_2(A) & v1_finset_1(A) & v3_friends1(A) ) )).
fof(rc1_fsm_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) ) => ? [C] : ( l1_fsm_3(C,A,B) & v1_fsm_3(C,A,B) ) ) )).
fof(rc1_funcop_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) )).
fof(rc1_funcsdom,axiom,( ? [A] : ( l6_algstr_0(A) & ~ v2_struct_0(A) & v7_struct_0(A) & v8_struct_0(A) & v13_struct_0(A,1) & v13_algstr_0(A) & v36_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v1_vectsp_1(A) & v3_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) ) )).
fof(rc1_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) ) )).
fof(rc1_funct_2,axiom,( ! [A] : ! [B] : ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) & v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,A,B) ) )).
fof(rc1_funct_3,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),A))) & v1_relat_1(B) & v4_relat_1(B,k2_zfmisc_1(A,A)) & v5_relat_1(B,A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v3_binop_1(B,A) ) )).
fof(rc1_funct_7,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_funcop_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) ) )).
fof(rc1_funct_8,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_numbers)) & v1_membered(A) & v1_funct_8(A) ) )).
fof(rc1_funct_9,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v2_funct_9(A) ) )).
fof(rc1_functor0,axiom,( ! [A] : ! [B] : ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),k2_zfmisc_1(B,B)))) & v1_relat_1(C) & v4_relat_1(C,k2_zfmisc_1(A,A)) & v5_relat_1(C,k2_zfmisc_1(B,B)) & 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) ) )).
fof(rc1_functor1,axiom,( ? [A] : ( l2_altcat_1(A) & ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & v1_altcat_2(A) ) )).
fof(rc1_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k1_numbers) & v5_relat_1(B,k1_rcomp_1(k5_numbers,1)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_partfun1(B,A) & v1_funct_2(B,A,k1_numbers) & v1_valued_0(B) & v2_valued_0(B) & v3_valued_0(B) ) ) )).
fof(rc1_fvaluat1,axiom,( ? [A] : ( m1_subset_1(A,k6_numbers) & v1_xxreal_0(A) & v2_xxreal_0(A) & v1_xreal_0(A) & v1_fvaluat1(A) ) )).
fof(rc1_gcd_1,axiom,( ? [A] : ( l6_algstr_0(A) & ~ 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) & v1_vectsp_2(A) ) )).
fof(rc1_geomtrap,axiom,( ? [A] : ( l1_geomtrap(A) & v1_geomtrap(A) ) )).
fof(rc1_glib_000,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) ) )).
fof(rc1_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ? [B] : ( m3_glib_001(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k2_xboole_0(k6_glib_000(A),k7_glib_000(A))) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v1_glib_001(B,A) & v2_glib_001(B,A) & v3_glib_001(B,A) ) ) )).
fof(rc1_glib_002,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & v4_glib_000(A) & v3_glib_002(A) ) )).
fof(rc1_glib_003,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) & v3_glib_003(A) ) )).
fof(rc1_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_glib_000(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v2_pre_poly(B) & v1_glib_000(B) & v2_glib_000(B) & v9_glib_000(B,A) & v3_glib_002(B) & v1_glib_003(B) & v4_glib_003(B,A) & v7_glib_003(B) ) ) )).
fof(rc1_goboard1,axiom,( ? [A] : ( m1_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) & v1_relat_1(A) & ~ v3_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) ) )).
fof(rc1_goboard5,axiom,( ? [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_struct_0(k15_euclid(2))) & v1_funct_1(A) & ~ v3_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_topreal1(A) & v2_topreal1(A) & v1_goboard5(A) & v2_goboard5(A) ) )).
fof(rc1_goboard9,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(A) & v1_convex1(A,k15_euclid(2)) ) )).
fof(rc1_goedelcp,axiom,( ? [A] : ( m1_qc_lang1(A) & v4_card_3(A) ) )).
fof(rc1_gr_cy_1,axiom,( ? [A] : ( l3_algstr_0(A) & ~ v2_struct_0(A) & v15_algstr_0(A) & v1_group_1(A) & v2_group_1(A) & v3_group_1(A) & v1_gr_cy_1(A) ) )).
fof(rc1_gr_cy_3,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v7_ordinal1(A) & ~ v8_ordinal1(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & v1_int_2(A) & v1_finset_1(A) & v1_card_1(A) & v1_xxreal_0(A) & v2_xxreal_0(A) & ~ v3_xxreal_0(A) & v1_gr_cy_3(A) ) )).
fof(rc1_graph_1,axiom,( ? [A] : ( l1_graph_1(A) & v1_graph_1(A) ) )).
fof(rc1_graph_2,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_graph_2(A) & v2_graph_2(A) ) )).
fof(rc1_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ? [B] : ( m1_graph_1(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u4_struct_0(A)) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v1_msscyc_1(B,A) ) ) )).
fof(rc1_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ? [B] : ( m1_graph_1(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u4_struct_0(A)) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v7_graph_1(B,A) & v1_graph_4(B,A) ) ) )).
fof(rc1_grcat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_algstr_0(A) & ~ v2_struct_0(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v13_vectsp_1(C,A,B) ) ) )).
fof(rc1_grnilp_1,axiom,( ? [A] : ( l3_algstr_0(A) & ~ v2_struct_0(A) & v15_algstr_0(A) & v1_group_1(A) & v2_group_1(A) & v3_group_1(A) & v1_grnilp_1(A) ) )).
fof(rc1_group_1,axiom,( ? [A] : ( l3_algstr_0(A) & ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) ) )).
fof(rc1_group_10,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l3_algstr_0(A) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_funct_2(B,B)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,k1_funct_2(B,B)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(A),k1_funct_2(B,B)) & v1_group_10(C,A,B) ) ) )).
fof(rc1_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ? [B] : ( m1_group_2(B,A) & ~ v2_struct_0(B) & v15_algstr_0(B) & v1_group_1(B) & v2_group_1(B) & v3_group_1(B) ) ) )).
fof(rc1_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ? [B] : ( m1_group_2(B,A) & ~ v2_struct_0(B) & v15_algstr_0(B) & v1_group_1(B) & v2_group_1(B) & v3_group_1(B) & v1_group_3(B,A) ) ) )).
fof(rc1_group_6,axiom,( ? [A] : ( l3_algstr_0(A) & ~ v2_struct_0(A) & v7_struct_0(A) & v15_algstr_0(A) & v1_group_1(A) & v2_group_1(A) & v3_group_1(A) ) )).
fof(rc1_group_7,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_group_7(B) ) )).
fof(rc1_group_9,axiom,( ! [A] : ? [B] : ( l1_group_9(B,A) & v2_group_9(B,A) ) )).
fof(rc1_groupp_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) & v7_ordinal1(B) ) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & v1_groupp_1(C,B,A) ) ) )).
fof(rc1_grsolv_1,axiom,( ? [A] : ( l3_algstr_0(A) & ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & v1_grsolv_1(A) ) )).
fof(rc1_hahnban,axiom,( ! [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) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_numbers))) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,k1_numbers) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_partfun1(B,u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v2_hahnban(B,A) & v3_hahnban(B,A) & v6_hahnban(B,A) ) ) )).
fof(rc1_hahnban1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(B)) & v5_relat_1(C,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_hahnban1(C,A,B) & v2_hahnban1(C,A,B) ) ) )).
fof(rc1_hallmar1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_finseq_1(B,k1_zfmisc_1(A)) & v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) ) ) )).
fof(rc1_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) & v1_henmodel(B,A) ) ) )).
fof(rc1_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k1_complfld)))) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,u1_struct_0(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) & v2_hahnban1(B,k1_complfld,A) & v1_hermitan(B,A) ) ) )).
fof(rc1_heyting1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k8_normform(A)) & ~ v1_xboole_0(B) ) )).
fof(rc1_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ? [B] : ( m1_subset_1(B,u1_struct_0(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A)))) & ~ v1_xboole_0(B) ) ) )).
fof(rc1_hilbert1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v5_hilbert1(A) ) )).
fof(rc1_hilbert3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & m1_subset_1(B,k1_hilbert1) & m1_subset_1(C,k1_hilbert1) & m1_subset_1(D,k1_hilbert1) ) => ? [E] : ( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k3_hilbert3(A,k3_hilbert1(B,C)),k3_hilbert3(A,k3_hilbert1(B,D))))) & v1_relat_1(E) & v4_relat_1(E,k3_hilbert3(A,k3_hilbert1(B,C))) & v5_relat_1(E,k3_hilbert3(A,k3_hilbert1(B,D))) & ~ v1_xboole_0(E) & v1_funct_1(E) & v1_partfun1(E,k3_hilbert3(A,k3_hilbert1(B,C))) & v1_funct_2(E,k3_hilbert3(A,k3_hilbert1(B,C)),k3_hilbert3(A,k3_hilbert1(B,D))) & v1_funcop_1(E) & v2_funcop_1(E) ) ) )).
fof(rc1_ideal_1,axiom,( ? [A] : ( l2_algstr_0(A) & ~ v2_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v1_algstr_1(A) ) )).
fof(rc1_incproj,axiom,( ? [A] : ( l1_incsp_1(A) & v1_incsp_1(A) & v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) ) )).
fof(rc1_incsp_1,axiom,( ? [A] : ( l1_incsp_1(A) & v1_incsp_1(A) ) )).
fof(rc1_index_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( ~ v1_xboole_0(B) & v1_relat_1(B) & ~ v3_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) ) )).
fof(rc1_instalg1,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) ) )).
fof(rc1_int_1,axiom,( ? [A] : ( v1_xxreal_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) ) )).
fof(rc1_int_2,axiom,( ? [A] : ( v1_xxreal_0(A) & ~ v3_xxreal_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v7_ordinal1(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & v1_int_2(A) ) )).
fof(rc1_int_3,axiom,( ? [A] : ( l6_algstr_0(A) & ~ v2_struct_0(A) & ~ v6_struct_0(A) & v13_algstr_0(A) & v36_algstr_0(A) & v1_group_1(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) & v2_vectsp_1(A) & v3_vectsp_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v1_vectsp_2(A) & v1_int_3(A) ) )).
fof(rc1_int_6,axiom,( ? [A] : ( v1_relat_1(A) & ~ v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) ) )).
fof(rc1_integr1c,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k2_numbers))) & v1_relat_1(A) & v4_relat_1(A,k1_numbers) & v5_relat_1(A,k2_numbers) & v1_funct_1(A) & v1_valued_0(A) & v1_integr1c(A) ) )).
fof(rc1_integra2,axiom,( ? [A] : ( m1_finseq_1(A,k1_numbers) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k1_numbers) & v1_funct_1(A) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_integra2(A) ) )).
fof(rc1_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_interva1(B,A) & ~ v1_xboole_0(B) ) ) )).
fof(rc1_intpro_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v7_intpro_1(A) ) )).
fof(rc1_isomichi,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v7_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v2_tdlat_3(A) ) )).
fof(rc1_jordan,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) & v4_funct_1(B) & v3_pre_topc(B,k15_euclid(A)) & v4_pre_topc(B,k15_euclid(A)) & ~ v9_rltopsp1(B,k15_euclid(A)) & v1_convex1(B,k15_euclid(A)) ) ) )).
fof(rc1_jordan10,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & v4_funct_1(A) & v2_connsp_1(A,k15_euclid(2)) & v2_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) ) )).
fof(rc1_jordan1a,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(A) & v1_topreal2(A) & v2_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) ) )).
fof(rc1_jordan1g,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_zfmisc_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) ) )).
fof(rc1_jordan1h,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v2_setfam_1(A) ) => ? [B] : ( m1_finseq_1(B,k3_finseq_2(A)) & v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k3_finseq_2(A)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v1_funcop_1(B) & v2_funcop_1(B) & v1_pre_poly(B) & v2_pre_poly(B) ) ) )).
fof(rc1_jordan1j,axiom,( ? [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_struct_0(k15_euclid(2))) & ~ v1_xboole_0(A) & ~ v1_zfmisc_1(A) & ~ v8_ordinal1(A) & v1_funct_1(A) & v2_funct_1(A) & ~ v3_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_topreal1(A) & v2_topreal1(A) & v3_topreal1(A) & v4_topreal1(A) & v1_goboard5(A) & v2_goboard5(A) ) )).
fof(rc1_jordan21,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(A) & v4_pre_topc(A,k15_euclid(2)) & v2_connsp_1(A,k15_euclid(2)) & v2_compts_1(A,k15_euclid(2)) & v9_rltopsp1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) & v1_topreal2(A) & v1_jordan21(A) ) )).
fof(rc1_jordan23,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v2_jordan23(A) ) )).
fof(rc1_jordan2c,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v6_tbsp_1(B,A) ) ) )).
fof(rc1_jordan5a,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( m1_pre_topc(B,k15_euclid(A)) & ~ v2_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v6_pre_topc(B) & v7_pre_topc(B) & v8_pre_topc(B) & v1_compts_1(B) ) ) )).
fof(rc1_knaster,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) & v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,A,B) & v6_cohsp_1(C) ) ) )).
fof(rc1_kurato_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k9_setfam_1(A)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) ) ) )).
fof(rc1_kurato_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_topmetr)))) & v1_setfam_1(A) & v3_setfam_1(A,u1_struct_0(k3_topmetr)) ) )).
fof(rc1_lang1,axiom,( ? [A] : ( l1_lang1(A) & v1_lang1(A) ) )).
fof(rc1_lattice2,axiom,( ? [A] : ( 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) & v10_lattices(A) & v1_lattice2(A) ) )).
fof(rc1_lattice3,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) ) )).
fof(rc1_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v20_lattices(B,A) & v21_lattices(B,A) ) ) )).
fof(rc1_lattice5,axiom,( ! [A] : ! [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) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,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) & v20_waybel_0(C,A,B) ) ) )).
fof(rc1_lattice6,axiom,( ? [A] : ( l3_lattices(A) & ~ v2_struct_0(A) & v8_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) ) )).
fof(rc1_lattice7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v6_orders_2(B,A) ) ) )).
fof(rc1_lattices,axiom,( ? [A] : ( l1_lattices(A) & v1_lattices(A) ) )).
fof(rc1_lexbfs,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k4_ordinal1))) & ~ v1_xboole_0(A) & v1_finset_1(A) & v5_finset_1(A) ) )).
fof(rc1_lfuzzy_0,axiom,( ? [A] : ( l1_orders_2(A) & v1_orders_2(A) & v2_lfuzzy_0(A) ) )).
fof(rc1_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),k1_numbers))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k2_zfmisc_1(A,A)) & v5_relat_1(B,k1_numbers) & v5_relat_1(B,k1_rcomp_1(k5_numbers,1)) & v1_funct_1(B) & v1_partfun1(B,k2_zfmisc_1(A,A)) & v1_funct_2(B,k2_zfmisc_1(A,A),k1_numbers) & v1_valued_0(B) & v2_valued_0(B) & v3_valued_0(B) & v1_lfuzzy_1(B,A) & v2_lfuzzy_1(B,A) & v3_lfuzzy_1(B,A) & v4_lfuzzy_1(B,A) ) ) )).
fof(rc1_lmod_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : ( m1_subset_1(D,C) & ~ v2_struct_0(D) & v13_algstr_0(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) & v2_rlvect_1(D) & v3_rlvect_1(D) & v4_rlvect_1(D) ) ) )).
fof(rc1_lopban_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(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) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v13_vectsp_1(C,A,B) & v1_lopban_1(C,A,B) ) ) )).
fof(rc1_lopban_2,axiom,( ? [A] : ( l1_normsp_1(A) & ~ v2_struct_0(A) & ~ v7_struct_0(A) & v12_algstr_0(A) & v13_algstr_0(A) & v14_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v8_rlvect_1(A) & v9_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & v2_normsp_1(A) & v3_lopban_1(A) ) )).
fof(rc1_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_lopban_3(B,A) ) ) )).
fof(rc1_lopclset,axiom,( ? [A] : ( l3_lattices(A) & ~ v2_struct_0(A) & ~ v7_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v11_lattices(A) & v12_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v16_lattices(A) & v17_lattices(A) ) )).
fof(rc1_lpspacc1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_ideal_1(B,A) & v1_lpspacc1(B,A) ) ) )).
fof(rc1_lpspace1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_ideal_1(B,A) & v1_lpspace1(B,A) ) ) )).
fof(rc1_lpspace2,axiom,( ? [A] : ( v1_xxreal_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_lpspace2(A) ) )).
fof(rc1_ltlaxio3,axiom,( ? [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) & ~ v2_ltlaxio3(A) & v3_ltlaxio3(A) ) )).
fof(rc1_ltlaxio4,axiom,( ! [A] : ? [B] : ( m1_finseq_2(B,A) & ~ v1_xboole_0(B) & v4_funct_1(B) & v1_finset_1(B) & v3_finseq_1(B) ) )).
fof(rc1_margrel1,axiom,( ? [A] : ( v3_finseq_1(A) & v2_card_3(A) ) )).
fof(rc1_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( m1_finseq_1(B,k3_finseq_2(k1_numbers)) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k3_finseq_2(k1_numbers)) & v1_funct_1(B) & v1_finseq_1(B) & v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & v1_matrix10(B) & v4_matrix10(B) ) ) )).
fof(rc1_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(k1_nat_1(A,2)),k2_finseq_1(k1_nat_1(A,2))))) & v1_relat_1(B) & v4_relat_1(B,k2_finseq_1(k1_nat_1(A,2))) & v5_relat_1(B,k2_finseq_1(k1_nat_1(A,2))) & v1_funct_1(B) & v2_funct_1(B) & ~ v1_xboole_0(B) & v1_partfun1(B,k2_finseq_1(k1_nat_1(A,2))) & v1_funct_2(B,k2_finseq_1(k1_nat_1(A,2)),k2_finseq_1(k1_nat_1(A,2))) & v2_funct_2(B,k2_finseq_1(k1_nat_1(A,2))) & v3_funct_2(B,k2_finseq_1(k1_nat_1(A,2)),k2_finseq_1(k1_nat_1(A,2))) & v1_finset_1(B) & ~ v5_matrix_2(B,k1_nat_1(A,2)) ) ) )).
fof(rc1_matrix13,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) & v1_xboole_0(A) & v1_finset_1(A) & v1_setfam_1(A) ) )).
fof(rc1_matrix17,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ? [C] : ( m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,k3_finseq_2(u1_struct_0(B))) & v1_funct_1(C) & v1_finseq_1(C) & v1_funcop_1(C) & v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & v1_matrix17(C,B,A) ) ) )).
fof(rc1_matrix_0,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v2_pre_poly(A) & v1_matrix_0(A) ) )).
fof(rc1_matrix_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v2_struct_0(B) & l6_algstr_0(B) ) => ? [C] : ( m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & v1_matrix_1(C,B) ) ) )).
fof(rc1_matrix_2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ? [C] : ( m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,k3_finseq_2(u1_struct_0(B))) & v1_funct_1(C) & v1_finset_1(C) & v1_finseq_1(C) & v2_finseq_1(C) & v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & v1_matrix_2(C,A,B) & v2_matrix_2(C,A,B) ) ) )).
fof(rc1_matrix_9,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( m1_subset_1(B,k5_finsub_1(k3_matrix_2(A))) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) )).
fof(rc1_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_finseq_1(B,k3_finseq_2(k3_finseq_2(A))) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k3_finseq_2(k3_finseq_2(A))) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v1_matrixj1(B,A) ) ) )).
fof(rc1_matrixj2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ? [B] : ( m1_finseq_1(B,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v1_funcop_1(B) & v2_funcop_1(B) & v1_matrixj2(B,A) ) ) )).
fof(rc1_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ? [B] : ( l1_vectsp_1(B,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) & v1_matrlin(B,A) ) ) )).
fof(rc1_matrprob,axiom,( ? [A] : ( m1_finseq_1(A,k1_numbers) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k1_numbers) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v1_matrprob(A) ) )).
fof(rc1_matrtop1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ? [C] : ( m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,k3_finseq_2(u1_struct_0(B))) & v1_funct_1(C) & v1_finset_1(C) & v1_finseq_1(C) & v2_finseq_1(C) & v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & v1_matrix_6(C,A,B) ) ) )).
fof(rc1_matrtop3,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) & v2_funcop_1(B) & v1_matrtop3(B,A) ) )).
fof(rc1_mazurulm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_normsp_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_partfun1(B,u1_struct_0(A)) & 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) & v2_mazurulm(B,A,A) & v3_mazurulm(B,A,A) ) ) )).
fof(rc1_measure1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v1_relat_1(C) & v4_relat_1(C,B) & v5_relat_1(C,k6_numbers) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,B) & v1_funct_2(C,B,k6_numbers) & v2_valued_0(C) & v10_valued_0(C) & v6_supinf_2(C) & v2_measure1(C,A,B) ) ) )).
fof(rc1_measure5,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v1_measure5(A) ) )).
fof(rc1_measure6,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v6_xxreal_2(A) ) )).
fof(rc1_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) & v1_funct_2(C,k4_ordinal1,B) & v1_prob_2(C) ) ) )).
fof(rc1_membered,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v6_membered(A) ) )).
fof(rc1_memstr_0,axiom,( ! [A] : ? [B] : ( l1_memstr_0(B,A) & v1_memstr_0(B,A) ) )).
fof(rc1_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k1_numbers) & v1_funct_1(B) & v1_valued_0(B) & v2_valued_0(B) & v3_valued_0(B) & v6_supinf_2(B) ) ) )).
fof(rc1_mesfunc2,axiom,( ! [A] : ! [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))) ) => ? [C] : ( m1_finseq_1(C,B) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,B) & v1_funct_1(C) & v1_finset_1(C) & v1_finseq_1(C) & v2_finseq_1(C) & v1_prob_2(C) ) ) )).
fof(rc1_mesfunc7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k6_numbers) & v1_funct_1(B) & v2_valued_0(B) & v6_supinf_2(B) ) ) )).
fof(rc1_mesfunc8,axiom,( ! [A] : ! [B] : ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,B)))) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,k4_partfun1(A,B)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,B)) & v1_mesfunc8(C,A,B) ) )).
fof(rc1_metric_1,axiom,( ? [A] : ( l1_metric_1(A) & v1_metric_1(A) ) )).
fof(rc1_metrizts,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v2_pre_topc(A) & v3_pcomps_1(A) & v1_metrizts(A) ) )).
fof(rc1_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) & v4_funct_1(B) & v1_mfold_1(B,A) ) ) )).
fof(rc1_midsp_1,axiom,( ? [A] : ( l1_midsp_1(A) & v1_midsp_1(A) ) )).
fof(rc1_midsp_2,axiom,( ? [A] : ( l2_algstr_0(A) & ~ v2_struct_0(A) & v8_algstr_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v2_midsp_2(A) ) )).
fof(rc1_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ? [B] : ( l1_midsp_3(B,A) & v1_midsp_3(B,A) ) ) )).
fof(rc1_mmlquer2,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,A) & v1_relat_2(B) & v4_relat_2(B) & v6_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A) ) )).
fof(rc1_mmlquery,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,A) & v1_mmlquery(B,A) ) )).
fof(rc1_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ? [B] : ( l1_mod_2(B,A) & v2_mod_2(B,A) ) ) )).
fof(rc1_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_partfun1(B,u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v13_vectsp_1(B,A,A) ) ) )).
fof(rc1_modcat_1,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) & m1_modcat_1(B,A) ) => ? [C] : ( m1_subset_1(C,B) & ~ 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) ) ) )).
fof(rc1_modelc_1,axiom,( ? [A] : ( m1_finseq_1(A,k4_ordinal1) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finseq_1(A) & v1_modelc_1(A) ) )).
fof(rc1_modelc_2,axiom,( ? [A] : ( m1_finseq_1(A,k4_ordinal1) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_modelc_2(A) ) )).
fof(rc1_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => ? [B] : ( l1_modelc_3(B,A) & v1_modelc_3(B,A) ) ) )).
fof(rc1_moebius1,axiom,( ? [A] : ( m1_subset_1(A,k4_ordinal1) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v7_ordinal1(A) & ~ v8_ordinal1(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & ~ v1_int_2(A) & v1_finset_1(A) & v1_card_1(A) & v1_xxreal_0(A) & ~ v3_xxreal_0(A) & v1_rat_1(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) & v6_membered(A) & v3_xxreal_2(A) & v4_xxreal_2(A) & v5_xxreal_2(A) ) )).
fof(rc1_monoid_0,axiom,( ? [A] : ( l1_struct_0(A) & v1_monoid_0(A) ) )).
fof(rc1_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v3_msualg_1(B,A) & v4_msualg_1(B,A) & v2_msafree(B,A) ) ) )).
fof(rc1_msafree1,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_prob_2(B) ) )).
fof(rc1_msafree2,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_struct_0(A) & v1_msafree2(A) ) )).
fof(rc1_msafree4,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v2_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v6_trees_3(A) & v4_card_3(A) ) )).
fof(rc1_msalimit,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( 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) & v2_funcop_1(D) & v1_msalimit(D,A,B,C) ) ) )).
fof(rc1_msinst_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v3_msualg_1(B,A) & v1_msualg_6(B,A) ) ) )).
fof(rc1_msscyc_1,axiom,( ? [A] : ( l1_graph_1(A) & ~ v2_struct_0(A) & v11_struct_0(A) & v14_struct_0(A) ) )).
fof(rc1_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ? [C] : ( m3_pboole(C,A,B) & v1_relat_1(C) & v3_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v2_finset_1(C) ) ) )).
fof(rc1_msualg_1,axiom,( ? [A] : ( l1_msualg_1(A) & v1_msualg_1(A) ) )).
fof(rc1_msualg_2,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_struct_0(A) & v1_msualg_1(A) & v2_msualg_2(A) ) )).
fof(rc1_msualg_3,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_funcop_1(B) & v2_funcop_1(B) & v1_msualg_3(B) ) )).
fof(rc1_msualg_4,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v2_funcop_1(B) ) )).
fof(rc1_msualg_5,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ? [C] : ( m1_msualg_4(C,A,B,B) & v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v2_funcop_1(C) & v1_msualg_4(C,A,B) ) ) )).
fof(rc1_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v4_msualg_1(B,A) ) ) )).
fof(rc1_msualg_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ? [B] : ( m2_nat_lat(B,A) & ~ v2_struct_0(B) & v4_lattices(B) & v5_lattices(B) & v6_lattices(B) & v7_lattices(B) & v8_lattices(B) & v9_lattices(B) & v10_lattices(B) & v4_lattice3(B) ) ) )).
fof(rc1_msualg_9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ? [C] : ( m1_subset_1(C,k6_closure2(A,B)) & v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v2_finset_1(C) ) ) )).
fof(rc1_mycielsk,axiom,( ! [A] : ? [B] : ( m1_eqrel_1(B,A) & ~ v10_ordinal1(B) & v1_finset_1(B) & v1_setfam_1(B) ) )).
fof(rc1_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & v1_nagata_1(B,A) ) ) )).
fof(rc1_nat_1,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v7_ordinal1(A) & ~ v8_ordinal1(A) & v1_xcmplx_0(A) & v1_xxreal_0(A) & v1_xreal_0(A) & v1_finset_1(A) & v1_card_1(A) ) )).
fof(rc1_nat_2,axiom,( ? [A] : ( v1_xxreal_0(A) & ~ v3_xxreal_0(A) & ~ v1_zfmisc_1(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v7_ordinal1(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) ) )).
fof(rc1_nat_3,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v4_valued_0(A) & v2_pre_poly(A) ) )).
fof(rc1_nat_lat,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ? [B] : ( m2_nat_lat(B,A) & ~ v2_struct_0(B) & v3_lattices(B) & v4_lattices(B) & v5_lattices(B) & v6_lattices(B) & v7_lattices(B) & v8_lattices(B) & v9_lattices(B) & v10_lattices(B) ) ) )).
fof(rc1_nattra_1,axiom,( ? [A] : ( l1_cat_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_struct_0(A) & v2_cat_1(A) & v3_cat_1(A) & v4_cat_1(A) & v5_cat_1(A) & v6_cat_1(A) & v4_nattra_1(A) ) )).
fof(rc1_ndiff_1,axiom,( ! [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) & v3_normsp_0(A) & v4_normsp_0(A) & v2_normsp_1(A) & l1_normsp_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_struct_0(A)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v12_struct_0(B,k4_ordinal1,A) & v1_ndiff_1(B,A,k4_struct_0(A)) ) ) )).
fof(rc1_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,k1_numbers) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_ndiff_3(B,A) ) ) )).
fof(rc1_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) & v1_relat_1(B) & v4_relat_1(B,k1_numbers) & v5_relat_1(B,k1_euclid(A)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_partfun1(B,k1_numbers) & v1_funct_2(B,k1_numbers,k1_euclid(A)) & v1_funcop_1(B) & v7_valued_2(B) & v8_valued_2(B) & v9_valued_2(B) & v1_ndiff_4(B,A) ) ) )).
fof(rc1_neckla_2,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v8_struct_0(A) & v1_orders_2(A) & v1_neckla_2(A) ) )).
fof(rc1_neckla_3,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v8_struct_0(A) & v1_orders_2(A) & v1_necklace(A) & v3_necklace(A) ) )).
fof(rc1_necklace,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v1_necklace(A) ) )).
fof(rc1_net_1,axiom,( ? [A] : ( l1_petri(A) & v1_petri(A) & v1_net_1(A) ) )).
fof(rc1_newton,axiom,( ? [A] : ( m1_subset_1(A,k4_ordinal1) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v7_ordinal1(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_xxreal_0(A) & ~ v3_xxreal_0(A) & v1_int_1(A) & v1_int_2(A) & v1_finset_1(A) & v1_card_1(A) & v1_rat_1(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) & v6_membered(A) ) )).
fof(rc1_nfcont_3,axiom,( ! [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) & l1_normsp_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,k1_numbers) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_nfcont_3(B,A) ) ) )).
fof(rc1_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) & v1_relat_1(B) & v4_relat_1(B,k1_numbers) & v5_relat_1(B,k1_euclid(A)) & v1_funct_1(B) & v1_funcop_1(B) & v7_valued_2(B) & v8_valued_2(B) & v9_valued_2(B) & v1_nfcont_4(B,A) ) ) )).
fof(rc1_normsp_1,axiom,( ? [A] : ( l1_normsp_1(A) & v1_normsp_1(A) ) )).
fof(rc1_openlatt,axiom,( ? [A] : ( l3_lattices(A) & ~ v2_struct_0(A) & ~ v7_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v11_lattices(A) & v12_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v1_lattice2(A) & v3_filter_0(A) ) )).
fof(rc1_oposet_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) & v1_relat_1(B) & v2_relat_2(B) & v5_relat_2(B) & v8_relat_2(B) ) )).
fof(rc1_ordeq_01,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_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) & l1_normsp_1(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k9_rsspace4(A,B)))) & v2_nfcont_1(C,k9_rsspace4(A,B)) ) ) )).
fof(rc1_orders_2,axiom,( ? [A] : ( l1_orders_2(A) & v1_orders_2(A) ) )).
fof(rc1_ordinal1,axiom,( ? [A] : v3_ordinal1(A) )).
fof(rc1_ordinal2,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal1(A) ) )).
fof(rc1_ordinal4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ? [B] : ( m1_subset_1(B,A) & v3_ordinal1(B) ) ) )).
fof(rc1_ordinal5,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v5_ordinal1(A) & v1_finset_1(A) ) )).
fof(rc1_ordinal6,axiom,( ? [A] : v1_ordinal6(A) )).
fof(rc1_osafree,axiom,( ? [A] : ( l3_osalg_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v4_osalg_1(A) & v5_osalg_1(A) & v8_osalg_1(A) & v10_osalg_1(A) & v2_osalg_4(A) ) )).
fof(rc1_osalg_3,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_msualg_2(C,A,B) & v12_osalg_1(C,A) & v13_osalg_1(C,A) ) ) )).
fof(rc1_osalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_partfun1(B,u1_struct_0(A)) & v2_funcop_1(B) & v11_osalg_1(B,A) ) ) )).
fof(rc1_parsp_1,axiom,( ? [A] : ( l1_parsp_1(A) & v1_parsp_1(A) ) )).
fof(rc1_partfun1,axiom,( ! [A] : ! [B] : ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) & v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,B) & v1_funct_1(C) ) )).
fof(rc1_partfun3,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k1_numbers) & v1_funct_1(B) & v1_partfun1(B,A) & v1_funct_2(B,A,k1_numbers) & v1_valued_0(B) & v2_valued_0(B) & v3_valued_0(B) & v2_partfun3(B) ) )).
fof(rc1_partfun4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_numbers))) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,k1_numbers) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_partfun1(B,u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v1_valued_0(B) & v2_valued_0(B) & v3_valued_0(B) & v1_pscomp_1(B,A) & v1_partfun3(B) ) ) )).
fof(rc1_pboole,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) )).
fof(rc1_pcomps_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v2_pre_topc(A) & v2_pcomps_1(A) ) )).
fof(rc1_pdiff_6,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(B),k1_euclid(A)))) & v1_relat_1(C) & v4_relat_1(C,k1_euclid(B)) & v5_relat_1(C,k1_euclid(A)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_partfun1(C,k1_euclid(B)) & v1_funct_2(C,k1_euclid(B),k1_euclid(A)) & v1_funcop_1(C) & v7_valued_2(C) & v8_valued_2(C) & v9_valued_2(C) & v1_pdiff_6(C,A,B) & v2_pdiff_6(C,A,B) ) ) )).
fof(rc1_pencil_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_partfun1(B,u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_pencil_2(B,A,A) ) ) )).
fof(rc1_petri,axiom,( ? [A] : ( l1_petri(A) & v1_petri(A) ) )).
fof(rc1_polyalg1,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( l1_polyalg1(B,A) & v1_polyalg1(B,A) ) ) )).
fof(rc1_polynom2,axiom,( ? [A] : ( l6_algstr_0(A) & ~ v2_struct_0(A) & ~ v7_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) ) )).
fof(rc1_polynom4,axiom,( ? [A] : ( l6_algstr_0(A) & ~ v2_struct_0(A) & ~ v6_struct_0(A) & ~ v7_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v36_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v1_group_1(A) & v3_group_1(A) & v5_group_1(A) & v5_vectsp_1(A) & v1_vectsp_2(A) ) )).
fof(rc1_polynom5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l6_algstr_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_partfun1(B,k4_ordinal1) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & v1_polynom5(B,A) ) ) )).
fof(rc1_polynom7,axiom,( ? [A] : ( l6_algstr_0(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) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v1_vectsp_2(A) & v1_algstr_1(A) ) )).
fof(rc1_polyred,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & ~ v7_struct_0(B) & l2_struct_0(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k15_pre_poly(A)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & v1_partfun1(C,k15_pre_poly(A)) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom7(C,A,B) & v3_polynom7(C,A,B) & v1_polynom1(C,B) ) ) )).
fof(rc1_poset_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v6_orders_2(B,A) ) ) )).
fof(rc1_pralg_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k3_finseq_2(A)) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,A) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_finset_1(B) & v4_card_3(B) & v1_finseq_1(B) & v2_finseq_1(B) ) ) )).
fof(rc1_pre_circ,axiom,( ! [A] : ? [B] : ( 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) ) )).
fof(rc1_pre_poly,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k3_finseq_2(A)) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,A) & v1_funct_1(B) & v1_xboole_0(B) & v1_finset_1(B) & v4_card_3(B) & v1_finseq_1(B) & v2_finseq_1(B) ) )).
fof(rc1_pre_topc,axiom,( ? [A] : ( l1_pre_topc(A) & v1_pre_topc(A) ) )).
fof(rc1_prepower,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k1_numbers) & v5_relat_1(A,k3_numbers) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_partfun1(A,k4_ordinal1) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) ) )).
fof(rc1_prob_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & ~ v1_xboole_0(B) & v2_finsub_1(B) & v1_prob_1(B,A) ) )).
fof(rc1_prob_3,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & v2_prob_3(B,A) & v3_prob_3(B,A) ) )).
fof(rc1_prob_4,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k9_setfam_1(A)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & v1_prob_2(B) ) )).
fof(rc1_prvect_1,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v4_card_3(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_prvect_1(A) ) )).
fof(rc1_prvect_2,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v4_card_3(A) & v1_prvect_2(A) ) )).
fof(rc1_pscomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_numbers))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,k1_numbers) & v1_funct_1(B) & v1_partfun1(B,u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v1_valued_0(B) & v2_valued_0(B) & v3_valued_0(B) & v1_comseq_2(B) ) ) )).
fof(rc1_pua2mss1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_finseq_1(B,k4_partfun1(k3_finseq_2(A),A)) & v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k4_partfun1(k3_finseq_2(A),A)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v4_card_3(B) & v4_margrel1(B,A) & v5_margrel1(B,A) ) ) )).
fof(rc1_pythtrip,axiom,( ? [A] : ( m1_subset_1(A,k4_ordinal1) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v7_ordinal1(A) & v1_xcmplx_0(A) & v1_xxreal_0(A) & ~ v3_xxreal_0(A) & v1_xreal_0(A) & v1_int_1(A) & v1_abian(A) & v1_pythtrip(A) ) )).
fof(rc1_qc_lang1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_qc_lang1(B) ) => ? [C] : ( m1_finseq_1(C,k2_qc_lang1(B)) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,k2_qc_lang1(B)) & v1_funct_1(C) & v1_finset_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & v2_finseq_1(C) ) ) )).
fof(rc1_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ? [B] : ( m1_qc_lang1(B) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_qc_trans(B,A) ) ) )).
fof(rc1_qmax_1,axiom,( ? [A] : ( l1_qmax_1(A) & v1_qmax_1(A) ) )).
fof(rc1_quaterni,axiom,( ? [A] : v1_quaterni(A) )).
fof(rc1_quofield,axiom,( ? [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) & v5_vectsp_1(A) & v6_vectsp_1(A) ) )).
fof(rc1_random_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_random_1(C,A,B) & v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,k1_numbers) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,A) & v1_funct_2(C,A,k1_numbers) & v1_valued_0(C) & v2_valued_0(C) & v3_valued_0(C) & v6_supinf_2(C) ) ) )).
fof(rc1_random_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) => ? [E] : ( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) & v1_relat_1(E) & v4_relat_1(E,A) & v5_relat_1(E,B) & ~ v1_xboole_0(E) & v1_funct_1(E) & v1_partfun1(E,A) & v1_funct_2(E,A,B) & v1_random_3(E,A,B,C,D) ) ) )).
fof(rc1_ranknull,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) => ? [C] : ( m1_vectsp_7(C,A,B) & v1_finset_1(C) ) ) )).
fof(rc1_rat_1,axiom,( ? [A] : ( v1_xxreal_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_rat_1(A) ) )).
fof(rc1_ratfunc1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & l2_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_partfun1(B,k4_ordinal1) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & ~ v1_ratfunc1(B,A) ) ) )).
fof(rc1_rcomp_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v3_rcomp_1(A) ) )).
fof(rc1_rcomp_3,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v3_rcomp_1(A) & v5_xxreal_2(A) & v6_xxreal_2(A) ) )).
fof(rc1_real_1,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xxreal_0(A) & v2_xxreal_0(A) & v1_xreal_0(A) ) )).
fof(rc1_real_3,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k1_numbers) & v5_relat_1(A,k4_numbers) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) ) )).
fof(rc1_realset2,axiom,( ? [A] : ( l6_algstr_0(A) & ~ v2_struct_0(A) & ~ v7_struct_0(A) & v36_algstr_0(A) & v3_rlvect_1(A) ) )).
fof(rc1_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ? [B] : ( m1_finseq_1(B,k1_zfmisc_1(A)) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k1_zfmisc_1(A)) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v1_rearran1(B) & v2_rearran1(B) & v3_rearran1(B,k1_zfmisc_1(A)) ) ) )).
fof(rc1_relat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) ) )).
fof(rc1_relset_1,axiom,( ! [A] : ! [B] : ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) & v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,B) ) )).
fof(rc1_revrot_1,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ? [B] : ( m1_finseq_1(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,A) & v1_funct_1(B) & ~ v3_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v1_finseq_6(B,A) ) ) )).
fof(rc1_rewrite1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v10_rewrite1(A) ) )).
fof(rc1_rewrite2,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_rewrite2(A) ) )).
fof(rc1_rewrite3,axiom,( ! [A] : ? [B] : ( l1_rewrite3(B,A) & v1_rewrite3(B,A) ) )).
fof(rc1_rfinseq,axiom,( ? [A] : ( m1_finseq_1(A,k1_numbers) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k1_numbers) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v8_valued_0(A) ) )).
fof(rc1_rfunct_2,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & v1_relat_1(A) & v4_relat_1(A,k1_numbers) & v5_relat_1(A,k1_numbers) & v1_funct_1(A) & v1_zfmisc_1(A) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) ) )).
fof(rc1_rfunct_3,axiom,( ! [A] : ! [B] : ? [C] : ( m1_rfunct_3(C,A,B) & ~ v1_xboole_0(C) ) )).
fof(rc1_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ 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) ) => ? [B] : ( 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) ) ) )).
fof(rc1_ringcat1,axiom,( ? [A] : ( l1_ringcat1(A) & v2_ringcat1(A) ) )).
fof(rc1_rlaffin1,axiom,( ! [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) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_card_1(B,1) & v1_rlaffin1(B,A) ) ) )).
fof(rc1_rlsub_1,axiom,( ! [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) ) => ? [B] : ( m1_rlsub_1(B,A) & ~ v2_struct_0(B) & v12_algstr_0(B) & v13_algstr_0(B) & v14_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) & v9_rlvect_1(B) ) ) )).
fof(rc1_rlsub_2,axiom,( ! [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) & v8_rlvect_1(A) & l1_rlvect_1(A) & m1_rlsub_1(B,A) ) => ? [C] : ( m1_rlsub_2(C,A,B) & ~ v2_struct_0(C) & v12_algstr_0(C) & v13_algstr_0(C) & v1_rlvect_1(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) & v9_rlvect_1(C) ) ) )).
fof(rc1_rltopsp1,axiom,( ? [A] : ( v1_xxreal_0(A) & ~ v8_ordinal1(A) & v1_xcmplx_0(A) & v1_xreal_0(A) ) )).
fof(rc1_rlvect_1,axiom,( ? [A] : ( l1_rlvect_1(A) & v1_rlvect_1(A) ) )).
fof(rc1_rlvect_3,axiom,( ! [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) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_rlvect_3(B,A) ) ) )).
fof(rc1_rlvect_5,axiom,( ? [A] : ( l1_rlvect_1(A) & ~ 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) & v1_rlvect_5(A) ) )).
fof(rc1_rlvect_x,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) ) => ? [C] : ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,A) & v1_funct_1(C) & v1_finset_1(C) & v3_card_1(C,B) & v1_finseq_1(C) & v2_finseq_1(C) ) ) )).
fof(rc1_rmod_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : ( 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) & v2_vectsp_2(C,A) & v4_vectsp_2(C,A) ) ) )).
fof(rc1_robbins2,axiom,( ? [A] : ( l2_robbins1(A) & ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v1_robbins2(A) ) )).
fof(rc1_robbins4,axiom,( ? [A] : ( l4_robbins1(A) & ~ v2_struct_0(A) & v7_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v12_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v17_lattices(A) & v10_robbins1(A) & v1_robbins3(A) & v2_robbins3(A) & v3_robbins3(A) & v8_robbins3(A) & v9_robbins3(A) & v1_robbins4(A) ) )).
fof(rc1_roughs_1,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & ~ v1_roughs_1(A) ) )).
fof(rc1_rsspace4,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,u1_struct_0(B)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_partfun1(C,A) & v1_funct_2(C,A,u1_struct_0(B)) & v1_rsspace4(C,A,B) ) ) )).
fof(rc1_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ? [B] : ( 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) & v1_bhsp_1(B) & v2_bhsp_1(B) ) ) )).
fof(rc1_rusub_2,axiom,( ! [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) & v8_rlvect_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) & m1_rusub_1(B,A) ) => ? [C] : ( m1_rusub_2(C,A,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) & v1_bhsp_1(C) & v2_bhsp_1(C) ) ) )).
fof(rc1_rusub_4,axiom,( ? [A] : ( l1_bhsp_1(A) & ~ v2_struct_0(A) & v12_algstr_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v8_rlvect_1(A) & v9_rlvect_1(A) & v1_bhsp_1(A) & v2_bhsp_1(A) & v1_rusub_4(A) ) )).
fof(rc1_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v4_valued_0(B) & v1_finset_1(B) & v3_card_1(B,A) & v1_finseq_1(B) & v2_finseq_1(B) ) ) )).
fof(rc1_scm_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) & m1_subset_1(B,k4_ordinal1) ) => ? [C] : ( m1_scm_1(C,A) & ~ 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(C,u1_struct_0(k1_ami_3)) & v5_memstr_0(C,k7_card_1(2),k1_ami_3,B) ) ) )).
fof(rc1_scm_halt,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) & v2_pre_poly(A) & v2_scm_halt(A) ) )).
fof(rc1_scmfsa6b,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) & v2_pre_poly(A) & v1_scmfsa6b(A) ) )).
fof(rc1_scmfsa6c,axiom,( ? [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) & v1_scmfsa6c(A) & v2_scmfsa6c(A) ) )).
fof(rc1_scmfsa7b,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & ~ v1_xboole_0(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) & v7_amistd_1(A,k7_card_1(3),k1_scmfsa_2) & v1_scmfsa7b(A) ) )).
fof(rc1_scmfsa8a,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) & v1_afinsq_1(A) & v2_compos_1(A,k1_scmfsa_2) & v1_scmfsa7b(A) ) )).
fof(rc1_scmfsa_2,axiom,( ? [A] : ( m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) & v1_ami_2(A) ) )).
fof(rc1_scmfsa_m,axiom,( ? [A] : ( m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) & v1_ami_2(A) & ~ v1_scmfsa_m(A) ) )).
fof(rc1_scmpds_2,axiom,( ? [A] : ( m1_subset_1(A,u1_struct_0(k1_scmpds_2)) & v1_ami_2(A) ) )).
fof(rc1_scmpds_5,axiom,( ? [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) & v6_compos_0(A,u1_compos_1(k1_scmpds_2)) & v4_scmpds_4(A) & v1_scmpds_5(A) ) )).
fof(rc1_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ? [B] : ( m1_subset_1(B,u1_struct_0(k1_scmring2(A))) & v1_ami_2(B) ) ) )).
fof(rc1_scmyciel,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v2_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) ) )).
fof(rc1_semi_af1,axiom,( ? [A] : ( l1_analoaf(A) & ~ v2_struct_0(A) & v1_semi_af1(A) ) )).
fof(rc1_seq_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k1_numbers) & v1_funct_1(A) & v9_ordinal1(A) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) ) )).
fof(rc1_seq_4,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v3_xxreal_2(A) & v4_xxreal_2(A) ) )).
fof(rc1_seqm_3,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k1_numbers) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_partfun1(A,k4_ordinal1) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v4_valued_0(A) & v5_valued_0(A) ) )).
fof(rc1_setfam_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) )).
fof(rc1_setwiseo,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k5_finsub_1(A)) & v1_xboole_0(B) & v1_finset_1(B) ) )).
fof(rc1_sfmastr1,axiom,( ? [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) & v1_scmfsa6c(A) & v1_amistd_2(A,k7_card_1(3),k1_scmfsa_2) & v3_amistd_2(A,k7_card_1(3),k1_scmfsa_2) & v1_sfmastr1(A) ) )).
fof(rc1_sgraph1,axiom,( ? [A] : ( l1_sgraph1(A) & v1_sgraph1(A) ) )).
fof(rc1_sheffer1,axiom,( ? [A] : ( l3_lattices(A) & ~ v2_struct_0(A) & v7_struct_0(A) & v8_struct_0(A) & v13_struct_0(A,1) & v10_lattices(A) & v17_lattices(A) & v7_robbins1(A) & v1_sheffer1(A) & v2_sheffer1(A) & v3_sheffer1(A) & v4_sheffer1(A) ) )).
fof(rc1_sheffer2,axiom,( ? [A] : ( l1_sheffer1(A) & ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & v1_sheffer2(A) ) )).
fof(rc1_simplex0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & ~ v2_setfam_1(B) & v1_finset_1(B) & v5_finset_1(B) & v1_classes1(B) ) ) )).
fof(rc1_simplex1,axiom,( ! [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) & v8_rlvect_1(A) & l1_rlvect_1(A) & m1_simplex0(B,u1_struct_0(A)) ) => ? [C] : ( m1_simplex1(C,A,B) & v1_matroid0(C) & v3_matroid0(C) ) ) )).
fof(rc1_simplex2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) ) => ? [C] : ( m1_simplex0(C,B) & ~ v3_pencil_1(C) & v1_matroid0(C) & v3_matroid0(C) & v1_simplex2(C,A) ) ) )).
fof(rc1_sppol_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(A) & v4_funct_1(A) & v2_compts_1(A,k15_euclid(2)) & v1_sppol_1(A) ) )).
fof(rc1_sppol_2,axiom,( ? [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_struct_0(k15_euclid(2))) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v4_topreal1(A) ) )).
fof(rc1_sprect_1,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & ~ v1_xboole_0(A) & v1_funct_1(A) & v3_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) ) )).
fof(rc1_sprect_2,axiom,( ? [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_struct_0(k15_euclid(2))) & ~ v1_xboole_0(A) & ~ v1_zfmisc_1(A) & ~ v8_ordinal1(A) & v1_funct_1(A) & ~ v3_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_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) ) )).
fof(rc1_sprect_3,axiom,( ? [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_struct_0(k15_euclid(2))) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_topreal1(A) & v2_topreal1(A) & v1_goboard5(A) & v1_sprect_1(A) ) )).
fof(rc1_stacks_1,axiom,( ? [A] : ( l1_stacks_1(A) & v1_stacks_1(A) ) )).
fof(rc1_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ? [B] : ( m1_subset_1(B,k2_zfmisc_1(k16_substut1(A),k3_qc_lang1(A))) & v1_sublemma(B,A) ) ) )).
fof(rc1_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) ) ) )).
fof(rc1_substlat,axiom,( ! [A] : ! [B] : ? [C] : ( m1_subset_1(C,k1_substlat(A,B)) & ~ v1_xboole_0(C) ) )).
fof(rc1_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ? [B] : ( m1_subset_1(B,k1_substut1(A)) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) ) ) )).
fof(rc1_supinf_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & ~ v1_xboole_0(B) & v1_setfam_1(B) ) ) )).
fof(rc1_supinf_2,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k6_numbers)) & ~ v1_xboole_0(A) & v2_membered(A) & v4_card_3(A) ) )).
fof(rc1_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ? [B] : ( l1_symsp_1(B,A) & v1_symsp_1(B,A) ) ) )).
fof(rc1_t_0topsp,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) ) )).
fof(rc1_t_1topsp,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v2_pre_topc(A) & v7_pre_topc(A) ) )).
fof(rc1_taxonom1,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xxreal_0(A) & ~ v3_xxreal_0(A) & v1_xreal_0(A) ) )).
fof(rc1_taxonom2,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v1_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_taxonom2(A) & v2_taxonom2(A) ) )).
fof(rc1_tbsp_1,axiom,( ? [A] : ( l1_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) & v5_tbsp_1(A) ) )).
fof(rc1_tdgroup,axiom,( ? [A] : ( l2_algstr_0(A) & ~ v2_struct_0(A) & v8_algstr_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) ) )).
fof(rc1_tdlat_3,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v1_pre_topc(A) & v1_tdlat_3(A) & v2_tdlat_3(A) ) )).
fof(rc1_termord,axiom,( ? [A] : ( l2_algstr_0(A) & ~ v7_struct_0(A) ) )).
fof(rc1_tex_1,axiom,( ? [A] : ( l1_pre_topc(A) & v13_struct_0(A,1) & v1_pre_topc(A) ) )).
fof(rc1_tex_2,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_zfmisc_1(B) & v1_subset_1(B,A) ) ) )).
fof(rc1_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v1_tex_3(B,A) ) ) )).
fof(rc1_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) & v4_tex_4(B,A) ) ) )).
fof(rc1_tietze,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k1_numbers) & v1_funct_1(A) & v3_funct_1(A) & v1_partfun1(A,k4_ordinal1) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v1_series_1(A) & v2_comseq_2(A) ) )).
fof(rc1_toler_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_toler_1(C,A,B) & v1_toler_1(C,A,B) ) ) )).
fof(rc1_topalg_2,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) & ~ v1_xboole_0(B) & v1_convex1(B,k15_euclid(A)) ) ) )).
fof(rc1_topalg_6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ? [C] : ( m1_borsuk_2(C,A,B,B) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(k5_topmetr)) & v5_relat_1(C,u1_struct_0(A)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v3_funct_1(C) & v1_partfun1(C,u1_struct_0(k5_topmetr)) & v1_funct_2(C,u1_struct_0(k5_topmetr),u1_struct_0(A)) & v5_pre_topc(C,k5_topmetr,A) ) ) )).
fof(rc1_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & ~ v1_xboole_0(B) & v2_topdim_1(B,A) ) ) )).
fof(rc1_topdim_2,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & v1_topdim_2(B,A) ) )).
fof(rc1_topgen_1,axiom,( ? [A] : ( l1_struct_0(A) & ~ v2_struct_0(A) & v1_orders_4(A) ) )).
fof(rc1_topgen_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & ~ v1_xboole_0(B) & v1_tops_2(B,A) ) ) )).
fof(rc1_topgen_4,axiom,( ? [A] : ( ~ v1_xboole_0(A) & ~ v4_card_3(A) ) )).
fof(rc1_topgrp_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,A) & v1_funct_1(B) & v2_funct_1(B) & v1_partfun1(B,A) & v1_funct_2(B,A,A) & v2_funct_2(B,A) ) )).
fof(rc1_topmetr,axiom,( ! [A] : ( ( v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ? [B] : ( m1_topmetr(B,A) & v1_metric_1(B) & v6_metric_1(B) & v7_metric_1(B) & v8_metric_1(B) & v9_metric_1(B) ) ) )).
fof(rc1_topreal2,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & v4_funct_1(A) & ~ v1_xboole_0(A) & v1_topreal2(A) ) )).
fof(rc1_topreal6,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(A) & v1_convex1(A,k15_euclid(2)) ) )).
fof(rc1_topreal8,axiom,( ? [A] : ( v1_zfmisc_1(A) & v1_relat_1(A) & v1_funct_1(A) ) )).
fof(rc1_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(A))))) & v1_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(A))) & v5_pre_topc(B,k15_euclid(A),k15_euclid(A)) & v13_vectsp_1(B,k15_euclid(A),k15_euclid(A)) & v1_topreal9(B,A) ) ) )).
fof(rc1_topreala,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v2_monoid_0(A) ) )).
fof(rc1_toprealb,axiom,( ? [A] : ( m1_pre_topc(A,k15_euclid(2)) & v1_pre_topc(A) & v2_pre_topc(A) & v1_monoid_0(A) & v2_monoid_0(A) & v1_toprealb(A) ) )).
fof(rc1_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A) ) ) )).
fof(rc1_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & v1_tops_2(B,A) ) ) )).
fof(rc1_transgeo,axiom,( ? [A] : ( l1_analoaf(A) & ~ v2_struct_0(A) & v1_analoaf(A) & v1_transgeo(A) ) )).
fof(rc1_trees_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_trees_1(A) ) )).
fof(rc1_trees_2,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_trees_2(A) ) )).
fof(rc1_trees_3,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_3(A) & v2_trees_3(A) ) )).
fof(rc1_trees_9,axiom,( ? [A] : ( v1_relat_1(A) & v1_zfmisc_1(A) & v1_funct_1(A) & v3_trees_2(A) ) )).
fof(rc1_trees_a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ? [B] : ( m4_trees_1(B,A) & ~ v1_xboole_0(B) & v2_trees_1(B) ) ) )).
fof(rc1_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) & v1_tsep_1(B,A) ) ) )).
fof(rc1_tsp_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v6_pre_topc(A) ) )).
fof(rc1_turing_1,axiom,( ? [A] : ( l1_turing_1(A) & v1_turing_1(A) ) )).
fof(rc1_unialg_1,axiom,( ? [A] : ( l1_unialg_1(A) & v1_unialg_1(A) ) )).
fof(rc1_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ? [B] : ( m1_unialg_2(B,A) & ~ v2_struct_0(B) & v1_unialg_1(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) ) ) )).
fof(rc1_unialg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ? [B] : ( m1_unialg_3(B,A) & ~ v1_xboole_0(B) ) ) )).
fof(rc1_uniroots,axiom,( ? [A] : ( l6_algstr_0(A) & ~ v2_struct_0(A) & ~ v6_struct_0(A) & ~ v7_struct_0(A) & v8_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v1_group_1(A) & v3_group_1(A) & v5_group_1(A) & v1_vectsp_1(A) & v2_vectsp_1(A) & v3_vectsp_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v1_vectsp_2(A) ) )).
fof(rc1_uproots,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & l2_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_partfun1(B,k4_ordinal1) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & v1_uproots(B,A) ) ) )).
fof(rc1_valued_0,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v4_valued_0(A) ) )).
fof(rc1_valued_1,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_valued_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) ) )).
fof(rc1_valued_2,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v6_valued_2(A) ) )).
fof(rc1_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v6_struct_0(A) & l6_algstr_0(A) ) => ? [B] : ( l1_vectsp_1(B,A) & ~ v7_struct_0(B) ) ) )).
fof(rc1_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ? [B] : ( l1_vectsp_1(B,A) & ~ 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) ) ) )).
fof(rc1_vectsp_1,axiom,( ? [A] : ( l2_algstr_0(A) & ~ v2_struct_0(A) & v8_algstr_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) ) )).
fof(rc1_vectsp_2,axiom,( ? [A] : ( l6_algstr_0(A) & ~ v2_struct_0(A) & v13_algstr_0(A) & v36_algstr_0(A) & v1_group_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) ) )).
fof(rc1_vectsp_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : ( m1_vectsp_4(C,A,B) & ~ 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) ) ) )).
fof(rc1_vectsp_7,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v1_finset_1(C) & v1_vectsp_7(C,A,B) ) ) )).
fof(rc1_vectsp_8,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) => ? [C] : ( m1_vectsp_8(C,A,B) & ~ v1_xboole_0(C) ) ) )).
fof(rc1_vectsp_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) )).
fof(rc1_waybel10,axiom,( ! [A] : ! [B] : ( ( l1_orders_2(A) & ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_orders_3(C,A,B) ) ) )).
fof(rc1_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_finset_1(B) & v1_waybel_0(B,A) ) ) )).
fof(rc1_waybel12,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_waybel12(C,A,B) & ~ v1_xboole_0(C) ) ) )).
fof(rc1_waybel13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( 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) & v14_waybel_0(B,A) ) ) )).
fof(rc1_waybel18,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_waybel18(B) ) )).
fof(rc1_waybel19,axiom,( ? [A] : ( l1_waybel_9(A) & ~ v2_struct_0(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) & v1_waybel_9(A) & ~ v1_yellow_3(A) & v1_waybel19(A) ) )).
fof(rc1_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_partfun1(B,u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v22_waybel_0(B,A,A) & v8_waybel_1(B,A) ) ) )).
fof(rc1_waybel21,axiom,( ! [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] : ( m1_yellow_0(B,A) & ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v4_yellow_0(B,A) & v5_yellow_0(B,A) & v7_yellow_0(B,A) & v3_waybel_0(B,A) & v4_waybel_0(B,A) & v2_lattice3(B) & v3_lattice3(B) ) ) )).
fof(rc1_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v3_waybel23(B,A) & v4_waybel23(B,A) ) ) )).
fof(rc1_waybel24,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_waybel_0(C,A,B) ) ) )).
fof(rc1_waybel25,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v6_pre_topc(A) & v2_waybel18(A) ) )).
fof(rc1_waybel26,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & ~ v7_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & v2_waybel18(A) & v1_waybel25(A) ) )).
fof(rc1_waybel27,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_waybel27(A) & v2_waybel27(A) & v3_waybel27(A) ) )).
fof(rc1_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v7_waybel_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_partfun1(B,u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_waybel28(B,A) ) ) )).
fof(rc1_waybel29,axiom,( ? [A] : ( l1_waybel_9(A) & ~ v2_struct_0(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_yellow_3(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) ) )).
fof(rc1_waybel30,axiom,( ? [A] : ( 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_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_waybel_9(A) & v4_waybel11(A) & v3_waybel_3(A) & ~ v1_yellow_3(A) & v2_waybel_2(A) ) )).
fof(rc1_waybel31,axiom,( ? [A] : ( l1_orders_2(A) & v8_struct_0(A) & v13_struct_0(A,1) & v1_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) ) )).
fof(rc1_waybel33,axiom,( ? [A] : ( l1_waybel_9(A) & ~ v2_struct_0(A) & 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) & v1_waybel33(A) ) )).
fof(rc1_waybel34,axiom,( ! [A] : ! [B] : ( ( 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) ) => ? [C] : ( m1_waybel_1(C,A,B) & v3_waybel_1(C,A,B) ) ) )).
fof(rc1_waybel35,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,u1_struct_0(A)) & v1_waybel_4(B,A) ) ) )).
fof(rc1_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_waybel_0(B,A) & v2_waybel_0(B,A) ) ) )).
fof(rc1_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_partfun1(B,u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v6_waybel_1(B,A) ) ) )).
fof(rc1_waybel_2,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v13_struct_0(A,1) & v1_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & ~ v1_yellow_3(A) & v1_lattice3(A) & v2_lattice3(A) ) )).
fof(rc1_waybel_3,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & v16_waybel_0(A) ) )).
fof(rc1_waybel_4,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v1_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) & v1_relat_1(B) & v5_waybel_4(B,A) ) ) )).
fof(rc1_waybel_5,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v2_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) ) )).
fof(rc1_waybel_6,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & 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) ) )).
fof(rc1_waybel_7,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & ~ v7_struct_0(A) & v1_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v11_waybel_1(A) & ~ v1_yellow_3(A) & v1_lattice3(A) & v2_lattice3(A) ) )).
fof(rc1_waybel_8,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v13_struct_0(A,1) & v1_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) ) )).
fof(rc1_waybel_9,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m2_yellow_6(C,A,B) & ~ v2_struct_0(C) & v4_orders_2(C) & v6_waybel_0(C,A) & v7_waybel_0(C) ) ) )).
fof(rc1_wellfnd1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & ~ v1_finset_1(A) & v1_card_1(A) & v1_card_5(A) ) )).
fof(rc1_xboole_0,axiom,( ? [A] : v1_xboole_0(A) )).
fof(rc1_xboolean,axiom,( ? [A] : v1_xboolean(A) )).
fof(rc1_xcmplx_0,axiom,( ? [A] : v1_xcmplx_0(A) )).
fof(rc1_xreal_0,axiom,( ? [A] : v1_xreal_0(A) )).
fof(rc1_xtuple_0,axiom,( ? [A] : v1_xtuple_0(A) )).
fof(rc1_xxreal_0,axiom,( ? [A] : v1_xxreal_0(A) )).
fof(rc1_xxreal_2,axiom,( ? [A] : ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) & v6_membered(A) & ~ v1_xboole_0(A) & v1_xxreal_2(A) & v2_xxreal_2(A) ) )).
fof(rc1_xxreal_3,axiom,( ? [A] : ( v1_xxreal_0(A) & v2_xxreal_0(A) & ~ v1_xreal_0(A) ) )).
fof(rc1_yellow11,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v8_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) ) )).
fof(rc1_yellow12,axiom,( ! [A] : ! [B] : ( ( l1_pre_topc(A) & l1_pre_topc(B) ) => ? [C] : ( m3_yellow_9(C,A,B) & v1_pre_topc(C) & v2_pre_topc(C) ) ) )).
fof(rc1_yellow13,axiom,( ! [A] : ! [B] : ( ( l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ? [C] : ( m1_yellow13(C,A,B) & ~ v1_xboole_0(C) ) ) )).
fof(rc1_yellow14,axiom,( ? [A] : ( l1_struct_0(A) & ~ v2_struct_0(A) & v1_monoid_0(A) ) )).
fof(rc1_yellow16,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v5_orders_3(C,A,B) & v22_waybel_0(C,A,B) ) ) )).
fof(rc1_yellow19,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) & ~ v2_struct_0(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ? [C] : ( m1_yellow_6(C,A,B) & ~ v2_struct_0(C) & v6_waybel_0(C,A) & v7_waybel_0(C) & v2_yellow_6(C,A,B) ) ) )).
fof(rc1_yellow21,axiom,( ? [A] : ( l2_altcat_1(A) & ~ v2_struct_0(A) & v2_altcat_1(A) & v6_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & v1_altcat_2(A) & v3_yellow21(A) ) )).
fof(rc1_yellow_0,axiom,( ? [A] : ( l1_orders_2(A) & v13_struct_0(A,1) & v1_orders_2(A) & v3_orders_2(A) ) )).
fof(rc1_yellow_1,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_yellow_1(B) ) )).
fof(rc1_yellow_3,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & ~ v1_yellow_3(A) ) )).
fof(rc1_yellow_6,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v3_funct_1(A) & ~ v1_xboole_0(A) & v2_pralg_1(A) ) )).
fof(rc1_yellow_7,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v7_struct_0(A) & v8_struct_0(A) & v13_struct_0(A,1) & v1_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v16_waybel_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & v2_waybel_1(A) & v9_waybel_1(A) & v1_waybel_5(A) ) )).
fof(rc1_yellow_8,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ? [C] : ( 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) ) ) )).
fof(rc1_yellow_9,axiom,( ? [A] : ( l1_waybel_9(A) & ~ v2_struct_0(A) & v13_struct_0(A,1) & 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_waybel_9(A) ) )).
fof(rc1_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ? [B] : ( m1_subset_1(B,A) & v1_relat_1(B) ) ) )).
fof(rc1_zf_lang,axiom,( ? [A] : ( m1_finseq_1(A,k4_ordinal1) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_zf_lang(A) ) )).
fof(rc1_zf_refle,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ? [B] : ( m1_subset_1(B,A) & ~ v1_xboole_0(B) ) ) )).
fof(rc1_zfmisc_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_zfmisc_1(A) ) )).
fof(rc1_zmodul01,axiom,( ? [A] : ( l1_zmodul01(A) & v1_zmodul01(A) ) )).
fof(rc1_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_zmodul02(B,A) ) ) )).
fof(rc1_zmodul03,axiom,( ? [A] : ( l1_zmodul01(A) & ~ v2_struct_0(A) & ~ v7_struct_0(A) & v5_algstr_0(A) & v6_algstr_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v1_algstr_1(A) & v2_algstr_1(A) & v3_algstr_1(A) & v4_algstr_1(A) & v2_zmodul01(A) & v3_zmodul01(A) & v4_zmodul01(A) & v5_zmodul01(A) ) )).
fof(rc20_comput_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v4_valued_0(A) & v2_margrel1(A) & v2_comput_1(A) & v8_comput_1(A,k5_numbers) ) )).
fof(rc20_fomodel0,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(A) & ~ v2_abian(A) ) )).
fof(rc20_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : ( 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(B) & v7_fomodel4(B,A) & v15_fomodel4(B,A) ) ) )).
fof(rc20_scmyciel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v10_ordinal1(A) & v5_finset_1(A) & v2_finsub_1(A) & ~ v1_setfam_1(A) & v1_classes1(A) & ~ v1_scmyciel(A) & v3_scmyciel(A,1) & v4_scmyciel(A) & v12_scmyciel(A) ) )).
fof(rc20_struct_0,axiom,( ? [A] : ( l2_struct_0(A) & ~ v2_struct_0(A) & v7_struct_0(A) ) )).
fof(rc21_comput_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v4_valued_0(A) & v2_margrel1(A) & v2_comput_1(A) & v8_comput_1(A,1) ) )).
fof(rc21_fomodel0,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_xboole_0(A) & v5_fomodel0(A) ) )).
fof(rc21_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : ( 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(B) & v7_fomodel4(B,A) & v13_fomodel4(B,2,A) & v15_fomodel4(B,A) ) ) )).
fof(rc21_struct_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_zfmisc_1(B) ) ) )).
fof(rc22_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & v19_aofa_a00(B,A) ) ) )).
fof(rc22_comput_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v4_valued_0(A) & v2_margrel1(A) & v2_comput_1(A) & v8_comput_1(A,2) ) )).
fof(rc22_struct_0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_zfmisc_1(B) ) ) )).
fof(rc23_comput_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v4_valued_0(A) & v2_margrel1(A) & v2_comput_1(A) & v8_comput_1(A,3) ) )).
fof(rc23_struct_0,axiom,( ! [A] : ( v1_card_1(A) => ? [B] : ( l1_struct_0(B) & v13_struct_0(B,A) ) ) )).
fof(rc24_aofa_a00,axiom,( ! [A] : ! [B] : ? [C] : ( l5_aofa_a00(C) & ~ v2_struct_0(C) & ~ v11_struct_0(C) & v14_struct_0(C) & v1_instalg1(C) & v12_aofa_a00(C) & v14_aofa_a00(C,4) & v21_aofa_a00(C,A,B,1) ) )).
fof(rc25_struct_0,axiom,( ? [A] : ( l5_struct_0(A) & ~ v15_struct_0(A) ) )).
fof(rc26_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v21_aofa_a00(A,1,1,11) & l6_aofa_a00(A) ) => ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & v19_aofa_a00(B,A) ) ) )).
fof(rc27_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(C) & ~ v11_struct_0(C) & v21_aofa_a00(C,A,B,1) & l5_aofa_a00(C) ) => ? [D] : ( l3_msualg_1(D,C) & v3_msualg_1(D,C) & v4_msualg_1(D,C) & ~ v1_catalg_1(D,C) & v22_aofa_a00(D,C,A,B,1) ) ) )).
fof(rc2_abcmiz_0,axiom,( ? [A] : ( l1_abcmiz_0(A) & v3_abcmiz_0(A) ) )).
fof(rc2_abcmiz_1,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_struct_0(A) & v1_msualg_1(A) & v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) ) )).
fof(rc2_abcmiz_a,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_struct_0(A) & v1_msualg_1(A) & v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & v1_abcmiz_a(A) ) )).
fof(rc2_abian,axiom,( ? [A] : ( m1_subset_1(A,k4_ordinal1) & v1_xxreal_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v7_ordinal1(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & v1_rat_1(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) & v6_membered(A) & v3_xxreal_2(A) & ~ v1_abian(A) ) )).
fof(rc2_afinsq_1,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v5_relat_1(B,A) & v5_ordinal1(B) & v1_funct_1(B) & v1_xboole_0(B) & v1_finset_1(B) ) )).
fof(rc2_afvect0,axiom,( ? [A] : ( l2_algstr_0(A) & ~ v2_struct_0(A) & ~ v7_struct_0(A) & v8_algstr_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) ) )).
fof(rc2_algstr_1,axiom,( ? [A] : ( l2_algstr_0(A) & ~ v2_struct_0(A) & v5_algstr_0(A) & v6_algstr_0(A) & v7_algstr_0(A) & v8_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v1_algstr_1(A) & v2_algstr_1(A) & v3_algstr_1(A) & v4_algstr_1(A) ) )).
fof(rc2_algstr_3,axiom,( ? [A] : ( l1_algstr_3(A) & ~ v2_struct_0(A) ) )).
fof(rc2_algstr_4,axiom,( ! [A] : ( l3_algstr_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,u1_struct_0(A)) & v1_partfun1(B,u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v3_relat_2(B) & v8_relat_2(B) & v1_algstr_4(B,A) ) ) )).
fof(rc2_altcat_1,axiom,( ? [A] : ( l2_altcat_1(A) & v6_altcat_1(A) ) )).
fof(rc2_altcat_2,axiom,( ? [A] : ( l1_altcat_1(A) & ~ v2_struct_0(A) & v1_altcat_2(A) ) )).
fof(rc2_ami_wstd,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) & v3_card_1(C,1) & v4_card_3(C) & v2_pre_poly(C) & v5_ami_wstd(C,A,B) ) ) )).
fof(rc2_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ? [B] : ( l1_extpro_1(B,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) ) ) )).
fof(rc2_amistd_2,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ? [B] : ( l1_extpro_1(B,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) & v2_amistd_2(B,A) ) ) )).
fof(rc2_amistd_5,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ? [B] : ( l1_extpro_1(B,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) ) ) )).
fof(rc2_analmetr,axiom,( ? [A] : ( l1_analmetr(A) & ~ v2_struct_0(A) ) )).
fof(rc2_analoaf,axiom,( ? [A] : ( l1_analoaf(A) & ~ v7_struct_0(A) & v1_analoaf(A) ) )).
fof(rc2_anproj_2,axiom,( ? [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) ) )).
fof(rc2_aofa_000,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(A),A))) & v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(A)) & v5_relat_1(B,A) & ~ v1_xboole_0(B) & v1_funct_1(B) & v2_margrel1(B) & v3_margrel1(B,A) & v8_comput_1(B,k5_numbers) ) ) )).
fof(rc2_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ? [B] : ( l1_aofa_a00(B,A) & v4_msualg_1(B,A) & v1_msafree1(B,A) ) ) )).
fof(rc2_aofa_a01,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) & v4_msualg_1(B,A) & v1_aofa_a01(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( l3_msualg_1(C,A) & v4_msualg_1(C,A) & v4_msafree4(C,A,B) & v6_msafree4(C,A,k5_msafree4(A,B)) & v17_aofa_a00(C,A) ) ) )).
fof(rc2_aofa_i00,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_card_1(A),A))) & v1_relat_1(B) & v4_relat_1(B,k1_card_1(A)) & v5_relat_1(B,A) & v1_funct_1(B) & v2_funct_1(B) & v1_funct_2(B,k1_card_1(A),A) & v2_funct_2(B,A) ) )).
fof(rc2_armstrng,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & v2_finsub_1(B) & v1_armstrng(B,A) ) )).
fof(rc2_arytm_3,axiom,( ? [A] : ( m1_subset_1(A,k5_arytm_3) & v1_xboole_0(A) ) )).
fof(rc2_asympt_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xxreal_0(A) & v3_xxreal_0(A) & v1_xreal_0(A) ) )).
fof(rc2_bcialg_3,axiom,( ? [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) & v5_bcialg_3(A) ) )).
fof(rc2_bcialg_4,axiom,( ? [A] : ( l1_bcialg_4(A) & ~ v2_struct_0(A) & v1_bcialg_4(A) ) )).
fof(rc2_bcialg_5,axiom,( ? [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_5(A) ) )).
fof(rc2_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) & ~ v1_xboole_0(B) & v3_bciideal(B,A) ) ) )).
fof(rc2_bhsp_1,axiom,( ? [A] : ( l1_bhsp_1(A) & ~ v2_struct_0(A) & v1_bhsp_1(A) ) )).
fof(rc2_bhsp_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ? [B] : ( m2_bhsp_5(B,A) & v1_finset_1(B) ) ) )).
fof(rc2_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) => ? [D] : ( 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(D) & v1_relat_1(D) & v4_relat_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C))) & v5_relat_1(D,u1_struct_0(A)) & v1_funct_1(D) & v1_partfun1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C))) & 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) ) ) )).
fof(rc2_bintree1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) & v2_bintree1(B) ) ) )).
fof(rc2_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v1_borsuk_1(B,A) ) ) )).
fof(rc2_borsuk_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ? [C] : ( m1_borsuk_2(C,A,B,B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(k5_topmetr)) & v5_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(k5_topmetr)) & v1_funct_2(C,u1_struct_0(k5_topmetr),u1_struct_0(A)) & v5_pre_topc(C,k5_topmetr,A) ) ) )).
fof(rc2_borsuk_5,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xreal_0(A) & v1_xxreal_0(A) & ~ v1_rat_1(A) ) )).
fof(rc2_borsuk_6,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v2_pre_topc(A) & v3_topmetr(A) ) )).
fof(rc2_c0sp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ? [B] : ( m1_c0sp1(B,A) & ~ v2_struct_0(B) & v12_algstr_0(B) & v13_algstr_0(B) & v14_algstr_0(B) & v36_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v9_rlvect_1(B) & v1_group_1(B) & v3_group_1(B) & v1_vectsp_1(B) & v2_vectsp_1(B) & v3_vectsp_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & v6_vectsp_1(B) ) ) )).
fof(rc2_cantor_1,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & v1_tops_2(B,A) & v2_cantor_1(B,A) ) ) )).
fof(rc2_card_1,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v1_finset_1(A) & v1_card_1(A) ) )).
fof(rc2_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ? [B] : ( m1_subset_1(B,k8_card_3(A)) & v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) ) ) )).
fof(rc2_card_fil,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & ~ v1_finset_1(A) & v1_card_1(A) & ~ v2_card_1(A) ) )).
fof(rc2_card_lar,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) & ~ v4_card_3(A) ) => ? [B] : ( m1_subset_1(B,A) & v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) & ~ v1_finset_1(B) & v1_card_1(B) ) ) )).
fof(rc2_cat_1,axiom,( ? [A] : ( l1_cat_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) ) )).
fof(rc2_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ? [B] : ( m3_cat_2(B,A) & ~ v2_struct_0(B) & ~ v11_struct_0(B) & v14_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & v1_cat_2(B,A) ) ) )).
fof(rc2_cat_4,axiom,( ? [A] : ( l1_cat_4(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) ) )).
fof(rc2_cat_5,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v2_cat_5(A) ) )).
fof(rc2_catalan2,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v5_ordinal1(A) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v4_valued_0(A) & v1_finset_1(A) & v4_partfun3(A) & v1_afinsq_1(A) & v1_catalan2(A) ) )).
fof(rc2_catalg_1,axiom,( ? [A] : ( v1_relat_1(A) & ~ v3_relat_1(A) & v1_funct_1(A) ) )).
fof(rc2_cayldick,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),A))) & v1_relat_1(B) & v4_relat_1(B,k2_zfmisc_1(A,A)) & v5_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,k2_zfmisc_1(A,A)) & v1_funct_2(B,k2_zfmisc_1(A,A),A) & v1_binop_1(B,A) & v2_binop_1(B,A) ) )).
fof(rc2_cc0sp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v3_c0sp1(B,A) & v1_cc0sp1(B,A) ) ) )).
fof(rc2_cfdiff_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k2_numbers) & v1_funct_1(A) & v3_funct_1(A) & ~ v1_xboole_0(A) & v1_partfun1(A,k4_ordinal1) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v1_valued_0(A) ) )).
fof(rc2_cfuncdom,axiom,( ? [A] : ( l1_cfuncdom(A) & ~ v2_struct_0(A) ) )).
fof(rc2_cgames_1,axiom,( ? [A] : ( l1_cgames_1(A) & v1_cgames_1(A) ) )).
fof(rc2_chain_1,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_zfmisc_1(B) & v1_finset_1(B) ) ) )).
fof(rc2_chord,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & ~ v4_glib_000(A) & v7_glib_000(A) & v2_chord(A) ) )).
fof(rc2_circcmb3,axiom,( ! [A] : ( ( v4_circcmb3(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v4_msualg_1(B,A) & v4_msafree2(B,A) & v5_circcmb3(B,A) ) ) )).
fof(rc2_circcomb,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v2_struct_0(A) & v3_circcomb(A) ) )).
fof(rc2_circled1,axiom,( ! [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) & v8_rlvect_1(A) & l1_rlvect_1(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : ( m2_rlvect_2(C,A,B) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,k1_numbers) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k1_numbers) & v1_valued_0(C) & v2_valued_0(C) & v3_valued_0(C) & v1_circled1(C,A) ) ) )).
fof(rc2_classes2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ? [B] : ( m1_subset_1(B,A) & ~ v1_xboole_0(B) ) ) )).
fof(rc2_clopban1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) & 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) ) ) )).
fof(rc2_clopban2,axiom,( ? [A] : ( l1_clopban2(A) & v1_clopban2(A) ) )).
fof(rc2_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v2_clopban3(B,A) ) ) )).
fof(rc2_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & v1_xboole_0(C) & v4_funct_1(C) & v1_finset_1(C) ) ) )).
fof(rc2_clvect_1,axiom,( ? [A] : ( l1_clvect_1(A) & ~ v2_struct_0(A) ) )).
fof(rc2_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ? [B] : ( m1_subset_1(B,A) & v1_finset_1(B) ) ) )).
fof(rc2_collsp,axiom,( ? [A] : ( l1_collsp(A) & ~ v2_struct_0(A) & v1_collsp(A) ) )).
fof(rc2_combgras,axiom,( ! [A] : ! [B] : ( ( l1_incsp_1(A) & l1_incsp_1(B) ) => ? [C] : ( l1_combgras(C,A,B) & v5_combgras(C,A,B) ) ) )).
fof(rc2_compact1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) ) )).
fof(rc2_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v2_compl_sp(B,A) ) ) )).
fof(rc2_compos_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_compos_0(A) & v2_compos_0(A) & v3_compos_0(A) ) )).
fof(rc2_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ? [B] : ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v3_card_1(B,1) & v1_afinsq_1(B) ) ) )).
fof(rc2_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ? [B] : ( m1_subset_1(B,u1_compos_1(A)) & v6_compos_0(B,u1_compos_1(A)) ) ) )).
fof(rc2_compts_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v8_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) ) )).
fof(rc2_comput_1,axiom,( ! [A] : ! [B] : ? [C] : ( m1_rfunct_3(C,A,B) & ~ v1_xboole_0(C) & v1_comput_1(C) ) )).
fof(rc2_comseq_2,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k2_numbers) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_partfun1(A,k4_ordinal1) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v1_valued_0(A) & v2_comseq_2(A) ) )).
fof(rc2_comseq_3,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k2_numbers) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_partfun1(A,k4_ordinal1) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v1_valued_0(A) & v1_comseq_3(A) ) )).
fof(rc2_conlat_1,axiom,( ? [A] : ( l1_conlat_1(A) & v1_conlat_1(A) ) )).
fof(rc2_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v1_convex1(B,A) ) ) )).
fof(rc2_convex2,axiom,( ! [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) & v8_rlvect_1(A) & l1_rlvect_1(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : ( m2_rlvect_2(C,A,B) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,k1_numbers) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k1_numbers) & v1_valued_0(C) & v2_valued_0(C) & v3_valued_0(C) & v2_convex1(C,A) ) ) )).
fof(rc2_convex3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v1_convex3(B,A) ) ) )).
fof(rc2_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v1_convex4(B,A) ) ) )).
fof(rc2_csspace,axiom,( ? [A] : ( l1_csspace(A) & ~ v2_struct_0(A) & v1_csspace(A) ) )).
fof(rc2_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) & v1_dilworth(B,A) ) ) )).
fof(rc2_diraf,axiom,( ? [A] : ( l1_analoaf(A) & ~ v2_struct_0(A) & ~ v7_struct_0(A) & v1_analoaf(A) & v1_diraf(A) & v2_diraf(A) ) )).
fof(rc2_e_siec,axiom,( ? [A] : ( l1_e_siec(A) & v2_e_siec(A) ) )).
fof(rc2_ec_pf_1,axiom,( ! [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) ) => ? [B] : ( m1_ec_pf_1(B,A) & ~ v2_struct_0(B) & ~ v6_struct_0(B) & ~ v7_struct_0(B) & v8_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v1_group_1(B) & v3_group_1(B) & v5_group_1(B) & v1_int_3(B) & v1_vectsp_1(B) & v2_vectsp_1(B) & v3_vectsp_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & v6_vectsp_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) ) ) )).
fof(rc2_endalg,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v4_vectsp_1(A) & l4_algstr_0(A) & ~ v2_struct_0(B) & v4_vectsp_1(B) & l4_algstr_0(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v6_group_1(C,A,B) & v1_group_6(C,A,B) ) ) )).
fof(rc2_entropy1,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( m1_finseq_1(B,k3_finseq_2(k1_numbers)) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k3_finseq_2(k1_numbers)) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & v1_entropy1(B,A) ) ) )).
fof(rc2_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_eqrel_1(B,A) & ~ v1_xboole_0(B) & v1_setfam_1(B) & ~ v10_ordinal1(B) ) ) )).
fof(rc2_equation,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_msualg_2(C,A,B) & v3_msualg_1(C,A) & v4_msualg_1(C,A) & v3_msafree2(C,A) ) ) )).
fof(rc2_euclid_7,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v3_euclid_7(A) ) )).
fof(rc2_euclmetr,axiom,( ? [A] : ( l1_analmetr(A) & ~ v2_struct_0(A) & v2_analmetr(A) & v1_euclmetr(A) & v2_euclmetr(A) & v3_euclmetr(A) & v4_euclmetr(A) & v5_euclmetr(A) & v6_euclmetr(A) & v7_euclmetr(A) ) )).
fof(rc2_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => ? [D] : ( v1_relat_1(D) & v4_relat_1(D,A) & v5_relat_1(D,C) & v5_relat_1(D,k4_numbers) & v1_funct_1(D) & v1_valued_0(D) & v3_valued_0(D) & v4_valued_0(D) & v1_finset_1(D) & v1_exchsort(D) & v2_exchsort(D,B) ) ) )).
fof(rc2_extpro_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ? [B] : ( l1_extpro_1(B,A) & ~ v2_struct_0(B) ) ) )).
fof(rc2_facirc_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & ~ v1_facirc_1(A) ) )).
fof(rc2_fcont_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & v1_relat_1(A) & v4_relat_1(A,k1_numbers) & v5_relat_1(A,k1_numbers) & v1_funct_1(A) & v1_xboole_0(A) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) ) )).
fof(rc2_fdiff_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & v1_relat_1(A) & v4_relat_1(A,k1_numbers) & v5_relat_1(A,k1_numbers) & v1_funct_1(A) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v2_fdiff_1(A) ) )).
fof(rc2_fin_topo,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v8_struct_0(A) & v1_orders_2(A) & v3_orders_2(A) ) )).
fof(rc2_finseq_1,axiom,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) & v1_xboole_0(B) & v1_finset_1(B) & v1_finseq_1(B) ) )).
fof(rc2_finseq_2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v1_xboole_0(B) ) => ? [C] : ( m1_finseq_1(C,B) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,B) & v1_funct_1(C) & v1_finset_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & v2_finseq_1(C) & v4_card_3(C) ) ) )).
fof(rc2_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_finseq_1(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,A) & ~ v1_xboole_0(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) ) ) )).
fof(rc2_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_finseq_1(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,A) & ~ v1_zfmisc_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v1_finseq_6(B,A) ) ) )).
fof(rc2_finset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) )).
fof(rc2_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_fintopo6(B,A) & ~ v2_struct_0(B) & v1_orders_2(B) ) ) )).
fof(rc2_fomodel0,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) ) => ? [C] : ( m1_subset_1(C,k3_finseq_2(A)) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,A) & v1_funct_1(C) & v1_finset_1(C) & v3_card_1(C,B) & v1_finseq_1(C) & v2_finseq_1(C) & v4_card_3(C) & v2_pre_poly(C) ) ) )).
fof(rc2_fomodel1,axiom,( ? [A] : ( l4_struct_0(A) & ~ v2_struct_0(A) & ~ v6_struct_0(A) & ~ v7_struct_0(A) & ~ v8_struct_0(A) ) )).
fof(rc2_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) ) => ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k9_funct_2(B,C)))) & ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,A) & v5_relat_1(D,k9_funct_2(B,C)) & v1_funct_1(D) & v1_partfun1(D,A) & v1_funct_2(D,A,k9_funct_2(B,C)) & v1_funcop_1(D) & v2_funcop_1(D) ) ) )).
fof(rc2_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) => ? [E] : ( m1_fomodel2(E,A,B,C) & ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_finseq_2(k1_int_2(k19_fomodel1(A,C)),B)) & v5_relat_1(E,k2_xboole_0(B,k6_margrel1)) & v1_funct_1(E) & v1_partfun1(E,k4_finseq_2(k1_int_2(k19_fomodel1(A,C)),B)) & v1_funct_2(E,k4_finseq_2(k1_int_2(k19_fomodel1(A,C)),B),k2_xboole_0(B,k6_margrel1)) & v2_fomodel3(E,A,B,C,D) ) ) )).
fof(rc2_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_fomodel4(A))) & v1_relat_1(B) & v2_fomodel4(B,A) ) ) )).
fof(rc2_freealg,axiom,( ? [A] : ( m1_finseq_1(A,k4_ordinal1) & ~ v1_xboole_0(A) & v1_relat_1(A) & ~ v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) ) )).
fof(rc2_fsm_1,axiom,( ! [A] : ? [B] : ( l1_fsm_1(B,A) & ~ v2_struct_0(B) & v8_struct_0(B) ) )).
fof(rc2_fsm_2,axiom,( ! [A] : ? [B] : ( l1_fsm_2(B,A) & ~ v2_struct_0(B) ) )).
fof(rc2_fsm_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) ) => ? [C] : ( l1_fsm_3(C,A,B) & ~ v2_struct_0(C) & v8_struct_0(C) & v1_fsm_3(C,A,B) & v2_fsm_3(C,A,B) ) ) )).
fof(rc2_funcop_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v3_funct_1(A) & ~ v1_xboole_0(A) ) )).
fof(rc2_funcsdom,axiom,( ? [A] : ( l1_funcsdom(A) & v1_funcsdom(A) ) )).
fof(rc2_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) )).
fof(rc2_funct_2,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_funct_2(B,A,A) & v3_funct_2(B,A,A) ) )).
fof(rc2_funct_7,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_funct_7(A) ) )).
fof(rc2_funct_8,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v1_funct_8(A) ) )).
fof(rc2_funct_9,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v2_funct_9(A) ) )).
fof(rc2_functor1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_altcat_2(A) & l2_altcat_1(A) ) => ? [B] : ( m1_altcat_2(B,A) & ~ v2_struct_0(B) & v1_altcat_2(B) ) ) )).
fof(rc2_fvaluat1,axiom,( ? [A] : ( v1_xxreal_0(A) & v2_xxreal_0(A) & v1_fvaluat1(A) ) )).
fof(rc2_gcd_1,axiom,( ? [A] : ( l6_algstr_0(A) & ~ v2_struct_0(A) & ~ v6_struct_0(A) & ~ v7_struct_0(A) & v13_algstr_0(A) & v1_group_1(A) & v3_group_1(A) & v5_group_1(A) & v1_vectsp_1(A) & v2_vectsp_1(A) & v3_vectsp_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v1_vectsp_2(A) & v3_gcd_1(A) ) )).
fof(rc2_geomtrap,axiom,( ? [A] : ( l1_geomtrap(A) & ~ v2_struct_0(A) & v1_geomtrap(A) ) )).
fof(rc2_glib_000,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) )).
fof(rc2_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ? [B] : ( m3_glib_001(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k2_xboole_0(k6_glib_000(A),k7_glib_000(A))) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v6_glib_001(B,A) ) ) )).
fof(rc2_glib_002,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & ~ v4_glib_000(A) & v3_glib_002(A) ) )).
fof(rc2_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_glib_000(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v2_pre_poly(B) & v1_glib_000(B) & v2_glib_000(B) & v3_glib_000(B) & v5_glib_000(B) & v6_glib_000(B) & v7_glib_000(B) & v8_glib_000(B) & v9_glib_000(B,A) & v1_glib_002(B) & v2_glib_002(B) & v3_glib_002(B) & v1_glib_003(B) & v4_glib_003(B,A) & v7_glib_003(B) & v1_glib_004(B,A) ) ) )).
fof(rc2_goboard9,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v3_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) ) )).
fof(rc2_gr_cy_1,axiom,( ? [A] : ( l3_algstr_0(A) & ~ v2_struct_0(A) & v8_struct_0(A) & v15_algstr_0(A) & v1_group_1(A) & v2_group_1(A) & v3_group_1(A) & v1_gr_cy_1(A) ) )).
fof(rc2_gr_cy_3,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v7_ordinal1(A) & ~ v8_ordinal1(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & v1_int_2(A) & v1_finset_1(A) & v1_card_1(A) & v1_xxreal_0(A) & v2_xxreal_0(A) & ~ v3_xxreal_0(A) & v2_gr_cy_3(A) ) )).
fof(rc2_graph_1,axiom,( ? [A] : ( l1_graph_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_graph_1(A) ) )).
fof(rc2_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ? [B] : ( m1_graph_1(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u4_struct_0(A)) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v3_graph_2(B,A) ) ) )).
fof(rc2_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ? [B] : ( m1_graph_1(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u4_struct_0(A)) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v7_graph_1(B,A) & v3_graph_2(B,A) ) ) )).
fof(rc2_grcat_1,axiom,( ? [A] : ( l1_grcat_1(A) & v1_grcat_1(A) ) )).
fof(rc2_group_1,axiom,( ? [A] : ( l3_algstr_0(A) & ~ v2_struct_0(A) & v15_algstr_0(A) & v1_group_1(A) & v2_group_1(A) & v3_group_1(A) & v5_group_1(A) ) )).
fof(rc2_group_10,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ? [B] : ( l3_algstr_0(B) & ~ v2_struct_0(B) & v8_struct_0(B) & v15_algstr_0(B) & v1_group_1(B) & v2_group_1(B) & v3_group_1(B) & v5_group_1(B) & v1_gr_cy_1(B) & v2_group_10(B,A) ) ) )).
fof(rc2_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ? [B] : ( m1_group_2(B,A) & ~ v2_struct_0(B) & v8_struct_0(B) & v15_algstr_0(B) & v1_group_1(B) & v2_group_1(B) & v3_group_1(B) ) ) )).
fof(rc2_group_6,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_group_6(C,A,B) ) ) )).
fof(rc2_group_7,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_group_7(A) ) )).
fof(rc2_group_9,axiom,( ! [A] : ? [B] : ( l1_group_9(B,A) & ~ v2_struct_0(B) ) )).
fof(rc2_groupp_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_int_2(A) & ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ? [C] : ( m1_group_2(C,B) & ~ v2_struct_0(C) & v1_group_1(C) & v2_group_1(C) & v3_group_1(C) & v2_group_10(C,A) ) ) )).
fof(rc2_hahnban1,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),k1_numbers))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(B)) & v5_relat_1(C,k1_numbers) & v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),k1_numbers) & v4_hahnban1(C,A,B) & v7_hahnban1(C,A,B) ) ) )).
fof(rc2_hallmar1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ? [B] : ( m1_finseq_1(B,k1_zfmisc_1(A)) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v1_hallmar1(B,A) ) ) )).
fof(rc2_hermitan,axiom,( ! [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) & 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] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k1_complfld)))) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,u1_struct_0(k1_complfld)) & ~ v1_zfmisc_1(B) & v1_funct_1(B) & ~ v3_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) ) ) )).
fof(rc2_hilbert3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & m1_subset_1(B,k1_hilbert1) & m1_subset_1(C,k1_hilbert1) & m1_subset_1(D,k1_hilbert1) ) => ? [E] : ( m1_subset_1(E,k3_hilbert3(A,k3_hilbert1(B,k3_hilbert1(C,D)))) & v1_relat_1(E) & v1_funct_1(E) & v1_funcop_1(E) & v2_funcop_1(E) ) ) )).
fof(rc2_ideal_1,axiom,( ? [A] : ( l6_algstr_0(A) & ~ v2_struct_0(A) & ~ v7_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) ) )).
fof(rc2_index_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_index_1(A) ) )).
fof(rc2_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ? [B] : ( m1_instalg1(B,A) & ~ v2_struct_0(B) & v1_instalg1(B) ) ) )).
fof(rc2_int_1,axiom,( ? [A] : v1_int_1(A) )).
fof(rc2_int_2,axiom,( ? [A] : ( v1_xxreal_0(A) & ~ v3_xxreal_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v7_ordinal1(A) & ~ v8_ordinal1(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & ~ v1_int_2(A) ) )).
fof(rc2_int_3,axiom,( ? [A] : ( l6_algstr_0(A) & ~ v2_struct_0(A) & ~ v6_struct_0(A) & ~ v7_struct_0(A) & v13_algstr_0(A) & v36_algstr_0(A) & v1_group_1(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) & v2_vectsp_1(A) & v3_vectsp_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v1_vectsp_2(A) & v1_int_3(A) ) )).
fof(rc2_int_6,axiom,( ? [A] : ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) ) )).
fof(rc2_interva1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & ~ v1_xboole_0(B) & v1_interva1(B,A) ) )).
fof(rc2_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_tops_1(B,A) & v1_isomichi(B,A) & v2_isomichi(B,A) ) ) )).
fof(rc2_jordan,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) & v4_funct_1(B) & ~ v1_xboole_0(B) & v4_pre_topc(B,k15_euclid(A)) & v9_rltopsp1(B,k15_euclid(A)) & v1_convex1(B,k15_euclid(A)) ) ) )).
fof(rc2_jordan23,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_finseq_1(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,A) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v1_finseq_6(B,A) & v2_jordan23(B) ) ) )).
fof(rc2_jordan5a,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v1_finset_1(A) & v5_xxreal_2(A) ) )).
fof(rc2_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v2_knaster(B,A) & v3_knaster(B,A) ) ) )).
fof(rc2_lang1,axiom,( ? [A] : ( l1_lang1(A) & ~ v2_struct_0(A) & v1_lang1(A) ) )).
fof(rc2_lattice2,axiom,( ? [A] : ( l3_lattices(A) & ~ v2_struct_0(A) & v3_lattices(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v1_lattice2(A) ) )).
fof(rc2_lattice3,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) ) )).
fof(rc2_lattice5,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ? [B] : ( m1_yellow_0(B,A) & v1_orders_2(B) & v5_yellow_0(B,A) & v6_yellow_0(B,A) ) ) )).
fof(rc2_lattice6,axiom,( ? [A] : ( 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) & v10_lattices(A) & v13_lattices(A) & v14_lattices(A) & v4_lattice3(A) & v1_lattice6(A) ) )).
fof(rc2_lattice7,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v8_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_waybel_1(A) & v1_lattice3(A) & v2_lattice3(A) ) )).
fof(rc2_lattice8,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ? [B] : ( m1_yellow_0(B,k1_lattice5(A)) & ~ v2_struct_0(B) & ~ v7_struct_0(B) & v4_yellow_0(B,k1_lattice5(A)) & v5_yellow_0(B,k1_lattice5(A)) & v6_yellow_0(B,k1_lattice5(A)) & v1_lattice8(B) ) ) )).
fof(rc2_lattices,axiom,( ? [A] : ( l2_lattices(A) & v2_lattices(A) ) )).
fof(rc2_lopban_1,axiom,( ! [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) & 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] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) & 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) ) ) )).
fof(rc2_lopban_2,axiom,( ? [A] : ( l1_lopban_2(A) & v1_lopban_2(A) ) )).
fof(rc2_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v2_lopban_3(B,A) ) ) )).
fof(rc2_lopclset,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k5_finsub_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) )).
fof(rc2_lpspace2,axiom,( ? [A] : ( v1_xxreal_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_lpspace2(A) ) )).
fof(rc2_margrel1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_margrel1(A) ) )).
fof(rc2_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( m1_finseq_1(B,k3_finseq_2(k1_numbers)) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k3_finseq_2(k1_numbers)) & v1_funct_1(B) & v1_finseq_1(B) & v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & v2_matrix10(B) & v3_matrix10(B) ) ) )).
fof(rc2_matrix13,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_setfam_1(A) ) )).
fof(rc2_matrix17,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ? [C] : ( m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,k3_finseq_2(u1_struct_0(B))) & v1_funct_1(C) & v1_finseq_1(C) & v1_funcop_1(C) & v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & v2_matrix17(C,B,A) ) ) )).
fof(rc2_matrix_0,axiom,( ! [A] : ? [B] : ( m1_finseq_1(B,k3_finseq_2(A)) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k3_finseq_2(A)) & v1_funct_1(B) & v1_funcop_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v1_pre_poly(B) & v2_pre_poly(B) & v1_matrix_0(B) ) )).
fof(rc2_matrix_2,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v3_matrix_2(A) ) )).
fof(rc2_matrix_9,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(A),k2_finseq_1(A)))) & v1_relat_1(B) & v4_relat_1(B,k2_finseq_1(A)) & v5_relat_1(B,k2_finseq_1(A)) & v1_funct_1(B) & v2_funct_1(B) & v1_partfun1(B,k2_finseq_1(A)) & v1_funct_2(B,k2_finseq_1(A),k2_finseq_1(A)) & v1_finset_1(B) & v1_finseq_1(B) ) ) )).
fof(rc2_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_finseq_1(B,k3_finseq_2(k3_finseq_2(A))) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k3_finseq_2(k3_finseq_2(A))) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v2_matrixj1(B,A) ) ) )).
fof(rc2_matrixj2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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] : ( m1_matrixj2(C,A,B) & v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) & v1_funct_1(C) & v1_finset_1(C) & v1_finseq_1(C) & v2_finseq_1(C) & v1_funcop_1(C) & v2_funcop_1(C) & v1_matrixj1(C,u1_struct_0(A)) & v2_matrixj1(C,u1_struct_0(A)) & v1_matrixj2(C,A) ) ) )).
fof(rc2_matroid0,axiom,( ! [A] : ( ( ~ v3_pencil_1(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A) ) ) )).
fof(rc2_matrprob,axiom,( ? [A] : ( m1_finseq_1(A,k3_finseq_2(k1_numbers)) & v1_relat_1(A) & ~ v3_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k3_finseq_2(k1_numbers)) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_funcop_1(A) & v1_matrix_0(A) & v1_pre_poly(A) & v4_matrprob(A) ) )).
fof(rc2_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(A))))) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(k15_euclid(A))) & v5_relat_1(B,u1_struct_0(k15_euclid(A))) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_partfun1(B,u1_struct_0(k15_euclid(A))) & v1_funct_2(B,u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(A))) & v1_topreal9(B,A) ) ) )).
fof(rc2_measure1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & ~ v1_xboole_0(B) & v2_finsub_1(B) & v1_prob_1(B,A) ) )).
fof(rc2_measure5,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v2_measure5(A) ) )).
fof(rc2_measure6,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_setfam_1(A) ) )).
fof(rc2_membered,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v6_membered(A) ) )).
fof(rc2_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ? [B] : ( l1_memstr_0(B,A) & v13_struct_0(B,1) ) ) )).
fof(rc2_mesfunc7,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v2_valued_0(A) ) )).
fof(rc2_metric_1,axiom,( ? [A] : ( l1_metric_1(A) & ~ v2_struct_0(A) & v1_metric_1(A) ) )).
fof(rc2_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) & ~ v1_xboole_0(B) & v4_funct_1(B) & v1_mfold_1(B,A) ) ) )).
fof(rc2_midsp_1,axiom,( ? [A] : ( l1_midsp_1(A) & ~ v2_struct_0(A) ) )).
fof(rc2_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ? [B] : ( l1_midsp_3(B,A) & ~ v2_struct_0(B) ) ) )).
fof(rc2_mmlquer2,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) & v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,A) ) )).
fof(rc2_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ? [B] : ( l1_mod_2(B,A) & v2_mod_2(B,A) & v3_mod_2(B,A) ) ) )).
fof(rc2_modcat_1,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) & m3_modcat_1(B,A) ) => ? [C] : ( m1_subset_1(C,B) & v2_mod_2(C,A) & v3_mod_2(C,A) ) ) )).
fof(rc2_modelc_2,axiom,( ? [A] : ( l1_modelc_2(A) & v9_modelc_2(A) ) )).
fof(rc2_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => ? [B] : ( l1_modelc_3(B,A) & v1_modelc_3(B,A) & v3_modelc_3(B,A) ) ) )).
fof(rc2_moebius1,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v7_ordinal1(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & v1_finset_1(A) & v1_card_1(A) & v1_xxreal_0(A) & ~ v3_xxreal_0(A) & ~ v1_moebius1(A) ) )).
fof(rc2_monoid_0,axiom,( ? [A] : ( l1_struct_0(A) & v2_monoid_0(A) ) )).
fof(rc2_msafree,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & v2_msafree(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_msafree(C,A,B) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) & v1_msafree(C,A,B) ) ) )).
fof(rc2_msafree1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v4_msualg_1(B,A) & v1_msafree1(B,A) ) ) )).
fof(rc2_msafree2,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_struct_0(A) & v1_msualg_1(A) & v2_msafree2(A) ) )).
fof(rc2_msafree4,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v2_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v4_trees_3(A) & v4_card_3(A) ) )).
fof(rc2_msalimit,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v2_msalimit(A) ) )).
fof(rc2_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ? [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) & v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) ) )).
fof(rc2_msualg_1,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v2_struct_0(A) & v11_struct_0(A) & v1_msualg_1(A) ) )).
fof(rc2_msualg_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_msualg_2(C,A,B) & v3_msualg_1(C,A) ) ) )).
fof(rc2_msualg_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_msualg_4(C,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,B)) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) & v2_funcop_1(C) & v2_msualg_4(C,A,B) ) ) )).
fof(rc2_msualg_6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_msualg_4(C,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,B)) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) & v2_funcop_1(C) & v2_msualg_4(C,A,B) & v3_msualg_6(C,A,B) & v4_msualg_6(C,A,B) ) ) )).
fof(rc2_msualg_9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ? [C] : ( m3_pboole(C,A,B) & v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v2_finset_1(C) ) ) )).
fof(rc2_mycielsk,axiom,( ? [A] : ( l1_orders_2(A) & v1_mycielsk(A) ) )).
fof(rc2_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & v1_xboole_0(B) & v1_nagata_1(B,A) ) ) )).
fof(rc2_nat_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v3_ordinal1(A) ) )).
fof(rc2_nat_3,axiom,( ! [A] : ? [B] : ( 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) ) )).
fof(rc2_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ? [B] : ( m3_cat_2(B,A) & ~ v2_struct_0(B) & ~ v11_struct_0(B) & v14_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) & v4_nattra_1(B) ) ) )).
fof(rc2_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_struct_0(A)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_ndiff_1(B,A,k4_struct_0(A)) ) ) )).
fof(rc2_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,k1_numbers) & v5_relat_1(B,u1_struct_0(A)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_partfun1(B,k1_numbers) & v1_funct_2(B,k1_numbers,u1_struct_0(A)) & v2_ndiff_3(B,A) ) ) )).
fof(rc2_newton,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v7_ordinal1(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_xxreal_0(A) & ~ v3_xxreal_0(A) & v1_int_1(A) & v1_int_2(A) & v1_finset_1(A) & v1_card_1(A) ) )).
fof(rc2_nfcont_3,axiom,( ! [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) & l1_normsp_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,k1_numbers) & v5_relat_1(B,u1_struct_0(A)) & v1_xboole_0(B) & v1_funct_1(B) ) ) )).
fof(rc2_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) & v1_relat_1(B) & v4_relat_1(B,k1_numbers) & v5_relat_1(B,k1_euclid(A)) & v1_xboole_0(B) & v1_funct_1(B) & v1_funcop_1(B) & v7_valued_2(B) & v8_valued_2(B) & v9_valued_2(B) ) ) )).
fof(rc2_normsp_1,axiom,( ? [A] : ( l1_normsp_1(A) & ~ v2_struct_0(A) & v1_normsp_1(A) ) )).
fof(rc2_oposet_1,axiom,( ? [A] : ( l2_qmax_1(A) & ~ v2_struct_0(A) & v3_qmax_1(A) ) )).
fof(rc2_orders_2,axiom,( ? [A] : ( l1_orders_2(A) & v13_struct_0(A,1) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) ) )).
fof(rc2_ordinal1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) ) )).
fof(rc2_ordinal2,axiom,( ? [A] : ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) )).
fof(rc2_ordinal4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ? [B] : ( m1_subset_1(B,A) & v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) & ~ v1_xboole_0(B) ) ) )).
fof(rc2_ordinal5,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v5_ordinal1(A) & v1_finset_1(A) & v1_ordinal2(A) & v2_ordinal2(A) & v1_ordinal5(A) & v2_ordinal5(A) & v3_ordinal5(A) ) )).
fof(rc2_ordinal6,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & ~ v1_xboole_0(A) & v1_ordinal2(A) & v2_ordinal2(A) & v3_ordinal2(A) ) )).
fof(rc2_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_msualg_4(D,u1_struct_0(A),B,C) & v1_relat_1(D) & v4_relat_1(D,u1_struct_0(A)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_partfun1(D,u1_struct_0(A)) & v2_funcop_1(D) & v1_osalg_4(D,A,B,C) ) ) )).
fof(rc2_papdesaf,axiom,( ? [A] : ( l1_analoaf(A) & ~ v2_struct_0(A) & ~ v7_struct_0(A) & v1_analoaf(A) & v1_diraf(A) & v2_diraf(A) & v2_aff_2(A) & v4_aff_2(A) & v7_aff_2(A) & v11_aff_2(A) & v1_translac(A) ) )).
fof(rc2_parsp_1,axiom,( ? [A] : ( l1_parsp_1(A) & ~ v2_struct_0(A) ) )).
fof(rc2_partfun1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,A) & v1_relat_2(B) & v3_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) & v1_partfun1(B,A) ) )).
fof(rc2_partfun3,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k1_numbers) & v1_funct_1(B) & v1_partfun1(B,A) & v1_funct_2(B,A,k1_numbers) & v1_valued_0(B) & v2_valued_0(B) & v3_valued_0(B) & v1_partfun3(B) ) )).
fof(rc2_partfun4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_numbers))) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,k1_numbers) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_partfun1(B,u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v1_valued_0(B) & v2_valued_0(B) & v3_valued_0(B) & v1_pscomp_1(B,A) & v2_partfun3(B) ) ) )).
fof(rc2_pboole,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v3_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) )).
fof(rc2_pcomps_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v8_pre_topc(A) ) )).
fof(rc2_petri,axiom,( ? [A] : ( l1_petri(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_petri(A) & v2_petri(A) & v3_petri(A) ) )).
fof(rc2_petri_2,axiom,( ? [A] : ( l1_petri_2(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) ) )).
fof(rc2_polyalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ? [B] : ( l1_polyalg1(B,A) & ~ v2_struct_0(B) & v1_polyalg1(B,A) ) ) )).
fof(rc2_polyform,axiom,( ? [A] : ( l1_polyform(A) & v2_polyform(A) & v3_polyform(A) & v4_polyform(A) ) )).
fof(rc2_polynom1,axiom,( ? [A] : ( l6_algstr_0(A) & ~ v2_struct_0(A) & ~ v7_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) ) )).
fof(rc2_polynom5,axiom,( ? [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) & v1_group_1(A) & v3_group_1(A) & v5_group_1(A) & v3_vectsp_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v2_polynom5(A) ) )).
fof(rc2_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v7_struct_0(B) & l2_struct_0(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,k15_pre_poly(A)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom7(C,A,B) ) ) )).
fof(rc2_polyred,axiom,( ? [A] : ( l6_algstr_0(A) & ~ v2_struct_0(A) & ~ v6_struct_0(A) & ~ v7_struct_0(A) & v5_algstr_0(A) & v6_algstr_0(A) & v7_algstr_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v1_group_1(A) & v3_group_1(A) & v5_group_1(A) & v1_vectsp_1(A) & v2_vectsp_1(A) & v3_vectsp_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v1_vectsp_2(A) & v1_algstr_1(A) & v2_algstr_1(A) & v3_algstr_1(A) & v4_algstr_1(A) ) )).
fof(rc2_poset_1,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v1_orders_2(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_poset_1(A) ) )).
fof(rc2_pre_poly,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k5_finsub_1(A))) & ~ v1_xboole_0(B) ) )).
fof(rc2_pre_topc,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) ) )).
fof(rc2_prob_1,axiom,( ! [A] : ? [B] : ( 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) ) )).
fof(rc2_prob_4,axiom,( ! [A] : ! [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))) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,B) & v5_relat_1(C,k9_setfam_1(A)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & v1_prob_2(C) ) ) )).
fof(rc2_prvect_2,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v4_card_3(A) & v2_prvect_2(A) ) )).
fof(rc2_pscomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_numbers))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,k1_numbers) & v1_funct_1(B) & v1_partfun1(B,u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v1_valued_0(B) & v2_valued_0(B) & v3_valued_0(B) & v1_pscomp_1(B,A) ) ) )).
fof(rc2_pythtrip,axiom,( ? [A] : ( m1_subset_1(A,k4_ordinal1) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v7_ordinal1(A) & v1_xcmplx_0(A) & v1_xxreal_0(A) & ~ v3_xxreal_0(A) & v1_xreal_0(A) & v1_int_1(A) & ~ v1_abian(A) & v1_pythtrip(A) ) )).
fof(rc2_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ? [B] : ( ~ v1_xboole_0(B) & v1_qc_lang1(B,A) ) ) )).
fof(rc2_qc_trans,axiom,( ! [A] : ! [B] : ( ( v4_card_3(A) & m1_qc_lang1(A) & v4_card_3(B) & m1_qc_lang1(B) ) => ? [C] : ( m1_qc_lang1(C) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_card_3(C) & v1_qc_trans(C,A) & v1_qc_trans(C,B) ) ) )).
fof(rc2_quantal1,axiom,( ? [A] : ( l1_quantal1(A) & ~ v2_struct_0(A) ) )).
fof(rc2_ranknull,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) => ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)))) & v1_relat_1(D) & v4_relat_1(D,u1_struct_0(B)) & v5_relat_1(D,u1_struct_0(C)) & 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) ) ) )).
fof(rc2_rat_1,axiom,( ? [A] : v1_rat_1(A) )).
fof(rc2_ratfunc1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & l2_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_partfun1(B,k4_ordinal1) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & ~ v2_ratfunc1(B,A) ) ) )).
fof(rc2_rcomp_3,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v2_rcomp_1(A) & v3_rcomp_1(A) & ~ v5_xxreal_2(A) & v6_xxreal_2(A) ) )).
fof(rc2_real_1,axiom,( ? [A] : ( m1_subset_1(A,k1_numbers) & v1_xcmplx_0(A) & v1_xxreal_0(A) & v2_xxreal_0(A) & v1_xreal_0(A) ) )).
fof(rc2_relat_1,axiom,( ? [A] : ( v1_relat_1(A) & v2_relat_1(A) ) )).
fof(rc2_rewrite2,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) & v1_relat_1(B) & v3_relat_2(B) ) )).
fof(rc2_rewrite3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) ) => ? [C] : ( l1_rewrite3(C,B) & ~ v2_struct_0(C) & v8_struct_0(C) & v1_rewrite3(C,B) & v2_rewrite3(C,A,B) ) ) )).
fof(rc2_ring_1,axiom,( ! [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) & l6_algstr_0(A) ) => ? [B] : ( 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) ) ) )).
fof(rc2_ringcat1,axiom,( ? [A] : ( l1_ringcat1(A) & v2_ringcat1(A) & v3_ringcat1(A) ) )).
fof(rc2_rlaffin1,axiom,( ! [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) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & v1_xboole_0(B) & v2_rlaffin1(B,A) ) ) )).
fof(rc2_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & ~ v1_xboole_0(B) & v1_rltopsp1(B,A) ) ) )).
fof(rc2_rlvect_1,axiom,( ? [A] : ( l1_rlvect_1(A) & ~ v2_struct_0(A) ) )).
fof(rc2_rlvect_5,axiom,( ! [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) ) => ? [B] : ( m1_rlsub_1(B,A) & ~ 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) & v1_rlvect_5(B) ) ) )).
fof(rc2_robbins1,axiom,( ? [A] : ( l2_robbins1(A) & v2_robbins1(A) ) )).
fof(rc2_robbins4,axiom,( ? [A] : ( l4_robbins1(A) & ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & v10_lattices(A) & v13_lattices(A) & v14_lattices(A) & v15_lattices(A) & v10_robbins1(A) & v1_robbins3(A) & v2_robbins3(A) & v3_robbins3(A) & v8_robbins3(A) & v9_robbins3(A) & v1_robbins4(A) ) )).
fof(rc2_roughs_1,axiom,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,A) & v1_funct_1(B) & v1_finset_1(B) & v1_prob_2(B) & v1_finseq_1(B) & v2_finseq_1(B) ) )).
fof(rc2_rusub_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ? [B] : ( m1_rusub_1(B,A) & ~ v2_struct_0(B) & v12_algstr_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v9_rlvect_1(B) & v1_bhsp_1(B) & v2_bhsp_1(B) & v1_rusub_4(B) ) ) )).
fof(rc2_rvsum_1,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v3_valued_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) ) )).
fof(rc2_scm_halt,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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_pre_poly(A) & v2_scm_halt(A) ) )).
fof(rc2_scmfsa6b,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) & v2_pre_poly(A) ) )).
fof(rc2_scmfsa8a,axiom,( ? [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) & v1_amistd_2(A,k7_card_1(3),k1_scmfsa_2) & v3_amistd_2(A,k7_card_1(3),k1_scmfsa_2) & v4_amistd_1(A,k7_card_1(3),k1_scmfsa_2) ) )).
fof(rc2_scmpds_5,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) & v2_compos_1(A,k1_scmpds_2) & v2_scmpds_4(A) & v3_scmpds_4(A) ) )).
fof(rc2_scmyciel,axiom,( ? [A] : v1_scmyciel(A) )).
fof(rc2_seq_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k1_numbers) & v1_funct_1(A) & v3_funct_1(A) & ~ v1_xboole_0(A) & v1_partfun1(A,k4_ordinal1) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) ) )).
fof(rc2_seqm_3,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_partfun1(A,k4_ordinal1) & v1_funct_2(A,k4_ordinal1,k4_ordinal1) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v4_valued_0(A) & v5_valued_0(A) ) )).
fof(rc2_setfam_1,axiom,( ? [A] : ~ v2_setfam_1(A) )).
fof(rc2_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k5_finsub_1(A)) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) )).
fof(rc2_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & v1_xboole_0(B) & v1_tops_2(B,A) ) ) )).
fof(rc2_simplex1,axiom,( ! [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) & 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)) ) => ? [C] : ( m1_simplex1(C,A,B) & ~ v3_pencil_1(C) & v1_matroid0(C) & v3_matroid0(C) ) ) )).
fof(rc2_simplex2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) ) => ? [B] : ( l1_pre_topc(B) & ~ v3_pencil_1(B) & v1_matroid0(B) & v3_matroid0(B) & v1_simplex2(B,A) ) ) )).
fof(rc2_sppol_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(A) & v4_funct_1(A) & v2_compts_1(A,k15_euclid(2)) & v2_sppol_1(A) ) )).
fof(rc2_sppol_2,axiom,( ? [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_struct_0(k15_euclid(2))) & ~ v1_zfmisc_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_topreal1(A) & v2_topreal1(A) & v3_topreal1(A) ) )).
fof(rc2_sprect_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ~ v1_xboole_0(A) & v2_compts_1(A,k15_euclid(2)) & ~ v1_sppol_1(A) & ~ v2_sppol_1(A) ) )).
fof(rc2_sprect_3,axiom,( ? [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_struct_0(k15_euclid(2))) & ~ v1_xboole_0(A) & ~ v1_zfmisc_1(A) & ~ v8_ordinal1(A) & v1_funct_1(A) & ~ v3_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_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_1(A) & v1_sprect_2(A) ) )).
fof(rc2_stacks_1,axiom,( ? [A] : ( l1_stacks_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_stacks_1(A) ) )).
fof(rc2_subset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_xboole_0(B) ) )).
fof(rc2_substlat,axiom,( ! [A] : ! [B] : ? [C] : ( m1_subset_1(C,k4_partfun1(A,B)) & v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) ) )).
fof(rc2_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ? [B] : ( ~ v1_xboole_0(B) & v1_substut1(B,A) ) ) )).
fof(rc2_supinf_2,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k6_numbers)) & ~ v1_xboole_0(A) & v2_membered(A) & v4_card_3(A) & v5_supinf_2(A) ) )).
fof(rc2_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ? [B] : ( l1_symsp_1(B,A) & ~ v2_struct_0(B) ) ) )).
fof(rc2_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v6_tbsp_1(B,A) ) ) )).
fof(rc2_tdgroup,axiom,( ? [A] : ( l1_analoaf(A) & ~ v2_struct_0(A) & ~ v7_struct_0(A) & v1_analoaf(A) & v2_tdgroup(A) ) )).
fof(rc2_tdlat_3,axiom,( ? [A] : ( l1_pre_topc(A) & v1_pre_topc(A) & v3_tdlat_3(A) ) )).
fof(rc2_termord,axiom,( ? [A] : ( l2_algstr_0(A) & ~ v2_struct_0(A) & ~ v7_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) ) )).
fof(rc2_tex_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v7_struct_0(A) & v1_pre_topc(A) ) )).
fof(rc2_tex_2,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & ~ v1_zfmisc_1(B) & ~ v1_subset_1(B,A) ) ) )).
fof(rc2_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v2_tex_3(B,A) ) ) )).
fof(rc2_tex_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) & ~ v1_tex_2(B,A) ) ) )).
fof(rc2_topalg_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ? [B] : ( m1_pre_topc(B,k15_euclid(A)) & ~ v2_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v1_topalg_2(B,A) ) ) )).
fof(rc2_topalg_6,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_topalg_2),u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(k2_topalg_2)) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v4_topalg_6(B,A) ) ) )).
fof(rc2_topdim_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_topdim_1(B,A) ) ) )).
fof(rc2_topgen_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v2_pre_topc(A) & v1_orders_4(A) ) )).
fof(rc2_topgen_2,axiom,( ? [A] : ( l1_pre_topc(A) & v2_pre_topc(A) & ~ v1_topgen_2(A) ) )).
fof(rc2_topgen_4,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & v4_card_3(B) & v1_tops_2(B,A) & v2_tops_2(B,A) ) ) )).
fof(rc2_topgrp_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ? [C] : ( m1_connsp_2(C,A,B) & ~ v1_xboole_0(C) & v3_pre_topc(C,A) ) ) )).
fof(rc2_topmetr,axiom,( ! [A] : ( ( ~ 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] : ( m1_topmetr(B,A) & ~ v2_struct_0(B) & v1_metric_1(B) & v6_metric_1(B) & v7_metric_1(B) & v8_metric_1(B) & v9_metric_1(B) ) ) )).
fof(rc2_topreal8,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v3_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) ) )).
fof(rc2_toprealc,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v2_toprealc(A) ) )).
fof(rc2_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A) & v4_pre_topc(B,A) ) ) )).
fof(rc2_trees_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) )).
fof(rc2_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ? [B] : ( m1_trees_2(B,A) & ~ v1_xboole_0(B) ) ) )).
fof(rc2_trees_3,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v3_trees_3(A) ) )).
fof(rc2_trees_9,axiom,( ? [A] : ( v1_relat_1(A) & ~ v1_zfmisc_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) ) )).
fof(rc2_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v1_tsep_1(B,A) ) ) )).
fof(rc2_tsp_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & ~ v6_pre_topc(A) ) )).
fof(rc2_unialg_1,axiom,( ? [A] : ( l1_unialg_1(A) & ~ v2_struct_0(A) & v1_unialg_1(A) ) )).
fof(rc2_unialg_2,axiom,( ? [A] : ( l1_unialg_1(A) & ~ v2_struct_0(A) & v1_unialg_1(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & v2_unialg_2(A) ) )).
fof(rc2_uniroots,axiom,( ? [A] : ( l6_algstr_0(A) & ~ v2_struct_0(A) & ~ v6_struct_0(A) & ~ v7_struct_0(A) & v8_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v1_group_1(A) & v3_group_1(A) & v1_vectsp_1(A) & v2_vectsp_1(A) & v3_vectsp_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) ) )).
fof(rc2_valued_0,axiom,( ? [A] : ( v1_relat_1(A) & v5_relat_1(A,k3_numbers) & v5_relat_1(A,k4_numbers) & ~ v1_xboole_0(A) & v1_funct_1(A) & v3_funct_1(A) & v4_valued_0(A) ) )).
fof(rc2_valued_1,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) ) )).
fof(rc2_valued_2,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v12_valued_2(A) ) )).
fof(rc2_vectmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,u1_struct_0(A)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_partfun1(B,u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v2_funct_2(B,u1_struct_0(A)) & v3_vectmetr(B,A) ) ) )).
fof(rc2_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ? [B] : ( l1_vectsp_1(B,A) & ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v7_vectsp_1(B,A) ) ) )).
fof(rc2_vectsp11,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) & ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(B)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,u1_struct_0(B)) & 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) & v1_vectsp11(C,A,B) ) ) )).
fof(rc2_vectsp_1,axiom,( ? [A] : ( l5_algstr_0(A) & ~ v2_struct_0(A) & v4_vectsp_1(A) ) )).
fof(rc2_vectsp_2,axiom,( ? [A] : ( l6_algstr_0(A) & ~ v2_struct_0(A) & ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v36_algstr_0(A) & v1_group_1(A) & v3_group_1(A) & v5_group_1(A) & v1_vectsp_1(A) & v2_vectsp_1(A) & v3_vectsp_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v1_vectsp_2(A) ) )).
fof(rc2_vectsp_9,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & v1_vectsp_7(C,A,B) ) ) )).
fof(rc2_waybel10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v2_funct_1(B) & ~ v1_xboole_0(B) & v1_partfun1(B,u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v17_waybel_0(B,A,A) & v18_waybel_0(B,A,A) & v7_waybel_1(B,A) & v8_waybel_1(B,A) ) ) )).
fof(rc2_waybel11,axiom,( ? [A] : ( l1_orders_2(A) & v8_struct_0(A) & v13_struct_0(A,1) & v1_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) ) )).
fof(rc2_waybel12,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & v2_waybel12(B,A) ) ) )).
fof(rc2_waybel18,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v4_waybel_3(B) & v1_waybel18(B) ) )).
fof(rc2_waybel19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_yellow_9(B,A) & ~ v2_struct_0(B) & v2_pre_topc(B) & v1_waybel_9(B) & v1_waybel19(B) ) ) )).
fof(rc2_waybel21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( l1_waybel_0(B,A) & ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v6_waybel_0(B,A) & v7_waybel_0(B) & v8_waybel_0(B,A) & v9_waybel_0(B,A) ) ) )).
fof(rc2_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v6_waybel23(B,A) ) ) )).
fof(rc2_waybel25,axiom,( ? [A] : ( 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_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_waybel_9(A) & v4_waybel11(A) ) )).
fof(rc2_waybel26,axiom,( ? [A] : ( l1_waybel_9(A) & ~ v2_struct_0(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) & v4_waybel11(A) ) )).
fof(rc2_waybel27,axiom,( ! [A] : ! [B] : ! [C] : ? [D] : ( v1_relat_1(D) & v4_relat_1(D,k1_funct_2(A,k1_funct_2(B,C))) & v1_funct_1(D) & v1_partfun1(D,k1_funct_2(A,k1_funct_2(B,C))) & v1_waybel27(D) ) )).
fof(rc2_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_partfun1(B,u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v1_waybel28(B,A) ) ) )).
fof(rc2_waybel29,axiom,( ! [A] : ( ( ~ 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] : ( m1_yellow_9(B,A) & ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & v1_waybel_9(B) & v4_waybel11(B) & ~ v1_yellow_3(B) ) ) )).
fof(rc2_waybel30,axiom,( ? [A] : ( l1_waybel_9(A) & ~ v2_struct_0(A) & v2_pre_topc(A) & v8_pre_topc(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v24_waybel_0(A) & v25_waybel_0(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_waybel_9(A) & v2_waybel19(A) & v3_waybel_3(A) & ~ v1_yellow_3(A) & v1_compts_1(A) ) )).
fof(rc2_waybel34,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & v2_yellow_0(B) & l1_orders_2(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v17_waybel_0(C,A,B) & v22_waybel_0(C,A,B) ) ) )).
fof(rc2_waybel35,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,u1_struct_0(A)) & v1_waybel_4(B,A) & v2_waybel_4(B,A) ) ) )).
fof(rc2_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_finset_1(B) & v1_waybel_0(B,A) & v2_waybel_0(B,A) ) ) )).
fof(rc2_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_partfun1(B,u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v7_waybel_1(B,A) ) ) )).
fof(rc2_waybel_3,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v1_orders_2(A) & v2_orders_2(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) ) )).
fof(rc2_waybel_4,axiom,( ! [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] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) & v1_relat_1(B) & v5_waybel_4(B,A) & v6_waybel_4(B,A) ) ) )).
fof(rc2_waybel_6,axiom,( ! [A] : ! [B] : ( ( 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) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,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) ) ) )).
fof(rc2_waybel_7,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_yellow_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_subset_1(B,u1_struct_0(A)) & v2_waybel_0(B,A) & v13_waybel_0(B,A) ) ) )).
fof(rc2_waybel_8,axiom,( ! [A] : ! [B] : ( ( 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) & 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_yellow_2(A,A,B)))) & ~ v1_xboole_0(C) & v1_waybel_0(C,k1_yellow_2(A,A,B)) ) ) )).
fof(rc2_waybel_9,axiom,( ? [A] : ( l1_waybel_9(A) & v1_waybel_9(A) ) )).
fof(rc2_xboole_0,axiom,( ? [A] : ~ v1_xboole_0(A) )).
fof(rc2_xcmplx_0,axiom,( ? [A] : ( ~ v8_ordinal1(A) & v1_xcmplx_0(A) ) )).
fof(rc2_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xxreal_0(A) & v2_xxreal_0(A) & v1_xreal_0(A) ) )).
fof(rc2_xtuple_0,axiom,( ? [A] : v2_xtuple_0(A) )).
fof(rc2_xxreal_0,axiom,( ? [A] : ( v1_xxreal_0(A) & v2_xxreal_0(A) ) )).
fof(rc2_xxreal_2,axiom,( ? [A] : ( v6_membered(A) & v1_finset_1(A) & ~ v1_xboole_0(A) ) )).
fof(rc2_xxreal_3,axiom,( ? [A] : ( v1_xxreal_0(A) & v3_xxreal_0(A) & ~ v1_xreal_0(A) ) )).
fof(rc2_yellow12,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) & l1_pre_topc(B) ) => ? [C] : ( m3_yellow_9(C,A,B) & ~ v2_struct_0(C) & v1_pre_topc(C) & v2_pre_topc(C) ) ) )).
fof(rc2_yellow13,axiom,( ! [A] : ! [B] : ( ( l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ? [C] : ( m1_yellow13(C,A,B) & v1_yellow13(C,A,B) ) ) )).
fof(rc2_yellow14,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v1_orders_2(A) & v1_monoid_0(A) ) )).
fof(rc2_yellow16,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_partfun1(B,u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v11_quantal1(B) ) ) )).
fof(rc2_yellow21,axiom,( ? [A] : ( l2_altcat_1(A) & ~ v2_struct_0(A) & v2_altcat_1(A) & v6_altcat_1(A) & v9_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & v1_altcat_2(A) & v2_yellow18(A) & v3_yellow18(A) & v4_yellow18(A) & v1_yellow21(A) & v2_yellow21(A) & v4_yellow21(A) ) )).
fof(rc2_yellow_0,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v2_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) ) )).
fof(rc2_yellow_6,axiom,( ! [A] : ? [B] : ( 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) ) )).
fof(rc2_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_yellow_8(B,A) ) ) )).
fof(rc2_yellow_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & v2_yellow_0(B) & l1_orders_2(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v17_waybel_0(C,A,B) ) ) )).
fof(rc2_zf_refle,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ? [B] : ( 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) ) ) )).
fof(rc2_zfmisc_1,axiom,( ? [A] : ~ v1_zfmisc_1(A) )).
fof(rc2_zmodul01,axiom,( ? [A] : ( l1_zmodul01(A) & ~ v2_struct_0(A) ) )).
fof(rc2_zmodul03,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) & v1_zmodul02(B,A) ) ) )).
fof(rc3_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ? [B] : ( m1_subset_1(B,u4_struct_0(A)) & v2_abcmiz_1(B,A) ) ) )).
fof(rc3_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => ? [B] : ( m1_instalg1(B,A) & v1_instalg1(B) & v1_abcmiz_1(B) ) ) )).
fof(rc3_abian,axiom,( ? [A] : ( v1_xxreal_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & v1_abian(A) ) )).
fof(rc3_afinsq_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( v1_relat_1(B) & v5_relat_1(B,A) & v5_ordinal1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) )).
fof(rc3_algstr_1,axiom,( ? [A] : ( l2_algstr_0(A) & ~ v2_struct_0(A) & v5_algstr_0(A) & v6_algstr_0(A) & v7_algstr_0(A) & v8_algstr_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v1_algstr_1(A) & v2_algstr_1(A) & v3_algstr_1(A) & v4_algstr_1(A) ) )).
fof(rc3_algstr_4,axiom,( ! [A] : ( l3_algstr_0(A) => ? [B] : ( m1_algstr_4(B,A) & v15_algstr_0(B) ) ) )).
fof(rc3_altcat_1,axiom,( ? [A] : ( l2_altcat_1(A) & ~ v2_struct_0(A) & v6_altcat_1(A) ) )).
fof(rc3_altcat_2,axiom,( ? [A] : ( l2_altcat_1(A) & ~ v2_struct_0(A) & v1_altcat_2(A) ) )).
fof(rc3_altcat_5,axiom,( ? [A] : ( l2_altcat_1(A) & ~ v2_struct_0(A) & v2_altcat_1(A) & v6_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & v1_altcat_5(A) ) )).
fof(rc3_amistd_2,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ? [B] : ( l1_extpro_1(B,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) ) ) )).
fof(rc3_amistd_5,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ? [B] : ( l1_extpro_1(B,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) ) ) )).
fof(rc3_analmetr,axiom,( ? [A] : ( l1_analmetr(A) & ~ v2_struct_0(A) & v1_analmetr(A) & v2_analmetr(A) ) )).
fof(rc3_analoaf,axiom,( ? [A] : ( l1_analoaf(A) & ~ v2_struct_0(A) & ~ v7_struct_0(A) & v1_analoaf(A) & v2_analoaf(A) ) )).
fof(rc3_aofa_a01,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) & v4_msualg_1(B,A) & v1_aofa_a01(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( l3_msualg_1(C,A) & v4_msualg_1(C,A) & v4_msafree4(C,A,B) & v6_msafree4(C,A,k5_msafree4(A,B)) & v17_aofa_a00(C,A) & v20_aofa_a00(C,4,1,A) ) ) )).
fof(rc3_armstrng,axiom,( ? [A] : ( l1_armstrng(A) & v2_armstrng(A) ) )).
fof(rc3_asympt_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xxreal_0(A) & v1_xreal_0(A) & v1_asympt_0(A) ) )).
fof(rc3_bcialg_1,axiom,( ? [A] : ( l2_bcialg_1(A) & v2_bcialg_1(A) ) )).
fof(rc3_bcialg_3,axiom,( ? [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) & v6_bcialg_3(A) ) )).
fof(rc3_bcialg_4,axiom,( ? [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) & v1_bcialg_4(A) & v2_bcialg_4(A) ) )).
fof(rc3_bcialg_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => ? [E] : ( 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) & v8_bcialg_1(E) ) ) )).
fof(rc3_bhsp_1,axiom,( ? [A] : ( l1_bhsp_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_bhsp_1(A) & v2_bhsp_1(A) ) )).
fof(rc3_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) => ? [D] : ( 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(D) & ~ v1_zfmisc_1(D) & v1_relat_1(D) & v4_relat_1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C))) & v5_relat_1(D,u1_struct_0(A)) & v1_funct_1(D) & ~ v3_funct_1(D) & v1_partfun1(D,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C))) & 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) ) ) )).
fof(rc3_bintree1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) & v2_bintree1(A) ) )).
fof(rc3_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_borsuk_1(B,A) & ~ v1_xboole_0(B) & v1_setfam_1(B) & v2_borsuk_1(B,A) ) ) )).
fof(rc3_borsuk_2,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v1_borsuk_2(A) ) )).
fof(rc3_borsuk_5,axiom,( ? [A] : ( ~ v8_ordinal1(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_xxreal_0(A) & v1_rat_1(A) ) )).
fof(rc3_borsuk_6,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v2_compts_1(B,A) ) ) )).
fof(rc3_c0sp1,axiom,( ! [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) & v2_funcsdom(A) & v3_group_1(A) & v5_group_1(A) & v1_vectsp_1(A) & v3_vectsp_1(A) & l1_funcsdom(A) ) => ? [B] : ( m2_c0sp1(B,A) & ~ v2_struct_0(B) & v12_algstr_0(B) & v13_algstr_0(B) & v14_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v9_rlvect_1(B) & v1_funcsdom(B) & v2_funcsdom(B) & v1_group_1(B) & v3_group_1(B) & v5_group_1(B) & v1_vectsp_1(B) & v3_vectsp_1(B) & v4_vectsp_1(B) & v6_vectsp_1(B) ) ) )).
fof(rc3_card_1,axiom,( ? [A] : ~ v1_finset_1(A) )).
fof(rc3_card_3,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v4_funct_1(A) & v2_card_3(A) ) )).
fof(rc3_cat_1,axiom,( ? [A] : ( l1_cat_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_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) ) )).
fof(rc3_cat_4,axiom,( ? [A] : ( l1_cat_4(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_struct_0(A) & v2_cat_1(A) & v3_cat_1(A) & v4_cat_1(A) & v5_cat_1(A) & v6_cat_1(A) & v2_cat_4(A) ) )).
fof(rc3_cat_5,axiom,( ? [A] : ( l1_cat_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_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) & v3_cat_5(A) ) )).
fof(rc3_catalg_1,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v2_struct_0(A) & v1_msualg_1(A) & v1_instalg1(A) & v2_catalg_1(A) ) )).
fof(rc3_cayldick,axiom,( ? [A] : ( l1_cayldick(A) & v1_cayldick(A) ) )).
fof(rc3_cfdiff_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) & v1_relat_1(A) & v4_relat_1(A,k2_numbers) & v5_relat_1(A,k2_numbers) & v1_funct_1(A) & v1_partfun1(A,k2_numbers) & v1_valued_0(A) & v2_cfdiff_1(A) ) )).
fof(rc3_cfuncdom,axiom,( ? [A] : ( l1_cfuncdom(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) & v3_group_1(A) & v5_group_1(A) & v1_vectsp_1(A) & v3_vectsp_1(A) & v1_cfuncdom(A) & v2_cfuncdom(A) ) )).
fof(rc3_cgames_1,axiom,( ? [A] : ( l1_cgames_1(A) & v1_cgames_1(A) & v2_cgames_1(A) ) )).
fof(rc3_chord,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & v4_glib_000(A) & v6_chord(A) ) )).
fof(rc3_circcmb3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ? [B] : ( m1_circcmb3(B,A) & ~ v2_struct_0(B) & ~ v11_struct_0(B) & v14_struct_0(B) & v1_msualg_1(B) & v2_msafree2(B) & v1_circcomb(B) & v2_circcomb(B) & v5_circcomb(B) & v4_circcmb3(B) ) ) )).
fof(rc3_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v3_msualg_1(B,A) & v6_circcomb(B,A) ) ) )).
fof(rc3_clopban1,axiom,( ? [A] : ( l2_clvect_1(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_clopban1(A) ) )).
fof(rc3_clopban2,axiom,( ? [A] : ( l1_clopban2(A) & ~ v2_struct_0(A) ) )).
fof(rc3_closure1,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( l1_closure1(B,A) & v5_closure1(B,A) ) ) )).
fof(rc3_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) & ~ v1_xboole_0(C) & v4_funct_1(C) & v2_card_3(C) & v1_closure2(C,A,B) & v2_closure2(C,A,B) & v3_closure2(C,A,B) & v4_closure2(C,A,B) & v5_closure2(C,A,B) & v6_closure2(C,A,B) ) ) )).
fof(rc3_clvect_1,axiom,( ? [A] : ( l1_clvect_1(A) & ~ 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) ) )).
fof(rc3_cohsp_1,axiom,( ? [A] : ( v1_finset_1(A) & v1_cohsp_1(A) & v2_cohsp_1(A) ) )).
fof(rc3_collsp,axiom,( ? [A] : ( l1_collsp(A) & ~ v2_struct_0(A) & v1_collsp(A) & v2_collsp(A) & v3_collsp(A) ) )).
fof(rc3_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v3_compl_sp(B,A) ) ) )).
fof(rc3_compos_0,axiom,( ? [A] : ( v1_compos_0(A) & v5_compos_0(A) ) )).
fof(rc3_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ? [B] : ( ~ v1_xboole_0(B) & v1_zfmisc_1(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) ) )).
fof(rc3_compts_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v2_compts_1(B,A) ) ) )).
fof(rc3_comput_1,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v4_valued_0(A) ) )).
fof(rc3_comseq_3,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k2_numbers) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_partfun1(A,k4_ordinal1) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v1_valued_0(A) & v2_comseq_3(A) ) )).
fof(rc3_conlat_1,axiom,( ? [A] : ( l1_conlat_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_conlat_1(A) ) )).
fof(rc3_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v2_convex4(B,A) ) ) )).
fof(rc3_dilworth,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_finset_1(B) & v1_dilworth(B,A) ) ) )).
fof(rc3_e_siec,axiom,( ? [A] : ( l1_e_siec(A) & v3_e_siec(A) ) )).
fof(rc3_ec_pf_1,axiom,( ? [A] : ( l6_algstr_0(A) & ~ v2_struct_0(A) & ~ v6_struct_0(A) & ~ v7_struct_0(A) & v8_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v36_algstr_0(A) & v1_group_1(A) & v3_group_1(A) & v5_group_1(A) & v1_int_3(A) & v1_vectsp_1(A) & v2_vectsp_1(A) & v3_vectsp_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) ) )).
fof(rc3_eqrel_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(k9_setfam_1(A)))) & ~ v1_xboole_0(B) & v1_eqrel_1(B,A) ) )).
fof(rc3_equation,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & v1_msualg_6(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_msualg_2(C,A,B) & v1_msualg_6(C,A) ) ) )).
fof(rc3_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) & v4_funct_1(B) & v3_finseq_1(B) & v3_euclid_7(B) ) ) )).
fof(rc3_exchsort,axiom,( ! [A] : ( v3_ordinal1(A) => ? [B] : ( v1_relat_1(B) & v5_relat_1(B,k4_numbers) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_valued_0(B) & v3_valued_0(B) & v4_valued_0(B) & v1_finset_1(B) & v1_exchsort(B) & v2_exchsort(B,A) ) ) )).
fof(rc3_extpro_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ? [B] : ( l1_extpro_1(B,A) & v13_struct_0(B,1) & v2_memstr_0(B,A) ) ) )).
fof(rc3_facirc_1,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v3_card_1(B,A) & v1_finseq_1(B) & v2_finseq_1(B) & v4_card_3(B) & v2_facirc_1(B) ) ) )).
fof(rc3_fcont_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & v1_relat_1(A) & v4_relat_1(A,k1_numbers) & v5_relat_1(A,k1_numbers) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_partfun1(A,k1_numbers) & v1_funct_2(A,k1_numbers,k1_numbers) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v1_fcont_1(A) ) )).
fof(rc3_fdiff_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & v1_relat_1(A) & v4_relat_1(A,k1_numbers) & v5_relat_1(A,k1_numbers) & v1_funct_1(A) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v3_fdiff_1(A) ) )).
fof(rc3_finseq_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) ) )).
fof(rc3_finseq_5,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & ~ v1_zfmisc_1(A) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) ) )).
fof(rc3_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) )).
fof(rc3_fomodel0,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) => ? [C] : v2_fomodel0(C,A,B) ) )).
fof(rc3_fomodel1,axiom,( ? [A] : ( l1_fomodel1(A) & ~ v6_struct_0(A) ) )).
fof(rc3_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( v1_relat_1(D) & v1_funct_1(D) & v2_fomodel2(D,A,B,C) ) ) )).
fof(rc3_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) => ? [E] : ( v1_relat_1(E) & v1_funct_1(E) & v1_fomodel3(E,C,D) ) ) )).
fof(rc3_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : v1_fomodel4(B,A) ) )).
fof(rc3_freealg,axiom,( ? [A] : ( m1_finseq_1(A,k4_ordinal1) & ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) ) )).
fof(rc3_fsm_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ? [C] : ( l2_fsm_1(C,A,B) & v2_fsm_1(C,A,B) ) ) )).
fof(rc3_fsm_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ? [C] : ( l2_fsm_2(C,A,B) & v6_fsm_2(C,A,B) ) ) )).
fof(rc3_fsm_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) ) => ? [C] : ( l2_fsm_3(C,A,B) & v3_fsm_3(C,A,B) ) ) )).
fof(rc3_funcop_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) & v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,A) ) ) )).
fof(rc3_funcsdom,axiom,( ? [A] : ( l1_funcsdom(A) & ~ v2_struct_0(A) ) )).
fof(rc3_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) )).
fof(rc3_funct_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & v1_xreal_0(A) ) => ? [B] : ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_funct_9(B,A) ) ) )).
fof(rc3_functor0,axiom,( ! [A] : ! [B] : ( ( l1_altcat_1(A) & l1_altcat_1(B) ) => ? [C] : ( l2_functor0(C,A,B) & v9_functor0(C,A,B) ) ) )).
fof(rc3_fvaluat1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v2_fvaluat1(A) ) )).
fof(rc3_gcd_1,axiom,( ? [A] : ( l4_algstr_0(A) & ~ v2_struct_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v3_gcd_1(A) ) )).
fof(rc3_geomtrap,axiom,( ? [A] : ( l1_geomtrap(A) & ~ v2_struct_0(A) & v1_geomtrap(A) & v2_geomtrap(A) ) )).
fof(rc3_glib_000,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v4_glib_000(A) & v7_glib_000(A) ) )).
fof(rc3_glib_001,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & m3_glib_001(B,A) ) => ? [C] : ( m4_glib_001(C,A,B) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,k2_xboole_0(k6_glib_000(A),k7_glib_000(A))) & v1_funct_1(C) & v1_finset_1(C) & v1_finseq_1(C) & v2_finseq_1(C) & v4_glib_001(C,A) & v5_glib_001(C,A) ) ) )).
fof(rc3_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ? [B] : ( m1_glib_000(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) & v2_glib_000(B) & v4_glib_000(B) & v3_glib_002(B) ) ) )).
fof(rc3_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) ) => ? [B] : ( m1_glib_000(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) & v1_glib_003(B) & v4_glib_003(B,A) ) ) )).
fof(rc3_graph_1,axiom,( ? [A] : ( l1_graph_1(A) & v6_graph_1(A) ) )).
fof(rc3_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ? [B] : ( m1_graph_1(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u4_struct_0(A)) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v3_graph_2(B,A) ) ) )).
fof(rc3_grcat_1,axiom,( ? [A] : ( l1_grcat_1(A) & v1_grcat_1(A) & v2_grcat_1(A) ) )).
fof(rc3_group_2,axiom,( ? [A] : ( l3_algstr_0(A) & ~ v2_struct_0(A) & v8_struct_0(A) & v15_algstr_0(A) & v1_group_1(A) & v2_group_1(A) & v3_group_1(A) ) )).
fof(rc3_group_7,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v2_pralg_1(B) & v1_group_7(B) & v2_group_7(B,A) & v3_group_7(B,A) & v4_group_7(B,A) ) )).
fof(rc3_group_9,axiom,( ! [A] : ? [B] : ( l1_group_9(B,A) & ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v2_group_9(B,A) & v3_group_9(B,A) ) )).
fof(rc3_groupp_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ? [B] : ( l3_algstr_0(B) & ~ v2_struct_0(B) & v8_struct_0(B) & v1_group_1(B) & v2_group_1(B) & v3_group_1(B) & v5_group_1(B) & v1_gr_cy_1(B) & v3_groupp_1(B,A) ) ) )).
fof(rc3_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_numbers))) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,k1_numbers) & v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v4_hahnban1(B,k1_complfld,A) & v5_hahnban1(B,A) & v6_hahnban1(B,A) ) ) )).
fof(rc3_hallmar1,axiom,( ! [A] : ( v1_finset_1(A) => ? [B] : ( m1_finseq_1(B,k1_zfmisc_1(A)) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k1_zfmisc_1(A)) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v1_hallmar1(B,A) ) ) )).
fof(rc3_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ? [B] : ( 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_relat_1(B) & v4_relat_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) & v5_relat_1(B,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) & v2_bilinear(B,k1_complfld,A,A) & v4_bilinear(B,k1_complfld,A,A) & v2_hermitan(B,A,A) & v3_hermitan(B,A) & v4_hermitan(B,A) & v5_hermitan(B,A) ) ) )).
fof(rc3_hilbert3,axiom,( ? [A] : ( m1_subset_1(A,k1_hilbert1) & v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_hilbert3(A) ) )).
fof(rc3_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_ideal_1(B,A) ) ) )).
fof(rc3_index_1,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_index_1(B) ) )).
fof(rc3_instalg1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ? [B] : ( m1_instalg1(B,A) & ~ v11_struct_0(B) & v1_instalg1(B) ) ) )).
fof(rc3_int_3,axiom,( ? [A] : ( l6_algstr_0(A) & ~ v2_struct_0(A) & v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v36_algstr_0(A) & v1_group_1(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) & v2_vectsp_1(A) & v3_vectsp_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) ) )).
fof(rc3_int_6,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v1_partfun3(A) ) )).
fof(rc3_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v5_tops_1(B,A) & v6_tops_1(B,A) ) ) )).
fof(rc3_jordan,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) & v4_funct_1(B) & ~ v1_xboole_0(B) & v3_pre_topc(B,k15_euclid(A)) & v9_rltopsp1(B,k15_euclid(A)) & v1_convex1(B,k15_euclid(A)) ) ) )).
fof(rc3_jordan23,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & ~ v1_xboole_0(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) ) )).
fof(rc3_lang1,axiom,( ? [A] : ( l2_lang1(A) & v2_lang1(A) ) )).
fof(rc3_lattice5,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,k2_zfmisc_1(A,A)) & v5_relat_1(C,u1_struct_0(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) ) ) )).
fof(rc3_lattice6,axiom,( ? [A] : ( 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) & v10_lattices(A) & v13_lattices(A) & v14_lattices(A) & v4_lattice3(A) & v2_lattice6(A) ) )).
fof(rc3_lattice7,axiom,( ? [A] : ( m2_lattice7(A) & ~ v1_xboole_0(A) ) )).
fof(rc3_lattices,axiom,( ? [A] : ( l3_lattices(A) & v3_lattices(A) ) )).
fof(rc3_lexbfs,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & v13_glib_000(A) & v2_lexbfs(A) & v3_lexbfs(A) ) )).
fof(rc3_lopban_1,axiom,( ? [A] : ( l1_normsp_1(A) & ~ v2_struct_0(A) & v12_algstr_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v8_rlvect_1(A) & v9_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & v2_normsp_1(A) & v3_lopban_1(A) ) )).
fof(rc3_lopban_2,axiom,( ? [A] : ( l1_lopban_2(A) & ~ v2_struct_0(A) ) )).
fof(rc3_margrel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(A),A))) & v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(A)) & v5_relat_1(B,A) & v1_funct_1(B) & ~ v1_xboole_0(B) & v2_margrel1(B) & v3_margrel1(B,A) ) ) )).
fof(rc3_matrix10,axiom,( ? [A] : ( m1_finseq_1(A,k3_finseq_2(k1_numbers)) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k3_finseq_2(k1_numbers)) & v1_funct_1(A) & v1_finseq_1(A) & v1_matrix_0(A) & v1_matrix10(A) & v4_matrix10(A) ) )).
fof(rc3_matrix13,axiom,( ! [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] : ( m1_finseq_1(B,k3_finseq_2(u1_struct_0(A))) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k3_finseq_2(u1_struct_0(A))) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v1_funcop_1(B) & v2_funcop_1(B) & v1_matrix_0(B) & v1_matrix_1(B,A) ) ) )).
fof(rc3_matrix17,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ? [C] : ( m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,k3_finseq_2(u1_struct_0(B))) & v1_funct_1(C) & v1_finseq_1(C) & v1_funcop_1(C) & v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & v3_matrix17(C,B,A) ) ) )).
fof(rc3_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_finseq_1(B,k3_finseq_2(A)) & v1_relat_1(B) & ~ v3_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k3_finseq_2(A)) & v1_funct_1(B) & v1_funcop_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v1_pre_poly(B) & v2_pre_poly(B) & v1_matrix_0(B) ) ) )).
fof(rc3_matrix_9,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(2),k2_finseq_1(2)))) & v1_relat_1(A) & v4_relat_1(A,k2_finseq_1(2)) & v5_relat_1(A,k2_finseq_1(2)) & v1_funct_1(A) & v2_funct_1(A) & ~ v1_xboole_0(A) & v1_partfun1(A,k2_finseq_1(2)) & v1_funct_2(A,k2_finseq_1(2),k2_finseq_1(2)) & v2_funct_2(A,k2_finseq_1(2)) & v3_funct_2(A,k2_finseq_1(2),k2_finseq_1(2)) & v1_finset_1(A) & ~ v5_matrix_2(A,2) ) )).
fof(rc3_matrixj2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ? [B] : ( m1_finseq_1(B,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) & v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v1_funcop_1(B) & v2_funcop_1(B) & v1_matrixj1(B,u1_struct_0(A)) & v2_matrixj1(B,u1_struct_0(A)) & v1_matrixj2(B,A) ) ) )).
fof(rc3_matroid0,axiom,( ! [A] : ( ( ~ v3_pencil_1(A) & v1_matroid0(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) & v3_pre_topc(B,A) ) ) )).
fof(rc3_matrprob,axiom,( ? [A] : ( m1_finseq_1(A,k3_finseq_2(k1_numbers)) & v1_relat_1(A) & ~ v3_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k3_finseq_2(k1_numbers)) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_funcop_1(A) & v1_matrix_0(A) & v1_pre_poly(A) & v6_matrprob(A) ) )).
fof(rc3_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(A))))) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(k15_euclid(A))) & v5_relat_1(B,u1_struct_0(k15_euclid(A))) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_partfun1(B,u1_struct_0(k15_euclid(A))) & v1_funct_2(B,u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(A))) & v1_funcop_1(B) & v2_funcop_1(B) & v1_pre_poly(B) & v3_matrtop3(B,A) ) ) )).
fof(rc3_measure1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & ~ v1_xboole_0(B) & v4_card_3(B) ) )).
fof(rc3_measure5,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v3_measure5(A) ) )).
fof(rc3_measure6,axiom,( ? [A] : ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) )).
fof(rc3_membered,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v6_membered(A) & v7_membered(A) ) )).
fof(rc3_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ? [B] : ( l1_memstr_0(B,A) & v2_memstr_0(B,A) ) ) )).
fof(rc3_metric_1,axiom,( ? [A] : ( l1_metric_1(A) & ~ v2_struct_0(A) & v1_metric_1(A) & v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) ) )).
fof(rc3_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( l1_pre_topc(B) & ~ v2_struct_0(B) & v2_pre_topc(B) & v2_mfold_1(B,A) ) ) )).
fof(rc3_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ? [B] : ( l1_midsp_2(B,A) & v4_midsp_2(B,A) ) ) )).
fof(rc3_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ? [B] : ( l1_midsp_3(B,k1_nat_1(A,2)) & ~ v2_struct_0(B) & v2_midsp_1(B) ) ) )).
fof(rc3_mod_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : ( m1_mod_2(D,A,B,C) & v2_mod_2(D,A) & v3_mod_2(D,A) ) ) )).
fof(rc3_modelc_1,axiom,( ? [A] : ( l2_modelc_1(A) & v9_modelc_1(A) ) )).
fof(rc3_modelc_2,axiom,( ? [A] : ( l1_modelc_2(A) & ~ v2_struct_0(A) ) )).
fof(rc3_modelc_3,axiom,( ? [A] : ( m1_finseq_1(A,k4_ordinal1) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_modelc_2(A) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v4_valued_0(A) & v5_modelc_3(A) ) )).
fof(rc3_moebius1,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v7_ordinal1(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & v1_finset_1(A) & v1_card_1(A) & v1_xxreal_0(A) & ~ v3_xxreal_0(A) & v1_moebius1(A) ) )).
fof(rc3_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v3_msualg_1(B,A) & v4_msualg_1(B,A) & v4_msafree2(B,A) ) ) )).
fof(rc3_msafree4,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_msafree4(B,A) ) )).
fof(rc3_msalimit,axiom,( ? [A] : ( l1_msualg_1(A) & v2_struct_0(A) & v11_struct_0(A) & v1_msualg_1(A) ) )).
fof(rc3_msscyc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_graph_1(A) ) => ? [B] : ( m1_graph_1(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v2_funct_1(B) & ~ v1_xboole_0(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v7_graph_1(B,A) ) ) )).
fof(rc3_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ? [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) & v1_relat_1(C) & v3_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v2_finset_1(C) ) ) )).
fof(rc3_msualg_1,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_msualg_1(A) ) )).
fof(rc3_msualg_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_msualg_2(C,A,B) & v3_msualg_1(C,A) & v4_msualg_1(C,A) ) ) )).
fof(rc3_msualg_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_msualg_4(C,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,B)) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) & v2_funcop_1(C) & v2_msualg_4(C,A,B) & v3_msualg_4(C,A,B) ) ) )).
fof(rc3_mycielsk,axiom,( ! [A] : ( ( v1_mycielsk(A) & l1_orders_2(A) ) => ? [B] : ( m1_eqrel_1(B,u1_struct_0(A)) & ~ v10_ordinal1(B) & v1_finset_1(B) & v1_setfam_1(B) & v6_dilworth(B,A) ) ) )).
fof(rc3_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_partfun1(B,k4_ordinal1) & v1_funct_2(B,k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & v2_nagata_1(B,A) ) ) )).
fof(rc3_nat_1,axiom,( ? [A] : ( m1_subset_1(A,k4_ordinal1) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v7_ordinal1(A) & ~ v8_ordinal1(A) & v1_xcmplx_0(A) & v1_xxreal_0(A) & v1_xreal_0(A) & v1_finset_1(A) & v1_card_1(A) ) )).
fof(rc3_nat_3,axiom,( ! [A] : ? [B] : ( 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) ) )).
fof(rc3_nattra_1,axiom,( ? [A] : ( l1_cat_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_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) & v4_nattra_1(A) ) )).
fof(rc3_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_struct_0(A)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v3_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) ) ) )).
fof(rc3_normsp_1,axiom,( ? [A] : ( l1_normsp_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) & v3_normsp_0(A) & v4_normsp_0(A) & v1_normsp_1(A) & v2_normsp_1(A) ) )).
fof(rc3_oposet_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) & v1_relat_1(B) & v1_funct_1(B) & v1_partfun1(B,A) & v1_funct_2(B,A,A) & v1_partit_2(B) ) )).
fof(rc3_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v6_orders_2(B,A) ) ) )).
fof(rc3_ordinal1,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) & v5_ordinal1(B) ) )).
fof(rc3_ordinal5,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v4_ordinal5(A) ) )).
fof(rc3_ordinal6,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & ~ v1_xboole_0(A) & v2_ordinal6(A) ) )).
fof(rc3_osalg_1,axiom,( ? [A] : ( l3_osalg_1(A) & v3_osalg_1(A) ) )).
fof(rc3_osalg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m2_osalg_2(C,A,B) & ~ v1_xboole_0(C) & 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)) ) ) )).
fof(rc3_osalg_4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_osalg_4(C,A,B) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) & v2_funcop_1(C) & v2_msualg_4(C,A,B) ) ) )).
fof(rc3_papdesaf,axiom,( ? [A] : ( l1_analoaf(A) & ~ v2_struct_0(A) & ~ v7_struct_0(A) & v1_analoaf(A) & v1_diraf(A) & v2_aff_2(A) & v4_aff_2(A) & v7_aff_2(A) & v11_aff_2(A) & v1_translac(A) ) )).
fof(rc3_parsp_1,axiom,( ? [A] : ( l1_parsp_1(A) & ~ v2_struct_0(A) & v1_parsp_1(A) & v2_parsp_1(A) ) )).
fof(rc3_partfun1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) & v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,B) & v1_funct_1(C) & ~ v1_xboole_0(C) ) ) )).
fof(rc3_partfun3,axiom,( ? [A] : ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) ) )).
fof(rc3_pboole,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) )).
fof(rc3_pcomps_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v3_pcomps_1(A) ) )).
fof(rc3_pcs_0,axiom,( ? [A] : ( l1_pcs_0(A) & v2_pcs_0(A) ) )).
fof(rc3_pencil_1,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v11_pencil_1(B) ) )).
fof(rc3_polynom1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,k15_pre_poly(A)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,k15_pre_poly(A)) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) ) ) )).
fof(rc3_polynom7,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & ~ v7_struct_0(B) & l2_struct_0(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,k15_pre_poly(A)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & v1_polynom7(C,A,B) ) ) )).
fof(rc3_poset_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,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) ) ) )).
fof(rc3_pralg_1,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v2_pralg_1(B) ) )).
fof(rc3_pre_poly,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k5_finsub_1(A))) & ~ v1_xboole_0(B) & v1_setfam_1(B) ) ) )).
fof(rc3_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) ) ) )).
fof(rc3_prob_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,B) & v5_relat_1(C,k9_setfam_1(A)) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) ) ) )).
fof(rc3_pscomp_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),k1_numbers))) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(B)) & v5_relat_1(C,k1_numbers) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(B),k1_numbers) & v1_valued_0(C) & v2_valued_0(C) & v3_valued_0(C) & v1_pscomp_1(C,B) ) ) )).
fof(rc3_pythtrip,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xxreal_0(A) & v1_xreal_0(A) & v1_int_1(A) & v1_abian(A) & v1_pythtrip(A) ) )).
fof(rc3_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) & ~ v1_xboole_0(B) & v1_henmodel(B,A) ) ) )).
fof(rc3_qmax_1,axiom,( ? [A] : ( l2_qmax_1(A) & v3_qmax_1(A) ) )).
fof(rc3_ranknull,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) & ~ v1_vectsp_7(C,A,B) ) ) )).
fof(rc3_ratfunc1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & l5_algstr_0(A) ) => ? [B] : ( m1_ratfunc1(B,A) & ~ v4_ratfunc1(B,A) ) ) )).
fof(rc3_rcomp_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(B,A) & v4_pre_topc(B,A) & v2_connsp_1(B,A) ) ) )).
fof(rc3_relat_1,axiom,( ! [A] : ! [B] : ? [C] : ( v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,B) ) )).
fof(rc3_ringcat1,axiom,( ! [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) & 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] : ( m1_ringcat1(C,A,B) & v2_ringcat1(C) & v3_ringcat1(C) ) ) )).
fof(rc3_rlaffin1,axiom,( ! [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) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & ~ v1_xboole_0(B) & v2_rlaffin1(B,A) ) ) )).
fof(rc3_rltopsp1,axiom,( ! [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) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v2_rltopsp1(B,A) ) ) )).
fof(rc3_rlvect_5,axiom,( ! [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_rlvect_5(A) & l1_rlvect_1(A) ) => ? [B] : ( m1_rlsub_1(B,A) & ~ 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) & v1_rlvect_5(B) ) ) )).
fof(rc3_roughs_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_finseq_1(B,A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,A) & v1_funct_1(B) & v1_finset_1(B) & v1_prob_2(B) & v1_finseq_1(B) & v2_finseq_1(B) ) ) )).
fof(rc3_rusub_4,axiom,( ! [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_bhsp_1(A) & v1_rusub_4(A) & l1_bhsp_1(A) ) => ? [B] : ( m1_rusub_1(B,A) & ~ v2_struct_0(B) & v12_algstr_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v9_rlvect_1(B) & v1_bhsp_1(B) & v2_bhsp_1(B) & v1_rusub_4(B) ) ) )).
fof(rc3_rvsum_1,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_valued_0(A) & v3_valued_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) ) )).
fof(rc3_scm_halt,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) & v2_pre_poly(A) & v2_scm_halt(A) & v3_scm_halt(A) ) )).
fof(rc3_scmpds_4,axiom,( ? [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) & v4_scmpds_4(A) ) )).
fof(rc3_scmyciel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v5_finset_1(A) ) )).
fof(rc3_seqm_3,axiom,( ? [A] : ( m1_finseq_1(A,k1_numbers) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k1_numbers) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v5_valued_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) ) )).
fof(rc3_setfam_1,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ? [B] : ( m1_subset_1(B,A) & ~ v1_xboole_0(B) ) ) )).
fof(rc3_simplex0,axiom,( ! [A] : ? [B] : ( m1_simplex0(B,A) & v2_struct_0(B) & v1_pre_topc(B) & v3_pencil_1(B) & v4_simplex0(B) ) )).
fof(rc3_simplex1,axiom,( ! [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) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_card_1(B,1) & v1_rlaffin1(B,A) ) ) )).
fof(rc3_simplex2,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( m1_simplex0(B,u1_struct_0(k15_euclid(A))) & ~ v3_pencil_1(B) & v1_matroid0(B) & v3_matroid0(B) & v4_matroid0(B) & v6_simplex0(B,u1_struct_0(k15_euclid(A))) & v1_simplex1(B,k15_euclid(A)) & v2_simplex1(B,k15_euclid(A)) & v2_simplex2(B,A) ) ) )).
fof(rc3_sppol_2,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & v5_topreal1(A) ) )).
fof(rc3_sprect_1,axiom,( ? [A] : ( m1_finseq_1(A,u1_struct_0(k15_euclid(2))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_struct_0(k15_euclid(2))) & v1_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_sprect_1(A) ) )).
fof(rc3_stacks_1,axiom,( ? [A] : ( l1_stacks_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_struct_0(A) & v1_stacks_1(A) & v2_stacks_1(A) & v3_stacks_1(A) & v4_stacks_1(A) & v5_stacks_1(A) & v6_stacks_1(A) ) )).
fof(rc3_subset_1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_subset_1(B,A) ) )).
fof(rc3_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ? [B] : ( l1_symsp_1(B,A) & ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) ) ) )).
fof(rc3_taxonom2,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & v4_taxonom2(B) ) )).
fof(rc3_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_finset_1(B) ) ) )).
fof(rc3_tdlat_3,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v1_tdlat_3(A) & v2_tdlat_3(A) ) )).
fof(rc3_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),k15_pre_poly(A)))) & v1_relat_1(B) & v4_relat_1(B,k15_pre_poly(A)) & v5_relat_1(B,k15_pre_poly(A)) & v1_partfun1(B,k15_pre_poly(A)) & v1_funct_2(B,k15_pre_poly(A),k15_pre_poly(A)) & v1_relat_2(B) & v4_relat_2(B) & v6_relat_2(B) & v8_relat_2(B) & v2_bagorder(B,A) ) ) )).
fof(rc3_tex_1,axiom,( ? [A] : ( l1_pre_topc(A) & v13_struct_0(A,1) & v1_pre_topc(A) & v2_pre_topc(A) ) )).
fof(rc3_tex_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_zfmisc_1(B) & v1_subset_1(B,u1_struct_0(A)) ) ) )).
fof(rc3_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v1_tsep_1(B,A) & v1_tex_3(B,A) ) ) )).
fof(rc3_topalg_2,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) & ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v6_xxreal_2(A) ) )).
fof(rc3_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_topalg_6(A)) & v1_relat_1(B) & v1_funct_1(B) & v7_topalg_6(B,A) ) ) )).
fof(rc3_topdim_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v2_pre_topc(A) & v3_topdim_1(A) ) )).
fof(rc3_topgen_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v2_pre_topc(A) & v7_pre_topc(A) ) )).
fof(rc3_topgen_4,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v2_pre_topc(A) & v5_waybel23(A) ) )).
fof(rc3_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_tops_1(B,A) ) ) )).
fof(rc3_topmetr,axiom,( ? [A] : ( l1_struct_0(A) & ~ v2_struct_0(A) & v3_topmetr(A) ) )).
fof(rc3_toprealc,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k3_topmetr)))) & v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,u1_struct_0(k3_topmetr)) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_partfun1(B,u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k3_topmetr)) & v1_valued_0(B) & v2_valued_0(B) & v3_valued_0(B) & v5_pre_topc(B,A,k3_topmetr) ) ) )).
fof(rc3_tops_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v3_pre_topc(B,A) & v4_pre_topc(B,A) ) ) )).
fof(rc3_trees_1,axiom,( ? [A] : v2_trees_1(A) )).
fof(rc3_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ? [B] : ( m1_trees_2(B,A) & v2_trees_2(B,A) ) ) )).
fof(rc3_trees_3,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_trees_3)) & ~ v1_xboole_0(A) & v1_trees_3(A) & v2_trees_3(A) ) )).
fof(rc3_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ? [B] : ( m1_subset_1(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k4_ordinal1) & v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) ) ) )).
fof(rc3_tsp_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & ~ v7_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v6_pre_topc(A) ) )).
fof(rc3_unialg_1,axiom,( ? [A] : ( l1_unialg_1(A) & ~ v2_struct_0(A) & v1_unialg_1(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) ) )).
fof(rc3_valued_0,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k4_ordinal1) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & v1_funct_2(A,k4_ordinal1,k4_ordinal1) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v4_valued_0(A) & v5_valued_0(A) ) )).
fof(rc3_valued_1,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) ) )).
fof(rc3_vectmetr,axiom,( ? [A] : ( l1_vectmetr(A) & v4_vectmetr(A) ) )).
fof(rc3_vectsp10,axiom,( ! [A] : ( ( ~ 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] : ( l1_vectsp_1(B,A) & ~ v2_struct_0(B) & v13_algstr_0(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) ) ) )).
fof(rc3_vectsp_1,axiom,( ? [A] : ( l3_algstr_0(A) & ~ v2_struct_0(A) & v3_group_1(A) & v5_group_1(A) ) )).
fof(rc3_vectsp_2,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( l1_vectsp_2(B,A) & v2_vectsp_2(B,A) ) ) )).
fof(rc3_vectsp_9,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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] : ( m1_vectsp_4(C,A,B) & ~ 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) & v1_matrlin(C,A) ) ) )).
fof(rc3_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_waybel11(B,A) & v3_waybel11(B,A) ) ) )).
fof(rc3_waybel12,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_finset_1(B) & v4_card_3(B) & v3_waybel12(B,A) ) ) )).
fof(rc3_waybel19,axiom,( ! [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] : ( m1_yellow_9(B,A) & ~ 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) & v1_yellow_0(B) & v2_yellow_0(B) & v3_yellow_0(B) & v24_waybel_0(B) & v25_waybel_0(B) & v1_waybel_9(B) & ~ v1_yellow_3(B) & v2_waybel19(B) ) ) )).
fof(rc3_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v7_waybel23(B,A) ) ) )).
fof(rc3_waybel27,axiom,( ! [A] : ! [B] : ! [C] : ? [D] : ( v1_relat_1(D) & v4_relat_1(D,k1_funct_2(k2_zfmisc_1(A,B),C)) & v1_funct_1(D) & v1_partfun1(D,k1_funct_2(k2_zfmisc_1(A,B),C)) & v2_waybel27(D) ) )).
fof(rc3_waybel32,axiom,( ! [A] : ( ( ~ 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] : ( m1_yellow_9(B,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) ) ) )).
fof(rc3_waybel34,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & l1_orders_2(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v18_waybel_0(C,A,B) & v21_waybel_0(C,A,B) ) ) )).
fof(rc3_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_yellow_0(B,A) & ~ v2_struct_0(B) & v1_orders_2(B) & v4_yellow_0(B,A) & v7_yellow_0(B,A) & v8_yellow_0(B,A) ) ) )).
fof(rc3_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_partfun1(B,u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v8_waybel_1(B,A) ) ) )).
fof(rc3_waybel_3,axiom,( ! [A] : ? [B] : ( 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) ) )).
fof(rc3_waybel_6,axiom,( ! [A] : ( ( 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] : ( 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) & v1_waybel_6(B,A) ) ) )).
fof(rc3_waybel_7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ? [B] : ( 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) & v1_waybel_7(B,A) ) ) )).
fof(rc3_waybel_9,axiom,( ? [A] : ( l1_waybel_9(A) & v8_struct_0(A) & v13_struct_0(A,1) & v1_tdlat_3(A) & v3_orders_2(A) & v1_waybel_9(A) ) )).
fof(rc3_wellfnd1,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_wellfnd1(B,A) ) ) )).
fof(rc3_xreal_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xxreal_0(A) & v3_xxreal_0(A) & v1_xreal_0(A) ) )).
fof(rc3_xtuple_0,axiom,( ? [A] : v3_xtuple_0(A) )).
fof(rc3_xxreal_0,axiom,( ? [A] : ( v1_xxreal_0(A) & v3_xxreal_0(A) ) )).
fof(rc3_xxreal_2,axiom,( ? [A] : ( v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_membered(A) & v5_membered(A) & v6_membered(A) & ~ v1_xboole_0(A) & v1_xxreal_2(A) & v5_xxreal_2(A) ) )).
fof(rc3_yellow12,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) & l1_pre_topc(B) ) => ? [C] : ( m3_yellow_9(C,B,A) & ~ v2_struct_0(C) & v1_pre_topc(C) & v2_pre_topc(C) ) ) )).
fof(rc3_yellow13,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ? [C] : ( m1_yellow13(C,A,B) & ~ v1_xboole_0(C) & v1_yellow13(C,A,B) ) ) )).
fof(rc3_yellow14,axiom,( ! [A] : ( ( v1_monoid_0(A) & l1_struct_0(A) ) => ? [B] : ( l1_waybel_0(B,A) & v6_waybel_0(B,A) & v1_yellow14(B,A) ) ) )).
fof(rc3_yellow16,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v4_waybel_3(B) & v1_yellow16(B) ) )).
fof(rc3_yellow21,axiom,( ? [A] : ( v1_relat_1(A) & v2_wellord1(A) ) )).
fof(rc3_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_yellow_0(B,A) & v1_orders_2(B) & v4_yellow_0(B,A) ) ) )).
fof(rc3_yellow_6,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v1_orders_2(A) & v4_orders_2(A) & v7_waybel_0(A) ) )).
fof(rc3_yellow_8,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v2_pre_topc(A) & v4_yellow_8(A) ) )).
fof(rc3_yellow_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & l1_orders_2(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v18_waybel_0(C,A,B) ) ) )).
fof(rc3_zmodul01,axiom,( ? [A] : ( l1_zmodul01(A) & ~ 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) ) )).
fof(rc3_zmodul03,axiom,( ? [A] : ( l1_zmodul01(A) & ~ v2_struct_0(A) & v5_algstr_0(A) & v6_algstr_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v1_algstr_1(A) & v2_algstr_1(A) & v3_algstr_1(A) & v4_algstr_1(A) & v1_zmodul01(A) & v2_zmodul01(A) & v3_zmodul01(A) & v4_zmodul01(A) & v5_zmodul01(A) & v1_zmodul03(A) ) )).
fof(rc4_abcmiz_0,axiom,( ? [A] : ( l2_abcmiz_0(A) & v7_abcmiz_0(A) ) )).
fof(rc4_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ? [B] : ( m1_subset_1(B,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) & ~ v1_xtuple_0(B) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) & v5_abcmiz_1(B,A,k28_abcmiz_1(A)) ) ) )).
fof(rc4_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ? [B] : ( m1_instalg1(B,A) & ~ v2_struct_0(B) & ~ v11_struct_0(B) & v14_struct_0(B) & v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) ) ) )).
fof(rc4_abian,axiom,( ? [A] : ( v1_xxreal_0(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & ~ v1_abian(A) ) )).
fof(rc4_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) & v3_card_1(B,A) ) ) )).
fof(rc4_algstr_0,axiom,( ? [A] : ( l2_algstr_0(A) & v8_algstr_0(A) ) )).
fof(rc4_algstr_1,axiom,( ? [A] : ( l4_algstr_0(A) & ~ v2_struct_0(A) & v21_algstr_0(A) & v22_algstr_0(A) & v4_vectsp_1(A) & v5_algstr_1(A) ) )).
fof(rc4_algstr_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ? [B] : ( m1_algstr_4(B,A) & ~ v2_struct_0(B) ) ) )).
fof(rc4_altcat_1,axiom,( ! [A] : ! [B] : ( ( v4_funct_1(A) & v4_funct_1(B) ) => ? [C] : ( 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_funcop_1(C) & v2_funcop_1(C) & v7_altcat_1(C) ) ) )).
fof(rc4_altcat_2,axiom,( ? [A] : ( l2_altcat_1(A) & v2_struct_0(A) & v6_altcat_1(A) ) )).
fof(rc4_altcat_5,axiom,( ? [A] : ( l2_altcat_1(A) & ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & v4_altcat_5(A) ) )).
fof(rc4_amistd_2,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ? [B] : ( l1_extpro_1(B,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) & v2_amistd_2(B,A) ) ) )).
fof(rc4_amistd_5,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ? [B] : ( l1_extpro_1(B,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) ) ) )).
fof(rc4_analmetr,axiom,( ? [A] : ( l1_analmetr(A) & ~ v2_struct_0(A) & v1_analmetr(A) & v3_analmetr(A) ) )).
fof(rc4_analoaf,axiom,( ? [A] : ( l1_analoaf(A) & ~ v2_struct_0(A) & ~ v7_struct_0(A) & v1_analoaf(A) & v2_analoaf(A) & v3_analoaf(A) ) )).
fof(rc4_aofa_a01,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(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] : ( l1_aofa_a00(C,A) & v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_msafree1(C,A) & v1_aofa_a01(C,A) ) ) )).
fof(rc4_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) => ? [D] : ( m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) & v1_relat_1(D) & v4_relat_1(D,k2_zfmisc_1(k9_funct_2(B,k4_numbers),u1_struct_0(A))) & v5_relat_1(D,k9_funct_2(B,k4_numbers)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_partfun1(D,k2_zfmisc_1(k9_funct_2(B,k4_numbers),u1_struct_0(A))) & v1_funct_2(D,k2_zfmisc_1(k9_funct_2(B,k4_numbers),u1_struct_0(A)),k9_funct_2(B,k4_numbers)) & v1_funcop_1(D) & v2_funcop_1(D) & v13_aofa_000(D,A,k9_funct_2(B,k4_numbers)) & v14_aofa_000(D,A,k9_funct_2(B,k4_numbers)) & v1_aofa_i00(D,A,B,C) ) ) )).
fof(rc4_armstrng,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k9_setfam_1(A)) & v5_relat_1(B,k9_setfam_1(A)) & v1_finset_1(B) ) )).
fof(rc4_asympt_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xxreal_0(A) & ~ v3_xxreal_0(A) & v1_xreal_0(A) ) )).
fof(rc4_bcialg_1,axiom,( ? [A] : ( l2_bcialg_1(A) & ~ v2_struct_0(A) & v2_bcialg_1(A) ) )).
fof(rc4_bcialg_4,axiom,( ? [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) & v1_bcialg_4(A) & v2_bcialg_4(A) ) )).
fof(rc4_bilinear,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) & ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ? [C] : ( 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(C) & v1_relat_1(C) & v4_relat_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) & v5_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & v1_partfun1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) & v7_bilinear(C,A,B) ) ) )).
fof(rc4_bintree1,axiom,( ? [A] : ( l1_lang1(A) & ~ v2_struct_0(A) & v1_lang1(A) & v1_dtconstr(A) & v2_dtconstr(A) & v3_dtconstr(A) & v3_bintree1(A) ) )).
fof(rc4_borsuk_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & m1_subset_1(B,u1_struct_0(A)) ) => ? [C] : ( m1_borsuk_2(C,A,B,B) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(k5_topmetr)) & v5_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & v3_funct_1(C) & v1_partfun1(C,u1_struct_0(k5_topmetr)) & v1_funct_2(C,u1_struct_0(k5_topmetr),u1_struct_0(A)) ) ) )).
fof(rc4_borsuk_5,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( 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) ) ) )).
fof(rc4_card_1,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v7_ordinal1(A) & ~ v8_ordinal1(A) & v1_card_1(A) ) )).
fof(rc4_card_3,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v3_card_3(A) ) )).
fof(rc4_cat_5,axiom,( ? [A] : ( l1_cat_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_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) & v1_cat_5(A) & v3_cat_5(A) & v4_cat_5(A) ) )).
fof(rc4_catalg_1,axiom,( ! [A] : ? [B] : ( m1_catalg_1(B,A) & v1_msualg_1(B) & v1_instalg1(B) & v2_catalg_1(B) ) )).
fof(rc4_cayldick,axiom,( ? [A] : ( l1_cayldick(A) & ~ v7_struct_0(A) & v1_cayldick(A) ) )).
fof(rc4_cfdiff_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) & v1_relat_1(A) & v4_relat_1(A,k2_numbers) & v5_relat_1(A,k2_numbers) & v1_funct_1(A) & v1_partfun1(A,k2_numbers) & v1_valued_0(A) & v3_cfdiff_1(A) ) )).
fof(rc4_cgames_1,axiom,( ? [A] : v2_cgames_1(A) )).
fof(rc4_chord,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & ~ v4_glib_000(A) & v7_glib_000(A) & v6_chord(A) ) )).
fof(rc4_circcmb3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v4_circcmb3(B) & m1_circcmb3(B,A) ) => ? [C] : ( m2_circcmb3(C,A,B) & v3_msualg_1(C,B) & v4_msualg_1(C,B) & v4_msafree2(C,B) & v4_circcomb(C,B) & v5_circcmb3(C,B) ) ) )).
fof(rc4_circcomb,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_struct_0(A) & v1_msualg_1(A) & v1_circcomb(A) & v2_circcomb(A) & v3_circcomb(A) & v5_circcomb(A) ) )).
fof(rc4_clopban2,axiom,( ? [A] : ( 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) & v1_clopban2(A) ) )).
fof(rc4_closure1,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( l1_closure1(B,A) & v4_msualg_1(B,A) & v5_closure1(B,A) & v6_closure1(B,A) & v7_closure1(B,A) & v8_closure1(B,A) & v9_closure1(B,A) & v10_closure1(B,A) & v11_closure1(B,A) ) ) )).
fof(rc4_clvect_1,axiom,( ! [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) ) => ? [B] : ( 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) & v1_clvect_1(B) & v2_clvect_1(B) & v3_clvect_1(B) & v4_clvect_1(B) & v5_clvect_1(B) ) ) )).
fof(rc4_cohsp_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_finset_1(B) & v1_cohsp_1(B) & v2_cohsp_1(B) ) ) )).
fof(rc4_collsp,axiom,( ? [A] : ( l1_collsp(A) & ~ v2_struct_0(A) & v1_collsp(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) ) )).
fof(rc4_compl_sp,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k9_setfam_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & v4_compl_sp(B,A) ) ) )).
fof(rc4_compos_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_compos_0(A) & v2_compos_0(A) & v3_compos_0(A) & v5_compos_0(A) ) )).
fof(rc4_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ? [B] : ( ~ v1_xboole_0(B) & v1_zfmisc_1(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) & v1_afinsq_1(B) & v3_compos_1(B,A) & v4_compos_1(B,A) ) ) )).
fof(rc4_compts_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & ~ v1_xboole_0(B) & v1_tops_2(B,A) ) ) )).
fof(rc4_comput_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_margrel1(A) ) )).
fof(rc4_comseq_3,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k2_numbers) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_partfun1(A,k4_ordinal1) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v1_valued_0(A) & v2_comseq_3(A) ) )).
fof(rc4_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l5_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) )).
fof(rc4_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v2_convex4(B,A) ) ) )).
fof(rc4_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_dilworth(B,A) ) ) )).
fof(rc4_e_siec,axiom,( ? [A] : ( l1_e_siec(A) & v1_e_siec(A) & v2_e_siec(A) & v3_e_siec(A) ) )).
fof(rc4_ec_pf_1,axiom,( ? [A] : ( l6_algstr_0(A) & ~ v2_struct_0(A) & ~ v6_struct_0(A) & ~ v7_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v1_group_1(A) & v3_group_1(A) & v5_group_1(A) & v1_int_3(A) & v1_vectsp_1(A) & v2_vectsp_1(A) & v3_vectsp_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v1_ec_pf_1(A) ) )).
fof(rc4_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_eqrel_1(B,A) & ~ v1_xboole_0(B) & v1_setfam_1(B) & ~ v10_ordinal1(B) ) ) )).
fof(rc4_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) & v4_funct_1(B) & v3_finseq_1(B) & v5_euclid_7(B,A) ) ) )).
fof(rc4_exchsort,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & ~ v1_xboole_0(B) ) => ? [C] : ( v1_relat_1(C) & v5_relat_1(C,B) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_exchsort(C) & v2_exchsort(C,A) ) ) )).
fof(rc4_extpro_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ? [B] : ( l1_extpro_1(B,A) & ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_extpro_1(B,A) ) ) )).
fof(rc4_facirc_1,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v4_card_3(A) & v2_facirc_1(A) ) )).
fof(rc4_finseq_1,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) ) )).
fof(rc4_finset_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) ) => ? [C] : ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v5_funct_1(C,B) & v1_finset_1(C) ) ) )).
fof(rc4_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : v3_fomodel0(B,A) ) )).
fof(rc4_fomodel1,axiom,( ? [A] : ( l1_fomodel1(A) & ~ v2_struct_0(A) & ~ v6_struct_0(A) & ~ v7_struct_0(A) & v11_fomodel1(A) ) )).
fof(rc4_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) ) => ? [C] : ( m1_subset_1(C,k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & ~ v8_ordinal1(C) & v1_finset_1(C) & v1_finseq_1(C) & v2_finseq_1(C) & v2_pre_poly(C) & v3_fomodel2(C,A,B) ) ) )).
fof(rc4_fomodel3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) & v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,B) & v2_funct_2(C,B) ) ) )).
fof(rc4_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : v2_fomodel4(B,A) ) )).
fof(rc4_freealg,axiom,( ? [A] : ( l1_unialg_1(A) & ~ v2_struct_0(A) & v1_unialg_1(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & v3_freealg(A) ) )).
fof(rc4_fsm_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ? [C] : ( l2_fsm_2(C,A,B) & ~ v2_struct_0(C) & v6_fsm_2(C,A,B) ) ) )).
fof(rc4_fsm_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) ) => ? [C] : ( l2_fsm_3(C,A,B) & ~ v2_struct_0(C) & v8_struct_0(C) & v3_fsm_3(C,A,B) & v4_fsm_3(C,A,B) ) ) )).
fof(rc4_funcop_1,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) )).
fof(rc4_funcsdom,axiom,( ? [A] : ( l1_funcsdom(A) & ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v1_vectsp_1(A) & v3_vectsp_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) & v1_funcsdom(A) & v2_funcsdom(A) ) )).
fof(rc4_funct_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) )).
fof(rc4_functor0,axiom,( ! [A] : ! [B] : ( ( l1_altcat_1(A) & l1_altcat_1(B) ) => ? [C] : ( l2_functor0(C,A,B) & v10_functor0(C,A,B) ) ) )).
fof(rc4_fvaluat1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k6_numbers) & v1_funct_1(B) & v1_funct_2(B,A,k6_numbers) & v2_fvaluat1(B) ) )).
fof(rc4_gcd_1,axiom,( ? [A] : ( l5_algstr_0(A) & ~ v2_struct_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v3_gcd_1(A) ) )).
fof(rc4_geomtrap,axiom,( ? [A] : ( l1_analoaf(A) & ~ v2_struct_0(A) & v1_analoaf(A) & v3_geomtrap(A) ) )).
fof(rc4_glib_000,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & ~ v4_glib_000(A) & v7_glib_000(A) ) )).
fof(rc4_glib_001,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_001(B,A) & m3_glib_001(B,A) ) => ? [C] : ( m4_glib_001(C,A,B) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,k2_xboole_0(k6_glib_000(A),k7_glib_000(A))) & v1_funct_1(C) & v1_finset_1(C) & v1_finseq_1(C) & v2_finseq_1(C) & v2_glib_001(C,A) & v4_glib_001(C,A) & v5_glib_001(C,A) ) ) )).
fof(rc4_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ? [B] : ( m1_glib_000(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) & v4_glib_002(B,A) ) ) )).
fof(rc4_grcat_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_grcat_1(C,A,B) & v1_grcat_1(C) & v2_grcat_1(C) ) ) )).
fof(rc4_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ? [C] : ( m1_group_9(C,A,B) & ~ v2_struct_0(C) & v1_group_1(C) & v2_group_1(C) & v3_group_1(C) & v2_group_9(C,A) & v3_group_9(C,A) ) ) )).
fof(rc4_groupp_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_int_2(A) & ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ? [C] : ( m1_group_2(C,B) & ~ v2_struct_0(C) & v8_struct_0(C) & v1_group_1(C) & v2_group_1(C) & v3_group_1(C) & v3_groupp_1(C,A) ) ) )).
fof(rc4_hermitan,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) & ~ v2_struct_0(B) & l1_vectsp_1(B,k1_complfld) ) => ? [C] : ( 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_relat_1(C) & v4_relat_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))) & v5_relat_1(C,u1_struct_0(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) ) ) )).
fof(rc4_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v2_ideal_1(B,A) ) ) )).
fof(rc4_index_1,axiom,( ! [A] : ! [B] : ? [C] : ( m1_index_1(C,A,B) & v2_index_1(C,A,B) & v3_index_1(C,A,B) ) )).
fof(rc4_int_3,axiom,( ? [A] : ( l6_algstr_0(A) & ~ v2_struct_0(A) & ~ v8_struct_0(A) & v13_algstr_0(A) & v36_algstr_0(A) & v1_group_1(A) & v3_group_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v1_vectsp_1(A) & v2_vectsp_1(A) & v3_vectsp_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v6_vectsp_1(A) ) )).
fof(rc4_int_6,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v1_partfun3(A) & v1_int_6(A) ) )).
fof(rc4_lang1,axiom,( ? [A] : ( l2_lang1(A) & ~ v2_struct_0(A) ) )).
fof(rc4_lattices,axiom,( ? [A] : ( l2_lattices(A) & v13_struct_0(A,1) & v2_lattices(A) ) )).
fof(rc4_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ? [B] : ( m1_lexbfs(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v4_lexbfs(B,A) ) ) )).
fof(rc4_lopban_2,axiom,( ? [A] : ( 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) & v1_lopban_2(A) ) )).
fof(rc4_margrel1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v2_margrel1(A) ) )).
fof(rc4_matrix10,axiom,( ? [A] : ( m1_finseq_1(A,k3_finseq_2(k1_numbers)) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k3_finseq_2(k1_numbers)) & v1_funct_1(A) & v1_finseq_1(A) & v1_matrix_0(A) & v2_matrix10(A) & v3_matrix10(A) ) )).
fof(rc4_matrix17,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ? [C] : ( m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,k3_finseq_2(u1_struct_0(B))) & v1_funct_1(C) & v1_finseq_1(C) & v1_funcop_1(C) & v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & v4_matrix17(C,u1_struct_0(B)) ) ) )).
fof(rc4_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & v7_ordinal1(C) ) => ? [D] : ( m1_finseq_1(D,k3_finseq_2(A)) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,k3_finseq_2(A)) & v1_funct_1(D) & v1_funcop_1(D) & v1_finset_1(D) & v1_finseq_1(D) & v2_finseq_1(D) & v1_pre_poly(D) & v2_pre_poly(D) & v1_matrix_0(D) & v2_matrix_0(D,A,B,C) ) ) )).
fof(rc4_matrix_9,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(A),k2_finseq_1(A)))) & v1_relat_1(B) & v4_relat_1(B,k2_finseq_1(A)) & v5_relat_1(B,k2_finseq_1(A)) & v1_funct_1(B) & v2_funct_1(B) & v1_partfun1(B,k2_finseq_1(A)) & v1_funct_2(B,k2_finseq_1(A),k2_finseq_1(A)) & v2_funct_2(B,k2_finseq_1(A)) & v3_funct_2(B,k2_finseq_1(A),k2_finseq_1(A)) & v1_finset_1(B) & v5_matrix_2(B,A) ) ) )).
fof(rc4_matrixj2,axiom,( ! [A] : ! [B] : ( ( l6_algstr_0(A) & ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(B)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(B)) & v2_matrixj2(C,A,B) ) ) )).
fof(rc4_matroid0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v4_taxonom2(A) & v1_setfam_1(A) ) )).
fof(rc4_measure1,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & ~ v1_xboole_0(B) & v1_prob_1(B,A) & v3_measure1(B,A) ) )).
fof(rc4_measure5,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v4_measure5(A) ) )).
fof(rc4_measure6,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v1_setfam_1(A) ) )).
fof(rc4_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ? [B] : ( l1_memstr_0(B,A) & ~ v2_struct_0(B) & v7_struct_0(B) & v8_struct_0(B) & v13_struct_0(B,1) & v1_memstr_0(B,A) & v2_memstr_0(B,A) & v3_memstr_0(B,A) ) ) )).
fof(rc4_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( l1_pre_topc(B) & ~ v2_struct_0(B) & v2_pre_topc(B) & v8_pre_topc(B) & v5_waybel23(B) & v2_mfold_1(B,A) ) ) )).
fof(rc4_modelc_1,axiom,( ? [A] : ( l2_modelc_1(A) & ~ v2_struct_0(A) ) )).
fof(rc4_modelc_2,axiom,( ? [A] : ( l1_modelc_2(A) & ~ v2_struct_0(A) & v10_modelc_2(A) ) )).
fof(rc4_modelc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( l2_modelc_3(B,A) & v7_modelc_3(B,A) ) ) )).
fof(rc4_msafree2,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v2_struct_0(A) & v8_struct_0(A) & ~ v11_struct_0(A) & v14_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) ) )).
fof(rc4_msafree4,axiom,( ! [A] : ( v4_card_3(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v2_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) ) ) )).
fof(rc4_msscyc_1,axiom,( ? [A] : ( l1_graph_1(A) & ~ v2_struct_0(A) & v14_struct_0(A) & v3_msscyc_1(A) ) )).
fof(rc4_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v2_finset_1(B) ) => ? [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) & v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v2_finset_1(C) ) ) )).
fof(rc4_mycielsk,axiom,( ? [A] : ( l1_orders_2(A) & v2_mycielsk(A) ) )).
fof(rc4_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_partfun1(B,k4_ordinal1) & v1_funct_2(B,k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & v3_nagata_1(B,A) ) ) )).
fof(rc4_ndiff_1,axiom,( ! [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) & 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] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & v2_ndiff_1(C,A,B) ) ) )).
fof(rc4_oposet_1,axiom,( ? [A] : ( l2_qmax_1(A) & ~ v2_struct_0(A) & v1_oposet_1(A) ) )).
fof(rc4_orders_2,axiom,( ? [A] : ( l1_orders_2(A) & v2_struct_0(A) & v1_orders_2(A) ) )).
fof(rc4_orders_3,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v4_orders_3(A) ) )).
fof(rc4_ordinal1,axiom,( ? [A] : v7_ordinal1(A) )).
fof(rc4_ordinal5,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v5_ordinal5(A) ) )).
fof(rc4_ordinal6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_ordinal1(A),k2_ordinal1(A)))) & v1_relat_1(B) & v4_relat_1(B,k2_ordinal1(A)) & v5_relat_1(B,k2_ordinal1(A)) & v1_funct_1(B) & v5_ordinal1(B) & ~ v1_xboole_0(B) & v1_partfun1(B,k2_ordinal1(A)) & v1_funct_2(B,k2_ordinal1(A),k2_ordinal1(A)) & v1_ordinal2(B) & v2_ordinal6(B) ) ) )).
fof(rc4_osalg_1,axiom,( ? [A] : ( l3_osalg_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v3_osalg_1(A) & v4_osalg_1(A) ) )).
fof(rc4_osalg_4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_osalg_4(C,A,B) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) & v2_funcop_1(C) & v2_msualg_4(C,A,B) & v3_msualg_4(C,A,B) ) ) )).
fof(rc4_pboole,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_funcop_1(B) ) )).
fof(rc4_pcs_0,axiom,( ? [A] : ( l1_pcs_0(A) & v2_struct_0(A) & v2_pcs_0(A) ) )).
fof(rc4_pencil_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v11_pencil_1(A) ) )).
fof(rc4_pre_poly,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_setfam_1(B) & m1_subset_1(B,k1_zfmisc_1(k5_finsub_1(A))) ) => ? [C] : ( m1_subset_1(C,B) & ~ v8_ordinal1(C) & ~ v1_xboole_0(C) ) ) )).
fof(rc4_pre_topc,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) ) ) )).
fof(rc4_prob_1,axiom,( ! [A] : ! [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))) ) => ? [C] : ( m1_subset_1(C,B) & v1_xboole_0(C) ) ) )).
fof(rc4_pscomp_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) ) )).
fof(rc4_pythtrip,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xxreal_0(A) & v1_xreal_0(A) & v1_int_1(A) & ~ v1_abian(A) & v1_pythtrip(A) ) )).
fof(rc4_quantal1,axiom,( ? [A] : ( l2_quantal1(A) & ~ v2_struct_0(A) ) )).
fof(rc4_random_3,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( v1_relat_1(C) & v1_funct_1(C) & v4_random_3(C,A,B) ) ) )).
fof(rc4_ratfunc1,axiom,( ! [A] : ( ( ~ 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) ) => ? [B] : ( m1_ratfunc1(B,A) & ~ v4_ratfunc1(B,A) & v5_ratfunc1(B,A) ) ) )).
fof(rc4_rcomp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_connsp_1(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v3_pre_topc(B,A) & v4_pre_topc(B,A) & v2_connsp_1(B,A) ) ) )).
fof(rc4_realset2,axiom,( ? [A] : ( l6_algstr_0(A) & ~ v2_struct_0(A) & ~ v6_struct_0(A) & ~ v7_struct_0(A) & v13_algstr_0(A) & v36_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_vectsp_1(A) & v1_realset2(A) ) )).
fof(rc4_ringcat1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v4_ringcat1(A) ) )).
fof(rc4_rltopsp1,axiom,( ! [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) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v3_rltopsp1(B,A) ) ) )).
fof(rc4_rlvect_1,axiom,( ? [A] : ( l2_algstr_0(A) & ~ v2_struct_0(A) & v8_algstr_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) ) )).
fof(rc4_robbins1,axiom,( ? [A] : ( l4_robbins1(A) & v4_robbins1(A) ) )).
fof(rc4_robbins3,axiom,( ? [A] : ( l3_robbins3(A) & v6_robbins3(A) ) )).
fof(rc4_roughs_1,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v8_struct_0(A) & v1_orders_3(A) & v2_roughs_1(A) ) )).
fof(rc4_rusub_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v2_rusub_4(B,A) ) ) )).
fof(rc4_scm_halt,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) & v2_pre_poly(A) & v1_scm_halt(A) ) )).
fof(rc4_scmyciel,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( ~ v1_xboole_0(B) & v1_classes1(B) & v3_scmyciel(B,A) ) ) )).
fof(rc4_seqm_3,axiom,( ? [A] : ( m1_finseq_1(A,k1_numbers) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,k1_numbers) & v1_funct_1(A) & v3_funct_1(A) & v1_valued_0(A) & v2_valued_0(A) & v3_valued_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) ) )).
fof(rc4_setfam_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & v3_setfam_1(B,A) ) ) )).
fof(rc4_simplex0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_simplex0(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & ~ v3_pencil_1(B) & v4_simplex0(B) & v6_simplex0(B,A) ) ) )).
fof(rc4_simplex1,axiom,( ! [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) ) => ? [B] : ( m1_simplex0(B,u1_struct_0(A)) & v1_matroid0(B) & v3_matroid0(B) & v2_simplex0(B) & ~ v4_simplex0(B) & v6_simplex0(B,u1_struct_0(A)) & v1_simplex1(B,A) & v2_simplex1(B,A) ) ) )).
fof(rc4_sppol_2,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & v1_topreal4(A) ) )).
fof(rc4_stacks_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ? [C] : ( m1_rewrite1(C,B) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,A) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_finset_1(C) & v1_finseq_1(C) & v2_finseq_1(C) ) ) )).
fof(rc4_struct_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) ) ) )).
fof(rc4_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v1_subset_1(B,A) ) ) )).
fof(rc4_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) & v1_borsuk_1(B,A) & v1_tsep_1(B,A) & v1_tdlat_3(B) & v3_tdlat_3(B) ) ) )).
fof(rc4_tex_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v7_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) ) )).
fof(rc4_tex_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & ~ v1_zfmisc_1(B) & ~ v1_subset_1(B,u1_struct_0(A)) ) ) )).
fof(rc4_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v1_borsuk_1(B,A) & v1_tsep_1(B,A) & v1_tdlat_3(B) & v3_tdlat_3(B) & ~ v3_tex_3(B,A) ) ) )).
fof(rc4_topalg_2,axiom,( ! [A] : ( ( v3_topmetr(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_membered(B) & v2_membered(B) & v3_membered(B) & v6_xxreal_2(B) ) ) )).
fof(rc4_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v3_pre_topc(B,A) ) ) )).
fof(rc4_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( 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) & v2_topgen_4(B,A) & v3_topgen_4(B,u1_struct_0(A)) & v4_topgen_4(B,u1_struct_0(A)) ) ) )).
fof(rc4_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_partfun1(B,u1_struct_0(A)) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A)) & v3_tops_2(B,A,A) ) ) )).
fof(rc4_topmetr,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v3_topmetr(A) ) )).
fof(rc4_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_tops_1(B,A) ) ) )).
fof(rc4_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ? [B] : ( m1_trees_2(B,A) & v1_finset_1(B) ) ) )).
fof(rc4_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_trees_3(B,A) & v4_funct_1(B) & ~ v1_xboole_0(B) & v1_finset_1(B) & v3_trees_3(B) ) ) )).
fof(rc4_tsp_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & ~ v7_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & ~ v6_pre_topc(A) & ~ v1_tdlat_3(A) ) )).
fof(rc4_valued_0,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,A) & v1_funct_1(B) & v3_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) ) )).
fof(rc4_valued_1,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v3_card_1(A,1) ) )).
fof(rc4_vectmetr,axiom,( ? [A] : ( l1_vectmetr(A) & ~ v2_struct_0(A) & v4_vectmetr(A) ) )).
fof(rc4_vectsp10,axiom,( ! [A] : ( ( ~ 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_vectsp_1(A) & v6_vectsp_1(A) & l6_algstr_0(A) ) => ? [B] : ( l1_vectsp_1(B,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) & 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) ) ) )).
fof(rc4_vectsp_1,axiom,( ? [A] : ( l4_algstr_0(A) & ~ v2_struct_0(A) & v1_group_1(A) & v3_group_1(A) & v5_group_1(A) ) )).
fof(rc4_vectsp_2,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( l1_vectsp_2(B,A) & ~ v2_struct_0(B) ) ) )).
fof(rc4_vectsp_9,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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] : ( m1_vectsp_4(C,A,B) & ~ 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) & v1_matrlin(C,A) ) ) )).
fof(rc4_waybel11,axiom,( ? [A] : ( l1_waybel_9(A) & ~ v2_struct_0(A) & v13_struct_0(A,1) & 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_waybel_9(A) & v4_waybel11(A) ) )).
fof(rc4_waybel19,axiom,( ? [A] : ( 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_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_waybel_9(A) & v4_waybel11(A) & ~ v1_yellow_3(A) ) )).
fof(rc4_waybel23,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v3_waybel_3(A) & l1_orders_2(A) ) => ? [B] : ( m1_waybel23(B,A) & v6_waybel23(B,A) ) ) )).
fof(rc4_waybel27,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v1_monoid_0(A) & v1_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & ~ v1_yellow_3(A) ) )).
fof(rc4_waybel34,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) & ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v18_waybel_0(C,A,B) ) ) )).
fof(rc4_waybel35,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,u1_struct_0(A)) & v4_waybel_4(B,A) ) ) )).
fof(rc4_waybel_0,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( l1_waybel_0(B,A) & v6_waybel_0(B,A) ) ) )).
fof(rc4_waybel_1,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v1_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v11_waybel_1(A) ) )).
fof(rc4_waybel_3,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v2_pre_topc(A) & v8_pre_topc(A) & v1_compts_1(A) ) )).
fof(rc4_waybel_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & v2_waybel_6(B,A) ) ) )).
fof(rc4_waybel_7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ? [B] : ( 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) & v2_waybel_7(B,A) ) ) )).
fof(rc4_xreal_0,axiom,( ? [A] : ( v8_ordinal1(A) & v1_xcmplx_0(A) & v1_xxreal_0(A) & v1_xreal_0(A) ) )).
fof(rc4_xxreal_0,axiom,( ? [A] : ( v8_ordinal1(A) & v1_xxreal_0(A) ) )).
fof(rc4_xxreal_2,axiom,( ? [A] : ( v2_membered(A) & ~ v1_xboole_0(A) & v6_xxreal_2(A) ) )).
fof(rc4_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : ( m2_yellow13(B,A) & ~ v1_xboole_0(B) ) ) )).
fof(rc4_yellow14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_monoid_0(A) & l1_struct_0(A) ) => ? [B] : ( l1_waybel_0(B,A) & ~ v2_struct_0(B) & v6_waybel_0(B,A) & v1_yellow14(B,A) ) ) )).
fof(rc4_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_yellow_0(B,A) & ~ v2_struct_0(B) & v1_orders_2(B) & v4_yellow_0(B,A) ) ) )).
fof(rc4_yellow_6,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v2_pralg_1(B) & v1_yellow_1(B) & v4_waybel_3(B) ) )).
fof(rc4_yellow_9,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_yellow_9(B,A) & v2_pre_topc(B) & v1_tdlat_3(B) & v1_waybel_9(B) ) ) )).
fof(rc4_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v7_zmodul01(B,A) ) ) )).
fof(rc4_zmodul03,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) & ~ v2_struct_0(B) & v5_algstr_0(B) & v6_algstr_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v1_algstr_1(B) & v2_algstr_1(B) & v3_algstr_1(B) & v4_algstr_1(B) & v1_zmodul01(B) & v2_zmodul01(B) & v3_zmodul01(B) & v4_zmodul01(B) & v5_zmodul01(B) & v1_zmodul03(B) ) ) )).
fof(rc5_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ? [B] : ( m1_abcmiz_1(B,A,k13_abcmiz_1(A)) & ~ v1_xtuple_0(B) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) & v6_abcmiz_1(B,A) ) ) )).
fof(rc5_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ? [B] : ( m1_abcmiz_1(B,A,k14_abcmiz_1(A)) & ~ v1_xboole_0(B) & v1_relat_1(B) & ~ v1_xtuple_0(B) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) & v3_trees_9(B) & ~ v5_abcmiz_1(B,A,k28_abcmiz_1(A)) ) ) )).
fof(rc5_abian,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) & ~ v1_xboole_0(B) & v1_finset_1(B) & v3_abian(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) )).
fof(rc5_algstr_0,axiom,( ? [A] : ( l2_algstr_0(A) & v13_struct_0(A,1) & v8_algstr_0(A) ) )).
fof(rc5_algstr_1,axiom,( ? [A] : ( l4_algstr_0(A) & ~ v2_struct_0(A) & v19_algstr_0(A) & v20_algstr_0(A) & v21_algstr_0(A) & v22_algstr_0(A) & v1_group_1(A) & v3_group_1(A) & v3_vectsp_1(A) & v4_vectsp_1(A) & v6_vectsp_1(A) & v5_algstr_1(A) ) )).
fof(rc5_algstr_4,axiom,( ! [A] : ( l3_algstr_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_algstr_4(B,A) ) ) )).
fof(rc5_altcat_1,axiom,( ? [A] : ( l2_altcat_1(A) & ~ v2_struct_0(A) & v6_altcat_1(A) & v10_altcat_1(A) ) )).
fof(rc5_altcat_2,axiom,( ! [A] : ( l2_altcat_1(A) => ? [B] : ( m1_altcat_2(B,A) & v6_altcat_1(B) ) ) )).
fof(rc5_amistd_2,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ? [B] : ( l1_extpro_1(B,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) & v2_amistd_2(B,A) & v4_amistd_2(B,A) ) ) )).
fof(rc5_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ? [B] : ( l1_extpro_1(B,A) & ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & v3_amistd_1(B,A) ) ) )).
fof(rc5_aofa_000,axiom,( ? [A] : ( ~ v1_finset_1(A) & v1_freealg(A) ) )).
fof(rc5_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ? [D] : ( m1_msafree(D,A,C) & ~ v1_xboole_0(D) & v1_relat_1(D) & v2_relat_1(D) & ~ v3_relat_1(D) & v4_relat_1(D,u1_struct_0(A)) & v1_funct_1(D) & v1_partfun1(D,u1_struct_0(A)) & v2_aofa_a01(D,A,B,C) ) ) )).
fof(rc5_armstrng,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k9_setfam_1(A)) & v5_relat_1(B,k9_setfam_1(A)) & v8_relat_2(B) & v3_armstrng(B,A) & v4_armstrng(B,A) & v5_armstrng(B,A) ) )).
fof(rc5_asympt_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xxreal_0(A) & ~ v2_xxreal_0(A) & v1_xreal_0(A) ) )).
fof(rc5_bcialg_4,axiom,( ? [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) ) )).
fof(rc5_bilinear,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) & ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ? [C] : ( 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(C) & v1_relat_1(C) & v4_relat_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) & v5_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & v1_partfun1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) & v1_funct_2(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)),u1_struct_0(A)) & v8_bilinear(C,A,B) ) ) )).
fof(rc5_borsuk_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v2_connsp_1(B,A) & v2_compts_1(B,A) ) ) )).
fof(rc5_card_1,axiom,( ! [A] : ( ~ v1_finset_1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_finset_1(B) ) ) )).
fof(rc5_card_3,axiom,( ? [A] : v5_card_3(A) )).
fof(rc5_cat_4,axiom,( ? [A] : ( l2_cat_4(A) & v5_cat_4(A) ) )).
fof(rc5_catalg_1,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v2_struct_0(A) & v1_msualg_1(A) & v1_instalg1(A) & v2_catalg_1(A) & v3_catalg_1(A) ) )).
fof(rc5_cayldick,axiom,( ? [A] : ( l1_cayldick(A) & ~ v2_struct_0(A) & ~ v6_struct_0(A) & v7_algstr_0(A) & v14_algstr_0(A) & v30_algstr_0(A) & v33_algstr_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) & v9_rlvect_1(A) & v2_funcsdom(A) & v3_normsp_0(A) & v4_normsp_0(A) & v2_normsp_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_lopban_2(A) & v3_lopban_2(A) & v4_lopban_2(A) & v3_topmetr(A) & v1_cayldick(A) & v3_cayldick(A) & v4_cayldick(A) & v5_cayldick(A) & v6_cayldick(A) ) )).
fof(rc5_cfdiff_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_numbers)) & v1_membered(A) & v6_cfdiff_1(A) ) )).
fof(rc5_cgames_1,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v3_cgames_1(A) ) )).
fof(rc5_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & v6_chord(A) ) => ? [B] : ( m3_chord(B,A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k6_glib_000(A)) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v7_chord(B,A) ) ) )).
fof(rc5_circcmb3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & m1_circcmb3(B,A) ) => ? [C] : ( m2_circcmb3(C,A,B) & v3_msualg_1(C,B) & v4_msualg_1(C,B) & v4_msafree2(C,B) & v4_circcomb(C,B) ) ) )).
fof(rc5_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_circcomb(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v3_msualg_1(B,A) & v4_circcomb(B,A) & v6_circcomb(B,A) ) ) )).
fof(rc5_clopban2,axiom,( ? [A] : ( 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) ) )).
fof(rc5_closure2,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( l1_closure2(B,A) & v11_closure2(B,A) ) ) )).
fof(rc5_clvect_1,axiom,( ? [A] : ( l2_clvect_1(A) & v7_clvect_1(A) ) )).
fof(rc5_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v4_finsub_1(B) ) ) )).
fof(rc5_compl_sp,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k9_setfam_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & v5_compl_sp(B,A) ) ) )).
fof(rc5_compos_0,axiom,( ! [A] : ( ( v1_compos_0(A) & v5_compos_0(A) ) => ? [B] : ( m1_subset_1(B,A) & v4_compos_0(B,A) ) ) )).
fof(rc5_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ? [B] : ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) ) )).
fof(rc5_comput_1,axiom,( ! [A] : ! [B] : ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(A),B))) & v1_relat_1(C) & v4_relat_1(C,k3_finseq_2(A)) & v5_relat_1(C,B) & v1_funct_1(C) & v2_margrel1(C) ) )).
fof(rc5_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l5_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u4_struct_0(A))) & ~ v1_xboole_0(B) ) ) )).
fof(rc5_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) & v2_dilworth(B,A) ) ) )).
fof(rc5_exchsort,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( v1_relat_1(B) & v5_relat_1(B,A) & ~ v1_xboole_0(B) & v1_funct_1(B) & v2_funct_2(B,A) ) ) )).
fof(rc5_extpro_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_setfam_1(A) & v2_memstr_0(B,A) & v3_extpro_1(B,A) & l1_extpro_1(B,A) ) => ? [C] : ( m1_subset_1(C,u1_compos_1(B)) & v2_extpro_1(C,A,B) ) ) )).
fof(rc5_finseq_1,axiom,( ? [A] : ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) ) )).
fof(rc5_finset_1,axiom,( ! [A] : ! [B] : ? [C] : ( v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,B) & v1_funct_1(C) & v1_finset_1(C) ) )).
fof(rc5_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,A) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v4_card_3(B) & v2_pre_poly(B) ) ) )).
fof(rc5_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : ( m1_subset_1(B,k1_fomodel1(A)) & v7_fomodel1(B,A) ) ) )).
fof(rc5_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : ( m1_subset_1(B,k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & ~ v8_ordinal1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v2_pre_poly(B) & v4_fomodel2(B,A) ) ) )).
fof(rc5_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( v1_relat_1(B) & v5_relat_1(B,A) & v2_funct_2(B,A) ) ) )).
fof(rc5_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) & v3_fomodel4(C,B) ) ) )).
fof(rc5_freealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & v3_freealg(A) & l1_unialg_1(A) ) => ? [B] : ( m1_freealg(B,A) & v2_freealg(B,A) ) ) )).
fof(rc5_fsm_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ? [C] : ( l2_fsm_1(C,A,B) & ~ v2_struct_0(C) & v8_struct_0(C) ) ) )).
fof(rc5_fsm_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ? [C] : ( l2_fsm_2(C,A,B) & ~ v2_struct_0(C) & v1_fsm_2(C,A) & v5_fsm_2(C,A) ) ) )).
fof(rc5_funct_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v3_funct_1(A) ) )).
fof(rc5_functor0,axiom,( ! [A] : ! [B] : ( ( l1_altcat_1(A) & l1_altcat_1(B) ) => ? [C] : ( l2_functor0(C,A,B) & v11_functor0(C,A,B) ) ) )).
fof(rc5_fvaluat1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : ( m2_fvaluat1(C,A,B) & ~ v2_struct_0(C) & v5_algstr_0(C) & v6_algstr_0(C) & v7_algstr_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) & v1_algstr_1(C) & v2_algstr_1(C) & v3_algstr_1(C) & v4_algstr_1(C) ) ) )).
fof(rc5_gcd_1,axiom,( ? [A] : ( l6_algstr_0(A) & ~ v2_struct_0(A) & ~ v6_struct_0(A) & v13_algstr_0(A) & v1_group_1(A) & v3_group_1(A) & 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) ) )).
fof(rc5_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ? [B] : ( m1_glib_000(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) & v4_glib_000(B) & v7_glib_000(B) ) ) )).
fof(rc5_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,k6_glib_000(A)) & ~ v5_glib_002(B,A) ) ) )).
fof(rc5_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ? [B] : ( m1_graph_1(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u4_struct_0(A)) & v1_funct_1(B) & v1_xboole_0(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) ) ) )).
fof(rc5_grcat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v3_grcat_1(A) ) )).
fof(rc5_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ? [C] : ( m1_group_9(C,A,B) & ~ v2_struct_0(C) & v1_group_1(C) & v2_group_1(C) & v3_group_1(C) & v2_group_9(C,A) & v3_group_9(C,A) & v4_group_9(C,A,B) ) ) )).
fof(rc5_hermitan,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) => ? [C] : ( 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_relat_1(C) & v4_relat_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))) & v5_relat_1(C,u1_struct_0(k1_complfld)) & ~ v1_zfmisc_1(C) & 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) ) ) )).
fof(rc5_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v3_ideal_1(B,A) ) ) )).
fof(rc5_lattices,axiom,( ? [A] : ( l1_lattices(A) & v13_struct_0(A,1) & v1_lattices(A) ) )).
fof(rc5_lopban_2,axiom,( ? [A] : ( l1_lopban_2(A) & ~ v2_struct_0(A) & v12_algstr_0(A) & v13_algstr_0(A) & v14_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v8_rlvect_1(A) & v9_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) ) )).
fof(rc5_margrel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_finseq_1(B,k4_partfun1(k3_finseq_2(A),A)) & v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k4_partfun1(k3_finseq_2(A),A)) & v1_funct_1(B) & v1_funcop_1(B) & v2_funcop_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v4_card_3(B) & v4_margrel1(B,A) & v5_margrel1(B,A) ) ) )).
fof(rc5_matrix_9,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(3),k2_finseq_1(3)))) & v1_relat_1(A) & v4_relat_1(A,k2_finseq_1(3)) & v5_relat_1(A,k2_finseq_1(3)) & v1_funct_1(A) & v2_funct_1(A) & ~ v1_xboole_0(A) & v1_partfun1(A,k2_finseq_1(3)) & v1_funct_2(A,k2_finseq_1(3),k2_finseq_1(3)) & v2_funct_2(A,k2_finseq_1(3)) & v3_funct_2(A,k2_finseq_1(3),k2_finseq_1(3)) & v1_finset_1(A) & ~ v5_matrix_2(A,3) ) )).
fof(rc5_matrixj2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(B)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,u1_struct_0(B)) & 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) ) ) )).
fof(rc5_measure1,axiom,( ! [A] : ! [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))) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,B) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,k4_ordinal1) & v1_funct_2(C,k4_ordinal1,B) & v1_prob_2(C) ) ) )).
fof(rc5_measure6,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & ~ v1_setfam_1(A) ) )).
fof(rc5_memstr_0,axiom,( ! [A] : ! [B] : ( ( ~ v1_setfam_1(A) & l1_memstr_0(B,A) ) => ? [C] : ( 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)) ) ) )).
fof(rc5_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( l1_pre_topc(B) & ~ v2_struct_0(B) & v2_pre_topc(B) & v3_mfold_1(B,A) ) ) )).
fof(rc5_modelc_1,axiom,( ? [A] : ( l2_modelc_1(A) & ~ v2_struct_0(A) & v10_modelc_1(A) ) )).
fof(rc5_monoid_0,axiom,( ! [A] : ( l3_algstr_0(A) => ? [B] : ( m1_monoid_0(B,A) & v22_algstr_0(B) ) ) )).
fof(rc5_msafree2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,k1_funct_1(u3_msualg_1(A,k11_msafree(A,B)),C)) & v1_relat_1(D) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v4_card_3(D) ) ) )).
fof(rc5_msafree4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_msafree4(B,A) ) => ? [C] : ( m2_pboole(C,A,B,k7_funcop_1(A,k4_ordinal1)) & v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v1_funcop_1(C) & v2_funcop_1(C) & v1_msualg_3(C) ) ) )).
fof(rc5_msscyc_1,axiom,( ? [A] : ( l1_graph_1(A) & ~ v2_struct_0(A) & v14_struct_0(A) & ~ v3_msscyc_1(A) ) )).
fof(rc5_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ? [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) & v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v1_mssubfam(C,A,B) & v2_mssubfam(C,A,B) & v3_mssubfam(C,A,B) & v4_mssubfam(C,A,B) & v5_mssubfam(C,A,B) & v6_mssubfam(C,A,B) ) ) )).
fof(rc5_msualg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v3_msualg_1(B,A) ) ) )).
fof(rc5_mycielsk,axiom,( ! [A] : ( ( v2_mycielsk(A) & l1_orders_2(A) ) => ? [B] : ( m1_eqrel_1(B,u1_struct_0(A)) & ~ v10_ordinal1(B) & v1_finset_1(B) & v1_setfam_1(B) & v5_dilworth(B,A) ) ) )).
fof(rc5_oposet_1,axiom,( ? [A] : ( l2_qmax_1(A) & ~ v2_struct_0(A) & v3_orders_2(A) & v3_qmax_1(A) ) )).
fof(rc5_ordinal1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v7_ordinal1(A) ) )).
fof(rc5_ordinal5,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v5_ordinal1(A) & v1_ordinal2(A) & v6_ordinal5(A) ) )).
fof(rc5_ordinal6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ? [B] : ( m1_subset_1(B,A) & v1_ordinal1(B) & v2_ordinal1(B) & v3_ordinal1(B) & ~ v1_zfmisc_1(B) & v1_finset_1(B) & v1_ordinal6(B) ) ) )).
fof(rc5_osalg_1,axiom,( ? [A] : ( l1_osalg_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) ) )).
fof(rc5_osalg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_msualg_2(C,A,B) & v12_osalg_1(C,A) ) ) )).
fof(rc5_osalg_4,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_osalg_4(A) ) )).
fof(rc5_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ? [C] : ( m3_pboole(C,A,B) & v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) ) )).
fof(rc5_pcs_0,axiom,( ? [A] : ( l1_pcs_0(A) & ~ v2_struct_0(A) & v2_pcs_0(A) & v4_pcs_0(A) & v6_pcs_0(A) ) )).
fof(rc5_pencil_1,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v15_pencil_1(B) ) )).
fof(rc5_polyalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( l1_polyalg1(B,A) & ~ v2_struct_0(B) & v1_polyalg1(B,A) ) ) )).
fof(rc5_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,k15_pre_poly(A)) & v5_relat_1(C,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) ) ) )).
fof(rc5_pre_poly,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k5_finsub_1(A))) & ~ v2_setfam_1(B) ) ) )).
fof(rc5_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) ) ) )).
fof(rc5_prelamb,axiom,( ? [A] : ( l2_prelamb(A) & ~ v2_struct_0(A) & v10_prelamb(A) ) )).
fof(rc5_pythtrip,axiom,( ? [A] : ( m1_pythtrip(A) & v1_finset_1(A) & ~ v2_pythtrip(A) & v3_pythtrip(A) ) )).
fof(rc5_quantal1,axiom,( ? [A] : ( l3_algstr_0(A) & ~ v2_struct_0(A) & v6_quantal1(A) ) )).
fof(rc5_ratfunc1,axiom,( ! [A] : ( ( ~ 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) ) => ? [B] : ( m1_ratfunc1(B,A) & ~ v4_ratfunc1(B,A) & ~ v5_ratfunc1(B,A) ) ) )).
fof(rc5_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_ringcat1(A) ) => ? [B] : ( m1_subset_1(B,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) & v1_group_1(B) & v3_group_1(B) & v1_vectsp_1(B) & v2_vectsp_1(B) & v3_vectsp_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & v6_vectsp_1(B) ) ) )).
fof(rc5_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & ~ v1_xboole_0(B) & v4_rltopsp1(B,A) ) ) )).
fof(rc5_rlvect_1,axiom,( ? [A] : ( l1_rlvect_1(A) & ~ 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) ) )).
fof(rc5_robbins1,axiom,( ? [A] : ( l4_robbins1(A) & v13_struct_0(A,1) & v4_robbins1(A) ) )).
fof(rc5_robbins3,axiom,( ? [A] : ( l1_robbins3(A) & ~ v2_struct_0(A) ) )).
fof(rc5_roughs_1,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v8_struct_0(A) & ~ v1_roughs_1(A) & v2_roughs_1(A) ) )).
fof(rc5_rusub_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v2_rusub_4(B,A) ) ) )).
fof(rc5_scm_halt,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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_pre_poly(A) & v2_scm_halt(A) ) )).
fof(rc5_scmyciel,axiom,( ? [A] : v4_scmyciel(A) )).
fof(rc5_sheffer1,axiom,( ? [A] : ( l1_sheffer1(A) & v13_struct_0(A,1) ) )).
fof(rc5_simplex0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_simplex0(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & v1_matroid0(B) & v2_simplex0(B) & ~ v4_simplex0(B) & ~ v5_simplex0(B) & v6_simplex0(B,A) ) ) )).
fof(rc5_sppol_2,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & v1_topreal4(A) ) )).
fof(rc5_stacks_1,axiom,( ? [A] : ( l1_stacks_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_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) ) )).
fof(rc5_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_xboole_0(B) & v1_zfmisc_1(B) ) ) )).
fof(rc5_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v2_pre_topc(B) & v2_tdlat_3(B) & v3_tdlat_3(B) ) ) )).
fof(rc5_tex_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v1_tdlat_3(A) & ~ v2_tdlat_3(A) ) )).
fof(rc5_tex_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_zfmisc_1(B) & v1_subset_1(B,u1_struct_0(A)) ) ) )).
fof(rc5_tex_3,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) & v1_borsuk_1(B,A) & v1_tsep_1(B,A) & v1_tdlat_3(B) & v3_tdlat_3(B) & ~ v1_tex_3(B,A) ) ) )).
fof(rc5_topalg_2,axiom,( ? [A] : ( m1_pre_topc(A,k3_topmetr) & ~ v2_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v3_topmetr(A) & v2_topalg_2(A) ) )).
fof(rc5_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v4_pre_topc(B,A) ) ) )).
fof(rc5_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ? [B] : ( 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)) & v3_measure1(B,u1_struct_0(A)) & v3_topgen_4(B,u1_struct_0(A)) ) ) )).
fof(rc5_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v2_tops_1(B,A) ) ) )).
fof(rc5_trees_2,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) )).
fof(rc5_trees_3,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v4_trees_3(A) & v5_trees_3(A) ) )).
fof(rc5_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & v6_pre_topc(B) ) ) )).
fof(rc5_valued_0,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) & v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,A) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v1_funct_2(B,k4_ordinal1,A) ) ) )).
fof(rc5_valued_1,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,k3_numbers) & v1_funct_1(B) & v1_partfun1(B,A) & v1_valued_0(B) & v2_valued_0(B) & v3_valued_0(B) & v4_valued_0(B) ) )).
fof(rc5_vectmetr,axiom,( ? [A] : ( l1_vectmetr(A) & ~ v2_struct_0(A) & v13_algstr_0(A) & v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & v9_metric_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) & v4_vectmetr(A) & v5_vectmetr(A) & v6_vectmetr(A) ) )).
fof(rc5_vectsp10,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v4_rlvect_1(A) & l2_algstr_0(A) & ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(B)) & v5_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & v13_vectsp_1(C,B,A) & v2_hahnban1(C,A,B) ) ) )).
fof(rc5_vectsp_1,axiom,( ? [A] : ( l6_algstr_0(A) & ~ v2_struct_0(A) & ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v36_algstr_0(A) & v2_rlvect_1(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) & v6_vectsp_1(A) ) )).
fof(rc5_vectsp_2,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & l1_struct_0(B) ) => ? [C] : ( l2_vectsp_2(C,A,B) & v3_vectsp_2(C,A,B) ) ) )).
fof(rc5_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v12_waybel_0(B,A) & v13_waybel_0(B,A) & v1_waybel11(B,A) & v2_waybel11(B,A) ) ) )).
fof(rc5_waybel19,axiom,( ? [A] : ( 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_lattice3(A) & v2_lattice3(A) & v3_lattice3(A) & v1_yellow_0(A) & v2_yellow_0(A) & v3_yellow_0(A) & v3_waybel_3(A) & v24_waybel_0(A) & v25_waybel_0(A) & v1_waybel_9(A) & ~ v1_yellow_3(A) & v2_waybel19(A) ) )).
fof(rc5_waybel23,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v3_waybel_3(A) & l1_orders_2(A) ) => ? [B] : ( m1_waybel23(B,A) & v7_waybel23(B,A) ) ) )).
fof(rc5_waybel27,axiom,( ? [A] : ( l1_struct_0(A) & ~ v2_struct_0(A) & v1_monoid_0(A) ) )).
fof(rc5_waybel35,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) & v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v5_relat_1(B,u1_struct_0(A)) & v1_waybel35(B,A) ) ) )).
fof(rc5_waybel_0,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( l1_waybel_0(B,A) & ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v6_waybel_0(B,A) & v7_waybel_0(B) ) ) )).
fof(rc5_waybel_1,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & v1_orders_2(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v9_waybel_1(A) ) )).
fof(rc5_waybel_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v2_yellow_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & v5_waybel_6(B,A) ) ) )).
fof(rc5_waybel_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(A)))) & ~ v1_xboole_0(B) & v2_waybel_0(B,k2_yellow_1(A)) & v13_waybel_0(B,k2_yellow_1(A)) & v3_waybel_7(B,k2_yellow_1(A)) ) ) )).
fof(rc5_xxreal_2,axiom,( ? [A] : ( v2_membered(A) & v1_xxreal_2(A) & v2_xxreal_2(A) & v6_xxreal_2(A) ) )).
fof(rc5_yellow14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_monoid_0(A) & l1_struct_0(A) ) => ? [B] : ( l1_waybel_0(B,A) & ~ v2_struct_0(B) & v4_orders_2(B) & v6_waybel_0(B,A) & v7_waybel_0(B) & v1_yellow14(B,A) ) ) )).
fof(rc5_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_yellow_0(B,A) & ~ v2_struct_0(B) & v1_orders_2(B) & v4_yellow_0(B,A) & v7_yellow_0(B,A) & v8_yellow_0(B,A) ) ) )).
fof(rc5_yellow_6,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & l1_waybel_0(B,A) ) => ? [C] : ( m1_yellow_6(C,A,B) & v6_waybel_0(C,A) & v2_yellow_6(C,A,B) ) ) )).
fof(rc5_yellow_9,axiom,( ! [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] : ( m1_yellow_9(B,A) & ~ 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) & v1_yellow_0(B) & v2_yellow_0(B) & v3_yellow_0(B) & v24_waybel_0(B) & v25_waybel_0(B) & v1_waybel_9(B) & v4_waybel11(B) ) ) )).
fof(rc5_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) & ~ v2_struct_0(B) & v5_algstr_0(B) & v6_algstr_0(B) & v7_algstr_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v1_algstr_1(B) & v2_algstr_1(B) & v3_algstr_1(B) & v4_algstr_1(B) & v1_zmodul01(B) & v2_zmodul01(B) & v3_zmodul01(B) & v4_zmodul01(B) & v5_zmodul01(B) ) ) )).
fof(rc5_zmodul03,axiom,( ? [A] : ( l1_zmodul01(A) & ~ v2_struct_0(A) & ~ v7_struct_0(A) & v5_algstr_0(A) & v6_algstr_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v1_algstr_1(A) & v2_algstr_1(A) & v3_algstr_1(A) & v4_algstr_1(A) & v2_zmodul01(A) & v3_zmodul01(A) & v4_zmodul01(A) & v5_zmodul01(A) & v1_zmodul03(A) ) )).
fof(rc6_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ? [B] : ( m1_abcmiz_1(B,A,k13_abcmiz_1(A)) & ~ v1_xtuple_0(B) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) & ~ v6_abcmiz_1(B,A) & v7_abcmiz_1(B,A) ) ) )).
fof(rc6_abian,axiom,( ! [A] : ! [B] : ( ~ v2_setfam_1(B) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) & v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,A,B) ) ) )).
fof(rc6_algstr_0,axiom,( ? [A] : ( l2_algstr_0(A) & v13_struct_0(A,1) & v7_algstr_0(A) & v8_algstr_0(A) & v14_algstr_0(A) ) )).
fof(rc6_altcat_1,axiom,( ? [A] : ( l2_altcat_1(A) & ~ v2_struct_0(A) & v2_altcat_1(A) & v6_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) ) )).
fof(rc6_altcat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ? [B] : ( m1_altcat_2(B,A) & ~ v2_struct_0(B) & v2_altcat_1(B) & v6_altcat_1(B) ) ) )).
fof(rc6_amistd_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_compos_1(B)) & v1_amistd_2(C,A,B) & v3_amistd_2(C,A,B) ) ) )).
fof(rc6_aofa_000,axiom,( ? [A] : ( l1_unialg_1(A) & ~ v2_struct_0(A) & v1_unialg_1(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) & v9_aofa_000(A) & ~ v10_aofa_000(A) & v11_aofa_000(A) & v12_aofa_000(A) ) )).
fof(rc6_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) & v2_aofa_a01(D,A,B,C) & m1_msafree(D,A,C) & m1_subset_1(E,u1_struct_0(A)) ) => ? [F] : ( m1_subset_1(F,k1_msafree4(u1_struct_0(A),D,E)) & v3_aofa_a01(F,A,B,C,D,E) ) ) )).
fof(rc6_armstrng,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) & v1_relat_1(B) & v4_relat_1(B,k9_setfam_1(A)) & v5_relat_1(B,k9_setfam_1(A)) & v6_armstrng(B,A) ) )).
fof(rc6_asympt_0,axiom,( ? [A] : ( v1_xcmplx_0(A) & v1_xxreal_0(A) & v1_xreal_0(A) & ~ v1_asympt_0(A) ) )).
fof(rc6_bcialg_4,axiom,( ? [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) ) )).
fof(rc6_bilinear,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) => ? [C] : ( 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(C) & v1_relat_1(C) & v4_relat_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) & v5_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & v1_partfun1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) & 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) ) ) )).
fof(rc6_card_1,axiom,( ! [A] : ( v1_card_1(A) => ? [B] : v3_card_1(B,A) ) )).
fof(rc6_card_3,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_finset_1(A) ) )).
fof(rc6_cat_4,axiom,( ? [A] : ( l2_cat_4(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) ) )).
fof(rc6_catalg_1,axiom,( ! [A] : ? [B] : ( m1_catalg_1(B,A) & v1_msualg_1(B) & v1_instalg1(B) & v2_catalg_1(B) & v3_catalg_1(B) ) )).
fof(rc6_cgames_1,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v3_cgames_1(A) & v4_cgames_1(A) ) )).
fof(rc6_circcmb3,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v2_funct_1(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v4_card_3(A) & v4_valued_0(A) ) )).
fof(rc6_circcomb,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) => ? [E] : ( l3_msualg_1(E,k5_circcomb(C,D)) & v3_msualg_1(E,k5_circcomb(C,D)) & v4_msualg_1(E,k5_circcomb(C,D)) & v4_msafree2(E,k5_circcomb(C,D)) & v4_circcomb(E,k5_circcomb(C,D)) ) ) )).
fof(rc6_closure2,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( l1_closure2(B,A) & v4_msualg_1(B,A) & v11_closure2(B,A) & v12_closure2(B,A) & v13_closure2(B,A) & v14_closure2(B,A) & v15_closure2(B,A) & v16_closure2(B,A) & v17_closure2(B,A) ) ) )).
fof(rc6_clvect_1,axiom,( ? [A] : ( l2_clvect_1(A) & ~ v2_struct_0(A) ) )).
fof(rc6_cohsp_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v2_finsub_1(A) & v1_classes1(A) & v1_coh_sp(A) & v3_cohsp_1(A) ) )).
fof(rc6_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) & v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k9_setfam_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & v4_compl_sp(B,A) ) ) )).
fof(rc6_compos_0,axiom,( ? [A] : ( ~ v1_xboole_0(A) & ~ v1_zfmisc_1(A) & v1_relat_1(A) & v1_compos_0(A) & v2_compos_0(A) & v3_compos_0(A) & v5_compos_0(A) ) )).
fof(rc6_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ? [B] : ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) & v1_afinsq_1(B) & ~ v2_compos_1(B,A) ) ) )).
fof(rc6_comput_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(A),B))) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k3_finseq_2(A)) & v5_relat_1(C,B) & v1_funct_1(C) & v2_margrel1(C) ) ) )).
fof(rc6_conlat_1,axiom,( ! [A] : ( l5_struct_0(A) => ? [B] : ( l2_conlat_1(B,A) & v3_conlat_1(B,A) ) ) )).
fof(rc6_dilworth,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_finset_1(B) & v2_dilworth(B,A) ) ) )).
fof(rc6_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) & v3_ordinal1(C) ) => ? [D] : ( m2_exchsort(D,A,B) & v1_relat_1(D) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_exchsort(D) & v2_exchsort(D,C) ) ) )).
fof(rc6_extpro_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ? [B] : ( l1_extpro_1(B,A) & ~ v2_struct_0(B) & v7_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & v1_extpro_1(B,A) ) ) )).
fof(rc6_finseq_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_finseq_1(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,A) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) ) ) )).
fof(rc6_finset_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ? [C] : ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,B) & v1_funct_1(C) & v1_finset_1(C) ) ) )).
fof(rc6_fomodel0,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) ) => ? [C] : ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,A) & v1_funct_1(C) & v1_finset_1(C) & v3_card_1(C,B) & v1_finseq_1(C) & v2_finseq_1(C) & v4_card_3(C) & v2_pre_poly(C) ) ) )).
fof(rc6_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : ( m1_subset_1(B,k1_fomodel1(A)) & v4_fomodel1(B,A) ) ) )).
fof(rc6_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ? [C] : ( m1_subset_1(C,k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & ~ v8_ordinal1(C) & v1_finset_1(C) & v1_finseq_1(C) & v2_finseq_1(C) & v2_pre_poly(C) & v3_fomodel2(C,A,B) & v4_fomodel2(C,A) & v5_fomodel2(C,A) ) ) )).
fof(rc6_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) => ? [D] : ( m1_subset_1(D,k15_fomodel2(A,B)) & v1_relat_1(D) & v4_relat_1(D,k37_fomodel1(A)) & v1_funct_1(D) & v1_partfun1(D,k37_fomodel1(A)) & v1_funcop_1(D) & v2_funcop_1(D) & v1_fomodel2(D,A,B) & v3_fomodel3(D,A,B,C) ) ) )).
fof(rc6_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : v3_fomodel4(B,A) ) )).
fof(rc6_fsm_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ? [C] : ( l3_fsm_1(C,A,B) & ~ v2_struct_0(C) & v8_struct_0(C) ) ) )).
fof(rc6_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( l1_fsm_2(B,A) & ~ v2_struct_0(B) & v1_fsm_2(B,A) & v5_fsm_2(B,A) ) ) )).
fof(rc6_funct_1,axiom,( ! [A] : ! [B] : ? [C] : ( v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,B) & v1_funct_1(C) ) )).
fof(rc6_functor0,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) & ~ v2_struct_0(B) & v1_altcat_2(B) & l1_altcat_1(B) ) => ? [C] : ( l2_functor0(C,A,B) & v8_functor0(C,A,B) & v10_functor0(C,A,B) & v11_functor0(C,A,B) ) ) )).
fof(rc6_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ? [B] : ( m1_glib_000(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) & v9_glib_000(B,A) ) ) )).
fof(rc6_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,k6_glib_000(A)) & v11_glib_000(B,A) ) ) )).
fof(rc6_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ? [B] : ( m3_graph_1(B,A) & ~ v2_struct_0(B) & v14_struct_0(B) & v1_graph_1(B) ) ) )).
fof(rc6_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_grcat_1(A) ) => ? [B] : ( m1_subset_1(B,A) & ~ v2_struct_0(B) & v5_algstr_0(B) & v6_algstr_0(B) & v7_algstr_0(B) & v8_algstr_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v1_algstr_1(B) & v2_algstr_1(B) & v3_algstr_1(B) & v4_algstr_1(B) ) ) )).
fof(rc6_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) => ? [D] : ( m1_group_9(D,A,C) & ~ v2_struct_0(D) & v1_group_1(D) & v2_group_1(D) & v3_group_1(D) & v3_group_9(D,A) & v4_group_9(D,A,C) ) ) )).
fof(rc6_hermitan,axiom,( ! [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) & 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] : ( 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_relat_1(B) & v4_relat_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) & v5_relat_1(B,u1_struct_0(k1_complfld)) & ~ v1_zfmisc_1(B) & v1_funct_1(B) & ~ v3_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) & v2_bilinear(B,k1_complfld,A,A) & v4_bilinear(B,k1_complfld,A,A) & v2_hermitan(B,A,A) & v3_hermitan(B,A) & v4_hermitan(B,A) & v5_hermitan(B,A) ) ) )).
fof(rc6_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ? [B] : ( 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) ) ) )).
fof(rc6_lattices,axiom,( ? [A] : ( l3_lattices(A) & v13_struct_0(A,1) & v3_lattices(A) ) )).
fof(rc6_measure1,axiom,( ! [A] : ! [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))) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & v1_relat_1(C) & v4_relat_1(C,B) & v5_relat_1(C,k6_numbers) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,B) & v1_funct_2(C,B,k6_numbers) & v2_valued_0(C) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) ) ) )).
fof(rc6_measure6,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & ~ v1_xboole_0(A) & v1_membered(A) & v2_membered(A) & v3_membered(A) & v5_xxreal_2(A) & v2_rcomp_1(A) ) )).
fof(rc6_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) => ? [D] : ( ~ v1_xboole_0(D) & 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) ) ) )).
fof(rc6_mfold_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v2_pre_topc(A) & v4_mfold_1(A) ) )).
fof(rc6_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l3_algstr_0(A) ) => ? [B] : ( m1_monoid_0(B,A) & ~ v2_struct_0(B) & v22_algstr_0(B) & v1_group_1(B) & v4_vectsp_1(B) ) ) )).
fof(rc6_msafree2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,k1_funct_1(u3_msualg_1(A,k11_msafree(A,B)),C)) & v1_relat_1(D) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v4_card_3(D) & v3_trees_2(D) ) ) )).
fof(rc6_msafree4,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v13_pencil_1(B) ) )).
fof(rc6_msscyc_1,axiom,( ? [A] : ( l1_graph_1(A) & ~ v2_struct_0(A) & v14_struct_0(A) & v2_msscyc_1(A) ) )).
fof(rc6_msualg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v3_msualg_1(B,A) & v4_msualg_1(B,A) ) ) )).
fof(rc6_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( m1_mycielsk(B,A) & v1_orders_2(B) & v3_necklace(B) ) ) )).
fof(rc6_oposet_1,axiom,( ? [A] : ( l2_qmax_1(A) & ~ v2_struct_0(A) & v3_necklace(A) & v3_qmax_1(A) ) )).
fof(rc6_ordinal1,axiom,( ? [A] : v8_ordinal1(A) )).
fof(rc6_ordinal6,axiom,( ? [A] : ( v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & ~ v1_zfmisc_1(A) & v1_finset_1(A) & v1_ordinal6(A) ) )).
fof(rc6_osalg_1,axiom,( ? [A] : ( l3_osalg_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_orders_3(A) & v3_osalg_1(A) & v4_osalg_1(A) & v5_osalg_1(A) & v6_osalg_1(A) ) )).
fof(rc6_osalg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_msualg_2(C,A,B) & v3_msualg_1(C,A) & v12_osalg_1(C,A) ) ) )).
fof(rc6_osalg_4,axiom,( ? [A] : ( l3_osalg_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v4_osalg_1(A) & v5_osalg_1(A) & v2_osalg_4(A) ) )).
fof(rc6_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ? [C] : ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v5_funct_1(C,B) & v1_partfun1(C,A) ) ) )).
fof(rc6_pcs_0,axiom,( ? [A] : ( l1_pcs_0(A) & ~ v2_struct_0(A) & v2_pcs_0(A) & v5_pcs_0(A) & v6_pcs_0(A) ) )).
fof(rc6_pencil_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) & v4_waybel_3(B) ) => ? [C] : ( m3_pboole(C,A,k12_pralg_1(A,B)) & v1_relat_1(C) & v2_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) ) ) )).
fof(rc6_polyalg1,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & l1_polyalg1(B,A) ) => ? [C] : ( m1_polyalg1(C,A,B) & v1_polyalg1(C,A) ) ) )).
fof(rc6_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,k15_pre_poly(A)) & v5_relat_1(C,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) ) ) )).
fof(rc6_pre_poly,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v2_setfam_1(B) & m1_subset_1(B,k1_zfmisc_1(k5_finsub_1(A))) ) => ? [C] : ( m1_subset_1(C,B) & ~ v1_xboole_0(C) & v1_finset_1(C) ) ) )).
fof(rc6_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_pre_topc(B,A) ) ) )).
fof(rc6_ratfunc1,axiom,( ! [A] : ( ( ~ 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) ) => ? [B] : ( m1_ratfunc1(B,A) & v6_ratfunc1(B,A) ) ) )).
fof(rc6_ringcat1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v5_ringcat1(A) ) )).
fof(rc6_rltopsp1,axiom,( ? [A] : ( l1_rltopsp1(A) & v5_rltopsp1(A) ) )).
fof(rc6_robbins1,axiom,( ? [A] : ( l2_robbins1(A) & v13_struct_0(A,1) & v2_robbins1(A) ) )).
fof(rc6_robbins3,axiom,( ? [A] : ( l2_robbins3(A) & ~ v2_struct_0(A) ) )).
fof(rc6_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v4_roughs_1(B,A) ) ) )).
fof(rc6_scmyciel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v10_ordinal1(A) & v5_finset_1(A) & v2_finsub_1(A) & ~ v1_setfam_1(A) & v1_classes1(A) & v1_scmyciel(A) & v3_scmyciel(A,1) & v4_scmyciel(A) ) )).
fof(rc6_simplex0,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v1_pre_topc(A) & v1_matroid0(A) & v2_simplex0(A) & ~ v4_simplex0(A) & ~ v5_simplex0(A) ) )).
fof(rc6_subset_1,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_zfmisc_1(B) ) ) )).
fof(rc6_tdlat_3,axiom,( ? [A] : ( l1_pre_topc(A) & v1_pre_topc(A) & v2_pre_topc(A) & v3_tdlat_3(A) ) )).
fof(rc6_tex_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & v2_tdlat_3(A) ) )).
fof(rc6_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & ~ v1_tex_2(B,A) ) ) )).
fof(rc6_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v3_tex_3(B,A) ) ) )).
fof(rc6_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v5_topgen_1(B,A) ) ) )).
fof(rc6_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & ~ v1_xboole_0(B) & v1_finsub_1(B) & v2_finsub_1(B) & v3_finsub_1(B) & v1_prob_1(B,u1_struct_0(A)) & v4_prob_1(B,u1_struct_0(A)) & v3_measure1(B,u1_struct_0(A)) & v1_topgen_4(B,A) & v3_topgen_4(B,u1_struct_0(A)) ) ) )).
fof(rc6_tops_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & ~ v2_tops_1(B,A) ) ) )).
fof(rc6_trees_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) & v3_trees_2(B) ) ) )).
fof(rc6_trees_3,axiom,( ? [A] : ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_finseq_1(A) & v2_finseq_1(A) & v6_trees_3(A) ) )).
fof(rc6_tsp_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & v6_pre_topc(B) & v1_tex_2(B,A) ) ) )).
fof(rc6_valued_0,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v4_valued_0(B) ) )).
fof(rc6_vectsp10,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) & ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(B)) & v5_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & v3_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) ) ) )).
fof(rc6_vectsp_1,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( l1_vectsp_1(B,A) & v7_vectsp_1(B,A) ) ) )).
fof(rc6_vectsp_2,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & l1_struct_0(B) ) => ? [C] : ( l2_vectsp_2(C,A,B) & ~ v2_struct_0(C) ) ) )).
fof(rc6_waybel11,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ? [B] : ( l1_waybel_0(B,A) & ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v6_waybel_0(B,A) & v7_waybel_0(B) & v8_waybel_0(B,A) ) ) )).
fof(rc6_waybel23,axiom,( ? [A] : ( l1_orders_2(A) & ~ v2_struct_0(A) & ~ v7_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_yellow_0(A) & v3_yellow_0(A) & v1_lattice3(A) & v2_lattice3(A) & v24_waybel_0(A) & v2_waybel_3(A) & v3_waybel_3(A) ) )).
fof(rc6_waybel34,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & l1_orders_2(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,u1_struct_0(A)) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v18_waybel_0(C,A,B) & v4_waybel34(C,A,B) ) ) )).
fof(rc6_waybel35,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ? [C] : ( m1_waybel35(C,A,B) & v3_card_1(C,1) ) ) )).
fof(rc6_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( l1_waybel_0(B,A) & ~ v2_struct_0(B) & v6_waybel_0(B,A) & v7_waybel_0(B) & v8_waybel_0(B,A) & v9_waybel_0(B,A) ) ) )).
fof(rc6_xxreal_2,axiom,( ? [A] : ( v2_membered(A) & ~ v1_xxreal_2(A) & v2_xxreal_2(A) & v6_xxreal_2(A) ) )).
fof(rc6_yellow_6,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ? [C] : ( m1_yellow_6(C,A,B) & ~ v2_struct_0(C) & v6_waybel_0(C,A) & v2_yellow_6(C,A,B) ) ) )).
fof(rc6_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) & ~ v2_struct_0(B) & v5_algstr_0(B) & v6_algstr_0(B) & v7_algstr_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v1_algstr_1(B) & v2_algstr_1(B) & v3_algstr_1(B) & v4_algstr_1(B) & v2_zmodul01(B) & v3_zmodul01(B) & v4_zmodul01(B) & v5_zmodul01(B) & v8_zmodul01(B,A) ) ) )).
fof(rc6_zmodul03,axiom,( ? [A] : ( l1_zmodul01(A) & ~ v2_struct_0(A) & v5_algstr_0(A) & v6_algstr_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v1_algstr_1(A) & v2_algstr_1(A) & v3_algstr_1(A) & v4_algstr_1(A) & v1_zmodul01(A) & v2_zmodul01(A) & v3_zmodul01(A) & v4_zmodul01(A) & v5_zmodul01(A) & v6_zmodul01(A) & v1_zmodul03(A) & v2_zmodul03(A) ) )).
fof(rc7_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ? [B] : ( m1_abcmiz_1(B,A,k13_abcmiz_1(A)) & ~ v1_xtuple_0(B) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) & v8_abcmiz_1(B,A) ) ) )).
fof(rc7_abian,axiom,( ? [A] : ( v1_xxreal_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v7_ordinal1(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & ~ v1_abian(A) ) )).
fof(rc7_algstr_0,axiom,( ? [A] : ( l3_algstr_0(A) & v15_algstr_0(A) ) )).
fof(rc7_altcat_1,axiom,( ? [A] : ( l2_altcat_1(A) & ~ v2_struct_0(A) & v7_struct_0(A) & v2_altcat_1(A) & v6_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & v14_altcat_1(A) ) )).
fof(rc7_altcat_2,axiom,( ! [A] : ( l2_altcat_1(A) => ? [B] : ( m1_altcat_2(B,A) & v6_altcat_1(B) & v2_altcat_2(B,A) ) ) )).
fof(rc7_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & v15_aofa_000(B,A) ) ) )).
fof(rc7_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ? [D] : ( l4_aofa_a00(D,A,B,C) & v4_aofa_a01(D,A,B,C) ) ) )).
fof(rc7_armstrng,axiom,( ! [A] : ( v1_finset_1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) & v1_relat_1(B) & v4_relat_1(B,k9_setfam_1(A)) & v5_relat_1(B,k9_setfam_1(A)) & v1_finset_1(B) & v4_card_3(B) & v6_armstrng(B,A) ) ) )).
fof(rc7_bcialg_1,axiom,( ! [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] : ( m2_bcialg_1(B,A) & ~ v1_xboole_0(B) & v12_bcialg_1(B,A) ) ) )).
fof(rc7_bilinear,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) => ? [C] : ( 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(C) & v1_relat_1(C) & v4_relat_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) & v5_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & v1_partfun1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) & 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) ) ) )).
fof(rc7_card_1,axiom,( ! [A] : ( v1_card_1(A) => ? [B] : ( v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) ) ) )).
fof(rc7_cat_4,axiom,( ? [A] : ( l2_cat_4(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_struct_0(A) & v2_cat_1(A) & v3_cat_1(A) & v4_cat_1(A) & v5_cat_1(A) & v6_cat_1(A) & v5_cat_4(A) ) )).
fof(rc7_catalg_1,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v2_struct_0(A) & v1_msualg_1(A) & v1_instalg1(A) & v2_catalg_1(A) & v3_catalg_1(A) ) )).
fof(rc7_circcmb3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ? [B] : ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v2_funct_1(B) & v1_finset_1(B) & v3_card_1(B,A) & v1_finseq_1(B) & v2_finseq_1(B) & v4_card_3(B) & v4_valued_0(B) ) ) )).
fof(rc7_clvect_1,axiom,( ? [A] : ( l2_clvect_1(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) & v7_clvect_1(A) & v8_clvect_1(A) ) )).
fof(rc7_cohsp_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) & ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) & v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,A,B) & v4_cohsp_1(C) & v7_cohsp_1(C) ) ) )).
fof(rc7_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) & v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k9_setfam_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & v5_compl_sp(B,A) ) ) )).
fof(rc7_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ? [B] : ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) & v1_afinsq_1(B) & ~ v2_compos_1(B,A) ) ) )).
fof(rc7_comput_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(A),A))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(A)) & v5_relat_1(B,A) & v1_funct_1(B) & v2_margrel1(B) & v3_margrel1(B,A) ) ) )).
fof(rc7_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l5_struct_0(A) ) => ? [B] : ( l2_conlat_1(B,A) & v3_conlat_1(B,A) & ~ v4_conlat_1(B,A) ) ) )).
fof(rc7_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_eqrel_1(B,u1_struct_0(A)) & ~ v10_ordinal1(B) & v1_setfam_1(B) & v5_dilworth(B,A) ) ) )).
fof(rc7_extpro_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ? [B] : ( l1_extpro_1(B,A) & ~ v2_struct_0(B) & v7_struct_0(B) & v8_struct_0(B) & v13_struct_0(B,1) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & v1_extpro_1(B,A) & v3_extpro_1(B,A) ) ) )).
fof(rc7_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v3_card_1(B,A) & v1_finseq_1(B) & v2_finseq_1(B) ) ) )).
fof(rc7_finset_1,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & ~ v1_zfmisc_1(B) & v1_finset_1(B) ) ) )).
fof(rc7_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,A) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v4_card_3(B) & v2_pre_poly(B) ) ) )).
fof(rc7_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : ( m1_subset_1(B,k1_fomodel1(A)) & v10_fomodel1(B,A) ) ) )).
fof(rc7_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ? [C] : ( m1_subset_1(C,k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) & ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & ~ v8_ordinal1(C) & v1_finset_1(C) & v1_finseq_1(C) & v2_finseq_1(C) & v2_pre_poly(C) & ~ v15_fomodel1(C,A) & v3_fomodel2(C,A,B) & v4_fomodel2(C,A) & v5_fomodel2(C,A) ) ) )).
fof(rc7_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) => ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & v1_funcop_1(D) & v2_funcop_1(D) & v1_fomodel2(D,A,B) & v3_fomodel3(D,A,B,C) ) ) )).
fof(rc7_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : ( m1_subset_1(B,k9_funct_2(k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A)))) & v1_relat_1(B) & v4_relat_1(B,k9_setfam_1(k1_fomodel4(A))) & v5_relat_1(B,k9_setfam_1(k1_fomodel4(A))) & v1_funct_1(B) & v1_partfun1(B,k9_setfam_1(k1_fomodel4(A))) & v1_funct_2(B,k9_setfam_1(k1_fomodel4(A)),k9_setfam_1(k1_fomodel4(A))) & v6_fomodel4(B,A) ) ) )).
fof(rc7_fsm_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ? [C] : ( l2_fsm_1(C,A,B) & ~ v2_struct_0(C) & v8_struct_0(C) & v5_fsm_1(C,A,B) ) ) )).
fof(rc7_funct_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v4_funct_1(A) ) )).
fof(rc7_functor0,axiom,( ? [A] : ( l2_altcat_1(A) & ~ v2_struct_0(A) & v1_altcat_2(A) ) )).
fof(rc7_grcat_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v4_grcat_1(A) ) )).
fof(rc7_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_ideal_1(B,A) & v3_ideal_1(B,A) ) ) )).
fof(rc7_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_isomichi(B,A) ) ) )).
fof(rc7_lattices,axiom,( ? [A] : ( l2_lattices(A) & ~ v2_struct_0(A) & v2_lattices(A) & v4_lattices(A) & v5_lattices(A) ) )).
fof(rc7_memstr_0,axiom,( ! [A] : ! [B] : ( ( ~ v1_setfam_1(A) & ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ? [C] : ( ~ 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)) ) ) )).
fof(rc7_monoid_0,axiom,( ! [A] : ( l3_algstr_0(A) => ? [B] : ( m2_monoid_0(B,A) & v15_algstr_0(B) ) ) )).
fof(rc7_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ? [B] : ( l3_msualg_1(B,A) & v3_msualg_1(B,A) & v4_msualg_1(B,A) & v1_msafree1(B,A) & v3_msafree4(B,A) ) ) )).
fof(rc7_msscyc_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & v4_msualg_1(B,A) & v3_msafree2(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( m1_msafree(C,A,B) & v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & ~ v1_xboole_0(C) & v2_finset_1(C) & v1_partfun1(C,u1_struct_0(A)) ) ) )).
fof(rc7_oposet_1,axiom,( ? [A] : ( l2_qmax_1(A) & ~ v2_struct_0(A) & v1_necklace(A) & v3_qmax_1(A) ) )).
fof(rc7_ordinal1,axiom,( ? [A] : v8_ordinal1(A) )).
fof(rc7_ordinal6,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & ~ v1_xboole_0(A) & v3_ordinal6(A) & v4_ordinal6(A) ) )).
fof(rc7_osalg_1,axiom,( ? [A] : ( l3_osalg_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v4_osalg_1(A) & v5_osalg_1(A) & v8_osalg_1(A) ) )).
fof(rc7_osalg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_msualg_2(C,A,B) & v3_msualg_1(C,A) & v4_msualg_1(C,A) & v12_osalg_1(C,A) ) ) )).
fof(rc7_osalg_4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_osalg_4(C,A,B) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) & v2_funcop_1(C) & v2_msualg_4(C,A,B) & v3_msualg_4(C,A,B) & v3_osalg_4(C,A,B) ) ) )).
fof(rc7_pboole,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(A) => ? [C] : ( v1_relat_1(C) & v4_relat_1(C,B) & v5_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,B) ) ) )).
fof(rc7_pcs_0,axiom,( ! [A] : ? [B] : ( 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) & v11_pcs_0(B) ) )).
fof(rc7_pencil_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) & v14_pencil_1(B) ) => ? [C] : ( m3_pboole(C,A,k12_pralg_1(A,B)) & v1_relat_1(C) & v2_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) ) ) )).
fof(rc7_polyalg1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) & ~ v2_struct_0(B) & l1_polyalg1(B,A) ) => ? [C] : ( m1_polyalg1(C,A,B) & ~ v2_struct_0(C) & v1_polyalg1(C,A) ) ) )).
fof(rc7_pre_poly,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_pre_poly(A) ) )).
fof(rc7_pre_topc,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v4_pre_topc(B,A) ) ) )).
fof(rc7_quantal1,axiom,( ? [A] : ( l2_quantal1(A) & ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) ) )).
fof(rc7_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v5_ringcat1(A) ) => ? [B] : ( m1_subset_1(B,A) & v2_ringcat1(B) & v3_ringcat1(B) ) ) )).
fof(rc7_rltopsp1,axiom,( ? [A] : ( l1_rltopsp1(A) & ~ v2_struct_0(A) & v5_rltopsp1(A) ) )).
fof(rc7_robbins3,axiom,( ? [A] : ( l3_robbins3(A) & ~ v2_struct_0(A) ) )).
fof(rc7_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v1_roughs_1(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v4_roughs_1(B,A) ) ) )).
fof(rc7_scmyciel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v10_ordinal1(A) & v1_finset_1(A) & v5_finset_1(A) & v2_finsub_1(A) & ~ v1_setfam_1(A) & v1_classes1(A) & v3_scmyciel(A,1) & v4_scmyciel(A) ) )).
fof(rc7_sheffer1,axiom,( ? [A] : ( l3_sheffer1(A) & v13_struct_0(A,1) ) )).
fof(rc7_simplex0,axiom,( ! [A] : ( ( ~ v5_simplex0(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_xboole_0(B) & v3_pre_topc(B,A) ) ) )).
fof(rc7_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v3_tdlat_3(B) ) ) )).
fof(rc7_tex_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & ~ v2_tdlat_3(A) ) )).
fof(rc7_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v13_struct_0(B,1) & v1_pre_topc(B) ) ) )).
fof(rc7_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & v1_tex_2(B,A) & v1_tex_3(B,A) ) ) )).
fof(rc7_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_tops_1(B,A) ) ) )).
fof(rc7_trees_2,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) ) )).
fof(rc7_trees_3,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v4_trees_3(A) & v5_trees_3(A) ) )).
fof(rc7_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v6_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) & ~ v6_pre_topc(B) ) ) )).
fof(rc7_vectsp10,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(B)) & v5_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & v3_funct_1(C) & ~ v1_xboole_0(C) & v1_partfun1(C,u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & v13_vectsp_1(C,B,A) & v2_hahnban1(C,A,B) ) ) )).
fof(rc7_vectsp_1,axiom,( ! [A] : ( l1_struct_0(A) => ? [B] : ( l1_vectsp_1(B,A) & ~ v2_struct_0(B) & v7_vectsp_1(B,A) ) ) )).
fof(rc7_vectsp_2,axiom,( ! [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) & l6_algstr_0(A) ) => ? [B] : ( l1_vectsp_1(B,A) & ~ v2_struct_0(B) & v13_algstr_0(B) & v7_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) ) ) )).
fof(rc7_waybel35,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) => ? [C] : ( m1_waybel35(C,A,B) & v3_card_1(C,1) ) ) )).
fof(rc7_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v12_waybel_0(B,A) & v13_waybel_0(B,A) ) ) )).
fof(rc7_xxreal_2,axiom,( ? [A] : ( v2_membered(A) & v1_xxreal_2(A) & ~ v2_xxreal_2(A) & v6_xxreal_2(A) ) )).
fof(rc7_zmodul03,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) & ~ v2_struct_0(B) & v5_algstr_0(B) & v6_algstr_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v1_algstr_1(B) & v2_algstr_1(B) & v3_algstr_1(B) & v4_algstr_1(B) & v1_zmodul01(B) & v2_zmodul01(B) & v3_zmodul01(B) & v4_zmodul01(B) & v5_zmodul01(B) & v6_zmodul01(B) & v1_zmodul03(B) & v2_zmodul03(B) ) ) )).
fof(rc8_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ? [B] : ( m1_abcmiz_1(B,A,k13_abcmiz_1(A)) & ~ v1_xtuple_0(B) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) & v6_abcmiz_1(B,A) & v8_abcmiz_1(B,A) ) ) )).
fof(rc8_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ? [B] : ( m2_abcmiz_1(B,A,k12_abcmiz_1(A)) & v2_abcmiz_1(B,A) & v4_abcmiz_a(B,A) ) ) )).
fof(rc8_abian,axiom,( ? [A] : ( v1_xxreal_0(A) & v1_ordinal1(A) & v2_ordinal1(A) & v3_ordinal1(A) & v7_ordinal1(A) & v1_xcmplx_0(A) & v1_xreal_0(A) & v1_int_1(A) & v1_abian(A) ) )).
fof(rc8_algstr_0,axiom,( ? [A] : ( l3_algstr_0(A) & v13_struct_0(A,1) & v15_algstr_0(A) ) )).
fof(rc8_altcat_1,axiom,( ? [A] : ( l2_altcat_1(A) & ~ v2_struct_0(A) & v7_struct_0(A) & v2_altcat_1(A) & v6_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & v13_altcat_1(A) & v14_altcat_1(A) ) )).
fof(rc8_altcat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ? [B] : ( m1_altcat_2(B,A) & ~ v2_struct_0(B) & v6_altcat_1(B) & v2_altcat_2(B,A) ) ) )).
fof(rc8_armstrng,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k9_setfam_1(A)) & v5_relat_1(B,k9_setfam_1(A)) & v8_relat_2(B) & v5_armstrng(B,A) & v7_armstrng(B,A) ) )).
fof(rc8_bcialg_4,axiom,( ? [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) & v8_bcialg_4(A) ) )).
fof(rc8_card_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v3_card_1(B,1) ) ) )).
fof(rc8_catalg_1,axiom,( ! [A] : ? [B] : ( m1_catalg_1(B,A) & v1_msualg_1(B) & v1_instalg1(B) & v2_catalg_1(B) & v3_catalg_1(B) ) )).
fof(rc8_circcmb3,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v2_struct_0(A) & v8_struct_0(A) & ~ v11_struct_0(A) & v14_struct_0(A) & v1_msualg_1(A) & v2_msafree2(A) & v1_circcomb(A) & v2_circcomb(A) & v5_circcomb(A) & v4_circcmb3(A) & v6_circcmb3(A) ) )).
fof(rc8_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ? [B] : ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v4_cohsp_1(B) & v7_cohsp_1(B) ) ) )).
fof(rc8_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ? [B] : ( v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) ) ) )).
fof(rc8_comput_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v4_valued_0(A) & v2_margrel1(A) & v2_comput_1(A) ) )).
fof(rc8_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l5_struct_0(A) ) => ? [B] : ( l2_conlat_1(B,A) & v3_conlat_1(B,A) & v5_conlat_1(B,A) ) ) )).
fof(rc8_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ? [B] : ( m1_eqrel_1(B,u1_struct_0(A)) & ~ v10_ordinal1(B) & v1_setfam_1(B) & v6_dilworth(B,A) ) ) )).
fof(rc8_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ? [B] : ( l1_extpro_1(B,A) & ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & v1_extpro_1(B,A) & v3_extpro_1(B,A) ) ) )).
fof(rc8_finseq_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v3_finseq_1(A) ) )).
fof(rc8_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_finset_1(A) & v5_finset_1(A) ) )).
fof(rc8_fomodel0,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v2_xxreal_0(A) & ~ v1_xboole_0(B) ) => ? [C] : ( m1_subset_1(C,k6_subset_1(k3_finseq_2(B),k1_tarski(k1_xboole_0))) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_finset_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & v2_finseq_1(C) & v4_card_3(C) & v2_pre_poly(C) ) ) )).
fof(rc8_fomodel1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ? [C] : ( m1_subset_1(C,k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0))) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & ~ v1_xboole_0(C) & ~ v8_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) & v1_finseq_1(C) & v2_finseq_1(C) & v4_card_3(C) & v2_pre_poly(C) & v14_fomodel1(C,A,B) ) ) )).
fof(rc8_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : ( m1_subset_1(B,k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & ~ v8_ordinal1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v2_pre_poly(B) & ~ v15_fomodel1(B,A) & v4_fomodel2(B,A) & v5_fomodel2(B,A) ) ) )).
fof(rc8_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : ( m1_subset_1(B,k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & ~ v8_ordinal1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v2_pre_poly(B) & v13_fomodel1(B,A) ) ) )).
fof(rc8_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : ( 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(B) & v7_fomodel4(B,A) ) ) )).
fof(rc8_fsm_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ? [C] : ( l2_fsm_1(C,A,B) & ~ v2_struct_0(C) & v8_struct_0(C) & v7_fsm_1(C,A,B) ) ) )).
fof(rc8_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ? [C] : ( v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v5_funct_1(C,B) ) ) )).
fof(rc8_functor0,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) & ~ v2_struct_0(B) & v1_altcat_2(B) & l1_altcat_1(B) ) => ? [C] : ( l2_functor0(C,A,B) & v6_functor0(C,A,B) & v8_functor0(C,A,B) ) ) )).
fof(rc8_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_grcat_1(A) ) => ? [B] : ( m1_subset_1(B,A) & v1_grcat_1(B) & v2_grcat_1(B) ) ) )).
fof(rc8_group_9,axiom,( ! [A] : ? [B] : ( l1_group_9(B,A) & ~ v2_struct_0(B) & v1_group_1(B) & v2_group_1(B) & v3_group_1(B) & v2_group_9(B,A) & v3_group_9(B,A) & v6_group_9(B,A) ) )).
fof(rc8_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ? [B] : ( 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) ) ) )).
fof(rc8_lattices,axiom,( ? [A] : ( l1_lattices(A) & ~ v2_struct_0(A) & v1_lattices(A) & v6_lattices(A) & v7_lattices(A) ) )).
fof(rc8_memstr_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) => ? [D] : ( 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_card_3(D) & v5_memstr_0(D,A,B,C) ) ) )).
fof(rc8_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ? [B] : ( m2_monoid_0(B,A) & ~ v2_struct_0(B) & v15_algstr_0(B) ) ) )).
fof(rc8_msafree4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( l3_msualg_1(C,A) & v3_msualg_1(C,A) & v4_msualg_1(C,A) & v1_msualg_6(C,A) & ~ v1_catalg_1(C,A) & v4_msafree4(C,A,B) ) ) )).
fof(rc8_msualg_1,axiom,( ? [A] : ( l1_msualg_1(A) & ~ v11_struct_0(A) & v13_struct_0(A,1) & v1_msualg_1(A) & v5_msualg_1(A) ) )).
fof(rc8_oposet_1,axiom,( ? [A] : ( l2_qmax_1(A) & ~ v2_struct_0(A) & v5_orders_2(A) & v1_necklace(A) & v3_qmax_1(A) ) )).
fof(rc8_ordinal1,axiom,( ? [A] : ~ v8_ordinal1(A) )).
fof(rc8_ordinal6,axiom,( ? [A] : ( v1_ordinal1(A) & ~ v1_xboole_0(A) & v1_classes1(A) & v2_classes1(A) & ~ v4_card_3(A) & v1_classes2(A) ) )).
fof(rc8_osalg_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) & v7_osalg_1(B,A) ) ) )).
fof(rc8_osalg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m2_osalg_2(C,A,B) & ~ v1_xboole_0(C) & 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(C,A,B) ) ) )).
fof(rc8_osalg_4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_osalg_4(C,A,B) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) & v2_funcop_1(C) & v2_msualg_4(C,A,B) & v3_osalg_4(C,A,B) ) ) )).
fof(rc8_pcs_0,axiom,( ! [A] : ? [B] : ( 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) & v11_pcs_0(B) ) )).
fof(rc8_pencil_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( 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) ) ) )).
fof(rc8_pre_poly,axiom,( ? [A] : ( v4_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) ) )).
fof(rc8_pre_topc,axiom,( ! [A] : ! [B] : ( ( v2_pre_topc(A) & l1_pre_topc(A) & ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v5_relat_1(C,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) ) ) )).
fof(rc8_random_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ? [B] : ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v6_random_3(B,A) ) ) )).
fof(rc8_rltopsp1,axiom,( ? [A] : ( l1_rltopsp1(A) & ~ 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) & v5_rltopsp1(A) & v6_rltopsp1(A) & v7_rltopsp1(A) ) )).
fof(rc8_robbins3,axiom,( ? [A] : ( l3_robbins3(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) ) )).
fof(rc8_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) & v5_finset_1(B) & v3_scmyciel(B,1) & v4_scmyciel(B) ) ) )).
fof(rc8_sheffer1,axiom,( ? [A] : ( l3_sheffer1(A) & ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & v8_robbins1(A) & v9_sheffer1(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) ) )).
fof(rc8_simplex0,axiom,( ! [A] : ( ( ~ v3_pencil_1(A) & v3_matroid0(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_finset_1(B) & v3_pre_topc(B,A) ) ) )).
fof(rc8_tdlat_3,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v4_tdlat_3(A) ) )).
fof(rc8_tex_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & ~ v2_tdlat_3(A) & v3_tdlat_3(A) ) )).
fof(rc8_tex_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v7_struct_0(B) & v1_pre_topc(B) & v1_tex_2(B,A) ) ) )).
fof(rc8_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & ~ v2_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & ~ v4_tex_3(B,A) ) ) )).
fof(rc8_trees_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) ) ) )).
fof(rc8_trees_3,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v6_trees_3(A) ) )).
fof(rc8_vectsp10,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) & v1_relat_1(C) & v4_relat_1(C,u1_struct_0(B)) & v5_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & ~ v3_funct_1(C) & ~ v1_xboole_0(C) & ~ v1_zfmisc_1(C) & v1_partfun1(C,u1_struct_0(B)) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(A)) & v13_vectsp_1(C,B,A) & v1_hahnban1(C,A,B) ) ) )).
fof(rc8_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ? [B] : ( l1_vectsp_1(B,A) & ~ 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) ) ) )).
fof(rc8_vectsp_2,axiom,( ! [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) & l6_algstr_0(A) ) => ? [B] : ( l1_vectsp_2(B,A) & ~ 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) ) ) )).
fof(rc8_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ? [B] : ( 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) ) ) )).
fof(rc8_xxreal_2,axiom,( ? [A] : ( v2_membered(A) & ~ v1_xboole_0(A) & ~ v1_xxreal_2(A) & ~ v2_xxreal_2(A) & v6_xxreal_2(A) ) )).
fof(rc8_yellow_6,axiom,( ! [A] : ! [B] : ( l1_struct_0(B) => ? [C] : ( m3_yellow_6(C,A,B) & v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v2_pralg_1(C) & v1_yellow_1(C) & v4_waybel_3(C) ) ) )).
fof(rc9_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ? [B] : ( m1_abcmiz_1(B,A,k13_abcmiz_1(A)) & ~ v1_xtuple_0(B) & ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) & v7_abcmiz_1(B,A) & v8_abcmiz_1(B,A) ) ) )).
fof(rc9_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ? [B] : ( m2_abcmiz_1(B,A,k13_abcmiz_1(A)) & v2_abcmiz_1(B,A) & v4_abcmiz_a(B,A) ) ) )).
fof(rc9_altcat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ? [B] : ( m1_altcat_2(B,A) & ~ v2_struct_0(B) & v6_altcat_1(B) & v2_altcat_2(B,A) & v3_altcat_2(B,A) ) ) )).
fof(rc9_bilinear,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) & ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ? [C] : ( 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(C) & v1_relat_1(C) & v4_relat_1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) & v5_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & v1_partfun1(C,k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B))) & 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) ) ) )).
fof(rc9_circcmb3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ? [B] : ( m1_circcmb3(B,A) & ~ v2_struct_0(B) & v8_struct_0(B) & ~ v11_struct_0(B) & v14_struct_0(B) & v1_msualg_1(B) & v2_msafree2(B) & v1_circcomb(B) & v2_circcomb(B) & v5_circcomb(B) & v4_circcmb3(B) & v6_circcmb3(B) ) ) )).
fof(rc9_cohsp_1,axiom,( ? [A] : ( v1_relat_1(A) & v1_funct_1(A) & v10_cohsp_1(A) ) )).
fof(rc9_compl_sp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) & v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,k9_setfam_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & v1_compl_sp(B,A) & v7_compl_sp(B,A) ) ) )).
fof(rc9_comput_1,axiom,( ! [A] : ? [B] : ( m1_finseq_1(B,A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,A) & v1_funct_1(B) & v1_finset_1(B) & v4_card_3(B) & v1_finseq_1(B) & v2_finseq_1(B) & v3_comput_1(B) ) )).
fof(rc9_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ? [B] : ( l2_conlat_1(B,A) & ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) ) ) )).
fof(rc9_extpro_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & ~ v2_compos_1(C,B) ) => ? [D] : ( ~ v1_xboole_0(D) & 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_card_3(D) & v4_extpro_1(D,A,B,C) & v5_extpro_1(D,A,B,C) ) ) )).
fof(rc9_finseq_1,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,A) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) ) )).
fof(rc9_finset_1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v2_finset_1(A) ) )).
fof(rc9_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,A) & v1_partfun1(B,A) & v1_relat_2(B) ) ) )).
fof(rc9_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : ( m1_subset_1(B,k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & ~ v1_xboole_0(B) & ~ v8_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v4_card_3(B) & v2_pre_poly(B) & v15_fomodel1(B,A) ) ) )).
fof(rc9_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : ( m1_subset_1(B,k1_fomodel1(A)) & ~ v4_fomodel1(B,A) ) ) )).
fof(rc9_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : ( m1_subset_1(B,k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & ~ v8_ordinal1(B) & v1_finset_1(B) & v1_finseq_1(B) & v2_finseq_1(B) & v2_pre_poly(B) & v15_fomodel1(B,A) ) ) )).
fof(rc9_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ? [B] : v12_fomodel4(B,A) ) )).
fof(rc9_fsm_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ? [C] : ( l2_fsm_1(C,A,B) & ~ v2_struct_0(C) & v8_struct_0(C) & v5_fsm_1(C,A,B) & v7_fsm_1(C,A,B) ) ) )).
fof(rc9_funct_1,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) ) )).
fof(rc9_functor0,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v12_altcat_1(A) & l2_altcat_1(A) & ~ v2_struct_0(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ? [C] : ( l2_functor0(C,A,B) & v6_functor0(C,A,B) & v8_functor0(C,A,B) & v9_functor0(C,A,B) & v12_functor0(C,A,B) ) ) )).
fof(rc9_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) => ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)))) & v1_relat_1(D) & v4_relat_1(D,u1_struct_0(B)) & v5_relat_1(D,u1_struct_0(C)) & v1_funct_1(D) & ~ v1_xboole_0(D) & v1_partfun1(D,u1_struct_0(B)) & 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) ) ) )).
fof(rc9_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v7_algstr_0(A) & v4_rlvect_1(A) & v5_vectsp_1(A) & v1_algstr_1(A) & l6_algstr_0(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & ~ v1_xboole_0(B) & v1_subset_1(B,u1_struct_0(A)) & v1_ideal_1(B,A) & v2_ideal_1(B,A) & v3_ideal_1(B,A) ) ) )).
fof(rc9_lattices,axiom,( ? [A] : ( l3_lattices(A) & ~ v2_struct_0(A) & v3_lattices(A) & v10_lattices(A) ) )).
fof(rc9_oposet_1,axiom,( ? [A] : ( l2_qmax_1(A) & ~ v2_struct_0(A) & v2_necklace(A) & v3_qmax_1(A) ) )).
fof(rc9_ordinal1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & ~ v10_ordinal1(A) ) )).
fof(rc9_osalg_1,axiom,( ? [A] : ( l3_osalg_1(A) & ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v4_osalg_1(A) & v5_osalg_1(A) & v8_osalg_1(A) & v10_osalg_1(A) ) )).
fof(rc9_pcs_0,axiom,( ! [A] : ? [B] : ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v7_pcs_0(B) ) )).
fof(rc9_pre_poly,axiom,( ! [A] : ? [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) & v1_relat_1(B) & v4_relat_1(B,A) & v5_relat_1(B,A) & v1_partfun1(B,A) & v1_funct_2(B,A,A) & v1_relat_2(B) & v4_relat_2(B) & v8_relat_2(B) & v2_wellord1(B) & v3_orders_1(B) ) )).
fof(rc9_pre_topc,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v2_pre_topc(A) & v7_pre_topc(A) ) )).
fof(rc9_random_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v6_random_3(B,A) ) => ? [C] : ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) & v7_random_3(C,A,B) ) ) )).
fof(rc9_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v9_rltopsp1(B,A) ) ) )).
fof(rc9_robbins1,axiom,( ? [A] : ( l4_robbins1(A) & ~ v2_struct_0(A) & v10_lattices(A) & v4_robbins1(A) & v5_robbins1(A) & v6_robbins1(A) ) )).
fof(rc9_robbins3,axiom,( ? [A] : ( l3_robbins3(A) & ~ v2_struct_0(A) & v10_lattices(A) ) )).
fof(rc9_scmyciel,axiom,( ? [A] : ( ~ v1_xboole_0(A) & v10_ordinal1(A) & v5_finset_1(A) & v2_finsub_1(A) & ~ v1_setfam_1(A) & v1_classes1(A) & v3_scmyciel(A,1) & v4_scmyciel(A) & v5_scmyciel(A) ) )).
fof(rc9_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ? [C] : ( m2_simplex0(C,A,B) & v2_struct_0(C) & v1_pre_topc(C) & v3_pencil_1(C) & v1_matroid0(C) & v3_matroid0(C) ) ) )).
fof(rc9_tdlat_3,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & v5_tdlat_3(A) ) )).
fof(rc9_tex_1,axiom,( ? [A] : ( l1_pre_topc(A) & ~ v2_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & ~ v3_tdlat_3(A) ) )).
fof(rc9_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v13_struct_0(B,1) ) ) )).
fof(rc9_tex_3,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ? [B] : ( m1_pre_topc(B,A) & v1_pre_topc(B) & v2_pre_topc(B) & ~ v2_tex_3(B,A) ) ) )).
fof(rc9_trees_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) & v1_relat_1(C) & ~ v1_xboole_0(C) ) ) )).
fof(rc9_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ? [B] : ( m4_trees_3(B,A) & ~ v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) ) ) )).
fof(rc9_vectsp_1,axiom,( ? [A] : ( l2_algstr_0(A) & ~ v2_struct_0(A) & v12_vectsp_1(A) ) )).
fof(rc9_vectsp_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) => ? [C] : ( l2_vectsp_2(C,A,B) & ~ v2_struct_0(C) & v13_algstr_0(C) & v2_rlvect_1(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v3_vectsp_2(C,A,B) ) ) )).
fof(rc9_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( 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) ) ) )).
fof(rc9_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( l1_waybel_0(B,A) & ~ v2_struct_0(B) & v4_orders_2(B) & v6_waybel_0(B,A) & v7_waybel_0(B) & v3_yellow_6(B,A) ) ) )).
fof(rd10_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k1_funct_1(k16_afinsq_1(A,B,C,D),1) = B )).
fof(rd10_fomodel0,axiom,( ! [A] : k32_fomodel0(k6_partfun1(A)) = A )).
fof(rd10_xtuple_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k5_xtuple_0(k6_xtuple_0(A,B,C,D)) = C )).
fof(rd11_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k1_funct_1(k16_afinsq_1(A,B,C,D),2) = C )).
fof(rd11_xtuple_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_xtuple_0(k6_xtuple_0(A,B,C,D)) = D )).
fof(rd12_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k1_funct_1(k16_afinsq_1(A,B,C,D),3) = D )).
fof(rd12_xtuple_0,axiom,( ! [A] : ( v3_xtuple_0(A) => k6_xtuple_0(k7_xtuple_0(A),k8_xtuple_0(A),k5_xtuple_0(A),k2_xtuple_0(A)) = A ) )).
fof(rd1_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => k1_ordinal4(A,k1_xboole_0) = A ) )).
fof(rd1_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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 ) )).
fof(rd1_cayldick,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_cayldick)) => k2_cayldick(k3_cayldick,A) = A ) )).
fof(rd1_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => k8_complex1(A) = A ) )).
fof(rd1_compos_1,axiom,( ! [A] : ! [B] : ( ( l1_compos_1(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) ) => k5_compos_1(A,B,k5_numbers) = B ) )).
fof(rd1_extpro_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k4_ordinal1) & 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,k5_numbers) = D ) )).
fof(rd1_fomodel0,axiom,( ! [A] : ! [B] : k13_fomodel0(B,A) = A )).
fof(rd1_funct_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => k1_funct_1(k4_relat_1(A),B) = B ) )).
fof(rd1_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) )).
fof(rd1_funct_4,axiom,( ! [A] : ! [B] : ( ( 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 ) )).
fof(rd1_int_1,axiom,( ! [A] : ( v1_int_1(A) => k10_subset_1(A,k4_numbers) = A ) )).
fof(rd1_lattices,axiom,( ! [A] : ! [B] : ( ( ~ 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 ) )).
fof(rd1_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => k10_subset_1(A,k4_ordinal1) = A ) )).
fof(rd1_nattra_1,axiom,( ! [A] : ( ( ~ 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) & v4_nattra_1(A) & l1_cat_1(A) ) => k10_nattra_1(A) = A ) )).
fof(rd1_relat_1,axiom,( ! [A] : k9_xtuple_0(k4_relat_1(A)) = A )).
fof(rd1_rlvect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_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)) & m1_subset_1(C,u1_struct_0(A)) ) => k1_algstr_0(A,B,C) = C ) )).
fof(rd1_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) ) => k61_valued_1(A,k5_numbers) = A ) )).
fof(rd1_vectsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v1_vectsp_1(A) & l6_algstr_0(A) & m1_subset_1(B,u1_struct_0(A)) & v9_struct_0(C,A) & m1_subset_1(C,u1_struct_0(A)) ) => k6_algstr_0(A,B,C) = C ) )).
fof(rd1_xcmplx_0,axiom,( ! [A] : ( v1_xcmplx_0(A) => k10_subset_1(A,k2_numbers) = A ) )).
fof(rd1_xreal_0,axiom,( ! [A] : ( v1_xreal_0(A) => k10_subset_1(A,k1_numbers) = A ) )).
fof(rd1_xtuple_0,axiom,( ! [A] : ! [B] : k1_xtuple_0(k4_tarski(A,B)) = A )).
fof(rd1_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => k10_subset_1(A,k6_numbers) = A ) )).
fof(rd1_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ 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_zmodul02(B,A) ) => k22_zmodul02(A,B,k19_zmodul02(A)) = B ) )).
fof(rd2_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => k1_ordinal4(k1_xboole_0,A) = A ) )).
fof(rd2_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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 ) )).
fof(rd2_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_cayldick(A) & l1_cayldick(A) ) => k2_cayldick(A,k4_struct_0(A)) = k4_struct_0(A) ) )).
fof(rd2_compos_1,axiom,( ! [A] : ! [B] : ( ( l1_compos_1(A) & v7_ordinal1(B) ) => k5_compos_1(A,k4_compos_1(A),B) = k4_compos_1(A) ) )).
fof(rd2_fomodel0,axiom,( ! [A] : k22_fomodel0(A) = A )).
fof(rd2_funct_4,axiom,( ! [A] : ! [B] : ( ( 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 ) )).
fof(rd2_lattices,axiom,( ! [A] : ! [B] : ( ( ~ 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 ) )).
fof(rd2_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => k10_subset_1(A,k4_ordinal1) = A ) )).
fof(rd2_relat_1,axiom,( ! [A] : k10_xtuple_0(k4_relat_1(A)) = A )).
fof(rd2_rlvect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_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)) & m1_subset_1(C,u1_struct_0(A)) ) => k1_algstr_0(A,C,B) = C ) )).
fof(rd2_vectsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v2_vectsp_1(A) & l6_algstr_0(A) & v9_struct_0(B,A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k6_algstr_0(A,B,C) = B ) )).
fof(rd2_xtuple_0,axiom,( ! [A] : ! [B] : k2_xtuple_0(k4_tarski(A,B)) = B )).
fof(rd2_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ 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_zmodul02(B,A) ) => k23_zmodul02(A,1,B) = B ) )).
fof(rd3_afinsq_1,axiom,( ! [A] : k1_funct_1(k5_afinsq_1(A),k5_numbers) = A )).
fof(rd3_cat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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 ) )).
fof(rd3_cayldick,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v31_algstr_0(A) & v33_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v8_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v3_cayldick(A) & v5_cayldick(A) & l1_cayldick(A) & m1_subset_1(B,u1_struct_0(A)) ) => k2_cayldick(A,k2_cayldick(A,B)) = B ) )).
fof(rd3_compos_1,axiom,( ! [A] : ! [B] : ( ( l1_compos_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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 ) )).
fof(rd3_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => k9_xtuple_0(k2_zfmisc_1(A,B)) = A ) )).
fof(rd3_funct_4,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(rd3_lattices,axiom,( ! [A] : ! [B] : ( ( ~ 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 ) )).
fof(rd3_relat_1,axiom,( ! [A] : k2_relat_1(k4_relat_1(A)) = k4_relat_1(A) )).
fof(rd3_rlvect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v8_rlvect_1(A) & l1_rlvect_1(A) & v9_struct_0(B,A) & m1_subset_1(B,u1_struct_0(A)) & v1_xreal_0(C) ) => k1_rlvect_1(A,B,C) = B ) )).
fof(rd3_vectsp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) & ~ v9_struct_0(B,A) & m1_subset_1(B,u1_struct_0(A)) ) => k11_algstr_0(A,k11_algstr_0(A,B)) = B ) )).
fof(rd3_xtuple_0,axiom,( ! [A] : ( v1_xtuple_0(A) => k4_tarski(k1_xtuple_0(A),k2_xtuple_0(A)) = A ) )).
fof(rd4_afinsq_1,axiom,( ! [A] : ! [B] : k1_funct_1(k6_afinsq_1(A,B),k5_numbers) = A )).
fof(rd4_cat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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 ) )).
fof(rd4_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v31_algstr_0(A) & v8_rlvect_1(A) & v6_vectsp_1(A) & v3_lopban_2(A) & v3_cayldick(A) & l1_cayldick(A) ) => k2_cayldick(A,k5_struct_0(A)) = k5_struct_0(A) ) )).
fof(rd4_compos_1,axiom,( ! [A] : ! [B] : ( ( l1_compos_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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 ) )).
fof(rd4_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => k10_xtuple_0(k2_zfmisc_1(B,A)) = A ) )).
fof(rd4_lattices,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(rd4_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => k5_relat_1(A,k9_xtuple_0(A)) = A ) )).
fof(rd4_rlvect_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_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)) ) => k4_algstr_0(A,B) = B ) )).
fof(rd4_xtuple_0,axiom,( ! [A] : ! [B] : ! [C] : k4_xtuple_0(k3_xtuple_0(A,B,C)) = A )).
fof(rd5_afinsq_1,axiom,( ! [A] : ! [B] : k1_funct_1(k6_afinsq_1(A,B),1) = B )).
fof(rd5_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v31_algstr_0(A) & v8_rlvect_1(A) & v3_vectsp_1(A) & v3_lopban_2(A) & v3_cayldick(A) & l1_cayldick(A) ) => k2_cayldick(A,k5_struct_0(A)) = k5_struct_0(A) ) )).
fof(rd5_compos_1,axiom,( ! [A] : ! [B] : ( ( l1_compos_1(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) ) => k6_compos_1(A,B,k5_numbers) = B ) )).
fof(rd5_fomodel0,axiom,( ! [A] : ! [B] : k2_xboole_0(k6_subset_1(A,B),k3_xboole_0(A,B)) = A )).
fof(rd5_lattices,axiom,( ! [A] : ! [B] : ( ( ~ 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 ) )).
fof(rd5_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(A) => k5_relat_1(k5_relat_1(A,B),B) = k5_relat_1(A,B) ) )).
fof(rd5_rlvect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) & m1_subset_1(B,u1_struct_0(A)) & v9_struct_0(C,A) & m1_subset_1(C,u1_struct_0(A)) ) => k5_algstr_0(A,B,C) = B ) )).
fof(rd5_xtuple_0,axiom,( ! [A] : ! [B] : ! [C] : k5_xtuple_0(k3_xtuple_0(A,B,C)) = B )).
fof(rd6_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : k1_funct_1(k7_afinsq_1(A,B,C),k5_numbers) = A )).
fof(rd6_compos_1,axiom,( ! [A] : ! [B] : ( ( l1_compos_1(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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 ) )).
fof(rd6_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & m1_subset_1(B,k1_zfmisc_1(k9_xtuple_0(A))) ) => k1_relset_1(B,k5_relat_1(A,B)) = B ) )).
fof(rd6_lattices,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(rd6_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => k6_relat_1(k10_xtuple_0(A),A) = A ) )).
fof(rd6_xtuple_0,axiom,( ! [A] : ! [B] : ! [C] : k2_xtuple_0(k3_xtuple_0(A,B,C)) = C )).
fof(rd7_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : k1_funct_1(k7_afinsq_1(A,B,C),1) = B )).
fof(rd7_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_partit_2(A) & m1_subset_1(B,k9_xtuple_0(A)) ) => k1_funct_1(A,k1_funct_1(A,B)) = B ) )).
fof(rd7_lattices,axiom,( ! [A] : ! [B] : ( ( ~ 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 ) )).
fof(rd7_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k6_relat_1(A,k6_relat_1(A,B)) = k6_relat_1(A,B) ) )).
fof(rd7_xtuple_0,axiom,( ! [A] : ( v2_xtuple_0(A) => k3_xtuple_0(k4_xtuple_0(A),k5_xtuple_0(A),k2_xtuple_0(A)) = A ) )).
fof(rd8_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : k1_funct_1(k7_afinsq_1(A,B,C),2) = C )).
fof(rd8_fomodel0,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k7_relset_1(A,A,k6_partfun1(A),B) = B ) )).
fof(rd8_relat_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) ) => k5_relat_1(B,A) = B ) )).
fof(rd8_xtuple_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k7_xtuple_0(k6_xtuple_0(A,B,C,D)) = A )).
fof(rd9_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k1_funct_1(k16_afinsq_1(A,B,C,D),k5_numbers) = A )).
fof(rd9_fomodel0,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k6_partfun1(A))) => k2_relat_1(B) = B ) )).
fof(rd9_relat_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) ) => k6_relat_1(A,B) = B ) )).
fof(rd9_xtuple_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k8_xtuple_0(k6_xtuple_0(A,B,C,D)) = B )).
fof(redefinition_k10_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [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) ) => k10_aofa_a00(A,B,C,D,E,F,G,H,I) = k9_aofa_a00(B,C,D,E,F,G,H,I) ) )).
fof(redefinition_k10_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k10_binarith,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k10_binarith(A,B) = k5_finseq_1(B) ) )).
fof(redefinition_k10_bspace,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) )).
fof(redefinition_k10_bvfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k10_catalg_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k10_clopban1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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) ) )).
fof(redefinition_k10_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => k10_comseq_3(A) = k2_series_1(A) ) )).
fof(redefinition_k10_cqc_lang,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k10_descip_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_finseq_2(A,k6_margrel1)) & v7_ordinal1(C) ) => k10_descip_1(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k10_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k10_euclid,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k1_euclid(A)) ) => k10_euclid(A,B) = k54_valued_1(B) ) )).
fof(redefinition_k10_filter_0,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k10_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k10_fomodel0,axiom,( ! [A] : ! [B] : k10_fomodel0(A,B) = k4_funct_3(A,B) )).
fof(redefinition_k10_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) & v7_ordinal1(C) & v8_ordinal1(C) ) => k10_fomodel3(A,B,C) = k9_fomodel3(A,B,C) ) )).
fof(redefinition_k10_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k10_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k10_funct_3,axiom,( ! [A] : ! [B] : k10_funct_3(A,B) = k8_funct_3(A,B) )).
fof(redefinition_k10_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k10_fvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & ~ 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) ) )).
fof(redefinition_k10_genealg1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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,k4_ordinal1) & m1_subset_1(E,k4_ordinal1) & m1_subset_1(F,k4_ordinal1) & m1_subset_1(G,k4_ordinal1) ) => k10_genealg1(A,B,C,D,E,F,G) = k4_genealg1(A,B,C,D,E,F,G) ) )).
fof(redefinition_k10_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => k10_glib_000(A) = k8_glib_000(A) ) )).
fof(redefinition_k10_group_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k10_laplace,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) ) => k10_laplace(A,B) = k5_finseq_1(B) ) )).
fof(redefinition_k10_margrel1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => k10_margrel1(A,B) = k4_xboolean(A,B) ) )).
fof(redefinition_k10_matrixj1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k10_measure8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k6_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => k10_measure8(A,B,C,D) = k3_relat_1(C,D) ) )).
fof(redefinition_k10_monoid_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k10_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k10_petri,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k10_pralg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k10_pre_poly,axiom,( ! [A] : ! [B] : ( m1_finseq_1(B,k3_finseq_2(A)) => k10_pre_poly(A,B) = k1_card_3(B) ) )).
fof(redefinition_k10_prvect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k10_pua2mss1,axiom,( ! [A] : ! [B] : ( ( v2_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) & m4_pua2mss1(B,A) ) => k10_pua2mss1(A,B) = k10_xtuple_0(B) ) )).
fof(redefinition_k10_quofield,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k10_rvsum_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k10_rvsum_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k10_seq_4,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k2_numbers) & v1_xcmplx_0(B) ) => k10_seq_4(A,B) = k24_valued_1(A,B) ) )).
fof(redefinition_k10_topalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k10_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,u1_struct_0(k15_euclid(A))) ) => k10_toprealc(A,B,C) = k18_valued_1(B,C) ) )).
fof(redefinition_k10_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k11_ami_3,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k11_aofa_000,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(redefinition_k11_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k11_arytm_3,axiom,( k11_arytm_3 = k1_xboole_0 )).
fof(redefinition_k11_card_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k11_chain_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_chain_1(B,A) & m1_subset_1(C,k4_ordinal1) ) => k11_chain_1(A,B,C) = k5_chain_1(A,B,C) ) )).
fof(redefinition_k11_cohsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k11_cqc_lang,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k11_cqc_sim1,axiom,( ! [A] : k11_cqc_sim1(A) = k4_relat_1(A) )).
fof(redefinition_k11_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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) ) )).
fof(redefinition_k11_euclid,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k1_euclid(A)) ) => k11_euclid(A,B) = k39_valued_1(B) ) )).
fof(redefinition_k11_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k11_filter_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) & m2_nat_lat(B,A) ) => k11_filter_2(A,B) = k1_lattice2(B) ) )).
fof(redefinition_k11_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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)) ) => k11_fomodel2(A,B,C,D,E) = k1_funct_1(D,E) ) )).
fof(redefinition_k11_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k11_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k11_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => k11_funct_7(A,B,C) = k10_funct_7(B,C) ) )).
fof(redefinition_k11_genealg1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( ~ 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,k4_ordinal1) & m1_subset_1(E,k4_ordinal1) & m1_subset_1(F,k4_ordinal1) & m1_subset_1(G,k4_ordinal1) & m1_subset_1(H,k4_ordinal1) ) => k11_genealg1(A,B,C,D,E,F,G,H) = k5_genealg1(A,B,C,D,E,F,G,H) ) )).
fof(redefinition_k11_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => k11_glib_000(A) = k9_glib_000(A) ) )).
fof(redefinition_k11_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k11_lang1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k11_ltlaxio3,axiom,( ! [A] : ! [B] : ( ( v2_funct_1(A) & m1_finseq_1(A,k1_hilbert1) & v2_funct_1(B) & m1_finseq_1(B,k1_hilbert1) ) => k11_ltlaxio3(A,B) = k4_tarski(A,B) ) )).
fof(redefinition_k11_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & v7_ordinal1(C) & m1_subset_1(D,A) ) => k11_matrix_0(A,B,C,D) = k10_matrix_0(B,C,D) ) )).
fof(redefinition_k11_matrixj1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k11_measure8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & v1_funct_1(D) & v1_funct_2(D,B,k6_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => k11_measure8(A,B,C,D) = k3_relat_1(C,D) ) )).
fof(redefinition_k11_monoid_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l3_algstr_0(A) ) => k11_monoid_1(A,B) = k9_monoid_1(A,B) ) )).
fof(redefinition_k11_nat_3,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => k11_nat_3(A,B) = k10_nat_3(A,B) ) )).
fof(redefinition_k11_newton,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => k11_newton(A,B) = k1_newton(A,B) ) )).
fof(redefinition_k11_openlatt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k11_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k11_polynom1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)))) ) => k11_polynom1(A,B,C,D) = k10_polynom1(A,B,C,D) ) )).
fof(redefinition_k11_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k11_prvect_1,axiom,( ! [A] : ! [B] : ( ( 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) = k6_funct_6(B) ) )).
fof(redefinition_k11_prvect_2,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k11_quaterni,axiom,( k11_quaterni = k4_quaterni )).
fof(redefinition_k11_ringcat1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v4_ringcat1(A) & m1_subset_1(B,k10_ringcat1(A)) ) => k11_ringcat1(A,B) = k1_ringcat1(B) ) )).
fof(redefinition_k11_rvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k11_rvsum_2,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k11_seq_4,axiom,( ! [A] : ( m1_finseq_1(A,k2_numbers) => k11_seq_4(A) = k54_valued_1(A) ) )).
fof(redefinition_k11_toprealc,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) ) => k11_toprealc(A,B) = k39_valued_1(B) ) )).
fof(redefinition_k12_abcmiz_a,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k12_ami_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k12_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k12_arytm_3,axiom,( k12_arytm_3 = k1_arytm_3 )).
fof(redefinition_k12_cgames_1,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & m1_subset_1(B,k2_cgames_1(A)) ) => k12_cgames_1(A,B) = k10_cgames_1(B) ) )).
fof(redefinition_k12_cqc_lang,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k12_descip_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & 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) ) )).
fof(redefinition_k12_diff_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)) & v1_diff_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)))) & m1_subset_1(B,k4_ordinal1) ) => k12_diff_1(A,B) = k1_funct_1(A,B) ) )).
fof(redefinition_k12_finseq_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k12_finseq_1(A,B) = k5_finseq_1(B) ) )).
fof(redefinition_k12_fomodel0,axiom,( ! [A] : ! [B] : k12_fomodel0(A,B) = k3_xboole_0(A,B) )).
fof(redefinition_k12_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k12_freealg,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(A,k4_ordinal1) & ~ v1_xboole_0(B) & v1_freealg(B) ) => k12_freealg(A,B) = k8_freealg(A,B) ) )).
fof(redefinition_k12_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k12_funct_3,axiom,( ! [A] : k12_funct_3(A) = k11_funct_3(A) )).
fof(redefinition_k12_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k12_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => k12_functor0(A) = k11_functor0(A) ) )).
fof(redefinition_k12_fvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & ~ 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) ) )).
fof(redefinition_k12_genealg1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [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,k4_ordinal1) & m1_subset_1(E,k4_ordinal1) & m1_subset_1(F,k4_ordinal1) & m1_subset_1(G,k4_ordinal1) & m1_subset_1(H,k4_ordinal1) & m1_subset_1(I,k4_ordinal1) ) => k12_genealg1(A,B,C,D,E,F,G,H,I) = k6_genealg1(A,B,C,D,E,F,G,H,I) ) )).
fof(redefinition_k12_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k12_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k12_lattice5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k12_lopban_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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) ) )).
fof(redefinition_k12_margrel1,axiom,( ! [A] : k12_margrel1(A) = k11_margrel1(A) )).
fof(redefinition_k12_monoid_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k12_openlatt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k12_polynom3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k12_polynom3(A) = k5_finseq_1(A) ) )).
fof(redefinition_k12_prvect_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k12_quaterni,axiom,( k12_quaterni = k5_quaterni )).
fof(redefinition_k12_rfunct_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k12_ringcat1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v4_ringcat1(A) & m1_subset_1(B,k10_ringcat1(A)) ) => k12_ringcat1(A,B) = k2_ringcat1(B) ) )).
fof(redefinition_k12_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => k12_rvsum_1(A) = k39_valued_1(A) ) )).
fof(redefinition_k12_rvsum_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k12_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k12_supinf_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_valued_0(A) ) => k12_supinf_2(A,B) = k1_funct_1(A,B) ) )).
fof(redefinition_k12_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,u1_struct_0(k15_euclid(A))) ) => k12_toprealc(A,B,C) = k50_valued_1(B,C) ) )).
fof(redefinition_k12_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k13_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k13_descip_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & 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) ) )).
fof(redefinition_k13_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [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) ) )).
fof(redefinition_k13_fomodel1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k13_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) => k13_fomodel2(A,B,C,D) = k12_fomodel2(A,B,C,D) ) )).
fof(redefinition_k13_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k13_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k13_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(D,A) ) => k13_funct_7(A,B,C,D) = k12_funct_7(B,C,D) ) )).
fof(redefinition_k13_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k13_lang1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => k13_lang1(A,B) = k18_finseq_1(B) ) )).
fof(redefinition_k13_lattice3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k13_lexbfs,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(redefinition_k13_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => k13_lopclset(A) = k8_lopclset(A) ) )).
fof(redefinition_k13_matrix_0,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k13_matrix_0(A,B) = k5_finseq_1(B) ) )).
fof(redefinition_k13_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k13_ordinal6,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v3_ordinal1(B) ) => k13_ordinal6(A,B) = k12_ordinal6(A,B) ) )).
fof(redefinition_k13_osalg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k13_polynom3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_group_1(A) & l6_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k13_polynom3(A,B,C) = k11_polynom3(A,B,C) ) )).
fof(redefinition_k13_prob_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(redefinition_k13_rvsum_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k4_finseq_2(A,k1_numbers)) ) => k13_rvsum_1(A,B) = k39_valued_1(B) ) )).
fof(redefinition_k13_seq_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,k12_seq_4(A)) & m1_subset_1(C,k12_seq_4(A)) ) => k13_seq_4(A,B,C) = k1_valued_1(B,C) ) )).
fof(redefinition_k13_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(D) ) => k13_toprealc(A,B,C,D) = k1_funct_7(B,C,D) ) )).
fof(redefinition_k13_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k14_abcmiz_a,axiom,( ! [A] : ( m1_subset_1(A,k5_abcmiz_a) => k14_abcmiz_a(A) = k13_abcmiz_a(A) ) )).
fof(redefinition_k14_borsuk_7,axiom,( ! [A] : ( v1_int_1(A) => k14_borsuk_7(A) = k13_borsuk_7(A) ) )).
fof(redefinition_k14_cat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) => k14_cat_2(A,B,C,D,E) = k13_funct_3(D,E) ) )).
fof(redefinition_k14_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k14_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) => k14_funct_7(A,B,C,D,E) = k1_funct_7(C,D,E) ) )).
fof(redefinition_k14_grcat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k14_lexbfs,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & m2_lexbfs(B,A) ) => k14_lexbfs(A,B) = k40_glib_000(B) ) )).
fof(redefinition_k14_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & m1_subset_1(C,k4_finseq_2(B,A)) ) => k14_matrix_0(A,B,C) = k5_finseq_1(C) ) )).
fof(redefinition_k14_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k14_prvect_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v1_prvect_1(A) & m1_subset_1(B,k4_finseq_1(A)) ) => k14_prvect_1(A,B) = k1_funct_1(A,B) ) )).
fof(redefinition_k14_rvsum_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k14_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k14_trees_3,axiom,( ! [A] : ( v7_ordinal1(A) => k14_trees_3(A) = k5_finseq_1(A) ) )).
fof(redefinition_k14_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k15_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k15_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k15_bvfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k15_cat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) => k15_cat_2(A,B,C,D,E,F) = k15_funct_3(E,F) ) )).
fof(redefinition_k15_clopban1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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) ) )).
fof(redefinition_k15_csspace,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) )).
fof(redefinition_k15_fomodel1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fomodel1(A) ) => k15_fomodel1(A) = k1_fomodel1(A) ) )).
fof(redefinition_k15_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & ~ v1_xboole_0(B) ) => k15_fomodel2(A,B) = k14_fomodel2(A,B) ) )).
fof(redefinition_k15_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(redefinition_k15_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => k15_glib_000(A) = k14_glib_000(A) ) )).
fof(redefinition_k15_glib_004,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(redefinition_k15_ideal_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k15_lattice5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k15_margrel1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k15_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) & m1_subset_1(D,A) & m1_subset_1(E,A) ) => k15_matrix_0(A,B,C,D,E) = k12_matrix_0(B,C,D,E) ) )).
fof(redefinition_k15_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k15_mesfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) & v1_xxreal_0(C) ) => k15_mesfunc1(A,B,C) = k11_mesfunc1(B,C) ) )).
fof(redefinition_k15_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k15_monoid_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k15_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k15_pre_poly,axiom,( ! [A] : k15_pre_poly(A) = k14_pre_poly(A) )).
fof(redefinition_k15_rvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k15_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => k15_seq_4(A) = k14_seq_4(A) ) )).
fof(redefinition_k15_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => k15_sin_cos(A) = k14_sin_cos(A) ) )).
fof(redefinition_k15_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k16_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k16_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k16_csspace,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k16_csspace(A,B,C) = k2_normsp_1(A,B,C) ) )).
fof(redefinition_k16_descip_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) & m1_subset_1(B,A) ) => k16_descip_1(A,B) = k1_ordinal1(B) ) )).
fof(redefinition_k16_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => k16_euclid(A) = k4_euclid(A) ) )).
fof(redefinition_k16_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k16_fomodel1(A) = k2_fomodel1(A) ) )).
fof(redefinition_k16_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k16_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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) ) )).
fof(redefinition_k16_margrel1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k16_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & v1_matrix_0(C) & v2_matrix_0(C,A,B,B) & m1_finseq_1(C,k3_finseq_2(A)) ) => k16_matrixj1(A,B,C) = k5_finseq_1(C) ) )).
fof(redefinition_k16_mesfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) & v1_xxreal_0(C) ) => k16_mesfunc1(A,B,C) = k12_mesfunc1(B,C) ) )).
fof(redefinition_k16_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k16_monoid_1,axiom,( ! [A] : ! [B] : k16_monoid_1(A,B) = k4_funct_3(A,B) )).
fof(redefinition_k16_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => k16_openlatt(A) = k8_openlatt(A) ) )).
fof(redefinition_k16_pralg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k16_pre_poly,axiom,( ! [A] : k16_pre_poly(A) = k1_pboole(A) )).
fof(redefinition_k16_prvect_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v1_prvect_1(A) & m1_subset_1(B,k4_finseq_1(k15_prvect_1(A))) ) => k16_prvect_1(A,B) = k1_funct_1(A,B) ) )).
fof(redefinition_k16_quatern2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_quatern2)) => k16_quatern2(A) = k26_quaterni(A) ) )).
fof(redefinition_k16_seq_4,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k12_seq_4(A)) ) => k16_seq_4(A,B) = k30_valued_1(B) ) )).
fof(redefinition_k16_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k17_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k16_coh_sp(A)) => k17_coh_sp(A,B) = k2_xtuple_0(B) ) )).
fof(redefinition_k17_finseq_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & m1_finseq_1(C,A) ) => k17_finseq_1(A,B,C) = k16_finseq_1(B,C) ) )).
fof(redefinition_k17_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & l1_fomodel1(A) ) => k17_fomodel1(A) = k10_fomodel1(A) ) )).
fof(redefinition_k17_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : k17_funcop_1(A,B,C) = k13_funcop_1(A,B,C) )).
fof(redefinition_k17_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) => k17_funct_3(A,B,C,D) = k5_relat_1(C,D) ) )).
fof(redefinition_k17_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => k17_glib_000(A) = k16_glib_000(A) ) )).
fof(redefinition_k17_lexbfs,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k17_lopban_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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) ) )).
fof(redefinition_k17_margrel1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k4_partfun1(k3_finseq_2(A),A)) ) => k17_margrel1(A,B) = k5_finseq_1(B) ) )).
fof(redefinition_k17_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & v1_matrix_0(C) & m1_finseq_1(C,k3_finseq_2(A)) ) => k17_matrix_0(A,B,C) = k2_finseq_3(B,C) ) )).
fof(redefinition_k17_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & v7_ordinal1(C) & v1_matrix_0(D) & v2_matrix_0(D,A,B,B) & m1_finseq_1(D,k3_finseq_2(A)) & v1_matrix_0(E) & v2_matrix_0(E,A,C,C) & m1_finseq_1(E,k3_finseq_2(A)) ) => k17_matrixj1(A,B,C,D,E) = k10_finseq_1(D,E) ) )).
fof(redefinition_k17_mesfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) & v1_xxreal_0(C) ) => k17_mesfunc1(A,B,C) = k13_mesfunc1(B,C) ) )).
fof(redefinition_k17_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k17_monoid_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => k17_monoid_1(A,B) = k2_funcop_1(A,B) ) )).
fof(redefinition_k17_rvsum_1,axiom,( ! [A] : ( m1_finseq_1(A,k2_numbers) => k17_rvsum_1(A) = k16_rvsum_1(A) ) )).
fof(redefinition_k17_seq_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,k12_seq_4(A)) & m1_subset_1(C,k12_seq_4(A)) ) => k17_seq_4(A,B,C) = k45_valued_1(B,C) ) )).
fof(redefinition_k17_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => k17_supinf_2(A) = k10_xtuple_0(A) ) )).
fof(redefinition_k17_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_xreal_0(B) & ~ v3_xxreal_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)))) ) => k17_toprealc(A,B,C) = k2_toprealc(C) ) )).
fof(redefinition_k17_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k18_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k18_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k16_coh_sp(A)) => k18_coh_sp(A,B) = k1_xtuple_0(B) ) )).
fof(redefinition_k18_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k18_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k18_fomodel1(A) = k7_fomodel1(A) ) )).
fof(redefinition_k18_funcop_1,axiom,( ! [A] : ! [B] : k18_funcop_1(A,B) = k16_funcop_1(A,B) )).
fof(redefinition_k18_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k18_mesfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) & v1_xxreal_0(C) ) => k18_mesfunc1(A,B,C) = k14_mesfunc1(B,C) ) )).
fof(redefinition_k18_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v1_lattice2(A) & l3_lattices(A) ) => k18_openlatt(A) = k8_openlatt(A) ) )).
fof(redefinition_k18_rvsum_1,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => k18_rvsum_1(A) = k16_rvsum_1(A) ) )).
fof(redefinition_k18_scmfsa_2,axiom,( ! [A] : ! [B] : ( ( 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(k7_card_1(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) ) )).
fof(redefinition_k18_seq_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,k12_seq_4(A)) & m1_subset_1(C,k2_numbers) ) => k18_seq_4(A,B,C) = k24_valued_1(B,C) ) )).
fof(redefinition_k18_substut1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k16_substut1(A)) ) => k18_substut1(A,B) = k1_xtuple_0(B) ) )).
fof(redefinition_k19_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => k19_bvfunc_1(A,B) = k8_xboolean(A,B) ) )).
fof(redefinition_k19_euclid,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => k19_euclid(A,B) = k10_finseq_1(A,B) ) )).
fof(redefinition_k19_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k19_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k19_grcat_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k19_margrel1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_margrel1(A) ) => k19_margrel1(A) = k18_margrel1(A) ) )).
fof(redefinition_k19_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k19_mesfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) & v1_xxreal_0(C) ) => k19_mesfunc1(A,B,C) = k10_relat_1(B,C) ) )).
fof(redefinition_k19_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k19_seq_4,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k12_seq_4(A)) ) => k19_seq_4(A,B) = k54_valued_1(B) ) )).
fof(redefinition_k19_substut1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k16_substut1(A)) ) => k19_substut1(A,B) = k2_xtuple_0(B) ) )).
fof(redefinition_k19_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(redefinition_k1_abian,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) => k1_abian(A,B,C) = k8_funct_7(B,C) ) )).
fof(redefinition_k1_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => k1_afinsq_1(A) = k1_card_1(A) ) )).
fof(redefinition_k1_altcat_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) & m1_subset_1(B,u1_struct_0(A)) & ~ v1_xboole_0(C) & 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)))) & m1_altcat_5(E,A,B,C,D) & m1_subset_1(F,C) ) => k1_altcat_5(A,B,C,D,E,F) = k1_funct_1(E,F) ) )).
fof(redefinition_k1_amistd_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) = k1_funct_7(C,D,E) ) )).
fof(redefinition_k1_aofa_000,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k1_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => k1_aofa_a00(A,B,C,D) = k1_funct_7(B,C,D) ) )).
fof(redefinition_k1_asympt_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k1_asympt_0(A,B) = k1_valued_1(A,B) ) )).
fof(redefinition_k1_binarith,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => k1_binarith(A,B) = k5_xboolean(A,B) ) )).
fof(redefinition_k1_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k1_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k1_bvfunc_2,axiom,( ! [A] : k1_bvfunc_2(A) = k1_partit1(A) )).
fof(redefinition_k1_card_fil,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_card_fil(B,A) ) => k1_card_fil(A,B) = k7_setfam_1(A,B) ) )).
fof(redefinition_k1_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(C,A) ) => k1_cat_3(A,B,C) = k16_funcop_1(B,C) ) )).
fof(redefinition_k1_cat_5,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k1_catalan2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) & v1_relat_1(B) & v5_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => k1_catalan2(A,B) = k1_ordinal4(A,B) ) )).
fof(redefinition_k1_chain_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k1_chain_1(A,B) = k1_zfmisc_1(B) ) )).
fof(redefinition_k1_circcomb,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( 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) ) )).
fof(redefinition_k1_circuit2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k1_classes2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) ) => k1_classes2(A,B) = k1_tarski(B) ) )).
fof(redefinition_k1_clopban2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_normsp_0(A) & v4_normsp_0(A) & 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) ) )).
fof(redefinition_k1_closure1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(redefinition_k1_closure3,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k1_convex4,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k1_descip_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k1_dist_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_finseq_1(B,A) => k1_dist_1(A,B,C) = k10_relat_1(B,C) ) )).
fof(redefinition_k1_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k1_dtconstr,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_trees_3(B,A) & m1_finseq_1(C,B) ) => k1_dtconstr(A,B,C) = k15_trees_3(C) ) )).
fof(redefinition_k1_dynkin,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) = k12_funct_7(B,C,D) ) )).
fof(redefinition_k1_ec_pf_1,axiom,( ! [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) ) )).
fof(redefinition_k1_euclid_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => k1_euclid_7(A,B,C) = k13_funct_3(B,C) ) )).
fof(redefinition_k1_euclid_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) ) => k1_euclid_8(A,B,C) = k11_finseq_1(A,B,C) ) )).
fof(redefinition_k1_euler_2,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k4_ordinal1) & v7_ordinal1(B) ) => k1_euler_2(A,B) = k24_valued_1(A,B) ) )).
fof(redefinition_k1_extreal1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_numbers) & m1_subset_1(B,k6_numbers) ) => k1_extreal1(A,B) = k4_xxreal_3(A,B) ) )).
fof(redefinition_k1_extreal2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_numbers) & m1_subset_1(B,k6_numbers) ) => k1_extreal2(A,B) = k4_xxreal_0(A,B) ) )).
fof(redefinition_k1_finance1,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => k1_finance1(A,B) = k2_xxreal_1(A,B) ) )).
fof(redefinition_k1_finseq_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) & v7_ordinal1(C) & m1_subset_1(D,A) ) => k1_finseq_7(A,B,C,D) = k1_funct_7(B,C,D) ) )).
fof(redefinition_k1_finseq_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => k1_finseq_8(A,B,C) = k7_finseq_1(B,C) ) )).
fof(redefinition_k1_finseqop,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k1_finsub_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k1_fintopo5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => k1_fintopo5(A,B,C,D) = k9_relat_1(C,D) ) )).
fof(redefinition_k1_flang_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k3_catalan2(A)) & m1_subset_1(C,k3_catalan2(A)) ) => k1_flang_1(A,B,C) = k1_ordinal4(B,C) ) )).
fof(redefinition_k1_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k1_fomodel2(A) = k8_fomodel1(A) ) )).
fof(redefinition_k1_funcsdom,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k1_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k1_functor3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k1_fuzzy_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v5_relat_1(C,k1_rcomp_1(k5_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))) ) => k1_fuzzy_4(A,B,C) = k2_funct_4(C) ) )).
fof(redefinition_k1_glib_003,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,A) & m1_subset_1(C,k1_zfmisc_1(B)) ) => k1_glib_003(A,B,C) = k15_finseq_1(C) ) )).
fof(redefinition_k1_goboard9,axiom,( ! [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))) ) => k1_goboard9(A) = k3_finseq_5(A) ) )).
fof(redefinition_k1_gr_cy_1,axiom,( ! [A] : ( m1_finseq_1(A,k4_numbers) => k1_gr_cy_1(A) = k16_rvsum_1(A) ) )).
fof(redefinition_k1_graph_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => k1_graph_3(A,B) = k5_graph_2(A,B) ) )).
fof(redefinition_k1_graphsp,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(A,k1_numbers) & v1_xreal_0(C) ) => k1_graphsp(A,B,C) = k1_funct_7(A,B,C) ) )).
fof(redefinition_k1_grnilp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k1_groeb_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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,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) ) )).
fof(redefinition_k1_groeb_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,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,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) ) )).
fof(redefinition_k1_group_10,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k1_group_14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) & 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)))) ) => k1_group_14(A,B,C,D,E) = k3_relat_1(D,E) ) )).
fof(redefinition_k1_group_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k1_index_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ 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) ) )).
fof(redefinition_k1_int_2,axiom,( ! [A] : ( v1_int_1(A) => k1_int_2(A) = k9_complex1(A) ) )).
fof(redefinition_k1_integr16,axiom,( ! [A] : ( m1_finseq_1(A,k2_numbers) => k1_integr16(A) = k3_comseq_3(A) ) )).
fof(redefinition_k1_integra2,axiom,( ! [A] : ! [B] : ( ( v3_membered(A) & v1_xreal_0(B) ) => k1_integra2(A,B) = k23_member_1(A,B) ) )).
fof(redefinition_k1_integra5,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k1_isocat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k1_jordan11,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) & v7_ordinal1(C) ) => k1_jordan11(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k1_jordan2b,axiom,( ! [A] : ( v1_xreal_0(A) => k1_jordan2b(A) = k5_finseq_1(A) ) )).
fof(redefinition_k1_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k1_kurato_0(A,B) = k3_card_3(B) ) )).
fof(redefinition_k1_laplace,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),k4_ordinal1),u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_ordinal1),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) ) )).
fof(redefinition_k1_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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) ) )).
fof(redefinition_k1_lmod_7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) )).
fof(redefinition_k1_lopban_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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) ) )).
fof(redefinition_k1_lopban_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & l1_normsp_1(A) & ~ v2_struct_0(B) & l1_normsp_1(B) & m1_subset_1(C,u1_struct_0(A)) & m1_subset_1(D,u1_struct_0(B)) ) => k1_lopban_7(A,B,C,D) = k4_tarski(C,D) ) )).
fof(redefinition_k1_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v1_membered(B) & m1_subset_1(C,k3_rfunct_3(A,B)) & m1_subset_1(D,k3_rfunct_3(A,B)) ) => k1_lpspacc1(A,B,C,D) = k1_valued_1(C,D) ) )).
fof(redefinition_k1_margrel1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(C,A) ) => k1_margrel1(A,B,C) = k2_funcop_1(B,C) ) )).
fof(redefinition_k1_matrix15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & v7_ordinal1(C) & v7_ordinal1(D) & v1_matrix_0(E) & v2_matrix_0(E,A,B,C) & m1_finseq_1(E,k3_finseq_2(A)) & v1_matrix_0(F) & v2_matrix_0(F,A,B,D) & m1_finseq_1(F,k3_finseq_2(A)) ) => k1_matrix15(A,B,C,D,E,F) = k8_pre_poly(E,F) ) )).
fof(redefinition_k1_matrix_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & m1_subset_1(D,u1_struct_0(B)) ) => k1_matrix_7(A,B,C,D) = k6_matrix_3(B,C,D) ) )).
fof(redefinition_k1_matrixr2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m1_finseq_1(B,k3_finseq_2(k1_numbers)) & v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m1_finseq_1(C,k3_finseq_2(k1_numbers)) ) => k1_matrixr2(A,B,C) = k6_matrixr1(B,C) ) )).
fof(redefinition_k1_matrlin,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & v1_matrix_0(C) & m1_finseq_1(C,k3_finseq_2(A)) ) => k1_matrlin(A,B,C) = k2_finseq_3(B,C) ) )).
fof(redefinition_k1_matrlin2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) )).
fof(redefinition_k1_matrprob,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,k3_finseq_2(A)) & v7_ordinal1(C) ) => k1_matrprob(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k1_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k1_measure1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k1_measure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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) ) )).
fof(redefinition_k1_measure3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => k1_measure3(A,B,C) = k10_xtuple_0(C) ) )).
fof(redefinition_k1_measure5,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_numbers) & m1_subset_1(B,k6_numbers) ) => k1_measure5(A,B) = k4_xxreal_1(A,B) ) )).
fof(redefinition_k1_measure6,axiom,( ! [A] : ! [B] : ( ( v3_membered(A) & v1_xreal_0(B) ) => k1_measure6(A,B) = k17_member_1(A,B) ) )).
fof(redefinition_k1_measure8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k1_member_1,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => k1_member_1(A) = k2_xxreal_3(A) ) )).
fof(redefinition_k1_mesfunc9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_valued_0(A) ) => k1_mesfunc9(A,B) = k1_funct_1(A,B) ) )).
fof(redefinition_k1_midsp_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_finseq_2(B,A)) & m1_subset_1(D,k4_ordinal1) & m1_subset_1(E,A) ) => k1_midsp_3(A,B,C,D,E) = k1_funct_7(C,D,E) ) )).
fof(redefinition_k1_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k1_mod_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k1_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) ) => k1_modelc_3(A) = k13_modelc_2(A) ) )).
fof(redefinition_k1_monoid_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => k1_monoid_0(A,B,C) = k7_finseq_1(B,C) ) )).
fof(redefinition_k1_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & m1_subset_1(C,A) ) => k1_msafree4(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k1_mssubfam,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k1_msualg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k1_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k1_msualg_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k1_nagata_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) & m1_subset_1(C,k4_ordinal1) ) => k1_nagata_1(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k1_nat_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k4_ordinal1) ) => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) )).
fof(redefinition_k1_nat_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k1_nat_5(A,B,C) = k5_relat_1(B,C) ) )).
fof(redefinition_k1_nat_d,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => k1_nat_d(A,B) = k4_int_1(A,B) ) )).
fof(redefinition_k1_ndiff_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & ~ v1_xboole_0(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) ) )).
fof(redefinition_k1_normsp_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v7_ordinal1(C) ) => k1_normsp_0(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k1_normsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v7_ordinal1(C) ) => k1_normsp_1(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k1_oppcat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k1_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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) ) )).
fof(redefinition_k1_partfun2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => k1_partfun2(A,B) = k4_relat_1(B) ) )).
fof(redefinition_k1_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => k1_pcs_0(A,B,C) = k1_relat_1(C) ) )).
fof(redefinition_k1_pdiff_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k1_pencil_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k1_pepin,axiom,( ! [A] : ( v1_int_1(A) => k1_pepin(A) = k1_square_1(A) ) )).
fof(redefinition_k1_polyform,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v7_ordinal1(B) ) => k1_polyform(A,B) = k3_xcmplx_0(A,B) ) )).
fof(redefinition_k1_polynom3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k4_ordinal1) & m1_finseq_1(C,A) ) => k1_polynom3(A,B,C) = k2_finseq_3(B,C) ) )).
fof(redefinition_k1_pralg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k1_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k1_prob_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k1_prob_1(A,B) = k3_card_3(B) ) )).
fof(redefinition_k1_prob_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & v7_ordinal1(D) ) => k1_prob_2(A,B,C,D) = k1_funct_1(C,D) ) )).
fof(redefinition_k1_prob_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & m1_subset_1(D,k4_ordinal1) ) => k1_prob_4(A,B,C,D) = k1_funct_1(C,D) ) )).
fof(redefinition_k1_prvect_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k1_prvect_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k1_pua2mss1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,k4_partfun1(k3_finseq_2(A),A)) ) => k1_pua2mss1(A,B) = k10_xtuple_0(B) ) )).
fof(redefinition_k1_quatern2,axiom,( k1_quatern2 = k17_quaterni )).
fof(redefinition_k1_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k1_random_1(A) = k1_zfmisc_1(A) ) )).
fof(redefinition_k1_rcomp_1,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => k1_rcomp_1(A,B) = k1_xxreal_1(A,B) ) )).
fof(redefinition_k1_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k1_real_1(A) = k4_xcmplx_0(A) ) )).
fof(redefinition_k1_rearran1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v3_membered(B) & v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) & v1_xreal_0(D) ) => k1_rearran1(A,B,C,D) = k24_valued_1(C,D) ) )).
fof(redefinition_k1_recdef_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v4_valued_0(A) ) => k1_recdef_1(A,B) = k1_funct_1(A,B) ) )).
fof(redefinition_k1_relset_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) ) => k1_relset_1(A,B) = k9_xtuple_0(B) ) )).
fof(redefinition_k1_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => k1_relset_2(A,B,C,D) = k9_relat_1(C,D) ) )).
fof(redefinition_k1_roughs_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,k1_zfmisc_1(A)) & v7_ordinal1(C) ) => k1_roughs_1(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k1_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v3_valued_0(A) ) => k1_rvsum_1(A) = k10_xtuple_0(A) ) )).
fof(redefinition_k1_rvsum_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_valued_0(A) ) => k1_rvsum_2(A) = k10_xtuple_0(A) ) )).
fof(redefinition_k1_scm_inst,axiom,( k1_scm_inst = k5_ordinal1 )).
fof(redefinition_k1_scmfsa_3,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k1_scmpds_4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_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,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => k1_scmpds_4(A,B) = k1_ordinal4(A,B) ) )).
fof(redefinition_k1_seq_4,axiom,( ! [A] : ( v1_xreal_0(A) => k1_seq_4(A) = k1_tarski(A) ) )).
fof(redefinition_k1_seqfunc,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,B)))) & v7_ordinal1(D) ) => k1_seqfunc(A,B,C,D) = k1_funct_1(C,D) ) )).
fof(redefinition_k1_series_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_membered(A) & v7_membered(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => k1_series_1(A,B,C) = k1_valued_1(B,C) ) )).
fof(redefinition_k1_stacks_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => k1_stacks_1(A,B,C) = k7_finseq_1(B,C) ) )).
fof(redefinition_k1_stirl2_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & v1_funct_1(C) & v1_funct_2(C,k7_card_1(A),B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(A),B))) ) => k1_stirl2_1(A,B,C,D) = k8_relat_1(C,D) ) )).
fof(redefinition_k1_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k1_substut2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k1_supinf_1,axiom,( k1_supinf_1 = k1_xxreal_0 )).
fof(redefinition_k1_supinf_2,axiom,( k1_supinf_2 = k5_ordinal1 )).
fof(redefinition_k1_toler_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(A) => k1_toler_1(A,B) = k2_wellord1(A,B) ) )).
fof(redefinition_k1_topalg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k1_topgen_3,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) )).
fof(redefinition_k1_transgeo,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k1_twoscomp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k1_unialg_3,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(redefinition_k1_valued_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) & v7_ordinal1(C) ) => k1_valued_0(A,B,C) = k7_nat_1(B,C) ) )).
fof(redefinition_k1_waybel10,axiom,( ! [A] : ! [B] : ( ( l1_orders_2(A) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => k1_waybel10(A,B) = k7_lattice3(B) ) )).
fof(redefinition_k1_waybel20,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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) ) )).
fof(redefinition_k1_waybel23,axiom,( ! [A] : ! [B] : ( ( ~ 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(k1_yellow_1(k7_waybel_0(A))))) ) => k1_waybel23(A,B) = k3_tarski(B) ) )).
fof(redefinition_k1_waybel27,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & ~ v2_struct_0(B) & l1_orders_2(B) & m1_subset_1(C,u1_struct_0(k5_yellow_1(A,B))) & m1_subset_1(D,A) ) => k1_waybel27(A,B,C,D) = k1_funct_1(C,D) ) )).
fof(redefinition_k1_waybel_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k1_waybel_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k1_yellow12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k1_yellow16,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k5_yellow_1(A,B)))) ) => k1_yellow16(A,B,C,D) = k5_card_3(C,D) ) )).
fof(redefinition_k1_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k1_zmodul03,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) & l1_vectsp_1(B,A) & m1_vectsp_6(C,A,B) & m1_subset_1(D,u1_struct_0(B)) ) => k1_zmodul03(A,B,C,D) = k1_funct_1(C,D) ) )).
fof(redefinition_k20_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => k20_bvfunc_1(A,B) = k9_xboolean(A,B) ) )).
fof(redefinition_k20_glib_001,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & m3_glib_001(B,A) & m1_subset_1(C,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => k20_glib_001(A,B,C,D) = k9_glib_001(A,B,C,D) ) )).
fof(redefinition_k20_grcat_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k20_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k20_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k20_rvsum_1,axiom,( ! [A] : ( m1_finseq_1(A,k2_numbers) => k20_rvsum_1(A) = k19_rvsum_1(A) ) )).
fof(redefinition_k20_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(redefinition_k21_abcmiz_1,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k4_abcmiz_1,k4_ordinal1)) => k21_abcmiz_1(A) = k1_xtuple_0(A) ) )).
fof(redefinition_k21_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k21_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => k21_bvfunc_1(A,B) = k7_xboolean(A,B) ) )).
fof(redefinition_k21_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => k21_euclid(A) = k20_euclid(A) ) )).
fof(redefinition_k21_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k21_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k21_rvsum_1,axiom,( ! [A] : ( m1_finseq_1(A,k1_numbers) => k21_rvsum_1(A) = k19_rvsum_1(A) ) )).
fof(redefinition_k22_abcmiz_1,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k4_abcmiz_1,k4_ordinal1)) => k22_abcmiz_1(A) = k2_xtuple_0(A) ) )).
fof(redefinition_k22_matrixj1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k22_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k22_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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) ) => k22_pre_poly(A,B) = k13_pre_poly(B) ) )).
fof(redefinition_k22_quaterni,axiom,( ! [A] : ! [B] : ( ( v1_quaterni(A) & v1_quaterni(B) ) => k22_quaterni(A,B) = k7_quaterni(A,B) ) )).
fof(redefinition_k22_substut1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k22_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(redefinition_k22_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k22_zmodul02,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & m1_zmodul02(B,A) & m1_zmodul02(C,A) ) => k22_zmodul02(A,B,C) = k1_valued_1(B,C) ) )).
fof(redefinition_k23_abcmiz_1,axiom,( ! [A] : ( m1_subset_1(A,k20_abcmiz_1) => k23_abcmiz_1(A) = k1_xtuple_0(A) ) )).
fof(redefinition_k23_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k23_lexbfs,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(redefinition_k23_monoid_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l3_algstr_0(A) ) => k23_monoid_1(A) = k22_monoid_1(A) ) )).
fof(redefinition_k23_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) => k23_pre_poly(A,B,C) = k3_relat_1(B,C) ) )).
fof(redefinition_k23_quaterni,axiom,( ! [A] : ! [B] : ( ( v1_quaterni(A) & v1_quaterni(B) ) => k23_quaterni(A,B) = k10_quaterni(A,B) ) )).
fof(redefinition_k23_substut1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k24_abcmiz_1,axiom,( ! [A] : ( m1_subset_1(A,k20_abcmiz_1) => k24_abcmiz_1(A) = k2_xtuple_0(A) ) )).
fof(redefinition_k24_fomodel1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k24_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k24_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(redefinition_k24_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => k24_quaterni(A) = k8_quaterni(A) ) )).
fof(redefinition_k24_turing_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k25_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ 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) ) )).
fof(redefinition_k25_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(redefinition_k25_quaterni,axiom,( ! [A] : ! [B] : ( ( v1_quaterni(A) & v1_quaterni(B) ) => k25_quaterni(A,B) = k9_quaterni(A,B) ) )).
fof(redefinition_k25_substut1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k25_turing_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k25_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k26_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ 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) ) )).
fof(redefinition_k26_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k26_fomodel1(A) = k11_fomodel1(A) ) )).
fof(redefinition_k26_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k26_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k27_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ 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) ) )).
fof(redefinition_k27_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k27_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => k27_quaterni(A) = k26_quaterni(A) ) )).
fof(redefinition_k28_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ 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) ) )).
fof(redefinition_k28_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k28_fomodel1(A) = k25_fomodel1(A) ) )).
fof(redefinition_k29_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k29_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k29_fomodel1(A) = k27_fomodel1(A) ) )).
fof(redefinition_k29_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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(k30_fomodel2(A),k30_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) ) )).
fof(redefinition_k29_modelc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) = k8_funct_7(B,C) ) )).
fof(redefinition_k2_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => k2_absvalue(A) = k1_absvalue(A) ) )).
fof(redefinition_k2_aff_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k2_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => k2_afinsq_1(A) = k9_xtuple_0(A) ) )).
fof(redefinition_k2_ami_2,axiom,( k2_ami_2 = k2_scm_inst )).
fof(redefinition_k2_asympt_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v2_xxreal_0(B) & v1_xreal_0(B) ) => k2_asympt_0(A,B) = k24_valued_1(A,B) ) )).
fof(redefinition_k2_bhsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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) ) )).
fof(redefinition_k2_binarith,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_margrel1) & m1_subset_1(B,k6_margrel1) ) => k2_binarith(A,B) = k10_xboolean(A,B) ) )).
fof(redefinition_k2_binop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k2_borsuk_7,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,u1_struct_0(k3_topmetr)) & v1_xreal_0(B) ) => k2_borsuk_7(A,B) = k2_xcmplx_0(A,B) ) )).
fof(redefinition_k2_bvfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k2_calcul_2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => k2_calcul_2(A,B) = k1_calcul_2(A,B) ) )).
fof(redefinition_k2_cat_5,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k2_chain_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_chain_1(B,A) & m1_subset_1(C,k2_finseq_1(A)) ) => k2_chain_1(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k2_classes2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) ) => k2_classes2(A,B) = k1_zfmisc_1(B) ) )).
fof(redefinition_k2_closure1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k2_closure2,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k2_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => k2_complfld(A) = k8_complex1(A) ) )).
fof(redefinition_k2_complsp2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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) ) )).
fof(redefinition_k2_compos_0,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_compos_0(A) & m1_subset_1(B,A) ) => k2_compos_0(A,B) = k4_xtuple_0(B) ) )).
fof(redefinition_k2_comseq_2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k2_comseq_3,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v7_ordinal1(B) ) => k2_comseq_3(A,B) = k1_newton(A,B) ) )).
fof(redefinition_k2_cqc_lang,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k2_descip_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & m1_finseq_1(C,A) ) => k2_descip_1(A,B,C) = k16_finseq_1(B,C) ) )).
fof(redefinition_k2_diff_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k2_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k2_dtconstr,axiom,( ! [A] : ! [B] : ! [C] : ( m1_finseq_1(C,k2_zfmisc_1(A,B)) => k2_dtconstr(A,B,C) = k11_mcart_1(C) ) )).
fof(redefinition_k2_ec_pf_2,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k2_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k2_euclid_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k2_extreal1,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => k2_extreal1(A,B) = k6_xxreal_3(A,B) ) )).
fof(redefinition_k2_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => k2_finseq_1(A) = k1_finseq_1(A) ) )).
fof(redefinition_k2_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k2_finseq_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) & v7_ordinal1(C) & v7_ordinal1(D) ) => k2_finseq_7(A,B,C,D) = k9_funct_7(B,C,D) ) )).
fof(redefinition_k2_finseqop,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k2_finsop_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) & m1_finseq_1(C,A) ) => k2_finsop_1(A,B,C) = k1_funct_4(B,C) ) )).
fof(redefinition_k2_finsub_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k2_flang_1,axiom,( ! [A] : k2_flang_1(A) = k4_afinsq_1(A) )).
fof(redefinition_k2_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))))) ) => k2_fomodel4(A,B,C) = k13_fomodel0(B,C) ) )).
fof(redefinition_k2_funcsdom,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k2_funct_2,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k2_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k2_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_finseq_1(B,A) & v7_ordinal1(C) & m1_subset_1(D,A) ) => k2_funct_7(A,B,C,D) = k1_funct_7(B,C,D) ) )).
fof(redefinition_k2_functor3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k2_graph_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_finseq_1(B,A) & v7_ordinal1(C) & v7_ordinal1(D) ) => k2_graph_2(A,B,C,D) = k1_graph_2(B,C,D) ) )).
fof(redefinition_k2_group_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k2_groupp_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k2_henmodel,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k2_heyting1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k7_normform(A)) => k2_heyting1(A,B) = k1_tarski(B) ) )).
fof(redefinition_k2_index_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k2_int_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_int_3)) => k2_int_3(A) = k9_complex1(A) ) )).
fof(redefinition_k2_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => k2_int_8(A) = k1_int_8(A) ) )).
fof(redefinition_k2_integr15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k4_ordinal1,k1_integra1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) & m2_integr15(D,A,B,C) & m1_subset_1(E,k4_ordinal1) ) => k2_integr15(A,B,C,D,E) = k1_funct_1(D,E) ) )).
fof(redefinition_k2_integr16,axiom,( ! [A] : ( m1_finseq_1(A,k2_numbers) => k2_integr16(A) = k4_comseq_3(A) ) )).
fof(redefinition_k2_integr18,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & 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,k4_ordinal1,k1_integra1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(B)))) & m2_integr18(E,A,B,C,D) & v7_ordinal1(F) ) => k2_integr18(A,B,C,D,E,F) = k1_funct_1(E,F) ) )).
fof(redefinition_k2_integra2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_integra1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) & v7_ordinal1(C) ) => k2_integra2(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k2_interva1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k2_jordan1h,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,k3_finseq_2(A)) ) => k2_jordan1h(A,B) = k9_matrix_0(B) ) )).
fof(redefinition_k2_kolmog01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k2_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k2_kurato_0(A,B) = k3_funct_6(B) ) )).
fof(redefinition_k2_kurato_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) & v7_ordinal1(C) ) => k2_kurato_2(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k2_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => k2_lattice3(A) = k8_filter_1(A) ) )).
fof(redefinition_k2_lfuzzy_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k2_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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) ) )).
fof(redefinition_k2_lopban_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & l1_normsp_1(A) & ~ v2_struct_0(B) & l1_normsp_1(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => k2_lopban_7(A,B,C,D) = k13_funct_3(C,D) ) )).
fof(redefinition_k2_lopclset,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k2_lpspace1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k2_matrix10,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m1_finseq_1(B,k3_finseq_2(k1_numbers)) ) => k2_matrix10(A,B) = k4_matrixr1(B) ) )).
fof(redefinition_k2_matrix13,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & ~ 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) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(C))) & m1_subset_1(E,u1_struct_0(C)) ) => k2_matrix13(A,B,C,D,E) = k6_matrix_3(C,D,E) ) )).
fof(redefinition_k2_matrix14,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) & m1_subset_1(B,k4_ordinal1) ) => k2_matrix14(A,B) = k1_matrix14(A,B) ) )).
fof(redefinition_k2_matrix_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_matrix_2(A) ) => k2_matrix_2(A) = k1_matrix_2(A) ) )).
fof(redefinition_k2_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k2_matrixj2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) )).
fof(redefinition_k2_matrixr2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m1_finseq_1(B,k3_finseq_2(k1_numbers)) ) => k2_matrixr2(A,B) = k1_matrixr1(B) ) )).
fof(redefinition_k2_matrlin,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) ) => k2_matrlin(A,B) = k5_finseq_1(B) ) )).
fof(redefinition_k2_matrprob,axiom,( ! [A] : ( v1_xreal_0(A) => k2_matrprob(A) = k5_finseq_1(A) ) )).
fof(redefinition_k2_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k2_measure1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k2_measure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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) ) )).
fof(redefinition_k2_measure4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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) ) )).
fof(redefinition_k2_measure7,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) & m1_measure7(B,A) & m1_subset_1(C,k4_ordinal1) ) => k2_measure7(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k2_member_1,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => k2_member_1(A) = k5_xxreal_3(A) ) )).
fof(redefinition_k2_metric_1,axiom,( k2_metric_1 = k7_funct_5 )).
fof(redefinition_k2_midsp_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_nat_1(A,2)) & m1_subset_1(C,u1_struct_0(B)) ) => k2_midsp_3(A,B,C) = k5_finseq_1(C) ) )).
fof(redefinition_k2_mmlquer2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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_mmlquer2(A,B,C) = k1_mmlquer2(B,C) ) )).
fof(redefinition_k2_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k2_morph_01,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k2_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) => k2_msafree4(A,B,C,D,E) = k1_funct_1(D,E) ) )).
fof(redefinition_k2_msaterm,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k2_mssubfam,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k2_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k2_multop_1,axiom,( ! [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_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) ) )).
fof(redefinition_k2_nagata_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) ) => k2_nagata_1(A,B) = k3_card_3(B) ) )).
fof(redefinition_k2_nat_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k4_ordinal1) ) => k2_nat_1(A,B) = k3_xcmplx_0(A,B) ) )).
fof(redefinition_k2_nat_3,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k1_numbers) & v7_ordinal1(B) ) => k2_nat_3(A,B) = k1_nat_3(A,B) ) )).
fof(redefinition_k2_nat_d,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => k2_nat_d(A,B) = k5_int_1(A,B) ) )).
fof(redefinition_k2_openlatt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k2_orders_1,axiom,( ! [A] : k2_orders_1(A) = k1_wellord2(A) )).
fof(redefinition_k2_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k2_partfun2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k2_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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) ) )).
fof(redefinition_k2_pencil_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k2_pencil_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k2_petri,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k2_pnproc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) & v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => k2_pnproc_1(A,B,C) = k1_valued_1(B,C) ) )).
fof(redefinition_k2_polyeq_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) & v1_xcmplx_0(D) ) => k2_polyeq_3(A,B,C,D) = k2_polyeq_1(A,B,C,D) ) )).
fof(redefinition_k2_polyform,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v7_ordinal1(B) ) => k2_polyform(A,B) = k1_newton(A,B) ) )).
fof(redefinition_k2_polynom3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => k2_polynom3(A,B,C) = k10_finseq_1(B,C) ) )).
fof(redefinition_k2_pralg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k2_pralg_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => k2_pralg_2(A) = k6_funct_6(A) ) )).
fof(redefinition_k2_pre_ff,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k3_finseq_2(k4_ordinal1)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k3_finseq_2(k4_ordinal1)))) & v7_ordinal1(B) ) => k2_pre_ff(A,B) = k1_funct_1(A,B) ) )).
fof(redefinition_k2_pre_poly,axiom,( ! [A] : k2_pre_poly(A) = k6_finseq_1(A) )).
fof(redefinition_k2_quatern2,axiom,( k2_quatern2 = k18_quaterni )).
fof(redefinition_k2_quatern3,axiom,( ! [A] : ( m1_subset_1(A,k1_quaterni) => k2_quatern3(A) = k1_quatern3(A) ) )).
fof(redefinition_k2_ranknull,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k2_rcomp_1,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => k2_rcomp_1(A,B) = k4_xxreal_1(A,B) ) )).
fof(redefinition_k2_real_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k2_real_1(A) = k5_xcmplx_0(A) ) )).
fof(redefinition_k2_relset_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) ) => k2_relset_1(A,B) = k10_xtuple_0(B) ) )).
fof(redefinition_k2_rfinseq,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & m1_finseq_1(C,A) ) => k2_rfinseq(A,B,C) = k1_rfinseq(B,C) ) )).
fof(redefinition_k2_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => k2_robbins3(A) = k8_filter_1(A) ) )).
fof(redefinition_k2_scm_comp,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k2_scmfsa_1,axiom,( k2_scmfsa_1 = k2_scm_inst )).
fof(redefinition_k2_scmfsa_2,axiom,( k2_scmfsa_2 = k2_scm_inst )).
fof(redefinition_k2_scmpds_i,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k2_scm_inst) & v1_int_1(B) ) => k2_scmpds_i(A,B) = k10_finseq_1(A,B) ) )).
fof(redefinition_k2_scmring2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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(k7_card_1(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) ) )).
fof(redefinition_k2_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k2_setlim_1(A,B) = k1_setlim_1(B) ) )).
fof(redefinition_k2_setwiseo,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k2_setwiseo(A,B) = k1_tarski(B) ) )).
fof(redefinition_k2_setwop_2,axiom,( ! [A] : ( v7_ordinal1(A) => k2_setwop_2(A) = k1_finseq_1(A) ) )).
fof(redefinition_k2_simplex0,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => k2_simplex0(A,B) = k1_simplex0(B) ) )).
fof(redefinition_k2_simplex2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k2_stacks_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(B) & m1_finseq_1(C,A) ) => k2_stacks_1(A,B,C) = k2_finseq_3(B,C) ) )).
fof(redefinition_k2_stirl2_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(B) & v1_funct_1(C) & v1_funct_2(C,A,k7_card_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k7_card_1(B)))) ) => k2_stirl2_1(A,B,C,D) = k1_funct_1(C,D) ) )).
fof(redefinition_k2_sublemma,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k38_substut1(A)) ) => k2_sublemma(A,B) = k1_xtuple_0(B) ) )).
fof(redefinition_k2_substlat,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k2_substut2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k2_supinf_1,axiom,( k2_supinf_1 = k2_xxreal_0 )).
fof(redefinition_k2_supinf_2,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => k2_supinf_2(A) = k2_xxreal_3(A) ) )).
fof(redefinition_k2_tbsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v7_ordinal1(C) ) => k2_tbsp_1(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k2_toler_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k2_topalg_2,axiom,( k2_topalg_2 = k3_topmetr )).
fof(redefinition_k2_topalg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k2_topalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k2_topalg_5,axiom,( ! [A] : ( v1_xreal_0(A) => k2_topalg_5(A) = k1_topalg_5(A) ) )).
fof(redefinition_k2_topgen_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k2_topreal7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k2_trees_4,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k2_trees_4(A,B) = k1_trees_4(B) ) )).
fof(redefinition_k2_trees_a,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & m1_subset_1(B,A) ) => k2_trees_a(A,B) = k1_tarski(B) ) )).
fof(redefinition_k2_turing_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k2_urysohn3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,B)))) & v7_ordinal1(D) ) => k2_urysohn3(A,B,C,D) = k1_funct_1(C,D) ) )).
fof(redefinition_k2_valuat_1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & ~ v1_xboole_0(B) ) => k2_valuat_1(A,B) = k1_valuat_1(A,B) ) )).
fof(redefinition_k2_valued_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_ordinal1) & v5_valued_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => k2_valued_0(A,B,C) = k3_relat_1(B,C) ) )).
fof(redefinition_k2_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(redefinition_k2_vectmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => k2_vectmetr(A) = k1_vectmetr(A) ) )).
fof(redefinition_k2_vectsp_8,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) )).
fof(redefinition_k2_waybel26,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k2_waybel28,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k2_waybel_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) = k6_funct_6(D) ) )).
fof(redefinition_k2_wsierp_1,axiom,( ! [A] : ( m1_finseq_1(A,k4_ordinal1) => k2_wsierp_1(A) = k16_rvsum_1(A) ) )).
fof(redefinition_k2_yellow14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k2_yellow16,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k2_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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) ) )).
fof(redefinition_k2_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k2_yellow_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k2_zf_lang1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) = k1_funct_7(B,C,D) ) )).
fof(redefinition_k2_zf_model,axiom,( ! [A] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) ) => k2_zf_model(A) = k1_zf_model(A) ) )).
fof(redefinition_k2_zf_refle,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k2_zfrefle1,axiom,( k2_zfrefle1 = k1_zfrefle1 )).
fof(redefinition_k30_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k30_fomodel2(A) = k26_fomodel2(A) ) )).
fof(redefinition_k31_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k31_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k31_fomodel2(A) = k7_fomodel1(A) ) )).
fof(redefinition_k31_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k31_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k32_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => k32_abcmiz_1(A) = k15_abcmiz_1(A) ) )).
fof(redefinition_k32_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k32_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k32_fomodel1(A) = k31_fomodel1(A) ) )).
fof(redefinition_k32_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) ) => k32_fomodel2(A,B) = k28_fomodel2(A,B) ) )).
fof(redefinition_k32_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(redefinition_k32_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k32_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k33_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => k33_abcmiz_1(A) = k16_abcmiz_1(A) ) )).
fof(redefinition_k33_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k33_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) ) => k33_fomodel2(A,B) = k27_fomodel2(A,B) ) )).
fof(redefinition_k33_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(redefinition_k33_substut1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k34_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k34_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & ~ v1_xboole_0(B) & m1_subset_1(C,k15_fomodel2(A,B)) & v4_fomodel1(D,A) & m1_subset_1(D,k1_fomodel1(A)) & m1_subset_1(E,B) ) => k34_fomodel2(A,B,C,D,E) = k5_fomodel2(C,D,E) ) )).
fof(redefinition_k34_substut1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k34_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k35_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k35_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k35_fomodel1(A) = k27_fomodel1(A) ) )).
fof(redefinition_k35_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(redefinition_k36_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k36_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k36_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k37_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k37_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k37_fomodel1(A) = k9_fomodel1(A) ) )).
fof(redefinition_k37_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k37_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k38_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k38_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v7_ordinal1(B) & ~ v8_ordinal1(B) & v3_card_1(C,B) & m1_subset_1(C,k3_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,k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k35_fomodel1(A))) ) => k38_fomodel4(A,B,C,D) = k37_fomodel4(A,B,C,D) ) )).
fof(redefinition_k38_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k39_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k39_fomodel1(A) = k25_fomodel1(A) ) )).
fof(redefinition_k39_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) => k39_fomodel2(A,B) = k38_fomodel2(A,B) ) )).
fof(redefinition_k39_substut1,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k38_substut1(A)) ) => k39_substut1(A,B) = k37_substut1(A,B) ) )).
fof(redefinition_k3_abcmiz_1,axiom,( ! [A] : ( m1_subset_1(A,k2_abcmiz_1) => k3_abcmiz_1(A) = k1_xtuple_0(A) ) )).
fof(redefinition_k3_ami_wstd,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k3_aofa_a01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & l6_aofa_a00(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)) & v5_msafree4(C,A,B) & l3_msualg_1(C,A) & l4_aofa_a00(D,A,B,C) & m1_subset_1(E,k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),u8_aofa_a00(A))) & v4_msualg_1(F,A) & v4_msafree4(F,A,C) & l3_msualg_1(F,A) & ~ v2_struct_0(G) & v2_unialg_1(G) & v3_unialg_1(G) & v4_unialg_1(G) & v3_aofa_000(G) & v4_aofa_000(G) & v5_aofa_000(G) & v6_aofa_000(G) & l1_unialg_1(G) & m1_aofa_000(H,G,k13_aofa_a00(A,C,F,u4_aofa_a00(A,B,C,D)),k14_aofa_a00(A,C,F,u4_aofa_a00(A,B,C,D),u8_aofa_a00(A),E,k2_aofa_a01(A,F))) & m1_subset_1(I,k13_aofa_a00(A,C,F,u4_aofa_a00(A,B,C,D))) & m1_subset_1(J,u1_struct_0(G)) ) => k3_aofa_a01(A,B,C,D,E,F,G,H,I,J) = k1_binop_1(H,I,J) ) )).
fof(redefinition_k3_asympt_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & ~ v3_xxreal_0(B) & v1_xreal_0(B) ) => k3_asympt_0(A,B) = k7_valued_1(A,B) ) )).
fof(redefinition_k3_binop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k3_boolealg,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k3_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k3_borsuk_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k3_borsuk_7,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,u1_struct_0(k3_topmetr)) & v1_xreal_0(B) ) => k3_borsuk_7(A,B) = k6_xcmplx_0(A,B) ) )).
fof(redefinition_k3_bvfunc26,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k3_catalan2,axiom,( ! [A] : k3_catalan2(A) = k8_afinsq_1(A) )).
fof(redefinition_k3_catalg_1,axiom,( ! [A] : k3_catalg_1(A) = k2_catalg_1(A) )).
fof(redefinition_k3_cgames_1,axiom,( k3_cgames_1 = k1_cgames_1 )).
fof(redefinition_k3_chord,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(redefinition_k3_classes1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => k3_classes1(A,B) = k2_classes1(A,B) ) )).
fof(redefinition_k3_classes2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) & m1_subset_1(B,A) ) => k3_classes2(A,B) = k3_tarski(B) ) )).
fof(redefinition_k3_closure1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k3_closure3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k3_cohsp_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & m1_subset_1(B,A) ) => k3_cohsp_1(A,B) = k5_finsub_1(B) ) )).
fof(redefinition_k3_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_complex1(A) = k1_complex1(A) ) )).
fof(redefinition_k3_complsp2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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) ) )).
fof(redefinition_k3_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_compos_1(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v7_ordinal1(C) ) => k3_compos_1(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k3_descip_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & m1_finseq_1(C,A) ) => k3_descip_1(A,B,C) = k1_rfinseq(B,C) ) )).
fof(redefinition_k3_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k3_dtconstr,axiom,( ! [A] : ! [B] : ! [C] : ( m1_finseq_1(C,k2_zfmisc_1(A,B)) => k3_dtconstr(A,B,C) = k12_mcart_1(C) ) )).
fof(redefinition_k3_ec_pf_2,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k3_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k3_euclid,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => k3_euclid(A) = k54_valued_1(A) ) )).
fof(redefinition_k3_finance1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k3_finance1(A,B) = k18_valued_1(A,B) ) )).
fof(redefinition_k3_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(A) = k1_card_1(A) ) )).
fof(redefinition_k3_finseq_2,axiom,( ! [A] : k3_finseq_2(A) = k13_finseq_1(A) )).
fof(redefinition_k3_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k3_finseq_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k3_finseq_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_finseq_1(B,A) & v7_ordinal1(C) & v7_ordinal1(D) ) => k3_finseq_8(A,B,C,D) = k2_finseq_8(B,C,D) ) )).
fof(redefinition_k3_finseqop,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k3_finsop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finsop_1(A) = k9_xtuple_0(A) ) )).
fof(redefinition_k3_finsub_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k3_flang_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k3_flang_1(A,B) = k3_afinsq_1(B) ) )).
fof(redefinition_k3_fomodel0,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k3_fomodel0(A,B) = k13_finseq_1(B) ) )).
fof(redefinition_k3_fomodel2,axiom,( ! [A] : k3_fomodel2(A) = k4_relat_1(A) )).
fof(redefinition_k3_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v3_fomodel4(B,A) & v3_fomodel4(C,A) ) => k3_fomodel4(A,B,C) = k13_fomodel0(B,C) ) )).
fof(redefinition_k3_funcsdom,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k3_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k3_functor3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k3_graph_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k3_graphsp,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k3_group_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k3_group_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k3_idea_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) => k3_idea_1(A,B,C) = k2_idea_1(A,B,C) ) )).
fof(redefinition_k3_int_5,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & m1_finseq_1(B,k1_zfmisc_1(A)) ) => k3_int_5(A,B) = k1_card_3(B) ) )).
fof(redefinition_k3_jgraph_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) ) => k3_jgraph_1(A,B) = k2_jgraph_1(B) ) )).
fof(redefinition_k3_jordan10,axiom,( ! [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_jordan10(A) = k1_jordan10(A) ) )).
fof(redefinition_k3_kolmog01,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(redefinition_k3_lattice5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k3_lattices,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k3_lfuzzy_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k3_lfuzzy_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => k3_lfuzzy_1(A,B) = k4_funct_3(A,B) ) )).
fof(redefinition_k3_lopclset,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k3_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v1_membered(B) & m1_subset_1(C,k3_rfunct_3(A,B)) & m1_subset_1(D,k3_rfunct_3(A,B)) ) => k3_lpspacc1(A,B,C,D) = k18_valued_1(C,D) ) )).
fof(redefinition_k3_matrix10,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m1_finseq_1(B,k3_finseq_2(k1_numbers)) ) => k3_matrix10(A,B) = k1_matrix10(B) ) )).
fof(redefinition_k3_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => k3_matrix13(A) = k1_tarski(A) ) )).
fof(redefinition_k3_matrix_7,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k3_matrix_2(A)) ) => k3_matrix_7(A,B) = k2_funct_1(B) ) )).
fof(redefinition_k3_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k3_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k3_measure1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k3_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => k3_measure6(A) = k5_member_1(A) ) )).
fof(redefinition_k3_measure8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) )).
fof(redefinition_k3_member_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_numbers) & m1_subset_1(B,k6_numbers) ) => k3_member_1(A,B) = k4_xxreal_3(A,B) ) )).
fof(redefinition_k3_mesfunc2,axiom,( ! [A] : ! [B] : k3_mesfunc2(A,B) = k4_funct_3(A,B) )).
fof(redefinition_k3_metric_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v8_metric_1(A) & l1_metric_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k3_metric_1(A,B,C) = k1_metric_1(A,B,C) ) )).
fof(redefinition_k3_midsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k3_midsp_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( m1_subset_1(A,k4_ordinal1) & ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_nat_1(A,2)) & m1_subset_1(C,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) & 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) ) )).
fof(redefinition_k3_modcat_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k3_monoid_0,axiom,( k3_monoid_0 = k2_gr_cy_1 )).
fof(redefinition_k3_monoid_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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) ) )).
fof(redefinition_k3_msafree,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k3_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => k3_msafree4(A,B,C,D) = k3_relat_1(C,D) ) )).
fof(redefinition_k3_msaterm,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k3_msualg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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) ) )).
fof(redefinition_k3_msualg_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k3_nagata_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k3_nat_d,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => k3_nat_d(A,B) = k4_int_1(A,B) ) )).
fof(redefinition_k3_openlatt,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k3_partfun2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k3_pencil_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k3_petri,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k3_polyform,axiom,( ! [A] : ( v1_int_1(A) => k3_polyform(A) = k5_finseq_1(A) ) )).
fof(redefinition_k3_polynom1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v2_struct_0(B) & 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)))) ) => k3_polynom1(A,B,C) = k2_polynom1(B,C) ) )).
fof(redefinition_k3_pre_poly,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k3_pre_poly(A,B) = k5_finseq_1(B) ) )).
fof(redefinition_k3_prvect_2,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k3_pscomp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k3_pua2mss1,axiom,( ! [A] : ! [B] : ( m2_pua2mss1(B,A) => k3_pua2mss1(A,B) = k10_xtuple_0(B) ) )).
fof(redefinition_k3_quatern2,axiom,( k3_quatern2 = k1_xcmplx_0 )).
fof(redefinition_k3_quaterni,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [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) ) )).
fof(redefinition_k3_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => k3_radix_1(A) = k2_radix_1(A) ) )).
fof(redefinition_k3_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => k3_radix_3(A) = k1_radix_3(A) ) )).
fof(redefinition_k3_random_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k3_ratfunc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v7_struct_0(A) & l5_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & ~ v1_ratfunc1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k3_ratfunc1(A,B,C) = k4_tarski(B,C) ) )).
fof(redefinition_k3_rcomp_1,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xxreal_0(B) ) => k3_rcomp_1(A,B) = k2_xxreal_1(A,B) ) )).
fof(redefinition_k3_real_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k3_real_1(A,B) = k2_xcmplx_0(A,B) ) )).
fof(redefinition_k3_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => k3_relset_1(A,B,C) = k2_relat_1(C) ) )).
fof(redefinition_k3_rewrite2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,k8_afinsq_1(A)) & v7_ordinal1(C) ) => k3_rewrite2(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k3_rfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k3_rfunct_3,axiom,( ! [A] : ! [B] : k3_rfunct_3(A,B) = k4_partfun1(A,B) )).
fof(redefinition_k3_rlvect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k3_rlvect_2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k3_rvsum_2,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k3_scm_comp,axiom,( ! [A] : ( m1_subset_1(A,k6_dtconstr(k1_scm_comp)) => k3_scm_comp(A) = k1_trees_4(A) ) )).
fof(redefinition_k3_scmfsa_1,axiom,( k3_scmfsa_1 = k1_scmfsa_i )).
fof(redefinition_k3_scmpds_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k2_ami_2) & v1_int_1(B) ) => k3_scmpds_1(A,B) = k10_finseq_1(A,B) ) )).
fof(redefinition_k3_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k3_series_1(A) = k2_series_1(A) ) )).
fof(redefinition_k3_setwiseo,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => k3_setwiseo(A,B,C) = k2_tarski(B,C) ) )).
fof(redefinition_k3_substut2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k3_supinf_2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_numbers) & m1_subset_1(B,k6_numbers) ) => k3_supinf_2(A,B) = k1_xxreal_3(A,B) ) )).
fof(redefinition_k3_topalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k3_topgen_2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k3_topgen_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k3_topreal7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k3_toprealb,axiom,( ! [A] : ! [B] : ( ( v1_xreal_0(A) & v1_xreal_0(B) ) => k3_toprealb(A,B) = k1_toprealb(A,B) ) )).
fof(redefinition_k3_trees_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k3_turing_1,axiom,( ! [A] : ( v7_ordinal1(A) => k3_turing_1(A) = k1_ordinal1(A) ) )).
fof(redefinition_k3_uproots,axiom,( ! [A] : ! [B] : ( ( 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) = k2_uproots(A,B) ) )).
fof(redefinition_k3_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(redefinition_k3_vfunct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k3_waybel27,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k3_waybel_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k3_waybel_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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(k1_funct_6(D)),k7_funcop_1(k4_card_3(k1_funct_6(D)),A),k7_funcop_1(k4_card_3(k1_funct_6(D)),B)) & m1_subset_1(F,k4_card_3(k1_funct_6(D))) ) => k3_waybel_5(A,B,C,D,E,F) = k1_funct_1(E,F) ) )).
fof(redefinition_k3_wsierp_1,axiom,( ! [A] : ( m1_finseq_1(A,k4_ordinal1) => k3_wsierp_1(A) = k19_rvsum_1(A) ) )).
fof(redefinition_k3_yellow20,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k3_yellow21,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k3_yellow_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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_yellow_1(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k3_yellow_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k3_zf_lang,axiom,( ! [A] : ( m1_subset_1(A,k1_zf_lang) => k3_zf_lang(A) = k5_finseq_1(A) ) )).
fof(redefinition_k40_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k41_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k41_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & v13_fomodel4(B,k5_numbers,A) & v13_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))))) & v11_fomodel4(C,A,B) ) => k41_fomodel4(A,B,C) = k40_fomodel4(A,B,C) ) )).
fof(redefinition_k41_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k42_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k42_fomodel1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) => k42_fomodel1(A,B,C) = k7_finseq_1(B,C) ) )).
fof(redefinition_k42_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k43_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) & m1_subset_1(B,k1_fomodel1(A)) ) => k43_fomodel1(A,B) = k5_finseq_1(B) ) )).
fof(redefinition_k43_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k40_fomodel2(A)) ) => k43_fomodel4(A,B,C,D) = k42_fomodel4(A,B,C,D) ) )).
fof(redefinition_k43_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k46_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(redefinition_k47_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k30_fomodel2(B)) ) => k47_fomodel4(A,B,C,D) = k46_fomodel4(A,B,C,D) ) )).
fof(redefinition_k47_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(redefinition_k48_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k49_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k4_altcat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k4_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k4_bvfunc26,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k4_bvfunc_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_eqrel_1(B,A) ) => k4_bvfunc_2(A,B) = k1_tarski(B) ) )).
fof(redefinition_k4_card_1,axiom,( ! [A] : ( v7_ordinal1(A) => k4_card_1(A) = k1_ordinal1(A) ) )).
fof(redefinition_k4_cat_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) )).
fof(redefinition_k4_chord,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(redefinition_k4_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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) ) )).
fof(redefinition_k4_clopban1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k4_closure3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k4_cohsp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k4_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k4_complex1(A) = k2_complex1(A) ) )).
fof(redefinition_k4_complsp2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_finseq_2(A,k2_numbers)) & v1_xcmplx_0(C) ) => k4_complsp2(A,B,C) = k24_valued_1(B,C) ) )).
fof(redefinition_k4_cqc_lang,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & 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) ) )).
fof(redefinition_k4_descip_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & m1_subset_1(C,k4_finseq_2(k3_xcmplx_0(2,B),A)) ) => k4_descip_1(A,B,C) = k16_finseq_1(B,C) ) )).
fof(redefinition_k4_dickson,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => k4_dickson(A,B) = k3_dickson(B) ) )).
fof(redefinition_k4_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k4_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k4_euclid_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k4_euclid_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xreal_0(A) & v1_xreal_0(B) & v1_xreal_0(C) ) => k4_euclid_5(A,B,C) = k11_finseq_1(A,B,C) ) )).
fof(redefinition_k4_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k4_finseq_1(A) = k9_xtuple_0(A) ) )).
fof(redefinition_k4_finseq_5,axiom,( ! [A] : ! [B] : ( m1_finseq_1(B,A) => k4_finseq_5(A,B) = k3_finseq_5(B) ) )).
fof(redefinition_k4_finseqop,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k4_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k3_catalan2(A)) => k4_flang_1(A,B) = k1_tarski(B) ) )).
fof(redefinition_k4_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k4_fomodel3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k4_funcsdom,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k4_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k4_functor2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k4_functor3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k4_fvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & ~ 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) ) )).
fof(redefinition_k4_glib_005,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(redefinition_k4_graph_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k4_graph_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => k4_graph_2(A,B,C) = k3_graph_2(B,C) ) )).
fof(redefinition_k4_graphsp,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k1_funct_2(A,A)) & m1_subset_1(C,A) ) => k4_graphsp(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k4_group_7,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k4_jgraph_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) ) => k4_jgraph_1(A,B) = k2_jgraph_1(B) ) )).
fof(redefinition_k4_jordan10,axiom,( ! [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)))) ) => k4_jordan10(A) = k2_jordan10(A) ) )).
fof(redefinition_k4_jordan1k,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ 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) ) )).
fof(redefinition_k4_lang1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k4_lattices,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k4_matrix10,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m1_finseq_1(B,k3_finseq_2(k1_numbers)) & v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m1_finseq_1(C,k3_finseq_2(k1_numbers)) ) => k4_matrix10(A,B,C) = k3_matrixr1(B,C) ) )).
fof(redefinition_k4_matrix11,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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)))) & v1_matrix_0(E) & v2_matrix_0(E,C,A,B) & m1_finseq_1(E,k3_finseq_2(C)) ) => k4_matrix11(A,B,C,D,E) = k3_relat_1(D,E) ) )).
fof(redefinition_k4_matrix13,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => k4_matrix13(A,B) = k2_tarski(A,B) ) )).
fof(redefinition_k4_matrixj1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(A)) ) => k4_matrixj1(A,B) = k5_finseq_1(B) ) )).
fof(redefinition_k4_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k4_measure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => k4_measure1(A,B,C) = k10_xtuple_0(C) ) )).
fof(redefinition_k4_measure7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k9_setfam_1(k1_numbers)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k1_numbers)))) & m2_measure7(B,A) & m1_subset_1(C,k4_ordinal1) ) => k4_measure7(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k4_mesfunc5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k3_rfunct_3(A,B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k3_rfunct_3(A,B)))) & v7_ordinal1(D) ) => k4_mesfunc5(A,B,C,D) = k1_funct_1(C,D) ) )).
fof(redefinition_k4_mesfunc7,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_numbers) & v7_ordinal1(B) ) => k4_mesfunc7(A,B) = k3_mesfunc7(A,B) ) )).
fof(redefinition_k4_mssubfam,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k4_multop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ( ( ~ 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) ) )).
fof(redefinition_k4_nat_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => k4_nat_1(A,B) = k3_xxreal_0(A,B) ) )).
fof(redefinition_k4_nat_d,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => k4_nat_d(A,B) = k5_int_1(A,B) ) )).
fof(redefinition_k4_nattra_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) => k4_nattra_1(A,B,C) = k1_nattra_1(A,B,C) ) )).
fof(redefinition_k4_newton,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => k4_newton(A,B) = k3_newton(A,B) ) )).
fof(redefinition_k4_normsp_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) => k4_normsp_0(A,B,C) = k3_normsp_0(B,C) ) )).
fof(redefinition_k4_ordinal4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k4_ordinal6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k4_partfun2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k4_petri,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k4_pnproc_1,axiom,( ! [A] : ! [B] : ( m1_pnproc_1(B,A) => k4_pnproc_1(A,B) = k1_xtuple_0(B) ) )).
fof(redefinition_k4_polyform,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_int_1(B) ) => k4_polyform(A,B) = k10_finseq_1(A,B) ) )).
fof(redefinition_k4_polynom1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) => k4_polynom1(A,B,C,D) = k1_funct_1(C,D) ) )).
fof(redefinition_k4_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k4_prob_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,k9_setfam_1(A)) & v7_ordinal1(C) ) => k4_prob_3(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k4_quatern3,axiom,( ! [A] : ( m1_subset_1(A,k1_quaterni) => k4_quatern3(A) = k3_quatern3(A) ) )).
fof(redefinition_k4_quofield,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k4_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => k4_radix_3(A) = k2_radix_3(A) ) )).
fof(redefinition_k4_random_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k4_ratfunc1,axiom,( ! [A] : ! [B] : ( ( ~ v7_struct_0(A) & l5_algstr_0(A) & m1_ratfunc1(B,A) ) => k4_ratfunc1(A,B) = k1_xtuple_0(B) ) )).
fof(redefinition_k4_rcomp_1,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xreal_0(B) ) => k4_rcomp_1(A,B) = k3_xxreal_1(A,B) ) )).
fof(redefinition_k4_real_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k4_real_1(A,B) = k3_xcmplx_0(A,B) ) )).
fof(redefinition_k4_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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) ) )).
fof(redefinition_k4_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,A))) => k4_relset_2(A,B,C) = k3_relset_2(B,C) ) )).
fof(redefinition_k4_rewrite2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k4_rfunct_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k4_robbins3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k4_rvsum_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k4_rvsum_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k4_scmfsa_m,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => k4_scmfsa_m(A) = k1_tarski(A) ) )).
fof(redefinition_k4_seq_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_membered(A) ) => k4_seq_4(A) = k2_xxreal_2(A) ) )).
fof(redefinition_k4_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k4_setlim_1(A,B) = k3_setlim_1(B) ) )).
fof(redefinition_k4_setwiseo,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k4_stacks_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k4_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(A) & 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) ) )).
fof(redefinition_k4_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k4_supinf_2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k6_numbers) & m1_subset_1(B,k6_numbers) ) => k4_supinf_2(A,B) = k3_xxreal_3(A,B) ) )).
fof(redefinition_k4_tex_4,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k4_topalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k4_topgen_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k4_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => k4_topgrp_1(A) = k3_struct_0(A) ) )).
fof(redefinition_k4_topreal7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k4_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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))) ) => k4_toprealc(A,B,C,D,E) = k1_funct_1(D,E) ) )).
fof(redefinition_k4_turing_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_finseq_1(B,k4_ordinal1) ) => k4_turing_1(A,B) = k16_finseq_1(A,B) ) )).
fof(redefinition_k4_urysohn1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k4_valuat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_qc_lang1(A) & ~ v1_xboole_0(B) & v7_ordinal1(C) & 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) ) )).
fof(redefinition_k4_waybel18,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k4_waybel35,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k4_waybel_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k4_yellow_1(A,B))) & m1_subset_1(D,A) ) => k4_waybel_3(A,B,C,D) = k1_funct_1(C,D) ) )).
fof(redefinition_k4_wsierp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & m1_finseq_1(C,A) ) => k4_wsierp_1(A,B,C) = k2_finseq_3(B,C) ) )).
fof(redefinition_k4_yellow20,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k4_yellow21,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k4_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k4_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k4_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) ) => k4_zf_lang1(A) = k3_zf_lang1(A) ) )).
fof(redefinition_k4_zf_refle,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k51_abcmiz_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => k51_abcmiz_1(A) = k1_lang1(A) ) )).
fof(redefinition_k51_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(redefinition_k52_abcmiz_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => k52_abcmiz_1(A) = k2_lang1(A) ) )).
fof(redefinition_k52_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(redefinition_k52_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k53_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k55_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k56_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k58_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k58_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k59_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k5_abcmiz_a,axiom,( k5_abcmiz_a = k17_abcmiz_1 )).
fof(redefinition_k5_afinsq_1,axiom,( ! [A] : k5_afinsq_1(A) = k3_afinsq_1(A) )).
fof(redefinition_k5_binop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k5_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k5_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k5_bvfunc26,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k5_bvfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k5_card_1,axiom,( ! [A] : ( v1_finset_1(A) => k5_card_1(A) = k1_card_1(A) ) )).
fof(redefinition_k5_cat_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ 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) ) )).
fof(redefinition_k5_cayldick,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,u1_struct_0(A)) ) => k5_cayldick(A,B,C) = k6_afinsq_1(B,C) ) )).
fof(redefinition_k5_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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) ) )).
fof(redefinition_k5_classes2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k5_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k5_complex1,axiom,( k5_complex1 = k5_ordinal1 )).
fof(redefinition_k5_complsp2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_finseq_2(A,k2_numbers)) ) => k5_complsp2(A,B) = k30_valued_1(B) ) )).
fof(redefinition_k5_comseq_3,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k5_convex4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k5_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => k5_cqc_lang(A) = k12_qc_lang1(A) ) )).
fof(redefinition_k5_descip_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k4_finseq_2(k2_nat_1(2,B),A)) ) => k5_descip_1(A,B,C) = k1_rfinseq(B,C) ) )).
fof(redefinition_k5_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( ~ 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) ) )).
fof(redefinition_k5_equation,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) & m1_subset_1(B,u1_struct_0(A)) & m1_subset_1(C,k1_funct_1(u3_msualg_1(A,k3_equation(A)),B)) & m1_subset_1(D,k1_funct_1(u3_msualg_1(A,k3_equation(A)),B)) ) => k5_equation(A,B,C,D) = k4_tarski(C,D) ) )).
fof(redefinition_k5_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => k5_euclid(A) = k4_euclid(A) ) )).
fof(redefinition_k5_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) = k9_funct_7(C,D,E) ) )).
fof(redefinition_k5_finseq_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & m1_subset_1(C,A) ) => k5_finseq_2(A,B,C) = k2_finseq_2(B,C) ) )).
fof(redefinition_k5_flang_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & v7_ordinal1(C) ) => k5_flang_1(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k5_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k5_funct_3,axiom,( ! [A] : ! [B] : k5_funct_3(A,B) = k4_funct_3(A,B) )).
fof(redefinition_k5_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k5_funct_5,axiom,( k5_funct_5 = k5_ordinal1 )).
fof(redefinition_k5_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k5_glib_004,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k5_groeb_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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(k12_polynom1(A,B)))) & m2_ideal_1(D,k12_polynom1(A,B),C) & m2_ideal_1(E,k12_polynom1(A,B),C) ) => k5_groeb_2(A,B,C,D,E) = k7_finseq_1(D,E) ) )).
fof(redefinition_k5_group_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k5_index_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k5_integr15,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( m1_subset_1(A,k4_ordinal1) & ~ 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,k4_ordinal1,k1_integra1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(B)))) & m4_integr15(E,A,B,C,D) & m1_subset_1(F,k4_ordinal1) ) => k5_integr15(A,B,C,D,E,F) = k1_funct_1(E,F) ) )).
fof(redefinition_k5_knaster,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k5_lang1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k5_lexbfs,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(redefinition_k5_lpspacc1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & v1_membered(B) & m1_subset_1(C,k3_rfunct_3(A,B)) & v1_xcmplx_0(D) ) => k5_lpspacc1(A,B,C,D) = k24_valued_1(C,D) ) )).
fof(redefinition_k5_matrix10,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m1_finseq_1(B,k3_finseq_2(k1_numbers)) & v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m1_finseq_1(C,k3_finseq_2(k1_numbers)) ) => k5_matrix10(A,B,C) = k5_matrixr1(B,C) ) )).
fof(redefinition_k5_matrix13,axiom,( ! [A] : ( ( v1_finset_1(A) & v1_setfam_1(A) & m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) ) => k5_matrix13(A) = k14_finseq_1(A) ) )).
fof(redefinition_k5_matrix_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & v7_ordinal1(C) & ~ 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) & v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(D),A,B) & m1_finseq_1(E,k3_finseq_2(u1_struct_0(D))) & v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(D),k1_matrix_0(E),C) & m1_finseq_1(F,k3_finseq_2(u1_struct_0(D))) ) => k5_matrix_3(A,B,C,D,E,F) = k4_matrix_3(D,E,F) ) )).
fof(redefinition_k5_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(A)) & v1_matrix_0(C) & m1_finseq_1(C,k3_finseq_2(A)) ) => k5_matrixj1(A,B,C) = k10_finseq_1(B,C) ) )).
fof(redefinition_k5_matrlin2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v7_ordinal1(A) & v7_ordinal1(B) & ~ 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) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(C))) & v1_matrix_0(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) ) )).
fof(redefinition_k5_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k5_midsp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k5_midsp_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( m1_subset_1(A,k4_ordinal1) & ~ v1_xboole_0(B) & m1_subset_1(C,k4_finseq_2(k1_nat_1(A,1),B)) & m1_midsp_3(D,A) ) => k5_midsp_3(A,B,C,D) = k1_funct_1(C,D) ) )).
fof(redefinition_k5_modal_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k5_monoid_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(C,A) ) => k5_monoid_1(A,B,C) = k2_funcop_1(B,C) ) )).
fof(redefinition_k5_mssubfam,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k5_msualg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k5_nat_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => k5_nat_1(A,B) = k4_xxreal_0(A,B) ) )).
fof(redefinition_k5_nat_d,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => k5_nat_d(A,B) = k2_int_2(A,B) ) )).
fof(redefinition_k5_normsp_0,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_normsp_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k5_normsp_0(A,B) = k3_normsp_0(A,B) ) )).
fof(redefinition_k5_numbers,axiom,( k5_numbers = k5_ordinal1 )).
fof(redefinition_k5_petri,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k5_pnproc_1,axiom,( ! [A] : ! [B] : ( m1_pnproc_1(B,A) => k5_pnproc_1(A,B) = k2_xtuple_0(B) ) )).
fof(redefinition_k5_polyform,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_int_1(A) & v1_int_1(B) & v1_int_1(C) ) => k5_polyform(A,B,C) = k11_finseq_1(A,B,C) ) )).
fof(redefinition_k5_pralg_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k5_prob_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_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) ) )).
fof(redefinition_k5_prob_3,axiom,( ! [A] : ! [B] : ( m1_finseq_1(B,k9_setfam_1(A)) => k5_prob_3(A,B) = k3_card_3(B) ) )).
fof(redefinition_k5_prvect_2,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k5_quatern2,axiom,( ! [A] : ! [B] : ( ( v1_quaterni(A) & v1_quaterni(B) ) => k5_quatern2(A,B) = k4_quatern2(A,B) ) )).
fof(redefinition_k5_quofield,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k5_random_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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_xreal_0(D) ) => k5_random_1(A,B,C,D) = k24_valued_1(C,D) ) )).
fof(redefinition_k5_ranknull,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) )).
fof(redefinition_k5_ratfunc1,axiom,( ! [A] : ! [B] : ( ( ~ v7_struct_0(A) & l5_algstr_0(A) & m1_ratfunc1(B,A) ) => k5_ratfunc1(A,B) = k2_xtuple_0(B) ) )).
fof(redefinition_k5_real_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k5_real_1(A,B) = k6_xcmplx_0(A,B) ) )).
fof(redefinition_k5_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => k5_relset_1(A,B,C,D) = k5_relat_1(C,D) ) )).
fof(redefinition_k5_rewrite2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k5_rfunct_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k5_ringcat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) )).
fof(redefinition_k5_robbins1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k5_robbins3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k5_rsspace3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l1_normsp_1(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v7_ordinal1(C) ) => k5_rsspace3(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k5_rvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k5_rvsum_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => k5_rvsum_2(A) = k30_valued_1(A) ) )).
fof(redefinition_k5_scmfsa_m,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k5_series_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => k5_series_1(A,B) = k2_power(A,B) ) )).
fof(redefinition_k5_setfam_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => k5_setfam_1(A,B) = k3_tarski(B) ) )).
fof(redefinition_k5_setlim_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k5_setlim_1(A,B,C) = k1_setlim_1(C) ) )).
fof(redefinition_k5_setwiseo,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k5_sublemma,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k38_substut1(A)) ) => k5_sublemma(A,B) = k20_substut1(A,B) ) )).
fof(redefinition_k5_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k5_substut2,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k16_substut1(A)) ) => k5_substut2(A,B) = k2_xtuple_0(B) ) )).
fof(redefinition_k5_supinf_2,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_zfmisc_1(k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => k5_supinf_2(A,B) = k8_member_1(A,B) ) )).
fof(redefinition_k5_topmetr,axiom,( k5_topmetr = k17_borsuk_1 )).
fof(redefinition_k5_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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)) ) => k5_toprealc(A,B,C,D,E,F) = k1_binop_1(D,E,F) ) )).
fof(redefinition_k5_trees_9,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) ) => k5_trees_9(A,B) = k3_trees_9(B) ) )).
fof(redefinition_k5_urysohn3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) => k5_urysohn3(A,B,C,D) = k1_funct_1(C,D) ) )).
fof(redefinition_k5_waybel18,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k5_waybel_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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(k4_yellow_1(A,B)))) ) => k5_waybel_3(A,B,C,D) = k5_card_3(C,D) ) )).
fof(redefinition_k5_waybel_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k5_yellow20,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k5_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k5_zf_model,axiom,( ! [A] : ! [B] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) & ~ v1_xboole_0(B) ) => k5_zf_model(A,B) = k4_zf_model(A,B) ) )).
fof(redefinition_k5_zf_refle,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k60_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k61_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k62_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k63_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k64_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k69_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k6_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k6_bcialg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k6_bhsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k6_bhsp_1(A,B,C) = k2_normsp_1(A,B,C) ) )).
fof(redefinition_k6_bilinear,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k6_borsuk_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k6_bvfunc26,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k6_bvfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k6_cat_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ 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) ) )).
fof(redefinition_k6_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k6_classes2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k6_closure2,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k6_cohsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k6_comseq_3,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k6_cqc_lang,axiom,( ! [A] : ! [B] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k3_cqc_lang(A)) ) => k6_cqc_lang(A,B) = k13_qc_lang1(A,B) ) )).
fof(redefinition_k6_domain_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k6_domain_1(A,B) = k1_tarski(B) ) )).
fof(redefinition_k6_dtconstr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dtconstr(A) & l1_lang1(A) ) => k6_dtconstr(A) = k1_lang1(A) ) )).
fof(redefinition_k6_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => k6_eqrel_1(A,B,C,D) = k9_relat_1(C,D) ) )).
fof(redefinition_k6_euclid,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k1_euclid(A)) ) => k6_euclid(A,B) = k30_valued_1(B) ) )).
fof(redefinition_k6_euclid_7,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => k6_euclid_7(A,B) = k6_matrixr2(A,B) ) )).
fof(redefinition_k6_filter_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k6_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k6_funct_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k6_funct_3(A,B) = k4_relat_1(B) ) )).
fof(redefinition_k6_fvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & ~ 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) ) )).
fof(redefinition_k6_graphsp,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k6_group_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k6_index_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k6_knaster,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k6_lattice3,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k6_lattice8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k6_lopban_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k6_matrix10,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & v1_xreal_0(B) & v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m1_finseq_1(C,k3_finseq_2(k1_numbers)) ) => k6_matrix10(A,B,C) = k7_matrixr1(B,C) ) )).
fof(redefinition_k6_matrix15,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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_0(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) ) )).
fof(redefinition_k6_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k6_matrlin2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) )).
fof(redefinition_k6_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k6_measure6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v3_membered(B) & v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => k6_measure6(A,B,C) = k35_valued_1(C) ) )).
fof(redefinition_k6_midsp_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_subset_1(A,k4_ordinal1) & ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_nat_1(A,2)) & m1_subset_1(C,k4_finseq_2(k1_nat_1(A,1),u1_struct_0(B))) & m1_subset_1(D,k4_ordinal1) & m1_subset_1(E,u1_struct_0(B)) ) => k6_midsp_3(A,B,C,D,E) = k1_funct_7(C,D,E) ) )).
fof(redefinition_k6_monoid_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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) ) )).
fof(redefinition_k6_msaterm,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k6_nat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) & v7_ordinal1(C) ) => k6_nat_1(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k6_nat_d,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => k6_nat_d(A,B) = k3_int_2(A,B) ) )).
fof(redefinition_k6_ordinal4,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) & v3_ordinal1(B) & m1_subset_1(B,A) ) => k6_ordinal4(A,B) = k1_ordinal1(B) ) )).
fof(redefinition_k6_partfun1,axiom,( ! [A] : k6_partfun1(A) = k4_relat_1(A) )).
fof(redefinition_k6_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k6_pdiff_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) & m1_subset_1(C,k1_euclid(A)) ) => k6_pdiff_1(A,B,C) = k5_pdiff_1(B,C) ) )).
fof(redefinition_k6_polyform,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k4_numbers) & m1_finseq_1(B,k4_numbers) ) => k6_polyform(A,B) = k7_finseq_1(A,B) ) )).
fof(redefinition_k6_polynom1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)))) ) => k6_polynom1(A,B,C,D) = k5_polynom1(A,B,C,D) ) )).
fof(redefinition_k6_prelamb,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k6_prob_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_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) ) )).
fof(redefinition_k6_qmax_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k6_random_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k6_real_1,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k1_numbers) & m1_subset_1(B,k1_numbers) ) => k6_real_1(A,B) = k7_xcmplx_0(A,B) ) )).
fof(redefinition_k6_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) => k6_relset_1(A,B,C,D) = k6_relat_1(C,D) ) )).
fof(redefinition_k6_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k6_rewrite2,axiom,( ! [A] : k6_rewrite2(A) = k4_relat_1(A) )).
fof(redefinition_k6_rfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k6_robbins1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k6_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => k6_rvsum_1(A) = k30_valued_1(A) ) )).
fof(redefinition_k6_rvsum_2,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v3_card_1(B,A) & m1_finseq_1(B,k2_numbers) ) => k6_rvsum_2(A,B) = k30_valued_1(B) ) )).
fof(redefinition_k6_scmfsa_m,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k6_scmring1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k6_setfam_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => k6_setfam_1(A,B) = k1_setfam_1(B) ) )).
fof(redefinition_k6_setlim_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k6_setlim_1(A,B,C) = k3_setlim_1(C) ) )).
fof(redefinition_k6_setwiseo,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k6_subset_1,axiom,( ! [A] : ! [B] : k6_subset_1(A,B) = k4_xboole_0(A,B) )).
fof(redefinition_k6_substut1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_qc_lang1(A) & m1_subset_1(B,k1_substut1(A)) ) => k6_substut1(A,B,C) = k5_relat_1(B,C) ) )).
fof(redefinition_k6_supinf_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k6_numbers)) => k6_supinf_2(A) = k4_member_1(A) ) )).
fof(redefinition_k6_topalg_5,axiom,( ! [A] : ( v1_int_1(A) => k6_topalg_5(A) = k5_topalg_5(A) ) )).
fof(redefinition_k6_topgrp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k6_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => k6_toprealc(A,B,C) = k7_valued_1(B,C) ) )).
fof(redefinition_k6_trees_2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k6_trees_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => k6_trees_3(A,B) = k7_funct_3(A,B) ) )).
fof(redefinition_k6_vfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k6_waybel35,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k6_waybel_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k6_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k6_zf_lang1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_zf_lang(A) & m1_finseq_1(A,k4_ordinal1) & 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) ) )).
fof(redefinition_k70_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k73_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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) ) )).
fof(redefinition_k74_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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) ) )).
fof(redefinition_k79_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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) ) )).
fof(redefinition_k7_abcmiz_a,axiom,( k7_abcmiz_a = k19_abcmiz_1 )).
fof(redefinition_k7_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k7_binom,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_ordinal1) ) => k7_binom(A,B) = k3_newton(A,B) ) )).
fof(redefinition_k7_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k7_card_1,axiom,( ! [A] : ( v7_ordinal1(A) => k7_card_1(A) = k6_card_1(A) ) )).
fof(redefinition_k7_cat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) => k7_cat_2(A,B,C,D) = k4_tarski(C,D) ) )).
fof(redefinition_k7_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ 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) ) )).
fof(redefinition_k7_chain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) & m1_chain_1(B,A) & m1_subset_1(C,k4_ordinal1) & 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) ) )).
fof(redefinition_k7_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k7_classes2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k7_clopban1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) )).
fof(redefinition_k7_closure2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k7_complex1,axiom,( k7_complex1 = k1_xcmplx_0 )).
fof(redefinition_k7_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => k7_comseq_3(A) = k3_comseq_3(A) ) )).
fof(redefinition_k7_cqc_lang,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k7_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) & m1_subset_1(C,A) ) => k7_domain_1(A,B,C) = k2_tarski(B,C) ) )).
fof(redefinition_k7_dtconstr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_dtconstr(A) & l1_lang1(A) ) => k7_dtconstr(A) = k2_lang1(A) ) )).
fof(redefinition_k7_dynkin,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_dynkin(B,A) & m1_subset_1(C,B) ) => k7_dynkin(A,B,C) = k6_dynkin(A,B,C) ) )).
fof(redefinition_k7_euclid,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k7_finseqop,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k7_fomodel3,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k7_fomodel3(A,B) = k5_fomodel3(A,B) ) )).
fof(redefinition_k7_funcop_1,axiom,( ! [A] : ! [B] : k7_funcop_1(A,B) = k2_funcop_1(A,B) )).
fof(redefinition_k7_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k7_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k7_genealg1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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,k4_ordinal1) ) => k7_genealg1(A,B,C,D) = k1_genealg1(A,B,C,D) ) )).
fof(redefinition_k7_group_1,axiom,( ! [A] : ( ( v8_struct_0(A) & l1_struct_0(A) ) => k7_group_1(A) = k7_struct_0(A) ) )).
fof(redefinition_k7_index_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k7_interva1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k7_lexbfs,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k7_lfuzzy_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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) ) )).
fof(redefinition_k7_margrel1,axiom,( k7_margrel1 = k1_xboolean )).
fof(redefinition_k7_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(A)) & v7_ordinal1(C) ) => k7_matrix_0(A,B,C) = k5_matrix_0(A,B,C) ) )).
fof(redefinition_k7_matrixj1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k7_matrixj2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) )).
fof(redefinition_k7_matrlin,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(A)) & v1_matrix_0(C) & m1_finseq_1(C,k3_finseq_2(A)) ) => k7_matrlin(A,B,C) = k8_pre_poly(B,C) ) )).
fof(redefinition_k7_matrlin2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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) ) )).
fof(redefinition_k7_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k7_monoid_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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) ) )).
fof(redefinition_k7_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) => k7_msafree4(A,B,C,D,E) = k1_funct_1(D,E) ) )).
fof(redefinition_k7_nat_d,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => k7_nat_d(A,B) = k1_xreal_0(A,B) ) )).
fof(redefinition_k7_newton,axiom,( ! [A] : ( v7_ordinal1(A) => k7_newton(A) = k2_newton(A) ) )).
fof(redefinition_k7_prob_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_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) ) )).
fof(redefinition_k7_qmax_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k7_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => k7_quatern2(A) = k6_quatern2(A) ) )).
fof(redefinition_k7_random_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k7_ranknull,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k7_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => k7_relset_1(A,B,C,D) = k7_relat_1(C,D) ) )).
fof(redefinition_k7_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(redefinition_k7_rfunct_1,axiom,( ! [A] : ! [B] : k7_rfunct_1(A,B) = k4_funct_3(A,B) )).
fof(redefinition_k7_rfunct_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k7_rlvect_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k7_rusub_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k7_rvsum_1,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & m1_subset_1(B,k4_finseq_2(A,k1_numbers)) ) => k7_rvsum_1(A,B) = k30_valued_1(B) ) )).
fof(redefinition_k7_rvsum_2,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k7_scmfsa_m,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k7_scmringi,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k7_seq_4,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k2_numbers) & m1_finseq_1(B,k2_numbers) ) => k7_seq_4(A,B) = k1_valued_1(A,B) ) )).
fof(redefinition_k7_sublemma,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k7_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k7_subset_1(A,B,C) = k4_xboole_0(B,C) ) )).
fof(redefinition_k7_supinf_2,axiom,( ! [A] : ( v2_membered(A) => k7_supinf_2(A) = k2_xxreal_2(A) ) )).
fof(redefinition_k7_topalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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) ) )).
fof(redefinition_k7_topgrp_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k7_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => k7_toprealc(A,B,C) = k13_valued_1(B,C) ) )).
fof(redefinition_k7_trees_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => k7_trees_3(A,B) = k8_funct_3(A,B) ) )).
fof(redefinition_k7_trees_4,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,k5_trees_3(A)) ) => k7_trees_4(A,B) = k1_funct_6(B) ) )).
fof(redefinition_k7_valuat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( m1_qc_lang1(A) & ~ v1_xboole_0(B) & v7_ordinal1(C) & 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) ) )).
fof(redefinition_k7_waybel_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k7_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k7_yellow_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k80_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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) ) )).
fof(redefinition_k84_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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) ) )).
fof(redefinition_k85_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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) ) )).
fof(redefinition_k89_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k8_cat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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)) ) => k8_cat_2(A,B,C,D) = k4_tarski(C,D) ) )).
fof(redefinition_k8_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ 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) ) )).
fof(redefinition_k8_cat_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ 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) ) )).
fof(redefinition_k8_catalg_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,A) ) => k8_catalg_1(A,B) = k5_catalg_1(B) ) )).
fof(redefinition_k8_closure2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k8_cohsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k8_compos_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( l1_compos_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k4_ordinal1) & 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) ) )).
fof(redefinition_k8_comput_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & m1_subset_1(B,k4_finseq_2(A,k4_ordinal1)) & m1_subset_1(C,k4_ordinal1) & m1_subset_1(D,k4_ordinal1) ) => k8_comput_1(A,B,C,D) = k1_funct_7(B,C,D) ) )).
fof(redefinition_k8_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => k8_comseq_3(A) = k4_comseq_3(A) ) )).
fof(redefinition_k8_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => k8_conlat_1(A) = k7_conlat_1(A) ) )).
fof(redefinition_k8_cqc_lang,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k8_cqc_sim1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k8_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k8_dtconstr,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k8_eqrel_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k8_euclid,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k8_finseq_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => k8_finseq_1(A,B,C) = k7_finseq_1(B,C) ) )).
fof(redefinition_k8_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))))) ) => k8_fomodel4(A,B,C) = k7_fomodel4(A,B,C) ) )).
fof(redefinition_k8_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(C,A) ) => k8_funcop_1(A,B,C) = k2_funcop_1(B,C) ) )).
fof(redefinition_k8_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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))) ) => k8_funct_4(A,B,C,D) = k3_funct_4(C,D) ) )).
fof(redefinition_k8_funct_5,axiom,( k8_funct_5 = k6_funct_5 )).
fof(redefinition_k8_fvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & ~ 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) ) )).
fof(redefinition_k8_genealg1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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,k4_ordinal1) & m1_subset_1(E,k4_ordinal1) ) => k8_genealg1(A,B,C,D,E) = k2_genealg1(A,B,C,D,E) ) )).
fof(redefinition_k8_graph_5,axiom,( k8_graph_5 = k2_arytm_2 )).
fof(redefinition_k8_group_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k8_index_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k8_interva1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k8_isocat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) )).
fof(redefinition_k8_lexbfs,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k8_lfuzzy_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v5_relat_1(C,k1_rcomp_1(k5_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) ) )).
fof(redefinition_k8_lpspace1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(B) ) => k8_lpspace1(A,B) = k2_funcop_1(A,B) ) )).
fof(redefinition_k8_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => k8_ltlaxio3(A) = k1_xtuple_0(A) ) )).
fof(redefinition_k8_margrel1,axiom,( k8_margrel1 = k2_xboolean )).
fof(redefinition_k8_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_matrix_0(B) & m1_finseq_1(B,k3_finseq_2(A)) & v7_ordinal1(C) ) => k8_matrix_0(A,B,C) = k6_matrix_0(A,B,C) ) )).
fof(redefinition_k8_matrix_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k8_matrixc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & 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) ) )).
fof(redefinition_k8_matrlin,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v1_xboole_0(A) & v7_ordinal1(B) & v7_ordinal1(C) & v7_ordinal1(D) & v1_matrix_0(E) & v2_matrix_0(E,A,B,D) & m1_finseq_1(E,k3_finseq_2(A)) & v1_matrix_0(F) & v2_matrix_0(F,A,C,D) & m1_finseq_1(F,k3_finseq_2(A)) ) => k8_matrlin(A,B,C,D,E,F) = k7_finseq_1(E,F) ) )).
fof(redefinition_k8_matrlin2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) )).
fof(redefinition_k8_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k8_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v3_rewrite1(B) & v4_rewrite1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) & m1_subset_1(C,A) ) => k8_msafree4(A,B,C) = k2_rewrite1(B,C) ) )).
fof(redefinition_k8_msaterm,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k8_nat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) & v7_ordinal1(C) ) => k8_nat_1(A,B,C) = k7_nat_1(B,C) ) )).
fof(redefinition_k8_nat_3,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k8_ordinal3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v7_ordinal1(A) & v3_ordinal1(B) & v7_ordinal1(B) ) => k8_ordinal3(A,B) = k10_ordinal2(A,B) ) )).
fof(redefinition_k8_polynom3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & l2_algstr_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k8_polynom3(A,B,C) = k2_normsp_1(A,B,C) ) )).
fof(redefinition_k8_prob_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) )).
fof(redefinition_k8_prob_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_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) ) )).
fof(redefinition_k8_prvect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k8_random_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v2_finset_1(A) & v1_partfun1(A,k4_ordinal1) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v7_random_3(B,A,k7_random_3(A)) & v7_ordinal1(C) ) => k8_random_3(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k8_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => k8_relset_1(A,B,C,D) = k8_relat_1(C,D) ) )).
fof(redefinition_k8_rvsum_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k8_rvsum_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k8_seq_4,axiom,( ! [A] : ! [B] : ( ( m1_finseq_1(A,k2_numbers) & m1_finseq_1(B,k2_numbers) ) => k8_seq_4(A,B) = k45_valued_1(A,B) ) )).
fof(redefinition_k8_setwiseo,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k8_sublemma,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k8_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k8_subset_1(A,B,C) = k3_xboole_0(B,C) ) )).
fof(redefinition_k8_supinf_2,axiom,( ! [A] : ( v2_membered(A) => k8_supinf_2(A) = k1_xxreal_2(A) ) )).
fof(redefinition_k8_topalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( ~ 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) ) )).
fof(redefinition_k8_topgrp_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(redefinition_k8_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => k8_toprealc(A,B,C) = k24_valued_1(B,C) ) )).
fof(redefinition_k8_trees_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k8_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k8_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k90_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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) ) )).
fof(redefinition_k91_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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) ) )).
fof(redefinition_k9_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k9_binarith,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(redefinition_k9_bspace,axiom,( ! [A] : k9_bspace(A) = k8_bspace(A) )).
fof(redefinition_k9_bvfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k9_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) )).
fof(redefinition_k9_cat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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,k6_cat_2(A,B),C) & m1_subset_1(E,u4_struct_0(A)) & m1_subset_1(F,u4_struct_0(B)) ) => k9_cat_2(A,B,C,D,E,F) = k1_binop_1(D,E,F) ) )).
fof(redefinition_k9_catalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k9_classes2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k9_compos_1,axiom,( ! [A] : ! [B] : ( ( l1_compos_1(A) & m1_subset_1(B,u1_compos_1(A)) ) => k9_compos_1(A,B) = k3_afinsq_1(B) ) )).
fof(redefinition_k9_comseq_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_ordinal1) & v5_valued_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => k9_comseq_3(A,B) = k3_relat_1(A,B) ) )).
fof(redefinition_k9_cqc_lang,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k9_domain_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k9_dtconstr,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k9_ec_pf_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k9_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k9_euclid,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,k1_euclid(A)) & v1_xreal_0(C) ) => k9_euclid(A,B,C) = k24_valued_1(B,C) ) )).
fof(redefinition_k9_filter_0,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(redefinition_k9_filter_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k9_finseq_1,axiom,( ! [A] : k9_finseq_1(A) = k5_finseq_1(A) )).
fof(redefinition_k9_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k9_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k9_fomodel0(A) = k8_fomodel0(A) ) )).
fof(redefinition_k9_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) => k9_fomodel4(A,B,C) = k4_tarski(B,C) ) )).
fof(redefinition_k9_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k9_funct_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => k9_funct_2(A,B) = k1_funct_2(A,B) ) )).
fof(redefinition_k9_funct_3,axiom,( ! [A] : ! [B] : k9_funct_3(A,B) = k7_funct_3(A,B) )).
fof(redefinition_k9_funct_5,axiom,( k9_funct_5 = k7_funct_5 )).
fof(redefinition_k9_functor3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k9_genealg1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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,k4_ordinal1) & m1_subset_1(E,k4_ordinal1) & m1_subset_1(F,k4_ordinal1) ) => k9_genealg1(A,B,C,D,E,F) = k3_genealg1(A,B,C,D,E,F) ) )).
fof(redefinition_k9_glib_003,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(redefinition_k9_glib_004,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(redefinition_k9_lfuzzy_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k9_lopban_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) )).
fof(redefinition_k9_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => k9_lopclset(A) = k8_lopclset(A) ) )).
fof(redefinition_k9_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => k9_ltlaxio3(A) = k2_xtuple_0(A) ) )).
fof(redefinition_k9_margrel1,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => k9_margrel1(A) = k3_xboolean(A) ) )).
fof(redefinition_k9_matrix13,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(A),B,C) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => k9_matrix13(A,B,C,D) = k10_xtuple_0(D) ) )).
fof(redefinition_k9_matrix_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(redefinition_k9_matrix_5,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => k9_matrix_5(A,B) = k1_funct_1(A,B) ) )).
fof(redefinition_k9_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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) ) )).
fof(redefinition_k9_measure8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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,k6_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,k6_numbers))) ) => k9_measure8(A,B,C) = k6_measure8(A,B,C) ) )).
fof(redefinition_k9_nat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) & v7_ordinal1(C) ) => k9_nat_1(A,B,C) = k1_funct_1(B,C) ) )).
fof(redefinition_k9_ordinal3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v7_ordinal1(A) & v3_ordinal1(B) & v7_ordinal1(B) ) => k9_ordinal3(A,B) = k11_ordinal2(A,B) ) )).
fof(redefinition_k9_osafree,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_k9_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k9_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k9_prob_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(redefinition_k9_prvect_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k9_rvsum_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(redefinition_k9_rvsum_2,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k9_scmfsa_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(redefinition_k9_seq_4,axiom,( ! [A] : ( m1_finseq_1(A,k2_numbers) => k9_seq_4(A) = k30_valued_1(A) ) )).
fof(redefinition_k9_setfam_1,axiom,( ! [A] : k9_setfam_1(A) = k1_zfmisc_1(A) )).
fof(redefinition_k9_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_matroid0(B) & m1_simplex0(B,A) & v1_int_1(C) ) => k9_simplex0(A,B,C) = k8_simplex0(A,B,C) ) )).
fof(redefinition_k9_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k9_subset_1(A,B,C) = k3_xboole_0(B,C) ) )).
fof(redefinition_k9_supinf_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_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) ) )).
fof(redefinition_k9_topalg_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(redefinition_k9_toprealc,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & m1_subset_1(B,u1_struct_0(k15_euclid(A))) & v1_xreal_0(C) ) => k9_toprealc(A,B,C) = k14_valued_2(B,C) ) )).
fof(redefinition_k9_valued_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(redefinition_k9_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(redefinition_m1_armstrng,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) ) => ! [C] : ( m1_armstrng(C,A,B) <=> m1_subset_1(C,B) ) ) )).
fof(redefinition_m1_autalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( m1_autalg_1(D,A,B,C) <=> m1_subset_1(D,C) ) ) )).
fof(redefinition_m1_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree1(A) ) => ! [B] : ( m1_bintree2(B,A) <=> m1_subset_1(B,A) ) ) )).
fof(redefinition_m1_bvfunc_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_eqrel_1(B,A) ) => ! [C] : ( m1_bvfunc_1(C,A,B) <=> m1_subset_1(C,B) ) ) )).
fof(redefinition_m1_card_lar,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( m1_card_lar(C,A,B) <=> m1_subset_1(C,B) ) ) )).
fof(redefinition_m1_cat_5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_cat_5(A) ) => ! [B] : ( m1_cat_5(B,A) <=> m1_subset_1(B,A) ) ) )).
fof(redefinition_m1_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( m1_closure2(D,A,B,C) <=> m1_subset_1(D,C) ) ) )).
fof(redefinition_m1_complfld,axiom,( ! [A] : ! [B] : ( ( m1_subset_1(A,u1_struct_0(k1_complfld)) & ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_complfld(C,A,B) <=> m1_comptrig(C,A,B) ) ) )).
fof(redefinition_m1_comput_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( m1_comput_1(E,A,B,C,D) <=> m1_subset_1(E,D) ) ) )).
fof(redefinition_m1_dist_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & m1_subset_1(B,k6_dist_1(A)) ) => ! [C] : ( m1_dist_2(C,A,B) <=> m1_subset_1(C,B) ) ) )).
fof(redefinition_m1_dtconstr,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_dtconstr(D,A,B,C) <=> m1_subset_1(D,C) ) ) )).
fof(redefinition_m1_fomodel0,axiom,( ! [A] : ! [B] : ( m1_fomodel0(B,A) <=> m1_finseq_1(B,A) ) )).
fof(redefinition_m1_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & m1_finseq_2(B,A) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ! [D] : ( m1_graph_3(D,A,B,C) <=> m1_subset_1(D,C) ) ) )).
fof(redefinition_m1_group_6,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) & m1_group_2(B,A) ) => ! [C] : ( m1_group_6(C,A,B) <=> m1_group_2(C,B) ) ) )).
fof(redefinition_m1_incproj,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_incproj(B,A) <=> m2_collsp(B,A) ) ) )).
fof(redefinition_m1_matrix_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_matrix_2(A) ) => ! [B] : ( m1_matrix_2(B,A) <=> m1_subset_1(B,A) ) ) )).
fof(redefinition_m1_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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,k10_xtuple_0(B)) ) => ! [D] : ( m1_msafree4(D,A,B,C) <=> m1_subset_1(D,C) ) ) )).
fof(redefinition_m1_orders_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_orders_3(A) ) => ! [B] : ( m1_orders_3(B,A) <=> m1_subset_1(B,A) ) ) )).
fof(redefinition_m1_osalg_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_osalg_1(C,A,B) <=> m1_subset_1(C,B) ) ) )).
fof(redefinition_m1_petri,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_petri(D,A,B,C) <=> m1_subset_1(D,C) ) ) )).
fof(redefinition_m1_pre_poly,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k5_finsub_1(A))) ) => ! [C] : ( m1_pre_poly(C,A,B) <=> m1_subset_1(C,B) ) ) )).
fof(redefinition_m1_prob_1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) <=> m1_subset_1(C,B) ) ) )).
fof(redefinition_m1_prob_3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( m1_prob_3(C,A,B) <=> m1_finseq_1(C,B) ) ) )).
fof(redefinition_m1_pua2mss1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k4_partfun1(A,B))) ) => ! [D] : ( m1_pua2mss1(D,A,B,C) <=> m1_subset_1(D,C) ) ) )).
fof(redefinition_m1_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) <=> m1_subset_1(B,A) ) ) )).
fof(redefinition_m1_trees_4,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_trees_4(C,A,B) <=> m1_finseq_1(C,B) ) ) )).
fof(redefinition_m2_conlat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) & m1_conlat_1(B,A) ) => ! [C] : ( m2_conlat_1(C,A,B) <=> m1_subset_1(C,B) ) ) )).
fof(redefinition_m2_finseq_1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) <=> m1_finseq_1(B,A) ) )).
fof(redefinition_m2_finseq_2,axiom,( ! [A] : ! [B] : ( m1_finseq_2(B,A) => ! [C] : ( m2_finseq_2(C,A,B) <=> m1_subset_1(C,B) ) ) )).
fof(redefinition_m2_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m2_fomodel2(D,A,B,C) <=> m1_fomodel2(D,A,B,C) ) ) )).
fof(redefinition_m2_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(B) & m1_funct_2(C,A,B) ) => ! [D] : ( m2_funct_2(D,A,B,C) <=> m1_subset_1(D,C) ) ) )).
fof(redefinition_m2_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_graph_1(B,A) <=> m1_graph_1(B,A) ) ) )).
fof(redefinition_m2_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_grcat_1(A) ) => ! [B] : ( m2_grcat_1(B,A) <=> m1_subset_1(B,A) ) ) )).
fof(redefinition_m2_lmod_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_group_1(A) & 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] : ( m2_lmod_7(D,A,B,C) <=> m1_subset_1(D,C) ) ) )).
fof(redefinition_m2_ltlaxio4,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_ltlaxio4(C,A,B) <=> m1_rlaffin3(C,B) ) ) )).
fof(redefinition_m2_modcat_1,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) & m1_modcat_1(B,A) ) => ! [C] : ( m2_modcat_1(C,A,B) <=> m1_subset_1(C,B) ) ) )).
fof(redefinition_m2_orders_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m2_orders_1(C,A,B) <=> m1_orders_1(C,B) ) ) )).
fof(redefinition_m2_prob_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m2_prob_4(D,A,B,C) <=> m1_prob_4(D,A,B,C) ) ) )).
fof(redefinition_m2_rfunct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(C) & m1_rfunct_3(C,A,B) ) => ! [D] : ( m2_rfunct_3(D,A,B,C) <=> m1_subset_1(D,C) ) ) )).
fof(redefinition_m2_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_ringcat1(A) ) => ! [B] : ( m2_ringcat1(B,A) <=> m1_subset_1(B,A) ) ) )).
fof(redefinition_m2_rlaffin3,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_rlaffin3(C,A,B) <=> m1_rlaffin3(C,B) ) ) )).
fof(redefinition_m2_subset_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_subset_1(C,A,B) <=> m1_subset_1(C,B) ) ) )).
fof(redefinition_m2_trees_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m2_trees_3(C,A,B) <=> m1_subset_1(C,B) ) ) )).
fof(redefinition_m2_unialg_3,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m2_unialg_3(C,A,B) <=> m1_subset_1(C,B) ) ) )).
fof(redefinition_m2_valued_0,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ! [C] : ( m2_valued_0(C,A,B) <=> m1_valued_0(C,B) ) ) )).
fof(redefinition_m2_vectsp_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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] : ( m2_vectsp_8(D,A,B,C) <=> m1_subset_1(D,C) ) ) )).
fof(redefinition_m3_conlat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) & ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) ) => ! [C] : ( m3_conlat_1(C,A,B) <=> m1_subset_1(C,B) ) ) )).
fof(redefinition_m3_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_grcat_1(A) ) => ! [B] : ( m3_grcat_1(B,A) <=> m1_subset_1(B,A) ) ) )).
fof(redefinition_m3_msalimit,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_msalimit(A) ) => ! [B] : ( m3_msalimit(B,A) <=> m1_subset_1(B,A) ) ) )).
fof(redefinition_m3_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m3_pnproc_1(C,A,B) <=> m1_subset_1(C,B) ) ) )).
fof(redefinition_m3_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v5_ringcat1(A) ) => ! [B] : ( m3_ringcat1(B,A) <=> m1_subset_1(B,A) ) ) )).
fof(redefinition_m3_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m3_topgrp_1(B,A) <=> m2_topgrp_1(B,A) ) ) )).
fof(redefinition_m3_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ! [B] : ( m3_trees_3(B,A) <=> m2_trees_1(B,A) ) ) )).
fof(redefinition_m4_modcat_1,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) & m3_modcat_1(B,A) ) => ! [C] : ( m4_modcat_1(C,A,B) <=> m1_subset_1(C,B) ) ) )).
fof(redefinition_m5_bcialg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m5_bcialg_2(C,A,B) <=> m4_bcialg_2(C,A,B) ) ) )).
fof(redefinition_m5_margrel1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & m4_margrel1(B,A) ) => ! [C] : ( m5_margrel1(C,A,B) <=> m1_subset_1(C,B) ) ) )).
fof(redefinition_m5_monoid_0,axiom,( ! [A] : ! [B] : ( ( l3_algstr_0(A) & m2_monoid_0(B,A) ) => ! [C] : ( m5_monoid_0(C,A,B) <=> m2_monoid_0(C,B) ) ) )).
fof(redefinition_m6_monoid_0,axiom,( ! [A] : ! [B] : ( ( l3_algstr_0(A) & m3_monoid_0(B,A) ) => ! [C] : ( m6_monoid_0(C,A,B) <=> m2_monoid_0(C,B) ) ) )).
fof(redefinition_m7_monoid_0,axiom,( ! [A] : ! [B] : ( ( l3_algstr_0(A) & m3_monoid_0(B,A) ) => ! [C] : ( m7_monoid_0(C,A,B) <=> m3_monoid_0(C,B) ) ) )).
fof(redefinition_r10_analmetr,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r1_boolealg,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) ) )).
fof(redefinition_r1_borsuk_3,axiom,( ! [A] : ! [B] : ( ( l1_pre_topc(A) & l1_pre_topc(B) ) => ( r1_borsuk_3(A,B) <=> r1_t_0topsp(A,B) ) ) )).
fof(redefinition_r1_borsuk_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r1_convex4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & m1_convex4(B,A) & m1_convex4(C,A) ) => ( r1_convex4(A,B,C) <=> B = C ) ) )).
fof(redefinition_r1_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r1_filter_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) ) )).
fof(redefinition_r1_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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 ) ) )).
fof(redefinition_r1_group_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) ) )).
fof(redefinition_r1_heyting1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r1_interva1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) ) )).
fof(redefinition_r1_lattice7,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(redefinition_r1_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v5_relat_1(C,k1_rcomp_1(k5_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(k5_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) ) ) )).
fof(redefinition_r1_margrel1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) ) )).
fof(redefinition_r1_mfold_2,axiom,( ! [A] : ! [B] : ( ( l1_pre_topc(A) & l1_pre_topc(B) ) => ( r1_mfold_2(A,B) <=> r1_t_0topsp(A,B) ) ) )).
fof(redefinition_r1_nat_d,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => ( r1_nat_d(A,B) <=> r1_int_1(A,B) ) ) )).
fof(redefinition_r1_ordinal1,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => ( r1_ordinal1(A,B) <=> r1_tarski(A,B) ) ) )).
fof(redefinition_r1_pnproc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) & v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ( r1_pnproc_1(A,B,C) <=> B = C ) ) )).
fof(redefinition_r1_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ( r1_relset_1(A,B,C,D) <=> r1_tarski(C,D) ) ) )).
fof(redefinition_r1_revrot_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) ) => ( r1_revrot_1(A,B,C) <=> r2_finseq_4(B,C) ) ) )).
fof(redefinition_r1_rlvect_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) ) )).
fof(redefinition_r1_rmod_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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 ) ) )).
fof(redefinition_r1_subset_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( r1_subset_1(A,B) <=> r1_xboole_0(A,B) ) ) )).
fof(redefinition_r1_vectsp_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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 ) ) )).
fof(redefinition_r1_yellow10,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(redefinition_r1_zmodul02,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & m1_zmodul02(B,A) & m1_zmodul02(C,A) ) => ( r1_zmodul02(A,B,C) <=> B = C ) ) )).
fof(redefinition_r2_abian,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r2_altcat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(redefinition_r2_borsuk_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r2_borsuk_3,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(redefinition_r2_clvect_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r2_clvect_2(A,B,C) <=> r1_clvect_2(A,B,C) ) ) )).
fof(redefinition_r2_compos_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) ) => ( r2_compos_2(A,B) <=> r1_compos_2(A,B) ) ) )).
fof(redefinition_r2_euclidlp,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k1_euclid(A)) & m1_subset_1(C,k1_euclid(A)) ) => ( r2_euclidlp(A,B,C) <=> r1_euclidlp(A,B,C) ) ) )).
fof(redefinition_r2_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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 ) ) )).
fof(redefinition_r2_fuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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) ) ) )).
fof(redefinition_r2_gcd_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r2_group_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r2_group_6,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(redefinition_r2_interva1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) ) )).
fof(redefinition_r2_metric_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r2_necklace,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & ~ v2_struct_0(B) & l1_orders_2(B) ) => ( r2_necklace(A,B) <=> r1_necklace(A,B) ) ) )).
fof(redefinition_r2_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(redefinition_r2_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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 ) ) )).
fof(redefinition_r2_subset_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( r2_subset_1(A,B) <=> r1_xboole_0(A,B) ) ) )).
fof(redefinition_r2_topalg_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r2_tsep_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r2_wellord2,axiom,( ! [A] : ! [B] : ( r2_wellord2(A,B) <=> r2_tarski(A,B) ) )).
fof(redefinition_r2_yellow_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(redefinition_r3_boolealg,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r3_finseq_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => ( r3_finseq_8(A,B,C) <=> r1_tarski(B,C) ) ) )).
fof(redefinition_r3_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r3_lattices,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r3_metric_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r3_orders_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r3_osalg_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r3_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r3_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r4_boolealg,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r4_borsuk_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(redefinition_r4_gcd_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r4_group_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r4_tsep_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r4_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r5_aff_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r6_group_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r6_msualg_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r6_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) ) )).
fof(redefinition_r7_gcd_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(redefinition_r8_binop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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 ) ) )).
fof(redefinition_r8_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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 ) ) )).
fof(redefinition_r9_analmetr,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(reflexivity_r1_abcmiz_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(reflexivity_r1_altcat_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => r1_altcat_2(A,A) ) )).
fof(reflexivity_r1_anproj_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) )).
fof(reflexivity_r1_bhsp_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r1_bhsp_3(A,B,B) ) )).
fof(reflexivity_r1_boolealg,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r1_borsuk_3,axiom,( ! [A] : ! [B] : ( ( l1_pre_topc(A) & l1_pre_topc(B) ) => r1_borsuk_3(A,A) ) )).
fof(reflexivity_r1_borsuk_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r1_bvfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r1_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) )).
fof(reflexivity_r1_circcomb,axiom,( ! [A] : ! [B] : ( ( l1_msualg_1(A) & l1_msualg_1(B) ) => r1_circcomb(A,A) ) )).
fof(reflexivity_r1_convex4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & m1_convex4(B,A) & m1_convex4(C,A) ) => r1_convex4(A,B,B) ) )).
fof(reflexivity_r1_dist_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(A) & m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => r1_dist_1(A,B,B) ) )).
fof(reflexivity_r1_ec_pf_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(reflexivity_r1_filter_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(reflexivity_r1_filter_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r1_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) )).
fof(reflexivity_r1_functor0,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(reflexivity_r1_functor2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(reflexivity_r1_functor3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(reflexivity_r1_fuzzy_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(reflexivity_r1_group_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r1_group_6,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(reflexivity_r1_heyting1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r1_int_1,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_int_1(B) ) => r1_int_1(A,A) ) )).
fof(reflexivity_r1_integra1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(reflexivity_r1_interva1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r1_isocat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) )).
fof(reflexivity_r1_lattice7,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(reflexivity_r1_lfuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & v5_relat_1(C,k1_rcomp_1(k5_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(k5_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) ) )).
fof(reflexivity_r1_lmod_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) )).
fof(reflexivity_r1_lopban_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r1_margrel1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_subset_1(B,k3_margrel1(A)) & m1_subset_1(C,k3_margrel1(A)) ) => r1_margrel1(A,B,B) ) )).
fof(reflexivity_r1_matrix_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => r1_matrix_6(A,B,C,C) ) )).
fof(reflexivity_r1_matrix_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => r1_matrix_8(A,B,C,C) ) )).
fof(reflexivity_r1_msuhom_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) & ~ v2_struct_0(B) & l1_msualg_1(B) ) => r1_msuhom_1(A,A) ) )).
fof(reflexivity_r1_nat_d,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => r1_nat_d(A,A) ) )).
fof(reflexivity_r1_nattra_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) )).
fof(reflexivity_r1_normform,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(reflexivity_r1_ordinal1,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => r1_ordinal1(A,A) ) )).
fof(reflexivity_r1_osalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r1_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r1_partfun1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => r1_partfun1(A,A) ) )).
fof(reflexivity_r1_pnproc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) & v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => r1_pnproc_1(A,B,B) ) )).
fof(reflexivity_r1_pzfmisc1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(reflexivity_r1_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => r1_relset_1(A,B,C,C) ) )).
fof(reflexivity_r1_ringcat1,axiom,( ! [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) & 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) ) )).
fof(reflexivity_r1_rlvect_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & m1_rlvect_2(B,A) & m1_rlvect_2(C,A) ) => r1_rlvect_2(A,B,B) ) )).
fof(reflexivity_r1_rmod_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) )).
fof(reflexivity_r1_roughs_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r1_setfam_1,axiom,( ! [A] : ! [B] : r1_setfam_1(A,A) )).
fof(reflexivity_r1_tarski,axiom,( ! [A] : ! [B] : r1_tarski(A,A) )).
fof(reflexivity_r1_unialg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(reflexivity_r1_vectsp_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(reflexivity_r1_xxreal_0,axiom,( ! [A] : ! [B] : ( ( v1_xxreal_0(A) & v1_xxreal_0(B) ) => r1_xxreal_0(A,A) ) )).
fof(reflexivity_r1_yellow18,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(reflexivity_r1_zmodul02,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & m1_zmodul02(B,A) & m1_zmodul02(C,A) ) => r1_zmodul02(A,B,B) ) )).
fof(reflexivity_r2_abcmiz_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(reflexivity_r2_altcat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(reflexivity_r2_altcat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r2_arytm_3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => r2_arytm_3(A,A) ) )).
fof(reflexivity_r2_borsuk_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r2_borsuk_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) & ~ v2_struct_0(B) & l1_pre_topc(B) ) => r2_borsuk_3(A,A) ) )).
fof(reflexivity_r2_circtrm1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) & ~ v2_struct_0(B) & l1_msualg_1(B) ) => r2_circtrm1(A,A) ) )).
fof(reflexivity_r2_classes1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => r2_classes1(A,A) ) )).
fof(reflexivity_r2_clvect_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_clvect_2(A,B,B) ) )).
fof(reflexivity_r2_compos_2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) ) => r2_compos_2(A,A) ) )).
fof(reflexivity_r2_cqc_sim1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(reflexivity_r2_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(reflexivity_r2_functor2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(reflexivity_r2_fuzzy_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & v5_relat_1(B,k1_rcomp_1(k5_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(k5_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) ) )).
fof(reflexivity_r2_gcd_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r2_group_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r2_group_6,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(reflexivity_r2_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r2_interva1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r2_isocat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) )).
fof(reflexivity_r2_matrix_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => r2_matrix_8(A,B,C,C) ) )).
fof(reflexivity_r2_metric_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r2_midsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r2_modelc_2,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(A) & m1_finseq_1(A,k4_ordinal1) & v1_modelc_2(B) & m1_finseq_1(B,k4_ordinal1) ) => r2_modelc_2(A,A) ) )).
fof(reflexivity_r2_nattra_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) )).
fof(reflexivity_r2_necklace,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & ~ v2_struct_0(B) & l1_orders_2(B) ) => r2_necklace(B,B) ) )).
fof(reflexivity_r2_ordinal2,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => r2_ordinal2(A,A) ) )).
fof(reflexivity_r2_osalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r2_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(reflexivity_r2_pnproc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) & v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => r2_pnproc_1(A,B,B) ) )).
fof(reflexivity_r2_polynom3,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k4_finseq_2(A,k4_ordinal1)) & m1_subset_1(C,k4_finseq_2(A,k4_ordinal1)) ) => r2_polynom3(A,B,B) ) )).
fof(reflexivity_r2_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(reflexivity_r2_qc_lang2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(reflexivity_r2_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(reflexivity_r2_roughs_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r2_setfam_1,axiom,( ! [A] : ! [B] : r2_setfam_1(B,B) )).
fof(reflexivity_r2_stacks_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r2_topalg_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r2_wellord2,axiom,( ! [A] : ! [B] : r2_wellord2(A,A) )).
fof(reflexivity_r2_zfrefle1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => r2_zfrefle1(A,A) ) )).
fof(reflexivity_r3_abcmiz_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(reflexivity_r3_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(B,k4_armstrng(A)) & m1_subset_1(C,k4_armstrng(A)) ) => r3_armstrng(A,B,B) ) )).
fof(reflexivity_r3_finseq_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(A) & m1_finseq_1(B,A) & m1_finseq_1(C,A) ) => r3_finseq_8(A,B,B) ) )).
fof(reflexivity_r3_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r3_lattices,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r3_nattra_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) )).
fof(reflexivity_r3_necklace,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & ~ v2_struct_0(B) & l1_orders_2(B) ) => r3_necklace(A,A) ) )).
fof(reflexivity_r3_orders_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r3_pcs_0,axiom,( ! [A] : ! [B] : ( ( l2_pcs_0(A) & l2_pcs_0(B) ) => r3_pcs_0(A,A) ) )).
fof(reflexivity_r3_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(reflexivity_r3_prelamb,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r3_qmax_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(reflexivity_r3_roughs_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r3_xboole_0,axiom,( ! [A] : ! [B] : r3_xboole_0(A,A) )).
fof(reflexivity_r3_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r3_zfrefle1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => r3_zfrefle1(A,A) ) )).
fof(reflexivity_r4_borsuk_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(reflexivity_r4_cqc_the3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(reflexivity_r4_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(reflexivity_r4_gcd_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r4_graph_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) & ~ v2_struct_0(B) & l1_graph_1(B) ) => r4_graph_1(A,A) ) )).
fof(reflexivity_r4_group_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r4_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(reflexivity_r4_qmax_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(reflexivity_r4_stacks_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(reflexivity_r4_yellow_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r5_abcmiz_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(reflexivity_r5_cqc_the3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(reflexivity_r5_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) )).
fof(reflexivity_r5_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => r5_glib_000(A,A) ) )).
fof(reflexivity_r5_waybel_1,axiom,( ! [A] : ! [B] : ( ( l1_orders_2(A) & l1_orders_2(B) ) => r5_waybel_1(A,A) ) )).
fof(reflexivity_r6_abcmiz_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(reflexivity_r6_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => r6_glib_000(A,A) ) )).
fof(reflexivity_r6_group_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r6_msualg_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r6_osalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(reflexivity_r6_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(reflexivity_r7_cqc_the3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(reflexivity_r7_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) )).
fof(reflexivity_r7_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(reflexivity_r8_binop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) )).
fof(reflexivity_r8_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) )).
fof(spc100_boole,axiom,( ~ v1_xboole_0(100) )).
fof(spc100_numerals,axiom,( v2_xxreal_0(100) & m1_subset_1(100,k4_ordinal1) )).
fof(spc105_boole,axiom,( ~ v1_xboole_0(105) )).
fof(spc105_numerals,axiom,( v2_xxreal_0(105) & m1_subset_1(105,k4_ordinal1) )).
fof(spc106_boole,axiom,( ~ v1_xboole_0(106) )).
fof(spc106_numerals,axiom,( v2_xxreal_0(106) & m1_subset_1(106,k4_ordinal1) )).
fof(spc108_boole,axiom,( ~ v1_xboole_0(108) )).
fof(spc108_numerals,axiom,( v2_xxreal_0(108) & m1_subset_1(108,k4_ordinal1) )).
fof(spc10_arithm,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) = k5_xcmplx_0(k3_xcmplx_0(A,B)) ) )).
fof(spc10_boole,axiom,( ~ v1_xboole_0(10) )).
fof(spc10_numerals,axiom,( v2_xxreal_0(10) & m1_subset_1(10,k4_ordinal1) )).
fof(spc117_boole,axiom,( ~ v1_xboole_0(117) )).
fof(spc117_numerals,axiom,( v2_xxreal_0(117) & m1_subset_1(117,k4_ordinal1) )).
fof(spc119_boole,axiom,( ~ v1_xboole_0(119) )).
fof(spc119_numerals,axiom,( v2_xxreal_0(119) & m1_subset_1(119,k4_ordinal1) )).
fof(spc11_arithm,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k7_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) = k7_xcmplx_0(B,A) ) )).
fof(spc11_boole,axiom,( ~ v1_xboole_0(11) )).
fof(spc11_numerals,axiom,( v2_xxreal_0(11) & m1_subset_1(11,k4_ordinal1) )).
fof(spc120_boole,axiom,( ~ v1_xboole_0(120) )).
fof(spc120_numerals,axiom,( v2_xxreal_0(120) & m1_subset_1(120,k4_ordinal1) )).
fof(spc121_boole,axiom,( ~ v1_xboole_0(121) )).
fof(spc121_numerals,axiom,( v2_xxreal_0(121) & m1_subset_1(121,k4_ordinal1) )).
fof(spc123_boole,axiom,( ~ v1_xboole_0(123) )).
fof(spc123_numerals,axiom,( v2_xxreal_0(123) & m1_subset_1(123,k4_ordinal1) )).
fof(spc126_boole,axiom,( ~ v1_xboole_0(126) )).
fof(spc126_numerals,axiom,( v2_xxreal_0(126) & m1_subset_1(126,k4_ordinal1) )).
fof(spc127_boole,axiom,( ~ v1_xboole_0(127) )).
fof(spc127_numerals,axiom,( v2_xxreal_0(127) & m1_subset_1(127,k4_ordinal1) )).
fof(spc128_boole,axiom,( ~ v1_xboole_0(128) )).
fof(spc128_numerals,axiom,( v2_xxreal_0(128) & m1_subset_1(128,k4_ordinal1) )).
fof(spc12_arithm,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k3_xcmplx_0(A,k5_xcmplx_0(B)) = k7_xcmplx_0(A,B) ) )).
fof(spc12_boole,axiom,( ~ v1_xboole_0(12) )).
fof(spc12_numerals,axiom,( v2_xxreal_0(12) & m1_subset_1(12,k4_ordinal1) )).
fof(spc136_boole,axiom,( ~ v1_xboole_0(136) )).
fof(spc136_numerals,axiom,( v2_xxreal_0(136) & m1_subset_1(136,k4_ordinal1) )).
fof(spc139_boole,axiom,( ~ v1_xboole_0(139) )).
fof(spc139_numerals,axiom,( v2_xxreal_0(139) & m1_subset_1(139,k4_ordinal1) )).
fof(spc13_boole,axiom,( ~ v1_xboole_0(13) )).
fof(spc13_numerals,axiom,( v2_xxreal_0(13) & m1_subset_1(13,k4_ordinal1) )).
fof(spc140_boole,axiom,( ~ v1_xboole_0(140) )).
fof(spc140_numerals,axiom,( v2_xxreal_0(140) & m1_subset_1(140,k4_ordinal1) )).
fof(spc149_boole,axiom,( ~ v1_xboole_0(149) )).
fof(spc149_numerals,axiom,( v2_xxreal_0(149) & m1_subset_1(149,k4_ordinal1) )).
fof(spc14_boole,axiom,( ~ v1_xboole_0(14) )).
fof(spc14_numerals,axiom,( v2_xxreal_0(14) & m1_subset_1(14,k4_ordinal1) )).
fof(spc152_boole,axiom,( ~ v1_xboole_0(152) )).
fof(spc152_numerals,axiom,( v2_xxreal_0(152) & m1_subset_1(152,k4_ordinal1) )).
fof(spc158_boole,axiom,( ~ v1_xboole_0(158) )).
fof(spc158_numerals,axiom,( v2_xxreal_0(158) & m1_subset_1(158,k4_ordinal1) )).
fof(spc159_boole,axiom,( ~ v1_xboole_0(159) )).
fof(spc159_numerals,axiom,( v2_xxreal_0(159) & m1_subset_1(159,k4_ordinal1) )).
fof(spc15_boole,axiom,( ~ v1_xboole_0(15) )).
fof(spc15_numerals,axiom,( v2_xxreal_0(15) & m1_subset_1(15,k4_ordinal1) )).
fof(spc160_boole,axiom,( ~ v1_xboole_0(160) )).
fof(spc160_numerals,axiom,( v2_xxreal_0(160) & m1_subset_1(160,k4_ordinal1) )).
fof(spc162_boole,axiom,( ~ v1_xboole_0(162) )).
fof(spc162_numerals,axiom,( v2_xxreal_0(162) & m1_subset_1(162,k4_ordinal1) )).
fof(spc163_boole,axiom,( ~ v1_xboole_0(163) )).
fof(spc163_numerals,axiom,( v2_xxreal_0(163) & m1_subset_1(163,k4_ordinal1) )).
fof(spc164_boole,axiom,( ~ v1_xboole_0(164) )).
fof(spc164_numerals,axiom,( v2_xxreal_0(164) & m1_subset_1(164,k4_ordinal1) )).
fof(spc166_boole,axiom,( ~ v1_xboole_0(166) )).
fof(spc166_numerals,axiom,( v2_xxreal_0(166) & m1_subset_1(166,k4_ordinal1) )).
fof(spc16_boole,axiom,( ~ v1_xboole_0(16) )).
fof(spc16_numerals,axiom,( v2_xxreal_0(16) & m1_subset_1(16,k4_ordinal1) )).
fof(spc172_boole,axiom,( ~ v1_xboole_0(172) )).
fof(spc172_numerals,axiom,( v2_xxreal_0(172) & m1_subset_1(172,k4_ordinal1) )).
fof(spc17_boole,axiom,( ~ v1_xboole_0(17) )).
fof(spc17_numerals,axiom,( v2_xxreal_0(17) & m1_subset_1(17,k4_ordinal1) )).
fof(spc185_boole,axiom,( ~ v1_xboole_0(185) )).
fof(spc185_numerals,axiom,( v2_xxreal_0(185) & m1_subset_1(185,k4_ordinal1) )).
fof(spc18_boole,axiom,( ~ v1_xboole_0(18) )).
fof(spc18_numerals,axiom,( v2_xxreal_0(18) & m1_subset_1(18,k4_ordinal1) )).
fof(spc192_boole,axiom,( ~ v1_xboole_0(192) )).
fof(spc192_numerals,axiom,( v2_xxreal_0(192) & m1_subset_1(192,k4_ordinal1) )).
fof(spc197_boole,axiom,( ~ v1_xboole_0(197) )).
fof(spc197_numerals,axiom,( v2_xxreal_0(197) & m1_subset_1(197,k4_ordinal1) )).
fof(spc198_boole,axiom,( ~ v1_xboole_0(198) )).
fof(spc198_numerals,axiom,( v2_xxreal_0(198) & m1_subset_1(198,k4_ordinal1) )).
fof(spc19_boole,axiom,( ~ v1_xboole_0(19) )).
fof(spc19_numerals,axiom,( v2_xxreal_0(19) & m1_subset_1(19,k4_ordinal1) )).
fof(spc1_arithm,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(A,k4_xcmplx_0(B)) = k6_xcmplx_0(A,B) ) )).
fof(spc1_boole,axiom,( ~ v1_xboole_0(1) )).
fof(spc1_numerals,axiom,( v2_xxreal_0(1) & m1_subset_1(1,k4_ordinal1) )).
fof(spc203_boole,axiom,( ~ v1_xboole_0(203) )).
fof(spc203_numerals,axiom,( v2_xxreal_0(203) & m1_subset_1(203,k4_ordinal1) )).
fof(spc20_boole,axiom,( ~ v1_xboole_0(20) )).
fof(spc20_numerals,axiom,( v2_xxreal_0(20) & m1_subset_1(20,k4_ordinal1) )).
fof(spc210_boole,axiom,( ~ v1_xboole_0(210) )).
fof(spc210_numerals,axiom,( v2_xxreal_0(210) & m1_subset_1(210,k4_ordinal1) )).
fof(spc211_boole,axiom,( ~ v1_xboole_0(211) )).
fof(spc211_numerals,axiom,( v2_xxreal_0(211) & m1_subset_1(211,k4_ordinal1) )).
fof(spc214_boole,axiom,( ~ v1_xboole_0(214) )).
fof(spc214_numerals,axiom,( v2_xxreal_0(214) & m1_subset_1(214,k4_ordinal1) )).
fof(spc216_boole,axiom,( ~ v1_xboole_0(216) )).
fof(spc216_numerals,axiom,( v2_xxreal_0(216) & m1_subset_1(216,k4_ordinal1) )).
fof(spc21_boole,axiom,( ~ v1_xboole_0(21) )).
fof(spc21_numerals,axiom,( v2_xxreal_0(21) & m1_subset_1(21,k4_ordinal1) )).
fof(spc220_boole,axiom,( ~ v1_xboole_0(220) )).
fof(spc220_numerals,axiom,( v2_xxreal_0(220) & m1_subset_1(220,k4_ordinal1) )).
fof(spc225_boole,axiom,( ~ v1_xboole_0(225) )).
fof(spc225_numerals,axiom,( v2_xxreal_0(225) & m1_subset_1(225,k4_ordinal1) )).
fof(spc22_boole,axiom,( ~ v1_xboole_0(22) )).
fof(spc22_numerals,axiom,( v2_xxreal_0(22) & m1_subset_1(22,k4_ordinal1) )).
fof(spc231_boole,axiom,( ~ v1_xboole_0(231) )).
fof(spc231_numerals,axiom,( v2_xxreal_0(231) & m1_subset_1(231,k4_ordinal1) )).
fof(spc234_boole,axiom,( ~ v1_xboole_0(234) )).
fof(spc234_numerals,axiom,( v2_xxreal_0(234) & m1_subset_1(234,k4_ordinal1) )).
fof(spc236_boole,axiom,( ~ v1_xboole_0(236) )).
fof(spc236_numerals,axiom,( v2_xxreal_0(236) & m1_subset_1(236,k4_ordinal1) )).
fof(spc23_boole,axiom,( ~ v1_xboole_0(23) )).
fof(spc23_numerals,axiom,( v2_xxreal_0(23) & m1_subset_1(23,k4_ordinal1) )).
fof(spc241_boole,axiom,( ~ v1_xboole_0(241) )).
fof(spc241_numerals,axiom,( v2_xxreal_0(241) & m1_subset_1(241,k4_ordinal1) )).
fof(spc242_boole,axiom,( ~ v1_xboole_0(242) )).
fof(spc242_numerals,axiom,( v2_xxreal_0(242) & m1_subset_1(242,k4_ordinal1) )).
fof(spc249_boole,axiom,( ~ v1_xboole_0(249) )).
fof(spc249_numerals,axiom,( v2_xxreal_0(249) & m1_subset_1(249,k4_ordinal1) )).
fof(spc24_boole,axiom,( ~ v1_xboole_0(24) )).
fof(spc24_numerals,axiom,( v2_xxreal_0(24) & m1_subset_1(24,k4_ordinal1) )).
fof(spc252_boole,axiom,( ~ v1_xboole_0(252) )).
fof(spc252_numerals,axiom,( v2_xxreal_0(252) & m1_subset_1(252,k4_ordinal1) )).
fof(spc255_boole,axiom,( ~ v1_xboole_0(255) )).
fof(spc255_numerals,axiom,( v2_xxreal_0(255) & m1_subset_1(255,k4_ordinal1) )).
fof(spc256_boole,axiom,( ~ v1_xboole_0(256) )).
fof(spc256_numerals,axiom,( v2_xxreal_0(256) & m1_subset_1(256,k4_ordinal1) )).
fof(spc257_boole,axiom,( ~ v1_xboole_0(257) )).
fof(spc257_numerals,axiom,( v2_xxreal_0(257) & m1_subset_1(257,k4_ordinal1) )).
fof(spc25_boole,axiom,( ~ v1_xboole_0(25) )).
fof(spc25_numerals,axiom,( v2_xxreal_0(25) & m1_subset_1(25,k4_ordinal1) )).
fof(spc261_boole,axiom,( ~ v1_xboole_0(261) )).
fof(spc261_numerals,axiom,( v2_xxreal_0(261) & m1_subset_1(261,k4_ordinal1) )).
fof(spc263_boole,axiom,( ~ v1_xboole_0(263) )).
fof(spc263_numerals,axiom,( v2_xxreal_0(263) & m1_subset_1(263,k4_ordinal1) )).
fof(spc26_boole,axiom,( ~ v1_xboole_0(26) )).
fof(spc26_numerals,axiom,( v2_xxreal_0(26) & m1_subset_1(26,k4_ordinal1) )).
fof(spc271_boole,axiom,( ~ v1_xboole_0(271) )).
fof(spc271_numerals,axiom,( v2_xxreal_0(271) & m1_subset_1(271,k4_ordinal1) )).
fof(spc27_boole,axiom,( ~ v1_xboole_0(27) )).
fof(spc27_numerals,axiom,( v2_xxreal_0(27) & m1_subset_1(27,k4_ordinal1) )).
fof(spc282_boole,axiom,( ~ v1_xboole_0(282) )).
fof(spc282_numerals,axiom,( v2_xxreal_0(282) & m1_subset_1(282,k4_ordinal1) )).
fof(spc288_boole,axiom,( ~ v1_xboole_0(288) )).
fof(spc288_numerals,axiom,( v2_xxreal_0(288) & m1_subset_1(288,k4_ordinal1) )).
fof(spc289_boole,axiom,( ~ v1_xboole_0(289) )).
fof(spc289_numerals,axiom,( v2_xxreal_0(289) & m1_subset_1(289,k4_ordinal1) )).
fof(spc28_boole,axiom,( ~ v1_xboole_0(28) )).
fof(spc28_numerals,axiom,( v2_xxreal_0(28) & m1_subset_1(28,k4_ordinal1) )).
fof(spc29_boole,axiom,( ~ v1_xboole_0(29) )).
fof(spc29_numerals,axiom,( v2_xxreal_0(29) & m1_subset_1(29,k4_ordinal1) )).
fof(spc2_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,k4_xcmplx_0(1)) = k4_xcmplx_0(A) ) )).
fof(spc2_boole,axiom,( ~ v1_xboole_0(2) )).
fof(spc2_numerals,axiom,( v2_xxreal_0(2) & m1_subset_1(2,k4_ordinal1) )).
fof(spc30_boole,axiom,( ~ v1_xboole_0(30) )).
fof(spc30_numerals,axiom,( v2_xxreal_0(30) & m1_subset_1(30,k4_ordinal1) )).
fof(spc315_boole,axiom,( ~ v1_xboole_0(315) )).
fof(spc315_numerals,axiom,( v2_xxreal_0(315) & m1_subset_1(315,k4_ordinal1) )).
fof(spc317_boole,axiom,( ~ v1_xboole_0(317) )).
fof(spc317_numerals,axiom,( v2_xxreal_0(317) & m1_subset_1(317,k4_ordinal1) )).
fof(spc31_boole,axiom,( ~ v1_xboole_0(31) )).
fof(spc31_numerals,axiom,( v2_xxreal_0(31) & m1_subset_1(31,k4_ordinal1) )).
fof(spc325_boole,axiom,( ~ v1_xboole_0(325) )).
fof(spc325_numerals,axiom,( v2_xxreal_0(325) & m1_subset_1(325,k4_ordinal1) )).
fof(spc32_boole,axiom,( ~ v1_xboole_0(32) )).
fof(spc32_numerals,axiom,( v2_xxreal_0(32) & m1_subset_1(32,k4_ordinal1) )).
fof(spc332_boole,axiom,( ~ v1_xboole_0(332) )).
fof(spc332_numerals,axiom,( v2_xxreal_0(332) & m1_subset_1(332,k4_ordinal1) )).
fof(spc335_boole,axiom,( ~ v1_xboole_0(335) )).
fof(spc335_numerals,axiom,( v2_xxreal_0(335) & m1_subset_1(335,k4_ordinal1) )).
fof(spc33_boole,axiom,( ~ v1_xboole_0(33) )).
fof(spc33_numerals,axiom,( v2_xxreal_0(33) & m1_subset_1(33,k4_ordinal1) )).
fof(spc342_boole,axiom,( ~ v1_xboole_0(342) )).
fof(spc342_numerals,axiom,( v2_xxreal_0(342) & m1_subset_1(342,k4_ordinal1) )).
fof(spc343_boole,axiom,( ~ v1_xboole_0(343) )).
fof(spc343_numerals,axiom,( v2_xxreal_0(343) & m1_subset_1(343,k4_ordinal1) )).
fof(spc344_boole,axiom,( ~ v1_xboole_0(344) )).
fof(spc344_numerals,axiom,( v2_xxreal_0(344) & m1_subset_1(344,k4_ordinal1) )).
fof(spc345_boole,axiom,( ~ v1_xboole_0(345) )).
fof(spc345_numerals,axiom,( v2_xxreal_0(345) & m1_subset_1(345,k4_ordinal1) )).
fof(spc346_boole,axiom,( ~ v1_xboole_0(346) )).
fof(spc346_numerals,axiom,( v2_xxreal_0(346) & m1_subset_1(346,k4_ordinal1) )).
fof(spc347_boole,axiom,( ~ v1_xboole_0(347) )).
fof(spc347_numerals,axiom,( v2_xxreal_0(347) & m1_subset_1(347,k4_ordinal1) )).
fof(spc348_boole,axiom,( ~ v1_xboole_0(348) )).
fof(spc348_numerals,axiom,( v2_xxreal_0(348) & m1_subset_1(348,k4_ordinal1) )).
fof(spc349_boole,axiom,( ~ v1_xboole_0(349) )).
fof(spc349_numerals,axiom,( v2_xxreal_0(349) & m1_subset_1(349,k4_ordinal1) )).
fof(spc34_boole,axiom,( ~ v1_xboole_0(34) )).
fof(spc34_numerals,axiom,( v2_xxreal_0(34) & m1_subset_1(34,k4_ordinal1) )).
fof(spc350_boole,axiom,( ~ v1_xboole_0(350) )).
fof(spc350_numerals,axiom,( v2_xxreal_0(350) & m1_subset_1(350,k4_ordinal1) )).
fof(spc351_boole,axiom,( ~ v1_xboole_0(351) )).
fof(spc351_numerals,axiom,( v2_xxreal_0(351) & m1_subset_1(351,k4_ordinal1) )).
fof(spc352_boole,axiom,( ~ v1_xboole_0(352) )).
fof(spc352_numerals,axiom,( v2_xxreal_0(352) & m1_subset_1(352,k4_ordinal1) )).
fof(spc353_boole,axiom,( ~ v1_xboole_0(353) )).
fof(spc353_numerals,axiom,( v2_xxreal_0(353) & m1_subset_1(353,k4_ordinal1) )).
fof(spc354_boole,axiom,( ~ v1_xboole_0(354) )).
fof(spc354_numerals,axiom,( v2_xxreal_0(354) & m1_subset_1(354,k4_ordinal1) )).
fof(spc355_boole,axiom,( ~ v1_xboole_0(355) )).
fof(spc355_numerals,axiom,( v2_xxreal_0(355) & m1_subset_1(355,k4_ordinal1) )).
fof(spc356_boole,axiom,( ~ v1_xboole_0(356) )).
fof(spc356_numerals,axiom,( v2_xxreal_0(356) & m1_subset_1(356,k4_ordinal1) )).
fof(spc357_boole,axiom,( ~ v1_xboole_0(357) )).
fof(spc357_numerals,axiom,( v2_xxreal_0(357) & m1_subset_1(357,k4_ordinal1) )).
fof(spc358_boole,axiom,( ~ v1_xboole_0(358) )).
fof(spc358_numerals,axiom,( v2_xxreal_0(358) & m1_subset_1(358,k4_ordinal1) )).
fof(spc359_boole,axiom,( ~ v1_xboole_0(359) )).
fof(spc359_numerals,axiom,( v2_xxreal_0(359) & m1_subset_1(359,k4_ordinal1) )).
fof(spc35_boole,axiom,( ~ v1_xboole_0(35) )).
fof(spc35_numerals,axiom,( v2_xxreal_0(35) & m1_subset_1(35,k4_ordinal1) )).
fof(spc360_boole,axiom,( ~ v1_xboole_0(360) )).
fof(spc360_numerals,axiom,( v2_xxreal_0(360) & m1_subset_1(360,k4_ordinal1) )).
fof(spc361_boole,axiom,( ~ v1_xboole_0(361) )).
fof(spc361_numerals,axiom,( v2_xxreal_0(361) & m1_subset_1(361,k4_ordinal1) )).
fof(spc362_boole,axiom,( ~ v1_xboole_0(362) )).
fof(spc362_numerals,axiom,( v2_xxreal_0(362) & m1_subset_1(362,k4_ordinal1) )).
fof(spc363_boole,axiom,( ~ v1_xboole_0(363) )).
fof(spc363_numerals,axiom,( v2_xxreal_0(363) & m1_subset_1(363,k4_ordinal1) )).
fof(spc364_boole,axiom,( ~ v1_xboole_0(364) )).
fof(spc364_numerals,axiom,( v2_xxreal_0(364) & m1_subset_1(364,k4_ordinal1) )).
fof(spc365_boole,axiom,( ~ v1_xboole_0(365) )).
fof(spc365_numerals,axiom,( v2_xxreal_0(365) & m1_subset_1(365,k4_ordinal1) )).
fof(spc36_boole,axiom,( ~ v1_xboole_0(36) )).
fof(spc36_numerals,axiom,( v2_xxreal_0(36) & m1_subset_1(36,k4_ordinal1) )).
fof(spc37_boole,axiom,( ~ v1_xboole_0(37) )).
fof(spc37_numerals,axiom,( v2_xxreal_0(37) & m1_subset_1(37,k4_ordinal1) )).
fof(spc38_boole,axiom,( ~ v1_xboole_0(38) )).
fof(spc38_numerals,axiom,( v2_xxreal_0(38) & m1_subset_1(38,k4_ordinal1) )).
fof(spc390_boole,axiom,( ~ v1_xboole_0(390) )).
fof(spc390_numerals,axiom,( v2_xxreal_0(390) & m1_subset_1(390,k4_ordinal1) )).
fof(spc39_boole,axiom,( ~ v1_xboole_0(39) )).
fof(spc39_numerals,axiom,( v2_xxreal_0(39) & m1_subset_1(39,k4_ordinal1) )).
fof(spc3_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(1,A) = k5_xcmplx_0(A) ) )).
fof(spc3_boole,axiom,( ~ v1_xboole_0(3) )).
fof(spc3_numerals,axiom,( v2_xxreal_0(3) & m1_subset_1(3,k4_ordinal1) )).
fof(spc40_boole,axiom,( ~ v1_xboole_0(40) )).
fof(spc40_numerals,axiom,( v2_xxreal_0(40) & m1_subset_1(40,k4_ordinal1) )).
fof(spc414_boole,axiom,( ~ v1_xboole_0(414) )).
fof(spc414_numerals,axiom,( v2_xxreal_0(414) & m1_subset_1(414,k4_ordinal1) )).
fof(spc416_boole,axiom,( ~ v1_xboole_0(416) )).
fof(spc416_numerals,axiom,( v2_xxreal_0(416) & m1_subset_1(416,k4_ordinal1) )).
fof(spc417_boole,axiom,( ~ v1_xboole_0(417) )).
fof(spc417_numerals,axiom,( v2_xxreal_0(417) & m1_subset_1(417,k4_ordinal1) )).
fof(spc419_boole,axiom,( ~ v1_xboole_0(419) )).
fof(spc419_numerals,axiom,( v2_xxreal_0(419) & m1_subset_1(419,k4_ordinal1) )).
fof(spc41_boole,axiom,( ~ v1_xboole_0(41) )).
fof(spc41_numerals,axiom,( v2_xxreal_0(41) & m1_subset_1(41,k4_ordinal1) )).
fof(spc42_boole,axiom,( ~ v1_xboole_0(42) )).
fof(spc42_numerals,axiom,( v2_xxreal_0(42) & m1_subset_1(42,k4_ordinal1) )).
fof(spc434_boole,axiom,( ~ v1_xboole_0(434) )).
fof(spc434_numerals,axiom,( v2_xxreal_0(434) & m1_subset_1(434,k4_ordinal1) )).
fof(spc43_boole,axiom,( ~ v1_xboole_0(43) )).
fof(spc43_numerals,axiom,( v2_xxreal_0(43) & m1_subset_1(43,k4_ordinal1) )).
fof(spc446_boole,axiom,( ~ v1_xboole_0(446) )).
fof(spc446_numerals,axiom,( v2_xxreal_0(446) & m1_subset_1(446,k4_ordinal1) )).
fof(spc449_boole,axiom,( ~ v1_xboole_0(449) )).
fof(spc449_numerals,axiom,( v2_xxreal_0(449) & m1_subset_1(449,k4_ordinal1) )).
fof(spc44_boole,axiom,( ~ v1_xboole_0(44) )).
fof(spc44_numerals,axiom,( v2_xxreal_0(44) & m1_subset_1(44,k4_ordinal1) )).
fof(spc453_boole,axiom,( ~ v1_xboole_0(453) )).
fof(spc453_numerals,axiom,( v2_xxreal_0(453) & m1_subset_1(453,k4_ordinal1) )).
fof(spc454_boole,axiom,( ~ v1_xboole_0(454) )).
fof(spc454_numerals,axiom,( v2_xxreal_0(454) & m1_subset_1(454,k4_ordinal1) )).
fof(spc458_boole,axiom,( ~ v1_xboole_0(458) )).
fof(spc458_numerals,axiom,( v2_xxreal_0(458) & m1_subset_1(458,k4_ordinal1) )).
fof(spc45_boole,axiom,( ~ v1_xboole_0(45) )).
fof(spc45_numerals,axiom,( v2_xxreal_0(45) & m1_subset_1(45,k4_ordinal1) )).
fof(spc46_boole,axiom,( ~ v1_xboole_0(46) )).
fof(spc46_numerals,axiom,( v2_xxreal_0(46) & m1_subset_1(46,k4_ordinal1) )).
fof(spc47_boole,axiom,( ~ v1_xboole_0(47) )).
fof(spc47_numerals,axiom,( v2_xxreal_0(47) & m1_subset_1(47,k4_ordinal1) )).
fof(spc487_boole,axiom,( ~ v1_xboole_0(487) )).
fof(spc487_numerals,axiom,( v2_xxreal_0(487) & m1_subset_1(487,k4_ordinal1) )).
fof(spc48_boole,axiom,( ~ v1_xboole_0(48) )).
fof(spc48_numerals,axiom,( v2_xxreal_0(48) & m1_subset_1(48,k4_ordinal1) )).
fof(spc49_boole,axiom,( ~ v1_xboole_0(49) )).
fof(spc49_numerals,axiom,( v2_xxreal_0(49) & m1_subset_1(49,k4_ordinal1) )).
fof(spc4_arithm,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k3_xcmplx_0(A,k7_xcmplx_0(B,C)) = k7_xcmplx_0(k3_xcmplx_0(A,B),C) ) )).
fof(spc4_boole,axiom,( ~ v1_xboole_0(4) )).
fof(spc4_numerals,axiom,( v2_xxreal_0(4) & m1_subset_1(4,k4_ordinal1) )).
fof(spc503_boole,axiom,( ~ v1_xboole_0(503) )).
fof(spc503_numerals,axiom,( v2_xxreal_0(503) & m1_subset_1(503,k4_ordinal1) )).
fof(spc50_boole,axiom,( ~ v1_xboole_0(50) )).
fof(spc50_numerals,axiom,( v2_xxreal_0(50) & m1_subset_1(50,k4_ordinal1) )).
fof(spc512_boole,axiom,( ~ v1_xboole_0(512) )).
fof(spc512_numerals,axiom,( v2_xxreal_0(512) & m1_subset_1(512,k4_ordinal1) )).
fof(spc51_boole,axiom,( ~ v1_xboole_0(51) )).
fof(spc51_numerals,axiom,( v2_xxreal_0(51) & m1_subset_1(51,k4_ordinal1) )).
fof(spc52_boole,axiom,( ~ v1_xboole_0(52) )).
fof(spc52_numerals,axiom,( v2_xxreal_0(52) & m1_subset_1(52,k4_ordinal1) )).
fof(spc53_boole,axiom,( ~ v1_xboole_0(53) )).
fof(spc53_numerals,axiom,( v2_xxreal_0(53) & m1_subset_1(53,k4_ordinal1) )).
fof(spc54_boole,axiom,( ~ v1_xboole_0(54) )).
fof(spc54_numerals,axiom,( v2_xxreal_0(54) & m1_subset_1(54,k4_ordinal1) )).
fof(spc553_boole,axiom,( ~ v1_xboole_0(553) )).
fof(spc553_numerals,axiom,( v2_xxreal_0(553) & m1_subset_1(553,k4_ordinal1) )).
fof(spc554_boole,axiom,( ~ v1_xboole_0(554) )).
fof(spc554_numerals,axiom,( v2_xxreal_0(554) & m1_subset_1(554,k4_ordinal1) )).
fof(spc55_boole,axiom,( ~ v1_xboole_0(55) )).
fof(spc55_numerals,axiom,( v2_xxreal_0(55) & m1_subset_1(55,k4_ordinal1) )).
fof(spc569_boole,axiom,( ~ v1_xboole_0(569) )).
fof(spc569_numerals,axiom,( v2_xxreal_0(569) & m1_subset_1(569,k4_ordinal1) )).
fof(spc56_boole,axiom,( ~ v1_xboole_0(56) )).
fof(spc56_numerals,axiom,( v2_xxreal_0(56) & m1_subset_1(56,k4_ordinal1) )).
fof(spc577_boole,axiom,( ~ v1_xboole_0(577) )).
fof(spc577_numerals,axiom,( v2_xxreal_0(577) & m1_subset_1(577,k4_ordinal1) )).
fof(spc578_boole,axiom,( ~ v1_xboole_0(578) )).
fof(spc578_numerals,axiom,( v2_xxreal_0(578) & m1_subset_1(578,k4_ordinal1) )).
fof(spc57_boole,axiom,( ~ v1_xboole_0(57) )).
fof(spc57_numerals,axiom,( v2_xxreal_0(57) & m1_subset_1(57,k4_ordinal1) )).
fof(spc58_boole,axiom,( ~ v1_xboole_0(58) )).
fof(spc58_numerals,axiom,( v2_xxreal_0(58) & m1_subset_1(58,k4_ordinal1) )).
fof(spc590_boole,axiom,( ~ v1_xboole_0(590) )).
fof(spc590_numerals,axiom,( v2_xxreal_0(590) & m1_subset_1(590,k4_ordinal1) )).
fof(spc59_boole,axiom,( ~ v1_xboole_0(59) )).
fof(spc59_numerals,axiom,( v2_xxreal_0(59) & m1_subset_1(59,k4_ordinal1) )).
fof(spc5_arithm,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k3_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) )).
fof(spc5_boole,axiom,( ~ v1_xboole_0(5) )).
fof(spc5_numerals,axiom,( v2_xxreal_0(5) & m1_subset_1(5,k4_ordinal1) )).
fof(spc602_boole,axiom,( ~ v1_xboole_0(602) )).
fof(spc602_numerals,axiom,( v2_xxreal_0(602) & m1_subset_1(602,k4_ordinal1) )).
fof(spc605_boole,axiom,( ~ v1_xboole_0(605) )).
fof(spc605_numerals,axiom,( v2_xxreal_0(605) & m1_subset_1(605,k4_ordinal1) )).
fof(spc60_boole,axiom,( ~ v1_xboole_0(60) )).
fof(spc60_numerals,axiom,( v2_xxreal_0(60) & m1_subset_1(60,k4_ordinal1) )).
fof(spc619_boole,axiom,( ~ v1_xboole_0(619) )).
fof(spc619_numerals,axiom,( v2_xxreal_0(619) & m1_subset_1(619,k4_ordinal1) )).
fof(spc61_boole,axiom,( ~ v1_xboole_0(61) )).
fof(spc61_numerals,axiom,( v2_xxreal_0(61) & m1_subset_1(61,k4_ordinal1) )).
fof(spc62_boole,axiom,( ~ v1_xboole_0(62) )).
fof(spc62_numerals,axiom,( v2_xxreal_0(62) & m1_subset_1(62,k4_ordinal1) )).
fof(spc631_boole,axiom,( ~ v1_xboole_0(631) )).
fof(spc631_numerals,axiom,( v2_xxreal_0(631) & m1_subset_1(631,k4_ordinal1) )).
fof(spc63_boole,axiom,( ~ v1_xboole_0(63) )).
fof(spc63_numerals,axiom,( v2_xxreal_0(63) & m1_subset_1(63,k4_ordinal1) )).
fof(spc64_boole,axiom,( ~ v1_xboole_0(64) )).
fof(spc64_numerals,axiom,( v2_xxreal_0(64) & m1_subset_1(64,k4_ordinal1) )).
fof(spc656_boole,axiom,( ~ v1_xboole_0(656) )).
fof(spc656_numerals,axiom,( v2_xxreal_0(656) & m1_subset_1(656,k4_ordinal1) )).
fof(spc672_boole,axiom,( ~ v1_xboole_0(672) )).
fof(spc672_numerals,axiom,( v2_xxreal_0(672) & m1_subset_1(672,k4_ordinal1) )).
fof(spc673_boole,axiom,( ~ v1_xboole_0(673) )).
fof(spc673_numerals,axiom,( v2_xxreal_0(673) & m1_subset_1(673,k4_ordinal1) )).
fof(spc688_boole,axiom,( ~ v1_xboole_0(688) )).
fof(spc688_numerals,axiom,( v2_xxreal_0(688) & m1_subset_1(688,k4_ordinal1) )).
fof(spc68_boole,axiom,( ~ v1_xboole_0(68) )).
fof(spc68_numerals,axiom,( v2_xxreal_0(68) & m1_subset_1(68,k4_ordinal1) )).
fof(spc691_boole,axiom,( ~ v1_xboole_0(691) )).
fof(spc691_numerals,axiom,( v2_xxreal_0(691) & m1_subset_1(691,k4_ordinal1) )).
fof(spc693_boole,axiom,( ~ v1_xboole_0(693) )).
fof(spc693_numerals,axiom,( v2_xxreal_0(693) & m1_subset_1(693,k4_ordinal1) )).
fof(spc69_boole,axiom,( ~ v1_xboole_0(69) )).
fof(spc69_numerals,axiom,( v2_xxreal_0(69) & m1_subset_1(69,k4_ordinal1) )).
fof(spc6_arithm,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k2_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(A,k2_xcmplx_0(B,C)) ) )).
fof(spc6_boole,axiom,( ~ v1_xboole_0(6) )).
fof(spc6_numerals,axiom,( v2_xxreal_0(6) & m1_subset_1(6,k4_ordinal1) )).
fof(spc70_boole,axiom,( ~ v1_xboole_0(70) )).
fof(spc70_numerals,axiom,( v2_xxreal_0(70) & m1_subset_1(70,k4_ordinal1) )).
fof(spc712_boole,axiom,( ~ v1_xboole_0(712) )).
fof(spc712_numerals,axiom,( v2_xxreal_0(712) & m1_subset_1(712,k4_ordinal1) )).
fof(spc71_boole,axiom,( ~ v1_xboole_0(71) )).
fof(spc71_numerals,axiom,( v2_xxreal_0(71) & m1_subset_1(71,k4_ordinal1) )).
fof(spc72_boole,axiom,( ~ v1_xboole_0(72) )).
fof(spc72_numerals,axiom,( v2_xxreal_0(72) & m1_subset_1(72,k4_ordinal1) )).
fof(spc733_boole,axiom,( ~ v1_xboole_0(733) )).
fof(spc733_numerals,axiom,( v2_xxreal_0(733) & m1_subset_1(733,k4_ordinal1) )).
fof(spc73_boole,axiom,( ~ v1_xboole_0(73) )).
fof(spc73_numerals,axiom,( v2_xxreal_0(73) & m1_subset_1(73,k4_ordinal1) )).
fof(spc744_boole,axiom,( ~ v1_xboole_0(744) )).
fof(spc744_numerals,axiom,( v2_xxreal_0(744) & m1_subset_1(744,k4_ordinal1) )).
fof(spc765_boole,axiom,( ~ v1_xboole_0(765) )).
fof(spc765_numerals,axiom,( v2_xxreal_0(765) & m1_subset_1(765,k4_ordinal1) )).
fof(spc792_boole,axiom,( ~ v1_xboole_0(792) )).
fof(spc792_numerals,axiom,( v2_xxreal_0(792) & m1_subset_1(792,k4_ordinal1) )).
fof(spc7_arithm,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) & v1_xcmplx_0(C) ) => k3_xcmplx_0(k3_xcmplx_0(A,B),C) = k3_xcmplx_0(A,k3_xcmplx_0(B,C)) ) )).
fof(spc7_boole,axiom,( ~ v1_xboole_0(7) )).
fof(spc7_numerals,axiom,( v2_xxreal_0(7) & m1_subset_1(7,k4_ordinal1) )).
fof(spc800_boole,axiom,( ~ v1_xboole_0(800) )).
fof(spc800_numerals,axiom,( v2_xxreal_0(800) & m1_subset_1(800,k4_ordinal1) )).
fof(spc809_boole,axiom,( ~ v1_xboole_0(809) )).
fof(spc809_numerals,axiom,( v2_xxreal_0(809) & m1_subset_1(809,k4_ordinal1) )).
fof(spc81_boole,axiom,( ~ v1_xboole_0(81) )).
fof(spc81_numerals,axiom,( v2_xxreal_0(81) & m1_subset_1(81,k4_ordinal1) )).
fof(spc82_boole,axiom,( ~ v1_xboole_0(82) )).
fof(spc82_numerals,axiom,( v2_xxreal_0(82) & m1_subset_1(82,k4_ordinal1) )).
fof(spc830_boole,axiom,( ~ v1_xboole_0(830) )).
fof(spc830_numerals,axiom,( v2_xxreal_0(830) & m1_subset_1(830,k4_ordinal1) )).
fof(spc83_boole,axiom,( ~ v1_xboole_0(83) )).
fof(spc83_numerals,axiom,( v2_xxreal_0(83) & m1_subset_1(83,k4_ordinal1) )).
fof(spc841_boole,axiom,( ~ v1_xboole_0(841) )).
fof(spc841_numerals,axiom,( v2_xxreal_0(841) & m1_subset_1(841,k4_ordinal1) )).
fof(spc847_boole,axiom,( ~ v1_xboole_0(847) )).
fof(spc847_numerals,axiom,( v2_xxreal_0(847) & m1_subset_1(847,k4_ordinal1) )).
fof(spc855_boole,axiom,( ~ v1_xboole_0(855) )).
fof(spc855_numerals,axiom,( v2_xxreal_0(855) & m1_subset_1(855,k4_ordinal1) )).
fof(spc869_boole,axiom,( ~ v1_xboole_0(869) )).
fof(spc869_numerals,axiom,( v2_xxreal_0(869) & m1_subset_1(869,k4_ordinal1) )).
fof(spc870_boole,axiom,( ~ v1_xboole_0(870) )).
fof(spc870_numerals,axiom,( v2_xxreal_0(870) & m1_subset_1(870,k4_ordinal1) )).
fof(spc873_boole,axiom,( ~ v1_xboole_0(873) )).
fof(spc873_numerals,axiom,( v2_xxreal_0(873) & m1_subset_1(873,k4_ordinal1) )).
fof(spc89_boole,axiom,( ~ v1_xboole_0(89) )).
fof(spc89_numerals,axiom,( v2_xxreal_0(89) & m1_subset_1(89,k4_ordinal1) )).
fof(spc8_arithm,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k2_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k4_xcmplx_0(k2_xcmplx_0(A,B)) ) )).
fof(spc8_boole,axiom,( ~ v1_xboole_0(8) )).
fof(spc8_numerals,axiom,( v2_xxreal_0(8) & m1_subset_1(8,k4_ordinal1) )).
fof(spc90_boole,axiom,( ~ v1_xboole_0(90) )).
fof(spc90_numerals,axiom,( v2_xxreal_0(90) & m1_subset_1(90,k4_ordinal1) )).
fof(spc91_boole,axiom,( ~ v1_xboole_0(91) )).
fof(spc91_numerals,axiom,( v2_xxreal_0(91) & m1_subset_1(91,k4_ordinal1) )).
fof(spc928_boole,axiom,( ~ v1_xboole_0(928) )).
fof(spc928_numerals,axiom,( v2_xxreal_0(928) & m1_subset_1(928,k4_ordinal1) )).
fof(spc936_boole,axiom,( ~ v1_xboole_0(936) )).
fof(spc936_numerals,axiom,( v2_xxreal_0(936) & m1_subset_1(936,k4_ordinal1) )).
fof(spc964_boole,axiom,( ~ v1_xboole_0(964) )).
fof(spc964_numerals,axiom,( v2_xxreal_0(964) & m1_subset_1(964,k4_ordinal1) )).
fof(spc96_boole,axiom,( ~ v1_xboole_0(96) )).
fof(spc96_numerals,axiom,( v2_xxreal_0(96) & m1_subset_1(96,k4_ordinal1) )).
fof(spc97_boole,axiom,( ~ v1_xboole_0(97) )).
fof(spc97_numerals,axiom,( v2_xxreal_0(97) & m1_subset_1(97,k4_ordinal1) )).
fof(spc988_boole,axiom,( ~ v1_xboole_0(988) )).
fof(spc988_numerals,axiom,( v2_xxreal_0(988) & m1_subset_1(988,k4_ordinal1) )).
fof(spc999_boole,axiom,( ~ v1_xboole_0(999) )).
fof(spc999_numerals,axiom,( v2_xxreal_0(999) & m1_subset_1(999,k4_ordinal1) )).
fof(spc9_arithm,axiom,( ! [A] : ! [B] : ( ( v1_xcmplx_0(A) & v1_xcmplx_0(B) ) => k6_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k6_xcmplx_0(B,A) ) )).
fof(spc9_boole,axiom,( ~ v1_xboole_0(9) )).
fof(spc9_numerals,axiom,( v2_xxreal_0(9) & m1_subset_1(9,k4_ordinal1) )).
fof(symmetry_r10_analmetr,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r10_rewrite1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => ( r10_rewrite1(A,B) => r10_rewrite1(B,A) ) ) )).
fof(symmetry_r11_rewrite1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => ( r11_rewrite1(A,B) => r11_rewrite1(B,A) ) ) )).
fof(symmetry_r12_rewrite1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => ( r12_rewrite1(A,B) => r12_rewrite1(B,A) ) ) )).
fof(symmetry_r1_afvect0,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r1_anproj_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) ) )).
fof(symmetry_r1_arytm_3,axiom,( ! [A] : ! [B] : ( ( v3_ordinal1(A) & v3_ordinal1(B) ) => ( r1_arytm_3(A,B) => r1_arytm_3(B,A) ) ) )).
fof(symmetry_r1_bhsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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) ) ) )).
fof(symmetry_r1_bhsp_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r1_bhsp_3(A,B,C) => r1_bhsp_3(A,C,B) ) ) )).
fof(symmetry_r1_boolealg,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r1_borsuk_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r1_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) ) )).
fof(symmetry_r1_chord,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) ) )).
fof(symmetry_r1_circcomb,axiom,( ! [A] : ! [B] : ( ( l1_msualg_1(A) & l1_msualg_1(B) ) => ( r1_circcomb(A,B) => r1_circcomb(B,A) ) ) )).
fof(symmetry_r1_connsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(symmetry_r1_convex4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r1_csspace,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) ) )).
fof(symmetry_r1_dist_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(symmetry_r1_ec_pf_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(symmetry_r1_filter_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(symmetry_r1_filter_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r1_fintopo4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r1_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ 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) ) ) )).
fof(symmetry_r1_functor0,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(symmetry_r1_functor3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(symmetry_r1_gobrd10,axiom,( ! [A] : ! [B] : ( ( v7_ordinal1(A) & v7_ordinal1(B) ) => ( r1_gobrd10(A,B) => r1_gobrd10(B,A) ) ) )).
fof(symmetry_r1_group_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r1_int_2,axiom,( ! [A] : ! [B] : ( ( v1_int_1(A) & v1_int_1(B) ) => ( r1_int_2(A,B) => r1_int_2(B,A) ) ) )).
fof(symmetry_r1_interva1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r1_isocat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) ) )).
fof(symmetry_r1_lopban_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r1_margrel1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r1_matrix_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r1_matrix_6(A,B,C,D) => r1_matrix_6(A,B,D,C) ) ) )).
fof(symmetry_r1_matrix_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r1_matrix_8(A,B,C,D) => r1_matrix_8(A,B,D,C) ) ) )).
fof(symmetry_r1_mfold_2,axiom,( ! [A] : ! [B] : ( ( l1_pre_topc(A) & l1_pre_topc(B) ) => ( r1_mfold_2(A,B) => r1_mfold_2(B,A) ) ) )).
fof(symmetry_r1_osalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r1_osalg_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r1_partfun1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_relat_1(B) & v1_funct_1(B) ) => ( r1_partfun1(A,B) => r1_partfun1(B,A) ) ) )).
fof(symmetry_r1_pnproc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) & v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ( r1_pnproc_1(A,B,C) => r1_pnproc_1(A,C,B) ) ) )).
fof(symmetry_r1_rlvect_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r1_rmod_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) ) )).
fof(symmetry_r1_rpr_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(symmetry_r1_rvsum_1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(symmetry_r1_subset_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( r1_subset_1(A,B) => r1_subset_1(B,A) ) ) )).
fof(symmetry_r1_topalg_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r1_tsep_1,axiom,( ! [A] : ! [B] : ( ( l1_struct_0(A) & l1_struct_0(B) ) => ( r1_tsep_1(A,B) => r1_tsep_1(B,A) ) ) )).
fof(symmetry_r1_tsep_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(symmetry_r1_unialg_2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(symmetry_r1_vectsp_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(symmetry_r1_xboole_0,axiom,( ! [A] : ! [B] : ( r1_xboole_0(A,B) => r1_xboole_0(B,A) ) )).
fof(symmetry_r1_yellow10,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(symmetry_r1_yellow18,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(symmetry_r1_yellow20,axiom,( ! [A] : ! [B] : ( ( l2_altcat_1(A) & l2_altcat_1(B) ) => ( r1_yellow20(A,B) => r1_yellow20(B,A) ) ) )).
fof(symmetry_r1_zmodul02,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) & m1_zmodul02(B,A) & m1_zmodul02(C,A) ) => ( r1_zmodul02(A,B,C) => r1_zmodul02(A,C,B) ) ) )).
fof(symmetry_r2_altcat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r2_borsuk_3,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(symmetry_r2_circtrm1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) & ~ v2_struct_0(B) & l1_msualg_1(B) ) => ( r2_circtrm1(A,B) => r2_circtrm1(B,A) ) ) )).
fof(symmetry_r2_classes1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v1_relat_1(B) ) => ( r2_classes1(A,B) => r2_classes1(B,A) ) ) )).
fof(symmetry_r2_clvect_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r2_clvect_2(A,B,C) => r2_clvect_2(A,C,B) ) ) )).
fof(symmetry_r2_cqc_sim1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(symmetry_r2_euclidlp,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k1_euclid(A)) & m1_subset_1(C,k1_euclid(A)) ) => ( r2_euclidlp(A,B,C) => r2_euclidlp(A,C,B) ) ) )).
fof(symmetry_r2_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(symmetry_r2_functor0,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(symmetry_r2_group_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r2_group_6,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(symmetry_r2_interva1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r2_isocat_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & 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) ) ) )).
fof(symmetry_r2_jordan12,axiom,( ! [A] : ! [B] : ! [C] : ( ( v7_ordinal1(A) & 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) ) ) )).
fof(symmetry_r2_matrix_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v7_ordinal1(A) & ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m1_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m1_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r2_matrix_6(A,B,C,D) => r2_matrix_6(A,B,D,C) ) ) )).
fof(symmetry_r2_midsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r2_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(symmetry_r2_quofield,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) & ~ v2_struct_0(B) & l6_algstr_0(B) ) => ( r2_quofield(A,B) => r2_quofield(B,A) ) ) )).
fof(symmetry_r2_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(symmetry_r2_stacks_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r2_subset_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( r2_subset_1(A,B) => r2_subset_1(B,A) ) ) )).
fof(symmetry_r2_topalg_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r2_tsep_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(symmetry_r2_tsep_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r2_wellord2,axiom,( ! [A] : ! [B] : ( r2_wellord2(A,B) => r2_wellord2(B,A) ) )).
fof(symmetry_r2_yellow18,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) & ~ v2_struct_0(B) & l2_altcat_1(B) ) => ( r2_yellow18(A,B) => r2_yellow18(B,A) ) ) )).
fof(symmetry_r2_yellow_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(symmetry_r2_zfrefle1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) => ( r2_zfrefle1(A,B) => r2_zfrefle1(B,A) ) ) )).
fof(symmetry_r3_boolealg,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r3_borsuk_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(symmetry_r3_euclidlp,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k1_euclid(A)) & m1_subset_1(C,k1_euclid(A)) ) => ( r3_euclidlp(A,B,C) => r3_euclidlp(A,C,B) ) ) )).
fof(symmetry_r3_gcd_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r3_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r3_metric_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r3_necklace,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) & ~ v2_struct_0(B) & l1_orders_2(B) ) => ( r3_necklace(A,B) => r3_necklace(B,A) ) ) )).
fof(symmetry_r3_osalg_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r3_prelamb,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r3_tsep_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(symmetry_r3_tsep_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r3_xboole_0,axiom,( ! [A] : ! [B] : ( r3_xboole_0(A,B) => r3_xboole_0(B,A) ) )).
fof(symmetry_r3_yellow18,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(symmetry_r4_boolealg,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r4_borsuk_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(symmetry_r4_cqc_the3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(symmetry_r4_euclidlp,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k1_euclid(A)) & m1_subset_1(C,k1_euclid(A)) ) => ( r4_euclidlp(A,B,C) => r4_euclidlp(A,C,B) ) ) )).
fof(symmetry_r4_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(symmetry_r4_gcd_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r4_group_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r4_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(symmetry_r4_qmax_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(symmetry_r4_stacks_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(symmetry_r4_tsep_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(symmetry_r4_tsep_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r5_abcmiz_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(symmetry_r5_aff_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r5_cqc_the3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(symmetry_r5_euclidlp,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k1_euclidlp(A)) & m1_subset_1(C,k1_euclidlp(A)) ) => ( r5_euclidlp(A,B,C) => r5_euclidlp(A,C,B) ) ) )).
fof(symmetry_r5_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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) ) ) )).
fof(symmetry_r5_glib_000,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ( r5_glib_000(A,B) => r5_glib_000(B,A) ) ) )).
fof(symmetry_r5_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(symmetry_r6_euclidlp,axiom,( ! [A] : ! [B] : ! [C] : ( ( m1_subset_1(A,k4_ordinal1) & m1_subset_1(B,k1_euclidlp(A)) & m1_subset_1(C,k1_euclidlp(A)) ) => ( r6_euclidlp(A,B,C) => r6_euclidlp(A,C,B) ) ) )).
fof(symmetry_r6_group_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r6_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(symmetry_r7_cqc_the3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(symmetry_r7_fsm_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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) ) ) )).
fof(symmetry_r7_gcd_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r8_binop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) ) )).
fof(symmetry_r8_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(symmetry_r9_analmetr,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(t100_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_abcmiz_1(B,A,k13_abcmiz_1(A)) => k46_abcmiz_1(A,k37_abcmiz_1(A,B)) = k46_abcmiz_1(A,B) ) ) )).
fof(t100_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(D)) => ! [F] : ( m1_subset_1(F,D) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t100_card_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) )).
fof(t100_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & v6_chord(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ~ ( B != C & ~ r1_chord(A,B,C) & ? [D] : ( m2_chord(D,A,B,C) & v4_chord(D,A,B,C) & ? [E] : ( 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] : ( m1_subset_1(F,k6_glib_000(E)) & B = F & ? [G] : ( m1_subset_1(G,k6_glib_000(A)) & ? [H] : ( m1_subset_1(H,k6_glib_000(A)) & r2_hidden(G,D) & r2_hidden(H,D) & ! [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t100_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_clvect_1(D,A) => ( ? [E] : ( m2_clvect_1(E,A,D) & r2_hidden(B,E) & r2_hidden(C,E) ) <=> r1_struct_0(D,k5_algstr_0(A,B,C)) ) ) ) ) ) )).
fof(t100_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [H] : ( v1_xreal_0(H) => ( ( 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_funct_1(E,H) = k5_numbers | k1_funct_1(F,H) = k5_numbers | k1_funct_1(G,H) = k5_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(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(B,H),k1_funct_1(E,H)),k3_xcmplx_0(k1_fdiff_1(E,H),k1_funct_1(B,H))),k1_square_1(k1_funct_1(E,H))),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(C,H),k1_funct_1(F,H)),k3_xcmplx_0(k1_fdiff_1(F,H),k1_funct_1(C,H))),k1_square_1(k1_funct_1(F,H))),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(D,H),k1_funct_1(G,H)),k3_xcmplx_0(k1_fdiff_1(G,H),k1_funct_1(D,H))),k1_square_1(k1_funct_1(G,H)))),A) ) ) ) ) ) ) ) ) ) ) )).
fof(t100_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ~ ( ~ r2_hidden(B,C) & v1_euclid_4(C,A) & ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t100_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) ) => k10_xtuple_0(A) = k10_xtuple_0(k15_finseq_1(A)) ) )).
fof(t100_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k4_finseq_2(3,A) = a_1_2_finseq_2(A) ) )).
fof(t100_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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) ) ) )).
fof(t100_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t100_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t100_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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))) ) ) ) ) )).
fof(t100_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ~ ( B != C & r2_hidden(B,k10_xtuple_0(k6_funct_4(A,B,C))) ) ) )).
fof(t100_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : r1_tarski(k10_xtuple_0(A),k2_xboole_0(k10_xtuple_0(k1_funct_7(A,B,C)),k1_tarski(k1_funct_1(A,B)))) ) )).
fof(t100_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t100_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t100_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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)) ) ) ) ) )).
fof(t100_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) )).
fof(t100_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v8_group_9(C,A,B) & m2_finseq_1(C,k6_group_9(A,B)) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t100_integra8,axiom,( ! [A] : ( ( ~ 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,k22_sin_cos,k22_sin_cos)) = k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k1_square_1(k1_funct_1(k22_sin_cos,k2_seq_4(A))),k1_square_1(k1_funct_1(k22_sin_cos,k3_seq_4(A))))) ) )).
fof(t100_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t100_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t100_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v3_limfunc1(B) & v3_limfunc1(C) & k4_limfunc1(B) = k4_limfunc1(C) & ! [D] : ( v1_xreal_0(D) => ? [E] : ( v1_xreal_0(E) & ~ r1_xxreal_0(E,D) & r2_hidden(E,k1_relset_1(k1_numbers,A)) ) ) ) => ( ! [D] : ( v1_xreal_0(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,C),k3_limfunc1(D))) & 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,B),k3_limfunc1(D))) & 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,C),k3_limfunc1(D))) ) ) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k3_limfunc1(D))) => ( r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(A,E)) & r1_xxreal_0(k1_funct_1(A,E),k1_funct_1(C,E)) ) ) ) ) ) | ( v3_limfunc1(A) & k4_limfunc1(A) = k4_limfunc1(B) ) ) ) ) ) ) )).
fof(t100_matrix13,axiom,( ! [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] : ( ( v1_matrix_0(B) & v1_matrix_1(B,A) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ( r1_tarski(k2_zfmisc_1(C,C),k2_matrix_0(B)) => v1_matrix_1(k6_matrix13(u1_struct_0(A),B,C,C),A) ) ) ) ) )).
fof(t100_member_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => k13_member_1(k2_tarski(A,B),k2_tarski(C,D)) = k2_enumset1(k3_xcmplx_0(A,C),k3_xcmplx_0(A,D),k3_xcmplx_0(B,C),k3_xcmplx_0(B,D)) ) ) ) ) )).
fof(t100_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ? [E] : ( 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)) ) ) ) ) ) ) )).
fof(t100_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t100_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ! [D] : ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t100_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t100_prepower,axiom,( ! [A] : ( v1_int_1(A) => ( A != k5_numbers => k3_prepower(k5_numbers,A) = k5_numbers ) ) )).
fof(t100_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => k6_relat_1(k1_xboole_0,A) = k1_xboole_0 ) )).
fof(t100_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k8_afinsq_1(C))) => ! [E] : ( ( ~ 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 ) ) ) ) ) )).
fof(t100_rvsum_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k19_rvsum_1(k11_finseq_1(A,B,C)) = k3_xcmplx_0(k3_xcmplx_0(A,B),C) ) ) ) )).
fof(t100_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ! [C] : ~ ( r2_hidden(k2_tarski(k4_tarski(B,k3_tarski(A)),C),k12_scmyciel(A)) & B = C ) ) )).
fof(t100_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ( ( r4_semi_af1(A,B,G,C,H,F) & r4_semi_af1(A,B,G,D,I,F) & r4_semi_af1(A,C,H,E,J,F) ) => r2_analoaf(A,D,E,I,J) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t100_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => r1_xxreal_0(k6_xcmplx_0(k20_seq_4(B),k20_seq_4(C)),k20_seq_4(k17_seq_4(A,B,C))) ) ) ) )).
fof(t100_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t100_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ~ ( ~ r1_xxreal_0(k4_sin_cos6(A),k5_numbers) & ~ r1_xxreal_0(k28_sin_cos,k4_sin_cos6(A)) ) ) ) )).
fof(t100_sin_cos9,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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),k7_xcmplx_0(1,2)))) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => ( k1_funct_1(B,C) = k3_xcmplx_0(2,C) & ~ r1_xxreal_0(k1_funct_1(B,C),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_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),k7_xcmplx_0(1,2)),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_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),k7_xcmplx_0(1,2)),A),C) = k4_xcmplx_0(k7_xcmplx_0(1,k2_xcmplx_0(1,k1_square_1(k3_xcmplx_0(2,C))))) ) ) ) ) ) ) )).
fof(t100_sincos10,axiom,( k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k4_sincos10,k1_rcomp_1(1,k3_square_1(2)))) = k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k7_xcmplx_0(k28_sin_cos,2)) )).
fof(t100_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v2_tdlat_2(B,A) => ! [C] : ( 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) ) ) ) ) ) ) ) )).
fof(t100_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( ~ 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))))) ) ) ) ) ) )).
fof(t100_xboole_1,axiom,( ! [A] : ! [B] : k4_xboole_0(A,B) = k5_xboole_0(A,k3_xboole_0(A,B)) )).
fof(t100_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k10_xboolean(A,k5_xboolean(A,B)) = k11_xboolean(B,A) ) ) )).
fof(t100_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k7_xcmplx_0(A,k7_xcmplx_0(1,B)) = k3_xcmplx_0(A,B) ) ) )).
fof(t100_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(A,C) & r1_xxreal_0(C,D) & r1_tarski(k1_xxreal_1(C,D),k1_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t100_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t100_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t100_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( r1_tarski(A,C) & r1_tarski(B,D) ) => k3_xboole_0(k2_zfmisc_1(A,D),k2_zfmisc_1(C,B)) = k2_zfmisc_1(A,B) ) )).
fof(t100_zmodul01,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t101_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m3_abcmiz_1(B,A) => k1_abcmiz_1(k48_abcmiz_1(A,B)) = k48_abcmiz_1(A,B) ) ) )).
fof(t101_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( m1_aofa_000(E,A,B,C) => ! [F] : ( ( v15_aofa_000(F,A) & m1_subset_1(F,u1_struct_0(A)) ) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t101_card_2,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ( ( r1_tarski(A,B) & k5_card_1(A) = k5_card_1(B) ) => A = B ) ) ) )).
fof(t101_card_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v5_funct_1(C,B) ) => ? [D] : ( m1_subset_1(D,k4_card_3(B)) & r1_tarski(C,D) ) ) ) )).
fof(t101_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ~ ( B != C & ~ r1_chord(A,B,C) & v3_chord(B,A) & v3_chord(C,A) ) ) ) ) ) )).
fof(t101_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_clvect_1(C,A) => ! [D] : ( m2_clvect_1(D,A,C) => ! [E] : ( m2_clvect_1(E,A,C) => ( ( r2_hidden(B,D) & r2_hidden(B,E) ) => D = E ) ) ) ) ) ) )).
fof(t101_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ( ( r1_fdiff_1(B,E) & r1_fdiff_1(C,E) & r1_fdiff_1(D,E) ) => ( k1_funct_1(B,E) = k5_numbers | k1_funct_1(C,E) = k5_numbers | k1_funct_1(D,E) = k5_numbers | A = k5_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(k7_xcmplx_0(k1_fdiff_1(B,E),k1_square_1(k1_funct_1(B,E))),k7_xcmplx_0(k1_fdiff_1(C,E),k1_square_1(k1_funct_1(C,E))),k7_xcmplx_0(k1_fdiff_1(D,E),k1_square_1(k1_funct_1(D,E)))),k7_xcmplx_0(1,A))) ) ) ) ) ) ) ) )).
fof(t101_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t101_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v3_card_1(B,3) & m2_finseq_1(B,A) ) => ? [C] : ( m1_subset_1(C,A) & ? [D] : ( m1_subset_1(D,A) & ? [E] : ( m1_subset_1(E,A) & B = k11_finseq_1(C,D,E) ) ) ) ) ) )).
fof(t101_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( r2_hidden(A,k1_relset_1(k4_ordinal1,B)) => k1_funct_1(k7_finseq_1(k9_finseq_1(C),B),k1_nat_1(A,1)) = k1_funct_1(B,A) ) ) ) )).
fof(t101_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => r1_tarski(k10_xtuple_0(k2_rfinseq(A,1,C)),k10_xtuple_0(k1_finseq_6(A,C,B))) ) ) ) )).
fof(t101_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t101_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) ) => ! [C] : ( r2_hidden(C,k9_xtuple_0(B)) => r2_hidden(k1_funct_1(B,C),A) ) ) )).
fof(t101_funct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(B))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t101_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( r2_hidden(B,k10_xtuple_0(A)) => r2_hidden(C,k10_xtuple_0(k6_funct_4(A,B,C))) ) ) )).
fof(t101_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( r2_hidden(B,k9_xtuple_0(A)) => r2_hidden(C,k10_xtuple_0(k1_funct_7(A,B,C))) ) ) )).
fof(t101_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t101_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ~ ( r2_hidden(C,k14_glib_001(A,B)) & ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => ! [E] : ( m1_subset_1(E,k6_glib_000(A)) => ! [F] : ( ( ~ v1_abian(F) & m1_subset_1(F,k4_ordinal1) ) => ~ ( r1_xxreal_0(k1_nat_1(F,2),k3_finseq_1(B)) & D = k1_funct_1(B,F) & C = k1_funct_1(B,k1_nat_1(F,1)) & E = k1_funct_1(B,k1_nat_1(F,2)) & r1_glib_000(A,D,E,C) ) ) ) ) ) ) ) )).
fof(t101_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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)) ) ) ) ) )).
fof(t101_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v8_struct_0(A) => v1_finset_1(k8_group_3(A,B)) ) ) ) )).
fof(t101_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( m1_group_9(D,A,B) => ! [E] : ( ( v8_group_9(E,A,B) & m2_finseq_1(E,k6_group_9(A,B)) ) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( 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) ) ) ) ) ) ) ) )).
fof(t101_integra8,axiom,( ! [A] : ( ( ~ 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,k22_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos))) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k16_sin_cos),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k16_sin_cos),k3_seq_4(A))) ) )).
fof(t101_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ! [B] : ( ( 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)) ) ) ) ) )).
fof(t101_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t101_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t101_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v3_limfunc1(B) & v3_limfunc1(C) & k4_limfunc1(B) = k4_limfunc1(C) ) => ( ! [D] : ( v1_xreal_0(D) => ~ ( r1_tarski(k3_limfunc1(D),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,A))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k3_limfunc1(D)) => ( r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(A,E)) & r1_xxreal_0(k1_funct_1(A,E),k1_funct_1(C,E)) ) ) ) ) ) | ( v3_limfunc1(A) & k4_limfunc1(A) = k4_limfunc1(B) ) ) ) ) ) ) )).
fof(t101_matrix13,axiom,( ! [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] : ( ( v1_matrix_0(B) & v1_matrix_1(B,A) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( C = a_2_1_matrix13(A,B) => k8_matrix13(A,B) = k1_card_1(C) ) ) ) )).
fof(t101_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => k14_member_1(A,B) = a_2_6_member_1(A,B) ) ) )).
fof(t101_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_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))) ) ) ) ) ) )).
fof(t101_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( 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] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t101_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t101_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t101_relat_1,axiom,( ! [A] : k6_relat_1(A,k1_xboole_0) = k1_xboole_0 )).
fof(t101_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_afinsq_1(C))) => ! [F] : ( ( ~ 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)) ) ) ) ) ) ) )).
fof(t101_rvsum_1,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k4_finseq_2(k5_numbers,k1_numbers)) => k21_rvsum_1(A) = 1 ) )).
fof(t101_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ( ( r1_scmpds_6(C,B,A) & r2_scmpds_6(C,B,A) ) => ( r1_xxreal_0(k5_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,k1_nat_1(k5_card_1(C),1))) ) ) ) ) ) ) ) )).
fof(t101_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ! [C] : ( ( 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) ) ) )).
fof(t101_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r1_semi_af1(A,B,C,D) & r5_semi_af1(A,B,D) ) ) ) ) )).
fof(t101_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => ( k20_seq_4(k17_seq_4(A,B,C)) = k5_numbers <=> B = C ) ) ) ) )).
fof(t101_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t101_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) => k4_sin_cos6(A) = k6_xcmplx_0(k28_sin_cos,k4_sin_cos6(k4_xcmplx_0(A))) ) ) )).
fof(t101_sin_cos9,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_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] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_1(k2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,B,C),A),D) = k3_xcmplx_0(2,D) ) ) ) ) ) ) ) )).
fof(t101_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,k3_square_1(2)) & k5_sincos10(A) = k5_numbers ) => A = 1 ) & ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,k3_square_1(2)) & k5_sincos10(A) = k7_xcmplx_0(k28_sin_cos,4) ) => A = k3_square_1(2) ) ) ) )).
fof(t101_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v2_tdlat_2(B,A) => ! [C] : ( 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) ) ) ) ) ) ) ) )).
fof(t101_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))))) ) ) ) ) )).
fof(t101_xboole_1,axiom,( ! [A] : ! [B] : k5_xboole_0(A,B) = k4_xboole_0(k2_xboole_0(A,B),k3_xboole_0(A,B)) )).
fof(t101_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ( k4_xboolean(A,B) = k2_xboolean => ( A = k2_xboolean & B = k2_xboolean ) ) ) ) )).
fof(t101_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t101_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(A,C) & ~ r1_xxreal_0(D,C) & r1_tarski(k4_xxreal_1(C,D),k2_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t101_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(C,k5_numbers) ) => r1_xxreal_0(k4_xxreal_3(B,C),k4_xxreal_3(A,C)) ) ) ) ) )).
fof(t101_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ~ 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)))) ) ) ) ) )).
fof(t101_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(t101_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( 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)) ) ) )).
fof(t102_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m3_abcmiz_1(B,A) => ! [C] : ( ( 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)) ) ) ) )).
fof(t102_aofa_000,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( ~ 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] : ( m1_aofa_000(D,C,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t102_card_3,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( ( r4_wellord1(A,B) & v1_finset_1(A) ) => v1_finset_1(B) ) ) ) )).
fof(t102_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & v6_chord(A) ) => ? [B] : ( m1_subset_1(B,k6_glib_000(A)) & v3_chord(B,A) ) ) )).
fof(t102_clvect_1,axiom,( ! [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) & l2_clvect_1(A) ) => k2_normsp_0(A,k4_struct_0(A)) = k5_numbers ) )).
fof(t102_euclid_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( v1_xreal_0(G) => ( ( 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(k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(B,G),k1_fdiff_1(F,G)),k3_xcmplx_0(k1_funct_1(C,G),k1_fdiff_1(E,G))),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(C,G),k1_fdiff_1(D,G)),k3_xcmplx_0(k1_funct_1(A,G),k1_fdiff_1(F,G))),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(A,G),k1_fdiff_1(E,G)),k3_xcmplx_0(k1_funct_1(B,G),k1_fdiff_1(D,G)))),k1_euclid_8(k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(B,G),k1_funct_1(F,G)),k3_xcmplx_0(k1_fdiff_1(C,G),k1_funct_1(E,G))),k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(C,G),k1_funct_1(D,G)),k3_xcmplx_0(k1_fdiff_1(A,G),k1_funct_1(F,G))),k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(A,G),k1_funct_1(E,G)),k3_xcmplx_0(k1_fdiff_1(B,G),k1_funct_1(D,G))))) ) ) ) ) ) ) ) ) )).
fof(t102_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(k1_euclid(A)),k5_euclidlp(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t102_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => r2_hidden(k11_finseq_1(B,C,D),k4_finseq_2(3,A)) ) ) ) ) )).
fof(t102_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ ( r2_hidden(A,k1_relset_1(k4_ordinal1,B)) & ! [C] : ( 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(k4_ordinal1,B)) => k2_finseq_3(A,B) = B ) ) ) ) )).
fof(t102_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ( r2_hidden(C,k6_subset_1(k10_xtuple_0(D),k10_xtuple_0(k1_finseq_5(A,D,B)))) => k1_finseq_6(A,k1_finseq_6(A,D,B),C) = k1_finseq_6(A,D,C) ) ) ) ) ) )).
fof(t102_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k8_afinsq_1(A))) => ( ( r1_tarski(B,k2_flang_2(A,D)) & r1_tarski(C,k2_flang_2(A,D)) ) => r1_tarski(k6_flang_1(A,B,C),k1_flang_2(A,D,k5_numbers,2)) ) ) ) ) )).
fof(t102_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t102_funct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t102_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : k6_funct_4(A,B,B) = A ) )).
fof(t102_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : k10_xtuple_0(k9_funct_7(A,B,C)) = k10_xtuple_0(A) ) )).
fof(t102_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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))) ) ) )).
fof(t102_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( r2_hidden(C,k14_glib_001(A,B)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & r2_hidden(D,k1_relset_1(k4_ordinal1,k12_glib_001(A,B))) & k1_funct_1(k12_glib_001(A,B),D) = C ) ) ) ) )).
fof(t102_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t102_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ! [C] : ( ( v15_algstr_0(C) & m1_group_2(C,A) ) => ( r5_group_3(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r1_group_2(A,C,k6_group_3(A,B,D)) ) ) ) ) ) )).
fof(t102_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ! [D] : ( ( 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) ) ) ) ) )).
fof(t102_integra8,axiom,( ! [A] : ( ( ~ 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,k22_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k16_sin_cos))) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k18_sin_cos),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k18_sin_cos),k3_seq_4(A))) ) )).
fof(t102_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ~ v2_funct_1(k7_jgraph_4(A)) ) ) )).
fof(t102_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t102_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t102_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v6_limfunc1(B) & v6_limfunc1(C) & k5_limfunc1(B) = k5_limfunc1(C) & ! [D] : ( v1_xreal_0(D) => ? [E] : ( v1_xreal_0(E) & ~ r1_xxreal_0(D,E) & r2_hidden(E,k1_relset_1(k1_numbers,A)) ) ) ) => ( ! [D] : ( v1_xreal_0(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,C),k10_prob_1(D))) & 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,B),k10_prob_1(D))) & 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,C),k10_prob_1(D))) ) ) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k10_prob_1(D))) => ( r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(A,E)) & r1_xxreal_0(k1_funct_1(A,E),k1_funct_1(C,E)) ) ) ) ) ) | ( v6_limfunc1(A) & k5_limfunc1(A) = k5_limfunc1(B) ) ) ) ) ) ) )).
fof(t102_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k6_prvect_1(B,A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k6_prvect_1(B,A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k6_prvect_1(B,A))) => ! [G] : ( m2_finseq_2(G,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [H] : ( m2_finseq_2(H,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [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)) & ( ( H = E & I = F ) => k4_fvsum_1(A,B,H,I) = k1_algstr_0(k6_prvect_1(B,A),E,F) ) & ( G = D => k10_fvsum_1(A,B,G,C) = k4_vectsp_1(B,k6_prvect_1(B,A),C,D) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t102_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r2_hidden(C,A) & r2_hidden(D,B) ) => r2_hidden(k6_xxreal_3(C,D),k14_member_1(A,B)) ) ) ) ) ) )).
fof(t102_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( k1_relset_1(A,D) = k1_relset_1(A,E) & r1_mesfunc5(A,B,C,E) & ! [F] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t102_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ( 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)) = k4_xxreal_3(E,k1_mesfunc6(A,B,C,D)) ) ) ) ) ) ) ) )).
fof(t102_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) => ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t102_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t102_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => k6_relat_1(A,k3_relat_1(B,C)) = k3_relat_1(B,k6_relat_1(A,C)) ) ) )).
fof(t102_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(E))) => ! [G] : ( ( ~ 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 ) ) ) ) )).
fof(t102_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => k19_rvsum_1(k5_finseq_2(k4_ordinal1,A,1)) = 1 ) )).
fof(t102_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ( r1_xxreal_0(k5_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,k1_nat_1(k5_card_1(C),1))) ) ) ) ) ) ) )).
fof(t102_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ! [C] : ( r2_hidden(k2_tarski(B,C),k1_scmyciel(A)) => r2_hidden(k2_tarski(k4_tarski(B,k3_tarski(A)),C),k12_scmyciel(A)) ) ) )).
fof(t102_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & B != C & C != D & D != B ) ) ) ) )).
fof(t102_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => ~ ( B != C & r1_xxreal_0(k20_seq_4(k17_seq_4(A,B,C)),k5_numbers) ) ) ) ) )).
fof(t102_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) )).
fof(t102_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,B) & k2_xcmplx_0(k1_square_1(A),k1_square_1(B)) = 1 ) => k17_sin_cos(k4_sin_cos6(A)) = B ) ) ) )).
fof(t102_sin_cos9,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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),k7_xcmplx_0(1,2)))) & C = k1_taylor_1(2) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_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),k7_xcmplx_0(1,2)),A) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_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),k7_xcmplx_0(1,2)),A),D) = k7_xcmplx_0(D,k2_xcmplx_0(1,k1_square_1(D))) ) ) ) ) ) ) ) )).
fof(t102_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( ( r1_xxreal_0(k4_xcmplx_0(k3_square_1(2)),A) & r1_xxreal_0(A,k4_xcmplx_0(1)) & k6_sincos10(A) = k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos) ) => A = k4_xcmplx_0(k3_square_1(2)) ) & ( ( r1_xxreal_0(k4_xcmplx_0(k3_square_1(2)),A) & r1_xxreal_0(A,k4_xcmplx_0(1)) & k6_sincos10(A) = k28_sin_cos ) => A = k4_xcmplx_0(1) ) ) ) )).
fof(t102_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => u1_struct_0(k12_tdlat_1(A)) = k9_tdlat_1(A) ) )).
fof(t102_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ( u1_struct_0(k8_tmap_1(A,B)) = u1_struct_0(A) & ! [C] : ( 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) ) ) ) ) ) )).
fof(t102_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(t102_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => k3_xboolean(k4_xboolean(A,k3_xboolean(A))) = k2_xboolean ) )).
fof(t102_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( 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)) ) ) )).
fof(t102_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r1_xxreal_0(k3_xcmplx_0(A,D),k3_xcmplx_0(C,B)) => ( r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(D,k5_numbers) | r1_xxreal_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,D)) ) ) ) ) ) ) )).
fof(t102_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(A,C) & ~ r1_xxreal_0(D,C) & r1_tarski(k3_xxreal_1(C,D),k2_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t102_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ~ ( ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(k5_numbers,C) & C != k2_xxreal_0 & r1_xxreal_0(k4_xxreal_3(A,C),k4_xxreal_3(B,C)) ) ) ) ) )).
fof(t102_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t102_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : 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))) )).
fof(t102_zmodul01,axiom,( ! [A] : ( ( ~ 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 ) )).
fof(t103_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m3_abcmiz_1(B,A) => ! [C] : ( ( 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)) ) ) ) )).
fof(t103_aofa_000,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( ~ 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] : ( m1_aofa_000(D,C,A,B) => ! [E] : ( 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] : ( m1_subset_1(F,A) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t103_card_3,axiom,( k10_card_3(k1_tarski(k1_xboole_0)) = k1_xboole_0 )).
fof(t103_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m3_chord(B,A) => k3_finseq_1(B) = k5_card_1(k6_glib_000(A)) ) ) )).
fof(t103_clvect_1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_normsp_0(A,k4_algstr_0(A,B)) = k2_normsp_0(A,B) ) ) )).
fof(t103_euclid_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [J] : ( v1_xreal_0(J) => ( ( 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(k3_xcmplx_0(k1_fdiff_1(G,J),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(B,J),k1_funct_1(F,J)),k3_xcmplx_0(k1_funct_1(C,J),k1_funct_1(E,J)))),k3_xcmplx_0(k1_fdiff_1(H,J),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(C,J),k1_funct_1(D,J)),k3_xcmplx_0(k1_funct_1(A,J),k1_funct_1(F,J)))),k3_xcmplx_0(k1_fdiff_1(I,J),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(A,J),k1_funct_1(E,J)),k3_xcmplx_0(k1_funct_1(B,J),k1_funct_1(D,J))))),k1_euclid_8(k3_xcmplx_0(k1_funct_1(G,J),k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(B,J),k1_funct_1(F,J)),k3_xcmplx_0(k1_fdiff_1(C,J),k1_funct_1(E,J)))),k3_xcmplx_0(k1_funct_1(H,J),k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(C,J),k1_funct_1(D,J)),k3_xcmplx_0(k1_fdiff_1(A,J),k1_funct_1(F,J)))),k3_xcmplx_0(k1_funct_1(I,J),k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(A,J),k1_funct_1(E,J)),k3_xcmplx_0(k1_fdiff_1(B,J),k1_funct_1(D,J)))))),k1_euclid_8(k3_xcmplx_0(k1_funct_1(G,J),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(B,J),k1_fdiff_1(F,J)),k3_xcmplx_0(k1_funct_1(C,J),k1_fdiff_1(E,J)))),k3_xcmplx_0(k1_funct_1(H,J),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(C,J),k1_fdiff_1(D,J)),k3_xcmplx_0(k1_funct_1(A,J),k1_fdiff_1(F,J)))),k3_xcmplx_0(k1_funct_1(I,J),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(A,J),k1_fdiff_1(E,J)),k3_xcmplx_0(k1_funct_1(B,J),k1_fdiff_1(D,J)))))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t103_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t103_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => k4_finseq_2(k2_xcmplx_0(A,B),C) = a_3_0_finseq_2(A,B,C) ) ) ) )).
fof(t103_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => m2_finseq_1(k2_finseq_3(A,C),B) ) ) ) )).
fof(t103_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ( r2_hidden(C,k6_subset_1(k10_xtuple_0(D),k10_xtuple_0(k2_finseq_5(A,D,B)))) => ( k4_finseq_4(D,C) = 1 | k1_finseq_6(A,k1_finseq_6(A,D,B),C) = k1_finseq_6(A,D,C) ) ) ) ) ) ) )).
fof(t103_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k2_flang_1(A),B) => ( r1_xxreal_0(C,k5_numbers) | r1_tarski(k2_flang_2(A,B),k7_flang_1(A,B,C)) ) ) ) ) )).
fof(t103_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v5_funct_1(k1_xboole_0,A) ) )).
fof(t103_funct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(B))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t103_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( ~ r2_hidden(B,k10_xtuple_0(A)) => k6_funct_4(A,B,C) = A ) ) )).
fof(t103_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( r1_funct_7(A,B,D) => r1_funct_7(k1_funct_4(A,C),k1_funct_4(B,C),D) ) ) ) ) )).
fof(t103_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k37_gfacirc1(A,B,C),k38_gfacirc1(A,B,C)))) & ? [E] : ( m1_subset_1(E,k6_margrel1) & ? [F] : ( m1_subset_1(F,k6_margrel1) & ? [G] : ( 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)))) ) ) ) ) ) ) )).
fof(t103_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ! [E] : ( ( 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)) ) ) ) ) )).
fof(t103_group_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_group_2(D,B) => ( r2_hidden(A,k13_group_2(B,D,C)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k6_algstr_0(B,C,E) & r1_struct_0(D,E) ) ) ) ) ) )).
fof(t103_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => r5_group_3(A,B,B) ) ) )).
fof(t103_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v8_group_9(C,A,B) & m2_finseq_1(C,k6_group_9(A,B)) ) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(D,k4_finseq_1(k20_group_9(A,B,C))) & ! [E] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t103_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(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)) ) ) ) )).
fof(t103_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t103_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(2,A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t103_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v6_limfunc1(B) & v6_limfunc1(C) & k5_limfunc1(B) = k5_limfunc1(C) ) => ( ! [D] : ( v1_xreal_0(D) => ~ ( r1_tarski(k10_prob_1(D),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,A))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k10_prob_1(D)) => ( r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(A,E)) & r1_xxreal_0(k1_funct_1(A,E),k1_funct_1(C,E)) ) ) ) ) ) | ( v6_limfunc1(A) & k5_limfunc1(A) = k5_limfunc1(B) ) ) ) ) ) ) )).
fof(t103_matrix13,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(D),B,C) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(D))) ) => ( r2_hidden(A,k9_matrix13(D,B,C,E)) <=> ? [F] : ( v7_ordinal1(F) & r2_hidden(F,k2_finseq_1(B)) & A = k7_matrix_0(u1_struct_0(D),E,F) ) ) ) ) ) ) )).
fof(t103_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( v2_membered(C) => ! [D] : ( v2_membered(D) => ( ( r1_tarski(A,B) & r1_tarski(C,D) ) => r1_tarski(k14_member_1(A,C),k14_member_1(B,D)) ) ) ) ) ) )).
fof(t103_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t103_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ! [D] : ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t103_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t103_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => k5_relat_1(k6_relat_1(B,C),A) = k6_relat_1(B,k5_relat_1(C,A)) ) )).
fof(t103_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k8_afinsq_1(C))) => ! [E] : ( ( ~ v2_struct_0(E) & l1_rewrite3(E,D) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(E)) => ( r2_hidden(F,k3_rewrite3(C,D,E,A,B)) <=> ? [G] : ( m1_subset_1(G,u1_struct_0(E)) & r2_hidden(G,B) & r4_rewrite3(C,D,E,G,A,F) ) ) ) ) ) ) )).
fof(t103_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) & v1_finseq_1(A) ) => ( ? [B] : ( v7_ordinal1(B) & r2_hidden(B,k4_finseq_1(A)) & k1_funct_1(A,B) = k5_numbers ) <=> k19_rvsum_1(A) = k5_numbers ) ) )).
fof(t103_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( 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)) = k1_nat_1(k5_card_1(C),1) ) ) ) ) ) )).
fof(t103_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ! [C] : ( ( 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) ) ) )).
fof(t103_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r5_semi_af1(A,B,C) & B = C ) ) ) ) )).
fof(t103_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => k20_seq_4(k17_seq_4(A,B,C)) = k20_seq_4(k17_seq_4(A,C,B)) ) ) ) )).
fof(t103_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t103_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(B,k5_numbers) & k2_xcmplx_0(k1_square_1(A),k1_square_1(B)) = 1 ) => k17_sin_cos(k4_sin_cos6(A)) = k4_xcmplx_0(B) ) ) ) )).
fof(t103_sin_cos9,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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),k7_xcmplx_0(1,2))))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) & C = k1_taylor_1(2) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_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),k7_xcmplx_0(1,2))),A) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_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),k7_xcmplx_0(1,2))),A),D) = k1_funct_1(k1_sin_cos9,D) ) ) ) ) ) ) ) )).
fof(t103_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( ( r1_xxreal_0(k4_xcmplx_0(k3_square_1(2)),A) & r1_xxreal_0(A,k4_xcmplx_0(1)) & k7_sincos10(A) = k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)) ) => A = k4_xcmplx_0(1) ) & ( ( r1_xxreal_0(k4_xcmplx_0(k3_square_1(2)),A) & r1_xxreal_0(A,k4_xcmplx_0(1)) & k7_sincos10(A) = k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)) ) => A = k4_xcmplx_0(k3_square_1(2)) ) ) ) )).
fof(t103_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k12_tdlat_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k12_tdlat_1(A))) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k9_tdlat_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t103_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t103_xboole_1,axiom,( ! [A] : ! [B] : r1_xboole_0(k3_xboole_0(A,B),k5_xboole_0(A,B)) )).
fof(t103_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => k6_xboolean(A,A) = k2_xboolean ) )).
fof(t103_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k3_xcmplx_0(k7_xcmplx_0(1,C),k7_xcmplx_0(A,B)) = k7_xcmplx_0(A,k3_xcmplx_0(B,C)) ) ) ) )).
fof(t103_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r1_xxreal_0(k3_xcmplx_0(A,D),k3_xcmplx_0(C,B)) => ( r1_xxreal_0(k5_numbers,B) | r1_xxreal_0(k5_numbers,D) | r1_xxreal_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,D)) ) ) ) ) ) ) )).
fof(t103_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(A,C) & ~ r1_xxreal_0(D,C) & r1_tarski(k2_xxreal_1(C,D),k2_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t103_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(A,B) => ( r1_xxreal_0(k5_numbers,C) | r1_xxreal_0(k6_xxreal_3(B,C),k6_xxreal_3(A,C)) ) ) ) ) ) )).
fof(t103_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ~ 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)) ) ) ) ) ) )).
fof(t103_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( r1_xboole_0(A,B) | r1_xboole_0(C,D) ) => r1_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ) )).
fof(t103_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_zmodul01(B) & m1_zmodul01(B,A) ) => k7_zmodul01(A,B,B) = B ) ) )).
fof(t104_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v9_abcmiz_1(B,A) & m1_abcmiz_1(B,A,k12_abcmiz_1(A)) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t104_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_aofa_000(D,A,B,C) => ! [E] : ( ( v15_aofa_000(E,A) & m1_subset_1(E,u1_struct_0(A)) ) => r5_aofa_000(A,B,C,E,D) ) ) ) ) ) )).
fof(t104_card_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) )).
fof(t104_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m3_chord(B,A) => r1_xxreal_0(1,k3_finseq_1(B)) ) ) )).
fof(t104_clvect_1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k2_normsp_0(A,k5_algstr_0(A,B,C)),k2_xcmplx_0(k2_normsp_0(A,B),k2_normsp_0(A,C))) ) ) ) )).
fof(t104_euclid_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [J] : ( v1_xreal_0(J) => ( ( 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(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k1_funct_1(H,J),k1_funct_1(B,J)),k1_fdiff_1(F,J)),k3_xcmplx_0(k3_xcmplx_0(k1_funct_1(I,J),k1_funct_1(C,J)),k1_fdiff_1(E,J))),k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k1_funct_1(I,J),k1_funct_1(C,J)),k1_fdiff_1(D,J)),k3_xcmplx_0(k3_xcmplx_0(k1_funct_1(G,J),k1_funct_1(A,J)),k1_fdiff_1(F,J))),k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k1_funct_1(G,J),k1_funct_1(A,J)),k1_fdiff_1(E,J)),k3_xcmplx_0(k3_xcmplx_0(k1_funct_1(H,J),k1_funct_1(B,J)),k1_fdiff_1(D,J)))),k1_euclid_8(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k1_funct_1(H,J),k1_fdiff_1(B,J)),k1_funct_1(F,J)),k3_xcmplx_0(k3_xcmplx_0(k1_funct_1(I,J),k1_fdiff_1(C,J)),k1_funct_1(E,J))),k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k1_funct_1(I,J),k1_fdiff_1(C,J)),k1_funct_1(D,J)),k3_xcmplx_0(k3_xcmplx_0(k1_funct_1(G,J),k1_fdiff_1(A,J)),k1_funct_1(F,J))),k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k1_funct_1(G,J),k1_fdiff_1(A,J)),k1_funct_1(E,J)),k3_xcmplx_0(k3_xcmplx_0(k1_funct_1(H,J),k1_fdiff_1(B,J)),k1_funct_1(D,J))))),k1_euclid_8(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(H,J),k1_funct_1(B,J)),k1_funct_1(F,J)),k3_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(I,J),k1_funct_1(C,J)),k1_funct_1(E,J))),k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(I,J),k1_funct_1(C,J)),k1_funct_1(D,J)),k3_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(G,J),k1_funct_1(A,J)),k1_funct_1(F,J))),k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(G,J),k1_funct_1(A,J)),k1_funct_1(E,J)),k3_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(H,J),k1_funct_1(B,J)),k1_funct_1(D,J))))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t104_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t104_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v3_card_1(D,k2_xcmplx_0(A,B)) & m2_finseq_1(D,C) ) => ? [E] : ( m2_finseq_2(E,C,k4_finseq_2(A,C)) & ? [F] : ( m2_finseq_2(F,C,k4_finseq_2(B,C)) & D = k8_finseq_1(C,E,F) ) ) ) ) ) ) )).
fof(t104_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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)) ) ) )).
fof(t104_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ( ( r2_hidden(C,k10_xtuple_0(k2_rfinseq(A,1,D))) & r2_finseq_4(D,C) ) => k1_finseq_6(A,k1_finseq_6(A,D,B),C) = k1_finseq_6(A,D,C) ) ) ) ) ) )).
fof(t104_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( 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)) ) ) )).
fof(t104_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_funct_1(B,A) ) => r1_tarski(k9_xtuple_0(B),k9_xtuple_0(A)) ) ) )).
fof(t104_funct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t104_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : 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))) ) )).
fof(t104_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( r1_funct_7(A,B,D) => r1_funct_7(k1_funct_4(C,A),k1_funct_4(C,B),D) ) ) ) ) )).
fof(t104_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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] : ( 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)) ) ) )).
fof(t104_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => r1_tarski(k14_glib_001(A,k8_glib_001(A,B,D,C)),k14_glib_001(A,B)) ) ) ) ) )).
fof(t104_group_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_group_2(D,B) => ( r2_hidden(A,k14_group_2(B,D,C)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k6_algstr_0(B,E,C) & r1_struct_0(D,E) ) ) ) ) ) )).
fof(t104_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ! [C] : ( ( v15_algstr_0(C) & m1_group_2(C,A) ) => ( r5_group_3(A,B,C) => r5_group_3(A,C,B) ) ) ) ) )).
fof(t104_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v8_group_9(C,A,B) & m2_finseq_1(C,k6_group_9(A,B)) ) => ! [D] : ( ( v8_group_9(D,A,B) & m2_finseq_1(D,k6_group_9(A,B)) ) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t104_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ! [C] : ( ( ~ 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] : ( 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) ) ) ) ) ) ) )).
fof(t104_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t104_jordan2c,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ~ v9_rltopsp1(k7_topreal1(A),k15_euclid(2)) ) )).
fof(t104_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_prvect_1(B,A)))) ) => ? [D] : ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),k5_card_1(C),A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) & v2_funct_1(D) & k9_matrix13(B,k5_card_1(C),A,D) = C ) ) ) ) )).
fof(t104_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t104_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( 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) = k4_xxreal_3(E,k2_mesfunc6(A,B,C,D,F)) ) ) ) ) ) ) ) ) )).
fof(t104_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t104_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t104_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r2_hidden(B,k7_relat_1(C,A)) <=> ? [D] : ( r2_hidden(D,k9_xtuple_0(C)) & r2_hidden(k4_tarski(D,B),C) & r2_hidden(D,A) ) ) ) )).
fof(t104_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ v2_struct_0(C) & l1_rewrite3(C,B) ) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t104_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => k19_rvsum_1(k2_finseq_2(k2_xcmplx_0(A,B),C)) = k3_xcmplx_0(k19_rvsum_1(k2_finseq_2(A,C)),k19_rvsum_1(k2_finseq_2(B,C))) ) ) ) )).
fof(t104_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( ~ r1_xxreal_0(k5_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) ) ) ) ) ) ) ) )).
fof(t104_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => A = k7_scmyciel(k12_scmyciel(A),k3_tarski(A)) ) )).
fof(t104_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r5_semi_af1(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( ~ r1_semi_af1(A,B,C,D) & r5_semi_af1(A,B,D) ) ) ) ) ) ) )).
fof(t104_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => ! [D] : ( m2_finseq_2(D,k2_numbers,k12_seq_4(A)) => r1_xxreal_0(k20_seq_4(k17_seq_4(A,C,D)),k2_xcmplx_0(k20_seq_4(k17_seq_4(A,C,B)),k20_seq_4(k17_seq_4(A,B,D)))) ) ) ) ) )).
fof(t104_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t104_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) => k17_sin_cos(k4_sin_cos6(A)) = k3_square_1(k6_xcmplx_0(1,k1_square_1(A))) ) ) )).
fof(t104_sin_cos9,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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),k7_xcmplx_0(1,2))))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) & C = k1_taylor_1(2) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_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),k7_xcmplx_0(1,2))),A) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_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),k7_xcmplx_0(1,2))),A),D) = k1_funct_1(k2_sin_cos9,D) ) ) ) ) ) ) ) )).
fof(t104_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,k3_square_1(2)) & k8_sincos10(A) = k7_xcmplx_0(k28_sin_cos,4) ) => A = k3_square_1(2) ) & ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,k3_square_1(2)) & k8_sincos10(A) = k7_xcmplx_0(k28_sin_cos,2) ) => A = 1 ) ) ) )).
fof(t104_tdlat_2,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t104_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t104_xboole_1,axiom,( ! [A] : ! [B] : ( ~ ( ~ r2_xboole_0(A,B) & A != B & ~ r2_xboole_0(B,A) ) <=> r3_xboole_0(A,B) ) )).
fof(t104_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k6_xboolean(A,k6_xboolean(B,A)) = k2_xboolean ) ) )).
fof(t104_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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)) ) ) ) )).
fof(t104_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r1_xxreal_0(k3_xcmplx_0(A,D),k3_xcmplx_0(C,B)) => ( r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(k5_numbers,D) | r1_xxreal_0(k7_xcmplx_0(C,D),k7_xcmplx_0(A,B)) ) ) ) ) ) ) )).
fof(t104_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(A,C) & r1_xxreal_0(C,D) & r1_tarski(k1_xxreal_1(C,D),k2_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t104_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ~ ( ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(k5_numbers,C) & C != k2_xxreal_0 & r1_xxreal_0(k6_xxreal_3(A,C),k6_xxreal_3(B,C)) ) ) ) ) )).
fof(t104_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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))) ) ) ) ) ) ) )).
fof(t104_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k1_tarski(C),D)) <=> ( A = C & r2_hidden(B,D) ) ) )).
fof(t104_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( m1_zmodul01(D,A) => k7_zmodul01(A,B,k7_zmodul01(A,C,D)) = k7_zmodul01(A,k7_zmodul01(A,B,C),D) ) ) ) ) )).
fof(t105_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v9_abcmiz_1(B,A) & m1_abcmiz_1(B,A,k12_abcmiz_1(A)) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t105_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_aofa_000(D,A,B,C) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t105_card_3,axiom,( ! [A] : ( ( v4_funct_1(A) & v2_card_3(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(B,A) => k9_xtuple_0(B) = k9_card_3(A) ) ) ) )).
fof(t105_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) & v2_glib_000(B) ) => ! [C] : ( m3_chord(C,A) => ( r5_glib_000(A,B) => m3_chord(C,B) ) ) ) ) )).
fof(t105_clvect_1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_xxreal_0(k5_numbers,k2_normsp_0(A,B)) ) ) )).
fof(t105_euclid_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [J] : ( v1_xreal_0(J) => ( ( 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(k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(H,J),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(A,J),k1_fdiff_1(E,J)),k3_xcmplx_0(k1_funct_1(B,J),k1_fdiff_1(D,J)))),k3_xcmplx_0(k1_funct_1(I,J),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(C,J),k1_fdiff_1(D,J)),k3_xcmplx_0(k1_funct_1(A,J),k1_fdiff_1(F,J))))),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(I,J),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(B,J),k1_fdiff_1(F,J)),k3_xcmplx_0(k1_funct_1(C,J),k1_fdiff_1(E,J)))),k3_xcmplx_0(k1_funct_1(G,J),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(A,J),k1_fdiff_1(E,J)),k3_xcmplx_0(k1_funct_1(B,J),k1_fdiff_1(D,J))))),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(G,J),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(C,J),k1_fdiff_1(D,J)),k3_xcmplx_0(k1_funct_1(A,J),k1_fdiff_1(F,J)))),k3_xcmplx_0(k1_funct_1(H,J),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(B,J),k1_fdiff_1(F,J)),k3_xcmplx_0(k1_funct_1(C,J),k1_fdiff_1(E,J)))))),k1_euclid_8(k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(H,J),k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(A,J),k1_funct_1(E,J)),k3_xcmplx_0(k1_fdiff_1(B,J),k1_funct_1(D,J)))),k3_xcmplx_0(k1_funct_1(I,J),k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(C,J),k1_funct_1(D,J)),k3_xcmplx_0(k1_fdiff_1(A,J),k1_funct_1(F,J))))),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(I,J),k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(B,J),k1_funct_1(F,J)),k3_xcmplx_0(k1_fdiff_1(C,J),k1_funct_1(E,J)))),k3_xcmplx_0(k1_funct_1(G,J),k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(A,J),k1_funct_1(E,J)),k3_xcmplx_0(k1_fdiff_1(B,J),k1_funct_1(D,J))))),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(G,J),k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(C,J),k1_funct_1(D,J)),k3_xcmplx_0(k1_fdiff_1(A,J),k1_funct_1(F,J)))),k3_xcmplx_0(k1_funct_1(H,J),k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(B,J),k1_funct_1(F,J)),k3_xcmplx_0(k1_fdiff_1(C,J),k1_funct_1(E,J))))))),k1_euclid_8(k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(H,J),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(A,J),k1_funct_1(E,J)),k3_xcmplx_0(k1_funct_1(B,J),k1_funct_1(D,J)))),k3_xcmplx_0(k1_fdiff_1(I,J),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(C,J),k1_funct_1(D,J)),k3_xcmplx_0(k1_funct_1(A,J),k1_funct_1(F,J))))),k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(I,J),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(B,J),k1_funct_1(F,J)),k3_xcmplx_0(k1_funct_1(C,J),k1_funct_1(E,J)))),k3_xcmplx_0(k1_fdiff_1(G,J),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(A,J),k1_funct_1(E,J)),k3_xcmplx_0(k1_funct_1(B,J),k1_funct_1(D,J))))),k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(G,J),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(C,J),k1_funct_1(D,J)),k3_xcmplx_0(k1_funct_1(A,J),k1_funct_1(F,J)))),k3_xcmplx_0(k1_fdiff_1(H,J),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(B,J),k1_funct_1(F,J)),k3_xcmplx_0(k1_funct_1(C,J),k1_funct_1(E,J))))))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t105_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(k1_euclid(A)),k5_euclidlp(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t105_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v3_card_1(D,A) & m2_finseq_1(D,C) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t105_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( C = k1_nat_1(B,1) & r2_hidden(A,k2_finseq_1(C)) ) => k3_finseq_1(k14_finseq_1(k7_subset_1(k4_ordinal1,k2_finseq_1(C),k1_tarski(A)))) = B ) ) ) ) )).
fof(t105_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ( ( v1_finseq_6(D,A) & r2_finseq_4(D,C) ) => k1_finseq_6(A,k1_finseq_6(A,D,B),C) = k1_finseq_6(A,D,C) ) ) ) ) ) )).
fof(t105_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t105_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(t105_funct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(t105_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ( k1_funct_1(A,D) != B => k1_funct_1(k6_funct_4(A,B,C),D) = k1_funct_1(A,D) ) ) )).
fof(t105_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t105_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(t105_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => k14_glib_001(A,B) = k14_glib_001(A,k6_glib_001(A,B)) ) ) )).
fof(t105_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t105_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( v15_algstr_0(C) & m1_group_2(C,A) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t105_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v8_group_9(C,A,B) & m2_finseq_1(C,k6_group_9(A,B)) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( v7_ordinal1(E) => ( ( D = k20_group_9(A,B,C) & r2_hidden(E,k4_finseq_1(D)) & ! [F] : ( ( ~ 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] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t105_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ! [B] : ( ( 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)) ) ) ) ) )).
fof(t105_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t105_jordan2c,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ~ v9_rltopsp1(k5_topreal1(A),k15_euclid(2)) ) )).
fof(t105_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ( k8_matrix13(C,D) = A => v2_funct_1(D) ) ) ) ) ) )).
fof(t105_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( 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))) ) ) ) )).
fof(t105_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( r1_mesfunc5(A,B,C,D) => ( r2_hidden(k8_relset_1(A,k6_numbers,D,k1_tarski(k1_supinf_1)),B) & r2_hidden(k8_relset_1(A,k6_numbers,D,k1_tarski(k2_supinf_1)),B) & k12_supinf_2(C,k8_relset_1(A,k6_numbers,D,k1_tarski(k1_supinf_1))) = k5_numbers & k12_supinf_2(C,k8_relset_1(A,k6_numbers,D,k1_tarski(k2_supinf_1))) = k5_numbers & r2_hidden(k4_subset_1(A,k8_relset_1(A,k6_numbers,D,k1_tarski(k1_supinf_1)),k8_relset_1(A,k6_numbers,D,k1_tarski(k2_supinf_1))),B) & k12_supinf_2(C,k4_subset_1(A,k8_relset_1(A,k6_numbers,D,k1_tarski(k1_supinf_1)),k8_relset_1(A,k6_numbers,D,k1_tarski(k2_supinf_1)))) = k5_numbers ) ) ) ) ) ) )).
fof(t105_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) => ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t105_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ~ ( ~ r4_pboole(A,C,D) & r4_pboole(A,k3_pboole(A,B,C),k3_pboole(A,B,D)) ) ) ) ) )).
fof(t105_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => r1_tarski(k7_relat_1(B,A),k10_xtuple_0(B)) ) )).
fof(t105_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k8_afinsq_1(C))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_afinsq_1(C))) => ! [F] : ( ( ~ v2_struct_0(F) & l1_rewrite3(F,D) ) => ! [G] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t105_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => k19_rvsum_1(k2_finseq_2(k3_xcmplx_0(A,B),C)) = k19_rvsum_1(k2_finseq_2(B,k19_rvsum_1(k2_finseq_2(A,C)))) ) ) ) )).
fof(t105_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( r1_xxreal_0(k5_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) ) ) ) ) ) ) ) )).
fof(t105_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,k3_tarski(B)) => C != k3_tarski(A) ) ) ) ) )).
fof(t105_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( ~ r1_semi_af1(A,D,E,C) & r1_semi_af1(A,D,E,B) & r5_semi_af1(A,D,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ r4_semi_af1(A,E,B,C,F,D) ) ) ) ) ) ) ) )).
fof(t105_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k12_seq_4(A))) => ( B = k1_xboole_0 => v1_seq_4(B,A) ) ) ) )).
fof(t105_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) )).
fof(t105_sin_cos6,axiom,( v6_valued_0(k5_relset_1(k1_numbers,k1_numbers,k3_sin_cos6,k1_rcomp_1(k4_xcmplx_0(1),1))) )).
fof(t105_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k1_funct_1(C,D) = k7_xcmplx_0(D,A) & ~ r1_xxreal_0(k1_funct_1(C,D),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_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] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_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) = k2_xcmplx_0(k1_funct_1(k1_sin_cos9,k7_xcmplx_0(D,A)),k7_xcmplx_0(D,k3_xcmplx_0(A,k2_xcmplx_0(1,k1_square_1(k7_xcmplx_0(D,A)))))) ) ) ) ) ) ) ) )).
fof(t105_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,k3_square_1(2)) ) => ( r1_xxreal_0(k5_numbers,k5_sincos10(A)) & r1_xxreal_0(k5_sincos10(A),k7_xcmplx_0(k28_sin_cos,4)) ) ) ) )).
fof(t105_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k12_tdlat_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k12_tdlat_1(A))) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k9_tdlat_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t105_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t105_xboole_1,axiom,( ! [A] : ! [B] : ~ ( r2_xboole_0(A,B) & k4_xboole_0(B,A) = k1_xboole_0 ) )).
fof(t105_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k6_xboolean(A,k6_xboolean(k6_xboolean(A,B),B)) = k2_xboolean ) ) )).
fof(t105_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r1_xxreal_0(k3_xcmplx_0(A,D),k3_xcmplx_0(C,B)) => ( r1_xxreal_0(k5_numbers,B) | r1_xxreal_0(D,k5_numbers) | r1_xxreal_0(k7_xcmplx_0(C,D),k7_xcmplx_0(A,B)) ) ) ) ) ) ) )).
fof(t105_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(A,C) & ~ r1_xxreal_0(D,C) & r1_tarski(k4_xxreal_1(C,D),k3_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t105_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => k1_xxreal_3(k6_xxreal_3(A,2),k6_xxreal_3(A,2)) = A ) )).
fof(t105_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t105_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(D,k1_tarski(C))) <=> ( r2_hidden(A,D) & B = C ) ) )).
fof(t105_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => m1_zmodul01(k7_zmodul01(A,B,C),B) ) ) ) )).
fof(t106_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t106_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_aofa_000(D,A,B,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r5_aofa_000(A,B,C,E,D) => ! [F] : r6_aofa_000(A,B,C,E,D,F) ) ) ) ) ) ) )).
fof(t106_card_3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v4_funct_1(B) ) => ( ! [C] : ( ( 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)) ) ) )).
fof(t106_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m3_chord(B,A) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ~ ( r1_xxreal_0(C,k3_finseq_1(B)) & v1_xboole_0(k4_chord(A,B,C)) ) ) ) ) )).
fof(t106_clvect_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => r1_xxreal_0(k2_normsp_0(C,k3_rlvect_1(C,k1_clvect_1(C,D,A),k1_clvect_1(C,E,B))),k2_xcmplx_0(k3_xcmplx_0(k9_complex1(A),k2_normsp_0(C,D)),k3_xcmplx_0(k9_complex1(B),k2_normsp_0(C,E)))) ) ) ) ) ) )).
fof(t106_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ~ ( r5_euclidlp(A,B,C) & B != C & ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t106_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k3_finseq_2(A) = k3_tarski(a_1_3_finseq_2(A)) ) )).
fof(t106_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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(k4_ordinal1,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(k4_ordinal1,k2_finseq_1(D),k1_tarski(B))),A) = k1_nat_1(A,1) ) ) ) ) ) ) ) )).
fof(t106_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t106_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t106_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v2_funct_1(A) & r1_tarski(B,k9_xtuple_0(A)) ) => k7_relat_1(k2_funct_1(A),k7_relat_1(A,B)) = B ) ) )).
fof(t106_funct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( 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)))) ) ) ) ) )).
fof(t106_funct_4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( ( r2_hidden(A,k9_xtuple_0(B)) & k1_funct_1(B,A) = C ) => k1_funct_1(k6_funct_4(B,C,D),A) = D ) ) )).
fof(t106_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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(k1_funct_7(k6_partfun1(k9_xtuple_0(D)),A,B),D),C) ) ) )).
fof(t106_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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))) )).
fof(t106_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ( r1_glib_000(A,C,D,B) <=> k14_glib_001(A,k2_glib_001(A,C,D,B)) = k1_tarski(B) ) ) )).
fof(t106_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t106_group_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_group_2(C,B) => ( r2_hidden(A,k9_group_3(B,C)) => ( v15_algstr_0(A) & m1_group_2(A,B) ) ) ) ) )).
fof(t106_group_9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( r2_hidden(D,k4_finseq_1(B)) & ? [F] : ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t106_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r1_xxreal_0(A,k7_xcmplx_0(k18_euclid(B),k12_euclid(B))) => ( r1_xxreal_0(1,A) | r1_xxreal_0(k17_euclid(B),k5_numbers) | ! [C] : ( 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),k5_numbers) & r1_xxreal_0(k5_numbers,k18_euclid(C)) ) ) ) ) ) ) ) )).
fof(t106_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t106_jordan2c,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ~ v9_rltopsp1(k4_topreal1(A),k15_euclid(2)) ) )).
fof(t106_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,B) & r2_hidden(C,k1_relset_1(k1_numbers,A)) & k1_funct_1(A,C) != k5_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)) = k5_numbers ) ) ) ) )).
fof(t106_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_vectsp_6(F,D,k6_prvect_1(D,C)) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(D),B,C) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(D))) ) => ( ( r2_hidden(A,k2_finseq_1(k3_finseq_1(G))) & E = k1_funct_1(F,k1_funct_1(G,A)) ) => k7_matrix_0(u1_struct_0(D),k10_matrix13(D,C,k3_vectsp_6(D,k6_prvect_1(D,C),k11_matrix13(D,B,C,G),F)),A) = k10_fvsum_1(k1_matrix_0(G),D,k7_matrix_0(u1_struct_0(D),G,A),E) ) ) ) ) ) ) ) ) )).
fof(t106_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t106_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_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)) ) ) ) ) ) ) )).
fof(t106_ncfcont1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t106_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t106_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k7_relat_1(B,A) = k7_relat_1(B,k3_xboole_0(k9_xtuple_0(B),A)) ) )).
fof(t106_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k19_rvsum_1(k2_finseq_2(A,k3_xcmplx_0(B,C))) = k3_xcmplx_0(k19_rvsum_1(k2_finseq_2(A,B)),k19_rvsum_1(k2_finseq_2(A,C))) ) ) ) )).
fof(t106_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => k5_card_1(k10_scmpds_6(A,B,C)) = k1_nat_1(k5_card_1(C),2) ) ) ) )).
fof(t106_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v6_scmyciel(A) ) => ( k8_scmyciel(A) = k5_numbers => ! [B] : ( ( 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) ) ) ) )).
fof(t106_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k12_seq_4(A))) => ( B = k12_seq_4(A) => v1_seq_4(B,A) ) ) ) )).
fof(t106_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) )).
fof(t106_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_fdiff_1(k3_sin_cos6,k2_rcomp_1(k4_xcmplx_0(1),1)) & ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & k1_fdiff_1(k3_sin_cos6,A) != k4_xcmplx_0(k7_xcmplx_0(1,k3_square_1(k6_xcmplx_0(1,k1_square_1(A))))) ) ) ) )).
fof(t106_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k1_funct_1(C,D) = k7_xcmplx_0(D,A) & ~ r1_xxreal_0(k1_funct_1(C,D),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_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] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_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) = k6_xcmplx_0(k1_funct_1(k2_sin_cos9,k7_xcmplx_0(D,A)),k7_xcmplx_0(D,k3_xcmplx_0(A,k2_xcmplx_0(1,k1_square_1(k7_xcmplx_0(D,A)))))) ) ) ) ) ) ) ) )).
fof(t106_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(k3_square_1(2)),A) & r1_xxreal_0(A,k4_xcmplx_0(1)) ) => ( r1_xxreal_0(k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos),k6_sincos10(A)) & r1_xxreal_0(k6_sincos10(A),k28_sin_cos) ) ) ) )).
fof(t106_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k12_tdlat_1(A)))) => ? [C] : ( m1_subset_1(C,u1_struct_0(k12_tdlat_1(A))) & r4_lattice3(k12_tdlat_1(A),C,B) & ! [D] : ( 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) ) ) ) ) ) )).
fof(t106_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( r1_tsep_1(B,C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t106_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(C,k4_xboole_0(A,B)) => ( r1_tarski(C,A) & r1_xboole_0(C,B) ) ) )).
fof(t106_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k6_xboolean(k6_xboolean(A,B),k6_xboolean(k6_xboolean(B,C),k6_xboolean(A,C))) = k2_xboolean ) ) ) )).
fof(t106_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( A != k5_numbers => k3_xcmplx_0(A,k7_xcmplx_0(1,A)) = 1 ) ) )).
fof(t106_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(k3_xcmplx_0(C,B),k3_xcmplx_0(A,D)) & r1_xxreal_0(k7_xcmplx_0(C,D),k7_xcmplx_0(A,B)) ) ) ) ) ) )).
fof(t106_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( r1_xxreal_0(C,A) & ~ r1_xxreal_0(D,C) & r1_tarski(k2_xxreal_1(C,D),k3_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t106_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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)))) ) ) ) ) ) ) )).
fof(t106_zfmisc_1,axiom,( ! [A] : ! [B] : ( B != k1_xboole_0 => ( k2_zfmisc_1(k1_tarski(A),B) != k1_xboole_0 & k2_zfmisc_1(B,k1_tarski(A)) != k1_xboole_0 ) ) )).
fof(t106_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( ( v1_zmodul01(C) & m1_zmodul01(C,A) ) => ( m1_zmodul01(C,B) <=> k7_zmodul01(A,C,B) = C ) ) ) ) )).
fof(t107_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t107_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_aofa_000(D,A,B,C) => ! [E] : ( ( v15_aofa_000(E,A) & m1_subset_1(E,u1_struct_0(A)) ) => ! [F] : r6_aofa_000(A,B,C,E,D,F) ) ) ) ) ) )).
fof(t107_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & v4_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ? [C] : ( m3_chord(C,A) & C = k12_finseq_1(k6_glib_000(A),B) & v7_chord(C,A) ) ) ) )).
fof(t107_clvect_1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_normsp_0(A,k5_algstr_0(A,B,C)) = k5_numbers <=> B = C ) ) ) ) )).
fof(t107_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ~ ( r6_euclidlp(A,B,C) & ~ r1_xboole_0(B,C) & ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t107_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ! [D] : ( ( v3_card_1(D,A) & m2_finseq_1(D,C) ) => m2_finseq_2(D,B,k4_finseq_2(A,B)) ) ) ) ) )).
fof(t107_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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(k4_ordinal1,C)) ) => k3_finseq_1(k2_finseq_3(B,C)) = A ) ) ) ) )).
fof(t107_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_zfmisc_1(B) & m2_finseq_1(B,A) ) => ~ ( ~ v1_xboole_0(B) & ! [C] : ( m1_subset_1(C,A) => B != k12_finseq_1(A,C) ) ) ) ) )).
fof(t107_flang_2,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(t107_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r2_hidden(B,A) & r2_hidden(B,k9_xtuple_0(C)) ) => r2_hidden(k1_funct_1(C,B),k7_relat_1(C,A)) ) ) )).
fof(t107_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,B))) ) => ! [F] : ( m1_subset_1(F,A) => ( r1_tarski(k2_relset_1(C,D),k1_relset_1(C,E)) => ( A = k1_xboole_0 | k1_funct_1(k8_funct_2(A,B,C,D,E),F) = k1_funct_1(E,k1_funct_1(D,F)) ) ) ) ) ) ) )).
fof(t107_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( ~ r2_hidden(B,k9_xtuple_0(A)) => r1_tarski(A,k1_funct_4(A,k16_funcop_1(B,C))) ) ) )).
fof(t107_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(k1_funct_7(k6_partfun1(k9_xtuple_0(C)),A,B),C) ) ) )).
fof(t107_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : v1_relat_1(k3_msafree2(k43_gfacirc1(A,B,C))) )).
fof(t107_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => r1_tarski(k14_glib_001(A,B),k21_glib_000(A,k13_glib_001(A,B))) ) ) )).
fof(t107_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t107_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ! [C] : ( ( v15_algstr_0(C) & m1_group_2(C,A) ) => ( r2_hidden(B,k9_group_3(A,C)) <=> r6_group_3(A,B,C) ) ) ) ) )).
fof(t107_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( ( v8_group_9(D,A,B) & m2_finseq_1(D,k6_group_9(A,B)) ) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t107_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(k17_euclid(B),k5_numbers) & ~ r1_xxreal_0(A,k7_xcmplx_0(k18_euclid(B),k12_euclid(B))) & ? [C] : ( 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),k5_numbers) & ~ r1_xxreal_0(k5_numbers,k18_euclid(C)) ) ) ) ) ) )).
fof(t107_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t107_jordan2c,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ~ v9_rltopsp1(k6_topreal1(A),k15_euclid(2)) ) )).
fof(t107_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(B,C) & r2_hidden(C,k1_relset_1(k1_numbers,A)) & k1_funct_1(A,C) != k5_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)) = k5_numbers ) ) ) ) )).
fof(t107_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( m1_vectsp_6(E,D,k6_prvect_1(D,C)) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(D),B,C) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(D))) ) => ( ( v2_funct_1(F) & r1_tarski(k1_vectsp_6(D,k6_prvect_1(D,C),E),k9_matrix13(D,B,C,F)) & r2_hidden(A,k2_finseq_1(C)) ) => k1_funct_1(k4_vectsp_6(D,k6_prvect_1(D,C),E),A) = k4_rlvect_1(D,k8_matrix_0(u1_struct_0(D),k10_matrix13(D,C,k3_vectsp_6(D,k6_prvect_1(D,C),k11_matrix13(D,B,C,F),E)),A)) ) ) ) ) ) ) ) )).
fof(t107_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( 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))) ) ) ) )).
fof(t107_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_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) ) ) ) ) ) ) )).
fof(t107_ncfcont1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t107_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t107_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => k7_relat_1(A,k9_xtuple_0(A)) = k10_xtuple_0(A) ) )).
fof(t107_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => k21_rvsum_1(k15_rvsum_1(A,B,C)) = k3_xcmplx_0(k21_rvsum_1(B),k21_rvsum_1(C)) ) ) ) )).
fof(t107_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ( r2_hidden(k5_numbers,k9_xtuple_0(k10_scmpds_6(A,B,C))) & r2_hidden(1,k9_xtuple_0(k10_scmpds_6(A,B,C))) ) ) ) ) )).
fof(t107_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( 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))) ) ) )).
fof(t107_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(k12_seq_4(A)))) => ( ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k12_seq_4(A))) => ( r2_hidden(C,B) => v1_seq_4(C,A) ) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k12_seq_4(A))) => ( C = k3_tarski(B) => v1_seq_4(C,A) ) ) ) ) ) )).
fof(t107_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) )).
fof(t107_sin_cos6,axiom,( v1_fcont_1(k5_relset_1(k1_numbers,k1_numbers,k3_sin_cos6,k1_rcomp_1(k4_xcmplx_0(1),1))) )).
fof(t107_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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,D,E))) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => k1_funct_1(D,F) = 1 ) ) & E = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k1_taylor_1(2)) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => k1_funct_1(C,F) = k7_xcmplx_0(F,A) ) ) ) => ( r2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,D,E),B) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => k1_funct_1(k2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,D,E),B),F) = k7_xcmplx_0(k3_xcmplx_0(2,F),k1_square_1(A)) ) ) ) ) ) ) ) ) ) )).
fof(t107_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(k3_square_1(2)),A) & r1_xxreal_0(A,k4_xcmplx_0(1)) ) => ( r1_xxreal_0(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_sincos10(A)) & r1_xxreal_0(k7_sincos10(A),k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4))) ) ) ) )).
fof(t107_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => v4_lattice3(k12_tdlat_1(A)) ) )).
fof(t107_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(t107_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(C,k5_xboole_0(A,B)) <=> ( r1_tarski(C,k2_xboole_0(A,B)) & r1_xboole_0(C,k3_xboole_0(A,B)) ) ) )).
fof(t107_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k6_xboolean(k6_xboolean(A,B),k6_xboolean(k6_xboolean(C,A),k6_xboolean(C,B))) = k2_xboolean ) ) ) )).
fof(t107_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(k5_numbers,D) & ~ r1_xxreal_0(k3_xcmplx_0(C,B),k3_xcmplx_0(A,D)) & r1_xxreal_0(k7_xcmplx_0(C,D),k7_xcmplx_0(A,B)) ) ) ) ) ) )).
fof(t107_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(A,C) & ~ r1_xxreal_0(D,C) & r1_tarski(k3_xxreal_1(C,D),k3_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t107_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t107_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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))) ) ) )).
fof(t107_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => k7_zmodul01(A,k3_zmodul01(A),B) = k3_zmodul01(A) ) ) )).
fof(t108_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t108_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_aofa_000(D,A,B,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => r7_aofa_000(A,B,C,E,D,B) ) ) ) ) ) )).
fof(t108_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m3_chord(B,A) => ( v7_chord(B,A) <=> ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => ! [E] : ( m1_subset_1(E,k6_glib_000(A)) => ( ( r1_chord(A,C,D) & r1_chord(A,C,E) ) => ( D = E | ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t108_clvect_1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_normsp_0(A,k5_algstr_0(A,B,C)) = k2_normsp_0(A,k5_algstr_0(A,C,B)) ) ) ) )).
fof(t108_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [F] : ( 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 ) ) ) ) ) ) ) )).
fof(t108_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ( ~ v1_xboole_0(D) => ( k4_finseq_2(A,D) = k4_finseq_2(B,C) => A = B ) ) ) ) )).
fof(t108_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t108_finseq_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ~ ( ~ r1_xxreal_0(A,k3_finseq_1(B)) & ( r1_xxreal_0(A,k1_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,k6_xcmplx_0(A,k3_finseq_1(B))) ) ) ) ) )).
fof(t108_flang_2,axiom,( ! [A] : ! [B] : ( 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) ) )).
fof(t108_funct_1,axiom,( ! [A] : ! [B] : ( ( 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 ) ) )).
fof(t108_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,B))) ) => ! [F] : ( m1_subset_1(F,A) => ( r1_tarski(k2_relset_1(C,D),k1_relset_1(C,E)) => ( A = k1_xboole_0 | k1_funct_1(k8_funct_2(A,B,C,D,E),F) = k7_partfun1(B,E,k1_funct_1(D,F)) ) ) ) ) ) ) )).
fof(t108_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ! [E] : ( ( 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))) ) ) ) )).
fof(t108_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => k1_funct_4(A,k16_funcop_1(B,k1_funct_1(A,B))) = A ) ) )).
fof(t108_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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) ) )).
fof(t108_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m3_glib_001(D,B) => ( C = D => k14_glib_001(A,C) = k14_glib_001(B,D) ) ) ) ) ) )).
fof(t108_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_group_2(C,A) => ( r2_hidden(B,k13_group_2(A,C,B)) & r2_hidden(B,k14_group_2(A,C,B)) ) ) ) ) )).
fof(t108_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v15_algstr_0(C) & m1_group_2(C,A) ) => r2_hidden(k6_group_3(A,C,B),k9_group_3(A,C)) ) ) ) )).
fof(t108_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( ( v8_group_9(D,A,B) & m2_finseq_1(D,k6_group_9(A,B)) ) => ! [E] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t108_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r1_xxreal_0(A,k7_xcmplx_0(k18_euclid(B),k12_euclid(B))) & r1_xxreal_0(A,k7_xcmplx_0(k18_euclid(C),k12_euclid(C))) ) => ( r1_xxreal_0(1,A) | r1_xxreal_0(k17_euclid(B),k5_numbers) | r1_xxreal_0(k17_euclid(C),k5_numbers) | r1_xxreal_0(k7_xcmplx_0(k18_euclid(C),k12_euclid(C)),k7_xcmplx_0(k18_euclid(B),k12_euclid(B))) | ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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(k7_xcmplx_0(k18_euclid(E),k12_euclid(E)),k7_xcmplx_0(k18_euclid(D),k12_euclid(D))) ) ) ) ) ) ) ) ) )).
fof(t108_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t108_jordan2c,axiom,( ! [A] : ( ( 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)) ) )).
fof(t108_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v3_limfunc1(A) & k4_limfunc1(A) = k5_numbers & ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,B) & r2_hidden(C,k1_relset_1(k1_numbers,A)) & k1_funct_1(A,C) != k5_numbers ) ) ) => ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & r2_hidden(C,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k3_limfunc1(B))) & ~ r1_xxreal_0(k5_numbers,k1_funct_1(A,C)) ) ) | v4_limfunc1(k6_rfunct_1(k1_numbers,k1_numbers,A)) ) ) ) )).
fof(t108_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( v2_membered(C) => k14_member_1(k12_member_1(A,B),C) = k12_member_1(A,k14_member_1(B,C)) ) ) ) )).
fof(t108_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( r1_mesfunc5(A,B,C,D) & r1_mesfunc5(A,B,C,E) ) => r1_mesfunc5(A,B,C,k3_mesfunc1(A,D,E)) ) ) ) ) ) ) )).
fof(t108_ncfcont1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t108_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => r5_pboole(A,C,k4_pboole(A,B,C)) ) ) )).
fof(t108_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => r1_tarski(k7_relat_1(B,A),k7_relat_1(B,k9_xtuple_0(B))) ) )).
fof(t108_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => k21_rvsum_1(k11_rvsum_1(A,C,B)) = k3_xcmplx_0(k19_rvsum_1(k2_finseq_2(A,B)),k21_rvsum_1(C)) ) ) ) )).
fof(t108_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ( k1_funct_1(k10_scmpds_6(A,B,C),k5_numbers) = k9_scmpds_2(A,B,2) & k1_funct_1(k10_scmpds_6(A,B,C),1) = k3_scmpds_2(k1_nat_1(k5_card_1(C),1)) ) ) ) ) )).
fof(t108_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v6_scmyciel(A) ) => ( k8_scmyciel(A) = 1 => ! [B] : ( ( 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) ) ) ) )).
fof(t108_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k12_seq_4(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k12_seq_4(A))) => ( ( v1_seq_4(B,A) & v1_seq_4(C,A) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k12_seq_4(A))) => ( D = k9_subset_1(k12_seq_4(A),B,C) => v1_seq_4(D,A) ) ) ) ) ) ) )).
fof(t108_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t108_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) => k2_xcmplx_0(k2_sin_cos6(A),k4_sin_cos6(A)) = k7_xcmplx_0(k28_sin_cos,2) ) ) )).
fof(t108_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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,D,E),k3_taylor_1),k7_xcmplx_0(A,2)))) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => k1_funct_1(D,F) = 1 ) ) & E = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k1_taylor_1(2)) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => k1_funct_1(C,F) = k7_xcmplx_0(F,A) ) ) ) => ( A = k5_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,D,E),k3_taylor_1),k7_xcmplx_0(A,2)),B) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => k1_funct_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,D,E),k3_taylor_1),k7_xcmplx_0(A,2)),B),F) = k7_xcmplx_0(F,k3_xcmplx_0(A,k2_xcmplx_0(1,k1_square_1(k7_xcmplx_0(F,A))))) ) ) ) ) ) ) ) ) ) ) )).
fof(t108_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,k3_square_1(2)) ) => ( r1_xxreal_0(k7_xcmplx_0(k28_sin_cos,4),k8_sincos10(A)) & r1_xxreal_0(k8_sincos10(A),k7_xcmplx_0(k28_sin_cos,2)) ) ) ) )).
fof(t108_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v3_tdlat_2(B,A) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t108_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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))))) ) ) ) ) ) )).
fof(t108_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(B,A) => r1_tarski(k3_xboole_0(B,C),A) ) )).
fof(t108_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k6_xboolean(k6_xboolean(A,k6_xboolean(A,B)),k6_xboolean(A,B)) = k2_xboolean ) ) )).
fof(t108_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( B != k5_numbers => A = k3_xcmplx_0(A,k3_xcmplx_0(k7_xcmplx_0(1,B),B)) ) ) ) )).
fof(t108_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(k5_numbers,D) & ~ r1_xxreal_0(k3_xcmplx_0(C,B),k3_xcmplx_0(A,D)) & r1_xxreal_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,D)) ) ) ) ) ) )).
fof(t108_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( r1_xxreal_0(C,A) & r1_xxreal_0(C,D) & r1_tarski(k1_xxreal_1(C,D),k3_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t108_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t108_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t108_zmodul01,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t109_abcmiz_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k49_abcmiz_1)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k49_abcmiz_1)) => ( r3_orders_2(k49_abcmiz_1,A,B) <=> r1_tarski(B,A) ) ) ) )).
fof(t109_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_aofa_000(D,A,B,C) => ! [E] : ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) )).
fof(t109_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & v6_chord(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) & v2_glib_000(B) & v6_chord(B) ) => ! [C] : ( ( v7_chord(C,A) & m3_chord(C,A) ) => ( r5_glib_000(A,B) => ( v7_chord(C,B) & m3_chord(C,B) ) ) ) ) ) )).
fof(t109_clvect_1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k6_xcmplx_0(k2_normsp_0(A,B),k2_normsp_0(A,C)),k2_normsp_0(A,k5_algstr_0(A,B,C))) ) ) ) )).
fof(t109_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t109_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => m2_finseq_2(k1_finseq_2(A),k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) ) )).
fof(t109_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ( ( k3_finseq_1(D) = k1_nat_1(B,1) & r2_hidden(C,k1_relset_1(k4_ordinal1,D)) & r1_xxreal_0(C,A) & r1_xxreal_0(A,B) ) => k1_funct_1(k2_finseq_3(C,D),A) = k1_funct_1(D,k1_nat_1(A,1)) ) ) ) ) ) )).
fof(t109_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( 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),k1_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),k1_nat_1(k3_finseq_1(C),1)) = k7_partfun1(A,C,k3_finseq_1(C)) ) ) ) ) )).
fof(t109_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => r1_tarski(k7_flang_1(A,k2_flang_2(A,B),C),k8_flang_1(A,B)) ) ) )).
fof(t109_funct_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_funct_1(A) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(t109_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,B))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,A,A) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( r1_tarski(k2_relset_1(C,D),k1_relset_1(C,E)) => r2_funct_2(A,B,k1_partfun1(A,A,A,B,F,k8_funct_2(A,B,C,D,E)),k8_funct_2(A,B,C,k1_partfun1(A,A,A,C,F,D),E)) ) ) ) ) ) )).
fof(t109_funct_4,axiom,( ! [A] : ! [B] : ! [C] : k9_xtuple_0(k1_funct_4(k7_funcop_1(C,B),k16_funcop_1(C,A))) = k1_ordinal1(C) )).
fof(t109_funct_7,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ( v1_funct_1(k1_funct_7(k1_funct_7(B,C,k1_funct_1(B,D)),D,k1_funct_1(B,C))) & v1_funct_2(k1_funct_7(k1_funct_7(B,C,k1_funct_1(B,D)),D,k1_funct_1(B,C)),A,A) & v3_funct_2(k1_funct_7(k1_funct_7(B,C,k1_funct_1(B,D)),D,k1_funct_1(B,C)),A,A) & m1_subset_1(k1_funct_7(k1_funct_7(B,C,k1_funct_1(B,D)),D,k1_funct_1(B,C)),k1_zfmisc_1(k2_zfmisc_1(A,A))) ) ) ) ) )).
fof(t109_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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) ) )).
fof(t109_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( 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)) ) ) ) )).
fof(t109_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t109_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => r2_hidden(B,k9_group_3(A,B)) ) ) )).
fof(t109_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v8_group_9(C,A,B) & m2_finseq_1(C,k6_group_9(A,B)) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ~ ( r2_hidden(E,k4_finseq_1(k20_group_9(A,B,C))) & ! [F] : ( ( ~ 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) ) ) ) ) ) ) ) ) )).
fof(t109_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(k17_euclid(B),k5_numbers) & ~ r1_xxreal_0(A,k7_xcmplx_0(k18_euclid(B),k12_euclid(B))) & ~ r1_xxreal_0(k17_euclid(C),k5_numbers) & ~ r1_xxreal_0(A,k7_xcmplx_0(k18_euclid(C),k12_euclid(C))) & ~ r1_xxreal_0(k7_xcmplx_0(k18_euclid(C),k12_euclid(C)),k7_xcmplx_0(k18_euclid(B),k12_euclid(B))) & ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) & ? [E] : ( 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(k7_xcmplx_0(k18_euclid(E),k12_euclid(E)),k7_xcmplx_0(k18_euclid(D),k12_euclid(D))) ) ) ) ) ) ) )).
fof(t109_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t109_jordan2c,axiom,( ! [A] : ( ( v2_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(t109_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v3_limfunc1(A) & k4_limfunc1(A) = k5_numbers & ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,B) & r2_hidden(C,k1_relset_1(k1_numbers,A)) & k1_funct_1(A,C) != k5_numbers ) ) ) => ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & r2_hidden(C,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k3_limfunc1(B))) & ~ r1_xxreal_0(k1_funct_1(A,C),k5_numbers) ) ) | v5_limfunc1(k6_rfunct_1(k1_numbers,k1_numbers,A)) ) ) ) )).
fof(t109_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( v2_membered(C) => k12_member_1(k14_member_1(A,B),C) = k14_member_1(k12_member_1(A,C),B) ) ) ) )).
fof(t109_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ~ ( r1_mesfunc5(A,B,C,D) & r1_mesfunc5(A,B,C,E) & ! [F] : ( 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,k6_numbers,D,F)),k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,E,F))) ) ) ) ) ) ) ) ) )).
fof(t109_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ! [D] : ( ( 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,k4_normsp_0(u1_struct_0(A),B,D)) ) ) ) ) ) )).
fof(t109_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) )).
fof(t109_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k10_xtuple_0(k5_relat_1(B,A)) = k7_relat_1(B,A) ) )).
fof(t109_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => k21_rvsum_1(k13_rvsum_1(A,B)) = k1_square_1(k21_rvsum_1(B)) ) ) )).
fof(t109_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ( ( r1_xxreal_0(k5_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) ) ) ) ) ) ) ) )).
fof(t109_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v6_scmyciel(A) ) => ( r1_xxreal_0(2,k8_scmyciel(A)) => ! [B] : ( ( 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)) ) ) ) )).
fof(t109_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => ! [D] : ( m2_finseq_2(D,k2_numbers,k12_seq_4(A)) => ( r2_hidden(D,k21_seq_4(A,C,B)) <=> ~ r1_xxreal_0(B,k20_seq_4(k17_seq_4(A,C,D))) ) ) ) ) ) )).
fof(t109_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) )).
fof(t109_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) => k6_xcmplx_0(k4_sin_cos6(k4_xcmplx_0(A)),k2_sin_cos6(A)) = k7_xcmplx_0(k28_sin_cos,2) ) ) )).
fof(t109_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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),k7_xcmplx_0(A,2))))) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => ( k1_funct_1(C,F) = k7_xcmplx_0(F,A) & ~ r1_xxreal_0(k1_funct_1(C,F),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(C,F)) ) ) ) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => k1_funct_1(D,F) = 1 ) ) & E = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k1_taylor_1(2)) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => k1_funct_1(C,F) = k7_xcmplx_0(F,A) ) ) ) => ( A = k5_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),k7_xcmplx_0(A,2))),B) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => k1_funct_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),k7_xcmplx_0(A,2))),B),F) = k1_funct_1(k1_sin_cos9,k7_xcmplx_0(F,A)) ) ) ) ) ) ) ) ) ) ) )).
fof(t109_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,1) & ~ r1_xxreal_0(k3_square_1(2),A) & ~ ( ~ r1_xxreal_0(k5_sincos10(A),k5_numbers) & ~ r1_xxreal_0(k7_xcmplx_0(k28_sin_cos,4),k5_sincos10(A)) ) ) ) )).
fof(t109_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v3_tdlat_2(B,A) => ! [C] : ( 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) ) ) ) ) ) ) ) )).
fof(t109_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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))))) ) ) ) )).
fof(t109_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(B,A) => r1_tarski(k4_xboole_0(B,C),A) ) )).
fof(t109_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k6_xboolean(k6_xboolean(A,k6_xboolean(B,C)),k6_xboolean(k6_xboolean(A,B),k6_xboolean(A,C))) = k2_xboolean ) ) ) )).
fof(t109_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( B != k5_numbers => A = k3_xcmplx_0(k3_xcmplx_0(A,k7_xcmplx_0(1,B)),B) ) ) ) )).
fof(t109_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(k3_xcmplx_0(C,B),k3_xcmplx_0(A,D)) & r1_xxreal_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,D)) ) ) ) ) ) )).
fof(t109_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( r1_xxreal_0(C,A) & r1_xxreal_0(C,D) & r1_tarski(k1_xxreal_1(C,D),k4_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t109_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t109_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( k2_zfmisc_1(A,C) = k2_zfmisc_1(B,D) => ( A = k1_xboole_0 | C = k1_xboole_0 | ( A = B & C = D ) ) ) )).
fof(t109_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_zmodul01(B) & m1_zmodul01(B,A) ) => k7_zmodul01(A,k4_zmodul01(A),B) = B ) ) )).
fof(t10_abcmiz_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l2_abcmiz_0(A) ) => ( v9_abcmiz_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t10_abcmiz_1,axiom,( ! [A] : k1_abcmiz_1(k3_tarski(A)) = k3_tarski(a_1_0_abcmiz_1(A)) )).
fof(t10_abcmiz_a,axiom,( ! [A] : ( ( 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)) ) )).
fof(t10_abian,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) => ! [D] : ( m1_subset_1(D,B) => k3_funct_2(B,B,k1_abian(B,C,k1_nat_1(A,1)),D) = k3_funct_2(B,B,C,k3_funct_2(B,B,k1_abian(B,C,A),D)) ) ) ) ) )).
fof(t10_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(k7_xcmplx_0(A,B),k5_numbers) => k3_square_1(k7_xcmplx_0(A,B)) = k7_xcmplx_0(k3_square_1(k9_complex1(A)),k3_square_1(k9_complex1(B))) ) ) ) )).
fof(t10_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r1_aff_1(A,B,C,E) & r1_aff_1(A,B,C,D) & r1_aff_1(A,E,D,F) ) => ( E = D | r1_aff_1(A,B,C,F) ) ) ) ) ) ) ) ) )).
fof(t10_aff_2,axiom,( ! [A] : ( ( ~ 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) ) ) ) )).
fof(t10_aff_3,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v4_aff_3(A) => v6_aff_3(A) ) ) )).
fof(t10_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) => ( ( r2_hidden(B,F) & r2_hidden(C,G) & r2_hidden(E,G) & B = D ) => ( ( ~ r5_aff_1(A,F,G) & ~ r5_aff_1(A,G,F) ) | F = G | ( ~ r2_analoaf(A,B,C,D,E) & ~ r2_analoaf(A,C,B,E,D) ) | C = E ) ) ) ) ) ) ) ) ) )).
fof(t10_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(t10_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => k2_afinsq_2(A,k5_numbers) = A ) )).
fof(t10_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_aff_4(B,A) => ! [C] : ( r2_hidden(C,k6_afproj(A,B)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & C = D & v1_aff_4(D,A) & r1_aff_4(A,B,D) ) ) ) ) ) )).
fof(t10_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( ( r2_analoaf(A,B,C,F,G) & r2_analoaf(A,D,E,C,B) & r2_analoaf(A,D,H,G,F) ) => E = H ) ) ) ) ) ) ) ) ) )).
fof(t10_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect01(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r1_afvect01(A,B,C) & r2_analoaf(A,B,C,C,D) ) => B = D ) ) ) ) ) )).
fof(t10_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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) ) ) ) ) ) )).
fof(t10_algspec1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( k9_xtuple_0(B) = A => k1_algspec1(A,B) = B ) ) )).
fof(t10_algstr_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k8_algstr_0)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k8_algstr_0)) => k6_algstr_0(k8_algstr_0,A,B) = k5_struct_0(k8_algstr_0) ) ) )).
fof(t10_algstr_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t10_altcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(E,k1_altcat_1(A,B,C)) & ? [F] : ( m1_subset_1(F,k1_altcat_1(A,C,D)) & ? [G] : ( v1_relat_1(G) & v1_funct_1(G) & ? [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t10_altcat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t10_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v7_altcat_3(C,A) & r2_altcat_3(A,B,C) ) => v7_altcat_3(B,A) ) ) ) ) )).
fof(t10_altcat_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,u1_struct_0(k7_altcat_1(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,u1_struct_0(k7_altcat_1(A))))) ) => r2_hidden(k4_card_3(C),A) ) => v4_altcat_5(k7_altcat_1(A)) ) ) )).
fof(t10_ami_2,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k3_ami_2,k4_ami_2))) => ! [B] : ( m2_subset_1(B,k1_ami_2,k2_ami_2) => ! [C] : ( v1_int_1(C) => k1_funct_1(k7_ami_2(A,B,C),B) = C ) ) ) )).
fof(t10_ami_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( A != B & k10_ami_3(A) = k10_ami_3(B) ) ) ) )).
fof(t10_ami_5,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => ~ ( k2_compos_0(u1_compos_1(k1_ami_3),A) = 4 & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_ami_3)) ) => A != k5_ami_3(B,C) ) ) ) ) )).
fof(t10_ami_6,axiom,( ! [A] : ( 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) ) ) )).
fof(t10_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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) ) ) )).
fof(t10_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t10_amistd_2,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v2_struct_0(C) & v2_memstr_0(C,A) & v3_memstr_0(C,A) & l1_extpro_1(C,A) ) => ! [D] : ( ( 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] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(C)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ! [G] : ( ( v1_relat_1(G) & v4_relat_1(G,k4_ordinal1) & v5_relat_1(G,u1_compos_1(C)) & v1_funct_1(G) & v1_partfun1(G,k4_ordinal1) ) => ( ( r1_tarski(E,F) & r1_tarski(E,G) & ! [H] : ( v7_ordinal1(H) => ( ~ 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] : ( v7_ordinal1(H) => ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ( v2_extpro_1(C,A,B) <=> v1_xboole_0(k2_amistd_4(A,B,C)) ) ) ) ) )).
fof(t10_amistd_5,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(B)) & v1_funct_1(D) & v1_finset_1(D) & ~ v2_compos_1(D,B) ) => ! [E] : ( ( 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] : ( ( 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] : ( ( v1_relat_1(G) & v4_relat_1(G,k4_ordinal1) & v5_relat_1(G,u1_compos_1(B)) & v1_funct_1(G) & v1_partfun1(G,k4_ordinal1) ) => ( r1_tarski(D,G) => ! [H] : ( v7_ordinal1(H) => r6_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r1_analmetr(A,E,F) & r2_analmetr(A,B,C,E,F) & r2_analmetr(A,B,D,E,F) ) => ( r2_analmetr(A,B,k3_rlvect_1(A,C,D),E,F) & r2_analmetr(A,B,k5_algstr_0(A,C,D),E,F) ) ) ) ) ) ) ) ) )).
fof(t10_analoaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analoaf(A,B,C,C,B) => B = C ) ) ) ) )).
fof(t10_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_analmetr(A,D,E) => k2_analort(A,D,E,k3_rlvect_1(A,B,C)) = k3_rlvect_1(A,k2_analort(A,D,E,B),k2_analort(A,D,E,C)) ) ) ) ) ) ) )).
fof(t10_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t10_anproj_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ? [C] : ( m2_funct_2(C,A,k1_numbers,k9_funct_2(A,k1_numbers)) & k3_funct_2(A,k1_numbers,C,B) = 1 & ! [D] : ( r2_hidden(D,A) => ( D = B | k1_funct_1(C,D) = k5_numbers ) ) ) ) ) )).
fof(t10_aofa_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ~ ( 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] : ( v7_ordinal1(E) => ~ ( k1_funct_1(k7_aofa_000(A,D,B),C) = k1_funct_1(k8_funct_7(A,E),C) & ~ r2_hidden(k1_funct_1(k8_funct_7(A,E),C),D) & ! [F] : ( v7_ordinal1(F) => ( ~ r1_xxreal_0(E,F) => r2_hidden(k1_funct_1(k8_funct_7(A,F),C),D) ) ) ) ) ) ) ) )).
fof(t10_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( k1_funct_1(k4_aofa_a00(A,B,C,D,E,F,G,H),D) = H & ( C != D => k1_funct_1(k4_aofa_a00(A,B,C,D,E,F,G,H),C) = G ) & ~ ( B != C & B != D & k1_funct_1(k4_aofa_a00(A,B,C,D,E,F,G,H),B) != F ) & ~ ( A != B & A != C & A != D & k1_funct_1(k4_aofa_a00(A,B,C,D,E,F,G,H),A) != E ) ) )).
fof(t10_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => k2_aofa_a01(A,D) = k7_margrel1 ) ) ) ) )).
fof(t10_aofa_i00,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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,k5_numbers),A) ) ) )).
fof(t10_armstrng,axiom,( ! [A] : ( l1_armstrng(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_armstrng(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_armstrng(A))) => ( r2_hidden(k4_tarski(B,C),k5_armstrng(A)) <=> r2_armstrng(A,B,C) ) ) ) ) )).
fof(t10_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,k1_numbers) => ( k5_arytm_0(A,B) = k5_arytm_0(C,D) => ( A = C & B = D ) ) ) ) ) ) )).
fof(t10_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ( ( r1_arytm_2(A,B) & k1_arytm_1(B,A) = k11_arytm_3 ) => A = B ) ) ) )).
fof(t10_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ~ ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( k7_arytm_2(A,C) != B & k7_arytm_2(B,C) != A ) ) ) ) )).
fof(t10_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ( ( r2_hidden(k1_xboole_0,B) & r2_arytm_3(A,B) ) => r1_ordinal1(A,B) ) ) ) )).
fof(t10_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_hidden(A,k6_asympt_0(A)) ) )).
fof(t10_autalg_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t10_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_funct_2(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_autgroup(A))) => ( B = C => k2_funct_1(B) = k2_group_1(k3_autgroup(A),C) ) ) ) ) )).
fof(t10_bagorder,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t10_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t10_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => k1_bcialg_2(A,k1_bcialg_2(A,B,C,D),C,E) = k1_bcialg_2(A,B,C,k1_nat_1(D,E)) ) ) ) ) ) )).
fof(t10_bcialg_3,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t10_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t10_bcialg_6,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( v7_ordinal1(C) => k3_bcialg_6(A,C,k2_bcialg_1(A,B)) = k3_bcialg_6(A,k4_xcmplx_0(C),B) ) ) ) )).
fof(t10_bciideal,axiom,( ! [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) ) => ( m2_bcialg_1(k5_bcialg_1(A),A) => ( v12_bcialg_1(k5_bcialg_1(A),A) & m2_bcialg_1(k5_bcialg_1(A),A) ) ) ) )).
fof(t10_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t10_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v3_funct_1(C) & r2_hidden(B,k10_xtuple_0(C)) ) => k1_bhsp_2(A,C) = B ) ) ) ) )).
fof(t10_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( m2_valued_0(C,u1_struct_0(A),B) & v1_bhsp_2(B,A) ) => k1_bhsp_2(A,C) = k1_bhsp_2(A,B) ) ) ) ) )).
fof(t10_bhsp_4,axiom,( ! [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_bhsp_1(A) & v3_bhsp_3(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_bhsp_4(B,A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & ? [F] : ( v7_ordinal1(F) & 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)))) ) ) ) ) ) ) ) ) )).
fof(t10_bhsp_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( 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] : ( ( 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] : ( 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] : ( 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),k9_binop_2) ) ) ) ) ) ) ) ) ) )).
fof(t10_bhsp_6,axiom,( ! [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_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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_bhsp_6(B,A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( ~ v1_xboole_0(D) & r1_tarski(D,B) & ! [E] : ( ( 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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(t10_binari_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k3_binari_2(k2_xcmplx_0(A,1),k9_binarith(A,1,k6_margrel1,B,k10_binarith(k6_margrel1,C))) = k6_xcmplx_0(k6_binarith(A,B),k15_funcop_1(k4_ordinal1,C,k7_margrel1,k5_numbers,k5_series_1(2,A))) ) ) ) )).
fof(t10_binari_3,axiom,( k1_binari_2(1) = k10_binarith(k6_margrel1,k8_margrel1) )).
fof(t10_binari_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k2_xcmplx_0(B,C),k6_xcmplx_0(k5_series_1(2,A),1)) => k8_binarith(A,k1_binari_3(A,B),k1_binari_3(A,C)) = k7_margrel1 ) ) ) ) )).
fof(t10_binarith,axiom,( ! [A] : ( v1_xboolean(A) => k5_xboolean(A,k8_margrel1) = k8_margrel1 ) )).
fof(t10_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t10_binop_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ( ( r3_binop_1(A,C,B) & r3_binop_1(A,D,B) ) => C = D ) ) ) ) )).
fof(t10_binop_2,axiom,( k4_binop_1(k4_ordinal1,k24_binop_2) = 1 )).
fof(t10_bintree1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dtconstr(A) & v2_dtconstr(A) & v3_bintree1(A) & l1_lang1(A) ) => ! [B] : ( m1_trees_4(B,k5_trees_3(u1_struct_0(A)),k4_dtconstr(A)) => ! [C] : ( 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] : ( m1_dtconstr(D,u1_struct_0(A),k5_trees_3(u1_struct_0(A)),k4_dtconstr(A)) & ? [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t10_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ( A = k3_finseq_2(k7_domain_1(k4_ordinal1,k5_numbers,1)) => ! [B] : ( v7_ordinal1(B) => r2_hidden(k5_euclid(B),k2_trees_2(A,B)) ) ) ) )).
fof(t10_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t10_boolmark,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m2_funct_2(B,u1_struct_0(A),k6_margrel1,k1_boolmark(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t10_bor_cant,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [E] : ( v7_ordinal1(E) => ( 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)) = k1_funct_1(k1_series_3(k8_prob_1(A,B,k2_prob_1(A,D),C)),E) ) ) ) ) ) ) )).
fof(t10_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_borsuk_1(A,B))) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & C = k4_borsuk_1(A,B,D,E) ) ) ) ) ) )).
fof(t10_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t10_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t10_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( k19_sin_cos(A) = k19_sin_cos(B) & ! [C] : ( v1_int_1(C) => ( A != k2_xcmplx_0(B,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)) & A != k2_xcmplx_0(k4_xcmplx_0(B),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)) ) ) ) ) ) )).
fof(t10_brouwer,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t10_bspace,axiom,( ! [A] : ! [B] : ( k3_bspace(A,B) = k4_struct_0(k2_bspace) <=> ~ r2_hidden(B,A) ) )).
fof(t10_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) )).
fof(t10_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t10_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t10_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t10_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t10_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t10_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(t10_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t10_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(t10_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t10_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t10_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t10_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t10_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t10_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m2_c0sp1(k7_c0sp1(A),k12_funcsdom(A)) ) )).
fof(t10_c0sp2,axiom,( ! [A] : ( l1_lopban_2(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & 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) ) ) ) ) )).
fof(t10_calcul_1,axiom,( ! [A] : ! [B] : ( ( 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(k4_ordinal1,k7_finseq_1(B,k9_finseq_1(A)))) ) ) )).
fof(t10_calcul_2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => k3_finseq_1(k14_finseq_1(k2_calcul_2(k3_finseq_1(C),k3_finseq_1(B)))) = k3_finseq_1(B) ) ) ) )).
fof(t10_cantor_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(k9_setfam_1(A)))) ) => ! [C] : ( 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)) ) ) ) )).
fof(t10_card_1,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_ordinal1(k1_card_1(A),k1_card_1(B)) ) )).
fof(t10_card_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t10_card_3,axiom,( k4_card_3(k1_xboole_0) = k1_tarski(k1_xboole_0) )).
fof(t10_card_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) ) => ! [B] : ( ( 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 ) ) ) )).
fof(t10_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_card_fil(B,A) => ! [C] : ( m2_card_fil(C,A) => ( ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ~ ( r2_hidden(D,B) & r2_hidden(D,k1_card_fil(A,B)) ) ) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ~ ( r2_hidden(D,C) & r2_hidden(D,k7_setfam_1(A,C)) ) ) ) ) ) ) )).
fof(t10_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ! [C] : ( B != C => k5_card_1(k1_card_fin(A,k5_numbers,B,C)) = 1 ) ) )).
fof(t10_card_lar,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t10_cardfin2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => k5_card_1(k2_cardfin2(A)) = k1_cardfin2(k7_xcmplx_0(k2_newton(k5_card_1(A)),k4_power)) ) )).
fof(t10_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k3_cat_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_cat_1(A,B))) => ! [E] : ( m1_subset_1(E,u4_struct_0(k3_cat_1(A,B))) => m1_cat_1(E,k3_cat_1(A,B),C,D) ) ) ) )).
fof(t10_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m3_cat_2(B,A) => ! [C] : ( 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 ) ) ) )).
fof(t10_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( 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) ) ) )).
fof(t10_cat_4,axiom,( ! [A] : ! [B] : v3_cat_4(k5_cat_4(A,B)) )).
fof(t10_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & 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) ) ) ) )).
fof(t10_catalan1,axiom,( k1_catalan1(k5_numbers) = k5_numbers )).
fof(t10_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v5_ordinal1(C) & v1_finset_1(C) ) => ( ( v1_catalan2(C) & r1_xxreal_0(B,k6_xcmplx_0(k1_nat_1(A,k1_afinsq_1(C)),k3_xcmplx_0(2,k7_afinsq_2(C)))) ) => v1_catalan2(k1_catalan2(k1_catalan2(k8_funcop_1(k4_ordinal1,A,k5_numbers),C),k8_funcop_1(k4_ordinal1,B,1))) ) ) ) ) )).
fof(t10_catalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_instalg1(A) & v2_catalg_1(A) & v3_catalg_1(A) & l1_msualg_1(A) ) => m1_catalg_1(A,k4_catalg_1(A)) ) )).
fof(t10_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ( v3_cayldick(A) & v4_normsp_0(A) & v3_normsp_0(A) & v2_normsp_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v8_rlvect_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v13_algstr_0(A) & v3_group_1(A) & v5_vectsp_1(A) & v4_vectsp_1(A) & v33_algstr_0(A) ) => ( v6_struct_0(A) | k2_cayldick(A,k4_algstr_0(A,B)) = k4_algstr_0(A,k2_cayldick(A,B)) ) ) ) ) )).
fof(t10_cayley,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t10_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t10_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_cc0sp2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_cc0sp2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_cc0sp2(A))) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(H,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k2_numbers,G,H) = k2_xcmplx_0(k3_funct_2(u1_struct_0(A),k2_numbers,E,H),k3_funct_2(u1_struct_0(A),k2_numbers,F,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( 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))) => v9_ordinal1(k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,A,B)) ) ) ) )).
fof(t10_cfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_numbers)) => ( v6_cfdiff_1(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( r2_hidden(B,A) & ! [C] : ( v1_xreal_0(C) => ~ r1_tarski(a_2_0_cfdiff_1(B,C),A) ) ) ) ) ) )).
fof(t10_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) )).
fof(t10_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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(k5_numbers)) = k8_relset_1(A,k2_numbers,B,k1_tarski(k5_numbers)) & k8_relset_1(A,k2_numbers,k31_valued_1(A,k2_numbers,B),k1_tarski(k5_numbers)) = k8_relset_1(A,k2_numbers,B,k1_tarski(k5_numbers)) ) ) ) )).
fof(t10_cgames_1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => ! [C] : ( 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)) ) ) ) )).
fof(t10_chain_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ? [B] : ( m1_subset_1(B,k1_numbers) & r2_hidden(B,A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => r1_xxreal_0(C,B) ) ) ) ) )).
fof(t10_chord,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_abian(A) ) => ( r1_xxreal_0(A,1) => A = k5_numbers ) ) )).
fof(t10_circcmb2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(A,D))) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ v2_struct_0(C) & ~ v11_struct_0(C) & v2_msafree2(C) & l1_msualg_1(C) ) => ( C = k2_circcomb(A,B) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ( r2_circcomb(A,B,D,E) => ! [F] : ( ( v4_msualg_1(F,C) & v4_msafree2(F,C) & l3_msualg_1(F,C) ) => ( F = k3_circcomb(A,B,D,E) => ! [G] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(C,F))) => ! [H] : ( 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] : ( 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) = k1_nat_1(k2_circcmb3(A,D,H),k2_circcmb3(B,E,I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v8_struct_0(B) & l1_msualg_1(B) ) => v8_struct_0(k2_circcomb(A,B)) ) ) )).
fof(t10_circled1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t10_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) => ! [D] : ( ( ~ 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)) ) ) ) ) )).
fof(t10_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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))) ) ) ) ) )).
fof(t10_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_msafree2(D,A,B) => ( r2_hidden(C,k2_msafree2(A)) => k5_circuit2(A,B,C,D) = k1_funct_1(D,C) ) ) ) ) ) )).
fof(t10_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_ckspace1(A,C,D,B) & r1_xxreal_0(E,D) ) => r1_ckspace1(A,C,E,B) ) ) ) ) ) ) )).
fof(t10_classes1,axiom,( ! [A] : ! [B] : ! [C] : ( v3_ordinal1(C) => ( r2_hidden(B,k3_classes1(A,k1_ordinal1(C))) <=> ~ ( ~ ( r1_tarski(B,k3_classes1(A,C)) & r2_hidden(B,k1_classes1(A)) ) & ! [D] : ~ ( r2_hidden(D,k3_classes1(A,C)) & ( r1_tarski(B,D) | B = k9_setfam_1(D) ) ) ) ) ) )).
fof(t10_classes2,axiom,( ! [A] : k2_ordinal1(k1_classes1(A)) = k1_card_1(k1_classes1(A)) )).
fof(t10_clopban1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t10_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(k6_clopban1(A,A)),k8_clopban1(A,A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(k6_clopban1(A,A)),k8_clopban1(A,A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t10_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v9_clvect_1(B,A) => ( ! [D] : ( v7_ordinal1(D) => ~ r2_funct_2(k4_ordinal1,u1_struct_0(A),B,k1_valued_0(u1_struct_0(A),C,D)) ) | v9_clvect_1(C,A) ) ) ) ) ) )).
fof(t10_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_pboole(C,A,B) => ! [D] : ( 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))) ) ) ) ) )).
fof(t10_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_closure2(C,A,B,k2_closure2(A,B)) => ! [D] : ( m1_closure2(D,A,B,k2_closure2(A,B)) => r2_hidden(k2_pboole(A,C,D),k2_closure2(A,B)) ) ) ) )).
fof(t10_closure3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t10_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t10_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v3_funct_1(C) & r2_hidden(B,k10_xtuple_0(C)) ) => k1_clvect_2(A,C) = B ) ) ) ) )).
fof(t10_clvect_3,axiom,( ! [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) & v2_csspace(A) & v4_clvect_2(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clvect_3(B,A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(D,E) & r1_xxreal_0(D,F) & r1_xxreal_0(C,k13_csspace(A,k5_algstr_0(A,k1_normsp_0(A,k1_bhsp_4(A,B),E),k1_normsp_0(A,k1_bhsp_4(A,B),F)))) ) ) ) ) ) ) ) ) )).
fof(t10_coh_sp,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ( r2_hidden(k3_tarski(A),A) => A = k9_setfam_1(k3_tarski(A)) ) ) )).
fof(t10_cohsp_1,axiom,( ! [A] : ! [B] : v1_cohsp_1(k1_enumset1(A,B,k2_xboole_0(A,B))) )).
fof(t10_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(B,k1_collsp(A,B,C)) & r2_hidden(C,k1_collsp(A,B,C)) ) ) ) ) )).
fof(t10_combgras,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ( r1_ordinal1(k1_nat_1(A,1),k1_card_1(B)) => ( r1_xxreal_0(A,k5_numbers) | ! [C] : ( m1_subset_1(C,u1_incsp_1(k1_combgras(A,B))) => ! [D] : ( m1_subset_1(D,u2_incsp_1(k1_combgras(A,B))) => ( r1_incsp_1(k1_combgras(A,B),C,D) <=> r1_tarski(C,D) ) ) ) ) ) ) ) )).
fof(t10_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => k3_complex1(k3_xcmplx_0(A,k7_complex1)) = k5_numbers ) )).
fof(t10_complex2,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( k17_sin_cos(A) = k5_numbers & k19_sin_cos(A) = k5_numbers ) ) )).
fof(t10_complfld,axiom,( ! [A] : ( 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) ) )).
fof(t10_complsp2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k2_numbers) => ! [D] : ( 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) = k4_xcmplx_0(C) ) ) ) ) ) )).
fof(t10_compos_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_compos_0(A) & v2_compos_0(A) ) => ! [B] : ( m1_subset_1(B,A) => ( k5_xtuple_0(B) = k1_xboole_0 => k3_compos_0(A,k2_compos_0(A,B)) = k6_domain_1(k4_ordinal1,k5_numbers) ) ) ) )).
fof(t10_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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)))) ) ) ) )).
fof(t10_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) ) ) )).
fof(t10_comptrig,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k1_rcomp_1(k28_sin_cos,k3_xcmplx_0(2,k28_sin_cos))) => r1_xxreal_0(k1_funct_1(k16_sin_cos,A),k5_numbers) ) ) )).
fof(t10_compts_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t10_comput_1,axiom,( ! [A] : ( ( v4_funct_1(A) & v1_comput_1(A) ) <=> ( v1_relat_1(k3_tarski(A)) & v1_funct_1(k3_tarski(A)) ) ) )).
fof(t10_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,C,k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)),k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,C,A),k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,C,B))) ) ) ) )).
fof(t10_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( v1_xcmplx_0(B) => ( ! [C] : ( v7_ordinal1(C) => k9_nat_1(k2_numbers,A,C) = B ) => k3_comseq_2(A) = B ) ) ) )).
fof(t10_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v2_comseq_2(A) & v2_comseq_2(B) & k3_comseq_2(k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)) = k5_complex1 ) => k3_comseq_2(A) = k3_comseq_2(B) ) ) ) )).
fof(t10_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t10_conmetr1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v2_aff_2(A) <=> v6_conmetr1(A) ) ) )).
fof(t10_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_connsp_1(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t10_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_pre_topc(A,B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k1_pre_topc(A,B)))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t10_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t10_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( B = k1_xboole_0 => v1_convex1(B,A) ) ) ) )).
fof(t10_convex2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(t10_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t10_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t10_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => r2_qc_lang2(A,B,k6_cqc_lang(A,B)) ) ) )).
fof(t10_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t10_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t10_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t10_csspace,axiom,( ! [A] : ( 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 ) )).
fof(t10_csspace2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v1_comseq_3(A) & ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(k5_numbers,k1_funct_1(k7_comseq_3(A),B)) & k1_funct_1(k8_comseq_3(A),B) = k5_numbers ) ) ) => k9_complex1(k11_comseq_3(A)) = k4_series_1(k55_valued_1(k4_ordinal1,k2_numbers,A)) ) ) )).
fof(t10_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k5_csspace4(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_csspace4(A,B))) => ! [E] : ( ( 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] : ( ( 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] : ( v1_xcmplx_0(G) => ( D = k1_clvect_1(k5_csspace4(A,B),C,G) <=> ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_decomp_1,axiom,( ! [A] : ( ( 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) ) )).
fof(t10_descip_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v1_int_1(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t10_dickson,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(t10_diff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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] : ( ( 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_funct_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,C),k26_valued_1(k1_numbers,k1_numbers,G,D)),B),k1_nat_1(A,1)),E) = k2_xcmplx_0(k3_xcmplx_0(C,k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(F,B),k1_nat_1(A,1)),E)),k3_xcmplx_0(D,k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(G,B),k1_nat_1(A,1)),E))) ) ) ) ) ) ) ) )).
fof(t10_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( ( 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] : ( ( 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) = k2_xcmplx_0(k3_xcmplx_0(A,k11_diff_1(G,C,D,E,F)),k3_xcmplx_0(B,k11_diff_1(H,C,D,E,F))) ) ) ) ) ) ) ) ) )).
fof(t10_diff_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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] : ( ( 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_funct_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,C),k26_valued_1(k1_numbers,k1_numbers,G,D)),B),k2_xcmplx_0(A,1)),E) = k6_xcmplx_0(k3_xcmplx_0(C,k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(F,B),k2_xcmplx_0(A,1)),E)),k3_xcmplx_0(D,k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(G,B),k2_xcmplx_0(A,1)),E))) ) ) ) ) ) ) ) )).
fof(t10_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( 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) = k7_xcmplx_0(k3_xcmplx_0(4,k3_xcmplx_0(k17_sin_cos(k2_xcmplx_0(B,A)),k17_sin_cos(k6_xcmplx_0(B,A)))),k3_xcmplx_0(k1_square_1(k6_xcmplx_0(k19_sin_cos(k2_xcmplx_0(A,B)),k19_sin_cos(k6_xcmplx_0(A,B)))),k6_xcmplx_0(A,B))) ) ) ) )).
fof(t10_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v1_finset_1(B) & v1_dilworth(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(C,k5_card_1(B)) & ! [D] : ( ( 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 ) ) ) ) ) ) )).
fof(t10_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_diraf(A,B,B,C) & r1_diraf(A,B,C,C) ) ) ) ) )).
fof(t10_dirort,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dirort(A) & l1_analoaf(A) ) => ( v4_dirort(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,A) => k1_funct_1(k7_dist_1(A),k5_dist_1(A,B)) = k4_dist_1(A,B) ) ) )).
fof(t10_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_dist_2(D,A,B) => ! [E] : ( ( 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] : ( F = C <=> k1_funct_1(E,F) = k8_margrel1 ) => k4_dist_2(A,B,D,E) = k3_dist_1(A,D,C) ) ) ) ) ) ) )).
fof(t10_domain_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ~ v1_xboole_0(E) => ( r2_hidden(A,k4_zfmisc_1(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,B) & ? [G] : ( m1_subset_1(G,C) & ? [H] : ( m1_subset_1(H,D) & ? [I] : ( m1_subset_1(I,E) & A = k6_xtuple_0(F,G,H,I) ) ) ) ) ) ) ) ) ) )).
fof(t10_dtconstr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dtconstr(A) & v2_dtconstr(A) & l1_lang1(A) ) => ! [B] : ( m1_dtconstr(B,u1_struct_0(A),k5_trees_3(u1_struct_0(A)),k4_dtconstr(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k7_dtconstr(A)) => ~ ( k1_funct_1(B,k1_xboole_0) = C & ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t10_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( 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)) ) ) ) )).
fof(t10_e_siec,axiom,( ! [A] : ! [B] : ( 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))) ) )).
fof(t10_ec_pf_1,axiom,( ! [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] : ( ( v36_algstr_0(B) & m1_ec_pf_1(B,A) ) => ( k1_ec_pf_1(A) = k7_struct_0(B) => B = A ) ) ) )).
fof(t10_ec_pf_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t10_endalg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k6_endalg(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k6_endalg(A,B))) => ! [E] : ( m1_autalg_1(E,u1_struct_0(A),u3_msualg_1(A,B),k4_endalg(A,B)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t10_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( 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))) ) ) ) ) )).
fof(t10_entropy1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( ( v4_partfun3(B) & r1_xxreal_0(k5_numbers,A) ) => v4_partfun3(k10_rvsum_1(B,A)) ) ) ) )).
fof(t10_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k3_enumset1(A,B,C,D,E) = k2_xboole_0(k2_enumset1(A,B,C,D),k1_tarski(E)) )).
fof(t10_eqrel_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(t10_equation,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,C) => ( r1_pzfmisc1(A,B,C) => r6_pboole(A,k1_equation(A,C,D),B) ) ) ) ) )).
fof(t10_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => r1_xxreal_0(k12_euclid(k8_euclid(A,B,C)),k2_xcmplx_0(k12_euclid(B),k12_euclid(C))) ) ) ) )).
fof(t10_euclid_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v3_valued_0(B) ) => ( k3_finseq_1(A) = k3_finseq_1(B) => k1_square_1(k12_euclid(k4_rvsum_1(A,B))) = k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k12_euclid(A)),k3_xcmplx_0(2,k22_rvsum_1(B,A))),k1_square_1(k12_euclid(B))) ) ) ) )).
fof(t10_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ( ( r2_hidden(D,k2_euclid_4(A,B,C)) & r2_hidden(E,k2_euclid_4(A,B,C)) ) => r1_tarski(k2_euclid_4(A,D,E),k2_euclid_4(A,B,C)) ) ) ) ) ) ) )).
fof(t10_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => k4_algstr_0(k15_euclid(3),A) = k4_euclid_5(k4_xcmplx_0(k1_euclid_5(A)),k4_xcmplx_0(k2_euclid_5(A)),k4_xcmplx_0(k3_euclid_5(A))) ) )).
fof(t10_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( r2_hidden(D,k1_rltopsp1(k15_euclid(2),B,C)) => ( D = B | k4_euclid_3(A,B,C) = k4_euclid_3(A,B,D) ) ) ) ) ) ) )).
fof(t10_euclid_7,axiom,( 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))) )).
fof(t10_euclid_8,axiom,( k22_rvsum_1(k2_euclid_8,k2_euclid_8) = 1 )).
fof(t10_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => ( r2_hidden(C,k8_metric_1(k14_euclid(A),D,B)) => ! [E] : ( ~ r1_xxreal_0(B,k9_complex1(k1_funct_1(k8_rvsum_1(C,D),E))) & ~ r1_xxreal_0(B,k9_complex1(k6_xcmplx_0(k1_funct_1(C,E),k1_funct_1(D,E)))) ) ) ) ) ) ) )).
fof(t10_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(B)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(B)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(B)) => ~ ( k8_euclid(B,E,C) = k9_euclid(B,D,A) & E != C & A = k5_numbers ) ) ) ) ) ) )).
fof(t10_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v2_euclmetr(A) <=> v2_conmetr(A) ) ) )).
fof(t10_euler_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_int_2(A,B) => ! [C] : ( v7_ordinal1(C) => ? [D] : ( v1_int_1(D) & ? [E] : ( v1_int_1(E) & k2_xcmplx_0(k3_xcmplx_0(D,A),k3_xcmplx_0(E,B)) = C ) ) ) ) ) ) )).
fof(t10_exchsort,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( v2_exchsort(B,A) & v1_exchsort(B) ) <=> ? [C] : ( v3_ordinal1(C) & k9_xtuple_0(B) = k6_subset_1(C,A) & r1_ordinal1(A,C) ) ) ) ) )).
fof(t10_extens_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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),k2_funct_6(k15_msafree(A,B)),B) ) ) )).
fof(t10_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(B)) & v1_funct_1(D) ) => ( r1_tarski(k16_funcop_1(C,k2_compos_1(B)),D) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t10_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( ~ r1_xxreal_0(B,k3_extreal1(A)) => ( ~ r1_xxreal_0(A,k2_xxreal_3(B)) & ~ r1_xxreal_0(B,A) ) ) ) ) )).
fof(t10_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t10_facirc_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t10_fcont_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r1_fcont_1(B,A) => ( k1_funct_1(B,A) = k5_numbers | r1_fcont_1(k6_rfunct_1(k1_numbers,k1_numbers,B),A) ) ) ) ) )).
fof(t10_fcont_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t10_fcont_3,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(t10_fdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( ( 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) ) ) ) )).
fof(t10_fdiff_10,axiom,( ! [A] : ( ( 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,k18_sin_cos,k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k18_sin_cos),A),B) = k3_xcmplx_0(k1_funct_1(k16_sin_cos,k1_funct_1(k18_sin_cos,B)),k1_funct_1(k16_sin_cos,B)) ) ) ) ) )).
fof(t10_fdiff_11,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(1),1)) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k1_sin_cos9,B),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_sin_cos9),A),B) = k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(k2_xcmplx_0(1,k1_square_1(B)),k2_xcmplx_0(1,k1_square_1(k1_funct_1(k1_sin_cos9,B)))))) ) ) ) ) ) )).
fof(t10_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ~ ( k1_funct_1(C,A) != B & r1_fdiff_1(C,A) & ! [D] : ( m1_rcomp_1(D,A) => ~ ( r1_tarski(D,k1_relset_1(k1_numbers,C)) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,D) & k1_funct_1(C,E) = B ) ) ) ) ) ) ) ) )).
fof(t10_fdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( 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)) = k2_xcmplx_0(k1_fdiff_3(C,A),k1_fdiff_3(C,B)) ) ) ) ) ) )).
fof(t10_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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,k2_xcmplx_0(A,B))))) & D = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,E,k3_taylor_1) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,C) => ( k1_funct_1(E,F) = k2_xcmplx_0(F,B) & ~ r1_xxreal_0(k1_funct_1(E,F),k5_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,k2_xcmplx_0(A,B))),C) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,C) => k1_funct_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,k2_xcmplx_0(A,B))),C),F) = k7_xcmplx_0(k6_xcmplx_0(F,A),k2_xcmplx_0(F,B)) ) ) ) ) ) ) ) ) ) )).
fof(t10_fdiff_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(C,D) = k3_xcmplx_0(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] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_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) = k3_xcmplx_0(k3_xcmplx_0(A,k3_prepower(k1_funct_1(k16_sin_cos,D),k6_xcmplx_0(A,1))),k1_funct_1(k16_sin_cos,k3_xcmplx_0(k2_xcmplx_0(A,1),D))) ) ) ) ) ) ) ) )).
fof(t10_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,C),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_rfunct_1(k1_numbers,k1_numbers,B,C),k3_taylor_1)))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => ( k1_funct_1(C,D) = D & ~ r1_xxreal_0(k1_funct_1(C,D),k5_numbers) & k1_funct_1(B,D) = k6_xcmplx_0(D,1) & ~ r1_xxreal_0(k1_funct_1(B,D),k5_numbers) ) ) ) ) => ( r2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k6_rfunct_1(k1_numbers,k1_numbers,C),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_rfunct_1(k1_numbers,k1_numbers,B,C),k3_taylor_1)),A) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_1(k2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k6_rfunct_1(k1_numbers,k1_numbers,C),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_rfunct_1(k1_numbers,k1_numbers,B,C),k3_taylor_1)),A),D) = k7_xcmplx_0(1,k3_xcmplx_0(k1_square_1(D),k6_xcmplx_0(D,1))) ) ) ) ) ) ) ) )).
fof(t10_fdiff_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos6,k1_taylor_1(A)),B) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos6,k1_taylor_1(A)),B),C) = k7_xcmplx_0(k3_xcmplx_0(A,k3_prepower(k1_funct_1(k1_sin_cos6,C),k6_xcmplx_0(A,1))),k3_square_1(k6_xcmplx_0(1,k1_square_1(C)))) ) ) ) ) ) ) )).
fof(t10_fdiff_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( 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,C)),k26_sin_cos))) & F = k1_taylor_1(2) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,D) => k1_funct_1(E,G) = k2_xcmplx_0(A,k3_xcmplx_0(B,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,C)),k26_sin_cos),D) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,D) => k1_funct_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,C)),k26_sin_cos),D),G) = k7_xcmplx_0(k2_xcmplx_0(B,k3_xcmplx_0(k3_xcmplx_0(2,C),G)),k1_square_1(k1_funct_1(k18_sin_cos,k2_xcmplx_0(k2_xcmplx_0(A,k3_xcmplx_0(B,G)),k3_xcmplx_0(C,k1_square_1(G)))))) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_fdiff_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( 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,C)),k1_fdiff_9))) & F = k1_taylor_1(2) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,D) => k1_funct_1(E,G) = k2_xcmplx_0(A,k3_xcmplx_0(B,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,C)),k1_fdiff_9),D) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,D) => k1_funct_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,C)),k1_fdiff_9),D),G) = k7_xcmplx_0(k3_xcmplx_0(k2_xcmplx_0(B,k3_xcmplx_0(k3_xcmplx_0(2,C),G)),k1_funct_1(k16_sin_cos,k2_xcmplx_0(k2_xcmplx_0(A,k3_xcmplx_0(B,G)),k3_xcmplx_0(C,k1_square_1(G))))),k1_square_1(k1_funct_1(k18_sin_cos,k2_xcmplx_0(k2_xcmplx_0(A,k3_xcmplx_0(B,G)),k3_xcmplx_0(C,k1_square_1(G)))))) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_ff_siec,axiom,( ! [A] : ( ( 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)))) ) ) )).
fof(t10_fib_num,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( k9_nat_1(k1_numbers,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B),C) = k6_real_1(k9_nat_1(k1_numbers,A,C),k9_nat_1(k1_numbers,B,C)) & k9_nat_1(k1_numbers,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B),C) = k4_real_1(k9_nat_1(k1_numbers,A,C),k2_real_1(k9_nat_1(k1_numbers,B,C))) ) ) ) ) )).
fof(t10_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_xreal_0(B) ) => k3_xcmplx_0(k2_power(B,A),k2_power(B,k4_xcmplx_0(A))) = 1 ) ) )).
fof(t10_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(B,A) => ( v1_abian(B) | r1_xxreal_0(k2_power(k2_fib_num,B),k2_power(k2_fib_num,A)) ) ) ) ) )).
fof(t10_filerec1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m2_finseq_1(E,D) => ( E = k11_finseq_1(A,B,C) => ( r2_hidden(A,D) & r2_hidden(B,D) & r2_hidden(C,D) ) ) ) ) )).
fof(t10_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t10_filter_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m2_filter_1(C,A,B) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t10_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t10_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t10_finance1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( v1_xreal_0(C) => r1_finance1(A,k1_numbers,B,k12_prob_1,k7_funcop_1(A,C)) ) ) ) )).
fof(t10_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => k2_finseq_1(A) = k7_subset_1(k4_ordinal1,k2_finseq_1(k1_nat_1(A,1)),k1_tarski(k1_nat_1(A,1))) ) )).
fof(t10_finseq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(A)) => r2_hidden(k1_funct_1(A,C),B) ) ) => m2_finseq_1(A,B) ) ) )).
fof(t10_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(k2_xcmplx_0(A,B),k2_finseq_1(A)) => B = k5_numbers ) ) ) )).
fof(t10_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r2_finseq_4(A,B) => k9_relat_1(A,k1_finseq_4(A,B)) = k1_tarski(B) ) ) )).
fof(t10_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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)))) ) ) ) ) )).
fof(t10_finseq_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => r1_tarski(A,k7_finseq_1(A,B)) ) ) )).
fof(t10_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,k3_finseq_1(B)) ) => ( E = D | k7_partfun1(A,k1_finseq_7(A,B,D,C),E) = k7_partfun1(A,B,E) ) ) ) ) ) ) ) )).
fof(t10_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => r1_xxreal_0(k3_finseq_1(k4_finseq_8(A,B,C)),k3_finseq_1(B)) ) ) ) )).
fof(t10_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( ( 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] : ( ( v3_card_1(H,F) & m2_finseq_1(H,A) ) => ! [I] : ( ( v3_card_1(I,F) & m2_finseq_1(I,B) ) => r2_relset_1(k4_ordinal1,C,k1_finseqop(A,B,C,G,k8_finseq_1(A,H,k12_finseq_1(A,D)),k8_finseq_1(B,I,k12_finseq_1(B,E))),k8_finseq_1(C,k1_finseqop(A,B,C,G,H,I),k12_finseq_1(C,k2_binop_1(A,B,C,G,D,E)))) ) ) ) ) ) ) ) ) ) )).
fof(t10_finset_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_finset_1(k9_xtuple_0(A)) <=> v1_finset_1(A) ) ) )).
fof(t10_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t10_finsub_1,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_tarski(k5_finsub_1(A),k5_finsub_1(B)) ) )).
fof(t10_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k8_fin_topo(A,C)) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k3_fintopo2(A,B,D) = k8_margrel1 => k1_fintopo2(A,B,D,C) = k8_margrel1 ) ) ) ) ) ) )).
fof(t10_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t10_fintopo4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t10_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t10_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k3_catalan2(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( k1_afinsq_1(B) = k2_xcmplx_0(C,D) & ! [E] : ( m1_subset_1(E,k3_catalan2(A)) => ! [F] : ( m1_subset_1(F,k3_catalan2(A)) => ~ ( k1_afinsq_1(E) = C & k1_afinsq_1(F) = D & B = k1_flang_1(A,E,F) ) ) ) ) ) ) ) )).
fof(t10_flang_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( k7_flang_1(A,C,D) = k1_tarski(B) & k7_flang_1(A,C,E) = k1_tarski(B) ) => ( D = E | B = k2_flang_1(A) ) ) ) ) ) )).
fof(t10_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k2_flang_1(A),k1_flang_3(A,B,C)) <=> ( C = k5_numbers | r2_hidden(k2_flang_1(A),B) ) ) ) ) )).
fof(t10_fomodel0,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( v8_ordinal1(B) => k4_finseq_2(B,A) = k1_tarski(k1_xboole_0) ) ) )).
fof(t10_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k6_subset_1(k5_fomodel1(A),k16_fomodel1(A)) = k3_fomodel1(A) ) )).
fof(t10_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v12_fomodel1(k32_fomodel1(A),A) ) )).
fof(t10_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( v4_fomodel1(C,B) & m1_subset_1(C,k1_fomodel1(B)) ) => ! [D] : ( ( 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] : ( m2_subset_1(E,k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0)),k35_fomodel1(B)) => ( k29_fomodel2(B,k37_fomodel3(B,C,E,D)) = k29_fomodel2(B,D) & ! [F] : ( m2_subset_1(F,k9_funct_2(k37_fomodel1(B),k3_rfunct_3(k3_finseq_2(A),k2_xboole_0(A,k6_margrel1))),k15_fomodel2(B,A)) => k25_fomodel2(B,A,F,k37_fomodel3(B,C,E,D)) = k25_fomodel2(B,A,k34_fomodel2(B,A,F,C,k3_funct_2(k35_fomodel1(B),A,k9_fomodel2(B,A,F),E)),D) ) ) ) ) ) ) ) )).
fof(t10_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C))))) => ! [E] : ( 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) & v9_fomodel4(B,C,D,A) ) => ( ( ~ v7_fomodel4(D,C) & ~ v7_fomodel4(E,C) ) | v9_fomodel4(B,C,E,A) ) ) ) ) ) )).
fof(t10_frechet,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ( A = k4_ordinal1 => v4_pre_topc(A,k3_topmetr) ) ) )).
fof(t10_friends1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_2(B) & v3_relat_2(B) & v1_finset_1(B) & v3_friends1(B) ) => ~ ( ~ v2_friends1(B) & r2_hidden(A,k1_relat_1(B)) & r1_xxreal_0(k5_card_1(k9_relat_1(B,A)),2) ) ) )).
fof(t10_fscirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t10_fscirc_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(A,B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => k4_fscirc_2(k1_nat_1(B,1),A,C,D) = k1_fscirc_1(k1_funct_1(C,k1_nat_1(B,1)),k1_funct_1(D,k1_nat_1(B,1)),k3_fscirc_2(B,C,D)) ) ) ) ) ) )).
fof(t10_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( ~ v2_struct_0(D) & l3_fsm_1(D,A,B) ) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t10_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => v2_fsm_2(u2_fsm_1(A,B),A,B) ) ) )).
fof(t10_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => ! [C] : ( 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] : ( m1_subset_1(D,k8_afinsq_1(A)) => ( k1_flang_1(A,B,D) != C & k1_flang_1(A,D,B) != C ) ) ) ) ) ) ) )).
fof(t10_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ( E != k4_tarski(k10_finseq_1(D,k12_gfacirc1(A,B,C)),k2_twoscomp) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t10_funcop_1,axiom,( ! [A] : ( 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 ) )).
fof(t10_funcsdom,axiom,( ! [A] : ! [B] : ( 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) ) )).
fof(t10_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( ! [D] : ( 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] : ( 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) ) ) ) ) )).
fof(t10_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ! [D] : ~ ( r2_hidden(D,B) & ! [E] : ~ ( r2_hidden(E,A) & D = k1_funct_1(C,E) ) ) => k2_relset_1(B,C) = B ) ) )).
fof(t10_funct_3,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(t10_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(t10_funct_5,axiom,( ! [A] : ( k9_xtuple_0(A) = k1_xboole_0 <=> k10_xtuple_0(A) = k1_xboole_0 ) )).
fof(t10_funct_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) ) ) )).
fof(t10_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t10_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t10_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t10_functor0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(t10_functor1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l1_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_altcat_2(C) & l1_altcat_1(C) ) => ! [D] : ( ( v8_functor0(D,A,B) & l2_functor0(D,A,B) ) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t10_functor2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ( ( r2_functor2(A,B,C,D) & r2_functor2(A,B,D,E) ) => ! [F] : ( m2_functor2(F,A,B,C,D) => ! [G] : ( m2_functor2(G,A,B,D,E) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t10_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ! [F] : ( ( v15_functor0(F,B,C) & m2_functor0(F,B,C) ) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t10_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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))) ) ) ) ) )).
fof(t10_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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)) ) ) ) )).
fof(t10_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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(k1_fuzzy_4(B,A,C),k1_fuzzy_4(B,A,D)) ) ) ) ) ) )).
fof(t10_fvaluat1,axiom,( ! [A] : ( v1_fvaluat1(A) => ! [B] : ( v1_fvaluat1(B) => ( ~ r1_xxreal_0(B,A) => r1_xxreal_0(k1_xxreal_3(A,1),B) ) ) ) )).
fof(t10_fvsum_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t10_gate_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(k5_gate_1(A,B)) <=> ( ~ ( ~ v1_xboole_0(A) & v1_xboole_0(B) ) & ~ ( ~ v1_xboole_0(B) & v1_xboole_0(A) ) ) ) )).
fof(t10_gcd_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_gcd_1(A,B,k5_struct_0(A)) = B ) ) )).
fof(t10_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v2_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( m1_genealg1(D,C) => ! [E] : ( m1_genealg1(E,C) => ( r1_xxreal_0(k3_finseq_1(D),B) => k8_genealg1(C,D,E,A,B) = k7_genealg1(C,D,E,A) ) ) ) ) ) ) )).
fof(t10_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t10_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(t10_gfacirc2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(A,B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t10_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( 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),k4_ordinal1) & 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)) ) ) ) ) )).
fof(t10_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( 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))) ) ) ) ) ) )).
fof(t10_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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)) ) ) )).
fof(t10_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) & v1_glib_003(B) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t10_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ! [C] : ( ( 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_funct_1(k5_glib_003(A),B)) ) ) ) )).
fof(t10_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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] : ( m1_subset_1(C,k6_glib_000(A)) => r2_hidden(C,k1_relset_1(k6_glib_000(A),k6_glib_005(A,B,C))) ) ) ) )).
fof(t10_goboard1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( k1_matrix_0(C) = k1_nat_1(A,1) & r2_hidden(B,k2_finseq_1(A)) ) => ( r1_xxreal_0(A,k5_numbers) | ( k8_matrix_0(u1_struct_0(k15_euclid(2)),k16_matrix_0(1,u1_struct_0(k15_euclid(2)),C),B) = k8_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(B,1)) & r2_hidden(B,k2_finseq_1(k1_matrix_0(k16_matrix_0(1,u1_struct_0(k15_euclid(2)),C)))) & r2_hidden(k1_nat_1(B,1),k2_finseq_1(k1_matrix_0(C))) ) ) ) ) ) ) )).
fof(t10_goboard2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ~ ( A != k1_xboole_0 & k2_goboard1(A) = k1_xboole_0 ) ) )).
fof(t10_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( v1_goboard1(B) & r1_xxreal_0(1,A) & r1_xxreal_0(A,k1_matrix_0(B)) ) => ( v3_relat_1(B) | k1_goboard5(B,k5_numbers) = a_2_9_goboard5(A,B) ) ) ) ) )).
fof(t10_goboard6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(2))) => ( ( E = k19_euclid(A,B) & r1_xxreal_0(k5_numbers,D) ) => ( r1_xxreal_0(C,D) | r2_hidden(k19_euclid(A,k6_xcmplx_0(B,D)),k8_metric_1(k14_euclid(2),E,C)) ) ) ) ) ) ) ) )).
fof(t10_goboard7,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( v7_ordinal1(B) => ~ ( v1_sppol_1(k2_topreal1(2,A,B)) & ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(k2_goboard2(A))) & ! [D] : ( 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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,C)) ) ) ) ) ) ) ) )).
fof(t10_goboard8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,2),k3_finseq_1(A)) ) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,2),k3_finseq_1(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_matrix_0(k2_goboard2(A))) ) => ( ( ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,k1_matrix_0(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k7_nat_d(k1_matrix_0(k2_goboard2(A)),1)) ) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,k1_matrix_0(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k7_nat_d(k1_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k7_nat_d(k1_matrix_0(k2_goboard2(A)),1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,2),k1_matrix_0(k2_goboard2(A)))),k7_xcmplx_0(1,2)),k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_matrix_0(k2_goboard2(A))),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,2),k1_matrix_0(k2_goboard2(A)))),k7_xcmplx_0(1,2)),k19_euclid(k5_numbers,1))),k3_topreal1(2,A)) ) ) ) ) ) ) )).
fof(t10_goboard9,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k3_finseq_1(A)) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(C,k3_finseq_1(k2_goboard2(A))) & r1_xxreal_0(D,k1_matrix_0(k2_goboard2(A))) & k3_goboard5(k2_goboard2(A),C,D) = k5_goboard5(A,B) ) ) ) ) ) ) )).
fof(t10_gobrd11,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t10_gobrd12,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t10_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [F] : ( ( ~ v3_relat_1(F) & v1_matrix_0(F) & v1_goboard1(F) & v2_goboard1(F) & v3_goboard1(F) & v4_goboard1(F) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_tarski(k9_matrix_0(E),k9_matrix_0(F)) & r2_hidden(k4_tarski(A,C),k2_matrix_0(E)) & r2_hidden(k4_tarski(B,D),k2_matrix_0(F)) & k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),F,B,D) ) => r1_tarski(k3_goboard5(F,B,D),k3_goboard5(E,A,C)) ) ) ) ) ) ) ) )).
fof(t10_gobrd14,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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_0(k1_jordan8(D,C))) & r2_hidden(k4_tarski(k1_nat_1(A,1),B),k2_matrix_0(k1_jordan8(D,C))) ) => k1_topreal6(2,k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(D,C),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(D,C),k1_nat_1(A,1),B)) = k7_xcmplx_0(k6_xcmplx_0(k8_pscomp_1(D),k6_pscomp_1(D)),k1_newton(2,C)) ) ) ) ) ) )).
fof(t10_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( ( v1_henmodel(D,A) & m1_subset_1(D,k1_zfmisc_1(k3_cqc_lang(A))) ) => ! [E] : ( m1_henmodel(E,A,D) => ( r1_valuat_1(A,k1_henmodel(A),k12_cqc_lang(A,C,B),E,k3_henmodel(A)) <=> ? [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t10_gr_cy_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v8_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k2_group_1(B,k5_group_1(B,A,C)) = k5_group_1(B,k6_xcmplx_0(k7_group_1(B),k4_nat_d(A,k7_group_1(B))),C) ) ) ) )).
fof(t10_gr_cy_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v2_struct_0(C) & v8_struct_0(C) & v2_group_1(C) & v3_group_1(C) & l3_algstr_0(C) ) => ! [D] : ( 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,B,D)))) = k7_group_1(k5_group_4(C,k6_domain_1(u1_struct_0(C),k5_group_1(C,A,D)))) & r1_struct_0(k5_group_4(C,k6_domain_1(u1_struct_0(C),k5_group_1(C,B,D))),k5_group_1(C,A,D)) ) => r1_group_2(C,k5_group_4(C,k6_domain_1(u1_struct_0(C),k5_group_1(C,B,D))),k5_group_4(C,k6_domain_1(u1_struct_0(C),k5_group_1(C,A,D)))) ) ) ) ) ) )).
fof(t10_gr_cy_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_gr_cy_3(A) ) => ? [B] : ( v7_ordinal1(B) & v1_int_2(B) & v2_gr_cy_3(B) & A = k1_nat_1(k3_xcmplx_0(2,B),1) ) ) )).
fof(t10_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_graph_1(C) ) => ( r1_graph_1(A,B,C) => r1_graph_1(A,C,B) ) ) ) ) )).
fof(t10_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( 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,k1_nat_1(B,1),C)),k1_graph_2(A,k1_nat_1(C,1),k3_finseq_1(A))) = A ) ) ) ) )).
fof(t10_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v2_funct_1(C) & v1_msscyc_1(C,A) & m2_graph_1(C,A) ) => ~ ( r2_hidden(B,k4_finseq_1(C)) & ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t10_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( ( 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 ) ) ) ) ) ) )).
fof(t10_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v7_graph_1(B,A) & m2_graph_1(B,A) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t10_graphsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ! [E] : ( ( 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 ) ) ) ) )).
fof(t10_grcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t10_grfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( r1_tarski(B,A) & v2_funct_1(A) ) => v2_funct_1(B) ) ) ) )).
fof(t10_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ( m1_group_6(C,A,B) => r1_tarski(k5_group_5(A,B,C),k8_group_2(A,B)) ) ) ) ) )).
fof(t10_groeb_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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))) ) ) ) ) )).
fof(t10_groeb_2,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t10_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [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) & v1_vectsp_2(B) & v1_algstr_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( ( 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(k3_polynom1(k15_pre_poly(A),B,C)) = k5_card_1(k3_polynom1(k15_pre_poly(A),B,k10_polynom1(A,B,D,C))) ) ) ) ) )).
fof(t10_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( k2_group_1(A,B) = k1_group_1(A) => B = k1_group_1(A) ) ) ) )).
fof(t10_group_10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ? [C] : ( v15_algstr_0(C) & m1_group_2(C,A) & r3_group_10(B,A,C) ) ) ) )).
fof(t10_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( v1_group_3(C,A) & m1_group_2(C,A) ) => ! [D] : ( ( v1_group_3(D,A) & m1_group_2(D,A) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t10_group_12,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k2_group_7(k2_finseq_1(A),B))) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k2_group_7(k2_finseq_1(A),B))) => ! [E] : ( m2_finseq_1(E,u1_struct_0(k2_group_7(k2_finseq_1(A),B))) => ( ( k3_finseq_1(D) = A & ! [F] : ( m2_subset_1(F,k4_ordinal1,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] : ( m2_subset_1(F,k4_ordinal1,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 ) ) ) ) ) ) )).
fof(t10_group_14,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v1_prvect_1(A) ) => ! [B] : ( ( ~ 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] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k4_prvect_3(k20_prvect_1(A),B)),u1_struct_0(k20_prvect_1(k7_finseq_1(A,k9_finseq_1(B))))) & v13_vectsp_1(C,k4_prvect_3(k20_prvect_1(A),B),k20_prvect_1(k7_finseq_1(A,k9_finseq_1(B)))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_prvect_3(k20_prvect_1(A),B)),u1_struct_0(k20_prvect_1(k7_finseq_1(A,k9_finseq_1(B))))))) & v3_funct_2(C,u1_struct_0(k4_prvect_3(k20_prvect_1(A),B)),u1_struct_0(k20_prvect_1(k7_finseq_1(A,k9_finseq_1(B))))) & ! [D] : ( m1_subset_1(D,u1_struct_0(k20_prvect_1(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ? [F] : ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) & ? [G] : ( 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) ) ) ) ) ) ) ) )).
fof(t10_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t10_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t10_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t10_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_group_5(A,k6_finseq_1(u1_struct_0(A)),B) = k1_xboole_0 ) ) )).
fof(t10_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => v7_struct_0(k6_group_2(A)) ) )).
fof(t10_group_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ~ v4_group_1(B,A) => ! [C] : ( v1_int_1(C) => k5_group_1(A,C,B) = k5_group_1(A,k5_int_1(C,k6_group_1(A,B)),B) ) ) ) ) )).
fof(t10_group_9,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(t10_groupp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t10_grsolv_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v15_algstr_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t10_hahnban,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t10_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t10_hallmar1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t10_hausdorf,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) ) => ? [B] : ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) & A = B & k3_weierstr(A) = k3_seq_4(B) ) ) )).
fof(t10_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k3_finseq_1(k8_glib_001(A,B,C,D)),k3_finseq_1(B)) ) ) ) ) )).
fof(t10_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t10_hermitan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ( k4_complex1(A) = k5_numbers => ( k3_complex1(k8_group_1(k1_complfld,A,B)) = k4_real_1(k3_complex1(A),k3_complex1(B)) & k4_complex1(k8_group_1(k1_complfld,A,B)) = k4_real_1(k3_complex1(A),k4_complex1(B)) ) ) ) ) )).
fof(t10_hessenbe,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t10_heyting1,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(t10_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( 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) ) ) ) )).
fof(t10_heyting3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( m1_subset_1(E,k5_finsub_1(k4_partfun1(A,C))) => ! [F] : ( 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) ) ) ) )).
fof(t10_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(A,B) => k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k16_sin_cos,B),3),A) = k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k18_sin_cos),A) ) ) ) )).
fof(t10_hilbasis,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ( k2_hilbasis(A,B) = k2_hilbasis(A,C) => B = C ) ) ) ) )).
fof(t10_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_hilbert1)) => ( r1_tarski(A,B) => r1_tarski(k5_hilbert1(A),k5_hilbert1(B)) ) ) ) )).
fof(t10_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => r1_xxreal_0(1,k3_finseq_1(A)) ) )).
fof(t10_hilbert3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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))) ) ) )).
fof(t10_holder_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(B) & ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,B,D)) ) & ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k2_power(k9_nat_1(k1_numbers,B,D),A) ) ) => ( v2_comseq_2(C) & k1_seq_2(C) = k2_power(k1_seq_2(B),A) ) ) ) ) ) ) )).
fof(t10_hurwitz,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k5_vfunct_1(k4_ordinal1,A,k5_vfunct_1(k4_ordinal1,A,B)),B) ) ) )).
fof(t10_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => k1_binari_3(A,k5_numbers) = k1_idea_1(A) ) )).
fof(t10_ideal_1,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(t10_incproj,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k3_incproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k3_incproj(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k3_incproj(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( B = E & C = F & D = G ) => ( r1_collsp(A,E,F,G) <=> ? [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_incsp_1,axiom,( ! [A] : ( l2_incsp_1(A) => ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_incsp_1(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t10_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ~ v1_xboole_0(k2_cat_1(A,C,D)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t10_instalg1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_instalg1(B,A) => ( r1_tarski(u1_struct_0(B),u1_struct_0(A)) & r1_tarski(u4_struct_0(B),u4_struct_0(A)) ) ) ) )).
fof(t10_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( k3_xcmplx_0(A,B) = k4_xcmplx_0(1) <=> ( ( A = k4_xcmplx_0(1) & B = 1 ) | ( A = 1 & B = k4_xcmplx_0(1) ) ) ) ) ) )).
fof(t10_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( 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)) ) ) ) ) )).
fof(t10_int_3,axiom,( 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)) )).
fof(t10_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t10_int_5,axiom,( r1_int_5(1,2) )).
fof(t10_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ~ ( r2_hidden(B,k4_finseq_1(A)) & ! [C] : ( v1_int_1(C) => k3_xcmplx_0(C,k1_funct_1(A,B)) != k19_rvsum_1(A) ) ) ) ) )).
fof(t10_int_7,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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) ) => k22_pre_poly(A,k5_nat_3(A,B,C)) = k9_subset_1(A,k22_pre_poly(A,B),k22_pre_poly(A,C)) ) ) )).
fof(t10_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r1_int_2(C,D) => ( r1_xxreal_0(D,1) | ( r2_int_1(k1_newton(C,A),k1_newton(C,B),D) <=> r2_int_1(A,B,k3_pepin(C,D)) ) ) ) ) ) ) ) )).
fof(t10_integr10,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( 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) = k2_xcmplx_0(k4_integr10(A,C),k4_integr10(B,C)) ) ) ) ) ) )).
fof(t10_integr11,axiom,( 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,k5_numbers),k3_sin_cos2),k1_sin_cos2),k1_numbers) & ! [A] : ( v1_xreal_0(A) => k1_funct_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,k5_numbers),k3_sin_cos2),k1_sin_cos2),k1_numbers),A) = k3_xcmplx_0(A,k1_funct_1(k1_sin_cos2,A)) ) )).
fof(t10_integr12,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k18_sin_cos,k22_sin_cos),k16_sin_cos)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k22_sin_cos)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k22_sin_cos)),k3_seq_4(A))) ) ) ) ) )).
fof(t10_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k18_sin_cos,k22_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,k18_sin_cos),k22_sin_cos),k7_xcmplx_0(1,2)))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_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,k18_sin_cos),k22_sin_cos),k7_xcmplx_0(1,2)),k2_seq_4(A)),k1_funct_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,k18_sin_cos),k22_sin_cos),k7_xcmplx_0(1,2)),k3_seq_4(A))) ) ) ) ) )).
fof(t10_integr14,axiom,( ! [A] : ( ( 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,k27_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,k27_sin_cos,k1_fdiff_9)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k1_fdiff_9)),A),B) = k7_xcmplx_0(k7_xcmplx_0(k1_funct_1(k16_sin_cos,k1_funct_1(k27_sin_cos,B)),k1_square_1(k1_funct_1(k16_sin_cos,B))),k1_square_1(k1_funct_1(k18_sin_cos,k1_funct_1(k27_sin_cos,B)))) ) ) ) ) ) )).
fof(t10_integr15,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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_comseq_2(B) => ( v3_integra1(B,A) <=> ? [C] : ( v1_xreal_0(C) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_integra1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) ) => ! [E] : ( m2_integr15(E,A,B,D) => ( ( v2_comseq_2(k2_integra3(A,D)) & k1_seq_2(k2_integra3(A,D)) = k5_numbers ) => ( v2_comseq_2(k3_integr15(A,B,D,E)) & k1_seq_2(k3_integr15(A,B,D,E)) = C ) ) ) ) ) ) ) ) ) )).
fof(t10_integr16,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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] : ( m1_integra1(C,A) => ! [D] : ( m1_integr16(D,A,B,C) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t10_integr18,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,u1_struct_0(C)))) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t10_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ( ( r1_xxreal_0(B,D) & r1_xxreal_0(D,E) & r1_xxreal_0(E,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)) ) => ( r1_integr15(A,k3_integra5(D,E),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(D,E)),A) ) ) ) ) ) ) ) ) ) )).
fof(t10_integra1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t10_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( ( v4_xxreal_2(B) & r1_xxreal_0(A,k5_numbers) ) => v3_xxreal_2(k1_integra2(B,A)) ) ) ) )).
fof(t10_integra3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( m1_integra1(C,B) => ! [D] : ( m1_integra1(D,B) => ! [E] : ( ( 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(k6_xcmplx_0(k18_rvsum_1(k5_integra1(B,E,D)),k18_rvsum_1(k5_integra1(B,E,C))),k3_xcmplx_0(k6_xcmplx_0(k2_seq_4(k1_rvsum_1(E)),k3_seq_4(k1_rvsum_1(E))),k1_integra3(B,C))) ) ) ) ) ) ) )).
fof(t10_integra4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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_comseq_2(k2_partfun1(A,k1_numbers,B,A)) => ( v1_integra1(B,A) & v2_integra1(B,A) ) ) ) ) )).
fof(t10_integra5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t10_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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)) = k3_xcmplx_0(C,k4_integra5(A,B,D)) ) ) ) ) ) )).
fof(t10_integra7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ! [D] : ( ( 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_funct_1(D,B) = k2_xcmplx_0(k4_integra5(A,B,k2_fdiff_1(D,C)),k1_funct_1(D,A)) ) ) ) ) )).
fof(t10_integra8,axiom,( k2_sin_cos6(k7_xcmplx_0(k3_square_1(2),2)) = k7_xcmplx_0(k28_sin_cos,4) )).
fof(t10_integra9,axiom,( ! [A] : ( ( 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),k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k18_sin_cos),A),B) = k6_xcmplx_0(k1_funct_1(k18_sin_cos,B),k3_xcmplx_0(B,k1_funct_1(k16_sin_cos,B))) ) ) ) ) )).
fof(t10_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => m1_interva1(k1_tarski(B),A) ) ) )).
fof(t10_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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)) ) ) ) ) )).
fof(t10_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => k1_funct_1(k2_irrat_1(k5_numbers),A) = 1 ) )).
fof(t10_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t10_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( k2_cat_1(k6_cat_2(A,B),k7_cat_2(A,B,C,E),k7_cat_2(A,B,D,F)) != k1_xboole_0 => ! [G] : ( m1_subset_1(G,u4_struct_0(A)) => ! [H] : ( m1_subset_1(H,u4_struct_0(B)) => ( m1_cat_1(k8_cat_2(A,B,G,H),k6_cat_2(A,B),k7_cat_2(A,B,C,E),k7_cat_2(A,B,D,F)) <=> ( m1_cat_1(G,A,C,D) & m1_cat_1(H,B,E,F) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) ) ) )).
fof(t10_jct_misc,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => r1_xxreal_0(k5_numbers,k1_jct_misc(A,B)) ) ) )).
fof(t10_jgraph_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( 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))) ) ) ) ) )).
fof(t10_jgraph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t10_jgraph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) != k5_numbers ) & ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( 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(G,k3_square_1(k2_xcmplx_0(1,k1_square_1(k7_xcmplx_0(F,G))))) ) ) ) ) & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).
fof(t10_jgraph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( v5_pre_topc(B,A,k3_topmetr) & v5_pre_topc(C,A,k3_topmetr) & E != k5_numbers & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,F) != k5_numbers ) & ! [F] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( v1_xreal_0(H) => ! [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) = k3_xcmplx_0(I,k3_square_1(k9_complex1(k6_xcmplx_0(1,k1_square_1(k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(H,I),D),E)))))) ) ) ) ) & v5_pre_topc(F,A,k3_topmetr) ) ) ) ) ) ) ) ) )).
fof(t10_jgraph_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k4_algstr_0(k15_euclid(A),k4_struct_0(k15_euclid(A))) = k4_struct_0(k15_euclid(A)) ) )).
fof(t10_jgraph_6,axiom,( k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k1_jgraph_3,k19_euclid(k4_xcmplx_0(1),k5_numbers)) = k19_euclid(k4_xcmplx_0(1),k5_numbers) )).
fof(t10_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t10_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t10_jordan10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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(k2_jordan9(B,A))) ) ) )).
fof(t10_jordan11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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(k5_jordan11(B,A),1)),B) ) ) ) )).
fof(t10_jordan12,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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))) ) ) )).
fof(t10_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( r1_jordan1h(A,B) => r1_xboole_0(A,k3_goboard9(k1_jordan13(A,B))) ) ) ) )).
fof(t10_jordan16,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t10_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ( r1_jordan17(A,B,C,D,E) => r1_jordan17(A,C,D,E,B) ) ) ) ) ) ) )).
fof(t10_jordan18,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => k3_seq_4(k7_relset_1(u1_struct_0(k15_euclid(2)),k1_numbers,k4_pscomp_1,k5_topreal1(A))) = k17_euclid(A) ) )).
fof(t10_jordan19,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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,k2_jordan9(B,A)))) ) ) )).
fof(t10_jordan1a,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( r1_tarski(B,k6_jordan6(A)) => v2_sppol_1(B) ) ) ) )).
fof(t10_jordan1b,axiom,( ! [A] : ( ( ~ v1_zfmisc_1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( 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)) ) ) )).
fof(t10_jordan1c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( 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] : ( v1_int_1(D) => ~ ( r2_hidden(B,k1_jordan2c(2,C)) & D = k1_int_1(k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k17_euclid(B),k6_pscomp_1(C)),k6_xcmplx_0(k8_pscomp_1(C),k6_pscomp_1(C))),k1_newton(2,A)),2)) & r1_xxreal_0(D,1) ) ) ) ) ) )).
fof(t10_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & ~ r1_xxreal_0(k3_finseq_1(k2_jordan9(B,A)),C) & r2_hidden(k23_pscomp_1(B),k4_goboard5(k2_jordan9(B,A),C)) ) ) ) )).
fof(t10_jordan1e,axiom,( ! [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] : ( v7_ordinal1(B) => k1_nat_1(k3_finseq_1(k1_jordan1e(A,B)),k3_finseq_1(k2_jordan1e(A,B))) = k1_nat_1(k3_finseq_1(k2_jordan9(A,B)),1) ) ) )).
fof(t10_jordan1f,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => r1_goboard1(u1_struct_0(k15_euclid(2)),k1_jordan1e(A,B),k1_jordan8(A,B)) ) ) )).
fof(t10_jordan1g,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t10_jordan1h,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => r2_relset_1(k4_ordinal1,k1_numbers,k1_goboard1(A),k1_partfun1(k4_ordinal1,u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k1_numbers,A,k4_pscomp_1)) ) )).
fof(t10_jordan1i,axiom,( ! [A] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(t10_jordan1j,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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)))) ) => ( r2_hidden(k22_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))),k10_xtuple_0(k2_jordan1e(B,A))) & r2_hidden(k22_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))),k3_topreal1(2,k2_jordan1e(B,A))) ) ) ) )).
fof(t10_jordan1k,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ 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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r2_hidden(E,C) => r1_xxreal_0(A,k3_metric_1(B,D,E)) ) ) => r1_xxreal_0(A,k1_funct_1(k6_weierstr(B,C),D)) ) ) ) ) ) )).
fof(t10_jordan20,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ~ ( 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) ) ) ) ) ) ) )).
fof(t10_jordan21,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => r1_xboole_0(k2_jordan2c(2,A),A) ) )).
fof(t10_jordan22,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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(D,C) & r2_hidden(k4_tarski(A,B),k2_matrix_0(k1_jordan8(E,C))) & r2_hidden(k4_tarski(k1_nat_1(A,1),B),k2_matrix_0(k1_jordan8(E,C))) & r1_xxreal_0(k1_topreal6(2,k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,C),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,C),k1_nat_1(A,1),B)),k1_topreal6(2,k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,D),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,D),k1_nat_1(A,1),B))) ) ) ) ) ) ) )).
fof(t10_jordan23,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v3_jordan23(A) => v3_jordan23(k3_finseq_5(A)) ) ) )).
fof(t10_jordan24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) ) )).
fof(t10_jordan2b,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( v1_xreal_0(C) => ( r2_hidden(B,k2_finseq_1(A)) => k16_rvsum_1(k1_funct_7(k5_euclid(A),B,C)) = C ) ) ) ) )).
fof(t10_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t10_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(B,k2_topreal1(2,A,1)) => k1_jordan3(A,B) = 1 ) ) ) )).
fof(t10_jordan4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( 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) ) ) ) ) ) ) )).
fof(t10_jordan5a,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t10_jordan5b,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t10_jordan5c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t10_jordan5d,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( 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_0(k2_goboard2(A))) & ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(D,k4_finseq_1(A)) & r2_hidden(k4_tarski(B,C),k2_matrix_0(k2_goboard2(A))) & k18_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),A,D)) = k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),B,C)) ) ) ) ) ) ) )).
fof(t10_jordan6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t10_jordan7,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t10_jordan8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(4,k3_finseq_1(k1_jordan8(A,B))) ) ) )).
fof(t10_jordan9,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r1_goboard1(u1_struct_0(k15_euclid(2)),B,A) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(B)) ) => ( v1_convex1(k1_tops_1(k15_euclid(2),k3_gobrd13(B,A,C)),k15_euclid(2)) & v1_convex1(k1_tops_1(k15_euclid(2),k2_gobrd13(B,A,C)),k15_euclid(2)) ) ) ) ) ) ) )).
fof(t10_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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)) ) ) ) )).
fof(t10_knaster,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t10_kolmog01,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [E] : ( 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] : ( m1_prob_1(F,A,B) => ! [G] : ( m1_prob_1(G,A,B) => ( ( r2_hidden(F,D) & r2_hidden(G,E) ) => r1_prob_2(A,B,C,F,G) ) ) ) ) => ! [F] : ( m1_prob_1(F,A,B) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t10_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ! [E] : ( v7_ordinal1(E) => k1_funct_1(D,E) = k3_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) => k3_kurato_0(A,D) = k9_subset_1(A,k3_kurato_0(A,B),k3_kurato_0(A,C)) ) ) ) ) )).
fof(t10_kurato_1,axiom,( k2_pre_topc(k3_topmetr,k6_kurato_1) = k4_subset_1(k1_numbers,k1_seq_4(1),k3_rcomp_1(2,k1_xxreal_0)) )).
fof(t10_kurato_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k14_euclid(A))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k14_euclid(A))) => ~ ( ~ r1_xboole_0(k8_metric_1(k14_euclid(A),E,B),k8_metric_1(k14_euclid(A),G,D)) & ~ r1_xboole_0(k8_metric_1(k14_euclid(A),G,D),k8_metric_1(k14_euclid(A),F,C)) & r1_xxreal_0(k2_xcmplx_0(k2_xcmplx_0(B,C),k3_xcmplx_0(2,D)),k3_metric_1(k14_euclid(A),E,F)) ) ) ) ) ) ) ) ) )).
fof(t10_lang1,axiom,( ! [A] : k1_lang1(k6_lang1(A)) = k1_xboole_0 )).
fof(t10_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)))) ) ) ) ) )).
fof(t10_latsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( r2_hidden(C,u1_struct_0(A)) => m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B))) ) ) ) )).
fof(t10_lattice2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( m1_subset_1(E,k5_finsub_1(A)) => ( ! [F] : ( m1_subset_1(F,A) => ( r2_hidden(F,E) => k1_funct_1(D,F) = k1_funct_1(C,F) ) ) => k7_funct_4(A,B,C,k2_partfun1(A,B,D,E)) = C ) ) ) ) ) )).
fof(t10_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_lattice3(A) <=> v2_lattice3(k7_lattice3(A)) ) ) )).
fof(t10_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_lattice4(A,k2_setwiseo(u1_struct_0(A),B)) = B ) ) )).
fof(t10_lattice5,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k1_lattice5(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_lattice5(A))) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t10_lattice6,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t10_lattice7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r2_hidden(B,k3_lattice7(A)) <=> ( B != k3_yellow_0(A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( B = k13_lattice3(A,C,D) & B != C & B != D ) ) ) ) ) ) ) )).
fof(t10_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t10_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( k4_lattices(A,D,B) = k4_lattices(A,D,C) & k3_lattices(A,D,B) = k3_lattices(A,D,C) ) => B = C ) ) ) ) ) )).
fof(t10_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & v2_lexbfs(A) & v3_lexbfs(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t10_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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,k1_fuzzy_4(A,A,k2_lfuzzy_1(k2_zfmisc_1(A,A),B,C)),k2_lfuzzy_1(k2_zfmisc_1(A,A),B,C)) ) ) ) ) )).
fof(t10_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_limfunc1(A) & v1_limfunc1(B) ) => v1_limfunc1(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) ) ) )).
fof(t10_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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)) ) ) ) )).
fof(t10_lmod_5,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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) ) ) )).
fof(t10_lmod_6,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m1_vectsp_4(D,B,C) => ( r2_hidden(A,k2_lmod_6(B,C,D,k2_struct_0(D))) <=> r1_struct_0(D,A) ) ) ) ) )).
fof(t10_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_vectsp_4(E,A,B) => ( r2_hidden(D,k3_vectsp_4(A,B,C,E)) <=> r1_struct_0(E,k5_algstr_0(B,C,D)) ) ) ) ) ) ) )).
fof(t10_lopban_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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))) ) ) ) )).
fof(t10_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(k8_lopban_1(A,A)),k10_lopban_1(A,A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(k8_lopban_1(A,A)),k10_lopban_1(A,A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t10_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_normsp_1(B,A) => ( ! [D] : ( v7_ordinal1(D) => ~ r2_funct_2(k4_ordinal1,u1_struct_0(A),B,k1_valued_0(u1_struct_0(A),C,D)) ) | v3_normsp_1(C,A) ) ) ) ) ) )).
fof(t10_lopban_6,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_normsp_2(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t10_lopban_7,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( ( m1_rlsub_1(A,B) & u1_struct_0(A) = C & u1_normsp_0(A) = k2_partfun1(u1_struct_0(B),k1_numbers,u1_normsp_0(B),u1_struct_0(A)) & v2_nfcont_1(C,B) ) => v3_lopban_1(A) ) ) ) ) )).
fof(t10_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k6_lopclset(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k6_lopclset(A))) => k3_lattices(k6_lopclset(A),B,C) = k2_xboole_0(B,C) ) ) ) )).
fof(t10_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_normsp_1(B) ) => ( B = g1_normsp_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)),k3_lp_space(A)) => ( u1_struct_0(B) = k2_lp_space(A) & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) <=> ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_series_1(k1_lp_space(k2_rsspace(C),A)) ) ) & k4_struct_0(B) = k5_rsspace & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => C = k2_rsspace(C) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k1_rlvect_1(B,D,C) = k26_valued_1(k4_ordinal1,k1_numbers,k2_rsspace(D),C) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( k4_algstr_0(B,C) = k32_valued_1(k4_ordinal1,k1_numbers,k2_rsspace(C)) & r2_funct_2(k4_ordinal1,k1_numbers,k2_rsspace(k4_algstr_0(B,C)),k32_valued_1(k4_ordinal1,k1_numbers,k2_rsspace(C))) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k5_algstr_0(B,C,D) = k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k2_rsspace(C),k2_rsspace(D)) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => v1_series_1(k1_lp_space(k2_rsspace(C),A)) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k2_normsp_0(B,C) = k2_power(k4_series_1(k1_lp_space(k2_rsspace(C),A)),k7_xcmplx_0(1,A)) ) ) ) ) ) ) )).
fof(t10_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_rfunct_3(B,A,k2_numbers,k3_rfunct_3(A,k2_numbers)) => k1_binop_1(k9_lpspacc1(A),B,k1_binop_1(k8_lpspacc1(A),k4_xcmplx_0(k6_complex1),B)) = k2_partfun1(A,k2_numbers,k10_lpspacc1(A),k1_relset_1(A,B)) ) ) )).
fof(t10_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_rfunct_3(B,A,k1_numbers,k3_rfunct_3(A,k1_numbers)) => ! [C] : ( 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)) ) ) ) )).
fof(t10_lpspace2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(C,B) => ( r1_xxreal_0(k3_extreal1(k5_real_1(k9_nat_1(k1_numbers,k3_series_1(A),B),k9_nat_1(k1_numbers,k3_series_1(A),C))),k5_real_1(k9_nat_1(k1_numbers,k3_series_1(k56_valued_1(k4_ordinal1,k1_numbers,A)),B),k9_nat_1(k1_numbers,k3_series_1(k56_valued_1(k4_ordinal1,k1_numbers,A)),C))) & r1_xxreal_0(k3_extreal1(k5_real_1(k9_nat_1(k1_numbers,k3_series_1(A),B),k9_nat_1(k1_numbers,k3_series_1(A),C))),k9_nat_1(k1_numbers,k3_series_1(k56_valued_1(k4_ordinal1,k1_numbers,A)),B)) ) ) ) ) ) )).
fof(t10_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => ( k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(C),k1_domain_1(k4_ordinal1,k1_hilbert1,B,k6_ltlaxio1(A))) = 1 <=> ! [D] : ( m1_subset_1(D,k4_ordinal1) => k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(C),k1_domain_1(k4_ordinal1,k1_hilbert1,k1_nat_1(B,D),A)) = 1 ) ) ) ) ) )).
fof(t10_ltlaxio2,axiom,( k7_partfun1(k1_hilbert1,k2_ltlaxio2(k6_finseq_1(k1_hilbert1)),k3_finseq_1(k2_ltlaxio2(k6_finseq_1(k1_hilbert1)))) = k3_ltlaxio1 )).
fof(t10_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( m1_subset_1(D,k1_hilbert1) => ~ ( r2_hidden(k4_hilbert1(C,D),k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,k4_ltlaxio1(A,B))) & ~ r2_hidden(k4_hilbert1(C,D),k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,A)) & ~ r2_hidden(k4_hilbert1(C,D),k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,B)) ) ) ) ) ) )).
fof(t10_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)))) => k3_ltlaxio4(k4_subset_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)),A,B)) = k4_subset_1(k1_hilbert1,k3_ltlaxio4(A),k3_ltlaxio4(B)) ) ) )).
fof(t10_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t10_margrel1,axiom,( ! [A] : ( 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 ) ) ) )).
fof(t10_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(C,D) => ( r1_tarski(k3_mathmorp(A,B,D),k3_mathmorp(A,B,C)) & r1_tarski(k6_rusub_4(A,B,C),k6_rusub_4(A,B,D)) ) ) ) ) ) ) )).
fof(t10_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( v4_matrix10(B) & v1_matrix10(C) ) => v1_matrix10(k4_matrix10(A,B,C)) ) ) ) ) )).
fof(t10_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_matrix_2(B,k3_matrix_2(k1_nat_1(A,2))) => ! [C] : ( m1_matrix_2(C,k3_matrix_2(k1_nat_1(A,2))) => ! [D] : ( m1_matrix_2(D,k3_matrix_2(k1_nat_1(A,2))) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [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(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),D,k1_partfun1(k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),C,B)) & v4_matrix_2(C,k2_matrix_2(k3_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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [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] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(E),C,D) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(E))) ) => k1_matrix12(C,D,E,F,B,A) = k1_matrix12(C,D,E,F,A,B) ) ) ) ) ) ) )).
fof(t10_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => k1_card_1(k2_sgraph1(k2_finseq_1(A))) = k4_newton(2,A) ) )).
fof(t10_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t10_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ! [E] : ( ( v1_finset_1(E) & v1_setfam_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ( r1_tarski(k2_zfmisc_1(C,E),k2_matrix_0(B)) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ~ ( r2_hidden(F,k7_subset_1(k4_ordinal1,k4_finseq_1(B),C)) & r2_hidden(G,k7_subset_1(k4_ordinal1,k2_finseq_1(k1_matrix_0(B)),D)) & k3_matrix_0(u1_struct_0(A),B,F,G) != k4_struct_0(A) & r1_tarski(D,E) & k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,u1_struct_0(A),k5_matrix13(E),k7_matrix_0(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))) ) ) ) ) ) ) ) ) ) )).
fof(t10_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(B),A,A) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(B))) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(B),A,A) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(B))) ) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(B),A,A) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(B))) ) => ( ( 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_3(B,k3_matrix_3(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)) ) ) ) ) ) ) ) ) ) )).
fof(t10_matrix17,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t10_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ( v1_matrix_0(k5_finseq_2(k4_finseq_2(A,C),B,k5_finseq_2(C,A,D))) & v2_matrix_0(k5_finseq_2(k4_finseq_2(A,C),B,k5_finseq_2(C,A,D)),C,B,A) & m2_finseq_1(k5_finseq_2(k4_finseq_2(A,C),B,k5_finseq_2(C,A,D)),k3_finseq_2(C)) ) ) ) ) ) )).
fof(t10_matrix_2,axiom,( ! [A] : ( v7_ordinal1(A) => v5_matrix_2(k6_partfun1(k2_finseq_1(A)),A) ) )).
fof(t10_matrix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k4_tarski(C,D),k2_matrix_0(k3_matrix_1(B,A))) => ( C = D | k1_funct_1(k8_matrix_0(u1_struct_0(B),k3_matrix_1(B,A),D),C) = k4_struct_0(B) ) ) ) ) ) ) )).
fof(t10_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) & k1_matrix_4(A,C,B) = C ) => B = k1_matrix_3(A,k3_finseq_1(B),k1_matrix_0(B)) ) ) ) ) )).
fof(t10_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => k7_matrix_5(1,A) = A ) )).
fof(t10_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => k4_matrix_0(u1_struct_0(B),k3_matrix_1(B,A)) = k3_matrix_1(B,A) ) ) )).
fof(t10_matrix_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k4_matrix_2(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_matrix_2(2))) => ~ ( ? [C] : ( m1_matrix_2(C,k3_matrix_2(2)) & C = A & v4_matrix_2(C,k2_matrix_2(k3_matrix_2(2))) ) & ? [C] : ( m1_matrix_2(C,k3_matrix_2(2)) & C = B & v4_matrix_2(C,k2_matrix_2(k3_matrix_2(2))) ) & k6_algstr_0(k4_matrix_2(2),A,B) != k10_finseq_1(1,2) ) ) ) )).
fof(t10_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_6(C,A,B) & v1_matrix_8(C,A,B) ) => C = k3_matrix_1(B,A) ) ) ) ) )).
fof(t10_matrix_9,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_matrix_2(F,k3_matrix_2(2)) => ( F = k3_finseq_5(k1_finseq_2(2)) => k10_matrix_3(2,A,k15_matrix_0(u1_struct_0(A),B,C,D,E),F) = k2_finseq_4(u1_struct_0(A),C,D) ) ) ) ) ) ) ) )).
fof(t10_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => k7_matrix_5(k4_xcmplx_0(1),A) = k4_matrix_5(A) ) )).
fof(t10_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( ( r2_hidden(A,k4_finseq_1(C)) & r2_hidden(B,k2_finseq_1(k7_partfun1(k4_ordinal1,C,A))) ) => ( r2_hidden(k1_nat_1(B,k2_wsierp_1(k17_finseq_1(k4_ordinal1,k7_nat_d(A,1),C))),k2_finseq_1(k2_wsierp_1(k17_finseq_1(k4_ordinal1,A,C)))) & k1_matrixj1(C,k1_nat_1(B,k2_wsierp_1(k17_finseq_1(k4_ordinal1,k7_nat_d(A,1),C)))) = A ) ) ) ) ) )).
fof(t10_matrixj2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => m1_matrixj2(k1_xboole_0,A,B) ) ) )).
fof(t10_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( 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 ) ) ) )).
fof(t10_matrixr2,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k4_tarski(B,C),k2_matrix_0(A)) => k3_matrix_0(k1_numbers,k4_matrixr1(A),B,C) = k1_real_1(k3_matrix_0(k1_numbers,A,B,C)) ) ) ) ) )).
fof(t10_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(B)) => ( ( k3_finseq_1(D) = k3_finseq_1(E) & ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t10_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t10_matroid0,axiom,( ! [A] : ( v4_taxonom2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_matroid0(A)))) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ( ! [D] : ( r2_hidden(D,B) => r2_hidden(D,k1_funct_1(C,D)) ) => ( v3_pre_topc(B,k2_matroid0(A)) <=> v2_funct_1(C) ) ) ) ) ) )).
fof(t10_matrprob,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) <=> ? [C] : ( v7_ordinal1(C) & ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(D,k4_finseq_1(B)) & ! [E] : ( m2_finseq_1(E,A) => ~ ( k1_funct_1(B,D) = E & k3_finseq_1(E) = C ) ) ) ) ) ) ) )).
fof(t10_matrtop1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_finseq_1(B) & v1_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) & v1_valued_0(C) ) => ! [D] : ( ( 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)))) ) ) ) ) )).
fof(t10_matrtop2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlvect_2(C,A) => m1_rlvect_2(k2_partfun1(u1_struct_0(A),k1_numbers,C,u1_struct_0(B)),B) ) ) ) )).
fof(t10_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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) = k1_funct_7(C,A,k4_xcmplx_0(k1_funct_1(C,A))) ) ) ) ) )).
fof(t10_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & v2_comseq_2(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k6_normsp_1(A,k2_ndiff_1(A,B,C)) = k1_rlvect_1(A,B,k1_seq_2(C)) ) ) ) )).
fof(t10_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)))) ) ) )).
fof(t10_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r2_hidden(C,k2_zfmisc_1(D,k2_tarski(A,B))) => ( r2_hidden(k1_xtuple_0(C),D) & ( k2_xtuple_0(C) = A | k2_xtuple_0(C) = B ) ) ) )).
fof(t10_measure1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( 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))) ) ) ) ) )).
fof(t10_measure2,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ( ( k9_nat_1(B,D,k5_numbers) = k9_nat_1(B,C,k5_numbers) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => k9_nat_1(B,D,k1_nat_1(F,1)) = k1_measure1(A,B,k9_nat_1(B,C,k1_nat_1(F,1)),k9_nat_1(B,D,F)) ) & k9_nat_1(B,E,k5_numbers) = k9_nat_1(B,C,k5_numbers) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => k9_nat_1(B,E,k1_nat_1(F,1)) = k3_measure1(A,B,k9_nat_1(B,C,k1_nat_1(F,1)),k9_nat_1(B,D,F)) ) ) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( ~ r1_xxreal_0(G,F) => r1_xboole_0(k9_nat_1(B,E,F),k9_nat_1(B,E,G)) ) ) ) ) ) ) ) ) )).
fof(t10_measure4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_measure4(D,C) => ( ( r2_hidden(A,k1_measure4(C,D)) & r2_hidden(B,k1_measure4(C,D)) ) => r2_hidden(k6_subset_1(A,B),k1_measure4(C,D)) ) ) )).
fof(t10_measure5,axiom,( k2_measure5(k1_xboole_0) = k1_supinf_2 )).
fof(t10_measure6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xxreal_0(B) => ( ? [C] : ( v1_xxreal_0(C) & r1_xxreal_0(B,C) & A = k1_xxreal_1(B,C) ) => B = k7_supinf_2(A) ) ) ) )).
fof(t10_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v6_supinf_2(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k4_ordinal1)) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k4_ordinal1))) ) => ( v2_funct_1(C) => r1_xxreal_0(k19_supinf_2(k1_measure7(B,k1_partfun1(B,k4_ordinal1,k4_ordinal1,k6_numbers,C,A))),k19_supinf_2(A)) ) ) ) ) ) )).
fof(t10_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => v6_supinf_2(k6_measure8(A,B,C)) ) ) )).
fof(t10_member_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k4_member_1(k2_tarski(A,B)) = k2_tarski(k2_xxreal_3(A),k2_xxreal_3(B)) ) ) )).
fof(t10_membered,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_membered(A) ) => ? [B] : ( v1_rat_1(B) & r2_hidden(B,A) ) ) )).
fof(t10_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) & v4_memstr_0(C,A,B) ) => ~ r2_hidden(k4_struct_0(B),k9_xtuple_0(C)) ) ) ) )).
fof(t10_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => k1_euclid_6(k4_struct_0(k15_euclid(2)),A,B) = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k17_euclid(A),k18_euclid(B)),k3_xcmplx_0(k17_euclid(B),k18_euclid(A))),2) ) ) )).
fof(t10_mesfun10,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [C] : ( m1_subset_1(C,k6_numbers) => ( ( r2_hidden(C,k1_numbers) & ! [D] : ( 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)) ) ) ) ) ) )).
fof(t10_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t10_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & v1_mesfunc8(B,A,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( v7_ordinal1(C) => r2_relset_1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,k5_mesfun7c(A,B),C),k3_mesfun7c(A,k8_nat_1(k4_partfun1(A,k1_numbers),B,C))) ) ) ) )).
fof(t10_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( 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)) ) ) ) )).
fof(t10_mesfunc1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,A) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_xxreal_0(k6_xcmplx_0(B,A),k2_extreal1(1,k1_nat_1(C,1))) ) ) ) ) )).
fof(t10_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( v3_valued_0(B) => v3_valued_0(k6_mesfunc1(A,B,C)) ) ) ) ) )).
fof(t10_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ! [C] : ~ ( r2_hidden(C,k1_relset_1(A,B)) & r1_xxreal_0(k12_supinf_2(B,C),k2_supinf_1) ) <=> v3_mesfunc5(B) ) ) ) )).
fof(t10_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,C))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( v1_xreal_0(F) => ( ! [G] : ( v7_ordinal1(G) => k1_funct_1(D,G) = k3_xboole_0(B,k12_mesfunc1(E,k6_xcmplx_0(F,k2_extreal1(1,k1_nat_1(G,1))))) ) => k3_xboole_0(B,k11_mesfunc1(E,F)) = k5_setfam_1(A,k4_measure1(A,C,D)) ) ) ) ) ) ) )).
fof(t10_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( m1_subset_1(C,A) => ( r2_hidden(C,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers))) => r2_funct_2(k4_ordinal1,k6_numbers,k3_mesfunc5(A,k4_mesfunc8(A,B),C),k4_rinfsup2(k3_mesfunc5(A,B,C))) ) ) ) ) )).
fof(t10_mesfunc9,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( v1_xxreal_0(B) => ( ( v10_mesfunc5(A) & ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(B,k12_supinf_2(A,C)) ) ) => r1_xxreal_0(B,k2_mesfunc5(A)) ) ) ) )).
fof(t10_metric_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => r1_xxreal_0(k5_binop_1(k1_numbers,k6_metric_1,A,B),k3_real_1(k5_binop_1(k1_numbers,k6_metric_1,A,C),k5_binop_1(k1_numbers,k6_metric_1,C,B))) ) ) ) )).
fof(t10_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,k1_metric_2(A,B)) & r2_hidden(D,k1_metric_2(A,B)) ) => k3_metric_1(A,C,D) = k5_numbers ) ) ) ) ) )).
fof(t10_metric_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))) => ( k2_binop_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,k10_metric_3(A,B),C,D) = k5_numbers <=> C = D ) ) ) ) ) )).
fof(t10_metric_6,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( v2_tbsp_1(B,A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ r1_metric_6(A,B,C) ) ) ) ) )).
fof(t10_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k1_pre_topc(A,C)))) => ( ( v5_topgen_4(B,A) & D = k9_subset_1(u1_struct_0(A),B,C) ) => v5_topgen_4(D,k1_pre_topc(A,C)) ) ) ) ) ) )).
fof(t10_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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))) ) ) )).
fof(t10_mfold_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t10_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_midsp_1(A,B,B,C,C) ) ) ) )).
fof(t10_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t10_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v2_struct_0(C) & v2_midsp_1(C) & l1_midsp_3(C,k1_nat_1(A,2)) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(C))) => ! [F] : ( m1_midsp_3(F,A) => ( F = B => k1_funct_1(k1_midsp_3(u1_struct_0(C),k1_nat_1(A,1),E,B,D),F) = D ) ) ) ) ) ) ) )).
fof(t10_mmlquer2,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => k1_relat_1(k1_mmlquer2(A,B)) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) ) ) )).
fof(t10_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [E] : ( v7_ordinal1(E) => ( r1_tarski(B,C) => ( E = k5_numbers | r1_tarski(k10_mmlquery(A,B,D,E),k4_mmlquery(A,D,C)) ) ) ) ) ) ) )).
fof(t10_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( v2_mod_2(B,A) & v3_mod_2(B,A) & l1_mod_2(B,A) ) => ? [C] : ( ~ 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] : ( ~ 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] : ( 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) ) ) ) ) ) )).
fof(t10_mod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t10_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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))) ) ) )).
fof(t10_modal_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( r2_hidden(C,A) => ! [D] : ( m1_trees_1(D,k5_trees_1(A,C,B)) => ! [E] : ( m1_trees_1(E,B) => ( D = k8_finseq_1(k4_ordinal1,C,E) => r2_wellord2(k1_trees_2(k5_trees_1(A,C,B),D),k1_trees_2(B,E)) ) ) ) ) ) ) ) )).
fof(t10_modcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_modcat_1(B,A) => ! [C] : ( m4_modcat_1(C,A,k4_modcat_1(A,B)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t10_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_1(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v2_struct_0(C) & v10_modelc_1(C) & l2_modelc_1(C) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t10_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ( v3_modelc_2(A) | v6_modelc_2(A) ) => ( k3_finseq_1(A) = k1_nat_1(1,k3_finseq_1(k10_modelc_2(A))) & ~ r1_xxreal_0(k3_finseq_1(A),k3_finseq_1(k10_modelc_2(A))) ) ) ) )).
fof(t10_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k13_modelc_2(B))) => ( r2_hidden(A,C) => k18_modelc_3(B,k7_subset_1(k13_modelc_2(B),C,k1_tarski(A))) = k6_xcmplx_0(k18_modelc_3(B,C),k3_finseq_1(A)) ) ) ) ) )).
fof(t10_moebius1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ( r1_nat_d(k1_newton(B,2),A) => r1_nat_d(B,A) ) ) ) )).
fof(t10_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v13_monoid_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & k6_algstr_0(A,B,D) = C & k6_algstr_0(A,E,B) = C ) ) ) ) ) ) )).
fof(t10_monoid_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t10_morph_01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t10_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t10_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t10_msafree3,axiom,( ! [A] : ( l1_msualg_1(A) => ! [B] : ! [C] : ( ( 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] : ( ~ ( 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 ) ) ) )).
fof(t10_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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] : ( r2_hidden(D,k5_trees_9(u1_struct_0(k5_msafree(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)) ) ) ) ) )).
fof(t10_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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] : ( m1_subset_1(D,u4_struct_0(A)) => ~ ( k1_funct_1(C,k1_xboole_0) = k4_tarski(D,u1_struct_0(A)) & ! [E] : ( m1_msaterm(E,A,B,k2_msaterm(A,B,D)) => C != k4_trees_4(k4_tarski(D,u1_struct_0(A)),E) ) ) ) ) ) ) )).
fof(t10_msscyc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v7_graph_1(B,A) & m1_graph_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( 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),k1_nat_1(C,1)) = k1_funct_1(u2_graph_1(A),k1_funct_1(B,C)) ) ) ) ) ) )).
fof(t10_mssubfam,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( B = k2_tarski(C,D) => k8_setfam_1(A,B) = k9_subset_1(A,C,D) ) ) ) ) )).
fof(t10_mssublat,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) ) ) )).
fof(t10_msualg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_finseq_1(k1_unialg_1(A)),k3_finseq_2(k1_tarski(k5_numbers))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_1(k1_unialg_1(A)),k3_finseq_2(k1_tarski(k5_numbers))))) ) => ! [C] : ( m1_subset_1(C,k1_tarski(k5_numbers)) => ( B = k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k3_finseq_2(k1_tarski(k5_numbers)),k1_unialg_1(A),k7_finseq_2(k5_numbers)) => k6_msualg_1(A) = g1_msualg_1(k1_tarski(k5_numbers),k4_finseq_1(k1_unialg_1(A)),B,k1_margrel1(k1_tarski(k5_numbers),k4_finseq_1(k1_unialg_1(A)),C)) ) ) ) ) )).
fof(t10_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_msualg_2(C,A,B) => m3_pboole(k2_msualg_2(A,B),u1_struct_0(A),u3_msualg_1(A,C)) ) ) ) )).
fof(t10_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( m2_pboole(E,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t10_msualg_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_msualg_4(C,A,B) & m1_msualg_4(C,A,B,B) ) => ! [D] : ( ( v1_msualg_4(D,A,B) & m1_msualg_4(D,A,B,B) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t10_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_msualg_6(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( 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))))) ) ) ) ) ) ) ) )).
fof(t10_msualg_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_msualg_5(A,B)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,k6_pboole(A,B,B)))) => ( D = C => ( v1_xboole_0(C) | ! [E] : ( ( v1_msualg_4(E,A,B) & m1_msualg_4(E,A,B,B) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t10_msualg_8,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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] : ( 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] : ( 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))),k3_tarski(D)) ) ) ) ) ) ) ) )).
fof(t10_msualg_9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,k1_pzfmisc1(A,B),C) => v1_msualg_3(D) ) ) ) )).
fof(t10_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t10_mycielsk,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v6_dilworth(B,A) & m1_eqrel_1(B,u1_struct_0(A)) ) => ! [C] : ( 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))) ) ) ) ) )).
fof(t10_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t10_nagata_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( ~ 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) ) ) ) )).
fof(t10_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(A,B) & ! [C] : ( v7_ordinal1(C) => B != k2_xcmplx_0(A,C) ) ) ) ) )).
fof(t10_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(A,B) => k2_power(2,B) = k3_xcmplx_0(k2_power(2,A),k2_power(2,k7_nat_d(B,A))) ) ) ) )).
fof(t10_nat_3,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => k2_nat_3(A,1) = A ) )).
fof(t10_nat_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( k6_nat_d(B,C) = 1 => ( B = k5_numbers | C = k5_numbers | k6_nat_d(k1_newton(B,A),C) = 1 ) ) ) ) ) )).
fof(t10_nat_5,axiom,( ! [A] : ! [B] : ! [C] : ( m2_finseq_1(C,k1_numbers) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ! [E] : ( m2_finseq_1(E,k1_numbers) => ( ( k2_xboole_0(A,B) = k4_finseq_1(C) & r1_xboole_0(A,B) & r2_relset_1(k4_ordinal1,k1_numbers,D,k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k1_numbers,k14_finseq_1(A),C)) & r2_relset_1(k4_ordinal1,k1_numbers,E,k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k1_numbers,k14_finseq_1(B),C)) ) => k18_rvsum_1(C) = k2_xcmplx_0(k18_rvsum_1(D),k18_rvsum_1(E)) ) ) ) ) )).
fof(t10_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_nat_d(B,C) & r1_nat_d(B,k2_xcmplx_0(C,A)) ) => r1_nat_d(B,A) ) ) ) ) )).
fof(t10_nat_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_nat_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_nat_lat)) => ! [C] : ( 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) ) ) ) ) )).
fof(t10_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t10_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) => ! [D] : ( 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] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ~ ( r2_hidden(G,k1_relset_1(u1_struct_0(B),C)) & ~ r1_xxreal_0(F,k2_normsp_0(B,k5_algstr_0(B,G,D))) & r1_xxreal_0(E,k2_normsp_0(A,k5_algstr_0(A,k7_partfun1(u1_struct_0(A),C,G),k7_partfun1(u1_struct_0(A),C,D)))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_ncfcont2,axiom,( ! [A] : ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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)) ) ) ) ) ) )).
fof(t10_ndiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,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)) ) ) ) ) )).
fof(t10_ndiff_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) ) )).
fof(t10_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => r1_ndiff_3(A,C,D) ) ) ) ) ) ) ) )).
fof(t10_ndiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(t10_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(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)) ) )).
fof(t10_neckla_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( l1_orders_2(B) => ! [C] : ( 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) ) ) ) ) ) ) )).
fof(t10_necklace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(B,C) => ( r1_xxreal_0(B,A) | r2_hidden(A,C) ) ) ) ) ) )).
fof(t10_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k2_net_1(A)) => r1_tarski(k3_net_1(A,B),k2_net_1(A)) ) ) )).
fof(t10_newton,axiom,( ! [A] : ( v7_ordinal1(A) => k1_newton(1,A) = 1 ) )).
fof(t10_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( 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] : ( m1_nfcont_1(E,B,k7_partfun1(u1_struct_0(B),C,D)) => ? [F] : ( m1_nfcont_1(F,A,D) & r1_tarski(k7_relset_1(u1_struct_0(A),u1_struct_0(B),C,F),E) ) ) ) ) ) ) ) ) )).
fof(t10_nfcont_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [C] : ( v1_xreal_0(C) => ( r1_nfcont_3(A,B,C) <=> ( r2_hidden(C,k1_relset_1(k1_numbers,B)) & ! [D] : ( m1_nfcont_1(D,A,k7_partfun1(u1_struct_0(A),B,C)) => ? [E] : ( m1_rcomp_1(E,C) & r1_tarski(k7_relset_1(k1_numbers,u1_struct_0(A),B,E),D) ) ) ) ) ) ) ) )).
fof(t10_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,u1_struct_0(k4_real_ns1(A))))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,u1_struct_0(k4_real_ns1(A))))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k1_euclid(A)))) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t10_normform,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_finsub_1(B) ) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t10_normsp_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_xxreal_0(k2_normsp_0(A,k5_algstr_0(A,B,D)),k2_xcmplx_0(k2_normsp_0(A,k5_algstr_0(A,B,C)),k2_normsp_0(A,k5_algstr_0(A,C,D)))) ) ) ) ) )).
fof(t10_normsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v8_pre_topc(A) & l1_pre_topc(A) ) => ( v6_waybel_3(A) => v2_yellow_8(A) ) ) )).
fof(t10_ntalgo_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => ! [B] : ( m1_subset_1(B,k4_numbers) => ! [C] : ( m1_subset_1(C,k4_numbers) => ( ( A = k5_int_1(B,C) & r1_int_2(B,C) ) => ( C = k5_numbers | r1_int_2(A,C) ) ) ) ) ) )).
fof(t10_numbers,axiom,( r2_xboole_0(k4_ordinal1,k2_numbers) )).
fof(t10_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t10_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t10_oposet_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v2_necklace(A) => v3_necklace(A) ) ) )).
fof(t10_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_oppcat_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_oppcat_1(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t10_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_ordeq_01(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_ordeq_01(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_ordeq_01(A,B))) => ! [F] : ( ( v1_funct_1(F) & v1_nfcont_3(F,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ! [G] : ( ( v1_funct_1(G) & v1_nfcont_3(G,B) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ! [H] : ( ( v1_funct_1(H) & v1_nfcont_3(H,B) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ( ( F = C & G = D & H = E & k1_relset_1(k1_numbers,F) = A & k1_relset_1(k1_numbers,G) = A & k1_relset_1(k1_numbers,H) = A ) => ( E = k3_rlvect_1(k2_ordeq_01(A,B),C,D) <=> ! [I] : ( m2_subset_1(I,k1_numbers,A) => k7_partfun1(u1_struct_0(B),H,I) = k3_rlvect_1(B,k7_partfun1(u1_struct_0(B),F,I),k7_partfun1(u1_struct_0(B),G,I)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_orders_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( ( r8_relat_2(C,A) & r1_tarski(B,A) ) => r8_relat_2(C,B) ) ) )).
fof(t10_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v6_orders_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t10_orders_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_orders_3(A) ) => ! [B] : ( m1_orders_3(B,A) => ! [C] : ( m1_orders_3(C,A) => r1_tarski(k1_orders_3(B,C),k1_ens_1(k2_orders_3(A))) ) ) ) )).
fof(t10_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ~ ( ~ r2_hidden(A,B) & A != B & ~ r2_hidden(B,A) ) ) ) )).
fof(t10_ordinal2,axiom,( ! [A] : r1_tarski(k3_ordinal1(A),A) )).
fof(t10_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => k2_ordinal2(k1_tarski(A)) = A ) )).
fof(t10_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( v3_ordinal1(B) => ( ( v2_ordinal2(A) & r2_hidden(B,k9_xtuple_0(A)) ) => r1_ordinal1(B,k1_funct_1(A,B)) ) ) ) )).
fof(t10_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) ) => ( ( r2_hidden(1,A) & ! [C] : ( v3_ordinal1(C) => ( r2_hidden(C,k9_xtuple_0(B)) => k1_funct_1(B,C) = k12_ordinal2(A,C) ) ) ) => v2_ordinal2(B) ) ) ) )).
fof(t10_ordinal6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t10_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => C = k4_struct_0(B) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => r1_orders_2(B,C,C) ) ) ) ) )).
fof(t10_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : 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)) ) ) ) ) ) ) ) )).
fof(t10_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t10_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t10_osalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t10_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v2_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t10_papdesaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( v1_xreal_0(G) => ( ( 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 = k5_numbers | r1_geomtrap(A,B,C,B,D) | ( F = k3_rlvect_1(A,E,k1_rlvect_1(A,k5_algstr_0(A,D,C),k5_xcmplx_0(k4_xcmplx_0(G)))) & F = k3_rlvect_1(A,B,k1_rlvect_1(A,k5_algstr_0(A,D,B),k5_xcmplx_0(k4_xcmplx_0(G)))) & k5_algstr_0(A,D,C) = k1_rlvect_1(A,k5_algstr_0(A,F,E),k4_xcmplx_0(G)) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) ) )).
fof(t10_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t10_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) )).
fof(t10_partfun2,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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 ) ) ) ) )).
fof(t10_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_partit1(A,B,C) => ( C = A | r1_partit1(A,B,k3_subset_1(A,C)) ) ) ) ) ) )).
fof(t10_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r2_diraf(A,B,C,D,E) & r2_diraf(A,B,C,F,G) & r1_diraf(A,B,D,F) & r3_diraf(A,C,E,G) ) => ( r3_diraf(A,B,D,C) | r1_diraf(A,C,E,G) ) ) ) ) ) ) ) ) ) )).
fof(t10_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t10_pcomps_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_finset_1(B) => v1_pcomps_1(B,A) ) ) ) )).
fof(t10_pcs_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v16_pcs_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k17_pcs_0(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k17_pcs_0(A,B))) => ( r1_orders_2(k17_pcs_0(A,B),C,D) <=> ? [E] : ? [F] : ( l2_pcs_0(F) & ? [G] : ( m1_subset_1(G,u1_struct_0(F)) & ? [H] : ( 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) ) ) ) ) ) ) ) )).
fof(t10_pdiff_1,axiom,( ! [A] : ( ( 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] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(1))) => ! [D] : ( v1_xreal_0(D) => ( ( A = k2_pdiff_1(B) & C = k9_finseq_1(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(k4_ordinal1,1)) = k9_finseq_1(k1_fdiff_1(B,D)) ) ) ) ) ) )).
fof(t10_pdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(2)) => ( r3_pdiff_1(2,2,A,B) <=> ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & B = k10_finseq_1(C,D) & ? [E] : ( m1_rcomp_1(E,D) & r1_tarski(E,k1_relset_1(k1_numbers,k1_pdiff_2(2,2,A,B))) & ? [F] : ( v1_funct_1(F) & v3_fdiff_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [G] : ( v1_funct_1(G) & v2_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,E) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(2,2,A,B),H),k1_funct_1(k1_pdiff_2(2,2,A,B),D)) = k2_xcmplx_0(k1_funct_1(F,k6_xcmplx_0(H,D)),k1_funct_1(G,k6_xcmplx_0(H,D))) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_pdiff_3,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(2)) => ! [B] : ( ( 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) ) ) ) )).
fof(t10_pdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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] : ( m1_rcomp_1(F,A) => ~ ( r1_tarski(F,k1_relset_1(k1_numbers,k1_pdiff_2(3,1,E,D))) & ? [G] : ( v1_funct_1(G) & v3_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [H] : ( v1_funct_1(H) & v2_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,F) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,1,E,D),I),k1_funct_1(k1_pdiff_2(3,1,E,D),A)) = k2_xcmplx_0(k1_funct_1(G,k6_xcmplx_0(I,A)),k1_funct_1(H,k6_xcmplx_0(I,A))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t10_pdiff_6,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [D] : ( 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)))) ) ) ) ) ) )).
fof(t10_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,A) ) => k1_funct_7(k5_euclid(A),D,k3_xcmplx_0(C,B)) = k10_rvsum_1(k1_funct_7(k5_euclid(A),D,B),C) ) ) ) ) ) )).
fof(t10_pdiff_8,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_1(D,A),k7_euclid(A,B,C)) = k3_real_1(k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_1(D,A),B),k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_1(D,A),C)) ) ) ) ) )).
fof(t10_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t10_pencil_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ! [D] : v16_pencil_1(k1_funct_7(k1_pzfmisc1(A,B),C,D),A) ) ) )).
fof(t10_pencil_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) )).
fof(t10_pencil_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( ~ 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))) ) ) ) ) )).
fof(t10_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( 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)) ) ) ) ) )).
fof(t10_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_int_1(B) => k5_int_1(k2_xcmplx_0(k3_xcmplx_0(B,A),1),A) = k4_nat_d(1,A) ) ) )).
fof(t10_petri,axiom,( ! [A] : ( ( ~ 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 ) )).
fof(t10_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ( ( r2_pnproc_1(A,B,C) & r2_pnproc_1(A,C,B) ) => r1_pnproc_1(A,B,C) ) ) ) )).
fof(t10_polyalg1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_polynom5(A,k11_polynom3(A,C,D),B),k11_polynom3(A,k3_polynom5(A,C,B),D)) ) ) ) ) )).
fof(t10_polyeq_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( A != k5_numbers => ! [B] : ( v1_xcmplx_0(B) => k2_polyeq_1(k5_numbers,k5_numbers,A,B) != k5_numbers ) ) ) )).
fof(t10_polyeq_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ( ! [K] : ( v1_xreal_0(K) => k1_polyeq_2(A,B,C,D,E,K) = k2_polyeq_2(A,G,H,I,J,K) ) => ( A = k5_numbers | k7_xcmplx_0(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,k1_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(k1_square_1(F),k1_square_1(F)),k3_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(G,H),I),k3_xcmplx_0(k1_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)),k1_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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_polyeq_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xcmplx_0(D) => ~ ( A != k5_numbers & r1_xxreal_0(k5_numbers,k1_quin_1(A,B,C)) & k4_polyeq_1(A,B,C,k5_numbers,D) = k5_numbers & D != k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A)) & D != k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A)) & D != k4_xcmplx_0(k7_xcmplx_0(B,k3_xcmplx_0(2,A))) & D != k5_numbers ) ) ) ) ) )).
fof(t10_polyeq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( B != k5_numbers & ~ r1_xxreal_0(k5_numbers,k7_xcmplx_0(C,B)) & v1_abian(D) & r1_xxreal_0(1,D) & k2_polyeq_1(B,C,k5_numbers,k1_newton(A,D)) = k5_numbers & A != k5_numbers & A != k1_power(D,k4_xcmplx_0(k7_xcmplx_0(C,B))) & A != k4_xcmplx_0(k1_power(D,k4_xcmplx_0(k7_xcmplx_0(C,B)))) ) ) ) ) ) )).
fof(t10_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k1_newton(B,2) = A <=> ( B = k1_polyeq_5(2,A) | B = k4_xcmplx_0(k1_polyeq_5(2,A)) ) ) ) ) )).
fof(t10_polyform,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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)))) ) ) ) )).
fof(t10_polynom1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t10_polynom2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,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),k3_polynom1(k15_pre_poly(A),B,C)) ) ) ) )).
fof(t10_polynom3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k6_polynom3(1,A) = k2_matrlin(k4_ordinal1,k3_pre_poly(k4_ordinal1,A)) ) )).
fof(t10_polynom4,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k1_nat_1(k1_algseq_1(A,B),k1_algseq_1(A,C)),1) ) ) ) ) )).
fof(t10_polynom5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => k1_polynom5(k2_polynom3(u1_struct_0(k1_complfld),A,B)) = k10_finseq_1(k9_complex1(A),k9_complex1(B)) ) ) )).
fof(t10_polynom6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( ( 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] : ( m2_subset_1(D,k14_pre_poly(A),k15_pre_poly(A)) => ! [E] : ( 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] : ( m2_subset_1(F,k14_pre_poly(A),k15_pre_poly(A)) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t10_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v7_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( ~ v9_struct_0(C,B) & m1_subset_1(C,u1_struct_0(B)) ) => ! [D] : ( ( 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 ) ) ) )).
fof(t10_polynom8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_polynom5(A,k3_polynom5(A,D,C),B),k3_polynom5(A,D,k6_algstr_0(A,B,C))) ) ) ) ) )).
fof(t10_polyred,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => r2_funct_2(k15_pre_poly(A),u1_struct_0(B),k5_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))) ) ) ) ) )).
fof(t10_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t10_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ v1_abian(B) => k1_power(B,A) = k4_xcmplx_0(k1_power(B,k4_xcmplx_0(A))) ) ) ) )).
fof(t10_pralg_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ( 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))) ) ) ) )).
fof(t10_pralg_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ! [E] : ( ( 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(t10_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( ( k1_msualg_1(B,D) = k1_xboole_0 & k9_xtuple_0(E) = A & ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t10_pre_circ,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) ) => ! [C] : ( m1_trees_1(C,A) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ~ ( r2_hidden(D,k5_trees_1(A,C,B)) & r1_tarski(C,D) & ! [E] : ( m1_trees_1(E,B) => D != k8_finseq_1(k4_ordinal1,C,E) ) ) ) ) ) ) )).
fof(t10_pre_ff,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(B,C) => ( r1_xxreal_0(A,1) | r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(k3_power(A,B),k3_power(A,C)) ) ) ) ) ) )).
fof(t10_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t10_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( l1_pre_topc(C) => ! [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)) & m1_pre_topc(C,A) ) => m1_pre_topc(D,B) ) ) ) ) ) )).
fof(t10_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_prelamb(A) ) => ! [B] : ( m1_prelamb(B,A) => ! [C] : ( 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)),k4_ordinal1),B,C)) = 7 & ! [D] : ( m1_trees_1(D,k9_xtuple_0(B)) => ! [E] : ( m1_trees_1(E,k9_xtuple_0(B)) => ! [F] : ( m2_finseq_1(F,u1_struct_0(A)) => ! [G] : ( m2_finseq_1(G,u1_struct_0(A)) => ! [H] : ( m2_finseq_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ~ ( D = k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,k5_numbers)) & E = k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,1)) & k1_xtuple_0(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k4_ordinal1),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)),k4_ordinal1),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)),k4_ordinal1),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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_newton(B,C),k1_newton(A,C)) ) ) ) ) )).
fof(t10_prgcor_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r1_xxreal_0(k5_numbers,A) => ( r1_xxreal_0(B,k5_numbers) | k1_prgcor_1(A,B) = k4_int_1(A,B) ) ) ) ) )).
fof(t10_prob_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(t10_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( 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] : ( m1_prob_1(D,A,B) => r1_xxreal_0(k5_numbers,k3_funct_2(B,k1_numbers,C,D)) ) & k1_funct_1(C,A) = 1 & ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m1_prob_1(E,A,B) => ( r1_xboole_0(D,E) => k3_funct_2(B,k1_numbers,C,k6_prob_1(A,B,D,E)) = k3_real_1(k3_funct_2(B,k1_numbers,C,D),k3_funct_2(B,k1_numbers,C,E)) ) ) ) & ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(D) => ( v2_comseq_2(k8_prob_1(A,B,D,C)) & k1_seq_2(k8_prob_1(A,B,D,C)) = k1_funct_1(C,k1_prob_1(A,D)) ) ) ) ) ) ) ) ) )).
fof(t10_prob_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => v2_prob_1(k1_prob_3(A,B)) ) )).
fof(t10_prob_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ( r1_funct_2(k4_ordinal1,k1_numbers,k4_ordinal1,k6_numbers,A,B) & v1_seq_2(A) ) => k1_rinfsup1(A) = k1_xxreal_2(k2_relset_1(k6_numbers,B)) ) ) ) )).
fof(t10_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t10_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_collsp(A,E,F,G) & r1_projdes1(A,B,C,D,E) & r1_projdes1(A,B,C,D,F) ) => ( E = F | r1_projdes1(A,B,C,D,G) ) ) ) ) ) ) ) ) ) )).
fof(t10_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t10_projred1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u2_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u2_incsp_1(A)) => ! [H] : ( m1_subset_1(H,u2_incsp_1(A)) => ! [I] : ( m1_subset_1(I,u2_incsp_1(A)) => ~ ( r1_incsp_1(A,E,F) & r1_incsp_1(A,E,G) & F != G & r1_incsp_1(A,B,F) & E != B & r1_incsp_1(A,C,G) & r1_incsp_1(A,D,G) & C != D & r1_incsp_1(A,B,H) & r1_incsp_1(A,C,H) & r1_incsp_1(A,D,I) & H = I ) ) ) ) ) ) ) ) ) ) )).
fof(t10_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t10_prvect_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_prvect_2(A))) => ! [D] : ( m1_subset_1(D,k4_card_3(k4_prvect_2(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k11_prvect_2(A,B))) => ( ( D = C & E = k1_funct_1(D,B) ) => r1_xxreal_0(k2_normsp_0(k11_prvect_2(A,B),E),k2_normsp_0(k14_prvect_2(A),C)) ) ) ) ) ) ) )).
fof(t10_prvect_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l1_rlvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_rlvect_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_prvect_3(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t10_pscomp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t10_pua2mss1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( r1_tarski(B,A) => ! [C] : ( m1_eqrel_1(C,A) => m1_eqrel_1(a_3_1_pua2mss1(A,B,C),B) ) ) ) )).
fof(t10_pythtrip,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( r1_int_2(A,B) & v1_abian(A) & v1_abian(B) ) ) ) )).
fof(t10_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) )).
fof(t10_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => r1_xxreal_0(1,k3_finseq_1(k11_qc_lang1(A,B))) ) ) )).
fof(t10_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ! [E] : ( m1_subset_1(E,k9_qc_lang1(A)) => ( k3_qc_lang2(A,B,C) = k3_qc_lang2(A,D,E) => ( B = D & C = E ) ) ) ) ) ) ) )).
fof(t10_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t10_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( r2_hidden(C,k10_xtuple_0(k2_qc_lang4(A,B))) <=> r2_qc_lang2(A,C,B) ) ) ) ) )).
fof(t10_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_henmodel(B,A) & m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) ) => ! [C] : ( ( v1_qc_trans(C,A) & m1_qc_lang1(C) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_cqc_lang(C))) => ( r1_tarski(B,D) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_valuat_1(F,C,E) => ! [G] : ( m2_funct_2(G,k3_qc_lang1(C),E,k2_valuat_1(C,E)) => ~ ( r6_calcul_1(C,D,E,F,G) & ! [H] : ( ~ v1_xboole_0(H) => ! [I] : ( m1_valuat_1(I,A,H) => ! [J] : ( m2_funct_2(J,k3_qc_lang1(A),H,k2_valuat_1(A,H)) => ~ r6_calcul_1(A,B,H,I,J) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_qmax_1,axiom,( ! [A] : ( ( v2_qmax_1(A) & l1_qmax_1(A) ) => ! [B] : ( m1_subset_1(B,k5_qmax_1(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t10_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t10_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ~ ( A != k5_numbers & r1_xxreal_0(k28_quaterni(A),k5_numbers) ) ) )).
fof(t10_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ( ( k14_quaterni(A) = k5_numbers & k15_quaterni(A) = k5_numbers & k16_quaterni(A) = k5_numbers ) => A = k13_quaterni(A) ) ) )).
fof(t10_quaterni,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ r2_hidden(k2_quaterni(k5_numbers,1,2,3,A,B,C,D),k2_numbers) ) ) ) ) )).
fof(t10_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ! [D] : ( v1_xreal_0(D) => r1_xxreal_0(k5_numbers,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k1_square_1(D)),k3_xcmplx_0(B,D)),C)) ) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(k1_quin_1(A,B,C),k5_numbers) ) ) ) ) ) )).
fof(t10_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t10_radix_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,k2_radix_1(B)) => v1_int_1(A) ) ) )).
fof(t10_radix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,k1_nat_1(B,1)) & m2_finseq_1(C,k3_radix_1(A)) ) => ! [D] : ( ( v3_card_1(D,B) & m2_finseq_1(D,k3_radix_1(A)) ) => ( ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k2_finseq_1(B)) => k1_funct_1(C,E) = k1_funct_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) ) ) ) ) ) )).
fof(t10_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => r1_tarski(k1_radix_3(A),k4_numbers) ) )).
fof(t10_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(2,A) => k11_radix_1(k1_radix_1(A)) = 1 ) ) )).
fof(t10_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(2,B) ) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t10_ramsey_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_finset_1(B) => ~ ( r1_xxreal_0(A,k5_card_1(B)) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => k5_card_1(C) != A ) ) ) ) )).
fof(t10_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k1_random_1(A),k6_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),k6_numbers))) ) => ! [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))) ) => ! [D] : ( m2_finseq_1(D,k6_numbers) => ! [E] : ( 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] : ( v7_ordinal1(F) => ( r2_hidden(F,k4_finseq_1(D)) => k12_supinf_2(D,F) = k4_xxreal_3(k12_supinf_2(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) ) ) ) ) ) ) ) )).
fof(t10_random_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ! [D] : ( m2_finseq_1(D,A) => ( ( v2_funct_1(D) & k2_relset_1(A,D) = C ) => k5_bhsp_5(k1_numbers,A,k9_binop_2,C,B) = k18_rvsum_1(k4_bhsp_5(k1_numbers,A,B,D)) ) ) ) ) ) )).
fof(t10_random_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & v1_random_3(E,A,B,C,D) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(B),D) => ( F != k1_xboole_0 => a_6_0_random_3(A,B,C,D,E,F) = k8_relset_1(A,B,E,F) ) ) ) ) ) ) ) )).
fof(t10_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t10_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => r1_xxreal_0(k5_xcmplx_0(k1_rat_1(A)),1) ) )).
fof(t10_ratfunc1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t10_rcomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_rcomp_1(A) => v5_xxreal_2(A) ) ) )).
fof(t10_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => k2_seq_4(k10_prob_1(A)) = A ) )).
fof(t10_real_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) <=> ( k9_xtuple_0(A) = k4_ordinal1 & ! [B] : ( r2_hidden(B,k4_ordinal1) => v7_ordinal1(k1_funct_1(A,B)) ) ) ) ) )).
fof(t10_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( m2_funct_2(C,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t10_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(k1_nat_1(A,1))) => k1_square_1(k12_euclid(B)) = k2_xcmplx_0(k1_square_1(k12_euclid(k17_finseq_1(k1_numbers,A,B))),k1_square_1(k1_funct_1(B,k1_nat_1(A,1)))) ) ) )).
fof(t10_realset2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t10_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t10_rearran1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_rearran1(C) & v2_rearran1(C) & m2_finseq_1(C,k1_zfmisc_1(B)) ) => ~ ( r1_xxreal_0(1,A) & r1_xxreal_0(A,k6_xcmplx_0(k3_finseq_1(C),1)) & ! [D] : ( m1_subset_1(D,B) => ~ ( k6_subset_1(k1_funct_1(C,k1_nat_1(A,1)),k1_funct_1(C,A)) = k1_tarski(D) & k1_funct_1(C,k1_nat_1(A,1)) = k2_xboole_0(k1_funct_1(C,A),k1_tarski(D)) & k6_subset_1(k1_funct_1(C,k1_nat_1(A,1)),k1_tarski(D)) = k1_funct_1(C,A) ) ) ) ) ) ) )).
fof(t10_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r1_tarski(A,B) => r1_tarski(k1_relat_1(A),k1_relat_1(B)) ) ) ) )).
fof(t10_relat_2,axiom,( ! [A] : ( 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)) ) ) )).
fof(t10_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ( ! [D] : ~ ( r2_hidden(D,B) & ! [E] : ~ r2_hidden(k4_tarski(E,D),C) ) <=> k2_relset_1(B,C) = B ) ) )).
fof(t10_relset_2,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( 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)) ) ) )).
fof(t10_revrot_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( 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(k1_nat_1(A,1),k4_finseq_4(D,C))) ) ) ) ) ) )).
fof(t10_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r1_tarski(A,B) => ! [C] : ( m1_rewrite1(C,A) => m1_rewrite1(C,B) ) ) ) ) )).
fof(t10_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ( r1_rewrite2(A,B,C,D) => r2_rewrite2(A,B,C,D) ) ) ) ) )).
fof(t10_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ( D = k1_flang_1(A,B,C) => ( B = k2_flang_1(A) | C = k2_flang_1(A) | ( ~ r1_xxreal_0(k1_afinsq_1(D),k1_afinsq_1(B)) & ~ r1_xxreal_0(k1_afinsq_1(D),k1_afinsq_1(C)) ) ) ) ) ) ) ) )).
fof(t10_rfinseq,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( k3_finseq_1(A) = k1_nat_1(C,2) & k1_funct_1(A,k1_nat_1(C,1)) = B ) => k3_rfinseq(k17_finseq_1(k1_numbers,k1_nat_1(C,1),A)) = k7_finseq_1(k17_finseq_1(k1_numbers,C,k3_rfinseq(A)),k9_finseq_1(B)) ) ) ) ) )).
fof(t10_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k3_finseq_1(A),k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & ~ ( k4_rfinseq2(k10_rvsum_1(A,B)) = k3_xcmplx_0(B,k4_rfinseq2(A)) & k2_rfinseq2(k10_rvsum_1(A,B)) = k2_rfinseq2(A) ) ) ) ) )).
fof(t10_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t10_rfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ( r1_tarski(k2_relset_1(A,C),k1_relset_1(A,B)) => ( r2_relset_1(k4_ordinal1,k1_numbers,k56_valued_1(k4_ordinal1,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,A,C,B)),k8_funct_2(k4_ordinal1,k1_numbers,A,C,k56_valued_1(A,k1_numbers,B))) & r2_relset_1(k4_ordinal1,k1_numbers,k32_valued_1(k4_ordinal1,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,A,C,B)),k8_funct_2(k4_ordinal1,k1_numbers,A,C,k32_valued_1(A,k1_numbers,B))) ) ) ) ) ) )).
fof(t10_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(k5_numbers,C) => k8_relset_1(A,k1_numbers,k56_valued_1(A,k1_numbers,B),k1_tarski(C)) = k1_xboole_0 ) ) ) ) )).
fof(t10_rfunct_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ! [C] : ( ( r1_rfunct_4(A,B) & r1_tarski(C,B) ) => r1_rfunct_4(A,C) ) ) )).
fof(t10_rinfsup1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(A,k1_funct_1(B,C)) ) <=> ( v2_seq_2(B) & r1_xxreal_0(A,k2_rinfsup1(B)) ) ) ) ) )).
fof(t10_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( r1_funct_2(k4_ordinal1,k6_numbers,k4_ordinal1,k1_numbers,A,B) & v1_comseq_2(B) ) => ( r1_funct_2(k4_ordinal1,k6_numbers,k4_ordinal1,k1_numbers,k3_rinfsup2(A),k3_rinfsup1(B)) & k6_rinfsup2(A) = k6_rinfsup1(B) ) ) ) ) )).
fof(t10_ring_1,axiom,( ! [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) & 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))) ) )).
fof(t10_ringcat1,axiom,( ! [A] : ( ( v2_ringcat1(A) & v3_ringcat1(A) & l1_ringcat1(A) ) => ! [B] : ( ( v2_ringcat1(B) & v3_ringcat1(B) & l1_ringcat1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t10_rlaffin1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) => k1_convex1(C,D,k3_xcmplx_0(A,B)) = k1_convex1(C,k1_convex1(C,D,B),A) ) ) ) ) )).
fof(t10_rlaffin2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ~ ( r2_hidden(A,k1_rlaffin2(B,C)) & ! [D] : ( m2_rlvect_2(D,B,C) => ~ ( v2_convex1(D,B) & A = k6_rlvect_2(B,D) ) ) ) ) ) )).
fof(t10_rlaffin3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_rlvect_1(B) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,u1_struct_0(B)))) ) => ! [E] : 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) ) ) ) ) )).
fof(t10_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => m1_subset_1(C,u1_struct_0(A)) ) ) ) )).
fof(t10_rlsub_2,axiom,( ! [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) ) => ( 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)) ) ) )).
fof(t10_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t10_rlvect_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v8_rlvect_1(B) & l1_rlvect_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( ( A = k5_numbers | C = k4_struct_0(B) ) => k1_rlvect_1(B,C,A) = k4_struct_0(B) ) ) ) ) )).
fof(t10_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t10_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t10_rlvect_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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] : ( v1_xreal_0(E) & A = k3_rlvect_1(B,C,k1_rlvect_1(B,D,E)) ) ) ) ) ) )).
fof(t10_rlvect_5,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlvect_2(C,A) => ( r1_tarski(k3_rlvect_2(A,C),u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t10_rlvect_x,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t10_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => m1_subset_1(D,u1_struct_0(B)) ) ) ) ) )).
fof(t10_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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 ) ) ) )).
fof(t10_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( ( 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),D,C)) = k5_algstr_0(B,k3_rlvect_1(B,k1_rmod_4(A,B,D),k1_rmod_4(A,B,C)),k1_rmod_4(A,B,k9_subset_1(u1_struct_0(B),D,C))) ) ) ) ) )).
fof(t10_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k3_robbins1(A,B) = k3_robbins1(A,C) => B = C ) ) ) ) )).
fof(t10_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t10_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t10_robbins4,axiom,( r1_tarski(u1_struct_0(k2_robbins4),k1_zfmisc_1(3)) )).
fof(t10_rolle,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,k2_rcomp_1(A,B)) & r1_xxreal_0(k5_numbers,k1_fdiff_1(C,D)) ) ) ) => v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,C,k2_rcomp_1(A,B))) ) ) ) ) )).
fof(t10_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ~ ( 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) ) ) ) )).
fof(t10_rpr_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ~ ( B != k1_xboole_0 & ! [C] : ( ( v3_card_1(C,1) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ~ r1_tarski(C,B) ) ) ) ) )).
fof(t10_rsspace,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace))) => k1_rlvect_1(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace),A,1) = A ) )).
fof(t10_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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)) ) ) )).
fof(t10_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( E = D & F = C ) => k5_algstr_0(B,E,F) = k5_algstr_0(A,D,C) ) ) ) ) ) ) ) )).
fof(t10_rusub_2,axiom,( ! [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_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)) ) ) )).
fof(t10_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t10_rusub_4,axiom,( ! [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_bhsp_1(A) & v1_rusub_4(A) & l1_bhsp_1(A) ) => k1_rusub_4(A) = k1_rusub_4(k2_rusub_1(A)) ) )).
fof(t10_rusub_5,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t10_rvsum_1,axiom,( r7_binop_1(k1_numbers,k7_binop_2,k9_binop_2) )).
fof(t10_rvsum_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t10_scm_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_ami_3)) ) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ( k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_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(k7_card_1(2),k1_ami_3,A,D,B),E) = k5_numbers => k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1))) = F ) & ( k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B),E) != k5_numbers => k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1))) = k1_nat_1(C,1) ) & ! [G] : ( ( v1_ami_2(G) & m1_subset_1(G,u1_struct_0(k1_ami_3)) ) => k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1)),G) = k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B),G) ) ) ) ) ) ) ) ) ) )).
fof(t10_scm_comp,axiom,( ! [A] : ( m2_subset_1(A,u1_struct_0(k1_scm_comp),k7_dtconstr(k1_scm_comp)) => ! [B] : ( m1_dtconstr(B,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [C] : ( 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)) = k5_nat_1(k17_scm_comp(B),k17_scm_comp(C)) ) ) ) )).
fof(t10_scm_inst,axiom,( ! [A] : ( m1_subset_1(A,k3_scm_inst) => r1_xxreal_0(k2_compos_0(k3_scm_inst,A),8) ) )).
fof(t10_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => ! [C] : ( m1_scmfsa_2(C) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( 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(E,D,C) & B != k15_scmfsa_2(E,D,C) ) | r2_hidden(C,k4_sf_mastr(A)) ) ) ) ) ) ) ) )).
fof(t10_scmfsa10,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( 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 ) ) )).
fof(t10_scmfsa6a,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => k6_scmfsa6a(A,B) = k4_scmfsa6a(A,k11_compos_1(k1_scmfsa_2,B)) ) ) )).
fof(t10_scmfsa6b,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(A,k7_card_1(3),k1_scmfsa_2,k5_numbers) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ( ( r1_tarski(B,D) & r1_extpro_1(k7_card_1(3),k1_scmfsa_2,D,A) ) => ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(E,k8_extpro_1(k7_card_1(3),k1_scmfsa_2,D,A)) => r8_pboole(u1_struct_0(k1_scmfsa_2),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,D,A,E),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(D,k3_scmfsa6a(B,C)),A,E)) ) ) ) ) ) ) ) )).
fof(t10_scmfsa6c,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => k4_sf_mastr(k1_scmfsa6c(A,B)) = k1_xboole_0 ) ) )).
fof(t10_scmfsa7b,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t10_scmfsa8a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t10_scmfsa8b,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => k5_card_1(k1_scmfsa8b(C,A,B)) = k1_nat_1(k1_nat_1(k5_card_1(A),k5_card_1(B)),4) ) ) ) )).
fof(t10_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(C,k7_card_1(3),k1_scmfsa_2,k5_numbers) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(D,k7_card_1(3),k1_scmfsa_2,k5_numbers) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,C) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,D) ) => ! [F] : ( v7_ordinal1(F) => ( k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C,F)) = k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,D,F)) & k3_extpro_1(k7_card_1(3),k1_scmfsa_2,A,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C,F)) = k3_extpro_1(k7_card_1(3),k1_scmfsa_2,B,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,D,F)) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C,F)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,D,F)) ) ) ) ) ) ) ) ) )).
fof(t10_scmfsa9a,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) => k4_sf_mastr(k2_scmfsa8b(A,B,C)) = k4_subset_1(k3_scmfsa_2,k4_sf_mastr(B),k4_sf_mastr(C)) ) ) ) )).
fof(t10_scmfsa_1,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k4_scmfsa_1,k5_scmfsa_1))) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k1_scmfsa_1,k2_scmfsa_1) => k1_funct_1(k6_scmfsa_1(A,B),C) = k1_funct_1(A,C) ) ) ) )).
fof(t10_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) ) )).
fof(t10_scmfsa_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( ~ 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(k7_card_1(3),k1_scmfsa_2)) & v1_finset_1(B) & v4_extpro_1(B,k7_card_1(3),k1_scmfsa_2,A) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ( ( r1_tarski(B,C) & r1_tarski(B,D) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( ( r1_tarski(A,E) & r1_tarski(A,F) ) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v1_ami_2(H) & m1_subset_1(H,u1_struct_0(k1_scmfsa_2)) ) => ! [I] : ( v7_ordinal1(I) => ( k3_extpro_1(k7_card_1(3),k1_scmfsa_2,E,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G)) = k13_scmfsa_2(I,H) => ( I = k1_ordinal1(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G))) | ( ~ ( ~ r1_xxreal_0(k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G),H),k5_numbers) & r1_xxreal_0(k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,D,G),H),k5_numbers) ) & ~ ( ~ r1_xxreal_0(k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,D,G),H),k5_numbers) & r1_xxreal_0(k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G),H),k5_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_scmfsa_9,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(6,C) => r2_hidden(k2_xcmplx_0(k5_card_1(B),C),k2_afinsq_1(k1_scmfsa_9(A,B))) ) ) ) ) )).
fof(t10_scmfsa_m,axiom,( r2_hidden(k4_scmfsa_2(k5_numbers),k9_xtuple_0(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))) )).
fof(t10_scmisort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( 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(k7_card_1(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(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa_9(B,C)),k1_scmfsa_m(D),k2_xcmplx_0(1,k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(D))))) = k1_nat_1(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(D),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(D)))),4) ) => k3_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa_9(B,C)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa_9(B,C)),k1_scmfsa_m(D),k2_xcmplx_0(1,k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(D))))) = k11_scmfsa_2(k1_nat_1(k5_card_1(C),4)) ) ) ) ) ) )).
fof(t10_scmp_gcd,axiom,( k1_funct_1(k4_scmp_gcd,k5_numbers) = k5_scmpds_2(k2_scmp_gcd,k5_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,k1_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) )).
fof(t10_scmpds_2,axiom,( ! [A] : ( ( 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 ) )).
fof(t10_scmpds_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( v7_ordinal1(G) => ! [H] : ( v1_int_1(H) => ! [I] : ( v1_int_1(I) => ! [J] : ( ( v1_ami_2(J) & m1_subset_1(J,u1_struct_0(k1_scmpds_2)) ) => ! [K] : ( ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_scmpds_4,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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)) ) ) ) )).
fof(t10_scmpds_6,axiom,( ! [A] : ( v1_int_1(A) => ( r2_hidden(k5_numbers,k9_xtuple_0(k1_scmpds_6(A))) & k1_funct_1(k1_scmpds_6(A),k5_numbers) = k3_scmpds_2(A) ) ) )).
fof(t10_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( 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,k5_numbers) ) => ! [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_partfun1(D,u1_struct_0(k1_scmpds_2)) & v5_memstr_0(D,2,k1_scmpds_2,k5_numbers) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(E) & 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] : ( v7_ordinal1(F) => 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) ) ) ) ) ) ) ) )).
fof(t10_scmpds_8,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( r1_xxreal_0(k5_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) ) ) ) ) ) ) ) )).
fof(t10_scmpds_9,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => k1_amistd_1(2,k1_scmpds_2,C,k12_scmpds_2(A,B,D,E)) = k1_tarski(k1_ordinal1(C)) ) ) ) ) ) )).
fof(t10_scmring1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k4_card_3(k3_relat_1(k3_ami_2,k1_scmring1(A)))) => ! [C] : ( m2_subset_1(C,k1_ami_2,k2_ami_2) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_funct_1(k4_scmring1(A,B,C,D),C) = D ) ) ) ) )).
fof(t10_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( v7_ordinal1(C) => k2_compos_0(u1_compos_1(k1_scmring2(A)),k9_scmring2(A,C,B)) = 7 ) ) ) )).
fof(t10_scmring4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(B))) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmring2(B))) ) => ! [E] : ( ( 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(k7_card_1(2),k1_scmring2(B))) & v1_partfun1(E,u1_struct_0(k1_scmring2(B))) ) => ! [F] : ( ( 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(k7_card_1(2),k1_scmring2(B))) & v1_partfun1(F,u1_struct_0(k1_scmring2(B))) ) => ! [G] : ( ( v1_relat_1(G) & v4_relat_1(G,k4_ordinal1) & v5_relat_1(G,u1_compos_1(k1_scmring2(B))) & v1_funct_1(G) & v1_partfun1(G,k4_ordinal1) ) => ! [H] : ( ( v1_relat_1(H) & v4_relat_1(H,k4_ordinal1) & v5_relat_1(H,u1_compos_1(k1_scmring2(B))) & v1_funct_1(H) & v1_partfun1(H,k4_ordinal1) ) => ! [I] : ( ( v1_relat_1(I) & v4_relat_1(I,k4_ordinal1) & 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] : ( ( 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(k7_card_1(2),k1_scmring2(B))) & ~ v1_xboole_0(J) & v1_finset_1(J) & v4_extpro_1(J,k7_card_1(2),k1_scmring2(B),I) ) => ( ( r1_tarski(J,E) & r1_tarski(J,F) & r1_tarski(I,G) & r1_tarski(I,H) & k3_extpro_1(k7_card_1(2),k1_scmring2(B),G,k5_extpro_1(k7_card_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(k7_card_1(2),k1_scmring2(B),G,E,A),C),k2_scmring2(B,k5_extpro_1(k7_card_1(2),k1_scmring2(B),G,E,A),D)) = k6_algstr_0(B,k2_scmring2(B,k5_extpro_1(k7_card_1(2),k1_scmring2(B),H,F,A),C),k2_scmring2(B,k5_extpro_1(k7_card_1(2),k1_scmring2(B),H,F,A),D)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( v7_ordinal1(B) => r2_hidden(k3_xtuple_0(6,k9_finseq_1(B),k1_xboole_0),k1_scmringi(A)) ) ) )).
fof(t10_scpinvar,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ( r2_hidden(k5_numbers,k9_xtuple_0(k4_scpinvar(A,B,C))) & r2_hidden(1,k9_xtuple_0(k4_scpinvar(A,B,C))) ) ) ) ) )).
fof(t10_scpisort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t10_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( k1_funct_1(B,k2_scmp_gcd) = k5_numbers & k1_funct_1(B,k1_scmp_gcd(2)) = C & r1_xxreal_0(k1_nat_1(D,1),C) & r1_xxreal_0(7,D) ) => ( r1_scmpds_6(k1_scpqsort,B,A) & r2_scmpds_6(k1_scpqsort,B,A) ) ) ) ) ) ) )).
fof(t10_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ~ r2_analoaf(A,B,C,D,E) => ( B != C & D != E ) ) ) ) ) ) ) )).
fof(t10_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_funct_2(k4_ordinal1,k1_numbers,A,k32_valued_1(k4_ordinal1,k1_numbers,B)) <=> ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,A,C) = k1_real_1(k9_nat_1(k1_numbers,B,C)) ) ) ) ) )).
fof(t10_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(A) => k1_seq_2(k32_valued_1(k4_ordinal1,k1_numbers,A)) = k4_xcmplx_0(k1_seq_2(A)) ) ) )).
fof(t10_seq_4,axiom,( ! [A] : ( v1_xreal_0(A) => k3_seq_4(k1_seq_4(A)) = k2_seq_4(k1_seq_4(A)) ) )).
fof(t10_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => r2_relset_1(k4_ordinal1,k4_partfun1(A,k1_numbers),k2_seqfunc(A,D,k3_xcmplx_0(C,B)),k2_seqfunc(A,k2_seqfunc(A,D,B),C)) ) ) ) ) )).
fof(t10_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v6_valued_0(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(k9_nat_1(k1_numbers,A,k5_numbers),k9_nat_1(k1_numbers,A,B)) ) ) ) ) )).
fof(t10_series_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_series_1(B) => ( v1_series_1(k26_valued_1(k4_ordinal1,k1_numbers,B,A)) & k4_series_1(k26_valued_1(k4_ordinal1,k1_numbers,B,A)) = k3_xcmplx_0(A,k4_series_1(B)) ) ) ) ) )).
fof(t10_series_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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(k1_square_1(A),k1_square_1(B)),k1_square_1(C))) ) ) ) )).
fof(t10_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => r1_xxreal_0(k7_xcmplx_0(2,k2_xcmplx_0(k7_xcmplx_0(1,A),k7_xcmplx_0(1,B))),k7_xcmplx_0(k2_xcmplx_0(A,B),2)) ) ) )).
fof(t10_setfam_1,axiom,( ! [A] : k1_setfam_1(k1_tarski(A)) = A )).
fof(t10_setlim_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ! [D] : ( v7_ordinal1(D) => k1_funct_1(C,D) = B ) => k1_kurato_0(A,C) = B ) ) ) )).
fof(t10_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) ) ) )).
fof(t10_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( m1_subset_1(D,k5_finsub_1(A)) => ( k7_relset_1(A,B,C,D) = k1_xboole_0 => D = k1_xboole_0 ) ) ) ) ) )).
fof(t10_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k5_finsub_1(A)) => ! [D] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t10_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( m1_scmfsa_2(E) => ! [F] : ( m1_scmfsa_2(F) => ( k15_scmfsa_2(C,A,E) = k15_scmfsa_2(D,B,F) => ( A = B & C = D & E = F ) ) ) ) ) ) ) ) )).
fof(t10_sfmastr2,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) & v1_scmfsa7b(D) ) => ! [E] : ( v7_ordinal1(E) => ( ( k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k3_sfmastr2(B,A,D,C),E),k4_scmfsa_2(k5_numbers)) = 1 & r5_scmfsa7b(D,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k3_sfmastr2(B,A,D,C),E),k1_funct_4(B,k1_sfmastr2(C,D))) & r6_scmfsa7b(D,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k3_sfmastr2(B,A,D,C),E),k1_funct_4(B,k1_sfmastr2(C,D))) ) => ( k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k3_sfmastr2(B,A,D,C),k1_nat_1(E,1)),k4_scmfsa_2(k5_numbers)) = 1 & ( ~ r1_xxreal_0(k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(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)))),k5_numbers) => k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k3_sfmastr2(B,A,D,C),k1_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(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(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) ) ) ) ) ) ) ) ) )).
fof(t10_sfmastr3,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & ~ v1_scmfsa_m(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( k1_funct_1(A,k4_scmfsa_2(k5_numbers)) = 1 => k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k1_sfmastr3(F,B,C,D,E,A),k5_numbers),k4_scmfsa_2(k5_numbers)) = 1 ) ) ) ) ) ) ) )).
fof(t10_sgraph1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(k2_tarski(B,C),k2_sgraph1(A)) => ( r2_hidden(B,A) & r2_hidden(C,A) & B != C ) ) )).
fof(t10_sheffer1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t10_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t10_simplex0,axiom,( ! [A] : ( ( v6_ordinal1(A) & v1_finset_1(A) ) => ( v1_setfam_1(A) => r1_ordinal1(k5_card_1(A),k1_card_1(k3_tarski(A))) ) ) )).
fof(t10_simplex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_simplex0(B,u1_struct_0(A)) => ! [C] : ( m1_simplex1(C,A,B) => k3_simplex1(A,B) = k3_simplex1(A,C) ) ) ) )).
fof(t10_simplex2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t10_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k9_nat_1(k2_numbers,k3_sin_cos(B),k5_numbers) = 1 & k9_nat_1(k2_numbers,k8_sin_cos(k5_numbers,B,A),k5_numbers) = 1 ) ) ) )).
fof(t10_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => k1_funct_1(k16_sin_cos,A) = k1_funct_1(k16_sin_cos,k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B),A)) ) ) )).
fof(t10_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A) = k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,k4_xcmplx_0(A)) ) )).
fof(t10_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k17_sin_cos(A) != k5_numbers => k2_sin_cos4(k3_xcmplx_0(2,A)) = k7_xcmplx_0(k6_xcmplx_0(k1_square_1(k2_sin_cos4(A)),1),k3_xcmplx_0(2,k2_sin_cos4(A))) ) ) )).
fof(t10_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => k1_funct_1(k18_sin_cos,A) = k1_funct_1(k18_sin_cos,k2_xcmplx_0(A,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B))) ) ) )).
fof(t10_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( r1_xxreal_0(1,A) & r1_xxreal_0(k2_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(A,1),2)),k3_square_1(k7_xcmplx_0(k6_xcmplx_0(A,1),2))),k5_numbers) ) ) )).
fof(t10_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( A != k5_numbers => ( k2_xcmplx_0(k1_sin_cos5(A),k6_sin_cos2(B)) = k7_xcmplx_0(k4_sin_cos2(k2_xcmplx_0(A,B)),k3_xcmplx_0(k2_sin_cos2(A),k4_sin_cos2(B))) & k6_xcmplx_0(k1_sin_cos5(A),k6_sin_cos2(B)) = k7_xcmplx_0(k4_sin_cos2(k6_xcmplx_0(A,B)),k3_xcmplx_0(k2_sin_cos2(A),k4_sin_cos2(B))) ) ) ) ) )).
fof(t10_sin_cos9,axiom,( v2_funct_1(k2_partfun1(k1_numbers,k1_numbers,k27_sin_cos,k2_rcomp_1(k5_numbers,k28_sin_cos))) )).
fof(t10_sincos10,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos))) )).
fof(t10_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) )).
fof(t10_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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))) ) ) ) ) )).
fof(t10_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( 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) ) ) ) )).
fof(t10_sprect_2,axiom,( ! [A] : ( ( v2_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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)) ) ) ) )).
fof(t10_sprect_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) )).
fof(t10_sprect_5,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t10_square_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k6_xcmplx_0(k1_square_1(A),k1_square_1(B)) != k5_numbers => k7_xcmplx_0(1,k2_xcmplx_0(A,B)) = k7_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(k1_square_1(A),k1_square_1(B))) ) ) ) )).
fof(t10_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ( k9_stacks_1(A,B) = k1_xboole_0 => r1_stacks_1(A,B) ) ) ) )).
fof(t10_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,k7_card_1(B)) => ( r1_xxreal_0(A,k6_xcmplx_0(B,1)) & m1_subset_1(k6_xcmplx_0(B,1),k4_ordinal1) ) ) ) ) )).
fof(t10_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v5_relat_1(C,k3_qc_lang1(A)) & v3_card_1(C,B) & m2_finseq_1(C,k2_qc_lang1(A)) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t10_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k4_subset_1(A,B,k3_subset_1(A,B)) = k2_subset_1(A) ) )).
fof(t10_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( v1_finset_1(D) => ~ ( r2_hidden(D,C) & ! [E] : ~ ( r1_tarski(E,D) & r2_hidden(E,k3_substlat(A,B,C)) ) ) ) ) )).
fof(t10_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) )).
fof(t10_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k1_substut1(A)) => ! [E] : ( 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] : ( m2_subset_1(F,k16_substut1(A),k38_substut1(A)) & F = k1_substut2(A,k11_cqc_lang(A,C,B),D) ) ) ) ) ) ) ) ) )).
fof(t10_supinf_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_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))) ) ) ) )).
fof(t10_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t10_sysrel,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) ) )).
fof(t10_t_0topsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( ? [C] : ( 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) ) ) ) )).
fof(t10_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t10_taxonom2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( B = k1_xboole_0 => v5_taxonom2(B,A) ) ) )).
fof(t10_taylor_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( k6_prepower(k1_funct_1(k22_sin_cos,1),A) = k1_funct_1(k22_sin_cos,A) & k2_power(k1_funct_1(k22_sin_cos,1),A) = k1_funct_1(k22_sin_cos,A) & k2_power(k4_power,A) = k1_funct_1(k22_sin_cos,A) & k6_prepower(k4_power,A) = k1_funct_1(k22_sin_cos,A) ) ) )).
fof(t10_taylor_2,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => r1_taylor_1(k22_sin_cos,B,A) ) ) )).
fof(t10_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ~ ( B != k1_xboole_0 & v6_tbsp_1(B,A) & ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & r2_hidden(D,B) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(E,B) => r1_xxreal_0(k1_metric_1(A,D,E),C) ) ) ) ) ) ) & ( ( v8_metric_1(A) & v9_metric_1(A) ) => ( ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(E,B) => r1_xxreal_0(k1_metric_1(A,D,E),C) ) ) ) ) ) | v6_tbsp_1(B,A) ) ) ) ) ) )).
fof(t10_tdgroup,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r1_tdgroup(A,B,C,D,E) ) ) ) ) ) )).
fof(t10_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t10_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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))) ) ) ) )).
fof(t10_tdlat_3,axiom,( ! [A] : ( 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)) ) ) )).
fof(t10_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t10_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t10_tex_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => ~ ( u1_struct_0(B) = u1_struct_0(A) & v1_tex_2(B,A) ) ) ) )).
fof(t10_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( v1_tops_1(B,A) & ! [C] : ( ( ~ v2_struct_0(C) & v1_pre_topc(C) & v1_tex_3(C,A) & m1_pre_topc(C,A) ) => B != u1_struct_0(C) ) ) ) ) )).
fof(t10_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v2_tex_4(k1_tex_4(A,B),A) ) ) )).
fof(t10_tietze,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( r1_seqfunc(A,k1_numbers,C,B) => ! [D] : ( ( v2_xxreal_0(D) & v1_xreal_0(D) ) => ! [E] : ( ( v2_xxreal_0(E) & v1_xreal_0(E) ) => ( ! [F] : ( 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,k2_power(E,F)),B) ) => ( r1_xxreal_0(1,E) | ! [F] : ( m1_subset_1(F,B) => ( r1_xxreal_0(k6_xcmplx_0(k1_funct_1(k1_seqfunc(A,k1_numbers,C,k5_numbers),F),k7_xcmplx_0(D,k6_xcmplx_0(1,E))),k1_funct_1(k11_seqfunc(A,C,B),F)) & r1_xxreal_0(k1_funct_1(k11_seqfunc(A,C,B),F),k2_xcmplx_0(k1_funct_1(k1_seqfunc(A,k1_numbers,C,k5_numbers),F),k7_xcmplx_0(D,k6_xcmplx_0(1,E)))) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( m1_pre_topc(B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & E = D ) ) ) ) ) ) )).
fof(t10_toler_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ( v3_relat_2(D) => v3_relat_2(k1_toler_1(D,C)) ) ) )).
fof(t10_topalg_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(B)) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,1) ) => r1_xxreal_0(k12_euclid(k9_euclid(B,C,A)),k12_euclid(C)) ) ) ) ) )).
fof(t10_topalg_2,axiom,( v2_topalg_2(k5_topmetr) )).
fof(t10_topalg_3,axiom,( ! [A] : ( 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) ) ) )).
fof(t10_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(C),u1_struct_0(k2_borsuk_1(A,B))) & v5_pre_topc(D,C,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))))) ) => v5_pre_topc(k4_topalg_4(A,B,C,D),C,B) ) ) ) ) )).
fof(t10_topalg_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t10_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t10_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ( k3_topdim_1(A,B) = k4_xcmplx_0(1) & v2_topdim_1(B,A) ) <=> r1_tarski(B,k6_domain_1(k1_zfmisc_1(u1_struct_0(A)),k1_struct_0(A))) ) ) ) )).
fof(t10_topdim_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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))) ) ) ) ) )).
fof(t10_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_tops_1(A,B)) <=> ! [D] : ( ( 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] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t10_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_pre_topc(A,B)) <=> ? [D] : ( 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] : ~ ( r2_hidden(E,D) & r1_xboole_0(E,B) ) ) ) ) ) ) )).
fof(t10_topgen_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( ( u1_struct_0(A) = u1_struct_0(B) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) )).
fof(t10_topgen_4,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t10_topgen_5,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v4_pre_topc(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( v4_pre_topc(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ! [E] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) ) )).
fof(t10_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) )).
fof(t10_topmetr,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => u1_struct_0(k2_topmetr(A,B)) = k1_rcomp_1(A,B) ) ) ) )).
fof(t10_topmetr3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(k2_topmetr(A,B))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k2_topmetr(A,B))))) ) => ( ( r1_funct_2(k4_ordinal1,u1_struct_0(k2_topmetr(A,B)),k4_ordinal1,k1_numbers,D,C) & r1_xxreal_0(A,B) & v8_valued_0(C) ) => v2_tbsp_1(D,k2_topmetr(A,B)) ) ) ) ) ) )).
fof(t10_topreal1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t10_topreal3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(B,C) => a_3_1_topreal3(A,B,C) = k1_rltopsp1(k15_euclid(2),k19_euclid(B,A),k19_euclid(C,A)) ) ) ) ) )).
fof(t10_topreal4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(2))) => ~ ( A != B & r2_hidden(A,k8_metric_1(k14_euclid(2),D,C)) & r2_hidden(B,k8_metric_1(k14_euclid(2),D,C)) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ~ ( r1_topreal4(E,A,B) & r1_tarski(E,k8_metric_1(k14_euclid(2),D,C)) ) ) ) ) ) ) ) )).
fof(t10_topreal5,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t10_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k12_rvsum_1(k10_finseq_1(A,B)) = k10_finseq_1(k1_square_1(A),k1_square_1(B)) ) ) )).
fof(t10_topreal7,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( 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)) ) ) )).
fof(t10_topreal8,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t10_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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 ) ) ) ) )).
fof(t10_topreala,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t10_toprealb,axiom,( ! [A] : ( 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)) ) )).
fof(t10_toprealc,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( 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),k1_square_1(A)) ) ) )).
fof(t10_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) )).
fof(t10_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t10_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) )).
fof(t10_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v2_tops_1(B,A) & B = u1_struct_0(A) ) ) ) )).
fof(t10_tops_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v3_pre_topc(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( r2_hidden(C,D) & ! [E] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t10_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) )).
fof(t10_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t10_treal_1,axiom,( r2_funct_2(u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k4_topmetr(k5_numbers,1)),k3_treal_1(k5_numbers,1,k1_treal_1(k5_numbers,1),k2_treal_1(k5_numbers,1)),k3_struct_0(k4_topmetr(k5_numbers,1))) )).
fof(t10_trees_1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) ) )).
fof(t10_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => m4_trees_1(k1_trees_2(A,B),A) ) ) )).
fof(t10_trees_3,axiom,( ! [A] : ! [B] : ( ( v3_trees_3(A) & v3_trees_3(B) ) => v3_trees_3(k5_xboole_0(A,B)) ) )).
fof(t10_trees_4,axiom,( ! [A] : ! [B] : ( ( 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(k1_funct_6(B)) ) )).
fof(t10_trees_9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ( r2_hidden(A,k3_trees_9(B)) <=> ? [C] : ( m1_trees_1(C,k9_xtuple_0(B)) & A = k5_trees_2(B,C) ) ) ) )).
fof(t10_trees_a,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ! [C] : ( m4_trees_1(C,k9_xtuple_0(A)) => ( C != k1_xboole_0 => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ~ ( r2_hidden(D,k9_xtuple_0(k3_trees_a(A,C,B))) & ? [E] : ( m2_finseq_1(E,k4_ordinal1) & r2_hidden(E,C) & ~ ( ~ r1_tarski(E,D) & k1_funct_1(k3_trees_a(A,C,B),D) = k1_funct_1(A,D) ) ) & ! [E] : ( m2_finseq_1(E,k4_ordinal1) => ! [F] : ( m2_finseq_1(F,k4_ordinal1) => ~ ( r2_hidden(E,C) & r2_hidden(F,k9_xtuple_0(B)) & D = k8_finseq_1(k4_ordinal1,E,F) & k1_funct_1(k3_trees_a(A,C,B),D) = k1_funct_1(B,F) ) ) ) ) ) ) ) ) ) )).
fof(t10_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : ( ~ v2_struct_0(C) & v1_pre_topc(C) & m1_pre_topc(C,A) & B = u1_struct_0(C) ) ) ) )).
fof(t10_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t10_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t10_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_tsp_2(B,A) ) ) )).
fof(t10_turing_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( l1_turing_1(C) => ! [D] : ( m1_subset_1(D,k3_zfmisc_1(u2_turing_1(C),k4_numbers,k9_funct_2(k4_numbers,u1_turing_1(C)))) => k9_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),k1_nat_1(A,B)) = k9_nat_1(k3_zfmisc_1(u2_turing_1(C),k4_numbers,k9_funct_2(k4_numbers,u1_turing_1(C))),k10_turing_1(C,k9_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) ) ) ) ) )).
fof(t10_twoscomp,axiom,( k1_funct_1(k8_twoscomp,k10_finseq_1(k5_numbers,k5_numbers)) = k5_numbers & k1_funct_1(k8_twoscomp,k10_finseq_1(k5_numbers,1)) = 1 & k1_funct_1(k8_twoscomp,k10_finseq_1(1,k5_numbers)) = 1 & k1_funct_1(k8_twoscomp,k10_finseq_1(1,1)) = 1 & k1_funct_1(k9_twoscomp,k10_finseq_1(k5_numbers,k5_numbers)) = 1 & k1_funct_1(k9_twoscomp,k10_finseq_1(k5_numbers,1)) = 1 & k1_funct_1(k9_twoscomp,k10_finseq_1(1,k5_numbers)) = k5_numbers & k1_funct_1(k9_twoscomp,k10_finseq_1(1,1)) = 1 & k1_funct_1(k10_twoscomp,k10_finseq_1(k5_numbers,k5_numbers)) = 1 & k1_funct_1(k10_twoscomp,k10_finseq_1(k5_numbers,1)) = 1 & k1_funct_1(k10_twoscomp,k10_finseq_1(1,k5_numbers)) = 1 & k1_funct_1(k10_twoscomp,k10_finseq_1(1,1)) = k5_numbers )).
fof(t10_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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 ) ) ) )).
fof(t10_unialg_3,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_unialg_1(B) & m1_unialg_2(B,A) ) => r1_tarski(k6_unialg_2(A),k1_funct_1(k3_unialg_3(A),B)) ) ) )).
fof(t10_uniroots,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k1_hahnban1(k19_sin_cos(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B),A)),k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B),A))) = k1_hahnban1(k19_sin_cos(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k4_nat_d(B,A)),A)),k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k4_nat_d(B,A)),A))) ) ) )).
fof(t10_uproots,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( 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 = k22_pre_poly(A,C) & k3_uproots(A,C) = k5_card_1(B) ) <=> r6_pboole(A,C,k1_uproots(A,B,1)) ) ) ) )).
fof(t10_urysohn1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_subset_1(B,k1_numbers,k1_urysohn1(A)) => ( B = k7_xcmplx_0(k6_urysohn1(A,B),k1_newton(2,A)) & r1_xxreal_0(k6_urysohn1(A,B),k1_newton(2,A)) ) ) ) )).
fof(t10_urysohn2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ( v3_measure5(A) => ( r1_xxreal_0(k5_numbers,B) | v4_measure5(k1_integra2(A,B)) ) ) ) ) )).
fof(t10_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_funct_2(C,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t10_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : k1_funct_1(k35_valued_1(A),B) = k5_xcmplx_0(k1_funct_1(A,B)) ) )).
fof(t10_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( 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) ) ) )).
fof(t10_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( r1_vectsp_5(A,B,C,D) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t10_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( m1_vectsp11(E,A,B,C) & m1_vectsp11(F,A,B,D) ) => ( ! [G] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t10_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( 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) ) ) ) ) ) )).
fof(t10_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k6_algstr_0(A,C,B) = k1_group_1(A) => ( B = k11_algstr_0(A,C) & C = k11_algstr_0(A,B) ) ) ) ) ) )).
fof(t10_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => m1_subset_1(D,u1_struct_0(B)) ) ) ) ) )).
fof(t10_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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)) ) ) ) )).
fof(t10_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t10_vectsp_7,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t10_vectsp_8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ! [C] : ( ( ~ 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] : ( 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) ) ) ) ) ) )).
fof(t10_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_7(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => r1_struct_0(k1_vectsp_7(A,B,C),D) ) ) ) ) )).
fof(t10_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t10_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t10_waybel10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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)))) ) ) ) )).
fof(t10_waybel11,axiom,( ! [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) ) => ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & l1_pre_topc(A) ) ) )).
fof(t10_waybel12,axiom,( ! [A] : ( ( v5_orders_2(A) & v1_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( 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))) ) ) )).
fof(t10_waybel13,axiom,( ! [A] : ( ( 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(k1_yellow_1(k7_waybel_0(A))) ) )).
fof(t10_waybel14,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t10_waybel15,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t10_waybel16,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_yellow_1(k8_waybel_0(k2_yellow_1(A)))))) ) => ( r2_yellow_0(k1_yellow_1(k8_waybel_0(k2_yellow_1(A))),B) & k2_yellow_0(k1_yellow_1(k8_waybel_0(k2_yellow_1(A))),B) = k1_setfam_1(B) ) ) )).
fof(t10_waybel17,axiom,( ! [A] : ( ( 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] : ( ( ~ 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) ) ) )).
fof(t10_waybel18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(t10_waybel19,axiom,( ! [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) & v1_waybel19(A) & l1_waybel_9(A) ) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & v2_waybel_0(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( ! [D] : ( 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)) ) ) ) ) )).
fof(t10_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v3_orders_2(D) & v5_orders_2(D) & l1_orders_2(D) ) => ! [E] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t10_waybel21,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) )).
fof(t10_waybel22,axiom,( ! [A] : k1_card_1(k1_waybel22(A)) = k1_card_1(A) )).
fof(t10_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k4_waybel_0(A,k6_waybel_0(A,B)) = k6_waybel_0(A,B) ) ) )).
fof(t10_waybel24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t10_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( ( v2_waybel18(B) & r1_waybel18(A,B) ) => v2_waybel18(A) ) ) ) )).
fof(t10_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t10_waybel27,axiom,( ! [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] : ( ( 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] : ( ( 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] : ( ( 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 ) ) ) ) )).
fof(t10_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t10_waybel29,axiom,( ! [A] : ( l1_pre_topc(A) => ! [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] : ( ( ~ v2_struct_0(C) & l1_waybel_9(C) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t10_waybel30,axiom,( ! [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) & l1_waybel_9(A) ) => r1_tarski(k5_waybel11(A),k2_waybel19(A)) ) )).
fof(t10_waybel32,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & v25_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t10_waybel33,axiom,( ! [A] : ( ( 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] : ( ( v1_waybel33(B) & m1_yellow_9(B,A) ) => k4_waybel28(A) = u1_pre_topc(B) ) ) )).
fof(t10_waybel34,axiom,( ! [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] : ( ( 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] : ( ( 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) ) ) ) )).
fof(t10_waybel35,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & m1_waybel35(C,A,B) ) => ( v2_waybel35(C,A,B) => v3_lattice3(k5_yellow_0(A,C)) ) ) ) ) )).
fof(t10_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( r2_waybel_0(A,B,C) <=> ~ r1_waybel_0(A,B,k6_subset_1(u1_struct_0(A),C)) ) ) ) )).
fof(t10_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(t10_waybel_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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))) ) ) )).
fof(t10_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_lattice3(A,k2_waybel_3(A,B),B) ) ) )).
fof(t10_waybel_4,axiom,( ! [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] : ( ( v5_waybel_4(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ( ( 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)))) ) ) ) ) )).
fof(t10_waybel_6,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t10_waybel_7,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v12_waybel_0(B,k2_yellow_1(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(A)))) ) => ( v1_waybel_0(B,k2_yellow_1(A)) <=> ! [C] : ( ( 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) ) ) ) ) )).
fof(t10_waybel_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( C = D => k2_waybel_8(A,C) = k2_waybel_8(B,D) ) ) ) ) ) ) )).
fof(t10_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t10_weddwitt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k7_group_3(A,B)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t10_weierstr,axiom,( ! [A] : ( ( 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] : ( 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) ) ) ) )).
fof(t10_wellord1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k2_wellord1(B,A) = k5_relat_1(k6_relat_1(A,B),A) ) )).
fof(t10_wellord2,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( r2_wellord1(B,A) => ( k1_relat_1(k2_wellord1(B,A)) = A & v2_wellord1(k2_wellord1(B,A)) ) ) ) )).
fof(t10_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( r1_int_2(B,C) => r1_int_2(k1_newton(B,A),C) ) ) ) ) )).
fof(t10_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(A,B) => r1_tarski(A,k2_xboole_0(C,B)) ) )).
fof(t10_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( 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)) ) ) ) )).
fof(t10_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t10_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(A,B) <=> r1_xxreal_0(k6_xcmplx_0(C,B),k6_xcmplx_0(C,A)) ) ) ) ) )).
fof(t10_xregular,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ~ ( r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(C,D) & r2_hidden(D,E) & r2_hidden(E,F) & r2_hidden(F,A) ) )).
fof(t10_xtuple_0,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_tarski(k11_xtuple_0(A),k11_xtuple_0(B)) ) )).
fof(t10_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( r2_hidden(A,k1_numbers) & r1_xxreal_0(A,B) & ~ r2_hidden(B,k1_numbers) & B != k1_xxreal_0 ) ) ) )).
fof(t10_xxreal_1,axiom,( ! [A] : ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ~ ( r2_hidden(A,k2_xxreal_1(B,C)) & ~ ( r2_hidden(A,k3_xxreal_1(B,C)) & A != C ) & A != B ) ) ) )).
fof(t10_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => k1_xxreal_2(k2_xboole_0(A,B)) = k4_xxreal_0(k1_xxreal_2(A),k1_xxreal_2(B)) ) ) )).
fof(t10_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( k2_xxreal_3(A) = k2_xxreal_3(B) => A = B ) ) ) )).
fof(t10_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_yellow_3(A,B))) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t10_yellow11,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ( ~ ( ? [B] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( 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] : ( ( 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) ) ) ) ) )).
fof(t10_yellow12,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t10_yellow13,axiom,( ! [A] : ( ( 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,k1_yellow_1(k7_waybel_0(A))) ) )).
fof(t10_yellow14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t10_yellow15,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( m2_finseq_1(E,k6_margrel1) => k3_finseq_1(k1_yellow15(A,k3_finseq_4(k1_zfmisc_1(A),B,C,D),E)) = 3 ) ) ) ) )).
fof(t10_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_yellow16(A,B,C) => k10_xtuple_0(C) = u1_struct_0(A) ) ) ) ) )).
fof(t10_yellow17,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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)) ) ) ) )).
fof(t10_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( C = D => k8_altcat_1(A,C) = k8_altcat_1(B,D) ) ) ) ) ) ) )).
fof(t10_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( r2_hidden(C,k2_yellow19(A,B)) <=> ( r1_waybel_0(A,B,C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) )).
fof(t10_yellow20,axiom,( ! [A] : ( l2_altcat_1(A) => ! [B] : ( l2_altcat_1(B) => ( r1_yellow20(A,B) <=> ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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) ) ) ) ) )).
fof(t10_yellow21,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_orders_2(A,C,B) & ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t10_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ! [C] : ! [D] : ( 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) ) ) ) ) )).
fof(t10_yellow_1,axiom,( ! [A] : ( l1_orders_2(A) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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),k2_orders_1(u1_struct_0(A))) ) ) )).
fof(t10_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(k1_yellow_2(A,B,C))) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,E) = D ) ) ) ) ) )).
fof(t10_yellow_3,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( 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] : ? [E] : C = k4_tarski(D,E) & ? [D] : ? [E] : k1_xtuple_0(C) = k4_tarski(D,E) & ? [D] : ? [E] : k2_xtuple_0(C) = k4_tarski(D,E) ) ) ) ) )).
fof(t10_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t10_yellow_5,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_orders_2(A,C,B) => k12_lattice3(A,B,C) = C ) ) ) ) )).
fof(t10_yellow_6,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_waybel_0(B,A) => ! [C] : ( m1_yellow_6(C,A,B) => r1_tarski(u1_struct_0(C),u1_struct_0(B)) ) ) ) )).
fof(t10_yellow_7,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( r1_yellow_0(A,B) <=> r2_yellow_0(k7_lattice3(A),B) ) ) )).
fof(t10_yellow_8,axiom,( ! [A] : ( l1_pre_topc(A) => ! [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)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => v3_pre_topc(C,A) ) ) ) ) )).
fof(t10_yellow_9,axiom,( ! [A] : ( ( 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)))) ) ) )).
fof(t10_zf_colla,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( k9_xtuple_0(B) = A & ! [C] : ( m1_subset_1(C,A) => k1_funct_1(B,C) = k7_relat_1(B,C) ) ) => v1_ordinal1(k10_xtuple_0(B)) ) ) ) )).
fof(t10_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t10_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ~ ( ~ v7_zf_lang(A) & ~ v4_zf_lang(A) & ~ v5_zf_lang(A) & ~ v6_zf_lang(A) ) ) )).
fof(t10_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => k10_zf_lang(A,B) = k11_zf_lang(k6_zf_lang(A),B) ) ) )).
fof(t10_zf_model,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ( v5_zf_lang(A) => ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(t10_zf_refle,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => v3_ordinal1(k3_card_3(A)) ) )).
fof(t10_zfmisc_1,axiom,( ! [A] : ! [B] : ~ ( r1_xboole_0(k1_tarski(A),k1_tarski(B)) & A = B ) )).
fof(t10_zfmodel1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t10_zfmodel2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( 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(k5_numbers),k8_zf_lang(k2_zf_lang(4),k12_zf_lang(B,k4_zf_lang(k2_zf_lang(4),k2_zf_lang(k5_numbers))))))) => ( r2_hidden(k2_zf_lang(k5_numbers),k2_zf_model(B)) | ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t10_zfrefle1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ( ( v1_zf_model(A) & r2_zfrefle1(A,B) & v1_ordinal1(B) ) => v1_zf_model(B) ) ) ) )).
fof(t10_zmodul01,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( ( v6_zmodul01(B) & k1_zmodul01(B,C,A) = k1_zmodul01(B,D,A) ) => ( A = k5_numbers | C = D ) ) ) ) ) ) )).
fof(t10_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m2_zmodul02(D,A,B) => ( r1_tarski(B,C) => m2_zmodul02(D,A,C) ) ) ) ) ) )).
fof(t10_zmodul03,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r1_tarski(k18_zmodul02(A,B),u1_struct_0(k33_zmodul02(A,C))) & ! [D] : ( m2_zmodul02(D,A,C) => k21_zmodul02(A,B) != k21_zmodul02(A,D) ) ) ) ) ) )).
fof(t110_abcmiz_1,axiom,( ! [A] : ( 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 ) ) )).
fof(t110_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_aofa_000(D,A,B,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t110_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ( ? [B] : ( m3_chord(B,A) & v7_chord(B,A) ) => v6_chord(A) ) ) )).
fof(t110_clvect_1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k2_normsp_0(A,B),k2_normsp_0(A,C))),k2_normsp_0(A,k5_algstr_0(A,B,C))) ) ) ) )).
fof(t110_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(k1_euclid(A)),k5_euclidlp(A)) => ( ( r1_tarski(D,F) & r1_tarski(E,F) & r6_euclidlp(A,D,E) & r2_hidden(B,F) & r5_euclidlp(A,C,E) & r2_hidden(B,C) ) => ( r1_tarski(C,F) & r6_euclidlp(A,C,D) ) ) ) ) ) ) ) ) )).
fof(t110_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => m2_finseq_2(k2_finseq_2(A,C),B,k4_finseq_2(A,B)) ) ) ) )).
fof(t110_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t110_finseq_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( k3_finseq_1(A) = 1 => k3_finseq_5(A) = A ) ) )).
fof(t110_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => r1_tarski(k2_flang_2(A,k7_flang_1(A,B,C)),k8_flang_1(A,B)) ) ) )).
fof(t110_funct_1,axiom,( ! [A] : ~ ( ! [B] : ~ ( r2_hidden(B,A) & B = k1_xboole_0 ) & ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ~ ( k9_xtuple_0(B) = A & ! [C] : ( r2_hidden(C,A) => r2_hidden(k1_funct_1(B,C),C) ) ) ) ) )).
fof(t110_funct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,B) & k2_relset_1(B,C) = k1_tarski(D) ) ) ) ) ) )).
fof(t110_funct_4,axiom,( ! [A] : ! [B] : ! [C] : k9_xtuple_0(k1_funct_4(k1_funct_4(k7_funcop_1(C,B),k16_funcop_1(C,A)),k16_funcop_1(k1_ordinal1(C),A))) = k1_ordinal1(k1_ordinal1(C)) )).
fof(t110_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ~ ( r2_hidden(B,k9_xtuple_0(A)) & r2_hidden(C,k9_xtuple_0(A)) & ! [D] : ( ( 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)))) ) => k1_funct_7(k1_funct_7(A,B,k1_funct_1(A,C)),C,k1_funct_1(A,B)) != k3_relat_1(D,A) ) ) ) )).
fof(t110_gfacirc1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ~ v1_facirc_1(k2_msafree2(k43_gfacirc1(A,B,C))) ) ) ) )).
fof(t110_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => k3_finseq_1(B) = k1_nat_1(k2_nat_1(2,k15_glib_001(A,B)),1) ) ) )).
fof(t110_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t110_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t110_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t110_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ~ r1_xxreal_0(k17_euclid(B),k5_numbers) & ~ r1_xxreal_0(k17_euclid(C),k5_numbers) & ~ r1_xxreal_0(k7_xcmplx_0(k18_euclid(C),k12_euclid(C)),k7_xcmplx_0(k18_euclid(B),k12_euclid(B))) & ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) & ? [E] : ( 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(k7_xcmplx_0(k18_euclid(E),k12_euclid(E)),k7_xcmplx_0(k18_euclid(D),k12_euclid(D))) ) ) ) ) ) ) )).
fof(t110_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t110_jordan2c,axiom,( ! [A] : ( ( v2_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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)) ) ) ) )).
fof(t110_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v6_limfunc1(A) & k5_limfunc1(A) = k5_numbers & ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(B,C) & r2_hidden(C,k1_relset_1(k1_numbers,A)) & k1_funct_1(A,C) != k5_numbers ) ) ) => ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & r2_hidden(C,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k10_prob_1(B))) & ~ r1_xxreal_0(k5_numbers,k1_funct_1(A,C)) ) ) | v7_limfunc1(k6_rfunct_1(k1_numbers,k1_numbers,A)) ) ) ) )).
fof(t110_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( v2_membered(C) => k14_member_1(k14_member_1(A,B),C) = k14_member_1(A,k12_member_1(B,C)) ) ) ) )).
fof(t110_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ( 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)) = k4_xxreal_3(E,k7_mesfunc5(A,B,C,D)) ) ) ) ) ) ) ) )).
fof(t110_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( 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,k4_normsp_0(u1_struct_0(A),B,D)) ) ) ) ) ) )).
fof(t110_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) )).
fof(t110_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( k7_relat_1(B,A) = k1_xboole_0 <=> r1_xboole_0(k9_xtuple_0(B),A) ) ) )).
fof(t110_rvsum_1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => k20_rvsum_1(A) = k1_finsop_1(k2_numbers,A,k5_binop_2) ) )).
fof(t110_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v6_scmyciel(A) ) => ( r1_xxreal_0(2,k8_scmyciel(A)) => k8_scmyciel(k12_scmyciel(A)) = k8_scmyciel(A) ) ) )).
fof(t110_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => ( ~ r1_xxreal_0(B,k5_numbers) => r2_hidden(C,k21_seq_4(A,C,B)) ) ) ) ) )).
fof(t110_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t110_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) => k6_xcmplx_0(k4_sin_cos6(A),k2_sin_cos6(k4_xcmplx_0(A))) = k7_xcmplx_0(k28_sin_cos,2) ) ) )).
fof(t110_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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),k7_xcmplx_0(A,2))))) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => ( k1_funct_1(C,F) = k7_xcmplx_0(F,A) & ~ r1_xxreal_0(k1_funct_1(C,F),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(C,F)) ) ) ) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => k1_funct_1(D,F) = 1 ) ) & E = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k1_taylor_1(2)) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => k1_funct_1(C,F) = k7_xcmplx_0(F,A) ) ) ) => ( A = k5_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),k7_xcmplx_0(A,2))),B) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => k1_funct_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),k7_xcmplx_0(A,2))),B),F) = k1_funct_1(k2_sin_cos9,k7_xcmplx_0(F,A)) ) ) ) ) ) ) ) ) ) ) )).
fof(t110_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(k3_square_1(2))) & ~ r1_xxreal_0(k4_xcmplx_0(1),A) & ~ ( ~ r1_xxreal_0(k6_sincos10(A),k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos)) & ~ r1_xxreal_0(k28_sin_cos,k6_sincos10(A)) ) ) ) )).
fof(t110_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v3_tdlat_2(B,A) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t110_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))))) ) ) ) ) )).
fof(t110_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r1_tarski(B,A) & r1_tarski(C,A) ) => r1_tarski(k5_xboole_0(B,C),A) ) )).
fof(t110_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k6_xboolean(k6_xboolean(A,k6_xboolean(B,C)),k6_xboolean(B,k6_xboolean(A,C))) = k2_xboolean ) ) ) )).
fof(t110_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( B != k5_numbers => A = k7_xcmplx_0(A,k3_xcmplx_0(B,k7_xcmplx_0(1,B))) ) ) ) )).
fof(t110_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(k5_numbers,D) & ~ r1_xxreal_0(k7_xcmplx_0(C,D),k3_xcmplx_0(A,B)) & r1_xxreal_0(k7_xcmplx_0(C,B),k3_xcmplx_0(A,D)) ) ) ) ) ) )).
fof(t110_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( r1_xxreal_0(C,A) & ~ r1_xxreal_0(D,C) & r1_tarski(k2_xxreal_1(C,D),k4_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t110_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t110_zfmisc_1,axiom,( ! [A] : ! [B] : ( ( r1_tarski(A,k2_zfmisc_1(A,B)) | r1_tarski(A,k2_zfmisc_1(B,A)) ) => A = k1_xboole_0 ) )).
fof(t110_zmodul01,axiom,( ! [A] : ( ( ~ 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 ) )).
fof(t111_abcmiz_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k49_abcmiz_1)) => ! [B] : ( 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) ) ) ) )).
fof(t111_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_aofa_000(D,A,B,C) => ! [E] : ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) )).
fof(t111_clvect_1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_xxreal_0(k2_normsp_0(A,k5_algstr_0(A,B,D)),k2_xcmplx_0(k2_normsp_0(A,k5_algstr_0(A,B,C)),k2_normsp_0(A,k5_algstr_0(A,C,D)))) ) ) ) ) )).
fof(t111_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t111_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v3_card_1(D,A) & m2_finseq_1(D,B) ) => ! [E] : ( ( 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(k4_ordinal1,B,B,C,D,E),C,k4_finseq_2(A,C)) ) ) ) ) ) )).
fof(t111_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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 ) ) ) )).
fof(t111_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => k3_finseq_1(k2_rfinseq(A,C,B)) = k7_nat_d(k3_finseq_1(B),C) ) ) ) )).
fof(t111_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) )).
fof(t111_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r1_tarski(A,C) & r1_tarski(B,C) & r1_xboole_0(A,B) ) => r1_xboole_0(k9_xtuple_0(A),k9_xtuple_0(B)) ) ) ) ) )).
fof(t111_funct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t111_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : k1_funct_4(k5_relat_1(A,B),A) = A ) )).
fof(t111_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( r2_hidden(B,k9_xtuple_0(A)) => k9_xtuple_0(A) = k9_xtuple_0(k1_funct_4(A,k16_funcop_1(B,C))) ) ) )).
fof(t111_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t111_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ( k3_finseq_1(B) = k3_finseq_1(C) <=> k15_glib_001(A,B) = k15_glib_001(A,C) ) ) ) ) )).
fof(t111_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t111_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t111_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v8_group_9(C,A,B) & m2_finseq_1(C,k6_group_9(A,B)) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t111_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t111_jordan2c,axiom,( ! [A] : ( ( v2_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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)) ) ) ) )).
fof(t111_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v6_limfunc1(A) & k5_limfunc1(A) = k5_numbers & ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(B,C) & r2_hidden(C,k1_relset_1(k1_numbers,A)) & k1_funct_1(A,C) != k5_numbers ) ) ) => ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & r2_hidden(C,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k10_prob_1(B))) & ~ r1_xxreal_0(k1_funct_1(A,C),k5_numbers) ) ) | v8_limfunc1(k6_rfunct_1(k1_numbers,k1_numbers,A)) ) ) ) )).
fof(t111_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & v1_matrix_1(C,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( k8_matrix13(B,C) = A => m1_vectsp_7(k9_matrix13(B,A,A,C),B,k6_prvect_1(B,A)) ) ) ) ) )).
fof(t111_member_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k14_member_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k6_xxreal_3(A,B)) ) ) )).
fof(t111_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t111_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( 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,k4_normsp_0(u1_struct_0(B),A,D)) ) ) ) ) ) )).
fof(t111_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t111_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ~ ( A != k1_xboole_0 & r1_tarski(A,k9_xtuple_0(B)) & k7_relat_1(B,A) = k1_xboole_0 ) ) )).
fof(t111_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k2_numbers) => k20_rvsum_1(k5_finseq_2(k2_numbers,k2_xcmplx_0(A,B),C)) = k3_xcmplx_0(k20_rvsum_1(k5_finseq_2(k2_numbers,A,C)),k20_rvsum_1(k5_finseq_2(k2_numbers,B,C))) ) ) ) )).
fof(t111_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ( ( r1_xxreal_0(k5_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,k1_nat_1(k5_card_1(C),2))) ) ) ) ) ) ) )).
fof(t111_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v11_scmyciel(A) ) => ? [B] : ( v10_scmyciel(B,k12_scmyciel(A)) & m1_eqrel_1(B,k3_tarski(k12_scmyciel(A))) & k1_card_1(B) = k2_xcmplx_0(1,k10_scmyciel(A)) ) ) )).
fof(t111_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => v1_seq_4(k21_seq_4(A,C,B),A) ) ) ) )).
fof(t111_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t111_sin_cos9,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A)),B),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A)),B)) ) ) ) ) => ( r2_hidden(k5_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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k4_xcmplx_0(k7_xcmplx_0(1,k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) ) )).
fof(t111_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(k3_square_1(2))) & ~ r1_xxreal_0(k4_xcmplx_0(1),A) & ~ ( ~ r1_xxreal_0(k7_sincos10(A),k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2))) & ~ r1_xxreal_0(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)),k7_sincos10(A)) ) ) ) )).
fof(t111_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t111_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : k4_xboole_0(k3_xboole_0(A,C),k3_xboole_0(B,C)) = k3_xboole_0(k4_xboole_0(A,B),C) )).
fof(t111_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k6_xboolean(k6_xboolean(k6_xboolean(A,B),C),k6_xboolean(B,C)) = k2_xboolean ) ) ) )).
fof(t111_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( A != k5_numbers & B != k5_numbers & k7_xcmplx_0(1,k3_xcmplx_0(A,B)) = k5_numbers ) ) ) )).
fof(t111_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(k7_xcmplx_0(C,D),k3_xcmplx_0(A,B)) & r1_xxreal_0(k7_xcmplx_0(C,B),k3_xcmplx_0(A,D)) ) ) ) ) ) )).
fof(t111_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(A,C) & ~ r1_xxreal_0(D,C) & r1_tarski(k3_xxreal_1(C,D),k4_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t111_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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))))) ) ) ) ) ) ) )).
fof(t111_zfmisc_1,axiom,( ! [A] : ? [B] : ( r2_hidden(A,B) & ! [C] : ! [D] : ( ( r2_hidden(C,B) & r1_tarski(D,C) ) => r2_hidden(D,B) ) & ! [C] : ( r2_hidden(C,B) => r2_hidden(k1_zfmisc_1(C),B) ) & ! [C] : ~ ( r1_tarski(C,B) & ~ r2_tarski(C,B) & ~ r2_hidden(C,B) ) ) )).
fof(t111_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => m1_zmodul01(k7_zmodul01(A,B,C),k6_zmodul01(A,B,C)) ) ) ) )).
fof(t112_abcmiz_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t112_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_aofa_000(D,A,B,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t112_clvect_1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & k2_normsp_0(A,k5_algstr_0(A,B,C)) = k5_numbers ) ) ) ) )).
fof(t112_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [F] : ( 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) & r5_euclidlp(A,C,D) & r5_euclidlp(A,D,E) & C != D & ~ r1_xboole_0(B,C) & ~ r1_xboole_0(B,D) & r1_xboole_0(B,E) ) ) ) ) ) ) ) )).
fof(t112_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,B) ) => ! [D] : ( ( 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),k4_ordinal1,B,D,C),B,k4_finseq_2(A,B)) ) ) ) ) ) )).
fof(t112_finseq_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_funct_1(k8_finseq_1(k4_ordinal1,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(k4_ordinal1,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(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)) & v3_funct_2(k8_finseq_1(k4_ordinal1,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(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)) & m1_subset_1(k8_finseq_1(k4_ordinal1,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(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)))) ) ) )).
fof(t112_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) => k4_finseq_5(A,k3_finseq_6(A,B,C,D)) = k3_finseq_6(A,k4_finseq_5(A,B),k1_nat_1(k7_nat_d(k3_finseq_1(B),D),1),k1_nat_1(k7_nat_d(k3_finseq_1(B),C),1)) ) ) ) ) ) )).
fof(t112_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( 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)) ) ) )).
fof(t112_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => k6_relat_1(A,B) = k5_relat_1(B,k8_relat_1(B,A)) ) )).
fof(t112_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ( m1_subset_1(E,B) => A != k1_funct_1(D,E) ) ) ) )).
fof(t112_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( ( k9_xtuple_0(C) = k1_tarski(B) & k10_xtuple_0(C) = k1_tarski(A) ) => C = k16_funcop_1(B,A) ) ) )).
fof(t112_funct_7,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ! [B] : ( m2_finseq_1(B,k4_numbers) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( 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 = k2_funct_7(k4_numbers,k2_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] : ( 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) ) ) ) ) ) ) )).
fof(t112_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t112_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m3_glib_001(D,B) => ( C = D => k15_glib_001(A,C) = k15_glib_001(B,D) ) ) ) ) ) )).
fof(t112_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t112_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ( v8_struct_0(A) => v1_finset_1(k9_group_3(A,B)) ) ) ) )).
fof(t112_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( m1_group_9(D,A,B) => ! [E] : ( ( v8_group_9(E,A,B) & m2_finseq_1(E,k6_group_9(A,B)) ) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t112_jgraph_4,axiom,( ! [A] : ( 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))) ) )).
fof(t112_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t112_jordan2c,axiom,( ! [A] : ( ( v2_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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)) ) ) ) )).
fof(t112_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v3_limfunc1(A) & k4_limfunc1(A) = k5_numbers ) => ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & r2_hidden(C,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k3_limfunc1(B))) & r1_xxreal_0(k1_funct_1(A,C),k5_numbers) ) ) | v4_limfunc1(k6_rfunct_1(k1_numbers,k1_numbers,A)) ) ) ) )).
fof(t112_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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 ) ) )).
fof(t112_member_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) )).
fof(t112_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ( r1_mesfunc5(A,B,C,D) => ( r1_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,F)) & k8_mesfunc5(A,B,C,k6_mesfunc1(A,D,E),F) = k4_xxreal_3(E,k8_mesfunc5(A,B,C,D,F)) ) ) ) ) ) ) ) ) )).
fof(t112_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ! [D] : ( ( 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) ) ) ) ) )).
fof(t112_pboole,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(t112_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(t112_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k2_numbers) => k20_rvsum_1(k5_finseq_2(k2_numbers,k3_xcmplx_0(A,B),C)) = k20_rvsum_1(k5_finseq_2(k2_numbers,B,k20_rvsum_1(k5_finseq_2(k2_numbers,A,C)))) ) ) ) )).
fof(t112_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ( ~ r1_xxreal_0(k5_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,k1_nat_1(k5_card_1(C),2))) ) ) ) ) ) ) )).
fof(t112_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v11_scmyciel(A) ) => k10_scmyciel(k12_scmyciel(A)) = k2_xcmplx_0(1,k10_scmyciel(A)) ) )).
fof(t112_seq_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => r1_xxreal_0(B,C) ) ) => ( A = k1_xboole_0 | r1_xxreal_0(B,k3_seq_4(A)) ) ) ) ) )).
fof(t112_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t112_sin_cos9,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A)),B),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A)),B)) ) ) ) ) => ( r2_hidden(k5_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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k7_xcmplx_0(1,k2_xcmplx_0(1,k1_square_1(B))) ) ) ) ) ) ) )).
fof(t112_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,1) & ~ r1_xxreal_0(k3_square_1(2),A) & ~ ( ~ r1_xxreal_0(k8_sincos10(A),k7_xcmplx_0(k28_sin_cos,4)) & ~ r1_xxreal_0(k7_xcmplx_0(k28_sin_cos,2),k8_sincos10(A)) ) ) ) )).
fof(t112_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ v2_struct_0(E) & m1_pre_topc(E,A) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(k1_tsep_1(A,D,E))) => ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t112_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : k5_xboole_0(k3_xboole_0(A,C),k3_xboole_0(B,C)) = k3_xboole_0(k5_xboole_0(A,B),C) )).
fof(t112_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => k6_xboolean(k6_xboolean(k2_xboolean,A),A) = k2_xboolean ) )).
fof(t112_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( A != k5_numbers & B != k5_numbers & k3_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(B,A)) != 1 ) ) ) )).
fof(t112_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(k5_numbers,D) & ~ r1_xxreal_0(k3_xcmplx_0(A,B),k7_xcmplx_0(C,D)) & r1_xxreal_0(k3_xcmplx_0(A,D),k7_xcmplx_0(C,B)) ) ) ) ) ) )).
fof(t112_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(A,C) & ~ r1_xxreal_0(D,C) & r1_tarski(k4_xxreal_1(C,D),k4_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t112_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t112_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( r2_hidden(A,k2_zfmisc_1(B,D)) & r2_hidden(A,k2_zfmisc_1(C,E)) ) => r2_hidden(A,k2_zfmisc_1(k3_xboole_0(B,C),k3_xboole_0(D,E))) ) )).
fof(t112_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( ( v1_zmodul01(C) & m1_zmodul01(C,A) ) => k6_zmodul01(A,k7_zmodul01(A,B,C),C) = C ) ) ) )).
fof(t113_abcmiz_1,axiom,( k4_yellow_0(k49_abcmiz_1) = k1_xboole_0 )).
fof(t113_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_aofa_000(D,A,B,C) => ! [E] : ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t113_clvect_1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v9_clvect_1(B,A) & v9_clvect_1(C,A) ) => v9_clvect_1(k2_normsp_1(A,B,C),A) ) ) ) ) )).
fof(t113_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t113_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,B) ) => ! [D] : ( ( 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),k4_ordinal1,B,D,C),A) & m2_finseq_1(k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k4_ordinal1,B,D,C),B) ) ) ) ) ) )).
fof(t113_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k10_xtuple_0(A))) => ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k1_relset_1(k4_ordinal1,A),k1_relset_1(k4_ordinal1,A)) & v3_funct_2(C,k1_relset_1(k4_ordinal1,A),k1_relset_1(k4_ordinal1,A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_relset_1(k4_ordinal1,A),k1_relset_1(k4_ordinal1,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) ) ) ) )).
fof(t113_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,A) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k2_xcmplx_0(C,B),k3_finseq_1(D)) ) => k1_funct_1(k2_rfinseq(A,B,D),C) = k1_funct_1(D,k2_xcmplx_0(C,B)) ) ) ) ) ) )).
fof(t113_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => r1_tarski(k1_flang_2(A,k2_flang_2(A,B),C,D),k8_flang_1(A,B)) ) ) ) )).
fof(t113_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(k10_xtuple_0(A),k10_xtuple_0(B)) => ! [C] : ~ ( r2_hidden(C,k9_xtuple_0(A)) & ! [D] : ~ ( r2_hidden(D,k9_xtuple_0(B)) & k1_funct_1(A,C) = k1_funct_1(B,D) ) ) ) ) ) )).
fof(t113_funct_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ( ! [E] : ( m1_subset_1(E,B) => r2_hidden(k3_funct_2(B,C,D,E),A) ) => r1_tarski(k2_relset_1(C,D),A) ) ) ) ) )).
fof(t113_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : k1_funct_1(k1_funct_4(A,k16_funcop_1(C,B)),C) = B ) )).
fof(t113_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ~ ( 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 ) ) )).
fof(t113_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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))) ) ) )).
fof(t113_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( 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))) ) ) ) ) ) )).
fof(t113_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_group_2(C,A) => ( r1_struct_0(C,B) <=> k13_group_2(A,C,B) = k8_group_2(A,C) ) ) ) ) )).
fof(t113_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t113_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v8_group_9(C,A,B) & m2_finseq_1(C,k6_group_9(A,B)) ) => r5_group_9(A,B,B,C,C) ) ) )).
fof(t113_jgraph_4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(B,k7_xcmplx_0(k17_euclid(A),k12_euclid(A))) => ( r1_xxreal_0(k5_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(k3_xcmplx_0(k12_euclid(A),k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k17_euclid(A),k12_euclid(A)),B),k6_xcmplx_0(1,B))),k3_xcmplx_0(k12_euclid(A),k4_xcmplx_0(k3_square_1(k6_xcmplx_0(1,k1_square_1(k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k17_euclid(A),k12_euclid(A)),B),k6_xcmplx_0(1,B)))))))) ) ) & ( r1_xxreal_0(k5_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 ) ) ) ) )).
fof(t113_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t113_jordan2c,axiom,( ! [A] : ( ( v2_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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)) ) ) ) )).
fof(t113_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v3_limfunc1(A) & k4_limfunc1(A) = k5_numbers ) => ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & r2_hidden(C,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k3_limfunc1(B))) & r1_xxreal_0(k5_numbers,k1_funct_1(A,C)) ) ) | v5_limfunc1(k6_rfunct_1(k1_numbers,k1_numbers,A)) ) ) ) )).
fof(t113_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ( ! [G] : ( v7_ordinal1(G) => ( r2_hidden(G,k2_finseq_1(A)) => k3_matrix_0(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(k4_ordinal1,k2_finseq_1(k1_matrix_0(D)),k3_matrix13(E)))) ) ) ) ) ) ) ) ) )).
fof(t113_member_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) )).
fof(t113_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( 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) ) ) ) ) )).
fof(t113_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t113_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t113_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k2_numbers) => ! [C] : ( m1_subset_1(C,k2_numbers) => k19_rvsum_1(k2_finseq_2(A,k3_xcmplx_0(B,C))) = k3_xcmplx_0(k20_rvsum_1(k5_finseq_2(k2_numbers,A,B)),k20_rvsum_1(k5_finseq_2(k2_numbers,A,C))) ) ) ) )).
fof(t113_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => k5_memstr_0(2,k1_scmpds_2,k6_scmpds_4(k10_scmpds_6(D,E,C),B,A)) = k1_nat_1(k5_card_1(C),2) ) ) ) ) ) )).
fof(t113_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => k1_funct_1(k13_scmyciel(A),k5_numbers) = A ) )).
fof(t113_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t113_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( 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,C)) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,D) => ( ~ r1_xxreal_0(k1_funct_1(E,H),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(E,H)) ) ) ) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,D) => k1_funct_1(F,H) = k2_xcmplx_0(A,k3_xcmplx_0(B,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,C)),k1_sin_cos9),D) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,D) => k1_funct_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,C)),k1_sin_cos9),D),H) = k7_xcmplx_0(k2_xcmplx_0(B,k3_xcmplx_0(k3_xcmplx_0(2,C),H)),k2_xcmplx_0(1,k1_square_1(k2_xcmplx_0(k2_xcmplx_0(A,k3_xcmplx_0(B,H)),k3_xcmplx_0(C,k1_square_1(H)))))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t113_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,k3_square_1(2)) ) => ( k1_funct_1(k16_sin_cos,k5_sincos10(A)) = k7_xcmplx_0(k3_square_1(k6_xcmplx_0(k1_square_1(A),1)),A) & k1_funct_1(k18_sin_cos,k5_sincos10(A)) = k7_xcmplx_0(1,A) ) ) ) )).
fof(t113_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ v2_struct_0(E) & m1_pre_topc(E,A) ) => ( A = k1_tsep_1(A,D,E) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t113_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : 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)) )).
fof(t113_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => ( k6_xboolean(A,B) = k2_xboolean => k6_xboolean(k6_xboolean(B,C),k6_xboolean(A,C)) = k2_xboolean ) ) ) ) )).
fof(t113_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( B != k5_numbers => k2_xcmplx_0(k7_xcmplx_0(A,B),C) = k7_xcmplx_0(k2_xcmplx_0(A,k3_xcmplx_0(B,C)),B) ) ) ) ) )).
fof(t113_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(k3_xcmplx_0(A,B),k7_xcmplx_0(C,D)) & r1_xxreal_0(k3_xcmplx_0(A,D),k7_xcmplx_0(C,B)) ) ) ) ) ) )).
fof(t113_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(D,C) & r1_tarski(k4_xxreal_1(C,D),k1_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t113_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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(B,k10_zf_lang(A,B))) & r2_zf_model(C,k11_zf_lang(B,k10_zf_lang(A,B))) ) ) ) ) ) )).
fof(t113_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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) ) ) ) )).
fof(t113_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( ( v1_zmodul01(C) & m1_zmodul01(C,A) ) => k7_zmodul01(A,C,k6_zmodul01(A,C,B)) = C ) ) ) )).
fof(t114_abcmiz_1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( k1_funct_1(B,C) = k1_xboole_0 & ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => k2_msualg_1(A,D) != C ) ) ) ) ) ) )).
fof(t114_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( m1_aofa_000(E,A,B,C) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t114_clvect_1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v9_clvect_1(B,A) & v9_clvect_1(C,A) ) => v9_clvect_1(k3_normsp_1(A,B,C),A) ) ) ) ) )).
fof(t114_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t114_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,B) ) => ! [D] : ( m1_subset_1(D,B) => k1_funct_1(k8_finseq_1(B,C,k12_finseq_1(B,D)),k1_nat_1(A,1)) = D ) ) ) ) )).
fof(t114_finseq_3,axiom,( ! [A] : ( ( 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 ) ) )).
fof(t114_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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,k2_xcmplx_0(k6_xcmplx_0(k3_finseq_1(C),B),1)) ) ) ) ) )).
fof(t114_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => r1_tarski(k2_flang_2(A,k1_flang_2(A,B,C,D)),k8_flang_1(A,B)) ) ) ) )).
fof(t114_funct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ! [F] : ( m1_subset_1(F,A) => ( v1_partfun1(E,B) => k3_funct_2(A,C,k8_funct_2(A,C,B,D,E),F) = k1_funct_1(E,k3_funct_2(A,B,D,F)) ) ) ) ) ) ) )).
fof(t114_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : 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)) ) )).
fof(t114_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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(k1_funct_7(E,C,D)) & v1_funct_2(k1_funct_7(E,C,D),A,B) & m1_subset_1(k1_funct_7(E,C,D),k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ) ) )).
fof(t114_gfacirc1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => k2_msafree2(k43_gfacirc1(A,B,C)) = k1_enumset1(A,B,C) ) ) ) )).
fof(t114_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m3_glib_001(D,B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t114_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t114_group_3,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t114_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v8_group_9(C,A,B) & m2_finseq_1(C,k6_group_9(A,B)) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t114_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t114_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,k5_numbers) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(A))) => ( C = k5_euclid(A) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(A))) => ( ( F = D & k1_rlvect_1(k15_euclid(A),F,B) = E ) => k3_xcmplx_0(B,k3_metric_1(k14_euclid(A),C,D)) = k3_metric_1(k14_euclid(A),C,E) ) ) ) ) ) ) ) ) ) )).
fof(t114_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v6_limfunc1(A) & k5_limfunc1(A) = k5_numbers ) => ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & r2_hidden(C,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k10_prob_1(B))) & r1_xxreal_0(k1_funct_1(A,C),k5_numbers) ) ) | v7_limfunc1(k6_rfunct_1(k1_numbers,k1_numbers,A)) ) ) ) )).
fof(t114_member_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t114_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( 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) ) ) ) ) )).
fof(t114_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,A) & v1_funct_1(E) & v1_partfun1(E,A) ) => ( ( r6_pboole(A,k2_pboole(A,D,E),k2_pboole(A,B,C)) & r5_pboole(A,B,D) & r5_pboole(A,C,E) ) => ( r6_pboole(A,B,E) & r6_pboole(A,C,D) ) ) ) ) ) ) )).
fof(t114_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t114_rvsum_1,axiom,( ! [A] : ( ( 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) ) )).
fof(t114_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( r1_xxreal_0(k5_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) ) ) ) ) ) ) ) )).
fof(t114_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k12_seq_4(A))) => ( D != k1_xboole_0 => r1_xxreal_0(k22_seq_4(A,k13_seq_4(A,B,C),D),k2_xcmplx_0(k22_seq_4(A,B,D),k20_seq_4(C))) ) ) ) ) ) )).
fof(t114_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t114_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( 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,C)) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,D) => ( ~ r1_xxreal_0(k1_funct_1(E,H),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(E,H)) ) ) ) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,D) => k1_funct_1(F,H) = k2_xcmplx_0(A,k3_xcmplx_0(B,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,C)),k2_sin_cos9),D) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,D) => k1_funct_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,C)),k2_sin_cos9),D),H) = k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,k3_xcmplx_0(k3_xcmplx_0(2,C),H)),k2_xcmplx_0(1,k1_square_1(k2_xcmplx_0(k2_xcmplx_0(A,k3_xcmplx_0(B,H)),k3_xcmplx_0(C,k1_square_1(H))))))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t114_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(k3_square_1(2)),A) & r1_xxreal_0(A,k4_xcmplx_0(1)) ) => ( k1_funct_1(k16_sin_cos,k6_sincos10(A)) = k4_xcmplx_0(k7_xcmplx_0(k3_square_1(k6_xcmplx_0(k1_square_1(A),1)),A)) & k1_funct_1(k18_sin_cos,k6_sincos10(A)) = k7_xcmplx_0(1,A) ) ) ) )).
fof(t114_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( r4_tsep_1(A,C,D) => ! [E] : ( ( 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)))) ) ) ) ) ) ) ) ) )).
fof(t114_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) )).
fof(t114_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ( k6_xboolean(A,k6_xboolean(A,B)) = k2_xboolean => k6_xboolean(A,B) = k2_xboolean ) ) ) )).
fof(t114_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( C != k5_numbers => k2_xcmplx_0(A,B) = k3_xcmplx_0(C,k2_xcmplx_0(k7_xcmplx_0(A,C),k7_xcmplx_0(B,C))) ) ) ) ) )).
fof(t114_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(k7_xcmplx_0(C,D),k3_xcmplx_0(A,B)) & r1_xxreal_0(k3_xcmplx_0(A,D),k7_xcmplx_0(C,B)) ) ) ) ) ) )).
fof(t114_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(D,C) & r1_tarski(k2_xxreal_1(C,D),k1_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t114_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t114_zfmisc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(t114_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( 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))) ) ) ) ) )).
fof(t115_abcmiz_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => ! [B] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t115_clvect_1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v9_clvect_1(C,A) => v9_clvect_1(k4_normsp_1(A,C,B),A) ) ) ) ) )).
fof(t115_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v3_card_1(C,k1_nat_1(A,1)) & m2_finseq_1(C,B) ) => ? [D] : ( m2_finseq_2(D,B,k4_finseq_2(A,B)) & ? [E] : ( m1_subset_1(E,B) & C = k8_finseq_1(B,D,k12_finseq_1(B,E)) ) ) ) ) ) )).
fof(t115_finseq_3,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => m2_finseq_1(A,k1_numbers) ) )).
fof(t115_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(1,C) => k3_finseq_6(A,B,1,C) = k17_finseq_1(A,C,B) ) ) ) ) )).
fof(t115_flang_2,axiom,( ! [A] : ! [B] : ( 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)))) ) )).
fof(t115_funct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ! [F] : ( m1_subset_1(F,A) => ( v1_partfun1(E,B) => k3_funct_2(A,C,k8_funct_2(A,C,B,D,E),F) = k7_partfun1(C,E,k3_funct_2(A,B,D,F)) ) ) ) ) ) ) )).
fof(t115_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r1_xboole_0(k9_xtuple_0(B),k9_xtuple_0(C)) => k1_funct_4(k1_funct_4(k1_funct_4(A,B),C),B) = k1_funct_4(k1_funct_4(A,B),C) ) ) ) ) )).
fof(t115_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( r1_tarski(k10_xtuple_0(B),A) => k6_funct_4(B,C,D) = k3_relat_1(B,k1_funct_7(k6_partfun1(A),C,D)) ) ) )).
fof(t115_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k43_gfacirc1(A,B,C),k44_gfacirc1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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)) ) ) ) ) ) ) )).
fof(t115_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( 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)) ) ) ) ) ) )).
fof(t115_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t115_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( v15_algstr_0(C) & v1_group_3(C,A) & m1_group_2(C,A) ) => v1_group_3(k10_group_2(A,B,C),A) ) ) ) )).
fof(t115_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v8_group_9(C,A,B) & m2_finseq_1(C,k6_group_9(A,B)) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t115_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t115_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(B,k5_numbers) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => ( D = k5_euclid(A) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( E = k8_metric_1(k14_euclid(A),D,C) => k1_convex1(k15_euclid(A),E,B) = k8_metric_1(k14_euclid(A),D,k3_xcmplx_0(B,C)) ) ) ) ) ) ) ) ) )).
fof(t115_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v6_limfunc1(A) & k5_limfunc1(A) = k5_numbers ) => ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & r2_hidden(C,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k10_prob_1(B))) & r1_xxreal_0(k5_numbers,k1_funct_1(A,C)) ) ) | v8_limfunc1(k6_rfunct_1(k1_numbers,k1_numbers,A)) ) ) ) )).
fof(t115_matrix13,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) ) => ( v1_vectsp_7(D,A,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t115_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => k15_member_1(A,B) = a_2_7_member_1(A,B) ) ) )).
fof(t115_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r13_ncfcont1(A,A,B,k1_partfun2(u1_struct_0(A),B)) ) ) )).
fof(t115_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t115_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r1_tarski(A,B) => r1_tarski(k7_relat_1(C,A),k7_relat_1(C,B)) ) ) )).
fof(t115_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t115_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( ~ r1_xxreal_0(k5_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) ) ) ) ) ) ) ) )).
fof(t115_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( v4_scmyciel(B) => ! [C] : ( v7_ordinal1(C) => k1_funct_1(k13_scmyciel(A),k1_nat_1(C,1)) = k12_scmyciel(k1_funct_1(k13_scmyciel(A),C)) ) ) ) )).
fof(t115_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k12_seq_4(A))) => ( r2_hidden(B,C) => k22_seq_4(A,B,C) = k5_numbers ) ) ) ) )).
fof(t115_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t115_sin_cos9,axiom,( ! [A] : ( ( 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,k22_sin_cos,k1_sin_cos9))) & ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & r1_xxreal_0(1,k1_funct_1(k22_sin_cos,B)) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_sin_cos9),A),B) = k7_xcmplx_0(k1_funct_1(k22_sin_cos,B),k2_xcmplx_0(1,k1_square_1(k1_funct_1(k22_sin_cos,B)))) ) ) ) ) ) )).
fof(t115_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(k3_square_1(2)),A) & r1_xxreal_0(A,k4_xcmplx_0(1)) ) => ( k1_funct_1(k16_sin_cos,k7_sincos10(A)) = k7_xcmplx_0(1,A) & k1_funct_1(k18_sin_cos,k7_sincos10(A)) = k4_xcmplx_0(k7_xcmplx_0(k3_square_1(k6_xcmplx_0(k1_square_1(A),1)),A)) ) ) ) )).
fof(t115_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_borsuk_1(C,A) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & v1_borsuk_1(D,A) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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)))) ) ) ) ) ) ) ) )).
fof(t115_xboole_1,axiom,( ! [A] : ~ r2_xboole_0(A,k1_xboole_0) )).
fof(t115_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => ( k6_xboolean(A,k6_xboolean(B,C)) = k2_xboolean => k6_xboolean(k6_xboolean(A,B),k6_xboolean(A,C)) = k2_xboolean ) ) ) ) )).
fof(t115_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( C != k5_numbers => k2_xcmplx_0(A,B) = k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)),C) ) ) ) ) )).
fof(t115_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(k5_numbers,D) & ~ r1_xxreal_0(k7_xcmplx_0(C,D),k3_xcmplx_0(A,B)) & r1_xxreal_0(k3_xcmplx_0(A,D),k7_xcmplx_0(C,B)) ) ) ) ) ) )).
fof(t115_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(D,C) & r1_tarski(k3_xxreal_1(C,D),k1_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t115_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t115_zfmisc_1,axiom,( ! [A] : ! [B] : ( r2_hidden(A,B) => k2_xboole_0(k4_xboole_0(B,k1_tarski(A)),k1_tarski(A)) = B ) )).
fof(t115_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t116_abcmiz_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t116_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( m1_aofa_000(E,A,B,C) => ! [F] : ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t116_clvect_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( v9_clvect_1(C,B) => v9_clvect_1(k6_clvect_1(B,C,A),B) ) ) ) ) )).
fof(t116_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,B) ) => k3_relat_1(k1_finseq_2(A),C) = C ) ) ) )).
fof(t116_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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(k4_ordinal1,A),k1_relset_1(k4_ordinal1,B)) ) ) ) )).
fof(t116_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ( 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) ) ) ) ) )).
fof(t116_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t116_funct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ! [D] : ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t116_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : 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)) ) ) )).
fof(t116_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k43_gfacirc1(A,B,C),k44_gfacirc1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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)) ) ) ) ) ) )).
fof(t116_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v1_glib_001(B,A) <=> k1_funct_1(B,1) = k1_funct_1(B,k3_finseq_1(B)) ) ) ) )).
fof(t116_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t116_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t116_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v8_group_9(C,A,B) & m2_finseq_1(C,k6_group_9(A,B)) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t116_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( 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] : ( 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) = k3_xcmplx_0(k12_euclid(D),k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k17_euclid(D),k12_euclid(D)),A),k6_xcmplx_0(1,A))) ) ) & ! [D] : ( 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),k5_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) ) ) ) ) ) )).
fof(t116_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t116_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r1_xxreal_0(C,D) => ( r1_xxreal_0(C,k5_numbers) | ! [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(A))) => ( E = k5_euclid(A) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( F = k8_metric_1(k14_euclid(A),E,B) => r1_tarski(k1_convex1(k15_euclid(A),F,C),k1_convex1(k15_euclid(A),F,D)) ) ) ) ) ) ) ) ) ) ) )).
fof(t116_matrix13,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( 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] : ( m1_subset_1(F,u1_struct_0(B)) & ? [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(t116_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( ( r2_hidden(C,A) & r2_hidden(D,B) ) => r2_hidden(k7_xcmplx_0(C,D),k15_member_1(A,B)) ) ) ) ) ) )).
fof(t116_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ! [D] : ( ( 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) ) ) ) ) )).
fof(t116_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t116_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => ( r1_tarski(B,C) => r1_tarski(k7_relat_1(B,A),k7_relat_1(C,A)) ) ) ) )).
fof(t116_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t116_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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) ) ) ) ) )).
fof(t116_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t116_sin_cos9,axiom,( ! [A] : ( ( 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,k22_sin_cos,k2_sin_cos9))) & ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & r1_xxreal_0(1,k1_funct_1(k22_sin_cos,B)) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k2_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k2_sin_cos9),A),B) = k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k22_sin_cos,B),k2_xcmplx_0(1,k1_square_1(k1_funct_1(k22_sin_cos,B))))) ) ) ) ) ) )).
fof(t116_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,k3_square_1(2)) ) => ( k1_funct_1(k16_sin_cos,k8_sincos10(A)) = k7_xcmplx_0(1,A) & k1_funct_1(k18_sin_cos,k8_sincos10(A)) = k7_xcmplx_0(k3_square_1(k6_xcmplx_0(k1_square_1(A),1)),A) ) ) ) )).
fof(t116_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_tsep_1(C,A) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & v1_tsep_1(D,A) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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)))) ) ) ) ) ) ) ) )).
fof(t116_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : k3_xboole_0(A,k3_xboole_0(B,C)) = k3_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)) )).
fof(t116_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ( ( k6_xboolean(A,B) = k2_xboolean & k6_xboolean(B,A) = k2_xboolean ) => A = B ) ) ) )).
fof(t116_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ~ ( B != k5_numbers & D != k5_numbers & k2_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,D)) != k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(C,B)),k3_xcmplx_0(B,D)) ) ) ) ) ) )).
fof(t116_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(k3_xcmplx_0(A,B),k7_xcmplx_0(C,D)) & r1_xxreal_0(k7_xcmplx_0(C,B),k3_xcmplx_0(A,D)) ) ) ) ) ) )).
fof(t116_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(D,B) & r1_xxreal_0(C,D) & r1_tarski(k1_xxreal_1(C,D),k1_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t116_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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,C),k11_zf_lang(k11_zf_lang(B,C),k11_zf_lang(k10_zf_lang(A,B),C)))) & r2_zf_model(D,k11_zf_lang(k11_zf_lang(A,C),k11_zf_lang(k11_zf_lang(B,C),k11_zf_lang(k10_zf_lang(A,B),C)))) ) ) ) ) ) ) )).
fof(t116_zfmisc_1,axiom,( ! [A] : ! [B] : ( ~ r2_hidden(A,B) => k4_xboole_0(k2_xboole_0(B,k1_tarski(A)),k1_tarski(A)) = B ) )).
fof(t116_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( m1_zmodul01(D,A) => m1_zmodul01(k6_zmodul01(A,C,k7_zmodul01(A,B,D)),k7_zmodul01(A,k6_zmodul01(A,B,C),k6_zmodul01(A,C,D))) ) ) ) ) )).
fof(t117_abcmiz_1,axiom,( ! [A] : ( l1_msualg_1(A) => ! [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] : ( ( 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) ) ) ) ) )).
fof(t117_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_aofa_000(D,A,B,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t117_clvect_1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v9_clvect_1(B,A) => v2_comseq_2(k5_normsp_0(A,B)) ) ) ) )).
fof(t117_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,B) ) => ! [D] : ( ( v3_card_1(D,A) & m2_finseq_1(D,B) ) => ( ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k2_finseq_1(A)) => k1_funct_1(C,E) = k1_funct_1(D,E) ) ) => C = D ) ) ) ) ) )).
fof(t117_finseq_3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( ( B != k5_numbers & A = k1_xboole_0 ) <=> k4_finseq_2(B,A) = k1_xboole_0 ) ) )).
fof(t117_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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(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)) = k1_nat_1(k7_nat_d(D,C),1) & ! [E] : ( v7_ordinal1(E) => ( ( 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_xcmplx_0(E,C),1)) ) ) ) ) & ( ~ r1_xxreal_0(C,D) => ( k3_finseq_1(k3_finseq_6(A,B,C,D)) = k1_nat_1(k7_nat_d(C,D),1) & ! [E] : ( v7_ordinal1(E) => ( ( 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,k1_nat_1(k7_nat_d(C,E),1)) ) ) ) ) ) ) ) ) ) ) )).
fof(t117_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t117_funct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ! [D] : ! [E] : ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,A,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [G] : ( ( 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))) ) ) ) ) ) )).
fof(t117_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r1_xboole_0(k9_xtuple_0(A),k9_xtuple_0(C)) & r1_tarski(A,B) ) => r1_tarski(A,k1_funct_4(B,C)) ) ) ) ) )).
fof(t117_funct_7,axiom,( ! [A] : ! [B] : k9_xtuple_0(k10_funct_7(A,B)) = k4_ordinal1 )).
fof(t117_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k43_gfacirc1(A,B,C),k44_gfacirc1(A,B,C)))) & ? [E] : ( m1_subset_1(E,k6_margrel1) & ? [F] : ( m1_subset_1(F,k6_margrel1) & ? [G] : ( 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)) ) ) ) ) ) ) )).
fof(t117_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v1_glib_001(B,A) <=> ? [C] : r1_glib_001(A,C,C,B) ) ) ) )).
fof(t117_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t117_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ( ( v1_group_3(B,A) & m1_group_2(B,A) ) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k13_group_2(A,B,C) = k14_group_2(A,B,C) ) ) ) ) )).
fof(t117_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v8_group_9(C,A,B) & m2_finseq_1(C,k6_group_9(A,B)) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t117_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( 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] : ( 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) = k3_xcmplx_0(k12_euclid(D),k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k17_euclid(D),k12_euclid(D)),A),k2_xcmplx_0(1,A))) ) ) & ! [D] : ( 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),k5_numbers) & D != k4_struct_0(k15_euclid(2)) ) ) ) ) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) | v5_pre_topc(C,k1_pre_topc(k15_euclid(2),B),k3_topmetr) ) ) ) ) ) )).
fof(t117_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t117_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(C),A,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(C))) ) => ( ( v1_vectsp_7(k9_matrix13(C,A,B,E),C,k6_prvect_1(C,B)) & v2_funct_1(E) ) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ( r2_hidden(G,k2_finseq_1(k3_finseq_1(E))) => ( F = G | ( v2_funct_1(k3_matrix11(F,A,B,u1_struct_0(C),E,k4_fvsum_1(k1_matrix_0(E),C,k7_matrix_0(u1_struct_0(C),E,F),k10_fvsum_1(k1_matrix_0(E),C,k7_matrix_0(u1_struct_0(C),E,G),D)))) & v1_vectsp_7(k9_matrix13(C,A,B,k3_matrix11(F,A,B,u1_struct_0(C),E,k4_fvsum_1(k1_matrix_0(E),C,k7_matrix_0(u1_struct_0(C),E,F),k10_fvsum_1(k1_matrix_0(E),C,k7_matrix_0(u1_struct_0(C),E,G),D)))),C,k6_prvect_1(C,B)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t117_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_membered(C) => ! [D] : ( v1_membered(D) => ( ( r1_tarski(A,B) & r1_tarski(C,D) ) => r1_tarski(k15_member_1(A,C),k15_member_1(B,D)) ) ) ) ) ) )).
fof(t117_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( 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) ) ) ) ) )).
fof(t117_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t117_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ! [D] : ( v1_relat_1(D) => ( ( r1_tarski(C,D) & r1_tarski(A,B) ) => r1_tarski(k7_relat_1(C,A),k7_relat_1(D,B)) ) ) ) )).
fof(t117_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) ) ) )).
fof(t117_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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) ) ) ) ) )).
fof(t117_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k12_seq_4(A))) => ( D != k1_xboole_0 => r1_xxreal_0(k22_seq_4(A,C,D),k2_xcmplx_0(k20_seq_4(k17_seq_4(A,C,B)),k22_seq_4(A,B,D))) ) ) ) ) ) )).
fof(t117_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t117_sin_cos9,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k3_taylor_1,B),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k1_sin_cos9),A),B) = k7_xcmplx_0(1,k3_xcmplx_0(B,k2_xcmplx_0(1,k1_square_1(k1_funct_1(k3_taylor_1,B))))) ) ) ) ) ) )).
fof(t117_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,1) & ~ r1_xxreal_0(k3_square_1(2),A) & k1_funct_1(k2_fdiff_9,k5_sincos10(A)) != k7_xcmplx_0(A,k3_square_1(k6_xcmplx_0(k1_square_1(A),1))) ) ) )).
fof(t117_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( r4_tsep_1(A,C,D) => ! [E] : ( ( 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)))) ) ) ) ) ) ) ) ) )).
fof(t117_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t117_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => ( ( k6_xboolean(A,B) = k2_xboolean & k6_xboolean(B,C) = k2_xboolean ) => k6_xboolean(A,C) = k2_xboolean ) ) ) ) )).
fof(t117_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( A != k5_numbers => k2_xcmplx_0(A,B) = k3_xcmplx_0(A,k2_xcmplx_0(1,k7_xcmplx_0(B,A))) ) ) ) )).
fof(t117_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(k5_numbers,D) & ~ r1_xxreal_0(k3_xcmplx_0(A,B),k7_xcmplx_0(C,D)) & r1_xxreal_0(k7_xcmplx_0(C,B),k3_xcmplx_0(A,D)) ) ) ) ) ) )).
fof(t117_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(D,C) & r1_tarski(k4_xxreal_1(C,D),k2_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t117_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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,C),k11_zf_lang(B,C)),k11_zf_lang(k10_zf_lang(A,B),C))) & r2_zf_model(D,k11_zf_lang(k7_zf_lang(k11_zf_lang(A,C),k11_zf_lang(B,C)),k11_zf_lang(k10_zf_lang(A,B),C))) ) ) ) ) ) ) )).
fof(t117_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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) ) ) )).
fof(t117_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t118_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t118_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_aofa_000(D,A,B,C) => ! [E] : ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t118_clvect_1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v9_clvect_1(C,A) & k7_clvect_1(A,C) = B ) => ( v2_comseq_2(k5_normsp_0(A,k4_normsp_1(A,C,B))) & k1_seq_2(k5_normsp_0(A,k4_normsp_1(A,C,B))) = k5_numbers ) ) ) ) ) )).
fof(t118_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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] : ( ( v3_card_1(F,A) & m2_finseq_1(F,B) ) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t118_finseq_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( 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(k4_ordinal1,k4_finseqop(A,B,C,D)) = k1_relset_1(k4_ordinal1,C) & k3_finseq_1(k4_finseqop(A,B,C,D)) = k3_finseq_1(C) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k1_relset_1(k4_ordinal1,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)) ) ) ) ) ) ) ) )).
fof(t118_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => r1_tarski(k10_xtuple_0(k3_finseq_6(A,B,C,D)),k10_xtuple_0(B)) ) ) ) ) )).
fof(t118_funct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t118_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r1_xboole_0(k9_xtuple_0(B),k9_xtuple_0(C)) => k1_funct_4(k1_funct_4(A,B),C) = k1_funct_4(k1_funct_4(A,C),B) ) ) ) ) )).
fof(t118_funct_7,axiom,( ! [A] : ! [B] : k1_funct_1(k10_funct_7(A,B),k5_numbers) = A )).
fof(t118_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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] : ( 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)) ) ) )).
fof(t118_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v1_glib_001(B,A) <=> v1_glib_001(k6_glib_001(A,B),A) ) ) ) )).
fof(t118_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t118_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ( ( v1_group_3(B,A) & m1_group_2(B,A) ) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_tarski(k13_group_2(A,B,C),k14_group_2(A,B,C)) ) ) ) ) )).
fof(t118_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v8_group_9(C,A,B) & m2_finseq_1(C,k6_group_9(A,B)) ) => ! [D] : ( ( v8_group_9(D,A,B) & m2_finseq_1(D,k6_group_9(A,B)) ) => ? [E] : ( v8_group_9(E,A,B) & m2_finseq_1(E,k6_group_9(A,B)) & ? [F] : ( 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) ) ) ) ) ) )).
fof(t118_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( 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] : ( 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) = k3_xcmplx_0(k12_euclid(D),k4_xcmplx_0(k3_square_1(k6_xcmplx_0(1,k1_square_1(k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k17_euclid(D),k12_euclid(D)),A),k6_xcmplx_0(1,A))))))) ) ) & ! [D] : ( 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),k5_numbers) & r1_xxreal_0(A,k7_xcmplx_0(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) ) ) ) ) ) )).
fof(t118_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t118_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(C),A,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(C))) ) => ( 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)) ) ) ) ) ) ) )).
fof(t118_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t118_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( 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) ) ) ) ) )).
fof(t118_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) )).
fof(t118_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => k7_relat_1(k3_relat_1(B,C),A) = k7_relat_1(C,k7_relat_1(B,A)) ) ) )).
fof(t118_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t118_scmyciel,axiom,( ! [A] : ( 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) ) ) )).
fof(t118_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k12_seq_4(A))) => ( r2_hidden(C,k23_seq_4(A,D,B)) <=> ~ r1_xxreal_0(B,k22_seq_4(A,C,D)) ) ) ) ) ) )).
fof(t118_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t118_sin_cos9,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k3_taylor_1,B),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k2_sin_cos9),A),B) = k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(B,k2_xcmplx_0(1,k1_square_1(k1_funct_1(k3_taylor_1,B)))))) ) ) ) ) ) )).
fof(t118_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(k3_square_1(2))) & ~ r1_xxreal_0(k4_xcmplx_0(1),A) & k1_funct_1(k2_fdiff_9,k6_sincos10(A)) != k4_xcmplx_0(k7_xcmplx_0(A,k3_square_1(k6_xcmplx_0(k1_square_1(A),1)))) ) ) )).
fof(t118_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ v2_struct_0(D) & v1_borsuk_1(D,A) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ 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)))) ) ) ) ) ) ) ) )).
fof(t118_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => k6_xboolean(k6_xboolean(k3_xboolean(A),A),A) = k2_xboolean ) )).
fof(t118_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( 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) ) ) )).
fof(t118_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(A,B) ) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(k7_xcmplx_0(C,B),k7_xcmplx_0(C,A)) ) ) ) ) ) )).
fof(t118_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( r1_xxreal_0(B,D) & ~ r1_xxreal_0(D,C) & r1_tarski(k3_xxreal_1(C,D),k2_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t118_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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)))) ) ) ) ) ) )).
fof(t118_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( r1_tarski(A,k2_zfmisc_1(C,E)) & r1_tarski(B,k2_zfmisc_1(D,F)) ) => r1_tarski(k2_xboole_0(A,B),k2_zfmisc_1(k2_xboole_0(C,D),k2_xboole_0(E,F))) ) )).
fof(t118_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( m1_zmodul01(D,A) => ( ( v1_zmodul01(B) & m1_zmodul01(B,D) ) => k6_zmodul01(A,B,k7_zmodul01(A,C,D)) = k7_zmodul01(A,k6_zmodul01(A,B,C),D) ) ) ) ) ) )).
fof(t119_abcmiz_1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [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] : ( ( 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))) ) ) ) ) )).
fof(t119_clvect_1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) )).
fof(t119_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t119_finseq_3,axiom,( ! [A] : ( ~ 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))) ) )).
fof(t119_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( r1_xxreal_0(1,k3_finseq_1(B)) => k3_finseq_6(A,B,1,k3_finseq_1(B)) = B ) ) ) )).
fof(t119_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( 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)))) ) ) ) ) )).
fof(t119_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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 ) ) ) )).
fof(t119_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(C,k5_numbers) => k1_funct_1(k10_funct_7(A,B),C) = B ) ) )).
fof(t119_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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))) )).
fof(t119_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m3_glib_001(D,B) => ( ( C = D & v1_glib_001(C,A) ) => v1_glib_001(D,B) ) ) ) ) ) )).
fof(t119_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_group_2(C,A) => ( r1_struct_0(C,B) <=> k14_group_2(A,C,B) = k8_group_2(A,C) ) ) ) ) )).
fof(t119_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ( ( v1_group_3(B,A) & m1_group_2(B,A) ) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_tarski(k14_group_2(A,B,C),k13_group_2(A,B,C)) ) ) ) ) )).
fof(t119_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( 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] : ( 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) = k3_xcmplx_0(k12_euclid(D),k4_xcmplx_0(k3_square_1(k6_xcmplx_0(1,k1_square_1(k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k17_euclid(D),k12_euclid(D)),A),k2_xcmplx_0(1,A))))))) ) ) & ! [D] : ( 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),k5_numbers) & r1_xxreal_0(k7_xcmplx_0(k17_euclid(D),k12_euclid(D)),A) & D != k4_struct_0(k15_euclid(2)) ) ) ) ) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) | v5_pre_topc(C,k1_pre_topc(k15_euclid(2),B),k3_topmetr) ) ) ) ) ) )).
fof(t119_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t119_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(C),A,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(C))) ) => ( ( 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)))) ) ) ) ) ) ) )).
fof(t119_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( 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))) ) ) ) )).
fof(t119_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t119_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => k10_xtuple_0(k3_relat_1(A,B)) = k7_relat_1(B,k10_xtuple_0(A)) ) ) )).
fof(t119_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => r1_xxreal_0(k5_numbers,k22_rvsum_1(A,A)) ) )).
fof(t119_scmyciel,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( v1_finset_1(B) & v4_scmyciel(B) & k8_scmyciel(B) = 2 & ~ r1_xxreal_0(k10_scmyciel(B),A) ) ) )).
fof(t119_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k12_seq_4(A))) => ( r2_hidden(C,D) => ( r1_xxreal_0(B,k5_numbers) | r2_hidden(C,k23_seq_4(A,D,B)) ) ) ) ) ) ) )).
fof(t119_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t119_sin_cos9,axiom,( ! [A] : ( ( 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,k22_sin_cos))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k22_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k22_sin_cos),A),B) = k7_xcmplx_0(k1_funct_1(k22_sin_cos,k1_funct_1(k1_sin_cos9,B)),k2_xcmplx_0(1,k1_square_1(B))) ) ) ) ) ) )).
fof(t119_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(k3_square_1(2))) & ~ r1_xxreal_0(k4_xcmplx_0(1),A) & k1_funct_1(k1_fdiff_9,k7_sincos10(A)) != k4_xcmplx_0(k7_xcmplx_0(A,k3_square_1(k6_xcmplx_0(k1_square_1(A),1)))) ) ) )).
fof(t119_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ v2_struct_0(D) & v1_tsep_1(D,A) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ 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)))) ) ) ) ) ) ) ) )).
fof(t119_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ( k3_xboolean(A) = k2_xboolean => k6_xboolean(A,B) = k2_xboolean ) ) ) )).
fof(t119_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( 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) ) ) )).
fof(t119_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(D,C) & r1_tarski(k2_xxreal_1(C,D),k2_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t119_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t119_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( ~ r2_hidden(A,C) & ~ r2_hidden(B,C) & C != k4_xboole_0(C,k2_tarski(A,B)) ) )).
fof(t119_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_zmodul01(B) & m1_zmodul01(B,A) ) => ! [C] : ( ( v1_zmodul01(C) & m1_zmodul01(C,A) ) => ( k6_zmodul01(A,B,C) = C <=> k7_zmodul01(A,B,C) = B ) ) ) ) )).
fof(t11_abcmiz_0,axiom,( ! [A] : ( l2_abcmiz_0(A) => ! [B] : ( 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] : ( m1_subset_1(C,u1_abcmiz_0(A)) => ! [D] : ( m1_subset_1(D,u1_abcmiz_0(B)) => ( C = D => k3_abcmiz_0(A,C) = k3_abcmiz_0(B,D) ) ) ) ) ) ) )).
fof(t11_abcmiz_1,axiom,( ! [A] : ! [B] : k1_abcmiz_1(k2_xboole_0(A,B)) = k2_xboole_0(k1_abcmiz_1(A),k1_abcmiz_1(B)) )).
fof(t11_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & v1_abcmiz_a(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ~ ( ! [C] : ( 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] : ( 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 ) ) ) ) ) ) )).
fof(t11_abian,axiom,( ! [A] : ( v1_int_1(A) => ( v1_abian(A) <=> ? [B] : ( v1_int_1(B) & A = k3_xcmplx_0(2,B) ) ) ) )).
fof(t11_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k5_numbers,k3_xcmplx_0(A,B)) => k9_complex1(k2_xcmplx_0(A,B)) = k2_xcmplx_0(k9_complex1(A),k9_complex1(B)) ) ) ) )).
fof(t11_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ~ ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_aff_1(A,B,C,D) ) ) ) ) )).
fof(t11_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v2_aff_2(A) => v4_aff_2(A) ) ) )).
fof(t11_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(B,D) & r2_hidden(C,D) & v1_aff_1(D,A) ) ) ) ) )).
fof(t11_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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 ) ) ) )).
fof(t11_afinsq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & v1_finset_1(C) ) => k2_afinsq_2(k1_ordinal4(B,C),k2_xcmplx_0(k1_afinsq_1(B),A)) = k2_afinsq_2(C,A) ) ) ) )).
fof(t11_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t11_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ( ( r2_analoaf(A,B,C,G,H) & r2_analoaf(A,D,E,I,J) & r2_analoaf(A,C,F,D,E) & r2_analoaf(A,H,K,I,J) ) => r2_analoaf(A,B,F,G,K) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect01(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r1_afvect01(A,B,C) & B = C ) ) ) ) )).
fof(t11_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_unialg_1(C) & v3_unialg_1(C) & v4_unialg_1(C) & l1_unialg_1(C) ) => ! [D] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(t11_algspec1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => r6_pboole(A,k1_algspec1(A,k1_algspec1(A,B)),k1_algspec1(A,B)) ) )).
fof(t11_algstr_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k6_algstr_0(A,B,k5_struct_0(A)) = B ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & k6_algstr_0(A,B,C) = k5_struct_0(A) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t11_algstr_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k1_algstr_0(A,B,k4_struct_0(A)) = B ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & k1_algstr_0(A,B,C) = k4_struct_0(A) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => k6_algstr_0(A,B,k5_struct_0(A)) = B ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ( B != k4_struct_0(A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_algstr_0(A,B,C) != k5_struct_0(A) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_algstr_0(A,B,k4_struct_0(A)) = k4_struct_0(A) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_algstr_0(A,k4_struct_0(A),B) = k4_struct_0(A) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t11_algstr_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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))) ) ) ) ) ) ) )).
fof(t11_altcat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t11_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v6_altcat_3(B,A) & r2_altcat_3(A,B,C) ) => v6_altcat_3(C,A) ) ) ) ) )).
fof(t11_ami_2,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k3_ami_2,k4_ami_2))) => ! [B] : ( m2_subset_1(B,k1_ami_2,k2_ami_2) => ! [C] : ( v1_int_1(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t11_ami_5,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => ~ ( k2_compos_0(u1_compos_1(k1_ami_3),A) = 5 & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_ami_3)) ) => A != k6_ami_3(B,C) ) ) ) ) )).
fof(t11_ami_6,axiom,( ! [A] : ( 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) ) ) )).
fof(t11_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k4_ordinal1) => k4_ami_wstd(A,B,C,k5_numbers) = C ) ) ) )).
fof(t11_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( v7_ordinal1(B) => k3_amistd_1(A,k4_amistd_1(A),B) = k2_tarski(B,k1_ordinal1(B)) ) ) )).
fof(t11_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_compos_1(B)) => ( v2_extpro_1(C,A,B) => v1_xboole_0(k3_amistd_4(A,B,C)) ) ) ) ) )).
fof(t11_amistd_5,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) & ~ v2_compos_1(C,B) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ( 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)) ) ) ) ) ) ) ) )).
fof(t11_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r1_analmetr(A,C,D) & r2_analmetr(A,B,B,C,D) ) => B = k4_struct_0(A) ) ) ) ) ) )).
fof(t11_analoaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t11_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_analmetr(A,D,E) => k2_analort(A,D,E,k5_algstr_0(A,B,C)) = k5_algstr_0(A,k2_analort(A,D,E,B),k2_analort(A,D,E,C)) ) ) ) ) ) ) )).
fof(t11_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t11_anproj_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( m2_funct_2(C,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [D] : ( m2_funct_2(D,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ( ( k3_funct_2(A,k1_numbers,B,E) = 1 & ! [H] : ( r2_hidden(H,A) => ( H = E | k1_funct_1(B,H) = k5_numbers ) ) & k3_funct_2(A,k1_numbers,C,F) = 1 & ! [H] : ( r2_hidden(H,A) => ( H = F | k1_funct_1(C,H) = k5_numbers ) ) & k3_funct_2(A,k1_numbers,D,G) = 1 & ! [H] : ( r2_hidden(H,A) => ( H = G | k1_funct_1(D,H) = k5_numbers ) ) ) => ( E = F | E = G | F = G | ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ( k1_binop_1(k5_funcsdom(A),k1_binop_1(k5_funcsdom(A),k1_funct_1(k7_funcsdom(A),k4_tarski(H,B)),k1_funct_1(k7_funcsdom(A),k4_tarski(I,C))),k1_funct_1(k7_funcsdom(A),k4_tarski(J,D))) = k8_funcsdom(A) => ( H = k5_numbers & I = k5_numbers & J = k5_numbers ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_aofa_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( ( 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)) ) ) ) )).
fof(t11_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ~ ( B != C & A != B & A != C & k10_xtuple_0(k1_borsuk_7(A,B,C,D,E,F)) != k1_enumset1(D,E,F) ) )).
fof(t11_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ( B = k10_subset_1(k1_funct_1(u7_aofa_a00(A),1),u4_struct_0(A)) => ( B = k1_funct_1(u7_aofa_a00(A),1) & k1_msualg_1(A,B) = k1_xboole_0 & k2_msualg_1(A,B) = u8_aofa_a00(A) ) ) ) ) )).
fof(t11_aofa_i00,axiom,( ! [A] : ( v4_card_3(A) => ! [B] : ( ( 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),k4_ordinal1) ) ) )).
fof(t11_armstrng,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_armstrng(A)) => ! [C] : ( m1_subset_1(C,k4_armstrng(A)) => ( ( r3_armstrng(A,C,B) & r3_armstrng(A,B,C) ) => B = C ) ) ) )).
fof(t11_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ( B = k5_numbers => k1_arytm_0(A,B) = A ) ) ) )).
fof(t11_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => r1_arytm_2(k1_arytm_1(A,B),A) ) ) )).
fof(t11_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( k7_arytm_2(A,B) = k7_arytm_2(A,C) => B = C ) ) ) ) )).
fof(t11_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ! [C] : ( ( v3_ordinal1(C) & v7_ordinal1(C) ) => ( ( r2_arytm_3(A,B) & r2_arytm_3(A,k8_ordinal3(B,C)) ) => r2_arytm_3(A,C) ) ) ) ) )).
fof(t11_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(A,k6_asympt_0(B)) => r1_tarski(k6_asympt_0(A),k6_asympt_0(B)) ) ) ) )).
fof(t11_asympt_1,axiom,( r2_hidden(k3_asympt_1(2),k6_asympt_0(k3_asympt_1(3))) )).
fof(t11_autalg_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(t11_autgroup,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t11_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ! [E] : ( m2_finseq_1(E,k4_ordinal1) => ( ( D = k23_pre_poly(A,k7_pre_poly(A,k22_pre_poly(A,B),k2_orders_1(A)),B) & E = k23_pre_poly(A,k7_pre_poly(A,k1_finsub_1(k1_zfmisc_1(A),k22_pre_poly(A,B),C),k2_orders_1(A)),B) ) => k2_wsierp_1(D) = k2_wsierp_1(E) ) ) ) ) ) ) )).
fof(t11_bcialg_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) ) ) )).
fof(t11_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => 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) ) ) ) ) ) ) )).
fof(t11_bcialg_3,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t11_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t11_bcialg_5,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => r1_bcialg_1(A,k1_bcialg_5(A,C,B,k1_nat_1(D,1),k1_nat_1(D,1)),k1_bcialg_5(A,B,C,D,k1_nat_1(D,1))) ) ) ) ) )).
fof(t11_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ! [C] : ( m2_bcialg_1(C,A) => ( k9_subset_1(u1_struct_0(A),B,C) = k1_tarski(k4_struct_0(A)) <=> ! [D] : ( m2_subset_1(D,u1_struct_0(A),B) => ! [E] : ( m2_subset_1(E,u1_struct_0(A),C) => k1_bcialg_1(A,D,E) = D ) ) ) ) ) ) )).
fof(t11_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k2_bhsp_1(A,k5_algstr_0(A,B,C),D) = k6_xcmplx_0(k2_bhsp_1(A,B,D),k2_bhsp_1(A,C,D)) ) ) ) ) )).
fof(t11_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_funct_1(C) => ( ! [D] : ( v7_ordinal1(D) => k1_normsp_1(A,C,D) != B ) | k1_bhsp_2(A,C) = B ) ) ) ) ) )).
fof(t11_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => 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) ) ) ) ) )).
fof(t11_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_bhsp_4(B,A) => v2_bhsp_3(k1_bhsp_4(A,B),A) ) ) ) )).
fof(t11_bhsp_5,axiom,( ! [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_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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_finset_1(C) & m2_bhsp_5(C,A) ) => ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(E,C) => k1_funct_1(D,E) = k1_square_1(k2_bhsp_1(A,B,E)) ) ) ) => ! [E] : ( ( 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] : ( 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),k9_binop_2,C,D) ) ) ) ) ) ) ) ) ) )).
fof(t11_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(t11_binari_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k6_margrel1) ) => ! [D] : ( m1_subset_1(D,k6_margrel1) => ! [E] : ( m1_subset_1(E,k6_margrel1) => k6_xcmplx_0(k2_xcmplx_0(k3_binari_2(k2_xcmplx_0(A,1),k7_binarith(k2_xcmplx_0(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(k4_ordinal1,k4_binari_2(k2_xcmplx_0(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,k5_numbers,k5_series_1(2,k1_nat_1(A,1)))),k15_funcop_1(k4_ordinal1,k5_binari_2(k2_xcmplx_0(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,k5_numbers,k5_series_1(2,k1_nat_1(A,1)))) = k2_xcmplx_0(k3_binari_2(k2_xcmplx_0(A,1),k9_binarith(A,1,k6_margrel1,B,k10_binarith(k6_margrel1,D))),k3_binari_2(k2_xcmplx_0(A,1),k9_binarith(A,1,k6_margrel1,C,k10_binarith(k6_margrel1,E)))) ) ) ) ) ) )).
fof(t11_binari_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => k6_binarith(A,k1_binari_2(A)) = 1 ) )).
fof(t11_binari_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k2_xcmplx_0(B,C),k6_xcmplx_0(k5_series_1(2,A),1)) => k6_binarith(A,k7_binarith(A,k1_binari_3(A,B),k1_binari_3(A,C))) = k2_xcmplx_0(B,C) ) ) ) ) )).
fof(t11_binarith,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k5_xboolean(k5_xboolean(A,B),C) = k5_xboolean(A,k5_xboolean(B,C)) ) ) ) )).
fof(t11_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k2_binom(A,k2_binom(A,B,C),D) = k2_binom(A,B,k3_xcmplx_0(C,D)) ) ) ) ) )).
fof(t11_binop_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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,C,B) <=> ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( 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)) & 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)) ) ) ) ) ) ) ) )).
fof(t11_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ( A = k3_finseq_2(k7_domain_1(k4_ordinal1,k5_numbers,1)) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( m2_finseq_2(C,k6_margrel1,k4_finseq_2(B,k6_margrel1)) => r2_hidden(C,k2_trees_2(A,B)) ) ) ) ) )).
fof(t11_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t11_boolmark,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m2_funct_2(B,u1_struct_0(A),k6_margrel1,k1_boolmark(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t11_bor_cant,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( r2_funct_2(k4_ordinal1,k9_setfam_1(A),k4_setlim_1(A,B),k7_bor_cant(A,B)) & r2_funct_2(k4_ordinal1,k9_setfam_1(A),k2_setlim_1(A,B),k9_bor_cant(A,B)) ) ) )).
fof(t11_borsuk_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(A,B)))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t11_borsuk_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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] : ( ( 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,k5_numbers) & C = k1_funct_1(E,1) & v5_pre_topc(F,k5_topmetr,A) & C = k1_funct_1(F,k5_numbers) & D = k1_funct_1(F,1) & ! [G] : ( ( 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,k5_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))) ) ) ) ) ) ) ) ) ) )).
fof(t11_borsuk_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v1_compts_1(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ~ ( r1_tarski(k2_zfmisc_1(k2_struct_0(B),k1_tarski(D)),C) & ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t11_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t11_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t11_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( k17_sin_cos(A) = k17_sin_cos(B) & k19_sin_cos(A) = k19_sin_cos(B) & ! [C] : ( v1_int_1(C) => A != k2_xcmplx_0(B,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)) ) ) ) ) )).
fof(t11_brouwer,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xxreal_0(A) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_brouwer(B,C,A))) => ! [E] : ( ( 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 ) ) ) ) ) ) ) )).
fof(t11_bspace,axiom,( ! [A] : ! [B] : ( k3_bspace(A,B) != k4_struct_0(k2_bspace) <=> k3_bspace(A,B) = k5_struct_0(k2_bspace) ) )).
fof(t11_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t11_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t11_bvfunc14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : 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) )).
fof(t11_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t11_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(t11_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t11_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( m1_eqrel_1(D,A) => r1_bvfunc_1(A,k6_bvfunc_2(A,C,B,D),C) ) ) ) ) )).
fof(t11_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t11_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t11_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t11_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t11_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t11_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t11_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t11_c0sp1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(t11_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( 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 ) ) )).
fof(t11_calcul_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(A,k5_numbers) => k3_finseq_1(k14_finseq_1(k4_subset_1(k4_ordinal1,k2_finseq_1(B),k6_domain_1(k4_ordinal1,k1_nat_1(B,A))))) = k1_nat_1(B,1) ) ) ) )).
fof(t11_calcul_2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => k1_relset_1(k4_ordinal1,k14_finseq_1(k2_calcul_2(k3_finseq_1(C),k3_finseq_1(B)))) = k1_relset_1(k4_ordinal1,B) ) ) ) )).
fof(t11_cantor_1,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(t11_card_1,axiom,( ! [A] : ! [B] : ( r1_ordinal1(k1_card_1(A),k1_card_1(B)) <=> ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & k9_xtuple_0(C) = B & r1_tarski(A,k10_xtuple_0(C)) ) ) )).
fof(t11_card_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( r2_wellord2(E,G) & r2_wellord2(F,H) ) => ( A = B | C = D | ( r2_wellord2(k2_xboole_0(k2_zfmisc_1(E,k1_tarski(A)),k2_zfmisc_1(F,k1_tarski(B))),k2_xboole_0(k2_zfmisc_1(G,k1_tarski(C)),k2_zfmisc_1(H,k1_tarski(D)))) & k1_card_1(k2_xboole_0(k2_zfmisc_1(E,k1_tarski(A)),k2_zfmisc_1(F,k1_tarski(B)))) = k1_card_1(k2_xboole_0(k2_zfmisc_1(G,k1_tarski(C)),k2_zfmisc_1(H,k1_tarski(D)))) ) ) ) )).
fof(t11_card_3,axiom,( ! [A] : ! [B] : k1_funct_2(A,B) = k4_card_3(k7_funcop_1(A,B)) )).
fof(t11_card_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ( v4_card_3(k9_xtuple_0(A)) & ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => v4_card_3(k1_funct_1(A,B)) ) ) => v4_card_3(k3_card_3(A)) ) ) )).
fof(t11_card_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) ) => ( v2_ordinal2(A) => v2_funct_1(A) ) ) )).
fof(t11_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_card_fil(B,A) => r2_hidden(k1_xboole_0,B) ) ) )).
fof(t11_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ! [C] : k5_card_1(k1_card_fin(A,k5_card_1(A),B,C)) = 1 ) )).
fof(t11_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t11_cardfin2,axiom,( k2_cardfin2(k1_xboole_0) = k1_tarski(k1_xboole_0) )).
fof(t11_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k3_cat_1(A,B))) => ! [D] : ( 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 ) ) )).
fof(t11_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m3_cat_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k8_cat_1(B,A,k5_cat_2(A,B),C) = C ) ) ) )).
fof(t11_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( 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))) ) ) )).
fof(t11_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => v10_cat_1(k1_cat_4(A),A) ) )).
fof(t11_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => v3_cat_5(k3_cat_1(A,k4_tarski(k4_tarski(A,A),k10_cat_1(A)))) ) )).
fof(t11_catalan1,axiom,( k1_catalan1(1) = 1 )).
fof(t11_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ( ( v1_catalan2(B) & k3_xcmplx_0(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 ) ) ) ) )).
fof(t11_catalg_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_catalg_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ( r2_hidden(k5_catalg_1(C),u4_struct_0(B)) & ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(k6_catalg_1(C,D),u1_struct_0(B)) & ! [E] : ( m1_subset_1(E,A) => r2_hidden(k7_catalg_1(C,D,E),u4_struct_0(B)) ) ) ) ) ) ) ) )).
fof(t11_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v3_cayldick(A) & v4_normsp_0(A) & v3_normsp_0(A) & v2_normsp_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v8_rlvect_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v13_algstr_0(A) & v3_group_1(A) & v5_vectsp_1(A) & v4_vectsp_1(A) & v33_algstr_0(A) & v4_cayldick(A) ) => ( v6_struct_0(A) | k2_cayldick(A,k5_algstr_0(A,B,C)) = k5_algstr_0(A,k2_cayldick(A,B),k2_cayldick(A,C)) ) ) ) ) ) )).
fof(t11_cayley,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t11_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t11_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_cc0sp2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_cc0sp2(A))) => ! [D] : ( ( 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] : ( ( 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] : ( v1_xcmplx_0(F) => ( ( D = B & E = C ) => ( C = k1_clvect_1(k3_cc0sp2(A),B,F) <=> ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t11_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( 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(k4_ordinal1,k2_numbers,k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,A,k2_cfunct_1(k2_numbers,B)),k36_valued_1(k4_ordinal1,k2_numbers,k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,A,B))) ) ) ) )).
fof(t11_cfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_numbers)) => ( ! [B] : ( v1_xcmplx_0(B) => ~ ( r2_hidden(B,A) & ! [C] : ( m1_cfdiff_1(C,B) => ~ r1_tarski(C,A) ) ) ) => v6_cfdiff_1(A) ) ) )).
fof(t11_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k2_numbers,k9_funct_2(A,k2_numbers)) => k1_binop_1(k1_cfuncdom(A),B,k1_funct_1(k3_cfuncdom(A),k4_tarski(k4_xcmplx_0(k6_complex1),B))) = k4_cfuncdom(A) ) ) )).
fof(t11_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)))) ) ) )).
fof(t11_cgames_1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t11_chain_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ? [B] : ( m1_subset_1(B,k1_numbers) & r2_hidden(B,A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => r1_xxreal_0(B,C) ) ) ) ) )).
fof(t11_chord,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_abian(A) ) => ~ ( r1_xxreal_0(A,3) & A != k5_numbers & A != 2 ) ) )).
fof(t11_circcmb2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(A,D))) => ! [H] : ( m1_subset_1(H,k4_card_3(u3_msualg_1(B,E))) => ! [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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(C,F))) => ! [H] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ 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))) ) ) ) ) )).
fof(t11_circled1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(B,k2_circled1(A,B)) ) ) )).
fof(t11_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) => ! [D] : ( r2_hidden(D,k2_msafree2(k1_circtrm1(A,B,C))) <=> ( r2_hidden(D,k9_trees_9(C)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( m1_subset_1(F,k1_funct_1(B,E)) & D = k1_trees_4(k4_tarski(F,E)) ) ) ) ) ) ) ) )).
fof(t11_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,k5_msafree2(A,B)),C)) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,k5_msafree2(A,B)),D)) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t11_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t11_classes1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v3_ordinal1(D) => ( ( r1_tarski(B,C) & r2_hidden(C,k3_classes1(A,D)) ) => r2_hidden(B,k3_classes1(A,k1_ordinal1(D))) ) ) )).
fof(t11_classes2,axiom,( ! [A] : ! [B] : ( ( v2_classes1(B) & r2_hidden(A,B) ) => r2_hidden(k1_card_1(A),B) ) )).
fof(t11_clopban1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k3_clopban1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_clopban1(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k3_clopban1(A,B))) => ( E = k3_rlvect_1(k3_clopban1(A,B),C,D) <=> ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t11_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(k6_clopban1(A,A)),k8_clopban1(A,A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(k6_clopban1(A,A)),k8_clopban1(A,A)) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t11_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v9_clvect_1(B,A) => ( ! [D] : ( v7_ordinal1(D) => ~ r2_funct_2(k4_ordinal1,u1_struct_0(A),B,k1_valued_0(u1_struct_0(A),C,D)) ) | k7_clvect_1(A,C) = k7_clvect_1(A,B) ) ) ) ) ) )).
fof(t11_clopban4,axiom,( ! [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) & 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] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ! [E] : ( v7_ordinal1(E) => ( 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) ) ) ) ) ) )).
fof(t11_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m1_closure2(D,A,C,k2_closure2(A,C)) => r2_hidden(k4_pboole(A,D,B),k2_closure2(A,C)) ) ) ) )).
fof(t11_closure3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) => ! [D] : ( 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))) ) ) ) )).
fof(t11_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xcmplx_0(D) => ( k1_clvect_1(A,C,D) = k1_clvect_1(A,B,D) => ( D = k5_numbers | C = B ) ) ) ) ) ) )).
fof(t11_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_funct_1(C) => ( ! [D] : ( v7_ordinal1(D) => k1_normsp_1(A,C,D) != B ) | k1_clvect_2(A,C) = B ) ) ) ) ) )).
fof(t11_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clvect_3(B,A) => v3_clvect_2(k1_bhsp_4(A,B),A) ) ) ) )).
fof(t11_coh_sp,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(t11_cohsp_1,axiom,( ! [A] : ! [B] : v2_cohsp_1(k1_enumset1(A,B,k3_xboole_0(A,B))) )).
fof(t11_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_collsp(A,B,C,D) <=> r2_hidden(D,k1_collsp(A,B,C)) ) ) ) ) ) )).
fof(t11_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ( v2_prob_1(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t11_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => k4_complex1(k3_xcmplx_0(A,k7_complex1)) = A ) )).
fof(t11_complex2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) & k17_sin_cos(A) = k17_sin_cos(B) & k19_sin_cos(A) = k19_sin_cos(B) ) => ( r1_xxreal_0(k3_xcmplx_0(2,k28_sin_cos),A) | r1_xxreal_0(k3_xcmplx_0(2,k28_sin_cos),B) | A = B ) ) ) ) )).
fof(t11_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( 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) ) ) )).
fof(t11_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( v1_xcmplx_0(B) => k4_finseq_1(k10_seq_4(A,B)) = k4_finseq_1(A) ) ) )).
fof(t11_compos_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_compos_0(B) & v2_compos_0(B) & v3_compos_0(B) & v5_compos_0(B) ) => ! [C] : ( m1_subset_1(C,B) => ( k5_compos_0(B,C,A) = k6_compos_0(B) => C = k6_compos_0(B) ) ) ) ) )).
fof(t11_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( 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) ) ) ) ) )).
fof(t11_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) ) ) )).
fof(t11_comptrig,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( r2_hidden(A,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))) & r1_xxreal_0(k1_funct_1(k18_sin_cos,A),k5_numbers) ) ) )).
fof(t11_compts_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t11_comput_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t11_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k31_valued_1(k4_ordinal1,k2_numbers,A),k25_valued_1(k4_ordinal1,k2_numbers,A,k4_xcmplx_0(k6_complex1))) ) )).
fof(t11_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v2_comseq_2(A) => k3_comseq_2(k2_comseq_2(k4_ordinal1,A)) = k8_complex1(k3_comseq_2(A)) ) ) )).
fof(t11_comseq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_comseq_3(A,k5_numbers) = k6_complex1 ) )).
fof(t11_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t11_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( ~ v4_conlat_1(k3_funct_2(u1_struct_0(A),u1_struct_0(k11_conlat_1(A)),k4_conlat_2(A),B),A) & v6_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) & ~ v4_conlat_1(k3_funct_2(u4_struct_0(A),u1_struct_0(k11_conlat_1(A)),k5_conlat_2(A),C),A) & v6_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) ) ) ) ) )).
fof(t11_conmetr1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v1_aff_2(A) <=> v4_conmetr1(A) ) ) )).
fof(t11_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_connsp_1(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t11_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t11_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t11_convex1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( 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) ) ) ) ) ) ) )).
fof(t11_convex2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(t11_convex4,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t11_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t11_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t11_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => v1_cqc_the1(k1_cqc_the1(A,B),A) ) ) )).
fof(t11_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t11_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t11_csspace,axiom,( ! [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) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t11_csspace2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(k5_numbers,k1_funct_1(k7_comseq_3(k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,k2_comseq_2(k4_ordinal1,A))),B)) & k1_funct_1(k8_comseq_3(k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,k2_comseq_2(k4_ordinal1,A))),B) = k5_numbers ) ) ) )).
fof(t11_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t11_decomp_1,axiom,( ! [A] : ( ( 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) ) )).
fof(t11_descip_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( r1_xxreal_0(1,k3_finseq_1(B)) => k8_descip_1(A,B,k5_numbers) = B ) ) ) )).
fof(t11_dickson,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) )).
fof(t11_diff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(C,A),1),B) = k6_xcmplx_0(k1_funct_1(k2_diff_1(C,A),B),k1_funct_1(C,B)) ) ) ) )).
fof(t11_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( ( 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) = k3_xcmplx_0(A,k1_diff_2(G,B,C,D,E,F)) ) ) ) ) ) ) ) )).
fof(t11_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t11_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(B,k1_relset_1(k1_numbers,k2_fdiff_9)) & r2_hidden(k2_xcmplx_0(B,A),k1_relset_1(k1_numbers,k2_fdiff_9)) ) => k1_funct_1(k3_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k2_fdiff_9),A),B) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(4,k17_sin_cos(k2_xcmplx_0(k3_xcmplx_0(2,B),A))),k17_sin_cos(A)),k1_square_1(k6_xcmplx_0(k19_sin_cos(k2_xcmplx_0(k3_xcmplx_0(2,B),A)),k19_sin_cos(A))))) ) ) ) )).
fof(t11_dilworth,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_dilworth(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t11_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t11_dirort,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dirort(A) & l1_analoaf(A) ) => ( v2_dirort(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_dist_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,A) ) => ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(C,k2_finseq_1(k5_card_1(A))) & ! [D] : ( m1_subset_1(D,A) => ~ ( k1_funct_1(k9_dist_1(A,B),C) = k2_dist_1(A,B,D) & D = k1_funct_1(k19_finseq_1(A),C) ) ) ) ) ) ) )).
fof(t11_dist_2,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k4_finseq_1(B))) => ( k3_finseq_1(k5_dist_2(A,B,C)) = k5_card_1(C) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(k5_dist_2(A,B,C))) => k1_funct_1(k5_dist_2(A,B,C),D) = k1_funct_1(B,k1_funct_1(k19_finseq_1(C),D)) ) ) ) ) ) )).
fof(t11_domain_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ~ v1_xboole_0(E) => ( ! [F] : ( r2_hidden(F,A) <=> ? [G] : ( m1_subset_1(G,B) & ? [H] : ( m1_subset_1(H,C) & ? [I] : ( m1_subset_1(I,D) & ? [J] : ( m1_subset_1(J,E) & F = k6_xtuple_0(G,H,I,J) ) ) ) ) ) => A = k4_zfmisc_1(B,C,D,E) ) ) ) ) ) ) )).
fof(t11_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_dynkin(k9_setfam_1(A),A) ) )).
fof(t11_e_siec,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t11_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => k5_numbers = k4_struct_0(k9_int_3(A)) ) )).
fof(t11_ec_pf_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t11_endalg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t11_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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 ) ) ) )).
fof(t11_entropy1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ( r1_entropy1(C,B) => ( A = B | k1_funct_1(C,A) = k5_numbers ) ) ) ) ) )).
fof(t11_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k1_tarski(A),k3_enumset1(B,C,D,E,F)) )).
fof(t11_eqrel_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,A)))) => ( ! [C] : ( 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))) ) ) ) ) )).
fof(t11_equation,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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,k2_funct_6(C)) => r6_pboole(A,k9_pboole(A,k1_equation(A,B,C),C),B) ) ) ) )).
fof(t11_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => r1_xxreal_0(k6_xcmplx_0(k12_euclid(B),k12_euclid(C)),k12_euclid(k7_euclid(A,B,C))) ) ) ) )).
fof(t11_euclid_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v3_valued_0(B) ) => ( k3_finseq_1(A) = k3_finseq_1(B) => k1_square_1(k12_euclid(k8_rvsum_1(A,B))) = k2_xcmplx_0(k6_xcmplx_0(k1_square_1(k12_euclid(A)),k3_xcmplx_0(2,k22_rvsum_1(B,A))),k1_square_1(k12_euclid(B))) ) ) ) )).
fof(t11_euclid_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k1_euclid_3(k4_xcmplx_0(A)) = k4_algstr_0(k15_euclid(2),k1_euclid_3(A)) ) )).
fof(t11_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ( ( r2_hidden(D,k2_euclid_4(A,B,C)) & r2_hidden(E,k2_euclid_4(A,B,C)) ) => ( D = E | r1_tarski(k2_euclid_4(A,B,C),k2_euclid_4(A,D,E)) ) ) ) ) ) ) ) )).
fof(t11_euclid_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k4_algstr_0(k15_euclid(3),k4_euclid_5(A,B,C)) = k4_euclid_5(k4_xcmplx_0(A),k4_xcmplx_0(B),k4_xcmplx_0(C)) ) ) ) )).
fof(t11_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( k4_euclid_3(A,C,B) = k28_sin_cos => r2_hidden(C,k1_rltopsp1(k15_euclid(2),A,B)) ) ) ) ) )).
fof(t11_euclid_7,axiom,( v1_funct_1(k12_finseq_1(k4_ordinal1,1)) & v1_funct_2(k12_finseq_1(k4_ordinal1,1),k6_domain_1(k4_ordinal1,1),k6_domain_1(k4_ordinal1,1)) & v3_funct_2(k12_finseq_1(k4_ordinal1,1),k6_domain_1(k4_ordinal1,1),k6_domain_1(k4_ordinal1,1)) & m1_subset_1(k12_finseq_1(k4_ordinal1,1),k1_zfmisc_1(k2_zfmisc_1(k6_domain_1(k4_ordinal1,1),k6_domain_1(k4_ordinal1,1)))) )).
fof(t11_euclid_8,axiom,( k22_rvsum_1(k3_euclid_8,k3_euclid_8) = 1 )).
fof(t11_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(A))) => ( ~ r1_xxreal_0(B,k5_numbers) => r2_hidden(C,k4_euclid_9(A,C,B)) ) ) ) ) )).
fof(t11_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(C)) => ( k9_euclid(C,D,k6_xcmplx_0(A,B)) = k7_euclid(C,k9_euclid(C,D,A),k9_euclid(C,D,k4_xcmplx_0(B))) & k9_euclid(C,D,k6_xcmplx_0(A,B)) = k7_euclid(C,k9_euclid(C,D,A),k6_euclid(C,k9_euclid(C,D,B))) & k9_euclid(C,D,k6_xcmplx_0(A,B)) = k8_euclid(C,k9_euclid(C,D,A),k9_euclid(C,D,B)) ) ) ) ) ) )).
fof(t11_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v3_euclmetr(A) <=> v1_conaffm(A) ) ) )).
fof(t11_euler_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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) ) ) ) )).
fof(t11_exchsort,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( v3_exchsort(B,A) & ~ v1_xboole_0(B) & v1_exchsort(B) ) <=> ? [C] : ( v3_ordinal1(C) & k9_xtuple_0(B) = k6_subset_1(A,C) & r2_hidden(C,A) ) ) ) ) )).
fof(t11_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(B)) & v1_funct_1(D) ) => ( r1_tarski(k16_funcop_1(C,k2_compos_1(B)),D) => ! [E] : ( ( 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] : ( ( 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] : ( v7_ordinal1(G) => k5_extpro_1(A,B,D,F,G) = F ) ) ) ) ) ) ) ) ) )).
fof(t11_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( ~ r1_xxreal_0(A,k2_xxreal_3(B)) & ~ r1_xxreal_0(B,A) & ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(B,k3_extreal1(A)) ) ) ) ) )).
fof(t11_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => k5_facirc_1(A,B,C,k5_numbers) = C ) ) ) )).
fof(t11_facirc_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) ) => ! [D] : ! [E] : ( k3_facirc_2(k1_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(k1_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(k1_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)) ) ) ) ) )).
fof(t11_fcont_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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)) & r1_fcont_1(B,A) & r1_fcont_1(C,A) ) => ( k1_funct_1(B,A) = k5_numbers | r1_fcont_1(k3_rfunct_1(k1_numbers,k1_numbers,C,B),A) ) ) ) ) ) )).
fof(t11_fcont_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( 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)) ) ) ) )).
fof(t11_fcont_3,axiom,( ! [A] : ! [B] : ( ( 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] : ( v1_xreal_0(C) => k7_relset_1(k1_numbers,k1_numbers,B,A) != k10_prob_1(C) ) | v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) ) ) )).
fof(t11_fdiff_1,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => k2_relset_1(k1_numbers,B) != k1_tarski(C) ) | ( r2_fdiff_1(B,A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(k2_fdiff_1(B,A),C) = k5_numbers ) ) ) ) ) ) ) )).
fof(t11_fdiff_10,axiom,( ! [A] : ( ( 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,k18_sin_cos,k27_sin_cos))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k27_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k27_sin_cos),A),B) = k6_xcmplx_0(k4_xcmplx_0(k1_funct_1(k18_sin_cos,B)),k7_xcmplx_0(k1_funct_1(k18_sin_cos,B),k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t11_fdiff_11,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(1),1)) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k2_sin_cos9,B),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k1_sin_cos9),A),B) = k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(k2_xcmplx_0(1,k1_square_1(B)),k2_xcmplx_0(1,k1_square_1(k1_funct_1(k2_sin_cos9,B)))))) ) ) ) ) ) )).
fof(t11_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r1_fdiff_1(B,A) <=> ( ? [C] : ( m1_rcomp_1(C,A) & r1_tarski(C,k1_relset_1(k1_numbers,B)) ) & ! [C] : ( ( v1_funct_1(C) & v9_ordinal1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & v1_fdiff_1(C,k5_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v3_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,D) = k1_tarski(A) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,D)),k1_relset_1(k1_numbers,B)) ) => v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,C),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,D),B),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,D,B)))) ) ) ) ) ) ) ) )).
fof(t11_fdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( 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)) = k6_xcmplx_0(k1_fdiff_3(C,A),k1_fdiff_3(C,B)) ) ) ) ) ) )).
fof(t11_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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,k6_xcmplx_0(B,A))))) & D = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,E,k3_taylor_1) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,C) => ( k1_funct_1(E,F) = k6_xcmplx_0(F,B) & ~ r1_xxreal_0(k1_funct_1(E,F),k5_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,k6_xcmplx_0(B,A))),C) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,C) => k1_funct_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,k6_xcmplx_0(B,A))),C),F) = k7_xcmplx_0(k6_xcmplx_0(F,A),k6_xcmplx_0(F,B)) ) ) ) ) ) ) ) ) ) )).
fof(t11_fdiff_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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,k18_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] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(C,D) = k3_xcmplx_0(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,k18_sin_cos),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k1_taylor_1(A))),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k18_sin_cos),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k1_taylor_1(A))),B),D) = k3_xcmplx_0(k3_xcmplx_0(A,k3_prepower(k1_funct_1(k16_sin_cos,D),k6_xcmplx_0(A,1))),k1_funct_1(k18_sin_cos,k3_xcmplx_0(k2_xcmplx_0(A,1),D))) ) ) ) ) ) ) ) )).
fof(t11_fdiff_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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,k22_sin_cos))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(C,D) = k3_xcmplx_0(D,k3_power(k4_power,A)) ) ) ) => ( r1_xxreal_0(A,k5_numbers) | ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k22_sin_cos),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k22_sin_cos),B),D) = k3_xcmplx_0(k6_prepower(A,D),k3_power(k4_power,A)) ) ) ) ) ) ) ) ) )).
fof(t11_fdiff_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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,k3_sin_cos6,k1_taylor_1(A)))) & r1_tarski(B,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_sin_cos6,k1_taylor_1(A)),B) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_sin_cos6,k1_taylor_1(A)),B),C) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(A,k3_prepower(k1_funct_1(k3_sin_cos6,C),k6_xcmplx_0(A,1))),k3_square_1(k6_xcmplx_0(1,k1_square_1(C))))) ) ) ) ) ) ) )).
fof(t11_fdiff_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( 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,C)),k27_sin_cos))) & F = k1_taylor_1(2) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,D) => k1_funct_1(E,G) = k2_xcmplx_0(A,k3_xcmplx_0(B,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,C)),k27_sin_cos),D) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,D) => k1_funct_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,C)),k27_sin_cos),D),G) = k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,k3_xcmplx_0(k3_xcmplx_0(2,C),G)),k1_square_1(k1_funct_1(k16_sin_cos,k2_xcmplx_0(k2_xcmplx_0(A,k3_xcmplx_0(B,G)),k3_xcmplx_0(C,k1_square_1(G))))))) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_fdiff_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( 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,C)),k2_fdiff_9))) & F = k1_taylor_1(2) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,D) => k1_funct_1(E,G) = k2_xcmplx_0(A,k3_xcmplx_0(B,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,C)),k2_fdiff_9),D) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,D) => k1_funct_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,C)),k2_fdiff_9),D),G) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k2_xcmplx_0(B,k3_xcmplx_0(k3_xcmplx_0(2,C),G)),k1_funct_1(k18_sin_cos,k2_xcmplx_0(k2_xcmplx_0(A,k3_xcmplx_0(B,G)),k3_xcmplx_0(C,k1_square_1(G))))),k1_square_1(k1_funct_1(k16_sin_cos,k2_xcmplx_0(k2_xcmplx_0(A,k3_xcmplx_0(B,G)),k3_xcmplx_0(C,k1_square_1(G))))))) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_ff_siec,axiom,( ! [A] : ( ( 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 ) ) )).
fof(t11_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => k2_power(k4_xcmplx_0(1),k4_xcmplx_0(A)) = k2_power(k4_xcmplx_0(1),A) ) )).
fof(t11_fib_num3,axiom,( k1_fib_num3(k5_numbers) = 2 & k1_fib_num3(1) = 1 & ! [A] : ( v7_ordinal1(A) => k1_fib_num3(k1_nat_1(k1_nat_1(A,1),1)) = k1_nat_1(k1_fib_num3(A),k1_fib_num3(k1_nat_1(A,1))) ) )).
fof(t11_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( v1_abian(A) & v1_abian(B) & r1_xxreal_0(B,A) ) => r1_xxreal_0(k2_power(k2_fib_num,A),k2_power(k2_fib_num,B)) ) ) ) )).
fof(t11_filerec1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ( C = k9_finseq_1(A) => k17_finseq_1(B,1,C) = k9_finseq_1(A) ) ) ) )).
fof(t11_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t11_filter_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m2_filter_1(C,A,B) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t11_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( C = E & D = F & r2_lattices(A,C,D) ) => r2_lattices(B,E,F) ) ) ) ) ) ) ) ) )).
fof(t11_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k12_fin_topo(A,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r2_hidden(D,C) & r2_hidden(B,k1_fin_topo(A,D)) ) ) ) ) ) )).
fof(t11_finance1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( m1_finance1(B) => ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(C,k5_numbers) => k4_finance1(C,A,B) = k2_xcmplx_0(k3_funct_2(k4_ordinal1,k1_numbers,A,k5_numbers),k5_finance1(C,A,B)) ) ) ) ) )).
fof(t11_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => m2_finseq_1(k10_finseq_1(B,C),A) ) ) ) )).
fof(t11_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,A) => r2_hidden(k1_nat_1(A,1),k2_finseq_1(B)) ) ) ) )).
fof(t11_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r2_finseq_4(A,B) => k8_relat_1(A,k1_tarski(B)) = k1_tarski(k1_finseq_4(A,B)) ) ) )).
fof(t11_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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 ) ) ) )).
fof(t11_finseq_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( r1_tarski(C,k4_finseq_1(A)) => k5_relat_1(k7_finseq_1(A,B),C) = k5_relat_1(A,C) ) ) ) )).
fof(t11_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( 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,D),E,C) = 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,C)),k17_finseq_1(A,k7_nat_d(k7_nat_d(F,E),1),k2_rfinseq(A,E,B))),k12_finseq_1(A,D)),k2_rfinseq(A,F,B)) ) ) ) ) ) ) ) ) )).
fof(t11_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( 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) ) ) ) )).
fof(t11_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( ( 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))) ) => ! [G] : ( ( v3_card_1(G,D) & m2_finseq_1(G,A) ) => ! [H] : ( ( v3_card_1(H,D) & m2_finseq_1(H,B) ) => ! [I] : ( ( v3_card_1(I,E) & m2_finseq_1(I,A) ) => ! [J] : ( ( v3_card_1(J,E) & m2_finseq_1(J,B) ) => r2_relset_1(k4_ordinal1,C,k1_finseqop(A,B,C,F,k8_finseq_1(A,G,I),k8_finseq_1(B,H,J)),k8_finseq_1(C,k1_finseqop(A,B,C,F,G,H),k1_finseqop(A,B,C,F,I,J))) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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 ) ) ) )).
fof(t11_finsub_1,axiom,( ! [A] : ! [B] : k5_finsub_1(k3_xboole_0(A,B)) = k3_xboole_0(k5_finsub_1(A),k5_finsub_1(B)) )).
fof(t11_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k9_fin_topo(A,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & k1_fintopo2(A,B,D,C) = k8_margrel1 ) ) ) ) ) )).
fof(t11_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t11_fintopo4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t11_fintopo5,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => v3_orders_2(k3_fintopo5(A,B)) ) ) )).
fof(t11_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_fin_topo(B,A) <=> ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_tarski(k1_fin_topo(A,C),B) => r2_hidden(C,B) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => r1_tarski(k1_fin_topo(A,C),B) ) ) ) ) ) ) )).
fof(t11_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k3_catalan2(A)) => ( k1_flang_1(A,B,B) = B => B = k1_xboole_0 ) ) )).
fof(t11_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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) ) ) ) )).
fof(t11_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ( k1_flang_3(A,B,C) = k8_flang_1(A,B) <=> ( r2_hidden(k2_flang_1(A),B) | C = k5_numbers ) ) ) ) )).
fof(t11_fomodel0,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => k4_finseq_2(B,A) = k1_funct_2(k2_finseq_1(B),A) ) )).
fof(t11_fomodel1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t11_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ~ 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)),k15_fomodel2(B,C),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0))),k20_fomodel2(B,C,k22_fomodel2(B,A,C))) = k2_zfmisc_1(k15_fomodel2(B,C),k28_fomodel2(B,A)) ) ) ) )).
fof(t11_fomodel3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( ( ~ v6_struct_0(D) & v11_fomodel1(D) & l1_fomodel1(D) ) => ! [E] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(C),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_fomodel2(C,B)) => ! [F] : ( m2_subset_1(F,k9_funct_2(k37_fomodel1(D),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_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,k9_fomodel2(C,B,E),k3_finseq_2(A)) = k2_partfun1(k35_fomodel1(D),B,k9_fomodel2(D,B,F),k3_finseq_2(A)) ) ) ) ) ) ) )).
fof(t11_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(D) & v11_fomodel1(D) & l1_fomodel1(D) ) => ! [E] : ( 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) & v9_fomodel4(C,D,E,A) ) => v9_fomodel4(C,D,E,B) ) ) ) )).
fof(t11_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( r2_funct_2(k4_ordinal1,u1_struct_0(B),E,k1_partfun1(k4_ordinal1,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)) ) ) ) ) ) ) ) )).
fof(t11_friends1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v2_relat_2(C) & v3_relat_2(C) & v1_finset_1(C) & v3_friends1(C) ) => ( ( r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k1_relat_1(C)) ) => ( v2_friends1(C) | k5_card_1(k9_relat_1(C,A)) = k5_card_1(k9_relat_1(C,B)) ) ) ) )).
fof(t11_fscirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t11_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( ( ~ v2_struct_0(E) & l2_fsm_1(E,A,B) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(E)) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t11_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t11_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : 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))) )).
fof(t11_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => k1_funct_1(A,C) = B ) => A = k2_funcop_1(k9_xtuple_0(A),B) ) ) )).
fof(t11_funcsdom,axiom,( ! [A] : ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => k1_binop_1(k5_funcsdom(A),B,k1_funct_1(k7_funcsdom(A),k4_tarski(k4_xcmplx_0(1),B))) = k8_funcsdom(A) ) )).
fof(t11_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,k9_xtuple_0(k3_relat_1(B,C))) <=> ( r2_hidden(A,k9_xtuple_0(B)) & r2_hidden(k1_funct_1(B,A),k9_xtuple_0(C)) ) ) ) ) )).
fof(t11_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ~ ( r2_hidden(E,A) & k1_funct_1(D,E) = C ) ) ) )).
fof(t11_funct_3,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(t11_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ~ r2_hidden(C,k9_xtuple_0(B)) => k1_funct_1(k1_funct_4(A,B),C) = k1_funct_1(A,C) ) ) ) )).
fof(t11_funct_5,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t11_funct_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) ) )).
fof(t11_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t11_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t11_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t11_functor0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(t11_functor1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l1_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_altcat_2(C) & l1_altcat_1(C) ) => ! [D] : ( ( v8_functor0(D,A,B) & l2_functor0(D,A,B) ) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t11_functor2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ! [F] : ( ( v15_functor0(F,A,B) & m2_functor0(F,A,B) ) => ! [G] : ( m2_functor2(G,A,B,C,D) => ! [H] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ! [F] : ( ( v15_functor0(F,B,C) & m2_functor0(F,B,C) ) => ! [G] : ( m1_functor2(G,A,B,D,E) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( r1_functor2(A,B,D,E) => k2_functor2(A,C,k1_functor3(A,B,C,D,F),k1_functor3(A,B,C,E,F),k5_functor3(A,B,C,D,E,G,F),H) = k6_functor0(B,C,F,k3_functor0(A,B,D,H),k3_functor0(A,B,E,H),k2_functor2(A,B,D,E,G,H)) ) ) ) ) ) ) ) ) ) )).
fof(t11_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v5_relat_1(k7_rfunct_1(k1_xboole_0,A),k1_rcomp_1(k5_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))) ) ) )).
fof(t11_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D,C)),k2_fuzzy_1(A,k1_fuzzy_2(A,B,D),k1_fuzzy_1(A,B,C))) ) ) ) ) )).
fof(t11_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,k1_fuzzy_4(B,A,k1_fuzzy_2(k2_zfmisc_1(A,B),C,D)),k1_fuzzy_2(k2_zfmisc_1(B,A),k1_fuzzy_4(B,A,C),k1_fuzzy_4(B,A,D))) ) ) ) ) )).
fof(t11_fvaluat1,axiom,( ! [A] : ( v1_fvaluat1(A) => ~ r1_xxreal_0(A,k2_xxreal_0) ) )).
fof(t11_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t11_gate_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(k5_gate_1(A,B)) <=> v1_xboole_0(k4_gate_1(A,B)) ) )).
fof(t11_gcd_1,axiom,( ! [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) & v1_vectsp_2(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(t11_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v2_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( m1_genealg1(D,C) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t11_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_analoaf(A,B,k1_geomtrap(A,B,C),k1_geomtrap(A,B,C),C) ) ) ) )).
fof(t11_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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))) )).
fof(t11_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( 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 ) ) )).
fof(t11_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( ~ r1_xxreal_0(k3_finseq_1(B),C) => ( r2_hidden(C,k1_relset_1(k4_ordinal1,B)) & r2_hidden(k1_nat_1(C,1),k1_relset_1(k4_ordinal1,B)) & r2_hidden(k1_nat_1(C,2),k1_relset_1(k4_ordinal1,B)) ) ) ) ) ) )).
fof(t11_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t11_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) ) => ! [B] : ( ( v1_glib_003(B) & v4_glib_003(B,A) & m1_glib_000(B,A) ) => ! [C] : ( r2_hidden(C,k25_glib_000(A,B)) => k1_funct_1(k5_glib_003(B),C) = k1_funct_1(k5_glib_003(A),C) ) ) ) )).
fof(t11_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k21_glib_000(A,B))) => ! [D] : ( ( v1_glib_003(D) & v4_glib_003(D,A) & m2_glib_000(D,A,B,C) ) => ! [E] : ! [F] : ( ( 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_funct_1(k5_glib_003(A),E)) = k4_glib_004(F) ) ) ) ) ) ) ) )).
fof(t11_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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] : ! [D] : ! [E] : ( 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(k2_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)))),k2_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)))) ) ) ) ) ) )).
fof(t11_goboard1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( k1_matrix_0(D) = k1_nat_1(B,1) & r2_hidden(C,k2_finseq_1(B)) & r2_hidden(A,k4_finseq_1(D)) ) => ( r1_xxreal_0(B,k5_numbers) | ( k3_matrix_0(u1_struct_0(k15_euclid(2)),k16_matrix_0(1,u1_struct_0(k15_euclid(2)),D),A,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),D,A,k1_nat_1(C,1)) & r2_hidden(1,k2_finseq_1(k1_matrix_0(D))) ) ) ) ) ) ) ) )).
fof(t11_goboard2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( v1_topreal1(A) => ! [C] : ( v7_ordinal1(C) => ( ( r2_hidden(C,k4_finseq_1(A)) & r2_hidden(k1_nat_1(C,1),k4_finseq_1(A)) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ~ ( r2_hidden(k4_tarski(D,E),k2_matrix_0(B)) & r2_hidden(k4_tarski(F,G),k2_matrix_0(B)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),B,D,E) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),B,F,G) & D != F & G != E ) ) ) ) ) ) ) ) ) ) )).
fof(t11_goboard5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( v7_ordinal1(B) => ~ ( r2_hidden(B,k4_finseq_1(A)) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(k4_tarski(C,D),k2_matrix_0(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,D) ) ) ) ) ) ) )).
fof(t11_goboard7,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( v7_ordinal1(B) => ~ ( v2_sppol_1(k2_topreal1(2,A,B)) & ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(k2_goboard2(A))) & ! [D] : ( 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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,1)) ) ) ) ) ) ) ) )).
fof(t11_goboard8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,2),k3_finseq_1(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k1_matrix_0(k2_goboard2(A))) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,2),k3_finseq_1(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_nat_1(D,1)) ) => ( ( ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,k1_nat_1(D,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,2),k1_nat_1(D,1)) ) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,k1_nat_1(D,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,2),k1_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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_nat_1(D,1))),k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,2),k1_nat_1(D,1))),k7_xcmplx_0(1,2))),k3_topreal1(2,A)) ) ) ) ) ) ) ) )).
fof(t11_goboard9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r1_xxreal_0(A,k1_matrix_0(B)) => v1_convex1(k1_tops_1(k15_euclid(2),k2_goboard5(B,A)),k15_euclid(2)) ) ) ) )).
fof(t11_gobrd11,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t11_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [F] : ( ( ~ v3_relat_1(F) & v1_matrix_0(F) & v1_goboard1(F) & v2_goboard1(F) & v3_goboard1(F) & v4_goboard1(F) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_tarski(k9_matrix_0(E),k9_matrix_0(F)) & r2_hidden(k4_tarski(A,C),k2_matrix_0(E)) & r2_hidden(k4_tarski(B,D),k2_matrix_0(F)) & k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),F,B,D) ) => r1_tarski(k3_goboard5(F,k7_nat_d(B,1),D),k3_goboard5(E,k7_nat_d(A,1),C)) ) ) ) ) ) ) ) )).
fof(t11_gobrd14,axiom,( ! [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] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ~ ( ~ r1_xxreal_0(D,1) & ~ r1_xxreal_0(B,k1_topreal6(2,k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,D),1,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,D),1,2))) & ~ r1_xxreal_0(C,k1_topreal6(2,k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,D),1,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,D),2,1))) ) ) ) ) ) ) )).
fof(t11_goedcpuc,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_henmodel(B,A) & m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) ) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ( v1_henmodel(k4_subset_1(k3_cqc_lang(A),B,k6_domain_1(k3_cqc_lang(A),C)),A) | v1_henmodel(k4_subset_1(k3_cqc_lang(A),B,k6_domain_1(k3_cqc_lang(A),k6_cqc_lang(A,C))),A) ) ) ) ) )).
fof(t11_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_valuat_1(E,A,D) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t11_gr_cy_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => B = k1_group_1(A) ) ) ) )).
fof(t11_gr_cy_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v2_struct_0(D) & v8_struct_0(D) & v2_group_1(D) & v3_group_1(D) & l3_algstr_0(D) ) => ! [E] : ( m1_group_2(E,D) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ( ( k7_group_1(D) = B & D = k5_group_4(D,k6_domain_1(u1_struct_0(D),F)) & k7_group_1(E) = C & E = k5_group_4(D,k6_domain_1(u1_struct_0(D),k5_group_1(D,A,F))) ) => r1_nat_d(B,k3_xcmplx_0(A,C)) ) ) ) ) ) ) ) )).
fof(t11_gr_cy_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_gr_cy_3(A) ) => ? [B] : ( v7_ordinal1(B) & v1_int_2(B) & v2_gr_cy_3(B) & k1_euler_1(A) = k3_xcmplx_0(2,B) ) ) )).
fof(t11_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_graph_1(A) & l1_graph_1(A) ) => r1_graph_1(A,A,A) ) )).
fof(t11_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_tarski(k10_xtuple_0(k1_graph_2(A,B,C)),k10_xtuple_0(A)) ) ) ) )).
fof(t11_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t11_graph_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( ( v7_graph_1(E,B) & m2_graph_1(E,B) ) => ! [F] : ( ( v7_graph_1(F,B) & m2_graph_1(F,B) ) => ( ( r3_graph_4(B,C,E) & F = k2_partfun1(k4_ordinal1,u4_struct_0(B),E,k2_finseq_1(A)) & D = k2_partfun1(k4_ordinal1,u1_struct_0(B),C,k2_finseq_1(k1_nat_1(A,1))) ) => r3_graph_4(B,D,F) ) ) ) ) ) ) ) )).
fof(t11_graph_5,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t11_grcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(t11_grfunc_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t11_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ( m1_group_6(C,A,B) => m1_group_6(k1_grnilp_1(A,B,C),A,B) ) ) ) ) )).
fof(t11_groeb_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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(k12_polynom1(A,C),D) = k7_ideal_1(k12_polynom1(A,C),k1_groeb_1(A,C,E)) ) => v9_rewrite1(k3_polyred(A,B,C,D)) ) ) ) ) ) )).
fof(t11_groeb_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k15_pre_poly(A))) ) => ? [D] : ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t11_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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,k8_polynom1(A,C)),k8_polynom1(A,C)) ) ) ) )).
fof(t11_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k6_algstr_0(A,C,B) = k1_group_1(A) => ( C = k2_group_1(A,B) & B = k2_group_1(A,C) ) ) ) ) ) )).
fof(t11_group_10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ~ ( r1_nat_d(B,k7_group_1(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_group_1(A,C) != B ) ) ) ) )).
fof(t11_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(t11_group_12,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k2_group_7(k2_finseq_1(A),B))) => ? [D] : ( m2_finseq_1(D,u1_struct_0(k2_group_7(k2_finseq_1(A),B))) & k3_finseq_1(D) = A & ! [E] : ( m2_subset_1(E,k4_ordinal1,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) ) ) ) ) )).
fof(t11_group_14,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( ~ v2_struct_0(g2_algstr_0(u1_struct_0(k9_int_3(A)),u1_algstr_0(k9_int_3(A)),u2_struct_0(k9_int_3(A)))) & v2_rlvect_1(g2_algstr_0(u1_struct_0(k9_int_3(A)),u1_algstr_0(k9_int_3(A)),u2_struct_0(k9_int_3(A)))) & v13_algstr_0(g2_algstr_0(u1_struct_0(k9_int_3(A)),u1_algstr_0(k9_int_3(A)),u2_struct_0(k9_int_3(A)))) & v3_rlvect_1(g2_algstr_0(u1_struct_0(k9_int_3(A)),u1_algstr_0(k9_int_3(A)),u2_struct_0(k9_int_3(A)))) & v4_rlvect_1(g2_algstr_0(u1_struct_0(k9_int_3(A)),u1_algstr_0(k9_int_3(A)),u2_struct_0(k9_int_3(A)))) ) ) )).
fof(t11_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t11_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t11_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t11_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t11_group_6,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) )).
fof(t11_group_7,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t11_group_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(t11_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( ( ~ 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) ) ) ) ) )).
fof(t11_groupp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t11_grsolv_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v15_algstr_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t11_hahnban,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rlsub_1(C,A) => ( ~ r1_struct_0(C,B) => ! [D] : ( 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(t11_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) )).
fof(t11_hallmar1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t11_hausdorf,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) ) => ? [B] : ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) & A = B & k2_weierstr(A) = k2_seq_4(B) ) ) )).
fof(t11_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( ~ v3_glib_001(k8_glib_001(A,B,C,D),A) & v3_glib_001(B,A) ) ) ) ) ) )).
fof(t11_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(k3_cqc_lang(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k3_cqc_lang(A))))) ) => ( ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(D,k1_relset_1(k4_ordinal1,B)) & r2_hidden(C,k1_relset_1(k4_ordinal1,B)) ) => ( r1_xxreal_0(D,C) | ( v1_henmodel(k9_nat_1(k9_setfam_1(k3_cqc_lang(A)),B,C),A) & r1_tarski(k9_nat_1(k9_setfam_1(k3_cqc_lang(A)),B,C),k9_nat_1(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) ) ) ) )).
fof(t11_hermitan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ( ( k4_complex1(A) = k5_numbers & k4_complex1(B) = k5_numbers ) => k4_complex1(k8_group_1(k1_complfld,A,B)) = k5_numbers ) ) ) )).
fof(t11_hessenbe,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t11_heyting1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(k7_normform(A))) => ! [C] : ( 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] : ( m2_funct_2(D,k7_normform(A),k1_heyting1(A),k9_funct_2(k7_normform(A),k1_heyting1(A))) => ~ ( ! [E] : ( 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)) ) ) ) ) ) )).
fof(t11_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( 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 ) ) ) )).
fof(t11_heyting3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(t11_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(A,C) => k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k16_sin_cos,C),B),A) = k1_funct_1(k16_sin_cos,k2_xcmplx_0(A,k7_xcmplx_0(k3_xcmplx_0(B,k28_sin_cos),2))) ) ) ) ) )).
fof(t11_hilbasis,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_ordinal1(A) ) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ v7_struct_0(C) & v4_vectsp_1(C) & l6_algstr_0(C) ) => ! [D] : ( ( 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)))) ) => k1_polynom2(A,k2_hilbasis(A,B),C,D) = k3_funct_2(A,u1_struct_0(C),D,B) ) ) ) ) )).
fof(t11_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => k5_hilbert1(k5_hilbert1(A)) = k5_hilbert1(A) ) )).
fof(t11_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( k1_funct_1(A,1) = 1 => v2_hilbert2(A) ) ) )).
fof(t11_hilbert3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,2,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(2,A))) ) => ? [C] : ( m1_subset_1(C,A) & ? [D] : ( m1_subset_1(D,A) & r1_funct_2(2,A,k2_tarski(k5_numbers,1),A,B,k5_funct_4(A,k5_numbers,1,C,D)) ) ) ) ) )).
fof(t11_holder_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_series_1(B) & ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,B,D)) ) & ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k2_power(k9_nat_1(k1_numbers,k3_series_1(B),D),A) ) ) => ( v2_comseq_2(C) & k1_seq_2(C) = k2_power(k4_series_1(B),A) & v7_valued_0(C) & ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k9_nat_1(k1_numbers,C,D),k2_power(k4_series_1(B),A)) ) ) ) ) ) ) ) )).
fof(t11_hurwitz,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k5_vfunct_1(k4_ordinal1,A,k8_polynom3(A,B,C)),k8_polynom3(A,k5_vfunct_1(k4_ordinal1,A,B),k5_vfunct_1(k4_ordinal1,A,C))) ) ) ) )).
fof(t11_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_idea_1(B,A) => k4_idea_1(B,A,k6_idea_1(B,A)) = k5_numbers ) ) ) )).
fof(t11_ideal_1,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(t11_incproj,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ~ ! [B] : ( m1_subset_1(B,u1_incsp_1(k3_incproj(A))) => ! [C] : ( m1_subset_1(C,u2_incsp_1(k3_incproj(A))) => r1_incsp_1(k3_incproj(A),B,C) ) ) ) )).
fof(t11_incsp_1,axiom,( ! [A] : ( l2_incsp_1(A) => ! [B] : ( m1_subset_1(B,u4_incsp_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_incsp_1(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t11_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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] : ( m4_index_1(C,u1_struct_0(A),u4_struct_0(A),u1_graph_1(A),u2_graph_1(A),B) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t11_instalg1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_instalg1(B,A) => ( r1_tarski(u2_msualg_1(B),u2_msualg_1(A)) & r1_tarski(u1_msualg_1(B),u1_msualg_1(A)) ) ) ) )).
fof(t11_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => r2_int_1(A,A,B) ) ) )).
fof(t11_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ~ ( r1_int_1(A,B) & r1_int_1(B,A) & A != B & A != k4_xcmplx_0(B) ) ) ) )).
fof(t11_int_3,axiom,( ! [A] : ( 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)) ) ) ) )).
fof(t11_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ( r2_int_1(A,B,D) => r2_int_1(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C),D) ) ) ) ) ) )).
fof(t11_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_int_5(A,C) & r2_int_1(A,B,C) ) => r1_int_5(B,C) ) ) ) ) )).
fof(t11_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r2_hidden(B,k4_finseq_1(A)) & r2_hidden(C,k4_finseq_1(A)) ) => ( C = B | k1_funct_1(A,C) = k5_numbers | v1_int_1(k7_xcmplx_0(k19_rvsum_1(A),k3_xcmplx_0(k1_funct_1(A,B),k1_funct_1(A,C)))) ) ) ) ) ) )).
fof(t11_int_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ( C = k3_int_2(A,B) => k22_pre_poly(k8_newton,k13_nat_3(C)) = k9_subset_1(k8_newton,k22_pre_poly(k8_newton,k13_nat_3(A)),k22_pre_poly(k8_newton,k13_nat_3(B))) ) ) ) ) )).
fof(t11_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_int_2(B,C) => ( r1_xxreal_0(C,1) | ( r2_int_1(k1_newton(B,A),1,C) <=> r1_nat_d(k3_pepin(B,C),A) ) ) ) ) ) ) )).
fof(t11_integr10,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( ( r1_tarski(k1_limfunc1(B),k1_relset_1(k1_numbers,A)) & r4_integr10(A,B) ) => ! [C] : ( v1_xreal_0(C) => ( r4_integr10(k26_valued_1(k1_numbers,k1_numbers,A,C),B) & k4_integr10(k26_valued_1(k1_numbers,k1_numbers,A,C),B) = k3_xcmplx_0(C,k4_integr10(A,B)) ) ) ) ) ) )).
fof(t11_integr11,axiom,( 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,k5_numbers),k1_sin_cos2),k3_sin_cos2),k1_numbers) & ! [A] : ( v1_xreal_0(A) => k1_funct_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,k5_numbers),k1_sin_cos2),k3_sin_cos2),k1_numbers),A) = k3_xcmplx_0(A,k1_funct_1(k3_sin_cos2,A)) ) )).
fof(t11_integr12,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,C) & r1_xxreal_0(D,k5_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,k18_sin_cos),k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,C)))) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k16_sin_cos),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k16_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t11_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k22_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos))) & r1_tarski(C,k1_relset_1(k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_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) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k16_sin_cos),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k16_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t11_integr14,axiom,( ! [A] : ( ( 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,k26_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,k26_sin_cos,k2_fdiff_9)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k2_fdiff_9)),A),B) = k7_xcmplx_0(k7_xcmplx_0(k1_funct_1(k18_sin_cos,k1_funct_1(k26_sin_cos,B)),k1_square_1(k1_funct_1(k18_sin_cos,B))),k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k26_sin_cos,B)))) ) ) ) ) ) )).
fof(t11_integr15,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_integra1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(B)))) ) => ! [E] : ( m4_integr15(E,A,B,C,D) => ( ( v1_integr15(C,A,B) & v2_integr15(C,A,B) & v2_comseq_2(k2_integra3(B,D)) & k1_seq_2(k2_integra3(B,D)) = k5_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) ) ) ) ) ) ) ) )).
fof(t11_integr16,axiom,( ! [A] : ( ( 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)) ) ) ) )).
fof(t11_integr18,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,u1_struct_0(C)))) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t11_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ( ( r1_xxreal_0(B,D) & r1_xxreal_0(D,E) & r1_xxreal_0(E,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)) ) => ( r1_integr15(A,k3_integra5(D,E),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(D,E)),A) ) ) ) ) ) ) ) ) ) )).
fof(t11_integra1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t11_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( ( v3_xxreal_2(B) & r1_xxreal_0(k5_numbers,A) ) => v3_xxreal_2(k1_integra2(B,A)) ) ) ) )).
fof(t11_integra3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( m1_integra1(C,B) => ! [D] : ( m1_integra1(D,B) => ! [E] : ( ( 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(k6_xcmplx_0(k18_rvsum_1(k4_integra1(B,E,C)),k18_rvsum_1(k4_integra1(B,E,D))),k3_xcmplx_0(k6_xcmplx_0(k2_seq_4(k1_rvsum_1(E)),k3_seq_4(k1_rvsum_1(E))),k1_integra3(B,C))) ) ) ) ) ) ) )).
fof(t11_integra4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ? [B] : ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_integra1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) & v2_comseq_2(k2_integra3(A,B)) & k1_seq_2(k2_integra3(A,B)) = k5_numbers ) ) )).
fof(t11_integra5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t11_integra6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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)) = k2_xcmplx_0(k2_integra5(A,B),k2_integra5(A,C)) & k2_integra5(A,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,B,C)) = k6_xcmplx_0(k2_integra5(A,B),k2_integra5(A,C)) ) ) ) ) ) )).
fof(t11_integra7,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r1_integra7(A,C,B) => r1_tarski(A,k1_relset_1(k1_numbers,C)) ) ) ) )).
fof(t11_integra8,axiom,( k2_sin_cos6(k4_xcmplx_0(k7_xcmplx_0(k3_square_1(2),2))) = k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)) )).
fof(t11_integra9,axiom,( ! [A] : ( ( 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),k18_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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),k18_sin_cos)),A),B) = k4_xcmplx_0(k3_xcmplx_0(B,k1_funct_1(k16_sin_cos,B))) ) ) ) ) )).
fof(t11_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) & ? [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) & r1_tarski(C,D) & B = k2_interva1(A,C,D) ) ) ) ) )).
fof(t11_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( 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) ) ) ) )).
fof(t11_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => k3_xcmplx_0(k7_xcmplx_0(1,k1_nat_1(A,1)),k7_xcmplx_0(1,k7_newton(A))) = k7_xcmplx_0(1,k7_newton(k1_nat_1(A,1))) ) )).
fof(t11_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ( v12_cat_1(C,A,B) => ( r2_funct_2(u4_struct_0(B),u4_struct_0(B),k9_cat_1(B,A,B,k1_isocat_1(A,B,C),C),k10_cat_1(B)) & r2_funct_2(u4_struct_0(A),u4_struct_0(A),k9_cat_1(A,B,A,C,k1_isocat_1(A,B,C)),k10_cat_1(A)) ) ) ) ) ) )).
fof(t11_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v6_tops_1(k2_struct_0(A),A) & v5_tops_1(k2_struct_0(A),A) ) ) )).
fof(t11_jct_misc,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ 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),k5_numbers) ) ) ) )).
fof(t11_jgraph_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t11_jgraph_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & r1_tarski(a_2_0_jgraph_2(A,C),B) ) ) ) ) ) )).
fof(t11_jgraph_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( 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] : ( 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) = k7_xcmplx_0(k17_euclid(C),k3_square_1(k2_xcmplx_0(1,k1_square_1(k7_xcmplx_0(k18_euclid(C),k17_euclid(C)))))) ) ) & ! [C] : ( 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) = k5_numbers ) ) ) => v5_pre_topc(B,k1_pre_topc(k15_euclid(2),A),k3_topmetr) ) ) ) )).
fof(t11_jgraph_4,axiom,( ! [A] : ( 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) ) ) )).
fof(t11_jgraph_5,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( m1_subset_1(G,u1_struct_0(k5_topmetr)) => ! [H] : ( m1_subset_1(H,u1_struct_0(k5_topmetr)) => ~ ( G = k5_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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t11_jgraph_6,axiom,( ! [A] : ( ( ~ 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(k4_xcmplx_0(1),k5_numbers)) = k18_pscomp_1(A) ) ) )).
fof(t11_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t11_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t11_jordan10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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(k2_jordan9(B,A))) ) ) )).
fof(t11_jordan11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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),k5_jordan11(B,A)),B) ) ) ) )).
fof(t11_jordan12,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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))) ) ) ) )).
fof(t11_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( r1_jordan1h(A,B) => r1_tarski(A,k2_goboard9(k1_jordan13(A,B))) ) ) ) )).
fof(t11_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( 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_0(k1_jordan8(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_topreal1(2,k2_jordan1e(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E),k3_topreal1(2,k1_jordan1e(B,A))) & ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ~ ( 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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,F),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,G)),k3_topreal1(2,k2_jordan1e(B,A))) = k1_tarski(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,F),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,G)),k3_topreal1(2,k1_jordan1e(B,A))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,G)) ) ) ) ) ) ) ) ) ) )).
fof(t11_jordan16,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t11_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ( r1_jordan17(A,B,C,D,E) => r1_jordan17(A,D,E,B,C) ) ) ) ) ) ) )).
fof(t11_jordan18,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( 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)) ) ) ) )).
fof(t11_jordan19,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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,k2_jordan9(B,A)))) ) ) )).
fof(t11_jordan1b,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => r1_xxreal_0(1,k1_jordan1a(A)) ) )).
fof(t11_jordan1c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( 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] : ( v1_int_1(D) => ( ( r2_hidden(B,k1_jordan2c(2,C)) & D = k1_int_1(k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k17_euclid(B),k6_pscomp_1(C)),k6_xcmplx_0(k8_pscomp_1(C),k6_pscomp_1(C))),k1_newton(2,A)),2)) ) => r1_xxreal_0(k2_xcmplx_0(D,1),k3_finseq_1(k1_jordan8(C,A))) ) ) ) ) ) )).
fof(t11_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & ~ r1_xxreal_0(k3_finseq_1(k2_jordan9(B,A)),C) & r2_hidden(k22_pscomp_1(B),k2_gobrd13(k2_jordan9(B,A),k1_jordan8(B,A),C)) ) ) ) )).
fof(t11_jordan1e,axiom,( ! [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] : ( v7_ordinal1(B) => k1_finseq_6(u1_struct_0(k15_euclid(2)),k2_jordan9(A,B),k18_pscomp_1(k3_topreal1(2,k2_jordan9(A,B)))) = k4_graph_2(u1_struct_0(k15_euclid(2)),k1_jordan1e(A,B),k2_jordan1e(A,B)) ) ) )).
fof(t11_jordan1g,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t11_jordan1h,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => r2_relset_1(k4_ordinal1,k1_numbers,k2_goboard1(A),k1_partfun1(k4_ordinal1,u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k1_numbers,A,k5_pscomp_1)) ) )).
fof(t11_jordan1i,axiom,( ! [A] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(t11_jordan1j,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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)))) ) => ( r2_hidden(k23_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))),k10_xtuple_0(k2_jordan1e(B,A))) & r2_hidden(k23_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))),k3_topreal1(2,k2_jordan1e(B,A))) ) ) ) )).
fof(t11_jordan1k,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => r1_xxreal_0(k5_numbers,k7_weierstr(A,B,C)) ) ) ) )).
fof(t11_jordan20,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) => ! [B] : ( v1_xreal_0(B) => ( A = k3_rcomp_1(k5_numbers,B) => v3_pre_topc(A,k5_topmetr) ) ) ) )).
fof(t11_jordan21,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t11_jordan22,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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)))) ) => ~ ( ~ r1_xxreal_0(B,A) & r1_xxreal_0(k1_topreal6(2,k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(C,A),1,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(C,A),2,1)),k1_topreal6(2,k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(C,B),1,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(C,B),2,1))) ) ) ) ) )).
fof(t11_jordan23,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( v1_jordan23(B) => ! [C] : ( m1_subset_1(C,A) => v1_jordan23(k1_finseq_6(A,B,C)) ) ) ) ) )).
fof(t11_jordan24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) ) )).
fof(t11_jordan2b,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r2_hidden(D,k2_finseq_1(A)) & B = C ) => ( r1_xxreal_0(k7_partfun1(k1_numbers,C,D),k12_euclid(B)) & r1_xxreal_0(k1_square_1(k7_partfun1(k1_numbers,C,D)),k1_square_1(k12_euclid(B))) ) ) ) ) ) ) )).
fof(t11_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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))) ) ) )).
fof(t11_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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 ) ) ) )).
fof(t11_jordan4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( 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) ) ) ) ) ) ) )).
fof(t11_jordan5a,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_tarski(A,k1_rcomp_1(B,C)) => ( ~ r2_hidden(B,A) & ~ r2_hidden(C,A) ) ) ) ) ) )).
fof(t11_jordan5b,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t11_jordan5c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) )).
fof(t11_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( 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))) ) ) ) ) )).
fof(t11_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t11_jordan7,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t11_jordan8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(C,B),2,A)) = k6_pscomp_1(C) ) ) ) ) )).
fof(t11_jordan9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [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(k1_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) ) ) ) ) ) )).
fof(t11_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) )).
fof(t11_knaster,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t11_kolmog01,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( m1_kolmog01(D,B,A,C) => ! [E] : ( ( ~ 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) ) ) ) ) ) )).
fof(t11_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ! [E] : ( v7_ordinal1(E) => k1_funct_1(D,E) = k2_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) => k4_kurato_0(A,D) = k4_subset_1(A,k4_kurato_0(A,B),k4_kurato_0(A,C)) ) ) ) ) )).
fof(t11_kurato_1,axiom,( 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)) )).
fof(t11_kurato_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t11_lang1,axiom,( ! [A] : k3_lang1(k6_lang1(A)) = k1_tarski(k1_xboole_0) )).
fof(t11_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,A) => ! [E] : ( ( 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(t11_latsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( r2_hidden(C,u1_struct_0(B)) => m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B))) ) ) ) )).
fof(t11_lattice2,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t11_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( v1_lattice3(k3_lattice3(A)) & v2_lattice3(k3_lattice3(A)) ) ) )).
fof(t11_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v11_lattices(B) & l3_lattices(B) ) => ! [C] : ( m1_lattice4(C,B,A) => ( v2_funct_2(C,u1_struct_0(A)) => v11_lattices(A) ) ) ) ) )).
fof(t11_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( v1_relat_1(D) => ! [E] : ( v1_relat_1(E) => ! [F] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t11_lattice6,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t11_lattice7,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ( r2_hidden(B,k3_lattice7(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_orders_2(A,C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_orders_2(A,D,B) => r3_orders_2(A,D,C) ) ) ) ) ) ) ) )).
fof(t11_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t11_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t11_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( ( v4_lexbfs(B,A) & m1_lexbfs(B,A) ) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t11_lfuzzy_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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] : ( m1_subset_1(C,u1_struct_0(k4_yellow_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_yellow_1(A,B))) => ! [E] : ( m1_subset_1(E,A) => k4_waybel_3(A,B,k11_lattice3(k4_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)) ) ) ) ) ) ) )).
fof(t11_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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(k3_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)) ) ) ) ) )).
fof(t11_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_limfunc1(A) & v2_limfunc1(B) ) => v2_limfunc1(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) ) ) )).
fof(t11_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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) ) ) ) ) )).
fof(t11_lmod_5,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t11_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => r1_tarski(C,k2_struct_0(k1_mod_3(A,B,C))) ) ) ) )).
fof(t11_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t11_lopban_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(k5_lopban_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_lopban_1(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_lopban_1(A,B))) => ( E = k3_rlvect_1(k5_lopban_1(A,B),C,D) <=> ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t11_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(k8_lopban_1(A,A)),k10_lopban_1(A,A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(k8_lopban_1(A,A)),k10_lopban_1(A,A)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => k4_lopban_2(A,k3_lopban_2(A,C,B),k3_xcmplx_0(D,E)) = k3_lopban_2(A,k4_lopban_2(A,C,E),k4_lopban_2(A,B,D)) ) ) ) ) ) )).
fof(t11_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_normsp_1(B,A) => ( ! [D] : ( v7_ordinal1(D) => ~ r2_funct_2(k4_ordinal1,u1_struct_0(A),B,k1_valued_0(u1_struct_0(A),C,D)) ) | k6_normsp_1(A,C) = k6_normsp_1(A,B) ) ) ) ) ) )).
fof(t11_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(E,B) => k9_nat_1(u1_struct_0(A),C,E) = k9_nat_1(u1_struct_0(A),D,E) ) ) => k9_nat_1(u1_struct_0(A),k1_bhsp_4(A,C),B) = k9_nat_1(u1_struct_0(A),k1_bhsp_4(A,D),B) ) ) ) ) ) )).
fof(t11_lopban_6,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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),k4_xcmplx_0(1)) ) ) ) )).
fof(t11_lopban_7,axiom,( ! [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) & v3_lopban_1(A) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & 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] : ( ( 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_lopban_7(C,A,B) => v3_lopban_1(k5_lopban_7(A,B,C)) ) ) ) ) )).
fof(t11_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k6_lopclset(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k6_lopclset(A))) => k4_lattices(k6_lopclset(A),B,C) = k3_xboole_0(B,C) ) ) ) )).
fof(t11_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,B,C) = k5_numbers ) => ( v1_series_1(k1_lp_space(B,A)) & k2_power(k4_series_1(k1_lp_space(B,A)),k7_xcmplx_0(1,A)) = k5_numbers ) ) ) ) ) )).
fof(t11_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_rfunct_3(B,A,k2_numbers,k3_rfunct_3(A,k2_numbers)) => k2_binop_1(k2_numbers,k3_rfunct_3(A,k2_numbers),k3_rfunct_3(A,k2_numbers),k8_lpspacc1(A),k6_complex1,B) = B ) ) )).
fof(t11_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_rfunct_3(B,A,k1_numbers,k3_rfunct_3(A,k1_numbers)) => ! [C] : ( m2_rfunct_3(C,A,k1_numbers,k3_rfunct_3(A,k1_numbers)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t11_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => ( k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(C),k1_domain_1(k4_ordinal1,k1_hilbert1,B,k7_ltlaxio1(A))) = 1 <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(C),k1_domain_1(k4_ordinal1,k1_hilbert1,k1_nat_1(B,D),A)) = 1 ) ) ) ) ) )).
fof(t11_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => k7_partfun1(k1_hilbert1,k2_ltlaxio2(k12_finseq_1(k1_hilbert1,A)),k3_finseq_1(k2_ltlaxio2(k12_finseq_1(k1_hilbert1,A)))) = A ) )).
fof(t11_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ~ ( r2_hidden(A,k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,B)) & A != B & r1_xxreal_0(k3_finseq_1(B),k3_finseq_1(A)) ) ) ) )).
fof(t11_ltlaxio4,axiom,( k3_ltlaxio4(k6_domain_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)),k11_ltlaxio3(k6_finseq_1(k1_hilbert1),k6_finseq_1(k1_hilbert1)))) = k6_domain_1(k1_hilbert1,k4_ltlaxio1(k3_ltlaxio1,k3_ltlaxio1)) )).
fof(t11_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t11_margrel1,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( 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 ) ) ) ) )).
fof(t11_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(k4_struct_0(A),C) => ( r1_tarski(k3_mathmorp(A,B,C),B) & r1_tarski(B,k6_rusub_4(A,B,C)) ) ) ) ) ) )).
fof(t11_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( v1_matrix10(B) & v2_matrix10(C) & r1_matrix10(k3_matrix10(A,C),k3_matrix10(A,B)) ) => v1_matrix10(k4_matrix10(A,B,C)) ) ) ) ) )).
fof(t11_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [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] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(E),C,D) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(E))) ) => ( ( r2_hidden(B,k4_finseq_1(F)) & r2_hidden(A,k4_finseq_1(F)) ) => k1_matrix12(C,D,E,k1_matrix12(C,D,E,F,B,A),B,A) = F ) ) ) ) ) ) ) )).
fof(t11_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t11_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ( ( r1_tarski(C,k4_finseq_1(B)) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k7_subset_1(k4_ordinal1,k4_finseq_1(B),C)) => k7_matrix_0(u1_struct_0(A),B,D) = k5_finseq_2(u1_struct_0(A),k1_matrix_0(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_0(B)))) ) ) ) ) )).
fof(t11_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v1_matrix16(C,u1_struct_0(B)) => v1_matrix16(k2_matrix_3(B,C),u1_struct_0(B)) ) ) ) ) )).
fof(t11_matrix17,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t11_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( v1_matrix_0(k12_finseq_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),B)) & v2_matrix_0(k12_finseq_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),B),A,1,k3_finseq_1(B)) & m2_finseq_1(k12_finseq_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),B),k3_finseq_2(A)) ) ) ) )).
fof(t11_matrix_2,axiom,( ! [A] : ( v7_ordinal1(A) => v1_finset_1(k3_matrix_2(A)) ) )).
fof(t11_matrix_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ 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) ) ) )).
fof(t11_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) ) => B = k1_matrix_4(A,B,k1_matrix_4(A,C,C)) ) ) ) ) )).
fof(t11_matrix_5,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_matrix_0(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)) ) ) ) ) )).
fof(t11_matrix_6,axiom,( ! [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] : ( v7_ordinal1(B) => k1_matrix_6(B,A,k4_matrix_0(u1_struct_0(A),k3_matrix_1(A,B))) = k3_matrix_1(A,B) ) ) )).
fof(t11_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_8(C,A,B) & v1_matrix_8(D,A,B) & r1_matrix_6(A,B,C,D) ) => v1_matrix_8(k4_matrix_3(B,C,D),A,B) ) ) ) ) ) )).
fof(t11_matrix_9,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t11_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => k1_matrixc1(k4_matrix_5(A)) = k4_matrix_5(k1_matrixc1(A)) ) )).
fof(t11_matrixj1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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(k4_ordinal1,B,A)) = k2_wsierp_1(k17_finseq_1(k4_ordinal1,C,A)) ) => ( ( r2_hidden(B,k4_finseq_1(A)) & k1_funct_1(A,B) = k5_numbers ) | ( r2_hidden(C,k4_finseq_1(A)) & k1_funct_1(A,C) = k5_numbers ) | B = C ) ) ) ) ) )).
fof(t11_matrixj2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( m1_subset_1(C,u1_struct_0(B)) => m1_matrixj2(k16_matrixj1(u1_struct_0(B),A,k2_matrixj2(B,C,A)),B,C) ) ) ) )).
fof(t11_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( 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)) ) ) ) ) )).
fof(t11_matrixr2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => k7_matrixr1(k3_xcmplx_0(A,B),C) = k7_matrixr1(A,k7_matrixr1(B,C)) ) ) ) )).
fof(t11_matrlin,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ( ! [C] : ( 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) ) ) ) )).
fof(t11_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(t11_matroid0,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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))) ) ) ) ) ) )).
fof(t11_matrprob,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k3_finseq_2(A)) => ( ? [C] : ( v7_ordinal1(C) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(B)) => k3_finseq_1(k1_matrprob(A,B,D)) = C ) ) ) <=> ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) ) ) )).
fof(t11_matrtop1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k2_xcmplx_0(E,D),A) <=> r2_hidden(E,B) ) ) => k5_relat_1(k61_valued_1(C,D),A) = k61_valued_1(k5_relat_1(C,B),D) ) ) ) )).
fof(t11_matrtop2,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_vectsp_4(C,k2_vectsp_1,k6_prvect_1(k2_vectsp_1,B)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t11_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,k2_finseq_1(B)) => v1_matrtop3(k3_matrtop1(B,B,k1_matrtop3(B,A)),k3_matrix13(A)) ) ) ) )).
fof(t11_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t11_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( r2_pboole(A,D,k4_pboole(A,B,C)) <=> ( r2_pboole(A,D,B) & r5_pboole(A,D,C) ) ) ) ) ) )).
fof(t11_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r2_hidden(D,k2_zfmisc_1(k2_tarski(A,B),k1_tarski(C))) => ( ( k1_xtuple_0(D) = A | k1_xtuple_0(D) = B ) & k2_xtuple_0(D) = C ) ) )).
fof(t11_measure1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ( r2_hidden(k1_xboole_0,B) & r2_hidden(A,B) & ! [D] : ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t11_measure2,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m1_measure2(D,A,B) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ( D = k4_measure1(A,B,E) => r1_xxreal_0(k3_funct_2(B,k6_numbers,C,k2_measure2(A,B,D)),k19_supinf_2(k1_partfun1(k4_ordinal1,B,B,k6_numbers,E,C))) ) ) ) ) ) )).
fof(t11_measure3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ( ( k9_nat_1(B,D,k5_numbers) = k1_xboole_0 & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( k9_nat_1(B,D,k1_nat_1(F,1)) = k3_measure1(A,B,k9_nat_1(B,E,k5_numbers),k9_nat_1(B,E,F)) & r1_tarski(k9_nat_1(B,E,k1_nat_1(F,1)),k9_nat_1(B,E,F)) ) ) ) => ( r1_xxreal_0(k1_supinf_1,k12_supinf_2(C,k9_nat_1(B,E,k5_numbers))) | k7_supinf_2(k17_supinf_2(k1_partfun1(k4_ordinal1,B,B,k6_numbers,E,C))) = k4_supinf_2(k12_supinf_2(C,k9_nat_1(B,E,k5_numbers)),k8_supinf_2(k17_supinf_2(k1_partfun1(k4_ordinal1,B,B,k6_numbers,D,C)))) ) ) ) ) ) ) )).
fof(t11_measure5,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ! [B] : ( m1_subset_1(B,k6_numbers) => ! [C] : ( ( v6_xxreal_2(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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 ) ) ) ) ) ) )).
fof(t11_measure6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xxreal_0(B) => ( ? [C] : ( v1_xxreal_0(C) & r1_xxreal_0(B,C) & A = k2_xxreal_1(B,C) ) => B = k7_supinf_2(A) ) ) ) )).
fof(t11_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v6_supinf_2(B) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,C,k4_ordinal1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,k4_ordinal1))) ) => ( ( v2_funct_1(D) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r2_hidden(E,C) => k12_supinf_2(A,E) = k12_supinf_2(k1_partfun1(C,k4_ordinal1,k4_ordinal1,k6_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)) ) ) ) ) ) ) )).
fof(t11_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => ( r2_hidden(B,A) <=> r2_hidden(k4_xcmplx_0(B),k5_member_1(A)) ) ) ) )).
fof(t11_membered,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v5_membered(A) ) => ? [B] : ( v1_int_1(B) & r2_hidden(B,A) ) ) )).
fof(t11_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t11_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => k1_euclid_6(k3_rlvect_1(k15_euclid(2),A,D),B,C) = k6_xcmplx_0(k2_xcmplx_0(k1_euclid_6(A,B,C),k1_euclid_6(D,B,C)),k1_euclid_6(k4_struct_0(k15_euclid(2)),B,C)) ) ) ) ) )).
fof(t11_mesfun10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers)) = k1_relset_1(A,k4_mesfunc5(A,k6_numbers,C,k5_numbers)) & v1_mesfunc8(B,A,k6_numbers) & k8_relset_1(A,k6_numbers,D,k6_domain_1(k6_numbers,k1_supinf_1)) = k1_xboole_0 & k8_relset_1(A,k6_numbers,D,k6_domain_1(k6_numbers,k2_supinf_1)) = k1_xboole_0 & ! [E] : ( v7_ordinal1(E) => r2_relset_1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,B,E),k3_mesfunc1(A,D,k4_mesfunc5(A,k6_numbers,C,E))) ) ) => ( r2_relset_1(A,k6_numbers,k5_mesfunc8(A,B),k3_mesfunc1(A,D,k5_mesfunc8(A,C))) & r2_relset_1(A,k6_numbers,k6_mesfunc8(A,B),k3_mesfunc1(A,D,k6_mesfunc8(A,C))) ) ) ) ) ) ) )).
fof(t11_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t11_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( m1_subset_1(C,A) => ( r2_hidden(C,k1_relset_1(A,k4_mesfunc5(A,k1_numbers,B,k5_numbers))) => r2_funct_2(k4_ordinal1,k6_numbers,k3_mesfunc5(A,k5_mesfun7c(A,B),C),k4_rinfsup2(k1_mesfunc5(k4_ordinal1,k10_seqfunc(A,B,C)))) ) ) ) ) )).
fof(t11_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( 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,k5_numbers)) ) ) ) ) )).
fof(t11_mesfunc1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_xxreal_0(k6_xcmplx_0(A,k2_extreal1(1,k1_nat_1(C,1))),B) ) => r1_xxreal_0(A,B) ) ) ) )).
fof(t11_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t11_mesfunc3,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => m2_finseq_1(A,k6_numbers) ) )).
fof(t11_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ! [C] : ~ ( r2_hidden(C,k1_relset_1(A,B)) & r1_xxreal_0(k1_supinf_1,k12_supinf_2(B,C)) ) <=> v4_mesfunc5(B) ) ) ) )).
fof(t11_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,C))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( v1_xreal_0(F) => ( ! [G] : ( v7_ordinal1(G) => k1_funct_1(D,G) = k3_xboole_0(B,k14_mesfunc1(E,k2_xcmplx_0(F,k2_extreal1(1,k1_nat_1(G,1))))) ) => k3_xboole_0(B,k13_mesfunc1(E,F)) = k5_setfam_1(A,k4_measure1(A,C,D)) ) ) ) ) ) ) )).
fof(t11_mesfunc7,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ( A = B => k4_mesfunc7(A,C) = k1_newton(B,C) ) ) ) ) )).
fof(t11_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ( ! [C] : ( 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,k6_numbers,k5_mesfunc8(A,B),k2_mesfunc8(A,k3_mesfunc8(A,B))) ) ) ) )).
fof(t11_metric_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( l1_metric_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r2_hidden(D,k8_metric_1(B,C,A)) <=> ( ~ v2_struct_0(B) & ~ r1_xxreal_0(A,k1_metric_1(B,C,D)) ) ) ) ) ) ) )).
fof(t11_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v7_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_metric_2(A,B,C) <=> B = C ) ) ) ) )).
fof(t11_metric_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))) => k2_binop_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,k10_metric_3(A,B),C,D) = k2_binop_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,k10_metric_3(A,B),D,C) ) ) ) ) )).
fof(t11_metric_6,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r1_metric_6(A,C,B) => k1_tbsp_1(A,C) = B ) ) ) ) )).
fof(t11_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k1_pre_topc(A,C)))) => ( ( v6_topgen_4(B,A) & D = k9_subset_1(u1_struct_0(A),B,C) ) => v6_topgen_4(D,k1_pre_topc(A,C)) ) ) ) ) ) )).
fof(t11_mfold_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_connsp_2(D,A,C) => ! [E] : ( ( v3_pre_topc(E,B) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) ) => ~ ( r1_metrizts(A,B,D,E) & ! [F] : ( ( v3_pre_topc(F,A) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t11_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t11_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_midsp_1(A,B,C,D,E) => r1_midsp_1(A,D,E,B,C) ) ) ) ) ) ) )).
fof(t11_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t11_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_nat_1(A,2)) ) => ! [C] : ( m1_midsp_3(C,A) => ( r2_midsp_3(A,C,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m2_finseq_2(F,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(B))) => ! [G] : ( m2_finseq_2(G,u1_struct_0(B),k4_finseq_2(k1_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)) ) ) ) ) ) ) ) ) ) )).
fof(t11_mmlquer2,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => r1_tarski(k1_mmlquer2(A,B),k2_xboole_0(A,B)) ) ) )).
fof(t11_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [D] : ( v7_ordinal1(D) => k12_mmlquery(A,B,C,k1_nat_1(D,1)) = k14_mmlquery(A,B,C,D) ) ) ) )).
fof(t11_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( v3_mod_2(B,A) & l1_mod_2(B,A) ) => ! [C] : ( ( v3_mod_2(C,A) & l1_mod_2(C,A) ) => ~ ( k2_mod_2(A,B) = k3_mod_2(A,C) & ! [D] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) ) ) ) )).
fof(t11_mod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t11_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_mod_4(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t11_modcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_modcat_1(B,A) => ! [C] : ( m4_modcat_1(C,A,k4_modcat_1(A,B)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t11_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t11_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ~ ( ~ v4_modelc_2(A) & ~ v5_modelc_2(A) & ~ v7_modelc_2(A) & ~ v8_modelc_2(A) ) => ( k3_finseq_1(A) = k1_nat_1(k1_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))) ) ) ) )).
fof(t11_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k13_modelc_2(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k13_modelc_2(B))) => ( D = k2_xboole_0(C,k1_tarski(A)) => ( r2_hidden(A,C) | k18_modelc_3(B,D) = k2_xcmplx_0(k18_modelc_3(B,C),k3_finseq_1(A)) ) ) ) ) ) ) )).
fof(t11_moebius1,axiom,( ! [A] : ( ( v1_int_2(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) ) => ~ ( r1_int_2(B,C) & r1_nat_d(k11_newton(A,2),k2_nat_1(B,C)) & ~ r1_nat_d(k11_newton(A,2),B) & ~ r1_nat_d(k11_newton(A,2),C) ) ) ) ) )).
fof(t11_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v14_monoid_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k6_algstr_0(A,B,C) = k6_algstr_0(A,B,D) => C = D ) ) ) ) ) ) )).
fof(t11_monoid_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(t11_morph_01,axiom,( ! [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) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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)) ) ) ) ) )).
fof(t11_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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)) ) ) )).
fof(t11_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ( r2_hidden(E,k1_relset_1(k4_ordinal1,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))) ) ) ) ) ) ) ) )).
fof(t11_msafree3,axiom,( ! [A] : ! [B] : ! [C] : ( l1_msualg_1(C) => ! [D] : ( r2_hidden(D,u1_struct_0(C)) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t11_msafree4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v6_trees_3(B) ) => r1_tarski(k10_xtuple_0(B),k3_trees_9(k4_trees_4(A,B))) ) )).
fof(t11_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) & r2_hidden(C,k7_msafree(A,B,D)) ) ) ) ) )).
fof(t11_msscyc_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t11_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t11_mssublat,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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] : ( 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) ) ) ) ) ) )).
fof(t11_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msualg_2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t11_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( m2_pboole(E,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t11_msualg_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_msualg_4(C,A,B) & m1_msualg_4(C,A,B,B) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t11_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_msualg_6(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( 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 ) ) ) ) ) ) ) )).
fof(t11_msualg_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m2_nat_lat(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t11_msualg_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t11_msualg_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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)) ) ) )).
fof(t11_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) )).
fof(t11_mycielsk,axiom,( ! [A] : ( ( v8_struct_0(A) & l1_orders_2(A) ) => r1_xxreal_0(k1_dilworth(A),k5_card_1(u1_struct_0(A))) ) )).
fof(t11_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_nagata_1(B,A) => v1_pcomps_1(B,A) ) ) ) )).
fof(t11_nagata_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,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(k4_ordinal1,k4_partfun1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_numbers)))) ) => ( ( ! [C] : ( v7_ordinal1(C) => ? [D] : ( 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] : ( 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] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t11_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(A,k2_xcmplx_0(A,B)) ) ) )).
fof(t11_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(A,B) => r1_nat_d(k2_power(2,A),k2_power(2,B)) ) ) ) )).
fof(t11_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => k2_nat_3(k2_pre_poly(k1_numbers),A) = k2_pre_poly(k1_numbers) ) )).
fof(t11_nat_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k4_nat_d(k1_newton(A,k3_xcmplx_0(2,B)),C) = k4_nat_d(k2_nat_1(k4_nat_d(k1_newton(A,B),C),k4_nat_d(k1_newton(A,B),C)),C) ) ) ) )).
fof(t11_nat_5,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ( ( r2_relset_1(k4_ordinal1,k1_numbers,C,k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k1_numbers,k14_finseq_1(A),B)) & r1_tarski(k7_subset_1(k4_ordinal1,k4_finseq_1(B),k8_relset_1(k4_ordinal1,k1_numbers,B,k6_domain_1(k4_ordinal1,k5_numbers))),A) & r1_tarski(A,k4_finseq_1(B)) ) => k18_rvsum_1(B) = k18_rvsum_1(C) ) ) ) )).
fof(t11_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_nat_d(B,C) & r1_nat_d(B,A) ) => r1_nat_d(B,k4_nat_d(C,A)) ) ) ) ) )).
fof(t11_nat_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_nat_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_nat_lat)) => ( k1_binop_1(k1_nat_lat,B,k1_binop_1(k2_nat_lat,B,A)) = B & k1_binop_1(k1_nat_lat,k1_binop_1(k2_nat_lat,A,B),B) = B & k1_binop_1(k1_nat_lat,B,k1_binop_1(k2_nat_lat,A,B)) = B & k1_binop_1(k1_nat_lat,k1_binop_1(k2_nat_lat,B,A),B) = B ) ) ) )).
fof(t11_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t11_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_numbers))) ) => ! [C] : ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_hidden(F,k1_relset_1(u1_struct_0(A),B)) & ~ r1_xxreal_0(E,k2_normsp_0(A,k5_algstr_0(A,F,C))) & r1_xxreal_0(D,k9_complex1(k5_real_1(k7_partfun1(k1_numbers,B,F),k7_partfun1(k1_numbers,B,C)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_ncfcont2,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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)) ) ) ) ) ) )).
fof(t11_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k1_ndiff_1(A,B,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,D)),k3_normsp_1(A,k1_ndiff_1(A,B,C),k1_ndiff_1(A,B,D))) ) ) ) ) )).
fof(t11_ndiff_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) ) ) )).
fof(t11_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t11_ndiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(B)))) ) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t11_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(A)) => ! [C] : ! [D] : ( ( 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(k1_funct_7(D,B,C),u1_struct_0(k14_prvect_2(A))) ) ) ) ) )).
fof(t11_neckla_3,axiom,( u1_orders_2(k3_necklace(k4_necklace(4))) = k11_domain_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,2),k1_domain_1(k4_ordinal1,k4_ordinal1,2,k5_numbers),k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,3),k1_domain_1(k4_ordinal1,k4_ordinal1,3,k5_numbers),k1_domain_1(k4_ordinal1,k4_ordinal1,1,3),k1_domain_1(k4_ordinal1,k4_ordinal1,3,1)) )).
fof(t11_necklace,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ( ( r2_necklace(B,A) & r2_necklace(C,B) ) => r2_necklace(C,A) ) ) ) ) )).
fof(t11_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k2_net_1(A)) => r1_tarski(k4_net_1(A,B),k2_net_1(A)) ) ) )).
fof(t11_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => k1_newton(k5_numbers,A) = k5_numbers ) ) )).
fof(t11_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,k1_relset_1(u1_struct_0(A),C)) => ( ! [E] : ( m1_nfcont_1(E,A,D) => k9_subset_1(u1_struct_0(A),k1_relset_1(u1_struct_0(A),C),E) != k1_tarski(D) ) | r1_nfcont_1(A,B,C,D) ) ) ) ) ) ) )).
fof(t11_nfcont_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( 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) & r1_nfcont_2(D,A,B,C) ) => v1_nfcont_1(k7_relset_1(u1_struct_0(A),u1_struct_0(B),C,D),B) ) ) ) ) ) )).
fof(t11_nfcont_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ( ? [D] : ( 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) ) ) ) ) )).
fof(t11_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k1_euclid(A))) => ~ ( ? [E] : ( v1_xreal_0(E) & ~ r1_xxreal_0(E,k5_numbers) & a_4_0_nfcont_4(A,B,C,E) = D ) & ! [E] : ( m1_rcomp_1(E,B) => ? [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t11_normform,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_finsub_1(B) ) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(A,B)) => ( C = k1_normform(A,B,C,D) => r1_normform(A,B,D,C) ) ) ) ) ) )).
fof(t11_normsp_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & k2_normsp_0(A,k5_algstr_0(A,B,C)) = k5_numbers ) ) ) ) )).
fof(t11_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => v4_frechet(k3_normsp_2(A)) ) )).
fof(t11_ntalgo_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,k2_zfmisc_1(k4_numbers,k4_numbers)) ) => ! [B] : ( m2_finseq_1(B,k4_numbers) => ! [C] : ( m2_finseq_1(C,k4_numbers) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k3_finseq_1(B) = k3_finseq_1(A) & ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(D,k2_finseq_1(k3_finseq_1(A))) & k1_funct_1(C,D) = k5_numbers ) ) & ! [D] : ( 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] : ( v7_ordinal1(D) => ! [E] : ( 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] : ( v7_ordinal1(D) => ( r2_hidden(D,k2_finseq_1(k3_finseq_1(A))) => k5_int_1(k4_ntalgo_1(A),k1_funct_1(C,D)) = k5_int_1(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) ) ) )).
fof(t11_numbers,axiom,( r1_tarski(k1_numbers,k2_numbers) )).
fof(t11_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t11_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t11_oposet_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v4_oposet_1(A) => v3_oposet_1(A) ) ) )).
fof(t11_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_cat_1(A,B,C) != k1_xboole_0 => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t11_ordeq_01,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(k2_ordeq_01(B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_ordeq_01(B,C))) => ! [F] : ( ( v1_funct_1(F) & v1_nfcont_3(F,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(C)))) ) => ! [G] : ( ( v1_funct_1(G) & v1_nfcont_3(G,C) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(C)))) ) => ( ( F = D & G = E & k1_relset_1(k1_numbers,F) = B & k1_relset_1(k1_numbers,G) = B ) => ( E = k1_rlvect_1(k2_ordeq_01(B,C),D,A) <=> ! [H] : ( m2_subset_1(H,k1_numbers,B) => k7_partfun1(u1_struct_0(C),G,H) = k1_rlvect_1(C,k7_partfun1(u1_struct_0(C),F,H),A) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_orders_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( ( r7_relat_2(C,A) & r1_tarski(B,A) ) => r7_relat_2(C,B) ) ) )).
fof(t11_orders_2,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ~ ( ? [D] : ( 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] : ( ( v6_orders_2(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( r2_hidden(B,D) & r2_hidden(C,D) ) ) ) ) ) ) ) )).
fof(t11_orders_3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => r1_tarski(k1_orders_3(A,B),k1_funct_2(u1_struct_0(A),u1_struct_0(B))) ) ) )).
fof(t11_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => r3_xboole_0(A,B) ) ) )).
fof(t11_ordinal2,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_tarski(k3_ordinal1(A),k3_ordinal1(B)) ) )).
fof(t11_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( r1_tarski(B,A) => v3_ordinal1(k1_setfam_1(B)) ) ) )).
fof(t11_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( v3_ordinal1(B) => ( v2_ordinal2(A) => v3_ordinal1(k8_relat_1(A,B)) ) ) ) )).
fof(t11_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( ( r2_hidden(k5_numbers,A) & v4_ordinal1(B) ) => ( v1_xboole_0(B) | ( r2_hidden(C,k12_ordinal2(A,B)) <=> ? [D] : ( v3_ordinal1(D) & r2_hidden(D,B) & r2_hidden(C,k12_ordinal2(A,D)) ) ) ) ) ) ) )).
fof(t11_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r1_ordinal1(A,B) <=> r1_ordinal1(k3_ordinal5(A),k3_ordinal5(B)) ) ) ) )).
fof(t11_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( ~ r1_orders_2(B,D,C) => r1_orders_2(B,k5_algstr_0(B,E,k4_vectsp_1(A,B,k1_ortsp_1(A,B,C,D,E),D)),C) ) ) ) ) ) ) )).
fof(t11_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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] : ( m1_subset_1(D,u4_struct_0(A)) => ( k1_funct_1(C,k1_xboole_0) = k4_tarski(D,u1_struct_0(A)) => ( ? [E] : ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : C != k1_trees_4(k4_tarski(F,E)) ) & ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t11_osalg_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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] : ( m1_subset_1(D,u4_struct_0(A)) => ~ r5_osalg_1(A,B,D,C) ) ) ) ) ) ) )).
fof(t11_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t11_osalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t11_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r3_orders_2(A,D,B) & r3_orders_2(A,D,C) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r3_orders_2(A,B,D) & r3_orders_2(A,C,D) ) ) ) ) ) ) )).
fof(t11_papdesaf,axiom,( ! [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) ) => ! [B] : ( ( ~ v7_struct_0(B) & v2_analoaf(B) & l1_analoaf(B) ) => ( B = k2_analoaf(A) => v6_papdesaf(B) ) ) ) )).
fof(t11_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A))) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t11_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t11_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) )).
fof(t11_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v2_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,B) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t11_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => v3_pasch(A) ) )).
fof(t11_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ~ ( r4_pboole(A,B,C) & ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t11_pcomps_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => v2_tops_2(k1_pcomps_1(A,B),A) ) ) )).
fof(t11_pcs_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v16_pcs_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k17_pcs_0(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k17_pcs_0(A,B))) => ( r1_orders_2(k17_pcs_0(A,B),C,D) <=> ? [E] : ( m1_subset_1(E,A) & ? [F] : ( m1_subset_1(F,u1_struct_0(k15_pcs_0(A,B,E))) & ? [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t11_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k4_pdiff_1(B,A) = k3_relat_1(k1_pdiff_1(B,A),k2_funct_1(k1_pdiff_1(1,1))) ) ) )).
fof(t11_pdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(2)) => ! [E] : ( ( 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 = k10_pdiff_1(2,1,E,D) <=> ? [F] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & D = k10_finseq_1(F,G) & ? [H] : ( m1_rcomp_1(H,F) & r1_tarski(H,k1_relset_1(k1_numbers,k1_pdiff_2(2,1,E,D))) & ? [I] : ( v1_funct_1(I) & v3_fdiff_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [J] : ( v1_funct_1(J) & v2_fdiff_1(J) & m1_subset_1(J,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & C = k1_funct_1(I,1) & ! [K] : ( v1_xreal_0(K) => ( r2_hidden(K,H) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(2,1,E,D),K),k1_funct_1(k1_pdiff_2(2,1,E,D),F)) = k2_xcmplx_0(k1_funct_1(I,k6_xcmplx_0(K,F)),k1_funct_1(J,k6_xcmplx_0(K,F))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_pdiff_3,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(2)) => ! [B] : ( ( 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) ) ) ) )).
fof(t11_pdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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] : ( m1_rcomp_1(F,B) => ~ ( r1_tarski(F,k1_relset_1(k1_numbers,k1_pdiff_2(3,2,E,D))) & ? [G] : ( v1_funct_1(G) & v3_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [H] : ( v1_funct_1(H) & v2_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,F) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,2,E,D),I),k1_funct_1(k1_pdiff_2(3,2,E,D),B)) = k2_xcmplx_0(k1_funct_1(G,k6_xcmplx_0(I,B)),k1_funct_1(H,k6_xcmplx_0(I,B))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t11_pdiff_6,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( 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) => k3_funct_2(k1_euclid(B),k1_euclid(A),C,k5_euclid(B)) = k5_euclid(A) ) ) ) ) )).
fof(t11_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(C,A) & B != k5_numbers & k1_finseq_7(k1_numbers,k5_euclid(A),C,B) = k5_euclid(A) ) ) ) ) )).
fof(t11_pdiff_8,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(A))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => 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)) ) ) ) ) )).
fof(t11_pdiff_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,B) ) => k12_euclid(k1_funct_1(k6_pdiff_1(B,A,k5_euclid(B)),C)) = k9_complex1(C) ) ) ) ) )).
fof(t11_pencil_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_pboole(C,A,k12_pralg_1(A,B)) => m3_pboole(k1_pzfmisc1(A,C),A,k12_pralg_1(A,B)) ) ) ) )).
fof(t11_pencil_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( ~ v13_pencil_1(C) & v16_pencil_1(C,A) & m3_pboole(C,A,k12_pralg_1(A,B)) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t11_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m1_vectsp_4(E,A,B) => ! [F] : ( m1_vectsp_4(F,A,B) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( k4_nat_d(k3_xcmplx_0(C,A),B) = k4_nat_d(A,B) & r1_int_2(A,B) ) => ( r1_xxreal_0(B,1) | k4_nat_d(C,B) = 1 ) ) ) ) ) )).
fof(t11_petri,axiom,( ! [A] : ( ( ~ 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 ) )).
fof(t11_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,k4_ordinal1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => 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))) ) ) ) )).
fof(t11_polyalg1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_polyalg1(B,A) => m1_polyalg1(B,A,B) ) ) )).
fof(t11_polyeq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => ( ! [F] : ( v1_xreal_0(F) => k2_polyeq_1(C,D,E,F) = k3_polyeq_1(C,F,A,B) ) => ( C = k5_numbers | ( k7_xcmplx_0(D,C) = k4_xcmplx_0(k2_xcmplx_0(A,B)) & k7_xcmplx_0(E,C) = k3_xcmplx_0(A,B) ) ) ) ) ) ) ) ) )).
fof(t11_polyeq_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ( ! [K] : ( v1_xreal_0(K) => k1_polyeq_2(A,B,C,D,E,K) = k2_polyeq_2(A,G,H,I,J,K) ) => ( A = k5_numbers | k7_xcmplx_0(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,k1_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)),k1_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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_polyeq_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xcmplx_0(D) => ~ ( A != k5_numbers & ~ r1_xxreal_0(k5_numbers,k1_quin_1(A,B,C)) & k4_polyeq_1(A,B,C,k5_numbers,D) = k5_numbers & D != k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,k3_xcmplx_0(2,A))),k3_xcmplx_0(k7_xcmplx_0(k3_square_1(k4_xcmplx_0(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A)),k7_complex1)) & D != k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,k3_xcmplx_0(2,A))),k3_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k3_square_1(k4_xcmplx_0(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A))),k7_complex1)) & D != k5_numbers ) ) ) ) ) )).
fof(t11_polyeq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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(k1_square_1(A),k3_xcmplx_0(A,B)),k1_square_1(B))) & k2_xcmplx_0(k1_newton(A,5),k1_newton(B,5)) = k3_xcmplx_0(k2_xcmplx_0(A,B),k2_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k1_newton(A,4),k3_xcmplx_0(k1_newton(A,3),B)),k3_xcmplx_0(k1_newton(A,2),k1_newton(B,2))),k3_xcmplx_0(A,k1_newton(B,3))),k1_newton(B,4))) ) ) ) )).
fof(t11_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => ( ( C = k4_xcmplx_0(k2_xcmplx_0(D,E)) & B = k3_xcmplx_0(D,E) ) => ( k2_xcmplx_0(k2_xcmplx_0(k1_newton(A,2),k3_xcmplx_0(C,A)),B) = k5_numbers <=> ( A = D | A = E ) ) ) ) ) ) ) ) )).
fof(t11_polyform,axiom,( ! [A] : ( v7_ordinal1(A) => ~ r1_xxreal_0(k2_xcmplx_0(A,2),1) ) )).
fof(t11_polynom1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t11_polynom2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( ( 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(k15_pre_poly(A),B,C) = k1_tarski(D) => ! [E] : ( ( 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)))) ) => k2_polynom2(A,B,C,E) = k6_algstr_0(B,k4_polynom1(A,B,C,D),k1_polynom2(A,D,B,E)) ) ) ) ) ) ) )).
fof(t11_polynom3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( k1_funct_1(k6_polynom3(2,C),A) = k2_polynom3(k4_ordinal1,D,k7_nat_d(C,D)) & k1_funct_1(k6_polynom3(2,C),B) = k2_polynom3(k4_ordinal1,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) ) ) ) ) ) ) ) ) )).
fof(t11_polynom4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k1_polynom4(A,B),k14_funct_7(k4_ordinal1,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)))) ) ) )).
fof(t11_polynom5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_complfld)) => k1_polynom5(k3_finseq_4(u1_struct_0(k1_complfld),A,B,C)) = k11_finseq_1(k9_complex1(A),k9_complex1(B),k9_complex1(C)) ) ) ) )).
fof(t11_polynom6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( m2_subset_1(C,k14_pre_poly(A),k15_pre_poly(A)) => ! [D] : ( m2_subset_1(D,k14_pre_poly(A),k15_pre_poly(A)) => ! [E] : ( m2_subset_1(E,k14_pre_poly(B),k15_pre_poly(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t11_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( 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) ) ) )).
fof(t11_polynom8,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r1_xxreal_0(k1_algseq_1(A,k2_polynom8(A,B,C)),k4_nat_1(k1_algseq_1(A,B),k1_algseq_1(A,C))) ) ) ) )).
fof(t11_polyred,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_group_1(B) & l5_algstr_0(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) )).
fof(t11_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) )).
fof(t11_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ ( ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) & v1_abian(C) ) => k1_power(C,k3_xcmplx_0(A,B)) = k3_xcmplx_0(k1_power(C,A),k1_power(C,B)) ) ) ) ) )).
fof(t11_pralg_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ( k9_xtuple_0(k1_funct_6(k12_pralg_2(A,B,C,D))) = A & ! [E] : ( m1_subset_1(E,A) => k1_funct_1(k1_funct_6(k12_pralg_2(A,B,C,D)),E) = k3_msualg_1(B,D,k5_pralg_2(A,B,C,E)) ) ) ) ) ) ) )).
fof(t11_pralg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( 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] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t11_pre_circ,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v4_trees_3(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(k1_nat_1(B,1),k4_finseq_1(A)) => k4_trees_1(k11_trees_3(A),k12_finseq_1(k4_ordinal1,B)) = k1_funct_1(A,k1_nat_1(B,1)) ) ) ) )).
fof(t11_pre_ff,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & k2_xcmplx_0(k1_int_1(k3_power(2,k3_xcmplx_0(2,A))),1) = k1_int_1(k3_power(2,k1_nat_1(k3_xcmplx_0(2,A),1))) ) ) )).
fof(t11_pre_poly,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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 ) ) ) )).
fof(t11_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).
fof(t11_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_prelamb(A) ) => ! [B] : ( m1_prelamb(B,A) => ! [C] : ( m1_trees_1(C,k9_xtuple_0(B)) => ~ ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(k5_numbers,D) & r1_xxreal_0(D,7) & k2_xtuple_0(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k4_ordinal1),B,C)) = D ) ) ) ) ) )).
fof(t11_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(1,A) => r1_xxreal_0(1,k1_newton(A,B)) ) ) ) )).
fof(t11_prgcor_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( ( B = k5_numbers & C = A & D = B ) => ( k4_int_1(A,B) = k5_numbers & k3_nat_d(C,D) = k5_numbers ) ) & ( ( r1_xxreal_0(k5_numbers,A) & C = A & D = B ) => ( r1_xxreal_0(B,k5_numbers) | k4_int_1(A,B) = k3_nat_d(C,D) ) ) & ( ( r1_xxreal_0(k5_numbers,A) & C = A & D = k4_xcmplx_0(B) ) => ( r1_xxreal_0(k5_numbers,B) | ( ( k2_nat_1(D,k3_nat_d(C,D)) = C => k4_int_1(A,B) = k4_xcmplx_0(k3_nat_d(C,D)) ) & ( k2_nat_1(D,k3_nat_d(C,D)) != C => k4_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(k5_numbers,A) | r1_xxreal_0(B,k5_numbers) | ( ( k2_nat_1(D,k3_nat_d(C,D)) = C => k4_int_1(A,B) = k4_xcmplx_0(k3_nat_d(C,D)) ) & ( k2_nat_1(D,k3_nat_d(C,D)) != C => k4_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(k5_numbers,A) | r1_xxreal_0(k5_numbers,B) | k4_int_1(A,B) = k3_nat_d(C,D) ) ) ) ) ) ) ) )).
fof(t11_prob_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => m1_subset_1(k3_tarski(k10_xtuple_0(B)),k1_zfmisc_1(A)) ) )).
fof(t11_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m1_prob_1(E,A,B) => ! [F] : ( m2_prob_1(F,A,B) => k3_funct_2(B,k1_numbers,F,k6_prob_1(A,B,k6_prob_1(A,B,C,D),E)) = k3_real_1(k5_real_1(k3_real_1(k3_real_1(k3_funct_2(B,k1_numbers,F,C),k3_funct_2(B,k1_numbers,F,D)),k3_funct_2(B,k1_numbers,F,E)),k3_real_1(k3_real_1(k3_funct_2(B,k1_numbers,F,k5_prob_1(A,B,C,D)),k3_funct_2(B,k1_numbers,F,k5_prob_1(A,B,D,E))),k3_funct_2(B,k1_numbers,F,k5_prob_1(A,B,C,E)))),k3_funct_2(B,k1_numbers,F,k5_prob_1(A,B,k5_prob_1(A,B,C,D),E))) ) ) ) ) ) ) )).
fof(t11_prob_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => v3_prob_1(k2_prob_3(A,B)) ) )).
fof(t11_prob_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ( r1_funct_2(k4_ordinal1,k1_numbers,k4_ordinal1,k6_numbers,A,B) & v2_seq_2(A) ) => k2_rinfsup1(A) = k2_xxreal_2(k2_relset_1(k6_numbers,B)) ) ) ) )).
fof(t11_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) )).
fof(t11_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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] : ( m1_subset_1(I,u1_struct_0(A)) => ~ ( r1_collsp(A,E,F,I) & r1_collsp(A,G,H,I) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t11_projred1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t11_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u2_incsp_1(A)) => m1_projred2(k6_partfun1(k1_projred2(A,B)),A) ) ) )).
fof(t11_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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] : ( m2_subset_1(C,k4_ordinal1,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)))) ) ) ) ) ) ) )).
fof(t11_prvect_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_prvect_2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_prvect_2(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k11_prvect_2(A,B))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k11_prvect_2(A,B))) => ! [G] : ( m1_subset_1(G,k4_card_3(k4_prvect_2(A))) => ! [H] : ( 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(k2_normsp_0(k11_prvect_2(A,B),k5_algstr_0(k11_prvect_2(A,B),F,E)),k2_normsp_0(k14_prvect_2(A),k5_algstr_0(k14_prvect_2(A),D,C))) ) ) ) ) ) ) ) ) ) )).
fof(t11_prvect_3,axiom,( ! [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) ) => ? [B] : ( 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] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) )).
fof(t11_pscomp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( 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(k5_numbers,k2_relset_1(k1_numbers,B)) | v1_pscomp_1(k6_measure6(u1_struct_0(A),k1_numbers,B),A) ) ) ) ) )).
fof(t11_pua2mss1,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) ) => ! [B] : ( m1_eqrel_1(B,k9_xtuple_0(A)) => m1_eqrel_1(a_2_1_pua2mss1(A,B),A) ) ) )).
fof(t11_pythtrip,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( k1_nat_1(k1_pepin(A),k1_pepin(B)) = k1_pepin(C) & r1_int_2(A,B) & ~ v1_abian(A) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( r1_xxreal_0(D,E) & A = k6_xcmplx_0(k1_pepin(E),k1_pepin(D)) & B = k2_nat_1(k2_nat_1(2,D),E) & C = k1_nat_1(k1_pepin(E),k1_pepin(D)) ) ) ) ) ) ) ) )).
fof(t11_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(t11_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(A),k8_qc_lang1(A,B)) => k7_qc_lang1(A,C) = B ) ) ) )).
fof(t11_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ! [E] : ( m1_subset_1(E,k9_qc_lang1(A)) => ( k2_qc_lang2(A,B,C) = k2_qc_lang2(A,D,E) => ( B = D & C = E ) ) ) ) ) ) ) )).
fof(t11_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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))) ) ) ) )).
fof(t11_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => k10_xtuple_0(k2_qc_lang4(A,B)) = k15_qc_lang2(A,B) ) ) )).
fof(t11_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_qc_trans(B,A) & m1_qc_lang1(B) ) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(B)) => ! [D] : ( m2_finseq_1(D,k3_cqc_lang(A)) => ( C = D => ( k1_calcul_1(k3_cqc_lang(B),C) = k1_calcul_1(k3_cqc_lang(A),D) & k2_calcul_1(B,C) = k2_calcul_1(A,D) ) ) ) ) ) ) )).
fof(t11_qmax_1,axiom,( ! [A] : ( ( v2_qmax_1(A) & l1_qmax_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k5_qmax_1(A))) => ! [C] : ( 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] : ( m1_subset_1(D,k5_qmax_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t11_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v10_lattices(A) & v4_lattice3(A) & v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t11_quatern2,axiom,( k1_quatern2 = k6_quaterni(k5_numbers,k5_numbers,k5_numbers,k5_numbers) )).
fof(t11_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k1_square_1(k28_quaterni(A)) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k13_quaterni(A)),k1_square_1(k14_quaterni(A))),k1_square_1(k15_quaterni(A))),k1_square_1(k16_quaterni(A))) ) )).
fof(t11_quaterni,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ( ( 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 ) ) )).
fof(t11_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ! [D] : ( v1_xreal_0(D) => r1_xxreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k1_square_1(D)),k3_xcmplx_0(B,D)),C),k5_numbers) ) => ( r1_xxreal_0(k5_numbers,A) | r1_xxreal_0(k1_quin_1(A,B,C),k5_numbers) ) ) ) ) ) )).
fof(t11_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t11_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => r1_tarski(k2_radix_1(A),k4_numbers) ) )).
fof(t11_radix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(1,B) => ! [C] : ( ( v3_card_1(C,B) & m2_finseq_1(C,k3_radix_1(A)) ) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t11_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t11_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(2,A) => k12_radix_1(k1_radix_1(A),A) = k5_numbers ) ) )).
fof(t11_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(2,B) => ! [C] : ( ( 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),k5_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))) ) ) ) ) )).
fof(t11_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k1_random_1(A),k6_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),k6_numbers))) ) => ! [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))) ) => ~ ( ~ r1_xxreal_0(k1_xxreal_0,k12_supinf_2(B,A)) & ! [D] : ( m2_finseq_1(D,k6_numbers) => ! [E] : ( 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] : ( v7_ordinal1(F) => ( r2_hidden(F,k4_finseq_1(D)) => k12_supinf_2(D,F) = k4_xxreal_3(k12_supinf_2(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) ) ) ) ) ) ) ) )).
fof(t11_random_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [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))) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( ~ v1_xboole_0(F) & v1_finset_1(F) & m1_subset_1(F,k1_zfmisc_1(A)) ) => ! [G] : ( m2_finseq_1(G,A) => ( ( v2_funct_1(G) & k2_relset_1(A,G) = F ) => ! [H] : ( m2_finseq_1(H,B) => ! [I] : ( m2_finseq_1(I,k2_zfmisc_1(A,B)) => ! [J] : ( ( ~ v1_xboole_0(J) & v1_finset_1(J) & m1_subset_1(J,k1_zfmisc_1(B)) ) => ! [K] : ( ( 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] : ! [M] : ( ( r2_hidden(L,F) & r2_hidden(M,J) ) => k1_binop_1(E,L,M) = k1_extreal1(k12_supinf_2(C,L),k12_supinf_2(D,M)) ) ) => k18_rvsum_1(k4_bhsp_5(k1_numbers,k2_zfmisc_1(A,B),E,I)) = k3_xcmplx_0(k18_rvsum_1(k4_bhsp_5(k1_numbers,A,C,G)),k18_rvsum_1(k4_bhsp_5(k1_numbers,B,D,H))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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)))) ) => r1_struct_0(k1_ranknull(A,B,C,D),k4_struct_0(B)) ) ) ) ) )).
fof(t11_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ( k2_rat_1(A) = k5_numbers <=> A = k5_numbers ) ) )).
fof(t11_ratfunc1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k14_polynom3(A))) => ( ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(C,k4_finseq_1(B)) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_funct_1(B,C) != k3_hurwitz(A,D,1) ) ) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( C = k3_group_4(k14_polynom3(A),B) & C = k9_polynom3(A) ) ) ) ) ) )).
fof(t11_rcomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( ( v5_xxreal_2(A) & v2_rcomp_1(A) ) => v1_rcomp_1(A) ) ) )).
fof(t11_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => k3_seq_4(k2_limfunc1(A)) = A ) )).
fof(t11_real_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) <=> ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) ) ) )).
fof(t11_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( m2_funct_2(C,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t11_realset2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t11_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t11_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [D] : ( ( v1_rearran1(D) & v2_rearran1(D) & v3_rearran1(D,k1_zfmisc_1(A)) & m2_finseq_1(D,k1_zfmisc_1(A)) ) => ( ( v1_partfun1(C,B) & k5_card_1(A) = k5_card_1(B) ) => k3_finseq_1(k3_rfinseq(k20_rfunct_3(B,C,B))) = k3_finseq_1(k15_rfunct_3(A,D)) ) ) ) ) ) )).
fof(t11_relat_1,axiom,( ! [A] : ! [B] : k1_relat_1(k1_tarski(k4_tarski(A,B))) = k2_tarski(A,B) )).
fof(t11_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ( v8_relat_2(A) <=> ! [B] : ! [C] : ! [D] : ( ( r2_hidden(k4_tarski(B,C),A) & r2_hidden(k4_tarski(C,D),A) ) => r2_hidden(k4_tarski(B,D),A) ) ) ) )).
fof(t11_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) ) )).
fof(t11_relset_2,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( 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)) ) ) )).
fof(t11_revrot_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t11_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r1_rewrite1(A,B,C) <=> ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) & ~ r1_xxreal_0(k3_finseq_1(D),k5_numbers) & k1_funct_1(D,1) = B & k1_funct_1(D,k3_finseq_1(D)) = C & ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(E,k4_finseq_1(D)) & r2_hidden(k1_nat_1(E,1),k4_finseq_1(D)) ) => r2_hidden(k4_tarski(k1_funct_1(D,E),k1_funct_1(D,k1_nat_1(E,1))),A) ) ) ) ) ) )).
fof(t11_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ~ ( r2_rewrite2(A,B,C,C) & ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t11_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(A)) => ( k1_flang_1(A,D,B) = k1_flang_1(A,E,C) => ( ( k1_afinsq_1(D) != k1_afinsq_1(E) & k1_afinsq_1(B) != k1_afinsq_1(C) ) | ( D = E & B = C ) ) ) ) ) ) ) ) )).
fof(t11_rfinseq,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( k3_finseq_1(A) = k1_nat_1(D,2) & k1_funct_1(A,k1_nat_1(D,1)) = B & k1_funct_1(A,k1_nat_1(D,2)) = C ) => k3_rfinseq(A) = k7_finseq_1(k17_finseq_1(k1_numbers,D,k3_rfinseq(A)),k10_finseq_1(k6_xcmplx_0(B,C),C)) ) ) ) ) ) )).
fof(t11_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( ~ r1_xxreal_0(k3_finseq_1(A),k5_numbers) => ( k3_rfinseq2(k6_rvsum_1(A)) = k4_xcmplx_0(k4_rfinseq2(A)) & k1_rfinseq2(k6_rvsum_1(A)) = k2_rfinseq2(A) ) ) ) )).
fof(t11_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_valued_0(C) ) => k18_valued_1(C,k1_valued_1(A,B)) = k1_valued_1(k18_valued_1(C,A),k18_valued_1(C,B)) ) ) ) )).
fof(t11_rfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ( r1_tarski(k2_relset_1(A,C),k1_relset_1(A,k6_rfunct_1(A,k1_numbers,B))) => v9_ordinal1(k8_funct_2(k4_ordinal1,k1_numbers,A,C,B)) ) ) ) ) )).
fof(t11_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ( E != k5_numbers => ( r2_classes1(C,D) <=> r2_classes1(k26_valued_1(A,k1_numbers,C,E),k26_valued_1(B,k1_numbers,D,E)) ) ) ) ) ) ) ) )).
fof(t11_rfunct_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( r1_rfunct_4(B,C) <=> r1_rfunct_4(k15_valued_1(k1_numbers,k1_numbers,B,A),C) ) ) ) )).
fof(t11_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_seq_2(A) <=> v2_seq_2(k32_valued_1(k4_ordinal1,k1_numbers,A)) ) ) )).
fof(t11_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v3_rinfsup2(A) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) ) )).
fof(t11_ring_1,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k2_ring_1(A,B))) => ? [D] : ( 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) ) ) ) ) )).
fof(t11_ringcat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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] : ( ( v2_ringcat1(B) & v3_ringcat1(B) & l1_ringcat1(B) ) => ( k2_ringcat1(B) = A => k6_ringcat1(k5_ringcat1(A),B) = B ) ) & ! [B] : ( ( v2_ringcat1(B) & v3_ringcat1(B) & l1_ringcat1(B) ) => ( k1_ringcat1(B) = A => k6_ringcat1(B,k5_ringcat1(A)) = B ) ) ) ) )).
fof(t11_rlaffin1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k1_convex1(A,B,1) = B ) ) )).
fof(t11_rlaffin2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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 ) ) ) ) )).
fof(t11_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => k4_struct_0(B) = k4_struct_0(A) ) ) )).
fof(t11_rlsub_2,axiom,( ! [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) ) => ! [B] : ( 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)) ) ) ) )).
fof(t11_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t11_rlvect_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ~ ( k1_rlvect_1(B,C,A) = k4_struct_0(B) & A != k5_numbers & C != k4_struct_0(B) ) ) ) ) )).
fof(t11_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t11_rlvect_3,axiom,( ! [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) ) => ! [B] : ( 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) ) ) ) )).
fof(t11_rlvect_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & A = k3_rlvect_1(B,k1_rlvect_1(B,C,E),k1_rlvect_1(B,D,F)) ) ) ) ) ) ) )).
fof(t11_rlvect_5,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlvect_2(C,B) => ? [D] : ( 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) ) ) ) ) )).
fof(t11_rlvect_x,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r2_hidden(k4_struct_0(A),k2_rlvect_x(A,B)) ) ) )).
fof(t11_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => k4_struct_0(C) = k4_struct_0(B) ) ) ) )).
fof(t11_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(t11_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( ( 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),D,C)) = k5_algstr_0(B,k3_rlvect_1(B,k1_rmod_4(A,B,D),k1_rmod_4(A,B,C)),k1_rmod_4(A,B,k4_subset_1(u1_struct_0(B),D,C))) ) ) ) ) )).
fof(t11_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_robbins1(A,B,k3_robbins1(A,k5_robbins1(A,C,k3_robbins1(A,C)))) = B ) ) ) )).
fof(t11_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t11_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t11_robbins4,axiom,( ! [A] : ( r2_hidden(A,u1_struct_0(k2_robbins4)) => r1_tarski(A,k1_enumset1(k5_numbers,1,2)) ) )).
fof(t11_rolle,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,k2_rcomp_1(A,B)) => r1_xxreal_0(k5_numbers,k1_fdiff_1(C,D)) ) ) ) => v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,C,k2_rcomp_1(A,B))) ) ) ) ) )).
fof(t11_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t11_rpr_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v3_card_1(B,1) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t11_rsspace,axiom,( ! [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) ) => ! [B] : ( 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,k9_rsspace(A,B),k7_rsspace(A,B),k8_rsspace(A,B)),A) ) ) ) ) )).
fof(t11_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t11_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => r1_struct_0(B,k4_struct_0(A)) ) ) )).
fof(t11_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t11_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_rlvect_3(B,A) & ! [C] : ( 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)) ) ) ) ) ) )).
fof(t11_rusub_4,axiom,( ! [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_bhsp_1(A) & v1_rusub_4(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ( k1_rusub_4(A) = k1_rusub_4(B) <=> k2_rusub_1(A) = k2_rusub_1(B) ) ) ) )).
fof(t11_rusub_5,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t11_rvsum_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(B,k1_numbers)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k4_finseq_2(B,k1_numbers)) => k1_funct_1(k5_rvsum_1(B,C,D),A) = k2_xcmplx_0(k1_funct_1(C,A),k1_funct_1(D,A)) ) ) ) )).
fof(t11_rvsum_2,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,B) & m2_finseq_1(C,k2_numbers) ) => ! [D] : ( ( v3_card_1(D,B) & m2_finseq_1(D,k2_numbers) ) => k1_funct_1(k8_rvsum_2(B,C,D),A) = k6_xcmplx_0(k1_funct_1(C,A),k1_funct_1(D,A)) ) ) ) )).
fof(t11_scm_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_ami_3)) ) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ( k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_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(k7_card_1(2),k1_ami_3,A,D,B),E),k5_numbers) => k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1))) = F ) & ( r1_xxreal_0(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B),E),k5_numbers) => k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1))) = k1_nat_1(C,1) ) & ! [G] : ( ( v1_ami_2(G) & m1_subset_1(G,u1_struct_0(k1_ami_3)) ) => k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1)),G) = k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B),G) ) ) ) ) ) ) ) ) ) )).
fof(t11_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => ! [C] : ( m1_scmfsa_2(C) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t11_scmfsa10,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( 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 ) ) )).
fof(t11_scmfsa6a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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)) = k1_nat_1(k5_card_1(A),k5_card_1(B)) ) ) )).
fof(t11_scmfsa7b,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( v7_ordinal1(B) => ~ r3_scmfsa7b(k11_scmfsa_2(B),A) ) ) )).
fof(t11_scmfsa8a,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( v7_ordinal1(D) => ( ~ r1_xxreal_0(k2_scmfsa8a(A,B,C),D) => ( r2_hidden(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),D)),k2_afinsq_1(C)) & k3_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),D)) != k2_compos_1(k1_scmfsa_2) ) ) ) ) ) ) ) )).
fof(t11_scmfsa8b,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => k5_card_1(k2_scmfsa8b(C,A,B)) = k1_nat_1(k1_nat_1(k5_card_1(A),k5_card_1(B)),4) ) ) ) )).
fof(t11_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(C,k7_card_1(3),k1_scmfsa_2,k5_numbers) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(D,k7_card_1(3),k1_scmfsa_2,k5_numbers) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,C) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,D) ) => k8_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C) = k8_extpro_1(k7_card_1(3),k1_scmfsa_2,B,D) ) ) ) ) ) ) )).
fof(t11_scmfsa9a,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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_sf_mastr(k1_scmfsa_9(A,B)) = k4_subset_1(k2_scmfsa_2,k4_scmfsa_m(A),k2_sf_mastr(B)) ) ) )).
fof(t11_scmfsa_1,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k4_scmfsa_1,k5_scmfsa_1))) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k1_scmfsa_1,k3_scmfsa_1) => k9_scmfsa_1(k6_scmfsa_1(A,B),C) = k9_scmfsa_1(A,C) ) ) ) )).
fof(t11_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( 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 ) ) )).
fof(t11_scmfsa_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( ~ 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(k7_card_1(3),k1_scmfsa_2)) & v1_finset_1(B) & v4_extpro_1(B,k7_card_1(3),k1_scmfsa_2,A) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ( ( r1_tarski(B,C) & r1_tarski(B,D) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( ( r1_tarski(A,E) & r1_tarski(A,F) ) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v1_ami_2(H) & m1_subset_1(H,u1_struct_0(k1_scmfsa_2)) ) => ! [I] : ( ( v1_ami_2(I) & m1_subset_1(I,u1_struct_0(k1_scmfsa_2)) ) => ! [J] : ( m1_scmfsa_2(J) => ( ( k3_extpro_1(k7_card_1(3),k1_scmfsa_2,E,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G)) = k14_scmfsa_2(H,I,J) & r2_hidden(H,k9_xtuple_0(B)) ) => ! [K] : ( m1_subset_1(K,k4_ordinal1) => ! [L] : ( m1_subset_1(L,k4_ordinal1) => ( ( K = k1_int_2(k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G),I)) & L = k1_int_2(k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,D,G),I)) ) => k7_partfun1(k4_numbers,k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G),J),K) = k7_partfun1(k4_numbers,k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,D,G),J),L) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_scmfsa_m,axiom,( k9_xtuple_0(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))) = k7_domain_1(u1_struct_0(k1_scmfsa_2),k4_scmfsa_2(k5_numbers),k4_struct_0(k1_scmfsa_2)) )).
fof(t11_scmisort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( 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),k5_numbers) | ( k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa_9(D,C)),k1_scmfsa_m(B),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(B)),3))) = k5_numbers & ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(E,k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(B)),3)) => r2_hidden(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_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))) ) ) ) ) ) ) ) ) ) )).
fof(t11_scmp_gcd,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( r1_tarski(k4_scmp_gcd,A) => ! [B] : ( ( 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,k5_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) = k5_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(k1_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)) ) ) ) ) )).
fof(t11_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( 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 ) ) )).
fof(t11_scmpds_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( v7_ordinal1(G) => ! [H] : ( v1_int_1(H) => ! [I] : ( v1_int_1(I) => ! [J] : ( ( v1_ami_2(J) & m1_subset_1(J,u1_struct_0(k1_scmpds_2)) ) => ! [K] : ( ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_scmpds_4,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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)) ) ) ) )).
fof(t11_scmpds_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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) ) ) ) ) )).
fof(t11_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ( v1_scmpds_4(A) <=> ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => r1_scmpds_6(A,B,C) ) ) ) ) )).
fof(t11_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t11_scmpds_9,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => k1_amistd_1(2,k1_scmpds_2,C,k13_scmpds_2(A,B,D,E)) = k1_tarski(k1_ordinal1(C)) ) ) ) ) ) )).
fof(t11_scmring1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k4_card_3(k3_relat_1(k3_ami_2,k1_scmring1(A)))) => ! [C] : ( m2_subset_1(C,k1_ami_2,k2_ami_2) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t11_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => ! [D] : ( ( 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(k7_card_1(2),k1_scmring2(A))) & v1_partfun1(D,u1_struct_0(k1_scmring2(A))) ) => ( k1_funct_1(k2_extpro_1(k7_card_1(2),k1_scmring2(A),k3_scmring2(A,B,C),D),k4_struct_0(k1_scmring2(A))) = k4_card_1(k5_memstr_0(k7_card_1(2),k1_scmring2(A),D)) & k2_scmring2(A,k2_extpro_1(k7_card_1(2),k1_scmring2(A),k3_scmring2(A,B,C),D),B) = k2_scmring2(A,D,C) & ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmring2(A))) ) => ( E != B => k2_scmring2(A,k2_extpro_1(k7_card_1(2),k1_scmring2(A),k3_scmring2(A,B,C),D),E) = k2_scmring2(A,D,E) ) ) ) ) ) ) ) )).
fof(t11_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmring2(A))) => ( k2_compos_0(u1_compos_1(k1_scmring2(A)),B) = k5_numbers => B = k2_compos_1(k1_scmring2(A)) ) ) ) )).
fof(t11_scmring4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(B))) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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(k7_card_1(2),k1_scmring2(B))) & v1_partfun1(E,u1_struct_0(k1_scmring2(B))) ) => ! [F] : ( ( 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(k7_card_1(2),k1_scmring2(B))) & v1_partfun1(F,u1_struct_0(k1_scmring2(B))) ) => ! [G] : ( ( v1_relat_1(G) & v4_relat_1(G,k4_ordinal1) & v5_relat_1(G,u1_compos_1(k1_scmring2(B))) & v1_funct_1(G) & v1_partfun1(G,k4_ordinal1) ) => ! [H] : ( ( v1_relat_1(H) & v4_relat_1(H,k4_ordinal1) & v5_relat_1(H,u1_compos_1(k1_scmring2(B))) & v1_funct_1(H) & v1_partfun1(H,k4_ordinal1) ) => ! [I] : ( ( v1_relat_1(I) & v4_relat_1(I,k4_ordinal1) & 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] : ( ( 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(k7_card_1(2),k1_scmring2(B))) & ~ v1_xboole_0(J) & v1_finset_1(J) & v4_extpro_1(J,k7_card_1(2),k1_scmring2(B),I) ) => ( ( r1_tarski(J,E) & r1_tarski(J,F) & r1_tarski(I,G) & r1_tarski(I,H) & k3_extpro_1(k7_card_1(2),k1_scmring2(B),G,k5_extpro_1(k7_card_1(2),k1_scmring2(B),G,E,A)) = k9_scmring2(B,D,C) ) => ( D = k1_ordinal1(k5_memstr_0(k7_card_1(2),k1_scmring2(B),k5_extpro_1(k7_card_1(2),k1_scmring2(B),G,E,A))) | ( k2_scmring2(B,k5_extpro_1(k7_card_1(2),k1_scmring2(B),G,E,A),C) = k4_struct_0(B) <=> k2_scmring2(B,k5_extpro_1(k7_card_1(2),k1_scmring2(B),H,F,A),C) = k4_struct_0(B) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k2_scm_inst) => ! [C] : ( v7_ordinal1(C) => r2_hidden(k3_xtuple_0(7,k9_finseq_1(C),k12_finseq_1(k2_scm_inst,B)),k1_scmringi(A)) ) ) ) )).
fof(t11_scmyciel,axiom,( ! [A] : ! [B] : ~ ( r2_hidden(B,k1_scmyciel(A)) & ! [C] : ! [D] : ~ ( C != D & r2_hidden(C,k3_tarski(A)) & r2_hidden(D,k3_tarski(A)) & B = k2_tarski(C,D) ) ) )).
fof(t11_scpinvar,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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),k5_numbers) = k7_scmpds_2(A,B,2) & k1_funct_1(k4_scpinvar(A,B,C),1) = k3_scmpds_2(k1_nat_1(k5_card_1(C),2)) & k1_funct_1(k4_scpinvar(A,B,C),k1_nat_1(k5_card_1(C),2)) = k3_scmpds_2(k4_xcmplx_0(k1_nat_1(k5_card_1(C),2))) ) ) ) ) )).
fof(t11_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( m2_finseq_1(F,k4_numbers) => ! [G] : ( m2_finseq_1(G,k4_numbers) => ( ( k1_funct_1(B,k2_scmp_gcd) = k5_numbers & k1_funct_1(B,k1_scmp_gcd(2)) = C & r1_xxreal_0(k1_nat_1(D,1),C) & r1_xxreal_0(k1_funct_1(B,k1_scmp_gcd(4)),k2_xcmplx_0(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))),k5_numbers) | ( k1_funct_1(k6_scmpds_4(k1_scpqsort,B,A),k2_scmp_gcd) = k5_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] : ( v7_ordinal1(H) & 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] : ( v7_ordinal1(I) => ( 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] : ( v7_ordinal1(I) => ( 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] : ( v7_ordinal1(I) => ( r1_xxreal_0(k1_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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r2_analoaf(A,B,C,B,E) & r2_analoaf(A,C,D,C,E) & r2_analoaf(A,D,B,D,E) ) => r2_analoaf(A,B,C,B,D) ) ) ) ) ) ) )).
fof(t11_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B),k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,k32_valued_1(k4_ordinal1,k1_numbers,B))) ) ) )).
fof(t11_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(A) & v2_comseq_2(B) ) => v2_comseq_2(k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) ) ) )).
fof(t11_seq_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v5_xxreal_2(A) => ( v1_xboole_0(A) | r1_xxreal_0(k3_seq_4(A),k2_seq_4(A)) ) ) ) )).
fof(t11_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => r2_relset_1(k4_ordinal1,k4_partfun1(A,k1_numbers),k2_seqfunc(A,B,1),B) ) ) )).
fof(t11_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v7_valued_0(A) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_nat_1(k1_numbers,A,k5_numbers),k9_nat_1(k1_numbers,A,B)) ) ) ) )).
fof(t11_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,B,C) = k3_funct_2(k4_ordinal1,k1_numbers,A,k5_numbers) ) => r2_funct_2(k4_ordinal1,k1_numbers,k3_series_1(k1_valued_0(k1_numbers,A,1)),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k1_valued_0(k1_numbers,k3_series_1(A),1),B)) ) ) ) )).
fof(t11_series_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => r1_xxreal_0(k3_xcmplx_0(3,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(B,C)),k3_xcmplx_0(A,C))),k1_square_1(k2_xcmplx_0(k2_xcmplx_0(A,B),C))) ) ) ) )).
fof(t11_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => r1_xxreal_0(k3_square_1(k3_xcmplx_0(A,B)),k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),2))) ) ) )).
fof(t11_setfam_1,axiom,( ! [A] : ! [B] : k1_setfam_1(k2_tarski(A,B)) = k3_xboole_0(A,B) )).
fof(t11_setlim_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ! [D] : ( v7_ordinal1(D) => k1_funct_1(C,D) = B ) => k3_prob_1(A,C) = B ) ) ) )).
fof(t11_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) ) ) )).
fof(t11_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t11_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_scmfsa_2(C) => ! [D] : ( m1_scmfsa_2(D) => ( k16_scmfsa_2(A,C) = k16_scmfsa_2(B,D) => ( A = B & C = D ) ) ) ) ) ) )).
fof(t11_sfmastr1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( v1_scmfsa6c(D) & m1_subset_1(D,u1_compos_1(k1_scmfsa_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmfsa_2)) ) => ( ( v7_amistd_1(C,k7_card_1(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(k7_card_1(3),k1_scmfsa_2,D,k1_scmfsa6b(C,B,A)),E) ) ) ) ) ) ) )).
fof(t11_sfmastr2,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ( ~ ( k1_funct_1(A,k4_scmfsa_2(k5_numbers)) != 1 & v1_scmfsa_m(C) ) => k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k3_sfmastr2(B,A,D,C),k5_numbers),C) = k1_funct_1(A,C) ) ) ) ) ) )).
fof(t11_sfmastr3,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & ~ v1_scmfsa_m(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k1_sfmastr3(F,B,C,D,E,A),k5_numbers),B) = k1_funct_1(A,C) ) ) ) ) ) ) )).
fof(t11_sgraph1,axiom,( k2_sgraph1(k1_xboole_0) = k1_xboole_0 )).
fof(t11_sheffer1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t11_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,C,B)) = B ) ) ) )).
fof(t11_simplex0,axiom,( ! [A] : ! [B] : ( v6_ordinal1(B) => v6_ordinal1(k2_xboole_0(B,k1_tarski(k2_xboole_0(k3_tarski(B),A)))) ) )).
fof(t11_simplex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_simplex0(B,u1_struct_0(A)) => m1_simplex1(B,A,B) ) ) )).
fof(t11_simplex2,axiom,( ! [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) ) => ! [B] : ( ( ~ v3_pencil_1(B) & v1_matroid0(B) & v3_matroid0(B) & m1_simplex0(B,u1_struct_0(A)) ) => ! [C] : ( ( v3_pre_topc(C,k4_simplex1(A,B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_simplex1(A,B)))) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_hidden(E,C) & r2_hidden(F,C) & ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( v1_xreal_0(I) => ~ ( 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(k5_numbers,I) & r1_xxreal_0(I,k7_xcmplx_0(k6_xcmplx_0(k5_card_1(k5_setfam_1(u1_struct_0(A),D)),1),k5_card_1(k5_setfam_1(u1_struct_0(A),D)))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(D,C) => k9_nat_1(k2_numbers,k10_sin_cos(k1_nat_1(C,1),B,A),D) = k2_xcmplx_0(k9_nat_1(k2_numbers,k10_sin_cos(C,B,A),D),k9_nat_1(k2_numbers,k9_sin_cos(k1_nat_1(C,1),B,A),D)) ) ) ) ) ) )).
fof(t11_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => k1_funct_1(k18_sin_cos,A) = k1_funct_1(k18_sin_cos,k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B),A)) ) ) )).
fof(t11_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,k2_xcmplx_0(A,B)) = k2_xcmplx_0(k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,B)),k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,B))) ) ) )).
fof(t11_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( k19_sin_cos(A) != k5_numbers & k19_sin_cos(B) != k5_numbers & k19_sin_cos(C) != k5_numbers & k17_sin_cos(k2_xcmplx_0(k2_xcmplx_0(A,B),C)) != k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k19_sin_cos(A),k19_sin_cos(B)),k19_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)))) ) ) ) ) )).
fof(t11_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k19_sin_cos(A) != k5_numbers => k1_square_1(k4_sin_cos4(A)) = k2_xcmplx_0(1,k1_square_1(k1_sin_cos4(A))) ) ) )).
fof(t11_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ~ ( ~ r1_xxreal_0(A,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)) & ~ r1_xxreal_0(k2_xcmplx_0(k28_sin_cos,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)),A) & r1_xxreal_0(k17_sin_cos(A),k5_numbers) ) ) ) )).
fof(t11_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(1,k1_square_1(A)) => ( ~ r1_xxreal_0(k2_xcmplx_0(A,1),k5_numbers) & ~ r1_xxreal_0(k6_xcmplx_0(1,A),k5_numbers) ) ) ) )).
fof(t11_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k3_xcmplx_0(k2_sin_cos2(A),k2_sin_cos2(B)) = k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k4_sin_cos2(k2_xcmplx_0(A,B)),k4_sin_cos2(k6_xcmplx_0(A,B)))) & k3_xcmplx_0(k2_sin_cos2(A),k4_sin_cos2(B)) = k3_xcmplx_0(k7_xcmplx_0(1,2),k2_xcmplx_0(k2_sin_cos2(k2_xcmplx_0(A,B)),k2_sin_cos2(k6_xcmplx_0(A,B)))) & k3_xcmplx_0(k4_sin_cos2(A),k2_sin_cos2(B)) = k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k2_sin_cos2(k2_xcmplx_0(A,B)),k2_sin_cos2(k6_xcmplx_0(A,B)))) & k3_xcmplx_0(k4_sin_cos2(A),k4_sin_cos2(B)) = k3_xcmplx_0(k7_xcmplx_0(1,2),k2_xcmplx_0(k4_sin_cos2(k2_xcmplx_0(A,B)),k4_sin_cos2(k6_xcmplx_0(A,B)))) ) ) ) )).
fof(t11_sin_cos9,axiom,( k2_relset_1(k1_numbers,k1_sin_cos9) = k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2)) )).
fof(t11_sincos10,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers))) )).
fof(t11_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => r1_sppol_1(A,B,k1_rltopsp1(k15_euclid(A),B,C)) ) ) ) )).
fof(t11_sppol_2,axiom,( k3_topreal1(2,k6_finseq_1(u1_struct_0(k15_euclid(2)))) = k1_xboole_0 )).
fof(t11_sprect_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t11_sprect_2,axiom,( ! [A] : ( ( v2_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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)) ) ) ) )).
fof(t11_sprect_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t11_sprect_5,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t11_square_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k6_xcmplx_0(k1_square_1(A),k1_square_1(B)) != k5_numbers => k7_xcmplx_0(1,k6_xcmplx_0(A,B)) = k7_xcmplx_0(k2_xcmplx_0(A,B),k6_xcmplx_0(k1_square_1(A),k1_square_1(B))) ) ) ) )).
fof(t11_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => k3_nat_1(A) = k5_numbers ) )).
fof(t11_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t11_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k4_subset_1(A,B,k2_subset_1(A)) = k2_subset_1(A) ) )).
fof(t11_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m2_subset_1(C,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B)) => k3_substlat(A,B,C) = C ) )).
fof(t11_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => ( v4_substut1(B,A) => v2_qc_lang1(k18_substut1(A,B),A) ) ) ) )).
fof(t11_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ( ! [D] : ( m1_subset_1(D,k1_substut1(A)) => ? [E] : ( m2_subset_1(E,k16_substut1(A),k38_substut1(A)) & k2_sublemma(A,E) = B & k19_substut1(A,E) = D ) ) => ! [D] : ( m1_subset_1(D,k1_substut1(A)) => ? [E] : ( 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 ) ) ) ) ) ) )).
fof(t11_supinf_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( m1_subset_1(B,k6_numbers) => ( m1_xxreal_2(B,A) <=> m2_xxreal_2(k2_supinf_2(B),k6_supinf_2(A)) ) ) ) )).
fof(t11_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( r1_orders_2(B,k5_algstr_0(B,C,D),F) & r1_orders_2(B,k5_algstr_0(B,C,E),F) ) => r1_orders_2(B,k5_algstr_0(B,D,E),F) ) ) ) ) ) ) ) )).
fof(t11_sysrel,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r1_tarski(A,B) => r1_tarski(k2_relat_1(A),k2_relat_1(B)) ) ) ) )).
fof(t11_t_0topsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v6_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t11_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => r1_setfam_1(k10_eqrel_1(A),k1_tarski(A)) ) )).
fof(t11_taxonom2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v4_taxonom2(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ( ! [D] : ( 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) ) ) ) ) ) )).
fof(t11_taylor_1,axiom,( ~ r1_xxreal_0(k4_power,2) )).
fof(t11_taylor_2,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k5_numbers,C) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( r2_hidden(E,k2_rcomp_1(k4_xcmplx_0(A),A)) => ( r1_xxreal_0(F,k5_numbers) | r1_xxreal_0(1,F) | r1_xxreal_0(k9_complex1(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k22_sin_cos,k2_rcomp_1(k4_xcmplx_0(A),A)),D),k3_xcmplx_0(F,E)),k1_newton(E,D)),k2_newton(D))),k7_xcmplx_0(k3_xcmplx_0(B,k1_newton(C,D)),k2_newton(D))) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ( v6_metric_1(A) => ( r1_xxreal_0(C,k5_numbers) | r2_hidden(B,k8_metric_1(A,B,C)) ) ) ) ) ) )).
fof(t11_tdgroup,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_tdgroup(A,B,C,E,F) & r1_tdgroup(A,B,D,E,G) ) => r1_tdgroup(A,C,D,F,G) ) ) ) ) ) ) ) ) )).
fof(t11_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t11_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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))) ) ) ) )).
fof(t11_tdlat_3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(t11_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t11_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( 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) ) ) )).
fof(t11_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t11_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_tex_3(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => ( v1_tops_1(D,B) <=> v1_tops_1(C,A) ) ) ) ) ) ) )).
fof(t11_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) )).
fof(t11_tietze,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( r1_seqfunc(A,k1_numbers,C,B) => ! [D] : ( ( v2_xxreal_0(D) & v1_xreal_0(D) ) => ! [E] : ( ( v2_xxreal_0(E) & v1_xreal_0(E) ) => ! [F] : ( ( 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] : ( v7_ordinal1(G) => r1_tietze(k45_valued_1(k1_seqfunc(A,k1_numbers,C,G),F),k3_xcmplx_0(D,k2_power(E,G)),B) ) => ( r1_xxreal_0(1,E) | ( r2_seqfunc(A,C,B) & k11_seqfunc(A,C,B) = F ) ) ) ) ) ) ) ) ) ) )).
fof(t11_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_tsep_1(A,B,C))) => ~ ( ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => E != D ) & ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => E != D ) ) ) ) ) ) )).
fof(t11_toler_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(B,A) => ( v1_relat_2(k1_toler_1(C,B)) & v3_relat_2(k1_toler_1(C,B)) & v1_partfun1(k1_toler_1(C,B),B) & m1_subset_1(k1_toler_1(C,B),k1_zfmisc_1(k2_zfmisc_1(B,B))) ) ) ) )).
fof(t11_topalg_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k17_borsuk_1)) => r1_xxreal_0(k12_euclid(k9_euclid(A,B,C)),k12_euclid(B)) ) ) ) )).
fof(t11_topalg_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => v1_borsuk_2(k4_topmetr(A,B)) ) ) ) )).
fof(t11_topalg_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( 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) ) ) )).
fof(t11_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t11_topalg_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(t11_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_topalg_6(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_borsuk_2(C,A,B,B) => ! [D] : ( m1_borsuk_2(D,A,B,B) => r3_borsuk_2(A,B,B,C,D) ) ) ) ) ) )).
fof(t11_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( v1_int_1(C) => ( ( ( v2_topdim_1(B,A) & r1_xxreal_0(k3_topdim_1(A,B),C) ) => ( r1_xxreal_0(k4_xcmplx_0(1),C) & ! [D] : ( 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(k4_xcmplx_0(1),C) & ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t11_topdim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v2_pre_topc(B) & v3_pcomps_1(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t11_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_tops_1(A,B)) <=> ? [D] : ( 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] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t11_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_tops_2(B,A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) => ? [C] : ( 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)) ) ) ) )).
fof(t11_topgen_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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))) ) ) ) )).
fof(t11_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ( v7_topgen_1(A) <=> v1_orders_4(A) ) ) )).
fof(t11_topgen_5,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v4_pre_topc(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( v4_pre_topc(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ( r1_xboole_0(C,D) => ! [E] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) ) )).
fof(t11_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => v2_funct_1(k3_group_1(A)) ) )).
fof(t11_topmetr,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k7_metric_1)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_metric_1)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( C = A & D = B ) => k3_metric_1(k7_metric_1,A,B) = k9_complex1(k6_xcmplx_0(C,D)) ) ) ) ) ) )).
fof(t11_topreal1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t11_topreal4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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(k7_xcmplx_0(k2_xcmplx_0(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)) ) ) ) ) ) ) )).
fof(t11_topreal5,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t11_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ( ( r2_hidden(B,k4_finseq_1(k3_euclid(C))) & A = k1_funct_1(C,B) ) => k1_funct_1(k3_euclid(C),B) = k9_complex1(A) ) ) ) ) )).
fof(t11_topreal7,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( 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)) ) ) )).
fof(t11_topreal8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t11_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => ( C = D => k8_metric_1(k14_euclid(A),D,B) = k1_topreal9(A,C,B) ) ) ) ) ) )).
fof(t11_topreala,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t11_toprealb,axiom,( ! [A] : ( ( v1_toprealb(A) & m1_pre_topc(A,k15_euclid(2)) ) => ! [B] : ( ( v1_toprealb(B) & m1_pre_topc(B,k15_euclid(2)) ) => r2_borsuk_3(A,B) ) ) )).
fof(t11_toprealc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k12_euclid(k8_rvsum_1(k2_finseq_2(A,B),k2_finseq_2(A,C))) = k3_xcmplx_0(k3_square_1(A),k9_complex1(k6_xcmplx_0(B,C))) ) ) ) )).
fof(t11_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => k3_toprns_1(A,B) = k2_toprns_1(k4_xcmplx_0(1),A,B) ) ) )).
fof(t11_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t11_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t11_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v2_tops_1(C,A) & r1_tarski(B,C) ) => v2_tops_1(B,A) ) ) ) ) )).
fof(t11_tops_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k3_topmetr)) => ! [D] : ( ( v1_xreal_0(D) & v2_xxreal_0(D) ) => ? [E] : ( 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)))) ) ) ) ) ) ) )).
fof(t11_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t11_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t11_treal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_topmetr(k5_numbers,1))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_topmetr(k5_numbers,1))) => ! [E] : ( 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(k5_numbers,1)),k4_treal_1(A,B,C,D),E) = k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(D,C),k6_xcmplx_0(B,A)),E),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(B,C),k3_xcmplx_0(A,D)),k6_xcmplx_0(B,A))) ) ) ) ) ) ) )).
fof(t11_trees_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( r2_hidden(A,k1_trees_1(B)) <=> r2_xboole_0(A,B) ) ) ) )).
fof(t11_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m4_trees_1(B,A) => ! [C] : ( m1_trees_2(C,A) => ? [D] : ( m1_trees_1(D,A) & r1_tarski(k9_subset_1(A,B,C),k1_tarski(D)) ) ) ) ) )).
fof(t11_trees_3,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(t11_trees_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v6_trees_3(C) ) => ( r2_hidden(B,k9_xtuple_0(k4_trees_4(A,C))) <=> ~ ( B != k1_xboole_0 & ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v3_trees_2(E) ) => ! [F] : ( m1_trees_1(F,k9_xtuple_0(E)) => ~ ( ~ r1_xxreal_0(k3_finseq_1(C),D) & E = k1_funct_1(C,k1_nat_1(D,1)) & B = k8_finseq_1(k4_ordinal1,k14_trees_3(D),F) ) ) ) ) ) ) ) )).
fof(t11_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => r2_hidden(A,k3_trees_9(A)) ) )).
fof(t11_trees_a,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) ) => ( r2_hidden(A,k9_xtuple_0(B)) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ~ ( 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] : ( m2_finseq_1(E,k4_ordinal1) => ~ ( r2_hidden(E,k9_xtuple_0(C)) & D = k8_finseq_1(k4_ordinal1,A,E) & k1_funct_1(k7_trees_2(B,A,C),D) = k1_funct_1(C,E) ) ) ) ) ) ) ) ) )).
fof(t11_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t11_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t11_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v1_tsp_1(B,A) ) ) )).
fof(t11_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t11_turing_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( l1_turing_1(C) => ! [D] : ( 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,k9_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)) = k9_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) ) => k9_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) = k9_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) ) ) ) ) ) )).
fof(t11_twoscomp,axiom,( k1_funct_1(k14_twoscomp,k10_finseq_1(k5_numbers,k5_numbers)) = k5_numbers & k1_funct_1(k14_twoscomp,k10_finseq_1(k5_numbers,1)) = 1 & k1_funct_1(k14_twoscomp,k10_finseq_1(1,k5_numbers)) = 1 & k1_funct_1(k14_twoscomp,k10_finseq_1(1,1)) = k5_numbers & k1_funct_1(k15_twoscomp,k10_finseq_1(k5_numbers,k5_numbers)) = 1 & k1_funct_1(k15_twoscomp,k10_finseq_1(k5_numbers,1)) = k5_numbers & k1_funct_1(k15_twoscomp,k10_finseq_1(1,k5_numbers)) = k5_numbers & k1_funct_1(k15_twoscomp,k10_finseq_1(1,1)) = 1 )).
fof(t11_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_unialg_2(B,A) => ! [C] : ( m1_unialg_2(C,A) => ( r1_tarski(u1_struct_0(B),u1_struct_0(C)) => m1_unialg_2(B,C) ) ) ) ) )).
fof(t11_unialg_3,axiom,( ! [A] : ( ( ~ 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] : ( m1_unialg_2(B,A) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k6_unialg_2(A)) => r2_hidden(C,u1_struct_0(B)) ) ) ) )).
fof(t11_uniform1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k9_complex1(k6_xcmplx_0(A,B)) = k9_complex1(k6_xcmplx_0(B,A)) ) ) )).
fof(t11_uniroots,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k8_group_1(k1_complfld,k1_hahnban1(k19_sin_cos(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B),A)),k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B),A))),k1_hahnban1(k19_sin_cos(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C),A)),k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C),A)))) = k1_hahnban1(k19_sin_cos(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k4_nat_d(k2_xcmplx_0(B,C),A)),A)),k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k4_nat_d(k2_xcmplx_0(B,C),A)),A))) ) ) ) )).
fof(t11_uproots,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( 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] : ( m2_finseq_1(D,k1_numbers) => ~ ( D = k3_relat_1(k19_finseq_1(B),C) & k2_uproots(A,C) = k18_rvsum_1(D) ) ) ) ) ) )).
fof(t11_urysohn1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_subset_1(B,k1_numbers,k1_urysohn1(A)) => ( ~ r1_xxreal_0(B,k7_xcmplx_0(k6_xcmplx_0(k6_urysohn1(A,B),1),k1_newton(2,A))) & ~ r1_xxreal_0(k7_xcmplx_0(k1_nat_1(k6_urysohn1(A,B),1),k1_newton(2,A)),B) ) ) ) )).
fof(t11_urysohn2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ( v4_measure5(A) => ( r1_xxreal_0(B,k5_numbers) | v4_measure5(k1_integra2(A,B)) ) ) ) ) )).
fof(t11_urysohn3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v10_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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] : ( m2_urysohn3(D,A,B,C) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ( ( F = k1_funct_1(k4_urysohn3(A,B,C,D),E) & r2_hidden(E,k3_urysohn1) ) => v3_pre_topc(F,A) ) ) ) ) ) ) ) ) ) )).
fof(t11_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t11_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ( k9_xtuple_0(k39_valued_1(A)) = k9_xtuple_0(A) & ! [B] : k1_funct_1(k39_valued_1(A),B) = k1_square_1(k1_funct_1(A,B)) ) ) )).
fof(t11_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( 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) ) ) )).
fof(t11_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r1_struct_0(D,E) => m1_subset_1(E,u1_struct_0(C)) ) ) ) ) ) ) )).
fof(t11_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => m2_vectsp11(C,A,B,k3_struct_0(B),k1_group_1(A)) ) ) ) ) )).
fof(t11_vectsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( 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) ) ) ) ) ) ) )).
fof(t11_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t11_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => k4_struct_0(C) = k4_struct_0(B) ) ) ) )).
fof(t11_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t11_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t11_vectsp_7,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( ( v7_vectsp_1(D,A) & m1_vectsp_4(D,A,B) ) => ( C = u1_struct_0(D) => k1_vectsp_7(A,B,C) = D ) ) ) ) ) )).
fof(t11_vectsp_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(t11_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t11_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t11_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t11_waybel10,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k5_yellow_1(A,B))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k5_yellow_1(A,B))) => ( ( E = C & F = D ) => ( r1_orders_2(k5_yellow_1(A,B),E,F) <=> r1_yellow_2(A,B,C,D) ) ) ) ) ) ) ) )).
fof(t11_waybel11,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => v4_pre_topc(k5_waybel_0(A,B),A) ) ) )).
fof(t11_waybel12,axiom,( ! [A] : ( ( v5_orders_2(A) & v1_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t11_waybel13,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) => ( v1_waybel_3(B,k1_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))) ) ) ) ) )).
fof(t11_waybel14,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t11_waybel15,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t11_waybel16,axiom,( ! [A] : ( ~ v1_xboole_0(k9_setfam_1(A)) & v2_waybel_0(k9_setfam_1(A),k2_yellow_1(A)) & v13_waybel_0(k9_setfam_1(A),k2_yellow_1(A)) & m1_subset_1(k9_setfam_1(A),k1_zfmisc_1(u1_struct_0(k2_yellow_1(A)))) ) )).
fof(t11_waybel17,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ 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) ) ) ) ) )).
fof(t11_waybel18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( v2_waybel18(A) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(t11_waybel19,axiom,( ! [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) & v1_waybel19(A) & l1_waybel_9(A) ) => ! [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) & v1_waybel19(B) & l1_waybel_9(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t11_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v5_orders_2(D) & l1_orders_2(D) ) => ! [E] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t11_waybel21,axiom,( ! [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] : ( ( ~ 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) ) ) )).
fof(t11_waybel22,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v2_waybel_0(B,k2_yellow_1(A)) & v13_waybel_0(B,k2_yellow_1(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(A)))) ) => B = k1_yellow_0(k1_yellow_1(k8_waybel_0(k2_yellow_1(A))),a_2_0_waybel22(A,B)) ) )).
fof(t11_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_yellow_0(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t11_waybel24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t11_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v2_waybel18(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( m1_pre_topc(A,B) => r1_waybel18(A,B) ) ) ) )).
fof(t11_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t11_waybel27,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ( m1_yellow_0(B,C) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t11_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t11_waybel29,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => v24_waybel_0(k2_yellow16(A,B,C)) ) => v24_waybel_0(k4_yellow_1(A,B)) ) ) ) )).
fof(t11_waybel30,axiom,( ! [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] : ( ( 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) ) ) ) )).
fof(t11_waybel31,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => r2_hidden(B,k2_waybel_8(A,B)) ) ) ) )).
fof(t11_waybel32,axiom,( ! [A] : ( ( 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] : ( m1_yellow_9(B,A) => ( u1_pre_topc(B) = k5_waybel11(A) => v4_waybel11(B) ) ) ) )).
fof(t11_waybel33,axiom,( ! [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] : ( ( ~ 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)) ) ) )).
fof(t11_waybel34,axiom,( ! [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] : ( ( 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] : ( ( 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) ) ) ) )).
fof(t11_waybel35,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( ( v4_waybel_4(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ( m1_waybel35(C,A,B) => ( v2_waybel35(C,A,B) => r2_hidden(k3_yellow_0(A),C) ) ) ) ) )).
fof(t11_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ( v10_waybel_0(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t11_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(t11_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t11_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t11_waybel_4,axiom,( ! [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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_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)))) ) ) ) )).
fof(t11_waybel_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_funcop_1(C) ) => ( ( k9_xtuple_0(B) = k9_xtuple_0(C) & ! [D] : ( 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)) ) ) ) ) )).
fof(t11_waybel_7,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v13_waybel_0(B,k2_yellow_1(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(A)))) ) => ( v2_waybel_0(B,k2_yellow_1(A)) <=> ! [C] : ( ( 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) ) ) ) ) )).
fof(t11_waybel_8,axiom,( ! [A] : ( l1_orders_2(A) => ! [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_struct_0(A) & v2_struct_0(B) ) ) ) )).
fof(t11_waybel_9,axiom,( ! [A] : ( 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))) ) )).
fof(t11_weddwitt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => m1_eqrel_1(a_2_1_weddwitt(A,B),u1_struct_0(A)) ) ) )).
fof(t11_weierstr,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ( v2_compts_1(A,k3_topmetr) => v5_xxreal_2(k1_weierstr(A)) ) ) )).
fof(t11_wellord1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k2_wellord1(B,A) = k6_relat_1(A,k5_relat_1(B,A)) ) )).
fof(t11_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ( r1_int_2(C,D) => r1_int_2(k1_newton(C,A),k1_newton(D,B)) ) ) ) ) ) )).
fof(t11_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(k2_xboole_0(A,B),C) => r1_tarski(A,C) ) )).
fof(t11_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k4_xboolean(A,k5_xboolean(k3_xboolean(A),B)) = k4_xboolean(A,B) ) ) )).
fof(t11_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(2,A) = k2_xcmplx_0(A,A) ) )).
fof(t11_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(A,k6_xcmplx_0(B,C)) => r1_xxreal_0(C,k6_xcmplx_0(B,A)) ) ) ) ) )).
fof(t11_xtuple_0,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_tarski(k12_xtuple_0(A),k12_xtuple_0(B)) ) )).
fof(t11_xxreal_0,axiom,( ~ r2_hidden(k2_xxreal_0,k1_numbers) )).
fof(t11_xxreal_1,axiom,( ! [A] : ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ~ ( r2_hidden(A,k3_xxreal_1(B,C)) & ~ ( r2_hidden(A,k2_xxreal_1(B,C)) & A != B ) & A != C ) ) ) )).
fof(t11_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => k1_xxreal_2(k1_tarski(A)) = A ) )).
fof(t11_xxreal_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( k1_xxreal_3(A,B) = k1_xxreal_3(A,C) => B = C ) ) ) ) )).
fof(t11_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B))) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t11_yellow11,axiom,( ! [A] : ( ( 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] : ( ( 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) ) ) ) )).
fof(t11_yellow12,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t11_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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) ) ) ) )).
fof(t11_yellow14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ( ( r5_waybel_1(A,B) & v2_lattice3(A) ) => v2_lattice3(B) ) ) ) )).
fof(t11_yellow15,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t11_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( 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)))) ) ) ) ) ) )).
fof(t11_yellow17,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_waybel18(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k3_waybel18(A,B))) => r2_hidden(k1_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))) ) ) ) ) ) )).
fof(t11_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_waybel_9(A,B,C) <=> r1_waybel_7(A,k2_yellow19(A,B),C) ) ) ) ) )).
fof(t11_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & l2_altcat_1(B) ) => ( r1_yellow20(A,B) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_subset_1(F,u1_struct_0(B)) & ? [G] : ( m1_subset_1(G,u1_struct_0(B)) & ? [H] : ( 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] : ( m1_subset_1(I,k1_altcat_1(A,C,D)) & ? [J] : ( m1_subset_1(J,k1_altcat_1(B,F,G)) & J = I & ? [K] : ( m1_subset_1(K,k1_altcat_1(A,D,E)) & ? [L] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t11_yellow21,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t11_yellow_0,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_lattice3(A,B,C) & r1_orders_2(A,C,D) ) => r2_lattice3(A,B,D) ) ) ) ) )).
fof(t11_yellow_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ! [B] : ! [C] : ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r2_hidden(k2_xboole_0(B,C),A) ) => v1_lattice3(k1_yellow_1(A)) ) ) )).
fof(t11_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => v5_orders_3(k3_struct_0(A),A,A) ) )).
fof(t11_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t11_yellow_4,axiom,( ! [A] : ( ( v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t11_yellow_5,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r6_waybel_1(A,B,C) <=> C = k7_waybel_1(A,B) ) ) ) ) )).
fof(t11_yellow_6,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_waybel_0(B,A) => ! [C] : ( m1_yellow_6(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ( ( D = F & E = G & r1_orders_2(C,F,G) ) => r1_orders_2(B,D,E) ) ) ) ) ) ) ) ) )).
fof(t11_yellow_7,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( r1_yellow_0(k7_lattice3(A),B) <=> r2_yellow_0(A,B) ) ) )).
fof(t11_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [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)))) ) => ! [C] : ( 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)) ) ) ) )).
fof(t11_yellow_9,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) ) ) )).
fof(t11_zf_colla,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( r2_zf_model(A,k6_zf_model) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ( ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,B) <=> r2_hidden(D,C) ) ) => B = C ) ) ) ) ) )).
fof(t11_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t11_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v7_zf_lang(A) => k3_finseq_1(A) = 3 ) ) )).
fof(t11_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,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) ) ) ) ) )).
fof(t11_zf_model,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ( v6_zf_lang(A) => ! [C] : ( ( 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] : ( ( 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] : ( m2_subset_1(E,k4_ordinal1,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)) ) ) ) ) ) )).
fof(t11_zf_refle,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_ordinal2(B) ) => v3_ordinal1(k3_card_3(k6_relat_1(A,B))) ) )).
fof(t11_zfmisc_1,axiom,( ! [A] : ! [B] : ( A != B => r1_xboole_0(k1_tarski(A),k1_tarski(B)) ) )).
fof(t11_zfmodel1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t11_zfmodel2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( 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(k5_numbers),k8_zf_lang(k2_zf_lang(4),k12_zf_lang(B,k4_zf_lang(k2_zf_lang(4),k2_zf_lang(k5_numbers))))))) ) => r2_funct_2(A,A,k1_zfmodel1(B,A,C),k2_zfmodel1(B,A)) ) ) ) ) )).
fof(t11_zfrefle1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t11_zmodul01,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( ~ 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] : ( 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 ) ) ) ) ) ) )).
fof(t11_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => m2_zmodul02(k19_zmodul02(A),A,B) ) ) )).
fof(t11_zmodul03,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul02(C,A) => ( r1_tarski(k18_zmodul02(A,C),u1_struct_0(B)) => ! [D] : ( m1_zmodul02(D,B) => ( D = k2_partfun1(u1_struct_0(A),k4_numbers,C,u1_struct_0(B)) => ( k18_zmodul02(A,C) = k18_zmodul02(B,D) & k21_zmodul02(A,C) = k21_zmodul02(B,D) ) ) ) ) ) ) ) )).
fof(t120_abcmiz_1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(t120_clvect_1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) )).
fof(t120_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,C) => ! [F] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t120_finseq_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m2_finseq_1(C,k8_eqrel_1(A,B)) => ? [D] : ( m2_finseq_1(D,A) & r1_finseq_3(A,B,C,D) ) ) ) ) )).
fof(t120_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t120_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(t120_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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 ) ) ) )).
fof(t120_funct_7,axiom,( ! [A] : ! [B] : ! [C] : k9_xtuple_0(k12_funct_7(A,B,C)) = k4_ordinal1 )).
fof(t120_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t120_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v2_glib_001(B,A) <=> ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( ~ r1_xxreal_0(k3_finseq_1(B),C) => r2_glib_000(A,k1_funct_1(B,C),k1_funct_1(B,k1_nat_1(C,2)),k1_funct_1(B,k1_nat_1(C,1))) ) ) ) ) ) )).
fof(t120_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t120_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ( ( v1_group_3(B,A) & m1_group_2(B,A) ) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => k11_group_2(A,B,C) = k12_group_2(A,B,C) ) ) ) ) )).
fof(t120_group_9,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( 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))) ) ) ) )).
fof(t120_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t120_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(C),A,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(C))) ) => ( ( 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))) ) ) ) ) ) ) )).
fof(t120_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => k15_member_1(A,k5_member_1(B)) = k5_member_1(k15_member_1(A,B)) ) ) )).
fof(t120_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ! [C] : ( ( 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) ) ) ) )).
fof(t120_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t120_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => r1_tarski(k7_relat_1(k5_relat_1(C,A),B),k7_relat_1(C,B)) ) )).
fof(t120_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) ) => k22_rvsum_1(k4_rvsum_1(A,B),C) = k2_xcmplx_0(k22_rvsum_1(A,C),k22_rvsum_1(B,C)) ) ) ) ) )).
fof(t120_scmyciel,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( v1_finset_1(B) & v4_scmyciel(B) & k11_scmyciel(B) = 2 & ~ r1_xxreal_0(k9_scmyciel(B),A) ) ) )).
fof(t120_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k12_seq_4(A))) => ( ~ r1_xxreal_0(B,k5_numbers) => r1_tarski(C,k23_seq_4(A,C,B)) ) ) ) ) )).
fof(t120_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t120_sin_cos9,axiom,( ! [A] : ( ( 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,k22_sin_cos))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k22_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k22_sin_cos),A),B) = k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k22_sin_cos,k1_funct_1(k2_sin_cos9,B)),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t120_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,1) & ~ r1_xxreal_0(k3_square_1(2),A) & k1_funct_1(k1_fdiff_9,k8_sincos10(A)) != k7_xcmplx_0(A,k3_square_1(k6_xcmplx_0(k1_square_1(A),1))) ) ) )).
fof(t120_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ 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)))) ) ) ) ) ) ) ) ) )).
fof(t120_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ( ( k6_xboolean(A,B) = k2_xboolean & k6_xboolean(A,k3_xboolean(B)) = k2_xboolean ) => k3_xboolean(A) = k2_xboolean ) ) ) )).
fof(t120_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k6_xcmplx_0(k7_xcmplx_0(A,C),k7_xcmplx_0(B,C)) = k7_xcmplx_0(k6_xcmplx_0(A,B),C) ) ) ) )).
fof(t120_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(C,k5_numbers) & r1_xxreal_0(A,B) ) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(C,B)) ) ) ) ) ) )).
fof(t120_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(D,C) & r1_tarski(k4_xxreal_1(C,D),k3_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t120_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t120_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( ~ r2_hidden(A,C) & ~ r2_hidden(B,C) & C != k4_xboole_0(k2_xboole_0(C,k2_tarski(A,B)),k2_tarski(A,B)) ) )).
fof(t120_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( ( v1_zmodul01(C) & m1_zmodul01(C,A) ) => ! [D] : ( ( v1_zmodul01(D) & m1_zmodul01(D,A) ) => ( m1_zmodul01(B,C) => m1_zmodul01(k6_zmodul01(A,B,D),k6_zmodul01(A,C,D)) ) ) ) ) ) )).
fof(t121_abcmiz_1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [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] : ( ( 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))) ) ) ) ) ) )).
fof(t121_clvect_1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(t121_finseq_3,axiom,( ! [A] : ! [B] : ( r2_hidden(A,k4_card_3(k9_finseq_1(B))) <=> ? [C] : ( r2_hidden(C,B) & A = k9_finseq_1(C) ) ) )).
fof(t121_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( 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,k1_nat_1(k7_nat_d(D,C),1)) & ~ r1_xxreal_0(E,k2_xcmplx_0(k6_xcmplx_0(D,C),1)) & ~ r1_xxreal_0(E,k6_xcmplx_0(k1_nat_1(D,1),C)) ) | ( k1_funct_1(k3_finseq_6(A,B,C,D),E) = k1_funct_1(B,k7_nat_d(k2_xcmplx_0(E,C),1)) & k1_funct_1(k3_finseq_6(A,B,C,D),E) = k1_funct_1(B,k2_xcmplx_0(k7_nat_d(E,1),C)) & k1_funct_1(k3_finseq_6(A,B,C,D),E) = k1_funct_1(B,k6_xcmplx_0(k2_xcmplx_0(E,C),1)) & k1_funct_1(k3_finseq_6(A,B,C,D),E) = k1_funct_1(B,k2_xcmplx_0(k6_xcmplx_0(E,1),C)) ) ) ) ) ) ) ) ) )).
fof(t121_funct_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => m1_funct_2(k1_funct_2(A,B),A,B) ) )).
fof(t121_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r1_xboole_0(k9_xtuple_0(B),k9_xtuple_0(C)) => k1_funct_4(k6_subset_1(A,B),C) = k6_subset_1(k1_funct_4(A,C),B) ) ) ) ) )).
fof(t121_funct_7,axiom,( ! [A] : ! [B] : ! [C] : k1_funct_1(k12_funct_7(A,B,C),k5_numbers) = A )).
fof(t121_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t121_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ! [E] : ! [F] : ( ( v2_glib_001(B,A) & r1_glib_001(A,D,E,B) & r2_glib_000(A,E,F,C) ) => ( v2_glib_001(k10_glib_001(A,B,C),A) & r1_glib_001(A,D,F,k10_glib_001(A,B,C)) ) ) ) ) )).
fof(t121_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t121_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ( ( v1_group_3(B,A) & m1_group_2(B,A) ) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => m1_group_2(B,k6_group_3(A,B,C)) ) ) ) ) )).
fof(t121_group_9,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => k3_relat_1(B,k5_relat_1(C,A)) = k3_relat_1(k6_relat_1(A,B),C) ) ) )).
fof(t121_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t121_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ( ( v1_vectsp_7(k9_matrix13(C,A,B,D),C,k6_prvect_1(C,B)) & v2_funct_1(D) ) <=> k8_matrix13(C,D) = A ) ) ) ) ) )).
fof(t121_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => k15_member_1(k5_member_1(A),B) = k5_member_1(k15_member_1(A,B)) ) ) )).
fof(t121_pboole,axiom,( r1_pboole(k1_xboole_0,k1_pboole(k1_xboole_0),k1_pboole(k1_xboole_0)) )).
fof(t121_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r1_tarski(B,C) => k7_relat_1(k5_relat_1(A,C),B) = k7_relat_1(A,B) ) ) )).
fof(t121_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => ! [C] : ( v1_xreal_0(C) => ( k3_finseq_1(A) = k3_finseq_1(B) => k22_rvsum_1(k10_rvsum_1(A,C),B) = k3_xcmplx_0(C,k22_rvsum_1(A,B)) ) ) ) ) )).
fof(t121_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k12_seq_4(A))) => ( C != k1_xboole_0 => v1_seq_4(k23_seq_4(A,C,B),A) ) ) ) ) )).
fof(t121_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,C,B)) ) ) ) )).
fof(t121_sin_cos9,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k1_partfun2(k1_numbers,A)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k1_partfun2(k1_numbers,A)),A),B) = k4_xcmplx_0(k7_xcmplx_0(k1_square_1(B),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t121_sincos10,axiom,( r2_fdiff_1(k1_sincos10,k7_relset_1(k1_numbers,k1_numbers,k1_fdiff_9,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(t121_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ v2_struct_0(D) & v1_borsuk_1(D,A) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ 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)))) ) ) ) ) ) ) ) ) )).
fof(t121_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( 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 ) ) ) )).
fof(t121_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,k7_xcmplx_0(A,2)) = k7_xcmplx_0(A,2) ) )).
fof(t121_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(D,B) & r1_xxreal_0(C,D) & r1_tarski(k1_xxreal_1(C,D),k3_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t121_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ~ v1_xboole_0(C) => ( ( r2_zf_model(C,k11_zf_lang(A,B)) & r2_zf_model(C,A) ) => r2_zf_model(C,B) ) ) ) ) )).
fof(t121_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : 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)) )).
fof(t121_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ( ~ ( ? [D] : ( 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] : ( m1_zmodul01(D,A) => u1_struct_0(D) != k2_xboole_0(u1_struct_0(B),u1_struct_0(C)) ) ) ) ) ) ) )).
fof(t122_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( r2_hidden(B,k51_abcmiz_1(k5_msafree(A,k28_abcmiz_1(A)))) <=> ? [C] : ( m1_subset_1(C,k2_abcmiz_1) & B = k1_domain_1(k2_abcmiz_1,u1_struct_0(A),C,k14_abcmiz_1(A)) ) ) ) )).
fof(t122_clvect_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(t122_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,B) ) => k4_finseq_1(C) = k2_finseq_1(A) ) ) ) )).
fof(t122_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(A,k4_card_3(k10_finseq_1(B,C))) <=> ? [D] : ? [E] : ( r2_hidden(D,B) & r2_hidden(E,C) & A = k10_finseq_1(D,E) ) ) )).
fof(t122_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t122_funct_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_relat_1(D) & v5_relat_1(D,A) & v1_funct_1(D) ) => k9_xtuple_0(k3_relat_1(D,C)) = k9_xtuple_0(D) ) ) ) )).
fof(t122_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t122_funct_7,axiom,( ! [A] : ! [B] : ! [C] : k1_funct_1(k12_funct_7(A,B,C),1) = B )).
fof(t122_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) ) )).
fof(t122_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v2_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => v2_glib_001(k8_glib_001(A,B,C,D),A) ) ) ) ) )).
fof(t122_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t122_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ( ( v1_group_3(B,A) & m1_group_2(B,A) ) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => m1_group_2(k6_group_3(A,B,C),B) ) ) ) ) )).
fof(t122_group_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( 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),k6_subset_1(k4_ordinal1,k1_tarski(k5_numbers))) ) => k14_finseq_1(k7_relset_1(k1_numbers,k1_numbers,C,B)) = k1_partfun1(k4_ordinal1,k4_ordinal1,k1_numbers,k1_numbers,k14_finseq_1(B),C) ) ) ) )).
fof(t122_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t122_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k6_prvect_1(C,B)))) => ~ ( r1_tarski(E,k9_matrix13(C,A,B,D)) & ! [F] : ( ( v1_finset_1(F) & v1_setfam_1(F) & m1_subset_1(F,k1_zfmisc_1(k4_ordinal1)) ) => ~ ( r1_tarski(F,k2_finseq_1(A)) & k9_matrix13(C,k5_card_1(F),k5_card_1(k2_finseq_1(B)),k6_matrix13(u1_struct_0(C),D,F,k2_finseq_1(B))) = E & v2_funct_1(k6_matrix13(u1_struct_0(C),D,F,k2_finseq_1(B))) ) ) ) ) ) ) ) ) )).
fof(t122_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( 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))) ) ) ) )).
fof(t122_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ( ? [D] : ( 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)) ) ) ) ) )).
fof(t122_pboole,axiom,( ! [A] : ( ( 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 ) )).
fof(t122_relat_1,axiom,( ! [A] : ! [B] : ( 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))) ) )).
fof(t122_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => ( k3_finseq_1(A) = k3_finseq_1(B) => k22_rvsum_1(k6_rvsum_1(A),B) = k4_xcmplx_0(k22_rvsum_1(A,B)) ) ) ) )).
fof(t122_seq_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( 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 ) ) ) )).
fof(t122_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t122_sin_cos9,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k4_xcmplx_0(k7_xcmplx_0(k1_square_1(B),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t122_sincos10,axiom,( r2_fdiff_1(k2_sincos10,k7_relset_1(k1_numbers,k1_numbers,k1_fdiff_9,k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos))) )).
fof(t122_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ v2_struct_0(D) & v1_tsep_1(D,A) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ 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)))) ) ) ) ) ) ) ) ) )).
fof(t122_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k5_xboolean(A,k6_xboolean(A,B)) = k2_xboolean ) ) )).
fof(t122_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t122_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k5_xcmplx_0(A),k5_numbers) ) & ~ ( ~ r1_xxreal_0(k5_xcmplx_0(A),k5_numbers) & r1_xxreal_0(A,k5_numbers) ) ) ) )).
fof(t122_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(D,C) & r1_tarski(k2_xxreal_1(C,D),k3_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t122_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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)))) ) ) ) ) ) )).
fof(t122_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(t122_zmodul01,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t123_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( 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] : ( ( v2_abcmiz_1(C,A) & m1_subset_1(C,u4_struct_0(A)) ) => B != k4_tarski(C,u1_struct_0(A)) ) ) ) ) )).
fof(t123_clvect_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( 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] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(F))) => ! [H] : ( m1_subset_1(H,u1_struct_0(F)) => ! [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) ) ) ) ) ) ) ) ) ) ) )).
fof(t123_finseq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t123_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r2_hidden(A,k4_card_3(k11_finseq_1(B,C,D))) <=> ? [E] : ? [F] : ? [G] : ( r2_hidden(E,B) & r2_hidden(F,C) & r2_hidden(G,D) & A = k11_finseq_1(E,F,G) ) ) )).
fof(t123_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( 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)) ) ) ) ) ) )).
fof(t123_funct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( ! [C] : ( m1_subset_1(C,A) => k3_funct_2(A,A,B,C) = C ) => r2_funct_2(A,A,B,k6_partfun1(A)) ) ) ) )).
fof(t123_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r1_tarski(A,B) => r1_tarski(k1_funct_4(A,C),k1_funct_4(B,C)) ) ) ) ) )).
fof(t123_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v7_ordinal1(D) => ( ~ r1_xxreal_0(D,1) => k1_funct_1(k12_funct_7(A,B,C),D) = C ) ) )).
fof(t123_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( C != k4_tarski(k10_finseq_1(A,B),k14_twoscomp) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k46_gfacirc1(A,B,C),k47_gfacirc1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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 ) ) ) ) ) ) ) )).
fof(t123_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( ~ v3_glib_001(B,A) <=> r1_xxreal_0(3,k3_finseq_1(B)) ) ) ) )).
fof(t123_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t123_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t123_group_9,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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] : ~ ( k14_finseq_1(D) = k3_relat_1(k14_finseq_1(A),k2_funct_1(k14_finseq_1(k7_subset_1(k4_ordinal1,k2_finseq_1(k1_nat_1(C,1)),k1_tarski(B))))) & r1_tarski(D,k2_finseq_1(C)) ) ) ) ) )).
fof(t123_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t123_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( k8_matrix13(C,D) = E <=> ( ? [F] : ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t123_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( 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))) ) ) ) )).
fof(t123_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ( ? [D] : ( 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)) ) ) ) ) )).
fof(t123_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t123_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r2_hidden(B,k8_relat_1(C,A)) <=> ? [D] : ( r2_hidden(D,k10_xtuple_0(C)) & r2_hidden(k4_tarski(B,D),C) & r2_hidden(D,A) ) ) ) )).
fof(t123_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => ( k3_finseq_1(A) = k3_finseq_1(B) => k22_rvsum_1(k6_rvsum_1(A),k6_rvsum_1(B)) = k22_rvsum_1(A,B) ) ) ) )).
fof(t123_seq_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( 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)) ) ) ) )).
fof(t123_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t123_sin_cos9,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_sin_cos9),A),B) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_funct_1(k1_sin_cos9,B)),k7_xcmplx_0(k1_funct_1(k22_sin_cos,B),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t123_sincos10,axiom,( r2_fdiff_1(k3_sincos10,k7_relset_1(k1_numbers,k1_numbers,k2_fdiff_9,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers))) )).
fof(t123_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( r3_tsep_1(A,B,C) <=> ( r1_tsep_1(B,C) & ! [D] : ( ( ~ v2_struct_0(D) & v2_pre_topc(D) & l1_pre_topc(D) ) => ! [E] : ( ( 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)))) ) ) ) ) ) ) ) ) ) )).
fof(t123_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k6_xboolean(A,k5_xboolean(A,B)) = k2_xboolean ) ) )).
fof(t123_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( k7_xcmplx_0(A,B) = k7_xcmplx_0(D,C) => ( B = k5_numbers | C = k5_numbers | B = C | k7_xcmplx_0(A,B) = k7_xcmplx_0(k6_xcmplx_0(A,D),k6_xcmplx_0(B,C)) ) ) ) ) ) ) )).
fof(t123_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ ( ~ r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,k5_xcmplx_0(A)) ) & ~ ( ~ r1_xxreal_0(k5_numbers,k5_xcmplx_0(A)) & r1_xxreal_0(k5_numbers,A) ) ) ) )).
fof(t123_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(D,C) & r1_tarski(k3_xxreal_1(C,D),k3_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t123_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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)))) ) ) ) ) ) )).
fof(t123_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( r1_tarski(A,B) & k3_xboole_0(B,C) = k1_tarski(D) & r2_hidden(D,A) ) => k3_xboole_0(A,C) = k1_tarski(D) ) )).
fof(t123_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ( r1_zmodul01(A,B,C) => m3_zmodul01(C,A,B) ) ) ) ) )).
fof(t124_abcmiz_1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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] : ( 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(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_numbers))))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),B,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_numbers)))))),k1_msaterm(A,k2_pboole(u1_struct_0(A),B,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_numbers))))) ) ) ) )).
fof(t124_finseq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(t124_finseq_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k4_card_3(k9_finseq_1(A)) = k4_finseq_2(1,A) ) )).
fof(t124_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,A) => k17_finseq_1(A,k1_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)) ) ) ) ) )).
fof(t124_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( ( 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) ) ) ) )).
fof(t124_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t124_funct_7,axiom,( ! [A] : ! [B] : ! [C] : k12_funct_7(A,B,C) = k1_funct_7(k10_funct_7(A,C),1,B) )).
fof(t124_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( C != k4_tarski(k10_finseq_1(A,B),k14_twoscomp) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k46_gfacirc1(A,B,C),k47_gfacirc1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( 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) ) ) ) ) ) ) ) )).
fof(t124_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t124_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t124_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ( ( v1_group_3(B,A) & m1_group_2(B,A) ) <=> ! [C] : ( 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)) ) ) ) ) ) )).
fof(t124_group_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t124_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [D] : ( ( 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,k4_xcmplx_0(1)) | r1_xxreal_0(1,A) | v5_pre_topc(D,k1_pre_topc(k15_euclid(2),B),k1_pre_topc(k15_euclid(2),C)) ) ) ) ) ) ) )).
fof(t124_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t124_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_membered(C) => k15_member_1(k13_member_1(A,B),C) = k13_member_1(A,k15_member_1(B,C)) ) ) ) )).
fof(t124_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) => ( ? [D] : ( 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)) ) ) ) ) )).
fof(t124_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ~ r3_pboole(A,B,k1_pboole(A)) ) ) )).
fof(t124_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => r1_tarski(k8_relat_1(B,A),k9_xtuple_0(B)) ) )).
fof(t124_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) ) => k22_rvsum_1(k8_rvsum_1(A,B),C) = k6_xcmplx_0(k22_rvsum_1(A,C),k22_rvsum_1(B,C)) ) ) ) ) )).
fof(t124_seq_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( 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)) = k2_xcmplx_0(k3_seq_4(A),k3_seq_4(B)) ) ) ) ) )).
fof(t124_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t124_sin_cos9,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k2_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k2_sin_cos9),A),B) = k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_funct_1(k2_sin_cos9,B)),k7_xcmplx_0(k1_funct_1(k22_sin_cos,B),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t124_sincos10,axiom,( r2_fdiff_1(k4_sincos10,k7_relset_1(k1_numbers,k1_numbers,k2_fdiff_9,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(t124_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( r3_tsep_1(A,B,C) <=> ( r1_tsep_1(B,C) & ! [D] : ( ( ~ v2_struct_0(D) & v2_pre_topc(D) & l1_pre_topc(D) ) => ! [E] : ( ( 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)))) ) ) ) ) ) ) ) ) ) )).
fof(t124_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k5_xboolean(k3_xboolean(B),k6_xboolean(k6_xboolean(B,A),A)) = k2_xboolean ) ) )).
fof(t124_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),D),C) = k6_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,C),k7_xcmplx_0(B,C)),k7_xcmplx_0(D,C)) ) ) ) ) )).
fof(t124_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A)) ) ) ) )).
fof(t124_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( r1_xxreal_0(B,D) & r1_xxreal_0(C,D) & r1_tarski(k1_xxreal_1(C,D),k4_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t124_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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)))) ) ) ) ) ) )).
fof(t124_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( r1_tarski(k3_xboole_0(B,C),k1_tarski(A)) & r2_hidden(A,D) & r1_xboole_0(D,C) ) => r1_xboole_0(k2_xboole_0(B,D),C) ) )).
fof(t124_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( v8_zmodul01(B,A) & m1_zmodul01(B,A) ) => ! [C] : ( m3_zmodul01(C,A,B) => ( r1_zmodul01(A,C,B) & r1_zmodul01(A,B,C) ) ) ) ) )).
fof(t125_abcmiz_1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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] : ( m1_dtconstr(C,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),B,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_numbers))))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),B,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_numbers)))))),k1_msaterm(A,k2_pboole(u1_struct_0(A),B,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_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(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_numbers))),C))) ) ) ) ) )).
fof(t125_finseq_2,axiom,( ! [A] : ! [B] : k10_xtuple_0(k10_finseq_1(A,B)) = k2_tarski(A,B) )).
fof(t125_finseq_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => k4_card_3(k10_finseq_1(A,B)) = a_2_0_finseq_3(A,B) ) ) )).
fof(t125_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( 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,k1_nat_1(C,1),D)) ) ) ) ) ) ) )).
fof(t125_funct_2,axiom,( ! [A] : r2_hidden(k6_partfun1(A),k1_funct_2(A,A)) )).
fof(t125_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t125_funct_7,axiom,( ! [A] : ! [B] : k10_xtuple_0(k10_funct_7(A,B)) = k2_tarski(A,B) )).
fof(t125_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( C != k4_tarski(k10_finseq_1(A,B),k14_twoscomp) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k46_gfacirc1(A,B,C),k47_gfacirc1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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 ) ) ) ) ) ) ) )).
fof(t125_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ~ ( k3_glib_001(A,B) != k4_glib_001(A,B) & v3_glib_001(B,A) ) ) ) )).
fof(t125_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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)) ) ) ) ) )).
fof(t125_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t125_group_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_1(E,k4_numbers) => ! [F] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t125_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [D] : ( ( 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,k4_xcmplx_0(1)) | r1_xxreal_0(1,A) | v5_pre_topc(D,k1_pre_topc(k15_euclid(2),B),k1_pre_topc(k15_euclid(2),C)) ) ) ) ) ) ) )).
fof(t125_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t125_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_membered(C) => k13_member_1(k15_member_1(A,B),C) = k15_member_1(k13_member_1(A,C),B) ) ) ) )).
fof(t125_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ! [D] : ( ( 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) ) ) ) ) )).
fof(t125_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t125_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k8_relat_1(B,A) = k8_relat_1(B,k3_xboole_0(k10_xtuple_0(B),A)) ) )).
fof(t125_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_valued_0(D) & v1_finseq_1(D) ) => ! [E] : ( ( 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) ) => k22_rvsum_1(k4_rvsum_1(k10_rvsum_1(C,A),k10_rvsum_1(D,B)),E) = k2_xcmplx_0(k3_xcmplx_0(A,k22_rvsum_1(C,E)),k3_xcmplx_0(B,k22_rvsum_1(D,E))) ) ) ) ) ) ) )).
fof(t125_seq_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( ( v3_xxreal_2(B) & ! [C] : ( v1_xreal_0(C) => ~ ( r2_hidden(C,A) & ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,B) & r1_xxreal_0(D,C) ) ) ) ) ) => ( A = k1_xboole_0 | r1_xxreal_0(k3_seq_4(B),k3_seq_4(A)) ) ) ) ) )).
fof(t125_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t125_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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),k7_xcmplx_0(1,A)),k1_partfun2(k1_numbers,B)))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k1_funct_1(C,D) = k3_xcmplx_0(A,D) & A != k5_numbers & ~ r1_xxreal_0(k1_funct_1(C,D),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_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),k7_xcmplx_0(1,A)),k1_partfun2(k1_numbers,B)),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_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),k7_xcmplx_0(1,A)),k1_partfun2(k1_numbers,B)),B),D) = k4_xcmplx_0(k7_xcmplx_0(k1_square_1(k3_xcmplx_0(A,D)),k2_xcmplx_0(1,k1_square_1(k3_xcmplx_0(A,D))))) ) ) ) ) ) ) ) )).
fof(t125_sincos10,axiom,( v3_rcomp_1(k7_relset_1(k1_numbers,k1_numbers,k1_fdiff_9,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(t125_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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] : ( ( ~ v2_struct_0(D) & v2_pre_topc(D) & l1_pre_topc(D) ) => ! [E] : ( ( 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)))) ) ) ) ) ) ) ) ) ) ) )).
fof(t125_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => k7_xboolean(A,A) = k2_xboolean ) )).
fof(t125_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => k7_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(A,B),D),C) = k2_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(A,C),k7_xcmplx_0(B,C)),k7_xcmplx_0(D,C)) ) ) ) ) )).
fof(t125_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_numbers,k5_xcmplx_0(A)) & ~ r1_xxreal_0(k5_xcmplx_0(B),k5_numbers) & r1_xxreal_0(B,A) ) ) ) )).
fof(t125_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(D,C) & r1_tarski(k2_xxreal_1(C,D),k4_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t125_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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)))) ) ) ) ) ) )).
fof(t125_zfmisc_1,axiom,( ! [A] : ! [B] : ( ! [C] : ! [D] : ( ( r2_hidden(C,A) & r2_hidden(D,B) ) => r1_xboole_0(C,D) ) => r1_xboole_0(k3_tarski(A),k3_tarski(B)) ) )).
fof(t125_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( v8_zmodul01(B,A) & m1_zmodul01(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(t126_abcmiz_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t126_finseq_2,axiom,( ! [A] : ! [B] : ! [C] : k10_xtuple_0(k11_finseq_1(A,B,C)) = k1_enumset1(A,B,C) )).
fof(t126_finseq_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k4_card_3(k10_finseq_1(A,A)) = k4_finseq_2(2,A) ) )).
fof(t126_funct_2,axiom,( k1_funct_2(k1_xboole_0,k1_xboole_0) = k1_tarski(k6_partfun1(k1_xboole_0)) )).
fof(t126_funct_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),A))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B,B),B))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(C,C),C))) ) => ( G = k1_realset1(E,C) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(D,D),D))) ) => ( H = k1_realset1(F,D) => k8_funct_4(C,D,G,H) = k1_realset1(k8_funct_4(A,B,E,F),k2_zfmisc_1(C,D)) ) ) ) ) ) ) ) ) ) ) )).
fof(t126_funct_7,axiom,( ! [A] : ! [B] : ! [C] : k10_xtuple_0(k12_funct_7(A,B,C)) = k1_enumset1(A,B,C) )).
fof(t126_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( C != k4_tarski(k10_finseq_1(A,B),k14_twoscomp) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k46_gfacirc1(A,B,C),k47_gfacirc1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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))) ) ) ) ) ) ) )).
fof(t126_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v3_glib_001(B,A) <=> ? [C] : ( m1_subset_1(C,k6_glib_000(A)) & r2_relset_1(k4_ordinal1,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B,k1_glib_001(A,C)) ) ) ) ) )).
fof(t126_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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)) ) ) ) ) )).
fof(t126_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( v15_algstr_0(C) & v1_group_3(C,A) & m1_group_2(C,A) ) => ? [D] : ( 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)) ) ) ) ) )).
fof(t126_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(2),B)))) => ! [D] : ( ( 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,k4_xcmplx_0(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)) ) ) ) ) ) ) )).
fof(t126_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t126_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_membered(C) => k15_member_1(k15_member_1(A,B),C) = k15_member_1(A,k13_member_1(B,C)) ) ) ) )).
fof(t126_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( 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) ) ) ) ) )).
fof(t126_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ~ r4_pboole(A,B,k1_pboole(A)) ) ) )).
fof(t126_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => k8_relat_1(A,k10_xtuple_0(A)) = k9_xtuple_0(A) ) )).
fof(t126_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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) ) => k22_rvsum_1(k4_rvsum_1(A,B),k4_rvsum_1(C,D)) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k22_rvsum_1(A,C),k22_rvsum_1(A,D)),k22_rvsum_1(B,C)),k22_rvsum_1(B,D)) ) ) ) ) ) )).
fof(t126_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k12_seq_4(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k12_seq_4(A))) => ~ ( B != k1_xboole_0 & C != k1_xboole_0 & ~ r1_xxreal_0(k5_numbers,k24_seq_4(A,B,C)) ) ) ) ) )).
fof(t126_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t126_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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),k4_xcmplx_0(k7_xcmplx_0(1,A))),k1_partfun2(k1_numbers,B)))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k1_funct_1(C,D) = k3_xcmplx_0(A,D) & A != k5_numbers & ~ r1_xxreal_0(k1_funct_1(C,D),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_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),k4_xcmplx_0(k7_xcmplx_0(1,A))),k1_partfun2(k1_numbers,B)),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_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),k4_xcmplx_0(k7_xcmplx_0(1,A))),k1_partfun2(k1_numbers,B)),B),D) = k4_xcmplx_0(k7_xcmplx_0(k1_square_1(k3_xcmplx_0(A,D)),k2_xcmplx_0(1,k1_square_1(k3_xcmplx_0(A,D))))) ) ) ) ) ) ) ) )).
fof(t126_sincos10,axiom,( v3_rcomp_1(k7_relset_1(k1_numbers,k1_numbers,k1_fdiff_9,k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos))) )).
fof(t126_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t126_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k7_xboolean(k7_xboolean(k7_xboolean(k7_xboolean(A,B),C),A),k7_xboolean(B,C)) = k2_xboolean ) ) ) )).
fof(t126_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( B != k5_numbers => k6_xcmplx_0(k7_xcmplx_0(A,B),C) = k7_xcmplx_0(k6_xcmplx_0(A,k3_xcmplx_0(C,B)),B) ) ) ) ) )).
fof(t126_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k5_numbers,A) ) => k5_numbers = k3_xcmplx_0(A,B) ) ) ) )).
fof(t126_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( r1_xxreal_0(B,D) & ~ r1_xxreal_0(D,C) & r1_tarski(k3_xxreal_1(C,D),k4_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t126_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ~ v1_xboole_0(C) => r2_zf_model(C,k11_zf_lang(k8_zf_lang(B,A),A)) ) ) ) )).
fof(t126_zfmisc_1,axiom,( ! [A] : ! [B] : ~ r2_hidden(A,k2_zfmisc_1(A,B)) )).
fof(t126_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( v8_zmodul01(B,A) & m1_zmodul01(B,A) ) => ! [C] : ( m3_zmodul01(C,A,B) => k7_zmodul01(A,B,C) = k3_zmodul01(A) ) ) ) )).
fof(t127_abcmiz_1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [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] : ( ( v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_msafree(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_msafree(A,C))) => ! [F] : ( m2_finseq_1(F,u1_struct_0(k5_msafree(A,B))) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t127_finseq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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 ) ) ) ) )).
fof(t127_finseq_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => k4_card_3(k11_finseq_1(A,B,C)) = a_3_1_finseq_3(A,B,C) ) ) ) )).
fof(t127_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( 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)) ) ) ) )).
fof(t127_funct_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( m1_subset_1(D,A) => ! [E] : k1_funct_1(k1_funct_7(C,D,E),D) = E ) ) ) ) )).
fof(t127_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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))) )).
fof(t127_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v3_glib_001(B,A) <=> v3_glib_001(k6_glib_001(A,B),A) ) ) ) )).
fof(t127_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_group_2(C,A) => ? [D] : ( 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)) ) ) ) ) )).
fof(t127_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => k15_group_2(A,B) = k16_group_2(A,B) ) ) )).
fof(t127_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(2),B)))) => ! [D] : ( ( 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,k4_xcmplx_0(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)) ) ) ) ) ) ) )).
fof(t127_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t127_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_membered(C) => k15_member_1(A,k15_member_1(B,C)) = k15_member_1(k13_member_1(A,C),B) ) ) ) )).
fof(t127_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( 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) ) ) ) ) )).
fof(t127_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t127_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => r1_tarski(k8_relat_1(B,A),k8_relat_1(B,k10_xtuple_0(B))) ) )).
fof(t127_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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) ) => k22_rvsum_1(k8_rvsum_1(A,B),k8_rvsum_1(C,D)) = k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k22_rvsum_1(A,C),k22_rvsum_1(A,D)),k22_rvsum_1(B,C)),k22_rvsum_1(B,D)) ) ) ) ) ) )).
fof(t127_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t127_sin_cos9,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k1_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k1_sin_cos9),A),B) = k2_xcmplx_0(k7_xcmplx_0(k1_funct_1(k1_sin_cos9,B),B),k7_xcmplx_0(k1_funct_1(k3_taylor_1,B),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t127_sincos10,axiom,( v3_rcomp_1(k7_relset_1(k1_numbers,k1_numbers,k2_fdiff_9,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers))) )).
fof(t127_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( A = k1_tsep_1(A,C,D) => ! [E] : ( ( 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))) ) ) ) ) ) ) )).
fof(t127_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => ( ( k7_xboolean(A,B) = k2_xboolean & k7_xboolean(B,C) = k2_xboolean ) => k7_xboolean(A,C) = k2_xboolean ) ) ) ) )).
fof(t127_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( B != k5_numbers => k6_xcmplx_0(C,k7_xcmplx_0(A,B)) = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(C,B),A),B) ) ) ) ) )).
fof(t127_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => r1_xxreal_0(k5_numbers,k3_xcmplx_0(A,B)) ) ) ) )).
fof(t127_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(D,C) & r1_tarski(k4_xxreal_1(C,D),k4_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t127_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ~ v1_xboole_0(C) => r2_zf_model(C,k11_zf_lang(A,k13_zf_lang(B,A))) ) ) ) )).
fof(t127_zfmisc_1,axiom,( ! [A] : ! [B] : ( B = k4_tarski(A,k1_tarski(A)) => r2_hidden(B,k2_zfmisc_1(k1_tarski(A),B)) ) )).
fof(t127_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ( r1_zmodul01(A,B,C) => r1_zmodul01(A,C,B) ) ) ) ) )).
fof(t128_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ~ ( B != k1_xboole_0 & ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m1_subset_1(D,A) => B != k8_finseq_1(A,k12_finseq_1(A,D),C) ) ) ) ) ) )).
fof(t128_finseq_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k4_card_3(k11_finseq_1(A,A,A)) = k4_finseq_2(3,A) ) )).
fof(t128_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ~ ( k1_funct_2(A,B) != k1_xboole_0 & k1_funct_2(B,C) != k1_xboole_0 & k1_funct_2(A,C) = k1_xboole_0 ) )).
fof(t128_funct_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( m1_subset_1(E,A) => ( ! [F] : ( 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,k14_funct_7(A,B,D,E,k3_funct_2(A,B,C,E))) ) ) ) ) ) ) )).
fof(t128_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : v1_relat_1(k3_msafree2(k49_gfacirc1(A,B,C))) )).
fof(t128_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ( v3_glib_001(C,A) => r2_relset_1(k4_ordinal1,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),k7_glib_001(A,B,C),B) ) ) ) ) )).
fof(t128_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_group_2(D,A) => r2_wellord2(k13_group_2(A,D,B),k13_group_2(A,D,C)) ) ) ) ) )).
fof(t128_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t128_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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) ) ) )).
fof(t128_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t128_member_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k15_member_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k7_xcmplx_0(A,B)) ) ) )).
fof(t128_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ( ! [C] : ( 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)) ) ) ) )).
fof(t128_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t128_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( k8_relat_1(B,A) = k1_xboole_0 <=> r1_xboole_0(k10_xtuple_0(B),A) ) ) )).
fof(t128_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => ( k3_finseq_1(A) = k3_finseq_1(B) => k22_rvsum_1(k4_rvsum_1(A,B),k4_rvsum_1(A,B)) = k2_xcmplx_0(k2_xcmplx_0(k22_rvsum_1(A,A),k3_xcmplx_0(2,k22_rvsum_1(A,B))),k22_rvsum_1(B,B)) ) ) ) )).
fof(t128_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k12_seq_4(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k12_seq_4(A))) => ~ ( C != k1_xboole_0 & D != k1_xboole_0 & ~ r1_xxreal_0(k24_seq_4(A,C,D),k2_xcmplx_0(k22_seq_4(A,B,C),k22_seq_4(A,B,D))) ) ) ) ) ) )).
fof(t128_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) )).
fof(t128_sin_cos9,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k2_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k2_sin_cos9),A),B) = k6_xcmplx_0(k7_xcmplx_0(k1_funct_1(k2_sin_cos9,B),B),k7_xcmplx_0(k1_funct_1(k3_taylor_1,B),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t128_sincos10,axiom,( v3_rcomp_1(k7_relset_1(k1_numbers,k1_numbers,k2_fdiff_9,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(t128_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( ~ r1_tsep_1(C,D) => ! [E] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t128_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t128_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( C != k5_numbers => k6_xcmplx_0(A,B) = k3_xcmplx_0(C,k6_xcmplx_0(k7_xcmplx_0(A,C),k7_xcmplx_0(B,C))) ) ) ) ) )).
fof(t128_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(B,k5_numbers) ) => r1_xxreal_0(k5_numbers,k3_xcmplx_0(A,B)) ) ) ) )).
fof(t128_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t128_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( ~ 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)))) ) ) ) ) ) )).
fof(t128_zfmisc_1,axiom,( ! [A] : ! [B] : ~ ( r2_hidden(B,k2_zfmisc_1(A,B)) & ! [C] : ~ ( r2_hidden(C,A) & B = k4_tarski(C,k1_tarski(C)) ) ) )).
fof(t128_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( v8_zmodul01(B,A) & m1_zmodul01(B,A) ) => ! [C] : ( m3_zmodul01(C,A,B) => m3_zmodul01(B,A,C) ) ) ) )).
fof(t129_abcmiz_1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t129_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,B) ) <=> r2_hidden(C,k4_finseq_2(A,B)) ) ) ) )).
fof(t129_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : k4_card_3(k2_finseq_2(A,B)) = k4_finseq_2(A,B) ) )).
fof(t129_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) ) => r1_funct_7(B,k1_funct_4(B,C),A) ) ) )).
fof(t129_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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) ) )).
fof(t129_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( ( 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 ) ) ) ) ) ) )).
fof(t129_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_group_2(D,A) => r2_wellord2(k13_group_2(A,D,B),k14_group_2(A,D,C)) ) ) ) ) )).
fof(t129_group_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( r1_struct_0(k10_group_3(B,C),A) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & k4_group_3(B,C,D) = C ) ) ) ) )).
fof(t129_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t129_member_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k15_member_1(k1_tarski(A),k2_tarski(B,C)) = k2_tarski(k7_xcmplx_0(A,B),k7_xcmplx_0(A,C)) ) ) ) )).
fof(t129_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t129_pboole,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t129_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ~ ( A != k1_xboole_0 & r1_tarski(A,k10_xtuple_0(B)) & k8_relat_1(B,A) = k1_xboole_0 ) ) )).
fof(t129_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => ( k3_finseq_1(A) = k3_finseq_1(B) => k22_rvsum_1(k8_rvsum_1(A,B),k8_rvsum_1(A,B)) = k2_xcmplx_0(k6_xcmplx_0(k22_rvsum_1(A,A),k3_xcmplx_0(2,k22_rvsum_1(A,B))),k22_rvsum_1(B,B)) ) ) ) )).
fof(t129_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k12_seq_4(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k12_seq_4(A))) => ( ~ r1_xboole_0(B,C) => k24_seq_4(A,B,C) = k5_numbers ) ) ) ) )).
fof(t129_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t129_sin_cos9,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(1),1)) ) => ( r2_hidden(k5_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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k1_square_1(B))),k7_xcmplx_0(1,k3_xcmplx_0(B,k2_xcmplx_0(1,k1_square_1(B))))) ) ) ) ) ) ) )).
fof(t129_sincos10,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k7_relset_1(k1_numbers,k1_numbers,k1_fdiff_9,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))))) )).
fof(t129_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t129_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => k3_xboolean(k7_xboolean(A,k3_xboolean(A))) = k2_xboolean ) )).
fof(t129_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( C != k5_numbers => k6_xcmplx_0(A,B) = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)),C) ) ) ) ) )).
fof(t129_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(k3_xcmplx_0(A,B),k5_numbers) ) ) ) )).
fof(t129_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t129_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( ~ 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))) ) ) ) ) ) ) )).
fof(t129_zfmisc_1,axiom,( ! [A] : ! [B] : ( ( r1_tarski(B,A) & v1_zfmisc_1(A) ) => v1_zfmisc_1(B) ) )).
fof(t129_zmodul01,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t12_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_abcmiz_0(A)) => k3_abcmiz_0(A,B) = a_2_0_abcmiz_0(A,B) ) ) )).
fof(t12_abcmiz_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ! [B] : ( m1_subset_1(B,A) => k1_abcmiz_1(B) = B ) => k1_abcmiz_1(k1_setfam_1(A)) = k1_setfam_1(A) ) ) )).
fof(t12_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t12_abian,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v1_abian(A) ) => r1_xxreal_0(1,A) ) )).
fof(t12_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k9_complex1(k2_xcmplx_0(A,B)) = k2_xcmplx_0(k9_complex1(A),k9_complex1(B)) => r1_xxreal_0(k5_numbers,k3_xcmplx_0(A,B)) ) ) ) )).
fof(t12_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_aff_1(A,B,C,D) ) ) ) ) ) )).
fof(t12_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v4_aff_2(A) => v7_aff_2(A) ) ) )).
fof(t12_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_aff_1(B,A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_hidden(C,B) ) ) ) ) )).
fof(t12_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ! [B] : ( ( 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 ) ) )).
fof(t12_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t12_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r2_analoaf(A,B,C,E,F) & r2_analoaf(A,B,D,G,F) ) => r2_analoaf(A,C,D,G,E) ) ) ) ) ) ) ) ) )).
fof(t12_alg_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t12_algspec1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(t12_algstr_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k6_algstr_0(A,B,k5_struct_0(A)) = B ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & k6_algstr_0(A,B,C) = k5_struct_0(A) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_algstr_0(A,B,C) = k6_algstr_0(A,C,B) ) ) ) ) ) )).
fof(t12_algstr_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k1_algstr_0(A,B,k4_struct_0(A)) = B ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & k1_algstr_0(A,B,C) = k4_struct_0(A) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => k6_algstr_0(A,B,k5_struct_0(A)) = B ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ( B != k4_struct_0(A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_algstr_0(A,B,C) != k5_struct_0(A) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_algstr_0(A,B,k4_struct_0(A)) = k4_struct_0(A) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_algstr_0(A,B,C) = k6_algstr_0(A,C,B) ) ) ) ) ) )).
fof(t12_algstr_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( v2_algstr_4(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( v1_group_6(C,A,B) => ( v2_algstr_4(k8_relset_1(u1_struct_0(A),u1_struct_0(B),C,D),A) & m1_subset_1(k8_relset_1(u1_struct_0(A),u1_struct_0(B),C,D),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) ) )).
fof(t12_altcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_altcat_1(A,B,B) != k1_xboole_0 ) ) )).
fof(t12_altcat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_hidden(k4_cat_1(A,B),k1_binop_1(k2_altcat_2(A),B,B)) ) ) )).
fof(t12_ami_2,axiom,( ~ r2_hidden(k4_ordinal1,k2_ami_2) )).
fof(t12_ami_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k10_ami_3(A) != B ) ) )).
fof(t12_ami_5,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => ~ ( k2_compos_0(u1_compos_1(k1_ami_3),A) = 6 & ! [B] : ( v7_ordinal1(B) => A != k7_ami_3(B) ) ) ) )).
fof(t12_ami_6,axiom,( ! [A] : ( 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) = k4_ordinal1 ) )).
fof(t12_ami_wstd,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_setfam_1(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( k4_ami_wstd(B,C,D,A) = k4_ami_wstd(B,C,E,A) => D = E ) ) ) ) ) ) )).
fof(t12_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t12_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ( v2_extpro_1(C,A,B) => v1_xboole_0(k4_amistd_4(A,B,C)) ) ) ) ) )).
fof(t12_amistd_5,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) & ~ v2_compos_1(C,B) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ( 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)) ) ) ) ) ) ) ) )).
fof(t12_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r1_analmetr(A,E,F) & r2_analmetr(A,B,k5_algstr_0(A,C,D),E,F) & r2_analmetr(A,C,k5_algstr_0(A,D,B),E,F) ) => r2_analmetr(A,D,k5_algstr_0(A,B,C),E,F) ) ) ) ) ) ) ) )).
fof(t12_analoaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t12_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ( r1_analmetr(A,C,D) => k2_analort(A,C,D,k1_rlvect_1(A,B,E)) = k1_rlvect_1(A,k2_analort(A,C,D,B),E) ) ) ) ) ) ) )).
fof(t12_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t12_anproj_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ~ ( B != C & B != D & C != D & ! [E] : ( m2_funct_2(E,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [F] : ( m2_funct_2(F,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [G] : ( m2_funct_2(G,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ? [H] : ( v1_xreal_0(H) & ? [I] : ( v1_xreal_0(I) & ? [J] : ( v1_xreal_0(J) & k1_binop_1(k5_funcsdom(A),k1_binop_1(k5_funcsdom(A),k1_funct_1(k7_funcsdom(A),k4_tarski(H,E)),k1_funct_1(k7_funcsdom(A),k4_tarski(I,F))),k1_funct_1(k7_funcsdom(A),k4_tarski(J,G))) = k8_funcsdom(A) & ~ ( H = k5_numbers & I = k5_numbers & J = k5_numbers ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_aofa_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( ( 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 ) ) ) ) )).
fof(t12_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ~ ( B != C & A != B & A != C & D != A & D != B & D != C & k10_xtuple_0(k4_aofa_a00(A,B,C,D,E,F,G,H)) != k2_enumset1(E,F,G,H) ) )).
fof(t12_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ( B = k10_subset_1(k1_funct_1(u7_aofa_a00(A),2),u4_struct_0(A)) => ( B = k1_funct_1(u7_aofa_a00(A),2) & k1_msualg_1(A,B) = k12_finseq_1(u1_struct_0(A),u8_aofa_a00(A)) & k2_msualg_1(A,B) = u8_aofa_a00(A) ) ) ) ) )).
fof(t12_aofa_i00,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k2_power(k5_numbers,k2_xcmplx_0(A,B)) = k3_xcmplx_0(k2_power(k5_numbers,A),k2_power(k5_numbers,B)) ) ) )).
fof(t12_armstrng,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_armstrng(A)) => ! [C] : ( m1_subset_1(C,k4_armstrng(A)) => ! [D] : ( m1_subset_1(D,k4_armstrng(A)) => ( ( r3_armstrng(A,C,B) & r3_armstrng(A,D,C) ) => r3_armstrng(A,D,B) ) ) ) ) )).
fof(t12_arrow,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m2_subset_1(D,k2_arrow(A),k3_arrow(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t12_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ( B = k5_numbers => k2_arytm_0(A,B) = k5_numbers ) ) ) )).
fof(t12_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( ( r1_arytm_2(B,A) & r1_arytm_2(B,C) ) => k7_arytm_2(A,k1_arytm_1(C,B)) = k7_arytm_2(k1_arytm_1(A,B),C) ) ) ) ) )).
fof(t12_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( 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) ) ) ) )).
fof(t12_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => r2_arytm_3(k2_arytm_3(A,B),k9_ordinal3(A,B)) ) ) )).
fof(t12_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & v2_asympt_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( r2_hidden(A,k6_asympt_0(B)) & r2_hidden(B,k6_asympt_0(C)) ) => r2_hidden(A,k6_asympt_0(C)) ) ) ) ) )).
fof(t12_asympt_1,axiom,( ~ r2_hidden(k3_asympt_1(2),k7_asympt_0(k3_asympt_1(3))) )).
fof(t12_autalg_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t12_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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)) ) ) )).
fof(t12_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(t12_bcialg_1,axiom,( ! [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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) )).
fof(t12_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => 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) ) ) ) )).
fof(t12_bcialg_3,axiom,( ! [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] : ( 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) ) ) ) )).
fof(t12_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_bcialg_1(A,C,k1_bcialg_4(A,B,k1_bcialg_1(A,C,B))) ) ) ) )).
fof(t12_bcialg_5,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => r1_bcialg_1(A,k1_bcialg_5(A,B,C,D,k1_nat_1(D,1)),k1_bcialg_5(A,C,B,D,D)) ) ) ) ) )).
fof(t12_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => v12_bcialg_1(B,A) ) ) )).
fof(t12_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k2_bhsp_1(A,B,k5_algstr_0(A,C,D)) = k6_xcmplx_0(k2_bhsp_1(A,B,C),k2_bhsp_1(A,B,D)) ) ) ) ) )).
fof(t12_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_bhsp_2(B,A) => ( ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & 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) ) ) ) ) ) )).
fof(t12_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => 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_xcmplx_0(C,D)) ) ) ) ) )).
fof(t12_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ! [D] : ( v7_ordinal1(D) => k1_normsp_1(A,C,D) = k1_normsp_1(A,B,k5_numbers) ) => r2_funct_2(k4_ordinal1,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)) ) ) ) ) )).
fof(t12_bhsp_5,axiom,( ! [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_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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_finset_1(C) & m2_bhsp_5(C,A) ) => ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ( r2_hidden(F,C) => k1_funct_1(E,F) = k1_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),k9_binop_2,C,E) ) ) ) ) ) ) ) ) ) )).
fof(t12_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) ) )).
fof(t12_binari_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k6_margrel1) ) => ! [D] : ( m1_subset_1(D,k6_margrel1) => ! [E] : ( m1_subset_1(E,k6_margrel1) => k3_binari_2(k2_xcmplx_0(A,1),k7_binarith(k2_xcmplx_0(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)))) = k2_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k3_binari_2(k2_xcmplx_0(A,1),k9_binarith(A,1,k6_margrel1,B,k10_binarith(k6_margrel1,D))),k3_binari_2(k2_xcmplx_0(A,1),k9_binarith(A,1,k6_margrel1,C,k10_binarith(k6_margrel1,E)))),k15_funcop_1(k4_ordinal1,k4_binari_2(k2_xcmplx_0(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,k5_numbers,k5_series_1(2,k1_nat_1(A,1)))),k15_funcop_1(k4_ordinal1,k5_binari_2(k2_xcmplx_0(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,k5_numbers,k5_series_1(2,k1_nat_1(A,1)))) ) ) ) ) ) )).
fof(t12_binari_3,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( 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 ) ) ) ) )).
fof(t12_binari_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t12_binarith,axiom,( ! [A] : ( v1_xboolean(A) => k5_xboolean(A,A) = A ) )).
fof(t12_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( k5_binom(A,B,k5_numbers) = k4_struct_0(A) & k6_binom(A,B,k5_numbers) = k4_struct_0(A) ) ) ) )).
fof(t12_binop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t12_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => r1_tarski(k2_finseq_1(k5_series_1(2,B)),k10_xtuple_0(k1_bintree2(A,B))) ) ) )).
fof(t12_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t12_bor_cant,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( r2_funct_2(k4_ordinal1,k9_setfam_1(A),k6_setlim_1(A,B,C),k7_bor_cant(A,C)) & r2_funct_2(k4_ordinal1,k9_setfam_1(A),k5_setlim_1(A,B,C),k9_bor_cant(A,C)) ) ) ) ) )).
fof(t12_borsuk_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( 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) ) ) ) )).
fof(t12_borsuk_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( 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,k5_numbers) = B & k1_funct_1(E,1) = C & k1_funct_1(F,k5_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),k5_numbers) = B & k1_funct_1(k1_borsuk_2(A,B,C,D,E,F),1) = D ) ) ) ) ) ) ) ) )).
fof(t12_borsuk_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v1_compts_1(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t12_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t12_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_metric_1)) => ( r2_hidden(B,k2_pre_topc(k3_topmetr,A)) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & r1_xboole_0(k8_metric_1(k7_metric_1,B,C),A) ) ) ) ) ) )).
fof(t12_borsuk_7,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( ( k9_complex1(B) = k9_complex1(C) & k1_comptrig(B) = k2_xcmplx_0(k1_comptrig(C),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A)) ) => B = C ) ) ) ) )).
fof(t12_brouwer,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xxreal_0(A) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(B))) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t12_bspace,axiom,( ! [A] : ! [B] : ! [C] : ( k3_bspace(A,B) = k3_bspace(A,C) <=> ( r2_hidden(B,A) <=> r2_hidden(C,A) ) ) )).
fof(t12_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t12_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t12_bvfunc14,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ( B != C => k1_funct_1(k1_funct_4(k1_funct_4(A,k16_funcop_1(B,D)),k16_funcop_1(C,E)),B) = D ) ) )).
fof(t12_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t12_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t12_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t12_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( m1_eqrel_1(D,A) => r1_bvfunc_1(A,C,k7_bvfunc_2(A,C,B,D)) ) ) ) ) )).
fof(t12_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t12_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(t12_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t12_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t12_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t12_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t12_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t12_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_c0sp1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_c0sp1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_c0sp1(A))) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(H,A) => k3_funct_2(A,k1_numbers,G,H) = k3_real_1(k3_funct_2(A,k1_numbers,E,H),k3_funct_2(A,k1_numbers,F,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => k1_c0sp2(A,k5_numbers) = k4_struct_0(k5_c0sp2(A)) ) )).
fof(t12_calcul_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(A,k5_numbers) => k1_relset_1(k4_ordinal1,k14_finseq_1(k4_subset_1(k4_ordinal1,k2_finseq_1(B),k6_domain_1(k4_ordinal1,k1_nat_1(B,A))))) = k2_finseq_1(k1_nat_1(B,1)) ) ) ) )).
fof(t12_calcul_2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => k2_relset_1(k4_ordinal1,k14_finseq_1(k2_calcul_2(k3_finseq_1(C),k3_finseq_1(B)))) = k2_calcul_2(k3_finseq_1(C),k3_finseq_1(B)) ) ) ) )).
fof(t12_cantor_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(t12_card_1,axiom,( ! [A] : ~ r2_wellord2(A,k1_zfmisc_1(A)) )).
fof(t12_card_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => k1_card_1(k10_ordinal2(A,B)) = k1_card_2(k1_card_1(A),k1_card_1(B)) ) ) )).
fof(t12_card_3,axiom,( ! [A] : ! [B] : ( ( 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) ) ) ) )).
fof(t12_card_4,axiom,( ! [A] : ( ( v4_card_3(A) & ! [B] : ( r2_hidden(B,A) => v4_card_3(B) ) ) => v4_card_3(k3_tarski(A)) ) )).
fof(t12_card_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) ) => ! [B] : ( ( 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 ) ) )).
fof(t12_card_fil,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t12_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ! [E] : ( ~ r2_hidden(C,A) => k5_card_1(k1_card_fin(A,B,D,E)) = k1_card_1(a_5_0_card_fin(A,B,C,D,E)) ) ) ) )).
fof(t12_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t12_cardfin2,axiom,( ! [A] : k2_cardfin2(k1_tarski(A)) = k1_xboole_0 )).
fof(t12_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k3_cat_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_cat_1(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k3_cat_1(A,B))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k3_cat_1(A,B))) => ! [G] : ( m1_cat_1(G,k3_cat_1(A,B),C,D) => ! [H] : ( m1_cat_1(H,k3_cat_1(A,B),E,F) => G = H ) ) ) ) ) ) )).
fof(t12_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u4_struct_0(k2_oppcat_1(C))) => ! [E] : ( 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))) ) ) ) ) )).
fof(t12_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_cat_1(C,A,B,k1_cat_4(A)) => ! [D] : ( m1_cat_1(D,A,B,k1_cat_4(A)) => C = D ) ) ) ) )).
fof(t12_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t12_catalan1,axiom,( k1_catalan1(2) = 1 )).
fof(t12_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v5_ordinal1(C) & v1_finset_1(C) ) => ( ( v1_catalan2(B) & k3_xcmplx_0(2,k7_afinsq_2(k5_relat_1(B,A))) = A & B = k1_catalan2(k5_relat_1(B,A),C) ) => v1_catalan2(C) ) ) ) ) )).
fof(t12_catalg_1,axiom,( ! [A] : ! [B] : ( k5_catalg_1(A) = k5_catalg_1(B) => A = B ) )).
fof(t12_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_cayldick(A))) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & B = k6_afinsq_1(C,D) ) ) ) ) )).
fof(t12_cayley,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t12_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t12_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_cc0sp2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_cc0sp2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_cc0sp2(A))) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(H,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k2_numbers,G,H) = k3_xcmplx_0(k3_funct_2(u1_struct_0(A),k2_numbers,E,H),k3_funct_2(u1_struct_0(A),k2_numbers,F,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_cfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_numbers)) => ( v6_cfdiff_1(A) <=> ! [B] : ( v1_xcmplx_0(B) => ~ ( r2_hidden(B,A) & ! [C] : ( m1_cfdiff_1(C,B) => ~ r1_tarski(C,A) ) ) ) ) ) )).
fof(t12_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) )).
fof(t12_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( v1_xcmplx_0(C) => ( C != k5_numbers => k8_relset_1(A,k2_numbers,k25_valued_1(A,k2_numbers,B,C),k1_tarski(k5_numbers)) = k8_relset_1(A,k2_numbers,B,k1_tarski(k5_numbers)) ) ) ) ) )).
fof(t12_cgames_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v2_cgames_1(B) => ( r2_hidden(B,k2_cgames_1(A)) <=> r1_ordinal1(k9_cgames_1(B),A) ) ) ) )).
fof(t12_chord,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_abian(A) ) => ~ ( r1_xxreal_0(A,5) & A != k5_numbers & A != 2 & A != 4 ) ) )).
fof(t12_circcmb2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(A,D))) => ! [H] : ( m1_subset_1(H,k4_card_3(u3_msualg_1(B,E))) => ! [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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_circcmb3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_card_1(D,C) & v1_finseq_1(D) ) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t12_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( r2_hidden(C,k2_msafree2(k2_circcomb(A,B))) => r2_hidden(C,k2_msafree2(B)) ) ) ) ) )).
fof(t12_circled1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t12_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m3_msaterm(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t12_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t12_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( m1_msafree2(D,A,B) => ( r1_tarski(D,C) => r1_tarski(D,k6_circuit2(A,B,C)) ) ) ) ) ) )).
fof(t12_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) ) => ! [D] : ( v1_xreal_0(D) => ( ( v1_pdiff_7(C,A) & B = k7_funcop_1(C,D) ) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ( r2_hidden(E,C) => ( r1_pdiff_7(A,B,E) & r1_funct_2(k1_euclid(A),k1_numbers,k1_euclid(A),k4_ordinal1,k1_pdiff_7(A,B,E),k8_funcop_1(k4_ordinal1,k1_euclid(A),k5_numbers)) ) ) ) ) ) ) ) ) )).
fof(t12_classes1,axiom,( ! [A] : ! [B] : ! [C] : ( v3_ordinal1(C) => ( r2_hidden(B,k3_classes1(A,C)) => r2_hidden(k9_setfam_1(B),k3_classes1(A,k1_ordinal1(C))) ) ) )).
fof(t12_classes2,axiom,( ! [A] : ! [B] : ( r2_hidden(A,k1_classes1(B)) => r2_hidden(k1_card_1(A),k1_classes1(B)) ) )).
fof(t12_clopban1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k3_clopban1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_clopban1(A,B))) => ! [E] : ( v1_xcmplx_0(E) => ( D = k1_clvect_1(k3_clopban1(A,B),C,E) <=> ! [F] : ( m1_subset_1(F,A) => k4_clopban1(A,B,D,F) = k1_clvect_1(B,k4_clopban1(A,B,C,F),E) ) ) ) ) ) ) ) )).
fof(t12_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(k6_clopban1(A,A)),k8_clopban1(A,A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(k6_clopban1(A,A)),k8_clopban1(A,A)) => ! [D] : ( v1_xcmplx_0(D) => k4_clopban2(A,k3_clopban2(A,C,B),D) = k3_clopban2(A,C,k4_clopban2(A,B,D)) ) ) ) ) )).
fof(t12_clopban4,axiom,( ! [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) & 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k2_normsp_0(A,k1_normsp_1(A,B,D)),k9_nat_1(k1_numbers,C,D)) ) & v2_comseq_2(C) & k1_seq_2(C) = k5_numbers ) => ( v9_clvect_1(B,A) & k7_clvect_1(A,B) = k4_struct_0(A) ) ) ) ) ) )).
fof(t12_closure1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t12_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_closure2(C,A,B,k2_closure2(A,B)) => ! [D] : ( m1_closure2(D,A,B,k2_closure2(A,B)) => r2_hidden(k5_pboole(A,C,D),k2_closure2(A,B)) ) ) ) )).
fof(t12_closure3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ! [D] : ( r2_hidden(D,C) => m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t12_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( k1_clvect_1(A,B,C) = k1_clvect_1(A,B,D) => ( B = k4_struct_0(A) | C = D ) ) ) ) ) ) )).
fof(t12_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clvect_2(B,A) => ( ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & 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) ) ) ) ) ) )).
fof(t12_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ! [D] : ( v7_ordinal1(D) => k1_normsp_0(A,C,D) = k1_normsp_0(A,B,k5_numbers) ) => 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) ) ) ) ) )).
fof(t12_coh_sp,axiom,( ! [A] : ! [B] : ( ( 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 ) )).
fof(t12_cohsp_1,axiom,( ! [A] : ( v1_cohsp_1(k5_finsub_1(A)) & v2_cohsp_1(k5_finsub_1(A)) ) )).
fof(t12_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_collsp(A,B,C,D) ) ) ) ) ) )).
fof(t12_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(t12_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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 ) ) ) )).
fof(t12_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( A != k5_numbers => ( ( ~ r1_xxreal_0(k28_sin_cos,k1_comptrig(A)) => k1_comptrig(k4_xcmplx_0(A)) = k2_xcmplx_0(k1_comptrig(A),k28_sin_cos) ) & ( r1_xxreal_0(k28_sin_cos,k1_comptrig(A)) => k1_comptrig(k4_xcmplx_0(A)) = k6_xcmplx_0(k1_comptrig(A),k28_sin_cos) ) ) ) ) )).
fof(t12_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => B = k5_algstr_0(k1_complfld,k3_rlvect_1(k1_complfld,B,A),A) ) ) )).
fof(t12_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xcmplx_0(C) => k9_matrix_5(k10_seq_4(A,C),B) = k3_xcmplx_0(C,k9_matrix_5(A,B)) ) ) ) )).
fof(t12_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k1_nat_1(k5_card_1(B),k5_card_1(C)),1) & k5_card_1(k7_compos_1(A,B,C)) = k7_nat_d(k1_nat_1(k5_card_1(B),k5_card_1(C)),1) ) ) ) ) )).
fof(t12_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( 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 ) ) ) )).
fof(t12_comptrig,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))) => r1_xxreal_0(k5_numbers,k1_funct_1(k18_sin_cos,A)) ) ) )).
fof(t12_compts_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ( v8_pre_topc(A) & v1_compts_1(A) ) => v9_pre_topc(A) ) ) )).
fof(t12_comput_1,axiom,( ! [A] : ( ( v4_funct_1(A) & v1_comput_1(A) ) => ! [B] : ( ( 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] : ( r2_hidden(C,k9_xtuple_0(B)) => k1_funct_1(k3_tarski(A),C) = k1_funct_1(B,C) ) ) ) ) ) )).
fof(t12_comseq_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k25_valued_1(k4_ordinal1,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,C),A),k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k25_valued_1(k4_ordinal1,k2_numbers,B,A),C)) ) ) ) )).
fof(t12_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & v2_comseq_2(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => k3_comseq_2(k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)) = k2_xcmplx_0(k3_comseq_2(A),k3_comseq_2(B)) ) ) )).
fof(t12_comseq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => r1_xxreal_0(k9_complex1(A),k2_xcmplx_0(k9_complex1(k3_complex1(A)),k9_complex1(k4_complex1(A)))) ) )).
fof(t12_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_waybel_1(C,A,B) => ! [D] : ( ( 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] : ( ( 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) => ( v2_conlat_1(C,A,B) <=> ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_conmetr1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v6_conmetr1(A) => v5_conmetr1(A) ) ) )).
fof(t12_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_connsp_1(A) <=> ! [B] : ( 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))) ) ) ) ) )).
fof(t12_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( C = D => r1_tarski(k1_connsp_1(B,D),k1_connsp_1(A,C)) ) ) ) ) ) )).
fof(t12_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t12_convex1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => r1_tarski(k1_convex1(A,B,k2_xcmplx_0(C,D)),k6_rusub_4(A,k1_convex1(A,B,C),k1_convex1(A,B,D))) ) ) ) ) )).
fof(t12_convex2,axiom,( ! [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) ) => ! [B] : ( ( v2_convex1(B,A) & m1_rlvect_2(B,A) ) => ! [C] : ( ( v2_convex1(C,A) & m1_rlvect_2(C,A) ) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ~ r1_xxreal_0(k3_xcmplx_0(D,E),k5_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))) ) ) ) ) ) ) )).
fof(t12_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t12_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => r2_qc_lang2(A,B,k11_cqc_lang(A,C,B)) ) ) ) )).
fof(t12_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t12_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t12_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ( r1_tarski(B,C) => r2_cqc_the3(A,C,B) ) ) ) ) )).
fof(t12_csspace,axiom,( v6_clvect_1(k11_csspace,k7_csspace) & ~ v1_xboole_0(k11_csspace) )).
fof(t12_csspace2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v2_comseq_3(A) & k4_series_1(k55_valued_1(k4_ordinal1,k2_numbers,A)) = k5_numbers ) => ! [B] : ( v7_ordinal1(B) => k1_funct_1(A,B) = k5_complex1 ) ) ) )).
fof(t12_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( 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)) ) ) ) )).
fof(t12_decomp_1,axiom,( ! [A] : ( ( 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) ) )).
fof(t12_descip_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( r1_xxreal_0(1,k3_finseq_1(B)) => k8_descip_1(A,B,k3_finseq_1(B)) = B ) ) ) )).
fof(t12_dickson,axiom,( ! [A] : ( v1_relat_1(A) => ( A = k3_dickson(A) <=> v5_relat_2(A) ) ) )).
fof(t12_diff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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] : ( 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))) ) ) ) ) )).
fof(t12_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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] : ( ( 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) = k2_xcmplx_0(k1_diff_2(F,A,B,C,D,E),k1_diff_2(G,A,B,C,D,E)) ) ) ) ) ) ) ) )).
fof(t12_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(B,k1_relset_1(k1_numbers,k2_fdiff_9)) & r2_hidden(k6_xcmplx_0(B,A),k1_relset_1(k1_numbers,k2_fdiff_9)) ) => k1_funct_1(k4_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k2_fdiff_9),A),B) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(4,k17_sin_cos(k6_xcmplx_0(k3_xcmplx_0(2,B),A))),k17_sin_cos(A)),k1_square_1(k6_xcmplx_0(k19_sin_cos(k6_xcmplx_0(k3_xcmplx_0(2,B),A)),k19_sin_cos(A))))) ) ) ) )).
fof(t12_dilworth,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_dilworth(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t12_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r1_diraf(A,B,C,D) & r1_diraf(A,C,D,E) ) => ( C = D | r1_diraf(A,B,D,E) ) ) ) ) ) ) ) )).
fof(t12_dirort,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dirort(A) & l1_analoaf(A) ) => ( v2_dirort(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,A) => k9_dist_1(A,B) = k10_rvsum_1(k4_dist_1(A,B),k3_finseq_1(B)) ) ) )).
fof(t12_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k4_finseq_1(B))) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( D = k19_finseq_1(C) => k3_relat_1(k2_funct_1(D),k5_dist_2(A,B,C)) = k2_partfun1(k4_ordinal1,A,B,C) ) ) ) ) ) )).
fof(t12_domain_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ~ v1_xboole_0(E) => ( A = k4_zfmisc_1(B,C,D,E) <=> ! [F] : ( r2_hidden(F,A) <=> ? [G] : ( m1_subset_1(G,B) & ? [H] : ( m1_subset_1(H,C) & ? [I] : ( m1_subset_1(I,D) & ? [J] : ( m1_subset_1(J,E) & F = k6_xtuple_0(G,H,I,J) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ( ! [C] : ( r2_hidden(C,B) => m1_dynkin(C,A) ) => m1_dynkin(k1_setfam_1(B),A) ) ) ) )).
fof(t12_e_siec,axiom,( ! [A] : ( ( v2_e_siec(A) & v3_e_siec(A) & l1_e_siec(A) ) => k1_sysrel(u1_e_siec(A)) = k1_sysrel(u2_e_siec(A)) ) )).
fof(t12_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => 1 = k5_struct_0(k9_int_3(A)) ) )).
fof(t12_ec_pf_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t12_endalg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m2_funct_2(B,u1_struct_0(A),u1_struct_0(A),k1_endalg(A)) => m2_pboole(k16_funcop_1(k5_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))) ) ) )).
fof(t12_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k2_ens_1(A)) => ! [C] : ( m1_subset_1(C,k2_ens_1(A)) => ( k3_ens_1(A,C) = k4_ens_1(A,B) => ( k2_xtuple_0(k6_ens_1(A,B,C)) = k3_relat_1(k2_xtuple_0(B),k2_xtuple_0(C)) & k3_ens_1(A,k6_ens_1(A,B,C)) = k3_ens_1(A,B) & k4_ens_1(A,k6_ens_1(A,B,C)) = k4_ens_1(A,C) ) ) ) ) ) )).
fof(t12_entropy1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( 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_funct_1(k14_rvsum_1(B,C),A) = k3_xcmplx_0(k1_funct_1(B,A),k1_funct_1(C,A)) ) ) ) ) ) )).
fof(t12_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k2_tarski(A,B),k2_enumset1(C,D,E,F)) )).
fof(t12_equation,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_funcop_1(B) ) => ! [C] : ( ( 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),k2_funct_6(B)) ) ) )).
fof(t12_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => r1_xxreal_0(k6_xcmplx_0(k12_euclid(B),k12_euclid(C)),k12_euclid(k8_euclid(A,B,C))) ) ) ) )).
fof(t12_euclid_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v3_valued_0(B) ) => ( k3_finseq_1(A) = k3_finseq_1(B) => k2_xcmplx_0(k1_square_1(k12_euclid(k4_rvsum_1(A,B))),k1_square_1(k12_euclid(k8_rvsum_1(A,B)))) = k3_xcmplx_0(2,k2_xcmplx_0(k1_square_1(k12_euclid(A)),k1_square_1(k12_euclid(B)))) ) ) ) )).
fof(t12_euclid_3,axiom,( ! [A] : ( 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(k4_xcmplx_0(k17_euclid(A)),k3_xcmplx_0(k4_xcmplx_0(k18_euclid(A)),k7_complex1)) ) )).
fof(t12_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t12_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(3))) => k5_algstr_0(k15_euclid(3),A,B) = k4_euclid_5(k6_xcmplx_0(k1_euclid_5(A),k1_euclid_5(B)),k6_xcmplx_0(k2_euclid_5(A),k2_euclid_5(B)),k6_xcmplx_0(k3_euclid_5(A),k3_euclid_5(B))) ) ) )).
fof(t12_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(D,k1_rltopsp1(k15_euclid(2),A,B)) & r2_hidden(D,k1_rltopsp1(k15_euclid(2),A,C)) & B != C & D != A & ~ r2_hidden(B,k1_rltopsp1(k15_euclid(2),A,C)) & ~ r2_hidden(C,k1_rltopsp1(k15_euclid(2),A,B)) ) ) ) ) ) )).
fof(t12_euclid_7,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( v2_funct_1(A) <=> v2_funct_1(k6_rfinseq2(A)) ) ) )).
fof(t12_euclid_8,axiom,( k22_rvsum_1(k4_euclid_8,k4_euclid_8) = 1 )).
fof(t12_euclid_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(k5_numbers))) => k4_euclid_9(k5_numbers,B,A) = k1_tarski(k1_xboole_0) ) ) )).
fof(t12_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(B)) => ! [D] : ( 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,k4_xcmplx_0(A))) & k9_euclid(B,k8_euclid(B,C,D),A) = k8_euclid(B,k9_euclid(B,C,A),k9_euclid(B,D,A)) ) ) ) ) ) )).
fof(t12_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v5_euclmetr(A) <=> v5_conmetr(A) ) ) )).
fof(t12_euler_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => k5_int_1(k2_xcmplx_0(A,k3_xcmplx_0(B,C)),C) = k5_int_1(A,C) ) ) ) )).
fof(t12_euler_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( k4_nat_d(k3_xcmplx_0(A,C),B) = k4_nat_d(C,B) & r1_int_2(B,C) ) => ( A = k5_numbers | r1_xxreal_0(B,1) | k4_nat_d(A,B) = 1 ) ) ) ) ) )).
fof(t12_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v2_exchsort(A,k2_ordinal2(k9_xtuple_0(A))) ) )).
fof(t12_extens_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,C) => ( v2_msualg_3(D,A,B,C) <=> ! [E] : ( ( v1_relat_1(E) & v2_relat_1(E) & v4_relat_1(E,A) & v1_funct_1(E) & v1_partfun1(E,A) ) => ! [F] : ( m2_pboole(F,A,C,E) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t12_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(B)) & v1_funct_1(D) ) => ( r1_tarski(k16_funcop_1(C,k2_compos_1(B)),D) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t12_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( ( r1_xxreal_0(k2_xxreal_3(B),A) & r1_xxreal_0(A,B) ) <=> r1_xxreal_0(k3_extreal1(A),B) ) ) ) )).
fof(t12_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t12_facirc_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( k3_facirc_2(k1_nat_1(A,1),B,C) = k2_circcomb(k3_facirc_2(A,B,C),k19_facirc_1(k1_funct_1(B,k1_nat_1(A,1)),k1_funct_1(C,k1_nat_1(A,1)),k5_facirc_2(A,B,C))) & k4_facirc_2(k1_nat_1(A,1),B,C) = k3_circcomb(k3_facirc_2(A,B,C),k19_facirc_1(k1_funct_1(B,k1_nat_1(A,1)),k1_funct_1(C,k1_nat_1(A,1)),k5_facirc_2(A,B,C)),k4_facirc_2(A,B,C),k20_facirc_1(k1_funct_1(B,k1_nat_1(A,1)),k1_funct_1(C,k1_nat_1(A,1)),k5_facirc_2(A,B,C))) & k5_facirc_2(k1_nat_1(A,1),B,C) = k17_facirc_1(k1_funct_1(B,k1_nat_1(A,1)),k1_funct_1(C,k1_nat_1(A,1)),k5_facirc_2(A,B,C)) ) ) ) ) )).
fof(t12_fcont_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,B,C))) & r1_fcont_1(B,A) & r1_fcont_1(C,k1_funct_1(B,A)) ) => r1_fcont_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) )).
fof(t12_fcont_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( ( 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)) ) ) ) )).
fof(t12_fcont_3,axiom,( ! [A] : ! [B] : ( ( 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] : ( v1_xreal_0(C) => k7_relset_1(k1_numbers,k1_numbers,B,A) != k3_limfunc1(C) ) | v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) ) ) )).
fof(t12_fdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_rcomp_1(C,B) => ( ( r1_fdiff_1(A,B) & r1_tarski(C,k1_relset_1(k1_numbers,A)) ) => ! [D] : ( ( v1_funct_1(D) & v9_ordinal1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,E) = k1_tarski(B) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),C) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),A),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,A)))) & k1_fdiff_1(A,B) = k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),A),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,A)))) ) ) ) ) ) ) ) ) )).
fof(t12_fdiff_10,axiom,( ! [A] : ( ( 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,k26_sin_cos))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k26_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k26_sin_cos),A),B) = k2_xcmplx_0(k1_funct_1(k16_sin_cos,B),k7_xcmplx_0(k1_funct_1(k16_sin_cos,B),k1_square_1(k1_funct_1(k18_sin_cos,B)))) ) ) ) ) ) )).
fof(t12_fdiff_11,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(1),1)) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k2_sin_cos9,B),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k2_sin_cos9),A),B) = k7_xcmplx_0(1,k3_xcmplx_0(k2_xcmplx_0(1,k1_square_1(B)),k2_xcmplx_0(1,k1_square_1(k1_funct_1(k2_sin_cos9,B))))) ) ) ) ) ) )).
fof(t12_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( m1_rcomp_1(D,A) & r1_tarski(D,k1_relset_1(k1_numbers,C)) ) & ! [D] : ( ( v1_funct_1(D) & v9_ordinal1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,E) = k1_tarski(A) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),k1_relset_1(k1_numbers,C)) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),C),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,C)))) & k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),C),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,C)))) = B ) ) ) ) ) ) & ( ! [D] : ( ( v1_funct_1(D) & v9_ordinal1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,E) = k1_tarski(A) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),k1_relset_1(k1_numbers,C)) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),C),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,C)))) & k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),C),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,C)))) = B ) ) ) ) => ( ! [D] : ( 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 ) ) ) ) ) ) ) )).
fof(t12_fdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( 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)) = k2_xcmplx_0(k3_xcmplx_0(k1_fdiff_3(C,A),k1_funct_1(B,C)),k3_xcmplx_0(k1_fdiff_3(C,B),k1_funct_1(A,C))) ) ) ) ) ) )).
fof(t12_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( 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,C)))) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,D) => k1_funct_1(E,G) = k2_xcmplx_0(A,k3_xcmplx_0(B,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,C)),D) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,D) => k1_funct_1(k2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,E,k26_valued_1(k1_numbers,k1_numbers,F,C)),D),G) = k2_xcmplx_0(B,k3_xcmplx_0(k3_xcmplx_0(2,C),G)) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_fdiff_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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,k18_sin_cos),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(A))))) & r1_xxreal_0(1,A) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(C,D) = k3_xcmplx_0(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,k18_sin_cos),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(A))),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k18_sin_cos),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(A))),B),D) = k4_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(A,k3_prepower(k1_funct_1(k18_sin_cos,D),k6_xcmplx_0(A,1))),k1_funct_1(k16_sin_cos,k3_xcmplx_0(k2_xcmplx_0(A,1),D)))) ) ) ) ) ) ) ) )).
fof(t12_fdiff_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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,k22_sin_cos),D),k7_xcmplx_0(1,k3_power(k4_power,A))))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => ( k1_funct_1(C,E) = k3_xcmplx_0(E,k3_power(k4_power,A)) & k1_funct_1(D,E) = k6_xcmplx_0(E,k7_xcmplx_0(1,k3_power(k4_power,A))) ) ) ) ) => ( r1_xxreal_0(A,k5_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,k22_sin_cos),D),k7_xcmplx_0(1,k3_power(k4_power,A))),B) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_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,k22_sin_cos),D),k7_xcmplx_0(1,k3_power(k4_power,A))),B),E) = k3_xcmplx_0(E,k6_prepower(A,E)) ) ) ) ) ) ) ) ) ) )).
fof(t12_fdiff_7,axiom,( ! [A] : ( ( 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)),k7_xcmplx_0(1,2)))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(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)),k7_xcmplx_0(1,2)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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)),k7_xcmplx_0(1,2)),A),B) = k7_xcmplx_0(k1_funct_1(k1_sin_cos6,B),k3_square_1(k6_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t12_fdiff_8,axiom,( ! [A] : ( ( 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,k22_sin_cos,k26_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k26_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k26_sin_cos),A),B) = k7_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_square_1(k1_funct_1(k18_sin_cos,k1_funct_1(k22_sin_cos,B)))) ) ) ) ) ) )).
fof(t12_fdiff_9,axiom,( ! [A] : ( ( 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,k22_sin_cos,k1_fdiff_9))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_fdiff_9),A),B) = k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_funct_1(k16_sin_cos,k1_funct_1(k22_sin_cos,B))),k1_square_1(k1_funct_1(k18_sin_cos,k1_funct_1(k22_sin_cos,B)))) ) ) ) ) ) )).
fof(t12_ff_siec,axiom,( ! [A] : ( ( 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 ) ) )).
fof(t12_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_nat_d(B,C) & r1_nat_d(B,A) ) => r1_nat_d(B,k1_nat_1(k2_nat_1(C,D),k2_nat_1(A,E))) ) ) ) ) ) ) )).
fof(t12_fib_num3,axiom,( ! [A] : ( v7_ordinal1(A) => k1_fib_num3(k1_nat_1(A,2)) = k1_nat_1(k1_fib_num3(A),k1_fib_num3(k1_nat_1(A,1))) ) )).
fof(t12_fib_num4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( r1_xxreal_0(B,A) => r1_xxreal_0(k1_fib_num3(B),k1_fib_num3(A)) ) ) ) )).
fof(t12_filerec1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_finseq_1(D,C) => ( D = k10_finseq_1(A,B) => k2_rfinseq(C,1,D) = k9_finseq_1(B) ) ) ) )).
fof(t12_filter_0,axiom,( ! [A] : ( ( ~ 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))) ) ) ) )).
fof(t12_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( C = D => k7_lattices(A,C) = k7_lattices(B,D) ) ) ) ) ) ) )).
fof(t12_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v1_fin_topo(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k9_fin_topo(A,B) = k12_fin_topo(A,B) ) ) ) )).
fof(t12_finance1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(C,k5_numbers) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k6_finance1(A,k1_numbers,B,k12_prob_1)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_finance1(A,k1_numbers,B,k12_prob_1)))) ) => ( r1_funct_2(A,k1_numbers,A,k1_tarski(k2_xcmplx_0(1,D)),k9_finance1(k5_numbers,A,k1_numbers,B,k12_prob_1,k6_finance1(A,k1_numbers,B,k12_prob_1),F),k7_funcop_1(A,k2_xcmplx_0(1,D))) => ! [G] : ( m1_subset_1(G,A) => k11_finance1(C,E,A,B,k6_finance1(A,k1_numbers,B,k12_prob_1),F,G) = k2_xcmplx_0(k3_xcmplx_0(k2_xcmplx_0(1,D),k3_funct_2(k4_ordinal1,k1_numbers,E,k5_numbers)),k12_finance1(C,E,A,B,k6_finance1(A,k1_numbers,B,k12_prob_1),F,G)) ) ) ) ) ) ) ) ) ) )).
fof(t12_finseq_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ ( r2_hidden(A,B) & ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(C,k4_finseq_1(B)) & A = k4_tarski(C,k1_funct_1(B,C)) ) ) ) ) )).
fof(t12_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => m2_finseq_1(k11_finseq_1(B,C,D),A) ) ) ) ) )).
fof(t12_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(A,k2_finseq_1(C)) => ( r1_xxreal_0(A,B) | r2_hidden(k6_xcmplx_0(A,B),k2_finseq_1(C)) ) ) ) ) ) )).
fof(t12_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v2_funct_1(A) & r2_hidden(B,k10_xtuple_0(A)) ) => k1_funct_1(k2_funct_1(A),B) = k1_finseq_4(A,B) ) ) )).
fof(t12_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( ( k4_finseq_1(B) = k4_finseq_1(C) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(B)) => k7_partfun1(A,B,D) = k7_partfun1(A,C,D) ) ) ) => B = C ) ) ) ) )).
fof(t12_finseq_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( r2_hidden(C,k10_xtuple_0(A)) => k5_finseq_4(k7_finseq_1(A,B),C) = k5_finseq_4(A,C) ) ) ) )).
fof(t12_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => k1_finseq_7(A,k12_finseq_1(A,B),1,C) = k12_finseq_1(A,C) ) ) ) )).
fof(t12_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( 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))) ) ) ) ) )).
fof(t12_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( ( 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))) ) => ! [G] : ( m2_finseq_1(G,B) => r2_relset_1(k4_ordinal1,C,k3_finseqop(A,B,C,F,D,k8_finseq_1(B,G,k12_finseq_1(B,E))),k8_finseq_1(C,k3_finseqop(A,B,C,F,D,G),k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)))) ) ) ) ) ) ) ) )).
fof(t12_finset_1,axiom,( ! [A] : ~ ( v1_finset_1(A) & A != k1_xboole_0 & v6_ordinal1(A) & ! [B] : ~ ( r2_hidden(B,A) & ! [C] : ( r2_hidden(C,A) => r1_tarski(C,B) ) ) ) )).
fof(t12_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t12_finsub_1,axiom,( ! [A] : ! [B] : r1_tarski(k2_xboole_0(k5_finsub_1(A),k5_finsub_1(B)),k5_finsub_1(k2_xboole_0(A,B))) )).
fof(t12_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( k4_fintopo2(A,B,C) = k8_margrel1 <=> r2_hidden(B,C) ) ) ) ) )).
fof(t12_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t12_fintopo4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_fin_topo(A) => ( v4_fin_topo(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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 ) ) ) ) ) ) ) )).
fof(t12_fintopo5,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => v1_fin_topo(k3_fintopo5(A,B)) ) ) )).
fof(t12_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_fintopo6(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t12_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( 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 ) ) ) ) )).
fof(t12_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) )).
fof(t12_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => k8_flang_1(A,B) = k4_subset_1(k8_afinsq_1(A),k1_flang_2(A,B,k5_numbers,C),k1_flang_3(A,B,k2_xcmplx_0(C,1))) ) ) )).
fof(t12_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( v7_ordinal1(C) => ( r2_hidden(B,k4_finseq_2(C,A)) => m2_finseq_1(B,A) ) ) )).
fof(t12_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t12_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ~ 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)),k15_fomodel2(B,C),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0))),k18_fomodel2(B,C,k22_fomodel2(B,A,C))) = k2_zfmisc_1(k15_fomodel2(B,C),k27_fomodel2(B,A)) ) ) ) )).
fof(t12_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ( ( k1_fomodel2(B) = k1_fomodel2(C) & k31_fomodel2(B) = k31_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] : ( m2_subset_1(D,k9_funct_2(k37_fomodel1(B),k3_rfunct_3(k3_finseq_2(A),k2_xboole_0(A,k6_margrel1))),k15_fomodel2(B,A)) => ! [E] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(C),k3_rfunct_3(k3_finseq_2(A),k2_xboole_0(A,k6_margrel1))),k15_fomodel2(C,A)) => ! [F] : ( ( 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] : ( ( 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 & k25_fomodel2(C,A,E,G) = k25_fomodel2(B,A,D,F) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C))))) => ( v9_fomodel4(B,C,D,A) => ( v4_fomodel2(B,C) & m2_subset_1(B,k3_finseq_2(k15_fomodel1(C)),k6_subset_1(k3_finseq_2(k15_fomodel1(C)),k1_tarski(k1_xboole_0))) ) ) ) ) )).
fof(t12_frechet,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t12_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( r2_funct_2(k4_ordinal1,u1_struct_0(B),E,k1_partfun1(k4_ordinal1,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)) ) ) ) ) ) ) ) ) )).
fof(t12_fscirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t12_fscirc_2,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(t12_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( ( ~ v2_struct_0(E) & l2_fsm_1(E,A,B) ) => ! [F] : ( ( ~ v2_struct_0(F) & l2_fsm_1(F,A,B) ) => ! [G] : ( m1_subset_1(G,u1_struct_0(E)) => ! [H] : ( m1_subset_1(H,u1_struct_0(E)) => ! [I] : ( m1_subset_1(I,u1_struct_0(F)) => ! [J] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_afinsq_1(C))) => ! [F] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t12_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : v1_relat_1(k3_msafree2(k7_ftacell1(A,B,C,D,E))) )).
fof(t12_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : k5_relat_1(k2_funcop_1(A,C),B) = k2_funcop_1(k3_xboole_0(A,B),C) )).
fof(t12_funcsdom,axiom,( ! [A] : ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => k1_binop_1(k7_funcsdom(A),1,B) = B ) )).
fof(t12_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,k9_xtuple_0(k3_relat_1(B,C))) => k1_funct_1(k3_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A)) ) ) ) )).
fof(t12_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ! [E] : ( r2_hidden(E,A) => k1_funct_1(C,E) = k1_funct_1(D,E) ) => r2_relset_1(A,B,C,D) ) ) ) )).
fof(t12_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => r1_tarski(k8_relat_1(k1_funct_3(D),A),k1_zfmisc_1(B)) ) ) )).
fof(t12_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( r2_hidden(C,k9_xtuple_0(k1_funct_4(A,B))) <=> ( r2_hidden(C,k9_xtuple_0(A)) | r2_hidden(C,k9_xtuple_0(B)) ) ) ) ) )).
fof(t12_funct_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( r2_hidden(k4_tarski(B,C),k9_xtuple_0(A)) => r2_hidden(B,k9_xtuple_0(k1_funct_5(A))) ) ) )).
fof(t12_funct_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)) ) ) ) )).
fof(t12_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ( ~ r1_xboole_0(A,k10_xtuple_0(k1_funct_4(k6_partfun1(B),k7_funcop_1(A,C)))) => r2_hidden(C,A) ) )).
fof(t12_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t12_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t12_functor0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t12_functor1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l1_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_altcat_2(C) & l1_altcat_1(C) ) => ! [D] : ( ( v8_functor0(D,A,B) & l2_functor0(D,A,B) ) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t12_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,B,C) & m2_functor0(E,B,C) ) => ! [F] : ( ( v15_functor0(F,B,C) & m2_functor0(F,B,C) ) => ! [G] : ( m1_functor2(G,B,C,E,F) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( r1_functor2(B,C,E,F) => k2_functor2(A,C,k1_functor3(A,B,C,D,E),k1_functor3(A,B,C,D,F),k6_functor3(A,B,C,E,F,D,G),H) = k2_functor2(B,C,E,F,G,k3_functor0(A,B,D,H)) ) ) ) ) ) ) ) ) ) )).
fof(t12_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( ( 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] : ( m1_subset_1(E,A) => ( r2_hidden(E,k1_relset_1(A,D)) => ( r1_xxreal_0(B,k1_funct_1(D,E)) & r1_xxreal_0(k1_funct_1(D,E),C) ) ) ) ) ) ) ) ) )).
fof(t12_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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))) ) ) ) )).
fof(t12_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,k1_fuzzy_4(B,A,k6_fuzzy_1(k2_zfmisc_1(A,B),C,D)),k6_fuzzy_1(k2_zfmisc_1(B,A),k1_fuzzy_4(B,A,C),k1_fuzzy_4(B,A,D))) ) ) ) ) )).
fof(t12_fvaluat1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t12_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r7_binop_1(u1_struct_0(A),k1_fvsum_1(A,B),u1_algstr_0(A)) ) ) )).
fof(t12_gate_1,axiom,( ! [A] : ! [B] : ( ~ ( ~ 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)) ) ) )).
fof(t12_gcd_1,axiom,( ! [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) & v1_vectsp_2(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t12_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( m1_genealg1(C,B) => ! [D] : ( m1_genealg1(D,B) => k8_genealg1(B,C,D,A,A) = C ) ) ) ) )).
fof(t12_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t12_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : v1_relat_1(k3_msafree2(k7_gfacirc1(A,B,C))) )).
fof(t12_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ! [C] : ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( D != E => ( r2_hidden(D,k1_relset_1(k4_ordinal1,k13_glib_000(k13_glib_000(A,D,B),E,C))) & r2_hidden(E,k1_relset_1(k4_ordinal1,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 ) ) ) ) ) )).
fof(t12_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t12_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t12_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v3_glib_001(B,A) => k8_glib_003(A,B) = k1_xboole_0 ) ) ) )).
fof(t12_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( v2_glib_001(B,A) & v5_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ! [D] : ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( 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))) ) ) ) ) ) )).
fof(t12_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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] : ! [D] : ! [E] : ( 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),k2_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))))) ) ) ) ) ) )).
fof(t12_goboard1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( k1_matrix_0(C) = k1_nat_1(A,1) & r2_hidden(B,k2_finseq_1(A)) ) => ( r1_xxreal_0(A,k5_numbers) | ( k8_matrix_0(u1_struct_0(k15_euclid(2)),k16_matrix_0(k1_matrix_0(C),u1_struct_0(k15_euclid(2)),C),B) = k8_matrix_0(u1_struct_0(k15_euclid(2)),C,B) & r2_hidden(B,k2_finseq_1(k1_matrix_0(k16_matrix_0(k1_matrix_0(C),u1_struct_0(k15_euclid(2)),C)))) ) ) ) ) ) ) )).
fof(t12_goboard2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ~ ( ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(C,k4_finseq_1(A)) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( r2_hidden(k4_tarski(D,E),k2_matrix_0(B)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),B,D,E) ) ) ) ) ) & v1_topreal1(A) & ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(C,k4_finseq_1(A)) & r2_hidden(k1_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,k1_nat_1(C,1)) ) ) & ! [C] : ( 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)) ) ) ) ) ) )).
fof(t12_goboard5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_goboard5(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( v7_ordinal1(B) => ( ( r2_hidden(B,k4_finseq_1(A)) & r2_hidden(k1_nat_1(B,1),k4_finseq_1(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( ( r2_hidden(k4_tarski(C,D),k2_matrix_0(k2_goboard2(A))) & r2_hidden(k4_tarski(E,F),k2_matrix_0(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,D) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),E,F) ) => k2_xcmplx_0(k9_complex1(k6_xcmplx_0(C,E)),k9_complex1(k6_xcmplx_0(D,F))) = 1 ) ) ) ) ) ) ) ) )).
fof(t12_goboard6,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => k1_tops_1(k15_euclid(2),k1_goboard5(A,k5_numbers)) = a_1_0_goboard6(A) ) )).
fof(t12_goboard7,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( v1_topreal1(A) & r1_xxreal_0(B,k3_finseq_1(k2_goboard2(A))) & r1_xxreal_0(C,k1_matrix_0(k2_goboard2(A))) ) => r1_xboole_0(k1_tops_1(k15_euclid(2),k3_goboard5(k2_goboard2(A),B,C)),k3_topreal1(2,A)) ) ) ) ) )).
fof(t12_goboard8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,2),k3_finseq_1(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,2),k1_matrix_0(k2_goboard2(A))) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,2),k3_finseq_1(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,1),k1_nat_1(C,1)) ) => ( ( ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,1),k1_nat_1(C,2)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,2),k1_nat_1(C,1)) ) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,1),k1_nat_1(C,2)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,2),k1_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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),D,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,1),k1_nat_1(C,1))),k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,1),C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,2),k1_nat_1(C,1))),k7_xcmplx_0(1,2))),k3_topreal1(2,A)) ) ) ) ) ) ) ) )).
fof(t12_goboard9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_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)) ) ) ) )).
fof(t12_gobrd11,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( v1_xreal_0(B) => ( A = a_1_1_gobrd11(B) => v4_pre_topc(A,k15_euclid(2)) ) ) ) )).
fof(t12_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [F] : ( ( ~ v3_relat_1(F) & v1_matrix_0(F) & v1_goboard1(F) & v2_goboard1(F) & v3_goboard1(F) & v4_goboard1(F) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_tarski(k9_matrix_0(E),k9_matrix_0(F)) & r2_hidden(k4_tarski(A,C),k2_matrix_0(E)) & r2_hidden(k4_tarski(B,D),k2_matrix_0(F)) & k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),F,B,D) ) => r1_tarski(k3_goboard5(F,B,k7_nat_d(D,1)),k3_goboard5(E,A,k7_nat_d(C,1))) ) ) ) ) ) ) ) )).
fof(t12_gobrd14,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(t12_gr_cy_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v15_algstr_0(C) & m1_group_2(C,B) ) => ( r1_group_2(B,C,k6_group_2(B)) | C = B ) ) ) ) ) )).
fof(t12_gr_cy_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ 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] : ( 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) = B ) => ( C = k5_group_4(C,k6_domain_1(u1_struct_0(C),k5_group_1(C,A,D))) <=> k6_nat_d(A,B) = 1 ) ) ) ) ) ) )).
fof(t12_gr_cy_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_gr_cy_3(A) ) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) & v1_gr_cy_3(B) ) => ! [C] : ( v7_ordinal1(C) => ~ ( A != B & C = k3_xcmplx_0(A,B) & ! [D] : ( ( v7_ordinal1(D) & v1_int_2(D) & v2_gr_cy_3(D) ) => ! [E] : ( ( v7_ordinal1(E) & v1_int_2(E) & v2_gr_cy_3(E) ) => k1_euler_1(C) != k3_xcmplx_0(k3_xcmplx_0(4,D),E) ) ) ) ) ) ) )).
fof(t12_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ( ? [C] : ( ~ 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) ) ) ) )).
fof(t12_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( 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) ) ) ) ) ) )).
fof(t12_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t12_graph_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v2_struct_0(D) & l1_graph_1(D) ) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t12_graph_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t12_graphsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v7_graph_1(B,A) & m2_graph_1(B,A) ) => ! [C] : ! [D] : ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( u1_struct_0(A) = k2_xboole_0(C,D) & r2_hidden(E,C) & ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( ( r2_hidden(G,C) & r2_hidden(H,D) ) => ! [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) ) ) ) ) ) )).
fof(t12_grcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( m1_grcat_1(C,A,B) => ? [D] : ( 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) ) ) ) ) )).
fof(t12_grfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( v2_funct_1(A) => v2_funct_1(k3_xboole_0(A,B)) ) ) ) )).
fof(t12_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ( m1_group_6(C,A,B) => m1_group_6(k1_grnilp_1(A,C,B),A,B) ) ) ) ) )).
fof(t12_groeb_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( v9_rewrite1(k3_polyred(A,B,C,D)) => v7_rewrite1(k3_polyred(A,B,C,D)) ) ) ) ) ) )).
fof(t12_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v1_vectsp_1(B) & v4_rlvect_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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,k5_polynom1(A,B,C,D)),k5_polynom1(A,B,k1_polyred(A,E,B,C),k1_polyred(A,E,B,D))) ) ) ) ) ) )).
fof(t12_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(D,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),k7_polynom1(A,B,C,D),k8_polynom1(A,B)) => r2_funct_2(k15_pre_poly(A),u1_struct_0(B),C,D) ) ) ) ) ) )).
fof(t12_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k6_algstr_0(A,D,B) = C <=> B = k6_algstr_0(A,k2_group_1(A,D),C) ) ) ) ) ) )).
fof(t12_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t12_group_12,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v5_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( m2_subset_1(D,k4_ordinal1,k2_finseq_1(A)) => m1_group_2(k1_group_7(k2_finseq_1(A),C,D),B) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ? [E] : ( m2_finseq_1(E,u1_struct_0(B)) & k3_finseq_1(E) = A & ! [F] : ( m2_subset_1(F,k4_ordinal1,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] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(B)) => ( ( k3_finseq_1(D) = A & ! [F] : ( m2_subset_1(F,k4_ordinal1,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] : ( m2_subset_1(F,k4_ordinal1,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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k2_group_7(k2_finseq_1(A),C))) => ? [F] : ( m2_finseq_1(F,u1_struct_0(B)) & k3_finseq_1(F) = A & ! [G] : ( m2_subset_1(G,k4_ordinal1,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) ) ) ) ) ) ) ) ) )).
fof(t12_group_14,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v1_prvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k20_prvect_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k20_prvect_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k20_prvect_1(A))) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) & v1_finseq_1(G) ) => ( ( B = E & C = F & D = G ) => ( D = k3_rlvect_1(k20_prvect_1(A),B,C) <=> ! [H] : ( m2_subset_1(H,k4_ordinal1,k4_finseq_1(k15_prvect_1(A))) => k1_funct_1(G,H) = k1_binop_1(u1_algstr_0(k16_prvect_1(A,H)),k1_funct_1(E,H),k1_funct_1(F,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t12_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t12_group_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( 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) ) ) ) )).
fof(t12_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t12_group_6,axiom,( ! [A] : ( ( ~ 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 ) )).
fof(t12_group_7,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t12_group_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v4_group_1(B,A) => v4_group_1(k2_group_1(A,B),A) ) ) ) )).
fof(t12_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( m1_group_9(D,A,B) => ( r1_tarski(u1_struct_0(C),u1_struct_0(D)) => m1_group_9(C,A,D) ) ) ) ) )).
fof(t12_groupp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ~ ( k7_group_1(B) != k7_group_1(A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_struct_0(B,C) ) ) ) ) )).
fof(t12_grsolv_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v15_algstr_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( v15_algstr_0(D) & m1_group_2(D,A) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t12_hahnban,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t12_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(t12_hallmar1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ! [E] : 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))) ) ) ) )).
fof(t12_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t12_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( v7_ordinal1(C) & ~ v1_abian(C) ) => ! [D] : ( ( v7_ordinal1(D) & ~ v1_abian(D) ) => ! [E] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t12_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( ~ v1_xboole_0(C) => ( ~ v1_henmodel(B,A) => ! [D] : ( m1_valuat_1(D,A,C) => ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ~ r6_calcul_1(A,B,C,D,E) ) ) ) ) ) ) )).
fof(t12_hermitan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ( k4_complex1(A) = k5_numbers => A = k2_complfld(A) ) ) )).
fof(t12_hessenbe,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( ~ r1_collsp(A,B,C,E) & r1_collsp(A,B,C,D) & r1_collsp(A,E,F,D) & D != F & C != D & r1_collsp(A,D,C,F) ) ) ) ) ) ) ) )).
fof(t12_heyting1,axiom,( ! [A] : 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)) )).
fof(t12_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( 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)) ) ) )).
fof(t12_heyting3,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k1_heyting3(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_heyting3(A,B))) => ( r3_orders_2(k1_heyting3(A,B),C,D) <=> ! [E] : ~ ( r2_hidden(E,C) & ! [F] : ~ ( r2_hidden(F,D) & r1_tarski(F,E) ) ) ) ) ) )).
fof(t12_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(A,B) => k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k18_sin_cos,B),2),A) = k4_xcmplx_0(k1_funct_1(k18_sin_cos,A)) ) ) ) )).
fof(t12_hilbasis,axiom,( ! [A] : ! [B] : ( ( ~ v7_struct_0(B) & v1_group_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,A) => ( k4_polynom1(A,B,k3_hilbasis(A,C,B),k2_hilbasis(A,C)) = k1_group_1(B) & ! [D] : ( ( 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) => k4_polynom1(A,B,k3_hilbasis(A,C,B),D) = k4_struct_0(B) ) ) ) ) ) )).
fof(t12_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => ( v6_hilbert1(A) <=> k5_hilbert1(A) = A ) ) )).
fof(t12_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( k1_funct_1(A,1) = 2 => v1_hilbert2(A) ) ) )).
fof(t12_hilbert3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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) ) )).
fof(t12_hurwitz,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r2_funct_2(k4_ordinal1,u1_struct_0(A),k5_vfunct_1(k4_ordinal1,A,k11_polynom3(A,B,C)),k11_polynom3(A,k5_vfunct_1(k4_ordinal1,A,B),C)) & r2_funct_2(k4_ordinal1,u1_struct_0(A),k5_vfunct_1(k4_ordinal1,A,k11_polynom3(A,B,C)),k11_polynom3(A,B,k5_vfunct_1(k4_ordinal1,A,C))) ) ) ) ) )).
fof(t12_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k4_idea_1(C,A,B) = k4_idea_1(C,B,A) ) ) ) )).
fof(t12_ideal_1,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(t12_incproj,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u2_incsp_1(k3_incproj(A))) => ? [C] : ( m1_subset_1(C,u1_incsp_1(k3_incproj(A))) & ? [D] : ( m1_subset_1(D,u1_incsp_1(k3_incproj(A))) & ? [E] : ( 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) ) ) ) ) ) )).
fof(t12_incsp_1,axiom,( ! [A] : ( l2_incsp_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_incsp_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_incsp_1(A))) => ( ( r1_tarski(C,B) & v3_incsp_1(B,A) ) => v3_incsp_1(C,A) ) ) ) ) )).
fof(t12_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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] : ( 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) ) ) ) )).
fof(t12_instalg1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t12_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( r2_int_1(A,k5_numbers,A) & r2_int_1(k5_numbers,A,A) ) ) )).
fof(t12_int_2,axiom,( ! [A] : ( v1_int_1(A) => ( r1_int_1(A,k5_numbers) & r1_int_1(1,A) & r1_int_1(k4_xcmplx_0(1),A) ) ) )).
fof(t12_int_4,axiom,( ! [A] : ( v1_int_1(A) => k5_numbers = k5_int_1(k5_numbers,A) ) )).
fof(t12_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r1_int_1(A,B) => k3_int_2(A,B) = k1_int_2(A) ) ) ) )).
fof(t12_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(B,k4_finseq_1(A)) & r2_hidden(C,k4_finseq_1(A)) & C != B & k1_funct_1(A,C) != k5_numbers & ! [D] : ( 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)) ) ) ) ) ) )).
fof(t12_int_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k8_newton) & v1_funct_1(A) & v1_partfun1(A,k8_newton) & v4_valued_0(A) & v2_pre_poly(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k8_newton) & v1_funct_1(B) & v1_partfun1(B,k8_newton) & v4_valued_0(B) & v2_pre_poly(B) ) => ( ( v1_int_7(A) & v1_int_7(B) & r1_xboole_0(k22_pre_poly(k8_newton,A),k22_pre_poly(k8_newton,B)) ) => r1_int_2(k8_nat_3(k8_newton,A),k8_nat_3(k8_newton,B)) ) ) ) )).
fof(t12_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( ( r1_int_2(A,B) & k3_finseq_1(C) = k3_pepin(A,B) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,C)) => k1_funct_1(C,D) = k1_newton(A,k7_nat_d(D,1)) ) ) ) => ( r1_xxreal_0(B,1) | ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( r2_hidden(D,k1_relset_1(k4_ordinal1,C)) & r2_hidden(E,k1_relset_1(k4_ordinal1,C)) & D != E & r2_int_1(k1_funct_1(C,D),k1_funct_1(C,E),B) ) ) ) ) ) ) ) ) )).
fof(t12_integr11,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( k3_xcmplx_0(A,k2_xcmplx_0(C,1)) != k5_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(k2_xcmplx_0(C,1))),k7_xcmplx_0(1,k3_xcmplx_0(A,k2_xcmplx_0(C,1)))),k1_numbers) & ! [D] : ( v1_xreal_0(D) => k1_funct_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(k2_xcmplx_0(C,1))),k7_xcmplx_0(1,k3_xcmplx_0(A,k2_xcmplx_0(C,1)))),k1_numbers),D) = k3_prepower(k2_xcmplx_0(k3_xcmplx_0(A,D),B),C) ) ) ) ) ) ) )).
fof(t12_integr12,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,C) & r1_xxreal_0(D,k5_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) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k18_sin_cos)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k18_sin_cos)),k3_seq_4(A))) ) ) ) ) )).
fof(t12_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k22_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k16_sin_cos))) & r1_tarski(C,k1_relset_1(k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k18_sin_cos))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k18_sin_cos),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k18_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t12_integr14,axiom,( ! [A] : ( ( 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,k27_sin_cos,k1_fdiff_9))) => ( r2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k1_fdiff_9)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k1_fdiff_9)),A),B) = k6_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B))),k1_funct_1(k18_sin_cos,B)),k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k27_sin_cos,B),k1_funct_1(k16_sin_cos,B)),k1_square_1(k1_funct_1(k18_sin_cos,B)))) ) ) ) ) ) )).
fof(t12_integr15,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) & ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_integra1(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(B)))) ) => ! [F] : ( m4_integr15(F,A,B,C,E) => ( ( v2_comseq_2(k2_integra3(B,E)) & k1_seq_2(k2_integra3(B,E)) = k5_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 ) ) ) ) ) ) ) ) ) ) )).
fof(t12_integr16,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k2_numbers))) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t12_integr18,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ 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] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,u1_struct_0(D)))) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t12_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ( ( r1_xxreal_0(B,D) & r1_xxreal_0(D,E) & r1_xxreal_0(E,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)) ) => ( r1_integr15(A,k3_integra5(D,E),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(D,E)),A) ) ) ) ) ) ) ) ) )).
fof(t12_integra1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t12_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( ( v3_xxreal_2(B) & r1_xxreal_0(A,k5_numbers) ) => v4_xxreal_2(k1_integra2(B,A)) ) ) ) )).
fof(t12_integra3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v1_xboole_0(D) & v2_measure5(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ! [E] : ( 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_funct_1(k3_finseq_6(k1_numbers,E,B,C),1),A) & ! [F] : ( ( ~ v1_xboole_0(F) & v2_measure5(F) & m1_subset_1(F,k1_zfmisc_1(k1_numbers)) ) => ~ ( A = k3_seq_4(F) & k2_seq_4(F) = k1_funct_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) ) ) ) ) ) ) ) ) )).
fof(t12_integra4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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_comseq_2(k2_partfun1(A,k1_numbers,B,A)) => ( v3_integra1(B,A) <=> ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_integra1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) ) => ( ( v2_comseq_2(k2_integra3(A,C)) & k1_seq_2(k2_integra3(A,C)) = k5_numbers ) => k6_xcmplx_0(k1_seq_2(k3_integra2(A,B,C)),k1_seq_2(k4_integra2(A,B,C))) = k5_numbers ) ) ) ) ) ) )).
fof(t12_integra5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( 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),k6_xcmplx_0(k1_funct_1(C,k2_seq_4(A)),k1_funct_1(C,k3_seq_4(A)))) & r1_xxreal_0(k6_xcmplx_0(k1_funct_1(C,k2_seq_4(A)),k1_funct_1(C,k3_seq_4(A))),k6_integra1(A,k1_integra5(k2_fdiff_1(C,B),A),D)) ) ) ) ) ) )).
fof(t12_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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)) = k2_xcmplx_0(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)) = k6_xcmplx_0(k4_integra5(A,B,C),k4_integra5(A,B,D)) ) ) ) ) ) ) )).
fof(t12_integra7,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_integra7(A,D,B) & r1_integra7(A,E,C) ) => ( r1_integra7(A,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,D,E),k3_valued_1(k1_numbers,k1_numbers,k1_numbers,B,C)) & r1_integra7(A,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,D,E),k47_valued_1(k1_numbers,k1_numbers,k1_numbers,B,C)) ) ) ) ) ) ) )).
fof(t12_integra8,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k5_numbers,k19_sin_cos(k7_xcmplx_0(A,2))) => k19_sin_cos(k7_xcmplx_0(A,2)) = k3_square_1(k7_xcmplx_0(k2_xcmplx_0(1,k19_sin_cos(A)),2)) ) ) )).
fof(t12_integra9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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)) = k6_xcmplx_0(k1_funct_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),k18_sin_cos)),k2_seq_4(A)),k1_funct_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),k18_sin_cos)),k3_seq_4(A))) ) ) ) )).
fof(t12_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t12_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => r1_tarski(A,k7_intpro_1(A)) ) )).
fof(t12_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t12_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u4_struct_0(A)) => ! [H] : ( 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(k8_cat_2(A,B,G,H),k2_cat_1(k6_cat_2(A,B),k7_cat_2(A,B,C,E),k7_cat_2(A,B,D,F))) ) ) ) ) ) ) ) ) ) )).
fof(t12_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k1_tops_1(A,k2_pre_topc(A,k1_struct_0(A))) = k1_struct_0(A) ) )).
fof(t12_jgraph_1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v3_topreal1(A) => v1_goboard5(A) ) ) )).
fof(t12_jgraph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) => ! [F] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_jgraph_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( 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] : ( 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) = k7_xcmplx_0(k18_euclid(C),k3_square_1(k2_xcmplx_0(1,k1_square_1(k7_xcmplx_0(k18_euclid(C),k17_euclid(C)))))) ) ) & ! [C] : ( 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) = k5_numbers ) ) ) => v5_pre_topc(B,k1_pre_topc(k15_euclid(2),A),k3_topmetr) ) ) ) )).
fof(t12_jgraph_4,axiom,( ! [A] : ( v7_ordinal1(A) => v5_pre_topc(k1_jgraph_4(A),k15_euclid(A),k3_topmetr) ) )).
fof(t12_jgraph_5,axiom,( ! [A] : ( ( 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] : ( ( 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,k5_numbers) = k1_funct_1(A,1) & k1_funct_1(B,1) = k1_funct_1(A,k5_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) ) ) ) ) )).
fof(t12_jgraph_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t12_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t12_jordan,axiom,( ! [A] : ( ( 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)) ) )).
fof(t12_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t12_jordan10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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,k2_jordan9(B,A)))) ) ) )).
fof(t12_jordan11,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( 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)) ) ) )).
fof(t12_jordan12,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r2_jordan12(2,A,B) => ! [C] : ( v7_ordinal1(C) => v1_finset_1(k9_subset_1(u1_struct_0(k15_euclid(2)),k3_topreal1(2,A),k2_topreal1(2,B,C))) ) ) ) ) )).
fof(t12_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( r1_jordan1h(A,B) => r1_tarski(A,k2_jordan2c(2,k3_topreal1(2,k1_jordan13(A,B)))) ) ) ) )).
fof(t12_jordan16,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( 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 ) ) ) ) ) ) ) )).
fof(t12_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ( r1_jordan17(A,B,C,D,E) => r1_jordan17(A,E,B,C,D) ) ) ) ) ) ) )).
fof(t12_jordan18,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( 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)) ) ) ) )).
fof(t12_jordan19,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D)),k3_topreal1(2,k1_jordan1e(B,A))) = k1_tarski(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D)),k3_topreal1(2,k2_jordan1e(B,A))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D)) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D)),k8_jordan6(B)) ) ) ) ) ) ) )).
fof(t12_jordan1b,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t12_jordan1c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( 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] : ( v1_int_1(D) => ( ( r2_hidden(B,k1_jordan2c(2,C)) & D = k1_int_1(k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k18_euclid(B),k9_pscomp_1(C)),k6_xcmplx_0(k7_pscomp_1(C),k9_pscomp_1(C))),k1_newton(2,A)),2)) ) => ( ~ r1_xxreal_0(D,1) & r1_xxreal_0(k2_xcmplx_0(D,1),k1_matrix_0(k1_jordan8(C,A))) ) ) ) ) ) ) )).
fof(t12_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & ~ r1_xxreal_0(k3_finseq_1(k2_jordan9(B,A)),C) & r2_hidden(k22_pscomp_1(B),k4_goboard5(k2_jordan9(B,A),C)) ) ) ) )).
fof(t12_jordan1e,axiom,( ! [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] : ( v7_ordinal1(B) => k3_topreal1(2,k2_jordan9(A,B)) = k3_topreal1(2,k4_graph_2(u1_struct_0(k15_euclid(2)),k1_jordan1e(A,B),k2_jordan1e(A,B))) ) ) )).
fof(t12_jordan1f,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => r1_goboard1(u1_struct_0(k15_euclid(2)),k2_jordan1e(A,B),k1_jordan8(A,B)) ) ) )).
fof(t12_jordan1g,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t12_jordan1h,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k2_finseq_1(k1_matrix_0(B))) => r1_tarski(k2_relset_1(A,k8_matrix_0(A,B,C)),k2_jordan1h(A,B)) ) ) ) ) )).
fof(t12_jordan1i,axiom,( ! [A] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(t12_jordan1j,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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)))) ) => ( r2_hidden(k24_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))),k10_xtuple_0(k2_jordan1e(B,A))) & r2_hidden(k24_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))),k3_topreal1(2,k2_jordan1e(B,A))) ) ) ) )).
fof(t12_jordan1k,axiom,( ! [A] : ( ( ~ 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] : ( ( v2_compts_1(B,k3_pcomps_1(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( ( 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) = k5_numbers ) ) ) ) )).
fof(t12_jordan20,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) => ! [B] : ( v1_xreal_0(B) => ( A = k4_rcomp_1(B,1) => v3_pre_topc(A,k5_topmetr) ) ) ) )).
fof(t12_jordan21,axiom,( ! [A] : ( ( 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(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)),2))))) ) )).
fof(t12_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ~ ( ~ r1_xxreal_0(E,B) & ~ r1_xxreal_0(C,k1_topreal6(2,k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,E),1,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,E),1,2))) & ~ r1_xxreal_0(D,k1_topreal6(2,k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,E),1,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,E),2,1))) ) ) ) ) ) ) ) )).
fof(t12_jordan23,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( ( v2_jordan23(B) & v1_finseq_6(B,A) ) => ! [C] : ( m1_subset_1(C,A) => v2_jordan23(k1_finseq_6(A,B,C)) ) ) ) ) )).
fof(t12_jordan24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)))))) ) ) ) ) ) )).
fof(t12_jordan2b,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( C = a_3_0_jordan2b(A,B,D) & r2_hidden(D,k2_finseq_1(A)) ) => v3_pre_topc(C,k15_euclid(A)) ) ) ) ) ) )).
fof(t12_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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))) ) ) )).
fof(t12_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) | k1_nat_1(k1_jordan3(A,B),1) = C ) ) ) ) ) )).
fof(t12_jordan4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( 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,k1_nat_1(k7_nat_d(C,D),1)) ) => k1_funct_1(k3_finseq_6(A,B,C,D),E) = k1_funct_1(B,k1_nat_1(k7_nat_d(C,E),1)) ) ) ) ) ) ) )).
fof(t12_jordan5a,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_numbers)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t12_jordan5b,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t12_jordan5c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t12_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( 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))) ) ) ) ) )).
fof(t12_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( r1_topreal1(k15_euclid(2),B,C,A) & ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(D,A) & k17_euclid(D) = k7_xcmplx_0(k2_xcmplx_0(k17_euclid(B),k17_euclid(C)),2) ) ) ) ) ) ) )).
fof(t12_jordan7,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t12_jordan8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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_0(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) ) ) ) ) )).
fof(t12_jordan9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( 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] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(1,D) & r1_xxreal_0(D,k1_matrix_0(B)) & ! [E] : ( 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_0(u1_struct_0(k15_euclid(2)),B,1,D)) ) ) ) ) ) ) ) ) )).
fof(t12_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t12_knaster,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t12_kolmog01,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( m2_prob_1(D,A,C) => ! [E] : ( m1_kolmog01(E,B,A,C) => ! [F] : ( ( ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(B)) ) => ! [G] : ( ( ~ v1_xboole_0(G) & m1_subset_1(G,k1_zfmisc_1(B)) ) => ( ( r2_kolmog01(A,C,D,B,E) & r1_subset_1(F,G) ) => ! [H] : ( m1_subset_1(H,k1_zfmisc_1(A)) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(A)) => ( ( r2_hidden(H,k7_kolmog01(A,C,B,F,E)) & r2_hidden(I,k7_kolmog01(A,C,B,G,E)) ) => k1_funct_1(D,k3_finsub_1(k1_zfmisc_1(A),H,I)) = k3_xcmplx_0(k1_funct_1(D,H),k1_funct_1(D,I)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ! [E] : ( v7_ordinal1(E) => k1_funct_1(D,E) = k2_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) => r1_tarski(k4_subset_1(A,k3_kurato_0(A,B),k3_kurato_0(A,C)),k3_kurato_0(A,D)) ) ) ) ) )).
fof(t12_kurato_1,axiom,( 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) )).
fof(t12_kurato_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( m2_valued_0(C,k9_setfam_1(u1_struct_0(A)),B) & ! [E] : ( v7_ordinal1(E) => k1_funct_1(B,E) = D ) ) => r2_funct_2(k4_ordinal1,k9_setfam_1(u1_struct_0(A)),C,B) ) ) ) ) ) )).
fof(t12_lang1,axiom,( ! [A] : ! [B] : ( A != B => k1_lang1(k7_lang1(A,B)) = k1_tarski(B) ) )).
fof(t12_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t12_latsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( r2_hidden(C,k3_xboole_0(u1_struct_0(A),u1_struct_0(B))) => m1_subset_1(C,u1_struct_0(A)) ) ) ) )).
fof(t12_lattice2,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(t12_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v3_lattice3(A) => ( v1_lattice3(A) & v2_lattice3(A) ) ) ) )).
fof(t12_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v13_lattices(B) & l3_lattices(B) ) => ! [C] : ( m1_lattice4(C,B,A) => ( v2_funct_2(C,u1_struct_0(A)) => ( v13_lattices(A) & r3_lattice4(B,A,C) ) ) ) ) ) )).
fof(t12_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ! [D] : ( v1_relat_1(D) => ! [E] : ( v1_relat_1(E) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ~ ( r1_xxreal_0(F,G) & r1_relat_2(D,A) & r1_relat_2(E,A) & ? [H] : ( ~ v1_xboole_0(H) & m2_finseq_1(H,A) & k3_finseq_1(H) = F & r1_lattice5(A,H,B,C,D,E) ) & ! [H] : ( ( ~ v1_xboole_0(H) & m2_finseq_1(H,A) ) => ~ ( k3_finseq_1(H) = G & r1_lattice5(A,H,B,C,D,E) ) ) ) ) ) ) ) ) )).
fof(t12_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v3_lattice6(B,A) => ( r1_lattice6(A,k3_lattice6(A,B),B) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_lattice6(A,C,B) => C = k3_lattice6(A,B) ) ) ) ) ) ) )).
fof(t12_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t12_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_lattices(A,k5_lattices(A),B) = B ) ) )).
fof(t12_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( ( v4_lexbfs(B,A) & m1_lexbfs(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t12_lfuzzy_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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] : ( m1_subset_1(C,u1_struct_0(k4_yellow_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_yellow_1(A,B))) => ! [E] : ( m1_subset_1(E,A) => k4_waybel_3(A,B,k10_lattice3(k4_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)) ) ) ) ) ) ) )).
fof(t12_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t12_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_limfunc1(A) & v1_seq_2(B) ) => v2_limfunc1(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) ) ) )).
fof(t12_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t12_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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) ) ) ) ) )).
fof(t12_lmod_5,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( ( 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 ) ) ) ) ) ) )).
fof(t12_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t12_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_subset_1(D,k7_lmod_7(A,B,C)) => ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & D = k8_lmod_7(A,B,C,E) ) ) ) ) ) )).
fof(t12_lopban_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(k5_lopban_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_lopban_1(A,B))) => ! [E] : ( v1_xreal_0(E) => ( D = k1_rlvect_1(k5_lopban_1(A,B),C,E) <=> ! [F] : ( m1_subset_1(F,A) => k6_lopban_1(A,B,D,F) = k1_rlvect_1(B,k6_lopban_1(A,B,C,F),E) ) ) ) ) ) ) ) )).
fof(t12_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(k8_lopban_1(A,A)),k10_lopban_1(A,A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(k8_lopban_1(A,A)),k10_lopban_1(A,A)) => ! [D] : ( v1_xreal_0(D) => k4_lopban_2(A,k3_lopban_2(A,C,B),D) = k3_lopban_2(A,C,k4_lopban_2(A,B,D)) ) ) ) ) )).
fof(t12_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k2_normsp_0(A,k9_nat_1(u1_struct_0(A),B,D)),k9_nat_1(k1_numbers,C,D)) ) & v2_comseq_2(C) & k1_seq_2(C) = k5_numbers ) => ( v3_normsp_1(B,A) & k6_normsp_1(A,B) = k4_struct_0(A) ) ) ) ) ) )).
fof(t12_lopban_6,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t12_lopban_7,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ( v1_lopban_7(C,A,B) <=> ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( r1_tarski(k2_relset_1(u1_struct_0(A),D),k1_relset_1(u1_struct_0(A),C)) & v3_normsp_1(D,A) & v3_normsp_1(k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),D,C),B) ) => ( r2_hidden(k6_normsp_1(A,D),k1_relset_1(u1_struct_0(A),C)) & k6_normsp_1(B,k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),D,C)) = k1_funct_1(C,k6_normsp_1(A,D)) ) ) ) ) ) ) ) )).
fof(t12_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => u1_struct_0(k6_lopclset(A)) = k1_lopclset(A) ) )).
fof(t12_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_series_1(k1_lp_space(B,A)) & k2_power(k4_series_1(k1_lp_space(B,A)),k7_xcmplx_0(1,A)) = k5_numbers ) => ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,B,C) = k5_numbers ) ) ) ) ) )).
fof(t12_lpspacc1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_rfunct_3(D,C,k2_numbers,k3_rfunct_3(C,k2_numbers)) => k1_binop_1(k8_lpspacc1(C),A,k1_binop_1(k8_lpspacc1(C),B,D)) = k1_binop_1(k8_lpspacc1(C),k3_xcmplx_0(A,B),D) ) ) ) ) )).
fof(t12_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_rfunct_3(B,A,k1_numbers,k3_rfunct_3(A,k1_numbers)) => ! [C] : ( 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)) ) ) ) )).
fof(t12_lpspace2,axiom,( ! [A] : ( ( v2_xxreal_0(A) & v1_xreal_0(A) ) => ! [B] : ( ~ v1_xboole_0(B) => r2_relset_1(B,k1_numbers,k2_mesfun6c(A,B,k8_lpspace1(B,k5_numbers)),k8_lpspace1(B,k5_numbers)) ) ) )).
fof(t12_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => ( k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(D),k1_domain_1(k4_ordinal1,k1_hilbert1,C,k8_ltlaxio1(A,B))) = 1 <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(D),k1_domain_1(k4_ordinal1,k1_hilbert1,k1_nat_1(C,E),B)) = 1 & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ~ r1_xxreal_0(E,F) => k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(D),k1_domain_1(k4_ordinal1,k1_hilbert1,k1_nat_1(C,F),A)) = 1 ) ) ) ) ) ) ) ) )).
fof(t12_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_xxreal_0(A,C) => k1_funct_1(k2_ltlaxio2(B),A) = k1_funct_1(k2_ltlaxio2(k17_finseq_1(k1_hilbert1,C,B)),A) ) ) ) ) )).
fof(t12_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => r1_tarski(k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,A),k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,k1_ltlaxio1(A))) ) )).
fof(t12_ltlaxio4,axiom,( r2_relset_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1),k4_ltlaxio4(k1_subset_1(k1_hilbert1)),k6_domain_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)),k11_ltlaxio3(k6_finseq_1(k1_hilbert1),k6_finseq_1(k1_hilbert1)))) )).
fof(t12_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) )).
fof(t12_margrel1,axiom,( ! [A] : ( v1_xboolean(A) => k4_xboolean(k7_margrel1,A) = k7_margrel1 ) )).
fof(t12_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => k6_rusub_4(A,B,C) = k6_rusub_4(A,C,B) ) ) ) )).
fof(t12_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( v1_matrix10(B) & v2_matrix10(C) ) => v1_matrix10(k5_matrix10(A,B,C)) ) ) ) ) )).
fof(t12_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_matrix_2(C,k3_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) ) ) ) ) )).
fof(t12_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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(B,k4_finseq_1(k3_matrix_1(D,C))) & r2_hidden(A,k4_finseq_1(k3_matrix_1(D,C))) ) => ( v1_matrix_6(k1_matrix12(C,C,D,k3_matrix_1(D,C),B,A),C,D) & k1_matrix_6(C,D,k1_matrix12(C,C,D,k3_matrix_1(D,C),B,A)) = k1_matrix12(C,C,D,k3_matrix_1(D,C),B,A) ) ) ) ) ) ) )).
fof(t12_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ! [F] : ( 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_0(u1_struct_0(B),C,E,F) = k4_struct_0(B) ) ) ) ) => ( v1_matrix_0(k4_matrix11(A,A,u1_struct_0(B),D,C)) & v2_matrix_0(k4_matrix11(A,A,u1_struct_0(B),D,C),u1_struct_0(B),A,A) & v1_matrix_2(k4_matrix11(A,A,u1_struct_0(B),D,C),A,B) & m2_finseq_1(k4_matrix11(A,A,u1_struct_0(B),D,C),k3_finseq_2(u1_struct_0(B))) ) ) ) ) ) ) )).
fof(t12_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t12_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ( ( r1_tarski(C,k2_finseq_1(k1_matrix_0(B))) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k7_subset_1(k4_ordinal1,k2_finseq_1(k1_matrix_0(B)),C)) => k8_matrix_0(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)) ) ) ) ) )).
fof(t12_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix16(C,u1_struct_0(B)) & v1_matrix16(D,u1_struct_0(B)) ) => v1_matrix16(k1_matrix_4(B,C,D),u1_struct_0(B)) ) ) ) ) ) )).
fof(t12_matrix17,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t12_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ! [D] : ( m2_finseq_1(D,B) => ( ( k3_finseq_1(C) = A & k3_finseq_1(D) = A ) => ( v1_matrix_0(k2_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B)),C,D)) & v2_matrix_0(k2_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B)),C,D),B,2,A) & m2_finseq_1(k2_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B)),C,D),k3_finseq_2(B)) ) ) ) ) ) ) )).
fof(t12_matrix_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => ( ( r2_hidden(C,k4_finseq_1(B)) & ! [D] : ( 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) ) ) ) ) )).
fof(t12_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(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)) ) ) ) ) )).
fof(t12_matrix_5,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_matrix_0(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)) ) ) ) ) )).
fof(t12_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r2_matrix_6(A,B,D,C) => ( r1_xxreal_0(A,k5_numbers) | r2_matrix_6(A,B,k4_matrix_0(u1_struct_0(B),C),k4_matrix_0(u1_struct_0(B),D)) ) ) ) ) ) ) )).
fof(t12_matrix_7,axiom,( ! [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] : ( ( v1_matrix_0(B) & v2_matrix_0(B,u1_struct_0(A),2,2) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => k12_matrix_3(2,A,B) = k5_algstr_0(A,k8_group_1(A,k3_matrix_0(u1_struct_0(A),B,1,1),k3_matrix_0(u1_struct_0(A),B,2,2)),k8_group_1(A,k3_matrix_0(u1_struct_0(A),B,1,2),k3_matrix_0(u1_struct_0(A),B,2,1))) ) ) )).
fof(t12_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_8(C,A,B) & v1_matrix_8(D,A,B) & r1_matrix_6(A,B,C,D) ) => v1_matrix_8(k4_matrix_3(B,k4_matrix_0(u1_struct_0(B),C),k4_matrix_0(u1_struct_0(B),D)),A,B) ) ) ) ) ) )).
fof(t12_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k2_numbers)) ) => ( k3_finseq_1(k5_matrix_5(A,B)) = k3_finseq_1(A) & k1_matrix_0(k5_matrix_5(A,B)) = k1_matrix_0(A) ) ) ) )).
fof(t12_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_matrixj1(k1_xboole_0,A) & m2_finseq_1(k1_xboole_0,k3_finseq_2(k3_finseq_2(A))) ) ) )).
fof(t12_matrixj2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_matrixj2(D,A,C) => 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),B))),A,k3_rlvect_1(A,C,B)) ) ) ) ) )).
fof(t12_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( 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) ) ) ) ) )).
fof(t12_matrixr2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => k7_matrixr1(k2_xcmplx_0(A,B),C) = k3_matrixr1(k7_matrixr1(A,C),k7_matrixr1(B,C)) ) ) ) )).
fof(t12_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t12_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) )).
fof(t12_matroid0,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r1_tarski(D,C) => ! [E] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t12_matrprob,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v1_matrix_0(C) ) => ( r2_hidden(k4_tarski(A,B),k2_matrix_0(C)) <=> ( r2_hidden(A,k2_finseq_1(k3_finseq_1(C))) & r2_hidden(B,k2_finseq_1(k1_matrix_0(C))) ) ) ) ) ) )).
fof(t12_matrtop1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ? [D] : ( m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) & 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] : ( v7_ordinal1(E) => ( ~ r1_xxreal_0(E,k5_numbers) => ( r2_hidden(E,D) <=> r2_hidden(k2_xcmplx_0(E,k3_finseq_1(B)),k9_subset_1(k4_ordinal1,A,k4_finseq_1(k7_finseq_1(B,C)))) ) ) ) ) ) ) )).
fof(t12_matrtop3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_vectsp_1)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_vectsp_1)) => ( ( C = k19_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,k15_matrix_0(u1_struct_0(k2_vectsp_1),C,D,k4_algstr_0(k2_vectsp_1,D),C),k3_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,k15_matrix_0(u1_struct_0(k2_vectsp_1),C,D,k4_algstr_0(k2_vectsp_1,D),C),k3_matrix_1(k2_vectsp_1,B)))) = k5_struct_0(k2_vectsp_1) ) ) ) ) ) )).
fof(t12_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t12_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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))) ) ) )).
fof(t12_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r2_hidden(D,k2_zfmisc_1(k1_tarski(A),k2_tarski(B,C))) => ( k1_xtuple_0(D) = A & ( k2_xtuple_0(D) = B | k2_xtuple_0(D) = C ) ) ) )).
fof(t12_measure1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( m1_measure1(E,A,B,C) => ( r1_tarski(D,E) => m1_measure1(D,A,B,C) ) ) ) ) ) )).
fof(t12_measure2,axiom,( ! [A] : ! [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))) ) => ! [C] : ( m1_measure2(C,A,B) => ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) & C = k4_measure1(A,B,D) ) ) ) )).
fof(t12_measure3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ( ! [E] : ( m1_subset_1(E,k4_ordinal1) => r1_tarski(k9_nat_1(B,D,k1_nat_1(E,1)),k9_nat_1(B,D,E)) ) => ( r1_xxreal_0(k1_supinf_1,k12_supinf_2(C,k9_nat_1(B,D,k5_numbers))) | k12_supinf_2(C,k1_measure2(A,B,k1_measure3(A,B,D))) = k7_supinf_2(k17_supinf_2(k1_partfun1(k4_ordinal1,B,B,k6_numbers,D,C))) ) ) ) ) ) )).
fof(t12_measure5,axiom,( ! [A] : ( ( v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t12_measure6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xxreal_0(B) => ( ? [C] : ( v1_xxreal_0(C) & r1_xxreal_0(C,B) & A = k2_rcomp_1(C,B) ) => B = k8_supinf_2(A) ) ) ) )).
fof(t12_measure7,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( m1_measure7(B,A) => v6_supinf_2(k3_measure7(A,B)) ) ) )).
fof(t12_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t12_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => ( r2_hidden(k4_xcmplx_0(B),A) <=> r2_hidden(B,k5_member_1(A)) ) ) ) )).
fof(t12_membered,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_membered(A) ) => ? [B] : ( v7_ordinal1(B) & r2_hidden(B,A) ) ) )).
fof(t12_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => r1_tarski(k6_memstr_0(A,B,C),C) ) ) ) )).
fof(t12_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t12_mesfun10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( r1_mesfunc5(A,B,C,D) & r1_mesfunc5(A,B,C,E) ) => r1_mesfunc5(A,B,C,k4_mesfunc1(A,D,E)) ) ) ) ) ) ) )).
fof(t12_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t12_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( 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(k4_ordinal1,k10_seqfunc(A,B,C))) ) ) ) ) )).
fof(t12_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( ( v1_mesfunc8(B,A,k1_numbers) & r1_tarski(E,k1_relset_1(A,k4_mesfunc5(A,k1_numbers,B,k5_numbers))) & r2_hidden(D,E) ) => k1_mesfunc9(k3_series_1(k10_seqfunc(A,B,D)),C) = k1_mesfunc9(k10_seqfunc(A,k2_mesfun9c(A,B),D),C) ) ) ) ) ) )).
fof(t12_mesfunc1,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ( ! [B] : ( v1_xreal_0(B) => ~ r1_xxreal_0(A,B) ) => A = k1_supinf_1 ) ) )).
fof(t12_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( m1_subset_1(C,A) => r1_xxreal_0(k1_supinf_2,k12_supinf_2(k1_mesfunc2(A,B),C)) ) ) ) )).
fof(t12_mesfunc3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ~ ( r1_mesfunc2(A,B,C) & ! [D] : ( ( v1_prob_2(D) & m2_finseq_1(D,B) ) => ! [E] : ( m2_finseq_1(E,k6_numbers) => ~ r1_mesfunc3(A,B,C,D,E) ) ) ) ) ) ) )).
fof(t12_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( v6_supinf_2(B) => v3_mesfunc5(B) ) ) ) )).
fof(t12_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( r1_mesfunc6(A,B,C,D) <=> ! [E] : ( v1_xreal_0(E) => r2_hidden(k8_subset_1(A,D,k11_mesfunc1(C,E)),B) ) ) ) ) ) ) )).
fof(t12_mesfunc7,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(k5_numbers,A) => r1_xxreal_0(k5_numbers,k4_mesfunc7(A,B)) ) ) ) )).
fof(t12_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ( ! [C] : ( 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,k6_numbers,k6_mesfunc8(A,B),k1_mesfunc8(A,k4_mesfunc8(A,B))) ) ) ) )).
fof(t12_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( ( ! [F] : ( v7_ordinal1(F) => r2_relset_1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,C,F),k2_partfun1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,B,F),E)) ) & r2_hidden(D,E) ) => ( ( v8_mesfunc5(k3_mesfunc5(A,B,D)) => v8_mesfunc5(k3_mesfunc5(A,C,D)) ) & ( v9_mesfunc5(k3_mesfunc5(A,B,D)) => v9_mesfunc5(k3_mesfunc5(A,C,D)) ) & ( v7_mesfunc5(k3_mesfunc5(A,B,D)) => v7_mesfunc5(k3_mesfunc5(A,C,D)) ) & ( v10_mesfunc5(k3_mesfunc5(A,B,D)) => v10_mesfunc5(k3_mesfunc5(A,C,D)) ) ) ) ) ) ) ) )).
fof(t12_metric_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( l1_metric_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r2_hidden(D,k9_metric_1(B,C,A)) <=> ( ~ v2_struct_0(B) & r1_xxreal_0(k1_metric_1(B,C,D),A) ) ) ) ) ) ) )).
fof(t12_metric_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k1_metric_2(A,B)) <=> C = B ) ) ) ) )).
fof(t12_metric_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(k5_numbers,D) ) => r1_xxreal_0(k3_square_1(k2_xcmplx_0(k1_square_1(k2_xcmplx_0(A,C)),k1_square_1(k2_xcmplx_0(B,D)))),k2_xcmplx_0(k3_square_1(k2_xcmplx_0(k1_square_1(A),k1_square_1(B))),k3_square_1(k2_xcmplx_0(k1_square_1(C),k1_square_1(D))))) ) ) ) ) ) )).
fof(t12_metric_6,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r1_metric_6(A,C,B) <=> ( v2_tbsp_1(C,A) & k1_tbsp_1(A,C) = B ) ) ) ) ) )).
fof(t12_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))))) ) ) ) ) )).
fof(t12_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( v2_mfold_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ? [D] : ( m1_connsp_2(D,B,C) & ? [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) ) ) ) ) ) ) )).
fof(t12_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t12_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_midsp_1(A,B,B,C,D) => C = D ) ) ) ) ) )).
fof(t12_midsp_2,axiom,( ! [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) ) => ! [B] : ( 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)) ) ) )).
fof(t12_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v2_struct_0(C) & v2_midsp_1(C) & l1_midsp_3(C,k1_nat_1(A,2)) ) => ! [D] : ( ( v4_midsp_2(D,C) & l1_midsp_2(D,C) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(u1_midsp_2(C,D))) => ! [F] : ( m2_finseq_2(F,u1_struct_0(u1_midsp_2(C,D)),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(u1_midsp_2(C,D)))) => ( r2_hidden(B,k2_finseq_1(k1_nat_1(A,1))) => ( k1_funct_1(k1_midsp_3(u1_struct_0(u1_midsp_2(C,D)),k1_nat_1(A,1),F,B,E),B) = E & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( r2_hidden(G,k7_subset_1(k4_ordinal1,k4_finseq_1(F),k1_tarski(B))) => k1_funct_1(k1_midsp_3(u1_struct_0(u1_midsp_2(C,D)),k1_nat_1(A,1),F,B,E),G) = k1_funct_1(F,G) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_mmlquer2,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => k1_mmlquer2(k1_mmlquer2(A,B),C) = k1_mmlquer2(A,k1_mmlquer2(B,C)) ) ) ) )).
fof(t12_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [D] : ( v7_ordinal1(D) => k11_mmlquery(A,B,C,D) = k13_mmlquery(A,B,C,k1_nat_1(D,1)) ) ) ) )).
fof(t12_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( m1_mod_2(E,A,C,D) => ! [F] : ( m1_mod_2(F,A,B,C) => ( v2_mod_2(k8_mod_2(A,E,F),A) & m1_mod_2(k8_mod_2(A,E,F),A,B,D) ) ) ) ) ) ) ) )).
fof(t12_mod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t12_mod_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & l1_vectsp_2(D,B) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t12_modal_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ( k8_trees_2(A,k1_modal_1(A)) = k5_numbers => ( k5_card_1(A) = 1 & A = k1_tarski(k1_xboole_0) ) ) ) )).
fof(t12_modcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u4_struct_0(k11_modcat_1(A,B))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t12_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t12_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( k1_funct_1(k3_modelc_2(A),1) = k5_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 ) ) ) )).
fof(t12_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k13_modelc_2(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k13_modelc_2(B))) => ( D = k2_xboole_0(C,k1_tarski(A)) => r1_xxreal_0(k18_modelc_3(B,D),k2_xcmplx_0(k18_modelc_3(B,C),k3_finseq_1(A))) ) ) ) ) ) )).
fof(t12_moebius1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v3_valued_0(B) & v2_pre_poly(B) ) => ( k13_pre_poly(B) = k1_tarski(A) => k2_uproots(k4_ordinal1,B) = k1_funct_1(B,A) ) ) ) )).
fof(t12_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v15_monoid_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k6_algstr_0(A,C,B) = k6_algstr_0(A,D,B) => C = D ) ) ) ) ) ) )).
fof(t12_monoid_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(t12_morph_01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t12_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t12_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( 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] : ( ( 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] : ( v7_ordinal1(G) => ( r2_hidden(G,k1_relset_1(k4_ordinal1,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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_msafree3,axiom,( ! [A] : ( l1_msualg_1(A) => ! [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] : ! [D] : ( ( 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] : ( ~ ( 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 ) ) ) ) )).
fof(t12_msafree4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ( r2_hidden(A,k3_trees_9(B)) => r1_tarski(k3_trees_9(A),k3_trees_9(B)) ) ) ) )).
fof(t12_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => r1_tarski(k7_msafree(A,B,C),k1_msaterm(A,B)) ) ) ) )).
fof(t12_msscyc_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v2_struct_0(C) & ~ v11_struct_0(C) & l1_graph_1(C) ) => ! [D] : ( ( v7_graph_1(D,C) & m1_graph_1(D,C) ) => ! [E] : ( ( 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,k1_nat_1(B,1)) ) ) ) ) ) ) )).
fof(t12_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t12_mssublat,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t12_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msualg_2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & m1_msualg_2(C,A,B) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t12_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( m2_pboole(E,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t12_msualg_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( ( 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] : ( ( 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] : ! [G] : ! [H] : ( ( v1_relat_1(H) & v1_funct_1(H) & v1_finseq_1(H) ) => ! [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),k1_nat_1(k3_finseq_1(H),1))),k2_msualg_4(A,B,D,k7_partfun1(u1_struct_0(A),k1_msualg_1(A,C),k1_nat_1(k3_finseq_1(H),1))),k2_msualg_4(A,B,E,k7_partfun1(u1_struct_0(A),k1_msualg_1(A,C),k1_nat_1(k3_finseq_1(H),1))))) => ! [J] : ( m1_subset_1(J,k3_msualg_1(A,C,B)) => ! [K] : ( 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)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( l3_msualg_1(D,A) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t12_msualg_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m2_nat_lat(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( D = E => ( r3_lattice3(A,D,C) <=> r3_lattice3(B,E,C) ) ) ) ) ) ) ) )).
fof(t12_msualg_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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 ) ) ) ) )).
fof(t12_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( 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) ) ) )).
fof(t12_mycielsk,axiom,( ! [A] : ( ( v8_struct_0(A) & l1_orders_2(A) ) => r1_xxreal_0(k2_dilworth(A),k5_card_1(u1_struct_0(A))) ) )).
fof(t12_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) ) => ( v2_nagata_1(B,A) => v3_nagata_1(B,A) ) ) ) )).
fof(t12_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => r1_xxreal_0(B,k2_xcmplx_0(C,A)) ) ) ) ) )).
fof(t12_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & k3_nat_d(B,A) = k5_numbers & r1_xxreal_0(A,B) ) ) ) )).
fof(t12_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => k1_nat_3(k9_finseq_1(B),A) = k9_finseq_1(k1_newton(B,A)) ) ) )).
fof(t12_nat_4,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ ( ~ v1_int_2(A) & ~ r1_xxreal_0(A,1) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( r1_nat_d(B,A) & ~ r1_xxreal_0(B,1) & ~ r1_xxreal_0(A,B) ) ) ) & ~ ( ~ ( ~ r1_xxreal_0(A,1) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( r1_nat_d(B,A) & ~ r1_xxreal_0(B,1) & ~ r1_xxreal_0(A,B) ) ) ) & v1_int_2(A) ) ) ) )).
fof(t12_nat_5,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( B = k1_finseq_3(A,k6_domain_1(k4_ordinal1,k5_numbers)) => k18_rvsum_1(A) = k18_rvsum_1(B) ) ) ) )).
fof(t12_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ( k4_nat_d(A,2) = k5_numbers | k4_nat_d(A,2) = 1 ) ) )).
fof(t12_nat_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_nat_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_nat_lat)) => ( k1_binop_1(k2_nat_lat,B,k1_binop_1(k1_nat_lat,B,A)) = B & k1_binop_1(k2_nat_lat,k1_binop_1(k1_nat_lat,A,B),B) = B & k1_binop_1(k2_nat_lat,B,k1_binop_1(k1_nat_lat,A,B)) = B & k1_binop_1(k2_nat_lat,k1_binop_1(k1_nat_lat,B,A),B) = B ) ) ) )).
fof(t12_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_cat_1(A,B,C) != k1_xboole_0 => ! [D] : ( m1_cat_1(D,A,B,C) => k9_cat_3(A,B,C,A,k10_cat_1(A),D) = D ) ) ) ) ) )).
fof(t12_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k2_numbers))) ) => ! [C] : ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_hidden(F,k1_relset_1(u1_struct_0(A),B)) & ~ r1_xxreal_0(E,k2_normsp_0(A,k5_algstr_0(A,F,C))) & r1_xxreal_0(D,k9_complex1(k6_xcmplx_0(k7_partfun1(k2_numbers,B,F),k7_partfun1(k2_numbers,B,C)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_ncfcont2,axiom,( ! [A] : ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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)) ) ) ) ) ) )).
fof(t12_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,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))) ) ) ) ) )).
fof(t12_ndiff_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k7_partfun1(u1_struct_0(A),k2_ndiff_3(A,C,B),D) = k4_struct_0(A) ) ) ) ) ) ) ) ) )).
fof(t12_ndiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(B)))) ) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t12_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_prvect_2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_prvect_2(A))) => ! [D] : ( m1_subset_1(D,k4_card_3(k4_prvect_2(A))) => ! [E] : ( m1_subset_1(E,k4_card_3(k4_prvect_2(A))) => ! [F] : ( 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] : ( m2_subset_1(G,k4_ordinal1,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)) ) ) ) ) ) ) ) ) ) )).
fof(t12_neckla_3,axiom,( ! [A] : ( l1_orders_2(A) => r1_xboole_0(u1_orders_2(A),u1_orders_2(k3_necklace(A))) ) )).
fof(t12_necklace,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ( ( r3_necklace(A,B) & r3_necklace(B,C) ) => r3_necklace(A,C) ) ) ) ) )).
fof(t12_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k2_net_1(A)) => r1_tarski(k4_net_1(A,B),k2_net_1(A)) ) ) )).
fof(t12_newton,axiom,( k2_newton(k5_numbers) = 1 )).
fof(t12_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),k8_funct_2(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,C),k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,D))) & r2_funct_2(k4_ordinal1,u1_struct_0(B),k8_funct_2(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,C),k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,D))) ) ) ) ) ) ) ) )).
fof(t12_nfcont_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_numbers))) ) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & r2_hidden(E,C) & k7_partfun1(k1_numbers,B,D) = k2_seq_4(k7_relset_1(u1_struct_0(A),k1_numbers,B,C)) & k7_partfun1(k1_numbers,B,E) = k3_seq_4(k7_relset_1(u1_struct_0(A),k1_numbers,B,C)) ) ) ) ) ) ) ) )).
fof(t12_nfcont_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t12_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k1_euclid(A))) => ~ ( ? [E] : ( v1_xreal_0(E) & ~ r1_xxreal_0(E,k5_numbers) & a_4_0_nfcont_4(A,B,C,E) = D ) & ! [E] : ( m1_rcomp_1(E,B) => ~ r1_tarski(k7_relset_1(k1_numbers,k1_euclid(A),C,E),D) ) ) ) ) ) ) ) ) )).
fof(t12_normform,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_finsub_1(B) ) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(A,B)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t12_normsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) <=> ( k9_xtuple_0(A) = k4_ordinal1 & ! [D] : ( r2_hidden(D,k4_ordinal1) => m1_subset_1(k1_funct_1(A,D),u1_struct_0(B)) ) ) ) ) ) ) )).
fof(t12_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k3_normsp_2(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k3_normsp_2(A))))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k3_normsp_2(A))) => ( ( r1_funct_2(k4_ordinal1,u1_struct_0(A),k4_ordinal1,u1_struct_0(k3_normsp_2(A)),B,C) & D = E ) => ( r1_frechet(k3_normsp_2(A),C,E) <=> ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( v7_ordinal1(G) => ? [H] : ( v7_ordinal1(H) & r1_xxreal_0(G,H) & r1_xxreal_0(F,k2_normsp_0(A,k5_algstr_0(A,k1_normsp_1(A,B,H),D))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_ntalgo_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => ! [B] : ( m1_subset_1(B,k4_numbers) => ! [C] : ( ( ~ v1_xboole_0(C) & m2_finseq_1(C,k4_numbers) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m2_finseq_1(D,k4_numbers) ) => ( ( r1_xxreal_0(2,k3_finseq_1(C)) & ! [E] : ( v7_ordinal1(E) => ! [F] : ( 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] : ( v7_ordinal1(E) => ( r2_hidden(E,k2_finseq_1(k3_finseq_1(C))) => k5_int_1(A,k1_funct_1(C,E)) = k5_int_1(B,k1_funct_1(C,E)) ) ) & k1_funct_1(D,1) = 1 ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,k3_finseq_1(C)) & ! [F] : ( 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)) ) ) ) => k5_int_1(A,k1_funct_1(D,k1_nat_1(E,1))) = k5_int_1(B,k1_funct_1(D,k1_nat_1(E,1))) ) ) ) ) ) ) ) )).
fof(t12_numbers,axiom,( r1_tarski(k3_numbers,k1_numbers) )).
fof(t12_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t12_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( r2_hidden(C,k1_funct_1(k8_openlatt(A),B)) <=> ? [D] : ( ~ 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) ) ) ) ) )).
fof(t12_oposet_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_qmax_1(A) ) => ( v8_oposet_1(A) => v3_necklace(A) ) ) )).
fof(t12_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_oppcat_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_oppcat_1(A))) => ( k2_cat_1(k2_oppcat_1(A),B,C) != k1_xboole_0 => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t12_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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(k2_ordeq_01(A,B)) = k8_funcop_1(u1_struct_0(B),A,k4_struct_0(B)) ) ) )).
fof(t12_orders_1,axiom,( ! [A] : ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => k1_relat_1(B) = A ) )).
fof(t12_orders_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ? [D] : ( 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) ) ) ) ) ) )).
fof(t12_orders_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_orders_3(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_orders_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_orders_3(A))) => ! [D] : ( m1_orders_3(D,A) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t12_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r1_ordinal1(A,B) | r2_hidden(B,A) ) ) ) )).
fof(t12_ordinal2,axiom,( ! [A] : r1_tarski(k3_ordinal1(A),k2_ordinal1(A)) )).
fof(t12_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( k2_xboole_0(A,B) = A | k2_xboole_0(A,B) = B ) ) ) )).
fof(t12_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(t12_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( ( r2_hidden(k5_numbers,A) & r2_hidden(k12_ordinal2(A,B),k12_ordinal2(A,C)) ) => r2_hidden(B,C) ) ) ) ) )).
fof(t12_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r2_hidden(A,B) <=> r2_hidden(k3_ordinal5(A),k3_ordinal5(B)) ) ) ) )).
fof(t12_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ~ r1_orders_2(B,D,C) => k1_ortsp_1(A,B,C,D,k4_vectsp_1(A,B,F,E)) = k8_group_1(A,F,k1_ortsp_1(A,B,C,D,E)) ) ) ) ) ) ) ) )).
fof(t12_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(k2_osafree(A,B))) => ! [D] : ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t12_osalg_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t12_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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))) ) ) ) )).
fof(t12_osalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ( v1_osalg_3(D,A) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( m1_subset_1(F,u4_struct_0(A)) => ( r6_osalg_1(A,E,F) => ! [G] : ( m1_subset_1(G,k3_msualg_1(A,E,B)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v2_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,B),D)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t12_papdesaf,axiom,( ! [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) ) => ! [B] : ( ( ~ v7_struct_0(B) & v2_analoaf(B) & l1_analoaf(B) ) => ( B = k2_analoaf(A) => ( v6_papdesaf(B) & v5_papdesaf(B) ) ) ) ) )).
fof(t12_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_parsp_1(A))) => ( r1_parsp_1(k9_parsp_1(A),B,C,D,E) <=> ? [F] : ( m1_subset_1(F,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) & ? [G] : ( m1_subset_1(G,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) & ? [H] : ( m1_subset_1(H,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) & ? [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) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ~ ( B != C & C != D & D != B ) => r1_parsp_2(A,B,C,D) ) ) ) ) ) )).
fof(t12_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) )).
fof(t12_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t12_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ? [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) & r2_hidden(C,D) & r2_hidden(D,B) ) ) ) ) )).
fof(t12_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t12_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r2_analoaf(A,B,F,F,C) & r2_analoaf(A,D,F,F,E) & r2_diraf(A,B,D,C,E) ) => ( r3_diraf(A,F,B,D) | r2_analoaf(A,B,D,E,C) ) ) ) ) ) ) ) ) )).
fof(t12_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t12_pcomps_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t12_pcs_0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v16_pcs_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k17_pcs_0(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k17_pcs_0(A,B))) => ( r1_pcs_0(k17_pcs_0(A,B),C,D) <=> ? [E] : ? [F] : ( l2_pcs_0(F) & ? [G] : ( m1_subset_1(G,u1_struct_0(F)) & ? [H] : ( 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) ) ) ) ) ) ) ) )).
fof(t12_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t12_pdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(2)) => ! [E] : ( ( 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 = k10_pdiff_1(2,2,E,D) <=> ? [F] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & D = k10_finseq_1(F,G) & ? [H] : ( m1_rcomp_1(H,G) & r1_tarski(H,k1_relset_1(k1_numbers,k1_pdiff_2(2,2,E,D))) & ? [I] : ( v1_funct_1(I) & v3_fdiff_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [J] : ( v1_funct_1(J) & v2_fdiff_1(J) & m1_subset_1(J,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & C = k1_funct_1(I,1) & ! [K] : ( v1_xreal_0(K) => ( r2_hidden(K,H) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(2,2,E,D),K),k1_funct_1(k1_pdiff_2(2,2,E,D),G)) = k2_xcmplx_0(k1_funct_1(I,k6_xcmplx_0(K,G)),k1_funct_1(J,k6_xcmplx_0(K,G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_pdiff_3,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(2)) => ! [B] : ( ( 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) ) ) ) )).
fof(t12_pdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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] : ( m1_rcomp_1(F,C) => ~ ( r1_tarski(F,k1_relset_1(k1_numbers,k1_pdiff_2(3,3,E,D))) & ? [G] : ( v1_funct_1(G) & v3_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [H] : ( v1_funct_1(H) & v2_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,F) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,3,E,D),I),k1_funct_1(k1_pdiff_2(3,3,E,D),C)) = k2_xcmplx_0(k1_funct_1(G,k6_xcmplx_0(I,C)),k1_funct_1(H,k6_xcmplx_0(I,C))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t12_pdiff_6,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( 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)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(k4_real_ns1(B)),u1_struct_0(k4_real_ns1(A))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(B)),u1_struct_0(k4_real_ns1(A))))) ) => ( r1_funct_2(k1_euclid(B),k1_euclid(A),u1_struct_0(k4_real_ns1(B)),u1_struct_0(k4_real_ns1(A)),C,D) => ( v1_pdiff_6(C,A,B) <=> v13_vectsp_1(D,k4_real_ns1(B),k4_real_ns1(A)) ) ) ) ) ) ) )).
fof(t12_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,A) & C = k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_1(E,A),D) ) => ( k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k1_finseq_7(k1_numbers,D,E,B),D) = k2_funct_7(k1_numbers,k5_euclid(A),E,k5_real_1(B,C)) & k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,k1_finseq_7(k1_numbers,D,E,B)) = k2_funct_7(k1_numbers,k5_euclid(A),E,k5_real_1(C,B)) ) ) ) ) ) ) ) )).
fof(t12_pdiff_8,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_1(D,A),k8_euclid(A,B,C)) = k5_real_1(k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_1(D,A),B),k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_1(D,A),C)) ) ) ) ) )).
fof(t12_pdiff_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(B)) => C = k3_funct_2(k1_numbers,k1_euclid(B),k6_pdiff_1(B,A,C),k3_funct_2(k1_euclid(B),k1_numbers,k1_pdiff_1(A,B),C)) ) ) ) )).
fof(t12_pencil_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ( C != k3_pencil_1(A,B) => v3_card_1(k1_funct_1(B,C),1) ) ) ) ) )).
fof(t12_pencil_2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(t12_pencil_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v15_pencil_1(B) ) => ! [C] : ( ( ~ v13_pencil_1(C) & v16_pencil_1(C,A) & m3_pboole(C,A,k12_pralg_1(A,B)) ) => ! [D] : ( m1_subset_1(D,u1_pre_topc(k2_pencil_1(A,B,k3_pencil_1(A,C)))) => m1_subset_1(k4_card_3(k1_funct_7(C,k3_pencil_1(A,C),D)),u1_pre_topc(k5_pencil_1(A,B))) ) ) ) ) )).
fof(t12_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( 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 ) ) ) ) )).
fof(t12_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k4_nat_d(k1_newton(C,A),B) = k4_nat_d(k1_newton(k4_nat_d(C,B),A),B) ) ) ) )).
fof(t12_petri,axiom,( ! [A] : ( ( ~ 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 ) )).
fof(t12_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,k4_ordinal1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,k4_ordinal1) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ( ( 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)) ) ) ) ) ) )).
fof(t12_polyalg1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_polyalg1(B,A) => ! [C] : ( l1_polyalg1(C,A) => ! [D] : ( l1_polyalg1(D,A) => ( ( m1_polyalg1(B,A,C) & m1_polyalg1(C,A,D) ) => m1_polyalg1(B,A,D) ) ) ) ) ) )).
fof(t12_polyeq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ( ! [I] : ( v1_xreal_0(I) => k4_polyeq_1(A,C,E,G,I) = k4_polyeq_1(B,D,F,H,I) ) => ( A = B & C = D & E = F & G = H ) ) ) ) ) ) ) ) ) ) )).
fof(t12_polyeq_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( k1_square_1(B) = A & B != k3_square_1(A) & B != k4_xcmplx_0(k3_square_1(A)) ) ) ) )).
fof(t12_polyeq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( B != k5_numbers & r1_xxreal_0(k5_numbers,k6_xcmplx_0(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(k3_xcmplx_0(2,B),C)),k3_xcmplx_0(3,k1_square_1(B)))) & k4_polyeq_1(B,C,C,B,A) = k5_numbers & A != k4_xcmplx_0(1) & A != k7_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(B,C),k3_square_1(k6_xcmplx_0(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(k3_xcmplx_0(2,B),C)),k3_xcmplx_0(3,k1_square_1(B))))),k3_xcmplx_0(2,B)) & A != k7_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(B,C),k3_square_1(k6_xcmplx_0(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(k3_xcmplx_0(2,B),C)),k3_xcmplx_0(3,k1_square_1(B))))),k3_xcmplx_0(2,B)) ) ) ) ) )).
fof(t12_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( D != k5_numbers => ( k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(D,k1_newton(A,2)),k3_xcmplx_0(C,A)),B) = k5_numbers <=> ( A = k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(2,D))),k7_xcmplx_0(k1_polyeq_5(2,k1_quin_1(B,C,D)),k3_xcmplx_0(2,D))) | A = k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(2,D))),k7_xcmplx_0(k1_polyeq_5(2,k1_quin_1(B,C,D)),k3_xcmplx_0(2,D))) ) ) ) ) ) ) ) )).
fof(t12_polyform,axiom,( k2_polyform(k4_xcmplx_0(1),2) = 1 )).
fof(t12_polynom1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t12_polynom2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( 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)))) ) => k2_polynom2(A,B,k8_polynom1(A,B),C) = k4_struct_0(B) ) ) ) )).
fof(t12_polynom3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( k1_funct_1(k6_polynom3(2,B),A) = k2_polynom3(k4_ordinal1,C,k7_nat_d(B,C)) & k1_funct_1(k6_polynom3(2,B),k1_nat_1(A,1)) = k2_polynom3(k4_ordinal1,D,k7_nat_d(B,D)) ) => D = k1_nat_1(C,1) ) ) ) ) ) )).
fof(t12_polynom4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( k1_algseq_1(A,B) = k5_numbers => r2_funct_2(k4_ordinal1,u1_struct_0(A),k1_polynom4(A,B),k9_polynom3(A)) ) ) ) )).
fof(t12_polynom5,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( 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)) ) ) )).
fof(t12_polynom6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( m2_subset_1(C,k14_pre_poly(A),k15_pre_poly(A)) => ! [D] : ( m2_subset_1(D,k14_pre_poly(B),k15_pre_poly(B)) => ! [E] : ( 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] : ( v7_ordinal1(F) => ~ ( r2_hidden(F,k4_finseq_1(k20_pre_poly(A,C))) & ! [G] : ( m2_subset_1(G,k14_pre_poly(A),k15_pre_poly(A)) => ! [H] : ( m2_finseq_1(H,k15_pre_poly(k10_ordinal2(A,B))) => ~ ( H = k9_pre_poly(k15_pre_poly(k10_ordinal2(A,B)),k4_ordinal1,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] : ( v7_ordinal1(I) => ~ ( r2_hidden(I,k4_finseq_1(H)) & ! [J] : ( 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) ) ) ) ) ) ) )).
fof(t12_polynom7,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( 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] : ( ( 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_polynom2(A,B,C,D) = k6_algstr_0(B,k3_polynom7(A,B,C),k1_polynom2(A,k2_polynom7(A,B,C),B,D)) ) ) ) ) )).
fof(t12_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => r2_funct_2(k15_pre_poly(A),u1_struct_0(B),k5_polynom7(A,B,k10_polynom1(A,B,C,D),E),k10_polynom1(A,B,C,k5_polynom7(A,B,D,E))) ) ) ) ) ) )).
fof(t12_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(t12_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(1,B) ) | ( A != k5_numbers & ~ v1_abian(B) ) ) => k1_power(B,k7_xcmplx_0(1,A)) = k7_xcmplx_0(1,k1_power(B,A)) ) ) ) )).
fof(t12_pralg_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(t12_pralg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( m2_pboole(E,u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D)) => ! [F] : ( m1_subset_1(F,k3_msualg_1(A,B,C)) => r2_hidden(F,k4_card_3(k1_funct_6(k3_relat_1(k1_msualg_1(A,B),E)))) ) ) ) ) ) ) )).
fof(t12_pre_circ,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v6_trees_3(A) ) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(k1_nat_1(B,1),k4_finseq_1(A)) => r2_hidden(k9_finseq_1(B),k11_trees_3(k1_funct_6(A))) ) ) ) )).
fof(t12_pre_ff,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => r1_xxreal_0(k1_int_1(k3_power(2,k1_nat_1(k3_xcmplx_0(2,A),1))),k2_xcmplx_0(k1_int_1(k3_power(2,k3_xcmplx_0(2,A))),1)) ) ) )).
fof(t12_pre_poly,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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)))) ) ) ) )).
fof(t12_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( B != k1_struct_0(A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ r2_hidden(C,B) ) ) ) ) )).
fof(t12_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t12_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(1,B) ) => r1_xxreal_0(A,k1_newton(A,B)) ) ) ) )).
fof(t12_prgcor_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => k2_prgcor_1(A,B) = k4_int_1(A,B) ) ) )).
fof(t12_prob_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( r2_hidden(B,k1_prob_1(A,C)) <=> ? [D] : ( v7_ordinal1(D) & r2_hidden(B,k9_nat_1(k9_setfam_1(A),C,D)) ) ) ) )).
fof(t12_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m2_prob_1(E,A,B) => k3_funct_2(B,k1_numbers,E,k7_prob_1(A,B,C,k5_prob_1(A,B,C,D))) = k5_real_1(k3_funct_2(B,k1_numbers,E,C),k3_funct_2(B,k1_numbers,E,k5_prob_1(A,B,C,D))) ) ) ) ) ) )).
fof(t12_prob_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ! [D] : ( r2_hidden(D,k1_prob_2(B,k9_setfam_1(B),k1_prob_3(B,C),A)) <=> ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(E,A) => r2_hidden(D,k1_prob_2(B,k9_setfam_1(B),C,E)) ) ) ) ) ) )).
fof(t12_prob_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ( r1_funct_2(k4_ordinal1,k1_numbers,k4_ordinal1,k6_numbers,A,B) & v4_partfun3(A) & v1_series_1(A) ) => k4_series_1(A) = k19_supinf_2(B) ) ) ) )).
fof(t12_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) )).
fof(t12_projdes1,axiom,( ! [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) ) => ~ ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => r1_projdes1(A,B,C,D,E) ) ) ) ) ) )).
fof(t12_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t12_projred1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & v9_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u1_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u1_incsp_1(A)) => ! [H] : ( m1_subset_1(H,u1_incsp_1(A)) => ! [I] : ( m1_subset_1(I,u1_incsp_1(A)) => ! [J] : ( m1_subset_1(J,u1_incsp_1(A)) => ! [K] : ( m1_subset_1(K,u1_incsp_1(A)) => ! [L] : ( m1_subset_1(L,u2_incsp_1(A)) => ! [M] : ( m1_subset_1(M,u2_incsp_1(A)) => ! [N] : ( m1_subset_1(N,u2_incsp_1(A)) => ! [O] : ( m1_subset_1(O,u2_incsp_1(A)) => ! [P] : ( m1_subset_1(P,u2_incsp_1(A)) => ! [Q] : ( m1_subset_1(Q,u2_incsp_1(A)) => ! [R] : ( m1_subset_1(R,u2_incsp_1(A)) => ! [S] : ( m1_subset_1(S,u2_incsp_1(A)) => ! [T] : ( 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] : ( m1_subset_1(U,u2_incsp_1(A)) => ~ r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),I,J,K),U) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t12_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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] : ( m2_subset_1(C,k4_ordinal1,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)))) ) ) ) ) ) ) )).
fof(t12_prvect_3,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => k1_binop_1(C,D,E) = k10_finseq_1(D,E) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(k5_prvect_3(A,B))) => ! [E] : ( 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] : ( m1_subset_1(D,u1_struct_0(k5_prvect_3(A,B))) => ! [E] : ( v1_xreal_0(E) => 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))) ) ) ) )).
fof(t12_pscomp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( 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] : ( 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)),k2_measure6(u1_struct_0(A),k1_numbers,B),C),A) ) ) ) ) )).
fof(t12_pua2mss1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k10_eqrel_1(A)) => ? [C] : ( m2_finseq_1(C,A) & k4_card_3(B) = k1_tarski(C) ) ) )).
fof(t12_pythtrip,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( A = k6_xcmplx_0(k1_pepin(E),k1_pepin(D)) & B = k2_nat_1(k2_nat_1(2,D),E) & C = k1_nat_1(k1_pepin(E),k1_pepin(D)) ) => k1_nat_1(k1_pepin(A),k1_pepin(B)) = k1_pepin(C) ) ) ) ) ) ) )).
fof(t12_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t12_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( ( k1_xtuple_0(k1_funct_1(k11_qc_lang1(A,B),1)) = k5_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] : ( v7_ordinal1(C) & 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) ) ) ) ) )).
fof(t12_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ! [E] : ( m1_subset_1(E,k9_qc_lang1(A)) => ( k4_qc_lang2(A,B,C) = k4_qc_lang2(A,D,E) => ( B = D & C = E ) ) ) ) ) ) ) )).
fof(t12_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t12_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_trees_1(C,k9_xtuple_0(k2_qc_lang4(A,B))) => ! [D] : ( m1_trees_1(D,k9_xtuple_0(k2_qc_lang4(A,B))) => ( r2_hidden(D,k1_trees_2(k9_xtuple_0(k2_qc_lang4(A,B)),C)) => r1_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)) ) ) ) ) ) )).
fof(t12_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_qc_trans(B,A) & m1_qc_lang1(B) ) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => k24_qc_lang1(A,C) = k24_qc_lang1(B,k1_qc_trans(A,B,C)) ) ) ) )).
fof(t12_qmax_1,axiom,( ! [A] : ( ( v2_qmax_1(A) & l1_qmax_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k5_qmax_1(A))) => ! [C] : ( 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] : ( m1_subset_1(D,k5_qmax_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t12_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v10_lattices(A) & v4_lattice3(A) & v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t12_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => k23_quaterni(k1_quatern2,A) = k5_numbers ) )).
fof(t12_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k1_square_1(k28_quaterni(A)) = k28_quaterni(k23_quaterni(A,k27_quaterni(A))) ) )).
fof(t12_quaterni,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ( k6_quaterni(A,B,C,D) = k6_quaterni(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) ) ) ) ) ) ) ) ) )).
fof(t12_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ! [D] : ( v1_xreal_0(D) => ~ r1_xxreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k1_square_1(D)),k3_xcmplx_0(B,D)),C),k5_numbers) ) & ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k5_numbers,k1_quin_1(A,B,C)) ) ) ) ) )).
fof(t12_quofield,axiom,( ! [A] : ( ( ~ 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] : ( 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 ) ) ) )).
fof(t12_radix_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t12_radix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t12_radix_3,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(k4_xcmplx_0(1),k5_radix_3(A,B)) & r1_xxreal_0(k5_radix_3(A,B),1) ) ) ) )).
fof(t12_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k3_radix_1(B)) ) => ! [D] : ( ( v3_card_1(D,A) & m2_finseq_1(D,k3_radix_1(B)) ) => ( ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t12_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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),k5_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))) ) ) ) ) )).
fof(t12_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m2_prob_1(B,A,k1_random_1(A)) => ! [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))) ) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ! [E] : ( 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] : ( v7_ordinal1(F) => ( r2_hidden(F,k4_finseq_1(D)) => k12_supinf_2(D,F) = k1_extreal1(k12_supinf_2(C,k1_funct_1(E,F)),k12_supinf_2(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) ) ) ) ) ) ) )).
fof(t12_random_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [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))) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( ~ v1_xboole_0(F) & v1_finset_1(F) & m1_subset_1(F,k1_zfmisc_1(A)) ) => ! [G] : ( ( ~ v1_xboole_0(G) & v1_finset_1(G) & m1_subset_1(G,k1_zfmisc_1(B)) ) => ! [H] : ( ( v1_finset_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ( H = k2_zfmisc_1(F,G) & ! [I] : ! [J] : ( ( r2_hidden(I,F) & r2_hidden(J,G) ) => k1_binop_1(E,I,J) = k1_extreal1(k12_supinf_2(C,I),k12_supinf_2(D,J)) ) ) => k5_bhsp_5(k1_numbers,k2_zfmisc_1(A,B),k9_binop_2,H,E) = k3_xcmplx_0(k5_bhsp_5(k1_numbers,A,k9_binop_2,F,C),k5_bhsp_5(k1_numbers,B,k9_binop_2,G,D)) ) ) ) ) ) ) ) ) ) )).
fof(t12_random_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( m2_prob_1(E,A,C) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,A,B) & v1_random_3(F,A,B,C,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => k12_supinf_2(k1_random_3(A,B,C,D,k2_prob_4(A,C,E),F),B) = 1 ) ) ) ) ) ) )).
fof(t12_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => m1_subset_1(k2_ranknull(B,C,D,E),k1_zfmisc_1(u1_struct_0(k3_ranknull(A,B,C,D)))) ) ) ) ) ) )).
fof(t12_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ( A = k7_xcmplx_0(k2_rat_1(A),k1_rat_1(A)) & A = k3_xcmplx_0(k2_rat_1(A),k5_xcmplx_0(k1_rat_1(A))) & A = k3_xcmplx_0(k5_xcmplx_0(k1_rat_1(A)),k2_rat_1(A)) ) ) )).
fof(t12_rcomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( ( v2_rcomp_1(A) & v4_xxreal_2(A) ) => ( A = k1_xboole_0 | r2_hidden(k2_seq_4(A),A) ) ) ) )).
fof(t12_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => k3_seq_4(k3_limfunc1(A)) = A ) )).
fof(t12_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k9_nat_1(k4_ordinal1,k2_real_3(B,A),1) = k3_nat_d(A,k9_nat_1(k4_ordinal1,k1_real_3(B,A),k5_numbers)) ) ) )).
fof(t12_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( 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) ) ) ) )).
fof(t12_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k4_real_ns1(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k4_real_ns1(A))))) ) => ( v1_rsspace3(B,k4_real_ns1(A)) => v3_normsp_1(B,k4_real_ns1(A)) ) ) ) )).
fof(t12_realset2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t12_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t12_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [D] : ( ( v1_rearran1(D) & v2_rearran1(D) & v3_rearran1(D,k1_zfmisc_1(A)) & m2_finseq_1(D,k1_zfmisc_1(A)) ) => ( ( v1_partfun1(C,B) & k5_card_1(A) = k5_card_1(B) ) => k1_relset_1(A,k3_rearran1(B,A,D,C)) = A ) ) ) ) ) )).
fof(t12_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => k1_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B)) ) ) )).
fof(t12_relset_1,axiom,( ! [A] : ! [B] : m1_subset_1(k1_xboole_0,k1_zfmisc_1(k2_zfmisc_1(A,B))) )).
fof(t12_relset_2,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( 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)) ) ) )).
fof(t12_revrot_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( 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(k1_nat_1(A,k4_finseq_4(D,C)),k3_finseq_1(D))) ) ) ) ) ) ) )).
fof(t12_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : r1_rewrite1(A,B,B) ) )).
fof(t12_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t12_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(A)) => ~ ( k1_flang_1(A,D,B) = k1_flang_1(A,E,C) & ( r1_xxreal_0(k1_afinsq_1(D),k1_afinsq_1(E)) | r1_xxreal_0(k1_afinsq_1(C),k1_afinsq_1(B)) ) & ! [F] : ( m1_subset_1(F,k8_afinsq_1(A)) => ~ ( k1_flang_1(A,D,F) = E & B = k1_flang_1(A,F,C) ) ) ) ) ) ) ) ) )).
fof(t12_rfinseq,axiom,( k3_rfinseq(k6_finseq_1(k1_numbers)) = k6_finseq_1(k1_numbers) )).
fof(t12_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( ~ r1_xxreal_0(k3_finseq_1(A),k5_numbers) => ( k4_rfinseq2(k6_rvsum_1(A)) = k4_xcmplx_0(k3_rfinseq2(A)) & k2_rfinseq2(k6_rvsum_1(A)) = k1_rfinseq2(A) ) ) ) )).
fof(t12_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( v1_xcmplx_0(C) => k24_valued_1(k18_valued_1(A,B),C) = k18_valued_1(k24_valued_1(A,C),B) ) ) ) )).
fof(t12_rfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ( r1_tarski(k2_relset_1(A,C),k1_relset_1(A,k6_rfunct_1(A,k1_numbers,B))) => r2_relset_1(k4_ordinal1,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,A,C,k6_rfunct_1(A,k1_numbers,B)),k37_valued_1(k4_ordinal1,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,A,C,B))) ) ) ) ) )).
fof(t12_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t12_rfunct_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ~ r1_xxreal_0(A,k5_numbers) => ( r1_rfunct_4(B,C) <=> r1_rfunct_4(k26_valued_1(k1_numbers,k1_numbers,B,A),C) ) ) ) ) )).
fof(t12_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_seq_2(A) <=> v1_seq_2(k32_valued_1(k4_ordinal1,k1_numbers,A)) ) ) )).
fof(t12_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r1_funct_2(k4_ordinal1,k6_numbers,k4_ordinal1,k1_numbers,A,B) => ( v2_rinfsup2(A) <=> v1_seq_2(B) ) ) ) ) )).
fof(t12_ring_1,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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))) ) ) ) )).
fof(t12_ringcat1,axiom,( ! [A] : ( ( v2_ringcat1(A) & v3_ringcat1(A) & l1_ringcat1(A) ) => ( ~ v1_xboole_0(k1_tarski(A)) & v5_ringcat1(k1_tarski(A)) ) ) )).
fof(t12_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k1_convex1(A,B,k5_numbers),k6_domain_1(u1_struct_0(A),k4_struct_0(A))) ) ) )).
fof(t12_rlaffin2,axiom,( ! [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) ) => ! [B] : ( ( v1_rlaffin1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t12_rlaffin3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( k1_card_1(C) = k1_card_1(k1_convex1(B,C,A)) <=> ~ ( A = k5_numbers & ~ v1_zfmisc_1(C) ) ) ) ) ) )).
fof(t12_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => k4_struct_0(B) = k4_struct_0(C) ) ) ) )).
fof(t12_rlsub_2,axiom,( ! [A] : ( ( ~ 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 ) )).
fof(t12_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t12_rlvect_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t12_rlvect_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t12_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( v1_xreal_0(D) => B != k1_rlvect_1(A,C,D) ) ) ) ) & ( ! [D] : ( v1_xreal_0(D) => 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) ) ) ) ) ) ) ) )).
fof(t12_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t12_rlvect_5,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlvect_2(C,A) => ~ ( r1_tarski(k3_rlvect_2(A,C),u1_struct_0(B)) & ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t12_rlvect_x,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( r2_hidden(A,C) => r2_hidden(A,k2_rlvect_x(B,C)) ) ) ) )).
fof(t12_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => k4_struct_0(C) = k4_struct_0(D) ) ) ) ) )).
fof(t12_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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 ) ) )).
fof(t12_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( ( 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),D,C)) = k5_algstr_0(B,k1_rmod_4(A,B,k4_subset_1(u1_struct_0(B),D,C)),k1_rmod_4(A,B,C)) ) ) ) ) )).
fof(t12_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_robbins1(A,B,B) = B ) ) )).
fof(t12_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t12_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t12_robbins4,axiom,( k3_lattice3(g3_lattices(u1_struct_0(k2_robbins4),u2_lattices(k2_robbins4),u1_lattices(k2_robbins4))) = k1_robbins4 )).
fof(t12_rolle,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,k2_rcomp_1(A,B)) => r1_xxreal_0(k1_fdiff_1(C,D),k5_numbers) ) ) ) => v8_valued_0(k2_partfun1(k1_numbers,k1_numbers,C,k2_rcomp_1(A,B))) ) ) ) ) )).
fof(t12_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k3_roughs_1(A,B),B) ) ) )).
fof(t12_rpr_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v3_card_1(B,1) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( v3_card_1(C,1) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ( B = C | r1_subset_1(B,C) ) ) ) ) )).
fof(t12_rsspace,axiom,( m1_rlsub_1(g1_rlvect_1(k10_rsspace,k9_rsspace(k6_rsspace,k10_rsspace),k7_rsspace(k6_rsspace,k10_rsspace),k8_rsspace(k6_rsspace,k10_rsspace)),k6_rsspace) )).
fof(t12_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t12_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => r1_struct_0(C,k4_struct_0(B)) ) ) ) )).
fof(t12_rusub_2,axiom,( ! [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_bhsp_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => k1_rusub_2(A,k2_rusub_1(A),k2_rusub_1(A)) = A ) )).
fof(t12_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( k1_rusub_3(A,B) = A & ! [C] : ( 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 ) ) ) ) ) )).
fof(t12_rusub_4,axiom,( ! [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_bhsp_1(A) & v1_rusub_4(A) & l1_bhsp_1(A) ) => ( k1_rusub_4(A) = k5_numbers <=> k2_rusub_1(A) = k1_rusub_1(A) ) ) )).
fof(t12_rusub_5,axiom,( ! [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) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t12_rvsum_1,axiom,( ! [A] : ( ( 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) ) )).
fof(t12_rvsum_2,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t12_scm_1,axiom,( k4_xtuple_0(k2_compos_1(k1_ami_3)) = k5_numbers & ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => k4_xtuple_0(k2_ami_3(A,B)) = 1 ) ) & ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => k4_xtuple_0(k3_ami_3(A,B)) = 2 ) ) & ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => k4_xtuple_0(k4_ami_3(A,B)) = 3 ) ) & ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => k4_xtuple_0(k5_ami_3(A,B)) = 4 ) ) & ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => k4_xtuple_0(k6_ami_3(A,B)) = 5 ) ) & ! [A] : ( m1_subset_1(A,k4_ordinal1) => k4_xtuple_0(k7_ami_3(A)) = 6 ) & ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k4_xtuple_0(k8_ami_3(B,A)) = 7 ) ) & ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k4_xtuple_0(k9_ami_3(B,A)) = 8 ) ) )).
fof(t12_scm_comp,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( m1_dtconstr(B,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r1_tarski(k61_valued_1(k15_scm_comp(B,C),D),A) => ! [E] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(E,u1_struct_0(k1_ami_3)) & v5_memstr_0(E,k7_card_1(2),k1_ami_3,D) ) => ~ ( ~ r1_xxreal_0(C,k17_scm_comp(B)) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(G,u1_struct_0(k1_ami_3)) ) => ~ ( G = k5_extpro_1(k7_card_1(2),k1_ami_3,A,E,k1_nat_1(F,1)) & k1_nat_1(F,1) = k1_afinsq_1(k15_scm_comp(B,C)) & k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,A,E,F)) = k1_nat_1(D,F) & k5_memstr_0(k7_card_1(2),k1_ami_3,G) = k1_nat_1(D,k1_nat_1(F,1)) & k1_funct_1(G,k10_ami_3(C)) = k12_scm_comp(E,B) & ! [H] : ( m1_subset_1(H,k4_ordinal1) => ( ~ r1_xxreal_0(C,H) => k1_funct_1(E,k10_ami_3(H)) = k1_funct_1(G,k10_ami_3(H)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => ! [C] : ( m1_scmfsa_2(C) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t12_scmfsa10,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( 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 ) ) )).
fof(t12_scmfsa6a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( v2_compos_1(A,k1_scmfsa_2) => k1_scmfsa6a(A,B) = A ) ) ) )).
fof(t12_scmfsa7b,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( v7_ordinal1(C) => ~ r3_scmfsa7b(k12_scmfsa_2(C,B),A) ) ) ) )).
fof(t12_scmfsa8a,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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] : ( v7_ordinal1(E) => ( r1_xxreal_0(E,k2_scmfsa8a(A,B,C)) => r8_pboole(u1_struct_0(k1_scmfsa_2),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),E),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k3_scmfsa6a(C,D)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),E)) ) ) ) ) ) ) ) )).
fof(t12_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( v1_ami_2(E) & ~ v1_scmfsa_m(E) & m1_subset_1(E,u1_struct_0(k1_scmfsa_2)) ) => ( ( k1_funct_1(B,E) = k5_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) ) ) ) ) ) ) ) )).
fof(t12_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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(k5_numbers)) = 1 & r5_scmfsa7b(E,C,A) & r6_scmfsa7b(E,C,A) & ! [F] : ( ( 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] : ( m1_scmfsa_2(F) => k18_scmfsa_2(C,F) = k18_scmfsa_2(D,F) ) ) => k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(E,C,A)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(E,D,B)) ) ) ) ) ) ) )).
fof(t12_scmfsa9a,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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_sf_mastr(k1_scmfsa_9(A,B)) = k4_sf_mastr(B) ) ) )).
fof(t12_scmfsa_1,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k4_scmfsa_1,k5_scmfsa_1))) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k1_funct_1(k6_scmfsa_1(A,B),C) = k1_funct_1(A,C) ) ) ) )).
fof(t12_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( 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 ) ) )).
fof(t12_scmfsa_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( ~ 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(k7_card_1(3),k1_scmfsa_2)) & v1_finset_1(B) & v4_extpro_1(B,k7_card_1(3),k1_scmfsa_2,A) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ( ( r1_tarski(B,C) & r1_tarski(B,D) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( ( r1_tarski(A,E) & r1_tarski(A,F) ) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v1_ami_2(H) & m1_subset_1(H,u1_struct_0(k1_scmfsa_2)) ) => ! [I] : ( ( v1_ami_2(I) & m1_subset_1(I,u1_struct_0(k1_scmfsa_2)) ) => ! [J] : ( m1_scmfsa_2(J) => ( ( k3_extpro_1(k7_card_1(3),k1_scmfsa_2,E,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G)) = k15_scmfsa_2(H,I,J) & r2_hidden(J,k9_xtuple_0(B)) ) => ! [K] : ( v7_ordinal1(K) => ! [L] : ( v7_ordinal1(L) => ( ( K = k1_int_2(k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G),I)) & L = k1_int_2(k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,D,G),I)) ) => k1_funct_7(k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G),J),K,k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G),H)) = k1_funct_7(k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,D,G),J),L,k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,D,G),H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_scmfsa_m,axiom,( k1_funct_1(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)),k4_scmfsa_2(k5_numbers)) = 1 )).
fof(t12_scmisort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( 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),k5_numbers) | ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(E,k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(B)),3)) => r2_hidden(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_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))) ) ) ) ) ) ) ) ) )).
fof(t12_scmp_gcd,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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),k5_numbers) & k1_funct_1(B,k2_scmp_gcd) = k5_numbers & r1_xxreal_0(k5_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] : ( v7_ordinal1(C) => ~ ( 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] : ( v7_ordinal1(D) => ( 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)) ) ) ) ) ) ) ) ) )).
fof(t12_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( 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 ) ) )).
fof(t12_scmpds_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( v7_ordinal1(G) => ! [H] : ( v1_int_1(H) => ! [I] : ( v1_int_1(I) => ! [J] : ( ( v1_ami_2(J) & m1_subset_1(J,u1_struct_0(k1_scmpds_2)) ) => ! [K] : ( ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_scmpds_4,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmpds_2)) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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)) ) ) ) )).
fof(t12_scmpds_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_scmpds_4(C) ) => ! [D] : ( v7_ordinal1(D) => ( ~ 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)) ) ) ) ) ) )).
fof(t12_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ( v2_scmpds_4(A) <=> ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => r2_scmpds_6(A,B,C) ) ) ) ) )).
fof(t12_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_scmpds_4(C) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t12_scmpds_9,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => k1_amistd_1(2,k1_scmpds_2,C,k14_scmpds_2(A,B,D,E)) = k1_tarski(k1_ordinal1(C)) ) ) ) ) ) )).
fof(t12_scmring1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k4_card_3(k3_relat_1(k3_ami_2,k1_scmring1(A)))) => k9_xtuple_0(B) = k1_ami_2 ) ) )).
fof(t12_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => ! [D] : ( ( 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(k7_card_1(2),k1_scmring2(A))) & v1_partfun1(D,u1_struct_0(k1_scmring2(A))) ) => ( k1_funct_1(k2_extpro_1(k7_card_1(2),k1_scmring2(A),k4_scmring2(A,B,C),D),k4_struct_0(k1_scmring2(A))) = k4_card_1(k5_memstr_0(k7_card_1(2),k1_scmring2(A),D)) & k2_scmring2(A,k2_extpro_1(k7_card_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] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmring2(A))) ) => ( E != B => k2_scmring2(A,k2_extpro_1(k7_card_1(2),k1_scmring2(A),k4_scmring2(A,B,C),D),E) = k2_scmring2(A,D,E) ) ) ) ) ) ) ) )).
fof(t12_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmring2(A))) => ~ ( k2_compos_0(u1_compos_1(k1_scmring2(A)),B) = 1 & ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmring2(A))) ) => B != k3_scmring2(A,C,D) ) ) ) ) ) )).
fof(t12_scmyciel,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(k2_tarski(B,C),A) => ( B = C | r2_hidden(k2_tarski(B,C),k1_scmyciel(A)) ) ) )).
fof(t12_scpqsort,axiom,( v2_compos_1(k1_scpqsort,k1_scmpds_2) & v3_scmpds_4(k1_scpqsort) )).
fof(t12_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t12_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_funct_2(k4_ordinal1,k1_numbers,B,k56_valued_1(k4_ordinal1,k1_numbers,A)) <=> ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,B,C) = k9_complex1(k9_nat_1(k1_numbers,A,C)) ) ) ) ) )).
fof(t12_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(A) & v2_comseq_2(B) ) => k1_seq_2(k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) = k6_xcmplx_0(k1_seq_2(A),k1_seq_2(B)) ) ) ) )).
fof(t12_seq_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v5_xxreal_2(A) => ( v1_xboole_0(A) | ( ~ ( ? [B] : ( v1_xreal_0(B) & ? [C] : ( v1_xreal_0(C) & r2_hidden(B,A) & r2_hidden(C,A) & C != B ) ) & r1_xxreal_0(k2_seq_4(A),k3_seq_4(A)) ) & ~ ( ~ r1_xxreal_0(k2_seq_4(A),k3_seq_4(A)) & ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( r2_hidden(B,A) & r2_hidden(C,A) & C != B ) ) ) ) ) ) ) ) )).
fof(t12_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => r2_relset_1(k4_ordinal1,k4_partfun1(A,k1_numbers),k8_seqfunc(A,k3_seqfunc(A,B),k3_seqfunc(A,C)),k3_seqfunc(A,k8_seqfunc(A,B,C))) ) ) ) )).
fof(t12_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v8_valued_0(A) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,A,k5_numbers)) ) ) ) )).
fof(t12_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_series_1(A) => ! [B] : ( v7_ordinal1(B) => v1_series_1(k1_valued_0(k1_numbers,A,B)) ) ) ) )).
fof(t12_series_3,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => r1_xxreal_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),B),C),k2_xcmplx_0(k2_xcmplx_0(k1_newton(A,3),k1_newton(B,3)),k1_newton(C,3))) ) ) ) )).
fof(t12_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => r1_xxreal_0(k7_xcmplx_0(2,k2_xcmplx_0(k7_xcmplx_0(1,A),k7_xcmplx_0(1,B))),k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),2))) ) ) )).
fof(t12_setfam_1,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_setfam_1(A,B) ) )).
fof(t12_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) )).
fof(t12_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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 ) ) ) ) ) )).
fof(t12_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k5_finsub_1(A)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( ( 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] : ( ( 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] : ( ( 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) & E = k4_binop_1(B,F) & r6_binop_1(B,G,F) & k5_binop_1(B,G,D,E) = E ) => k5_binop_1(B,G,D,k7_setwiseo(A,B,F,C,H)) = k7_setwiseo(A,B,F,C,k10_funcop_1(B,A,G,D,H)) ) ) ) ) ) ) ) ) ) )).
fof(t12_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_scmfsa_2(C) => ! [D] : ( m1_scmfsa_2(D) => ( k17_scmfsa_2(A,C) = k17_scmfsa_2(B,D) => ( A = B & C = D ) ) ) ) ) ) )).
fof(t12_sfmastr1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( v1_scmfsa6c(D) & m1_subset_1(D,u1_compos_1(k1_scmfsa_2)) ) => ! [E] : ( m1_scmfsa_2(E) => ( ( v7_amistd_1(C,k7_card_1(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(k7_card_1(3),k1_scmfsa_2,D,k1_scmfsa6b(C,B,A)),E) ) ) ) ) ) ) )).
fof(t12_sfmastr2,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( m1_scmfsa_2(D) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & ~ v1_xboole_0(E) & v1_funct_1(E) & v1_finset_1(E) & v1_afinsq_1(E) ) => k18_scmfsa_2(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k3_sfmastr2(B,A,E,C),k5_numbers),D) = k18_scmfsa_2(A,D) ) ) ) ) ) )).
fof(t12_sfmastr3,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & ~ v1_scmfsa_m(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( B != C => k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k1_sfmastr3(F,B,C,D,E,A),k5_numbers),C) = k1_funct_1(A,C) ) ) ) ) ) ) ) )).
fof(t12_sgraph1,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_tarski(k2_sgraph1(A),k2_sgraph1(B)) ) )).
fof(t12_sheffer1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t12_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t12_simplex0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( 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] : ~ ( r2_hidden(C,B) & k1_card_1(C) != 1 & ! [D] : ~ ( r2_hidden(D,C) & r2_hidden(k6_subset_1(C,k1_tarski(D)),B) ) ) ) ) )).
fof(t12_simplex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_simplex0(B,u1_struct_0(A)) => m1_simplex1(k5_simplex0(u1_struct_0(B),u1_pre_topc(B)),A,B) ) ) )).
fof(t12_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v7_ordinal1(C) => k9_nat_1(k2_numbers,k10_comseq_3(k10_sin_cos(k1_nat_1(C,1),B,A)),C) = k2_xcmplx_0(k9_nat_1(k2_numbers,k10_comseq_3(k10_sin_cos(C,B,A)),C),k9_nat_1(k2_numbers,k10_comseq_3(k9_sin_cos(k1_nat_1(C,1),B,A)),C)) ) ) ) )).
fof(t12_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k22_sin_cos,k2_xcmplx_0(A,B)) = k3_xcmplx_0(k1_funct_1(k22_sin_cos,A),k1_funct_1(k22_sin_cos,B)) ) ) )).
fof(t12_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,k6_xcmplx_0(A,B)) = k6_xcmplx_0(k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,B)),k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,B))) ) ) )).
fof(t12_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( k19_sin_cos(A) != k5_numbers & k19_sin_cos(B) != k5_numbers & k19_sin_cos(C) != k5_numbers & k19_sin_cos(k2_xcmplx_0(k2_xcmplx_0(A,B),C)) != k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k19_sin_cos(A),k19_sin_cos(B)),k19_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)))) ) ) ) ) )).
fof(t12_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => k2_sin_cos4(A) = k7_xcmplx_0(1,k1_sin_cos4(A)) ) )).
fof(t12_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ~ ( ~ r1_xxreal_0(A,k2_xcmplx_0(k28_sin_cos,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B))) & ~ r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)),A) & r1_xxreal_0(k5_numbers,k17_sin_cos(A)) ) ) ) )).
fof(t12_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( A != 1 & r1_xxreal_0(k1_square_1(k6_xcmplx_0(1,A)),k5_numbers) ) ) )).
fof(t12_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k6_xcmplx_0(k1_square_1(k2_sin_cos2(A)),k1_square_1(k4_sin_cos2(B))) = k6_xcmplx_0(k3_xcmplx_0(k2_sin_cos2(k2_xcmplx_0(A,B)),k2_sin_cos2(k6_xcmplx_0(A,B))),1) ) ) )).
fof(t12_sin_cos9,axiom,( k2_relset_1(k1_numbers,k2_sin_cos9) = k2_rcomp_1(k5_numbers,k28_sin_cos) )).
fof(t12_sincos10,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(t12_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => r1_sppol_1(A,C,k1_rltopsp1(k15_euclid(A),B,C)) ) ) ) )).
fof(t12_sppol_2,axiom,( ! [A] : ( 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 ) )).
fof(t12_sprect_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t12_sprect_2,axiom,( ! [A] : ( ( v2_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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)) ) ) ) )).
fof(t12_sprect_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(B,C) & r1_xxreal_0(C,k1_matrix_0(D)) & r1_xxreal_0(1,A) & r1_xxreal_0(A,k3_finseq_1(D)) ) => r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,A,B)),k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,A,C))) ) ) ) ) ) )).
fof(t12_sprect_5,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t12_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( k5_numbers != A & r1_xxreal_0(k1_square_1(A),k5_numbers) ) ) )).
fof(t12_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k4_ordinal1)) ) => ( r1_tarski(B,k7_card_1(A)) => r1_xxreal_0(k3_nat_1(B),k6_xcmplx_0(A,1)) ) ) ) )).
fof(t12_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t12_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_tarski(B,C) <=> r1_tarski(k3_subset_1(A,C),k3_subset_1(A,B)) ) ) ) )).
fof(t12_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( 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)) ) ) )).
fof(t12_supinf_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( m1_subset_1(B,k6_numbers) => ( m2_xxreal_2(B,A) <=> m1_xxreal_2(k2_supinf_2(B),k6_supinf_2(A)) ) ) ) )).
fof(t12_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_orders_2(B,k5_algstr_0(B,E,k4_vectsp_1(A,B,F,D)),C) & r1_orders_2(B,k5_algstr_0(B,E,k4_vectsp_1(A,B,G,D)),C) ) => ( r1_orders_2(B,D,C) | F = G ) ) ) ) ) ) ) ) ) )).
fof(t12_sysrel,axiom,( ! [A] : k3_relat_1(k4_relat_1(A),k4_relat_1(A)) = k4_relat_1(A) )).
fof(t12_t_0topsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v6_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(t12_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_taxonom1(k1_tarski(k1_tarski(A)),A) ) )).
fof(t12_taylor_1,axiom,( ! [A] : ( v1_xreal_0(A) => k3_power(k4_power,k23_sin_cos(A)) = A ) )).
fof(t12_taylor_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(D,E) & r1_xxreal_0(C,k7_xcmplx_0(k3_xcmplx_0(A,k1_newton(B,E)),k2_newton(E))) ) ) ) ) ) ) ) )).
fof(t12_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(C,k5_numbers) => k8_metric_1(A,B,C) = k1_xboole_0 ) ) ) ) )).
fof(t12_tdgroup,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r1_tdgroup(A,B,D,D,C) ) ) ) ) )).
fof(t12_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t12_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t12_tdlat_3,axiom,( ! [A] : ( ( v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) )).
fof(t12_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t12_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( 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) ) ) )).
fof(t12_tex_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [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_tdlat_3(A) ) => v1_tdlat_3(B) ) ) ) )).
fof(t12_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_tex_3(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( m1_pre_topc(C,A) => ( m1_pre_topc(B,C) => v1_tex_3(C,A) ) ) ) ) )).
fof(t12_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(t12_tietze,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( ~ r1_tsep_1(B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_tsep_1(A,B,C))) => ( ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & E = D ) & ? [E] : ( m1_subset_1(E,u1_struct_0(C)) & E = D ) ) ) ) ) ) ) )).
fof(t12_toler_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t12_topalg_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k14_euclid(C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k14_euclid(C))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k14_euclid(C))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k14_euclid(C))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k15_euclid(C))) => ! [K] : ( m1_subset_1(K,u1_struct_0(k15_euclid(C))) => ! [L] : ( m1_subset_1(L,u1_struct_0(k15_euclid(C))) => ! [M] : ( 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,k3_metric_1(k14_euclid(C),D,E)) & ~ r1_xxreal_0(B,k3_metric_1(k14_euclid(C),F,G)) & r1_xxreal_0(k2_xcmplx_0(A,B),k3_metric_1(k14_euclid(C),H,I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_topalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_topalg_2(A) & m1_pre_topc(A,k2_topalg_2) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( m1_borsuk_2(E,A,B,C) => r4_borsuk_2(A,B,C,D,E) ) ) ) ) ) )).
fof(t12_topalg_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_tops_2(B,A) & v4_taxonom2(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( v2_connsp_1(C,A) & r2_hidden(D,B) & m1_setfam_1(B,C) ) => ( r1_xboole_0(D,C) | r1_tarski(C,D) ) ) ) ) ) )).
fof(t12_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t12_topalg_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t12_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v2_topalg_6(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_borsuk_6(A,B,C) & ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t12_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t12_topdim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t12_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)))) ) ) ) )).
fof(t12_topgen_2,axiom,( ! [A] : k1_card_1(k10_eqrel_1(A)) = k1_card_1(A) )).
fof(t12_topgen_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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))) ) ) ) )).
fof(t12_topgen_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v3_topgen_4(B,A) => r2_hidden(k1_xboole_0,B) ) ) )).
fof(t12_topgen_5,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v3_pre_topc(C,A) & v4_pre_topc(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) )).
fof(t12_topgrp_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t12_topmetr,axiom,( ! [A] : ( 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) ) ) )).
fof(t12_topreal1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t12_topreal3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(A,k1_rltopsp1(k15_euclid(2),k19_euclid(C,B),k19_euclid(D,B))) => k18_euclid(A) = B ) ) ) ) ) )).
fof(t12_topreal4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)),k7_xcmplx_0(k2_xcmplx_0(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)) ) ) ) ) ) ) )).
fof(t12_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k3_euclid(k10_finseq_1(A,B)) = k10_finseq_1(k9_complex1(A),k9_complex1(B)) ) ) )).
fof(t12_topreal7,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ( ( k3_finseq_1(A) = k3_finseq_1(C) & k3_finseq_1(B) = k3_finseq_1(D) ) => k12_rvsum_1(k4_rvsum_1(k8_finseq_1(k1_numbers,A,B),k8_finseq_1(k1_numbers,C,D))) = k8_finseq_1(k1_numbers,k12_rvsum_1(k4_rvsum_1(A,C)),k12_rvsum_1(k4_rvsum_1(B,D))) ) ) ) ) ) )).
fof(t12_topreal8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(t12_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => ( C = D => k9_metric_1(k14_euclid(A),D,B) = k2_topreal9(A,C,B) ) ) ) ) ) )).
fof(t12_topreala,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_tsep_1(C,B) & m1_pre_topc(C,B) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t12_toprealb,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ( m1_subset_1(B,u1_struct_0(k8_toprealb(A))) => k12_euclid(B) = 1 ) ) ) )).
fof(t12_toprealc,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xcmplx_0(C) => k39_valued_1(k1_funct_7(k5_euclid(B),A,C)) = k1_funct_7(k5_euclid(B),A,k1_square_1(C)) ) ) )).
fof(t12_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) )).
fof(t12_tops_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_pre_topc(A,B)) <=> ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t12_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t12_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_tops_1(B,A) <=> ! [C] : ( 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) ) ) ) ) ) )).
fof(t12_tops_4,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(k3_topmetr)) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => ? [D] : ( 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)))) ) ) ) ) ) )).
fof(t12_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t12_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t12_treal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_topmetr(k5_numbers,1))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_topmetr(k5_numbers,1))) => v5_pre_topc(k4_treal_1(A,B,C,D),k4_topmetr(A,B),k4_topmetr(k5_numbers,1)) ) ) ) ) ) )).
fof(t12_trees_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t12_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k7_finseq_1(B,k9_finseq_1(C)),k1_trees_2(A,B)) <=> r2_hidden(k7_finseq_1(B,k9_finseq_1(C)),A) ) ) ) ) )).
fof(t12_trees_3,axiom,( ! [A] : ( v1_trees_3(k1_tarski(A)) <=> ( ~ v1_xboole_0(A) & v1_trees_1(A) ) ) )).
fof(t12_trees_4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v6_trees_3(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_trees_2(D) ) => ! [E] : ( m1_trees_1(E,k9_xtuple_0(D)) => ( D = k1_funct_1(B,k1_nat_1(C,1)) => ( r1_xxreal_0(k3_finseq_1(B),C) | k1_funct_1(k4_trees_4(A,B),k8_finseq_1(k4_ordinal1,k14_trees_3(C),E)) = k1_funct_1(D,E) ) ) ) ) ) ) )).
fof(t12_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( ( 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 ) ) ) )).
fof(t12_trees_a,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ! [C] : ( m4_trees_1(C,k9_xtuple_0(A)) => ( C != k1_xboole_0 => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( 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) ) ) ) ) ) ) )).
fof(t12_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_borsuk_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => ( v4_pre_topc(D,B) <=> v4_pre_topc(C,A) ) ) ) ) ) ) )).
fof(t12_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t12_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v1_tsp_1(k6_domain_1(u1_struct_0(A),B),A) ) ) )).
fof(t12_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( v1_tsp_2(B,A) & ! [C] : ( ( ~ v2_struct_0(C) & v1_pre_topc(C) & m1_pre_topc(C,A) ) => ~ ( v2_tsp_2(C,A) & B = u1_struct_0(C) ) ) ) ) ) )).
fof(t12_turing_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( l1_turing_1(C) => ! [D] : ( 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)),k9_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) ) => k9_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) = k9_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) ) ) ) ) ) )).
fof(t12_twoscomp,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( 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)) ) ) ) ) )).
fof(t12_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( v1_unialg_1(B) & m1_unialg_2(B,A) ) => ! [C] : ( ( v1_unialg_1(C) & m1_unialg_2(C,A) ) => ( u1_struct_0(B) = u1_struct_0(C) => B = C ) ) ) ) )).
fof(t12_unialg_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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))) ) ) ) )).
fof(t12_uniform1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r2_hidden(A,k1_rcomp_1(C,D)) & r2_hidden(B,k1_rcomp_1(C,D)) ) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(A,B)),k6_xcmplx_0(D,C)) ) ) ) ) ) )).
fof(t12_uniroots,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k1_binop_1(k4_group_1(A),B,k3_xcmplx_0(C,D)) = k1_binop_1(k4_group_1(A),k1_binop_1(k4_group_1(A),B,C),D) ) ) ) ) )).
fof(t12_uproots,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) => ( r6_pboole(A,B,k11_pre_poly(A,C,D)) => k2_uproots(A,B) = k2_xcmplx_0(k2_uproots(A,C),k2_uproots(A,D)) ) ) ) ) )).
fof(t12_urysohn1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_subset_1(B,k1_numbers,k1_urysohn1(A)) => ~ r1_xxreal_0(k7_xcmplx_0(k1_nat_1(k6_urysohn1(A,B),1),k1_newton(2,A)),k7_xcmplx_0(k6_xcmplx_0(k6_urysohn1(A,B),1),k1_newton(2,A))) ) ) )).
fof(t12_urysohn2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ( v4_measure5(A) => ( r1_xxreal_0(k5_numbers,B) | v3_measure5(k1_integra2(A,B)) ) ) ) ) )).
fof(t12_urysohn3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v10_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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] : ( m2_urysohn3(D,A,B,C) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( ( r2_hidden(E,k3_urysohn1) & r2_hidden(F,k3_urysohn1) ) => ( r1_xxreal_0(F,E) | ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) => ( G = k1_funct_1(k4_urysohn3(A,B,C,D),E) => r1_tarski(k2_pre_topc(A,G),k1_funct_1(k4_urysohn3(A,B,C,D),F)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t12_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_funct_2(C,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t12_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v4_valued_0(A) <=> ! [B] : v7_ordinal1(k1_funct_1(A,B)) ) ) )).
fof(t12_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t12_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(t12_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m1_vectsp_4(E,A,B) => ! [F] : ( m1_vectsp_4(F,A,E) => ! [G] : ( m1_vectsp_4(G,A,E) => ( ( F = C & G = D ) => k1_vectsp_5(A,E,F,G) = k1_vectsp_5(A,B,C,D) ) ) ) ) ) ) ) ) )).
fof(t12_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp11(C,A,B,k3_struct_0(B)) => C = k1_group_1(A) ) ) ) )).
fof(t12_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_algstr_0(A,B,C) = k4_struct_0(A) <=> k4_algstr_0(A,B) = C ) ) ) ) )).
fof(t12_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t12_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => k4_struct_0(C) = k4_struct_0(D) ) ) ) ) )).
fof(t12_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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 ) ) )).
fof(t12_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( ( 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)) ) ) ) ) ) ) )).
fof(t12_vectsp_7,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( C = u1_struct_0(B) => k1_vectsp_7(A,B,C) = B ) ) ) ) )).
fof(t12_vectsp_8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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)) ) ) ) ) ) )).
fof(t12_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t12_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t12_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t12_waybel10,axiom,( ! [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] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(k2_waybel10(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t12_waybel11,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => v3_pre_topc(k3_subset_1(u1_struct_0(A),k5_waybel_0(A,B)),A) ) ) )).
fof(t12_waybel12,axiom,( ! [A] : ( ( v5_orders_2(A) & v2_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( 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))) ) ) )).
fof(t12_waybel13,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) => ( v1_waybel_3(B,k1_yellow_1(k7_waybel_0(A))) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & B = k5_waybel_0(A,C) ) ) ) ) )).
fof(t12_waybel14,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t12_waybel15,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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 ) ) ) ) )).
fof(t12_waybel16,axiom,( ! [A] : ( ~ v1_xboole_0(k1_tarski(A)) & v2_waybel_0(k1_tarski(A),k2_yellow_1(A)) & v13_waybel_0(k1_tarski(A),k2_yellow_1(A)) & m1_subset_1(k1_tarski(A),k1_zfmisc_1(u1_struct_0(k2_yellow_1(A)))) ) )).
fof(t12_waybel17,axiom,( ! [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) & l1_orders_2(A) ) => ! [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) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) )).
fof(t12_waybel18,axiom,( ! [A] : ( ( v4_waybel11(A) & m1_yellow_9(A,k2_yellow_1(k1_tarski(k5_numbers))) ) => u1_pre_topc(A) = u1_pre_topc(k9_waybel18) ) )).
fof(t12_waybel19,axiom,( ! [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) & v1_waybel19(A) & l1_waybel_9(A) ) => ! [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) & v1_waybel19(B) & l1_waybel_9(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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) ) ) ) ) )).
fof(t12_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v3_orders_2(D) & v5_orders_2(D) & l1_orders_2(D) ) => ! [E] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t12_waybel21,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( l1_orders_2(C) => ! [D] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t12_waybel22,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( 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),k1_yellow_1(k8_waybel_0(k2_yellow_1(A))),B) ) ) )).
fof(t12_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_yellow_0(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t12_waybel24,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_lattice3(C) & v2_lattice3(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) )).
fof(t12_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t12_waybel27,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ( ( v4_yellow_0(B,C) & m1_yellow_0(B,C) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t12_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t12_waybel30,axiom,( ! [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) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k2_waybel19(A)) <=> v3_pre_topc(B,A) ) ) ) )).
fof(t12_waybel31,axiom,( ! [A] : ( ( 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) ) )).
fof(t12_waybel32,axiom,( ! [A] : ( ( 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] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => k5_waybel11(A) = u1_pre_topc(B) ) ) )).
fof(t12_waybel33,axiom,( ! [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] : ( ( ~ v1_xboole_0(B) & v1_subset_1(B,u1_struct_0(k2_yellow_1(k2_struct_0(A)))) & v2_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t12_waybel34,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ! [C] : ! [D] : ~ ( r2_hidden(D,k1_binop_1(u1_altcat_1(A),B,C)) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) )).
fof(t12_waybel35,axiom,( ! [A] : ( ( ~ 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] : ( ( v2_waybel_4(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ( m1_waybel35(C,A,B) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t12_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ( v11_waybel_0(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t12_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t12_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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))) ) ) )).
fof(t12_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t12_waybel_4,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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)) ) ) ) )).
fof(t12_waybel_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_funcop_1(C) ) => ( ( k9_xtuple_0(B) = k9_xtuple_0(C) & ! [D] : ( 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)) ) ) ) ) )).
fof(t12_waybel_6,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t12_waybel_7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & r2_hidden(D,B) ) ) ) ) ) ) ) )).
fof(t12_waybel_8,axiom,( ! [A] : ( l1_orders_2(A) => ! [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) ) => v3_orders_2(B) ) ) ) )).
fof(t12_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(t12_weddwitt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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)) ) ) )).
fof(t12_weierstr,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ( v2_compts_1(A,k3_topmetr) => v2_rcomp_1(k1_weierstr(A)) ) ) )).
fof(t12_wellord1,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) ) ) )).
fof(t12_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ( k3_int_2(C,D) = 1 => ( k3_int_2(C,k1_newton(D,B)) = 1 & k3_int_2(k1_newton(C,A),k1_newton(D,B)) = 1 ) ) ) ) ) ) )).
fof(t12_xboole_1,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => k2_xboole_0(A,B) = B ) )).
fof(t12_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k5_xboolean(A,k4_xboolean(k3_xboolean(A),B)) = k5_xboolean(A,B) ) ) )).
fof(t12_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(3,A) = k2_xcmplx_0(k2_xcmplx_0(A,A),A) ) )).
fof(t12_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k6_xcmplx_0(A,B),C) => r1_xxreal_0(k6_xcmplx_0(A,C),B) ) ) ) ) )).
fof(t12_xtuple_0,axiom,( ! [A] : ! [B] : ~ ( r2_hidden(A,k11_xtuple_0(B)) & ! [C] : ! [D] : ~ r2_hidden(k3_xtuple_0(A,C,D),B) ) )).
fof(t12_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ~ ( r2_hidden(A,k1_numbers) & r1_xxreal_0(A,k2_xxreal_0) ) ) )).
fof(t12_xxreal_1,axiom,( ! [A] : ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(A,k3_xxreal_1(B,C)) => ( r2_hidden(A,k1_xxreal_1(B,C)) & A != B ) ) ) ) )).
fof(t12_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k4_xxreal_0(A,B) = k1_xxreal_2(k2_tarski(A,B)) ) ) )).
fof(t12_xxreal_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( k3_xxreal_3(A,B) = k3_xxreal_3(A,C) => B = C ) ) ) ) )).
fof(t12_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B))) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t12_yellow11,axiom,( ! [A] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t12_yellow12,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t12_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v19_waybel_0(k4_waybel_1(A,B),A,A) ) ) )).
fof(t12_yellow14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ( ( r5_waybel_1(A,B) & v1_lattice3(A) ) => v1_lattice3(B) ) ) ) )).
fof(t12_yellow15,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k9_setfam_1(A)) => m1_subset_1(a_2_0_yellow15(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) )).
fof(t12_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t12_yellow17,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(k4_waybel18(A,B,C))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t12_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t12_yellow20,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) )).
fof(t12_yellow21,axiom,( ! [A] : ( ~ v2_setfam_1(A) => r1_tarski(u1_struct_0(k6_yellow21(A)),k2_yellow21(A)) ) )).
fof(t12_yellow_0,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r1_lattice3(A,B,C) & r1_orders_2(A,D,C) ) => r1_lattice3(A,B,D) ) ) ) ) )).
fof(t12_yellow_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ! [B] : ! [C] : ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r2_hidden(k3_xboole_0(B,C),A) ) => v2_lattice3(k1_yellow_1(A)) ) ) )).
fof(t12_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t12_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t12_yellow_4,axiom,( ! [A] : ( ( v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => r2_yellow_4(A,B,k2_yellow_4(A,B,C)) ) ) ) )).
fof(t12_yellow_5,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t12_yellow_6,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_yellow_6(C,A,B) & m1_yellow_6(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ( ( D = F & E = G & r1_orders_2(B,D,E) ) => r1_orders_2(C,F,G) ) ) ) ) ) ) ) ) )).
fof(t12_yellow_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( r1_yellow_0(A,B) | r2_yellow_0(k7_lattice3(A),B) ) => k1_yellow_0(A,B) = k2_yellow_0(k7_lattice3(A),B) ) ) )).
fof(t12_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(D,C) => ( v3_pre_topc(D,A) & r2_hidden(B,D) ) ) ) ) ) ) )).
fof(t12_yellow_9,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( 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) ) ) ) )).
fof(t12_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t12_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ~ ( ~ v7_zf_lang(A) & ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ~ r1_xxreal_0(k1_nat_1(k3_finseq_1(B),1),k3_finseq_1(A)) ) ) ) )).
fof(t12_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,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) ) ) ) ) )).
fof(t12_zf_model,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,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) ) ) ) ) ) )).
fof(t12_zf_refle,axiom,( ! [A] : ( v3_ordinal1(A) => k2_ordinal1(k4_classes1(A)) = A ) )).
fof(t12_zfmisc_1,axiom,( ! [A] : ! [B] : ( k3_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A) => A = B ) )).
fof(t12_zfmodel1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t12_zfmodel2,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t12_zfrefle1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t12_zmodul01,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ 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] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ( ( k3_finseq_1(C) = k3_finseq_1(D) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( 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) ) ) ) ) ) )).
fof(t12_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m2_zmodul02(B,A,k1_subset_1(u1_struct_0(A))) => r2_funct_2(u1_struct_0(A),k4_numbers,B,k19_zmodul02(A)) ) ) )).
fof(t12_zmodul03,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul02(C,B) => ? [D] : ( m1_zmodul02(D,A) & k18_zmodul02(B,C) = k18_zmodul02(A,D) & k21_zmodul02(B,C) = k21_zmodul02(A,D) ) ) ) ) )).
fof(t130_abcmiz_1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ 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] : ( m4_abcmiz_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m2_finseq_1(E,k1_funct_1(u3_msualg_1(A,k1_msafree3(A,B)),D)) => ( m2_finseq_1(k1_partfun1(k4_ordinal1,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(k4_ordinal1,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) ) ) ) ) ) ) )).
fof(t130_finseq_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t130_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( k1_funct_6(k9_finseq_1(A)) = k9_finseq_1(k9_xtuple_0(A)) & k2_funct_6(k9_finseq_1(A)) = k9_finseq_1(k10_xtuple_0(A)) ) ) )).
fof(t130_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) ) => r1_funct_7(B,C,A) ) ) )).
fof(t130_gfacirc1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => k2_msafree2(k49_gfacirc1(A,B,C)) = k1_enumset1(A,B,C) ) ) ) )).
fof(t130_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ~ ( r1_glib_000(A,k4_glib_001(A,B),D,C) & v3_glib_001(k10_glib_001(A,B,C),A) ) ) ) )).
fof(t130_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_group_2(D,A) => r2_wellord2(k14_group_2(A,D,B),k14_group_2(A,D,C)) ) ) ) ) )).
fof(t130_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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)) ) ) )).
fof(t130_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ! [C] : ( ( r2_hidden(B,C) & C = a_0_2_jgraph_4 ) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) | r1_xxreal_0(1,A) | r2_hidden(k1_funct_1(k9_jgraph_4(A),B),C) ) ) ) )).
fof(t130_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t130_member_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k15_member_1(k2_tarski(A,B),k1_tarski(C)) = k2_tarski(k7_xcmplx_0(A,C),k7_xcmplx_0(B,C)) ) ) ) )).
fof(t130_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t130_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( ( v3_relat_1(C) & r2_pboole(A,B,C) ) => v3_relat_1(B) ) ) ) )).
fof(t130_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(t130_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k4_finseq_2(A,k1_numbers)) => k22_rvsum_1(k5_rvsum_1(A,B,C),D) = k2_xcmplx_0(k22_rvsum_1(B,D),k22_rvsum_1(C,D)) ) ) ) ) )).
fof(t130_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k12_seq_4(A))) => ( r2_hidden(B,k25_seq_4(A)) <=> v1_seq_4(B,A) ) ) ) )).
fof(t130_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t130_sin_cos9,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(1),1)) ) => ( r2_hidden(k5_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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k2_sin_cos9,B),k1_square_1(B))),k7_xcmplx_0(1,k3_xcmplx_0(B,k2_xcmplx_0(1,k1_square_1(B))))) ) ) ) ) ) ) )).
fof(t130_sincos10,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k2_sincos10,k7_relset_1(k1_numbers,k1_numbers,k1_fdiff_9,k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos)))) )).
fof(t130_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t130_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t130_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ~ ( B != k5_numbers & D != k5_numbers & k6_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(C,D)) != k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(C,B)),k3_xcmplx_0(B,D)) ) ) ) ) ) )).
fof(t130_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k3_xcmplx_0(A,B),k5_numbers) ) ) ) )).
fof(t130_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t130_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( ~ v1_xboole_0(D) => ( ~ r2_hidden(C,k2_zf_model(B)) => r2_zf_model(D,k11_zf_lang(k8_zf_lang(C,k11_zf_lang(A,B)),k11_zf_lang(k13_zf_lang(C,A),B))) ) ) ) ) ) )).
fof(t130_zfmisc_1,axiom,( ! [A] : ~ ( ~ v1_xboole_0(A) & v1_zfmisc_1(A) & ! [B] : A != k1_tarski(B) ) )).
fof(t130_zmodul01,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t131_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_abcmiz_1)) => ( k1_relset_1(k2_abcmiz_1,k54_abcmiz_1(A,B)) = B & ! [C] : ( 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) ) ) ) ) ) )).
fof(t131_finseq_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,A) => ( r2_hidden(C,k4_finseq_2(B,A)) <=> k3_finseq_1(C) = B ) ) ) )).
fof(t131_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( k1_funct_6(k10_finseq_1(A,B)) = k10_finseq_1(k9_xtuple_0(A),k9_xtuple_0(B)) & k2_funct_6(k10_finseq_1(A,B)) = k10_finseq_1(k10_xtuple_0(A),k10_xtuple_0(B)) ) ) ) )).
fof(t131_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => r1_funct_7(k1_funct_4(D,B),k1_funct_4(D,C),A) ) ) ) )).
fof(t131_gfacirc1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ~ v1_facirc_1(k2_msafree2(k49_gfacirc1(A,B,C))) ) ) ) )).
fof(t131_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ~ ( ~ v3_glib_001(B,A) & ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ~ ( C = k6_xcmplx_0(k3_finseq_1(B),2) & r2_relset_1(k4_ordinal1,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,k1_nat_1(C,1))),B) ) ) ) ) ) )).
fof(t131_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t131_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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] : ( v1_finset_1(C) => ~ ( C = k8_group_3(A,B) & k5_card_1(C) = k18_group_2(A,k10_group_3(A,B)) ) ) ) ) ) )).
fof(t131_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t131_member_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => k15_member_1(k2_tarski(A,B),k2_tarski(C,D)) = k2_enumset1(k7_xcmplx_0(A,C),k7_xcmplx_0(A,D),k7_xcmplx_0(B,C),k7_xcmplx_0(B,D)) ) ) ) ) )).
fof(t131_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r1_tarski(B,k1_relset_1(u1_struct_0(A),C)) & ! [F] : ( 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) ) ) ) ) ) )).
fof(t131_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t131_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t131_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [D] : ( v1_xreal_0(D) => k22_rvsum_1(k11_rvsum_1(A,B,D),C) = k3_xcmplx_0(D,k22_rvsum_1(B,C)) ) ) ) ) )).
fof(t131_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k12_seq_4(A))) => ( v2_seq_4(B,A) <=> v1_seq_4(k3_subset_1(k12_seq_4(A),B),A) ) ) ) )).
fof(t131_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t131_sincos10,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k3_sincos10,k7_relset_1(k1_numbers,k1_numbers,k2_fdiff_9,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers)))) )).
fof(t131_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ v2_struct_0(E) & m1_pre_topc(E,A) ) => ! [F] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(t131_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t131_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( A != k5_numbers => k6_xcmplx_0(A,B) = k3_xcmplx_0(A,k6_xcmplx_0(1,k7_xcmplx_0(B,A))) ) ) ) )).
fof(t131_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(B,k5_numbers) ) => r1_xxreal_0(k3_xcmplx_0(A,B),k5_numbers) ) ) ) )).
fof(t131_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t131_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( ~ v1_xboole_0(D) => ( r2_zf_model(D,k11_zf_lang(A,B)) => ( r2_hidden(C,k2_zf_model(B)) | r2_zf_model(D,k11_zf_lang(k13_zf_lang(C,A),B)) ) ) ) ) ) ) )).
fof(t131_zfmisc_1,axiom,( ! [A] : ! [B] : ( v1_zfmisc_1(B) => ( r2_hidden(A,B) => B = k1_tarski(A) ) ) )).
fof(t131_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( m2_zmodul01(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t132_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_abcmiz_1,k34_abcmiz_1(A)))) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t132_finseq_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => r1_tarski(k4_finseq_2(B,A),k3_finseq_2(A)) ) )).
fof(t132_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( k1_funct_6(k11_finseq_1(A,B,C)) = k11_finseq_1(k9_xtuple_0(A),k9_xtuple_0(B),k9_xtuple_0(C)) & k2_funct_6(k11_finseq_1(A,B,C)) = k11_finseq_1(k10_xtuple_0(A),k10_xtuple_0(B),k10_xtuple_0(C)) ) ) ) ) )).
fof(t132_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t132_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ( r1_tarski(k14_glib_001(A,C),k14_glib_001(A,B)) => ( v3_glib_001(C,A) | r1_tarski(k13_glib_001(A,C),k13_glib_001(A,B)) ) ) ) ) ) )).
fof(t132_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t132_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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))) ) ) )).
fof(t132_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ~ v5_pre_topc(k9_jgraph_4(A),k15_euclid(2),k15_euclid(2)) ) ) )).
fof(t132_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t132_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(C,A) => r2_hidden(k1_xxreal_3(B,C),k16_member_1(A,B)) ) ) ) ) )).
fof(t132_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_numbers))) ) => ( ! [C] : ( 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) = k2_normsp_0(A,C) ) ) => r11_ncfcont1(A,B,k1_relset_1(u1_struct_0(A),B)) ) ) ) )).
fof(t132_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t132_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t132_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => k22_rvsum_1(k7_rvsum_1(A,B),C) = k4_xcmplx_0(k22_rvsum_1(B,C)) ) ) ) )).
fof(t132_seq_4,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A != k1_xboole_0 => ( v4_xxreal_2(A) & r2_hidden(k2_seq_4(A),A) & v3_xxreal_2(A) & r2_hidden(k3_seq_4(A),A) ) ) ) )).
fof(t132_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,C,B)) = C ) ) ) )).
fof(t132_sincos10,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k4_sincos10,k7_relset_1(k1_numbers,k1_numbers,k2_fdiff_9,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))))) )).
fof(t132_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( ~ r1_tsep_1(C,D) => ! [E] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) ) ) )).
fof(t132_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ( k7_xboolean(A,B) = k2_xboolean <=> ( k6_xboolean(A,B) = k2_xboolean & k6_xboolean(B,A) = k2_xboolean ) ) ) ) )).
fof(t132_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( A != k5_numbers => C = k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,C),B),B),A) ) ) ) ) )).
fof(t132_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k5_numbers,k3_xcmplx_0(A,B)) ) ) ) )).
fof(t132_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t132_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( ~ 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)) ) ) ) ) ) )).
fof(t132_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( r2_hidden(A,D) & r2_hidden(B,D) & r2_hidden(C,D) ) => r1_tarski(k1_enumset1(A,B,C),D) ) )).
fof(t132_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ( r1_zmodul01(A,B,C) <=> ! [D] : ( m2_zmodul01(D,A,B) => ! [E] : ( m2_zmodul01(E,A,C) => ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t133_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_abcmiz_1,k34_abcmiz_1(A)))) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t133_finseq_2,axiom,( ! [A] : ! [B] : ( r2_hidden(B,k4_finseq_2(1,A)) <=> ? [C] : ( r2_hidden(C,A) & B = k9_finseq_1(C) ) ) )).
fof(t133_finseq_3,axiom,( ! [A] : ( k3_card_3(k9_finseq_1(A)) = A & k3_funct_6(k9_finseq_1(A)) = A ) )).
fof(t133_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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) ) ) ) )).
fof(t133_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t133_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( ~ v3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ~ ( r2_hidden(C,k13_glib_001(A,B)) & v10_glib_000(C,A) ) ) ) ) ) )).
fof(t133_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v8_struct_0(C) & m1_group_2(C,A) ) => ? [D] : ( v1_finset_1(D) & ? [E] : ( 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) ) ) ) ) ) )).
fof(t133_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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] : ( 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))) ) ) ) ) ) )).
fof(t133_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ~ v2_funct_1(k9_jgraph_4(A)) ) ) )).
fof(t133_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t133_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => k16_member_1(A,B) = a_2_8_member_1(A,B) ) ) )).
fof(t133_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => k7_partfun1(k1_numbers,C,D) = k2_normsp_0(A,D) ) ) ) => r11_ncfcont1(A,C,B) ) ) ) )).
fof(t133_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t133_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r1_tarski(A,B) => r1_tarski(k8_relat_1(C,A),k8_relat_1(C,B)) ) ) )).
fof(t133_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => k22_rvsum_1(k7_rvsum_1(A,B),k7_rvsum_1(A,C)) = k22_rvsum_1(B,C) ) ) ) )).
fof(t133_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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)) ) ) ) ) ) )).
fof(t133_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,k5_sheffer1(A,C,B),k5_sheffer1(A,B,B)) = B ) ) ) )).
fof(t133_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( r1_tsep_1(C,D) => ! [E] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) ) ) )).
fof(t133_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t133_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k4_xcmplx_0(A) = k4_xcmplx_0(B) => A = B ) ) ) )).
fof(t133_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_numbers,k3_xcmplx_0(A,B)) & ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(k5_numbers,B) ) & ~ ( ~ r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,k5_numbers) ) ) ) ) )).
fof(t133_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t133_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( ~ 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)) ) ) ) ) ) )).
fof(t133_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(k4_tarski(A,B),C) => ( r2_hidden(A,k3_tarski(k3_tarski(C))) & r2_hidden(B,k3_tarski(k3_tarski(C))) ) ) )).
fof(t133_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t134_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_abcmiz_1(B,A) & m1_subset_1(B,u4_struct_0(A)) ) => ! [C] : ( m1_trees_4(C,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A)))),k34_abcmiz_1(A)) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t134_finseq_2,axiom,( ! [A] : ! [B] : ( r2_hidden(k9_finseq_1(B),k4_finseq_2(1,A)) => r2_hidden(B,A) ) )).
fof(t134_finseq_3,axiom,( ! [A] : ! [B] : ( k3_card_3(k10_finseq_1(A,B)) = k2_xboole_0(A,B) & k3_funct_6(k10_finseq_1(A,B)) = k3_xboole_0(A,B) ) )).
fof(t134_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( ( k9_xtuple_0(C) = k9_xtuple_0(D) & r1_tarski(B,k9_xtuple_0(C)) & r1_xboole_0(A,B) & r1_funct_7(C,D,A) ) => k5_relat_1(C,B) = k5_relat_1(D,B) ) ) ) )).
fof(t134_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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))) ) ) )).
fof(t134_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v3_glib_001(B,A) <=> k14_glib_001(A,B) = k1_xboole_0 ) ) ) )).
fof(t134_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(t134_group_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( v15_algstr_0(C) & m1_group_2(C,B) ) => ( r1_struct_0(k11_group_3(B,C),A) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = D & r1_group_2(B,k6_group_3(B,C,D),C) ) ) ) ) )).
fof(t134_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(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)) ) ) ) )).
fof(t134_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t134_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ~ ( r2_hidden(C,k16_member_1(A,B)) & ! [D] : ( m1_subset_1(D,k6_numbers) => ~ ( C = k1_xxreal_3(B,D) & r2_hidden(D,A) ) ) ) ) ) )).
fof(t134_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => ( r1_tarski(B,C) => r1_tarski(k8_relat_1(B,A),k8_relat_1(C,A)) ) ) ) )).
fof(t134_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k4_finseq_2(A,k1_numbers)) => k22_rvsum_1(k9_rvsum_1(A,B,C),D) = k6_xcmplx_0(k22_rvsum_1(B,D),k22_rvsum_1(C,D)) ) ) ) ) )).
fof(t134_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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)) ) ) ) ) ) )).
fof(t134_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t134_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_borsuk_1(C,A) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & v1_borsuk_1(D,A) & m1_pre_topc(D,A) ) => ( ~ r1_tsep_1(C,D) => ! [E] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) ) ) )).
fof(t134_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => k3_xboolean(k9_xboolean(A,k3_xboolean(A))) = k2_xboolean ) )).
fof(t134_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k4_xcmplx_0(A) = k5_numbers => A = k5_numbers ) ) )).
fof(t134_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k3_xcmplx_0(A,B),k5_numbers) & ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) ) & ~ ( ~ r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(k5_numbers,B) ) ) ) ) )).
fof(t134_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t134_zf_lang1,axiom,( r1_tarski(k9_zf_lang,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) )).
fof(t134_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( r1_tarski(C,k2_xboole_0(B,k1_tarski(A))) & ~ r2_hidden(A,C) & ~ r1_tarski(C,B) ) )).
fof(t134_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_zmodul01(A,B,C) & k3_rlvect_1(A,F,G) = k3_rlvect_1(A,D,E) & r1_struct_0(B,F) & r1_struct_0(B,D) & r1_struct_0(C,G) & r1_struct_0(C,E) ) => ( F = D & G = E ) ) ) ) ) ) ) ) ) )).
fof(t135_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_abcmiz_1(B,A,k13_abcmiz_1(A)) => ! [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,k30_abcmiz_1(A,k32_abcmiz_1(A),B)) = k30_abcmiz_1(A,k32_abcmiz_1(A),k56_abcmiz_1(A,C,B)) ) ) ) )).
fof(t135_finseq_2,axiom,( ! [A] : ! [B] : ( r2_hidden(B,k4_finseq_2(2,A)) <=> ? [C] : ? [D] : ( r2_hidden(C,A) & r2_hidden(D,A) & B = k10_finseq_1(C,D) ) ) )).
fof(t135_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : ( k3_card_3(k11_finseq_1(A,B,C)) = k2_xboole_0(k2_xboole_0(A,B),C) & k3_funct_6(k11_finseq_1(A,B,C)) = k3_xboole_0(k3_xboole_0(A,B),C) ) )).
fof(t135_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,C) & v1_funct_1(D) & v1_partfun1(D,C) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,C) & v1_funct_1(E) & v1_partfun1(E,C) ) => ( ( r1_tarski(C,k2_xboole_0(A,B)) & k5_relat_1(D,B) = k5_relat_1(E,B) ) => r1_funct_7(D,E,A) ) ) ) )).
fof(t135_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k49_gfacirc1(A,B,C),k50_gfacirc1(A,B,C)))) & ? [E] : ( m1_subset_1(E,k6_margrel1) & ? [F] : ( m1_subset_1(F,k6_margrel1) & ? [G] : ( 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)))) ) ) ) ) ) ) )).
fof(t135_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m3_glib_001(D,B) => ( ( C = D & v3_glib_001(C,A) ) => v3_glib_001(D,B) ) ) ) ) ) )).
fof(t135_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t135_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t135_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ! [C] : ( ( ~ 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] : ( 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) ) ) ) ) ) ) )).
fof(t135_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t135_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( v1_xreal_0(C) => ( r1_tarski(k16_member_1(A,C),k16_member_1(B,C)) => r1_tarski(A,B) ) ) ) ) )).
fof(t135_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( ! [D] : ( ( 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) ) ) ) )).
fof(t135_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ! [D] : ( v1_relat_1(D) => ( ( r1_tarski(C,D) & r1_tarski(A,B) ) => r1_tarski(k8_relat_1(C,A),k8_relat_1(D,B)) ) ) ) )).
fof(t135_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [F] : ( m2_finseq_2(F,k1_numbers,k4_finseq_2(A,k1_numbers)) => k22_rvsum_1(k5_rvsum_1(A,k11_rvsum_1(A,D,B),k11_rvsum_1(A,E,C)),F) = k2_xcmplx_0(k3_xcmplx_0(B,k22_rvsum_1(D,F)),k3_xcmplx_0(C,k22_rvsum_1(E,F))) ) ) ) ) ) ) )).
fof(t135_seq_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(C)) ) => k7_partfun1(A,k8_finseq_1(A,B,C),k1_nat_1(D,k3_finseq_1(B))) = k7_partfun1(A,C,D) ) ) ) ) ) )).
fof(t135_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,k5_sheffer1(A,C,B),k5_sheffer1(A,C,C)) = C ) ) ) )).
fof(t135_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_tsep_1(C,A) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & v1_tsep_1(D,A) & m1_pre_topc(D,A) ) => ( ~ r1_tsep_1(C,D) => ! [E] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) ) ) )).
fof(t135_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => k8_xboolean(A,k3_xboolean(A)) = k2_xboolean ) )).
fof(t135_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k2_xcmplx_0(A,k4_xcmplx_0(B)) = k5_numbers => A = B ) ) ) )).
fof(t135_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(B,k5_numbers) ) => r1_xxreal_0(k5_numbers,k7_xcmplx_0(A,B)) ) ) ) )).
fof(t135_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t135_zf_lang1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ( A != k5_numbers & A != 1 & A != 2 & A != 3 & A != 4 ) ) )).
fof(t135_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(A,k2_xboole_0(C,k1_tarski(B))) <=> ( r2_hidden(A,C) | A = B ) ) )).
fof(t135_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ( A = k6_zmodul01(A,B,C) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( 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) ) ) ) ) ) )).
fof(t136_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_abcmiz_1(B,A,k12_abcmiz_1(A)) => ! [C] : ( m1_abcmiz_1(C,A,k13_abcmiz_1(A)) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t136_finseq_2,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(k10_finseq_1(B,C),k4_finseq_2(2,A)) => ( r2_hidden(B,A) & r2_hidden(C,A) ) ) )).
fof(t136_finseq_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r2_hidden(A,k9_xtuple_0(B)) => ( k4_funct_6(k9_finseq_1(B),1,A) = k1_funct_1(B,A) & k4_funct_6(k10_finseq_1(B,C),1,A) = k1_funct_1(B,A) & k4_funct_6(k11_finseq_1(B,C,D),1,A) = k1_funct_1(B,A) ) ) ) ) ) )).
fof(t136_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,C) & v1_funct_1(D) & v1_partfun1(D,C) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,C) & v1_funct_1(E) & v1_partfun1(E,C) ) => ( ( r1_tarski(B,C) & r1_xboole_0(A,B) & r1_funct_7(D,E,A) ) => k5_relat_1(D,B) = k5_relat_1(E,B) ) ) ) )).
fof(t136_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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] : ( 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)) ) ) )).
fof(t136_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v4_glib_001(B,A) <=> ! [C] : ( ( v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ~ ( 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) ) ) ) ) ) ) )).
fof(t136_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => r2_wellord2(k15_group_2(A,B),k16_group_2(A,B)) ) ) )).
fof(t136_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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] : ( v1_finset_1(C) => ~ ( C = k9_group_3(A,B) & k5_card_1(C) = k18_group_2(A,k11_group_3(A,B)) ) ) ) ) ) )).
fof(t136_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ! [B] : ( ( 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)) ) ) ) ) )).
fof(t136_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t136_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( v1_xreal_0(C) => ( k16_member_1(A,C) = k16_member_1(B,C) => A = B ) ) ) ) )).
fof(t136_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v2_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( ! [E] : ( ( 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)) ) ) ) ) )).
fof(t136_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => k8_relat_1(k3_relat_1(B,C),A) = k8_relat_1(B,k8_relat_1(C,A)) ) ) )).
fof(t136_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k4_finseq_2(A,k1_numbers)) => k22_rvsum_1(k5_rvsum_1(A,B,C),k5_rvsum_1(A,D,E)) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k22_rvsum_1(B,D),k22_rvsum_1(B,E)),k22_rvsum_1(C,D)),k22_rvsum_1(C,E)) ) ) ) ) ) )).
fof(t136_seq_4,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( v5_valued_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r2_hidden(B,k4_finseq_1(A)) & r2_hidden(C,k4_finseq_1(A)) & r1_xxreal_0(B,C) ) => r1_xxreal_0(k1_funct_1(A,B),k1_funct_1(A,C)) ) ) ) ) ) )).
fof(t136_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t136_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_borsuk_1(C,A) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & v1_borsuk_1(D,A) & m1_pre_topc(D,A) ) => ( r1_tsep_1(C,D) => ! [E] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) ) )).
fof(t136_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k5_xboolean(A,k8_xboolean(A,B)) = k2_xboolean ) ) )).
fof(t136_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => A = k2_xcmplx_0(k2_xcmplx_0(A,B),k4_xcmplx_0(B)) ) ) )).
fof(t136_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => r1_xxreal_0(k5_numbers,k7_xcmplx_0(A,B)) ) ) ) )).
fof(t136_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t136_zf_lang1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ~ r2_hidden(A,k3_enumset1(k5_numbers,1,2,3,4)) ) )).
fof(t136_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(k2_xboole_0(C,k1_tarski(A)),B) <=> ( r2_hidden(A,B) & r1_tarski(C,B) ) ) )).
fof(t136_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t137_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_abcmiz_1)) => k56_abcmiz_1(A,k54_abcmiz_1(A,C),B) = B ) ) ) )).
fof(t137_finseq_2,axiom,( ! [A] : ! [B] : ( r2_hidden(B,k4_finseq_2(3,A)) <=> ? [C] : ? [D] : ? [E] : ( r2_hidden(C,A) & r2_hidden(D,A) & r2_hidden(E,A) & B = k11_finseq_1(C,D,E) ) ) )).
fof(t137_finseq_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r2_hidden(A,k9_xtuple_0(C)) => ( k4_funct_6(k10_finseq_1(B,C),2,A) = k1_funct_1(C,A) & k4_funct_6(k11_finseq_1(B,C,D),2,A) = k1_funct_1(C,A) ) ) ) ) ) )).
fof(t137_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( r1_tarski(A,B) => ( r2_hidden(C,k9_xtuple_0(A)) | r1_tarski(A,k1_funct_7(B,C,D)) ) ) ) ) )).
fof(t137_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( r1_xxreal_0(k3_finseq_1(B),3) => v4_glib_001(B,A) ) ) ) )).
fof(t137_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t137_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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 ) ) ) )).
fof(t137_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r1_xxreal_0(A,k7_xcmplx_0(k17_euclid(B),k12_euclid(B))) => ( r1_xxreal_0(1,A) | r1_xxreal_0(k5_numbers,k18_euclid(B)) | ! [C] : ( 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(k5_numbers,k18_euclid(C)) & r1_xxreal_0(k5_numbers,k17_euclid(C)) ) ) ) ) ) ) ) )).
fof(t137_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t137_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t137_pboole,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(t137_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => k9_xtuple_0(k3_relat_1(A,B)) = k8_relat_1(A,k9_xtuple_0(B)) ) ) )).
fof(t137_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k4_finseq_2(A,k1_numbers)) => k22_rvsum_1(k9_rvsum_1(A,B,C),k9_rvsum_1(A,D,E)) = k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k22_rvsum_1(B,D),k22_rvsum_1(B,E)),k22_rvsum_1(C,D)),k22_rvsum_1(C,E)) ) ) ) ) ) )).
fof(t137_seq_4,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( v5_valued_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(B,k4_finseq_1(A)) & r2_hidden(C,k4_finseq_1(A)) & B != C & k1_funct_1(A,B) = k1_funct_1(A,C) ) ) ) ) ) )).
fof(t137_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)))) ) ) ) ) ) ) )).
fof(t137_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_tsep_1(C,A) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & v1_tsep_1(D,A) & m1_pre_topc(D,A) ) => ( r1_tsep_1(C,D) => ! [E] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) ) )).
fof(t137_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k8_xboolean(A,k9_xboolean(A,B)) = k2_xboolean ) ) )).
fof(t137_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => A = k2_xcmplx_0(A,k2_xcmplx_0(B,k4_xcmplx_0(B))) ) ) )).
fof(t137_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(B,k5_numbers) ) => r1_xxreal_0(k7_xcmplx_0(A,B),k5_numbers) ) ) ) )).
fof(t137_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t137_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( r2_hidden(B,k3_zf_lang1(A)) => ( B != k5_numbers & B != 1 & B != 2 & B != 3 & B != 4 ) ) ) )).
fof(t137_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( r1_tarski(B,C) & r1_tarski(C,k2_xboole_0(B,k1_tarski(A))) & k2_xboole_0(B,k1_tarski(A)) != C & B != C ) )).
fof(t137_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t138_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( 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)))))) ) ) )).
fof(t138_finseq_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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) ) ) )).
fof(t138_finseq_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r2_hidden(A,k9_xtuple_0(D)) => k4_funct_6(k11_finseq_1(B,C,D),3,A) = k1_funct_1(D,A) ) ) ) ) )).
fof(t138_funct_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ! [F] : k1_funct_4(B,k4_funct_4(C,D,E,F)) = k1_funct_7(k1_funct_7(B,C,E),D,F) ) ) ) ) )).
fof(t138_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v4_glib_001(B,A) <=> v4_glib_001(k6_glib_001(A,B),A) ) ) ) )).
fof(t138_group_2,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t138_group_3,axiom,( ! [A] : ( ( ~ 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 ) )).
fof(t138_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(B)) & ~ r1_xxreal_0(A,k7_xcmplx_0(k17_euclid(B),k12_euclid(B))) & ? [C] : ( 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(k5_numbers,k18_euclid(C)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(C)) ) ) ) ) ) )).
fof(t138_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t138_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k10_xtuple_0(B)) => ? [D] : ( r2_hidden(D,A) & C = k1_funct_1(B,D) ) ) ) ) )).
fof(t138_relat_1,axiom,( ! [A] : ! [B] : ( 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))) ) )).
fof(t138_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => k22_rvsum_1(k5_rvsum_1(A,B,C),k5_rvsum_1(A,B,C)) = k2_xcmplx_0(k2_xcmplx_0(k22_rvsum_1(B,B),k3_xcmplx_0(2,k22_rvsum_1(B,C))),k22_rvsum_1(C,C)) ) ) ) )).
fof(t138_seq_4,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( v7_ordinal1(C) => ( ( v5_valued_0(A) & r2_relset_1(k4_ordinal1,k1_numbers,B,k2_partfun1(k4_ordinal1,k1_numbers,A,k2_finseq_1(C))) ) => v5_valued_0(B) ) ) ) ) )).
fof(t138_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)))) ) ) ) ) ) )).
fof(t138_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( r3_tsep_1(A,B,C) <=> ( r1_tsep_1(B,C) & ! [D] : ( ( ~ v2_struct_0(D) & v2_pre_topc(D) & l1_pre_topc(D) ) => ! [E] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) ) ) )).
fof(t138_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => k4_xboolean(A,k3_xboolean(A)) = k1_xboolean ) )).
fof(t138_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => A = k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),A),B) ) ) )).
fof(t138_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k5_numbers,B) ) => r1_xxreal_0(k7_xcmplx_0(A,B),k5_numbers) ) ) ) )).
fof(t138_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t138_zf_lang1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => k3_zf_lang1(k4_zf_lang(A,B)) = k2_tarski(A,B) ) ) )).
fof(t138_zfmisc_1,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) <=> ! [B] : ~ v1_xboole_0(k4_xboole_0(A,k1_tarski(B))) ) )).
fof(t138_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( v8_zmodul01(B,A) & m1_zmodul01(B,A) ) => ! [C] : ( m3_zmodul01(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t139_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [C] : ( ( 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 ) ) ) )).
fof(t139_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( r2_hidden(C,k4_finseq_2(A,B)) => ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) ) ) ) )).
fof(t139_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( k9_xtuple_0(k5_funct_6(k9_finseq_1(A))) = k9_xtuple_0(A) & ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => k1_funct_1(k5_funct_6(k9_finseq_1(A)),B) = k9_finseq_1(k1_funct_1(A,B)) ) ) ) )).
fof(t139_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v4_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => v4_glib_001(k8_glib_001(A,B,C,D),A) ) ) ) ) )).
fof(t139_group_2,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t139_group_3,axiom,( ! [A] : ( ( ~ 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 ) )).
fof(t139_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r1_xxreal_0(A,k7_xcmplx_0(k17_euclid(B),k12_euclid(B))) & r1_xxreal_0(A,k7_xcmplx_0(k17_euclid(C),k12_euclid(C))) ) => ( r1_xxreal_0(1,A) | r1_xxreal_0(k5_numbers,k18_euclid(B)) | r1_xxreal_0(k5_numbers,k18_euclid(C)) | r1_xxreal_0(k7_xcmplx_0(k17_euclid(C),k12_euclid(C)),k7_xcmplx_0(k17_euclid(B),k12_euclid(B))) | ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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(k7_xcmplx_0(k17_euclid(E),k12_euclid(E)),k7_xcmplx_0(k17_euclid(D),k12_euclid(D))) ) ) ) ) ) ) ) ) )).
fof(t139_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t139_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( r2_hidden(C,A) => m1_subset_1(k1_funct_1(B,C),k10_xtuple_0(B)) ) ) )).
fof(t139_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v3_relat_1(A) <=> ! [B] : ( r2_hidden(B,k10_xtuple_0(A)) => B = k1_xboole_0 ) ) ) )).
fof(t139_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => k22_rvsum_1(k9_rvsum_1(A,B,C),k9_rvsum_1(A,B,C)) = k2_xcmplx_0(k6_xcmplx_0(k22_rvsum_1(B,B),k3_xcmplx_0(2,k22_rvsum_1(B,C))),k22_rvsum_1(C,C)) ) ) ) )).
fof(t139_seq_4,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ? [B] : ( 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) ) ) )).
fof(t139_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t139_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( A = k1_tsep_1(A,C,D) => ! [E] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) ) ) )).
fof(t139_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ( k4_xboolean(A,A) = k1_xboolean => A = k1_xboolean ) ) )).
fof(t139_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k4_xcmplx_0(k2_xcmplx_0(A,B)) = k2_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) ) ) )).
fof(t139_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(k7_xcmplx_0(A,B),k5_numbers) ) ) ) )).
fof(t139_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => k3_xboole_0(k2_xxreal_1(C,D),k2_xxreal_1(A,B)) = k2_xxreal_1(k4_xxreal_0(C,A),k3_xxreal_0(D,B)) ) ) ) ) )).
fof(t139_zf_lang1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => k3_zf_lang1(k5_zf_lang(A,B)) = k2_tarski(A,B) ) ) )).
fof(t139_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( v8_zmodul01(B,A) & m1_zmodul01(B,A) ) => ! [C] : ( m3_zmodul01(C,A,B) => ! [D] : ( 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 ) ) ) ) )).
fof(t13_abcmiz_0,axiom,( ! [A] : ( l2_abcmiz_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_abcmiz_0(A)) => ( r2_hidden(C,k2_abcmiz_0(A,B)) <=> r2_hidden(B,k3_abcmiz_0(A,C)) ) ) ) ) )).
fof(t13_abcmiz_1,axiom,( ! [A] : ! [B] : 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)) )).
fof(t13_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & v1_abcmiz_a(A) & l1_msualg_1(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(t13_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r1_aff_1(A,E,C,D) & r2_analoaf(A,B,C,B,D) ) => ( r1_aff_1(A,E,B,C) | C = D ) ) ) ) ) ) ) )).
fof(t13_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v8_aff_2(A) => v12_aff_2(A) ) ) )).
fof(t13_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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 ) ) ) ) )).
fof(t13_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) )).
fof(t13_afinsq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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 ) ) )).
fof(t13_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t13_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & B != C & ~ r1_afvect0(A,B,C) ) ) ) )).
fof(t13_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t13_algspec1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(B,k6_partfun1(A)) => r6_pboole(A,k1_algspec1(A,B),k6_partfun1(A)) ) ) )).
fof(t13_algstr_1,axiom,( ! [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] : ( 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) ) ) ) )).
fof(t13_algstr_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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_group_6(C,A,B) & v1_group_6(D,A,B) ) => ( v2_algstr_4(a_4_0_algstr_4(A,B,C,D),A) & m1_subset_1(a_4_0_algstr_4(A,B,C,D),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) ) )).
fof(t13_altcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_hidden(k8_altcat_1(A,B),k1_altcat_1(A,B,B)) ) ) )).
fof(t13_altcat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_cat_1(E,A,B,C) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t13_altcat_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_altcat_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_altcat_1(A))) => ( k1_altcat_1(k7_altcat_1(A),B,C) != k1_xboole_0 => ! [D] : ( m1_subset_1(D,k1_altcat_1(k7_altcat_1(A),B,C)) => ! [E] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t13_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v16_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(t13_ami_2,axiom,( r2_hidden(k4_ordinal1,k1_ami_2) )).
fof(t13_ami_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( k4_struct_0(k1_ami_3) != k10_ami_3(A) & k4_struct_0(k1_ami_3) != A ) ) )).
fof(t13_ami_5,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => ~ ( k2_compos_0(u1_compos_1(k1_ami_3),A) = 7 & ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_ami_3)) ) => A != k8_ami_3(B,C) ) ) ) ) )).
fof(t13_ami_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( 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) = k4_ordinal1 ) ) )).
fof(t13_ami_wstd,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_setfam_1(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,k4_ordinal1) => k2_xcmplx_0(k3_ami_wstd(B,C,D),A) = k3_ami_wstd(B,C,k4_ami_wstd(B,C,D,A)) ) ) ) ) )).
fof(t13_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ~ ( ~ v1_xboole_0(k2_amistd_1(A,B,C)) & v4_amistd_1(C,A,B) ) ) ) ) )).
fof(t13_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ( v2_extpro_1(C,A,B) => v1_xboole_0(k5_amistd_4(A,B,C)) ) ) ) ) )).
fof(t13_amistd_5,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) & ~ v2_compos_1(C,B) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => 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))) ) ) ) ) ) ) )).
fof(t13_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r1_analmetr(A,D,E) & B != k4_struct_0(A) & ! [F] : ( v1_xreal_0(F) => ~ r2_analmetr(A,k5_algstr_0(A,C,k1_rlvect_1(A,B,F)),B,D,E) ) ) ) ) ) ) ) )).
fof(t13_analoaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_analoaf(A,B,C,C,D) => r1_analoaf(A,B,C,B,D) ) ) ) ) ) )).
fof(t13_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r1_analmetr(A,D,E) & k2_analort(A,D,E,B) = k2_analort(A,D,E,C) ) => B = C ) ) ) ) ) ) )).
fof(t13_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k3_rlvect_1(A,B,C) = k4_struct_0(A) => r1_anproj_1(A,B,C) ) ) ) ) )).
fof(t13_anproj_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( m2_funct_2(C,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [D] : ( m2_funct_2(D,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ( ( A = k8_domain_1(A,E,F,G) & k3_funct_2(A,k1_numbers,B,E) = 1 & ! [H] : ( r2_hidden(H,A) => ( H = E | k1_funct_1(B,H) = k5_numbers ) ) & k3_funct_2(A,k1_numbers,C,F) = 1 & ! [H] : ( r2_hidden(H,A) => ( H = F | k1_funct_1(C,H) = k5_numbers ) ) & k3_funct_2(A,k1_numbers,D,G) = 1 & ! [H] : ( r2_hidden(H,A) => ( H = G | k1_funct_1(D,H) = k5_numbers ) ) ) => ( E = F | E = G | F = G | ! [H] : ( m2_funct_2(H,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ? [I] : ( v1_xreal_0(I) & ? [J] : ( v1_xreal_0(J) & ? [K] : ( v1_xreal_0(K) & H = k1_binop_1(k5_funcsdom(A),k1_binop_1(k5_funcsdom(A),k1_funct_1(k7_funcsdom(A),k4_tarski(I,B)),k1_funct_1(k7_funcsdom(A),k4_tarski(J,C))),k1_funct_1(k7_funcsdom(A),k4_tarski(K,D))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t13_aofa_000,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,k4_ordinal1) ) => ? [C] : ( ~ 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 ) ) ) )).
fof(t13_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( r2_hidden(B,A) & r2_hidden(C,A) & r2_hidden(D,A) & r2_hidden(E,A) & r2_hidden(F,A) & r2_hidden(G,A) ) => r1_tarski(k4_enumset1(B,C,D,E,F,G),A) ) )).
fof(t13_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ( B = k10_subset_1(k1_funct_1(u7_aofa_a00(A),3),u4_struct_0(A)) => ( B = k1_funct_1(u7_aofa_a00(A),3) & k1_msualg_1(A,B) = k2_finseq_4(u1_struct_0(A),u8_aofa_a00(A),u8_aofa_a00(A)) & k2_msualg_1(A,B) = u8_aofa_a00(A) ) ) ) ) )).
fof(t13_aofa_i00,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k2_power(k2_power(A,B),C) = k2_power(A,k3_xcmplx_0(B,C)) ) ) ) )).
fof(t13_armstrng,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t13_arrow,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_subset_1(B,k2_arrow(A),k3_arrow(A)) => ! [C] : ( m1_subset_1(C,k2_arrow(A)) => ( ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ~ ( ~ r1_arrow(B,E,D) & r1_arrow(C,E,D) ) ) ) <=> ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t13_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => k2_arytm_0(A,k2_arytm_0(B,C)) = k2_arytm_0(k2_arytm_0(A,B),C) ) ) ) )).
fof(t13_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( r1_arytm_2(C,B) => k7_arytm_2(A,k1_arytm_1(B,C)) = k1_arytm_1(k7_arytm_2(A,B),C) ) ) ) ) )).
fof(t13_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( 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)) ) ) ) )).
fof(t13_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ( B != k1_xboole_0 => r2_arytm_3(k6_ordinal3(k9_ordinal3(A,B),k2_arytm_3(A,B)),A) ) ) ) )).
fof(t13_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v2_xxreal_0(B) & v1_xreal_0(B) ) => k6_asympt_0(A) = k6_asympt_0(k2_asympt_0(A,B)) ) ) )).
fof(t13_asympt_1,axiom,( ? [A] : ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v4_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & r2_funct_2(k4_ordinal1,k1_numbers,A,k1_asympt_1(2,1,1)) & r2_hidden(k1_asympt_1(2,1,k5_numbers),k8_asympt_0(A)) ) )).
fof(t13_autalg_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( 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) ) ) ) ) )).
fof(t13_autgroup,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t13_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t13_bcialg_1,axiom,( ! [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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) )).
fof(t13_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k1_bcialg_2(A,k4_struct_0(A),B,k1_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))) ) ) ) ) )).
fof(t13_bcialg_3,axiom,( ! [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) ) => ( v19_bcialg_1(A) => ( v4_bcialg_3(A) & v5_bcialg_3(A) ) ) ) )).
fof(t13_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t13_bcialg_5,axiom,( ! [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] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( m1_bcialg_5(A,B,C,D,E) <=> m1_bcialg_5(A,D,E,B,C) ) ) ) ) ) ) )).
fof(t13_bcialg_6,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( v1_int_1(C) => r2_hidden(k3_bcialg_6(A,C,B),k5_bcialg_1(A)) ) ) ) )).
fof(t13_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( v14_bcialg_1(A) => v12_bcialg_1(B,A) ) ) ) )).
fof(t13_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k2_bhsp_1(A,k5_algstr_0(A,B,C),k5_algstr_0(A,D,E)) = k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k2_bhsp_1(A,B,D),k2_bhsp_1(A,B,E)),k2_bhsp_1(A,C,D)),k2_bhsp_1(A,C,E)) ) ) ) ) ) )).
fof(t13_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) )).
fof(t13_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( v7_ordinal1(D) => 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)) ) ) ) ) )).
fof(t13_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) ) )).
fof(t13_binari_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => k6_binarith(A,k3_binarith(A,B)) = k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(k6_binarith(A,B)),k5_series_1(2,A)),1) ) ) )).
fof(t13_binari_3,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( 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 ) ) ) ) )).
fof(t13_binari_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k2_xcmplx_0(B,C),k6_xcmplx_0(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 ) ) ) ) )).
fof(t13_binarith,axiom,( k2_binarith(k8_margrel1,k7_margrel1) = k8_margrel1 )).
fof(t13_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_binom(A,B,1) = B ) ) )).
fof(t13_binop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t13_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => k1_funct_1(k1_bintree2(A,B),k5_euclid(B)) = 1 ) ) )).
fof(t13_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r3_boolealg(A,B,C) & r3_lattices(A,C,D) ) => r3_boolealg(A,B,D) ) ) ) ) ) )).
fof(t13_borsuk_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t13_borsuk_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( ? [D] : ( 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,k5_numbers) = B & k1_funct_1(D,1) = C ) & ! [D] : ( ( 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,k5_numbers) = C & k1_funct_1(D,1) = B ) ) ) ) ) ) )).
fof(t13_borsuk_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( 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) ) ) ) )).
fof(t13_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(B,C) & A = k1_rcomp_1(B,C) ) => ( r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(C,1) ) ) ) ) ) )).
fof(t13_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k7_metric_1)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_metric_1)) => ( r1_xxreal_0(A,B) => k3_metric_1(k7_metric_1,A,B) = k6_xcmplx_0(B,A) ) ) ) )).
fof(t13_borsuk_7,axiom,( ! [A] : ( v7_ordinal1(A) => k6_euclid(A,k5_euclid(A)) = k5_euclid(A) ) )).
fof(t13_brouwer,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t13_bspace,axiom,( ! [A] : ! [B] : ! [C] : ( k3_bspace(A,C) = k3_bspace(B,C) <=> ( r2_hidden(C,A) <=> r2_hidden(C,B) ) ) )).
fof(t13_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) ) ) )).
fof(t13_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t13_bvfunc14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ~ ( 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 ) )).
fof(t13_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t13_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) ) )).
fof(t13_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t13_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t13_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t13_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(t13_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t13_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t13_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) )).
fof(t13_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)))) ) ) ) )).
fof(t13_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t13_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_c0sp1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_c0sp1(A))) => ! [E] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,A) => k3_funct_2(A,k1_numbers,F,G) = k3_xcmplx_0(B,k3_funct_2(A,k1_numbers,E,G)) ) ) ) ) ) ) ) ) ) )).
fof(t13_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_c0sp2(A))) => r1_xxreal_0(k5_numbers,k2_normsp_0(k5_c0sp2(A),B)) ) ) )).
fof(t13_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => ( ~ r1_xxreal_0(k3_finseq_1(B),k5_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)))) ) ) ) ) )).
fof(t13_calcul_2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => ! [D] : ( m2_finseq_1(D,k3_cqc_lang(A)) => ( r2_hidden(B,k1_relset_1(k4_ordinal1,k14_finseq_1(k2_calcul_2(k3_finseq_1(D),k3_finseq_1(C))))) => k1_funct_1(k14_finseq_1(k2_calcul_2(k3_finseq_1(D),k3_finseq_1(C))),B) = k1_nat_1(k3_finseq_1(D),B) ) ) ) ) ) )).
fof(t13_cantor_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(t13_card_1,axiom,( ! [A] : r2_hidden(k1_card_1(A),k1_card_1(k1_zfmisc_1(A))) )).
fof(t13_card_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => k1_card_1(k11_ordinal2(A,B)) = k2_card_2(k1_card_1(A),k1_card_1(B)) ) ) )).
fof(t13_card_3,axiom,( ! [A] : k5_card_3(A,k1_xboole_0) = k1_xboole_0 )).
fof(t13_card_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v4_card_3(A) => v4_card_3(k3_finseq_2(A)) ) ) )).
fof(t13_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_card_fil(C,A) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( r2_hidden(D,k2_card_fil(A,C,B)) <=> ? [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) & r2_hidden(E,C) & r1_tarski(k9_subset_1(A,E,B),D) ) ) ) ) ) ) )).
fof(t13_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ! [E] : ~ ( ~ r2_hidden(C,A) & D != E & k5_card_1(k1_card_fin(A,B,D,E)) != k1_card_1(a_5_1_card_fin(A,B,C,D,E)) ) ) ) )).
fof(t13_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( ( v3_card_lar(B,A) & r1_tarski(B,C) ) => v3_card_lar(C,A) ) ) ) ) )).
fof(t13_cardfin2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( v1_int_1(B) => k3_xcmplx_0(B,k7_afinsq_2(A)) = k2_xcmplx_0(k7_afinsq_2(k5_relat_1(k24_valued_1(A,B),k7_nat_d(k1_afinsq_1(A),1))),k3_xcmplx_0(B,k1_funct_1(A,k7_nat_d(k1_afinsq_1(A),1)))) ) ) )).
fof(t13_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( k3_graph_1(A,C) = k4_graph_1(A,B) <=> r2_hidden(k4_tarski(C,B),k9_xtuple_0(u1_cat_1(A))) ) ) ) ) )).
fof(t13_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m3_cat_2(B,A) => ( v13_cat_1(k5_cat_2(A,B),B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( C = E & D = F ) => k2_cat_1(B,C,D) = k2_cat_1(A,E,F) ) ) ) ) ) ) ) ) )).
fof(t13_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( 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) ) ) )).
fof(t13_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_cat_1(A,B,k1_cat_4(A)) != k1_xboole_0 ) ) )).
fof(t13_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t13_catalan1,axiom,( ! [A] : ( v7_ordinal1(A) => v1_int_1(k1_catalan1(A)) ) )).
fof(t13_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v5_ordinal1(C) & v1_finset_1(C) ) => ( ( v1_catalan2(C) & k3_xcmplx_0(2,k7_afinsq_2(k5_relat_1(C,A))) = A & A = k1_nat_1(B,1) ) => k5_relat_1(C,A) = k1_catalan2(k5_relat_1(C,B),k8_funcop_1(k4_ordinal1,1,1)) ) ) ) ) )).
fof(t13_catalg_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( k6_catalg_1(A,C) = k6_catalg_1(B,D) => ( A = B & C = D ) ) )).
fof(t13_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_cayldick(k4_cayldick(A)))) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & B = k6_afinsq_1(k6_afinsq_1(C,D),k6_afinsq_1(E,F)) ) ) ) ) ) ) )).
fof(t13_cayley,axiom,( ! [A] : ! [B] : ( r2_tarski(A,B) => r2_group_6(k2_cayley(A),k2_cayley(B)) ) )).
fof(t13_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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_funct_1(k6_cc0sp1(A),B) = k2_seq_4(k5_cc0sp1(A,B)) ) ) ) )).
fof(t13_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => k4_struct_0(k3_cc0sp2(A)) = k1_cc0sp2(A,k5_complex1) ) )).
fof(t13_cfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_numbers)) => ! [B] : ( m1_subset_1(B,k2_numbers) => ! [C] : ( v1_xreal_0(C) => ( A = a_2_1_cfdiff_1(B,C) => v6_cfdiff_1(A) ) ) ) ) )).
fof(t13_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => k1_funct_1(k3_cfuncdom(A),k4_tarski(C,k1_funct_1(k3_cfuncdom(A),k4_tarski(D,B)))) = k1_funct_1(k3_cfuncdom(A),k4_tarski(k3_xcmplx_0(C,D),B)) ) ) ) ) )).
fof(t13_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t13_cgames_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v2_cgames_1(B) => ( r2_hidden(k9_cgames_1(B),A) <=> ? [C] : ( v3_ordinal1(C) & r2_hidden(C,A) & r2_hidden(B,k2_cgames_1(C)) ) ) ) ) )).
fof(t13_chain_1,axiom,( ! [A] : ( ( ~ v1_zfmisc_1(A) & v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ? [B] : ( v1_xreal_0(B) & ? [C] : ( v1_xreal_0(C) & r2_hidden(B,A) & r2_hidden(C,A) & ~ r1_xxreal_0(B,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => ( r1_xxreal_0(C,D) & r1_xxreal_0(D,B) ) ) ) ) ) ) )).
fof(t13_chord,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_abian(A) ) => ~ ( r1_xxreal_0(A,7) & A != k5_numbers & A != 2 & A != 4 & A != 6 ) ) )).
fof(t13_circcmb2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(C,F))) => ! [H] : ( m1_subset_1(H,k4_card_3(u3_msualg_1(A,D))) => ( H = k5_relat_1(G,u1_struct_0(A)) => ! [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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t13_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k10_xtuple_0(k7_finseq_4(A,B,C,D)) = k2_enumset1(A,B,C,D) )).
fof(t13_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ( r1_circcomb(A,B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_msafree2(k2_circcomb(A,B))) => r2_hidden(C,k2_msafree2(A)) ) ) ) ) ) )).
fof(t13_circled1,axiom,( ! [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) ) => ! [B] : ( ( v3_rltopsp1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => k2_circled1(A,B) = B ) ) )).
fof(t13_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m3_msaterm(D,A,B) => ! [E] : ( m1_subset_1(E,u4_struct_0(k1_circtrm1(A,B,D))) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t13_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(E,u4_struct_0(A)) => k1_funct_1(D,k1_xboole_0) != k4_tarski(E,u1_struct_0(A)) ) ) ) ) ) ) )).
fof(t13_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) ) => ! [D] : ( v1_xreal_0(D) => ( ( v1_pdiff_7(C,A) & B = k7_funcop_1(C,D) ) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( v1_xreal_0(F) => ~ ( r2_hidden(E,C) & ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( v1_xreal_0(G) => ~ ( ~ r1_xxreal_0(G,k5_numbers) & ! [H] : ( 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] : ( m2_finseq_2(I,k1_numbers,k1_euclid(A)) => r1_xxreal_0(k9_complex1(k5_real_1(k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_7(A,B,H),I),k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_7(A,B,E),I))),k3_xcmplx_0(F,k12_euclid(I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t13_classes1,axiom,( ! [A] : ! [B] : ! [C] : ( v3_ordinal1(C) => ( v4_ordinal1(C) => ( C = k1_xboole_0 | ( r2_hidden(B,k3_classes1(A,C)) <=> ? [D] : ( v3_ordinal1(D) & r2_hidden(D,C) & r2_hidden(B,k3_classes1(A,D)) ) ) ) ) ) )).
fof(t13_classes2,axiom,( ! [A] : ! [B] : ( ( v2_classes1(B) & r2_hidden(A,k1_card_1(B)) ) => r2_hidden(A,B) ) )).
fof(t13_clopban1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t13_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_clopban2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_clopban2(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t13_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ! [C] : ( v7_ordinal1(C) => k1_normsp_0(A,B,C) = k4_struct_0(A) ) => v2_clopban3(B,A) ) ) ) )).
fof(t13_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => ( k1_normsp_1(A,k1_clopban4(A,B),k1_nat_1(C,1)) = k6_algstr_0(A,k1_clvect_1(A,B,k7_xcmplx_0(k6_complex1,k1_nat_1(C,1))),k1_normsp_1(A,k1_clopban4(A,B),C)) & k1_normsp_1(A,k1_clopban4(A,B),k5_numbers) = k5_struct_0(A) & r1_xxreal_0(k2_normsp_0(A,k1_normsp_1(A,k1_clopban4(A,B),C)),k9_nat_1(k1_numbers,k4_sin_cos(k2_normsp_0(A,B)),C)) ) ) ) ) )).
fof(t13_closure1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t13_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) ) => k9_xtuple_0(k3_closure2(C)) = A ) ) )).
fof(t13_closure3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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)))) ) ) ) )).
fof(t13_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) )).
fof(t13_coh_sp,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => k2_coh_sp(k3_tarski(A),k1_coh_sp(A)) = A ) )).
fof(t13_cohsp_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ~ ( v1_cohsp_1(A) & r1_tarski(B,k3_tarski(A)) & v1_finset_1(B) & ! [C] : ~ ( r2_hidden(C,A) & r1_tarski(B,C) ) ) ) )).
fof(t13_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( B = C => k1_collsp(A,B,C) = u1_struct_0(A) ) ) ) ) )).
fof(t13_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ~ ( r1_tarski(k2_relset_1(k9_setfam_1(u1_struct_0(A)),C),B) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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] : ( v7_ordinal1(E) => k9_nat_1(k9_setfam_1(u1_struct_0(A)),D,E) = k1_setfam_1(a_3_1_compl_sp(A,C,E)) ) ) ) ) ) ) ) )).
fof(t13_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(k3_complex1(A),k3_xcmplx_0(k4_complex1(A),k7_complex1)) = A ) )).
fof(t13_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k1_comptrig(A) = k5_numbers <=> A = k9_complex1(A) ) ) )).
fof(t13_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => B = k3_rlvect_1(k1_complfld,k5_algstr_0(k1_complfld,B,A),A) ) ) )).
fof(t13_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( v1_xcmplx_0(B) => k1_complsp2(k10_seq_4(A,B)) = k10_seq_4(k1_complsp2(A),k8_complex1(B)) ) ) )).
fof(t13_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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))) ) ) ) )).
fof(t13_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t13_comptrig,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( r2_hidden(A,k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos))) & r1_xxreal_0(k5_numbers,k1_funct_1(k18_sin_cos,A)) ) ) )).
fof(t13_comput_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t13_comseq_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k25_valued_1(k4_ordinal1,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,C),A),k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,k25_valued_1(k4_ordinal1,k2_numbers,C,A))) ) ) ) )).
fof(t13_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & v2_comseq_2(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => k3_comseq_2(k2_comseq_2(k4_ordinal1,k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B))) = k2_xcmplx_0(k8_complex1(k3_comseq_2(A)),k8_complex1(k3_comseq_2(B))) ) ) )).
fof(t13_comseq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( r1_xxreal_0(k9_complex1(k3_complex1(A)),k9_complex1(A)) & r1_xxreal_0(k9_complex1(k4_complex1(A)),k9_complex1(A)) ) ) )).
fof(t13_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_waybel_1(C,A,B) => ( v2_conlat_1(C,A,B) => ! [D] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t13_conmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( ( v1_conmetr(A) & v1_conaffm(A) ) => v2_conmetr(A) ) ) )).
fof(t13_conmetr1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v3_conmetr1(k3_analmetr(A)) <=> v6_conmetr(A) ) ) )).
fof(t13_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_connsp_1(A) <=> ! [B] : ( 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) ) ) ) ) )).
fof(t13_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r1_connsp_2(A,B) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t13_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t13_convex1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(k5_numbers,D) & v1_convex1(B,A) ) => k7_rusub_4(A,k1_convex1(A,B,C),k1_convex1(A,B,D)) = k1_convex1(A,B,k2_xcmplx_0(C,D)) ) ) ) ) ) )).
fof(t13_convex2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_classes1(A,B) => ! [C] : ! [D] : ~ ( r2_hidden(C,k9_xtuple_0(A)) & r2_hidden(D,k9_xtuple_0(A)) & C != D & ! [E] : ! [F] : ~ ( 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) ) ) ) ) ) )).
fof(t13_convex4,axiom,( ! [A] : ( ( ~ 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] : ( m2_convex4(B,A,k1_subset_1(u1_struct_0(A))) => k4_convex4(A,B) = k4_struct_0(A) ) ) )).
fof(t13_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t13_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => r1_tarski(B,k1_cqc_the1(A,B)) ) ) )).
fof(t13_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t13_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => r2_cqc_the3(A,B,k4_cqc_the1(A)) ) ) )).
fof(t13_csspace,axiom,( 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) )).
fof(t13_csspace2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,A),k55_valued_1(k4_ordinal1,k2_numbers,k2_comseq_2(k4_ordinal1,A))) ) )).
fof(t13_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( 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)) ) ) ) ) )).
fof(t13_decomp_1,axiom,( ! [A] : ( ( 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) ) )).
fof(t13_descip_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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 ) ) ) )).
fof(t13_dickson,axiom,( ! [A] : ( v1_relat_1(A) => ( v8_relat_2(A) => v8_relat_2(k3_dickson(A)) ) ) )).
fof(t13_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( ( 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] : ( ( 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) = k2_xcmplx_0(k3_xcmplx_0(A,k1_diff_2(H,C,D,E,F,G)),k3_xcmplx_0(B,k1_diff_2(I,C,D,E,F,G))) ) ) ) ) ) ) ) ) ) )).
fof(t13_diff_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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_funct_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,C),F),B),k2_xcmplx_0(A,1)),D) = k2_xcmplx_0(k3_xcmplx_0(C,k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(E,B),k2_xcmplx_0(A,1)),D)),k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(F,B),k2_xcmplx_0(A,1)),D)) ) ) ) ) ) ) )).
fof(t13_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(k2_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k2_fdiff_9)) & r2_hidden(k6_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k2_fdiff_9)) ) => k1_funct_1(k5_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k2_fdiff_9),A),B) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(4,k17_sin_cos(k3_xcmplx_0(2,B))),k17_sin_cos(A)),k1_square_1(k6_xcmplx_0(k19_sin_cos(k3_xcmplx_0(2,B)),k19_sin_cos(A))))) ) ) ) )).
fof(t13_dilworth,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) ) )).
fof(t13_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r1_diraf(A,B,C,D) & C != D ) ) ) ) )).
fof(t13_dirort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t13_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,A) => k16_rvsum_1(k9_dist_1(A,B)) = k3_xcmplx_0(k3_finseq_1(B),k18_rvsum_1(k4_dist_1(A,B))) ) ) )).
fof(t13_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) ) => ! [C] : ( ( 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] : ( r2_hidden(D,k9_xtuple_0(B)) => ( r2_hidden(D,k3_dist_2(k3_relat_1(B,C))) <=> r2_hidden(k1_funct_1(B,D),k3_dist_2(C)) ) ) ) ) ) )).
fof(t13_domain_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) => ( A = k4_mcart_1(B,C,D,E,F) <=> ! [G] : ( m1_subset_1(G,B) => ! [H] : ( m1_subset_1(H,C) => ! [I] : ( m1_subset_1(I,D) => ! [J] : ( m1_subset_1(J,E) => ( F = k5_domain_1(B,C,D,E,G,H,I,J) => A = G ) ) ) ) ) ) ) ) ) ) ) )).
fof(t13_dtconstr,axiom,( ! [A] : ( ( 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(k4_ordinal1,k5_numbers) ) ) )).
fof(t13_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(t13_e_siec,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t13_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ? [C] : ( v7_ordinal1(C) & B = k4_nat_d(C,A) ) ) ) )).
fof(t13_ec_pf_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t13_endalg,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t13_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k2_ens_1(A)) => ! [C] : ( m1_subset_1(C,k2_ens_1(A)) => ! [D] : ( m1_subset_1(D,k2_ens_1(A)) => ( ( k3_ens_1(A,C) = k4_ens_1(A,B) & k3_ens_1(A,D) = k4_ens_1(A,C) ) => k6_ens_1(A,k6_ens_1(A,B,C),D) = k6_ens_1(A,B,k6_ens_1(A,C,D)) ) ) ) ) ) )).
fof(t13_entropy1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( r1_entropy1(B,A) => k18_rvsum_1(B) = k1_funct_1(B,A) ) ) ) )).
fof(t13_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k1_enumset1(A,B,C),k1_enumset1(D,E,F)) )).
fof(t13_eqrel_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) )).
fof(t13_equation,axiom,( ! [A] : ! [B] : ( ( 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,k1_funct_6(B),B),k2_funct_6(B)) ) )).
fof(t13_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ( k12_euclid(k8_euclid(A,B,C)) = k5_numbers <=> B = C ) ) ) ) )).
fof(t13_euclid_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v3_valued_0(B) ) => ( k3_finseq_1(A) = k3_finseq_1(B) => k6_xcmplx_0(k1_square_1(k12_euclid(k4_rvsum_1(A,B))),k1_square_1(k12_euclid(k8_rvsum_1(A,B)))) = k3_xcmplx_0(4,k22_rvsum_1(A,B)) ) ) ) )).
fof(t13_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => k2_euclid_3(k4_algstr_0(k15_euclid(2),A)) = k4_xcmplx_0(k2_euclid_3(A)) ) )).
fof(t13_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ~ ( v1_euclid_4(B,A) & ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & C != D ) ) ) ) ) ) )).
fof(t13_euclid_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => k5_algstr_0(k15_euclid(3),k4_euclid_5(A,C,E),k4_euclid_5(B,D,F)) = k4_euclid_5(k6_xcmplx_0(A,B),k6_xcmplx_0(C,D),k6_xcmplx_0(E,F)) ) ) ) ) ) ) )).
fof(t13_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(D,k1_rltopsp1(k15_euclid(2),A,C)) & D != A & D != C & k2_xcmplx_0(k4_euclid_3(A,D,B),k4_euclid_3(B,D,C)) != k28_sin_cos & k2_xcmplx_0(k4_euclid_3(A,D,B),k4_euclid_3(B,D,C)) != k3_xcmplx_0(3,k28_sin_cos) ) ) ) ) ) )).
fof(t13_euclid_7,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ~ ( v2_funct_1(A) & ! [B] : ( ( 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] : ( m2_finseq_1(C,k4_ordinal1) => ~ ( C = k1_partfun1(k4_finseq_1(A),k4_finseq_1(A),k4_ordinal1,k4_ordinal1,B,A) & v5_valued_0(C) & k4_finseq_1(A) = k4_finseq_1(C) & k2_relset_1(k4_ordinal1,A) = k2_relset_1(k4_ordinal1,C) ) ) ) ) ) )).
fof(t13_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => k22_rvsum_1(A,k1_euclid_8(k5_numbers,k5_numbers,k5_numbers)) = k5_numbers ) )).
fof(t13_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t13_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(D)) => k9_euclid(D,E,k6_xcmplx_0(k6_xcmplx_0(A,B),C)) = k8_euclid(D,k8_euclid(D,k9_euclid(D,E,A),k9_euclid(D,E,B)),k9_euclid(D,E,C)) ) ) ) ) ) )).
fof(t13_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v6_euclmetr(A) <=> v8_conmetr(A) ) ) )).
fof(t13_euler_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_nat_d(C,k3_xcmplx_0(A,B)) & r1_int_2(A,C) ) => r1_nat_d(C,B) ) ) ) ) )).
fof(t13_euler_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => k2_euler_2(k2_euler_2(B,A),A) = k2_euler_2(B,A) ) ) )).
fof(t13_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v3_exchsort(A,k3_ordinal2(k9_xtuple_0(A))) ) )).
fof(t13_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & ~ v2_compos_1(C,B) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t13_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => r1_xxreal_0(k3_extreal1(k1_xxreal_3(A,B)),k3_supinf_2(k3_extreal1(A),k3_extreal1(B))) ) ) )).
fof(t13_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t13_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( r1_tarski(k2_relset_1(k1_numbers,C),A) & v2_comseq_2(C) & r2_hidden(k1_seq_2(C),A) ) => ( v2_comseq_2(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,C,B)) & k1_funct_1(B,k1_seq_2(C)) = k1_seq_2(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,C,B)) ) ) ) ) ) ) )).
fof(t13_fcont_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( 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] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & k1_funct_1(A,C) = k2_seq_4(k7_relset_1(k1_numbers,k1_numbers,A,B)) & k1_funct_1(A,D) = k3_seq_4(k7_relset_1(k1_numbers,k1_numbers,A,B)) ) ) ) ) ) ) )).
fof(t13_fcont_3,axiom,( ! [A] : ! [B] : ( ( 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] : ( v1_xreal_0(C) => k7_relset_1(k1_numbers,k1_numbers,B,A) != k1_limfunc1(C) ) | v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) ) ) )).
fof(t13_fdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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) = k2_xcmplx_0(k1_fdiff_1(B,A),k1_fdiff_1(C,A)) ) ) ) ) ) )).
fof(t13_fdiff_10,axiom,( ! [A] : ( ( 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,k27_sin_cos))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k27_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k27_sin_cos),A),B) = k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,B),k1_funct_1(k27_sin_cos,B)),k7_xcmplx_0(1,k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t13_fdiff_11,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k16_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k16_sin_cos),A),B) = k7_xcmplx_0(k1_funct_1(k18_sin_cos,k1_funct_1(k1_sin_cos9,B)),k2_xcmplx_0(1,k1_square_1(B))) ) ) ) ) ) )).
fof(t13_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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_funct_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) = k3_xcmplx_0(k1_fdiff_1(C,k1_funct_1(B,A)),k1_fdiff_1(B,A)) ) ) ) ) ) )).
fof(t13_fdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( r4_fdiff_3(A,C) & r4_fdiff_3(B,C) ) => ( k1_funct_1(B,C) = k5_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)) = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_3(C,A),k1_funct_1(B,C)),k3_xcmplx_0(k1_fdiff_3(C,B),k1_funct_1(A,C))),k1_square_1(k1_funct_1(B,C))) ) ) ) ) ) ) )).
fof(t13_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( 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,C)),k3_taylor_1))) & F = k1_taylor_1(2) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,D) => ( k1_funct_1(E,G) = k2_xcmplx_0(A,k3_xcmplx_0(B,G)) & ~ r1_xxreal_0(k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,E,k26_valued_1(k1_numbers,k1_numbers,F,C)),G),k5_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,C)),k3_taylor_1),D) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,D) => k1_funct_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,C)),k3_taylor_1),D),G) = k7_xcmplx_0(k2_xcmplx_0(B,k3_xcmplx_0(k3_xcmplx_0(2,C),G)),k2_xcmplx_0(k2_xcmplx_0(A,k3_xcmplx_0(B,G)),k3_xcmplx_0(C,k1_newton(G,2)))) ) ) ) ) ) ) ) ) ) ) )).
fof(t13_fdiff_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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,k18_sin_cos,k1_taylor_1(A))))) & r1_xxreal_0(1,A) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(C,D) = k3_xcmplx_0(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,k18_sin_cos,k1_taylor_1(A))),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_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,k18_sin_cos,k1_taylor_1(A))),B),D) = k3_xcmplx_0(k3_xcmplx_0(A,k3_prepower(k1_funct_1(k18_sin_cos,D),k6_xcmplx_0(A,1))),k1_funct_1(k18_sin_cos,k3_xcmplx_0(k2_xcmplx_0(A,1),D))) ) ) ) ) ) ) ) )).
fof(t13_fdiff_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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,k22_sin_cos),k22_sin_cos),k7_xcmplx_0(1,k2_xcmplx_0(1,k3_power(k4_power,A)))))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(C,D) = k3_xcmplx_0(D,k3_power(k4_power,A)) ) ) ) => ( r1_xxreal_0(A,k5_numbers) | A = k7_xcmplx_0(1,k4_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,k22_sin_cos),k22_sin_cos),k7_xcmplx_0(1,k2_xcmplx_0(1,k3_power(k4_power,A)))),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_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,k22_sin_cos),k22_sin_cos),k7_xcmplx_0(1,k2_xcmplx_0(1,k3_power(k4_power,A)))),B),D) = k3_xcmplx_0(k6_prepower(A,D),k1_funct_1(k22_sin_cos,D)) ) ) ) ) ) ) ) ) )).
fof(t13_fdiff_7,axiom,( ! [A] : ( ( 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,k3_sin_cos6,k1_taylor_1(2)),k7_xcmplx_0(1,2)))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_sin_cos6,k1_taylor_1(2)),k7_xcmplx_0(1,2)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_sin_cos6,k1_taylor_1(2)),k7_xcmplx_0(1,2)),A),B) = k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k3_sin_cos6,B),k3_square_1(k6_xcmplx_0(1,k1_square_1(B))))) ) ) ) ) ) )).
fof(t13_fdiff_8,axiom,( ! [A] : ( ( 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,k22_sin_cos,k27_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k27_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k27_sin_cos),A),B) = k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k22_sin_cos,B))))) ) ) ) ) ) )).
fof(t13_fdiff_9,axiom,( ! [A] : ( ( 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,k22_sin_cos,k2_fdiff_9))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k2_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k2_fdiff_9),A),B) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_funct_1(k18_sin_cos,k1_funct_1(k22_sin_cos,B))),k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k22_sin_cos,B))))) ) ) ) ) ) )).
fof(t13_ff_siec,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t13_fib_num2,axiom,( ! [A] : ( ( 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)) ) )).
fof(t13_fib_num3,axiom,( ! [A] : ( v7_ordinal1(A) => k1_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)) ) )).
fof(t13_fib_num4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ~ r1_xxreal_0(k2_power(k1_fib_num,A),k2_power(k2_fib_num,A)) ) )).
fof(t13_filerec1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m2_finseq_1(E,D) => ( E = k11_finseq_1(A,B,C) => k17_finseq_1(D,1,E) = k9_finseq_1(A) ) ) ) )).
fof(t13_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t13_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t13_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t13_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(B,k9_fin_topo(A,B)) ) ) )).
fof(t13_finance1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(C,k5_numbers) => ! [D] : ( v1_xreal_0(D) => ( ~ r1_xxreal_0(D,k4_xcmplx_0(1)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [F] : ( m1_finance1(F) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k4_ordinal1,k6_finance1(A,k1_numbers,B,k12_prob_1)) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_finance1(A,k1_numbers,B,k12_prob_1)))) ) => ( r1_funct_2(A,k1_numbers,A,k1_tarski(k2_xcmplx_0(1,D)),k9_finance1(k5_numbers,A,k1_numbers,B,k12_prob_1,k6_finance1(A,k1_numbers,B,k12_prob_1),G),k7_funcop_1(A,k2_xcmplx_0(1,D))) => ! [H] : ( m1_subset_1(H,A) => ( r1_xxreal_0(k4_finance1(C,E,F),k5_numbers) => r1_xxreal_0(k11_finance1(C,E,A,B,k6_finance1(A,k1_numbers,B,k12_prob_1),G,H),k6_xcmplx_0(k12_finance1(C,E,A,B,k6_finance1(A,k1_numbers,B,k12_prob_1),G,H),k3_xcmplx_0(k2_xcmplx_0(1,D),k5_finance1(C,E,F)))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t13_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ( k4_finseq_1(A) = k4_finseq_1(B) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(A)) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) => A = B ) ) ) )).
fof(t13_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t13_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(k6_xcmplx_0(A,B),k2_finseq_1(A)) <=> ~ r1_xxreal_0(A,B) ) ) ) )).
fof(t13_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r1_finseq_4(A,B) => k1_finseq_4(A,k1_funct_1(A,B)) = B ) ) )).
fof(t13_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & ! [D] : ( 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 ) ) ) ) )).
fof(t13_finseq_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t13_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => k1_finseq_7(A,k2_finseq_4(A,B,C),1,D) = k2_finseq_4(A,D,C) ) ) ) ) )).
fof(t13_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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 ) ) ) )).
fof(t13_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t13_finsub_1,axiom,( ! [A] : r1_tarski(k5_finsub_1(A),k1_zfmisc_1(A)) )).
fof(t13_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k6_fin_topo(A,C)) <=> ( ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( 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 ) ) ) ) ) )).
fof(t13_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k3_fintopo3(A,B,k1_nat_1(C,1)) = k9_fin_topo(A,k3_fintopo3(A,B,C)) ) ) ) )).
fof(t13_fintopo4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_fin_topo(A) => ( v4_fin_topo(B,A) <=> ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(t13_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_fintopo6(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t13_flang_1,axiom,( ! [A] : ! [B] : ( 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 ) ) )).
fof(t13_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k2_flang_1(A),C) => ( r1_tarski(B,k6_flang_1(A,B,k7_flang_1(A,C,D))) & r1_tarski(B,k6_flang_1(A,k7_flang_1(A,C,D),B)) ) ) ) ) ) )).
fof(t13_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ( r1_tarski(B,C) => r1_tarski(k1_flang_3(A,B,D),k1_flang_3(A,C,D)) ) ) ) ) )).
fof(t13_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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(k6_fomodel0(A,C),k12_finseq_1(A,B)) = B & ! [D] : ( ( ~ v1_xboole_0(D) & m2_finseq_1(D,A) ) => k1_funct_1(k6_fomodel0(A,C),k1_monoid_0(A,D,k12_finseq_1(A,B))) = k1_binop_1(C,k1_funct_1(k6_fomodel0(A,C),D),B) ) ) ) ) ) )).
fof(t13_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ 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) & m1_fomodel0(A,k15_fomodel1(B)) ) ) ) )).
fof(t13_fomodel2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k8_relset_1(k4_finseq_2(2,A),k6_margrel1,k2_fomodel2(A),k6_domain_1(k4_ordinal1,1)) = a_1_1_fomodel2(A) ) )).
fof(t13_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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] : ( m2_subset_1(D,k9_funct_2(k37_fomodel1(B),k3_rfunct_3(k3_finseq_2(A),k2_xboole_0(A,k6_margrel1))),k15_fomodel2(B,A)) => ! [E] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(B),k3_rfunct_3(k3_finseq_2(A),k2_xboole_0(A,k6_margrel1))),k15_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))) => k25_fomodel2(B,A,D,C) = k25_fomodel2(B,A,E,C) ) ) ) ) ) ) )).
fof(t13_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( v10_fomodel4(D,B,C) => v10_fomodel4(A,B,C) ) ) ) ) )).
fof(t13_frechet,axiom,( ! [A] : ! [B] : ( r1_tarski(B,A) => k7_relset_1(A,A,k6_partfun1(A),B) = B ) )).
fof(t13_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t13_friends1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_2(A) & v3_relat_2(A) & v1_finset_1(A) & v3_friends1(A) ) => ! [B] : ( m1_subset_1(B,k1_relat_1(A)) => ! [C] : ( m1_subset_1(C,k1_relat_1(A)) => ~ ( v1_friends1(B,A) & B != C & ! [D] : ~ ( k9_relat_1(A,C) = k2_tarski(B,D) & k9_relat_1(A,D) = k2_tarski(B,C) ) ) ) ) ) )).
fof(t13_fscirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t13_fscirc_2,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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) ) )).
fof(t13_fsm_3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(B)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k8_afinsq_1(B))) => ! [E] : ( ( ~ v2_struct_0(E) & l1_rewrite3(E,D) ) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t13_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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) ) ) ) ) ) )).
fof(t13_funcop_1,axiom,( ! [A] : ! [B] : ( k9_xtuple_0(k2_funcop_1(A,B)) = A & r1_tarski(k10_xtuple_0(k2_funcop_1(A,B)),k1_tarski(B)) ) )).
fof(t13_funcsdom,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ! [D] : ( m2_funct_2(D,C,k1_numbers,k9_funct_2(C,k1_numbers)) => k1_binop_1(k7_funcsdom(C),A,k1_binop_1(k7_funcsdom(C),B,D)) = k1_binop_1(k7_funcsdom(C),k3_xcmplx_0(A,B),D) ) ) ) )).
fof(t13_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t13_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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) ) ) ) )).
fof(t13_funct_3,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(t13_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( r2_hidden(C,k9_xtuple_0(B)) => k1_funct_1(k1_funct_4(A,B),C) = k1_funct_1(B,C) ) ) ) )).
fof(t13_funct_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( ( r2_hidden(k4_tarski(C,D),k9_xtuple_0(A)) & B = k1_funct_1(k1_funct_5(A),C) ) => ( r2_hidden(D,k9_xtuple_0(B)) & k1_funct_1(B,D) = k1_binop_1(A,C,D) ) ) ) ) )).
fof(t13_funct_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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))) ) ) ) )).
fof(t13_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ~ ( A != B & r2_hidden(A,k10_xtuple_0(k1_funct_4(k6_partfun1(C),k16_funcop_1(A,B)))) ) )).
fof(t13_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t13_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) ) => ( v1_funct_9(B,A) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t13_functor0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(t13_functor1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_altcat_2(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_altcat_2(C) & m1_altcat_2(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_altcat_2(D,A) ) => ! [E] : ( ( ~ v2_struct_0(E) & m1_altcat_2(E,C) ) => ( D = E => ! [F] : ( l2_functor0(F,A,B) => k14_functor0(A,B,D,F) = k14_functor0(C,B,E,k14_functor0(A,B,C,F)) ) ) ) ) ) ) ) )).
fof(t13_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ! [F] : ( ( v15_functor0(F,A,B) & m2_functor0(F,A,B) ) => ! [G] : ( ( v15_functor0(G,B,C) & m2_functor0(G,B,C) ) => ! [H] : ( m1_functor2(H,A,B,D,E) => ! [I] : ( m1_functor2(I,A,B,E,F) => ( ( r1_functor2(A,B,D,E) & r1_functor2(A,B,E,F) ) => r8_pboole(u1_struct_0(A),k5_functor3(A,B,C,D,F,k3_functor2(A,B,D,E,F,H,I),G),k3_functor2(A,C,k1_functor3(A,B,C,D,G),k1_functor3(A,B,C,E,G),k1_functor3(A,B,C,F,G),k5_functor3(A,B,C,D,E,H,G),k5_functor3(A,B,C,E,F,I,G))) ) ) ) ) ) ) ) ) ) ) )).
fof(t13_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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) ) ) )).
fof(t13_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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)) ) ) ) )).
fof(t13_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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] : ( ( v5_relat_1(F,k1_rcomp_1(k5_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,k3_fuzzy_4(A,B,C,D,k2_fuzzy_1(k2_zfmisc_1(B,C),E,F)),k2_fuzzy_1(k2_zfmisc_1(A,C),k3_fuzzy_4(A,B,C,D,E),k3_fuzzy_4(A,B,C,D,F))) ) ) ) ) ) ) )).
fof(t13_fvaluat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k2_fvaluat1(A,B,1) = B ) ) )).
fof(t13_fvsum_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t13_gate_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(k7_gate_1(A,B)) <=> ( v1_xboole_0(A) & v1_xboole_0(B) ) ) )).
fof(t13_gcd_1,axiom,( ! [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) & v1_vectsp_2(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) ) ) )).
fof(t13_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v2_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( m1_genealg1(D,C) => ! [E] : ( m1_genealg1(E,C) => k8_genealg1(C,D,E,A,B) = k8_genealg1(C,D,E,B,A) ) ) ) ) ) )).
fof(t13_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_analoaf(A,B,D,D,C) => r1_analoaf(A,k1_geomtrap(A,B,D),D,D,k1_geomtrap(A,D,C)) ) ) ) ) ) )).
fof(t13_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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) ) )).
fof(t13_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ( r1_glib_000(A,C,D,B) => ( r2_hidden(C,k6_glib_000(A)) & r2_hidden(D,k6_glib_000(A)) ) ) ) )).
fof(t13_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ( r1_glib_000(A,C,D,B) => k3_finseq_1(k2_glib_001(A,C,D,B)) = 3 ) ) )).
fof(t13_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(B)) => ( C = D => r1_tarski(k1_glib_002(B,D),k1_glib_002(A,C)) ) ) ) ) ) )).
fof(t13_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) ) => ! [B] : ( m3_glib_001(B,A) => k3_finseq_1(k8_glib_003(A,B)) = k15_glib_001(A,B) ) ) )).
fof(t13_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( v2_glib_001(B,A) & v5_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ( ( v2_glib_001(C,A) & v5_glib_001(C,A) & m3_glib_001(C,A) ) => ! [D] : ! [E] : ( ( r2_glib_004(A,B,D,E) & r2_glib_004(A,C,D,E) ) => k10_glib_003(A,B) = k10_glib_003(A,C) ) ) ) ) )).
fof(t13_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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] : ( 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),k5_numbers) ) ) ) ) )).
fof(t13_goboard1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( k1_matrix_0(D) = k1_nat_1(B,1) & r2_hidden(C,k2_finseq_1(B)) & r2_hidden(A,k4_finseq_1(D)) ) => ( r1_xxreal_0(B,k5_numbers) | ( r2_hidden(C,k2_finseq_1(k1_matrix_0(D))) & k3_matrix_0(u1_struct_0(k15_euclid(2)),k16_matrix_0(k1_matrix_0(D),u1_struct_0(k15_euclid(2)),D),A,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),D,A,C) & r2_hidden(k1_matrix_0(D),k2_finseq_1(k1_matrix_0(D))) ) ) ) ) ) ) ) )).
fof(t13_goboard2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ( k3_finseq_1(k2_goboard2(A)) = k1_card_1(k10_xtuple_0(k1_goboard1(A))) & k1_matrix_0(k2_goboard2(A)) = k1_card_1(k10_xtuple_0(k2_goboard1(A))) ) ) )).
fof(t13_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( v1_goboard1(C) & v4_goboard1(C) & r1_xxreal_0(1,B) ) => ( v3_relat_1(C) | r1_xxreal_0(k3_finseq_1(C),A) | r1_xxreal_0(k1_matrix_0(C),B) | r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),k1_nat_1(B,1))),k1_goboard5(C,A)) ) ) ) ) ) )).
fof(t13_goboard6,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_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) ) )).
fof(t13_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_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_nat_1(B,2),k1_matrix_0(C)) ) => k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_nat_1(B,1))),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_nat_1(B,2)))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_nat_1(B,1))) ) ) ) ) )).
fof(t13_goboard8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,2),k3_finseq_1(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,2),k1_matrix_0(k2_goboard2(A))) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,2),k3_finseq_1(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,1),k1_nat_1(C,1)) ) => ( ( ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,1),k1_nat_1(C,2)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),D,k1_nat_1(C,1)) ) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,1),k1_nat_1(C,2)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),D,k1_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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),D,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,1),k1_nat_1(C,1))),k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,1),C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,2),k1_nat_1(C,1))),k7_xcmplx_0(1,2))),k3_topreal1(2,A)) ) ) ) ) ) ) ) )).
fof(t13_goboard9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_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_0(C)) & k1_tops_1(k15_euclid(2),k3_goboard5(C,A,B)) = k1_xboole_0 ) ) ) ) )).
fof(t13_gobrd11,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( v1_xreal_0(B) => ( A = a_1_3_gobrd11(B) => v4_pre_topc(A,k15_euclid(2)) ) ) ) )).
fof(t13_gobrd14,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( 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] : ( 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] : ( 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) ) ) ) ) ) )).
fof(t13_goedcpuc,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_henmodel(B,A) & m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) ) => ! [C] : ( ( v1_henmodel(C,A) & m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) ) => ( ( r1_tarski(B,C) & v2_goedelcp(B,A) ) => v2_goedelcp(C,A) ) ) ) ) )).
fof(t13_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => k7_cqc_sim1(A,k12_cqc_lang(A,C,B)) = k1_nat_1(k7_cqc_sim1(A,B),1) ) ) ) )).
fof(t13_gr_cy_1,axiom,( k1_group_1(k2_gr_cy_1) = k5_numbers )).
fof(t13_gr_cy_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & v1_gr_cy_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t13_gr_cy_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_gr_cy_3(A) ) => ? [B] : ( v7_ordinal1(B) & v1_int_2(B) & v2_gr_cy_3(B) & k7_group_1(k3_int_7(A)) = k3_xcmplx_0(2,B) ) ) )).
fof(t13_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_graph_1(C) ) => ( ? [D] : ( ~ 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)) ) ) ) ) )).
fof(t13_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( B != k1_xboole_0 => k1_nat_1(k3_finseq_1(k3_graph_2(A,B)),1) = k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)) ) ) ) )).
fof(t13_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t13_graph_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v2_struct_0(C) & l1_graph_1(C) ) => ! [D] : ( m2_finseq_1(D,u1_struct_0(C)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(C)) => ! [F] : ( ( v7_graph_1(F,C) & m2_graph_1(F,C) ) => ! [G] : ( ( 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,k1_nat_1(B,1)) ) => r3_graph_4(C,E,G) ) ) ) ) ) ) ) ) )).
fof(t13_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t13_graphsp,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( ( ~ v2_struct_0(C) & v6_graph_1(C) & l1_graph_1(C) ) => ! [D] : ( ( v7_graph_1(D,C) & m2_graph_1(D,C) ) => ! [E] : ( ( v7_graph_1(E,C) & m2_graph_1(E,C) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ! [H] : ( 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] : ~ ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t13_grcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( v1_grcat_1(C) & m1_grcat_1(C,A,B) ) => ? [D] : ( 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) ) ) ) ) )).
fof(t13_grfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(t13_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,A) => ( m1_group_6(k1_grnilp_1(A,C,k7_group_2(A)),A,D) => m1_group_6(k1_grnilp_1(A,k10_group_2(A,C,B),B),A,k10_group_2(A,D,B)) ) ) ) ) ) )).
fof(t13_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( v7_rewrite1(k3_polyred(A,B,C,D)) => v4_rewrite1(k3_polyred(A,B,C,D)) ) ) ) ) ) )).
fof(t13_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t13_groeb_3,axiom,( ! [A] : ! [B] : ( ( ~ 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,k8_polynom1(A,B)),k8_polynom1(A,B)) ) )).
fof(t13_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k6_algstr_0(A,B,D) = C <=> B = k6_algstr_0(A,C,k2_group_1(A,D)) ) ) ) ) ) )).
fof(t13_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t13_group_12,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( m2_subset_1(D,k4_ordinal1,k2_finseq_1(A)) => k1_group_7(k2_finseq_1(A),C,D) = k2_group_12(k2_finseq_1(A),B,D) ) & ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k2_group_7(k2_finseq_1(A),C))) => ? [F] : ( m2_finseq_1(F,u1_struct_0(k2_group_7(k2_finseq_1(A),B))) & k3_finseq_1(F) = A & ! [G] : ( m2_subset_1(G,k4_ordinal1,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) ) ) ) ) ) ) ) ) )).
fof(t13_group_14,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ! [C] : ( v1_int_1(C) => ( r2_hidden(B,k4_finseq_1(A)) => k5_int_1(k5_int_1(C,k19_rvsum_1(A)),k1_funct_1(A,B)) = k5_int_1(C,k1_funct_1(A,B)) ) ) ) ) )).
fof(t13_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t13_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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)) ) ) ) ) )).
fof(t13_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t13_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ! [C] : ( ( v1_group_3(C,A) & m1_group_2(C,A) ) => ~ ( r2_hidden(B,k15_group_2(A,C)) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( B = k13_group_2(A,C,D) & B = k14_group_2(A,C,D) ) ) ) ) ) )).
fof(t13_group_7,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t13_group_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v4_group_1(B,A) <=> ! [C] : ( v1_int_1(C) => ( k5_group_1(A,C,B) = k1_group_1(A) => C = k5_numbers ) ) ) ) ) )).
fof(t13_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( m1_group_9(D,A,B) => ( ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r1_struct_0(C,E) => r1_struct_0(D,E) ) ) => m1_group_9(C,A,D) ) ) ) ) )).
fof(t13_groupp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => v1_groupp_1(k1_group_1(A),B,A) ) ) )).
fof(t13_grsolv_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v15_algstr_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( v15_algstr_0(D) & m1_group_2(D,A) ) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t13_hahnban,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t13_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t13_hallmar1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ! [E] : ( ~ r2_hidden(C,E) => k1_hallmar1(A,B,E) = k1_hallmar1(A,k2_hallmar1(A,B,C,D),E) ) ) ) ) )).
fof(t13_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => r1_xxreal_0(k1_funct_1(k6_weierstr(A,B),C),k3_metric_1(A,C,D)) ) ) ) ) ) )).
fof(t13_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ( r1_tarski(B,C) => r1_tarski(k13_glib_001(A,B),k13_glib_001(A,C)) ) ) ) ) )).
fof(t13_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => v1_henmodel(k6_domain_1(k3_cqc_lang(A),k5_cqc_lang(A)),A) ) )).
fof(t13_hermitan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => k8_group_1(k1_complfld,A,k2_complfld(A)) = k1_square_1(k9_complex1(A)) ) )).
fof(t13_hessenbe,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( ~ r1_collsp(A,B,C,E) & r1_collsp(A,B,C,D) & r1_collsp(A,E,F,B) & B != D & B != F & r1_collsp(A,D,B,F) ) ) ) ) ) ) ) )).
fof(t13_heyting1,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(t13_heyting2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t13_heyting3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(t13_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(A,B) => k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k18_sin_cos,B),3),A) = k1_funct_1(k16_sin_cos,A) ) ) ) )).
fof(t13_hilbasis,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ 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) ) => k3_polynom1(k15_pre_poly(A),C,k3_hilbasis(A,B,C)) = k6_domain_1(k15_pre_poly(A),k2_hilbasis(A,B)) ) ) )).
fof(t13_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => ( v6_hilbert1(A) => r1_tarski(k6_hilbert1,A) ) ) )).
fof(t13_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ( k1_funct_1(B,1) = k1_nat_1(3,A) => v3_hilbert2(B) ) ) ) )).
fof(t13_hilbert3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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)) ) ) ) )).
fof(t13_holder_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,1) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k1_numbers) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [G] : ( v7_ordinal1(G) => ( k9_nat_1(k1_numbers,D,G) = k2_power(k9_complex1(k9_nat_1(k1_numbers,B,G)),A) & k9_nat_1(k1_numbers,E,G) = k2_power(k9_complex1(k9_nat_1(k1_numbers,C,G)),A) & k9_nat_1(k1_numbers,F,G) = k2_power(k9_complex1(k3_real_1(k9_nat_1(k1_numbers,B,G),k9_nat_1(k1_numbers,C,G))),A) ) ) & v1_series_1(D) & v1_series_1(E) ) => ( v1_series_1(F) & r1_xxreal_0(k2_power(k4_series_1(F),k7_xcmplx_0(1,A)),k2_xcmplx_0(k2_power(k4_series_1(D),k7_xcmplx_0(1,A)),k2_power(k4_series_1(E),k7_xcmplx_0(1,A)))) ) ) ) ) ) ) ) ) ) )).
fof(t13_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_idea_1(B,A) => k4_idea_1(B,k5_numbers,A) = A ) ) ) )).
fof(t13_ideal_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & v2_ideal_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => r2_hidden(k4_algstr_0(A,C),B) ) ) ) ) )).
fof(t13_incproj,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_incsp_1(k3_incproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k3_incproj(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k3_incproj(A))) => ! [E] : ( m1_subset_1(E,u1_incsp_1(k3_incproj(A))) => ! [F] : ( m1_subset_1(F,u1_incsp_1(k3_incproj(A))) => ! [G] : ( m1_subset_1(G,u2_incsp_1(k3_incproj(A))) => ! [H] : ( m1_subset_1(H,u2_incsp_1(k3_incproj(A))) => ! [I] : ( m1_subset_1(I,u2_incsp_1(k3_incproj(A))) => ! [J] : ( m1_subset_1(J,u2_incsp_1(k3_incproj(A))) => ~ ( r1_incsp_1(k3_incproj(A),B,I) & r1_incsp_1(k3_incproj(A),C,I) & r1_incsp_1(k3_incproj(A),D,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) & r1_incsp_1(k3_incproj(A),B,G) & r1_incsp_1(k3_incproj(A),D,G) & r1_incsp_1(k3_incproj(A),C,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) & I != J & ! [K] : ( m1_subset_1(K,u1_incsp_1(k3_incproj(A))) => ~ ( r1_incsp_1(k3_incproj(A),K,G) & r1_incsp_1(k3_incproj(A),K,H) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t13_incsp_1,axiom,( ! [A] : ( l2_incsp_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_incsp_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_incsp_1(A))) => ( ( r1_tarski(C,B) & v4_incsp_1(B,A) ) => v4_incsp_1(C,A) ) ) ) ) )).
fof(t13_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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] : ( m4_index_1(C,u1_struct_0(A),u4_struct_0(A),u1_graph_1(A),u2_graph_1(A),B) => ! [D] : ( 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) ) ) ) ) )).
fof(t13_instalg1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t13_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => r2_int_1(A,B,1) ) ) )).
fof(t13_int_2,axiom,( ! [A] : ( v1_int_1(A) => ~ ( ( r1_int_1(A,1) | r1_int_1(A,k4_xcmplx_0(1)) ) & A != 1 & A != k4_xcmplx_0(1) ) ) )).
fof(t13_int_3,axiom,( k5_struct_0(k1_int_3) = 1 )).
fof(t13_int_4,axiom,( ! [A] : ( v1_int_1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ! [B] : ( v1_int_1(B) => ? [C] : ( v1_int_1(C) & ? [D] : ( v1_int_1(D) & B = k2_xcmplx_0(k3_xcmplx_0(A,C),D) & r1_xxreal_0(k5_numbers,D) & ~ r1_xxreal_0(A,D) ) ) ) ) ) )).
fof(t13_int_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ( k5_int_1(B,D) = k5_int_1(C,D) => k5_int_1(k1_newton(B,A),D) = k5_int_1(k1_newton(C,A),D) ) ) ) ) ) )).
fof(t13_int_6,axiom,( ! [A] : ( v1_int_1(A) => ( r1_int_1(k1_int_2(A),A) & r1_int_1(A,k1_int_2(A)) ) ) )).
fof(t13_int_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k8_newton) & v1_funct_1(A) & v1_partfun1(A,k8_newton) & v4_valued_0(A) & v2_pre_poly(A) ) => ~ ( v1_int_7(A) & k8_nat_3(k8_newton,A) = k5_numbers ) ) )).
fof(t13_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( ( r1_int_2(A,B) & k3_finseq_1(C) = k3_pepin(A,B) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,C)) => k1_funct_1(C,D) = k1_newton(A,k7_nat_d(D,1)) ) ) ) => ( r1_xxreal_0(B,1) | ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,C)) => k4_nat_d(k1_newton(k1_funct_1(C,D),k3_pepin(A,B)),B) = 1 ) ) ) ) ) ) ) )).
fof(t13_integr11,axiom,( ! [A] : ( ( ~ 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)) = k6_xcmplx_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,2),k5_numbers),k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(2,k5_numbers),k16_sin_cos),k7_xcmplx_0(1,4))),k2_seq_4(A)),k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,2),k5_numbers),k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(2,k5_numbers),k16_sin_cos),k7_xcmplx_0(1,4))),k3_seq_4(A))) ) )).
fof(t13_integr12,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k22_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k18_sin_cos))) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k16_sin_cos),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k16_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t13_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,D) & r2_relset_1(k1_numbers,k1_numbers,C,k1_taylor_1(2)) & r2_relset_1(k1_numbers,k1_numbers,B,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,k18_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,k18_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)),k26_sin_cos))) & D = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,D)),k26_sin_cos),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,D)),k26_sin_cos),k3_seq_4(A))) ) ) ) ) ) )).
fof(t13_integr14,axiom,( ! [A] : ( ( 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,k27_sin_cos,k2_fdiff_9))) => ( r2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k2_fdiff_9)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k2_fdiff_9)),A),B) = k2_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B))),k1_funct_1(k16_sin_cos,B)),k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k27_sin_cos,B),k1_funct_1(k18_sin_cos,B)),k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t13_integr15,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t13_integr16,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(t13_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t13_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ( ( r1_xxreal_0(B,D) & r1_xxreal_0(D,E) & r1_xxreal_0(E,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)) ) => ( r1_integr15(A,k3_integra5(D,E),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(D,E)),A) ) ) ) ) ) ) ) ) ) )).
fof(t13_integra1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t13_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( ( v4_xxreal_2(B) & r1_xxreal_0(k5_numbers,A) ) => k2_seq_4(k1_integra2(B,A)) = k3_xcmplx_0(A,k2_seq_4(B)) ) ) ) )).
fof(t13_integra3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( m1_integra1(C,B) => ! [D] : ( m1_integra1(D,B) => ! [E] : ( ( 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) = k5_numbers | r1_xxreal_0(A,k3_seq_4(B)) | r1_xxreal_0(k6_xcmplx_0(k18_rvsum_1(k5_integra1(B,E,D)),k18_rvsum_1(k5_integra1(B,E,C))),k3_xcmplx_0(k6_xcmplx_0(k2_seq_4(k1_rvsum_1(E)),k3_seq_4(k1_rvsum_1(E))),k1_integra3(B,C))) ) ) ) ) ) ) ) )).
fof(t13_integra4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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_partfun1(k18_rfunct_3(A,B),A) & v1_partfun1(k19_rfunct_3(A,B),A) ) ) ) )).
fof(t13_integra5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ! [C] : ( ( 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)) = k6_xcmplx_0(k1_funct_1(C,k2_seq_4(A)),k1_funct_1(C,k3_seq_4(A))) ) ) ) )).
fof(t13_integra6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t13_integra7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r1_integra7(B,D,C) => r1_integra7(B,k26_valued_1(k1_numbers,k1_numbers,D,A),k26_valued_1(k1_numbers,k1_numbers,C,A)) ) ) ) ) )).
fof(t13_integra8,axiom,( k19_sin_cos(k7_xcmplx_0(k28_sin_cos,4)) = k7_xcmplx_0(k3_square_1(2),2) )).
fof(t13_integra9,axiom,( ! [A] : ( ( 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,k18_sin_cos),k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k16_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k18_sin_cos),k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k16_sin_cos)),A),B) = k4_xcmplx_0(k3_xcmplx_0(B,k1_funct_1(k18_sin_cos,B))) ) ) ) ) )).
fof(t13_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t13_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1)) => ( r1_tarski(A,B) => r1_tarski(k7_intpro_1(A),k7_intpro_1(B)) ) ) ) )).
fof(t13_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k1_irrat_1(A),B),k5_numbers) & r1_xxreal_0(k1_funct_1(k1_irrat_1(A),B),1) ) ) ) ) )).
fof(t13_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t13_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,k6_cat_2(A,B),C) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( k2_cat_1(A,E,F) != k1_xboole_0 => ! [G] : ( m1_cat_1(G,A,E,F) => ( r2_nattra_1(B,C,k10_cat_2(A,B,C,D,E),k10_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,k10_cat_2(A,B,C,D,E),k10_cat_2(A,B,C,D,F)) ) ) ) ) ) ) ) ) ) )).
fof(t13_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t13_jct_misc,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t13_jgraph_1,axiom,( ! [A] : ( 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) ) ) )).
fof(t13_jgraph_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ~ ( ~ ( r1_xxreal_0(k18_euclid(A),k17_euclid(A)) & r1_xxreal_0(k4_xcmplx_0(k17_euclid(A)),k18_euclid(A)) ) & ~ ( r1_xxreal_0(k17_euclid(A),k18_euclid(A)) & r1_xxreal_0(k18_euclid(A),k4_xcmplx_0(k17_euclid(A))) ) & ~ ( r1_xxreal_0(k17_euclid(A),k18_euclid(A)) & r1_xxreal_0(k4_xcmplx_0(k18_euclid(A)),k17_euclid(A)) ) & ~ ( r1_xxreal_0(k18_euclid(A),k17_euclid(A)) & r1_xxreal_0(k17_euclid(A),k4_xcmplx_0(k18_euclid(A))) ) ) ) )).
fof(t13_jgraph_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( 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] : ( 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) = k7_xcmplx_0(k18_euclid(C),k3_square_1(k2_xcmplx_0(1,k1_square_1(k7_xcmplx_0(k17_euclid(C),k18_euclid(C)))))) ) ) & ! [C] : ( 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) = k5_numbers ) ) ) => v5_pre_topc(B,k1_pre_topc(k15_euclid(2),A),k3_topmetr) ) ) ) )).
fof(t13_jgraph_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t13_jgraph_5,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k5_topmetr)) => ! [I] : ( m1_subset_1(I,u1_struct_0(k5_topmetr)) => ~ ( H = k5_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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t13_jgraph_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(B))) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t13_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t13_jordan,axiom,( ! [A] : ( ( 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)) ) )).
fof(t13_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( E = a_4_1_jordan1(A,B,C,D) => v2_connsp_1(E,k15_euclid(2)) ) ) ) ) ) ) )).
fof(t13_jordan11,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(C,k2_jordan2c(2,A)) & r2_hidden(B,k1_jordan2c(2,A)) & r1_xxreal_0(k1_topreal6(2,C,B),k5_jordan1k(2,C,A)) ) ) ) ) )).
fof(t13_jordan12,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t13_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( r1_jordan1h(A,B) => r1_tarski(k1_jordan2c(2,k3_topreal1(2,k1_jordan13(A,B))),k1_jordan2c(2,A)) ) ) ) )).
fof(t13_jordan16,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t13_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ~ ( B != C & r1_jordan17(A,B,C,D,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ~ ( F != B & F != C & r1_jordan17(A,B,F,C,D) ) ) ) ) ) ) ) ) )).
fof(t13_jordan18,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( 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)) ) ) ) )).
fof(t13_jordan19,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D)),k3_topreal1(2,k1_jordan1e(B,A))) = k1_tarski(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D)),k3_topreal1(2,k2_jordan1e(B,A))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D)) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D)),k9_jordan6(B)) ) ) ) ) ) ) )).
fof(t13_jordan1a,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t13_jordan1b,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_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)) ) )).
fof(t13_jordan1c,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v1_int_1(D) => ( D = k1_int_1(k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k17_euclid(C),k6_pscomp_1(A)),k6_xcmplx_0(k8_pscomp_1(A),k6_pscomp_1(A))),k1_newton(2,B)),2)) => r1_xxreal_0(k2_xcmplx_0(k6_pscomp_1(A),k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k8_pscomp_1(A),k6_pscomp_1(A)),k1_newton(2,B)),k6_xcmplx_0(D,2))),k17_euclid(C)) ) ) ) ) ) )).
fof(t13_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & ~ r1_xxreal_0(k3_finseq_1(k2_jordan9(B,A)),C) & r2_hidden(k25_pscomp_1(B),k2_gobrd13(k2_jordan9(B,A),k1_jordan8(B,A),C)) ) ) ) )).
fof(t13_jordan1e,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => k3_topreal1(2,k2_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))) ) ) )).
fof(t13_jordan1f,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( k17_euclid(C) = k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(B),k8_pscomp_1(B)),2) & k18_euclid(C) = k3_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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,1),k1_jordan1a(k1_jordan8(B,1)),1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,1),k1_jordan1a(k1_jordan8(B,1)),k1_matrix_0(k1_jordan8(B,1)))),k8_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))))) & ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(1,D) & r1_xxreal_0(D,k1_matrix_0(k1_jordan8(B,k1_nat_1(A,1)))) & C = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),D) ) ) ) ) ) ) )).
fof(t13_jordan1g,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t13_jordan1h,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => r1_tarski(k2_relset_1(A,k7_matrix_0(A,B,C)),k2_jordan1h(A,B)) ) ) ) ) )).
fof(t13_jordan1j,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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)))) ) => ( r2_hidden(k25_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))),k10_xtuple_0(k2_jordan1e(B,A))) & r2_hidden(k25_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))),k3_topreal1(2,k2_jordan1e(B,A))) ) ) ) )).
fof(t13_jordan1k,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ 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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(B)))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(B)))) ) => ( ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( r2_hidden(E,C) & r2_hidden(F,D) ) => r1_xxreal_0(A,k3_metric_1(B,E,F)) ) ) ) => r1_xxreal_0(A,k7_weierstr(B,C,D)) ) ) ) ) ) )).
fof(t13_jordan20,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(2),A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_topmetr))) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( ( r1_xxreal_0(E,1) & B = a_3_0_jordan20(A,D,E) & C = k3_rcomp_1(k5_numbers,E) ) => k7_relset_1(u1_struct_0(k5_topmetr),u1_struct_0(k1_pre_topc(k15_euclid(2),A)),D,C) = B ) ) ) ) ) ) )).
fof(t13_jordan21,axiom,( ! [A] : ( ( 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(k7_xcmplx_0(k2_xcmplx_0(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(k7_xcmplx_0(k2_xcmplx_0(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(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)),2))))) ) ) )).
fof(t13_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,k5_numbers) => k2_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,k2_jordan9(A,B)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),k3_finseq_1(k1_jordan8(A,B))))))) = k2_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,k2_jordan9(A,B)),k6_jordan6(k7_xcmplx_0(k2_xcmplx_0(k8_pscomp_1(k3_topreal1(2,k2_jordan9(A,B))),k6_pscomp_1(k3_topreal1(2,k2_jordan9(A,B)))),2))))) ) ) ) )).
fof(t13_jordan23,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( ( v3_jordan23(B) & v1_finseq_6(B,A) ) => ! [C] : ( m1_subset_1(C,A) => v3_jordan23(k1_finseq_6(A,B,C)) ) ) ) ) )).
fof(t13_jordan24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( ( 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))) ) ) ) ) ) ) ) )).
fof(t13_jordan2b,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( C = a_3_1_jordan2b(A,B,D) & r2_hidden(D,k2_finseq_1(A)) ) => v3_pre_topc(C,k15_euclid(A)) ) ) ) ) ) )).
fof(t13_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t13_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( v3_topreal1(A) & r2_hidden(B,k2_topreal1(2,A,C)) & C != k1_jordan3(A,B) & C != k1_nat_1(k1_jordan3(A,B),1) ) ) ) ) )).
fof(t13_jordan4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( 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,k1_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),k2_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(D,E),1),A),1)) & k2_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(D,E),1),A),1) = k1_nat_1(k7_nat_d(k1_nat_1(k7_nat_d(D,E),1),A),1) ) ) ) ) ) ) ) )).
fof(t13_jordan5a,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(k4_topmetr(A,B))) => ! [H] : ( ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t13_jordan5b,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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) ) ) ) )).
fof(t13_jordan5c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t13_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( 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))))) ) ) ) )).
fof(t13_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t13_jordan7,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t13_jordan8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(C,B),A,2)) = k9_pscomp_1(C) ) ) ) ) )).
fof(t13_jordan9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( 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] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(B)) & ! [E] : ( 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_0(u1_struct_0(k15_euclid(2)),B,D,1)) ) ) ) ) ) ) ) ) )).
fof(t13_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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))) ) ) ) )).
fof(t13_kolmog01,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( m1_kolmog01(D,B,A,C) => ! [E] : ( ( ~ 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)) ) ) ) ) ) ) )).
fof(t13_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ! [E] : ( v7_ordinal1(E) => k1_funct_1(D,E) = k3_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) => r1_tarski(k4_kurato_0(A,D),k9_subset_1(A,k4_kurato_0(A,B),k4_kurato_0(A,C))) ) ) ) ) )).
fof(t13_kurato_1,axiom,( 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) )).
fof(t13_lang1,axiom,( ! [A] : ! [B] : ( A != B => k3_lang1(k7_lang1(A,B)) = k1_tarski(k9_finseq_1(B)) ) )).
fof(t13_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(D,k2_finseq_1(A)) & r2_hidden(E,k2_finseq_1(A)) ) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( 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_0(u1_struct_0(B),k2_laplace(D,E,A,B,C),F,G) != k3_matrix_0(u1_struct_0(B),C,F,G) ) & ( r1_xxreal_0(E,G) => ( r1_xxreal_0(D,F) | k3_matrix_0(u1_struct_0(B),k2_laplace(D,E,A,B,C),F,G) = k3_matrix_0(u1_struct_0(B),C,F,k1_nat_1(G,1)) ) ) & ( r1_xxreal_0(D,F) => ( r1_xxreal_0(E,G) | k3_matrix_0(u1_struct_0(B),k2_laplace(D,E,A,B,C),F,G) = k3_matrix_0(u1_struct_0(B),C,k1_nat_1(F,1),G) ) ) & ( ( r1_xxreal_0(D,F) & r1_xxreal_0(E,G) ) => k3_matrix_0(u1_struct_0(B),k2_laplace(D,E,A,B,C),F,G) = k3_matrix_0(u1_struct_0(B),C,k1_nat_1(F,1),k1_nat_1(G,1)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t13_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k1_funct_1(k1_latsubgr(A),B)) <=> r1_struct_0(B,C) ) ) ) ) )).
fof(t13_latsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( r2_hidden(C,k3_xboole_0(u1_struct_0(A),u1_struct_0(B))) => m1_subset_1(C,u1_struct_0(B)) ) ) ) )).
fof(t13_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_lattices(A) & l3_lattices(A) ) => k1_lattice2(k1_lattice2(A)) = A ) )).
fof(t13_lattice3,axiom,( ! [A] : ( ( v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k10_lattice3(A,B,C) = k10_lattice3(A,C,B) ) ) ) )).
fof(t13_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t13_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_yellow_0(B,k1_lattice5(A)) & v6_yellow_0(B,k1_lattice5(A)) & m1_yellow_0(B,k1_lattice5(A)) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ! [D] : ( ( 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] : ( ( 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] : ! [G] : ~ ( 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] : ( ( ~ v1_xboole_0(H) & m2_finseq_1(H,A) ) => ~ ( k3_finseq_1(H) = k1_nat_1(C,2) & r1_lattice5(A,H,F,G,D,E) ) ) ) ) ) => ( ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t13_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v4_lattice6(B,A) => ( r1_lattice6(A,B,k4_lattice6(A,B)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_lattice6(A,B,C) => C = k4_lattice6(A,B) ) ) ) ) ) ) )).
fof(t13_lattice7,axiom,( ! [A] : ( ( 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] : ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_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(k1_yellow_1(k4_lattice7(k5_yellow_0(A,k3_lattice7(A)))))))) & v23_waybel_0(B,A,k1_yellow_1(k4_lattice7(k5_yellow_0(A,k3_lattice7(A))))) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k1_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)) ) ) ) )).
fof(t13_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(t13_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k4_lattices(A,k5_lattices(A),B) = k5_lattices(A) ) ) )).
fof(t13_lfuzzy_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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(k4_yellow_1(A,B)) & v9_waybel_1(k4_yellow_1(A,B)) ) ) ) ) )).
fof(t13_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t13_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( ( v1_limfunc1(A) => ( r1_xxreal_0(B,k5_numbers) | v1_limfunc1(k26_valued_1(k4_ordinal1,k1_numbers,A,B)) ) ) & ( v1_limfunc1(A) => ( r1_xxreal_0(k5_numbers,B) | v2_limfunc1(k26_valued_1(k4_ordinal1,k1_numbers,A,B)) ) ) & ( B = k5_numbers => ( k10_xtuple_0(k26_valued_1(k4_ordinal1,k1_numbers,A,B)) = k1_tarski(k5_numbers) & v3_funct_1(k26_valued_1(k4_ordinal1,k1_numbers,A,B)) ) ) ) ) ) )).
fof(t13_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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) ) ) ) ) ) )).
fof(t13_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t13_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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) ) ) ) ) )).
fof(t13_lmod_5,axiom,( ! [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) ) => ! [B] : ( ( ~ 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] : ( 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 ) ) ) ) ) )).
fof(t13_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(t13_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t13_lopban_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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)) ) ) )).
fof(t13_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_lopban_2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_lopban_2(A))) => ! [D] : ( 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] : ( 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)) ) ) ) ) ) )).
fof(t13_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ! [C] : ( v7_ordinal1(C) => k5_rsspace3(A,B,C) = k4_struct_0(A) ) => v2_lopban_3(B,A) ) ) ) )).
fof(t13_lopban_4,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k3_xcmplx_0(k2_newton(k7_nat_d(A,1)),A) = k2_newton(A) ) ) & ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(B,A) => k3_xcmplx_0(k2_newton(k7_nat_d(A,B)),k6_xcmplx_0(k1_nat_1(A,1),B)) = k2_newton(k7_nat_d(k1_nat_1(A,1),B)) ) ) ) )).
fof(t13_lopban_6,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t13_lopban_7,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( ( 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)))) ) => ( ( v2_lopban_1(D,A,B) & v2_nfcont_1(k1_relset_1(u1_struct_0(A),C),A) & r2_relset_1(u1_struct_0(A),u1_struct_0(B),C,D) ) => v1_lopban_7(C,A,B) ) ) ) ) ) )).
fof(t13_lopclset,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t13_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_normsp_1(B) ) => ( B = g1_normsp_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)),k3_lp_space(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( v1_xreal_0(E) => ( ( k2_normsp_0(B,C) = k5_numbers => C = k4_struct_0(B) ) & ( C = k4_struct_0(B) => k2_normsp_0(B,C) = k5_numbers ) & r1_xxreal_0(k5_numbers,k2_normsp_0(B,C)) & r1_xxreal_0(k2_normsp_0(B,k1_algstr_0(B,C,D)),k2_xcmplx_0(k2_normsp_0(B,C),k2_normsp_0(B,D))) & k2_normsp_0(B,k1_rlvect_1(B,C,E)) = k3_xcmplx_0(k9_complex1(E),k2_normsp_0(B,C)) ) ) ) ) ) ) ) ) )).
fof(t13_lpspacc1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_rfunct_3(D,C,k2_numbers,k3_rfunct_3(C,k2_numbers)) => k1_binop_1(k9_lpspacc1(C),k1_binop_1(k8_lpspacc1(C),A,D),k1_binop_1(k8_lpspacc1(C),B,D)) = k1_binop_1(k8_lpspacc1(C),k2_xcmplx_0(A,B),D) ) ) ) ) )).
fof(t13_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_rfunct_3(B,A,k1_numbers,k3_rfunct_3(A,k1_numbers)) => ! [C] : ( m2_rfunct_3(C,A,k1_numbers,k3_rfunct_3(A,k1_numbers)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t13_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : 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)) ) ) )).
fof(t13_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(1,A) & r1_xxreal_0(A,k3_finseq_1(B)) ) => k7_partfun1(k1_hilbert1,k2_ltlaxio2(B),A) = k7_partfun1(k1_hilbert1,k2_ltlaxio2(k17_finseq_1(k1_hilbert1,C,B)),A) ) ) ) ) )).
fof(t13_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => r1_tarski(k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,B),k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,k4_ltlaxio1(A,B))) ) ) )).
fof(t13_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ( r1_ltlaxio4(A,B) => v3_ltlaxio3(B) ) ) ) )).
fof(t13_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ( r2_hidden(C,k4_cqc_the1(A)) => r2_hidden(k8_cqc_lang(A,B,C),k4_cqc_the1(A)) ) ) ) ) )).
fof(t13_margrel1,axiom,( ! [A] : ( v1_xboolean(A) => k4_xboolean(k8_margrel1,A) = A ) )).
fof(t13_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_tarski(k1_mathmorp(A,E,C),k1_mathmorp(A,D,B)) <=> r1_tarski(k1_mathmorp(A,k5_algstr_0(A,E,D),C),B) ) ) ) ) ) ) )).
fof(t13_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( r1_matrix10(C,B) => v1_matrix10(k5_matrix10(A,B,C)) ) ) ) ) )).
fof(t13_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_matrix_2(C,k3_matrix_2(k1_nat_1(A,2))) => ! [D] : ( m1_matrix_2(D,k3_matrix_2(k1_nat_1(A,2))) => ! [E] : ( m1_matrix_2(E,k3_matrix_2(k1_nat_1(A,2))) => ( ( r2_funct_2(k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),E,k1_partfun1(k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),D,C)) & v4_matrix_2(D,k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))) ) => k2_matrix11(A,B,E) = k4_algstr_0(B,k2_matrix11(A,B,C)) ) ) ) ) ) ) )).
fof(t13_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( m1_subset_1(E,u1_struct_0(D)) => ( ( r2_hidden(B,k4_finseq_1(k3_matrix_1(D,C))) & r2_hidden(A,k4_finseq_1(k3_matrix_1(D,C))) ) => ( A = B | ( v1_matrix_6(k3_matrix12(C,C,D,k3_matrix_1(D,C),B,A,E),C,D) & k1_matrix_6(C,D,k3_matrix12(C,C,D,k3_matrix_1(D,C),B,A,E)) = k3_matrix12(C,C,D,k3_matrix_1(D,C),B,A,k4_algstr_0(D,E)) ) ) ) ) ) ) ) ) )).
fof(t13_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ! [F] : ( 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_0(u1_struct_0(B),C,E,F) = k4_struct_0(B) ) ) ) ) ) => ( v1_matrix_0(k4_matrix11(A,A,u1_struct_0(B),D,C)) & v2_matrix_0(k4_matrix11(A,A,u1_struct_0(B),D,C),u1_struct_0(B),A,A) & v2_matrix_2(k4_matrix11(A,A,u1_struct_0(B),D,C),A,B) & m2_finseq_1(k4_matrix11(A,A,u1_struct_0(B),D,C),k3_finseq_2(u1_struct_0(B))) ) ) ) ) ) ) )).
fof(t13_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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] : ( 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)) ) ) ) )).
fof(t13_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t13_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(B),A,A) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix16(E,u1_struct_0(B)) & v1_matrix16(F,u1_struct_0(B)) ) => v1_matrix16(k1_matrix_4(B,k2_matrix13(A,A,B,E,C),k2_matrix13(A,A,B,F,D)),u1_struct_0(B)) ) ) ) ) ) ) ) )).
fof(t13_matrix17,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t13_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ( v1_matrix_0(k1_xboole_0) & v2_matrix_0(k1_xboole_0,B,k5_numbers,A) & m2_finseq_1(k1_xboole_0,k3_finseq_2(B)) ) ) ) )).
fof(t13_matrix_3,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => k3_finseq_1(k11_fvsum_1(A,B,C)) = k4_nat_1(k3_finseq_1(B),k3_finseq_1(C)) ) ) ) )).
fof(t13_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) ) => k1_matrix_4(A,B,k1_matrix_4(A,B,C)) = C ) ) ) ) )).
fof(t13_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => k3_matrix_5(A,A) = k7_matrix_5(2,A) ) )).
fof(t13_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v1_matrix_6(C,A,B) => ( r1_xxreal_0(A,k5_numbers) | k1_matrix_6(A,B,k4_matrix_0(u1_struct_0(B),C)) = k4_matrix_0(u1_struct_0(B),k1_matrix_6(A,B,C)) ) ) ) ) ) )).
fof(t13_matrix_7,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( k3_finseq_1(k1_matrix_3(A,B,C)) = B & k4_finseq_1(k1_matrix_3(A,B,C)) = k2_finseq_1(B) ) ) ) ) )).
fof(t13_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_8(C,A,B) & v1_matrix_8(D,A,B) & v1_matrix_6(C,A,B) ) => v1_matrix_8(k4_matrix_3(B,C,D),A,B) ) ) ) ) ) )).
fof(t13_matrix_9,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k12_matrix_3(2,A,k15_matrix_0(u1_struct_0(A),B,C,D,E)) = k5_algstr_0(A,k8_group_1(A,B,E),k8_group_1(A,C,D)) ) ) ) ) ) )).
fof(t13_matrixc1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k2_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(k2_numbers)) ) => ( ( k3_finseq_1(C) = k3_finseq_1(D) & k1_matrix_0(C) = k1_matrix_0(D) & r2_hidden(k4_tarski(A,B),k2_matrix_0(C)) ) => k3_matrix_0(k2_numbers,k5_matrix_5(C,D),A,B) = k6_xcmplx_0(k3_matrix_0(k2_numbers,C,A,B),k3_matrix_0(k2_numbers,D,A,B)) ) ) ) ) ) )).
fof(t13_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrixj1(B,A) & m2_finseq_1(B,k3_finseq_2(k3_finseq_2(A))) ) => ( k2_wsierp_1(k10_matrixj1(A,B)) = k5_numbers => k2_wsierp_1(k11_matrixj1(A,B)) = k5_numbers ) ) ) )).
fof(t13_matrixj2,axiom,( ! [A] : ( l6_algstr_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( v7_ordinal1(D) & r2_funct_2(u1_struct_0(B),u1_struct_0(B),k1_vectsp11(B,C,D),k6_grcat_1(B,B)) ) ) ) ) ) )).
fof(t13_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( 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) ) ) ) ) )).
fof(t13_matrixr2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => k7_matrixr1(k6_xcmplx_0(A,B),C) = k5_matrixr1(k7_matrixr1(A,C),k7_matrixr1(B,C)) ) ) ) )).
fof(t13_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( k3_finseq_1(C) = k5_numbers => k4_rlvect_1(B,k6_matrlin(B,C)) = k4_struct_0(B) ) ) ) ) )).
fof(t13_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( m2_finseq_1(D,u1_struct_0(C)) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t13_matroid0,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v1_vectsp_7(C,A,B) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t13_matrprob,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(C)) ) => ( r2_hidden(k4_tarski(A,B),k2_matrix_0(D)) <=> ( r2_hidden(A,k4_finseq_1(D)) & r2_hidden(B,k4_finseq_1(k1_matrprob(C,D,A))) ) ) ) ) ) ) )).
fof(t13_matrtop1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ( ( k3_finseq_1(D) = k3_finseq_1(B) & r1_xxreal_0(k3_finseq_1(E),k3_finseq_1(C)) ) => k15_finseq_1(k5_relat_1(k7_finseq_1(B,C),k8_relat_1(k7_finseq_1(D,E),A))) = k7_finseq_1(k15_finseq_1(k5_relat_1(B,k8_relat_1(D,A))),k15_finseq_1(k5_relat_1(C,k8_relat_1(E,A)))) ) ) ) ) ) )).
fof(t13_matrtop2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( k8_matrix13(k2_vectsp_1,C) = A => m1_matrlin(C,k2_vectsp_1,k1_vectsp_7(k2_vectsp_1,k6_prvect_1(k2_vectsp_1,B),k9_matrix13(k2_vectsp_1,A,B,C))) ) ) ) ) )).
fof(t13_matrtop3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t13_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t13_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( r2_pboole(A,D,k5_pboole(A,B,C)) <=> ( r2_pboole(A,D,k2_pboole(A,B,C)) & r5_pboole(A,D,k3_pboole(A,B,C)) ) ) ) ) ) )).
fof(t13_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( r2_hidden(E,k2_zfmisc_1(k2_tarski(A,B),k2_tarski(C,D))) => ( ( k1_xtuple_0(E) = A | k1_xtuple_0(E) = B ) & ( k2_xtuple_0(E) = C | k2_xtuple_0(E) = D ) ) ) )).
fof(t13_measure1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ! [D] : ( m1_measure1(D,A,B,C) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t13_measure2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( k1_funct_1(B,k5_numbers) = k1_xboole_0 & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( k1_funct_1(B,k1_nat_1(C,1)) = k6_subset_1(k1_funct_1(A,k5_numbers),k1_funct_1(A,C)) & r1_tarski(k1_funct_1(A,k1_nat_1(C,1)),k1_funct_1(A,C)) ) ) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_tarski(k1_funct_1(B,C),k1_funct_1(B,k1_nat_1(C,1))) ) ) ) ) )).
fof(t13_measure3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & v1_prob_2(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => r1_xxreal_0(k19_supinf_2(k1_partfun1(k4_ordinal1,B,B,k6_numbers,D,C)),k12_supinf_2(C,k2_measure2(A,B,k1_measure3(A,B,D)))) ) ) ) )).
fof(t13_measure4,axiom,( ! [A] : ! [B] : ( m1_measure4(B,A) => ( v1_funct_1(k3_measure4(A,B)) & v1_funct_2(k3_measure4(A,B),k1_measure4(A,B),k6_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),k6_numbers))) ) ) )).
fof(t13_measure5,axiom,( ! [A] : ( ( v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => r1_xxreal_0(k1_supinf_2,k2_measure5(A)) ) )).
fof(t13_measure6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xxreal_0(B) => ( ? [C] : ( v1_xxreal_0(C) & r1_xxreal_0(C,B) & A = k3_xxreal_1(C,B) ) => B = k8_supinf_2(A) ) ) ) )).
fof(t13_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k9_setfam_1(k1_numbers)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k1_numbers)))) ) => ! [B] : ( m2_measure7(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_xxreal_0(k1_supinf_2,k12_supinf_2(k7_measure7(A,B),C)) ) ) ) )).
fof(t13_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ( r1_tarski(A,B) <=> r1_tarski(k5_member_1(A),k5_member_1(B)) ) ) ) )).
fof(t13_membered,axiom,( ! [A] : ( v1_membered(A) => ( ! [B] : ( v1_xcmplx_0(B) => r2_hidden(B,A) ) => A = k2_numbers ) ) )).
fof(t13_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_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)) ) ) ) )).
fof(t13_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( B != C => ( r1_euclid_6(A,B,C) <=> r2_hidden(A,k4_euclid_4(2,B,C)) ) ) ) ) ) )).
fof(t13_mesfun10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ~ ( r1_mesfunc5(A,B,C,D) & r1_mesfunc5(A,B,C,E) & ! [F] : ( 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,k6_numbers,D,F)),k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,k7_mesfunc1(A,E),F))) ) ) ) ) ) ) ) ) )).
fof(t13_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t13_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( 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(k4_ordinal1,k10_seqfunc(A,B,C))) ) ) ) ) )).
fof(t13_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( v1_mesfunc8(B,A,k1_numbers) & r1_tarski(D,k1_relset_1(A,k4_mesfunc5(A,k1_numbers,B,k5_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)) ) ) ) ) ) )).
fof(t13_mesfunc1,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ( ! [B] : ( v1_xreal_0(B) => ~ r1_xxreal_0(B,A) ) => A = k2_supinf_1 ) ) )).
fof(t13_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( m1_subset_1(C,A) => r1_xxreal_0(k1_supinf_2,k12_supinf_2(k2_mesfunc2(A,B),C)) ) ) ) )).
fof(t13_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( v2_mesfunc5(B) => v4_mesfunc5(B) ) ) ) )).
fof(t13_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( r1_tarski(D,k1_relset_1(A,C)) => ( r1_mesfunc6(A,B,C,D) <=> ! [E] : ( v1_xreal_0(E) => r2_hidden(k8_subset_1(A,D,k14_mesfunc1(C,E)),B) ) ) ) ) ) ) ) )).
fof(t13_mesfunc7,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => k4_mesfunc7(k1_supinf_1,A) = k1_supinf_1 ) ) )).
fof(t13_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( m1_subset_1(C,A) => ( r2_hidden(C,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers))) => ( v10_mesfunc5(k3_mesfunc5(A,B,C)) <=> k12_supinf_2(k6_mesfunc8(A,B),C) = k12_supinf_2(k5_mesfunc8(A,B),C) ) ) ) ) ) )).
fof(t13_metric_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( l1_metric_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r2_hidden(D,k10_metric_1(B,C,A)) <=> ( ~ v2_struct_0(B) & k1_metric_1(B,C,D) = A ) ) ) ) ) ) )).
fof(t13_metric_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k1_metric_2(A,B) = k6_domain_1(u1_struct_0(A),B) ) ) )).
fof(t13_metric_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))) => ! [E] : ( m1_subset_1(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))) => r1_xxreal_0(k2_binop_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,k10_metric_3(A,B),C,E),k3_real_1(k2_binop_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,k10_metric_3(A,B),C,D),k2_binop_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,k10_metric_3(A,B),D,E))) ) ) ) ) ) )).
fof(t13_metric_6,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( v2_tbsp_1(B,A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r1_metric_6(A,B,C) & k1_tbsp_1(A,B) = C ) ) ) ) ) )).
fof(t13_metrizts,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( ! [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] : ( 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] : ( 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) ) ) ) ) ) )).
fof(t13_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( v2_mfold_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ? [D] : ( m1_connsp_2(D,B,C) & r1_metrizts(B,k15_euclid(A),D,k2_struct_0(k15_euclid(A))) ) ) ) ) ) )).
fof(t13_mfold_2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k4_finseq_1(k14_rvsum_1(A,B))) => ( k1_funct_1(k14_rvsum_1(A,B),C) = k3_xcmplx_0(k7_partfun1(k1_numbers,A,C),k7_partfun1(k1_numbers,B,C)) & k7_partfun1(k1_numbers,k14_rvsum_1(A,B),C) = k3_xcmplx_0(k7_partfun1(k1_numbers,A,C),k7_partfun1(k1_numbers,B,C)) ) ) ) ) ) )).
fof(t13_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_midsp_1(A,B,C,D,D) => B = C ) ) ) ) ) )).
fof(t13_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_midsp_1(A) ) => ! [B] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t13_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v2_struct_0(C) & v2_midsp_1(C) & l1_midsp_3(C,k1_nat_1(A,2)) ) => ! [D] : ( ( v4_midsp_2(D,C) & l1_midsp_2(D,C) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(u1_midsp_2(C,D))) => ! [F] : ( m2_finseq_2(F,u1_struct_0(u1_midsp_2(C,D)),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(u1_midsp_2(C,D)))) => ( ! [G] : ( 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)),k1_nat_1(A,1),F,B,E),G) = E ) ) & ! [G] : ( m1_midsp_3(G,A) => ! [H] : ( 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)),k1_nat_1(A,1),F,H,E),G) = k5_midsp_3(A,u1_struct_0(u1_midsp_2(C,D)),F,G) ) ) ) ) ) ) ) ) ) ) )).
fof(t13_mmlquer2,axiom,( ! [A] : ! [B] : ( ( v1_relat_2(B) & v6_relat_2(B) & v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => r2_relset_1(A,A,k2_mmlquer2(A,B,C),B) ) ) )).
fof(t13_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(t13_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( m1_mod_2(E,A,C,D) => ! [F] : ( m1_mod_2(F,A,B,C) => ! [G] : ( ( 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] : ( ( v1_funct_1(H) & v1_funct_2(H,u1_struct_0(B),u1_struct_0(C)) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)))) ) => ( ( E = g1_mod_2(A,C,D,G) & F = g1_mod_2(A,B,C,H) ) => ( k9_mod_2(A,B,C,D,E,F) = g1_mod_2(A,B,D,k1_partfun1(u1_struct_0(B),u1_struct_0(C),u1_struct_0(C),u1_struct_0(D),H,G)) & k8_mod_2(A,E,F) = g1_mod_2(A,B,D,k1_partfun1(u1_struct_0(B),u1_struct_0(C),u1_struct_0(C),u1_struct_0(D),H,G)) ) ) ) ) ) ) ) ) ) ) )).
fof(t13_mod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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))) ) ) ) ) )).
fof(t13_mod_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & l1_vectsp_2(D,B) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t13_modal_1,axiom,( ! [A] : ( ( ~ 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(k4_ordinal1,k4_ordinal1)),k14_trees_3(k5_numbers)) ) ) )).
fof(t13_modcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u4_struct_0(k11_modcat_1(A,B))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t13_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k48_modelc_1(A,B,D))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t13_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r1_modelc_2(B,k3_modelc_2(A)) <=> B = A ) ) ) )).
fof(t13_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => k18_modelc_3(A,k7_modelc_3(A)) = k5_numbers ) )).
fof(t13_moebius1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ( r1_nat_d(B,A) => a_2_0_moebius1(A,B) = a_2_1_moebius1(A,B) ) ) ) )).
fof(t13_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v16_monoid_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t13_monoid_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(t13_morph_01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t13_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => k12_msafree(A,B,C) = a_3_1_msafree(A,B,C) ) ) ) )).
fof(t13_msafree3,axiom,( ! [A] : ! [B] : ! [C] : ( l1_msualg_1(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,u1_struct_0(C)) & v1_funct_1(D) & v1_partfun1(D,u1_struct_0(C)) ) => ! [E] : ( r2_hidden(E,u1_struct_0(C)) => ! [F] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t13_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ( r2_hidden(D,k3_msualg_1(A,C,k1_msafree3(A,B))) => k1_funct_1(k5_msualg_1(A,C,k1_msafree3(A,B)),D) = k4_trees_4(k4_tarski(C,u1_struct_0(A)),D) ) ) ) ) ) )).
fof(t13_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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)) ) ) )).
fof(t13_msscyc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v7_graph_1(B,A) & m1_graph_1(B,A) ) => k1_funct_1(k7_graph_2(A,B),k1_nat_1(k3_finseq_1(B),1)) = k1_funct_1(u2_graph_1(A),k1_funct_1(B,k3_finseq_1(B))) ) ) )).
fof(t13_mssubfam,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v1_funcop_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( ( r2_hidden(B,A) & D = k1_funct_1(C,B) ) => k1_funct_1(k2_funct_6(C),B) = k10_xtuple_0(D) ) ) ) )).
fof(t13_mssublat,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t13_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m3_pboole(C,u1_struct_0(A),u3_msualg_1(A,B)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t13_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t13_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v4_msualg_1(D,A) & l3_msualg_1(D,A) ) => ~ ( r2_hidden(k4_tarski(B,C),k3_msualg_6(A)) & ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ~ r1_msualg_6(A,B,C,D,E) ) ) ) ) ) ) )).
fof(t13_msualg_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m2_nat_lat(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( D = E => ( r4_lattice3(A,D,C) <=> r4_lattice3(B,E,C) ) ) ) ) ) ) ) )).
fof(t13_msualg_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(t13_msualg_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(A,B))) => ( ! [E] : 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) ) ) ) ) ) )).
fof(t13_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(t13_mycielsk,axiom,( ! [A] : ( ( v8_struct_0(A) & l1_orders_2(A) ) => r1_xxreal_0(k2_mycielsk(A),k5_card_1(u1_struct_0(A))) ) )).
fof(t13_nagata_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_complex1(k9_nat_1(k1_numbers,k3_series_1(A),B)),k9_nat_1(k1_numbers,k3_series_1(k56_valued_1(k4_ordinal1,k1_numbers,A)),B)) ) ) )).
fof(t13_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(k1_nat_1(B,1),A) <=> r1_xxreal_0(A,B) ) ) ) )).
fof(t13_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(A,B) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(1,k3_nat_d(B,A)) ) ) ) ) )).
fof(t13_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_1(C,k1_numbers) => k1_nat_3(k7_finseq_1(C,k9_finseq_1(B)),A) = k7_finseq_1(k2_nat_3(C,A),k1_nat_3(k9_finseq_1(B),A)) ) ) ) )).
fof(t13_nat_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( r1_nat_d(A,B) & ~ r1_xxreal_0(A,1) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r1_nat_d(C,B) & r1_xxreal_0(C,A) & v1_int_2(C) ) ) ) ) ) )).
fof(t13_nat_5,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => m2_finseq_1(A,k1_numbers) ) )).
fof(t13_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k4_nat_d(k3_xcmplx_0(A,B),A) = k5_numbers ) ) )).
fof(t13_nat_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k10_nat_lat)) => ! [B] : ( 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)) ) ) )).
fof(t13_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t13_ncfcont1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k2_numbers))) ) => ! [C] : ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_hidden(F,k1_relset_1(u1_struct_0(A),B)) & ~ r1_xxreal_0(E,k2_normsp_0(A,k5_algstr_0(A,F,C))) & r1_xxreal_0(D,k9_complex1(k6_xcmplx_0(k7_partfun1(k2_numbers,B,F),k7_partfun1(k2_numbers,B,C)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t13_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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)) ) ) ) ) )).
fof(t13_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v2_comseq_2(B) & v3_normsp_1(C,A) ) => v3_normsp_1(k1_ndiff_1(A,C,B),A) ) ) ) ) )).
fof(t13_ndiff_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(t13_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_rcomp_1(D,C) => ( ( r1_ndiff_3(A,B,C) & r1_tarski(D,k1_relset_1(k1_numbers,B)) ) => ! [E] : ( ( v9_ordinal1(E) & v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & v1_fdiff_1(E,k5_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & v3_funct_1(F) & v1_funct_2(F,k4_ordinal1,k1_numbers) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,F) = k1_tarski(C) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,E,F)),D) ) => ( v3_normsp_1(k1_ndiff_1(A,k3_normsp_1(A,k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,E,F),B),k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,F,B)),k37_valued_1(k4_ordinal1,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(k4_ordinal1,u1_struct_0(A),k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,E,F),B),k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,F,B)),k37_valued_1(k4_ordinal1,k1_numbers,E))) ) ) ) ) ) ) ) ) ) )).
fof(t13_ndiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( 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) ) ) ) ) ) ) ) ) )).
fof(t13_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_prvect_2(A))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k4_card_3(k4_prvect_2(A))) => ! [E] : ( m1_subset_1(E,k4_card_3(k4_prvect_2(A))) => ( B = E => ( k1_rlvect_1(k14_prvect_2(A),B,C) = D <=> ! [F] : ( m2_subset_1(F,k4_ordinal1,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) ) ) ) ) ) ) ) ) )).
fof(t13_neckla_3,axiom,( ! [A] : ( l1_orders_2(A) => r1_xboole_0(k6_partfun1(u1_struct_0(A)),u1_orders_2(k3_necklace(A))) ) )).
fof(t13_necklace,axiom,( ! [A] : ( 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))) ) ) )).
fof(t13_net_1,axiom,( ! [A] : ! [B] : ( ( v1_net_1(B) & l1_petri(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t13_newton,axiom,( k2_newton(1) = 1 )).
fof(t13_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( v1_xreal_0(E) => ( r1_tarski(k2_relset_1(u1_struct_0(A),D),k1_relset_1(u1_struct_0(A),C)) => r2_funct_2(k4_ordinal1,u1_struct_0(B),k8_funct_2(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),D,C),E)) ) ) ) ) ) ) )).
fof(t13_nfcont_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t13_nfcont_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( ( 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) ) ) ) ) ) )).
fof(t13_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ( ? [D] : ( 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) ) ) ) ) )).
fof(t13_normform,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_finsub_1(B) ) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ! [D] : ( 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) ) ) ) ) )).
fof(t13_normsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & k10_xtuple_0(C) = k6_domain_1(u1_struct_0(A),B) ) ) ) )).
fof(t13_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k3_normsp_2(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k3_normsp_2(A))))) ) => ( r1_funct_2(k4_ordinal1,u1_struct_0(A),k4_ordinal1,u1_struct_0(k3_normsp_2(A)),B,C) => ( v2_frechet(C,k3_normsp_2(A)) <=> v3_normsp_1(B,A) ) ) ) ) ) )).
fof(t13_ntalgo_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ( k3_finseq_1(A) = 1 => k19_rvsum_1(A) = k1_funct_1(A,1) ) ) )).
fof(t13_numbers,axiom,( r1_tarski(k3_numbers,k2_numbers) )).
fof(t13_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t13_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( r2_hidden(B,k9_openlatt(A)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & B = k1_funct_1(k8_openlatt(A),C) ) ) ) )).
fof(t13_oposet_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_oposet_1(A) & l2_qmax_1(A) ) => ( v5_orders_2(A) => v6_oposet_1(A) ) ) )).
fof(t13_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_oppcat_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_oppcat_1(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t13_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_nfcont_3(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ( k1_relset_1(k1_numbers,C) = A => r2_relset_1(k1_numbers,u1_struct_0(B),k4_ordeq_01(A,B,C),C) ) ) ) ) )).
fof(t13_orders_1,axiom,( ! [A] : ! [B] : ( 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 ) ) ) )).
fof(t13_orders_2,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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))) ) ) ) ) )).
fof(t13_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => v3_ordinal1(k1_ordinal1(A)) ) )).
fof(t13_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( k3_xboole_0(A,B) = A | k3_xboole_0(A,B) = B ) ) ) )).
fof(t13_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_ordinal2(B) ) => ~ ( v2_ordinal2(A) & v2_ordinal2(B) & ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_ordinal2(C) ) => ~ ( C = k3_relat_1(B,A) & v2_ordinal2(C) ) ) ) ) ) )).
fof(t13_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => k1_ordinal5(A,k5_numbers) = 1 ) )).
fof(t13_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) ) => ( v2_ordinal5(B) => v2_ordinal5(k5_relat_1(B,A)) ) ) ) )).
fof(t13_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ~ r1_orders_2(B,D,C) => k1_ortsp_1(A,B,C,D,k3_rlvect_1(B,E,F)) = k3_rlvect_1(A,k1_ortsp_1(A,B,C,D,E),k1_ortsp_1(A,B,C,D,F)) ) ) ) ) ) ) ) )).
fof(t13_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( ( 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),k15_trees_3(D)) ) ) ) ) ) ) )).
fof(t13_osalg_1,axiom,( ! [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) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( m2_finseq_2(E,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ( ( r3_osalg_1(A,B,C,E) & r3_osalg_1(A,B,D,E) ) => C = D ) ) ) ) ) ) )).
fof(t13_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v12_osalg_1(C,A) & m1_msualg_2(C,A,B) ) => m2_osalg_2(k3_osalg_2(A,B),A,C) ) ) ) )).
fof(t13_osalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & v13_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t13_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v2_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,B),D)) => ( r3_orders_2(A,D,E) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t13_papdesaf,axiom,( ! [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) ) => ! [B] : ( ( ~ v7_struct_0(B) & v2_analoaf(B) & l1_analoaf(B) ) => ( B = k2_analoaf(A) => v2_aff_2(k2_diraf(B)) ) ) ) )).
fof(t13_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A))) => r1_parsp_1(k9_parsp_1(A),B,C,C,B) ) ) ) )).
fof(t13_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t13_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) )).
fof(t13_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t13_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => k2_partit1(A,B,B) = B ) ) )).
fof(t13_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t13_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r2_analoaf(A,F,B,F,D) & r2_analoaf(A,F,C,F,E) & r2_diraf(A,B,C,D,E) ) => ( r3_diraf(A,F,B,C) | r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) ) )).
fof(t13_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t13_pcomps_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t13_pcs_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v16_pcs_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k17_pcs_0(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k17_pcs_0(A,B))) => ( r1_pcs_0(k17_pcs_0(A,B),C,D) <=> ? [E] : ( m1_subset_1(E,A) & ? [F] : ( m1_subset_1(F,u1_struct_0(k15_pcs_0(A,B,E))) & ? [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t13_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(A))) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t13_pdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(2)) => ! [D] : ( ( 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) ) => k10_pdiff_1(2,1,D,C) = k1_fdiff_1(k1_pdiff_2(2,1,D,C),A) ) ) ) ) ) )).
fof(t13_pdiff_3,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(2)) => ! [B] : ( ( 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) = k10_pdiff_1(2,1,k1_pdiff_3(1,2,B),A) ) ) ) )).
fof(t13_pdiff_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r3_pdiff_1(3,1,A,B) <=> ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & B = k11_finseq_1(C,D,E) & ? [F] : ( m1_rcomp_1(F,C) & r1_tarski(F,k1_relset_1(k1_numbers,k1_pdiff_2(3,1,A,B))) & ? [G] : ( v1_funct_1(G) & v3_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [H] : ( v1_funct_1(H) & v2_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,F) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,1,A,B),I),k1_funct_1(k1_pdiff_2(3,1,A,B),C)) = k2_xcmplx_0(k1_funct_1(G,k6_xcmplx_0(I,C)),k1_funct_1(H,k6_xcmplx_0(I,C))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t13_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t13_pdiff_6,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( 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)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(k4_real_ns1(B)),u1_struct_0(k4_real_ns1(A))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(B)),u1_struct_0(k4_real_ns1(A))))) ) => ( r1_funct_2(k1_euclid(B),k1_euclid(A),u1_struct_0(k4_real_ns1(B)),u1_struct_0(k4_real_ns1(A)),C,D) => ( v2_pdiff_6(C,A,B) <=> v1_lopban_1(D,k4_real_ns1(B),k4_real_ns1(A)) ) ) ) ) ) ) )).
fof(t13_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( 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)),k3_real_1(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)) ) ) ) ) ) )).
fof(t13_pdiff_8,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k16_lopban_1(k4_real_ns1(A),k4_real_ns1(B)))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( 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(k2_normsp_0(k16_lopban_1(k4_real_ns1(A),k4_real_ns1(1)),E),k2_normsp_0(k16_lopban_1(k4_real_ns1(A),k4_real_ns1(B)),C)) ) ) ) ) ) ) )).
fof(t13_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t13_pencil_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t13_pencil_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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)))) ) ) ) )).
fof(t13_pencil_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v15_pencil_1(B) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_pencil_1(A,B,C))) => ! [E] : ( ( ~ 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(k1_funct_7(E,C,k6_domain_1(u1_struct_0(k2_pencil_1(A,B,C)),D))) & v16_pencil_1(k1_funct_7(E,C,k6_domain_1(u1_struct_0(k2_pencil_1(A,B,C)),D)),A) & m3_pboole(k1_funct_7(E,C,k6_domain_1(u1_struct_0(k2_pencil_1(A,B,C)),D)),A,k12_pralg_1(A,B)) ) ) ) ) ) ) ) )).
fof(t13_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t13_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ( A != k5_numbers => k4_nat_d(k1_square_1(A),k1_nat_1(A,1)) = 1 ) ) )).
fof(t13_petri,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t13_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ( r2_pnproc_1(A,B,C) => r2_pnproc_1(A,k3_pnproc_1(A,C,B),C) ) ) ) )).
fof(t13_polyalg1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_polyalg1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t13_polyeq_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ! [D] : ( 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(k1_square_1(D),k1_square_1(A))) ) => ( A = k5_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) = k5_numbers ) ) ) ) ) )).
fof(t13_polyeq_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( ( k4_complex1(D) = k5_numbers & k4_polyeq_1(A,k5_numbers,B,C,D) = k5_numbers ) => ( A = k5_numbers | ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ~ ( k3_complex1(D) = k2_xcmplx_0(E,F) & k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,F),E),k7_xcmplx_0(B,A)) = k5_numbers & D != k2_xcmplx_0(k1_power(3,k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(2,A))),k3_square_1(k2_xcmplx_0(k7_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,k1_square_1(A))),k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(3,A)),3))))),k1_power(3,k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(2,A))),k3_square_1(k2_xcmplx_0(k7_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,k1_square_1(A))),k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(3,A)),3)))))) & D != k2_xcmplx_0(k1_power(3,k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(2,A))),k3_square_1(k2_xcmplx_0(k7_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,k1_square_1(A))),k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(3,A)),3))))),k1_power(3,k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(2,A))),k3_square_1(k2_xcmplx_0(k7_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,k1_square_1(A))),k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(3,A)),3)))))) & D != k2_xcmplx_0(k1_power(3,k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(2,A))),k3_square_1(k2_xcmplx_0(k7_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,k1_square_1(A))),k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(3,A)),3))))),k1_power(3,k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(2,A))),k3_square_1(k2_xcmplx_0(k7_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,k1_square_1(A))),k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(3,A)),3)))))) ) ) ) ) ) ) ) ) ) )).
fof(t13_polyeq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( k1_polyeq_4(B,C,D,D,C,B,A) = k5_numbers => ( B = k5_numbers | r1_xxreal_0(k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(C),k3_xcmplx_0(k3_xcmplx_0(2,B),C)),k3_xcmplx_0(5,k1_square_1(B))),k3_xcmplx_0(k3_xcmplx_0(4,B),D)),k5_numbers) | ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ~ ( E = k7_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(B,C),k3_square_1(k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(C),k3_xcmplx_0(k3_xcmplx_0(2,B),C)),k3_xcmplx_0(5,k1_square_1(B))),k3_xcmplx_0(k3_xcmplx_0(4,B),D)))),k3_xcmplx_0(2,B)) & F = k7_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(B,C),k3_square_1(k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(C),k3_xcmplx_0(k3_xcmplx_0(2,B),C)),k3_xcmplx_0(5,k1_square_1(B))),k3_xcmplx_0(k3_xcmplx_0(4,B),D)))),k3_xcmplx_0(2,B)) & A != k4_xcmplx_0(1) & A != k7_xcmplx_0(k2_xcmplx_0(E,k3_square_1(k1_quin_1(1,k4_xcmplx_0(E),1))),2) & A != k7_xcmplx_0(k2_xcmplx_0(F,k3_square_1(k1_quin_1(1,k4_xcmplx_0(F),1))),2) & A != k7_xcmplx_0(k6_xcmplx_0(E,k3_square_1(k1_quin_1(1,k4_xcmplx_0(E),1))),2) & A != k7_xcmplx_0(k6_xcmplx_0(F,k3_square_1(k1_quin_1(1,k4_xcmplx_0(F),1))),2) ) ) ) ) ) ) ) ) ) )).
fof(t13_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( v1_xcmplx_0(F) => ! [G] : ( v1_xcmplx_0(G) => ( ( A = k6_xcmplx_0(E,k7_xcmplx_0(D,3)) & F = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(3,C),k1_newton(D,2)),9) & G = k7_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(9,D),C),k3_xcmplx_0(2,k1_newton(D,3))),k3_xcmplx_0(27,B)),54) ) => ( k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_newton(A,3),k3_xcmplx_0(D,k1_newton(A,2))),k3_xcmplx_0(C,A)),B) = k5_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)) = k5_numbers ) ) ) ) ) ) ) ) ) )).
fof(t13_polyform,axiom,( ! [A] : ( v7_ordinal1(A) => k2_polyform(k4_xcmplx_0(1),A) = k2_polyform(k4_xcmplx_0(1),k2_xcmplx_0(A,2)) ) )).
fof(t13_polynom1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t13_polynom2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( 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)))) ) => k2_polynom2(A,B,k9_polynom1(A,B),C) = k5_struct_0(B) ) ) ) )).
fof(t13_polynom3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k1_funct_1(k6_polynom3(2,A),1) = k2_polynom3(k4_ordinal1,k5_numbers,A) ) )).
fof(t13_polynom4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k1_polynom4(A,k9_polynom3(A)),k9_polynom3(A)) ) )).
fof(t13_polynom5,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( 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))) = k7_finseq_1(k1_polynom5(A),k9_finseq_1(k9_complex1(B))) & k1_polynom5(k8_finseq_1(u1_struct_0(k1_complfld),k12_finseq_1(u1_struct_0(k1_complfld),B),A)) = k7_finseq_1(k9_finseq_1(k9_complex1(B)),k1_polynom5(A)) ) ) ) )).
fof(t13_polynom6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( m2_subset_1(C,k14_pre_poly(A),k15_pre_poly(A)) => ! [D] : ( m2_subset_1(D,k14_pre_poly(A),k15_pre_poly(A)) => ! [E] : ( m2_subset_1(E,k14_pre_poly(A),k15_pre_poly(A)) => ! [F] : ( m2_subset_1(F,k14_pre_poly(B),k15_pre_poly(B)) => ! [G] : ( m2_subset_1(G,k14_pre_poly(B),k15_pre_poly(B)) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t13_polynom7,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( 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] : ( ( 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)))) ) => k2_polynom2(A,B,k1_polynom7(A,B,C,D),E) = k6_algstr_0(B,C,k1_polynom2(A,D,B,E)) ) ) ) ) ) )).
fof(t13_polynom8,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k3_polynom8(A,B,k5_numbers) = k5_struct_0(A) ) ) )).
fof(t13_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( ~ v2_struct_0(D) & l2_struct_0(D) ) => ! [E] : ( ( 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)))) ) => k4_polynom1(A,D,k1_polyred(A,B,D,E),k11_pre_poly(A,C,B)) = k4_polynom1(A,D,E,C) ) ) ) ) ) )).
fof(t13_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(1,C) ) | ( B != k5_numbers & ~ v1_abian(C) ) ) => k1_power(C,k7_xcmplx_0(A,B)) = k7_xcmplx_0(k1_power(C,A),k1_power(C,B)) ) ) ) ) )).
fof(t13_pralg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( m2_pboole(E,u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D)) => ! [F] : ( m1_subset_1(F,k3_msualg_1(A,B,C)) => ! [G] : ( r2_hidden(G,k1_relset_1(k4_ordinal1,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)) ) ) ) ) ) ) ) )).
fof(t13_pre_circ,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v4_trees_3(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v4_trees_3(B) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & r2_hidden(k1_nat_1(C,1),k4_finseq_1(A)) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(A)) => ( D = k1_nat_1(C,1) | k1_funct_1(A,D) = k1_funct_1(B,D) ) ) ) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_trees_1(D) ) => ( k1_funct_1(B,k1_nat_1(C,1)) = D => k11_trees_3(B) = k5_trees_1(k11_trees_3(A),k12_finseq_1(k4_ordinal1,C),D) ) ) ) ) ) ) )).
fof(t13_pre_ff,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k1_int_1(k3_power(2,k3_xcmplx_0(2,A))) = k1_int_1(k3_power(2,k1_nat_1(k3_xcmplx_0(2,A),1))) ) ) )).
fof(t13_pre_poly,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ~ ! [C] : ( m1_subset_1(C,k4_partfun1(A,B)) => C = k1_xboole_0 ) ) ) )).
fof(t13_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v4_pre_topc(C,B) <=> ? [D] : ( 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 ) ) ) ) ) )).
fof(t13_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t13_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(A,1) & r1_xxreal_0(2,B) & r1_xxreal_0(k1_newton(A,B),A) ) ) ) )).
fof(t13_prob_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( r2_hidden(C,k3_prob_1(A,B)) <=> ! [D] : ( v7_ordinal1(D) => r2_hidden(C,k9_nat_1(k9_setfam_1(A),B,D)) ) ) ) )).
fof(t13_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m2_prob_1(E,A,B) => ( r1_xxreal_0(k3_funct_2(B,k1_numbers,E,k5_prob_1(A,B,C,D)),k3_funct_2(B,k1_numbers,E,D)) & r1_xxreal_0(k3_funct_2(B,k1_numbers,E,k5_prob_1(A,B,C,D)),k3_funct_2(B,k1_numbers,E,C)) ) ) ) ) ) ) )).
fof(t13_prob_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(C)))) ) => ( r2_hidden(B,k1_prob_2(C,k9_setfam_1(C),k2_prob_3(C,D),A)) <=> ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(E,A) & r2_hidden(B,k1_prob_2(C,k9_setfam_1(C),D,E)) ) ) ) ) )).
fof(t13_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) ) ) ) )).
fof(t13_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t13_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( ~ r1_collsp(A,B,C,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => r1_projdes1(A,B,C,D,E) ) ) ) ) ) ) )).
fof(t13_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t13_projred1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) ) => ( ? [B] : ( m1_subset_1(B,u2_incsp_1(A)) & ? [C] : ( m1_subset_1(C,u1_incsp_1(A)) & ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & ? [E] : ( m1_subset_1(E,u1_incsp_1(A)) & ? [F] : ( 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] : ( m1_subset_1(B,u2_incsp_1(A)) => ? [C] : ( m1_subset_1(C,u1_incsp_1(A)) & ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & ? [E] : ( m1_subset_1(E,u1_incsp_1(A)) & ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t13_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u2_incsp_1(A)) => ! [F] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t13_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,k4_card_3(A)) => ! [E] : ( m2_subset_1(E,k4_ordinal1,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) ) ) ) ) )).
fof(t13_prvect_3,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_prvect_2(A) ) => ! [B] : ( ( v1_relat_1(B) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_prvect_2(B) ) => ? [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(k10_prvect_2(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k10_prvect_2(B))) => ? [F] : ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) & ? [G] : ( 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] : ( m1_subset_1(D,u1_struct_0(k5_prvect_3(k10_prvect_2(A),k10_prvect_2(B)))) => ! [E] : ( 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] : ( m1_subset_1(D,u1_struct_0(k5_prvect_3(k10_prvect_2(A),k10_prvect_2(B)))) => ! [E] : ( 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))) ) ) ) )).
fof(t13_pscomp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( 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] : ( 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)),k2_measure6(u1_struct_0(A),k1_numbers,B),C),A) ) ) ) ) )).
fof(t13_pua2mss1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) ) => ( ( k3_card_3(B) = A & ! [C] : ! [D] : ( ( 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) ) ) )).
fof(t13_pythtrip,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( ~ r1_xxreal_0(A,2) & ! [B] : ( m1_pythtrip(B) => ~ ( ~ v2_pythtrip(B) & r2_hidden(A,B) ) ) ) ) )).
fof(t13_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t13_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t13_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ! [E] : ( m1_subset_1(E,k9_qc_lang1(A)) => ( k5_qc_lang2(A,B,D) = k5_qc_lang2(A,C,E) => ( B = C & D = E ) ) ) ) ) ) ) )).
fof(t13_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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))) ) ) ) )).
fof(t13_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_trees_1(C,k9_xtuple_0(k2_qc_lang4(A,B))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t13_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_qc_trans(B,A) & m1_qc_lang1(B) ) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(B),k3_cqc_lang(B)) => ! [D] : ( m1_subset_1(D,k1_substut1(A)) => ! [E] : ( m1_subset_1(E,k1_substut1(B)) => ! [F] : ( m2_subset_1(F,k2_qc_lang1(B),k3_qc_lang1(B)) => ! [G] : ( m2_subset_1(G,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [H] : ( m2_subset_1(H,k9_qc_lang1(A),k3_cqc_lang(A)) => ( ( H = C & D = E & G = F ) => k7_substut1(A,G,H,D) = k7_substut1(B,F,C,E) ) ) ) ) ) ) ) ) ) )).
fof(t13_qmax_1,axiom,( ! [A] : ( ( 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))) ) )).
fof(t13_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v10_lattices(A) & v4_lattice3(A) & v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t13_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => k23_quaterni(A,k1_quatern2) = k5_numbers ) )).
fof(t13_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k1_square_1(k28_quaterni(A)) = k13_quaterni(k23_quaterni(A,k27_quaterni(A))) ) )).
fof(t13_quaterni,axiom,( k10_quaterni(k1_xcmplx_0,k1_xcmplx_0) = k4_xcmplx_0(1) )).
fof(t13_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ! [D] : ( v1_xreal_0(D) => ~ r1_xxreal_0(k5_numbers,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k1_square_1(D)),k3_xcmplx_0(B,D)),C)) ) & ~ r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,k1_quin_1(A,B,C)) ) ) ) ) )).
fof(t13_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t13_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => r2_hidden(k5_numbers,k2_radix_1(A)) ) )).
fof(t13_radix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t13_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) ) ) )).
fof(t13_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k3_radix_1(B)) ) => ! [D] : ( ( v3_card_1(D,A) & m2_finseq_1(D,k3_radix_1(B)) ) => ( ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t13_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(2,B) ) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t13_ramsey_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t13_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m2_prob_1(B,A,k1_random_1(A)) => ! [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))) ) => ? [D] : ( m2_finseq_1(D,k1_numbers) & ? [E] : ( 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] : ( v7_ordinal1(F) => ( r2_hidden(F,k4_finseq_1(D)) => k12_supinf_2(D,F) = k1_extreal1(k12_supinf_2(C,k1_funct_1(E,F)),k12_supinf_2(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) ) ) ) ) ) )).
fof(t13_random_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ( ! [D] : ( r2_hidden(D,C) => r1_xxreal_0(k5_numbers,k12_supinf_2(B,D)) ) => r1_xxreal_0(k5_numbers,k5_bhsp_5(k1_numbers,A,k9_binop_2,C,B)) ) ) ) ) )).
fof(t13_random_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( m2_prob_1(E,A,C) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,A,B) & v1_random_3(F,A,B,C,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => r1_funct_2(D,k1_numbers,D,k6_numbers,k2_random_3(A,B,C,D,E,F),k1_random_3(A,B,C,D,k2_prob_4(A,C,E),F)) ) ) ) ) ) ) )).
fof(t13_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(C)) => ( r1_struct_0(k3_ranknull(A,B,C,D),E) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & E = k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,F) ) ) ) ) ) ) ) )).
fof(t13_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ( A != k5_numbers => k1_rat_1(A) = k7_xcmplx_0(k2_rat_1(A),A) ) ) )).
fof(t13_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_polynom5(A,B,C) => r1_polynom5(A,k5_vfunct_1(k4_ordinal1,A,B),C) ) ) ) ) )).
fof(t13_rcomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( ( v2_rcomp_1(A) & v3_xxreal_2(A) ) => ( A = k1_xboole_0 | r2_hidden(k3_seq_4(A),A) ) ) ) )).
fof(t13_rcomp_3,axiom,( ! [A] : ( ( v5_xxreal_2(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( ( r2_hidden(k3_seq_4(A),A) & r2_hidden(k2_seq_4(A),A) ) => A = k1_rcomp_1(k3_seq_4(A),k2_seq_4(A)) ) ) )).
fof(t13_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k9_nat_1(k4_ordinal1,k1_real_3(B,A),1) = k4_nat_d(A,k9_nat_1(k4_ordinal1,k1_real_3(B,A),k5_numbers)) ) ) )).
fof(t13_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( 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) ) ) ) )).
fof(t13_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_real_ns1(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k7_real_ns1(A))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t13_realset2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k8_group_1(A,B,k4_struct_0(A)) = k4_struct_0(A) ) ) )).
fof(t13_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t13_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [E] : ( ( 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] : ( m1_subset_1(F,k4_ordinal1) => ( ( r1_xxreal_0(1,F) & r2_hidden(C,k6_subset_1(k1_funct_1(E,k1_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) = k7_finseq_1(k2_finseq_2(F,k5_numbers),k3_rfinseq(k2_rfinseq(k1_numbers,F,k20_rfunct_3(B,D,B)))) ) ) ) ) ) ) ) ) ) ) )).
fof(t13_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( 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))) ) ) )).
fof(t13_relset_1,axiom,( ! [A] : r1_tarski(k4_relat_1(A),k2_zfmisc_1(A,A)) )).
fof(t13_relset_2,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( 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)))) ) ) )).
fof(t13_revrot_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( 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(k1_nat_1(A,k3_finseq_1(D)),k4_finseq_4(D,C))) ) ) ) ) ) ) )).
fof(t13_rewrite1,axiom,( ! [A] : ! [B] : ( r1_rewrite1(k1_xboole_0,A,B) => A = B ) )).
fof(t13_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(A)) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t13_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(A)) => ~ ( k1_flang_1(A,D,B) = k1_flang_1(A,E,C) & ! [F] : ( m1_subset_1(F,k8_afinsq_1(A)) => ~ ( k1_flang_1(A,D,F) = E & B = k1_flang_1(A,F,C) ) ) & ! [F] : ( m1_subset_1(F,k8_afinsq_1(A)) => ~ ( k1_flang_1(A,E,F) = D & C = k1_flang_1(A,F,B) ) ) ) ) ) ) ) ) )).
fof(t13_rfinseq,axiom,( ! [A] : ( v1_xreal_0(A) => k3_rfinseq(k9_finseq_1(A)) = k9_finseq_1(A) ) )).
fof(t13_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( v7_ordinal1(B) => ( ~ 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))) ) ) ) ) )).
fof(t13_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( v1_xcmplx_0(C) => k24_valued_1(k18_valued_1(A,B),C) = k18_valued_1(A,k24_valued_1(B,C)) ) ) ) )).
fof(t13_rfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ( ( v1_partfun1(B,A) & v1_partfun1(C,A) ) => ( r2_relset_1(k4_ordinal1,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,A,D,k3_valued_1(A,k1_numbers,k1_numbers,B,C)),k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,A,D,B),k8_funct_2(k4_ordinal1,k1_numbers,A,D,C))) & r2_relset_1(k4_ordinal1,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,A,D,k47_valued_1(A,k1_numbers,k1_numbers,B,C)),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,A,D,B),k8_funct_2(k4_ordinal1,k1_numbers,A,D,C))) & r2_relset_1(k4_ordinal1,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,A,D,k20_valued_1(A,k1_numbers,k1_numbers,B,C)),k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,A,D,B),k8_funct_2(k4_ordinal1,k1_numbers,A,D,C))) ) ) ) ) ) ) )).
fof(t13_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t13_rfunct_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t13_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_seq_2(A) => k1_rinfsup1(A) = k4_xcmplx_0(k2_rinfsup1(k32_valued_1(k4_ordinal1,k1_numbers,A))) ) ) )).
fof(t13_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r1_funct_2(k4_ordinal1,k6_numbers,k4_ordinal1,k1_numbers,A,B) => ( v1_rinfsup2(A) <=> v2_seq_2(B) ) ) ) ) )).
fof(t13_ring_1,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_ring_1(A,B))) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t13_ringcat1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(D,A) => m1_ringcat1(D,B,C) ) ) ) ) ) )).
fof(t13_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_rlvect_2(C,A) => ! [D] : ( 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)) ) ) ) ) )).
fof(t13_rlaffin2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ~ v1_xboole_0(k1_rlaffin2(A,B)) => v1_finset_1(B) ) ) ) )).
fof(t13_rlaffin3,axiom,( ! [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) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_rlaffin3(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t13_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_rlsub_1(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ( ( E = C & F = B ) => k3_rlvect_1(D,E,F) = k3_rlvect_1(A,C,B) ) ) ) ) ) ) ) )).
fof(t13_rlsub_2,axiom,( ! [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) ) => ! [B] : ( ( v1_rlvect_1(B) & m1_rlsub_1(B,A) ) => k2_rlsub_2(A,B,B) = B ) ) )).
fof(t13_rltopsp1,axiom,( ! [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) ) => ! [B] : ( v1_xreal_0(B) => 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)) ) ) )).
fof(t13_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_algstr_0(A,B,k4_struct_0(A)) = B ) ) )).
fof(t13_rlvect_2,axiom,( ! [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) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t13_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( B != C & v1_rlvect_3(k7_domain_1(u1_struct_0(A),B,C),A) ) <=> ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( k3_rlvect_1(A,k1_rlvect_1(A,B,D),k1_rlvect_1(A,C,E)) = k4_struct_0(A) => ( D = k5_numbers & E = k5_numbers ) ) ) ) ) ) ) ) )).
fof(t13_rlvect_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & A = k3_rlvect_1(B,k3_rlvect_1(B,C,k1_rlvect_1(B,D,F)),k1_rlvect_1(B,E,G)) ) ) ) ) ) ) ) )).
fof(t13_rlvect_5,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_3(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_struct_0(k1_rlvect_3(A,B),C) ) ) ) )).
fof(t13_rlvect_x,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t13_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_rmod_2(E,A,B) => ! [F] : ( m1_subset_1(F,u1_struct_0(E)) => ! [G] : ( m1_subset_1(G,u1_struct_0(E)) => ( ( F = D & G = C ) => k3_rlvect_1(E,F,G) = k3_rlvect_1(B,D,C) ) ) ) ) ) ) ) ) )).
fof(t13_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v2_vectsp_2(C,A) & m1_rmod_2(C,A,B) ) => k2_rmod_3(A,B,C,C) = C ) ) ) )).
fof(t13_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( ( 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),D,C)) = k5_algstr_0(B,k1_rmod_4(A,B,D),k1_rmod_4(A,B,k9_subset_1(u1_struct_0(B),D,C))) ) ) ) ) )).
fof(t13_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_robbins1(A,B,k7_robbins1(A)) = B ) ) )).
fof(t13_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) )).
fof(t13_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t13_robbins4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_robbins4)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_robbins4)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_robbins4)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t13_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(B,k4_roughs_1(A,B)) ) ) )).
fof(t13_rpr_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t13_rsspace,axiom,( ~ v2_struct_0(g1_rlvect_1(k10_rsspace,k9_rsspace(k6_rsspace,k10_rsspace),k7_rsspace(k6_rsspace,k10_rsspace),k8_rsspace(k6_rsspace,k10_rsspace))) & v13_algstr_0(g1_rlvect_1(k10_rsspace,k9_rsspace(k6_rsspace,k10_rsspace),k7_rsspace(k6_rsspace,k10_rsspace),k8_rsspace(k6_rsspace,k10_rsspace))) & v2_rlvect_1(g1_rlvect_1(k10_rsspace,k9_rsspace(k6_rsspace,k10_rsspace),k7_rsspace(k6_rsspace,k10_rsspace),k8_rsspace(k6_rsspace,k10_rsspace))) & v3_rlvect_1(g1_rlvect_1(k10_rsspace,k9_rsspace(k6_rsspace,k10_rsspace),k7_rsspace(k6_rsspace,k10_rsspace),k8_rsspace(k6_rsspace,k10_rsspace))) & v4_rlvect_1(g1_rlvect_1(k10_rsspace,k9_rsspace(k6_rsspace,k10_rsspace),k7_rsspace(k6_rsspace,k10_rsspace),k8_rsspace(k6_rsspace,k10_rsspace))) & v5_rlvect_1(g1_rlvect_1(k10_rsspace,k9_rsspace(k6_rsspace,k10_rsspace),k7_rsspace(k6_rsspace,k10_rsspace),k8_rsspace(k6_rsspace,k10_rsspace))) & v6_rlvect_1(g1_rlvect_1(k10_rsspace,k9_rsspace(k6_rsspace,k10_rsspace),k7_rsspace(k6_rsspace,k10_rsspace),k8_rsspace(k6_rsspace,k10_rsspace))) & v7_rlvect_1(g1_rlvect_1(k10_rsspace,k9_rsspace(k6_rsspace,k10_rsspace),k7_rsspace(k6_rsspace,k10_rsspace),k8_rsspace(k6_rsspace,k10_rsspace))) & v8_rlvect_1(g1_rlvect_1(k10_rsspace,k9_rsspace(k6_rsspace,k10_rsspace),k7_rsspace(k6_rsspace,k10_rsspace),k8_rsspace(k6_rsspace,k10_rsspace))) & l1_rlvect_1(g1_rlvect_1(k10_rsspace,k9_rsspace(k6_rsspace,k10_rsspace),k7_rsspace(k6_rsspace,k10_rsspace),k8_rsspace(k6_rsspace,k10_rsspace))) )).
fof(t13_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t13_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => r1_struct_0(A,k4_struct_0(B)) ) ) )).
fof(t13_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_bhsp_1(B) & m1_rusub_1(B,A) ) => k2_rusub_2(A,B,B) = B ) ) )).
fof(t13_rusub_3,axiom,( ! [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_bhsp_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_rlvect_3(B,A) & ! [C] : ( m1_rusub_3(C,A) => ~ r1_tarski(B,C) ) ) ) ) )).
fof(t13_rusub_4,axiom,( ! [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_bhsp_1(A) & v1_rusub_4(A) & l1_bhsp_1(A) ) => ( k1_rusub_4(A) = 1 <=> ? [B] : ( 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)) ) ) ) )).
fof(t13_rusub_5,axiom,( ! [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) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_rusub_4(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t13_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k4_rvsum_1(k9_finseq_1(A),k9_finseq_1(B)) = k9_finseq_1(k2_xcmplx_0(A,B)) ) ) )).
fof(t13_rvsum_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k7_rvsum_2(k9_finseq_1(A),k9_finseq_1(B)) = k9_finseq_1(k6_xcmplx_0(A,B)) ) ) )).
fof(t13_scm_comp,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( m1_dtconstr(B,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r1_tarski(k61_valued_1(k1_ordinal4(k15_scm_comp(B,C),k5_afinsq_1(k2_compos_1(k1_ami_3))),D),A) => ! [E] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(E,u1_struct_0(k1_ami_3)) & v5_memstr_0(E,k7_card_1(2),k1_ami_3,D) ) => ( ~ r1_xxreal_0(C,k17_scm_comp(B)) => ( r1_extpro_1(k7_card_1(2),k1_ami_3,A,E) & k1_funct_1(k6_extpro_1(k7_card_1(2),k1_ami_3,A,E),k10_ami_3(C)) = k12_scm_comp(E,B) & k8_extpro_1(k7_card_1(2),k1_ami_3,A,E) = k1_afinsq_1(k15_scm_comp(B,C)) ) ) ) ) ) ) ) ) )).
fof(t13_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ( ( r1_tarski(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_3(k4_scmfsa_2(k5_numbers),1)),D) & r1_tarski(k3_scmfsa6a(B,C),A) ) => ( k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D,k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),D),1))) = k5_card_1(B) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D,k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),D),1))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_funct_4(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),D,k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),D)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_3(k4_scmfsa_2(k5_numbers),1)))) & r1_tarski(k6_compos_1(k1_scmfsa_2,C,k5_card_1(B)),A) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D,k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),D),1)),k4_scmfsa_2(k5_numbers)) = 1 & r1_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D) & k8_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D) = k2_xcmplx_0(k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),D),1),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(k1_funct_4(A,B),C),k1_funct_4(k6_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,B),D),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_3(k4_scmfsa_2(k5_numbers),1))))) & ( v1_scmfsa6b(C) => k1_funct_1(k6_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D),k4_scmfsa_2(k5_numbers)) = 1 ) ) ) ) ) ) ) )).
fof(t13_scmfsa10,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( 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 ) ) )).
fof(t13_scmfsa6a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k6_compos_1(k1_scmfsa_2,k2_scmfsa6a(A),B) = k1_scmfsa6a(k6_compos_1(k1_scmfsa_2,A,B),k1_nat_1(k5_card_1(A),B)) ) ) )).
fof(t13_scmfsa7b,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( v7_ordinal1(C) => ~ r3_scmfsa7b(k13_scmfsa_2(C,B),A) ) ) ) )).
fof(t13_scmfsa8a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( v7_ordinal1(B) => k5_card_1(k1_scmfsa6a(A,B)) = k5_card_1(A) ) ) )).
fof(t13_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( v1_ami_2(E) & ~ v1_scmfsa_m(E) & m1_subset_1(E,u1_struct_0(k1_scmfsa_2)) ) => ( ( k1_funct_1(B,E) = k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),3)))) ) ) ) ) ) ) )).
fof(t13_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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(k5_numbers)) = 1 & r5_scmfsa7b(E,C,A) & r6_scmfsa7b(E,C,A) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,C) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,D) ) => k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(E,C,A)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(E,D,B)) ) ) ) ) ) ) )).
fof(t13_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => r1_scmfsa9a(A,B,C,D) ) ) ) ) )).
fof(t13_scmfsa_1,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k4_scmfsa_1,k5_scmfsa_1))) => ! [B] : ( m2_subset_1(B,k1_scmfsa_1,k2_scmfsa_1) => ! [C] : ( v1_int_1(C) => k1_funct_1(k7_scmfsa_1(A,B,C),k4_ordinal1) = k1_funct_1(A,k4_ordinal1) ) ) ) )).
fof(t13_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( 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 ) ) )).
fof(t13_scmfsa_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( ~ 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(k7_card_1(3),k1_scmfsa_2)) & v1_finset_1(B) & v4_extpro_1(B,k7_card_1(3),k1_scmfsa_2,A) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ( ( r1_tarski(B,C) & r1_tarski(B,D) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( ( r1_tarski(A,E) & r1_tarski(A,F) ) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v1_ami_2(H) & m1_subset_1(H,u1_struct_0(k1_scmfsa_2)) ) => ! [I] : ( m1_scmfsa_2(I) => ( ( k3_extpro_1(k7_card_1(3),k1_scmfsa_2,E,k5_extpro_1(k7_card_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(k7_card_1(3),k1_scmfsa_2,E,C,G),I)) = k3_finseq_1(k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,D,G),I)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t13_scmfsa_m,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) ) => r1_tarski(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)),k1_scmfsa_m(A)) ) )).
fof(t13_scmisort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( 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),k5_numbers) | ( k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa_9(D,C)),k1_scmfsa_m(B),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(B)),3))) = k5_numbers & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa_9(D,C)),k1_scmfsa_m(B),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(B)),3))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(B),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(B)))) ) ) ) ) ) ) ) )).
fof(t13_scmp_gcd,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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),k5_numbers) & k1_funct_1(B,k2_scmp_gcd) = k5_numbers & r1_xxreal_0(k5_numbers,k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,k3_scmp_gcd),3))) & r1_xxreal_0(k5_numbers,k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,k3_scmp_gcd),2))) & ! [C] : ( v7_ordinal1(C) => ~ ( 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] : ( v7_ordinal1(D) => ( 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)) ) ) ) ) ) ) ) ) )).
fof(t13_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( 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 ) ) ) )).
fof(t13_scmpds_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( v7_ordinal1(G) => ! [H] : ( v1_int_1(H) => ! [I] : ( v1_int_1(I) => ! [J] : ( ( v1_ami_2(J) & m1_subset_1(J,u1_struct_0(k1_scmpds_2)) ) => ! [K] : ( ( 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))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t13_scmpds_4,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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)) ) ) ) )).
fof(t13_scmpds_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_scmpds_4(C) ) => ! [D] : ( v7_ordinal1(D) => ( ( 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) ) ) ) ) ) )).
fof(t13_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(E) & 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) ) ) ) ) ) ) )).
fof(t13_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( v7_ordinal1(D) => ( ( 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)) ) ) ) ) ) ) )).
fof(t13_scmpds_9,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => k1_amistd_1(2,k1_scmpds_2,C,k15_scmpds_2(A,B,D,E)) = k1_tarski(k1_ordinal1(C)) ) ) ) ) ) )).
fof(t13_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => ! [D] : ( ( 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(k7_card_1(2),k1_scmring2(A))) & v1_partfun1(D,u1_struct_0(k1_scmring2(A))) ) => ( k1_funct_1(k2_extpro_1(k7_card_1(2),k1_scmring2(A),k5_scmring2(A,B,C),D),k4_struct_0(k1_scmring2(A))) = k4_card_1(k5_memstr_0(k7_card_1(2),k1_scmring2(A),D)) & k2_scmring2(A,k2_extpro_1(k7_card_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] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmring2(A))) ) => ( E != B => k2_scmring2(A,k2_extpro_1(k7_card_1(2),k1_scmring2(A),k5_scmring2(A,B,C),D),E) = k2_scmring2(A,D,E) ) ) ) ) ) ) ) )).
fof(t13_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmring2(A))) => ~ ( k2_compos_0(u1_compos_1(k1_scmring2(A)),B) = 2 & ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmring2(A))) ) => B != k4_scmring2(A,C,D) ) ) ) ) ) )).
fof(t13_scmyciel,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(k2_tarski(B,C),k1_scmyciel(A)) => ( B != C & r2_hidden(B,k3_tarski(A)) & r2_hidden(C,k3_tarski(A)) ) ) )).
fof(t13_scpinvar,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),F)) = k5_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,k1_nat_1(k5_card_1(C),3))) ) ) ) ) ) ) ) )).
fof(t13_scpisort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ! [F] : ( v7_ordinal1(F) => ( ! [G] : ( ( 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,k5_numbers) ) => ! [H] : ( ( v1_relat_1(H) & v4_relat_1(H,k4_ordinal1) & v5_relat_1(H,u1_compos_1(k1_scmpds_2)) & v1_funct_1(H) & v1_partfun1(H,k4_ordinal1) ) => ( 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)),k5_numbers) | r1_xxreal_0(F,k5_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) ) ) ) ) ) ) ) ) ) )).
fof(t13_scpqsort,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k5_card_1(k2_scpqsort(A,B)) = 57 ) ) )).
fof(t13_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_analoaf(A,B,C,B,D) ) ) ) ) ) )).
fof(t13_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B),C),k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C))) ) ) ) )).
fof(t13_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(A) => v1_comseq_2(A) ) ) )).
fof(t13_seq_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(A) => v2_comseq_2(k56_valued_1(k4_ordinal1,k1_numbers,A)) ) ) )).
fof(t13_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( B != k5_numbers => r2_relset_1(k4_ordinal1,k4_partfun1(A,k1_numbers),k3_seqfunc(A,k2_seqfunc(A,C,B)),k2_seqfunc(A,k3_seqfunc(A,C),k5_xcmplx_0(B))) ) ) ) ) )).
fof(t13_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) <=> ! [B] : ( v7_ordinal1(B) => m1_subset_1(k9_nat_1(k1_numbers,A,B),k4_ordinal1) ) ) ) )).
fof(t13_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ? [B] : ( v7_ordinal1(B) & v1_series_1(k1_valued_0(k1_numbers,A,B)) ) => v1_series_1(A) ) ) )).
fof(t13_series_3,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => r1_xxreal_0(k3_xcmplx_0(k3_xcmplx_0(A,B),C),k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_newton(A,3),k1_newton(B,3)),k1_newton(C,3)),3)) ) ) ) )).
fof(t13_series_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(1,k9_complex1(A)) & ~ r1_xxreal_0(1,k9_complex1(B)) & ~ r1_xxreal_0(k9_complex1(k7_xcmplx_0(k2_xcmplx_0(A,B),k2_xcmplx_0(1,k3_xcmplx_0(A,B)))),1) ) ) ) )).
fof(t13_setfam_1,axiom,( ! [A] : ! [B] : ( r1_setfam_1(A,B) => r1_tarski(k3_tarski(A),k3_tarski(B)) ) )).
fof(t13_setlim_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ( v3_funct_1(C) & k3_funct_1(C) = B ) => ! [D] : ( v7_ordinal1(D) => k3_tarski(a_3_3_setlim_1(A,C,D)) = B ) ) ) ) )).
fof(t13_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) ) ) )).
fof(t13_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,k5_finsub_1(A)) => ! [E] : ( ( 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] : ( m1_subset_1(F,B) => ( F = k7_setwiseo(A,B,C,D,E) <=> ? [G] : ( 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] : ( m1_subset_1(H,B) => ( r3_binop_1(B,H,C) => k1_funct_1(G,k1_xboole_0) = H ) ) & ! [H] : ( m1_subset_1(H,A) => k1_funct_1(G,k1_tarski(H)) = k3_funct_2(A,B,E,H) ) & ! [H] : ( m1_subset_1(H,k5_finsub_1(A)) => ( r1_tarski(H,D) => ( H = k1_xboole_0 | ! [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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t13_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k5_finsub_1(A)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( ( 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] : ( ( 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] : ( ( 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) & E = k4_binop_1(B,F) & r6_binop_1(B,G,F) & k5_binop_1(B,G,E,D) = E ) => k5_binop_1(B,G,k7_setwiseo(A,B,F,C,H),D) = k7_setwiseo(A,B,F,C,k9_funcop_1(B,A,G,H,D)) ) ) ) ) ) ) ) ) ) )).
fof(t13_sf_mastr,axiom,( k1_sf_mastr(k2_compos_1(k1_scmfsa_2)) = k1_xboole_0 )).
fof(t13_sfmastr1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( v1_scmfsa6c(D) & m1_subset_1(D,u1_compos_1(k1_scmfsa_2)) ) => ( ( v7_amistd_1(C,k7_card_1(3),k1_scmfsa_2) | ( r6_scmfsa7b(C,k1_scmfsa_m(B),A) & r5_scmfsa7b(C,k1_scmfsa_m(B),A) ) ) => k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(k5_scmfsa6a(C,D),B,A)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k2_extpro_1(k7_card_1(3),k1_scmfsa_2,D,k1_scmfsa6b(C,B,A))) ) ) ) ) ) )).
fof(t13_sfmastr2,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) => r1_sfmastr2(B,A,C,D) ) ) ) ) ) )).
fof(t13_sfmastr3,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & ~ v1_scmfsa_m(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( B != D => k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k1_sfmastr3(F,B,C,D,E,A),k5_numbers),D) = k1_funct_1(A,D) ) ) ) ) ) ) ) )).
fof(t13_sgraph1,axiom,( ! [A] : ( v1_finset_1(A) => v1_finset_1(k2_sgraph1(A)) ) )).
fof(t13_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => v1_sheffer1(A) ) )).
fof(t13_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t13_simplex1,axiom,( ! [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) ) => ! [B] : ( ( v1_matroid0(B) & m1_simplex0(B,u1_struct_0(A)) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t13_simplex2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( ( v6_tbsp_1(C,k14_euclid(A)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k14_euclid(A)))) ) => ( C = B => ! [D] : ( 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),k9_metric_1(k14_euclid(A),D,k3_tbsp_1(k14_euclid(A),C))) ) ) ) ) ) ) )).
fof(t13_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v7_ordinal1(C) => k9_nat_1(k2_numbers,k3_sin_cos(B),C) = k9_nat_1(k2_numbers,k9_sin_cos(C,B,A),C) ) ) ) )).
fof(t13_sin_cos2,axiom,( k1_funct_1(k22_sin_cos,k5_numbers) = 1 )).
fof(t13_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,k6_xcmplx_0(A,B)) = k6_xcmplx_0(k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,B)),k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,B))) ) ) )).
fof(t13_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( k19_sin_cos(A) != k5_numbers & k19_sin_cos(B) != k5_numbers & k19_sin_cos(C) != k5_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)))) ) ) ) ) )).
fof(t13_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( k19_sin_cos(A) != k5_numbers & k17_sin_cos(A) != k5_numbers & ~ ( k4_sin_cos4(k3_xcmplx_0(2,A)) = k7_xcmplx_0(k1_square_1(k4_sin_cos4(A)),k6_xcmplx_0(1,k1_square_1(k1_sin_cos4(A)))) & k4_sin_cos4(k3_xcmplx_0(2,A)) = k7_xcmplx_0(k2_xcmplx_0(k2_sin_cos4(A),k1_sin_cos4(A)),k6_xcmplx_0(k2_sin_cos4(A),k1_sin_cos4(A))) ) ) ) )).
fof(t13_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ~ ( ~ r1_xxreal_0(A,k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B))) & ~ r1_xxreal_0(k2_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)),A) & r1_xxreal_0(k19_sin_cos(A),k5_numbers) ) ) ) )).
fof(t13_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(1,k1_square_1(A)) => r1_xxreal_0(k5_numbers,k7_xcmplx_0(k2_xcmplx_0(k1_square_1(A),1),k6_xcmplx_0(1,k1_square_1(A)))) ) ) )).
fof(t13_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k6_xcmplx_0(k1_square_1(k6_xcmplx_0(k2_sin_cos2(A),k2_sin_cos2(B))),k1_square_1(k6_xcmplx_0(k4_sin_cos2(A),k4_sin_cos2(B)))) = k3_xcmplx_0(4,k1_square_1(k2_sin_cos2(k7_xcmplx_0(k6_xcmplx_0(A,B),2)))) & k6_xcmplx_0(k1_square_1(k2_xcmplx_0(k4_sin_cos2(A),k4_sin_cos2(B))),k1_square_1(k2_xcmplx_0(k2_sin_cos2(A),k2_sin_cos2(B)))) = k3_xcmplx_0(4,k1_square_1(k4_sin_cos2(k7_xcmplx_0(k6_xcmplx_0(A,B),2)))) ) ) ) )).
fof(t13_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))) => k1_funct_1(k26_sin_cos,A) = k1_sin_cos4(A) ) ) )).
fof(t13_sincos10,axiom,( v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(t13_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t13_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(B,k3_topreal1(2,A)) & ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(A)) & r2_hidden(B,k2_topreal1(2,A,C)) ) ) ) ) ) )).
fof(t13_sprect_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t13_sprect_2,axiom,( ! [A] : ( ( v2_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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)) ) ) ) )).
fof(t13_sprect_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(B,k1_matrix_0(D)) & r1_xxreal_0(1,A) & r1_xxreal_0(A,C) & r1_xxreal_0(C,k3_finseq_1(D)) ) => r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,A,B)),k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,C,B))) ) ) ) ) ) )).
fof(t13_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(t13_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) & r1_xxreal_0(A,k1_square_1(A)) ) ) )).
fof(t13_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t13_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k4_ordinal1)) ) => ~ ( r1_tarski(B,k7_card_1(A)) & B != k1_seq_4(k6_xcmplx_0(A,1)) & r1_xxreal_0(k6_xcmplx_0(A,1),k3_nat_1(B)) ) ) ) )).
fof(t13_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [E] : ( m2_subset_1(E,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [F] : ( ( v5_relat_1(F,k3_qc_lang1(A)) & v3_card_1(F,B) & m2_finseq_1(F,k2_qc_lang1(A)) ) => ! [G] : ( m1_subset_1(G,k1_substut1(A)) => r2_relset_1(k4_ordinal1,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)) ) ) ) ) ) ) ) )).
fof(t13_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k7_subset_1(A,B,C) = k9_subset_1(A,B,k3_subset_1(A,C)) ) ) )).
fof(t13_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( 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)) ) ) )).
fof(t13_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => ! [C] : ( m1_subset_1(C,k16_substut1(A)) => ( k19_substut1(A,B) = k19_substut1(A,C) => v6_substut1(k21_substut1(A,B,C),A) ) ) ) ) )).
fof(t13_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( 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) ) ) ) )).
fof(t13_supinf_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => k7_supinf_2(k6_supinf_2(A)) = k2_supinf_2(k8_supinf_2(A)) ) )).
fof(t13_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(t13_sysrel,axiom,( ! [A] : k4_relat_1(k1_tarski(A)) = k1_tarski(k4_tarski(A,A)) )).
fof(t13_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_taxonom1(k1_tarski(k10_eqrel_1(A)),A) ) )).
fof(t13_taxonom2,axiom,( ! [A] : ! [B] : ( ( v3_abian(B,k1_zfmisc_1(k1_zfmisc_1(A))) & m1_taxonom2(B,A) ) => ! [C] : ( ( v4_taxonom2(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ( ( r1_tarski(C,B) & ! [D] : ( ( 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) ) ) ) )).
fof(t13_taylor_1,axiom,( ! [A] : ( v1_xreal_0(A) => k3_power(k4_power,k1_funct_1(k22_sin_cos,A)) = A ) )).
fof(t13_taylor_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & r2_hidden(E,k2_rcomp_1(k4_xcmplx_0(A),A)) & ~ r1_xxreal_0(F,k5_numbers) & ~ r1_xxreal_0(1,F) & r1_xxreal_0(B,k9_complex1(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k22_sin_cos,k2_rcomp_1(k4_xcmplx_0(A),A)),D),k3_xcmplx_0(F,E)),k1_newton(E,D)),k2_newton(D)))) ) ) ) ) ) ) ) )).
fof(t13_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t13_tdgroup,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r1_tdgroup(A,B,C,C,D) & r1_tdgroup(A,B,E,E,D) ) => C = E ) ) ) ) ) ) )).
fof(t13_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t13_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(t13_tdlat_3,axiom,( ! [A] : ( ( v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t13_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t13_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t13_tex_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [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)) & v2_tdlat_3(A) ) => v2_tdlat_3(B) ) ) ) )).
fof(t13_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_tex_3(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( m1_pre_topc(B,C) => ( v1_tex_3(B,C) & m1_pre_topc(B,C) ) ) ) ) ) )).
fof(t13_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v1_tex_4(k5_setfam_1(u1_struct_0(A),k1_tex_4(A,B)),A) ) ) )).
fof(t13_tietze,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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] : ( ( 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))) ) ) ) ) ) ) ) )).
fof(t13_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_tsep_1(A,B,C))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ! [F] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t13_toler_1,axiom,( ! [A] : ! [B] : ( ( 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 ) ) )).
fof(t13_topalg_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k14_euclid(C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k14_euclid(C))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k15_euclid(C))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k15_euclid(C))) => ~ ( D = H & E = I & F = k1_rlvect_1(k15_euclid(C),H,B) & G = k1_rlvect_1(k15_euclid(C),I,B) & ~ r1_xxreal_0(A,k3_metric_1(k14_euclid(C),D,E)) & B != k5_numbers & r1_xxreal_0(k3_xcmplx_0(k9_complex1(B),A),k3_metric_1(k14_euclid(C),F,G)) ) ) ) ) ) ) ) ) ) ) )).
fof(t13_topalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_topalg_2(A) & m1_pre_topc(A,k2_topalg_2) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t13_topalg_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t13_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t13_topalg_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_connsp_2(A) <=> v2_connsp_2(k2_struct_0(A),A) ) ) )).
fof(t13_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t13_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t13_topdim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v2_pre_topc(B) & v3_pcomps_1(B) & l1_pre_topc(B) ) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v3_pre_topc(E,B) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) ) => ~ ( r2_hidden(D,E) & ! [F] : ( ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t13_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(t13_topgen_2,axiom,( ! [A] : ( ( ~ 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] : ( ( 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) ) ) ) )).
fof(t13_topgen_3,axiom,( ! [A] : ( 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))) ) ) )).
fof(t13_topgen_4,axiom,( ! [A] : ! [B] : ( 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) ) ) ) )).
fof(t13_topgen_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => r2_hidden(B,k1_topreal9(A,B,C)) ) ) ) )).
fof(t13_topgrp_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t13_topmetr,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & m1_topmetr(B,A) ) => m1_pre_topc(k3_pcomps_1(B),k3_pcomps_1(A)) ) ) )).
fof(t13_topreal1,axiom,( k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,k5_numbers),k19_euclid(k5_numbers,1)) = a_0_0_topreal1 & k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,1),k19_euclid(1,1)) = a_0_1_topreal1 & k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,k5_numbers),k19_euclid(1,k5_numbers)) = a_0_2_topreal1 & k1_rltopsp1(k15_euclid(2),k19_euclid(1,k5_numbers),k19_euclid(1,1)) = a_0_3_topreal1 )).
fof(t13_topreal3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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(k7_xcmplx_0(k2_xcmplx_0(k17_euclid(A),k17_euclid(B)),2),k18_euclid(A)),k1_rltopsp1(k15_euclid(2),A,B)) ) ) ) ) )).
fof(t13_topreal4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v7_ordinal1(D) => ( ( v4_topreal1(B) & r2_hidden(D,k4_finseq_1(B)) & r2_hidden(k1_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)) ) ) ) ) ) ) ) )).
fof(t13_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(C,D) ) => k2_xcmplx_0(k9_complex1(k6_xcmplx_0(B,A)),k9_complex1(k6_xcmplx_0(D,C))) = k2_xcmplx_0(k6_xcmplx_0(B,A),k6_xcmplx_0(D,C)) ) ) ) ) ) )).
fof(t13_topreal7,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ( ( k3_finseq_1(A) = k3_finseq_1(C) & k3_finseq_1(B) = k3_finseq_1(D) ) => k3_euclid(k4_rvsum_1(k8_finseq_1(k1_numbers,A,B),k8_finseq_1(k1_numbers,C,D))) = k8_finseq_1(k1_numbers,k3_euclid(k4_rvsum_1(A,C)),k3_euclid(k4_rvsum_1(B,D))) ) ) ) ) ) )).
fof(t13_topreal8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m2_finseq_1(C,B) => ( r1_xxreal_0(1,A) => k2_graph_2(B,C,k1_nat_1(A,1),k3_finseq_1(C)) = k2_rfinseq(B,A,C) ) ) ) )).
fof(t13_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => ( C = D => k10_metric_1(k14_euclid(A),D,B) = k3_topreal9(A,C,B) ) ) ) ) ) )).
fof(t13_topreala,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(t13_toprealb,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( m1_subset_1(A,u1_struct_0(k8_toprealb(2))) => ( r1_xxreal_0(k4_xcmplx_0(1),k17_euclid(A)) & r1_xxreal_0(k17_euclid(A),1) & r1_xxreal_0(k4_xcmplx_0(1),k18_euclid(A)) & r1_xxreal_0(k18_euclid(A),1) ) ) ) )).
fof(t13_toprealc,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => ( r2_hidden(A,k2_finseq_1(B)) => k12_euclid(k1_funct_7(k5_euclid(B),A,C)) = k9_complex1(C) ) ) ) )).
fof(t13_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => k2_toprns_1(k3_xcmplx_0(C,B),A,D) = k2_toprns_1(C,A,k2_toprns_1(B,A,D)) ) ) ) ) )).
fof(t13_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) ) )).
fof(t13_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t13_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_tops_1(B,A) <=> ! [C] : ( 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) ) ) ) ) ) )).
fof(t13_tops_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( ( v1_xreal_0(D) & v2_xxreal_0(D) ) => ? [E] : ( 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))) ) ) ) ) ) ) )).
fof(t13_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t13_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(t13_treal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_topmetr(k5_numbers,1))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_topmetr(k5_numbers,1))) => ( k3_funct_2(u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(k5_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(k5_numbers,1)),k4_treal_1(A,B,C,D),k2_treal_1(A,B)) = D ) ) ) ) ) ) )).
fof(t13_trees_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t13_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => ( B = k1_xboole_0 => k2_trees_2(A,1) = k1_trees_2(A,B) ) ) ) )).
fof(t13_trees_3,axiom,( ! [A] : ( v2_trees_3(k1_tarski(A)) <=> ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) ) )).
fof(t13_trees_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(t13_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( m1_trees_1(B,k9_xtuple_0(A)) => r1_tarski(k3_trees_9(k5_trees_2(A,B)),k3_trees_9(A)) ) ) )).
fof(t13_trees_a,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) ) => ( r2_hidden(A,k9_xtuple_0(B)) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( 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) ) ) ) ) ) ) )).
fof(t13_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_borsuk_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( v1_borsuk_1(C,B) & m1_pre_topc(C,B) ) => ( v1_borsuk_1(C,A) & m1_pre_topc(C,A) ) ) ) ) )).
fof(t13_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t13_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t13_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v6_pre_topc(B) & m1_pre_topc(B,A) ) => ? [C] : ( v1_pre_topc(C) & m1_pre_topc(C,A) & m1_pre_topc(B,C) & v2_tsp_2(C,A) ) ) ) )).
fof(t13_twoscomp,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( 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))) ) ) ) ) )).
fof(t13_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t13_unialg_3,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t13_uniroots,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ( v1_int_1(B) => v1_int_1(k2_binop_1(u1_struct_0(k1_complfld),k4_ordinal1,u1_struct_0(k1_complfld),k4_group_1(k1_complfld),B,A)) ) ) ) )).
fof(t13_uproots,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & v3_group_1(A) & v5_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( ( 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),k4_ordinal1,u1_struct_0(A),D,B) => k3_group_4(A,C) = k3_group_4(A,B) ) ) ) ) ) )).
fof(t13_urysohn1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_subset_1(B,k1_numbers,k1_urysohn1(k1_nat_1(A,1))) => ( ~ r2_hidden(B,k1_urysohn1(A)) => ( r2_hidden(k7_xcmplx_0(k6_xcmplx_0(k6_urysohn1(k1_nat_1(A,1),B),1),k11_newton(2,k1_nat_1(A,1))),k1_urysohn1(A)) & r2_hidden(k7_xcmplx_0(k1_nat_1(k6_urysohn1(k1_nat_1(A,1),B),1),k11_newton(2,k1_nat_1(A,1))),k1_urysohn1(A)) ) ) ) ) )).
fof(t13_urysohn2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,k5_numbers) => ! [C] : ( ( ~ 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( D = k7_supinf_2(A) & E = k8_supinf_2(A) ) => ( k7_supinf_2(C) = k3_xcmplx_0(B,D) & k8_supinf_2(C) = k3_xcmplx_0(B,E) ) ) ) ) ) ) ) ) ) ) )).
fof(t13_urysohn3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m2_urysohn3(D,A,B,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => r1_tarski(k6_urysohn3(A,B,C,D,E),k2_urysohn1) ) ) ) ) ) )).
fof(t13_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t13_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v3_funct_1(A) & v1_valued_0(A) ) => ? [B] : ( v1_xcmplx_0(B) & ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => k1_funct_1(A,C) = B ) ) ) )).
fof(t13_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(t13_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(t13_vectsp10,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t13_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t13_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t13_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ( B != k4_struct_0(A) & k11_algstr_0(A,B) = k4_struct_0(A) ) ) ) )).
fof(t13_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_vectsp_4(E,A,B) => ! [F] : ( m1_subset_1(F,u1_struct_0(E)) => ! [G] : ( m1_subset_1(G,u1_struct_0(E)) => ( ( F = D & G = C ) => k3_rlvect_1(E,F,G) = k3_rlvect_1(B,D,C) ) ) ) ) ) ) ) ) )).
fof(t13_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( v7_vectsp_1(C,A) & m1_vectsp_4(C,A,B) ) => k2_vectsp_5(A,B,C,C) = C ) ) ) )).
fof(t13_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t13_vectsp_7,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t13_vectsp_8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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)) ) ) ) ) ) )).
fof(t13_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_7(D,A,C) => ? [E] : ( m1_vectsp_7(E,A,B) & r1_tarski(D,E) ) ) ) ) ) )).
fof(t13_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ( v1_xreal_0(E) => 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))) ) ) ) ) ) )).
fof(t13_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ( v1_xcmplx_0(E) => 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))) ) ) ) ) ) )).
fof(t13_waybel10,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t13_waybel11,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t13_waybel12,axiom,( ! [A] : ( ( v5_orders_2(A) & v2_yellow_0(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t13_waybel13,axiom,( ! [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] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_waybel_8(k1_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(k1_yellow_1(k7_waybel_0(A))))))) ) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k1_waybel_8(k1_yellow_1(k7_waybel_0(A)))),B,C) = k5_waybel_0(A,C) ) => v23_waybel_0(B,A,k1_waybel_8(k1_yellow_1(k7_waybel_0(A)))) ) ) ) )).
fof(t13_waybel14,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t13_waybel15,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k2_yellow_1(A)),u1_struct_0(k2_yellow_1(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_yellow_1(A)),u1_struct_0(k2_yellow_1(A))))) ) => ( ( v11_quantal1(B) & v22_waybel_0(B,k2_yellow_1(A),k2_yellow_1(A)) ) => v22_waybel_0(k3_waybel_1(k2_yellow_1(A),k2_yellow_1(A),B),k1_yellow_2(k2_yellow_1(A),k2_yellow_1(A),B),k2_yellow_1(A)) ) ) )).
fof(t13_waybel16,axiom,( ! [A] : v2_yellow_0(k1_yellow_1(k8_waybel_0(k2_yellow_1(A)))) )).
fof(t13_waybel18,axiom,( ! [A] : ( ~ 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)))))) ) ) )).
fof(t13_waybel19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_orders_2(A) & v4_orders_2(A) & v1_waybel19(A) & l1_waybel_9(A) ) => ! [B] : ( 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) ) ) )).
fof(t13_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(t13_waybel21,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t13_waybel22,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( 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(k1_yellow_1(k8_waybel_0(k2_yellow_1(A)))),u1_struct_0(B),k2_waybel22(A,B,C),k4_yellow_0(k1_yellow_1(k8_waybel_0(k2_yellow_1(A))))) = k4_yellow_0(B) ) ) )).
fof(t13_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_yellow_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( C = D => r1_tarski(k5_waybel_0(B,D),k5_waybel_0(A,C)) ) ) ) ) ) )).
fof(t13_waybel24,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_lattice3(C) & v2_lattice3(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) )).
fof(t13_waybel25,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [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)) => k1_waybel25(A) = k1_waybel25(B) ) ) ) )).
fof(t13_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v6_pre_topc(B) & v1_waybel25(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & v6_pre_topc(C) & v1_waybel25(C) & l1_pre_topc(C) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t13_waybel27,axiom,( ! [A] : ! [B] : ( 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(k5_numbers)) = k6_subset_1(A,B) ) ) )).
fof(t13_waybel28,axiom,( ! [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] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( r2_hidden(B,k6_yellow_6(A)) & C = k1_waybel11(A,B) & ! [D] : ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t13_waybel29,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => ! [C] : ( ( v4_waybel11(C) & m1_yellow_9(C,A) ) => u1_pre_topc(B) = u1_pre_topc(C) ) ) ) )).
fof(t13_waybel30,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_waybel11(B,A) => v3_waybel11(k4_waybel_0(A,B),A) ) ) ) )).
fof(t13_waybel31,axiom,( ! [A] : ( ( 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] : ( ( v6_waybel23(B,A) & m1_waybel23(B,A) ) => ( k5_card_1(B) = k1_waybel31(A) <=> B = u1_struct_0(k1_waybel_8(A)) ) ) ) )).
fof(t13_waybel32,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t13_waybel33,axiom,( ! [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] : ( ( ~ v1_xboole_0(B) & v1_subset_1(B,u1_struct_0(k2_yellow_1(k2_struct_0(A)))) & v2_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_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)) ) ) )).
fof(t13_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t13_waybel35,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t13_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t13_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t13_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t13_waybel_3,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_orders_2(A,B,C) => r1_waybel_3(A,B,C) ) ) ) ) )).
fof(t13_waybel_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ! [C] : ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(C,k5_waybel_4(A,D,B)) <=> r2_hidden(k4_tarski(C,D),B) ) ) ) ) )).
fof(t13_waybel_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( 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] : ~ ( r2_hidden(D,k9_xtuple_0(C)) & A = k4_yellow_2(B,k1_funct_1(C,D)) ) ) & ( ? [D] : ( 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] : ~ ( r2_hidden(D,k9_xtuple_0(C)) & A = k5_yellow_2(B,k1_funct_1(C,D)) ) ) & ( ? [D] : ( 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))) ) ) ) ) )).
fof(t13_waybel_6,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t13_waybel_7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( ~ 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))) ) ) ) ) ) )).
fof(t13_waybel_8,axiom,( ! [A] : ( l1_orders_2(A) => ! [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)) & v4_orders_2(A) ) => v4_orders_2(B) ) ) ) )).
fof(t13_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => r1_tarski(u1_struct_0(k4_waybel_9(A,B,C)),u1_struct_0(B)) ) ) ) )).
fof(t13_weddwitt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k7_group_1(A) = k2_nat_1(k5_card_1(k7_group_3(A,B)),k7_group_1(k1_weddwitt(A,B))) ) ) )).
fof(t13_weierstr,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ( v2_compts_1(A,k3_topmetr) => v1_rcomp_1(k1_weierstr(A)) ) ) )).
fof(t13_wellord1,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(t13_wellord2,axiom,( ! [A] : r1_relat_2(k1_wellord2(A),A) )).
fof(t13_wsierp_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r1_int_1(k1_int_2(B),A) <=> r1_int_1(B,A) ) ) ) )).
fof(t13_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( r1_tarski(A,B) & r1_tarski(C,D) ) => r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)) ) )).
fof(t13_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k6_xboolean(A,k6_xboolean(A,B)) = k6_xboolean(A,B) ) ) )).
fof(t13_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(4,A) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,A),A),A) ) )).
fof(t13_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t13_xtuple_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r2_hidden(k3_xtuple_0(A,B,C),D) => r2_hidden(A,k11_xtuple_0(D)) ) )).
fof(t13_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( r2_hidden(A,k1_numbers) & r1_xxreal_0(B,A) & ~ r2_hidden(B,k1_numbers) & B != k2_xxreal_0 ) ) ) )).
fof(t13_xxreal_1,axiom,( ! [A] : ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(A,k2_xxreal_1(B,C)) => ( r2_hidden(A,k1_xxreal_1(B,C)) & A != C ) ) ) ) )).
fof(t13_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => k2_xxreal_2(k1_tarski(A)) = A ) )).
fof(t13_xxreal_3,axiom,( ! [A] : ( 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 ) ) ) )).
fof(t13_yellow10,axiom,( ! [A] : ( ( v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t13_yellow11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t13_yellow12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t13_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( 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)))) ) ) ) )).
fof(t13_yellow14,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_struct_0(A) => v3_yellow_0(A) ) ) )).
fof(t13_yellow15,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => k2_yellow15(A,B) = k1_tarski(A) ) )).
fof(t13_yellow16,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t13_yellow17,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(k4_waybel18(A,B,C))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k4_waybel18(A,B,D)))) => ! [G] : ( 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(k1_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)) ) ) ) ) ) ) ) ) ) )).
fof(t13_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t13_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))))) ) => k7_subset_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))),B,k1_tarski(k1_xboole_0)) = k2_yellow19(A,k3_yellow19(A,k2_struct_0(A),B)) ) ) )).
fof(t13_yellow21,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t13_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [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_yellow_0(A) => v1_yellow_0(B) ) & ( v2_yellow_0(A) => v2_yellow_0(B) ) ) ) ) ) )).
fof(t13_yellow_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( r2_hidden(k1_xboole_0,A) => k3_yellow_0(k1_yellow_1(A)) = k1_xboole_0 ) ) )).
fof(t13_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t13_yellow_3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) )).
fof(t13_yellow_4,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(B,k2_yellow_4(A,B,B)) ) ) )).
fof(t13_yellow_5,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t13_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k4_yellow_6(B,k3_yellow_6(A,B,C)) = C ) ) ) )).
fof(t13_yellow_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( r2_yellow_0(A,B) | r1_yellow_0(k7_lattice3(A),B) ) => k2_yellow_0(A,B) = k1_yellow_0(k7_lattice3(A),B) ) ) )).
fof(t13_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(B,D) & v3_pre_topc(D,A) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(E,C) & r1_tarski(E,D) ) ) ) ) ) ) ) )).
fof(t13_yellow_9,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( 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) ) ) ) )).
fof(t13_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( v8_zf_fund1(B,A) & v1_finset_1(C) & ! [D] : ( r2_hidden(D,C) => r2_hidden(D,B) ) ) => r2_hidden(C,B) ) ) ) )).
fof(t13_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => r1_xxreal_0(3,k3_finseq_1(A)) ) )).
fof(t13_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,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)) ) ) ) ) ) )).
fof(t13_zf_model,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,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)) ) ) ) ) ) )).
fof(t13_zf_refle,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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) ) ) )).
fof(t13_zfmisc_1,axiom,( ! [A] : ! [B] : k3_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k1_tarski(A) )).
fof(t13_zfmodel2,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t13_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( v1_int_1(B) => k1_zmodul01(A,k4_rlvect_1(A,k6_finseq_1(u1_struct_0(A))),B) = k4_struct_0(A) ) ) )).
fof(t13_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),k4_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_numbers))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r2_hidden(E,k4_finseq_1(C)) & B = k1_funct_1(C,E) ) => k1_funct_1(k20_zmodul02(A,C,D),E) = k1_zmodul01(A,B,k3_funct_2(u1_struct_0(A),k4_numbers,D,B)) ) ) ) ) ) ) )).
fof(t13_zmodul03,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul02(C,A) => ~ ( r1_tarski(k18_zmodul02(A,C),u1_struct_0(B)) & ! [D] : ( m1_zmodul02(D,B) => ~ ( k18_zmodul02(B,D) = k18_zmodul02(A,C) & k21_zmodul02(B,D) = k21_zmodul02(A,C) ) ) ) ) ) ) )).
fof(t140_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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)))))) ) ) )).
fof(t140_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( k9_xtuple_0(k5_funct_6(k10_finseq_1(A,B))) = k3_xboole_0(k9_xtuple_0(A),k9_xtuple_0(B)) & ! [C] : ( r2_hidden(C,k3_xboole_0(k9_xtuple_0(A),k9_xtuple_0(B))) => k1_funct_1(k5_funct_6(k10_finseq_1(A,B)),C) = k10_finseq_1(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ) )).
fof(t140_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v4_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t140_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t140_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(B)) & ~ r1_xxreal_0(A,k7_xcmplx_0(k17_euclid(B),k12_euclid(B))) & ~ r1_xxreal_0(k5_numbers,k18_euclid(C)) & ~ r1_xxreal_0(A,k7_xcmplx_0(k17_euclid(C),k12_euclid(C))) & ~ r1_xxreal_0(k7_xcmplx_0(k17_euclid(C),k12_euclid(C)),k7_xcmplx_0(k17_euclid(B),k12_euclid(B))) & ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) & ? [E] : ( 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(k7_xcmplx_0(k17_euclid(E),k12_euclid(E)),k7_xcmplx_0(k17_euclid(D),k12_euclid(D))) ) ) ) ) ) ) )).
fof(t140_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t140_pboole,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t140_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ! [D] : ( ( 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)) ) ) ) )).
fof(t140_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => r1_xxreal_0(k22_rvsum_1(B,C),k2_xcmplx_0(k22_rvsum_1(B,B),k22_rvsum_1(C,C))) ) ) ) )).
fof(t140_seq_4,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( 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 ) ) ) )).
fof(t140_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(t140_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_borsuk_1(C,A) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & v1_borsuk_1(D,A) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) ) )).
fof(t140_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ~ ( k4_xboolean(A,B) = k1_xboolean & A != k1_xboolean & B != k1_xboolean ) ) ) )).
fof(t140_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k4_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B)) = k2_xcmplx_0(A,k4_xcmplx_0(B)) ) ) )).
fof(t140_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k7_xcmplx_0(A,B),k5_numbers) ) ) ) )).
fof(t140_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => k3_xboole_0(k1_xxreal_1(C,D),k1_xxreal_1(A,B)) = k1_xxreal_1(k4_xxreal_0(C,A),k3_xxreal_0(D,B)) ) ) ) ) )).
fof(t140_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => k3_zf_lang1(k6_zf_lang(A)) = k3_zf_lang1(A) ) )).
fof(t140_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( v8_zmodul01(B,A) & m1_zmodul01(B,A) ) => ! [C] : ( m3_zmodul01(C,A,B) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t141_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_abcmiz_1(B,A,k13_abcmiz_1(A)) => ! [C] : ( ( 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)) ) ) ) )).
fof(t141_finseq_2,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( k2_finseq_2(C,A) = k2_finseq_2(B,A) => C = B ) ) ) )).
fof(t141_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( k9_xtuple_0(k6_funct_6(k9_finseq_1(A))) = k4_card_3(k9_finseq_1(k9_xtuple_0(A))) & k10_xtuple_0(k6_funct_6(k9_finseq_1(A))) = k4_card_3(k9_finseq_1(k10_xtuple_0(A))) & ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => k1_funct_1(k6_funct_6(k9_finseq_1(A)),k9_finseq_1(B)) = k9_finseq_1(k1_funct_1(A,B)) ) ) ) )).
fof(t141_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v4_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t141_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t141_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ~ r1_xxreal_0(k5_numbers,k18_euclid(B)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(C)) & ~ r1_xxreal_0(k7_xcmplx_0(k17_euclid(C),k12_euclid(C)),k7_xcmplx_0(k17_euclid(B),k12_euclid(B))) & ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) & ? [E] : ( 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(k7_xcmplx_0(k17_euclid(E),k12_euclid(E)),k7_xcmplx_0(k17_euclid(D),k12_euclid(D))) ) ) ) ) ) ) )).
fof(t141_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( r2_hidden(C,A) => r2_hidden(k2_xcmplx_0(B,C),k17_member_1(A,B)) ) ) ) ) )).
fof(t141_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v5_funct_1(C,B) ) => ? [D] : ( 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) ) ) ) )).
fof(t141_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => ( ( r1_tarski(k9_xtuple_0(C),A) & r1_tarski(C,B) ) => r1_tarski(C,k5_relat_1(B,A)) ) ) ) )).
fof(t141_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t141_seq_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v3_xxreal_2(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => k3_seq_4(k4_subset_1(k1_numbers,A,B)) = k3_xxreal_0(k3_seq_4(A),k3_seq_4(B)) ) ) )).
fof(t141_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(t141_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_tsep_1(C,A) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & v1_tsep_1(D,A) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) ) )).
fof(t141_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => k3_xboolean(k6_xboolean(A,A)) = k1_xboolean ) )).
fof(t141_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k2_xcmplx_0(A,B) = k4_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B))) ) ) )).
fof(t141_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(k5_numbers,k7_xcmplx_0(A,B)) ) ) ) )).
fof(t141_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => k3_xboole_0(k3_xxreal_1(C,D),k3_xxreal_1(A,B)) = k3_xxreal_1(k4_xxreal_0(C,A),k3_xxreal_0(D,B)) ) ) ) ) )).
fof(t141_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => k3_zf_lang1(k7_zf_lang(A,B)) = k2_xboole_0(k3_zf_lang1(A),k3_zf_lang1(B)) ) ) )).
fof(t141_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( v8_zmodul01(B,A) & m1_zmodul01(B,A) ) => ! [C] : ( m3_zmodul01(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t142_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : k3_relat_1(k2_finseq_2(A,B),k16_funcop_1(B,C)) = k2_finseq_2(A,C) ) )).
fof(t142_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( k9_xtuple_0(k6_funct_6(k10_finseq_1(A,B))) = k4_card_3(k10_finseq_1(k9_xtuple_0(A),k9_xtuple_0(B))) & k10_xtuple_0(k6_funct_6(k10_finseq_1(A,B))) = k4_card_3(k10_finseq_1(k10_xtuple_0(A),k10_xtuple_0(B))) & ! [C] : ! [D] : ( ( r2_hidden(C,k9_xtuple_0(A)) & r2_hidden(D,k9_xtuple_0(B)) ) => k1_funct_1(k6_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)) ) ) ) ) )).
fof(t142_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t142_group_2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t142_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => k17_member_1(A,B) = a_2_9_member_1(A,B) ) ) )).
fof(t142_pboole,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) )).
fof(t142_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r1_xboole_0(B,k9_xtuple_0(A)) => k5_relat_1(A,B) = k1_xboole_0 ) ) )).
fof(t142_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k16_rvsum_1(k7_finseq_4(A,B,C,D)) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C),D) ) ) ) ) )).
fof(t142_seq_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_xxreal_2(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => k2_seq_4(k4_subset_1(k1_numbers,A,B)) = k4_xxreal_0(k2_seq_4(A),k2_seq_4(B)) ) ) )).
fof(t142_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t142_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => k7_xboolean(A,k3_xboolean(A)) = k1_xboolean ) )).
fof(t142_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k4_xcmplx_0(k6_xcmplx_0(A,B)) = k6_xcmplx_0(B,A) ) ) )).
fof(t142_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(k5_numbers,k7_xcmplx_0(B,A)) ) ) ) )).
fof(t142_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => k3_xboole_0(k4_xxreal_1(C,D),k4_xxreal_1(A,B)) = k4_xxreal_1(k4_xxreal_0(C,A),k3_xxreal_0(D,B)) ) ) ) ) )).
fof(t142_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => k3_zf_lang1(k8_zf_lang(B,A)) = k2_xboole_0(k3_zf_lang1(A),k1_tarski(B)) ) ) )).
fof(t142_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( v8_zmodul01(B,A) & m1_zmodul01(B,A) ) => ! [C] : ( m3_zmodul01(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t143_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ( ( 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) ) ) ) ) )).
fof(t143_finseq_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r2_hidden(A,k9_xtuple_0(B)) & r2_hidden(A,k9_xtuple_0(C)) ) => ! [D] : ! [E] : ( k1_funct_1(k13_funct_3(B,C),A) = k4_tarski(D,E) <=> k1_funct_1(k5_funct_6(k10_finseq_1(B,C)),A) = k10_finseq_1(D,E) ) ) ) ) )).
fof(t143_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( r1_xxreal_0(k3_finseq_1(B),3) => v5_glib_001(B,A) ) ) ) )).
fof(t143_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ( k15_group_2(A,B) = k1_tarski(u1_struct_0(A)) => B = A ) ) ) )).
fof(t143_jgraph_4,axiom,( ! [A] : ( 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))) ) )).
fof(t143_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ~ ( r2_hidden(C,k17_member_1(A,B)) & ! [D] : ( v1_xcmplx_0(D) => ~ ( C = k2_xcmplx_0(B,D) & r2_hidden(D,A) ) ) ) ) ) )).
fof(t143_pboole,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m1_subset_1(D,A) => k1_funct_1(C,D) = k7_partfun1(B,C,D) ) ) ) ) )).
fof(t143_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ! [D] : ( ( r1_tarski(C,D) & k5_relat_1(A,D) = k5_relat_1(B,D) ) => k5_relat_1(A,C) = k5_relat_1(B,C) ) ) ) )).
fof(t143_rvsum_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(t143_seq_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => r1_xxreal_0(C,B) ) ) => r1_xxreal_0(k2_seq_4(A),B) ) ) ) )).
fof(t143_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t143_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => k3_xboolean(k7_xboolean(A,A)) = k1_xboolean ) )).
fof(t143_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k6_xcmplx_0(k4_xcmplx_0(A),B) = k6_xcmplx_0(k4_xcmplx_0(B),A) ) ) )).
fof(t143_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_numbers,k7_xcmplx_0(A,B)) & ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(A,k5_numbers) ) & ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(k5_numbers,A) ) ) ) ) )).
fof(t143_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(C,A) & r1_xxreal_0(D,B) ) => k3_xboole_0(k1_xxreal_1(C,D),k1_xxreal_1(A,B)) = k1_xxreal_1(A,D) ) ) ) ) ) )).
fof(t143_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => k3_zf_lang1(k10_zf_lang(A,B)) = k2_xboole_0(k3_zf_lang1(A),k3_zf_lang1(B)) ) ) )).
fof(t143_zmodul01,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(t144_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_abcmiz_1,k34_abcmiz_1(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k38_abcmiz_1(A))) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t144_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( ( r2_hidden(A,k9_xtuple_0(C)) & r2_hidden(B,k9_xtuple_0(D)) ) => ! [E] : ! [F] : ( k1_binop_1(k15_funct_3(C,D),A,B) = k4_tarski(E,F) <=> k1_funct_1(k6_funct_6(k10_finseq_1(C,D)),k10_finseq_1(A,B)) = k10_finseq_1(E,F) ) ) ) ) )).
fof(t144_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( ( 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) ) ) ) )).
fof(t144_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ( k16_group_2(A,B) = k1_tarski(u1_struct_0(A)) => B = A ) ) ) )).
fof(t144_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ( r1_tarski(A,B) <=> r1_tarski(k17_member_1(A,C),k17_member_1(B,C)) ) ) ) ) )).
fof(t144_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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 ) ) )).
fof(t144_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( 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)))) ) ) )).
fof(t144_rvsum_1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( 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)) ) ) )).
fof(t144_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t144_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k4_xboolean(A,k9_xboolean(A,B)) = k1_xboolean ) ) )).
fof(t144_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => A = k6_xcmplx_0(k4_xcmplx_0(B),k6_xcmplx_0(k4_xcmplx_0(A),B)) ) ) )).
fof(t144_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k7_xcmplx_0(A,B),k5_numbers) & ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(A,k5_numbers) ) & ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(k5_numbers,A) ) ) ) ) )).
fof(t144_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(C,A) & r1_xxreal_0(D,B) ) => k3_xboole_0(k2_xxreal_1(C,D),k1_xxreal_1(A,B)) = k2_xxreal_1(A,D) ) ) ) ) ) )).
fof(t144_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => k3_zf_lang1(k11_zf_lang(A,B)) = k2_xboole_0(k3_zf_lang1(A),k3_zf_lang1(B)) ) ) )).
fof(t144_zmodul01,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t145_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_abcmiz_1,k34_abcmiz_1(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k38_abcmiz_1(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t145_finseq_3,axiom,( ! [A] : ! [B] : k7_funct_6(k9_finseq_1(A),B) = k9_finseq_1(k1_funct_2(A,B)) )).
fof(t145_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v5_glib_001(B,A) & m3_glib_001(B,A) ) => ( ~ v1_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ~ ( ~ r1_xxreal_0(D,C) & r1_xxreal_0(D,k3_finseq_1(B)) & k1_funct_1(B,C) = k1_funct_1(B,D) ) ) ) ) ) ) )).
fof(t145_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t145_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ( k17_member_1(A,C) = k17_member_1(B,C) => A = B ) ) ) ) )).
fof(t145_pboole,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,B) & v1_funct_1(C) ) => ? [D] : ( 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) ) ) ) )).
fof(t145_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ~ ( ~ v3_relat_1(k5_relat_1(B,A)) & v3_relat_1(B) ) ) )).
fof(t145_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => m2_finseq_1(A,k1_numbers) ) )).
fof(t145_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t145_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k9_xboolean(A,k6_xboolean(A,B)) = k1_xboolean ) ) )).
fof(t145_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t145_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(A,B) & r1_xxreal_0(k2_xcmplx_0(B,1),A) ) ) ) )).
fof(t145_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(A,C) => ( r1_xxreal_0(D,B) | k3_xboole_0(k2_xxreal_1(C,D),k1_xxreal_1(A,B)) = k1_xxreal_1(C,B) ) ) ) ) ) ) )).
fof(t145_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => k3_zf_lang1(k12_zf_lang(A,B)) = k2_xboole_0(k3_zf_lang1(A),k3_zf_lang1(B)) ) ) )).
fof(t145_zmodul01,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t146_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_abcmiz_1,k34_abcmiz_1(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k38_abcmiz_1(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t146_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : k7_funct_6(k10_finseq_1(A,B),C) = k10_finseq_1(k1_funct_2(A,C),k1_funct_2(B,C)) )).
fof(t146_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v5_glib_001(B,A) <=> v5_glib_001(k6_glib_001(A,B),A) ) ) ) )).
fof(t146_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ( v1_finset_1(k15_group_2(A,B)) => ( ? [C] : ( v1_finset_1(C) & C = k15_group_2(A,B) & k18_group_2(A,B) = k5_card_1(C) ) & ? [C] : ( v1_finset_1(C) & C = k16_group_2(A,B) & k18_group_2(A,B) = k5_card_1(C) ) ) ) ) ) )).
fof(t146_member_1,axiom,( ! [A] : ( v1_membered(A) => k17_member_1(A,k5_numbers) = A ) )).
fof(t146_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t146_relat_1,axiom,( ! [A] : ! [B] : ( 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) ) )).
fof(t146_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) & v1_finseq_1(A) ) => m2_finseq_1(A,k2_numbers) ) )).
fof(t146_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t146_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k9_xboolean(A,k8_xboolean(A,B)) = k1_xboolean ) ) )).
fof(t146_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t146_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ r1_xxreal_0(A,k6_xcmplx_0(A,1)) ) )).
fof(t146_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(D,B) => ( r1_xxreal_0(A,C) | k3_xboole_0(k3_xxreal_1(C,D),k1_xxreal_1(A,B)) = k1_xxreal_1(A,D) ) ) ) ) ) ) )).
fof(t146_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => k3_zf_lang1(k13_zf_lang(B,A)) = k2_xboole_0(k3_zf_lang1(A),k1_tarski(B)) ) ) )).
fof(t146_zmodul01,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(t147_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_abcmiz_1,k34_abcmiz_1(A)))) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t147_finseq_3,axiom,( ! [A] : ! [B] : k8_funct_6(A,k9_finseq_1(B)) = k9_finseq_1(k1_funct_2(A,B)) )).
fof(t147_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v5_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => v5_glib_001(k8_glib_001(A,B,C,D),A) ) ) ) ) )).
fof(t147_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => k7_group_1(A) = k2_nat_1(k7_group_1(B),k18_group_2(A,B)) ) ) )).
fof(t147_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k17_member_1(A,k2_xcmplx_0(B,C)) = k17_member_1(k17_member_1(A,C),B) ) ) ) )).
fof(t147_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k5_relat_1(B,A) = k5_relat_1(B,k3_xboole_0(k9_xtuple_0(B),A)) ) )).
fof(t147_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t147_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => k10_xboolean(A,A) = k1_xboolean ) )).
fof(t147_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t147_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(A,B) & r1_xxreal_0(B,k6_xcmplx_0(A,1)) ) ) ) )).
fof(t147_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(B,D) ) => k3_xboole_0(k3_xxreal_1(C,D),k1_xxreal_1(A,B)) = k3_xxreal_1(C,B) ) ) ) ) ) )).
fof(t147_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => k3_zf_lang1(k14_zf_lang(B,C,A)) = k2_xboole_0(k3_zf_lang1(A),k2_tarski(B,C)) ) ) ) )).
fof(t147_zmodul01,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t148_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_abcmiz_1,k34_abcmiz_1(A)))) ) => ! [C] : ( m3_abcmiz_1(C,A) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t148_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : k8_funct_6(A,k10_finseq_1(B,C)) = k10_finseq_1(k1_funct_2(A,B),k1_funct_2(A,C)) )).
fof(t148_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v5_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ! [D] : ( ( r1_glib_000(A,k4_glib_001(A,B),D,C) & ! [E] : ( ( ~ v1_abian(E) & m1_subset_1(E,k4_ordinal1) ) => ~ ( ~ 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) ) ) ) ) )).
fof(t148_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => r1_nat_d(k7_group_1(B),k7_group_1(A)) ) ) )).
fof(t148_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => k17_member_1(k9_member_1(A,B),C) = k9_member_1(k17_member_1(A,C),B) ) ) ) )).
fof(t148_relat_1,axiom,( ! [A] : ! [B] : r1_tarski(k9_xtuple_0(k2_zfmisc_1(A,B)),A) )).
fof(t148_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t148_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k6_xcmplx_0(k6_xcmplx_0(C,A),k6_xcmplx_0(C,B)) = k4_xcmplx_0(k6_xcmplx_0(A,B)) ) ) ) )).
fof(t148_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & r1_xxreal_0(k2_xcmplx_0(1,A),k5_numbers) ) ) )).
fof(t148_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(D,B) => ( r1_xxreal_0(A,C) | k3_xboole_0(k4_xxreal_1(C,D),k1_xxreal_1(A,B)) = k2_xxreal_1(A,D) ) ) ) ) ) ) )).
fof(t148_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => k3_zf_lang1(k15_zf_lang(B,C,A)) = k2_xboole_0(k3_zf_lang1(A),k2_tarski(B,C)) ) ) ) )).
fof(t148_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_zmodul01(B) & m1_zmodul01(B,A) ) => ! [C] : ( ( v1_zmodul01(C) & m1_zmodul01(C,A) ) => ! [D] : ( ( v1_zmodul01(D) & m1_zmodul01(D,A) ) => ( m1_zmodul01(B,C) => m1_zmodul01(k7_zmodul01(A,B,D),k7_zmodul01(A,C,D)) ) ) ) ) ) )).
fof(t149_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_abcmiz_1,k34_abcmiz_1(A)))) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t149_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) ) ) )).
fof(t149_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v5_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ! [D] : ( 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) ) ) ) ) )).
fof(t149_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,C) => ( B = D => k18_group_2(A,B) = k2_nat_1(k18_group_2(C,D),k18_group_2(A,C)) ) ) ) ) ) )).
fof(t149_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t149_relat_1,axiom,( ! [A] : ! [B] : r1_tarski(k10_xtuple_0(k2_zfmisc_1(A,B)),B) )).
fof(t149_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t149_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(k5_numbers,A) = k4_xcmplx_0(A) ) )).
fof(t149_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(1,A) & r1_xxreal_0(k6_xcmplx_0(1,A),k5_numbers) ) ) )).
fof(t149_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(A,C) => ( r1_xxreal_0(D,B) | k3_xboole_0(k4_xxreal_1(C,D),k1_xxreal_1(A,B)) = k3_xxreal_1(C,B) ) ) ) ) ) ) )).
fof(t149_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,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)) ) ) ) ) )).
fof(t149_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_zmodul01(B) & m1_zmodul01(B,A) ) => ( ! [C] : ( 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)) ) ) ) )).
fof(t14_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t14_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & v1_abcmiz_a(A) & l1_msualg_1(A) ) => ! [B] : ( 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 ) ) ) ) ) )).
fof(t14_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( k2_absvalue(A) = 1 & r1_xxreal_0(A,k5_numbers) ) ) )).
fof(t14_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t14_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v7_aff_2(A) => v11_aff_2(A) ) ) )).
fof(t14_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t14_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ? [C] : ( 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 ) ) ) )).
fof(t14_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(B,C) => k3_afinsq_2(A,B,C) = k1_xboole_0 ) ) ) ) )).
fof(t14_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( r2_hidden(B,k7_afproj(A)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & B = k5_afproj(A,C) & v1_aff_1(C,A) ) ) ) )).
fof(t14_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t14_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t14_algspec1,axiom,( ! [A] : r6_pboole(A,k1_algspec1(A,k1_xboole_0),k6_partfun1(A)) )).
fof(t14_algstr_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l5_algstr_0(A) ) => ( v7_algstr_1(A) <=> ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != k4_struct_0(A) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k6_algstr_0(A,B,D) != C ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != k4_struct_0(A) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k6_algstr_0(A,D,B) != C ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => k6_algstr_0(A,B,k4_struct_0(A)) = k4_struct_0(A) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_algstr_0(A,k4_struct_0(A),B) = k4_struct_0(A) ) ) ) ) )).
fof(t14_algstr_4,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_xboole_0(B) <=> v2_struct_0(k9_algstr_4(A,B)) ) ) ) )).
fof(t14_altcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_altcat_1(A,B,C) != k1_xboole_0 => ! [D] : ( m1_subset_1(D,k1_altcat_1(A,B,C)) => k5_altcat_1(A,B,C,C,D,k8_altcat_1(A,C)) = D ) ) ) ) ) )).
fof(t14_altcat_2,axiom,( ! [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) & l1_cat_1(A) ) => v3_altcat_1(k3_altcat_2(A),u1_struct_0(A),k2_altcat_2(A)) ) )).
fof(t14_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l2_altcat_1(B) ) => ! [C] : ( ( v11_functor0(C,A,B) & l2_functor0(C,A,B) ) => ( v18_functor0(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t14_ami_2,axiom,( ! [A] : ~ ( r2_hidden(A,k2_ami_2) & ! [B] : ( v7_ordinal1(B) => A != k4_tarski(1,B) ) ) )).
fof(t14_ami_3,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => ~ ( ? [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(B,u1_struct_0(k1_ami_3)) & k1_funct_1(k2_extpro_1(k7_card_1(2),k1_ami_3,A,B),k4_struct_0(k1_ami_3)) = k4_card_1(k5_memstr_0(k7_card_1(2),k1_ami_3,B)) ) & v2_extpro_1(A,k7_card_1(2),k1_ami_3) ) ) )).
fof(t14_ami_5,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => ~ ( k2_compos_0(u1_compos_1(k1_ami_3),A) = 8 & ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_ami_3)) ) => A != k9_ami_3(B,C) ) ) ) ) )).
fof(t14_ami_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( 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) = k4_ordinal1 ) ) )).
fof(t14_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k4_ordinal1) => k5_ami_wstd(A,B,C) = k1_ami_wstd(A,B,k1_nat_1(k3_ami_wstd(A,B,C),1)) ) ) ) )).
fof(t14_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) ) => ( v5_amistd_1(C,A,B) <=> ! [D] : ( ( 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(k4_ordinal1,C)) => ! [E] : ( v7_ordinal1(E) => r2_hidden(k5_memstr_0(A,B,k5_extpro_1(A,B,C,D,E)),k1_relset_1(k4_ordinal1,C)) ) ) ) ) ) ) ) )).
fof(t14_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(t14_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ~ ( ( r1_analoaf(A,B,D,C,E) | r1_analoaf(A,B,D,E,C) ) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( k1_rlvect_1(A,k5_algstr_0(A,D,B),F) = k1_rlvect_1(A,k5_algstr_0(A,E,C),G) & ~ ( F = k5_numbers & G = k5_numbers ) ) ) ) ) & ~ ( ? [F] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & k1_rlvect_1(A,k5_algstr_0(A,D,B),F) = k1_rlvect_1(A,k5_algstr_0(A,E,C),G) & ~ ( F = k5_numbers & G = k5_numbers ) ) ) & ~ r1_analoaf(A,B,D,C,E) & ~ r1_analoaf(A,B,D,E,C) ) ) ) ) ) ) ) )).
fof(t14_analoaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t14_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_analmetr(A,C,D) => k2_analort(A,C,D,k2_analort(A,C,D,B)) = k4_algstr_0(A,B) ) ) ) ) ) )).
fof(t14_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t14_anproj_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ~ ( A = k8_domain_1(A,B,C,D) & B != C & B != D & C != D & ! [E] : ( m2_funct_2(E,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [F] : ( m2_funct_2(F,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [G] : ( m2_funct_2(G,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ? [H] : ( m2_funct_2(H,A,k1_numbers,k9_funct_2(A,k1_numbers)) & ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ! [K] : ( v1_xreal_0(K) => H != k1_binop_1(k5_funcsdom(A),k1_binop_1(k5_funcsdom(A),k1_funct_1(k7_funcsdom(A),k4_tarski(I,E)),k1_funct_1(k7_funcsdom(A),k4_tarski(J,F))),k1_funct_1(k7_funcsdom(A),k4_tarski(K,G))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ( ( r2_hidden(B,A) & r2_hidden(C,A) & r2_hidden(D,A) & r2_hidden(E,A) & r2_hidden(F,A) & r2_hidden(G,A) & r2_hidden(H,A) & r2_hidden(I,A) & r2_hidden(J,A) ) => r1_tarski(k7_enumset1(B,C,D,E,F,G,H,I,J),A) ) )).
fof(t14_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v19_aofa_a00(B,A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( C = k10_subset_1(k1_funct_1(u7_aofa_a00(A),4),u4_struct_0(A)) => ( k1_msualg_1(A,C) = k1_xboole_0 & k2_msualg_1(A,C) = B ) ) ) ) ) )).
fof(t14_aofa_i00,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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))) ) ) )).
fof(t14_armstrng,axiom,( ! [A] : ! [B] : ( r2_hidden(B,k7_armstrng(A)) <=> ? [C] : ( m1_subset_1(C,k4_armstrng(A)) & ? [D] : ( m1_subset_1(D,k4_armstrng(A)) & B = k4_tarski(C,D) & r3_armstrng(A,D,C) ) ) ) )).
fof(t14_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( 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)) ) ) ) )).
fof(t14_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( ( r1_arytm_2(C,A) & r1_arytm_2(B,C) ) => k7_arytm_2(k1_arytm_1(A,C),B) = k1_arytm_1(A,k1_arytm_1(C,B)) ) ) ) ) )).
fof(t14_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ~ ( A != k11_arytm_3 & ! [B] : ( m1_subset_1(B,k2_arytm_2) => k8_arytm_2(A,B) != k12_arytm_3 ) ) ) )).
fof(t14_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ( k3_arytm_3(A,k1_xboole_0) = A & k2_arytm_3(A,k1_xboole_0) = k1_xboole_0 ) ) )).
fof(t14_asympt_0,axiom,( ! [A] : ( ( ~ v3_xxreal_0(A) & v1_xreal_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & v2_asympt_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(B,k6_asympt_0(C)) => r2_hidden(B,k6_asympt_0(k3_asympt_0(C,A))) ) ) ) ) )).
fof(t14_asympt_1,axiom,( ~ r2_hidden(k4_asympt_1(k5_numbers),k8_asympt_0(k4_asympt_1(1))) )).
fof(t14_autalg_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t14_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_funct_2(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) => ! [C] : ( 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) ) ) ) )).
fof(t14_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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) = k5_numbers <=> B = k16_pre_poly(A) ) ) ) )).
fof(t14_bcialg_1,axiom,( ! [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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) )).
fof(t14_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k2_bcialg_1(A,k1_bcialg_2(A,k4_struct_0(A),B,k1_nat_1(D,C))) = k1_bcialg_1(A,k2_bcialg_1(A,k1_bcialg_2(A,k4_struct_0(A),B,D)),k1_bcialg_2(A,k4_struct_0(A),B,C)) ) ) ) ) )).
fof(t14_bcialg_3,axiom,( ! [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) & 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) ) ) )).
fof(t14_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t14_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_bcialg_5(E,A,B,C,D) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => m1_bcialg_5(E,k1_nat_1(A,F),B,C,k1_nat_1(D,F)) ) ) ) ) ) ) )).
fof(t14_bcialg_6,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( v7_ordinal1(C) => k2_bcialg_1(A,k3_bcialg_6(A,k1_nat_1(C,1),B)) = k1_bcialg_1(A,k2_bcialg_1(A,k3_bcialg_6(A,C,B)),B) ) ) ) )).
fof(t14_bciideal,axiom,( ! [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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( m1_bciideal(B,A) => m2_bcialg_1(B,A) ) ) ) )).
fof(t14_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_bhsp_1(A,k4_struct_0(A),B) = k5_numbers ) ) )).
fof(t14_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) )).
fof(t14_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => k1_valued_0(u1_struct_0(A),k5_vfunct_1(k4_ordinal1,A,B),C) = k5_vfunct_1(k4_ordinal1,A,k1_valued_0(u1_struct_0(A),B,C)) ) ) ) )).
fof(t14_bhsp_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(B)) ) => ( r1_xboole_0(D,E) => ! [F] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(t14_binari_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k2_binari_2(k2_xcmplx_0(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))))) ) ) ) )).
fof(t14_binari_3,axiom,( k3_binarith(1,k10_binarith(k6_margrel1,k7_margrel1)) = k10_binarith(k6_margrel1,k8_margrel1) )).
fof(t14_binari_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ( r1_xxreal_0(k2_xcmplx_0(A,B),k6_xcmplx_0(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))) = k2_xcmplx_0(A,B) ) ) ) ) )).
fof(t14_binarith,axiom,( ! [A] : ( ( v3_card_1(A,1) & m2_finseq_1(A,k6_margrel1) ) => ( A = k14_trees_3(k7_margrel1) | A = k14_trees_3(k8_margrel1) ) ) )).
fof(t14_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_algstr_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_binom(A,B,1) = B ) ) )).
fof(t14_binop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t14_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t14_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t14_bor_cant,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ( ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(C)))) ) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( ~ ( ? [G] : ( v7_ordinal1(G) & r2_hidden(F,k1_funct_1(k1_valued_0(k9_setfam_1(C),D,E),G)) ) & ! [G] : ( v7_ordinal1(G) => ~ ( r1_xxreal_0(E,G) & r2_hidden(F,k1_funct_1(D,G)) ) ) ) & ~ ( ? [G] : ( v7_ordinal1(G) & r1_xxreal_0(E,G) & r2_hidden(F,k1_funct_1(D,G)) ) & ! [G] : ( v7_ordinal1(G) => ~ r2_hidden(F,k1_funct_1(k1_valued_0(k9_setfam_1(C),D,E),G)) ) ) ) ) ) & ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(C)))) ) => ! [E] : ( r2_hidden(E,k3_prob_1(C,k7_bor_cant(C,D))) <=> ! [F] : ( v7_ordinal1(F) => ? [G] : ( v7_ordinal1(G) & r1_xxreal_0(F,G) & r2_hidden(E,k1_funct_1(D,G)) ) ) ) ) & ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( r2_hidden(D,k2_prob_2(A,B,k7_bor_cant(A,C))) <=> ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(E,F) & r2_hidden(D,k1_prob_2(A,B,C,F)) ) ) ) ) & ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(C)))) ) => ! [E] : ( r2_hidden(E,k1_prob_1(C,k9_bor_cant(C,D))) <=> ? [F] : ( v7_ordinal1(F) & ! [G] : ( v7_ordinal1(G) => ( r1_xxreal_0(F,G) => r2_hidden(E,k1_funct_1(D,G)) ) ) ) ) ) & ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( r2_hidden(D,k1_prob_1(A,k9_bor_cant(A,C))) <=> ? [E] : ( v7_ordinal1(E) & ! [F] : ( v7_ordinal1(F) => ( r1_xxreal_0(E,F) => r2_hidden(D,k1_prob_2(A,B,C,F)) ) ) ) ) ) & ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,k1_prob_1(A,k9_bor_cant(A,k2_prob_1(A,C)))) <=> ? [E] : ( v7_ordinal1(E) & ! [F] : ( v7_ordinal1(F) => ~ ( r1_xxreal_0(E,F) & r2_hidden(D,k1_prob_2(A,B,C,F)) ) ) ) ) ) ) ) ) ) )).
fof(t14_borsuk_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(t14_borsuk_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t14_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_topmetr))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t14_borsuk_5,axiom,( ! [A] : ( 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) ) ) )).
fof(t14_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ( v3_topmetr(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v1_xreal_0(B) ) ) ) )).
fof(t14_borsuk_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ~ ( B != k5_euclid(A) & k30_valued_1(B) = k5_euclid(A) ) ) ) )).
fof(t14_brouwer,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xxreal_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( 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) ) ) ) )).
fof(t14_bspace,axiom,( ! [A] : k3_bspace(k1_xboole_0,A) = k4_struct_0(k2_bspace) )).
fof(t14_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(t14_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t14_bvfunc14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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)) ) ) )).
fof(t14_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t14_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) ) )).
fof(t14_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t14_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t14_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t14_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(t14_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t14_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t14_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t14_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t14_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t14_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_c0sp1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_c0sp1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_c0sp1(A))) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(H,A) => k3_funct_2(A,k1_numbers,G,H) = k4_real_1(k3_funct_2(A,k1_numbers,E,H),k3_funct_2(A,k1_numbers,F,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_c0sp2(A))) => ( B = k4_struct_0(k5_c0sp2(A)) => k5_numbers = k2_normsp_0(k5_c0sp2(A),B) ) ) ) )).
fof(t14_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ! [C] : ! [D] : ( m2_finseq_1(D,k3_cqc_lang(A)) => ( r2_hidden(1,k1_relset_1(k4_ordinal1,k10_finseq_1(B,C))) & r2_hidden(2,k1_relset_1(k4_ordinal1,k10_finseq_1(B,C))) & k1_funct_1(k7_finseq_1(D,k10_finseq_1(B,C)),k1_nat_1(k3_finseq_1(D),1)) = B & k1_funct_1(k7_finseq_1(D,k10_finseq_1(B,C)),k1_nat_1(k3_finseq_1(D),2)) = C ) ) ) )).
fof(t14_calcul_2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => r1_tarski(k2_calcul_2(k3_finseq_1(C),k3_finseq_1(B)),k1_relset_1(k4_ordinal1,k8_finseq_1(k3_cqc_lang(A),C,B))) ) ) ) )).
fof(t14_cantor_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t14_card_1,axiom,( ! [A] : r2_hidden(k1_xboole_0,k2_card_1(A)) )).
fof(t14_card_2,axiom,( ! [A] : ! [B] : ( r2_wellord2(k2_xboole_0(k2_zfmisc_1(A,k1_tarski(k5_numbers)),k2_zfmisc_1(B,k1_tarski(1))),k2_xboole_0(k2_zfmisc_1(B,k1_tarski(k5_numbers)),k2_zfmisc_1(A,k1_tarski(1)))) & k1_card_1(k2_xboole_0(k2_zfmisc_1(A,k1_tarski(k5_numbers)),k2_zfmisc_1(B,k1_tarski(1)))) = k1_card_1(k2_xboole_0(k2_zfmisc_1(B,k1_tarski(k5_numbers)),k2_zfmisc_1(A,k1_tarski(1)))) ) )).
fof(t14_card_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => k5_card_3(A,k1_tarski(B)) = k1_tarski(k1_funct_1(B,A)) ) )).
fof(t14_card_5,axiom,( ! [A] : ( v1_card_1(A) => r2_hidden(A,k3_card_2(2,A)) ) )).
fof(t14_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_card_fil(C,A) => ( ! [D] : ( 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)) ) ) ) ) ) )).
fof(t14_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ! [E] : ~ ( D != E & ~ r2_hidden(C,A) & k5_card_1(k1_card_fin(k2_xboole_0(A,k1_tarski(C)),k1_nat_1(B,1),D,E)) != k1_nat_1(k5_card_1(k1_card_fin(A,k1_nat_1(B,1),D,E)),k5_card_1(k1_card_fin(A,B,D,E))) ) ) ) )).
fof(t14_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ! [C] : ( ( r4_card_lar(A,B) & r1_tarski(B,C) & r1_tarski(C,A) ) => r4_card_lar(A,C) ) ) )).
fof(t14_cardfin2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k4_numbers) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ( k1_afinsq_1(B) = k1_nat_1(k1_afinsq_1(A),1) => ! [C] : ( v1_int_1(C) => ( k5_relat_1(B,k1_afinsq_1(A)) = k24_valued_1(A,C) => k7_afinsq_2(B) = k2_xcmplx_0(k3_xcmplx_0(C,k7_afinsq_2(A)),k1_funct_1(B,k1_afinsq_1(A))) ) ) ) ) ) )).
fof(t14_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( k3_graph_1(A,C) = k4_graph_1(A,B) => k1_cat_1(A,B,C) = k1_binop_1(u1_cat_1(A),C,B) ) ) ) ) )).
fof(t14_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m3_cat_2(B,A) => ( v1_cat_2(B,A) <=> v13_cat_1(k5_cat_2(A,B),B,A) ) ) ) )).
fof(t14_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u4_struct_0(C)) => ! [E] : ( m1_subset_1(E,u4_struct_0(C)) => ! [F] : ( 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,E,F),D),k5_funct_4(u4_struct_0(C),A,B,k1_cat_1(C,D,E),k1_cat_1(C,D,F))) ) ) ) ) ) )).
fof(t14_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_cat_4(A,B) = k10_cat_3(A,B,k1_cat_4(A)) ) ) )).
fof(t14_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ 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)) ) ) ) )).
fof(t14_catalan1,axiom,( ! [A] : ( v7_ordinal1(A) => k1_catalan1(k1_nat_1(A,1)) = k7_xcmplx_0(k7_newton(k3_xcmplx_0(2,A)),k2_nat_1(k7_newton(A),k7_newton(k1_nat_1(A,1)))) ) )).
fof(t14_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ~ ( A = k3_nat_1(a_1_0_catalan2(B)) & ~ r1_xxreal_0(A,k5_numbers) & v1_catalan2(B) & ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v5_ordinal1(C) & v1_finset_1(C) ) => ~ ( k5_relat_1(B,A) = k1_catalan2(k1_catalan2(k8_funcop_1(k4_ordinal1,1,k5_numbers),C),k8_funcop_1(k4_ordinal1,1,1)) & v1_catalan2(C) ) ) ) ) ) )).
fof(t14_catalg_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( k7_catalg_1(A,C,E) = k7_catalg_1(B,D,F) => ( A = B & C = D & E = F ) ) )).
fof(t14_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v9_algstr_0(B,A) & v9_algstr_0(C,A) ) => v9_algstr_0(k5_cayldick(A,B,C),k4_cayldick(A)) ) ) ) ) )).
fof(t14_cayley,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t14_cc0sp1,axiom,( ! [A] : ( l1_clopban2(A) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t14_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => k1_group_1(k3_cc0sp2(A)) = k1_cc0sp2(A,k6_complex1) ) )).
fof(t14_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [C] : ( ( 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(k4_ordinal1,k2_numbers,k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,A,k2_valued_1(k2_numbers,k2_numbers,k2_numbers,B,C)),k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,A,B),k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,A,C))) & r2_relset_1(k4_ordinal1,k2_numbers,k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,A,k46_valued_1(k2_numbers,k2_numbers,k2_numbers,B,C)),k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,A,B),k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,A,C))) & r2_relset_1(k4_ordinal1,k2_numbers,k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,A,k19_valued_1(k2_numbers,k2_numbers,k2_numbers,B,C)),k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,A,B),k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,A,C))) ) ) ) ) ) )).
fof(t14_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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))) = k1_funct_1(k3_cfuncdom(A),k4_tarski(k2_xcmplx_0(C,D),B)) ) ) ) ) )).
fof(t14_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t14_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ! [B] : ( v2_cgames_1(B) => ( r2_hidden(B,k8_cgames_1(A)) => r2_hidden(k9_cgames_1(B),k9_cgames_1(A)) ) ) ) )).
fof(t14_chain_1,axiom,( ! [A] : ( ( ~ v1_zfmisc_1(A) & v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( m2_chain_1(k4_tarski(B,C),A) <=> ( r2_hidden(B,A) & r2_hidden(C,A) & ( ( ~ r1_xxreal_0(C,B) & ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,A) & ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(C,D) ) ) ) | ( ~ r1_xxreal_0(B,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => ( r1_xxreal_0(D,B) & r1_xxreal_0(C,D) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( ( v2_funct_1(A) & r1_xxreal_0(B,k3_finseq_1(A)) ) => k4_finseq_4(A,k1_funct_1(A,B)) = B ) ) ) )).
fof(t14_circcmb2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(C,F))) => ! [H] : ( m1_subset_1(H,k4_card_3(u3_msualg_1(B,E))) => ( H = k5_relat_1(G,u1_struct_0(B)) => ! [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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k10_xtuple_0(k8_finseq_4(A,B,C,D,E)) = k3_enumset1(A,B,C,D,E) )).
fof(t14_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(B)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t14_circled1,axiom,( ! [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) ) => k2_circled1(A,k1_struct_0(A)) = k1_xboole_0 ) )).
fof(t14_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k1_msaterm(A,B))) ) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t14_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t14_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_pboole(C,k2_msafree2(A),k7_funcop_1(k2_msafree2(A),k4_ordinal1),k5_relat_1(u3_msualg_1(A,B),k2_msafree2(A))) => ( v3_funct_1(k9_funct_6(C)) => ( v1_xboole_0(k2_msafree2(A)) | ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(A,B))) => ! [E] : ( m1_msafree2(E,A,B) => ( E = k1_funct_1(k9_funct_6(C),k5_numbers) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => r1_tarski(E,k9_nat_1(k4_card_3(u3_msualg_1(A,B)),k9_circuit2(A,B,C,D),F)) ) ) ) ) ) ) ) ) ) )).
fof(t14_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) ) => ! [D] : ( v1_xreal_0(D) => ( ( v1_pdiff_7(C,A) & B = k7_funcop_1(C,D) ) => ( r2_pdiff_9(C,A,B) & k1_relset_1(k1_euclid(A),k2_pdiff_9(A,C,B)) = C & ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ( r2_hidden(E,C) => k7_partfun1(k9_funct_2(k1_euclid(A),k1_numbers),k2_pdiff_9(A,C,B),E) = k8_funcop_1(k4_ordinal1,k1_euclid(A),k5_numbers) ) ) ) ) ) ) ) ) )).
fof(t14_classes1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v3_ordinal1(D) => ( ( v4_ordinal1(D) & r2_hidden(B,k3_classes1(A,D)) ) => ( D = k1_xboole_0 | ( ~ r1_tarski(C,B) & C != k9_setfam_1(B) ) | r2_hidden(C,k3_classes1(A,D)) ) ) ) )).
fof(t14_classes2,axiom,( ! [A] : ! [B] : ( r2_hidden(A,k1_card_1(k1_classes1(B))) => r2_hidden(A,k1_classes1(B)) ) )).
fof(t14_clopban1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t14_clopban2,axiom,( ! [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) & 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)) ) ) )).
fof(t14_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clopban3(B,A) => ( v9_clvect_1(B,A) & k7_clvect_1(A,B) = k4_struct_0(A) ) ) ) ) )).
fof(t14_clopban4,axiom,( ! [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) & 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] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ~ r1_xxreal_0(B,k5_numbers) => k1_normsp_1(A,k4_lopban_4(A,C),B) = k1_normsp_1(A,C,k7_nat_d(B,1)) ) ) ) ) )).
fof(t14_closure1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t14_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) => ( ~ v1_xboole_0(C) => ! [D] : ( r2_hidden(D,A) => k1_funct_1(k4_closure2(A,B,C),D) = a_4_0_closure2(A,B,C,D) ) ) ) ) )).
fof(t14_clvect_1,axiom,( ! [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) ) => ! [B] : ( v1_xcmplx_0(B) => k1_clvect_1(A,k4_rlvect_1(A,k6_finseq_1(u1_struct_0(A))),B) = k4_struct_0(A) ) ) )).
fof(t14_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) )).
fof(t14_coh_sp,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_partfun1(C,B) & v1_relat_2(C) & v3_relat_2(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) => ( r2_hidden(A,k2_coh_sp(B,C)) <=> m1_toler_1(A,B,C) ) ) )).
fof(t14_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( v1_cohsp_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => r2_hidden(k3_tarski(B),A) ) ) )).
fof(t14_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m2_collsp(B,A) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & C != D & r2_hidden(C,B) & r2_hidden(D,B) ) ) ) ) )).
fof(t14_combgras,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ( ( r1_xxreal_0(2,A) & r1_ordinal1(k1_nat_1(A,2),k1_card_1(B)) ) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t14_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( ( k4_complex1(A) = k5_numbers & k4_complex1(B) = k5_numbers ) => ( k3_complex1(k3_xcmplx_0(A,B)) = k4_real_1(k3_complex1(A),k3_complex1(B)) & k4_complex1(k3_xcmplx_0(A,B)) = k5_numbers ) ) ) ) )).
fof(t14_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( A != k5_numbers => ( ~ r1_xxreal_0(k28_sin_cos,k1_comptrig(A)) <=> r1_xxreal_0(k28_sin_cos,k1_comptrig(k4_xcmplx_0(A))) ) ) ) )).
fof(t14_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( 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 ) ) ) ) )).
fof(t14_complsp2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k2_numbers,k4_finseq_2(A,k2_numbers)) => ! [D] : ( m2_finseq_2(D,k2_numbers,k4_finseq_2(A,k2_numbers)) => k9_matrix_5(k3_complsp2(A,C,D),B) = k2_xcmplx_0(k9_matrix_5(C,B),k9_matrix_5(D,B)) ) ) ) ) )).
fof(t14_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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))) ) ) ) )).
fof(t14_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( v6_compos_0(D,u1_compos_1(A)) & m1_subset_1(D,u1_compos_1(A)) ) => ! [E] : ( ( 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 ) ) ) ) ) )).
fof(t14_comptrig,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos))) => r1_xxreal_0(k1_funct_1(k18_sin_cos,A),k5_numbers) ) ) )).
fof(t14_compts_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t14_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B),C),k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,C),k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,C))) ) ) ) )).
fof(t14_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( v1_xcmplx_0(B) => k3_comseq_2(k25_valued_1(k4_ordinal1,k2_numbers,A,B)) = k3_xcmplx_0(B,k3_comseq_2(A)) ) ) )).
fof(t14_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( r2_funct_2(k4_ordinal1,k1_numbers,k7_comseq_3(A),k7_comseq_3(B)) & r2_funct_2(k4_ordinal1,k1_numbers,k8_comseq_3(A),k8_comseq_3(B)) ) => r2_funct_2(k4_ordinal1,k2_numbers,A,B) ) ) ) )).
fof(t14_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => v2_conlat_1(k1_waybel_1(k2_yellow_1(u1_struct_0(A)),k2_yellow_1(u4_struct_0(A)),k3_conlat_1(A),k4_conlat_1(A)),k2_yellow_1(u1_struct_0(A)),k2_yellow_1(u4_struct_0(A))) ) )).
fof(t14_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_conlat_1(B) ) => ( r1_filter_1(k11_conlat_1(B),A) <=> ? [C] : ( 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] : ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t14_conmetr1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v5_conmetr(A) <=> v7_aff_2(k3_analmetr(A)) ) ) )).
fof(t14_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t14_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r1_connsp_2(A,B) <=> ! [C] : ( ( ~ 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(t14_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t14_convex1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t14_convex2,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r1_tarski(C,k3_rlvect_2(A,B)) & ! [D] : ( m1_rlvect_2(D,A) => k3_rlvect_2(A,D) != C ) ) ) ) ) )).
fof(t14_convex4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t14_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t14_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t14_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t14_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => r2_cqc_the3(A,k1_subset_1(k3_cqc_lang(A)),k4_cqc_the1(A)) ) )).
fof(t14_csspace,axiom,( ~ 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))) )).
fof(t14_csspace2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v2_comseq_2(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [D] : ( v7_ordinal1(D) => k1_funct_1(C,D) = k3_xcmplx_0(k9_complex1(k6_xcmplx_0(k1_funct_1(B,D),A)),k9_complex1(k6_xcmplx_0(k1_funct_1(B,D),A))) ) => ( v2_comseq_2(C) & k1_seq_2(C) = k3_xcmplx_0(k9_complex1(k6_xcmplx_0(k3_comseq_2(B),A)),k9_complex1(k6_xcmplx_0(k3_comseq_2(B),A))) ) ) ) ) ) ) )).
fof(t14_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( 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) ) ) ) )).
fof(t14_decomp_1,axiom,( ! [A] : ( ( 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) ) )).
fof(t14_descip_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( v1_int_1(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t14_dickson,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( v4_relat_2(A) => ( r2_hidden(k4_tarski(B,C),k3_dickson(A)) <=> ( r2_hidden(k4_tarski(B,C),A) & B != C ) ) ) ) )).
fof(t14_diff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(k26_valued_1(k1_numbers,k1_numbers,E,C),B),k1_nat_1(A,1)),D) = k3_xcmplx_0(C,k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(E,B),k1_nat_1(A,1)),D)) ) ) ) ) ) )).
fof(t14_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( ( 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) = k3_xcmplx_0(A,k2_diff_2(H,B,C,D,E,F,G)) ) ) ) ) ) ) ) ) )).
fof(t14_diff_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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_funct_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,C)),B),k2_xcmplx_0(A,1)),D) = k2_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(E,B),k2_xcmplx_0(A,1)),D),k3_xcmplx_0(C,k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(F,B),k2_xcmplx_0(A,1)),D))) ) ) ) ) ) ) )).
fof(t14_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( 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) = k7_xcmplx_0(k3_xcmplx_0(4,k3_xcmplx_0(k17_sin_cos(k2_xcmplx_0(A,B)),k17_sin_cos(k6_xcmplx_0(A,B)))),k3_xcmplx_0(k1_square_1(k2_xcmplx_0(k19_sin_cos(k2_xcmplx_0(A,B)),k19_sin_cos(k6_xcmplx_0(A,B)))),k6_xcmplx_0(A,B))) ) ) ) )).
fof(t14_dilworth,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t14_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r1_diraf(A,B,C,D) & r1_diraf(A,C,B,D) ) => B = C ) ) ) ) ) )).
fof(t14_dirort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t14_dist_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,A) ) => ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(C,k4_finseq_1(B)) & ! [D] : ( 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(k19_finseq_1(A),D) ) ) ) ) ) ) )).
fof(t14_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) ) => ! [C] : ( ( 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_dist_2(k3_relat_1(B,C)) = k8_relat_1(B,k3_dist_2(C)) ) ) ) )).
fof(t14_domain_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) => ( A = k5_mcart_1(B,C,D,E,F) <=> ! [G] : ( m1_subset_1(G,B) => ! [H] : ( m1_subset_1(H,C) => ! [I] : ( m1_subset_1(I,D) => ! [J] : ( m1_subset_1(J,E) => ( F = k5_domain_1(B,C,D,E,G,H,I,J) => A = H ) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_dtconstr,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_dtconstr)) => k18_dtconstr(k5_dtconstr,A) = k6_domain_1(k3_finseq_2(k4_ordinal1),k3_pre_poly(k4_ordinal1,k5_numbers)) ) )).
fof(t14_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(t14_e_siec,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t14_ec_pf_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => m1_subset_1(k5_int_1(A,B),u1_struct_0(k9_int_3(B))) ) ) )).
fof(t14_ec_pf_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t14_endalg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( k9_xtuple_0(B) = k1_endalg(A) & ! [C] : ( r2_hidden(C,k1_endalg(A)) => k1_funct_1(B,C) = k16_funcop_1(k5_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)))))) ) ) ) ) )).
fof(t14_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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 ) ) ) )).
fof(t14_entropy1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( v4_partfun3(A) => ! [B] : ( v7_ordinal1(B) => ( ( r2_hidden(B,k4_finseq_1(A)) & k1_funct_1(A,B) = k18_rvsum_1(A) ) => r1_entropy1(A,B) ) ) ) ) )).
fof(t14_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k2_enumset1(A,B,C,D),k2_tarski(E,F)) )).
fof(t14_eqrel_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t14_equation,axiom,( ! [A] : ! [B] : ( ( 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,k2_funct_6(B),B),k1_funct_6(B)) ) )).
fof(t14_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ~ ( B != C & r1_xxreal_0(k12_euclid(k8_euclid(A,B,C)),k5_numbers) ) ) ) ) )).
fof(t14_euclid_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => ! [B] : ( ( 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(k9_complex1(k22_rvsum_1(A,B)),k3_xcmplx_0(k12_euclid(A),k12_euclid(B))) ) ) ) )).
fof(t14_euclid_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( 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)) ) ) )).
fof(t14_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) => ~ ( v1_euclid_4(C,A) & ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ~ ( B != D & r2_hidden(D,C) ) ) ) ) ) ) )).
fof(t14_euclid_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t14_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( r2_hidden(D,k1_rltopsp1(k15_euclid(2),A,B)) => ( D = A | D = B | ( k4_euclid_3(C,D,A) != k7_xcmplx_0(k28_sin_cos,2) & k4_euclid_3(C,D,A) != k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos) ) | k4_euclid_3(A,D,C) = k4_euclid_3(C,D,B) ) ) ) ) ) ) )).
fof(t14_euclid_7,axiom,( ! [A] : ( v1_euclid_7(A) <=> ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v3_valued_0(B) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t14_euclid_8,axiom,( k5_euclid_8(k2_euclid_8,k3_euclid_8) = k4_euclid_8 )).
fof(t14_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => ( r2_hidden(D,k4_euclid_9(A,C,B)) => ( ( A = k5_numbers & r1_xxreal_0(B,k5_numbers) ) | ! [E] : ( ~ r1_xxreal_0(B,k9_complex1(k1_funct_1(k8_rvsum_1(D,C),E))) & ~ r1_xxreal_0(B,k9_complex1(k6_xcmplx_0(k1_funct_1(D,E),k1_funct_1(C,E)))) ) ) ) ) ) ) ) )).
fof(t14_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(D)) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(D)) => ! [G] : ( m2_finseq_2(G,k1_numbers,k1_euclid(D)) => ! [H] : ( 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,k4_xcmplx_0(A)),k9_euclid(D,G,k4_xcmplx_0(B))),k9_euclid(D,H,k4_xcmplx_0(C)))) ) ) ) ) ) ) ) ) )).
fof(t14_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v7_euclmetr(A) => v3_euclmetr(A) ) ) )).
fof(t14_euler_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_int_2(A,C) & r1_int_2(B,C) ) => ( A = k5_numbers | C = k5_numbers | r1_int_2(k3_xcmplx_0(A,B),C) ) ) ) ) ) )).
fof(t14_euler_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => k2_euler_2(k1_euler_2(k2_euler_2(C,B),A),B) = k2_euler_2(k1_euler_2(C,A),B) ) ) ) )).
fof(t14_exchsort,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( v3_exchsort(C,B) & r2_hidden(A,k9_xtuple_0(C)) ) => r2_hidden(A,B) ) ) ) ) )).
fof(t14_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & ~ v2_compos_1(C,B) ) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t14_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ~ ( ~ r1_xxreal_0(A,k2_supinf_1) & ~ r1_xxreal_0(k1_supinf_1,A) & A != k5_numbers & k1_extreal1(k3_extreal1(A),k3_extreal1(k2_extreal1(k8_mesfunc1,A))) != k8_mesfunc1 ) ) )).
fof(t14_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => k5_facirc_1(A,B,C,1) = k6_circuit2(A,B,C) ) ) ) )).
fof(t14_facirc_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => k3_msafree2(k3_facirc_2(k1_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,k1_nat_1(A,1)),k1_funct_1(C,k1_nat_1(A,1)),k5_facirc_2(A,B,C)))) ) ) ) )).
fof(t14_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(C,A) & ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ~ ( r2_hidden(F,A) & ~ r1_xxreal_0(E,k9_complex1(k6_xcmplx_0(F,C))) & r1_xxreal_0(D,k9_complex1(k6_xcmplx_0(k1_funct_1(B,F),k1_funct_1(B,C)))) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_fcont_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t14_fcont_3,axiom,( ! [A] : ! [B] : ( ( 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] : ( v1_xreal_0(C) => k7_relset_1(k1_numbers,k1_numbers,B,A) != k2_limfunc1(C) ) | v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) ) ) )).
fof(t14_fdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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) = k6_xcmplx_0(k1_fdiff_1(B,A),k1_fdiff_1(C,A)) ) ) ) ) ) )).
fof(t14_fdiff_10,axiom,( ! [A] : ( ( 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,k18_sin_cos,k26_sin_cos))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k26_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k26_sin_cos),A),B) = k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k1_square_1(k1_funct_1(k16_sin_cos,B)),k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(1,k1_funct_1(k18_sin_cos,B))) ) ) ) ) ) )).
fof(t14_fdiff_11,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k16_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k16_sin_cos),A),B) = k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k18_sin_cos,k1_funct_1(k2_sin_cos9,B)),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t14_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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) ) => ( k1_funct_1(C,A) = k5_numbers | ( r1_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,B,C),A) & k1_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,B,C),A) = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(B,A),k1_funct_1(C,A)),k3_xcmplx_0(k1_fdiff_1(C,A),k1_funct_1(B,A))),k1_square_1(k1_funct_1(C,A))) ) ) ) ) ) ) )).
fof(t14_fdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r4_fdiff_3(A,B) => ( k1_funct_1(A,B) = k5_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)) = k4_xcmplx_0(k7_xcmplx_0(k1_fdiff_3(B,A),k1_square_1(k1_funct_1(A,B)))) ) ) ) ) ) )).
fof(t14_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k1_funct_1(C,D) = k2_xcmplx_0(A,D) & k1_funct_1(C,D) != k5_numbers ) ) ) ) => ( r2_fdiff_1(k6_rfunct_1(k1_numbers,k1_numbers,C),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(k2_fdiff_1(k6_rfunct_1(k1_numbers,k1_numbers,C),B),D) = k4_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k2_xcmplx_0(A,D)))) ) ) ) ) ) ) ) )).
fof(t14_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k22_sin_cos))) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(B,C) = k4_xcmplx_0(C) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k22_sin_cos),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k22_sin_cos),A),C) = k4_xcmplx_0(k23_sin_cos(k4_xcmplx_0(C))) ) ) ) ) ) ) )).
fof(t14_fdiff_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => ( k1_funct_1(D,E) = k2_xcmplx_0(k3_xcmplx_0(A,E),B) & ~ r1_xxreal_0(k1_funct_1(D,E),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(D,E)) ) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k1_sin_cos6),C) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k1_sin_cos6),C),E) = k7_xcmplx_0(A,k3_square_1(k6_xcmplx_0(1,k1_square_1(k2_xcmplx_0(k3_xcmplx_0(A,E),B))))) ) ) ) ) ) ) ) ) )).
fof(t14_fdiff_8,axiom,( ! [A] : ( ( 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,k26_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k26_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k26_sin_cos),A),B) = k7_xcmplx_0(1,k3_xcmplx_0(B,k1_square_1(k1_funct_1(k18_sin_cos,k1_funct_1(k3_taylor_1,B))))) ) ) ) ) ) )).
fof(t14_fdiff_9,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k1_fdiff_9),A),B) = k7_xcmplx_0(k1_funct_1(k16_sin_cos,k1_funct_1(k3_taylor_1,B)),k3_xcmplx_0(B,k1_square_1(k1_funct_1(k18_sin_cos,k1_funct_1(k3_taylor_1,B))))) ) ) ) ) ) )).
fof(t14_ff_siec,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t14_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( C != k5_numbers & r1_xxreal_0(k2_xcmplx_0(C,B),A) & r1_xxreal_0(A,B) ) ) ) ) )).
fof(t14_fib_num3,axiom,( k1_fib_num3(2) = 3 )).
fof(t14_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( ~ r1_xxreal_0(A,1) & r1_xxreal_0(k2_power(k2_fib_num,A),k4_xcmplx_0(k7_xcmplx_0(1,2))) ) ) )).
fof(t14_filerec1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m2_finseq_1(E,D) => ( E = k11_finseq_1(A,B,C) => k17_finseq_1(D,2,E) = k10_finseq_1(A,B) ) ) ) )).
fof(t14_filter_0,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(t14_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t14_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t14_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t14_finance1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(C,k5_numbers) => ! [D] : ( v1_xreal_0(D) => ( ~ r1_xxreal_0(D,k4_xcmplx_0(1)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [F] : ( m1_finance1(F) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k4_ordinal1,k6_finance1(A,k1_numbers,B,k12_prob_1)) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_finance1(A,k1_numbers,B,k12_prob_1)))) ) => ( ( r1_funct_2(A,k1_numbers,A,k1_tarski(k2_xcmplx_0(1,D)),k9_finance1(k5_numbers,A,k1_numbers,B,k12_prob_1,k6_finance1(A,k1_numbers,B,k12_prob_1),G),k7_funcop_1(A,k2_xcmplx_0(1,D))) & r1_xxreal_0(k4_finance1(C,E,F),k5_numbers) ) => ( r1_tarski(a_5_0_finance1(A,B,C,E,G),a_7_0_finance1(A,B,C,D,E,F,G)) & r1_tarski(a_5_1_finance1(A,B,C,E,G),a_7_1_finance1(A,B,C,D,E,F,G)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & ! [C] : ( 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 ) ) ) )).
fof(t14_finseq_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => k3_finseq_1(k7_finseq_1(B,k9_finseq_1(A))) = k1_nat_1(k3_finseq_1(B),1) ) )).
fof(t14_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => r1_xboole_0(k2_finseq_1(A),k1_tarski(k1_nat_1(A,1))) ) )).
fof(t14_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r2_finseq_4(A,B) => r1_finseq_4(A,k1_finseq_4(A,B)) ) ) )).
fof(t14_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( k3_finseq_1(B) = 1 => B = k12_finseq_1(A,k7_partfun1(A,B,1)) ) ) ) )).
fof(t14_finseq_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( v7_ordinal1(C) => k5_relat_1(k7_finseq_1(A,B),k2_finseq_1(k2_xcmplx_0(k3_finseq_1(A),C))) = k7_finseq_1(A,k5_relat_1(B,k2_finseq_1(C))) ) ) ) )).
fof(t14_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => k1_finseq_7(A,k2_finseq_4(A,B,C),2,D) = k2_finseq_4(A,B,D) ) ) ) ) )).
fof(t14_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( 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 ) ) ) ) )).
fof(t14_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( ( 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))) ) => ! [G] : ( m2_finseq_1(G,A) => r2_relset_1(k4_ordinal1,C,k2_finseqop(A,B,C,F,k8_finseq_1(A,G,k12_finseq_1(A,D)),E),k8_finseq_1(C,k2_finseqop(A,B,C,F,G,E),k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)))) ) ) ) ) ) ) ) )).
fof(t14_finset_1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( v1_finset_1(A) & r1_tarski(A,k2_zfmisc_1(B,C)) & ! [D] : ~ ( v1_finset_1(D) & r1_tarski(D,B) & r1_tarski(A,k2_zfmisc_1(D,C)) ) ) )).
fof(t14_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t14_finsub_1,axiom,( ! [A] : ( v1_finset_1(A) => k5_finsub_1(A) = k1_zfmisc_1(A) ) )).
fof(t14_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k7_fin_topo(A,C)) <=> ( ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( 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 ) ) ) ) ) )).
fof(t14_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k3_fintopo3(A,B,k5_numbers) = B ) ) )).
fof(t14_fintopo4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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,k5_numbers) => r2_fintopo4(A,B,D,C) ) ) ) ) ) )).
fof(t14_fintopo5,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => v3_orders_2(k5_fintopo5(A,B)) ) ) )).
fof(t14_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_fintopo6(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t14_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t14_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k8_afinsq_1(A))) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( ( r1_tarski(B,k7_flang_1(A,D,E)) & r1_tarski(C,k7_flang_1(A,D,F)) ) => r1_tarski(k6_flang_1(A,B,C),k7_flang_1(A,D,k2_xcmplx_0(E,F))) ) ) ) ) ) ) )).
fof(t14_flang_3,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(B,C) & B != k2_flang_1(A) & k1_flang_3(A,C,D) = k4_flang_1(A,k2_flang_1(A)) ) ) ) )).
fof(t14_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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),k9_fomodel0(A),B) = k1_funct_1(k6_fomodel0(k3_finseq_2(A),k11_monoid_0(A)),B) ) ) )).
fof(t14_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ( v1_funct_1(k28_fomodel1(A)) & v1_funct_2(k28_fomodel1(A),k4_ordinal1,k9_setfam_1(k3_finseq_2(k15_fomodel1(A)))) & m1_subset_1(k28_fomodel1(A),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k3_finseq_2(k15_fomodel1(A)))))) ) ) )).
fof(t14_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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) != k31_fomodel2(A) => k13_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),k9_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) = k31_fomodel2(A) => k13_fomodel2(A,B,D,C) = k1_funct_1(k2_fomodel2(B),k3_relat_1(k34_fomodel1(A,C),k9_fomodel2(A,B,D))) ) ) ) ) ) ) )).
fof(t14_fomodel3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( ~ v6_struct_0(D) & v11_fomodel1(D) & l1_fomodel1(D) ) => ! [E] : ( ( v4_fomodel1(E,D) & m1_subset_1(E,k1_fomodel1(D)) ) => ! [F] : ( m2_subset_1(F,k9_funct_2(k37_fomodel1(D),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_fomodel2(D,B)) => ( v10_fomodel2(A,B,D,F) => ( v7_fomodel2(E,A,D) | v10_fomodel2(A,B,D,k34_fomodel2(D,B,F,E,C)) ) ) ) ) ) ) ) )).
fof(t14_frechet,axiom,( ! [A] : ! [B] : ! [C] : k9_xtuple_0(k1_funct_4(k6_partfun1(A),k7_funcop_1(B,C))) = k2_xboole_0(A,B) )).
fof(t14_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k1_frechet2(A,B),k2_pre_topc(A,B)) ) ) )).
fof(t14_fscirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t14_fscirc_2,axiom,( ! [A] : ! [B] : ! [C] : 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))) )).
fof(t14_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ( ( v3_fsm_2(B,A) & v1_fsm_2(B,A) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t14_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t14_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( 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))) ) )).
fof(t14_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(C,B) => k8_relat_1(k2_funcop_1(A,C),B) = A ) )).
fof(t14_funcsdom,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ! [D] : ( m2_funct_2(D,C,k1_numbers,k9_funct_2(C,k1_numbers)) => k1_binop_1(k5_funcsdom(C),k1_binop_1(k7_funcsdom(C),A,D),k1_binop_1(k7_funcsdom(C),B,D)) = k1_binop_1(k7_funcsdom(C),k2_xcmplx_0(A,B),D) ) ) ) )).
fof(t14_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,k10_xtuple_0(k3_relat_1(B,C))) => r2_hidden(A,k10_xtuple_0(C)) ) ) ) )).
fof(t14_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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 ) ) ) ) )).
fof(t14_funct_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t14_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t14_funct_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( r2_hidden(k4_tarski(B,C),k9_xtuple_0(A)) => r2_hidden(C,k9_xtuple_0(k3_funct_5(A))) ) ) )).
fof(t14_funct_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) ) )).
fof(t14_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(t14_funct_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_8(B) & m1_subset_1(B,k1_zfmisc_1(k2_numbers)) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t14_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t14_functor0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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)) ) ) )).
fof(t14_functor1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_altcat_2(B,A) ) => ( v2_altcat_2(B,A) <=> v18_functor0(k10_functor0(A,B),B,A) ) ) ) )).
fof(t14_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,B,C) & m2_functor0(E,B,C) ) => ! [F] : ( ( v15_functor0(F,B,C) & m2_functor0(F,B,C) ) => ! [G] : ( ( v15_functor0(G,B,C) & m2_functor0(G,B,C) ) => ! [H] : ( m1_functor2(H,B,C,E,F) => ! [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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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)) ) ) )).
fof(t14_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D,C)),k1_fuzzy_1(A,k1_fuzzy_2(A,B,D),k1_fuzzy_2(A,B,C))) ) ) ) ) )).
fof(t14_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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] : ( ( v5_relat_1(F,k1_rcomp_1(k5_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,k3_fuzzy_4(A,B,C,k2_fuzzy_1(k2_zfmisc_1(A,B),D,E),F),k2_fuzzy_1(k2_zfmisc_1(A,C),k3_fuzzy_4(A,B,C,D,F),k3_fuzzy_4(A,B,C,E,F))) ) ) ) ) ) ) )).
fof(t14_fvaluat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k2_fvaluat1(A,B,2) = k14_ideal_1(A,B,B) ) ) )).
fof(t14_fvsum_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t14_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(k8_gate_1(A,B,C)) <=> ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ~ v1_xboole_0(C) ) ) )).
fof(t14_gcd_1,axiom,( ! [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) & v1_vectsp_2(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t14_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v2_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( m1_genealg1(E,D) => ! [F] : ( m1_genealg1(F,D) => m1_genealg1(k3_genealg1(D,E,F,A,B,C),D) ) ) ) ) ) ) )).
fof(t14_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_analoaf(A,B,D,C,E) => r1_analoaf(A,B,D,k1_geomtrap(A,B,C),k1_geomtrap(A,D,E)) ) ) ) ) ) ) )).
fof(t14_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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) ) )).
fof(t14_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ( r1_glib_000(A,C,D,B) => r1_glib_000(A,D,C,B) ) ) )).
fof(t14_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ( 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)) ) ) ) )).
fof(t14_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ( ? [B] : ( m1_subset_1(B,k6_glib_000(A)) & k1_glib_002(A,B) = k6_glib_000(A) ) => v1_glib_002(A) ) ) )).
fof(t14_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) ) => ! [B] : ! [C] : ! [D] : ( 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)) ) ) )).
fof(t14_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( v2_glib_001(B,A) & v5_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ! [D] : ( r2_glib_004(A,B,C,D) => k1_glib_004(A,C,D) = k10_glib_003(A,B) ) ) ) )).
fof(t14_goboard1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_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(k8_matrix_0(u1_struct_0(k15_euclid(2)),E,D))) & r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),A,B),k10_xtuple_0(k7_matrix_0(u1_struct_0(k15_euclid(2)),E,C))) & r2_hidden(B,k4_finseq_1(A)) & r2_hidden(D,k2_finseq_1(k1_matrix_0(E))) & r2_hidden(C,k4_finseq_1(E)) ) => ( r1_xxreal_0(k1_matrix_0(E),1) | r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),A,B),k10_xtuple_0(k7_matrix_0(u1_struct_0(k15_euclid(2)),k16_matrix_0(D,u1_struct_0(k15_euclid(2)),E),C))) ) ) ) ) ) ) ) )).
fof(t14_goboard2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( v7_ordinal1(B) => ~ ( r2_hidden(B,k4_finseq_1(A)) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(k4_tarski(C,D),k2_matrix_0(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,D) ) ) ) ) ) ) )).
fof(t14_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( v1_goboard1(C) & v4_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_0(C),B) | r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_nat_1(B,1))),k1_goboard5(C,A)) ) ) ) ) ) )).
fof(t14_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_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) ) ) ) ) )).
fof(t14_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,2),k3_finseq_1(C)) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k1_matrix_0(C)) ) => k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),B)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,2),B))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),B)) ) ) ) ) )).
fof(t14_goboard8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,2),k3_finseq_1(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k1_matrix_0(k2_goboard2(A))) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,2),k3_finseq_1(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,1),C) ) => ( ( ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),D,C) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,2),C) ) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),D,C) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),D,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,1),k1_nat_1(C,1))),k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,1),C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,2),k1_nat_1(C,1))),k7_xcmplx_0(1,2))),k3_topreal1(2,A)) ) ) ) ) ) ) ) )).
fof(t14_goboard9,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k3_finseq_1(A)) & k1_tops_1(k15_euclid(2),k5_goboard5(A,B)) = k1_xboole_0 ) ) ) )).
fof(t14_gobrd11,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( v1_xreal_0(B) => ( A = a_1_7_gobrd11(B) => v4_pre_topc(A,k15_euclid(2)) ) ) ) )).
fof(t14_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(D)) & r1_goboard1(u1_struct_0(k15_euclid(2)),D,E) & r2_hidden(k4_tarski(A,B),k2_matrix_0(E)) & r2_hidden(k4_tarski(A,k1_nat_1(B,1)),k2_matrix_0(E)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,k1_nat_1(B,1)) ) => k3_gobrd13(D,E,C) = k3_goboard5(E,k7_nat_d(A,1),B) ) ) ) ) ) ) )).
fof(t14_gobrd14,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t14_goedcpuc,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ( r7_calcul_1(A,B,C) => r1_henmodel(A,B,C) ) ) ) ) )).
fof(t14_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t14_gr_cy_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => k1_group_1(k4_gr_cy_1(A)) = k5_numbers ) )).
fof(t14_gr_cy_3,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( k7_group_1(A) = k3_xcmplx_0(B,C) & ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t14_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => m2_graph_1(k1_xboole_0,A) ) )).
fof(t14_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( 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) ) ) ) ) )).
fof(t14_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( r1_graph_2(A,C,B) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( 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,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)) ) ) ) ) ) ) ) )).
fof(t14_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( ( v7_graph_1(D,A) & m2_graph_1(D,A) ) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t14_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v7_graph_1(B,A) & v1_graph_4(B,A) & m2_graph_1(B,A) ) => ! [C] : ( 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] : ( m1_subset_1(D,k4_ordinal1) => ~ ( 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) ) ) ) ) ) ) )).
fof(t14_graphsp,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_graph_1(B) & v6_graph_1(B) & l1_graph_1(B) ) => ! [C] : ( ( v7_graph_1(C,B) & m2_graph_1(C,B) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t14_grcat_1,axiom,( ! [A] : ( ( v2_grcat_1(A) & l1_grcat_1(A) ) => ? [B] : ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) & ? [C] : ( ~ 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) ) ) ) )).
fof(t14_grfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r1_tarski(A,C) & r1_tarski(B,C) ) => ( v1_relat_1(k2_xboole_0(A,B)) & v1_funct_1(k2_xboole_0(A,B)) ) ) ) ) ) )).
fof(t14_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => m1_group_6(k1_grnilp_1(A,B,C),A,k1_grnilp_1(A,B,k7_group_2(A))) ) ) ) )).
fof(t14_groeb_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( v4_rewrite1(k3_polyred(A,B,C,D)) => v8_rewrite1(k3_polyred(A,B,C,D)) ) ) ) ) ) )).
fof(t14_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v6_algstr_0(B) & v1_vectsp_1(B) & v1_algstr_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t14_groeb_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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),k7_polynom1(A,B,k8_polynom1(A,B),C),k5_vfunct_1(k15_pre_poly(A),B,C)) ) ) )).
fof(t14_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & k6_algstr_0(A,B,D) = C ) ) ) ) )).
fof(t14_group_10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => k1_card_1(a_2_2_group_10(A,B)) = k1_card_1(B) ) ) )).
fof(t14_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t14_group_14,axiom,( ! [A] : ( ( 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] : ( ( v1_relat_1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_finseq_1(B) & v1_prvect_1(B) ) => ~ ( k3_finseq_1(A) = k3_finseq_1(B) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r2_hidden(C,k4_finseq_1(B)) & ! [D] : ( ( v7_ordinal1(D) & ~ v8_ordinal1(D) ) => ~ ( D = k1_funct_1(A,C) & k1_funct_1(B,C) = k2_group_14(D) ) ) ) ) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k2_group_14(k19_rvsum_1(A))),u1_struct_0(k20_prvect_1(B))) & v13_vectsp_1(C,k2_group_14(k19_rvsum_1(A)),k20_prvect_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_group_14(k19_rvsum_1(A))),u1_struct_0(k20_prvect_1(B))))) ) => ? [D] : ( v1_int_1(D) & r2_hidden(D,u1_struct_0(k2_group_14(k19_rvsum_1(A)))) & k1_funct_1(C,D) != k1_int_6(D,A) ) ) ) ) ) )).
fof(t14_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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))) ) ) ) ) )).
fof(t14_group_3,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t14_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t14_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t14_group_7,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t14_group_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ( ~ ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => B = k1_group_1(A) ) => ( ! [B] : ( ( 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] : ( m1_subset_1(B,k4_ordinal1) & k7_struct_0(A) = B & v1_int_2(B) ) ) ) ) ) )).
fof(t14_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v2_group_9(C,A) & m1_group_9(C,A,B) ) => ! [D] : ( ( v2_group_9(D,A) & m1_group_9(D,A,B) ) => ( u1_struct_0(C) = u1_struct_0(D) => C = D ) ) ) ) )).
fof(t14_groupp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v7_ordinal1(D) & v1_int_2(D) ) => ( v1_groupp_1(k2_group_3(A,B,C),D,A) => v1_groupp_1(B,D,A) ) ) ) ) ) )).
fof(t14_grsolv_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v15_algstr_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t14_hahnban,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( m1_rlsub_1(D,A) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( 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) ) ) ) ) ) ) )).
fof(t14_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t14_hallmar1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ! [E] : ( ( 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))) ) ) ) ) )).
fof(t14_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(E,B) => r1_xxreal_0(C,k3_metric_1(A,D,E)) ) ) => r1_xxreal_0(C,k1_funct_1(k6_weierstr(A,B),D)) ) ) ) ) ) )).
fof(t14_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ( r1_tarski(B,C) => r1_tarski(k14_glib_001(A,B),k14_glib_001(A,C)) ) ) ) ) )).
fof(t14_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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 ) ) ) )).
fof(t14_hermitan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ( ( r1_xxreal_0(k5_numbers,k3_complex1(A)) & k4_complex1(A) = k5_numbers ) => k9_complex1(A) = k3_complex1(A) ) ) )).
fof(t14_hessenbe,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t14_heyting1,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t14_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m2_subset_1(C,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B)) => ! [D] : ( m1_subset_1(D,k4_partfun1(A,B)) => ! [E] : ( 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] : ( v1_finset_1(F) => ~ ( r2_hidden(F,k2_heyting2(A,B,C)) & r1_tarski(F,D) ) ) ) ) ) ) ) )).
fof(t14_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => r2_hidden(k1_domain_1(k4_ordinal1,k4_ordinal1,k1_nat_1(k2_nat_1(2,A),1),B),k3_heyting3(A,B)) ) ) )).
fof(t14_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(A,C) => k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k18_sin_cos,C),B),A) = k1_funct_1(k18_sin_cos,k2_xcmplx_0(A,k7_xcmplx_0(k3_xcmplx_0(B,k28_sin_cos),2))) ) ) ) ) )).
fof(t14_hilbasis,axiom,( ! [A] : ( ( ~ 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] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t14_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => r2_hidden(k3_hilbert1(A,A),k6_hilbert1) ) )).
fof(t14_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( k1_funct_1(A,1) = k5_numbers => A = k2_hilbert1 ) ) )).
fof(t14_hilbert3,axiom,( v1_funct_1(k5_funct_4(k4_ordinal1,k5_numbers,1,1,k5_numbers)) & v1_funct_2(k5_funct_4(k4_ordinal1,k5_numbers,1,1,k5_numbers),2,2) & v3_funct_2(k5_funct_4(k4_ordinal1,k5_numbers,1,1,k5_numbers),2,2) & m1_subset_1(k5_funct_4(k4_ordinal1,k5_numbers,1,1,k5_numbers),k1_zfmisc_1(k2_zfmisc_1(2,2))) )).
fof(t14_hurwitz,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_polynom5(A,k3_polynom5(A,B,D),C),k3_polynom5(A,B,k6_algstr_0(A,C,D))) ) ) ) ) )).
fof(t14_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k4_idea_1(D,k4_idea_1(D,A,B),C) = k4_idea_1(D,A,k4_idea_1(D,B,C)) ) ) ) ) )).
fof(t14_ideal_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & v3_ideal_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => r2_hidden(k4_algstr_0(A,C),B) ) ) ) ) )).
fof(t14_incproj,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & r1_collsp(A,B,C,F) & r1_collsp(A,D,E,F) ) ) ) ) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(k3_incproj(A))) => ! [C] : ( m1_subset_1(C,u2_incsp_1(k3_incproj(A))) => ? [D] : ( 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) ) ) ) ) ) )).
fof(t14_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u4_incsp_1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t14_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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] : ( ( ~ 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) ) ) ) ) )).
fof(t14_instalg1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t14_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( r2_int_1(A,B,C) => r2_int_1(B,A,C) ) ) ) ) )).
fof(t14_int_2,axiom,( ! [A] : ( v1_int_1(A) => ( ( A = 1 | A = k4_xcmplx_0(1) ) => ( r1_int_1(A,1) & r1_int_1(A,k4_xcmplx_0(1)) ) ) ) )).
fof(t14_int_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,1) => k5_struct_0(k9_int_3(A)) = 1 ) ) )).
fof(t14_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( r2_int_1(A,B,C) => k3_int_2(A,C) = k3_int_2(B,C) ) ) ) ) )).
fof(t14_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => ( ( k3_int_2(A,C) = 1 & k5_int_1(k6_xcmplx_0(k1_pepin(B),A),C) = k5_numbers ) => r1_int_2(B,C) ) ) ) ) )).
fof(t14_int_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => k3_int_2(A,B) = k3_int_2(A,k1_int_2(B)) ) ) )).
fof(t14_int_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k8_newton) & v1_funct_1(A) & v1_partfun1(A,k8_newton) & v4_valued_0(A) & v2_pre_poly(A) ) => ( v1_int_7(A) => ( k8_nat_3(k8_newton,A) = 1 <=> k22_pre_poly(k8_newton,A) = k1_xboole_0 ) ) ) )).
fof(t14_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_int_2(A,C) => ( r1_xxreal_0(C,1) | k3_pepin(k1_newton(A,B),C) = k3_nat_d(k3_pepin(A,C),k6_nat_d(k3_pepin(A,C),B)) ) ) ) ) ) )).
fof(t14_integr10,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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(k5_numbers) & k1_relset_1(k1_numbers,B) = k2_limfunc1(k5_numbers) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,k3_limfunc1(k5_numbers)) => r3_integr10(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,A,k6_integr10(C)),k5_numbers) ) ) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,k3_limfunc1(k5_numbers)) => r3_integr10(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,B,k6_integr10(C)),k5_numbers) ) ) ) => ( ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,k3_limfunc1(k5_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)),k5_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))) ) ) ) ) )).
fof(t14_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k28_sin_cos) => k2_integra5(A,k41_valued_1(k1_numbers,k1_numbers,k16_sin_cos)) = k7_xcmplx_0(k28_sin_cos,2) ) ) )).
fof(t14_integr12,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k22_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k16_sin_cos))) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k18_sin_cos)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k18_sin_cos)),k3_seq_4(A))) ) ) ) ) )).
fof(t14_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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,k18_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)),k27_sin_cos))) & D = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,D)),k27_sin_cos),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,D)),k27_sin_cos),k3_seq_4(A))) ) ) ) ) ) )).
fof(t14_integr14,axiom,( ! [A] : ( ( 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,k18_sin_cos,k27_sin_cos))) => ( r2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k27_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k27_sin_cos)),A),B) = k2_xcmplx_0(k1_funct_1(k18_sin_cos,B),k7_xcmplx_0(k1_funct_1(k18_sin_cos,B),k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t14_integr15,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t14_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t14_integr19,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t14_integra1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => v3_funct_1(k2_partfun1(A,k1_numbers,k7_rfunct_1(A,A),A)) ) )).
fof(t14_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( ( v4_xxreal_2(B) & r1_xxreal_0(A,k5_numbers) ) => k3_seq_4(k1_integra2(B,A)) = k3_xcmplx_0(A,k2_seq_4(B)) ) ) ) )).
fof(t14_integra3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( m1_integra1(C,B) => ! [D] : ( m1_integra1(D,B) => ! [E] : ( ( 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) = k5_numbers | r1_xxreal_0(A,k3_seq_4(B)) | r1_xxreal_0(k6_xcmplx_0(k18_rvsum_1(k4_integra1(B,E,C)),k18_rvsum_1(k4_integra1(B,E,D))),k3_xcmplx_0(k6_xcmplx_0(k2_seq_4(k1_rvsum_1(E)),k3_seq_4(k1_rvsum_1(E))),k1_integra3(B,C))) ) ) ) ) ) ) ) )).
fof(t14_integra4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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)) ) ) ) )).
fof(t14_integra5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(t14_integra6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t14_integra7,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_integra7(A,D,B) & r1_integra7(A,E,C) ) => r1_integra7(A,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,D,E),k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,B,E),k20_valued_1(k1_numbers,k1_numbers,k1_numbers,D,C))) ) ) ) ) ) )).
fof(t14_integra8,axiom,( k19_sin_cos(k7_xcmplx_0(k3_xcmplx_0(3,k28_sin_cos),4)) = k4_xcmplx_0(k7_xcmplx_0(k3_square_1(2),2)) )).
fof(t14_integra9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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)),k18_sin_cos)) = k6_xcmplx_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k18_sin_cos),k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k16_sin_cos)),k2_seq_4(A)),k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k18_sin_cos),k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k16_sin_cos)),k3_seq_4(A))) ) ) ) )).
fof(t14_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => ! [C] : ( r2_hidden(C,B) <=> ( r1_tarski(k5_interva1(A,B),C) & r1_tarski(C,k6_interva1(A,B)) ) ) ) ) )).
fof(t14_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => k7_intpro_1(k7_intpro_1(A)) = k7_intpro_1(A) ) )).
fof(t14_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,k5_numbers) => ( r1_xxreal_0(k5_numbers,k1_funct_1(k2_irrat_1(A),B)) & r1_xxreal_0(k1_funct_1(k2_irrat_1(A),B),k7_xcmplx_0(1,k7_newton(A))) & r1_xxreal_0(k1_funct_1(k2_irrat_1(A),B),k1_funct_1(k5_irrat_1,A)) & r1_xxreal_0(k5_numbers,k1_funct_1(k3_irrat_1(B),A)) & r1_xxreal_0(k1_funct_1(k3_irrat_1(B),A),k7_xcmplx_0(1,k7_newton(A))) & r1_xxreal_0(k1_funct_1(k3_irrat_1(B),A),k1_funct_1(k5_irrat_1,A)) ) ) ) ) )).
fof(t14_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ! [C] : r1_isocat_1(k6_cat_2(k3_cat_1(B,C),A),A) ) )).
fof(t14_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,k6_cat_2(A,B),C) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => r2_nattra_1(B,C,k10_cat_2(A,B,C,D,k3_graph_1(A,E)),k10_cat_2(A,B,C,D,k4_graph_1(A,E))) ) ) ) ) ) )).
fof(t14_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t14_jct_misc,axiom,( ! [A] : ( 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)) ) ) )).
fof(t14_jgraph_1,axiom,( ! [A] : ( 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) ) ) )).
fof(t14_jgraph_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( 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] : ( 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) = k7_xcmplx_0(k17_euclid(C),k3_square_1(k2_xcmplx_0(1,k1_square_1(k7_xcmplx_0(k17_euclid(C),k18_euclid(C)))))) ) ) & ! [C] : ( 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) = k5_numbers ) ) ) => v5_pre_topc(B,k1_pre_topc(k15_euclid(2),A),k3_topmetr) ) ) ) )).
fof(t14_jgraph_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(A))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( D = k9_metric_1(k14_euclid(A),B,C) => ( v9_rltopsp1(D,k15_euclid(A)) & v4_pre_topc(D,k15_euclid(A)) ) ) ) ) ) ) )).
fof(t14_jgraph_5,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k5_topmetr)) => ! [I] : ( m1_subset_1(I,u1_struct_0(k5_topmetr)) => ~ ( H = k5_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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_jgraph_6,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k5_topmetr)) => ! [I] : ( m1_subset_1(I,u1_struct_0(k5_topmetr)) => ~ ( H = k5_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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_jordan,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( 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) ) ) ) )).
fof(t14_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ( v3_pre_topc(a_1_0_jordan1(A),k15_euclid(2)) & m1_subset_1(a_1_0_jordan1(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ) )).
fof(t14_jordan10,axiom,( ! [A] : ( ( 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) ) )).
fof(t14_jordan11,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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))) ) ) ) )).
fof(t14_jordan12,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( 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] : ( 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) ) ) ) ) ) )).
fof(t14_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( r1_jordan1h(A,B) => r1_tarski(k2_jordan2c(2,A),k2_jordan2c(2,k3_topreal1(2,k1_jordan13(A,B)))) ) ) ) )).
fof(t14_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( 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_0(k1_jordan8(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_topreal1(2,k2_jordan1e(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C),k3_topreal1(2,k1_jordan1e(B,A))) & ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ~ ( 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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),F,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),G,C)),k3_topreal1(2,k2_jordan1e(B,A))) = k1_tarski(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),F,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),G,C)),k3_topreal1(2,k1_jordan1e(B,A))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),G,C)) ) ) ) ) ) ) ) ) ) )).
fof(t14_jordan16,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t14_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ~ ( B != C & r1_jordan17(A,B,C,D,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ~ ( F != B & F != C & r1_jordan17(A,B,F,C,E) ) ) ) ) ) ) ) ) )).
fof(t14_jordan18,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( 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)) ) ) ) )).
fof(t14_jordan19,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & ~ r1_xxreal_0(A,k5_numbers) & k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k9_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) = k1_tarski(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k8_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D)) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k8_jordan6(B)) ) ) ) ) ) ) )).
fof(t14_jordan1a,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( 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)) ) ) ) )).
fof(t14_jordan1b,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t14_jordan1c,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v1_int_1(D) => ~ ( D = k1_int_1(k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k17_euclid(C),k6_pscomp_1(A)),k6_xcmplx_0(k8_pscomp_1(A),k6_pscomp_1(A))),k1_newton(2,B)),2)) & r1_xxreal_0(k2_xcmplx_0(k6_pscomp_1(A),k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k8_pscomp_1(A),k6_pscomp_1(A)),k1_newton(2,B)),k6_xcmplx_0(D,1))),k17_euclid(C)) ) ) ) ) ) )).
fof(t14_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & ~ r1_xxreal_0(k3_finseq_1(k2_jordan9(B,A)),C) & r2_hidden(k25_pscomp_1(B),k4_goboard5(k2_jordan9(B,A),C)) ) ) ) )).
fof(t14_jordan1e,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => k18_pscomp_1(A) != k23_pscomp_1(A) ) )).
fof(t14_jordan1g,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t14_jordan1h,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v4_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)))) ) )).
fof(t14_jordan1j,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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)))) ) => ( r2_hidden(k18_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))),k10_xtuple_0(k2_jordan1e(B,A))) & r2_hidden(k18_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))),k3_topreal1(2,k2_jordan1e(B,A))) ) ) ) )).
fof(t14_jordan1k,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t14_jordan20,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(2),A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_topmetr))) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( ( r1_xxreal_0(k5_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 ) ) ) ) ) ) )).
fof(t14_jordan21,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => r2_hidden(k10_jordan6(A),A) ) )).
fof(t14_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,k5_numbers) => k3_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,k2_jordan9(A,B)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),k3_finseq_1(k1_jordan8(A,B))))))) = k3_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,k2_jordan9(A,B)),k6_jordan6(k7_xcmplx_0(k2_xcmplx_0(k8_pscomp_1(k3_topreal1(2,k2_jordan9(A,B))),k6_pscomp_1(k3_topreal1(2,k2_jordan9(A,B)))),2))))) ) ) ) )).
fof(t14_jordan23,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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)) ) ) ) ) )).
fof(t14_jordan24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( ( 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))) ) ) ) ) ) ) ) )).
fof(t14_jordan2b,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( B = a_4_0_jordan2b(A,C,D,E) & r2_hidden(E,k2_finseq_1(A)) ) => v3_pre_topc(B,k15_euclid(A)) ) ) ) ) ) ) )).
fof(t14_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t14_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( v2_topreal1(A) & v3_topreal1(A) & r1_xxreal_0(k1_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) ) ) ) ) ) )).
fof(t14_jordan4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( 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,k1_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),k2_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(E,D),1),A),1)) & k2_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(E,D),1),A),1) = k1_nat_1(k7_nat_d(k1_nat_1(k7_nat_d(E,D),1),A),1) ) ) ) ) ) ) ) )).
fof(t14_jordan5a,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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))) ) ) ) ) ) ) ) ) )).
fof(t14_jordan5b,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t14_jordan5c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t14_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( 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))))) ) ) ) )).
fof(t14_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t14_jordan7,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t14_jordan8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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_0(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) ) ) ) ) )).
fof(t14_jordan9,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( ( r1_goboard1(u1_struct_0(k15_euclid(2)),B,A) & v1_topreal1(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(C,k3_finseq_1(A)) & r1_xxreal_0(D,k1_matrix_0(A)) ) => r1_xboole_0(k1_tops_1(k15_euclid(2),k3_goboard5(A,C,D)),k3_topreal1(2,B)) ) ) ) ) ) ) )).
fof(t14_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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)) ) ) )).
fof(t14_kolmog01,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( m2_prob_1(D,A,C) => ! [E] : ( m1_kolmog01(E,B,A,C) => ! [F] : ( ( ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(B)) ) => ! [G] : ( ( ~ v1_xboole_0(G) & m1_subset_1(G,k1_zfmisc_1(B)) ) => ( ( r2_kolmog01(A,C,D,B,E) & r1_subset_1(F,G) ) => ! [H] : ( m1_prob_1(H,A,C) => ! [I] : ( m1_prob_1(I,A,C) => ( ( r2_hidden(H,k4_kolmog01(B,A,C,E,F)) & r2_hidden(I,k4_kolmog01(B,A,C,E,G)) ) => k3_funct_2(C,k1_numbers,D,k5_prob_1(A,C,H,I)) = k3_xcmplx_0(k3_funct_2(C,k1_numbers,D,H),k3_funct_2(C,k1_numbers,D,I)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( ! [D] : ( v7_ordinal1(D) => k1_funct_1(B,D) = C ) => k4_kurato_0(A,B) = C ) ) ) )).
fof(t14_kurato_1,axiom,( 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) )).
fof(t14_kurato_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(A)))))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => ( C = D => ( r2_hidden(C,k1_kurato_2(k15_euclid(A),B)) <=> ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v7_ordinal1(F) => ? [G] : ( v7_ordinal1(G) & ~ r1_xxreal_0(G,F) & r1_xboole_0(k1_funct_1(B,G),k8_metric_1(k14_euclid(A),D,E)) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_lang1,axiom,( ! [A] : ! [B] : ( A != B => k1_lang1(k8_lang1(A,B)) = k1_tarski(B) ) )).
fof(t14_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(D,k2_finseq_1(A)) & r2_hidden(E,k2_finseq_1(A)) ) => k4_matrix_0(u1_struct_0(B),k2_laplace(D,E,A,B,C)) = k2_laplace(E,D,A,B,k4_matrix_0(u1_struct_0(B),C)) ) ) ) ) ) ) )).
fof(t14_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => r2_hidden(k1_group_1(A),k1_funct_1(k1_latsubgr(A),B)) ) ) )).
fof(t14_latsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B))) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t14_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_lattices(A,B,C) = C ) => B = k5_lattices(A) ) ) ) )).
fof(t14_lattice3,axiom,( ! [A] : ( ( v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t14_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(t14_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(t14_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & v1_lattice6(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v3_lattice6(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r1_lattice6(A,C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_lattice6(A,D,B) => D = C ) ) ) ) ) ) )).
fof(t14_lattice7,axiom,( ! [A] : ( ( 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,k1_yellow_1(k4_lattice7(k5_yellow_0(A,k3_lattice7(A))))) ) )).
fof(t14_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r3_lattices(A,k5_lattices(A),B) ) ) )).
fof(t14_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( ( v4_lexbfs(B,A) & m1_lexbfs(B,A) ) => ! [C] : ( v7_ordinal1(C) => k2_relset_1(k4_ordinal1,k5_lexbfs(A,B,C)) = k2_finsub_1(k1_zfmisc_1(k4_ordinal1),k2_finseq_1(k39_glib_000(B)),k2_finseq_1(k7_nat_d(k39_glib_000(B),C))) ) ) ) )).
fof(t14_lfuzzy_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => u1_struct_0(k4_lfuzzy_0(A)) = k9_funct_2(A,k1_rcomp_1(k5_numbers,1)) ) )).
fof(t14_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t14_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( ( v2_limfunc1(A) => ( r1_xxreal_0(B,k5_numbers) | v2_limfunc1(k26_valued_1(k4_ordinal1,k1_numbers,A,B)) ) ) & ( v2_limfunc1(A) => ( r1_xxreal_0(k5_numbers,B) | v1_limfunc1(k26_valued_1(k4_ordinal1,k1_numbers,A,B)) ) ) & ( B = k5_numbers => ( k10_xtuple_0(k26_valued_1(k4_ordinal1,k1_numbers,A,B)) = k1_tarski(k5_numbers) & v3_funct_1(k26_valued_1(k4_ordinal1,k1_numbers,A,B)) ) ) ) ) ) )).
fof(t14_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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) ) ) ) ) ) )).
fof(t14_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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) ) ) ) ) ) )).
fof(t14_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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) ) ) ) ) )).
fof(t14_lmod_5,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t14_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( r1_lmod_6(A,B,C) => ( ( r1_struct_0(B,D) => r1_struct_0(C,D) ) & ( m1_subset_1(D,u1_struct_0(B)) => m1_subset_1(D,u1_struct_0(C)) ) ) ) ) ) ) )).
fof(t14_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t14_lopban_1,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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)) ) ) )).
fof(t14_lopban_2,axiom,( ! [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) & 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)) ) ) )).
fof(t14_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_lopban_3(B,A) => ( v3_normsp_1(B,A) & k6_normsp_1(A,B) = k4_struct_0(A) ) ) ) ) )).
fof(t14_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => ( k9_nat_1(u1_struct_0(A),k1_lopban_4(A,B),k1_nat_1(C,1)) = k6_algstr_0(A,k1_rlvect_1(A,B,k7_xcmplx_0(1,k1_nat_1(C,1))),k9_nat_1(u1_struct_0(A),k1_lopban_4(A,B),C)) & k9_nat_1(u1_struct_0(A),k1_lopban_4(A,B),k5_numbers) = k5_struct_0(A) & r1_xxreal_0(k2_normsp_0(A,k9_nat_1(u1_struct_0(A),k1_lopban_4(A,B),C)),k9_nat_1(k1_numbers,k4_sin_cos(k2_normsp_0(A,B)),C)) ) ) ) ) )).
fof(t14_lopban_6,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r1_xxreal_0(C,D) => r1_tarski(k1_lopban_5(A,B,C),k1_lopban_5(A,B,D)) ) ) ) ) ) )).
fof(t14_lopban_7,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) => ( ( v1_lopban_7(C,A,B) & v2_funct_1(C) & D = k2_funct_1(C) ) => v1_lopban_7(D,B,A) ) ) ) ) ) )).
fof(t14_lopclset,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t14_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_normsp_1(B) ) => ( B = g1_normsp_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)),k3_lp_space(A)) => ( v4_normsp_0(B) & v3_normsp_0(B) & v2_normsp_1(B) ) ) ) ) ) )).
fof(t14_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_rfunct_3(B,A,k2_numbers,k3_rfunct_3(A,k2_numbers)) => ! [C] : ( m2_rfunct_3(C,A,k2_numbers,k3_rfunct_3(A,k2_numbers)) => ! [D] : ( m2_rfunct_3(D,A,k2_numbers,k3_rfunct_3(A,k2_numbers)) => r2_relset_1(A,k2_numbers,k2_lpspace1(A,k2_numbers,k7_lpspacc1(A),B,k2_lpspace1(A,k2_numbers,k9_lpspacc1(A),C,D)),k2_lpspace1(A,k2_numbers,k9_lpspacc1(A),k2_lpspace1(A,k2_numbers,k7_lpspacc1(A),B,C),k2_lpspace1(A,k2_numbers,k7_lpspacc1(A),B,D))) ) ) ) ) )).
fof(t14_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) )).
fof(t14_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t14_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(C),k1_domain_1(k4_ordinal1,k1_hilbert1,B,k1_ltlaxio1(k2_ltlaxio1(A)))) = k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(C),k1_domain_1(k4_ordinal1,k1_hilbert1,B,k2_ltlaxio1(k1_ltlaxio1(A)))) ) ) ) )).
fof(t14_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => k4_ltlaxio2(k12_finseq_1(k1_hilbert1,A)) = k12_finseq_1(k1_hilbert1,k1_ltlaxio1(A)) ) )).
fof(t14_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => r1_tarski(k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,B),k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,k5_ltlaxio1(A,B))) ) ) )).
fof(t14_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)))) ) => ( r2_hidden(A,B) => r1_relset_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1),k5_ltlaxio4(A),k6_ltlaxio4(B)) ) ) ) )).
fof(t14_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t14_margrel1,axiom,( ! [A] : ( v1_xboolean(A) => ( k4_xboolean(A,A) = k7_margrel1 => A = k7_margrel1 ) ) )).
fof(t14_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t14_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,B,B) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( v1_matrix10(C) => ( r1_xxreal_0(A,k5_numbers) | v1_matrix10(k6_matrix10(B,A,C)) ) ) ) ) ) )).
fof(t14_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_matrix_2(C,k3_matrix_2(k1_nat_1(A,2))) => ( v4_matrix_2(C,k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))) => k2_matrix11(A,B,C) = k4_algstr_0(B,k1_group_1(B)) ) ) ) ) )).
fof(t14_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( m1_subset_1(D,u1_struct_0(C)) => ( r2_hidden(A,k4_finseq_1(k3_matrix_1(C,B))) => ( D = k4_struct_0(C) | ( v1_matrix_6(k2_matrix12(B,B,C,k3_matrix_1(C,B),A,D),B,C) & k1_matrix_6(B,C,k2_matrix12(B,B,C,k3_matrix_1(C,B),A,D)) = k2_matrix12(B,B,C,k3_matrix_1(C,B),A,k11_algstr_0(C,D)) ) ) ) ) ) ) ) )).
fof(t14_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ( k3_matrix_1(A,k5_numbers) = k2_matrix_1(A,k5_numbers) & k3_matrix_1(A,k5_numbers) = k1_xboole_0 ) ) )).
fof(t14_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t14_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(B),A,A) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(B))) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(B),A,A) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(B))) ) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(B),A,A) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix16(F,u1_struct_0(B)) & v1_matrix16(G,u1_struct_0(B)) & v1_matrix16(H,u1_struct_0(B)) ) => v1_matrix16(k1_matrix_4(B,k3_matrix_3(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)) ) ) ) ) ) ) ) ) ) )).
fof(t14_matrix17,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ( v5_matrix17(D,u1_struct_0(A)) => 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(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))) ) ) ) ) ) )).
fof(t14_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_matrix_0(k9_finseq_1(k1_xboole_0)) & v2_matrix_0(k9_finseq_1(k1_xboole_0),A,1,k5_numbers) & m2_finseq_1(k9_finseq_1(k1_xboole_0),k3_finseq_2(A)) ) ) )).
fof(t14_matrix_3,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( v7_ordinal1(D) => ( ( k1_funct_1(B,D) = k5_struct_0(A) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(B)) => ( E = D | k1_funct_1(B,E) = k4_struct_0(A) ) ) ) ) => ! [E] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t14_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(D) & k1_matrix_4(A,B,D) = k1_matrix_4(A,C,D) ) => B = C ) ) ) ) ) )).
fof(t14_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => k3_matrix_5(k3_matrix_5(A,A),A) = k7_matrix_5(3,A) ) )).
fof(t14_matrix_6,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(A),B,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(A),B,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(A),B,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(A))) ) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(A),B,B) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(A))) ) => ( ( r2_matrix_6(B,A,E,C) & r2_matrix_6(B,A,F,D) ) => r2_matrix_6(B,A,k4_matrix_3(A,E,F),k4_matrix_3(A,D,C)) ) ) ) ) ) ) ) )).
fof(t14_matrix_7,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( m1_matrix_2(C,k3_matrix_2(B)) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k2_finseq_1(B)) => r2_hidden(k1_funct_1(C,D),k2_finseq_1(B)) ) ) ) ) ) )).
fof(t14_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_8(C,A,B) & v4_matrix_6(C,A,B) ) => v2_matrix_6(C,A,B) ) ) ) ) )).
fof(t14_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k2_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k1_matrix_0(A) = k1_matrix_0(B) ) => k1_matrixc1(k5_matrix_5(A,B)) = k5_matrix_5(k1_matrixc1(A),k1_matrixc1(B)) ) ) ) )).
fof(t14_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrixj1(B,A) & m2_finseq_1(B,k3_finseq_2(k3_finseq_2(A))) ) => ! [C] : ( ( 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(k4_ordinal1,k10_matrixj1(A,B),k10_matrixj1(A,C)) ) ) ) )).
fof(t14_matrixj2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( ~ 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] : ( ( 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)))))) ) ) ) ) ) )).
fof(t14_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => A = k8_rvsum_1(k4_rvsum_1(A,B),B) ) ) ) )).
fof(t14_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(k3_finseq_1(C),k5_numbers) & k4_matrix_3(B,k1_matrix_3(B,A,k3_finseq_1(C)),C) != k1_matrix_3(B,A,k1_matrix_0(C)) ) ) ) ) )).
fof(t14_matrlin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( ~ 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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),k1_nat_1(A,1),k5_numbers) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => k4_rlvect_1(C,k6_matrlin(C,D)) = k4_struct_0(C) ) ) ) ) )).
fof(t14_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( m1_vectsp_4(E,A,B) => ! [F] : ( m2_finseq_1(F,u1_struct_0(E)) => ( D = F => k5_matrlin(A,B,C,D) = k5_matrlin(A,E,C,F) ) ) ) ) ) ) ) )).
fof(t14_matroid0,axiom,( ! [A] : ( ( ~ v3_pencil_1(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r1_tarski(C,B) & v3_pre_topc(C,A) & ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t14_matrprob,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(C)) ) => ( r2_hidden(k4_tarski(A,B),k2_matrix_0(D)) => k3_matrix_0(C,D,A,B) = k1_funct_1(k1_matrprob(C,D,A),B) ) ) ) ) ) )).
fof(t14_matrtop1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,D,B,C) & m2_finseq_1(E,k3_finseq_2(D)) ) => ( v1_matrix_0(k1_finseq_3(E,A)) & v2_matrix_0(k1_finseq_3(E,A),D,k7_nat_d(B,k5_card_1(k8_relat_1(E,A))),C) & m2_finseq_1(k1_finseq_3(E,A),k3_finseq_2(D)) ) ) ) ) ) )).
fof(t14_matrtop2,axiom,( ! [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] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t14_matrtop3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(E))) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(C,E) & r2_hidden(D,k2_finseq_1(E)) ) => ( r1_xxreal_0(C,B) | D = B | D = C | k13_fvsum_1(k2_vectsp_1,k1_matrtop1(F),k8_matrix_0(u1_struct_0(k2_vectsp_1),k2_matrtop3(E,A,B,C),D)) = k1_funct_1(F,D) ) ) ) ) ) ) ) ) )).
fof(t14_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t14_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( ( r2_pboole(A,C,B) | r2_pboole(A,D,B) ) => r2_pboole(A,k3_pboole(A,C,D),B) ) ) ) ) )).
fof(t14_mcart_1,axiom,( ! [A] : ( ? [B] : ? [C] : A = k4_tarski(B,C) => ( A != k1_xtuple_0(A) & A != k2_xtuple_0(A) ) ) )).
fof(t14_measure1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t14_measure2,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m1_measure2(D,A,B) => ( ! [E] : ( r2_hidden(E,D) => m2_measure1(E,A,B,C) ) => m2_measure1(k2_measure2(A,B,D),A,B,C) ) ) ) ) )).
fof(t14_measure3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ( ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & v1_prob_2(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => r1_xxreal_0(k12_supinf_2(C,k2_measure2(A,B,k1_measure3(A,B,D))),k19_supinf_2(k1_partfun1(k4_ordinal1,B,B,k6_numbers,D,C))) ) => ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) ) ) ) )).
fof(t14_measure4,axiom,( ! [A] : ! [B] : ( m1_measure4(B,A) => ( v1_funct_1(k3_measure4(A,B)) & v1_funct_2(k3_measure4(A,B),k1_measure4(A,B),k6_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),k6_numbers))) ) ) )).
fof(t14_measure5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( ( ~ v1_xboole_0(A) & v2_measure5(A) ) <=> ? [B] : ( v1_xreal_0(B) & ? [C] : ( v1_xreal_0(C) & r1_xxreal_0(B,C) & A = k1_rcomp_1(B,C) ) ) ) ) )).
fof(t14_measure6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xxreal_0(B) => ( ? [C] : ( v1_xxreal_0(C) & r1_xxreal_0(C,B) & A = k1_xxreal_1(C,B) ) => B = k8_supinf_2(A) ) ) ) )).
fof(t14_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_zfmisc_1(k4_ordinal1,k4_ordinal1)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_zfmisc_1(k4_ordinal1,k4_ordinal1)))) ) => ( ( v2_funct_1(A) & k11_funcop_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,A) = k2_zfmisc_1(k4_ordinal1,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ? [C] : ( m1_subset_1(C,k4_ordinal1) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(k1_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k1_numbers)))) ) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t14_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ( k5_member_1(A) = k5_member_1(B) => A = B ) ) ) )).
fof(t14_membered,axiom,( ! [A] : ( v2_membered(A) => ( ! [B] : ( v1_xxreal_0(B) => r2_hidden(B,A) ) => A = k6_numbers ) ) )).
fof(t14_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => k9_subset_1(u1_struct_0(B),k9_xtuple_0(C),k8_struct_0(B)) = k9_xtuple_0(k6_memstr_0(A,B,C)) ) ) ) )).
fof(t14_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_euclid_6(A,B,C) & D = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),B,k6_xcmplx_0(1,E)),k1_rlvect_1(k15_euclid(2),C,E)) & A = D ) ) ) ) ) ) )).
fof(t14_mesfun10,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ! [C] : ( 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)) ) ) ) ) )).
fof(t14_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( ( r1_mesfun6c(A,B,C,E) & D = k9_subset_1(A,k1_relset_1(A,C),E) ) => r1_mesfun6c(A,B,k2_partfun1(A,k2_numbers,C,E),D) ) ) ) ) ) ) )).
fof(t14_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( 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(k4_ordinal1,k10_seqfunc(A,B,C))) ) ) ) ) )).
fof(t14_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( 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,k5_numbers))) & r2_hidden(D,k1_relset_1(A,C)) & k1_mesfunc9(C,D) = k4_series_1(k10_seqfunc(A,B,D)) ) => k1_mesfunc9(C,D) = k1_seq_2(k10_seqfunc(A,k2_mesfun9c(A,B),D)) ) ) ) ) ) )).
fof(t14_mesfunc1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ! [D] : ( v1_xxreal_0(D) => ( 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))) ) ) ) )).
fof(t14_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => r2_relset_1(A,k6_numbers,k2_mesfunc2(A,B),k1_mesfunc2(A,k7_mesfunc1(A,B))) ) ) )).
fof(t14_mesfunc3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ~ ( r1_mesfunc2(A,B,C) & ! [D] : ( r2_hidden(D,k1_relset_1(A,C)) => r1_xxreal_0(k1_supinf_2,k1_funct_1(C,D)) ) & ! [D] : ( ( v1_prob_2(D) & m2_finseq_1(D,B) ) => ! [E] : ( m2_finseq_1(E,k6_numbers) => ~ ( r1_mesfunc3(A,B,C,D,E) & k12_supinf_2(E,1) = k1_supinf_2 & ! [F] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( r1_mesfunc2(A,B,C) => ( v4_mesfunc5(C) & v3_mesfunc5(C) ) ) ) ) ) )).
fof(t14_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( r1_mesfunc6(A,B,C,D) <=> ! [E] : ( v1_xreal_0(E) => r2_hidden(k8_subset_1(A,D,k12_mesfunc1(C,E)),B) ) ) ) ) ) ) )).
fof(t14_mesfunc7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t14_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t14_metric_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( l1_metric_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => r1_tarski(k8_metric_1(B,C,A),k9_metric_1(B,C,A)) ) ) ) )).
fof(t14_metric_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( m1_metric_2(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & B = k6_domain_1(u1_struct_0(A),C) ) ) ) ) )).
fof(t14_metric_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(D,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C))) => ! [E] : ( m1_subset_1(E,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C))) => ( k2_binop_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,k13_metric_3(A,B,C),D,E) = k5_numbers <=> D = E ) ) ) ) ) ) )).
fof(t14_metric_6,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r1_metric_6(A,C,B) <=> ( v2_comseq_2(k2_metric_6(A,C,B)) & k1_seq_2(k2_metric_6(A,C,B)) = k5_numbers ) ) ) ) ) )).
fof(t14_metrizts,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ! [B] : ( ( v2_pre_topc(B) & v3_pcomps_1(B) & l1_pre_topc(B) ) => ( ! [C] : ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v2_tex_2(C,B) => r1_ordinal1(k1_card_1(C),A) ) ) ) ) ) )).
fof(t14_mfold_2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t14_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_midsp_1(A,B,C,B,C) ) ) ) )).
fof(t14_midsp_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_nat_1(A,2)) ) => ! [C] : ( ( v4_midsp_2(C,B) & l1_midsp_2(C,B) ) => ! [D] : ( m2_finseq_2(D,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(u1_midsp_2(B,C)))) => ! [E] : ( m2_finseq_2(E,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(u1_midsp_2(B,C)))) => ( ! [F] : ( 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 ) ) ) ) ) ) )).
fof(t14_mmlquer2,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ( r1_mmlquery(C,D,k3_mmlquer2(A,k4_mmlquer2(A,B))) <=> ~ r1_xxreal_0(k5_card_1(k1_mmlquery(A,B,D)),k5_card_1(k1_mmlquery(A,B,C))) ) ) ) ) ) )).
fof(t14_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(t14_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( v2_mod_2(B,A) & v3_mod_2(B,A) & l1_mod_2(B,A) ) => ! [C] : ( ( 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] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_mod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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) ) ) )).
fof(t14_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_2(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_mod_4(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t14_modal_1,axiom,( ! [A] : ( ( ~ 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(k4_ordinal1,k4_ordinal1)),k14_trees_3(k5_numbers),k14_trees_3(1)) ) ) )).
fof(t14_modcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u4_struct_0(k11_modcat_1(A,B))) => ! [D] : ( m1_subset_1(D,u4_struct_0(k11_modcat_1(A,B))) => ! [E] : ( m4_modcat_1(E,B,k4_modcat_1(B,k3_modcat_1(A,B))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t14_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [E] : ( 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] : ( m1_modelc_1(F,A,B) & k3_funct_2(k4_ordinal1,A,F,k5_numbers) = C & r3_modelc_1(A,B,D,k3_funct_2(k4_ordinal1,A,F,1),E) ) ) ) ) ) ) ) )).
fof(t14_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r1_modelc_2(B,k6_modelc_2(A)) <=> B = A ) ) ) )).
fof(t14_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k13_modelc_2(B))) => ( C = k1_tarski(A) => k18_modelc_3(B,C) = k3_finseq_1(A) ) ) ) ) )).
fof(t14_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ? [B] : ( m1_subset_1(B,k4_ordinal1) & r1_tarski(k22_pre_poly(k8_newton,k13_nat_3(A)),k2_finseq_1(B)) ) ) )).
fof(t14_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v17_monoid_0(A) <=> ( v1_setwiseo(u2_algstr_0(A),u1_struct_0(A)) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) ) ) )).
fof(t14_monoid_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(t14_morph_01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( ( ~ 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))) ) ) ) )).
fof(t14_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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)) ) ) )).
fof(t14_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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) ) ) ) )).
fof(t14_msafree4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( r2_pboole(A,C,D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,B,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => r2_pboole(B,k3_msafree4(A,B,E,C),k3_msafree4(A,B,E,D)) ) ) ) ) ) )).
fof(t14_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(B,D)) => ( C = k1_trees_4(k4_tarski(E,D)) => k7_msaterm(A,B,C) = D ) ) ) ) ) ) )).
fof(t14_msscyc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v7_graph_1(B,A) & m1_graph_1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v7_graph_1(C,A) & m1_graph_1(C,A) ) => ( k1_funct_1(k7_graph_2(A,B),k1_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) ) ) ) ) ) )).
fof(t14_mssubfam,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v1_funcop_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( ( r2_hidden(B,A) & D = k1_funct_1(C,B) ) => k1_funct_1(k1_funct_6(C),B) = k9_xtuple_0(D) ) ) ) )).
fof(t14_mssublat,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) )).
fof(t14_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t14_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t14_msualg_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,k3_msualg_1(A,C,B)) => ! [H] : ( m1_subset_1(H,k3_msualg_1(A,C,B)) => ( ! [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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_msualg_6(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_rewrite1(E,k3_msualg_6(A)) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) & v1_funcop_1(F) ) => ( ( k3_finseq_1(E) = k1_nat_1(k3_finseq_1(F),1) & C = k1_funct_1(E,1) & D = k1_funct_1(E,k3_finseq_1(E)) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ! [H] : ( ( v1_relat_1(H) & v1_funct_1(H) ) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( 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,k1_nat_1(G,1)) ) => r1_msualg_6(A,I,J,B,H) ) ) ) ) ) ) => ( v1_funct_1(k3_funct_7(k1_funct_1(u3_msualg_1(A,B),C),F)) & v1_funct_2(k3_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(k3_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 ) ) ) ) ) ) ) ) ) ) )).
fof(t14_msualg_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m2_nat_lat(B,A) => ( v1_msualg_7(B,A) => v4_lattice3(B) ) ) ) )).
fof(t14_msualg_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_msualg_5(A,B)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_msualg_5(A,B)))) => ! [E] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t14_msualg_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_pralg_2(D,B,A) => ! [E] : ( m1_subset_1(E,k4_card_3(k9_pralg_2(B,A,C,D))) => ! [F] : ( m1_subset_1(F,k4_card_3(k9_pralg_2(B,A,C,D))) => ( ! [G] : ( 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) ) ) ) ) ) ) ) )).
fof(t14_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(k6_msualg_1(A))) => ! [C] : ( m1_subset_1(C,k3_msualg_1(k6_msualg_1(A),B,k9_msualg_1(A))) => m2_finseq_1(C,u1_struct_0(A)) ) ) ) )).
fof(t14_mycielsk,axiom,( ! [A] : ( ( v8_struct_0(A) & l1_orders_2(A) ) => r1_xxreal_0(k3_mycielsk(A),k5_card_1(u1_struct_0(A))) ) )).
fof(t14_nagata_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => r2_hidden(k7_subset_1(u1_struct_0(B),k2_struct_0(B),k9_metric_1(B,C,A)),k2_pcomps_1(B)) ) ) ) )).
fof(t14_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(1,A) => A = k5_numbers ) ) )).
fof(t14_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( A != k5_numbers => k3_nat_d(k2_xcmplx_0(B,A),A) = k1_nat_1(k3_nat_d(B,A),1) ) ) ) )).
fof(t14_nat_4,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_int_2(A) <=> ( ~ r1_xxreal_0(A,1) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( ~ r1_xxreal_0(B,1) & r1_xxreal_0(k2_nat_1(B,B),A) & v1_int_2(B) & r1_nat_d(B,A) ) ) ) ) ) )).
fof(t14_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t14_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,1) => k4_nat_d(1,A) = 1 ) ) )).
fof(t14_nat_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k10_nat_lat)) => ! [B] : ( 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)) ) ) )).
fof(t14_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t14_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( 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] : ( m1_ncfcont1(E,B,k7_partfun1(u1_struct_0(B),C,D)) => ? [F] : ( m1_ncfcont1(F,A,D) & ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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)) ) ) ) ) )).
fof(t14_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k1_seq_2(B)) ) ) ) ) )).
fof(t14_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t14_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( 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)) ) ) ) ) ) ) ) )).
fof(t14_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m1_subset_1(B,k4_card_3(k4_prvect_2(A))) => ( k4_struct_0(k14_prvect_2(A)) = B <=> ! [C] : ( m2_subset_1(C,k4_ordinal1,k4_finseq_1(A)) => k1_ndiff_5(A,B,C) = k4_struct_0(k11_prvect_2(A,C)) ) ) ) ) )).
fof(t14_neckla_3,axiom,( ! [A] : ( 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))) ) )).
fof(t14_necklace,axiom,( ! [A] : ( v7_ordinal1(A) => v2_necklace(k1_necklace(A)) ) )).
fof(t14_net_1,axiom,( ! [A] : ! [B] : ( ( v1_net_1(B) & l1_petri(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t14_newton,axiom,( k2_newton(2) = 2 )).
fof(t14_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,k1_numbers,k5_normsp_0(B,k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),D,C)),k8_funct_2(k4_ordinal1,k1_numbers,u1_struct_0(A),D,k4_normsp_0(u1_struct_0(A),B,C))) & r2_funct_2(k4_ordinal1,u1_struct_0(B),k5_vfunct_1(k4_ordinal1,B,k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),D,C)),k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),D,k5_vfunct_1(u1_struct_0(A),B,C))) ) ) ) ) ) ) )).
fof(t14_nfcont_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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(k4_normsp_0(k1_numbers,B,C),A) & r1_nfcont_3(B,k5_vfunct_1(k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t14_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t14_normform,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_finsub_1(B) ) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(A,B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t14_normsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ! [D] : ( v7_ordinal1(D) => k1_normsp_0(A,B,D) = C ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k10_xtuple_0(B) != k6_domain_1(u1_struct_0(A),C) ) ) ) ) )).
fof(t14_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k3_normsp_2(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k3_normsp_2(A))))) ) => ( ( r1_funct_2(k4_ordinal1,u1_struct_0(A),k4_ordinal1,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) ) ) ) ) ) )).
fof(t14_ntalgo_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ? [B] : ( ~ v1_xboole_0(B) & m2_finseq_1(B,k4_numbers) & k3_finseq_1(B) = k1_nat_1(k3_finseq_1(A),1) & k1_funct_1(B,1) = 1 & ! [C] : ( 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,k1_nat_1(k3_finseq_1(A),1)) ) ) )).
fof(t14_numbers,axiom,( r1_tarski(k4_numbers,k3_numbers) )).
fof(t14_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t14_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t14_oposet_1,axiom,( v9_oposet_1(u1_robbins1(k1_oposet_1),k1_oposet_1) )).
fof(t14_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_cat_1(E,A,B,C) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t14_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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(k5_ordeq_01(A,B)) ) ) )).
fof(t14_orders_1,axiom,( ! [A] : ! [B] : ( ( 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 ) ) )).
fof(t14_orders_2,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t14_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => v3_ordinal1(k3_tarski(A)) ) )).
fof(t14_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( r2_hidden(A,B) => r1_ordinal1(k2_ordinal2(B),A) ) ) )).
fof(t14_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ( r2_hidden(A,1) => A = k1_xboole_0 ) ) )).
fof(t14_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_ordinal2(C) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t14_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => k1_ordinal5(A,k1_ordinal1(B)) = k12_ordinal2(A,k1_ordinal5(A,B)) ) ) )).
fof(t14_ordinal6,axiom,( k1_ordinal6(k1_xboole_0) = k5_numbers )).
fof(t14_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( ~ r1_orders_2(B,D,C) & F != k4_struct_0(A) & k1_ortsp_1(A,B,C,k4_vectsp_1(A,B,F,D),E) != k8_group_1(A,k11_algstr_0(A,F),k1_ortsp_1(A,B,C,D,E)) ) ) ) ) ) ) ) )).
fof(t14_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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))) ) ) ) )).
fof(t14_osalg_1,axiom,( ! [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) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t14_osalg_2,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t14_osalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & v13_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v12_osalg_1(C,A) & m1_msualg_2(C,A,B) ) => v13_osalg_1(C,A) ) ) ) )).
fof(t14_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( ( v4_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v2_msualg_4(D,A,C) & v3_msualg_4(D,A,C) & m1_osalg_4(D,A,C) ) => ! [E] : ~ ( 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] : ( m1_subset_1(F,k3_msualg_1(A,B,C)) => E != k9_osalg_4(A,B,C,D,F) ) ) ) ) ) ) )).
fof(t14_papdesaf,axiom,( ! [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) ) => ! [B] : ( ( ~ v7_struct_0(B) & v2_analoaf(B) & l1_analoaf(B) ) => ( B = k2_analoaf(A) => v4_aff_2(k2_diraf(B)) ) ) ) )).
fof(t14_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A))) => r1_parsp_1(k9_parsp_1(A),B,C,D,D) ) ) ) ) )).
fof(t14_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_parsp_2(A,B,C,D) ) ) ) ) ) )).
fof(t14_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( v1_funct_1(k5_relat_1(k6_relat_1(B,C),A)) & m1_subset_1(k5_relat_1(k6_relat_1(B,C),A),k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ) )).
fof(t14_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,A) => ! [F] : ( 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) ) ) ) ) ) )).
fof(t14_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => k2_partit1(A,k2_partit1(A,B,C),D) = k2_partit1(A,B,k2_partit1(A,C,D)) ) ) ) ) )).
fof(t14_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ( v2_bvfunc_2(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( 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)))) ) ) ) ) ) ) )).
fof(t14_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r2_diraf(A,E,B,C,D) & r2_diraf(A,E,C,B,D) ) => ( r3_diraf(A,E,B,C) | ( r2_analoaf(A,E,B,C,D) & r2_analoaf(A,E,C,B,D) ) ) ) ) ) ) ) ) )).
fof(t14_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) )).
fof(t14_pcomps_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t14_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ( l2_pcs_0(B) => ( u1_struct_0(k19_pcs_0(A,B)) = k2_xboole_0(u1_struct_0(A),u1_struct_0(B)) & u1_orders_2(k19_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(k19_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)) ) ) ) )).
fof(t14_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(A))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t14_pdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(2)) => ! [D] : ( ( 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) ) => k10_pdiff_1(2,2,D,C) = k1_fdiff_1(k1_pdiff_2(2,2,D,C),B) ) ) ) ) ) )).
fof(t14_pdiff_3,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(2)) => ! [B] : ( ( 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) = k10_pdiff_1(2,2,k1_pdiff_3(1,2,B),A) ) ) ) )).
fof(t14_pdiff_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r3_pdiff_1(3,2,A,B) <=> ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & B = k11_finseq_1(C,D,E) & ? [F] : ( m1_rcomp_1(F,D) & r1_tarski(F,k1_relset_1(k1_numbers,k1_pdiff_2(3,2,A,B))) & ? [G] : ( v1_funct_1(G) & v3_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [H] : ( v1_funct_1(H) & v2_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,F) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,2,A,B),I),k1_funct_1(k1_pdiff_2(3,2,A,B),D)) = k2_xcmplx_0(k1_funct_1(G,k6_xcmplx_0(I,D)),k1_funct_1(H,k6_xcmplx_0(I,D))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t14_pdiff_6,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k1_euclid(B),k1_euclid(A)) & v1_pdiff_6(C,A,B) & v2_pdiff_6(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(B),k1_euclid(A)))) ) <=> ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k4_real_ns1(B)),u1_struct_0(k4_real_ns1(A))) & v13_vectsp_1(C,k4_real_ns1(B),k4_real_ns1(A)) & v1_lopban_1(C,k4_real_ns1(B),k4_real_ns1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(B)),u1_struct_0(k4_real_ns1(A))))) ) ) ) ) )).
fof(t14_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(1))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(1))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( 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)) ) ) ) ) ) )).
fof(t14_pdiff_8,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k16_lopban_1(k4_real_ns1(A),k4_real_ns1(B)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k16_lopban_1(k4_real_ns1(A),k4_real_ns1(B)))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k16_lopban_1(k4_real_ns1(A),k4_real_ns1(1)))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k16_lopban_1(k4_real_ns1(A),k4_real_ns1(1)))) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( ( 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(k2_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)),k2_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))) ) ) ) ) ) ) ) ) )).
fof(t14_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) => ! [D] : ( ( 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] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ( r2_hidden(E,C) => r1_pdiff_1(A,B,D,E) ) ) ) ) ) ) ) ) ) )).
fof(t14_pencil_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t14_pencil_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(t14_pencil_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v15_pencil_1(B) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k2_pencil_1(A,B,C)))) => ! [E] : ( ( ~ v13_pencil_1(E) & v16_pencil_1(E,A) & m3_pboole(E,A,k12_pralg_1(A,B)) ) => m1_subset_1(k4_card_3(k1_funct_7(E,C,D)),k1_zfmisc_1(u1_struct_0(k5_pencil_1(A,B)))) ) ) ) ) ) )).
fof(t14_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t14_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( k4_nat_d(A,B) = C => ( r1_xxreal_0(B,k1_square_1(C)) | k4_nat_d(k1_square_1(A),B) = k1_square_1(C) ) ) ) ) ) )).
fof(t14_petri,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t14_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,k4_ordinal1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,k4_ordinal1) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ( ( 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)) ) ) ) ) ) )).
fof(t14_polyalg1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_polyalg1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t14_polyeq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_newton(k2_xcmplx_0(B,A),3) = k2_xcmplx_0(k2_xcmplx_0(k1_newton(B,3),k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),k1_square_1(B)),k3_xcmplx_0(k3_xcmplx_0(3,k1_square_1(A)),B))),k1_newton(A,3)) ) ) )).
fof(t14_polyeq_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( k4_polyeq_1(A,k5_numbers,B,C,D) = k5_numbers => ( A = k5_numbers | k4_complex1(D) = k5_numbers | ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ~ ( k3_complex1(D) = k2_xcmplx_0(E,F) & k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,F),E),k7_xcmplx_0(B,k3_xcmplx_0(4,A))) = k5_numbers & D != k2_xcmplx_0(k2_xcmplx_0(k1_power(3,k2_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(16,A)),k3_square_1(k2_xcmplx_0(k1_square_1(k7_xcmplx_0(C,k3_xcmplx_0(16,A))),k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(12,A)),3))))),k1_power(3,k6_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(16,A)),k3_square_1(k2_xcmplx_0(k1_square_1(k7_xcmplx_0(C,k3_xcmplx_0(16,A))),k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(12,A)),3)))))),k3_xcmplx_0(k3_square_1(k2_xcmplx_0(k3_xcmplx_0(3,k1_square_1(k2_xcmplx_0(k1_power(3,k2_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(16,A)),k3_square_1(k2_xcmplx_0(k1_square_1(k7_xcmplx_0(C,k3_xcmplx_0(16,A))),k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(12,A)),3))))),k1_power(3,k6_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(16,A)),k3_square_1(k2_xcmplx_0(k1_square_1(k7_xcmplx_0(C,k3_xcmplx_0(16,A))),k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(12,A)),3)))))))),k7_xcmplx_0(B,A))),k7_complex1)) & D != k6_xcmplx_0(k2_xcmplx_0(k1_power(3,k2_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(16,A)),k3_square_1(k2_xcmplx_0(k1_square_1(k7_xcmplx_0(C,k3_xcmplx_0(16,A))),k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(12,A)),3))))),k1_power(3,k6_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(16,A)),k3_square_1(k2_xcmplx_0(k1_square_1(k7_xcmplx_0(C,k3_xcmplx_0(16,A))),k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(12,A)),3)))))),k3_xcmplx_0(k3_square_1(k2_xcmplx_0(k3_xcmplx_0(3,k1_square_1(k2_xcmplx_0(k1_power(3,k2_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(16,A)),k3_square_1(k2_xcmplx_0(k1_square_1(k7_xcmplx_0(C,k3_xcmplx_0(16,A))),k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(12,A)),3))))),k1_power(3,k6_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(16,A)),k3_square_1(k2_xcmplx_0(k1_square_1(k7_xcmplx_0(C,k3_xcmplx_0(16,A))),k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(12,A)),3)))))))),k7_xcmplx_0(B,A))),k7_complex1)) & D != k2_xcmplx_0(k3_xcmplx_0(2,k1_power(3,k2_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(16,A)),k3_square_1(k2_xcmplx_0(k1_square_1(k7_xcmplx_0(C,k3_xcmplx_0(16,A))),k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(12,A)),3)))))),k3_xcmplx_0(k3_square_1(k2_xcmplx_0(k3_xcmplx_0(3,k1_square_1(k3_xcmplx_0(2,k1_power(3,k2_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(16,A)),k3_square_1(k2_xcmplx_0(k1_square_1(k7_xcmplx_0(C,k3_xcmplx_0(16,A))),k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(12,A)),3)))))))),k7_xcmplx_0(B,A))),k7_complex1)) & D != k6_xcmplx_0(k3_xcmplx_0(2,k1_power(3,k2_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(16,A)),k3_square_1(k2_xcmplx_0(k1_square_1(k7_xcmplx_0(C,k3_xcmplx_0(16,A))),k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(12,A)),3)))))),k3_xcmplx_0(k3_square_1(k2_xcmplx_0(k3_xcmplx_0(3,k1_square_1(k3_xcmplx_0(2,k1_power(3,k2_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(16,A)),k3_square_1(k2_xcmplx_0(k1_square_1(k7_xcmplx_0(C,k3_xcmplx_0(16,A))),k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(12,A)),3)))))))),k7_xcmplx_0(B,A))),k7_complex1)) & D != k2_xcmplx_0(k3_xcmplx_0(2,k1_power(3,k6_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(16,A)),k3_square_1(k2_xcmplx_0(k1_square_1(k7_xcmplx_0(C,k3_xcmplx_0(16,A))),k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(12,A)),3)))))),k3_xcmplx_0(k3_square_1(k2_xcmplx_0(k3_xcmplx_0(3,k1_square_1(k3_xcmplx_0(2,k1_power(3,k6_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(16,A)),k3_square_1(k2_xcmplx_0(k1_square_1(k7_xcmplx_0(C,k3_xcmplx_0(16,A))),k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(12,A)),3)))))))),k7_xcmplx_0(B,A))),k7_complex1)) & D != k6_xcmplx_0(k3_xcmplx_0(2,k1_power(3,k6_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(16,A)),k3_square_1(k2_xcmplx_0(k1_square_1(k7_xcmplx_0(C,k3_xcmplx_0(16,A))),k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(12,A)),3)))))),k3_xcmplx_0(k3_square_1(k2_xcmplx_0(k3_xcmplx_0(3,k1_square_1(k3_xcmplx_0(2,k1_power(3,k6_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(16,A)),k3_square_1(k2_xcmplx_0(k1_square_1(k7_xcmplx_0(C,k3_xcmplx_0(16,A))),k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(12,A)),3)))))))),k7_xcmplx_0(B,A))),k7_complex1)) ) ) ) ) ) ) ) ) ) )).
fof(t14_polyeq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( k2_xcmplx_0(A,B) = C & k3_xcmplx_0(A,B) = D & r1_xxreal_0(k5_numbers,k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D))) & ~ ( A = k7_xcmplx_0(k2_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2) & B = k7_xcmplx_0(k6_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2) ) & ~ ( A = k7_xcmplx_0(k6_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2) & B = k7_xcmplx_0(k2_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2) ) ) ) ) ) ) )).
fof(t14_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( v1_xcmplx_0(F) => ! [G] : ( v1_xcmplx_0(G) => ( ( D = k4_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(E,F),G)) & C = k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(E,F),k3_xcmplx_0(E,G)),k3_xcmplx_0(F,G)) & B = k4_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(E,F),G)) ) => ( k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_newton(A,3),k3_xcmplx_0(D,k1_newton(A,2))),k3_xcmplx_0(C,A)),B) = k5_numbers <=> ~ ( A != E & A != F & A != G ) ) ) ) ) ) ) ) ) ) )).
fof(t14_polynom2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( ( 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_polynom2(A,B,k5_vfunct_1(k15_pre_poly(A),B,C),D) = k4_algstr_0(B,k2_polynom2(A,B,C,D)) ) ) ) ) )).
fof(t14_polynom4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v6_struct_0(A) & l5_algstr_0(A) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k1_polynom4(A,k10_polynom3(A)),k10_polynom3(A)) ) )).
fof(t14_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( 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,k8_polynom1(A,B)) | k3_polynom1(k15_pre_poly(A),B,C) = k6_domain_1(k15_pre_poly(A),k16_pre_poly(A)) ) ) ) ) )).
fof(t14_polynom8,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k3_polynom8(A,B,1) = B ) ) )).
fof(t14_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( ( 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(k3_polynom1(k15_pre_poly(A),B,k1_polyred(A,D,B,C)),a_4_0_polyred(A,B,C,D)) ) ) ) ) )).
fof(t14_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(1,C) & r1_xxreal_0(1,B) ) | ( ~ v1_abian(C) & ~ v1_abian(B) ) ) => k1_power(C,k1_power(B,A)) = k1_power(k2_nat_1(C,B),A) ) ) ) ) )).
fof(t14_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ! [E] : ( m1_subset_1(E,k3_msualg_1(B,D,k14_pralg_2(A,B,C))) => r2_hidden(E,k1_funct_2(k1_relset_1(k4_ordinal1,k1_msualg_1(B,D)),k1_funct_2(A,k3_tarski(a_3_1_pralg_3(A,B,C))))) ) ) ) ) ) )).
fof(t14_pre_ff,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k2_xcmplx_0(k1_int_1(k3_power(2,A)),1) = k1_int_1(k3_power(2,k1_nat_1(k3_xcmplx_0(2,A),1))) ) ) )).
fof(t14_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k4_partfun1(A,B)) => ! [D] : ( r1_tarski(D,C) => r2_hidden(D,k4_partfun1(A,B)) ) ) )).
fof(t14_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ! [C] : ( 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) ) ) ) )).
fof(t14_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t14_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(A,1) & r1_xxreal_0(1,B) ) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(k1_newton(A,B),A) ) ) ) ) )).
fof(t14_prob_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k3_prob_1(A,k11_funct_7(k1_zfmisc_1(A),B,C)) = k9_subset_1(A,B,C) ) ) )).
fof(t14_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m1_prob_1(E,A,B) => ! [F] : ( m2_prob_1(F,A,B) => ( E = k3_subset_1(A,D) => k3_funct_2(B,k1_numbers,F,C) = k3_real_1(k3_funct_2(B,k1_numbers,F,k5_prob_1(A,B,C,D)),k3_funct_2(B,k1_numbers,F,k5_prob_1(A,B,C,E))) ) ) ) ) ) ) ) )).
fof(t14_prob_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k3_prob_1(A,k1_prob_3(A,B)) = k3_prob_1(A,B) ) )).
fof(t14_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( k1_funct_1(C,A) = 1 => m2_prob_1(C,A,B) ) ) ) ) )).
fof(t14_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t14_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t14_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u2_incsp_1(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t14_projred1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & v8_incproj(A) & l1_incsp_1(A) ) => ? [B] : ( m1_subset_1(B,u1_incsp_1(A)) & ? [C] : ( m1_subset_1(C,u1_incsp_1(A)) & ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & ? [E] : ( m1_subset_1(E,u1_incsp_1(A)) & ? [F] : ( m1_subset_1(F,u1_incsp_1(A)) & ? [G] : ( m1_subset_1(G,u1_incsp_1(A)) & ? [H] : ( m1_subset_1(H,u1_incsp_1(A)) & ? [I] : ( m1_subset_1(I,u2_incsp_1(A)) & ? [J] : ( m1_subset_1(J,u2_incsp_1(A)) & ? [K] : ( m1_subset_1(K,u2_incsp_1(A)) & ? [L] : ( m1_subset_1(L,u2_incsp_1(A)) & ? [M] : ( m1_subset_1(M,u2_incsp_1(A)) & ? [N] : ( m1_subset_1(N,u2_incsp_1(A)) & ? [O] : ( m1_subset_1(O,u2_incsp_1(A)) & ? [P] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u1_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u1_incsp_1(A)) => ! [H] : ( m1_subset_1(H,u1_incsp_1(A)) => ! [I] : ( m1_subset_1(I,u2_incsp_1(A)) => ! [J] : ( m1_subset_1(J,u2_incsp_1(A)) => ! [K] : ( m1_subset_1(K,u2_incsp_1(A)) => ! [L] : ( m1_subset_1(L,u2_incsp_1(A)) => ! [M] : ( m1_subset_1(M,u2_incsp_1(A)) => ! [N] : ( m1_subset_1(N,u2_incsp_1(A)) => ! [O] : ( m1_subset_1(O,u2_incsp_1(A)) => ! [P] : ( m1_subset_1(P,u2_incsp_1(A)) => ( ( r1_incsp_1(A,D,L) & r1_incsp_1(A,D,N) & r1_incsp_1(A,D,P) & r1_incsp_1(A,B,O) & r1_incsp_1(A,C,O) & r1_incsp_1(A,E,N) & r1_incsp_1(A,E,M) & r1_incsp_1(A,B,I) & r1_incsp_1(A,E,I) & r1_incsp_1(A,F,L) & r1_incsp_1(A,F,I) & r1_incsp_1(A,H,O) & r1_incsp_1(A,H,J) & r1_incsp_1(A,F,J) & r1_incsp_1(A,G,J) & r1_incsp_1(A,E,K) & r1_incsp_1(A,C,K) & r1_incsp_1(A,G,K) & r1_incsp_1(A,G,P) ) => ( r1_incsp_1(A,B,L) | r1_incsp_1(A,C,M) | r1_incsp_1(A,B,N) | r1_incsp_1(A,C,N) | r1_projred2(A,L,M,N) | r1_incsp_1(A,C,P) | L = P | r1_projred2(A,M,N,O) | H = B | r1_incsp_1(A,H,L) | r1_incsp_1(A,H,P) | k3_relat_1(k1_projred1(A,L,N,B),k1_projred1(A,N,M,C)) = k3_relat_1(k1_projred1(A,L,P,H),k1_projred1(A,P,M,C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) ) => ! [B] : ( m2_prvect_1(B,A) => ( k1_funct_6(B) = A & r1_tarski(k4_card_3(k2_funct_6(B)),k4_card_3(A)) ) ) ) )).
fof(t14_prvect_3,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(k10_prvect_2(k10_finseq_1(A,B)))) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & C = k10_finseq_1(D,E) ) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(k10_prvect_2(k10_finseq_1(A,B)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k10_prvect_2(k10_finseq_1(A,B)))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( 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] : ( m1_subset_1(C,u1_struct_0(k10_prvect_2(k10_finseq_1(A,B)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_subset_1(C,u1_struct_0(k10_prvect_2(k10_finseq_1(A,B)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t14_pscomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t14_pua2mss1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_eqrel_1(C,B) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t14_pythtrip,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ! [B] : ( m1_pythtrip(B) => ~ ( ~ v2_pythtrip(B) & v3_pythtrip(B) & r2_hidden(k2_nat_1(4,A),B) ) ) ) ) )).
fof(t14_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t14_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)))) ) ) ) )).
fof(t14_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t14_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t14_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_trees_1(C,k9_xtuple_0(k2_qc_lang4(A,B))) => ! [D] : ( 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)))) ) ) ) ) ) )).
fof(t14_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_qc_trans(B,A) & m1_qc_lang1(B) ) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(B),k3_cqc_lang(B)) => ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_substut1(A)) ) => ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,k1_substut1(B)) ) => ! [F] : ( m2_subset_1(F,k9_qc_lang1(A),k3_cqc_lang(A)) => ( ( D = E & F = C ) => k13_substut1(A,D,F) = k13_substut1(B,E,C) ) ) ) ) ) ) ) )).
fof(t14_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v10_lattices(A) & v4_lattice3(A) & v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t14_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => k23_quaterni(A,k2_quatern2) = A ) )).
fof(t14_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k3_xcmplx_0(2,k13_quaterni(A)) = k13_quaterni(k22_quaterni(A,k27_quaterni(A))) ) )).
fof(t14_quaterni,axiom,( k10_quaterni(k11_quaterni,k11_quaterni) = k4_xcmplx_0(1) )).
fof(t14_quin_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k1_square_1(D)),k3_xcmplx_0(B,D)),C) = k5_numbers => ( A = k5_numbers | k6_xcmplx_0(k1_square_1(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,A),D),B)),k1_quin_1(A,B,C)) = k5_numbers ) ) ) ) ) ) )).
fof(t14_quofield,axiom,( ! [A] : ( ( ~ 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] : ( 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 ) ) ) )).
fof(t14_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v3_card_1(D,C) & m2_finseq_1(D,k3_radix_1(B)) ) => ( r2_hidden(A,k2_finseq_1(C)) => m2_subset_1(k1_funct_1(D,A),k4_numbers,k3_radix_1(B)) ) ) ) ) ) )).
fof(t14_radix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k5_radix_2(C,B,A) = k10_radix_1(C,B,A) ) ) ) )).
fof(t14_radix_3,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(2,B) => r2_hidden(k5_radix_3(A,B),k3_radix_3(B)) ) ) ) )).
fof(t14_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(2,B) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k3_radix_1(B)) ) => ! [D] : ( ( v3_card_1(D,A) & m2_finseq_1(D,k3_radix_1(B)) ) => ! [E] : ( ( v3_card_1(E,A) & m2_finseq_1(E,k3_radix_1(B)) ) => ! [F] : ( ( v3_card_1(F,A) & m2_finseq_1(F,k3_radix_1(B)) ) => ( ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t14_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(t14_ramsey_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ( ( 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 != k5_numbers & ~ v1_finset_1(C) & ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t14_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ~ ( v2_prob_1(B) & ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & k9_nat_1(k9_setfam_1(A),B,C) != k9_nat_1(k9_setfam_1(A),B,D) ) ) ) ) ) )).
fof(t14_random_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ( ( r1_tarski(C,D) & ! [E] : ( r2_hidden(E,D) => r1_xxreal_0(k5_numbers,k12_supinf_2(B,E)) ) ) => r1_xxreal_0(k5_bhsp_5(k1_numbers,A,k9_binop_2,C,B),k5_bhsp_5(k1_numbers,A,k9_binop_2,D,B)) ) ) ) ) ) )).
fof(t14_random_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( m2_prob_1(E,A,C) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,A,B) & v1_random_3(F,A,B,C,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [G] : ( r2_hidden(G,D) => k12_supinf_2(k2_random_3(A,B,C,D,E,F),G) = k12_supinf_2(E,k8_relset_1(A,B,F,G)) ) ) ) ) ) ) ) )).
fof(t14_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k1_ranknull(A,B,C,D))) => k1_funct_1(D,E) = k4_struct_0(C) ) ) ) ) ) )).
fof(t14_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ( v1_int_1(A) => ( k1_rat_1(A) = 1 & k2_rat_1(A) = A ) ) ) )).
fof(t14_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_ratfunc1(A,B,C,D) => r1_polynom5(A,k8_polynom3(A,B,C),D) ) ) ) ) ) )).
fof(t14_rcomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_rcomp_1(A) => ( A = k1_xboole_0 | ( r2_hidden(k2_seq_4(A),A) & r2_hidden(k3_seq_4(A),A) ) ) ) ) )).
fof(t14_rcomp_3,axiom,( ! [A] : ( ( v5_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( ~ r2_hidden(k3_seq_4(A),A) => r1_tarski(A,k4_rcomp_1(k3_seq_4(A),k2_seq_4(A))) ) ) )).
fof(t14_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(A,B) & k9_nat_1(k4_ordinal1,k1_real_3(D,C),A) = k5_numbers ) => k9_nat_1(k4_ordinal1,k1_real_3(D,C),B) = k5_numbers ) ) ) ) ) )).
fof(t14_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( 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),C,B),B),B) ) ) ) )).
fof(t14_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_real_ns1(A))) => ( B = C => k1_square_1(k2_normsp_0(k4_real_ns1(A),B)) = k2_bhsp_1(k7_real_ns1(A),C,C) ) ) ) ) )).
fof(t14_realset2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k8_group_1(A,k4_struct_0(A),B) = k4_struct_0(A) ) ) )).
fof(t14_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) )).
fof(t14_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [E] : ( ( 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_funct_1(k3_rearran1(B,A,E,D),C) = k1_funct_1(k20_rfunct_3(B,D,B),1) ) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ( r1_xxreal_0(1,F) & r2_hidden(C,k6_subset_1(k1_funct_1(E,k1_nat_1(F,1)),k1_funct_1(E,F))) ) => ( r1_xxreal_0(k3_finseq_1(E),F) | k1_funct_1(k3_rearran1(B,A,E,D),C) = k1_funct_1(k20_rfunct_3(B,D,B),k1_nat_1(F,1)) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_relat_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(t14_relset_1,axiom,( ! [A] : m1_subset_1(k4_relat_1(A),k1_zfmisc_1(k2_zfmisc_1(A,A))) )).
fof(t14_relset_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( v1_relat_1(C) => k7_relat_1(C,k5_setfam_1(A,B)) = k3_tarski(a_3_0_relset_2(A,B,C)) ) ) )).
fof(t14_revrot_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => k3_finseq_1(k1_finseq_6(A,C,B)) = k3_finseq_1(C) ) ) ) )).
fof(t14_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r1_rewrite1(A,B,C) => ( r2_hidden(B,k1_relat_1(A)) | B = C ) ) ) )).
fof(t14_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t14_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( l1_rewrite3(C,B) => ( k9_xtuple_0(u1_rewrite3(B,C)) = k1_xboole_0 => v2_rewrite3(C,A,B) ) ) ) ) )).
fof(t14_rfinseq,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k3_rfinseq(k10_finseq_1(A,B)) = k10_finseq_1(k6_xcmplx_0(A,B),B) ) ) )).
fof(t14_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( r2_classes1(A,B) => k3_rfinseq2(A) = k3_rfinseq2(B) ) ) ) )).
fof(t14_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t14_rfunct_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ( v1_partfun1(C,B) => r2_relset_1(k4_ordinal1,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,B,D,k26_valued_1(B,k1_numbers,C,A)),k26_valued_1(k4_ordinal1,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,B,D,C),A)) ) ) ) ) ) )).
fof(t14_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => v1_binop_1(k13_rfunct_3(A),k3_rfunct_3(A,k1_numbers)) ) )).
fof(t14_rfunct_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t14_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_seq_2(A) => k2_rinfsup1(A) = k4_xcmplx_0(k1_rinfsup1(k32_valued_1(k4_ordinal1,k1_numbers,A))) ) ) )).
fof(t14_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( r1_funct_2(k4_ordinal1,k6_numbers,k4_ordinal1,k1_numbers,A,B) & v2_comseq_2(B) ) => ( v7_mesfunc5(A) & v10_mesfunc5(A) & k2_mesfunc5(A) = k1_seq_2(B) ) ) ) ) )).
fof(t14_ring_1,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_ring_1(A,B))) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t14_ringcat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_ringcat1(C,A,B) => m4_ringcat1(k1_tarski(C),A,B) ) ) ) )).
fof(t14_rlaffin1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_rlvect_2(C,B) => ! [D] : ( 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) ) ) ) ) )).
fof(t14_rlaffin2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( ( 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,k6_xcmplx_0(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)))) ) ) ) ) ) ) ) )).
fof(t14_rlaffin3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( m2_rlaffin3(D,B,C) => ( m2_rlaffin3(k4_vfunct_1(k4_ordinal1,B,D,A),B,k1_convex1(B,C,A)) <=> ~ ( A = k5_numbers & ~ v1_zfmisc_1(C) ) ) ) ) ) ) )).
fof(t14_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_rlsub_1(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ( E = B => k1_rlvect_1(D,E,C) = k1_rlvect_1(A,B,C) ) ) ) ) ) ) )).
fof(t14_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => k2_rlsub_2(A,B,C) = k2_rlsub_2(A,C,B) ) ) ) )).
fof(t14_rltopsp1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( ~ v8_ordinal1(C) & v1_xreal_0(C) ) => ( r2_hidden(k4_struct_0(A),k1_convex1(A,B,C)) => r2_hidden(k4_struct_0(A),B) ) ) ) ) )).
fof(t14_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_algstr_0(A,k4_struct_0(A),B) = k4_algstr_0(A,B) ) ) )).
fof(t14_rlvect_2,axiom,( ! [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) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t14_rlvect_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( r1_struct_0(k1_rlvect_3(B,C),A) <=> ? [D] : ( m2_rlvect_2(D,B,C) & A = k6_rlvect_2(B,D) ) ) ) ) )).
fof(t14_rlvect_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(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)) ) ) ) ) ) ) ) ) )).
fof(t14_rlvect_5,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t14_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_rmod_2(E,A,C) => ! [F] : ( m1_subset_1(F,u1_struct_0(E)) => ( F = D => k5_vectsp_2(A,E,B,F) = k5_vectsp_2(A,C,B,D) ) ) ) ) ) ) ) )).
fof(t14_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => k2_rmod_3(A,B,C,D) = k2_rmod_3(A,B,D,C) ) ) ) ) )).
fof(t14_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( ( 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),D,C)) = k5_algstr_0(B,k1_rmod_4(A,B,k4_subset_1(u1_struct_0(B),D,C)),k1_rmod_4(A,B,k9_subset_1(u1_struct_0(B),D,C))) ) ) ) ) )).
fof(t14_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_robbins1(A,B,k6_lattices(A)) = B ) ) )).
fof(t14_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_robbins1(A,k1_lattices(A,B,C)) = k3_robbins1(A,k1_lattices(A,C,B)) ) ) ) )).
fof(t14_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t14_robbins4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_robbins4)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_robbins4)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_robbins4)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t14_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k3_roughs_1(A,B),k4_roughs_1(A,B)) ) ) )).
fof(t14_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v3_card_1(B,1) & m1_subset_1(B,k1_zfmisc_1(A)) ) => k1_rpr_1(A,B) = k7_xcmplx_0(1,k5_card_1(A)) ) ) )).
fof(t14_rsspace,axiom,( u1_struct_0(k6_rsspace) = k1_rsspace & ! [A] : ( m1_subset_1(A,u1_struct_0(k6_rsspace)) <=> ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k6_rsspace)) => A = k2_rsspace(A) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k6_rsspace)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k6_rsspace)) => k3_rlvect_1(k6_rsspace,A,B) = k1_series_1(k1_numbers,k2_rsspace(A),k2_rsspace(B)) ) ) & ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k6_rsspace)) => k1_rlvect_1(k6_rsspace,B,A) = k26_valued_1(k4_ordinal1,k1_numbers,k2_rsspace(B),A) ) ) )).
fof(t14_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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_funct_1(k8_rsspace4(A,B),C) = k2_seq_4(k7_rsspace4(A,B,C)) ) ) ) )).
fof(t14_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t14_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => k2_rusub_2(A,B,C) = k2_rusub_2(A,C,B) ) ) ) )).
fof(t14_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( k1_rusub_3(A,B) = A & ! [C] : ( m1_rusub_3(C,A) => ~ r1_tarski(C,B) ) ) ) ) )).
fof(t14_rusub_4,axiom,( ! [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_bhsp_1(A) & v1_rusub_4(A) & l1_bhsp_1(A) ) => ( k1_rusub_4(A) = 2 <=> ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( 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)) ) ) ) ) )).
fof(t14_rusub_5,axiom,( ! [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) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_rusub_4(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_rusub_4(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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 ) ) ) ) ) )).
fof(t14_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k4_rvsum_1(k2_finseq_2(A,B),k2_finseq_2(A,C)) = k2_finseq_2(A,k2_xcmplx_0(B,C)) ) ) ) )).
fof(t14_rvsum_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k7_rvsum_2(k2_finseq_2(A,B),k2_finseq_2(A,C)) = k2_finseq_2(A,k6_xcmplx_0(B,C)) ) ) ) )).
fof(t14_scm_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( r1_tarski(k5_afinsq_1(k2_compos_1(k1_ami_3)),A) => ! [B] : ( ( v5_memstr_0(B,k7_card_1(2),k1_ami_3,k5_numbers) & m1_scm_1(B,k6_finseq_1(k4_numbers)) ) => ( r1_extpro_1(k7_card_1(2),k1_ami_3,A,B) & k8_extpro_1(k7_card_1(2),k1_ami_3,A,B) = k5_numbers & k6_extpro_1(k7_card_1(2),k1_ami_3,A,B) = B ) ) ) ) )).
fof(t14_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_finset_1(E) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(G,u1_struct_0(k1_scmfsa_2)) ) => ! [H] : ( ( 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(k7_card_1(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] : ( m1_subset_1(I,k4_ordinal1) => ( r2_hidden(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,G,I)),k9_xtuple_0(F)) & r2_hidden(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,H,I)),k9_xtuple_0(F)) ) ) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,G,D),k4_struct_0(k1_scmfsa_2)) = k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,H,D),k4_struct_0(k1_scmfsa_2)) & k5_relat_1(k5_extpro_1(k7_card_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(k7_card_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(k7_card_1(3),k1_scmfsa_2,A,G,C),k4_struct_0(k1_scmfsa_2)) = k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,H,C),k4_struct_0(k1_scmfsa_2)) & k5_relat_1(k5_extpro_1(k7_card_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(k7_card_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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_scmfsa10,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( 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 ) ) )).
fof(t14_scmfsa6a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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)) ) ) )).
fof(t14_scmfsa7b,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( m1_scmfsa_2(D) => ~ ( A != B & r3_scmfsa7b(k14_scmfsa_2(B,C,D),A) ) ) ) ) ) )).
fof(t14_scmfsa8a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(t14_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( 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) = k5_numbers | ( r5_scmfsa7b(k1_scmfsa8b(E,C,D),B,A) & r6_scmfsa7b(k1_scmfsa8b(E,C,D),B,A) ) ) ) ) ) ) ) ) )).
fof(t14_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,B),k1_funct_4(A,C),C) & k2_scmfsa8a(B,A,C) = k2_scmfsa8a(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),k1_funct_4(A,C),C) ) ) ) ) ) )).
fof(t14_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ( ( 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) ) ) ) ) ) ) )).
fof(t14_scmfsa_1,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k4_scmfsa_1,k5_scmfsa_1))) => ! [B] : ( m2_subset_1(B,k1_scmfsa_1,k2_scmfsa_1) => ! [C] : ( v1_int_1(C) => k1_funct_1(k7_scmfsa_1(A,B,C),B) = C ) ) ) )).
fof(t14_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( 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 ) ) )).
fof(t14_scmfsa_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( ~ 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(k7_card_1(3),k1_scmfsa_2)) & v1_finset_1(B) & v4_extpro_1(B,k7_card_1(3),k1_scmfsa_2,A) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ( ( r1_tarski(B,C) & r1_tarski(B,D) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( ( r1_tarski(A,E) & r1_tarski(A,F) ) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v1_ami_2(H) & m1_subset_1(H,u1_struct_0(k1_scmfsa_2)) ) => ! [I] : ( m1_scmfsa_2(I) => ( ( k3_extpro_1(k7_card_1(3),k1_scmfsa_2,E,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G)) = k17_scmfsa_2(H,I) & r2_hidden(I,k9_xtuple_0(B)) ) => ! [J] : ( v7_ordinal1(J) => ! [K] : ( v7_ordinal1(K) => ( ( J = k1_int_2(k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G),H)) & K = k1_int_2(k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,D,G),H)) ) => k5_finseq_2(k4_ordinal1,J,k5_numbers) = k5_finseq_2(k4_ordinal1,K,k5_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_scmfsa_9,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(k1_nat_1(k5_card_1(B),6),C) => r2_hidden(C,k2_afinsq_1(k1_scmfsa_9(A,B))) ) ) ) ) )).
fof(t14_scmfsa_m,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) ) => ~ r2_hidden(k2_scmfsa_m(A),A) ) )).
fof(t14_scmisort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( 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),k5_numbers) & ! [E] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(E,u1_struct_0(k1_scmfsa_2)) ) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( r8_pboole(u1_struct_0(k1_scmfsa_2),E,k1_scmfsa_m(B)) & F = k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(B)),3) & k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa_9(D,C)),E,F)) = k5_numbers & ! [G] : ( ( v1_ami_2(G) & m1_subset_1(G,u1_struct_0(k1_scmfsa_2)) ) => k1_funct_1(k5_extpro_1(k7_card_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] : ( m1_scmfsa_2(G) => k18_scmfsa_2(k5_extpro_1(k7_card_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) ) ) ) ) ) ) ) ) ) )).
fof(t14_scmp_gcd,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ( r1_tarski(k4_scmp_gcd,A) => ! [C] : ( v1_int_1(C) => ! [D] : ( 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(k5_numbers,C) & r1_xxreal_0(k5_numbers,D) ) => k1_funct_1(k6_extpro_1(2,k1_scmpds_2,A,B),k1_scmp_gcd(9)) = k3_int_2(C,D) ) ) ) ) ) ) )).
fof(t14_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( 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 ) ) ) )).
fof(t14_scmpds_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ! [I] : ( ( v1_ami_2(I) & m1_subset_1(I,u1_struct_0(k1_scmpds_2)) ) => ! [J] : ( v1_int_1(J) => ! [K] : ( 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(k5_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)) = k5_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)) = k5_numbers ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_scmpds_4,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmpds_2)) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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)) ) ) ) )).
fof(t14_scmpds_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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) ) ) ) ) )).
fof(t14_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => ! [D] : ( ( 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(k7_card_1(2),k1_scmring2(A))) & v1_partfun1(D,u1_struct_0(k1_scmring2(A))) ) => ( k1_funct_1(k2_extpro_1(k7_card_1(2),k1_scmring2(A),k6_scmring2(A,B,C),D),k4_struct_0(k1_scmring2(A))) = k4_card_1(k5_memstr_0(k7_card_1(2),k1_scmring2(A),D)) & k2_scmring2(A,k2_extpro_1(k7_card_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] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmring2(A))) ) => ( E != B => k2_scmring2(A,k2_extpro_1(k7_card_1(2),k1_scmring2(A),k6_scmring2(A,B,C),D),E) = k2_scmring2(A,D,E) ) ) ) ) ) ) ) )).
fof(t14_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmring2(A))) => ~ ( k2_compos_0(u1_compos_1(k1_scmring2(A)),B) = 3 & ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmring2(A))) ) => B != k5_scmring2(A,C,D) ) ) ) ) ) )).
fof(t14_scmyciel,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_tarski(k1_scmyciel(A),k1_scmyciel(B)) ) )).
fof(t14_scpinvar,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ( k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),E)) = k5_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)) = k1_nat_1(k5_card_1(C),3) ) ) ) ) ) ) )).
fof(t14_scpisort,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k5_card_1(k1_scpisort(A,B)) = 23 ) ) )).
fof(t14_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t14_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B),C),k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C))) ) ) ) )).
fof(t14_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(A) & v2_comseq_2(B) ) => v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) ) ) )).
fof(t14_seq_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(A) => k1_seq_2(k56_valued_1(k4_ordinal1,k1_numbers,A)) = k9_complex1(k1_seq_2(A)) ) ) )).
fof(t14_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => r2_relset_1(k4_ordinal1,k4_partfun1(A,k1_numbers),k3_seqfunc(A,k5_seqfunc(A,B)),k5_seqfunc(A,k3_seqfunc(A,B))) ) ) )).
fof(t14_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_ordinal1) & v5_valued_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(B,k9_nat_1(k4_ordinal1,A,B)) ) ) )).
fof(t14_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k9_nat_1(k1_numbers,A,C),k9_nat_1(k1_numbers,B,C)) ) => ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k9_nat_1(k1_numbers,k3_series_1(A),C),k9_nat_1(k1_numbers,k3_series_1(B),C)) ) ) ) ) )).
fof(t14_series_3,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => r1_xxreal_0(k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(B,A),k7_xcmplx_0(C,B)),k7_xcmplx_0(A,C)),k2_xcmplx_0(k2_xcmplx_0(k1_newton(k7_xcmplx_0(A,B),3),k1_newton(k7_xcmplx_0(B,C),3)),k1_newton(k7_xcmplx_0(C,A),3))) ) ) ) )).
fof(t14_series_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(k7_xcmplx_0(k9_complex1(k2_xcmplx_0(A,B)),k2_xcmplx_0(1,k9_complex1(k2_xcmplx_0(A,B)))),k2_xcmplx_0(k7_xcmplx_0(k9_complex1(A),k2_xcmplx_0(1,k9_complex1(A))),k7_xcmplx_0(k9_complex1(B),k2_xcmplx_0(1,k9_complex1(B))))) ) ) )).
fof(t14_setfam_1,axiom,( ! [A] : ! [B] : ( r2_setfam_1(A,B) => ( B = k1_xboole_0 | r1_tarski(k1_setfam_1(A),k1_setfam_1(B)) ) ) )).
fof(t14_setlim_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ( v3_funct_1(C) & k3_funct_1(C) = B ) => ! [D] : ( v7_ordinal1(D) => k1_setfam_1(a_3_3_setlim_1(A,C,D)) = B ) ) ) ) )).
fof(t14_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) ) ) )).
fof(t14_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ( v1_binop_1(C,B) & v2_binop_1(C,B) ) => ! [E] : ( m1_subset_1(E,A) => k7_setwiseo(A,B,C,k2_setwiseo(A,E),D) = k3_funct_2(A,B,D,E) ) ) ) ) ) ) )).
fof(t14_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k5_finsub_1(A)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t14_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t14_sfmastr1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_scmfsa6c(D) & v1_sfmastr1(D) & m1_subset_1(D,u1_compos_1(k1_scmfsa_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmfsa_2)) ) => ( ( v7_amistd_1(C,k7_card_1(3),k1_scmfsa_2) | ( r6_scmfsa7b(C,k2_extpro_1(k7_card_1(3),k1_scmfsa_2,D,k1_scmfsa_m(B)),A) & r5_scmfsa7b(C,k2_extpro_1(k7_card_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(k7_card_1(3),k1_scmfsa_2,D,k1_scmfsa_m(B)),A),E) ) ) ) ) ) ) )).
fof(t14_sfmastr2,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) & v1_scmfsa7b(D) ) => ( r1_sfmastr2(B,A,C,D) => ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(E,k1_funct_1(A,C)) => k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k3_sfmastr2(B,A,D,C),E),k4_scmfsa_2(k5_numbers)) = 1 ) ) ) ) ) ) ) )).
fof(t14_sfmastr3,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & ~ v1_scmfsa_m(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmfsa_2)) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & 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] : ( ( v1_relat_1(G) & v4_relat_1(G,k4_ordinal1) & v5_relat_1(G,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(G) & v1_partfun1(G,k4_ordinal1) ) => ( r2_hidden(E,k2_sf_mastr(F)) => ( B = E | k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k1_sfmastr3(G,B,C,D,F,A),k5_numbers),E) = k1_funct_1(A,E) ) ) ) ) ) ) ) ) ) )).
fof(t14_sheffer1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t14_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t14_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)) ) ) ) )).
fof(t14_simplex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_simplex0(B,u1_struct_0(A)) => ! [C] : ( m1_simplex1(C,A,B) => ! [D] : ( m1_simplex1(D,A,C) => m1_simplex1(D,A,B) ) ) ) ) )).
fof(t14_simplex2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t14_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v7_ordinal1(C) => k9_nat_1(k2_numbers,k10_comseq_3(k3_sin_cos(k2_xcmplx_0(B,A))),C) = k9_nat_1(k2_numbers,k10_comseq_3(k10_sin_cos(C,B,A)),C) ) ) ) )).
fof(t14_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ( k6_xcmplx_0(k1_square_1(k1_funct_1(k3_sin_cos2,A)),k1_square_1(k1_funct_1(k1_sin_cos2,A))) = 1 & k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(k3_sin_cos2,A),k1_funct_1(k3_sin_cos2,A)),k3_xcmplx_0(k1_funct_1(k1_sin_cos2,A),k1_funct_1(k1_sin_cos2,A))) = 1 ) ) )).
fof(t14_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,k2_xcmplx_0(A,B)) = k2_xcmplx_0(k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,B)),k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,B))) ) ) )).
fof(t14_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( k17_sin_cos(A) != k5_numbers & k17_sin_cos(B) != k5_numbers & k17_sin_cos(C) != k5_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)) ) ) ) ) )).
fof(t14_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k17_sin_cos(A) != k5_numbers => k1_square_1(k3_sin_cos4(A)) = k2_xcmplx_0(1,k1_square_1(k2_sin_cos4(A))) ) ) )).
fof(t14_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ~ ( ~ r1_xxreal_0(A,k2_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B))) & ~ r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)),A) & r1_xxreal_0(k5_numbers,k19_sin_cos(A)) ) ) ) )).
fof(t14_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(1,k1_square_1(A)) & r1_xxreal_0(1,k1_square_1(k7_xcmplx_0(k3_xcmplx_0(2,A),k2_xcmplx_0(1,k1_square_1(A))))) ) ) )).
fof(t14_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k7_xcmplx_0(k2_xcmplx_0(k2_sin_cos2(A),k2_sin_cos2(B)),k6_xcmplx_0(k2_sin_cos2(A),k2_sin_cos2(B))) = k3_xcmplx_0(k6_sin_cos2(k7_xcmplx_0(k2_xcmplx_0(A,B),2)),k1_sin_cos5(k7_xcmplx_0(k6_xcmplx_0(A,B),2))) ) ) )).
fof(t14_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k2_rcomp_1(k5_numbers,k28_sin_cos)) => k1_funct_1(k27_sin_cos,A) = k2_sin_cos4(A) ) ) )).
fof(t14_sincos10,axiom,( v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos))) )).
fof(t14_sppol_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( k17_euclid(A) != k17_euclid(B) & k18_euclid(A) != k18_euclid(B) & ! [C] : ( 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) ) ) ) ) ) )).
fof(t14_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(B,k3_topreal1(2,A)) & ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_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,k1_nat_1(C,1)))) ) ) ) ) ) )).
fof(t14_sprect_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t14_sprect_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t14_sprect_3,axiom,( ! [A] : ( 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))) ) )).
fof(t14_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(t14_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,1) & r1_xxreal_0(k1_square_1(A),A) ) ) )).
fof(t14_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( ( r2_stacks_1(A,B,C) & r1_stacks_1(A,B) ) => r1_stacks_1(A,C) ) ) ) ) )).
fof(t14_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k4_ordinal1)) => ( r1_tarski(B,k7_card_1(A)) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(k3_nat_1(B),k6_xcmplx_0(A,1)) ) ) ) ) )).
fof(t14_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [D] : ( ( v5_relat_1(D,k3_qc_lang1(A)) & v3_card_1(D,B) & m2_finseq_1(D,k2_qc_lang1(A)) ) => ! [E] : ( m1_subset_1(E,k1_substut1(A)) => k2_sublemma(A,k4_sublemma(B,A,C,D,E)) = k4_cqc_lang(B,A,C,D) ) ) ) ) ) )).
fof(t14_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( 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) ) ) )).
fof(t14_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( m1_subset_1(D,k5_finsub_1(k4_partfun1(A,B))) => ! [E] : ( 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)) ) ) ) ) )).
fof(t14_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k16_substut1(A),k3_qc_lang1(A))) => ! [C] : ( m1_substut1(C,A,B) => ( v3_substut1(B,A) => v7_substut1(k24_substut1(A,B,C),A) ) ) ) ) )).
fof(t14_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( m2_subset_1(E,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t14_supinf_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => k8_supinf_2(k6_supinf_2(A)) = k2_supinf_2(k7_supinf_2(A)) ) )).
fof(t14_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( ~ r1_orders_2(B,D,C) => r1_orders_2(B,k5_algstr_0(B,E,k4_vectsp_1(A,B,k1_symsp_1(A,B,C,D,E),D)),C) ) ) ) ) ) ) )).
fof(t14_sysrel,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(t14_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ( B = k2_tarski(k1_tarski(A),k10_eqrel_1(A)) => m1_taxonom1(B,A) ) ) ) )).
fof(t14_taylor_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k23_sin_cos(k3_power(k4_power,A)) = A ) ) )).
fof(t14_taylor_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & ? [E] : ( v1_xreal_0(E) & r2_hidden(E,k2_rcomp_1(k4_xcmplx_0(A),A)) & r1_xxreal_0(B,k9_complex1(k6_xcmplx_0(k1_funct_1(k22_sin_cos,E),k9_nat_1(k1_numbers,k3_series_1(k1_taylor_2(k22_sin_cos,k2_rcomp_1(k4_xcmplx_0(A),A),E)),D)))) ) ) ) ) ) ) )).
fof(t14_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t14_tdgroup,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_tdgroup(A,B,C,D,E) => r1_tdgroup(A,B,D,C,E) ) ) ) ) ) ) )).
fof(t14_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => v4_tops_1(k1_struct_0(A),A) ) )).
fof(t14_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(t14_tdlat_3,axiom,( ! [A] : ( ( 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) ) ) ) )).
fof(t14_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t14_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( B != k1_xboole_0 => v1_tops_1(B,A) ) ) => v2_tdlat_3(A) ) ) )).
fof(t14_tex_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [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)) & v3_tdlat_3(A) ) => v3_tdlat_3(B) ) ) ) )).
fof(t14_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_tex_3(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t14_tex_4,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t14_tietze,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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] : ( ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t14_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_tsep_1(A,B,C))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ! [F] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t14_toler_1,axiom,( 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))) )).
fof(t14_topalg_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( m1_subset_1(F,u1_struct_0(k14_euclid(E))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k14_euclid(E))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k14_euclid(E))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k14_euclid(E))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k14_euclid(E))) => ! [K] : ( m1_subset_1(K,u1_struct_0(k14_euclid(E))) => ! [L] : ( m1_subset_1(L,u1_struct_0(k15_euclid(E))) => ! [M] : ( m1_subset_1(M,u1_struct_0(k15_euclid(E))) => ! [N] : ( m1_subset_1(N,u1_struct_0(k15_euclid(E))) => ! [O] : ( 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,C),k1_rlvect_1(k15_euclid(E),N,D)) & K = k3_rlvect_1(k15_euclid(E),k1_rlvect_1(k15_euclid(E),M,C),k1_rlvect_1(k15_euclid(E),O,D)) & ~ r1_xxreal_0(A,k3_metric_1(k14_euclid(E),F,G)) & ~ r1_xxreal_0(B,k3_metric_1(k14_euclid(E),H,I)) & C != k5_numbers & D != k5_numbers & r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(k9_complex1(C),A),k3_xcmplx_0(k9_complex1(D),B)),k3_metric_1(k14_euclid(E),J,K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_topalg_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_topmetr(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_topmetr(A,B))) => ! [E] : ( m1_borsuk_2(E,k4_topmetr(A,B),C,D) => ! [F] : ( m1_borsuk_2(F,k4_topmetr(A,B),C,D) => r3_borsuk_2(k4_topmetr(A,B),C,D,E,F) ) ) ) ) ) ) ) )).
fof(t14_topalg_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t14_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t14_topalg_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_tsep_1(B,A) & m1_pre_topc(B,A) ) => ( v1_connsp_2(A) => v1_connsp_2(B) ) ) ) )).
fof(t14_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t14_topdim_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k4_topdim_1(k1_compts_1(A)) = k5_numbers ) )).
fof(t14_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t14_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => k2_waybel23(A) = k1_card_1(u1_struct_0(A)) ) )).
fof(t14_topgen_3,axiom,( ! [A] : ( 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))) ) ) )).
fof(t14_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) ) ) )).
fof(t14_topgen_5,axiom,( ! [A] : ! [B] : ( r2_hidden(k10_finseq_1(A,B),k1_topgen_5) <=> ( r2_hidden(A,k1_numbers) & B = k5_numbers ) ) )).
fof(t14_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(t14_topmetr,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v9_metric_1(B) & l1_metric_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(B)))) => ( D = k8_metric_1(B,C,A) => v3_pre_topc(D,k3_pcomps_1(B)) ) ) ) ) ) )).
fof(t14_topmetr3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [E] : ( ( ~ 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 ) ) ) ) ) ) )).
fof(t14_topreal1,axiom,( k1_topreal1 = a_0_4_topreal1 )).
fof(t14_topreal3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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),k7_xcmplx_0(k2_xcmplx_0(k18_euclid(A),k18_euclid(B)),2)),k1_rltopsp1(k15_euclid(2),A,B)) ) ) ) ) )).
fof(t14_topreal4,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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(k7_xcmplx_0(k2_xcmplx_0(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))) ) ) ) ) ) )).
fof(t14_topreal5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( v1_topreal2(A) => ! [B] : ( v1_xreal_0(B) => ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & r2_hidden(C,A) & k18_euclid(C) != B ) ) ) ) )).
fof(t14_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,k5_numbers) => r2_hidden(A,k2_rcomp_1(k6_xcmplx_0(A,B),k2_xcmplx_0(A,B))) ) ) ) )).
fof(t14_topreal7,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ( ( k3_finseq_1(A) = k3_finseq_1(C) & k3_finseq_1(B) = k3_finseq_1(D) ) => k12_rvsum_1(k8_rvsum_1(k8_finseq_1(k1_numbers,A,B),k8_finseq_1(k1_numbers,C,D))) = k8_finseq_1(k1_numbers,k12_rvsum_1(k8_rvsum_1(A,C)),k12_rvsum_1(k8_rvsum_1(B,D))) ) ) ) ) ) )).
fof(t14_topreal8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( 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) ) ) ) )).
fof(t14_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => r1_tarski(k1_topreal9(A,C,B),k2_topreal9(A,C,B)) ) ) ) )).
fof(t14_topreala,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(t14_toprealb,axiom,( ! [A] : ( 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) = k5_numbers ) ) )).
fof(t14_toprealc,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => k1_funct_7(k16_euclid(B),A,k5_numbers) = k16_euclid(B) ) )).
fof(t14_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) )).
fof(t14_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t14_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t14_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_tops_1(B,A) <=> ! [C] : ( 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)) ) ) ) ) ) )).
fof(t14_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t14_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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(C,A) & v7_transgeo(D,A) & r2_funct_2(u1_struct_0(A),u1_struct_0(A),B,k1_transgeo(u1_struct_0(A),C,C)) & r2_funct_2(u1_struct_0(A),u1_struct_0(A),B,k1_transgeo(u1_struct_0(A),D,D)) ) => r2_funct_2(u1_struct_0(A),u1_struct_0(A),C,D) ) ) ) ) ) )).
fof(t14_treal_1,axiom,( r2_funct_2(u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k4_topmetr(k5_numbers,1)),k4_treal_1(k5_numbers,1,k1_treal_1(k5_numbers,1),k2_treal_1(k5_numbers,1)),k3_struct_0(k4_topmetr(k5_numbers,1))) )).
fof(t14_trees_1,axiom,( k1_trees_1(k1_xboole_0) = k1_xboole_0 )).
fof(t14_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => A = k3_tarski(a_1_0_trees_2(A)) ) )).
fof(t14_trees_3,axiom,( ! [A] : ( v3_trees_3(k1_tarski(A)) <=> ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) ) )).
fof(t14_trees_4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ! [C] : ( ( 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)) ) ) )).
fof(t14_trees_9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ( r2_hidden(A,k6_trees_9(B)) <=> ? [C] : ( m1_trees_1(C,k9_xtuple_0(B)) & A = k4_tarski(C,k5_trees_2(B,C)) ) ) ) )).
fof(t14_trees_a,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ! [C] : ( m4_trees_1(C,k9_xtuple_0(A)) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ~ ( r2_hidden(D,k9_xtuple_0(k3_trees_a(A,C,B))) & r2_hidden(D,a_3_1_trees_a(A,B,C)) & ! [E] : ( m1_trees_1(E,k9_xtuple_0(A)) => ! [F] : ( m1_trees_1(F,k9_xtuple_0(B)) => ~ ( D = k8_finseq_1(k4_ordinal1,E,F) & r2_hidden(E,C) & k1_funct_1(k3_trees_a(A,C,B),D) = k1_funct_1(B,F) ) ) ) ) ) ) ) ) )).
fof(t14_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t14_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t14_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v6_pre_topc(C) & m1_pre_topc(C,A) ) => ( m1_pre_topc(B,C) => v6_pre_topc(B) ) ) ) ) )).
fof(t14_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(t14_turing_1,axiom,( k1_funct_1(k13_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers)) = k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers,1) & k1_funct_1(k13_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,1)) = k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,1,k5_numbers,1) & k1_funct_1(k13_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,1,1)) = k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,1,1,1) & k1_funct_1(k13_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,1,k5_numbers)) = k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,2,1,1) & k1_funct_1(k13_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,2,1)) = k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,2,1,1) & k1_funct_1(k13_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,2,k5_numbers)) = k3_xtuple_0(3,k5_numbers,k4_xcmplx_0(1)) & k1_funct_1(k13_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,3,1)) = k3_xtuple_0(4,k5_numbers,k4_xcmplx_0(1)) & k1_funct_1(k13_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,4,1)) = k3_xtuple_0(4,1,k4_xcmplx_0(1)) & k1_funct_1(k13_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,4,k5_numbers)) = k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,5,k5_numbers,k5_numbers) )).
fof(t14_twoscomp,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( 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)) ) ) ) ) )).
fof(t14_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t14_unialg_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_unialg_3(A))) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t14_uniroots,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k1_complfld)) => ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(B,k4_finseq_1(A)) => v1_int_1(k1_funct_1(A,B)) ) ) => v1_int_1(k4_rlvect_1(k1_complfld,A)) ) ) )).
fof(t14_uproots,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_uproots(B,A) <=> ~ r1_xxreal_0(k1_algseq_1(A,B),k5_numbers) ) ) ) )).
fof(t14_urysohn1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_subset_1(B,k1_numbers,k1_urysohn1(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t14_urysohn2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,k5_numbers) => ! [C] : ( ( ~ 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( D = k7_supinf_2(A) & E = k8_supinf_2(A) ) => ( k7_supinf_2(C) = k3_xcmplx_0(B,D) & k8_supinf_2(C) = k3_xcmplx_0(B,E) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_urysohn3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m2_urysohn3(D,A,B,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( ( ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(k6_numbers)) ) => ( F = k6_urysohn3(A,B,C,D,E) => ! [G] : ( m1_subset_1(G,k6_numbers) => ( G = 1 => ( r1_xxreal_0(k1_supinf_2,k8_supinf_2(F)) & r1_xxreal_0(k8_supinf_2(F),G) ) ) ) ) ) ) ) ) ) ) )).
fof(t14_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_funct_2(C,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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 ) ) ) ) ) )).
fof(t14_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v3_funct_1(A) & v2_valued_0(A) ) => ? [B] : ( v1_xxreal_0(B) & ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => k1_funct_1(A,C) = B ) ) ) )).
fof(t14_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( k9_xtuple_0(C) = k9_xtuple_0(k45_valued_1(A,B)) & ! [D] : ( 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) ) ) ) ) )).
fof(t14_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(t14_vectsp10,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_vectsp_4(D,A,B) => ( ~ r1_struct_0(D,C) => ! [E] : ( 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] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t14_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( 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))))) ) ) ) ) ) )).
fof(t14_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t14_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( B != k4_struct_0(A) => k11_algstr_0(A,k11_algstr_0(A,B)) = B ) ) ) )).
fof(t14_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_vectsp_4(E,A,B) => ! [F] : ( m1_subset_1(F,u1_struct_0(E)) => ( F = D => k4_vectsp_1(A,E,C,F) = k4_vectsp_1(A,B,C,D) ) ) ) ) ) ) ) )).
fof(t14_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t14_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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] : ( m2_vectsp_6(D,A,B,C) => r2_hidden(k4_vectsp_6(A,B,D),C) ) ) ) ) ) ) )).
fof(t14_vectsp_7,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t14_vectsp_8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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)) ) ) ) ) ) )).
fof(t14_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v1_vectsp_7(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r2_hidden(D,C) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t14_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => r2_relset_1(A,u1_struct_0(B),k4_vfunct_1(A,B,C,k3_xcmplx_0(D,E)),k4_vfunct_1(A,B,k4_vfunct_1(A,B,C,E),D)) ) ) ) ) ) )).
fof(t14_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => r2_relset_1(A,u1_struct_0(B),k2_vfunct_2(A,B,C,k3_xcmplx_0(D,E)),k2_vfunct_2(A,B,k2_vfunct_2(A,B,C,E),D)) ) ) ) ) ) )).
fof(t14_waybel10,axiom,( ! [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] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t14_waybel12,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( 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 ) ) )).
fof(t14_waybel13,axiom,( ! [A] : ( ( 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(k1_yellow_1(k7_waybel_0(A))) ) )).
fof(t14_waybel14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v6_waybel_6(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t14_waybel15,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(t14_waybel16,axiom,( ! [A] : v1_yellow_0(k1_yellow_1(k8_waybel_0(k2_yellow_1(A)))) )).
fof(t14_waybel17,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t14_waybel18,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k2_yellow_1(A)),u1_struct_0(k4_yellow_1(A,k7_funcop_1(A,k2_yellow_1(k1_tarski(k5_numbers)))))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_yellow_1(A)),u1_struct_0(k4_yellow_1(A,k7_funcop_1(A,k2_yellow_1(k1_tarski(k5_numbers)))))))) & v23_waybel_0(B,k2_yellow_1(A),k4_yellow_1(A,k7_funcop_1(A,k2_yellow_1(k1_tarski(k5_numbers))))) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k1_funct_1(B,C) = k5_funct_3(C,A) ) ) ) )).
fof(t14_waybel19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)))) ) ) ) ) )).
fof(t14_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(t14_waybel21,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ( v5_yellow_0(B,A) <=> ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t14_waybel22,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( 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(k1_yellow_1(k8_waybel_0(k2_yellow_1(A)))),u1_struct_0(B),k2_waybel22(A,B,C),k1_waybel22(A)) = C ) ) )).
fof(t14_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_yellow_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( C = D => r1_tarski(k6_waybel_0(B,D),k6_waybel_0(A,C)) ) ) ) ) ) )).
fof(t14_waybel24,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_lattice3(C) & v2_lattice3(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(t14_waybel25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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(k4_yellow_1(A,k7_funcop_1(A,k1_waybel25(B)))),u1_orders_2(k4_yellow_1(A,k7_funcop_1(A,k1_waybel25(B))))) ) ) )).
fof(t14_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t14_waybel27,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_yellow_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_yellow_1(A,B))) => ( r1_orders_2(k5_yellow_1(A,B),C,D) <=> ! [E] : ( m1_subset_1(E,A) => r1_orders_2(B,k1_waybel27(A,B,C,E),k1_waybel27(A,B,D,E)) ) ) ) ) ) ) )).
fof(t14_waybel28,axiom,( ! [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] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( C = k1_waybel11(A,B) & ! [D] : ( ( 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] : ( m2_yellow_6(D,A,B) => C = k1_waybel11(A,D) ) ) ) ) ) )).
fof(t14_waybel29,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & l1_waybel_9(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t14_waybel30,axiom,( ! [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_waybel_2(A) & l1_waybel_9(A) ) => ! [B] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t14_waybel31,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_waybel31(A,k1_struct_0(A),B) = k2_waybel_3(A,B) ) ) )).
fof(t14_waybel32,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t14_waybel33,axiom,( ! [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] : ( ( ~ v1_xboole_0(B) & v1_subset_1(B,u1_struct_0(k2_yellow_1(k2_struct_0(A)))) & v2_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))))) ) => r2_hidden(k3_yellow19(A,k2_struct_0(A),B),k6_yellow_6(A)) ) ) )).
fof(t14_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_waybel34(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_waybel34(A))) => ! [D] : ( 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))))) ) ) ) ) ) )).
fof(t14_waybel35,axiom,( ! [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] : ( ( 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] : ( m1_waybel35(C,A,B) => ( ( v2_waybel35(C,A,B) & v8_waybel_4(B,A) ) => r1_waybel35(A,C,B) ) ) ) ) )).
fof(t14_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k3_waybel_0(A,B) = a_2_0_waybel_0(A,B) ) ) )).
fof(t14_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(t14_waybel_2,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t14_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t14_waybel_4,axiom,( ! [A] : ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r2_hidden(A,k6_waybel_4(B,D,C)) <=> r2_hidden(k4_tarski(D,A),C) ) ) ) ) )).
fof(t14_waybel_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,C) & v1_funct_1(D) & v1_partfun1(D,C) ) => ! [E] : ( 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] : ( m1_subset_1(F,C) => A != k4_yellow_2(B,k1_waybel_5(C,u1_struct_0(B),D,E,F)) ) ) & ( ? [F] : ( 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] : ( m1_subset_1(F,C) => A != k5_yellow_2(B,k1_waybel_5(C,u1_struct_0(B),D,E,F)) ) ) & ( ? [F] : ( 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))) ) ) ) ) ) ) )).
fof(t14_waybel_6,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( ~ r3_orders_2(A,C,B) & ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t14_waybel_8,axiom,( ! [A] : ( l1_orders_2(A) => ! [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)) & v5_orders_2(A) ) => v5_orders_2(B) ) ) ) )).
fof(t14_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t14_weddwitt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,k3_weddwitt(A)) => ( ( v2_funct_1(B) & k2_relset_1(k3_weddwitt(A),B) = k3_weddwitt(A) ) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( ( k3_finseq_1(C) = k3_finseq_1(B) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k4_finseq_1(C)) => k1_funct_1(C,D) = k1_card_1(k1_funct_1(B,D)) ) ) ) => k7_group_1(A) = k2_wsierp_1(C) ) ) ) ) ) )).
fof(t14_weierstr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t14_wellord1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => r1_tarski(k1_wellord1(k2_wellord1(C,B),A),k1_wellord1(C,A)) ) )).
fof(t14_wellord2,axiom,( ! [A] : r8_relat_2(k1_wellord2(A),A) )).
fof(t14_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_nat_d(A,B) => r1_nat_d(k1_newton(A,C),k1_newton(B,C)) ) ) ) ) )).
fof(t14_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r1_tarski(B,A) & r1_tarski(C,A) & ! [D] : ( ( r1_tarski(B,D) & r1_tarski(C,D) ) => r1_tarski(A,D) ) ) => A = k2_xboole_0(B,C) ) )).
fof(t14_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k4_xboolean(A,k6_xboolean(A,B)) = k4_xboolean(A,B) ) ) )).
fof(t14_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,A) = k5_numbers ) )).
fof(t14_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t14_xtuple_0,axiom,( ! [A] : ! [B] : ~ ( r2_hidden(A,k12_xtuple_0(B)) & ! [C] : ! [D] : ~ r2_hidden(k3_xtuple_0(C,A,D),B) ) )).
fof(t14_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ~ ( ~ r2_hidden(A,k1_numbers) & A != k1_xxreal_0 & A != k2_xxreal_0 ) ) )).
fof(t14_xxreal_1,axiom,( ! [A] : ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(A,k4_xxreal_1(B,C)) => ( r2_hidden(A,k2_xxreal_1(B,C)) & A != B ) ) ) ) )).
fof(t14_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k2_xxreal_2(k2_tarski(A,B)) = k3_xxreal_0(A,B) ) ) )).
fof(t14_xxreal_3,axiom,( ! [A] : ( 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 ) ) ) )).
fof(t14_yellow10,axiom,( ! [A] : ( ( v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t14_yellow12,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & v2_waybel_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t14_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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)) ) ) ) )).
fof(t14_yellow14,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ( ( r5_waybel_1(A,B) & v1_yellow_0(A) ) => v1_yellow_0(B) ) ) ) )).
fof(t14_yellow15,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t14_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) ) )).
fof(t14_yellow17,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ( v1_compts_1(A) <=> ! [B] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t14_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t14_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_subset_1(B,u1_struct_0(k2_yellow_1(k2_struct_0(A)))) & v2_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))))) ) => B = k2_yellow19(A,k3_yellow19(A,k2_struct_0(A),B)) ) ) )).
fof(t14_yellow20,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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)) ) ) ) )).
fof(t14_yellow21,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( ( 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) ) ) ) ) ) )).
fof(t14_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [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] : ( ( r1_yellow_0(A,C) => r1_yellow_0(B,C) ) & ( r2_yellow_0(A,C) => r2_yellow_0(B,C) ) ) ) ) ) )).
fof(t14_yellow_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( r2_hidden(k3_tarski(A),A) => k4_yellow_0(k1_yellow_1(A)) = k3_tarski(A) ) ) )).
fof(t14_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t14_yellow_3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ( ~ v2_struct_0(k3_yellow_3(A,B)) => ( ~ v2_struct_0(A) & ~ v2_struct_0(B) ) ) ) ) )).
fof(t14_yellow_4,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t14_yellow_5,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t14_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => m2_yellow_6(B,A,B) ) ) )).
fof(t14_yellow_7,axiom,( ! [A] : ( l1_orders_2(A) => ! [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_lattice3(A) ) => v2_lattice3(B) ) ) ) )).
fof(t14_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ( r1_tarski(B,u1_pre_topc(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( 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)))) ) ) ) ) )).
fof(t14_yellow_9,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( r2_hidden(A,B) => ! [C] : ( r2_hidden(C,k2_cantor_1(A,B)) <=> ? [D] : ( ~ 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) ) ) ) ) )).
fof(t14_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ! [D] : ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t14_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( k3_finseq_1(A) = 3 => v7_zf_lang(A) ) ) )).
fof(t14_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ! [E] : ( m2_subset_1(E,k4_ordinal1,k1_zf_lang) => ! [F] : ( m2_subset_1(F,k4_ordinal1,k1_zf_lang) => ( k14_zf_lang(C,E,A) = k14_zf_lang(D,F,B) => ( C = D & E = F & A = B ) ) ) ) ) ) ) ) )).
fof(t14_zf_model,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ( r1_zf_model(A,B,C) <=> ~ r1_zf_model(A,B,k6_zf_lang(C)) ) ) ) ) )).
fof(t14_zf_refle,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( v3_ordinal1(B) & m1_subset_1(B,A) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t14_zfmisc_1,axiom,( ! [A] : ! [B] : ( k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A) <=> A != B ) )).
fof(t14_zfmodel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_zfmodel1(B,A) => r2_zfmodel1(B,A) ) ) ) )).
fof(t14_zfmodel2,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( ( 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(k5_numbers),k8_zf_lang(k2_zf_lang(4),k12_zf_lang(D,k4_zf_lang(k2_zf_lang(4),k2_zf_lang(k5_numbers))))))) => ( r2_hidden(k2_zf_lang(k5_numbers),k2_zf_model(D)) | r2_hidden(A,k4_zf_lang1(D)) | r2_hidden(B,k2_zf_model(D)) | A = k2_zf_lang(k5_numbers) | A = k2_zf_lang(3) | A = k2_zf_lang(4) | ( ~ r2_hidden(k2_zf_lang(k5_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(k5_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(k5_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)))) ) ) ) ) ) ) ) ) )).
fof(t14_zfrefle1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_ordinal2(B) ) => ( v2_ordinal2(B) => v2_ordinal2(k1_ordinal3(A,B)) ) ) ) )).
fof(t14_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t14_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k4_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_numbers))) ) => k20_zmodul02(A,k6_finseq_1(u1_struct_0(A)),B) = k6_finseq_1(u1_struct_0(A)) ) ) )).
fof(t14_zmodul03,axiom,( ! [A] : ( ( ~ 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) & v1_zmodul03(A) & l1_zmodul01(A) ) => ! [B] : ( m1_zmodul03(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_struct_0(k33_zmodul02(A,B),C) ) ) ) )).
fof(t150_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k38_abcmiz_1(A))) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_abcmiz_1,k34_abcmiz_1(A)))) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t150_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( 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) ) ) ) )).
fof(t150_group_2,axiom,( ! [A] : ( ( ~ 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 ) )).
fof(t150_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t150_relat_1,axiom,( ! [A] : ! [B] : ~ ( 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 ) ) )).
fof(t150_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t150_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k2_xcmplx_0(A,B) = k6_xcmplx_0(A,k4_xcmplx_0(B)) ) ) )).
fof(t150_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(A,1) & r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(B,1) & k3_xcmplx_0(A,B) = 1 ) => A = 1 ) ) ) )).
fof(t150_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(C,A) & r1_xxreal_0(D,B) ) => k3_xboole_0(k2_xxreal_1(C,D),k2_xxreal_1(A,B)) = k2_xxreal_1(A,D) ) ) ) ) ) )).
fof(t150_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,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)) ) ) ) ) )).
fof(t150_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m2_zmodul01(D,A,B) & r2_hidden(C,D) ) ) ) ) )).
fof(t151_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m3_abcmiz_1(B,A) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_abcmiz_1,k34_abcmiz_1(A)))) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t151_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) ) => k3_finseq_1(B) = A ) ) )).
fof(t151_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( r1_xxreal_0(C,k3_finseq_1(B)) => k19_glib_001(A,B,C) = C ) ) => v5_glib_001(B,A) ) ) ) )).
fof(t151_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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 ) ) ) )).
fof(t151_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t151_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( ( k9_xtuple_0(B) = k1_xboole_0 & k9_xtuple_0(A) = k1_xboole_0 ) => B = A ) ) ) )).
fof(t151_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)))))) ) ) ) ) ) )).
fof(t151_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => A = k6_xcmplx_0(A,k2_xcmplx_0(B,k4_xcmplx_0(B))) ) ) )).
fof(t151_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(1,B) ) => r1_xxreal_0(A,k3_xcmplx_0(A,B)) ) ) ) )).
fof(t151_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(B,D) ) => k3_xboole_0(k2_xxreal_1(C,D),k2_xxreal_1(A,B)) = k2_xxreal_1(C,B) ) ) ) ) ) )).
fof(t151_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => r1_tarski(k2_zf_model(A),k3_zf_lang1(A)) ) )).
fof(t151_zmodul01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_numbers) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( 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) ) ) ) ) ) )).
fof(t152_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(1,D) & r1_xxreal_0(D,A) & k1_funct_1(k7_finseq_1(B,C),D) != k1_funct_1(B,D) ) ) ) ) ) )).
fof(t152_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(C,A) => r2_hidden(k3_xxreal_3(B,C),k18_member_1(A,B)) ) ) ) ) )).
fof(t152_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( ( k10_xtuple_0(B) = k1_xboole_0 & k10_xtuple_0(A) = k1_xboole_0 ) => B = A ) ) ) )).
fof(t152_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t152_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( k6_xcmplx_0(A,C) = k2_xcmplx_0(B,k4_xcmplx_0(C)) => A = B ) ) ) ) )).
fof(t152_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(B,1) ) => r1_xxreal_0(A,k3_xcmplx_0(A,B)) ) ) ) )).
fof(t152_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(A,C) & ~ r1_xxreal_0(B,D) & k3_xboole_0(k3_xxreal_1(C,D),k2_xxreal_1(A,B)) != k1_xxreal_1(A,D) ) ) ) ) ) )).
fof(t152_zf_lang1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ! [E] : ( m2_subset_1(E,k4_ordinal1,k1_zf_lang) => ! [F] : ( m2_subset_1(F,k4_ordinal1,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 ) ) ) ) ) ) ) ) ) )).
fof(t152_zmodul01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_numbers) => ( C = k5_numbers => k2_binop_1(k4_numbers,u1_struct_0(A),u1_struct_0(A),k12_zmodul01(A),C,B) = k4_struct_0(A) ) ) ) ) )).
fof(t153_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,B) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_card_1(D,A) & v1_finseq_1(D) ) => ! [E] : ( v7_ordinal1(E) => ~ ( r1_xxreal_0(1,E) & r1_xxreal_0(E,A) & k1_funct_1(k7_finseq_1(C,D),k2_xcmplx_0(B,E)) != k1_funct_1(D,E) ) ) ) ) ) ) )).
fof(t153_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v6_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ! [D] : ( 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) ) ) ) ) )).
fof(t153_group_2,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t153_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => k18_member_1(A,B) = a_2_10_member_1(A,B) ) ) )).
fof(t153_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => ( k9_xtuple_0(B) = k9_xtuple_0(A) => k9_xtuple_0(k3_relat_1(C,B)) = k9_xtuple_0(k3_relat_1(C,A)) ) ) ) ) )).
fof(t153_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t153_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( k6_xcmplx_0(C,A) = k2_xcmplx_0(C,k4_xcmplx_0(B)) => A = B ) ) ) ) )).
fof(t153_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(B,1) ) => r1_xxreal_0(k3_xcmplx_0(A,B),A) ) ) ) )).
fof(t153_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(B,D) ) => k3_xboole_0(k3_xxreal_1(C,D),k2_xxreal_1(A,B)) = k4_xxreal_1(C,B) ) ) ) ) ) )).
fof(t153_zf_lang1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ? [E] : ( m2_subset_1(E,k4_ordinal1,k1_zf_lang) & ? [F] : ( m2_subset_1(F,k4_ordinal1,k1_zf_lang) & k5_zf_lang1(k4_zf_lang(A,B),C,D) = k4_zf_lang(E,F) ) ) ) ) ) ) )).
fof(t153_zmodul01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k2_binop_1(k4_ordinal1,u1_struct_0(A),u1_struct_0(A),k3_binom(A),B,k4_struct_0(A)) = k4_struct_0(A) ) ) )).
fof(t154_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k1_relset_1(k4_ordinal1,A)) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,B) ) => r2_hidden(C,k1_relset_1(k4_ordinal1,A)) ) ) ) ) ) )).
fof(t154_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( r1_glib_000(A,C,C,B) => v8_glib_001(k2_glib_001(A,C,C,B),A) ) ) )).
fof(t154_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t154_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ~ ( r2_hidden(C,k18_member_1(A,B)) & ! [D] : ( m1_subset_1(D,k6_numbers) => ~ ( C = k3_xxreal_3(B,D) & r2_hidden(D,A) ) ) ) ) ) )).
fof(t154_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => ( k10_xtuple_0(B) = k10_xtuple_0(A) => k10_xtuple_0(k3_relat_1(B,C)) = k10_xtuple_0(k3_relat_1(A,C)) ) ) ) ) )).
fof(t154_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t154_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t154_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(1,B) ) => r1_xxreal_0(k3_xcmplx_0(A,B),A) ) ) ) )).
fof(t154_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(D,B) => ( r1_xxreal_0(A,C) | k3_xboole_0(k4_xxreal_1(C,D),k2_xxreal_1(A,B)) = k2_xxreal_1(A,D) ) ) ) ) ) ) )).
fof(t154_zf_lang1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ! [E] : ( m2_subset_1(E,k4_ordinal1,k1_zf_lang) => ! [F] : ( m2_subset_1(F,k4_ordinal1,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 ) ) ) ) ) ) ) ) ) )).
fof(t154_zmodul01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( 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) ) ) )).
fof(t155_finseq_3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) ) => ( C = k1_tarski(k4_tarski(B,A)) => k15_finseq_1(C) = k9_finseq_1(A) ) ) ) )).
fof(t155_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ! [E] : ~ ( r1_glib_000(A,D,E,C) & r2_hidden(C,k14_glib_001(A,B)) & v8_glib_001(B,A) & ! [F] : ( m3_glib_001(F,A) => ~ ( r1_glib_001(A,D,E,F) & ~ r2_hidden(C,k14_glib_001(A,F)) ) ) ) ) ) )).
fof(t155_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(t155_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( v1_xreal_0(C) => ( r1_tarski(k18_member_1(A,C),k18_member_1(B,C)) => r1_tarski(A,B) ) ) ) ) )).
fof(t155_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( 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) ) ) ) )).
fof(t155_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t155_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t155_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,1) & r1_xxreal_0(k3_xcmplx_0(A,B),A) ) ) ) )).
fof(t155_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(B,D) ) => k3_xboole_0(k4_xxreal_1(C,D),k2_xxreal_1(A,B)) = k4_xxreal_1(C,B) ) ) ) ) ) )).
fof(t155_zf_lang1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ? [E] : ( m2_subset_1(E,k4_ordinal1,k1_zf_lang) & ? [F] : ( m2_subset_1(F,k4_ordinal1,k1_zf_lang) & k5_zf_lang1(k5_zf_lang(A,B),C,D) = k5_zf_lang(E,F) ) ) ) ) ) ) )).
fof(t155_zmodul01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t156_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) ) => k5_card_1(A) = k3_finseq_1(k15_finseq_1(A)) ) )).
fof(t156_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => m4_glib_001(B,A,B) ) ) )).
fof(t156_group_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_finset_1(B) => ~ ( ! [C] : ~ ( r2_hidden(C,B) & ! [D] : ( v1_finset_1(D) => ~ ( D = C & k5_card_1(D) = A & ! [E] : ( r2_hidden(E,B) => ( C = E | ( r2_wellord2(C,E) & r1_xboole_0(C,E) ) ) ) ) ) ) & ! [C] : ( v1_finset_1(C) => ~ ( C = k3_tarski(B) & k5_card_1(C) = k2_nat_1(A,k5_card_1(B)) ) ) ) ) ) )).
fof(t156_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( v1_xreal_0(C) => ( k18_member_1(A,C) = k18_member_1(B,C) => A = B ) ) ) ) )).
fof(t156_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => ( k5_relat_1(B,A) = k5_relat_1(C,A) => k7_relat_1(B,A) = k7_relat_1(C,A) ) ) ) )).
fof(t156_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t156_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t156_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(1,B) & r1_xxreal_0(k3_xcmplx_0(A,B),A) ) ) ) )).
fof(t156_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(C,A) & r1_xxreal_0(D,B) ) => k3_xboole_0(k3_xxreal_1(C,D),k3_xxreal_1(A,B)) = k3_xxreal_1(A,D) ) ) ) ) ) )).
fof(t156_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ( k6_zf_lang(A) = k5_zf_lang1(k6_zf_lang(B),C,D) <=> A = k5_zf_lang1(B,C,D) ) ) ) ) ) )).
fof(t156_zmodul01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(C,D) & E = k6_xcmplx_0(D,C) ) => k2_binop_1(k4_ordinal1,u1_struct_0(A),u1_struct_0(A),k3_binom(A),E,B) = k5_algstr_0(A,k2_binop_1(k4_ordinal1,u1_struct_0(A),u1_struct_0(A),k3_binom(A),D,B),k2_binop_1(k4_ordinal1,u1_struct_0(A),u1_struct_0(A),k3_binom(A),C,B)) ) ) ) ) ) ) )).
fof(t157_finseq_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_finseq_1(B) ) => ~ ( k15_finseq_1(B) = k9_finseq_1(A) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => B != k1_tarski(k4_tarski(C,A)) ) ) ) )).
fof(t157_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m4_glib_001(C,A,B) => ! [D] : ( m4_glib_001(D,A,C) => m4_glib_001(D,A,B) ) ) ) ) )).
fof(t157_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t157_relat_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) ) => ! [C] : ( r2_hidden(C,k10_xtuple_0(B)) => r2_hidden(C,A) ) ) )).
fof(t157_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))))) ) ) ) ) ) )).
fof(t157_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t157_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,B) & r1_xxreal_0(A,k3_xcmplx_0(A,B)) ) ) ) )).
fof(t157_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(B,D) ) => k3_xboole_0(k3_xxreal_1(C,D),k3_xxreal_1(A,B)) = k3_xxreal_1(C,B) ) ) ) ) ) )).
fof(t157_zmodul01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k4_algstr_0(A,k2_binop_1(k4_ordinal1,u1_struct_0(A),u1_struct_0(A),k3_binom(A),C,B)) = k2_binop_1(k4_ordinal1,u1_struct_0(A),u1_struct_0(A),k3_binom(A),C,k4_algstr_0(A,B)) ) ) ) )).
fof(t158_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ! [E] : ( m4_glib_001(B,A,C) => ( r1_glib_001(A,D,E,B) <=> r1_glib_001(A,D,E,C) ) ) ) ) ) )).
fof(t158_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t158_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(C,A) => k9_relat_1(k2_zfmisc_1(A,B),C) = B ) )).
fof(t158_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))))) ) ) ) ) ) )).
fof(t158_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t158_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,1) & r1_xxreal_0(A,k3_xcmplx_0(A,B)) ) ) ) )).
fof(t158_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(C,A) & r1_xxreal_0(D,B) ) => k3_xboole_0(k4_xxreal_1(C,D),k3_xxreal_1(A,B)) = k4_xxreal_1(A,D) ) ) ) ) ) )).
fof(t158_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( m2_subset_1(E,k4_ordinal1,k1_zf_lang) => ! [F] : ( m2_subset_1(F,k4_ordinal1,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) ) ) ) ) ) ) ) ) )).
fof(t158_zmodul01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_numbers) => ! [D] : ( m1_subset_1(D,k4_numbers) => ( r2_hidden(C,k4_ordinal1) => ( r2_hidden(D,k4_ordinal1) | 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)) ) ) ) ) ) ) )).
fof(t159_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t159_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t159_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r2_hidden(k4_tarski(A,B),C) <=> r2_hidden(B,k9_relat_1(C,A)) ) ) )).
fof(t159_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))))) ) ) ) ) ) )).
fof(t159_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t159_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(1,B) ) => r1_xxreal_0(1,k3_xcmplx_0(A,B)) ) ) ) )).
fof(t159_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(A,C) => ( r1_xxreal_0(D,B) | k3_xboole_0(k4_xxreal_1(C,D),k3_xxreal_1(A,B)) = k3_xxreal_1(C,B) ) ) ) ) ) ) )).
fof(t159_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ! [E] : ( m2_subset_1(E,k4_ordinal1,k1_zf_lang) => ( E != C => ( k8_zf_lang(E,A) = k6_zf_lang1(k8_zf_lang(E,B),C,D) <=> A = k6_zf_lang1(B,C,D) ) ) ) ) ) ) ) )).
fof(t159_zmodul01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_numbers) => ! [D] : ( 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)) ) ) ) ) )).
fof(t15_abcmiz_0,axiom,( ! [A] : ( ( ~ v4_abcmiz_0(A) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_abcmiz_0(A,B) = a_2_1_abcmiz_0(A,B) ) ) )).
fof(t15_abcmiz_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( ( k1_funct_1(A,k5_numbers) = a_0_0_abcmiz_1 & ! [B] : ( v7_ordinal1(B) => k1_funct_1(A,k1_nat_1(B,1)) = a_2_0_abcmiz_1(A,B) ) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_abcmiz_1)) ) => ? [C] : ( m1_subset_1(C,k4_ordinal1) & r1_tarski(B,k1_funct_1(A,C)) ) ) ) ) )).
fof(t15_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & v1_abcmiz_a(A) & l1_msualg_1(A) ) => ! [B] : ( 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))))) ) ) ) )).
fof(t15_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( k2_absvalue(A) = k4_xcmplx_0(1) & r1_xxreal_0(k5_numbers,A) ) ) )).
fof(t15_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r2_hidden(D,k2_aff_1(A,B,C)) & r2_hidden(E,k2_aff_1(A,B,C)) ) => ( D = E | r1_tarski(k2_aff_1(A,D,E),k2_aff_1(A,B,C)) ) ) ) ) ) ) ) )).
fof(t15_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v11_aff_2(A) => v13_aff_2(A) ) ) )).
fof(t15_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r5_aff_1(A,B,C) => k1_aff_4(A,B,C) = C ) ) ) ) )).
fof(t15_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ( k1_afinsq_1(A) = k5_numbers <=> A = k1_xboole_0 ) ) )).
fof(t15_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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(k1_nat_1(C,1),B)) ) ) ) ) )).
fof(t15_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( r2_hidden(B,k8_afproj(A)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & B = k6_afproj(A,C) & v1_aff_4(C,A) ) ) ) )).
fof(t15_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t15_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(t15_algspec1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(A,k9_xtuple_0(B)) => k1_algspec1(A,B) = k5_relat_1(B,A) ) ) )).
fof(t15_algstr_1,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(t15_algstr_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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))) ) ) ) ) ) )).
fof(t15_altcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_subset_1(F,k1_altcat_1(A,B,C)) => ! [G] : ( m1_subset_1(G,k1_altcat_1(A,C,D)) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t15_altcat_2,axiom,( ! [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) & 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)) ) ) )).
fof(t15_altcat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( m1_subset_1(D,k1_altcat_1(A,B,C)) & v1_altcat_3(D,A,B,C) & ~ v5_altcat_3(D,A,B,C) ) ) ) ) ) )).
fof(t15_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l2_altcat_1(B) ) => ! [C] : ( ( v11_functor0(C,A,B) & l2_functor0(C,A,B) ) => ( v17_functor0(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => v2_funct_1(k7_functor0(A,B,C,E,D)) ) ) ) ) ) ) )).
fof(t15_ami_2,axiom,( ! [A] : ( v7_ordinal1(A) => r2_hidden(k4_tarski(1,A),k2_ami_2) ) )).
fof(t15_ami_3,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => ( A = k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0) => v2_extpro_1(A,k7_card_1(2),k1_ami_3) ) ) )).
fof(t15_ami_5,axiom,( ! [A] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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(k7_card_1(2),k1_ami_3,B)),C) ) ) ) )).
fof(t15_ami_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k1_amistd_1(k7_card_1(2),k1_ami_3,A,k7_ami_3(B)) = k1_tarski(B) ) ) )).
fof(t15_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k4_ordinal1) => C != k5_ami_wstd(A,B,C) ) ) ) )).
fof(t15_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) ) => ( ( v5_amistd_1(C,A,B) & r2_hidden(k5_numbers,k1_relset_1(k4_ordinal1,C)) ) => v6_amistd_1(C,A,B) ) ) ) ) )).
fof(t15_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ( ~ ! [D] : ( ( 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)) ) ) ) ) )).
fof(t15_amistd_5,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) & ~ v2_compos_1(C,B) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t15_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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,D),k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,E)),k1_diraf(u1_struct_0(A),k1_analoaf(A))) <=> ? [F] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & k1_rlvect_1(A,k5_algstr_0(A,D,B),F) = k1_rlvect_1(A,k5_algstr_0(A,E,C),G) & ~ ( F = k5_numbers & G = k5_numbers ) ) ) ) ) ) ) ) ) )).
fof(t15_analoaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k5_algstr_0(A,C,B) = k5_algstr_0(A,E,D) => r1_analoaf(A,B,C,D,E) ) ) ) ) ) ) )).
fof(t15_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r1_analmetr(A,C,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k2_analort(A,C,D,E) != B ) ) ) ) ) ) )).
fof(t15_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( ~ r2_anproj_1(A,D,E,F) & r2_anproj_1(A,D,E,B) & r2_anproj_1(A,E,F,C) & ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( r2_anproj_1(A,D,F,G) & r2_anproj_1(A,B,C,G) & ~ v9_struct_0(G,A) ) ) ) ) ) ) ) ) ) )).
fof(t15_anproj_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ~ ( A = k8_domain_1(A,B,C,D) & B != C & B != D & C != D & ! [E] : ( m2_funct_2(E,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [F] : ( m2_funct_2(F,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [G] : ( m2_funct_2(G,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ~ ( ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ( k1_binop_1(k5_funcsdom(A),k1_binop_1(k5_funcsdom(A),k1_funct_1(k7_funcsdom(A),k4_tarski(H,E)),k1_funct_1(k7_funcsdom(A),k4_tarski(I,F))),k1_funct_1(k7_funcsdom(A),k4_tarski(J,G))) = k8_funcsdom(A) => ( H = k5_numbers & I = k5_numbers & J = k5_numbers ) ) ) ) ) & ! [H] : ( m2_funct_2(H,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ? [I] : ( v1_xreal_0(I) & ? [J] : ( v1_xreal_0(J) & ? [K] : ( v1_xreal_0(K) & H = k1_binop_1(k5_funcsdom(A),k1_binop_1(k5_funcsdom(A),k1_funct_1(k7_funcsdom(A),k4_tarski(I,E)),k1_funct_1(k7_funcsdom(A),k4_tarski(J,F))),k1_funct_1(k7_funcsdom(A),k4_tarski(K,G))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t15_aofa_000,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r2_hidden(B,k4_finseq_1(A)) & C = k1_recdef_1(A,B) ) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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] : ( ~ 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 ) ) ) ) ) ) ) )).
fof(t15_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ( ( r2_hidden(B,A) & r2_hidden(C,A) & r2_hidden(D,A) & r2_hidden(E,A) & r2_hidden(F,A) & r2_hidden(G,A) & r2_hidden(H,A) & r2_hidden(I,A) & r2_hidden(J,A) & r2_hidden(K,A) ) => r1_tarski(k8_enumset1(B,C,D,E,F,G,H,I,J,K),A) ) )).
fof(t15_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v19_aofa_a00(B,A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( C = k10_subset_1(k1_funct_1(u7_aofa_a00(A),5),u4_struct_0(A)) => ( k1_msualg_1(A,C) = k1_xboole_0 & k2_msualg_1(A,C) = B ) ) ) ) ) )).
fof(t15_aofa_i00,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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,k5_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) ) ) ) )).
fof(t15_armstrng,axiom,( ! [A] : 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)) )).
fof(t15_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => k2_arytm_0(k3_arytm_0(A),B) = k3_arytm_0(k2_arytm_0(A,B)) ) ) )).
fof(t15_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( ( r1_arytm_2(B,A) & r1_arytm_2(B,C) ) => k7_arytm_2(k1_arytm_1(C,B),A) = k7_arytm_2(k1_arytm_1(A,B),C) ) ) ) ) )).
fof(t15_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ( A = k12_arytm_3 => k8_arytm_2(A,B) = B ) ) ) )).
fof(t15_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ( k3_arytm_3(A,B) = k1_xboole_0 => A = k1_xboole_0 ) ) ) )).
fof(t15_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v4_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v4_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) => ( r1_xxreal_0(k1_seq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)),k5_numbers) | k6_asympt_0(A) = k6_asympt_0(B) ) ) ) ) )).
fof(t15_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(A,k6_asympt_0(k3_asympt_1(1))) => r2_hidden(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,A),k6_asympt_0(k3_asympt_1(2))) ) ) )).
fof(t15_autalg_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v2_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( m2_pboole(E,A,B,C) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t15_autgroup,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t15_bagorder,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k1_bagorder(C,A,B,k16_pre_poly(C)) = k16_pre_poly(k7_nat_d(B,A)) ) ) ) )).
fof(t15_bcialg_1,axiom,( ! [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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) )).
fof(t15_bcialg_3,axiom,( ! [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) ) => ( ( ~ 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) ) ) )).
fof(t15_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t15_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_bcialg_5(E,A,B,C,D) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => m1_bcialg_5(E,A,k1_nat_1(B,F),k1_nat_1(C,F),D) ) ) ) ) ) ) )).
fof(t15_bcialg_6,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k5_bcialg_1(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t15_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( m1_bciideal(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t15_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_bhsp_1(A,B,k4_struct_0(A)) = k5_numbers ) ) )).
fof(t15_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(t15_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( v7_ordinal1(D) => 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)) ) ) ) ) )).
fof(t15_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k3_bhsp_4(A,B,k5_numbers) = k1_normsp_1(A,B,k5_numbers) ) ) )).
fof(t15_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(t15_binari_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k2_xcmplx_0(k3_binari_2(k2_xcmplx_0(A,1),k2_binari_2(k2_xcmplx_0(A,1),k9_binarith(A,1,k6_margrel1,B,k10_binarith(k6_margrel1,C)))),k15_funcop_1(k4_ordinal1,k4_binari_2(k1_nat_1(A,1),k3_binarith(k2_xcmplx_0(A,1),k9_binarith(A,1,k6_margrel1,B,k10_binarith(k6_margrel1,C))),k1_binari_2(k1_nat_1(A,1))),k7_margrel1,k5_numbers,k5_series_1(2,k1_nat_1(A,1)))) = k4_xcmplx_0(k3_binari_2(k2_xcmplx_0(A,1),k9_binarith(A,1,k6_margrel1,B,k10_binarith(k6_margrel1,C)))) ) ) ) )).
fof(t15_binari_3,axiom,( k3_binarith(1,k10_binarith(k6_margrel1,k8_margrel1)) = k10_binarith(k6_margrel1,k7_margrel1) )).
fof(t15_binari_4,axiom,( ! [A] : ( ( v3_card_1(A,1) & m2_finseq_1(A,k6_margrel1) ) => ( A = k12_finseq_1(k6_margrel1,k8_margrel1) => k3_binari_2(1,A) = k4_xcmplx_0(1) ) ) )).
fof(t15_binarith,axiom,( ! [A] : ( ( v3_card_1(A,1) & m2_finseq_1(A,k6_margrel1) ) => ( A = k14_trees_3(k7_margrel1) => k6_binarith(1,A) = k5_numbers ) ) )).
fof(t15_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_algstr_1(A) & v3_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k5_binom(A,B,k1_nat_1(C,D)) = k1_algstr_0(A,k5_binom(A,B,C),k5_binom(A,B,D)) ) ) ) ) )).
fof(t15_binop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t15_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => k1_funct_1(k2_bintree2(A,B),1) = k5_euclid(B) ) ) )).
fof(t15_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r3_boolealg(A,B,k1_boolealg(A,C,D)) => r3_boolealg(A,B,C) ) ) ) ) ) )).
fof(t15_bor_cant,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) & k3_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 ) ) ) ) ) )).
fof(t15_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(A,B)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k2_borsuk_1(A,B))))) => ( ! [E] : ( r2_hidden(E,D) => ( r1_tarski(E,C) & ? [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & ? [G] : ( 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) ) ) ) ) ) )).
fof(t15_borsuk_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_pre_topc(C,A) => m1_pre_topc(k2_borsuk_1(B,C),k2_borsuk_1(B,A)) ) ) ) )).
fof(t15_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_topmetr)) => ! [B] : ( 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))) ) ) )).
fof(t15_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( A = k2_rcomp_1(B,C) => ( B = C | k2_pre_topc(k3_topmetr,A) = k1_rcomp_1(B,C) ) ) ) ) ) )).
fof(t15_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k12_rvsum_1(k11_finseq_1(A,B,C)) = k11_finseq_1(k1_square_1(A),k1_square_1(B),k1_square_1(C)) ) ) ) )).
fof(t15_brouwer,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xxreal_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( 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] : ( 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 ) ) ) ) )).
fof(t15_bspace,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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)) ) ) ) )).
fof(t15_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t15_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t15_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ! [G] : ! [H] : ! [I] : ! [J] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t15_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)))) ) ) ) )).
fof(t15_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t15_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t15_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t15_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t15_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(t15_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t15_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t15_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t15_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) )).
fof(t15_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t15_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k4_struct_0(k7_c0sp1(A)) = k8_funcop_1(k4_ordinal1,A,k5_numbers) ) )).
fof(t15_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_c0sp2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_c0sp2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_c0sp2(A))) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(H,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k1_numbers,G,H) = k3_real_1(k3_funct_2(u1_struct_0(A),k1_numbers,E,H),k3_funct_2(u1_struct_0(A),k1_numbers,F,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t15_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t15_calcul_2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => k1_relset_1(k4_ordinal1,k5_relset_1(k4_ordinal1,k3_cqc_lang(A),k8_finseq_1(k3_cqc_lang(A),C,B),k2_calcul_2(k3_finseq_1(C),k3_finseq_1(B)))) = k2_calcul_2(k3_finseq_1(C),k3_finseq_1(B)) ) ) ) )).
fof(t15_cantor_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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)))) ) ) )).
fof(t15_card_1,axiom,( ! [A] : ! [B] : ( k1_card_1(A) = k1_card_1(B) => k2_card_1(A) = k2_card_1(B) ) )).
fof(t15_card_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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))) ) )).
fof(t15_card_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) )).
fof(t15_card_4,axiom,( ! [A] : ( v1_card_1(A) => ( ~ v1_finset_1(A) => k2_card_2(A,A) = A ) ) )).
fof(t15_card_5,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ? [B] : ( v3_ordinal1(B) & A = k3_card_1(B) ) ) )).
fof(t15_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( r2_hidden(B,k3_card_fil(A)) <=> m1_card_fil(B,A) ) ) )).
fof(t15_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ( C != D => k5_card_1(k1_card_fin(A,B,C,D)) = k4_newton(B,k5_card_1(A)) ) ) ) )).
fof(t15_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v3_card_lar(B,A) => v1_card_lar(B,A) ) ) ) )).
fof(t15_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t15_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t15_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u4_struct_0(C)) => ! [E] : ( m1_subset_1(E,u4_struct_0(C)) => ! [F] : ( 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))) ) ) ) ) ) )).
fof(t15_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t15_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ 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) ) ) ) )).
fof(t15_catalan1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( ~ r1_xxreal_0(A,1) & r1_xxreal_0(k1_catalan1(k1_nat_1(A,1)),k1_catalan1(A)) ) ) )).
fof(t15_catalan2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ~ ( r1_tarski(k2_relset_1(k4_ordinal1,A),k7_domain_1(k4_ordinal1,k5_numbers,1)) & ~ v1_catalan2(A) & ! [B] : ( v7_ordinal1(B) => ~ ( k1_nat_1(k3_xcmplx_0(2,B),1) = k3_nat_1(a_1_1_catalan2(A)) & r1_xxreal_0(k1_nat_1(k3_xcmplx_0(2,B),1),k1_relset_1(k4_ordinal1,A)) & B = k7_afinsq_2(k5_relat_1(A,k3_xcmplx_0(2,B))) & k1_recdef_1(A,k3_xcmplx_0(2,B)) = 1 ) ) ) ) )).
fof(t15_catalg_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_catalg_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ? [D] : ( m1_subset_1(D,A) & ? [E] : ( m1_subset_1(E,A) & C = k9_catalg_1(A,D,E) ) ) ) ) ) )).
fof(t15_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v9_algstr_0(k5_cayldick(A,B,C),k4_cayldick(A)) => ( v9_algstr_0(B,A) & v9_algstr_0(C,A) ) ) ) ) ) )).
fof(t15_cc0sp1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(t15_cc0sp2,axiom,( ! [A] : ( ( ~ 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] : ( m1_cc0sp1(B,A) => ! [C] : ( m1_cc0sp1(C,A) => ( r1_tarski(u1_struct_0(B),u1_struct_0(C)) => m1_cc0sp1(B,C) ) ) ) ) )).
fof(t15_cfcont_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( 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(k4_ordinal1,k2_numbers,k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,B,k25_valued_1(k2_numbers,k2_numbers,C,A)),k25_valued_1(k4_ordinal1,k2_numbers,k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,B,C),A)) ) ) ) ) )).
fof(t15_cfdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [B] : ( ( 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] : ( v1_xcmplx_0(C) => ( r2_hidden(C,B) => r1_cfdiff_1(A,C) ) ) ) ) ) ) )).
fof(t15_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ! [C] : ( m2_funct_2(C,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t15_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t15_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ! [B] : ( v2_cgames_1(B) => ( ( r2_hidden(B,k6_cgames_1(A)) | r2_hidden(B,k7_cgames_1(A)) ) => r2_hidden(k9_cgames_1(B),k9_cgames_1(A)) ) ) ) )).
fof(t15_chain_1,axiom,( ! [A] : ( ( ~ v1_zfmisc_1(A) & v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( A = k2_tarski(B,C) => ( m2_chain_1(k4_tarski(D,E),A) <=> ( ( D = B & E = C ) | ( D = C & E = B ) ) ) ) ) ) ) ) ) )).
fof(t15_chord,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k10_xtuple_0(A))) ) => ? [C] : ( r2_hidden(C,B) & ! [D] : ( r2_hidden(D,B) => r1_xxreal_0(k4_finseq_4(A,C),k4_finseq_4(A,D)) ) ) ) ) )).
fof(t15_circcmb2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(C,F))) => ! [H] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t15_circcmb3,axiom,( ! [A] : ( ( v4_circcmb3(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( A = k5_circcomb(C,B) => k3_circcmb3(A) = k4_tarski(B,C) ) ) ) )).
fof(t15_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & ~ v11_struct_0(C) & v2_msafree2(C) & l1_msualg_1(C) ) => ( C = k2_circcomb(A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r2_hidden(D,k3_msafree2(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ( D = E => ( r2_hidden(E,k3_msafree2(C)) & k4_msafree2(C,E) = k4_msafree2(B,D) ) ) ) ) ) ) ) ) ) )).
fof(t15_circled1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v1_xreal_0(C) => k1_convex1(A,k2_circled1(A,B),C) = k2_circled1(A,k1_convex1(A,B,C)) ) ) ) )).
fof(t15_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v4_msafree2(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m3_msaterm(D,A,B) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t15_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ r1_xxreal_0(k4_circuit1(A,B,C),k5_numbers) ) ) ) )).
fof(t15_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) ) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( v1_pdiff_7(C,A) & B = k7_funcop_1(C,D) & r1_xxreal_0(1,E) & r1_xxreal_0(E,A) ) => ( r3_pdiff_9(A,C,E,B) & r1_pdiff_9(A,C,k3_pdiff_9(A,C,E,B)) ) ) ) ) ) ) ) )).
fof(t15_classes1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => r1_tarski(k3_classes1(A,B),k3_classes1(A,k1_ordinal1(B))) ) )).
fof(t15_classes2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( ( v2_classes1(B) & r2_hidden(A,k1_card_1(B)) ) => r2_hidden(A,B) ) ) )).
fof(t15_clopban1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k6_clopban1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k6_clopban1(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k6_clopban1(A,B))) => ( E = k3_rlvect_1(k6_clopban1(A,B),C,D) <=> ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t15_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k8_clopban2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k8_clopban2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k8_clopban2(A))) => ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t15_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,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))) ) ) ) )).
fof(t15_closure1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t15_closure2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k9_xtuple_0(k3_closure2(k1_tarski(A))) = k9_xtuple_0(A) ) )).
fof(t15_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xcmplx_0(D) => k1_clvect_1(A,k4_rlvect_1(A,k2_finseq_4(u1_struct_0(A),C,B)),D) = k3_rlvect_1(A,k1_clvect_1(A,C,D),k1_clvect_1(A,B,D)) ) ) ) ) )).
fof(t15_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(t15_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k2_clvect_3(A,B,k5_numbers) = k1_normsp_0(A,B,k5_numbers) ) ) )).
fof(t15_coh_sp,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t15_cohsp_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( r1_cohsp_1(A,A) => ( v1_cohsp_1(A) & v2_cohsp_1(A) ) ) ) )).
fof(t15_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( m2_collsp(D,A) => ~ ( r2_hidden(B,D) & r2_hidden(C,D) ) ) ) ) ) ) )).
fof(t15_combgras,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ( ( r1_xxreal_0(2,A) & r1_ordinal1(k1_nat_1(A,2),k1_card_1(B)) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t15_compl_sp,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t15_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( ( k3_complex1(A) = k5_numbers & k3_complex1(B) = k5_numbers ) => ( k3_complex1(k3_xcmplx_0(A,B)) = k1_real_1(k4_real_1(k4_complex1(A),k4_complex1(B))) & k4_complex1(k3_xcmplx_0(A,B)) = k5_numbers ) ) ) ) )).
fof(t15_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( ~ ( A = B & k6_xcmplx_0(A,B) = k5_numbers ) => ( ~ r1_xxreal_0(k28_sin_cos,k1_comptrig(k6_xcmplx_0(A,B))) <=> r1_xxreal_0(k28_sin_cos,k1_comptrig(k6_xcmplx_0(B,A))) ) ) ) ) )).
fof(t15_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ~ ( B != k4_struct_0(k1_complfld) & ( k8_group_1(k1_complfld,A,B) = k5_struct_0(k1_complfld) | k8_group_1(k1_complfld,B,A) = k5_struct_0(k1_complfld) ) & A != k11_algstr_0(k1_complfld,B) ) ) ) )).
fof(t15_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => k1_complsp2(k7_seq_4(A,B)) = k7_seq_4(k1_complsp2(A),k1_complsp2(B)) ) ) ) )).
fof(t15_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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)),k5_numbers) ) ) ) )).
fof(t15_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( v6_compos_0(D,u1_compos_1(A)) & m1_subset_1(D,u1_compos_1(A)) ) => ! [E] : ( ( v6_compos_0(E,u1_compos_1(A)) & m1_subset_1(E,u1_compos_1(A)) ) => ! [F] : ( ( 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 ) ) ) ) ) ) )).
fof(t15_comptrig,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( r2_hidden(A,k2_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(2,k28_sin_cos))) & r1_xxreal_0(k1_funct_1(k18_sin_cos,A),k5_numbers) ) ) )).
fof(t15_compts_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( ~ v2_struct_0(C) & l1_pre_topc(C) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t15_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( v1_relat_1(C) => ( r1_tarski(k9_xtuple_0(C),k4_finseq_2(A,B)) => v2_margrel1(C) ) ) ) ) )).
fof(t15_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,C,A),k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,C,B)),k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,C,k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B))) ) ) ) )).
fof(t15_comseq_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & v2_comseq_2(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => k3_comseq_2(k2_comseq_2(k4_ordinal1,k25_valued_1(k4_ordinal1,k2_numbers,B,A))) = k3_xcmplx_0(k8_complex1(A),k8_complex1(k3_comseq_2(B))) ) ) )).
fof(t15_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( r2_funct_2(k4_ordinal1,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(k4_ordinal1,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))) ) ) ) )).
fof(t15_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [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(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)) ) ) ) )).
fof(t15_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => r1_filter_1(k11_conlat_1(k6_conlat_2(A)),A) ) )).
fof(t15_conmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v3_conaffm(A) => v1_conmetr(A) ) ) )).
fof(t15_conmetr1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v11_aff_2(k3_analmetr(A)) <=> v8_conmetr(A) ) ) )).
fof(t15_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_connsp_1(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t15_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_connsp_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_connsp_1(B,A) => v3_pre_topc(B,A) ) ) ) ) )).
fof(t15_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t15_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ! [C] : ( 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) ) ) ) )).
fof(t15_convex4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( B != C => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t15_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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) ) ) )).
fof(t15_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v5_relat_1(C,k3_qc_lang1(A)) & v3_card_1(C,B) & m2_finseq_1(C,k2_qc_lang1(A)) ) => ! [D] : ( m2_subset_1(D,k6_qc_lang1(A),k8_qc_lang1(A,B)) => k7_cqc_sim1(A,k4_cqc_lang(B,A,D,C)) = k5_numbers ) ) ) ) )).
fof(t15_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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) ) ) )).
fof(t15_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) )).
fof(t15_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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) ) ) ) )).
fof(t15_csspace,axiom,( u1_struct_0(k7_csspace) = k1_csspace & ! [A] : ( m1_subset_1(A,u1_struct_0(k7_csspace)) <=> ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k7_csspace)) <=> ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k7_csspace)) => A = k2_csspace(A) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k7_csspace)) => ! [B] : ( 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] : ( v1_xcmplx_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_csspace)) => k1_clvect_1(k7_csspace,B,A) = k25_valued_1(k4_ordinal1,k2_numbers,k2_csspace(B),A) ) ) )).
fof(t15_csspace2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v2_comseq_2(C) & v2_comseq_2(B) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [E] : ( v7_ordinal1(E) => k1_funct_1(D,E) = k2_xcmplx_0(k3_xcmplx_0(k9_complex1(k6_xcmplx_0(k1_funct_1(C,E),A)),k9_complex1(k6_xcmplx_0(k1_funct_1(C,E),A))),k1_funct_1(B,E)) ) => ( v2_comseq_2(D) & k1_seq_2(D) = k2_xcmplx_0(k3_xcmplx_0(k9_complex1(k6_xcmplx_0(k3_comseq_2(C),A)),k9_complex1(k6_xcmplx_0(k3_comseq_2(C),A))),k1_seq_2(B)) ) ) ) ) ) ) ) )).
fof(t15_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( 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_funct_1(k8_csspace4(A,B),C) = k2_seq_4(k7_csspace4(A,B,C)) ) ) ) )).
fof(t15_decomp_1,axiom,( ! [A] : ( ( 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) ) )).
fof(t15_descip_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t15_dickson,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_wellfnd1(A) => v1_wellfnd1(k5_dickson(A)) ) ) )).
fof(t15_diff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( ( 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_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,D,E),B),k1_nat_1(A,1)),C) = k2_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(D,B),k1_nat_1(A,1)),C),k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(E,B),k1_nat_1(A,1)),C)) ) ) ) ) ) )).
fof(t15_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( ( 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] : ( ( 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) = k2_xcmplx_0(k2_diff_2(G,A,B,C,D,E,F),k2_diff_2(H,A,B,C,D,E,F)) ) ) ) ) ) ) ) ) )).
fof(t15_diff_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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] : ( ( 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_funct_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,C),k26_valued_1(k1_numbers,k1_numbers,G,D)),B),k2_xcmplx_0(A,1)),E) = k6_xcmplx_0(k3_xcmplx_0(C,k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(F,B),k2_xcmplx_0(A,1)),E)),k3_xcmplx_0(D,k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(G,B),k2_xcmplx_0(A,1)),E))) ) ) ) ) ) ) ) )).
fof(t15_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(B,k1_relset_1(k1_numbers,k1_fdiff_9)) & r2_hidden(k2_xcmplx_0(B,A),k1_relset_1(k1_numbers,k1_fdiff_9)) ) => k1_funct_1(k3_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fdiff_9,k1_fdiff_9),A),B) = k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(4,k17_sin_cos(k2_xcmplx_0(k3_xcmplx_0(2,B),A))),k17_sin_cos(A)),k1_square_1(k2_xcmplx_0(k19_sin_cos(k2_xcmplx_0(k3_xcmplx_0(2,B),A)),k19_sin_cos(A)))) ) ) ) )).
fof(t15_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v1_dilworth(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v2_dilworth(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ! [E] : ( ( r2_hidden(D,C) & r2_hidden(E,C) & r2_hidden(D,B) & r2_hidden(E,B) ) => D = E ) ) ) ) )).
fof(t15_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t15_dirort,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dirort(A) & l1_analoaf(A) ) => ( v4_dirort(A) => v3_dirort(A) ) ) )).
fof(t15_dist_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ( ( v1_prob_2(A) & k9_xtuple_0(A) = k4_finseq_1(B) & ! [C] : ( 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) ) ) ) ) )).
fof(t15_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => ! [C] : ( m1_dist_2(C,A,B) => ! [D] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(k4_finseq_1(k9_dist_1(A,C)))) & E = k3_dist_2(k1_partfun1(k4_ordinal1,A,A,k6_margrel1,k19_finseq_1(A),D)) & k5_card_1(k3_dist_2(k1_partfun1(k4_ordinal1,A,A,k6_margrel1,C,D))) = k16_rvsum_1(k5_dist_2(k4_ordinal1,k9_dist_1(A,C),E)) ) ) ) ) ) )).
fof(t15_e_siec,axiom,( ! [A] : ( ( 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 ) ) )).
fof(t15_ec_pf_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(C))) => ( ( D = k5_int_1(A,C) & E = k5_int_1(B,C) ) => k3_rlvect_1(k9_int_3(C),D,E) = k5_int_1(k2_xcmplx_0(A,B),C) ) ) ) ) ) ) )).
fof(t15_ec_pf_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t15_endalg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( 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] : ( r2_hidden(C,k1_endalg(A)) => k1_funct_1(B,C) = k16_funcop_1(k5_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)))) ) ) ) )).
fof(t15_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t15_entropy1,axiom,( ! [A] : ( ( v1_matrprob(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( v7_ordinal1(B) => ( ( r2_hidden(B,k4_finseq_1(A)) & k1_funct_1(A,B) = 1 ) => r1_entropy1(A,B) ) ) ) )).
fof(t15_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k3_enumset1(A,B,C,D,E),k1_tarski(F)) )).
fof(t15_eqrel_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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)) ) ) )).
fof(t15_equation,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t15_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => k12_euclid(k8_euclid(A,B,C)) = k12_euclid(k8_euclid(A,C,B)) ) ) ) )).
fof(t15_euclid_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => ! [B] : ( ( 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)),k2_xcmplx_0(k12_euclid(A),k12_euclid(B))) ) ) ) )).
fof(t15_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => k2_euclid_3(k5_algstr_0(k15_euclid(2),A,B)) = k6_xcmplx_0(k2_euclid_3(A),k2_euclid_3(B)) ) ) )).
fof(t15_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => k12_euclid(B) = k3_square_1(k22_rvsum_1(B,B)) ) ) )).
fof(t15_euclid_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => k5_euclid_5(k4_euclid_5(A,C,E),k4_euclid_5(B,D,F)) = k4_euclid_5(k6_xcmplx_0(k3_xcmplx_0(C,F),k3_xcmplx_0(E,D)),k6_xcmplx_0(k3_xcmplx_0(E,B),k3_xcmplx_0(A,F)),k6_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(C,B))) ) ) ) ) ) ) )).
fof(t15_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ( ( r2_hidden(E,k1_rltopsp1(k15_euclid(2),A,C)) & r2_hidden(E,k1_rltopsp1(k15_euclid(2),B,D)) ) => ( E = A | E = B | E = C | E = D | k4_euclid_3(A,E,B) = k4_euclid_3(C,E,D) ) ) ) ) ) ) ) )).
fof(t15_euclid_7,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t15_euclid_8,axiom,( k5_euclid_8(k3_euclid_8,k4_euclid_8) = k2_euclid_8 )).
fof(t15_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => ~ ( A != k5_numbers & r2_hidden(D,k4_euclid_9(A,C,B)) & r1_xxreal_0(k3_xcmplx_0(A,k1_square_1(B)),k18_rvsum_1(k12_rvsum_1(k8_rvsum_1(D,C)))) ) ) ) ) ) )).
fof(t15_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(D)) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(D)) => k8_euclid(D,E,k9_euclid(D,F,k2_xcmplx_0(k2_xcmplx_0(A,B),C))) = k7_euclid(D,k7_euclid(D,k7_euclid(D,E,k9_euclid(D,F,k4_xcmplx_0(A))),k9_euclid(D,F,k4_xcmplx_0(B))),k9_euclid(D,F,k4_xcmplx_0(C))) ) ) ) ) ) ) )).
fof(t15_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( ( v1_euclmetr(A) & v3_euclmetr(A) ) => v2_euclmetr(A) ) ) )).
fof(t15_euler_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ~ ( B != k5_numbers & ~ r1_xxreal_0(A,k5_numbers) & k3_int_2(k3_xcmplx_0(A,B),k3_xcmplx_0(A,C)) != k3_xcmplx_0(A,k3_int_2(B,C)) ) ) ) ) )).
fof(t15_euler_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => k2_euler_2(k8_finseq_1(k4_ordinal1,B,C),A) = k8_finseq_1(k4_ordinal1,k2_euler_2(B,A),k2_euler_2(C,A)) ) ) ) )).
fof(t15_exchsort,axiom,( k1_exchsort(k1_xboole_0) = k5_numbers & k2_exchsort(k1_xboole_0) = k5_numbers & k3_exchsort(k1_xboole_0) = k5_numbers )).
fof(t15_extens_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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] : ( ( v4_msualg_1(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( m2_pboole(F,u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,E)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t15_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & ~ v2_compos_1(C,B) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t15_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ( ( A = k1_supinf_1 | A = k2_supinf_1 ) => k1_extreal1(k3_extreal1(A),k3_extreal1(k2_extreal1(k8_mesfunc1,A))) = k5_numbers ) ) )).
fof(t15_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(t15_facirc_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(A,B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => k6_facirc_2(k1_nat_1(B,1),A,C,D) = k12_facirc_1(k1_funct_1(C,k1_nat_1(B,1)),k1_funct_1(D,k1_nat_1(B,1)),k5_facirc_2(B,C,D)) ) ) ) ) ) )).
fof(t15_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t15_fcont_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_xxreal_0(B,A) & r1_tarski(k1_rcomp_1(B,A),k1_relset_1(k1_numbers,C)) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A))) ) => ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,k4_subset_1(k1_numbers,k1_rcomp_1(k1_funct_1(C,B),k1_funct_1(C,A)),k1_rcomp_1(k1_funct_1(C,A),k1_funct_1(C,B)))) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k1_rcomp_1(B,A)) & D = k1_funct_1(C,E) ) ) ) ) ) ) ) ) )).
fof(t15_fcont_3,axiom,( ! [A] : ! [B] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => 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)) ) ) ) )).
fof(t15_fdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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) = k3_xcmplx_0(B,k1_fdiff_1(C,A)) ) ) ) ) ) )).
fof(t15_fdiff_10,axiom,( ! [A] : ( ( 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,k18_sin_cos))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),A),B) = k6_xcmplx_0(k1_square_1(k1_funct_1(k18_sin_cos,B)),k1_square_1(k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t15_fdiff_11,axiom,( ! [A] : ( ( 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,k18_sin_cos))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k18_sin_cos),A),B) = k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k16_sin_cos,k1_funct_1(k1_sin_cos9,B)),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t15_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r1_fdiff_1(B,A) => ( k1_funct_1(B,A) = k5_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) = k4_xcmplx_0(k7_xcmplx_0(k1_fdiff_1(B,A),k1_square_1(k1_funct_1(B,A)))) ) ) ) ) ) )).
fof(t15_fdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( ( r3_fdiff_3(A,B) & k2_fdiff_3(B,A) = C ) => ( ? [D] : ( v1_xreal_0(D) & ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k1_rcomp_1(B,k2_xcmplx_0(B,D)),k1_relset_1(k1_numbers,A)) ) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v9_ordinal1(D) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k10_xtuple_0(E) = k1_tarski(B) & r1_tarski(k10_xtuple_0(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),k1_relset_1(k1_numbers,A)) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ r1_xxreal_0(k3_funct_2(k4_ordinal1,k1_numbers,D,F),k5_numbers) ) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),A),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,A)))) & k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),A),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,A)))) = C ) ) ) ) ) ) & ( ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v9_ordinal1(D) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k10_xtuple_0(E) = k1_tarski(B) & r1_tarski(k10_xtuple_0(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),k1_relset_1(k1_numbers,A)) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ r1_xxreal_0(k3_funct_2(k4_ordinal1,k1_numbers,D,F),k5_numbers) ) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),A),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,A)))) & k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),A),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,A)))) = C ) ) ) ) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k1_rcomp_1(B,k2_xcmplx_0(B,D)),k1_relset_1(k1_numbers,A)) ) ) | ( r3_fdiff_3(A,B) & k2_fdiff_3(B,A) = C ) ) ) ) ) ) ) )).
fof(t15_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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),k4_xcmplx_0(1)))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k1_funct_1(C,D) = k2_xcmplx_0(A,D) & k1_funct_1(C,D) != k5_numbers ) ) ) ) => ( r2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k6_rfunct_1(k1_numbers,k1_numbers,C),k4_xcmplx_0(1)),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(k2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k6_rfunct_1(k1_numbers,k1_numbers,C),k4_xcmplx_0(1)),B),D) = k7_xcmplx_0(1,k1_square_1(k2_xcmplx_0(A,D))) ) ) ) ) ) ) ) )).
fof(t15_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k22_sin_cos)))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => ( k1_funct_1(B,D) = k6_xcmplx_0(k4_xcmplx_0(D),1) & k1_funct_1(C,D) = k4_xcmplx_0(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,k22_sin_cos)),A) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_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,k22_sin_cos)),A),D) = k7_xcmplx_0(D,k23_sin_cos(D)) ) ) ) ) ) ) ) )).
fof(t15_fdiff_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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,k3_sin_cos6))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => ( k1_funct_1(D,E) = k2_xcmplx_0(k3_xcmplx_0(A,E),B) & ~ r1_xxreal_0(k1_funct_1(D,E),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(D,E)) ) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k3_sin_cos6),C) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k3_sin_cos6),C),E) = k4_xcmplx_0(k7_xcmplx_0(A,k3_square_1(k6_xcmplx_0(1,k1_square_1(k2_xcmplx_0(k3_xcmplx_0(A,E),B)))))) ) ) ) ) ) ) ) ) )).
fof(t15_fdiff_8,axiom,( ! [A] : ( ( 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,k27_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k27_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k27_sin_cos),A),B) = k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(B,k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k3_taylor_1,B)))))) ) ) ) ) ) )).
fof(t15_fdiff_9,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k2_fdiff_9),A),B) = k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k18_sin_cos,k1_funct_1(k3_taylor_1,B)),k3_xcmplx_0(B,k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k3_taylor_1,B)))))) ) ) ) ) ) )).
fof(t15_ff_siec,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t15_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ~ ( ~ r1_xxreal_0(A,k5_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))) ) ) ) ) )).
fof(t15_fib_num3,axiom,( k1_fib_num3(3) = 4 )).
fof(t15_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,2) => r1_xxreal_0(k4_xcmplx_0(k7_xcmplx_0(1,k3_square_1(5))),k2_power(k2_fib_num,A)) ) ) )).
fof(t15_filerec1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m2_finseq_1(E,D) => ( E = k11_finseq_1(A,B,C) => k2_rfinseq(D,1,E) = k10_finseq_1(B,C) ) ) ) )).
fof(t15_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_filter_0(A,B)) <=> r3_lattices(A,B,C) ) ) ) ) )).
fof(t15_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t15_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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))) ) ) ) ) ) )).
fof(t15_finance1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [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))) ) => ( 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) ) ) ) ) ) )).
fof(t15_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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))) ) ) ) )).
fof(t15_finseq_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t15_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => k7_subset_1(k4_ordinal1,k2_finseq_1(k1_nat_1(A,1)),k2_finseq_1(A)) = k1_tarski(k1_nat_1(A,1)) ) )).
fof(t15_finseq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( 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) ) ) ) )).
fof(t15_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => k7_partfun1(A,k8_finseq_1(A,k12_finseq_1(A,B),C),1) = B ) ) ) )).
fof(t15_finseq_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( r2_hidden(C,k6_subset_1(k10_xtuple_0(B),k10_xtuple_0(A))) => k5_finseq_4(k7_finseq_1(A,B),C) = k7_finseq_1(A,k5_finseq_4(B,C)) ) ) ) )).
fof(t15_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t15_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( k3_finseq_1(k5_finseq_8(A,B,C)) = k6_xcmplx_0(k1_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(k1_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)) = k1_nat_1(k3_finseq_1(B),k7_nat_d(k3_finseq_1(C),k3_finseq_1(k4_finseq_8(A,B,C)))) ) ) ) ) )).
fof(t15_finset_1,axiom,( ! [A] : ! [B] : ~ ( ~ v1_finset_1(B) & r2_hidden(B,k2_zfmisc_1(A,B)) ) )).
fof(t15_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t15_finsub_1,axiom,( k5_finsub_1(k1_xboole_0) = k1_tarski(k1_xboole_0) )).
fof(t15_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k5_fintopo2(A,B,C) = k8_margrel1 <=> B = C ) ) ) ) )).
fof(t15_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k3_fintopo3(A,B,1) = k9_fin_topo(A,B) ) ) )).
fof(t15_fintopo4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t15_fintopo5,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => v1_fin_topo(k5_fintopo5(A,B)) ) ) )).
fof(t15_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t15_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t15_flang_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ~ ( r2_hidden(B,C) & B != k2_flang_1(A) & k8_flang_1(A,C) = k4_flang_1(A,k2_flang_1(A)) ) ) )).
fof(t15_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( 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 = k5_numbers & B = k1_xboole_0 ) ) ) ) ) )).
fof(t15_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_2(B,A,k3_finseq_2(A)) => ! [C] : ( m2_finseq_2(C,A,k3_finseq_2(A)) => k1_funct_1(k9_fomodel0(A),k10_finseq_1(B,C)) = k1_monoid_0(A,B,C) ) ) ) )).
fof(t15_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_fomodel1(A)) => ~ ( B != k8_fomodel1(A) & B != k18_fomodel1(A) & ~ r2_hidden(B,k37_fomodel1(A)) ) ) ) )).
fof(t15_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_fomodel2(C,A,B) ) => ! [D] : ( ( 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) = k31_fomodel2(A) => ( k13_fomodel2(A,B,C,D) = 1 <=> k1_funct_1(k9_fomodel2(A,B,C),k1_funct_1(k34_fomodel1(A,D),1)) = k1_funct_1(k9_fomodel2(A,B,C),k1_funct_1(k34_fomodel1(A,D),2)) ) ) ) ) ) ) )).
fof(t15_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( ( v4_fomodel1(D,C) & m1_subset_1(D,k1_fomodel1(C)) ) => ! [E] : ( ( 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] : ( ( 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))),k15_fomodel2(C,A)) ) => k34_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,k34_fomodel2(C,A,F,D,B)) ) ) ) ) ) ) )).
fof(t15_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v13_fomodel4(B,k5_numbers,A) & v13_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] : ( v11_fomodel4(C,A,B) => ! [D] : ( ( 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,k8_eqrel_1(k35_fomodel1(A),k8_fomodel4(A,B,C)),k41_fomodel4(A,B,C),D) = 1 <=> r2_hidden(D,C) ) ) ) ) ) )).
fof(t15_frechet,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(t15_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m2_valued_0(C,u1_struct_0(A),B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_frechet(A,B,D) => r1_frechet(A,C,D) ) ) ) ) ) )).
fof(t15_fscirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t15_fscirc_2,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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) ) )).
fof(t15_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( ( ~ v2_struct_0(D) & l2_fsm_1(D,A,B) ) => ! [E] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t15_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ( ( v3_fsm_2(B,A) & v1_fsm_2(B,A) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t15_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( ( ~ v2_struct_0(D) & l1_fsm_3(D,A,C) ) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t15_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( 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))) ) )).
fof(t15_funcop_1,axiom,( ! [A] : ! [B] : k8_relat_1(k2_funcop_1(A,B),k1_tarski(B)) = A )).
fof(t15_funcsdom,axiom,( ! [A] : ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( m2_funct_2(C,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [D] : ( 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))) ) ) ) )).
fof(t15_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( k9_xtuple_0(k3_relat_1(A,B)) = k9_xtuple_0(A) => r1_tarski(k10_xtuple_0(A),k9_xtuple_0(B)) ) ) ) )).
fof(t15_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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)) ) ) ) ) )).
fof(t15_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ( r1_tarski(A,k1_zfmisc_1(B)) => k7_relat_1(D,k3_tarski(A)) = k3_tarski(k7_relat_1(k1_funct_3(D),A)) ) ) ) )).
fof(t15_funct_4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t15_funct_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( ( r2_hidden(k4_tarski(C,D),k9_xtuple_0(A)) & B = k1_funct_1(k3_funct_5(A),D) ) => ( r2_hidden(C,k9_xtuple_0(B)) & k1_funct_1(B,C) = k1_binop_1(A,C,D) ) ) ) ) )).
fof(t15_funct_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) ) )).
fof(t15_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : 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)) ) )).
fof(t15_funct_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_8(B) & m1_subset_1(B,k1_zfmisc_1(k2_numbers)) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t15_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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) = k5_numbers | v1_funct_9(C,k2_xcmplx_0(A,B)) ) ) ) ) ) )).
fof(t15_functor0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t15_functor1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l2_altcat_1(B) ) => ! [C] : ( ( v10_functor0(C,A,B) & l2_functor0(C,A,B) ) => ( v18_functor0(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t15_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v2_altcat_1(D) & v12_altcat_1(D) & l2_altcat_1(D) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ! [F] : ( ( v15_functor0(F,B,C) & m2_functor0(F,B,C) ) => ! [G] : ( ( v15_functor0(G,C,D) & m2_functor0(G,C,D) ) => ! [H] : ( ( v15_functor0(H,C,D) & m2_functor0(H,C,D) ) => ! [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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t15_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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(k3_funct_2(A,k1_numbers,k4_fuzzy_1(A),B),k3_funct_2(A,k1_numbers,C,B)) & r1_xxreal_0(k3_funct_2(A,k1_numbers,C,B),k3_funct_2(A,k1_numbers,k5_fuzzy_1(A),B)) ) ) ) ) )).
fof(t15_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D,C)),k2_fuzzy_1(A,k1_fuzzy_2(A,B,D),k1_fuzzy_2(A,B,C))) ) ) ) ) )).
fof(t15_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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] : ( ( v5_relat_1(F,k1_rcomp_1(k5_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(k3_fuzzy_4(A,B,C,D,k1_fuzzy_1(k2_zfmisc_1(B,C),E,F)),k1_fuzzy_1(k2_zfmisc_1(A,C),k3_fuzzy_4(A,B,C,D,E),k3_fuzzy_4(A,B,C,D,F))) ) ) ) ) ) ) )).
fof(t15_fvsum_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t15_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ ( ~ 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)) ) ) )).
fof(t15_gcd_1,axiom,( ! [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) & v1_vectsp_2(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t15_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v2_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( m1_genealg1(E,D) => ! [F] : ( m1_genealg1(F,D) => ( k9_genealg1(D,E,F,k5_numbers,B,C) = k8_genealg1(D,F,E,B,C) & k9_genealg1(D,E,F,A,k5_numbers,C) = k8_genealg1(D,F,E,A,C) & k9_genealg1(D,E,F,A,B,k5_numbers) = k8_genealg1(D,F,E,A,B) ) ) ) ) ) ) ) )).
fof(t15_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_analmetr(A,D,E) => r2_geomtrap(A,D,E,B,B,C,C) ) ) ) ) ) ) )).
fof(t15_gfacirc1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ~ v1_facirc_1(k2_msafree2(k7_gfacirc1(A,B,C))) ) ) ) )).
fof(t15_gfacirc2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ( ( k1_funct_1(C,k5_numbers) = k5_circcomb(k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k8_margrel1),k1_xboole_0) & k1_funct_1(D,k5_numbers) = k7_circcomb(k5_ordinal1,k6_margrel1,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k8_margrel1),k1_xboole_0) & k1_funct_1(E,k5_numbers) = k4_tarski(k1_xboole_0,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k8_margrel1)) & ! [F] : ( v7_ordinal1(F) => ! [G] : ( ( ~ v2_struct_0(G) & l1_msualg_1(G) ) => ! [H] : ( ( v4_msualg_1(H,G) & l3_msualg_1(H,G) ) => ! [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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t15_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ~ ( r1_glib_000(A,C,E,B) & r1_glib_000(A,D,F,B) & ~ ( C = D & E = F ) & ~ ( C = F & E = D ) ) ) )).
fof(t15_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t15_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ( v1_glib_002(A) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => k1_glib_002(A,B) = k6_glib_000(A) ) ) ) )).
fof(t15_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) ) => ! [B] : ( m3_glib_001(B,A) => k8_glib_003(A,k6_glib_001(A,B)) = k3_finseq_5(k8_glib_003(A,B)) ) ) )).
fof(t15_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( 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)))) = k1_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)))) = k1_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) ) ) ) ) )).
fof(t15_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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] : ! [D] : ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t15_goboard1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m2_finseq_1(C,B) => ! [D] : ( ( v1_matrix_0(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) ) ) ) ) ) )).
fof(t15_goboard2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( ( r2_hidden(A,k4_finseq_1(B)) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => r1_xxreal_0(k1_funct_1(k1_goboard1(B),A),k1_funct_1(k1_goboard1(B),C)) ) ) ) => r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),B,A),k10_xtuple_0(k7_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(B),1))) ) ) ) )).
fof(t15_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( v2_goboard1(C) & v3_goboard1(C) & r1_xxreal_0(1,A) ) => ( v3_relat_1(C) | r1_xxreal_0(k1_matrix_0(C),B) | r1_xxreal_0(k3_finseq_1(C),A) | r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),k1_nat_1(B,1))),k2_goboard5(C,B)) ) ) ) ) ) )).
fof(t15_goboard6,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => k1_tops_1(k15_euclid(2),k2_goboard5(A,k5_numbers)) = a_1_2_goboard6(A) ) )).
fof(t15_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(C)) ) => k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_nat_1(B,1))),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),k1_nat_1(B,1)))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_nat_1(B,1))) ) ) ) ) )).
fof(t15_goboard8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,2),k3_finseq_1(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,2),k1_matrix_0(k2_goboard2(A))) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,2),k3_finseq_1(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,1),k1_nat_1(C,1)) ) => ( ( ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,1),C) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,2),k1_nat_1(C,1)) ) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,1),C) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,2),k1_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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),D,k1_nat_1(C,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,1),k1_nat_1(C,2))),k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,1),k1_nat_1(C,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,2),k1_nat_1(C,2))),k7_xcmplx_0(1,2))),k3_topreal1(2,A)) ) ) ) ) ) ) ) )).
fof(t15_goboard9,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k3_finseq_1(A)) & k1_tops_1(k15_euclid(2),k4_goboard5(A,B)) = k1_xboole_0 ) ) ) )).
fof(t15_gobrd11,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( v1_xreal_0(B) => ( A = a_1_5_gobrd11(B) => v4_pre_topc(A,k15_euclid(2)) ) ) ) )).
fof(t15_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(D)) & r1_goboard1(u1_struct_0(k15_euclid(2)),D,E) & r2_hidden(k4_tarski(A,B),k2_matrix_0(E)) & r2_hidden(k4_tarski(A,k1_nat_1(B,1)),k2_matrix_0(E)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,k1_nat_1(B,1)) ) => k2_gobrd13(D,E,C) = k3_goboard5(E,A,B) ) ) ) ) ) ) )).
fof(t15_gobrd14,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t15_gr_cy_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k2_gr_cy_1)) => k2_group_1(k2_gr_cy_1,A) = k4_xcmplx_0(A) ) )).
fof(t15_gr_cy_2,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t15_gr_cy_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_gr_cy_3(A) ) => ? [B] : ( v7_ordinal1(B) & v1_int_2(B) & v2_gr_cy_3(B) & ? [C] : ( v15_algstr_0(C) & m1_group_2(C,k3_int_7(A)) & ? [D] : ( v15_algstr_0(D) & m1_group_2(D,k3_int_7(A)) & ? [E] : ( v15_algstr_0(E) & m1_group_2(E,k3_int_7(A)) & ? [F] : ( 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) = k3_xcmplx_0(2,B) & ! [G] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t15_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v1_graph_1(B) & m3_graph_1(B,A) ) => ! [C] : ( ( 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 ) ) ) ) )).
fof(t15_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_xxreal_0(1,C) => ( r1_xxreal_0(k3_finseq_1(B),C) | k1_funct_1(k3_graph_2(A,B),k1_nat_1(k3_finseq_1(A),C)) = k1_funct_1(B,k1_nat_1(C,1)) ) ) ) ) ) )).
fof(t15_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t15_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( ( v7_graph_1(E,A) & m2_graph_1(E,A) ) => ! [F] : ( ( v7_graph_1(F,A) & m2_graph_1(F,A) ) => ! [G] : ( ( v7_graph_1(G,A) & m2_graph_1(G,A) ) => ( ( r3_graph_4(A,C,F) & r3_graph_4(A,D,G) & k1_funct_1(C,k3_finseq_1(C)) = k1_funct_1(D,1) & E = k8_finseq_1(u4_struct_0(A),F,G) & B = k4_graph_2(u1_struct_0(A),C,D) ) => r3_graph_4(A,B,E) ) ) ) ) ) ) ) ) )).
fof(t15_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v7_graph_1(B,A) & v1_graph_4(B,A) & m2_graph_1(B,A) ) => v2_funct_1(B) ) ) )).
fof(t15_graphsp,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(C) & v2_graph_1(C) & v6_graph_1(C) & l1_graph_1(C) ) => ! [D] : ( ( v7_graph_1(D,C) & m2_graph_1(D,C) ) => ! [E] : ( ( v7_graph_1(E,C) & m2_graph_1(E,C) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(C)) => ! [H] : ( m1_subset_1(H,u1_struct_0(C)) => ! [I] : ( m1_subset_1(I,u1_struct_0(C)) => ( ( r2_hidden(B,u4_struct_0(C)) & r8_graph_5(C,G,H,D,A,F) & E = k7_finseq_1(D,k9_finseq_1(B)) & r1_graph_4(C,H,I,B) & r2_hidden(G,A) & ! [J] : ( m1_subset_1(J,u1_struct_0(C)) => ( r2_hidden(J,A) => ! [K] : ~ ( 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(A,k1_tarski(H)),F) ) ) ) ) ) ) ) ) ) )).
fof(t15_grcat_1,axiom,( ! [A] : ( ( v1_grcat_1(A) & v2_grcat_1(A) & l1_grcat_1(A) ) => ? [B] : ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) & ? [C] : ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) & ? [D] : ( 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) ) ) ) ) )).
fof(t15_grfunc_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( ( r2_hidden(A,k9_xtuple_0(C)) & D = k2_xboole_0(B,C) ) => k1_funct_1(D,A) = k1_funct_1(C,A) ) ) ) ) )).
fof(t15_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t15_groeb_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ( v8_rewrite1(k3_polyred(A,B,C,D)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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(k12_polynom1(A,C),D)) => r1_rewrite1(k3_polyred(A,B,C,D),E,k8_polynom1(A,C)) ) ) ) ) ) ) ) )).
fof(t15_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v1_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => r8_pboole(k15_pre_poly(A),k5_polynom7(A,B,k5_polynom1(A,B,C,D),E),k5_polynom1(A,B,k5_polynom7(A,B,C,E),k5_polynom7(A,B,D,E))) ) ) ) ) ) )).
fof(t15_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l6_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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),k7_polynom1(A,C,D,k6_termord(A,B,C,D)),k5_termord(A,B,C,D)) ) ) ) ) )).
fof(t15_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & k6_algstr_0(A,D,B) = C ) ) ) ) )).
fof(t15_group_10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v7_ordinal1(D) & v1_int_2(D) ) => ~ ( A = k3_xcmplx_0(k1_newton(D,C),B) & ~ r1_nat_d(D,B) & k4_nat_d(k4_newton(k1_newton(D,C),A),D) = k5_numbers ) ) ) ) ) )).
fof(t15_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t15_group_14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(A,B),k2_zfmisc_1(A,k4_card_3(k9_finseq_1(B)))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),k2_zfmisc_1(A,k4_card_3(k9_finseq_1(B)))))) & v2_funct_1(C) & v2_funct_2(C,k2_zfmisc_1(A,k4_card_3(k9_finseq_1(B)))) & ! [D] : ! [E] : ( ( r2_hidden(D,A) & r2_hidden(E,B) ) => k1_binop_1(C,D,E) = k4_tarski(D,k9_finseq_1(E)) ) ) ) ) )).
fof(t15_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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))) ) ) ) ) )).
fof(t15_group_3,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t15_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( ( 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),k4_ordinal1,u1_struct_0(A),D,B) => k3_group_4(A,B) = k3_group_4(A,C) ) ) ) ) ) ) )).
fof(t15_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t15_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ! [C] : ( ( 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))) ) ) ) )).
fof(t15_group_7,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t15_group_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_subset_1(F,u1_struct_0(A)) & D = k6_algstr_0(A,k6_algstr_0(A,B,F),C) & r2_hidden(F,E) ) ) ) ) ) ) ) )).
fof(t15_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => k4_group_9(A,B) = k4_group_9(A,C) ) ) )).
fof(t15_groupp_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v8_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_group_2(C,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( ( v2_group_10(C,A) & r1_struct_0(C,D) ) => v1_groupp_1(D,A,B) ) ) ) ) ) )).
fof(t15_grsolv_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v15_algstr_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( v15_algstr_0(D) & m1_group_2(D,A) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t15_hahnban,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( 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] : ( 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] : ( 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] : ( m1_subset_1(G,u1_struct_0(C)) & ? [H] : ( v1_xreal_0(H) & 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t15_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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] : ( ( 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))) ) ) ) ) ) )).
fof(t15_hallmar1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,k1_zfmisc_1(A)) ) => ( v1_hallmar1(B,A) => v2_relat_1(B) ) ) ) )).
fof(t15_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_xxreal_0(k1_funct_1(k6_weierstr(A,B),C),k2_xcmplx_0(k3_metric_1(A,C,D),k1_funct_1(k6_weierstr(A,B),D))) ) ) ) ) )).
fof(t15_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => r1_tarski(B,k7_glib_001(A,B,C)) ) ) ) )).
fof(t15_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)))) ) ) )).
fof(t15_hermitan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => k3_real_1(k3_complex1(A),k3_complex1(k2_complfld(A))) = k3_xcmplx_0(2,k3_complex1(A)) ) )).
fof(t15_hessenbe,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( ~ r1_collsp(A,F,B,C) & r1_collsp(A,F,B,D) & r1_collsp(A,F,C,E) & F != D & F != E & r1_collsp(A,F,D,E) ) ) ) ) ) ) ) )).
fof(t15_heyting1,axiom,( ! [A] : ( 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) ) )).
fof(t15_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( m1_subset_1(D,k5_finsub_1(k4_partfun1(A,B))) => ! [E] : ~ ( r2_hidden(E,k3_heyting2(A,B,C,D)) & ! [F] : ( ( 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 ) ) ) ) ) ) )).
fof(t15_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => r1_xboole_0(k3_heyting3(A,B),k6_domain_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,k1_nat_1(k2_nat_1(2,A),3),B))) ) ) )).
fof(t15_hfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t15_hilbasis,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k14_polynom3(A))) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( B = C => k4_algstr_0(k14_polynom3(A),B) = k5_vfunct_1(k4_ordinal1,A,C) ) ) ) ) )).
fof(t15_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ( r2_hidden(B,k6_hilbert1) => r2_hidden(k3_hilbert1(A,B),k6_hilbert1) ) ) ) )).
fof(t15_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( 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)) ) ) ) )).
fof(t15_hilbert3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ! [D] : ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,C,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,A))) ) => ! [F] : ( ( 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) ) ) ) ) )).
fof(t15_hurwitz,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k5_vfunct_1(k4_ordinal1,A,k3_polynom5(A,B,C)),k3_polynom5(A,B,k4_algstr_0(A,C))) ) ) ) )).
fof(t15_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => r1_idea_1(C,k4_idea_1(C,A,B)) ) ) ) )).
fof(t15_ideal_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t15_incproj,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_collsp(A,B,C,F) & r1_collsp(A,D,E,F) ) ) ) ) ) ) & ! [B] : ( m1_subset_1(B,u2_incsp_1(k3_incproj(A))) => ! [C] : ( m1_subset_1(C,u2_incsp_1(k3_incproj(A))) => ? [D] : ( 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) ) ) ) ) ) )).
fof(t15_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => v3_incsp_1(k8_domain_1(u1_incsp_1(A),B,B,C),A) ) ) ) )).
fof(t15_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & 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)) ) ) ) )).
fof(t15_instalg1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => m1_instalg1(A,A) ) )).
fof(t15_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ( ( r2_int_1(A,B,D) & r2_int_1(B,C,D) ) => r2_int_1(A,C,D) ) ) ) ) ) )).
fof(t15_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( r2_int_1(A,B,C) <=> r1_int_1(C,k6_xcmplx_0(A,B)) ) ) ) ) )).
fof(t15_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ~ ( r1_int_2(A,C) & ! [D] : ( v1_int_1(D) => k5_int_1(k6_xcmplx_0(k3_xcmplx_0(A,D),B),C) != k5_numbers ) ) ) ) ) )).
fof(t15_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ~ ( ~ r1_xxreal_0(B,2) & k3_int_2(A,B) = 1 & r1_int_5(A,B) & ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ~ ( k5_int_1(k6_xcmplx_0(k1_pepin(C),A),B) = k5_numbers & k5_int_1(k6_xcmplx_0(k1_pepin(D),A),B) = k5_numbers & ~ r2_int_1(C,D,B) ) ) ) ) ) ) )).
fof(t15_int_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r1_int_2(A,B) => k2_int_2(A,B) = k1_int_2(k3_xcmplx_0(A,B)) ) ) ) )).
fof(t15_int_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k8_newton) & v1_funct_1(A) & v1_partfun1(A,k8_newton) & v4_valued_0(A) & v2_pre_poly(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k8_newton) & v1_funct_1(B) & v1_partfun1(B,k8_newton) & v4_valued_0(B) & v2_pre_poly(B) ) => ( ( v1_int_7(A) & v1_int_7(B) & k8_nat_3(k8_newton,A) = k8_nat_3(k8_newton,B) ) => r8_pboole(k8_newton,A,B) ) ) ) )).
fof(t15_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_int_2(B,C) => ( r1_xxreal_0(C,1) | ( r1_int_2(k3_pepin(B,C),A) <=> k3_pepin(k1_newton(B,A),C) = k3_pepin(B,C) ) ) ) ) ) ) )).
fof(t15_integr10,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( ( k1_relset_1(k1_numbers,A) = k2_limfunc1(k5_numbers) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,k3_limfunc1(k5_numbers)) => r3_integr10(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,A,k6_integr10(C)),k5_numbers) ) ) ) => ( ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,k3_limfunc1(k5_numbers)) => r3_integr10(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_valued_1(k1_numbers,k1_numbers,A,B),k6_integr10(C)),k5_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)) ) ) ) ) )).
fof(t15_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k3_xcmplx_0(2,k28_sin_cos)) => k2_integra5(A,k41_valued_1(k1_numbers,k1_numbers,k16_sin_cos)) = k28_sin_cos ) ) )).
fof(t15_integr12,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( 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,E,F),k3_taylor_1))) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,G) => ( k1_funct_1(D,H) = k7_xcmplx_0(H,A) & ~ r1_xxreal_0(k1_funct_1(D,H),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(D,H)) & k1_funct_1(E,H) = 1 ) ) ) & r2_relset_1(k1_numbers,k1_numbers,F,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k1_taylor_1(2))) & G = k1_relset_1(k1_numbers,C) & r2_relset_1(k1_numbers,k1_numbers,C,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k1_sin_cos9)) ) => ( A = k5_numbers | k2_integra5(B,C) = k6_xcmplx_0(k1_funct_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,D,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,E,F),k3_taylor_1),k7_xcmplx_0(A,2))),k2_seq_4(B)),k1_funct_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,D,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,E,F),k3_taylor_1),k7_xcmplx_0(A,2))),k3_seq_4(B))) ) ) ) ) ) ) ) ) ) )).
fof(t15_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k18_sin_cos),k1_partfun2(k1_numbers,C)),k3_rfunct_1(k1_numbers,k1_numbers,k3_taylor_1,k41_valued_1(k1_numbers,k1_numbers,k18_sin_cos)))) & r1_tarski(C,k1_relset_1(k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k26_sin_cos))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k26_sin_cos),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k26_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t15_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k7_xcmplx_0(k1_funct_1(k16_sin_cos,k7_xcmplx_0(1,D)),k3_xcmplx_0(k1_square_1(D),k1_square_1(k1_funct_1(k18_sin_cos,k7_xcmplx_0(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) = k6_xcmplx_0(k1_funct_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)),k2_seq_4(A)),k1_funct_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)),k3_seq_4(A))) ) ) ) ) )).
fof(t15_integr15,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_euclid(B)))) ) => ! [E] : ( ( 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)))) ) ) ) ) ) )).
fof(t15_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t15_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t15_integra1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => k1_rvsum_1(k7_rfunct_1(B,B)) = k1_seq_4(1) ) ) )).
fof(t15_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( ( v3_xxreal_2(B) & r1_xxreal_0(k5_numbers,A) ) => k3_seq_4(k1_integra2(B,A)) = k3_xcmplx_0(A,k3_seq_4(B)) ) ) ) )).
fof(t15_integra4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t15_integra5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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)) ) => ( k3_seq_4(k1_rvsum_1(k2_partfun1(k1_numbers,k1_numbers,B,A))) = k1_funct_1(B,k3_seq_4(A)) & k2_seq_4(k1_rvsum_1(k2_partfun1(k1_numbers,k1_numbers,B,A))) = k1_funct_1(B,k2_seq_4(A)) ) ) ) ) )).
fof(t15_integra7,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( ! [F] : ~ ( r2_hidden(F,A) & k1_funct_1(E,F) = k5_numbers ) & r1_integra7(A,D,B) & r1_integra7(A,E,C) ) => r1_integra7(A,k3_rfunct_1(k1_numbers,k1_numbers,D,E),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,B,E),k20_valued_1(k1_numbers,k1_numbers,k1_numbers,D,C)),k20_valued_1(k1_numbers,k1_numbers,k1_numbers,E,E))) ) ) ) ) ) )).
fof(t15_integra8,axiom,( k4_sin_cos6(k7_xcmplx_0(k3_square_1(2),2)) = k7_xcmplx_0(k28_sin_cos,4) )).
fof(t15_integra9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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),k18_sin_cos))) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k16_sin_cos),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k16_sin_cos),k3_seq_4(A))) ) ) ) )).
fof(t15_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => B = k2_interva1(A,k5_interva1(A,B),k6_interva1(A,B)) ) ) )).
fof(t15_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ( v8_intpro_1(A) <=> k7_intpro_1(A) = A ) ) )).
fof(t15_irrat_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_series_1(k1_valued_0(k1_numbers,A,1)) => ( v1_series_1(A) & k4_series_1(A) = k2_xcmplx_0(k1_funct_1(A,k5_numbers),k4_series_1(k1_valued_0(k1_numbers,A,1))) ) ) ) )).
fof(t15_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & 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(k6_cat_2(A,B),k6_cat_2(B,A)) ) ) )).
fof(t15_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,k6_cat_2(A,B),C) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => k2_nattra_1(B,C,k10_cat_2(A,B,C,D,k3_graph_1(A,E)),k10_cat_2(A,B,C,D,k4_graph_1(A,E)),k4_isocat_2(A,B,C,D,E),F) = k9_cat_2(A,B,C,D,E,k4_cat_1(B,F)) ) ) ) ) ) ) )).
fof(t15_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t15_jct_misc,axiom,( ! [A] : ( ( 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)) ) )).
fof(t15_jgraph_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(t15_jgraph_4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k14_euclid(2))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( C = k9_metric_1(k14_euclid(2),A,B) => v2_compts_1(C,k15_euclid(2)) ) ) ) ) )).
fof(t15_jgraph_5,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k5_topmetr)) => ! [I] : ( m1_subset_1(I,u1_struct_0(k5_topmetr)) => ~ ( H = k5_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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t15_jgraph_6,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k5_topmetr)) => ! [I] : ( m1_subset_1(I,u1_struct_0(k5_topmetr)) => ~ ( H = k5_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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t15_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t15_jordan,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( 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) ) ) ) )).
fof(t15_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ( v3_pre_topc(a_1_1_jordan1(A),k15_euclid(2)) & m1_subset_1(a_1_1_jordan1(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ) )).
fof(t15_jordan10,axiom,( ! [A] : ( ( 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))) ) )).
fof(t15_jordan11,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t15_jordan12,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(t15_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( r1_jordan1h(A,B) => r1_tarski(k3_goboard9(k1_jordan13(A,B)),k1_jordan2c(2,A)) ) ) ) )).
fof(t15_jordan16,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t15_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ~ ( C != D & r1_jordan17(A,B,C,D,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ~ ( F != C & F != D & r1_jordan17(A,B,C,F,D) ) ) ) ) ) ) ) ) )).
fof(t15_jordan18,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ~ ( r1_topreal1(k15_euclid(2),C,D,B) & r1_tarski(B,A) & ! [E] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(t15_jordan19,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & ~ r1_xxreal_0(A,k5_numbers) & k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k9_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) = k1_tarski(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k8_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D)) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k9_jordan6(B)) ) ) ) ) ) ) )).
fof(t15_jordan1b,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t15_jordan1c,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v1_int_1(D) => ( D = k1_int_1(k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k18_euclid(C),k9_pscomp_1(A)),k6_xcmplx_0(k7_pscomp_1(A),k9_pscomp_1(A))),k1_newton(2,B)),2)) => r1_xxreal_0(k2_xcmplx_0(k9_pscomp_1(A),k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k7_pscomp_1(A),k9_pscomp_1(A)),k1_newton(2,B)),k6_xcmplx_0(D,2))),k18_euclid(C)) ) ) ) ) ) )).
fof(t15_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & ~ r1_xxreal_0(k3_finseq_1(k2_jordan9(B,A)),C) & r2_hidden(k24_pscomp_1(B),k2_gobrd13(k2_jordan9(B,A),k1_jordan8(B,A),C)) ) ) ) )).
fof(t15_jordan1e,axiom,( ! [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] : ( v7_ordinal1(B) => ( r1_xxreal_0(3,k3_finseq_1(k1_jordan1e(A,B))) & r1_xxreal_0(3,k3_finseq_1(k2_jordan1e(A,B))) ) ) ) )).
fof(t15_jordan1g,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t15_jordan1h,axiom,( ! [A] : ( ( v1_matrix_0(A) & v1_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)) ) )).
fof(t15_jordan1k,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => k1_jordan2c(A,k1_struct_0(k15_euclid(A))) = k1_struct_0(k15_euclid(A)) ) ) )).
fof(t15_jordan20,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(2),A)))) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( ( 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)) ) ) ) ) ) )).
fof(t15_jordan21,axiom,( ! [A] : ( ( 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)) ) )).
fof(t15_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,k5_numbers) => k1_jordan21(k3_topreal1(2,k2_jordan9(A,B))) = k19_euclid(k7_xcmplx_0(k2_xcmplx_0(k8_pscomp_1(k3_topreal1(2,k2_jordan9(A,B))),k6_pscomp_1(k3_topreal1(2,k2_jordan9(A,B)))),2),k2_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,k2_jordan9(A,B)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),k3_finseq_1(k1_jordan8(A,B)))))))) ) ) ) )).
fof(t15_jordan23,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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) = k13_matrix_0(u1_struct_0(k15_euclid(2)),B) ) ) ) )).
fof(t15_jordan24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t15_jordan2b,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( m1_subset_1(E,k4_ordinal1) => ( ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t15_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => r1_xboole_0(k1_jordan2c(A,B),k2_jordan2c(A,B)) ) ) )).
fof(t15_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) )).
fof(t15_jordan4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ( ( 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 ) ) ) ) ) )).
fof(t15_jordan5a,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k4_topmetr(A,B))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k4_topmetr(A,B))) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ! [K] : ( v1_xreal_0(K) => ~ ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t15_jordan5b,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( v4_topreal1(B) & r1_xxreal_0(1,A) & r1_xxreal_0(k1_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,k1_nat_1(A,1)),C) ) ) ) ) )).
fof(t15_jordan5c,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t15_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( 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))))) ) ) ) )).
fof(t15_jordan7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t15_jordan8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t15_jordan9,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( ( r1_goboard1(u1_struct_0(k15_euclid(2)),B,A) & v1_topreal1(B) ) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(B)) ) => ( r1_xboole_0(k1_tops_1(k15_euclid(2),k3_gobrd13(B,A,C)),k3_topreal1(2,B)) & r1_xboole_0(k1_tops_1(k15_euclid(2),k2_gobrd13(B,A,C)),k3_topreal1(2,B)) ) ) ) ) ) ) )).
fof(t15_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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) ) ) )).
fof(t15_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v3_ordinal1(D) => k3_knaster(A,B,C,k1_ordinal1(D)) = k1_funct_1(B,k3_knaster(A,B,C,D)) ) ) ) ) )).
fof(t15_kolmog01,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( m1_kolmog01(D,B,A,C) => ( ~ v1_xboole_0(k6_kolmog01(B,A,C,D)) & v1_prob_1(k6_kolmog01(B,A,C,D),A) & v4_prob_1(k6_kolmog01(B,A,C,D),A) & m1_subset_1(k6_kolmog01(B,A,C,D),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ) ) ) )).
fof(t15_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( ! [D] : ( v7_ordinal1(D) => k1_funct_1(B,D) = C ) => k3_kurato_0(A,B) = C ) ) ) )).
fof(t15_kurato_1,axiom,( 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) )).
fof(t15_kurato_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => k2_pre_topc(A,k1_kurato_2(A,B)) = k1_kurato_2(A,B) ) ) )).
fof(t15_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t15_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => k1_funct_1(k1_latsubgr(A),B) != k1_xboole_0 ) ) )).
fof(t15_latsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t15_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ! [C] : ( 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) ) ) ) )).
fof(t15_lattice3,axiom,( ! [A] : ( ( v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k11_lattice3(A,B,C) = k11_lattice3(A,C,B) ) ) ) )).
fof(t15_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t15_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t15_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & v2_lattice6(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v4_lattice6(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r1_lattice6(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_lattice6(A,B,D) => D = C ) ) ) ) ) ) )).
fof(t15_lattice7,axiom,( ! [A] : ( ( 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)))) ) )).
fof(t15_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v3_ordinal1(B) => k3_lattice8(A,k1_ordinal1(B)) = k1_lattice8(k3_lattice8(A,B)) ) ) )).
fof(t15_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k4_lattices(A,k6_lattices(A),B) = B ) ) )).
fof(t15_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( ( v4_lexbfs(B,A) & m1_lexbfs(B,A) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t15_lfuzzy_0,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t15_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t15_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_limfunc1(A) => v2_limfunc1(k32_valued_1(k4_ordinal1,k1_numbers,A)) ) & ( v2_limfunc1(A) => v1_limfunc1(k32_valued_1(k4_ordinal1,k1_numbers,A)) ) ) ) )).
fof(t15_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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) ) ) ) ) ) )).
fof(t15_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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) ) ) ) ) ) )).
fof(t15_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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) ) ) ) ) )).
fof(t15_lmod_5,axiom,( ! [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) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t15_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ! [H] : ( m1_subset_1(H,u1_struct_0(D)) => ! [I] : ( m1_subset_1(I,u1_struct_0(D)) => ! [J] : ( m1_subset_1(J,u1_struct_0(D)) => ( r1_lmod_6(A,C,D) => ( k4_struct_0(C) = k4_struct_0(D) & ( ( F = I & G = J ) => k1_algstr_0(C,F,G) = k1_algstr_0(D,I,J) ) & ( E = H => k4_vectsp_1(A,C,B,E) = k4_vectsp_1(A,D,B,H) ) & ( E = H => k4_algstr_0(D,H) = k4_algstr_0(C,E) ) & ( ( F = I & G = J ) => k5_algstr_0(C,F,G) = k5_algstr_0(D,I,J) ) & r1_struct_0(C,k4_struct_0(D)) & r1_struct_0(D,k4_struct_0(C)) & ( ( r1_struct_0(C,I) & r1_struct_0(C,J) ) => r1_struct_0(C,k1_algstr_0(D,I,J)) ) & ( r1_struct_0(C,H) => r1_struct_0(C,k4_vectsp_1(A,D,B,H)) ) & ( r1_struct_0(C,H) => r1_struct_0(C,k4_algstr_0(D,H)) ) & ( ( r1_struct_0(C,I) & r1_struct_0(C,J) ) => r1_struct_0(C,k5_algstr_0(D,I,J)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t15_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(k13_lmod_7(A,B,C))) => ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & D = k14_lmod_7(A,B,C,E) ) ) ) ) ) )).
fof(t15_lopban_1,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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),k9_rsspace(k5_lopban_1(u1_struct_0(A),B),k7_lopban_1(A,B)),k7_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))),k5_lopban_1(u1_struct_0(A),B)) ) ) )).
fof(t15_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k8_lopban_2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k8_lopban_2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k8_lopban_2(A))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( 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] : ( 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,k2_xcmplx_0(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,k3_xcmplx_0(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),k3_xcmplx_0(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)) ) ) ) ) ) ) ) )).
fof(t15_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,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))) ) ) ) )).
fof(t15_lopban_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( ~ r1_xxreal_0(A,k5_numbers) => k9_nat_1(u1_struct_0(B),k4_lopban_4(B,C),A) = k9_nat_1(u1_struct_0(B),C,k7_nat_d(A,1)) ) ) ) ) )).
fof(t15_lopban_7,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r1_xxreal_0(k2_normsp_0(A,C),k2_normsp_0(k7_prvect_3(A,B),k1_lopban_7(A,B,C,D))) & r1_xxreal_0(k2_normsp_0(B,D),k2_normsp_0(k7_prvect_3(A,B),k1_lopban_7(A,B,C,D))) ) ) ) ) ) )).
fof(t15_lopclset,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v7_struct_0(B) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B) ) => ( r2_hidden(A,k7_lopclset(B)) <=> ? [C] : ( ~ 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) ) ) ) )).
fof(t15_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_normsp_1(B) ) => ( B = g1_normsp_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_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) ) ) ) ) ) )).
fof(t15_lpspacc1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_rfunct_3(C,B,k2_numbers,k3_rfunct_3(B,k2_numbers)) => ! [D] : ( m2_rfunct_3(D,B,k2_numbers,k3_rfunct_3(B,k2_numbers)) => k1_binop_1(k7_lpspacc1(B),k1_binop_1(k8_lpspacc1(B),A,C),D) = k1_binop_1(k8_lpspacc1(B),A,k2_lpspace1(B,k2_numbers,k7_lpspacc1(B),C,D)) ) ) ) ) )).
fof(t15_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) )).
fof(t15_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( ( A = k1_relset_1(A,D) & ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,k1_relset_1(A,D)) => k5_numbers = k1_funct_1(D,E) ) ) ) => ( r3_mesfunc6(A,B,C,D) & k1_mesfunc6(A,B,C,D) = k5_numbers ) ) ) ) ) ) )).
fof(t15_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(C),k1_domain_1(k4_ordinal1,k1_hilbert1,B,k3_hilbert1(k1_ltlaxio1(k2_ltlaxio1(A)),k2_ltlaxio1(k1_ltlaxio1(A))))) = 1 ) ) ) )).
fof(t15_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m2_finseq_1(B,k1_hilbert1) => k4_ltlaxio2(k8_finseq_1(k1_hilbert1,B,k12_finseq_1(k1_hilbert1,A))) = k8_finseq_1(k1_hilbert1,k4_ltlaxio2(B),k12_finseq_1(k1_hilbert1,k1_ltlaxio1(A))) ) ) )).
fof(t15_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => k5_ltlaxio3(A) = k3_tarski(a_1_0_ltlaxio3(A)) ) )).
fof(t15_ltlaxio4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) ) => ? [B] : ( m1_subset_1(B,k1_hilbert1) & r2_hidden(B,k5_ltlaxio3(A)) & k5_ltlaxio3(k7_subset_1(k1_hilbert1,k5_ltlaxio3(A),k6_domain_1(k1_hilbert1,B))) = k7_subset_1(k1_hilbert1,k5_ltlaxio3(A),k6_domain_1(k1_hilbert1,B)) ) ) )).
fof(t15_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ( r2_hidden(k8_cqc_lang(A,D,k8_cqc_lang(A,C,B)),k4_cqc_the1(A)) => r2_hidden(k8_cqc_lang(A,C,k8_cqc_lang(A,D,B)),k4_cqc_the1(A)) ) ) ) ) ) )).
fof(t15_margrel1,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k4_xboolean(B,k4_xboolean(C,A)) = k4_xboolean(k4_xboolean(B,C),A) ) ) ) )).
fof(t15_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t15_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,B,B) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( v2_matrix10(C) => ( r1_xxreal_0(k5_numbers,A) | v1_matrix10(k6_matrix10(B,A,C)) ) ) ) ) ) )).
fof(t15_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k4_matrix_2(k1_nat_1(A,2)))) => ! [D] : ( m1_matrix_2(D,k3_matrix_2(k1_nat_1(A,2))) => ( ( D = k3_group_4(k4_matrix_2(k1_nat_1(A,2)),C) & ! [E] : ( v7_ordinal1(E) => ~ ( r2_hidden(E,k4_finseq_1(C)) & ! [F] : ( m1_matrix_2(F,k3_matrix_2(k1_nat_1(A,2))) => ~ ( k1_funct_1(C,E) = F & v4_matrix_2(F,k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))) ) ) ) ) ) => ( ( k4_nat_d(k3_finseq_1(C),2) = k5_numbers => 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)) ) ) ) ) ) ) ) )).
fof(t15_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [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] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(E),C,D) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(E))) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(E),C,D) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(E))) ) => ( ( r2_hidden(B,k2_finseq_1(k1_matrix_0(F))) & r2_hidden(A,k2_finseq_1(k1_matrix_0(F))) & G = k4_matrix_0(u1_struct_0(E),F) ) => ( r1_xxreal_0(C,k5_numbers) | r1_xxreal_0(D,k5_numbers) | k4_matrix_0(u1_struct_0(E),k1_matrix12(C,D,E,G,B,A)) = k4_matrix12(C,D,E,F,B,A) ) ) ) ) ) ) ) ) ) )).
fof(t15_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & v1_matrix_2(D,A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & v1_matrix_2(E,A,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ( C = k4_matrix_3(B,D,E) => ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & v1_matrix_2(C,A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & k13_matrix_3(A,B,C) = k11_fvsum_1(B,k13_matrix_3(A,B,D),k13_matrix_3(A,B,E)) ) ) ) ) ) ) ) )).
fof(t15_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,u1_struct_0(A),k5_numbers,k5_numbers) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ( B = k1_xboole_0 & B = k3_matrix_1(A,k5_numbers) & B = k2_matrix_1(A,k5_numbers) ) ) ) )).
fof(t15_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,D,C,B) & m2_finseq_1(E,k3_finseq_2(D)) ) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,D,C,A) & m2_finseq_1(F,k3_finseq_2(D)) ) => ! [G] : ( v7_ordinal1(G) => ( r2_hidden(G,k2_finseq_1(C)) => k7_matrix_0(D,k1_matrix15(D,C,B,A,E,F),G) = k8_finseq_1(D,k7_matrix_0(D,E,G),k7_matrix_0(D,F,G)) ) ) ) ) ) ) ) ) )).
fof(t15_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(B),A,A) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(B))) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(B),A,A) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(B))) ) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(B),A,A) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix16(F,u1_struct_0(B)) & v1_matrix16(G,u1_struct_0(B)) & v1_matrix16(H,u1_struct_0(B)) ) => v1_matrix16(k1_matrix_4(B,k1_matrix_4(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)) ) ) ) ) ) ) ) ) ) )).
fof(t15_matrix17,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t15_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ( v1_matrix_0(k12_finseq_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),k12_finseq_1(A,B))) & v2_matrix_0(k12_finseq_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),k12_finseq_1(A,B)),A,1,1) & m2_finseq_1(k12_finseq_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),k12_finseq_1(A,B)),k3_finseq_2(A)) ) ) ) )).
fof(t15_matrix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k4_tarski(C,D),k2_matrix_0(k3_matrix_1(B,A))) => ( ( C = D => k1_funct_1(k7_matrix_0(u1_struct_0(B),k3_matrix_1(B,A),C),D) = k5_struct_0(B) ) & ( C != D => k1_funct_1(k7_matrix_0(u1_struct_0(B),k3_matrix_1(B,A),C),D) = k4_struct_0(B) ) ) ) ) ) ) ) )).
fof(t15_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(D) & k1_matrix_4(A,D,B) = k1_matrix_4(A,D,C) ) => B = C ) ) ) ) ) )).
fof(t15_matrix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k1_matrix_5(k8_matrix_5(A,B)) = k1_matrix_3(k1_complfld,A,B) ) ) )).
fof(t15_matrix_6,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(A),B,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(A),B,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ( r2_matrix_6(B,A,D,C) => r1_matrix_6(B,A,C,D) ) ) ) ) ) )).
fof(t15_matrix_7,axiom,( ! [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] : ( v7_ordinal1(B) => ( r1_xxreal_0(1,B) => k12_matrix_3(B,A,k1_matrix_3(A,B,B)) = k4_struct_0(A) ) ) ) )).
fof(t15_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( k4_matrix_3(B,D,C) = k3_matrix_1(B,A) => v1_matrix_8(k4_matrix_3(B,C,D),A,B) ) ) ) ) ) )).
fof(t15_matrix_9,axiom,( k3_finseq_5(k1_finseq_2(3)) = k3_finseq_4(k4_ordinal1,3,2,1) )).
fof(t15_matrixc1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k2_numbers) => ! [C] : ( m2_finseq_2(C,k2_numbers,k4_finseq_2(A,k2_numbers)) => ! [D] : ( m2_finseq_2(D,k2_numbers,k4_finseq_2(A,k2_numbers)) => k10_seq_4(k5_matrixc1(C,D),B) = k5_matrixc1(k10_seq_4(C,B),D) ) ) ) ) )).
fof(t15_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => k10_matrixj1(A,k4_matrixj1(A,B)) = k13_matrix_0(k4_ordinal1,k3_finseq_1(B)) ) ) )).
fof(t15_matrixj2,axiom,( ! [A] : ( l6_algstr_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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) = k5_numbers <=> k2_struct_0(B) = k6_domain_1(u1_struct_0(B),k4_struct_0(B)) ) ) ) ) )).
fof(t15_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => A = k4_rvsum_1(k8_rvsum_1(A,B),B) ) ) ) )).
fof(t15_matrixr2,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( k3_finseq_1(B) = k1_matrix_0(C) => ( r1_xxreal_0(k3_finseq_1(C),k5_numbers) | r1_xxreal_0(k3_finseq_1(B),k5_numbers) | k4_matrix_3(A,k2_matrix_3(A,C),B) = k2_matrix_3(A,k4_matrix_3(A,C,B)) ) ) ) ) ) )).
fof(t15_matrlin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => k2_matrlin(A,k3_pre_poly(A,B)) = k4_matrix_0(A,k2_matrlin(A,k3_pre_poly(A,B))) ) ) )).
fof(t15_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m2_finseq_1(E,u1_struct_0(D)) => ( C = E => k4_rlvect_1(B,C) = k4_rlvect_1(D,E) ) ) ) ) ) ) )).
fof(t15_matroid0,axiom,( ! [A] : ( ( ~ v3_pencil_1(A) & v1_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ? [C] : ( v3_pre_topc(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & r1_matroid0(A,C,B) ) ) ) )).
fof(t15_matrprob,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(C)) ) => ( r2_hidden(k4_tarski(A,B),k2_matrix_0(D)) <=> ( r2_hidden(A,k4_finseq_1(k8_matrix_0(C,D,B))) & r2_hidden(B,k4_finseq_1(k7_matrix_0(C,D,A))) ) ) ) ) ) ) )).
fof(t15_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,D,A,B) & m2_finseq_1(E,k3_finseq_2(D)) ) => ! [F] : ( v7_ordinal1(F) => ( r2_hidden(F,k2_finseq_1(k1_matrix_0(E))) => k8_matrix_0(D,k4_matrix11(A,B,D,C,E),F) = k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k4_ordinal1,D,C,k8_matrix_0(D,E,F)) ) ) ) ) ) ) ) )).
fof(t15_matrtop2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & v3_valued_0(C) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k2_finseq_1(A))) => ~ ( v2_funct_1(k2_partfun1(k4_ordinal1,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(k4_ordinal1,k3_finseq_2(u1_struct_0(k2_vectsp_1)),D,E)) = k9_matrix13(k2_vectsp_1,A,B,D) & ! [F] : ( m2_vectsp_6(F,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),F) = k1_funct_1(k3_matrtop1(A,B,D),C) & ! [G] : ( v7_ordinal1(G) => ( r2_hidden(G,E) => k1_funct_1(F,k7_matrix_0(u1_struct_0(k2_vectsp_1),D,G)) = k16_rvsum_1(k15_finseq_1(k5_relat_1(C,k8_relset_1(k4_ordinal1,k3_finseq_2(u1_struct_0(k2_vectsp_1)),D,k1_tarski(k7_matrix_0(u1_struct_0(k2_vectsp_1),D,G)))))) ) ) ) ) ) ) ) ) ) ) )).
fof(t15_matrtop3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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),k8_matrix_0(u1_struct_0(k2_vectsp_1),k2_matrtop3(D,A,B,C),B)) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(E,B),k19_sin_cos(A)),k3_xcmplx_0(k1_funct_1(E,C),k4_xcmplx_0(k17_sin_cos(A)))) ) ) ) ) ) ) ) )).
fof(t15_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t15_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( r2_pboole(A,C,B) => r2_pboole(A,k4_pboole(A,C,D),B) ) ) ) ) )).
fof(t15_mcart_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( r2_hidden(A,B) => A = k4_tarski(k1_xtuple_0(A),k2_xtuple_0(A)) ) ) )).
fof(t15_measure1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & k2_relset_1(k9_setfam_1(A),C) = k1_tarski(B) ) ) )).
fof(t15_measure2,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m1_measure2(D,A,B) => ( ? [E] : ( r2_hidden(E,D) & m2_measure1(E,A,B,C) ) => m2_measure1(k1_measure2(A,B,D),A,B,C) ) ) ) ) )).
fof(t15_measure3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k2_measure3(A,B,C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_measure3(A,B,C)))) ) => ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => r2_hidden(k9_nat_1(B,E,F),k3_measure3(A,B,C,k9_nat_1(k2_measure3(A,B,C),D,F))) ) ) ) ) ) )).
fof(t15_measure4,axiom,( ! [A] : ! [B] : ( m1_measure4(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( k12_supinf_2(B,C) = k1_supinf_2 => r2_hidden(C,k1_measure4(A,B)) ) ) ) )).
fof(t15_measure6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xxreal_0(B) => ( ? [C] : ( v1_xxreal_0(C) & r1_xxreal_0(C,B) & A = k2_xxreal_1(C,B) ) => B = k8_supinf_2(A) ) ) ) )).
fof(t15_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k9_setfam_1(k1_numbers)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(k1_numbers)))) ) => ! [B] : ( 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))) ) ) )).
fof(t15_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => k5_member_1(k2_xboole_0(A,B)) = k2_xboole_0(k5_member_1(A),k5_member_1(B)) ) ) )).
fof(t15_membered,axiom,( ! [A] : ( v3_membered(A) => ( ! [B] : ( v1_xreal_0(B) => r2_hidden(B,A) ) => A = k1_numbers ) ) )).
fof(t15_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [C] : ( v7_ordinal1(C) => r2_hidden(k4_struct_0(B),k9_xtuple_0(k7_memstr_0(A,B,C))) ) ) ) )).
fof(t15_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t15_mesfun10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ( ( k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers)) = k1_relset_1(A,k4_mesfunc5(A,k6_numbers,C,k5_numbers)) & v1_mesfunc8(B,A,k6_numbers) & ! [D] : ( v7_ordinal1(D) => r2_relset_1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,B,D),k7_mesfunc1(A,k4_mesfunc5(A,k6_numbers,C,D))) ) ) => ( r2_relset_1(A,k6_numbers,k5_mesfunc8(A,B),k7_mesfunc1(A,k6_mesfunc8(A,C))) & r2_relset_1(A,k6_numbers,k6_mesfunc8(A,B),k7_mesfunc1(A,k5_mesfunc8(A,C))) ) ) ) ) ) )).
fof(t15_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t15_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t15_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( v7_ordinal1(D) => ( ! [E] : ( 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)) ) ) ) ) ) )).
fof(t15_mesfunc1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ! [D] : ( v1_xxreal_0(D) => ( 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))) ) ) ) )).
fof(t15_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( 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 ) ) ) ) )).
fof(t15_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( v6_supinf_2(C) => v6_supinf_2(k2_partfun1(A,k6_numbers,C,B)) ) ) ) )).
fof(t15_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( r1_tarski(D,k1_relset_1(A,C)) => ( r1_mesfunc6(A,B,C,D) <=> ! [E] : ( v1_xreal_0(E) => r2_hidden(k8_subset_1(A,D,k13_mesfunc1(C,E)),B) ) ) ) ) ) ) ) )).
fof(t15_mesfunc7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t15_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k6_numbers)) & v1_mesfunc8(C,A,k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [E] : ( v1_xreal_0(E) => ( ! [F] : ( v7_ordinal1(F) => k9_nat_1(k9_setfam_1(A),D,F) = k9_subset_1(A,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,C,k5_numbers)),k17_mesfunc1(A,k4_mesfunc5(A,k6_numbers,C,F),E)) ) => k3_tarski(k2_relset_1(B,D)) = k9_subset_1(A,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,C,k5_numbers)),k17_mesfunc1(A,k2_mesfunc8(A,C),E)) ) ) ) ) ) ) )).
fof(t15_metric_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( l1_metric_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => r1_tarski(k10_metric_1(B,C,A),k9_metric_1(B,C,A)) ) ) ) )).
fof(t15_metric_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_metric_1(B) ) => ( r2_hidden(A,k2_metric_2(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & A = k1_metric_2(B,C) ) ) ) )).
fof(t15_metric_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(D,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C))) => ! [E] : ( m1_subset_1(E,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C))) => k2_binop_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,k13_metric_3(A,B,C),D,E) = k2_binop_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,k13_metric_3(A,B,C),E,D) ) ) ) ) ) )).
fof(t15_metric_6,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r1_metric_6(A,C,B) => ! [D] : ( v1_xreal_0(D) => ( ~ r1_xxreal_0(D,k5_numbers) => r2_metric_6(A,k8_metric_1(A,B,D),C) ) ) ) ) ) ) )).
fof(t15_metrizts,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v2_tex_2(C,B) => r1_ordinal1(k1_card_1(C),A) ) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) => ( ( v1_tops_2(C,B) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t15_mfold_2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k3_finseq_1(C) = k3_finseq_1(D) ) => k22_rvsum_1(k8_finseq_1(k1_numbers,A,C),k8_finseq_1(k1_numbers,B,D)) = k2_xcmplx_0(k22_rvsum_1(A,B),k22_rvsum_1(C,D)) ) ) ) ) ) )).
fof(t15_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r1_midsp_1(A,B,C,D,E) ) ) ) ) ) )).
fof(t15_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ( ! [B] : ( 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] : ( m1_subset_1(B,u1_struct_0(k15_midsp_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_midsp_1(A))) => ! [D] : ( m1_midsp_1(D,A) => ! [E] : ( m1_midsp_1(E,A) => ( ( B = D & C = E ) => k3_rlvect_1(k15_midsp_1(A),B,C) = k7_midsp_1(A,D,E) ) ) ) ) ) ) ) )).
fof(t15_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_nat_1(A,2)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(B))) => ! [E] : ( ( v4_midsp_2(E,B) & l1_midsp_2(E,B) ) => ! [F] : ( m2_finseq_2(F,u1_struct_0(u1_midsp_2(B,E)),k4_finseq_2(k1_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 ) ) ) ) ) ) ) )).
fof(t15_mmlquer2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ r2_hidden(A,k10_xtuple_0(B)) => k6_mmlquer2(B,A) = k5_numbers ) ) )).
fof(t15_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(t15_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( v2_mod_2(B,A) & v3_mod_2(B,A) & l1_mod_2(B,A) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t15_mod_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t15_mod_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & l1_vectsp_2(D,B) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t15_modal_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(t15_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [E] : ( 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] : ( m1_modelc_1(F,A,B) & k3_funct_2(k4_ordinal1,A,F,k5_numbers) = C & ! [G] : ( m1_subset_1(G,k4_ordinal1) => r3_modelc_1(A,B,D,k3_funct_2(k4_ordinal1,A,F,G),E) ) ) ) ) ) ) ) ) )).
fof(t15_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ( r1_modelc_2(C,k4_modelc_2(A,B)) <=> ( C = A | C = B ) ) ) ) ) )).
fof(t15_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k13_modelc_2(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t15_moebius1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ( ~ r2_hidden(B,k22_pre_poly(k8_newton,k13_nat_3(A))) => k11_nat_3(A,B) = k5_numbers ) ) ) )).
fof(t15_monoid_0,axiom,( ! [A] : ( ( ~ 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)) ) ) ) ) )).
fof(t15_monoid_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t15_morph_01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( ( ~ 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))) ) ) ) )).
fof(t15_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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) ) ) )).
fof(t15_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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)) ) ) ) )).
fof(t15_msafree4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r2_pboole(A,B,C) => ! [D] : ( m2_finseq_1(D,A) => r2_pboole(k4_finseq_1(D),k3_relat_1(D,B),k3_relat_1(D,C)) ) ) ) ) )).
fof(t15_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( l3_msualg_1(C,A) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( ( 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 ) ) ) ) ) ) )).
fof(t15_msscyc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v7_graph_1(B,A) & m1_graph_1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v7_graph_1(C,A) & m1_graph_1(C,A) ) => ! [D] : ( ( ~ 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),k1_nat_1(k3_finseq_1(B),1)) = k1_funct_1(k7_graph_2(A,D),k1_nat_1(k3_finseq_1(D),1)) ) ) ) ) ) ) )).
fof(t15_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_funcop_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t15_mssublat,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) )).
fof(t15_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(t15_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( m2_pboole(E,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t15_msualg_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t15_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_rewrite1(k3_msualg_6(A),C,D) => ! [E] : ( m1_rewrite1(E,k3_msualg_6(A)) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) & v1_funcop_1(F) ) => ( ( k3_finseq_1(E) = k1_nat_1(k3_finseq_1(F),1) & C = k1_funct_1(E,1) & D = k1_funct_1(E,k3_finseq_1(E)) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ! [H] : ( ( v1_relat_1(H) & v1_funct_1(H) ) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( 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,k1_nat_1(G,1)) ) => r1_msualg_6(A,I,J,B,H) ) ) ) ) ) ) => m2_msualg_6(k3_funct_7(k1_funct_1(u3_msualg_1(A,B),C),F),A,B,C,D) ) ) ) ) ) ) ) ) )).
fof(t15_msualg_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m2_nat_lat(B,A) => ( v2_msualg_7(B,A) => v4_lattice3(B) ) ) ) )).
fof(t15_msualg_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(t15_msualg_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & m1_msualg_2(D,A,B) ) => ! [E] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t15_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u4_struct_0(k6_msualg_1(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t15_mycielsk,axiom,( ! [A] : ( ( v3_dilworth(A) & v1_mycielsk(A) & l1_orders_2(A) ) => r1_xxreal_0(k1_dilworth(A),k2_mycielsk(A)) ) )).
fof(t15_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v3_pcomps_1(A) => ( v9_pre_topc(A) & v7_pre_topc(A) ) ) ) )).
fof(t15_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k3_xcmplx_0(A,B) = 1 => A = 1 ) ) ) )).
fof(t15_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_nat_d(B,C) & r1_xxreal_0(1,C) & r1_xxreal_0(1,A) & r1_xxreal_0(A,B) ) => k3_nat_d(k7_nat_d(C,A),B) = k6_xcmplx_0(k3_nat_d(C,B),1) ) ) ) ) )).
fof(t15_nat_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t15_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( ( r2_hidden(C,k3_moebius1(A)) & r2_hidden(E,k3_moebius1(B)) & r2_hidden(D,k3_moebius1(A)) & r2_hidden(F,k3_moebius1(B)) & r1_int_2(A,B) & k3_xcmplx_0(C,E) = k3_xcmplx_0(D,F) ) => ( C = D & E = F ) ) ) ) ) ) ) ) )).
fof(t15_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( k4_nat_d(A,D) = k5_numbers & B = k6_xcmplx_0(A,k3_xcmplx_0(C,D)) ) => k4_nat_d(B,D) = k5_numbers ) ) ) ) ) )).
fof(t15_nat_lat,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => m2_nat_lat(A,A) ) )).
fof(t15_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ( r1_nattra_1(A,B,C,D) => ! [E] : ( m1_nattra_1(E,A,B,C,D) => ! [F] : ( m1_nattra_1(F,A,B,C,D) => ( ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => k2_nattra_1(A,B,C,D,E,G) = k2_nattra_1(A,B,C,D,F,G) ) => r2_funct_2(u1_struct_0(A),u4_struct_0(B),E,F) ) ) ) ) ) ) ) ) )).
fof(t15_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( 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] : ( m1_nfcont_1(E,B,k7_partfun1(u1_struct_0(B),C,D)) => ? [F] : ( m1_ncfcont1(F,A,D) & ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t15_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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)) ) ) ) ) )).
fof(t15_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( v7_ordinal1(D) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k1_valued_0(u1_struct_0(A),k2_normsp_1(A,B,C),D),k2_normsp_1(A,k1_valued_0(u1_struct_0(A),B,D),k1_valued_0(u1_struct_0(A),C,D))) ) ) ) ) )).
fof(t15_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t15_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( 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)) ) ) ) ) ) ) ) ) )).
fof(t15_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_prvect_2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_prvect_2(A))) => ! [D] : ( m1_subset_1(D,k4_card_3(k4_prvect_2(A))) => ! [E] : ( m1_subset_1(E,k4_card_3(k4_prvect_2(A))) => ! [F] : ( 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] : ( m2_subset_1(G,k4_ordinal1,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)) ) ) ) ) ) ) ) ) ) )).
fof(t15_neckla_3,axiom,( ! [A] : ( ( v1_orders_2(A) & v3_necklace(A) & l1_orders_2(A) ) => ( v7_struct_0(A) => k3_necklace(A) = A ) ) )).
fof(t15_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t15_newton,axiom,( ! [A] : ( v7_ordinal1(A) => k2_newton(k1_nat_1(A,1)) = k3_xcmplx_0(k2_newton(A),k1_nat_1(A,1)) ) )).
fof(t15_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r1_nfcont_1(A,B,C,E) & r1_nfcont_1(A,B,D,E) ) => ( r1_nfcont_1(A,B,k6_vfunct_1(u1_struct_0(A),B,C,D),E) & r1_nfcont_1(A,B,k2_vfunct_1(u1_struct_0(A),B,C,D),E) ) ) ) ) ) ) ) )).
fof(t15_nfcont_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t15_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t15_normform,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_finsub_1(B) ) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(A,B)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t15_normsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & k10_xtuple_0(B) = k6_domain_1(u1_struct_0(A),C) ) => ! [C] : ( v7_ordinal1(C) => k1_normsp_0(A,B,C) = k1_normsp_0(A,B,k1_nat_1(C,1)) ) ) ) ) )).
fof(t15_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t15_ntalgo_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,k2_zfmisc_1(k4_numbers,k4_numbers)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,k4_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m2_finseq_1(C,k4_numbers) ) => ! [D] : ( m1_subset_1(D,k4_numbers) => ! [E] : ( m1_subset_1(E,k4_numbers) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k3_finseq_1(B) = k3_finseq_1(A) & ! [F] : ( v7_ordinal1(F) => ~ ( r2_hidden(F,k2_finseq_1(k3_finseq_1(A))) & k1_funct_1(C,F) = k5_numbers ) ) & ! [F] : ( 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] : ( v7_ordinal1(F) => ! [G] : ( 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] : ( v7_ordinal1(F) => ( r2_hidden(F,k2_finseq_1(k3_finseq_1(A))) => k5_int_1(D,k1_funct_1(C,F)) = k5_int_1(k1_funct_1(B,F),k1_funct_1(C,F)) ) ) & E = k19_rvsum_1(C) ) => k5_int_1(k4_ntalgo_1(A),E) = k5_int_1(D,E) ) ) ) ) ) ) )).
fof(t15_numbers,axiom,( r1_tarski(k4_numbers,k1_numbers) )).
fof(t15_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t15_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t15_oposet_1,axiom,( v11_oposet_1(k1_oposet_1) )).
fof(t15_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_cat_1(E,A,B,C) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t15_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_ordeq_01(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_ordeq_01(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_ordeq_01(A,B))) => ! [F] : ( ( v1_funct_1(F) & v1_nfcont_3(F,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ! [G] : ( ( v1_funct_1(G) & v1_nfcont_3(G,B) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ! [H] : ( ( v1_funct_1(H) & v1_nfcont_3(H,B) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ( ( F = C & G = D & H = E & k1_relset_1(k1_numbers,F) = A & k1_relset_1(k1_numbers,G) = A & k1_relset_1(k1_numbers,H) = A ) => ( E = k1_algstr_0(k5_ordeq_01(A,B),C,D) <=> ! [I] : ( m2_subset_1(I,k1_numbers,A) => k7_partfun1(u1_struct_0(B),H,I) = k3_rlvect_1(B,k7_partfun1(u1_struct_0(B),F,I),k7_partfun1(u1_struct_0(B),G,I)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t15_orders_1,axiom,( ! [A] : ! [B] : ( ( 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 ) )).
fof(t15_orders_2,axiom,( ! [A] : ( ( ~ 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 ) )).
fof(t15_ordinal1,axiom,( ! [A] : ( ! [B] : ( r2_hidden(B,A) => ( v3_ordinal1(B) & r1_tarski(B,A) ) ) => v3_ordinal1(A) ) )).
fof(t15_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ! [C] : ( v3_ordinal1(C) => ( r2_hidden(C,B) => r1_ordinal1(A,C) ) ) => ( k2_ordinal1(B) = k5_ordinal1 | r1_ordinal1(A,k2_ordinal2(B)) ) ) ) )).
fof(t15_ordinal3,axiom,( 1 = k1_tarski(k1_xboole_0) )).
fof(t15_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( v3_ordinal1(B) => ( v2_ordinal2(A) => v2_ordinal2(k5_relat_1(A,B)) ) ) ) )).
fof(t15_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => k1_ordinal6(k1_tarski(A)) = 1 ) )).
fof(t15_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( ~ r1_orders_2(B,D,C) & F != k4_struct_0(A) & k1_ortsp_1(A,B,k4_vectsp_1(A,B,F,C),D,E) != k1_ortsp_1(A,B,C,D,E) ) ) ) ) ) ) ) )).
fof(t15_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t15_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ( v2_relat_1(k3_osalg_1(A,B)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t15_osalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t15_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t15_papdesaf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ( v4_aff_2(A) => v7_aff_2(A) ) ) )).
fof(t15_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_parsp_1(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k9_parsp_1(A))) => ! [G] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t15_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t15_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ~ ( r2_hidden(A,k7_relat_1(D,B)) & ! [E] : ( m1_subset_1(E,B) => ~ ( r2_hidden(E,k1_relset_1(B,D)) & A = k1_funct_1(D,E) ) ) ) ) )).
fof(t15_partfun2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ( r2_relset_1(B,C,E,k2_partfun1(B,C,D,A)) <=> ( k1_relset_1(B,E) = k8_subset_1(B,k1_relset_1(B,D),A) & ! [F] : ( m1_subset_1(F,B) => ( r2_hidden(F,k1_relset_1(B,E)) => k7_partfun1(C,E,F) = k7_partfun1(C,D,F) ) ) ) ) ) ) ) ) )).
fof(t15_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => r1_setfam_1(k2_partit1(A,B,C),B) ) ) ) )).
fof(t15_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t15_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r1_diraf(A,F,D,C) & r2_analoaf(A,D,E,C,B) & r2_analoaf(A,F,E,F,B) ) => ( r3_diraf(A,F,B,C) | F = D | r1_diraf(A,F,E,B) ) ) ) ) ) ) ) ) )).
fof(t15_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) )).
fof(t15_pcomps_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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)) ) ) ) )).
fof(t15_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ( l2_pcs_0(B) => k19_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))) ) ) )).
fof(t15_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(A))) => ! [F] : ( 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(k4_ordinal1,1)) = k9_finseq_1(k10_pdiff_1(A,B,D,F)) ) ) ) ) ) ) ) )).
fof(t15_pdiff_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_euclid(2))) => ! [B] : ( ( 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] : ( m2_finseq_2(C,k1_numbers,k1_euclid(2)) => ( r2_hidden(C,A) => r3_pdiff_1(2,1,B,C) ) ) ) ) ) ) )).
fof(t15_pdiff_3,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(2)) => ! [B] : ( ( 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) = k10_pdiff_1(2,1,k1_pdiff_3(2,2,B),A) ) ) ) )).
fof(t15_pdiff_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r3_pdiff_1(3,3,A,B) <=> ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & B = k11_finseq_1(C,D,E) & ? [F] : ( m1_rcomp_1(F,E) & r1_tarski(F,k1_relset_1(k1_numbers,k1_pdiff_2(3,3,A,B))) & ? [G] : ( v1_funct_1(G) & v3_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [H] : ( v1_funct_1(H) & v2_fdiff_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,F) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,3,A,B),I),k1_funct_1(k1_pdiff_2(3,3,A,B),E)) = k2_xcmplx_0(k1_funct_1(G,k6_xcmplx_0(I,E)),k1_funct_1(H,k6_xcmplx_0(I,E))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t15_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t15_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,A) ) => k1_funct_1(k6_pdiff_1(A,D,k5_euclid(A)),k3_xcmplx_0(C,B)) = k10_rvsum_1(k1_funct_1(k6_pdiff_1(A,D,k5_euclid(A)),B),C) ) ) ) ) ) )).
fof(t15_pdiff_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(B)) => ( ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,B) ) => r1_xxreal_0(k9_complex1(k1_funct_1(C,D)),A) ) ) => r1_xxreal_0(k12_euclid(C),k3_xcmplx_0(B,A)) ) ) ) ) )).
fof(t15_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t15_pencil_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => v3_pencil_1(k1_pencil_1(A,B,C)) ) & v3_pencil_1(k5_pencil_1(A,B)) ) ) ) )).
fof(t15_pencil_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(t15_pencil_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,A) => v3_card_1(k1_funct_1(k1_pzfmisc1(A,B),C),1) ) ) ) )).
fof(t15_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( m1_vectsp_4(C,A,D) => ! [E] : ( v7_ordinal1(E) => ( ( k1_nat_1(k1_vectsp_9(A,C),1) = E & k1_vectsp_9(A,D) = k1_nat_1(E,1) ) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t15_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( v1_int_2(B) & k4_nat_d(A,B) = k4_xcmplx_0(1) ) => k4_nat_d(k1_square_1(A),B) = 1 ) ) ) )).
fof(t15_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k7_petri(k11_petri(A),k12_petri(A,B)) = k6_petri(A,B) ) ) )).
fof(t15_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ( r2_pnproc_1(A,B,C) => r1_pnproc_1(A,C,k2_pnproc_1(A,k3_pnproc_1(A,C,B),B)) ) ) ) )).
fof(t15_polyalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_polyalg1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_polyalg1(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ( ( D = F & E = G ) => k1_algstr_0(B,D,E) = k1_algstr_0(C,F,G) ) ) ) ) ) ) ) ) )).
fof(t15_polyeq_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xcmplx_0(E) => ( ( k4_polyeq_1(A,B,C,D,E) = k5_numbers & k4_complex1(E) = k5_numbers ) => ( A = k5_numbers | ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ~ ( H = k2_xcmplx_0(k3_complex1(E),k7_xcmplx_0(B,k3_xcmplx_0(3,A))) & k3_complex1(E) = k6_xcmplx_0(k2_xcmplx_0(F,G),k7_xcmplx_0(B,k3_xcmplx_0(3,A))) & k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,F),G),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),C),k1_square_1(B)),k3_xcmplx_0(3,k1_square_1(A)))) = k5_numbers & E != k2_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k1_power(3,k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(3,A)),3)),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),D),k3_xcmplx_0(B,C)),k3_xcmplx_0(6,k1_square_1(A)))),k3_square_1(k2_xcmplx_0(k7_xcmplx_0(k1_square_1(k2_xcmplx_0(k3_xcmplx_0(2,k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(3,A)),3)),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),D),k3_xcmplx_0(B,C)),k3_xcmplx_0(3,k1_square_1(A))))),4),k1_newton(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),C),k1_square_1(B)),k3_xcmplx_0(9,k1_square_1(A))),3))))),k1_power(3,k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(3,A)),3)),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),D),k3_xcmplx_0(B,C)),k3_xcmplx_0(6,k1_square_1(A)))),k3_square_1(k2_xcmplx_0(k7_xcmplx_0(k1_square_1(k2_xcmplx_0(k3_xcmplx_0(2,k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(3,A)),3)),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),D),k3_xcmplx_0(B,C)),k3_xcmplx_0(3,k1_square_1(A))))),4),k1_newton(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),C),k1_square_1(B)),k3_xcmplx_0(9,k1_square_1(A))),3)))))),k7_xcmplx_0(B,k3_xcmplx_0(3,A))),k3_xcmplx_0(k5_numbers,k7_complex1)) & E != k2_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k1_power(3,k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(3,A)),3)),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),D),k3_xcmplx_0(B,C)),k3_xcmplx_0(6,k1_square_1(A)))),k3_square_1(k2_xcmplx_0(k7_xcmplx_0(k1_square_1(k2_xcmplx_0(k3_xcmplx_0(2,k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(3,A)),3)),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),D),k3_xcmplx_0(B,C)),k3_xcmplx_0(3,k1_square_1(A))))),4),k1_newton(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),C),k1_square_1(B)),k3_xcmplx_0(9,k1_square_1(A))),3))))),k1_power(3,k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(3,A)),3)),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),D),k3_xcmplx_0(B,C)),k3_xcmplx_0(6,k1_square_1(A)))),k3_square_1(k2_xcmplx_0(k7_xcmplx_0(k1_square_1(k2_xcmplx_0(k3_xcmplx_0(2,k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(3,A)),3)),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),D),k3_xcmplx_0(B,C)),k3_xcmplx_0(3,k1_square_1(A))))),4),k1_newton(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),C),k1_square_1(B)),k3_xcmplx_0(9,k1_square_1(A))),3)))))),k7_xcmplx_0(B,k3_xcmplx_0(3,A))),k3_xcmplx_0(k5_numbers,k7_complex1)) & E != k2_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k1_power(3,k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(3,A)),3)),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),D),k3_xcmplx_0(B,C)),k3_xcmplx_0(6,k1_square_1(A)))),k3_square_1(k2_xcmplx_0(k7_xcmplx_0(k1_square_1(k2_xcmplx_0(k3_xcmplx_0(2,k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(3,A)),3)),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),D),k3_xcmplx_0(B,C)),k3_xcmplx_0(3,k1_square_1(A))))),4),k1_newton(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),C),k1_square_1(B)),k3_xcmplx_0(9,k1_square_1(A))),3))))),k1_power(3,k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(3,A)),3)),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),D),k3_xcmplx_0(B,C)),k3_xcmplx_0(6,k1_square_1(A)))),k3_square_1(k2_xcmplx_0(k7_xcmplx_0(k1_square_1(k2_xcmplx_0(k3_xcmplx_0(2,k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(3,A)),3)),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),D),k3_xcmplx_0(B,C)),k3_xcmplx_0(3,k1_square_1(A))))),4),k1_newton(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),C),k1_square_1(B)),k3_xcmplx_0(9,k1_square_1(A))),3)))))),k7_xcmplx_0(B,k3_xcmplx_0(3,A))),k3_xcmplx_0(k5_numbers,k7_complex1)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t15_polyeq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( k2_xcmplx_0(k1_newton(A,E),k1_newton(B,E)) = C & k3_xcmplx_0(k1_newton(A,E),k1_newton(B,E)) = D & r1_xxreal_0(k5_numbers,k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D))) & ~ v1_abian(E) & ~ ( A = k1_power(E,k7_xcmplx_0(k2_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2)) & B = k1_power(E,k7_xcmplx_0(k6_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2)) ) & ~ ( A = k1_power(E,k7_xcmplx_0(k6_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2)) & B = k1_power(E,k7_xcmplx_0(k2_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2)) ) ) ) ) ) ) ) )).
fof(t15_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( v1_xcmplx_0(F) => ! [G] : ( v1_xcmplx_0(G) => ! [H] : ( v1_xcmplx_0(H) => ! [I] : ( v1_xcmplx_0(I) => ( ( G = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(3,C),k1_newton(D,2)),9) & H = k7_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(9,D),C),k3_xcmplx_0(2,k1_newton(D,3))),k3_xcmplx_0(27,B)),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 = k4_xcmplx_0(k7_xcmplx_0(G,E)) ) => ( G = k5_numbers | ( k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_newton(A,3),k3_xcmplx_0(D,k1_newton(A,2))),k3_xcmplx_0(C,A)),B) = k5_numbers <=> ~ ( A != k6_xcmplx_0(k2_xcmplx_0(E,F),k7_xcmplx_0(D,3)) & A != k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(E,F),2)),k7_xcmplx_0(D,3)),k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(E,F),k1_polyeq_5(2,3)),k7_complex1),2)) & A != k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(E,F),2)),k7_xcmplx_0(D,3)),k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(E,F),k1_polyeq_5(2,3)),k7_complex1),2)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t15_polyform,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t15_polynom1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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) ) => k4_polynom1(A,B,k5_polynom1(A,B,C,D),E) = k1_algstr_0(B,k4_polynom1(A,B,C,E),k4_polynom1(A,B,D,E)) ) ) ) ) )).
fof(t15_polynom2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(D,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [E] : ( ( 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)))) ) => k2_polynom2(A,B,k6_polynom1(A,B,C,D),E) = k3_rlvect_1(B,k2_polynom2(A,B,C,E),k2_polynom2(A,B,D,E)) ) ) ) ) ) )).
fof(t15_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( m2_finseq_1(E,k4_finseq_2(3,k4_ordinal1)) => ! [F] : ( ( 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] : ( m2_finseq_1(G,k4_finseq_2(3,k4_ordinal1)) => ( G = k1_partfun1(k4_finseq_1(E),k4_finseq_1(E),k4_ordinal1,k4_finseq_2(3,k4_ordinal1),F,E) => k7_polynom3(A,B,C,D,G) = k1_partfun1(k4_finseq_1(E),k4_finseq_1(E),k4_ordinal1,u1_struct_0(A),F,k7_polynom3(A,B,C,D,E)) ) ) ) ) ) ) ) ) )).
fof(t15_polynom4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k1_algseq_1(A,k1_polynom4(A,B)) = k1_algseq_1(A,B) ) ) )).
fof(t15_polynom5,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k2_polynom5(A,B,k5_numbers),k10_polynom3(A)) ) ) )).
fof(t15_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( 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)))) ) => ( k3_polynom1(k15_pre_poly(A),B,C) = k1_xboole_0 | k3_polynom1(k15_pre_poly(A),B,C) = k6_domain_1(k15_pre_poly(A),k16_pre_poly(A)) ) ) ) )).
fof(t15_polynom8,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k3_polynom8(A,B,k4_xcmplx_0(1)) = k11_algstr_0(A,B) ) ) )).
fof(t15_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(D,A,C) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t15_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(1,C) & r1_xxreal_0(1,B) ) | ( ~ v1_abian(C) & ~ v1_abian(B) ) ) => k3_xcmplx_0(k1_power(C,A),k1_power(B,A)) = k1_power(k2_nat_1(C,B),k1_newton(A,k1_nat_1(C,B))) ) ) ) ) )).
fof(t15_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ! [E] : ( m1_subset_1(E,k3_msualg_1(B,D,k14_pralg_2(A,B,C))) => ! [F] : ( r2_hidden(F,k1_relset_1(k4_ordinal1,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))) ) ) ) ) ) ) )).
fof(t15_pre_circ,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => ~ ( B != k1_xboole_0 & r1_xxreal_0(k5_card_1(A),k5_card_1(k4_trees_1(A,B))) ) ) ) )).
fof(t15_pre_ff,axiom,( k3_pre_ff(k5_numbers) = k5_numbers & k3_pre_ff(1) = 1 & ! [A] : ( v7_ordinal1(A) => ( k3_pre_ff(k3_xcmplx_0(2,A)) = k3_pre_ff(A) & k3_pre_ff(k1_nat_1(k3_xcmplx_0(2,A),1)) = k1_nat_1(k3_pre_ff(A),k3_pre_ff(k1_nat_1(A,1))) ) ) )).
fof(t15_pre_poly,axiom,( ! [A] : ! [B] : r1_tarski(k4_partfun1(A,B),k9_setfam_1(k2_zfmisc_1(A,B))) )).
fof(t15_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( r2_hidden(C,u1_struct_0(A)) => ( r2_hidden(C,k2_pre_topc(A,B)) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( v4_pre_topc(D,A) & r1_tarski(B,D) ) => r2_hidden(C,D) ) ) ) ) ) ) )).
fof(t15_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_prelamb(A,k12_finseq_1(u1_struct_0(A),k1_prelamb(A,C,B)),k1_prelamb(A,k1_prelamb(A,D,C),k1_prelamb(A,D,B))) ) ) ) ) )).
fof(t15_prob_1,axiom,( ! [A] : ! [B] : ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( r1_tarski(k10_xtuple_0(C),B) => r2_hidden(k3_prob_1(A,C),B) ) ) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r2_hidden(C,B) => r2_hidden(k3_subset_1(A,C),B) ) ) ) ) ) )).
fof(t15_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m2_prob_1(E,A,B) => r1_xxreal_0(k6_xcmplx_0(k3_real_1(k3_funct_2(B,k1_numbers,E,C),k3_funct_2(B,k1_numbers,E,D)),1),k3_funct_2(B,k1_numbers,E,k5_prob_1(A,B,C,D))) ) ) ) ) ) )).
fof(t15_prob_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k1_kurato_0(A,k2_prob_3(A,B)) = k1_kurato_0(A,B) ) )).
fof(t15_prob_4,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(B) => r2_funct_2(k4_ordinal1,k9_setfam_1(A),k2_prob_3(A,B),B) ) ) )).
fof(t15_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t15_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( ~ r1_projdes1(A,B,D,E,F) & r1_collsp(A,F,B,C) & B != C & r1_projdes1(A,B,D,E,C) ) ) ) ) ) ) ) )).
fof(t15_projpl_1,axiom,( ! [A] : ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ~ r5_projpl_1(A,B,C,D,E) ) ) ) ) ) ) )).
fof(t15_projred1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & v8_incproj(A) & l1_incsp_1(A) ) => ? [B] : ( m1_subset_1(B,u1_incsp_1(A)) & ? [C] : ( m1_subset_1(C,u2_incsp_1(A)) & ? [D] : ( m1_subset_1(D,u2_incsp_1(A)) & ? [E] : ( m1_subset_1(E,u2_incsp_1(A)) & ? [F] : ( 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) ) ) ) ) ) ) )).
fof(t15_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u1_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u1_incsp_1(A)) => ! [H] : ( m1_subset_1(H,u1_incsp_1(A)) => ! [I] : ( m1_subset_1(I,u1_incsp_1(A)) => ! [J] : ( m1_subset_1(J,u1_incsp_1(A)) => ! [K] : ( m1_subset_1(K,u2_incsp_1(A)) => ! [L] : ( m1_subset_1(L,u2_incsp_1(A)) => ! [M] : ( m1_subset_1(M,u2_incsp_1(A)) => ! [N] : ( m1_subset_1(N,u2_incsp_1(A)) => ! [O] : ( m1_subset_1(O,u2_incsp_1(A)) => ! [P] : ( m1_subset_1(P,u2_incsp_1(A)) => ! [Q] : ( m1_subset_1(Q,u2_incsp_1(A)) => ! [R] : ( m1_subset_1(R,u2_incsp_1(A)) => ( ( r4_incsp_1(A,k7_domain_1(u1_incsp_1(A),D,G),N) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),G,I,E),O) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),D,E,H),P) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),B,C,E),Q) & r4_incsp_1(A,k7_domain_1(u1_incsp_1(A),D,J),R) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),B,G,H),K) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),C,H,J),L) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),G,J,F),M) & r1_incsp_1(A,F,Q) ) => ( r1_incsp_1(A,B,N) | r1_incsp_1(A,B,P) | r1_incsp_1(A,C,O) | r1_incsp_1(A,C,P) | r1_incsp_1(A,C,R) | r1_projred2(A,N,O,P) | B = C | C = F | N = R | k3_relat_1(k1_projred1(A,N,P,B),k1_projred1(A,P,O,C)) = k3_relat_1(k1_projred1(A,N,R,F),k1_projred1(A,R,O,C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t15_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) ) => ! [B] : ( m2_prvect_1(B,A) => ! [C] : ( m1_subset_1(C,k4_card_3(A)) => ! [D] : ( m2_subset_1(D,k4_ordinal1,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)) ) ) ) ) )).
fof(t15_prvect_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ? [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => k1_binop_1(C,D,E) = k10_finseq_1(D,E) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(k7_prvect_3(A,B))) => ! [E] : ( 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] : ( m1_subset_1(D,u1_struct_0(k7_prvect_3(A,B))) => ! [E] : ( v1_xreal_0(E) => 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] : ( m1_subset_1(D,u1_struct_0(k7_prvect_3(A,B))) => k2_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)) = k2_normsp_0(k7_prvect_3(A,B),D) ) ) ) ) )).
fof(t15_pua2mss1,axiom,( ! [A] : ( ( v2_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [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),k8_pua2mss1(A,B,k5_numbers),B) & r2_relset_1(u1_struct_0(A),u1_struct_0(A),k8_pua2mss1(A,B,1),k7_pua2mss1(A,B)) ) ) ) )).
fof(t15_pythtrip,axiom,( ~ v2_pythtrip(k8_domain_1(k4_ordinal1,3,4,5)) & v3_pythtrip(k8_domain_1(k4_ordinal1,3,4,5)) & m1_pythtrip(k8_domain_1(k4_ordinal1,3,4,5)) )).
fof(t15_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t15_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)))) ) ) ) ) )).
fof(t15_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( m2_subset_1(E,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [F] : ( m2_subset_1(F,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t15_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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))) ) ) ) )).
fof(t15_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_trees_1(C,k9_xtuple_0(k2_qc_lang4(A,B))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t15_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_qc_trans(B,A) & m1_qc_lang1(B) ) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(B),k3_cqc_lang(B)) => ! [D] : ( m1_subset_1(D,k1_substut1(A)) => ! [E] : ( m1_subset_1(E,k1_substut1(B)) => ! [F] : ( m2_subset_1(F,k2_qc_lang1(B),k3_qc_lang1(B)) => ! [G] : ( m2_subset_1(G,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [H] : ( m2_subset_1(H,k9_qc_lang1(A),k3_cqc_lang(A)) => ( ( H = C & D = E & G = F ) => k14_substut1(A,G,H,k7_substut1(A,G,k11_cqc_lang(A,G,H),D)) = k14_substut1(B,F,C,k7_substut1(B,F,k11_cqc_lang(B,F,C),E)) ) ) ) ) ) ) ) ) ) )).
fof(t15_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v10_lattices(A) & v4_lattice3(A) & v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v18_quantal1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t15_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => k23_quaterni(k2_quatern2,A) = A ) )).
fof(t15_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ( v1_xreal_0(B) => k27_quaterni(k23_quaterni(B,A)) = k23_quaterni(k27_quaterni(B),k27_quaterni(A)) ) ) ) )).
fof(t15_quaterni,axiom,( k10_quaterni(k12_quaterni,k12_quaterni) = k4_xcmplx_0(1) )).
fof(t15_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( B != k5_numbers & r1_xxreal_0(k5_numbers,k1_quin_1(B,C,D)) & k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(A)),k3_xcmplx_0(C,A)),D) = k5_numbers & A != k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B)) & A != k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B)) ) ) ) ) ) )).
fof(t15_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t15_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v3_card_1(D,C) & m2_finseq_1(D,k3_radix_1(B)) ) => ( r2_hidden(A,k2_finseq_1(C)) => m2_subset_1(k4_radix_1(A,B,C,D),k4_numbers,k3_radix_1(B)) ) ) ) ) ) )).
fof(t15_radix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_radix_1(A,B,C) => B = k3_radix_2(A,C,k5_radix_2(C,A,B)) ) ) ) ) ) )).
fof(t15_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t15_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(2,B) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k3_radix_1(B)) ) => ! [D] : ( ( v3_card_1(D,A) & m2_finseq_1(D,k3_radix_1(B)) ) => ! [E] : ( ( v3_card_1(E,A) & m2_finseq_1(E,k3_radix_1(B)) ) => ( ! [F] : ( 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) = k5_numbers ) & ~ ( k4_radix_1(F,B,A,D) = k4_radix_1(F,B,A,E) & k4_radix_1(F,B,A,C) = k5_numbers ) ) ) => k2_xcmplx_0(k8_radix_1(A,B,E),k8_radix_1(A,B,k10_radix_1(B,A,k5_numbers))) = k2_xcmplx_0(k8_radix_1(A,B,C),k8_radix_1(A,B,D)) ) ) ) ) ) ) ) )).
fof(t15_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(t15_ramsey_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_finset_1(C) => ! [D] : ( m1_eqrel_1(D,k3_group_10(C,A)) => ~ ( k1_card_1(D) = B & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(C)) => ~ ( ~ v1_finset_1(E) & r1_ramsey_1(C,A,E,D) ) ) ) ) ) ) ) )).
fof(t15_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ~ ( v2_prob_1(B) & ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & k3_prob_1(A,B) != k9_nat_1(k9_setfam_1(A),B,D) ) ) ) ) ) )).
fof(t15_random_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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(C) & v1_funct_2(C,A,B) & v1_random_3(C,A,B,k1_random_1(A),k1_random_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ) ) ) )).
fof(t15_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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) ) ) ) ) ) )).
fof(t15_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ( ( k2_rat_1(A) = A | k1_rat_1(A) = 1 ) => v1_int_1(A) ) ) )).
fof(t15_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_ratfunc1(A,B,C,D) => r1_polynom5(A,k5_vfunct_1(k4_ordinal1,A,k8_polynom3(A,B,C)),D) ) ) ) ) ) )).
fof(t15_rcomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ~ ( v1_rcomp_1(A) & ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r1_tarski(k1_rcomp_1(B,C),A) ) ) ) & ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => A != k1_rcomp_1(B,C) ) ) ) ) )).
fof(t15_rcomp_3,axiom,( ! [A] : ( ( v5_xxreal_2(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(k2_seq_4(A),A) => ( r2_hidden(k3_seq_4(A),A) | A = k4_rcomp_1(k3_seq_4(A),k2_seq_4(A)) ) ) ) )).
fof(t15_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( 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) ) ) ) )).
fof(t15_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k4_real_ns1(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k4_real_ns1(A))))) ) <=> ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k7_real_ns1(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k7_real_ns1(A))))) ) ) ) )).
fof(t15_realset2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t15_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_binop_1(u1_struct_0(A),k1_realset3(A),B,k4_struct_0(A)) = B ) ) )).
fof(t15_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => k1_relat_1(A) = k1_relat_1(k2_relat_1(A)) ) )).
fof(t15_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) => ( r1_tarski(k4_relat_1(A),D) => ( r1_tarski(A,k1_relset_1(B,D)) & r1_tarski(A,k2_relset_1(C,D)) ) ) ) )).
fof(t15_relset_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => B = k3_tarski(a_2_0_relset_2(A,B)) ) ) )).
fof(t15_revrot_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => k4_finseq_1(k1_finseq_6(A,C,B)) = k4_finseq_1(C) ) ) ) )).
fof(t15_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r2_hidden(k4_tarski(B,C),A) => r1_rewrite1(A,B,C) ) ) )).
fof(t15_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(A)) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t15_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( l1_rewrite3(E,D) => ( r1_rewrite3(D,E,A,B,C) => ( r1_struct_0(E,A) & r2_hidden(B,D) & r1_struct_0(E,C) & r2_hidden(A,k9_xtuple_0(k9_xtuple_0(u1_rewrite3(D,E)))) & r2_hidden(B,k10_xtuple_0(k9_xtuple_0(u1_rewrite3(D,E)))) & r2_hidden(C,k10_xtuple_0(u1_rewrite3(D,E))) ) ) ) )).
fof(t15_rfinseq,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k2_rfinseq(k1_numbers,B,k3_rfinseq(A)) = k3_rfinseq(k2_rfinseq(k1_numbers,B,A)) ) ) )).
fof(t15_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( r2_classes1(A,B) => k4_rfinseq2(A) = k4_rfinseq2(B) ) ) ) )).
fof(t15_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_valued_0(C) ) => k45_valued_1(k18_valued_1(C,A),k18_valued_1(C,B)) = k18_valued_1(C,k45_valued_1(A,B)) ) ) ) )).
fof(t15_rfunct_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ( r1_tarski(k2_relset_1(B,D),k1_relset_1(B,k2_partfun1(B,k1_numbers,C,A))) => r2_relset_1(k4_ordinal1,k1_numbers,k56_valued_1(k4_ordinal1,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,B,D,k2_partfun1(B,k1_numbers,C,A))),k8_funct_2(k4_ordinal1,k1_numbers,B,D,k2_partfun1(B,k1_numbers,k56_valued_1(B,k1_numbers,C),A))) ) ) ) ) )).
fof(t15_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => v2_binop_1(k13_rfunct_3(A),k3_rfunct_3(A,k1_numbers)) ) )).
fof(t15_rfunct_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( r1_rfunct_4(C,E) & r1_rfunct_4(D,E) ) => ( ( ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k5_numbers,B) ) & ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,k5_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) ) ) ) ) ) ) )).
fof(t15_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_seq_2(A) & v2_seq_2(B) ) => r1_xxreal_0(k2_xcmplx_0(k2_rinfsup1(A),k2_rinfsup1(B)),k2_rinfsup1(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B))) ) ) ) )).
fof(t15_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( r1_funct_2(k4_ordinal1,k6_numbers,k4_ordinal1,k1_numbers,A,B) & v7_mesfunc5(A) ) => ( v2_comseq_2(B) & k2_mesfunc5(A) = k1_seq_2(B) ) ) ) ) )).
fof(t15_ring_1,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t15_ringcat1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r2_ringcat1(A,B) & r2_ringcat1(A,C) ) => B = C ) )).
fof(t15_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( ( 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 ) ) ) ) ) ) )).
fof(t15_rlaffin2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ? [D] : ( 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) = k3_xcmplx_0(A,k5_card_1(C)) & D = k1_funct_4(k4_rlvect_2(B),k7_funcop_1(C,A)) ) ) ) ) )).
fof(t15_rlaffin3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( k8_matrix13(k2_vectsp_1,C) = A => ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t15_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ( D = B => k4_algstr_0(A,B) = k4_algstr_0(C,D) ) ) ) ) ) )).
fof(t15_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( 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) ) ) ) ) )).
fof(t15_rltopsp1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( ~ v8_ordinal1(D) & v1_xreal_0(D) ) => 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) ) ) ) ) )).
fof(t15_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_algstr_0(A,B,B) = k4_struct_0(A) ) ) )).
fof(t15_rlvect_2,axiom,( ! [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) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t15_rlvect_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( r2_hidden(A,C) => r1_struct_0(k1_rlvect_3(B,C),A) ) ) ) )).
fof(t15_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t15_rlvect_5,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t15_rlvect_x,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t15_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ( E = C => k4_algstr_0(B,C) = k4_algstr_0(D,E) ) ) ) ) ) ) )).
fof(t15_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t15_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( ( 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),D,C)) = k3_rlvect_1(B,k1_rmod_4(A,B,k7_subset_1(u1_struct_0(B),D,C)),k1_rmod_4(A,B,k7_subset_1(u1_struct_0(B),C,D))) ) ) ) ) )).
fof(t15_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_robbins1(A,B,k3_robbins1(A,B)) = k7_robbins1(A) ) ) )).
fof(t15_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t15_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t15_robbins4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_robbins4)) => ! [B] : ( 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) = k5_numbers ) ) ) ) )).
fof(t15_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ~ v4_roughs_1(B,A) <=> k3_roughs_1(A,B) = B ) ) ) )).
fof(t15_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => k1_rpr_1(A,k2_subset_1(A)) = 1 ) )).
fof(t15_rsspace,axiom,( ! [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))) ) => ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v8_rlvect_1(A) & l1_rlvect_1(A) ) ) ) )).
fof(t15_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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)) ) ) )).
fof(t15_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r1_struct_0(B,C) => r1_struct_0(B,k1_rlvect_1(A,C,D)) ) ) ) ) ) )).
fof(t15_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( 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) ) ) ) ) )).
fof(t15_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_rlvect_3(B,A) & ! [C] : ( m1_rusub_3(C,A) => ~ r1_tarski(B,C) ) ) ) ) )).
fof(t15_rusub_4,axiom,( ! [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_bhsp_1(A) & v1_rusub_4(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => k1_nat_1(k1_rusub_4(k1_rusub_2(A,B,C)),k1_rusub_4(k2_rusub_2(A,B,C))) = k1_nat_1(k1_rusub_4(B),k1_rusub_4(C)) ) ) ) )).
fof(t15_rusub_5,axiom,( ! [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) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_rusub_4(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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))) ) ) ) ) )).
fof(t15_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t15_rvsum_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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 ) ) )).
fof(t15_scm_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( r1_tarski(k1_ordinal4(k5_afinsq_1(k2_ami_3(k10_ami_3(k5_numbers),k10_ami_3(1))),k5_afinsq_1(k2_compos_1(k1_ami_3))),A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( ( v5_memstr_0(D,k7_card_1(2),k1_ami_3,k5_numbers) & m1_scm_1(D,k6_afinsq_1(B,C)) ) => ( r1_extpro_1(k7_card_1(2),k1_ami_3,A,D) & k8_extpro_1(k7_card_1(2),k1_ami_3,A,D) = 1 & k1_funct_1(k6_extpro_1(k7_card_1(2),k1_ami_3,A,D),k10_ami_3(k5_numbers)) = C & ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_ami_3)) ) => ( E != k10_ami_3(k5_numbers) => k1_funct_1(k6_extpro_1(k7_card_1(2),k1_ami_3,A,D),E) = k1_funct_1(D,E) ) ) ) ) ) ) ) ) )).
fof(t15_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(F,u1_struct_0(k1_scmfsa_2)) ) => ! [G] : ( ( 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(k7_card_1(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] : ( m1_subset_1(H,k4_ordinal1) => ( r2_hidden(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,F,H)),k9_xtuple_0(E)) & r2_hidden(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,G,H)),k9_xtuple_0(E)) ) ) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,F,D),k4_struct_0(k1_scmfsa_2)) = k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,G,D),k4_struct_0(k1_scmfsa_2)) & k5_relat_1(k5_extpro_1(k7_card_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(k7_card_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(k7_card_1(3),k1_scmfsa_2,A,F,C),k4_struct_0(k1_scmfsa_2)) = k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,G,C),k4_struct_0(k1_scmfsa_2)) & k5_relat_1(k5_extpro_1(k7_card_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(k7_card_1(3),k1_scmfsa_2,B,G,C),k2_xboole_0(k4_sf_mastr(E),k2_sf_mastr(E))) ) ) ) ) ) ) ) ) ) )).
fof(t15_scmfsa10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => k5_xtuple_0(k12_scmfsa_2(A,B)) = k9_finseq_1(A) ) ) )).
fof(t15_scmfsa6a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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)) ) ) ) )).
fof(t15_scmfsa7b,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( m1_scmfsa_2(D) => ~ r3_scmfsa7b(k15_scmfsa_2(B,C,D),A) ) ) ) ) )).
fof(t15_scmfsa8a,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( v7_ordinal1(D) => ( r1_xxreal_0(D,k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A))) => ( r8_pboole(u1_struct_0(k1_scmfsa_2),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),D),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k2_scmfsa6a(C)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),D)) & k3_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k2_scmfsa6a(C)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k2_scmfsa6a(C)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),D)) != k2_compos_1(k1_scmfsa_2) ) ) ) ) ) ) ) )).
fof(t15_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & ~ v1_scmfsa_m(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( 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(k7_card_1(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) = k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k5_card_1(B),k5_card_1(C)),3)))) ) ) ) ) ) ) ) )).
fof(t15_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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,k7_card_1(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) ) ) ) ) ) ) )).
fof(t15_scmfsa_1,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k4_scmfsa_1,k5_scmfsa_1))) => ! [B] : ( m2_subset_1(B,k1_scmfsa_1,k2_scmfsa_1) => ! [C] : ( v1_int_1(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t15_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( 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 ) ) )).
fof(t15_scmfsa_m,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t15_scmisort,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => r8_pboole(u1_struct_0(k1_scmfsa_2),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k1_scmisort(A,B,C,E),k1_nat_1(D,1)),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k1_scmisort(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k1_scmisort(A,B,C,E),D),B,C,E),1)) ) ) ) ) ) )).
fof(t15_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( 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 ) ) ) )).
fof(t15_scmpds_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ! [I] : ( ( v1_ami_2(I) & m1_subset_1(I,u1_struct_0(k1_scmpds_2)) ) => ! [J] : ( v1_int_1(J) => ! [K] : ( 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(k5_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)),k5_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)),k5_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)),k5_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)),k5_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t15_scmpds_4,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmpds_2)) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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)) ) ) ) )).
fof(t15_scmpds_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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) ) ) ) ) )).
fof(t15_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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)) ) ) ) ) ) )).
fof(t15_scmpds_8,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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)) = k1_nat_1(k5_card_1(C),2) ) ) ) )).
fof(t15_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmring2(A))) => ~ ( k2_compos_0(u1_compos_1(k1_scmring2(A)),B) = 4 & ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmring2(A))) ) => B != k6_scmring2(A,C,D) ) ) ) ) ) )).
fof(t15_scpinvar,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),F)) = k5_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) ) ) ) ) ) ) ) )).
fof(t15_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(7,C) & ! [E] : ( m2_finseq_1(E,k4_numbers) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t15_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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) ) ) ) ) ) ) ) ) ) ) )).
fof(t15_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B),C),k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,C),k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C))) ) ) ) )).
fof(t15_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(A) & v2_comseq_2(B) ) => k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) = k3_xcmplx_0(k1_seq_2(A),k1_seq_2(B)) ) ) ) )).
fof(t15_seq_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(k56_valued_1(k4_ordinal1,k1_numbers,A)) & k1_seq_2(k56_valued_1(k4_ordinal1,k1_numbers,A)) = k5_numbers ) => ( v2_comseq_2(A) & k1_seq_2(A) = k5_numbers ) ) ) )).
fof(t15_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => r2_relset_1(k4_ordinal1,k4_partfun1(A,k1_numbers),k5_seqfunc(A,k8_seqfunc(A,B,C)),k8_seqfunc(A,k5_seqfunc(A,B),k5_seqfunc(A,C))) ) ) ) )).
fof(t15_seqm_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k1_valued_0(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C),A) = k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k1_valued_0(k1_numbers,B,A),k1_valued_0(k1_numbers,C,A)) ) ) ) )).
fof(t15_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_series_1(A) => ! [B] : ( v7_ordinal1(B) => k4_series_1(A) = k2_xcmplx_0(k9_nat_1(k1_numbers,k3_series_1(A),B),k4_series_1(k1_valued_0(k1_numbers,A,k1_nat_1(B,1)))) ) ) ) )).
fof(t15_series_3,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => r1_xxreal_0(k3_xcmplx_0(3,k1_power(3,k3_xcmplx_0(k3_xcmplx_0(A,B),C))),k2_xcmplx_0(k2_xcmplx_0(A,B),C)) ) ) ) )).
fof(t15_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => ! [D] : ( ( v1_xreal_0(D) & v2_xxreal_0(D) ) => ~ r1_xxreal_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,k2_xcmplx_0(k2_xcmplx_0(A,B),D)),k7_xcmplx_0(B,k2_xcmplx_0(k2_xcmplx_0(A,B),C))),k7_xcmplx_0(C,k2_xcmplx_0(k2_xcmplx_0(B,C),D))),k7_xcmplx_0(D,k2_xcmplx_0(k2_xcmplx_0(A,C),D))),1) ) ) ) ) )).
fof(t15_setfam_1,axiom,( ! [A] : r1_setfam_1(k1_xboole_0,A) )).
fof(t15_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( k9_xtuple_0(C) = k4_ordinal1 & ! [D] : ( v7_ordinal1(D) => k1_funct_1(C,D) = k1_setfam_1(a_3_3_setlim_1(A,B,D)) ) ) => ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) ) ) )).
fof(t15_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) )).
fof(t15_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ( v3_binop_1(C,B) & v1_binop_1(C,B) & v2_binop_1(C,B) ) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => k7_setwiseo(A,B,C,k3_setwiseo(A,E,F),D) = k5_binop_1(B,C,k3_funct_2(A,B,D,E),k3_funct_2(A,B,D,F)) ) ) ) ) ) ) ) )).
fof(t15_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k5_finsub_1(A)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t15_sf_mastr,axiom,( ! [A] : ( v7_ordinal1(A) => k1_sf_mastr(k11_scmfsa_2(A)) = k1_xboole_0 ) )).
fof(t15_sfmastr1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_scmfsa6c(D) & v1_sfmastr1(D) & m1_subset_1(D,u1_compos_1(k1_scmfsa_2)) ) => ! [E] : ( m1_scmfsa_2(E) => ( ( v7_amistd_1(C,k7_card_1(3),k1_scmfsa_2) | ( r6_scmfsa7b(C,k2_extpro_1(k7_card_1(3),k1_scmfsa_2,D,k1_scmfsa_m(B)),A) & r5_scmfsa7b(C,k2_extpro_1(k7_card_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(k7_card_1(3),k1_scmfsa_2,D,k1_scmfsa_m(B)),A),E) ) ) ) ) ) ) )).
fof(t15_sfmastr2,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) & v1_scmfsa7b(D) ) => ( r1_sfmastr2(B,A,C,D) => ( ( k1_funct_1(A,k4_scmfsa_2(k5_numbers)) != 1 & v1_scmfsa_m(C) ) | ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(E,k1_funct_1(A,C)) => k2_xcmplx_0(k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(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) ) ) ) ) ) ) ) ) )).
fof(t15_sfmastr3,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & ~ v1_scmfsa_m(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( m1_scmfsa_2(E) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & 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] : ( ( v1_relat_1(G) & v4_relat_1(G,k4_ordinal1) & v5_relat_1(G,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(G) & v1_partfun1(G,k4_ordinal1) ) => k18_scmfsa_2(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k1_sfmastr3(G,B,C,D,F,A),k5_numbers),E) = k18_scmfsa_2(A,E) ) ) ) ) ) ) ) )).
fof(t15_sgraph1,axiom,( ! [A] : k2_sgraph1(k1_tarski(A)) = k1_xboole_0 )).
fof(t15_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => v2_sheffer1(A) ) )).
fof(t15_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t15_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_xboole_0(k4_simplex0(A)) <=> v4_simplex0(A) ) ) )).
fof(t15_simplex2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( ( v6_tbsp_1(C,k14_euclid(A)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k14_euclid(A)))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t15_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v7_ordinal1(C) => k6_xcmplx_0(k3_xcmplx_0(k9_nat_1(k2_numbers,k10_comseq_3(k3_sin_cos(B)),C),k9_nat_1(k2_numbers,k10_comseq_3(k3_sin_cos(A)),C)),k9_nat_1(k2_numbers,k10_comseq_3(k3_sin_cos(k2_xcmplx_0(B,A))),C)) = k9_nat_1(k2_numbers,k10_comseq_3(k12_sin_cos(B,A,C)),C) ) ) ) )).
fof(t15_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_funct_1(k3_sin_cos2,A) != k5_numbers & ~ r1_xxreal_0(k1_funct_1(k3_sin_cos2,A),k5_numbers) & k1_funct_1(k3_sin_cos2,k5_numbers) = 1 ) ) )).
fof(t15_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,k3_xcmplx_0(k7_complex1,A)) = k3_xcmplx_0(k7_complex1,k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A)) ) )).
fof(t15_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k2_xcmplx_0(k17_sin_cos(A),k17_sin_cos(B)) = k3_xcmplx_0(2,k3_xcmplx_0(k19_sin_cos(k7_xcmplx_0(k6_xcmplx_0(A,B),2)),k17_sin_cos(k7_xcmplx_0(k2_xcmplx_0(A,B),2)))) ) ) )).
fof(t15_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( k19_sin_cos(A) != k5_numbers & k17_sin_cos(A) != k5_numbers & ~ ( k3_sin_cos4(k3_xcmplx_0(2,A)) = k7_xcmplx_0(k3_xcmplx_0(k4_sin_cos4(A),k3_sin_cos4(A)),2) & k3_sin_cos4(k3_xcmplx_0(2,A)) = k7_xcmplx_0(k2_xcmplx_0(k1_sin_cos4(A),k2_sin_cos4(A)),2) ) ) ) )).
fof(t15_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ~ ( ~ r1_xxreal_0(A,k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B))) & ~ r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)),A) & r1_xxreal_0(k19_sin_cos(A),k5_numbers) ) ) ) )).
fof(t15_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) & r1_xxreal_0(k7_xcmplx_0(k2_xcmplx_0(1,A),k6_xcmplx_0(1,A)),k5_numbers) ) ) )).
fof(t15_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k7_xcmplx_0(k2_xcmplx_0(k4_sin_cos2(A),k4_sin_cos2(B)),k6_xcmplx_0(k4_sin_cos2(A),k4_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))) ) ) )).
fof(t15_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_funct_1(k18_sin_cos,A) != k5_numbers => k1_funct_1(k26_sin_cos,A) = k1_sin_cos4(A) ) ) )).
fof(t15_sincos10,axiom,( v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers))) )).
fof(t15_sppol_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t15_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_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,k1_nat_1(C,1)))) ) => r2_hidden(B,k3_topreal1(2,A)) ) ) ) ) )).
fof(t15_sprect_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t15_sprect_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => k4_finseq_1(k1_goboard1(A)) = k4_finseq_1(A) ) )).
fof(t15_sprect_3,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t15_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(t15_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,B) ) => r1_xxreal_0(k1_square_1(A),k1_square_1(B)) ) ) ) )).
fof(t15_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( ( r1_stacks_1(A,B) & r1_stacks_1(A,C) ) => r2_stacks_1(A,B,C) ) ) ) ) )).
fof(t15_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k7_card_1(B),k7_card_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(B),k7_card_1(A)))) ) => ( ( B = k5_numbers & A = k5_numbers ) => ( v2_funct_2(C,k7_card_1(A)) & v1_stirl2_1(C,B,A) ) ) ) ) ) )).
fof(t15_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_valuat_1(D,A,C) => ! [E] : ( m2_subset_1(E,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [F] : ( ( v5_relat_1(F,k3_qc_lang1(A)) & v3_card_1(F,B) & m2_finseq_1(F,k2_qc_lang1(A)) ) => ! [G] : ( m1_subset_1(G,k1_substut1(A)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t15_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( 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))) ) ) )).
fof(t15_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( m1_subset_1(D,k5_finsub_1(k4_partfun1(A,B))) => ! [E] : ~ ( r2_hidden(E,k4_substlat(A,B,C,D)) & ! [F] : ! [G] : ~ ( r2_hidden(F,C) & r2_hidden(G,D) & E = k2_xboole_0(F,G) ) ) ) ) )).
fof(t15_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => ! [C] : ( m1_subset_1(C,k16_substut1(A)) => ( k20_substut1(A,B) = k20_substut1(A,C) => B = C ) ) ) ) )).
fof(t15_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [D] : ( ( v5_relat_1(D,k3_qc_lang1(A)) & v3_card_1(D,B) & m2_finseq_1(D,k2_qc_lang1(A)) ) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t15_supinf_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k6_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t15_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ~ r1_orders_2(B,D,C) => k1_symsp_1(A,B,C,D,k4_vectsp_1(A,B,F,E)) = k8_group_1(A,F,k1_symsp_1(A,B,C,D,E)) ) ) ) ) ) ) ) )).
fof(t15_sysrel,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_tarski(k4_relat_1(A),k4_relat_1(B)) ) )).
fof(t15_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ( B = k2_tarski(k1_tarski(A),k10_eqrel_1(A)) => m2_taxonom1(B,A) ) ) ) )).
fof(t15_taylor_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k1_funct_1(k22_sin_cos,k3_power(k4_power,A)) = A ) ) )).
fof(t15_taylor_2,axiom,( ! [A] : ( v1_xreal_0(A) => v2_series_1(k4_sin_cos(A)) ) )).
fof(t15_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t15_tdgroup,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = C ) ) => ( ~ ! [B] : ( m1_subset_1(B,u1_struct_0(k2_tdgroup(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_tdgroup(A))) => B = C ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(k2_tdgroup(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_tdgroup(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_tdgroup(A))) => ( r2_analoaf(k2_tdgroup(A),B,C,D,D) => B = C ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(k2_tdgroup(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_tdgroup(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_tdgroup(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_tdgroup(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_tdgroup(A))) => ! [G] : ( 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] : ( m1_subset_1(B,u1_struct_0(k2_tdgroup(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_tdgroup(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_tdgroup(A))) => ? [E] : ( m1_subset_1(E,u1_struct_0(k2_tdgroup(A))) & r2_analoaf(k2_tdgroup(A),B,C,D,E) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(k2_tdgroup(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_tdgroup(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_tdgroup(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_tdgroup(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_tdgroup(A))) => ! [G] : ( 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] : ( m1_subset_1(B,u1_struct_0(k2_tdgroup(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_tdgroup(A))) => ? [D] : ( m1_subset_1(D,u1_struct_0(k2_tdgroup(A))) & r2_analoaf(k2_tdgroup(A),B,D,D,C) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(k2_tdgroup(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_tdgroup(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_tdgroup(A))) => ! [E] : ( 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] : ( m1_subset_1(B,u1_struct_0(k2_tdgroup(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_tdgroup(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_tdgroup(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t15_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => v4_tops_1(k2_struct_0(A),A) ) )).
fof(t15_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(t15_tdlat_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_tdlat_3(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => v3_pre_topc(B,A) ) ) ) )).
fof(t15_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t15_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( 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) ) ) )).
fof(t15_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t15_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t15_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ v3_tex_4(B,A) ) ) )).
fof(t15_tietze,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t15_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_tsep_1(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ( ( E = D & F = D ) => ! [G] : ( m1_connsp_2(G,B,E) => ! [H] : ( m1_connsp_2(H,C,F) => ? [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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t15_toler_1,axiom,( ! [A] : ! [B] : ( ( 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] : ! [D] : ( r2_hidden(k4_tarski(C,D),B) => m1_toler_1(k2_tarski(C,D),A,B) ) ) )).
fof(t15_topalg_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t15_topalg_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_topmetr(A,B))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t15_topalg_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v4_pre_topc(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t15_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t15_topalg_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t15_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_topalg_6(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_borsuk_2(C,A,B,B) => ! [D] : ( m1_borsuk_2(D,A,B,B) => r3_borsuk_2(A,B,B,C,D) ) ) ) ) )).
fof(t15_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( ? [B] : ( v7_ordinal1(B) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v3_pre_topc(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( r2_hidden(C,D) & ! [E] : ( ( 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)),k6_xcmplx_0(B,1)) ) ) ) ) ) ) => v3_topdim_1(A) ) ) )).
fof(t15_topdim_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & v5_waybel23(A) & v3_topdim_1(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(t15_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( r1_topgen_1(A,B,C) => m1_subset_1(C,u1_struct_0(A)) ) ) ) )).
fof(t15_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_topgen_2(A) & l1_pre_topc(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)))) & ? [C] : ( 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] : ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t15_topgen_3,axiom,( ! [A] : ( 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))) ) ) )).
fof(t15_topgen_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v1_prob_1(B,A) => B = k7_setfam_1(A,B) ) ) )).
fof(t15_topgen_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r2_hidden(k19_euclid(A,B),k1_topgen_5) <=> B = k5_numbers ) ) ) )).
fof(t15_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(t15_topmetr,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ( v3_pre_topc(B,k3_pcomps_1(A)) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k8_metric_1(A,C,D),B) ) ) ) ) ) ) ) )).
fof(t15_topmetr3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) ) )).
fof(t15_topreal3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( D = k11_finseq_1(A,B,C) => ( E = k5_numbers | r1_xxreal_0(F,k1_nat_1(E,1)) | k2_topreal1(2,D,F) = k1_xboole_0 ) ) ) ) ) ) ) ) )).
fof(t15_topreal4,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)),k7_xcmplx_0(k2_xcmplx_0(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))) ) ) ) ) ) )).
fof(t15_topreal5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( v1_topreal2(A) => ! [B] : ( v1_xreal_0(B) => ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & r2_hidden(C,A) & k17_euclid(C) != B ) ) ) ) )).
fof(t15_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k5_numbers,B) => r2_hidden(A,k1_rcomp_1(k6_xcmplx_0(A,B),k2_xcmplx_0(A,B))) ) ) ) )).
fof(t15_topreal7,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ( ( k3_finseq_1(A) = k3_finseq_1(C) & k3_finseq_1(B) = k3_finseq_1(D) ) => k3_euclid(k8_rvsum_1(k8_finseq_1(k1_numbers,A,B),k8_finseq_1(k1_numbers,C,D))) = k8_finseq_1(k1_numbers,k3_euclid(k8_rvsum_1(A,C)),k3_euclid(k8_rvsum_1(B,D))) ) ) ) ) ) )).
fof(t15_topreal8,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & m2_finseq_1(C,B) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(t15_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => r1_tarski(k3_topreal9(A,C,B),k2_topreal9(A,C,B)) ) ) ) )).
fof(t15_topreala,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t15_toprealb,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( ( m1_subset_1(A,u1_struct_0(k8_toprealb(2))) & k17_euclid(A) = k4_xcmplx_0(1) ) => k18_euclid(A) = k5_numbers ) ) )).
fof(t15_toprealc,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_card_1(D,B) & v1_finseq_1(D) & v3_valued_0(D) ) => k14_rvsum_1(D,k1_funct_7(k16_euclid(B),A,C)) = k1_funct_7(k16_euclid(B),A,k3_xcmplx_0(k1_funct_1(D,A),C)) ) ) ) )).
fof(t15_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(t15_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k1_tops_1(A,k2_struct_0(A)) = k2_struct_0(A) ) )).
fof(t15_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t15_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t15_tops_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( ( 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] : ( ( 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),k8_metric_1(B,E,F)) ) ) ) ) ) ) ) ) ) ) )).
fof(t15_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),k2_zfmisc_1(A,A)))) => ( ( ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,A) => ! [I] : ( m1_subset_1(I,A) => ! [J] : ( 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] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( 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) ) ) ) ) ) )).
fof(t15_treal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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(k5_numbers,1)),u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k4_topmetr(A,B)),k4_treal_1(A,B,k1_treal_1(k5_numbers,1),k2_treal_1(k5_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(k5_numbers,1)),u1_struct_0(k4_topmetr(k5_numbers,1)),k3_struct_0(k4_topmetr(k5_numbers,1)),k1_partfun1(u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(k5_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(k5_numbers,1),k2_treal_1(k5_numbers,1)))) ) ) ) ) )).
fof(t15_trees_1,axiom,( ! [A] : k1_trees_1(k9_finseq_1(A)) = k1_tarski(k1_xboole_0) )).
fof(t15_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => A = k3_tarski(a_1_1_trees_2(A)) ) )).
fof(t15_trees_3,axiom,( ! [A] : ! [B] : ( v1_trees_3(k2_tarski(A,B)) <=> ( ~ v1_xboole_0(A) & v1_trees_1(A) & ~ v1_xboole_0(B) & v1_trees_1(B) ) ) )).
fof(t15_trees_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v6_trees_3(C) ) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t15_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => r2_hidden(k4_tarski(k1_xboole_0,A),k6_trees_9(A)) ) )).
fof(t15_trees_a,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) ) => ( r2_hidden(A,k9_xtuple_0(B)) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ~ ( r2_hidden(D,k9_xtuple_0(k7_trees_2(B,A,C))) & r2_hidden(D,a_2_4_trees_a(A,C)) & ! [E] : ( m1_trees_1(E,k9_xtuple_0(C)) => ~ ( D = k8_finseq_1(k4_ordinal1,A,E) & k1_funct_1(k7_trees_2(B,A,C),D) = k1_funct_1(C,E) ) ) ) ) ) ) ) ) )).
fof(t15_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( v4_pre_topc(B,A) & ! [C] : ( ( ~ v2_struct_0(C) & v1_pre_topc(C) & v1_borsuk_1(C,A) & m1_pre_topc(C,A) ) => B != u1_struct_0(C) ) ) ) ) )).
fof(t15_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t15_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v6_pre_topc(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( ~ r1_tsep_1(B,C) => v6_pre_topc(k2_tsep_1(A,B,C)) ) ) ) ) )).
fof(t15_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(C,A) <=> ( C = k3_tex_4(A,C) & ? [D] : ( 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)) ) ) ) ) ) ) )).
fof(t15_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( m2_funct_2(B,k4_numbers,u1_turing_1(A),k9_funct_2(k4_numbers,u1_turing_1(A))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_turing_1(k2_finseq_4(k4_ordinal1,C,D),A,B) => r1_turing_1(A,B,C,k1_nat_1(k1_nat_1(C,D),2)) ) ) ) ) ) )).
fof(t15_twoscomp,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( 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))) ) ) ) ) )).
fof(t15_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_unialg_2(B,A) => m1_subset_1(k6_unialg_2(A),k1_zfmisc_1(u1_struct_0(B))) ) ) )).
fof(t15_unialg_3,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k12_unialg_2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k12_unialg_2(A))) => ! [D] : ( ( v1_unialg_1(D) & m1_unialg_2(D,A) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t15_uniroots,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t15_uproots,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( ~ r1_xxreal_0(k1_algseq_1(A,B),k5_numbers) & k1_normsp_1(A,B,k7_nat_d(k1_algseq_1(A,B),1)) = k4_struct_0(A) ) ) ) )).
fof(t15_urysohn1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_subset_1(B,k1_numbers,k1_urysohn1(A)) => ! [C] : ( m2_subset_1(C,k1_numbers,k1_urysohn1(A)) => ( ~ r1_xxreal_0(C,B) => ( r1_xxreal_0(B,k7_xcmplx_0(k6_xcmplx_0(k6_urysohn1(A,C),1),k1_newton(2,A))) & r1_xxreal_0(k7_xcmplx_0(k1_nat_1(k6_urysohn1(A,B),1),k1_newton(2,A)),C) ) ) ) ) ) )).
fof(t15_urysohn2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,k5_numbers) => ! [C] : ( ( ~ 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( D = k7_supinf_2(A) & E = k8_supinf_2(A) ) => ( k7_supinf_2(C) = k3_xcmplx_0(B,D) & k8_supinf_2(C) = k3_xcmplx_0(B,E) ) ) ) ) ) ) ) ) ) ) )).
fof(t15_urysohn3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v10_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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] : ( m2_urysohn3(D,A,B,C) => ! [E] : ( m2_subset_1(E,k1_numbers,k3_urysohn1) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ~ r1_xxreal_0(E,k12_supinf_2(k7_urysohn3(A,B,C,D),F)) => r2_hidden(F,k5_urysohn3(k3_urysohn1,A,k4_urysohn3(A,B,C,D),E)) ) ) ) ) ) ) ) ) ) )).
fof(t15_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_funct_2(C,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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 ) ) ) ) ) )).
fof(t15_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v3_funct_1(A) & v3_valued_0(A) ) => ? [B] : ( v1_xreal_0(B) & ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => k1_funct_1(A,C) = B ) ) ) )).
fof(t15_valued_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_membered(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_membered(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [F] : ( 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)) ) ) ) ) ) )).
fof(t15_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(t15_vectsp10,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t15_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( m1_matrlin(D,A,C) => ! [E] : ( m1_matrlin(E,A,C) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t15_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t15_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( 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 ) ) ) ) )).
fof(t15_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ( E = C => k4_algstr_0(B,C) = k4_algstr_0(D,E) ) ) ) ) ) ) )).
fof(t15_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t15_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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) ) ) )).
fof(t15_vectsp_7,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t15_vectsp_8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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)))) ) ) )).
fof(t15_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_7(C,A,B) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r1_xboole_0(D,C) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t15_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ( v1_xreal_0(E) => 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))) ) ) ) ) ) )).
fof(t15_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ( v1_xcmplx_0(E) => 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))) ) ) ) ) ) )).
fof(t15_waybel10,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_waybel10(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t15_waybel11,axiom,( ! [A] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t15_waybel12,axiom,( ! [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] : ( 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 ) ) )).
fof(t15_waybel13,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t15_waybel14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t15_waybel15,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(t15_waybel16,axiom,( ! [A] : k4_yellow_0(k1_yellow_1(k8_waybel_0(k2_yellow_1(A)))) = k9_setfam_1(A) )).
fof(t15_waybel17,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( 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))) ) ) ) ) ) ) )).
fof(t15_waybel18,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v4_waybel11(B) & m1_yellow_9(B,k4_yellow_1(A,k7_funcop_1(A,k2_yellow_1(k1_tarski(k5_numbers))))) ) => u1_pre_topc(B) = u1_pre_topc(k3_waybel18(A,k7_funcop_1(A,k9_waybel18))) ) ) )).
fof(t15_waybel19,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( v2_pre_topc(C) & v1_waybel19(C) & m1_yellow_9(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t15_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ( ( r5_waybel_1(A,B) & v3_orders_2(A) ) => v3_orders_2(B) ) ) ) )).
fof(t15_waybel21,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ( v6_yellow_0(B,A) <=> ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t15_waybel22,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( 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] : ( m1_waybel16(D,k1_yellow_1(k8_waybel_0(k2_yellow_1(A))),B) => ( k2_partfun1(u1_struct_0(k1_yellow_1(k8_waybel_0(k2_yellow_1(A)))),u1_struct_0(B),D,k1_waybel22(A)) = C => r2_funct_2(u1_struct_0(k1_yellow_1(k8_waybel_0(k2_yellow_1(A)))),u1_struct_0(B),D,k2_waybel22(A,B,C)) ) ) ) ) )).
fof(t15_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_waybel23(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t15_waybel24,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_lattice3(C) & v2_lattice3(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t15_waybel25,axiom,( ! [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) ) => k1_waybel25(A) = g1_waybel_9(u1_struct_0(A),u1_orders_2(A),u1_pre_topc(A)) ) )).
fof(t15_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & v6_pre_topc(C) & v1_waybel25(C) & l1_pre_topc(C) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t15_waybel27,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ 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)) => k5_yellow_1(A,B) = k5_yellow_1(A,C) ) ) ) )).
fof(t15_waybel28,axiom,( ! [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] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( 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] : ( m2_yellow_6(D,A,B) => ( r2_hidden(D,k6_yellow_6(A)) => C = k1_waybel11(A,D) ) ) ) ) ) ) ) )).
fof(t15_waybel29,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t15_waybel30,axiom,( ! [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_waybel_2(A) & l1_waybel_9(A) ) => ! [B] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t15_waybel31,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k4_waybel_0(A,B)) => k2_waybel31(A,B,C) = k1_xboole_0 ) ) ) ) )).
fof(t15_waybel33,axiom,( ! [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] : ( ( ~ v1_xboole_0(B) & v2_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v3_waybel_7(B,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t15_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t15_waybel35,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ! [D] : ( r2_hidden(C,k3_waybel35(A,B,D)) <=> ( r2_hidden(k4_tarski(C,D),A) & r2_hidden(C,B) ) ) ) )).
fof(t15_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k4_waybel_0(A,B) = a_2_1_waybel_0(A,B) ) ) )).
fof(t15_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(t15_waybel_2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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)) ) ) ) )).
fof(t15_waybel_3,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t15_waybel_4,axiom,( ! [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] : ( ( v1_waybel_4(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t15_waybel_5,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_funcop_1(C) ) => ( ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r2_hidden(D,k1_relset_1(k4_card_3(k1_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) ) ) ) ) )).
fof(t15_waybel_6,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_waybel_6(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & C = k2_yellow_0(A,D) ) ) ) ) ) )).
fof(t15_waybel_7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( ~ 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))) ) ) ) ) ) )).
fof(t15_waybel_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t15_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t15_weddwitt,axiom,( ! [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] : ( ( ~ 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] : ( v7_ordinal1(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t15_weierstr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t15_wellord1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( v1_relat_2(B) => v1_relat_2(k2_wellord1(B,A)) ) ) )).
fof(t15_wellord2,axiom,( ! [A] : r4_relat_2(k1_wellord2(A),A) )).
fof(t15_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_nat_d(A,1) => A = 1 ) ) )).
fof(t15_xboole_1,axiom,( ! [A] : ! [B] : ( k2_xboole_0(A,B) = k1_xboole_0 => A = k1_xboole_0 ) )).
fof(t15_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k6_xboolean(A,k4_xboolean(A,B)) = k6_xboolean(A,B) ) ) )).
fof(t15_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k6_xcmplx_0(A,B) = k5_numbers => A = B ) ) ) )).
fof(t15_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t15_xtuple_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r2_hidden(k3_xtuple_0(A,B,C),D) => r2_hidden(B,k12_xtuple_0(D)) ) )).
fof(t15_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( k3_xxreal_0(A,B) = A | k3_xxreal_0(A,B) = B ) ) ) )).
fof(t15_xxreal_1,axiom,( ! [A] : ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(A,k4_xxreal_1(B,C)) => ( r2_hidden(A,k3_xxreal_1(B,C)) & A != C ) ) ) ) )).
fof(t15_xxreal_2,axiom,( ! [A] : ( ( v3_membered(A) & ~ v1_xboole_0(A) ) => ( v3_xxreal_2(A) => r2_hidden(k2_xxreal_2(A),k1_numbers) ) ) )).
fof(t15_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => k3_xxreal_3(A,k5_numbers) = A ) )).
fof(t15_yellow10,axiom,( ! [A] : ( ( v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t15_yellow12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v3_waybel_3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t15_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [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)))) ) => ! [C] : ( 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)))) ) ) ) ) )).
fof(t15_yellow14,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ( ( r5_waybel_1(A,B) & v2_yellow_0(A) ) => v2_yellow_0(B) ) ) ) )).
fof(t15_yellow15,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => k5_setfam_1(A,k2_yellow15(A,B)) = A ) )).
fof(t15_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( 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] : ( 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)) ) ) ) ) ) )).
fof(t15_yellow17,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ~ ( r1_tarski(k2_struct_0(A),k3_tarski(C)) & ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(C)) ) => ~ r1_tarski(k2_struct_0(A),k3_tarski(D)) ) ) ) ) ) ) )).
fof(t15_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t15_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))))) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t15_yellow20,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( 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) ) ) ) ) )).
fof(t15_yellow21,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k6_yellow21(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k6_yellow21(A))) => ! [D] : ( 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))))) ) ) ) ) ) )).
fof(t15_yellow_0,axiom,( ! [A] : ( ( v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( r1_yellow_0(A,B) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r2_lattice3(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_lattice3(A,B,D) => r1_orders_2(A,C,D) ) ) ) ) ) )).
fof(t15_yellow_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v2_yellow_0(k1_yellow_1(A)) => r2_hidden(k3_tarski(A),A) ) ) )).
fof(t15_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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) ) ) ) ) ) )).
fof(t15_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ( v3_orders_2(k3_yellow_3(A,B)) => ( v3_orders_2(A) & v3_orders_2(B) ) ) ) ) )).
fof(t15_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(t15_yellow_5,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r2_yellow_5(A,B,B) <=> B != k3_yellow_0(A) ) ) ) )).
fof(t15_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(t15_yellow_7,axiom,( ! [A] : ( l1_orders_2(A) => ! [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_lattice3(A) ) => v1_lattice3(B) ) ) ) )).
fof(t15_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v2_yellow_8(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ( v4_card_3(B) & ! [C] : ( 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) ) ) ) ) )).
fof(t15_yellow_9,axiom,( ! [A] : ! [B] : ( 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) ) )).
fof(t15_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t15_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ( k1_funct_1(k4_zf_lang(A,B),1) = k5_numbers & k1_funct_1(k5_zf_lang(A,B),1) = 1 ) ) ) )).
fof(t15_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ! [E] : ( m2_subset_1(E,k4_ordinal1,k1_zf_lang) => ! [F] : ( m2_subset_1(F,k4_ordinal1,k1_zf_lang) => ! [G] : ( m2_subset_1(G,k4_ordinal1,k1_zf_lang) => ! [H] : ( m2_subset_1(H,k4_ordinal1,k1_zf_lang) => ( k16_zf_lang(C,E,G,A) = k16_zf_lang(D,F,H,B) => ( C = D & E = F & G = H & A = B ) ) ) ) ) ) ) ) ) ) )).
fof(t15_zf_model,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ( r1_zf_model(A,B,k7_zf_lang(C,D)) <=> ( r1_zf_model(A,B,C) & r1_zf_model(A,B,D) ) ) ) ) ) ) )).
fof(t15_zf_refle,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( v3_ordinal1(B) & m1_subset_1(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t15_zfmisc_1,axiom,( ! [A] : ! [B] : ( k4_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_xboole_0 => A = B ) )).
fof(t15_zfmodel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_ordinal1(A) => ( ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r1_xboole_0(k1_enumset1(k2_zf_lang(k5_numbers),k2_zf_lang(1),k2_zf_lang(2)),k2_zf_model(B)) => r2_zf_model(A,k11_zf_model(B)) ) ) <=> ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( 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(k5_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(k5_numbers),k8_zf_lang(k2_zf_lang(4),k12_zf_lang(B,k4_zf_lang(k2_zf_lang(4),k2_zf_lang(k5_numbers))))))) ) => ! [D] : ( m1_subset_1(D,A) => r2_hidden(k7_relset_1(A,A,k1_zfmodel1(B,A,C),D),A) ) ) ) ) ) ) ) )).
fof(t15_zfmodel2,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ( ~ r2_hidden(A,k4_zf_lang1(D)) => ( r2_zf_model(C,k6_zf_lang1(D,B,A)) <=> r2_zf_model(C,D) ) ) ) ) ) ) )).
fof(t15_zfrefle1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_ordinal2(C) ) => k5_relat_1(k1_ordinal3(B,C),A) = k1_ordinal3(B,k5_relat_1(C,A)) ) ) ) )).
fof(t15_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t15_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),k4_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_numbers))) ) => k20_zmodul02(A,k12_finseq_1(u1_struct_0(A),B),C) = k12_finseq_1(u1_struct_0(A),k1_zmodul01(A,B,k3_funct_2(u1_struct_0(A),k4_numbers,C,B))) ) ) ) )).
fof(t15_zmodul03,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v1_zmodul02(C,B) => ( v1_zmodul02(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) )).
fof(t160_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ( m4_glib_001(B,A,C) => r1_xxreal_0(k3_finseq_1(B),k3_finseq_1(C)) ) ) ) ) )).
fof(t160_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( r2_hidden(C,A) => r2_hidden(k6_xcmplx_0(B,C),k19_member_1(A,B)) ) ) ) ) )).
fof(t160_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( r2_hidden(A,k9_xtuple_0(B)) <=> k9_relat_1(B,A) != k1_xboole_0 ) ) )).
fof(t160_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t160_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k4_xcmplx_0(k2_xcmplx_0(A,B)) = k6_xcmplx_0(k4_xcmplx_0(B),A) ) ) )).
fof(t160_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,1) & r1_xxreal_0(B,1) ) => r1_xxreal_0(k3_xcmplx_0(A,B),1) ) ) ) )).
fof(t160_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(C,A) & r1_xxreal_0(D,B) ) => k3_xboole_0(k4_xxreal_1(C,D),k4_xxreal_1(A,B)) = k4_xxreal_1(A,D) ) ) ) ) ) )).
fof(t160_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ( k8_zf_lang(D,A) = k6_zf_lang1(k8_zf_lang(C,B),C,D) <=> A = k6_zf_lang1(B,C,D) ) ) ) ) ) )).
fof(t160_zmodul01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k2_binop_1(k4_ordinal1,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(k4_ordinal1,u1_struct_0(A),u1_struct_0(A),k3_binom(A),D,B),k2_binop_1(k4_ordinal1,u1_struct_0(A),u1_struct_0(A),k3_binom(A),D,C)) ) ) ) ) )).
fof(t161_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t161_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => k19_member_1(A,B) = a_2_11_member_1(A,B) ) ) )).
fof(t161_relat_1,axiom,( ! [A] : ! [B] : ( v4_relat_1(k1_xboole_0,A) & v5_relat_1(k1_xboole_0,B) ) )).
fof(t161_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => v1_sheffer2(A) ) )).
fof(t161_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k4_xcmplx_0(k6_xcmplx_0(A,B)) = k2_xcmplx_0(k4_xcmplx_0(A),B) ) ) )).
fof(t161_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,1) & r1_xxreal_0(1,B) & r1_xxreal_0(k3_xcmplx_0(A,B),1) ) ) ) )).
fof(t161_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => r1_tarski(k2_xboole_0(k2_xxreal_1(C,D),k2_xxreal_1(A,B)),k2_xxreal_1(k3_xxreal_0(C,A),k4_xxreal_0(D,B))) ) ) ) ) )).
fof(t161_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( m2_subset_1(E,k4_ordinal1,k1_zf_lang) => ! [F] : ( m2_subset_1(F,k4_ordinal1,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) ) ) ) ) ) ) ) ) )).
fof(t161_zmodul01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t162_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ( m4_glib_001(B,A,C) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ~ ( r1_xxreal_0(D,k3_finseq_1(B)) & ! [E] : ( ( ~ v1_abian(E) & m1_subset_1(E,k4_ordinal1) ) => ~ ( r1_xxreal_0(D,E) & r1_xxreal_0(E,k3_finseq_1(C)) & k1_funct_1(B,D) = k1_funct_1(C,E) ) ) ) ) ) ) ) ) )).
fof(t162_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ~ ( r2_hidden(C,k19_member_1(A,B)) & ! [D] : ( v1_xcmplx_0(D) => ~ ( C = k6_xcmplx_0(B,D) & r2_hidden(D,A) ) ) ) ) ) )).
fof(t162_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r1_xboole_0(A,B) => k5_relat_1(k5_relat_1(C,A),B) = k1_xboole_0 ) ) )).
fof(t162_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k4_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),B)) = k6_xcmplx_0(A,B) ) ) )).
fof(t162_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(1,A) & r1_xxreal_0(B,1) & r1_xxreal_0(1,k3_xcmplx_0(A,B)) ) ) ) )).
fof(t162_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ~ r1_xboole_0(k2_xxreal_1(C,D),k2_xxreal_1(A,B)) => k2_xboole_0(k2_xxreal_1(C,D),k2_xxreal_1(A,B)) = k2_xxreal_1(k3_xxreal_0(C,A),k4_xxreal_0(D,B)) ) ) ) ) ) )).
fof(t162_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( m2_subset_1(E,k4_ordinal1,k1_zf_lang) => ! [F] : ( m2_subset_1(F,k4_ordinal1,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) ) ) ) ) ) ) ) ) )).
fof(t162_zmodul01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k2_binop_1(k4_ordinal1,u1_struct_0(A),u1_struct_0(A),k3_binom(A),k2_nat_1(C,D),B) = k2_binop_1(k4_ordinal1,u1_struct_0(A),u1_struct_0(A),k3_binom(A),C,k2_binop_1(k4_ordinal1,u1_struct_0(A),u1_struct_0(A),k3_binom(A),D,B)) ) ) ) ) )).
fof(t163_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ( m4_glib_001(B,A,C) => ! [D] : ( ( v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ~ ( r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(B)) & ! [E] : ( ( v1_abian(E) & m1_subset_1(E,k4_ordinal1) ) => ~ ( r1_xxreal_0(D,E) & r1_xxreal_0(E,k3_finseq_1(C)) & k1_funct_1(B,D) = k1_funct_1(C,E) ) ) ) ) ) ) ) ) )).
fof(t163_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ( r1_tarski(A,B) <=> r1_tarski(k19_member_1(A,C),k19_member_1(B,C)) ) ) ) ) )).
fof(t163_relat_1,axiom,( ! [A] : k1_relat_1(k1_tarski(k4_tarski(A,A))) = k1_tarski(A) )).
fof(t163_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k2_xcmplx_0(A,B) = k4_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B)) ) ) )).
fof(t163_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t163_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => r1_tarski(k2_xboole_0(k3_xxreal_1(C,D),k3_xxreal_1(A,B)),k3_xxreal_1(k3_xxreal_0(C,A),k4_xxreal_0(D,B))) ) ) ) ) )).
fof(t163_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( m2_subset_1(E,k4_ordinal1,k1_zf_lang) => ! [F] : ( m2_subset_1(F,k4_ordinal1,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) ) ) ) ) ) ) ) ) )).
fof(t163_zmodul01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_numbers) => ! [D] : ( 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)) ) ) ) ) )).
fof(t164_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ( k19_member_1(A,C) = k19_member_1(B,C) => A = B ) ) ) ) )).
fof(t164_relat_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) ) => B = k5_relat_1(B,A) ) )).
fof(t164_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t164_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t164_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ~ r1_xboole_0(k3_xxreal_1(C,D),k3_xxreal_1(A,B)) => k2_xboole_0(k3_xxreal_1(C,D),k3_xxreal_1(A,B)) = k3_xxreal_1(k3_xxreal_0(C,A),k4_xxreal_0(D,B)) ) ) ) ) ) )).
fof(t164_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ! [E] : ( m2_subset_1(E,k4_ordinal1,k1_zf_lang) => ( E != C => ( k13_zf_lang(E,A) = k6_zf_lang1(k13_zf_lang(E,B),C,D) <=> A = k6_zf_lang1(B,C,D) ) ) ) ) ) ) ) )).
fof(t164_zmodul01,axiom,( ! [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) ) => ( ~ 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))) ) ) )).
fof(t165_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( m3_glib_001(C,B) => m3_glib_001(C,A) ) ) ) )).
fof(t165_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t165_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) ) => ( r1_tarski(C,B) => r1_tarski(C,k5_relat_1(B,A)) ) ) ) )).
fof(t165_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t165_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(A,k5_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) ) ) ) )).
fof(t165_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t165_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ( k13_zf_lang(D,A) = k6_zf_lang1(k13_zf_lang(C,B),C,D) <=> A = k6_zf_lang1(B,C,D) ) ) ) ) ) )).
fof(t166_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t166_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t166_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r1_tarski(k9_xtuple_0(C),B) => k6_subset_1(C,k5_relat_1(C,A)) = k5_relat_1(C,k6_subset_1(B,A)) ) ) )).
fof(t166_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t166_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(A,k5_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)) ) ) ) )).
fof(t166_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t166_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ( v2_zf_lang(A) <=> v2_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) )).
fof(t167_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t167_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t167_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k9_xtuple_0(k6_subset_1(B,k5_relat_1(B,A))) = k6_subset_1(k9_xtuple_0(B),A) ) )).
fof(t167_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t167_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,1) => r1_xxreal_0(B,k3_xcmplx_0(A,C)) ) ) => r1_xxreal_0(B,A) ) ) ) )).
fof(t167_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t167_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ( v3_zf_lang(A) <=> v3_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) )).
fof(t168_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t168_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(C,A) => r2_hidden(k3_xxreal_3(C,B),k20_member_1(A,B)) ) ) ) ) )).
fof(t168_relat_1,axiom,( ! [A] : ! [B] : ( 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))) ) )).
fof(t168_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t168_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t168_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ( v4_zf_lang(A) <=> v4_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) )).
fof(t169_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & ~ v4_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t169_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => k20_member_1(A,B) = a_2_12_member_1(A,B) ) ) )).
fof(t169_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r1_xboole_0(k9_xtuple_0(A),k9_xtuple_0(B)) => r1_xboole_0(A,B) ) ) ) )).
fof(t169_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t169_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(1,C) & ~ r1_xxreal_0(A,k3_xcmplx_0(C,B)) ) ) => r1_xxreal_0(A,k5_numbers) ) ) ) )).
fof(t169_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t169_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ( v5_zf_lang(A) <=> v5_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) )).
fof(t16_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_abcmiz_0(A) ) => k4_abcmiz_0(A,k1_subset_1(u1_abcmiz_0(A))) = u1_struct_0(A) ) )).
fof(t16_abcmiz_1,axiom,( r1_tarski(a_0_0_abcmiz_1,k2_abcmiz_1) )).
fof(t16_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & v1_abcmiz_a(A) & l1_msualg_1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t16_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ( k2_absvalue(A) = k5_numbers => A = k5_numbers ) ) )).
fof(t16_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r2_hidden(D,k2_aff_1(A,B,C)) & r2_hidden(E,k2_aff_1(A,B,C)) ) => ( B = C | r1_tarski(k2_aff_1(A,B,C),k2_aff_1(A,D,E)) ) ) ) ) ) ) ) )).
fof(t16_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t16_afinsq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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) ) ) )).
fof(t16_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => r1_subset_1(u1_struct_0(A),k7_afproj(A)) ) )).
fof(t16_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_afvect0(A,B,C,D) => r2_afvect0(A,D,C,B) ) ) ) ) ) )).
fof(t16_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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 ) ) ) ) ) )).
fof(t16_algspec1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k1_algspec1(k1_xboole_0,A) = k1_xboole_0 ) )).
fof(t16_algstr_4,axiom,( ! [A] : k11_algstr_4(A,k5_numbers) = k1_xboole_0 )).
fof(t16_altcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ( v14_altcat_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_altcat_1(A,B,B) = k1_tarski(k8_altcat_1(A,B)) ) ) ) )).
fof(t16_altcat_2,axiom,( ! [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) & l1_cat_1(A) ) => v11_altcat_1(k4_altcat_2(A)) ) )).
fof(t16_altcat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( m1_subset_1(D,k1_altcat_1(A,B,C)) & v2_altcat_3(D,A,B,C) & ~ v4_altcat_3(D,A,B,C) ) ) ) ) ) )).
fof(t16_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l2_altcat_1(B) ) => ! [C] : ( ( v10_functor0(C,A,B) & l2_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(G,k1_altcat_1(A,D,E)) => F != k6_functor0(A,B,C,D,E,G) ) ) ) ) ) ) ) ) )).
fof(t16_ami_2,axiom,( ! [A] : ( m1_subset_1(A,k1_ami_2) => ( A = k4_ordinal1 | r2_hidden(A,k2_ami_2) ) ) )).
fof(t16_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ~ v2_extpro_1(k2_ami_3(A,B),k7_card_1(2),k1_ami_3) ) ) )).
fof(t16_ami_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( ~ 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(k7_card_1(2),k1_ami_3)) & v1_finset_1(B) & v4_extpro_1(B,k7_card_1(2),k1_ami_3,A) ) => ! [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(C,u1_struct_0(k1_ami_3)) ) => ! [D] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ( ( r1_tarski(B,C) & r1_tarski(B,D) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_ami_3)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_ami_3)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( ( r1_tarski(A,E) & r1_tarski(A,F) ) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v1_ami_2(H) & m1_subset_1(H,u1_struct_0(k1_ami_3)) ) => ! [I] : ( ( v1_ami_2(I) & m1_subset_1(I,u1_struct_0(k1_ami_3)) ) => ! [J] : ( m1_subset_1(J,u1_compos_1(k1_ami_3)) => ( ( J = k3_extpro_1(k7_card_1(2),k1_ami_3,E,k5_extpro_1(k7_card_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(k7_card_1(2),k1_ami_3,E,C,G),I) = k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,F,D,G),I) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_ami_6,axiom,( ! [A] : ( v7_ordinal1(A) => k2_amistd_1(k7_card_1(2),k1_ami_3,k7_ami_3(A)) = k1_tarski(A) ) )).
fof(t16_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( k5_ami_wstd(A,B,C) = k5_ami_wstd(A,B,D) => C = D ) ) ) ) ) )).
fof(t16_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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(k5_numbers,k2_compos_1(B)),A,B) ) ) )).
fof(t16_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(t16_analmetr,axiom,( ! [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) ) => u1_struct_0(k2_diraf(k2_analoaf(A))) = u1_struct_0(A) ) )).
fof(t16_analoaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( E = k5_algstr_0(A,k3_rlvect_1(A,C,D),B) => ( r1_analoaf(A,B,C,D,E) & r1_analoaf(A,B,D,C,E) ) ) ) ) ) ) ) )).
fof(t16_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_analmetr(A,F,G) & r1_analoaf(A,B,D,C,E) ) => r1_analoaf(A,k2_analort(A,F,G,B),k2_analort(A,F,G,D),k2_analort(A,F,G,C),k2_analort(A,F,G,E)) ) ) ) ) ) ) ) ) )).
fof(t16_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t16_anproj_2,axiom,( ? [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) & l1_rlvect_1(A) & ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( 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 = k5_numbers & F = k5_numbers & G = k5_numbers ) ) ) ) ) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ? [F] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & 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)) ) ) ) ) ) ) ) ) )).
fof(t16_aofa_000,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => ! [B] : ~ ( r2_hidden(B,k4_dtconstr(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,k1_lang1(A)) & B = k2_trees_4(u1_struct_0(A),C) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t16_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : k2_xboole_0(k1_tarski(A),k6_enumset1(B,C,D,E,F,G,H,I)) = k7_enumset1(A,B,C,D,E,F,G,H,I) )).
fof(t16_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v19_aofa_a00(B,A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( C = k10_subset_1(k1_funct_1(u7_aofa_a00(A),6),u4_struct_0(A)) => ( k1_msualg_1(A,C) = k12_finseq_1(u1_struct_0(A),B) & k2_msualg_1(A,C) = B ) ) ) ) ) )).
fof(t16_aofa_i00,axiom,( ! [A] : ( m4_aofa_i00(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k9_funct_2(k4_ordinal1,k4_numbers),k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_funct_2(k4_ordinal1,k4_numbers),k4_ordinal1))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k9_funct_2(k4_ordinal1,k4_numbers),k4_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k9_funct_2(k4_ordinal1,k4_numbers),k4_numbers))) ) => r2_aofa_i00(k7_freealg(k19_aofa_000,k26_aofa_i00),k4_ordinal1,k1_aofa_i00(k9_funct_2(k4_ordinal1,k4_numbers),k5_numbers,k5_numbers),A,B,C) ) ) ) )).
fof(t16_armstrng,axiom,( ! [A] : 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)) )).
fof(t16_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => r2_hidden(k2_arytm_0(A,A),k2_arytm_2) ) )).
fof(t16_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( 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)) ) ) ) ) )).
fof(t16_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( 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) ) ) ) )).
fof(t16_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ( k3_arytm_3(A,A) = A & k2_arytm_3(A,A) = A ) ) )).
fof(t16_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v4_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v4_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) & k1_seq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) = k5_numbers ) => ( r2_hidden(A,k6_asympt_0(B)) & ~ r2_hidden(B,k6_asympt_0(A)) ) ) ) ) )).
fof(t16_asympt_1,axiom,( ? [A] : ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v4_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & r2_funct_2(k4_ordinal1,k1_numbers,A,k1_asympt_1(2,1,k5_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,k5_numbers),k6_asympt_0(A)) ) )).
fof(t16_autalg_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v2_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( m2_pboole(E,A,B,C) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(t16_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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)) ) ) )).
fof(t16_bagorder,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t16_bcialg_1,axiom,( ! [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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) )).
fof(t16_bcialg_3,axiom,( ! [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) ) => ( v4_bcialg_3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)))) ) ) ) ) )).
fof(t16_bcialg_4,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t16_bcialg_5,axiom,( ! [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] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( v8_bcialg_1(A) & m1_bcialg_5(A,B,C,D,E) ) <=> ( v8_bcialg_1(A) & m1_bcialg_5(A,D,E,B,C) ) ) ) ) ) ) ) )).
fof(t16_bcialg_6,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k5_bcialg_1(A)) => ! [D] : ( v7_ordinal1(D) => k3_bcialg_6(A,k4_xcmplx_0(D),k6_bcialg_1(A,B,C)) = k1_bcialg_1(A,k3_bcialg_6(A,k4_xcmplx_0(D),B),k3_bcialg_6(A,k4_xcmplx_0(D),C)) ) ) ) ) )).
fof(t16_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( m1_bciideal(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t16_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_bhsp_1(A,k3_rlvect_1(A,B,C),k3_rlvect_1(A,B,C)) = k2_xcmplx_0(k2_xcmplx_0(k2_bhsp_1(A,B,B),k3_xcmplx_0(2,k2_bhsp_1(A,B,C))),k2_bhsp_1(A,C,C)) ) ) ) )).
fof(t16_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_bhsp_2(B,A) => k1_bhsp_2(A,k5_vfunct_1(k4_ordinal1,A,B)) = k4_algstr_0(A,k1_bhsp_2(A,B)) ) ) ) )).
fof(t16_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( v7_ordinal1(D) => 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) ) ) ) ) )).
fof(t16_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k3_bhsp_4(A,B,1) = k3_rlvect_1(A,k3_bhsp_4(A,B,k5_numbers),k1_normsp_1(A,B,1)) ) ) )).
fof(t16_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t16_binari_3,axiom,( k7_binarith(1,k10_binarith(k6_margrel1,k7_margrel1),k10_binarith(k6_margrel1,k7_margrel1)) = k10_binarith(k6_margrel1,k7_margrel1) )).
fof(t16_binari_4,axiom,( ! [A] : ( ( v3_card_1(A,1) & m2_finseq_1(A,k6_margrel1) ) => ( A = k12_finseq_1(k6_margrel1,k7_margrel1) => k3_binari_2(1,A) = k5_numbers ) ) )).
fof(t16_binarith,axiom,( ! [A] : ( ( v3_card_1(A,1) & m2_finseq_1(A,k6_margrel1) ) => ( A = k14_trees_3(k8_margrel1) => k6_binarith(1,A) = 1 ) ) )).
fof(t16_binop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t16_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t16_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ~ r4_boolealg(A,B,k5_lattices(A)) ) ) )).
fof(t16_bor_cant,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) = k5_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))) = k5_numbers & k1_funct_1(C,k4_kurato_0(A,D)) = 1 ) ) ) ) ) ) ) )).
fof(t16_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k2_borsuk_1(A,B))))) => ! [D] : ~ ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t16_borsuk_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v1_compts_1(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t16_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_topmetr)) => ! [B] : ( 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))) ) ) )).
fof(t16_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ v1_rat_1(A) <=> r2_hidden(A,k1_borsuk_5) ) ) )).
fof(t16_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k18_rvsum_1(k12_rvsum_1(k11_finseq_1(A,B,C))) = k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(C)) ) ) ) )).
fof(t16_bspace,axiom,( ! [A] : ! [B] : ( A = B <=> ! [C] : k3_bspace(A,C) = k3_bspace(B,C) ) )).
fof(t16_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(t16_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t16_bvfunc14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ! [F] : ! [G] : ! [H] : ! [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) ) ) )).
fof(t16_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)))) ) ) ) )).
fof(t16_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t16_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t16_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t16_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t16_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t16_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t16_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t16_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t16_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t16_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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,D),k9_bvfunc_1(A,C,k1_bvfunc_1(A,D))),k5_bvfunc_1(A,k1_bvfunc_1(A,B),k1_bvfunc_1(A,C))) ) ) ) ) )).
fof(t16_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k1_group_1(k7_c0sp1(A)) = k8_funcop_1(k4_ordinal1,A,1) ) )).
fof(t16_c0sp2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v1_compts_1(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_c0sp2(B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_c0sp2(B))) => ! [E] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(B)) => k3_funct_2(u1_struct_0(B),k1_numbers,F,G) = k3_xcmplx_0(A,k3_funct_2(u1_struct_0(B),k1_numbers,E,G)) ) ) ) ) ) ) ) ) ) )).
fof(t16_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t16_calcul_2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => k15_finseq_1(k5_relset_1(k4_ordinal1,k3_cqc_lang(A),k8_finseq_1(k3_cqc_lang(A),C,B),k2_calcul_2(k3_finseq_1(C),k3_finseq_1(B)))) = k4_relset_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k3_cqc_lang(A),k14_finseq_1(k2_calcul_2(k3_finseq_1(C),k3_finseq_1(B))),k8_finseq_1(k3_cqc_lang(A),C,B)) ) ) ) )).
fof(t16_cantor_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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)))))) ) ) ) )).
fof(t16_card_1,axiom,( ! [A] : ! [B] : ( r2_wellord2(A,B) => k2_card_1(A) = k2_card_1(B) ) )).
fof(t16_card_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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)))) ) )).
fof(t16_card_3,axiom,( ! [A] : ! [B] : ! [C] : k5_card_3(A,k2_xboole_0(B,C)) = k2_xboole_0(k5_card_3(A,B),k5_card_3(A,C)) )).
fof(t16_card_4,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ( r2_hidden(k5_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 ) ) ) ) ) )).
fof(t16_card_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_finset_1(B) & v1_card_1(B) ) => ( B != k5_numbers & B != 1 & B != 2 & B != k5_card_1(A) & r2_hidden(k5_card_1(A),B) & r1_tarski(k4_ordinal1,B) ) ) ) )).
fof(t16_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t16_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ! [C] : ! [D] : ( C != D => r2_hidden(k1_funct_4(k7_funcop_1(B,D),k7_funcop_1(A,C)),k1_card_fin(k2_xboole_0(A,B),k5_card_1(A),C,D)) ) ) ) )).
fof(t16_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( r1_tarski(k8_subset_1(A,D,C),B) => r1_tarski(k9_subset_1(A,C,k2_card_lar(A,D)),k1_ordinal1(B)) ) ) ) ) ) )).
fof(t16_cardfin2,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ( r1_xxreal_0(k5_card_1(A),k5_card_1(B)) => k5_card_1(k4_cardfin2(A,B)) = k6_xcmplx_0(k11_newton(k5_card_1(B),k5_card_1(A)),k7_xcmplx_0(k2_newton(k5_card_1(B)),k2_newton(k7_nat_d(k5_card_1(B),k5_card_1(A))))) ) ) ) )).
fof(t16_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t16_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(B)) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t16_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_cat_1(A,B,k1_cat_4(A)) = k1_tarski(k6_cat_4(A,B)) ) ) )).
fof(t16_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k7_cat_5(B) = B ) ) )).
fof(t16_catalan1,axiom,( ! [A] : ( v7_ordinal1(A) => r1_xxreal_0(k1_catalan1(A),k1_catalan1(k1_nat_1(A,1))) ) )).
fof(t16_catalan2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ! [C] : ( v7_ordinal1(C) => ( ( k5_relat_1(A,k1_nat_1(k3_xcmplx_0(2,C),k1_afinsq_1(B))) = k1_catalan2(k1_catalan2(k8_funcop_1(k4_ordinal1,C,k5_numbers),B),k8_funcop_1(k4_ordinal1,C,1)) & v1_catalan2(B) & k3_xcmplx_0(2,k7_afinsq_2(B)) = k1_afinsq_1(B) ) => ( r1_xxreal_0(C,k5_numbers) | k3_nat_1(a_1_0_catalan2(A)) = k1_nat_1(k3_xcmplx_0(2,C),k1_afinsq_1(B)) ) ) ) ) ) )).
fof(t16_catalg_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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 ) ) ) ) )).
fof(t16_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v10_algstr_0(B,A) & v10_algstr_0(C,A) ) => v10_algstr_0(k5_cayldick(A,B,C),k4_cayldick(A)) ) ) ) ) )).
fof(t16_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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 ) ) )).
fof(t16_cc0sp2,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t16_cfcont_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( 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(k5_numbers)) = k1_xboole_0 ) => r2_relset_1(k4_ordinal1,k2_numbers,k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,B,k5_relset_1(k2_numbers,k2_numbers,k2_cfunct_1(k2_numbers,C),A)),k36_valued_1(k4_ordinal1,k2_numbers,k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,B,k5_relset_1(k2_numbers,k2_numbers,C,A)))) ) ) ) )).
fof(t16_cfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_numbers)) => ! [B] : ( ( 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) ) ) ) )).
fof(t16_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ! [C] : ( m2_funct_2(C,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ! [D] : ( v1_xcmplx_0(D) => k1_binop_1(k2_cfuncdom(A),k1_funct_1(k3_cfuncdom(A),k4_tarski(D,B)),C) = k1_funct_1(k3_cfuncdom(A),k4_tarski(D,k1_funcsdom(A,k2_numbers,k2_cfuncdom(A),B,C))) ) ) ) ) )).
fof(t16_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( 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,D,k2_valued_1(A,k2_numbers,k2_numbers,B,C)),k2_valued_1(A,k2_numbers,k2_numbers,k19_valued_1(A,k2_numbers,k2_numbers,D,B),k19_valued_1(A,k2_numbers,k2_numbers,D,C))) ) ) ) ) )).
fof(t16_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ~ r2_hidden(A,k8_cgames_1(A)) ) )).
fof(t16_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : ( 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)) ) ) ) ) )).
fof(t16_circcmb2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & ~ v11_struct_0(C) & v2_msafree2(C) & l1_msualg_1(C) ) => ( C = k2_circcomb(A,B) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(C,F))) => ! [H] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_circcmb3,axiom,( ! [A] : ( ( v4_circcmb3(A) & l1_msualg_1(A) ) => k3_msafree2(A) = k1_tarski(k3_circcmb3(A)) ) )).
fof(t16_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ( r1_circcomb(A,B) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t16_circled1,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ~ ( v1_circled1(B,A) & k3_rlvect_2(A,B) = k1_xboole_0 ) ) ) )).
fof(t16_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v4_msafree2(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m3_msaterm(D,A,B) => ! [E] : ( m1_subset_1(E,u4_struct_0(k1_circtrm1(A,B,D))) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t16_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_funct_1(u3_msualg_1(A,k5_msafree2(A,B)),C)) => ! [E] : ( ( 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] : ( m1_subset_1(F,k4_ordinal1) => ~ ( r2_hidden(F,k1_relset_1(k4_ordinal1,E)) & ! [G] : ( 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) ) ) ) ) ) ) )).
fof(t16_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_pboole(C,k2_msafree2(A),k7_funcop_1(k2_msafree2(A),k4_ordinal1),k5_relat_1(u3_msualg_1(A,B),k2_msafree2(A))) => ( v3_funct_1(k9_funct_6(C)) => ( v1_xboole_0(k2_msafree2(A)) | ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(A,B))) => ! [E] : ( m1_msafree2(E,A,B) => ( E = k1_funct_1(k9_funct_6(C),k5_numbers) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( r1_xxreal_0(k6_circuit1(A,B,G),F) => k1_funct_1(k9_nat_1(k4_card_3(u3_msualg_1(A,B)),k9_circuit2(A,B,C,D),F),G) = k5_circuit2(A,B,G,E) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k1_euclid(A))) ) => ! [E] : ( v1_xreal_0(E) => ( ( v1_pdiff_7(D,A) & C = k7_funcop_1(D,E) & r1_xxreal_0(1,B) & r1_xxreal_0(B,A) ) => k3_pdiff_9(A,D,B,C) = k8_funcop_1(k4_ordinal1,D,k5_numbers) ) ) ) ) ) ) )).
fof(t16_classes1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r1_ordinal1(B,C) => r1_tarski(k3_classes1(A,B),k3_classes1(A,C)) ) ) ) )).
fof(t16_classes2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( r2_hidden(A,k1_card_1(k1_classes1(B))) => r2_hidden(A,k1_classes1(B)) ) ) )).
fof(t16_clopban1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k6_clopban1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k6_clopban1(A,B))) => ! [E] : ( v1_xcmplx_0(E) => ( D = k1_clvect_1(k6_clopban1(A,B),C,E) <=> ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t16_clopban2,axiom,( ! [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) & 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)) ) ) )).
fof(t16_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,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))) ) ) ) )).
fof(t16_clopban4,axiom,( ! [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) & 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] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t16_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m2_pboole(C,A,k5_mssubfam(A,B),k5_mssubfam(A,B)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t16_closure2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t16_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t16_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clvect_2(B,A) => k1_clvect_2(A,k5_vfunct_1(k4_ordinal1,A,B)) = k4_algstr_0(A,k1_clvect_2(A,B)) ) ) ) )).
fof(t16_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k2_clvect_3(A,B,1) = k3_rlvect_1(A,k2_clvect_3(A,B,k5_numbers),k1_normsp_0(A,B,1)) ) ) )).
fof(t16_coh_sp,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k3_coh_sp(C)) => ( r2_hidden(k2_tarski(A,B),D) => ( r2_hidden(A,k3_tarski(D)) & r2_hidden(B,k3_tarski(D)) ) ) ) )).
fof(t16_cohsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) ) )).
fof(t16_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m2_collsp(E,A) => ( ( r2_hidden(B,E) & r2_hidden(C,E) & r2_hidden(D,E) ) => r1_collsp(A,B,C,D) ) ) ) ) ) ) )).
fof(t16_combgras,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( l1_incsp_1(B) => ! [C] : ( l1_combgras(C,A,B) => ! [D] : ( l1_combgras(D,A,B) => ( ( ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => k2_combgras(A,B,C,E) = k2_combgras(A,B,D,E) ) & ! [E] : ( 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)) ) ) ) ) ) )).
fof(t16_compl_sp,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t16_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k3_complex1(k3_xcmplx_0(A,A)) = k6_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A))) & k4_complex1(k3_xcmplx_0(A,A)) = k3_xcmplx_0(2,k4_real_1(k3_complex1(A),k4_complex1(A))) ) ) )).
fof(t16_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( r2_hidden(k1_comptrig(A),k2_rcomp_1(k5_numbers,k28_sin_cos)) <=> ~ r1_xxreal_0(k4_complex1(A),k5_numbers) ) ) )).
fof(t16_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_complfld)) => ~ ( B != k4_struct_0(k1_complfld) & ( k8_group_1(k1_complfld,A,B) = C | k8_group_1(k1_complfld,B,A) = C ) & ~ ( A = k8_group_1(k1_complfld,C,k11_algstr_0(k1_complfld,B)) & A = k8_group_1(k1_complfld,k11_algstr_0(k1_complfld,B),C) ) ) ) ) ) )).
fof(t16_complsp2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k2_numbers,k4_finseq_2(A,k2_numbers)) => ! [D] : ( m2_finseq_2(D,k2_numbers,k4_finseq_2(A,k2_numbers)) => k9_matrix_5(k2_complsp2(A,C,D),B) = k6_xcmplx_0(k9_matrix_5(C,B),k9_matrix_5(D,B)) ) ) ) ) )).
fof(t16_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(A)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t16_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( v6_compos_0(D,u1_compos_1(A)) & m1_subset_1(D,u1_compos_1(A)) ) => ! [E] : ( ( v6_compos_0(E,u1_compos_1(A)) & m1_subset_1(E,u1_compos_1(A)) ) => ! [F] : ( ( v6_compos_0(F,u1_compos_1(A)) & m1_subset_1(F,u1_compos_1(A)) ) => ! [G] : ( ( 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 ) ) ) ) ) ) ) )).
fof(t16_comptrig,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k1_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(2,k28_sin_cos))) => r1_xxreal_0(k5_numbers,k1_funct_1(k18_sin_cos,A)) ) ) )).
fof(t16_compts_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) ) )).
fof(t16_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v4_valued_0(A) & v2_comput_1(A) ) => ( v1_funct_1(A) & v3_margrel1(A,k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(k4_ordinal1),k4_ordinal1))) ) ) )).
fof(t16_comseq_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k25_valued_1(k4_ordinal1,k2_numbers,k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,C),A),k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k25_valued_1(k4_ordinal1,k2_numbers,B,A),k25_valued_1(k4_ordinal1,k2_numbers,C,A))) ) ) ) )).
fof(t16_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => k3_comseq_2(k31_valued_1(k4_ordinal1,k2_numbers,A)) = k4_xcmplx_0(k3_comseq_2(A)) ) )).
fof(t16_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( r2_funct_2(k4_ordinal1,k1_numbers,k32_valued_1(k4_ordinal1,k1_numbers,k7_comseq_3(A)),k7_comseq_3(k31_valued_1(k4_ordinal1,k2_numbers,A))) & r2_funct_2(k4_ordinal1,k1_numbers,k32_valued_1(k4_ordinal1,k1_numbers,k8_comseq_3(A)),k8_comseq_3(k31_valued_1(k4_ordinal1,k2_numbers,A))) ) ) )).
fof(t16_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u4_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t16_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( v4_lattice3(A) <=> ? [B] : ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_conlat_1(B) & r1_filter_1(k11_conlat_1(B),A) ) ) ) )).
fof(t16_conmetr1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v2_conmetr(A) <=> v2_aff_2(k3_analmetr(A)) ) ) )).
fof(t16_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t16_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r1_connsp_2(A,B) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t16_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(t16_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_rusub_4(B,A) => v1_convex1(B,A) ) ) ) )).
fof(t16_convex4,axiom,( ! [A] : ( ( ~ 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] : ( m1_convex4(B,A) => ( k1_convex4(A,B) = k1_xboole_0 => k4_convex4(A,B) = k4_struct_0(A) ) ) ) )).
fof(t16_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( 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,k5_numbers),B))) ) ) ) ) )).
fof(t16_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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) ) ) )).
fof(t16_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ( v1_cqc_the1(B,A) <=> k1_cqc_the1(A,B) = B ) ) ) )).
fof(t16_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t16_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => r3_cqc_the3(A,k4_cqc_the1(A)) ) )).
fof(t16_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => k12_csspace(A,k4_struct_0(A),k4_struct_0(A)) = k5_numbers ) )).
fof(t16_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t16_decomp_1,axiom,( ! [A] : ( ( 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) ) )).
fof(t16_descip_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( r1_xxreal_0(1,k3_finseq_1(B)) => k8_descip_1(A,B,1) = k6_descip_1(B) ) ) ) )).
fof(t16_dickson,axiom,( ! [A] : ( l1_orders_2(A) => ( ( v1_wellfnd1(k5_dickson(A)) & v5_orders_2(A) ) => v1_wellfnd1(A) ) ) )).
fof(t16_diff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( ( 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_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,D,E),B),k1_nat_1(A,1)),C) = k6_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(D,B),k1_nat_1(A,1)),C),k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(E,B),k1_nat_1(A,1)),C)) ) ) ) ) ) )).
fof(t16_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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) = k2_xcmplx_0(k3_xcmplx_0(A,k2_diff_2(I,C,D,E,F,G,H)),k3_xcmplx_0(B,k2_diff_2(J,C,D,E,F,G,H))) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t16_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(B,k1_relset_1(k1_numbers,k1_fdiff_9)) & r2_hidden(k6_xcmplx_0(B,A),k1_relset_1(k1_numbers,k1_fdiff_9)) ) => k1_funct_1(k4_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fdiff_9,k1_fdiff_9),A),B) = k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(4,k17_sin_cos(k6_xcmplx_0(k3_xcmplx_0(2,B),A))),k17_sin_cos(A)),k1_square_1(k2_xcmplx_0(k19_sin_cos(k6_xcmplx_0(k3_xcmplx_0(2,B),A)),k19_sin_cos(A)))) ) ) ) )).
fof(t16_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v2_dilworth(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ( v2_dilworth(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) )).
fof(t16_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t16_dirort,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dirort(A) & l1_analoaf(A) ) => ( v4_dirort(A) => v2_dirort(A) ) ) )).
fof(t16_dist_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,A) ) => k16_rvsum_1(k9_dist_1(A,B)) = k3_finseq_1(B) ) ) )).
fof(t16_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => ! [C] : ( m1_dist_2(C,A,B) => k9_dist_1(A,C) = k26_valued_1(k4_ordinal1,k1_numbers,k4_dist_1(A,C),k3_finseq_1(C)) ) ) ) )).
fof(t16_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ( ( m1_dynkin(B,A) & v2_finsub_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( r1_tarski(k10_xtuple_0(C),B) => r1_tarski(k10_xtuple_0(k4_dynkin(A,C)),B) ) ) ) ) ) )).
fof(t16_e_siec,axiom,( ! [A] : ( ( 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 ) ) )).
fof(t16_ec_pf_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(B))) => ( C = k5_int_1(A,B) => k4_algstr_0(k9_int_3(B),C) = k5_int_1(k6_xcmplx_0(B,A),B) ) ) ) ) )).
fof(t16_ec_pf_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t16_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t16_entropy1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( v1_matrprob(k2_finseq_2(A,k7_xcmplx_0(1,A))) & m2_finseq_1(k2_finseq_2(A,k7_xcmplx_0(1,A)),k1_numbers) ) ) )).
fof(t16_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k1_tarski(A),k4_enumset1(B,C,D,E,F,G)) )).
fof(t16_eqrel_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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) ) ) )).
fof(t16_equation,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t16_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => r1_xxreal_0(k12_euclid(k8_euclid(A,C,D)),k2_xcmplx_0(k12_euclid(k8_euclid(A,C,B)),k12_euclid(k8_euclid(A,B,D)))) ) ) ) ) )).
fof(t16_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => k22_rvsum_1(k3_rlvect_1(k15_euclid(A),B,C),D) = k2_xcmplx_0(k22_rvsum_1(B,D),k22_rvsum_1(C,D)) ) ) ) ) )).
fof(t16_euclid_3,axiom,( k1_euclid_3(k5_complex1) = k4_struct_0(k15_euclid(2)) )).
fof(t16_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ( k22_rvsum_1(B,B) = k5_numbers <=> k12_euclid(B) = k5_numbers ) ) ) )).
fof(t16_euclid_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(3))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t16_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( k12_euclid(k5_algstr_0(k15_euclid(2),C,A)) = k12_euclid(k5_algstr_0(k15_euclid(2),B,C)) => ( A = B | k4_euclid_3(C,A,B) = k4_euclid_3(A,B,C) ) ) ) ) ) )).
fof(t16_euclid_7,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) )).
fof(t16_euclid_8,axiom,( k5_euclid_8(k4_euclid_8,k2_euclid_8) = k3_euclid_8 )).
fof(t16_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => ~ ( A != k5_numbers & r2_hidden(D,k4_euclid_9(A,C,B)) & r1_xxreal_0(k3_xcmplx_0(B,k3_square_1(A)),k3_metric_1(k14_euclid(A),D,C)) ) ) ) ) ) )).
fof(t16_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t16_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t16_euler_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_int_1(C) => ( A != k5_numbers => k3_int_2(k2_xcmplx_0(A,k3_xcmplx_0(C,B)),B) = k3_int_2(A,B) ) ) ) ) )).
fof(t16_euler_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => k2_euler_2(k1_euler_2(k8_finseq_1(k4_ordinal1,C,D),A),B) = k8_finseq_1(k4_ordinal1,k2_euler_2(k1_euler_2(C,A),B),k2_euler_2(k1_euler_2(D,A),B)) ) ) ) ) )).
fof(t16_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k2_exchsort(A) = k3_ordinal2(k9_xtuple_0(A)) ) )).
fof(t16_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) & r1_compos_1(B,C,k5_memstr_0(A,B,k5_extpro_1(A,B,C,D,E))) ) ) ) ) ) ) )).
fof(t16_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ( A != k5_numbers => k3_extreal1(k2_extreal1(k8_mesfunc1,A)) = k2_extreal1(k8_mesfunc1,k3_extreal1(A)) ) ) )).
fof(t16_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( 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) ) ) ) ) )).
fof(t16_fcont_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t16_fcont_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_xxreal_0(B,A) & r1_tarski(k1_rcomp_1(B,A),k1_relset_1(k1_numbers,C)) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A))) ) => ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,k1_rcomp_1(k3_seq_4(k7_relset_1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A))),k2_seq_4(k7_relset_1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A))))) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k1_rcomp_1(B,A)) & D = k1_funct_1(C,E) ) ) ) ) ) ) ) ) )).
fof(t16_fcont_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t16_fdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(C,A),k1_fdiff_1(B,A)),k3_xcmplx_0(k1_funct_1(B,A),k1_fdiff_1(C,A))) ) ) ) ) ) )).
fof(t16_fdiff_10,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k16_sin_cos),A),B) = k2_xcmplx_0(k7_xcmplx_0(k1_funct_1(k16_sin_cos,B),B),k3_xcmplx_0(k1_funct_1(k3_taylor_1,B),k1_funct_1(k18_sin_cos,B))) ) ) ) ) ) )).
fof(t16_fdiff_11,axiom,( ! [A] : ( ( 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,k18_sin_cos))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k18_sin_cos),A),B) = k7_xcmplx_0(k1_funct_1(k16_sin_cos,k1_funct_1(k2_sin_cos9,B)),k2_xcmplx_0(1,k1_square_1(B))) ) ) ) ) ) )).
fof(t16_fdiff_2,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(t16_fdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( 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)) = k2_xcmplx_0(k2_fdiff_3(C,A),k2_fdiff_3(C,B)) ) ) ) ) ) )).
fof(t16_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k1_funct_1(C,D) = k6_xcmplx_0(A,D) & k1_funct_1(C,D) != k5_numbers ) ) ) ) => ( r2_fdiff_1(k6_rfunct_1(k1_numbers,k1_numbers,C),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(k2_fdiff_1(k6_rfunct_1(k1_numbers,k1_numbers,C),B),D) = k7_xcmplx_0(1,k1_square_1(k6_xcmplx_0(A,D))) ) ) ) ) ) ) ) )).
fof(t16_fdiff_5,axiom,( ! [A] : ( ( 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(k7_xcmplx_0(1,2))))) => ( r2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k4_taylor_1(k7_xcmplx_0(1,2))),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k4_taylor_1(k7_xcmplx_0(1,2))),A),B) = k2_xcmplx_0(k1_funct_1(k18_sin_cos,B),k3_xcmplx_0(k7_xcmplx_0(1,2),k6_prepower(B,k4_xcmplx_0(k7_xcmplx_0(1,2))))) ) ) ) ) ) )).
fof(t16_fdiff_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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,k22_sin_cos)))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(C,D) = k4_xcmplx_0(k3_xcmplx_0(D,k3_power(k4_power,A))) ) ) ) => ( r1_xxreal_0(A,k5_numbers) | ( r2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k22_sin_cos)),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(k2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k22_sin_cos)),B),D) = k3_xcmplx_0(k6_prepower(A,k4_xcmplx_0(D)),k3_power(k4_power,A)) ) ) ) ) ) ) ) ) )).
fof(t16_fdiff_7,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k1_sin_cos6),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k1_sin_cos6),A),B) = k2_xcmplx_0(k1_funct_1(k1_sin_cos6,B),k7_xcmplx_0(B,k3_square_1(k6_xcmplx_0(1,k1_square_1(B))))) ) ) ) ) ) )).
fof(t16_fdiff_8,axiom,( ! [A] : ( ( 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,k26_sin_cos,k22_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k22_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k22_sin_cos),A),B) = k7_xcmplx_0(k1_funct_1(k22_sin_cos,k1_funct_1(k26_sin_cos,B)),k1_square_1(k1_funct_1(k18_sin_cos,B))) ) ) ) ) ) )).
fof(t16_fdiff_9,axiom,( ! [A] : ( ( 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,k22_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fdiff_9,k22_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fdiff_9,k22_sin_cos),A),B) = k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k22_sin_cos,k1_funct_1(k1_fdiff_9,B)),k1_funct_1(k16_sin_cos,B)),k1_square_1(k1_funct_1(k18_sin_cos,B))) ) ) ) ) ) )).
fof(t16_ff_siec,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t16_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t16_fib_num3,axiom,( k1_fib_num3(4) = 7 )).
fof(t16_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(2,A) => r1_xxreal_0(k2_power(k2_fib_num,A),k7_xcmplx_0(1,k3_square_1(5))) ) ) )).
fof(t16_filerec1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m2_finseq_1(E,D) => ( E = k11_finseq_1(A,B,C) => k2_rfinseq(D,2,E) = k9_finseq_1(C) ) ) ) )).
fof(t16_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t16_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t16_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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))) ) ) ) ) ) )).
fof(t16_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) )).
fof(t16_finance1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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(k6_finance1(A,k1_numbers,B,k12_prob_1),k3_random_2(A,B)) ) ) )).
fof(t16_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(t16_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ ( k3_finseq_1(B) = k1_nat_1(A,1) & ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : B != k7_finseq_1(C,k9_finseq_1(D)) ) ) ) ) )).
fof(t16_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => k2_finseq_1(A) != k2_finseq_1(k1_nat_1(A,1)) ) )).
fof(t16_finseq_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => k7_partfun1(A,k12_finseq_1(A,B),1) = B ) ) )).
fof(t16_finseq_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k3_finseq_1(k16_finseq_1(B,A)),k3_finseq_1(A)) ) ) )).
fof(t16_finseq_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( r2_finseq_4(k7_finseq_1(A,B),C) => r2_hidden(C,k5_xboole_0(k10_xtuple_0(A),k10_xtuple_0(B))) ) ) ) )).
fof(t16_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t16_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t16_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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(k4_ordinal1,B,k4_finseqop(A,B,k5_finseq_2(A,D,C),E),k5_finseq_2(B,D,k3_funct_2(A,B,E,C))) ) ) ) ) ) )).
fof(t16_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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 ) ) ) )).
fof(t16_finsub_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(A)) => v1_finset_1(B) ) )).
fof(t16_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( k1_fintopo2(A,B,D,C) = k8_margrel1 & k5_fintopo2(A,B,D) = k7_margrel1 ) ) ) ) ) ) ) )).
fof(t16_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) )).
fof(t16_fintopo4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( ( 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,k5_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)) ) ) ) ) ) ) )).
fof(t16_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t16_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_catalan2(A))) => ( r2_hidden(k2_flang_1(A),C) => ( r1_tarski(B,k6_flang_1(A,B,C)) & r1_tarski(B,k6_flang_1(A,C,B)) ) ) ) ) )).
fof(t16_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k2_flang_1(A),B) => ( r1_xxreal_0(C,k5_numbers) | k8_flang_1(A,k7_flang_1(A,B,C)) = k8_flang_1(A,B) ) ) ) ) )).
fof(t16_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => k1_flang_3(A,B,k2_xcmplx_0(C,1)) = k6_flang_1(A,k1_flang_3(A,B,C),B) ) ) )).
fof(t16_fomodel0,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(t16_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( 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,k5_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 ) ) ) ) )).
fof(t16_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( 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,k30_fomodel2(A)) ) ) )).
fof(t16_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ( ( k31_fomodel2(B) = k31_fomodel2(C) & k1_fomodel2(B) = k1_fomodel2(C) ) => ! [D] : ( m2_subset_1(D,k9_funct_2(k37_fomodel1(B),k3_rfunct_3(k3_finseq_2(A),k2_xboole_0(A,k6_margrel1))),k15_fomodel2(B,A)) => ! [E] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(C),k3_rfunct_3(k3_finseq_2(A),k2_xboole_0(A,k6_margrel1))),k15_fomodel2(C,A)) => ! [F] : ( ( 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))) ) => ~ ( 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(F),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(F),k37_fomodel1(B))) & k5_relat_1(D,k9_subset_1(k15_fomodel1(B),k10_xtuple_0(F),k37_fomodel1(B))) = k5_relat_1(E,k9_subset_1(k15_fomodel1(B),k10_xtuple_0(F),k37_fomodel1(B))) & ! [G] : ( ( 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))) ) => F != G ) ) ) ) ) ) ) ) ) )).
fof(t16_frechet,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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)) ) )).
fof(t16_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m2_valued_0(C,u1_struct_0(A),B) => r1_tarski(k2_frechet(A,B),k2_frechet(A,C)) ) ) ) )).
fof(t16_fscirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t16_fscirc_2,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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) ) )).
fof(t16_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t16_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ( ( v3_fsm_2(B,A) & v1_fsm_2(B,A) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t16_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t16_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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))) ) ) ) ) ) ) )).
fof(t16_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ r2_hidden(C,B) => k8_relat_1(k2_funcop_1(A,C),B) = k1_xboole_0 ) )).
fof(t16_funcsdom,axiom,( ! [A] : ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( m2_funct_2(C,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [D] : ( m2_funct_2(D,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [E] : ( v1_xreal_0(E) => k1_binop_1(k6_funcsdom(A),k1_binop_1(k7_funcsdom(A),E,B),C) = k1_binop_1(k7_funcsdom(A),E,k1_funcsdom(A,k1_numbers,k6_funcsdom(A),B,C)) ) ) ) ) )).
fof(t16_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( r1_tarski(k10_xtuple_0(B),A) & ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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) ) ) )).
fof(t16_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( D != k1_xboole_0 => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,B,D) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,D))) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t16_funct_3,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(t16_funct_4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t16_funct_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k9_xtuple_0(k3_funct_5(A)) = k10_xtuple_0(k9_xtuple_0(A)) ) )).
fof(t16_funct_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)) ) ) ) )).
fof(t16_funct_7,axiom,( k4_numbers != k3_finseq_2(k4_numbers) )).
fof(t16_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t16_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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) = k5_numbers | v1_funct_9(C,k6_xcmplx_0(A,B)) ) ) ) ) ) )).
fof(t16_functor0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( 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))) ) ) ) ) )).
fof(t16_functor1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l2_altcat_1(B) ) => ! [C] : ( ( v10_functor0(C,A,B) & l2_functor0(C,A,B) ) => ( v17_functor0(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => v2_funct_1(k5_functor0(A,B,C,D,E)) ) ) ) ) ) ) )).
fof(t16_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v2_altcat_1(D) & v12_altcat_1(D) & l2_altcat_1(D) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ! [F] : ( ( v15_functor0(F,B,C) & m2_functor0(F,B,C) ) => ! [G] : ( ( v15_functor0(G,B,C) & m2_functor0(G,B,C) ) => ! [H] : ( ( v15_functor0(H,C,D) & m2_functor0(H,C,D) ) => ! [I] : ( m1_functor2(I,B,C,F,G) => ( r1_functor2(B,C,F,G) => r8_pboole(u1_struct_0(A),k6_functor3(A,B,D,k1_functor3(B,C,D,F,H),k1_functor3(B,C,D,G,H),E,k5_functor3(B,C,D,F,G,I,H)),k5_functor3(A,C,D,k1_functor3(A,B,C,E,F),k1_functor3(A,B,C,E,G),k6_functor3(A,B,C,F,G,E,I),H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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)) ) ) ) ) )).
fof(t16_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D),C),k1_fuzzy_2(A,B,k2_fuzzy_1(A,D,C))) ) ) ) ) )).
fof(t16_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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] : ( ( v5_relat_1(F,k1_rcomp_1(k5_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(k3_fuzzy_4(A,B,C,k1_fuzzy_1(k2_zfmisc_1(A,B),D,E),F),k1_fuzzy_1(k2_zfmisc_1(A,C),k3_fuzzy_4(A,B,C,D,F),k3_fuzzy_4(A,B,C,E,F))) ) ) ) ) ) ) )).
fof(t16_fvaluat1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ~ ( C != k4_struct_0(B) & k3_fvaluat1(B,C,A) = k4_struct_0(B) ) ) ) ) )).
fof(t16_fvsum_1,axiom,( ! [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) ) => r7_binop_1(u1_struct_0(A),k5_vectsp_1(A),u1_algstr_0(A)) ) )).
fof(t16_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ ( ~ 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)) ) ) )).
fof(t16_gcd_1,axiom,( ! [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) & v1_vectsp_2(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r4_gcd_1(A,B,k4_struct_0(A)) => B = k4_struct_0(A) ) ) ) )).
fof(t16_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v2_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( m1_genealg1(E,D) => ! [F] : ( m1_genealg1(F,D) => ( k9_genealg1(D,E,F,k5_numbers,k5_numbers,C) = k7_genealg1(D,E,F,C) & k9_genealg1(D,E,F,A,k5_numbers,k5_numbers) = k7_genealg1(D,E,F,A) & k9_genealg1(D,E,F,k5_numbers,B,k5_numbers) = k7_genealg1(D,E,F,B) ) ) ) ) ) ) ) )).
fof(t16_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_analmetr(A,D,E) => r2_geomtrap(A,D,E,B,C,B,C) ) ) ) ) ) ) )).
fof(t16_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t16_gfacirc2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( k5_gfacirc2(k5_numbers,A,B) = k5_circcomb(k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k8_margrel1),k1_xboole_0) & k6_gfacirc2(k5_numbers,A,B) = k7_circcomb(k5_ordinal1,k6_margrel1,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k8_margrel1),k1_xboole_0) & k7_gfacirc2(k5_numbers,A,B) = k4_tarski(k1_xboole_0,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k8_margrel1)) ) ) ) )).
fof(t16_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ( r1_glib_000(A,C,D,B) <=> ( r2_glib_000(A,C,D,B) | r2_glib_000(A,D,C,B) ) ) ) )).
fof(t16_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( r1_glib_001(A,C,D,B) <=> ( k1_funct_1(B,1) = C & k1_funct_1(B,k3_finseq_1(B)) = D ) ) ) ) )).
fof(t16_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t16_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t16_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(t16_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( v7_ordinal1(D) => ( B != C => r1_glib_005(A,k1_funct_1(k12_glib_005(A,B,C),D),B,C) ) ) ) ) ) )).
fof(t16_goboard1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(C)) ) => ( ( ! [E] : ( v7_ordinal1(E) => ~ ( r2_hidden(E,k4_finseq_1(A)) & ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ~ ( r2_hidden(k4_tarski(F,G),k2_matrix_0(D)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,E) = k3_matrix_0(C,D,F,G) ) ) ) ) ) & ! [E] : ( v7_ordinal1(E) => ~ ( r2_hidden(E,k4_finseq_1(B)) & ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ~ ( r2_hidden(k4_tarski(F,G),k2_matrix_0(D)) & k7_partfun1(u1_struct_0(k15_euclid(2)),B,E) = k3_matrix_0(C,D,F,G) ) ) ) ) ) ) => ! [E] : ( v7_ordinal1(E) => ~ ( r2_hidden(E,k4_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(2)),A,B))) & ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ~ ( r2_hidden(k4_tarski(F,G),k2_matrix_0(D)) & k7_partfun1(u1_struct_0(k15_euclid(2)),k8_finseq_1(u1_struct_0(k15_euclid(2)),A,B),E) = k3_matrix_0(C,D,F,G) ) ) ) ) ) ) ) ) ) )).
fof(t16_goboard2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( ( r2_hidden(A,k4_finseq_1(B)) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => r1_xxreal_0(k1_funct_1(k1_goboard1(B),C),k1_funct_1(k1_goboard1(B),A)) ) ) ) => r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),B,A),k10_xtuple_0(k7_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(B),k3_finseq_1(k2_goboard2(B))))) ) ) ) )).
fof(t16_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( v2_goboard1(C) & v3_goboard1(C) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k1_matrix_0(C)) & r1_xxreal_0(1,A) ) => ( v3_relat_1(C) | r1_xxreal_0(k3_finseq_1(C),A) | r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),B)),k2_goboard5(C,B)) ) ) ) ) ) )).
fof(t16_goboard6,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_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_0(A))) = a_1_3_goboard6(A) ) )).
fof(t16_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(C)) ) => k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),k1_nat_1(B,1))),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),k1_nat_1(B,1)))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),k1_nat_1(B,1))) ) ) ) ) )).
fof(t16_goboard8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,2),k3_finseq_1(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,2),k1_matrix_0(k2_goboard2(A))) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,2),k3_finseq_1(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,1),k1_nat_1(C,1)) ) => ( ( ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,1),C) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),D,k1_nat_1(C,1)) ) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,1),C) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),D,k1_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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),D,k1_nat_1(C,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,1),k1_nat_1(C,2))),k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,1),k1_nat_1(C,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(D,2),k1_nat_1(C,2))),k7_xcmplx_0(1,2))),k3_topreal1(2,A)) ) ) ) ) ) ) ) )).
fof(t16_goboard9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_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_0(C)) ) => v1_convex1(k1_tops_1(k15_euclid(2),k3_goboard5(C,A,B)),k15_euclid(2)) ) ) ) ) )).
fof(t16_gobrd11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => v4_pre_topc(k2_goboard5(B,A),k15_euclid(2)) ) ) )).
fof(t16_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(D)) & r1_goboard1(u1_struct_0(k15_euclid(2)),D,E) & r2_hidden(k4_tarski(A,B),k2_matrix_0(E)) & r2_hidden(k4_tarski(k1_nat_1(A,1),B),k2_matrix_0(E)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,k1_nat_1(A,1),B) ) => k3_gobrd13(D,E,C) = k3_goboard5(E,A,B) ) ) ) ) ) ) )).
fof(t16_gobrd14,axiom,( ! [A] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(t16_gr_cy_1,axiom,( ! [A] : ( v1_int_1(A) => A = k5_group_1(k2_gr_cy_1,A,k5_gr_cy_1(1)) ) )).
fof(t16_gr_cy_3,axiom,( k1_gr_cy_3(k5_numbers) = k5_numbers )).
fof(t16_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_graph_1(B) & l1_graph_1(B) ) => ( ( r4_graph_1(A,B) & r4_graph_1(B,A) ) => A = B ) ) ) )).
fof(t16_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ r1_xxreal_0(k3_finseq_1(B),1) => k1_funct_1(k3_graph_2(A,B),k3_finseq_1(k3_graph_2(A,B))) = k1_funct_1(B,k3_finseq_1(B)) ) ) ) )).
fof(t16_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => k1_graph_3(A,k1_xboole_0) = k1_xboole_0 ) )).
fof(t16_graph_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( ( v7_graph_1(C,B) & m2_graph_1(C,B) ) => ( v7_graph_1(k2_partfun1(k4_ordinal1,u4_struct_0(B),C,k2_finseq_1(A)),B) & m2_graph_1(k2_partfun1(k4_ordinal1,u4_struct_0(B),C,k2_finseq_1(A)),B) ) ) ) ) )).
fof(t16_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u4_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u4_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t16_graphsp,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(C) & v2_graph_1(C) & v6_graph_1(C) & l1_graph_1(C) ) => ! [D] : ( ( v7_graph_1(D,C) & m2_graph_1(D,C) ) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ( ( u1_struct_0(C) = k2_xboole_0(A,B) & r2_hidden(F,A) & ! [H] : ( m1_subset_1(H,u1_struct_0(C)) => ! [I] : ( m1_subset_1(I,u1_struct_0(C)) => ( ( r2_hidden(H,A) & r2_hidden(I,B) ) => ! [J] : ~ ( 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) ) ) ) ) ) ) ) )).
fof(t16_grcat_1,axiom,( ! [A] : ( ( v2_grcat_1(A) & l1_grcat_1(A) ) => ! [B] : ( ( v2_grcat_1(B) & l1_grcat_1(B) ) => ~ ( k7_grcat_1(A) = k8_grcat_1(B) & ! [C] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v13_algstr_0(D) & v3_rlvect_1(D) & v4_rlvect_1(D) & l2_algstr_0(D) ) => ! [E] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(t16_grfunc_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ~ ( r2_hidden(A,k9_xtuple_0(D)) & D = k2_xboole_0(B,C) & k1_funct_1(D,A) != k1_funct_1(B,A) & k1_funct_1(D,A) != k1_funct_1(C,A) ) ) ) ) )).
fof(t16_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,k2_grnilp_1(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( 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) ) ) ) ) ) )).
fof(t16_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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(k12_polynom1(A,C),D)) => r1_rewrite1(k3_polyred(A,B,C,D),E,k8_polynom1(A,C)) ) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(E,A,C) & v1_polynom1(E,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(k12_polynom1(A,C),D)) => r7_polyred(A,B,C,E,D) ) ) ) ) ) ) ) )).
fof(t16_groeb_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l6_algstr_0(B) ) => ! [C] : ( 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))) ) ) )).
fof(t16_groeb_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k15_pre_poly(A))) => ( k3_polynom1(k15_pre_poly(A),B,k2_groeb_3(A,B,C,D)) = k3_xboole_0(k3_polynom1(k15_pre_poly(A),B,C),D) & ! [E] : ( ( 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,k3_polynom1(k15_pre_poly(A),B,k2_groeb_3(A,B,C,D))) => k4_polynom1(A,B,k2_groeb_3(A,B,C,D),E) = k4_polynom1(A,B,C,E) ) ) ) ) ) ) )).
fof(t16_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_group_1(A,k6_algstr_0(A,C,B)) = k6_algstr_0(A,k2_group_1(A,B),k2_group_1(A,C)) ) ) ) )).
fof(t16_group_10,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => k7_group_1(k4_gr_cy_1(A)) = A ) )).
fof(t16_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_group_2(C,A) => r1_tarski(k1_group_11(A,B,C),B) ) ) ) )).
fof(t16_group_14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k1_card_1(k4_card_3(k9_finseq_1(A))) = k1_card_1(A) ) )).
fof(t16_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t16_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k2_group_3(A,B,D) = k2_group_3(A,C,D) => B = C ) ) ) ) ) )).
fof(t16_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t16_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t16_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t16_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => m1_group_9(k4_group_9(A,B),A,C) ) ) )).
fof(t16_groupp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => v2_group_10(k6_group_2(A),B) ) ) )).
fof(t16_hahnban,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( 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] : ( 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] : ( 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] : ( 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] : ( m1_subset_1(H,u1_struct_0(C)) => ! [I] : ( m1_subset_1(I,u1_struct_0(C)) => ! [J] : ( v1_xreal_0(J) => ! [K] : ( v1_xreal_0(K) => ( ( 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,k2_xcmplx_0(J,K))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t16_hallmar1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r2_hidden(C,k4_finseq_1(B)) & v1_hallmar1(B,A) ) => r1_xxreal_0(1,k5_card_1(k1_funct_1(B,C))) ) ) ) ) )).
fof(t16_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t16_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( 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 ) ) ) ) )).
fof(t16_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_henmodel(B,A) & m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t16_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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) ) ) )).
fof(t16_hessenbe,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ( ( r1_collsp(A,B,C,D) & r1_collsp(A,E,F,G) & r1_collsp(A,B,F,J) & r1_collsp(A,E,C,J) & r1_collsp(A,B,G,I) & r1_collsp(A,D,E,I) & r1_collsp(A,C,G,H) & r1_collsp(A,D,F,H) ) => ( C = D | B = D | F = G | E = F | E = G | r1_collsp(A,B,C,E) | r1_collsp(A,H,I,J) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_heyting1,axiom,( k7_normform(k1_xboole_0) = k1_tarski(k4_tarski(k1_xboole_0,k1_xboole_0)) )).
fof(t16_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k3_heyting3(k1_nat_1(A,1),B) = k2_xboole_0(k3_heyting3(A,B),k6_domain_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,k1_nat_1(k2_nat_1(2,A),3),B))) ) ) )).
fof(t16_hfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t16_hilbasis,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k14_polynom3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_polynom3(A))) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( B = D & C = E ) => k5_algstr_0(k14_polynom3(A),B,C) = k3_normsp_1(A,D,E) ) ) ) ) ) ) )).
fof(t16_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => r2_hidden(k3_hilbert1(A,k2_hilbert1),k6_hilbert1) ) )).
fof(t16_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( 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)) ) ) ) )).
fof(t16_hilbert3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ! [D] : ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,C,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,A))) ) => ! [F] : ( ( 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) ) ) ) ) )).
fof(t16_hurwitz,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k5_vfunct_1(k4_ordinal1,A,k3_polynom5(A,B,C)),k3_polynom5(A,k5_vfunct_1(k4_ordinal1,A,B),C)) ) ) ) )).
fof(t16_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => r1_idea_1(B,k6_idea_1(B,A)) ) ) )).
fof(t16_ideal_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t16_incproj,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( 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] : ( m1_subset_1(B,u1_incsp_1(k3_incproj(A))) => ! [C] : ( m1_subset_1(C,u2_incsp_1(k3_incproj(A))) => ! [D] : ( m1_subset_1(D,u2_incsp_1(k3_incproj(A))) => ? [E] : ( m1_subset_1(E,u1_incsp_1(k3_incproj(A))) & ? [F] : ( m1_subset_1(F,u1_incsp_1(k3_incproj(A))) & ? [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t16_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => v4_incsp_1(k9_domain_1(u1_incsp_1(A),B,B,C,D),A) ) ) ) ) )).
fof(t16_instalg1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_instalg1(B,A) => ! [C] : ( m1_instalg1(C,B) => m1_instalg1(C,A) ) ) ) )).
fof(t16_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => ( ( r2_int_1(A,B,E) & r2_int_1(C,D,E) ) => r2_int_1(k2_xcmplx_0(A,C),k2_xcmplx_0(B,D),E) ) ) ) ) ) ) )).
fof(t16_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r1_int_1(A,B) <=> r1_int_1(k1_int_2(A),k1_int_2(B)) ) ) ) )).
fof(t16_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & r1_int_2(A,C) & ! [D] : ( v7_ordinal1(D) => k5_int_1(k6_xcmplx_0(k3_xcmplx_0(A,D),B),C) != k5_numbers ) ) ) ) ) )).
fof(t16_int_5,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ~ ( ~ r1_xxreal_0(A,2) & ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ~ ( k3_finseq_1(B) = k3_nat_d(k7_nat_d(A,1),2) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => k3_int_2(k1_recdef_1(B,C),A) = 1 ) ) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => r1_int_5(k1_recdef_1(B,C),A) ) ) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t16_int_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => k3_int_2(k3_xcmplx_0(A,B),k3_xcmplx_0(A,C)) = k3_xcmplx_0(k1_int_2(A),k3_int_2(B,C)) ) ) ) )).
fof(t16_int_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k8_newton) & v1_funct_1(A) & v1_partfun1(A,k8_newton) & v4_valued_0(A) & v2_pre_poly(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( ( v1_int_7(A) & B = k8_nat_3(k8_newton,A) ) => r8_pboole(k8_newton,k13_nat_3(B),A) ) ) ) )).
fof(t16_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_int_2(A,D) & k3_pepin(A,D) = k3_xcmplx_0(B,C) ) => ( r1_xxreal_0(D,1) | k3_pepin(k1_newton(A,B),D) = C ) ) ) ) ) ) )).
fof(t16_integr11,axiom,( ! [A] : ( ( ~ 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,k18_sin_cos)) = k6_xcmplx_0(k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,2),k5_numbers),k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(2,k5_numbers),k16_sin_cos),k7_xcmplx_0(1,4))),k2_seq_4(A)),k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,2),k5_numbers),k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(2,k5_numbers),k16_sin_cos),k7_xcmplx_0(1,4))),k3_seq_4(A))) ) )).
fof(t16_integr12,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( 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,E,F),k3_taylor_1))) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,G) => ( k1_funct_1(D,H) = k7_xcmplx_0(H,A) & ~ r1_xxreal_0(k1_funct_1(D,H),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(D,H)) & k1_funct_1(E,H) = 1 ) ) ) & r2_relset_1(k1_numbers,k1_numbers,F,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k1_taylor_1(2))) & G = k1_relset_1(k1_numbers,C) & r2_relset_1(k1_numbers,k1_numbers,C,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k2_sin_cos9)) ) => ( A = k5_numbers | k2_integra5(B,C) = k6_xcmplx_0(k1_funct_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,D,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,E,F),k3_taylor_1),k7_xcmplx_0(A,2))),k2_seq_4(B)),k1_funct_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,D,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,E,F),k3_taylor_1),k7_xcmplx_0(A,2))),k3_seq_4(B))) ) ) ) ) ) ) ) ) ) )).
fof(t16_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k18_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,k27_sin_cos))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k27_sin_cos),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k27_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t16_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k7_xcmplx_0(k1_funct_1(k18_sin_cos,k7_xcmplx_0(1,D)),k3_xcmplx_0(k1_square_1(D),k1_square_1(k1_funct_1(k16_sin_cos,k7_xcmplx_0(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) = k6_xcmplx_0(k1_funct_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),k2_seq_4(A)),k1_funct_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),k3_seq_4(A))) ) ) ) ) )).
fof(t16_integr15,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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)) ) ) ) ) )).
fof(t16_integr16,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k2_numbers))) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t16_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( C = k1_rcomp_1(D,E) => k5_integr18(A,C,B) = k6_integr18(A,B,D,E) ) ) ) ) ) ) )).
fof(t16_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t16_integra1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ~ 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) ) ) ) )).
fof(t16_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( ( v3_xxreal_2(B) & r1_xxreal_0(A,k5_numbers) ) => k2_seq_4(k1_integra2(B,A)) = k3_xcmplx_0(A,k3_seq_4(B)) ) ) ) )).
fof(t16_integra3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( m1_integra1(C,B) => ( r2_hidden(A,k1_rvsum_1(C)) => ( r1_xxreal_0(k1_funct_1(C,1),A) & r1_xxreal_0(A,k1_funct_1(C,k3_finseq_1(C))) ) ) ) ) ) )).
fof(t16_integra4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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)) ) ) ) )).
fof(t16_integra5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t16_integra8,axiom,( k4_sin_cos6(k4_xcmplx_0(k7_xcmplx_0(k3_square_1(2),2))) = k7_xcmplx_0(k3_xcmplx_0(3,k28_sin_cos),4) )).
fof(t16_integra9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k18_sin_cos),k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k16_sin_cos))) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B)),k18_sin_cos),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B)),k18_sin_cos),k3_seq_4(A))) ) ) ) )).
fof(t16_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => r1_tarski(k5_interva1(A,B),k6_interva1(A,B)) ) ) )).
fof(t16_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ( v8_intpro_1(A) => r1_tarski(k8_intpro_1,A) ) ) )).
fof(t16_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( 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,k1_nat_1(A,1)) ) ) ) ) ) )).
fof(t16_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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(k6_cat_2(k6_cat_2(A,B),C),k6_cat_2(A,k6_cat_2(B,C))) ) ) ) )).
fof(t16_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,k6_cat_2(A,B),C) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => r2_funct_2(u1_struct_0(B),u4_struct_0(C),k4_nattra_1(B,C,k10_cat_2(A,B,C,D,E)),k4_isocat_2(A,B,C,D,k4_cat_1(A,E))) ) ) ) ) ) )).
fof(t16_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t16_jgraph_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ~ ( ? [E] : ( 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)) ) ) ) ) ) )).
fof(t16_jgraph_4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(B,k7_xcmplx_0(k18_euclid(A),k12_euclid(A))) => ( r1_xxreal_0(k5_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(k3_xcmplx_0(k12_euclid(A),k4_xcmplx_0(k3_square_1(k6_xcmplx_0(1,k1_square_1(k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k18_euclid(A),k12_euclid(A)),B),k6_xcmplx_0(1,B))))))),k3_xcmplx_0(k12_euclid(A),k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k18_euclid(A),k12_euclid(A)),B),k6_xcmplx_0(1,B)))) ) ) & ( r1_xxreal_0(k5_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 ) ) ) ) )).
fof(t16_jgraph_5,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( 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,k5_numbers) = k19_euclid(k4_xcmplx_0(1),k5_numbers) & k1_funct_1(A,1) = k19_euclid(1,k5_numbers) & k1_funct_1(B,1) = k19_euclid(k5_numbers,1) & k1_funct_1(B,k5_numbers) = k19_euclid(k5_numbers,k4_xcmplx_0(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)) ) ) ) ) )).
fof(t16_jgraph_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ 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] : ( 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] : ( ( 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] : ( ( 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,k5_numbers) = C & k1_funct_1(G,1) = A & k1_funct_1(H,k5_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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_jordan,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => r2_hidden(C,k1_topreal9(A,C,B)) ) ) ) )).
fof(t16_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ( v3_pre_topc(a_1_2_jordan1(A),k15_euclid(2)) & m1_subset_1(a_1_2_jordan1(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ) )).
fof(t16_jordan10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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(k2_jordan9(B,A))) ) ) )).
fof(t16_jordan11,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t16_jordan12,axiom,( ! [A] : ( ( ~ 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] : ! [C] : ! [D] : ~ ( ? [E] : ( 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] : ( 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] : ( 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) ) ) ) ) )).
fof(t16_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( r1_jordan1h(A,B) => r1_tarski(k2_jordan2c(2,A),k2_goboard9(k1_jordan13(A,B))) ) ) ) )).
fof(t16_jordan16,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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] : ( ( 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] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ~ ( v3_tops_2(F,k5_topmetr,k1_pre_topc(k15_euclid(2),A)) & k1_funct_1(F,k5_numbers) = B & k1_funct_1(F,1) = C & k1_funct_1(F,G) = D & k1_funct_1(F,H) = E & r1_xxreal_0(k5_numbers,G) & r1_xxreal_0(G,H) & r1_xxreal_0(H,1) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ~ ( C != D & r1_jordan17(A,B,C,D,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ~ ( F != C & F != D & r1_jordan17(A,C,F,D,E) ) ) ) ) ) ) ) ) )).
fof(t16_jordan19,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E),k3_topreal1(2,k2_jordan1e(B,A))) & r2_hidden(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k8_jordan6(B)) ) ) ) ) ) ) )).
fof(t16_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_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_0(C)) ) => r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_matrix_0(C)))) ) ) ) ) )).
fof(t16_jordan1b,axiom,( ! [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] : ( v7_ordinal1(B) => k1_jordan1a(k1_jordan8(A,B)) = k1_nat_1(k11_newton(2,k7_nat_d(B,1)),2) ) ) )).
fof(t16_jordan1c,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v1_int_1(D) => ~ ( D = k1_int_1(k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k18_euclid(C),k9_pscomp_1(A)),k6_xcmplx_0(k7_pscomp_1(A),k9_pscomp_1(A))),k1_newton(2,B)),2)) & r1_xxreal_0(k2_xcmplx_0(k9_pscomp_1(A),k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k7_pscomp_1(A),k9_pscomp_1(A)),k1_newton(2,B)),k6_xcmplx_0(D,1))),k18_euclid(C)) ) ) ) ) ) )).
fof(t16_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & ~ r1_xxreal_0(k3_finseq_1(k2_jordan9(B,A)),C) & r2_hidden(k24_pscomp_1(B),k4_goboard5(k2_jordan9(B,A),C)) ) ) ) )).
fof(t16_jordan1e,axiom,( ! [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] : ( v7_ordinal1(B) => 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,k2_jordan9(A,B))),k22_pscomp_1(k3_topreal1(2,k2_jordan9(A,B)))) ) ) )).
fof(t16_jordan1g,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t16_jordan1h,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v4_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))) ) )).
fof(t16_jordan1k,axiom,( ! [A] : ( v7_ordinal1(A) => k1_jordan2c(A,k2_struct_0(k15_euclid(A))) = k1_struct_0(k15_euclid(A)) ) )).
fof(t16_jordan20,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(2),A)))) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(k5_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)) ) ) ) ) ) )).
fof(t16_jordan21,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => k10_jordan6(A) != k11_jordan6(A) ) )).
fof(t16_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,k5_numbers) => k2_jordan21(k3_topreal1(2,k2_jordan9(A,B))) = k19_euclid(k7_xcmplx_0(k2_xcmplx_0(k8_pscomp_1(k3_topreal1(2,k2_jordan9(A,B))),k6_pscomp_1(k3_topreal1(2,k2_jordan9(A,B)))),2),k3_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,k2_jordan9(A,B)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),k3_finseq_1(k1_jordan8(A,B)))))))) ) ) ) )).
fof(t16_jordan23,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v2_funct_1(A) => v2_jordan23(A) ) ) )).
fof(t16_jordan24,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( 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)) ) ) ) )).
fof(t16_jordan2b,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(B)))) => ( F = k8_metric_1(B,E,D) => ( r1_xxreal_0(D,k5_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)) ) ) ) ) )).
fof(t16_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) )).
fof(t16_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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,k1_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_xcmplx_0(k1_jordan3(A,C),D),1))) ) ) ) ) ) )).
fof(t16_jordan4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => k3_finseq_6(A,B,k5_numbers,k5_numbers) = k17_finseq_1(A,1,B) ) ) )).
fof(t16_jordan5a,axiom,( ! [A] : ( ( 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,k5_numbers) = k5_numbers & k1_funct_1(A,1) = 1 ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_topmetr)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_topmetr)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t16_jordan5b,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ( ( 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 ) ) ) )).
fof(t16_jordan5c,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( 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)))) ) ) ) ) )).
fof(t16_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( 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))))) ) ) ) )).
fof(t16_jordan7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(t16_jordan8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t16_jordan9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(C)) ) => ( k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B)) = k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_nat_1(B,1))) & k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B)) = k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),B)) & k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),k1_nat_1(B,1))) = k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),B)) & k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),k1_nat_1(B,1))) = k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_nat_1(B,1))) ) ) ) ) ) )).
fof(t16_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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))) ) ) ) ) )).
fof(t16_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v3_ordinal1(D) => k4_knaster(A,B,C,k1_ordinal1(D)) = k1_funct_1(B,k4_knaster(A,B,C,D)) ) ) ) ) )).
fof(t16_kolmog01,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( m2_prob_1(D,A,C) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),C) => ! [F] : ( 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) != k5_numbers & k3_funct_2(C,k1_numbers,D,E) != 1 ) ) ) ) ) ) ) )).
fof(t16_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( ! [E] : ( v7_ordinal1(E) => k1_funct_1(C,E) = k5_xboole_0(D,k1_funct_1(B,E)) ) => r1_tarski(k5_subset_1(A,D,k3_kurato_0(A,B)),k4_kurato_0(A,C)) ) ) ) ) )).
fof(t16_kurato_1,axiom,( 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)) )).
fof(t16_lang1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k1_lang1(k9_lang1(A)) = A ) )).
fof(t16_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,D,C,B) & m2_finseq_1(E,k3_finseq_2(D)) ) => ! [F] : ( m2_finseq_1(F,D) => ! [G] : ( v7_ordinal1(G) => ( r2_hidden(G,k2_finseq_1(k1_matrix_0(E))) => ( ( ( G = A & k3_finseq_1(F) = k3_finseq_1(E) ) => k8_matrix_0(D,k3_laplace(A,C,B,D,E,F),G) = F ) & ( G != A => k8_matrix_0(D,k3_laplace(A,C,B,D,E,F),G) = k8_matrix_0(D,E,G) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t16_latsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_waybel_0(B,A) & v12_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k13_lattice3(A,C,D),B) ) ) ) ) ) )).
fof(t16_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k4_lattices(A,B,C) = C ) => B = k6_lattices(A) ) ) ) )).
fof(t16_lattice3,axiom,( ! [A] : ( ( v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t16_lattice4,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t16_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t16_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v3_lattice6(B,A) => v2_waybel_6(k4_lattice3(A,B),k3_lattice3(A)) ) ) ) )).
fof(t16_lattice7,axiom,( ! [A] : ( ( 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] : ( ~ v1_xboole_0(B) & m2_lattice7(B) & r5_waybel_1(A,k1_yellow_1(B)) ) ) ) )).
fof(t16_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_lattices(A,k6_lattices(A),B) = k6_lattices(A) ) ) )).
fof(t16_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( ( v4_lexbfs(B,A) & m1_lexbfs(B,A) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( ~ r1_xxreal_0(D,k7_nat_d(k39_glib_000(B),C)) & r1_xxreal_0(D,k39_glib_000(B)) & ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t16_lfuzzy_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( 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)) ) ) ) ) )).
fof(t16_lfuzzy_1,axiom,( ! [A] : ( ~ 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) ) ) )).
fof(t16_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_seq_2(A) & v2_limfunc1(B) ) => v1_limfunc1(k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) ) ) )).
fof(t16_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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) ) ) ) ) ) )).
fof(t16_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r2_limfunc3(B,A) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & v2_seq_2(k2_partfun1(k1_numbers,k1_numbers,C,k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,D),A),k2_rcomp_1(A,k2_xcmplx_0(A,D))))) ) ) | r2_limfunc3(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t16_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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) ) ) ) ) )).
fof(t16_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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,D) & r1_lmod_6(A,C,D) ) => ( k4_struct_0(B) = k4_struct_0(C) & r1_struct_0(C,k4_struct_0(B)) & ( r1_tarski(u1_struct_0(B),u1_struct_0(C)) => r1_lmod_6(A,B,C) ) & ( ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ( r1_struct_0(B,E) => r1_struct_0(C,E) ) ) => r1_lmod_6(A,B,C) ) & ( ( u1_struct_0(B) = u1_struct_0(C) & v7_vectsp_1(B,A) & v7_vectsp_1(C,A) ) => B = C ) & r1_lmod_6(A,k1_vectsp_4(A,B),C) ) ) ) ) ) ) )).
fof(t16_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t16_lopban_1,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(k8_lopban_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k8_lopban_1(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k8_lopban_1(A,B))) => ( E = k3_rlvect_1(k8_lopban_1(A,B),C,D) <=> ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t16_lopban_2,axiom,( ! [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) & 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)) ) ) )).
fof(t16_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,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))) ) ) ) )).
fof(t16_lopban_6,axiom,( ! [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) & v3_lopban_1(A) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t16_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_tarski(a_2_0_lopclset(A,B),k7_lopclset(A)) ) ) )).
fof(t16_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( ( r2_hidden(k1_relset_1(A,D),B) & ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,k1_relset_1(A,D)) => k5_numbers = k1_funct_1(D,E) ) ) ) => ( r2_mesfun6c(A,B,C,D) & k1_mesfun6c(A,B,C,D) = k5_numbers ) ) ) ) ) ) )).
fof(t16_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_rfunct_3(B,A,k1_numbers,k3_rfunct_3(A,k1_numbers)) => k1_binop_1(k13_rfunct_3(A),B,k1_binop_1(k4_lpspace1(A),k4_xcmplx_0(1),B)) = k2_partfun1(A,k1_numbers,k5_lpspace1(A),k1_relset_1(A,B)) ) ) )).
fof(t16_lpspace2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_numbers) => ( r1_xxreal_0(k2_power(k9_complex1(k2_xcmplx_0(A,B)),C),k2_power(k2_xcmplx_0(k9_complex1(A),k9_complex1(B)),C)) & r1_xxreal_0(k2_power(k2_xcmplx_0(k9_complex1(A),k9_complex1(B)),C),k2_power(k3_xcmplx_0(2,k4_xxreal_0(k9_complex1(A),k9_complex1(B))),C)) & r1_xxreal_0(k2_power(k9_complex1(k2_xcmplx_0(A,B)),C),k2_power(k3_xcmplx_0(2,k4_xxreal_0(k9_complex1(A),k9_complex1(B))),C)) ) ) ) ) ) )).
fof(t16_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(C),k1_domain_1(k4_ordinal1,k1_hilbert1,B,k3_hilbert1(k2_ltlaxio1(k1_ltlaxio1(A)),k1_ltlaxio1(k2_ltlaxio1(A))))) = 1 ) ) ) )).
fof(t16_ltlaxio2,axiom,( ! [A] : ( m2_finseq_1(A,k1_hilbert1) => ! [B] : ( m2_finseq_1(B,k1_hilbert1) => k4_ltlaxio2(k8_finseq_1(k1_hilbert1,A,B)) = k8_finseq_1(k1_hilbert1,k4_ltlaxio2(A),k4_ltlaxio2(B)) ) ) )).
fof(t16_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => r1_tarski(A,k5_ltlaxio3(A)) ) )).
fof(t16_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ( ( r2_hidden(k8_cqc_lang(A,D,k8_cqc_lang(A,C,B)),k4_cqc_the1(A)) & r2_hidden(C,k4_cqc_the1(A)) ) => r2_hidden(k8_cqc_lang(A,D,B),k4_cqc_the1(A)) ) ) ) ) ) )).
fof(t16_margrel1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t16_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t16_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( v1_matrix10(B) => v2_matrix10(k2_matrix10(A,B)) ) ) ) )).
fof(t16_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(B,A) & r2_hidden(A,k2_finseq_1(C)) & r2_hidden(B,k2_finseq_1(C)) & ! [D] : ( m1_matrix_2(D,k3_matrix_2(C)) => ~ ( v4_matrix_2(D,k2_matrix_2(k3_matrix_2(C))) & k1_funct_1(D,A) = B ) ) ) ) ) ) )).
fof(t16_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(D),B,C) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(D))) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(D),B,C) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(D))) ) => ( ( r2_hidden(A,k2_finseq_1(k1_matrix_0(F))) & G = k4_matrix_0(u1_struct_0(D),F) ) => ( r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(C,k5_numbers) | k4_matrix_0(u1_struct_0(D),k2_matrix12(B,C,D,G,A,E)) = k5_matrix12(B,C,D,F,A,E) ) ) ) ) ) ) ) ) ) )).
fof(t16_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & v2_matrix_2(D,A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & v2_matrix_2(E,A,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ( C = k4_matrix_3(B,D,E) => ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & v2_matrix_2(C,A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & k13_matrix_3(A,B,C) = k11_fvsum_1(B,k13_matrix_3(A,B,D),k13_matrix_3(A,B,E)) ) ) ) ) ) ) ) )).
fof(t16_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,u1_struct_0(A),k5_numbers,k5_numbers) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => v1_matrix_6(B,k5_numbers,A) ) ) )).
fof(t16_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,D,C,B) & m2_finseq_1(E,k3_finseq_2(D)) ) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,D,C,A) & m2_finseq_1(F,k3_finseq_2(D)) ) => ! [G] : ( v7_ordinal1(G) => ( r2_hidden(G,k2_finseq_1(k1_matrix_0(E))) => k8_matrix_0(D,k1_matrix15(D,C,B,A,E,F),G) = k8_matrix_0(D,E,G) ) ) ) ) ) ) ) ) )).
fof(t16_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(B),A,A) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(B))) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(B),A,A) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(B))) ) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(B),A,A) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(B))) ) => ( ( 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_3(B,k1_matrix_4(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)) ) ) ) ) ) ) ) ) ) )).
fof(t16_matrix17,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t16_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_matrix_0(k10_finseq_1(k1_xboole_0,k1_xboole_0)) & v2_matrix_0(k10_finseq_1(k1_xboole_0,k1_xboole_0),A,2,k5_numbers) & m2_finseq_1(k10_finseq_1(k1_xboole_0,k1_xboole_0),k3_finseq_2(A)) ) ) )).
fof(t16_matrix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k4_tarski(C,D),k2_matrix_0(k3_matrix_1(B,A))) => ( ( C = D => k1_funct_1(k8_matrix_0(u1_struct_0(B),k3_matrix_1(B,A),D),C) = k5_struct_0(B) ) & ( C != D => k1_funct_1(k8_matrix_0(u1_struct_0(B),k3_matrix_1(B,A),D),C) = k4_struct_0(B) ) ) ) ) ) ) ) )).
fof(t16_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(D) ) => k1_matrix_4(A,k1_matrix_4(A,B,C),D) = k1_matrix_4(A,k1_matrix_4(A,B,D),C) ) ) ) ) ) )).
fof(t16_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k2_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k1_matrix_0(A) = k1_matrix_0(B) & A = k3_matrix_5(A,B) ) => B = k8_matrix_5(k3_finseq_1(A),k1_matrix_0(A)) ) ) ) )).
fof(t16_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v1_matrix_6(C,A,B) => ( v1_matrix_6(k1_matrix_6(A,B,C),A,B) & k1_matrix_6(A,B,k1_matrix_6(A,B,C)) = C ) ) ) ) ) )).
fof(t16_matrix_7,axiom,( ! [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] : ( v7_ordinal1(B) => ( r1_xxreal_0(1,B) => k12_matrix_3(B,A,k3_matrix_1(A,B)) = k1_group_1(A) ) ) ) )).
fof(t16_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_8(C,A,B) & v4_matrix_6(C,A,B) ) => C = k3_matrix_1(B,A) ) ) ) ) )).
fof(t16_matrix_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t16_matrixc1,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k2_numbers)) ) => k1_matrixc1(k7_matrixc1(B,A)) = k7_matrix_5(k8_complex1(A),k1_matrixc1(B)) ) ) )).
fof(t16_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => k2_wsierp_1(k10_matrixj1(A,k5_matrixj1(A,B,C))) = k1_nat_1(k3_finseq_1(B),k3_finseq_1(C)) ) ) ) )).
fof(t16_matrixj2,axiom,( ! [A] : ( l6_algstr_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) & ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t16_matrixr1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_finseq_1(k9_fvsum_1(A,B,C)) = k3_finseq_1(B) ) ) ) )).
fof(t16_matrixr2,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(C) = k3_finseq_1(D) & k1_matrix_0(C) = k1_matrix_0(D) & k3_finseq_1(B) = k1_matrix_0(C) ) => ( r1_xxreal_0(k3_finseq_1(C),k5_numbers) | r1_xxreal_0(k3_finseq_1(B),k5_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)) ) ) ) ) ) ) )).
fof(t16_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t16_matrlin2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( ~ 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] : ( m2_finseq_1(D,u1_struct_0(C)) => ( r2_hidden(A,k4_finseq_1(D)) => k4_rlvect_1(C,k5_matrlin(B,C,k7_matrix_0(u1_struct_0(B),k3_matrix_1(B,k3_finseq_1(D)),A),D)) = k7_partfun1(u1_struct_0(C),D,A) ) ) ) ) ) )).
fof(t16_matroid0,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v3_pre_topc(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t16_matrprob,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(B)) ) => ( C = D => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(C)) => k7_matrix_0(A,C,E) = k7_matrix_0(B,D,E) ) ) ) ) ) ) ) )).
fof(t16_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ~ ( k8_matrix13(C,D) = A & ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(C),k7_nat_d(B,A),B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(C))) ) => k8_matrix13(C,k8_matrlin(u1_struct_0(C),A,k7_nat_d(B,A),B,D,E)) != B ) ) ) ) ) ) )).
fof(t16_matrtop2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & v3_valued_0(C) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ~ ( v2_funct_1(D) & ! [E] : ( 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] : ( v7_ordinal1(F) => ( r2_hidden(F,k4_finseq_1(C)) => k1_funct_1(E,k7_matrix_0(u1_struct_0(k2_vectsp_1),D,F)) = k1_funct_1(C,F) ) ) ) ) ) ) ) ) ) )).
fof(t16_matrtop3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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),k8_matrix_0(u1_struct_0(k2_vectsp_1),k2_matrtop3(D,A,B,C),C)) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(E,B),k17_sin_cos(A)),k3_xcmplx_0(k1_funct_1(E,C),k19_sin_cos(A))) ) ) ) ) ) ) ) )).
fof(t16_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t16_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( ( r2_pboole(A,C,B) & r2_pboole(A,D,B) ) => r2_pboole(A,k5_pboole(A,C,D),B) ) ) ) ) )).
fof(t16_mcart_1,axiom,( ! [A] : ! [B] : ~ ( A != k1_xboole_0 & B != k1_xboole_0 & ~ ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => C = k4_tarski(k1_xtuple_0(C),k2_xtuple_0(C)) ) ) )).
fof(t16_measure1,axiom,( ! [A] : ? [B] : ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_tarski(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_tarski(A)))) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => k9_nat_1(k1_tarski(A),B,C) = A ) ) )).
fof(t16_measure2,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m1_measure2(D,A,B) => ( ! [E] : ( r2_hidden(E,D) => m2_measure1(E,A,B,C) ) => m2_measure1(k1_measure2(A,B,D),A,B,C) ) ) ) ) )).
fof(t16_measure3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k2_measure3(A,B,C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_measure3(A,B,C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ? [F] : ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => k9_nat_1(k9_setfam_1(A),F,G) = k6_subset_1(k9_nat_1(k2_measure3(A,B,C),D,G),k9_nat_1(B,E,G)) ) ) ) ) ) ) )).
fof(t16_measure4,axiom,( ! [A] : ! [B] : ( m1_measure4(B,A) => r1_measure3(A,k1_measure4(A,B),k3_measure4(A,B)) ) )).
fof(t16_measure6,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t16_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => k5_member_1(k3_xboole_0(A,B)) = k3_xboole_0(k5_member_1(A),k5_member_1(B)) ) ) )).
fof(t16_membered,axiom,( ! [A] : ( v4_membered(A) => ( ! [B] : ( v1_rat_1(B) => r2_hidden(B,A) ) => A = k3_numbers ) ) )).
fof(t16_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( v7_ordinal1(D) => k5_memstr_0(A,B,k1_funct_4(C,k7_memstr_0(A,B,D))) = D ) ) ) ) )).
fof(t16_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( ( D = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),B,k6_xcmplx_0(1,F)),k1_rlvect_1(k15_euclid(2),C,F)) & E = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),C,k6_xcmplx_0(1,G)),k1_rlvect_1(k15_euclid(2),A,G)) ) => ( r1_euclid_6(A,B,C) | G = 1 | ( ~ ( k2_xcmplx_0(k6_xcmplx_0(1,G),k3_xcmplx_0(F,G)) != k5_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)) & k2_xcmplx_0(k6_xcmplx_0(1,G),k3_xcmplx_0(F,G)) = k5_numbers ) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_mesfun10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & v1_mesfunc8(B,A,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,C,k6_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,k6_numbers))) ) => ! [E] : ( m1_subset_1(E,C) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( E = k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers)) & E = k1_relset_1(A,F) & ! [G] : ( v7_ordinal1(G) => r1_mesfunc1(A,C,k4_mesfunc5(A,k6_numbers,B,G),E) ) & r1_mesfunc5(A,C,D,F) & ! [G] : ( m1_subset_1(G,A) => ! [H] : ( v7_ordinal1(H) => ( r2_hidden(G,E) => r1_xxreal_0(k12_supinf_2(k10_mesfunc1(A,k4_mesfunc5(A,k6_numbers,B,H)),G),k12_supinf_2(F,G)) ) ) ) ) => ( ! [G] : ( v7_ordinal1(G) => r1_mesfunc5(A,C,D,k10_mesfunc1(A,k4_mesfunc5(A,k6_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))) ) ) ) ) ) ) ) ) )).
fof(t16_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t16_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & v1_mesfunc8(C,A,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [E] : ( v1_xreal_0(E) => ( ! [F] : ( v7_ordinal1(F) => k1_funct_1(D,F) = k8_subset_1(A,k1_relset_1(A,k4_mesfunc5(A,k1_numbers,C,k5_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,k5_numbers)),k17_mesfunc1(A,k3_mesfun7c(A,C),E)) ) ) ) ) ) ) )).
fof(t16_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [E] : ( v7_ordinal1(E) => ( ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t16_mesfunc1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ! [D] : ( v1_xxreal_0(D) => ( 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))) ) ) ) )).
fof(t16_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( 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 ) ) ) ) )).
fof(t16_mesfunc3,axiom,( ! [A] : ( m2_finseq_1(A,k6_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( A = B => k4_extreal1(A) = k18_rvsum_1(B) ) ) ) )).
fof(t16_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_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)) ) ) ) ) )).
fof(t16_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( ( r1_tarski(E,D) & r1_mesfunc6(A,B,C,D) ) => r1_mesfunc6(A,B,C,E) ) ) ) ) ) ) )).
fof(t16_mesfunc7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( v5_xxreal_2(k10_xtuple_0(B)) => v3_valued_0(B) ) ) ) )).
fof(t16_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k6_numbers)) & v1_mesfunc8(C,A,k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [E] : ( v1_xreal_0(E) => ( ! [F] : ( v7_ordinal1(F) => k9_nat_1(k9_setfam_1(A),D,F) = k9_subset_1(A,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,C,k5_numbers)),k18_mesfunc1(A,k4_mesfunc5(A,k6_numbers,C,F),E)) ) => k1_setfam_1(k2_relset_1(B,D)) = k9_subset_1(A,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,C,k5_numbers)),k18_mesfunc1(A,k1_mesfunc8(A,C),E)) ) ) ) ) ) ) )).
fof(t16_mesfunc9,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v6_supinf_2(A) => ( v6_supinf_2(k2_mesfunc9(A)) & v7_valued_0(k2_mesfunc9(A)) ) ) ) )).
fof(t16_metric_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( l1_metric_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k4_subset_1(u1_struct_0(B),k10_metric_1(B,C,A),k8_metric_1(B,C,A)) = k9_metric_1(B,C,A) ) ) ) )).
fof(t16_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_hidden(k1_metric_2(A,B),k2_metric_2(A)) ) ) )).
fof(t16_metric_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => r1_xxreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k3_xcmplx_0(A,D)),k3_xcmplx_0(C,B)),k3_xcmplx_0(k3_xcmplx_0(2,k3_xcmplx_0(A,F)),k3_xcmplx_0(E,C))),k3_xcmplx_0(k3_xcmplx_0(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(k1_square_1(k3_xcmplx_0(A,D)),k1_square_1(k3_xcmplx_0(C,B))),k1_square_1(k3_xcmplx_0(A,F))),k1_square_1(k3_xcmplx_0(E,C))),k1_square_1(k3_xcmplx_0(B,F))),k1_square_1(k3_xcmplx_0(E,D)))) ) ) ) ) ) ) )).
fof(t16_metric_6,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ! [D] : ( v1_xreal_0(D) => ( ~ r1_xxreal_0(D,k5_numbers) => r2_metric_6(A,k8_metric_1(A,B,D),C) ) ) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t16_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ( r2_hidden(B,k2_finseq_1(A)) => k1_funct_1(k3_rlvect_1(k15_euclid(A),C,D),B) = k2_xcmplx_0(k1_funct_1(C,B),k1_funct_1(D,B)) ) ) ) ) ) )).
fof(t16_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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 ) ) ) ) ) ) ) )).
fof(t16_midsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( B = k4_algstr_0(A,B) => B = k4_struct_0(A) ) ) ) )).
fof(t16_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_nat_1(A,2)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( v4_midsp_2(D,B) & l1_midsp_2(D,B) ) => ! [E] : ( m2_finseq_2(E,u1_struct_0(u1_midsp_2(B,D)),k4_finseq_2(k1_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 ) ) ) ) ) )).
fof(t16_mmlquer2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( r2_hidden(A,k10_xtuple_0(B)) => ( r2_hidden(k6_mmlquer2(B,A),k1_relset_1(k4_ordinal1,B)) & A = k1_funct_1(B,k6_mmlquer2(B,A)) ) ) ) )).
fof(t16_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(t16_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( ( v2_mod_2(F,A) & m1_mod_2(F,A,B,C) ) => ! [G] : ( ( v2_mod_2(G,A) & m1_mod_2(G,A,C,D) ) => ! [H] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t16_mod_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => C != k4_vectsp_1(A,B,E,D) ) ) ) ) & ( ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t16_mod_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & l1_vectsp_2(D,B) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t16_modal_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(t16_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k48_modelc_1(A,B,D))) => ! [F] : ( 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] : ( m1_modelc_1(G,A,B) & k3_funct_2(k4_ordinal1,A,G,k5_numbers) = C & ? [H] : ( m1_subset_1(H,k4_ordinal1) & ! [I] : ( m1_subset_1(I,k4_ordinal1) => ( ~ r1_xxreal_0(H,I) => r3_modelc_1(A,B,D,k3_funct_2(k4_ordinal1,A,G,I),E) ) ) & r3_modelc_1(A,B,D,k3_funct_2(k4_ordinal1,A,G,H),F) ) ) ) ) ) ) ) ) ) )).
fof(t16_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ( r1_modelc_2(C,k5_modelc_2(A,B)) <=> ( C = A | C = B ) ) ) ) ) )).
fof(t16_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( 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) ) ) ) )).
fof(t16_moebius1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ( r1_tarski(k22_pre_poly(k8_newton,k13_nat_3(B)),k2_finseq_1(k1_nat_1(A,1))) => ( r1_tarski(k22_pre_poly(k8_newton,k13_nat_3(B)),k2_finseq_1(A)) | ( v7_ordinal1(k1_nat_1(A,1)) & v1_int_2(k1_nat_1(A,1)) ) ) ) ) ) )).
fof(t16_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ( v4_vectsp_1(A) <=> ! [B] : ( 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 ) ) ) ) )).
fof(t16_monoid_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( ~ v1_xboole_0(F) => ! [G] : ( ~ v1_xboole_0(G) => ! [H] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t16_morph_01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t16_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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)) ) ) )).
fof(t16_msafree3,axiom,( ! [A] : ! [B] : ( ( ~ v11_struct_0(B) & v1_instalg1(B) & l1_msualg_1(B) ) => ! [C] : ( ( 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] : ( ( v1_relat_1(D) & v4_relat_1(D,u1_struct_0(B)) & v1_funct_1(D) & v1_partfun1(D,u1_struct_0(B)) ) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t16_msafree4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r2_pboole(A,B,C) => r1_tarski(k4_card_3(B),k4_card_3(C)) ) ) ) )).
fof(t16_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( l3_msualg_1(C,A) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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 ) ) ) ) ) ) ) )).
fof(t16_msscyc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ 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),k1_nat_1(k3_finseq_1(B),1)) ) ) ) )).
fof(t16_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m2_pboole(C,A,B,k1_pboole(A)) => r6_pboole(A,C,k1_pboole(A)) ) ) )).
fof(t16_mssublat,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t16_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t16_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t16_msualg_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t16_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(t16_msualg_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m2_nat_lat(B,A) => ( v1_msualg_7(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => k16_lattice3(A,C) = k16_lattice3(B,C) ) ) ) ) )).
fof(t16_msualg_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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] : ( 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(t16_msualg_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t16_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(t16_nagata_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( 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) = k5_numbers ) ) ) ) ) ) )).
fof(t16_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( A != k5_numbers & r1_xxreal_0(k2_xcmplx_0(B,A),B) ) ) ) )).
fof(t16_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(A,B) => k3_nat_d(k2_power(2,B),k2_power(2,A)) = k2_power(2,k7_nat_d(B,A)) ) ) ) )).
fof(t16_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) & v3_valued_0(C) ) => ( A != k5_numbers => k13_pre_poly(C) = k13_pre_poly(k4_nat_3(B,C,A)) ) ) ) )).
fof(t16_nat_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ~ ( B != k5_numbers & C = k1_newton(A,k11_nat_3(B,A)) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( D = C & r1_xxreal_0(1,D) & r1_xxreal_0(D,B) ) ) ) ) ) )).
fof(t16_nat_5,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(C,k3_moebius1(A)) & r2_hidden(D,k3_moebius1(B)) ) => r2_hidden(k3_xcmplx_0(C,D),k3_moebius1(k3_xcmplx_0(A,B))) ) ) ) ) ) )).
fof(t16_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( k4_nat_d(A,C) = k5_numbers => ( C = k5_numbers | r1_xxreal_0(C,B) | k4_nat_d(k2_xcmplx_0(A,B),C) = B ) ) ) ) ) )).
fof(t16_nat_lat,axiom,( m2_nat_lat(k10_nat_lat,k3_nat_lat) )).
fof(t16_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k2_nattra_1(A,B,C,C,k1_nattra_1(A,B,C),D) = k4_cat_1(B,k8_cat_1(A,B,C,D)) ) ) ) ) )).
fof(t16_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) => ! [D] : ( 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] : ( m1_ncfcont1(E,A,k7_partfun1(u1_struct_0(A),C,D)) => ? [F] : ( m1_nfcont_1(F,B,D) & ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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,k4_normsp_0(u1_struct_0(B),C,D)) ) ) ) ) )).
fof(t16_ndiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => r2_funct_2(k4_ordinal1,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))) ) ) ) ) )).
fof(t16_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [D] : ( v1_xreal_0(D) => ( 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) ) ) ) ) ) ) )).
fof(t16_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( 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)) ) ) ) ) ) ) ) ) )).
fof(t16_ndiff_5,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_tarski(k2_ndiff_5(A,B,C),k1_rltopsp1(A,B,C)) ) ) ) )).
fof(t16_neckla_3,axiom,( ! [A] : ( ( v1_orders_2(A) & v3_necklace(A) & l1_orders_2(A) ) => k3_necklace(k3_necklace(A)) = A ) )).
fof(t16_necklace,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ( r5_waybel_1(A,B) => k1_card_1(u1_orders_2(A)) = k1_card_1(u1_orders_2(B)) ) ) ) )).
fof(t16_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t16_nfcont_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r1_nfcont_1(B,C,D,E) => r1_nfcont_1(B,C,k4_vfunct_1(u1_struct_0(B),C,D,A),E) ) ) ) ) ) ) )).
fof(t16_nfcont_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) & ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(C,k9_complex1(k3_xcmplx_0(B,k2_power(A,D)))) ) ) ) ) ) )).
fof(t16_nfcont_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( r1_tarski(k2_relset_1(k1_numbers,D),B) & v2_comseq_2(D) & r2_hidden(k1_seq_2(D),B) ) => ( v3_normsp_1(k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,D,C),A) & k7_partfun1(u1_struct_0(A),C,k1_seq_2(D)) = k6_normsp_1(A,k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,D,C)) ) ) ) ) ) ) ) )).
fof(t16_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t16_normform,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,k5_finsub_1(B)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t16_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t16_numbers,axiom,( r1_tarski(k4_numbers,k2_numbers) )).
fof(t16_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t16_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t16_oposet_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_qmax_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t16_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(k2_oppcat_1(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t16_ordeq_01,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(k5_ordeq_01(B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_ordeq_01(B,C))) => ! [F] : ( ( v1_funct_1(F) & v1_nfcont_3(F,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(C)))) ) => ! [G] : ( ( v1_funct_1(G) & v1_nfcont_3(G,C) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(C)))) ) => ( ( F = D & G = E & k1_relset_1(k1_numbers,F) = B & k1_relset_1(k1_numbers,G) = B ) => ( E = k1_rlvect_1(k5_ordeq_01(B,C),D,A) <=> ! [H] : ( m2_subset_1(H,k1_numbers,B) => k7_partfun1(u1_struct_0(C),G,H) = k1_rlvect_1(C,k7_partfun1(u1_struct_0(C),F,H),A) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_orders_1(A) => v1_orders_1(k2_relat_1(A)) ) ) )).
fof(t16_orders_2,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t16_ordinal1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => ~ ( r1_tarski(A,B) & A != k1_xboole_0 & ! [C] : ( v3_ordinal1(C) => ~ ( r2_hidden(C,A) & ! [D] : ( v3_ordinal1(D) => ( r2_hidden(D,A) => r1_ordinal1(C,D) ) ) ) ) ) ) )).
fof(t16_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ! [C] : ( ( r2_hidden(A,B) & r1_tarski(B,C) ) => r1_ordinal1(k2_ordinal2(C),k2_ordinal2(B)) ) ) )).
fof(t16_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ~ ( r1_ordinal1(A,1) & A != k1_xboole_0 & A != 1 ) ) )).
fof(t16_ordinal4,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t16_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => k1_ordinal5(A,1) = A ) )).
fof(t16_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( A != B => k1_ordinal6(k2_tarski(A,B)) = 2 ) ) ) )).
fof(t16_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( r1_orders_2(B,F,C) => ( r1_orders_2(B,D,C) | ( k1_ortsp_1(A,B,C,k3_rlvect_1(B,D,F),E) = k1_ortsp_1(A,B,C,D,E) & k1_ortsp_1(A,B,C,D,k3_rlvect_1(B,E,F)) = k1_ortsp_1(A,B,C,D,E) ) ) ) ) ) ) ) ) ) )).
fof(t16_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( r2_hidden(D,k1_funct_1(B,C)) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t16_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ~ v1_xboole_0(B) => v11_osalg_1(k3_osalg_1(A,B),A) ) ) )).
fof(t16_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_osalg_2(C,A,B) => r1_tarski(k5_osalg_2(A,B,C),k5_msualg_2(A,B,C)) ) ) ) )).
fof(t16_osalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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] : ( m2_pboole(E,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,k6_msualg_3(A,B,C,D))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t16_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t16_papdesaf,axiom,( ! [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) ) => ! [B] : ( ( ~ v7_struct_0(B) & v2_analoaf(B) & l1_analoaf(B) ) => ( B = k2_analoaf(A) => v7_aff_2(k2_diraf(B)) ) ) ) )).
fof(t16_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t16_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t16_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(t16_partfun2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t16_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => r1_setfam_1(B,k3_partit1(A,B,C)) ) ) ) )).
fof(t16_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t16_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r1_diraf(A,F,E,B) & r2_analoaf(A,D,E,C,B) & r2_analoaf(A,F,D,F,C) ) => ( r3_diraf(A,F,B,C) | F = D | r1_diraf(A,F,D,C) ) ) ) ) ) ) ) ) )).
fof(t16_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( ( r2_pboole(A,B,D) & r2_pboole(A,C,D) ) => r2_pboole(A,k2_pboole(A,B,C),D) ) ) ) ) )).
fof(t16_pcomps_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t16_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ( l2_pcs_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k19_pcs_0(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k19_pcs_0(A,B))) => ( r1_orders_2(k19_pcs_0(A,B),C,D) <=> ~ ( ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( E = C & F = D & r1_orders_2(A,E,F) ) ) ) & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ~ ( E = C & F = D & r1_orders_2(B,E,F) ) ) ) ) ) ) ) ) ) )).
fof(t16_pdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( 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] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(B),k1_euclid(C)))) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(k4_real_ns1(B))) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t16_pdiff_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_euclid(2))) => ! [B] : ( ( 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] : ( m2_finseq_2(C,k1_numbers,k1_euclid(2)) => ( r2_hidden(C,A) => r3_pdiff_1(2,2,B,C) ) ) ) ) ) ) )).
fof(t16_pdiff_3,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(2)) => ! [B] : ( ( 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) = k10_pdiff_1(2,2,k1_pdiff_3(2,2,B),A) ) ) ) )).
fof(t16_pdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(3)) => ! [F] : ( ( 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 = k10_pdiff_1(3,1,F,E) <=> ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & ? [I] : ( v1_xreal_0(I) & E = k11_finseq_1(G,H,I) & ? [J] : ( m1_rcomp_1(J,G) & r1_tarski(J,k1_relset_1(k1_numbers,k1_pdiff_2(3,1,F,E))) & ? [K] : ( v1_funct_1(K) & v3_fdiff_1(K) & m1_subset_1(K,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [L] : ( v1_funct_1(L) & v2_fdiff_1(L) & m1_subset_1(L,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & D = k1_funct_1(K,1) & ! [M] : ( v1_xreal_0(M) => ( r2_hidden(M,J) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,1,F,E),M),k1_funct_1(k1_pdiff_2(3,1,F,E),G)) = k2_xcmplx_0(k1_funct_1(K,k6_xcmplx_0(M,G)),k1_funct_1(L,k6_xcmplx_0(M,G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t16_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(1))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( 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) ) ) ) ) ) )).
fof(t16_pdiff_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(B))) => ( ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,B) ) => r1_xxreal_0(k2_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(k2_normsp_0(k4_real_ns1(B),C),k3_xcmplx_0(B,A)) ) ) ) ) )).
fof(t16_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t16_pencil_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ( ~ v4_pencil_1(k1_pencil_1(A,B,C)) & ~ ! [D] : ( m1_subset_1(D,A) => v3_pencil_1(k1_pencil_1(A,B,D)) ) ) ) & v4_pencil_1(k5_pencil_1(A,B)) ) ) ) )).
fof(t16_pencil_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t16_pencil_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v15_pencil_1(C) ) => ! [D] : ( m1_subset_1(D,u1_pre_topc(k2_pencil_1(A,C,B))) => ! [E] : ( m1_pboole(E,A,k12_pralg_1(A,C)) => m1_subset_1(k4_card_3(k1_funct_7(k1_pzfmisc1(A,E),B,D)),u1_pre_topc(k5_pencil_1(A,C))) ) ) ) ) ) )).
fof(t16_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( m1_vectsp_4(C,A,D) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t16_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( v1_abian(A) & v1_abian(k1_nat_1(A,1)) ) ) )).
fof(t16_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k6_petri(k11_petri(A),k12_petri(A,B)) = k7_petri(A,B) ) ) )).
fof(t16_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => r1_pnproc_1(A,k3_pnproc_1(A,k2_pnproc_1(A,B,C),B),C) ) ) )).
fof(t16_polyalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_polyalg1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_polyalg1(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ( ( D = F & E = G ) => k6_algstr_0(B,D,E) = k6_algstr_0(C,F,G) ) ) ) ) ) ) ) ) )).
fof(t16_polyeq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( k4_polyeq_1(A,B,C,D,E) = k5_numbers => ( A = k5_numbers | ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ( ( J = k2_xcmplx_0(E,k7_xcmplx_0(B,k3_xcmplx_0(3,A))) & I = k4_xcmplx_0(k7_xcmplx_0(B,k3_xcmplx_0(3,A))) & F = k7_xcmplx_0(B,A) & G = k7_xcmplx_0(C,A) & H = k7_xcmplx_0(D,A) ) => k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_newton(J,3),k3_xcmplx_0(k5_numbers,k1_square_1(J))),k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),C),k1_square_1(B)),k3_xcmplx_0(3,k1_square_1(A))),J)),k2_xcmplx_0(k3_xcmplx_0(2,k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(3,A)),3)),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),D),k3_xcmplx_0(B,C)),k3_xcmplx_0(3,k1_square_1(A))))) = k5_numbers ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_polyeq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( k1_polyeq_1(B,C,A) = k5_numbers => ( B = k5_numbers | A = k4_xcmplx_0(k7_xcmplx_0(C,B)) ) ) ) ) ) )).
fof(t16_polyeq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( k2_xcmplx_0(k1_newton(A,E),k1_newton(B,E)) = C & k3_xcmplx_0(k1_newton(A,E),k1_newton(B,E)) = D & r1_xxreal_0(k5_numbers,k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D))) & ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(D,k5_numbers) & v1_abian(E) & r1_xxreal_0(1,E) & ~ ( A = k1_power(E,k7_xcmplx_0(k2_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2)) & B = k1_power(E,k7_xcmplx_0(k6_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2)) ) & ~ ( A = k4_xcmplx_0(k1_power(E,k7_xcmplx_0(k2_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2))) & B = k1_power(E,k7_xcmplx_0(k6_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2)) ) & ~ ( A = k1_power(E,k7_xcmplx_0(k2_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2)) & B = k4_xcmplx_0(k1_power(E,k7_xcmplx_0(k6_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2))) ) & ~ ( A = k4_xcmplx_0(k1_power(E,k7_xcmplx_0(k2_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2))) & B = k4_xcmplx_0(k1_power(E,k7_xcmplx_0(k6_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2))) ) & ~ ( A = k1_power(E,k7_xcmplx_0(k6_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2)) & B = k1_power(E,k7_xcmplx_0(k2_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2)) ) & ~ ( A = k4_xcmplx_0(k1_power(E,k7_xcmplx_0(k6_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2))) & B = k1_power(E,k7_xcmplx_0(k2_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2)) ) & ~ ( A = k1_power(E,k7_xcmplx_0(k6_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2)) & B = k4_xcmplx_0(k1_power(E,k7_xcmplx_0(k2_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2))) ) & ~ ( A = k4_xcmplx_0(k1_power(E,k7_xcmplx_0(k6_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2))) & B = k4_xcmplx_0(k1_power(E,k7_xcmplx_0(k2_xcmplx_0(C,k3_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(4,D)))),2))) ) ) ) ) ) ) ) )).
fof(t16_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( v1_xcmplx_0(F) => ! [G] : ( v1_xcmplx_0(G) => ( ( F = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(3,C),k1_newton(D,2)),9) & F = k5_numbers & G = k7_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(9,D),C),k3_xcmplx_0(2,k1_newton(D,3))),k3_xcmplx_0(27,B)),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(D,k1_newton(A,2))),k3_xcmplx_0(C,A)),B) = k5_numbers <=> ~ ( A != k6_xcmplx_0(E,k7_xcmplx_0(D,3)) & A != k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(E,2)),k7_xcmplx_0(D,3)),k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(E,k1_polyeq_5(2,3)),k7_complex1),2)) & A != k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(E,2)),k7_xcmplx_0(D,3)),k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(E,k1_polyeq_5(2,3)),k7_complex1),2)) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_polyform,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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 ) ) )).
fof(t16_polynom1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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) ) => k4_polynom1(A,B,E,F) = k1_algstr_0(B,k4_polynom1(A,B,C,F),k4_polynom1(A,B,D,F)) ) => r2_funct_2(k15_pre_poly(A),u1_struct_0(B),E,k5_polynom1(A,B,C,D)) ) ) ) ) ) )).
fof(t16_polynom2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(D,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [E] : ( ( 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)))) ) => k2_polynom2(A,B,k7_polynom1(A,B,C,D),E) = k5_algstr_0(B,k2_polynom2(A,B,C,E),k2_polynom2(A,B,D,E)) ) ) ) ) ) )).
fof(t16_polynom3,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k3_finseq_2(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k10_pre_poly(A,k17_finseq_1(k3_finseq_2(A),C,B)) = k17_finseq_1(k4_ordinal1,C,k10_pre_poly(A,B)) ) ) )).
fof(t16_polynom5,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k2_polynom5(A,B,1),B) ) ) )).
fof(t16_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( 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) = k4_polynom1(A,B,C,k16_pre_poly(A)) ) ) ) )).
fof(t16_polynom8,axiom,( ! [A] : ( ( ~ 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] : ( v1_int_1(B) => k3_polynom8(A,k5_struct_0(A),B) = k5_struct_0(A) ) ) )).
fof(t16_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( 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] : ( ( 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,k3_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))) ) ) ) ) ) ) ) )).
fof(t16_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_xxreal_0(A,B) => ( ( ~ ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(1,C) ) & v1_abian(C) ) | r1_xxreal_0(k1_power(C,A),k1_power(C,B)) ) ) ) ) ) )).
fof(t16_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( r2_hidden(F,k1_relset_1(k4_ordinal1,k1_msualg_1(B,D))) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ( G = k1_funct_1(k1_msualg_1(B,D),F) => ! [H] : ( m1_subset_1(H,k3_msualg_1(B,D,k14_pralg_2(A,B,C))) => ! [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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_pre_circ,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) ) => ! [C] : ( m1_trees_1(C,A) => k1_nat_1(k5_card_1(k5_trees_1(A,C,B)),k5_card_1(k4_trees_1(A,C))) = k1_nat_1(k5_card_1(A),k5_card_1(B)) ) ) ) )).
fof(t16_pre_ff,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( A != k5_numbers & r1_xxreal_0(k3_xcmplx_0(2,A),A) ) ) )).
fof(t16_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k4_partfun1(A,B)) ) )).
fof(t16_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & ! [D] : ( 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) ) ) ) )).
fof(t16_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t16_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) => r1_xxreal_0(k2_xcmplx_0(1,k3_xcmplx_0(B,A)),k1_newton(k2_xcmplx_0(1,A),B)) ) ) ) )).
fof(t16_prob_1,axiom,( ! [A] : ! [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))) ) => ( ~ v1_xboole_0(B) & v2_finsub_1(B) & v1_prob_1(B,A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ) )).
fof(t16_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m2_prob_1(D,A,B) => k3_funct_2(B,k1_numbers,D,C) = k6_xcmplx_0(1,k3_funct_2(B,k1_numbers,D,k7_prob_1(A,B,k4_prob_1(A,B),C))) ) ) ) ) )).
fof(t16_prob_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(C)))) ) => ( r2_hidden(B,k1_prob_2(C,k9_setfam_1(C),k3_prob_3(C,D),A)) <=> ( r2_hidden(B,k1_prob_2(C,k9_setfam_1(C),D,A)) & ! [E] : ( v7_ordinal1(E) => ~ ( ~ r1_xxreal_0(A,E) & r2_hidden(B,k1_prob_2(C,k9_setfam_1(C),D,E)) ) ) ) ) ) ) )).
fof(t16_prob_4,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(B) => ( k1_prob_4(A,k9_setfam_1(A),k3_prob_3(A,B),k5_numbers) = k1_prob_4(A,k9_setfam_1(A),B,k5_numbers) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => k1_prob_4(A,k9_setfam_1(A),k3_prob_3(A,B),k1_nat_1(C,1)) = k3_measure1(A,k9_setfam_1(A),k1_prob_4(A,k9_setfam_1(A),B,k1_nat_1(C,1)),k1_prob_4(A,k9_setfam_1(A),B,C)) ) ) ) ) )).
fof(t16_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t16_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ( ( r1_projdes1(A,B,D,F,H) & r1_projdes1(A,B,D,F,I) & r1_projdes1(A,B,D,F,J) & r1_projdes1(A,C,E,G,H) & r1_projdes1(A,C,E,G,I) & r1_projdes1(A,C,E,G,J) ) => ( r1_collsp(A,B,D,F) | r1_collsp(A,C,E,G) | r1_projdes1(A,B,D,F,C) | r1_collsp(A,H,I,J) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_projpl_1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t16_projred1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & v8_incproj(A) & l1_incsp_1(A) ) => ? [B] : ( m1_subset_1(B,u1_incsp_1(A)) & ? [C] : ( m1_subset_1(C,u1_incsp_1(A)) & ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & ? [E] : ( m1_subset_1(E,u1_incsp_1(A)) & ? [F] : ( 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) ) ) ) ) ) ) )).
fof(t16_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u1_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u1_incsp_1(A)) => ! [H] : ( m1_subset_1(H,u1_incsp_1(A)) => ! [I] : ( m1_subset_1(I,u2_incsp_1(A)) => ! [J] : ( m1_subset_1(J,u2_incsp_1(A)) => ! [K] : ( m1_subset_1(K,u2_incsp_1(A)) => ! [L] : ( m1_subset_1(L,u2_incsp_1(A)) => ! [M] : ( m1_subset_1(M,u2_incsp_1(A)) => ! [N] : ( m1_subset_1(N,u2_incsp_1(A)) => ! [O] : ( m1_subset_1(O,u2_incsp_1(A)) => ! [P] : ( m1_subset_1(P,u2_incsp_1(A)) => ( ( r4_incsp_1(A,k7_domain_1(u1_incsp_1(A),D,F),L) & r1_incsp_1(A,E,M) & r4_incsp_1(A,k7_domain_1(u1_incsp_1(A),D,E),N) & 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),D,G),P) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),B,E,F),I) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),H,F,G),J) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),C,E,G),K) ) => ( r1_incsp_1(A,B,L) | r1_incsp_1(A,B,N) | r1_incsp_1(A,C,N) | r1_incsp_1(A,C,P) | r1_projred2(A,L,M,N) | r1_projred2(A,M,N,O) | L = P | P = N | B = C | ( H != B & H != C & ~ r1_incsp_1(A,H,L) & ~ r1_incsp_1(A,H,P) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,k4_card_3(A)) => ! [E] : ( m1_subset_1(E,k4_card_3(A)) => ! [F] : ( m2_subset_1(F,k4_ordinal1,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) ) ) ) ) )).
fof(t16_prvect_3,axiom,( ! [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) & l1_normsp_1(A) ) => ? [B] : ( 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] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => k2_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)) = k2_normsp_0(A,C) ) ) ) )).
fof(t16_pscomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v2_compts_1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t16_pua2mss1,axiom,( ! [A] : ( ( v2_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( 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,k1_nat_1(B,1)),k7_pua2mss1(A,k8_pua2mss1(A,C,B))) ) ) ) )).
fof(t16_pythtrip,axiom,( ~ v1_finset_1(a_0_0_pythtrip) )).
fof(t16_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t16_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)))) ) ) ) )).
fof(t16_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( m1_subset_1(E,k9_qc_lang1(A)) => ! [F] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t16_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t16_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_trees_1(C,k9_xtuple_0(k2_qc_lang4(A,B))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t16_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_qc_trans(B,A) & m1_qc_lang1(B) ) => ! [C] : ( m2_subset_1(C,k16_substut1(A),k38_substut1(A)) => ! [D] : ( m2_subset_1(D,k16_substut1(B),k38_substut1(B)) => ( ( v5_qc_lang1(k2_sublemma(A,C),A) & v5_qc_lang1(k2_sublemma(B,D),B) & k21_qc_lang1(A,k2_sublemma(A,C)) = k21_qc_lang1(B,k2_sublemma(B,D)) & k22_qc_lang1(A,k2_sublemma(A,C)) = k22_qc_lang1(B,k2_sublemma(B,D)) & C = D ) => k35_substut1(A,k32_substut1(A,C)) = k35_substut1(B,k32_substut1(B,D)) ) ) ) ) ) )).
fof(t16_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v10_lattices(A) & v4_lattice3(A) & v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t16_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k23_quaterni(k23_quaterni(A,B),C) = k23_quaterni(A,k23_quaterni(B,C)) ) ) ) )).
fof(t16_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k27_quaterni(k23_quaterni(A,B)) = k23_quaterni(k27_quaterni(B),k27_quaterni(A)) ) ) )).
fof(t16_quaterni,axiom,( k10_quaterni(k1_xcmplx_0,k11_quaterni) = k12_quaterni )).
fof(t16_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r1_xxreal_0(k5_numbers,k1_quin_1(B,C,D)) => ( B = k5_numbers | k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(A)),k3_xcmplx_0(C,A)),D) = k3_xcmplx_0(k3_xcmplx_0(B,k6_xcmplx_0(A,k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B)))),k6_xcmplx_0(A,k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B)))) ) ) ) ) ) ) )).
fof(t16_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t16_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v3_card_1(B,1) & m2_finseq_1(B,k4_numbers) ) => ( k7_partfun1(k4_numbers,B,1) = A => B = k9_finseq_1(A) ) ) ) )).
fof(t16_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => k5_radix_3(k5_numbers,A) = k5_numbers ) )).
fof(t16_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(2,C) => ! [D] : ( 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))) = k5_numbers ) ) ) ) ) ) )).
fof(t16_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(t16_ramsey_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(2,B) & r1_xxreal_0(2,A) & ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(C,k4_newton(k7_nat_d(B,1),k7_nat_d(k2_xcmplx_0(B,A),2))) & r1_xxreal_0(2,C) & ! [D] : ( v1_finset_1(D) => ! [E] : ( ( 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] : ( m1_subset_1(F,k1_zfmisc_1(D)) => ( ~ ( 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(1) ) & ~ ( 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(2) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ~ ( v3_prob_1(B) & ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & k9_nat_1(k9_setfam_1(A),B,C) != k9_nat_1(k9_setfam_1(A),B,D) ) ) ) ) ) )).
fof(t16_random_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( m2_prob_1(C,A,k1_random_1(A)) => ! [D] : ( m2_prob_1(D,B,k1_random_1(B)) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(A)) ) => ! [F] : ( ( ~ v1_xboole_0(F) & v1_finset_1(F) & m1_subset_1(F,k1_zfmisc_1(B)) ) => k12_supinf_2(k2_random_2(A,B,C,D),k2_zfmisc_1(E,F)) = k1_extreal1(k12_supinf_2(C,E),k12_supinf_2(D,F)) ) ) ) ) ) ) )).
fof(t16_random_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,A) ) => ( v1_funct_1(B) & v1_funct_2(B,k2_finseq_1(k3_finseq_1(B)),A) & v1_random_3(B,k2_finseq_1(k3_finseq_1(B)),A,k1_random_1(k2_finseq_1(k3_finseq_1(B))),k1_random_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(k3_finseq_1(B)),A))) ) ) ) )).
fof(t16_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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)) = k5_numbers ) ) )).
fof(t16_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ( k2_rat_1(A) = A <=> k1_rat_1(A) = 1 ) ) )).
fof(t16_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_ratfunc1(A,B,C,D) => r1_polynom5(A,k8_polynom3(A,B,C),D) ) ) ) ) ) )).
fof(t16_rcomp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_rcomp_1(B,A) => r2_hidden(A,B) ) ) )).
fof(t16_rcomp_3,axiom,( ! [A] : ( ( v5_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( ~ r2_hidden(k2_seq_4(A),A) => r1_tarski(A,k3_rcomp_1(k3_seq_4(A),k2_seq_4(A))) ) ) )).
fof(t16_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( 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) ) ) ) )).
fof(t16_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k4_real_ns1(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k4_real_ns1(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k7_real_ns1(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k7_real_ns1(A))))) ) => ( r1_funct_2(k4_ordinal1,u1_struct_0(k4_real_ns1(A)),k4_ordinal1,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) ) ) ) ) ) ) ) )).
fof(t16_realset2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) )).
fof(t16_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t16_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [D] : ( ( v1_rearran1(D) & v2_rearran1(D) & v3_rearran1(D,k1_zfmisc_1(A)) & m2_finseq_1(D,k1_zfmisc_1(A)) ) => ( ( v1_partfun1(C,B) & k5_card_1(A) = k5_card_1(B) ) => r2_classes1(k3_rearran1(B,A,D,C),k20_rfunct_3(B,C,B)) ) ) ) ) ) )).
fof(t16_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => k2_relat_1(k3_xboole_0(A,B)) = k3_xboole_0(k2_relat_1(A),k2_relat_1(B)) ) ) )).
fof(t16_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ( r1_tarski(k4_relat_1(A),C) => ( A = k1_relset_1(A,C) & r1_tarski(A,k2_relset_1(B,C)) ) ) ) )).
fof(t16_relset_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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))) ) ) )).
fof(t16_revrot_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_finseq_6(B,A) & m2_finseq_1(B,A) ) => ! [C] : ( m1_subset_1(C,A) => ( ! [D] : ( v7_ordinal1(D) => ~ ( ~ 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 ) ) ) ) )).
fof(t16_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ! [D] : ( ( r1_rewrite1(A,B,C) & r1_rewrite1(A,C,D) ) => r1_rewrite1(A,B,D) ) ) )).
fof(t16_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t16_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( l1_rewrite3(F,D) => ! [G] : ( l1_rewrite3(G,E) => ( ( u1_rewrite3(D,F) = u1_rewrite3(E,G) & r1_rewrite3(D,F,A,B,C) ) => r1_rewrite3(E,G,A,B,C) ) ) ) )).
fof(t16_rfinseq,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( k3_finseq_1(A) != k5_numbers => k18_rvsum_1(k3_rfinseq(A)) = k1_funct_1(A,1) ) ) )).
fof(t16_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( ( k3_finseq_1(A) = k5_numbers | k3_finseq_1(A) = 1 ) => v1_integra2(A) ) ) )).
fof(t16_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(t16_rfunct_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k5_numbers)) = k1_xboole_0 ) => r2_relset_1(k4_ordinal1,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,B,D,k2_partfun1(B,k1_numbers,k6_rfunct_1(B,k1_numbers,C),A)),k37_valued_1(k4_ordinal1,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,B,D,k2_partfun1(B,k1_numbers,C,A)))) ) ) ) ) )).
fof(t16_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => r3_binop_1(k3_rfunct_3(A,k1_numbers),k7_funcop_1(k2_subset_1(A),k5_numbers),k13_rfunct_3(A)) ) )).
fof(t16_rfunct_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( r2_rfunct_3(A,B) <=> ( r1_tarski(B,k9_xtuple_0(A)) & ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( 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(k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(A,E),k1_funct_1(A,C)),k6_xcmplx_0(E,C)),k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(A,D),k1_funct_1(A,C)),k6_xcmplx_0(D,C))) & r1_xxreal_0(k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(A,D),k1_funct_1(A,C)),k6_xcmplx_0(D,C)),k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(A,D),k1_funct_1(A,E)),k6_xcmplx_0(D,E))) ) ) ) ) ) ) ) ) ) )).
fof(t16_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_seq_2(A) & v1_seq_2(B) ) => r1_xxreal_0(k1_rinfsup1(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)),k2_xcmplx_0(k1_rinfsup1(A),k1_rinfsup1(B))) ) ) ) )).
fof(t16_rinfsup2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v7_mesfunc5(k1_valued_0(k6_numbers,B,A)) => ( v7_mesfunc5(B) & v10_mesfunc5(B) & k2_mesfunc5(B) = k2_mesfunc5(k1_valued_0(k6_numbers,B,A)) ) ) ) ) )).
fof(t16_ring_1,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t16_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ? [B] : ( r2_hidden(B,A) & r2_ringcat1(B,k18_mod_2) ) ) )).
fof(t16_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( 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) ) ) ) )).
fof(t16_rlaffin2,axiom,( ! [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) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t16_rlaffin3,axiom,( ! [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) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ! [D] : ( m2_rlaffin3(D,A,B) => k3_finseq_1(k1_rlaffin3(A,B,D,C)) = k5_card_1(B) ) ) ) )).
fof(t16_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_rlsub_1(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ( ( E = C & F = B ) => k5_algstr_0(D,E,F) = k5_algstr_0(A,C,B) ) ) ) ) ) ) ) )).
fof(t16_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t16_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_connsp_2(C,A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(C,D) => m1_connsp_2(D,A,B) ) ) ) ) ) )).
fof(t16_rlvect_1,axiom,( ! [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) & v8_rlvect_1(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k4_algstr_0(A,B) = k1_rlvect_1(A,B,k4_xcmplx_0(1)) ) ) )).
fof(t16_rlvect_2,axiom,( ! [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) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t16_rlvect_3,axiom,( ! [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) ) => k1_rlvect_3(A,k1_subset_1(u1_struct_0(A))) = k1_rlsub_1(A) ) )).
fof(t16_rlvect_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & ? [I] : ( v1_xreal_0(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)) ) ) ) ) ) ) ) ) ) )).
fof(t16_rlvect_5,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlvect_3(C,B) => ? [D] : ( m1_rlvect_3(D,A) & r1_tarski(C,D) ) ) ) ) )).
fof(t16_rlvect_x,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ( r2_hidden(A,k2_rlvect_x(B,k6_domain_1(u1_struct_0(B),C))) <=> ? [D] : ( v1_int_1(D) & A = k1_rlvect_1(B,C,D) ) ) ) ) )).
fof(t16_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_rmod_2(E,A,B) => ! [F] : ( m1_subset_1(F,u1_struct_0(E)) => ! [G] : ( m1_subset_1(G,u1_struct_0(E)) => ( ( F = D & G = C ) => k5_algstr_0(E,F,G) = k5_algstr_0(B,D,C) ) ) ) ) ) ) ) ) )).
fof(t16_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t16_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ! [D] : ( m1_rmod_4(D,A,B) => ( r2_hidden(C,k2_rmod_4(A,B,D)) <=> ? [E] : ( 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) ) ) ) ) ) )).
fof(t16_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t16_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t16_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_lattices(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( C = E & D = F ) => k1_lattices(A,C,D) = k1_lattices(B,E,F) ) ) ) ) ) ) ) ) )).
fof(t16_robbins4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_robbins4)) => ! [B] : ( 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) = k5_numbers ) ) ) ) )).
fof(t16_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ~ v4_roughs_1(B,A) <=> k4_roughs_1(A,B) = B ) ) ) )).
fof(t16_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_xboole_0(B,C) => k1_rpr_1(A,k9_subset_1(A,B,C)) = k5_numbers ) ) ) ) )).
fof(t16_rsspace,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => k1_funct_1(A,B) = k5_numbers ) => ( v1_series_1(A) & k4_series_1(A) = k5_numbers ) ) ) )).
fof(t16_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_rsspace4(A,B))) => ! [D] : ( ( 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] : ( m1_subset_1(E,A) => r1_xxreal_0(k2_normsp_0(B,k3_funct_2(A,u1_struct_0(B),D,E)),k2_normsp_0(k9_rsspace4(A,B),C)) ) ) ) ) ) ) )).
fof(t16_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_struct_0(B,C) => r1_struct_0(B,k4_algstr_0(A,C)) ) ) ) ) )).
fof(t16_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t16_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ~ ( r1_tarski(k10_xtuple_0(D),u1_struct_0(k1_rusub_3(A,C))) & ! [E] : ( m2_rlvect_2(E,A,C) => k4_rlvect_1(A,k5_rlvect_2(A,D,B)) != k6_rlvect_2(A,E) ) ) ) ) ) ) )).
fof(t16_rusub_4,axiom,( ! [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_bhsp_1(A) & v1_rusub_4(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => r1_xxreal_0(k6_xcmplx_0(k1_nat_1(k1_rusub_4(B),k1_rusub_4(C)),k1_rusub_4(A)),k1_rusub_4(k2_rusub_2(A,B,C))) ) ) ) )).
fof(t16_rusub_5,axiom,( ! [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) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_rusub_4(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t16_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => k4_rvsum_1(B,k2_finseq_2(A,k5_numbers)) = B ) ) )).
fof(t16_rvsum_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t16_scm_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( r1_tarski(k1_ordinal4(k5_afinsq_1(k3_ami_3(k10_ami_3(k5_numbers),k10_ami_3(1))),k5_afinsq_1(k2_compos_1(k1_ami_3))),A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( ( v5_memstr_0(D,k7_card_1(2),k1_ami_3,k5_numbers) & m1_scm_1(D,k6_afinsq_1(B,C)) ) => ( r1_extpro_1(k7_card_1(2),k1_ami_3,A,D) & k8_extpro_1(k7_card_1(2),k1_ami_3,A,D) = 1 & k1_funct_1(k6_extpro_1(k7_card_1(2),k1_ami_3,A,D),k10_ami_3(k5_numbers)) = k2_xcmplx_0(B,C) & ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_ami_3)) ) => ( E != k10_ami_3(k5_numbers) => k1_funct_1(k6_extpro_1(k7_card_1(2),k1_ami_3,A,D),E) = k1_funct_1(D,E) ) ) ) ) ) ) ) ) )).
fof(t16_scm_halt,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k3_scmfsa6a(C,D)),k1_scmfsa_m(A)) = k2_xcmplx_0(k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k1_scmfsa_m(A)),1),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(k1_funct_4(B,C),D),k1_funct_4(k6_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k1_scmfsa_m(A)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_3(k4_scmfsa_2(k5_numbers),1))))) ) ) ) ) )).
fof(t16_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( 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)) ) ) ) ) )).
fof(t16_scmfsa10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => k5_xtuple_0(k13_scmfsa_2(A,B)) = k9_finseq_1(A) ) ) )).
fof(t16_scmfsa6a,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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)) ) ) ) )).
fof(t16_scmfsa7b,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_scmfsa_2(C) => ~ ( A != B & r3_scmfsa7b(k16_scmfsa_2(B,C),A) ) ) ) ) )).
fof(t16_scmfsa8a,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k2_scmfsa6a(C)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A)),1))) = k5_card_1(C) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A)))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k2_scmfsa6a(C)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A)),1))) ) ) ) ) ) )).
fof(t16_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [E] : ( ( 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),k7_card_1(3),k1_scmfsa_2) & ( k1_funct_1(B,E) = k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),3)))) ) & ( k1_funct_1(B,E) != k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),3)))) ) ) ) ) ) ) ) )).
fof(t16_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,C) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,D) & r1_scmfsa8a(C,A,E) ) => r1_scmfsa8a(D,B,E) ) ) ) ) ) ) )).
fof(t16_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_ami_2(B) & ~ v1_scmfsa_m(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(D,k7_card_1(3),k1_scmfsa_2,k5_numbers) ) => ( r1_tarski(k1_scmfsa_9(B,C),A) => ( k1_funct_1(D,B) = k5_numbers | ( k8_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D) = 4 & ! [E] : ( v7_ordinal1(E) => k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D,E)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,D) ) ) ) ) ) ) ) ) )).
fof(t16_scmfsa_1,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k4_scmfsa_1,k5_scmfsa_1))) => ! [B] : ( m2_subset_1(B,k1_scmfsa_1,k2_scmfsa_1) => ! [C] : ( v1_int_1(C) => ! [D] : ( 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) ) ) ) ) )).
fof(t16_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => k2_compos_0(u1_compos_1(k1_scmfsa_2),k11_scmfsa_2(A)) = 6 ) )).
fof(t16_scmfsa_m,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k3_scmfsa_2)) ) => ~ r2_hidden(k3_scmfsa_m(A),A) ) )).
fof(t16_scmisort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => r8_pboole(u1_struct_0(k1_scmfsa_2),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k1_scmisort(D,B,C,A),k1_nat_1(k5_numbers,1)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa_9(C,B)),k1_scmfsa_m(D),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(k1_funct_4(A,k2_scmfsa_9(C,B)),B),k1_scmfsa_m(D)),3))) ) ) ) ) )).
fof(t16_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( 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 ) ) ) )).
fof(t16_scmpds_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ! [I] : ( ( v1_ami_2(I) & m1_subset_1(I,u1_struct_0(k1_scmpds_2)) ) => ! [J] : ( v1_int_1(J) => ! [K] : ( 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(k5_numbers,k2_xcmplx_0(H,K)) ) => ( K = 1 | ( ~ ( ~ r1_xxreal_0(k5_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(k5_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(k5_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(k5_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))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_scmpds_4,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmpds_2)) => ! [C] : ( 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)) ) ) ) )).
fof(t16_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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] : ( v7_ordinal1(E) => ( 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))) ) ) ) ) ) ) )).
fof(t16_scmpds_8,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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(k1_nat_1(k5_card_1(D),2),C) <=> r2_hidden(C,k9_xtuple_0(k2_scmpds_8(A,B,D))) ) ) ) ) ) )).
fof(t16_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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(k7_card_1(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(k7_card_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(k7_card_1(2),k1_scmring2(A),k9_scmring2(A,D,B),E),k4_struct_0(k1_scmring2(A))) = k4_card_1(k5_memstr_0(k7_card_1(2),k1_scmring2(A),E)) ) & k2_scmring2(A,k2_extpro_1(k7_card_1(2),k1_scmring2(A),k9_scmring2(A,D,B),E),C) = k2_scmring2(A,E,C) ) ) ) ) ) ) )).
fof(t16_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmring2(A))) => ~ ( k2_compos_0(u1_compos_1(k1_scmring2(A)),B) = 5 & ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => B != k7_scmring2(A,C,D) ) ) ) ) ) )).
fof(t16_scpinvar,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_scmpds_2)) ) => ! [G] : ( v1_int_1(G) => ! [H] : ( 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] : ( ( 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,k5_numbers) ) => ! [J] : ( ( v1_relat_1(J) & v4_relat_1(J,k4_ordinal1) & v5_relat_1(J,u1_compos_1(k1_scmpds_2)) & v1_funct_1(J) & v1_partfun1(J,k4_ordinal1) ) => ( ( 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),k5_numbers) | r1_xxreal_0(k1_funct_1(I,F),k5_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),k5_numbers) | r1_xxreal_0(k1_funct_1(B,E),k5_numbers) | r1_xxreal_0(k1_funct_1(B,F),k5_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)) != k5_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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t16_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)),k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,A),k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,B))) ) ) ) )).
fof(t16_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( v2_comseq_2(A) & k1_seq_2(A) != k5_numbers & ! [B] : ( v7_ordinal1(B) => ? [C] : ( v7_ordinal1(C) & r1_xxreal_0(B,C) & r1_xxreal_0(k9_complex1(k1_funct_1(A,C)),k7_xcmplx_0(k9_complex1(k1_seq_2(A)),2)) ) ) ) ) )).
fof(t16_seq_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( m2_valued_0(B,k1_numbers,A) & v2_comseq_2(A) ) => v2_comseq_2(B) ) ) ) )).
fof(t16_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => r2_relset_1(k4_ordinal1,k4_partfun1(A,k1_numbers),k5_seqfunc(A,k9_seqfunc(A,C,B)),k9_seqfunc(A,k5_seqfunc(A,C),k5_seqfunc(A,B))) ) ) ) )).
fof(t16_seqm_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k1_valued_0(k1_numbers,k32_valued_1(k4_ordinal1,k1_numbers,B),A) = k32_valued_1(k4_ordinal1,k1_numbers,k1_valued_0(k1_numbers,B,A)) ) ) )).
fof(t16_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,A,B)) ) => v7_valued_0(k3_series_1(A)) ) ) )).
fof(t16_series_3,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => r1_xxreal_0(k1_power(3,k3_xcmplx_0(k3_xcmplx_0(A,B),C)),k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C),3)) ) ) ) )).
fof(t16_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => ! [D] : ( ( v1_xreal_0(D) & v2_xxreal_0(D) ) => ~ r1_xxreal_0(2,k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,k2_xcmplx_0(k2_xcmplx_0(A,B),D)),k7_xcmplx_0(B,k2_xcmplx_0(k2_xcmplx_0(A,B),C))),k7_xcmplx_0(C,k2_xcmplx_0(k2_xcmplx_0(B,C),D))),k7_xcmplx_0(D,k2_xcmplx_0(k2_xcmplx_0(A,C),D)))) ) ) ) ) )).
fof(t16_setfam_1,axiom,( ! [A] : ( r1_setfam_1(A,k1_xboole_0) => A = k1_xboole_0 ) )).
fof(t16_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( k9_xtuple_0(C) = k4_ordinal1 & ! [D] : ( v7_ordinal1(D) => k1_funct_1(C,D) = k3_tarski(a_3_3_setlim_1(A,B,D)) ) ) => ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) ) ) ) )).
fof(t16_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => k8_nat_1(k9_setfam_1(B),k5_setlim_2(B,D,C),A) = k5_setlim_2(B,k8_nat_1(k9_setfam_1(B),D,A),C) ) ) ) )).
fof(t16_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ( v3_binop_1(C,B) & v1_binop_1(C,B) & v2_binop_1(C,B) ) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => k7_setwiseo(A,B,C,k4_setwiseo(A,E,F,G),D) = k5_binop_1(B,C,k5_binop_1(B,C,k3_funct_2(A,B,D,E),k3_funct_2(A,B,D,F)),k3_funct_2(A,B,D,G)) ) ) ) ) ) ) ) ) )).
fof(t16_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k5_finsub_1(A)) => ! [E] : ( ( 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] : ( ( v1_funct_1(F) & v1_funct_2(F,A,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [G] : ( ( 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] : ( ( 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(E,B) & v2_binop_1(E,B) & v1_setwiseo(E,B) & v1_binop_1(G,C) & v2_binop_1(G,C) & v1_setwiseo(G,C) & k3_funct_2(B,C,H,k4_binop_1(B,E)) = k4_binop_1(C,G) & ! [I] : ( m1_subset_1(I,B) => ! [J] : ( m1_subset_1(J,B) => k3_funct_2(B,C,H,k5_binop_1(B,E,I,J)) = k5_binop_1(C,G,k3_funct_2(B,C,H,I),k3_funct_2(B,C,H,J)) ) ) ) => k3_funct_2(B,C,H,k7_setwiseo(A,B,E,D,F)) = k7_setwiseo(A,C,G,D,k1_partfun1(A,B,B,C,F,H)) ) ) ) ) ) ) ) ) ) )).
fof(t16_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t16_sfmastr1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_scmfsa6c(D) & v1_sfmastr1(D) & m1_subset_1(D,u1_compos_1(k1_scmfsa_2)) ) => ( ( v7_amistd_1(C,k7_card_1(3),k1_scmfsa_2) | ( r6_scmfsa7b(C,k2_extpro_1(k7_card_1(3),k1_scmfsa_2,D,k1_scmfsa_m(B)),A) & r5_scmfsa7b(C,k2_extpro_1(k7_card_1(3),k1_scmfsa_2,D,k1_scmfsa_m(B)),A) ) ) => k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(k4_scmfsa6a(D,C),B,A)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(C,k2_extpro_1(k7_card_1(3),k1_scmfsa_2,D,k1_scmfsa_m(B)),A)) ) ) ) ) ) )).
fof(t16_sfmastr3,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & ~ v1_scmfsa_m(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( k1_funct_1(A,k4_scmfsa_2(k5_numbers)) = 1 => ! [G] : ( ( 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(k7_card_1(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(k5_numbers))),k6_scmfsa_2(B,C)),A,F)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_funct_7(k1_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))) ) ) ) ) ) ) ) ) ) )).
fof(t16_sgraph1,axiom,( ! [A] : r2_hidden(g1_sgraph1(k1_xboole_0,k1_subset_1(k2_sgraph1(k1_xboole_0))),k3_sgraph1(A)) )).
fof(t16_sheffer1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t16_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t16_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => k4_simplex0(A) = k5_setfam_1(u1_struct_0(A),u1_pre_topc(A)) ) )).
fof(t16_simplex1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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(k5_numbers,A,B) = B ) ) ) )).
fof(t16_simplex2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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)),k3_xcmplx_0(k7_xcmplx_0(k6_simplex0(B),k2_xcmplx_0(k6_simplex0(B),1)),k3_simplex2(A,B))) ) ) ) )).
fof(t16_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(k9_complex1(k9_nat_1(k2_numbers,k10_comseq_3(k3_sin_cos(A)),B)),k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k9_complex1(A))),B)) & r1_xxreal_0(k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k9_complex1(A))),B),k4_series_1(k4_sin_cos(k9_complex1(A)))) & r1_xxreal_0(k9_complex1(k9_nat_1(k2_numbers,k10_comseq_3(k3_sin_cos(A)),B)),k4_series_1(k4_sin_cos(k9_complex1(A)))) ) ) ) )).
fof(t16_sin_cos2,axiom,( k1_funct_1(k1_sin_cos2,k5_numbers) = k5_numbers )).
fof(t16_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,k3_xcmplx_0(k7_complex1,A)) = k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A) ) )).
fof(t16_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k6_xcmplx_0(k17_sin_cos(A),k17_sin_cos(B)) = k3_xcmplx_0(2,k3_xcmplx_0(k19_sin_cos(k7_xcmplx_0(k2_xcmplx_0(A,B),2)),k17_sin_cos(k7_xcmplx_0(k6_xcmplx_0(A,B),2)))) ) ) )).
fof(t16_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => k17_sin_cos(k3_xcmplx_0(3,A)) = k2_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(4,k1_newton(k17_sin_cos(A),3))),k3_xcmplx_0(3,k17_sin_cos(A))) ) )).
fof(t16_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ( ( r1_xxreal_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B),A) & r1_xxreal_0(A,k2_xcmplx_0(k28_sin_cos,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B))) ) => r1_xxreal_0(k5_numbers,k17_sin_cos(A)) ) ) ) )).
fof(t16_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) & r1_xxreal_0(1,k1_square_1(A)) ) ) )).
fof(t16_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k6_xcmplx_0(A,B) != k5_numbers => k7_xcmplx_0(k2_xcmplx_0(k2_sin_cos2(A),k2_sin_cos2(B)),k2_xcmplx_0(k4_sin_cos2(A),k4_sin_cos2(B))) = k7_xcmplx_0(k6_xcmplx_0(k4_sin_cos2(A),k4_sin_cos2(B)),k6_xcmplx_0(k2_sin_cos2(A),k2_sin_cos2(B))) ) ) ) )).
fof(t16_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_funct_1(k16_sin_cos,A) != k5_numbers => k1_funct_1(k27_sin_cos,A) = k2_sin_cos4(A) ) ) )).
fof(t16_sincos10,axiom,( v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(t16_sppol_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t16_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_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,k1_nat_1(B,1))),k3_topreal1(2,A)) ) ) ) )).
fof(t16_sprect_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t16_sprect_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => k4_finseq_1(k2_goboard1(A)) = k4_finseq_1(A) ) )).
fof(t16_sprect_3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)),k13_matrix_0(u1_struct_0(k15_euclid(2)),B),A)) ) ) ) ) )).
fof(t16_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(t16_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(k1_square_1(B),k1_square_1(A)) ) ) ) )).
fof(t16_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t16_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k7_card_1(C),k7_card_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(C),k7_card_1(A)))) ) => ( ~ r1_xxreal_0(C,k5_numbers) => r1_xxreal_0(k3_nat_1(k1_stirl2_1(C,k7_card_1(A),D,k1_seq_4(B))),k6_xcmplx_0(C,1)) ) ) ) ) ) )).
fof(t16_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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) ) ) ) )).
fof(t16_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_tarski(B,k3_subset_1(A,C)) => r1_tarski(C,k3_subset_1(A,B)) ) ) ) )).
fof(t16_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( m1_subset_1(D,k5_finsub_1(k4_partfun1(A,B))) => ! [E] : ( m1_subset_1(E,k4_partfun1(A,B)) => ! [F] : ( 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)) ) ) ) ) ) )).
fof(t16_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => k27_substut1(A,k20_substut1(A,B)) = B ) ) )).
fof(t16_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m1_subset_1(C,k1_substut1(A)) => k2_substut2(A,k6_cqc_lang(A,B),C) = k5_sublemma(A,k2_substut2(A,B,C)) ) ) ) )).
fof(t16_supinf_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k6_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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(k6_numbers,A,k5_supinf_2(B,C),k13_supinf_2(A,B,C,D,E)),k3_supinf_2(k10_supinf_2(k6_numbers,A,B,D),k10_supinf_2(k6_numbers,A,C,E))) ) ) ) ) ) )).
fof(t16_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ~ r1_orders_2(B,D,C) => k1_symsp_1(A,B,C,D,k3_rlvect_1(B,E,F)) = k3_rlvect_1(A,k1_symsp_1(A,B,C,D,E),k1_symsp_1(A,B,C,D,F)) ) ) ) ) ) ) ) )).
fof(t16_sysrel,axiom,( ! [A] : ! [B] : k6_subset_1(k4_relat_1(k6_subset_1(A,B)),k4_relat_1(A)) = k1_xboole_0 )).
fof(t16_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( v2_metric_1(B,A) & r1_xxreal_0(k5_numbers,C) ) => r1_relat_2(k1_taxonom1(A,B,C),A) ) ) ) ) )).
fof(t16_taylor_1,axiom,( v2_funct_1(k22_sin_cos) & r2_fdiff_1(k22_sin_cos,k1_numbers) & r2_fdiff_1(k22_sin_cos,k2_subset_1(k1_numbers)) & ! [A] : ( v1_xreal_0(A) => k1_fdiff_1(k22_sin_cos,A) = k1_funct_1(k22_sin_cos,A) ) & ! [A] : ( v1_xreal_0(A) => ~ r1_xxreal_0(k1_fdiff_1(k22_sin_cos,A),k5_numbers) ) & k1_relset_1(k1_numbers,k22_sin_cos) = k2_subset_1(k1_numbers) & k2_relset_1(k1_numbers,k22_sin_cos) = k3_limfunc1(k5_numbers) )).
fof(t16_taylor_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(A,k5_numbers) => ( r2_funct_2(k4_ordinal1,k1_numbers,k1_taylor_2(k22_sin_cos,k2_rcomp_1(k4_xcmplx_0(A),A),B),k4_sin_cos(B)) & v2_series_1(k1_taylor_2(k22_sin_cos,k2_rcomp_1(k4_xcmplx_0(A),A),B)) & k1_funct_1(k22_sin_cos,B) = k4_series_1(k1_taylor_2(k22_sin_cos,k2_rcomp_1(k4_xcmplx_0(A),A),B)) ) ) ) ) )).
fof(t16_tdgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ( ( ~ ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = C ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,D) => B = C ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_analoaf(A,B,C,D,E) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r2_analoaf(A,B,D,D,C) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) )).
fof(t16_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t16_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) )).
fof(t16_tdlat_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_tdlat_3(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => v4_pre_topc(B,A) ) ) ) )).
fof(t16_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t16_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( k2_pre_topc(A,B) = B & k1_tops_1(A,B) = B ) ) ) )).
fof(t16_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ( v1_tex_2(k1_tex_2(A,B),A) & v7_struct_0(A) ) ) ) )).
fof(t16_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t16_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t16_tietze,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t16_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_tsep_1(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ( ( E = D & F = D ) => ! [G] : ( m1_connsp_2(G,B,E) => ! [H] : ( m1_connsp_2(H,C,F) => ? [I] : ( m1_connsp_2(I,k1_tsep_1(A,B,C),D) & r1_tarski(I,k2_xboole_0(G,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_toler_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( r2_hidden(C,A) => m1_toler_1(k1_tarski(C),A,B) ) ) )).
fof(t16_topalg_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v2_struct_0(D) & v2_pre_topc(D) & l1_pre_topc(D) ) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t16_topalg_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_topmetr)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_topmetr)) => ! [C] : ( m1_borsuk_2(C,k5_topmetr,A,B) => ! [D] : ( m1_borsuk_2(D,k5_topmetr,A,B) => r4_borsuk_2(k5_topmetr,A,B,C,D) ) ) ) ) )).
fof(t16_topalg_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t16_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( r1_borsuk_6(A,C,D) & r1_borsuk_6(B,E,F) ) => ! [G] : ( m1_borsuk_2(G,A,C,D) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t16_topalg_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ? [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)))) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => v2_connsp_1(C,A) ) ) ) => v1_connsp_2(A) ) ) )).
fof(t16_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,C,C) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t16_topdim_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v2_pre_topc(B) & v3_topdim_1(B) & l1_pre_topc(B) ) => ( r1_xxreal_0(k4_topdim_1(B),A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( v3_pre_topc(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ~ ( r2_hidden(C,D) & ! [E] : ( ( 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)),k6_xcmplx_0(A,1)) ) ) ) ) ) ) ) ) )).
fof(t16_topdim_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & v5_waybel23(A) & v3_topdim_1(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & v5_waybel23(B) & v3_topdim_1(B) & v3_pcomps_1(B) & l1_pre_topc(B) ) => ( k4_topdim_1(B) = k5_numbers => k4_topdim_1(k2_borsuk_1(A,B)) = k4_topdim_1(A) ) ) ) )).
fof(t16_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( r2_hidden(C,k2_topgen_1(A,B)) <=> r1_topgen_1(A,B,C) ) ) ) )).
fof(t16_topgen_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(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)))) ) => ! [C] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(E,k1_funct_1(D,E)) & ! [F] : ( ( 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) ) ) ) ) ) )).
fof(t16_topgen_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( 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) ) ) ) )).
fof(t16_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(t16_topreal3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t16_topreal4,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ( ( 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))) ) ) ) ) ) ) )).
fof(t16_topreal5,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t16_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,A) => ( k3_seq_4(k2_rcomp_1(A,B)) = A & k2_seq_4(k2_rcomp_1(A,B)) = B ) ) ) ) )).
fof(t16_topreal7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( k3_finseq_1(B) = A => r2_hidden(B,u1_struct_0(k14_euclid(A))) ) ) ) )).
fof(t16_topreal8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,A) ) => ! [C] : ( ( ~ 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 ) ) ) ) )).
fof(t16_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t16_topreala,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t16_toprealb,axiom,( ! [A] : ( 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) = k5_numbers ) ) )).
fof(t16_toprealc,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_card_1(D,B) & v1_finseq_1(D) & v3_valued_0(D) ) => k22_rvsum_1(D,k1_funct_7(k16_euclid(B),A,C)) = k3_xcmplx_0(k1_funct_1(D,A),C) ) ) ) )).
fof(t16_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => k2_toprns_1(1,A,B) = B ) ) )).
fof(t16_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k1_tops_1(A,B),B) ) ) )).
fof(t16_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t16_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => v1_tops_1(k2_struct_0(A),A) ) )).
fof(t16_tops_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( 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] : ( ( 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,k8_metric_1(B,D,F)),E) ) ) ) ) ) ) ) ) )).
fof(t16_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) )).
fof(t16_treal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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(k5_numbers,1)),u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k4_topmetr(A,B)),k4_treal_1(A,B,k2_treal_1(k5_numbers,1),k1_treal_1(k5_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(k5_numbers,1)),u1_struct_0(k4_topmetr(k5_numbers,1)),k3_struct_0(k4_topmetr(k5_numbers,1)),k1_partfun1(u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(k5_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(k5_numbers,1),k1_treal_1(k5_numbers,1)))) ) ) ) ) )).
fof(t16_trees_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t16_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m2_trees_2(B,A) => ? [C] : ( v7_ordinal1(C) & B = k2_trees_2(A,C) ) ) ) )).
fof(t16_trees_3,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(t16_trees_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) ) ) )).
fof(t16_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ( k6_trees_9(A) = k6_trees_9(B) => A = B ) ) ) )).
fof(t16_trees_a,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ! [C] : ( 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) ) ) ) )).
fof(t16_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t16_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t16_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v6_pre_topc(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t16_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(t16_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( m2_funct_2(B,k4_numbers,u1_turing_1(A),k9_funct_2(k4_numbers,u1_turing_1(A))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r1_turing_1(A,B,C,k1_nat_1(k1_nat_1(C,D),2)) => r2_turing_1(k2_finseq_4(k4_ordinal1,C,D),A,B) ) ) ) ) ) )).
fof(t16_twoscomp,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( 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)) ) ) ) ) )).
fof(t16_unialg_2,axiom,( ! [A] : ( ( ~ 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] : ( 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))) ) ) ) )).
fof(t16_unialg_3,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k12_unialg_2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k12_unialg_2(A))) => ! [D] : ( ( v1_unialg_1(D) & m1_unialg_2(D,A) ) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t16_uniroots,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_uniroots(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t16_uproots,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( k1_algseq_1(A,B) = 1 => ( r2_funct_2(k4_ordinal1,u1_struct_0(A),B,k2_algseq_1(A,k1_normsp_1(A,B,k5_numbers))) & k1_normsp_1(A,B,k5_numbers) != k4_struct_0(A) ) ) ) ) )).
fof(t16_urysohn1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_subset_1(B,k1_numbers,k1_urysohn1(k1_nat_1(A,1))) => ! [C] : ( m2_subset_1(C,k1_numbers,k1_urysohn1(k1_nat_1(A,1))) => ~ ( ~ r1_xxreal_0(C,B) & ~ r2_hidden(B,k1_urysohn1(A)) & ~ r2_hidden(C,k1_urysohn1(A)) & ~ r1_xxreal_0(k7_xcmplx_0(k1_nat_1(k6_urysohn1(k1_nat_1(A,1),B),1),k11_newton(2,k1_nat_1(A,1))),k7_xcmplx_0(k6_xcmplx_0(k6_urysohn1(k1_nat_1(A,1),C),1),k11_newton(2,k1_nat_1(A,1)))) ) ) ) ) )).
fof(t16_urysohn2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,k5_numbers) => ! [C] : ( ( ~ 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( D = k7_supinf_2(A) & E = k8_supinf_2(A) ) => ( k7_supinf_2(C) = k3_xcmplx_0(B,D) & k8_supinf_2(C) = k3_xcmplx_0(B,E) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_urysohn3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v10_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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] : ( m2_urysohn3(D,A,B,C) => ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k4_subset_1(k1_numbers,k2_urysohn1,k3_limfunc1(1))) => ( r1_xxreal_0(E,k5_numbers) | ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( r2_hidden(F,k1_funct_1(k4_urysohn3(A,B,C,D),E)) => r1_xxreal_0(k12_supinf_2(k7_urysohn3(A,B,C,D),F),E) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [E] : ( ( v5_relat_1(E,k3_qc_lang1(A)) & v3_card_1(E,B) & m2_finseq_1(E,k2_qc_lang1(A)) ) => ! [F] : ( m1_valuat_1(F,A,C) => ! [G] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t16_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k3_numbers) & ~ v1_xboole_0(A) & v1_funct_1(A) & v3_funct_1(A) ) => ? [B] : ( v1_rat_1(B) & ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => k1_funct_1(A,C) = B ) ) ) )).
fof(t16_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t16_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(t16_vectsp10,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & 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] : ( ( ~ 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] : ( ( 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) ) ) ) )).
fof(t16_vectsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( 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 ) ) ) ) ) )).
fof(t16_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(t16_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_vectsp_4(E,A,B) => ! [F] : ( m1_subset_1(F,u1_struct_0(E)) => ! [G] : ( m1_subset_1(G,u1_struct_0(E)) => ( ( F = D & G = C ) => k5_algstr_0(E,F,G) = k5_algstr_0(B,D,C) ) ) ) ) ) ) ) ) )).
fof(t16_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ( ! [D] : ( ( 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] : ( m1_vectsp_4(D,A,B) => ( k2_vectsp_5(A,B,D,C) = D => m1_vectsp_4(D,A,C) ) ) ) ) ) ) )).
fof(t16_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m2_vectsp_6(C,A,B,k1_subset_1(u1_struct_0(B))) => k4_vectsp_6(A,B,C) = k4_struct_0(B) ) ) ) )).
fof(t16_vectsp_7,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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))) ) ) ) ) )).
fof(t16_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t16_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( 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),k4_xcmplx_0(1))) ) ) ) ) )).
fof(t16_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( 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),k4_xcmplx_0(k6_complex1))) ) ) ) ) )).
fof(t16_waybel10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t16_waybel11,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t16_waybel12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t16_waybel13,axiom,( ! [A] : ( ( 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] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_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(k1_yellow_1(k7_waybel_0(k1_waybel_8(A))))))) ) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(k1_waybel_8(A)))),B,C) = k2_waybel_8(A,C) ) => v23_waybel_0(B,A,k1_yellow_1(k7_waybel_0(k1_waybel_8(A)))) ) ) ) )).
fof(t16_waybel14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t16_waybel15,axiom,( ! [A] : ( ( 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] : ( 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] : ( 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) ) ) ) ) )).
fof(t16_waybel16,axiom,( ! [A] : k3_yellow_0(k1_yellow_1(k8_waybel_0(k2_yellow_1(A)))) = k1_tarski(A) )).
fof(t16_waybel17,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_waybel_0(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( 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))) ) ) ) ) ) ) )).
fof(t16_waybel18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t16_waybel19,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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)) ) ) )).
fof(t16_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ( ( r5_waybel_1(A,B) & v4_orders_2(A) ) => v4_orders_2(B) ) ) ) )).
fof(t16_waybel21,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t16_waybel22,axiom,( ! [A] : r1_waybel22(k1_yellow_1(k8_waybel_0(k2_yellow_1(A))),k1_waybel22(A)) )).
fof(t16_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_waybel23(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t16_waybel24,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_lattice3(C) & v2_lattice3(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t16_waybel25,axiom,( ! [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] : ( ( 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)) ) ) )).
fof(t16_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t16_waybel27,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(t16_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & v1_yellow_6(B,A) & l1_waybel_0(B,A) ) => ! [C] : ( m2_yellow_6(C,A,B) => ( v1_yellow_6(C,A) & k4_yellow_6(A,B) = k4_yellow_6(A,C) ) ) ) ) )).
fof(t16_waybel29,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) ) )).
fof(t16_waybel30,axiom,( ! [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_waybel_2(A) & l1_waybel_9(A) ) => ! [B] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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)))) ) ) ) ) ) ) ) )).
fof(t16_waybel31,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t16_waybel32,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(t16_waybel33,axiom,( ! [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] : ( ( ~ v1_xboole_0(B) & v2_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v3_waybel_7(B,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))))) ) => ! [C] : ( 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) ) ) ) )).
fof(t16_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_waybel34(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_waybel34(A))) => ! [D] : ( 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))))) ) ) ) ) ) )).
fof(t16_waybel35,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v1_waybel_4(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_lattice3(A,k4_waybel35(A,B,C,D),D) ) ) ) )).
fof(t16_waybel_0,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t16_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) ) )).
fof(t16_waybel_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) )).
fof(t16_waybel_4,axiom,( ! [A] : ( ( 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),k5_yellow_1(u1_struct_0(A),k1_yellow_1(k7_waybel_0(A)))) & m1_yellow_0(k8_waybel_4(A),k5_yellow_1(u1_struct_0(A),k1_yellow_1(k7_waybel_0(A)))) ) ) )).
fof(t16_waybel_5,axiom,( ! [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] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) ) => ! [D] : ( 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))) ) ) ) ) )).
fof(t16_waybel_7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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)))) ) ) ) )).
fof(t16_waybel_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(t16_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t16_weddwitt,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => r1_tarski(u1_struct_0(k4_weddwitt(A)),u1_struct_0(A)) ) )).
fof(t16_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => v5_pre_topc(k4_weierstr(A,B),k3_pcomps_1(A),k3_topmetr) ) ) )).
fof(t16_wellord1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( v6_relat_2(B) => v6_relat_2(k2_wellord1(B,A)) ) ) )).
fof(t16_wellord2,axiom,( ! [A] : k1_wellord2(k1_tarski(A)) = k1_tarski(k4_tarski(A,A)) )).
fof(t16_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_nat_d(C,A) & k3_int_2(A,B) = 1 ) => k3_int_2(C,B) = 1 ) ) ) ) )).
fof(t16_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : k3_xboole_0(k3_xboole_0(A,B),C) = k3_xboole_0(A,k3_xboole_0(B,C)) )).
fof(t16_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k4_xboolean(A,k3_xboolean(k6_xboolean(A,B))) = k4_xboolean(A,k3_xboolean(B)) ) ) )).
fof(t16_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k6_xcmplx_0(B,A) = B => A = k5_numbers ) ) ) )).
fof(t16_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t16_xtuple_0,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_tarski(k13_xtuple_0(A),k13_xtuple_0(B)) ) )).
fof(t16_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( k4_xxreal_0(A,B) = A | k4_xxreal_0(A,B) = B ) ) ) )).
fof(t16_xxreal_1,axiom,( ! [A] : ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(A,k4_xxreal_1(B,C)) => ( r2_hidden(A,k1_xxreal_1(B,C)) & A != B & A != C ) ) ) ) )).
fof(t16_xxreal_2,axiom,( ! [A] : ( ( v3_membered(A) & ~ v1_xboole_0(A) ) => ( v4_xxreal_2(A) => r2_hidden(k1_xxreal_2(A),k1_numbers) ) ) )).
fof(t16_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( k1_xxreal_3(A,B) = k1_xxreal_0 & A != k1_xxreal_0 & B != k1_xxreal_0 ) ) ) )).
fof(t16_yellow10,axiom,( ! [A] : ( ( v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t16_yellow12,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t16_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_pre_topc(A,B)) <=> ! [D] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(E,D) & r1_xboole_0(B,E) ) ) ) ) ) ) ) )).
fof(t16_yellow14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t16_yellow15,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ! [C] : ! [D] : ( ( r2_hidden(C,k2_yellow15(A,B)) & r2_hidden(D,k2_yellow15(A,B)) ) => ( C = D | r1_xboole_0(C,D) ) ) ) )).
fof(t16_yellow16,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) )).
fof(t16_yellow17,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ~ ( r2_hidden(C,k2_waybel18(A,B)) & ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t16_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t16_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_subset_1(B,u1_struct_0(k2_yellow_1(k2_struct_0(A)))) & v2_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))))) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t16_yellow20,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,B) & v1_funct_1(E) & v1_partfun1(E,B) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,B) & v1_funct_1(F) & v1_partfun1(F,B) ) => ! [G] : ( ( 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] : ( ( 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] : ( m2_pboole(I,A,C,D) => ! [J] : ( m2_pboole(J,B,E,F) => ( ! [K] : ( ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t16_yellow21,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( ( 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) ) ) ) ) ) )).
fof(t16_yellow_0,axiom,( ! [A] : ( ( v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( r2_yellow_0(A,B) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r1_lattice3(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_lattice3(A,B,D) => r1_orders_2(A,D,C) ) ) ) ) ) )).
fof(t16_yellow_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_yellow_0(k1_yellow_1(A)) => r2_hidden(k1_setfam_1(A),A) ) ) )).
fof(t16_yellow_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t16_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t16_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t16_yellow_5,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ( v2_waybel_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t16_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & v1_yellow_6(B,A) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k2_waybel_0(A,B,C) = k4_yellow_6(A,B) ) ) ) )).
fof(t16_yellow_7,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_lattice3(A) <=> v1_lattice3(k7_lattice3(A)) ) ) )).
fof(t16_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(B,A) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t16_yellow_9,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t16_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(A)) ) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( ( 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(D,k1_funct_2(G,B)) & r1_tarski(C,k1_funct_2(k4_subset_1(k4_ordinal1,G,k6_domain_1(k4_ordinal1,F)),B)) & r2_hidden(C,E) ) => ( r2_hidden(F,G) | r2_hidden(a_5_1_zf_fund1(A,B,C,D,F),E) ) ) ) ) ) ) ) ) ) )).
fof(t16_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => k1_funct_1(k7_zf_lang(A,B),1) = 3 ) ) )).
fof(t16_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ! [E] : ( m2_subset_1(E,k4_ordinal1,k1_zf_lang) => ! [F] : ( m2_subset_1(F,k4_ordinal1,k1_zf_lang) => ! [G] : ( m2_subset_1(G,k4_ordinal1,k1_zf_lang) => ( k16_zf_lang(C,D,E,A) = k14_zf_lang(G,F,B) => ( C = G & D = F & k8_zf_lang(E,A) = B ) ) ) ) ) ) ) ) ) )).
fof(t16_zf_model,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ( r1_zf_model(A,B,k8_zf_lang(D,C)) <=> ! [E] : ( ( 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] : ( m2_subset_1(F,k4_ordinal1,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) ) ) ) ) ) ) ) )).
fof(t16_zf_refle,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( v3_ordinal1(B) & m1_subset_1(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t16_zfmisc_1,axiom,( ! [A] : ! [B] : k4_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k1_xboole_0 )).
fof(t16_zfmodel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_ordinal1(A) => ( ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r1_xboole_0(k1_enumset1(k2_zf_lang(k5_numbers),k2_zf_lang(1),k2_zf_lang(2)),k2_zf_model(B)) => r2_zf_model(A,k11_zf_model(B)) ) ) <=> ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_zfmodel1(B,A) => ! [C] : ( r2_hidden(C,A) => r2_hidden(k7_relat_1(B,C),A) ) ) ) ) ) ) )).
fof(t16_zfmodel2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( 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(k5_numbers),k2_zf_model(C)) & r1_zf_model(A,D,k8_zf_lang(k2_zf_lang(3),k13_zf_lang(k2_zf_lang(k5_numbers),k8_zf_lang(k2_zf_lang(4),k12_zf_lang(C,k4_zf_lang(k2_zf_lang(4),k2_zf_lang(k5_numbers))))))) & ! [E] : ( ( v1_zf_lang(E) & m2_finseq_1(E,k4_ordinal1) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_ordinal1) => ~ ( ~ r1_xxreal_0(B,G) & r2_hidden(k2_zf_lang(G),k4_zf_lang1(E)) & G != 3 & G != 4 ) ) & ~ r2_hidden(k2_zf_lang(k5_numbers),k2_zf_model(E)) & r1_zf_model(A,F,k8_zf_lang(k2_zf_lang(3),k13_zf_lang(k2_zf_lang(k5_numbers),k8_zf_lang(k2_zf_lang(4),k12_zf_lang(E,k4_zf_lang(k2_zf_lang(4),k2_zf_lang(k5_numbers))))))) & r2_funct_2(A,A,k1_zfmodel1(C,A,D),k1_zfmodel1(E,A,F)) ) ) ) ) ) ) ) ) )).
fof(t16_zfrefle1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t16_zmodul01,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(t16_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),k4_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_numbers))) ) => k20_zmodul02(A,k2_finseq_4(u1_struct_0(A),B,C),D) = k2_finseq_4(u1_struct_0(A),k1_zmodul01(A,B,k3_funct_2(u1_struct_0(A),k4_numbers,D,B)),k1_zmodul01(A,C,k3_funct_2(u1_struct_0(A),k4_numbers,D,C))) ) ) ) ) )).
fof(t16_zmodul03,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_zmodul02(C,A) & r1_tarski(C,u1_struct_0(B)) ) => ( v1_zmodul02(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) ) ) ) ) )).
fof(t170_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( 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) ) ) ) ) )).
fof(t170_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ~ ( r2_hidden(C,k20_member_1(A,B)) & ! [D] : ( m1_subset_1(D,k6_numbers) => ~ ( C = k3_xxreal_3(D,B) & r2_hidden(D,A) ) ) ) ) ) )).
fof(t170_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r1_xboole_0(k10_xtuple_0(A),k10_xtuple_0(B)) => r1_xboole_0(A,B) ) ) ) )).
fof(t170_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t170_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(C,1) & r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) & k2_xcmplx_0(k3_xcmplx_0(C,A),k3_xcmplx_0(k6_xcmplx_0(1,C),B)) = k5_numbers & ~ ( C = k5_numbers & B = k5_numbers ) & ~ ( C = 1 & A = k5_numbers ) & ~ ( A = k5_numbers & B = k5_numbers ) ) ) ) ) )).
fof(t170_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t170_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ( v6_zf_lang(A) <=> v6_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) )).
fof(t171_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ! [D] : ! [E] : ( r1_glib_000(B,C,D,E) => k2_glib_001(A,C,D,E) = k2_glib_001(B,C,D,E) ) ) ) )).
fof(t171_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => k20_member_1(A,B) = k4_member_1(k18_member_1(A,B)) ) ) )).
fof(t171_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r1_tarski(A,B) => k5_relat_1(k6_subset_1(C,k5_relat_1(C,B)),A) = k1_xboole_0 ) ) )).
fof(t171_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t171_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(A,B) ) => r1_xxreal_0(A,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(1,C),A),k3_xcmplx_0(C,B))) ) ) ) ) )).
fof(t171_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t171_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,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) ) ) ) ) )).
fof(t172_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m3_glib_001(D,B) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t172_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => k18_member_1(A,B) = k4_member_1(k20_member_1(A,B)) ) ) )).
fof(t172_relat_1,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) ) => v4_relat_1(C,B) ) ) )).
fof(t172_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t172_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(C,1) & r1_xxreal_0(A,B) ) => r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(1,C),A),k3_xcmplx_0(C,B)),B) ) ) ) ) )).
fof(t172_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t172_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,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) ) ) ) ) ) )).
fof(t173_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( 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) ) ) ) ) ) ) )).
fof(t173_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t173_relat_1,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,A) ) => v5_relat_1(C,B) ) ) )).
fof(t173_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t173_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(k5_numbers,D) & r1_xxreal_0(D,1) & r1_xxreal_0(A,B) & r1_xxreal_0(A,C) ) => r1_xxreal_0(A,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(1,D),B),k3_xcmplx_0(D,C))) ) ) ) ) ) )).
fof(t173_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t173_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,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) ) ) ) ) ) ) )).
fof(t174_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t174_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t174_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r1_tarski(A,B) <=> r1_tarski(A,k5_relat_1(B,k9_xtuple_0(A))) ) ) ) )).
fof(t174_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k3_xcmplx_0(k4_xcmplx_0(A),B) = k4_xcmplx_0(k3_xcmplx_0(A,B)) ) ) )).
fof(t174_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(k5_numbers,D) & r1_xxreal_0(D,1) & r1_xxreal_0(B,A) & r1_xxreal_0(C,A) ) => r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(1,D),B),k3_xcmplx_0(D,C)),A) ) ) ) ) ) )).
fof(t174_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(A,D) & r1_xxreal_0(C,B) & r1_xxreal_0(D,C) ) => k2_xboole_0(k1_xxreal_1(A,C),k1_xxreal_1(D,B)) = k1_xxreal_1(A,B) ) ) ) ) ) )).
fof(t174_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ( v8_zf_lang(A) <=> v8_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) )).
fof(t175_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( ( r5_glib_000(A,B) & m1_glib_001(C,A) ) => m1_glib_001(C,B) ) ) ) )).
fof(t175_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t175_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,B) ) => r1_tarski(C,k2_zfmisc_1(A,B)) ) )).
fof(t175_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k3_xcmplx_0(k4_xcmplx_0(A),B) = k3_xcmplx_0(A,k4_xcmplx_0(B)) ) ) )).
fof(t175_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( r1_xxreal_0(k5_numbers,D) & r1_xxreal_0(D,1) & ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(C,A) & r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(1,D),B),k3_xcmplx_0(D,C)),A) ) ) ) ) ) )).
fof(t175_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(A,D) & r1_xxreal_0(C,B) ) => ( r1_xxreal_0(C,D) | k2_xboole_0(k2_xxreal_1(A,C),k3_xxreal_1(D,B)) = k1_xxreal_1(A,B) ) ) ) ) ) ) )).
fof(t175_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ( v9_zf_lang(A) <=> v9_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) )).
fof(t176_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( ( r5_glib_000(A,B) & m2_glib_001(C,A) ) => m2_glib_001(C,B) ) ) ) )).
fof(t176_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( r2_hidden(C,A) => r2_hidden(k6_xcmplx_0(C,B),k21_member_1(A,B)) ) ) ) ) )).
fof(t176_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => r1_tarski(k9_xtuple_0(k6_relat_1(A,B)),k9_xtuple_0(B)) ) )).
fof(t176_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k3_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k3_xcmplx_0(A,B) ) ) )).
fof(t176_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( r1_xxreal_0(k5_numbers,D) & r1_xxreal_0(D,1) & ~ r1_xxreal_0(A,B) & ~ r1_xxreal_0(A,C) & r1_xxreal_0(A,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(1,D),B),k3_xcmplx_0(D,C))) ) ) ) ) ) )).
fof(t176_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(A,D) & r1_xxreal_0(D,C) ) => ( r1_xxreal_0(B,C) | k2_xboole_0(k1_xxreal_1(A,C),k2_xxreal_1(D,B)) = k2_xxreal_1(A,B) ) ) ) ) ) ) )).
fof(t176_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ( v10_zf_lang(A) => v10_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) )).
fof(t177_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( ( r5_glib_000(A,B) & m3_glib_001(C,A) ) => m3_glib_001(C,B) ) ) ) )).
fof(t177_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => k21_member_1(A,B) = a_2_13_member_1(A,B) ) ) )).
fof(t177_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ! [D] : ( v1_relat_1(D) => ( r1_xboole_0(A,B) => r1_xboole_0(k5_relat_1(C,A),k5_relat_1(D,B)) ) ) ) )).
fof(t177_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k4_xcmplx_0(k3_xcmplx_0(A,k4_xcmplx_0(B))) = k3_xcmplx_0(A,B) ) ) )).
fof(t177_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(1,D) & r1_xxreal_0(A,B) & ~ r1_xxreal_0(C,A) & r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(1,D),B),k3_xcmplx_0(D,C)),A) ) ) ) ) ) )).
fof(t177_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(C,B) & r1_xxreal_0(D,C) ) => ( r1_xxreal_0(D,A) | k2_xboole_0(k3_xxreal_1(A,C),k1_xxreal_1(D,B)) = k3_xxreal_1(A,B) ) ) ) ) ) ) )).
fof(t177_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ( v11_zf_lang(A) <=> v11_zf_lang(k6_zf_lang1(A,B,C)) ) ) ) ) )).
fof(t178_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ! [D] : ! [E] : ( r5_glib_000(A,B) => k2_glib_001(A,D,E,C) = k2_glib_001(B,D,E,C) ) ) ) )).
fof(t178_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ~ ( r2_hidden(C,k21_member_1(A,B)) & ! [D] : ( v1_xcmplx_0(D) => ~ ( C = k6_xcmplx_0(D,B) & r2_hidden(D,A) ) ) ) ) ) )).
fof(t178_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => r1_tarski(k6_relat_1(A,B),k5_relat_1(B,k8_relat_1(B,A))) ) )).
fof(t178_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k4_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(A),B)) = k3_xcmplx_0(A,B) ) ) )).
fof(t178_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(1,D) & ~ r1_xxreal_0(A,B) & r1_xxreal_0(C,A) & r1_xxreal_0(A,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(1,D),B),k3_xcmplx_0(D,C))) ) ) ) ) ) )).
fof(t178_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(D,C) => ( r1_xxreal_0(D,A) | r1_xxreal_0(B,C) | k2_xboole_0(k3_xxreal_1(A,C),k2_xxreal_1(D,B)) = k4_xxreal_1(A,B) ) ) ) ) ) ) )).
fof(t178_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,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) ) ) ) ) ) )).
fof(t179_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t179_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ( r1_tarski(A,B) <=> r1_tarski(k21_member_1(A,C),k21_member_1(B,C)) ) ) ) ) )).
fof(t179_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( ( k9_xtuple_0(A) = k1_tarski(B) & k10_xtuple_0(A) = k1_tarski(C) ) => A = k1_tarski(k4_tarski(B,C)) ) ) )).
fof(t179_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(k4_xcmplx_0(1),A) = k4_xcmplx_0(A) ) )).
fof(t179_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(C,1) & r1_xxreal_0(A,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(1,C),A),k3_xcmplx_0(C,B))) ) => ( r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(1,C),A),k3_xcmplx_0(C,B)),B) | C = k5_numbers ) ) ) ) ) )).
fof(t179_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(A,D) & r1_xxreal_0(C,B) & r1_xxreal_0(D,B) ) => k2_xboole_0(k2_xboole_0(k2_xxreal_1(A,C),k1_xxreal_1(C,D)),k3_xxreal_1(D,B)) = k1_xxreal_1(A,B) ) ) ) ) ) )).
fof(t179_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,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) ) ) ) ) ) )).
fof(t17_abcmiz_0,axiom,( ! [A] : ( l2_abcmiz_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t17_abcmiz_1,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_abcmiz_1)) ) => ! [B] : ( v7_ordinal1(B) => r2_hidden(k4_tarski(k1_abcmiz_1(A),B),k2_abcmiz_1) ) ) )).
fof(t17_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & v1_abcmiz_a(A) & l1_msualg_1(A) ) => ! [B] : ( 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] : ( m1_subset_1(C,k2_abcmiz_1) => ~ ( C = k1_xtuple_0(k1_funct_1(B,k1_xboole_0)) & B = k35_abcmiz_1(C,A) ) ) ) ) ) )).
fof(t17_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => A = k3_xcmplx_0(k9_complex1(A),k2_absvalue(A)) ) )).
fof(t17_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t17_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) => ! [H] : ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(A))) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(A))) => ! [J] : ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(F,G) & r2_hidden(B,G) & r2_hidden(C,G) & r2_hidden(F,H) & r2_hidden(D,H) & r2_hidden(E,H) & ~ r2_hidden(F,I) & ~ r2_hidden(F,J) & G != H & r2_hidden(B,I) & r2_hidden(D,I) & r2_hidden(C,J) & r2_hidden(E,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] : ( m1_subset_1(K,u1_struct_0(A)) => ~ ( r2_hidden(K,I) & r2_hidden(K,J) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => k1_afinsq_1(k1_ordinal4(A,B)) = k1_nat_1(k1_afinsq_1(A),k1_afinsq_1(B)) ) ) )).
fof(t17_afinsq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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 ) ) ) )).
fof(t17_afproj,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t17_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_afvect0(A,B,C,C) <=> B = C ) ) ) ) )).
fof(t17_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_alg_1(B,A) => r1_alg_1(A,k4_alg_1(A,B),k5_alg_1(A,B)) ) ) )).
fof(t17_algspec1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r1_tarski(A,B) => k5_relat_1(k1_algspec1(B,C),A) = k1_algspec1(A,C) ) ) )).
fof(t17_algstr_4,axiom,( ! [A] : k11_algstr_4(A,1) = A )).
fof(t17_altcat_1,axiom,( v14_altcat_1(k7_altcat_1(k1_tarski(k5_numbers))) & v13_struct_0(k7_altcat_1(k1_tarski(k5_numbers)),1) )).
fof(t17_altcat_2,axiom,( ! [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) & l1_cat_1(A) ) => v12_altcat_1(k4_altcat_2(A)) ) )).
fof(t17_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l2_altcat_1(B) ) => ! [C] : ( ( v11_functor0(C,A,B) & l2_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(G,k1_altcat_1(A,D,E)) => F != k8_functor0(A,B,C,D,E,G) ) ) ) ) ) ) ) ) )).
fof(t17_ami_2,axiom,( k9_xtuple_0(k3_relat_1(k3_ami_2,k4_ami_2)) = k1_ami_2 )).
fof(t17_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ~ v2_extpro_1(k3_ami_3(A,B),k7_card_1(2),k1_ami_3) ) ) )).
fof(t17_ami_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( ~ 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(k7_card_1(2),k1_ami_3)) & v1_finset_1(B) & v4_extpro_1(B,k7_card_1(2),k1_ami_3,A) ) => ! [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(C,u1_struct_0(k1_ami_3)) ) => ! [D] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ( ( r1_tarski(B,C) & r1_tarski(B,D) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_ami_3)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_ami_3)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( ( r1_tarski(A,E) & r1_tarski(A,F) ) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v1_ami_2(H) & m1_subset_1(H,u1_struct_0(k1_ami_3)) ) => ! [I] : ( ( v1_ami_2(I) & m1_subset_1(I,u1_struct_0(k1_ami_3)) ) => ! [J] : ( m1_subset_1(J,u1_compos_1(k1_ami_3)) => ( ( J = k3_extpro_1(k7_card_1(2),k1_ami_3,E,k5_extpro_1(k7_card_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(k7_card_1(2),k1_ami_3,E,C,G),H),k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,E,C,G),I)) = k2_xcmplx_0(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,F,D,G),H),k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,F,D,G),I)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_ami_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k1_amistd_1(k7_card_1(2),k1_ami_3,B,k8_ami_3(C,A)) = k2_tarski(C,k1_ordinal1(B)) ) ) ) )).
fof(t17_ami_wstd,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_setfam_1(B) => k1_ami_wstd(B,k4_amistd_1(B),A) = A ) ) )).
fof(t17_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ( ~ ! [D] : ( ( 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)) ) ) ) ) )).
fof(t17_analmetr,axiom,( ! [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) ) => u1_analoaf(k2_diraf(k2_analoaf(A))) = k1_diraf(u1_struct_0(A),k1_analoaf(A)) ) )).
fof(t17_analoaf,axiom,( ! [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) ) => ( ~ ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = C ) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r1_analoaf(A,B,C,D,E) & r1_analoaf(A,B,D,C,E) & C != E ) ) ) ) ) ) )).
fof(t17_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_analmetr(A,F,G) & r1_analoaf(A,B,D,C,E) ) => r1_analoaf(A,k1_analort(A,F,G,B),k1_analort(A,F,G,D),k1_analort(A,F,G,C),k1_analort(A,F,G,E)) ) ) ) ) ) ) ) ) )).
fof(t17_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ~ r2_anproj_1(A,B,C,D) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( ~ v9_struct_0(G,A) & ~ r2_anproj_1(A,E,F,G) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_anproj_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( m2_funct_2(C,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [D] : ( m2_funct_2(D,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [E] : ( m2_funct_2(E,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,A) => ! [I] : ( m1_subset_1(I,A) => ( ( k3_funct_2(A,k1_numbers,B,F) = 1 & ! [J] : ( r2_hidden(J,A) => ( J = F | k1_funct_1(B,J) = k5_numbers ) ) & k3_funct_2(A,k1_numbers,C,G) = 1 & ! [J] : ( r2_hidden(J,A) => ( J = G | k1_funct_1(C,J) = k5_numbers ) ) & k3_funct_2(A,k1_numbers,D,H) = 1 & ! [J] : ( r2_hidden(J,A) => ( J = H | k1_funct_1(D,J) = k5_numbers ) ) & k3_funct_2(A,k1_numbers,E,I) = 1 & ! [J] : ( r2_hidden(J,A) => ( J = I | k1_funct_1(E,J) = k5_numbers ) ) ) => ( F = G | F = H | F = I | G = H | G = I | H = I | ! [J] : ( v1_xreal_0(J) => ! [K] : ( v1_xreal_0(K) => ! [L] : ( v1_xreal_0(L) => ! [M] : ( v1_xreal_0(M) => ( k1_binop_1(k5_funcsdom(A),k1_binop_1(k5_funcsdom(A),k1_binop_1(k5_funcsdom(A),k1_funct_1(k7_funcsdom(A),k4_tarski(J,B)),k1_funct_1(k7_funcsdom(A),k4_tarski(K,C))),k1_funct_1(k7_funcsdom(A),k4_tarski(L,D))),k1_funct_1(k7_funcsdom(A),k4_tarski(M,E))) = k8_funcsdom(A) => ( J = k5_numbers & K = k5_numbers & L = k5_numbers & M = k5_numbers ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : k2_xboole_0(k1_tarski(A),k7_enumset1(B,C,D,E,F,G,H,I,J)) = k8_enumset1(A,B,C,D,E,F,G,H,I,J) )).
fof(t17_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v19_aofa_a00(B,A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( C = k10_subset_1(k1_funct_1(u7_aofa_a00(A),7),u4_struct_0(A)) => ( k1_msualg_1(A,C) = k2_finseq_4(u1_struct_0(A),B,B) & k2_msualg_1(A,C) = B ) ) ) ) ) )).
fof(t17_aofa_i00,axiom,( ! [A] : ( m4_aofa_i00(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k9_funct_2(k4_ordinal1,k4_numbers),k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_funct_2(k4_ordinal1,k4_numbers),k4_ordinal1))) ) => m2_aofa_i00(B,k7_freealg(k19_aofa_000,k26_aofa_i00),k4_ordinal1,k1_aofa_i00(k9_funct_2(k4_ordinal1,k4_numbers),k5_numbers,k5_numbers),A) ) ) )).
fof(t17_armstrng,axiom,( ! [A] : 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)) )).
fof(t17_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ( k1_arytm_0(k2_arytm_0(A,A),k2_arytm_0(B,B)) = k5_numbers => A = k5_numbers ) ) ) )).
fof(t17_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( 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)) ) ) ) ) )).
fof(t17_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_arytm_2)) => ( ( r2_hidden(k5_ordinal1,A) & ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( 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) ) ) )).
fof(t17_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ! [C] : ( ( v3_ordinal1(C) & v7_ordinal1(C) ) => k3_arytm_3(k9_ordinal3(A,C),k9_ordinal3(B,C)) = k9_ordinal3(k3_arytm_3(A,B),C) ) ) ) )).
fof(t17_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v4_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v4_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_limfunc1(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) => ( ~ r2_hidden(A,k6_asympt_0(B)) & r2_hidden(B,k6_asympt_0(A)) ) ) ) ) )).
fof(t17_asympt_1,axiom,( ~ r1_xxreal_0(k7_xcmplx_0(159,100),k3_power(2,3)) => ( r2_hidden(k3_asympt_1(k3_power(2,3)),k6_asympt_0(k3_asympt_1(k7_xcmplx_0(159,100)))) & ~ r2_hidden(k3_asympt_1(k3_power(2,3)),k7_asympt_0(k3_asympt_1(k7_xcmplx_0(159,100)))) & ~ r2_hidden(k3_asympt_1(k3_power(2,3)),k8_asympt_0(k3_asympt_1(k7_xcmplx_0(159,100)))) ) )).
fof(t17_autalg_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,C) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t17_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_funct_2(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t17_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(t17_bcialg_1,axiom,( ! [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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) )).
fof(t17_bcialg_3,axiom,( ! [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) ) => ( v4_bcialg_3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t17_bcialg_4,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t17_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( v8_bcialg_1(E) & m1_bcialg_5(E,A,B,C,D) ) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( v8_bcialg_1(E) & m1_bcialg_5(E,k1_nat_1(A,F),B,C,k1_nat_1(D,F)) ) ) ) ) ) ) ) )).
fof(t17_bcialg_6,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( v7_ordinal1(C) => k3_bcialg_6(A,C,k2_bcialg_1(A,B)) = k2_bcialg_1(A,k3_bcialg_6(A,C,B)) ) ) ) )).
fof(t17_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( ! [C] : ( 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) ) ) ) ) )).
fof(t17_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_bhsp_1(A,k3_rlvect_1(A,B,C),k5_algstr_0(A,B,C)) = k6_xcmplx_0(k2_bhsp_1(A,B,B),k2_bhsp_1(A,C,C)) ) ) ) )).
fof(t17_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(t17_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => ( 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) ) ) ) ) ) )).
fof(t17_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k3_bhsp_4(A,B,1) = k3_rlvect_1(A,k1_normsp_1(A,B,k5_numbers),k1_normsp_1(A,B,1)) ) ) )).
fof(t17_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t17_binari_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t17_binari_3,axiom,( 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) )).
fof(t17_binari_4,axiom,( ! [A] : ( v1_xboolean(A) => k5_xboolean(k8_margrel1,A) = k8_margrel1 ) )).
fof(t17_binarith,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k6_margrel1) ) => ! [D] : ( m1_subset_1(D,k6_margrel1) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( v7_ordinal1(F) => ( r2_hidden(F,k2_finseq_1(A)) => k7_partfun1(k6_margrel1,k4_binarith(k2_xcmplx_0(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) ) ) ) ) ) ) ) )).
fof(t17_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_algstr_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k5_binom(A,B,C) = k6_binom(A,B,C) ) ) ) )).
fof(t17_binop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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) ) ) ) )).
fof(t17_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( v7_ordinal1(C) => ( 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))) ) ) ) ) )).
fof(t17_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( ~ r4_boolealg(A,B,D) & r3_lattices(A,C,D) & r4_boolealg(A,B,C) ) ) ) ) ) )).
fof(t17_bor_cant,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) = k5_numbers & k1_funct_1(C,k4_kurato_0(A,D)) = 1 ) ) ) ) ) ) ) )).
fof(t17_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k2_borsuk_1(A,B))))) => ! [D] : ~ ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t17_borsuk_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v1_compts_1(B) & l1_pre_topc(B) ) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t17_borsuk_4,axiom,( ! [A] : ( 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)) ) ) )).
fof(t17_borsuk_5,axiom,( ! [A] : ( v1_rat_1(A) => ! [B] : ( ( v1_xreal_0(B) & ~ v1_rat_1(B) ) => ~ v1_rat_1(k2_xcmplx_0(A,B)) ) ) )).
fof(t17_borsuk_7,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( 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),k1_square_1(A)) ) ) )).
fof(t17_bspace,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k2_bspace)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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)) ) ) ) )).
fof(t17_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t17_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t17_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) ) => ! [H] : ! [I] : ! [J] : ! [K] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t17_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t17_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)))) ) ) ) )).
fof(t17_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t17_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t17_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t17_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => r1_bvfunc_1(A,k6_bvfunc_2(A,B,C,D),k7_bvfunc_2(A,B,C,E)) ) ) ) ) ) )).
fof(t17_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t17_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t17_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t17_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t17_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t17_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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_comseq_2(k2_partfun1(A,k1_numbers,B,A)) => v4_xxreal_2(k9_c0sp1(A,B)) ) ) ) )).
fof(t17_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_c0sp2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_c0sp2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_c0sp2(A))) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(H,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k1_numbers,G,H) = k4_real_1(k3_funct_2(u1_struct_0(A),k1_numbers,E,H),k3_funct_2(u1_struct_0(A),k1_numbers,F,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_valuat_1(C,A,B) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [E] : ( m2_finseq_1(E,k3_cqc_lang(A)) => ( ~ r1_xxreal_0(k3_finseq_1(E),k5_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) ) ) ) ) ) ) ) )).
fof(t17_calcul_2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => k1_relset_1(k4_ordinal1,k15_finseq_1(k5_relset_1(k4_ordinal1,k3_cqc_lang(A),k8_finseq_1(k3_cqc_lang(A),C,B),k2_calcul_2(k3_finseq_1(C),k3_finseq_1(B))))) = k1_relset_1(k4_ordinal1,B) ) ) ) )).
fof(t17_cantor_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_pre_topc(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_pre_topc(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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 ) ) ) ) )).
fof(t17_card_1,axiom,( ! [A] : ( v3_ordinal1(A) => r2_hidden(A,k2_card_1(A)) ) )).
fof(t17_card_3,axiom,( ! [A] : ! [B] : ! [C] : r1_tarski(k5_card_3(A,k3_xboole_0(B,C)),k3_xboole_0(k5_card_3(A,B),k5_card_3(A,C))) )).
fof(t17_card_4,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t17_card_5,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( ( ~ v1_finset_1(B) & v1_card_1(B) ) => ( ( r1_ordinal1(B,A) | r2_hidden(B,A) ) => ( ~ v1_finset_1(A) & v1_card_1(A) ) ) ) ) )).
fof(t17_card_fin,axiom,( ! [A] : ! [B] : ! [C] : ( v1_finset_1(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t17_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_tarski(C,B) => r1_tarski(k2_card_lar(A,C),k1_ordinal1(B)) ) ) ) ) )).
fof(t17_cardfin2,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ~ ( k5_card_1(A) = 23 & k5_card_1(B) = 365 & r1_xxreal_0(k2_nat_1(2,k5_card_1(k4_cardfin2(A,B))),k5_card_1(k9_funct_2(A,B))) ) ) ) )).
fof(t17_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t17_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,C,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,C,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,B))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(C,C),C))) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t17_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(B)) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t17_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t17_cat_5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_cat_5(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ~ ( ! [C] : ( m1_cat_5(C,A) => ! [D] : ( m1_cat_5(D,A) => ! [E] : ( m1_cat_5(E,A) => ! [F] : ( m2_cat_1(F,C,D) => ! [G] : ( 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] : ( m1_cat_5(C,A) => r2_hidden(k10_cat_1(C),B) ) & ! [C] : ( ( ~ 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] : ( m1_cat_5(D,A) => ! [E] : ( m1_cat_5(E,A) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t17_catalan1,axiom,( ! [A] : ( v7_ordinal1(A) => r1_xxreal_0(k5_numbers,k1_catalan1(A)) ) )).
fof(t17_catalan2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ~ ( v1_catalan2(A) & a_1_0_catalan2(A) = k1_xboole_0 & ~ r1_xxreal_0(k1_afinsq_1(A),k5_numbers) & ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ~ ( A = k1_catalan2(k5_afinsq_1(k5_numbers),B) & v1_catalan2(B) ) ) ) ) )).
fof(t17_catalg_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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] : ( m1_subset_1(C,A) => B != k8_catalg_1(A,C) ) ) ) ) )).
fof(t17_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v10_algstr_0(k5_cayldick(A,B,C),k4_cayldick(A)) => ( v10_algstr_0(B,A) & v10_algstr_0(C,A) ) ) ) ) ) )).
fof(t17_cc0sp1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(t17_cc0sp2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t17_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( m2_valued_0(B,k2_numbers,A) & v2_comseq_2(A) ) => v2_comseq_2(B) ) ) ) )).
fof(t17_cfuncdom,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ? [C] : ( m2_funct_2(C,B,k2_numbers,k9_funct_2(B,k2_numbers)) & ? [D] : ( m2_funct_2(D,B,k2_numbers,k9_funct_2(B,k2_numbers)) & ! [E] : ( r2_hidden(E,B) => ( ( E = A => k1_funct_1(C,E) = k6_complex1 ) & ( E != A => k1_funct_1(C,E) = k5_numbers ) ) ) & ! [E] : ( r2_hidden(E,B) => ( ( E = A => k1_funct_1(D,E) = k5_numbers ) & ( E != A => k1_funct_1(D,E) = k6_complex1 ) ) ) ) ) ) )).
fof(t17_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( v1_xcmplx_0(D) => 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)) ) ) ) ) )).
fof(t17_cgames_1,axiom,( ! [A] : ! [B] : ( v2_cgames_1(B) => ( r2_hidden(A,k8_cgames_1(B)) => ( v2_cgames_1(A) & l1_cgames_1(A) ) ) ) )).
fof(t17_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( A = k7_finseq_1(k9_finseq_1(C),B) => ! [D] : ( ( v7_ordinal1(D) & ~ v8_ordinal1(D) ) => k1_chord(A,k1_nat_1(D,1)) = k1_chord(B,D) ) ) ) ) )).
fof(t17_circcmb2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & ~ v11_struct_0(C) & v2_msafree2(C) & l1_msualg_1(C) ) => ( C = k2_circcomb(A,B) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(C,F))) => ( v1_circuit2(G,C,F) => ( ! [H] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_circcmb3,axiom,( ! [A] : ( ( v4_circcmb3(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msafree2(B,A) & v5_circcmb3(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_finset_1(D) ) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t17_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_msualg_1(C) ) => ( ( r1_circcomb(A,C) & B = k2_circcomb(A,C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,k3_msafree2(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( D = E => ( r2_hidden(E,k3_msafree2(B)) & k4_msafree2(B,E) = k4_msafree2(A,D) ) ) ) ) ) ) ) ) ) )).
fof(t17_circled1,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( 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),k5_numbers) & r2_hidden(C,k3_rlvect_2(A,B)) ) ) ) ) )).
fof(t17_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v4_msafree2(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( ~ 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)) ) ) ) ) )).
fof(t17_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k6_circuit1(A,B,C),k7_circuit1(A,B)) ) ) ) )).
fof(t17_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_pboole(C,k2_msafree2(A),k7_funcop_1(k2_msafree2(A),k4_ordinal1),k5_relat_1(u3_msualg_1(A,B),k2_msafree2(A))) => ! [D] : ( m1_msafree2(D,A,B) => ( ( v3_funct_1(k9_funct_6(C)) & D = k1_funct_1(k9_funct_6(C),k5_numbers) ) => ( v1_xboole_0(k2_msafree2(A)) | ! [E] : ( m1_subset_1(E,k4_card_3(u3_msualg_1(A,B))) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( G = k7_circuit1(A,B) => k1_funct_1(k9_nat_1(k4_card_3(u3_msualg_1(A,B)),k9_circuit2(A,B,C,E),G),F) = k5_circuit2(A,B,F,D) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ( ( v1_pdiff_7(C,A) & D = k7_funcop_1(C,E) & r1_tarski(k2_relset_1(k4_ordinal1,B),k2_finseq_1(A)) ) => ( k1_seqfunc(k1_euclid(A),k1_numbers,k4_pdiff_9(A,C,B,D),k5_numbers) = k7_funcop_1(C,E) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ( r1_xxreal_0(1,F) & r1_xxreal_0(F,k3_finseq_1(B)) ) => k1_seqfunc(k1_euclid(A),k1_numbers,k4_pdiff_9(A,C,B,D),F) = k8_funcop_1(k4_ordinal1,C,k5_numbers) ) ) ) ) ) ) ) ) ) )).
fof(t17_classes1,axiom,( ! [A] : ? [B] : ( v3_ordinal1(B) & k3_classes1(A,B) = k3_classes1(A,k1_ordinal1(B)) ) )).
fof(t17_classes2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( ( v2_classes1(B) & r2_hidden(A,B) ) => r1_tarski(A,B) ) ) )).
fof(t17_clopban1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t17_clopban2,axiom,( ! [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) & v3_normsp_0(A) & v4_normsp_0(A) & 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] : ( m1_subset_1(B,u1_struct_0(A)) & k2_normsp_0(A,B) = 1 ) ) )).
fof(t17_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) ) )).
fof(t17_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v7_ordinal1(D) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_clopban4(D,A,C,B),k6_clvect_1(A,k2_clopban4(D,A,C,B),k7_xcmplx_0(k6_complex1,k2_newton(D)))) ) ) ) ) )).
fof(t17_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m2_pboole(C,A,k5_mssubfam(A,B),k5_mssubfam(A,B)) => ( ( v1_closure1(C,A,B) & ! [D] : ( m1_pboole(D,A,k5_mssubfam(A,B)) => r2_pboole(A,k2_closure1(A,B,C,D),D) ) ) => v3_closure1(C,A,B) ) ) ) )).
fof(t17_closure2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t17_clvect_1,axiom,( ! [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) ) => ! [B] : ( 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,k2_xcmplx_0(k6_complex1,k6_complex1)) ) ) )).
fof(t17_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(t17_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k2_clvect_3(A,B,1) = k3_rlvect_1(A,k1_normsp_0(A,B,k5_numbers),k1_normsp_0(A,B,1)) ) ) )).
fof(t17_coh_sp,axiom,( ! [A] : ! [B] : ( r2_hidden(A,k4_coh_sp(B)) <=> ? [C] : ( m1_subset_1(C,k3_coh_sp(B)) & ? [D] : ( 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)))) ) ) ) )).
fof(t17_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v4_cohsp_1(A) => ! [B] : ! [C] : ( ( 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)) ) ) ) )).
fof(t17_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m2_collsp(B,A) => ! [C] : ( m2_collsp(C,A) => ( r1_tarski(B,C) => B = C ) ) ) ) )).
fof(t17_combgras,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( l1_incsp_1(B) => ! [C] : ( l1_combgras(C,A,B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t17_compl_sp,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k1_topmetr(A,B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_topmetr(A,B))))) ) => ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) ) ) )).
fof(t17_complex1,axiom,( ! [A] : ( 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)) ) ) )).
fof(t17_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k1_comptrig(A) != k5_numbers => ( ~ ( ~ r1_xxreal_0(k28_sin_cos,k1_comptrig(A)) & r1_xxreal_0(k17_sin_cos(k1_comptrig(A)),k5_numbers) ) & ~ ( ~ r1_xxreal_0(k17_sin_cos(k1_comptrig(A)),k5_numbers) & r1_xxreal_0(k28_sin_cos,k1_comptrig(A)) ) ) ) ) )).
fof(t17_complfld,axiom,( k11_algstr_0(k1_complfld,k5_struct_0(k1_complfld)) = k5_struct_0(k1_complfld) )).
fof(t17_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => k1_complsp2(k8_seq_4(A,B)) = k8_seq_4(k1_complsp2(A),k1_complsp2(B)) ) ) ) )).
fof(t17_compos_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( l1_compos_1(B) => k5_compos_1(B,k4_compos_1(B),A) = k4_compos_1(B) ) ) )).
fof(t17_compos_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) ) => ~ r2_hidden(k62_valued_1(A),k9_xtuple_0(k63_valued_1(A))) ) )).
fof(t17_comptrig,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(k3_xcmplx_0(2,k28_sin_cos),A) & k17_sin_cos(A) = k5_numbers & A != k5_numbers & A != k28_sin_cos ) ) )).
fof(t17_compts_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t17_comput_1,axiom,( k19_margrel1(k1_xboole_0) = k5_numbers )).
fof(t17_comseq_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k25_valued_1(k4_ordinal1,k2_numbers,C,k3_xcmplx_0(A,B)),k25_valued_1(k4_ordinal1,k2_numbers,k25_valued_1(k4_ordinal1,k2_numbers,C,B),A)) ) ) ) )).
fof(t17_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => k3_comseq_2(k2_comseq_2(k4_ordinal1,k31_valued_1(k4_ordinal1,k2_numbers,A))) = k4_xcmplx_0(k8_complex1(k3_comseq_2(A))) ) )).
fof(t17_comseq_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k3_xcmplx_0(A,k3_complex1(B)) = k3_complex1(k3_xcmplx_0(A,B)) & k3_xcmplx_0(A,k4_complex1(B)) = k4_complex1(k3_xcmplx_0(A,B)) ) ) ) )).
fof(t17_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => k1_funct_1(k1_conlat_1(A),k1_xboole_0) = u4_struct_0(A) ) )).
fof(t17_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_conlat_1(A) & l1_conlat_1(A) ) => k7_conlat_2(k7_conlat_2(A)) = A ) )).
fof(t17_conmetr1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v1_conaffm(A) <=> v4_aff_2(k3_analmetr(A)) ) ) )).
fof(t17_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t17_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_connsp_2(A) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t17_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(t17_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( B = a_3_1_convex1(A,C,D) => v1_convex1(B,A) ) ) ) ) ) )).
fof(t17_convex4,axiom,( ! [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) ) => ! [B] : ( m1_convex4(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t17_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_subset_1(D,k6_qc_lang1(A),k8_qc_lang1(A,C)) => ! [E] : ( ( v3_card_1(E,C) & m2_finseq_1(E,k2_qc_lang1(A)) ) => k13_cqc_lang(A,k10_qc_lang1(A,D,E),B) = k10_qc_lang1(A,D,k1_cqc_lang(A,E,k2_cqc_lang(A,k3_qc_lang3(A,k5_numbers),B))) ) ) ) ) ) )).
fof(t17_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => k7_cqc_sim1(A,k7_cqc_lang(A,B,C)) = k1_nat_1(k7_cqc_sim1(A,B),k7_cqc_sim1(A,C)) ) ) ) )).
fof(t17_cqc_the1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,9) & ~ r2_hidden(A,k2_cqc_the1) ) ) )).
fof(t17_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ( r3_cqc_the3(A,B) <=> r1_tarski(B,k4_cqc_the1(A)) ) ) ) )).
fof(t17_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t17_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k9_csspace4(A,B))) => ! [D] : ( ( 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] : ( m1_subset_1(E,A) => r1_xxreal_0(k2_normsp_0(B,k3_funct_2(A,u1_struct_0(B),D,E)),k2_normsp_0(k9_csspace4(A,B),C)) ) ) ) ) ) ) )).
fof(t17_decomp_1,axiom,( ! [A] : ( ( 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) ) )).
fof(t17_descip_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1)) => ! [C] : ( m2_finseq_2(C,k6_margrel1,k4_finseq_2(A,k6_margrel1)) => k12_descip_1(A,k12_descip_1(A,B,C),C) = B ) ) ) )).
fof(t17_dickson,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ! [C] : ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t17_diff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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] : ( ( 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_funct_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,C),k26_valued_1(k1_numbers,k1_numbers,G,D)),B),k1_nat_1(A,1)),E) = k2_xcmplx_0(k3_xcmplx_0(C,k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(F,B),k1_nat_1(A,1)),E)),k3_xcmplx_0(D,k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(G,B),k1_nat_1(A,1)),E))) ) ) ) ) ) ) ) )).
fof(t17_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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) = k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(k1_funct_1(D,A),k3_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(A,C))),k7_xcmplx_0(k1_funct_1(D,B),k3_xcmplx_0(k6_xcmplx_0(B,A),k6_xcmplx_0(B,C)))),k7_xcmplx_0(k1_funct_1(D,C),k3_xcmplx_0(k6_xcmplx_0(C,A),k6_xcmplx_0(C,B)))) ) ) ) ) ) )).
fof(t17_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(k2_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k1_fdiff_9)) & r2_hidden(k6_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k1_fdiff_9)) ) => k1_funct_1(k5_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fdiff_9,k1_fdiff_9),A),B) = k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(4,k17_sin_cos(k3_xcmplx_0(2,B))),k17_sin_cos(A)),k1_square_1(k2_xcmplx_0(k19_sin_cos(k3_xcmplx_0(2,B)),k19_sin_cos(A)))) ) ) ) )).
fof(t17_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v1_finset_1(B) & v2_dilworth(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(C,k5_card_1(B)) & ! [D] : ( ( v1_finset_1(D) & v2_dilworth(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => k5_card_1(D) != C ) ) ) ) ) )).
fof(t17_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r1_diraf(A,B,C,E) & r1_diraf(A,B,D,E) & ~ r1_diraf(A,B,C,D) & ~ r1_diraf(A,B,D,C) ) ) ) ) ) ) )).
fof(t17_dirort,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dirort(A) & l1_analoaf(A) ) => ( v2_dirort(A) => ( v3_dirort(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_dist_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,A) ) => k18_rvsum_1(k4_dist_1(A,B)) = 1 ) ) )).
fof(t17_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => ! [C] : ( m1_dist_2(C,A,B) => ! [D] : ( m1_dist_2(D,A,B) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,k6_margrel1) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => k4_dist_2(A,B,C,E) = k4_dist_2(A,B,D,E) ) ) ) ) ) )).
fof(t17_domain_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) => ! [F] : ( 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 ) ) ) ) ) ) ) )).
fof(t17_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ( ( m1_dynkin(B,A) & v2_finsub_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( r1_tarski(k10_xtuple_0(C),B) => r2_hidden(k3_tarski(k10_xtuple_0(C)),B) ) ) ) ) ) )).
fof(t17_e_siec,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) ) )).
fof(t17_ec_pf_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(C))) => ( ( D = k5_int_1(A,C) & E = k5_int_1(B,C) ) => k5_algstr_0(k9_int_3(C),D,E) = k5_int_1(k6_xcmplx_0(A,B),C) ) ) ) ) ) ) )).
fof(t17_ec_pf_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t17_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => r1_tarski(k7_ens_1(A,B,C),k2_ens_1(A)) ) ) ) )).
fof(t17_entropy1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( A = k1_xboole_0 => k5_matrprob(A) = k5_numbers ) ) )).
fof(t17_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k2_tarski(A,B),k3_enumset1(C,D,E,F,G)) )).
fof(t17_eqrel_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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) ) ) )).
fof(t17_equation,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => m1_msualg_2(B,A,g3_msualg_1(A,u3_msualg_1(A,B),u4_msualg_1(A,B))) ) ) )).
fof(t17_euclid,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t17_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( v1_xreal_0(D) => k22_rvsum_1(k1_rlvect_1(k15_euclid(A),B,D),C) = k3_xcmplx_0(D,k22_rvsum_1(B,C)) ) ) ) ) )).
fof(t17_euclid_3,axiom,( k2_euclid_3(k4_struct_0(k15_euclid(2))) = k5_complex1 )).
fof(t17_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ( k22_rvsum_1(B,B) = k5_numbers <=> B = k5_euclid(A) ) ) ) )).
fof(t17_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => ! [B] : ( 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)) ) ) )).
fof(t17_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( r2_hidden(D,k1_rltopsp1(k15_euclid(2),A,B)) => ( D = B | ( k22_rvsum_1(k5_algstr_0(k15_euclid(2),C,D),k5_algstr_0(k15_euclid(2),B,A)) = k5_numbers <=> k22_rvsum_1(k5_algstr_0(k15_euclid(2),C,D),k5_algstr_0(k15_euclid(2),B,D)) = k5_numbers ) ) ) ) ) ) ) )).
fof(t17_euclid_7,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_euclid(k5_numbers))) => ( v5_euclid_7(A,k5_numbers) => A = k1_xboole_0 ) ) )).
fof(t17_euclid_8,axiom,( k5_euclid_8(k4_euclid_8,k3_euclid_8) = k6_euclid(3,k2_euclid_8) )).
fof(t17_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(A))) => ( A != k5_numbers => r1_tarski(k4_euclid_9(A,C,k7_xcmplx_0(B,k3_square_1(A))),k8_metric_1(k14_euclid(A),C,B)) ) ) ) ) )).
fof(t17_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(A)) => ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(t17_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( ~ r5_analmetr(A,B,C,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r4_analmetr(A,B,E,B,F) & r4_analmetr(A,C,E,D,F) ) ) ) ) ) ) ) ) )).
fof(t17_euler_1,axiom,( k1_euler_1(1) = 1 )).
fof(t17_euler_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_int_2(A,B) => ( A = k5_numbers | B = k5_numbers | ! [C] : ( v7_ordinal1(C) => r1_int_2(k1_newton(A,C),B) ) ) ) ) ) )).
fof(t17_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v3_exchsort(A,k2_exchsort(A)) ) )).
fof(t17_extens_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m3_pboole(C,u1_struct_0(A),u3_msualg_1(A,B)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t17_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) ) => ! [D] : ( ( 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(t17_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( ~ ( ( A = k2_supinf_1 | A = k1_supinf_1 ) & ( B = k2_supinf_1 | B = k1_supinf_1 ) ) & B != k5_numbers & k3_extreal1(k2_extreal1(A,B)) != k2_extreal1(k3_extreal1(A),k3_extreal1(B)) ) ) ) )).
fof(t17_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( r1_facirc_1(A,B,C,D) => ! [E] : ( v7_ordinal1(E) => r1_facirc_1(A,B,k5_facirc_1(A,B,C,E),D) ) ) ) ) ) )).
fof(t17_facirc_2,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(t17_fcont_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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))) ) ) )).
fof(t17_fcont_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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(B,A),k1_relset_1(k1_numbers,C)) & r1_xxreal_0(B,A) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A))) & ~ v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A))) & ~ v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A))) ) ) ) ) )).
fof(t17_fcont_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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(B,A),k1_relset_1(k1_numbers,C)) => ( ( ~ v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,C,k2_rcomp_1(B,A))) & ~ v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,C,k2_rcomp_1(B,A))) ) | 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(B,A))),k7_relset_1(k1_numbers,k1_numbers,C,k2_rcomp_1(B,A)))) ) ) ) ) ) )).
fof(t17_fdiff_10,axiom,( ! [A] : ( ( 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,k18_sin_cos))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k18_sin_cos),A),B) = k6_xcmplx_0(k7_xcmplx_0(k1_funct_1(k18_sin_cos,B),B),k3_xcmplx_0(k1_funct_1(k3_taylor_1,B),k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t17_fdiff_11,axiom,( ! [A] : ( ( 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,k26_sin_cos))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k26_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k26_sin_cos),A),B) = k7_xcmplx_0(1,k3_xcmplx_0(k1_square_1(k1_funct_1(k18_sin_cos,k1_funct_1(k1_sin_cos9,B))),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t17_fdiff_2,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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))) ) ) ) ) ) )).
fof(t17_fdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( 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)) = k6_xcmplx_0(k2_fdiff_3(C,A),k2_fdiff_3(C,B)) ) ) ) ) ) )).
fof(t17_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_1(C,E) = k1_square_1(A) ) ) & D = k1_taylor_1(2) ) => ( r2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,C,D),B) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_1(k2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,C,D),B),E) = k3_xcmplx_0(2,E) ) ) ) ) ) ) ) ) )).
fof(t17_fdiff_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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,k22_sin_cos)),D),k7_xcmplx_0(1,k3_power(k4_power,A))))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => ( k1_funct_1(C,E) = k4_xcmplx_0(k3_xcmplx_0(E,k3_power(k4_power,A))) & k1_funct_1(D,E) = k2_xcmplx_0(E,k7_xcmplx_0(1,k3_power(k4_power,A))) ) ) ) ) => ( r1_xxreal_0(A,k5_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,k22_sin_cos)),D),k7_xcmplx_0(1,k3_power(k4_power,A))),B) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_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,k22_sin_cos)),D),k7_xcmplx_0(1,k3_power(k4_power,A))),B),E) = k7_xcmplx_0(E,k6_prepower(A,E)) ) ) ) ) ) ) ) ) ) )).
fof(t17_fdiff_7,axiom,( ! [A] : ( ( 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),k3_sin_cos6))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k3_sin_cos6),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k3_sin_cos6),A),B) = k6_xcmplx_0(k1_funct_1(k3_sin_cos6,B),k7_xcmplx_0(B,k3_square_1(k6_xcmplx_0(1,k1_square_1(B))))) ) ) ) ) ) )).
fof(t17_fdiff_8,axiom,( ! [A] : ( ( 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,k27_sin_cos,k22_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k22_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k22_sin_cos),A),B) = k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k22_sin_cos,k1_funct_1(k27_sin_cos,B)),k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t17_fdiff_9,axiom,( ! [A] : ( ( 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,k22_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k22_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k22_sin_cos),A),B) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k22_sin_cos,k1_funct_1(k2_fdiff_9,B)),k1_funct_1(k18_sin_cos,B)),k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t17_ff_siec,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t17_fib_num2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( 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))) ) ) ) )).
fof(t17_fib_num3,axiom,( ! [A] : ( v7_ordinal1(A) => r1_xxreal_0(A,k1_fib_num3(A)) ) )).
fof(t17_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(k2_xcmplx_0(k7_xcmplx_0(k2_power(k2_fib_num,A),k3_square_1(5)),k7_xcmplx_0(1,2)),k5_numbers) & ~ r1_xxreal_0(1,k2_xcmplx_0(k7_xcmplx_0(k2_power(k2_fib_num,A),k3_square_1(5)),k7_xcmplx_0(1,2))) ) ) )).
fof(t17_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( k3_finseq_1(B) = k5_numbers => k4_finseq_5(A,B) = B ) ) ) )).
fof(t17_filter_0,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t17_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t17_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t17_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) )).
fof(t17_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t17_finseq_2,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ~ ( k3_finseq_1(B) != k5_numbers & ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m1_subset_1(D,A) => B != k7_finseq_1(C,k9_finseq_1(D)) ) ) ) ) )).
fof(t17_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k2_finseq_1(A) = k2_finseq_1(k2_xcmplx_0(A,B)) => B = k5_numbers ) ) ) )).
fof(t17_finseq_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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 ) ) ) ) )).
fof(t17_finseq_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k3_finseq_1(k16_finseq_1(B,A)),B) ) ) )).
fof(t17_finseq_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( r2_finseq_4(k7_finseq_1(A,B),C) & r2_hidden(C,k10_xtuple_0(A)) ) => r2_finseq_4(A,C) ) ) ) )).
fof(t17_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t17_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( r1_finseq_8(A,B) <=> k3_finseq_1(k4_finseq_8(A,k2_rfinseq(A,1,B),B)) = k5_numbers ) ) ) )).
fof(t17_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( ( 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(k4_ordinal1,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))) ) ) ) ) ) ) ) )).
fof(t17_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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) ) ) ) )).
fof(t17_finsub_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(A)) => m1_subset_1(B,k1_zfmisc_1(A)) ) )).
fof(t17_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) & k1_fintopo2(A,B,D,C) = k8_margrel1 & k5_fintopo2(A,B,D) = k7_margrel1 ) ) ) ) ) ) )).
fof(t17_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => 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)) ) ) ) ) )).
fof(t17_fintopo4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( ( 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,k5_numbers) & D = k7_relset_1(u1_struct_0(A),u1_struct_0(B),E,C) ) => v4_fin_topo(D,B) ) ) ) ) ) ) )).
fof(t17_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t17_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_catalan2(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_catalan2(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k3_catalan2(A))) => ( ( r1_tarski(B,D) & r1_tarski(C,E) ) => r1_tarski(k6_flang_1(A,B,C),k6_flang_1(A,D,E)) ) ) ) ) ) )).
fof(t17_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( 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) ) ) ) )).
fof(t17_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => k6_flang_1(A,k1_flang_3(A,B,C),k8_flang_1(A,B)) = k1_flang_3(A,B,C) ) ) )).
fof(t17_fomodel0,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t17_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t17_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v4_fomodel1(B,A) & m1_subset_1(B,k1_fomodel1(A)) ) => ! [C] : ( ( 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] : ( ( 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))) ) => ( k29_fomodel2(A,k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k1_fomodel2(A)),C),D)) = k2_xcmplx_0(1,k4_xxreal_0(k29_fomodel2(A,C),k29_fomodel2(A,D))) & k29_fomodel2(A,k42_fomodel1(A,k43_fomodel1(A,B),C)) = k1_nat_1(k29_fomodel2(A,C),1) ) ) ) ) ) )).
fof(t17_fomodel3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( ( ~ v6_struct_0(D) & v11_fomodel1(D) & l1_fomodel1(D) ) => ! [E] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(C),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_fomodel2(C,B)) => ! [F] : ( m2_subset_1(F,k9_funct_2(k37_fomodel1(D),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_fomodel2(D,B)) => ( ( v16_fomodel1(D,C) & r1_tarski(A,k30_fomodel2(C)) & k5_relat_1(E,k37_fomodel1(C)) = k5_relat_1(F,k37_fomodel1(C)) ) => ( v10_fomodel2(A,B,C,E) <=> v10_fomodel2(A,B,D,F) ) ) ) ) ) ) ) )).
fof(t17_fomodel4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C))))) => ! [E] : ( v4_funct_1(E) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k40_fomodel2(C)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k40_fomodel2(C)))) ) => ( ( v7_fomodel4(D,C) & r2_hidden(k25_fomodel4(C),D) & r2_hidden(k35_fomodel4(C),D) & r2_hidden(k26_fomodel4(C),D) & r2_hidden(k32_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)))))) | v10_fomodel4(E,C,D) | ( r1_tarski(k9_nat_1(k9_setfam_1(k2_xboole_0(E,k30_fomodel2(C))),k44_fomodel4(E,C,D,F),A),k9_nat_1(k9_setfam_1(k2_xboole_0(E,k30_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)),k9_nat_1(k9_setfam_1(k2_xboole_0(E,k30_fomodel2(C))),k44_fomodel4(E,C,D,F),B),k6_subset_1(k3_finseq_2(k1_fomodel1(C)),k1_tarski(k1_xboole_0)))))) & ~ v10_fomodel4(k9_nat_1(k9_setfam_1(k2_xboole_0(E,k30_fomodel2(C))),k44_fomodel4(E,C,D,F),B),C,D) ) ) ) ) ) ) ) ) ) )).
fof(t17_frechet,axiom,( ! [A] : ! [B] : ! [C] : ( ~ r2_hidden(C,A) => k8_relat_1(k1_funct_4(k6_partfun1(A),k7_funcop_1(B,C)),k1_tarski(C)) = B ) )).
fof(t17_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => k1_frechet2(A,k1_struct_0(A)) = k1_xboole_0 ) )).
fof(t17_fscirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t17_fscirc_2,axiom,( ! [A] : ! [B] : ! [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))) )).
fof(t17_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( ( ~ v2_struct_0(E) & l2_fsm_1(E,A,B) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(E)) => ! [G] : ( m1_subset_1(G,u1_struct_0(E)) => ( G = 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,C)) => ! [H] : ( m1_subset_1(H,k4_ordinal1) => ( r2_hidden(H,k2_finseq_1(k1_nat_1(k3_finseq_1(D),1))) => k1_funct_1(k2_fsm_1(A,E,F,k8_finseq_1(A,k12_finseq_1(A,C),D)),k1_nat_1(H,1)) = k1_funct_1(k2_fsm_1(A,E,G,D),H) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( ( ~ v2_struct_0(D) & l2_fsm_3(D,A,C) ) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t17_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ! [E] : ! [F] : ( 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] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( m1_subset_1(H,k6_margrel1) => ! [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)) ) ) ) ) ) ) ) ) ) )).
fof(t17_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( 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)) ) ) )).
fof(t17_funcsdom,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ? [C] : ( m2_funct_2(C,B,k1_numbers,k9_funct_2(B,k1_numbers)) & ? [D] : ( m2_funct_2(D,B,k1_numbers,k9_funct_2(B,k1_numbers)) & ! [E] : ( r2_hidden(E,B) => ( ( E = A => k1_funct_1(C,E) = 1 ) & ( E != A => k1_funct_1(C,E) = k5_numbers ) ) ) & ! [E] : ( r2_hidden(E,B) => ( ( E = A => k1_funct_1(D,E) = k5_numbers ) & ( E != A => k1_funct_1(D,E) = 1 ) ) ) ) ) ) )).
fof(t17_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k4_relat_1(A) <=> ( k9_xtuple_0(B) = A & ! [C] : ( r2_hidden(C,A) => k1_funct_1(B,C) = C ) ) ) ) )).
fof(t17_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) ) )).
fof(t17_funct_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t17_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t17_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) ) ) ) )).
fof(t17_funct_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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))) ) ) ) )).
fof(t17_funct_7,axiom,( k3_finseq_2(k1_xboole_0) = k1_tarski(k1_xboole_0) )).
fof(t17_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t17_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) ) => ( ! [C] : ( 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 = k5_numbers | ( v1_funct_9(B,k3_xcmplx_0(2,A)) & v2_funct_9(B) ) ) ) ) ) )).
fof(t17_functor0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,B,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,B) & v1_funct_1(F) & v1_partfun1(F,B) ) => ! [G] : ( ( v1_relat_1(G) & v4_relat_1(G,C) & v1_funct_1(G) & v1_partfun1(G,C) ) => ! [H] : ( 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) ) ) ) ) ) ) ) )).
fof(t17_functor1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t17_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v2_altcat_1(D) & v12_altcat_1(D) & l2_altcat_1(D) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ! [F] : ( ( v15_functor0(F,A,B) & m2_functor0(F,A,B) ) => ! [G] : ( ( v15_functor0(G,B,C) & m2_functor0(G,B,C) ) => ! [H] : ( ( v15_functor0(H,C,D) & m2_functor0(H,C,D) ) => ! [I] : ( m1_functor2(I,A,B,E,F) => ( r1_functor2(A,B,E,F) => r8_pboole(u1_struct_0(A),k5_functor3(A,B,D,E,F,I,k1_functor3(B,C,D,G,H)),k5_functor3(A,C,D,k1_functor3(A,B,C,E,G),k1_functor3(A,B,C,F,G),k5_functor3(A,B,C,E,F,I,G),H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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)) ) ) ) )).
fof(t17_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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))) ) ) ) )).
fof(t17_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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,k1_fuzzy_4(C,A,k3_fuzzy_4(A,B,C,D,E)),k3_fuzzy_4(C,B,A,k1_fuzzy_4(C,B,E),k1_fuzzy_4(B,A,D))) ) ) ) ) ) )).
fof(t17_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => k3_funct_2(u1_struct_0(A),k6_numbers,B,k5_struct_0(A)) = k5_numbers ) ) ) )).
fof(t17_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v7_ordinal1(F) => ( ( 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) ) ) ) ) ) ) ) )).
fof(t17_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ ( ~ 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)) ) ) )).
fof(t17_gcd_1,axiom,( ! [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) & v1_vectsp_2(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t17_genealg1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_genealg1(B,A) => ! [C] : ( m1_genealg1(C,A) => k9_genealg1(A,B,C,k5_numbers,k5_numbers,k5_numbers) = C ) ) ) )).
fof(t17_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_geomtrap(A,D,E,B,C,C,B) => B = C ) ) ) ) ) ) )).
fof(t17_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t17_gfacirc2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( C = k4_tarski(k1_xboole_0,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k8_margrel1)) => ( k5_gfacirc2(1,A,B) = k2_circcomb(k5_circcomb(k1_margrel1(k6_margrel1,k4_finseq_2(k5_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(k5_numbers,k6_margrel1),k8_margrel1),k1_xboole_0),k25_gfacirc1(k1_funct_1(A,1),k1_funct_1(B,1),C),k7_circcomb(k5_ordinal1,k6_margrel1,k1_margrel1(k6_margrel1,k4_finseq_2(k5_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) ) ) ) ) )).
fof(t17_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( r1_glib_000(A,E,F,D) => ( ( ~ ( r2_hidden(E,B) & r2_hidden(F,C) ) & ~ ( r2_hidden(E,C) & r2_hidden(F,B) ) ) | r3_glib_000(A,B,C,D) ) ) ) )).
fof(t17_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( r1_glib_001(A,C,D,B) => ( m1_subset_1(C,k6_glib_000(A)) & m1_subset_1(D,k6_glib_000(A)) ) ) ) ) )).
fof(t17_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => r2_hidden(B,k2_glib_002(A,B)) ) ) )).
fof(t17_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( 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))) ) ) ) )).
fof(t17_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( 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) ) ) )).
fof(t17_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ( B != C => v13_glib_000(k12_glib_005(A,B,C)) ) ) ) ) )).
fof(t17_goboard1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(C)) ) => ( ( ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(E,k4_finseq_1(A)) & r2_hidden(k1_nat_1(E,1),k4_finseq_1(A)) ) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ! [I] : ( v7_ordinal1(I) => ( ( r2_hidden(k4_tarski(F,G),k2_matrix_0(D)) & r2_hidden(k4_tarski(H,I),k2_matrix_0(D)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,E) = k3_matrix_0(C,D,F,G) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(E,1)) = k3_matrix_0(C,D,H,I) ) => k2_xcmplx_0(k9_complex1(k6_xcmplx_0(F,H)),k9_complex1(k6_xcmplx_0(G,I))) = 1 ) ) ) ) ) ) ) & ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(E,k4_finseq_1(B)) & r2_hidden(k1_nat_1(E,1),k4_finseq_1(B)) ) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ! [I] : ( v7_ordinal1(I) => ( ( r2_hidden(k4_tarski(F,G),k2_matrix_0(D)) & r2_hidden(k4_tarski(H,I),k2_matrix_0(D)) & k7_partfun1(u1_struct_0(k15_euclid(2)),B,E) = k3_matrix_0(C,D,F,G) & k7_partfun1(u1_struct_0(k15_euclid(2)),B,k1_nat_1(E,1)) = k3_matrix_0(C,D,H,I) ) => k2_xcmplx_0(k9_complex1(k6_xcmplx_0(F,H)),k9_complex1(k6_xcmplx_0(G,I))) = 1 ) ) ) ) ) ) ) & ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ( ( r2_hidden(k4_tarski(E,F),k2_matrix_0(D)) & r2_hidden(k4_tarski(G,H),k2_matrix_0(D)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k3_finseq_1(A)) = k3_matrix_0(C,D,E,F) & k7_partfun1(u1_struct_0(k15_euclid(2)),B,1) = k3_matrix_0(C,D,G,H) & r2_hidden(k3_finseq_1(A),k4_finseq_1(A)) & r2_hidden(1,k4_finseq_1(B)) ) => k2_xcmplx_0(k9_complex1(k6_xcmplx_0(E,G)),k9_complex1(k6_xcmplx_0(F,H))) = 1 ) ) ) ) ) ) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(E,k4_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(2)),A,B))) & r2_hidden(k1_nat_1(E,1),k4_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(2)),A,B))) ) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ! [I] : ( v7_ordinal1(I) => ( ( r2_hidden(k4_tarski(F,G),k2_matrix_0(D)) & r2_hidden(k4_tarski(H,I),k2_matrix_0(D)) & k7_partfun1(u1_struct_0(k15_euclid(2)),k8_finseq_1(u1_struct_0(k15_euclid(2)),A,B),E) = k3_matrix_0(C,D,F,G) & k7_partfun1(u1_struct_0(k15_euclid(2)),k8_finseq_1(u1_struct_0(k15_euclid(2)),A,B),k1_nat_1(E,1)) = k3_matrix_0(C,D,H,I) ) => k2_xcmplx_0(k9_complex1(k6_xcmplx_0(F,H)),k9_complex1(k6_xcmplx_0(G,I))) = 1 ) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_goboard2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( ( r2_hidden(A,k4_finseq_1(B)) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => r1_xxreal_0(k1_funct_1(k2_goboard1(B),A),k1_funct_1(k2_goboard1(B),C)) ) ) ) => r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),B,A),k10_xtuple_0(k8_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(B),1))) ) ) ) )).
fof(t17_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( v2_goboard1(C) & v3_goboard1(C) & r1_xxreal_0(1,A) & r1_xxreal_0(A,k3_finseq_1(C)) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(C)) ) => r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_nat_1(B,1))),k2_goboard5(C,B)) ) ) ) ) )).
fof(t17_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_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_0(B),A) | k1_tops_1(k15_euclid(2),k2_goboard5(B,A)) = a_2_1_goboard6(A,B) ) ) ) ) )).
fof(t17_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(C)) ) => k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),B)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_nat_1(B,1)))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B)) ) ) ) ) )).
fof(t17_goboard8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,2),k3_finseq_1(A)) ) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,2),k1_matrix_0(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,k1_nat_1(C,1)) ) => ( ( ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,k1_nat_1(C,2)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),2,k1_nat_1(C,1)) ) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,k1_nat_1(C,2)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),2,k1_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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,k1_nat_1(C,1))),k7_xcmplx_0(1,2)),k19_euclid(1,k5_numbers)),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),2,k1_nat_1(C,1))),k7_xcmplx_0(1,2))),k3_topreal1(2,A)) ) ) ) ) ) ) )).
fof(t17_goboard9,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k3_finseq_1(A)) ) => v1_convex1(k1_tops_1(k15_euclid(2),k5_goboard5(A,B)),k15_euclid(2)) ) ) ) )).
fof(t17_gobrd11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => v4_pre_topc(k1_goboard5(B,A),k15_euclid(2)) ) ) )).
fof(t17_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(D)) & r1_goboard1(u1_struct_0(k15_euclid(2)),D,E) & r2_hidden(k4_tarski(A,B),k2_matrix_0(E)) & r2_hidden(k4_tarski(k1_nat_1(A,1),B),k2_matrix_0(E)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,k1_nat_1(A,1),B) ) => k2_gobrd13(D,E,C) = k3_goboard5(E,A,k7_nat_d(B,1)) ) ) ) ) ) ) )).
fof(t17_gobrd14,axiom,( ! [A] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(t17_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_henmodel(B,A) & m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) ) => ! [C] : ( m1_henmodel(C,A,B) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t17_gr_cy_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( v1_int_1(D) & C = k5_group_1(A,D,B) ) ) ) ) ) )).
fof(t17_gr_cy_2,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) ) )).
fof(t17_gr_cy_3,axiom,( k1_gr_cy_3(1) = 1 )).
fof(t17_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_graph_1(C) ) => ( ( r4_graph_1(A,B) & r4_graph_1(B,C) ) => r4_graph_1(A,C) ) ) ) ) )).
fof(t17_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t17_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ! [C] : ~ ( r2_hidden(B,u4_struct_0(A)) & r2_hidden(B,C) & v1_xboole_0(k1_graph_3(A,C)) ) ) )).
fof(t17_graph_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( ( v7_graph_1(C,B) & v3_graph_2(C,B) & m2_graph_1(C,B) ) => ( v7_graph_1(k2_partfun1(k4_ordinal1,u4_struct_0(B),C,k2_finseq_1(A)),B) & v3_graph_2(k2_partfun1(k4_ordinal1,u4_struct_0(B),C,k2_finseq_1(A)),B) & m2_graph_1(k2_partfun1(k4_ordinal1,u4_struct_0(B),C,k2_finseq_1(A)),B) ) ) ) ) )).
fof(t17_graph_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m2_finseq_1(C,u4_struct_0(B)) => ( r1_tarski(k2_graph_5(B,C),A) <=> ! [D] : ( 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) ) ) ) ) ) )).
fof(t17_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(A,k4_finseq_1(C)) => ( A = B | k1_funct_1(k2_graphsp(A,B,C,D),A) = B ) ) ) ) ) ) )).
fof(t17_grcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( m1_grcat_1(D,B,C) => ! [E] : ( m1_grcat_1(E,A,B) => m1_grcat_1(k13_grcat_1(D,E),A,C) ) ) ) ) ) )).
fof(t17_grfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t17_grnilp_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t17_groeb_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(E,A,C) & v1_polynom1(E,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(k12_polynom1(A,C),D)) => r7_polyred(A,B,C,E,D) ) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(E,A,C) & v1_polynom1(E,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(k12_polynom1(A,C),D)) => r10_polyred(A,B,C,E,D) ) ) ) ) ) ) ) )).
fof(t17_groeb_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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] : ( ( 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] : ( ( 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,k11_polynom1(A,C,G,E)),k5_termord(A,B,C,k11_polynom1(A,C,H,F))) => r1_rewrite1(k3_polyred(A,B,C,D),k7_polynom1(A,C,k11_polynom1(A,C,G,E),k11_polynom1(A,C,H,F)),k8_polynom1(A,C)) ) ) ) ) ) ) ) => r1_groeb_1(A,B,C,D) ) ) ) ) ) )).
fof(t17_groeb_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k15_pre_poly(A))) => r1_tarski(k3_polynom1(k15_pre_poly(A),B,k2_groeb_3(A,B,C,D)),k3_polynom1(k15_pre_poly(A),B,C)) ) ) ) )).
fof(t17_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t17_group_10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_card_1(B) = k1_card_1(k5_group_2(A,C,B)) ) ) ) )).
fof(t17_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_group_2(C,A) => r1_tarski(B,k2_group_11(A,B,C)) ) ) ) )).
fof(t17_group_14,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(k4_card_3(A),B),k4_card_3(k7_finseq_1(A,k9_finseq_1(B)))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_card_3(A),B),k4_card_3(k7_finseq_1(A,k9_finseq_1(B)))))) & v2_funct_1(C) & v2_funct_2(C,k4_card_3(k7_finseq_1(A,k9_finseq_1(B)))) & ! [D] : ! [E] : ~ ( r2_hidden(D,k4_card_3(A)) & r2_hidden(E,B) & ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) & v1_finseq_1(G) ) => ~ ( D = F & k9_finseq_1(E) = G & k1_binop_1(C,D,E) = k7_finseq_1(F,G) ) ) ) ) ) ) ) )).
fof(t17_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t17_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_group_3(A,k1_group_1(A),B) = k1_group_1(A) ) ) )).
fof(t17_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(E,k4_ordinal1) => ( 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)) ) ) ) ) ) )).
fof(t17_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t17_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => u1_struct_0(k5_group_6(A,B)) = k15_group_2(A,B) ) ) )).
fof(t17_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t17_group_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v15_algstr_0(D) & m1_group_2(D,A) ) => ! [E] : ( ( v15_algstr_0(E) & m1_group_2(E,A) ) => ( r2_hidden(C,k11_group_2(A,E,k14_group_2(A,D,B))) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & C = k6_algstr_0(A,k6_algstr_0(A,F,B),G) & r1_struct_0(D,F) & r1_struct_0(E,G) ) ) ) ) ) ) ) ) )).
fof(t17_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t17_groupp_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v8_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => v1_groupp_1(C,A,B) ) => v2_group_10(B,A) ) ) ) )).
fof(t17_hahnban,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( 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] : ( 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] : ( 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] : ( m1_subset_1(G,u1_struct_0(C)) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( 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,k3_xcmplx_0(H,I))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t17_hallmar1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,k1_zfmisc_1(A)) ) => ~ ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k4_finseq_1(B)) => k5_card_1(k1_funct_1(B,C)) = 1 ) ) & v1_hallmar1(B,A) & ! [C] : ~ r1_hallmar1(A,B,C) ) ) ) )).
fof(t17_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t17_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v4_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t17_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [D] : ( ( v5_relat_1(D,k3_qc_lang1(A)) & v3_card_1(D,B) & m2_finseq_1(D,k2_qc_lang1(A)) ) => ! [E] : ( ( v1_henmodel(E,A) & m1_subset_1(E,k1_zfmisc_1(k3_cqc_lang(A))) ) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t17_hermitan,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t17_hessenbe,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ( ( r1_collsp(A,B,C,J) & r1_collsp(A,E,F,J) & r1_collsp(A,C,D,H) & r1_collsp(A,F,G,H) & r1_collsp(A,B,D,I) & r1_collsp(A,E,G,I) & r1_collsp(A,K,B,E) & r1_collsp(A,K,C,F) & r1_collsp(A,K,D,G) ) => ( K = E | B = E | K = F | C = F | K = G | D = G | r1_collsp(A,K,B,C) | r1_collsp(A,K,B,D) | r1_collsp(A,K,C,D) | r1_collsp(A,H,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_heyting1,axiom,( ! [A] : m2_subset_1(k1_tarski(k4_tarski(k1_xboole_0,k1_xboole_0)),k5_finsub_1(k7_normform(A)),k8_normform(A)) )).
fof(t17_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_substlat(A,B))) => ! [D] : ( r1_tarski(D,C) => m1_subset_1(D,u1_struct_0(k5_substlat(A,B))) ) ) ) )).
fof(t17_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => r2_xboole_0(k3_heyting3(A,B),k3_heyting3(k1_nat_1(A,1),B)) ) ) )).
fof(t17_hfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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))) ) ) ) ) ) ) )).
fof(t17_hilbasis,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k14_polynom3(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) ) ) )).
fof(t17_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => r2_hidden(k3_hilbert1(k3_hilbert1(A,B),k3_hilbert1(A,A)),k6_hilbert1) ) ) )).
fof(t17_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( A = k7_finseq_1(B,C) => A = B ) ) ) ) )).
fof(t17_hilbert3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k15_pralg_1(k1_xboole_0,A) = k1_xboole_0 ) )).
fof(t17_hurwitz,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_funct_2(k4_ordinal1,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))) ) ) ) ) )).
fof(t17_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( 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),k5_numbers) ) ) ) ) )).
fof(t17_incproj,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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] : ( m1_subset_1(B,u1_incsp_1(k3_incproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k3_incproj(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k3_incproj(A))) => ! [E] : ( m1_subset_1(E,u1_incsp_1(k3_incproj(A))) => ! [F] : ( m1_subset_1(F,u1_incsp_1(k3_incproj(A))) => ! [G] : ( m1_subset_1(G,u1_incsp_1(k3_incproj(A))) => ! [H] : ( m1_subset_1(H,u1_incsp_1(k3_incproj(A))) => ! [I] : ( m1_subset_1(I,u2_incsp_1(k3_incproj(A))) => ! [J] : ( m1_subset_1(J,u2_incsp_1(k3_incproj(A))) => ! [K] : ( m1_subset_1(K,u2_incsp_1(k3_incproj(A))) => ! [L] : ( m1_subset_1(L,u2_incsp_1(k3_incproj(A))) => ! [M] : ( m1_subset_1(M,u2_incsp_1(k3_incproj(A))) => ! [N] : ( m1_subset_1(N,u2_incsp_1(k3_incproj(A))) => ! [O] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t17_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ 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] : ( 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)) ) ) ) )).
fof(t17_instalg1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t17_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => ( ( r2_int_1(A,B,E) & r2_int_1(C,D,E) ) => r2_int_1(k6_xcmplx_0(A,C),k6_xcmplx_0(B,D),E) ) ) ) ) ) ) )).
fof(t17_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => m1_subset_1(k2_int_2(A,B),k4_ordinal1) ) ) )).
fof(t17_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ~ ( C != k5_numbers & ~ r1_int_1(k3_int_2(A,C),B) & ? [D] : ( v1_int_1(D) & k5_int_1(k6_xcmplx_0(k3_xcmplx_0(A,D),B),C) = k5_numbers ) ) ) ) ) )).
fof(t17_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ( ( k3_int_2(A,B) = 1 & r1_int_5(A,B) ) => ( r1_xxreal_0(B,2) | k5_int_1(k1_newton(A,k3_nat_d(k7_nat_d(B,1),2)),B) = 1 ) ) ) ) )).
fof(t17_int_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => k3_int_2(k3_xcmplx_0(A,B),A) = k1_int_2(A) ) ) )).
fof(t17_int_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( r1_xxreal_0(1,A) & r1_xxreal_0(1,B) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( k2_int_2(A,B) = k2_nat_1(D,C) & k3_int_2(D,C) = 1 & r1_int_1(D,A) & r1_int_1(C,B) & D != k5_numbers & C != k5_numbers ) ) ) ) ) ) )).
fof(t17_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_int_2(A,C) & r1_int_2(B,C) & r1_int_2(k3_pepin(A,C),k3_pepin(B,C)) ) => ( r1_xxreal_0(C,1) | k3_pepin(k3_xcmplx_0(A,B),C) = k2_nat_1(k3_pepin(A,C),k3_pepin(B,C)) ) ) ) ) ) )).
fof(t17_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k28_sin_cos) => k2_integra5(A,k41_valued_1(k1_numbers,k1_numbers,k18_sin_cos)) = k7_xcmplx_0(k28_sin_cos,2) ) ) )).
fof(t17_integr12,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( 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,E,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,D,k41_valued_1(k1_numbers,k1_numbers,E)),A)))) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,F) => ( k1_funct_1(D,G) = 1 & k1_funct_1(E,G) = k7_xcmplx_0(G,A) & ~ r1_xxreal_0(k1_funct_1(E,G),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(E,G)) ) ) ) & F = k1_relset_1(k1_numbers,C) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,B)) ) => k2_integra5(B,C) = k6_xcmplx_0(k1_funct_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,E,k1_sin_cos9)),k2_seq_4(B)),k1_funct_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,E,k1_sin_cos9)),k3_seq_4(B))) ) ) ) ) ) ) ) )).
fof(t17_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k26_sin_cos,k1_partfun2(k1_numbers,C)),k3_rfunct_1(k1_numbers,k1_numbers,k3_taylor_1,k41_valued_1(k1_numbers,k1_numbers,k18_sin_cos)))) & r1_tarski(C,k1_relset_1(k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k26_sin_cos))) & r1_tarski(C,k1_relset_1(k1_numbers,k26_sin_cos)) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k26_sin_cos),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k26_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t17_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k22_sin_cos,D),k1_funct_1(k16_sin_cos,k1_funct_1(k22_sin_cos,D))),k1_square_1(k1_funct_1(k18_sin_cos,k1_funct_1(k22_sin_cos,D)))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_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) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_fdiff_9),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_fdiff_9),k3_seq_4(A))) ) ) ) ) )).
fof(t17_integr15,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t17_integr16,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k2_numbers))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t17_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( k3_integra1(C) = k5_numbers & r1_tarski(C,k1_relset_1(k1_numbers,B)) ) => ( r1_integr18(A,C,B) & k5_integr18(A,C,B) = k4_struct_0(A) ) ) ) ) ) )).
fof(t17_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t17_integra1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( m1_integra1(C,B) => ( r2_hidden(A,k4_finseq_1(C)) => k3_integra1(k2_integra1(B,C,A)) = k1_funct_1(k5_integra1(B,k7_rfunct_1(B,B),C),A) ) ) ) ) )).
fof(t17_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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) ) ) ) )).
fof(t17_integra3,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( 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_funct_1(A,B),k1_funct_1(A,D)) & r1_xxreal_0(k1_funct_1(A,D),k1_funct_1(A,C)) ) => r2_hidden(k1_funct_1(A,D),k1_rvsum_1(k3_finseq_6(k1_numbers,A,B,C))) ) ) ) ) ) )).
fof(t17_integra4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t17_integra5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t17_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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) = k2_xcmplx_0(k4_integra5(A,C,D),k4_integra5(C,B,D)) ) ) ) ) ) ) )).
fof(t17_integra7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( 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_funct_1(D,E) = k2_xcmplx_0(k4_integra5(F,E,C),k1_funct_1(D,F)) ) ) ) ) ) ) ) )).
fof(t17_integra8,axiom,( k1_funct_1(k1_sin_cos2,1) = k7_xcmplx_0(k6_xcmplx_0(k1_square_1(k4_power),1),k3_xcmplx_0(2,k4_power)) )).
fof(t17_integra9,axiom,( ! [A] : ( ( ~ 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,k5_numbers),k22_sin_cos)) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_fcont_1(1,k4_xcmplx_0(1))),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_fcont_1(1,k4_xcmplx_0(1))),k3_seq_4(A))) ) )).
fof(t17_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => ! [C] : ( ( ~ 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))) ) ) ) )).
fof(t17_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => r2_hidden(k3_intpro_1(A,A),k8_intpro_1) ) )).
fof(t17_irrat_1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( ~ r1_xxreal_0(k3_finseq_1(A),k5_numbers) => k18_rvsum_1(A) = k2_xcmplx_0(k1_funct_1(A,1),k18_rvsum_1(k2_rfinseq(k1_numbers,1,A))) ) ) )).
fof(t17_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( ( ~ 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(k6_cat_2(A,C),k6_cat_2(B,D)) ) ) ) ) ) )).
fof(t17_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t17_jgraph_1,axiom,( ! [A] : ( 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,k1_nat_1(1,1))),k1_tarski(k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_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) ) ) )).
fof(t17_jgraph_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) ) )).
fof(t17_jgraph_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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] : ( ( 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(k4_xcmplx_0(1),k5_numbers) & k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,B) = k19_euclid(k5_numbers,1) & k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,C) = k19_euclid(1,k5_numbers) & k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,D) = k19_euclid(k5_numbers,k4_xcmplx_0(1)) ) ) | ! [F] : ( ( 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] : ( ( 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,k5_numbers) = A & k1_funct_1(F,1) = C & k1_funct_1(G,k5_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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_jgraph_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ 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] : ( 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] : ( ( 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] : ( ( 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,k5_numbers) = C & k1_funct_1(G,1) = A & k1_funct_1(H,k5_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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_jordan,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_xreal_0(B) & ~ v3_xxreal_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => m1_subset_1(C,u1_struct_0(k2_brouwer(A,C,B))) ) ) ) )).
fof(t17_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ( v3_pre_topc(a_1_3_jordan1(A),k15_euclid(2)) & m1_subset_1(a_1_3_jordan1(A),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ) )).
fof(t17_jordan10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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(k2_jordan9(B,A))) ) ) )).
fof(t17_jordan11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => r1_tarski(k3_topreal1(2,k2_jordan9(B,A)),k2_jordan2c(2,B)) ) ) )).
fof(t17_jordan12,axiom,( ! [A] : ( ( ~ 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] : ! [C] : ! [D] : ~ ( 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] : ( 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] : ( 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] : ( 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) ) ) ) ) )).
fof(t17_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( r1_jordan1h(A,B) => r1_xboole_0(k2_jordan2c(2,A),k1_jordan2c(2,k3_topreal1(2,k1_jordan13(A,B)))) ) ) ) )).
fof(t17_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( 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_0(k1_jordan8(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_topreal1(2,k1_jordan1e(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E),k3_topreal1(2,k2_jordan1e(B,A))) & ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ~ ( 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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,F),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,G)),k3_topreal1(2,k1_jordan1e(B,A))) = k1_tarski(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,F),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,G)),k3_topreal1(2,k2_jordan1e(B,A))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,G)) ) ) ) ) ) ) ) ) ) )).
fof(t17_jordan16,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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] : ( ( 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] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ~ ( v3_tops_2(F,k5_topmetr,k1_pre_topc(k15_euclid(2),A)) & k1_funct_1(F,k5_numbers) = B & k1_funct_1(F,1) = C & k1_funct_1(F,G) = D & k1_funct_1(F,H) = E & r1_xxreal_0(k5_numbers,G) & ~ r1_xxreal_0(H,G) & r1_xxreal_0(H,1) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ~ ( D != E & r1_jordan17(A,B,C,D,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ~ ( F != D & F != E & r1_jordan17(A,B,D,F,E) ) ) ) ) ) ) ) ) )).
fof(t17_jordan19,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E),k3_topreal1(2,k2_jordan1e(B,A))) & r2_hidden(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k9_jordan6(B)) ) ) ) ) ) ) )).
fof(t17_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_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_0(C)) ) => r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k3_finseq_1(C),B))) ) ) ) ) )).
fof(t17_jordan1b,axiom,( ! [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)))) ) => r1_tarski(A,k3_goboard5(k1_jordan8(A,k5_numbers),2,2)) ) )).
fof(t17_jordan1c,axiom,( ! [A] : ( ( v4_pre_topc(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(2))) => ~ ( r2_hidden(B,k1_jordan2c(2,A)) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & r1_tarski(k8_metric_1(k14_euclid(2),B,C),k1_jordan2c(2,A)) ) ) ) ) ) )).
fof(t17_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & ~ r1_xxreal_0(k3_finseq_1(k2_jordan9(B,A)),C) & r2_hidden(k18_pscomp_1(B),k2_gobrd13(k2_jordan9(B,A),k1_jordan8(B,A),C)) ) ) ) )).
fof(t17_jordan1e,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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)))) ) => r1_sprect_2(k2_jordan9(B,A),k1_jordan1e(B,A)) ) ) )).
fof(t17_jordan1h,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v3_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => r1_xxreal_0(k1_matrix_0(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)))) ) )).
fof(t17_jordan20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( ( 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,k5_numbers) = D & k1_funct_1(F,1) = E ) ) ) ) ) ) ) ) )).
fof(t17_jordan21,axiom,( ! [A] : ( ( 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)) ) )).
fof(t17_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k18_euclid(k1_jordan21(k3_topreal1(2,k2_jordan9(A,B)))),k18_euclid(k1_jordan21(A))) ) ) )).
fof(t17_jordan23,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v2_jordan23(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t17_jordan2b,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k7_metric_1)) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( C = A => k8_metric_1(k7_metric_1,A,B) = a_2_1_jordan2b(B,C) ) ) ) ) )).
fof(t17_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) )).
fof(t17_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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,k1_nat_1(k1_jordan3(A,C),1),k3_finseq_1(A))) ) => ( C = k1_funct_1(A,k1_nat_1(k1_jordan3(A,C),1)) | r1_jordan3(B,C,k7_partfun1(u1_struct_0(k15_euclid(2)),A,k3_finseq_1(A))) ) ) ) ) ) )).
fof(t17_jordan4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(C,k3_finseq_1(B)) => k3_finseq_6(A,B,C,C) = k6_finseq_1(A) ) ) ) ) )).
fof(t17_jordan5a,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B)))) ) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [H] : ( 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,k3_seq_4(k1_weierstr(G))) = k3_seq_4(k1_weierstr(H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_jordan5b,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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) = k13_matrix_0(u1_struct_0(k15_euclid(2)),B) ) ) ) )).
fof(t17_jordan5c,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t17_jordan5d,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)))) ) ) ) )).
fof(t17_jordan7,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( r1_topreal1(k15_euclid(2),B,C,A) & ! [D] : ( ( 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,k5_numbers) = B & k1_funct_1(D,1) = C ) ) ) ) ) ) )).
fof(t17_jordan8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,k3_finseq_1(k1_jordan8(A,C))) => r1_xboole_0(k3_goboard5(k1_jordan8(A,C),B,k5_numbers),A) ) ) ) ) )).
fof(t17_jordan9,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(A)) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k1_matrix_0(A)) ) => ( r2_hidden(B,k3_goboard5(A,C,D)) <=> ( r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),A,C,D)),k17_euclid(B)) & r1_xxreal_0(k17_euclid(B),k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),A,k1_nat_1(C,1),D))) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),A,C,D)),k18_euclid(B)) & r1_xxreal_0(k18_euclid(B),k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),A,C,k1_nat_1(D,1)))) ) ) ) ) ) ) ) )).
fof(t17_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t17_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( ! [E] : ( v7_ordinal1(E) => k1_funct_1(C,E) = k5_xboole_0(D,k1_funct_1(B,E)) ) => r1_tarski(k5_subset_1(A,D,k4_kurato_0(A,B)),k4_kurato_0(A,C)) ) ) ) ) )).
fof(t17_kurato_1,axiom,( 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)) )).
fof(t17_kurato_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ( ! [D] : ( v7_ordinal1(D) => r1_tarski(k1_funct_1(B,D),k1_funct_1(C,D)) ) => r1_tarski(k1_kurato_2(A,B),k1_kurato_2(A,C)) ) ) ) ) )).
fof(t17_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,D,C,B) & m2_finseq_1(E,k3_finseq_2(D)) ) => ! [F] : ( m2_finseq_1(F,D) => ( ~ r2_hidden(A,k2_finseq_1(k1_matrix_0(E))) => k3_laplace(A,C,B,D,E,F) = E ) ) ) ) ) ) ) )).
fof(t17_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t17_latsum_1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ! [D] : ( ( 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)) ) ) ) )).
fof(t17_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ! [C] : ( 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) ) ) ) )).
fof(t17_lattice3,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k13_lattice3(A,k12_lattice3(A,B,C),C) = C ) ) ) )).
fof(t17_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t17_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & v1_lattice6(A) & l3_lattices(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(t17_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v3_ordinal1(B) => r1_tarski(A,k3_lattice8(A,B)) ) ) )).
fof(t17_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r3_lattices(A,B,k6_lattices(A)) ) ) )).
fof(t17_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( ( v4_lexbfs(B,A) & m1_lexbfs(B,A) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => r1_relset_1(k6_glib_000(A),k4_ordinal1,k5_lexbfs(A,B,C),k5_lexbfs(A,B,D)) ) ) ) ) ) )).
fof(t17_lfuzzy_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_lfuzzy_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_lfuzzy_0(A))) => ( r1_orders_2(k4_lfuzzy_0(A),B,C) <=> ! [D] : ( 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)) ) ) ) ) ) )).
fof(t17_lfuzzy_1,axiom,( ! [A] : ( ~ 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) ) ) )).
fof(t17_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_seq_2(A) & v1_limfunc1(B) ) => v2_limfunc1(k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) ) ) )).
fof(t17_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r2_limfunc2(B,A) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & v2_seq_2(k2_partfun1(k1_numbers,k1_numbers,C,k2_rcomp_1(k6_xcmplx_0(A,D),A))) ) ) | r2_limfunc2(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t17_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r2_limfunc3(B,A) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,k9_subset_1(k1_numbers,k9_xtuple_0(C),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,D),A),k2_rcomp_1(A,k2_xcmplx_0(A,D))))) => r1_xxreal_0(E,k1_funct_1(C,F)) ) ) ) ) ) | r2_limfunc3(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t17_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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) ) ) ) ) )).
fof(t17_lmod_5,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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))) ) ) ) ) )).
fof(t17_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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 ) ) ) ) )).
fof(t17_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t17_lopban_1,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(k8_lopban_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k8_lopban_1(A,B))) => ! [E] : ( v1_xreal_0(E) => ( D = k1_rlvect_1(k8_lopban_1(A,B),C,E) <=> ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t17_lopban_2,axiom,( ! [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) & v3_normsp_0(A) & v4_normsp_0(A) & v2_normsp_1(A) & l1_normsp_1(A) ) => ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & k2_normsp_0(A,B) = 1 ) ) )).
fof(t17_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) ) )).
fof(t17_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) = k9_nat_1(u1_struct_0(A),k1_bhsp_4(A,k5_lopban_4(B,A,C,D)),B) ) ) ) ) ) )).
fof(t17_lopclset,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v7_struct_0(B) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( r2_hidden(A,k1_funct_1(k8_lopclset(B),C)) <=> ? [D] : ( ~ 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) ) ) ) ) )).
fof(t17_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( ( r2_hidden(D,k13_lpspacc1(A,B,C)) & r2_hidden(E,k13_lpspacc1(A,B,C)) ) => r2_hidden(k2_valued_1(A,k2_numbers,k2_numbers,D,E),k13_lpspacc1(A,B,C)) ) ) ) ) ) ) )).
fof(t17_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_rfunct_3(B,A,k1_numbers,k3_rfunct_3(A,k1_numbers)) => k1_binop_1(k4_lpspace1(A),1,B) = B ) ) )).
fof(t17_lpspace2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => ( r1_xxreal_0(C,k5_numbers) | r1_xxreal_0(k2_power(k4_xxreal_0(A,B),C),k2_xcmplx_0(k2_power(A,C),k2_power(B,C))) ) ) ) ) ) )).
fof(t17_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(D),k1_domain_1(k4_ordinal1,k1_hilbert1,C,k3_hilbert1(k2_ltlaxio1(k3_hilbert1(A,B)),k3_hilbert1(k2_ltlaxio1(A),k2_ltlaxio1(B))))) = 1 ) ) ) ) )).
fof(t17_ltlaxio2,axiom,( ! [A] : ( m2_finseq_1(A,k1_hilbert1) => ! [B] : ( m2_finseq_1(B,k1_hilbert1) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k1_hilbert1,k6_margrel1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_hilbert1,k6_margrel1))) ) => k3_funct_2(k1_hilbert1,k6_margrel1,k12_ltlaxio1(C),k7_partfun1(k1_hilbert1,k2_ltlaxio2(k8_finseq_1(k1_hilbert1,A,B)),k3_finseq_1(k2_ltlaxio2(k8_finseq_1(k1_hilbert1,A,B))))) = k10_margrel1(k3_funct_2(k1_hilbert1,k6_margrel1,k12_ltlaxio1(C),k7_partfun1(k1_hilbert1,k2_ltlaxio2(A),k3_finseq_1(k2_ltlaxio2(A)))),k3_funct_2(k1_hilbert1,k6_margrel1,k12_ltlaxio1(C),k7_partfun1(k1_hilbert1,k2_ltlaxio2(B),k3_finseq_1(k2_ltlaxio2(B))))) ) ) ) )).
fof(t17_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => k5_ltlaxio3(k5_ltlaxio3(A)) = k5_ltlaxio3(A) ) )).
fof(t17_ltlaxio4,axiom,( ! [A] : ( ( ~ v2_ltlaxio3(A) & m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) ) => ! [B] : ( m2_finseq_1(B,k1_hilbert1) => ( k2_relset_1(k1_hilbert1,B) = k3_ltlaxio4(k5_ltlaxio4(A)) => r8_ltlaxio1(k1_subset_1(k1_hilbert1),k3_hilbert1(k12_ltlaxio3(A),k1_ltlaxio1(k7_partfun1(k1_hilbert1,k2_ltlaxio2(k4_ltlaxio2(B)),k3_finseq_1(k2_ltlaxio2(k4_ltlaxio2(B))))))) ) ) ) )).
fof(t17_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ( ( r2_hidden(k8_cqc_lang(A,D,k8_cqc_lang(A,C,B)),k4_cqc_the1(A)) & r2_hidden(C,k4_cqc_the1(A)) & r2_hidden(D,k4_cqc_the1(A)) ) => r2_hidden(B,k4_cqc_the1(A)) ) ) ) ) ) )).
fof(t17_margrel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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))) ) ) ) )).
fof(t17_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t17_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( v2_matrix10(B) & v2_matrix10(C) ) => v2_matrix10(k4_matrix10(A,B,C)) ) ) ) ) )).
fof(t17_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_matrix_2(B,k3_matrix_2(k1_nat_1(A,1))) => ~ ( k1_funct_1(B,k1_nat_1(A,1)) != k1_nat_1(A,1) & ! [C] : ( m1_matrix_2(C,k3_matrix_2(k1_nat_1(A,1))) => ~ ( v4_matrix_2(C,k2_matrix_2(k3_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(k2_matrix_2(k3_matrix_2(k1_nat_1(A,1)))),k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,1)))),k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,1)))),k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,1)))),B,C),k1_nat_1(A,1)) = k1_nat_1(A,1) ) ) ) ) ) )).
fof(t17_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [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] : ( m1_subset_1(F,u1_struct_0(E)) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(E),C,D) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(E))) ) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(E),C,D) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(E))) ) => ( ( r2_hidden(B,k2_finseq_1(k1_matrix_0(G))) & r2_hidden(A,k2_finseq_1(k1_matrix_0(G))) & H = k4_matrix_0(u1_struct_0(E),G) ) => ( r1_xxreal_0(C,k5_numbers) | r1_xxreal_0(D,k5_numbers) | k4_matrix_0(u1_struct_0(E),k3_matrix12(C,D,E,H,B,A,F)) = k6_matrix12(C,D,E,G,B,A,F) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( ( v1_matrix_0(F) & m2_finseq_1(F,k3_finseq_2(A)) ) => ! [G] : ( m2_finseq_2(G,k4_ordinal1,k4_finseq_2(E,k4_ordinal1)) => ! [H] : ( m2_finseq_2(H,k4_ordinal1,k4_finseq_2(D,k4_ordinal1)) => ( r1_tarski(k2_zfmisc_1(k10_xtuple_0(G),k10_xtuple_0(H)),k2_matrix_0(F)) => ( r2_hidden(k4_tarski(B,C),k2_matrix_0(k1_matrix13(A,F,E,D,G,H))) <=> r2_hidden(k4_tarski(k1_funct_1(G,B),k1_funct_1(H,C)),k2_matrix_0(F)) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => k4_matrix_3(B,k4_matrix_3(B,C,D),E) = k4_matrix_3(B,C,k4_matrix_3(B,D,E)) ) ) ) ) ) )).
fof(t17_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,D,C,B) & m2_finseq_1(E,k3_finseq_2(D)) ) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,D,C,A) & m2_finseq_1(F,k3_finseq_2(D)) ) => ! [G] : ( v7_ordinal1(G) => ( r2_hidden(G,k2_finseq_1(k1_matrix_0(F))) => k8_matrix_0(D,k1_matrix15(D,C,B,A,E,F),k2_xcmplx_0(k1_matrix_0(E),G)) = k8_matrix_0(D,F,G) ) ) ) ) ) ) ) ) )).
fof(t17_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,B,A,A) & m2_finseq_1(C,k3_finseq_2(B)) ) => ( v3_matrix16(C,B) => ( r1_xxreal_0(A,k5_numbers) | v1_matrix16(k4_matrix_0(B,C),B) ) ) ) ) ) )).
fof(t17_matrix17,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v4_matrix17(C,u1_struct_0(B)) => k4_matrix_0(u1_struct_0(B),C) = C ) ) ) ) )).
fof(t17_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ( v1_matrix_0(k12_finseq_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),k2_finseq_4(A,B,C))) & v2_matrix_0(k12_finseq_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),k2_finseq_4(A,B,C)),A,1,2) & m2_finseq_1(k12_finseq_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),k2_finseq_4(A,B,C)),k3_finseq_2(A)) ) ) ) ) )).
fof(t17_matrix_3,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( 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) ) ) ) ) ) )).
fof(t17_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(D) ) => k1_matrix_4(A,B,D) = k1_matrix_4(A,k1_matrix_4(A,B,C),k1_matrix_4(A,D,C)) ) ) ) ) ) )).
fof(t17_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k2_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k1_matrix_0(A) = k1_matrix_0(B) & k3_matrix_5(A,B) = k8_matrix_5(k3_finseq_1(A),k1_matrix_0(A)) ) => B = k4_matrix_5(A) ) ) ) )).
fof(t17_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( k4_matrix_3(B,C,D) = k1_matrix_3(B,A,A) & v1_matrix_6(C,A,B) ) => ( r1_xxreal_0(A,k5_numbers) | r1_matrix_6(A,B,C,D) ) ) ) ) ) ) )).
fof(t17_matrix_7,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(A),B,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( r1_xxreal_0(1,B) & v1_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)) ) ) ) ) )).
fof(t17_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v2_matrix_6(C,A,B) => v2_matrix_6(k4_matrix_3(B,C,k4_matrix_0(u1_struct_0(B),C)),A,B) ) ) ) ) )).
fof(t17_matrix_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(k7_finseq_1(B,C),k3_matrix_2(A)) => r2_hidden(k7_finseq_1(B,k3_finseq_5(C)),k3_matrix_2(A)) ) ) ) ) )).
fof(t17_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(k5_matrixc1(A,B))) => k9_matrix_5(k5_matrixc1(A,B),C) = k3_xcmplx_0(k9_matrix_5(A,C),k9_matrix_5(B,C)) ) ) ) ) )).
fof(t17_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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(k4_ordinal1,A,k10_matrixj1(B,C)) ) ) ) )).
fof(t17_matrixj2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( ( 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)))) ) ) ) ) ) ) )).
fof(t17_matrixr1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_vectsp_1)) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t17_matrixr2,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k1_matrix_0(A) = k1_matrix_0(B) & k3_finseq_1(C) = k1_matrix_0(A) ) => ( r1_xxreal_0(k3_finseq_1(A),k5_numbers) | r1_xxreal_0(k3_finseq_1(C),k5_numbers) | k6_matrixr1(k5_matrixr1(A,B),C) = k5_matrixr1(k6_matrixr1(A,C),k6_matrixr1(B,C)) ) ) ) ) ) )).
fof(t17_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( ( 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] : ( m2_finseq_1(E,u1_struct_0(A)) => ! [F] : ( m2_finseq_1(F,u1_struct_0(B)) => ( ( k3_finseq_1(F) = k3_finseq_1(E) & v13_vectsp_1(D,B,C) & v1_mod_2(D,A,B,C) ) => k4_finseqop(u1_struct_0(B),u1_struct_0(C),k5_matrlin(A,B,E,F),D) = k5_matrlin(A,C,E,k4_finseqop(u1_struct_0(B),u1_struct_0(C),F,D)) ) ) ) ) ) ) ) )).
fof(t17_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_matrlin(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t17_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t17_matrprob,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(B)) ) => ( C = D => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k2_finseq_1(k1_matrix_0(C))) => k8_matrix_0(A,C,E) = k8_matrix_0(B,D,E) ) ) ) ) ) ) ) )).
fof(t17_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ~ ( k8_matrix13(C,D) = B & ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(C),A,k7_nat_d(A,B)) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(C))) ) => k8_matrix13(C,k1_matrix15(u1_struct_0(C),A,B,k7_nat_d(A,B),D,E)) != A ) ) ) ) ) ) )).
fof(t17_matrtop2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & v3_valued_0(C) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ! [E] : ( 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] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t17_matrtop3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(D,E) ) => ( r1_xxreal_0(D,C) | k4_matrix_3(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) ) ) ) ) ) ) ) )).
fof(t17_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(t17_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)))) ) ) )).
fof(t17_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : 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)) )).
fof(t17_measure1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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,k5_numbers) = B & k1_prob_2(A,k9_setfam_1(A),E,1) = C & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ~ r1_xxreal_0(F,1) => k1_prob_2(A,k9_setfam_1(A),E,F) = D ) ) ) ) ) ) )).
fof(t17_measure3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ~ ( ! [E] : ( m1_subset_1(E,k4_ordinal1) => m1_measure3(k9_nat_1(k9_setfam_1(A),D,E),A,B,C) ) & ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ~ ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_tarski(k9_nat_1(k9_setfam_1(A),D,F),k9_nat_1(B,E,F)) & k12_supinf_2(C,k9_nat_1(B,E,F)) = k1_supinf_2 ) ) ) ) ) ) ) )).
fof(t17_measure6,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t17_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m3_measure8(D,A,C,B) => ~ ( r2_hidden(C,B) & ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,B) & v1_prob_2(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ~ ( C = k3_tarski(k2_relset_1(B,E)) & ! [F] : ( v7_ordinal1(F) => r1_tarski(k9_nat_1(B,E,F),k1_measure8(A,B,D,F)) ) ) ) ) ) ) ) )).
fof(t17_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => k5_member_1(k6_subset_1(A,B)) = k6_subset_1(k5_member_1(A),k5_member_1(B)) ) ) )).
fof(t17_membered,axiom,( ! [A] : ( v5_membered(A) => ( ! [B] : ( v1_int_1(B) => r2_hidden(B,A) ) => A = k4_numbers ) ) )).
fof(t17_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t17_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( ( D = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),B,k6_xcmplx_0(1,G)),k1_rlvect_1(k15_euclid(2),C,G)) & E = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),C,k6_xcmplx_0(1,H)),k1_rlvect_1(k15_euclid(2),A,H)) & F = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),A,k6_xcmplx_0(1,I)),k1_rlvect_1(k15_euclid(2),B,I)) ) => k1_euclid_6(D,E,F) = k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(1,G),k6_xcmplx_0(1,H)),k6_xcmplx_0(1,I)),k3_xcmplx_0(k3_xcmplx_0(G,H),I)),k1_euclid_6(A,B,C)) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_mesfun10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & v1_mesfunc8(B,A,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,C,k6_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,k6_numbers))) ) => ! [E] : ( m1_subset_1(E,C) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ~ ( E = k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers)) & E = k1_relset_1(A,F) & ! [G] : ( v7_ordinal1(G) => r1_mesfunc1(A,C,k4_mesfunc5(A,k6_numbers,B,G),E) ) & r1_mesfunc5(A,C,D,F) & v6_supinf_2(F) & ! [G] : ( m1_subset_1(G,A) => ! [H] : ( v7_ordinal1(H) => ( r2_hidden(G,E) => r1_xxreal_0(k12_supinf_2(k10_mesfunc1(A,k4_mesfunc5(A,k6_numbers,B,H)),G),k12_supinf_2(F,G)) ) ) ) & ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k4_ordinal1,k6_numbers) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ~ ( ! [H] : ( v7_ordinal1(H) => k12_supinf_2(G,H) = k7_mesfunc5(A,C,D,k4_mesfunc5(A,k6_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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t17_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & v1_mesfunc8(C,A,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [E] : ( v1_xreal_0(E) => ( ! [F] : ( v7_ordinal1(F) => k1_funct_1(D,F) = k8_subset_1(A,k1_relset_1(A,k4_mesfunc5(A,k1_numbers,C,k5_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,k5_numbers)),k18_mesfunc1(A,k2_mesfun7c(A,C),E)) ) ) ) ) ) ) )).
fof(t17_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( v1_mesfunc8(B,A,k1_numbers) => v1_mesfunc8(k2_mesfun9c(A,B),A,k1_numbers) ) ) ) )).
fof(t17_mesfunc1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ! [D] : ( v1_xxreal_0(D) => ( 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))) ) ) ) )).
fof(t17_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_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))) ) ) ) )).
fof(t17_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_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)) ) ) ) ) )).
fof(t17_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t17_mesfunc7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ! [G] : ( ( ~ v1_xboole_0(G) & m1_subset_1(G,k1_zfmisc_1(k6_numbers)) ) => ( ( k9_subset_1(A,k1_relset_1(A,D),k1_relset_1(A,E)) = F & k10_xtuple_0(D) = G & v3_valued_0(E) & r1_mesfunc1(A,B,D,F) & v5_xxreal_2(k10_xtuple_0(D)) & r1_mesfunc5(A,B,C,E) ) => ( r1_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,k5_mesfunc1(A,D,E),F)) & ? [H] : ( 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,k6_numbers,k5_mesfunc1(A,D,k10_mesfunc1(A,E)),F)) = k4_xxreal_3(H,k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,k10_mesfunc1(A,E),F))) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k6_numbers)) & v1_mesfunc8(C,A,k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [E] : ( v1_xreal_0(E) => ( ! [F] : ( v7_ordinal1(F) => k9_nat_1(k9_setfam_1(A),D,F) = k9_subset_1(A,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,C,k5_numbers)),k17_mesfunc1(A,k4_mesfunc5(A,k6_numbers,C,F),E)) ) => ! [F] : ( v7_ordinal1(F) => k9_nat_1(k9_setfam_1(A),k6_setlim_1(A,B,D),F) = k9_subset_1(A,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,C,k5_numbers)),k17_mesfunc1(A,k4_mesfunc5(A,k6_numbers,k4_mesfunc8(A,C),F),E)) ) ) ) ) ) ) ) )).
fof(t17_metric_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_metric_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k8_metric_1(B,C,A) = a_3_3_metric_1(A,B,C) ) ) ) )).
fof(t17_metric_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_metric_1(B) ) => ( r2_hidden(A,k2_metric_2(B)) <=> m1_metric_2(A,B) ) ) )).
fof(t17_metric_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => r1_xxreal_0(k1_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(k1_square_1(A),k1_square_1(B)),k1_square_1(E)),k2_xcmplx_0(k2_xcmplx_0(k1_square_1(C),k1_square_1(D)),k1_square_1(F)))) ) ) ) ) ) ) )).
fof(t17_metric_6,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ! [D] : ( 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) ) ) ) ) )).
fof(t17_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(t17_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_rlvect_2(B,k10_funcsdom(k2_finseq_1(A))) <=> m1_rlvect_2(B,k15_euclid(A)) ) ) )).
fof(t17_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_midsp_1(A,F,G,B,C) & r1_midsp_1(A,F,G,D,E) ) => r1_midsp_1(A,B,C,D,E) ) ) ) ) ) ) ) ) )).
fof(t17_midsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_midsp_2(A,B) = k1_midsp_2(A,C) => B = C ) ) ) ) )).
fof(t17_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_nat_1(A,2)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(B))) => ! [E] : ( ( 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 ) ) ) ) ) )).
fof(t17_mmlquer2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ ( k6_mmlquer2(B,A) = k5_numbers & r2_hidden(A,k10_xtuple_0(B)) ) ) )).
fof(t17_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( ( r1_relset_1(A,A,E,F) & r1_tarski(B,C) & r1_relset_1(A,A,D,G) ) => r1_tarski(k7_mmlquery(A,D,B,F),k7_mmlquery(A,G,C,E)) ) ) ) ) ) ) ) )).
fof(t17_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( v2_mod_2(B,A) & v3_mod_2(B,A) & l1_mod_2(B,A) ) => ! [C] : ( ( v2_mod_2(C,A) & v3_mod_2(C,A) & l1_mod_2(C,A) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t17_mod_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t17_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v36_algstr_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t17_modal_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ! [B] : ( 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),k14_trees_3(k5_numbers),k4_trees_1(A,B)) ) ) ) )).
fof(t17_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k48_modelc_1(A,B,D))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t17_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ( r1_modelc_2(C,k7_modelc_2(A,B)) <=> ( C = A | C = B ) ) ) ) ) )).
fof(t17_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k13_modelc_2(A))) => r1_xxreal_0(k5_numbers,k18_modelc_3(A,B)) ) ) )).
fof(t17_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => r1_xxreal_0(k11_nat_3(A,C),k11_nat_3(B,C)) ) => r1_tarski(k22_pre_poly(k8_newton,k13_nat_3(A)),k22_pre_poly(k8_newton,k13_nat_3(B))) ) ) ) )).
fof(t17_monoid_0,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t17_monoid_1,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(t17_morph_01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(t17_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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) ) ) )).
fof(t17_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) ) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t17_msafree4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_rewrite1(B) & v4_rewrite1(B) ) => ( r3_rewrite1(B,A) => k2_rewrite1(B,A) = A ) ) )).
fof(t17_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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] : ( 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) ) ) ) ) ) )).
fof(t17_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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,k1_funct_6(D),B) & r2_pboole(A,k2_funct_6(D),C) ) ) ) ) ) )).
fof(t17_mssublat,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v13_struct_0(A,1) & v5_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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)))) ) ) ) )).
fof(t17_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( m3_pboole(D,u1_struct_0(A),u3_msualg_1(A,C)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t17_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ( r6_msualg_3(A,B,C) => r6_msualg_3(A,C,B) ) ) ) ) )).
fof(t17_msualg_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t17_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t17_msualg_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m2_nat_lat(B,A) => ( v2_msualg_7(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => k15_lattice3(A,C) = k15_lattice3(B,C) ) ) ) ) )).
fof(t17_msualg_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k5_msualg_5(u1_struct_0(A),u3_msualg_1(A,B))))) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t17_msualg_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( m1_subset_1(F,k3_msualg_1(A,E,C)) => ? [G] : ( m1_subset_1(G,k3_msualg_1(A,E,B)) & k5_msualg_3(A,B,C,E,D,G) = F ) ) ) ) ) ) ) ) )).
fof(t17_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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(k5_numbers)) & v1_funct_1(k2_msuhom_1(A,B,C)) & v1_partfun1(k2_msuhom_1(A,B,C),k1_tarski(k5_numbers)) ) ) ) ) ) )).
fof(t17_mycielsk,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_necklace(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t17_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(u1_struct_0(A))))) ) => ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => v3_pre_topc(k9_nat_1(k1_zfmisc_1(u1_struct_0(A)),B,C),A) ) => v3_pre_topc(k1_prob_1(u1_struct_0(A),B),A) ) ) ) )).
fof(t17_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ! [B] : ( v7_ordinal1(B) => ? [C] : ( v7_ordinal1(C) & ? [D] : ( v7_ordinal1(D) & B = k2_xcmplx_0(k3_xcmplx_0(A,C),D) & ~ r1_xxreal_0(A,D) ) ) ) ) ) )).
fof(t17_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k4_nat_d(k2_power(2,A),2) = k5_numbers ) ) )).
fof(t17_nat_3,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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))) ) ) )).
fof(t17_nat_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( v1_int_2(B) & r1_nat_d(D,k2_nat_1(A,k11_newton(B,k1_nat_1(C,1)))) ) => ( r1_nat_d(D,k2_nat_1(A,k11_newton(B,C))) | r1_nat_d(k11_newton(B,k1_nat_1(C,1)),D) ) ) ) ) ) ) )).
fof(t17_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ( r1_int_2(B,C) => k6_nat_d(A,k3_xcmplx_0(B,C)) = k2_nat_1(k6_nat_d(A,B),k6_nat_d(A,C)) ) ) ) ) )).
fof(t17_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( k4_nat_d(A,C) = k5_numbers => k4_nat_d(k2_xcmplx_0(A,B),C) = k4_nat_d(B,C) ) ) ) ) )).
fof(t17_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ( r1_nattra_1(A,B,C,D) => ! [E] : ( m1_nattra_1(E,A,B,C,D) => ( r2_funct_2(u1_struct_0(A),u4_struct_0(B),k3_nattra_1(A,B,C,D,D,E,k1_nattra_1(A,B,D)),E) & r2_funct_2(u1_struct_0(A),u4_struct_0(B),k3_nattra_1(A,B,C,C,D,k1_nattra_1(A,B,C),E),E) ) ) ) ) ) ) ) )).
fof(t17_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( 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] : ( m1_ncfcont1(E,B,k7_partfun1(u1_struct_0(B),C,D)) => ? [F] : ( m1_ncfcont1(F,A,D) & r1_tarski(k7_relset_1(u1_struct_0(A),u1_struct_0(B),C,F),E) ) ) ) ) ) ) ) ) )).
fof(t17_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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,k4_normsp_0(u1_struct_0(C),B,D)) ) ) ) ) )).
fof(t17_ndiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( v12_struct_0(C,k4_ordinal1,B) => v12_struct_0(k1_valued_0(u1_struct_0(B),C,A),k4_ordinal1,B) ) ) ) ) )).
fof(t17_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( 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)) ) ) ) ) ) ) ) ) )).
fof(t17_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(k2_ndiff_4(A,C,B),D) = k5_euclid(A) ) ) ) ) ) ) ) )).
fof(t17_neckla_3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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)) ) ) ) )).
fof(t17_necklace,axiom,( ! [A] : ( v7_ordinal1(A) => u1_orders_2(k4_necklace(A)) = k2_xboole_0(a_1_0_necklace(A),a_1_1_necklace(A)) ) )).
fof(t17_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t17_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ~ r1_xxreal_0(k2_newton(A),k5_numbers) ) )).
fof(t17_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_nfcont_1(A,B,C,D) => ( r2_nfcont_1(A,k4_normsp_0(u1_struct_0(A),B,C),D) & r1_nfcont_1(A,B,k5_vfunct_1(u1_struct_0(A),B,C),D) ) ) ) ) ) ) )).
fof(t17_nfcont_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(D,A) & ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( v1_xreal_0(G) => ~ ( r2_hidden(G,A) & ~ r1_xxreal_0(F,k9_complex1(k6_xcmplx_0(G,D))) & r1_xxreal_0(E,k2_normsp_0(B,k5_algstr_0(B,k7_partfun1(u1_struct_0(B),C,G),k7_partfun1(u1_struct_0(B),C,D)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t17_normform,axiom,( ! [A] : 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)) )).
fof(t17_normsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k1_normsp_0(A,B,C) = k1_normsp_0(A,B,k2_xcmplx_0(C,D)) ) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k1_normsp_0(A,B,C) = k1_normsp_0(A,B,D) ) ) ) ) ) )).
fof(t17_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_normsp_2(A)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t17_numbers,axiom,( r1_tarski(k4_ordinal1,k4_numbers) )).
fof(t17_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t17_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( r2_hidden(D,k7_subset_1(k1_zfmisc_1(u1_struct_0(A)),k10_openlatt(A,C),k10_openlatt(A,B))) => ( ~ 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(C,D) & ~ r2_hidden(B,D) ) ) ) ) ) )).
fof(t17_oposet_1,axiom,( v12_oposet_1(k1_oposet_1) )).
fof(t17_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,B,C) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t17_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_ordeq_01(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_rsspace4(A,B))) => ( C = D => k2_normsp_0(k5_ordeq_01(A,B),C) = k2_normsp_0(k9_rsspace4(A,B),D) ) ) ) ) ) )).
fof(t17_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v2_orders_1(A) => v2_orders_1(k2_relat_1(A)) ) ) )).
fof(t17_orders_2,axiom,( ! [A] : ( ( ~ 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 ) )).
fof(t17_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r2_hidden(A,B) <=> r1_ordinal1(k1_ordinal1(A),B) ) ) ) )).
fof(t17_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( r2_hidden(A,B) => r2_hidden(k2_ordinal2(B),B) ) ) )).
fof(t17_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t17_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_ordinal2(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_ordinal2(C) ) => ( ( v2_ordinal2(B) & v3_ordinal2(B) & v3_ordinal2(C) & A = k3_relat_1(B,C) ) => v3_ordinal2(A) ) ) ) ) )).
fof(t17_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => k1_ordinal6(A) = A ) )).
fof(t17_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( r1_orders_2(B,F,D) & r1_orders_2(B,F,E) ) => ( r1_orders_2(B,D,C) | k1_ortsp_1(A,B,k3_rlvect_1(B,C,F),D,E) = k1_ortsp_1(A,B,C,D,E) ) ) ) ) ) ) ) ) )).
fof(t17_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m1_subset_1(D,k3_msualg_1(A,C,k8_osafree(A,B))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t17_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t17_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_osalg_2(C,A,B) => r2_hidden(u3_msualg_1(A,B),k5_osalg_2(A,B,C)) ) ) ) )).
fof(t17_osalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t17_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t17_papdesaf,axiom,( ! [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) ) => ! [B] : ( ( ~ v7_struct_0(B) & v2_analoaf(B) & l1_analoaf(B) ) => ( B = k2_analoaf(A) => v11_aff_2(k2_diraf(B)) ) ) ) )).
fof(t17_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A))) => ? [E] : ( 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) ) ) ) ) ) )).
fof(t17_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t17_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_tarski(A),B))) ) => v2_funct_1(C) ) )).
fof(t17_partfun2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t17_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => k3_partit1(A,B,B) = B ) ) )).
fof(t17_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t17_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( ~ r3_diraf(A,F,B,C) & r2_analoaf(A,F,C,F,D) & r2_analoaf(A,C,B,D,E) & F != E & r1_diraf(A,B,F,E) ) ) ) ) ) ) ) )).
fof(t17_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( ( r2_pboole(A,D,B) & r2_pboole(A,D,C) ) => r2_pboole(A,D,k3_pboole(A,B,C)) ) ) ) ) )).
fof(t17_pcomps_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => r1_setfam_1(B,k1_pcomps_1(A,B)) ) ) )).
fof(t17_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ( l2_pcs_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k19_pcs_0(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k19_pcs_0(A,B))) => ( r1_pcs_0(k19_pcs_0(A,B),C,D) <=> ~ ( ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( E = C & F = D & r1_pcs_0(A,E,F) ) ) ) & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ~ ( E = C & F = D & r1_pcs_0(B,E,F) ) ) ) ) ) ) ) ) ) )).
fof(t17_pdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( 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] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(B),k1_euclid(C)))) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(k4_real_ns1(B))) => ! [G] : ( 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(k4_ordinal1,1)) = k11_pdiff_1(B,C,A,E,G) ) ) ) ) ) ) ) ) )).
fof(t17_pdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(2)) => ! [C] : ( m1_rcomp_1(C,k3_funct_2(k1_euclid(2),k1_numbers,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] : ( ( v9_ordinal1(D) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,E) = k1_tarski(k3_funct_2(k1_euclid(2),k1_numbers,k1_pdiff_1(1,2),B)) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),C) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(2,1,A,B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(2,1,A,B))))) & k10_pdiff_1(2,1,A,B) = k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(2,1,A,B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(2,1,A,B))))) ) ) ) ) ) ) ) ) )).
fof(t17_pdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(2)) => ! [C] : ( m1_rcomp_1(C,k3_funct_2(k1_euclid(2),k1_numbers,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] : ( ( v9_ordinal1(D) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,E) = k1_tarski(k3_funct_2(k1_euclid(2),k1_numbers,k1_pdiff_1(1,2),B)) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),C) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(2,1,k1_pdiff_3(1,2,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(2,1,k1_pdiff_3(1,2,A),B))))) & k2_pdiff_3(A,B) = k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(2,1,k1_pdiff_3(1,2,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(2,1,k1_pdiff_3(1,2,A),B))))) ) ) ) ) ) ) ) ) )).
fof(t17_pdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(3)) => ! [F] : ( ( 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 = k10_pdiff_1(3,2,F,E) <=> ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & ? [I] : ( v1_xreal_0(I) & E = k11_finseq_1(G,H,I) & ? [J] : ( m1_rcomp_1(J,H) & r1_tarski(J,k1_relset_1(k1_numbers,k1_pdiff_2(3,2,F,E))) & ? [K] : ( v1_funct_1(K) & v3_fdiff_1(K) & m1_subset_1(K,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [L] : ( v1_funct_1(L) & v2_fdiff_1(L) & m1_subset_1(L,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & D = k1_funct_1(K,1) & ! [M] : ( v1_xreal_0(M) => ( r2_hidden(M,J) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,2,F,E),M),k1_funct_1(k1_pdiff_2(3,2,F,E),H)) = k2_xcmplx_0(k1_funct_1(K,k6_xcmplx_0(M,H)),k1_funct_1(L,k6_xcmplx_0(M,H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t17_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(C,A) & B != k5_numbers & k3_funct_2(k1_numbers,k1_euclid(A),k6_pdiff_1(A,C,k5_euclid(A)),B) = k5_euclid(A) ) ) ) ) )).
fof(t17_pdiff_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(B)) => ( ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,B) ) => r1_xxreal_0(k9_complex1(k3_funct_2(k1_euclid(B),k1_numbers,k1_pdiff_1(D,B),C)),A) ) ) => r1_xxreal_0(k12_euclid(C),k3_xcmplx_0(B,A)) ) ) ) ) )).
fof(t17_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [E] : ( v1_xreal_0(E) => ( r1_pdiff_6(C,B,A,D) => ( r1_pdiff_6(C,B,A,k9_integr15(B,E,k1_euclid(A),D)) & ! [F] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t17_pencil_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ( v5_pencil_1(k1_pencil_1(A,B,C)) & ~ ! [D] : ( m1_subset_1(D,A) => v3_pencil_1(k1_pencil_1(A,B,D)) ) ) ) => v5_pencil_1(k5_pencil_1(A,B)) ) ) ) )).
fof(t17_pencil_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t17_pencil_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v15_pencil_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_pencil_1(A,B))) => ! [D] : ( 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] : ( ( v1_relat_1(E) & v4_relat_1(E,A) & v1_funct_1(E) & v1_partfun1(E,A) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,A) & v1_funct_1(F) & v1_partfun1(F,A) ) => ~ ( E = C & F = D & ! [G] : ( m1_subset_1(G,A) => ~ ( ! [H] : ( m1_subset_1(H,u1_struct_0(k2_pencil_1(A,B,G))) => ! [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] : ( m1_subset_1(H,A) => ( H != G => k1_funct_1(E,H) = k1_funct_1(F,H) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( 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)) ) ) ) ) )).
fof(t17_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( ~ r1_xxreal_0(A,2) & v1_int_2(A) & v1_abian(A) ) ) )).
fof(t17_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_petri(B,A) <=> v6_petri(k12_petri(A,B),k11_petri(A)) ) ) ) )).
fof(t17_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,k4_ordinal1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ( r2_pnproc_1(A,k2_pnproc_1(A,C,D),B) => r1_pnproc_1(A,k3_pnproc_1(A,k3_pnproc_1(A,B,C),D),k3_pnproc_1(A,B,k2_pnproc_1(A,C,D))) ) ) ) ) )).
fof(t17_polyalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_polyalg1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_polyalg1(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ( E = F => k4_vectsp_1(A,B,D,E) = k4_vectsp_1(A,C,D,F) ) ) ) ) ) ) ) )).
fof(t17_polyeq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_newton(E,3),k3_xcmplx_0(k5_numbers,k1_square_1(E))),k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),C),k1_square_1(B)),k3_xcmplx_0(3,k1_square_1(A))),E)),k2_xcmplx_0(k3_xcmplx_0(2,k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(3,A)),3)),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),D),k3_xcmplx_0(B,C)),k3_xcmplx_0(3,k1_square_1(A))))) = k5_numbers => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( ( F = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),C),k1_square_1(B)),k3_xcmplx_0(3,k1_square_1(A))) & G = k2_xcmplx_0(k3_xcmplx_0(2,k1_newton(k7_xcmplx_0(B,k3_xcmplx_0(3,A)),3)),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,A),D),k3_xcmplx_0(B,C)),k3_xcmplx_0(3,k1_square_1(A)))) ) => k4_polyeq_1(1,k5_numbers,F,G,E) = k5_numbers ) ) ) ) ) ) ) ) ) )).
fof(t17_polyeq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( v1_xcmplx_0(F) => ( ! [G] : ( v1_xcmplx_0(G) => k2_polyeq_1(A,B,C,G) = k2_polyeq_1(D,E,F,G) ) => ( A = D & B = E & C = F ) ) ) ) ) ) ) ) )).
fof(t17_polyeq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( k2_xcmplx_0(k1_newton(A,E),k1_newton(B,E)) = C & k6_xcmplx_0(k1_newton(A,E),k1_newton(B,E)) = D & v1_abian(E) & r1_xxreal_0(1,E) & ~ r1_xxreal_0(k2_xcmplx_0(C,D),k5_numbers) & ~ r1_xxreal_0(k6_xcmplx_0(C,D),k5_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))) ) ) ) ) ) ) ) )).
fof(t17_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t17_polyform,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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 ) ) )).
fof(t17_polynom1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( 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) ) => k4_polynom1(A,B,k5_vfunct_1(k15_pre_poly(A),B,C),D) = k4_algstr_0(B,k4_polynom1(A,B,C,D)) ) ) ) )).
fof(t17_polynom3,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ( A = B => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k17_finseq_1(k1_numbers,C,A) = k17_finseq_1(k4_ordinal1,C,B) ) ) ) ) )).
fof(t17_polynom4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_polynom4(A,k9_polynom3(A),B) = k4_struct_0(A) ) ) )).
fof(t17_polynom5,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k2_polynom5(A,B,2),k13_polynom3(A,B,B)) ) ) )).
fof(t17_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(t17_polynom8,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( k3_polynom8(A,B,k1_nat_1(C,1)) = k8_group_1(A,k3_polynom8(A,B,C),B) & k3_polynom8(A,B,k1_nat_1(C,1)) = k8_group_1(A,B,k3_polynom8(A,B,C)) ) ) ) ) )).
fof(t17_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t17_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( ~ r1_xxreal_0(B,A) & ~ ( ~ ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(1,C) ) & v1_abian(C) ) & r1_xxreal_0(k1_power(C,B),k1_power(C,A)) ) ) ) ) )).
fof(t17_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ! [E] : ( 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(k9_funct_6(E),k4_card_3(k1_funct_6(k12_pralg_2(A,B,C,D)))) ) ) ) ) ) ) )).
fof(t17_pre_circ,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) ) => ! [C] : ( m1_trees_1(C,k9_xtuple_0(A)) => k1_nat_1(k5_card_1(k7_trees_2(A,C,B)),k5_card_1(k5_trees_2(A,C))) = k1_nat_1(k5_card_1(A),k5_card_1(B)) ) ) ) )).
fof(t17_pre_ff,axiom,( ! [A] : ( v7_ordinal1(A) => ~ r1_xxreal_0(k1_nat_1(k3_xcmplx_0(2,A),1),A) ) )).
fof(t17_pre_poly,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( r1_tarski(k1_relat_1(B),A) => m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) ) )).
fof(t17_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t17_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t17_prob_1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => r2_hidden(k1_prob_1(A,C),B) ) ) )).
fof(t17_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m2_prob_1(D,A,B) => ( ~ ( ~ r1_xxreal_0(1,k3_funct_2(B,k1_numbers,D,C)) & r1_xxreal_0(k3_funct_2(B,k1_numbers,D,k7_prob_1(A,B,k4_prob_1(A,B),C)),k5_numbers) ) & ~ ( ~ r1_xxreal_0(k3_funct_2(B,k1_numbers,D,k7_prob_1(A,B,k4_prob_1(A,B),C)),k5_numbers) & r1_xxreal_0(1,k3_funct_2(B,k1_numbers,D,C)) ) ) ) ) ) ) )).
fof(t17_prob_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => r1_tarski(k1_prob_2(B,k9_setfam_1(B),k3_prob_3(B,C),A),k1_prob_2(B,k9_setfam_1(B),C,A)) ) ) )).
fof(t17_prob_4,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k1_prob_4(A,k9_setfam_1(A),B,k1_nat_1(C,1)) = k1_measure1(A,k9_setfam_1(A),k1_prob_4(A,k9_setfam_1(A),k3_prob_3(A,B),k1_nat_1(C,1)),k1_prob_4(A,k9_setfam_1(A),B,C)) ) ) ) )).
fof(t17_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t17_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ( ( r1_collsp(A,H,B,C) & r1_collsp(A,B,D,I) & r1_collsp(A,C,E,I) & r1_collsp(A,D,F,J) & r1_collsp(A,E,G,J) & r1_collsp(A,B,F,K) & r1_collsp(A,C,G,K) ) => ( B = C | r1_projdes1(A,B,D,F,H) | r1_collsp(A,C,E,G) | r1_collsp(A,I,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ~ ( ~ ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => r4_projpl_1(A,B,C,D) ) ) ) & ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ? [D] : ( m1_subset_1(D,u2_incsp_1(A)) & r4_incsp_1(A,k7_domain_1(u1_incsp_1(A),B,C),D) ) ) ) & ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => r1_incsp_1(A,B,C) ) ) ) ) )).
fof(t17_projred1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & v8_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ? [C] : ( m1_subset_1(C,u1_incsp_1(A)) & ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & ? [E] : ( m1_subset_1(E,u1_incsp_1(A)) & ? [F] : ( 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) ) ) ) ) ) ) )).
fof(t17_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u1_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u1_incsp_1(A)) => ! [H] : ( m1_subset_1(H,u1_incsp_1(A)) => ! [I] : ( m1_subset_1(I,u1_incsp_1(A)) => ! [J] : ( m1_subset_1(J,u1_incsp_1(A)) => ! [K] : ( m1_subset_1(K,u2_incsp_1(A)) => ! [L] : ( m1_subset_1(L,u2_incsp_1(A)) => ! [M] : ( m1_subset_1(M,u2_incsp_1(A)) => ! [N] : ( m1_subset_1(N,u2_incsp_1(A)) => ! [O] : ( m1_subset_1(O,u2_incsp_1(A)) => ! [P] : ( m1_subset_1(P,u2_incsp_1(A)) => ! [Q] : ( m1_subset_1(Q,u2_incsp_1(A)) => ! [R] : ( m1_subset_1(R,u2_incsp_1(A)) => ( ( r4_incsp_1(A,k7_domain_1(u1_incsp_1(A),D,G),N) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),G,I,E),O) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),D,E,H),P) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),B,C,E),Q) & r4_incsp_1(A,k7_domain_1(u1_incsp_1(A),D,J),R) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),B,G,H),K) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),C,H,J),L) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),G,J,F),M) & r1_incsp_1(A,F,Q) ) => ( r1_incsp_1(A,B,N) | r1_incsp_1(A,B,P) | r1_incsp_1(A,C,O) | r1_incsp_1(A,C,P) | r1_incsp_1(A,C,R) | r1_projred2(A,N,O,P) | B = C | N = R | ( ~ r1_incsp_1(A,F,N) & ~ r1_incsp_1(A,F,R) & C != F ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) ) => ! [B] : ( m1_prvect_1(B,A) => ( ! [C] : ( m2_subset_1(C,k4_ordinal1,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)) ) ) ) )).
fof(t17_prvect_3,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( ( v1_relat_1(B) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finseq_1(B) & v2_prvect_2(B) ) => ? [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(k14_prvect_2(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_prvect_2(B))) => ? [F] : ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) & ? [G] : ( 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] : ( m1_subset_1(D,u1_struct_0(k7_prvect_3(k14_prvect_2(A),k14_prvect_2(B)))) => ! [E] : ( 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] : ( m1_subset_1(D,u1_struct_0(k7_prvect_3(k14_prvect_2(A),k14_prvect_2(B)))) => ! [E] : ( 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] : ( m1_subset_1(D,u1_struct_0(k7_prvect_3(k14_prvect_2(A),k14_prvect_2(B)))) => k2_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)) = k2_normsp_0(k7_prvect_3(k14_prvect_2(A),k14_prvect_2(B)),D) ) ) ) ) )).
fof(t17_pscomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v2_compts_1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t17_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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,B,C) ) ) ) )).
fof(t17_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ( k1_xtuple_0(C) != k5_numbers & k1_xtuple_0(C) != 1 & k1_xtuple_0(C) != 2 & k1_xtuple_0(C) != 3 ) ) ) ) )).
fof(t17_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( m2_subset_1(E,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [F] : ( m2_subset_1(F,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t17_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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))) ) ) ) )).
fof(t17_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t17_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_qc_trans(B,A) & m1_qc_lang1(B) ) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(B),k3_cqc_lang(B)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(B),k3_qc_lang1(B)) => ! [E] : ( m2_subset_1(E,k2_qc_lang1(B),k3_qc_lang1(B)) => ! [F] : ( m2_subset_1(F,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [G] : ( m2_subset_1(G,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [H] : ( m2_subset_1(H,k2_qc_lang1(A),k3_qc_lang1(A)) => ( ( F = C & G = D & H = E ) => k4_substut2(A,F,G,H) = k4_substut2(B,C,D,E) ) ) ) ) ) ) ) ) ) )).
fof(t17_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v10_lattices(A) & v4_lattice3(A) & v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t17_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k23_quaterni(A,k22_quaterni(B,C)) = k22_quaterni(k23_quaterni(A,B),k23_quaterni(A,C)) ) ) ) )).
fof(t17_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k1_square_1(k28_quaterni(k23_quaterni(A,B))) = k3_xcmplx_0(k1_square_1(k28_quaterni(A)),k1_square_1(k28_quaterni(B))) ) ) )).
fof(t17_quaterni,axiom,( k10_quaterni(k11_quaterni,k12_quaterni) = k1_xcmplx_0 )).
fof(t17_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(k1_quin_1(A,B,C),k5_numbers) & r1_xxreal_0(k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A)),k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A))) ) ) ) ) )).
fof(t17_quofield,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(t17_radix_1,axiom,( k11_radix_1(k5_numbers) = k5_numbers )).
fof(t17_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v3_card_1(D,B) & m2_finseq_1(D,k3_radix_1(C)) ) => ( ( r1_xxreal_0(2,C) & r2_hidden(A,k2_finseq_1(k2_xcmplx_0(B,1))) ) => m2_subset_1(k8_radix_3(A,C,B,D),k4_numbers,k4_radix_3(C)) ) ) ) ) ) )).
fof(t17_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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,k5_numbers)) ) ) ) ) ) )).
fof(t17_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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),k5_numbers))) ) ) ) ) )).
fof(t17_ramsey_1,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( v7_ordinal1(B) & ! [C] : ( v1_finset_1(C) => ! [D] : ( m1_eqrel_1(D,k3_group_10(C,2)) => ~ ( r1_xxreal_0(B,k5_card_1(C)) & k5_card_1(D) = 2 & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(C)) => ~ ( r1_xxreal_0(A,k5_card_1(E)) & r1_ramsey_1(C,2,E,D) ) ) ) ) ) ) ) )).
fof(t17_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ~ ( v3_prob_1(B) & ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & k1_prob_1(A,B) != k9_nat_1(k9_setfam_1(A),B,D) ) ) ) ) ) )).
fof(t17_random_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( m2_prob_1(C,A,k1_random_1(A)) => ! [D] : ( m2_prob_1(D,B,k1_random_1(B)) => ! [E] : ! [F] : ( ( r2_hidden(E,A) & r2_hidden(F,B) ) => k12_supinf_2(k2_random_2(A,B,C,D),k1_tarski(k4_tarski(E,F))) = k1_extreal1(k12_supinf_2(C,k1_tarski(E)),k12_supinf_2(D,k1_tarski(F))) ) ) ) ) ) )).
fof(t17_random_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & v1_random_3(C,A,B,k1_random_1(A),k1_random_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( r2_hidden(D,k1_random_1(B)) => k12_supinf_2(k2_random_3(A,B,k1_random_1(A),k1_random_1(B),k2_random_1(A),C),D) = k7_xcmplx_0(k5_card_1(k8_relset_1(A,B,C,D)),k5_card_1(A)) ) ) ) ) )).
fof(t17_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( 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) => r1_struct_0(k1_ranknull(A,B,C,D),k5_algstr_0(B,E,F)) ) ) ) ) ) ) ) )).
fof(t17_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ( r1_xxreal_0(k5_numbers,A) => ( ( k2_rat_1(A) != A & k1_rat_1(A) != 1 ) | m1_subset_1(A,k4_ordinal1) ) ) ) )).
fof(t17_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( r1_hurwitz(A,C,B) & v1_polynom5(B,A) ) => r2_ratfunc1(A,B,C) ) ) ) ) )).
fof(t17_rcomp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_rcomp_1(B,A) => ! [C] : ( m1_rcomp_1(C,A) => ? [D] : ( m1_rcomp_1(D,A) & r1_tarski(D,B) & r1_tarski(D,C) ) ) ) ) )).
fof(t17_rcomp_3,axiom,( ! [A] : ( ( v5_xxreal_2(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(k3_seq_4(A),A) => ( r2_hidden(k2_seq_4(A),A) | A = k3_rcomp_1(k3_seq_4(A),k2_seq_4(A)) ) ) ) )).
fof(t17_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(A,B) & k9_nat_1(k4_ordinal1,k2_real_3(D,C),A) = k5_numbers ) => ( A = k5_numbers | k9_nat_1(k4_ordinal1,k2_real_3(D,C),B) = k5_numbers ) ) ) ) ) ) )).
fof(t17_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( 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) ) ) ) )).
fof(t17_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k4_real_ns1(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k4_real_ns1(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k7_real_ns1(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k7_real_ns1(A))))) ) => ( ( r1_funct_2(k4_ordinal1,u1_struct_0(k4_real_ns1(A)),k4_ordinal1,u1_struct_0(k7_real_ns1(A)),B,C) & v1_rsspace3(B,k4_real_ns1(A)) ) => v1_bhsp_3(C,k7_real_ns1(A)) ) ) ) ) )).
fof(t17_realset2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) )).
fof(t17_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t17_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [D] : ( ( v1_rearran1(D) & v2_rearran1(D) & v3_rearran1(D,k1_zfmisc_1(A)) & m2_finseq_1(D,k1_zfmisc_1(A)) ) => ( ( v1_partfun1(C,B) & k5_card_1(A) = k5_card_1(B) ) => k20_rfunct_3(A,k3_rearran1(B,A,D,C),A) = k20_rfunct_3(B,C,B) ) ) ) ) ) )).
fof(t17_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => k2_relat_1(k2_xboole_0(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) ) ) )).
fof(t17_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) ) ) )).
fof(t17_relset_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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)) ) ) ) )).
fof(t17_revrot_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( 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(k1_nat_1(A,k4_finseq_4(D,C)),k3_finseq_1(D))) ) ) ) ) ) )).
fof(t17_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( m1_rewrite1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( 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)) ) ) ) ) ) )).
fof(t17_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t17_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(E))) => ! [G] : ( 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 ) ) ) ) )).
fof(t17_rfinseq,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(k3_finseq_1(A),B) => k18_rvsum_1(k3_rfinseq(k2_rfinseq(k1_numbers,B,A))) = k1_funct_1(A,k1_nat_1(B,1)) ) ) ) )).
fof(t17_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( v1_integra2(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r2_hidden(B,k4_finseq_1(A)) & r2_hidden(C,k4_finseq_1(A)) ) => ( r1_xxreal_0(C,B) | r1_xxreal_0(k1_funct_1(A,B),k1_funct_1(A,C)) ) ) ) ) ) ) )).
fof(t17_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k24_valued_1(A,k3_xcmplx_0(B,C)) = k24_valued_1(k24_valued_1(A,C),B) ) ) ) )).
fof(t17_rfunct_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(t17_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k4_binop_1(k3_rfunct_3(A,k1_numbers),k13_rfunct_3(A)) = k7_funcop_1(k2_subset_1(A),k5_numbers) ) )).
fof(t17_rfunct_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( r1_rfunct_4(A,B) <=> ( r1_tarski(B,k9_xtuple_0(A)) & ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( 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(k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(A,D),k1_funct_1(A,C)),k6_xcmplx_0(D,C)),k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(A,E),k1_funct_1(A,C)),k6_xcmplx_0(E,C))) & ~ r1_xxreal_0(k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(A,D),k1_funct_1(A,E)),k6_xcmplx_0(D,E)),k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(A,D),k1_funct_1(A,C)),k6_xcmplx_0(D,C))) ) ) ) ) ) ) ) ) ) )).
fof(t17_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v4_partfun3(B) => v4_partfun3(k1_valued_0(k1_numbers,B,A)) ) ) ) )).
fof(t17_rinfsup2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v10_mesfunc5(k1_valued_0(k6_numbers,B,A)) => ( v10_mesfunc5(B) & k2_mesfunc5(B) = k2_mesfunc5(k1_valued_0(k6_numbers,B,A)) ) ) ) ) )).
fof(t17_ring_1,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t17_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => r2_hidden(k18_mod_2,k9_ringcat1(A)) ) )).
fof(t17_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_rlvect_2(C,A) => ! [D] : ( 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))) ) ) ) ) )).
fof(t17_rlaffin2,axiom,( ! [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) ) => ! [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)) => 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))) ) ) ) )).
fof(t17_rlaffin3,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_finset_1(D) & v1_rlaffin1(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ! [E] : ( m2_rlaffin3(E,A,D) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t17_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => r1_struct_0(B,k4_struct_0(A)) ) ) )).
fof(t17_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( ( v1_rlvect_1(C) & m1_rlsub_1(C,A) ) => ( m1_rlsub_1(C,B) <=> k2_rlsub_2(A,C,B) = C ) ) ) ) )).
fof(t17_rltopsp1,axiom,( ! [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) ) => ! [B] : ( ( v1_convex1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => k3_convex1(A,B) = B ) ) )).
fof(t17_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k4_algstr_0(A,k4_algstr_0(A,B)) = B ) ) )).
fof(t17_rlvect_2,axiom,( ! [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) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t17_rlvect_3,axiom,( ! [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) ) => ! [B] : ( 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)) ) ) ) )).
fof(t17_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t17_rlvect_5,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_rlvect_3(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t17_rlvect_x,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_hidden(B,k2_rlvect_x(A,k6_domain_1(u1_struct_0(A),B))) ) ) )).
fof(t17_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => r1_struct_0(C,k4_struct_0(B)) ) ) ) )).
fof(t17_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ( ! [D] : ( ( 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] : ( m1_rmod_2(D,A,B) => ( k2_rmod_3(A,B,D,C) = D => m1_rmod_2(D,A,C) ) ) ) ) ) ) )).
fof(t17_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t17_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t17_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t17_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lattices(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( C = E & D = F ) => k2_lattices(A,C,D) = k2_lattices(B,E,F) ) ) ) ) ) ) ) ) )).
fof(t17_robbins4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_robbins4)) => ! [B] : ( 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) = k5_numbers ) ) ) ) )).
fof(t17_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( B = k3_roughs_1(A,B) <=> B = k4_roughs_1(A,B) ) ) ) )).
fof(t17_rsspace,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k5_numbers,k1_funct_1(A,B)) ) & v1_series_1(A) & k4_series_1(A) = k5_numbers ) => ! [B] : ( v7_ordinal1(B) => k1_funct_1(A,B) = k5_numbers ) ) ) )).
fof(t17_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_rsspace4(A,B))) => r1_xxreal_0(k5_numbers,k2_normsp_0(k9_rsspace4(A,B),C)) ) ) ) )).
fof(t17_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t17_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( ( v1_bhsp_1(C) & m1_rusub_1(C,A) ) => ( m1_rusub_1(C,B) <=> k2_rusub_2(A,C,B) = C ) ) ) ) )).
fof(t17_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( 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] : ( m2_rlvect_2(D,A,C) => k6_rlvect_2(A,B) != k6_rlvect_2(A,D) ) ) ) ) ) )).
fof(t17_rusub_4,axiom,( ! [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_bhsp_1(A) & v1_rusub_4(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ( r1_rusub_2(A,B,C) => k1_rusub_4(A) = k1_nat_1(k1_rusub_4(B),k1_rusub_4(C)) ) ) ) ) )).
fof(t17_rusub_5,axiom,( ! [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) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_rusub_4(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t17_rvsum_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => k1_funct_1(k30_valued_1(B),A) = k4_xcmplx_0(k1_funct_1(B,A)) ) )).
fof(t17_rvsum_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t17_scm_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( r1_tarski(k1_ordinal4(k5_afinsq_1(k4_ami_3(k10_ami_3(k5_numbers),k10_ami_3(1))),k5_afinsq_1(k2_compos_1(k1_ami_3))),A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( ( v5_memstr_0(D,k7_card_1(2),k1_ami_3,k5_numbers) & m1_scm_1(D,k6_afinsq_1(B,C)) ) => ( r1_extpro_1(k7_card_1(2),k1_ami_3,A,D) & k8_extpro_1(k7_card_1(2),k1_ami_3,A,D) = 1 & k1_funct_1(k6_extpro_1(k7_card_1(2),k1_ami_3,A,D),k10_ami_3(k5_numbers)) = k6_xcmplx_0(B,C) & ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_ami_3)) ) => ( E != k10_ami_3(k5_numbers) => k1_funct_1(k6_extpro_1(k7_card_1(2),k1_ami_3,A,D),E) = k1_funct_1(D,E) ) ) ) ) ) ) ) ) )).
fof(t17_scm_halt,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(D,k1_scmfsa6b(C,A,B),B),k5_card_1(C))) ) ) ) ) )).
fof(t17_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,k4_ordinal1) => k2_sf_mastr(k1_scmfsa6a(A,B)) = k2_sf_mastr(A) ) ) )).
fof(t17_scmfsa6a,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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)) ) ) ) )).
fof(t17_scmfsa6b,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) & v1_scmfsa6b(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k3_scmfsa6a(C,D)),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))) = k2_xcmplx_0(k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))),1),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(k1_funct_4(B,C),D),k1_funct_4(k6_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))))) ) ) ) ) )).
fof(t17_scmfsa7b,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_scmfsa_2(C) => ~ r3_scmfsa7b(k17_scmfsa_2(B,C),A) ) ) ) )).
fof(t17_scmfsa8a,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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)) ) ) ) ) )).
fof(t17_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k5_numbers)) = 1 => ( r1_scmfsa8a(B,A,C) <=> r1_scmfsa8a(k1_scmfsa_m(B),A,C) ) ) ) ) ) )).
fof(t17_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ( ( r5_scmfsa7b(D,B,A) & r6_scmfsa7b(D,B,A) & k1_funct_1(B,C) = k5_numbers ) => k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa_9(C,D)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,D),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B)),3))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,D),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,D),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B)))) ) ) ) ) ) )).
fof(t17_scmfsa_1,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k4_scmfsa_1,k5_scmfsa_1))) => ! [B] : ( m2_subset_1(B,k1_scmfsa_1,k3_scmfsa_1) => ! [C] : ( m2_finseq_1(C,k4_numbers) => k9_scmfsa_1(k8_scmfsa_1(A,B,C),B) = C ) ) ) )).
fof(t17_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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 ) ) )).
fof(t17_scmfsa_m,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t17_scmisort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ( k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k1_scmisort(D,B,C,A),E)) = k5_numbers & r8_pboole(u1_struct_0(k1_scmfsa_2),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k1_scmisort(D,B,C,A),E),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa_9(C,B)),k1_scmfsa_m(D),F)) & k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k1_scmisort(D,B,C,A),E),k4_scmfsa_2(k5_numbers)) = 1 ) => ( r8_pboole(u1_struct_0(k1_scmfsa_2),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k1_scmisort(D,B,C,A),E),k1_scmfsa_m(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k1_scmisort(D,B,C,A),E))) & r8_pboole(u1_struct_0(k1_scmfsa_2),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k1_scmisort(D,B,C,A),k1_nat_1(E,1)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa_9(C,B)),k1_scmfsa_m(D),k1_nat_1(F,k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(k1_funct_4(A,k2_scmfsa_9(C,B)),B),k1_scmfsa_m(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k1_scmisort(D,B,C,A),E))),3)))) ) ) ) ) ) ) ) ) )).
fof(t17_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( 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 ) ) ) )).
fof(t17_scmpds_4,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v7_ordinal1(B) => ~ r2_hidden(A,k9_xtuple_0(k7_memstr_0(2,k1_scmpds_2,B))) ) ) )).
fof(t17_scmpds_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_scmpds_4(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( v7_ordinal1(E) => ( 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) ) ) ) ) ) ) )).
fof(t17_scmpds_6,axiom,( ! [A] : ( ( 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] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( v7_ordinal1(D) => ( ( 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)) ) ) ) ) ) ) )).
fof(t17_scmpds_7,axiom,( ! [A] : ( ( 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] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( v7_ordinal1(E) => ( ( 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) ) ) ) ) ) ) )).
fof(t17_scmpds_8,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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),k5_numbers) = k8_scmpds_2(A,B,k1_nat_1(k5_card_1(C),2)) & k1_funct_1(k2_scmpds_8(A,B,C),k1_nat_1(k5_card_1(C),1)) = k3_scmpds_2(k4_xcmplx_0(k1_nat_1(k5_card_1(C),1))) ) ) ) ) )).
fof(t17_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => ! [D] : ( ( 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(k7_card_1(2),k1_scmring2(A))) & v1_partfun1(D,u1_struct_0(k1_scmring2(A))) ) => ( k1_funct_1(k2_extpro_1(k7_card_1(2),k1_scmring2(A),k7_scmring2(A,C,B),D),k4_struct_0(k1_scmring2(A))) = k4_card_1(k5_memstr_0(k7_card_1(2),k1_scmring2(A),D)) & k2_scmring2(A,k2_extpro_1(k7_card_1(2),k1_scmring2(A),k7_scmring2(A,C,B),D),C) = B & ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmring2(A))) ) => ( E != C => k2_scmring2(A,k2_extpro_1(k7_card_1(2),k1_scmring2(A),k7_scmring2(A,C,B),D),E) = k2_scmring2(A,D,E) ) ) ) ) ) ) ) )).
fof(t17_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmring2(A))) => ~ ( k2_compos_0(u1_compos_1(k1_scmring2(A)),B) = 6 & ! [C] : ( v7_ordinal1(C) => B != k8_scmring2(A,C) ) ) ) ) )).
fof(t17_scmyciel,axiom,( ! [A] : ( v1_scmyciel(A) => k1_scmyciel(A) = k1_xboole_0 ) )).
fof(t17_scpinvar,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_scmpds_2)) ) => ! [G] : ( v1_int_1(G) => ! [H] : ( 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] : ( ( 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,k5_numbers) ) => ! [J] : ( ( v1_relat_1(J) & v4_relat_1(J,k4_ordinal1) & v5_relat_1(J,u1_compos_1(k1_scmpds_2)) & v1_funct_1(J) & v1_partfun1(J,k4_ordinal1) ) => ( ( 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),k5_numbers) | r1_xxreal_0(k1_funct_1(I,F),k5_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),k5_numbers) | r1_xxreal_0(k1_funct_1(B,F),k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t17_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k32_valued_1(k4_ordinal1,k1_numbers,A),k26_valued_1(k4_ordinal1,k1_numbers,A,k4_xcmplx_0(1))) ) )).
fof(t17_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(A) & ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k5_numbers,k1_funct_1(A,B)) ) ) => r1_xxreal_0(k5_numbers,k1_seq_2(A)) ) ) )).
fof(t17_seq_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( m2_valued_0(B,k1_numbers,A) & v2_comseq_2(A) ) => k1_seq_2(B) = k1_seq_2(A) ) ) ) )).
fof(t17_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => r2_relset_1(k4_ordinal1,k4_partfun1(A,k1_numbers),k5_seqfunc(A,k2_seqfunc(A,C,B)),k2_seqfunc(A,k5_seqfunc(A,C),k9_complex1(B))) ) ) ) )).
fof(t17_seqm_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k1_valued_0(k1_numbers,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C),A) = k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k1_valued_0(k1_numbers,B,A),k1_valued_0(k1_numbers,C,A)) ) ) ) )).
fof(t17_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,A,B)) ) => ( v1_seq_2(k3_series_1(A)) <=> v1_series_1(A) ) ) ) )).
fof(t17_series_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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)),k7_xcmplx_0(1,3)) ) ) ) ) )).
fof(t17_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( 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(k7_xcmplx_0(9,k2_xcmplx_0(k2_xcmplx_0(A,B),C)),k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(1,k6_xcmplx_0(k2_xcmplx_0(A,B),C)),k7_xcmplx_0(1,k6_xcmplx_0(k2_xcmplx_0(B,C),A))),k7_xcmplx_0(1,k6_xcmplx_0(k2_xcmplx_0(C,A),B)))) ) ) ) ) )).
fof(t17_setfam_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r1_setfam_1(A,B) & r1_setfam_1(B,C) ) => r1_setfam_1(A,C) ) )).
fof(t17_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k3_funct_2(k4_ordinal1,k9_setfam_1(A),k2_setlim_1(A,B),k5_numbers) = k3_prob_1(A,B) ) )).
fof(t17_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => k8_nat_1(k9_setfam_1(B),k6_setlim_2(B,D,C),A) = k6_setlim_2(B,k8_nat_1(k9_setfam_1(B),D,A),C) ) ) ) )).
fof(t17_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,k5_finsub_1(A)) => ! [E] : ( ( 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 | ! [F] : ( m1_subset_1(F,A) => k7_setwiseo(A,B,C,k5_setwiseo(A,D,k2_setwiseo(A,F)),E) = k5_binop_1(B,C,k7_setwiseo(A,B,C,D,E),k3_funct_2(A,B,E,F)) ) ) ) ) ) ) ) ) )).
fof(t17_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_scmfsa_2(C) => ! [D] : ( m1_subset_1(D,u1_compos_1(k1_scmfsa_2)) => ( ( D = k14_scmfsa_2(B,A,C) | D = k15_scmfsa_2(B,A,C) ) => k1_sf_mastr(D) = k5_scmfsa_m(A,B) ) ) ) ) ) )).
fof(t17_sfmastr1,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(t17_sfmastr2,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ( k1_funct_1(A,k4_scmfsa_2(k5_numbers)) = 1 => k11_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k3_sfmastr2(B,A,D,C),k5_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)) ) ) ) ) ) )).
fof(t17_sfmastr3,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => r1_sfmastr3(E,B,C,D,F,A) ) ) ) ) ) ) )).
fof(t17_sgraph1,axiom,( ! [A] : ! [B] : ( r2_hidden(B,k3_sgraph1(A)) <=> ? [C] : ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(A)) & ? [D] : ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_sgraph1(C))) & B = g1_sgraph1(C,D) ) ) ) )).
fof(t17_sheffer1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t17_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t17_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) => r1_tarski(B,k4_simplex0(A)) ) ) ) )).
fof(t17_simplex1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t17_simplex2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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)),k3_xcmplx_0(k1_newton(k7_xcmplx_0(k6_simplex0(C),k2_xcmplx_0(k6_simplex0(C),1)),B),k3_simplex2(A,C))) ) ) ) ) )).
fof(t17_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => r1_xxreal_0(1,k4_series_1(k4_sin_cos(k9_complex1(A)))) ) )).
fof(t17_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => k1_funct_1(k5_sin_cos2,A) = k7_xcmplx_0(k1_funct_1(k1_sin_cos2,A),k1_funct_1(k3_sin_cos2,A)) ) )).
fof(t17_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,k3_xcmplx_0(k7_complex1,A)) = k3_xcmplx_0(k7_complex1,k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,A)) ) )).
fof(t17_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k2_xcmplx_0(k19_sin_cos(A),k19_sin_cos(B)) = k3_xcmplx_0(2,k3_xcmplx_0(k19_sin_cos(k7_xcmplx_0(k2_xcmplx_0(A,B),2)),k19_sin_cos(k7_xcmplx_0(k6_xcmplx_0(A,B),2)))) ) ) )).
fof(t17_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => k19_sin_cos(k3_xcmplx_0(3,A)) = k6_xcmplx_0(k3_xcmplx_0(4,k1_newton(k19_sin_cos(A),3)),k3_xcmplx_0(3,k19_sin_cos(A))) ) )).
fof(t17_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ( ( r1_xxreal_0(k2_xcmplx_0(k28_sin_cos,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)),A) & r1_xxreal_0(A,k2_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B))) ) => r1_xxreal_0(k17_sin_cos(A),k5_numbers) ) ) ) )).
fof(t17_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) & r1_xxreal_0(k7_xcmplx_0(1,k3_square_1(k6_xcmplx_0(1,k1_square_1(A)))),1) ) ) )).
fof(t17_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k2_xcmplx_0(A,B) != k5_numbers => k7_xcmplx_0(k6_xcmplx_0(k2_sin_cos2(A),k2_sin_cos2(B)),k2_xcmplx_0(k4_sin_cos2(A),k4_sin_cos2(B))) = k7_xcmplx_0(k6_xcmplx_0(k4_sin_cos2(A),k4_sin_cos2(B)),k2_xcmplx_0(k2_sin_cos2(A),k2_sin_cos2(B))) ) ) ) )).
fof(t17_sin_cos9,axiom,( k1_funct_1(k26_sin_cos,k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4))) = k4_xcmplx_0(1) & k1_sin_cos4(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4))) = k4_xcmplx_0(1) )).
fof(t17_sincos10,axiom,( v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k3_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(t17_sppol_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( ( r2_hidden(B,k1_rltopsp1(k15_euclid(2),A,D)) & r2_hidden(C,k1_rltopsp1(k15_euclid(2),A,D)) & k18_euclid(B) = k18_euclid(C) ) => ( k17_euclid(B) = k17_euclid(C) | v1_sppol_1(k1_rltopsp1(k15_euclid(2),A,D)) ) ) ) ) ) ) )).
fof(t17_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(B,k2_topreal1(2,A,C)) => r2_hidden(B,k3_topreal1(2,A)) ) ) ) ) )).
fof(t17_sprect_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t17_sprect_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t17_sprect_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v4_topreal1(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t17_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(t17_square_1,axiom,( k3_square_1(k5_numbers) = k5_numbers )).
fof(t17_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t17_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k7_card_1(B),k7_card_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(B),k7_card_1(A)))) ) => ( v2_funct_2(C,k7_card_1(A)) => r1_xxreal_0(A,B) ) ) ) ) )).
fof(t17_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_valuat_1(C,A,B) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t17_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_tarski(k3_subset_1(A,B),C) => r1_tarski(k3_subset_1(A,C),B) ) ) ) )).
fof(t17_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( 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)) ) ) )).
fof(t17_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => ! [C] : ( m1_subset_1(C,k16_substut1(A)) => ! [D] : ( m1_subset_1(D,k16_substut1(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t17_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t17_supinf_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k6_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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(k6_numbers,A,B,D),k11_supinf_2(k6_numbers,A,C,E)),k11_supinf_2(k6_numbers,A,k5_supinf_2(B,C),k13_supinf_2(A,B,C,D,E))) ) ) ) ) ) )).
fof(t17_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( ~ r1_orders_2(B,D,C) & F != k4_struct_0(A) & k1_symsp_1(A,B,C,k4_vectsp_1(A,B,F,D),E) != k8_group_1(A,k11_algstr_0(A,F),k1_symsp_1(A,B,C,D,E)) ) ) ) ) ) ) ) )).
fof(t17_sysrel,axiom,( ! [A] : ( v1_relat_1(A) => ( r1_tarski(A,k4_relat_1(k9_xtuple_0(A))) => A = k4_relat_1(k9_xtuple_0(A)) ) ) )).
fof(t17_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( v4_metric_1(B,A) => r3_relat_2(k1_taxonom1(A,B,C),A) ) ) ) ) )).
fof(t17_taxonom2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( ( r2_hidden(D,C) & r1_tarski(B,D) ) => ! [E] : ( m1_eqrel_1(E,A) => ( ( r2_hidden(B,E) & ! [F] : ~ ( r2_hidden(F,E) & ~ r1_tarski(F,D) & ~ r1_tarski(D,F) & ~ r1_xboole_0(D,F) ) ) => ! [F] : ( ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t17_taylor_1,axiom,( r2_fdiff_1(k2_partfun2(k1_numbers,k1_numbers,k22_sin_cos),k1_relset_1(k1_numbers,k2_partfun2(k1_numbers,k1_numbers,k22_sin_cos))) & ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k1_relset_1(k1_numbers,k2_partfun2(k1_numbers,k1_numbers,k22_sin_cos))) => k1_fdiff_1(k2_partfun2(k1_numbers,k1_numbers,k22_sin_cos),A) = k7_xcmplx_0(1,A) ) ) )).
fof(t17_taylor_2,axiom,( ! [A] : ( ( 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,k18_sin_cos,A) & k2_fdiff_1(k18_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,k18_sin_cos,A)) = A ) ) )).
fof(t17_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ( v1_finset_1(B) & ! [C] : ( 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) ) ) ) )).
fof(t17_tdgroup,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t17_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t17_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => v1_tops_2(k1_tdlat_2(A,B),A) ) ) )).
fof(t17_tdlat_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( B = k1_tarski(C) => v3_pre_topc(B,A) ) ) ) => v1_tdlat_3(A) ) ) )).
fof(t17_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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,k8_polynom1(A,C)) ) ) ) ) ) )).
fof(t17_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k2_pre_topc(A,B) = B ) => v1_tdlat_3(A) ) ) )).
fof(t17_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( v13_struct_0(B,1) & m1_pre_topc(B,A) ) => ? [C] : ( 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))) ) ) ) )).
fof(t17_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( v1_tops_3(B,A) & ! [C] : ( ( ~ v2_struct_0(C) & v1_pre_topc(C) & v2_tex_3(C,A) & m1_pre_topc(C,A) ) => B != u1_struct_0(C) ) ) ) ) )).
fof(t17_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t17_tietze,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v4_pre_topc(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( v10_pre_topc(B) => ( r1_xxreal_0(A,k5_numbers) | ! [D] : ( ( 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] : ( ( 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,k7_xcmplx_0(A,3),k1_relset_1(u1_struct_0(B),E)) & r1_tietze(k45_valued_1(D,E),k7_xcmplx_0(k3_xcmplx_0(2,A),3),C) ) ) ) ) ) ) ) ) ) )).
fof(t17_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( m1_pre_topc(B,C) => ( ~ r1_tsep_1(B,C) & ~ r1_tsep_1(C,B) ) ) ) ) ) )).
fof(t17_toler_1,axiom,( ! [A] : ! [B] : ( ( 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] : ! [D] : ( m1_toler_1(C,A,B) => m1_toler_1(k3_xboole_0(C,D),A,B) ) ) )).
fof(t17_topalg_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k17_borsuk_1)) => k1_binop_1(B,C,D) = k1_rlvect_1(k15_euclid(A),C,k6_xcmplx_0(1,D)) ) ) => v5_pre_topc(B,k2_borsuk_1(k15_euclid(A),k17_borsuk_1),k15_euclid(A)) ) ) ) )).
fof(t17_topalg_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_topmetr)) => ! [B] : ( 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)) ) ) )).
fof(t17_topalg_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t17_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_borsuk_2(G,k2_borsuk_1(A,B),k4_borsuk_1(A,B,C,E),k4_borsuk_1(A,B,D,F)) => ! [H] : ( m1_borsuk_2(H,k2_borsuk_1(A,B),k4_borsuk_1(A,B,C,E),k4_borsuk_1(A,B,D,F)) => ! [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] : ( m1_borsuk_2(J,A,C,D) => ! [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_topalg_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => v1_connsp_2(k4_topmetr(A,B)) ) ) ) )).
fof(t17_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_borsuk_2(C,A,B,B) => v3_topalg_6(C,A,B) ) ) => v1_topalg_6(A) ) ) )).
fof(t17_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t17_topdim_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k14_euclid(1))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( k9_finseq_1(C) = A => k9_metric_1(k14_euclid(1),A,B) = a_2_0_topdim_2(B,C) ) ) ) ) )).
fof(t17_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_topgen_1(A,B)) <=> ! [D] : ( ( v3_pre_topc(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( r2_hidden(C,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,k9_subset_1(u1_struct_0(A),B,D)) & C != E ) ) ) ) ) ) ) ) )).
fof(t17_topgen_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(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)))) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,k1_funct_1(C,D)) & ! [E] : ( ( 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) ) ) ) ) )).
fof(t17_topgen_3,axiom,( k1_card_1(k3_numbers) = k4_ordinal1 )).
fof(t17_topgen_4,axiom,( ! [A] : ! [B] : ( 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) ) ) ) ) )).
fof(t17_topgen_5,axiom,( ! [A] : ! [B] : ( r2_hidden(k10_finseq_1(A,B),k2_topgen_5) <=> ( r2_hidden(A,k1_numbers) & ? [C] : ( v1_xreal_0(C) & B = C & r1_xxreal_0(k5_numbers,C) ) ) ) )).
fof(t17_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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))) ) ) )).
fof(t17_topmetr,axiom,( u1_struct_0(k3_topmetr) = k1_numbers )).
fof(t17_topreal3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r2_hidden(C,k4_finseq_1(k17_finseq_1(u1_struct_0(k15_euclid(2)),B,A))) & r2_hidden(k1_nat_1(C,1),k4_finseq_1(k17_finseq_1(u1_struct_0(k15_euclid(2)),B,A))) ) => k2_topreal1(2,A,C) = k2_topreal1(2,k17_finseq_1(u1_struct_0(k15_euclid(2)),B,A),C) ) ) ) ) )).
fof(t17_topreal4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ~ ( A != k7_partfun1(u1_struct_0(k15_euclid(2)),B,1) & v4_topreal1(B) & r2_hidden(A,k2_topreal1(2,B,C)) & ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t17_topreal5,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t17_topreal6,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( ( r1_t_0topsp(A,B) & v1_connsp_1(A) ) => v1_connsp_1(B) ) ) ) )).
fof(t17_topreal7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( k3_finseq_1(B) = A => r2_hidden(B,u1_struct_0(k15_euclid(A))) ) ) ) )).
fof(t17_topreal8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,A) ) => ! [C] : ( ( ~ 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 ) ) ) ) )).
fof(t17_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => r1_xboole_0(k1_topreal9(A,C,B),k3_topreal9(A,C,B)) ) ) ) )).
fof(t17_topreala,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t17_toprealb,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( ( m1_subset_1(A,u1_struct_0(k8_toprealb(2))) & k18_euclid(A) = k4_xcmplx_0(1) ) => k17_euclid(A) = k5_numbers ) ) )).
fof(t17_toprealc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_card_1(D,B) & v1_finseq_1(D) & v1_valued_0(D) ) => k45_valued_1(k1_funct_7(D,A,C),D) = k1_funct_7(k5_euclid(B),A,k6_xcmplx_0(C,k1_funct_1(D,A))) ) ) ) ) )).
fof(t17_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => k3_toprns_1(A,k3_toprns_1(A,B)) = B ) ) )).
fof(t17_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t17_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t17_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_tops_1(B,A) & B = k1_xboole_0 ) ) ) )).
fof(t17_tops_4,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( ( v1_xreal_0(F) & v2_xxreal_0(F) ) => ~ ( E = k1_funct_1(C,D) & ! [G] : ( ( 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,k8_metric_1(A,D,G)),k8_metric_1(B,E,F)) ) ) ) ) ) ) ) ) ) )).
fof(t17_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t17_treal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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(k5_numbers,1),k4_topmetr(A,B)) & r2_funct_2(u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(k5_numbers,1)),k2_tops_2(u1_struct_0(k4_topmetr(k5_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(k5_numbers,1),k2_treal_1(k5_numbers,1))) & v3_tops_2(k4_treal_1(A,B,k1_treal_1(k5_numbers,1),k2_treal_1(k5_numbers,1)),k4_topmetr(A,B),k4_topmetr(k5_numbers,1)) & r2_funct_2(u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k4_topmetr(A,B)),k2_tops_2(u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(k5_numbers,1)),k4_treal_1(A,B,k1_treal_1(k5_numbers,1),k2_treal_1(k5_numbers,1))),k3_treal_1(A,B,k1_treal_1(A,B),k2_treal_1(A,B))) ) ) ) ) )).
fof(t17_trees_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t17_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ~ ( v1_trees_2(A) & ! [B] : ( v7_ordinal1(B) => ? [C] : ( m1_trees_1(C,A) & ! [D] : ( v1_finset_1(D) => ~ ( D = k1_trees_2(A,C) & r1_xxreal_0(k5_card_1(D),B) ) ) ) ) ) ) )).
fof(t17_trees_3,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(t17_trees_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) ) ) )).
fof(t17_trees_9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ! [C] : ( r2_hidden(A,k7_trees_9(B,C)) <=> ? [D] : ( 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) ) ) ) ) )).
fof(t17_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_tsep_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => ( v3_pre_topc(D,B) <=> v3_pre_topc(C,A) ) ) ) ) ) ) )).
fof(t17_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t17_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v6_pre_topc(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t17_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(C,A) <=> ( C = k3_tex_4(A,C) & ? [D] : ( 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)) ) ) ) ) ) ) )).
fof(t17_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( m2_funct_2(B,k4_numbers,u1_turing_1(A),k9_funct_2(k4_numbers,u1_turing_1(A))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_turing_1(k2_finseq_4(k4_ordinal1,C,D),A,B) => ( k1_funct_1(B,C) = k5_numbers & k1_funct_1(B,k1_nat_1(k1_nat_1(C,D),2)) = k5_numbers & ! [E] : ( v1_int_1(E) => ~ ( ~ r1_xxreal_0(E,C) & ~ r1_xxreal_0(k1_nat_1(k1_nat_1(C,D),2),E) & k1_funct_1(B,E) != 1 ) ) ) ) ) ) ) ) )).
fof(t17_twoscomp,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( 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)) ) ) ) ) )).
fof(t17_unialg_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_unialg_2(B,A) => ! [C] : ( m1_unialg_2(C,A) => ~ r2_subset_1(u1_struct_0(B),u1_struct_0(C)) ) ) ) )).
fof(t17_unialg_3,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t17_uniroots,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t17_uproots,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k11_polynom3(A,B,k9_polynom3(A)),k9_polynom3(A)) ) ) )).
fof(t17_urysohn1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & ! [D] : ( m1_connsp_2(D,A,C) => ~ r1_tarski(D,B) ) ) ) ) ) ) )).
fof(t17_urysohn2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ( v6_xxreal_2(k1_integra2(A,B)) & m1_subset_1(k1_integra2(A,B),k1_zfmisc_1(k1_numbers)) ) ) ) )).
fof(t17_urysohn3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v10_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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] : ( m2_urysohn3(D,A,B,C) => ! [E] : ( m2_subset_1(E,k1_numbers,k3_urysohn1) => ( ~ r1_xxreal_0(E,k5_numbers) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( ~ r1_xxreal_0(k12_supinf_2(k7_urysohn3(A,B,C,D),F),E) & r2_hidden(F,k5_urysohn3(k3_urysohn1,A,k4_urysohn3(A,B,C,D),E)) ) ) ) ) ) ) ) ) ) ) )).
fof(t17_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_funct_2(C,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t17_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & ~ v1_xboole_0(A) & v1_funct_1(A) & v3_funct_1(A) ) => ? [B] : ( v1_int_1(B) & ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => k1_funct_1(A,C) = B ) ) ) )).
fof(t17_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : k1_funct_1(k50_valued_1(A,B),C) = k7_xcmplx_0(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) )).
fof(t17_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t17_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m1_vectsp_4(E,A,B) => ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & ? [G] : ( 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) ) ) ) ) ) ) ) )).
fof(t17_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t17_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t17_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( B != k4_struct_0(A) => k1_vectsp_2(A,B,B) = k1_group_1(A) ) ) ) )).
fof(t17_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => r1_struct_0(C,k4_struct_0(B)) ) ) ) )).
fof(t17_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t17_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) )).
fof(t17_vectsp_7,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ~ ( v1_vectsp_7(C,A,B) & ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t17_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t17_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t17_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t17_waybel10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( l1_orders_2(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_waybel10(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t17_waybel11,axiom,( ! [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] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t17_waybel12,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t17_waybel13,axiom,( ! [A] : ( ( 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] : ( 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) ) ) ) )).
fof(t17_waybel14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v3_yellow_8(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ( C = k3_subset_1(u1_struct_0(A),B) => v5_waybel_6(C,k1_yellow_1(u1_pre_topc(A))) ) ) ) ) )).
fof(t17_waybel15,axiom,( ! [A] : ( ( 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] : ( 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] : ( 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) ) ) ) ) )).
fof(t17_waybel16,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_yellow_1(A)))) ) => ( r1_yellow_0(k1_yellow_1(A),B) => r1_tarski(k3_tarski(B),k1_yellow_0(k1_yellow_1(A),B)) ) ) ) )).
fof(t17_waybel17,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( 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))) ) ) ) ) ) ) )).
fof(t17_waybel18,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v4_waybel11(B) & m1_yellow_9(B,k4_yellow_1(A,k7_funcop_1(A,k2_yellow_1(k1_tarski(k5_numbers))))) ) => v2_waybel18(B) ) ) )).
fof(t17_waybel19,axiom,( ! [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) & v1_waybel19(A) & l1_waybel_9(A) ) => ! [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) & v1_waybel19(B) & l1_waybel_9(B) ) => ( m1_yellow_9(B,k3_yellow_3(A,A)) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t17_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ( ( r5_waybel_1(A,B) & v5_orders_2(A) ) => v5_orders_2(B) ) ) ) )).
fof(t17_waybel21,axiom,( ! [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] : ( ( ~ 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) ) ) ) )).
fof(t17_waybel22,axiom,( ! [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) & l1_orders_2(A) ) => ! [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) & l1_orders_2(B) ) => ! [C] : ! [D] : ( ( r1_waybel22(A,C) & r1_waybel22(B,D) & k1_card_1(C) = k1_card_1(D) ) => r5_waybel_1(A,B) ) ) ) )).
fof(t17_waybel23,axiom,( ! [A] : ( ( v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_waybel23(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t17_waybel24,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v1_lattice3(C) & v2_lattice3(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( ( 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))) ) ) ) ) ) ) ) ) )).
fof(t17_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t17_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & v1_waybel25(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(t17_waybel27,axiom,( ! [A] : ? [B] : ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k2_yellow_1(A)),u1_struct_0(k5_yellow_1(A,k2_yellow_1(k1_tarski(k5_numbers))))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_yellow_1(A)),u1_struct_0(k5_yellow_1(A,k2_yellow_1(k1_tarski(k5_numbers))))))) & v23_waybel_0(B,k2_yellow_1(A),k5_yellow_1(A,k2_yellow_1(k1_tarski(k5_numbers)))) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k1_funct_1(B,C) = k5_funct_3(C,A) ) ) )).
fof(t17_waybel28,axiom,( ! [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) ) => v4_yellow_6(k3_waybel28(A),A) ) )).
fof(t17_waybel29,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(t17_waybel30,axiom,( ! [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_waybel_2(A) & l1_waybel_9(A) ) => ! [B] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => ! [C] : ( ( v13_waybel_0(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => k1_tops_1(A,C) = k1_tops_1(B,D) ) ) ) ) ) )).
fof(t17_waybel31,axiom,( ! [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) ) => ( ~ v8_struct_0(A) => ! [B] : ( ( v6_waybel23(B,A) & m1_waybel23(B,A) ) => ~ v1_finset_1(B) ) ) ) )).
fof(t17_waybel32,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => r3_orders_2(A,C,k1_yellow_0(A,B)) ) ) ) ) )).
fof(t17_waybel33,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ~ ( r2_waybel_0(A,B,C) & ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t17_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => u1_struct_0(k4_waybel34(A)) = u1_struct_0(k5_waybel34(A)) ) )).
fof(t17_waybel35,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v2_waybel_4(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t17_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k5_waybel_0(A,B)) <=> r1_orders_2(A,C,B) ) ) ) ) )).
fof(t17_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( 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) ) ) ) ) ) ) )).
fof(t17_waybel_2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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) ) ) ) )).
fof(t17_waybel_3,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => v1_waybel_3(B,A) ) ) ) )).
fof(t17_waybel_4,axiom,( ! [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] : ( ( v2_waybel_4(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t17_waybel_5,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v3_waybel_3(A) & ! [D] : ( 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) ) ) ) ) )).
fof(t17_waybel_6,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_waybel_6(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( ~ r3_orders_2(A,D,C) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,B) & r3_orders_2(A,C,E) & ~ r3_orders_2(A,D,E) ) ) ) ) ) ) ) ) )).
fof(t17_waybel_7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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)))) ) ) ) )).
fof(t17_waybel_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t17_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => m2_yellow_6(k4_waybel_9(A,B,C),A,B) ) ) ) )).
fof(t17_weddwitt,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r1_struct_0(k4_weddwitt(A),B) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_algstr_0(A,B,C) = k6_algstr_0(A,C,B) ) ) ) ) )).
fof(t17_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t17_wellord1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( v8_relat_2(B) => v8_relat_2(k2_wellord1(B,A)) ) ) )).
fof(t17_wellord2,axiom,( ! [A] : r1_tarski(k1_wellord2(A),k2_zfmisc_1(A,A)) )).
fof(t17_wsierp_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( A != k5_numbers => ( r1_int_1(A,B) <=> v1_int_1(k7_xcmplx_0(B,A)) ) ) ) ) )).
fof(t17_xboole_1,axiom,( ! [A] : ! [B] : r1_tarski(k3_xboole_0(A,B),A) )).
fof(t17_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k5_xboolean(k3_xboolean(A),k6_xboolean(A,B)) = k6_xboolean(A,B) ) ) )).
fof(t17_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => A = k6_xcmplx_0(A,k6_xcmplx_0(B,B)) ) ) )).
fof(t17_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t17_xtuple_0,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_tarski(k14_xtuple_0(A),k14_xtuple_0(B)) ) )).
fof(t17_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => r1_xxreal_0(k3_xxreal_0(A,B),A) ) ) )).
fof(t17_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => k1_xxreal_1(A,A) = k1_tarski(A) ) )).
fof(t17_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => m2_xxreal_2(A,k1_xxreal_1(A,B)) ) ) )).
fof(t17_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( k1_xxreal_3(A,B) = k2_xxreal_0 & A != k2_xxreal_0 & B != k2_xxreal_0 ) ) ) )).
fof(t17_yellow10,axiom,( ! [A] : ( ( v5_orders_2(A) & v3_yellow_0(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v5_orders_2(B) & v3_yellow_0(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t17_yellow12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_yellow_0(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t17_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_pre_topc(A,B)) <=> ? [D] : ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(E,D) & r1_xboole_0(B,E) ) ) ) ) ) ) ) )).
fof(t17_yellow14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t17_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t17_yellow17,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_waybel18(A,B,C))) => ! [E] : ~ ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t17_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t17_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_subset_1(B,u1_struct_0(k2_yellow_1(k2_struct_0(A)))) & v2_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))))) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t17_yellow20,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( ( 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] : ( 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) ) ) ) )).
fof(t17_yellow21,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( ( 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) ) ) ) ) ) )).
fof(t17_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( r1_yellow_0(A,B) & r2_yellow_0(A,B) ) ) )).
fof(t17_yellow_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k2_yellow_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_yellow_1(A))) => ( k13_lattice3(k2_yellow_1(A),B,C) = k2_xboole_0(B,C) & k12_lattice3(k2_yellow_1(A),B,C) = k3_xboole_0(B,C) ) ) ) )).
fof(t17_yellow_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t17_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t17_yellow_4,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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))) ) ) ) ) )).
fof(t17_yellow_5,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t17_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ! [D] : ~ ( r1_waybel_0(A,B,C) & r1_waybel_0(A,B,D) & r1_xboole_0(C,D) ) ) ) )).
fof(t17_yellow_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v3_lattice3(A) <=> v3_lattice3(k7_lattice3(A)) ) ) )).
fof(t17_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v3_yellow_8(k2_pre_topc(A,k6_domain_1(u1_struct_0(A),B)),A) ) ) )).
fof(t17_yellow_9,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => k2_cantor_1(A,B) = k1_tarski(A) ) )).
fof(t17_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t17_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => k1_funct_1(k8_zf_lang(A,B),1) = 4 ) ) )).
fof(t17_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ! [E] : ( m2_subset_1(E,k4_ordinal1,k1_zf_lang) => ! [F] : ( m2_subset_1(F,k4_ordinal1,k1_zf_lang) => ( k15_zf_lang(C,E,A) = k15_zf_lang(D,F,B) => ( C = D & E = F & A = B ) ) ) ) ) ) ) ) )).
fof(t17_zf_model,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ( r1_zf_model(A,B,k10_zf_lang(C,D)) <=> ( r1_zf_model(A,B,C) | r1_zf_model(A,B,D) ) ) ) ) ) ) )).
fof(t17_zfmisc_1,axiom,( ! [A] : ! [B] : ( A != B => k4_xboole_0(k2_tarski(A,B),k1_tarski(B)) = k1_tarski(A) ) )).
fof(t17_zfmodel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_zf_model(A) => ( v1_ordinal1(A) & ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ( ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,B) <=> r2_hidden(D,C) ) ) => B = C ) ) ) & ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => r2_hidden(k2_tarski(B,C),A) ) ) & ! [B] : ( m1_subset_1(B,A) => r2_hidden(k3_tarski(B),A) ) & ? [B] : ( m1_subset_1(B,A) & B != k1_xboole_0 & ! [C] : ( m1_subset_1(C,A) => ~ ( r2_hidden(C,B) & ! [D] : ( m1_subset_1(D,A) => ~ ( r2_xboole_0(C,D) & r2_hidden(D,B) ) ) ) ) ) & ! [B] : ( m1_subset_1(B,A) => r2_hidden(k3_xboole_0(A,k1_zfmisc_1(B)),A) ) & ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( 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(k5_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(k5_numbers),k8_zf_lang(k2_zf_lang(4),k12_zf_lang(B,k4_zf_lang(k2_zf_lang(4),k2_zf_lang(k5_numbers))))))) ) => ! [D] : ( m1_subset_1(D,A) => r2_hidden(k7_relset_1(A,A,k1_zfmodel1(B,A,C),D),A) ) ) ) ) ) ) ) )).
fof(t17_zfmodel2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( 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(k5_numbers),k2_zf_model(B)) & r1_zf_model(A,C,k8_zf_lang(k2_zf_lang(3),k13_zf_lang(k2_zf_lang(k5_numbers),k8_zf_lang(k2_zf_lang(4),k12_zf_lang(B,k4_zf_lang(k2_zf_lang(4),k2_zf_lang(k5_numbers))))))) & ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( ( 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(k5_numbers),k2_zf_model(D)) & r1_zf_model(A,E,k8_zf_lang(k2_zf_lang(3),k13_zf_lang(k2_zf_lang(k5_numbers),k8_zf_lang(k2_zf_lang(4),k12_zf_lang(D,k4_zf_lang(k2_zf_lang(4),k2_zf_lang(k5_numbers))))))) & r2_funct_2(A,A,k1_zfmodel1(B,A,C),k1_zfmodel1(D,A,E)) ) ) ) ) ) ) ) )).
fof(t17_zfrefle1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_ordinal2(B) ) => ( r2_hidden(A,k10_xtuple_0(B)) => v3_ordinal1(A) ) ) )).
fof(t17_zmodul01,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ 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] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ( ( k3_finseq_1(C) = k3_finseq_1(D) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( 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) ) ) ) ) ) )).
fof(t17_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(A),k4_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_numbers))) ) => k20_zmodul02(A,k3_finseq_4(u1_struct_0(A),B,C,D),E) = k3_finseq_4(u1_struct_0(A),k1_zmodul01(A,B,k3_funct_2(u1_struct_0(A),k4_numbers,E,B)),k1_zmodul01(A,C,k3_funct_2(u1_struct_0(A),k4_numbers,E,C)),k1_zmodul01(A,D,k3_funct_2(u1_struct_0(A),k4_numbers,E,D))) ) ) ) ) ) )).
fof(t17_zmodul03,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_zmodul02(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => ! [D] : ( 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(k33_zmodul02(A,D),C) ) ) ) ) ) ) ) )).
fof(t180_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ( k21_member_1(A,C) = k21_member_1(B,C) => A = B ) ) ) ) )).
fof(t180_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(1)) = A ) )).
fof(t180_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(C,1) & r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(1,C),A),k3_xcmplx_0(C,B)),A) ) => ( r1_xxreal_0(B,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(1,C),A),k3_xcmplx_0(C,B))) | C = k5_numbers ) ) ) ) ) )).
fof(t180_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(C,A) & ~ r1_xxreal_0(D,A) & ~ r1_xxreal_0(B,C) & ~ r1_xxreal_0(B,D) & k2_xboole_0(k2_xboole_0(k3_xxreal_1(A,C),k4_xxreal_1(C,D)),k2_xxreal_1(D,B)) != k4_xxreal_1(A,B) ) ) ) ) ) )).
fof(t180_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,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) ) ) ) ) ) )).
fof(t181_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => k21_member_1(A,B) = k5_member_1(k19_member_1(A,B)) ) ) )).
fof(t181_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k3_xcmplx_0(A,B) = k4_xcmplx_0(B) => ( B = k5_numbers | A = k4_xcmplx_0(1) ) ) ) ) )).
fof(t181_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(1,k7_xcmplx_0(B,A)) ) ) ) ) )).
fof(t181_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(C,D) & r1_xxreal_0(D,B) ) => k2_xboole_0(k2_xboole_0(k1_xxreal_1(A,C),k4_xxreal_1(C,D)),k1_xxreal_1(D,B)) = k1_xxreal_1(A,B) ) ) ) ) ) )).
fof(t181_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,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) ) ) ) ) ) ) )).
fof(t182_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => k19_member_1(A,B) = k5_member_1(k21_member_1(A,B)) ) ) )).
fof(t182_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ~ ( k3_xcmplx_0(A,A) = 1 & A != 1 & A != k4_xcmplx_0(1) ) ) )).
fof(t182_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(B,A) => ( r1_xxreal_0(k5_numbers,A) | r1_xxreal_0(1,k7_xcmplx_0(B,A)) ) ) ) ) )).
fof(t182_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t182_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ( ~ r2_hidden(B,k4_zf_lang1(A)) => k6_zf_lang1(A,B,C) = A ) ) ) ) )).
fof(t183_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t183_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(k4_xcmplx_0(A),k3_xcmplx_0(2,A)) = A ) )).
fof(t183_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,B) ) => r1_xxreal_0(k7_xcmplx_0(A,B),1) ) ) ) )).
fof(t183_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t183_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => k6_zf_lang1(A,B,B) = A ) ) )).
fof(t184_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t184_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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)) ) ) ) )).
fof(t184_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(B,A) & r1_xxreal_0(A,k5_numbers) ) => r1_xxreal_0(k7_xcmplx_0(A,B),1) ) ) ) )).
fof(t184_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t184_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ~ ( B != C & r2_hidden(B,k4_zf_lang1(k6_zf_lang1(A,B,C))) ) ) ) ) )).
fof(t185_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t185_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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)) ) ) ) )).
fof(t185_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(B,A) ) => r1_xxreal_0(k7_xcmplx_0(B,A),1) ) ) ) )).
fof(t185_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t185_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ( r2_hidden(B,k4_zf_lang1(A)) => r2_hidden(C,k4_zf_lang1(k6_zf_lang1(A,B,C))) ) ) ) ) )).
fof(t186_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(C,A) => r2_hidden(k4_xxreal_3(B,C),k22_member_1(A,B)) ) ) ) ) )).
fof(t186_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,k3_xcmplx_0(2,A)) = k4_xcmplx_0(A) ) )).
fof(t186_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t186_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ( B != C => k6_zf_lang1(k6_zf_lang1(A,B,C),B,D) = k6_zf_lang1(A,B,C) ) ) ) ) ) )).
fof(t187_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => k22_member_1(A,B) = a_2_14_member_1(A,B) ) ) )).
fof(t187_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k4_xcmplx_0(k7_xcmplx_0(A,B)) = k7_xcmplx_0(k4_xcmplx_0(A),B) ) ) )).
fof(t187_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(k7_xcmplx_0(B,A),1) ) ) ) )).
fof(t187_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t187_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,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))) ) ) ) )).
fof(t188_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ~ ( r2_hidden(C,k22_member_1(A,B)) & ! [D] : ( m1_subset_1(D,k6_numbers) => ~ ( C = k4_xxreal_3(B,D) & r2_hidden(D,A) ) ) ) ) ) )).
fof(t188_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k7_xcmplx_0(A,k4_xcmplx_0(B)) = k4_xcmplx_0(k7_xcmplx_0(A,B)) ) ) )).
fof(t188_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(A,B) & r1_xxreal_0(k7_xcmplx_0(B,A),1) ) ) ) )).
fof(t188_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t189_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( v1_xreal_0(C) => ( C != k5_numbers => k22_member_1(k3_xboole_0(A,B),C) = k3_xboole_0(k22_member_1(A,C),k22_member_1(B,C)) ) ) ) ) )).
fof(t189_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k4_xcmplx_0(k7_xcmplx_0(A,k4_xcmplx_0(B))) = k7_xcmplx_0(A,B) ) ) )).
fof(t189_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(1,k7_xcmplx_0(A,B)) ) ) ) )).
fof(t189_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t18_abcmiz_0,axiom,( ! [A] : ( ( v8_abcmiz_0(A) & l2_abcmiz_0(A) ) => ! [B] : ( 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))) ) ) )).
fof(t18_abcmiz_1,axiom,( k2_abcmiz_1 = a_0_1_abcmiz_1 )).
fof(t18_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & v1_abcmiz_a(A) & l1_msualg_1(A) ) => ! [B] : ( 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] : ( m1_abcmiz_1(C,A,k13_abcmiz_1(A)) => ! [D] : ( m1_abcmiz_1(D,A,k12_abcmiz_1(A)) => B != k6_trees_4(k4_tarski(k9_abcmiz_1,3),C,D) ) ) ) ) ) )).
fof(t18_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k2_absvalue(k3_xcmplx_0(A,B)) = k3_xcmplx_0(k2_absvalue(A),k2_absvalue(B)) ) ) )).
fof(t18_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_aff_1(B,A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & C != D ) ) ) ) ) ) )).
fof(t18_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) => ! [H] : ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(A))) => ! [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] : ( m1_subset_1(J,u1_struct_0(A)) => ~ ( r2_hidden(J,H) & r2_hidden(J,I) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t18_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( 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_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))) ) ) ) ) ) )).
fof(t18_afinsq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => k3_afinsq_2(B,k5_numbers,A) = k3_afinsq_2(B,1,A) ) ) )).
fof(t18_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( r2_hidden(B,k2_zfmisc_1(k1_afproj(A),k1_tarski(1))) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & B = k4_tarski(C,1) & v1_aff_1(C,A) ) ) ) )).
fof(t18_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_afvect0(A,B,C,B) <=> ( B = C | r1_afvect0(A,B,C) ) ) ) ) ) )).
fof(t18_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_alg_1(B,A) => r3_alg_1(A,k4_alg_1(A,B),k5_alg_1(A,B)) ) ) )).
fof(t18_algspec1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) )).
fof(t18_algstr_4,axiom,( ! [A] : k11_algstr_4(A,2) = k2_zfmisc_1(k2_zfmisc_1(A,A),k1_tarski(1)) )).
fof(t18_altcat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_altcat_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_altcat_1(A))) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t18_altcat_2,axiom,( ! [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) & l1_cat_1(A) ) => v2_altcat_1(k4_altcat_2(A)) ) )).
fof(t18_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t18_ami_2,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k3_ami_2,k4_ami_2))) => k9_xtuple_0(A) = k1_ami_2 ) )).
fof(t18_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ~ v2_extpro_1(k4_ami_3(A,B),k7_card_1(2),k1_ami_3) ) ) )).
fof(t18_ami_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( ~ 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(k7_card_1(2),k1_ami_3)) & v1_finset_1(B) & v4_extpro_1(B,k7_card_1(2),k1_ami_3,A) ) => ! [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(C,u1_struct_0(k1_ami_3)) ) => ! [D] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ( ( r1_tarski(B,C) & r1_tarski(B,D) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_ami_3)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_ami_3)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( ( r1_tarski(A,E) & r1_tarski(A,F) ) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v1_ami_2(H) & m1_subset_1(H,u1_struct_0(k1_ami_3)) ) => ! [I] : ( ( v1_ami_2(I) & m1_subset_1(I,u1_struct_0(k1_ami_3)) ) => ! [J] : ( m1_subset_1(J,u1_compos_1(k1_ami_3)) => ( ( J = k3_extpro_1(k7_card_1(2),k1_ami_3,E,k5_extpro_1(k7_card_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(k7_card_1(2),k1_ami_3,E,C,G),H),k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,E,C,G),I)) = k6_xcmplx_0(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,F,D,G),H),k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,F,D,G),I)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t18_ami_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( v7_ordinal1(B) => k2_amistd_1(k7_card_1(2),k1_ami_3,k8_ami_3(B,A)) = k1_tarski(B) ) ) )).
fof(t18_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(k4_amistd_1(A))) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t18_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_extpro_1(A))) => k2_compos_0(u1_compos_1(k1_extpro_1(A)),B) = k5_numbers ) ) )).
fof(t18_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(t18_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_diraf(k2_analoaf(A)))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k2_diraf(k2_analoaf(A)))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k2_diraf(k2_analoaf(A)))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k2_diraf(k2_analoaf(A)))) => ( ( F = B & H = D & G = C & I = E ) => ( r2_analoaf(k2_diraf(k2_analoaf(A)),F,H,G,I) <=> ? [J] : ( v1_xreal_0(J) & ? [K] : ( v1_xreal_0(K) & k1_rlvect_1(A,k5_algstr_0(A,D,B),J) = k1_rlvect_1(A,k5_algstr_0(A,E,C),K) & ~ ( J = k5_numbers & K = k5_numbers ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t18_analoaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( B != D & r1_analoaf(A,D,B,B,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_analoaf(A,C,B,B,F) & r1_analoaf(A,C,D,E,F) ) ) ) ) ) ) ) ) )).
fof(t18_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_analmetr(A,F,G) & r1_analort(A,F,G,B,C,D,E) ) => r1_analort(A,F,G,D,E,C,B) ) ) ) ) ) ) ) ) )).
fof(t18_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ~ ( r2_anproj_1(A,E,F,C) & r2_anproj_1(A,G,H,C) & r2_anproj_1(A,E,G,B) & r2_anproj_1(A,F,H,B) & r2_anproj_1(A,E,H,D) & r2_anproj_1(A,F,G,D) & r2_anproj_1(A,B,C,D) & ~ v9_struct_0(B,A) & ~ v9_struct_0(C,A) & ~ v9_struct_0(D,A) & ~ r2_anproj_1(A,E,F,H) & ~ r2_anproj_1(A,E,F,G) & ~ r2_anproj_1(A,E,G,H) & ~ r2_anproj_1(A,F,G,H) ) ) ) ) ) ) ) ) ) )).
fof(t18_anproj_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ~ ( B != C & B != D & B != E & C != D & C != E & D != E & ! [F] : ( m2_funct_2(F,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [G] : ( m2_funct_2(G,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [H] : ( m2_funct_2(H,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [I] : ( m2_funct_2(I,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ? [J] : ( v1_xreal_0(J) & ? [K] : ( v1_xreal_0(K) & ? [L] : ( v1_xreal_0(L) & ? [M] : ( v1_xreal_0(M) & k1_binop_1(k5_funcsdom(A),k1_binop_1(k5_funcsdom(A),k1_binop_1(k5_funcsdom(A),k1_funct_1(k7_funcsdom(A),k4_tarski(J,F)),k1_funct_1(k7_funcsdom(A),k4_tarski(K,G))),k1_funct_1(k7_funcsdom(A),k4_tarski(L,H))),k1_funct_1(k7_funcsdom(A),k4_tarski(M,I))) = k8_funcsdom(A) & ~ ( J = k5_numbers & K = k5_numbers & L = k5_numbers & M = k5_numbers ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t18_aofa_000,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k9_aofa_000(A,B,k5_numbers) = B ) ) )).
fof(t18_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : k2_xboole_0(k1_enumset1(A,B,C),k4_enumset1(D,E,F,G,H,I)) = k7_enumset1(A,B,C,D,E,F,G,H,I) )).
fof(t18_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v19_aofa_a00(B,A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( C = k10_subset_1(k1_funct_1(u7_aofa_a00(A),8),u4_struct_0(A)) => ( k1_msualg_1(A,C) = k2_finseq_4(u1_struct_0(A),B,B) & k2_msualg_1(A,C) = B ) ) ) ) ) )).
fof(t18_aofa_i00,axiom,( ! [A] : ( m4_aofa_i00(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k9_funct_2(k4_ordinal1,k4_numbers),k4_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_funct_2(k4_ordinal1,k4_numbers),k4_numbers))) ) => m3_aofa_i00(B,k7_freealg(k19_aofa_000,k26_aofa_i00),k4_ordinal1,k1_aofa_i00(k9_funct_2(k4_ordinal1,k4_numbers),k5_numbers,k5_numbers),A) ) ) )).
fof(t18_armstrng,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ( v8_relat_2(B) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t18_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ( ( k2_arytm_0(A,B) = 1 & k2_arytm_0(A,C) = 1 ) => ( A = k5_numbers | B = C ) ) ) ) ) )).
fof(t18_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => k2_arytm_1(A,A) = k11_arytm_3 ) )).
fof(t18_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ( r2_hidden(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ( r2_hidden(B,A) <=> ( r2_hidden(B,k4_ordinal1) & B != A & r1_arytm_2(B,A) ) ) ) ) ) )).
fof(t18_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ( B != k1_xboole_0 => ( k3_arytm_3(A,B) != k1_xboole_0 & k6_ordinal3(B,k3_arytm_3(A,B)) != k1_xboole_0 ) ) ) ) )).
fof(t18_asympt_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(A,k7_asympt_0(B)) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) ) )).
fof(t18_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => k9_nat_1(k1_numbers,A,C) = k5_int_1(C,2) ) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => k9_nat_1(k1_numbers,B,C) = k5_int_1(k1_nat_1(C,1),2) ) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & v2_asympt_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v2_asympt_0(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( r2_funct_2(k4_ordinal1,k1_numbers,C,A) & r2_funct_2(k4_ordinal1,k1_numbers,D,B) & ~ r2_hidden(C,k6_asympt_0(D)) & ~ r2_hidden(D,k6_asympt_0(C)) ) ) ) ) ) ) )).
fof(t18_autalg_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t18_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_autgroup(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_autgroup(A))) => ! [D] : ( m2_funct_2(D,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t18_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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(k22_pre_poly(A,C),k22_pre_poly(A,B)) ) ) ) ) )).
fof(t18_bcialg_1,axiom,( ! [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) ) => ( 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) ) ) ) )).
fof(t18_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => 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)) ) ) ) ) )).
fof(t18_bcialg_3,axiom,( ! [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) ) => ( v4_bcialg_3(A) <=> ! [B] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k7_bcialg_1(A,B)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t18_bcialg_4,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t18_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( v8_bcialg_1(E) & m1_bcialg_5(E,A,B,C,D) ) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( v8_bcialg_1(E) & m1_bcialg_5(E,A,k1_nat_1(B,F),k1_nat_1(C,F),D) ) ) ) ) ) ) ) )).
fof(t18_bcialg_6,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => k3_bcialg_6(A,C,k2_bcialg_1(A,B)) = k2_bcialg_1(A,k3_bcialg_6(A,C,B)) ) ) ) )).
fof(t18_bciideal,axiom,( ! [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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( m2_bciideal(B,A) => m2_bcialg_1(B,A) ) ) ) )).
fof(t18_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_bhsp_1(A,k5_algstr_0(A,B,C),k5_algstr_0(A,B,C)) = k2_xcmplx_0(k6_xcmplx_0(k2_bhsp_1(A,B,B),k3_xcmplx_0(2,k2_bhsp_1(A,B,C))),k2_bhsp_1(A,C,C)) ) ) ) )).
fof(t18_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(t18_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_bhsp_2(B,A) => ( ! [D] : ( v7_ordinal1(D) => B != k1_valued_0(u1_struct_0(A),C,D) ) | v1_bhsp_2(C,A) ) ) ) ) ) )).
fof(t18_bhsp_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => k3_bhsp_4(B,C,k1_nat_1(A,1)) = k3_rlvect_1(B,k3_bhsp_4(B,C,A),k1_normsp_1(B,C,k1_nat_1(A,1))) ) ) ) )).
fof(t18_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) ) )).
fof(t18_binari_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k6_margrel1) ) => ! [D] : ( m1_subset_1(D,k6_margrel1) => ! [E] : ( m1_subset_1(E,k6_margrel1) => k6_binari_2(k2_xcmplx_0(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))))) ) ) ) ) ) )).
fof(t18_binari_3,axiom,( k7_binarith(1,k10_binarith(k6_margrel1,k8_margrel1),k10_binarith(k6_margrel1,k8_margrel1)) = k10_binarith(k6_margrel1,k7_margrel1) )).
fof(t18_binarith,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k6_margrel1) ) => ! [D] : ( m1_subset_1(D,k6_margrel1) => ! [E] : ( m1_subset_1(E,k6_margrel1) => k8_binarith(A,B,C) = k7_partfun1(k6_margrel1,k4_binarith(k2_xcmplx_0(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)) ) ) ) ) ) )).
fof(t18_binop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t18_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree2(A) ) => ! [B] : ( v7_ordinal1(B) => k5_card_1(k2_trees_2(A,B)) = k5_series_1(2,B) ) ) )).
fof(t18_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t18_bor_cant,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( r1_bor_cant(A,B,C,D) => ( ( k1_funct_1(C,k3_kurato_0(A,k2_prob_1(A,D))) = k5_numbers | k1_funct_1(C,k3_kurato_0(A,k2_prob_1(A,D))) = 1 ) & ( k1_funct_1(C,k4_kurato_0(A,D)) = k5_numbers | k1_funct_1(C,k4_kurato_0(A,D)) = 1 ) ) ) ) ) ) ) )).
fof(t18_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t18_borsuk_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v1_compts_1(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t18_borsuk_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_connsp_1(A,k5_topmetr) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_topmetr)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_topmetr)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t18_borsuk_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v1_rat_1(A) ) => ~ v1_rat_1(k4_xcmplx_0(A)) ) )).
fof(t18_borsuk_7,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( 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),k1_square_1(A)) ) ) )).
fof(t18_bspace,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k2_bspace)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_bspace)) => ! [D] : ( 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)) ) ) ) )).
fof(t18_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t18_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t18_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,A) => ! [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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t18_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t18_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t18_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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))) ) ) ) )).
fof(t18_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(t18_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t18_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t18_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t18_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t18_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t18_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t18_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) )).
fof(t18_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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_comseq_2(k2_partfun1(A,k1_numbers,B,A)) <=> v4_xxreal_2(k9_c0sp1(A,B)) ) ) ) )).
fof(t18_c0sp2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v1_compts_1(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_c0sp2(B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_c0sp2(B))) => ( ( k2_normsp_0(k5_c0sp2(B),C) = k5_numbers => C = k4_struct_0(k5_c0sp2(B)) ) & ( C = k4_struct_0(k5_c0sp2(B)) => k2_normsp_0(k5_c0sp2(B),C) = k5_numbers ) & k2_normsp_0(k5_c0sp2(B),k1_rlvect_1(k5_c0sp2(B),C,A)) = k3_xcmplx_0(k9_complex1(A),k2_normsp_0(k5_c0sp2(B),C)) & r1_xxreal_0(k2_normsp_0(k5_c0sp2(B),k3_rlvect_1(k5_c0sp2(B),C,D)),k2_xcmplx_0(k2_normsp_0(k5_c0sp2(B),C),k2_normsp_0(k5_c0sp2(B),D))) ) ) ) ) ) )).
fof(t18_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => ( ( r2_relset_1(k4_ordinal1,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)) ) ) ) ) ) )).
fof(t18_calcul_2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => r2_calcul_1(A,B,k8_finseq_1(k3_cqc_lang(A),C,B)) ) ) ) )).
fof(t18_cantor_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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))))))) ) ) ) )).
fof(t18_card_1,axiom,( ! [A] : ( v3_ordinal1(A) => k3_card_1(k1_ordinal1(A)) = k2_card_1(k3_card_1(A)) ) )).
fof(t18_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ! [C] : ( v1_card_1(C) => k1_card_2(k1_card_2(A,B),C) = k1_card_2(A,k1_card_2(B,C)) ) ) ) )).
fof(t18_card_3,axiom,( ! [A] : ! [B] : ! [C] : r1_tarski(k6_subset_1(k5_card_3(A,B),k5_card_3(A,C)),k5_card_3(A,k6_subset_1(B,C))) )).
fof(t18_card_4,axiom,( ! [A] : ( ~ v1_finset_1(A) => ( r2_wellord2(k2_zfmisc_1(A,A),A) & k1_card_1(k2_zfmisc_1(A,A)) = k1_card_1(A) ) ) )).
fof(t18_card_5,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( ( ~ 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 ) ) ) ) )).
fof(t18_card_fil,axiom,( ! [A] : ( ~ v1_finset_1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t18_card_fin,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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] : ( ( r2_hidden(E,k9_xtuple_0(D)) & k1_funct_1(D,E) = A ) => r2_hidden(B,k1_funct_1(C,E)) ) ) ) ) ) )).
fof(t18_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => v2_card_lar(k2_card_lar(A,B),A) ) ) )).
fof(t18_cardfin2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ 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)),k7_xcmplx_0(1,2)) ) ) ) )).
fof(t18_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t18_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t18_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t18_cat_5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_cat_5(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( m1_cat_5(E,A) => ! [F] : ( m1_cat_5(F,A) => ! [G] : ( 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] : ( m1_cat_5(E,A) => ! [F] : ( m1_cat_5(F,A) => ! [G] : ( 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 ) ) ) ) ) )).
fof(t18_catalan1,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k1_catalan1(A),k4_ordinal1) ) )).
fof(t18_catalan2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ( v1_catalan2(A) => ( v1_catalan2(k1_catalan2(k5_afinsq_1(k5_numbers),A)) & a_1_2_catalan2(A) = k1_xboole_0 ) ) ) )).
fof(t18_catalg_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => B != k10_catalg_1(A,C,D,E) ) ) ) ) ) ) )).
fof(t18_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v11_algstr_0(B,A) & v11_algstr_0(C,A) ) => v11_algstr_0(k5_cayldick(A,B,C),k4_cayldick(A)) ) ) ) ) )).
fof(t18_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k8_funcop_1(k4_ordinal1,A,k5_numbers) = k4_struct_0(k7_cc0sp1(A)) ) )).
fof(t18_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( 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 ) ) )).
fof(t18_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( m2_valued_0(B,k2_numbers,A) & v2_comseq_2(A) ) => k3_comseq_2(B) = k3_comseq_2(A) ) ) ) )).
fof(t18_cfdiff_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k1_valued_0(k2_numbers,k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,C),A),k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k1_valued_0(k2_numbers,B,A),k1_valued_0(k2_numbers,C,A))) ) ) ) )).
fof(t18_cfuncdom,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_funct_2(D,C,k2_numbers,k9_funct_2(C,k2_numbers)) => ! [E] : ( m2_funct_2(E,C,k2_numbers,k9_funct_2(C,k2_numbers)) => ( ( r2_hidden(A,C) & r2_hidden(B,C) & ! [F] : ( r2_hidden(F,C) => ( ( F = A => k1_funct_1(D,F) = k6_complex1 ) & ( F != A => k1_funct_1(D,F) = k5_numbers ) ) ) & ! [F] : ( r2_hidden(F,C) => ( ( F = A => k1_funct_1(E,F) = k5_numbers ) & ( F != A => k1_funct_1(E,F) = k6_complex1 ) ) ) ) => ( A = B | ! [F] : ( v1_xcmplx_0(F) => ! [G] : ( v1_xcmplx_0(G) => ( k1_binop_1(k1_cfuncdom(C),k1_funct_1(k3_cfuncdom(C),k4_tarski(F,D)),k1_funct_1(k3_cfuncdom(C),k4_tarski(G,E))) = k4_cfuncdom(C) => ( F = k5_complex1 & G = k5_complex1 ) ) ) ) ) ) ) ) ) )).
fof(t18_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( v1_xcmplx_0(D) => 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))) ) ) ) ) )).
fof(t18_cgames_1,axiom,( ! [A] : ! [B] : ( 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) ) ) ) )).
fof(t18_chain_1,axiom,( ! [A] : ( ( ~ v1_zfmisc_1(A) & v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( m2_chain_1(k4_tarski(B,C),A) & m2_chain_1(k4_tarski(B,D),A) ) => C = D ) ) ) ) ) )).
fof(t18_chord,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ( k3_finseq_1(k15_finseq_1(C)) = k3_finseq_1(B) => k15_finseq_1(C) = B ) ) ) )).
fof(t18_circcmb2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(A,D))) => ! [H] : ( m1_subset_1(H,k4_card_3(u3_msualg_1(B,E))) => ! [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] : ( v7_ordinal1(J) => k5_relat_1(k5_facirc_1(C,F,I,J),u1_struct_0(B)) = k5_facirc_1(B,E,H,J) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t18_circcmb3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( 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] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_card_1(D,A) & v1_finseq_1(D) ) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t18_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => r2_circcomb(A,A,B,B) ) ) )).
fof(t18_circled1,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ~ ( v1_circled1(B,A) & B = k4_rlvect_2(A) ) ) ) )).
fof(t18_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m3_msaterm(C,A,B) => ! [D] : ( m3_msaterm(D,A,B) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t18_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k6_circuit1(A,B,C) = k5_numbers <=> ( r2_hidden(C,k2_msafree2(A)) | r2_hidden(C,k1_msafree2(A)) ) ) ) ) ) )).
fof(t18_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_pboole(C,k2_msafree2(A),k7_funcop_1(k2_msafree2(A),k4_ordinal1),k5_relat_1(u3_msualg_1(A,B),k2_msafree2(A))) => ( v3_funct_1(k9_funct_6(C)) => ( v1_xboole_0(k2_msafree2(A)) | ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(A,B))) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( E = k7_circuit1(A,B) => v1_circuit2(k9_nat_1(k4_card_3(u3_msualg_1(A,B)),k9_circuit2(A,B,C,D),E),A,B) ) ) ) ) ) ) ) ) )).
fof(t18_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ( ( v1_pdiff_7(C,A) & D = k7_funcop_1(C,E) & r1_tarski(k2_relset_1(k4_ordinal1,B),k2_finseq_1(A)) ) => ( r4_pdiff_9(A,C,B,D) & r1_pdiff_9(A,C,k5_pdiff_9(A,C,B,D)) ) ) ) ) ) ) ) )).
fof(t18_classes1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => ( k3_classes1(A,B) = k3_classes1(A,k1_ordinal1(B)) => k3_classes1(A,B) = k1_classes1(A) ) ) )).
fof(t18_classes2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( r2_hidden(A,k1_classes1(B)) => r1_tarski(A,k1_classes1(B)) ) ) )).
fof(t18_clopban1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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)))) ) ) ) )).
fof(t18_clopban2,axiom,( ! [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) & v3_normsp_0(A) & v4_normsp_0(A) & 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 ) )).
fof(t18_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) ) )).
fof(t18_clopban4,axiom,( ! [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) & 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] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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),k7_xcmplx_0(k6_complex1,k2_newton(B))) = k1_normsp_1(A,k1_bhsp_4(A,k3_clopban4(B,A,C,D)),B) ) ) ) ) ) )).
fof(t18_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m2_pboole(C,A,k5_mssubfam(A,B),k5_mssubfam(A,B)) => ! [D] : ( m1_pboole(D,A,k5_mssubfam(A,B)) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t18_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( 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)) ) ) ) ) )).
fof(t18_clvect_1,axiom,( ! [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) ) => ! [B] : ( 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,k4_xcmplx_0(k2_xcmplx_0(k6_complex1,k6_complex1))) ) ) )).
fof(t18_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(t18_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => k2_clvect_3(A,B,k1_nat_1(C,1)) = k3_rlvect_1(A,k2_clvect_3(A,B,C),k1_normsp_0(A,B,k1_nat_1(C,1))) ) ) ) )).
fof(t18_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_coh_sp(A)) => ? [C] : ( m1_subset_1(C,k4_coh_sp(A)) & ? [D] : ( m1_subset_1(D,k3_coh_sp(A)) & ? [E] : ( 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] : ! [G] : ( r2_hidden(k2_tarski(F,G),D) => r2_hidden(k2_tarski(k1_funct_1(C,F),k1_funct_1(C,G)),E) ) ) ) ) ) )).
fof(t18_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v4_cohsp_1(A) => k1_funct_1(A,k1_xboole_0) = k1_xboole_0 ) ) )).
fof(t18_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_collsp(D,A) => ( ( r2_hidden(B,D) & r2_hidden(C,D) ) => ( B = C | r1_tarski(k1_collsp(A,B,C),D) ) ) ) ) ) ) )).
fof(t18_combgras,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( l1_incsp_1(B) => ! [C] : ( l1_combgras(C,A,B) => ! [D] : ( 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) ) ) ) ) )).
fof(t18_compl_sp,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k1_topmetr(A,B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_topmetr(A,B))))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r1_funct_2(k4_ordinal1,u1_struct_0(k1_topmetr(A,B)),k4_ordinal1,u1_struct_0(A),C,D) => ( v3_tbsp_1(D,A) <=> v3_tbsp_1(C,k1_topmetr(A,B)) ) ) ) ) ) ) )).
fof(t18_complex1,axiom,( k3_xcmplx_0(k7_complex1,k7_complex1) = k4_xcmplx_0(k6_complex1) )).
fof(t18_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( ~ r1_xxreal_0(k28_sin_cos,k1_comptrig(A)) & ~ r1_xxreal_0(k28_sin_cos,k1_comptrig(B)) & r1_xxreal_0(k28_sin_cos,k1_comptrig(k2_xcmplx_0(A,B))) ) ) ) )).
fof(t18_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( 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)) ) ) ) )).
fof(t18_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => k1_complsp2(k1_complsp2(A)) = A ) )).
fof(t18_compos_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( l1_compos_1(B) => k61_valued_1(k4_compos_1(B),A) = k16_funcop_1(A,k2_compos_1(B)) ) ) )).
fof(t18_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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)) ) ) ) ) )).
fof(t18_comptrig,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(k3_xcmplx_0(2,k28_sin_cos),A) & k19_sin_cos(A) = k5_numbers & A != k7_xcmplx_0(k28_sin_cos,2) & A != k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos) ) ) )).
fof(t18_compts_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_finset_1(u1_struct_0(A)) => v1_compts_1(A) ) ) )).
fof(t18_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_margrel1(A) ) => ( k9_xtuple_0(A) = k1_tarski(k1_xboole_0) => k18_margrel1(A) = k5_numbers ) ) )).
fof(t18_comseq_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k25_valued_1(k4_ordinal1,k2_numbers,k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,C),A),k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k25_valued_1(k4_ordinal1,k2_numbers,B,A),k25_valued_1(k4_ordinal1,k2_numbers,C,A))) ) ) ) )).
fof(t18_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & v2_comseq_2(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => k3_comseq_2(k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)) = k6_xcmplx_0(k3_comseq_2(A),k3_comseq_2(B)) ) ) )).
fof(t18_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( r2_funct_2(k4_ordinal1,k1_numbers,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k7_comseq_3(A),k7_comseq_3(B)),k7_comseq_3(k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B))) & r2_funct_2(k4_ordinal1,k1_numbers,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_comseq_3(A),k8_comseq_3(B)),k8_comseq_3(k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B))) ) ) ) )).
fof(t18_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => k1_funct_1(k2_conlat_1(A),k1_xboole_0) = u1_struct_0(A) ) )).
fof(t18_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( 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) ) ) )).
fof(t18_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v2_connsp_1(C,A) & r1_tarski(C,B) & r1_tarski(B,k2_pre_topc(A,C)) ) => v2_connsp_1(B,A) ) ) ) ) )).
fof(t18_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_connsp_2(A) <=> ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t18_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t18_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( B = a_3_2_convex1(A,C,D) => v1_convex1(B,A) ) ) ) ) ) )).
fof(t18_convex4,axiom,( ! [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) ) => ! [B] : ( m1_convex4(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t18_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t18_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => k7_cqc_sim1(A,k11_cqc_lang(A,C,B)) = k1_nat_1(k7_cqc_sim1(A,B),1) ) ) ) )).
fof(t18_cqc_the1,axiom,( v1_finset_1(k2_cqc_the1) )).
fof(t18_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t18_csspace,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k12_csspace(B,C,k1_clvect_1(B,D,A)) = k3_xcmplx_0(k8_complex1(A),k12_csspace(B,C,D)) ) ) ) ) )).
fof(t18_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k9_csspace4(A,B))) => r1_xxreal_0(k5_numbers,k2_normsp_0(k9_csspace4(A,B),C)) ) ) ) )).
fof(t18_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(t18_descip_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t18_diff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(C,A),1),B) = k6_xcmplx_0(k1_funct_1(C,B),k1_funct_1(k2_diff_1(C,k4_xcmplx_0(A)),B)) ) ) ) )).
fof(t18_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t18_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( 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) = k7_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(4,k3_xcmplx_0(k19_sin_cos(k2_xcmplx_0(B,A)),k17_sin_cos(k6_xcmplx_0(B,A)))),k3_xcmplx_0(k17_sin_cos(k3_xcmplx_0(2,A)),k17_sin_cos(k3_xcmplx_0(2,B)))),k6_xcmplx_0(A,B)) ) ) ) )).
fof(t18_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t18_dirort,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dirort(A) & l1_analoaf(A) ) => ( v3_dirort(A) => ( ( ~ v5_dirort(A) & ~ v6_dirort(A) ) | v4_dirort(A) ) ) ) )).
fof(t18_dist_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t18_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m2_finseq_2(B,A,k3_finseq_2(A)) => ! [C] : ( ( 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_hidden(k10_relat_1(k1_partfun1(k4_ordinal1,A,A,k6_margrel1,B,C),k8_margrel1),k9_setfam_1(k4_finseq_1(B))) ) ) ) )).
fof(t18_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_dynkin(B,A) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(A),B) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( r1_xboole_0(C,D) => r2_hidden(k4_subset_1(A,C,D),B) ) ) ) ) ) )).
fof(t18_e_siec,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t18_ec_pf_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(C))) => ( ( D = k5_int_1(A,C) & E = k5_int_1(B,C) ) => k8_group_1(k9_int_3(C),D,E) = k5_int_1(k3_xcmplx_0(A,B),C) ) ) ) ) ) ) )).
fof(t18_ec_pf_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k9_int_3(C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k9_int_3(C))) => ( ( D = k5_int_1(A,C) & E = k5_int_1(B,C) & F = k5_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) ) ) ) ) ) ) ) ) )).
fof(t18_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k2_ens_1(A) = k3_tarski(a_1_2_ens_1(A)) ) )).
fof(t18_entropy1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => k4_finseq_1(k1_matrprob(A,B,C)) = k2_finseq_1(k1_matrix_0(B)) ) ) ) ) )).
fof(t18_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k1_enumset1(A,B,C),k2_enumset1(D,E,F,G)) )).
fof(t18_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r2_hidden(B,k9_relat_1(C,A)) <=> r2_hidden(k4_tarski(A,B),C) ) ) )).
fof(t18_equation,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_msualg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( r2_hidden(E,k3_msualg_1(A,D,C)) => r2_hidden(E,k3_msualg_1(A,D,B)) ) ) ) ) ) )).
fof(t18_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => r1_pcomps_1(k1_euclid(A),k13_euclid(A)) ) )).
fof(t18_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( v1_xreal_0(D) => k22_rvsum_1(B,k1_rlvect_1(k15_euclid(A),C,D)) = k3_xcmplx_0(D,k22_rvsum_1(B,C)) ) ) ) ) )).
fof(t18_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( k2_euclid_3(A) = k5_complex1 => A = k4_struct_0(k15_euclid(2)) ) ) )).
fof(t18_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => k22_rvsum_1(B,k5_euclid(A)) = k5_numbers ) ) )).
fof(t18_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => ! [B] : ( 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)) ) ) )).
fof(t18_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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 | D = A | ( k4_euclid_3(C,D,A) != k7_xcmplx_0(k28_sin_cos,2) & k4_euclid_3(C,D,A) != k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos) ) | k4_euclid_3(A,C,D) = k4_euclid_3(D,C,B) ) ) ) ) ) ) )).
fof(t18_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ( ( v5_euclid_7(B,A) & ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ( r2_hidden(D,B) => k22_rvsum_1(D,C) = k5_numbers ) ) ) => C = k5_euclid(A) ) ) ) ) )).
fof(t18_euclid_8,axiom,( k5_euclid_8(k2_euclid_8,k4_euclid_8) = k6_euclid(3,k3_euclid_8) )).
fof(t18_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(A))) => ( A != k5_numbers => r1_tarski(k4_euclid_9(A,C,B),k8_metric_1(k14_euclid(A),C,k3_xcmplx_0(B,k3_square_1(A)))) ) ) ) ) )).
fof(t18_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t18_euclmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( 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] : ( v1_xreal_0(H) => ~ ( H != k5_numbers & E = k3_rlvect_1(A,k1_rlvect_1(A,B,k3_xcmplx_0(H,G)),k1_rlvect_1(A,C,k4_xcmplx_0(k3_xcmplx_0(H,F)))) ) ) ) ) ) ) ) ) ) ) )).
fof(t18_euler_1,axiom,( k1_euler_1(2) = 1 )).
fof(t18_euler_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_int_2(A,B) => ( A = k5_numbers | r1_xxreal_0(B,1) | k4_nat_d(k1_newton(A,k1_euler_1(B)),B) = 1 ) ) ) ) )).
fof(t18_exchsort,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v1_xboole_0(B) => v2_exchsort(B,A) ) ) )).
fof(t18_extens_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_msualg_2(C,A,B) => ! [D] : ( m3_pboole(D,u1_struct_0(A),u3_msualg_1(A,B)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t18_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ( 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) ) ) ) ) ) ) )).
fof(t18_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => k3_extreal1(A) = k3_extreal1(k2_xxreal_3(A)) ) )).
fof(t18_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( r2_hidden(D,k2_msafree2(A)) => r1_facirc_1(A,B,C,D) ) ) ) ) )).
fof(t18_facirc_2,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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) ) )).
fof(t18_fcont_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t18_fcont_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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(B,A) & r1_tarski(k1_rcomp_1(B,A),k1_relset_1(k1_numbers,C)) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A))) & ~ ( k3_seq_4(k7_relset_1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A))) = k1_funct_1(C,B) & k2_seq_4(k7_relset_1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A))) = k1_funct_1(C,A) ) & ~ ( k3_seq_4(k7_relset_1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A))) = k1_funct_1(C,A) & k2_seq_4(k7_relset_1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A))) = k1_funct_1(C,B) ) ) ) ) ) )).
fof(t18_fcont_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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)))) ) ) ) ) )).
fof(t18_fdiff_1,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_1(k2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,B,C),A),D) = k2_xcmplx_0(k1_fdiff_1(B,D),k1_fdiff_1(C,D)) ) ) ) ) ) ) ) )).
fof(t18_fdiff_10,axiom,( ! [A] : ( ( 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,k22_sin_cos))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k22_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k22_sin_cos),A),B) = k2_xcmplx_0(k7_xcmplx_0(k1_funct_1(k22_sin_cos,B),B),k3_xcmplx_0(k1_funct_1(k3_taylor_1,B),k1_funct_1(k22_sin_cos,B))) ) ) ) ) ) )).
fof(t18_fdiff_11,axiom,( ! [A] : ( ( 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,k26_sin_cos))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k26_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k26_sin_cos),A),B) = k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(k1_square_1(k1_funct_1(k18_sin_cos,k1_funct_1(k2_sin_cos9,B))),k2_xcmplx_0(1,k1_square_1(B))))) ) ) ) ) ) )).
fof(t18_fdiff_2,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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))) ) ) ) ) ) )).
fof(t18_fdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( 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)) = k2_xcmplx_0(k3_xcmplx_0(k2_fdiff_3(C,A),k1_funct_1(B,C)),k3_xcmplx_0(k2_fdiff_3(C,B),k1_funct_1(A,C))) ) ) ) ) ) )).
fof(t18_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => ( k1_funct_1(C,E) = k1_square_1(A) & ~ r1_xxreal_0(k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,C,D),E),k5_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] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_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) = k7_xcmplx_0(k3_xcmplx_0(2,E),k2_xcmplx_0(k1_square_1(A),k1_newton(E,2))) ) ) ) ) ) ) ) ) )).
fof(t18_fdiff_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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,k22_sin_cos),k22_sin_cos),k7_xcmplx_0(1,k6_xcmplx_0(k3_power(k4_power,A),1))))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(C,D) = k3_xcmplx_0(D,k3_power(k4_power,A)) ) ) ) => ( r1_xxreal_0(A,k5_numbers) | A = k4_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,k22_sin_cos),k22_sin_cos),k7_xcmplx_0(1,k6_xcmplx_0(k3_power(k4_power,A),1))),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_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,k22_sin_cos),k22_sin_cos),k7_xcmplx_0(1,k6_xcmplx_0(k3_power(k4_power,A),1))),B),D) = k7_xcmplx_0(k6_prepower(A,D),k1_funct_1(k22_sin_cos,D)) ) ) ) ) ) ) ) ) )).
fof(t18_fdiff_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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(k4_xcmplx_0(1),1)) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(D,E) = k2_xcmplx_0(k3_xcmplx_0(A,E),B) ) ) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k1_sin_cos6),C) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k1_sin_cos6),C),E) = k2_xcmplx_0(k3_xcmplx_0(A,k1_funct_1(k1_sin_cos6,E)),k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,E),B),k3_square_1(k6_xcmplx_0(1,k1_square_1(E))))) ) ) ) ) ) ) ) ) )).
fof(t18_fdiff_8,axiom,( ! [A] : ( ( 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,k26_sin_cos,k3_taylor_1))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k3_taylor_1),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k3_taylor_1),A),B) = k7_xcmplx_0(1,k3_xcmplx_0(k1_funct_1(k18_sin_cos,B),k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t18_fdiff_9,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fdiff_9,k3_taylor_1),A),B) = k7_xcmplx_0(k1_funct_1(k16_sin_cos,B),k1_funct_1(k18_sin_cos,B)) ) ) ) ) ) )).
fof(t18_ff_siec,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t18_fib_num2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) ) => ( C = k1_tarski(k4_tarski(1,B)) => k61_valued_1(C,A) = k1_tarski(k4_tarski(k1_nat_1(1,A),B)) ) ) ) )).
fof(t18_fib_num3,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => r1_xxreal_0(k1_fib_num3(A),k1_fib_num3(k1_nat_1(A,1))) ) )).
fof(t18_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => k1_int_1(k2_xcmplx_0(k7_xcmplx_0(k2_power(k1_fib_num,A),k3_square_1(5)),k7_xcmplx_0(1,2))) = k1_pre_ff(A) ) )).
fof(t18_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( 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)) ) ) ) ) )).
fof(t18_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( v13_lattices(A) => ! [B] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t18_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) ) ) ) ) )).
fof(t18_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_lattice2(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t18_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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))) ) ) )).
fof(t18_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m2_finseq_1(C,B) => m2_finseq_1(k2_partfun1(k4_ordinal1,B,C,k2_finseq_1(A)),B) ) ) )).
fof(t18_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( ( C = k5_relat_1(B,k2_finseq_1(A)) & r1_xxreal_0(k3_finseq_1(B),A) ) => B = C ) ) ) ) )).
fof(t18_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => r1_tarski(k2_finseq_1(A),k2_finseq_1(k2_xcmplx_0(A,B))) ) ) )).
fof(t18_finseq_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t18_finseq_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => r1_tarski(k4_finseq_1(k16_finseq_1(B,A)),k4_finseq_1(A)) ) ) )).
fof(t18_finseq_6,axiom,( ! [A] : k4_finseq_4(k9_finseq_1(A),A) = 1 )).
fof(t18_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k3_finseq_1(k2_finseq_7(A,B,C,D)) = k3_finseq_1(B) ) ) ) ) )).
fof(t18_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(D,E) & r2_finseq_8(A,B,C,E) ) => r2_finseq_8(A,B,C,D) ) ) ) ) ) ) )).
fof(t18_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( ( 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(k4_ordinal1,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))) ) ) ) ) ) ) ) )).
fof(t18_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( v2_binop_1(C,A) => ( ( ~ v1_setwiseo(C,A) & ~ ( D != k5_numbers & E != k5_numbers ) ) | k1_finsop_1(A,k5_finseq_2(A,k1_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)) ) ) ) ) ) ) ) )).
fof(t18_finsub_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_finset_1(A) => m1_subset_1(B,k5_finsub_1(A)) ) ) )).
fof(t18_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k12_fin_topo(A,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & k4_fintopo2(A,D,C) = k8_margrel1 & k3_fintopo2(A,D,B) = k8_margrel1 ) ) ) ) ) )).
fof(t18_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k5_fintopo3(A,B,k1_nat_1(C,1)) = k8_fin_topo(A,k5_fintopo3(A,B,C)) ) ) ) )).
fof(t18_fintopo4,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => v3_orders_2(k2_fintopo4(A)) ) ) )).
fof(t18_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t18_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_catalan2(A))) => ! [D] : ( 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)) ) ) ) )).
fof(t18_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t18_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) )).
fof(t18_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r1_tarski(C,A) => r1_tarski(k8_funct_7(C,B),k8_funct_7(A,B)) ) ) ) ) )).
fof(t18_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ~ ( ~ v1_finset_1(k9_subset_1(k15_fomodel1(B),A,k16_fomodel1(B))) & ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ~ ( k37_fomodel1(C) = k9_subset_1(k15_fomodel1(B),A,k37_fomodel1(B)) & v16_fomodel1(B,C) ) ) ) ) )).
fof(t18_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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))) ) => ( k29_fomodel2(B,C) = k1_nat_1(A,1) => ( ( v5_fomodel2(C,B) => r2_hidden(C,k33_fomodel2(B,A)) ) & ( r2_hidden(C,k33_fomodel2(B,A)) => v5_fomodel2(C,B) ) & ( ~ v5_fomodel2(C,B) => r2_hidden(C,k32_fomodel2(B,A)) ) & ~ ( r2_hidden(C,k32_fomodel2(B,A)) & v5_fomodel2(C,B) ) ) ) ) ) ) )).
fof(t18_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( v4_fomodel1(C,B) & m1_subset_1(C,k1_fomodel1(B)) ) => ! [D] : ( ( v1_partfun1(D,A) & v1_relat_2(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [E] : ( m2_fomodel2(E,B,A,C) => v2_fomodel3(E,B,A,C,D) ) ) ) ) ) )).
fof(t18_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ! [D] : ( v4_funct_1(D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k40_fomodel2(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k40_fomodel2(B)))) ) => ( ( v7_fomodel4(C,B) & r2_hidden(k25_fomodel4(B),C) & r2_hidden(k35_fomodel4(B),C) & r2_hidden(k26_fomodel4(B),C) & r2_hidden(k32_fomodel4(B),C) & r1_tarski(k45_fomodel4(D,B,C,E),A) & k10_xtuple_0(E) = k40_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)))))) | v10_fomodel4(A,B,C) | v14_fomodel4(A,B) ) ) ) ) ) ) )).
fof(t18_frechet,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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) ) ) )).
fof(t18_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(B,k1_frechet2(A,B)) ) ) )).
fof(t18_fscirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t18_fscirc_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( 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(k5_numbers,k6_margrel1),k8_margrel1) & k9_xtuple_0(k2_xtuple_0(k3_fscirc_2(C,A,B))) = k4_finseq_2(k5_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) ) ) ) ) ) )).
fof(t18_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( ( ~ v2_struct_0(E) & l2_fsm_1(E,A,B) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(E)) => ! [G] : ( m1_subset_1(G,u1_struct_0(E)) => ( G = 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,C)) => k4_fsm_1(A,B,E,F,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,F,C))),k4_fsm_1(A,B,E,G,D)) ) ) ) ) ) ) ) ) )).
fof(t18_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( ~ v2_struct_0(D) & l2_fsm_2(D,A,B) ) => ~ ( v1_fsm_2(D,A) & r2_fsm_2(A,C,D) & ! [E] : ( ( ~ v8_ordinal1(E) & m1_subset_1(E,k4_ordinal1) ) => ~ ( ! [F] : ( m2_finseq_1(F,A) => ( ( r1_xxreal_0(E,k1_nat_1(k3_finseq_1(F),1)) & k1_funct_1(F,1) = C ) => r2_hidden(k1_funct_1(k2_fsm_1(A,D,u2_fsm_1(A,D),F),E),u1_fsm_2(A,D)) ) ) & ! [F] : ( m2_finseq_1(F,A) => ! [G] : ( ( ~ v8_ordinal1(G) & m1_subset_1(G,k4_ordinal1) ) => ~ ( r1_xxreal_0(G,k1_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(A,D,u2_fsm_1(A,D),F),G),u1_fsm_2(A,D)) ) ) ) ) ) ) ) ) ) ) )).
fof(t18_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( ( ~ v2_struct_0(D) & l2_fsm_3(D,A,C) ) => ( r2_hidden(B,k6_fsm_3(A,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(D)) & ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t18_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t18_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ~ ( 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 ) ) )).
fof(t18_funcsdom,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_funct_2(D,C,k1_numbers,k9_funct_2(C,k1_numbers)) => ! [E] : ( m2_funct_2(E,C,k1_numbers,k9_funct_2(C,k1_numbers)) => ( ( r2_hidden(A,C) & r2_hidden(B,C) & ! [F] : ( r2_hidden(F,C) => ( ( F = A => k1_funct_1(D,F) = 1 ) & ( F != A => k1_funct_1(D,F) = k5_numbers ) ) ) & ! [F] : ( r2_hidden(F,C) => ( ( F = A => k1_funct_1(E,F) = k5_numbers ) & ( F != A => k1_funct_1(E,F) = 1 ) ) ) ) => ( A = B | ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( k1_binop_1(k5_funcsdom(C),k1_funct_1(k7_funcsdom(C),k4_tarski(F,D)),k1_funct_1(k7_funcsdom(C),k4_tarski(G,E))) = k8_funcsdom(C) => ( F = k5_numbers & G = k5_numbers ) ) ) ) ) ) ) ) ) )).
fof(t18_funct_1,axiom,( ! [A] : ! [B] : ( r2_hidden(B,A) => k1_funct_1(k4_relat_1(A),B) = B ) )).
fof(t18_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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 ) ) ) )).
fof(t18_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t18_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => r1_tarski(k10_xtuple_0(B),k10_xtuple_0(k1_funct_4(A,B))) ) ) )).
fof(t18_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) ) )).
fof(t18_funct_6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_funcop_1(C) ) => ( ( r2_hidden(A,k9_xtuple_0(C)) & B = k1_funct_1(C,A) ) => ( r2_hidden(A,k9_xtuple_0(k1_funct_6(C))) & k1_funct_1(k1_funct_6(C),A) = k9_xtuple_0(B) & r2_hidden(A,k9_xtuple_0(k2_funct_6(C))) & k1_funct_1(k2_funct_6(C),A) = k10_xtuple_0(B) ) ) ) ) )).
fof(t18_funct_7,axiom,( ! [A] : ! [B] : ( r2_hidden(k9_finseq_1(B),k3_finseq_2(A)) <=> r2_hidden(B,A) ) )).
fof(t18_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t18_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) ) => ( ! [D] : ( 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) = k5_numbers | ( v1_funct_9(C,k2_xcmplx_0(A,B)) & v2_funct_9(C) ) ) ) ) ) ) )).
fof(t18_functor1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & v1_altcat_2(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & v1_altcat_2(B) & l2_altcat_1(B) ) => ! [C] : ( ( v8_functor0(C,A,B) & l2_functor0(C,A,B) ) => ( v21_functor0(C,A,B) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t18_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t18_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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) ) ) ) ) ) )).
fof(t18_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D),C) & r1_fuzzy_1(k1_fuzzy_2(A,D,B),C) ) => r1_fuzzy_1(k6_fuzzy_1(A,B,D),C) ) ) ) ) ) )).
fof(t18_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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] : ( ( v5_relat_1(F,k1_rcomp_1(k5_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] : ( ( v5_relat_1(G,k1_rcomp_1(k5_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] : ( ( r2_hidden(H,A) & r2_hidden(I,C) & ! [J] : ( r2_hidden(J,B) => ( r1_xxreal_0(k1_funct_1(D,k4_tarski(H,J)),k1_funct_1(E,k4_tarski(H,J))) & r1_xxreal_0(k1_funct_1(F,k4_tarski(J,I)),k1_funct_1(G,k4_tarski(J,I))) ) ) ) => r1_xxreal_0(k1_funct_1(k3_fuzzy_4(A,B,C,D,F),k4_tarski(H,I)),k1_funct_1(k3_fuzzy_4(A,B,C,E,G),k4_tarski(H,I))) ) ) ) ) ) ) ) ) )).
fof(t18_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_fvaluat1(C,A) => ~ ( v3_fvaluat1(A) & B != k4_struct_0(A) & k3_funct_2(u1_struct_0(A),k6_numbers,C,B) = k1_xxreal_0 ) ) ) ) )).
fof(t18_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_algstr_0(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m2_finseq_2(F,u1_struct_0(C),k4_finseq_2(A,u1_struct_0(C))) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t18_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ ( ~ 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)) ) ) )).
fof(t18_gcd_1,axiom,( ! [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) & v1_vectsp_2(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r4_gcd_1(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & v1_gcd_1(D,A) & k8_group_1(A,B,D) = C ) ) ) ) ) )).
fof(t18_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v2_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( m1_genealg1(E,D) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t18_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r1_analmetr(A,E,F) & r2_geomtrap(A,E,F,C,B,B,D) ) => ( C = B & B = D ) ) ) ) ) ) ) ) )).
fof(t18_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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))) ) ) )).
fof(t18_gfacirc2,axiom,( ! [A] : ! [B] : ! [C] : ( C = k4_tarski(k1_xboole_0,k1_margrel1(k6_margrel1,k4_finseq_2(k5_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(k5_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(k5_numbers,k6_margrel1),k8_margrel1),k1_xboole_0),k25_gfacirc1(A,B,C),k7_circcomb(k5_ordinal1,k6_margrel1,k1_margrel1(k6_margrel1,k4_finseq_2(k5_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) ) ) )).
fof(t18_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ( v3_glib_000(A) <=> ! [B] : ! [C] : ~ r1_glib_000(A,B,B,C) ) ) )).
fof(t18_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ! [D] : ! [E] : ( m3_glib_001(E,A) => ! [F] : ( m3_glib_001(F,B) => ( E = F => ( r1_glib_001(A,C,D,E) <=> r1_glib_001(B,C,D,F) ) ) ) ) ) ) )).
fof(t18_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ( m1_subset_1(E,k6_glib_000(A)) => ( ( r2_hidden(C,k2_glib_002(A,E)) & r2_glib_000(A,C,D,B) ) => r2_hidden(D,k2_glib_002(A,E)) ) ) ) )).
fof(t18_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m4_glib_001(C,A,B) => ? [D] : ( 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) ) ) ) ) )).
fof(t18_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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] : ! [D] : ( ( r1_glib_005(A,B,C,D) & ! [E] : ( ( 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) ) ) ) )).
fof(t18_goboard1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( 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_0(B))) & r1_xboole_0(k10_xtuple_0(C),k10_xtuple_0(k8_matrix_0(u1_struct_0(k15_euclid(2)),B,A))) ) => ( r1_xxreal_0(k1_matrix_0(B),1) | r1_goboard1(u1_struct_0(k15_euclid(2)),C,k16_matrix_0(A,u1_struct_0(k15_euclid(2)),B)) ) ) ) ) ) )).
fof(t18_goboard2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( ( r2_hidden(A,k4_finseq_1(B)) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => r1_xxreal_0(k1_funct_1(k2_goboard1(B),C),k1_funct_1(k2_goboard1(B),A)) ) ) ) => r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),B,A),k10_xtuple_0(k8_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(B),k1_matrix_0(k2_goboard2(B))))) ) ) ) )).
fof(t18_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_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_0(C),B) | r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),k1_nat_1(B,1))),k3_goboard5(C,A,B)) ) ) ) ) ) )).
fof(t18_goboard6,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => k1_tops_1(k15_euclid(2),k3_goboard5(A,k5_numbers,k5_numbers)) = a_1_4_goboard6(A) ) )).
fof(t18_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(C)) ) => k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),B)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),k1_nat_1(B,1)))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),B)) ) ) ) ) )).
fof(t18_goboard8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,2),k3_finseq_1(A)) ) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,2),k1_matrix_0(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,k1_nat_1(C,1)) ) => ( ( ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,C) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),2,k1_nat_1(C,1)) ) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,C) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),2,k1_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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,k1_nat_1(C,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,k1_nat_1(C,2))),k7_xcmplx_0(1,2)),k19_euclid(1,k5_numbers)),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,k1_nat_1(C,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),2,k1_nat_1(C,2))),k7_xcmplx_0(1,2))),k3_topreal1(2,A)) ) ) ) ) ) ) )).
fof(t18_goboard9,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k3_finseq_1(A)) ) => v1_convex1(k1_tops_1(k15_euclid(2),k4_goboard5(A,B)),k15_euclid(2)) ) ) ) )).
fof(t18_gobrd11,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( v1_goboard1(A) => k1_goboard5(A,k5_numbers) = a_1_9_gobrd11(A) ) ) )).
fof(t18_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(D)) & r1_goboard1(u1_struct_0(k15_euclid(2)),D,E) & r2_hidden(k4_tarski(A,B),k2_matrix_0(E)) & r2_hidden(k4_tarski(k1_nat_1(A,1),B),k2_matrix_0(E)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,k1_nat_1(A,1),B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,B) ) => k3_gobrd13(D,E,C) = k3_goboard5(E,A,k7_nat_d(B,1)) ) ) ) ) ) ) )).
fof(t18_gobrd14,axiom,( ! [A] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(t18_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ( v4_card_3(A) => v4_card_3(k9_qc_lang1(A)) ) ) )).
fof(t18_gr_cy_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( v7_ordinal1(D) & C = k5_group_1(A,D,B) ) ) ) ) ) )).
fof(t18_gr_cy_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) )).
fof(t18_gr_cy_3,axiom,( k1_gr_cy_3(2) = 3 )).
fof(t18_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_graph_1(C) ) => ( r1_graph_1(A,B,C) => ( r4_graph_1(B,A) & r4_graph_1(C,A) ) ) ) ) ) )).
fof(t18_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(t18_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ( v5_graph_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( m1_graph_1(D,A) => ! [E] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t18_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v7_graph_1(B,A) & v3_graph_2(B,A) & m2_graph_1(B,A) ) => ! [C] : ( ( v7_graph_1(C,A) & m2_graph_1(C,A) ) => ( C = B => v1_graph_4(C,A) ) ) ) ) )).
fof(t18_graph_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m2_finseq_1(C,u4_struct_0(B)) => ~ ( ~ r1_tarski(k2_graph_5(B,C),A) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m2_finseq_1(E,u4_struct_0(B)) => ! [F] : ( m2_finseq_1(F,u4_struct_0(B)) => ~ ( r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(C)) & ~ r1_tarski(k1_graph_5(B,k7_partfun1(u4_struct_0(B),C,k1_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) ) ) ) ) ) ) ) )).
fof(t18_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_2(D,k1_numbers,k3_finseq_2(k1_numbers)) => ! [E] : ( v1_xreal_0(E) => ~ ( C != A & C != B & k1_funct_1(k2_graphsp(A,B,D,E),C) != k1_funct_1(D,C) ) ) ) ) ) ) )).
fof(t18_grcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( m1_grcat_1(D,B,C) => ! [E] : ( m1_grcat_1(E,A,B) => ! [F] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t18_grfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) => ! [B] : ! [C] : ( r2_hidden(k4_tarski(C,B),k2_funct_1(A)) <=> r2_hidden(k4_tarski(B,C),A) ) ) ) )).
fof(t18_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,k2_grnilp_1(A)) => m2_finseq_1(B,k1_group_3(A)) ) ) )).
fof(t18_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(E,A,C) & v1_polynom1(E,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(k12_polynom1(A,C),D)) => r10_polyred(A,B,C,E,D) ) ) => ! [E] : ( ( 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(k12_polynom1(A,C),D))) & ! [F] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t18_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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(k12_polynom1(A,C),D)) ) ) ) ) ) ) ) )).
fof(t18_groeb_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( 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,k3_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))),k8_polynom1(A,B)) ) ) ) )).
fof(t18_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t18_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_group_2(C,A) => r1_tarski(k1_group_11(A,B,C),k2_group_11(A,B,C)) ) ) ) )).
fof(t18_group_14,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_finseq_1(B) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k4_finseq_1(B)) => k1_card_1(k1_funct_1(B,C)) = k1_funct_1(A,C) ) ) ) => k1_card_1(k4_card_3(B)) = k3_wsierp_1(A) ) ) ) )).
fof(t18_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t18_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_group_3(A,B,C) = k1_group_1(A) => B = k1_group_1(A) ) ) ) ) )).
fof(t18_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t18_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t18_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t18_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t18_group_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v15_algstr_0(D) & m1_group_2(D,A) ) => ! [E] : ( ( 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] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t18_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( m1_group_9(D,A,B) => ( ! [E] : ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t18_groupp_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v8_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t18_hahnban,axiom,( ! [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) ) => ! [B] : ( ( 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] : ( 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)) ) ) ) )).
fof(t18_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t18_hallmar1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ( ? [C] : r1_hallmar1(A,B,C) => v1_hallmar1(B,A) ) ) ) )).
fof(t18_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t18_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v5_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t18_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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] : ( ( 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))) ) ) ) )).
fof(t18_heyting1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(k7_normform(A))) => ! [C] : ( m1_subset_1(C,k5_finsub_1(k7_normform(A))) => ! [D] : ( 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] : ( 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)))) ) ) ) ) ) ) )).
fof(t18_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ r1_tarski(k2_heyting3(A,B),k3_heyting3(C,B)) ) ) ) )).
fof(t18_hfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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))) ) ) ) ) ) ) )).
fof(t18_hilbasis,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( C != k4_struct_0(A) => k1_algseq_1(A,k5_hilbasis(A,B,C)) = k1_nat_1(B,1) ) & ( C = k4_struct_0(A) => k1_algseq_1(A,k5_hilbasis(A,B,C)) = k5_numbers ) & r1_xxreal_0(k1_algseq_1(A,k5_hilbasis(A,B,C)),k1_nat_1(B,1)) ) ) ) ) )).
fof(t18_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => r2_hidden(k3_hilbert1(k3_hilbert1(B,A),k3_hilbert1(A,A)),k6_hilbert1) ) ) )).
fof(t18_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( m1_subset_1(D,k1_hilbert1) => ( k7_finseq_1(A,B) = k7_finseq_1(C,D) => ( A = C & B = D ) ) ) ) ) ) )).
fof(t18_hilbert3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t18_hurwitz,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_funct_2(k4_ordinal1,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))) ) ) ) ) )).
fof(t18_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_idea_1(A,B) & r1_idea_1(A,C) & k7_idea_1(A,B) = k7_idea_1(A,C) ) => B = C ) ) ) ) )).
fof(t18_incproj,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( 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] : ( m1_subset_1(B,u1_incsp_1(k3_incproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k3_incproj(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k3_incproj(A))) => ! [E] : ( m1_subset_1(E,u1_incsp_1(k3_incproj(A))) => ! [F] : ( m1_subset_1(F,u1_incsp_1(k3_incproj(A))) => ! [G] : ( m1_subset_1(G,u1_incsp_1(k3_incproj(A))) => ! [H] : ( m1_subset_1(H,u1_incsp_1(k3_incproj(A))) => ! [I] : ( m1_subset_1(I,u1_incsp_1(k3_incproj(A))) => ! [J] : ( m1_subset_1(J,u1_incsp_1(k3_incproj(A))) => ! [K] : ( m1_subset_1(K,u1_incsp_1(k3_incproj(A))) => ! [L] : ( m1_subset_1(L,u2_incsp_1(k3_incproj(A))) => ! [M] : ( m1_subset_1(M,u2_incsp_1(k3_incproj(A))) => ! [N] : ( m1_subset_1(N,u2_incsp_1(k3_incproj(A))) => ! [O] : ( m1_subset_1(O,u2_incsp_1(k3_incproj(A))) => ! [P] : ( m1_subset_1(P,u2_incsp_1(k3_incproj(A))) => ! [Q] : ( m1_subset_1(Q,u2_incsp_1(k3_incproj(A))) => ! [R] : ( m1_subset_1(R,u2_incsp_1(k3_incproj(A))) => ! [S] : ( m1_subset_1(S,u2_incsp_1(k3_incproj(A))) => ! [T] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t18_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t18_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ 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] : ( m2_cat_1(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t18_instalg1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_instalg1(B,A) => ! [C] : ( l1_msualg_1(C) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( 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))) ) ) ) ) ) ) )).
fof(t18_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => ( ( r2_int_1(A,B,E) & r2_int_1(C,D,E) ) => r2_int_1(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D),E) ) ) ) ) ) ) )).
fof(t18_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => r1_int_1(A,k2_int_2(A,B)) ) ) )).
fof(t18_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ~ ( C != k5_numbers & r1_int_1(k3_int_2(A,C),B) & ! [D] : ( v1_int_1(D) => k5_int_1(k6_xcmplx_0(k3_xcmplx_0(A,D),B),C) != k5_numbers ) ) ) ) ) )).
fof(t18_int_5,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t18_int_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => k3_int_2(A,k3_int_2(B,C)) = k3_int_2(k3_int_2(A,B),C) ) ) ) )).
fof(t18_int_7,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,1) => k5_card_1(k1_int_7(A)) = k6_xcmplx_0(A,1) ) ) )).
fof(t18_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_int_2(A,C) & r1_int_2(B,C) & k3_pepin(k3_xcmplx_0(A,B),C) = k2_nat_1(k3_pepin(A,C),k3_pepin(B,C)) ) => ( r1_xxreal_0(C,1) | r1_int_2(k3_pepin(A,C),k3_pepin(B,C)) ) ) ) ) ) )).
fof(t18_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k3_xcmplx_0(2,k28_sin_cos)) => k2_integra5(A,k41_valued_1(k1_numbers,k1_numbers,k18_sin_cos)) = k28_sin_cos ) ) )).
fof(t18_integr12,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( 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,E,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,D,k41_valued_1(k1_numbers,k1_numbers,E)),A)))) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,F) => ( k1_funct_1(D,G) = 1 & k1_funct_1(E,G) = k7_xcmplx_0(G,A) & ~ r1_xxreal_0(k1_funct_1(E,G),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(E,G)) ) ) ) & F = k1_relset_1(k1_numbers,C) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,B)) ) => k2_integra5(B,C) = k6_xcmplx_0(k1_funct_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,E,k2_sin_cos9)),k2_seq_4(B)),k1_funct_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,E,k2_sin_cos9)),k3_seq_4(B))) ) ) ) ) ) ) ) )).
fof(t18_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k27_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,k27_sin_cos))) & r1_tarski(C,k1_relset_1(k1_numbers,k27_sin_cos)) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k27_sin_cos),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k27_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t18_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k22_sin_cos,D),k1_funct_1(k18_sin_cos,k1_funct_1(k22_sin_cos,D))),k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k22_sin_cos,D)))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_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) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k2_fdiff_9)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k2_fdiff_9)),k3_seq_4(A))) ) ) ) ) )).
fof(t18_integr15,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t18_integr16,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( 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)))) ) ) ) )).
fof(t18_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( 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) ) ) ) ) ) ) )).
fof(t18_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t18_integra1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( m1_integra1(C,B) => ( r2_hidden(A,k4_finseq_1(C)) => k3_integra1(k2_integra1(B,C,A)) = k1_funct_1(k4_integra1(B,k7_rfunct_1(B,B),C),A) ) ) ) ) )).
fof(t18_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t18_integra3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( m1_integra1(C,B) => ! [D] : ( ( 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(k3_seq_4(k1_rvsum_1(k2_partfun1(B,k1_numbers,D,k2_integra1(B,C,A)))),k2_seq_4(k1_rvsum_1(D))) ) ) ) ) ) )).
fof(t18_integra4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ! [C] : ( ( 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))) ) ) ) )).
fof(t18_integra5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v2_measure5(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ! [E] : ( ( r1_tarski(B,E) & r2_fdiff_1(A,E) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_1(A,E),B)) & k3_seq_4(B) = k3_seq_4(C) & k2_seq_4(C) = k3_seq_4(D) & k2_seq_4(D) = k2_seq_4(B) ) => ( r1_tarski(C,B) & r1_tarski(D,B) & k2_integra5(B,k2_fdiff_1(A,E)) = k2_xcmplx_0(k2_integra5(C,k2_fdiff_1(A,E)),k2_integra5(D,k2_fdiff_1(A,E))) ) ) ) ) ) ) )).
fof(t18_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(C,D) & r1_xxreal_0(D,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)) ) => ( r1_integra5(k3_integra5(C,D),E) & v1_comseq_2(k2_partfun1(k1_numbers,k1_numbers,E,k3_integra5(C,D))) & r1_tarski(k3_integra5(C,D),k9_xtuple_0(E)) ) ) ) ) ) ) ) )).
fof(t18_integra7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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,E,D) & r1_integra5(k3_integra5(A,B),D) & v1_comseq_2(k2_partfun1(k1_numbers,k1_numbers,D,k3_integra5(A,B))) ) => k1_funct_1(E,B) = k2_xcmplx_0(k4_integra5(A,B,D),k1_funct_1(E,A)) ) ) ) ) ) )).
fof(t18_integra8,axiom,( k1_funct_1(k3_sin_cos2,k5_numbers) = 1 )).
fof(t18_integra9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( r2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_taylor_1(k2_xcmplx_0(A,1)),k7_xcmplx_0(1,k2_xcmplx_0(A,1))),k1_numbers) & ! [B] : ( v1_xreal_0(B) => k1_funct_1(k2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_taylor_1(k2_xcmplx_0(A,1)),k7_xcmplx_0(1,k2_xcmplx_0(A,1))),k1_numbers),B) = k3_prepower(B,A) ) ) ) )).
fof(t18_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => ! [C] : ( ( ~ 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))) ) ) ) )).
fof(t18_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ( r2_hidden(B,k8_intpro_1) => r2_hidden(k3_intpro_1(A,B),k8_intpro_1) ) ) ) )).
fof(t18_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ( ( k3_finseq_1(C) = A & ! [D] : ( v7_ordinal1(D) => ( ~ r1_xxreal_0(A,D) => k1_funct_1(B,D) = k1_funct_1(C,k1_nat_1(D,1)) ) ) & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(A,D) => k1_funct_1(B,D) = k5_numbers ) ) ) => ( v1_series_1(B) & k4_series_1(B) = k18_rvsum_1(C) ) ) ) ) ) )).
fof(t18_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,B,C) => ! [E] : ( m2_cat_1(E,B,C) => ( r1_nattra_1(B,C,D,E) => ! [F] : ( m2_cat_1(F,A,B) => ! [G] : ( m1_nattra_1(G,B,C,D,E) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => k2_nattra_1(A,C,k9_cat_1(A,B,C,F,D),k9_cat_1(A,B,C,F,E),k3_isocat_1(A,B,C,D,E,F,G),H) = k2_nattra_1(B,C,D,E,G,k8_cat_1(A,B,F,H)) ) ) ) ) ) ) ) ) ) )).
fof(t18_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,k6_cat_2(A,B),C) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k8_cat_1(A,k9_nattra_1(B,C),k5_isocat_2(A,B,C,D),E) = k10_cat_2(A,B,C,D,E) ) ) ) ) ) )).
fof(t18_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_tops_1(B,A) <=> ? [C] : ( 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)) ) ) ) ) )).
fof(t18_jgraph_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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 ) ) ) ) ) )).
fof(t18_jgraph_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) ) ) )).
fof(t18_jgraph_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ~ r1_xxreal_0(k18_euclid(B),k5_numbers) & ? [C] : ( 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),k5_numbers) ) ) ) ) )).
fof(t18_jgraph_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ 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] : ( 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] : ( ( 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] : ( ( 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,k5_numbers) = A & k1_funct_1(G,1) = C & k1_funct_1(H,k5_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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t18_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t18_jordan,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t18_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( v3_pre_topc(a_4_0_jordan1(A,B,C,D),k15_euclid(2)) & m1_subset_1(a_4_0_jordan1(A,B,C,D),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ) ) ) ) )).
fof(t18_jordan10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( ( 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,k2_jordan9(C,A))) ) ) ) ) )).
fof(t18_jordan12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_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)) ) ) ) )).
fof(t18_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( r1_jordan1h(A,B) => r1_xboole_0(k2_jordan2c(2,A),k3_goboard9(k1_jordan13(A,B))) ) ) ) )).
fof(t18_jordan16,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ~ ( r1_jordan5c(A,B,C,D,E) & v1_xboole_0(k5_jordan6(A,B,C,D,E)) ) ) ) ) ) ) )).
fof(t18_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ~ ( D != E & r1_jordan17(A,B,C,D,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ~ ( F != D & F != E & r1_jordan17(A,C,D,F,E) ) ) ) ) ) ) ) ) )).
fof(t18_jordan19,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & ~ r1_xxreal_0(A,k5_numbers) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E),k9_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k8_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k8_jordan6(B)) ) ) ) ) ) ) )).
fof(t18_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(E)) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k1_matrix_0(E)) & r1_xxreal_0(1,A) & r1_xxreal_0(A,B) & r1_xxreal_0(B,k3_finseq_1(E)) ) => r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,C)),k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),E,B,D))) ) ) ) ) ) ) )).
fof(t18_jordan1b,axiom,( ! [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)))) ) => ~ r1_tarski(k3_goboard5(k1_jordan8(A,k5_numbers),2,2),k1_jordan2c(2,A)) ) )).
fof(t18_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & ~ r1_xxreal_0(k3_finseq_1(k2_jordan9(B,A)),C) & r2_hidden(k18_pscomp_1(B),k4_goboard5(k2_jordan9(B,A),C)) ) ) ) )).
fof(t18_jordan1e,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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)))) ) => r1_sprect_2(k2_jordan9(B,A),k2_jordan1e(B,A)) ) ) )).
fof(t18_jordan1g,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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)),k2_jordan9(B,A),k22_pscomp_1(k3_topreal1(2,k2_jordan9(B,A)))),k18_pscomp_1(k3_topreal1(2,k2_jordan9(B,A)))) ) ) )).
fof(t18_jordan1h,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(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,k5_pscomp_1,k2_jordan1h(u1_struct_0(k15_euclid(2)),A))),k1_matrix_0(A)) ) )).
fof(t18_jordan1k,axiom,( ! [A] : ( v7_ordinal1(A) => k2_jordan2c(A,k2_struct_0(k15_euclid(A))) = k1_struct_0(k15_euclid(A)) ) )).
fof(t18_jordan20,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(2),A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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] : ( ( 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,k5_numbers) = C & k1_funct_1(F,1) = D ) ) ) ) ) ) ) ) ) ) )).
fof(t18_jordan21,axiom,( ! [A] : ( ( 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)) ) )).
fof(t18_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k18_euclid(k2_jordan21(A)),k18_euclid(k2_jordan21(k3_topreal1(2,k2_jordan9(A,B))))) ) ) )).
fof(t18_jordan23,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ( ( 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) | k1_nat_1(k1_jordan3(A,B),1) = C ) ) ) ) ) )).
fof(t18_jordan2b,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( m1_subset_1(C,k4_ordinal1) => ( ( r2_hidden(C,k2_finseq_1(A)) & ! [D] : ( 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) ) ) ) ) )).
fof(t18_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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) ) ) )).
fof(t18_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t18_jordan4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k3_finseq_6(A,B,C,D) = k4_finseq_5(A,k3_finseq_6(A,B,D,C)) ) ) ) ) )).
fof(t18_jordan5a,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B)))) ) => ! [G] : ( ( ~ v1_xboole_0(G) & m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B)))) ) => ! [H] : ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [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,k2_seq_4(k1_weierstr(H))) = k2_seq_4(k1_weierstr(I)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t18_jordan5b,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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 ) ) ) ) )).
fof(t18_jordan5c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t18_jordan5d,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)))) ) ) ) )).
fof(t18_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t18_jordan7,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( ( 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] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ( ( 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,k5_numbers) = B & k1_funct_1(F,1) = C & k1_funct_1(F,G) = D & r1_xxreal_0(k5_numbers,G) & r1_xxreal_0(G,1) & k1_funct_1(F,H) = E & r1_xxreal_0(k5_numbers,H) & r1_xxreal_0(H,1) & r1_xxreal_0(G,H) ) => r1_jordan5c(A,B,C,D,E) ) ) ) ) ) ) ) ) ) )).
fof(t18_jordan8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,k3_finseq_1(k1_jordan8(A,C))) => r1_xboole_0(k3_goboard5(k1_jordan8(A,C),k5_numbers,B),A) ) ) ) ) )).
fof(t18_jordan_a,axiom,( ! [A] : ( ( 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)) ) )).
fof(t18_kurato_1,axiom,( 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)) )).
fof(t18_kurato_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ( ! [E] : ( v7_ordinal1(E) => k1_funct_1(D,E) = k2_xboole_0(k1_funct_1(B,E),k1_funct_1(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)) ) ) ) ) ) )).
fof(t18_lang1,axiom,( ! [A] : ( v1_relat_1(A) => r1_tarski(A,k18_finseq_1(A)) ) )).
fof(t18_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,D,C,B) & m2_finseq_1(E,k3_finseq_2(D)) ) => k3_laplace(A,C,B,D,E,k8_matrix_0(D,E,A)) = E ) ) ) ) ) )).
fof(t18_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t18_latsum_1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t18_lattice2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t18_lattice3,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k12_lattice3(A,B,k13_lattice3(A,B,C)) = B ) ) ) )).
fof(t18_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v14_lattices(B) & l3_lattices(B) ) => ! [C] : ( m1_lattice4(C,B,A) => ( v2_funct_2(C,u1_struct_0(A)) => ( v14_lattices(A) & r2_lattice4(B,A,C) ) ) ) ) ) )).
fof(t18_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t18_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v4_lattice6(B,A) => v3_waybel_6(k4_lattice3(A,B),k3_lattice3(A)) ) ) ) )).
fof(t18_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k4_lattices(A,k7_lattices(A,B),B) = k5_lattices(A) ) ) )).
fof(t18_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( ( v4_lexbfs(B,A) & m1_lexbfs(B,A) ) => ! [C] : ( v7_ordinal1(C) => v2_funct_1(k5_lexbfs(A,B,C)) ) ) ) )).
fof(t18_lfuzzy_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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)) ) ) ) )).
fof(t18_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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,k1_fuzzy_4(A,A,B)),A) ) ) )).
fof(t18_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_limfunc1(A) & v2_comseq_2(B) ) => v1_limfunc1(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) ) ) )).
fof(t18_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r2_limfunc2(B,A) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,C),k2_rcomp_1(k6_xcmplx_0(A,D),A))) => r1_xxreal_0(E,k1_funct_1(C,F)) ) ) ) ) ) | r2_limfunc2(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t18_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r2_limfunc3(C,B) => ( r1_xxreal_0(A,k5_numbers) | r2_limfunc3(k26_valued_1(k1_numbers,k1_numbers,C,A),B) ) ) & ( r2_limfunc3(C,B) => ( r1_xxreal_0(k5_numbers,A) | r3_limfunc3(k26_valued_1(k1_numbers,k1_numbers,C,A),B) ) ) & ( r3_limfunc3(C,B) => ( r1_xxreal_0(A,k5_numbers) | r3_limfunc3(k26_valued_1(k1_numbers,k1_numbers,C,A),B) ) ) & ( r3_limfunc3(C,B) => ( r1_xxreal_0(k5_numbers,A) | r2_limfunc3(k26_valued_1(k1_numbers,k1_numbers,C,A),B) ) ) ) ) ) ) )).
fof(t18_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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) ) ) ) ) )).
fof(t18_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) )).
fof(t18_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t18_lopban_1,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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)) ) ) )).
fof(t18_lopban_2,axiom,( ! [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) & v3_normsp_0(A) & v4_normsp_0(A) & v2_normsp_1(A) & l1_normsp_1(A) ) => k1_funct_1(k15_lopban_1(A,A),k6_partfun1(u1_struct_0(A))) = 1 ) )).
fof(t18_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) ) )).
fof(t18_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v7_ordinal1(D) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k6_lopban_4(D,A,C,B),k5_normsp_1(A,k5_lopban_4(D,A,C,B),k7_xcmplx_0(1,k2_newton(D)))) ) ) ) ) )).
fof(t18_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t18_lpspacc1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,C,k6_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,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => ( r2_hidden(E,k13_lpspacc1(B,C,D)) => r2_hidden(k25_valued_1(B,k2_numbers,E,A),k13_lpspacc1(B,C,D)) ) ) ) ) ) ) )).
fof(t18_lpspace1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_rfunct_3(D,C,k1_numbers,k3_rfunct_3(C,k1_numbers)) => k1_binop_1(k4_lpspace1(C),A,k1_binop_1(k4_lpspace1(C),B,D)) = k1_binop_1(k4_lpspace1(C),k3_xcmplx_0(A,B),D) ) ) ) ) )).
fof(t18_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ~ r1_xxreal_0(D,k5_numbers) => r2_relset_1(A,k1_numbers,k26_valued_1(A,k1_numbers,k2_mesfun6c(D,A,k56_valued_1(A,k1_numbers,B)),k2_power(k9_complex1(C),D)),k2_mesfun6c(D,A,k56_valued_1(A,k1_numbers,k26_valued_1(A,k1_numbers,B,C)))) ) ) ) ) ) )).
fof(t18_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(C),k1_domain_1(k4_ordinal1,k1_hilbert1,B,k3_hilbert1(k6_ltlaxio1(A),k4_ltlaxio1(A,k2_ltlaxio1(k6_ltlaxio1(A)))))) = 1 ) ) ) )).
fof(t18_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k1_hilbert1) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k1_hilbert1,k6_margrel1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_hilbert1,k6_margrel1))) ) => ( r2_hidden(A,k4_finseq_1(B)) => k3_funct_2(k1_hilbert1,k6_margrel1,k12_ltlaxio1(C),k7_partfun1(k1_hilbert1,k2_ltlaxio2(B),k3_finseq_1(k2_ltlaxio2(B)))) = k10_margrel1(k10_margrel1(k3_funct_2(k1_hilbert1,k6_margrel1,k12_ltlaxio1(C),k7_partfun1(k1_hilbert1,k2_ltlaxio2(k17_finseq_1(k1_hilbert1,k7_nat_d(A,1),B)),k3_finseq_1(k2_ltlaxio2(k17_finseq_1(k1_hilbert1,k7_nat_d(A,1),B))))),k3_funct_2(k1_hilbert1,k6_margrel1,k12_ltlaxio1(C),k7_partfun1(k1_hilbert1,B,A))),k3_funct_2(k1_hilbert1,k6_margrel1,k12_ltlaxio1(C),k7_partfun1(k1_hilbert1,k2_ltlaxio2(k2_rfinseq(k1_hilbert1,A,B)),k3_finseq_1(k2_ltlaxio2(k2_rfinseq(k1_hilbert1,A,B)))))) ) ) ) ) )).
fof(t18_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => ( v1_ltlaxio3(A) => k5_ltlaxio3(A) = A ) ) )).
fof(t18_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ! [B] : ( m2_subset_1(B,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)),k8_ltlaxio4(A)) => r8_ltlaxio1(k1_subset_1(k1_hilbert1),k3_hilbert1(k12_ltlaxio3(A),k2_ltlaxio1(k12_ltlaxio3(B)))) ) ) )).
fof(t18_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t18_margrel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => m1_subset_1(k16_funcop_1(k6_finseq_1(A),B),k4_partfun1(k3_finseq_2(A),A)) ) ) )).
fof(t18_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t18_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( r1_matrix10(B,k2_matrix10(A,C)) => v2_matrix10(k4_matrix10(A,B,C)) ) ) ) ) )).
fof(t18_matrix11,axiom,( ! [A] : ! [B] : ( ~ r2_hidden(B,A) => ! [C] : ( ( 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] : ( ( 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 ) ) ) ) )).
fof(t18_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(D),C,C) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(D))) ) => ( ( r2_hidden(B,k4_finseq_1(k3_matrix_1(D,C))) & r2_hidden(A,k4_finseq_1(k3_matrix_1(D,C))) ) => ( r1_xxreal_0(C,k5_numbers) | k4_matrix_3(D,E,k4_matrix12(C,C,D,k3_matrix_1(D,C),B,A)) = k4_matrix12(C,C,D,E,B,A) ) ) ) ) ) ) ) )).
fof(t18_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(A)) ) => ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(C,k4_ordinal1)) => ! [F] : ( m2_finseq_2(F,k4_ordinal1,k4_finseq_2(B,k4_ordinal1)) => ~ ( r1_tarski(k2_zfmisc_1(k10_xtuple_0(E),k10_xtuple_0(F)),k2_matrix_0(D)) & ( C = k5_numbers => B = k5_numbers ) & ( B = k5_numbers => C = k5_numbers ) & k4_matrix_0(A,k1_matrix13(A,D,C,B,E,F)) != k1_matrix13(A,k4_matrix_0(A,D),B,C,F,E) ) ) ) ) ) ) ) )).
fof(t18_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( ( v1_matrix_6(C,A,B) & D = k1_matrix_6(A,B,C) ) => ( k4_matrix_3(B,D,C) = k3_matrix_1(B,A) & k4_matrix_3(B,C,D) = k3_matrix_1(B,A) ) ) & ( ( k4_matrix_3(B,D,C) = k3_matrix_1(B,A) & k4_matrix_3(B,C,D) = k3_matrix_1(B,A) ) => ( v1_matrix_6(C,A,B) & D = k1_matrix_6(A,B,C) ) ) ) ) ) ) ) )).
fof(t18_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,E,D,C) & m2_finseq_1(F,k3_finseq_2(E)) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,E,D,B) & m2_finseq_1(G,k3_finseq_2(E)) ) => ! [H] : ( m2_finseq_1(H,E) => ! [I] : ( m2_finseq_1(I,E) => ( ( k3_finseq_1(H) = k1_matrix_0(F) & k3_finseq_1(I) = k1_matrix_0(G) ) => k3_matrix11(A,D,k2_xcmplx_0(k1_matrix_0(F),k1_matrix_0(G)),E,k1_matrix15(E,D,C,B,F,G),k8_finseq_1(E,H,I)) = k1_matrix15(E,D,C,B,k3_matrix11(A,D,C,E,F,H),k3_matrix11(A,D,B,E,G,I)) ) ) ) ) ) ) ) ) ) ) )).
fof(t18_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,B,A,A) & m2_finseq_1(D,k3_finseq_2(B)) ) => ( r2_matrix16(B,D,C) => ( r1_xxreal_0(A,k5_numbers) | C = k8_matrix_0(B,D,1) ) ) ) ) ) ) )).
fof(t18_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ( v1_matrix_0(k2_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),k12_finseq_1(A,B),k12_finseq_1(A,C))) & v2_matrix_0(k2_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),k12_finseq_1(A,B),k12_finseq_1(A,C)),A,2,1) & m2_finseq_1(k2_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),k12_finseq_1(A,B),k12_finseq_1(A,C)),k3_finseq_2(A)) ) ) ) ) )).
fof(t18_matrix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => k4_matrix_3(B,k3_matrix_1(B,A),C) = C ) ) ) )).
fof(t18_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(D) ) => k1_matrix_4(A,k1_matrix_4(A,D,B),k1_matrix_4(A,D,C)) = k1_matrix_4(A,C,B) ) ) ) ) ) )).
fof(t18_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k2_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k1_matrix_0(A) = k1_matrix_0(B) & k5_matrix_5(B,A) = B ) => A = k8_matrix_5(k3_finseq_1(A),k1_matrix_0(A)) ) ) ) )).
fof(t18_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( C = k4_matrix_3(B,C,D) & v1_matrix_6(C,A,B) ) => r1_matrix_6(A,B,C,D) ) ) ) ) ) )).
fof(t18_matrix_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_matrix_2(B,k3_matrix_2(A)) => m1_matrix_2(k2_funct_2(k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),B),k3_matrix_2(A)) ) ) )).
fof(t18_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v2_matrix_6(C,A,B) => v2_matrix_6(k4_matrix_3(B,k4_matrix_0(u1_struct_0(B),C),C),A,B) ) ) ) ) )).
fof(t18_matrix_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(k7_finseq_1(B,C),k3_matrix_2(A)) => r2_hidden(k7_finseq_1(C,B),k3_matrix_2(A)) ) ) ) ) )).
fof(t18_matrixc1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_2(C,k2_numbers,k4_finseq_2(A,k2_numbers)) => ! [D] : ( m2_finseq_2(D,k2_numbers,k4_finseq_2(A,k2_numbers)) => k9_matrix_5(k5_matrixc1(C,D),B) = k3_xcmplx_0(k9_matrix_5(C,B),k9_matrix_5(D,B)) ) ) ) ) )).
fof(t18_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrixj1(B,A) & m2_finseq_1(B,k3_finseq_2(k3_finseq_2(A))) ) => ! [C] : ( ( 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(k4_ordinal1,k11_matrixj1(A,B),k11_matrixj1(A,C)) ) ) ) )).
fof(t18_matrixj2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( ~ 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] : ( m1_vectsp_4(D,B,C) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t18_matrixr1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => k2_matrix_0(k6_matrix_3(A,C,B)) = k2_matrix_0(C) ) ) ) )).
fof(t18_matrixr2,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ~ ( ~ r1_xxreal_0(k1_matrix_0(C),k5_numbers) & ~ r1_xxreal_0(k3_finseq_1(C),k5_numbers) & k4_matrix_3(A,C,k1_matrix_3(A,k1_matrix_0(C),B)) != k1_matrix_3(A,k3_finseq_1(C),B) ) ) ) ) ) )).
fof(t18_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( ( 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] : ( m1_matrlin(E,A,B) => ! [F] : ( m2_finseq_1(F,u1_struct_0(A)) => ( ( k3_finseq_1(F) = k3_finseq_1(E) & 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,k5_matrlin(A,B,F,E))) = k4_rlvect_1(C,k5_matrlin(A,C,F,k4_finseqop(u1_struct_0(B),u1_struct_0(C),E,D))) ) ) ) ) ) ) ) )).
fof(t18_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( m1_matrlin(D,A,C) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t18_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ? [C] : ( 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) ) ) ) )).
fof(t18_matrprob,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,A) => ( k3_finseq_1(D) = C => ( v1_matrix_0(k2_finseq_2(B,D)) & v2_matrix_0(k2_finseq_2(B,D),A,B,C) & m2_finseq_1(k2_finseq_2(B,D),k3_finseq_2(A)) ) ) ) ) ) ) )).
fof(t18_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_card_1(D,A) & v1_finseq_1(D) & v3_valued_0(D) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,B) ) => ( A = k5_numbers | k1_funct_1(k1_funct_1(k3_matrtop1(A,B,E),D),C) = k13_fvsum_1(k2_vectsp_1,k1_matrtop1(D),k8_matrix_0(u1_struct_0(k2_vectsp_1),E,C)) ) ) ) ) ) ) ) )).
fof(t18_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(B,C) ) => ( r1_xxreal_0(B,A) | k2_matrtop3(C,k5_numbers,A,B) = k3_matrix_1(k2_vectsp_1,C) ) ) ) ) ) )).
fof(t18_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( 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] : ( 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 ) ) ) ) ) )).
fof(t18_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r2_pboole(A,C,B) <=> r1_pboole(A,C,k1_mboolean(A,B)) ) ) ) )).
fof(t18_mcart_1,axiom,( ! [A] : ! [B] : ~ ( A != k1_xboole_0 & B != k1_xboole_0 & ~ ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ( C != k1_xtuple_0(C) & C != k2_xtuple_0(C) ) ) ) )).
fof(t18_measure1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t18_measure3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ( ! [E] : ( r2_hidden(E,D) <=> ? [F] : ( r2_hidden(F,B) & ? [G] : ( 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))) ) ) ) ) ) )).
fof(t18_measure6,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t18_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ( v1_measure8(C,A,B) => ! [D] : ( r2_hidden(D,B) => k1_mesfunc9(C,D) = k1_mesfunc9(k9_measure8(A,B,C),D) ) ) ) ) )).
fof(t18_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => k5_member_1(k5_xboole_0(A,B)) = k5_xboole_0(k5_member_1(A),k5_member_1(B)) ) ) )).
fof(t18_membered,axiom,( ! [A] : ( v6_membered(A) => ( ! [B] : ( v7_ordinal1(B) => r2_hidden(B,A) ) => A = k4_ordinal1 ) ) )).
fof(t18_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_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))) ) ) ) )).
fof(t18_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( ( D = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),B,k6_xcmplx_0(1,G)),k1_rlvect_1(k15_euclid(2),C,G)) & E = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),C,k6_xcmplx_0(1,H)),k1_rlvect_1(k15_euclid(2),A,H)) & F = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),A,k6_xcmplx_0(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) <=> k3_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(G,k6_xcmplx_0(1,G)),k7_xcmplx_0(H,k6_xcmplx_0(1,H))),k7_xcmplx_0(I,k6_xcmplx_0(1,I))) = k4_xcmplx_0(1) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t18_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( ? [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) & k1_relset_1(A,C) = D ) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t18_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & v1_mesfunc8(C,A,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( ( k1_relset_1(A,k4_mesfunc5(A,k1_numbers,C,k5_numbers)) = D & ! [E] : ( v7_ordinal1(E) => r1_mesfunc6(A,B,k4_mesfunc5(A,k1_numbers,C,E),D) ) ) => r1_mesfunc1(A,B,k7_mesfun7c(A,C),D) ) ) ) ) ) )).
fof(t18_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( ( k1_relset_1(A,k4_mesfunc5(A,k1_numbers,D,k5_numbers)) = C & v1_mesfunc8(D,A,k1_numbers) & ! [E] : ( v7_ordinal1(E) => r1_mesfunc6(A,B,k4_mesfunc5(A,k1_numbers,k2_mesfun9c(A,D),E),C) ) & ! [E] : ( 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) ) ) ) ) ) )).
fof(t18_mesfunc1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ! [D] : ( v1_xxreal_0(D) => 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)) ) ) )).
fof(t18_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( 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 ) ) ) ) ) )).
fof(t18_mesfunc3,axiom,( ! [A] : ( m2_finseq_1(A,k6_numbers) => ! [B] : ( m1_subset_1(B,k6_numbers) => ! [C] : ( m1_subset_1(C,k6_numbers) => ( ( C = k3_finseq_1(A) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(A)) => k12_supinf_2(A,D) = B ) ) ) => k4_extreal1(A) = k1_extreal1(C,B) ) ) ) ) )).
fof(t18_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( 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] : ( v1_xreal_0(F) => ! [G] : ( m2_subset_1(G,k1_zfmisc_1(A),B) => ( ( v3_mesfunc5(C) & v3_mesfunc5(D) & ! [H] : ( v1_rat_1(H) => k1_funct_1(E,H) = k9_subset_1(A,k9_subset_1(A,G,k15_mesfunc1(A,C,H)),k9_subset_1(A,G,k15_mesfunc1(A,D,k6_xcmplx_0(F,H)))) ) ) => k9_subset_1(A,G,k15_mesfunc1(A,k3_mesfunc1(A,C,D),F)) = k3_tarski(k2_relset_1(B,E)) ) ) ) ) ) ) ) ) )).
fof(t18_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( ( 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) ) ) ) ) ) ) ) )).
fof(t18_mesfunc7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : k2_partfun1(A,k6_numbers,k10_mesfunc1(A,B),C) = k10_mesfunc1(A,k2_partfun1(A,k6_numbers,B,C)) ) ) )).
fof(t18_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k6_numbers)) & v1_mesfunc8(C,A,k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [E] : ( v1_xreal_0(E) => ( ! [F] : ( v7_ordinal1(F) => k9_nat_1(k9_setfam_1(A),D,F) = k9_subset_1(A,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,C,k5_numbers)),k18_mesfunc1(A,k4_mesfunc5(A,k6_numbers,C,F),E)) ) => ! [F] : ( v7_ordinal1(F) => k9_nat_1(k9_setfam_1(A),k5_setlim_1(A,B,D),F) = k9_subset_1(A,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,C,k5_numbers)),k18_mesfunc1(A,k4_mesfunc5(A,k6_numbers,k3_mesfunc8(A,C),F),E)) ) ) ) ) ) ) ) )).
fof(t18_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [D] : ( ( v1_mesfunc8(B,A,k6_numbers) & ! [E] : ( v7_ordinal1(E) => r2_relset_1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,C,E),k2_partfun1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,B,E),D)) ) ) => v1_mesfunc8(C,A,k6_numbers) ) ) ) ) )).
fof(t18_metric_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_metric_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k9_metric_1(B,C,A) = a_3_4_metric_1(A,B,C) ) ) ) )).
fof(t18_metric_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => r2_hidden(k6_domain_1(u1_struct_0(A),B),k2_metric_2(A)) ) ) )).
fof(t18_metric_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(D,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C))) => ! [E] : ( m1_subset_1(E,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C))) => ! [F] : ( m1_subset_1(F,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C))) => r1_xxreal_0(k2_binop_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,k13_metric_3(A,B,C),D,F),k3_real_1(k2_binop_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,k13_metric_3(A,B,C),D,E),k2_binop_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,k13_metric_3(A,B,C),E,F))) ) ) ) ) ) ) )).
fof(t18_metric_6,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r1_metric_6(A,C,B) <=> ! [D] : ( v1_xreal_0(D) => ( ~ r1_xxreal_0(D,k5_numbers) => r2_metric_6(A,k8_metric_1(A,B,D),C) ) ) ) ) ) ) )).
fof(t18_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_finset_1(B) & v1_card_1(B) ) => ( r1_ordinal1(k2_waybel23(A),B) <=> ! [C] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t18_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( ( 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] : ( m2_finseq_1(D,u1_struct_0(k10_funcsdom(k2_finseq_1(A)))) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t18_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_midsp_1(A,B,C,E,F) & r1_midsp_1(A,C,D,F,G) ) => r1_midsp_1(A,B,D,E,G) ) ) ) ) ) ) ) ) )).
fof(t18_midsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t18_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_nat_1(A,2)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(B))) => ! [F] : ( ( v4_midsp_2(F,B) & l1_midsp_2(F,B) ) => ! [G] : ( m1_subset_1(G,u1_struct_0(u1_midsp_2(B,F))) => ! [H] : ( m2_finseq_2(H,u1_struct_0(u1_midsp_2(B,F)),k4_finseq_2(k1_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 ) ) ) ) ) ) ) ) ) ) )).
fof(t18_mmlquer2,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( k7_relat_1(k8_funct_7(B,C),A) = k1_xboole_0 & r1_xxreal_0(C,D) ) => k7_relat_1(k8_funct_7(B,D),A) = k1_xboole_0 ) ) ) ) )).
fof(t18_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( ( r1_relset_1(A,A,E,F) & r1_tarski(B,C) & r1_relset_1(A,A,D,G) ) => r1_tarski(k9_mmlquery(A,D,B,F),k9_mmlquery(A,G,C,E)) ) ) ) ) ) ) ) )).
fof(t18_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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] : ( ( 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] : ( ( 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 ) ) ) ) ) )).
fof(t18_mod_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ~ ( v1_lmod_5(C,A,B) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ~ ( r1_tarski(C,D) & v1_mod_3(D,A,B) ) ) ) ) ) ) )).
fof(t18_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v36_algstr_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t18_modal_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) ) => ! [C] : ( 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)),k14_trees_3(k5_numbers),k5_trees_2(B,C)) ) ) ) ) )).
fof(t18_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_partfun1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(k30_modelc_1(B))) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t18_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ( r1_modelc_2(C,k8_modelc_2(A,B)) <=> ( C = A | C = B ) ) ) ) ) )).
fof(t18_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k13_modelc_2(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k13_modelc_2(A))) => ! [D] : ( 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),k2_xcmplx_0(k18_modelc_3(A,C),k18_modelc_3(A,D))) ) ) ) ) ) )).
fof(t18_moebius1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ~ ( r1_tarski(k22_pre_poly(k8_newton,k13_nat_3(B)),k2_finseq_1(k1_nat_1(A,1))) & ! [C] : ( ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( r1_tarski(k22_pre_poly(k8_newton,k13_nat_3(C)),k2_finseq_1(A)) & B = k2_nat_1(C,k11_newton(k1_nat_1(A,1),D)) & ! [E] : ( ( v7_ordinal1(E) & v1_int_2(E) ) => ( ( r2_hidden(E,k22_pre_poly(k8_newton,k13_nat_3(C))) => k11_nat_3(C,E) = k11_nat_3(B,E) ) & ( ~ r2_hidden(E,k22_pre_poly(k8_newton,k13_nat_3(C))) => r1_xxreal_0(k11_nat_3(C,E),k11_nat_3(B,E)) ) ) ) ) ) ) ) ) ) )).
fof(t18_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( C = E & D = F ) => k6_algstr_0(B,C,D) = k6_algstr_0(A,E,F) ) ) ) ) ) ) ) ) )).
fof(t18_monoid_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)))) ) ) ) )).
fof(t18_morph_01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t18_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( v3_msualg_1(C,A) & v4_msualg_1(C,A) & v2_msafree(C,A) & l3_msualg_1(C,A) & ? [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,B)) & r2_msualg_3(A,C,B,D) ) ) ) ) )).
fof(t18_msafree3,axiom,( ! [A] : ! [B] : ( ( ~ v11_struct_0(B) & v1_instalg1(B) & l1_msualg_1(B) ) => ! [C] : ( ( 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] : ( ( v1_relat_1(D) & v4_relat_1(D,u1_struct_0(B)) & v1_funct_1(D) & v1_partfun1(D,u1_struct_0(B)) ) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t18_msafree4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_rewrite1(B) & v4_rewrite1(B) ) => k2_rewrite1(B,k2_rewrite1(B,A)) = k2_rewrite1(B,A) ) )).
fof(t18_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) )).
fof(t18_msscyc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( m1_trees_1(B,k9_xtuple_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => m1_trees_1(k17_finseq_1(k4_ordinal1,C,B),k9_xtuple_0(A)) ) ) ) )).
fof(t18_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t18_mssublat,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v13_struct_0(A,1) & v5_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & m1_msualg_2(C,A,B) ) => ! [D] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t18_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( m3_pboole(D,u1_struct_0(A),u3_msualg_1(A,C)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t18_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t18_msualg_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t18_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m2_msualg_6(F,A,B,C,D) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t18_msualg_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m2_nat_lat(B,A) => ( v1_msualg_7(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => k16_lattice3(A,C) = k16_lattice3(B,D) ) ) ) ) ) ) )).
fof(t18_msualg_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t18_msualg_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t18_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(t18_mycielsk,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_necklace(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t18_nagata_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t18_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( ( C = k2_xcmplx_0(k3_xcmplx_0(B,A),E) & C = k2_xcmplx_0(k3_xcmplx_0(B,D),F) ) => ( r1_xxreal_0(B,E) | r1_xxreal_0(B,F) | ( A = D & E = F ) ) ) ) ) ) ) ) ) )).
fof(t18_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ( k4_nat_d(A,2) = k5_numbers <=> k4_nat_d(k7_nat_d(A,1),2) = 1 ) ) ) )).
fof(t18_nat_3,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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))) ) ) )).
fof(t18_nat_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r1_nat_d(A,k11_newton(B,C)) & v1_int_2(B) & v1_int_2(A) ) => B = A ) ) ) ) )).
fof(t18_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ~ ( r1_int_2(B,C) & r2_hidden(A,k3_moebius1(k3_xcmplx_0(B,C))) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( r2_hidden(D,k3_moebius1(B)) & r2_hidden(E,k3_moebius1(C)) & A = k3_xcmplx_0(D,E) ) ) ) ) ) ) ) )).
fof(t18_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( A != k5_numbers => k3_nat_d(k3_xcmplx_0(A,B),A) = B ) ) ) )).
fof(t18_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ! [F] : ( 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] : ( m1_nattra_1(G,A,B,C,D) => ! [H] : ( m1_nattra_1(H,A,B,D,E) => ! [I] : ( m1_nattra_1(I,A,B,E,F) => r2_funct_2(u1_struct_0(A),u4_struct_0(B),k3_nattra_1(A,B,C,D,F,G,k3_nattra_1(A,B,D,E,F,H,I)),k3_nattra_1(A,B,C,E,F,k3_nattra_1(A,B,C,D,E,G,H),I)) ) ) ) ) ) ) ) ) ) ) )).
fof(t18_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( 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] : ( m1_nfcont_1(E,B,k7_partfun1(u1_struct_0(B),C,D)) => ? [F] : ( m1_ncfcont1(F,A,D) & r1_tarski(k7_relset_1(u1_struct_0(A),u1_struct_0(B),C,F),E) ) ) ) ) ) ) ) ) )).
fof(t18_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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,k4_normsp_0(u1_struct_0(B),C,D)) ) ) ) ) )).
fof(t18_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_funct_1(B) => ( v3_normsp_1(B,A) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => k6_normsp_1(A,B) = k1_normsp_1(A,B,C) ) ) ) ) ) )).
fof(t18_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( 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)) ) ) ) ) ) ) ) ) )).
fof(t18_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ( ( r1_tarski(B,k1_relset_1(k1_numbers,C)) & ! [F] : ( v1_xreal_0(F) => ( 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] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => k1_funct_1(k2_ndiff_4(A,C,B),F) = D ) ) ) ) ) ) ) ) ) )).
fof(t18_neckla_3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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)) ) ) ) )).
fof(t18_necklace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( r2_hidden(B,u1_orders_2(k4_necklace(A))) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & ~ r1_xxreal_0(A,k1_nat_1(C,1)) & ( B = k4_tarski(C,k1_nat_1(C,1)) | B = k4_tarski(k1_nat_1(C,1),C) ) ) ) ) )).
fof(t18_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t18_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k3_xcmplx_0(k2_newton(A),k2_newton(B)) != k5_numbers ) ) )).
fof(t18_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ( r3_nfcont_1(A,B,D,C) <=> ( r1_tarski(C,k1_relset_1(u1_struct_0(A),D)) & ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( r1_tarski(k2_relset_1(u1_struct_0(A),E),C) & v3_normsp_1(E,A) & r2_hidden(k6_normsp_1(A,E),C) ) => ( v3_normsp_1(k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,D),B) & k7_partfun1(u1_struct_0(B),D,k6_normsp_1(A,E)) = k6_normsp_1(B,k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,D)) ) ) ) ) ) ) ) ) )).
fof(t18_nfcont_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( 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) ) ) ) )).
fof(t18_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t18_normform,axiom,( ! [A] : v1_setwiseo(k5_normform(A),k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))) )).
fof(t18_normsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k1_normsp_0(A,B,C) = k1_normsp_0(A,B,D) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ! [D] : ( v7_ordinal1(D) => k1_normsp_0(A,B,D) = C ) ) ) ) ) )).
fof(t18_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t18_numbers,axiom,( r1_tarski(k4_ordinal1,k3_numbers) )).
fof(t18_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t18_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ~ ( D != k1_xboole_0 & r1_tarski(D,k7_subset_1(k1_zfmisc_1(u1_struct_0(A)),k10_openlatt(A,C),k10_openlatt(A,B))) & v6_ordinal1(D) & ! [E] : ~ ( r2_hidden(E,k7_subset_1(k1_zfmisc_1(u1_struct_0(A)),k10_openlatt(A,C),k10_openlatt(A,B))) & ! [F] : ( r2_hidden(F,D) => r1_tarski(F,E) ) ) ) ) ) ) )).
fof(t18_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(t18_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_ordeq_01(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_ordeq_01(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_rsspace4(A,B))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k9_rsspace4(A,B))) => ( ( E = C & F = D ) => k1_algstr_0(k5_ordeq_01(A,B),C,D) = k3_rlvect_1(k9_rsspace4(A,B),E,F) ) ) ) ) ) ) ) )).
fof(t18_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v3_orders_1(A) => v3_orders_1(k2_relat_1(A)) ) ) )).
fof(t18_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(B,C) & r2_hidden(B,k1_orders_2(A,C)) ) ) ) ) )).
fof(t18_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r2_hidden(A,k1_ordinal1(B)) <=> r1_ordinal1(A,B) ) ) ) )).
fof(t18_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => k3_ordinal2(A) = A ) )).
fof(t18_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ! [D] : ( v3_ordinal1(D) => ( ( r1_ordinal1(A,B) & r1_ordinal1(C,D) ) => r1_ordinal1(k10_ordinal2(A,C),k10_ordinal2(B,D)) ) ) ) ) ) )).
fof(t18_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( v3_ordinal1(B) => ( ! [C] : ( v3_ordinal1(C) => ( r2_hidden(C,k9_xtuple_0(A)) => k1_funct_1(A,C) = k10_ordinal2(B,C) ) ) => v2_ordinal2(A) ) ) ) )).
fof(t18_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => k1_ordinal5(A,2) = k12_ordinal2(A,A) ) )).
fof(t18_ordinal6,axiom,( ! [A] : ( k9_xtuple_0(k2_ordinal6(A)) = k1_ordinal6(A) & k10_xtuple_0(k2_ordinal6(A)) = k2_ordinal1(A) ) )).
fof(t18_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r1_orders_2(B,k5_algstr_0(B,E,D),C) => ( r1_orders_2(B,D,C) | k1_ortsp_1(A,B,C,D,E) = k1_group_1(A) ) ) ) ) ) ) ) )).
fof(t18_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t18_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t18_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_osalg_2(C,A,B) => r1_tarski(k5_osalg_2(A,B,C),k6_osalg_2(A,B)) ) ) ) )).
fof(t18_osalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v3_msualg_1(B,A) & v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t18_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t18_papdesaf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => v1_translac(k2_diraf(A)) ) )).
fof(t18_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_parsp_1(A,B,C,B,C) ) ) ) )).
fof(t18_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( ~ r1_parsp_2(A,D,B,C) & r1_parsp_2(A,D,B,E) & r1_parsp_2(A,D,C,E) & D != E ) ) ) ) ) ) )).
fof(t18_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_tarski(A),C))) ) => r1_tarski(k7_relat_1(D,B),k1_tarski(k1_funct_1(D,A))) ) )).
fof(t18_partfun2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t18_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ! [D] : ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( 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) ) ) ) ) )).
fof(t18_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k1_relat_1(k4_relat_1(A)) = A ) )).
fof(t18_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_analoaf(A,E,C,E,D) & C != E & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_analoaf(A,E,B,E,F) & r2_analoaf(A,C,B,D,F) ) ) ) ) ) ) ) ) )).
fof(t18_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t18_pcs_0,axiom,( ! [A] : ( ( v14_pcs_0(A) & l2_pcs_0(A) ) => ! [B] : ( ( v14_pcs_0(B) & l2_pcs_0(B) ) => ( r1_tsep_1(A,B) => v8_relat_2(u1_orders_2(k19_pcs_0(A,B))) ) ) ) )).
fof(t18_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t18_pdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(2)) => ! [C] : ( m1_rcomp_1(C,k3_funct_2(k1_euclid(2),k1_numbers,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] : ( ( v9_ordinal1(D) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,E) = k1_tarski(k3_funct_2(k1_euclid(2),k1_numbers,k1_pdiff_1(2,2),B)) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),C) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(2,2,A,B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(2,2,A,B))))) & k10_pdiff_1(2,2,A,B) = k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(2,2,A,B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(2,2,A,B))))) ) ) ) ) ) ) ) ) )).
fof(t18_pdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(2)) => ! [C] : ( m1_rcomp_1(C,k3_funct_2(k1_euclid(2),k1_numbers,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] : ( ( v9_ordinal1(D) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,E) = k1_tarski(k3_funct_2(k1_euclid(2),k1_numbers,k1_pdiff_1(2,2),B)) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),C) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(2,2,k1_pdiff_3(1,2,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(2,2,k1_pdiff_3(1,2,A),B))))) & k3_pdiff_3(A,B) = k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(2,2,k1_pdiff_3(1,2,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(2,2,k1_pdiff_3(1,2,A),B))))) ) ) ) ) ) ) ) ) )).
fof(t18_pdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(3)) => ! [F] : ( ( 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 = k10_pdiff_1(3,3,F,E) <=> ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & ? [I] : ( v1_xreal_0(I) & E = k11_finseq_1(G,H,I) & ? [J] : ( m1_rcomp_1(J,I) & r1_tarski(J,k1_relset_1(k1_numbers,k1_pdiff_2(3,3,F,E))) & ? [K] : ( v1_funct_1(K) & v3_fdiff_1(K) & m1_subset_1(K,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [L] : ( v1_funct_1(L) & v2_fdiff_1(L) & m1_subset_1(L,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & D = k1_funct_1(K,1) & ! [M] : ( v1_xreal_0(M) => ( r2_hidden(M,J) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(3,3,F,E),M),k1_funct_1(k1_pdiff_2(3,3,F,E),I)) = k2_xcmplx_0(k1_funct_1(K,k6_xcmplx_0(M,I)),k1_funct_1(L,k6_xcmplx_0(M,I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t18_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t18_pdiff_6,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [D] : ( 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))))) ) ) ) ) ) ) )).
fof(t18_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(1))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( 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)) ) ) ) ) )).
fof(t18_pdiff_8,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k16_lopban_1(k4_real_ns1(A),k4_real_ns1(B)))) => ! [D] : ( v1_xreal_0(D) => ( ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( 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(k2_normsp_0(k16_lopban_1(k4_real_ns1(A),k4_real_ns1(1)),F),D) ) ) ) => r1_xxreal_0(k2_normsp_0(k16_lopban_1(k4_real_ns1(A),k4_real_ns1(B)),C),k3_xcmplx_0(B,D)) ) ) ) ) ) )).
fof(t18_pdiff_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k16_lopban_1(k4_real_ns1(1),k4_real_ns1(A)))) => ? [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(A))) & C = k1_funct_1(B,k12_finseq_1(k4_ordinal1,1)) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(1))) => ( E = k9_finseq_1(D) => k17_lopban_1(k4_real_ns1(1),k4_real_ns1(A),B,E) = k1_rlvect_1(k4_real_ns1(A),C,D) ) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(k4_real_ns1(1))) => k2_normsp_0(k4_real_ns1(A),k17_lopban_1(k4_real_ns1(1),k4_real_ns1(A),B,D)) = k3_xcmplx_0(k2_normsp_0(k4_real_ns1(A),C),k2_normsp_0(k4_real_ns1(1),D)) ) ) ) ) )).
fof(t18_pencil_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t18_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( 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)) ) ) ) ) )).
fof(t18_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => v1_abian(k2_power(2,A)) ) ) )).
fof(t18_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_petri(B,A) <=> v4_petri(k12_petri(A,B),k11_petri(A)) ) ) ) )).
fof(t18_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,k4_ordinal1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ( ( r2_pnproc_1(A,D,C) & r2_pnproc_1(A,C,B) ) => r1_pnproc_1(A,k3_pnproc_1(A,B,k3_pnproc_1(A,C,D)),k2_pnproc_1(A,k3_pnproc_1(A,B,C),D)) ) ) ) ) )).
fof(t18_polyalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_polyalg1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_polyalg1(C,A,B) ) => ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & u1_struct_0(C) = D & v3_polyalg1(D,A,B) ) ) ) ) )).
fof(t18_polyeq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( k4_polyeq_1(1,k5_numbers,A,B,C) = k5_numbers => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( C = k2_xcmplx_0(D,E) & k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,E),D),A) = k5_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)) = k1_newton(k4_xcmplx_0(k7_xcmplx_0(A,3)),3) ) ) ) ) ) ) ) ) )).
fof(t18_polyeq_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k5_numbers,k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),k3_square_1(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)))),2)) & r1_xxreal_0(k5_numbers,k7_xcmplx_0(k2_xcmplx_0(A,k3_square_1(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)))),2)) ) ) ) )).
fof(t18_polyeq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( k2_xcmplx_0(k3_xcmplx_0(C,k1_newton(A,F)),k3_xcmplx_0(D,k1_newton(B,F))) = E & k3_xcmplx_0(A,B) = k5_numbers & ~ v1_abian(F) & k3_xcmplx_0(C,D) != k5_numbers & ~ ( A = k5_numbers & B = k1_power(F,k7_xcmplx_0(E,D)) ) & ~ ( A = k1_power(F,k7_xcmplx_0(E,C)) & B = k5_numbers ) ) ) ) ) ) ) ) )).
fof(t18_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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 ) ) ) )).
fof(t18_polyform,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t18_polynom1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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) ) => k4_polynom1(A,B,D,E) = k4_algstr_0(B,k4_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)) ) ) ) ) )).
fof(t18_polynom3,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_xxreal_0(B,C) => r1_xxreal_0(k2_wsierp_1(k17_finseq_1(k4_ordinal1,B,A)),k2_wsierp_1(k17_finseq_1(k4_ordinal1,C,A))) ) ) ) ) )).
fof(t18_polynom4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k2_polynom4(A,k10_polynom3(A),B) = k5_struct_0(A) ) ) )).
fof(t18_polynom5,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k2_polynom5(A,B,3),k13_polynom3(A,k13_polynom3(A,B,B),B)) ) ) )).
fof(t18_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l5_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( k4_polynom1(A,B,k4_polynom7(A,B,C),k16_pre_poly(A)) = C & ! [D] : ( ( 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) => k4_polynom1(A,B,k4_polynom7(A,B,C),D) = k4_struct_0(B) ) ) ) ) ) )).
fof(t18_polynom8,axiom,( ! [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) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t18_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) ) )).
fof(t18_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( 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) ) ) ) ) )).
fof(t18_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ! [E] : ( 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))))) ) ) ) ) ) ) )).
fof(t18_pre_circ,axiom,( ! [A] : k5_card_1(k1_trees_4(A)) = 1 )).
fof(t18_pre_ff,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => B = k1_nat_1(k2_nat_1(A,k3_pre_ff(k5_numbers)),k2_nat_1(B,k3_pre_ff(1))) ) ) )).
fof(t18_pre_poly,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) => k1_card_1(A) = k1_card_1(k10_xtuple_0(A)) ) )).
fof(t18_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(B,k2_pre_topc(A,B)) ) ) )).
fof(t18_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_prelamb(A,k12_finseq_1(u1_struct_0(A),k2_prelamb(A,C,k1_prelamb(A,k2_prelamb(A,C,B),C))),k2_prelamb(A,C,B)) ) ) ) )).
fof(t18_prob_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(t18_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m2_prob_1(D,A,B) => ( ~ ( ~ r1_xxreal_0(1,k3_funct_2(B,k1_numbers,D,k7_prob_1(A,B,k4_prob_1(A,B),C))) & r1_xxreal_0(k3_funct_2(B,k1_numbers,D,C),k5_numbers) ) & ~ ( ~ r1_xxreal_0(k3_funct_2(B,k1_numbers,D,C),k5_numbers) & r1_xxreal_0(1,k3_funct_2(B,k1_numbers,D,k7_prob_1(A,B,k4_prob_1(A,B),C))) ) ) ) ) ) ) )).
fof(t18_prob_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => r1_tarski(k1_prob_2(B,k9_setfam_1(B),k3_prob_3(B,C),A),k1_prob_2(B,k9_setfam_1(B),k2_prob_3(B,C),A)) ) ) )).
fof(t18_prob_4,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_xboole_0(k1_prob_4(A,k9_setfam_1(A),k3_prob_3(A,B),k1_nat_1(C,1)),k1_prob_4(A,k9_setfam_1(A),B,C)) ) ) ) )).
fof(t18_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t18_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t18_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ~ ( ? [B] : ( m1_subset_1(B,u1_incsp_1(A)) & ? [C] : ( m1_subset_1(C,u1_incsp_1(A)) & ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & ? [E] : ( m1_subset_1(E,u1_incsp_1(A)) & r5_projpl_1(A,B,C,D,E) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => r4_projpl_1(A,B,C,D) ) ) ) ) ) )).
fof(t18_projred1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ( ~ r1_incsp_1(A,B,C) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t18_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u1_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u1_incsp_1(A)) => ! [H] : ( m1_subset_1(H,u1_incsp_1(A)) => ! [I] : ( m1_subset_1(I,u2_incsp_1(A)) => ! [J] : ( m1_subset_1(J,u2_incsp_1(A)) => ! [K] : ( m1_subset_1(K,u2_incsp_1(A)) => ! [L] : ( m1_subset_1(L,u2_incsp_1(A)) => ! [M] : ( m1_subset_1(M,u2_incsp_1(A)) => ! [N] : ( m1_subset_1(N,u2_incsp_1(A)) => ! [O] : ( m1_subset_1(O,u2_incsp_1(A)) => ! [P] : ( m1_subset_1(P,u2_incsp_1(A)) => ( ( r4_incsp_1(A,k7_domain_1(u1_incsp_1(A),D,F),L) & r1_incsp_1(A,E,M) & r4_incsp_1(A,k7_domain_1(u1_incsp_1(A),D,E),N) & 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),D,G),P) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),B,E,F),I) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),H,F,G),J) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),C,E,G),K) ) => ( r1_incsp_1(A,B,L) | r1_incsp_1(A,B,N) | r1_incsp_1(A,C,N) | r1_incsp_1(A,H,L) | r1_projred2(A,L,M,N) | r1_projred2(A,M,N,O) | B = C | C = H | H = B | ( P != L & P != N & ~ r1_incsp_1(A,H,P) & ~ r1_incsp_1(A,C,P) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t18_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) ) => ! [B] : ( m1_prvect_1(B,A) => ( ! [C] : ( m2_subset_1(C,k4_ordinal1,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)) ) ) ) )).
fof(t18_prvect_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(k7_prvect_3(A,B))) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & C = k1_domain_1(u1_struct_0(A),u1_struct_0(B),D,E) ) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(k7_prvect_3(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_prvect_3(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( 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] : ( m1_subset_1(C,u1_struct_0(k7_prvect_3(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_subset_1(C,u1_struct_0(k7_prvect_3(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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] : ( m1_subset_1(C,u1_struct_0(k7_prvect_3(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ~ ( C = k1_domain_1(u1_struct_0(A),u1_struct_0(B),D,E) & ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(2)) => ~ ( F = k10_finseq_1(k2_normsp_0(A,D),k2_normsp_0(B,E)) & k2_normsp_0(k7_prvect_3(A,B),C) = k12_euclid(F) ) ) ) ) ) ) ) ) ) )).
fof(t18_pua2mss1,axiom,( ! [A] : ( ( v2_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(t18_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) )).
fof(t18_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( k1_xtuple_0(k1_funct_1(k11_qc_lang1(A,k12_qc_lang1(A)),1)) = k5_numbers & ~ ( v2_qc_lang1(B,A) & ! [C] : ( v7_ordinal1(C) => ~ 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 ) ) ) ) )).
fof(t18_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( m1_subset_1(E,k9_qc_lang1(A)) => ! [F] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t18_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t18_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_trees_1(C,k9_xtuple_0(k2_qc_lang4(A,B))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t18_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_qc_trans(B,A) & m1_qc_lang1(B) ) => ! [C] : ( ( v1_henmodel(C,B) & m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(B))) ) => ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => v2_qc_trans(C,B,A) ) ) ) ) )).
fof(t18_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k23_quaterni(k22_quaterni(A,B),C) = k22_quaterni(k23_quaterni(A,C),k23_quaterni(B,C)) ) ) ) )).
fof(t18_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k25_quaterni(k23_quaterni(k3_quatern2,A),k23_quaterni(A,k3_quatern2)) = k6_quaterni(k5_numbers,k5_numbers,k4_xcmplx_0(k3_xcmplx_0(2,k16_quaterni(A))),k3_xcmplx_0(2,k15_quaterni(A))) ) )).
fof(t18_quaterni,axiom,( k10_quaterni(k12_quaterni,k1_xcmplx_0) = k11_quaterni )).
fof(t18_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(k1_quin_1(B,C,D),k5_numbers) & ~ ( ~ r1_xxreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(A)),k3_xcmplx_0(C,A)),D),k5_numbers) <=> ( ~ r1_xxreal_0(A,k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B))) & ~ r1_xxreal_0(k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B)),A) ) ) ) ) ) ) ) )).
fof(t18_quofield,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(t18_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => k12_radix_1(k5_numbers,A) = k5_numbers ) )).
fof(t18_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t18_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t18_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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)),k5_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))) ) ) ) ) )).
fof(t18_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_random_1(C,A,B) => ! [D] : ( m1_random_1(D,A,B) => m1_random_1(k3_valued_1(A,k1_numbers,k1_numbers,C,D),A,B) ) ) ) ) )).
fof(t18_random_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,A) ) => ! [C] : ~ ( r2_hidden(C,A) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k2_finseq_1(k3_finseq_1(B)),A) & v1_random_3(D,k2_finseq_1(k3_finseq_1(B)),A,k1_random_1(k2_finseq_1(k3_finseq_1(B))),k1_random_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(k3_finseq_1(B)),A))) ) => ~ ( D = B & k12_supinf_2(k2_random_3(k2_finseq_1(k3_finseq_1(B)),A,k1_random_1(k2_finseq_1(k3_finseq_1(B))),k1_random_1(A),k2_random_1(k2_finseq_1(k3_finseq_1(B))),D),k1_tarski(C)) = k3_dist_1(A,B,C) ) ) ) ) ) )).
fof(t18_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t18_rat_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(t18_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( 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)) ) ) ) )).
fof(t18_rcomp_1,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & ! [C] : ( m1_rcomp_1(C,B) => ~ r1_tarski(C,A) ) ) ) ) )).
fof(t18_rcomp_3,axiom,( ! [A] : ( ( v5_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ~ ( ~ r2_hidden(k3_seq_4(A),A) & ~ r2_hidden(k2_seq_4(A),A) & ~ r1_tarski(A,k2_rcomp_1(k3_seq_4(A),k2_seq_4(A))) ) ) )).
fof(t18_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( k9_nat_1(k4_ordinal1,k1_real_3(D,C),A) = k5_numbers => ( r1_xxreal_0(B,A) | k9_nat_1(k4_ordinal1,k2_real_3(D,C),B) = k5_numbers ) ) ) ) ) ) )).
fof(t18_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( 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),C,B),B),B) ) ) ) )).
fof(t18_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k4_real_ns1(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k4_real_ns1(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k7_real_ns1(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k7_real_ns1(A))))) ) => ( ( r1_funct_2(k4_ordinal1,u1_struct_0(k4_real_ns1(A)),k4_ordinal1,u1_struct_0(k7_real_ns1(A)),B,C) & v1_bhsp_3(C,k7_real_ns1(A)) ) => v1_rsspace3(B,k4_real_ns1(A)) ) ) ) ) )).
fof(t18_realset2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t18_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t18_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [D] : ( ( v1_rearran1(D) & v2_rearran1(D) & v3_rearran1(D,k1_zfmisc_1(A)) & m2_finseq_1(D,k1_zfmisc_1(A)) ) => ( ( v1_partfun1(C,B) & k5_card_1(A) = k5_card_1(B) ) => k21_rfunct_3(A,k3_rearran1(B,A,D,C),A) = k21_rfunct_3(B,C,B) ) ) ) ) ) )).
fof(t18_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => k2_relat_1(k6_subset_1(A,B)) = k6_subset_1(k2_relat_1(A),k2_relat_1(B)) ) ) )).
fof(t18_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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))) ) )).
fof(t18_revrot_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( 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(k1_nat_1(A,k3_finseq_1(D)),k4_finseq_4(D,C))) ) ) ) ) ) )).
fof(t18_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r1_rewrite1(A,B,C) => ( B = C | ( r2_hidden(B,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) ) ) ) ) )).
fof(t18_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t18_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k8_afinsq_1(C))) => ! [E] : ( 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) ) ) ) ) )).
fof(t18_rfinseq,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( ( k3_finseq_1(A) = k5_numbers | k3_finseq_1(A) = 1 ) => v8_valued_0(A) ) ) )).
fof(t18_rfinseq2,axiom,( ! [A] : ( ( v1_integra2(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( v7_ordinal1(B) => ( v1_integra2(k17_finseq_1(k1_numbers,B,A)) & m2_finseq_1(k17_finseq_1(k1_numbers,B,A),k1_numbers) ) ) ) )).
fof(t18_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(t18_rfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) & k2_seq_4(k2_relset_1(k1_numbers,B)) = k3_seq_4(k2_relset_1(k1_numbers,B)) ) => v3_funct_1(B) ) ) ) )).
fof(t18_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => v1_setwiseo(k13_rfunct_3(A),k3_rfunct_3(A,k1_numbers)) ) )).
fof(t18_rfunct_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v1_partfun1(A,k1_numbers) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(B,k1_numbers)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k4_finseq_2(B,k1_numbers)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k4_finseq_2(B,k1_numbers)) => ( ( k18_rvsum_1(C) = 1 & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r2_hidden(F,k4_finseq_1(C)) => ( r1_xxreal_0(k5_numbers,k1_funct_1(C,F)) & k1_funct_1(E,F) = k1_funct_1(A,k1_funct_1(D,F)) ) ) ) ) => r1_xxreal_0(k1_funct_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) ) ) )).
fof(t18_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_seq_2(A) & v4_partfun3(A) ) => r1_xxreal_0(k5_numbers,k2_rinfsup1(A)) ) ) )).
fof(t18_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ~ ( k5_rinfsup2(A) = k6_rinfsup2(A) & r2_hidden(k6_rinfsup2(A),k1_numbers) & ! [B] : ( v7_ordinal1(B) => ~ v3_rinfsup2(k1_valued_0(k6_numbers,A,B)) ) ) ) )).
fof(t18_ring_1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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)) ) ) ) ) )).
fof(t18_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t18_rlaffin1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t18_rlaffin2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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) = k7_xcmplx_0(1,k5_card_1(C)) ) ) ) ) )).
fof(t18_rlaffin3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( v1_finset_1(D) & v1_rlaffin1(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ! [E] : ( m2_rlaffin3(E,B,D) => ! [F] : ( m2_rlaffin3(F,B,k1_convex1(B,D,A)) => ( ( r2_hidden(C,k4_rlaffin1(B,D)) & F = k4_vfunct_1(k4_ordinal1,B,E,A) ) => ( A = k5_numbers | k1_rlaffin3(B,D,E,C) = k1_rlaffin3(B,k1_convex1(B,D,A),F,k1_rlvect_1(B,C,A)) ) ) ) ) ) ) ) ) )).
fof(t18_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => r1_struct_0(C,k4_struct_0(B)) ) ) ) )).
fof(t18_rlsub_2,axiom,( ! [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) ) => ! [B] : ( 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) ) ) ) )).
fof(t18_rltopsp1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v1_xreal_0(C) => k1_convex1(A,k3_convex1(A,B),C) = k3_convex1(A,k1_convex1(A,B,C)) ) ) ) )).
fof(t18_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k4_algstr_0(A,B) = k4_algstr_0(A,C) => B = C ) ) ) ) )).
fof(t18_rlvect_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t18_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v1_rlvect_1(C) & m1_rlsub_1(C,A) ) => ( B = u1_struct_0(C) => k1_rlvect_3(A,B) = C ) ) ) ) )).
fof(t18_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t18_rlvect_5,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_3(B,A) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( r1_xboole_0(C,B) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t18_rlvect_x,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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] : ( v1_int_1(E) & A = k3_rlvect_1(B,C,k1_rlvect_1(B,D,E)) ) ) ) ) ) )).
fof(t18_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => r1_struct_0(D,k4_struct_0(C)) ) ) ) ) )).
fof(t18_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t18_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(t18_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_robbins1(A,B,B) = B ) ) )).
fof(t18_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) )).
fof(t18_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_robbins1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_robbins1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t18_robbins4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_robbins4)) => ! [B] : ( 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) = k5_numbers ) ) ) ) )).
fof(t18_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => k3_roughs_1(A,k1_struct_0(A)) = k1_xboole_0 ) )).
fof(t18_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => r1_xxreal_0(k5_numbers,k1_rpr_1(A,B)) ) ) )).
fof(t18_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_rsspace4(A,B))) => ( C = k4_struct_0(k9_rsspace4(A,B)) => k5_numbers = k2_normsp_0(k9_rsspace4(A,B),C) ) ) ) ) )).
fof(t18_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t18_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t18_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rlvect_2(C,A) => ( r1_tarski(k3_rlvect_2(A,C),u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t18_rusub_4,axiom,( ! [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_bhsp_1(A) & v1_rusub_4(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_xxreal_0(C,k1_rusub_4(A)) <=> ? [D] : ( v1_bhsp_1(D) & m1_rusub_1(D,A) & k1_rusub_4(D) = C ) ) ) ) ) )).
fof(t18_rusub_5,axiom,( ! [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) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t18_rvsum_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => k1_funct_1(k6_rvsum_1(B),A) = k4_xcmplx_0(k1_funct_1(B,A)) ) )).
fof(t18_rvsum_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k2_numbers) ) => ! [C] : ( ( 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 ) ) ) ) )).
fof(t18_scm_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( r1_tarski(k1_ordinal4(k5_afinsq_1(k5_ami_3(k10_ami_3(k5_numbers),k10_ami_3(1))),k5_afinsq_1(k2_compos_1(k1_ami_3))),A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( ( v5_memstr_0(D,k7_card_1(2),k1_ami_3,k5_numbers) & m1_scm_1(D,k6_afinsq_1(B,C)) ) => ( r1_extpro_1(k7_card_1(2),k1_ami_3,A,D) & k8_extpro_1(k7_card_1(2),k1_ami_3,A,D) = 1 & k1_funct_1(k6_extpro_1(k7_card_1(2),k1_ami_3,A,D),k10_ami_3(k5_numbers)) = k3_xcmplx_0(B,C) & ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_ami_3)) ) => ( E != k10_ami_3(k5_numbers) => k1_funct_1(k6_extpro_1(k7_card_1(2),k1_ami_3,A,D),E) = k1_funct_1(D,E) ) ) ) ) ) ) ) ) )).
fof(t18_scm_halt,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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) ) ) ) ) ) )).
fof(t18_scmbsort,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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(k5_numbers))) ) ) )).
fof(t18_scmfsa10,axiom,( ! [A] : ( 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) ) ) )).
fof(t18_scmfsa6a,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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)) ) ) ) )).
fof(t18_scmfsa6b,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) & v1_scmfsa6b(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => r8_pboole(u1_struct_0(k1_scmfsa_2),k1_scmfsa6b(k3_scmfsa6a(C,D),A,B),k9_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(D,k1_scmfsa6b(C,A,B),B),k5_card_1(C))) ) ) ) ) )).
fof(t18_scmfsa7b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) <=> ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => r5_scmfsa7b(A,B,C) ) ) ) ) )).
fof(t18_scmfsa8a,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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)) = k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A)),1) ) ) ) ) )).
fof(t18_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( 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),k5_numbers) | ( r5_scmfsa7b(k2_scmfsa8b(E,C,D),B,A) & r6_scmfsa7b(k2_scmfsa8b(E,C,D),B,A) ) ) ) ) ) ) ) ) )).
fof(t18_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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] : ( v7_ordinal1(E) => ( k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(B,D,C,A),E),C) != k5_numbers => k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(B,D,C,A),k1_nat_1(E,1))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(B,D,C,A),E)) ) ) ) ) ) ) )).
fof(t18_scmfsa_1,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k4_scmfsa_1,k5_scmfsa_1))) => ! [B] : ( m2_subset_1(B,k1_scmfsa_1,k3_scmfsa_1) => ! [C] : ( m2_finseq_1(C,k4_numbers) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t18_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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 ) ) )).
fof(t18_scmfsa_9,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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),k1_nat_1(k5_card_1(B),4)) = k11_scmfsa_2(k5_numbers) ) ) )).
fof(t18_scmfsa_m,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ( k1_funct_1(A,k4_scmfsa_2(k5_numbers)) = 1 => k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A) = k1_scmfsa_m(A) ) ) )).
fof(t18_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmpds_2)) ) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t18_scmpds_4,axiom,( ! [A] : ( ( 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] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ~ ( 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) ) ) ) ) )).
fof(t18_scmpds_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_scmpds_4(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( v7_ordinal1(E) => ( 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) ) ) ) ) ) ) )).
fof(t18_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [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_partfun1(D,u1_struct_0(k1_scmpds_2)) & v5_memstr_0(D,2,k1_scmpds_2,k5_numbers) ) => ! [E] : ( v7_ordinal1(E) => ( ( 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)) ) ) ) ) ) ) ) )).
fof(t18_scmpds_7,axiom,( ! [A] : ( ( 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] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( v7_ordinal1(E) => ( ( 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) ) ) ) ) ) ) )).
fof(t18_scmpds_8,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ( r1_xxreal_0(k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),E)),k5_numbers) => ( r1_scmpds_6(k2_scmpds_8(D,E,C),B,A) & r2_scmpds_6(k2_scmpds_8(D,E,C),B,A) ) ) ) ) ) ) ) )).
fof(t18_scmpds_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k3_amistd_1(2,k1_scmpds_2,A) = k4_ordinal1 ) )).
fof(t18_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmring2(A))) => ~ ( ? [C] : ( 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(k7_card_1(2),k1_scmring2(A))) & v1_partfun1(C,u1_struct_0(k1_scmring2(A))) & k1_funct_1(k2_extpro_1(k7_card_1(2),k1_scmring2(A),B,C),k4_struct_0(k1_scmring2(A))) = k4_card_1(k5_memstr_0(k7_card_1(2),k1_scmring2(A),C)) ) & v2_extpro_1(B,k7_card_1(2),k1_scmring2(A)) ) ) ) )).
fof(t18_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmring2(A))) => ~ ( k2_compos_0(u1_compos_1(k1_scmring2(A)),B) = 7 & ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => ! [D] : ( v7_ordinal1(D) => B != k9_scmring2(A,D,C) ) ) ) ) ) )).
fof(t18_scmyciel,axiom,( ! [A] : ~ ( k3_tarski(A) = k1_xboole_0 & A != k1_xboole_0 & A != k1_tarski(k1_xboole_0) ) )).
fof(t18_scpinvar,axiom,( k5_card_1(k5_scpinvar) = 12 )).
fof(t18_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t18_seq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k26_valued_1(k4_ordinal1,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C),A),k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k26_valued_1(k4_ordinal1,k1_numbers,B,A),C)) ) ) ) )).
fof(t18_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(A) & v2_comseq_2(B) & ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) => r1_xxreal_0(k1_seq_2(A),k1_seq_2(B)) ) ) ) )).
fof(t18_seq_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(A) => ( ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & k9_nat_1(k1_numbers,B,D) != k9_nat_1(k1_numbers,A,D) ) ) | v2_comseq_2(B) ) ) ) ) )).
fof(t18_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( r2_seqfunc(A,B,C) <=> ( r1_seqfunc(A,k1_numbers,B,C) & ? [D] : ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) & C = k1_relset_1(A,D) & ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,C) => ( v2_comseq_2(k10_seqfunc(A,B,E)) & k1_seq_2(k10_seqfunc(A,B,E)) = k1_funct_1(D,E) ) ) ) ) ) ) ) ) )).
fof(t18_seqm_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k1_valued_0(k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,B),A) = k37_valued_1(k4_ordinal1,k1_numbers,k1_valued_0(k1_numbers,B,A)) ) ) )).
fof(t18_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_series_1(A) & ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,A,B)) ) ) => r1_xxreal_0(k5_numbers,k4_series_1(A)) ) ) )).
fof(t18_series_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k2_xcmplx_0(A,B) = 1 => r1_xxreal_0(k3_xcmplx_0(A,B),k7_xcmplx_0(1,4)) ) ) ) )).
fof(t18_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => ! [D] : ( ( v1_xreal_0(D) & v2_xxreal_0(D) ) => r1_xxreal_0(k2_xcmplx_0(k3_square_1(k3_xcmplx_0(A,C)),k3_square_1(k3_xcmplx_0(B,D))),k3_square_1(k3_xcmplx_0(k2_xcmplx_0(A,B),k2_xcmplx_0(C,D)))) ) ) ) ) )).
fof(t18_setfam_1,axiom,( ! [A] : ! [B] : ( r1_setfam_1(B,k1_tarski(A)) => ! [C] : ( r2_hidden(C,B) => r1_tarski(C,A) ) ) )).
fof(t18_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k3_funct_2(k4_ordinal1,k9_setfam_1(A),k4_setlim_1(A,B),k5_numbers) = k1_kurato_0(A,B) ) )).
fof(t18_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => k8_nat_1(k9_setfam_1(B),k7_setlim_2(B,D,C),A) = k7_setlim_2(B,k8_nat_1(k9_setfam_1(B),D,A),C) ) ) ) )).
fof(t18_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ( v3_binop_1(C,B) & v1_binop_1(C,B) & v2_binop_1(C,B) ) => ! [E] : ( m1_subset_1(E,k5_finsub_1(A)) => ! [F] : ( m1_subset_1(F,k5_finsub_1(A)) => ~ ( E != k1_xboole_0 & F != k1_xboole_0 & k7_setwiseo(A,B,C,k5_setwiseo(A,E,F),D) != k5_binop_1(B,C,k7_setwiseo(A,B,C,E,D),k7_setwiseo(A,B,C,F,D)) ) ) ) ) ) ) ) ) )).
fof(t18_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k5_finsub_1(A)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) ) )).
fof(t18_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( m1_scmfsa_2(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t18_sfmastr2,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) & v1_scmfsa7b(D) ) => ! [E] : ( v7_ordinal1(E) => ( ( k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k3_sfmastr2(B,A,D,C),E),k4_scmfsa_2(k5_numbers)) = 1 & r6_scmfsa7b(D,k1_scmfsa_m(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(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(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(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(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(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)))),k5_numbers) | k11_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k3_sfmastr2(B,A,D,C),k1_nat_1(E,1)),k2_xboole_0(k2_sf_mastr(D),k3_scmfsa_2)) = k5_relat_1(k1_scmfsa6b(D,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(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)) ) ) ) ) ) ) ) )).
fof(t18_sgraph1,axiom,( ! [A] : ! [B] : ( m1_sgraph1(B,A) => ( r1_tarski(u1_struct_0(B),A) & r1_tarski(u1_sgraph1(B),k2_sgraph1(u1_struct_0(B))) ) ) )).
fof(t18_sheffer1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t18_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t18_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ( v2_simplex0(A) => v1_finset_1(u1_pre_topc(A)) ) ) )).
fof(t18_simplex1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( ~ 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) ) ) ) ) )).
fof(t18_simplex2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(C,k3_simplex2(A,k5_simplex1(D,k15_euclid(A),B))) ) ) ) ) ) ) )).
fof(t18_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,k4_sin_cos(k9_complex1(A)),B)) ) ) )).
fof(t18_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_square_1(k1_funct_1(k1_sin_cos2,A)) = k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k1_funct_1(k3_sin_cos2,k3_xcmplx_0(2,A)),1)) & k1_square_1(k1_funct_1(k3_sin_cos2,A)) = k3_xcmplx_0(k7_xcmplx_0(1,2),k2_xcmplx_0(k1_funct_1(k3_sin_cos2,k3_xcmplx_0(2,A)),1)) ) ) )).
fof(t18_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,k3_xcmplx_0(k7_complex1,A)) = k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,A) ) )).
fof(t18_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k6_xcmplx_0(k19_sin_cos(A),k19_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))))) ) ) )).
fof(t18_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k19_sin_cos(A) != k5_numbers => k1_sin_cos4(k3_xcmplx_0(3,A)) = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(3,k1_sin_cos4(A)),k1_newton(k1_sin_cos4(A),3)),k6_xcmplx_0(1,k3_xcmplx_0(3,k1_square_1(k1_sin_cos4(A))))) ) ) )).
fof(t18_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ( ( r1_xxreal_0(k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)),A) & r1_xxreal_0(A,k2_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B))) ) => r1_xxreal_0(k5_numbers,k19_sin_cos(A)) ) ) ) )).
fof(t18_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) & r1_xxreal_0(k7_xcmplx_0(k3_xcmplx_0(2,A),k6_xcmplx_0(1,k1_square_1(A))),k5_numbers) ) ) )).
fof(t18_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k7_xcmplx_0(k2_xcmplx_0(k2_sin_cos2(A),k2_sin_cos2(B)),k2_xcmplx_0(k4_sin_cos2(A),k4_sin_cos2(B))) = k6_sin_cos2(k2_xcmplx_0(k7_xcmplx_0(A,2),k7_xcmplx_0(B,2))) & k7_xcmplx_0(k6_xcmplx_0(k2_sin_cos2(A),k2_sin_cos2(B)),k2_xcmplx_0(k4_sin_cos2(A),k4_sin_cos2(B))) = k6_sin_cos2(k6_xcmplx_0(k7_xcmplx_0(A,2),k7_xcmplx_0(B,2))) ) ) ) )).
fof(t18_sin_cos9,axiom,( k1_funct_1(k27_sin_cos,k7_xcmplx_0(k28_sin_cos,4)) = 1 & k2_sin_cos4(k7_xcmplx_0(k28_sin_cos,4)) = 1 & k1_funct_1(k27_sin_cos,k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos)) = k4_xcmplx_0(1) & k2_sin_cos4(k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos)) = k4_xcmplx_0(1) )).
fof(t18_sincos10,axiom,( v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k4_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos))) )).
fof(t18_sppol_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( ( r2_hidden(B,k1_rltopsp1(k15_euclid(2),A,D)) & r2_hidden(C,k1_rltopsp1(k15_euclid(2),A,D)) & k17_euclid(B) = k17_euclid(C) ) => ( k18_euclid(B) = k18_euclid(C) | v2_sppol_1(k1_rltopsp1(k15_euclid(2),A,D)) ) ) ) ) ) ) )).
fof(t18_sppol_2,axiom,( ! [A] : ( 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)) ) ) )).
fof(t18_sprect_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t18_sprect_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t18_sprect_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t18_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(t18_square_1,axiom,( k3_square_1(1) = 1 )).
fof(t18_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t18_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k7_card_1(B),k7_card_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(B),k7_card_1(A)))) ) => ( ( v2_funct_2(C,k7_card_1(A)) & v1_stirl2_1(C,B,A) ) => ! [D] : ( v7_ordinal1(D) => ( ~ r1_xxreal_0(A,D) => r1_xxreal_0(D,k3_nat_1(k1_stirl2_1(B,k7_card_1(A),C,k1_seq_4(D)))) ) ) ) ) ) ) )).
fof(t18_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_funct_2(C,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t18_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( r1_tarski(B,k3_subset_1(A,B)) <=> B = k1_subset_1(A) ) ) )).
fof(t18_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( m1_subset_1(D,k5_finsub_1(k4_partfun1(A,B))) => ! [E] : ( 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)) ) ) ) ) )).
fof(t18_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => ! [C] : ( m1_subset_1(C,k16_substut1(A)) => ( k19_substut1(A,B) = k19_substut1(A,C) => k28_substut1(A,k21_substut1(A,B,C)) = B ) ) ) ) )).
fof(t18_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ( ! [C] : ( 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] : ( 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))) ) ) ) ) )).
fof(t18_supinf_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t18_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( ~ r1_orders_2(B,D,C) & F != k4_struct_0(A) & k1_symsp_1(A,B,k4_vectsp_1(A,B,F,C),D,E) != k1_symsp_1(A,B,C,D,E) ) ) ) ) ) ) ) )).
fof(t18_sysrel,axiom,( ! [A] : ! [B] : ( 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)) ) ) ) )).
fof(t18_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_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))) ) ) ) ) ) )).
fof(t18_taxonom2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ( r1_tarski(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ( ! [D] : ~ ( r2_hidden(D,C) & ~ r1_tarski(D,B) & ~ r1_tarski(B,D) & ~ r1_xboole_0(B,D) ) => ( ! [D] : ~ ( r2_hidden(D,C) & r1_tarski(D,B) ) | ! [D] : ( ! [E] : ( 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] : ( m1_eqrel_1(E,A) => ( r1_setfam_1(C,E) => ! [F] : ( ( r2_hidden(F,E) & r1_tarski(B,F) ) => r1_setfam_1(k2_xboole_0(D,k1_tarski(B)),E) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t18_taylor_1,axiom,( r2_relset_1(k1_numbers,k1_numbers,k3_taylor_1,k2_partfun2(k1_numbers,k1_numbers,k22_sin_cos)) & v2_funct_1(k3_taylor_1) & k1_relset_1(k1_numbers,k3_taylor_1) = k3_limfunc1(k5_numbers) & k2_relset_1(k1_numbers,k3_taylor_1) = k1_numbers & r2_fdiff_1(k3_taylor_1,k3_limfunc1(k5_numbers)) & ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => r1_fdiff_1(k3_taylor_1,A) ) ) & ! [A] : ( m2_subset_1(A,k1_numbers,k3_limfunc1(k5_numbers)) => k1_fdiff_1(k3_taylor_1,A) = k7_xcmplx_0(1,A) ) & ! [A] : ( m2_subset_1(A,k1_numbers,k3_limfunc1(k5_numbers)) => ~ r1_xxreal_0(k1_fdiff_1(k3_taylor_1,A),k5_numbers) ) )).
fof(t18_taylor_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( 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)) ) ) ) )).
fof(t18_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ( v5_tbsp_1(A) <=> v6_tbsp_1(k2_struct_0(A),A) ) ) )).
fof(t18_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => v5_tops_1(k1_struct_0(A),A) ) )).
fof(t18_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t18_tdlat_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v2_tdlat_3(A) <=> ! [B] : ( 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) ) ) ) ) )).
fof(t18_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => k4_polynom1(A,C,k5_termord(A,B,C,D),k3_termord(A,B,C,D)) = k4_polynom1(A,C,D,k3_termord(A,B,C,D)) ) ) ) ) )).
fof(t18_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k1_tops_1(A,B) = B ) => v1_tdlat_3(A) ) ) )).
fof(t18_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(t18_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tex_3(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => ( v1_tops_3(D,B) <=> v1_tops_3(C,A) ) ) ) ) ) ) )).
fof(t18_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_tarski(k6_domain_1(u1_struct_0(A),B),k2_tex_4(A,B)) ) ) )).
fof(t18_tietze,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( ( ~ v1_xboole_0(B) & v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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] : ( ( 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(k5_numbers) & k7_relset_1(u1_struct_0(A),u1_struct_0(k3_topmetr),D,C) = k1_tarski(1) ) ) ) ) ) => v10_pre_topc(A) ) ) )).
fof(t18_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(t18_toler_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_2(C) & v3_relat_2(C) & v1_partfun1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( m1_toler_1(B,A,C) => r1_tarski(B,A) ) ) )).
fof(t18_topalg_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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)) ) ) ) )).
fof(t18_topalg_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v1_topalg_2(B,A) & m1_pre_topc(B,k15_euclid(A)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_borsuk_2(E,B,C,D) => ! [F] : ( m1_borsuk_2(F,B,C,D) => m1_borsuk_6(k1_topalg_2(A,B,E,F),B,C,D,E,F) ) ) ) ) ) ) )).
fof(t18_topalg_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t18_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_borsuk_2(G,k2_borsuk_1(A,B),k4_borsuk_1(A,B,C,E),k4_borsuk_1(A,B,D,F)) => ! [H] : ( m1_borsuk_2(H,k2_borsuk_1(A,B),k4_borsuk_1(A,B,C,E),k4_borsuk_1(A,B,D,F)) => ! [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] : ( m1_borsuk_2(J,B,E,F) => ! [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t18_topalg_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( m1_borsuk_6(F,A,B,C,D,E) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t18_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_borsuk_2(E,A,B,B) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t18_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_topdim_1(k1_pre_topc(A,B)) => v1_topdim_1(B,A) ) ) ) )).
fof(t18_topdim_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(1))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( k9_finseq_1(C) = A => ( r1_xxreal_0(B,k5_numbers) | k2_tops_1(k15_euclid(1),k1_topreal9(1,A,B)) = k2_tarski(k9_finseq_1(k3_xxreal_3(C,B)),k9_finseq_1(k1_xxreal_3(C,B))) ) ) ) ) ) )).
fof(t18_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_topgen_1(A,B)) <=> ! [D] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(E,D) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_hidden(F,k9_subset_1(u1_struct_0(A),B,E)) & C != F ) ) ) ) ) ) ) ) ) )).
fof(t18_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(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)))) ) => ? [C] : ( 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) ) ) ) )).
fof(t18_topgen_4,axiom,( ! [A] : ( v1_xboole_0(k1_xboole_0) & m1_subset_1(k1_xboole_0,k1_zfmisc_1(k1_zfmisc_1(A))) ) )).
fof(t18_topgen_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r2_hidden(k19_euclid(A,B),k2_topgen_5) <=> r1_xxreal_0(k5_numbers,B) ) ) ) )).
fof(t18_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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))) ) ) )).
fof(t18_topmetr,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => u1_struct_0(k4_topmetr(A,B)) = k1_rcomp_1(A,B) ) ) ) )).
fof(t18_topreal3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ( ( r2_hidden(C,k4_finseq_1(A)) & r2_hidden(k1_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) ) ) ) ) )).
fof(t18_topreal4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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] : ( 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)) ) ) ) ) ) )).
fof(t18_topreal5,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t18_topreal7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_metric_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => k1_metric_1(k1_topreal7(A,B),k2_topreal7(A,B,C,E),k2_topreal7(A,B,D,F)) = k4_xxreal_0(k1_metric_1(A,C,D),k1_metric_1(B,E,F)) ) ) ) ) ) ) )).
fof(t18_topreal8,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,A) ) => ! [C] : ( ( ~ v1_zfmisc_1(C) & m2_finseq_1(C,A) ) => ( ( k7_partfun1(A,C,1) = k7_partfun1(A,B,k3_finseq_1(B)) & ! [D] : ( v7_ordinal1(D) => ~ ( 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) ) ) ) ) )).
fof(t18_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ~ ( ~ v1_xboole_0(k1_topreal9(A,C,B)) & r1_xxreal_0(B,k5_numbers) ) ) ) ) )).
fof(t18_topreala,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( r2_hidden(D,k1_relset_1(k1_numbers,B)) => k1_funct_1(A,D) = k1_funct_1(B,D) ) & ! [D] : ( 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))) ) ) ) ) )).
fof(t18_toprealb,axiom,( m1_pre_topc(k8_toprealb(2),k1_topreala(k4_xcmplx_0(1),1,k4_xcmplx_0(1),1)) )).
fof(t18_toprealc,axiom,( ! [A] : ( v1_xreal_0(A) => k12_euclid(k9_finseq_1(A)) = k9_complex1(A) ) )).
fof(t18_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => k4_toprns_1(A,B,k3_toprns_1(A,C)) = k1_toprns_1(A,B,C) ) ) ) )).
fof(t18_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => k1_tops_1(A,k1_struct_0(A)) = k1_struct_0(A) ) )).
fof(t18_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t18_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t18_tops_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v1_xreal_0(E) & v2_xxreal_0(E) ) => ? [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t18_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t18_treal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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(k5_numbers,1),k4_topmetr(A,B)) & r2_funct_2(u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(k5_numbers,1)),k2_tops_2(u1_struct_0(k4_topmetr(k5_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(k5_numbers,1),k1_treal_1(k5_numbers,1))) & v3_tops_2(k4_treal_1(A,B,k2_treal_1(k5_numbers,1),k1_treal_1(k5_numbers,1)),k4_topmetr(A,B),k4_topmetr(k5_numbers,1)) & r2_funct_2(u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k4_topmetr(A,B)),k2_tops_2(u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(k5_numbers,1)),k4_treal_1(A,B,k2_treal_1(k5_numbers,1),k1_treal_1(k5_numbers,1))),k3_treal_1(A,B,k2_treal_1(A,B),k1_treal_1(A,B))) ) ) ) ) )).
fof(t18_trees_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ( r2_hidden(A,B) => m2_finseq_1(A,k4_ordinal1) ) ) )).
fof(t18_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => ( v1_trees_2(A) => v1_finset_1(k1_trees_2(A,B)) ) ) ) )).
fof(t18_trees_3,axiom,( ! [A] : ! [B] : ( ( v1_trees_3(A) & r1_tarski(B,A) ) => v1_trees_3(B) ) )).
fof(t18_trees_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(C)) => k1_funct_1(D,E) = k1_trees_4(k1_funct_1(C,E)) ) ) ) ) ) ) )).
fof(t18_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( v1_xboole_0(k7_trees_9(A,B)) <=> ( v1_zfmisc_1(A) & ~ r2_hidden(k1_funct_1(A,k1_xboole_0),B) ) ) ) )).
fof(t18_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_tsep_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( v1_tsep_1(C,B) & m1_pre_topc(C,B) ) => ( v1_tsep_1(C,A) & m1_pre_topc(C,A) ) ) ) ) )).
fof(t18_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t18_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( v1_tsp_1(B,A) & ! [C] : ( ( ~ v2_struct_0(C) & v1_pre_topc(C) & v6_pre_topc(C) & m1_pre_topc(C,A) ) => B != u1_struct_0(C) ) ) ) ) )).
fof(t18_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( D = u1_struct_0(B) & ! [E] : ( 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)))) ) ) ) ) ) ) )).
fof(t18_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( m2_funct_2(B,k4_numbers,u1_turing_1(A),k9_funct_2(k4_numbers,u1_turing_1(A))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_turing_1(k3_finseq_4(k4_ordinal1,C,D,E),A,B) => ( r1_turing_1(A,B,C,k1_nat_1(k1_nat_1(C,D),2)) & r1_turing_1(A,B,k1_nat_1(k1_nat_1(C,D),2),k1_nat_1(k1_nat_1(k1_nat_1(C,D),E),4)) ) ) ) ) ) ) ) )).
fof(t18_twoscomp,axiom,( k1_funct_1(k17_twoscomp,k11_finseq_1(k5_numbers,k5_numbers,k5_numbers)) = k5_numbers & k1_funct_1(k17_twoscomp,k11_finseq_1(k5_numbers,k5_numbers,1)) = k5_numbers & k1_funct_1(k17_twoscomp,k11_finseq_1(k5_numbers,1,k5_numbers)) = k5_numbers & k1_funct_1(k17_twoscomp,k11_finseq_1(k5_numbers,1,1)) = k5_numbers & k1_funct_1(k17_twoscomp,k11_finseq_1(1,k5_numbers,k5_numbers)) = k5_numbers & k1_funct_1(k17_twoscomp,k11_finseq_1(1,k5_numbers,1)) = k5_numbers & k1_funct_1(k17_twoscomp,k11_finseq_1(1,1,k5_numbers)) = k5_numbers & k1_funct_1(k17_twoscomp,k11_finseq_1(1,1,1)) = 1 )).
fof(t18_unialg_2,axiom,( ! [A] : ( ( ~ 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 ) )).
fof(t18_unialg_3,axiom,( ! [A] : ( ( ~ 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] : ( ( 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)) ) ) )).
fof(t18_uniroots,axiom,( ! [A] : ( ( ~ 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)) = k6_xcmplx_0(k7_group_1(A),1) ) )).
fof(t18_uproots,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( r2_funct_2(k4_ordinal1,u1_struct_0(A),k11_polynom3(A,B,C),k9_polynom3(A)) & ~ r2_funct_2(k4_ordinal1,u1_struct_0(A),B,k9_polynom3(A)) & ~ r2_funct_2(k4_ordinal1,u1_struct_0(A),C,k9_polynom3(A)) ) ) ) ) )).
fof(t18_urysohn1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => m1_connsp_2(B,A,C) ) ) => v3_pre_topc(B,A) ) ) ) )).
fof(t18_urysohn2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k6_numbers) => ( ( B = C & r1_xxreal_0(k5_numbers,C) ) => k8_supinf_2(k1_integra2(A,B)) = k1_extreal1(C,k8_supinf_2(A)) ) ) ) ) )).
fof(t18_urysohn3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v10_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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] : ( m2_urysohn3(D,A,B,C) => ( v5_pre_topc(k7_urysohn3(A,B,C,D),A,k3_topmetr) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_xxreal_0(k5_numbers,k12_supinf_2(k7_urysohn3(A,B,C,D),E)) & r1_xxreal_0(k12_supinf_2(k7_urysohn3(A,B,C,D),E),1) & ( r2_hidden(E,B) => k12_supinf_2(k7_urysohn3(A,B,C,D),E) = k5_numbers ) & ( r2_hidden(E,C) => k12_supinf_2(k7_urysohn3(A,B,C,D),E) = 1 ) ) ) ) ) ) ) ) ) ) )).
fof(t18_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_funct_2(C,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t18_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v3_funct_1(A) & v4_valued_0(A) ) => ? [B] : ( v7_ordinal1(B) & ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => k1_funct_1(A,C) = B ) ) ) )).
fof(t18_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : k1_funct_1(k54_valued_1(A),B) = k9_complex1(k1_funct_1(A,B)) ) )).
fof(t18_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t18_vectsp10,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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] : ( 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] : ( 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] : ( m1_subset_1(H,u1_struct_0(D)) & ? [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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t18_vectsp11,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( 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,k5_numbers),k3_struct_0(A)) ) ) )).
fof(t18_vectsp_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t18_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( C != k4_struct_0(A) & D != k4_struct_0(A) & k1_vectsp_2(A,B,C) != k1_vectsp_2(A,k6_algstr_0(A,B,D),k6_algstr_0(A,C,D)) ) ) ) ) ) )).
fof(t18_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => r1_struct_0(D,k4_struct_0(C)) ) ) ) ) )).
fof(t18_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m1_vectsp_4(E,A,B) => ( m1_vectsp_4(C,A,E) => m1_vectsp_4(k2_vectsp_5(A,B,C,D),A,E) ) ) ) ) ) ) )).
fof(t18_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( C != D => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t18_vectsp_7,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ~ ( k1_vectsp_7(A,B,C) = B & ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t18_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ! [E] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t18_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t18_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( 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) ) ) ) )).
fof(t18_waybel10,axiom,( ! [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] : ( ( 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)) ) ) )).
fof(t18_waybel11,axiom,( ! [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] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t18_waybel12,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t18_waybel13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t18_waybel14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ( k13_lattice3(k1_yellow_1(u1_pre_topc(A)),B,C) = k2_xboole_0(B,C) & k12_lattice3(k1_yellow_1(u1_pre_topc(A)),B,C) = k3_xboole_0(B,C) ) ) ) ) )).
fof(t18_waybel15,axiom,( ! [A] : ( ( 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] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k2_yellow_1(B)),u1_struct_0(k2_yellow_1(B))) & v6_waybel_1(C,k2_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_yellow_1(B)),u1_struct_0(k2_yellow_1(B))))) ) => ~ ( v22_waybel_0(C,k2_yellow_1(B),k2_yellow_1(B)) & r5_waybel_1(A,k1_yellow_2(k2_yellow_1(B),k2_yellow_1(B),C)) ) ) ) ) & ( ? [B] : ? [C] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k2_yellow_1(B)),u1_struct_0(k2_yellow_1(B))) & v6_waybel_1(C,k2_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_yellow_1(B)),u1_struct_0(k2_yellow_1(B))))) & v22_waybel_0(C,k2_yellow_1(B),k2_yellow_1(B)) & r5_waybel_1(A,k1_yellow_2(k2_yellow_1(B),k2_yellow_1(B),C)) ) => v3_waybel_3(A) ) ) ) )).
fof(t18_waybel16,axiom,( ! [A] : ( ( 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(k1_yellow_1(k8_waybel_0(A))) ) )).
fof(t18_waybel17,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ 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) ) ) ) ) ) )).
fof(t18_waybel18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( ~ v1_xboole_0(B) & ? [C] : ( 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)) ) ) ) )).
fof(t18_waybel19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(t18_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ( ( r5_waybel_1(A,B) & v3_lattice3(A) ) => v3_lattice3(B) ) ) ) )).
fof(t18_waybel21,axiom,( ! [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] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ( v7_yellow_0(B,A) => v3_lattice3(B) ) ) ) )).
fof(t18_waybel22,axiom,( ! [A] : ! [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) & l1_orders_2(B) ) => ! [C] : ( ( r1_waybel22(B,C) & k1_card_1(C) = k1_card_1(A) ) => r5_waybel_1(B,k1_yellow_1(k8_waybel_0(k2_yellow_1(A)))) ) ) )).
fof(t18_waybel23,axiom,( ! [A] : ( ( v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_waybel23(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t18_waybel24,axiom,( ! [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] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) )).
fof(t18_waybel25,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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)) ) ) ) ) ) )).
fof(t18_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v6_pre_topc(B) & v1_waybel25(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,B) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t18_waybel27,axiom,( ! [A] : r5_waybel_1(k2_yellow_1(A),k5_yellow_1(A,k2_yellow_1(k1_tarski(k5_numbers)))) )).
fof(t18_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => v5_yellow_6(k3_waybel28(A),A) ) )).
fof(t18_waybel29,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t18_waybel30,axiom,( ! [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_waybel_2(A) & l1_waybel_9(A) ) => ! [B] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => ! [C] : ( ( v12_waybel_0(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => k2_pre_topc(A,C) = k2_pre_topc(B,D) ) ) ) ) ) )).
fof(t18_waybel31,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_waybel_3(B,A) => B = k2_yellow_0(A,k2_waybel_3(A,B)) ) ) ) )).
fof(t18_waybel32,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => v1_waybel11(B,A) ) ) )).
fof(t18_waybel33,axiom,( ! [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) & v1_waybel33(A) & l1_waybel_9(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v4_pre_topc(B,A) <=> ! [C] : ( ( ~ v1_xboole_0(C) & v2_waybel_0(C,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(C,k2_yellow_1(k2_struct_0(A))) & v3_waybel_7(C,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))))) ) => ( r2_hidden(B,C) => r2_hidden(k1_waybel33(A,k2_struct_0(A),C),B) ) ) ) ) ) )).
fof(t18_waybel34,axiom,( ! [A] : ( ~ 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) ) ) )).
fof(t18_waybel35,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v1_waybel_4(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ! [D] : ( 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)) ) ) ) ) )).
fof(t18_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k6_waybel_0(A,B)) <=> r1_orders_2(A,B,C) ) ) ) ) )).
fof(t18_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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)) ) ) ) ) ) ) )).
fof(t18_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t18_waybel_3,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_waybel_3(A,B,C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r3_orders_2(A,C,k1_yellow_0(A,D)) & ! [E] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t18_waybel_4,axiom,( ! [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] : ( ( 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))) ) ) )).
fof(t18_waybel_5,axiom,( ! [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] : ( ~ v1_xboole_0(B) => ( r2_hidden(B,k1_yellow_6(u1_struct_0(A))) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) ) => ( ! [D] : ( m1_subset_1(D,B) => r2_hidden(k1_funct_1(C,D),k1_yellow_6(u1_struct_0(A))) ) => ! [D] : ( m2_pboole(D,B,C,k7_funcop_1(B,u1_struct_0(A))) => ( ! [E] : ( 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) ) ) )).
fof(t18_waybel_6,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t18_waybel_7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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 ) ) ) ) )).
fof(t18_waybel_8,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t18_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(t18_weddwitt,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => r1_struct_0(k4_weddwitt(A),k4_struct_0(A)) ) )).
fof(t18_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t18_wellord1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( v4_relat_2(B) => v4_relat_2(k2_wellord1(B,A)) ) ) )).
fof(t18_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(A,k6_xcmplx_0(B,C)) => ( r1_xxreal_0(A,B) & r1_xxreal_0(C,B) ) ) ) ) ) )).
fof(t18_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(A,k3_xboole_0(B,C)) => r1_tarski(A,B) ) )).
fof(t18_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k4_xboolean(k3_xboolean(A),k6_xboolean(A,B)) = k5_xboolean(k3_xboolean(A),k4_xboolean(k3_xboolean(A),B)) ) ) )).
fof(t18_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k6_xcmplx_0(A,k6_xcmplx_0(A,B)) = B ) ) )).
fof(t18_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t18_xtuple_0,axiom,( ! [A] : ! [B] : ~ ( r2_hidden(A,k13_xtuple_0(B)) & ! [C] : ! [D] : ! [E] : ~ r2_hidden(k6_xtuple_0(A,C,D,E),B) ) )).
fof(t18_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t18_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => k2_xxreal_1(A,A) = k1_xboole_0 ) )).
fof(t18_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => m2_xxreal_2(A,k3_xxreal_1(A,B)) ) ) )).
fof(t18_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( k3_xxreal_3(A,B) = k1_xxreal_0 & A != k1_xxreal_0 & B != k2_xxreal_0 ) ) ) )).
fof(t18_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t18_yellow12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_yellow_0(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t18_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => m1_yellow13(k9_setfam_1(u1_struct_0(A)),A,B) ) ) )).
fof(t18_yellow14,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ( ~ ( ~ r1_t_0topsp(A,B) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t18_yellow15,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => v1_yellow15(B,A) ) ) )).
fof(t18_yellow16,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ~ ( r2_yellow16(B,A,C) & ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t18_yellow17,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( ( ~ 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))) ) ) ) ) ) )).
fof(t18_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v11_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(t18_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k2_pre_topc(A,C)) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_subset_1(D,u1_struct_0(k2_yellow_1(k2_struct_0(A)))) & v2_waybel_0(D,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(D,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))))) ) => ( D = k1_yellow19(A,B) => r2_waybel_0(A,k3_yellow19(A,k2_struct_0(A),D),C) ) ) ) ) ) ) )).
fof(t18_yellow20,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t18_yellow21,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_yellow21(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_yellow21(A))) => ! [D] : ( 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))))) ) ) ) ) ) )).
fof(t18_yellow_0,axiom,( ! [A] : ( ( v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t18_yellow_1,axiom,( ! [A] : k3_yellow_0(k2_yellow_1(A)) = k1_xboole_0 )).
fof(t18_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t18_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t18_yellow_4,axiom,( ! [A] : ( ( v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v13_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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))) ) ) ) ) )).
fof(t18_yellow_5,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t18_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m2_yellow_6(C,A,B) => ! [D] : ( r2_waybel_0(A,C,D) => r2_waybel_0(A,B,D) ) ) ) ) )).
fof(t18_yellow_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t18_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) )).
fof(t18_yellow_9,axiom,( ! [A] : ! [B] : ( 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 ) ) ) )).
fof(t18_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v2_zf_lang(A) => k1_funct_1(A,1) = k5_numbers ) ) )).
fof(t18_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,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)) ) ) ) ) ) )).
fof(t18_zf_model,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ( r1_zf_model(A,B,k11_zf_lang(C,D)) <=> ( r1_zf_model(A,B,C) => r1_zf_model(A,B,D) ) ) ) ) ) ) )).
fof(t18_zf_refle,axiom,( ! [A] : r1_tarski(k3_ordinal2(A),k1_ordinal1(k3_tarski(k2_ordinal1(A)))) )).
fof(t18_zfmisc_1,axiom,( ! [A] : ! [B] : ( r1_tarski(k1_tarski(A),k1_tarski(B)) => A = B ) )).
fof(t18_zfmodel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ( v1_ordinal1(A) & ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => r2_hidden(k2_tarski(B,C),A) ) ) & ! [B] : ( m1_subset_1(B,A) => r2_hidden(k3_tarski(B),A) ) & ! [B] : ( m1_subset_1(B,A) => r2_hidden(k3_xboole_0(A,k1_zfmisc_1(B)),A) ) & ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( 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(k5_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(k5_numbers),k8_zf_lang(k2_zf_lang(4),k12_zf_lang(B,k4_zf_lang(k2_zf_lang(4),k2_zf_lang(k5_numbers))))))) ) => ! [D] : ( m1_subset_1(D,A) => r2_hidden(k7_relset_1(A,A,k1_zfmodel1(B,A,C),D),A) ) ) ) ) ) => ( ! [B] : ( m1_subset_1(B,A) => ~ ( B != k1_xboole_0 & ! [C] : ( m1_subset_1(C,A) => ~ ( r2_hidden(C,B) & ! [D] : ( m1_subset_1(D,A) => ~ ( r2_xboole_0(C,D) & r2_hidden(D,B) ) ) ) ) ) ) | v1_zf_model(A) ) ) ) )).
fof(t18_zfmodel2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r1_zfmodel1(B,A) & r1_zfmodel1(C,A) ) => r1_zfmodel1(k3_relat_1(C,B),A) ) ) ) ) )).
fof(t18_zfrefle1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => r1_tarski(k10_xtuple_0(A),k4_ordinal2(A)) ) )).
fof(t18_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(t18_zmodul03,axiom,( ! [A] : ( ( ~ 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) & v1_zmodul03(A) & l1_zmodul01(A) ) => ! [B] : ( m1_zmodul03(B,A) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( r1_xboole_0(C,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( D = k4_subset_1(u1_struct_0(A),B,C) & v1_zmodul02(D,A) ) ) ) ) ) ) )).
fof(t190_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t190_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k4_xcmplx_0(k7_xcmplx_0(k4_xcmplx_0(A),B)) = k7_xcmplx_0(A,B) ) ) )).
fof(t190_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(A,B) & r1_xxreal_0(1,k7_xcmplx_0(A,B)) ) ) ) )).
fof(t190_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(B,C) => k6_subset_1(k1_xxreal_1(A,C),k1_xxreal_1(B,C)) = k2_xxreal_1(A,B) ) ) ) ) )).
fof(t191_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( v1_xreal_0(C) => ( C != k5_numbers => k22_member_1(k6_subset_1(A,B),C) = k6_subset_1(k22_member_1(A,C),k22_member_1(B,C)) ) ) ) ) )).
fof(t191_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k7_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k7_xcmplx_0(A,B) ) ) )).
fof(t191_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(A,B) & r1_xxreal_0(1,k7_xcmplx_0(B,A)) ) ) ) )).
fof(t191_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(B,C) => k6_subset_1(k3_xxreal_1(A,C),k1_xxreal_1(B,C)) = k4_xxreal_1(A,B) ) ) ) ) )).
fof(t192_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( v1_xreal_0(C) => ( C != k5_numbers => k22_member_1(k5_xboole_0(A,B),C) = k5_xboole_0(k22_member_1(A,C),k22_member_1(B,C)) ) ) ) ) )).
fof(t192_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k7_xcmplx_0(k4_xcmplx_0(A),B) = k7_xcmplx_0(A,k4_xcmplx_0(B)) ) ) )).
fof(t192_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(1,k7_xcmplx_0(B,A)) ) ) ) )).
fof(t192_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ~ r1_xxreal_0(C,B) => k6_subset_1(k1_xxreal_1(A,C),k3_xxreal_1(B,C)) = k1_xxreal_1(A,B) ) ) ) ) )).
fof(t193_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( r2_hidden(C,A) => r2_hidden(k3_xcmplx_0(B,C),k23_member_1(A,B)) ) ) ) ) )).
fof(t193_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k4_xcmplx_0(A) = k7_xcmplx_0(A,k4_xcmplx_0(1)) ) )).
fof(t193_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ~ r1_xxreal_0(C,B) => k6_subset_1(k3_xxreal_1(A,C),k3_xxreal_1(B,C)) = k3_xxreal_1(A,B) ) ) ) ) )).
fof(t194_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => k23_member_1(A,B) = a_2_15_member_1(A,B) ) ) )).
fof(t194_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => A = k7_xcmplx_0(k4_xcmplx_0(A),k4_xcmplx_0(1)) ) )).
fof(t194_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k4_xcmplx_0(A),B) ) => r1_xxreal_0(k4_xcmplx_0(1),k7_xcmplx_0(A,B)) ) ) ) )).
fof(t194_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ~ r1_xxreal_0(C,B) => k6_subset_1(k2_xxreal_1(A,C),k2_xxreal_1(B,C)) = k2_xxreal_1(A,B) ) ) ) ) )).
fof(t195_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ~ ( r2_hidden(C,k23_member_1(A,B)) & ! [D] : ( v1_xcmplx_0(D) => ~ ( C = k3_xcmplx_0(B,D) & r2_hidden(D,A) ) ) ) ) ) )).
fof(t195_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k7_xcmplx_0(A,B) = k4_xcmplx_0(1) => ( A = k4_xcmplx_0(B) & B = k4_xcmplx_0(A) ) ) ) ) )).
fof(t195_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ~ r1_xxreal_0(C,B) => k6_subset_1(k4_xxreal_1(A,C),k2_xxreal_1(B,C)) = k4_xxreal_1(A,B) ) ) ) ) )).
fof(t196_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ( r1_tarski(k23_member_1(A,C),k23_member_1(B,C)) => ( C = k5_numbers | r1_tarski(A,B) ) ) ) ) ) )).
fof(t196_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k7_xcmplx_0(B,A) = k4_xcmplx_0(B) => ( B = k5_numbers | A = k4_xcmplx_0(1) ) ) ) ) )).
fof(t196_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ~ r1_xxreal_0(C,B) => k6_subset_1(k2_xxreal_1(A,C),k4_xxreal_1(B,C)) = k1_xxreal_1(A,B) ) ) ) ) )).
fof(t197_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ( k23_member_1(A,C) = k23_member_1(B,C) => ( C = k5_numbers | A = B ) ) ) ) ) )).
fof(t197_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( A != k5_numbers => k7_xcmplx_0(k4_xcmplx_0(A),A) = k4_xcmplx_0(1) ) ) )).
fof(t197_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(A,k4_xcmplx_0(B)) & r1_xxreal_0(k7_xcmplx_0(A,B),k4_xcmplx_0(1)) ) ) ) )).
fof(t197_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ~ r1_xxreal_0(C,B) => k6_subset_1(k4_xxreal_1(A,C),k4_xxreal_1(B,C)) = k3_xxreal_1(A,B) ) ) ) ) )).
fof(t198_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ( C != k5_numbers => k23_member_1(k3_xboole_0(A,B),C) = k3_xboole_0(k23_member_1(A,C),k23_member_1(B,C)) ) ) ) ) )).
fof(t198_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( A != k5_numbers => k7_xcmplx_0(A,k4_xcmplx_0(A)) = k4_xcmplx_0(1) ) ) )).
fof(t198_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(B,k4_xcmplx_0(A)) & r1_xxreal_0(k7_xcmplx_0(A,B),k4_xcmplx_0(1)) ) ) ) )).
fof(t198_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t199_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ( C != k5_numbers => k23_member_1(k6_subset_1(A,B),C) = k6_subset_1(k23_member_1(A,C),k23_member_1(B,C)) ) ) ) ) )).
fof(t199_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ~ ( A != k5_numbers & A = k7_xcmplx_0(1,A) & A != 1 & A != k4_xcmplx_0(1) ) ) )).
fof(t199_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(k4_xcmplx_0(B),A) & r1_xxreal_0(k7_xcmplx_0(A,B),k4_xcmplx_0(1)) ) ) ) )).
fof(t199_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t19_abcmiz_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v9_abcmiz_0(A) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_abcmiz_0(A)) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t19_abcmiz_1,axiom,( k1_abcmiz_1(k2_abcmiz_1) = k2_abcmiz_1 )).
fof(t19_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & v1_abcmiz_a(A) & l1_msualg_1(A) ) => ! [B] : ( 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] : ( m1_abcmiz_1(C,A,k13_abcmiz_1(A)) => B != k5_trees_4(k4_tarski(k10_abcmiz_1,3),C) ) ) ) ) )).
fof(t19_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(k2_absvalue(k2_xcmplx_0(A,B)),k2_xcmplx_0(k2_xcmplx_0(k2_absvalue(A),k2_absvalue(B)),1)) ) ) )).
fof(t19_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_aff_1(C,A) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( B != D & r2_hidden(D,C) ) ) ) ) ) ) )).
fof(t19_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t19_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( 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))) ) ) ) ) ) )).
fof(t19_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => k3_afinsq_2(k1_ordinal4(A,B),k1_nat_1(k1_afinsq_1(A),1),k1_nat_1(k1_afinsq_1(A),k1_afinsq_1(B))) = B ) ) )).
fof(t19_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( r2_hidden(B,k2_zfmisc_1(k8_afproj(A),k1_tarski(2))) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & B = k4_tarski(k6_afproj(A,C),2) & v1_aff_4(C,A) ) ) ) )).
fof(t19_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r2_afvect0(A,B,D,C) ) ) ) ) )).
fof(t19_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) ) )).
fof(t19_algspec1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => r1_partfun1(k1_algspec1(A,C),k1_algspec1(B,C)) ) )).
fof(t19_algstr_4,axiom,( ! [A] : 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))) )).
fof(t19_altcat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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)) ) ) )).
fof(t19_altcat_2,axiom,( ! [A] : ( ( v2_struct_0(A) & v6_altcat_1(A) & l2_altcat_1(A) ) => A = k5_altcat_2 ) )).
fof(t19_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t19_ami_2,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k3_ami_2,k4_ami_2))) => ( v1_relat_1(A) & v4_relat_1(A,k1_ami_2) & v1_funct_1(A) & v1_partfun1(A,k1_ami_2) ) ) )).
fof(t19_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ~ v2_extpro_1(k5_ami_3(A,B),k7_card_1(2),k1_ami_3) ) ) )).
fof(t19_ami_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( ~ 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(k7_card_1(2),k1_ami_3)) & v1_finset_1(B) & v4_extpro_1(B,k7_card_1(2),k1_ami_3,A) ) => ! [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(C,u1_struct_0(k1_ami_3)) ) => ! [D] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ( ( r1_tarski(B,C) & r1_tarski(B,D) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_ami_3)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_ami_3)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( ( r1_tarski(A,E) & r1_tarski(A,F) ) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v1_ami_2(H) & m1_subset_1(H,u1_struct_0(k1_ami_3)) ) => ! [I] : ( ( v1_ami_2(I) & m1_subset_1(I,u1_struct_0(k1_ami_3)) ) => ! [J] : ( m1_subset_1(J,u1_compos_1(k1_ami_3)) => ( ( J = k3_extpro_1(k7_card_1(2),k1_ami_3,E,k5_extpro_1(k7_card_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(k7_card_1(2),k1_ami_3,E,C,G),H),k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,E,C,G),I)) = k3_xcmplx_0(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,F,D,G),H),k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,F,D,G),I)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t19_ami_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k1_amistd_1(k7_card_1(2),k1_ami_3,B,k9_ami_3(C,A)) = k2_tarski(C,k1_ordinal1(B)) ) ) ) )).
fof(t19_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( 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(k4_ordinal1,k5_ami_wstd(A,k4_amistd_1(A),B)) ) ) ) ) )).
fof(t19_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ! [D] : ( v7_ordinal1(D) => r1_tarski(k2_amistd_1(A,B,C),k1_amistd_1(A,B,D,C)) ) ) ) ) )).
fof(t19_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t19_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t19_analoaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( k3_rlvect_1(A,k1_rlvect_1(A,B,D),k1_rlvect_1(A,C,E)) = k4_struct_0(A) => ( D = k5_numbers & E = k5_numbers ) ) ) ) => ( B != C & B != k4_struct_0(A) & C != k4_struct_0(A) ) ) ) ) ) )).
fof(t19_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_analmetr(A,F,G) & r2_analort(A,F,G,B,C,D,E) ) => r2_analort(A,F,G,D,E,B,C) ) ) ) ) ) ) ) ) )).
fof(t19_anproj_1,axiom,( ! [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) ) => ! [B] : ! [C] : ( 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)) ) ) ) )).
fof(t19_anproj_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( m2_funct_2(C,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [D] : ( m2_funct_2(D,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [E] : ( m2_funct_2(E,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,A) => ! [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] : ( r2_hidden(J,A) => ( J = F | k1_funct_1(B,J) = k5_numbers ) ) & k3_funct_2(A,k1_numbers,C,G) = 1 & ! [J] : ( r2_hidden(J,A) => ( J = G | k1_funct_1(C,J) = k5_numbers ) ) & k3_funct_2(A,k1_numbers,D,H) = 1 & ! [J] : ( r2_hidden(J,A) => ( J = H | k1_funct_1(D,J) = k5_numbers ) ) & k3_funct_2(A,k1_numbers,E,I) = 1 & ! [J] : ( r2_hidden(J,A) => ( J = I | k1_funct_1(E,J) = k5_numbers ) ) ) => ( F = G | F = H | F = I | G = H | G = I | H = I | ! [J] : ( m2_funct_2(J,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ? [K] : ( v1_xreal_0(K) & ? [L] : ( v1_xreal_0(L) & ? [M] : ( v1_xreal_0(M) & ? [N] : ( v1_xreal_0(N) & J = k1_binop_1(k5_funcsdom(A),k1_binop_1(k5_funcsdom(A),k1_binop_1(k5_funcsdom(A),k1_funct_1(k7_funcsdom(A),k4_tarski(K,B)),k1_funct_1(k7_funcsdom(A),k4_tarski(L,C))),k1_funct_1(k7_funcsdom(A),k4_tarski(M,D))),k1_funct_1(k7_funcsdom(A),k4_tarski(N,E))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t19_aofa_000,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t19_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ~ ( A != B & A != C & A != D & B != C & B != D & C != D & ~ v2_funct_1(k7_finseq_4(A,B,C,D)) ) )).
fof(t19_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v19_aofa_a00(B,A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( C = k10_subset_1(k1_funct_1(u7_aofa_a00(A),9),u4_struct_0(A)) => ( k1_msualg_1(A,C) = k2_finseq_4(u1_struct_0(A),B,B) & k2_msualg_1(A,C) = B ) ) ) ) ) )).
fof(t19_aofa_i00,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_card_3(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(A,k4_numbers))) => ! [C] : ( ( 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] : ( m6_aofa_i00(D,A,B,C) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t19_armstrng,axiom,( ! [A] : ( v3_armstrng(k4_armstrng(A),A) & v8_relat_2(k4_armstrng(A)) & v4_armstrng(k4_armstrng(A),A) & v5_armstrng(k4_armstrng(A),A) ) )).
fof(t19_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ( B = 1 => k2_arytm_0(A,B) = A ) ) ) )).
fof(t19_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( 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) ) ) ) ) )).
fof(t19_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( A = k7_arytm_2(B,C) => r1_arytm_2(C,A) ) ) ) ) )).
fof(t19_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(t19_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(A,k7_asympt_0(B)) <=> r2_hidden(B,k6_asympt_0(A)) ) ) ) )).
fof(t19_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( k6_asympt_0(A) = k6_asympt_0(B) <=> r2_hidden(A,k8_asympt_0(B)) ) ) ) )).
fof(t19_autalg_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r1_pzfmisc1(A,B,C) => ! [D] : ( r2_hidden(D,k4_autalg_1(A,B,C)) => m2_pboole(D,A,B,C) ) ) ) ) )).
fof(t19_autgroup,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t19_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => v2_bagorder(k17_pre_poly(A),A) ) )).
fof(t19_bcialg_1,axiom,( ! [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) ) => r2_hidden(k4_struct_0(A),k4_bcialg_1(A)) ) )).
fof(t19_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_bcialg_1(A,B,C) => r1_bcialg_1(A,k1_bcialg_2(A,B,D,E),k1_bcialg_2(A,C,D,E)) ) ) ) ) ) ) )).
fof(t19_bcialg_3,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)))) ) ) ) ) ) ) )).
fof(t19_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k6_bcialg_4(A,B,k5_numbers) = k4_struct_0(A) ) ) )).
fof(t19_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( v8_bcialg_1(E) & m1_bcialg_5(E,A,B,C,D) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(E)) => ! [G] : ( m1_subset_1(G,u1_struct_0(E)) => k1_bcialg_2(E,F,G,k1_nat_1(A,1)) = k1_bcialg_2(E,F,G,k1_nat_1(D,1)) ) ) ) ) ) ) ) )).
fof(t19_bcialg_6,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( v7_ordinal1(C) => k3_bcialg_6(A,k4_xcmplx_0(C),k2_bcialg_1(A,B)) = k2_bcialg_1(A,k3_bcialg_6(A,k4_xcmplx_0(C),B)) ) ) ) )).
fof(t19_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( m2_bciideal(B,A) => r1_tarski(k4_bcialg_1(A),B) ) ) ) )).
fof(t19_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k9_complex1(k2_bhsp_1(A,B,C)),k3_xcmplx_0(k3_square_1(k2_bhsp_1(A,B,B)),k3_square_1(k2_bhsp_1(A,C,C)))) ) ) ) )).
fof(t19_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_bhsp_2(C,A) => ( k1_bhsp_2(A,C) = B <=> ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(E,F) & r1_xxreal_0(D,k3_bhsp_1(A,k5_algstr_0(A,k1_normsp_1(A,C,F),B))) ) ) ) ) ) ) ) ) ) )).
fof(t19_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_bhsp_3(B,A) => ( ! [D] : ( v7_ordinal1(D) => B != k1_valued_0(u1_struct_0(A),C,D) ) | v1_bhsp_3(C,A) ) ) ) ) ) )).
fof(t19_bhsp_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => k1_normsp_1(B,C,k1_nat_1(A,1)) = k5_algstr_0(B,k3_bhsp_4(B,C,k1_nat_1(A,1)),k3_bhsp_4(B,C,A)) ) ) ) )).
fof(t19_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) ) )).
fof(t19_binari_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k6_margrel1) ) => ! [D] : ( m1_subset_1(D,k6_margrel1) => ! [E] : ( m1_subset_1(E,k6_margrel1) => k2_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k3_binari_2(k2_xcmplx_0(A,1),k6_binari_2(k2_xcmplx_0(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(k4_ordinal1,k4_binari_2(k2_xcmplx_0(A,1),k9_binarith(A,1,k6_margrel1,B,k10_binarith(k6_margrel1,D)),k2_binari_2(k2_xcmplx_0(A,1),k9_binarith(A,1,k6_margrel1,C,k10_binarith(k6_margrel1,E)))),k7_margrel1,k5_numbers,k5_series_1(2,k1_nat_1(A,1)))),k15_funcop_1(k4_ordinal1,k5_binari_2(k2_xcmplx_0(A,1),k9_binarith(A,1,k6_margrel1,B,k10_binarith(k6_margrel1,D)),k2_binari_2(k2_xcmplx_0(A,1),k9_binarith(A,1,k6_margrel1,C,k10_binarith(k6_margrel1,E)))),k7_margrel1,k5_numbers,k5_series_1(2,k1_nat_1(A,1)))),k15_funcop_1(k4_ordinal1,k4_binari_2(k1_nat_1(A,1),k3_binarith(k2_xcmplx_0(A,1),k9_binarith(A,1,k6_margrel1,C,k10_binarith(k6_margrel1,E))),k1_binari_2(k1_nat_1(A,1))),k7_margrel1,k5_numbers,k5_series_1(2,k1_nat_1(A,1)))) = k6_xcmplx_0(k3_binari_2(k2_xcmplx_0(A,1),k9_binarith(A,1,k6_margrel1,B,k10_binarith(k6_margrel1,D))),k3_binari_2(k2_xcmplx_0(A,1),k9_binarith(A,1,k6_margrel1,C,k10_binarith(k6_margrel1,E)))) ) ) ) ) ) )).
fof(t19_binari_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( 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] : ( ( v7_ordinal1(D) & ~ v8_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 ) ) ) ) ) ) ) ) )).
fof(t19_binari_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k6_margrel1) ) => ( ( B = k5_euclid(A) & C = k5_euclid(A) ) => r1_binarith(A,B,C) ) ) ) ) )).
fof(t19_binarith,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k6_margrel1) ) => ! [D] : ( m1_subset_1(D,k6_margrel1) => ! [E] : ( m1_subset_1(E,k6_margrel1) => k7_binarith(k2_xcmplx_0(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)))) ) ) ) ) ) )).
fof(t19_binom,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k6_algstr_0(A,k5_binom(A,B,D),C) = k5_binom(A,k6_algstr_0(A,B,C),D) ) ) ) ) )).
fof(t19_binop_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( k9_xtuple_0(C) = k2_zfmisc_1(A,B) => ( v3_funct_1(C) <=> ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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) ) ) ) ) )).
fof(t19_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => k3_finseq_1(k2_bintree2(A,B)) = k5_series_1(2,B) ) ) )).
fof(t19_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t19_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t19_borsuk_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v1_compts_1(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [D] : ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t19_borsuk_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_connsp_1(A,k5_topmetr) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r1_tarski(k1_rcomp_1(B,C),A) ) ) ) ) )).
fof(t19_borsuk_5,axiom,( ! [A] : ( v1_rat_1(A) => ! [B] : ( ( v1_xreal_0(B) & ~ v1_rat_1(B) ) => ~ v1_rat_1(k6_xcmplx_0(A,B)) ) ) )).
fof(t19_borsuk_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => ( k16_rvsum_1(A) != k5_numbers => k16_rvsum_1(k14_valued_2(A,k16_rvsum_1(A))) = 1 ) ) )).
fof(t19_bspace,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k4_bspace(A,k5_struct_0(k2_bspace),B) = B ) )).
fof(t19_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t19_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t19_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ! [H] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(t19_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t19_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t19_bvfunc_1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(t19_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(t19_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t19_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ( r3_bvfunc_2(A,B,C,D) => r1_bvfunc_1(A,k7_bvfunc_2(A,B,C,D),B) ) ) ) ) ) )).
fof(t19_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t19_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t19_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t19_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)))) ) ) ) )).
fof(t19_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t19_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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_comseq_2(k2_partfun1(A,k1_numbers,B,A)) => r2_relset_1(A,k1_numbers,k8_c0sp1(A,B),B) ) ) ) )).
fof(t19_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_c0sp2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_c0sp2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_c0sp2(A))) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(H,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k1_numbers,G,H) = k5_real_1(k3_funct_2(u1_struct_0(A),k1_numbers,E,H),k3_funct_2(u1_struct_0(A),k1_numbers,F,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t19_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => ! [D] : ( m2_finseq_1(D,k3_cqc_lang(A)) => ( ( r2_relset_1(k4_ordinal1,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) ) ) ) ) ) ) )).
fof(t19_calcul_2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)) & v3_funct_2(C,k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)))) ) => k1_relset_1(k4_ordinal1,k3_calcul_2(k3_cqc_lang(A),B,C)) = k1_relset_1(k4_ordinal1,B) ) ) ) )).
fof(t19_card_1,axiom,( ! [A] : ( v3_ordinal1(A) => ( v4_ordinal1(A) => ( A = k1_xboole_0 | ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) ) => ( ( k9_xtuple_0(B) = A & ! [C] : ( 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)) ) ) ) ) ) )).
fof(t19_card_2,axiom,( ! [A] : ( v1_card_1(A) => k2_card_2(A,k5_numbers) = k5_numbers ) )).
fof(t19_card_3,axiom,( ! [A] : ! [B] : ! [C] : r1_tarski(k5_xboole_0(k5_card_3(A,B),k5_card_3(A,C)),k5_card_3(A,k5_xboole_0(B,C))) )).
fof(t19_card_4,axiom,( ! [A] : ! [B] : ( 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) ) ) ) )).
fof(t19_card_5,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ( k1_card_2(A,A) = A & k2_card_2(A,A) = A ) ) )).
fof(t19_card_fil,axiom,( ! [A] : ( ~ v1_finset_1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t19_card_fin,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t19_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ~ ( v1_card_lar(B,A) & ~ v1_card_lar(k2_card_lar(A,B),A) & ! [C] : ( v3_ordinal1(C) => ~ ( r2_hidden(C,A) & r3_card_lar(A,a_3_2_card_lar(A,B,C)) ) ) ) ) ) )).
fof(t19_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,B,C) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t19_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & 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(k6_cat_2(A,B)) = k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)) & u4_struct_0(k6_cat_2(A,B)) = k2_zfmisc_1(u4_struct_0(A),u4_struct_0(B)) & r1_funct_2(u4_struct_0(k6_cat_2(A,B)),u1_struct_0(k6_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(k6_cat_2(A,B)),k16_funct_3(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(k6_cat_2(A,B)),u1_struct_0(k6_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(k6_cat_2(A,B)),k16_funct_3(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(k6_cat_2(A,B)) = k8_funct_4(u4_struct_0(A),u4_struct_0(B),u1_cat_1(A),u1_cat_1(B)) ) ) ) )).
fof(t19_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u4_struct_0(C)) => ! [E] : ( m1_subset_1(E,u4_struct_0(C)) => ! [F] : ( m1_subset_1(F,u4_struct_0(C)) => ! [G] : ( 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))) ) ) ) ) ) ) )).
fof(t19_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t19_cat_5,axiom,( ! [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) & v4_cat_5(A) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ 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)) ) ) ) )).
fof(t19_catalan1,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k1_catalan1(k1_nat_1(A,1)) = k3_xcmplx_0(k3_xcmplx_0(2,k6_xcmplx_0(2,k7_xcmplx_0(3,k1_nat_1(A,1)))),k1_catalan1(A)) ) ) )).
fof(t19_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ( ( r1_tarski(k2_relset_1(k4_ordinal1,B),k7_domain_1(k4_ordinal1,k5_numbers,1)) & k1_nat_1(k3_xcmplx_0(2,A),1) = k3_nat_1(a_1_1_catalan2(B)) ) => v1_catalan2(k5_relat_1(B,k3_xcmplx_0(2,A))) ) ) ) )).
fof(t19_catalg_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t19_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v11_algstr_0(k5_cayldick(A,B,C),k4_cayldick(A)) => ( v11_algstr_0(B,A) & v11_algstr_0(C,A) ) ) ) ) ) )).
fof(t19_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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] : ( 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(k9_complex1(k3_funct_2(A,k2_numbers,C,B)),k2_normsp_0(k7_cc0sp1(A),D)) ) ) ) ) ) )).
fof(t19_cc0sp2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t19_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v2_comseq_2(A) => ( ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & k9_nat_1(k2_numbers,B,D) != k9_nat_1(k2_numbers,A,D) ) ) | v2_comseq_2(B) ) ) ) ) )).
fof(t19_cfdiff_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k1_valued_0(k2_numbers,k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,C),A),k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k1_valued_0(k2_numbers,B,A),k1_valued_0(k2_numbers,C,A))) ) ) ) )).
fof(t19_cfuncdom,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ~ ( r2_hidden(A,C) & r2_hidden(B,C) & A != B & ! [D] : ( m2_funct_2(D,C,k2_numbers,k9_funct_2(C,k2_numbers)) => ! [E] : ( m2_funct_2(E,C,k2_numbers,k9_funct_2(C,k2_numbers)) => ? [F] : ( v1_xcmplx_0(F) & ? [G] : ( v1_xcmplx_0(G) & k1_binop_1(k1_cfuncdom(C),k1_funct_1(k3_cfuncdom(C),k4_tarski(F,D)),k1_funct_1(k3_cfuncdom(C),k4_tarski(G,E))) = k4_cfuncdom(C) & ~ ( F = k5_numbers & G = k5_numbers ) ) ) ) ) ) ) )).
fof(t19_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t19_cgames_1,axiom,( ! [A] : ( ( v1_cgames_1(A) & l1_cgames_1(A) ) => ( v2_cgames_1(A) <=> ! [B] : ( r2_hidden(B,k2_xboole_0(u1_cgames_1(A),u2_cgames_1(A))) => v2_cgames_1(B) ) ) ) )).
fof(t19_chain_1,axiom,( ! [A] : ( ( ~ v1_zfmisc_1(A) & v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( m2_chain_1(k4_tarski(B,C),A) & m2_chain_1(k4_tarski(D,C),A) ) => B = D ) ) ) ) ) )).
fof(t19_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) => ! [C] : ( m2_glib_000(C,A,B,k21_glib_000(A,B)) => ! [D] : ! [E] : ( ( r2_hidden(D,B) & r2_hidden(E,B) ) => ! [F] : ( r1_glib_000(A,D,E,F) => r1_glib_000(C,D,E,F) ) ) ) ) ) )).
fof(t19_circcmb2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ! [I] : ( m1_subset_1(I,k4_card_3(u3_msualg_1(C,F))) => ! [J] : ( m1_subset_1(J,k4_card_3(u3_msualg_1(A,D))) => ! [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t19_circcmb3,axiom,( ! [A] : ( ( v4_circcmb3(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msafree2(B,A) & v5_circcmb3(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => v1_circuit2(k6_circuit2(A,B,C),A,B) ) ) ) )).
fof(t19_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( l3_msualg_1(D,B) => ( r2_circcomb(A,B,C,D) => r2_circcomb(B,A,D,C) ) ) ) ) ) )).
fof(t19_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m3_msaterm(C,A,B) => ! [D] : ( m3_msaterm(D,A,B) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t19_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t19_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_pboole(C,k2_msafree2(A),k7_funcop_1(k2_msafree2(A),k4_ordinal1),k5_relat_1(u3_msualg_1(A,B),k2_msafree2(A))) => ( v3_funct_1(k9_funct_6(C)) => ( v1_xboole_0(k2_msafree2(A)) | ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(A,B))) => ! [E] : ( m1_subset_1(E,k4_card_3(u3_msualg_1(A,B))) => r8_pboole(u1_struct_0(A),k9_nat_1(k4_card_3(u3_msualg_1(A,B)),k9_circuit2(A,B,C,D),k7_circuit1(A,B)),k9_nat_1(k4_card_3(u3_msualg_1(A,B)),k9_circuit2(A,B,C,E),k7_circuit1(A,B))) ) ) ) ) ) ) ) )).
fof(t19_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ( ( v1_pdiff_7(C,A) & D = k7_funcop_1(C,E) ) => r1_ckspace1(A,D,B,C) ) ) ) ) ) ) )).
fof(t19_classes1,axiom,( ! [A] : ? [B] : ( v3_ordinal1(B) & k3_classes1(A,B) = k1_classes1(A) ) )).
fof(t19_classes2,axiom,( ! [A] : ( v2_classes1(A) => v4_ordinal1(k1_card_1(A)) ) )).
fof(t19_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v9_clvect_1(B,A) & k7_clvect_1(A,B) = C ) => ( v2_comseq_2(k5_normsp_0(A,B)) & k1_seq_2(k5_normsp_0(A,B)) = k2_normsp_0(A,C) ) ) ) ) ) )).
fof(t19_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_clopban2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_clopban2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_clopban2(A))) => ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( 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 ) ) ) ) ) ) ) )).
fof(t19_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v1_xcmplx_0(C) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k1_bhsp_4(A,k6_clvect_1(A,B,C)),k6_clvect_1(A,k1_bhsp_4(A,B),C)) ) ) ) )).
fof(t19_clopban4,axiom,( ! [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) & 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) ) ) )).
fof(t19_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m2_pboole(C,A,k5_mssubfam(A,B),k5_mssubfam(A,B)) => ! [D] : ( m1_pboole(D,A,k5_mssubfam(A,B)) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t19_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t19_clvect_1,axiom,( ! [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) ) => ! [B] : ( 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,k2_xcmplx_0(k2_xcmplx_0(k6_complex1,k6_complex1),k6_complex1)) ) ) )).
fof(t19_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clvect_2(C,A) => ( k1_clvect_2(A,C) = B <=> ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(E,F) & r1_xxreal_0(D,k13_csspace(A,k5_algstr_0(A,k1_normsp_1(A,C,F),B))) ) ) ) ) ) ) ) ) ) )).
fof(t19_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => k1_normsp_0(A,B,k1_nat_1(C,1)) = k5_algstr_0(A,k2_clvect_3(A,B,k1_nat_1(C,1)),k2_clvect_3(A,B,C)) ) ) ) )).
fof(t19_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k3_coh_sp(A)) => ! [C] : ( m1_subset_1(C,k3_coh_sp(A)) => ! [D] : ( ( 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] : ! [F] : ( 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)) ) ) ) ) ) )).
fof(t19_cohsp_1,axiom,( ! [A] : k3_tarski(k5_finsub_1(A)) = A )).
fof(t19_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_collsp(D,A) => ( ( r2_hidden(B,D) & r2_hidden(C,D) ) => ( B = C | k1_collsp(A,B,C) = D ) ) ) ) ) ) )).
fof(t19_combgras,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( l1_incsp_1(B) => ! [C] : ( l1_combgras(C,A,B) => ! [D] : ( 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) ) ) ) ) )).
fof(t19_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k3_complex1(k6_xcmplx_0(A,B)) = k5_real_1(k3_complex1(A),k3_complex1(B)) & k4_complex1(k6_xcmplx_0(A,B)) = k5_real_1(k4_complex1(A),k4_complex1(B)) ) ) ) )).
fof(t19_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k1_comptrig(A) = k5_numbers <=> ( r1_xxreal_0(k5_numbers,k3_complex1(A)) & k4_complex1(A) = k5_numbers ) ) ) )).
fof(t19_complfld,axiom,( ! [A] : ( 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)) ) ) )).
fof(t19_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => k1_complsp2(k9_seq_4(A)) = k9_seq_4(k1_complsp2(A)) ) )).
fof(t19_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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 ) ) )).
fof(t19_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( r2_compos_2(B,C) & r1_compos_2(C,D) ) => r1_compos_2(B,D) ) ) ) ) )).
fof(t19_comptrig,axiom,( v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k16_sin_cos,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(t19_compts_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => ( v2_compts_1(C,A) <=> v2_compts_1(D,B) ) ) ) ) ) ) )).
fof(t19_comput_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(t19_comseq_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k25_valued_1(k4_ordinal1,k2_numbers,k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,C,B),A),k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k25_valued_1(k4_ordinal1,k2_numbers,C,A),B)) ) ) ) )).
fof(t19_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & v2_comseq_2(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => k3_comseq_2(k2_comseq_2(k4_ordinal1,k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B))) = k6_xcmplx_0(k8_complex1(k3_comseq_2(A)),k8_complex1(k3_comseq_2(B))) ) ) )).
fof(t19_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r2_funct_2(k4_ordinal1,k1_numbers,k26_valued_1(k4_ordinal1,k1_numbers,k7_comseq_3(A),B),k7_comseq_3(k25_valued_1(k4_ordinal1,k2_numbers,A,B))) & r2_funct_2(k4_ordinal1,k1_numbers,k26_valued_1(k4_ordinal1,k1_numbers,k8_comseq_3(A),B),k8_comseq_3(k25_valued_1(k4_ordinal1,k2_numbers,A,B))) ) ) ) )).
fof(t19_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ~ v4_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) & v6_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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u4_struct_0(A))) => ( ( ~ v4_conlat_1(g2_conlat_1(A,C,D),A) & v6_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) ) ) ) ) ) ) )).
fof(t19_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( 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) ) ) )).
fof(t19_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t19_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_connsp_2(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t19_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => m1_connsp_3(k1_struct_0(A),A) ) )).
fof(t19_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( B = a_3_3_convex1(A,C,D) => v1_convex1(B,A) ) ) ) ) ) )).
fof(t19_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_convex4(B,A) => ! [C] : ( 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))) ) ) ) )).
fof(t19_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t19_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => v1_finset_1(k24_qc_lang1(A,B)) ) ) )).
fof(t19_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k2_zfmisc_1(k3_cqc_lang(A),k2_cqc_the1)) => ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(B)) & ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(k5_numbers,D) & r1_xxreal_0(D,9) & k2_xtuple_0(k1_funct_1(B,C)) = D ) ) ) ) ) ) )).
fof(t19_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t19_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t19_csspace,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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,k8_complex1(A))) ) ) ) ) )).
fof(t19_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k9_csspace4(A,B))) => ( C = k4_struct_0(k9_csspace4(A,B)) => k5_numbers = k2_normsp_0(k9_csspace4(A,B),C) ) ) ) ) )).
fof(t19_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(t19_dickson,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v3_dickson(A) & r2_hidden(C,k6_dickson(A,B)) ) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t19_diff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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] : ( 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))) ) ) ) ) )).
fof(t19_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t19_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(k2_xcmplx_0(B,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))) ) => k1_funct_1(k3_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k1_fdiff_9),A),B) = k4_xcmplx_0(k3_xcmplx_0(4,k7_xcmplx_0(k3_xcmplx_0(k19_sin_cos(k2_xcmplx_0(k3_xcmplx_0(2,B),A)),k17_sin_cos(A)),k3_xcmplx_0(k17_sin_cos(k3_xcmplx_0(2,k2_xcmplx_0(B,A))),k17_sin_cos(k3_xcmplx_0(2,B)))))) ) ) ) )).
fof(t19_dilworth,axiom,( ! [A] : ( ( 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))) ) ) ) )).
fof(t19_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_diraf(A,B,C,C,B) & r2_diraf(A,B,C,B,C) ) ) ) ) )).
fof(t19_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,A) => ( v1_dist_1(B,A) => v3_funct_1(k4_dist_1(A,B)) ) ) ) )).
fof(t19_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ? [C] : ( 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_relat_1(C,k8_margrel1) = B ) ) ) )).
fof(t19_domain_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => k2_zfmisc_1(A,B) = a_2_0_domain_1(A,B) ) ) )).
fof(t19_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_dynkin(B,A) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(A),B) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( r1_tarski(C,D) => r2_hidden(k7_subset_1(A,D,C),B) ) ) ) ) ) )).
fof(t19_e_siec,axiom,( ! [A] : ( ( 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)))) ) )).
fof(t19_ec_pf_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(C))) => ( ( D = k5_int_1(A,C) & k5_int_1(k3_xcmplx_0(A,B),C) = 1 ) => k11_algstr_0(k9_int_3(C),D) = k5_int_1(B,C) ) ) ) ) ) )).
fof(t19_ec_pf_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k9_int_3(C))) => ( ( D = k5_int_1(A,C) & E = k5_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) ) ) ) ) ) ) ) )).
fof(t19_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t19_entropy1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( v2_matrprob(A) <=> ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => v4_partfun3(k7_matrix_0(k1_numbers,A,B)) ) ) ) ) )).
fof(t19_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k2_enumset1(A,B,C,D),k1_enumset1(E,F,G)) )).
fof(t19_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_relat_2(D) & v1_partfun1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( r2_hidden(C,k6_eqrel_1(A,A,D,B)) <=> r2_hidden(k4_tarski(C,B),D) ) ) )).
fof(t19_equation,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_msualg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t19_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => u1_struct_0(k15_euclid(A)) = k1_euclid(A) ) )).
fof(t19_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => k22_rvsum_1(k4_algstr_0(k15_euclid(A),B),C) = k4_xcmplx_0(k22_rvsum_1(B,C)) ) ) ) )).
fof(t19_euclid_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xreal_0(B) => k1_euclid_3(k3_xcmplx_0(B,A)) = k1_rlvect_1(k15_euclid(2),k1_euclid_3(A),B) ) ) )).
fof(t19_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => k22_rvsum_1(k5_euclid(A),B) = k5_numbers ) ) )).
fof(t19_euclid_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k5_euclid_5(k4_euclid_5(k5_numbers,k5_numbers,k5_numbers),k4_euclid_5(A,B,C)) = k4_struct_0(k15_euclid(3)) ) ) ) )).
fof(t19_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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)) => k22_rvsum_1(k5_algstr_0(k15_euclid(2),C,D),k5_algstr_0(k15_euclid(2),B,A)) = k5_numbers ) & ( k22_rvsum_1(k5_algstr_0(k15_euclid(2),C,D),k5_algstr_0(k15_euclid(2),B,A)) = k5_numbers => k4_euclid_3(A,C,D) = k4_euclid_3(D,C,B) ) ) ) ) ) ) ) ) )).
fof(t19_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => v6_euclid_7(k6_domain_1(k1_euclid(A),k5_euclid(A)),A) ) )).
fof(t19_euclid_8,axiom,( k5_euclid_8(k3_euclid_8,k2_euclid_8) = k6_euclid(3,k4_euclid_8) )).
fof(t19_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => ~ ( r2_hidden(D,k8_metric_1(k14_euclid(A),C,B)) & ! [E] : ( ( ~ v8_ordinal1(E) & m1_subset_1(E,k4_ordinal1) ) => ~ r1_tarski(k4_euclid_9(A,D,k7_xcmplx_0(1,E)),k8_metric_1(k14_euclid(A),C,B)) ) ) ) ) ) ) )).
fof(t19_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(A)) => ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(t19_euclmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( v1_xreal_0(F) => ~ ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ( 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,k3_xcmplx_0(F,H)),k1_rlvect_1(A,C,k4_xcmplx_0(k3_xcmplx_0(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,k3_xcmplx_0(F,H)),k1_rlvect_1(A,C,k4_xcmplx_0(k3_xcmplx_0(F,G)))),E),B,C) ) ) ) ) ) ) ) ) ) ) )).
fof(t19_euler_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,1) => r1_xxreal_0(k1_euler_1(A),k6_xcmplx_0(A,1)) ) ) )).
fof(t19_euler_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( v1_int_2(B) & r1_int_2(A,B) ) => ( A = k5_numbers | k4_nat_d(k1_newton(A,B),B) = k4_nat_d(A,B) ) ) ) ) )).
fof(t19_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_exchsort(A) ) => ( v3_exchsort(A,k5_numbers) <=> v1_xboole_0(A) ) ) )).
fof(t19_extens_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m1_msafree(D,A,B) => ! [E] : ( m2_pboole(E,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t19_extpro_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & ~ v1_setfam_1(C) ) => ( r1_xxreal_0(A,B) => ! [D] : ( ( ~ 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] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(D)) & v1_funct_1(E) ) => ! [F] : ( ( 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))) ) ) ) ) ) ) ) ) )).
fof(t19_extreal2,axiom,( k3_extreal1(k1_supinf_1) = k1_supinf_1 & k3_extreal1(k2_supinf_1) = k1_supinf_1 )).
fof(t19_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ( ! [E] : ( 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)) ) ) ) ) ) )).
fof(t19_facirc_2,axiom,( ! [A] : ! [B] : ! [C] : 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))) )).
fof(t19_fcont_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t19_fcont_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_xxreal_0(B,A) & r1_tarski(k1_rcomp_1(B,A),k1_relset_1(k1_numbers,C)) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A))) ) => k7_relset_1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A)) = k1_rcomp_1(k3_seq_4(k7_relset_1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A))),k2_seq_4(k7_relset_1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A)))) ) ) ) ) )).
fof(t19_fcont_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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)))) ) ) ) ) )).
fof(t19_fdiff_1,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_1(k2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,B,C),A),D) = k6_xcmplx_0(k1_fdiff_1(B,D),k1_fdiff_1(C,D)) ) ) ) ) ) ) ) )).
fof(t19_fdiff_10,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & r1_xxreal_0(B,k5_numbers) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k3_taylor_1),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k3_taylor_1),A),B) = k7_xcmplx_0(1,k3_xcmplx_0(k1_funct_1(k3_taylor_1,B),B)) ) ) ) ) ) )).
fof(t19_fdiff_11,axiom,( ! [A] : ( ( 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,k27_sin_cos))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k27_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k27_sin_cos),A),B) = k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k1_sin_cos9,B))),k2_xcmplx_0(1,k1_square_1(B))))) ) ) ) ) ) )).
fof(t19_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(t19_fdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( r3_fdiff_3(A,C) & r3_fdiff_3(B,C) ) => ( k1_funct_1(B,C) = k5_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)) = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k2_fdiff_3(C,A),k1_funct_1(B,C)),k3_xcmplx_0(k2_fdiff_3(C,B),k1_funct_1(A,C))),k1_square_1(k1_funct_1(B,C))) ) ) ) ) ) ) )).
fof(t19_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => ( k1_funct_1(C,E) = k1_square_1(A) & ~ r1_xxreal_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,C,D),E),k5_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] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_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) = k7_xcmplx_0(k3_xcmplx_0(2,E),k6_xcmplx_0(k1_square_1(A),k1_newton(E,2))) ) ) ) ) ) ) ) ) )).
fof(t19_fdiff_5,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k3_taylor_1,A),B) = k7_xcmplx_0(1,B) ) ) ) ) ) )).
fof(t19_fdiff_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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,k22_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k22_sin_cos)),k7_xcmplx_0(1,k6_xcmplx_0(1,k3_power(k4_power,A)))))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(C,D) = k3_xcmplx_0(D,k3_power(k4_power,A)) ) ) ) => ( r1_xxreal_0(A,k5_numbers) | A = k4_power | ( r2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k3_rfunct_1(k1_numbers,k1_numbers,k22_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k22_sin_cos)),k7_xcmplx_0(1,k6_xcmplx_0(1,k3_power(k4_power,A)))),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(k2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k3_rfunct_1(k1_numbers,k1_numbers,k22_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k22_sin_cos)),k7_xcmplx_0(1,k6_xcmplx_0(1,k3_power(k4_power,A)))),B),D) = k7_xcmplx_0(k1_funct_1(k22_sin_cos,D),k6_prepower(A,D)) ) ) ) ) ) ) ) ) )).
fof(t19_fdiff_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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,k3_sin_cos6))) & r1_tarski(C,k2_rcomp_1(k4_xcmplx_0(1),1)) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(D,E) = k2_xcmplx_0(k3_xcmplx_0(A,E),B) ) ) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k3_sin_cos6),C) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k3_sin_cos6),C),E) = k6_xcmplx_0(k3_xcmplx_0(A,k1_funct_1(k3_sin_cos6,E)),k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,E),B),k3_square_1(k6_xcmplx_0(1,k1_square_1(E))))) ) ) ) ) ) ) ) ) )).
fof(t19_fdiff_8,axiom,( ! [A] : ( ( 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,k27_sin_cos,k3_taylor_1))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k3_taylor_1),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k3_taylor_1),A),B) = k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(k1_funct_1(k16_sin_cos,B),k1_funct_1(k18_sin_cos,B)))) ) ) ) ) ) )).
fof(t19_fdiff_9,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k3_taylor_1),A),B) = k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k18_sin_cos,B),k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t19_ff_siec,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t19_fib_num2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r1_tarski(k9_xtuple_0(A),k2_finseq_1(B)) & ~ r1_xxreal_0(C,B) & ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ~ ( r1_tarski(A,D) & k4_finseq_1(D) = k2_finseq_1(C) ) ) ) ) ) ) )).
fof(t19_fib_num3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k2_nat_1(2,k1_fib_num3(k1_nat_1(A,2))) = k1_nat_1(k1_fib_num3(A),k1_fib_num3(k1_nat_1(A,3))) ) )).
fof(t19_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ( A != k5_numbers => k2_int_1(k6_xcmplx_0(k7_xcmplx_0(k2_power(k1_fib_num,A),k3_square_1(5)),k7_xcmplx_0(1,2))) = k1_pre_ff(A) ) ) )).
fof(t19_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( 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) = k1_nat_1(k3_finseq_1(B),1) ) ) ) ) ) )).
fof(t19_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ( ~ ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k4_lattices(A,B,C) = B ) & k2_filter_0(A,B) = u1_struct_0(A) ) ) ) )).
fof(t19_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t19_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_lattice2(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t19_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) )).
fof(t19_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ? [C] : ( m2_finseq_1(C,B) & k3_finseq_1(C) = A ) ) ) )).
fof(t19_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( C = k5_relat_1(B,k2_finseq_1(A)) => k3_finseq_1(C) = k3_xxreal_0(A,k3_finseq_1(B)) ) ) ) ) )).
fof(t19_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => r3_xboole_0(k2_finseq_1(A),k2_finseq_1(B)) ) ) )).
fof(t19_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_hidden(B,k10_xtuple_0(A)) => k1_funct_1(A,k4_finseq_4(A,B)) = B ) ) )).
fof(t19_finseq_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => r1_tarski(k10_xtuple_0(k16_finseq_1(B,A)),k10_xtuple_0(A)) ) ) )).
fof(t19_finseq_6,axiom,( ! [A] : ! [B] : k4_finseq_4(k10_finseq_1(A,B),A) = 1 )).
fof(t19_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => k2_finseq_7(A,B,C,C) = B ) ) ) )).
fof(t19_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( r1_xxreal_0(1,k3_finseq_1(B)) => r2_finseq_8(A,B,B,1) ) ) ) )).
fof(t19_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( ( 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(k4_ordinal1,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))) ) ) ) ) ) ) ) )).
fof(t19_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k8_fintopo2(A,C)) <=> ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(t19_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k5_fintopo3(A,B,k5_numbers) = B ) ) )).
fof(t19_fintopo4,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => v1_fin_topo(k2_fintopo4(A)) ) ) )).
fof(t19_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t19_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_catalan2(A))) => ! [D] : ( 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))) ) ) ) ) )).
fof(t19_flang_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(B,k1_flang_2(A,C,D,E)) <=> ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(D,F) & r1_xxreal_0(F,E) & r2_hidden(B,k7_flang_1(A,C,F)) ) ) ) ) ) )).
fof(t19_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ~ r1_xxreal_0(D,k5_numbers) => k7_flang_1(A,k1_flang_3(A,B,C),D) = k1_flang_3(A,B,k3_xcmplx_0(C,D)) ) ) ) ) )).
fof(t19_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(C,k1_funct_2(A,B)) => r1_tarski(k3_tarski(C),k2_zfmisc_1(A,B)) ) )).
fof(t19_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v4_fomodel1(C,A) & m1_subset_1(C,k1_fomodel1(A)) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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] : ( m2_subset_1(G,k9_funct_2(k37_fomodel1(A),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_fomodel2(A,B)) => ( ~ ( k25_fomodel2(A,B,G,k42_fomodel1(A,k43_fomodel1(A,C),D)) = k8_margrel1 & ! [H] : ( m1_subset_1(H,B) => k25_fomodel2(A,B,k34_fomodel2(A,B,G,C,H),D) != 1 ) ) & ( ? [H] : ( m1_subset_1(H,B) & k25_fomodel2(A,B,k34_fomodel2(A,B,G,C,H),D) = 1 ) => k25_fomodel2(A,B,G,k42_fomodel1(A,k43_fomodel1(A,C),D)) = k8_margrel1 ) & ( k25_fomodel2(A,B,G,k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k1_fomodel2(A)),E),F)) = k8_margrel1 => ( k25_fomodel2(A,B,G,E) = k7_margrel1 & k25_fomodel2(A,B,G,F) = k7_margrel1 ) ) & ( ( k25_fomodel2(A,B,G,E) = k7_margrel1 & k25_fomodel2(A,B,G,F) = k7_margrel1 ) => k25_fomodel2(A,B,G,k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k1_fomodel2(A)),E),F)) = k8_margrel1 ) ) ) ) ) ) ) ) ) )).
fof(t19_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v1_orders_4(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ~ ( v13_fomodel4(C,2,B) & v7_fomodel4(C,B) & v15_fomodel4(C,B) & ~ v10_fomodel4(A,B,C) & r1_tarski(A,k30_fomodel2(B)) & ! [D] : ( ( ~ v1_xboole_0(D) & v4_card_3(D) ) => ! [E] : ( m2_subset_1(E,k9_funct_2(k37_fomodel1(B),k3_rfunct_3(k3_finseq_2(D),k2_xboole_0(D,k6_margrel1))),k15_fomodel2(B,D)) => ~ v10_fomodel2(A,D,B,E) ) ) ) ) ) )).
fof(t19_frechet,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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) ) ) )).
fof(t19_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t19_fscirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => k2_msafree2(k8_fscirc_1(A,B,C)) = k1_enumset1(A,B,C) ) ) ) )).
fof(t19_fscirc_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( 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) ) ) ) ) )).
fof(t19_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ( r5_fsm_1(A,B,C,D,E) <=> ! [F] : ( m1_subset_1(F,A) => ( k3_funct_2(k2_zfmisc_1(u1_struct_0(C),A),B,u3_fsm_1(A,B,C),k1_domain_1(u1_struct_0(C),A,D,F)) = k3_funct_2(k2_zfmisc_1(u1_struct_0(C),A),B,u3_fsm_1(A,B,C),k1_domain_1(u1_struct_0(C),A,E,F)) & r5_fsm_1(A,B,C,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,F)),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,E,F))) ) ) ) ) ) ) ) ) )).
fof(t19_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( ~ 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))) ) ) ) ) ) )).
fof(t19_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t19_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t19_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : k3_relat_1(A,k2_funcop_1(B,C)) = k2_funcop_1(k8_relat_1(A,B),C) ) )).
fof(t19_funcsdom,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ~ ( r2_hidden(A,C) & r2_hidden(B,C) & A != B & ! [D] : ( m2_funct_2(D,C,k1_numbers,k9_funct_2(C,k1_numbers)) => ! [E] : ( m2_funct_2(E,C,k1_numbers,k9_funct_2(C,k1_numbers)) => ? [F] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & k1_binop_1(k5_funcsdom(C),k1_funct_1(k7_funcsdom(C),k4_tarski(F,D)),k1_funct_1(k7_funcsdom(C),k4_tarski(G,E))) = k8_funcsdom(C) & ~ ( F = k5_numbers & G = k5_numbers ) ) ) ) ) ) ) )).
fof(t19_funct_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t19_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ! [E] : ( ( r2_hidden(D,A) & r2_hidden(E,A) & k1_funct_1(C,D) = k1_funct_1(C,E) ) => D = E ) ) ) ) )).
fof(t19_funct_3,axiom,( ! [A] : ( ( 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))))) ) ) )).
fof(t19_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(k9_xtuple_0(A),k9_xtuple_0(B)) => k1_funct_4(A,B) = B ) ) ) )).
fof(t19_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) ) )).
fof(t19_funct_6,axiom,( k1_funct_6(k1_xboole_0) = k1_xboole_0 & k2_funct_6(k1_xboole_0) = k1_xboole_0 )).
fof(t19_funct_7,axiom,( ! [A] : ! [B] : ( r1_tarski(k3_finseq_2(A),k3_finseq_2(B)) => r1_tarski(A,B) ) )).
fof(t19_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t19_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) ) => ( ! [D] : ( 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) = k5_numbers | ( v1_funct_9(C,k6_xcmplx_0(A,B)) & v2_funct_9(C) ) ) ) ) ) ) )).
fof(t19_functor0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,B,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,A) & v1_funct_1(F) & v1_partfun1(F,A) ) => ! [G] : ( ( v1_relat_1(G) & v4_relat_1(G,B) & v1_funct_1(G) & v1_partfun1(G,B) ) => ! [H] : ( ( v1_relat_1(H) & v4_relat_1(H,C) & v1_funct_1(H) & v1_partfun1(H,C) ) => ! [I] : ( m1_functor0(I,A,B,D,F,G) => ! [J] : ( m1_functor0(J,A,C,k1_partfun1(A,B,B,C,D,E),k3_relat_1(D,G),H) => ( ! [K] : ~ ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t19_functor1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & v1_altcat_2(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & v1_altcat_2(B) & l2_altcat_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t19_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t19_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D) => r1_fuzzy_1(k2_fuzzy_1(A,B,C),k2_fuzzy_1(A,D,C)) ) ) ) ) ) )).
fof(t19_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D,C)),k1_fuzzy_2(A,k1_fuzzy_1(A,B,D),k1_fuzzy_1(A,B,C))) ) ) ) ) )).
fof(t19_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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] : ( ( v5_relat_1(F,k1_rcomp_1(k5_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] : ( ( v5_relat_1(G,k1_rcomp_1(k5_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(k3_fuzzy_4(A,B,C,D,F),k3_fuzzy_4(A,B,C,E,G)) ) ) ) ) ) ) ) ) )).
fof(t19_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => k3_funct_2(u1_struct_0(A),k6_numbers,B,k4_algstr_0(A,k5_struct_0(A))) = k5_numbers ) ) ) )).
fof(t19_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_fvsum_1(A,k12_finseq_1(u1_struct_0(A),B),k12_finseq_1(u1_struct_0(A),C)) = k12_finseq_1(u1_struct_0(A),k1_algstr_0(A,B,C)) ) ) ) )).
fof(t19_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(k13_gate_1(A,B,C)) <=> ( v1_xboole_0(A) & v1_xboole_0(B) & v1_xboole_0(C) ) ) )).
fof(t19_gcd_1,axiom,( ! [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) & v1_vectsp_2(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t19_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v2_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( m1_genealg1(E,D) => ! [F] : ( m1_genealg1(F,D) => ( r1_xxreal_0(k3_finseq_1(E),B) => k9_genealg1(D,E,F,A,B,C) = k8_genealg1(D,E,F,A,C) ) ) ) ) ) ) ) )).
fof(t19_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ( ( r1_analmetr(A,H,I) & r2_geomtrap(A,H,I,B,E,C,F) & r2_geomtrap(A,H,I,B,E,D,G) ) => ( B = E | r2_geomtrap(A,H,I,C,F,D,G) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t19_gfacirc1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => k2_msafree2(k7_gfacirc1(A,B,C)) = k1_enumset1(A,B,C) ) ) ) )).
fof(t19_gfacirc2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t19_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & v3_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => k35_glib_000(A,B) = k5_card_1(k28_glib_000(A,B)) ) ) )).
fof(t19_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m3_glib_001(D,B) => ( C = D => ! [E] : ( m1_subset_1(E,k4_ordinal1) => k5_glib_001(A,C,E) = k5_glib_001(B,D,E) ) ) ) ) ) ) )).
fof(t19_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => r1_tarski(k2_glib_002(A,B),k1_glib_002(A,B)) ) ) )).
fof(t19_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) & v1_glib_003(B) ) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t19_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t19_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ( C != B => r2_glib_005(A,k13_glib_005(A,C,B),B,C) ) ) ) ) )).
fof(t19_goboard1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( 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] : ( v7_ordinal1(D) => ~ ( r2_hidden(D,k4_finseq_1(B)) & r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),C,A),k10_xtuple_0(k7_matrix_0(u1_struct_0(k15_euclid(2)),B,D))) ) ) ) ) ) ) )).
fof(t19_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_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_0(C),B) | r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_nat_1(B,1))),k3_goboard5(C,A,B)) ) ) ) ) ) )).
fof(t19_goboard6,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => k1_tops_1(k15_euclid(2),k3_goboard5(A,k5_numbers,k1_matrix_0(A))) = a_1_5_goboard6(A) ) )).
fof(t19_goboard7,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(A)) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k1_matrix_0(A)) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(A)) & r1_xxreal_0(1,E) & r1_xxreal_0(k1_nat_1(E,1),k1_matrix_0(A)) ) => ( r1_xboole_0(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,k1_nat_1(C,1))),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,D,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,D,k1_nat_1(E,1)))) | ( B = D & r1_xxreal_0(k1_int_2(k6_xcmplx_0(C,E)),1) ) ) ) ) ) ) ) ) )).
fof(t19_goboard8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,2),k3_finseq_1(A)) ) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,2),k1_matrix_0(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k3_finseq_1(k2_goboard2(A)),k1_nat_1(C,1)) ) => ( ( ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k3_finseq_1(k2_goboard2(A)),k1_nat_1(C,2)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k7_nat_d(k3_finseq_1(k2_goboard2(A)),1),k1_nat_1(C,1)) ) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k3_finseq_1(k2_goboard2(A)),k1_nat_1(C,2)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k7_nat_d(k3_finseq_1(k2_goboard2(A)),1),k1_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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k7_nat_d(k3_finseq_1(k2_goboard2(A)),1),C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k3_finseq_1(k2_goboard2(A)),k1_nat_1(C,1))),k7_xcmplx_0(1,2)),k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k3_finseq_1(k2_goboard2(A)),C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k3_finseq_1(k2_goboard2(A)),k1_nat_1(C,1))),k7_xcmplx_0(1,2)),k19_euclid(1,k5_numbers))),k3_topreal1(2,A)) ) ) ) ) ) ) )).
fof(t19_goboard9,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k3_finseq_1(A)) ) => r1_tarski(k1_tops_1(k15_euclid(2),k5_goboard5(A,B)),k2_goboard9(A)) ) ) ) )).
fof(t19_gobrd11,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( v1_goboard1(A) => k1_goboard5(A,k3_finseq_1(A)) = a_1_10_gobrd11(A) ) ) )).
fof(t19_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(D)) & r1_goboard1(u1_struct_0(k15_euclid(2)),D,E) & r2_hidden(k4_tarski(A,B),k2_matrix_0(E)) & r2_hidden(k4_tarski(k1_nat_1(A,1),B),k2_matrix_0(E)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,k1_nat_1(A,1),B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,B) ) => k2_gobrd13(D,E,C) = k3_goboard5(E,A,B) ) ) ) ) ) ) )).
fof(t19_gobrd14,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t19_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ( v4_card_3(A) => v4_card_3(k3_cqc_lang(A)) ) ) )).
fof(t19_gr_cy_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) & k6_group_1(A,B) = k7_group_1(A) ) ) ) )).
fof(t19_gr_cy_2,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) ) )).
fof(t19_gr_cy_3,axiom,( k1_gr_cy_3(3) = 7 )).
fof(t19_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ 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)) ) ) ) ) )).
fof(t19_graph_2,axiom,( ! [A] : ( ( 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] : ? [C] : ( B != C & k10_xtuple_0(A) = k2_tarski(B,C) ) ) ) ) )).
fof(t19_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [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) ) ) ) )).
fof(t19_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u4_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u4_struct_0(A)) => ( r1_tarski(k10_xtuple_0(C),k10_xtuple_0(B)) => r1_tarski(k2_graph_5(A,C),k2_graph_5(A,B)) ) ) ) ) )).
fof(t19_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(B,k4_finseq_1(C)) => k1_funct_1(k2_graphsp(A,B,C,D),B) = D ) ) ) ) ) )).
fof(t19_grcat_1,axiom,( ! [A] : ( ( v1_grcat_1(A) & v2_grcat_1(A) & l1_grcat_1(A) ) => ! [B] : ( ( v1_grcat_1(B) & v2_grcat_1(B) & l1_grcat_1(B) ) => ~ ( k7_grcat_1(B) = k8_grcat_1(A) & ! [C] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v13_algstr_0(D) & v3_rlvect_1(D) & v4_rlvect_1(D) & l2_algstr_0(D) ) => ! [E] : ( ( ~ v2_struct_0(E) & v13_algstr_0(E) & v3_rlvect_1(E) & v4_rlvect_1(E) & l2_algstr_0(E) ) => ! [F] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t19_grfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( A = k1_xboole_0 => k2_funct_1(A) = k1_xboole_0 ) ) )).
fof(t19_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t19_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( ! [E] : ( ( 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(k12_polynom1(A,C),D))) & ! [F] : ( ( 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(k12_polynom1(A,C),D)),k3_groeb_1(A,k2_groeb_1(A,B,C,D))) ) ) ) ) ) )).
fof(t19_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( 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] : ( ( 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),k8_polynom1(A,C)) ) ) ) ) ) )).
fof(t19_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(E,k5_card_1(k3_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)) = k3_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 ) ) ) ) ) ) ) )).
fof(t19_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t19_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(t19_group_14,axiom,( ! [A] : ( ( 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] : ( ( v1_relat_1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_finseq_1(B) & v1_prvect_1(B) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r2_hidden(C,k4_finseq_1(B)) & ! [D] : ( ( v7_ordinal1(D) & ~ v8_ordinal1(D) ) => ~ ( D = k1_funct_1(A,C) & k1_funct_1(B,C) = k2_group_14(D) ) ) ) ) ) => k1_card_1(u1_struct_0(k20_prvect_1(B))) = k19_rvsum_1(A) ) ) ) )).
fof(t19_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t19_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_group_3(A,B,k1_group_1(A)) = B ) ) )).
fof(t19_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,k4_numbers) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t19_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t19_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_group_6(A,B))) => ! [D] : ( 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) ) ) ) ) )).
fof(t19_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t19_group_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,C) => ( ( D = k10_group_2(A,C,B) & v8_struct_0(A) ) => r1_xxreal_0(k18_group_2(C,D),k18_group_2(A,B)) ) ) ) ) ) )).
fof(t19_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v2_group_9(C,A) & m1_group_9(C,A,B) ) => k17_group_9(A,B,C,C) = C ) ) )).
fof(t19_groupp_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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] : ( m1_group_2(C,B) => ! [D] : ( m1_group_2(D,B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t19_hahnban,axiom,( ! [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) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k1_numbers,B,k5_algstr_0(A,C,D)) = k5_real_1(k3_funct_2(u1_struct_0(A),k1_numbers,B,C),k3_funct_2(u1_struct_0(A),k1_numbers,B,D)) ) ) ) ) )).
fof(t19_hahnban1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => k3_funct_2(u1_struct_0(A),k1_numbers,B,k4_vectsp_1(k1_complfld,A,k1_hahnban1(k5_numbers,D),C)) = k3_xcmplx_0(D,k3_funct_2(u1_struct_0(A),k1_numbers,B,k4_vectsp_1(k1_complfld,A,k2_hahnban1,C))) ) ) ) ) ) )).
fof(t19_hallmar1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_hallmar1(D,A,B,C) => m2_hallmar1(D,A,B) ) ) ) ) )).
fof(t19_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r2_hidden(D,B) & r1_xxreal_0(k1_funct_1(k6_weierstr(A,B),C),k3_metric_1(A,D,C)) ) ) ) ) )).
fof(t19_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v5_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ( ( 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) ) ) ) ) ) ) )).
fof(t19_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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))) ) ) )).
fof(t19_heyting1,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [C] : ( 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] : ( 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) ) ) ) ) ) )).
fof(t19_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( 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)) ) ) )).
fof(t19_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_xxreal_0(A,C) => r1_tarski(k3_heyting3(A,B),k3_heyting3(C,B)) ) ) ) ) )).
fof(t19_hfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t19_hilbasis,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(E,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k1_normsp_1(A,k11_polynom3(A,k5_hilbasis(A,B,D),E),k1_nat_1(C,B)) = k6_algstr_0(A,D,k1_normsp_1(A,E,C)) ) ) ) ) ) )).
fof(t19_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => r2_hidden(k3_hilbert1(k3_hilbert1(B,C),k3_hilbert1(k3_hilbert1(A,B),k3_hilbert1(A,C))),k6_hilbert1) ) ) ) )).
fof(t19_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( m1_subset_1(D,k1_hilbert1) => ( k4_hilbert1(A,B) = k4_hilbert1(C,D) => ( A = C & D = B ) ) ) ) ) ) )).
fof(t19_hurwitz,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k11_polynom3(A,B,k3_polynom5(A,C,D)),k3_polynom5(A,k11_polynom3(A,B,C),D)) ) ) ) ) )).
fof(t19_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_idea_1(B,A) => r1_idea_1(B,k8_idea_1(B,A)) ) ) ) )).
fof(t19_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t19_incproj,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( 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] : ( m1_subset_1(B,u1_incsp_1(k3_incproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k3_incproj(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k3_incproj(A))) => ! [E] : ( m1_subset_1(E,u1_incsp_1(k3_incproj(A))) => ! [F] : ( m1_subset_1(F,u1_incsp_1(k3_incproj(A))) => ! [G] : ( m1_subset_1(G,u1_incsp_1(k3_incproj(A))) => ! [H] : ( m1_subset_1(H,u1_incsp_1(k3_incproj(A))) => ! [I] : ( m1_subset_1(I,u1_incsp_1(k3_incproj(A))) => ! [J] : ( m1_subset_1(J,u1_incsp_1(k3_incproj(A))) => ! [K] : ( m1_subset_1(K,u1_incsp_1(k3_incproj(A))) => ! [L] : ( m1_subset_1(L,u2_incsp_1(k3_incproj(A))) => ! [M] : ( m1_subset_1(M,u2_incsp_1(k3_incproj(A))) => ! [N] : ( m1_subset_1(N,u2_incsp_1(k3_incproj(A))) => ! [O] : ( m1_subset_1(O,u2_incsp_1(k3_incproj(A))) => ! [P] : ( m1_subset_1(P,u2_incsp_1(k3_incproj(A))) => ! [Q] : ( m1_subset_1(Q,u2_incsp_1(k3_incproj(A))) => ! [R] : ( m1_subset_1(R,u2_incsp_1(k3_incproj(A))) => ! [S] : ( m1_subset_1(S,u2_incsp_1(k3_incproj(A))) => ! [T] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t19_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t19_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ 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] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t19_instalg1,axiom,( ! [A] : ( l1_msualg_1(A) => ! [B] : ( ( v1_instalg1(B) & l1_msualg_1(B) ) => ! [C] : ( m1_instalg1(C,B) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r3_pua2mss1(A,C,D,E) => r3_pua2mss1(A,B,D,E) ) ) ) ) ) ) )).
fof(t19_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ( r2_int_1(k2_xcmplx_0(A,B),C,D) <=> r2_int_1(A,k6_xcmplx_0(C,B),D) ) ) ) ) ) )).
fof(t19_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( r1_int_1(A,C) & r1_int_1(B,C) ) => r1_int_1(k2_int_2(A,B),C) ) ) ) ) )).
fof(t19_int_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(A,k5_numbers) & k4_nat_d(k3_xcmplx_0(A,B),k1_newton(A,C)) != k3_xcmplx_0(A,k4_nat_d(B,k1_newton(A,k7_nat_d(C,1)))) ) ) ) ) )).
fof(t19_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ( k3_int_2(A,B) = 1 => ( r1_xxreal_0(B,2) | r1_int_5(A,B) | k5_int_1(k1_newton(A,k3_nat_d(k7_nat_d(B,1),2)),B) = k6_xcmplx_0(B,1) ) ) ) ) )).
fof(t19_int_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( r1_int_2(A,B) => k3_int_2(A,k3_xcmplx_0(B,C)) = k3_int_2(A,C) ) ) ) ) )).
fof(t19_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_int_2(A,C) & k4_nat_d(k3_xcmplx_0(A,B),C) = 1 ) => ( r1_xxreal_0(C,1) | k3_pepin(A,C) = k3_pepin(B,C) ) ) ) ) ) )).
fof(t19_integr11,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ 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)),k18_sin_cos)) = k6_xcmplx_0(k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k1_taylor_1(k2_xcmplx_0(A,1))),k7_xcmplx_0(1,k2_xcmplx_0(A,1))),k2_seq_4(B)),k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k1_taylor_1(k2_xcmplx_0(A,1))),k7_xcmplx_0(1,k2_xcmplx_0(A,1))),k3_seq_4(B))) ) ) )).
fof(t19_integr12,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v3_rcomp_1(E) & m1_subset_1(E,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,E) & r1_tarski(E,k2_rcomp_1(k4_xcmplx_0(1),1)) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => k1_funct_1(D,F) = 1 ) ) & E = k1_relset_1(k1_numbers,C) & 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,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,k1_sin_cos6,k1_taylor_1(k6_xcmplx_0(A,1))),A),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k1_taylor_1(2)),k4_taylor_1(k7_xcmplx_0(1,2))))) ) => ( r1_xxreal_0(A,1) | k2_integra5(B,C) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos6,k1_taylor_1(A)),k2_seq_4(B)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos6,k1_taylor_1(A)),k3_seq_4(B))) ) ) ) ) ) ) ) )).
fof(t19_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,D) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => k1_funct_1(C,E) = 1 ) ) & r2_relset_1(k1_numbers,k1_numbers,B,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,C,k1_taylor_1(2))))) & r1_tarski(D,k2_rcomp_1(k4_xcmplx_0(1),1)) & D = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k1_sin_cos9),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k1_sin_cos9),k3_seq_4(A))) ) ) ) ) ) )).
fof(t19_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k7_xcmplx_0(k1_funct_1(k16_sin_cos,k1_funct_1(k3_taylor_1,D)),k3_xcmplx_0(D,k1_square_1(k1_funct_1(k18_sin_cos,k1_funct_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) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k1_fdiff_9),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k1_fdiff_9),k3_seq_4(A))) ) ) ) ) )).
fof(t19_integr15,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( C = k1_rcomp_1(D,E) => k11_integr15(A,C,B) = k12_integr15(D,E,A,B) ) ) ) ) ) ) )).
fof(t19_integr16,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k2_numbers))) ) => ! [C] : ( ( 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)) = k2_xcmplx_0(k7_integr16(A,B),k7_integr16(A,C)) & k7_integr16(A,k46_valued_1(k1_numbers,k2_numbers,k2_numbers,B,C)) = k6_xcmplx_0(k7_integr16(A,B),k7_integr16(A,C)) ) ) ) ) ) )).
fof(t19_integr19,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t19_integra1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k3_finseq_1(A) = k3_finseq_1(C) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k4_finseq_1(A)) => k1_funct_1(C,D) = k3_real_1(k7_partfun1(k1_numbers,A,D),k7_partfun1(k1_numbers,B,D)) ) ) ) => k18_rvsum_1(C) = k2_xcmplx_0(k18_rvsum_1(A),k18_rvsum_1(B)) ) ) ) ) )).
fof(t19_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( m1_integra1(D,B) => ( ( v1_comseq_2(k2_partfun1(B,k1_numbers,C,B)) & r1_xxreal_0(k5_numbers,A) ) => r1_xxreal_0(k3_xcmplx_0(k3_xcmplx_0(A,k3_seq_4(k1_rvsum_1(C))),k3_integra1(B)),k1_funct_1(k8_integra1(B,k26_valued_1(B,k1_numbers,C,A)),D)) ) ) ) ) ) )).
fof(t19_integra3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( m1_integra1(C,B) => ! [D] : ( ( 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(k3_seq_4(k1_rvsum_1(D)),k2_seq_4(k1_rvsum_1(k2_partfun1(B,k1_numbers,D,k2_integra1(B,C,A))))) ) ) ) ) ) )).
fof(t19_integra4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ! [C] : ( ( 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))) ) ) ) )).
fof(t19_integra5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( B = k1_rcomp_1(C,D) => k2_integra5(B,A) = k4_integra5(C,D,A) ) ) ) ) ) )).
fof(t19_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(C,D) & r1_xxreal_0(D,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)) ) => ( 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))) ) ) ) ) ) ) ) ) )).
fof(t19_integra7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t19_integra8,axiom,( k1_funct_1(k3_sin_cos2,1) = k7_xcmplx_0(k2_xcmplx_0(k1_square_1(k4_power),1),k3_xcmplx_0(2,k4_power)) )).
fof(t19_integra9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => k2_integra5(B,k1_taylor_1(A)) = k6_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,k2_xcmplx_0(A,1)),k1_newton(k2_seq_4(B),k2_xcmplx_0(A,1))),k3_xcmplx_0(k7_xcmplx_0(1,k2_xcmplx_0(A,1)),k1_newton(k3_seq_4(B),k2_xcmplx_0(A,1)))) ) ) )).
fof(t19_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => r1_interva1(A,k4_interva1(A,B,B),B) ) ) )).
fof(t19_intpro_1,axiom,( r2_hidden(k10_intpro_1,k8_intpro_1) )).
fof(t19_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r1_xxreal_0(A,B) => k1_funct_1(k5_newton(C,D,B),k1_nat_1(A,1)) = k3_xcmplx_0(k3_xcmplx_0(k4_newton(A,B),k2_power(C,k6_xcmplx_0(B,A))),k2_power(D,A)) ) ) ) ) ) )).
fof(t19_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ( r1_nattra_1(A,B,D,E) => ! [F] : ( m1_nattra_1(F,A,B,D,E) => ! [G] : ( m2_cat_1(G,B,C) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => k2_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,k2_nattra_1(A,B,D,E,F,H)) ) ) ) ) ) ) ) ) ) )).
fof(t19_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,k6_cat_2(A,B),C) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => m2_cat_1(k8_cat_1(A,k9_nattra_1(B,C),k5_isocat_2(A,B,C,D),E),B,C) ) ) ) ) ) )).
fof(t19_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_tops_1(B,A) <=> ? [C] : ( 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) ) ) ) ) )).
fof(t19_jgraph_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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)) ) ) ) ) ) )).
fof(t19_jgraph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( 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) ) ) ) ) ) ) )).
fof(t19_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( 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] : ( 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) = k3_xcmplx_0(k12_euclid(D),k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k18_euclid(D),k12_euclid(D)),A),k6_xcmplx_0(1,A))) ) ) & ! [D] : ( 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),k5_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) ) ) ) ) ) )).
fof(t19_jgraph_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r1_xxreal_0(k5_numbers,k18_euclid(B)) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) | r1_xxreal_0(1,A) | ! [C] : ( 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(k5_numbers,k18_euclid(C)) ) ) ) ) ) ) )).
fof(t19_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t19_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t19_jordan,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( 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) ) ) ) )).
fof(t19_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( v3_pre_topc(a_4_1_jordan1(A,B,C,D),k15_euclid(2)) & m1_subset_1(a_4_1_jordan1(A,B,C,D),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ) ) ) ) )).
fof(t19_jordan10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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,k2_jordan9(B,A))) ) ) )).
fof(t19_jordan12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r1_xxreal_0(A,k1_matrix_0(B)) => v1_convex1(k2_goboard5(B,A),k15_euclid(2)) ) ) ) )).
fof(t19_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( v7_ordinal1(C) => ( ( r1_jordan1h(A,C) & r2_jordan2c(2,A,B) ) => r1_xboole_0(B,k3_topreal1(2,k1_jordan13(A,C))) ) ) ) ) )).
fof(t19_jordan16,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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))) ) ) ) ) )).
fof(t19_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ~ ( E != B & r1_jordan17(A,B,C,D,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ~ ( F != E & F != B & r1_jordan17(A,B,C,E,F) ) ) ) ) ) ) ) ) )).
fof(t19_jordan19,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & ~ r1_xxreal_0(A,k5_numbers) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E),k9_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k8_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k9_jordan6(B)) ) ) ) ) ) ) )).
fof(t19_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_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_0(E)) ) => r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,C)),k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),E,B,D))) ) ) ) ) ) ) )).
fof(t19_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & ~ r1_xxreal_0(k3_finseq_1(k2_jordan9(B,A)),C) & r2_hidden(k19_pscomp_1(B),k2_gobrd13(k2_jordan9(B,A),k1_jordan8(B,A),C)) ) ) ) )).
fof(t19_jordan1g,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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)))) ) => k4_finseq_4(k1_jordan1e(B,A),k18_pscomp_1(k3_topreal1(2,k2_jordan9(B,A)))) = 1 ) ) )).
fof(t19_jordan1h,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v2_goboard1(A) & v3_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => k1_matrix_0(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))) ) )).
fof(t19_jordan1k,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v2_connsp_1(B,k15_euclid(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t19_jordan20,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t19_jordan21,axiom,( ! [A] : ( ( 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)) ) )).
fof(t19_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(k1_jordan8(A,B))) & k1_jordan21(k3_topreal1(2,k2_jordan9(A,B))) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),C) ) ) ) ) ) )).
fof(t19_jordan23,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v2_jordan23(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(t19_jordan2b,axiom,( ! [A] : ( v1_xreal_0(A) => k3_euclid(k9_finseq_1(A)) = k9_finseq_1(k9_complex1(A)) ) )).
fof(t19_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( B = k1_euclid(A) => v2_connsp_1(B,k15_euclid(A)) ) ) ) )).
fof(t19_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t19_jordan4,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( 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(k1_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_xcmplx_0(D,B),1)) ) ) ) ) ) ) )).
fof(t19_jordan5a,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => ( k3_seq_4(k1_rcomp_1(A,B)) = A & k2_seq_4(k1_rcomp_1(A,B)) = B ) ) ) ) )).
fof(t19_jordan5b,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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))) ) ) ) ) )).
fof(t19_jordan5c,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( v7_ordinal1(C) => ( ( v4_pre_topc(B,k15_euclid(2)) & v4_topreal1(A) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_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,k1_nat_1(C,1))) ) ) ) ) ) )).
fof(t19_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( B = a_1_0_jordan5d(A) => k3_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)))) ) ) ) )).
fof(t19_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => r1_tarski(k3_jordan6(A,B,C,D),A) ) ) ) ) )).
fof(t19_jordan7,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( ( 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] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ( ( 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,k5_numbers) = B & k1_funct_1(F,1) = C & k1_funct_1(F,G) = D & r1_xxreal_0(k5_numbers,G) & r1_xxreal_0(G,1) & k1_funct_1(F,H) = E & r1_xxreal_0(k5_numbers,H) & r1_xxreal_0(H,1) & r1_jordan5c(A,B,C,D,E) ) => r1_xxreal_0(G,H) ) ) ) ) ) ) ) ) ) )).
fof(t19_jordan9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ~ ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(C)) & r2_hidden(D,k9_matrix_0(C)) & r2_hidden(D,k3_goboard5(C,A,B)) & D != k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B) & D != k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_nat_1(B,1)) & D != k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),k1_nat_1(B,1)) & D != k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),B) ) ) ) ) ) )).
fof(t19_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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)) ) ) ) )).
fof(t19_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( v2_prob_1(B) => ( ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & ~ r1_xxreal_0(E,D) & ~ r2_hidden(C,k1_funct_1(B,E)) ) ) | r2_hidden(C,k2_kurato_0(A,B)) ) ) ) )).
fof(t19_kurato_1,axiom,( 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) )).
fof(t19_kurato_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ( ! [E] : ( v7_ordinal1(E) => k1_funct_1(D,E) = k3_xboole_0(k1_funct_1(B,E),k1_funct_1(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))) ) ) ) ) ) )).
fof(t19_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m2_finseq_1(E,D) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,D,C,B) & m2_finseq_1(F,k3_finseq_2(D)) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,D,B,C) & m2_finseq_1(G,k3_finseq_2(D)) ) => ( G = k4_matrix_0(D,F) => ( ( B = k5_numbers & C != k5_numbers ) | k3_laplace(A,C,B,D,F,E) = k4_matrix_0(D,k3_matrix11(A,B,C,D,G,E)) ) ) ) ) ) ) ) ) ) )).
fof(t19_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t19_latsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t19_lattice2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t19_lattice4,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t19_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(t19_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & v2_lattice6(A) & l3_lattices(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(t19_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m1_lattice5(D,A,B,C) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t19_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_lattices(A,k7_lattices(A,B),B) = k6_lattices(A) ) ) )).
fof(t19_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( ( v4_lexbfs(B,A) & m1_lexbfs(B,A) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t19_lfuzzy_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_lfuzzy_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t19_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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,k1_fuzzy_4(A,A,B)),A) ) ) )).
fof(t19_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_limfunc1(A) & v2_comseq_2(B) ) => v2_limfunc1(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) ) ) )).
fof(t19_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r5_limfunc2(B,A) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & v2_seq_2(k2_partfun1(k1_numbers,k1_numbers,C,k2_rcomp_1(A,k2_xcmplx_0(A,D)))) ) ) | r5_limfunc2(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t19_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t19_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(k6_xcmplx_0(A,D),A))) & r1_xxreal_0(k1_limfunc2(B,A),k1_funct_1(B,E)) ) ) ) ) | r2_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t19_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) )).
fof(t19_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( 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))) ) ) ) ) )).
fof(t19_lopban_1,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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)))) ) ) ) )).
fof(t19_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_lopban_2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_lopban_2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_lopban_2(A))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( 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] : ( 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 ) ) ) ) ) ) ) )).
fof(t19_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v1_xreal_0(C) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k1_bhsp_4(A,k5_normsp_1(A,B,C)),k5_normsp_1(A,k1_bhsp_4(A,B),C)) ) ) ) )).
fof(t19_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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),k7_xcmplx_0(1,k2_newton(B))) = k9_nat_1(u1_struct_0(A),k1_bhsp_4(A,k6_lopban_4(B,A,C,D)),B) ) ) ) ) ) )).
fof(t19_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(t19_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(k14_lpspacc1(A,B,C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k14_lpspacc1(A,B,C))) => ( ( D = F & E = G ) => k2_valued_1(A,k2_numbers,k2_numbers,D,E) = k3_rlvect_1(k14_lpspacc1(A,B,C),F,G) ) ) ) ) ) ) ) ) )).
fof(t19_lpspace1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_rfunct_3(D,C,k1_numbers,k3_rfunct_3(C,k1_numbers)) => k1_binop_1(k13_rfunct_3(C),k1_binop_1(k4_lpspace1(C),A,D),k1_binop_1(k4_lpspace1(C),B,D)) = k1_binop_1(k4_lpspace1(C),k2_xcmplx_0(A,B),D) ) ) ) ) )).
fof(t19_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(D,k5_numbers) & ~ r2_relset_1(A,k1_numbers,k26_valued_1(A,k1_numbers,k2_mesfun6c(D,A,k56_valued_1(A,k1_numbers,B)),k2_power(C,D)),k2_mesfun6c(D,A,k26_valued_1(A,k1_numbers,k56_valued_1(A,k1_numbers,B),C))) ) ) ) ) ) )).
fof(t19_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(D),k1_domain_1(k4_ordinal1,k1_hilbert1,C,k3_hilbert1(k4_hilbert1(A,B),k5_ltlaxio1(k2_ltlaxio1(B),k2_ltlaxio1(k4_ltlaxio1(A,k4_hilbert1(A,B))))))) = 1 ) ) ) ) )).
fof(t19_ltlaxio2,axiom,( ! [A] : ( m2_finseq_1(A,k1_hilbert1) => ! [B] : ( ( 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),k7_partfun1(k1_hilbert1,k2_ltlaxio2(A),k3_finseq_1(k2_ltlaxio2(A)))) = 1 <=> ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(A)) => k3_funct_2(k1_hilbert1,k6_margrel1,k12_ltlaxio1(B),k7_partfun1(k1_hilbert1,A,C)) = 1 ) ) ) ) ) )).
fof(t19_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_hilbert1)) => ( r2_hidden(k3_hilbert1(A,B),k5_ltlaxio3(C)) => ( r2_hidden(A,k5_ltlaxio3(C)) & r2_hidden(B,k5_ltlaxio3(C)) ) ) ) ) ) )).
fof(t19_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ( ( r2_hidden(B,k9_ltlaxio4(A)) & r2_hidden(C,k8_ltlaxio4(A)) ) => r1_ltlaxio4(C,B) ) ) ) ) )).
fof(t19_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t19_margrel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t19_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t19_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( v1_matrix10(B) & v2_matrix10(C) & r1_matrix10(k3_matrix10(A,B),k3_matrix10(A,C)) ) => v2_matrix10(k4_matrix10(A,B,C)) ) ) ) ) )).
fof(t19_matrix11,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,k2_xboole_0(B,k1_tarski(A)),k2_xboole_0(B,k1_tarski(A))) & v3_funct_2(E,k2_xboole_0(B,k1_tarski(A)),k2_xboole_0(B,k1_tarski(A))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k2_xboole_0(B,k1_tarski(A)),k2_xboole_0(B,k1_tarski(A))))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k2_xboole_0(B,k1_tarski(A)),k2_xboole_0(B,k1_tarski(A))) & v3_funct_2(F,k2_xboole_0(B,k1_tarski(A)),k2_xboole_0(B,k1_tarski(A))) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k2_xboole_0(B,k1_tarski(A)),k2_xboole_0(B,k1_tarski(A))))) ) => ( ( k2_partfun1(k2_xboole_0(B,k1_tarski(A)),k2_xboole_0(B,k1_tarski(A)),E,B) = C & k2_partfun1(k2_xboole_0(B,k1_tarski(A)),k2_xboole_0(B,k1_tarski(A)),F,B) = D & k1_funct_1(E,A) = A & k1_funct_1(F,A) = A ) => ( k2_partfun1(k2_xboole_0(B,k1_tarski(A)),k2_xboole_0(B,k1_tarski(A)),k1_partfun1(k2_xboole_0(B,k1_tarski(A)),k2_xboole_0(B,k1_tarski(A)),k2_xboole_0(B,k1_tarski(A)),k2_xboole_0(B,k1_tarski(A)),F,E),B) = k1_partfun1(B,B,B,B,D,C) & k1_funct_1(k1_partfun1(k2_xboole_0(B,k1_tarski(A)),k2_xboole_0(B,k1_tarski(A)),k2_xboole_0(B,k1_tarski(A)),k2_xboole_0(B,k1_tarski(A)),F,E),A) = A ) ) ) ) ) ) )).
fof(t19_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(C),B,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(C))) ) => ( r2_hidden(A,k4_finseq_1(k3_matrix_1(C,B))) => ( r1_xxreal_0(B,k5_numbers) | k4_matrix_3(C,E,k5_matrix12(B,B,C,k3_matrix_1(C,B),A,D)) = k5_matrix12(B,B,C,E,A,D) ) ) ) ) ) ) ) )).
fof(t19_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(A)) ) => ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(C,k4_ordinal1)) => ! [F] : ( m2_finseq_2(F,k4_ordinal1,k4_finseq_2(B,k4_ordinal1)) => ( r1_tarski(k2_zfmisc_1(k10_xtuple_0(E),k10_xtuple_0(F)),k2_matrix_0(D)) => ( ( B = k5_numbers & C != k5_numbers ) | k1_matrix13(A,D,C,B,E,F) = k4_matrix_0(A,k1_matrix13(A,k4_matrix_0(A,D),B,C,F,E)) ) ) ) ) ) ) ) ) )).
fof(t19_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v1_matrix_6(C,A,B) <=> ? [D] : ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) & k4_matrix_3(B,D,C) = k3_matrix_1(B,A) & k4_matrix_3(B,C,D) = k3_matrix_1(B,A) ) ) ) ) ) )).
fof(t19_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,D,C,B) & m2_finseq_1(E,k3_finseq_2(D)) ) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,D,C,A) & m2_finseq_1(F,k3_finseq_2(D)) ) => ( k6_matrix13(D,k1_matrix15(D,C,B,A,E,F),k2_finseq_1(C),k2_finseq_1(k1_matrix_0(E))) = E & k6_matrix13(D,k1_matrix15(D,C,B,A,E,F),k2_finseq_1(C),k7_subset_1(k4_ordinal1,k2_finseq_1(k2_xcmplx_0(k1_matrix_0(E),k1_matrix_0(F))),k2_finseq_1(k1_matrix_0(E)))) = F ) ) ) ) ) ) ) )).
fof(t19_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( ~ v1_xboole_0(F) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,F,D,D) & m2_finseq_1(G,k3_finseq_2(F)) ) => ( ( v3_matrix16(G,F) & r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k2_finseq_1(D),k2_finseq_1(D))) & C = k2_xcmplx_0(A,1) & E = k2_xcmplx_0(B,1) ) => ( r1_xxreal_0(D,A) | r1_xxreal_0(D,B) | k3_matrix_0(F,G,A,B) = k3_matrix_0(F,G,C,E) ) ) ) ) ) ) ) ) ) )).
fof(t19_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ( v1_matrix_0(k2_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),k2_finseq_4(A,B,C),k2_finseq_4(A,D,E))) & v2_matrix_0(k2_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),k2_finseq_4(A,B,C),k2_finseq_4(A,D,E)),A,2,2) & m2_finseq_1(k2_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),k2_finseq_4(A,B,C),k2_finseq_4(A,D,E)),k3_finseq_2(A)) ) ) ) ) ) ) )).
fof(t19_matrix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => k4_matrix_3(B,C,k3_matrix_1(B,A)) = C ) ) ) )).
fof(t19_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ! [E] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(D) & k1_matrix_0(D) = k1_matrix_0(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) ) ) ) ) ) ) )).
fof(t19_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => k3_matrix_5(A,k8_matrix_5(k3_finseq_1(A),k1_matrix_0(A))) = A ) )).
fof(t19_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( C = k4_matrix_3(B,D,C) & v1_matrix_6(C,A,B) ) => r1_matrix_6(A,B,C,D) ) ) ) ) ) )).
fof(t19_matrix_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t19_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_6(C,A,B) & k4_matrix_3(B,C,D) = k4_matrix_3(B,C,E) ) => D = E ) ) ) ) ) ) )).
fof(t19_matrix_9,axiom,( k3_matrix_2(3) = k4_enumset1(k3_finseq_4(k4_ordinal1,1,2,3),k3_finseq_4(k4_ordinal1,3,2,1),k3_finseq_4(k4_ordinal1,1,3,2),k3_finseq_4(k4_ordinal1,2,3,1),k3_finseq_4(k4_ordinal1,2,1,3),k3_finseq_4(k4_ordinal1,3,1,2)) )).
fof(t19_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => k11_matrixj1(A,k4_matrixj1(A,B)) = k9_finseq_1(k1_matrix_0(B)) ) ) )).
fof(t19_matrixj2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( ~ 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] : ( ( ~ 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] : ( m1_vectsp_4(E,B,C) => ! [F] : ( m1_vectsp_4(F,B,C) => ! [G] : ( m1_vectsp_4(G,B,D) => ! [H] : ( m1_vectsp_4(H,B,D) => ! [I] : ( m1_matrlin(I,B,C) => ! [J] : ( m2_finseq_1(J,u1_struct_0(D)) => ! [K] : ( m1_matrlin(K,B,E) => ! [L] : ( m1_matrlin(L,B,F) => ! [M] : ( m2_finseq_1(M,u1_struct_0(G)) => ! [N] : ( m2_finseq_1(N,u1_struct_0(H)) => ! [O] : ( ( v1_matrix_0(O) & v2_matrix_0(O,u1_struct_0(B),k3_finseq_1(I),k3_finseq_1(J)) & m2_finseq_1(O,k3_finseq_2(u1_struct_0(B))) ) => ! [P] : ( ( v1_matrix_0(P) & v2_matrix_0(P,u1_struct_0(B),k3_finseq_1(K),k3_finseq_1(M)) & m2_finseq_1(P,k3_finseq_2(u1_struct_0(B))) ) => ! [Q] : ( ( v1_matrix_0(Q) & v2_matrix_0(Q,u1_struct_0(B),k3_finseq_1(L),k3_finseq_1(N)) & m2_finseq_1(Q,k3_finseq_2(u1_struct_0(B))) ) => ( ( 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_0(P) = k3_finseq_1(M) & k1_matrix_0(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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t19_matrixr1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,k1_matrix_0(D)) ) => k8_matrix_0(u1_struct_0(B),k6_matrix_3(B,D,C),A) = k10_fvsum_1(k3_finseq_1(D),B,k8_matrix_0(u1_struct_0(B),D,A),C) ) ) ) ) ) )).
fof(t19_matrixr2,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( k1_matrix_0(B) = k3_finseq_1(C) => ( r1_xxreal_0(k3_finseq_1(B),k5_numbers) | r1_xxreal_0(k3_finseq_1(C),k5_numbers) | k4_matrix_3(A,B,k2_matrix_3(A,C)) = k2_matrix_3(A,k4_matrix_3(A,B,C)) ) ) ) ) ) )).
fof(t19_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( m1_vectsp_6(E,A,B) => ! [F] : ( ( 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),k4_ordinal1,u1_struct_0(B),F,C) => k3_vectsp_6(A,B,D,E) = k1_partfun1(k9_xtuple_0(C),k9_xtuple_0(C),k4_ordinal1,u1_struct_0(B),F,k3_vectsp_6(A,B,C,E)) ) ) ) ) ) ) ) )).
fof(t19_matrlin2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( ~ 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] : ( 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)) = k7_matrix_0(u1_struct_0(B),k3_matrix_1(B,k3_finseq_1(D)),A) ) ) ) ) ) )).
fof(t19_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t19_matrprob,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( m2_finseq_1(E,A) => ! [F] : ( m2_finseq_1(F,A) => ~ ( k3_finseq_1(E) = D & k3_finseq_1(F) = D & ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,A,C,D) & m2_finseq_1(G,k3_finseq_2(A)) ) => ? [H] : ( v7_ordinal1(H) & r2_hidden(H,k2_finseq_1(C)) & ~ ( ( 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 ) ) ) ) ) ) ) ) ) ) ) )).
fof(t19_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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,k3_matrix_1(B,A))) = A ) ) )).
fof(t19_matrtop2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ~ ( 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 ) ) ) ) ) )).
fof(t19_matrtop3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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) & k1_matrix_6(D,k2_vectsp_1,k2_matrtop3(D,A,B,C)) = k2_matrtop3(D,k4_xcmplx_0(A),B,C) ) ) ) ) ) ) ) )).
fof(t19_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t19_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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))) ) ) )).
fof(t19_mcart_1,axiom,( ! [A] : ~ ( A != k1_xboole_0 & ! [B] : ~ ( r2_hidden(B,A) & ! [C] : ! [D] : ! [E] : ~ ( ( r2_hidden(C,A) | r2_hidden(D,A) ) & B = k3_xtuple_0(C,D,E) ) ) ) )).
fof(t19_measure1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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,k5_numbers) = B & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ~ r1_xxreal_0(E,k5_numbers) => k1_prob_2(A,k9_setfam_1(A),D,E) = C ) ) ) ) ) )).
fof(t19_measure2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( k1_funct_1(B,k5_numbers) = k1_funct_1(A,k5_numbers) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( k1_funct_1(B,k1_nat_1(C,1)) = k6_subset_1(k1_funct_1(A,k1_nat_1(C,1)),k1_funct_1(A,C)) & r1_tarski(k1_funct_1(A,C),k1_funct_1(A,k1_nat_1(C,1))) ) ) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ~ r1_xxreal_0(D,C) => r1_xboole_0(k1_funct_1(B,C),k1_funct_1(B,D)) ) ) ) ) ) ) )).
fof(t19_measure3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ! [E] : ( ( r2_hidden(D,B) & r2_hidden(E,B) ) => ! [F] : ( m1_measure3(F,A,B,C) => ! [G] : ( 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) ) ) ) ) ) ) )).
fof(t19_measure6,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t19_measure8,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_measure4(C,A) => ( ! [D] : ( 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)) ) ) ) )).
fof(t19_member_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k5_member_1(k1_tarski(A)) = k1_tarski(k4_xcmplx_0(A)) ) )).
fof(t19_membered,axiom,( ! [A] : ! [B] : ( v1_membered(B) => ( r1_tarski(A,B) => v1_membered(A) ) ) )).
fof(t19_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_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)) ) ) ) ) )).
fof(t19_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(2))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k15_euclid(2))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k15_euclid(2))) => ! [J] : ( v1_xreal_0(J) => ! [K] : ( v1_xreal_0(K) => ! [L] : ( v1_xreal_0(L) => ( ( D = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),B,k6_xcmplx_0(1,J)),k1_rlvect_1(k15_euclid(2),C,J)) & E = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),C,k6_xcmplx_0(1,K)),k1_rlvect_1(k15_euclid(2),A,K)) & F = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),A,k6_xcmplx_0(1,L)),k1_rlvect_1(k15_euclid(2),B,L)) & r1_euclid_6(A,D,I) & r1_euclid_6(B,E,I) & r1_euclid_6(B,E,G) & r1_euclid_6(C,F,G) & r1_euclid_6(A,D,H) & r1_euclid_6(C,F,H) ) => ( r1_euclid_6(A,B,C) | J = 1 | K = 1 | L = 1 | ( k3_xcmplx_0(k3_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(1,K),k3_xcmplx_0(J,K)),k2_xcmplx_0(k6_xcmplx_0(1,J),k3_xcmplx_0(L,J))),k2_xcmplx_0(k6_xcmplx_0(1,L),k3_xcmplx_0(K,L))) != k5_numbers & k1_euclid_6(G,H,I) = k3_xcmplx_0(k7_xcmplx_0(k1_square_1(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(K,L),J),k3_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(1,K),k6_xcmplx_0(1,L)),k6_xcmplx_0(1,J)))),k3_xcmplx_0(k3_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(1,K),k3_xcmplx_0(J,K)),k2_xcmplx_0(k6_xcmplx_0(1,J),k3_xcmplx_0(L,J))),k2_xcmplx_0(k6_xcmplx_0(1,L),k3_xcmplx_0(K,L)))),k1_euclid_6(A,B,C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t19_mesfun10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & v1_mesfunc8(B,A,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,C,k6_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,k6_numbers))) ) => ! [E] : ( m1_subset_1(E,C) => ( ( E = k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers)) & ! [F] : ( v7_ordinal1(F) => r1_mesfunc1(A,C,k4_mesfunc5(A,k6_numbers,B,F),E) ) & v1_mesfun10(B,A) & ! [F] : ( 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] : ( v7_ordinal1(F) => r1_mesfunc5(A,C,D,k4_mesfunc5(A,k6_numbers,B,F)) ) & r1_mesfunc5(A,C,D,k7_mesfunc8(A,B)) & ? [F] : ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k6_numbers) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) & ! [G] : ( v7_ordinal1(G) => k12_supinf_2(F,G) = k7_mesfunc5(A,C,D,k4_mesfunc5(A,k6_numbers,B,G)) ) & v10_mesfunc5(F) & k2_mesfunc5(F) = k7_mesfunc5(A,C,D,k7_mesfunc8(A,B)) ) ) ) ) ) ) ) ) ) )).
fof(t19_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( k12_supinf_2(C,E) = k5_numbers => ( ! [F] : ( 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,k6_numbers,D,E)) ) ) ) ) ) ) ) )).
fof(t19_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & v1_mesfunc8(C,A,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( ( k1_relset_1(A,k4_mesfunc5(A,k1_numbers,C,k5_numbers)) = D & ! [E] : ( v7_ordinal1(E) => r1_mesfunc6(A,B,k4_mesfunc5(A,k1_numbers,C,E),D) ) ) => r1_mesfunc1(A,B,k6_mesfun7c(A,C),D) ) ) ) ) ) )).
fof(t19_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( ! [E] : ( v7_ordinal1(E) => r3_mesfunc6(A,B,C,k4_mesfunc5(A,k1_numbers,D,E)) ) => ! [E] : ( v7_ordinal1(E) => r3_mesfunc6(A,B,C,k4_mesfunc5(A,k1_numbers,k2_mesfun9c(A,D),E)) ) ) ) ) ) ) )).
fof(t19_mesfunc1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ! [F] : ( v1_xreal_0(F) => ( ! [G] : ( m1_subset_1(G,k4_ordinal1) => k9_nat_1(B,C,G) = k9_subset_1(A,E,k17_mesfunc1(A,D,k6_xcmplx_0(F,k2_extreal1(1,k1_nat_1(G,1))))) ) => k9_subset_1(A,E,k18_mesfunc1(A,D,F)) = k1_measure2(A,B,k1_measure3(A,B,C)) ) ) ) ) ) )).
fof(t19_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( 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 ) ) ) ) )).
fof(t19_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( v1_xreal_0(F) => ( ( 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) ) ) ) ) ) ) ) )).
fof(t19_mesfunc7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_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))) ) ) ) ) )).
fof(t19_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [D] : ( ( r1_tarski(D,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers))) & ! [E] : ( v7_ordinal1(E) => r2_relset_1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,C,E),k2_partfun1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,B,E),D)) ) & ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,D) => v10_mesfunc5(k3_mesfunc5(A,B,E)) ) ) ) => r2_relset_1(A,k6_numbers,k2_partfun1(A,k6_numbers,k7_mesfunc8(A,B),D),k7_mesfunc8(A,C)) ) ) ) ) )).
fof(t19_metric_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_metric_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k10_metric_1(B,C,A) = a_3_5_metric_1(A,B,C) ) ) ) )).
fof(t19_metric_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) & A = k6_domain_1(u1_struct_0(B),C) ) ) ) )).
fof(t19_metric_3,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers)) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k1_numbers,k1_numbers)) => ( k2_binop_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers,k16_metric_3,A,B) = k5_numbers <=> A = B ) ) ) )).
fof(t19_metric_6,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r1_metric_6(A,C,B) <=> ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t19_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_finset_1(B) & v1_card_1(B) ) => ( r1_ordinal1(k2_waybel23(A),B) <=> ! [C] : ( 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) ) ) ) ) ) )).
fof(t19_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t19_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t19_midsp_2,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & l1_midsp_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t19_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_nat_1(A,2)) ) => ! [C] : ( ( v4_midsp_2(C,B) & l1_midsp_2(C,B) ) => ( v2_midsp_3(B,A) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m2_finseq_2(F,u1_struct_0(u1_midsp_2(B,C)),k4_finseq_2(k1_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) ) ) ) ) ) ) ) )).
fof(t19_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( ( r1_relset_1(A,A,E,F) & r1_tarski(B,C) & r1_relset_1(A,A,D,G) ) => r1_tarski(k6_mmlquery(A,G,B,E),k6_mmlquery(A,D,C,F)) ) ) ) ) ) ) ) )).
fof(t19_mod_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => m1_subset_1(k1_enumset1(B,C,D),A) ) ) ) ) )).
fof(t19_mod_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ~ ( k1_mod_3(A,B,C) = B & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ~ ( r1_tarski(D,C) & v1_mod_3(D,A,B) ) ) ) ) ) ) )).
fof(t19_mod_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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)) ) ) ) )).
fof(t19_modal_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => ! [C] : ( m1_trees_1(C,A) => ( ( B = k14_trees_3(k5_numbers) & C = k14_trees_3(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),k14_trees_3(k5_numbers),k4_trees_1(A,B)),k14_trees_3(1),k4_trees_1(A,C)) ) ) ) ) )).
fof(t19_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_partfun1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(k30_modelc_1(B))) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t19_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ~ ( v2_modelc_2(A) & r1_modelc_2(B,A) ) ) ) )).
fof(t19_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_3(B,A) & l1_modelc_3(B,A) ) => ! [C] : ( ( v1_modelc_3(C,A) & l1_modelc_3(C,A) ) => ( r2_modelc_3(A,B,C) => r1_xxreal_0(k18_modelc_3(A,u2_modelc_3(A,C)),k6_xcmplx_0(k18_modelc_3(A,u2_modelc_3(A,B)),1)) ) ) ) ) )).
fof(t19_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( ! [C] : ( ( 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) ) ) ) )).
fof(t19_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t19_monoid_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(t19_morph_01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( ( ~ 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))) ) ) ) )).
fof(t19_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v3_msualg_1(B,A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ? [C] : ( v3_msualg_1(C,A) & v4_msualg_1(C,A) & v2_msafree(C,A) & l3_msualg_1(C,A) & ? [D] : ( 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 ) ) ) ) )).
fof(t19_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) ) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t19_msafree4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,C) => m3_pboole(k2_funct_6(D),A,C) ) ) ) )).
fof(t19_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( l3_msualg_1(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) )).
fof(t19_msscyc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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] : ( m1_subset_1(D,u4_struct_0(A)) => k1_funct_1(C,k1_xboole_0) != k4_tarski(D,u1_struct_0(A)) ) ) ) ) ) )).
fof(t19_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( ( v2_relat_1(C) & v2_finset_1(k6_pboole(A,B,C)) ) => v2_finset_1(B) ) ) ) )).
fof(t19_mssublat,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v13_struct_0(A,1) & v5_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & m1_msualg_2(C,A,B) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(t19_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( 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)) ) ) ) ) )).
fof(t19_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t19_msualg_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t19_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_rewrite1(k3_msualg_6(A),C,D) => ! [F] : ( m2_msualg_6(F,A,B,C,D) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t19_msualg_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m2_nat_lat(B,A) => ( v2_msualg_7(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => k15_lattice3(A,C) = k15_lattice3(B,D) ) ) ) ) ) ) )).
fof(t19_msualg_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t19_msualg_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( m2_pboole(E,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [F] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t19_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(t19_mycielsk,axiom,( ! [A] : ( ( v1_necklace(A) & l1_orders_2(A) ) => ! [B] : ( ( 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)))) ) ) ) )).
fof(t19_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v9_pre_topc(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( v3_pre_topc(C,A) & r2_hidden(D,C) & ! [E] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t19_nagata_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ( v9_pre_topc(A) & v7_pre_topc(A) & ? [B] : ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) & v6_nagata_1(B,A) ) ) <=> v3_pcomps_1(A) ) ) )).
fof(t19_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(k2_xcmplx_0(A,B),A) <=> r1_xxreal_0(1,B) ) ) ) )).
fof(t19_nat_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ~ ( A != 1 & r1_xxreal_0(A,1) ) ) )).
fof(t19_nat_3,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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(k22_pre_poly(A,B),k22_pre_poly(A,C)) => k8_nat_3(A,k11_pre_poly(A,B,C)) = k3_xcmplx_0(k8_nat_3(A,B),k8_nat_3(A,C)) ) ) ) )).
fof(t19_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( v1_int_2(B) => k3_moebius1(k1_newton(B,A)) = a_2_0_nat_5(A,B) ) ) ) )).
fof(t19_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( k4_nat_d(A,C) = k5_numbers => k3_nat_d(k2_xcmplx_0(A,B),C) = k1_nat_1(k3_nat_d(A,C),k3_nat_d(B,C)) ) ) ) ) )).
fof(t19_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t19_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) => ! [D] : ( 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] : ( m1_ncfcont1(E,A,k7_partfun1(u1_struct_0(A),C,D)) => ? [F] : ( m1_nfcont_1(F,B,D) & r1_tarski(k7_relset_1(u1_struct_0(B),u1_struct_0(A),C,F),E) ) ) ) ) ) ) ) ) )).
fof(t19_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t19_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( 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) ) ) ) ) ) ) ) ) )).
fof(t19_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [C] : ( v1_xreal_0(C) => ( r1_ndiff_4(A,B,C) => r1_nfcont_4(A,B,C) ) ) ) ) )).
fof(t19_neckla_3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( 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))) ) ) )).
fof(t19_necklace,axiom,( ! [A] : ( v7_ordinal1(A) => u1_struct_0(k4_necklace(A)) = A ) )).
fof(t19_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t19_newton,axiom,( ! [A] : ( v7_ordinal1(A) => k3_newton(k5_numbers,A) = 1 ) )).
fof(t19_nfcont_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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) <=> ( r1_tarski(A,k1_relset_1(u1_struct_0(B),D)) & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( v1_xreal_0(F) => ~ ( r2_hidden(E,A) & ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( v1_xreal_0(G) => ~ ( ~ r1_xxreal_0(G,k5_numbers) & ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ~ ( r2_hidden(H,A) & ~ r1_xxreal_0(G,k2_normsp_0(B,k5_algstr_0(B,H,E))) & r1_xxreal_0(F,k2_normsp_0(C,k5_algstr_0(C,k7_partfun1(u1_struct_0(C),D,H),k7_partfun1(u1_struct_0(C),D,E)))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t19_nfcont_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t19_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(k4_real_ns1(A))) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t19_normform,axiom,( ! [A] : 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)) )).
fof(t19_normsp_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v3_normsp_1(B,A) & v3_normsp_1(C,A) ) => v3_normsp_1(k2_normsp_1(A,B,C),A) ) ) ) ) )).
fof(t19_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t19_numbers,axiom,( r1_tarski(k4_ordinal1,k1_numbers) )).
fof(t19_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t19_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ~ r3_lattices(A,C,B) => r2_hidden(k2_filter_0(A,C),k7_subset_1(k1_zfmisc_1(u1_struct_0(A)),k10_openlatt(A,C),k10_openlatt(A,B))) ) ) ) ) )).
fof(t19_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(t19_ordeq_01,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(k5_ordeq_01(B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_rsspace4(B,C))) => ( E = D => k1_rlvect_1(k5_ordeq_01(B,C),D,A) = k1_rlvect_1(k9_rsspace4(B,C),E,A) ) ) ) ) ) ) )).
fof(t19_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v2_wellord1(A) => ( v1_orders_1(A) & v2_orders_1(A) & v3_orders_1(A) ) ) ) )).
fof(t19_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ~ r2_hidden(B,k1_orders_2(A,k6_domain_1(u1_struct_0(A),B))) ) ) )).
fof(t19_ordinal1,axiom,( ! [A] : ( ! [B] : ( r2_hidden(B,A) => v3_ordinal1(B) ) => v3_ordinal1(k3_tarski(A)) ) )).
fof(t19_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( r2_hidden(A,B) => r2_hidden(A,k3_ordinal2(B)) ) ) )).
fof(t19_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t19_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( v3_ordinal1(B) => ( ! [C] : ( 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) ) ) ) ) )).
fof(t19_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => k1_ordinal5(A,3) = k12_ordinal2(A,k12_ordinal2(A,A)) ) )).
fof(t19_ordinal6,axiom,( ! [A] : ( v1_ordinal6(A) => k10_xtuple_0(k2_ordinal6(A)) = A ) )).
fof(t19_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( ~ r1_orders_2(B,D,C) => k1_ortsp_1(A,B,C,D,D) = k1_group_1(A) ) ) ) ) ) )).
fof(t19_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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] : ( 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] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t19_osalg_1,axiom,( ! [A] : ( ( ~ 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] : ( l3_msualg_1(B,A) => v12_osalg_1(B,A) ) ) )).
fof(t19_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_osalg_2(C,A,B) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t19_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t19_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_parsp_1(A,B,C,D,E) => r1_parsp_1(A,D,E,B,C) ) ) ) ) ) ) )).
fof(t19_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r1_parsp_2(A,F,B,C) & r1_parsp_2(A,F,B,D) & r1_parsp_2(A,F,C,E) ) => ( F = B | F = C | r1_parsp_1(A,B,C,D,E) ) ) ) ) ) ) ) ) )).
fof(t19_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) ) )).
fof(t19_partfun2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ( r2_relset_1(B,C,E,k3_partfun2(B,C,A,D)) <=> ( ! [F] : ( m1_subset_1(F,B) => ( r2_hidden(F,k1_relset_1(B,E)) <=> ( r2_hidden(F,k1_relset_1(B,D)) & r2_hidden(k7_partfun1(C,D,F),A) ) ) ) & ! [F] : ( m1_subset_1(F,B) => ( r2_hidden(F,k1_relset_1(B,E)) => k7_partfun1(C,E,F) = k7_partfun1(C,D,F) ) ) ) ) ) ) ) ) )).
fof(t19_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ! [D] : ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( 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) ) ) ) ) )).
fof(t19_partit_2,axiom,( k8_funct_5 = k1_tarski(k4_tarski(k1_xboole_0,k1_xboole_0)) )).
fof(t19_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r1_diraf(A,E,D,C) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_diraf(A,E,F,B) & r2_analoaf(A,C,B,D,F) ) ) ) ) ) ) ) ) )).
fof(t19_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t19_pcomps_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(t19_pcs_0,axiom,( ! [A] : ( ( v14_pcs_0(A) & l2_pcs_0(A) ) => ! [B] : ( ( v14_pcs_0(B) & l2_pcs_0(B) ) => ( r1_tsep_1(A,B) => v13_pcs_0(k19_pcs_0(A,B)) ) ) ) )).
fof(t19_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( ( 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) ) => k11_pdiff_1(A,1,B,E,D) = k9_finseq_1(k10_pdiff_1(A,B,C,D)) ) ) ) ) ) ) )).
fof(t19_pdiff_2,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(2)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t19_pdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(2)) => ! [C] : ( m1_rcomp_1(C,k3_funct_2(k1_euclid(2),k1_numbers,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] : ( ( v9_ordinal1(D) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,E) = k1_tarski(k3_funct_2(k1_euclid(2),k1_numbers,k1_pdiff_1(1,2),B)) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),C) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(2,1,k1_pdiff_3(2,2,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(2,1,k1_pdiff_3(2,2,A),B))))) & k4_pdiff_3(A,B) = k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(2,1,k1_pdiff_3(2,2,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(2,1,k1_pdiff_3(2,2,A),B))))) ) ) ) ) ) ) ) ) )).
fof(t19_pdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) => k10_pdiff_1(3,1,E,D) = k1_fdiff_1(k1_pdiff_2(3,1,E,D),A) ) ) ) ) ) ) )).
fof(t19_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( 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) ) ) ) )).
fof(t19_pdiff_6,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [D] : ( 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)))) ) ) ) ) ) ) )).
fof(t19_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,A) & C = k3_funct_2(k1_euclid(A),k1_numbers,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)),k5_real_1(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)),k5_real_1(C,B)) ) ) ) ) ) ) ) )).
fof(t19_pdiff_8,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k16_lopban_1(k4_real_ns1(A),k4_real_ns1(B)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k16_lopban_1(k4_real_ns1(A),k4_real_ns1(B)))) => ! [E] : ( v1_xreal_0(E) => ( ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( m1_subset_1(G,u1_struct_0(k16_lopban_1(k4_real_ns1(A),k4_real_ns1(1)))) => ! [H] : ( 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(k2_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(k2_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)),k3_xcmplx_0(B,E)) ) ) ) ) ) ) )).
fof(t19_pdiff_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k16_lopban_1(k4_real_ns1(1),k4_real_ns1(A)))) => ? [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(A))) & C = k1_funct_1(B,k12_finseq_1(k4_ordinal1,1)) & k2_normsp_0(k4_real_ns1(A),C) = k2_normsp_0(k16_lopban_1(k4_real_ns1(1),k4_real_ns1(A)),B) ) ) ) )).
fof(t19_pencil_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t19_pencil_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t19_pencil_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( 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,k1_funct_7(C,D,k1_funct_1(B,D))),1) ) ) ) ) ) )).
fof(t19_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( 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)) ) ) ) ) ) )).
fof(t19_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ v1_abian(A) & ~ v1_abian(B) & v1_abian(k3_xcmplx_0(A,B)) ) ) ) )).
fof(t19_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t19_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( m1_pnproc_1(C,A) => ! [D] : ( 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))) ) ) ) ) )).
fof(t19_polyalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_polyalg1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ~ ( v3_polyalg1(C,A,B) & ! [D] : ( ( v1_polyalg1(D,A) & m1_polyalg1(D,A,B) ) => u1_struct_0(D) != C ) ) ) ) ) )).
fof(t19_polyeq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( k4_polyeq_1(1,k5_numbers,A,B,C) = k5_numbers => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( C = k2_xcmplx_0(D,E) & k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,E),D),A) = k5_numbers & C != k2_xcmplx_0(k1_power(3,k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,2)),k3_square_1(k2_xcmplx_0(k7_xcmplx_0(k1_square_1(B),4),k1_newton(k7_xcmplx_0(A,3),3))))),k1_power(3,k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,2)),k3_square_1(k2_xcmplx_0(k7_xcmplx_0(k1_square_1(B),4),k1_newton(k7_xcmplx_0(A,3),3)))))) & C != k2_xcmplx_0(k1_power(3,k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,2)),k3_square_1(k2_xcmplx_0(k7_xcmplx_0(k1_square_1(B),4),k1_newton(k7_xcmplx_0(A,3),3))))),k1_power(3,k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,2)),k3_square_1(k2_xcmplx_0(k7_xcmplx_0(k1_square_1(B),4),k1_newton(k7_xcmplx_0(A,3),3)))))) & C != k2_xcmplx_0(k1_power(3,k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,2)),k3_square_1(k2_xcmplx_0(k7_xcmplx_0(k1_square_1(B),4),k1_newton(k7_xcmplx_0(A,3),3))))),k1_power(3,k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,2)),k3_square_1(k2_xcmplx_0(k7_xcmplx_0(k1_square_1(B),4),k1_newton(k7_xcmplx_0(A,3),3)))))) ) ) ) ) ) ) ) )).
fof(t19_polyeq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( k1_square_1(B) = A & r1_xxreal_0(k5_numbers,k4_complex1(A)) & B != k2_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(A),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A))))),2)),k3_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(A)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A))))),2)),k7_complex1)) & B != k2_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(A),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A))))),2))),k3_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(A)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A))))),2))),k7_complex1)) ) ) ) )).
fof(t19_polyeq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( k2_xcmplx_0(k3_xcmplx_0(C,k1_newton(A,F)),k3_xcmplx_0(D,k1_newton(B,F))) = E & k3_xcmplx_0(A,B) = k5_numbers & v1_abian(F) & r1_xxreal_0(1,F) & ~ r1_xxreal_0(k7_xcmplx_0(E,D),k5_numbers) & ~ r1_xxreal_0(k7_xcmplx_0(E,C),k5_numbers) & k3_xcmplx_0(C,D) != k5_numbers & ~ ( A = k5_numbers & B = k1_power(F,k7_xcmplx_0(E,D)) ) & ~ ( A = k5_numbers & B = k4_xcmplx_0(k1_power(F,k7_xcmplx_0(E,D))) ) & ~ ( A = k1_power(F,k7_xcmplx_0(E,C)) & B = k5_numbers ) & ~ ( A = k4_xcmplx_0(k1_power(F,k7_xcmplx_0(E,C))) & B = k5_numbers ) ) ) ) ) ) ) ) )).
fof(t19_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t19_polyform,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( m2_finseq_1(B,k4_numbers) => k16_rvsum_1(k6_polyform(k3_polyform(A),B)) = k2_xcmplx_0(A,k16_rvsum_1(B)) ) ) )).
fof(t19_polynom1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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))) ) ) )).
fof(t19_polynom3,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ r1_xxreal_0(k3_finseq_1(B),C) => k17_finseq_1(A,k1_nat_1(C,1),B) = k7_finseq_1(k17_finseq_1(A,C,B),k9_finseq_1(k1_funct_1(B,k1_nat_1(C,1)))) ) ) ) )).
fof(t19_polynom4,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(t19_polynom5,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k2_polynom5(A,B,k1_nat_1(C,1)),k13_polynom3(A,k2_polynom5(A,B,C),B)) ) ) ) )).
fof(t19_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ 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)),k8_polynom1(A,B)) ) )).
fof(t19_polynom8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t19_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => r1_tarski(k3_polynom1(k15_pre_poly(A),B,k5_polynom7(A,B,C,D)),k3_polynom1(k15_pre_poly(A),B,C)) ) ) ) ) )).
fof(t19_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) => ( v1_abian(B) | ( r1_xxreal_0(k1_power(B,A),k4_xcmplx_0(1)) & r1_xxreal_0(A,k1_power(B,A)) ) ) ) ) ) )).
fof(t19_pralg_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ! [E] : ( 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))) ) ) ) ) )).
fof(t19_pre_circ,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => k6_xcmplx_0(k5_card_1(A),1) = k7_nat_d(k5_card_1(A),1) ) )).
fof(t19_pre_ff,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( k3_pre_ff(D) = k1_nat_1(k2_nat_1(B,k3_pre_ff(k1_nat_1(k3_xcmplx_0(2,A),1))),k2_nat_1(C,k3_pre_ff(k1_nat_1(k1_nat_1(k3_xcmplx_0(2,A),1),1)))) => k3_pre_ff(D) = k1_nat_1(k2_nat_1(B,k3_pre_ff(A)),k2_nat_1(k2_xcmplx_0(C,B),k3_pre_ff(k1_nat_1(A,1)))) ) ) ) ) ) )).
fof(t19_pre_poly,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ( ( r2_hidden(D,B) & r3_orders_1(C,B) & ! [E] : ( 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 ) ) ) ) ) )).
fof(t19_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t19_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t19_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(1,B) ) => ( k1_newton(k2_prepower(B,A),B) = A & k2_prepower(B,k1_newton(A,B)) = A ) ) ) ) )).
fof(t19_prob_1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => m1_prob_1(k9_subset_1(A,C,D),A,B) ) ) ) )).
fof(t19_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m2_prob_1(E,A,B) => ( r1_prob_2(A,B,E,C,D) => r1_prob_2(A,B,E,D,C) ) ) ) ) ) ) )).
fof(t19_prob_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => r2_funct_2(k4_ordinal1,k9_setfam_1(A),k2_prob_3(A,k3_prob_3(A,B)),k2_prob_3(A,B)) ) )).
fof(t19_prob_4,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(C) => r2_funct_2(k4_ordinal1,k9_setfam_1(A),k2_prob_3(A,C),C) ) ) ) )).
fof(t19_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t19_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( ( r1_collsp(A,H,B,C) & r1_collsp(A,H,D,E) & r1_collsp(A,H,F,G) ) => ( r1_projdes1(A,B,D,F,H) | H = C | H = E | H = G | ( ~ r1_collsp(A,C,E,G) & ~ r1_projdes1(A,C,E,G,H) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t19_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u2_incsp_1(A)) => ! [F] : ( 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 ) ) ) ) ) ) ) )).
fof(t19_projred1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t19_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u1_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u1_incsp_1(A)) => ! [H] : ( m1_subset_1(H,u1_incsp_1(A)) => ! [I] : ( m1_subset_1(I,u1_incsp_1(A)) => ! [J] : ( m1_subset_1(J,u1_incsp_1(A)) => ! [K] : ( m1_subset_1(K,u2_incsp_1(A)) => ! [L] : ( m1_subset_1(L,u2_incsp_1(A)) => ! [M] : ( m1_subset_1(M,u2_incsp_1(A)) => ! [N] : ( m1_subset_1(N,u2_incsp_1(A)) => ! [O] : ( m1_subset_1(O,u2_incsp_1(A)) => ! [P] : ( m1_subset_1(P,u2_incsp_1(A)) => ! [Q] : ( m1_subset_1(Q,u2_incsp_1(A)) => ! [R] : ( m1_subset_1(R,u2_incsp_1(A)) => ( ( r4_incsp_1(A,k7_domain_1(u1_incsp_1(A),D,G),N) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),G,I,E),O) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),D,E,H),P) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),B,C,E),Q) & r4_incsp_1(A,k7_domain_1(u1_incsp_1(A),D,J),R) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),B,G,H),K) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),C,H,J),L) & r4_incsp_1(A,k8_domain_1(u1_incsp_1(A),G,J,F),M) & r1_incsp_1(A,F,Q) ) => ( r1_incsp_1(A,B,N) | r1_incsp_1(A,B,P) | r1_incsp_1(A,C,O) | r1_incsp_1(A,C,P) | r1_incsp_1(A,F,N) | r1_projred2(A,N,O,P) | B = C | C = F | ( ~ r1_incsp_1(A,C,R) & ~ r1_incsp_1(A,F,R) & N != R ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t19_prvect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) ) => ! [B] : ( m1_prvect_1(B,A) => ! [C] : ( m1_subset_1(C,k4_card_3(A)) => ( ! [D] : ( m2_subset_1(D,k4_ordinal1,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)) ) ) ) ) )).
fof(t19_prvect_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(k14_prvect_2(k10_finseq_1(A,B)))) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & C = k10_finseq_1(D,E) ) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(k14_prvect_2(k10_finseq_1(A,B)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_prvect_2(k10_finseq_1(A,B)))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( 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] : ( m1_subset_1(C,u1_struct_0(k14_prvect_2(k10_finseq_1(A,B)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_subset_1(C,u1_struct_0(k14_prvect_2(k10_finseq_1(A,B)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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] : ( m1_subset_1(C,u1_struct_0(k14_prvect_2(k10_finseq_1(A,B)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ~ ( C = k10_finseq_1(D,E) & ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(2)) => ~ ( F = k10_finseq_1(k2_normsp_0(A,D),k2_normsp_0(B,E)) & k2_normsp_0(k14_prvect_2(k10_finseq_1(A,B)),C) = k12_euclid(F) ) ) ) ) ) ) ) ) ) )).
fof(t19_pua2mss1,axiom,( ! [A] : ( ( v2_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [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),k7_pua2mss1(A,B),B) ) ) )).
fof(t19_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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 ) ) ) )).
fof(t19_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) != k5_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 ) ) ) ) )).
fof(t19_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t19_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t19_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => k3_qc_lang4(A,B,C) = a_3_0_qc_lang4(A,B,C) ) ) ) )).
fof(t19_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v10_lattices(A) & v4_lattice3(A) & v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t19_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => k24_quaterni(A) = k23_quaterni(k24_quaterni(k2_quatern2),A) ) )).
fof(t19_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k22_quaterni(k23_quaterni(k3_quatern2,A),k23_quaterni(A,k3_quatern2)) = k6_quaterni(k4_xcmplx_0(k3_xcmplx_0(2,k14_quaterni(A))),k3_xcmplx_0(2,k13_quaterni(A)),k5_numbers,k5_numbers) ) )).
fof(t19_quaterni,axiom,( k10_quaterni(k1_xcmplx_0,k11_quaterni) = k8_quaterni(k10_quaterni(k11_quaterni,k1_xcmplx_0)) )).
fof(t19_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(k1_quin_1(B,C,D),k5_numbers) & ~ ( ~ ( ~ r1_xxreal_0(k5_numbers,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(A)),k3_xcmplx_0(C,A)),D)) & r1_xxreal_0(k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B)),A) & r1_xxreal_0(A,k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B))) ) & ~ ( ~ ( r1_xxreal_0(k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B)),A) & r1_xxreal_0(A,k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B))) ) & r1_xxreal_0(k5_numbers,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(A)),k3_xcmplx_0(C,A)),D)) ) ) ) ) ) ) ) )).
fof(t19_quofield,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t19_radix_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t19_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t19_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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))) ) ) ) ) )).
fof(t19_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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 ) ) ) ) ) )).
fof(t19_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_random_1(C,A,B) => ! [D] : ( m1_random_1(D,A,B) => m1_random_1(k47_valued_1(A,k1_numbers,k1_numbers,C,D),A,B) ) ) ) ) )).
fof(t19_random_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( k1_funct_1(k5_random_3(A),k5_numbers) = k1_funct_1(A,k5_numbers) & k1_funct_1(k5_random_3(A),1) = k2_zfmisc_1(k1_funct_1(A,k5_numbers),k1_funct_1(A,1)) & k1_funct_1(k5_random_3(A),2) = k3_zfmisc_1(k1_funct_1(A,k5_numbers),k1_funct_1(A,1),k1_funct_1(A,2)) & k1_funct_1(k5_random_3(A),3) = k4_zfmisc_1(k1_funct_1(A,k5_numbers),k1_funct_1(A,1),k1_funct_1(A,2),k1_funct_1(A,3)) ) ) )).
fof(t19_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( 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))) ) ) ) ) ) )).
fof(t19_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ( ~ ( ~ r1_xxreal_0(1,k5_xcmplx_0(k1_rat_1(A))) & v1_int_1(A) ) & ~ ( ~ v1_int_1(A) & r1_xxreal_0(1,k5_xcmplx_0(k1_rat_1(A))) ) ) ) )).
fof(t19_ratfunc1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & l5_algstr_0(A) ) => ! [B] : ( m1_ratfunc1(B,A) => B = k3_ratfunc1(A,k4_ratfunc1(A,B),k5_ratfunc1(A,B)) ) ) )).
fof(t19_rcomp_1,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & r1_tarski(k2_rcomp_1(k6_xcmplx_0(B,C),k2_xcmplx_0(B,C)),A) ) ) ) ) ) )).
fof(t19_rcomp_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v5_xxreal_2(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ~ ( ~ r2_hidden(k3_seq_4(A),A) & ~ r2_hidden(k2_seq_4(A),A) & A != k2_rcomp_1(k3_seq_4(A),k2_seq_4(A)) ) ) )).
fof(t19_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( A != k5_numbers => B = k1_nat_1(k3_xcmplx_0(k9_nat_1(k4_ordinal1,k2_real_3(B,A),k5_numbers),A),k9_nat_1(k4_ordinal1,k1_real_3(B,A),k5_numbers)) ) ) ) )).
fof(t19_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( 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) ) ) ) )).
fof(t19_realset2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t19_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t19_rearran1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,k1_numbers))) ) => ! [E] : ( ( v1_rearran1(E) & v2_rearran1(E) & v3_rearran1(E,k1_zfmisc_1(B)) & m2_finseq_1(E,k1_zfmisc_1(B)) ) => ( ( v1_partfun1(D,C) & k5_card_1(B) = k5_card_1(C) ) => ( k20_rfunct_3(B,k15_valued_1(B,k1_numbers,k3_rearran1(C,B,E,D),A),B) = k20_rfunct_3(C,k15_valued_1(C,k1_numbers,D,A),C) & k21_rfunct_3(B,k15_valued_1(B,k1_numbers,k3_rearran1(C,B,E,D),A),B) = k21_rfunct_3(C,k15_valued_1(C,k1_numbers,D,A),C) ) ) ) ) ) ) ) )).
fof(t19_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => r1_tarski(k9_xtuple_0(k3_relat_1(A,B)),k9_xtuple_0(A)) ) ) )).
fof(t19_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,C))) => ( r1_tarski(A,B) => r2_relset_1(A,C,k5_relset_1(A,C,D,B),D) ) ) )).
fof(t19_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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) ) ) )).
fof(t19_revrot_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => k16_euclid(A) != k22_euclid(A) ) )).
fof(t19_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r1_rewrite1(A,B,C) => ( r2_hidden(B,k1_relat_1(A)) <=> r2_hidden(C,k1_relat_1(A)) ) ) ) )).
fof(t19_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t19_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(D)) => ! [F] : ( m1_subset_1(F,k8_afinsq_1(D)) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k8_afinsq_1(D))) => ! [H] : ( ( 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] : ( m1_subset_1(I,k8_afinsq_1(D)) => ( k1_flang_1(D,E,I) != F & k1_flang_1(D,F,I) != E ) ) ) ) ) ) ) ) ) )).
fof(t19_rfinseq,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( v8_valued_0(A) <=> ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r2_hidden(B,k4_finseq_1(A)) & r2_hidden(C,k4_finseq_1(A)) ) => ( r1_xxreal_0(C,B) | r1_xxreal_0(k1_funct_1(A,C),k1_funct_1(A,B)) ) ) ) ) ) ) )).
fof(t19_rfinseq2,axiom,( ! [A] : ( ( v1_integra2(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( ( v1_integra2(B) & m2_finseq_1(B,k1_numbers) ) => ( r2_classes1(A,B) => A = B ) ) ) )).
fof(t19_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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),k4_xcmplx_0(1)) ) ) )).
fof(t19_rfunct_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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)) & k2_seq_4(k7_relset_1(B,k1_numbers,C,A)) = k3_seq_4(k7_relset_1(B,k1_numbers,C,A)) ) => v3_funct_1(k2_partfun1(B,k1_numbers,C,A)) ) ) ) )).
fof(t19_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k14_rfunct_3(A,k6_finseq_1(k3_rfunct_3(A,k1_numbers))) = k7_funcop_1(k2_subset_1(A),k5_numbers) ) )).
fof(t19_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_seq_2(A) & v4_partfun3(A) ) => r1_xxreal_0(k5_numbers,k1_rinfsup1(A)) ) ) )).
fof(t19_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ~ ( v7_mesfunc5(A) & ! [B] : ( v7_ordinal1(B) => ~ v3_rinfsup2(k1_valued_0(k6_numbers,A,B)) ) ) ) )).
fof(t19_ring_1,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t19_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_ringcat1(A) ) => ! [B] : ( m3_ringcat1(B,k10_ringcat1(A)) => ! [C] : ( m3_ringcat1(C,k10_ringcat1(A)) => ~ ( k11_ringcat1(A,B) = k12_ringcat1(A,C) & ! [D] : ( m2_ringcat1(D,A) => ! [E] : ( m2_ringcat1(E,A) => ! [F] : ( m2_ringcat1(F,A) => ~ ( r1_ringcat1(D,E) & r1_ringcat1(E,F) & m1_ringcat1(B,E,F) & m1_ringcat1(C,D,E) ) ) ) ) ) ) ) ) )).
fof(t19_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t19_rlaffin2,axiom,( ! [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) ) => ! [B] : ( ( 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 ) ) ) )).
fof(t19_rlaffin3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_rlaffin1(C,k15_euclid(A)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [D] : ( m2_rlaffin3(D,k15_euclid(A),C) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( k8_matrix13(k2_vectsp_1,E) = A => ! [F] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t19_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => r1_struct_0(A,k4_struct_0(B)) ) ) )).
fof(t19_rlsub_2,axiom,( ! [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) ) => ( 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) ) ) )).
fof(t19_rltopsp1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t19_rlvect_1,axiom,( ! [A] : ( ( ~ 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) & v8_rlvect_1(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B = k4_algstr_0(A,B) => B = k4_struct_0(A) ) ) ) )).
fof(t19_rlvect_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k3_funct_2(u1_struct_0(A),k1_numbers,B,C) = k5_numbers <=> ~ r2_hidden(C,k3_rlvect_2(A,B)) ) ) ) ) )).
fof(t19_rlvect_3,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( B = u1_struct_0(A) => k1_rlvect_3(A,B) = A ) ) ) )).
fof(t19_rlvect_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( v1_rlvect_3(k7_domain_1(u1_struct_0(B),C,D),B) => ( C = D | A = k5_numbers | v1_rlvect_3(k7_domain_1(u1_struct_0(B),C,k1_rlvect_1(B,D,A)),B) ) ) ) ) ) ) )).
fof(t19_rlvect_5,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t19_rlvect_x,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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] : ( v1_int_1(E) & ? [F] : ( v1_int_1(F) & A = k3_rlvect_1(B,k1_rlvect_1(B,C,E),k1_rlvect_1(B,D,F)) ) ) ) ) ) ) )).
fof(t19_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => r1_struct_0(B,k4_struct_0(C)) ) ) ) )).
fof(t19_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( m1_rmod_2(E,A,B) => ( m1_rmod_2(C,A,E) => m1_rmod_2(k2_rmod_3(A,B,C,D),A,E) ) ) ) ) ) ) )).
fof(t19_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( m2_rmod_4(E,A,B,C) => ( r1_tarski(C,D) => m2_rmod_4(E,A,B,D) ) ) ) ) ) ) )).
fof(t19_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_robbins1(A,B,k6_lattices(A)) = k6_lattices(A) ) ) )).
fof(t19_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) )).
fof(t19_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_robbins1(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t19_robbins4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k2_robbins4)) => ! [B] : ( 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) = k5_numbers ) ) ) ) )).
fof(t19_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => k4_roughs_1(A,k1_struct_0(A)) = k1_xboole_0 ) )).
fof(t19_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t19_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_rsspace4(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_rsspace4(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_rsspace4(A,B))) => ! [F] : ( ( 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] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t19_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => m1_rusub_1(A,A) ) )).
fof(t19_rusub_2,axiom,( ! [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_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) ) ) )).
fof(t19_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rlvect_2(C,B) => ? [D] : ( 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) ) ) ) ) )).
fof(t19_rusub_4,axiom,( ! [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_bhsp_1(A) & v1_rusub_4(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( r1_xxreal_0(B,k1_rusub_4(A)) & v1_xboole_0(k2_rusub_4(A,B)) ) ) ) )).
fof(t19_rusub_5,axiom,( ! [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) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_rusub_4(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t19_rvsum_1,axiom,( k6_rvsum_1(k6_finseq_1(k1_numbers)) = k6_finseq_1(k1_numbers) )).
fof(t19_rvsum_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k2_numbers) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k2_numbers) ) => C = k8_rvsum_2(A,k4_rvsum_2(A,C,B),B) ) ) ) )).
fof(t19_scm_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( r1_tarski(k1_ordinal4(k5_afinsq_1(k6_ami_3(k10_ami_3(k5_numbers),k10_ami_3(1))),k5_afinsq_1(k2_compos_1(k1_ami_3))),A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( ( v5_memstr_0(D,k7_card_1(2),k1_ami_3,k5_numbers) & m1_scm_1(D,k6_afinsq_1(B,C)) ) => ( r1_extpro_1(k7_card_1(2),k1_ami_3,A,D) & k8_extpro_1(k7_card_1(2),k1_ami_3,A,D) = 1 & k1_funct_1(k6_extpro_1(k7_card_1(2),k1_ami_3,A,D),k10_ami_3(k5_numbers)) = k4_int_1(B,C) & k1_funct_1(k6_extpro_1(k7_card_1(2),k1_ami_3,A,D),k10_ami_3(1)) = k5_int_1(B,C) & ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_ami_3)) ) => ~ ( E != k10_ami_3(k5_numbers) & E != k10_ami_3(1) & k1_funct_1(k6_extpro_1(k7_card_1(2),k1_ami_3,A,D),E) != k1_funct_1(D,E) ) ) ) ) ) ) ) ) )).
fof(t19_scm_halt,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( m1_scmfsa_2(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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) ) ) ) ) ) )).
fof(t19_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,k4_ordinal1) => k4_sf_mastr(k1_scmfsa6a(A,B)) = k4_sf_mastr(A) ) ) )).
fof(t19_scmfsa10,axiom,( ! [A] : ( 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) ) ) )).
fof(t19_scmfsa6a,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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)) ) ) ) )).
fof(t19_scmfsa6b,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ~ r1_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_7(B,k5_memstr_0(k7_card_1(3),k1_scmfsa_2,A),k11_scmfsa_2(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,A))),A) ) ) )).
fof(t19_scmfsa7b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) <=> ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => r6_scmfsa7b(A,B,C) ) ) ) ) )).
fof(t19_scmfsa8a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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) ) ) )).
fof(t19_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & ~ v1_scmfsa_m(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( 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(k7_card_1(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),k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k5_card_1(B),k5_card_1(C)),3)))) ) ) ) ) ) ) ) )).
fof(t19_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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] : ( v7_ordinal1(E) => ( ( k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(B,D,C,A),E),C) = k5_numbers & k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(B,D,C,A),E),k4_scmfsa_2(k5_numbers)) = 1 ) => ( ( ~ ( r6_scmfsa7b(D,k1_scmfsa_m(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(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(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(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,k7_card_1(3),k1_scmfsa_2) ) | k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(B,D,C,A),k1_nat_1(E,1))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(D,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(B,D,C,A),E),k1_funct_4(A,k1_scmfsa_9(C,D)))) ) ) ) ) ) ) ) )).
fof(t19_scmfsa_1,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k4_scmfsa_1,k5_scmfsa_1))) => ! [B] : ( m2_subset_1(B,k1_scmfsa_1,k3_scmfsa_1) => ! [C] : ( m2_finseq_1(C,k4_numbers) => ! [D] : ( 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) ) ) ) ) )).
fof(t19_scmfsa_2,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( 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(C,B,A)) = 9 ) ) ) )).
fof(t19_scmfsa_m,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ( k1_funct_1(A,k4_scmfsa_2(k5_numbers)) = 1 => k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_m(A)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,A) ) ) )).
fof(t19_scmisort,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( v1_ami_2(B) & ~ v1_scmfsa_m(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ( ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ~ ( ~ r1_xxreal_0(k1_funct_1(C,B),k5_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)) ) ) ) )).
fof(t19_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmpds_2)) ) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t19_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) & v2_compos_1(B,k1_scmpds_2) ) => ! [C] : ( ( 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] : ( v7_ordinal1(D) => ~ ( 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) ) ) ) ) ) )).
fof(t19_scmpds_7,axiom,( ! [A] : ( ( 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] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( v7_ordinal1(E) => ( ( 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))) ) ) ) ) ) ) )).
fof(t19_scmpds_8,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( r1_xxreal_0(k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),F)),k5_numbers) => k6_scmpds_4(k2_scmpds_8(D,F,C),B,A) = k1_funct_4(B,k7_memstr_0(2,k1_scmpds_2,k1_nat_1(k5_card_1(C),2))) ) ) ) ) ) ) ) )).
fof(t19_scmyciel,axiom,( ! [A] : ! [B] : ( k1_card_1(k3_tarski(A)) = 1 => v2_scmyciel(A) ) )).
fof(t19_scpinvar,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( v1_int_1(C) => ! [D] : ( 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,k5_numbers) | r1_xxreal_0(D,k5_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) ) ) ) ) ) ) ) )).
fof(t19_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(t19_seq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k26_valued_1(k4_ordinal1,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C),A),k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,k26_valued_1(k4_ordinal1,k1_numbers,C,A))) ) ) ) )).
fof(t19_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(A) & v2_comseq_2(B) & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(k1_funct_1(A,D),k1_funct_1(C,D)) & r1_xxreal_0(k1_funct_1(C,D),k1_funct_1(B,D)) ) ) & k1_seq_2(A) = k1_seq_2(B) ) => v2_comseq_2(C) ) ) ) ) )).
fof(t19_seq_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(A) => ( ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & k9_nat_1(k1_numbers,B,D) != k9_nat_1(k1_numbers,A,D) ) ) | k1_seq_2(A) = k1_seq_2(B) ) ) ) ) )).
fof(t19_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( r2_seqfunc(A,B,C) <=> ( r1_seqfunc(A,k1_numbers,B,C) & ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,C) => v2_comseq_2(k10_seqfunc(A,B,D)) ) ) ) ) ) ) )).
fof(t19_seqm_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k1_valued_0(k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C),A) = k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k1_valued_0(k1_numbers,B,A),k1_valued_0(k1_numbers,C,A)) ) ) ) )).
fof(t19_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,B,C)) ) & v1_series_1(A) ) => ( ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & ~ r1_xxreal_0(k9_nat_1(k1_numbers,B,D),k9_nat_1(k1_numbers,A,D)) ) ) | v1_series_1(B) ) ) ) ) )).
fof(t19_series_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k2_xcmplx_0(A,B) = 1 => r1_xxreal_0(k7_xcmplx_0(1,2),k2_xcmplx_0(k1_square_1(A),k1_square_1(B))) ) ) ) )).
fof(t19_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => ! [D] : ( ( 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)))) ) ) ) ) )).
fof(t19_setfam_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_setfam_1(C,k2_tarski(A,B)) => ! [D] : ~ ( r2_hidden(D,C) & ~ r1_tarski(D,A) & ~ r1_tarski(D,B) ) ) )).
fof(t19_setlim_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(A,k1_funct_1(k2_setlim_1(B,C),D)) <=> ! [E] : ( v7_ordinal1(E) => r2_hidden(A,k1_funct_1(C,k2_xcmplx_0(D,E))) ) ) ) ) )).
fof(t19_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => k8_nat_1(k9_setfam_1(B),k8_setlim_2(B,D,C),A) = k8_setlim_2(B,k8_nat_1(k9_setfam_1(B),D,A),C) ) ) ) )).
fof(t19_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,k5_finsub_1(A)) => ! [E] : ( ( 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] : ( m1_subset_1(F,A) => ( r2_hidden(F,D) => k5_binop_1(B,C,k3_funct_2(A,B,E,F),k7_setwiseo(A,B,C,D,E)) = k7_setwiseo(A,B,C,D,E) ) ) ) ) ) ) ) ) )).
fof(t19_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k5_finsub_1(A)) => ! [D] : ( ( 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] : ( ( 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))) ) ) ) ) ) ) )).
fof(t19_sf_mastr,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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)) ) ) ) )).
fof(t19_sfmastr2,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) & v1_scmfsa7b(D) ) => ! [E] : ( v7_ordinal1(E) => ~ ( ( r1_sfmastr2(B,A,C,D) | v7_amistd_1(D,k7_card_1(3),k1_scmfsa_2) ) & ~ r1_xxreal_0(k1_funct_1(A,C),E) & ~ ( k1_funct_1(A,k4_scmfsa_2(k5_numbers)) != 1 & v1_scmfsa_m(C) ) & k11_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k3_sfmastr2(B,A,D,C),k1_nat_1(E,1)),k2_xboole_0(k2_sf_mastr(D),k3_scmfsa_2)) != k5_relat_1(k1_scmfsa6b(D,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(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)) ) ) ) ) ) ) )).
fof(t19_sfmastr3,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & ~ v1_scmfsa_m(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( ( k1_funct_1(A,k4_scmfsa_2(k5_numbers)) = 1 & r1_sfmastr3(F,B,C,D,E,A) ) => ! [G] : ( v7_ordinal1(G) => ( r1_xxreal_0(G,k2_xcmplx_0(k6_xcmplx_0(k1_funct_1(A,D),k1_funct_1(A,C)),1)) => ( k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k1_sfmastr3(F,B,C,D,E,A),G),k4_scmfsa_2(k5_numbers)) = 1 & ( ~ r4_scmfsa7b(E,B) => ( k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(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(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(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(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(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) ) ) ) ) ) ) ) ) ) ) )).
fof(t19_sgraph1,axiom,( ! [A] : ! [B] : ( m1_sgraph1(B,A) => ! [C] : ~ ( r2_hidden(C,u1_sgraph1(B)) & ! [D] : ! [E] : ~ ( r2_hidden(D,u1_struct_0(B)) & r2_hidden(E,u1_struct_0(B)) & D != E & C = k2_tarski(D,E) ) ) ) )).
fof(t19_sheffer1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t19_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t19_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ~ ( v1_finset_1(u1_pre_topc(A)) & ~ v2_simplex0(A) & v3_matroid0(A) ) ) )).
fof(t19_simplex1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( ~ 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) ) ) ) ) )).
fof(t19_simplex2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ? [C] : ( 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(k2_xcmplx_0(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(k2_xcmplx_0(A,B)))))) & v3_tops_2(C,k2_borsuk_1(k15_euclid(A),k15_euclid(B)),k15_euclid(k2_xcmplx_0(A,B))) & ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(B))) => k1_binop_1(C,D,E) = k7_finseq_1(D,E) ) ) ) ) ) )).
fof(t19_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( k9_complex1(k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k9_complex1(A))),C)) = k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k9_complex1(A))),C) & ( r1_xxreal_0(C,B) => k9_complex1(k5_real_1(k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k9_complex1(A))),B),k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k9_complex1(A))),C))) = k5_real_1(k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k9_complex1(A))),B),k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k9_complex1(A))),C)) ) ) ) ) ) )).
fof(t19_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_funct_1(k3_sin_cos2,k4_xcmplx_0(A)) = k1_funct_1(k3_sin_cos2,A) & k1_funct_1(k1_sin_cos2,k4_xcmplx_0(A)) = k4_xcmplx_0(k1_funct_1(k1_sin_cos2,A)) & k1_funct_1(k5_sin_cos2,k4_xcmplx_0(A)) = k4_xcmplx_0(k1_funct_1(k5_sin_cos2,A)) ) ) )).
fof(t19_sin_cos3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k15_sin_cos(k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1))) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(k22_sin_cos,A),k1_funct_1(k18_sin_cos,B)),k3_xcmplx_0(k3_xcmplx_0(k1_funct_1(k22_sin_cos,A),k1_funct_1(k16_sin_cos,B)),k7_complex1)) ) ) )).
fof(t19_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( k19_sin_cos(A) != k5_numbers & k19_sin_cos(B) != k5_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(k19_sin_cos(A),k19_sin_cos(B))) ) ) ) )).
fof(t19_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k17_sin_cos(A) != k5_numbers => k2_sin_cos4(k3_xcmplx_0(3,A)) = k7_xcmplx_0(k6_xcmplx_0(k1_newton(k2_sin_cos4(A),3),k3_xcmplx_0(3,k2_sin_cos4(A))),k6_xcmplx_0(k3_xcmplx_0(3,k1_square_1(k2_sin_cos4(A))),1)) ) ) )).
fof(t19_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ( ( r1_xxreal_0(k2_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)),A) & r1_xxreal_0(A,k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B))) ) => r1_xxreal_0(k19_sin_cos(A),k5_numbers) ) ) ) )).
fof(t19_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) & r1_xxreal_0(k1_square_1(k6_xcmplx_0(1,k1_square_1(A))),k5_numbers) ) ) )).
fof(t19_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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))) = k7_xcmplx_0(k2_sin_cos2(k2_xcmplx_0(A,B)),k2_sin_cos2(k6_xcmplx_0(A,B))) ) ) )).
fof(t19_sin_cos9,axiom,( ! [A] : ( r2_hidden(A,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)),k7_xcmplx_0(k28_sin_cos,4))) => r2_hidden(k1_funct_1(k26_sin_cos,A),k1_rcomp_1(k4_xcmplx_0(1),1)) ) )).
fof(t19_sincos10,axiom,( v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers))) )).
fof(t19_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t19_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t19_sprect_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t19_sprect_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t19_sprect_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(1,A) => ( r1_xxreal_0(B,A) | ! [C] : ( 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,k1_nat_1(A,1),B))) ) ) ) ) ) ) )).
fof(t19_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(t19_square_1,axiom,( ~ r1_xxreal_0(k3_square_1(2),1) )).
fof(t19_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(t19_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k7_card_1(B),k7_card_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(B),k7_card_1(A)))) ) => ( ( v2_funct_2(C,k7_card_1(A)) & v1_stirl2_1(C,B,A) ) => ! [D] : ( v7_ordinal1(D) => ( ~ r1_xxreal_0(A,D) => r1_xxreal_0(k3_nat_1(k1_stirl2_1(B,k7_card_1(A),C,k1_seq_4(D))),k2_xcmplx_0(k6_xcmplx_0(B,A),D)) ) ) ) ) ) ) )).
fof(t19_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_valuat_1(C,A,B) => ! [D] : ( m2_subset_1(D,k16_substut1(A),k38_substut1(A)) => ( ! [E] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t19_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( r1_tarski(k3_subset_1(A,B),B) <=> B = k2_subset_1(A) ) ) )).
fof(t19_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( 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)) ) ) )).
fof(t19_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => ! [C] : ( m1_subset_1(C,k16_substut1(A)) => ( k19_substut1(A,B) = k19_substut1(A,C) => k29_substut1(A,k21_substut1(A,B,C)) = C ) ) ) ) )).
fof(t19_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t19_supinf_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => ! [C] : ( ( 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(k6_numbers,A,k6_supinf_2(B),k14_supinf_2(A,B,C)) = k2_supinf_2(k10_supinf_2(k6_numbers,A,B,C)) & k10_supinf_2(k6_numbers,A,k6_supinf_2(B),k14_supinf_2(A,B,C)) = k2_supinf_2(k11_supinf_2(k6_numbers,A,B,C)) ) ) ) ) )).
fof(t19_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( r1_orders_2(B,F,C) => ( r1_orders_2(B,D,C) | ( k1_symsp_1(A,B,C,k3_rlvect_1(B,D,F),E) = k1_symsp_1(A,B,C,D,E) & k1_symsp_1(A,B,C,D,k3_rlvect_1(B,E,F)) = k1_symsp_1(A,B,C,D,E) ) ) ) ) ) ) ) ) ) )).
fof(t19_sysrel,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( r1_tarski(k4_relat_1(A),B) => r1_tarski(k4_relat_1(A),k2_relat_1(B)) ) ) )).
fof(t19_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r1_xxreal_0(C,D) => r1_relset_1(A,A,k1_taxonom1(A,B,C),k1_taxonom1(A,B,D)) ) ) ) ) ) )).
fof(t19_taylor_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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,k22_sin_cos),A) & k1_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k22_sin_cos),A) = k3_xcmplx_0(k1_funct_1(k22_sin_cos,k1_funct_1(B,A)),k1_fdiff_1(B,A)) ) ) ) ) )).
fof(t19_taylor_2,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k16_sin_cos,A),k2_nat_1(2,B)) = k26_valued_1(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k16_sin_cos,A),k1_newton(k4_xcmplx_0(1),B)) & k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k16_sin_cos,A),k1_nat_1(k2_nat_1(2,B),1)) = k26_valued_1(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k18_sin_cos,A),k1_newton(k4_xcmplx_0(1),B)) & k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k18_sin_cos,A),k2_nat_1(2,B)) = k26_valued_1(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k18_sin_cos,A),k1_newton(k4_xcmplx_0(1),B)) & k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k18_sin_cos,A),k1_nat_1(k2_nat_1(2,B),1)) = k26_valued_1(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k16_sin_cos,A),k1_newton(k4_xcmplx_0(1),k1_nat_1(B,1))) ) ) ) )).
fof(t19_tbsp_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t19_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => v5_tops_1(k2_struct_0(A),A) ) )).
fof(t19_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t19_tdlat_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v2_tdlat_3(A) <=> ! [B] : ( 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) ) ) ) ) )).
fof(t19_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( 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) => k4_polynom1(A,C,k5_termord(A,B,C,D),E) = k4_struct_0(C) ) ) ) ) ) ) )).
fof(t19_tex_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( k2_tex_1(A) = k1_compts_1(A) <=> ? [B] : ( m1_subset_1(B,A) & A = k6_domain_1(A,B) ) ) ) )).
fof(t19_tex_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t19_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_tex_3(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( m1_pre_topc(C,A) => ( m1_pre_topc(B,C) => v2_tex_3(C,A) ) ) ) ) )).
fof(t19_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t19_tietze,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_tmap_1(A,k3_topmetr,B,C) <=> ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v3_pre_topc(E,A) & r2_hidden(C,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_hidden(F,E) & r1_xxreal_0(D,k9_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)))) ) ) ) ) ) ) ) ) ) ) )).
fof(t19_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(t19_toler_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_toler_1(C,A,B) => ? [D] : ( v1_toler_1(D,A,B) & m1_toler_1(D,A,B) & r1_tarski(C,D) ) ) ) )).
fof(t19_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r1_borsuk_6(A,B,C) & r1_borsuk_6(A,C,D) ) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(t19_topalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_topalg_2(A) & m1_pre_topc(A,k2_topalg_2) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( m1_borsuk_2(E,A,B,C) => m1_borsuk_6(k3_topalg_2(A,D,E),A,B,C,D,E) ) ) ) ) ) )).
fof(t19_topalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v2_pre_topc(D) & l1_pre_topc(D) ) => ! [E] : ( ( ~ v2_struct_0(E) & v2_pre_topc(E) & l1_pre_topc(E) ) => ! [F] : ( ( 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] : ( ( 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] : ( ( v4_pre_topc(H,B) & m1_subset_1(H,k1_zfmisc_1(u1_struct_0(B))) ) => ! [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] : ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t19_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_borsuk_2(G,k2_borsuk_1(A,B),k4_borsuk_1(A,B,C,E),k4_borsuk_1(A,B,D,F)) => ! [H] : ( m1_borsuk_2(H,k2_borsuk_1(A,B),k4_borsuk_1(A,B,C,E),k4_borsuk_1(A,B,D,F)) => ! [I] : ( m1_borsuk_2(I,A,C,D) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t19_topalg_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( m1_borsuk_6(F,A,B,C,D,E) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t19_topalg_6,axiom,( ! [A] : ( 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)))) ) ) )).
fof(t19_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(t19_topdim_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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),k5_numbers) ) ) ) ) )).
fof(t19_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_topgen_1(A,B)) <=> ? [D] : ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(E,D) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_hidden(F,k9_subset_1(u1_struct_0(A),B,E)) & C != F ) ) ) ) ) ) ) ) ) )).
fof(t19_topgen_2,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) ) ) )).
fof(t19_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t19_topgen_5,axiom,( r1_tarski(k1_topgen_5,k2_topgen_5) )).
fof(t19_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => v3_tops_2(k3_struct_0(A),A,A) ) )).
fof(t19_topmetr,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t19_topreal1,axiom,( r1_subset_1(k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,k5_numbers),k19_euclid(1,k5_numbers)),k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,1),k19_euclid(1,1))) )).
fof(t19_topreal3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( v7_ordinal1(C) => r1_tarski(k2_topreal1(A,B,C),k3_topreal1(A,B)) ) ) ) )).
fof(t19_topreal4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( 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)),k8_metric_1(k14_euclid(2),E,D)) & r2_hidden(A,k8_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),k8_metric_1(k14_euclid(2),E,D))) ) ) ) ) ) ) ) ) )).
fof(t19_topreal5,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t19_topreal6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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))) ) )).
fof(t19_topreal7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_metric_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_topreal7(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_topreal7(A,B))) => k1_metric_1(k1_topreal7(A,B),C,D) = k4_xxreal_0(k1_metric_1(A,k3_topreal7(A,B,C),k3_topreal7(A,B,D)),k1_metric_1(B,k4_topreal7(A,B,C),k4_topreal7(A,B,D))) ) ) ) ) )).
fof(t19_topreal8,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t19_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ( v1_xboole_0(k1_topreal9(A,C,B)) => r1_xxreal_0(B,k5_numbers) ) ) ) ) )).
fof(t19_topreala,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_topmetr)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ! [C] : ( 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) ) ) ) ) )).
fof(t19_toprealc,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => m2_finseq_1(A,k1_numbers) ) )).
fof(t19_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(t19_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t19_tops_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t19_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tops_1(B,A) <=> ! [C] : ( 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) ) ) ) ) ) )).
fof(t19_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t19_treal_1,axiom,( v1_connsp_1(k17_borsuk_1) )).
fof(t19_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( ( r2_hidden(B,A) & r1_tarski(C,B) ) => r2_hidden(C,A) ) ) ) ) )).
fof(t19_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => m1_trees_2(k1_xboole_0,A) ) )).
fof(t19_trees_3,axiom,( ! [A] : ! [B] : ( ( v2_trees_3(A) & r1_tarski(B,A) ) => v2_trees_3(B) ) )).
fof(t19_trees_4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v6_trees_3(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ( r2_hidden(k7_finseq_1(k14_trees_3(C),D),k9_xtuple_0(k4_trees_4(A,B))) => k1_funct_1(k4_trees_4(A,B),k7_finseq_1(k14_trees_3(C),D)) = k4_funct_6(B,k1_nat_1(C,1),D) ) ) ) ) )).
fof(t19_trees_9,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v3_trees_3(B) ) => ( r2_hidden(A,k9_trees_9(B)) <=> ? [C] : ( m1_subset_1(C,B) & ? [D] : ( m1_trees_1(D,k9_xtuple_0(C)) & A = k5_trees_2(C,D) ) ) ) ) )).
fof(t19_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_tsep_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t19_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t19_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v6_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( ~ v1_tsp_1(B,A) & ! [C] : ( ( v1_pre_topc(C) & ~ v6_pre_topc(C) & m1_pre_topc(C,A) ) => B != u1_struct_0(C) ) ) ) ) )).
fof(t19_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)))) ) ) ) ) ) )).
fof(t19_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( m2_funct_2(B,k4_numbers,u1_turing_1(A),k9_funct_2(k4_numbers,u1_turing_1(A))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_turing_1(k3_finseq_4(k4_ordinal1,C,D,E),A,B) => ( k1_funct_1(B,C) = k5_numbers & k1_funct_1(B,k1_nat_1(k1_nat_1(C,D),2)) = k5_numbers & k1_funct_1(B,k1_nat_1(k1_nat_1(k1_nat_1(C,D),E),4)) = k5_numbers & ! [F] : ( v1_int_1(F) => ~ ( ~ r1_xxreal_0(F,C) & ~ r1_xxreal_0(k1_nat_1(k1_nat_1(C,D),2),F) & k1_funct_1(B,F) != 1 ) ) & ! [F] : ( v1_int_1(F) => ~ ( ~ r1_xxreal_0(F,k1_nat_1(k1_nat_1(C,D),2)) & ~ r1_xxreal_0(k1_nat_1(k1_nat_1(k1_nat_1(C,D),E),4),F) & k1_funct_1(B,F) != 1 ) ) ) ) ) ) ) ) ) )).
fof(t19_twoscomp,axiom,( k1_funct_1(k18_twoscomp,k11_finseq_1(k5_numbers,k5_numbers,k5_numbers)) = k5_numbers & k1_funct_1(k18_twoscomp,k11_finseq_1(k5_numbers,k5_numbers,1)) = k5_numbers & k1_funct_1(k18_twoscomp,k11_finseq_1(k5_numbers,1,k5_numbers)) = k5_numbers & k1_funct_1(k18_twoscomp,k11_finseq_1(k5_numbers,1,1)) = 1 & k1_funct_1(k18_twoscomp,k11_finseq_1(1,k5_numbers,k5_numbers)) = k5_numbers & k1_funct_1(k18_twoscomp,k11_finseq_1(1,k5_numbers,1)) = k5_numbers & k1_funct_1(k18_twoscomp,k11_finseq_1(1,1,k5_numbers)) = k5_numbers & k1_funct_1(k18_twoscomp,k11_finseq_1(1,1,1)) = k5_numbers )).
fof(t19_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( v1_unialg_1(B) & m1_unialg_2(B,A) ) => ! [C] : ( ( ~ 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 ) ) ) ) )).
fof(t19_unialg_3,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t19_uniroots,axiom,( ! [A] : ( ( ~ 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] : ( r2_hidden(B,u1_struct_0(k1_uniroots(A))) => r2_hidden(B,u1_struct_0(A)) ) ) )).
fof(t19_uproots,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) ) ) ) )).
fof(t19_urysohn1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v7_pre_topc(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v4_pre_topc(k6_domain_1(u1_struct_0(A),B),A) ) ) ) )).
fof(t19_urysohn2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k6_numbers) => ( ( B = C & r1_xxreal_0(k5_numbers,C) ) => k7_supinf_2(k1_integra2(A,B)) = k1_extreal1(C,k7_supinf_2(A)) ) ) ) ) )).
fof(t19_urysohn3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v10_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_xxreal_0(k5_numbers,k12_supinf_2(D,E)) & r1_xxreal_0(k12_supinf_2(D,E),1) & ( r2_hidden(E,B) => k12_supinf_2(D,E) = k5_numbers ) & ( r2_hidden(E,C) => k12_supinf_2(D,E) = 1 ) ) ) ) ) ) ) ) ) )).
fof(t19_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( 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 ) ) ) ) ) ) ) )).
fof(t19_valued_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => m2_valued_0(B,A,B) ) ) )).
fof(t19_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( k9_xtuple_0(C) = k9_subset_1(k4_ordinal1,k4_finseq_1(A),k4_finseq_1(B)) => ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) ) ) ) ) )).
fof(t19_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t19_vectsp10,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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] : ( 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] : ( 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] : ( 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] : ( m1_subset_1(I,u1_struct_0(D)) => ! [J] : ( m1_subset_1(J,u1_struct_0(D)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ! [L] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t19_vectsp11,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( 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) ) ) )).
fof(t19_vectsp_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t19_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C != k4_struct_0(A) => ( k4_algstr_0(A,k1_vectsp_2(A,B,C)) = k1_vectsp_2(A,k4_algstr_0(A,B),C) & k1_vectsp_2(A,B,k4_algstr_0(A,C)) = k4_algstr_0(A,k1_vectsp_2(A,B,C)) ) ) ) ) ) )).
fof(t19_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => r1_struct_0(B,k4_struct_0(C)) ) ) ) )).
fof(t19_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t19_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t19_vectsp_7,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ~ ( v1_vectsp_7(C,A,B) & ! [D] : ( m1_vectsp_7(D,A,B) => ~ r1_tarski(C,D) ) ) ) ) ) )).
fof(t19_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t19_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t19_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t19_waybel10,axiom,( ! [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] : ( ( 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) ) ) )).
fof(t19_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t19_waybel12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t19_waybel13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t19_waybel14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ( v5_waybel_6(B,k1_yellow_1(u1_pre_topc(A))) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ~ ( r1_tarski(k3_xboole_0(C,D),B) & ~ r1_tarski(C,B) & ~ r1_tarski(D,B) ) ) ) ) ) ) )).
fof(t19_waybel15,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r2_hidden(B,k4_waybel_6(k7_lattice3(A))) <=> v6_waybel_6(B,A) ) ) ) )).
fof(t19_waybel16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t19_waybel17,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ 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] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t19_waybel18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & l1_pre_topc(A) ) => ~ ( v2_waybel18(A) & ! [B] : ( ~ v1_xboole_0(B) => ~ r1_waybel18(A,k3_waybel18(B,k7_funcop_1(B,k9_waybel18))) ) ) ) )).
fof(t19_waybel19,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m3_yellow_9(C,A,B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t19_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t19_waybel21,axiom,( ! [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] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ( v8_yellow_0(B,A) => v3_lattice3(B) ) ) ) )).
fof(t19_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_waybel23(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ( r2_yellow_0(A,C) => r2_hidden(k2_yellow_0(A,C),B) ) ) ) ) ) )).
fof(t19_waybel24,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_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)))) ) ) ) )).
fof(t19_waybel25,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r1_borsuk_3(A,B) => r5_waybel_1(k1_waybel25(A),k1_waybel25(B)) ) ) ) )).
fof(t19_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v6_pre_topc(B) & v1_waybel25(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,B) ) => ( r1_borsuk_1(B,C) => r3_yellow16(k1_waybel26(A,C),k1_waybel26(A,B)) ) ) ) ) )).
fof(t19_waybel28,axiom,( ! [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) & l1_orders_2(A) ) => v6_yellow_6(k3_waybel28(A),A) ) )).
fof(t19_waybel29,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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(k1_yellow_1(u1_pre_topc(A))),k4_waybel29(A)),B) = k5_funct_3(B,u1_struct_0(A)) ) ) )).
fof(t19_waybel30,axiom,( ! [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] : ( ( 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] : ( ( v2_pre_topc(C) & v2_waybel19(C) & m1_yellow_9(C,A) ) => ! [D] : ( ( v2_pre_topc(D) & v2_waybel19(D) & m1_yellow_9(D,B) ) => ( v3_waybel_3(k1_yellow_1(k5_waybel11(B))) => u1_pre_topc(k2_borsuk_1(C,D)) = k2_waybel19(k3_yellow_3(A,B)) ) ) ) ) ) )).
fof(t19_waybel31,axiom,( ! [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) ) => ( ~ v8_struct_0(A) => ! [B] : ( ( v6_waybel23(B,A) & m1_waybel23(B,A) ) => r1_ordinal1(k1_card_1(a_2_0_waybel31(A,B)),k1_card_1(B)) ) ) ) )).
fof(t19_waybel32,axiom,( ! [A] : ( ( 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] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => v3_pre_topc(k3_subset_1(u1_struct_0(B),k5_waybel_0(B,C)),B) ) ) ) )).
fof(t19_waybel33,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => r1_tarski(k5_waybel11(A),k4_waybel28(A)) ) )).
fof(t19_waybel34,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(t19_waybel35,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_waybel35(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ( ( v3_waybel35(C,A,B) & m1_waybel35(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & r2_hidden(E,C) & r2_orders_2(A,D,E) & ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t19_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k5_waybel_0(A,B) = k5_waybel_0(A,C) => B = C ) ) ) ) )).
fof(t19_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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) ) ) ) ) ) )).
fof(t19_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t19_waybel_3,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r3_orders_2(A,C,k1_yellow_0(A,D)) & ! [E] : ( ( 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) ) ) ) ) )).
fof(t19_waybel_4,axiom,( ! [A] : ( ( 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))) ) )).
fof(t19_waybel_5,axiom,( ! [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) ) => ( v3_waybel_3(A) <=> ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) ) => ! [D] : ( m2_pboole(D,B,C,k7_funcop_1(B,u1_struct_0(A))) => ( ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t19_waybel_6,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t19_waybel_7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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(k1_yellow_1(k7_waybel_0(A)))) ) ) ) )).
fof(t19_waybel_8,axiom,( ! [A] : ( ( 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)) ) ) ) )).
fof(t19_waybel_9,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t19_weddwitt,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => r1_struct_0(k4_weddwitt(A),k1_group_1(A)) ) )).
fof(t19_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ( v2_compts_1(B,k3_pcomps_1(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(C,B) => ( r1_xxreal_0(k3_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)),k3_metric_1(A,C,D)) ) ) ) ) ) ) ) )).
fof(t19_wellord1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => k2_wellord1(k2_wellord1(C,A),B) = k2_wellord1(C,k3_xboole_0(A,B)) ) )).
fof(t19_wsierp_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) )).
fof(t19_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r1_tarski(C,A) & r1_tarski(C,B) ) => r1_tarski(C,k3_xboole_0(A,B)) ) )).
fof(t19_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k7_xboolean(k7_xboolean(A,B),C) = k7_xboolean(A,k7_xboolean(B,C)) ) ) ) )).
fof(t19_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( k6_xcmplx_0(A,C) = k6_xcmplx_0(B,C) => A = B ) ) ) ) )).
fof(t19_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k2_xcmplx_0(A,B),C) <=> r1_xxreal_0(A,k6_xcmplx_0(C,B)) ) ) ) ) )).
fof(t19_xtuple_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( r2_hidden(k6_xtuple_0(A,B,C,D),E) => r2_hidden(A,k13_xtuple_0(E)) ) )).
fof(t19_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t19_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => k3_xxreal_1(A,A) = k1_xboole_0 ) )).
fof(t19_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => m2_xxreal_2(A,k2_xxreal_1(A,B)) ) ) )).
fof(t19_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( k3_xxreal_3(A,B) = k2_xxreal_0 & A != k2_xxreal_0 & B != k1_xxreal_0 ) ) ) )).
fof(t19_yellow10,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t19_yellow12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t19_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_yellow13(C,A,B) => ~ v1_xboole_0(C) ) ) ) )).
fof(t19_yellow14,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t19_yellow15,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t19_yellow16,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) ) )).
fof(t19_yellow17,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_waybel18(A,B,C))) => ! [E] : ( 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] : ~ ( 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)) ) ) ) ) ) ) )).
fof(t19_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v11_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(t19_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ! [C] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ( r1_waybel_0(A,C,B) => ! [D] : ( m2_yellow_6(D,A,C) => r1_waybel_0(A,D,B) ) ) ) ) )).
fof(t19_yellow20,axiom,( ! [A] : ( l2_altcat_1(A) => ! [B] : ( l2_altcat_1(B) => ( r1_yellow20(A,B) => k2_yellow20(A,B) = k2_yellow20(B,A) ) ) ) )).
fof(t19_yellow21,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k8_yellow21(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k8_yellow21(A))) => ! [D] : ( 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))))) ) ) ) ) ) )).
fof(t19_yellow_0,axiom,( ! [A] : ( ( v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t19_yellow_1,axiom,( ! [A] : k4_yellow_0(k2_yellow_1(A)) = A )).
fof(t19_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t19_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t19_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t19_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r1_orders_2(A,B,k3_yellow_0(A)) => B = k3_yellow_0(A) ) ) ) )).
fof(t19_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( r1_waybel_0(A,B,C) => r2_waybel_0(A,B,C) ) ) ) )).
fof(t19_yellow_7,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t19_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_yellow_8(A,k6_domain_1(u1_struct_0(A),B),B) ) ) )).
fof(t19_yellow_9,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [D] : ( 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) ) ) ) ) )).
fof(t19_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ~ v1_xboole_0(C) => ( ( v8_zf_fund1(B,A) & r2_hidden(C,B) ) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ( r2_hidden(k5_zf_fund1(D,C),B) => r2_hidden(k5_zf_fund1(k6_zf_lang(D),C),B) ) ) ) ) ) ) )).
fof(t19_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v3_zf_lang(A) => k1_funct_1(A,1) = 1 ) ) )).
fof(t19_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ! [E] : ( m2_subset_1(E,k4_ordinal1,k1_zf_lang) => ! [F] : ( m2_subset_1(F,k4_ordinal1,k1_zf_lang) => ! [G] : ( m2_subset_1(G,k4_ordinal1,k1_zf_lang) => ! [H] : ( m2_subset_1(H,k4_ordinal1,k1_zf_lang) => ( k17_zf_lang(C,E,G,A) = k17_zf_lang(D,F,H,B) => ( C = D & E = F & G = H & A = B ) ) ) ) ) ) ) ) ) ) )).
fof(t19_zf_model,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ( r1_zf_model(A,B,k12_zf_lang(C,D)) <=> ( r1_zf_model(A,B,C) <=> r1_zf_model(A,B,D) ) ) ) ) ) ) )).
fof(t19_zf_refle,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( r2_hidden(B,A) => r2_hidden(k3_ordinal2(B),A) ) ) )).
fof(t19_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( r1_tarski(k1_tarski(C),k2_tarski(A,B)) & C != A & C != B ) )).
fof(t19_zfmodel2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( 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(k5_numbers),k2_zf_model(B)) => ( r1_zf_model(A,C,k8_zf_lang(k2_zf_lang(3),k13_zf_lang(k2_zf_lang(k5_numbers),k8_zf_lang(k2_zf_lang(4),k12_zf_lang(B,k4_zf_lang(k2_zf_lang(4),k2_zf_lang(k5_numbers))))))) <=> ! [D] : ( m1_subset_1(D,A) => ? [E] : ( m1_subset_1(E,A) & ! [F] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t19_zfrefle1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( ( r2_ordinal2(A,B) & r2_ordinal2(B,C) ) => r2_ordinal2(A,C) ) ) ) ) )).
fof(t19_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v7_zmodul01(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => r2_hidden(k4_algstr_0(A,C),B) ) ) ) ) ) )).
fof(t19_zmodul02,axiom,( ! [A] : ( ( ~ 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) ) => k21_zmodul02(A,k19_zmodul02(A)) = k4_struct_0(A) ) )).
fof(t19_zmodul03,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(C,u1_struct_0(B)) => m1_zmodul01(k33_zmodul02(A,C),B) ) ) ) ) )).
fof(t1_abcmiz_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v1_abcmiz_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t1_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => r1_tarski(k1_funct_1(B,A),k3_card_3(B)) ) )).
fof(t1_abcmiz_a,axiom,( ! [A] : ( v1_xtuple_0(A) => A = k4_tarski(k1_xtuple_0(A),k2_xtuple_0(A)) ) )).
fof(t1_abian,axiom,( ! [A] : ( v1_int_1(A) => ( ~ ( ~ v1_abian(A) & ! [B] : ( v1_int_1(B) => A != k2_xcmplx_0(k3_xcmplx_0(2,B),1) ) ) & ~ ( ? [B] : ( v1_int_1(B) & A = k2_xcmplx_0(k3_xcmplx_0(2,B),1) ) & v1_abian(A) ) ) ) )).
fof(t1_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ( k9_complex1(A) = A | k9_complex1(A) = k4_xcmplx_0(A) ) ) )).
fof(t1_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_analoaf(A,B,C,C,B) & r2_analoaf(A,B,C,B,C) ) ) ) ) )).
fof(t1_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v2_aff_2(A) <=> v3_aff_2(A) ) ) )).
fof(t1_aff_3,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v1_aff_3(A) => v2_aff_3(A) ) ) )).
fof(t1_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( ( r1_aff_1(A,E,B,D) | r1_aff_1(A,E,D,B) ) & E != B & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_aff_1(A,E,C,F) & r2_analoaf(A,B,C,D,F) ) ) ) ) ) ) ) ) )).
fof(t1_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( A = k3_xboole_0(A,B) => r1_xxreal_0(A,B) ) ) ) )).
fof(t1_afinsq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( r2_hidden(B,A) => m1_subset_1(B,k4_ordinal1) ) ) )).
fof(t1_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t1_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_analoaf(A,B,C,B,C) ) ) ) )).
fof(t1_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect01(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_analoaf(A,B,C,B,C) ) ) ) )).
fof(t1_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t1_algseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( r1_xxreal_0(k1_algseq_1(B,C),A) => k1_funct_1(C,A) = k4_struct_0(B) ) ) ) ) )).
fof(t1_algspec1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t1_algstr_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_algstr_0(A,D,k4_struct_0(A)) = D ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & k1_algstr_0(A,D,E) = k4_struct_0(A) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) )).
fof(t1_algstr_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( A != B & ! [E] : ( v1_xreal_0(E) => k2_xcmplx_0(k3_xcmplx_0(A,E),C) != k2_xcmplx_0(k3_xcmplx_0(B,E),D) ) ) ) ) ) ) )).
fof(t1_algstr_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(t1_altcat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(B)) => ! [F] : ! [G] : ( ( 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) ) ) ) ) )).
fof(t1_altcat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : 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))) )).
fof(t1_altcat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t1_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_altcat_1(A,B,C)) => ! [F] : ( m1_subset_1(F,k1_altcat_1(A,B,D)) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t1_altcat_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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)))) ) => m1_altcat_5(k1_xboole_0,A,B,k1_xboole_0,C) ) ) ) )).
fof(t1_ami_2,axiom,( k1_funct_1(k3_relat_1(k3_ami_2,k4_ami_2),k4_ordinal1) = k4_ordinal1 )).
fof(t1_ami_3,axiom,( k4_struct_0(k1_ami_3) = k4_ordinal1 )).
fof(t1_ami_4,axiom,( k9_xtuple_0(k1_ami_4) = 5 )).
fof(t1_ami_5,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ? [B] : ( v7_ordinal1(B) & A = k10_ami_3(B) ) ) )).
fof(t1_ami_6,axiom,( ! [A] : ( m1_subset_1(A,k1_compos_0(u1_compos_1(k1_ami_3))) => ~ ! [B] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(B,8) & A = B ) ) ) )).
fof(t1_ami_wstd,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_setfam_1(B) => ! [C] : ( ( ~ v2_struct_0(C) & v2_memstr_0(C,B) & v3_memstr_0(C,B) & l1_extpro_1(C,B) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r1_ami_wstd(B,C,D,E) & r1_ami_wstd(B,C,E,A) ) => r1_ami_wstd(B,C,D,A) ) ) ) ) ) ) )).
fof(t1_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ( ! [D] : ( v7_ordinal1(D) => k1_amistd_1(A,B,D,C) = k1_tarski(D) ) => v1_xboole_0(k2_amistd_1(A,B,C)) ) ) ) ) )).
fof(t1_amistd_2,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(k4_amistd_1(A))) => k5_xtuple_0(B) = k5_numbers ) ) )).
fof(t1_amistd_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_setfam_1(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) => ( D = k1_tarski(A) => k1_amistd_3(B,C,D) = k16_funcop_1(k5_numbers,A) ) ) ) ) ) )).
fof(t1_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_compos_1(B)) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t1_amistd_5,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ( v2_amistd_1(C,A,B) => ! [D] : ( v7_ordinal1(D) => v2_amistd_1(k5_compos_0(u1_compos_1(B),C,D),A,B) ) ) ) ) ) )).
fof(t1_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_analmetr(A,D,E) => ( r2_analmetr(A,B,C,D,E) <=> ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( ( 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)) ) => k2_xcmplx_0(k3_xcmplx_0(F,H),k3_xcmplx_0(G,I)) = k5_numbers ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t1_analoaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k3_rlvect_1(A,k5_algstr_0(A,D,C),k5_algstr_0(A,C,B)) = k5_algstr_0(A,D,B) ) ) ) ) )).
fof(t1_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_analmetr(A,D,E) => k1_analort(A,D,E,k3_rlvect_1(A,B,C)) = k3_rlvect_1(A,k1_analort(A,D,E,B),k1_analort(A,D,E,C)) ) ) ) ) ) ) )).
fof(t1_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_anproj_1(A,B,C) <=> ? [D] : ( v1_xreal_0(D) & D != k5_numbers & B = k1_rlvect_1(A,C,D) ) ) ) ) ) )).
fof(t1_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( 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 = k5_numbers & F = k5_numbers & G = k5_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) ) ) ) ) ) ) )).
fof(t1_aofa_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( r1_tarski(D,k9_xtuple_0(A)) & r1_tarski(D,k9_xtuple_0(B)) & r1_tarski(k10_xtuple_0(C),D) & ! [E] : ( r2_hidden(E,D) => k1_funct_1(A,E) = k1_funct_1(B,E) ) ) => k3_relat_1(C,A) = k3_relat_1(C,B) ) ) ) ) )).
fof(t1_aofa_a01,axiom,( k4_nat_d(1,2) = 1 & k4_nat_d(2,2) = k5_numbers )).
fof(t1_aofa_i00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ~ ( D != E & E != F & F != D & ! [G] : ( ( 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 ) ) ) )).
fof(t1_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,k5_numbers) = A ) )).
fof(t1_armstrng,axiom,( ! [A] : ( v2_finsub_1(A) => ! [B] : ! [C] : ( ( 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) ) ) ) )).
fof(t1_arrow,axiom,( ! [A] : ( v1_finset_1(A) => ( r1_xxreal_0(2,k5_card_1(A)) => ! [B] : ( m1_subset_1(B,A) => ~ ! [C] : ( m1_subset_1(C,A) => C = B ) ) ) ) )).
fof(t1_arytm_0,axiom,( r1_tarski(k2_arytm_2,k1_numbers) )).
fof(t1_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ( k7_arytm_2(A,B) = B => A = k11_arytm_3 ) ) ) )).
fof(t1_arytm_2,axiom,( r1_tarski(k5_arytm_3,k2_arytm_2) )).
fof(t1_arytm_3,axiom,( ~ r1_arytm_3(k1_xboole_0,k1_xboole_0) )).
fof(t1_autalg_1,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t1_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) )).
fof(t1_axioms,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ~ ( ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r2_hidden(C,A) & r2_hidden(D,B) ) => r1_xxreal_0(C,D) ) ) ) & ! [C] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & r2_hidden(D,A) & r2_hidden(E,B) & ~ ( r1_xxreal_0(D,C) & r1_xxreal_0(C,E) ) ) ) ) ) ) ) )).
fof(t1_bagorder,axiom,( ! [A] : ! [B] : ! [C] : ( ( r2_hidden(C,A) & r2_hidden(C,B) & k6_subset_1(A,k1_tarski(C)) = k6_subset_1(B,k1_tarski(C)) ) => A = B ) )).
fof(t1_bcialg_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t1_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_2(A,B,C,k5_numbers) = B ) ) ) )).
fof(t1_bcialg_3,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t1_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t1_bcialg_5,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t1_bcialg_6,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k5_bcialg_1(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t1_bciideal,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t1_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => k2_bhsp_1(A,k4_struct_0(A),k4_struct_0(A)) = k5_numbers ) )).
fof(t1_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_funct_1(B) => v1_bhsp_2(B,A) ) ) ) )).
fof(t1_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_bhsp_3(B,A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & ? [F] : ( v7_ordinal1(F) & 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)))) ) ) ) ) ) ) ) ) )).
fof(t1_bhsp_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,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))) ) ) ) )).
fof(t1_bhsp_5,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( 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] : ( 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) ) ) ) ) ) )).
fof(t1_bhsp_6,axiom,( ! [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_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] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t1_bhsp_7,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( ~ v1_xboole_0(E) & r1_tarski(E,B) & ! [F] : ( ( 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,k9_complex1(k5_bhsp_5(k1_numbers,u1_struct_0(A),k9_binop_2,F,C))) ) ) ) ) ) ) ) ) ) ) )).
fof(t1_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t1_binari_2,axiom,( ! [A] : ( ( 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) = k5_numbers ) ) )).
fof(t1_binari_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ~ r1_xxreal_0(k5_series_1(2,A),k6_binarith(A,B)) ) ) )).
fof(t1_binari_4,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => r1_xxreal_0(k2_xcmplx_0(A,1),k3_xcmplx_0(A,2)) ) ) )).
fof(t1_binarith,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t1_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_algstr_0(A) & v2_vectsp_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_algstr_0(A,k4_struct_0(A),B) = k4_struct_0(A) ) ) )).
fof(t1_binop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ( ( 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] : ! [G] : ( ( 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) ) ) ) )).
fof(t1_binop_2,axiom,( k4_binop_1(k2_numbers,k3_binop_2) = k5_numbers )).
fof(t1_bintree1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) & v3_trees_2(B) ) => k15_trees_3(k9_finseq_1(B)) = k3_pre_poly(A,k1_bintree1(A,B)) ) ) )).
fof(t1_bintree2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(B,k3_finseq_2(A)) => r2_hidden(k5_relat_1(B,k2_finseq_1(C)),k3_finseq_2(A)) ) ) ) )).
fof(t1_birkhoff,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( m2_pboole(D,u1_struct_0(A),C,u3_msualg_1(A,B)) => r2_pboole(u1_struct_0(A),k2_funct_6(D),k2_funct_6(k1_birkhoff(A,C,B,D))) ) ) ) ) )).
fof(t1_boole,axiom,( ! [A] : k2_xboole_0(A,k1_xboole_0) = A )).
fof(t1_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r3_lattices(A,k3_lattices(A,B,C),D) => r3_lattices(A,B,D) ) ) ) ) ) )).
fof(t1_borsuk_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => r1_tarski(u1_struct_0(B),u1_struct_0(A)) ) ) )).
fof(t1_borsuk_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v2_pre_topc(D) & l1_pre_topc(D) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(D)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(D)))) ) => ! [F] : ( ( 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)))) ) => ~ ( m1_pre_topc(B,A) & m1_pre_topc(C,A) & k2_xboole_0(k2_struct_0(B),k2_struct_0(C)) = k2_struct_0(A) & v1_compts_1(B) & v1_compts_1(C) & v8_pre_topc(A) & v5_pre_topc(E,B,D) & v5_pre_topc(F,C,D) & ! [G] : ( r2_hidden(G,k9_subset_1(u1_struct_0(C),k2_struct_0(B),k2_struct_0(C))) => k1_funct_1(E,G) = k1_funct_1(F,G) ) & ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,u1_struct_0(A),u1_struct_0(D)) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(D)))) ) => ~ ( G = k1_funct_4(E,F) & v5_pre_topc(G,A,D) ) ) ) ) ) ) ) ) ) )).
fof(t1_borsuk_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t1_borsuk_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t1_borsuk_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : k4_enumset1(A,B,C,D,E,F) = k2_xboole_0(k1_enumset1(A,C,F),k1_enumset1(B,D,E)) )).
fof(t1_borsuk_6,axiom,( u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)) = k8_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(k5_numbers,1),k1_rcomp_1(k5_numbers,1)) )).
fof(t1_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) & k1_square_1(A) = k1_square_1(B) ) => A = B ) ) ) )).
fof(t1_brouwer,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( r2_hidden(C,k1_brouwer(A,B)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & C = k4_borsuk_1(A,B,D,E) & D != E ) ) ) ) ) )).
fof(t1_brouwer2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( v1_xreal_0(D) => k3_rlvect_1(k15_euclid(A),k1_rlvect_1(k15_euclid(A),B,k6_xcmplx_0(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)) ) ) ) ) )).
fof(t1_bspace,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( r2_hidden(B,k4_finseq_1(C)) => r1_struct_0(A,k1_funct_1(C,B)) ) ) ) ) )).
fof(t1_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t1_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ( r1_setfam_1(C,D) => r1_tarski(k15_bvfunc_1(A,B,C),k15_bvfunc_1(A,B,D)) ) ) ) ) ) )).
fof(t1_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( 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)) ) ) ) ) )).
fof(t1_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t1_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t1_bvfunc_1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(t1_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t1_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t1_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t1_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t1_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t1_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) )).
fof(t1_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t1_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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] : ( ( 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] : ( ( ~ 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t1_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t1_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) & r1_tarski(k2_relset_1(k3_cqc_lang(A),B),k2_relset_1(k3_cqc_lang(A),k2_partfun1(k4_ordinal1,k3_cqc_lang(A),C,D))) ) ) ) ) ) ) )).
fof(t1_calcul_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k2_calcul_2(A,B)) <=> ( r1_xxreal_0(k2_xcmplx_0(1,A),C) & r1_xxreal_0(C,k2_xcmplx_0(B,A)) ) ) ) ) ) )).
fof(t1_cantor_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => r1_tarski(B,k1_cantor_1(A,B)) ) )).
fof(t1_card_1,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ( r2_wellord2(A,B) => A = B ) ) ) )).
fof(t1_card_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( r2_hidden(A,B) & r2_wellord2(B,C) ) => ( C != k1_xboole_0 & ? [D] : r2_hidden(D,C) ) ) )).
fof(t1_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) ) => k1_card_3(A) = A ) )).
fof(t1_card_4,axiom,( ! [A] : ( v1_finset_1(A) => v4_card_3(A) ) )).
fof(t1_card_5,axiom,( ! [A] : k2_card_1(k1_card_1(A)) = k2_card_1(A) )).
fof(t1_card_fil,axiom,( ! [A] : ! [B] : ( ~ v1_finset_1(B) => r2_hidden(k5_card_1(k1_tarski(A)),k1_card_1(B)) ) )).
fof(t1_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ! [C] : ! [D] : ~ ( ( 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)) ) ) ) )).
fof(t1_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( r3_card_lar(A,B) <=> ( v2_card_lar(B,A) & v1_card_lar(B,A) ) ) ) ) )).
fof(t1_cardfin2,axiom,( ~ v2_abian(k6_partfun1(k1_xboole_0)) )).
fof(t1_cat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t1_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(B),k7_cat_1(A,B,k1_cat_2(A,B,C)),D) = C ) ) ) ) )).
fof(t1_cat_3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ! [E] : ( r2_hidden(E,A) => k7_partfun1(B,C,E) = k7_partfun1(B,D,E) ) => r2_funct_2(A,B,C,D) ) ) ) ) )).
fof(t1_cat_4,axiom,( ! [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) & l1_cat_1(A) ) => ( v1_cat_4(A) <=> ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & v10_cat_1(B,A) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u4_struct_0(A)) & ? [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t1_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t1_catalan1,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,1) => r1_xxreal_0(k7_nat_d(A,1),k7_nat_d(k3_xcmplx_0(2,A),3)) ) ) )).
fof(t1_catalan2,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,A) & v1_funct_1(C) & v5_ordinal1(C) & v1_finset_1(C) ) => ? [D] : ( v1_relat_1(D) & v5_relat_1(D,A) & v1_funct_1(D) & v5_ordinal1(D) & v1_finset_1(D) & C = k1_ordinal4(k5_relat_1(C,B),D) ) ) ) )).
fof(t1_catalg_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(t1_cayldick,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => r1_xxreal_0(k2_xcmplx_0(k1_square_1(k2_xcmplx_0(A,B)),k1_square_1(k2_xcmplx_0(C,D))),k1_square_1(k2_xcmplx_0(k3_square_1(k2_xcmplx_0(k1_square_1(A),k1_square_1(C))),k3_square_1(k2_xcmplx_0(k1_square_1(B),k1_square_1(D)))))) ) ) ) ) )).
fof(t1_cayley,axiom,( ! [A] : ! [B] : ( 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))) ) ) )).
fof(t1_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t1_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t1_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( r2_relset_1(k4_ordinal1,k2_numbers,A,k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,C)) <=> ! [D] : ( v7_ordinal1(D) => k9_nat_1(k2_numbers,A,D) = k6_xcmplx_0(k9_nat_1(k2_numbers,B,D),k9_nat_1(k2_numbers,C,D)) ) ) ) ) ) )).
fof(t1_cfdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( r1_funct_2(k4_ordinal1,k1_numbers,k4_ordinal1,k2_numbers,A,B) & v2_comseq_2(A) ) => v2_comseq_2(B) ) ) ) )).
fof(t1_cfdiff_2,axiom,( ! [A] : ( ( 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 ) ) ) )).
fof(t1_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ! [C] : ( m2_funct_2(C,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ! [D] : ( m2_funct_2(D,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ( r2_funct_2(A,k2_numbers,D,k1_funcsdom(A,k2_numbers,k1_cfuncdom(A),B,C)) <=> ! [E] : ( m1_subset_1(E,A) => k3_funct_2(A,k2_numbers,D,E) = k2_xcmplx_0(k3_funct_2(A,k2_numbers,B,E),k3_funct_2(A,k2_numbers,C,E)) ) ) ) ) ) ) )).
fof(t1_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( 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] : ( 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) = k2_xcmplx_0(k7_partfun1(k2_numbers,B,D),k7_partfun1(k2_numbers,C,D)) ) ) ) ) ) ) )).
fof(t1_cgames_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( r2_hidden(B,k2_cgames_1(A)) <=> ? [C] : ( v1_cgames_1(C) & l1_cgames_1(C) & B = C & ! [D] : ~ ( r2_hidden(D,k2_xboole_0(u1_cgames_1(C),u2_cgames_1(C))) & ! [E] : ( v3_ordinal1(E) => ~ ( r2_hidden(E,A) & r2_hidden(D,k2_cgames_1(E)) ) ) ) ) ) ) )).
fof(t1_chain_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,A) & ! [C] : ( m1_subset_1(C,k1_numbers) => ~ ( ~ r1_xxreal_0(C,A) & ~ r1_xxreal_0(B,C) ) ) ) ) ) )).
fof(t1_chord,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( v7_ordinal1(k6_xcmplx_0(A,1)) & r1_xxreal_0(1,A) ) ) )).
fof(t1_circcmb2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,B) & v1_finseq_1(C) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u4_struct_0(k5_circcomb(D,C))) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t1_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( r2_hidden(D,k2_msafree2(A)) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => k1_funct_1(k5_facirc_1(A,B,C,E),D) = k1_funct_1(C,D) ) ) ) ) ) )).
fof(t1_circcomb,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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)) ) ) ) )).
fof(t1_circled1,axiom,( ! [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) ) => ! [B] : ( ( v3_rltopsp1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v3_rltopsp1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => v3_rltopsp1(k1_rusub_5(A,B,C),A) ) ) ) )).
fof(t1_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t1_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m2_pboole(C,u1_struct_0(A),u3_msualg_1(A,k11_msafree(A,B)),u3_msualg_1(A,k11_msafree(A,B))) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_funcop_1(D) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) & v6_trees_3(F) ) => ! [G] : ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t1_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ! [C] : ( ( ~ v1_xboole_0(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( 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) => k1_relset_1(k1_euclid(A),k5_pdiff_9(A,B,C,D)) = B ) ) ) ) )).
fof(t1_classes1,axiom,( ! [A] : ( v2_classes1(A) <=> ( v1_classes1(A) & ! [B] : ( r2_hidden(B,A) => r2_hidden(k9_setfam_1(B),A) ) & ! [B] : ( ( r1_tarski(B,A) & r2_hidden(k1_card_1(B),k1_card_1(A)) ) => r2_hidden(B,A) ) ) ) )).
fof(t1_classes2,axiom,( ! [A] : ! [B] : ( ( v1_classes1(B) & r2_hidden(A,B) ) => ( ~ r2_tarski(A,B) & r2_hidden(k1_card_1(A),k1_card_1(B)) ) ) )).
fof(t1_clopban1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,A) => k3_funct_2(A,u1_struct_0(B),k4_lopban_1(A,B),C) = k4_struct_0(B) ) ) ) )).
fof(t1_clopban2,axiom,( ! [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) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) )).
fof(t1_clopban4,axiom,( ! [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) & 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(t1_closure1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( r1_tarski(B,C) => r1_tarski(a_2_0_closure1(A,C),a_2_0_closure1(A,B)) ) ) )).
fof(t1_closure2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t1_closure3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => k1_funct_4(B,C) = C ) ) ) )).
fof(t1_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xcmplx_0(C) => ( ( C = k5_numbers | B = k4_struct_0(A) ) => k1_clvect_1(A,B,C) = k4_struct_0(A) ) ) ) ) )).
fof(t1_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) )).
fof(t1_coh_sp,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => r2_hidden(k1_xboole_0,A) ) )).
fof(t1_cohsp_1,axiom,( ! [A] : ! [B] : ( r2_hidden(B,k1_cohsp_1(A)) <=> ~ ( B != k1_xboole_0 & ! [C] : ~ ( B = k1_tarski(C) & r2_hidden(C,A) ) ) ) )).
fof(t1_collsp,axiom,( ! [A] : ~ ( A != k1_xboole_0 & ! [B] : ( k1_tarski(B) != A & ! [C] : ! [D] : ~ ( C != D & r2_hidden(C,A) & r2_hidden(D,A) ) ) ) )).
fof(t1_combgras,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( 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(k1_nat_1(A,1),k1_card_1(k2_xboole_0(B,C))) ) ) ) ) )).
fof(t1_compact1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v8_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t1_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & v1_compl_sp(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => v2_seq_2(k1_compl_sp(A,B)) ) ) )).
fof(t1_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k2_xcmplx_0(k1_square_1(A),k1_square_1(B)) = k5_numbers => A = k5_numbers ) ) ) )).
fof(t1_complex2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v1_xreal_0(C) => ~ ( C = k2_xcmplx_0(k3_xcmplx_0(B,k4_xcmplx_0(k1_int_1(k7_xcmplx_0(A,B)))),A) & r1_xxreal_0(k5_numbers,C) & ~ r1_xxreal_0(B,C) ) ) ) ) ) )).
fof(t1_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( ( A = C & B = D ) => k3_rlvect_1(k1_complfld,A,B) = k2_xcmplx_0(C,D) ) ) ) ) ) )).
fof(t1_complsp1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => u1_pre_topc(k1_complsp1(A)) = k25_seq_4(A) ) )).
fof(t1_complsp2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( m2_finseq_1(C,k2_numbers) => ( r2_hidden(A,k4_finseq_1(k7_seq_4(B,C))) => k9_matrix_5(k7_seq_4(B,C),A) = k2_xcmplx_0(k9_matrix_5(B,A),k9_matrix_5(C,A)) ) ) ) ) )).
fof(t1_compos_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_compos_0(A) ) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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 ) ) ) ) )).
fof(t1_compos_1,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_compos_1)) => k2_compos_0(u1_compos_1(k1_compos_1),A) = k5_numbers ) )).
fof(t1_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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)) ) ) ) ) )).
fof(t1_comptrig,axiom,( ! [A] : ( v1_xcmplx_0(A) => r1_xxreal_0(k4_xcmplx_0(k9_complex1(A)),k3_complex1(A)) ) )).
fof(t1_compts_1,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_compts_1(A) <=> v2_compts_1(k2_struct_0(A),A) ) ) )).
fof(t1_comput_1,axiom,( ! [A] : ! [B] : ! [C] : ( k1_funct_7(k10_finseq_1(A,B),1,C) = k10_finseq_1(C,B) & k1_funct_7(k10_finseq_1(A,B),2,C) = k10_finseq_1(A,C) ) )).
fof(t1_comseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) <=> ( k9_xtuple_0(A) = k4_ordinal1 & ! [B] : ( r2_hidden(B,k4_ordinal1) => m1_subset_1(k1_funct_1(A,B),k2_numbers) ) ) ) ) )).
fof(t1_comseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( k1_nat_1(A,1) != k5_complex1 & k3_xcmplx_0(k1_nat_1(A,1),k7_complex1) != k5_complex1 ) ) )).
fof(t1_conaffm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v4_conaffm(A) => v1_conaffm(A) ) ) )).
fof(t1_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( 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) ) ) )).
fof(t1_conmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r5_analmetr(A,B,C,D) & B != C & C != D & D != B ) ) ) ) )).
fof(t1_conmetr1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v4_conmetr1(A) <=> ( v5_conmetr1(A) & v6_conmetr1(A) ) ) ) )).
fof(t1_connsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_connsp_1(A,B,C) => r1_xboole_0(B,C) ) ) ) ) )).
fof(t1_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t1_connsp_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ? [C] : ( 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)) ) ) ) )).
fof(t1_convex1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v1_xreal_0(C) => ( v1_convex1(B,A) => v1_convex1(k1_convex1(A,B,C),A) ) ) ) ) )).
fof(t1_convex2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( v1_convex1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t1_convex3,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( v2_convex1(C,A) & m1_rlvect_2(C,A) & k6_rlvect_2(A,C) = B & ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t1_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_convex4(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t1_convfun1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_rlvect_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k3_convfun1(A,B))) => ! [F] : ( v1_xreal_0(F) => ( 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)) ) ) ) ) ) ) ) )).
fof(t1_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t1_cqc_sim1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => k9_relat_1(k1_funct_4(C,k16_funcop_1(A,B)),A) = k1_tarski(B) ) )).
fof(t1_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t1_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t1_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ( r2_hidden(B,C) => r3_cqc_the1(A,C,B) ) ) ) ) )).
fof(t1_csspace,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_funct_2(k4_ordinal1,k2_numbers,k2_csspace(A),A) ) )).
fof(t1_csspace2,axiom,( u1_struct_0(k18_csspace) = k11_csspace & ! [A] : ( m1_subset_1(A,u1_struct_0(k18_csspace)) <=> ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & v1_series_1(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,k2_csspace(A)),k55_valued_1(k4_ordinal1,k2_numbers,k2_csspace(A)))) ) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k18_csspace)) <=> ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & v2_comseq_3(k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k2_csspace(A),k2_comseq_2(k4_ordinal1,k2_csspace(A)))) ) ) & k4_struct_0(k18_csspace) = k6_csspace & ! [A] : ( m1_subset_1(A,u1_struct_0(k18_csspace)) => A = k2_csspace(A) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k18_csspace)) => ! [B] : ( 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] : ( v1_xcmplx_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k18_csspace)) => k1_clvect_1(k18_csspace,B,A) = k25_valued_1(k4_ordinal1,k2_numbers,k2_csspace(B),A) ) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k18_csspace)) => ( k4_algstr_0(k18_csspace,A) = k31_valued_1(k4_ordinal1,k2_numbers,k2_csspace(A)) & r2_funct_2(k4_ordinal1,k2_numbers,k2_csspace(k4_algstr_0(k18_csspace,A)),k31_valued_1(k4_ordinal1,k2_numbers,k2_csspace(A))) ) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k18_csspace)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k18_csspace)) => k5_algstr_0(k18_csspace,A,B) = k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k2_csspace(A),k2_csspace(B)) ) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k18_csspace)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k18_csspace)) => ( v1_series_1(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,k2_csspace(A)),k55_valued_1(k4_ordinal1,k2_numbers,k2_csspace(B)))) & ! [C] : ( m1_subset_1(C,u1_struct_0(k18_csspace)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k18_csspace)) => k12_csspace(k18_csspace,C,D) = k11_comseq_3(k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k2_csspace(C),k2_comseq_2(k4_ordinal1,k2_csspace(D)))) ) ) ) ) ) )).
fof(t1_csspace3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(B) & ! [D] : ( v7_ordinal1(D) => k1_funct_1(C,D) = k9_complex1(k6_xcmplx_0(k1_funct_1(B,D),A)) ) ) => ( v2_comseq_2(C) & k1_seq_2(C) = k9_complex1(k6_xcmplx_0(k3_comseq_2(B),A)) ) ) ) ) ) )).
fof(t1_csspace4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v1_comseq_2(A) & k2_seq_4(k2_relset_1(k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,A))) = k5_numbers ) <=> ! [B] : ( v7_ordinal1(B) => k1_funct_1(A,B) = k5_complex1 ) ) ) )).
fof(t1_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t1_descip_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t1_dickson,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( k9_xtuple_0(A) = k1_tarski(B) => A = k16_funcop_1(B,k1_funct_1(A,B)) ) ) )).
fof(t1_diff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r2_hidden(B,k1_relset_1(k1_numbers,C)) & r2_hidden(k2_xcmplx_0(B,A),k1_relset_1(k1_numbers,C)) ) => k1_funct_1(k3_diff_1(C,A),B) = k6_xcmplx_0(k1_funct_1(C,k2_xcmplx_0(B,A)),k1_funct_1(C,B)) ) ) ) ) )).
fof(t1_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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,B,k2_xcmplx_0(B,A)) = k7_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(C,A),1),B),A) ) ) ) )).
fof(t1_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k5_diff_1(C,A),B) = k6_xcmplx_0(k1_funct_1(k3_diff_1(C,k7_xcmplx_0(A,2)),B),k1_funct_1(k3_diff_1(C,k4_xcmplx_0(k7_xcmplx_0(A,2))),B)) ) ) ) )).
fof(t1_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & k6_xcmplx_0(k3_power(k4_power,A),k3_power(k4_power,B)) != k3_power(k4_power,k7_xcmplx_0(A,B)) ) ) ) )).
fof(t1_dilworth,axiom,( ! [A] : ! [B] : ! [C] : ( ~ r2_hidden(C,A) => k6_subset_1(A,k2_xboole_0(B,k1_tarski(C))) = k6_subset_1(A,B) ) )).
fof(t1_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_analoaf(A,B,C,B,C) ) ) ) )).
fof(t1_dirort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(k5_analort(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_analort(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k5_analort(A,B,C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k5_analort(A,B,C))) => ! [H] : ( 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] : ( m1_subset_1(D,u1_struct_0(k5_analort(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_analort(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k5_analort(A,B,C))) => ? [G] : ( 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] : ( m1_subset_1(D,u1_struct_0(k5_analort(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_analort(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k5_analort(A,B,C))) => ? [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t1_dist_1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ~ ( r2_hidden(C,k9_xtuple_0(B)) & ! [D] : ( m1_subset_1(D,A) => ~ r2_hidden(C,k1_dist_1(A,B,D)) ) ) ) )).
fof(t1_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m2_finseq_1(B,A) => ( ( A = k6_domain_1(k4_ordinal1,1) & B = k2_matrprob(1) ) => k4_dist_1(A,B) = k2_matrprob(1) ) ) ) )).
fof(t1_domain_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ~ ( r2_hidden(A,k2_zfmisc_1(B,C)) & ! [D] : ( m1_subset_1(D,B) => ! [E] : ( m1_subset_1(E,C) => A != k4_tarski(D,E) ) ) ) ) ) )).
fof(t1_dtconstr,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,k5_trees_3(A)) => m2_finseq_1(B,k4_trees_3(A)) ) ) )).
fof(t1_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( r2_hidden(C,k10_xtuple_0(B)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & k9_nat_1(k9_setfam_1(A),B,D) = C ) ) ) ) )).
fof(t1_e_siec,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( 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 ) ) ) ) )).
fof(t1_ec_pf_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) )).
fof(t1_ec_pf_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( B = k4_algstr_0(A,C) => k2_binom(A,B,2) = k2_binom(A,C,2) ) ) ) ) )).
fof(t1_endalg,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t1_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( r2_hidden(B,k1_ens_1(A)) <=> ? [C] : ( m1_subset_1(C,A) & ? [D] : ( 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))) ) ) ) ) )).
fof(t1_entropy1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( C != k5_numbers & ~ r1_xxreal_0(D,A) & r1_xxreal_0(D,B) & r1_nat_d(C,D) & r1_xxreal_0(k3_nat_d(B,C),k3_nat_d(A,C)) ) ) ) ) ) )).
fof(t1_enumset1,axiom,( ! [A] : ! [B] : k2_tarski(A,B) = k2_xboole_0(k1_tarski(A),k1_tarski(B)) )).
fof(t1_eqrel_1,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(t1_equation,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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 ) ) ) ) ) )).
fof(t1_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => k10_euclid(A,k5_euclid(A)) = k2_finseq_2(A,k5_numbers) ) )).
fof(t1_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(B,k1_numbers)) => k1_funct_1(k14_rvsum_1(C,k5_euclid(B)),A) = k5_numbers ) ) ) )).
fof(t1_euclid_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_euclid_3(k1_euclid_3(A)) = A ) )).
fof(t1_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ( k7_euclid(A,k9_euclid(A,B,k5_numbers),B) = B & k7_euclid(A,B,k5_euclid(A)) = B ) ) ) )).
fof(t1_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => ? [B] : ( v1_xreal_0(B) & ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & A = k11_finseq_1(B,C,D) ) ) ) ) )).
fof(t1_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ( ( k17_sin_cos(k4_euclid_3(A,B,C)) = k17_sin_cos(k4_euclid_3(D,E,F)) & k19_sin_cos(k4_euclid_3(A,B,C)) = k19_sin_cos(k4_euclid_3(D,E,F)) ) => k4_euclid_3(A,B,C) = k4_euclid_3(D,E,F) ) ) ) ) ) ) ) )).
fof(t1_euclid_7,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r1_tarski(k10_xtuple_0(A),B) => k8_relat_1(A,B) = k9_xtuple_0(A) ) ) )).
fof(t1_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => A = k1_euclid_8(k1_funct_1(A,1),k1_funct_1(A,2),k1_funct_1(A,3)) ) )).
fof(t1_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) ) => ( v1_xboole_0(B) => A = k5_numbers ) ) ) )).
fof(t1_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(D)) => ( k9_euclid(D,k9_euclid(D,E,C),k7_xcmplx_0(A,B)) = k9_euclid(D,E,k7_xcmplx_0(k3_xcmplx_0(A,C),B)) & k9_euclid(D,k9_euclid(D,E,C),k7_xcmplx_0(1,B)) = k9_euclid(D,E,k7_xcmplx_0(C,B)) ) ) ) ) ) ) )).
fof(t1_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ~ r5_analmetr(A,B,C,D) => ( B != C & C != D & B != D ) ) ) ) ) ) )).
fof(t1_euler_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_int_2(A,A) <=> A = 1 ) ) )).
fof(t1_euler_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_int_2(A,B) <=> r1_int_2(A,B) ) ) ) )).
fof(t1_exchsort,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( r2_hidden(C,k6_subset_1(k10_ordinal2(A,B),A)) <=> ? [D] : ( v3_ordinal1(D) & C = k10_ordinal2(A,D) & r2_hidden(D,B) ) ) ) ) )).
fof(t1_extens_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,C) => ! [E] : ( m3_pboole(E,A,B) => ( r2_pboole(A,B,E) => r6_pboole(A,k1_msafree(A,B,C,E,D),D) ) ) ) ) ) )).
fof(t1_extreal1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( A = C & B = D ) => k4_xxreal_3(A,B) = k3_xcmplx_0(C,D) ) ) ) ) ) )).
fof(t1_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( A = B => k3_extreal1(A) = k9_complex1(B) ) ) ) )).
fof(t1_facirc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ~ ( v2_facirc_1(A) & v1_facirc_1(k10_xtuple_0(A)) ) ) )).
fof(t1_facirc_2,axiom,( ! [A] : ! [B] : ! [C] : ~ ( A != C & B != C & k6_subset_1(k2_tarski(A,B),k1_tarski(C)) != k2_tarski(A,B) ) )).
fof(t1_fcont_1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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) ) ) ) )).
fof(t1_fcont_2,axiom,( ! [A] : ! [B] : ( ( 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] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ~ ( 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,k9_complex1(k6_xcmplx_0(E,F))) & r1_xxreal_0(C,k9_complex1(k6_xcmplx_0(k1_funct_1(B,E),k1_funct_1(B,F)))) ) ) ) ) ) ) ) ) ) )).
fof(t1_fcont_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( r2_hidden(B,k2_rcomp_1(k6_xcmplx_0(A,C),k2_xcmplx_0(A,C))) & r1_xxreal_0(C,k9_complex1(k6_xcmplx_0(B,A))) ) ) ) ) )).
fof(t1_fdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) <=> r2_hidden(B,k1_numbers) ) ) <=> A = k1_numbers ) ) )).
fof(t1_fdiff_10,axiom,( ! [A] : ( ( 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,k27_sin_cos,k26_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k26_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k26_sin_cos),A),B) = k3_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,k1_funct_1(k27_sin_cos,B)))),k4_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B))))) ) ) ) ) ) )).
fof(t1_fdiff_11,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k16_sin_cos,B),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k1_sin_cos9),A),B) = k7_xcmplx_0(k1_funct_1(k18_sin_cos,B),k2_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t1_fdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(A) & v2_comseq_2(B) & k1_seq_2(A) = k1_seq_2(B) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( k3_funct_2(k4_ordinal1,k1_numbers,C,k2_nat_1(2,D)) = k3_funct_2(k4_ordinal1,k1_numbers,A,D) & k3_funct_2(k4_ordinal1,k1_numbers,C,k1_nat_1(k2_nat_1(2,D),1)) = k3_funct_2(k4_ordinal1,k1_numbers,B,D) ) ) ) => ( v2_comseq_2(C) & k1_seq_2(C) = k1_seq_2(A) ) ) ) ) ) )).
fof(t1_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k1_funct_1(C,D) = k2_xcmplx_0(A,D) & ~ r1_xxreal_0(k1_funct_1(C,D),k5_numbers) ) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1),B),D) = k7_xcmplx_0(1,k2_xcmplx_0(A,D)) ) ) ) ) ) ) ) )).
fof(t1_fdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => ( k1_funct_1(C,E) = k2_xcmplx_0(A,E) & k1_funct_1(D,E) = k6_xcmplx_0(A,E) & k1_funct_1(D,E) != k5_numbers ) ) ) ) => ( r2_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,C,D),B) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_1(k2_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,C,D),B),E) = k7_xcmplx_0(k3_xcmplx_0(2,A),k1_square_1(k6_xcmplx_0(A,E))) ) ) ) ) ) ) ) ) )).
fof(t1_fdiff_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,k5_numbers) => k1_funct_1(k22_sin_cos,k3_xcmplx_0(A,k3_power(k4_power,B))) = k6_prepower(B,A) ) ) ) )).
fof(t1_fdiff_7,axiom,( ! [A] : ( v1_xreal_0(A) => k3_prepower(A,2) = k1_square_1(A) ) )).
fof(t1_fdiff_8,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( r2_hidden(A,k1_relset_1(k1_numbers,k26_sin_cos)) & k1_funct_1(k18_sin_cos,A) = k5_numbers ) ) )).
fof(t1_fdiff_9,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_funct_1(k18_sin_cos,A) != k5_numbers => ( r1_fdiff_1(k1_fdiff_9,A) & k1_fdiff_1(k1_fdiff_9,A) = k7_xcmplx_0(k1_funct_1(k16_sin_cos,A),k1_square_1(k1_funct_1(k18_sin_cos,A))) ) ) ) )).
fof(t1_ff_siec,axiom,( ! [A] : ! [B] : ( 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 ) ) )).
fof(t1_fib_num,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k3_int_2(A,B) = k3_int_2(A,k1_nat_1(B,A)) ) ) )).
fof(t1_fib_num2,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => k1_nat_1(k7_nat_d(A,1),2) = k1_nat_1(A,1) ) )).
fof(t1_fib_num3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( k2_power(A,B) = k5_numbers => A = k5_numbers ) ) ) )).
fof(t1_fib_num4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => k2_power(k7_xcmplx_0(A,B),C) = k7_xcmplx_0(k2_power(A,C),k2_power(B,C)) ) ) ) )).
fof(t1_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t1_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t1_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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))) ) ) ) ) )).
fof(t1_filter_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t1_finance1,axiom,( ! [A] : ( v1_xreal_0(A) => k6_subset_1(k1_numbers,k3_rcomp_1(A,k1_xxreal_0)) = k2_rcomp_1(k2_xxreal_0,A) ) )).
fof(t1_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,k2_finseq_1(B)) <=> ( r1_xxreal_0(1,A) & r1_xxreal_0(A,B) ) ) ) ) )).
fof(t1_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( C = k3_xxreal_0(A,B) => k9_subset_1(k4_ordinal1,k2_finseq_1(A),k2_finseq_1(B)) = k2_finseq_1(C) ) ) ) ) )).
fof(t1_finseq_3,axiom,( k2_finseq_1(3) = k1_enumset1(1,2,3) )).
fof(t1_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r1_finseq_4(A,B) => r2_hidden(B,k9_xtuple_0(A)) ) ) )).
fof(t1_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(A,B) => m1_subset_1(k2_xcmplx_0(k6_xcmplx_0(B,A),1),k4_ordinal1) ) ) ) )).
fof(t1_finseq_6,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( ( r1_tarski(A,k2_finseq_1(B)) & r2_hidden(1,A) ) => k1_funct_1(k14_finseq_1(A),1) = 1 ) ) )).
fof(t1_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t1_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( 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 ) ) ) ) )).
fof(t1_finseqop,axiom,( ! [A] : ( ( 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 ) ) )).
fof(t1_finset_1,axiom,( ! [A] : ! [B] : ( ( r1_tarski(A,B) & v1_finset_1(B) ) => v1_finset_1(A) ) )).
fof(t1_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ~ ( k9_nat_1(A,D,1) = k1_funct_1(B,1) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( k5_numbers != E & ~ r1_xxreal_0(k3_finseq_1(B),E) & k9_nat_1(A,D,k1_nat_1(E,1)) != k1_binop_1(C,k9_nat_1(A,D,E),k1_funct_1(B,k1_nat_1(E,1))) ) ) & k1_finsop_1(A,B,C) = k9_nat_1(A,D,k3_finseq_1(B)) ) ) ) ) ) ) )).
fof(t1_finsub_1,axiom,( ! [A] : ( v4_finsub_1(A) <=> ! [B] : ! [C] : ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => ( r2_hidden(k2_xboole_0(B,C),A) & r2_hidden(k6_subset_1(B,C),A) ) ) ) )).
fof(t1_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t1_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_orders_2(A) => r1_tarski(B,k12_fin_topo(A,B)) ) ) ) )).
fof(t1_fintopo4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r1_xxreal_0(C,D) => r1_tarski(k7_fintopo3(A,B,C),k7_fintopo3(A,B,D)) ) ) ) ) ) )).
fof(t1_fintopo5,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( 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 ) ) ) ) )).
fof(t1_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => k9_fin_topo(A,k1_struct_0(A)) = k1_xboole_0 ) )).
fof(t1_flang_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ ( r1_xxreal_0(B,A) & r1_xxreal_0(C,A) ) & r1_xxreal_0(k2_xcmplx_0(B,C),A) ) ) ) ) )).
fof(t1_flang_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(k2_xcmplx_0(C,B),A) & r1_xxreal_0(A,k2_xcmplx_0(D,B)) & ! [E] : ( v7_ordinal1(E) => ~ ( k2_xcmplx_0(E,B) = A & r1_xxreal_0(C,E) & r1_xxreal_0(E,D) ) ) ) ) ) ) ) )).
fof(t1_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ( r1_tarski(C,k8_flang_1(A,B)) => ( r1_tarski(k6_flang_1(A,k8_flang_1(A,B),C),k8_flang_1(A,B)) & r1_tarski(k6_flang_1(A,C,k8_flang_1(A,B)),k8_flang_1(A,B)) ) ) ) ) )).
fof(t1_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(t1_fomodel1,axiom,( ! [A] : ( ( ~ 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)) = k1_tarski(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)) ) ) )).
fof(t1_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v14_fomodel1(B,k5_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 = k43_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)) ) ) )).
fof(t1_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m2_subset_1(C,k1_zfmisc_1(A),k8_eqrel_1(A,B)) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),k8_eqrel_1(A,B)) => ( ~ r2_subset_1(C,D) => C = D ) ) ) ) ) )).
fof(t1_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))))) => ! [D] : ( v2_fomodel4(D,B) => ~ ( v4_fomodel4(k1_tarski(A),B,C,D) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ v5_fomodel4(A,E,B,C,D) ) ) ) ) ) )).
fof(t1_fraenkel,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( r2_relset_1(A,B,k2_partfun1(A,B,C,E),k2_partfun1(A,B,D,E)) => ! [F] : ( m1_subset_1(F,A) => ( r2_hidden(F,E) => k1_funct_1(C,F) = k1_funct_1(D,F) ) ) ) ) ) )).
fof(t1_frechet,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => m1_subset_1(k2_relset_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(t1_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_ordinal1) & v5_valued_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ( v1_funct_1(k2_valued_0(u1_struct_0(A),C,B)) & v1_funct_2(k2_valued_0(u1_struct_0(A),C,B),k4_ordinal1,u1_struct_0(A)) & m1_subset_1(k2_valued_0(u1_struct_0(A),C,B),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) ) ) )).
fof(t1_freealg,axiom,( ! [A] : ( ( ~ 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] : ( 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 ) ) ) ) )).
fof(t1_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : v1_relat_1(k3_msafree2(k4_fscirc_1(A,B,C))) )).
fof(t1_fscirc_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ( ( k1_funct_1(C,k5_numbers) = k5_circcomb(k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k8_margrel1),k1_xboole_0) & k1_funct_1(D,k5_numbers) = k7_circcomb(k5_ordinal1,k6_margrel1,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k8_margrel1),k1_xboole_0) & k1_funct_1(E,k5_numbers) = k4_tarski(k1_xboole_0,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k8_margrel1)) & ! [F] : ( v7_ordinal1(F) => ! [G] : ( ( ~ v2_struct_0(G) & l1_msualg_1(G) ) => ! [H] : ( ( v4_msualg_1(H,G) & l3_msualg_1(H,G) ) => ! [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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t1_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(t1_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ v2_struct_0(C) & l1_fsm_1(C,A) ) => ! [D] : ( 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))) ) ) ) ) )).
fof(t1_fsm_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k2_xcmplx_0(B,C),A) => r1_xxreal_0(B,A) ) ) ) ) )).
fof(t1_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : 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))) )).
fof(t1_funcop_1,axiom,( ! [A] : k12_funct_3(A) = k13_funct_3(k6_partfun1(A),k6_partfun1(A)) )).
fof(t1_funcsdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( m2_funct_2(C,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [D] : ( m2_funct_2(D,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ( r2_funct_2(A,k1_numbers,D,k1_funcsdom(A,k1_numbers,k5_funcsdom(A),B,C)) <=> ! [E] : ( m1_subset_1(E,A) => k3_funct_2(A,k1_numbers,D,E) = k3_real_1(k3_funct_2(A,k1_numbers,B,E),k3_funct_2(A,k1_numbers,C,E)) ) ) ) ) ) ) )).
fof(t1_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) ) )).
fof(t1_funct_2,axiom,( ! [A] : ( ( 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)))) ) ) )).
fof(t1_funct_3,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => k4_relat_1(A) = k5_relat_1(k4_relat_1(B),A) ) )).
fof(t1_funct_4,axiom,( ! [A] : ~ ( ! [B] : ~ ( r2_hidden(B,A) & ! [C] : ! [D] : B != k4_tarski(C,D) ) & ! [B] : ! [C] : ~ r1_tarski(A,k2_zfmisc_1(B,C)) ) )).
fof(t1_funct_5,axiom,( k2_funct_4(k1_xboole_0) = k1_xboole_0 )).
fof(t1_funct_6,axiom,( ! [A] : ( ( 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))) ) )).
fof(t1_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r1_tarski(k10_xtuple_0(A),B) => k3_relat_1(A,k6_partfun1(B)) = A ) ) )).
fof(t1_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k2_xcmplx_0(k1_funct_1(B,C),k1_funct_1(B,k4_xcmplx_0(C))) = k5_numbers ) ) ) ) ) ) )).
fof(t1_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) ) => ( v1_funct_9(B,A) <=> ( A != k5_numbers & ! [C] : ( 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)) ) ) ) ) ) ) ) )).
fof(t1_functor0,axiom,( ! [A] : ( 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))) ) )).
fof(t1_functor1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ! [D] : ( ( ~ 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))) ) ) ) ) ) )).
fof(t1_functor2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(t1_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v5_relat_1(k7_rfunct_1(A,A),k1_rcomp_1(k5_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))) ) ) )).
fof(t1_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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(k5_numbers,k3_funct_2(A,k1_numbers,C,B)) & r1_xxreal_0(k3_funct_2(A,k1_numbers,C,B),1) ) ) ) ) )).
fof(t1_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( r2_hidden(C,k1_relset_1(A,B)) => r1_xxreal_0(k1_funct_1(B,C),k2_seq_4(k2_relset_1(k1_numbers,B))) ) & ! [C] : ( r2_hidden(C,k1_relset_1(A,B)) => r1_xxreal_0(k3_seq_4(k2_relset_1(k1_numbers,B)),k1_funct_1(B,C)) ) ) ) ) )).
fof(t1_fvaluat1,axiom,( ! [A] : ( v1_xxreal_0(A) => ( A = k2_xxreal_3(A) => A = k5_numbers ) ) )).
fof(t1_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & l2_algstr_0(A) ) => v1_binop_1(u1_algstr_0(A),u1_struct_0(A)) ) )).
fof(t1_gate_1,axiom,( k1_gate_1(k1_tarski(k1_xboole_0)) = k1_xboole_0 & k1_gate_1(k1_xboole_0) = k1_tarski(k1_xboole_0) )).
fof(t1_gate_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ! [Q] : ! [R] : ! [S] : ! [T] : ! [U] : ! [V] : ~ ( ~ ( ~ 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) ) ) ) )).
fof(t1_gate_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ~ ( ~ ( ~ 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) ) ) ) )).
fof(t1_gate_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ! [Q] : ! [R] : ! [S] : ! [T] : ! [U] : ! [V] : ! [W] : ! [X] : ! [Y] : ! [Z] : ! [A1] : ! [B1] : ! [C1] : ! [D1] : ! [E1] : ! [F1] : ! [G1] : ! [H1] : ! [I1] : ! [J1] : ! [K1] : ! [L1] : ~ ( ~ v1_xboole_0(M) & ~ ( ~ v1_xboole_0(Z) & v1_xboole_0(k4_gate_1(L1,k2_gate_1(A,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(L1,k2_gate_1(A,Y))) & v1_xboole_0(Z) ) & ~ ( ~ v1_xboole_0(A1) & v1_xboole_0(k4_gate_1(N,k2_gate_1(B,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(N,k2_gate_1(B,Y))) & v1_xboole_0(A1) ) & ~ ( ~ v1_xboole_0(B1) & v1_xboole_0(k4_gate_1(O,k2_gate_1(C,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(O,k2_gate_1(C,Y))) & v1_xboole_0(B1) ) & ~ ( ~ v1_xboole_0(C1) & v1_xboole_0(k4_gate_1(P,k2_gate_1(D,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(P,k2_gate_1(D,Y))) & v1_xboole_0(C1) ) & ~ ( ~ v1_xboole_0(D1) & v1_xboole_0(k4_gate_1(Q,k2_gate_1(E,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(Q,k2_gate_1(E,Y))) & v1_xboole_0(D1) ) & ~ ( ~ v1_xboole_0(E1) & v1_xboole_0(k4_gate_1(R,k2_gate_1(F,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(R,k2_gate_1(F,Y))) & v1_xboole_0(E1) ) & ~ ( ~ v1_xboole_0(F1) & v1_xboole_0(k4_gate_1(S,k2_gate_1(G,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(S,k2_gate_1(G,Y))) & v1_xboole_0(F1) ) & ~ ( ~ v1_xboole_0(G1) & v1_xboole_0(k4_gate_1(T,k2_gate_1(H,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(T,k2_gate_1(H,Y))) & v1_xboole_0(G1) ) & ~ ( ~ v1_xboole_0(H1) & v1_xboole_0(k4_gate_1(U,k2_gate_1(I,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(U,k2_gate_1(I,Y))) & v1_xboole_0(H1) ) & ~ ( ~ v1_xboole_0(I1) & v1_xboole_0(k4_gate_1(V,k2_gate_1(J,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(V,k2_gate_1(J,Y))) & v1_xboole_0(I1) ) & ~ ( ~ v1_xboole_0(J1) & v1_xboole_0(k4_gate_1(W,k2_gate_1(K,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(W,k2_gate_1(K,Y))) & v1_xboole_0(J1) ) & ~ ( ~ v1_xboole_0(K1) & v1_xboole_0(k4_gate_1(X,k2_gate_1(L,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(X,k2_gate_1(L,Y))) & v1_xboole_0(K1) ) & ~ ( ~ ( ~ v1_xboole_0(Y) & v1_xboole_0(k2_gate_1(M,Y)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(M,Y)) & v1_xboole_0(Y) ) & ~ ( ~ v1_xboole_0(X) & v1_xboole_0(k4_gate_1(K1,k2_gate_1(L,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(K1,k2_gate_1(L,Y))) & v1_xboole_0(X) ) & ~ ( ~ v1_xboole_0(W) & v1_xboole_0(k4_gate_1(J1,k2_gate_1(K,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(J1,k2_gate_1(K,Y))) & v1_xboole_0(W) ) & ~ ( ~ v1_xboole_0(V) & v1_xboole_0(k4_gate_1(I1,k2_gate_1(J,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(I1,k2_gate_1(J,Y))) & v1_xboole_0(V) ) & ~ ( ~ v1_xboole_0(U) & v1_xboole_0(k4_gate_1(H1,k2_gate_1(I,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(H1,k2_gate_1(I,Y))) & v1_xboole_0(U) ) & ~ ( ~ v1_xboole_0(T) & v1_xboole_0(k4_gate_1(G1,k2_gate_1(H,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(G1,k2_gate_1(H,Y))) & v1_xboole_0(T) ) & ~ ( ~ v1_xboole_0(S) & v1_xboole_0(k4_gate_1(F1,k2_gate_1(G,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(F1,k2_gate_1(G,Y))) & v1_xboole_0(S) ) & ~ ( ~ v1_xboole_0(R) & v1_xboole_0(k4_gate_1(E1,k2_gate_1(F,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(E1,k2_gate_1(F,Y))) & v1_xboole_0(R) ) & ~ ( ~ v1_xboole_0(Q) & v1_xboole_0(k4_gate_1(D1,k2_gate_1(E,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(D1,k2_gate_1(E,Y))) & v1_xboole_0(Q) ) & ~ ( ~ v1_xboole_0(P) & v1_xboole_0(k4_gate_1(C1,k2_gate_1(D,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(C1,k2_gate_1(D,Y))) & v1_xboole_0(P) ) & ~ ( ~ v1_xboole_0(O) & v1_xboole_0(k4_gate_1(B1,k2_gate_1(C,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(B1,k2_gate_1(C,Y))) & v1_xboole_0(O) ) & ~ ( ~ v1_xboole_0(N) & v1_xboole_0(k4_gate_1(A1,k2_gate_1(B,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(A1,k2_gate_1(B,Y))) & v1_xboole_0(N) ) & ~ ( ~ v1_xboole_0(L1) & v1_xboole_0(k4_gate_1(Z,k2_gate_1(A,Y))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(Z,k2_gate_1(A,Y))) & v1_xboole_0(L1) ) ) ) )).
fof(t1_gate_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ~ ( ~ ( ~ 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) ) ) ) )).
fof(t1_gcd_1,axiom,( ! [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) & v1_vectsp_2(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) ) ) )).
fof(t1_genealg1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t1_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t1_gfacirc1,axiom,( ! [A] : ( 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(k4_ordinal1,k5_numbers)) = 1 & k1_funct_1(k1_gfacirc1,k10_binarith(k4_ordinal1,1)) = k5_numbers ) ) )).
fof(t1_gfacirc2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ( ( k1_funct_1(C,k5_numbers) = k5_circcomb(k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1),k1_xboole_0) & k1_funct_1(D,k5_numbers) = k7_circcomb(k5_ordinal1,k6_margrel1,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1),k1_xboole_0) & k1_funct_1(E,k5_numbers) = k4_tarski(k1_xboole_0,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1)) & ! [F] : ( v7_ordinal1(F) => ! [G] : ( ( ~ v2_struct_0(G) & l1_msualg_1(G) ) => ! [H] : ( ( v4_msualg_1(H,G) & l3_msualg_1(H,G) ) => ! [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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t1_glib_000,axiom,( k1_glib_000 = 1 & k2_glib_000 = 2 & k3_glib_000 = 3 & k4_glib_000 = 4 )).
fof(t1_glib_001,axiom,( ! [A] : ( ( ~ v1_abian(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_abian(B) & m1_subset_1(B,k4_ordinal1) ) => ( ~ r1_xxreal_0(B,A) <=> r1_xxreal_0(k1_nat_1(A,2),B) ) ) ) )).
fof(t1_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & ~ v4_glib_000(A) & v1_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ~ v10_glib_000(B,A) ) ) )).
fof(t1_glib_003,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ( ( 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 ) ) ) )).
fof(t1_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t1_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( ( 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] : ( m3_glib_001(C,A) => ( v3_glib_001(C,A) => r5_glib_005(A,B,C) ) ) ) ) )).
fof(t1_goboard1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ( ( 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)) ) ) ) )).
fof(t1_goboard2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r2_hidden(B,k4_finseq_1(A)) & r2_hidden(k1_nat_1(B,1),k4_finseq_1(A)) & r2_hidden(C,k4_finseq_1(A)) & r2_hidden(k1_nat_1(C,1),k4_finseq_1(A)) ) => ( r1_xxreal_0(C,k1_nat_1(B,1)) | r1_xboole_0(k2_topreal1(2,A,B),k2_topreal1(2,A,C)) ) ) ) ) => v3_topreal1(A) ) ) )).
fof(t1_goboard3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ~ ( ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(C,k4_finseq_1(A)) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( r2_hidden(k4_tarski(D,E),k2_matrix_0(B)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),B,D,E) ) ) ) ) ) & v2_funct_1(A) & v2_topreal1(A) & v3_topreal1(A) & v1_topreal1(A) & ! [C] : ( 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)) ) ) ) ) ) )).
fof(t1_goboard4,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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(k7_matrix_0(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(k7_matrix_0(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(k8_matrix_0(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(k8_matrix_0(u1_struct_0(k15_euclid(2)),A,k1_matrix_0(A)))) & r1_xboole_0(k10_xtuple_0(B),k10_xtuple_0(C)) ) ) ) ) )).
fof(t1_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( v2_goboard1(C) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k1_matrix_0(C)) & r1_xxreal_0(1,A) & r1_xxreal_0(A,k3_finseq_1(C)) ) => k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B)) = k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,B)) ) ) ) ) )).
fof(t1_goboard6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_numbers) => r2_hidden(B,k8_metric_1(A,B,C)) ) ) ) ) )).
fof(t1_goboard7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(k9_complex1(k6_xcmplx_0(B,C)),A) & r1_xxreal_0(C,k2_xcmplx_0(B,A)) & r1_xxreal_0(B,k2_xcmplx_0(C,A)) ) ) ) ) )).
fof(t1_goboard8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,2),k3_finseq_1(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(k2_goboard2(A))) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,2),k1_matrix_0(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_nat_1(D,1)) ) => ( ( ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),D) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_nat_1(D,2)) ) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),D) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_nat_1(D,1))),k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,k1_nat_1(D,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_nat_1(D,2))),k7_xcmplx_0(1,2))),k3_topreal1(2,A)) ) ) ) ) ) ) ) )).
fof(t1_goboard9,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t1_gobrd10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_gobrd10(A,B) => r1_gobrd10(k1_nat_1(A,1),k1_nat_1(B,1)) ) ) ) )).
fof(t1_gobrd11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t1_gobrd12,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(B,k3_finseq_1(k2_goboard2(A))) & r1_xxreal_0(C,k1_matrix_0(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))) ) ) ) ) )).
fof(t1_goedcpuc,axiom,( ! [A] : ( m1_qc_lang1(A) => ? [B] : ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ~ r2_hidden(k4_tarski(B,k1_domain_1(k3_qc_lang1(A),k3_cqc_lang(A),D,C)),k1_qc_lang1(A)) ) ) ) )).
fof(t1_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(t1_gr_cy_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => ( A = k5_numbers => r3_binop_1(k4_numbers,A,k20_binop_2) ) ) )).
fof(t1_gr_cy_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( ~ r1_xxreal_0(k6_group_1(A,B),1) & B = k5_group_1(A,D,C) & D = k5_numbers ) ) ) ) ) )).
fof(t1_gr_cy_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ! [C] : ( v7_ordinal1(C) => ~ ( r1_nat_d(C,k3_xcmplx_0(A,B)) & C != 1 & C != A & C != B & C != k3_xcmplx_0(A,B) ) ) ) ) )).
fof(t1_graph_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t1_graph_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(k1_nat_1(A,1),B) & r1_xxreal_0(B,C) ) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & r1_xxreal_0(A,D) & ~ r1_xxreal_0(C,D) & B = k1_nat_1(D,1) ) ) ) ) ) )).
fof(t1_graph_3,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( ( v1_abian(A) <=> v1_abian(B) ) <=> v1_abian(k6_xcmplx_0(A,B)) ) ) ) )).
fof(t1_graph_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r1_graph_4(B,C,D,A) => r2_graph_1(B,C,D,A) ) ) ) ) )).
fof(t1_graph_5,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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] : ~ ( r2_hidden(D,k9_xtuple_0(C)) & k1_funct_1(B,A) = k1_funct_1(C,D) ) ) ) ) )).
fof(t1_graphsp,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( ~ r2_hidden(B,k10_xtuple_0(A)) & v2_funct_1(A) ) <=> v2_funct_1(k7_finseq_1(A,k9_finseq_1(B))) ) ) )).
fof(t1_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(k3_xtuple_0(B,C,D),A) & r2_hidden(k6_xtuple_0(B,C,D,E),A) ) ) ) ) ) ) )).
fof(t1_grfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r1_tarski(B,A) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) )).
fof(t1_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t1_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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] : ( ( 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 != k7_polynom1(A,C,D,k10_polynom1(A,C,G,E)) ) ) ) ) ) ) ) ) )).
fof(t1_groeb_3,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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 ) ) )).
fof(t1_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k6_algstr_0(A,C,B) = C & k6_algstr_0(A,B,C) = C & ? [D] : ( 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) ) ) ) ) )).
fof(t1_group_10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ~ ( r1_ordinal1(k5_card_1(A),k1_card_1(B)) & v1_xboole_0(k3_group_10(B,A)) ) ) ) )).
fof(t1_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t1_group_12,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( 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] : ( m1_subset_1(F,A) => ( F != C => k1_funct_1(D,F) = k1_group_1(k1_group_7(A,B,F)) ) ) ) <=> D = k1_funct_7(k1_group_1(k2_group_7(A,B)),C,E) ) ) ) ) ) ) )).
fof(t1_group_14,axiom,( ! [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) ) => ? [B] : ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k20_prvect_1(k9_finseq_1(A)))) & v13_vectsp_1(B,A,k20_prvect_1(k9_finseq_1(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k20_prvect_1(k9_finseq_1(A)))))) & v3_funct_2(B,u1_struct_0(A),u1_struct_0(k20_prvect_1(k9_finseq_1(A)))) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k20_prvect_1(k9_finseq_1(A))),B,C) = k12_finseq_1(u1_struct_0(A),C) ) ) ) )).
fof(t1_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v8_struct_0(A) => v1_finset_1(B) ) ) ) )).
fof(t1_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t1_group_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_group_2(D,B) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ( C = E => k5_group_1(B,A,C) = k5_group_1(D,A,E) ) ) ) ) ) ) )).
fof(t1_group_5,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(t1_group_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ( k3_funct_2(A,B,C,D) = k3_funct_2(A,B,C,E) => D = E ) ) ) ) ) ) ) )).
fof(t1_group_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,B) & v1_funct_1(F) & v1_partfun1(F,B) & v1_group_7(F) ) => ! [G] : ( ( ~ v2_struct_0(G) & l3_algstr_0(G) ) => ! [H] : ( m1_subset_1(H,u1_struct_0(k2_group_7(B,F))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k2_group_7(B,F))) => ! [J] : ( m1_subset_1(J,u1_struct_0(G)) => ! [K] : ( m1_subset_1(K,u1_struct_0(G)) => ( ( r2_hidden(A,B) & G = k1_funct_1(F,A) & C = H & D = I & E = k6_algstr_0(k2_group_7(B,F),H,I) & k1_funct_1(C,A) = J & k1_funct_1(D,A) = K ) => k6_algstr_0(G,J,K) = k1_funct_1(E,A) ) ) ) ) ) ) ) ) ) ) )).
fof(t1_group_8,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => k6_group_1(B,C) != A ) ) ) ) )).
fof(t1_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( r1_struct_0(C,D) => r1_struct_0(B,D) ) ) ) )).
fof(t1_groupp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ~ ( ! [C] : ( v7_ordinal1(C) => A != k1_newton(B,C) ) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( v1_int_2(C) & r1_int_1(C,A) & C != B ) ) ) ) ) )).
fof(t1_grsolv_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ! [C] : ( ( v15_algstr_0(C) & m1_group_2(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t1_hahnban,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => r1_tarski(u1_struct_0(B),u1_struct_0(k1_rlsub_2(A,B,C))) ) ) ) )).
fof(t1_hahnban1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t1_hallmar1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => k1_nat_1(k5_card_1(k2_xboole_0(A,B)),k5_card_1(k3_xboole_0(A,B))) = k1_nat_1(k5_card_1(A),k5_card_1(B)) ) ) )).
fof(t1_hausdorf,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & k4_xxreal_0(A,B) = k5_numbers ) => A = k5_numbers ) ) ) )).
fof(t1_heine,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_topmetr(C,k7_metric_1) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ( ( A = D & B = E ) => k3_metric_1(C,D,E) = k9_complex1(k6_xcmplx_0(A,B)) ) ) ) ) ) ) )).
fof(t1_helly,axiom,( ! [A] : ( ( ~ 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 ) )).
fof(t1_henmodel,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k4_ordinal1)) ) => ! [C] : ( ( 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] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( 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] : ( v7_ordinal1(D) => k4_card_1(D) != A ) | k1_funct_1(C,k3_tarski(A)) = k3_tarski(k2_relset_1(B,C)) ) ) ) ) ) )).
fof(t1_hermitan,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( A = k8_complex1(A) => k4_complex1(A) = k5_numbers ) ) )).
fof(t1_hessenbe,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t1_heyting1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t1_heyting2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( r2_hidden(D,k1_substlat(A,B)) & r2_hidden(C,D) ) => ( v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) ) ) )).
fof(t1_heyting3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) ) => ? [B] : ( m1_subset_1(B,k4_ordinal1) & r1_tarski(A,k1_finsub_1(k1_zfmisc_1(k4_ordinal1),k2_finseq_1(B),k6_domain_1(k4_ordinal1,k5_numbers))) ) ) )).
fof(t1_hfdiff_1,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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 ) ) )).
fof(t1_hilbasis,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t1_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => r2_hidden(k2_hilbert1,k5_hilbert1(A)) ) )).
fof(t1_hilbert2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ( ! [C] : ( 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] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k3_card_3(B) => k9_xtuple_0(C) = k3_tarski(A) ) ) ) ) )).
fof(t1_hilbert3,axiom,( ! [A] : ( v1_int_1(A) => ( v1_abian(A) <=> ~ v1_abian(k6_xcmplx_0(A,1)) ) ) )).
fof(t1_holder_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & ? [C] : ( v1_xreal_0(C) & r1_xxreal_0(k5_numbers,C) & k3_xcmplx_0(k2_power(C,A),k2_power(C,B)) != k2_power(C,k2_xcmplx_0(A,B)) ) ) ) ) )).
fof(t1_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ( ( r1_aff_1(A,D,B,C) & r1_aff_1(A,D,B,I) & r1_aff_1(A,D,B,J) & r1_aff_1(A,D,E,F) & r1_aff_1(A,D,E,G) & r1_aff_1(A,D,E,H) & r2_analoaf(A,B,E,C,F) & r2_analoaf(A,B,G,C,H) & r2_analoaf(A,I,E,J,F) & v4_aff_2(A) ) => ( r1_aff_1(A,D,B,E) | E = G | D = G | D = I | r2_analoaf(A,I,G,J,H) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t1_hurwitz,axiom,( ! [A] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(t1_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( v1_int_2(B) & ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(B,C) & A != k5_numbers & ! [D] : ( v7_ordinal1(D) => ~ ( k4_nat_d(k3_xcmplx_0(D,A),B) = C & ~ r1_xxreal_0(B,D) ) ) ) ) ) ) )).
fof(t1_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v1_algstr_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t1_incproj,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_incproj(B,A) <=> m1_subset_1(B,k1_incproj(A)) ) ) )).
fof(t1_incsp_1,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t1_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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(k7_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))) ) ) ) ) )).
fof(t1_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( ( 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] : ( m1_msaterm(D,A,C,k2_msaterm(A,C,B)) <=> m1_subset_1(D,k3_msualg_1(A,B,k11_msafree(A,C))) ) ) ) ) )).
fof(t1_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ( ( A = B | A = k4_xcmplx_0(B) ) => v1_int_1(A) ) ) ) )).
fof(t1_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( r1_int_1(A,B) & r1_int_1(A,k2_xcmplx_0(B,C)) ) => r1_int_1(A,C) ) ) ) ) )).
fof(t1_int_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_int_3)) => k3_funct_2(u1_struct_0(k1_int_3),k4_ordinal1,k3_int_3,A) = k2_int_3(A) ) )).
fof(t1_int_4,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( v1_xreal_0(B) => r2_tarski(A,k1_measure6(A,B)) ) ) )).
fof(t1_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( r1_int_1(A,B) & r1_int_1(A,C) ) => r1_int_1(A,k6_xcmplx_0(B,C)) ) ) ) ) )).
fof(t1_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_valued_0(B) ) => k3_finseq_1(k1_valued_1(A,B)) = k4_nat_1(k3_finseq_1(A),k3_finseq_1(B)) ) ) )).
fof(t1_int_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) ) => ( k13_pre_poly(C) = k1_tarski(A) => r6_pboole(B,C,k1_funct_7(k8_funcop_1(k4_ordinal1,B,k5_numbers),A,k1_funct_1(C,A))) ) ) )).
fof(t1_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => r1_tarski(k1_int_8(A),k2_finseq_1(A)) ) )).
fof(t1_integr10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,A) & ~ r1_xxreal_0(B,E) & ~ r1_xxreal_0(C,k3_xcmplx_0(k6_xcmplx_0(B,E),D)) ) ) ) ) ) ) ) )).
fof(t1_integr11,axiom,( r2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,2),k5_numbers),k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(2,k5_numbers),k16_sin_cos),k7_xcmplx_0(1,4))),k1_numbers) & ! [A] : ( v1_xreal_0(A) => k1_funct_1(k2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,2),k5_numbers),k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(2,k5_numbers),k16_sin_cos),k7_xcmplx_0(1,4))),k1_numbers),A) = k1_square_1(k1_funct_1(k16_sin_cos,A)) ) )).
fof(t1_integr12,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_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] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(k2_fdiff_1(k6_rfunct_1(k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B)),C),D) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(2,D),k1_square_1(k2_xcmplx_0(1,k1_newton(D,2))))) ) ) ) ) ) ) ) )).
fof(t1_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k18_sin_cos))) & r1_tarski(C,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_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) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k3_taylor_1),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k3_taylor_1),k3_seq_4(A))) ) ) ) ) )).
fof(t1_integr14,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k7_xcmplx_0(k1_funct_1(k16_sin_cos,k7_xcmplx_0(1,B)),k3_xcmplx_0(k1_square_1(B),k1_square_1(k1_funct_1(k18_sin_cos,k7_xcmplx_0(1,B))))) ) ) ) ) ) )).
fof(t1_integr15,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => ! [C] : ( m1_integra1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t1_integr16,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xreal_0(B) => ( k3_complex1(k3_xcmplx_0(B,A)) = k3_xcmplx_0(B,k3_complex1(A)) & k4_complex1(k3_xcmplx_0(B,A)) = k3_xcmplx_0(B,k4_complex1(A)) ) ) ) )).
fof(t1_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t1_integr19,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t1_integr1c,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t1_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( v3_xxreal_2(A) & v4_xxreal_2(A) ) ) )).
fof(t1_integra2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) <=> ( r1_xxreal_0(k3_seq_4(A),B) & r1_xxreal_0(B,k2_seq_4(A)) ) ) ) ) )).
fof(t1_integra3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [C] : ( m1_integra1(C,A) => ( r1_integra1(B,C) => r1_xxreal_0(k1_integra3(A,C),k1_integra3(A,B)) ) ) ) ) )).
fof(t1_integra4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ( k3_integra1(A) = k5_numbers => k3_finseq_1(B) = 1 ) ) ) )).
fof(t1_integra5,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ( B = k7_finseq_1(k9_finseq_1(D),A) | B = k7_finseq_1(A,k9_finseq_1(D)) ) & ( C = k7_finseq_1(k9_finseq_1(E),A) | C = k7_finseq_1(A,k9_finseq_1(E)) ) & k18_rvsum_1(k8_rvsum_1(B,C)) != k6_xcmplx_0(D,E) ) ) ) ) ) ) )).
fof(t1_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t1_integra7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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] : ( r2_hidden(E,B) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k1_funct_1(C,E),k1_funct_1(D,E))),A) ) ) => ( r1_xxreal_0(k6_xcmplx_0(k2_seq_4(k1_rvsum_1(C)),k2_seq_4(k1_rvsum_1(D))),A) & r1_xxreal_0(k6_xcmplx_0(k2_seq_4(k1_rvsum_1(D)),k2_seq_4(k1_rvsum_1(C))),A) ) ) ) ) ) ) )).
fof(t1_integra8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k17_sin_cos(k2_xcmplx_0(A,k3_xcmplx_0(k2_nat_1(2,B),k28_sin_cos))) = k17_sin_cos(A) ) ) )).
fof(t1_integra9,axiom,( r2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k4_xcmplx_0(1),k5_numbers),k22_sin_cos)),k1_numbers) & ! [A] : ( v1_xreal_0(A) => k1_funct_1(k2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k4_xcmplx_0(1),k5_numbers),k22_sin_cos)),k1_numbers),A) = k23_sin_cos(k4_xcmplx_0(A)) ) )).
fof(t1_interva1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( r2_hidden(D,k1_interva1(A,B,C)) <=> ( r1_tarski(B,D) & r1_tarski(D,C) ) ) ) ) )).
fof(t1_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => r2_hidden(k3_intpro_1(B,k3_intpro_1(C,B)),k7_intpro_1(A)) ) ) ) )).
fof(t1_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( v1_int_2(A) & v1_rat_1(k3_square_1(A)) ) ) )).
fof(t1_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_cat_1(F,A,D,E) => ( v9_cat_1(F,A,D,E) => v9_cat_1(k9_cat_3(A,D,E,B,C,F),B,k8_cat_1(A,B,C,D),k8_cat_1(A,B,C,E)) ) ) ) ) ) ) ) )).
fof(t1_isocat_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t1_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)))) ) ) ) )).
fof(t1_jct_misc,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r2_hidden(A,k1_rcomp_1(C,D)) & r2_hidden(B,k1_rcomp_1(C,D)) ) => r2_hidden(k7_xcmplx_0(k2_xcmplx_0(A,B),2),k1_rcomp_1(C,D)) ) ) ) ) ) )).
fof(t1_jgraph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v7_graph_1(B,A) & m2_graph_1(B,A) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( ( v1_graph_4(B,A) & r3_graph_4(A,C,B) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t1_jgraph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v2_pre_topc(D) & l1_pre_topc(D) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(D)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(D)))) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) => ! [H] : ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(A))) => ~ ( m1_pre_topc(B,A) & m1_pre_topc(C,A) & G = k2_struct_0(B) & H = k2_struct_0(C) & k2_xboole_0(k2_struct_0(B),k2_struct_0(C)) = k2_struct_0(A) & v4_pre_topc(G,A) & v4_pre_topc(H,A) & v5_pre_topc(E,B,D) & v5_pre_topc(F,C,D) & ! [I] : ( r2_hidden(I,k9_subset_1(u1_struct_0(C),k2_struct_0(B),k2_struct_0(C))) => k1_funct_1(E,I) = k1_funct_1(F,I) ) & ! [I] : ( ( v1_funct_1(I) & v1_funct_2(I,u1_struct_0(A),u1_struct_0(D)) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(D)))) ) => ~ ( I = k1_funct_4(E,F) & v5_pre_topc(I,A,D) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t1_jgraph_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( k12_euclid(A) = k3_square_1(k2_xcmplx_0(k1_square_1(k17_euclid(A)),k1_square_1(k18_euclid(A)))) & k1_square_1(k12_euclid(A)) = k2_xcmplx_0(k1_square_1(k17_euclid(A)),k1_square_1(k18_euclid(A))) ) ) )).
fof(t1_jgraph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t1_jgraph_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( r1_xxreal_0(k12_euclid(A),1) => ( r1_xxreal_0(k4_xcmplx_0(1),k17_euclid(A)) & r1_xxreal_0(k17_euclid(A),1) & r1_xxreal_0(k4_xcmplx_0(1),k18_euclid(A)) & r1_xxreal_0(k18_euclid(A),1) ) ) ) )).
fof(t1_jgraph_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t1_jordan,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( 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),k7_xcmplx_0(1,2)) = B ) ) ) ) )).
fof(t1_jordan1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( 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,k5_numbers) & C = k1_funct_1(D,1) ) ) ) => v1_connsp_1(A) ) ) )).
fof(t1_jordan10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(k2_jordan9(E,D))) & r2_hidden(k4_tarski(A,B),k2_matrix_0(k1_jordan8(E,D))) & r2_hidden(k4_tarski(A,k1_nat_1(B,1)),k2_matrix_0(k1_jordan8(E,D))) & k7_partfun1(u1_struct_0(k15_euclid(2)),k2_jordan9(E,D),C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,D),A,B) & k7_partfun1(u1_struct_0(k15_euclid(2)),k2_jordan9(E,D),k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,D),A,k1_nat_1(B,1)) & r1_xxreal_0(k3_finseq_1(k1_jordan8(E,D)),A) ) ) ) ) ) ) )).
fof(t1_jordan11,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => r1_xxreal_0(1,k3_jordan11(A)) ) )).
fof(t1_jordan12,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( ~ r1_xxreal_0(A,1) & r1_xxreal_0(k7_nat_d(A,1),k5_numbers) ) ) )).
fof(t1_jordan14,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t1_jordan15,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( 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)) ) ) ) )).
fof(t1_jordan16,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => k9_jordan6(A) != k8_jordan6(A) ) )).
fof(t1_jordan17,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( 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] : ( ( 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] : ( v1_xreal_0(G) => ~ ( v3_tops_2(F,k17_borsuk_1,k1_pre_topc(k15_euclid(A),E)) & k1_funct_1(F,k5_numbers) = C & k1_funct_1(F,1) = D & r1_xxreal_0(k5_numbers,G) & r1_xxreal_0(G,1) & k1_funct_1(F,G) = B ) ) ) ) ) ) ) ) ) )).
fof(t1_jordan18,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_square_1(k6_xcmplx_0(A,B)) = k1_square_1(k6_xcmplx_0(B,A)) ) ) )).
fof(t1_jordan19,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(A,B) => ( A = k5_numbers | r1_xxreal_0(k7_xcmplx_0(k1_nat_1(B,1),B),k7_xcmplx_0(k1_nat_1(A,1),A)) ) ) ) ) )).
fof(t1_jordan1a,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( ~ v1_abian(k3_finseq_1(A)) => k3_finseq_1(A) = k6_xcmplx_0(k3_xcmplx_0(2,k1_jordan1a(A)),1) ) ) )).
fof(t1_jordan1b,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_xboole_0(A) <=> v1_xboole_0(k3_finseq_5(A)) ) ) )).
fof(t1_jordan1c,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(k4_tarski(B,C),k2_matrix_0(k1_jordan8(A,D))) & r2_hidden(k4_tarski(k2_xcmplx_0(B,1),C),k2_matrix_0(k1_jordan8(A,D))) ) => k1_topreal6(2,k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,D),1,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,D),2,1)) = k6_xcmplx_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,D),k2_xcmplx_0(B,1),C)),k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,D),B,C))) ) ) ) ) ) )).
fof(t1_jordan1d,axiom,( ! [A] : ! [B] : ( ! [C] : ~ ( r2_hidden(C,A) & ! [D] : ~ ( r1_tarski(D,B) & r1_tarski(C,k3_tarski(D)) ) ) => r1_tarski(k3_tarski(A),k3_tarski(B)) ) )).
fof(t1_jordan1e,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r1_sprect_2(B,A) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t1_jordan1f,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_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_0(u1_struct_0(k15_euclid(2)),E,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,C)),k3_topreal1(2,D)) & r2_hidden(k4_tarski(A,B),k2_matrix_0(E)) & r2_hidden(k4_tarski(A,C),k2_matrix_0(E)) & r1_xxreal_0(B,C) & ! [F] : ( v7_ordinal1(F) => ~ ( r1_xxreal_0(B,F) & r1_xxreal_0(F,C) & k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,F)) = k3_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_0(u1_struct_0(k15_euclid(2)),E,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,C)),k3_topreal1(2,D)))) ) ) ) ) ) ) ) ) )).
fof(t1_jordan1g,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_zfmisc_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ~ ( ~ v1_xboole_0(A) & ! [B] : A != k9_finseq_1(B) ) ) )).
fof(t1_jordan1h,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)))) ) ) ) )).
fof(t1_jordan1i,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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_jordan9(B,A),k18_pscomp_1(k3_topreal1(2,k2_jordan9(B,A)))),1) ) ) )).
fof(t1_jordan1j,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( r1_xxreal_0(1,D) & r1_xxreal_0(D,k1_matrix_0(A)) & r1_xxreal_0(1,E) & r1_xxreal_0(E,k1_matrix_0(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_0(u1_struct_0(k15_euclid(2)),A,C,E)),k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,D))) ) ) ) ) ) ) )).
fof(t1_jordan1k,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,B) => ? [E] : ( r2_hidden(E,A) & D = k1_funct_1(C,E) ) ) ) ) ) )).
fof(t1_jordan20,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t1_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => r1_tarski(k2_kurato_2(k15_euclid(2),k1_jordan19(A),B),k2_pre_topc(k15_euclid(2),k3_goboard9(k2_jordan9(A,k5_numbers)))) ) ) )).
fof(t1_jordan23,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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))) ) ) ) )).
fof(t1_jordan2b,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v7_ordinal1(B) => ? [C] : ( 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] : ( 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) ) ) ) ) )).
fof(t1_jordan2c,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v5_valued_0(C) & m2_finseq_1(C,k1_numbers) ) => ( ( k2_relset_1(k1_numbers,C) = k2_tarski(A,B) & k3_finseq_1(C) = 2 & r1_xxreal_0(A,B) ) => ( k1_funct_1(C,1) = A & k1_funct_1(C,2) = B ) ) ) ) ) )).
fof(t1_jordan3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) ) ) )).
fof(t1_jordan4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(A,B) & ~ r1_xxreal_0(k2_xcmplx_0(B,B),A) & k4_nat_d(A,B) = k5_numbers ) ) ) )).
fof(t1_jordan5a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t1_jordan5b,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( r1_xxreal_0(1,A) & r1_xxreal_0(A,k7_nat_d(A,1)) ) ) )).
fof(t1_jordan5c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( ( 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] : ( v1_xreal_0(G) => ( ( 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,k5_numbers) = C & k1_funct_1(F,1) = D & r1_xxreal_0(k5_numbers,G) & r1_xxreal_0(G,1) & ! [H] : ( v1_xreal_0(H) => ~ ( r1_xxreal_0(k5_numbers,H) & ~ r1_xxreal_0(G,H) & r2_hidden(k1_funct_1(F,H),B) ) ) ) => ! [H] : ( ( 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] : ( v1_xreal_0(I) => ( ( v3_tops_2(H,k5_topmetr,k1_pre_topc(k15_euclid(2),A)) & k1_funct_1(H,k5_numbers) = C & k1_funct_1(H,1) = D & k1_funct_1(H,I) = E & r1_xxreal_0(k5_numbers,I) & r1_xxreal_0(I,1) ) => ! [J] : ( v1_xreal_0(J) => ~ ( r1_xxreal_0(k5_numbers,J) & ~ r1_xxreal_0(I,J) & r2_hidden(k1_funct_1(H,J),B) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t1_jordan5d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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))) ) ) ) )).
fof(t1_jordan6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(B,A) => ( r1_xxreal_0(B,k7_xcmplx_0(k2_xcmplx_0(B,A),2)) & r1_xxreal_0(k7_xcmplx_0(k2_xcmplx_0(B,A),2),A) ) ) ) ) )).
fof(t1_jordan7,axiom,( ! [A] : ( ( ~ 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)) ) ) ) )).
fof(t1_jordan9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t1_jordan_a,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(t1_knaster,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( C = k2_xboole_0(A,B) & r1_xboole_0(k9_xtuple_0(A),k9_xtuple_0(B)) ) => ( v2_funct_1(C) <=> ( v2_funct_1(A) & v2_funct_1(B) & r1_xboole_0(k10_xtuple_0(A),k10_xtuple_0(B)) ) ) ) ) ) ) )).
fof(t1_kolmog01,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ~ ( r1_tarski(B,k9_xtuple_0(A)) & B != k1_xboole_0 & k10_xtuple_0(k5_relat_1(A,B)) = k1_xboole_0 ) ) )).
fof(t1_kurato_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => r1_tarski(k3_funct_6(A),k1_funct_1(A,B)) ) ) )).
fof(t1_kurato_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(t1_kurato_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(A))) => ! [C] : ( v1_xreal_0(C) => ( v3_pre_topc(k8_metric_1(k14_euclid(A),B,C),k15_euclid(A)) & m1_subset_1(k8_metric_1(k14_euclid(A),B,C),k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) ) ) ) )).
fof(t1_l_hospit,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( ( r1_fcont_1(A,B) & ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(B,C) & ~ r1_xxreal_0(D,B) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ~ ( ~ 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) ) ) ) )).
fof(t1_lang1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => k2_xboole_0(k1_lang1(A),k2_lang1(A)) = u1_struct_0(A) ) )).
fof(t1_laplace,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t1_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(t1_latsum_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ~ ( 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)) ) ) )).
fof(t1_lattice2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( ( 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 ) ) ) )).
fof(t1_lattice3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k1_lattice3(A))) => ! [C] : ( 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) ) ) ) )).
fof(t1_lattice4,axiom,( ! [A] : ~ ( A != k1_xboole_0 & ! [B] : ~ ( B != k1_xboole_0 & r1_tarski(B,A) & v6_ordinal1(B) & ! [C] : ~ ( r2_hidden(C,A) & ! [D] : ( r2_hidden(D,B) => r1_tarski(D,C) ) ) ) & ! [B] : ~ ( r2_hidden(B,A) & ! [C] : ~ ( r2_hidden(C,A) & C != B & r1_tarski(B,C) ) ) ) )).
fof(t1_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( v1_lattice6(A) <=> v2_lattice6(k1_lattice2(A)) ) ) )).
fof(t1_lattice7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t1_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(t1_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t1_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( 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) ) ) ) ) )).
fof(t1_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v7_valued_0(A) => v2_seq_2(A) ) & ( v8_valued_0(A) => v1_seq_2(A) ) ) ) )).
fof(t1_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( v2_comseq_2(B) & ~ r1_xxreal_0(k1_seq_2(B),A) & ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & r1_xxreal_0(k1_funct_1(B,D),A) ) ) ) ) ) )).
fof(t1_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t1_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( r1_tarski(k10_xtuple_0(C),k8_subset_1(k1_numbers,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)),D)) => ( r1_tarski(k10_xtuple_0(C),k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) & r1_tarski(k10_xtuple_0(C),D) & r1_tarski(k10_xtuple_0(C),k1_relset_1(k1_numbers,A)) & r1_tarski(k10_xtuple_0(C),k8_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),D)) & r1_tarski(k10_xtuple_0(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,C,A)),k1_relset_1(k1_numbers,B)) ) ) ) ) ) )).
fof(t1_lmod_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t1_lmod_6,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) )).
fof(t1_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t1_lopban_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) ) => ! [C] : ( m2_funct_2(C,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => ! [D] : ( m2_funct_2(D,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => ! [E] : ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t1_lopban_2,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( ~ 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] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) )).
fof(t1_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(t1_lopban_5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( ( v1_comseq_2(A) & r1_xxreal_0(k5_numbers,B) ) => k6_rinfsup1(k26_valued_1(k4_ordinal1,k1_numbers,A,B)) = k3_xcmplx_0(B,k6_rinfsup1(A)) ) ) ) )).
fof(t1_lopban_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,A) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(k7_xcmplx_0(B,k2_xcmplx_0(1,C)),A) & ~ r1_xxreal_0(B,k7_xcmplx_0(B,k2_xcmplx_0(1,C))) ) ) ) ) ) )).
fof(t1_lopban_7,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( 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)))) ) => ( 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)) & v13_vectsp_1(k2_funct_1(C),B,A) & v1_lopban_1(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)))) & k10_xtuple_0(k2_funct_1(C)) = u1_struct_0(A) ) ) ) ) ) )).
fof(t1_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k1_lopclset(A)) => v3_pre_topc(B,A) ) ) ) )).
fof(t1_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(C,k5_numbers) & r1_xxreal_0(k2_power(B,C),k2_power(A,C)) ) ) ) ) )).
fof(t1_lpspacc1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_clvect_1(B,A) <=> ( v1_ideal_1(B,A) & v1_lpspacc1(B,A) ) ) ) ) )).
fof(t1_lpspace1,axiom,( ! [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) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t1_lpspace2,axiom,( ! [A] : ( ( v2_xxreal_0(A) & v1_xreal_0(A) ) => ! [B] : ( ( v2_xxreal_0(B) & v1_xreal_0(B) ) => ~ ( k3_supinf_2(k2_extreal1(1,A),k2_extreal1(1,B)) = 1 & r1_xxreal_0(A,1) ) ) ) )).
fof(t1_ltlaxio1,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k6_xboolean(k6_xboolean(A,k4_xboolean(B,C)),k6_xboolean(A,B)) = 1 ) ) ) )).
fof(t1_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ ( ~ r1_xxreal_0(k3_finseq_1(B),k5_numbers) & ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k3_finseq_1(k16_finseq_1(A,B)),k5_numbers) ) ) ) )).
fof(t1_ltlaxio3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(B)) => k2_rfinseq(A,C,B) = k7_finseq_1(k9_finseq_1(k1_funct_1(B,k1_nat_1(C,1))),k2_rfinseq(A,k1_nat_1(C,1),B)) ) ) ) ) )).
fof(t1_ltlaxio4,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & m1_finseq_2(B,A) ) => ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & r2_hidden(C,B) & ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ( r2_hidden(D,B) => r1_xxreal_0(k3_finseq_1(D),k3_finseq_1(C)) ) ) ) ) )).
fof(t1_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t1_margrel1,axiom,( ! [A] : ! [B] : ( ( v3_finseq_1(B) & v2_card_3(B) ) => ( r1_tarski(A,B) => ( v3_finseq_1(A) & v2_card_3(A) ) ) ) )).
fof(t1_mathmorp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k2_mathmorp(A,k2_mathmorp(A,B)) = B ) ) )).
fof(t1_matrix10,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k2_vectsp_1)) => ! [B] : ( v1_xreal_0(B) => ( A = B => k4_algstr_0(k2_vectsp_1,A) = k4_xcmplx_0(B) ) ) ) )).
fof(t1_matrix11,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,k2_sgraph1(k2_finseq_1(B))) <=> ? [C] : ( v7_ordinal1(C) & ? [D] : ( 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) ) ) ) ) )).
fof(t1_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(C),A,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(C))) ) => k1_matrix_0(D) = k1_matrix_0(E) ) ) ) ) ) )).
fof(t1_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,A,C,B) & m2_finseq_1(D,k3_finseq_2(A)) ) => ( ( C = k5_numbers => B = k5_numbers ) <=> ( k3_finseq_1(D) = C & k1_matrix_0(D) = B ) ) ) ) ) ) )).
fof(t1_matrix14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( 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))) ) ) )).
fof(t1_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ( k1_matrix_0(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) ) ) ) ) ) )).
fof(t1_matrix16,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => k9_fvsum_1(A,B,k1_group_1(A)) = B ) ) )).
fof(t1_matrix17,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(A),B,B) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(A))) ) => ( ( r2_hidden(k4_tarski(C,D),k2_matrix_0(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_0(u1_struct_0(A),G,C,D) = k4_struct_0(A) ) ) ) ) ) ) ) ) )).
fof(t1_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => v1_matrix_0(k12_finseq_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),k12_finseq_1(A,B))) ) ) )).
fof(t1_matrix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v2_struct_0(D) & l6_algstr_0(D) ) => ( r2_hidden(k4_tarski(A,B),k2_matrix_0(k2_matrix_1(D,C))) => k3_matrix_0(u1_struct_0(D),k2_matrix_1(D,C),A,B) = k4_struct_0(D) ) ) ) ) ) )).
fof(t1_matrix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k5_matrix_1(B,A,k11_matrix_0(u1_struct_0(B),A,A,C),k11_matrix_0(u1_struct_0(B),A,A,D)) = k11_matrix_0(u1_struct_0(B),A,A,k1_algstr_0(B,C,D)) ) ) ) ) )).
fof(t1_matrix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(D,E),k2_matrix_0(k1_matrix_3(C,A,B))) => k3_matrix_0(u1_struct_0(C),k1_matrix_3(C,A,B),D,E) = k4_struct_0(C) ) ) ) ) ) ) )).
fof(t1_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => k2_matrix_3(A,k2_matrix_3(A,B)) = B ) ) )).
fof(t1_matrix_5,axiom,( 1 = k1_group_1(k1_complfld) )).
fof(t1_matrix_6,axiom,( ! [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] : ( ( v1_matrix_0(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_0(B)) ) ) )).
fof(t1_matrix_7,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t1_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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(k3_matrix_1(B,A),A,B) & v3_matrix_8(k3_matrix_1(B,A),A,B) ) ) ) )).
fof(t1_matrix_9,axiom,( ! [A] : ! [B] : ( r2_hidden(A,B) => r2_hidden(k1_tarski(A),k5_finsub_1(B)) ) )).
fof(t1_matrixc1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v1_matrix_0(C) ) => ( r2_hidden(k4_tarski(A,B),k2_matrix_0(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_0(C)) ) ) ) ) ) )).
fof(t1_matrixj1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t1_matrixj2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( 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) ) ) ) )).
fof(t1_matrixr1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_vectsp_1)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_vectsp_1)) => ( ( A = C & B = D ) => k2_xcmplx_0(A,B) = k3_rlvect_1(k2_vectsp_1,C,D) ) ) ) ) ) )).
fof(t1_matrixr2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( 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) ) ) ) ) )).
fof(t1_matrlin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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 ) ) ) )).
fof(t1_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m1_vectsp_4(E,A,B) => ! [F] : ( m1_vectsp_4(F,A,E) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t1_matroid0,axiom,( ! [A] : ( ( ~ v3_pencil_1(A) & v1_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( ( v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( r1_tarski(C,B) => ( v3_pre_topc(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) )).
fof(t1_matrprob,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ! [D] : ( m2_finseq_1(D,A) => ( ( k3_finseq_1(D) = C & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(D)) => k1_funct_1(D,E) = B ) ) ) <=> D = k5_finseq_2(A,C,B) ) ) ) ) ) )).
fof(t1_matrtop1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t1_matrtop2,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( m1_vectsp_6(A,k2_vectsp_1,k6_prvect_1(k2_vectsp_1,B)) <=> m1_rlvect_2(A,k15_euclid(B)) ) ) )).
fof(t1_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( 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,k4_matrix_0(u1_struct_0(B),k4_matrix11(A,A,u1_struct_0(B),D,k4_matrix_0(u1_struct_0(B),k4_matrix11(A,A,u1_struct_0(B),D,C))))) = k12_matrix_3(A,B,C) & ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( r2_hidden(k4_tarski(E,F),k2_matrix_0(C)) => k3_matrix_0(u1_struct_0(B),k4_matrix_0(u1_struct_0(B),k4_matrix11(A,A,u1_struct_0(B),D,k4_matrix_0(u1_struct_0(B),k4_matrix11(A,A,u1_struct_0(B),D,C)))),E,F) = k3_matrix_0(u1_struct_0(B),C,k1_funct_1(D,E),k1_funct_1(D,F)) ) ) ) ) ) ) ) ) )).
fof(t1_mazurulm,axiom,( v1_tops_1(k2_urysohn1,k5_topmetr) & m1_subset_1(k2_urysohn1,k1_zfmisc_1(u1_struct_0(k5_topmetr))) )).
fof(t1_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t1_mcart_1,axiom,( ! [A] : ! [B] : ( k1_xtuple_0(k4_tarski(A,B)) = A & k2_xtuple_0(k4_tarski(A,B)) = B ) )).
fof(t1_measure1,axiom,( ! [A] : ! [B] : k3_tarski(k1_enumset1(A,B,k1_xboole_0)) = k3_tarski(k2_tarski(A,B)) )).
fof(t1_measure2,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => v6_supinf_2(k1_partfun1(k4_ordinal1,B,B,k6_numbers,D,C)) ) ) ) )).
fof(t1_measure3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => 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)) ) ) ) )).
fof(t1_measure4,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( ! [F] : ( m1_subset_1(F,k4_ordinal1) => k9_nat_1(B,D,F) = k8_subset_1(A,E,k9_nat_1(B,C,F)) ) => k3_tarski(k2_relset_1(B,D)) = k8_subset_1(A,E,k3_tarski(k2_relset_1(B,C))) ) ) ) ) ) )).
fof(t1_measure5,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t1_measure6,axiom,( ? [A] : ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_zfmisc_1(k4_ordinal1,k4_ordinal1)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_zfmisc_1(k4_ordinal1,k4_ordinal1)))) & v2_funct_1(A) & k1_relset_1(k4_ordinal1,A) = k4_ordinal1 & k11_funcop_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,A) = k2_zfmisc_1(k4_ordinal1,k4_ordinal1) ) )).
fof(t1_measure8,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => r2_funct_2(k4_ordinal1,k6_numbers,k18_supinf_2(A),k2_mesfunc9(A)) ) )).
fof(t1_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => ( r2_hidden(B,A) <=> r2_hidden(k2_xxreal_3(B),k4_member_1(A)) ) ) ) )).
fof(t1_membered,axiom,( ! [A] : ( v1_membered(A) => r1_tarski(A,k2_numbers) ) )).
fof(t1_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( v13_struct_0(B,1) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_partfun1(C,u1_struct_0(B)) ) => ! [D] : ( ( 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 ) ) ) ) ) )).
fof(t1_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( k17_euclid(k3_rlvect_1(k15_euclid(2),A,B)) = k2_xcmplx_0(k17_euclid(A),k17_euclid(B)) & k18_euclid(k3_rlvect_1(k15_euclid(2),A,B)) = k2_xcmplx_0(k18_euclid(A),k18_euclid(B)) ) ) ) )).
fof(t1_mesfun10,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ! [C] : ( 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))) ) ) ) )).
fof(t1_mesfun6c,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k2_xcmplx_0(A,B) = k2_xcmplx_0(A,B) & k4_xcmplx_0(A) = k4_xcmplx_0(A) & k6_xcmplx_0(A,B) = k6_xcmplx_0(A,B) & k3_xcmplx_0(A,B) = k3_xcmplx_0(A,B) ) ) ) )).
fof(t1_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( m1_subset_1(C,A) => r1_funct_2(k4_ordinal1,k1_numbers,k4_ordinal1,k6_numbers,k10_seqfunc(A,B,C),k3_mesfunc5(A,k1_mesfun7c(A,B),C)) ) ) ) )).
fof(t1_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t1_mesfunc1,axiom,( r2_tarski(k4_ordinal1,k1_mesfunc1) )).
fof(t1_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => r2_relset_1(A,k6_numbers,B,k6_mesfunc1(A,B,1)) ) ) )).
fof(t1_mesfunc5,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ! [B] : ( m1_subset_1(B,k6_numbers) => k3_extreal1(k4_supinf_2(A,B)) = k3_extreal1(k4_supinf_2(B,A)) ) ) )).
fof(t1_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => r2_relset_1(A,k6_numbers,k10_mesfunc1(A,k1_mesfunc5(A,B)),k1_mesfunc5(A,k56_valued_1(A,k1_numbers,B))) ) ) )).
fof(t1_mesfunc7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ! [D] : ( 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)) ) ) ) ) )).
fof(t1_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_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)) ) ) ) ) )).
fof(t1_metric_1,axiom,( ! [A] : ( l1_metric_1(A) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_metric_1(A,B,B) = k5_numbers ) <=> v6_metric_1(A) ) ) )).
fof(t1_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t1_metric_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))) => ( k2_binop_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,k1_metric_3(A,B),C,D) = k5_numbers <=> C = D ) ) ) ) ) )).
fof(t1_metric_6,axiom,( ! [A] : ( ( v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k3_metric_1(A,B,D),k3_metric_1(A,C,D))),k3_metric_1(A,B,C)) ) ) ) ) )).
fof(t1_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t1_mfold_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => r2_borsuk_3(A,k1_pre_topc(A,k2_struct_0(A))) ) )).
fof(t1_mfold_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : k9_xtuple_0(k6_relat_1(B,A)) = k8_relat_1(A,B) ) )).
fof(t1_midsp_1,axiom,( u1_struct_0(k2_midsp_1) = k1_tarski(k1_xboole_0) )).
fof(t1_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_midsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( 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 ) ) ) ) ) )).
fof(t1_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_finseq_1(D,C) => ~ ( k3_finseq_1(D) = k1_nat_1(k1_nat_1(A,1),B) & ! [E] : ( m2_finseq_1(E,C) => ! [F] : ( m2_finseq_1(F,C) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t1_mmlquer2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => r1_tarski(k1_relat_1(B),A) ) )).
fof(t1_mmlquery,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r1_tarski(A,B) <=> ! [C] : r1_tarski(k9_relat_1(A,C),k9_relat_1(B,C)) ) ) ) )).
fof(t1_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_mod_2(A))) => B = k4_struct_0(k1_mod_2(A)) ) ) )).
fof(t1_mod_3,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t1_mod_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,B) => k2_binop_1(A,B,C,D,E,F) = k2_binop_1(B,A,C,k1_mod_4(A,B,C,D),F,E) ) ) ) ) ) ) )).
fof(t1_modal_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ~ ( A != B & r3_xboole_0(k14_trees_3(A),k8_finseq_1(k4_ordinal1,k14_trees_3(B),C)) ) ) ) ) )).
fof(t1_modcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v2_mod_2(B,A) & v3_mod_2(B,A) & l1_mod_2(B,A) ) => m3_modcat_1(k1_tarski(B),A) ) ) )).
fof(t1_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) <=> r2_hidden(A,k12_modelc_1) ) )).
fof(t1_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) <=> r2_hidden(A,k9_modelc_2) ) )).
fof(t1_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_3(C,B) & l1_modelc_3(C,B) ) => ! [D] : ( 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))) ) ) ) ) ) ) ) )).
fof(t1_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( A != 1 => r1_xxreal_0(2,A) ) ) )).
fof(t1_monoid_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t1_monoid_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : k3_relat_1(B,k5_relat_1(A,C)) = k3_relat_1(k6_relat_1(C,B),A) ) ) )).
fof(t1_morph_01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t1_msafree,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_relat_1(D) & v4_relat_1(D,B) & v1_funct_1(D) & v1_partfun1(D,B) ) => ! [E] : ( m2_finseq_2(E,B,k3_finseq_2(B)) => ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t1_msafree1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t1_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_struct_0(A) & l1_msualg_1(A) ) => k2_msafree2(A) = u1_struct_0(A) ) )).
fof(t1_msafree3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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,k1_funct_6(C)) ) => r6_pboole(A,k1_equation(A,k9_pboole(A,B,C),C),B) ) ) ) )).
fof(t1_msafree4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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(B),k3_card_3(C)) ) ) ) )).
fof(t1_msalimit,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( ~ v2_struct_0(E) & ~ v11_struct_0(E) & l1_msualg_1(E) ) => ! [F] : ( m1_msalimit(F,A,E) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t1_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t1_msinst_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ( ~ v2_struct_0(C) & ~ v11_struct_0(C) & l1_msualg_1(C) ) ) ) ) ) )).
fof(t1_msscyc_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t1_msscyc_2,axiom,( ! [A] : ( l1_msualg_1(A) => r1_tarski(k1_msscyc_2(A),k2_zfmisc_1(u4_struct_0(A),u1_struct_0(A))) ) )).
fof(t1_mssubfam,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(t1_mssublat,axiom,( ! [A] : k3_funct_2(k4_ordinal1,k3_finseq_2(k1_tarski(A)),k7_finseq_2(A),k5_numbers) = k1_xboole_0 )).
fof(t1_msualg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ~ v1_xboole_0(k5_msualg_1(A,B,C)) ) ) ) )).
fof(t1_msualg_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( 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))) ) ) ) ) )).
fof(t1_msualg_3,axiom,( ! [A] : ! [B] : ( ( 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] : ( r2_hidden(C,A) => v2_funct_1(k1_funct_1(B,C)) ) ) ) )).
fof(t1_msualg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)))) ) ) ) ) ) )).
fof(t1_msualg_5,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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))) ) ) )).
fof(t1_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( r2_hidden(D,k3_msualg_1(A,C,B)) => ( v1_relat_1(D) & v1_funct_1(D) ) ) ) ) ) )).
fof(t1_msualg_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t1_msualg_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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(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(k3_finseq_1(B),A) ) ) ) ) ) )).
fof(t1_msualg_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(t1_msuhom_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( r1_tarski(k10_xtuple_0(A),C) => k3_relat_1(A,k5_relat_1(B,C)) = k3_relat_1(A,B) ) ) ) )).
fof(t1_multop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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] : ( ( 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] : ! [H] : ! [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) ) ) ) ) )).
fof(t1_mycielsk,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k5_numbers,A) => k3_xcmplx_0(A,k1_xreal_0(B,C)) = k1_xreal_0(k3_xcmplx_0(A,B),k3_xcmplx_0(A,C)) ) ) ) ) )).
fof(t1_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ? [C] : ( 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) ) ) ) )).
fof(t1_nagata_2,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => A != k2_nat_1(k1_newton(2,B),k1_nat_1(k3_xcmplx_0(2,C),1)) ) ) ) ) )).
fof(t1_nat_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( ( r2_hidden(k5_numbers,A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => r2_hidden(k2_xcmplx_0(B,1),A) ) ) ) => ! [B] : ( v7_ordinal1(B) => r2_hidden(B,A) ) ) ) )).
fof(t1_nat_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(B,k7_xcmplx_0(A,k2_xcmplx_0(k1_int_1(k7_xcmplx_0(A,B)),1))) ) ) ) )).
fof(t1_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_nat_d(A,C) & r1_nat_d(B,D) ) => r1_nat_d(k3_xcmplx_0(A,B),k3_xcmplx_0(C,D)) ) ) ) ) ) )).
fof(t1_nat_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(k3_xcmplx_0(A,A),k3_xcmplx_0(B,B)) & r1_xxreal_0(A,B) ) ) ) )).
fof(t1_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ~ r1_xxreal_0(k6_xcmplx_0(k11_newton(2,k1_nat_1(A,2)),1),k11_newton(2,k1_nat_1(A,1))) ) )).
fof(t1_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(A,k4_nat_d(B,A)) ) ) ) )).
fof(t1_nat_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_nat_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_nat_lat)) => k1_lattices(k3_nat_lat,A,B) = k5_nat_d(A,B) ) ) )).
fof(t1_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_hidden(k8_cat_2(k6_cat_2(A,A),A,k8_cat_2(A,A,k4_cat_1(A,B),k4_cat_1(A,B)),k4_cat_1(A,B)),u1_cat_1(A)) ) ) )).
fof(t1_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k5_vfunct_1(k4_ordinal1,A,B),k6_clvect_1(A,B,k4_xcmplx_0(k6_complex1))) ) ) )).
fof(t1_ncfcont2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t1_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_nfcont_1(C,A,B) => ! [D] : ( m1_nfcont_1(D,A,B) => ? [E] : ( m1_nfcont_1(E,A,B) & r1_tarski(E,C) & r1_tarski(E,D) ) ) ) ) ) )).
fof(t1_ndiff_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r1_ndiff_1(A,B,C,D) & ! [E] : ( m1_nfcont_1(E,A,D) => ~ ( r1_tarski(E,k1_relset_1(u1_struct_0(A),C)) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( ( v9_ordinal1(G) & v1_funct_1(G) & v1_funct_2(G,k4_ordinal1,k1_numbers) & v1_fdiff_1(G,k5_numbers) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [H] : ( ( v1_funct_1(H) & v3_funct_1(H) & v1_funct_2(H,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( k2_relset_1(u1_struct_0(A),H) = k1_tarski(D) & r1_tarski(k2_relset_1(u1_struct_0(A),k2_normsp_1(A,k2_ndiff_1(A,F,G),H)),E) ) => ( v3_normsp_1(k1_ndiff_1(B,k3_normsp_1(B,k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),k2_normsp_1(A,k2_ndiff_1(A,F,G),H),C),k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),H,C)),k37_valued_1(k4_ordinal1,k1_numbers,G)),B) & k17_lopban_1(A,B,k3_ndiff_1(A,B,C,D),F) = k6_normsp_1(B,k1_ndiff_1(B,k3_normsp_1(B,k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),k2_normsp_1(A,k2_ndiff_1(A,F,G),H),C),k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),H,C)),k37_valued_1(k4_ordinal1,k1_numbers,G))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t1_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( ! [D] : ( m1_subset_1(D,k4_ordinal1) => r1_xxreal_0(k2_normsp_0(A,k1_normsp_1(A,C,D)),k9_nat_1(k1_numbers,B,D)) ) & v2_comseq_2(B) & k1_seq_2(B) = k5_numbers ) => ( v3_normsp_1(C,A) & k6_normsp_1(A,C) = k4_struct_0(A) ) ) ) ) ) )).
fof(t1_ndiff_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t1_ndiff_5,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( E != k5_numbers & ~ r1_xxreal_0(D,k9_complex1(E)) & r1_xxreal_0(C,k3_xcmplx_0(k5_xcmplx_0(k9_complex1(E)),k2_normsp_0(A,k10_funct_2(k1_numbers,u1_struct_0(A),B,E)))) ) ) ) ) ) ) ) ) ) )).
fof(t1_neckla_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ! [C] : ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) => r2_hidden(D,A) ) ) ) )).
fof(t1_neckla_3,axiom,( ! [A] : ! [B] : 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))) )).
fof(t1_necklace,axiom,( 4 = k2_enumset1(k5_numbers,1,2,3) )).
fof(t1_net_1,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(t1_newton,axiom,( ! [A] : ( 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)) ) ) )).
fof(t1_nfcont_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_normsp_1(A,B,C),k2_normsp_1(A,B,k5_vfunct_1(k4_ordinal1,A,C))) ) ) ) )).
fof(t1_nfcont_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t1_nfcont_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( 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(k9_nat_1(k1_numbers,C,A),k1_relset_1(k1_numbers,D)) ) ) ) ) ) )).
fof(t1_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t1_normform,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_finsub_1(B) ) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(A,B)) => ( ( r1_normform(A,B,C,D) & r1_normform(A,B,D,C) ) => C = D ) ) ) ) ) )).
fof(t1_normsp_1,axiom,( ! [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) & l1_normsp_1(A) ) => k2_normsp_0(A,k4_struct_0(A)) = k5_numbers ) )).
fof(t1_normsp_2,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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] : ( v7_ordinal1(C) => r2_hidden(k3_subset_1(u1_struct_0(A),k9_nat_1(k9_setfam_1(u1_struct_0(A)),B,C)),k2_pcomps_1(A)) ) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k8_metric_1(A,E,D),k9_nat_1(k9_setfam_1(u1_struct_0(A)),B,C)) ) ) ) ) ) ) ) )).
fof(t1_ntalgo_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => k5_int_1(k5_int_1(A,B),B) = k5_int_1(A,B) ) ) )).
fof(t1_numbers,axiom,( r2_xboole_0(k1_numbers,k2_numbers) )).
fof(t1_numerals,axiom,( m1_subset_1(k1_xboole_0,k4_ordinal1) )).
fof(t1_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v11_o_ring_1(B,A) => v13_o_ring_1(B,A) ) ) ) )).
fof(t1_openlatt,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(t1_oposet_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) ) )).
fof(t1_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_oppcat_1(k2_oppcat_1(A),k3_oppcat_1(A,B)) = B ) ) )).
fof(t1_ordeq_01,axiom,( ! [A] : r1_abian(A,k1_tarski(k4_tarski(A,A))) )).
fof(t1_orders_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ r2_hidden(k1_xboole_0,k1_orders_1(A)) ) )).
fof(t1_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_orders_2(A,B,B) ) ) )).
fof(t1_orders_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_orders_3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_orders_2(A,B,C) <=> B = C ) ) ) ) )).
fof(t1_orders_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(A,B) => ( v4_yellow_0(k1_yellow_1(A),k1_yellow_1(B)) & m1_yellow_0(k1_yellow_1(A),k1_yellow_1(B)) ) ) ) ) )).
fof(t1_ordinal1,axiom,( ! [A] : ! [B] : ~ ( r2_hidden(B,A) & r1_tarski(A,B) ) )).
fof(t1_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r1_ordinal1(A,B) <=> r1_ordinal1(k1_ordinal1(A),k1_ordinal1(B)) ) ) ) )).
fof(t1_ordinal3,axiom,( ! [A] : r1_tarski(A,k1_ordinal1(A)) )).
fof(t1_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( v3_ordinal1(B) => ( k9_xtuple_0(A) = k1_ordinal1(B) => ( r1_ordinal2(k1_ordinal2(A),A) & k8_ordinal2(A) = k1_ordinal2(A) ) ) ) ) )).
fof(t1_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ~ ( r1_ordinal1(A,k1_ordinal1(B)) & ~ r1_ordinal1(A,B) & A != k1_ordinal1(B) ) ) ) )).
fof(t1_ordinal6,axiom,( ! [A] : ( v1_ordinal6(A) <=> ! [B] : ( r2_hidden(B,A) => v3_ordinal1(B) ) ) )).
fof(t1_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => r1_orders_2(B,k4_struct_0(B),C) ) ) ) )).
fof(t1_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v3_msualg_1(B,A) & v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m3_pboole(C,u1_struct_0(A),u3_msualg_1(A,B)) => ( m1_osafree(C,A,B) <=> ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t1_osalg_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t1_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t1_osalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(t1_osalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [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] : ( ( v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) ) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t1_papdesaf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(t1_pardepap,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v2_aff_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t1_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t1_parsp_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) ) ) )).
fof(t1_partfun1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ~ ( ! [C] : ( 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] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => k2_xboole_0(A,B) != C ) ) ) ) )).
fof(t1_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,A) => ( r2_hidden(E,k1_relset_1(A,C)) => k7_partfun1(B,C,E) = k7_partfun1(B,D,E) ) ) ) => r2_relset_1(A,B,C,D) ) ) ) ) ) )).
fof(t1_partfun3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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 ) ) )).
fof(t1_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ! [D] : ( ( r2_hidden(C,B) & r2_hidden(D,B) & r1_tarski(C,D) ) => C = D ) ) ) )).
fof(t1_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k2_bvfunc_2(A,k1_subset_1(k1_bvfunc_2(A))) = k6_partit1(A) ) )).
fof(t1_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_analoaf(A,C,E,E,D) & E != D & C != E & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_analoaf(A,B,E,E,F) & r2_diraf(A,B,C,D,F) & D != F & E != F ) ) ) ) ) ) ) ) )).
fof(t1_pboole,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_relat_1(A) => v1_setfam_1(k10_xtuple_0(A)) ) ) )).
fof(t1_pcomps_1,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r1_xxreal_0(C,D) => r1_tarski(k8_metric_1(A,B,C),k8_metric_1(A,B,D)) ) ) ) ) ) )).
fof(t1_pcomps_2,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r2_wellord1(A,B) => ( r2_wellord1(k2_wellord1(A,B),B) & B = k1_relat_1(k2_wellord1(A,B)) ) ) ) )).
fof(t1_pcs_0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v8_relat_2(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [D] : ( ( 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)) ) ) ) )).
fof(t1_pdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( 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] : ( v1_xreal_0(A) => ( k1_funct_1(k1_pdiff_1(1,1),k9_finseq_1(A)) = A & k1_funct_1(k2_funct_1(k1_pdiff_1(1,1)),A) = k9_finseq_1(A) ) ) )).
fof(t1_pdiff_2,axiom,( 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] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k1_pdiff_1(1,2),k10_finseq_1(A,B)) = A ) ) )).
fof(t1_pdiff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(2)) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t1_pdiff_4,axiom,( 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] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k1_funct_1(k1_pdiff_1(1,3),k11_finseq_1(A,B,C)) = A ) ) ) )).
fof(t1_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t1_pdiff_6,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(B),k1_euclid(A)))) ) <=> ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(B)),u1_struct_0(k4_real_ns1(A))))) ) ) ) ) )).
fof(t1_pdiff_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r1_xxreal_0(A,B) => k17_finseq_1(k1_numbers,A,k5_euclid(B)) = k5_euclid(A) ) ) ) )).
fof(t1_pdiff_8,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ( ( r2_hidden(B,k2_finseq_1(A)) & C = D ) => r1_xxreal_0(k9_complex1(k7_partfun1(k1_numbers,D,B)),k12_euclid(C)) ) ) ) ) ) )).
fof(t1_pdiff_9,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k16_lopban_1(A,B))) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(k5_numbers,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_xxreal_0(k2_normsp_0(A,E),1) => r1_xxreal_0(k2_normsp_0(B,k17_lopban_1(A,B,C,E)),k3_xcmplx_0(D,k2_normsp_0(A,E))) ) ) ) => r1_xxreal_0(k2_normsp_0(k16_lopban_1(A,B),C),D) ) ) ) ) ) )).
fof(t1_pencil_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( k4_card_3(A) = k4_card_3(B) & v2_relat_1(A) ) => v2_relat_1(B) ) ) ) )).
fof(t1_pencil_2,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => r1_tarski(k2_relset_1(A,k1_pencil_2(A,B,C,D)),k2_relset_1(A,B)) ) ) ) )).
fof(t1_pencil_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t1_pencil_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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) ) ) ) )).
fof(t1_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => r1_int_2(A,k1_nat_1(A,1)) ) )).
fof(t1_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k6_petri(A,B) = a_2_2_petri(A,B) ) ) )).
fof(t1_petri_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( m1_petri_2(C,A,B) => ? [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) & ? [E] : ( 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) ) ) ) ) )).
fof(t1_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => r2_pnproc_1(A,k1_pnproc_1(A),B) ) )).
fof(t1_polyalg1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(t1_polyeq_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( k1_polyeq_2(A,k5_numbers,B,k5_numbers,C,D) = k5_numbers => ( A = k5_numbers | C = k5_numbers | r1_xxreal_0(k6_xcmplx_0(k1_square_1(B),k3_xcmplx_0(k3_xcmplx_0(4,A),C)),k5_numbers) | ( D != k5_numbers & ~ ( D != k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A))) & D != k3_square_1(k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A))) & D != k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A)))) & D != k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A)))) ) ) ) ) ) ) ) ) )).
fof(t1_polyeq_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xcmplx_0(D) => ~ ( A != k5_numbers & r1_xxreal_0(k5_numbers,k1_quin_1(A,B,C)) & k2_polyeq_3(A,B,C,D) = k5_numbers & D != k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A)) & D != k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A)) & D != k4_xcmplx_0(k7_xcmplx_0(B,k3_xcmplx_0(2,A))) ) ) ) ) ) )).
fof(t1_polyeq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k5_numbers,k1_quin_1(A,B,C)) => ( r1_xxreal_0(k5_numbers,k7_xcmplx_0(B,A)) | r1_xxreal_0(k7_xcmplx_0(C,A),k5_numbers) | ( ~ r1_xxreal_0(k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A)),k5_numbers) & ~ r1_xxreal_0(k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A)),k5_numbers) ) ) ) ) ) ) )).
fof(t1_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,A) = k1_newton(A,2) ) )).
fof(t1_polyform,axiom,( ! [A] : ! [B] : ! [C] : ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => ( ! [D] : ! [E] : ~ ( D != E & A = k2_tarski(D,E) ) | B = C | A = k2_tarski(B,C) ) ) )).
fof(t1_polynom1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t1_polynom2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k4_group_1(A),B,k1_nat_1(C,D)) = k6_algstr_0(A,k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k4_group_1(A),B,C),k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k4_group_1(A),B,D)) ) ) ) ) )).
fof(t1_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( 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) ) ) ) )).
fof(t1_polynom4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( 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)) ) ) ) ) )).
fof(t1_polynom5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( A != k5_numbers & B != k5_numbers & ~ r1_xxreal_0(k5_numbers,k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k2_nat_1(A,B),A),B),1)) ) ) ) )).
fof(t1_polynom6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( ! [D] : ( r2_hidden(D,C) <=> ? [E] : ( v3_ordinal1(E) & D = k10_ordinal2(A,E) & r2_hidden(E,B) ) ) => k10_ordinal2(A,B) = k2_xboole_0(A,C) ) ) ) )).
fof(t1_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( 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,k8_polynom1(A,B)) <=> k3_polynom1(k15_pre_poly(A),B,C) = k1_xboole_0 ) ) ) )).
fof(t1_polynom8,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v6_struct_0(B) & v4_vectsp_1(B) & v1_vectsp_2(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ~ ( C != k4_struct_0(B) & k2_binom(B,C,A) = k4_struct_0(B) ) ) ) ) )).
fof(t1_polyred,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( 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] : ( ( 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,k6_polynom1(A,B,C,D)),k6_polynom1(A,B,k5_vfunct_1(k15_pre_poly(A),B,C),k5_vfunct_1(k15_pre_poly(A),B,D))) ) ) ) )).
fof(t1_poset_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v6_orders_2(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t1_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( v1_abian(B) => k1_newton(k4_xcmplx_0(A),B) = k1_newton(A,B) ) ) ) )).
fof(t1_pralg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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))) ) ) ) ) )).
fof(t1_pralg_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( r2_hidden(A,k4_card_3(B)) => r2_hidden(k5_relat_1(A,C),k4_card_3(k5_relat_1(B,C))) ) ) ) )).
fof(t1_pre_circ,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t1_pre_ff,axiom,( k1_pre_ff(k5_numbers) = k5_numbers & k1_pre_ff(1) = 1 & ! [A] : ( v7_ordinal1(A) => k1_pre_ff(k1_nat_1(k1_nat_1(A,1),1)) = k1_nat_1(k1_pre_ff(A),k1_pre_ff(k1_nat_1(A,1))) ) )).
fof(t1_pre_poly,axiom,( ! [A] : ! [B] : ( m2_finseq_2(B,A,k3_finseq_2(A)) => k5_pre_poly(A,k3_pre_poly(k3_finseq_2(A),B)) = B ) )).
fof(t1_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => r2_hidden(k1_xboole_0,u1_pre_topc(A)) ) )).
fof(t1_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_prelamb(A) ) => ! [B] : ( m1_prelamb(B,A) => ! [C] : ( m1_trees_1(C,k9_xtuple_0(B)) => ( k8_trees_2(k9_xtuple_0(B),C) = 1 => r2_hidden(k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,k5_numbers)),k9_xtuple_0(B)) ) ) ) ) )).
fof(t1_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(B) & ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(A,k1_funct_1(B,C)) ) ) => r1_xxreal_0(A,k1_seq_2(B)) ) ) ) )).
fof(t1_prgcor_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k7_nat_d(k1_nat_1(A,C),k1_nat_1(B,C)) = k7_nat_d(A,B) ) ) ) )).
fof(t1_prgcor_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ( ( r1_tarski(k4_ordinal1,A) & v7_ordinal1(k1_funct_1(B,k5_numbers)) & r2_hidden(k1_funct_1(B,k5_numbers),k1_afinsq_1(B)) ) => r1_prgcor_2(A,B,k12_afinsq_1(A,B)) ) ) ) )).
fof(t1_prob_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ? [C] : ( v7_ordinal1(C) & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => k9_nat_1(k1_numbers,B,D) = A ) ) ) => ( v2_comseq_2(B) & k1_seq_2(B) = A ) ) ) ) )).
fof(t1_prob_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( A != k5_numbers & B != k5_numbers & ~ ( k7_xcmplx_0(D,B) = k7_xcmplx_0(C,A) <=> k3_xcmplx_0(D,A) = k3_xcmplx_0(C,B) ) ) ) ) ) ) )).
fof(t1_prob_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ~ r2_hidden(k5_numbers,k9_xtuple_0(A)) ) )).
fof(t1_prob_4,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => r1_tarski(k4_measure1(A,k9_setfam_1(A),C),B) ) ) )).
fof(t1_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) )).
fof(t1_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t1_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u2_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u2_incsp_1(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t1_projred1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ~ ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => r1_incsp_1(A,C,B) ) ) ) )).
fof(t1_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ( ~ ( B != C & C != D & D != B ) => r1_projred2(A,B,C,D) ) ) ) ) ) )).
fof(t1_prvect_1,axiom,( ! [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) ) => r3_binop_1(u1_struct_0(A),k4_struct_0(A),u1_algstr_0(A)) ) )).
fof(t1_prvect_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ! [D] : ( m1_subset_1(D,k4_ordinal1) => k3_funct_2(k4_ordinal1,k1_numbers,B,D) = k9_complex1(k6_xcmplx_0(k3_funct_2(k4_ordinal1,k1_numbers,A,D),C)) ) => ( ( ( v2_comseq_2(A) & k1_seq_2(A) = C ) => ( v2_comseq_2(B) & k1_seq_2(B) = k5_numbers ) ) & ( ( v2_comseq_2(B) & k1_seq_2(B) = k5_numbers ) => ( v2_comseq_2(A) & k1_seq_2(A) = C ) ) ) ) ) ) ) )).
fof(t1_pscomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k1_pscomp_1(A,B),k3_funct_2(u1_struct_0(A),k1_numbers,B,C)) ) ) ) )).
fof(t1_pua2mss1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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] : ( r2_hidden(C,k9_xtuple_0(A)) => r1_tarski(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ) ) )).
fof(t1_pythtrip,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( v1_pythtrip(k2_nat_1(A,B)) & r1_int_2(A,B) ) => ( v1_pythtrip(A) & v1_pythtrip(B) ) ) ) ) )).
fof(t1_pzfmisc1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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 ) ) )).
fof(t1_qc_lang1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,A) => r1_tarski(k2_zfmisc_1(k1_tarski(C),B),k2_zfmisc_1(A,B)) ) ) )).
fof(t1_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => k18_qc_lang1(A,k13_qc_lang1(A,B)) = B ) ) )).
fof(t1_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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))) ) ) )).
fof(t1_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t1_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v5_relat_1(C,k3_qc_lang1(A)) & v3_card_1(C,B) & m2_finseq_1(C,k2_qc_lang1(A)) ) => ! [D] : ( m2_subset_1(D,k6_qc_lang1(A),k8_qc_lang1(A,B)) => k7_qc_lang1(A,D) = k3_finseq_1(C) ) ) ) ) )).
fof(t1_qmax_1,axiom,( ! [A] : ( ( v2_qmax_1(A) & l1_qmax_1(A) ) => ! [B] : ( m1_subset_1(B,k3_qmax_1(A)) => ! [C] : ( m1_subset_1(C,k5_qmax_1(A)) => ! [D] : ( 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)) = k6_xcmplx_0(1,k3_funct_2(k12_prob_1,k1_numbers,k4_qmax_1(A,k6_qmax_1(A,C),B),D)) ) ) ) ) ) )).
fof(t1_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t1_quatern2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k6_quaterni(A,B,C,D) = k22_quaterni(k22_quaterni(k19_quaterni(A,k21_quaterni(B,k7_complex1)),k21_quaterni(C,k11_quaterni)),k21_quaterni(D,k12_quaterni)) ) ) ) ) )).
fof(t1_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k13_quaterni(k23_quaterni(A,B)) = k13_quaterni(k23_quaterni(B,A)) ) ) )).
fof(t1_quaterni,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : k9_xtuple_0(k2_quaterni(E,F,G,H,A,B,C,D)) = k2_enumset1(E,F,G,H) )).
fof(t1_quin_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( A != k5_numbers => k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k1_square_1(D)),k3_xcmplx_0(B,D)),C) = k6_xcmplx_0(k3_xcmplx_0(A,k1_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))) ) ) ) ) ) )).
fof(t1_quofield,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v6_struct_0(A) & l5_algstr_0(A) ) => ~ v1_xboole_0(k1_quofield(A)) ) )).
fof(t1_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k4_nat_d(B,A) = k6_xcmplx_0(A,1) => k4_nat_d(k2_xcmplx_0(B,1),A) = k5_numbers ) ) ) )).
fof(t1_radix_2,axiom,( ! [A] : ( v7_ordinal1(A) => k4_nat_d(A,1) = k5_numbers ) )).
fof(t1_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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))) ) ) ) ) )).
fof(t1_radix_4,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( r1_xxreal_0(2,A) & r1_xxreal_0(k1_radix_1(A),2) ) ) )).
fof(t1_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(2,A) => r2_hidden(k6_xcmplx_0(k1_radix_1(A),1),k3_radix_1(A)) ) ) )).
fof(t1_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t1_ramsey_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t1_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( v1_xreal_0(F) => ( ( r1_mesfunc5(A,B,C,D) & r1_tarski(E,k1_relset_1(A,D)) & ! [G] : ( m1_subset_1(G,A) => ( r2_hidden(G,E) => r1_xxreal_0(F,k12_supinf_2(D,G)) ) ) ) => ( r1_xxreal_0(k1_xxreal_0,k3_funct_2(B,k6_numbers,C,E)) | r1_xxreal_0(k4_xxreal_3(F,k3_funct_2(B,k6_numbers,C,E)),k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,E))) ) ) ) ) ) ) ) ) )).
fof(t1_random_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_xtuple_0(A))) => ! [C] : ( 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))) ) ) ) ) )).
fof(t1_random_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => k8_relat_1(B,k3_tarski(A)) = k3_tarski(a_2_0_random_3(A,B)) ) ) )).
fof(t1_ranknull,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t1_rat_1,axiom,( ! [A] : ~ ( r2_hidden(A,k3_numbers) & ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ~ ( C != k5_numbers & A = k7_xcmplx_0(B,C) ) ) ) ) )).
fof(t1_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ( ( k3_finseq_1(C) = k3_finseq_1(D) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( 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)) ) ) ) ) ) )).
fof(t1_rcomp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r2_hidden(B,k2_rcomp_1(k6_xcmplx_0(C,A),k2_xcmplx_0(C,A))) <=> ~ r1_xxreal_0(A,k9_complex1(k6_xcmplx_0(B,C))) ) ) ) ) )).
fof(t1_rcomp_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_membered(A) & v3_xxreal_2(A) ) => ! [B] : ( ( v2_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,B) => r2_hidden(k3_seq_4(A),B) ) ) ) )).
fof(t1_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(A,B) & v2_xxreal_0(A) ) => v2_xxreal_0(B) ) ) ) )).
fof(t1_real_1,axiom,( k2_arytm_2 = a_0_0_real_1 )).
fof(t1_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) & r1_xxreal_0(k7_xcmplx_0(1,A),1) ) ) )).
fof(t1_real_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_real_lat)) => ! [B] : ( 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) ) ) )).
fof(t1_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(A))) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ( B = C => k2_normsp_0(k4_real_ns1(A),B) = k12_euclid(C) ) ) ) ) )).
fof(t1_realset2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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))) ) ) )).
fof(t1_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) )).
fof(t1_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ( v3_rearran1(B,k1_zfmisc_1(A)) <=> k3_finseq_1(B) = k5_card_1(A) ) ) ) )).
fof(t1_recdef_2,axiom,( ! [A] : ( ? [B] : ? [C] : ? [D] : A = k3_xtuple_0(B,C,D) => A = k3_xtuple_0(k4_xtuple_0(A),k5_xtuple_0(A),k2_xtuple_0(A)) ) )).
fof(t1_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => r1_tarski(A,k2_zfmisc_1(k9_xtuple_0(A),k10_xtuple_0(A))) ) )).
fof(t1_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_relat_2(A) <=> r1_tarski(k4_relat_1(k1_relat_1(A)),A) ) ) )).
fof(t1_reloc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) )).
fof(t1_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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))) ) ) )).
fof(t1_relset_2,axiom,( ! [A] : ! [B] : ( r2_hidden(A,k10_eqrel_1(B)) <=> ? [C] : ( A = k1_tarski(C) & r2_hidden(C,B) ) ) )).
fof(t1_revrot_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t1_rewrite1,axiom,( ! [A] : ( ( 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 ) ) )).
fof(t1_rewrite2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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 = k5_numbers ) ) ) ) )).
fof(t1_rewrite3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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) ) ) ) )).
fof(t1_rfinseq,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t1_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(A)) ) => ( r1_xxreal_0(k1_funct_1(A,B),k1_funct_1(A,k1_rfinseq2(A))) & r1_xxreal_0(k1_funct_1(A,B),k3_rfinseq2(A)) ) ) ) ) )).
fof(t1_rfunct_1,axiom,( ! [A] : ( ( 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(k5_numbers)))) = k6_subset_1(k9_xtuple_0(A),k8_relat_1(A,k1_tarski(k5_numbers))) ) ) )).
fof(t1_rfunct_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_relset_1(k4_ordinal1,k1_numbers,A,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C)) <=> ! [D] : ( v7_ordinal1(D) => k1_funct_1(A,D) = k6_xcmplx_0(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) ) )).
fof(t1_rfunct_3,axiom,( ! [A] : ( v1_xreal_0(A) => A = k6_xcmplx_0(k1_rfunct_3(A),k2_rfunct_3(A)) ) )).
fof(t1_rfunct_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(k3_xxreal_0(A,B),k4_xxreal_0(A,B)) ) ) )).
fof(t1_rinfsup1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( ~ r1_xxreal_0(C,k6_xcmplx_0(B,A)) & ~ r1_xxreal_0(k2_xcmplx_0(B,A),C) ) <=> ~ r1_xxreal_0(A,k9_complex1(k6_xcmplx_0(C,B))) ) ) ) ) )).
fof(t1_rinfsup2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( ( ~ 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) = k2_seq_4(B) ) ) ) ) )).
fof(t1_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_algstr_0(A,k5_algstr_0(A,B,C),C) = B ) ) ) )).
fof(t1_ringcat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l6_algstr_0(C) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t1_rlaffin1,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) )).
fof(t1_rlaffin2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) != k5_numbers & ! [E] : ( 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,k6_xcmplx_0(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),k7_xcmplx_0(1,k3_funct_2(u1_struct_0(A),k1_numbers,D,B))),k1_rlvect_1(A,E,k6_xcmplx_0(1,k7_xcmplx_0(1,k3_funct_2(u1_struct_0(A),k1_numbers,D,B))))) = B ) ) ) ) ) ) ) )).
fof(t1_rlaffin3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v3_valued_0(B) ) => ! [C] : ( 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) ) ) ) )).
fof(t1_rlsub_1,axiom,( ! [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) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t1_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( r1_struct_0(k1_rlsub_2(A,B,C),D) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( 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) ) ) ) ) ) ) )).
fof(t1_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(C,B) => r2_hidden(k1_rlvect_1(A,C,D),k1_convex1(A,B,D)) ) ) ) ) ) )).
fof(t1_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_struct_0(A,B) ) ) )).
fof(t1_rlvect_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_rlvect_2(A,B) = B ) ) )).
fof(t1_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(t1_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t1_rlvect_5,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_rlvect_2(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t1_rlvect_x,axiom,( ! [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) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t1_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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) ) ) ) ) ) )).
fof(t1_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( r1_struct_0(k1_rmod_3(A,B,C,D),E) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & ? [G] : ( 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) ) ) ) ) ) ) ) )).
fof(t1_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(B)) => ( ( k3_finseq_1(D) = k3_finseq_1(E) & ! [F] : ( v7_ordinal1(F) => ! [G] : ( 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)) ) ) ) ) ) ) )).
fof(t1_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) )).
fof(t1_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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 ) ) ) ) ) ) )).
fof(t1_robbins3,axiom,( ! [A] : ( ( ~ 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) ) ) ) )).
fof(t1_robbins4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t1_rolle,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,A) => ! [C] : ( ( 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_funct_1(C,A) = k1_funct_1(C,B) & r2_fdiff_1(C,k2_rcomp_1(A,B)) & ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,k2_rcomp_1(A,B)) & k1_fdiff_1(C,D) = k5_numbers ) ) ) ) ) ) ) )).
fof(t1_roughs_1,axiom,( ! [A] : ( r1_relset_1(A,A,k1_eqrel_1(A),k6_partfun1(A)) => v1_zfmisc_1(A) ) )).
fof(t1_rpr_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( r1_tarski(C,B) <=> ( C = k1_xboole_0 | C = B ) ) ) ) ) )).
fof(t1_rsspace,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k2_rsspace(A),A) ) )).
fof(t1_rsspace4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_comseq_2(A) & k2_seq_4(k2_relset_1(k1_numbers,k56_valued_1(k4_ordinal1,k1_numbers,A))) = k5_numbers ) <=> ! [B] : ( v7_ordinal1(B) => k1_funct_1(A,B) = k5_numbers ) ) ) )).
fof(t1_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( ( r1_struct_0(B,D) & m1_rusub_1(B,C) ) => r1_struct_0(C,D) ) ) ) ) )).
fof(t1_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( r1_struct_0(k1_rusub_2(A,B,C),D) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( 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) ) ) ) ) ) ) )).
fof(t1_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( r1_struct_0(k1_rusub_3(A,B),C) <=> ? [D] : ( m2_rlvect_2(D,A,B) & C = k6_rlvect_2(A,D) ) ) ) ) )).
fof(t1_rusub_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t1_rusub_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_rlvect_1(A) & l1_rlvect_1(A) ) => ! [B] : ( ( v2_rusub_4(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => r1_rusub_5(A,B,B) ) ) )).
fof(t1_rvsum_1,axiom,( r3_binop_1(k1_numbers,k5_numbers,k9_binop_2) )).
fof(t1_scheme1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( A != k2_nat_1(2,B) & A != k1_nat_1(k2_nat_1(2,B),1) ) ) ) )).
fof(t1_scm_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( ( v5_memstr_0(F,k7_card_1(2),k1_ami_3,E) & m1_scm_1(F,k16_afinsq_1(A,B,C,D)) ) => ( k1_funct_1(F,k10_ami_3(k5_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 ) ) ) ) ) ) ) )).
fof(t1_scm_comp,axiom,( ! [A] : ( m2_subset_1(A,u1_struct_0(k1_scm_comp),k7_dtconstr(k1_scm_comp)) => ~ ! [B] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(B,4) & A = k4_tarski(k5_numbers,B) ) ) ) )).
fof(t1_scm_inst,axiom,( r2_hidden(k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0),k3_scm_inst) )).
fof(t1_scmfsa6a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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))) ) )).
fof(t1_scmfsa6b,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(A,k7_card_1(3),k1_scmfsa_2,k5_numbers) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( r1_tarski(B,C) => r1_extpro_1(k7_card_1(3),k1_scmfsa_2,C,A) ) ) ) ) )).
fof(t1_scmfsa6c,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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,k7_card_1(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) ) ) ) ) ) )).
fof(t1_scmfsa8a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => ( ( k1_funct_1(A,C) = k2_compos_1(k1_scmfsa_2) => k1_funct_1(k1_scmfsa6a(A,B),C) = k11_scmfsa_2(B) ) & ( k1_funct_1(A,C) != k2_compos_1(k1_scmfsa_2) => k1_funct_1(k1_scmfsa6a(A,B),C) = k1_funct_1(A,C) ) ) ) ) ) )).
fof(t1_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ( r5_scmfsa7b(B,C,A) => r2_hidden(k5_numbers,k9_xtuple_0(B)) ) ) ) ) )).
fof(t1_scmfsa9a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => k2_sf_mastr(k16_funcop_1(A,B)) = k1_sf_mastr(B) ) ) )).
fof(t1_scmfsa_1,axiom,( r1_tarski(k1_ami_2,k1_scmfsa_1) )).
fof(t1_scmfsa_2,axiom,( k4_struct_0(k1_scmfsa_2) = k4_ordinal1 )).
fof(t1_scmfsa_3,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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(k7_card_1(3),k1_scmfsa_2,B)),C) ) ) ) )).
fof(t1_scmfsa_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k5_compos_0(u1_compos_1(k1_scmfsa_2),k11_scmfsa_2(B),A) = k11_scmfsa_2(k2_xcmplx_0(B,A)) ) ) )).
fof(t1_scmfsa_7,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( 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))) ) ) )).
fof(t1_scmfsa_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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(k5_numbers)),k4_compos_1(k1_scmfsa_2))) = k1_nat_1(k5_card_1(A),6) ) ) )).
fof(t1_scmfsa_i,axiom,( r1_tarski(k3_scm_inst,k2_scmfsa_i) )).
fof(t1_scmfsa_m,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ~ ( 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) ) ) )).
fof(t1_scmp_gcd,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k2_scmpds_2(A,B) = k1_scmp_gcd(k2_xcmplx_0(A,B)) ) ) )).
fof(t1_scmpds_1,axiom,( ! [A] : ( m2_subset_1(A,k1_ami_2,k2_ami_2) => r2_hidden(A,k2_xboole_0(k2_ami_2,k4_numbers)) ) )).
fof(t1_scmpds_2,axiom,( k4_struct_0(k1_scmpds_2) = k4_ordinal1 )).
fof(t1_scmpds_4,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( ( 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(k5_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)) ) ) ) )).
fof(t1_scmpds_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & 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))) ) ) )).
fof(t1_scmpds_6,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => k5_card_1(k2_scmpds_4(A,B)) = k1_nat_1(k5_card_1(B),1) ) ) )).
fof(t1_scmpds_7,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( k5_memstr_0(2,k1_scmpds_2,A) = B => k17_scmpds_2(A,k6_xcmplx_0(C,B)) = C ) ) ) ) )).
fof(t1_scmpds_9,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ! [C] : ( ( 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)) ) ) ) )).
fof(t1_scmpds_i,axiom,( ! [A] : ( v1_int_1(A) => r2_hidden(A,k2_xboole_0(k2_scm_inst,k4_numbers)) ) )).
fof(t1_scmring2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(t1_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => k4_memstr_0(k7_card_1(2),k1_scmring2(A),B) = u1_struct_0(A) ) ) )).
fof(t1_scmring4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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) = k4_tarski(1,A) ) ) )).
fof(t1_scmringi,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k7_card_1(8)) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( m1_subset_1(C,k1_scmringi(B)) => ! [D] : ( m1_subset_1(D,k2_scm_inst) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t1_scmyciel,axiom,( ! [A] : ! [B] : ~ r2_hidden(k4_tarski(A,B),B) )).
fof(t1_scpinvar,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmpds_2)) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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),k5_numbers) = A & k1_funct_1(k1_scmpds_4(k4_scmpds_4(A,B),C),1) = B ) ) ) ) )).
fof(t1_scpisort,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ? [D] : ( m2_finseq_1(D,k4_numbers) & k3_finseq_1(D) = B & ! [E] : ( v7_ordinal1(E) => ( ( 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_xcmplx_0(C,E))) ) ) ) ) ) ) )).
fof(t1_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v3_scmpds_4(D) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_scmpds_2)) ) => ! [G] : ( 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)),k5_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) ) ) ) ) ) ) ) ) ) )).
fof(t1_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_analoaf(A,B,C,B,C) ) ) ) )).
fof(t1_seq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) <=> ( k9_xtuple_0(A) = k4_ordinal1 & ! [B] : ( r2_hidden(B,k4_ordinal1) => v1_xreal_0(k1_funct_1(A,B)) ) ) ) ) )).
fof(t1_seq_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( ~ r1_xxreal_0(A,k4_xcmplx_0(B)) & ~ r1_xxreal_0(B,A) ) <=> ~ r1_xxreal_0(B,k9_complex1(A)) ) ) ) )).
fof(t1_seq_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ~ ( ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(C,A) & r2_hidden(D,B) & r1_xxreal_0(D,C) ) ) ) & ! [C] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & r2_hidden(D,A) & r2_hidden(E,B) & ~ ( r1_xxreal_0(D,C) & r1_xxreal_0(C,E) ) ) ) ) ) ) ) )).
fof(t1_seqfunc,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,B)))) ) <=> ( k9_xtuple_0(C) = k4_ordinal1 & ! [D] : ( v7_ordinal1(D) => ( v1_funct_1(k1_funct_1(C,D)) & m1_subset_1(k1_funct_1(C,D),k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ) ) ) ) )).
fof(t1_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v5_valued_0(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(C,B) & r1_xxreal_0(k9_nat_1(k1_numbers,A,C),k9_nat_1(k1_numbers,A,B)) ) ) ) ) ) )).
fof(t1_series_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,B,C) = k2_power(A,k1_nat_1(C,1)) ) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(1,A) | ( v2_comseq_2(B) & k1_seq_2(B) = k5_numbers ) ) ) ) ) )).
fof(t1_series_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k9_complex1(k1_newton(k4_xcmplx_0(1),A)) = 1 ) )).
fof(t1_series_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k5_numbers,A) ) => ( r1_xxreal_0(C,B) | r1_xxreal_0(k7_xcmplx_0(B,C),k7_xcmplx_0(k2_xcmplx_0(B,A),k2_xcmplx_0(C,A))) ) ) ) ) ) )).
fof(t1_series_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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)) ) ) ) )).
fof(t1_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => r1_xxreal_0(4,k3_xcmplx_0(k2_xcmplx_0(A,B),k2_xcmplx_0(k7_xcmplx_0(1,A),k7_xcmplx_0(1,B)))) ) ) )).
fof(t1_setfam_1,axiom,( k1_setfam_1(k1_xboole_0) = k1_xboole_0 )).
fof(t1_setlim_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,C))) ) => r2_hidden(k1_funct_1(D,k2_xcmplx_0(A,B)),a_3_0_setlim_1(A,C,D)) ) ) ) )).
fof(t1_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => k9_nat_1(k9_setfam_1(B),k2_setlim_1(B,C),A) = k3_prob_1(B,k8_nat_1(k9_setfam_1(B),C,A)) ) ) )).
fof(t1_setwiseo,axiom,( ! [A] : ! [B] : ! [C] : r1_tarski(k1_tarski(A),k1_enumset1(A,B,C)) )).
fof(t1_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t1_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ( k6_scmfsa_2(A,C) = k6_scmfsa_2(B,D) => ( A = B & C = D ) ) ) ) ) ) )).
fof(t1_sfmastr1,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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) ) ) ) )).
fof(t1_sfmastr2,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ( ( 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) ) ) ) ) ) ) )).
fof(t1_sfmastr3,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ( ( 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) ) ) ) ) ) ) )).
fof(t1_sgraph1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( r2_hidden(C,k1_sgraph1(A,B)) <=> ? [D] : ( v7_ordinal1(D) & C = D & r1_xxreal_0(A,D) & r1_xxreal_0(D,B) ) ) ) ) )).
fof(t1_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t1_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t1_simplex0,axiom,( ! [A] : ( v1_classes1(A) <=> ! [B] : ( r2_hidden(B,A) => r1_tarski(k9_setfam_1(B),A) ) ) )).
fof(t1_simplex2,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t1_sin_cos,axiom,( ! [A] : ( v7_ordinal1(A) => ( k2_newton(k5_numbers) = 1 & k2_newton(A) != k5_numbers & k2_newton(k1_nat_1(A,1)) = k2_nat_1(k2_newton(A),k1_nat_1(A,1)) ) ) )).
fof(t1_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => r1_xxreal_0(k3_xcmplx_0(2,k3_square_1(k3_xcmplx_0(A,B))),k2_xcmplx_0(A,B)) ) ) ) )).
fof(t1_sin_cos3,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => k2_xcmplx_0(k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,A)),k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,A))) = 1 ) )).
fof(t1_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => k1_sin_cos4(k4_xcmplx_0(A)) = k4_xcmplx_0(k1_sin_cos4(A)) ) )).
fof(t1_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k19_sin_cos(A) != k5_numbers => k3_sin_cos4(A) = k7_xcmplx_0(k4_sin_cos4(A),k1_sin_cos4(A)) ) ) )).
fof(t1_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k5_numbers,A) => ( r1_xxreal_0(B,A) | k1_int_1(k7_xcmplx_0(A,B)) = k5_numbers ) ) ) ) )).
fof(t1_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k7_xcmplx_0(1,A) = k2_power(A,k4_xcmplx_0(1)) ) ) )).
fof(t1_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ( k6_sin_cos2(A) = k7_xcmplx_0(k2_sin_cos2(A),k4_sin_cos2(A)) & k6_sin_cos2(k5_numbers) = k5_numbers ) ) )).
fof(t1_sin_cos9,axiom,( r1_tarski(k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2)),k1_relset_1(k1_numbers,k26_sin_cos)) )).
fof(t1_sincos10,axiom,( r1_tarski(k3_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)),k1_relset_1(k1_numbers,k1_fdiff_9)) )).
fof(t1_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,A) => r1_xxreal_0(A,k6_xcmplx_0(B,1)) ) ) ) )).
fof(t1_sppol_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( k19_euclid(A,B) = k19_euclid(C,D) => ( A = C & B = D ) ) ) ) ) ) )).
fof(t1_sprect_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t1_sprect_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( 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_xcmplx_0(C,A),1),k4_finseq_1(E)) ) ) ) ) ) ) )).
fof(t1_sprect_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(t1_sprect_4,axiom,( ! [A] : ( ( v4_topreal1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( ( 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)))) ) ) ) )).
fof(t1_sprect_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,k10_xtuple_0(k17_finseq_1(A,k4_finseq_4(B,C),B))) => r1_xxreal_0(k4_finseq_4(B,D),k4_finseq_4(B,C)) ) ) ) ) ) )).
fof(t1_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k2_xcmplx_0(k3_xxreal_0(A,B),k4_xxreal_0(A,B)) = k2_xcmplx_0(A,B) ) ) )).
fof(t1_stacks_1,axiom,( ! [A] : ( v7_ordinal1(A) => k2_finseq_3(A,k1_xboole_0) = k1_xboole_0 ) )).
fof(t1_stirl2_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) ) => k4_seq_4(A) = k3_nat_1(A) ) )).
fof(t1_struct_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r2_hidden(B,k8_struct_0(A)) <=> ~ v9_struct_0(B,A) ) ) ) )).
fof(t1_sublemma,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t1_subset,axiom,( ! [A] : ! [B] : ( r2_hidden(A,B) => m1_subset_1(A,B) ) )).
fof(t1_subset_1,axiom,( ! [A] : m1_subset_1(k1_xboole_0,k1_zfmisc_1(A)) )).
fof(t1_substlat,axiom,( ! [A] : ! [B] : r2_hidden(k1_xboole_0,k1_substlat(A,B)) )).
fof(t1_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ! [C] : ( 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)) ) ) ) )).
fof(t1_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_substut1(A)) => ? [C] : ( m2_subset_1(C,k16_substut1(A),k38_substut1(A)) & k2_sublemma(A,C) = k5_cqc_lang(A) & k19_substut1(A,C) = B ) ) ) )).
fof(t1_supinf_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ( r1_tarski(A,B) => ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(C,k3_supinf_1(B)) => r2_hidden(C,k3_supinf_1(A)) ) ) ) ) ) )).
fof(t1_supinf_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( A = C & B = D ) => k1_xxreal_3(A,B) = k2_xcmplx_0(C,D) ) ) ) ) ) )).
fof(t1_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => r1_orders_2(B,k4_struct_0(B),C) ) ) ) )).
fof(t1_sysrel,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) ) )).
fof(t1_t_0topsp,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( ! [E] : ( m1_subset_1(E,A) => ! [F] : ( 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 ) ) ) ) ) )).
fof(t1_t_1topsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) ) => ! [C] : ( 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) ) ) ) )).
fof(t1_taxonom1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(k1_nat_1(B,1),k4_finseq_1(A)) => ( r2_hidden(B,k4_finseq_1(A)) | B = k5_numbers ) ) ) ) )).
fof(t1_taxonom2,axiom,( ! [A] : ( ~ v2_struct_0(k1_yellow_1(k1_tarski(k1_tarski(A)))) & v3_orders_2(k1_yellow_1(k1_tarski(k1_tarski(A)))) & v4_orders_2(k1_yellow_1(k1_tarski(k1_tarski(A)))) & v5_orders_2(k1_yellow_1(k1_tarski(k1_tarski(A)))) & v1_taxonom2(k1_yellow_1(k1_tarski(k1_tarski(A)))) & v2_taxonom2(k1_yellow_1(k1_tarski(k1_tarski(A)))) ) )).
fof(t1_taylor_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k3_prepower(A,k2_xcmplx_0(C,B)) = k3_xcmplx_0(k3_prepower(A,C),k3_prepower(A,B)) ) ) ) )).
fof(t1_taylor_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => k9_complex1(k1_newton(A,B)) = k1_newton(k9_complex1(A),B) ) ) )).
fof(t1_tbsp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) & ? [B] : ( v7_ordinal1(B) & ? [C] : ( v7_ordinal1(C) & r1_xxreal_0(B,C) & ~ r1_xxreal_0(k2_power(A,C),k2_power(A,B)) ) ) ) ) )).
fof(t1_tdgroup,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_vectsp_1)) => ? [B] : ( m1_subset_1(B,u1_struct_0(k1_vectsp_1)) & k3_rlvect_1(k1_vectsp_1,B,B) = A ) ) )).
fof(t1_tdlat_1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t1_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(t1_tdlat_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(t1_termord,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(t1_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t1_tex_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v3_card_1(B,1) => ( r1_tarski(A,B) => A = B ) ) ) )).
fof(t1_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t1_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) )).
fof(t1_tietze,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k9_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)) ) ) ) ) ) )).
fof(t1_tmap_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ( r1_subset_1(C,D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,C,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,B))) ) => ! [F] : ( ( 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 ) ) ) ) ) ) ) ) )).
fof(t1_toler_1,axiom,( ! [A] : k2_relset_1(A,k1_eqrel_1(A)) = A )).
fof(t1_topalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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) ) ) ) )).
fof(t1_topalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_borsuk_2(G,B,E,F) => ( ( C = E & D = F & r1_borsuk_6(B,E,F) ) => m1_borsuk_2(G,A,C,D) ) ) ) ) ) ) ) ) )).
fof(t1_topalg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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))) ) ) ) )).
fof(t1_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_group_7(k2_tarski(1,2),k10_finseq_1(A,B)))) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & C = k5_group_7(A,B,D,E) ) ) ) ) ) )).
fof(t1_topalg_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_topmetr(B,C))) => ~ ( k8_metric_1(k2_topmetr(B,C),D,A) != k1_rcomp_1(B,C) & k8_metric_1(k2_topmetr(B,C),D,A) != k3_rcomp_1(B,k2_xcmplx_0(D,A)) & k8_metric_1(k2_topmetr(B,C),D,A) != k4_rcomp_1(k6_xcmplx_0(D,A),C) & k8_metric_1(k2_topmetr(B,C),D,A) != k2_rcomp_1(k6_xcmplx_0(D,A),k2_xcmplx_0(D,A)) ) ) ) ) ) ) )).
fof(t1_topalg_6,axiom,( r2_funct_2(u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k4_topmetr(k5_numbers,1)),k1_borsuk_6(k5_numbers,1,k5_numbers,1),k3_struct_0(k4_topmetr(k5_numbers,1))) )).
fof(t1_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k1_pre_topc(A,B)))) => ( D = k9_subset_1(u1_struct_0(A),C,B) => r1_tarski(k2_tops_1(k1_pre_topc(A,B),D),k9_subset_1(u1_struct_0(A),k2_tops_1(A,C),B)) ) ) ) ) ) )).
fof(t1_topdim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( 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) ) ) ) )).
fof(t1_topgen_1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t1_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(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)))) ) => ! [C] : ( 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)))) ) ) ) ) )).
fof(t1_topgen_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v3_abian(B,k1_zfmisc_1(k1_zfmisc_1(A))) <=> ! [C] : ~ ( r2_hidden(C,A) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ~ ( r2_hidden(D,B) & r2_hidden(C,D) ) ) ) ) ) )).
fof(t1_topgen_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v4_card_3(B) <=> v4_card_3(k7_setfam_1(A,B)) ) ) )).
fof(t1_topgen_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_partfun1(A,B) => ! [C] : k8_relat_1(k1_funct_4(A,B),C) = k2_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)) ) ) ) )).
fof(t1_topgrp_1,axiom,( ! [A] : ( l1_struct_0(A) => k2_relset_1(u1_struct_0(A),k3_struct_0(A)) = k2_struct_0(A) ) )).
fof(t1_topmetr,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)) ) ) ) )).
fof(t1_topmetr2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( v2_funct_1(A) & v2_funct_1(B) & ! [C] : ! [D] : ~ ( 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)) ) ) ) )).
fof(t1_topmetr3,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ( ( v2_tbsp_1(B,A) & ! [D] : ( v7_ordinal1(D) => 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) ) ) ) ) )).
fof(t1_topreal1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_topreal1(A,C,D,B) => ( r2_hidden(C,B) & r2_hidden(D,B) ) ) ) ) ) ) )).
fof(t1_topreal2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( A != B & r2_hidden(A,k1_topreal1) & r2_hidden(B,k1_topreal1) & ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t1_topreal3,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t1_topreal4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( r1_topreal4(A,B,C) => v5_topreal1(A) ) ) ) ) )).
fof(t1_topreal5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t1_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,B) ) => r1_xxreal_0(k9_complex1(A),k9_complex1(B)) ) ) ) )).
fof(t1_topreal7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => r1_xxreal_0(k4_xxreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,D)),k2_xcmplx_0(k4_xxreal_0(A,B),k4_xxreal_0(C,D))) ) ) ) ) )).
fof(t1_topreal8,axiom,( ! [A] : ! [B] : ! [C] : ( ( r1_tarski(A,k2_tarski(B,C)) & r2_hidden(B,A) ) => ( r2_hidden(C,A) | A = k1_tarski(B) ) ) )).
fof(t1_topreala,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( ( 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) ) ) )).
fof(t1_toprealb,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k17_sin_cos(k2_xcmplx_0(k3_xcmplx_0(A,C),B)) = k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,B),k16_sin_cos),C) ) ) ) )).
fof(t1_toprealc,axiom,( ! [A] : ( v1_zfmisc_1(A) => ! [B] : ( r2_tarski(A,B) => v1_zfmisc_1(B) ) ) )).
fof(t1_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) <=> ( k9_xtuple_0(B) = k4_ordinal1 & ! [C] : ( v7_ordinal1(C) => m1_subset_1(k1_funct_1(B,C),u1_struct_0(k15_euclid(A))) ) ) ) ) ) )).
fof(t1_tops_1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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 ) ) ) ) )).
fof(t1_tops_2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => r1_tarski(B,k9_setfam_1(k2_struct_0(A))) ) ) )).
fof(t1_tops_3,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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 ) ) ) ) )).
fof(t1_tops_4,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( v2_pre_topc(D) & l1_pre_topc(D) ) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t1_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) & k3_funct_2(A,A,C,D) = B ) ) ) ) )).
fof(t1_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r1_aff_1(A,B,C,D) & B != C & B != D & C != D ) ) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r1_aff_1(A,B,C,D) & B != D & C != D ) ) ) ) ) )).
fof(t1_treal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ( C = k1_rcomp_1(A,B) => v4_pre_topc(C,k3_topmetr) ) ) ) ) )).
fof(t1_trees_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( r1_tarski(A,B) <=> ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & B = k7_finseq_1(A,C) ) ) ) ) )).
fof(t1_trees_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t1_trees_3,axiom,( ! [A] : ( v1_trees_3(A) <=> r1_tarski(A,k1_trees_3) ) )).
fof(t1_trees_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_tarski(k2_trees_1(A),k2_trees_1(B)) => r1_xxreal_0(A,B) ) ) ) )).
fof(t1_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => k5_trees_2(A,k6_finseq_1(k4_ordinal1)) = A ) )).
fof(t1_trees_a,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t1_triang_1,axiom,( ! [A] : k2_wellord1(k1_xboole_0,A) = k1_xboole_0 )).
fof(t1_tsep_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => m1_subset_1(u1_struct_0(B),k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(t1_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(t1_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v3_pre_topc(C,A) & ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t1_tsp_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t1_turing_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(B,k3_turing_1(A)) <=> r1_xxreal_0(B,A) ) ) ) )).
fof(t1_twoscomp,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( 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)) ) ) ) )).
fof(t1_unialg_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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)))) ) ) ) ) )).
fof(t1_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t1_unialg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( r2_hidden(B,k1_unialg_3(A)) <=> ? [C] : ( v1_unialg_1(C) & m1_unialg_2(C,A) & B = C ) ) ) )).
fof(t1_uniform1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(A,k7_xcmplx_0(1,B)) ) ) ) ) )).
fof(t1_uniroots,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t1_uproots,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( r2_hidden(B,k4_finseq_1(A)) & k1_recdef_1(A,B) = k5_numbers ) ) => ( k2_wsierp_1(A) = k3_finseq_1(A) <=> A = k5_finseq_2(k4_ordinal1,k3_finseq_1(A),1) ) ) ) )).
fof(t1_urysohn1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,k1_urysohn1(A)) => ( r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(B,1) ) ) ) ) )).
fof(t1_urysohn2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( v1_xreal_0(B) => ( B != k5_numbers => k1_integra2(k1_integra2(A,B),k5_xcmplx_0(B)) = A ) ) ) )).
fof(t1_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( 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))) ) ) ) ) )).
fof(t1_valued_0,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ( v1_relat_1(B) & v1_valued_0(B) ) => ( r1_tarski(A,B) => v1_valued_0(A) ) ) ) )).
fof(t1_valued_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_membered(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_membered(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [F] : ( 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)) ) ) ) ) ) )).
fof(t1_valued_2,axiom,( ! [A] : m1_subset_1(k3_valued_2(A),k1_zfmisc_1(k2_valued_2(A))) )).
fof(t1_vectsp10,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( 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) ) ) ) ) ) )).
fof(t1_vectsp11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ! [E] : ( ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(C))) ) => ! [F] : ( m2_finseq_2(F,k4_ordinal1,k4_finseq_2(B,k4_ordinal1)) => ! [G] : ( m2_finseq_2(G,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ( r1_tarski(k2_zfmisc_1(k10_xtuple_0(F),k10_xtuple_0(G)),k2_matrix_0(D)) => k1_matrix13(u1_struct_0(C),k3_matrix_3(C,D,E),B,A,F,G) = k5_matrlin2(B,A,C,k1_matrix13(u1_struct_0(C),D,B,A,F,G),k1_matrix13(u1_struct_0(C),E,B,A,F,G)) ) ) ) ) ) ) ) ) )).
fof(t1_vectsp_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t1_vectsp_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) ) )).
fof(t1_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t1_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( r1_struct_0(k1_vectsp_5(A,B,C,D),E) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & ? [G] : ( 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) ) ) ) ) ) ) ) )).
fof(t1_vectsp_6,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m1_vectsp_6(D,B,C) => ( r2_hidden(A,k1_vectsp_6(B,C,D)) <=> ? [E] : ( 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) ) ) ) ) ) )).
fof(t1_vectsp_7,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t1_vectsp_8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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)) ) ) ) )).
fof(t1_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(B)) => ! [F] : ( ( 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),k4_ordinal1,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)) ) ) ) ) ) ) ) )).
fof(t1_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( 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(k5_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))))) ) ) ) ) )).
fof(t1_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( 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(k5_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))))) ) ) ) ) )).
fof(t1_waybel10,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t1_waybel11,axiom,( ! [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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t1_waybel12,axiom,( ! [A] : ! [B] : ( ( r1_ordinal1(k1_card_1(A),k1_card_1(B)) & v4_card_3(B) ) => v4_card_3(A) ) )).
fof(t1_waybel13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t1_waybel14,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ? [C] : ( 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] : ( 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)))) ) ) ) ) )).
fof(t1_waybel15,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( ( v4_yellow_0(C,B) & m1_yellow_0(C,B) ) => ( v4_yellow_0(C,A) & m1_yellow_0(C,A) ) ) ) ) )).
fof(t1_waybel16,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t1_waybel17,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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) ) ) ) ) ) )).
fof(t1_waybel18,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( 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) ) ) ) )).
fof(t1_waybel19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ? [B] : ( v2_pre_topc(B) & v1_waybel_9(B) & m1_yellow_9(B,A) & v1_waybel19(B) ) ) )).
fof(t1_waybel20,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k6_partfun1(A))) => k9_xtuple_0(B) = k10_xtuple_0(B) ) )).
fof(t1_waybel21,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_yellow_0(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( m1_waybel21(C,A,B) => k2_yellow_6(u1_struct_0(A),B,C,k4_yellow_0(A)) = k4_yellow_0(B) ) ) ) )).
fof(t1_waybel22,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,k1_yellow_1(k8_waybel_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_yellow_1(k8_waybel_0(A))))) ) => k1_yellow_0(k1_yellow_1(k8_waybel_0(A)),B) = k3_tarski(B) ) ) )).
fof(t1_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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))) ) ) )).
fof(t1_waybel24,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( 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)))) ) ) ) ) )).
fof(t1_waybel25,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k9_waybel18)) => ( A = k5_numbers => v4_pre_topc(k6_domain_1(u1_struct_0(k9_waybel18),A),k9_waybel18) ) ) )).
fof(t1_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( 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))))) ) ) ) ) )).
fof(t1_waybel28,axiom,( ! [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] : ( ( ~ 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)) ) ) )).
fof(t1_waybel29,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_yellow_0(D,k5_yellow_1(k2_zfmisc_1(A,B),C)) ) => ! [E] : ( ( ~ v2_struct_0(E) & m1_yellow_0(E,k5_yellow_1(A,k5_yellow_1(B,C))) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t1_waybel30,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => k3_xboole_0(A,k3_tarski(B)) = k3_tarski(a_2_0_waybel30(A,B)) ) )).
fof(t1_waybel31,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v3_waybel_3(A) & l1_orders_2(A) ) => ! [B] : ( ( v6_waybel23(B,A) & m1_waybel23(B,A) ) => r1_ordinal1(k1_waybel31(A),k1_card_1(B)) ) ) )).
fof(t1_waybel32,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) => v13_waybel_0(B,A) ) ) ) )).
fof(t1_waybel33,axiom,( ! [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] : ( ( 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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v2_waybel_0(E,k2_yellow_1(C)) & v13_waybel_0(E,k2_yellow_1(C)) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k2_yellow_1(C)))) ) => ! [F] : ( ( ~ v1_xboole_0(F) & v2_waybel_0(F,k2_yellow_1(D)) & v13_waybel_0(F,k2_yellow_1(D)) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k2_yellow_1(D)))) ) => ( E = F => k1_waybel33(A,C,E) = k1_waybel33(B,D,F) ) ) ) ) ) ) ) ) )).
fof(t1_waybel34,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ 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] : ( m1_waybel_1(E,A,B) => ! [F] : ( m1_waybel_1(F,C,D) => ( ( E = F & v3_waybel_1(E,A,B) ) => v3_waybel_1(F,C,D) ) ) ) ) ) ) ) ) )).
fof(t1_waybel35,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( v1_zfmisc_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => m1_waybel35(B,A,C) ) ) ) )).
fof(t1_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) ) <=> ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r2_hidden(D,B) & r2_lattice3(A,C,D) ) ) ) ) ) )).
fof(t1_waybel_1,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t1_waybel_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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)) ) ) ) )).
fof(t1_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_waybel_3(A,B,C) => r3_orders_2(A,B,C) ) ) ) ) )).
fof(t1_waybel_4,axiom,( ! [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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t1_waybel_5,axiom,( ! [A] : ( ( 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] : ( 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] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t1_waybel_6,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t1_waybel_7,axiom,( ! [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] : ! [C] : ( 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)) ) ) ) )).
fof(t1_waybel_8,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t1_waybel_9,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & l1_orders_2(D) ) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t1_weddwitt,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ( k1_newton(B,A) = 1 => ( r1_xxreal_0(B,1) | A = k5_numbers ) ) ) ) )).
fof(t1_weierstr,axiom,( ! [A] : ( ( v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( v1_xreal_0(G) & r1_tarski(k4_subset_1(u1_struct_0(A),k8_metric_1(A,B,D),k8_metric_1(A,C,E)),k8_metric_1(A,F,G)) ) ) ) ) ) ) ) )).
fof(t1_wellfnd1,axiom,( ! [A] : ( v4_funct_1(A) => ( ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t1_wellord1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r2_hidden(B,k1_wellord1(C,A)) <=> ( B != A & r2_hidden(k4_tarski(B,A),C) ) ) ) )).
fof(t1_wellord2,axiom,( ! [A] : ! [B] : ( r1_tarski(B,A) => k2_wellord1(k1_wellord2(A),B) = k1_wellord2(B) ) )).
fof(t1_wellset1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r2_hidden(B,k1_relat_1(A)) <=> ~ ! [C] : ( ~ r2_hidden(k4_tarski(B,C),A) & ~ r2_hidden(k4_tarski(C,B),A) ) ) ) )).
fof(t1_wsierp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_newton(A,2) = k3_xcmplx_0(A,A) & k1_newton(k4_xcmplx_0(A),2) = k1_newton(A,2) ) ) )).
fof(t1_xboole_0,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(C,k5_xboole_0(A,B)) <=> ~ ( r2_hidden(C,A) <=> r2_hidden(C,B) ) ) )).
fof(t1_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r1_tarski(A,B) & r1_tarski(B,C) ) => r1_tarski(A,C) ) )).
fof(t1_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => k4_xboolean(A,A) = A ) )).
fof(t1_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k2_xcmplx_0(A,k2_xcmplx_0(B,C)) = k2_xcmplx_0(k2_xcmplx_0(A,B),C) ) ) ) )).
fof(t1_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(B,A) ) ) )).
fof(t1_xregular,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( r2_hidden(B,A) & r1_xboole_0(B,A) ) ) )).
fof(t1_xtuple_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( k4_tarski(A,B) = k4_tarski(C,D) => ( A = C & B = D ) ) )).
fof(t1_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(B,A) ) => A = B ) ) ) )).
fof(t1_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(C,k1_xxreal_1(A,B)) <=> ( r1_xxreal_0(A,C) & r1_xxreal_0(C,B) ) ) ) ) ) )).
fof(t1_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( m1_xxreal_2(B,k1_tarski(A)) <=> r1_xxreal_0(A,B) ) ) ) )).
fof(t1_xxreal_3,axiom,( ! [A] : ( ( v1_xxreal_0(A) & v2_xxreal_0(A) & ~ v1_xreal_0(A) ) => A = k1_xxreal_0 ) )).
fof(t1_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ( v2_yellow_0(k3_yellow_3(A,B)) => ( v2_yellow_0(A) & v2_yellow_0(B) ) ) ) ) )).
fof(t1_yellow11,axiom,( 3 = k8_domain_1(k4_ordinal1,k5_numbers,1,2) )).
fof(t1_yellow12,axiom,( ! [A] : ! [B] : r1_relset_1(B,B,k7_relset_1(B,k2_zfmisc_1(B,B),k12_funct_3(B),A),k2_zfmisc_1(A,A)) )).
fof(t1_yellow14,axiom,( k9_setfam_1(k1_tarski(k5_numbers)) = k2_tarski(k5_numbers,1) )).
fof(t1_yellow15,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k9_setfam_1(A)) => ! [C] : ( m2_finseq_1(C,k6_margrel1) => k4_finseq_1(k1_yellow15(A,B,C)) = k4_finseq_1(B) ) ) )).
fof(t1_yellow16,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_yellow_0(C,B) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t1_yellow17,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ( 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) ) ) ) )).
fof(t1_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ( ( ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k3_functor0(A,B,C,E) = k3_functor0(A,B,D,E) ) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( k1_altcat_1(A,E,F) != k1_xboole_0 => ! [G] : ( 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)) ) ) ) ) ) )).
fof(t1_yellow19,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_subset_1(B,u1_struct_0(k2_yellow_1(A))) & v2_waybel_0(B,k2_yellow_1(A)) & v13_waybel_0(B,k2_yellow_1(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(A)))) ) => ! [C] : ~ ( r2_hidden(C,B) & v1_xboole_0(C) ) ) ) )).
fof(t1_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t1_yellow21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & v1_yellow21(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_yellow18(A,B) = u1_struct_0(k1_yellow21(B)) ) ) )).
fof(t1_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t1_yellow_1,axiom,( ! [A] : ( u1_struct_0(k1_yellow_1(A)) = A & u1_orders_2(k1_yellow_1(A)) = k2_orders_1(A) ) )).
fof(t1_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(C,k5_waybel_0(A,B)) <=> r2_lattice3(A,C,B) ) ) ) ) )).
fof(t1_yellow_3,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t1_yellow_4,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ! [C] : ( 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)) ) ) ) )).
fof(t1_yellow_5,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k13_lattice3(A,B,B) = B ) ) )).
fof(t1_yellow_6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t1_yellow_7,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_lattice3(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t1_yellow_8,axiom,( ! [A] : ! [B] : ! [C] : ( ( r2_hidden(B,k5_finsub_1(A)) & r1_tarski(C,B) ) => r2_hidden(C,k5_finsub_1(A)) ) )).
fof(t1_yellow_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t1_yoneda_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( m1_subset_1(D,u4_struct_0(k1_yoneda_1(A))) => ! [E] : ( 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(k7_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(k7_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(k7_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) ) ) ) ) ) ) )).
fof(t1_zf_colla,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v3_ordinal1(B) => k1_zf_colla(A,B) = a_2_1_zf_colla(A,B) ) ) )).
fof(t1_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ! [D] : ( 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) ) ) ) ) )).
fof(t1_zf_fund2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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(k5_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)) ) ) ) ) )).
fof(t1_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ( k4_zf_lang(A,B) = k4_zf_lang(C,D) => ( A = C & B = D ) ) ) ) ) ) )).
fof(t1_zf_lang1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ( k18_zf_lang(k4_zf_lang(A,B)) = A & k19_zf_lang(k4_zf_lang(A,B)) = B ) ) ) )).
fof(t1_zf_model,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ( 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))) ) ) ) )).
fof(t1_zf_refle,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => r2_zf_model(A,k7_zf_model) ) )).
fof(t1_zfmisc_1,axiom,( k1_zfmisc_1(k1_xboole_0) = k1_tarski(k1_xboole_0) )).
fof(t1_zfmodel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_ordinal1(A) => r2_zf_model(A,k6_zf_model) ) ) )).
fof(t1_zfmodel2,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => 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))) ) ) ) )).
fof(t1_zfrefle1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => r1_zfrefle1(A,k1_subset_1(k9_zf_lang)) ) )).
fof(t1_zmodul01,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ( ( A = k5_numbers | C = k4_struct_0(B) ) => k1_zmodul01(B,C,A) = k4_struct_0(B) ) ) ) ) )).
fof(t1_zmodul02,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ 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] : ( m1_zmodul01(C,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(k10_zmodul02(B,C))) => ( C = k5_zmodul02(B,A) => k1_zmodul01(k10_zmodul02(B,C),D,A) = k4_struct_0(k10_zmodul02(B,C)) ) ) ) ) ) )).
fof(t1_zmodul03,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_zmodul02(C,A) & k3_funct_2(u1_struct_0(A),k4_numbers,C,B) = 1 & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( D != B => k3_funct_2(u1_struct_0(A),k4_numbers,C,D) = k5_numbers ) ) ) ) ) )).
fof(t200_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ( C != k5_numbers => k23_member_1(k5_xboole_0(A,B),C) = k5_xboole_0(k23_member_1(A,C),k23_member_1(B,C)) ) ) ) ) )).
fof(t200_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( k7_xcmplx_0(A,B) = k7_xcmplx_0(D,C) => ( B = k5_numbers | C = k5_numbers | B = k4_xcmplx_0(C) | k7_xcmplx_0(A,B) = k7_xcmplx_0(k2_xcmplx_0(A,D),k2_xcmplx_0(B,C)) ) ) ) ) ) ) )).
fof(t200_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(k4_xcmplx_0(A),B) & r1_xxreal_0(k7_xcmplx_0(A,B),k4_xcmplx_0(1)) ) ) ) )).
fof(t200_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(D,B) ) => k6_subset_1(k1_xxreal_1(A,B),k2_xboole_0(k1_xxreal_1(A,C),k1_xxreal_1(D,B))) = k4_xxreal_1(C,D) ) ) ) ) ) )).
fof(t201_member_1,axiom,( ! [A] : ( v1_membered(A) => r1_tarski(k23_member_1(A,k5_numbers),k1_tarski(k5_numbers)) ) )).
fof(t201_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k5_xcmplx_0(A) = k5_xcmplx_0(B) => A = B ) ) ) )).
fof(t201_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,k4_xcmplx_0(B)) => ( r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(k7_xcmplx_0(A,B),k4_xcmplx_0(1)) ) ) ) ) )).
fof(t201_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t202_member_1,axiom,( ! [A] : ( v1_membered(A) => ( A != k1_xboole_0 => k23_member_1(A,k5_numbers) = k1_tarski(k5_numbers) ) ) )).
fof(t202_xcmplx_1,axiom,( k5_xcmplx_0(k5_numbers) = k5_numbers )).
fof(t202_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(B,k4_xcmplx_0(A)) => ( r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(k7_xcmplx_0(A,B),k4_xcmplx_0(1)) ) ) ) ) )).
fof(t202_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t203_member_1,axiom,( ! [A] : ( v1_membered(A) => k23_member_1(A,1) = A ) )).
fof(t203_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( B != k5_numbers => A = k3_xcmplx_0(k3_xcmplx_0(A,B),k5_xcmplx_0(B)) ) ) ) )).
fof(t203_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k4_xcmplx_0(B),A) => ( r1_xxreal_0(k5_numbers,B) | r1_xxreal_0(k7_xcmplx_0(A,B),k4_xcmplx_0(1)) ) ) ) ) )).
fof(t203_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t204_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k23_member_1(A,k3_xcmplx_0(B,C)) = k23_member_1(k23_member_1(A,C),B) ) ) ) )).
fof(t204_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) = k5_xcmplx_0(k3_xcmplx_0(A,B)) ) ) )).
fof(t204_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k4_xcmplx_0(A),B) => ( r1_xxreal_0(k5_numbers,B) | r1_xxreal_0(k7_xcmplx_0(A,B),k4_xcmplx_0(1)) ) ) ) ) )).
fof(t204_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t205_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => k23_member_1(k13_member_1(A,B),C) = k13_member_1(k23_member_1(A,C),B) ) ) ) )).
fof(t205_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k5_xcmplx_0(k3_xcmplx_0(A,k5_xcmplx_0(B))) = k3_xcmplx_0(k5_xcmplx_0(A),B) ) ) )).
fof(t205_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(k4_xcmplx_0(B),A) & r1_xxreal_0(k4_xcmplx_0(1),k7_xcmplx_0(A,B)) ) ) ) )).
fof(t205_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ~ r2_hidden(B,k2_xboole_0(k4_xxreal_1(A,B),k4_xxreal_1(B,C))) ) ) ) )).
fof(t206_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => r1_tarski(k23_member_1(A,k2_xcmplx_0(B,C)),k9_member_1(k23_member_1(A,B),k23_member_1(A,C))) ) ) ) )).
fof(t206_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k5_xcmplx_0(k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B))) = k3_xcmplx_0(A,B) ) ) )).
fof(t206_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(k4_xcmplx_0(A),B) & r1_xxreal_0(k4_xcmplx_0(1),k7_xcmplx_0(A,B)) ) ) ) )).
fof(t206_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ~ r2_hidden(B,k2_xboole_0(k2_xxreal_1(A,B),k4_xxreal_1(B,C))) ) ) ) )).
fof(t207_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => r1_tarski(k23_member_1(A,k6_xcmplx_0(B,C)),k11_member_1(k23_member_1(A,B),k23_member_1(A,C))) ) ) ) )).
fof(t207_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( A != k5_numbers & B != k5_numbers & k3_xcmplx_0(A,k5_xcmplx_0(B)) = k5_numbers ) ) ) )).
fof(t207_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(A,k4_xcmplx_0(B)) & r1_xxreal_0(k4_xcmplx_0(1),k7_xcmplx_0(A,B)) ) ) ) )).
fof(t207_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ~ r2_hidden(B,k2_xboole_0(k4_xxreal_1(A,B),k3_xxreal_1(B,C))) ) ) ) )).
fof(t208_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t208_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( A != k5_numbers & B != k5_numbers & k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) = k5_numbers ) ) ) )).
fof(t208_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(B,k4_xcmplx_0(A)) & r1_xxreal_0(k4_xcmplx_0(1),k7_xcmplx_0(A,B)) ) ) ) )).
fof(t208_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ~ r2_hidden(B,k2_xboole_0(k2_xxreal_1(A,B),k3_xxreal_1(B,C))) ) ) ) )).
fof(t209_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t209_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k3_xcmplx_0(A,k5_xcmplx_0(B)) = 1 => A = B ) ) ) )).
fof(t209_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(1,C) & ~ r1_xxreal_0(B,k7_xcmplx_0(A,C)) ) ) => r1_xxreal_0(B,A) ) ) ) )).
fof(t209_xxreal_1,axiom,( k1_xxreal_1(k2_xxreal_0,k1_xxreal_0) = k6_numbers )).
fof(t20_abcmiz_0,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t20_abcmiz_1,axiom,( ! [A] : ( v1_finset_1(k6_classes1(A)) => v1_finset_1(A) ) )).
fof(t20_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & v1_abcmiz_a(A) & l1_msualg_1(A) ) => ! [B] : ( 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] : ( 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)) ) ) ) ) ) )).
fof(t20_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ( A != k5_numbers => k3_xcmplx_0(k2_absvalue(A),k2_absvalue(k7_xcmplx_0(1,A))) = 1 ) ) )).
fof(t20_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_aff_1(A,B,C,D) <=> ? [E] : ( 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) ) ) ) ) ) ) )).
fof(t20_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t20_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( 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] : ( v7_ordinal1(D) => ~ ( r2_hidden(D,k2_afinsq_1(C)) & A = k2_xcmplx_0(k1_afinsq_1(B),D) ) ) ) ) ) ) )).
fof(t20_afinsq_2,axiom,( ! [A] : ( ( v1_finset_1(A) & v6_membered(A) ) => k1_afinsq_1(k4_afinsq_2(A)) = k5_card_1(A) ) )).
fof(t20_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k13_afproj(A))) <=> ~ ( ~ m1_subset_1(B,u1_struct_0(A)) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( B = k5_afproj(A,C) & v1_aff_1(C,A) ) ) ) ) ) )).
fof(t20_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t20_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(t20_algspec1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(t20_algstr_4,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(2,B) & ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ~ ( k3_finseq_1(C) = k6_xcmplx_0(B,1) & ! [D] : ( 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)) ) ) ) ) )).
fof(t20_altcat_2,axiom,( ! [A] : ( l2_altcat_1(A) => m1_altcat_2(A,A) ) )).
fof(t20_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t20_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ~ v2_extpro_1(k6_ami_3(A,B),k7_card_1(2),k1_ami_3) ) ) )).
fof(t20_ami_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( ~ 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(k7_card_1(2),k1_ami_3)) & v1_finset_1(B) & v4_extpro_1(B,k7_card_1(2),k1_ami_3,A) ) => ! [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(C,u1_struct_0(k1_ami_3)) ) => ! [D] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ( ( r1_tarski(B,C) & r1_tarski(B,D) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_ami_3)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_ami_3)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( ( r1_tarski(A,E) & r1_tarski(A,F) ) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v1_ami_2(H) & m1_subset_1(H,u1_struct_0(k1_ami_3)) ) => ! [I] : ( ( v1_ami_2(I) & m1_subset_1(I,u1_struct_0(k1_ami_3)) ) => ! [J] : ( m1_subset_1(J,u1_compos_1(k1_ami_3)) => ( ( J = k3_extpro_1(k7_card_1(2),k1_ami_3,E,k5_extpro_1(k7_card_1(2),k1_ami_3,E,C,G)) & J = k6_ami_3(H,I) & r2_hidden(H,k9_xtuple_0(B)) ) => ( H = I | k4_int_1(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,E,C,G),H),k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,E,C,G),I)) = k4_int_1(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,F,D,G),H),k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,F,D,G),I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t20_ami_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( v7_ordinal1(B) => k2_amistd_1(k7_card_1(2),k1_ami_3,k9_ami_3(B,A)) = k1_tarski(B) ) ) )).
fof(t20_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k3_amistd_1(A,k4_amistd_1(A),B) = k7_domain_1(k4_ordinal1,B,k5_ami_wstd(A,k4_amistd_1(A),B)) ) ) )).
fof(t20_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(k4_amistd_1(A))) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t20_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_analmetr(k2_analmetr(A,B,C)) = k2_diraf(k2_analoaf(A)) ) ) ) )).
fof(t20_analoaf,axiom,( ! [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) ) => ~ ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( k3_rlvect_1(A,k1_rlvect_1(A,B,D),k1_rlvect_1(A,C,E)) = k4_struct_0(A) => ( D = k5_numbers & E = k5_numbers ) ) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( ~ r1_analoaf(A,B,C,D,E) & ~ r1_analoaf(A,B,C,E,D) ) ) ) ) ) ) ) )).
fof(t20_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => r1_analort(A,E,F,B,B,C,D) ) ) ) ) ) ) )).
fof(t20_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t20_anproj_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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] : ( m2_funct_2(F,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [G] : ( m2_funct_2(G,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [H] : ( m2_funct_2(H,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [I] : ( m2_funct_2(I,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ? [J] : ( m2_funct_2(J,A,k1_numbers,k9_funct_2(A,k1_numbers)) & ! [K] : ( v1_xreal_0(K) => ! [L] : ( v1_xreal_0(L) => ! [M] : ( v1_xreal_0(M) => ! [N] : ( v1_xreal_0(N) => J != k1_binop_1(k5_funcsdom(A),k1_binop_1(k5_funcsdom(A),k1_binop_1(k5_funcsdom(A),k1_funct_1(k7_funcsdom(A),k4_tarski(K,F)),k1_funct_1(k7_funcsdom(A),k4_tarski(L,G))),k1_funct_1(k7_funcsdom(A),k4_tarski(M,H))),k1_funct_1(k7_funcsdom(A),k4_tarski(N,I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t20_aofa_000,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( r2_hidden(D,k9_aofa_000(A,B,k1_nat_1(C,1))) <=> ~ ( ~ r2_hidden(D,k9_aofa_000(A,B,C)) & ! [E] : ( m2_subset_1(E,k4_ordinal1,k4_finseq_1(u1_unialg_1(A))) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t20_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) & v1_finseq_1(G) ) => ( G = k5_aofa_a00(A,B,C,D,E,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 ) ) ) )).
fof(t20_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v19_aofa_a00(B,A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( C = k10_subset_1(k1_funct_1(u7_aofa_a00(A),10),u4_struct_0(A)) => ( k1_msualg_1(A,C) = k2_finseq_4(u1_struct_0(A),B,B) & k2_msualg_1(A,C) = u8_aofa_a00(A) ) ) ) ) ) )).
fof(t20_aofa_i00,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_card_3(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(A,k4_numbers))) => ! [C] : ( ( 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] : ( m6_aofa_i00(D,A,B,C) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t20_armstrng,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => v1_finset_1(B) ) ) )).
fof(t20_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ( B != k5_numbers => k2_arytm_0(k2_arytm_0(A,B),k4_arytm_0(B)) = A ) ) ) )).
fof(t20_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( r1_arytm_2(C,B) => k7_arytm_2(A,k1_arytm_1(B,C)) = k2_arytm_1(k7_arytm_2(A,B),C) ) ) ) ) )).
fof(t20_arytm_2,axiom,( r2_hidden(k11_arytm_3,k2_arytm_2) & r2_hidden(k12_arytm_3,k2_arytm_2) )).
fof(t20_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ( r1_arytm_3(A,B) <=> k3_arytm_3(A,B) = 1 ) ) ) )).
fof(t20_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_hidden(A,k7_asympt_0(A)) ) )).
fof(t20_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(A,k8_asympt_0(B)) <=> k8_asympt_0(A) = k8_asympt_0(B) ) ) ) )).
fof(t20_autalg_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r1_pzfmisc1(A,B,C) => ! [D] : ( m2_pboole(D,A,B,C) => r2_hidden(D,k4_autalg_1(A,B,C)) ) ) ) ) )).
fof(t20_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_funct_2(B,u1_struct_0(A),u1_struct_0(A),k4_autgroup(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_autgroup(A))) => ( B = C => k2_funct_1(B) = k2_group_1(k5_autgroup(A),C) ) ) ) ) )).
fof(t20_bcialg_1,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k4_bcialg_1(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k4_bcialg_1(A)) => r2_hidden(k1_bcialg_1(A,B,C),k4_bcialg_1(A)) ) ) ) )).
fof(t20_bcialg_3,axiom,( ! [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) ) => ( v4_bcialg_3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t20_bcialg_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => k6_bcialg_4(B,C,k1_nat_1(A,1)) = k1_bcialg_4(B,k6_bcialg_4(B,C,A),C) ) ) ) )).
fof(t20_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( v8_bcialg_1(E) & m1_bcialg_5(E,A,B,C,D) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(E)) => ! [G] : ( m1_subset_1(G,u1_struct_0(E)) => k1_bcialg_2(E,F,G,k1_nat_1(B,1)) = k1_bcialg_2(E,F,G,k1_nat_1(C,1)) ) ) ) ) ) ) ) )).
fof(t20_bcialg_6,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k5_bcialg_1(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t20_bciideal,axiom,( ! [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) ) => m2_bciideal(k4_bcialg_1(A),A) ) )).
fof(t20_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_bhsp_1(A,B,C) => r1_bhsp_1(A,B,k4_algstr_0(A,C)) ) ) ) ) )).
fof(t20_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_bhsp_2(B,A) => v2_comseq_2(k2_bhsp_2(A,B)) ) ) ) )).
fof(t20_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( v7_ordinal1(D) => ( r1_bhsp_3(A,B,C) => r1_bhsp_3(A,k1_valued_0(u1_struct_0(A),B,D),k1_valued_0(u1_struct_0(A),C,D)) ) ) ) ) ) )).
fof(t20_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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,k5_numbers)) ) ) )).
fof(t20_bilinear,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t20_binari_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t20_binari_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v1_int_1(B) => k5_int_1(k3_xcmplx_0(B,A),A) = k5_numbers ) ) )).
fof(t20_binarith,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k6_binarith(k2_xcmplx_0(A,1),k9_binarith(A,1,k6_margrel1,B,k10_binarith(k6_margrel1,C))) = k1_nat_1(k6_binarith(A,B),k15_funcop_1(k4_ordinal1,C,k7_margrel1,k5_numbers,k5_series_1(2,A))) ) ) ) )).
fof(t20_binom,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k6_algstr_0(A,C,k5_binom(A,B,D)) = k6_binom(A,k6_algstr_0(A,C,B),D) ) ) ) ) )).
fof(t20_binop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C))) ) => ! [E] : ( ( 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] : ! [G] : ( 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) ) ) ) )).
fof(t20_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => k4_finseq_1(k2_bintree2(A,B)) = k2_finseq_1(k5_series_1(2,B)) ) ) )).
fof(t20_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t20_bor_cant,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [E] : ( v7_ordinal1(E) => k3_funct_2(B,k1_numbers,C,k1_prob_2(A,B,k9_bor_cant(A,k2_prob_1(A,D)),E)) = k6_xcmplx_0(1,k3_funct_2(B,k1_numbers,C,k1_prob_2(A,B,k7_bor_cant(A,D),E))) ) ) ) ) ) )).
fof(t20_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( 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 ) ) ) ) )).
fof(t20_borsuk_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v1_compts_1(B) & l1_pre_topc(B) ) => ! [C] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t20_borsuk_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_topmetr))) => ( C = k1_rcomp_1(A,B) => v4_pre_topc(C,k5_topmetr) ) ) ) ) )).
fof(t20_borsuk_5,axiom,( ! [A] : ( v1_rat_1(A) => ! [B] : ( ( v1_xreal_0(B) & ~ v1_rat_1(B) ) => ~ v1_rat_1(k6_xcmplx_0(B,A)) ) ) )).
fof(t20_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : k9_xtuple_0(k1_borsuk_7(A,B,C,D,E,F)) = k1_enumset1(A,B,C) )).
fof(t20_bspace,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k2_bspace)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_bspace)) => ! [D] : ( 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) ) ) ) )).
fof(t20_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(t20_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t20_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t20_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t20_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t20_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t20_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(E,A) => ( r3_bvfunc_2(A,D,B,E) => r2_funct_2(A,k6_margrel1,k6_bvfunc_2(A,k9_bvfunc_1(A,D,C),B,E),k9_bvfunc_1(A,D,k6_bvfunc_2(A,C,B,E))) ) ) ) ) ) ) )).
fof(t20_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t20_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ( r3_bvfunc_2(A,B,C,D) => r1_bvfunc_1(A,B,k6_bvfunc_2(A,B,C,D)) ) ) ) ) ) )).
fof(t20_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t20_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t20_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t20_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) )).
fof(t20_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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,D),k9_bvfunc_1(A,C,D)),k9_bvfunc_1(A,k5_bvfunc_1(A,B,C),D)) ) ) ) ) )).
fof(t20_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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_comseq_2(k2_partfun1(A,k1_numbers,B,A)) => k1_funct_1(k10_c0sp1(A),B) = k2_seq_4(k9_c0sp1(A,B)) ) ) ) )).
fof(t20_c0sp2,axiom,( ! [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) & v3_lopban_1(A) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) ) )).
fof(t20_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => ( ( r2_relset_1(k4_ordinal1,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))) ) ) ) ) )).
fof(t20_calcul_2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t20_card_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r2_hidden(A,B) <=> r2_hidden(k3_card_1(A),k3_card_1(B)) ) ) ) )).
fof(t20_card_2,axiom,( ! [A] : ( v1_card_1(A) => k2_card_2(A,1) = A ) )).
fof(t20_card_4,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ! [C] : ( v1_card_1(C) => ! [D] : ( v1_card_1(D) => ( ( r2_hidden(B,A) & r2_hidden(C,D) ) => ( r2_hidden(k2_card_2(B,C),k2_card_2(A,D)) & r2_hidden(k2_card_2(C,B),k2_card_2(A,D)) ) ) ) ) ) ) )).
fof(t20_card_5,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( ( ~ v1_finset_1(B) & v1_card_1(B) ) => r1_ordinal1(A,k3_card_2(A,B)) ) ) )).
fof(t20_card_fil,axiom,( ! [A] : ( ~ v1_finset_1(A) => ! [B] : ( m1_card_fil(B,A) => ( r1_tarski(k4_card_fil(A),B) => v1_card_fil(B,A) ) ) ) )).
fof(t20_card_fin,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ~ v1_xboole_0(k2_card_fin(B,C,A)) => ! [D] : ! [E] : ~ ( 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)) ) ) ) ) )).
fof(t20_card_lar,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_card_lar(B,A) => r1_ordinal1(k1_card_5(A),k1_card_1(B)) ) ) ) )).
fof(t20_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t20_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k6_cat_2(A,B))) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & C = k7_cat_2(A,B,D,E) ) ) ) ) ) )).
fof(t20_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(B)) => ! [D] : ( ( 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))) ) ) ) )).
fof(t20_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t20_cat_5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_cat_5(A) ) => ? [B] : ( ~ 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 ) ) )).
fof(t20_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v5_ordinal1(C) & v1_finset_1(C) ) => ( r2_hidden(C,k2_catalan2(B,A)) <=> ( v1_catalan2(C) & k1_relset_1(k4_ordinal1,C) = B & k7_afinsq_2(C) = A ) ) ) ) ) )).
fof(t20_catalg_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t20_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v2_algstr_0(B,A) & v2_algstr_0(C,A) ) => v2_algstr_0(k5_cayldick(A,B,C),k4_cayldick(A)) ) ) ) ) )).
fof(t20_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_cc0sp1(A))) => r1_xxreal_0(k5_numbers,k2_normsp_0(k7_cc0sp1(A),B)) ) ) )).
fof(t20_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => k1_cc0sp2(A,k5_numbers) = k4_struct_0(k5_cc0sp2(A)) ) )).
fof(t20_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v2_comseq_2(A) => ( ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & k9_nat_1(k2_numbers,B,D) != k9_nat_1(k2_numbers,A,D) ) ) | k3_comseq_2(A) = k3_comseq_2(B) ) ) ) ) )).
fof(t20_cfdiff_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k1_valued_0(k2_numbers,k36_valued_1(k4_ordinal1,k2_numbers,B),A),k36_valued_1(k4_ordinal1,k2_numbers,k1_valued_0(k2_numbers,B,A))) ) ) )).
fof(t20_cfuncdom,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_funct_2(D,C,k2_numbers,k9_funct_2(C,k2_numbers)) => ! [E] : ( m2_funct_2(E,C,k2_numbers,k9_funct_2(C,k2_numbers)) => ( ( C = k2_tarski(A,B) & ! [F] : ( r2_hidden(F,C) => ( ( F = A => k1_funct_1(D,F) = k6_complex1 ) & ( F != A => k1_funct_1(D,F) = k5_numbers ) ) ) & ! [F] : ( r2_hidden(F,C) => ( ( F = A => k1_funct_1(E,F) = k5_numbers ) & ( F != A => k1_funct_1(E,F) = k6_complex1 ) ) ) ) => ( A = B | ! [F] : ( m2_funct_2(F,C,k2_numbers,k9_funct_2(C,k2_numbers)) => ? [G] : ( v1_xcmplx_0(G) & ? [H] : ( v1_xcmplx_0(H) & F = k1_binop_1(k1_cfuncdom(C),k1_funct_1(k3_cfuncdom(C),k4_tarski(G,D)),k1_funct_1(k3_cfuncdom(C),k4_tarski(H,E))) ) ) ) ) ) ) ) ) )).
fof(t20_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( 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,D,B),k19_valued_1(A,k2_numbers,k2_numbers,D,C)),k19_valued_1(A,k2_numbers,k2_numbers,D,k46_valued_1(A,k2_numbers,k2_numbers,B,C))) ) ) ) ) )).
fof(t20_cgames_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(t20_chain_1,axiom,( ! [A] : ( ( ~ v1_zfmisc_1(A) & v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( m2_chain_1(k4_tarski(B,C),A) & m2_chain_1(k4_tarski(D,E),A) ) => ( r1_xxreal_0(B,C) | r1_xxreal_0(D,E) | ( B = D & C = E ) ) ) ) ) ) ) ) )).
fof(t20_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v4_glib_001(B,A) <=> k3_finseq_1(B) = k1_nat_1(k2_nat_1(2,k5_card_1(k14_glib_001(A,B))),1) ) ) ) )).
fof(t20_circcmb2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ( ( ! [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] : ( m1_subset_1(I,k4_card_3(u3_msualg_1(B,E))) => v1_circuit2(k5_facirc_1(B,E,I,H),B,E) ) ) => ! [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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t20_circcmb3,axiom,( ! [A] : ( ( v4_circcmb3(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msafree2(B,A) & v5_circcmb3(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(t20_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_msualg_1(C) ) => ! [D] : ( ( v4_msualg_1(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t20_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( m3_msaterm(D,A,C) => ! [E] : ( m1_subset_1(E,k4_card_3(u3_msualg_1(k1_circtrm1(A,C,D),k6_circtrm1(A,C,D,B)))) => ! [F] : ( m1_circtrm1(F,A,C,D,B,E) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => m1_circtrm1(F,A,C,D,B,k5_facirc_1(k1_circtrm1(A,C,D),k6_circtrm1(A,C,D,B),E,G)) ) ) ) ) ) ) ) )).
fof(t20_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_pdiff_7(C,A) & m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_ckspace1(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_ckspace1(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_ckspace1(A,B,C))) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ( ( G = D & H = E & I = F ) => ( F = k3_rlvect_1(k2_ckspace1(A,B,C),D,E) <=> ! [J] : ( m2_subset_1(J,k1_euclid(A),C) => k1_funct_1(I,J) = k2_xcmplx_0(k1_funct_1(G,J),k1_funct_1(H,J)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t20_classes2,axiom,( ! [A] : ( v2_classes1(A) => ( A = k1_xboole_0 | ( k1_card_1(A) != k5_numbers & k1_card_1(A) != k1_xboole_0 & v4_ordinal1(k1_card_1(A)) ) ) ) )).
fof(t20_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t20_clopban2,axiom,( ! [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) & 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)) ) ) )).
fof(t20_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_clopban3(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t20_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_normsp_1(A,k1_clopban4(A,C),k5_numbers) = k5_struct_0(A) & k1_normsp_1(A,k2_clopban4(k5_numbers,A,C,B),k5_numbers) = k5_struct_0(A) ) ) ) ) )).
fof(t20_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m2_pboole(C,A,k5_mssubfam(A,B),k5_mssubfam(A,B)) => ! [D] : ( 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) ) ) ) ) )).
fof(t20_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ! [F] : ( 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)) ) ) ) ) ) )).
fof(t20_clvect_1,axiom,( ! [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) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t20_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clvect_2(B,A) => v2_comseq_2(k2_clvect_2(A,B)) ) ) ) )).
fof(t20_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k1_normsp_0(A,B,1) = k5_algstr_0(A,k2_clvect_3(A,B,1),k2_clvect_3(A,B,k5_numbers)) ) ) )).
fof(t20_coh_sp,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(t20_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v8_cohsp_1(A) ) => ( v1_classes1(k9_xtuple_0(A)) => ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => k1_funct_1(A,B) = k3_tarski(k7_relat_1(A,k5_finsub_1(B))) ) ) ) )).
fof(t20_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_collsp(D,A) => ! [E] : ( m2_collsp(E,A) => ( ( r2_hidden(B,D) & r2_hidden(C,D) & r2_hidden(B,E) & r2_hidden(C,E) ) => ( B = C | D = E ) ) ) ) ) ) ) )).
fof(t20_combgras,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( l1_combgras(B,A,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t20_compl_sp,axiom,( ! [A] : ( l1_pre_topc(A) => ( v1_compts_1(A) => v8_compl_sp(A) ) ) )).
fof(t20_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k3_complex1(k5_xcmplx_0(A)) = k7_xcmplx_0(k3_complex1(A),k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A)))) & k4_complex1(k5_xcmplx_0(A)) = k7_xcmplx_0(k1_real_1(k4_complex1(A)),k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A)))) ) ) )).
fof(t20_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k1_comptrig(A) = k28_sin_cos <=> ( ~ r1_xxreal_0(k5_numbers,k3_complex1(A)) & k4_complex1(A) = k5_numbers ) ) ) )).
fof(t20_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( 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))) ) ) ) )).
fof(t20_complsp2,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(A,k8_complex1(A)) = k3_xcmplx_0(2,k3_complex1(A)) ) )).
fof(t20_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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 ) ) )).
fof(t20_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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))) ) ) )).
fof(t20_comptrig,axiom,( v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k16_sin_cos,k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos)))) )).
fof(t20_compts_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_pre_topc(D,A) => ! [E] : ( m1_pre_topc(E,A) => ! [F] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) ) ) )).
fof(t20_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v2_margrel1(A) ) => r1_tarski(k1_relset_1(k3_finseq_2(k4_ordinal1),A),k4_finseq_2(k19_margrel1(A),k4_ordinal1)) ) )).
fof(t20_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,C)),k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B),C)) ) ) ) )).
fof(t20_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & v2_comseq_2(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => k3_comseq_2(k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)) = k3_xcmplx_0(k3_comseq_2(A),k3_comseq_2(B)) ) ) )).
fof(t20_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( v1_xcmplx_0(B) => ( r2_funct_2(k4_ordinal1,k1_numbers,k7_comseq_3(k25_valued_1(k4_ordinal1,k2_numbers,A,B)),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k26_valued_1(k4_ordinal1,k1_numbers,k7_comseq_3(A),k3_complex1(B)),k26_valued_1(k4_ordinal1,k1_numbers,k8_comseq_3(A),k4_complex1(B)))) & r2_funct_2(k4_ordinal1,k1_numbers,k8_comseq_3(k25_valued_1(k4_ordinal1,k2_numbers,A,B)),k1_series_1(k1_numbers,k26_valued_1(k4_ordinal1,k1_numbers,k8_comseq_3(A),k3_complex1(B)),k26_valued_1(k4_ordinal1,k1_numbers,k7_comseq_3(A),k4_complex1(B)))) ) ) ) )).
fof(t20_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u4_struct_0(A))) & ~ v4_conlat_1(g2_conlat_1(A,B,C),A) & v6_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 ) ) ) )).
fof(t20_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_conlat_1(A) & l1_conlat_1(A) ) => ! [B] : ( ( v3_conlat_1(B,A) & ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) & l2_conlat_1(B,A) ) => k8_conlat_2(k7_conlat_2(A),k8_conlat_2(A,B)) = B ) ) )).
fof(t20_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t20_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v10_pre_topc(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t20_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( B = u1_struct_0(A) => m1_connsp_3(B,A) ) ) ) )).
fof(t20_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( B = a_3_4_convex1(A,C,D) => v1_convex1(B,A) ) ) ) ) ) )).
fof(t20_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_convex4(C,A) => ! [D] : ( m1_convex4(D,A) => ( ( m2_convex4(C,A,B) & m2_convex4(D,A,B) ) => m2_convex4(k5_convex4(A,C,D),A,B) ) ) ) ) ) )).
fof(t20_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t20_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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) ) ) ) )).
fof(t20_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( 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 ) ) ) ) )).
fof(t20_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t20_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t20_csspace,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(t20_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k9_csspace4(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_csspace4(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_csspace4(A,B))) => ! [F] : ( ( 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] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t20_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(t20_descip_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,A) => ! [I] : ( m1_subset_1(I,A) => ? [J] : ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(t20_dickson,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v1_wellfnd1(k5_dickson(A)) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( B != k1_xboole_0 & ! [C] : ~ r2_hidden(C,k6_dickson(A,B)) ) ) ) ) )).
fof(t20_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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) = k5_numbers ) ) ) ) ) )).
fof(t20_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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,B,k2_xcmplx_0(B,A)) = k7_xcmplx_0(k1_funct_1(k3_diff_1(C,A),B),A) ) ) ) )).
fof(t20_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(k6_xcmplx_0(B,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))) ) => k1_funct_1(k4_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k1_fdiff_9),A),B) = k4_xcmplx_0(k3_xcmplx_0(4,k7_xcmplx_0(k3_xcmplx_0(k19_sin_cos(k6_xcmplx_0(k3_xcmplx_0(2,B),A)),k17_sin_cos(A)),k3_xcmplx_0(k17_sin_cos(k3_xcmplx_0(2,B)),k17_sin_cos(k3_xcmplx_0(2,k6_xcmplx_0(B,A))))))) ) ) ) )).
fof(t20_dilworth,axiom,( ! [A] : ( ( ~ 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 ) ) )).
fof(t20_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_diraf(A,B,C,D,D) & r2_diraf(A,D,D,B,C) ) ) ) ) ) )).
fof(t20_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( ( v1_dist_1(B,A) & r1_dist_1(A,B,C) ) => v1_dist_1(C,A) ) ) ) ) )).
fof(t20_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m2_finseq_2(B,A,k3_finseq_2(A)) => ! [C] : ( ( 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] : ( ( ~ v1_xboole_0(D) & v1_prob_1(D,k4_finseq_1(B)) & v4_prob_1(D,k4_finseq_1(B)) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(k4_finseq_1(B)))) ) => ( D = k9_setfam_1(k4_finseq_1(B)) => m1_prob_1(k10_relat_1(k1_partfun1(k4_ordinal1,A,A,k6_margrel1,B,C),k8_margrel1),k4_finseq_1(B),D) ) ) ) ) ) )).
fof(t20_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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))) ) ) ) ) )).
fof(t20_e_siec,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t20_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ( ( B = k5_numbers | C = k5_numbers ) <=> k8_group_1(k9_int_3(A),B,C) = k5_numbers ) ) ) ) )).
fof(t20_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ( B = k5_int_1(2,A) => k3_rlvect_1(k9_int_3(A),C,C) = k8_group_1(k9_int_3(A),B,C) ) ) ) ) )).
fof(t20_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t20_entropy1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => k8_matrix_0(k1_numbers,k10_matrixr1(A),B) = k2_matrprob(k1_funct_1(A,B)) ) ) ) )).
fof(t20_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k3_enumset1(A,B,C,D,E),k2_tarski(F,G)) )).
fof(t20_eqrel_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( r2_hidden(C,A) => r2_hidden(C,k6_eqrel_1(A,A,B,C)) ) ) )).
fof(t20_equation,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( m1_msualg_2(D,B,k14_pralg_2(A,B,C)) => ! [E] : ( m1_subset_1(E,u4_struct_0(B)) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t20_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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))) ) ) ) )).
fof(t20_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => k22_rvsum_1(B,k4_algstr_0(k15_euclid(A),C)) = k4_xcmplx_0(k22_rvsum_1(B,C)) ) ) ) )).
fof(t20_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => k22_rvsum_1(k7_euclid(A,B,C),D) = k2_xcmplx_0(k22_rvsum_1(B,D),k22_rvsum_1(C,D)) ) ) ) ) )).
fof(t20_euclid_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k5_euclid_5(k4_euclid_5(A,k5_numbers,k5_numbers),k4_euclid_5(B,k5_numbers,k5_numbers)) = k4_struct_0(k15_euclid(3)) ) ) )).
fof(t20_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) != k28_sin_cos & k4_euclid_3(B,C,A) != k28_sin_cos & k4_euclid_3(C,A,B) != k28_sin_cos ) ) ) ) ) )).
fof(t20_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k1_euclid(A)) => ! [C] : ( m2_finseq_1(C,k1_euclid(A)) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t20_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => k5_euclid_8(A,k1_euclid_8(k5_numbers,k5_numbers,k5_numbers)) = k1_euclid_8(k5_numbers,k5_numbers,k5_numbers) ) )).
fof(t20_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => ~ ( A != k5_numbers & r2_hidden(D,k4_euclid_9(A,C,B)) & r1_xxreal_0(B,k1_funct_1(k3_euclid(k8_rvsum_1(D,C)),k1_euclid_9(A,D,C))) ) ) ) ) ) )).
fof(t20_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(B)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(B)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t20_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( ( r1_analmetr(B,C,D) & A = k2_analmetr(B,C,D) ) => v5_conaffm(A) ) ) ) ) ) )).
fof(t20_euler_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_int_2(A) => k1_euler_1(A) = k6_xcmplx_0(A,1) ) ) )).
fof(t20_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k1_exchsort(A) = k2_ordinal2(k9_xtuple_0(A)) ) )).
fof(t20_extpro_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & ~ v1_setfam_1(C) ) => ( r1_xxreal_0(A,B) => ! [D] : ( ( ~ 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] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(D)) & v1_funct_1(E) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t20_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( ( v1_xreal_0(A) | v1_xreal_0(B) ) => r1_xxreal_0(k4_supinf_2(k3_extreal1(A),k3_extreal1(B)),k3_extreal1(k3_xxreal_3(A,B))) ) ) ) )).
fof(t20_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( 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))) ) ) ) ) )).
fof(t20_facirc_2,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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) ) )).
fof(t20_fcont_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ! [C] : ( ( 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)) ) ) ) )).
fof(t20_fcont_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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(B,A) & r1_tarski(k1_rcomp_1(B,A),k1_relset_1(k1_numbers,C)) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A))) ) => v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k2_partfun2(k1_numbers,k1_numbers,C),k1_rcomp_1(k3_seq_4(k7_relset_1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A))),k2_seq_4(k7_relset_1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A)))))) ) ) ) ) )).
fof(t20_fcont_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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)))) ) ) ) ) )).
fof(t20_fdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(k2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,C,A),B),D) = k3_xcmplx_0(A,k1_fdiff_1(C,D)) ) ) ) ) ) ) ) )).
fof(t20_fdiff_10,axiom,( ! [A] : ( ( 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,k22_sin_cos,k22_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k22_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k22_sin_cos),A),B) = k3_xcmplx_0(k1_funct_1(k22_sin_cos,k1_funct_1(k22_sin_cos,B)),k1_funct_1(k22_sin_cos,B)) ) ) ) ) ) )).
fof(t20_fdiff_11,axiom,( ! [A] : ( ( 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,k27_sin_cos))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k27_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k27_sin_cos),A),B) = k7_xcmplx_0(1,k3_xcmplx_0(k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k2_sin_cos9,B))),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t20_fdiff_2,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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)))) ) ) ) ) ) )).
fof(t20_fdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r3_fdiff_3(A,B) => ( k1_funct_1(A,B) = k5_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)) = k4_xcmplx_0(k7_xcmplx_0(k2_fdiff_3(B,A),k1_square_1(k1_funct_1(A,B)))) ) ) ) ) ) )).
fof(t20_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_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] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_1(k2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,C,D),B),E) = k3_xcmplx_0(3,k1_newton(E,2)) ) ) ) ) ) ) ) ) )).
fof(t20_fdiff_5,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k3_taylor_1),A),B) = k2_xcmplx_0(1,k1_funct_1(k3_taylor_1,B)) ) ) ) ) ) )).
fof(t20_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k22_sin_cos,B),k3_taylor_1))) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_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,k22_sin_cos,B),k3_taylor_1),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,B),k3_taylor_1),A),C) = k7_xcmplx_0(k1_funct_1(k22_sin_cos,C),k2_xcmplx_0(k1_funct_1(k22_sin_cos,C),1)) ) ) ) ) ) ) )).
fof(t20_fdiff_7,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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),k7_xcmplx_0(1,2)))) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => ( k1_funct_1(B,C) = k3_xcmplx_0(2,C) & ~ r1_xxreal_0(k1_funct_1(B,C),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_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),k7_xcmplx_0(1,2)),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_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),k7_xcmplx_0(1,2)),A),C) = k7_xcmplx_0(1,k3_square_1(k6_xcmplx_0(1,k1_square_1(k3_xcmplx_0(2,C))))) ) ) ) ) ) ) )).
fof(t20_fdiff_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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,k26_sin_cos,k1_taylor_1(A)))) & r1_xxreal_0(1,A) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_taylor_1(A)),B) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_taylor_1(A)),B),C) = k7_xcmplx_0(k3_xcmplx_0(A,k3_prepower(k1_funct_1(k16_sin_cos,C),k6_xcmplx_0(A,1))),k3_prepower(k1_funct_1(k18_sin_cos,C),k1_nat_1(A,1))) ) ) ) ) ) ) )).
fof(t20_fdiff_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fdiff_9,k1_taylor_1(A)),B),C) = k7_xcmplx_0(k3_xcmplx_0(A,k1_funct_1(k16_sin_cos,C)),k3_prepower(k1_funct_1(k18_sin_cos,C),k1_nat_1(A,1))) ) ) ) ) ) ) )).
fof(t20_ff_siec,axiom,( ! [A] : ( ( 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 ) ) )).
fof(t20_fib_num2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) ) => ? [B] : ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & r1_tarski(A,B) ) ) )).
fof(t20_fib_num3,axiom,( ! [A] : ( v7_ordinal1(A) => k1_fib_num3(k1_nat_1(A,1)) = k1_nat_1(k1_pre_ff(A),k1_pre_ff(k1_nat_1(A,2))) ) )).
fof(t20_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ( A != k5_numbers => k1_int_1(k7_xcmplx_0(k2_power(k1_fib_num,k3_xcmplx_0(2,A)),k3_square_1(5))) = k1_pre_ff(k3_xcmplx_0(2,A)) ) ) )).
fof(t20_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t20_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( 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] : ( ( ~ 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) ) ) ) ) ) )).
fof(t20_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t20_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)))) ) ) ) )).
fof(t20_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)))) ) ) ) ) )).
fof(t20_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( A != k1_xboole_0 <=> r1_xxreal_0(1,k3_finseq_1(A)) ) ) )).
fof(t20_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ~ ( k3_finseq_1(C) = k2_xcmplx_0(A,B) & ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t20_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( k2_finseq_1(A) = k1_tarski(B) => ( A = 1 & B = 1 ) ) ) )).
fof(t20_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_hidden(B,k10_xtuple_0(A)) => r2_hidden(k4_finseq_4(A,B),k4_finseq_1(A)) ) ) )).
fof(t20_finseq_5,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ( ~ v1_xboole_0(B) => k17_finseq_1(A,1,B) = k9_finseq_1(k7_partfun1(A,B,1)) ) ) )).
fof(t20_finseq_6,axiom,( ! [A] : ! [B] : ( A != B => k4_finseq_4(k10_finseq_1(A,B),B) = 2 ) )).
fof(t20_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k2_finseq_7(A,k2_finseq_7(A,B,C,D),D,C) = B ) ) ) ) )).
fof(t20_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r2_finseq_8(A,B,C,k5_numbers) => r2_finseq_8(A,B,C,1) ) ) ) ) )).
fof(t20_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( ( 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))) ) => ! [G] : ( ( v3_card_1(G,E) & m2_finseq_1(G,B) ) => r2_relset_1(k4_ordinal1,C,k1_finseqop(A,B,C,F,k5_finseq_2(A,E,D),G),k3_finseqop(A,B,C,F,D,G)) ) ) ) ) ) ) ) )).
fof(t20_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t20_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k9_fintopo2(A,C)) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(D,k6_fintopo2(A,B)) & r1_xboole_0(D,C) ) ) ) ) ) ) )).
fof(t20_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k5_fintopo3(A,B,1) = k8_fin_topo(A,B) ) ) )).
fof(t20_fintopo4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( ~ r1_xxreal_0(A,k5_numbers) => v3_orders_2(k4_fintopo4(A)) ) ) )).
fof(t20_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_xboole_0(k6_fin_topo(A,B),k7_fin_topo(A,B)) ) ) )).
fof(t20_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_catalan2(A))) => ! [D] : ( 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) ) ) ) ) )).
fof(t20_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(D,C) & r1_xxreal_0(C,E) ) => r1_tarski(k7_flang_1(A,B,C),k1_flang_2(A,B,D,E)) ) ) ) ) ) )).
fof(t20_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => k8_flang_1(A,k1_flang_3(A,B,C)) = k2_flang_2(A,k1_flang_3(A,B,C)) ) ) )).
fof(t20_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => A = a_1_1_fomodel0(A) ) )).
fof(t20_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( ( 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(k4_ordinal1,k35_fomodel1(B),C,k9_funct_2(k35_fomodel1(B),C),k7_fomodel2(B,C,D,E),k1_nat_1(A,1)),k9_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,k9_fomodel2(B,C,E),k9_nat_1(k9_setfam_1(k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0))),k39_fomodel1(B),A))) ) ) ) ) ) )).
fof(t20_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v1_orders_4(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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,k30_fomodel2(B)) & v13_fomodel2(C,A,B) ) => v17_fomodel4(C,A,B) ) ) ) )).
fof(t20_frechet,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t20_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ( v3_frechet(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k2_pre_topc(A,B) = k1_frechet2(A,B) ) ) ) )).
fof(t20_fscirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ 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))) ) ) ) )).
fof(t20_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( ~ v2_struct_0(D) & l2_fsm_2(D,A,B) ) => ~ ( v1_fsm_2(D,A) & r2_fsm_2(A,C,D) & ! [E] : ( m1_subset_1(E,B) => ~ r3_fsm_2(A,B,D,C,E) ) ) ) ) ) ) )).
fof(t20_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t20_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ( E != k4_tarski(k10_finseq_1(D,k24_gfacirc1(A,B,C)),k4_twoscomp) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t20_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : k1_funcop_1(k2_funcop_1(A,k4_tarski(C,B))) = k2_funcop_1(A,k4_tarski(B,C)) )).
fof(t20_funcsdom,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_funct_2(D,C,k1_numbers,k9_funct_2(C,k1_numbers)) => ! [E] : ( m2_funct_2(E,C,k1_numbers,k9_funct_2(C,k1_numbers)) => ( ( C = k2_tarski(A,B) & ! [F] : ( r2_hidden(F,C) => ( ( F = A => k1_funct_1(D,F) = 1 ) & ( F != A => k1_funct_1(D,F) = k5_numbers ) ) ) & ! [F] : ( r2_hidden(F,C) => ( ( F = A => k1_funct_1(E,F) = k5_numbers ) & ( F != A => k1_funct_1(E,F) = 1 ) ) ) ) => ( A = B | ! [F] : ( m2_funct_2(F,C,k1_numbers,k9_funct_2(C,k1_numbers)) => ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & F = k1_binop_1(k5_funcsdom(C),k1_funct_1(k7_funcsdom(C),k4_tarski(G,D)),k1_funct_1(k7_funcsdom(C),k4_tarski(H,E))) ) ) ) ) ) ) ) ) )).
fof(t20_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(B,k3_xboole_0(k9_xtuple_0(C),A)) => k1_funct_1(C,B) = k1_funct_1(k3_relat_1(k4_relat_1(A),C),B) ) ) )).
fof(t20_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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) ) ) ) ) )).
fof(t20_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k1_funct_4(k1_xboole_0,A) = A ) )).
fof(t20_funct_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ! [B] : ! [C] : ~ r2_hidden(k4_tarski(B,C),k9_xtuple_0(A)) => ( k1_funct_5(A) = k1_xboole_0 & k3_funct_5(A) = k1_xboole_0 ) ) ) )).
fof(t20_funct_6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( k1_funct_6(k7_funcop_1(A,B)) = k7_funcop_1(A,k9_xtuple_0(B)) & k2_funct_6(k7_funcop_1(A,B)) = k7_funcop_1(A,k10_xtuple_0(B)) ) ) )).
fof(t20_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t20_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) ) => ( ! [C] : ( 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 = k5_numbers | ( v1_funct_9(B,k3_xcmplx_0(2,A)) & v2_funct_9(B) ) ) ) ) ) )).
fof(t20_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_altcat_2(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l1_altcat_1(B) ) => ! [C] : ( l1_functor0(C,A,B) => ( v7_functor0(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & k3_functor0(A,B,C,E) = D ) ) ) ) ) ) )).
fof(t20_functor1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & v1_altcat_2(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & v1_altcat_2(B) & l2_altcat_1(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t20_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t20_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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,D) & r1_fuzzy_1(C,E) ) => r1_fuzzy_1(k2_fuzzy_1(A,B,C),k2_fuzzy_1(A,D,E)) ) ) ) ) ) ) )).
fof(t20_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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))) ) ) ) )).
fof(t20_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ( k1_funct_1(k4_fuzzy_2(A,B),C) = k5_numbers & k1_funct_1(k5_fuzzy_2(A,B),C) = 1 ) ) ) ) )).
fof(t20_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_fvaluat1(C,A) => ( v3_fvaluat1(A) => k3_funct_2(u1_struct_0(A),k6_numbers,C,k4_algstr_0(A,B)) = k3_funct_2(u1_struct_0(A),k6_numbers,C,B) ) ) ) ) )).
fof(t20_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t20_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ 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) ) ) )).
fof(t20_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & l4_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t20_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v2_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( m1_genealg1(E,D) => ! [F] : ( m1_genealg1(F,D) => ( r1_xxreal_0(k3_finseq_1(E),C) => k9_genealg1(D,E,F,A,B,C) = k8_genealg1(D,E,F,A,B) ) ) ) ) ) ) ) )).
fof(t20_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_analmetr(A,E,F) & ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ~ r2_geomtrap(A,E,F,B,D,C,G) & ~ r2_geomtrap(A,E,F,B,D,G,C) ) ) ) ) ) ) ) ) ) )).
fof(t20_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k7_gfacirc1(A,B,C),k8_gfacirc1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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) ) ) ) ) ) ) )).
fof(t20_gfacirc2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) ) => ! [D] : ! [E] : ( 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)) ) ) ) ) )).
fof(t20_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & ~ v4_glib_000(A) ) => ! [B] : ( 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))) ) ) )).
fof(t20_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( k3_finseq_1(B) = k3_finseq_1(k6_glib_001(A,B)) & k1_relset_1(k4_ordinal1,B) = k1_relset_1(k4_ordinal1,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)) ) ) ) )).
fof(t20_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(B)) => ( C = D => r1_tarski(k2_glib_002(B,D),k2_glib_002(A,C)) ) ) ) ) ) )).
fof(t20_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) ) => ! [B] : ( ( v1_glib_003(B) & v4_glib_003(B,A) & m1_glib_000(B,A) ) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m3_glib_001(D,B) => ( C = D => k8_glib_003(A,C) = k8_glib_003(B,D) ) ) ) ) ) )).
fof(t20_goboard1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ~ ( r1_goboard1(u1_struct_0(k15_euclid(2)),D,C) & r2_hidden(B,k4_finseq_1(D)) & r2_hidden(k1_nat_1(B,1),k4_finseq_1(D)) & r2_hidden(A,k4_finseq_1(C)) & r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),D,B),k10_xtuple_0(k7_matrix_0(u1_struct_0(k15_euclid(2)),C,A))) & ~ r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(B,1)),k10_xtuple_0(k7_matrix_0(u1_struct_0(k15_euclid(2)),C,A))) & ? [E] : ( v7_ordinal1(E) & r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(B,1)),k10_xtuple_0(k7_matrix_0(u1_struct_0(k15_euclid(2)),C,E))) & r2_hidden(E,k4_finseq_1(C)) & k9_complex1(k6_xcmplx_0(A,E)) != 1 ) ) ) ) ) ) )).
fof(t20_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( v1_goboard1(C) & v4_goboard1(C) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k1_matrix_0(C)) & r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) ) => r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),B)),k1_goboard5(C,A)) ) ) ) ) )).
fof(t20_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_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_0(B),A) | k1_tops_1(k15_euclid(2),k3_goboard5(B,k5_numbers,A)) = a_2_2_goboard6(A,B) ) ) ) ) )).
fof(t20_goboard7,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k3_finseq_1(A)) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(A)) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(A)) & r1_xxreal_0(1,E) & r1_xxreal_0(E,k1_matrix_0(A)) ) => ( r1_xboole_0(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1),C)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,D,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,k1_nat_1(D,1),E))) | ( C = E & r1_xxreal_0(k1_int_2(k6_xcmplx_0(B,D)),1) ) ) ) ) ) ) ) ) )).
fof(t20_goboard8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,2),k3_finseq_1(A)) ) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,2),k1_matrix_0(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k3_finseq_1(k2_goboard2(A)),k1_nat_1(C,1)) ) => ( ( ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(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,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k7_nat_d(k3_finseq_1(k2_goboard2(A)),1),k1_nat_1(C,1)) ) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k7_nat_d(k3_finseq_1(k2_goboard2(A)),1),k1_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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k7_nat_d(k3_finseq_1(k2_goboard2(A)),1),k1_nat_1(C,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k3_finseq_1(k2_goboard2(A)),k1_nat_1(C,2))),k7_xcmplx_0(1,2)),k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k3_finseq_1(k2_goboard2(A)),k1_nat_1(C,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k3_finseq_1(k2_goboard2(A)),k1_nat_1(C,2))),k7_xcmplx_0(1,2)),k19_euclid(1,k5_numbers))),k3_topreal1(2,A)) ) ) ) ) ) ) )).
fof(t20_goboard9,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t20_gobrd11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( v1_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) ) ) ) ) )).
fof(t20_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(D)) & r1_goboard1(u1_struct_0(k15_euclid(2)),D,E) & r2_hidden(k4_tarski(A,k1_nat_1(B,1)),k2_matrix_0(E)) & r2_hidden(k4_tarski(A,B),k2_matrix_0(E)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,B) ) => k3_gobrd13(D,E,C) = k3_goboard5(E,A,B) ) ) ) ) ) ) )).
fof(t20_gobrd14,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t20_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ( v4_card_3(A) => ( ~ v1_xboole_0(k1_goedelcp(A)) & v4_card_3(k1_goedelcp(A)) ) ) ) )).
fof(t20_gr_cy_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ( v1_gr_cy_1(A) => v1_gr_cy_1(B) ) ) ) )).
fof(t20_gr_cy_2,axiom,( ! [A] : ( ( ~ 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] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ( r1_group_2(A,B,k6_group_2(A)) | B = A ) ) ) ) )).
fof(t20_gr_cy_3,axiom,( k1_gr_cy_3(5) = 31 )).
fof(t20_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ( ? [C] : ( ~ 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)) ) ) ) ) )).
fof(t20_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : r1_tarski(k2_graph_3(A,B,C),k5_graph_3(A,B)) ) ) )).
fof(t20_graph_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(C) & l1_graph_1(C) ) => ! [D] : ( m2_finseq_1(D,u4_struct_0(C)) => ! [E] : ( m2_finseq_1(E,u4_struct_0(C)) => ( ( r1_tarski(k10_xtuple_0(E),k10_xtuple_0(D)) & 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) ) ) ) ) )).
fof(t20_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => ! [D] : ( v1_xreal_0(D) => k4_finseq_1(k2_graphsp(A,B,C,D)) = k4_finseq_1(C) ) ) ) ) )).
fof(t20_grcat_1,axiom,( ! [A] : ( ( v1_grcat_1(A) & v2_grcat_1(A) & l1_grcat_1(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t20_grfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r2_hidden(B,k9_xtuple_0(C)) & r2_hidden(B,A) ) <=> r2_hidden(k4_tarski(B,k1_funct_1(C,B)),k5_relat_1(C,A)) ) ) )).
fof(t20_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t20_groeb_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( r1_tarski(k2_groeb_1(A,B,C,k7_ideal_1(k12_polynom1(A,C),D)),k3_groeb_1(A,k2_groeb_1(A,B,C,D))) => v9_rewrite1(k3_polyred(A,B,C,D)) ) ) ) ) ) )).
fof(t20_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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,k8_polynom1(A,C)),k8_polynom1(A,C)) & r8_pboole(k15_pre_poly(A),k3_groeb_2(A,B,C,k8_polynom1(A,C),D),k8_polynom1(A,C)) ) ) ) ) ) )).
fof(t20_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(E,k5_card_1(k3_polynom1(k15_pre_poly(A),C,D))) => ! [F] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t20_group_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t20_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(t20_group_14,axiom,( ! [A] : ( ( 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] : ( ( v1_relat_1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_finseq_1(B) & v1_prvect_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k2_group_14(k19_rvsum_1(A))),u1_struct_0(k20_prvect_1(B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_group_14(k19_rvsum_1(A))),u1_struct_0(k20_prvect_1(B))))) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( r2_hidden(D,k4_finseq_1(B)) & ! [E] : ( ( v7_ordinal1(E) & ~ v8_ordinal1(E) ) => ~ ( E = k1_funct_1(A,D) & k1_funct_1(B,D) = k2_group_14(E) ) ) ) ) & ! [D] : ( v1_int_1(D) => ( r2_hidden(D,u1_struct_0(k2_group_14(k19_rvsum_1(A)))) => k1_funct_1(C,D) = k1_int_6(D,A) ) ) ) => v2_funct_1(C) ) ) ) ) )).
fof(t20_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k2_group_2(A,k7_domain_1(u1_struct_0(A),C,D),k6_domain_1(u1_struct_0(A),B)) = k7_domain_1(u1_struct_0(A),k6_algstr_0(A,C,B),k6_algstr_0(A,D,B)) ) ) ) ) )).
fof(t20_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_group_3(A,B,B) = B ) ) )).
fof(t20_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t20_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_group_5(A,B,B) = k1_group_1(A) ) ) )).
fof(t20_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_group_6(A,B))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t20_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t20_group_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ~ r1_xxreal_0(k18_group_2(A,B),k5_numbers) ) ) )).
fof(t20_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( m1_group_9(D,A,B) => ! [E] : ( 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)) ) ) ) ) )).
fof(t20_groupp_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v8_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_group_2(C,B) => ! [D] : ( 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] : ( ( v15_algstr_0(E) & m1_group_2(E,B) ) => ~ ( u1_struct_0(E) = k7_group_4(B,C,D) & v2_group_10(E,A) ) ) ) ) ) ) ) )).
fof(t20_hahnban,axiom,( ! [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) ) => ! [B] : ( ( 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)) = k5_numbers ) ) )).
fof(t20_hahnban1,axiom,( ! [A] : ( ( ~ 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] : ( m1_vectsp_4(B,k1_complfld,A) => m1_rlsub_1(k10_hahnban1(B),k10_hahnban1(A)) ) ) )).
fof(t20_hallmar1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( r2_hidden(C,k4_finseq_1(B)) => m1_hallmar1(k2_hallmar1(A,B,C,D),A,B,C) ) ) ) ) )).
fof(t20_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(D,B) & v2_compts_1(B,k3_pcomps_1(A)) ) => r1_xxreal_0(k3_metric_1(A,C,D),k1_funct_1(k5_weierstr(A,B),C)) ) ) ) ) ) )).
fof(t20_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v5_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t20_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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] : ( 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))) ) ) ) )).
fof(t20_heyting1,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k12_normform(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k12_normform(A))) => ~ ( ! [E] : ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ~ ( r2_hidden(E,C) & ! [F] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t20_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_substlat(A,B))) => ! [D] : ( 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) ) ) ) )).
fof(t20_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k2_heyting3(1,A) = k7_domain_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,1,A),k1_domain_1(k4_ordinal1,k4_ordinal1,2,A)) ) )).
fof(t20_hfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t20_hilbasis,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(E,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k1_normsp_1(A,k11_polynom3(A,E,k5_hilbasis(A,B,D)),k1_nat_1(C,B)) = k6_algstr_0(A,k1_normsp_1(A,E,C),D) ) ) ) ) ) )).
fof(t20_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) ) )).
fof(t20_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( m1_subset_1(D,k1_hilbert1) => ( k3_hilbert1(A,B) = k3_hilbert1(C,D) => ( A = C & D = B ) ) ) ) ) ) )).
fof(t20_hilbert3,axiom,( ! [A] : ! [B] : ! [C] : ( ( B = k1_xboole_0 => A = k1_xboole_0 ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) )).
fof(t20_hurwitz,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( k2_hurwitz(A,B) = k4_xcmplx_0(1) <=> r2_funct_2(k4_ordinal1,u1_struct_0(A),B,k9_polynom3(A)) ) ) ) )).
fof(t20_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( k8_idea_1(A,B) = k8_idea_1(A,C) => ( B = k5_numbers | C = k5_numbers | B = C ) ) ) ) ) )).
fof(t20_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_vectsp_1(A) & v6_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( v1_gcd_1(C,A) & r2_hidden(C,B) ) ) ) ) ) )).
fof(t20_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ~ ( ! [D] : ( m1_subset_1(D,u4_incsp_1(A)) => ~ ( r3_incsp_1(A,B,D) & r3_incsp_1(A,C,D) ) ) & B = C ) ) ) ) )).
fof(t20_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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] : ( 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) ) ) ) )).
fof(t20_instalg1,axiom,( ! [A] : ( l1_msualg_1(A) => ! [B] : ( ( v1_instalg1(B) & l1_msualg_1(B) ) => ! [C] : ( m1_instalg1(C,B) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t20_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => ( ( k3_xcmplx_0(D,E) = C & r2_int_1(A,B,C) ) => r2_int_1(A,B,D) ) ) ) ) ) ) )).
fof(t20_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => m1_subset_1(k3_int_2(A,B),k4_ordinal1) ) ) )).
fof(t20_int_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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)) ) ) ) )).
fof(t20_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ( ( k3_int_2(A,B) = 1 & r1_int_5(A,B) ) => ( r1_xxreal_0(B,2) | k5_int_1(k6_xcmplx_0(k1_newton(A,k3_nat_d(k7_nat_d(B,1),2)),1),B) = k5_numbers ) ) ) ) )).
fof(t20_int_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r1_int_2(A,B) => r1_int_1(k3_xcmplx_0(A,B),k2_int_2(A,B)) ) ) ) )).
fof(t20_int_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_int_7(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_int_7(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t20_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_int_2(A,C) & r1_nat_d(B,C) ) => ( r1_xxreal_0(C,1) | r1_xxreal_0(B,1) | r1_nat_d(k3_pepin(A,B),k3_pepin(A,C)) ) ) ) ) ) )).
fof(t20_integr11,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( B = k1_rcomp_1(k5_numbers,k28_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)),k18_sin_cos)) = k5_numbers ) ) ) )).
fof(t20_integr12,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v3_rcomp_1(E) & m1_subset_1(E,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,E) & r1_tarski(E,k2_rcomp_1(k4_xcmplx_0(1),1)) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => k1_funct_1(D,F) = 1 ) ) & r1_tarski(E,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_sin_cos6,k1_taylor_1(A)))) & E = k1_relset_1(k1_numbers,C) & 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,k3_sin_cos6,k1_taylor_1(k6_xcmplx_0(A,1))),A),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k1_taylor_1(2)),k4_taylor_1(k7_xcmplx_0(1,2))))) ) => ( r1_xxreal_0(A,1) | k2_integra5(B,C) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_sin_cos6,k1_taylor_1(A))),k2_seq_4(B)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_sin_cos6,k1_taylor_1(A))),k3_seq_4(B))) ) ) ) ) ) ) ) )).
fof(t20_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,D) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => k1_funct_1(C,E) = 1 ) ) & r2_relset_1(k1_numbers,k1_numbers,B,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,C,k1_taylor_1(2))))) & r1_tarski(D,k2_rcomp_1(k4_xcmplx_0(1),1)) & D = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k2_sin_cos9),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k2_sin_cos9),k3_seq_4(A))) ) ) ) ) ) )).
fof(t20_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k7_xcmplx_0(k1_funct_1(k18_sin_cos,k1_funct_1(k3_taylor_1,D)),k3_xcmplx_0(D,k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_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) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k2_fdiff_9)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k2_fdiff_9)),k3_seq_4(A))) ) ) ) ) )).
fof(t20_integr15,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( C = k1_rcomp_1(E,D) => k6_euclid(A,k11_integr15(A,C,B)) = k12_integr15(D,E,A,B) ) ) ) ) ) ) )).
fof(t20_integr16,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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)) = k3_xcmplx_0(A,k7_integr16(B,C)) ) ) ) ) ) )).
fof(t20_integr19,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t20_integra1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k3_finseq_1(A) = k3_finseq_1(C) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k4_finseq_1(A)) => k1_funct_1(C,D) = k5_real_1(k7_partfun1(k1_numbers,A,D),k7_partfun1(k1_numbers,B,D)) ) ) ) => k18_rvsum_1(C) = k6_xcmplx_0(k18_rvsum_1(A),k18_rvsum_1(B)) ) ) ) ) )).
fof(t20_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( m1_integra1(D,B) => ( ( v1_comseq_2(k2_partfun1(B,k1_numbers,C,B)) & r1_xxreal_0(A,k5_numbers) ) => r1_xxreal_0(k3_xcmplx_0(k3_xcmplx_0(A,k2_seq_4(k1_rvsum_1(C))),k3_integra1(B)),k1_funct_1(k8_integra1(B,k26_valued_1(B,k1_numbers,C,A)),D)) ) ) ) ) ) )).
fof(t20_integra4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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_comseq_2(k2_partfun1(A,k1_numbers,B,A)) & v3_integra1(B,A) ) => v3_integra1(k18_rfunct_3(A,B),A) ) ) ) )).
fof(t20_integra5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( B = k1_rcomp_1(D,C) => k4_xcmplx_0(k2_integra5(B,A)) = k4_integra5(C,D,A) ) ) ) ) ) )).
fof(t20_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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) = k2_xcmplx_0(k4_integra5(A,C,E),k4_integra5(C,D,E)) ) ) ) ) ) ) )).
fof(t20_integra7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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_funct_1(E,B) = k2_xcmplx_0(k4_integra5(A,B,D),k1_funct_1(E,A)) ) ) ) ) ) )).
fof(t20_integra8,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t20_integra9,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( ~ 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))) ) ) ) )).
fof(t20_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => r1_interva1(A,k3_interva1(A,B,B),B) ) ) )).
fof(t20_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( 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) ) ) )).
fof(t20_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(A,B) => ( r1_xxreal_0(B,k5_numbers) | k1_funct_1(k3_irrat_1(B),A) = k1_funct_1(k5_newton(1,k7_xcmplx_0(1,B),B),k1_nat_1(A,1)) ) ) ) ) )).
fof(t20_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,B,C) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t20_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,k6_cat_2(A,B),C) => ! [E] : ( m2_cat_1(E,k6_cat_2(A,B),C) => ( r2_funct_2(u4_struct_0(A),u4_struct_0(k9_nattra_1(B,C)),k5_isocat_2(A,B,C,D),k5_isocat_2(A,B,C,E)) => r2_funct_2(u4_struct_0(k6_cat_2(A,B)),u4_struct_0(C),D,E) ) ) ) ) ) ) )).
fof(t20_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)))) ) ) ) ) )).
fof(t20_jgraph_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(t20_jgraph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( v1_xreal_0(B) => ? [C] : ( 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] : ( 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) ) ) ) )).
fof(t20_jgraph_3,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(t20_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( 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] : ( 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) = k3_xcmplx_0(k12_euclid(D),k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k18_euclid(D),k12_euclid(D)),A),k2_xcmplx_0(1,A))) ) ) & ! [D] : ( 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),k5_numbers) & D != k4_struct_0(k15_euclid(2)) ) ) ) ) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) | v5_pre_topc(C,k1_pre_topc(k15_euclid(2),B),k3_topmetr) ) ) ) ) ) )).
fof(t20_jgraph_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r1_xxreal_0(k5_numbers,k18_euclid(B)) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) | r1_xxreal_0(1,A) | r1_xxreal_0(A,k7_xcmplx_0(k17_euclid(B),k12_euclid(B))) | k12_euclid(B) = k5_numbers | ! [C] : ( 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(k5_numbers,k18_euclid(C)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(C)) ) ) ) ) ) ) ) )).
fof(t20_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t20_jordan,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(B))) => ( r2_hidden(D,k3_topreal9(B,C,A)) => r1_tarski(k7_subset_1(u1_struct_0(k15_euclid(B)),k1_rltopsp1(k15_euclid(B),C,D),k7_domain_1(u1_struct_0(k15_euclid(B)),C,D)),k1_topreal9(B,C,A)) ) ) ) ) ) )).
fof(t20_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( E = a_4_0_jordan1(A,B,C,D) & F = a_4_1_jordan1(A,B,C,D) ) => r1_xboole_0(E,F) ) ) ) ) ) ) ) )).
fof(t20_jordan10,axiom,( ! [A] : ( ( 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) ) )).
fof(t20_jordan12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_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_0(C)) ) => v1_convex1(k3_goboard5(C,A,B),k15_euclid(2)) ) ) ) ) )).
fof(t20_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( r1_jordan1h(A,B) => r1_subset_1(k2_jordan2c(2,A),k3_topreal1(2,k1_jordan13(A,B))) ) ) ) )).
fof(t20_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( 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_0(k1_jordan8(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_topreal1(2,k1_jordan1e(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C),k3_topreal1(2,k2_jordan1e(B,A))) & ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ~ ( 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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),F,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),G,C)),k3_topreal1(2,k1_jordan1e(B,A))) = k1_tarski(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),F,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),G,C)),k3_topreal1(2,k2_jordan1e(B,A))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),G,C)) ) ) ) ) ) ) ) ) ) )).
fof(t20_jordan16,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_funct_2(u1_struct_0(k3_topmetr),u1_struct_0(k3_topmetr),k1_numbers,k1_numbers,A,k1_fcont_1(B,C)) => ( B = k5_numbers | v3_tops_2(A,k3_topmetr,k3_topmetr) ) ) ) ) ) )).
fof(t20_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ~ ( E != B & r1_jordan17(A,B,C,D,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ~ ( F != E & F != B & r1_jordan17(A,B,D,E,F) ) ) ) ) ) ) ) ) )).
fof(t20_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( ~ 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_0(u1_struct_0(k15_euclid(2)),B,A,k1_matrix_0(B)))) ) ) ) ) )).
fof(t20_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & ~ r1_xxreal_0(k3_finseq_1(k2_jordan9(B,A)),C) & r2_hidden(k19_pscomp_1(B),k4_goboard5(k2_jordan9(B,A),C)) ) ) ) )).
fof(t20_jordan1g,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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)))) ) => ~ r1_xxreal_0(k4_finseq_4(k1_jordan1e(B,A),k19_pscomp_1(k3_topreal1(2,k2_jordan9(B,A)))),k4_finseq_4(k1_jordan1e(B,A),k18_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))))) ) ) )).
fof(t20_jordan1h,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r1_goboard1(u1_struct_0(k15_euclid(2)),B,A) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(B)) ) => r1_tarski(k2_topreal1(2,B,C),k3_gobrd13(B,A,C)) ) ) ) ) ) )).
fof(t20_jordan20,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [E] : ( ( ~ 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 ) ) ) ) ) ) )).
fof(t20_jordan21,axiom,( ! [A] : ( ( 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)) ) )).
fof(t20_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(k1_jordan8(A,B))) & k2_jordan21(k3_topreal1(2,k2_jordan9(A,B))) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k1_jordan1a(k1_jordan8(A,B)),C) ) ) ) ) ) )).
fof(t20_jordan23,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v2_jordan23(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(t20_jordan2b,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(1))) => ? [B] : ( v1_xreal_0(B) & A = k9_finseq_1(B) ) ) )).
fof(t20_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t20_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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,k1_nat_1(k1_jordan3(A,B),1)) ) => ( B = k1_funct_1(A,k3_finseq_1(A)) | k1_nat_1(k1_nat_1(k1_jordan3(k4_finseq_5(u1_struct_0(k15_euclid(2)),A),B),k1_jordan3(A,B)),1) = k3_finseq_1(A) ) ) ) ) )).
fof(t20_jordan4,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( 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(k1_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)) ) ) ) ) ) ) )).
fof(t20_jordan5a,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t20_jordan5b,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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))) ) ) ) ) )).
fof(t20_jordan5c,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( v7_ordinal1(C) => ( ( v4_pre_topc(B,k15_euclid(2)) & v4_topreal1(A) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_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,k1_nat_1(C,1))) ) ) ) ) ) )).
fof(t20_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( B = a_1_0_jordan5d(A) => k2_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)))) ) ) ) )).
fof(t20_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => r1_tarski(k4_jordan6(A,B,C,D),A) ) ) ) ) )).
fof(t20_jordan7,axiom,( ! [A] : ( ( ~ 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] : ( v1_xreal_0(B) => ~ ( v1_topreal2(A) & ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( 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] : ( v7_ordinal1(D) => ( 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,k1_nat_1(D,1))) ) ) ) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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,k1_nat_1(D,1))) & r1_xxreal_0(B,k3_tbsp_1(k14_euclid(2),E)) ) ) ) & ! [D] : ( 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] : ( v7_ordinal1(D) => ( r1_xxreal_0(1,D) => ( r1_xxreal_0(k3_finseq_1(C),k1_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,k1_nat_1(D,1))),k1_jordan7(A,k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_nat_1(D,1)),k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_nat_1(D,2)))) = k1_tarski(k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_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] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( 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,k1_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,k1_nat_1(E,1)))) ) ) ) ) & ! [D] : ( v7_ordinal1(D) => ~ ( ~ r1_xxreal_0(D,1) & ~ r1_xxreal_0(k3_finseq_1(C),k1_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,k1_nat_1(D,1)))) ) ) ) ) ) ) ) )).
fof(t20_jordan9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(C)) ) => ( r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B),k3_goboard5(C,A,B)) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_nat_1(B,1)),k3_goboard5(C,A,B)) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),k1_nat_1(B,1)),k3_goboard5(C,A,B)) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),B),k3_goboard5(C,A,B)) ) ) ) ) ) )).
fof(t20_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t20_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v2_prob_1(B) => k3_kurato_0(A,B) = k2_kurato_0(A,B) ) ) )).
fof(t20_kurato_1,axiom,( 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) )).
fof(t20_kurato_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ( ! [D] : ( v7_ordinal1(D) => k2_kurato_2(A,C,D) = k2_pre_topc(A,k2_kurato_2(A,B,D)) ) => k1_kurato_2(A,C) = k1_kurato_2(A,B) ) ) ) ) )).
fof(t20_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t20_latsum_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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)) ) ) ) )).
fof(t20_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => r6_binop_1(u1_struct_0(A),u2_lattices(A),u2_lattices(A)) ) )).
fof(t20_lattice3,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t20_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t20_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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 ) ) ) )).
fof(t20_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( 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) ) ) ) ) ) )).
fof(t20_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k7_lattices(A,k7_lattices(A,B)) = B ) ) )).
fof(t20_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( ( v4_lexbfs(B,A) & m1_lexbfs(B,A) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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 ) ) ) ) ) )).
fof(t20_lfuzzy_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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)) ) ) ) )).
fof(t20_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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,k1_fuzzy_4(A,A,B)),C) ) ) ) ) )).
fof(t20_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => k1_funct_1(A,B) = B ) => v1_limfunc1(A) ) ) )).
fof(t20_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r5_limfunc2(B,A) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,C),k2_rcomp_1(A,k2_xcmplx_0(A,D)))) => r1_xxreal_0(E,k1_funct_1(C,F)) ) ) ) ) ) | r5_limfunc2(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t20_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,C) & ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ~ ( ~ 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] : ( v1_xreal_0(C) => ~ ( v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(k6_xcmplx_0(A,C),A))) & v8_valued_0(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(A,k2_xcmplx_0(A,C)))) & ~ v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(k6_xcmplx_0(A,C),A))) & ~ v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(A,k2_xcmplx_0(A,C)))) ) ) | r2_limfunc3(B,A) ) ) ) ) )).
fof(t20_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(k6_xcmplx_0(A,D),A))) & r1_xxreal_0(k1_limfunc2(B,A),k1_funct_1(B,E)) ) ) ) ) | r3_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t20_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) )).
fof(t20_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(k17_lmod_7(A,B,C))) => ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & D = k18_lmod_7(A,B,C,E) ) ) ) ) ) )).
fof(t20_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v3_normsp_1(B,A) & k6_normsp_1(A,B) = C ) => ( v2_comseq_2(k5_normsp_0(A,B)) & k1_seq_2(k5_normsp_0(A,B)) = k2_normsp_0(A,C) ) ) ) ) ) )).
fof(t20_lopban_2,axiom,( ! [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) & 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)) ) ) )).
fof(t20_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_lopban_3(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v1_xreal_0(C) => ( 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) ) ) ) ) )).
fof(t20_lopban_4,axiom,( ! [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) & 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) ) ) )).
fof(t20_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t20_lpspacc1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,C,k6_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,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(k14_lpspacc1(B,C,D))) => ( E = F => k25_valued_1(B,k2_numbers,E,A) = k1_clvect_1(k14_lpspacc1(B,C,D),F,A) ) ) ) ) ) ) ) )).
fof(t20_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_rfunct_3(B,A,k1_numbers,k3_rfunct_3(A,k1_numbers)) => ! [C] : ( m2_rfunct_3(C,A,k1_numbers,k3_rfunct_3(A,k1_numbers)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t20_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : 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)) ) ) ) )).
fof(t20_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(D),k1_domain_1(k4_ordinal1,k1_hilbert1,C,k3_hilbert1(k5_ltlaxio1(k2_ltlaxio1(B),k2_ltlaxio1(k4_ltlaxio1(A,k4_hilbert1(A,B)))),k4_hilbert1(A,B)))) = 1 ) ) ) ) )).
fof(t20_ltlaxio2,axiom,( ! [A] : ( m2_finseq_1(A,k1_hilbert1) => ! [B] : ( ( 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),k1_ltlaxio1(k7_partfun1(k1_hilbert1,k2_ltlaxio2(k4_ltlaxio2(A)),k3_finseq_1(k2_ltlaxio2(k4_ltlaxio2(A)))))) = k5_numbers <=> ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(A)) => k3_funct_2(k1_hilbert1,k6_margrel1,k12_ltlaxio1(B),k7_partfun1(k1_hilbert1,A,C)) = k5_numbers ) ) ) ) ) )).
fof(t20_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_hilbert1)) => ( r2_hidden(k4_ltlaxio1(A,B),k5_ltlaxio3(C)) => ( r2_hidden(A,k5_ltlaxio3(C)) & r2_hidden(B,k5_ltlaxio3(C)) ) ) ) ) ) )).
fof(t20_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ( r2_hidden(B,k9_ltlaxio4(A)) => v3_ltlaxio3(B) ) ) ) )).
fof(t20_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t20_margrel1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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) ) ) ) )).
fof(t20_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(B,k3_mathmorp(A,k6_rusub_4(A,B,C),C)) ) ) ) )).
fof(t20_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( r1_matrix10(B,C) => v2_matrix10(k5_matrix10(A,B,C)) ) ) ) ) )).
fof(t20_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_matrix_2(B,k3_matrix_2(A)) => ( v4_matrix_2(B,k2_matrix_2(k3_matrix_2(A))) => ( k1_partfun1(k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),B,B) = k1_finseq_2(A) & r2_funct_2(k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),B,k2_funct_2(k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),B)) ) ) ) ) )).
fof(t20_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(D),C,C) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(D))) ) => ( ( r2_hidden(B,k4_finseq_1(k3_matrix_1(D,C))) & r2_hidden(A,k4_finseq_1(k3_matrix_1(D,C))) ) => ( r1_xxreal_0(C,k5_numbers) | k4_matrix_3(D,F,k6_matrix12(C,C,D,k3_matrix_1(D,C),B,A,E)) = k6_matrix12(C,C,D,F,B,A,E) ) ) ) ) ) ) ) ) )).
fof(t20_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,A,1,1) & m2_finseq_1(B,k3_finseq_2(A)) ) => B = k2_matrlin(A,k13_matrix_0(A,k3_matrix_0(A,B,1,1))) ) ) )).
fof(t20_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => k13_fvsum_1(A,B,k2_matrix14(A,k3_finseq_1(B))) = k4_struct_0(A) ) ) )).
fof(t20_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(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))) ) ) ) ) ) )).
fof(t20_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( v3_matrix16(D,u1_struct_0(B)) => v3_matrix16(k2_matrix13(A,A,B,D,C),u1_struct_0(B)) ) ) ) ) ) )).
fof(t20_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ( ~ r1_xxreal_0(k3_finseq_1(B),k5_numbers) => ! [C] : ( v7_ordinal1(C) => ( ( v1_matrix_0(B) & v2_matrix_0(B,A,k3_finseq_1(B),C) & m2_finseq_1(B,k3_finseq_2(A)) ) <=> C = k1_matrix_0(B) ) ) ) ) ) )).
fof(t20_matrix_3,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k4_matrix_3(A,k14_matrix_0(u1_struct_0(A),1,k13_matrix_0(u1_struct_0(A),B)),k14_matrix_0(u1_struct_0(A),1,k13_matrix_0(u1_struct_0(A),C))) = k14_matrix_0(u1_struct_0(A),1,k13_matrix_0(u1_struct_0(A),k8_group_1(A,B,C))) ) ) ) )).
fof(t20_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) ) => B = k3_matrix_3(A,B,k1_matrix_4(A,C,C)) ) ) ) ) )).
fof(t20_matrix_5,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(C) = k3_finseq_1(D) & k1_matrix_0(C) = k1_matrix_0(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)) ) ) ) ) ) )).
fof(t20_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k4_matrix_0(u1_struct_0(B),k11_matrix_0(u1_struct_0(B),A,A,C)) = k11_matrix_0(u1_struct_0(B),A,A,C) ) ) ) )).
fof(t20_matrix_7,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t20_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_6(C,A,B) & k4_matrix_3(B,D,C) = k4_matrix_3(B,E,C) ) => D = E ) ) ) ) ) ) )).
fof(t20_matrix_9,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( ( v1_matrix_0(K) & v2_matrix_0(K,u1_struct_0(A),3,3) & m2_finseq_1(K,k3_finseq_2(u1_struct_0(A))) ) => ( K = k3_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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] : ( m1_matrix_2(L,k3_matrix_2(3)) => ( L = k3_finseq_4(k4_ordinal1,1,2,3) => k10_matrix_3(3,A,K,L) = k3_finseq_4(u1_struct_0(A),B,F,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t20_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ( r1_xxreal_0(1,k3_finseq_1(k1_complsp2(A))) => k1_finsop_1(k2_numbers,k1_complsp2(A),k3_binop_2) = k8_complex1(k1_finsop_1(k2_numbers,A,k3_binop_2)) ) ) )).
fof(t20_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => k2_wsierp_1(k11_matrixj1(A,k5_matrixj1(A,B,C))) = k2_xcmplx_0(k1_matrix_0(B),k1_matrix_0(C)) ) ) ) )).
fof(t20_matrixj2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( m1_matrlin(D,A,B) => ! [E] : ( m2_finseq_1(E,u1_struct_0(C)) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(A),k3_finseq_1(D),k3_finseq_1(E)) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(A))) ) => ! [G] : ( ( 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] : ( v7_ordinal1(H) => ! [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,k7_matrix_0(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_0(k2_matrixj1(u1_struct_0(A),G,I)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t20_matrixr1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(C)) ) => k7_matrix_0(u1_struct_0(A),k6_matrix_3(A,C,B),D) = k10_fvsum_1(k1_matrix_0(C),A,k7_matrix_0(u1_struct_0(A),C,D),B) ) ) ) ) ) )).
fof(t20_matrixr2,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(C) = k3_finseq_1(D) & k1_matrix_0(C) = k1_matrix_0(D) & k3_finseq_1(C) = k1_matrix_0(B) ) => ( r1_xxreal_0(k3_finseq_1(C),k5_numbers) | r1_xxreal_0(k3_finseq_1(B),k5_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)) ) ) ) ) ) ) )).
fof(t20_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t20_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( 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)) ) ) ) )).
fof(t20_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t20_matrprob,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( k3_finseq_1(k3_matrprob(A)) = k3_finseq_1(A) & ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k2_finseq_1(k3_finseq_1(A))) => k1_funct_1(k3_matrprob(A),B) = k18_rvsum_1(k7_matrix_0(k1_numbers,A,B)) ) ) ) ) )).
fof(t20_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ! [D] : ( m1_matrlin(D,k2_vectsp_1,k6_prvect_1(k2_vectsp_1,A)) => ! [E] : ( m1_matrlin(E,k2_vectsp_1,k6_prvect_1(k2_vectsp_1,B)) => ( ( D = k11_matrix13(k2_vectsp_1,A,A,k3_matrix_1(k2_vectsp_1,A)) & E = k11_matrix13(k2_vectsp_1,B,B,k3_matrix_1(k2_vectsp_1,B)) ) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(k2_vectsp_1),k3_finseq_1(D),k3_finseq_1(E)) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( 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)) ) ) ) ) ) ) ) ) )).
fof(t20_matrtop2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & v3_valued_0(C) ) => ! [D] : ( m1_matrlin(D,k2_vectsp_1,k6_prvect_1(k2_vectsp_1,A)) => ( D = k11_matrix13(k2_vectsp_1,A,A,k3_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(k4_ordinal1,k7_nat_d(A,B),k5_numbers)) ) ) ) ) ) ) )).
fof(t20_matrtop3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(E))) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(C,E) ) => ( r1_xxreal_0(C,B) | D = B | D = C | k1_funct_1(k3_funct_2(u1_struct_0(k15_euclid(E)),u1_struct_0(k15_euclid(E)),k3_matrtop1(E,E,k2_matrtop3(E,A,B,C)),F),D) = k1_funct_1(F,D) ) ) ) ) ) ) ) ) )).
fof(t20_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_normsp_0(A,k5_algstr_0(A,k3_funct_2(u1_struct_0(A),u1_struct_0(A),k1_mazurulm(A,B),C),B)) = k2_normsp_0(A,k5_algstr_0(A,C,B)) ) ) ) )).
fof(t20_mcart_1,axiom,( ! [A] : ~ ( A != k1_xboole_0 & ! [B] : ~ ( r2_hidden(B,A) & ! [C] : ! [D] : ! [E] : ! [F] : ~ ( ( r2_hidden(C,A) | r2_hidden(D,A) ) & B = k6_xtuple_0(C,D,E,F) ) ) ) )).
fof(t20_measure1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t20_measure3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => r1_measure3(A,k2_measure3(A,B,C),k4_measure3(A,B,C)) ) ) )).
fof(t20_measure6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v6_xxreal_2(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t20_member_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k5_member_1(k2_tarski(A,B)) = k2_tarski(k4_xcmplx_0(A),k4_xcmplx_0(B)) ) ) )).
fof(t20_membered,axiom,( ! [A] : ! [B] : ( v2_membered(B) => ( r1_tarski(A,B) => v2_membered(A) ) ) )).
fof(t20_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [C] : ( v7_ordinal1(C) => k6_memstr_0(A,B,k7_memstr_0(A,B,C)) = k1_xboole_0 ) ) ) )).
fof(t20_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(2))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k15_euclid(2))) => ! [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,k7_xcmplx_0(2,3)),k1_rlvect_1(k15_euclid(2),C,k7_xcmplx_0(1,3))) & E = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),C,k7_xcmplx_0(2,3)),k1_rlvect_1(k15_euclid(2),A,k7_xcmplx_0(1,3))) & F = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),A,k7_xcmplx_0(2,3)),k1_rlvect_1(k15_euclid(2),B,k7_xcmplx_0(1,3))) & r1_euclid_6(A,D,I) & r1_euclid_6(B,E,I) & r1_euclid_6(B,E,G) & r1_euclid_6(C,F,G) & r1_euclid_6(A,D,H) & r1_euclid_6(C,F,H) ) => ( r1_euclid_6(A,B,C) | k1_euclid_6(G,H,I) = k7_xcmplx_0(k1_euclid_6(A,B,C),7) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t20_mesfun10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( r1_mesfun10(A,B,C) => ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers))) => ( v10_mesfunc5(k3_mesfunc5(A,B,D)) & k2_mesfunc5(k3_mesfunc5(A,B,D)) = k12_supinf_2(C,D) ) ) ) ) ) ) ) )).
fof(t20_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ( k12_supinf_2(C,F) = k5_numbers => ( ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t20_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( m1_subset_1(C,A) => ( ( r2_hidden(C,k1_relset_1(A,k4_mesfunc5(A,k1_numbers,B,k5_numbers))) & v2_comseq_2(k10_seqfunc(A,B,C)) ) => v1_rinfsup2(k3_mesfunc5(A,k5_mesfun7c(A,B),C)) ) ) ) ) )).
fof(t20_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( 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))) ) ) ) )).
fof(t20_mesfunc1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,C))) ) => ! [E] : ! [F] : ( v1_xreal_0(F) => ( ! [G] : ( m1_subset_1(G,k4_ordinal1) => k9_nat_1(C,D,G) = k9_subset_1(A,E,k15_mesfunc1(A,B,k2_xcmplx_0(F,k2_extreal1(1,k1_nat_1(G,1))))) ) => k9_subset_1(A,E,k16_mesfunc1(A,B,F)) = k1_measure2(A,C,k1_measure3(A,C,D)) ) ) ) ) ) )).
fof(t20_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t20_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => r2_relset_1(A,k6_numbers,k1_mesfunc5(A,k26_valued_1(A,k1_numbers,B,C)),k6_mesfunc1(A,k1_mesfunc5(A,B),C)) ) ) ) )).
fof(t20_mesfunc7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => k3_mesfunc1(A,k2_partfun1(A,k6_numbers,k10_mesfunc1(A,B),k1_relset_1(A,k10_mesfunc1(A,k3_mesfunc1(A,B,C)))),k2_partfun1(A,k6_numbers,k10_mesfunc1(A,C),k1_relset_1(A,k10_mesfunc1(A,k3_mesfunc1(A,B,C))))) = k2_partfun1(A,k6_numbers,k3_mesfunc1(A,k10_mesfunc1(A,B),k10_mesfunc1(A,C)),k1_relset_1(A,k10_mesfunc1(A,k3_mesfunc1(A,B,C)))) ) ) ) )).
fof(t20_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(A),B) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [F] : ( v7_ordinal1(F) => ( ( v1_mesfunc8(D,A,k6_numbers) & r1_tarski(C,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,D,k5_numbers))) & ! [G] : ( v7_ordinal1(G) => ( r1_mesfunc1(A,B,k4_mesfunc5(A,k6_numbers,D,G),C) & r2_relset_1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,E,G),k2_partfun1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,D,G),C)) ) ) ) => r1_mesfunc1(A,B,k4_mesfunc5(A,k6_numbers,E,F),C) ) ) ) ) ) ) ) )).
fof(t20_metric_1,axiom,( ! [A] : k1_binop_1(k2_metric_1,A,A) = k5_numbers )).
fof(t20_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k2_metric_2(A)) => ! [C] : ( m1_subset_1(C,k2_metric_2(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r2_hidden(D,B) & r2_hidden(F,C) & r2_hidden(E,B) & r2_hidden(G,C) ) => k3_metric_1(A,D,F) = k3_metric_1(A,E,G) ) ) ) ) ) ) ) ) )).
fof(t20_metric_3,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers)) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k1_numbers,k1_numbers)) => k2_binop_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers,k16_metric_3,A,B) = k2_binop_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers,k16_metric_3,B,A) ) ) )).
fof(t20_metric_6,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ! [D] : ( v1_xreal_0(D) => ( ~ r1_xxreal_0(D,k5_numbers) => r2_metric_6(A,k8_metric_1(A,B,D),C) ) ) <=> ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t20_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_finset_1(B) & v1_card_1(B) ) => ( r1_ordinal1(k2_waybel23(A),B) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v2_tex_2(C,A) => r1_ordinal1(k1_card_1(C),B) ) ) ) ) ) )).
fof(t20_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_rlvect_2(B,k10_funcsdom(k2_finseq_1(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t20_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t20_midsp_2,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & l1_midsp_1(B) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t20_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => r2_hidden(1,k2_finseq_1(k1_nat_1(A,1))) ) )).
fof(t20_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( ( r1_relset_1(A,A,E,F) & r1_tarski(B,C) & r1_relset_1(A,A,D,G) ) => r1_tarski(k8_mmlquery(A,G,B,E),k8_mmlquery(A,D,C,F)) ) ) ) ) ) ) ) )).
fof(t20_mod_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,A) => m1_subset_1(k1_ordinal1(B),A) ) ) )).
fof(t20_mod_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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) ) ) )).
fof(t20_mod_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t20_modal_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) & v3_trees_2(B) ) => ! [C] : ( m1_trees_1(C,k9_xtuple_0(B)) => ! [D] : ( m1_trees_1(D,k9_xtuple_0(B)) => ( ( C = k14_trees_3(k5_numbers) & D = k14_trees_3(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)),k14_trees_3(k5_numbers),k5_trees_2(B,C)),k14_trees_3(1),k5_trees_2(B,D)) ) ) ) ) ) )).
fof(t20_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_1(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_partfun1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,C))) ) => ! [E] : ( m1_subset_1(E,C) => ! [F] : ( ( ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(k30_modelc_1(C))) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t20_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( v3_modelc_2(A) => ( r1_modelc_2(B,A) <=> B = k10_modelc_2(A) ) ) ) ) )).
fof(t20_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_3(B,A) & l1_modelc_3(B,A) ) => ! [C] : ( ( v1_modelc_3(C,A) & l1_modelc_3(C,A) ) => ( r3_modelc_3(A,B,C) => r1_xxreal_0(k18_modelc_3(A,u2_modelc_3(A,C)),k6_xcmplx_0(k18_modelc_3(A,u2_modelc_3(A,B)),1)) ) ) ) ) )).
fof(t20_moebius1,axiom,( ! [A] : ( v7_ordinal1(A) => ( ? [B] : ( v7_ordinal1(B) & ~ v8_ordinal1(B) & B != 1 & r1_nat_d(k1_newton(B,2),A) ) => v1_moebius1(A) ) ) )).
fof(t20_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v22_algstr_0(B) & v4_vectsp_1(B) & m1_monoid_0(B,A) ) => ! [C] : ( ( v22_algstr_0(C) & v4_vectsp_1(C) & m1_monoid_0(C,A) ) => B = C ) ) ) )).
fof(t20_monoid_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_monoid_1(B,A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_monoid_1(B,A))) => ( ! [E] : ( r2_hidden(E,A) => k1_funct_1(C,E) = k1_funct_1(D,E) ) => C = D ) ) ) ) )).
fof(t20_morph_01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t20_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) ) ) )).
fof(t20_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t20_msscyc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_msafree(C,A,B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t20_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t20_mssublat,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v13_struct_0(A,1) & v5_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & m1_msualg_2(C,A,B) ) => m1_unialg_2(k12_msualg_1(A,C),k12_msualg_1(A,B)) ) ) ) )).
fof(t20_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t20_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t20_msualg_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t20_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_rewrite1(k3_msualg_6(A),D,E) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ( r1_msualg_6(A,C,D,B,F) => ! [G] : ( m2_msualg_6(G,A,B,D,E) => m2_msualg_6(k3_relat_1(F,G),A,B,C,E) ) ) ) ) ) ) ) ) ) )).
fof(t20_msualg_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => v4_lattice3(k1_msualg_7(A,B)) ) ) ) )).
fof(t20_msualg_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t20_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(t20_mycielsk,axiom,( ! [A] : ( ( v1_necklace(A) & l1_orders_2(A) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(t20_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,A) => m1_subset_1(k6_xcmplx_0(B,1),k4_ordinal1) ) ) ) )).
fof(t20_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(B,A) => ( r1_xxreal_0(k2_xcmplx_0(B,B),A) | k3_nat_d(A,B) = 1 ) ) ) ) )).
fof(t20_nat_3,axiom,( ! [A] : k8_nat_3(A,k16_pre_poly(A)) = 1 )).
fof(t20_nat_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ~ ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( v1_int_2(C) => r1_xxreal_0(k11_nat_3(A,C),k11_nat_3(B,C)) ) ) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => B != k2_nat_1(A,C) ) ) ) ) )).
fof(t20_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( k4_nat_d(k3_xcmplx_0(A,C),B) = k4_nat_d(k3_xcmplx_0(A,D),B) & v1_int_2(B) ) => ( k5_numbers = A | r1_xxreal_0(B,A) | r1_xxreal_0(B,C) | r1_xxreal_0(B,D) | C = D ) ) ) ) ) ) )).
fof(t20_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( A != k5_numbers => k3_nat_d(k3_xcmplx_0(B,A),A) = B ) ) ) )).
fof(t20_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ( r2_nattra_1(A,B,C,D) => ! [E] : ( m2_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,k4_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,k4_nattra_1(A,B,C),E),E) ) ) ) ) ) ) ) )).
fof(t20_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,k1_relset_1(u1_struct_0(A),C)) => ( ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t20_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t20_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(k2_ndiff_3(A,C,B),D) = k4_struct_0(A) ) ) ) ) ) ) ) )).
fof(t20_ndiff_4,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t20_ndiff_5,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( 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] : ( m1_subset_1(H,u1_struct_0(A)) => ( r2_hidden(H,k1_rltopsp1(A,D,E)) => r1_nfcont_1(A,B,C,H) ) ) & ! [H] : ( 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] : ( m1_subset_1(H,u1_struct_0(A)) => ( r2_hidden(H,k2_ndiff_5(A,D,E)) => r1_xxreal_0(k2_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(k2_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)))),k3_xcmplx_0(F,k2_normsp_0(A,k5_algstr_0(A,E,D)))) ) ) ) ) ) ) ) ) )).
fof(t20_neckla_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_necklace(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t20_necklace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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))) ) ) ) )).
fof(t20_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t20_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(B,A) & C = k6_xcmplx_0(A,B) ) => k3_newton(B,A) = k3_newton(C,A) ) ) ) ) )).
fof(t20_nfcont_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(D,A) & ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ~ ( r2_hidden(G,A) & ~ r1_xxreal_0(F,k2_normsp_0(B,k5_algstr_0(B,G,D))) & r1_xxreal_0(E,k9_complex1(k5_real_1(k7_partfun1(k1_numbers,C,G),k7_partfun1(k1_numbers,C,D)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t20_nfcont_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t20_nfcont_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t20_normform,axiom,( ! [A] : ! [B] : ( 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) ) )).
fof(t20_normsp_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v3_normsp_1(B,A) & v3_normsp_1(C,A) ) => v3_normsp_1(k3_normsp_1(A,B,C),A) ) ) ) ) )).
fof(t20_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_normsp_2(A)))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t20_numbers,axiom,( r1_tarski(k4_ordinal1,k2_numbers) )).
fof(t20_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t20_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( ~ r3_lattices(A,C,B) & ! [D] : ( ( ~ 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(B,D) & r2_hidden(C,D) ) ) ) ) ) ) )).
fof(t20_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t20_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_ordeq_01(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_ordeq_01(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_ordeq_01(A,B))) => ! [F] : ( ( v1_funct_1(F) & v1_nfcont_3(F,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ! [G] : ( ( v1_funct_1(G) & v1_nfcont_3(G,B) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ! [H] : ( ( v1_funct_1(H) & v1_nfcont_3(H,B) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ( ( F = C & G = D & H = E & k1_relset_1(k1_numbers,F) = A & k1_relset_1(k1_numbers,G) = A & k1_relset_1(k1_numbers,H) = A ) => ( E = k5_algstr_0(k5_ordeq_01(A,B),C,D) <=> ! [I] : ( m2_subset_1(I,k1_numbers,A) => k7_partfun1(u1_struct_0(B),H,I) = k5_algstr_0(B,k7_partfun1(u1_struct_0(B),F,I),k7_partfun1(u1_struct_0(B),G,I)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t20_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v3_orders_1(A) => ( v1_orders_1(A) & v2_orders_1(A) ) ) ) )).
fof(t20_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(B,C) & r2_hidden(B,k2_orders_2(A,C)) ) ) ) ) )).
fof(t20_ordinal1,axiom,( ! [A] : ~ ( ! [B] : ( r2_hidden(B,A) => v3_ordinal1(B) ) & ! [B] : ( v3_ordinal1(B) => ~ r1_tarski(A,B) ) ) )).
fof(t20_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ! [C] : ( v3_ordinal1(C) => ( r2_hidden(C,B) => r2_hidden(C,A) ) ) => r1_ordinal1(k3_ordinal2(B),A) ) ) )).
fof(t20_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ! [D] : ( v3_ordinal1(D) => ( ( r1_ordinal1(A,B) & r1_ordinal1(C,D) ) => r1_ordinal1(k11_ordinal2(A,C),k11_ordinal2(B,D)) ) ) ) ) ) )).
fof(t20_ordinal4,axiom,( ! [A] : ( v3_ordinal1(A) => ( A != k1_xboole_0 => k12_ordinal2(k1_xboole_0,A) = k1_xboole_0 ) ) )).
fof(t20_ordinal6,axiom,( ! [A] : k1_card_1(k9_xtuple_0(k2_ordinal6(A))) = k1_card_1(k2_ordinal1(A)) )).
fof(t20_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( ~ r1_orders_2(B,D,C) => ( r1_orders_2(B,E,C) <=> k1_ortsp_1(A,B,C,D,E) = k4_struct_0(A) ) ) ) ) ) ) ) )).
fof(t20_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ( ? [E] : ( 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)) ) ) ) ) ) )).
fof(t20_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ! [C] : ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t20_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_osalg_2(C,A,B) => ( r2_hidden(C,k6_osalg_2(A,B)) <=> v3_msualg_2(C,A,B) ) ) ) ) )).
fof(t20_osalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t20_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_parsp_1(A,B,B,C,D) ) ) ) ) )).
fof(t20_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t20_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,k1_tarski(B)))) ) => ( r2_hidden(A,k1_relset_1(C,D)) => k1_funct_1(D,A) = B ) ) )).
fof(t20_partfun2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t20_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ( r1_setfam_1(B,C) <=> r1_tarski(k4_partit1(A,B),k4_partit1(A,C)) ) ) ) ) )).
fof(t20_partit_2,axiom,( ! [A] : ! [B] : k1_relat_1(k1_partit_2(A,B)) = k1_xboole_0 )).
fof(t20_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( E != C & r1_diraf(A,E,C,D) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_diraf(A,E,B,F) & r2_analoaf(A,C,B,D,F) ) ) ) ) ) ) ) ) )).
fof(t20_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t20_pcomps_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t20_pcs_0,axiom,( ! [A] : ( ( v14_pcs_0(A) & l2_pcs_0(A) ) => ! [B] : ( ( v14_pcs_0(B) & l2_pcs_0(B) ) => ( r1_tsep_1(A,B) => ( v14_pcs_0(k19_pcs_0(A,B)) & l2_pcs_0(k19_pcs_0(A,B)) ) ) ) ) )).
fof(t20_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(A))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t20_pdiff_2,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(2)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t20_pdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(2)) => ! [C] : ( m1_rcomp_1(C,k3_funct_2(k1_euclid(2),k1_numbers,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] : ( ( v9_ordinal1(D) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,E) = k1_tarski(k3_funct_2(k1_euclid(2),k1_numbers,k1_pdiff_1(2,2),B)) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),C) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(2,2,k1_pdiff_3(2,2,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(2,2,k1_pdiff_3(2,2,A),B))))) & k5_pdiff_3(A,B) = k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(2,2,k1_pdiff_3(2,2,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(2,2,k1_pdiff_3(2,2,A),B))))) ) ) ) ) ) ) ) ) )).
fof(t20_pdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) => k10_pdiff_1(3,2,E,D) = k1_fdiff_1(k1_pdiff_2(3,2,E,D),B) ) ) ) ) ) ) )).
fof(t20_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( 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) ) ) ) )).
fof(t20_pdiff_6,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(B),k1_euclid(A)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(B),k1_euclid(A)))) ) => ! [E] : ( 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))) ) ) ) ) ) ) ) )).
fof(t20_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(1))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(1))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t20_pdiff_8,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k4_real_ns1(A)))) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( 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)),k14_pdiff_1(A,B,E,C,D),D) ) <=> ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ( 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)),k14_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) ) ) ) ) ) ) ) ) ) ) )).
fof(t20_pdiff_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k16_lopban_1(k4_real_ns1(1),k4_real_ns1(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(1))) => k2_normsp_0(k4_real_ns1(A),k17_lopban_1(k4_real_ns1(1),k4_real_ns1(A),B,C)) = k3_xcmplx_0(k2_normsp_0(k16_lopban_1(k4_real_ns1(1),k4_real_ns1(A)),B),k2_normsp_0(k4_real_ns1(1),C)) ) ) ) )).
fof(t20_pencil_1,axiom,( ! [A] : ( ( v6_pencil_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_pre_topc(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = B => v1_pencil_1(C,A) ) ) ) ) )).
fof(t20_pencil_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t20_pencil_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v15_pencil_1(B) ) => ! [C] : ( m1_pencil_2(C,A,B) => ! [D] : ( m1_pencil_2(D,A,B) => ( r1_pencil_3(A,B,C,D) => ! [E] : ( ( 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] : ( m1_pencil_2(F,A,B) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t20_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( 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)) ) ) ) ) ) )).
fof(t20_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t20_pnproc_1,axiom,( ! [A] : ! [B] : ( m1_pnproc_1(B,A) => r1_tarski(k10_xtuple_0(k7_pnproc_1(A,B)),k9_funct_2(A,k4_ordinal1)) ) )).
fof(t20_polyalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_polyalg1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) => ( ! [E] : ( r2_hidden(E,D) <=> ( r1_tarski(E,u1_struct_0(B)) & ? [F] : ( 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) ) ) ) ) ) )).
fof(t20_polyeq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( A != k5_numbers & ~ r1_xxreal_0(k1_quin_1(A,B,C),k5_numbers) & k4_polyeq_1(k5_numbers,A,B,C,D) = k5_numbers & D != k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A)) & D != k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A)) ) ) ) ) ) )).
fof(t20_polyeq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( k1_square_1(B) = A & k4_complex1(A) = k5_numbers & ~ r1_xxreal_0(k3_complex1(A),k5_numbers) & B != k3_square_1(k3_complex1(A)) & B != k4_xcmplx_0(k3_square_1(k3_complex1(A))) ) ) ) )).
fof(t20_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => ( E != k5_numbers => ( k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(E,k1_newton(A,3)),k3_xcmplx_0(D,k1_newton(A,2))),k3_xcmplx_0(C,A)),B) = k5_numbers <=> ~ ( A != k2_polyeq_5(k7_xcmplx_0(B,E),k7_xcmplx_0(C,E),k7_xcmplx_0(D,E)) & A != k3_polyeq_5(k7_xcmplx_0(B,E),k7_xcmplx_0(C,E),k7_xcmplx_0(D,E)) & A != k4_polyeq_5(k7_xcmplx_0(B,E),k7_xcmplx_0(C,E),k7_xcmplx_0(D,E)) ) ) ) ) ) ) ) ) )).
fof(t20_polyform,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ! [B] : ( m2_finseq_1(B,k4_numbers) => ! [C] : ( 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)) ) ) ) )).
fof(t20_polynom1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( 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(k3_polynom1(k15_pre_poly(A),B,k5_polynom1(A,B,C,D)),k4_subset_1(k15_pre_poly(A),k3_polynom1(k15_pre_poly(A),B,C),k3_polynom1(k15_pre_poly(A),B,D))) ) ) ) )).
fof(t20_polynom3,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(k3_finseq_1(A),B) => k18_rvsum_1(k17_finseq_1(k1_numbers,k1_nat_1(B,1),A)) = k2_xcmplx_0(k18_rvsum_1(k17_finseq_1(k1_numbers,B,A)),k1_funct_1(A,k1_nat_1(B,1))) ) ) ) )).
fof(t20_polynom4,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_polynom4(A,k5_vfunct_1(k4_ordinal1,A,B),C) = k4_algstr_0(A,k2_polynom4(A,B,C)) ) ) ) )).
fof(t20_polynom5,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k4_ordinal1) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k2_polynom5(A,k9_polynom3(A),k1_nat_1(B,1)),k9_polynom3(A)) ) ) )).
fof(t20_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ 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)),k9_polynom1(A,B)) ) )).
fof(t20_polynom8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( 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))) ) ) ) ) )).
fof(t20_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v7_struct_0(B) & v1_vectsp_2(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( ( ~ v9_struct_0(D,B) & m1_subset_1(D,u1_struct_0(B)) ) => r1_tarski(k3_polynom1(k15_pre_poly(A),B,C),k3_polynom1(k15_pre_poly(A),B,k5_polynom7(A,B,C,D))) ) ) ) ) )).
fof(t20_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( r1_xxreal_0(k5_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)) ) ) ) ) ) )).
fof(t20_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,u4_struct_0(B)) => ( k1_msualg_1(B,E) != k1_xboole_0 => ! [F] : ( ( v4_msualg_1(F,B) & l3_msualg_1(F,B) ) => ! [G] : ( m1_subset_1(G,k3_msualg_1(B,E,k14_pralg_2(A,B,C))) => m1_subset_1(k1_funct_1(k9_funct_6(G),D),k3_msualg_1(B,E,k5_pralg_2(A,B,C,D))) ) ) ) ) ) ) ) ) )).
fof(t20_pre_circ,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_tarski(k9_xtuple_0(A),k9_xtuple_0(B)) <=> r2_tarski(A,B) ) ) ) )).
fof(t20_pre_ff,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( k3_pre_ff(D) = k1_nat_1(k2_nat_1(B,k3_pre_ff(k3_xcmplx_0(2,A))),k2_nat_1(C,k3_pre_ff(k1_nat_1(k3_xcmplx_0(2,A),1)))) => k3_pre_ff(D) = k1_nat_1(k2_nat_1(k2_xcmplx_0(B,C),k3_pre_ff(A)),k2_nat_1(C,k3_pre_ff(k1_nat_1(A,1)))) ) ) ) ) ) )).
fof(t20_pre_poly,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ( ( r2_hidden(D,B) & r3_orders_1(C,B) & ! [E] : ( 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 ) ) ) ) ) )).
fof(t20_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t20_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t20_prepower,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => k2_prepower(A,1) = 1 ) ) )).
fof(t20_prob_1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => m1_prob_1(k3_subset_1(A,C),A,B) ) ) )).
fof(t20_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m1_prob_1(E,A,B) => ! [F] : ( m2_prob_1(F,A,B) => ( r2_prob_2(A,B,F,C,D,E) <=> ( k3_funct_2(B,k1_numbers,F,k5_prob_1(A,B,k5_prob_1(A,B,C,D),E)) = k4_real_1(k4_real_1(k3_funct_2(B,k1_numbers,F,C),k3_funct_2(B,k1_numbers,F,D)),k3_funct_2(B,k1_numbers,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) ) ) ) ) ) ) ) ) )).
fof(t20_prob_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k1_kurato_0(A,k3_prob_3(A,B)) = k1_kurato_0(A,B) ) )).
fof(t20_prob_4,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(C) => ( k1_prob_4(A,B,k3_prob_3(A,C),k5_numbers) = k1_prob_4(A,B,C,k5_numbers) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => k1_prob_4(A,B,k3_prob_3(A,C),k1_nat_1(D,1)) = k3_measure1(A,B,k1_prob_4(A,B,C,k1_nat_1(D,1)),k1_prob_4(A,B,C,D)) ) ) ) ) ) )).
fof(t20_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t20_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ! [L] : ( m1_subset_1(L,u1_struct_0(A)) => ~ ( r1_projdes1(A,B,D,F,I) & ~ r1_projdes1(A,B,D,F,G) & ~ r1_projdes1(A,B,D,G,I) & r1_collsp(A,I,G,H) & r1_collsp(A,I,B,C) & r1_collsp(A,I,D,E) & r1_collsp(A,B,G,J) & r1_collsp(A,C,H,J) & r1_collsp(A,D,G,K) & r1_collsp(A,E,H,K) & r1_collsp(A,F,G,L) & I != C & G != H & I != E & r1_collsp(A,J,K,L) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t20_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u2_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u2_incsp_1(A)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t20_projred1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u2_incsp_1(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t20_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u2_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u2_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u2_incsp_1(A)) => ! [H] : ( 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,H) & ~ r1_incsp_1(A,C,H) & D != H & B != C & r1_incsp_1(A,B,G) & r1_incsp_1(A,C,G) & ! [I] : ( m1_subset_1(I,u1_incsp_1(A)) => ~ ( r1_incsp_1(A,I,G) & ~ r1_incsp_1(A,I,D) & ~ r1_incsp_1(A,I,H) & k3_relat_1(k1_projred1(A,D,F,B),k1_projred1(A,F,E,C)) = k3_relat_1(k1_projred1(A,D,H,I),k1_projred1(A,H,E,C)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t20_prvect_3,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( ( v1_relat_1(B) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finseq_1(B) & v2_prvect_2(B) ) => ? [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(k14_prvect_2(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_prvect_2(B))) => ? [F] : ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) & ? [G] : ( 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] : ( m1_subset_1(D,u1_struct_0(k14_prvect_2(k10_finseq_1(k14_prvect_2(A),k14_prvect_2(B))))) => ! [E] : ( 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] : ( m1_subset_1(D,u1_struct_0(k14_prvect_2(k10_finseq_1(k14_prvect_2(A),k14_prvect_2(B))))) => ! [E] : ( 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] : ( m1_subset_1(D,u1_struct_0(k14_prvect_2(k10_finseq_1(k14_prvect_2(A),k14_prvect_2(B))))) => k2_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)) = k2_normsp_0(k14_prvect_2(k10_finseq_1(k14_prvect_2(A),k14_prvect_2(B))),D) ) ) ) ) )).
fof(t20_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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,B,C) ) ) ) )).
fof(t20_qc_lang1,axiom,( ! [A] : ( 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] : ( 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) ) ) ) ) ) )).
fof(t20_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t20_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ( v6_qc_lang1(k12_qc_lang1(A),A) & v6_qc_lang1(k1_qc_lang2(A),A) ) ) )).
fof(t20_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( r2_qc_lang2(A,C,B) <=> k3_qc_lang4(A,B,C) != k1_xboole_0 ) ) ) ) )).
fof(t20_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) ) => ? [C] : ( v4_card_3(C) & m1_qc_lang1(C) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(C))) & v1_qc_trans(A,C) ) ) ) )).
fof(t20_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k23_quaterni(k24_quaterni(A),B) = k24_quaterni(k23_quaterni(A,B)) ) ) )).
fof(t20_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k25_quaterni(k23_quaterni(k11_quaterni,A),k23_quaterni(A,k11_quaterni)) = k6_quaterni(k5_numbers,k3_xcmplx_0(2,k16_quaterni(A)),k5_numbers,k4_xcmplx_0(k3_xcmplx_0(2,k14_quaterni(A)))) ) )).
fof(t20_quaterni,axiom,( k10_quaterni(k11_quaterni,k12_quaterni) = k8_quaterni(k10_quaterni(k12_quaterni,k11_quaterni)) )).
fof(t20_quin_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( ( k1_quin_1(A,B,C) = k5_numbers & k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k1_square_1(D)),k3_xcmplx_0(B,D)),C) = k5_numbers ) => ( A = k5_numbers | D = k4_xcmplx_0(k7_xcmplx_0(B,k3_xcmplx_0(2,A))) ) ) ) ) ) ) )).
fof(t20_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t20_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_radix_1(1,B,A) => k4_radix_1(1,A,1,k10_radix_1(A,1,B)) = B ) ) ) )).
fof(t20_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(D,k2_finseq_1(A)) & r1_xxreal_0(2,C) ) => k7_radix_3(D,C,k2_xcmplx_0(k2_xcmplx_0(A,1),1),k10_radix_3(k2_xcmplx_0(A,1),C,k10_radix_1(C,k2_xcmplx_0(A,1),B))) = k7_radix_3(D,C,k2_xcmplx_0(A,1),k10_radix_3(A,C,k10_radix_1(C,A,k4_nat_d(B,k1_newton(k1_radix_1(C),A))))) ) ) ) ) ) )).
fof(t20_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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)),k5_numbers) & r1_xxreal_0(k8_radix_1(k2_xcmplx_0(A,2),C,k8_radix_6(A,C,D)),k5_numbers) ) ) ) ) ) ) )).
fof(t20_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_random_1(C,A,B) => ! [D] : ( v1_xreal_0(D) => m1_random_1(k26_valued_1(A,k1_numbers,C,D),A,B) ) ) ) ) )).
fof(t20_random_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v2_finset_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v7_random_3(B,A,k7_random_3(A)) ) => ! [C] : ( v7_ordinal1(C) => m2_prob_1(k1_funct_1(k9_random_3(A,B),C),k1_funct_1(k5_random_3(A),C),k1_random_1(k1_funct_1(k5_random_3(A),C))) ) ) ) )).
fof(t20_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(t20_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ( k2_rat_1(A) = k1_rat_1(A) <=> A = 1 ) ) )).
fof(t20_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( m1_ratfunc1(B,A) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t20_rcomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( ! [B] : ( m1_subset_1(B,k1_numbers) => ~ ( r2_hidden(B,A) & ! [C] : ( m1_rcomp_1(C,B) => ~ r1_tarski(C,A) ) ) ) => v3_rcomp_1(A) ) ) )).
fof(t20_rcomp_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v4_xxreal_2(A) => r1_tarski(A,k1_limfunc1(k2_seq_4(A))) ) ) )).
fof(t20_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( A != k5_numbers => k7_xcmplx_0(B,A) = k2_xcmplx_0(k9_nat_1(k4_ordinal1,k2_real_3(B,A),k5_numbers),k7_xcmplx_0(1,k7_xcmplx_0(A,k9_nat_1(k4_ordinal1,k1_real_3(B,A),k5_numbers)))) ) ) ) )).
fof(t20_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( m2_funct_2(C,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t20_realset2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_algstr_0(A,B,C) = k6_algstr_0(A,C,B) ) ) ) )).
fof(t20_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) )).
fof(t20_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [D] : ( ( v1_rearran1(D) & v2_rearran1(D) & v3_rearran1(D,k1_zfmisc_1(A)) & m2_finseq_1(D,k1_zfmisc_1(A)) ) => ( ( v1_partfun1(C,B) & k5_card_1(A) = k5_card_1(B) ) => k1_relset_1(A,k4_rearran1(B,A,D,C)) = A ) ) ) ) ) )).
fof(t20_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => r1_tarski(k10_xtuple_0(k3_relat_1(A,B)),k10_xtuple_0(B)) ) ) )).
fof(t20_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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,C))) ) )).
fof(t20_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t20_revrot_1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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))) ) ) ) )).
fof(t20_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r1_rewrite1(A,B,C) <=> ( B = C | r2_hidden(k4_tarski(B,C),k18_finseq_1(A)) ) ) ) )).
fof(t20_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ~ r2_rewrite2(A,k1_partit_2(k8_afinsq_1(A),k8_afinsq_1(A)),B,C) ) ) )).
fof(t20_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(E))) => ! [G] : ( 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))) ) ) ) ) ) )).
fof(t20_rfinseq,axiom,( ! [A] : ( ( v8_valued_0(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( v8_valued_0(k17_finseq_1(k1_numbers,B,A)) & m2_finseq_1(k17_finseq_1(k1_numbers,B,A),k1_numbers) ) ) ) )).
fof(t20_rfinseq2,axiom,( ! [A] : ( ( v8_valued_0(A) & m2_finseq_1(A,k1_numbers) ) => k5_rfinseq2(A) = A ) )).
fof(t20_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t20_rfunct_2,axiom,( ! [A] : ! [B] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( 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_funct_1(B,D),k1_funct_1(B,C)) ) ) ) ) ) )).
fof(t20_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,k3_rfunct_3(A,k1_numbers)) => ! [C] : ( 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)) ) ) ) )).
fof(t20_rfunct_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v6_xxreal_2(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( v1_xreal_0(C) => ( r2_rfunct_3(A,B) => ( ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(D,B) & r2_hidden(E,B) & ~ r1_xxreal_0(C,D) & ~ r1_xxreal_0(E,C) ) ) ) | r1_fcont_1(A,C) ) ) ) ) ) )).
fof(t20_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_seq_2(A) & v4_partfun3(A) & v2_seq_2(B) & v4_partfun3(B) ) => ( v2_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) & r1_xxreal_0(k3_xcmplx_0(k2_rinfsup1(A),k2_rinfsup1(B)),k2_rinfsup1(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B))) ) ) ) ) )).
fof(t20_rinfsup2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v7_mesfunc5(B) => ( v7_mesfunc5(k1_valued_0(k6_numbers,B,A)) & v10_mesfunc5(k1_valued_0(k6_numbers,B,A)) & k2_mesfunc5(B) = k2_mesfunc5(k1_valued_0(k6_numbers,B,A)) ) ) ) ) )).
fof(t20_ring_1,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t20_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_ringcat1(A) ) => ! [B] : ( m3_ringcat1(B,k10_ringcat1(A)) => ! [C] : ( m3_ringcat1(C,k10_ringcat1(A)) => ( k11_ringcat1(A,B) = k12_ringcat1(A,C) => r2_hidden(k6_ringcat1(B,C),k10_ringcat1(A)) ) ) ) ) )).
fof(t20_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_rlvect_2(A,k1_rlaffin1(A,k4_rlvect_2(A),B),k4_rlvect_2(A)) ) ) )).
fof(t20_rlaffin2,axiom,( ! [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) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t20_rlaffin3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_finset_1(C) & v1_rlaffin1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( m2_rlaffin3(D,B,C) => ! [E] : ( 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] : ( 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) = k5_numbers ) ) ) ) ) ) ) ) )).
fof(t20_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t20_rlsub_2,axiom,( ! [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) ) => ! [B] : ( ( 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 ) ) ) )).
fof(t20_rltopsp1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t20_rlvect_1,axiom,( ! [A] : ( ( ~ 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) & v8_rlvect_1(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( k1_algstr_0(A,B,B) = k4_struct_0(A) => B = k4_struct_0(A) ) ) ) )).
fof(t20_rlvect_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k1_numbers,k4_rlvect_2(A),B) = k5_numbers ) ) )).
fof(t20_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t20_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t20_rlvect_5,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => k1_rlvect_3(A,C) = k1_rlvect_3(B,D) ) ) ) ) ) )).
fof(t20_rlvect_x,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_hidden(B,k2_rlvect_x(A,k7_domain_1(u1_struct_0(A),B,C))) ) ) ) )).
fof(t20_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t20_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t20_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => m2_rmod_4(k3_rmod_4(A,B),A,B,C) ) ) ) )).
fof(t20_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_robbins1(A,B,k6_robbins1(A,B,C)) = B ) ) ) )).
fof(t20_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t20_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_robbins1(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t20_robbins4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k2_robbins4)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_robbins4)) => ( ( A = k6_subset_1(3,2) & B = 1 ) => k3_lattices(k2_robbins4,A,B) = 3 ) ) ) )).
fof(t20_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => k3_roughs_1(A,k2_struct_0(A)) = k2_struct_0(A) ) )).
fof(t20_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k1_rpr_1(A,k4_subset_1(A,B,C)) = k6_xcmplx_0(k2_xcmplx_0(k1_rpr_1(A,B),k1_rpr_1(A,C)),k1_rpr_1(A,k9_subset_1(A,B,C))) ) ) ) )).
fof(t20_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_rsspace4(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_rsspace4(A,B))) => ! [E] : ( ( 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] : ( ( 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] : ( v1_xreal_0(G) => ( D = k1_rlvect_1(k9_rsspace4(A,B),C,G) <=> ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t20_rusub_1,axiom,( ! [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_bhsp_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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 ) ) ) )).
fof(t20_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( 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 ) ) ) )).
fof(t20_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rlvect_2(C,A) => ~ ( r1_tarski(k3_rlvect_2(A,C),u1_struct_0(B)) & ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t20_rusub_4,axiom,( ! [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_bhsp_1(A) & v1_rusub_4(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(B,k1_rusub_4(A)) => k2_rusub_4(A,B) = k1_xboole_0 ) ) ) )).
fof(t20_rusub_5,axiom,( ! [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) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_rusub_4(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : ( ~ 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) ) ) ) )).
fof(t20_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => k6_rvsum_1(k9_finseq_1(A)) = k9_finseq_1(k4_xcmplx_0(A)) ) )).
fof(t20_rvsum_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k2_numbers) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k2_numbers) ) => C = k4_rvsum_2(A,k8_rvsum_2(A,C,B),B) ) ) ) )).
fof(t20_scm_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( r1_tarski(k1_ordinal4(k5_afinsq_1(k7_ami_3(1)),k5_afinsq_1(k2_compos_1(k1_ami_3))),A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( ( v5_memstr_0(D,k7_card_1(2),k1_ami_3,k5_numbers) & m1_scm_1(D,k6_afinsq_1(B,C)) ) => ( r1_extpro_1(k7_card_1(2),k1_ami_3,A,D) & k8_extpro_1(k7_card_1(2),k1_ami_3,A,D) = 1 & ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_ami_3)) ) => k1_funct_1(k6_extpro_1(k7_card_1(2),k1_ami_3,A,D),E) = k1_funct_1(D,E) ) ) ) ) ) ) ) )).
fof(t20_scmbsort,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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) ) ) )).
fof(t20_scmfsa10,axiom,( ! [A] : ( 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) ) ) )).
fof(t20_scmfsa6a,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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)) ) ) ) )).
fof(t20_scmfsa7b,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ( ~ r3_scmfsa7b(A,B) => k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C),B) = k1_funct_1(C,B) ) ) ) ) )).
fof(t20_scmfsa8a,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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] : ( v7_ordinal1(E) => ( r1_xxreal_0(E,k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A))) => ( k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k2_scmfsa6a(C)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),E)) = k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k3_scmfsa6a(C,D)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),E)) & k3_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k2_scmfsa6a(C)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k2_scmfsa6a(C)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),E)) = k3_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k3_scmfsa6a(C,D)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k3_scmfsa6a(C,D)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),E)) ) ) ) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k2_scmfsa6a(C)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A)),1))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k3_scmfsa6a(C,D)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A)),1))) & k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k2_scmfsa6a(C)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A)),1))) = k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k3_scmfsa6a(C,D)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A)),1))) ) ) ) ) ) ) )).
fof(t20_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( 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),k5_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) ) ) ) ) ) ) ) )).
fof(t20_scmfsa8c,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ~ r1_xxreal_0(k1_nat_1(k1_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) ) ) ) ) ) ) )).
fof(t20_scmfsa_1,axiom,( r1_subset_1(k3_scmfsa_1,k1_ami_2) )).
fof(t20_scmfsa_2,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( 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 ) ) ) )).
fof(t20_scmfsa_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( v1_ami_2(D) & ~ v1_scmfsa_m(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( v7_ordinal1(E) => r6_pboole(u1_struct_0(k1_scmfsa_2),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(B,C,D,A),k1_nat_1(E,1)),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(B,C,D,A),E),C,D,A),1)) ) ) ) ) ) )).
fof(t20_scmfsa_m,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ( ( k1_funct_1(A,k4_scmfsa_2(k5_numbers)) = k1_funct_1(B,k4_scmfsa_2(k5_numbers)) & ! [C] : ( ( 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] : ( m1_scmfsa_2(C) => k18_scmfsa_2(A,C) = k18_scmfsa_2(B,C) ) ) => k6_memstr_0(k7_card_1(3),k1_scmfsa_2,A) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,B) ) ) ) )).
fof(t20_scmisort,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( v1_ami_2(B) & ~ v1_scmfsa_m(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ( ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ~ ( 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),k5_numbers) ) ) ) => v2_scm_halt(k2_scmfsa_9(B,A)) ) ) ) )).
fof(t20_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmpds_2)) ) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t20_scmpds_4,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_scmpds_4(A,B) & r1_xxreal_0(B,C) ) => r1_scmpds_4(A,C) ) ) ) ) )).
fof(t20_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) & v2_compos_1(B,k1_scmpds_2) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t20_scmpds_7,axiom,( ! [A] : ( ( 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] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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) ) ) ) ) ) )).
fof(t20_scmpds_8,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ( r1_xxreal_0(k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),E)),k5_numbers) => k5_memstr_0(2,k1_scmpds_2,k6_scmpds_4(k2_scmpds_8(D,E,C),B,A)) = k1_nat_1(k5_card_1(C),2) ) ) ) ) ) ) )).
fof(t20_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmring2(A))) => ( v2_extpro_1(B,k7_card_1(2),k1_scmring2(A)) => B = k2_compos_1(k1_scmring2(A)) ) ) ) )).
fof(t20_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t20_scmyciel,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) ) => r2_hidden(k1_xboole_0,A) ) )).
fof(t20_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t20_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B),C),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,C),k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C))) ) ) ) )).
fof(t20_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(A) & v2_comseq_2(B) & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(k1_funct_1(A,D),k1_funct_1(C,D)) & r1_xxreal_0(k1_funct_1(C,D),k1_funct_1(B,D)) ) ) & k1_seq_2(A) = k1_seq_2(B) ) => k1_seq_2(C) = k1_seq_2(A) ) ) ) ) )).
fof(t20_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(B) => k1_seq_2(k1_valued_0(k1_numbers,B,A)) = k1_seq_2(B) ) ) ) )).
fof(t20_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ! [D] : ( ( 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] : ( m1_subset_1(E,A) => ( r2_hidden(E,C) => ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( v7_ordinal1(G) => ? [H] : ( v7_ordinal1(H) & r1_xxreal_0(G,H) & r1_xxreal_0(F,k9_complex1(k6_xcmplx_0(k1_funct_1(k1_seqfunc(A,k1_numbers,B,H),E),k1_funct_1(D,E)))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t20_seqm_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k1_valued_0(k1_numbers,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C),A) = k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k1_valued_0(k1_numbers,B,A),k1_valued_0(k1_numbers,C,A)) ) ) ) )).
fof(t20_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,A,C)) & r1_xxreal_0(k9_nat_1(k1_numbers,A,C),k9_nat_1(k1_numbers,B,C)) ) ) & v1_series_1(B) ) => ( v1_series_1(A) & r1_xxreal_0(k4_series_1(A),k4_series_1(B)) ) ) ) ) )).
fof(t20_series_3,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ( k2_xcmplx_0(A,B) = 1 => r1_xxreal_0(9,k3_xcmplx_0(k2_xcmplx_0(1,k7_xcmplx_0(1,A)),k2_xcmplx_0(1,k7_xcmplx_0(1,B)))) ) ) ) )).
fof(t20_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => r1_xxreal_0(3,k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,B),k7_xcmplx_0(B,C)),k7_xcmplx_0(C,A))) ) ) ) )).
fof(t20_setfam_1,axiom,( ! [A] : r1_setfam_1(A,k2_setfam_1(A,A)) )).
fof(t20_setlim_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(A,k1_funct_1(k4_setlim_1(B,C),D)) <=> ? [E] : ( v7_ordinal1(E) & r2_hidden(A,k1_funct_1(C,k2_xcmplx_0(D,E))) ) ) ) ) )).
fof(t20_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => k8_nat_1(k9_setfam_1(B),k9_setlim_2(B,D,C),A) = k9_setlim_2(B,k8_nat_1(k9_setfam_1(B),D,A),C) ) ) ) )).
fof(t20_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ( v1_binop_1(C,B) & v2_binop_1(C,B) & v3_binop_1(C,B) ) => ! [E] : ( m1_subset_1(E,k5_finsub_1(A)) => ! [F] : ( m1_subset_1(F,k5_finsub_1(A)) => ( r1_tarski(E,F) => ( E = k1_xboole_0 | k5_binop_1(B,C,k7_setwiseo(A,B,C,E,D),k7_setwiseo(A,B,C,F,D)) = k7_setwiseo(A,B,C,F,D) ) ) ) ) ) ) ) ) ) )).
fof(t20_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t20_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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))) ) ) )).
fof(t20_sfmastr2,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ( ( r1_xxreal_0(k1_funct_1(A,C),k5_numbers) & k1_funct_1(A,k4_scmfsa_2(k5_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)) ) ) ) ) ) )).
fof(t20_sgraph1,axiom,( ! [A] : ! [B] : ( m1_sgraph1(B,A) => ! [C] : ! [D] : ( 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 ) ) ) )).
fof(t20_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & v3_sheffer1(A) & l3_lattices(A) ) => k6_lattices(A) = k1_sheffer1(A) ) )).
fof(t20_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,B,C) = k5_sheffer1(A,C,B) ) ) ) )).
fof(t20_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v1_matroid0(A) & v1_finset_1(u1_pre_topc(A)) ) => v2_simplex0(A) ) ) )).
fof(t20_simplex1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( ~ 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(k2_xcmplx_0(A,1),B,C) = k4_simplex1(B,k5_simplex1(A,B,C)) ) ) ) ) )).
fof(t20_simplex2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( 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(k2_xcmplx_0(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(k2_xcmplx_0(A,B)))))) ) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(B))) => k1_binop_1(C,D,E) = k7_finseq_1(D,E) ) ) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k14_euclid(B))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k14_euclid(k2_xcmplx_0(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(k2_xcmplx_0(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(k2_xcmplx_0(A,B),G,D) ) ) ) ) ) ) ) ) ) )).
fof(t20_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k9_complex1(k9_nat_1(k1_numbers,k3_series_1(k55_valued_1(k4_ordinal1,k2_numbers,k12_sin_cos(B,A,C))),D)) = k9_nat_1(k1_numbers,k3_series_1(k55_valued_1(k4_ordinal1,k2_numbers,k12_sin_cos(B,A,C))),D) ) ) ) ) )).
fof(t20_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k1_funct_1(k3_sin_cos2,k2_xcmplx_0(A,B)) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(k3_sin_cos2,A),k1_funct_1(k3_sin_cos2,B)),k3_xcmplx_0(k1_funct_1(k1_sin_cos2,A),k1_funct_1(k1_sin_cos2,B))) & k1_funct_1(k3_sin_cos2,k6_xcmplx_0(A,B)) = k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(k3_sin_cos2,A),k1_funct_1(k3_sin_cos2,B)),k3_xcmplx_0(k1_funct_1(k1_sin_cos2,A),k1_funct_1(k1_sin_cos2,B))) ) ) ) )).
fof(t20_sin_cos3,axiom,( k15_sin_cos(k5_complex1) = 1 )).
fof(t20_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( k19_sin_cos(A) != k5_numbers & k19_sin_cos(B) != k5_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(k19_sin_cos(A),k19_sin_cos(B))) ) ) ) )).
fof(t20_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => k1_square_1(k17_sin_cos(A)) = k7_xcmplx_0(k6_xcmplx_0(1,k19_sin_cos(k3_xcmplx_0(2,A))),2) ) )).
fof(t20_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ( ( r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)),A) & r1_xxreal_0(A,k2_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B))) ) => r1_xxreal_0(k5_numbers,k19_sin_cos(A)) ) ) ) )).
fof(t20_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) & r1_xxreal_0(k7_xcmplx_0(k2_xcmplx_0(1,k1_square_1(A)),k6_xcmplx_0(1,k1_square_1(A))),1) ) ) )).
fof(t20_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_sin_cos2(k6_xcmplx_0(A,B)),k2_sin_cos2(A)),k2_sin_cos2(k2_xcmplx_0(A,B))),k2_xcmplx_0(k2_xcmplx_0(k4_sin_cos2(k6_xcmplx_0(A,B)),k4_sin_cos2(A)),k4_sin_cos2(k2_xcmplx_0(A,B)))) = k6_sin_cos2(A) ) ) )).
fof(t20_sin_cos9,axiom,( ! [A] : ( r2_hidden(A,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos))) => r2_hidden(k1_funct_1(k27_sin_cos,A),k1_rcomp_1(k4_xcmplx_0(1),1)) ) )).
fof(t20_sincos10,axiom,( v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k4_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(t20_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ~ ( v2_funct_1(B) & r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(B)) & v1_zfmisc_1(k2_topreal1(2,B,A)) ) ) ) )).
fof(t20_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t20_sprect_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t20_sprect_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t20_sprect_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t20_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(t20_square_1,axiom,( k3_square_1(4) = 2 )).
fof(t20_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(t20_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k7_card_1(B),k7_card_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(B),k7_card_1(A)))) ) => ( ( v2_funct_2(C,k7_card_1(A)) & v1_stirl2_1(C,B,A) & B = A ) => C = k6_partfun1(B) ) ) ) ) )).
fof(t20_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k16_substut1(A),k38_substut1(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t20_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( ( r1_tarski(B,C) & r1_tarski(B,k3_subset_1(A,C)) ) => B = k1_xboole_0 ) ) )).
fof(t20_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( 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)) ) ) )).
fof(t20_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k16_substut1(A),k3_qc_lang1(A))) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(k16_substut1(A),k3_qc_lang1(A))) => ! [D] : ( m1_substut1(D,A,B) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t20_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t20_supinf_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => ! [C] : ( ( 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(k6_numbers,A,B,C)) & ~ r1_xxreal_0(k11_supinf_2(k6_numbers,A,B,C),k2_supinf_1) ) ) ) ) ) )).
fof(t20_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( r1_orders_2(B,F,D) & r1_orders_2(B,F,E) ) => ( r1_orders_2(B,D,C) | k1_symsp_1(A,B,k3_rlvect_1(B,C,F),D,E) = k1_symsp_1(A,B,C,D,E) ) ) ) ) ) ) ) ) )).
fof(t20_sysrel,axiom,( ! [A] : ! [B] : ( 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)) ) ) ) )).
fof(t20_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),k1_numbers))) ) => ! [C] : ! [D] : ( ( v1_taxonom1(B,A) & v2_metric_1(B,A) & v3_metric_1(B,A) & r2_hidden(k4_tarski(C,D),k1_taxonom1(A,B,k5_numbers)) ) => C = D ) ) ) )).
fof(t20_taylor_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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_funct_1(B,A),k5_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) = k7_xcmplx_0(k1_fdiff_1(B,A),k1_funct_1(B,A)) ) ) ) ) ) )).
fof(t20_taylor_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(B,k5_numbers) => ( k3_funct_2(k4_ordinal1,k1_numbers,k1_taylor_2(k16_sin_cos,k2_rcomp_1(k4_xcmplx_0(B),B),C),k2_nat_1(2,A)) = k5_numbers & k3_funct_2(k4_ordinal1,k1_numbers,k1_taylor_2(k16_sin_cos,k2_rcomp_1(k4_xcmplx_0(B),B),C),k1_nat_1(k2_nat_1(2,A),1)) = k7_xcmplx_0(k3_xcmplx_0(k1_newton(k4_xcmplx_0(1),A),k1_newton(C,k1_nat_1(k2_nat_1(2,A),1))),k2_newton(k1_nat_1(k2_nat_1(2,A),1))) & k3_funct_2(k4_ordinal1,k1_numbers,k1_taylor_2(k18_sin_cos,k2_rcomp_1(k4_xcmplx_0(B),B),C),k2_nat_1(2,A)) = k7_xcmplx_0(k3_xcmplx_0(k1_newton(k4_xcmplx_0(1),A),k1_newton(C,k2_nat_1(2,A))),k2_newton(k2_nat_1(2,A))) & k3_funct_2(k4_ordinal1,k1_numbers,k1_taylor_2(k18_sin_cos,k2_rcomp_1(k4_xcmplx_0(B),B),C),k1_nat_1(k2_nat_1(2,A),1)) = k5_numbers ) ) ) ) ) )).
fof(t20_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k1_tarski(B) => k3_tbsp_1(A,C) = k5_numbers ) ) ) )).
fof(t20_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => v6_tops_1(k1_struct_0(A),A) ) )).
fof(t20_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t20_tdlat_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) )).
fof(t20_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => r1_tarski(k3_polynom1(k15_pre_poly(A),C,k5_termord(A,B,C,D)),k3_polynom1(k15_pre_poly(A),C,D)) ) ) ) ) )).
fof(t20_tex_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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) ) ) ) ) ) ) )).
fof(t20_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t20_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tex_3(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( m1_pre_topc(B,C) => ( v2_tex_3(B,C) & m1_pre_topc(B,C) ) ) ) ) ) )).
fof(t20_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v3_tex_4(k2_tex_4(A,B),A) ) ) )).
fof(t20_tietze,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(u1_struct_0(A),k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(u1_struct_0(A),k1_numbers)))) ) => ( ( r3_seqfunc(u1_struct_0(A),B,u1_struct_0(A)) & ! [C] : ( v7_ordinal1(C) => ( 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)))) ) ) ) ) )).
fof(t20_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t20_toler_1,axiom,( ! [A] : ! [B] : ( ( 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] : ! [D] : ~ ( r2_hidden(k4_tarski(C,D),B) & ! [E] : ( ( v1_toler_1(E,A,B) & m1_toler_1(E,A,B) ) => ~ ( r2_hidden(C,E) & r2_hidden(D,E) ) ) ) ) )).
fof(t20_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t20_topalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v2_pre_topc(D) & l1_pre_topc(D) ) => ! [E] : ( ( ~ v2_struct_0(E) & v2_pre_topc(E) & l1_pre_topc(E) ) => ! [F] : ( ( 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] : ( ( 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] : ( ( v4_pre_topc(H,B) & m1_subset_1(H,k1_zfmisc_1(u1_struct_0(B))) ) => ! [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] : ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t20_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_borsuk_2(G,k2_borsuk_1(A,B),k4_borsuk_1(A,B,C,E),k4_borsuk_1(A,B,D,F)) => ! [H] : ( m1_borsuk_2(H,k2_borsuk_1(A,B),k4_borsuk_1(A,B,C,E),k4_borsuk_1(A,B,D,F)) => ! [I] : ( m1_borsuk_2(I,B,E,F) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t20_topalg_5,axiom,( ! [A] : ( 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)) ) )).
fof(t20_topalg_6,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( 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)) ) ) )).
fof(t20_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_topdim_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_xxreal_0(k2_topdim_1(A,B),k4_topdim_1(A)) ) ) )).
fof(t20_topdim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(A,1) => k4_topdim_1(k15_euclid(A)) = A ) ) )).
fof(t20_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( r2_hidden(C,k7_subset_1(u1_struct_0(A),B,k2_topgen_1(A,B))) <=> r2_topgen_1(A,B,C) ) ) ) )).
fof(t20_topgen_2,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) ) ) )).
fof(t20_topgen_3,axiom,( k1_card_1(a_0_0_topgen_3) = k3_topgen_3 )).
fof(t20_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t20_topgen_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_numbers) => ( r1_tarski(k1_topreal9(2,k19_euclid(A,B),C),k2_topgen_5) <=> r1_xxreal_0(C,B) ) ) ) ) ) )).
fof(t20_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => m1_connsp_2(k2_struct_0(A),A,B) ) ) )).
fof(t20_topmetr,axiom,( k4_topmetr(k5_numbers,1) = k17_borsuk_1 )).
fof(t20_topreal1,axiom,( r1_subset_1(k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,k5_numbers),k19_euclid(k5_numbers,1)),k1_rltopsp1(k15_euclid(2),k19_euclid(1,k5_numbers),k19_euclid(1,1))) )).
fof(t20_topreal3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => r1_tarski(k3_topreal1(2,k17_finseq_1(u1_struct_0(k15_euclid(2)),B,A)),k3_topreal1(2,A)) ) ) )).
fof(t20_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( 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)))) ) ) )).
fof(t20_topreal7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v6_metric_1(B) & l1_metric_1(B) ) => v6_metric_1(k1_topreal7(A,B)) ) ) )).
fof(t20_topreal8,axiom,( ! [A] : ( ( v1_goboard5(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(k3_finseq_1(A),B) => v3_topreal1(k17_finseq_1(u1_struct_0(k15_euclid(2)),B,A)) ) ) ) )).
fof(t20_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ( ~ v1_xboole_0(k2_topreal9(A,C,B)) => r1_xxreal_0(k5_numbers,B) ) ) ) ) )).
fof(t20_topreala,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_topmetr)) => ! [B] : ( m1_connsp_2(B,k3_topmetr,A) => ? [C] : ( m1_rcomp_1(C,A) & r1_tarski(C,B) ) ) ) )).
fof(t20_toprealb,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => r2_borsuk_3(k7_toprealb(A,D,B),k7_toprealb(A,E,C)) ) ) ) ) ) )).
fof(t20_toprealc,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => ~ ( k12_euclid(A) != k5_numbers & ! [B] : ( v7_ordinal1(B) => ~ ( r2_hidden(B,k4_finseq_1(A)) & k1_funct_1(A,B) != k5_numbers ) ) ) ) )).
fof(t20_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(t20_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t20_tops_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t20_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tops_1(B,A) <=> ! [C] : ( 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)) ) ) ) ) ) )).
fof(t20_tops_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k15_euclid(B)),u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(B)),u1_struct_0(k15_euclid(A))))) ) => ( v5_pre_topc(C,k15_euclid(B),k15_euclid(A)) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(B))) => ! [E] : ( ( v1_xreal_0(E) & v2_xxreal_0(E) ) => ? [F] : ( v1_xreal_0(F) & v2_xxreal_0(F) & r1_tarski(k7_relset_1(u1_struct_0(k15_euclid(B)),u1_struct_0(k15_euclid(A)),C,k1_topreal9(B,D,F)),k1_topreal9(A,k3_funct_2(u1_struct_0(k15_euclid(B)),u1_struct_0(k15_euclid(A)),C,D),E)) ) ) ) ) ) ) ) )).
fof(t20_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),k2_zfmisc_1(A,A)))) => ( ( ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,A) => ! [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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( 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) ) ) ) ) )).
fof(t20_treal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => v1_connsp_1(k4_topmetr(A,B)) ) ) ) )).
fof(t20_trees_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(k7_finseq_1(A,C),B) => r2_hidden(A,B) ) ) ) ) )).
fof(t20_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => m1_trees_2(k1_tarski(k1_xboole_0),A) ) )).
fof(t20_trees_3,axiom,( ! [A] : ! [B] : ( ( v3_trees_3(A) & r1_tarski(B,A) ) => v3_trees_3(B) ) )).
fof(t20_trees_4,axiom,( ! [A] : ( k3_trees_4(A,k1_xboole_0) = k1_trees_4(A) & k4_trees_4(A,k1_xboole_0) = k1_trees_4(A) ) )).
fof(t20_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v3_trees_3(B) ) => ( r2_hidden(A,B) => r2_hidden(A,k9_trees_9(B)) ) ) ) )).
fof(t20_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( v3_pre_topc(B,A) & ! [C] : ( ( ~ v2_struct_0(C) & v1_pre_topc(C) & v1_tsep_1(C,A) & m1_pre_topc(C,A) ) => B != u1_struct_0(C) ) ) ) ) )).
fof(t20_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t20_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( D = u1_struct_0(B) & ! [E] : ( 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) ) ) ) ) ) )).
fof(t20_turing_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r1_xxreal_0(1,k3_finseq_1(A)) => ( k1_gr_cy_1(k4_turing_1(1,k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,B),A))) = B & k1_gr_cy_1(k4_turing_1(2,k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,B),A))) = k1_nat_1(B,k7_partfun1(k4_ordinal1,A,1)) ) ) ) ) )).
fof(t20_twoscomp,axiom,( k1_funct_1(k19_twoscomp,k11_finseq_1(k5_numbers,k5_numbers,k5_numbers)) = k5_numbers & k1_funct_1(k19_twoscomp,k11_finseq_1(k5_numbers,k5_numbers,1)) = 1 & k1_funct_1(k19_twoscomp,k11_finseq_1(k5_numbers,1,k5_numbers)) = k5_numbers & k1_funct_1(k19_twoscomp,k11_finseq_1(k5_numbers,1,1)) = k5_numbers & k1_funct_1(k19_twoscomp,k11_finseq_1(1,k5_numbers,k5_numbers)) = k5_numbers & k1_funct_1(k19_twoscomp,k11_finseq_1(1,k5_numbers,1)) = k5_numbers & k1_funct_1(k19_twoscomp,k11_finseq_1(1,1,k5_numbers)) = k5_numbers & k1_funct_1(k19_twoscomp,k11_finseq_1(1,1,1)) = k5_numbers )).
fof(t20_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_unialg_2(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t20_unialg_3,axiom,( ! [A] : ( ( ~ 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] : ( m1_unialg_2(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t20_uniroots,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t20_uproots,axiom,( ! [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) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) )).
fof(t20_urysohn1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v10_pre_topc(A) => ! [B] : ( ( v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t20_urysohn2,axiom,( ! [A] : ( ( v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_numbers,B) & C = k2_measure5(A) ) => k3_xcmplx_0(B,C) = k2_measure5(k1_integra2(A,B)) ) ) ) ) )).
fof(t20_urysohn3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v10_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v4_pre_topc(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( r1_xboole_0(B,C) & ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_xxreal_0(k5_numbers,k12_supinf_2(D,E)) & r1_xxreal_0(k12_supinf_2(D,E),1) & ( r2_hidden(E,B) => k12_supinf_2(D,E) = k5_numbers ) & ( r2_hidden(E,C) => k12_supinf_2(D,E) = 1 ) ) ) ) ) ) ) ) ) )).
fof(t20_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( m1_valuat_1(F,A,B) => ( r1_valuat_1(A,B,k11_cqc_lang(A,C,E),F,D) <=> ! [G] : ( m2_funct_2(G,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ( ! [H] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t20_valued_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ( ( m2_valued_0(B,A,C) & m2_valued_0(C,A,D) ) => m2_valued_0(B,A,D) ) ) ) ) ) )).
fof(t20_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( v7_ordinal1(C) => ( r1_tarski(A,B) => r1_tarski(k61_valued_1(A,C),k61_valued_1(B,C)) ) ) ) ) )).
fof(t20_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t20_vectsp10,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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] : ( 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] : ( 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] : ( m1_subset_1(H,u1_struct_0(D)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t20_vectsp11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( l1_struct_0(C) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t20_vectsp_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( B != k4_struct_0(A) => k11_algstr_0(A,k11_algstr_0(A,B)) = B ) ) ) )).
fof(t20_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( D != k4_struct_0(A) => ( k3_rlvect_1(A,k1_vectsp_2(A,B,D),k1_vectsp_2(A,C,D)) = k1_vectsp_2(A,k3_rlvect_1(A,B,C),D) & k5_algstr_0(A,k1_vectsp_2(A,B,D),k1_vectsp_2(A,C,D)) = k1_vectsp_2(A,k5_algstr_0(A,B,C),D) ) ) ) ) ) ) )).
fof(t20_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t20_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t20_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t20_vectsp_7,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ~ ( k1_vectsp_7(A,B,C) = B & ! [D] : ( m1_vectsp_7(D,A,B) => ~ r1_tarski(D,C) ) ) ) ) ) )).
fof(t20_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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] : ( m1_vectsp_7(C,A,B) => v1_finset_1(C) ) ) ) ) )).
fof(t20_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t20_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t20_waybel10,axiom,( ! [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) ) => ( 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))))) ) ) )).
fof(t20_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t20_waybel12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t20_waybel13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(t20_waybel14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ( v6_waybel_6(B,k1_yellow_1(u1_pre_topc(A))) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ~ ( r1_tarski(B,k2_xboole_0(C,D)) & ~ r1_tarski(B,C) & ~ r1_tarski(B,D) ) ) ) ) ) ) )).
fof(t20_waybel15,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_waybel15(B,A) <=> ( v6_waybel_6(B,A) & B != k3_yellow_0(A) ) ) ) ) )).
fof(t20_waybel16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_waybel16(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r2_orders_2(A,B,C) & ! [D] : ( 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)) ) ) ) ) )).
fof(t20_waybel17,axiom,( ! [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] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ v2_struct_0(D) & v4_orders_2(D) & v7_waybel_0(D) & l1_waybel_0(D,A) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( 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))) ) ) ) ) ) ) ) )).
fof(t20_waybel19,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m3_yellow_9(C,A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) => ( ( E = D & v3_pre_topc(D,A) ) => v3_pre_topc(E,C) ) ) ) ) ) ) )).
fof(t20_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t20_waybel21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v4_yellow_0(C,A) & m1_yellow_0(C,A) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(t20_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_waybel23(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ( r1_yellow_0(A,C) => r2_hidden(k1_yellow_0(A,C),B) ) ) ) ) ) )).
fof(t20_waybel24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v3_orders_2(B) & l1_waybel_9(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_waybel24(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_waybel24(A,B))) => ( r1_orders_2(k3_waybel24(A,B),C,D) <=> ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t20_waybel25,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t20_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t20_waybel27,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v4_yellow_0(D,k5_yellow_1(A,k5_yellow_1(B,C))) & m1_yellow_0(D,k5_yellow_1(A,k5_yellow_1(B,C))) ) => ! [E] : ( ( ~ v2_struct_0(E) & v4_yellow_0(E,k5_yellow_1(k2_zfmisc_1(A,B),C)) & m1_yellow_0(E,k5_yellow_1(k2_zfmisc_1(A,B),C)) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t20_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ! [C] : ( r2_hidden(k4_tarski(B,C),k3_waybel28(A)) => r2_hidden(B,k6_yellow_6(A)) ) ) )).
fof(t20_waybel29,axiom,( k1_waybel25(k9_waybel18) = k1_waybel29(k2_yellow_1(k1_tarski(k5_numbers))) )).
fof(t20_waybel30,axiom,( ! [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] : ( ( 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] : ( ( v2_pre_topc(C) & v2_waybel19(C) & m1_yellow_9(C,k3_yellow_3(A,B)) ) => ! [D] : ( ( v2_pre_topc(D) & v2_waybel19(D) & m1_yellow_9(D,A) ) => ! [E] : ( ( v2_pre_topc(E) & v2_waybel19(E) & m1_yellow_9(E,B) ) => ( v3_waybel_3(k1_yellow_1(k5_waybel11(B))) => g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = k2_borsuk_1(D,E) ) ) ) ) ) ) )).
fof(t20_waybel32,axiom,( ! [A] : ( ( 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] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t20_waybel33,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t20_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => r2_functor0(k4_waybel34(A),k5_waybel34(A)) ) )).
fof(t20_waybel35,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_waybel35(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_waybel35(C,A,B) ) => ( ( v4_waybel35(C,A) & ! [D] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,C) => D = k1_yellow_0(A,k4_waybel35(A,B,C,D)) ) ) ) ) ) ) )).
fof(t20_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k6_waybel_0(A,B) = k6_waybel_0(A,C) => B = C ) ) ) ) )).
fof(t20_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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))) ) ) ) ) ) ) )).
fof(t20_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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] : ( ( ~ 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) ) ) ) ) ) )).
fof(t20_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_waybel_3(A,B,C) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t20_waybel_4,axiom,( ! [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] : ( ( 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),k1_yellow_1(k7_waybel_0(A)),k7_waybel_4(A,B),k3_yellow_2(A)) ) ) )).
fof(t20_waybel_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t20_waybel_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v2_yellow_0(A) & l1_orders_2(A) ) => v5_waybel_6(k4_yellow_0(A),A) ) )).
fof(t20_waybel_7,axiom,( ! [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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) | r2_hidden(k7_waybel_1(A,C),B) ) ) ) ) ) )).
fof(t20_waybel_8,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t20_waybel_9,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t20_weddwitt,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t20_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(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)))),k3_metric_1(A,C,D)) ) ) ) ) ) ) )).
fof(t20_wellord1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => k2_wellord1(k2_wellord1(C,A),B) = k2_wellord1(k2_wellord1(C,B),A) ) )).
fof(t20_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r1_tarski(A,B) & r1_tarski(A,C) & ! [D] : ( ( r1_tarski(D,B) & r1_tarski(D,C) ) => r1_tarski(D,A) ) ) => A = k3_xboole_0(B,C) ) )).
fof(t20_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k4_xboolean(A,k7_xboolean(A,B)) = k4_xboolean(A,B) ) ) )).
fof(t20_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( k6_xcmplx_0(C,A) = k6_xcmplx_0(C,B) => A = B ) ) ) ) )).
fof(t20_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(A,k2_xcmplx_0(B,C)) <=> r1_xxreal_0(k6_xcmplx_0(A,B),C) ) ) ) ) )).
fof(t20_xtuple_0,axiom,( ! [A] : ! [B] : ~ ( r2_hidden(A,k14_xtuple_0(B)) & ! [C] : ! [D] : ! [E] : ~ r2_hidden(k6_xtuple_0(C,A,D,E),B) ) )).
fof(t20_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(A,C) ) => r1_xxreal_0(A,k3_xxreal_0(B,C)) ) ) ) ) )).
fof(t20_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => k4_xxreal_1(A,A) = k1_xboole_0 ) )).
fof(t20_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => m2_xxreal_2(A,k4_xxreal_1(A,B)) ) ) )).
fof(t20_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t20_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t20_yellow12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t20_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) )).
fof(t20_yellow14,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t20_yellow15,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v3_waybel23(k2_struct_0(A),A) & v4_waybel23(k2_struct_0(A),A) ) ) )).
fof(t20_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t20_yellow17,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_waybel18(A,B))) => ( ! [E] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k4_waybel18(A,B,C))) => ! [F] : ( ( 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] : ~ ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t20_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(B)) & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & E = C & F = D & ? [G] : ( m1_subset_1(G,k1_altcat_1(A,C,D)) & ? [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t20_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ! [C] : ! [D] : ( ( r1_tarski(B,C) & r2_waybel_7(A,B,D) ) => r2_waybel_7(A,C,D) ) ) )).
fof(t20_yellow20,axiom,( ! [A] : ( l2_altcat_1(A) => ! [B] : ( l2_altcat_1(B) => ( r1_yellow20(A,B) => m1_altcat_2(k2_yellow20(A,B),A) ) ) ) )).
fof(t20_yellow_0,axiom,( ! [A] : ( ( v5_orders_2(A) & l1_orders_2(A) ) => ( v1_lattice3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_yellow_0(A,k2_tarski(B,C)) ) ) ) ) )).
fof(t20_yellow_1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(A)))) ) => k2_yellow_0(k2_yellow_1(A),B) = k1_setfam_1(B) ) )).
fof(t20_yellow_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( ( 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 ) ) ) )).
fof(t20_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t20_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t20_yellow_5,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t20_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t20_yellow_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t20_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t20_yellow_9,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [D] : ( 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)) ) ) ) )).
fof(t20_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ~ v1_xboole_0(C) => ( ( v8_zf_fund1(B,A) & r2_hidden(C,B) ) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( ( v1_zf_lang(E) & m2_finseq_1(E,k4_ordinal1) ) => ( ( 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) ) ) ) ) ) ) ) )).
fof(t20_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v4_zf_lang(A) => k1_funct_1(A,1) = 2 ) ) )).
fof(t20_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ! [E] : ( m2_subset_1(E,k4_ordinal1,k1_zf_lang) => ! [F] : ( m2_subset_1(F,k4_ordinal1,k1_zf_lang) => ! [G] : ( m2_subset_1(G,k4_ordinal1,k1_zf_lang) => ( k17_zf_lang(C,D,E,A) = k15_zf_lang(G,F,B) => ( C = G & D = F & k13_zf_lang(E,A) = B ) ) ) ) ) ) ) ) ) )).
fof(t20_zf_model,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ( r1_zf_model(A,B,k13_zf_lang(D,C)) <=> ? [E] : ( 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] : ( m2_subset_1(F,k4_ordinal1,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) ) ) ) ) ) ) )).
fof(t20_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(k2_tarski(A,B),k1_tarski(C)) => A = C ) )).
fof(t20_zfmodel2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( ( k9_xtuple_0(E) = A & ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t20_zfrefle1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r2_ordinal2(A,B) => r1_ordinal1(B,A) ) ) ) )).
fof(t20_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v7_zmodul01(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t20_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m2_zmodul02(B,A,k1_subset_1(u1_struct_0(A))) => k21_zmodul02(A,B) = k4_struct_0(A) ) ) )).
fof(t20_zmodul03,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => k33_zmodul02(A,C) = k33_zmodul02(B,D) ) ) ) ) ) )).
fof(t210_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(C,A) => r2_hidden(k6_xxreal_3(B,C),k24_member_1(A,B)) ) ) ) ) )).
fof(t210_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k3_xcmplx_0(A,B) = 1 => A = k5_xcmplx_0(B) ) ) ) )).
fof(t210_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,1) => r1_xxreal_0(k7_xcmplx_0(A,C),B) ) ) => r1_xxreal_0(A,B) ) ) ) )).
fof(t210_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => k4_xxreal_1(A,k2_xxreal_0) = k1_xboole_0 ) )).
fof(t211_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => k24_member_1(A,B) = a_2_16_member_1(A,B) ) ) )).
fof(t211_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( A != k5_numbers & B != k5_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))) ) ) ) )).
fof(t211_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => r1_xxreal_0(k5_xcmplx_0(A),1) ) ) )).
fof(t211_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => k2_xxreal_1(A,k2_xxreal_0) = k1_xboole_0 ) )).
fof(t212_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ~ ( r2_hidden(C,k24_member_1(A,B)) & ! [D] : ( m1_subset_1(D,k6_numbers) => ~ ( C = k6_xxreal_3(B,D) & r2_hidden(D,A) ) ) ) ) ) )).
fof(t212_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( A != k5_numbers & B != k5_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))) ) ) ) )).
fof(t212_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,1) & r1_xxreal_0(1,k5_xcmplx_0(A)) ) ) )).
fof(t212_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => k3_xxreal_1(A,k2_xxreal_0) = k1_xboole_0 ) )).
fof(t213_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( r2_hidden(C,A) => r2_hidden(k7_xcmplx_0(B,C),k25_member_1(A,B)) ) ) ) ) )).
fof(t213_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k5_xcmplx_0(k7_xcmplx_0(A,B)) = k7_xcmplx_0(B,A) ) ) )).
fof(t213_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) => r1_xxreal_0(k4_xcmplx_0(1),k5_xcmplx_0(A)) ) ) )).
fof(t213_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ( A != k2_xxreal_0 => k1_xxreal_1(A,k2_xxreal_0) = k1_xboole_0 ) ) )).
fof(t214_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => k25_member_1(A,B) = a_2_17_member_1(A,B) ) ) )).
fof(t214_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k7_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) = k7_xcmplx_0(B,A) ) ) )).
fof(t214_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(k5_xcmplx_0(A),k4_xcmplx_0(1)) ) ) )).
fof(t214_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => k4_xxreal_1(k1_xxreal_0,A) = k1_xboole_0 ) )).
fof(t215_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ~ ( r2_hidden(C,k25_member_1(A,B)) & ! [D] : ( v1_xcmplx_0(D) => ~ ( C = k7_xcmplx_0(B,D) & r2_hidden(D,A) ) ) ) ) ) )).
fof(t215_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(1,A) = k5_xcmplx_0(A) ) )).
fof(t215_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k7_xcmplx_0(A,2),k5_numbers) ) ) )).
fof(t215_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => k2_xxreal_1(k1_xxreal_0,A) = k1_xboole_0 ) )).
fof(t216_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ( r1_tarski(k25_member_1(A,C),k25_member_1(B,C)) => ( C = k5_numbers | r1_tarski(A,B) ) ) ) ) ) )).
fof(t216_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(1,k5_xcmplx_0(A)) = A ) )).
fof(t216_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(A,k7_xcmplx_0(A,2)) ) ) )).
fof(t216_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => k3_xxreal_1(k1_xxreal_0,A) = k1_xboole_0 ) )).
fof(t217_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ( k25_member_1(A,C) = k25_member_1(B,C) => ( C = k5_numbers | A = B ) ) ) ) ) )).
fof(t217_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k5_xcmplx_0(k7_xcmplx_0(1,A)) = A ) )).
fof(t217_xreal_1,axiom,( ! [A] : ( 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),k5_numbers) ) ) )).
fof(t217_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ( A != k1_xxreal_0 => k1_xxreal_1(k1_xxreal_0,A) = k1_xboole_0 ) ) )).
fof(t218_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ( C != k5_numbers => k25_member_1(k3_xboole_0(A,B),C) = k3_xboole_0(k25_member_1(A,C),k25_member_1(B,C)) ) ) ) ) )).
fof(t218_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k7_xcmplx_0(1,A) = k5_xcmplx_0(B) => A = B ) ) ) )).
fof(t218_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(A,k7_xcmplx_0(1,2)) => r1_xxreal_0(k5_numbers,k6_xcmplx_0(1,k3_xcmplx_0(2,A))) ) ) )).
fof(t218_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( ~ r1_xxreal_0(A,B) => r2_hidden(A,k3_xxreal_1(B,k1_xxreal_0)) ) ) ) )).
fof(t219_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ( C != k5_numbers => k25_member_1(k6_subset_1(A,B),C) = k6_subset_1(k25_member_1(A,C),k25_member_1(B,C)) ) ) ) ) )).
fof(t219_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k7_xcmplx_0(A,k5_xcmplx_0(B)) = k3_xcmplx_0(A,B) ) ) )).
fof(t219_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k7_xcmplx_0(1,2),A) => r1_xxreal_0(k5_numbers,k6_xcmplx_0(k3_xcmplx_0(2,A),1)) ) ) )).
fof(t219_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( r1_xxreal_0(B,A) => r2_hidden(A,k1_xxreal_1(B,k1_xxreal_0)) ) ) ) )).
fof(t21_abcmiz_0,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t21_abcmiz_1,axiom,( ! [A] : k6_classes1(k1_abcmiz_1(A)) = k6_classes1(A) )).
fof(t21_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & v1_abcmiz_a(A) & l1_msualg_1(A) ) => ! [B] : ( 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 ) ) ) ) )).
fof(t21_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => k7_xcmplx_0(1,k2_absvalue(A)) = k2_absvalue(k7_xcmplx_0(1,A)) ) )).
fof(t21_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(D,k2_aff_1(A,B,C)) => ( B = C | ( r2_hidden(E,k2_aff_1(A,B,C)) <=> r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) ) )).
fof(t21_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,C) & r2_hidden(E,D) ) ) ) ) ) ) ) )).
fof(t21_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) ) => r1_ordinal1(k9_xtuple_0(A),k9_xtuple_0(k1_ordinal4(A,B))) ) ) )).
fof(t21_afinsq_2,axiom,( ! [A] : ( ( v1_finset_1(A) & v6_membered(A) ) => ! [B] : ( ( 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),k5_numbers),k1_recdef_1(k4_afinsq_2(A),k5_numbers)) ) ) ) ) )).
fof(t21_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k14_afproj(A))) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & B = k5_afproj(A,C) & v1_aff_1(C,A) ) ) ) )).
fof(t21_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r2_afvect0(A,B,C,D) ) ) ) ) )).
fof(t21_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t21_algspec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t21_algstr_4,axiom,( ! [A] : ! [B] : ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(2,C) & r2_hidden(B,k11_algstr_4(A,C)) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t21_altcat_2,axiom,( ! [A] : ( l2_altcat_1(A) => ! [B] : ( l2_altcat_1(B) => ! [C] : ( l2_altcat_1(C) => ( ( m1_altcat_2(A,B) & m1_altcat_2(B,C) ) => m1_altcat_2(A,C) ) ) ) ) )).
fof(t21_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t21_ami_3,axiom,( ! [A] : ( v7_ordinal1(A) => ~ v2_extpro_1(k7_ami_3(A),k7_card_1(2),k1_ami_3) ) )).
fof(t21_ami_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( ~ 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(k7_card_1(2),k1_ami_3)) & v1_finset_1(B) & v4_extpro_1(B,k7_card_1(2),k1_ami_3,A) ) => ! [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(C,u1_struct_0(k1_ami_3)) ) => ! [D] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ( ( r1_tarski(B,C) & r1_tarski(B,D) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_ami_3)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_ami_3)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( ( r1_tarski(A,E) & r1_tarski(A,F) ) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v1_ami_2(H) & m1_subset_1(H,u1_struct_0(k1_ami_3)) ) => ! [I] : ( ( v1_ami_2(I) & m1_subset_1(I,u1_struct_0(k1_ami_3)) ) => ! [J] : ( m1_subset_1(J,u1_compos_1(k1_ami_3)) => ( ( J = k3_extpro_1(k7_card_1(2),k1_ami_3,E,k5_extpro_1(k7_card_1(2),k1_ami_3,E,C,G)) & J = k6_ami_3(H,I) & r2_hidden(I,k9_xtuple_0(B)) ) => k5_int_1(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,E,C,G),H),k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,E,C,G),I)) = k5_int_1(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,F,D,G),H),k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,F,D,G),I)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_ami_6,axiom,( ! [A] : ( v7_ordinal1(A) => k3_amistd_1(k7_card_1(2),k1_ami_3,A) = k2_tarski(A,k1_ordinal1(A)) ) )).
fof(t21_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,u1_compos_1(B)) => ( v3_ami_wstd(D,A,B) => k1_amistd_1(A,B,C,D) = k6_domain_1(k4_ordinal1,k5_ami_wstd(A,B,C)) ) ) ) ) ) )).
fof(t21_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) ) => ( v5_amistd_1(C,A,B) <=> ! [D] : ( ( 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(k4_ordinal1,C)) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(B)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ( r1_tarski(C,E) => ! [F] : ( v7_ordinal1(F) => r2_hidden(k5_memstr_0(A,B,k5_extpro_1(A,B,E,D,F)),k1_relset_1(k4_ordinal1,C)) ) ) ) ) ) ) ) ) ) )).
fof(t21_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(k2_analmetr(A,F,G))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k2_analmetr(A,F,G))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k2_analmetr(A,F,G))) => ! [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_analoaf,axiom,( ! [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) ) => ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & k3_rlvect_1(A,k1_rlvect_1(A,B,E),k1_rlvect_1(A,C,F)) = D ) ) ) ) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( ~ r1_analoaf(A,B,C,D,E) & ~ r1_analoaf(A,B,C,E,D) & ! [F] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => r2_analort(A,E,F,B,B,C,D) ) ) ) ) ) ) )).
fof(t21_anproj_1,axiom,( ! [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) & l1_rlvect_1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t21_anproj_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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] : ( m2_funct_2(F,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [G] : ( m2_funct_2(G,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [H] : ( m2_funct_2(H,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [I] : ( m2_funct_2(I,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ~ ( ! [J] : ( v1_xreal_0(J) => ! [K] : ( v1_xreal_0(K) => ! [L] : ( v1_xreal_0(L) => ! [M] : ( v1_xreal_0(M) => ( k1_binop_1(k5_funcsdom(A),k1_binop_1(k5_funcsdom(A),k1_binop_1(k5_funcsdom(A),k1_funct_1(k7_funcsdom(A),k4_tarski(J,F)),k1_funct_1(k7_funcsdom(A),k4_tarski(K,G))),k1_funct_1(k7_funcsdom(A),k4_tarski(L,H))),k1_funct_1(k7_funcsdom(A),k4_tarski(M,I))) = k8_funcsdom(A) => ( J = k5_numbers & K = k5_numbers & L = k5_numbers & M = k5_numbers ) ) ) ) ) ) & ! [J] : ( m2_funct_2(J,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ? [K] : ( v1_xreal_0(K) & ? [L] : ( v1_xreal_0(L) & ? [M] : ( v1_xreal_0(M) & ? [N] : ( v1_xreal_0(N) & J = k1_binop_1(k5_funcsdom(A),k1_binop_1(k5_funcsdom(A),k1_binop_1(k5_funcsdom(A),k1_funct_1(k7_funcsdom(A),k4_tarski(K,F)),k1_funct_1(k7_funcsdom(A),k4_tarski(L,G))),k1_funct_1(k7_funcsdom(A),k4_tarski(M,H))),k1_funct_1(k7_funcsdom(A),k4_tarski(N,I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : k10_xtuple_0(k5_aofa_a00(A,B,C,D,E,F)) = k4_enumset1(A,B,C,D,E,F) )).
fof(t21_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ( k1_msualg_1(A,B) = k1_xboole_0 => ! [C] : ( l3_msualg_1(C,A) => k3_msualg_1(A,B,C) = k1_tarski(k1_xboole_0) ) ) ) ) )).
fof(t21_aofa_i00,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_card_3(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_funct_2(A,k4_numbers))) => ! [C] : ( ( 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] : ( m6_aofa_i00(D,A,B,C) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t21_armstrng,axiom,( ! [A] : ! [B] : ( 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) ) ) ) )).
fof(t21_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ~ ( k2_arytm_0(A,B) = k5_numbers & A != k5_numbers & B != k5_numbers ) ) ) )).
fof(t21_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( ~ r1_arytm_2(C,B) => k2_arytm_1(A,k1_arytm_1(C,B)) = k2_arytm_1(k7_arytm_2(A,B),C) ) ) ) ) )).
fof(t21_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ~ ( r2_hidden(A,k5_arytm_3) & r2_hidden(B,k5_arytm_3) & ! [C] : ( m1_subset_1(C,k5_arytm_3) => ! [D] : ( m1_subset_1(D,k5_arytm_3) => ~ ( A = C & B = D & k8_arytm_2(A,B) = k10_arytm_3(C,D) ) ) ) ) ) ) )).
fof(t21_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => k9_ordinal3(k4_arytm_3(A,B),k3_arytm_3(A,B)) = A ) ) )).
fof(t21_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & v2_asympt_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( r2_hidden(A,k7_asympt_0(B)) & r2_hidden(B,k7_asympt_0(C)) ) => r2_hidden(A,k7_asympt_0(C)) ) ) ) ) )).
fof(t21_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ r1_xxreal_0(C,k5_numbers) => k9_nat_1(k1_numbers,B,C) = k3_xcmplx_0(C,k3_power(2,C)) ) ) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & v4_asympt_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( r2_funct_2(k4_ordinal1,k1_numbers,C,B) & r1_tarski(k6_asympt_0(C),k6_asympt_0(k3_asympt_1(k2_xcmplx_0(1,A)))) & k6_asympt_0(C) != k6_asympt_0(k3_asympt_1(k2_xcmplx_0(1,A))) ) ) ) ) ) )).
fof(t21_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t21_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t21_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k4_bcialg_1(A)) => r1_bcialg_1(A,k1_bcialg_1(A,B,C),B) ) ) ) )).
fof(t21_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => r1_bcialg_1(A,k1_bcialg_1(A,k1_bcialg_2(A,B,D,E),k1_bcialg_2(A,C,D,E)),k1_bcialg_1(A,B,C)) ) ) ) ) ) )).
fof(t21_bcialg_3,axiom,( ! [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) ) => ( v4_bcialg_3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t21_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k6_bcialg_4(A,B,1) = B ) ) )).
fof(t21_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( v8_bcialg_1(E) & m1_bcialg_5(E,A,B,C,D) ) => ( v8_bcialg_1(E) & m1_bcialg_5(E,A,B,B,D) ) ) ) ) ) ) )).
fof(t21_bcialg_6,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)))) ) ) ) )).
fof(t21_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( m2_bciideal(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & r1_bcialg_1(A,C,D) ) => r2_hidden(D,B) ) ) ) ) ) ) )).
fof(t21_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_bhsp_1(A,B,C) => r1_bhsp_1(A,k4_algstr_0(A,B),C) ) ) ) ) )).
fof(t21_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_bhsp_2(C,A) & k1_bhsp_2(A,C) = B ) => ( v2_comseq_2(k2_bhsp_2(A,C)) & k1_seq_2(k2_bhsp_2(A,C)) = k3_bhsp_1(A,B) ) ) ) ) ) )).
fof(t21_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v3_bhsp_3(A) & v1_bhsp_3(B,A) ) => v2_bhsp_3(B,A) ) ) ) )).
fof(t21_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k4_bhsp_4(A,B,1,k5_numbers) = k1_normsp_1(A,B,1) ) ) )).
fof(t21_bilinear,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t21_binari_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t21_binari_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,A) => r1_xxreal_0(k1_binari_4(C,B),k1_binari_4(C,A)) ) ) ) ) )).
fof(t21_binarith,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k6_margrel1) ) => k1_nat_1(k6_binarith(A,k7_binarith(A,B,C)),k15_funcop_1(k4_ordinal1,k8_binarith(A,B,C),k7_margrel1,k5_numbers,k5_series_1(2,A))) = k1_nat_1(k6_binarith(A,B),k6_binarith(A,C)) ) ) ) )).
fof(t21_binom,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k6_algstr_0(A,k6_binom(A,B,D),C) = k6_algstr_0(A,B,k5_binom(A,C,D)) ) ) ) ) )).
fof(t21_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => k10_xtuple_0(k2_bintree2(A,B)) = k2_trees_2(A,B) ) ) )).
fof(t21_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t21_bor_cant,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [E] : ( v7_ordinal1(E) => ( ( 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)) = k1_funct_1(k1_series_3(k8_prob_1(A,B,D,C)),E) ) & ( r1_bor_cant(A,B,C,D) => k6_xcmplx_0(1,k3_funct_2(B,k1_numbers,C,k1_prob_2(A,B,k2_prob_3(A,D),E))) = k1_funct_1(k1_series_3(k8_prob_1(A,B,k2_prob_1(A,D),C)),E) ) ) ) ) ) ) ) )).
fof(t21_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k2_borsuk_1(A,B))))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t21_borsuk_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_pre_topc(C,A) => ! [D] : ( m1_pre_topc(D,B) => m1_pre_topc(k2_borsuk_1(C,D),k2_borsuk_1(A,B)) ) ) ) ) )).
fof(t21_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_topmetr)) => ! [B] : ( 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))) ) ) ) ) )).
fof(t21_borsuk_5,axiom,( ! [A] : ( v1_rat_1(A) => ! [B] : ( ( v1_xreal_0(B) & ~ v1_rat_1(B) ) => ~ ( A != k5_numbers & v1_rat_1(k3_xcmplx_0(A,B)) ) ) ) )).
fof(t21_borsuk_6,axiom,( 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)))) )).
fof(t21_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : r1_tarski(k10_xtuple_0(k1_borsuk_7(A,B,C,D,E,F)),k1_enumset1(D,E,F)) )).
fof(t21_bspace,axiom,( ! [A] : v2_rlvect_1(k7_bspace(A)) )).
fof(t21_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t21_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t21_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t21_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t21_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t21_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t21_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(E,A) => ( r3_bvfunc_2(A,D,B,E) => r2_funct_2(A,k6_margrel1,k6_bvfunc_2(A,k9_bvfunc_1(A,C,D),B,E),k9_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),D)) ) ) ) ) ) ) )).
fof(t21_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(E,A) => ( r3_bvfunc_2(A,D,B,E) => r1_bvfunc_1(A,k7_bvfunc_2(A,k9_bvfunc_1(A,D,C),B,E),k9_bvfunc_1(A,D,k7_bvfunc_2(A,C,B,E))) ) ) ) ) ) ) )).
fof(t21_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t21_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t21_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(t21_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t21_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t21_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) )).
fof(t21_c0sp1,axiom,( ! [A] : ( l1_lopban_2(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & 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) ) ) ) ) )).
fof(t21_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(t21_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t21_calcul_2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t21_card_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( k3_card_1(A) = k3_card_1(B) => A = B ) ) ) )).
fof(t21_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ! [C] : ( v1_card_1(C) => k2_card_2(k2_card_2(A,B),C) = k2_card_2(A,k2_card_2(B,C)) ) ) ) )).
fof(t21_card_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ~ ( r2_hidden(A,k3_card_3(k2_card_3(B))) & ! [C] : ! [D] : A != k4_tarski(C,D) ) ) )).
fof(t21_card_4,axiom,( ! [A] : ( ~ v1_finset_1(A) => k1_card_1(A) = k2_card_2(k4_ordinal1,k1_card_1(A)) ) )).
fof(t21_card_5,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => k3_tarski(A) = A ) )).
fof(t21_card_fil,axiom,( ! [A] : ( ~ v1_finset_1(A) => ! [B] : ( m1_card_fil(B,A) => ( ( v1_card_fil(B,A) & v3_card_fil(B,A) ) => r1_tarski(k4_card_fil(A),B) ) ) ) )).
fof(t21_card_fin,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ~ ( r2_hidden(B,k2_card_fin(C,D,A)) & r2_hidden(A,k10_xtuple_0(D)) & ! [E] : ~ ( r2_hidden(E,k9_xtuple_0(D)) & k1_funct_1(D,E) = A & r2_hidden(B,k1_funct_1(C,E)) ) ) ) ) )).
fof(t21_card_lar,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) & ~ v4_card_3(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( ! [C] : ( m1_card_lar(C,A,B) => v2_card_lar(C,A) ) => v2_card_lar(k6_setfam_1(A,B),A) ) ) ) )).
fof(t21_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_cat_1(F,A,B,C) => ! [G] : ( m1_cat_1(G,A,C,D) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t21_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(k6_cat_2(A,B))) => ? [D] : ( m1_subset_1(D,u4_struct_0(A)) & ? [E] : ( m1_subset_1(E,u4_struct_0(B)) & C = k8_cat_2(A,B,D,E) ) ) ) ) ) )).
fof(t21_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(B)) => ! [D] : ( ( 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)) ) ) ) )).
fof(t21_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => v1_cat_4(A) ) )).
fof(t21_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ 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) ) ) ) )).
fof(t21_catalan1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k3_xcmplx_0(4,k1_catalan1(A)),k1_catalan1(k1_nat_1(A,1))) ) ) )).
fof(t21_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => r1_tarski(k2_catalan2(B,A),k1_card_fin(B,A,1,k5_numbers)) ) ) )).
fof(t21_catalg_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t21_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v2_algstr_0(k5_cayldick(A,B,C),k4_cayldick(A)) => ( v2_algstr_0(B,A) & v2_algstr_0(C,A) ) ) ) ) ) )).
fof(t21_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_cc0sp1(A))) => ( B = k4_struct_0(k7_cc0sp1(A)) => k5_numbers = k2_normsp_0(k7_cc0sp1(A),B) ) ) ) )).
fof(t21_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_cc0sp2(A))) => r1_xxreal_0(k5_numbers,k2_normsp_0(k5_cc0sp2(A),B)) ) ) )).
fof(t21_cfcont_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(t21_cfdiff_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k1_valued_0(k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,C),A),k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k1_valued_0(k2_numbers,B,A),k1_valued_0(k2_numbers,C,A))) ) ) ) )).
fof(t21_cfuncdom,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ~ ( C = k2_tarski(A,B) & A != B & ! [D] : ( m2_funct_2(D,C,k2_numbers,k9_funct_2(C,k2_numbers)) => ! [E] : ( m2_funct_2(E,C,k2_numbers,k9_funct_2(C,k2_numbers)) => ? [F] : ( m2_funct_2(F,C,k2_numbers,k9_funct_2(C,k2_numbers)) & ! [G] : ( v1_xcmplx_0(G) => ! [H] : ( v1_xcmplx_0(H) => F != k1_binop_1(k1_cfuncdom(C),k1_funct_1(k3_cfuncdom(C),k4_tarski(G,D)),k1_funct_1(k3_cfuncdom(C),k4_tarski(H,E))) ) ) ) ) ) ) ) )).
fof(t21_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( v1_xcmplx_0(D) => 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))) ) ) ) ) )).
fof(t21_cgames_1,axiom,( ! [A] : ( ( 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] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(A)) => ! [C] : ( m2_subset_1(C,k4_ordinal1,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))) ) ) ) ) )).
fof(t21_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ( r2_hidden(D,k3_chain_1(A,B,C)) <=> ~ ( ~ ! [E] : ( m2_subset_1(E,k4_ordinal1,k2_finseq_1(A)) => ( r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(D,E)) & r1_xxreal_0(k1_funct_1(D,E),k1_funct_1(C,E)) ) ) & ! [E] : ( m2_subset_1(E,k4_ordinal1,k2_finseq_1(A)) => ~ ( ~ r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(C,E)) & ( r1_xxreal_0(k1_funct_1(D,E),k1_funct_1(C,E)) | r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(D,E)) ) ) ) ) ) ) ) ) ) )).
fof(t21_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) => ! [C] : ( 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] : ( m3_glib_001(D,A) => ( ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t21_circcmb2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(C,F))) => ! [H] : ( m1_subset_1(H,k4_card_3(u3_msualg_1(A,D))) => ( H = k5_relat_1(G,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,k4_card_3(u3_msualg_1(B,E))) => ( I = k5_relat_1(G,u1_struct_0(B)) => ! [J] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_circcmb3,axiom,( ! [A] : ( ( v4_circcmb3(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msafree2(B,A) & v5_circcmb3(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => r1_xxreal_0(k2_circcmb3(A,B,C),1) ) ) ) )).
fof(t21_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t21_circled1,axiom,( ! [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) ) => ! [B] : ( ( v1_circled1(B,A) & m1_rlvect_2(B,A) ) => ! [C] : ( ( v1_circled1(C,A) & m1_rlvect_2(C,A) ) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ~ r1_xxreal_0(k3_xcmplx_0(D,E),k5_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))) ) ) ) ) ) ) )).
fof(t21_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( m3_msaterm(D,A,C) => ! [E] : ( m1_subset_1(E,k4_card_3(u3_msualg_1(k1_circtrm1(A,C,D),k6_circtrm1(A,C,D,B)))) => ! [F] : ( m1_circtrm1(F,A,C,D,B,E) => ! [G] : ( 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_xcmplx_0(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_xcmplx_0(1,k6_trees_1(k9_xtuple_0(G)))),G) = k7_circtrm1(A,B,C,G,F) ) ) ) ) ) ) ) ) ) )).
fof(t21_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_pdiff_7(C,A) & m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_ckspace1(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_ckspace1(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_ckspace1(A,B,C))) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [J] : ( v1_xreal_0(J) => ( ( G = D & H = E ) => ( E = k1_rlvect_1(k2_ckspace1(A,B,C),D,J) <=> ! [K] : ( m2_subset_1(K,k1_euclid(A),C) => k1_funct_1(H,K) = k3_xcmplx_0(J,k1_funct_1(G,K)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_classes2,axiom,( ! [A] : ( k1_card_1(k1_classes1(A)) != k5_numbers & k1_card_1(k1_classes1(A)) != k1_xboole_0 & v4_ordinal1(k1_card_1(k1_classes1(A))) ) )).
fof(t21_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t21_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => k5_struct_0(k7_clopban2(A)) = k6_clopban2(A) ) )).
fof(t21_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ! [D] : ( v7_ordinal1(D) => k1_normsp_0(A,C,D) = k1_normsp_0(A,B,k5_numbers) ) => r2_funct_2(k4_ordinal1,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)) ) ) ) ) )).
fof(t21_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(E,D) => k1_normsp_1(A,k4_clopban4(k1_nat_1(D,1),A,C,B),E) = k3_rlvect_1(A,k1_normsp_1(A,k4_clopban4(D,A,C,B),E),k1_normsp_1(A,k3_clopban4(k1_nat_1(D,1),A,C,B),E)) ) ) ) ) ) ) )).
fof(t21_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m2_pboole(C,A,k5_mssubfam(A,B),k5_mssubfam(A,B)) => ! [D] : ( 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) ) ) ) ) )).
fof(t21_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,C))) => ( r2_hidden(B,D) => r1_pboole(A,B,k5_closure2(A,C,D)) ) ) ) ) )).
fof(t21_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_clvect_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => r2_hidden(k4_algstr_0(A,C),B) ) ) ) ) ) )).
fof(t21_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_clvect_2(C,A) & k1_clvect_2(A,C) = B ) => ( v2_comseq_2(k2_clvect_2(A,C)) & k1_seq_2(k2_clvect_2(A,C)) = k13_csspace(A,B) ) ) ) ) ) )).
fof(t21_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k3_clvect_3(A,B,1,k5_numbers) = k1_normsp_0(A,B,1) ) ) )).
fof(t21_coh_sp,axiom,( ! [A] : ! [B] : ( 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] : ! [D] : ( 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)) ) ) ) )).
fof(t21_cohsp_1,axiom,( ! [A] : ( ( 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] : ! [C] : ~ ( r2_hidden(B,k9_xtuple_0(A)) & r2_hidden(C,k1_funct_1(A,B)) & ! [D] : ~ ( v1_finset_1(D) & r1_tarski(D,B) & r2_hidden(C,k1_funct_1(A,D)) ) ) ) ) ) ) )).
fof(t21_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m2_collsp(B,A) => ! [C] : ( m2_collsp(C,A) => ~ ( B != C & ~ r1_xboole_0(B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k3_xboole_0(B,C) != k6_domain_1(u1_struct_0(A),D) ) ) ) ) ) )).
fof(t21_combgras,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( l1_combgras(B,A,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t21_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v8_compl_sp(A) <=> ! [B] : ( 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 ) ) ) ) )).
fof(t21_complex1,axiom,( k5_xcmplx_0(k7_complex1) = k4_xcmplx_0(k7_complex1) )).
fof(t21_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k4_complex1(A) = k5_numbers <=> ( k1_comptrig(A) = k5_numbers | k1_comptrig(A) = k28_sin_cos ) ) ) )).
fof(t21_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( 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))) ) ) ) )).
fof(t21_complsp2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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) = k6_xcmplx_0(k9_matrix_5(B,A),k9_matrix_5(C,A)) ) ) ) ) )).
fof(t21_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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)) ) ) ) ) )).
fof(t21_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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 ) ) ) ) )).
fof(t21_comptrig,axiom,( v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k18_sin_cos,k2_rcomp_1(k5_numbers,k28_sin_cos))) )).
fof(t21_compts_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_pre_topc(C,B) => ! [D] : ( m1_pre_topc(D,B) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_comput_1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(t21_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k25_valued_1(k4_ordinal1,k2_numbers,A,k6_complex1),A) ) )).
fof(t21_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & v2_comseq_2(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => k3_comseq_2(k2_comseq_2(k4_ordinal1,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B))) = k3_xcmplx_0(k8_complex1(k3_comseq_2(A)),k8_complex1(k3_comseq_2(B))) ) ) )).
fof(t21_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( r2_funct_2(k4_ordinal1,k1_numbers,k7_comseq_3(k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k7_comseq_3(A),k7_comseq_3(B)),k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_comseq_3(A),k8_comseq_3(B)))) & r2_funct_2(k4_ordinal1,k1_numbers,k8_comseq_3(k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)),k1_series_1(k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k7_comseq_3(A),k8_comseq_3(B)),k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_comseq_3(A),k7_comseq_3(B)))) ) ) ) )).
fof(t21_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u4_struct_0(A))) => ( ~ v4_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) & v6_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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u4_struct_0(A))) => ( ( ~ v4_conlat_1(g2_conlat_1(A,C,D),A) & v6_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) ) ) ) ) ) ) )).
fof(t21_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(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)))) ) )).
fof(t21_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t21_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ( v1_connsp_2(A) & v10_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t21_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t21_convex1,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ~ ( v2_convex1(B,A) & k3_rlvect_2(A,B) = k1_xboole_0 ) ) ) )).
fof(t21_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_convex4(B,A) => ! [C] : ( m1_convex4(C,A) => r1_convex4(A,k5_convex4(A,B,C),k5_convex4(A,C,B)) ) ) ) )).
fof(t21_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t21_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t21_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t21_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t21_csspace,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( 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(k8_complex1(A),k12_csspace(C,D,E)),k3_xcmplx_0(k8_complex1(B),k12_csspace(C,D,F))) ) ) ) ) ) ) )).
fof(t21_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k9_csspace4(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_csspace4(A,B))) => ! [E] : ( ( 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] : ( ( 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] : ( v1_xcmplx_0(G) => ( D = k1_clvect_1(k9_csspace4(A,B),C,G) <=> ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(t21_descip_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,A) => ! [I] : ( m1_subset_1(I,A) => ! [J] : ( m1_subset_1(J,A) => ! [K] : ( m1_subset_1(K,A) => ! [L] : ( m1_subset_1(L,A) => ! [M] : ( m1_subset_1(M,A) => ! [N] : ( m1_subset_1(N,A) => ! [O] : ( m1_subset_1(O,A) => ! [P] : ( m1_subset_1(P,A) => ! [Q] : ( m1_subset_1(Q,A) => ? [R] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_dickson,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t21_diff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(k26_valued_1(k1_numbers,k1_numbers,E,C),B),k1_nat_1(A,1)),D) = k3_xcmplx_0(C,k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(E,B),k1_nat_1(A,1)),D)) ) ) ) ) ) )).
fof(t21_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( A != B => k9_diff_1(k1_fcont_1(C,D),A,B) = C ) ) ) ) ) )).
fof(t21_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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,k6_xcmplx_0(B,A),B) = k7_xcmplx_0(k1_funct_1(k4_diff_1(C,A),B),A) ) ) ) )).
fof(t21_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(k2_xcmplx_0(B,k7_xcmplx_0(A,2)),k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,k2_fdiff_9),k1_relset_1(k1_numbers,k1_fdiff_9))) & r2_hidden(k6_xcmplx_0(B,k7_xcmplx_0(A,2)),k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,k2_fdiff_9),k1_relset_1(k1_numbers,k1_fdiff_9))) ) => k1_funct_1(k5_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k1_fdiff_9),A),B) = k4_xcmplx_0(k3_xcmplx_0(4,k7_xcmplx_0(k3_xcmplx_0(k19_sin_cos(k3_xcmplx_0(2,B)),k17_sin_cos(A)),k3_xcmplx_0(k17_sin_cos(k2_xcmplx_0(k3_xcmplx_0(2,B),A)),k17_sin_cos(k6_xcmplx_0(k3_xcmplx_0(2,B),A)))))) ) ) ) )).
fof(t21_dilworth,axiom,( ! [A] : ( ( 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))) ) ) ) )).
fof(t21_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_diraf(A,B,C,B,D) => r2_diraf(A,C,B,C,D) ) ) ) ) ) )).
fof(t21_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( ( v1_dist_1(B,A) & v1_dist_1(C,A) ) => r1_dist_1(A,B,C) ) ) ) ) )).
fof(t21_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m2_finseq_2(B,A,k3_finseq_2(A)) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,A,k6_margrel1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => k10_relat_1(k1_partfun1(k4_ordinal1,A,A,k6_margrel1,B,k5_bvfunc_1(A,C,D)),k8_margrel1) = k2_xboole_0(k10_relat_1(k1_partfun1(k4_ordinal1,A,A,k6_margrel1,B,C),k8_margrel1),k10_relat_1(k1_partfun1(k4_ordinal1,A,A,k6_margrel1,B,D),k8_margrel1)) ) ) ) ) )).
fof(t21_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t21_e_siec,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t21_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ( k2_binom(k9_int_3(A),B,k5_numbers) = k1_group_1(k9_int_3(A)) & k2_binom(k9_int_3(A),B,k5_numbers) = 1 ) ) ) )).
fof(t21_ec_pf_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k9_int_3(C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k9_int_3(C))) => ( ( D = k5_int_1(A,C) & E = k5_int_1(B,C) & F = k5_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) ) ) ) ) ) ) ) ) )).
fof(t21_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => m1_subset_1(B,u1_struct_0(k11_ens_1(A))) ) ) )).
fof(t21_entropy1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( ( v1_matrix_0(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_0(C) = k3_finseq_1(B) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(D,E),k2_matrix_0(C)) => k3_matrix_0(k1_numbers,C,D,E) = k3_xcmplx_0(k1_funct_1(A,D),k1_funct_1(B,E)) ) ) ) ) ) ) ) ) )).
fof(t21_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : k5_enumset1(A,B,C,D,E,F,G) = k2_xboole_0(k4_enumset1(A,B,C,D,E,F),k1_tarski(G)) )).
fof(t21_eqrel_1,axiom,( ! [A] : ! [B] : ( ( 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] : ~ ( r2_hidden(C,A) & ! [D] : ~ r2_hidden(C,k6_eqrel_1(A,A,B,D)) ) ) )).
fof(t21_equation,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( m1_msualg_2(D,A,C) => ! [E] : ( 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] : ( m2_pboole(F,u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,B)) => ! [G] : ( 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] : ( m1_subset_1(H,u4_struct_0(A)) => ! [I] : ( m1_subset_1(I,k3_msualg_1(A,H,C)) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => m2_finseq_1(B,k1_numbers) ) ) )).
fof(t21_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => k22_rvsum_1(k4_algstr_0(k15_euclid(A),B),k4_algstr_0(k15_euclid(A),C)) = k22_rvsum_1(B,C) ) ) ) )).
fof(t21_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => k9_complex1(k2_euclid_3(A)) = k3_square_1(k2_xcmplx_0(k1_square_1(k17_euclid(A)),k1_square_1(k18_euclid(A)))) ) )).
fof(t21_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( v1_xreal_0(D) => k22_rvsum_1(k9_euclid(A,B,D),C) = k3_xcmplx_0(D,k22_rvsum_1(B,C)) ) ) ) ) )).
fof(t21_euclid_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k5_euclid_5(k4_euclid_5(k5_numbers,A,k5_numbers),k4_euclid_5(k5_numbers,B,k5_numbers)) = k4_struct_0(k15_euclid(3)) ) ) )).
fof(t21_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => k9_euclid(3,k2_euclid_8,A) = k1_euclid_8(A,k5_numbers,k5_numbers) ) )).
fof(t21_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => r1_tarski(k4_euclid_9(A,D,k6_xcmplx_0(B,k1_funct_1(k3_euclid(k8_rvsum_1(D,C)),k1_euclid_9(A,D,C)))),k4_euclid_9(A,C,B)) ) ) ) ) )).
fof(t21_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(D)) => ! [F] : ( 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,k3_xcmplx_0(A,B)),k9_euclid(D,F,k3_xcmplx_0(A,C))) ) ) ) ) ) ) )).
fof(t21_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_euler_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) = k2_nat_1(k1_euler_1(A),k1_euler_1(B)) ) ) ) ) )).
fof(t21_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => v2_exchsort(A,k1_exchsort(A)) ) )).
fof(t21_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) & r1_compos_1(B,C,k5_memstr_0(A,B,k5_extpro_1(A,B,C,D,E))) ) => ! [E] : ( v7_ordinal1(E) => k6_extpro_1(A,B,C,D) = k6_extpro_1(A,B,C,k5_extpro_1(A,B,C,D,E)) ) ) ) ) ) ) )).
fof(t21_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => r1_xxreal_0(k3_extreal1(k3_xxreal_3(A,B)),k3_supinf_2(k3_extreal1(A),k3_extreal1(B))) ) ) )).
fof(t21_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_circcomb(A) & v2_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_circcomb(B) & v2_circcomb(B) & l1_msualg_1(B) ) => ! [C] : ( r2_hidden(C,k3_msafree2(A)) => ( r2_hidden(C,k3_msafree2(k2_circcomb(A,B))) & r2_hidden(C,k3_msafree2(k2_circcomb(B,A))) ) ) ) ) )).
fof(t21_facirc_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t21_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) ) )).
fof(t21_fcont_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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)))) ) ) ) ) )).
fof(t21_fdiff_1,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,B,C),A),D) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(C,D),k1_fdiff_1(B,D)),k3_xcmplx_0(k1_funct_1(B,D),k1_fdiff_1(C,D))) ) ) ) ) ) ) ) )).
fof(t21_fdiff_10,axiom,( ! [A] : ( ( 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,k26_sin_cos,k16_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k16_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k16_sin_cos),A),B) = k7_xcmplx_0(k19_sin_cos(k1_funct_1(k26_sin_cos,B)),k1_square_1(k1_funct_1(k18_sin_cos,B))) ) ) ) ) ) )).
fof(t21_fdiff_11,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k1_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k1_fdiff_9),A),B) = k7_xcmplx_0(k1_funct_1(k16_sin_cos,k1_funct_1(k1_sin_cos9,B)),k3_xcmplx_0(k1_square_1(k1_funct_1(k18_sin_cos,k1_funct_1(k1_sin_cos9,B))),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t21_fdiff_2,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,A) & k1_funct_1(C,D) = k5_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))) ) ) ) ) ) )).
fof(t21_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => ( k1_funct_1(C,E) = A & ~ r1_xxreal_0(k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,C,D),E),k5_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] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_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) = k7_xcmplx_0(k3_xcmplx_0(3,k1_newton(E,2)),k2_xcmplx_0(A,k1_newton(E,3))) ) ) ) ) ) ) ) ) )).
fof(t21_fdiff_5,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ~ ( r2_hidden(C,A) & r1_xxreal_0(C,k5_numbers) ) ) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,B,k3_taylor_1),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,B,k3_taylor_1),A),C) = k2_xcmplx_0(C,k3_xcmplx_0(k3_xcmplx_0(2,C),k1_funct_1(k3_taylor_1,C))) ) ) ) ) ) ) )).
fof(t21_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k22_sin_cos,B),k3_taylor_1))) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => ( k1_funct_1(B,C) = 1 & ~ r1_xxreal_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,B),C),k5_numbers) ) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,B),k3_taylor_1),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,B),k3_taylor_1),A),C) = k7_xcmplx_0(k1_funct_1(k22_sin_cos,C),k6_xcmplx_0(k1_funct_1(k22_sin_cos,C),1)) ) ) ) ) ) ) )).
fof(t21_fdiff_7,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k3_sin_cos6),k7_xcmplx_0(1,2)))) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => ( k1_funct_1(B,C) = k3_xcmplx_0(2,C) & ~ r1_xxreal_0(k1_funct_1(B,C),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(B,C)) ) ) ) ) => ( r2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k3_sin_cos6),k7_xcmplx_0(1,2)),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(k2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k3_sin_cos6),k7_xcmplx_0(1,2)),A),C) = k4_xcmplx_0(k7_xcmplx_0(1,k3_square_1(k6_xcmplx_0(1,k1_square_1(k3_xcmplx_0(2,C)))))) ) ) ) ) ) ) )).
fof(t21_fdiff_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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,k27_sin_cos,k1_taylor_1(A)))) & r1_xxreal_0(1,A) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k1_taylor_1(A)),B) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k1_taylor_1(A)),B),C) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(A,k3_prepower(k1_funct_1(k18_sin_cos,C),k6_xcmplx_0(A,1))),k3_prepower(k1_funct_1(k16_sin_cos,C),k1_nat_1(A,1)))) ) ) ) ) ) ) )).
fof(t21_fdiff_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k1_taylor_1(A)),B),C) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(A,k1_funct_1(k18_sin_cos,C)),k3_prepower(k1_funct_1(k16_sin_cos,C),k1_nat_1(A,1)))) ) ) ) ) ) ) )).
fof(t21_ff_siec,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t21_fib_num2,axiom,( k1_pre_ff(2) = 1 )).
fof(t21_fib_num3,axiom,( ! [A] : ( v7_ordinal1(A) => k1_fib_num3(A) = k2_xcmplx_0(k2_power(k1_fib_num,A),k2_power(k2_fib_num,A)) ) )).
fof(t21_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => k2_int_1(k7_xcmplx_0(k2_power(k1_fib_num,k2_xcmplx_0(k3_xcmplx_0(2,A),1)),k3_square_1(5))) = k1_pre_ff(k2_xcmplx_0(k3_xcmplx_0(2,A),1)) ) )).
fof(t21_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t21_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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 ) ) )).
fof(t21_filter_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( m1_subset_1(F,B) => ! [G] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t21_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & r3_lattices(A,D,C) ) => r2_hidden(D,B) ) ) ) ) ) ) ) )).
fof(t21_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t21_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t21_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_finseq_1(D,C) => ~ ( k3_finseq_1(D) = k2_xcmplx_0(A,B) & ! [E] : ( m2_finseq_1(E,C) => ! [F] : ( m2_finseq_1(F,C) => ~ ( k3_finseq_1(E) = A & k3_finseq_1(F) = B & D = k8_finseq_1(C,E,F) ) ) ) ) ) ) ) ) )).
fof(t21_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : ( v7_ordinal1(C) => ( k2_finseq_1(C) = k2_tarski(A,B) => ( A = B | ( C = 2 & k2_tarski(A,B) = k2_tarski(1,2) ) ) ) ) )).
fof(t21_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t21_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( 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)))) ) ) ) ) )).
fof(t21_finseq_6,axiom,( ! [A] : ! [B] : ! [C] : k4_finseq_4(k11_finseq_1(A,B,C),A) = 1 )).
fof(t21_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k2_finseq_7(A,B,C,D) = k2_finseq_7(A,B,D,C) ) ) ) ) )).
fof(t21_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r1_tarski(C,B) => ( r1_xxreal_0(k3_finseq_1(C),k5_numbers) | k1_funct_1(C,1) = k1_funct_1(B,1) ) ) ) ) ) )).
fof(t21_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( ( 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))) ) => ! [G] : ( ( v3_card_1(G,E) & m2_finseq_1(G,A) ) => k3_funcop_1(F,G,k5_finseq_2(A,E,D)) = k4_funcop_1(F,G,D) ) ) ) ) ) ) ) )).
fof(t21_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t21_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k10_fintopo2(A,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(D,k6_fintopo2(A,B)) & r1_tarski(D,C) ) ) ) ) ) )).
fof(t21_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) )).
fof(t21_fintopo4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( ~ r1_xxreal_0(A,k5_numbers) => v1_fin_topo(k4_fintopo4(A)) ) ) )).
fof(t21_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) )).
fof(t21_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_catalan2(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t21_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( k1_flang_2(A,B,C,D) = k1_xboole_0 <=> ~ ( r1_xxreal_0(C,D) & ~ ( ~ r1_xxreal_0(C,k5_numbers) & B = k1_xboole_0 ) ) ) ) ) ) )).
fof(t21_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k8_afinsq_1(A))) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( ( r1_tarski(B,k1_flang_3(A,D,E)) & r1_tarski(C,k1_flang_3(A,D,F)) ) => r1_tarski(k6_flang_1(A,B,C),k1_flang_3(A,D,k2_xcmplx_0(E,F))) ) ) ) ) ) ) )).
fof(t21_fomodel0,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(t21_fomodel4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( v4_card_3(C) & m1_subset_1(C,k1_zfmisc_1(k30_fomodel2(B))) ) => ! [D] : ( m2_subset_1(D,k9_funct_2(k37_fomodel1(B),k3_rfunct_3(k3_finseq_2(A),k2_xboole_0(A,k6_margrel1))),k15_fomodel2(B,A)) => ~ ( v10_fomodel2(C,A,B,D) & ! [E] : ( ( ~ v1_xboole_0(E) & v4_card_3(E) ) => ! [F] : ( m2_subset_1(F,k9_funct_2(k37_fomodel1(B),k3_rfunct_3(k3_finseq_2(E),k2_xboole_0(E,k6_margrel1))),k15_fomodel2(B,E)) => ~ v10_fomodel2(C,E,B,F) ) ) ) ) ) ) ) )).
fof(t21_frechet,axiom,( v1_frechet(k3_topmetr) )).
fof(t21_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v3_frechet(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t21_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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)) ) ) ) )).
fof(t21_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( v7_ordinal1(E) => r6_fsm_1(A,B,C,D,D,E) ) ) ) ) ) )).
fof(t21_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( ~ v2_struct_0(D) & l2_fsm_2(D,A,B) ) => ( r2_fsm_2(A,C,D) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( m1_subset_1(F,B) => ( ( r3_fsm_2(A,B,D,C,E) & r3_fsm_2(A,B,D,C,F) ) => E = F ) ) ) ) ) ) ) ) )).
fof(t21_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t21_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : 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))) )).
fof(t21_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( ( k9_xtuple_0(D) = k9_xtuple_0(k3_funcop_1(C,A,B)) & ! [E] : ( 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) ) ) ) ) ) )).
fof(t21_funcsdom,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ~ ( C = k2_tarski(A,B) & A != B & ! [D] : ( m2_funct_2(D,C,k1_numbers,k9_funct_2(C,k1_numbers)) => ! [E] : ( m2_funct_2(E,C,k1_numbers,k9_funct_2(C,k1_numbers)) => ? [F] : ( m2_funct_2(F,C,k1_numbers,k9_funct_2(C,k1_numbers)) & ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => F != k1_binop_1(k5_funcsdom(C),k1_funct_1(k7_funcsdom(C),k4_tarski(G,D)),k1_funct_1(k7_funcsdom(C),k4_tarski(H,E))) ) ) ) ) ) ) ) )).
fof(t21_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(B,k9_xtuple_0(k3_relat_1(C,k4_relat_1(A)))) <=> ( r2_hidden(B,k9_xtuple_0(C)) & r2_hidden(k1_funct_1(C,B),A) ) ) ) )).
fof(t21_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,D,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(D,A))) ) => ! [F] : ( ( 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) ) ) ) ) ) ) )).
fof(t21_funct_3,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(t21_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k1_funct_4(A,k1_xboole_0) = A ) )).
fof(t21_funct_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ! [B] : ~ ( 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 ) ) ) )).
fof(t21_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( A != k1_xboole_0 => ! [B] : ( r2_hidden(B,k3_funct_6(A)) <=> ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => r2_hidden(B,k1_funct_1(A,C)) ) ) ) ) )).
fof(t21_funct_7,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ? [C] : ( m2_subset_1(C,k1_zfmisc_1(A),B) & ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( r1_tarski(D,C) => D = C ) ) ) ) ) )).
fof(t21_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t21_funct_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & v1_int_1(A) ) => v1_funct_9(k16_sin_cos,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A)) ) )).
fof(t21_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_altcat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( k1_altcat_1(B,C,C) != k1_xboole_0 => ! [D] : ( m1_subset_1(D,k1_altcat_1(B,C,C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k3_functor0(A,B,k9_functor0(A,B,C,D),E) = C ) ) ) ) ) ) )).
fof(t21_functor1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & v1_altcat_2(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & v1_altcat_2(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v12_altcat_1(C) & v1_altcat_2(C) & l2_altcat_1(C) ) => ! [D] : ( ( v8_functor0(D,A,B) & l2_functor0(D,A,B) ) => ! [E] : ( ( v8_functor0(E,B,C) & l2_functor0(E,B,C) ) => ! [F] : ( ( v8_functor0(F,B,A) & l2_functor0(F,B,A) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t21_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( m1_functor2(E,A,B,C,D) => ( r1_functor2(A,B,C,D) => r8_pboole(u1_struct_0(A),k6_functor3(A,A,B,C,D,k12_functor0(A),E),E) ) ) ) ) ) ) )).
fof(t21_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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) ) ) ) ) )).
fof(t21_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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))) ) ) ) )).
fof(t21_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ! [D] : ( r2_hidden(k4_tarski(C,D),k2_zfmisc_1(A,B)) => ( k1_funct_1(k4_fuzzy_2(A,B),k4_tarski(C,D)) = k5_numbers & k1_funct_1(k5_fuzzy_2(A,B),k4_tarski(C,D)) = 1 ) ) ) ) )).
fof(t21_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_fvaluat1(C,A) => ( v3_fvaluat1(A) => ( B = k4_struct_0(A) | k3_funct_2(u1_struct_0(A),k6_numbers,C,k11_algstr_0(A,B)) = k2_supinf_2(k3_funct_2(u1_struct_0(A),k6_numbers,C,B)) ) ) ) ) ) )).
fof(t21_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v1_algstr_1(B) & v2_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t21_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ ( ~ 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)) ) ) )).
fof(t21_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_vectsp_1(A) & l4_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(B,k3_gcd_1(A)) & v1_xboole_0(B) ) ) ) )).
fof(t21_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v2_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( m1_genealg1(E,D) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t21_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( r2_geomtrap(A,F,G,B,D,C,E) => r2_geomtrap(A,F,G,C,E,B,D) ) ) ) ) ) ) ) ) )).
fof(t21_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k7_gfacirc1(A,B,C),k8_gfacirc1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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) ) ) ) ) ) )).
fof(t21_gfacirc2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t21_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & ~ v4_glib_000(A) ) => ~ ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => B = C ) ) ) )).
fof(t21_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t21_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v3_glib_001(B,A) => k10_glib_003(A,B) = k5_numbers ) ) ) )).
fof(t21_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( 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)))) = k4_nat_1(k1_nat_1(C,1),k5_card_1(k2_glib_002(A,B))) ) ) ) )).
fof(t21_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r1_xxreal_0(1,A) => ( r1_xxreal_0(k1_matrix_0(C),B) | r1_xxreal_0(k3_finseq_1(C),A) | r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),k1_nat_1(B,1))),k3_goboard5(C,A,B)) ) ) ) ) ) )).
fof(t21_goboard6,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_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),k5_numbers)) = a_1_6_goboard6(A) ) )).
fof(t21_goboard7,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(A)) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k1_matrix_0(A)) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(A)) & r1_xxreal_0(1,E) & r1_xxreal_0(E,k1_matrix_0(A)) ) => ( r1_xboole_0(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,k1_nat_1(C,1))),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,D,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,k1_nat_1(D,1),E))) | ( ( B = D | B = k1_nat_1(D,1) ) & ( C = E | k1_nat_1(C,1) = E ) ) ) ) ) ) ) ) ) )).
fof(t21_goboard9,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t21_gobrd11,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( v2_goboard1(A) => k2_goboard5(A,k5_numbers) = a_1_11_gobrd11(A) ) ) )).
fof(t21_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(D)) & r1_goboard1(u1_struct_0(k15_euclid(2)),D,E) & r2_hidden(k4_tarski(A,k1_nat_1(B,1)),k2_matrix_0(E)) & r2_hidden(k4_tarski(A,B),k2_matrix_0(E)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,B) ) => k2_gobrd13(D,E,C) = k3_goboard5(E,k7_nat_d(A,1),B) ) ) ) ) ) ) )).
fof(t21_gobrd14,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t21_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ( r2_hidden(C,B) => r1_henmodel(A,B,C) ) ) ) ) )).
fof(t21_gr_cy_1,axiom,( ! [A] : ( ( ~ 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) ) ) ) )).
fof(t21_gr_cy_2,axiom,( ! [A] : ( ( ~ 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) ) ) ) )).
fof(t21_gr_cy_3,axiom,( k1_gr_cy_3(7) = 127 )).
fof(t21_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_graph_1(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & l1_graph_1(D) ) => ( ( r4_graph_1(B,D) & r4_graph_1(C,D) & r1_graph_1(A,B,C) ) => r4_graph_1(A,D) ) ) ) ) ) )).
fof(t21_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_graph_2(A) & v2_graph_2(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(A)) & k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) ) ) )).
fof(t21_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : r1_tarski(k3_graph_3(A,B,C),k6_graph_3(A,B)) ) ) )).
fof(t21_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( ( v7_graph_1(C,A) & m2_graph_1(C,A) ) => ~ ( r3_graph_4(A,B,C) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(C)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(B)) => ! [F] : ( ( v7_graph_1(F,A) & v3_graph_2(F,A) & m2_graph_1(F,A) ) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t21_graph_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(C) & l1_graph_1(C) ) => ! [D] : ( m2_finseq_1(D,u4_struct_0(C)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t21_graphsp,axiom,( ! [A] : ( 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] : ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k4_graphsp(k3_finseq_2(k1_numbers),k9_nat_1(k1_funct_2(k3_finseq_2(k1_numbers),k3_finseq_2(k1_numbers)),k5_graphsp(k3_finseq_2(k1_numbers),A),k5_numbers),B) = B ) ) ) ) )).
fof(t21_grcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v13_algstr_0(D) & v3_rlvect_1(D) & v4_rlvect_1(D) & l2_algstr_0(D) ) => ! [E] : ( ( v1_grcat_1(E) & m1_grcat_1(E,A,B) ) => ! [F] : ( ( v1_grcat_1(F) & m1_grcat_1(F,B,C) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t21_grfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(B,A) => k5_relat_1(A,k9_xtuple_0(B)) = B ) ) ) )).
fof(t21_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ( v1_grnilp_1(A) <=> ? [B] : ( m2_finseq_1(B,k2_grnilp_1(A)) & ~ r1_xxreal_0(k3_finseq_1(B),k5_numbers) & k1_funct_1(B,1) = k7_group_2(A) & k1_funct_1(B,k3_finseq_1(B)) = k6_group_2(A) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(k2_xcmplx_0(C,1),k4_finseq_1(B)) ) => ! [D] : ( ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) ) => ! [E] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t21_groeb_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_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)) ) ) ) ) ) ) )).
fof(t21_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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),k8_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))) ) ) ) ) ) ) )).
fof(t21_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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_numbers) = k1_xboole_0 & k4_groeb_3(A,B,C,D,k5_numbers) = k3_polynom1(k15_pre_poly(A),C,D) ) ) ) ) ) )).
fof(t21_group_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t21_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( m1_group_2(D,A) => ( r1_tarski(B,C) => r1_tarski(k1_group_11(A,B,D),k1_group_11(A,C,D)) ) ) ) ) ) )).
fof(t21_group_14,axiom,( ! [A] : ( ( 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] : ( ( v1_relat_1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_finseq_1(B) & v1_prvect_1(B) ) => ~ ( k3_finseq_1(A) = k3_finseq_1(B) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r2_hidden(C,k4_finseq_1(B)) & ! [D] : ( ( v7_ordinal1(D) & ~ v8_ordinal1(D) ) => ~ ( D = k1_funct_1(A,C) & k1_funct_1(B,C) = k2_group_14(D) ) ) ) ) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k2_group_14(k19_rvsum_1(A))),u1_struct_0(k20_prvect_1(B))) & v13_vectsp_1(C,k2_group_14(k19_rvsum_1(A)),k20_prvect_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_group_14(k19_rvsum_1(A))),u1_struct_0(k20_prvect_1(B))))) ) => ~ ( v3_funct_2(C,u1_struct_0(k2_group_14(k19_rvsum_1(A))),u1_struct_0(k20_prvect_1(B))) & ! [D] : ( v1_int_1(D) => ( r2_hidden(D,u1_struct_0(k2_group_14(k19_rvsum_1(A)))) => k1_funct_1(C,D) = k1_int_6(D,A) ) ) ) ) ) ) ) )).
fof(t21_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k2_group_2(A,k7_domain_1(u1_struct_0(A),B,E),k7_domain_1(u1_struct_0(A),C,D)) = k9_domain_1(u1_struct_0(A),k6_algstr_0(A,B,C),k6_algstr_0(A,B,D),k6_algstr_0(A,E,C),k6_algstr_0(A,E,D)) ) ) ) ) ) )).
fof(t21_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t21_group_4,axiom,( ! [A] : ( ( ~ 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 ) )).
fof(t21_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t21_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_group_6(A,B))) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & C = k13_group_2(A,B,D) & C = k14_group_2(A,B,D) ) ) ) ) )).
fof(t21_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & v5_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t21_group_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ( v8_struct_0(A) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,B) => ! [D] : ( m1_group_2(D,B) => ! [E] : ( m1_group_2(E,C) => ( E = k10_group_2(B,C,D) => ! [F] : ( m1_group_2(F,D) => ( F = k10_group_2(B,C,D) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(t21_groupp_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v8_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( v1_group_3(C,B) & m1_group_2(C,B) ) => ! [D] : ( ( v1_group_3(D,B) & m1_group_2(D,B) ) => ~ ( v2_group_10(C,A) & v2_group_10(D,A) & ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t21_hahnban,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( v1_xreal_0(F) => ? [G] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t21_hahnban1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(t21_hallmar1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( r2_hidden(C,k4_finseq_1(B)) => m2_hallmar1(k2_hallmar1(A,B,C,D),A,B) ) ) ) ) )).
fof(t21_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( v2_compts_1(B,k3_pcomps_1(A)) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,B) & r1_xxreal_0(k3_metric_1(A,D,C),k1_funct_1(k5_weierstr(A,B),C)) ) ) ) ) ) ) )).
fof(t21_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v7_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( ( v7_ordinal1(D) & ~ v1_abian(D) ) => ( ( r1_xxreal_0(D,k3_finseq_1(B)) & r1_xxreal_0(D,k3_finseq_1(C)) & ! [E] : ( ( v7_ordinal1(E) & ~ v1_abian(E) ) => ( r1_xxreal_0(E,D) => k1_funct_1(B,E) = k1_funct_1(C,E) ) ) ) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,D) ) => k1_funct_1(B,E) = k1_funct_1(C,E) ) ) ) ) ) ) ) )).
fof(t21_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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] : ( ( 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))) ) ) ) )).
fof(t21_heyting1,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A)) => k10_normform(A,B,k6_heyting1(A,B)) = k1_xboole_0 ) )).
fof(t21_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m1_subset_1(C,k4_partfun1(A,B)) => ( v1_finset_1(C) => ! [D] : ( r2_hidden(D,k3_funct_2(k4_partfun1(A,B),u1_struct_0(k5_substlat(A,B)),k8_heyting2(A,B),C)) => D = C ) ) ) ) )).
fof(t21_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ~ ( r2_hidden(C,k4_heyting3(k1_nat_1(A,1),B)) & ! [D] : ~ ( r2_hidden(D,k4_heyting3(A,B)) & r1_tarski(D,C) ) ) ) ) )).
fof(t21_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t21_hilbasis,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r1_xxreal_0(k1_algseq_1(A,k11_polynom3(A,B,C)),k7_nat_d(k1_nat_1(k1_algseq_1(A,B),k1_algseq_1(A,C)),1)) ) ) ) )).
fof(t21_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(t21_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( k1_hilbert2(B) = k1_hilbert2(A) => B = A ) ) ) )).
fof(t21_hilbert3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ ( C = k1_xboole_0 & B != k1_xboole_0 & A != k1_xboole_0 ) => ! [D] : ( ( 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) ) ) )).
fof(t21_hurwitz,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) )).
fof(t21_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k9_idea_1(C,A,B) = k9_idea_1(C,B,A) ) ) ) )).
fof(t21_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( v1_gcd_1(C,A) & r2_hidden(C,B) ) ) ) ) ) )).
fof(t21_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ~ ( ! [E] : ( 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] : ( 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 ) ) ) ) ) )).
fof(t21_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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] : ( 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 ) ) ) )).
fof(t21_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( l3_msualg_1(C,B) => ! [D] : ( 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] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t21_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( r2_int_1(A,B,C) <=> r2_int_1(k2_xcmplx_0(A,C),B,C) ) ) ) ) )).
fof(t21_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => r1_int_1(k3_int_2(A,B),A) ) ) )).
fof(t21_int_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & v1_int_2(A) & r1_int_2(A,B) & r1_nat_d(A,k4_nat_d(B,k1_newton(A,C))) ) ) ) ) )).
fof(t21_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ( k3_int_2(A,B) = 1 => ( r1_xxreal_0(B,2) | r1_int_5(A,B) | k5_int_1(k2_xcmplx_0(k1_newton(A,k3_nat_d(k7_nat_d(B,1),2)),1),B) = k5_numbers ) ) ) ) )).
fof(t21_int_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t21_int_7,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t21_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_int_2(B,C) & r1_int_2(A,k3_xcmplx_0(B,C)) ) => ( r1_xxreal_0(C,1) | r1_xxreal_0(B,1) | k3_pepin(A,k3_xcmplx_0(B,C)) = k5_nat_d(k3_pepin(A,B),k3_pepin(A,C)) ) ) ) ) ) )).
fof(t21_integr11,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( B = k1_rcomp_1(k5_numbers,k3_xcmplx_0(2,k28_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)),k18_sin_cos)) = k5_numbers ) ) ) )).
fof(t21_integr12,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,D) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => k1_funct_1(C,E) = 1 ) ) & r1_tarski(D,k2_rcomp_1(k4_xcmplx_0(1),1)) & D = k1_relset_1(k1_numbers,B) & r2_relset_1(k1_numbers,k1_numbers,B,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,C,k1_taylor_1(2)),k4_taylor_1(k7_xcmplx_0(1,2)))))) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,D),k1_sin_cos6),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,D),k1_sin_cos6),k3_seq_4(A))) ) ) ) ) ) )).
fof(t21_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k26_sin_cos,k22_sin_cos),k41_valued_1(k1_numbers,k1_numbers,k18_sin_cos))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k22_sin_cos),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k22_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t21_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k22_sin_cos),k3_rfunct_1(k1_numbers,k1_numbers,k16_sin_cos,k41_valued_1(k1_numbers,k1_numbers,k18_sin_cos)))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fdiff_9,k22_sin_cos),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fdiff_9,k22_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t21_integr15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k1_euclid(A)))) ) => ! [E] : ( ( 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)) ) ) ) ) )).
fof(t21_integr16,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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)) = k3_xcmplx_0(A,k7_integr16(B,C)) ) ) ) ) ) )).
fof(t21_integr19,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t21_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => k18_rvsum_1(k5_integra1(A,k7_rfunct_1(A,A),B)) = k3_integra1(A) ) ) )).
fof(t21_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( m1_integra1(D,B) => ( ( v1_comseq_2(k2_partfun1(B,k1_numbers,C,B)) & r1_xxreal_0(k5_numbers,A) ) => r1_xxreal_0(k1_funct_1(k9_integra1(B,k26_valued_1(B,k1_numbers,C,A)),D),k3_xcmplx_0(k3_xcmplx_0(A,k2_seq_4(k1_rvsum_1(C))),k3_integra1(B))) ) ) ) ) ) )).
fof(t21_integra4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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))) ) ) )).
fof(t21_integra5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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)) = k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(B,k2_seq_4(A)),k1_funct_1(C,k2_seq_4(A))),k3_xcmplx_0(k1_funct_1(B,k3_seq_4(A)),k1_funct_1(C,k3_seq_4(A)))),k2_integra5(A,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,B,k2_fdiff_1(C,D)))) ) ) ) ) ) )).
fof(t21_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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(k9_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))) ) ) ) ) ) ) ) )).
fof(t21_integra7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_xxreal_0(B,A) & r1_tarski(k3_integra5(B,A),C) & r1_integra5(k3_integra5(B,A),D) & r1_integra5(k3_integra5(B,A),E) & v1_comseq_2(k2_partfun1(k1_numbers,k1_numbers,D,k3_integra5(B,A))) & v1_comseq_2(k2_partfun1(k1_numbers,k1_numbers,E,k3_integra5(B,A))) & 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) ) => k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(F,A),k1_funct_1(G,A)),k3_xcmplx_0(k1_funct_1(F,B),k1_funct_1(G,B))) = k2_xcmplx_0(k4_integra5(B,A,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,D,G)),k4_integra5(B,A,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,F,E))) ) ) ) ) ) ) ) )).
fof(t21_integra8,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t21_integra9,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( ~ 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)) ) ) ) ) )).
fof(t21_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_interva1(C,A) ) => r1_interva1(A,k4_interva1(A,B,C),k4_interva1(A,C,B)) ) ) ) )).
fof(t21_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => r2_hidden(k3_intpro_1(k3_intpro_1(B,A),k3_intpro_1(A,A)),k8_intpro_1) ) ) )).
fof(t21_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ( v1_series_1(k3_irrat_1(A)) & k4_series_1(k3_irrat_1(A)) = k2_power(k2_xcmplx_0(1,k7_xcmplx_0(1,A)),A) & k4_series_1(k3_irrat_1(A)) = k1_funct_1(k4_irrat_1,A) ) ) ) )).
fof(t21_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ( r2_nattra_1(A,B,D,E) => ! [F] : ( m2_nattra_1(F,A,B,D,E) => ! [G] : ( m2_cat_1(G,B,C) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => k2_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,k2_nattra_1(A,B,D,E,F,H)) ) ) ) ) ) ) ) ) ) )).
fof(t21_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)))) ) ) ) )).
fof(t21_jgraph_1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ~ ( r1_jgraph_1(u1_struct_0(k15_euclid(2)),A,B) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(B)) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( r1_xxreal_0(1,D) & r1_xxreal_0(k1_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,k1_nat_1(D,1)) = k7_partfun1(u1_struct_0(k15_euclid(2)),B,k1_nat_1(C,1)) & k1_funct_1(A,D) = k1_funct_1(B,C) & k1_funct_1(A,k1_nat_1(D,1)) = k1_funct_1(B,k1_nat_1(C,1)) ) ) ) ) ) ) )).
fof(t21_jgraph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( 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) ) ) ) ) ) ) )).
fof(t21_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( 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] : ( 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) = k3_xcmplx_0(k12_euclid(D),k4_xcmplx_0(k3_square_1(k6_xcmplx_0(1,k1_square_1(k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k18_euclid(D),k12_euclid(D)),A),k6_xcmplx_0(1,A))))))) ) ) & ! [D] : ( 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),k5_numbers) & r1_xxreal_0(A,k7_xcmplx_0(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) ) ) ) ) ) )).
fof(t21_jgraph_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r1_xxreal_0(k5_numbers,k18_euclid(B)) & r1_xxreal_0(k5_numbers,k18_euclid(C)) ) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) | r1_xxreal_0(1,A) | k12_euclid(B) = k5_numbers | k12_euclid(C) = k5_numbers | r1_xxreal_0(k7_xcmplx_0(k17_euclid(C),k12_euclid(C)),k7_xcmplx_0(k17_euclid(B),k12_euclid(B))) | ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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(k7_xcmplx_0(k17_euclid(E),k12_euclid(E)),k7_xcmplx_0(k17_euclid(D),k12_euclid(D))) ) ) ) ) ) ) ) ) )).
fof(t21_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_jordan,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t21_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => a_4_2_jordan1(A,B,C,D) = a_4_3_jordan1(A,B,C,D) ) ) ) ) )).
fof(t21_jordan12,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k3_finseq_1(A)) ) => v1_convex1(k5_goboard5(A,B),k15_euclid(2)) ) ) ) )).
fof(t21_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( r1_jordan1h(A,B) => r1_tarski(k3_topreal1(2,k1_jordan13(A,B)),k1_jordan2c(2,A)) ) ) ) )).
fof(t21_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E),k3_topreal1(2,k1_jordan1e(B,A))) & r2_hidden(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k9_jordan6(B)) ) ) ) ) ) ) )).
fof(t21_jordan16,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t21_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ( ( r1_jordan17(A,B,C,D,E) & r1_jordan17(A,C,B,D,E) ) => ( B = D | B = E | C = E | B = C ) ) ) ) ) ) ) )).
fof(t21_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( ~ 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_0(B)) ) => r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,A)),k6_pscomp_1(k3_topreal1(2,C))) ) ) ) ) )).
fof(t21_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(k1_jordan8(B,A))) & k20_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,k1_matrix_0(k1_jordan8(B,A))) ) ) ) )).
fof(t21_jordan1g,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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)))) ) => r1_xxreal_0(k4_finseq_4(k1_jordan1e(B,A),k19_pscomp_1(k3_topreal1(2,k2_jordan9(B,A)))),k4_finseq_4(k1_jordan1e(B,A),k20_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))))) ) ) )).
fof(t21_jordan1h,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(B)) ) => k3_gobrd13(B,k2_goboard2(B),A) = k5_goboard5(B,A) ) ) ) )).
fof(t21_jordan1k,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => k1_topreal6(2,k3_rlvect_1(k15_euclid(2),B,A),k3_rlvect_1(k15_euclid(2),C,A)) = k1_topreal6(2,B,C) ) ) ) )).
fof(t21_jordan20,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t21_jordan21,axiom,( ! [A] : ( ( 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(k7_xcmplx_0(k2_xcmplx_0(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(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)),2))))) ) ) )).
fof(t21_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,k5_numbers) => k1_jordan21(k3_topreal1(2,k2_jordan9(A,B))) = k1_jordan21(k8_jordan6(k3_topreal1(2,k2_jordan9(A,B)))) ) ) ) )).
fof(t21_jordan23,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t21_jordan2b,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_rlvect_1(k15_euclid(1),k1_jordan2b(A),B) = k1_jordan2b(k3_xcmplx_0(B,A)) ) ) )).
fof(t21_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( v9_rltopsp1(B,k15_euclid(A)) <=> ? [C] : ( v1_xreal_0(C) & ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ~ ( r2_hidden(D,B) & r1_xxreal_0(C,k12_euclid(D)) ) ) ) ) ) ) )).
fof(t21_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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,k1_nat_1(k1_jordan3(A,B),1)) | k1_nat_1(k1_jordan3(k4_finseq_5(u1_struct_0(k15_euclid(2)),A),B),k1_jordan3(A,B)) = k3_finseq_1(A) ) ) ) ) )).
fof(t21_jordan4,axiom,( ! [A] : ( ( 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) ) )).
fof(t21_jordan5a,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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] : ( 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] : ( 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] : ( v1_xreal_0(G) & v3_tops_2(F,k5_topmetr,k1_pre_topc(k15_euclid(2),A)) & k1_funct_1(F,k5_numbers) = C & k1_funct_1(F,1) = D & k1_funct_1(F,G) = E & r1_xxreal_0(k5_numbers,G) & r1_xxreal_0(G,1) & ! [H] : ( v1_xreal_0(H) => ~ ( r1_xxreal_0(k5_numbers,H) & ~ r1_xxreal_0(G,H) & r2_hidden(k1_funct_1(F,H),B) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_jordan5b,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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) = k13_matrix_0(u1_struct_0(k15_euclid(2)),B) ) ) ) )).
fof(t21_jordan5c,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_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) ) ) ) )).
fof(t21_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( B = a_1_1_jordan5d(A) => k3_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)))) ) ) ) )).
fof(t21_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) )).
fof(t21_jordan9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(C)) & r2_hidden(D,k9_matrix_0(C)) & r2_hidden(D,k3_goboard5(C,A,B)) ) => r1_sppol_1(2,D,k3_goboard5(C,A,B)) ) ) ) ) ) )).
fof(t21_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_jordan_a(B,A) => ! [C] : ( v7_ordinal1(C) => ( ( 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) ) ) ) ) )).
fof(t21_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) & r2_abian(u1_struct_0(A),C,B) ) ) ) )).
fof(t21_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(B) => k4_kurato_0(A,B) = k1_kurato_0(A,B) ) ) )).
fof(t21_kurato_1,axiom,( 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) )).
fof(t21_kurato_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(A)))))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ( ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) & v3_toprns_1(D,A) & ! [E] : ( v7_ordinal1(E) => r2_hidden(k1_jordan11(A,D,E),k2_kurato_2(k15_euclid(A),B,E)) ) & C = k6_toprns_1(A,D) ) => r2_hidden(C,k1_kurato_2(k15_euclid(A),B)) ) ) ) ) )).
fof(t21_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_group_3(A)) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_group_3(A))) ) => ( C = k1_tarski(B) => k2_latsubgr(A,C) = B ) ) ) ) )).
fof(t21_latsum_1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ! [D] : ( ( 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)) ) ) ) )).
fof(t21_lattice2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t21_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t21_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(t21_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v5_lattice6(B,A) => v4_lattice6(B,A) ) ) ) )).
fof(t21_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ! [D] : ( v3_ordinal1(D) => ( r1_ordinal1(C,D) => r1_tarski(k3_lattice8(A,C),k3_lattice8(A,D)) ) ) ) ) ) )).
fof(t21_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t21_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( ( v4_lexbfs(B,A) & m1_lexbfs(B,A) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t21_lfuzzy_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_lfuzzy_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t21_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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,k1_fuzzy_4(A,A,B))) ) ) ) ) )).
fof(t21_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => k1_funct_1(A,B) = k4_xcmplx_0(B) ) => v2_limfunc1(A) ) ) )).
fof(t21_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r2_limfunc2(C,B) => ( r1_xxreal_0(A,k5_numbers) | r2_limfunc2(k26_valued_1(k1_numbers,k1_numbers,C,A),B) ) ) & ( r2_limfunc2(C,B) => ( r1_xxreal_0(k5_numbers,A) | r3_limfunc2(k26_valued_1(k1_numbers,k1_numbers,C,A),B) ) ) & ( r3_limfunc2(C,B) => ( r1_xxreal_0(A,k5_numbers) | r3_limfunc2(k26_valued_1(k1_numbers,k1_numbers,C,A),B) ) ) & ( r3_limfunc2(C,B) => ( r1_xxreal_0(k5_numbers,A) | r2_limfunc2(k26_valued_1(k1_numbers,k1_numbers,C,A),B) ) ) ) ) ) ) )).
fof(t21_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,C) & ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ~ ( ~ 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] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(k6_xcmplx_0(A,C),A))) & v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(A,k2_xcmplx_0(A,C)))) & ~ v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(k6_xcmplx_0(A,C),A))) & ~ v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(A,k2_xcmplx_0(A,C)))) ) ) | r2_limfunc3(B,A) ) ) ) ) )).
fof(t21_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(k6_xcmplx_0(A,D),A))) & r1_xxreal_0(k1_funct_1(B,E),k1_limfunc2(B,A)) ) ) ) ) | r2_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t21_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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)) ) ) ) ) )).
fof(t21_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t21_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t21_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => k5_struct_0(k7_lopban_2(A)) = k6_lopban_2(A) ) )).
fof(t21_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ! [D] : ( v7_ordinal1(D) => k5_rsspace3(A,C,D) = k5_rsspace3(A,B,k5_numbers) ) => r2_funct_2(k4_ordinal1,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)) ) ) ) ) )).
fof(t21_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k9_nat_1(u1_struct_0(A),k1_lopban_4(A,C),k5_numbers) = k5_struct_0(A) & k9_nat_1(u1_struct_0(A),k5_lopban_4(k5_numbers,A,C,B),k5_numbers) = k5_struct_0(A) ) ) ) ) )).
fof(t21_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t21_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_lpspacc1(A,B,C))) => ( D = E => ( k3_rlvect_1(k14_lpspacc1(A,B,C),E,k1_clvect_1(k14_lpspacc1(A,B,C),E,k4_xcmplx_0(k6_complex1))) = k2_partfun1(A,k2_numbers,k8_funcop_1(k2_numbers,A,k5_complex1),k1_relset_1(A,D)) & ? [F] : ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) & ? [G] : ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) & r2_hidden(F,k13_lpspacc1(A,B,C)) & r2_hidden(G,k13_lpspacc1(A,B,C)) & F = k3_rlvect_1(k14_lpspacc1(A,B,C),E,k1_clvect_1(k14_lpspacc1(A,B,C),E,k4_xcmplx_0(k6_complex1))) & r2_relset_1(A,k2_numbers,G,k8_funcop_1(k2_numbers,A,k5_complex1)) & r1_lpspacc1(A,B,C,F,G) ) ) ) ) ) ) ) ) ) )).
fof(t21_lpspace1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_rfunct_3(C,B,k1_numbers,k3_rfunct_3(B,k1_numbers)) => ! [D] : ( m2_rfunct_3(D,B,k1_numbers,k3_rfunct_3(B,k1_numbers)) => k1_binop_1(k3_lpspace1(B),k1_binop_1(k4_lpspace1(B),A,C),D) = k1_binop_1(k4_lpspace1(B),A,k2_lpspace1(B,k1_numbers,k3_lpspace1(B),C,D)) ) ) ) ) )).
fof(t21_lpspace2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_numbers) => r1_xxreal_0(k2_power(k9_complex1(k2_xcmplx_0(A,B)),C),k3_xcmplx_0(k2_power(2,C),k2_xcmplx_0(k2_power(k9_complex1(A),C),k2_power(k9_complex1(B),C)))) ) ) ) ) )).
fof(t21_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(D),k1_domain_1(k4_ordinal1,k1_hilbert1,C,k3_hilbert1(k4_hilbert1(A,B),k2_ltlaxio1(k7_ltlaxio1(B))))) = 1 ) ) ) ) )).
fof(t21_ltlaxio2,axiom,( ! [A] : ( m2_finseq_1(A,k1_hilbert1) => ! [B] : ( m2_finseq_1(B,k1_hilbert1) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k1_hilbert1,k6_margrel1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_hilbert1,k6_margrel1))) ) => ( k2_relset_1(k1_hilbert1,A) = k2_relset_1(k1_hilbert1,B) => k3_funct_2(k1_hilbert1,k6_margrel1,k12_ltlaxio1(C),k7_partfun1(k1_hilbert1,k2_ltlaxio2(A),k3_finseq_1(k2_ltlaxio2(A)))) = k3_funct_2(k1_hilbert1,k6_margrel1,k12_ltlaxio1(C),k7_partfun1(k1_hilbert1,k2_ltlaxio2(B),k3_finseq_1(k2_ltlaxio2(B)))) ) ) ) ) )).
fof(t21_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_hilbert1)) => ( r2_hidden(k5_ltlaxio1(A,B),k5_ltlaxio3(C)) => ( r2_hidden(A,k5_ltlaxio3(C)) & r2_hidden(B,k5_ltlaxio3(C)) ) ) ) ) ) )).
fof(t21_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ( ( r2_hidden(k4_hilbert1(A,B),k2_relset_1(k1_hilbert1,k9_ltlaxio3(C))) & r2_hidden(D,k9_ltlaxio4(C)) ) => r2_hidden(k1_ltlaxio2(A,B),k2_relset_1(k1_hilbert1,k9_ltlaxio3(D))) ) ) ) ) ) )).
fof(t21_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t21_margrel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) )).
fof(t21_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k1_mathmorp(A,k4_struct_0(A),B) = B ) ) )).
fof(t21_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( v1_matrix10(B) & v2_matrix10(C) ) => v2_matrix10(k5_matrix10(A,C,B)) ) ) ) ) )).
fof(t21_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_matrix_2(B,k3_matrix_2(A)) => ? [C] : ( m2_finseq_1(C,u1_struct_0(k4_matrix_2(A))) & B = k3_group_4(k4_matrix_2(A),C) & ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(D,k4_finseq_1(C)) & ! [E] : ( m1_matrix_2(E,k3_matrix_2(A)) => ~ ( k1_funct_1(C,D) = E & v4_matrix_2(E,k2_matrix_2(k3_matrix_2(A))) ) ) ) ) ) ) ) )).
fof(t21_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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(B,k4_finseq_1(k3_matrix_1(D,C))) & r2_hidden(A,k4_finseq_1(k3_matrix_1(D,C))) ) => ( r1_xxreal_0(C,k5_numbers) | k1_matrix_6(C,D,k4_matrix12(C,C,D,k3_matrix_1(D,C),B,A)) = k4_matrix12(C,C,D,k3_matrix_1(D,C),B,A) ) ) ) ) ) ) )).
fof(t21_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(A)) ) => ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(C,k4_ordinal1)) => ! [F] : ( m2_finseq_2(F,k4_ordinal1,k4_finseq_2(B,k4_ordinal1)) => ( ( C = 1 & B = 1 ) => k1_matrix13(A,D,C,B,E,F) = k2_matrlin(A,k13_matrix_0(A,k3_matrix_0(A,D,k1_funct_1(E,1),k1_funct_1(F,1)))) ) ) ) ) ) ) ) )).
fof(t21_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => k13_fvsum_1(A,k2_matrix14(A,k3_finseq_1(B)),B) = k4_struct_0(A) ) ) )).
fof(t21_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(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)) ) ) ) ) )).
fof(t21_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v3_matrix16(C,u1_struct_0(B)) & v3_matrix16(D,u1_struct_0(B)) ) => v3_matrix16(k3_matrix_3(B,C,D),u1_struct_0(B)) ) ) ) ) ) )).
fof(t21_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(D,E),k2_matrix_0(B)) => k3_matrix_0(A,B,D,E) = k3_matrix_0(A,C,D,E) ) ) ) ) => B = C ) ) ) ) )).
fof(t21_matrix_3,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => k4_matrix_3(A,k15_matrix_0(u1_struct_0(A),B,D,F,H),k15_matrix_0(u1_struct_0(A),C,E,G,I)) = k15_matrix_0(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))) ) ) ) ) ) ) ) ) ) )).
fof(t21_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) ) => B = k1_matrix_4(A,k3_matrix_3(A,B,C),C) ) ) ) ) )).
fof(t21_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k2_numbers)) ) => ! [C] : ( v1_xcmplx_0(C) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k1_matrix_0(A) = k1_matrix_0(B) ) => k7_matrix_5(C,k3_matrix_5(A,B)) = k3_matrix_5(k7_matrix_5(C,A),k7_matrix_5(C,B)) ) ) ) ) )).
fof(t21_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => v2_matrix_6(k11_matrix_0(u1_struct_0(B),A,A,C),A,B) ) ) ) )).
fof(t21_matrix_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t21_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_6(C,A,B) & k4_matrix_3(B,D,C) = k2_matrix_1(B,A) ) => D = k2_matrix_1(B,A) ) ) ) ) ) )).
fof(t21_matrix_9,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( ( v1_matrix_0(K) & v2_matrix_0(K,u1_struct_0(A),3,3) & m2_finseq_1(K,k3_finseq_2(u1_struct_0(A))) ) => ( K = k3_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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] : ( m1_matrix_2(L,k3_matrix_2(3)) => ( L = k3_finseq_4(k4_ordinal1,3,2,1) => k10_matrix_3(3,A,K,L) = k3_finseq_4(u1_struct_0(A),D,F,H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ( r1_xxreal_0(1,k3_finseq_1(A)) => k17_rvsum_1(k1_complsp2(A)) = k8_complex1(k17_rvsum_1(A)) ) ) )).
fof(t21_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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(k4_ordinal1,A,k11_matrixj1(B,C)) ) ) ) )).
fof(t21_matrixj2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( 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,k7_matrix_0(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))) ) ) ) ) ) )).
fof(t21_matrixr2,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k1_matrix_0(A) = k1_matrix_0(B) & k1_matrix_0(C) = k3_finseq_1(A) ) => ( r1_xxreal_0(k3_finseq_1(C),k5_numbers) | r1_xxreal_0(k3_finseq_1(A),k5_numbers) | k6_matrixr1(C,k5_matrixr1(A,B)) = k5_matrixr1(k6_matrixr1(C,A),k6_matrixr1(C,B)) ) ) ) ) ) )).
fof(t21_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ! [G] : ( m2_finseq_1(G,u1_struct_0(B)) => ( ( r1_tarski(k10_xtuple_0(G),F) & 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) & ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ( r2_hidden(H,F) => k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,H) = k3_funct_2(u1_struct_0(B),u1_struct_0(C),E,H) ) ) ) => k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,k4_rlvect_1(B,G)) = k3_funct_2(u1_struct_0(B),u1_struct_0(C),E,k4_rlvect_1(B,G)) ) ) ) ) ) ) ) )).
fof(t21_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_matrlin(C,A,B) => k3_finseq_1(C) = k1_vectsp_9(A,B) ) ) ) )).
fof(t21_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t21_matrprob,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( ~ r1_xxreal_0(k1_matrix_0(A),k5_numbers) => k3_matrprob(A) = k4_matrprob(k4_matrix_0(k1_numbers,A)) ) ) )).
fof(t21_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & v3_valued_0(C) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ! [E] : ( ( 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)))) ) => ( k1_funct_1(k3_matrtop1(A,B,D),C) = k1_funct_1(k3_matrtop1(A,B,k4_matrix11(A,B,u1_struct_0(k2_vectsp_1),E,D)),k3_relat_1(E,C)) & v3_card_1(k3_relat_1(E,C),A) & m2_finseq_1(k3_relat_1(E,C),k1_numbers) ) ) ) ) ) ) )).
fof(t21_matrtop2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m1_matrlin(C,k2_vectsp_1,k6_prvect_1(k2_vectsp_1,A)) => ( C = k11_matrix13(k2_vectsp_1,A,A,k3_matrix_1(k2_vectsp_1,A)) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(k2_vectsp_1),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( ( 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))) ) ) ) ) ) ) ) )).
fof(t21_matrtop3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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_funct_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) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(E,B),k19_sin_cos(A)),k3_xcmplx_0(k1_funct_1(E,C),k4_xcmplx_0(k17_sin_cos(A)))) ) ) ) ) ) ) ) )).
fof(t21_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t21_mboolean,axiom,( ! [A] : r6_pboole(A,k2_mboolean(A,k1_pboole(A)),k1_pboole(A)) )).
fof(t21_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( A != k1_xboole_0 & B != k1_xboole_0 & C != k1_xboole_0 ) <=> k3_zfmisc_1(A,B,C) != k1_xboole_0 ) )).
fof(t21_measure1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(t21_measure2,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ( ( k9_nat_1(B,D,k5_numbers) = k9_nat_1(B,C,k5_numbers) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( k9_nat_1(B,D,k1_nat_1(E,1)) = k3_measure1(A,B,k9_nat_1(B,C,k1_nat_1(E,1)),k9_nat_1(B,C,E)) & r1_tarski(k9_nat_1(B,C,E),k9_nat_1(B,C,k1_nat_1(E,1))) ) ) ) => ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & v1_prob_2(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) ) ) ) ) )).
fof(t21_measure6,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( v3_membered(B) => ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,k9_member_1(B,A)) <=> ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & r2_hidden(D,B) & r2_hidden(E,A) & C = k2_xcmplx_0(D,E) ) ) ) ) ) ) )).
fof(t21_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m2_measure8(C,A,B) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,k6_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( v1_funct_1(k1_partfun1(k4_ordinal1,k9_setfam_1(A),B,k6_numbers,C,D)) & v1_funct_2(k1_partfun1(k4_ordinal1,k9_setfam_1(A),B,k6_numbers,C,D),k4_ordinal1,k6_numbers) & m1_subset_1(k1_partfun1(k4_ordinal1,k9_setfam_1(A),B,k6_numbers,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) ) ) ) )).
fof(t21_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => ( r2_hidden(B,A) => r2_hidden(k5_xxreal_3(B),k6_member_1(A)) ) ) ) )).
fof(t21_membered,axiom,( ! [A] : ! [B] : ( v3_membered(B) => ( r1_tarski(A,B) => v3_membered(A) ) ) )).
fof(t21_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t21_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( ( D = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),B,k6_xcmplx_0(1,G)),k1_rlvect_1(k15_euclid(2),C,G)) & E = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),C,k6_xcmplx_0(1,H)),k1_rlvect_1(k15_euclid(2),A,H)) & F = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),A,k6_xcmplx_0(1,I)),k1_rlvect_1(k15_euclid(2),B,I)) ) => ( r1_euclid_6(A,B,C) | G = 1 | H = 1 | I = 1 | k2_xcmplx_0(k6_xcmplx_0(1,H),k3_xcmplx_0(G,H)) = k5_numbers | k2_xcmplx_0(k6_xcmplx_0(1,G),k3_xcmplx_0(I,G)) = k5_numbers | k2_xcmplx_0(k6_xcmplx_0(1,I),k3_xcmplx_0(H,I)) = k5_numbers | ( k3_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(G,k6_xcmplx_0(1,G)),k7_xcmplx_0(H,k6_xcmplx_0(1,H))),k7_xcmplx_0(I,k6_xcmplx_0(1,I))) = 1 <=> ? [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_mesfun10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & v1_mesfunc8(B,A,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,C,k6_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,k6_numbers))) ) => ! [E] : ( m1_subset_1(E,C) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( E = k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers)) & ! [G] : ( v7_ordinal1(G) => r1_mesfunc5(A,C,D,k4_mesfunc5(A,k6_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] : ( v1_funct_1(G) & v1_funct_2(G,k4_ordinal1,k6_numbers) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) & ! [H] : ( v7_ordinal1(H) => k12_supinf_2(G,H) = k7_mesfunc5(A,C,D,k4_mesfunc5(A,k6_numbers,B,H)) ) & v10_mesfunc5(G) & k2_mesfunc5(G) = k7_mesfunc5(A,C,D,F) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( k12_supinf_2(C,E) = k5_numbers => ( ! [F] : ( 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)) = k5_numbers ) ) ) ) ) ) ) ) )).
fof(t21_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & v1_mesfunc8(C,A,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( ( k1_relset_1(A,k4_mesfunc5(A,k1_numbers,C,k5_numbers)) = D & ! [E] : ( v7_ordinal1(E) => r1_mesfunc6(A,B,k4_mesfunc5(A,k1_numbers,C,E),D) ) & ! [E] : ( 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) ) ) ) ) ) )).
fof(t21_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => r2_funct_2(k4_ordinal1,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)) ) ) )).
fof(t21_mesfunc1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,C))) ) => ! [E] : ! [F] : ( v1_xreal_0(F) => ( ! [G] : ( m1_subset_1(G,k4_ordinal1) => k9_nat_1(C,D,G) = k9_subset_1(A,E,k16_mesfunc1(A,B,k6_xcmplx_0(F,k2_extreal1(1,k1_nat_1(G,1))))) ) => k9_subset_1(A,E,k15_mesfunc1(A,B,F)) = k2_measure2(A,C,k1_measure3(A,C,D)) ) ) ) ) ) )).
fof(t21_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( 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 ) ) ) ) )).
fof(t21_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ! [D] : ( 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)) ) ) ) ) )).
fof(t21_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( v1_xreal_0(E) => ( ( 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) ) ) ) ) ) ) )).
fof(t21_mesfunc7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(t21_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [E] : ( v1_xreal_0(E) => ( ! [F] : ( v7_ordinal1(F) => k9_nat_1(k9_setfam_1(A),D,F) = k9_subset_1(A,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,C,k5_numbers)),k18_mesfunc1(A,k4_mesfunc5(A,k6_numbers,k4_mesfunc8(A,C),F),E)) ) => k2_kurato_0(A,D) = k9_subset_1(A,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,C,k5_numbers)),k18_mesfunc1(A,k6_mesfunc8(A,C),E)) ) ) ) ) ) ) )).
fof(t21_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(A),B) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ( ( r1_tarski(C,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,D,k5_numbers))) & v1_mesfunc8(E,A,k6_numbers) & ! [F] : ( m1_subset_1(F,A) => ( r2_hidden(F,C) => v1_mesfunc9(k3_mesfunc5(A,D,F)) ) ) & ! [F] : ( v7_ordinal1(F) => r2_relset_1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,E,F),k2_partfun1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,D,F),C)) ) ) => ! [F] : ( m1_subset_1(F,A) => ( r2_hidden(F,C) => v1_mesfunc9(k3_mesfunc5(A,E,F)) ) ) ) ) ) ) ) ) )).
fof(t21_metric_1,axiom,( ! [A] : ( m1_subset_1(A,1) => ! [B] : ( m1_subset_1(B,1) => ~ ( A != B & r1_xxreal_0(k1_binop_1(k2_metric_1,A,B),k5_numbers) ) ) ) )).
fof(t21_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k2_metric_2(A)) => ! [C] : ( m1_subset_1(C,k2_metric_2(A)) => ! [D] : ( v1_xreal_0(D) => ( r4_metric_2(A,B,C,D) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & r2_hidden(E,B) & r2_hidden(F,C) & k3_metric_1(A,E,F) = D ) ) ) ) ) ) ) )).
fof(t21_metric_3,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers)) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k1_numbers,k1_numbers)) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(k1_numbers,k1_numbers)) => r1_xxreal_0(k2_binop_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers,k16_metric_3,A,C),k3_real_1(k2_binop_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers,k16_metric_3,A,B),k2_binop_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers,k16_metric_3,B,C))) ) ) ) )).
fof(t21_metric_6,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v2_tbsp_1(B,A) & v2_tbsp_1(C,A) ) => k3_metric_1(A,k1_tbsp_1(A,B),k1_tbsp_1(A,C)) = k1_seq_2(k3_metric_6(A,B,C)) ) ) ) ) )).
fof(t21_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_finset_1(B) & v1_card_1(B) ) => ( r1_ordinal1(k2_waybel23(A),B) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ( v1_tops_2(C,A) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t21_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k10_funcsdom(k2_finseq_1(A))))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t21_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t21_midsp_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t21_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => m1_midsp_3(1,A) ) )).
fof(t21_mmlquer2,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ! [D] : ( ( v1_relat_2(D) & v4_relat_2(D) & v6_relat_2(D) & v8_relat_2(D) & v1_partfun1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( k10_mmlquer2(A,D,k4_subset_1(A,B,C)) = k1_ordinal4(k10_mmlquer2(A,D,B),k10_mmlquer2(A,D,C)) <=> ! [E] : ! [F] : ( ( r2_hidden(E,B) & r2_hidden(F,C) ) => ( E != F & r1_mmlquery(E,F,D) ) ) ) ) ) ) )).
fof(t21_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [D] : ( 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)) ) ) ) )).
fof(t21_mod_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ( m1_subset_1(k5_numbers,A) & m1_subset_1(1,A) & m1_subset_1(2,A) ) ) )).
fof(t21_mod_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ~ ( v1_lmod_5(C,A,B) & ! [D] : ( m1_mod_3(D,A,B) => ~ r1_tarski(C,D) ) ) ) ) ) )).
fof(t21_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t21_modal_1,axiom,( r1_subset_1(k4_modal_1,k3_modal_1) )).
fof(t21_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_1(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_partfun1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,C))) ) => ! [E] : ( m1_subset_1(E,C) => ! [F] : ( ( ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(k30_modelc_1(C))) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t21_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( v6_modelc_2(A) => ( r1_modelc_2(B,A) <=> B = k10_modelc_2(A) ) ) ) ) )).
fof(t21_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_3(B,A) & l1_modelc_3(B,A) ) => ! [C] : ( ( v1_modelc_3(C,A) & l1_modelc_3(C,A) ) => ( r4_modelc_3(A,B,C) => r1_xxreal_0(k21_modelc_3(A,C),k6_xcmplx_0(k21_modelc_3(A,B),1)) ) ) ) ) )).
fof(t21_moebius1,axiom,( v1_moebius1(k5_numbers) )).
fof(t21_monoid_0,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( m3_monoid_0(B,A) => m2_monoid_0(B,A) ) ) )).
fof(t21_monoid_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_monoid_1(B,A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_monoid_1(B,A))) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t21_morph_01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t21_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( 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)) ) ) ) )).
fof(t21_msafree4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => r1_pzfmisc1(A,B,C) ) ) )).
fof(t21_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t21_msscyc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v2_relat_1(C) & m1_msafree(C,A,B) ) => ? [D] : ( 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) ) ) ) ) )).
fof(t21_mssubfam,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t21_mssublat,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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))) ) ) ) ) )).
fof(t21_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t21_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t21_msualg_5,axiom,( ! [A] : ! [B] : ( 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))) ) ) )).
fof(t21_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r2_hidden(F,k4_finseq_1(k1_msualg_1(A,E))) => ! [G] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(t21_msualg_7,axiom,( ? [A] : ( m2_nat_lat(A,k1_msualg_7(k10_subset_1(k5_numbers,k1_numbers),k10_subset_1(1,k1_numbers))) & v2_msualg_7(A,k1_msualg_7(k10_subset_1(k5_numbers,k1_numbers),k10_subset_1(1,k1_numbers))) & ~ v1_msualg_7(A,k1_msualg_7(k10_subset_1(k5_numbers,k1_numbers),k10_subset_1(1,k1_numbers))) ) )).
fof(t21_msualg_9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v2_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t21_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t21_mycielsk,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( 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)))) ) ) ) )).
fof(t21_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k1_binop_1(C,D,E) = k9_complex1(k5_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)) ) ) ) ) ) )).
fof(t21_nagata_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ~ ( v3_pcomps_1(A) & ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) ) => ~ v5_nagata_1(B,A) ) ) ) )).
fof(t21_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(A,B) => m1_subset_1(k6_xcmplx_0(B,A),k4_ordinal1) ) ) ) )).
fof(t21_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_abian(A) <=> k4_nat_d(A,2) = k5_numbers ) ) )).
fof(t21_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( A != 1 => k11_nat_3(1,A) = k5_numbers ) ) )).
fof(t21_nat_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( v1_int_2(C) => k11_nat_3(A,C) = k11_nat_3(B,C) ) ) => A = B ) ) ) )).
fof(t21_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(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)) ) ) ) ) )).
fof(t21_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k4_nat_d(B,C) = k4_nat_d(k2_xcmplx_0(k3_xcmplx_0(C,A),B),C) ) ) ) )).
fof(t21_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ( ( r2_nattra_1(A,B,C,D) & r2_nattra_1(A,B,D,E) ) => ! [F] : ( m2_nattra_1(F,A,B,C,D) => ! [G] : ( m2_nattra_1(G,A,B,D,E) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => k2_nattra_1(A,B,C,E,k5_nattra_1(A,B,C,D,E,F,G),H) = k5_cat_1(B,k8_cat_1(A,B,C,H),k8_cat_1(A,B,D,H),k8_cat_1(A,B,E,H),k2_nattra_1(A,B,C,D,F,H),k2_nattra_1(A,B,D,E,G,H)) ) ) ) ) ) ) ) ) ) )).
fof(t21_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,k1_relset_1(u1_struct_0(A),C)) => ( ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t21_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t21_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v9_ordinal1(B) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v1_fdiff_1(B,k5_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C != k4_struct_0(A) => ( v12_struct_0(k2_ndiff_1(A,C,B),k4_ordinal1,A) & v1_ndiff_1(k2_ndiff_1(A,C,B),A,k4_struct_0(A)) ) ) ) ) ) )).
fof(t21_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ! [E] : ( ( 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] : ( v1_xreal_0(F) => ( 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] : ( v1_xreal_0(F) => ( r2_hidden(F,D) => k1_funct_1(k2_ndiff_3(A,E,D),F) = B ) ) ) ) ) ) ) ) ) )).
fof(t21_ndiff_4,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t21_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k11_prvect_2(A,B))) => k2_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)) = k2_normsp_0(k11_prvect_2(A,B),C) ) ) ) )).
fof(t21_neckla_3,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( l1_orders_2(B) => ( ? [C] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) )).
fof(t21_necklace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( r2_hidden(B,u1_struct_0(k4_necklace(A))) & r1_xxreal_0(A,B) ) ) ) )).
fof(t21_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k2_net_1(A)) => ! [C] : ( r2_hidden(B,C) => ( k2_net_1(A) = k1_xboole_0 | r2_hidden(k5_net_1(A,B),k10_net_1(A,C)) ) ) ) ) )).
fof(t21_newton,axiom,( ! [A] : ( v7_ordinal1(A) => k3_newton(A,A) = 1 ) )).
fof(t21_nfcont_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t21_nfcont_3,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t21_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(A)),k1_numbers))) ) => ! [D] : ( m1_subset_1(D,k1_euclid(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t21_normsp_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_normsp_1(C,A) => v3_normsp_1(k4_normsp_1(A,C,B),A) ) ) ) ) )).
fof(t21_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_normsp_2(A)))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t21_numbers,axiom,( k1_numbers != k2_numbers )).
fof(t21_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t21_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t21_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_cat_1(A,B,C) != k1_xboole_0 => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t21_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_ordeq_01(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_ordeq_01(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_rsspace4(A,B))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k9_rsspace4(A,B))) => ( ( E = C & F = D ) => k5_algstr_0(k5_ordeq_01(A,B),C,D) = k5_algstr_0(k9_rsspace4(A,B),E,F) ) ) ) ) ) ) ) )).
fof(t21_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v2_orders_1(A) => v1_orders_1(A) ) ) )).
fof(t21_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ~ r2_hidden(B,k2_orders_2(A,k6_domain_1(u1_struct_0(A),B))) ) ) )).
fof(t21_ordinal1,axiom,( ! [A] : ~ ! [B] : ( r2_hidden(B,A) <=> v3_ordinal1(B) ) )).
fof(t21_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ~ ( r2_hidden(A,k3_ordinal2(B)) & ! [C] : ( v3_ordinal1(C) => ~ ( r2_hidden(C,B) & r1_ordinal1(A,C) ) ) ) ) )).
fof(t21_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( k10_ordinal2(A,B) = k10_ordinal2(A,C) => B = C ) ) ) ) )).
fof(t21_ordinal4,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( v4_ordinal1(A) => ( A = k1_xboole_0 | ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_ordinal2(C) ) => ( ( k9_xtuple_0(C) = A & ! [D] : ( v3_ordinal1(D) => ( r2_hidden(D,A) => k1_funct_1(C,D) = k12_ordinal2(B,D) ) ) ) => r1_ordinal2(k12_ordinal2(B,A),C) ) ) ) ) ) ) )).
fof(t21_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( ( r1_ordinal1(A,B) & r2_hidden(k5_numbers,C) ) => r1_ordinal1(k1_ordinal5(C,A),k1_ordinal5(C,B)) ) ) ) ) )).
fof(t21_ordinal6,axiom,( ! [A] : r3_wellord1(k1_wellord2(k1_ordinal6(A)),k1_wellord2(k2_ordinal1(A)),k2_ordinal6(A)) )).
fof(t21_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ~ ( ~ r1_orders_2(B,D,C) & ~ r1_orders_2(B,F,C) & k8_group_1(A,k1_ortsp_1(A,B,C,D,E),k11_algstr_0(A,k1_ortsp_1(A,B,C,D,F))) != k1_ortsp_1(A,B,C,F,E) ) ) ) ) ) ) ) )).
fof(t21_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ! [C] : ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t21_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_osalg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t21_osalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t21_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_parsp_1(A,B,C,D,E) => r1_parsp_1(A,C,B,D,E) ) ) ) ) ) ) )).
fof(t21_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t21_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_tarski(A)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k1_tarski(A)))) ) => ( k1_relset_1(B,C) = k1_relset_1(B,D) => C = D ) ) ) )).
fof(t21_partfun2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t21_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ! [E] : ! [F] : ! [G] : ( 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] : ( m1_subset_1(H,k4_ordinal1) => ~ ( r1_xxreal_0(1,H) & ~ r1_xxreal_0(k3_finseq_1(G),H) & ! [I] : ! [J] : ! [K] : ~ ( 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,k1_nat_1(H,1)),J) ) ) ) & r1_partit1(A,B,D) & r1_partit1(A,C,D) ) => r2_hidden(F,D) ) ) ) ) ) )).
fof(t21_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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 ) ) ) ) )).
fof(t21_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( ~ r3_diraf(A,E,B,C) & r1_diraf(A,E,D,C) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_diraf(A,E,F,B) & r2_analoaf(A,B,C,F,D) ) ) ) ) ) ) ) ) )).
fof(t21_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t21_pcomps_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t21_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ( r1_tarski(u1_struct_0(A),u1_struct_0(k20_pcs_0(A,B))) & r1_relset_1(u1_struct_0(A),u1_struct_0(A),u1_orders_2(A),u1_orders_2(k20_pcs_0(A,B))) & r1_relset_1(u1_struct_0(A),u1_struct_0(A),u1_pcs_0(A),u1_pcs_0(k20_pcs_0(A,B))) ) ) )).
fof(t21_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(A))) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t21_pdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( 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),k3_funct_2(k1_euclid(2),k1_numbers,k1_pdiff_1(1,2),B)) ) ) ) )).
fof(t21_pdiff_3,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(2)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [C] : ( ( 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) & k10_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) = k2_xcmplx_0(k2_pdiff_3(B,A),k2_pdiff_3(C,A)) ) ) ) ) ) )).
fof(t21_pdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) => k10_pdiff_1(3,3,E,D) = k1_fdiff_1(k1_pdiff_2(3,3,E,D),C) ) ) ) ) ) ) )).
fof(t21_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( 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) ) ) ) )).
fof(t21_pdiff_6,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(B),k1_euclid(A)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(B),k1_euclid(A)))) ) => ! [E] : ( 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))) ) ) ) ) ) ) ) )).
fof(t21_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t21_pdiff_8,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( 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] : ( 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] : ( m1_subset_1(E,k4_ordinal1) => ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t21_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [E] : ( ( 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] : ( m1_subset_1(F,k1_zfmisc_1(k1_euclid(A))) => ! [G] : ( 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] : ( m2_finseq_2(H,k1_numbers,k1_euclid(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(k4_real_ns1(A))) => ( ( r2_hidden(H,F) & H = I ) => k11_pdiff_1(A,B,C,D,H) = k1_funct_1(k9_pdiff_1(A,B,C,E,I),k12_finseq_1(k4_ordinal1,1)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_pencil_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,u1_pre_topc(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = B => v2_pencil_1(C,A) ) ) ) ) )).
fof(t21_pencil_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t21_pencil_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v15_pencil_1(B) ) => ! [C] : ( m1_pencil_2(C,A,B) => ! [D] : ( m1_pencil_2(D,A,B) => ( r1_xboole_0(C,D) => ( r1_pencil_3(A,B,C,D) <=> ! [E] : ( ( ~ v13_pencil_1(E) & v16_pencil_1(E,A) & m3_pboole(E,A,k12_pralg_1(A,B)) ) => ! [F] : ( ( ~ 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] : ( m1_subset_1(G,A) & G != k3_pencil_1(A,E) & ! [H] : ( m1_subset_1(H,A) => ( H != G => k1_funct_1(E,H) = k1_funct_1(F,H) ) ) & ! [H] : ( m1_subset_1(H,u1_struct_0(k2_pencil_1(A,B,G))) => ! [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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( 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)) ) ) ) ) ) ) )).
fof(t21_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( v1_abian(A) => ( r1_xxreal_0(B,k5_numbers) | v1_abian(k1_newton(A,B)) ) ) ) ) )).
fof(t21_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( m1_pnproc_1(C,A) => ! [D] : ( m1_pnproc_1(D,A) => k6_pnproc_1(A,k6_pnproc_1(A,B,C),D) = k1_funct_1(k3_relat_1(k7_pnproc_1(A,C),k7_pnproc_1(A,D)),B) ) ) ) )).
fof(t21_polyalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_polyalg1(B,A) ) => ! [C] : ( ( ~ 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 ) ) ) ) )).
fof(t21_polyeq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( k1_square_1(B) = A & k4_complex1(A) = k5_numbers & ~ r1_xxreal_0(k5_numbers,k3_complex1(A)) & B != k3_xcmplx_0(k3_square_1(k1_real_1(k3_complex1(A))),k7_complex1) & B != k4_xcmplx_0(k3_xcmplx_0(k3_square_1(k1_real_1(k3_complex1(A))),k7_complex1)) ) ) ) )).
fof(t21_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( v1_xcmplx_0(F) => ! [G] : ( v1_xcmplx_0(G) => ! [H] : ( v1_xcmplx_0(H) => ! [I] : ( v1_xcmplx_0(I) => ( ( A = k6_xcmplx_0(F,k7_xcmplx_0(E,4)) & I = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(8,D),k3_xcmplx_0(3,k1_newton(E,2))),32) & G = k7_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(8,C),k3_xcmplx_0(k3_xcmplx_0(4,D),E)),k1_newton(E,3)),64) & H = k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(256,B),k3_xcmplx_0(k3_xcmplx_0(64,E),C)),k3_xcmplx_0(k3_xcmplx_0(16,k1_newton(E,2)),D)),k3_xcmplx_0(3,k1_newton(E,4))),1024) ) => ( k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_newton(A,4),k3_xcmplx_0(E,k1_newton(A,3))),k3_xcmplx_0(D,k1_newton(A,2))),k3_xcmplx_0(C,A)),B) = k5_numbers <=> k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_newton(F,4),k3_xcmplx_0(k3_xcmplx_0(4,I),k1_newton(F,2))),k3_xcmplx_0(k3_xcmplx_0(8,G),F)),k3_xcmplx_0(4,H)) = k5_numbers ) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_polyform,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k2_bspace)) => k4_rlvect_1(k2_bspace,k3_pre_poly(u1_struct_0(k2_bspace),A)) = A ) )).
fof(t21_polynom1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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),k5_polynom1(A,B,k5_polynom1(A,B,C,D),E),k5_polynom1(A,B,C,k5_polynom1(A,B,D,E))) ) ) ) ) )).
fof(t21_polynom3,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(1,E) & r1_xxreal_0(D,k1_recdef_1(A,k1_nat_1(B,1))) & r1_xxreal_0(E,k1_recdef_1(A,k1_nat_1(C,1))) & k1_nat_1(k2_wsierp_1(k17_finseq_1(k4_ordinal1,B,A)),D) = k1_nat_1(k2_wsierp_1(k17_finseq_1(k4_ordinal1,C,A)),E) ) => ( r1_xxreal_0(k3_finseq_1(A),B) | r1_xxreal_0(k3_finseq_1(A),C) | ( B = C & D = E ) ) ) ) ) ) ) ) )).
fof(t21_polynom4,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(t21_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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 ) ) ) ) )).
fof(t21_polynom8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t21_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( ~ 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) ) ) ) ) ) )).
fof(t21_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r1_xxreal_0(A,k5_numbers) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) | v1_abian(B) | ( r1_xxreal_0(k1_power(B,A),A) & ~ r1_xxreal_0(k1_power(B,A),k4_xcmplx_0(1)) ) ) ) ) ) )).
fof(t21_pre_circ,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( 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)) = k1_nat_1(k5_card_1(A),k5_card_1(B)) ) ) ) )).
fof(t21_pre_poly,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_card_3(A) <=> ! [B] : ( r2_hidden(B,k10_xtuple_0(A)) => v1_card_1(B) ) ) ) )).
fof(t21_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t21_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),k2_prelamb(A,k2_prelamb(A,C,k1_prelamb(A,B,C)),B)) & r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),k1_prelamb(A,B,k1_prelamb(A,k2_prelamb(A,C,B),C))) ) ) ) ) )).
fof(t21_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k5_numbers,A) => k2_prepower(1,A) = A ) ) )).
fof(t21_prob_1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => m1_prob_1(k4_subset_1(A,C,D),A,B) ) ) ) )).
fof(t21_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m1_prob_1(E,A,B) => ! [F] : ( m2_prob_1(F,A,B) => ( r2_prob_2(A,B,F,C,D,E) => r2_prob_2(A,B,F,D,C,E) ) ) ) ) ) ) ) )).
fof(t21_prob_3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( r2_funct_2(k4_ordinal1,k9_setfam_1(A),D,k1_prob_3(A,C)) => ( k1_prob_2(A,B,D,k5_numbers) = k1_prob_2(A,B,C,k5_numbers) & ! [E] : ( v7_ordinal1(E) => k1_prob_2(A,B,D,k1_nat_1(E,1)) = k5_prob_1(A,B,k1_prob_2(A,B,D,E),k1_prob_2(A,B,C,k1_nat_1(E,1))) ) ) ) ) ) ) )).
fof(t21_prob_4,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(C) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => r1_xboole_0(k1_prob_4(A,B,k3_prob_3(A,C),k1_nat_1(D,1)),k1_prob_4(A,B,C,D)) ) ) ) ) )).
fof(t21_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t21_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ( ( r1_collsp(A,H,B,C) & r1_collsp(A,H,D,E) & r1_collsp(A,H,F,G) & r1_collsp(A,B,D,I) & r1_collsp(A,C,E,I) & r1_collsp(A,D,F,K) & r1_collsp(A,E,G,K) & r1_collsp(A,B,F,J) & r1_collsp(A,C,G,J) ) => ( r1_collsp(A,H,B,D) | r1_collsp(A,H,D,F) | r1_collsp(A,H,B,F) | B = C | D = E | H = C | H = E | H = G | r1_collsp(A,K,J,I) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u2_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u2_incsp_1(A)) => ! [H] : ( m1_subset_1(H,u2_incsp_1(A)) => ! [I] : ( m1_subset_1(I,u2_incsp_1(A)) => ( ( v1_projpl_1(A) & r3_projpl_1(A,B,G,H,I) & r1_zfmisc_1(G,H,I) & r2_projpl_1(A,C,F,G) & r2_projpl_1(A,D,F,H) & r2_projpl_1(A,E,F,I) ) => ( r1_incsp_1(A,B,F) | r1_zfmisc_1(C,D,E) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_projred1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t21_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u2_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u2_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u2_incsp_1(A)) => ! [H] : ( 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,H) & ~ r1_incsp_1(A,B,H) & E != H & B != C & r1_incsp_1(A,B,G) & r1_incsp_1(A,C,G) & ! [I] : ( m1_subset_1(I,u1_incsp_1(A)) => ~ ( r1_incsp_1(A,I,G) & ~ r1_incsp_1(A,I,E) & ~ r1_incsp_1(A,I,H) & k3_relat_1(k1_projred1(A,D,F,B),k1_projred1(A,F,E,C)) = k3_relat_1(k1_projred1(A,D,H,B),k1_projred1(A,H,E,I)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_prvect_3,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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(k4_ordinal1,u1_struct_0(B))),D,k12_finseq_1(u1_struct_0(B),E)) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(k5_prvect_3(A,B))) => ! [E] : ( 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] : ( m1_subset_1(D,u1_struct_0(k5_prvect_3(A,B))) => ! [E] : ( 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)))) ) ) ) )).
fof(t21_pua2mss1,axiom,( ! [A] : ( ( 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)) ) )).
fof(t21_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) )).
fof(t21_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k1_qc_lang1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t21_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( m2_subset_1(E,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [F] : ( m2_subset_1(F,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [G] : ( m2_subset_1(G,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [H] : ( m2_subset_1(H,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [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 ) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v6_qc_lang1(B,A) <=> v6_qc_lang1(k13_qc_lang1(A,B),A) ) ) ) )).
fof(t21_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m1_trees_1(D,k9_xtuple_0(k2_qc_lang4(A,C))) => ! [E] : ( m1_trees_1(E,k9_xtuple_0(k2_qc_lang4(A,C))) => ( ( E = k7_finseq_1(D,k9_finseq_1(B)) & v3_qc_lang1(k3_trees_2(k9_qc_lang1(A),k2_qc_lang4(A,C),D),A) ) => ( k3_trees_2(k9_qc_lang1(A),k2_qc_lang4(A,C),E) = k18_qc_lang1(A,k3_trees_2(k9_qc_lang1(A),k2_qc_lang4(A,C),D)) & B = k5_numbers ) ) ) ) ) ) ) )).
fof(t21_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_henmodel(B,A) & m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) ) => ! [C] : ( ( v1_qc_trans(C,A) & m1_qc_lang1(C) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_cqc_lang(C))) => ( B = D => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_valuat_1(F,A,E) => ! [G] : ( m2_funct_2(G,k3_qc_lang1(A),E,k2_valuat_1(A,E)) => ~ ( r6_calcul_1(A,B,E,F,G) & ! [H] : ( ~ v1_xboole_0(H) => ! [I] : ( m1_valuat_1(I,C,H) => ! [J] : ( m2_funct_2(J,k3_qc_lang1(C),H,k2_valuat_1(C,H)) => ~ r6_calcul_1(C,D,H,I,J) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_quantal1,axiom,( ! [A] : ( ( ~ 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) ) ) ) )).
fof(t21_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k23_quaterni(A,k24_quaterni(B)) = k24_quaterni(k23_quaterni(A,B)) ) ) )).
fof(t21_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k22_quaterni(k23_quaterni(k11_quaterni,A),k23_quaterni(A,k11_quaterni)) = k6_quaterni(k4_xcmplx_0(k3_xcmplx_0(2,k15_quaterni(A))),k5_numbers,k3_xcmplx_0(2,k13_quaterni(A)),k5_numbers) ) )).
fof(t21_quaterni,axiom,( k10_quaterni(k12_quaterni,k1_xcmplx_0) = k8_quaterni(k10_quaterni(k1_xcmplx_0,k12_quaterni)) )).
fof(t21_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(k6_xcmplx_0(k1_square_1(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,B),A),C)),k1_quin_1(B,C,D)),k5_numbers) & r1_xxreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(A)),k3_xcmplx_0(C,A)),D),k5_numbers) ) ) ) ) ) )).
fof(t21_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [C] : ( 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) ) ) ) )).
fof(t21_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(1,B) => ! [C] : ( v7_ordinal1(C) => ( r1_radix_1(B,C,A) => C = k8_radix_1(B,A,k10_radix_1(A,B,C)) ) ) ) ) ) )).
fof(t21_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => r2_relset_1(A,k6_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))) ) ) ) )).
fof(t21_random_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v2_finset_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v7_random_3(B,A,k7_random_3(A)) ) => ! [C] : ( v7_ordinal1(C) => ? [D] : ( m2_prob_1(D,k1_funct_1(k5_random_3(A),C),k1_random_1(k1_funct_1(k5_random_3(A),C))) & D = k1_funct_1(k9_random_3(A,B),C) & k1_funct_1(k9_random_3(A,B),k1_nat_1(C,1)) = k2_random_2(k1_funct_1(k5_random_3(A),C),k1_funct_1(A,k1_nat_1(C,1)),D,k8_random_3(A,B,k1_nat_1(C,1))) ) ) ) ) )).
fof(t21_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t21_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ( k2_rat_1(A) = k4_xcmplx_0(k1_rat_1(A)) <=> A = k4_xcmplx_0(1) ) ) )).
fof(t21_rcomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ~ ( v3_rcomp_1(A) & v4_xxreal_2(A) & r2_hidden(k2_seq_4(A),A) ) ) )).
fof(t21_rcomp_3,axiom,( ! [A] : ( ( v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( ( v4_xxreal_2(A) & r2_hidden(k2_seq_4(A),A) ) => ( v3_xxreal_2(A) | A = k1_limfunc1(k2_seq_4(A)) ) ) ) )).
fof(t21_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k6_real_lat(A))) => ! [C] : ( 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) ) ) ) )).
fof(t21_realset2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t21_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t21_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [E] : ( ( 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_funct_1(k4_rearran1(B,A,E,D),C) = k1_funct_1(k20_rfunct_3(B,D,B),1) ) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ( r1_xxreal_0(1,F) & r2_hidden(C,k6_subset_1(k1_funct_1(k2_rearran1(A,E),k1_nat_1(F,1)),k1_funct_1(k2_rearran1(A,E),F))) ) => ( r1_xxreal_0(k3_finseq_1(k2_rearran1(A,E)),F) | k1_funct_1(k4_rearran1(B,A,E,D),C) = k1_funct_1(k20_rfunct_3(B,D,B),k1_nat_1(F,1)) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r1_tarski(k10_xtuple_0(B),k9_xtuple_0(A)) => k9_xtuple_0(k3_relat_1(B,A)) = k9_xtuple_0(B) ) ) ) )).
fof(t21_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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) ) ) )).
fof(t21_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( 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))))) ) ) )).
fof(t21_revrot_1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t21_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r1_rewrite1(A,B,C) <=> r1_rewrite1(k18_finseq_1(A),B,C) ) ) )).
fof(t21_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t21_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(E))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k8_afinsq_1(E))) => ! [H] : ( l1_rewrite3(H,F) => ! [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) ) ) ) ) ) ) )).
fof(t21_rfinseq,axiom,( ! [A] : ( ( v8_valued_0(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => v8_valued_0(k2_rfinseq(k1_numbers,B,A)) ) ) )).
fof(t21_rfinseq2,axiom,( ! [A] : ( ( v1_integra2(A) & m2_finseq_1(A,k1_numbers) ) => k6_rfinseq2(A) = A ) )).
fof(t21_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => k24_valued_1(A,1) = A ) )).
fof(t21_rfunct_2,axiom,( ! [A] : ! [B] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( 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_funct_1(B,C),k1_funct_1(B,D)) ) ) ) ) ) )).
fof(t21_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,k3_rfunct_3(A,k1_numbers)) => ! [C] : ( 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))) ) ) ) )).
fof(t21_rfunct_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t21_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_seq_2(A) & v4_partfun3(A) & v1_seq_2(B) & v4_partfun3(B) ) => ( v1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) & r1_xxreal_0(k1_rinfsup1(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)),k3_xcmplx_0(k1_rinfsup1(A),k1_rinfsup1(B))) ) ) ) ) )).
fof(t21_rinfsup2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v10_mesfunc5(B) => ( v10_mesfunc5(k1_valued_0(k6_numbers,B,A)) & k2_mesfunc5(B) = k2_mesfunc5(k1_valued_0(k6_numbers,B,A)) ) ) ) ) )).
fof(t21_ring_1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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)) ) ) ) ) )).
fof(t21_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(k17_ringcat1(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t21_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => r1_rlvect_2(A,k1_rlaffin1(A,B,k4_struct_0(A)),B) ) ) )).
fof(t21_rlaffin2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( 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 ) ) ) ) )).
fof(t21_rlaffin3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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] : ( ( v1_finset_1(D) & v1_rlaffin1(D,C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) ) => ! [E] : ( m2_rlaffin3(E,C,D) => ( r2_hidden(A,k4_rlaffin1(C,D)) => ( r2_hidden(A,k4_rlaffin1(C,k7_relset_1(k4_ordinal1,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)),k5_finseq_2(k4_ordinal1,k7_nat_d(k5_card_1(D),B),k5_numbers)) ) ) ) ) ) ) )).
fof(t21_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_rlsub_1(D,A) => ( r1_struct_0(D,B) => r1_struct_0(D,k1_rlvect_1(A,B,C)) ) ) ) ) ) )).
fof(t21_rlsub_2,axiom,( ! [A] : ( ( ~ 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 ) )).
fof(t21_rltopsp1,axiom,( ! [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) ) => ! [B] : ( ( v1_convex1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(C,1) & r2_hidden(k4_struct_0(A),B) ) => r1_tarski(k1_convex1(A,B,C),B) ) ) ) ) )).
fof(t21_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k5_algstr_0(A,B,C) = k4_struct_0(A) => B = C ) ) ) ) )).
fof(t21_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m2_rlvect_2(D,A,B) => ( r1_tarski(B,C) => m2_rlvect_2(D,A,C) ) ) ) ) ) )).
fof(t21_rlvect_3,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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 ) ) ) ) )).
fof(t21_rlvect_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( 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) ) ) ) ) ) )).
fof(t21_rlvect_5,axiom,( ! [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) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t21_rlvect_x,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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] : ( v1_int_1(F) & ? [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(t21_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_rmod_2(E,A,C) => ( r1_struct_0(E,D) => r1_struct_0(E,k5_vectsp_2(A,C,B,D)) ) ) ) ) ) ) )).
fof(t21_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(t21_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(t21_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_robbins1(A,B,k5_robbins1(A,B,C)) = B ) ) ) )).
fof(t21_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_robbins1(A,k1_lattices(A,B,B)) = k3_robbins1(A,B) ) ) )).
fof(t21_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_robbins1(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t21_robbins4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k2_robbins4)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_robbins4)) => ( ( A = k6_subset_1(3,1) & B = 1 ) => k3_lattices(k2_robbins4,A,B) = 3 ) ) ) )).
fof(t21_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => k4_roughs_1(A,k2_struct_0(A)) = k2_struct_0(A) ) )).
fof(t21_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_xboole_0(B,C) => k1_rpr_1(A,k4_subset_1(A,B,C)) = k2_xcmplx_0(k1_rpr_1(A,B),k1_rpr_1(A,C)) ) ) ) ) )).
fof(t21_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_rsspace4(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_rsspace4(A,B))) => ! [E] : ( v1_xreal_0(E) => ( ( k2_normsp_0(k9_rsspace4(A,B),C) = k5_numbers => C = k4_struct_0(k9_rsspace4(A,B)) ) & ( C = k4_struct_0(k9_rsspace4(A,B)) => k2_normsp_0(k9_rsspace4(A,B),C) = k5_numbers ) & k2_normsp_0(k9_rsspace4(A,B),k1_rlvect_1(k9_rsspace4(A,B),C,E)) = k3_xcmplx_0(k9_complex1(E),k2_normsp_0(k9_rsspace4(A,B),C)) & r1_xxreal_0(k2_normsp_0(k9_rsspace4(A,B),k1_algstr_0(k9_rsspace4(A,B),C,D)),k2_xcmplx_0(k2_normsp_0(k9_rsspace4(A,B),C),k2_normsp_0(k9_rsspace4(A,B),D))) ) ) ) ) ) ) )).
fof(t21_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( ~ 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) ) ) ) ) )).
fof(t21_rusub_2,axiom,( ! [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_bhsp_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => k2_rusub_2(A,k2_rusub_1(A),k2_rusub_1(A)) = A ) )).
fof(t21_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_3(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_struct_0(k1_rusub_3(A,B),C) ) ) ) )).
fof(t21_rusub_4,axiom,( ! [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_bhsp_1(A) & v1_rusub_4(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_tarski(k2_rusub_4(B,C),k2_rusub_4(A,C)) ) ) ) )).
fof(t21_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => r1_struct_0(k2_rusub_5(A,B),k4_struct_0(A)) ) ) )).
fof(t21_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => k6_rvsum_1(k2_finseq_2(A,B)) = k2_finseq_2(A,k4_xcmplx_0(B)) ) ) )).
fof(t21_rvsum_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k9_rvsum_2(k9_finseq_1(B),A) = k9_finseq_1(k3_xcmplx_0(A,B)) ) ) )).
fof(t21_scm_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( r1_tarski(k1_ordinal4(k5_afinsq_1(k8_ami_3(1,k10_ami_3(k5_numbers))),k5_afinsq_1(k2_compos_1(k1_ami_3))),A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( ( v5_memstr_0(D,k7_card_1(2),k1_ami_3,k5_numbers) & m1_scm_1(D,k6_afinsq_1(B,C)) ) => ( r1_extpro_1(k7_card_1(2),k1_ami_3,A,D) & k8_extpro_1(k7_card_1(2),k1_ami_3,A,D) = 1 & ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_ami_3)) ) => k1_funct_1(k6_extpro_1(k7_card_1(2),k1_ami_3,A,D),E) = k1_funct_1(D,E) ) ) ) ) ) ) ) )).
fof(t21_scm_halt,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2,E,k1_scmfsa6b(D,A,C)),B) ) ) ) ) ) )).
fof(t21_scmfsa10,axiom,( ! [A] : ( 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) ) ) )).
fof(t21_scmfsa6a,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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)) ) ) ) )).
fof(t21_scmfsa7b,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ( r5_scmfsa7b(C,A,B) => ( r4_scmfsa7b(C,D) | ! [E] : ( v7_ordinal1(E) => k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),E),D) = k1_funct_1(A,D) ) ) ) ) ) ) ) )).
fof(t21_scmfsa8a,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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] : ( v7_ordinal1(E) => ( r1_xxreal_0(E,k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))))) => ( k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k2_scmfsa6a(C)),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),E)) = k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k3_scmfsa6a(C,D)),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),E)) & k3_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k2_scmfsa6a(C)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k2_scmfsa6a(C)),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),E)) = k3_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k3_scmfsa6a(C,D)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k3_scmfsa6a(C,D)),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),E)) ) ) ) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k2_scmfsa6a(C)),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))),1))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k3_scmfsa6a(C,D)),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))),1))) & k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k2_scmfsa6a(C)),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))),1))) = k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k3_scmfsa6a(C,D)),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))),1))) ) ) ) ) ) ) )).
fof(t21_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & ~ v1_scmfsa_m(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(E,u1_struct_0(k1_scmfsa_2)) ) => ( ( r1_xxreal_0(k1_funct_1(E,D),k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k5_card_1(B),k5_card_1(C)),3)))) ) ) ) ) ) ) )).
fof(t21_scmfsa8c,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ~ r1_xxreal_0(k1_nat_1(k1_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) ) ) ) ) ) ) )).
fof(t21_scmfsa_1,axiom,( k9_xtuple_0(k3_relat_1(k4_scmfsa_1,k5_scmfsa_1)) = k1_scmfsa_1 )).
fof(t21_scmfsa_2,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( ( 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 ) ) )).
fof(t21_scmfsa_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => r6_pboole(u1_struct_0(k1_scmfsa_2),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(D,B,C,A),k1_nat_1(k5_numbers,1)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa_9(C,B)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(k1_funct_4(A,k1_scmfsa_9(C,B)),B),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D)),3))) ) ) ) ) )).
fof(t21_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmpds_2)) ) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t21_scmpds_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) & v3_scmpds_4(A) ) => ! [B] : ( v1_int_1(B) => ( r1_xxreal_0(k5_numbers,k2_xcmplx_0(k5_card_1(A),B)) => v3_scmpds_4(k3_scmpds_4(A,k3_scmpds_2(B))) ) ) ) )).
fof(t21_scmpds_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) & v2_scmpds_4(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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_xcmplx_0(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)))) ) ) ) ) )).
fof(t21_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [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_partfun1(D,u1_struct_0(k1_scmpds_2)) & v5_memstr_0(D,2,k1_scmpds_2,k5_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(k1_nat_1(k5_card_1(C),1))),C),D,A) & r1_scmpds_6(k1_scmpds_4(k1_scmpds_4(B,k1_scmpds_6(k1_nat_1(k5_card_1(C),1))),C),D,A) ) ) ) ) ) ) )).
fof(t21_scmpds_7,axiom,( ! [A] : ( ( 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] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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))) ) ) ) ) ) ) )).
fof(t21_scmpds_8,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( r1_xxreal_0(k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),F)),k5_numbers) => k1_funct_1(k6_scmpds_4(k2_scmpds_8(D,F,C),B,A),E) = k1_funct_1(B,E) ) ) ) ) ) ) ) )).
fof(t21_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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(k5_numbers,k1_xboole_0,k1_xboole_0) ) )).
fof(t21_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t21_scmyciel,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v3_scmyciel(B,A) => ! [C] : ( m1_subset_1(C,B) => ( r2_hidden(C,B) => r1_xxreal_0(k5_card_1(C),k1_nat_1(A,1)) ) ) ) ) )).
fof(t21_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ~ ( B != C & B != D & C != D ) => r2_analoaf(A,B,C,B,D) ) ) ) ) ) )).
fof(t21_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,A),k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,B)),k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B))) ) ) ) )).
fof(t21_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(A) & v9_ordinal1(A) ) => ( k1_seq_2(A) = k5_numbers | v2_comseq_2(k37_valued_1(k4_ordinal1,k1_numbers,A)) ) ) ) )).
fof(t21_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(k1_valued_0(k1_numbers,B,A)) => v2_comseq_2(B) ) ) ) )).
fof(t21_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( r3_seqfunc(A,B,C) => r2_seqfunc(A,B,C) ) ) ) )).
fof(t21_seqm_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k1_valued_0(k1_numbers,k26_valued_1(k4_ordinal1,k1_numbers,C,B),A) = k26_valued_1(k4_ordinal1,k1_numbers,k1_valued_0(k1_numbers,C,A),B) ) ) ) )).
fof(t21_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_series_1(A) <=> ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & r1_xxreal_0(B,k9_complex1(k5_real_1(k9_nat_1(k1_numbers,k3_series_1(A),D),k9_nat_1(k1_numbers,k3_series_1(A),C)))) ) ) ) ) ) ) )).
fof(t21_series_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k2_xcmplx_0(A,B) = 1 => r1_xxreal_0(k7_xcmplx_0(1,4),k2_xcmplx_0(k1_newton(A,3),k1_newton(B,3))) ) ) ) )).
fof(t21_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( 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(k3_square_1(3),k2_xcmplx_0(k2_xcmplx_0(A,B),C)) ) ) ) ) )).
fof(t21_setfam_1,axiom,( ! [A] : r1_setfam_1(k3_setfam_1(A,A),A) )).
fof(t21_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( v7_ordinal1(C) => k1_funct_1(k2_setlim_1(A,B),C) = k8_subset_1(A,k3_funct_2(k4_ordinal1,k9_setfam_1(A),k2_setlim_1(A,B),k1_nat_1(C,1)),k1_funct_1(B,C)) ) ) )).
fof(t21_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v2_prob_1(C) => v2_prob_1(k5_setlim_2(A,C,B)) ) ) ) )).
fof(t21_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,k5_finsub_1(A)) => ! [E] : ( ( 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) ) => ( D = k1_xboole_0 | ! [F] : ( m1_subset_1(F,B) => ( ! [G] : ( m1_subset_1(G,A) => ( r2_hidden(G,D) => k3_funct_2(A,B,E,G) = F ) ) => k7_setwiseo(A,B,C,D,E) = F ) ) ) ) ) ) ) ) ) )).
fof(t21_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => k2_partfun1(k4_ordinal1,A,k1_setwop_2(A,C,B),k4_finseq_1(C)) = C ) ) ) )).
fof(t21_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) ) => ( r1_xboole_0(k1_relset_1(k4_ordinal1,A),k1_relset_1(k4_ordinal1,B)) => k2_sf_mastr(k1_funct_4(A,B)) = k4_subset_1(k2_scmfsa_2,k2_sf_mastr(A),k2_sf_mastr(B)) ) ) ) )).
fof(t21_sgraph1,axiom,( ! [A] : ! [B] : ( 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)))) ) ) )).
fof(t21_sheffer1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t21_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,B,B)) = B ) ) ) )).
fof(t21_simplex0,axiom,( ! [A] : ( 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)) ) ) )).
fof(t21_simplex1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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),k5_numbers) ) => g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = k4_simplex1(A,B) ) ) ) )).
fof(t21_simplex2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( v9_rltopsp1(B,k15_euclid(A)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(A))) & ? [D] : ( v1_xreal_0(D) & r1_tarski(B,k4_euclid_9(A,C,D)) ) ) ) ) ) )).
fof(t21_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(D,E) & r1_xxreal_0(C,k9_complex1(k9_nat_1(k1_numbers,k3_series_1(k55_valued_1(k4_ordinal1,k2_numbers,k12_sin_cos(B,A,E))),E))) ) ) ) ) ) ) )).
fof(t21_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k1_funct_1(k1_sin_cos2,k2_xcmplx_0(A,B)) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_sin_cos2,A),k1_funct_1(k3_sin_cos2,B)),k3_xcmplx_0(k1_funct_1(k3_sin_cos2,A),k1_funct_1(k1_sin_cos2,B))) & k1_funct_1(k1_sin_cos2,k6_xcmplx_0(A,B)) = k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_sin_cos2,A),k1_funct_1(k3_sin_cos2,B)),k3_xcmplx_0(k1_funct_1(k3_sin_cos2,A),k1_funct_1(k1_sin_cos2,B))) ) ) ) )).
fof(t21_sin_cos3,axiom,( k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,k5_complex1) = k5_numbers )).
fof(t21_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => k1_square_1(k19_sin_cos(A)) = k7_xcmplx_0(k2_xcmplx_0(1,k19_sin_cos(k3_xcmplx_0(2,A))),2) ) )).
fof(t21_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ~ ( r1_xxreal_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B),A) & ~ r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)),A) & k17_sin_cos(A) = k5_numbers & A != k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B) & A != k2_xcmplx_0(k28_sin_cos,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)) ) ) ) )).
fof(t21_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(k1_square_1(A),1) & r1_xxreal_0(1,k1_square_1(k7_xcmplx_0(1,A))) ) ) )).
fof(t21_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( k2_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(k6_sin_cos2(A),k6_sin_cos2(B)),k6_sin_cos2(C)),k3_xcmplx_0(k3_xcmplx_0(k6_sin_cos2(A),k6_sin_cos2(B)),k6_sin_cos2(C))),k4_sin_cos2(A)),k4_sin_cos2(B)),k4_sin_cos2(C)) & k4_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(k6_sin_cos2(A),k6_sin_cos2(B))),k3_xcmplx_0(k6_sin_cos2(B),k6_sin_cos2(C))),k3_xcmplx_0(k6_sin_cos2(C),k6_sin_cos2(A))),k4_sin_cos2(A)),k4_sin_cos2(B)),k4_sin_cos2(C)) & k6_sin_cos2(k2_xcmplx_0(k2_xcmplx_0(A,B),C)) = k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k6_sin_cos2(A),k6_sin_cos2(B)),k6_sin_cos2(C)),k3_xcmplx_0(k3_xcmplx_0(k6_sin_cos2(A),k6_sin_cos2(B)),k6_sin_cos2(C))),k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(1,k3_xcmplx_0(k6_sin_cos2(B),k6_sin_cos2(C))),k3_xcmplx_0(k6_sin_cos2(C),k6_sin_cos2(A))),k3_xcmplx_0(k6_sin_cos2(A),k6_sin_cos2(B)))) ) ) ) ) )).
fof(t21_sin_cos9,axiom,( k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k26_sin_cos,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)),k7_xcmplx_0(k28_sin_cos,4)))) = k1_rcomp_1(k4_xcmplx_0(1),1) )).
fof(t21_sincos10,axiom,( v2_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k3_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(t21_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ~ ( v2_funct_1(B) & r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(B)) & v2_sppol_1(k2_topreal1(2,B,A)) & v1_sppol_1(k2_topreal1(2,B,A)) ) ) ) )).
fof(t21_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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) ) ) )).
fof(t21_sprect_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t21_sprect_2,axiom,( ! [A] : ( ( ~ v1_zfmisc_1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => r1_sprect_2(A,A) ) )).
fof(t21_sprect_3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) ) )).
fof(t21_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t21_square_1,axiom,( ~ r1_xxreal_0(2,k3_square_1(2)) )).
fof(t21_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t21_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k7_card_1(B),k7_card_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(B),k7_card_1(A)))) ) => ( C = k6_partfun1(B) => ( r1_xxreal_0(B,k5_numbers) | v1_stirl2_1(C,B,A) ) ) ) ) ) )).
fof(t21_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k16_substut1(A),k38_substut1(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t21_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( 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)) ) ) )).
fof(t21_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( m1_subset_1(D,k5_finsub_1(k4_partfun1(A,B))) => ! [E] : ( 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) ) ) ) )).
fof(t21_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k16_substut1(A),k3_qc_lang1(A))) => ! [C] : ( m1_substut1(C,A,B) => ( v3_substut1(B,A) => k31_substut1(A,k24_substut1(A,B,C)) = k22_substut1(A,B) ) ) ) ) )).
fof(t21_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ( ( ! [D] : ( 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] : ( 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] : ( 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))) ) ) ) ) ) )).
fof(t21_supinf_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t21_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r1_orders_2(B,k5_algstr_0(B,E,D),C) => ( r1_orders_2(B,D,C) | k1_symsp_1(A,B,C,D,E) = k1_group_1(A) ) ) ) ) ) ) ) )).
fof(t21_sysrel,axiom,( ! [A] : ! [B] : ( 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) ) ) ) )).
fof(t21_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),k1_numbers))) ) => ! [C] : ( 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,k5_numbers)) ) ) ) ) )).
fof(t21_taylor_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,k5_numbers) => ( r1_fdiff_1(k4_taylor_1(A),B) & k1_fdiff_1(k4_taylor_1(A),B) = k3_xcmplx_0(A,k6_prepower(B,k6_xcmplx_0(A,1))) ) ) ) ) )).
fof(t21_taylor_2,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r1_taylor_1(k16_sin_cos,B,A) & r1_taylor_1(k18_sin_cos,B,A) ) ) ) )).
fof(t21_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_tbsp_1(B,A) => r1_xxreal_0(k5_numbers,k3_tbsp_1(A,B)) ) ) ) )).
fof(t21_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => v6_tops_1(k2_struct_0(A),A) ) )).
fof(t21_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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)) ) ) ) )).
fof(t21_tdlat_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v3_tdlat_3(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) => v4_pre_topc(B,A) ) ) ) ) )).
fof(t21_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ( k3_polynom1(k15_pre_poly(A),C,k5_termord(A,B,C,D)) = k1_xboole_0 | k3_polynom1(k15_pre_poly(A),C,k5_termord(A,B,C,D)) = k1_tarski(k3_termord(A,B,C,D)) ) ) ) ) ) )).
fof(t21_tex_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ( ~ v1_xboole_0(k6_subset_1(A,k6_domain_1(A,B))) => ! [C] : ( 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) ) ) ) ) ) ) ) )).
fof(t21_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t21_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tex_3(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_tex_3(C,B) & m1_pre_topc(C,B) ) => ( v2_tex_3(C,A) & m1_pre_topc(C,A) ) ) ) ) )).
fof(t21_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t21_tietze,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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))))) ) ) ) ) ) )).
fof(t21_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t21_toler_1,axiom,( ! [A] : ! [B] : ( ( 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] : ~ ( r2_hidden(C,A) & ! [D] : ( ( v1_toler_1(D,A,B) & m1_toler_1(D,A,B) ) => ~ r2_hidden(C,D) ) ) ) )).
fof(t21_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r1_borsuk_6(A,B,C) & r1_borsuk_6(A,D,C) ) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t21_topalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k17_borsuk_1)) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t21_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_borsuk_2(G,k2_borsuk_1(A,B),k4_borsuk_1(A,B,C,E),k4_borsuk_1(A,B,D,F)) => ! [H] : ( m1_borsuk_2(H,k2_borsuk_1(A,B),k4_borsuk_1(A,B,C,E),k4_borsuk_1(A,B,D,F)) => ! [I] : ( m1_borsuk_2(I,A,C,D) => ! [J] : ( m1_borsuk_2(J,A,C,D) => ! [K] : ( m1_borsuk_2(K,B,E,F) => ! [L] : ( m1_borsuk_2(L,B,E,F) => ! [M] : ( m1_borsuk_6(M,A,C,D,I,J) => ! [N] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_topalg_6,axiom,( ! [A] : ( l1_pre_topc(A) => m2_subset_1(k1_xboole_0,k4_partfun1(k1_numbers,k2_struct_0(A)),k1_topalg_6(A)) ) )).
fof(t21_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t21_topdim_2,axiom,( ! [A] : ( v7_ordinal1(A) => r1_xxreal_0(k4_topdim_1(k15_euclid(A)),A) ) )).
fof(t21_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_topgen_1(A,B,C) <=> ! [D] : ( ( v3_pre_topc(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( r2_hidden(C,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( E != C & r2_hidden(E,B) & r2_hidden(E,D) ) ) ) ) ) ) ) ) )).
fof(t21_topgen_2,axiom,( ! [A] : ! [B] : ! [C] : ( 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)))) ) ) )).
fof(t21_topgen_3,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(1,B) & ~ v1_series_1(k4_topgen_3(A,B)) ) ) )).
fof(t21_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t21_topgen_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k5_numbers,B) => ( r1_xxreal_0(C,k5_numbers) | ( r1_xboole_0(k1_topreal9(2,k19_euclid(A,B),C),k1_topgen_5) <=> r1_xxreal_0(C,B) ) ) ) ) ) ) )).
fof(t21_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_connsp_2(E,A,D) => ? [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t21_topmetr,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) & ? [C] : ( v1_xreal_0(C) & ! [D] : ( v1_xreal_0(D) => k1_funct_1(A,D) = k2_xcmplx_0(k3_xcmplx_0(B,D),C) ) ) ) => v5_pre_topc(A,k3_topmetr,k3_topmetr) ) ) )).
fof(t21_topreal1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(B))) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) ) => ( r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(B)),C,A),k2_topreal1(B,C,A)) & r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(B)),C,k1_nat_1(A,1)),k2_topreal1(B,C,A)) ) ) ) ) ) )).
fof(t21_topreal3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(B))) => ( ( r2_hidden(C,k8_metric_1(k14_euclid(B),E,A)) & r2_hidden(D,k8_metric_1(k14_euclid(B),E,A)) ) => r1_tarski(k1_rltopsp1(k15_euclid(B),C,D),k8_metric_1(k14_euclid(B),E,A)) ) ) ) ) ) ) )).
fof(t21_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => ( k12_euclid(k19_euclid(k5_numbers,A)) = k9_complex1(A) & k12_euclid(k19_euclid(A,k5_numbers)) = k9_complex1(A) ) ) )).
fof(t21_topreal7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v8_metric_1(B) & l1_metric_1(B) ) => v8_metric_1(k1_topreal7(A,B)) ) ) )).
fof(t21_topreal8,axiom,( ! [A] : ( ( v1_goboard5(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(1,B) => v3_topreal1(k2_rfinseq(u1_struct_0(k15_euclid(2)),B,A)) ) ) ) )).
fof(t21_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ~ ( v1_xboole_0(k2_topreal9(A,C,B)) & r1_xxreal_0(k5_numbers,B) ) ) ) ) )).
fof(t21_topreala,axiom,( ! [A] : ( ( 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] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t21_toprealb,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k8_toprealb(2))) => ~ m1_subset_1(A,u1_struct_0(k11_toprealb(A))) ) )).
fof(t21_toprealc,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => r1_xxreal_0(k9_complex1(k16_rvsum_1(A)),k18_rvsum_1(k3_euclid(A))) ) )).
fof(t21_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ( v1_toprns_1(C,A) => ( B = k5_numbers | v1_toprns_1(k2_toprns_1(B,A,C),A) ) ) ) ) ) )).
fof(t21_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t21_tops_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t21_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t21_tops_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_xreal_0(D) & v2_xxreal_0(D) ) => ? [E] : ( 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))) ) ) ) ) ) ) )).
fof(t21_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t21_treal_1,axiom,( ! [A] : ( ( 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] : ( 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 ) ) )).
fof(t21_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ( r2_hidden(k1_xboole_0,A) & r2_hidden(k6_finseq_1(k4_ordinal1),A) ) ) )).
fof(t21_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( m1_trees_2(D,A) => ~ ( r2_hidden(B,D) & r2_hidden(C,D) & ~ r2_hidden(B,k1_trees_1(C)) & ~ r1_tarski(C,B) ) ) ) ) ) )).
fof(t21_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => r1_tarski(k5_trees_3(A),k4_trees_3(A)) ) )).
fof(t21_trees_4,axiom,( ! [A] : ! [B] : k3_trees_4(A,k9_finseq_1(B)) = k7_trees_2(k7_funcop_1(k2_trees_1(1),A),k14_trees_3(k5_numbers),k1_trees_4(B)) )).
fof(t21_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v3_trees_3(B) ) => ( r1_tarski(A,B) => r1_tarski(k9_trees_9(A),k9_trees_9(B)) ) ) ) )).
fof(t21_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ 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)) ) ) ) ) )).
fof(t21_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t21_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t21_turing_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r1_xxreal_0(3,k3_finseq_1(A)) => ( k1_gr_cy_1(k4_turing_1(1,k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,B),A))) = B & k1_gr_cy_1(k4_turing_1(2,k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,B),A))) = k1_nat_1(B,k7_partfun1(k4_ordinal1,A,1)) & k1_gr_cy_1(k4_turing_1(3,k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,B),A))) = k1_nat_1(k1_nat_1(B,k7_partfun1(k4_ordinal1,A,1)),k7_partfun1(k4_ordinal1,A,2)) & k1_gr_cy_1(k4_turing_1(4,k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,B),A))) = k1_nat_1(k1_nat_1(k1_nat_1(B,k7_partfun1(k4_ordinal1,A,1)),k7_partfun1(k4_ordinal1,A,2)),k7_partfun1(k4_ordinal1,A,3)) ) ) ) ) )).
fof(t21_twoscomp,axiom,( k1_funct_1(k20_twoscomp,k11_finseq_1(k5_numbers,k5_numbers,k5_numbers)) = 1 & k1_funct_1(k20_twoscomp,k11_finseq_1(k5_numbers,k5_numbers,1)) = k5_numbers & k1_funct_1(k20_twoscomp,k11_finseq_1(k5_numbers,1,k5_numbers)) = k5_numbers & k1_funct_1(k20_twoscomp,k11_finseq_1(k5_numbers,1,1)) = k5_numbers & k1_funct_1(k20_twoscomp,k11_finseq_1(1,k5_numbers,k5_numbers)) = k5_numbers & k1_funct_1(k20_twoscomp,k11_finseq_1(1,k5_numbers,1)) = k5_numbers & k1_funct_1(k20_twoscomp,k11_finseq_1(1,1,k5_numbers)) = k5_numbers & k1_funct_1(k20_twoscomp,k11_finseq_1(1,1,1)) = k5_numbers )).
fof(t21_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_unialg_2(B,A) => ! [C] : ( m1_unialg_2(C,A) => k8_unialg_2(A,B,C) = k8_unialg_2(A,C,B) ) ) ) )).
fof(t21_unialg_3,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(t21_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ( r2_hidden(B,k2_uniroots(A)) <=> m1_comptrig(B,k1_group_1(k1_complfld),A) ) ) ) )).
fof(t21_uproots,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_polynom3(A))) => ( B = C => k5_vfunct_1(k4_ordinal1,A,B) = k4_algstr_0(k14_polynom3(A),C) ) ) ) ) )).
fof(t21_urysohn1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v9_pre_topc(A) <=> ! [B] : ( ( v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & ! [D] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t21_urysohn2,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k3_xcmplx_0(k1_newton(2,B),A),1) ) ) ) )).
fof(t21_urysohn3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v8_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v4_pre_topc(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( r1_xboole_0(B,C) & ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_xxreal_0(k5_numbers,k12_supinf_2(D,E)) & r1_xxreal_0(k12_supinf_2(D,E),1) & ( r2_hidden(E,B) => k12_supinf_2(D,E) = k5_numbers ) & ( r2_hidden(E,C) => k12_supinf_2(D,E) = 1 ) ) ) ) ) ) ) ) ) )).
fof(t21_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t21_valued_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ! [C] : ( m2_valued_0(C,A,B) => r1_tarski(k2_relset_1(A,C),k2_relset_1(A,B)) ) ) ) )).
fof(t21_valued_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(t21_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t21_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(t21_vectsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t21_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( C != k4_struct_0(A) & D != k4_struct_0(A) & k1_vectsp_2(A,B,k1_vectsp_2(A,C,D)) != k1_vectsp_2(A,k6_algstr_0(A,B,D),C) ) ) ) ) ) )).
fof(t21_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_vectsp_4(E,A,B) => ( r1_struct_0(E,D) => r1_struct_0(E,k4_vectsp_1(A,B,C,D)) ) ) ) ) ) ) )).
fof(t21_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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 ) ) ) ) )).
fof(t21_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t21_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v1_vectsp_7(C,A,B) => v1_finset_1(C) ) ) ) ) ) )).
fof(t21_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => r2_relset_1(A,k1_numbers,k4_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),k4_normsp_0(A,B,C))) ) ) ) ) )).
fof(t21_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => r2_relset_1(A,k1_numbers,k4_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),k4_normsp_0(A,B,C))) ) ) ) ) )).
fof(t21_waybel10,axiom,( ! [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] : ( ( 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) ) ) )).
fof(t21_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t21_waybel12,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( 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 ) ) )).
fof(t21_waybel13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t21_waybel14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)))) ) ) ) ) ) ) ) )).
fof(t21_waybel15,axiom,( ! [A] : ( ( 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))) ) )).
fof(t21_waybel16,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t21_waybel17,axiom,( ! [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] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ 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))) ) ) ) ) ) )).
fof(t21_waybel19,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( u1_struct_0(A) = u1_struct_0(B) => ! [C] : ( m3_yellow_9(C,A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) => ( ( E = D & v4_pre_topc(D,A) ) => v4_pre_topc(E,C) ) ) ) ) ) ) ) )).
fof(t21_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t21_waybel21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v4_yellow_0(C,A) & m1_yellow_0(C,A) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(t21_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v3_waybel23(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t21_waybel24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v3_orders_2(B) & l1_waybel_9(B) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t21_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t21_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t21_waybel27,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v4_yellow_0(D,k5_yellow_1(A,k5_yellow_1(B,C))) & m1_yellow_0(D,k5_yellow_1(A,k5_yellow_1(B,C))) ) => ! [E] : ( ( ~ v2_struct_0(E) & v4_yellow_0(E,k5_yellow_1(k2_zfmisc_1(A,B),C)) & m1_yellow_0(E,k5_yellow_1(k2_zfmisc_1(A,B),C)) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t21_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) => ! [C] : ( 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))) ) ) ) ) )).
fof(t21_waybel29,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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(k4_yellow_1(A,k2_funcop_1(A,B))) ) ) )).
fof(t21_waybel30,axiom,( ! [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_waybel_2(A) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v5_pre_topc(k4_waybel_1(A,B),A,A) ) ) )).
fof(t21_waybel31,axiom,( ! [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] : ( ( v2_pre_topc(B) & v2_waybel19(B) & m1_yellow_9(B,A) ) => ! [C] : ( ( 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)))) ) ) ) ) )).
fof(t21_waybel32,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( ! [C] : ( 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) ) ) ) )).
fof(t21_waybel33,axiom,( ! [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) ) => r1_tarski(k1_waybel19(A),k4_waybel28(A)) ) )).
fof(t21_waybel34,axiom,( ! [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] : ( ( 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] : ( ( 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] : ( ( v4_waybel11(D) & m1_yellow_9(D,B) ) => ! [E] : ( ( v4_waybel11(E) & m1_yellow_9(E,A) ) => ! [F] : ( ( 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))) ) ) ) ) ) ) ) ) )).
fof(t21_waybel35,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_waybel_4(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ( m1_waybel35(C,A,B) => ( ! [D] : ( 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) ) ) ) ) )).
fof(t21_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t21_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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)) ) ) ) ) ) )).
fof(t21_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) ) )).
fof(t21_waybel_3,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ! [D] : ( ( ~ 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) ) ) ) ) )).
fof(t21_waybel_4,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) )).
fof(t21_waybel_5,axiom,( ! [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) ) => ( v3_waybel_3(A) <=> ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( 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)))) ) ) ) ) ) ) )).
fof(t21_waybel_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => v6_waybel_6(k3_yellow_0(A),A) ) )).
fof(t21_waybel_7,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v2_waybel_0(B,k2_yellow_1(A)) & v13_waybel_0(B,k2_yellow_1(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(A)))) ) => ( v2_waybel_7(B,k2_yellow_1(A)) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r2_hidden(C,B) | r2_hidden(k6_subset_1(A,C),B) ) ) ) ) )).
fof(t21_waybel_8,axiom,( ! [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_8(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v4_waybel_7(B,A) => v5_waybel_6(B,A) ) ) ) )).
fof(t21_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_yellow_6(A,B))) => m1_connsp_2(C,A,B) ) ) ) )).
fof(t21_weddwitt,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t21_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( ( E = k1_funct_1(k5_weierstr(A,B),C) & F = k1_funct_1(k5_weierstr(A,B),D) ) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(E,F)),k3_metric_1(A,C,D)) ) ) ) ) ) ) ) ) ) )).
fof(t21_wellord1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k2_wellord1(k2_wellord1(B,A),A) = k2_wellord1(B,A) ) )).
fof(t21_xboole_1,axiom,( ! [A] : ! [B] : k3_xboole_0(A,k2_xboole_0(A,B)) = A )).
fof(t21_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k4_xboolean(k3_xboolean(A),k7_xboolean(A,B)) = k4_xboolean(k3_xboolean(A),k3_xboolean(B)) ) ) )).
fof(t21_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k6_xcmplx_0(k6_xcmplx_0(A,B),C) = k6_xcmplx_0(k6_xcmplx_0(A,C),B) ) ) ) )).
fof(t21_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t21_xtuple_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( r2_hidden(k6_xtuple_0(B,A,C,D),E) => r2_hidden(A,k14_xtuple_0(E)) ) )).
fof(t21_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ~ ( ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(C,A) & r1_xxreal_0(k3_xxreal_0(B,C),A) ) ) ) ) )).
fof(t21_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => r1_tarski(k4_xxreal_1(A,B),k3_xxreal_1(A,B)) ) ) )).
fof(t21_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => m1_xxreal_2(B,k1_xxreal_1(A,B)) ) ) )).
fof(t21_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t21_yellow10,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t21_yellow12,axiom,( ! [A] : ( ( v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t21_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t21_yellow14,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t21_yellow15,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v6_waybel23(k2_struct_0(A),A) & v7_waybel23(k2_struct_0(A),A) ) ) )).
fof(t21_yellow16,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t21_yellow17,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_waybel18(A,B))) => ( ! [E] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k4_waybel18(A,B,C))) => ! [F] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(B)) & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & E = C & F = D & ? [G] : ( m1_subset_1(G,k1_altcat_1(A,C,D)) & ? [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_pre_topc(A,B)) <=> ? [D] : ( ~ 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) ) ) ) ) ) )).
fof(t21_yellow20,axiom,( ! [A] : ( l2_altcat_1(A) => ! [B] : ( l2_altcat_1(B) => ( r1_yellow20(A,B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(k2_yellow20(A,B))) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t21_yellow_0,axiom,( ! [A] : ( ( v5_orders_2(A) & l1_orders_2(A) ) => ( v2_lattice3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_yellow_0(A,k2_tarski(B,C)) ) ) ) ) )).
fof(t21_yellow_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(A)))) => k1_yellow_0(k2_yellow_1(A),B) = k3_tarski(B) ) )).
fof(t21_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => v11_quantal1(k3_struct_0(A)) ) )).
fof(t21_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t21_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t21_yellow_5,axiom,( ! [A] : ( ( v5_orders_2(A) & v1_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t21_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( r2_waybel_0(A,B,C) => ( ~ v2_struct_0(k5_yellow_6(A,B,C)) & v7_waybel_0(k5_yellow_6(A,B,C)) ) ) ) ) )).
fof(t21_yellow_7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t21_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v8_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v3_yellow_8(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v1_zfmisc_1(B) ) ) )).
fof(t21_yellow_9,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(t21_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ~ v1_xboole_0(C) => ( ( v8_zf_fund1(B,A) & r2_hidden(C,B) ) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( m2_subset_1(E,k4_ordinal1,k1_zf_lang) => ( r2_hidden(k5_zf_fund1(D,C),B) => r2_hidden(k5_zf_fund1(k8_zf_lang(E,D),C),B) ) ) ) ) ) ) ) )).
fof(t21_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v5_zf_lang(A) => k1_funct_1(A,1) = 3 ) ) )).
fof(t21_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,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) ) ) ) ) ) )).
fof(t21_zf_model,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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] : ( ( 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] : ( m2_subset_1(G,k4_ordinal1,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) ) ) ) ) ) ) ) ) )).
fof(t21_zf_refle,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) & ~ v4_card_3(A) ) => ( v6_card_fil(A) => v1_zf_model(k4_classes1(A)) ) ) )).
fof(t21_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(k2_tarski(A,B),k1_tarski(C)) => k2_tarski(A,B) = k1_tarski(C) ) )).
fof(t21_zfrefle1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( ( r2_ordinal2(A,B) & r2_ordinal2(B,A) ) => A = B ) ) ) )).
fof(t21_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( u1_struct_0(A) = B => v7_zmodul01(B,A) ) ) ) )).
fof(t21_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_zmodul02(C,A,k6_domain_1(u1_struct_0(A),B)) => k21_zmodul02(A,C) = k1_zmodul01(A,B,k3_funct_2(u1_struct_0(A),k4_numbers,C,B)) ) ) ) )).
fof(t21_zmodul03,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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) & v1_zmodul03(B) & l1_zmodul01(B) ) => ! [C] : ( m1_zmodul03(C,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ~ ( D != E & r2_hidden(D,C) & r2_hidden(E,C) & k13_zmodul02(A,B,D) = k13_zmodul02(A,B,E) ) ) ) ) ) ) )).
fof(t220_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ( C != k5_numbers => k25_member_1(k5_xboole_0(A,B),C) = k5_xboole_0(k25_member_1(A,C),k25_member_1(B,C)) ) ) ) ) )).
fof(t220_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k3_xcmplx_0(k5_xcmplx_0(A),k7_xcmplx_0(C,B)) = k7_xcmplx_0(C,k3_xcmplx_0(A,B)) ) ) ) )).
fof(t220_xreal_1,axiom,( ! [A] : ( 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)),k5_numbers) ) ) )).
fof(t220_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( r1_xxreal_0(A,B) => r2_hidden(A,k1_xxreal_1(k2_xxreal_0,B)) ) ) ) )).
fof(t221_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => r1_tarski(k25_member_1(A,k2_xcmplx_0(B,C)),k9_member_1(k25_member_1(A,B),k25_member_1(A,C))) ) ) ) )).
fof(t221_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k7_xcmplx_0(k5_xcmplx_0(A),B) = k5_xcmplx_0(k3_xcmplx_0(A,B)) ) ) )).
fof(t221_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(A,k7_xcmplx_0(A,3)) ) ) )).
fof(t221_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( ~ r1_xxreal_0(B,A) => r2_hidden(A,k2_xxreal_1(k2_xxreal_0,B)) ) ) ) )).
fof(t222_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => r1_tarski(k25_member_1(A,k6_xcmplx_0(B,C)),k11_member_1(k25_member_1(A,B),k25_member_1(A,C))) ) ) ) )).
fof(t222_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k5_xcmplx_0(k4_xcmplx_0(A)) = k4_xcmplx_0(k5_xcmplx_0(A)) ) )).
fof(t222_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k7_xcmplx_0(A,3),k5_numbers) ) ) )).
fof(t222_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t223_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(C,A) => r2_hidden(k6_xxreal_3(C,B),k26_member_1(A,B)) ) ) ) ) )).
fof(t223_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ~ ( A != k5_numbers & A = k5_xcmplx_0(A) & A != 1 & A != k4_xcmplx_0(1) ) ) )).
fof(t223_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(A,k7_xcmplx_0(A,4)) ) ) )).
fof(t223_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( r1_xxreal_0(B,C) & r1_xxreal_0(C,D) & r2_hidden(B,k2_xboole_0(k4_xxreal_1(C,D),k4_xxreal_1(D,A))) ) ) ) ) ) )).
fof(t224_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => k26_member_1(A,B) = a_2_18_member_1(A,B) ) ) )).
fof(t224_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C),B) = k2_xcmplx_0(A,C) ) ) ) )).
fof(t224_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k7_xcmplx_0(A,4),k5_numbers) ) ) )).
fof(t224_xxreal_1,axiom,( k1_numbers = k4_xxreal_1(k2_xxreal_0,k1_xxreal_0) )).
fof(t225_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ~ ( r2_hidden(C,k26_member_1(A,B)) & ! [D] : ( m1_subset_1(D,k6_numbers) => ~ ( C = k6_xxreal_3(D,B) & r2_hidden(D,A) ) ) ) ) ) )).
fof(t225_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k2_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(A,B),C),B) = k2_xcmplx_0(A,C) ) ) ) )).
fof(t225_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( B != k5_numbers & ! [C] : ( v1_xreal_0(C) => A != k7_xcmplx_0(B,C) ) ) ) ) )).
fof(t225_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => r1_tarski(k4_xxreal_1(A,B),k1_numbers) ) ) )).
fof(t226_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( r2_hidden(C,A) => r2_hidden(k7_xcmplx_0(C,B),k27_member_1(A,B)) ) ) ) ) )).
fof(t226_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k6_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),C),B) = k6_xcmplx_0(A,C) ) ) ) )).
fof(t226_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)) ) ) ) ) )).
fof(t226_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( r2_hidden(A,k1_numbers) => r1_tarski(k2_xxreal_1(A,B),k1_numbers) ) ) ) )).
fof(t227_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => k27_member_1(A,B) = a_2_19_member_1(A,B) ) ) )).
fof(t227_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(A,B),C),B) = k6_xcmplx_0(A,C) ) ) ) )).
fof(t227_xreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( ~ r1_xxreal_0(B,A) & ! [C] : ( v1_xxreal_0(C) => ~ ( ~ r1_xxreal_0(C,A) & ~ r1_xxreal_0(B,C) ) ) ) ) ) )).
fof(t227_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( r2_hidden(B,k1_numbers) => r1_tarski(k3_xxreal_1(A,B),k1_numbers) ) ) ) )).
fof(t228_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ~ ( r2_hidden(C,k27_member_1(A,B)) & ! [D] : ( v1_xcmplx_0(D) => ~ ( C = k7_xcmplx_0(D,B) & r2_hidden(D,A) ) ) ) ) ) )).
fof(t228_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k6_xcmplx_0(k6_xcmplx_0(A,A),B) = k4_xcmplx_0(B) ) ) )).
fof(t228_xreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ! [D] : ( 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) ) ) ) ) ) )).
fof(t228_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( ( r2_hidden(A,k1_numbers) & r2_hidden(B,k1_numbers) ) => r1_tarski(k1_xxreal_1(A,B),k1_numbers) ) ) ) )).
fof(t229_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ( r1_tarski(k27_member_1(A,C),k27_member_1(B,C)) => ( C = k5_numbers | r1_tarski(A,B) ) ) ) ) ) )).
fof(t229_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(A),A),B) = k4_xcmplx_0(B) ) ) )).
fof(t229_xreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ! [D] : ( 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) ) ) ) ) ) )).
fof(t229_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => k4_xxreal_1(k2_xxreal_0,A) = a_1_0_xxreal_1(A) ) )).
fof(t22_abcmiz_0,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t22_abcmiz_1,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k4_classes1(k4_ordinal1))) ) => r2_hidden(A,k4_classes1(k4_ordinal1)) ) )).
fof(t22_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & v1_abcmiz_a(A) & l1_msualg_1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t22_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(k6_xcmplx_0(k2_xcmplx_0(k2_absvalue(A),k2_absvalue(B)),1),k2_absvalue(k2_xcmplx_0(A,B))) ) ) )).
fof(t22_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t22_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_aff_4(D,A) & v1_aff_1(B,A) & v1_aff_1(C,A) & r1_tarski(B,D) & r1_tarski(C,D) & ~ r5_aff_1(A,B,C) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,B) & r2_hidden(E,C) ) ) ) ) ) ) ) )).
fof(t22_afinsq_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ~ ( r2_hidden(A,k2_afinsq_1(C)) & ! [D] : ( v7_ordinal1(D) => ~ ( D = A & r2_hidden(k2_xcmplx_0(k1_afinsq_1(B),D),k2_afinsq_1(k1_ordinal4(B,C))) ) ) ) ) ) )).
fof(t22_afinsq_2,axiom,( ! [A] : ( v7_ordinal1(A) => k1_recdef_1(k4_afinsq_2(k1_tarski(A)),k5_numbers) = A ) )).
fof(t22_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k14_afproj(A))) => m1_subset_1(B,u1_incsp_1(k13_afproj(A))) ) ) )).
fof(t22_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r2_afvect0(A,B,C,D) & r2_afvect0(A,B,C,E) ) => D = E ) ) ) ) ) ) )).
fof(t22_algspec1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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] : k3_relat_1(k1_algspec1(C,B),A) = k5_relat_1(A,C) ) ) ) )).
fof(t22_algstr_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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))) ) ) ) )).
fof(t22_altcat_2,axiom,( ! [A] : ( l2_altcat_1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t22_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v16_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t22_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( v7_ordinal1(B) => ~ v2_extpro_1(k8_ami_3(B,A),k7_card_1(2),k1_ami_3) ) ) )).
fof(t22_ami_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( ~ 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(k7_card_1(2),k1_ami_3)) & v1_finset_1(B) & v4_extpro_1(B,k7_card_1(2),k1_ami_3,A) ) => ! [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(C,u1_struct_0(k1_ami_3)) ) => ! [D] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ( ( r1_tarski(B,C) & r1_tarski(B,D) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_ami_3)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_ami_3)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( ( r1_tarski(A,E) & r1_tarski(A,F) ) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v1_ami_2(H) & m1_subset_1(H,u1_struct_0(k1_ami_3)) ) => ! [I] : ( v7_ordinal1(I) => ! [J] : ( m1_subset_1(J,u1_compos_1(k1_ami_3)) => ( ( J = k3_extpro_1(k7_card_1(2),k1_ami_3,E,k5_extpro_1(k7_card_1(2),k1_ami_3,E,C,G)) & J = k8_ami_3(I,H) ) => ( I = k1_ordinal1(k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,E,C,G))) | ( k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,E,C,G),H) = k5_numbers <=> k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,F,D,G),H) = k5_numbers ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t22_ami_6,axiom,( ! [A] : ( v7_ordinal1(A) => ( r2_hidden(k2_xcmplx_0(A,1),k3_amistd_1(k7_card_1(2),k1_ami_3,A)) & ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k3_amistd_1(k7_card_1(2),k1_ami_3,A)) => r1_xxreal_0(A,B) ) ) ) ) )).
fof(t22_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_compos_1(B)) => ~ ( v3_ami_wstd(C,A,B) & v2_extpro_1(C,A,B) ) ) ) ) )).
fof(t22_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(k2_analmetr(A,F,G))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k2_analmetr(A,F,G))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k2_analmetr(A,F,G))) => ! [K] : ( m1_subset_1(K,u1_struct_0(k2_analmetr(A,F,G))) => ( ( H = B & J = D & I = C & K = E ) => ( r2_analoaf(k2_analmetr(A,F,G),H,J,I,K) <=> ? [L] : ( v1_xreal_0(L) & ? [M] : ( v1_xreal_0(M) & k1_rlvect_1(A,k5_algstr_0(A,D,B),L) = k1_rlvect_1(A,k5_algstr_0(A,E,C),M) & ~ ( L = k5_numbers & M = k5_numbers ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t22_analoaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t22_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => r1_analort(A,E,F,B,C,D,D) ) ) ) ) ) ) )).
fof(t22_anproj_1,axiom,( ! [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) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t22_anproj_2,axiom,( ? [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) & l1_rlvect_1(A) & ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( 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 = k5_numbers & G = k5_numbers & H = k5_numbers & I = k5_numbers ) ) ) ) ) ) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & ? [I] : ( v1_xreal_0(I) & ? [J] : ( v1_xreal_0(J) & 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t22_aofa_000,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(B,C) => ! [D] : ( v7_ordinal1(D) => r1_tarski(k9_aofa_000(A,B,D),k9_aofa_000(A,C,D)) ) ) ) ) ) )).
fof(t22_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( v1_relat_1(H) & v1_funct_1(H) & v1_finseq_1(H) ) => ( H = k7_aofa_a00(A,B,C,D,E,F,G) <=> ( k3_finseq_1(H) = 7 & k1_funct_1(H,1) = A & k1_funct_1(H,2) = B & k1_funct_1(H,3) = C & k1_funct_1(H,4) = D & k1_funct_1(H,5) = E & k1_funct_1(H,6) = F & k1_funct_1(H,7) = G ) ) ) )).
fof(t22_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( k1_msualg_1(A,C) = k12_finseq_1(u1_struct_0(A),B) => ! [D] : ( l3_msualg_1(D,A) => k3_msualg_1(A,C,D) = k4_card_3(k12_finseq_1(k10_xtuple_0(u3_msualg_1(A,D)),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,D),B))) ) ) ) ) ) )).
fof(t22_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t22_armstrng,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(t22_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( 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)) ) ) )).
fof(t22_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( r1_arytm_2(B,A) => ( r1_arytm_2(B,C) | k2_arytm_1(A,k1_arytm_1(B,C)) = k7_arytm_2(k1_arytm_1(A,B),C) ) ) ) ) ) )).
fof(t22_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t22_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v4_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v4_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) => ( r1_xxreal_0(k1_seq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)),k5_numbers) | k7_asympt_0(A) = k7_asympt_0(B) ) ) ) ) )).
fof(t22_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ~ r1_xxreal_0(1,A) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ r1_xxreal_0(C,1) => k9_nat_1(k1_numbers,B,C) = k7_xcmplx_0(k5_series_1(C,2),k3_power(2,C)) ) ) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & v4_asympt_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( r2_funct_2(k4_ordinal1,k1_numbers,C,B) & r1_tarski(k6_asympt_0(k3_asympt_1(k2_xcmplx_0(1,A))),k6_asympt_0(C)) & k6_asympt_0(k3_asympt_1(k2_xcmplx_0(1,A))) != k6_asympt_0(C) ) ) ) ) ) )).
fof(t22_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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))) ) ) ) )).
fof(t22_autgroup,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t22_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => v2_wellord1(k4_bagorder(A)) ) )).
fof(t22_bcialg_1,axiom,( ! [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) ) => m1_bcialg_1(A,A) ) )).
fof(t22_bcialg_3,axiom,( ! [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) & v6_bcialg_3(A) & l2_bcialg_1(A) ) => ( v7_bcialg_3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v2_bcialg_3(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t22_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k6_bcialg_4(A,B,2) = k1_bcialg_4(A,B,B) ) ) )).
fof(t22_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( v8_bcialg_1(E) & m1_bcialg_5(E,A,B,C,D) ) => ( v8_bcialg_1(E) & m1_bcialg_5(E,D,B,C,D) ) ) ) ) ) ) )).
fof(t22_bcialg_6,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => k1_bcialg_1(A,k3_bcialg_6(A,C,B),k3_bcialg_6(A,D,B)) = k3_bcialg_6(A,k6_xcmplx_0(C,D),B) ) ) ) ) )).
fof(t22_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( m2_bciideal(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t22_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t22_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) & k1_seq_2(k2_bhsp_2(A,k4_normsp_1(A,C,B))) = k5_numbers ) ) ) ) ) )).
fof(t22_bhsp_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => k4_bhsp_4(B,C,k1_nat_1(A,1),A) = k1_normsp_1(B,C,k1_nat_1(A,1)) ) ) ) )).
fof(t22_bilinear,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t22_binari_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t22_binari_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(C,B) => r1_xxreal_0(k1_binari_4(C,A),k1_binari_4(B,A)) ) ) ) ) )).
fof(t22_binarith,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k6_margrel1) ) => ( r1_binarith(A,B,C) => k6_binarith(A,k7_binarith(A,B,C)) = k1_nat_1(k6_binarith(A,B),k6_binarith(A,C)) ) ) ) ) )).
fof(t22_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_relset_1(k4_ordinal1,u1_struct_0(A),k8_binom(A,B,C,k5_numbers),k12_finseq_1(u1_struct_0(A),k1_group_1(A))) ) ) ) )).
fof(t22_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree2(A) ) => k1_funct_1(k2_bintree2(A,1),1) = k10_binarith(k4_ordinal1,k5_numbers) ) )).
fof(t22_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t22_borsuk_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( m1_setfam_1(C,D) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ~ ( r1_tarski(E,C) & m1_setfam_1(E,D) & ! [F] : ~ ( r2_hidden(F,E) & r1_xboole_0(F,D) ) ) ) ) ) ) ) ) )).
fof(t22_borsuk_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(B,A)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t22_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( B = A => ( v4_xxreal_2(B) & v3_xxreal_2(B) ) ) ) ) )).
fof(t22_borsuk_5,axiom,( ! [A] : ( v1_rat_1(A) => ! [B] : ( ( v1_xreal_0(B) & ~ v1_rat_1(B) ) => ~ ( A != k5_numbers & v1_rat_1(k7_xcmplx_0(B,A)) ) ) ) )).
fof(t22_borsuk_6,axiom,( 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)))) )).
fof(t22_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k1_borsuk_7(A,A,A,B,C,D) = k16_funcop_1(A,D) )).
fof(t22_bspace,axiom,( ! [A] : v3_rlvect_1(k7_bspace(A)) )).
fof(t22_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(t22_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t22_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t22_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t22_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t22_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t22_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(E,A) => ( r3_bvfunc_2(A,D,B,E) => r2_funct_2(A,k6_margrel1,k6_bvfunc_2(A,k5_bvfunc_1(A,D,C),B,E),k5_bvfunc_1(A,D,k6_bvfunc_2(A,C,B,E))) ) ) ) ) ) ) )).
fof(t22_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(E,A) => ( r3_bvfunc_2(A,D,B,E) => 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),D)) ) ) ) ) ) ) )).
fof(t22_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t22_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t22_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(t22_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t22_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t22_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t22_c0sp1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(t22_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k5_c0sp2(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k5_c0sp2(A))))) ) => ( v1_rsspace3(B,k5_c0sp2(A)) => v3_normsp_1(B,k5_c0sp2(A)) ) ) ) )).
fof(t22_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t22_calcul_2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t22_card_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r1_ordinal1(A,B) <=> r1_ordinal1(k3_card_1(A),k3_card_1(B)) ) ) ) )).
fof(t22_card_2,axiom,( ! [A] : ( v1_card_1(A) => k2_card_2(2,A) = k1_card_2(A,A) ) )).
fof(t22_card_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) ) )).
fof(t22_card_4,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(t22_card_5,axiom,( k1_card_5(k4_ordinal1) = k4_ordinal1 )).
fof(t22_card_fil,axiom,( ! [A] : ( ~ v1_finset_1(A) => ! [B] : ( ( v3_card_fil(B,A) & m1_card_fil(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r2_hidden(C,B) <=> ~ r2_hidden(C,k1_card_fil(A,B)) ) ) ) ) )).
fof(t22_card_fin,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t22_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_hidden(k4_cat_1(A,B),k2_cat_1(A,B,B)) ) ) )).
fof(t22_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ( k3_graph_1(k6_cat_2(A,B),k8_cat_2(A,B,C,D)) = k7_cat_2(A,B,k3_graph_1(A,C),k3_graph_1(B,D)) & k4_graph_1(k6_cat_2(A,B),k8_cat_2(A,B,C,D)) = k7_cat_2(A,B,k4_graph_1(A,C),k4_graph_1(B,D)) ) ) ) ) ) )).
fof(t22_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_cat_1(D,A,B,C) => ( v1_cat_3(D,A,B,C) => v8_cat_1(D,A,B,C) ) ) ) ) ) )).
fof(t22_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t22_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ 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] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t22_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( v1_xboole_0(k2_catalan2(B,A)) <=> ~ r1_xxreal_0(k3_xcmplx_0(2,A),B) ) ) ) )).
fof(t22_catalg_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t22_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v3_algstr_0(B,A) & v3_algstr_0(C,A) ) => v3_algstr_0(k5_cayldick(A,B,C),k4_cayldick(A)) ) ) ) ) )).
fof(t22_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k7_cc0sp1(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k7_cc0sp1(A))) => ! [G] : ( 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] : ( m1_subset_1(H,A) => k3_funct_2(A,k2_numbers,D,H) = k2_xcmplx_0(k3_funct_2(A,k2_numbers,B,H),k3_funct_2(A,k2_numbers,C,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t22_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k5_cc0sp2(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k5_cc0sp2(A))) => ! [G] : ( 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] : ( m1_subset_1(H,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k2_numbers,D,H) = k2_xcmplx_0(k3_funct_2(u1_struct_0(A),k2_numbers,B,H),k3_funct_2(u1_struct_0(A),k2_numbers,C,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t22_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v2_comseq_2(A) => ( ! [C] : ( v7_ordinal1(C) => ~ r2_relset_1(k4_ordinal1,k2_numbers,A,k1_valued_0(k2_numbers,B,C)) ) | v2_comseq_2(B) ) ) ) ) )).
fof(t22_cfuncdom,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ~ ( C = k2_tarski(A,B) & A != B & ! [D] : ( m2_funct_2(D,C,k2_numbers,k9_funct_2(C,k2_numbers)) => ! [E] : ( m2_funct_2(E,C,k2_numbers,k9_funct_2(C,k2_numbers)) => ~ ( ! [F] : ( v1_xcmplx_0(F) => ! [G] : ( v1_xcmplx_0(G) => ( k1_binop_1(k1_cfuncdom(C),k1_funct_1(k3_cfuncdom(C),k4_tarski(F,D)),k1_funct_1(k3_cfuncdom(C),k4_tarski(G,E))) = k4_cfuncdom(C) => ( F = k5_numbers & G = k5_numbers ) ) ) ) & ! [F] : ( m2_funct_2(F,C,k2_numbers,k9_funct_2(C,k2_numbers)) => ? [G] : ( v1_xcmplx_0(G) & ? [H] : ( v1_xcmplx_0(H) & F = k1_binop_1(k1_cfuncdom(C),k1_funct_1(k3_cfuncdom(C),k4_tarski(G,D)),k1_funct_1(k3_cfuncdom(C),k4_tarski(H,E))) ) ) ) ) ) ) ) ) )).
fof(t22_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => r2_relset_1(A,k2_numbers,k25_valued_1(A,k2_numbers,B,k3_xcmplx_0(C,D)),k25_valued_1(A,k2_numbers,k25_valued_1(A,k2_numbers,B,D),C)) ) ) ) ) )).
fof(t22_cgames_1,axiom,( ! [A] : ( ( 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] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(A)) => ! [C] : ( m2_subset_1(C,k4_ordinal1,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))) ) ) ) ) )).
fof(t22_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ( ! [E] : ( m2_subset_1(E,k4_ordinal1,k2_finseq_1(A)) => r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) => ( r2_hidden(D,k3_chain_1(A,B,C)) <=> ! [E] : ( m2_subset_1(E,k4_ordinal1,k2_finseq_1(A)) => ( r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(D,E)) & r1_xxreal_0(k1_funct_1(D,E),k1_funct_1(C,E)) ) ) ) ) ) ) ) ) )).
fof(t22_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( B != C => ! [D] : ( m3_glib_001(D,A) => ~ ( k13_glib_001(A,D) = k2_tarski(B,C) & ! [E] : ~ r1_glib_000(A,B,C,E) ) ) ) ) )).
fof(t22_circcmb2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ! [I] : ( m1_subset_1(I,k4_card_3(u3_msualg_1(C,F))) => ! [J] : ( m1_subset_1(J,k4_card_3(u3_msualg_1(A,D))) => ( J = k5_relat_1(I,u1_struct_0(A)) => ! [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t22_circcmb3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( k4_finseq_2(C,A) = k4_finseq_2(D,B) => ( C = k5_numbers | ( A = B & C = D ) ) ) ) ) ) ) )).
fof(t22_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t22_circled1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t22_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_pdiff_7(C,A) & m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_ckspace1(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_ckspace1(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_ckspace1(A,B,C))) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ( ( G = D & H = E & I = F ) => ( F = k8_group_1(k2_ckspace1(A,B,C),D,E) <=> ! [J] : ( m2_subset_1(J,k1_euclid(A),C) => k1_funct_1(I,J) = k3_xcmplx_0(k1_funct_1(G,J),k1_funct_1(H,J)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t22_classes1,axiom,( ! [A] : ( v1_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( B != k1_xboole_0 => v1_ordinal1(k3_classes1(A,B)) ) ) ) )).
fof(t22_classes2,axiom,( ! [A] : ! [B] : ( v2_classes1(B) => ( ( ~ ( r2_hidden(A,B) & v1_ordinal1(B) ) & ~ ( r2_hidden(A,B) & r1_tarski(A,B) ) & ~ ( r2_hidden(k1_card_1(A),k1_card_1(B)) & r1_tarski(A,B) ) ) | r1_tarski(k1_funct_2(A,B),B) ) ) )).
fof(t22_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t22_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => k5_struct_0(k8_clopban2(A)) = k6_clopban2(A) ) )).
fof(t22_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v7_ordinal1(D) => k1_normsp_1(A,k1_bhsp_4(A,k4_clopban4(k1_nat_1(D,1),A,C,B)),D) = k3_rlvect_1(A,k1_normsp_1(A,k1_bhsp_4(A,k4_clopban4(D,A,C,B)),D),k1_normsp_1(A,k1_bhsp_4(A,k3_clopban4(k1_nat_1(D,1),A,C,B)),D)) ) ) ) ) )).
fof(t22_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m2_pboole(C,A,k5_mssubfam(A,B),k5_mssubfam(A,B)) => ! [D] : ( 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) ) ) ) ) )).
fof(t22_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k1_closure2(A,D))) => ( E = k2_tarski(B,C) => r6_pboole(A,k2_mboolean(A,k5_closure2(A,D,E)),k2_pboole(A,B,C)) ) ) ) ) ) )).
fof(t22_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v6_clvect_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t22_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) & k1_seq_2(k2_clvect_2(A,k4_normsp_1(A,C,B))) = k5_numbers ) ) ) ) ) )).
fof(t22_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => k3_clvect_3(A,B,k1_nat_1(C,1),C) = k1_normsp_0(A,B,k1_nat_1(C,1)) ) ) ) )).
fof(t22_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_coh_sp(A)) => ! [C] : ( m1_subset_1(C,k5_coh_sp(A)) => ( k6_coh_sp(A,C) = k7_coh_sp(A,B) => ( k2_xtuple_0(k9_coh_sp(A,B,C)) = k3_relat_1(k2_xtuple_0(B),k2_xtuple_0(C)) & k6_coh_sp(A,k9_coh_sp(A,B,C)) = k6_coh_sp(A,B) & k7_coh_sp(A,k9_coh_sp(A,B,C)) = k7_coh_sp(A,C) ) ) ) ) )).
fof(t22_cohsp_1,axiom,( ! [A] : ( ( 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] : ! [C] : ~ ( r2_hidden(B,k9_xtuple_0(A)) & r2_hidden(C,k1_funct_1(A,B)) & ! [D] : ~ ( v1_finset_1(D) & r1_tarski(D,B) & r2_hidden(C,k1_funct_1(A,D)) & ! [E] : ( ( r1_tarski(E,B) & r2_hidden(C,k1_funct_1(A,E)) ) => r1_tarski(D,E) ) ) ) ) ) ) ) )).
fof(t22_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & k1_collsp(A,B,C) = u1_struct_0(A) ) ) ) ) )).
fof(t22_combgras,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( l1_combgras(B,A,A) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t22_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v8_compl_sp(A) <=> ! [B] : ( ( v2_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & v5_compl_sp(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ~ ( v2_prob_1(B) & k2_kurato_0(u1_struct_0(A),B) = k1_xboole_0 ) ) ) ) )).
fof(t22_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k4_complex1(A) = k5_numbers => ( k3_complex1(A) = k5_numbers | ( k3_complex1(k5_xcmplx_0(A)) = k2_real_1(k3_complex1(A)) & k4_complex1(k5_xcmplx_0(A)) = k5_numbers ) ) ) ) )).
fof(t22_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( r1_xxreal_0(k1_comptrig(A),k28_sin_cos) => r1_xxreal_0(k5_numbers,k4_complex1(A)) ) ) )).
fof(t22_complfld,axiom,( ! [A] : ( 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) ) ) )).
fof(t22_complsp2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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) = k2_xcmplx_0(k9_matrix_5(B,A),k9_matrix_5(C,A)) ) ) ) ) )).
fof(t22_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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)) ) ) ) )).
fof(t22_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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 ) ) ) ) )).
fof(t22_comptrig,axiom,( v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k18_sin_cos,k2_rcomp_1(k28_sin_cos,k3_xcmplx_0(2,k28_sin_cos)))) )).
fof(t22_compts_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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)))))) ) ) ) )).
fof(t22_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & 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(k4_ordinal1),A) = k4_finseq_2(k19_margrel1(A),k4_ordinal1) ) ) )).
fof(t22_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k31_valued_1(k4_ordinal1,k2_numbers,k31_valued_1(k4_ordinal1,k2_numbers,A)),A) ) )).
fof(t22_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ~ ( k3_comseq_2(A) != k5_complex1 & ! [B] : ( v7_ordinal1(B) => ? [C] : ( v7_ordinal1(C) & r1_xxreal_0(B,C) & r1_xxreal_0(k9_complex1(k9_nat_1(k2_numbers,A,C)),k7_xcmplx_0(k9_complex1(k3_comseq_2(A)),2)) ) ) ) ) )).
fof(t22_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_ordinal1) & v5_valued_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ( r2_funct_2(k4_ordinal1,k1_numbers,k7_comseq_3(k9_comseq_3(B,A)),k2_valued_0(k1_numbers,B,k7_comseq_3(A))) & r2_funct_2(k4_ordinal1,k1_numbers,k8_comseq_3(k9_comseq_3(B,A)),k2_valued_0(k1_numbers,B,k8_comseq_3(A))) ) ) ) )).
fof(t22_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u4_struct_0(A))) => ( ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & ~ v4_conlat_1(g2_conlat_1(A,C,B),A) & v6_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 ) ) ) )).
fof(t22_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => r1_filter_1(k11_conlat_1(k7_conlat_2(A)),k1_lattice2(k11_conlat_1(A))) ) )).
fof(t22_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v2_connsp_1(C,A) & ~ r1_xboole_0(C,B) & k7_subset_1(u1_struct_0(A),C,B) != k1_struct_0(A) & r1_xboole_0(C,k2_tops_1(A,B)) ) ) ) ) )).
fof(t22_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ~ ( ! [D] : ( 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 ) ) ) ) )).
fof(t22_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t22_convex1,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( v2_convex1(B,A) & r1_xxreal_0(k1_funct_1(B,C),k5_numbers) & r2_hidden(C,k3_rlvect_2(A,B)) ) ) ) ) )).
fof(t22_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_convex4(B,A) => ! [C] : ( m1_convex4(C,A) => ! [D] : ( 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)) ) ) ) ) )).
fof(t22_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t22_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => k13_cqc_sim1(A,k5_cqc_lang(A)) = k26_qc_lang1(A) ) )).
fof(t22_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_finseq_1(C,k2_zfmisc_1(k3_cqc_lang(A),k2_cqc_the1)) => ~ ( r2_cqc_the1(A,B,C) & ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(k5_numbers,D) & r1_xxreal_0(D,6) & k2_xtuple_0(k1_funct_1(C,1)) = D ) ) ) ) ) ) )).
fof(t22_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ! [E] : ( m2_subset_1(E,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t22_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t22_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t22_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k9_csspace4(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_csspace4(A,B))) => ! [E] : ( v1_xcmplx_0(E) => ( ( k2_normsp_0(k9_csspace4(A,B),C) = k5_numbers => C = k4_struct_0(k9_csspace4(A,B)) ) & ( C = k4_struct_0(k9_csspace4(A,B)) => k2_normsp_0(k9_csspace4(A,B),C) = k5_numbers ) & k2_normsp_0(k9_csspace4(A,B),k1_clvect_1(k9_csspace4(A,B),C,E)) = k3_xcmplx_0(k9_complex1(E),k2_normsp_0(k9_csspace4(A,B),C)) & r1_xxreal_0(k2_normsp_0(k9_csspace4(A,B),k1_algstr_0(k9_csspace4(A,B),C,D)),k2_xcmplx_0(k2_normsp_0(k9_csspace4(A,B),C),k2_normsp_0(k9_csspace4(A,B),D))) ) ) ) ) ) ) )).
fof(t22_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(t22_descip_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,A) => ! [I] : ( m1_subset_1(I,A) => ! [J] : ( m1_subset_1(J,A) => ! [K] : ( m1_subset_1(K,A) => ! [L] : ( m1_subset_1(L,A) => ! [M] : ( m1_subset_1(M,A) => ! [N] : ( m1_subset_1(N,A) => ! [O] : ( m1_subset_1(O,A) => ! [P] : ( m1_subset_1(P,A) => ! [Q] : ( m1_subset_1(Q,A) => ! [R] : ( m1_subset_1(R,A) => ! [S] : ( m1_subset_1(S,A) => ! [T] : ( m1_subset_1(T,A) => ! [U] : ( m1_subset_1(U,A) => ! [V] : ( m1_subset_1(V,A) => ! [W] : ( m1_subset_1(W,A) => ! [X] : ( m1_subset_1(X,A) => ! [Y] : ( m1_subset_1(Y,A) => ! [Z] : ( m1_subset_1(Z,A) => ! [A1] : ( m1_subset_1(A1,A) => ! [B1] : ( m1_subset_1(B1,A) => ! [C1] : ( m1_subset_1(C1,A) => ! [D1] : ( m1_subset_1(D1,A) => ! [E1] : ( m1_subset_1(E1,A) => ! [F1] : ( m1_subset_1(F1,A) => ! [G1] : ( m1_subset_1(G1,A) => ? [H1] : ( m2_finseq_1(H1,A) & v3_card_1(H1,32) & k1_funct_1(H1,1) = B & k1_funct_1(H1,2) = C & k1_funct_1(H1,3) = D & k1_funct_1(H1,4) = E & k1_funct_1(H1,5) = F & k1_funct_1(H1,6) = G & k1_funct_1(H1,7) = H & k1_funct_1(H1,8) = I & k1_funct_1(H1,9) = J & k1_funct_1(H1,10) = K & k1_funct_1(H1,11) = L & k1_funct_1(H1,12) = M & k1_funct_1(H1,13) = N & k1_funct_1(H1,14) = O & k1_funct_1(H1,15) = P & k1_funct_1(H1,16) = Q & k1_funct_1(H1,17) = R & k1_funct_1(H1,18) = S & k1_funct_1(H1,19) = T & k1_funct_1(H1,20) = U & k1_funct_1(H1,21) = V & k1_funct_1(H1,22) = W & k1_funct_1(H1,23) = X & k1_funct_1(H1,24) = Y & k1_funct_1(H1,25) = Z & k1_funct_1(H1,26) = A1 & k1_funct_1(H1,27) = B1 & k1_funct_1(H1,28) = C1 & k1_funct_1(H1,29) = D1 & k1_funct_1(H1,30) = E1 & k1_funct_1(H1,31) = F1 & k1_funct_1(H1,32) = G1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t22_dickson,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ~ ( r2_hidden(C,k6_dickson(A,B)) & v1_xboole_0(C) ) ) ) )).
fof(t22_diff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( ( 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_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,D,E),B),k1_nat_1(A,1)),C) = k2_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(D,B),k1_nat_1(A,1)),C),k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(E,B),k1_nat_1(A,1)),C)) ) ) ) ) ) )).
fof(t22_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( r1_zfmisc_1(A,B,C) => k10_diff_1(k1_fcont_1(D,E),A,B,C) = k5_numbers ) ) ) ) ) ) )).
fof(t22_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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,k6_xcmplx_0(B,k7_xcmplx_0(A,2)),k2_xcmplx_0(B,k7_xcmplx_0(A,2))) = k7_xcmplx_0(k1_funct_1(k5_diff_1(C,A),B),A) ) ) ) )).
fof(t22_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(A,k1_relset_1(k1_numbers,k26_sin_cos)) & r2_hidden(B,k1_relset_1(k1_numbers,k26_sin_cos)) ) => k9_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k26_sin_cos),k18_sin_cos),A,B) = k9_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k16_sin_cos),A,B) ) ) ) )).
fof(t22_dilworth,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v2_dilworth(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( r2_hidden(C,k4_dilworth(A,B)) & r2_hidden(C,k3_dilworth(A,B)) ) => r2_hidden(C,B) ) ) ) )).
fof(t22_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t22_dist_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => k10_dist_1(A) = k8_dist_1(A,k11_dist_1(A)) ) )).
fof(t22_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m2_finseq_2(B,A,k3_finseq_2(A)) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,A,k6_margrel1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => k10_relat_1(k1_partfun1(k4_ordinal1,A,A,k6_margrel1,B,k2_bvfunc_1(A,C,D)),k8_margrel1) = k3_xboole_0(k10_relat_1(k1_partfun1(k4_ordinal1,A,A,k6_margrel1,B,C),k8_margrel1),k10_relat_1(k1_partfun1(k4_ordinal1,A,A,k6_margrel1,B,D),k8_margrel1)) ) ) ) ) )).
fof(t22_domain_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => B = a_2_1_domain_1(A,B) ) ) )).
fof(t22_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t22_e_siec,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t22_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( 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) ) ) )).
fof(t22_ec_pf_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k9_int_3(C))) => ( ( D = k5_int_1(A,C) & E = k5_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 ) ) ) ) ) ) ) )).
fof(t22_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k11_ens_1(A))) => m1_subset_1(B,A) ) ) )).
fof(t22_entropy1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( ( v1_matrix_0(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_0(C) = k3_finseq_1(B) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(C)) => k7_matrix_0(k1_numbers,C,D) = k10_rvsum_1(B,k1_funct_1(A,D)) ) ) ) ) ) ) ) )).
fof(t22_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : 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)) )).
fof(t22_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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(C,k6_eqrel_1(A,A,E,B)) & r2_hidden(D,k6_eqrel_1(A,A,E,B)) ) => r2_hidden(k4_tarski(C,D),E) ) ) )).
fof(t22_equation,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v1_msualg_6(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v1_msualg_6(D,A) & m1_msualg_2(D,A,C) ) => ! [E] : ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t22_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => k13_rvsum_1(A,k10_euclid(A,B)) = k11_euclid(A,B) ) ) )).
fof(t22_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => k22_rvsum_1(k5_algstr_0(k15_euclid(A),B,C),D) = k6_xcmplx_0(k22_rvsum_1(B,D),k22_rvsum_1(C,D)) ) ) ) ) )).
fof(t22_euclid_3,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( k3_finseq_1(A) = 2 => k12_euclid(A) = k3_square_1(k2_xcmplx_0(k1_square_1(k1_funct_1(A,1)),k1_square_1(k1_funct_1(A,2)))) ) ) )).
fof(t22_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( v1_xreal_0(D) => k22_rvsum_1(B,k9_euclid(A,C,D)) = k3_xcmplx_0(D,k22_rvsum_1(B,C)) ) ) ) ) )).
fof(t22_euclid_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k5_euclid_5(k4_euclid_5(k5_numbers,k5_numbers,A),k4_euclid_5(k5_numbers,k5_numbers,B)) = k4_struct_0(k15_euclid(3)) ) ) )).
fof(t22_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( 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) | ( k3_xcmplx_0(k12_euclid(k5_algstr_0(k15_euclid(2),B,C)),k12_euclid(k5_algstr_0(k15_euclid(2),D,F))) = k3_xcmplx_0(k12_euclid(k5_algstr_0(k15_euclid(2),C,A)),k12_euclid(k5_algstr_0(k15_euclid(2),E,D))) & k3_xcmplx_0(k12_euclid(k5_algstr_0(k15_euclid(2),B,C)),k12_euclid(k5_algstr_0(k15_euclid(2),F,E))) = k3_xcmplx_0(k12_euclid(k5_algstr_0(k15_euclid(2),A,B)),k12_euclid(k5_algstr_0(k15_euclid(2),E,D))) & k3_xcmplx_0(k12_euclid(k5_algstr_0(k15_euclid(2),C,A)),k12_euclid(k5_algstr_0(k15_euclid(2),F,E))) = k3_xcmplx_0(k12_euclid(k5_algstr_0(k15_euclid(2),A,B)),k12_euclid(k5_algstr_0(k15_euclid(2),D,F))) ) ) ) ) ) ) ) ) ) )).
fof(t22_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k1_euclid(A)) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k1_euclid(A)) => ( ( v5_valued_0(C) & r1_tarski(k2_relset_1(k4_ordinal1,C),k4_finseq_1(B)) & r2_relset_1(k4_ordinal1,k1_euclid(A),D,k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k1_euclid(A),C,B)) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k4_finseq_1(B)) => ( r2_hidden(E,k2_relset_1(k4_ordinal1,C)) | k1_funct_1(B,E) = k5_euclid(A) ) ) ) ) => k5_euclid_7(A,B) = k5_euclid_7(A,D) ) ) ) ) ) )).
fof(t22_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => k9_euclid(3,k3_euclid_8,A) = k1_euclid_8(k5_numbers,A,k5_numbers) ) )).
fof(t22_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(A))) => r1_tarski(k8_metric_1(k14_euclid(A),C,B),k4_euclid_9(A,C,B)) ) ) ) )).
fof(t22_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(E)) => ! [G] : ( m2_finseq_2(G,k1_numbers,k1_euclid(E)) => ! [H] : ( 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,k3_xcmplx_0(A,B)),k9_euclid(E,G,k3_xcmplx_0(A,C))),k9_euclid(E,H,k3_xcmplx_0(A,D))) ) ) ) ) ) ) ) ) )).
fof(t22_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( ( r1_analmetr(B,C,D) & A = k2_analmetr(B,C,D) ) => v7_euclmetr(A) ) ) ) ) ) )).
fof(t22_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_exchsort(A) ) => k9_xtuple_0(A) = k6_subset_1(k2_exchsort(A),k1_exchsort(A)) ) )).
fof(t22_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ( r1_extpro_1(A,B,C,D) <=> r1_extpro_1(A,B,C,k5_extpro_1(A,B,C,D,E)) ) ) ) ) ) ) )).
fof(t22_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(k3_extreal1(A),D) & r1_xxreal_0(k3_extreal1(B),C) ) => r1_xxreal_0(k3_extreal1(k1_xxreal_3(A,B)),k1_xxreal_3(D,C)) ) ) ) ) ) )).
fof(t22_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( r2_hidden(C,k3_msafree2(B)) => r2_hidden(C,k3_msafree2(k2_circcomb(A,B))) ) ) ) )).
fof(t22_facirc_2,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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) ) )).
fof(t22_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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(k5_numbers)) = k1_xboole_0 ) => v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k6_rfunct_1(k1_numbers,k1_numbers,B),A)) ) ) )).
fof(t22_fcont_3,axiom,( ! [A] : ( ( 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))) ) ) ) )).
fof(t22_fdiff_1,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(k2_fdiff_1(B,A),C) = k5_numbers ) ) ) ) ) ) )).
fof(t22_fdiff_10,axiom,( ! [A] : ( ( 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,k27_sin_cos,k16_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k16_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k16_sin_cos),A),B) = k4_xcmplx_0(k7_xcmplx_0(k19_sin_cos(k1_funct_1(k27_sin_cos,B)),k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t22_fdiff_11,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k1_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k1_fdiff_9),A),B) = k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k16_sin_cos,k1_funct_1(k2_sin_cos9,B)),k3_xcmplx_0(k1_square_1(k1_funct_1(k18_sin_cos,k1_funct_1(k2_sin_cos9,B))),k2_xcmplx_0(1,k1_square_1(B))))) ) ) ) ) ) )).
fof(t22_fdiff_2,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r2_fdiff_1(B,A) & ! [C] : ( v1_xreal_0(C) => ~ ( r2_hidden(C,A) & k1_funct_1(B,C) = k5_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)))) ) ) ) ) )).
fof(t22_fdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( 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) ) ) ) ) )).
fof(t22_fdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_1(C,E) = A ) ) & D = k1_taylor_1(2) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,B) & r1_xxreal_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,C,D),E),k5_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] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_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) = k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(4,A),E),k1_newton(k6_xcmplx_0(A,k1_newton(E,2)),2)) ) ) ) ) ) ) ) ) )).
fof(t22_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k22_sin_cos),k3_taylor_1)))) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => ( k1_funct_1(B,C) = 1 & ~ r1_xxreal_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,B,k22_sin_cos),C),k5_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,k22_sin_cos),k3_taylor_1)),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_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,k22_sin_cos),k3_taylor_1)),A),C) = k7_xcmplx_0(k1_funct_1(k22_sin_cos,C),k6_xcmplx_0(1,k1_funct_1(k22_sin_cos,C))) ) ) ) ) ) ) )).
fof(t22_fdiff_7,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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(k7_xcmplx_0(1,2))))) & B = k47_valued_1(k1_numbers,k1_numbers,k1_numbers,C,D) & D = k1_taylor_1(2) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,A) => ( k1_funct_1(C,E) = 1 & ~ r1_xxreal_0(k1_funct_1(B,E),k5_numbers) ) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k4_taylor_1(k7_xcmplx_0(1,2))),A) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k4_taylor_1(k7_xcmplx_0(1,2))),A),E) = k4_xcmplx_0(k3_xcmplx_0(E,k6_prepower(k6_xcmplx_0(1,k3_prepower(E,2)),k4_xcmplx_0(k7_xcmplx_0(1,2))))) ) ) ) ) ) ) ) ) )).
fof(t22_fdiff_8,axiom,( ! [A] : ( ( 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,k26_sin_cos,k6_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos)))) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( k2_xcmplx_0(1,k1_funct_1(k16_sin_cos,B)) != k5_numbers & k6_xcmplx_0(1,k1_funct_1(k16_sin_cos,B)) != k5_numbers ) ) ) ) => ( r2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k6_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k6_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos)),A),B) = k7_xcmplx_0(1,k6_xcmplx_0(1,k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t22_fdiff_9,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fdiff_9,k1_partfun2(k1_numbers,A)),A),B) = k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(k16_sin_cos,B),k1_square_1(k1_funct_1(k18_sin_cos,B))),k1_square_1(k1_funct_1(k18_sin_cos,B))) ) ) ) ) ) )).
fof(t22_ff_siec,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t22_fib_num2,axiom,( k1_pre_ff(3) = 2 )).
fof(t22_fib_num3,axiom,( ! [A] : ( v7_ordinal1(A) => k1_nat_1(k2_nat_1(2,k1_fib_num3(A)),k1_fib_num3(k1_nat_1(A,1))) = k2_nat_1(5,k1_pre_ff(k1_nat_1(A,1))) ) )).
fof(t22_fib_num4,axiom,( ! [A] : ( 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)) ) ) )).
fof(t22_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => r1_filerec1(A,B,k6_finseq_1(A),B) ) ) )).
fof(t22_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t22_filter_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t22_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t22_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k8_fin_topo(A,B),B) ) ) )).
fof(t22_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => k3_finseq_1(k7_finseq_1(A,B)) = k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)) ) ) )).
fof(t22_finseq_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m2_finseq_1(C,B) => m2_finseq_1(C,A) ) ) )).
fof(t22_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( r2_hidden(C,k1_relset_1(k4_ordinal1,A)) => r2_hidden(C,k1_relset_1(k4_ordinal1,k7_finseq_1(A,B))) ) ) ) )).
fof(t22_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_hidden(B,k10_xtuple_0(A)) => ( m1_subset_1(k6_xcmplx_0(k4_finseq_4(A,B),1),k4_ordinal1) & m1_subset_1(k6_xcmplx_0(k3_finseq_1(A),k4_finseq_4(A,B)),k4_ordinal1) ) ) ) )).
fof(t22_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m2_finseq_1(C,B) => ! [D] : ( 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) ) ) ) ) )).
fof(t22_finseq_6,axiom,( ! [A] : ! [B] : ! [C] : ( A != B => k4_finseq_4(k11_finseq_1(A,B,C),B) = 2 ) )).
fof(t22_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k10_xtuple_0(k2_finseq_7(A,B,C,D)) = k10_xtuple_0(B) ) ) ) ) )).
fof(t22_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( k3_finseq_1(C) = k5_numbers => r4_finseq_8(A,B,C) ) ) ) ) )).
fof(t22_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( ( 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))) ) => ! [G] : ( ( v3_card_1(G,E) & m2_finseq_1(G,B) ) => k3_finseqop(A,B,C,F,D,G) = k3_relat_1(G,k5_funcop_1(F,D,k6_partfun1(B))) ) ) ) ) ) ) ) )).
fof(t22_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k11_fintopo2(A,C)) <=> ( r2_hidden(B,C) & ? [D] : ( 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) ) ) ) ) ) ) )).
fof(t22_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => 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)) ) ) ) ) )).
fof(t22_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t22_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_catalan2(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t22_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => k1_flang_2(A,B,C,C) = k7_flang_1(A,B,C) ) ) )).
fof(t22_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k1_flang_3(A,B,k2_xcmplx_0(D,C)) = k6_flang_1(A,k1_flang_3(A,B,D),k7_flang_1(A,B,C)) ) ) ) )).
fof(t22_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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))) ) ) ) )).
fof(t22_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ( v4_fomodel1(B,A) & m1_subset_1(B,k1_fomodel1(A)) ) => ! [C] : ( ( 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] : ( ( 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(k29_fomodel2(A,k42_fomodel1(A,k43_fomodel1(A,B),C)),k29_fomodel2(A,C)) & ~ r1_xxreal_0(k29_fomodel2(A,k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k1_fomodel2(A)),C),D)),k29_fomodel2(A,C)) & ~ r1_xxreal_0(k29_fomodel2(A,k42_fomodel1(A,k42_fomodel1(A,k43_fomodel1(A,k1_fomodel2(A)),C),D)),k29_fomodel2(A,D)) ) ) ) ) ) )).
fof(t22_frechet,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r2_funct_2(k4_ordinal1,u1_struct_0(A),C,k8_funcop_1(u1_struct_0(A),k4_ordinal1,B)) => r1_frechet(A,C,B) ) ) ) ) )).
fof(t22_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ( v4_frechet(A) & ! [B] : ( 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) ) ) )).
fof(t22_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : v1_relat_1(k3_msafree2(k8_fscirc_1(A,B,C))) )).
fof(t22_fscirc_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k4_fscirc_1(A,B,C),k7_fscirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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) ) ) ) ) ) )).
fof(t22_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( v7_ordinal1(F) => ( r6_fsm_1(A,B,C,D,E,F) => r6_fsm_1(A,B,C,E,D,F) ) ) ) ) ) ) ) )).
fof(t22_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,A) => ! [E] : ( 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] : ( m1_subset_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t22_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( ( ~ 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] : ( 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 ) ) ) ) ) ) )).
fof(t22_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : v1_relat_1(k3_msafree2(k13_ftacell1(A,B,C,D,E))) )).
fof(t22_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(t22_funcsdom,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ~ ( C = k2_tarski(A,B) & A != B & ! [D] : ( m2_funct_2(D,C,k1_numbers,k9_funct_2(C,k1_numbers)) => ! [E] : ( m2_funct_2(E,C,k1_numbers,k9_funct_2(C,k1_numbers)) => ~ ( ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( k1_binop_1(k5_funcsdom(C),k1_funct_1(k7_funcsdom(C),k4_tarski(F,D)),k1_funct_1(k7_funcsdom(C),k4_tarski(G,E))) = k8_funcsdom(C) => ( F = k5_numbers & G = k5_numbers ) ) ) ) & ! [F] : ( m2_funct_2(F,C,k1_numbers,k9_funct_2(C,k1_numbers)) => ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & F = k1_binop_1(k5_funcsdom(C),k1_funct_1(k7_funcsdom(C),k4_tarski(G,D)),k1_funct_1(k7_funcsdom(C),k4_tarski(H,E))) ) ) ) ) ) ) ) ) )).
fof(t22_funct_1,axiom,( ! [A] : ! [B] : k3_relat_1(k4_relat_1(B),k4_relat_1(A)) = k4_relat_1(k3_xboole_0(A,B)) )).
fof(t22_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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 ) ) ) ) )).
fof(t22_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => r1_tarski(k10_xtuple_0(k3_funct_3(A)),k1_zfmisc_1(k9_xtuple_0(A))) ) )).
fof(t22_funct_4,axiom,( ! [A] : ! [B] : k1_funct_4(k6_partfun1(A),k6_partfun1(B)) = k6_partfun1(k2_xboole_0(A,B)) )).
fof(t22_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ( ( 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] : ( r2_hidden(F,B) => k1_funct_1(E,F) = k1_binop_1(D,C,F) ) ) ) ) ) )).
fof(t22_funct_6,axiom,( ! [A] : ( k3_card_3(k7_funcop_1(k1_xboole_0,A)) = k1_xboole_0 & k3_funct_6(k7_funcop_1(k1_xboole_0,A)) = k1_xboole_0 ) )).
fof(t22_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( k3_finseq_1(A) = k1_nat_1(k3_finseq_1(B),1) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) <=> ( r2_hidden(C,k4_finseq_1(A)) & r2_hidden(k1_nat_1(C,1),k4_finseq_1(A)) ) ) ) ) ) ) )).
fof(t22_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t22_funct_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & v1_int_1(A) ) => v1_funct_9(k18_sin_cos,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A)) ) )).
fof(t22_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_altcat_1(B) ) => ! [C] : ( ( v10_functor0(C,A,B) & l2_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t22_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ! [F] : ( ( v15_functor0(F,B,C) & m2_functor0(F,B,C) ) => ! [G] : ( ( v15_functor0(G,B,C) & m2_functor0(G,B,C) ) => ! [H] : ( m1_functor2(H,A,B,D,E) => ! [I] : ( m2_functor2(I,B,C,F,G) => ( ( r1_functor2(A,B,D,E) & r2_functor2(B,C,F,G) ) => r8_pboole(u1_struct_0(A),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,D,G),k1_functor3(A,B,C,E,G),k6_functor3(A,B,C,F,G,D,I),k5_functor3(A,B,C,D,E,H,G))) ) ) ) ) ) ) ) ) ) ) )).
fof(t22_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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)) ) ) ) )).
fof(t22_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D),C),k2_fuzzy_1(A,k1_fuzzy_2(A,B,k2_fuzzy_1(A,D,C)),k1_fuzzy_2(A,D,k2_fuzzy_1(A,B,C)))) ) ) ) ) )).
fof(t22_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_numbers,1)) & v1_funct_1(D) & v1_funct_2(D,k2_zfmisc_1(B,C),k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B,C),k1_numbers))) ) => r2_relset_1(k2_zfmisc_1(A,C),k1_numbers,k3_fuzzy_4(A,B,C,k4_fuzzy_2(A,B),D),k4_fuzzy_2(A,C)) ) ) ) ) )).
fof(t22_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_fvaluat1(D,A) => ( v3_fvaluat1(A) => ( C = k4_struct_0(A) | k3_funct_2(u1_struct_0(A),k6_numbers,D,k1_vectsp_2(A,B,C)) = k4_supinf_2(k3_funct_2(u1_struct_0(A),k6_numbers,D,B),k3_funct_2(u1_struct_0(A),k6_numbers,D,C)) ) ) ) ) ) ) )).
fof(t22_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t22_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ ( ~ 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)) ) ) )).
fof(t22_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v4_vectsp_1(A) & l4_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ( r2_hidden(k5_struct_0(A),B) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m2_subset_1(D,u1_struct_0(A),B) & r4_gcd_1(A,D,C) ) ) & ! [C] : ( m2_subset_1(C,u1_struct_0(A),B) => ! [D] : ( m2_subset_1(D,u1_struct_0(A),B) => ~ ( C != D & r3_gcd_1(A,C,D) ) ) ) ) ) ) )).
fof(t22_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v2_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( m1_genealg1(E,D) => ! [F] : ( m1_genealg1(F,D) => ( ( r1_xxreal_0(k3_finseq_1(E),A) & r1_xxreal_0(k3_finseq_1(E),C) ) => k9_genealg1(D,E,F,A,B,C) = k7_genealg1(D,E,F,B) ) ) ) ) ) ) ) )).
fof(t22_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( r2_geomtrap(A,F,G,B,D,C,E) => r2_geomtrap(A,F,G,D,B,E,C) ) ) ) ) ) ) ) ) )).
fof(t22_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k7_gfacirc1(A,B,C),k8_gfacirc1(A,B,C)))) & ? [E] : ( m1_subset_1(E,k6_margrel1) & ? [F] : ( m1_subset_1(F,k6_margrel1) & ? [G] : ( 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) ) ) ) ) ) ) )).
fof(t22_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v4_glib_000(A) ) => ? [B] : ( m1_subset_1(B,k6_glib_000(A)) & k6_glib_000(A) = k6_domain_1(k6_glib_000(A),B) ) ) )).
fof(t22_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( r1_glib_001(A,C,D,B) <=> r1_glib_001(A,D,C,k6_glib_001(A,B)) ) ) ) )).
fof(t22_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_glib_002(B) & m1_glib_000(B,A) ) => ( v9_glib_000(B,A) => v1_glib_002(A) ) ) ) )).
fof(t22_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( r1_glib_000(A,B,C,D) => k10_glib_003(A,k2_glib_001(A,B,C,D)) = k1_funct_1(k5_glib_003(A),D) ) ) ) ) )).
fof(t22_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( 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))))) ) ) ) )).
fof(t22_goboard1,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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(k7_matrix_0(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(k7_matrix_0(u1_struct_0(k15_euclid(2)),A,k3_finseq_1(A)))) & r1_goboard1(u1_struct_0(k15_euclid(2)),B,A) ) => ( ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(A)) & ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(D,k4_finseq_1(B)) & r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),B,D),k10_xtuple_0(k7_matrix_0(u1_struct_0(k15_euclid(2)),A,C))) ) ) ) ) & ! [C] : ( v7_ordinal1(C) => ~ ( 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(k7_matrix_0(u1_struct_0(k15_euclid(2)),A,C))) ) ) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ~ ( 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(k7_matrix_0(u1_struct_0(k15_euclid(2)),A,C))) & ! [G] : ( v7_ordinal1(G) => ( ( r2_hidden(G,k4_finseq_1(B)) & r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),B,G),k10_xtuple_0(k7_matrix_0(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(k7_matrix_0(u1_struct_0(k15_euclid(2)),A,D))) & r1_xxreal_0(D,C) ) ) ) ) ) ) ) ) ) )).
fof(t22_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_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_0(C)) ) => ( r1_xxreal_0(k3_finseq_1(C),A) | r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),B)),k3_goboard5(C,A,B)) ) ) ) ) ) )).
fof(t22_goboard6,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_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_0(A))) = a_1_7_goboard6(A) ) )).
fof(t22_goboard7,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(A)) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k1_matrix_0(A)) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(A)) & r1_xxreal_0(1,E) & r1_xxreal_0(k1_nat_1(E,1),k1_matrix_0(A)) & ~ r1_xboole_0(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,k1_nat_1(C,1))),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,D,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,D,k1_nat_1(E,1)))) & ~ ( C = E & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,k1_nat_1(C,1))) = k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,D,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,D,k1_nat_1(E,1))) ) & ~ ( C = k1_nat_1(E,1) & k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,k1_nat_1(C,1))),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,D,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,D,k1_nat_1(E,1)))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,C)) ) & ~ ( k1_nat_1(C,1) = E & k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,k1_nat_1(C,1))),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,D,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,D,k1_nat_1(E,1)))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),A,D,E)) ) ) ) ) ) ) ) )).
fof(t22_goboard9,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t22_gobrd11,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( v2_goboard1(A) => k2_goboard5(A,k1_matrix_0(A)) = a_1_12_gobrd11(A) ) ) )).
fof(t22_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_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) ) ) ) ) )).
fof(t22_gobrd14,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t22_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t22_gr_cy_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r1_nat_d(C,A) & ! [D] : ( ( v15_algstr_0(D) & m1_group_2(D,B) ) => ~ ( k7_group_1(D) = C & ! [E] : ( ( v15_algstr_0(E) & m1_group_2(E,B) ) => ( k7_group_1(E) = C => r1_group_2(B,E,D) ) ) ) ) ) ) ) ) ) )).
fof(t22_gr_cy_3,axiom,( k1_gr_cy_3(11) = k2_nat_1(23,89) )).
fof(t22_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_graph_1(C) ) => ( ( r4_graph_1(B,A) & r4_graph_1(C,A) ) => r4_graph_1(k5_graph_1(B,C),A) ) ) ) ) )).
fof(t22_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_graph_2(A) & v2_graph_2(A) ) => ! [B] : ( ( 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] : ( ( 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 ) ) ) ) ) ) )).
fof(t22_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_card_1(k5_graph_3(A,B)) = k8_graph_1(A,B) ) ) )).
fof(t22_graph_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t22_graph_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m2_finseq_1(C,u4_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t22_graphsp,axiom,( ! [A] : ( 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] : ( 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] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k4_graphsp(k3_finseq_2(k1_numbers),k9_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)),k1_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),k9_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))) ) ) ) ) )).
fof(t22_grcat_1,axiom,( ! [A] : ( ( v1_grcat_1(A) & v2_grcat_1(A) & l1_grcat_1(A) ) => ! [B] : ( ( v1_grcat_1(B) & v2_grcat_1(B) & l1_grcat_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t22_grfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r2_hidden(B,k9_xtuple_0(C)) & r2_hidden(k1_funct_1(C,B),A) ) <=> r2_hidden(k4_tarski(B,k1_funct_1(C,B)),k6_relat_1(A,C)) ) ) )).
fof(t22_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) ) => ! [E] : ( m1_group_6(E,A,B) => ! [F] : ( ( 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))) ) ) ) ) ) ) ) )).
fof(t22_groeb_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(k12_polynom1(A,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k12_polynom1(A,C))) => ! [F] : ( ( ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ( r1_groeb_1(A,B,C,F) => ( r11_polyred(k12_polynom1(A,C),k7_ideal_1(k12_polynom1(A,C),F),D,E) <=> k2_rewrite1(k3_polyred(A,B,C,F),D) = k2_rewrite1(k3_polyred(A,B,C,F),E) ) ) ) ) ) ) ) ) )).
fof(t22_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(D,A,C) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(E,A,C) & v1_polynom1(E,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)) ) ) ) ) ) ) )).
fof(t22_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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(k3_polynom1(k15_pre_poly(A),C,D))) = k3_polynom1(k15_pre_poly(A),C,D) & k4_groeb_3(A,B,C,D,k5_card_1(k3_polynom1(k15_pre_poly(A),C,D))) = k1_xboole_0 ) ) ) ) ) )).
fof(t22_group_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t22_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( m1_group_2(D,A) => ( r1_tarski(B,C) => r1_tarski(k2_group_11(A,B,D),k2_group_11(A,C,D)) ) ) ) ) ) )).
fof(t22_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( 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 ) ) ) )).
fof(t22_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t22_group_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(t22_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_group_1(A,k2_group_5(A,B,C)) = k2_group_5(A,C,B) ) ) ) )).
fof(t22_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t22_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v4_group_9(C,A,B) & m1_group_9(C,A,B) ) => k3_tarski(k7_group_9(A,B,C)) = u1_struct_0(B) ) ) )).
fof(t22_groupp_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v15_algstr_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t22_hahnban,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t22_hahnban1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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))) ) ) ) )).
fof(t22_hallmar1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ! [C] : ( m2_hallmar1(C,A,B) => ! [D] : ( m2_hallmar1(D,A,C) => m2_hallmar1(D,A,B) ) ) ) ) )).
fof(t22_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t22_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ~ ( k3_glib_001(A,B) = k3_glib_001(A,C) & v1_abian(k3_finseq_1(k1_helly(B,C))) ) ) ) ) )).
fof(t22_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t22_heyting1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k12_normform(A))) => ! [C] : ( 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) ) ) )).
fof(t22_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_substlat(A,B))) => ! [D] : ( m2_subset_1(D,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B)) => ! [E] : ( m2_subset_1(E,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B)) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t22_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ r2_hidden(k3_heyting3(A,B),k4_heyting3(k1_nat_1(A,1),B)) ) ) )).
fof(t22_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t22_hilbasis,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( ( ~ 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] : ( ( 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))) ) ) ) ) ) ) )).
fof(t22_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) ) )).
fof(t22_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( m1_subset_1(D,k1_hilbert1) => k4_hilbert1(A,B) != k3_hilbert1(C,D) ) ) ) ) )).
fof(t22_hilbert3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ ( C = k1_xboole_0 & B != k1_xboole_0 & A != k1_xboole_0 ) => ! [D] : ( ( 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)) ) ) )).
fof(t22_hurwitz,axiom,( ! [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) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) ) ) ) )).
fof(t22_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_idea_1(B,A) => k9_idea_1(B,1,A) = A ) ) ) )).
fof(t22_ideal_1,axiom,( ! [A] : ( ( ~ 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) ) => ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) <=> ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t22_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u4_incsp_1(A)) => ( ( r3_incsp_1(A,C,E) & r3_incsp_1(A,D,E) ) => ( r3_incsp_1(A,B,E) | C = D | ! [F] : ( m1_subset_1(F,u4_incsp_1(A)) => ~ ( r3_incsp_1(A,B,F) & r3_incsp_1(A,C,F) & r3_incsp_1(A,D,F) ) ) ) ) ) ) ) ) ) )).
fof(t22_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( 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] : ( m2_cat_1(F,A,B) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t22_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v4_msualg_1(C,B) & l3_msualg_1(C,B) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t22_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( r2_int_1(A,B,C) <=> r2_int_1(k6_xcmplx_0(A,C),B,C) ) ) ) ) )).
fof(t22_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( r1_int_1(C,A) & r1_int_1(C,B) ) => r1_int_1(C,k3_int_2(A,B)) ) ) ) ) )).
fof(t22_int_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(C,k5_numbers) => ( k5_int_1(k6_xcmplx_0(A,B),C) = k5_numbers <=> k4_nat_d(A,C) = k4_nat_d(B,C) ) ) ) ) ) )).
fof(t22_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ! [C] : ( v1_int_1(C) => ( ( r1_int_5(A,B) & r1_int_5(C,B) ) => r1_int_5(k3_xcmplx_0(A,C),B) ) ) ) ) )).
fof(t22_int_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ~ ( r1_int_2(A,B) & ! [C] : ( v1_int_1(C) => ~ r2_int_1(k3_xcmplx_0(C,A),1,B) ) ) ) ) )).
fof(t22_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => r1_int_8(k2_int_8(A),A) ) )).
fof(t22_integr11,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ 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,k18_sin_cos,k1_taylor_1(A)),k16_sin_cos)) = k6_xcmplx_0(k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(k2_xcmplx_0(A,1))),k4_xcmplx_0(k7_xcmplx_0(1,k2_xcmplx_0(A,1)))),k2_seq_4(B)),k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(k2_xcmplx_0(A,1))),k4_xcmplx_0(k7_xcmplx_0(1,k2_xcmplx_0(A,1)))),k3_seq_4(B))) ) ) )).
fof(t22_integr12,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,D) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => k1_funct_1(C,E) = 1 ) ) & r1_tarski(D,k2_rcomp_1(k4_xcmplx_0(1),1)) & D = k1_relset_1(k1_numbers,B) & r2_relset_1(k1_numbers,k1_numbers,B,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_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,C,k1_taylor_1(2)),k4_taylor_1(k7_xcmplx_0(1,2)))))) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,D),k3_sin_cos6),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,D),k3_sin_cos6),k3_seq_4(A))) ) ) ) ) ) )).
fof(t22_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k27_sin_cos,k22_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) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k22_sin_cos),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k22_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t22_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k22_sin_cos),k3_rfunct_1(k1_numbers,k1_numbers,k18_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) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k22_sin_cos)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k22_sin_cos)),k3_seq_4(A))) ) ) ) ) )).
fof(t22_integr15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k1_euclid(A)))) ) => ! [E] : ( ( 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)) ) ) ) ) )).
fof(t22_integr16,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k2_numbers))) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( B = k1_rcomp_1(C,D) => k7_integr16(B,A) = k8_integr16(C,D,A) ) ) ) ) ) )).
fof(t22_integr19,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( ~ v8_ordinal1(E) & m1_subset_1(E,k4_ordinal1) ) => ! [F] : ( ( 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))) ) ) ) ) ) ) ) ) )).
fof(t22_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => k18_rvsum_1(k4_integra1(A,k7_rfunct_1(A,A),B)) = k3_integra1(A) ) ) )).
fof(t22_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( m1_integra1(D,B) => ( ( v1_comseq_2(k2_partfun1(B,k1_numbers,C,B)) & r1_xxreal_0(A,k5_numbers) ) => r1_xxreal_0(k1_funct_1(k9_integra1(B,k26_valued_1(B,k1_numbers,C,A)),D),k3_xcmplx_0(k3_xcmplx_0(A,k3_seq_4(k1_rvsum_1(C))),k3_integra1(B))) ) ) ) ) ) )).
fof(t22_integra4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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_comseq_2(k2_partfun1(A,k1_numbers,B,A)) & v3_integra1(B,A) ) => v3_integra1(k19_rfunct_3(A,B),A) ) ) ) )).
fof(t22_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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(k9_complex1(k4_integra5(C,D,E)),k4_integra5(C,D,k56_valued_1(k1_numbers,k1_numbers,E))) & r1_xxreal_0(k9_complex1(k4_integra5(D,C,E)),k4_integra5(C,D,k56_valued_1(k1_numbers,k1_numbers,E))) ) ) ) ) ) ) ) )).
fof(t22_integra7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_xxreal_0(B,A) & r1_tarski(k1_rcomp_1(B,A),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) ) => k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(F,A),k1_funct_1(G,A)),k3_xcmplx_0(k1_funct_1(F,B),k1_funct_1(G,B))) = k2_xcmplx_0(k4_integra5(B,A,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,D,G)),k4_integra5(B,A,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,F,E))) ) ) ) ) ) ) ) )).
fof(t22_integra8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( 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) = k4_xcmplx_0(k1_fdiff_1(A,B)) ) ) ) ) )).
fof(t22_integra9,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( ~ 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)) ) ) ) ) )).
fof(t22_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_interva1(C,A) ) => r1_interva1(A,k3_interva1(A,B,C),k3_interva1(A,C,B)) ) ) ) )).
fof(t22_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => r2_hidden(k3_intpro_1(k3_intpro_1(B,C),k3_intpro_1(k3_intpro_1(A,B),k3_intpro_1(A,C))),k8_intpro_1) ) ) ) )).
fof(t22_irrat_1,axiom,( v2_comseq_2(k4_irrat_1) & k1_seq_2(k4_irrat_1) = k4_power )).
fof(t22_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,B,C) => ! [E] : ( m2_cat_1(E,B,C) => ( r2_nattra_1(B,C,D,E) => ! [F] : ( m2_cat_1(F,A,B) => ! [G] : ( m2_nattra_1(G,B,C,D,E) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => k2_nattra_1(A,C,k9_cat_1(A,B,C,F,D),k9_cat_1(A,B,C,F,E),k5_isocat_1(A,B,C,D,E,F,G),H) = k2_nattra_1(B,C,D,E,G,k8_cat_1(A,B,F,H)) ) ) ) ) ) ) ) ) ) )).
fof(t22_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(t22_jgraph_1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t22_jgraph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t22_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( 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] : ( 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) = k3_xcmplx_0(k12_euclid(D),k4_xcmplx_0(k3_square_1(k6_xcmplx_0(1,k1_square_1(k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k18_euclid(D),k12_euclid(D)),A),k2_xcmplx_0(1,A))))))) ) ) & ! [D] : ( 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),k5_numbers) & r1_xxreal_0(k7_xcmplx_0(k18_euclid(D),k12_euclid(D)),A) & D != k4_struct_0(k15_euclid(2)) ) ) ) ) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) | v5_pre_topc(C,k1_pre_topc(k15_euclid(2),B),k3_topmetr) ) ) ) ) ) )).
fof(t22_jgraph_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ~ r1_xxreal_0(k17_euclid(B),k5_numbers) & ? [C] : ( 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),k5_numbers) ) ) ) ) )).
fof(t22_jgraph_6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal2(A) => v2_compts_1(A,k15_euclid(2)) ) ) )).
fof(t22_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t22_jordan,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t22_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => a_4_4_jordan1(A,B,C,D) = a_4_5_jordan1(A,B,C,D) ) ) ) ) )).
fof(t22_jordan12,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_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)) ) ) ) ) )).
fof(t22_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( 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_0(k1_jordan8(A,E))) & k7_partfun1(u1_struct_0(k15_euclid(2)),k1_jordan13(A,E),D) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,E),B,C) & r1_xxreal_0(B,1) ) ) ) ) ) ) )).
fof(t22_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E),k3_topreal1(2,k1_jordan1e(B,A))) & r2_hidden(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k8_jordan6(B)) ) ) ) ) ) ) )).
fof(t22_jordan16,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t22_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t22_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( ~ 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_0(u1_struct_0(k15_euclid(2)),B,A,1)),k9_pscomp_1(k3_topreal1(2,C))) ) ) ) ) )).
fof(t22_jordan1g,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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)))) ) => ~ r1_xxreal_0(k4_finseq_4(k1_jordan1e(B,A),k21_pscomp_1(k3_topreal1(2,k2_jordan9(B,A)))),k4_finseq_4(k1_jordan1e(B,A),k20_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))))) ) ) )).
fof(t22_jordan1h,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r1_goboard1(u1_struct_0(k15_euclid(2)),B,A) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(B)) ) => r1_tarski(k2_topreal1(2,B,C),k2_gobrd13(B,A,C)) ) ) ) ) ) )).
fof(t22_jordan1k,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( A != B & r1_xxreal_0(k1_topreal6(2,A,B),k5_numbers) ) ) ) )).
fof(t22_jordan20,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t22_jordan21,axiom,( ! [A] : ( ( 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(k7_xcmplx_0(k2_xcmplx_0(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(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)),2))))) ) ) )).
fof(t22_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,k5_numbers) => k2_jordan21(k3_topreal1(2,k2_jordan9(A,B))) = k2_jordan21(k9_jordan6(k3_topreal1(2,k2_jordan9(A,B)))) ) ) ) )).
fof(t22_jordan23,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t22_jordan2b,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_jordan2b(k2_xcmplx_0(A,B)) = k3_rlvect_1(k15_euclid(1),k1_jordan2b(A),k1_jordan2b(B)) ) ) )).
fof(t22_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( r1_xxreal_0(1,A) & v9_rltopsp1(k2_struct_0(k15_euclid(A)),k15_euclid(A)) ) ) )).
fof(t22_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t22_jordan4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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 ) ) ) )).
fof(t22_jordan5a,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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] : ( 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] : ( 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] : ( v1_xreal_0(G) & v3_tops_2(F,k5_topmetr,k1_pre_topc(k15_euclid(2),A)) & k1_funct_1(F,k5_numbers) = C & k1_funct_1(F,1) = D & k1_funct_1(F,G) = E & r1_xxreal_0(k5_numbers,G) & r1_xxreal_0(G,1) & ! [H] : ( v1_xreal_0(H) => ~ ( r1_xxreal_0(H,1) & ~ r1_xxreal_0(H,G) & r2_hidden(k1_funct_1(F,H),B) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t22_jordan5b,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t22_jordan5c,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_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,k1_nat_1(B,1)) ) ) ) )).
fof(t22_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( B = a_1_1_jordan5d(A) => k2_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)))) ) ) ) )).
fof(t22_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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 ) ) ) ) )).
fof(t22_jordan9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(2))) => ~ ( r1_xxreal_0(2,k3_finseq_1(B)) & r1_xxreal_0(2,k1_matrix_0(B)) & r1_goboard1(u1_struct_0(k15_euclid(2)),C,B) & r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(B)) & r1_xxreal_0(1,E) & r1_xxreal_0(k1_nat_1(E,1),k1_matrix_0(B)) & r1_tarski(k2_topreal1(2,C,A),k3_goboard5(B,D,E)) ) ) ) ) ) ) ) )).
fof(t22_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_jordan_a(C,A) => ( r2_hidden(B,k4_finseq_1(C)) => r1_tarski(k2_jordan_a(A,B,C),A) ) ) ) ) )).
fof(t22_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( 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] : ( v3_ordinal1(D) => r3_lattices(A,C,k5_knaster(A,B,C,D)) ) ) ) ) ) )).
fof(t22_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_funct_1(B) => m1_subset_1(k3_funct_1(B),k1_zfmisc_1(A)) ) ) )).
fof(t22_kurato_1,axiom,( 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) )).
fof(t22_kurato_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ( ! [D] : ( v7_ordinal1(D) => r1_tarski(k2_kurato_2(A,C,D),B) ) => r1_tarski(k1_kurato_2(A,C),k2_pre_topc(A,B)) ) ) ) ) )).
fof(t22_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(k11_group_4(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t22_latsum_1,axiom,( ! [A] : ! [B] : ! [C] : ( l1_orders_2(C) => ! [D] : ( 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))) ) ) ) ) )).
fof(t22_lattice2,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t22_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t22_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t22_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v3_ordinal1(B) => k8_lattice5(A,k1_ordinal1(B)) = k5_lattice5(k8_lattice5(A,B)) ) ) )).
fof(t22_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v6_lattice6(B,A) => v3_lattice6(B,A) ) ) ) )).
fof(t22_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t22_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( ( v4_lexbfs(B,A) & m1_lexbfs(B,A) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t22_lfuzzy_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,C) => k8_lfuzzy_0(A,C,k3_fuzzy_4(A,B,C,D,E),F,G) = k1_yellow_0(k1_lfuzzy_0(k1_rcomp_1(k5_numbers,1)),a_7_0_lfuzzy_0(A,B,C,D,E,F,G)) ) ) ) ) ) ) ) )).
fof(t22_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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,k3_fuzzy_4(A,A,A,k4_fuzzy_4(A,A),B),B) ) ) )).
fof(t22_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_limfunc1(A) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(C,k1_funct_1(B,D)) ) ) ) | v1_limfunc1(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).
fof(t22_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r5_limfunc2(C,B) => ( r1_xxreal_0(A,k5_numbers) | r5_limfunc2(k26_valued_1(k1_numbers,k1_numbers,C,A),B) ) ) & ( r5_limfunc2(C,B) => ( r1_xxreal_0(k5_numbers,A) | r6_limfunc2(k26_valued_1(k1_numbers,k1_numbers,C,A),B) ) ) & ( r6_limfunc2(C,B) => ( r1_xxreal_0(A,k5_numbers) | r6_limfunc2(k26_valued_1(k1_numbers,k1_numbers,C,A),B) ) ) & ( r6_limfunc2(C,B) => ( r1_xxreal_0(k5_numbers,A) | r5_limfunc2(k26_valued_1(k1_numbers,k1_numbers,C,A),B) ) ) ) ) ) ) )).
fof(t22_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,C) & ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ~ ( ~ 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] : ( v1_xreal_0(C) => ~ ( v8_valued_0(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(k6_xcmplx_0(A,C),A))) & v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(A,k2_xcmplx_0(A,C)))) & ~ v2_seq_2(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(k6_xcmplx_0(A,C),A))) & ~ v2_seq_2(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(A,k2_xcmplx_0(A,C)))) ) ) | r3_limfunc3(B,A) ) ) ) ) )).
fof(t22_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(k6_xcmplx_0(A,D),A))) & r1_xxreal_0(k1_funct_1(B,E),k1_limfunc2(B,A)) ) ) ) ) | r3_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t22_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t22_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t22_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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)) ) ) )).
fof(t22_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => k5_struct_0(k8_lopban_2(A)) = k6_lopban_2(A) ) )).
fof(t22_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(E,D) => k9_nat_1(u1_struct_0(A),k7_lopban_4(k1_nat_1(D,1),A,C,B),E) = k3_rlvect_1(A,k9_nat_1(u1_struct_0(A),k7_lopban_4(D,A,C,B),E),k9_nat_1(u1_struct_0(A),k6_lopban_4(k1_nat_1(D,1),A,C,B),E)) ) ) ) ) ) ) )).
fof(t22_lopclset,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t22_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => r1_lpspacc1(A,B,C,D,D) ) ) ) ) )).
fof(t22_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,k1_relset_1(A,D)) => k5_numbers = k1_funct_1(D,E) ) ) => ( ! [E] : ( 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) = k5_numbers ) ) ) ) ) ) ) )).
fof(t22_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v2_xxreal_0(D) & v1_xreal_0(D) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( 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)))) ) ) ) ) ) ) ) ) )).
fof(t22_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_hilbert1)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => ( ( r2_ltlaxio1(C,A) & r2_ltlaxio1(C,B) ) <=> r2_ltlaxio1(C,k4_subset_1(k1_hilbert1,A,B)) ) ) ) ) )).
fof(t22_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(A,k3_ltlaxio1)) ) )).
fof(t22_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_hilbert1)) => ( r2_hidden(k1_ltlaxio2(A,B),k5_ltlaxio3(C)) => ( r2_hidden(A,k5_ltlaxio3(C)) & r2_hidden(B,k5_ltlaxio3(C)) & r2_hidden(k4_hilbert1(A,B),k5_ltlaxio3(C)) ) ) ) ) ) )).
fof(t22_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ( ( r2_hidden(k4_hilbert1(A,B),k2_relset_1(k1_hilbert1,k8_ltlaxio3(C))) & r2_hidden(D,k9_ltlaxio4(C)) ) => r2_hidden(k1_ltlaxio2(A,B),k2_relset_1(k1_hilbert1,k8_ltlaxio3(D))) ) ) ) ) ) )).
fof(t22_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t22_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(t22_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,B,B) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( v1_matrix10(C) => ( r1_xxreal_0(k5_numbers,A) | v2_matrix10(k6_matrix10(B,A,C)) ) ) ) ) ) )).
fof(t22_matrix11,axiom,( ! [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)) ) ) )).
fof(t22_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( m1_subset_1(E,u1_struct_0(D)) => ( ( r2_hidden(B,k4_finseq_1(k3_matrix_1(D,C))) & r2_hidden(A,k4_finseq_1(k3_matrix_1(D,C))) ) => ( A = B | r1_xxreal_0(C,k5_numbers) | k1_matrix_6(C,D,k6_matrix12(C,C,D,k3_matrix_1(D,C),B,A,E)) = k6_matrix12(C,C,D,k3_matrix_1(D,C),B,A,k4_algstr_0(D,E)) ) ) ) ) ) ) ) )).
fof(t22_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,A,2,2) & m2_finseq_1(B,k3_finseq_2(A)) ) => B = k15_matrix_0(A,k3_matrix_0(A,B,1,1),k3_matrix_0(A,B,1,2),k3_matrix_0(A,B,2,1),k3_matrix_0(A,B,2,2)) ) ) )).
fof(t22_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) )).
fof(t22_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k5_numbers ) => ( k7_matrlin(u1_struct_0(A),B,C) = C & k7_matrlin(u1_struct_0(A),C,B) = C ) ) ) ) ) )).
fof(t22_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ( ( v3_matrix16(C,u1_struct_0(B)) & v3_matrix16(D,u1_struct_0(B)) & v3_matrix16(E,u1_struct_0(B)) ) => v3_matrix16(k3_matrix_3(B,k3_matrix_3(B,C,D),E),u1_struct_0(B)) ) ) ) ) ) ) )).
fof(t22_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,B,k5_numbers,A) & m2_finseq_1(C,k3_finseq_2(B)) ) => ( k3_finseq_1(C) = k5_numbers & k1_matrix_0(C) = k5_numbers & k2_matrix_0(C) = k1_xboole_0 ) ) ) ) )).
fof(t22_matrix_3,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( k1_matrix_0(B) = k3_finseq_1(C) => ( k1_matrix_0(C) = k5_numbers | k4_matrix_0(u1_struct_0(A),k4_matrix_3(A,B,C)) = k4_matrix_3(A,k4_matrix_0(u1_struct_0(A),C),k4_matrix_0(u1_struct_0(A),B)) ) ) ) ) ) )).
fof(t22_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) ) => B = k3_matrix_3(A,k1_matrix_4(A,B,C),C) ) ) ) ) )).
fof(t22_matrix_5,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( k1_matrix_0(B) = k3_finseq_1(C) => ( r1_xxreal_0(k3_finseq_1(B),k5_numbers) | r1_xxreal_0(k3_finseq_1(C),k5_numbers) | k4_matrix_3(A,k1_matrix_3(A,k3_finseq_1(B),k1_matrix_0(B)),C) = k1_matrix_3(A,k3_finseq_1(B),k1_matrix_0(C)) ) ) ) ) ) )).
fof(t22_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v2_matrix_6(C,A,B) & v2_matrix_6(D,A,B) ) => ( r1_xxreal_0(A,k5_numbers) | ( r1_matrix_6(A,B,C,D) <=> v2_matrix_6(k4_matrix_3(B,C,D),A,B) ) ) ) ) ) ) ) )).
fof(t22_matrix_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k4_matrix_7(A,k13_matrix_0(u1_struct_0(A),B)) = k13_matrix_0(u1_struct_0(A),k2_group_1(A,B)) ) ) )).
fof(t22_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_6(C,A,B) & k4_matrix_3(B,D,C) = k2_matrix_1(B,A) ) => D = k2_matrix_1(B,A) ) ) ) ) ) )).
fof(t22_matrix_9,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( ( v1_matrix_0(K) & v2_matrix_0(K,u1_struct_0(A),3,3) & m2_finseq_1(K,k3_finseq_2(u1_struct_0(A))) ) => ( K = k3_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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] : ( m1_matrix_2(L,k3_matrix_2(3)) => ( L = k3_finseq_4(k4_ordinal1,1,3,2) => k10_matrix_3(3,A,K,L) = k3_finseq_4(u1_struct_0(A),B,G,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t22_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( 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)) ) ) ) )).
fof(t22_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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 ) ) ) ) )).
fof(t22_matrixj2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( ~ 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] : ( 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,k7_matrix_0(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))) ) ) ) ) ) ) ) )).
fof(t22_matrixr1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ( k1_matrix_0(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) ) ) ) ) ) )).
fof(t22_matrixr2,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k1_matrix_0(A) = k1_matrix_0(B) & k3_finseq_1(C) = k3_finseq_1(A) & k1_matrix_0(C) = k1_matrix_0(A) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(D,E),k2_matrix_0(A)) => k3_matrix_0(k1_numbers,C,D,E) = k5_real_1(k3_matrix_0(k1_numbers,A,D,E),k3_matrix_0(k1_numbers,B,D,E)) ) ) ) ) => C = k5_matrixr1(A,B) ) ) ) ) )).
fof(t22_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( ( 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] : ( ( 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)))) ) => ( ( 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) ) => ! [F] : ( m1_matrlin(F,A,B) => ( k4_finseqop(u1_struct_0(B),u1_struct_0(C),F,D) = k4_finseqop(u1_struct_0(B),u1_struct_0(C),F,E) => ( r1_xxreal_0(k3_finseq_1(F),k5_numbers) | r2_funct_2(u1_struct_0(B),u1_struct_0(C),D,E) ) ) ) ) ) ) ) ) ) )).
fof(t22_matrlin2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( ~ 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] : ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t22_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_matroid0(B,A) => ! [C] : ( m1_matroid0(C,A) => k5_card_1(B) = k5_card_1(C) ) ) ) )).
fof(t22_matrprob,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => k4_matrprob(A) = k3_matrprob(k4_matrix_0(k1_numbers,A)) ) )).
fof(t22_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & v3_valued_0(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_card_1(D,A) & v1_finseq_1(D) & v3_valued_0(D) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => 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)) ) ) ) ) ) )).
fof(t22_matrtop2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_rlvect_3(B,k15_euclid(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [C] : ( ( 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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(k2_vectsp_1),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ~ ( 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)) ) ) ) ) ) ) )).
fof(t22_matrtop3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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_funct_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) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(E,B),k17_sin_cos(A)),k3_xcmplx_0(k1_funct_1(E,C),k19_sin_cos(A))) ) ) ) ) ) ) ) )).
fof(t22_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_normsp_0(A,k5_algstr_0(A,k3_funct_2(u1_struct_0(A),u1_struct_0(A),k1_mazurulm(A,B),C),C)) = k4_xxreal_3(2,k2_normsp_0(A,k5_algstr_0(A,C,B))) ) ) ) )).
fof(t22_mboolean,axiom,( ! [A] : ! [B] : r6_pboole(A,k2_mboolean(A,k7_funcop_1(A,B)),k7_funcop_1(A,k3_tarski(B))) )).
fof(t22_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( 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 ) ) ) )).
fof(t22_measure1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ( ( ! [C] : ( r2_hidden(C,B) => r2_hidden(k6_subset_1(A,C),B) ) & ! [C] : ( ( ~ 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))) ) ) ) )).
fof(t22_measure2,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ( ( k9_nat_1(B,D,k5_numbers) = k9_nat_1(B,C,k5_numbers) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( k9_nat_1(B,D,k1_nat_1(E,1)) = k3_measure1(A,B,k9_nat_1(B,C,k1_nat_1(E,1)),k9_nat_1(B,C,E)) & r1_tarski(k9_nat_1(B,C,E),k9_nat_1(B,C,k1_nat_1(E,1))) ) ) ) => ( k9_nat_1(B,C,k5_numbers) = k9_nat_1(B,D,k5_numbers) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => k9_nat_1(B,C,k1_nat_1(E,1)) = k1_measure1(A,B,k9_nat_1(B,D,k1_nat_1(E,1)),k9_nat_1(B,C,E)) ) ) ) ) ) ) )).
fof(t22_measure6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t22_measure8,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,k6_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( v1_funct_1(k1_partfun1(k4_ordinal1,k9_setfam_1(A),B,k6_numbers,C,D)) & v1_funct_2(k1_partfun1(k4_ordinal1,k9_setfam_1(A),B,k6_numbers,C,D),k4_ordinal1,k6_numbers) & m1_subset_1(k1_partfun1(k4_ordinal1,k9_setfam_1(A),B,k6_numbers,C,D),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) ) ) ) )).
fof(t22_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ( r1_tarski(A,B) => r1_tarski(k6_member_1(A),k6_member_1(B)) ) ) ) )).
fof(t22_membered,axiom,( ! [A] : ! [B] : ( v4_membered(B) => ( r1_tarski(A,B) => v4_membered(A) ) ) )).
fof(t22_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t22_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( ( D = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),B,k6_xcmplx_0(1,G)),k1_rlvect_1(k15_euclid(2),C,G)) & E = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),C,k6_xcmplx_0(1,H)),k1_rlvect_1(k15_euclid(2),A,H)) & F = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),A,k6_xcmplx_0(1,I)),k1_rlvect_1(k15_euclid(2),B,I)) ) => ( r1_euclid_6(A,B,C) | G = 1 | H = 1 | I = 1 | ( k3_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(G,k6_xcmplx_0(1,G)),k7_xcmplx_0(H,k6_xcmplx_0(1,H))),k7_xcmplx_0(I,k6_xcmplx_0(1,I))) = 1 <=> r1_menelaus(k4_euclid_4(2,A,D),k4_euclid_4(2,B,E),k4_euclid_4(2,C,F)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t22_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( 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) = k5_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) ) ) ) ) ) ) ) )).
fof(t22_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & v1_mesfunc8(C,A,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( ( k1_relset_1(A,k4_mesfunc5(A,k1_numbers,C,k5_numbers)) = E & ! [F] : ( v7_ordinal1(F) => r1_mesfunc6(A,B,k4_mesfunc5(A,k1_numbers,C,F),E) ) & k1_relset_1(A,D) = E & ! [F] : ( m1_subset_1(F,A) => ( r2_hidden(F,E) => ( v2_comseq_2(k10_seqfunc(A,C,F)) & k12_supinf_2(D,F) = k1_seq_2(k10_seqfunc(A,C,F)) ) ) ) ) => r1_mesfunc1(A,B,D,E) ) ) ) ) ) ) )).
fof(t22_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => r2_funct_2(k4_ordinal1,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)) ) ) )).
fof(t22_mesfunc1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ! [F] : ( v1_xreal_0(F) => ( ! [G] : ( m1_subset_1(G,k4_ordinal1) => k9_nat_1(B,C,G) = k9_subset_1(A,E,k18_mesfunc1(A,D,k2_xcmplx_0(F,k2_extreal1(1,k1_nat_1(G,1))))) ) => k9_subset_1(A,E,k17_mesfunc1(A,D,F)) = k2_measure2(A,B,k1_measure3(A,B,C)) ) ) ) ) ) )).
fof(t22_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t22_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_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)) ) ) ) ) ) )).
fof(t22_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => v3_valued_0(k1_mesfunc5(A,B)) ) ) )).
fof(t22_mesfunc7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ~ ( r1_mesfunc5(A,B,C,D) & r1_mesfunc5(A,B,C,E) & ! [F] : ( 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,k6_numbers,k10_mesfunc1(A,k3_mesfunc1(A,D,E)),F)),k3_supinf_2(k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,k10_mesfunc1(A,D),F)),k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,k10_mesfunc1(A,E),F)))) ) ) ) ) ) ) ) ) )).
fof(t22_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [E] : ( v1_xreal_0(E) => ( ! [F] : ( v7_ordinal1(F) => k9_nat_1(k9_setfam_1(A),D,F) = k9_subset_1(A,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,C,k5_numbers)),k17_mesfunc1(A,k4_mesfunc5(A,k6_numbers,k3_mesfunc8(A,C),F),E)) ) => k3_tarski(k2_relset_1(B,D)) = k9_subset_1(A,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,C,k5_numbers)),k17_mesfunc1(A,k5_mesfunc8(A,C),E)) ) ) ) ) ) ) )).
fof(t22_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( r2_hidden(E,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,k4_mesfunc9(A,B),C))) & r1_xxreal_0(D,C) ) => ( r2_hidden(E,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,k4_mesfunc9(A,B),D))) & r2_hidden(E,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,D))) ) ) ) ) ) ) )).
fof(t22_metric_1,axiom,( ! [A] : ( m1_subset_1(A,1) => ! [B] : ( m1_subset_1(B,1) => k1_binop_1(k2_metric_1,A,B) = k1_binop_1(k2_metric_1,B,A) ) ) )).
fof(t22_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k2_metric_2(A)) => ! [C] : ( m1_subset_1(C,k2_metric_2(A)) => ! [D] : ( m1_subset_1(D,k1_numbers) => ( r4_metric_2(A,B,C,D) => r4_metric_2(A,C,B,D) ) ) ) ) ) )).
fof(t22_metric_3,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers)) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k1_numbers,k1_numbers)) => ( k2_binop_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers,k18_metric_3,A,B) = k5_numbers <=> A = B ) ) ) )).
fof(t22_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_finset_1(B) & v1_card_1(B) ) => ( r1_ordinal1(k2_waybel23(A),B) <=> r1_ordinal1(k4_topgen_1(A),B) ) ) ) )).
fof(t22_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ~ ( C = k8_euclid_7(A) & ! [D] : ( m2_rlvect_2(D,k15_euclid(A),C) => B != k6_rlvect_2(k15_euclid(A),D) ) ) ) ) ) )).
fof(t22_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) => ( ( r2_midsp_1(A,B,D) & r2_midsp_1(A,C,D) ) => r2_midsp_1(A,B,C) ) ) ) ) ) )).
fof(t22_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t22_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_midsp_3(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v4_midsp_2(E,B) & l1_midsp_2(E,B) ) => ! [F] : ( m2_finseq_2(F,u1_struct_0(u1_midsp_2(B,E)),k4_finseq_2(k1_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) ) ) ) ) ) ) )).
fof(t22_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t22_mod_2,axiom,( k4_struct_0(k18_mod_2) = k5_numbers & k5_struct_0(k18_mod_2) = 1 & m1_subset_1(k4_struct_0(k18_mod_2),k1_enumset1(k5_numbers,1,2)) & m1_subset_1(k5_struct_0(k18_mod_2),k1_enumset1(k5_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(k5_numbers,1,2),k1_enumset1(k5_numbers,1,2)),k1_enumset1(k5_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(k5_numbers,1,2),k1_enumset1(k5_numbers,1,2)),k1_enumset1(k5_numbers,1,2),u2_algstr_0(k18_mod_2),k14_mod_2) )).
fof(t22_mod_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ~ ( k1_mod_3(A,B,C) = B & ! [D] : ( m1_mod_3(D,A,B) => ~ r1_tarski(D,C) ) ) ) ) ) )).
fof(t22_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t22_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k6_modal_1) => m1_subset_1(k7_trees_2(k8_funcop_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k2_trees_1(1),k1_domain_1(k4_ordinal1,k4_ordinal1,1,k5_numbers)),k14_trees_3(k5_numbers),A),k6_modal_1) ) )).
fof(t22_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_partfun1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(k30_modelc_1(B))) ) => ! [F] : ( ( 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] : ( m1_modelc_1(G,B,C) & k3_funct_2(k4_ordinal1,B,G,k5_numbers) = D & r4_modelc_1(B,C,E,F,k3_funct_2(k4_ordinal1,B,G,1),A) ) ) ) ) ) ) ) ) )).
fof(t22_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( v4_modelc_2(A) => ( r1_modelc_2(B,A) <=> ( B = k11_modelc_2(A) | B = k12_modelc_2(A) ) ) ) ) ) )).
fof(t22_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_3(B,A) & l1_modelc_3(B,A) ) => ( r1_xxreal_0(k21_modelc_3(A,B),k5_numbers) => u2_modelc_3(A,B) = k7_modelc_3(A) ) ) ) )).
fof(t22_moebius1,axiom,( ~ v1_moebius1(1) )).
fof(t22_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l4_algstr_0(B) ) => ( m2_monoid_0(A,A) & m3_monoid_0(B,B) ) ) ) )).
fof(t22_monoid_1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(t22_morph_01,axiom,( ! [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) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t22_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( 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)) ) ) ) )).
fof(t22_msafree4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v2_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( m2_pboole(E,A,B,C) => ( m3_pboole(C,A,D) => m2_pboole(E,A,B,D) ) ) ) ) ) )).
fof(t22_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t22_msscyc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v2_relat_1(C) & m1_msafree(C,A,B) ) => ~ ( ~ v4_msafree2(B,A) & v4_msafree2(k11_msafree(A,C),A) ) ) ) ) )).
fof(t22_mssublat,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t22_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_msualg_2(C,A,B) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t22_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & m1_msualg_2(C,A,B) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t22_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msualg_6(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k4_finseq_1(k1_msualg_1(A,D))) => ! [F] : ( 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))) ) ) ) ) ) ) ) )).
fof(t22_msualg_7,axiom,( ? [A] : ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) & ? [B] : ( m2_nat_lat(B,A) & v2_msualg_7(B,A) & ~ v1_msualg_7(B,A) ) ) )).
fof(t22_msualg_9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v2_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t22_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t22_mycielsk,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( 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))) ) ) ) )).
fof(t22_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t22_nagata_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ( v9_pre_topc(A) & v7_pre_topc(A) & ? [B] : ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))))) & v5_nagata_1(B,A) ) ) <=> v3_pcomps_1(A) ) ) )).
fof(t22_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(k1_nat_1(B,1),A) & r1_xxreal_0(B,A) & A != B ) ) ) )).
fof(t22_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ v1_abian(A) <=> k4_nat_d(A,2) = 1 ) ) )).
fof(t22_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,1) => k11_nat_3(A,A) = 1 ) ) )).
fof(t22_nat_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ! [C] : ( ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) ) => ( k1_newton(A,k11_nat_3(C,A)) = k1_newton(B,k11_nat_3(C,B)) => ( r1_xxreal_0(k11_nat_3(C,A),k5_numbers) | A = B ) ) ) ) ) )).
fof(t22_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_int_2(A) <=> ( k4_nat_d(k1_nat_1(k7_newton(k7_nat_d(A,1)),1),A) = k5_numbers & ~ r1_xxreal_0(A,1) ) ) ) )).
fof(t22_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k4_nat_d(k2_xcmplx_0(A,C),B) = k4_nat_d(k2_xcmplx_0(k4_nat_d(A,B),C),B) ) ) ) )).
fof(t22_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,A,B) => ! [G] : ( m2_nattra_1(G,A,B,C,D) => ! [H] : ( 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] : ( m2_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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t22_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r2_hidden(D,k1_relset_1(u1_struct_0(B),C)) => ( ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t22_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( 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) ) ) ) )).
fof(t22_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) <=> r2_hidden(C,u1_struct_0(A)) ) ) <=> B = u1_struct_0(A) ) ) ) )).
fof(t22_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [C] : ( v1_xreal_0(C) => ( r1_ndiff_3(A,B,C) => r1_nfcont_3(A,B,C) ) ) ) ) )).
fof(t22_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t22_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_prvect_2(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t22_neckla_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => r2_necklace(B,A) ) ) )).
fof(t22_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k2_net_1(A)) => ! [C] : ( r2_hidden(B,C) => ( k2_net_1(A) = k1_xboole_0 | r2_hidden(k6_net_1(A,B),k11_net_1(A,C)) ) ) ) ) )).
fof(t22_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k3_newton(k1_nat_1(A,1),k1_nat_1(B,1)) = k2_xcmplx_0(k3_newton(k1_nat_1(A,1),B),k3_newton(A,B)) ) ) )).
fof(t22_nfcont_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t22_nfcont_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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,k4_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) ) ) ) ) )).
fof(t22_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t22_normform,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k5_finsub_1(B)) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t22_normsp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( v3_normsp_1(C,B) => v3_normsp_1(k5_normsp_1(B,C,A),B) ) ) ) ) )).
fof(t22_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k4_normsp_2(A)))) => ( v3_pre_topc(B,k4_normsp_2(A)) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(a_3_2_normsp_2(A,C,D),B) ) ) ) ) ) ) ) )).
fof(t22_numbers,axiom,( k3_numbers != k1_numbers )).
fof(t22_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t22_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & k1_funct_1(k8_openlatt(A),B) = k1_funct_1(k8_openlatt(A),C) ) ) ) ) )).
fof(t22_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t22_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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_nfcont_1(k1_ordeq_01(A,B),k9_rsspace4(A,B)) & m1_subset_1(k1_ordeq_01(A,B),k1_zfmisc_1(u1_struct_0(k9_rsspace4(A,B)))) ) ) ) )).
fof(t22_orders_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t22_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_orders_2(A,C,B) <=> r2_hidden(B,k1_orders_2(A,k6_domain_1(u1_struct_0(A),C))) ) ) ) ) )).
fof(t22_ordinal1,axiom,( ! [A] : ~ ! [B] : ( v3_ordinal1(B) => r2_hidden(B,A) ) )).
fof(t22_ordinal2,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_ordinal1(k3_ordinal2(A),k3_ordinal2(B)) ) )).
fof(t22_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r2_hidden(k10_ordinal2(A,B),k10_ordinal2(A,C)) => r2_hidden(B,C) ) ) ) ) )).
fof(t22_ordinal4,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ~ ( B != k1_xboole_0 & k12_ordinal2(B,A) = k1_xboole_0 ) ) ) )).
fof(t22_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) ) => ( ( r2_hidden(k5_numbers,A) & ! [C] : ( v3_ordinal1(C) => ( r2_hidden(C,k9_xtuple_0(B)) => k1_funct_1(B,C) = k1_ordinal5(A,C) ) ) ) => v2_ordinal5(B) ) ) ) )).
fof(t22_ordinal6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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_ordinal1(k1_funct_1(D,B),k1_funct_1(D,C)) ) ) ) )).
fof(t22_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ~ ( ~ r1_orders_2(B,D,C) & ~ r1_orders_2(B,E,C) & k1_ortsp_1(A,B,C,D,E) != k11_algstr_0(A,k1_ortsp_1(A,B,C,E,D)) ) ) ) ) ) ) )).
fof(t22_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( ( r6_osalg_1(A,B,C) & r6_osalg_1(A,C,B) ) => B = C ) ) ) ) )).
fof(t22_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_osalg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_tarski(k8_osalg_2(A,B,C,D),k8_msualg_2(A,B,C,D)) ) ) ) ) )).
fof(t22_osalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v2_msualg_4(C,A,B) & v3_osalg_4(C,A,B) & m1_osalg_4(C,A,B) ) => v3_msualg_4(C,A,B) ) ) ) )).
fof(t22_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_parsp_1(A,B,C,D,E) => r1_parsp_1(A,B,C,E,D) ) ) ) ) ) ) )).
fof(t22_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t22_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => r1_relset_1(A,B,k3_partfun1(C,A,B),C) ) )).
fof(t22_partfun2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(C)) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ( D = k7_relset_1(B,C,E,A) <=> ! [F] : ( m1_subset_1(F,C) => ( r2_hidden(F,D) <=> ? [G] : ( m1_subset_1(G,B) & r2_hidden(G,k1_relset_1(B,E)) & r2_hidden(G,A) & F = k7_partfun1(C,E,G) ) ) ) ) ) ) ) ) )).
fof(t22_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m2_finseq_1(D,A) => ! [E] : ! [F] : ( ( 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] : ( m1_subset_1(G,k4_ordinal1) => ~ ( r1_xxreal_0(1,G) & ~ r1_xxreal_0(k3_finseq_1(D),G) & ! [H] : ~ ( 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,k1_nat_1(G,1))),k3_eqrel_1(A,B,C)) ) ) ) ) => r2_hidden(k4_tarski(E,F),k5_eqrel_1(A,B,C)) ) ) ) ) ) )).
fof(t22_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( r3_relat_2(B,A) => v3_relat_2(B) ) ) ) )).
fof(t22_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_analoaf(A,B,E,C,D) & r2_analoaf(A,B,C,E,D) ) ) ) ) ) )).
fof(t22_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t22_pcomps_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_compts_1(A) => v2_pcomps_1(A) ) ) )).
fof(t22_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k20_pcs_0(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k20_pcs_0(A,B))) => ( C = B => r1_orders_2(k20_pcs_0(A,B),C,D) ) ) ) ) )).
fof(t22_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( 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] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [G] : ( m1_subset_1(G,u1_struct_0(k4_real_ns1(A))) => ! [H] : ( 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,C,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(D,B))) = k2_pdiff_1(k1_partfun1(k1_numbers,k1_euclid(A),k1_euclid(A),k1_numbers,k6_pdiff_1(A,C,H),k1_partfun1(k1_euclid(A),k1_euclid(B),k1_euclid(B),k1_numbers,F,k1_pdiff_1(D,B)))) ) ) ) ) ) ) ) ) ) )).
fof(t22_pdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( 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),k3_funct_2(k1_euclid(2),k1_numbers,k1_pdiff_1(2,2),B)) ) ) ) )).
fof(t22_pdiff_3,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(2)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [C] : ( ( 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) & k10_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) = k2_xcmplx_0(k3_pdiff_3(B,A),k3_pdiff_3(C,A)) ) ) ) ) ) )).
fof(t22_pdiff_4,axiom,( ! [A] : ! [B] : ( ( 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] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => ( r2_hidden(C,A) => r3_pdiff_1(3,1,B,C) ) ) ) ) ) )).
fof(t22_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( 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) ) ) ) )).
fof(t22_pdiff_6,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(B),k1_euclid(A)))) ) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(B)) => ! [E] : ( v1_xreal_0(E) => ( 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))) ) ) ) ) ) ) ) )).
fof(t22_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(B),k1_euclid(A)))) ) => ! [E] : ( 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) & k11_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(k4_ordinal1,1)) ) ) ) ) ) ) ) )).
fof(t22_pdiff_8,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k4_real_ns1(A)))) => ( v3_nfcont_1(D,k4_real_ns1(A)) => ( ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( 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)),k14_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) ) ) ) ) ) ) ) )).
fof(t22_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [E] : ( ( 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] : ( m1_subset_1(F,k1_zfmisc_1(k1_euclid(A))) => ! [G] : ( 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] : ( m2_finseq_2(H,k1_numbers,k1_euclid(A)) => ! [I] : ( m2_finseq_2(I,k1_numbers,k1_euclid(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(k4_real_ns1(A))) => ! [K] : ( 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))) = k2_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))),k14_pdiff_1(A,B,C,E,G),K),k7_partfun1(u1_struct_0(k16_lopban_1(k4_real_ns1(1),k4_real_ns1(B))),k14_pdiff_1(A,B,C,E,G),J))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t22_pencil_1,axiom,( ! [A] : ( ( ~ v3_pencil_1(A) & l1_pre_topc(A) ) => v1_pencil_1(k2_struct_0(A),A) ) )).
fof(t22_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(D,k1_vectsp_9(A,B)) & v1_xboole_0(k6_pencil_4(A,B,C,D)) ) ) ) ) ) )).
fof(t22_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_nat_d(2,A) <=> v1_abian(A) ) ) )).
fof(t22_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => k8_pnproc_1(A,B,k2_pre_poly(B)) = k6_partfun1(k9_funct_2(A,k4_ordinal1)) ) )).
fof(t22_polyalg1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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)) ) ) ) )).
fof(t22_polyeq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( A != k5_numbers & r1_xxreal_0(k5_numbers,k1_quin_1(A,B,C)) & k4_polyeq_1(A,B,C,k5_numbers,D) = k5_numbers & D != k5_numbers & D != k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A)) & D != k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A)) ) ) ) ) ) )).
fof(t22_polyeq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( k1_square_1(B) = A & ~ r1_xxreal_0(k5_numbers,k4_complex1(A)) & B != k2_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(A),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A))))),2)),k3_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(A)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A))))),2))),k7_complex1)) & B != k2_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(A),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A))))),2))),k3_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(A)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A))))),2)),k7_complex1)) ) ) ) )).
fof(t22_polyeq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k2_power(A,B) = 1 => ( r1_xxreal_0(A,k5_numbers) | A = 1 | B = k5_numbers ) ) ) ) )).
fof(t22_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( v1_xcmplx_0(F) => ! [G] : ( v1_xcmplx_0(G) => ! [H] : ( v1_xcmplx_0(H) => ! [I] : ( v1_xcmplx_0(I) => ( ( G = k4_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(E,F),H),I)) & D = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(E,F),k3_xcmplx_0(E,H)),k3_xcmplx_0(E,I)),k3_xcmplx_0(F,H)),k3_xcmplx_0(F,I)),k3_xcmplx_0(H,I)) & C = k4_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(E,F),H),k3_xcmplx_0(k3_xcmplx_0(E,F),I)),k3_xcmplx_0(k3_xcmplx_0(E,H),I)),k3_xcmplx_0(k3_xcmplx_0(F,H),I))) & B = k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(E,F),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(C,A)),B) = k5_numbers <=> ~ ( A != E & A != F & A != H & A != I ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t22_polyform,axiom,( ! [A] : ! [B] : 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)))) )).
fof(t22_polynom1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( 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) ) => k4_polynom1(A,B,k8_polynom1(A,B),C) = k4_struct_0(B) ) ) )).
fof(t22_polynom3,axiom,( ! [A] : ! [B] : ! [C] : ( m2_finseq_1(C,k3_finseq_2(A)) => ! [D] : ( m2_finseq_1(D,k3_finseq_2(B)) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ! [H] : ( m1_subset_1(H,k4_ordinal1) => ( ( 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) & k1_nat_1(k2_wsierp_1(k17_finseq_1(k4_ordinal1,k7_nat_d(E,1),k10_pre_poly(A,C))),G) = k1_nat_1(k2_wsierp_1(k17_finseq_1(k4_ordinal1,k7_nat_d(F,1),k10_pre_poly(B,D))),H) ) => ( E = F & G = H ) ) ) ) ) ) ) ) )).
fof(t22_polynom4,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( 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),k4_ordinal1,u1_struct_0(A),k4_group_1(A),C,k7_nat_d(k1_algseq_1(A,B),1))) ) ) ) )).
fof(t22_polynom5,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k2_polynom4(A,k2_polynom5(A,B,D),C) = k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k4_group_1(A),k2_polynom4(A,B,C),D) ) ) ) ) )).
fof(t22_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( k3_polynom1(k15_pre_poly(A),B,k4_polynom7(A,B,C)) = k1_xboole_0 | k3_polynom1(k15_pre_poly(A),B,k4_polynom7(A,B,C)) = k6_domain_1(k15_pre_poly(A),k16_pre_poly(A)) ) ) ) )).
fof(t22_polynom8,axiom,( ! [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) & v2_vectsp_1(A) & v4_vectsp_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( 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)) ) ) ) ) )).
fof(t22_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( 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),k10_polynom1(A,B,k1_polynom7(A,B,E,D),C)) ) ) ) ) ) )).
fof(t22_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r1_xxreal_0(1,B) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(k6_xcmplx_0(k1_power(B,A),1),k7_xcmplx_0(k6_xcmplx_0(A,1),B)) ) ) ) ) )).
fof(t22_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ( k1_msualg_1(B,D) != k1_xboole_0 => ! [E] : ( m1_subset_1(E,k3_msualg_1(B,D,k14_pralg_2(A,B,C))) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( ( 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(k9_funct_6(E),F)) ) ) ) ) ) ) ) ) ) )).
fof(t22_pre_circ,axiom,( ! [A] : ( v7_ordinal1(A) => ~ v1_finset_1(a_1_0_pre_circ(A)) ) )).
fof(t22_pre_poly,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : k1_card_3(k5_relat_1(A,B)) = k5_relat_1(k1_card_3(A),B) ) )).
fof(t22_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t22_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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,D),k2_prelamb(A,C,D)),k2_prelamb(A,B,C))) & r2_prelamb(A,k6_finseq_1(u1_struct_0(A)),k1_prelamb(A,k1_prelamb(A,C,B),k1_prelamb(A,k1_prelamb(A,D,C),k1_prelamb(A,D,B)))) ) ) ) ) ) )).
fof(t22_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_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)) ) ) ) ) )).
fof(t22_prob_1,axiom,( ! [A] : ! [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))) ) => m1_prob_1(k1_xboole_0,A,B) ) )).
fof(t22_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m1_prob_1(E,A,B) => ! [F] : ( m2_prob_1(F,A,B) => ( r2_prob_2(A,B,F,C,D,E) => r2_prob_2(A,B,F,C,E,D) ) ) ) ) ) ) ) )).
fof(t22_prob_3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( r2_funct_2(k4_ordinal1,k9_setfam_1(A),D,k2_prob_3(A,C)) => ( k1_prob_2(A,B,D,k5_numbers) = k1_prob_2(A,B,C,k5_numbers) & ! [E] : ( v7_ordinal1(E) => k1_prob_2(A,B,D,k1_nat_1(E,1)) = k6_prob_1(A,B,k1_prob_2(A,B,D,E),k1_prob_2(A,B,C,k1_nat_1(E,1))) ) ) ) ) ) ) )).
fof(t22_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ( r1_prob_4(A,B,C) <=> r1_measure3(A,B,k2_prob_4(A,B,C)) ) ) ) ) )).
fof(t22_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) )).
fof(t22_projdes1,axiom,( ! [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) ) => v5_anproj_2(A) ) )).
fof(t22_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ( ( v1_projpl_1(A) & ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ? [D] : ( m1_subset_1(D,u2_incsp_1(A)) & r4_incsp_1(A,k7_domain_1(u1_incsp_1(A),B,C),D) ) ) ) & ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & r2_projpl_1(A,D,B,C) ) ) ) ) => ( ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ~ r5_projpl_1(A,B,C,D,E) ) ) ) ) | ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ? [C] : ( m1_subset_1(C,u1_incsp_1(A)) & ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & ? [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t22_projred1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u2_incsp_1(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t22_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u1_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u1_incsp_1(A)) => ! [H] : ( m1_subset_1(H,u2_incsp_1(A)) => ! [I] : ( m1_subset_1(I,u2_incsp_1(A)) => ! [J] : ( m1_subset_1(J,u2_incsp_1(A)) => ! [K] : ( m1_subset_1(K,u2_incsp_1(A)) => ! [L] : ( m1_subset_1(L,u2_incsp_1(A)) => ! [M] : ( 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,M) & r1_incsp_1(A,E,M) & r1_incsp_1(A,D,L) & r1_incsp_1(A,C,L) & r1_incsp_1(A,G,H) & r1_incsp_1(A,G,M) & r1_incsp_1(A,F,I) & r1_incsp_1(A,F,L) & r1_incsp_1(A,G,K) & r1_incsp_1(A,F,K) ) => ( 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,K,C),k1_projred1(A,K,I,B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t22_prvect_3,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_prvect_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( 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] : ( m1_subset_1(D,u1_struct_0(k10_prvect_2(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ? [F] : ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) & ? [G] : ( 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] : ( m1_subset_1(D,u1_struct_0(k5_prvect_3(k10_prvect_2(A),B))) => ! [E] : ( 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] : ( m1_subset_1(D,u1_struct_0(k5_prvect_3(k10_prvect_2(A),B))) => ! [E] : ( 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)))) ) ) ) )).
fof(t22_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(B,A) => k1_funct_1(k3_pscomp_1(k15_euclid(2),k4_pscomp_1,A),B) = k17_euclid(B) ) ) ) )).
fof(t22_pua2mss1,axiom,( ! [A] : ( ( v2_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( 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))) ) ) )).
fof(t22_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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 ) ) ) )).
fof(t22_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_qc_lang1(A)) => r1_qc_lang1(A,B,B) ) ) )).
fof(t22_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( m1_subset_1(E,k9_qc_lang1(A)) => ! [F] : ( m1_subset_1(F,k9_qc_lang1(A)) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t22_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t22_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m1_trees_1(D,k9_xtuple_0(k2_qc_lang4(A,C))) => ! [E] : ( m1_trees_1(E,k9_xtuple_0(k2_qc_lang4(A,C))) => ~ ( E = k7_finseq_1(D,k9_finseq_1(B)) & v4_qc_lang1(k3_trees_2(k9_qc_lang1(A),k2_qc_lang4(A,C),D),A) & ~ ( k3_trees_2(k9_qc_lang1(A),k2_qc_lang4(A,C),E) = k19_qc_lang1(A,k3_trees_2(k9_qc_lang1(A),k2_qc_lang4(A,C),D)) & B = k5_numbers ) & ~ ( k3_trees_2(k9_qc_lang1(A),k2_qc_lang4(A,C),E) = k20_qc_lang1(A,k3_trees_2(k9_qc_lang1(A),k2_qc_lang4(A,C),D)) & B = 1 ) ) ) ) ) ) ) )).
fof(t22_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_henmodel(B,A) & m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ( r1_tarski(C,B) => v1_henmodel(C,A) ) ) ) ) )).
fof(t22_quantal1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k5_quantal1(A,k5_quantal1(A,B)) = B ) ) )).
fof(t22_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k23_quaterni(k24_quaterni(A),k24_quaterni(B)) = k23_quaterni(A,B) ) ) )).
fof(t22_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k25_quaterni(k23_quaterni(k12_quaterni,A),k23_quaterni(A,k12_quaterni)) = k6_quaterni(k5_numbers,k4_xcmplx_0(k3_xcmplx_0(2,k15_quaterni(A))),k3_xcmplx_0(2,k14_quaterni(A)),k5_numbers) ) )).
fof(t22_quaterni,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) & ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & A = k2_quaterni(k5_numbers,1,2,3,B,C,D,E) ) ) ) ) ) )).
fof(t22_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( k1_quin_1(B,C,D) = k5_numbers => ( r1_xxreal_0(B,k5_numbers) | ( ~ ( ~ r1_xxreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(A)),k3_xcmplx_0(C,A)),D),k5_numbers) & A = k4_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(2,B))) ) & ~ ( A != k4_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(2,B))) & r1_xxreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(A)),k3_xcmplx_0(C,A)),D),k5_numbers) ) ) ) ) ) ) ) ) )).
fof(t22_quofield,axiom,( ! [A] : ( ( ~ 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] : ( 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 ) ) ) )).
fof(t22_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_radix_1(1,B,A) & r1_radix_1(1,C,A) ) => k11_radix_1(k2_xcmplx_0(k4_radix_1(1,A,1,k10_radix_1(A,1,B)),k4_radix_1(1,A,1,k10_radix_1(A,1,C)))) = k11_radix_1(k2_xcmplx_0(B,C)) ) ) ) ) )).
fof(t22_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_random_1(C,A,B) => ! [D] : ( m1_random_1(D,A,B) => m1_random_1(k20_valued_1(A,k1_numbers,k1_numbers,C,D),A,B) ) ) ) ) )).
fof(t22_random_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v2_finset_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) & v7_random_3(B,A,k7_random_3(A)) ) => ( k1_funct_1(k9_random_3(A,B),k5_numbers) = k8_random_3(A,B,k5_numbers) & k1_funct_1(k9_random_3(A,B),1) = k2_random_2(k1_funct_1(A,k5_numbers),k1_funct_1(A,1),k8_random_3(A,B,k5_numbers),k8_random_3(A,B,1)) & ? [C] : ( m2_prob_1(C,k2_zfmisc_1(k1_funct_1(A,k5_numbers),k1_funct_1(A,1)),k1_random_1(k2_zfmisc_1(k1_funct_1(A,k5_numbers),k1_funct_1(A,1)))) & C = k1_funct_1(k9_random_3(A,B),1) & k1_funct_1(k9_random_3(A,B),2) = k2_random_2(k2_zfmisc_1(k1_funct_1(A,k5_numbers),k1_funct_1(A,1)),k1_funct_1(A,2),C,k8_random_3(A,B,2)) ) & ? [C] : ( m2_prob_1(C,k3_zfmisc_1(k1_funct_1(A,k5_numbers),k1_funct_1(A,1),k1_funct_1(A,2)),k1_random_1(k3_zfmisc_1(k1_funct_1(A,k5_numbers),k1_funct_1(A,1),k1_funct_1(A,2)))) & C = k1_funct_1(k9_random_3(A,B),2) & k1_funct_1(k9_random_3(A,B),3) = k2_random_2(k3_zfmisc_1(k1_funct_1(A,k5_numbers),k1_funct_1(A,1),k1_funct_1(A,2)),k1_funct_1(A,3),C,k8_random_3(A,B,3)) ) & ? [C] : ( m2_prob_1(C,k4_zfmisc_1(k1_funct_1(A,k5_numbers),k1_funct_1(A,1),k1_funct_1(A,2),k1_funct_1(A,3)),k1_random_1(k4_zfmisc_1(k1_funct_1(A,k5_numbers),k1_funct_1(A,1),k1_funct_1(A,2),k1_funct_1(A,3)))) & C = k1_funct_1(k9_random_3(A,B),3) & k1_funct_1(k9_random_3(A,B),4) = k2_random_2(k4_zfmisc_1(k1_funct_1(A,k5_numbers),k1_funct_1(A,1),k1_funct_1(A,2),k1_funct_1(A,3)),k1_funct_1(A,4),C,k8_random_3(A,B,4)) ) ) ) ) )).
fof(t22_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ! [F] : ( m1_vectsp_7(F,A,B) => ( ( m1_vectsp_7(E,A,k1_ranknull(A,B,C,D)) & r1_tarski(E,F) ) => v2_funct_1(k2_partfun1(u1_struct_0(B),u1_struct_0(C),D,k7_subset_1(u1_struct_0(B),F,E))) ) ) ) ) ) ) ) )).
fof(t22_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ( k4_xcmplx_0(k2_rat_1(A)) = k1_rat_1(A) <=> A = k4_xcmplx_0(1) ) ) )).
fof(t22_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v4_ratfunc1(B,A) & m1_ratfunc1(B,A) ) => ! [C] : ( m1_ratfunc1(C,A) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & ~ v1_ratfunc1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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] : ( m2_finseq_1(E,u1_struct_0(k14_polynom3(A))) => ~ ( D = k3_group_4(k14_polynom3(A),E) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( r2_hidden(F,k4_finseq_1(E)) & ! [G] : ( 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) ) ) ) ) ) ) )).
fof(t22_rcomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ~ ( v3_rcomp_1(A) & v3_xxreal_2(A) & r2_hidden(k3_seq_4(A),A) ) ) )).
fof(t22_rcomp_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v4_xxreal_2(A) => ( r2_hidden(k2_seq_4(A),A) | r1_tarski(A,k10_prob_1(k2_seq_4(A))) ) ) ) )).
fof(t22_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k6_real_lat(A))) => ! [C] : ( 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) ) ) ) )).
fof(t22_realset2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(A),k8_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t22_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t22_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( 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) ) ) ) )).
fof(t22_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) ) )).
fof(t22_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t22_revrot_1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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))) ) ) ) )).
fof(t22_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r1_tarski(A,B) => ! [C] : ! [D] : ( r1_rewrite1(A,C,D) => r1_rewrite1(B,C,D) ) ) ) ) )).
fof(t22_rewrite2,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(t22_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(C))) => ! [G] : ( l1_rewrite3(G,F) => ~ ( r2_rewrite3(C,F,G,A,D,B,E) & ! [H] : ( m1_subset_1(H,k8_afinsq_1(C)) => ~ ( r1_rewrite3(F,G,A,H,B) & D = k1_flang_1(C,H,E) ) ) ) ) ) ) ) ) )).
fof(t22_rfinseq,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ? [B] : ( v8_valued_0(B) & m2_finseq_1(B,k1_numbers) & r2_classes1(A,B) ) ) )).
fof(t22_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( v8_valued_0(A) => v1_integra2(k6_rvsum_1(A)) ) ) )).
fof(t22_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t22_rfunct_2,axiom,( ! [A] : ! [B] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( 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_funct_1(B,C),k1_funct_1(B,D)) ) ) ) ) ) ) )).
fof(t22_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,k3_rfunct_3(A,k1_numbers)) => ! [C] : ( 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))) ) ) ) )).
fof(t22_rfunct_4,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) ) )).
fof(t22_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v7_valued_0(A) & v1_seq_2(A) ) => v1_comseq_2(A) ) ) )).
fof(t22_rinfsup2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ( v2_rinfsup2(B) => v2_rinfsup2(k1_valued_0(k6_numbers,B,A)) ) & ( v1_rinfsup2(B) => v1_rinfsup2(k1_valued_0(k6_numbers,B,A)) ) ) ) ) )).
fof(t22_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(k17_ringcat1(A))) => ! [C] : ( m3_ringcat1(C,k10_ringcat1(k9_ringcat1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k17_ringcat1(A))) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t22_rlaffin1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(t22_rlaffin2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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))),k6_xcmplx_0(1,k7_xcmplx_0(1,k5_card_1(C)))),k1_rlvect_1(A,B,k7_xcmplx_0(1,k5_card_1(C)))) ) ) ) ) ) )).
fof(t22_rlaffin3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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] : ( ( v1_finset_1(D) & v1_rlaffin1(D,C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) ) => ! [E] : ( 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(k4_ordinal1,u1_struct_0(C),E,k2_finseq_1(B))))) <=> k1_rlaffin3(C,D,E,A) = k7_finseq_1(k5_finseq_2(k4_ordinal1,B,k5_numbers),k2_rfinseq(k1_numbers,B,k1_rlaffin3(C,D,E,A))) ) ) ) ) ) ) )).
fof(t22_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rlsub_1(C,A) => ( r1_struct_0(C,B) => r1_struct_0(C,k4_algstr_0(A,B)) ) ) ) ) )).
fof(t22_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => m1_rlsub_1(k2_rlsub_2(A,B,C),k1_rlsub_2(A,B,C)) ) ) ) )).
fof(t22_rltopsp1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_convex1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r1_tarski(k1_rltopsp1(A,C,D),B) ) ) ) ) ) ) )).
fof(t22_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & k5_algstr_0(A,C,D) = B ) ) ) ) )).
fof(t22_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => m2_rlvect_2(k4_rlvect_2(A),A,B) ) ) )).
fof(t22_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t22_rlvect_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( 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) ) ) ) ) )).
fof(t22_rlvect_5,axiom,( ! [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) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t22_rlvect_x,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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] : ( v1_int_1(F) & ? [G] : ( v1_int_1(G) & ? [H] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t22_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_rmod_2(D,A,B) => ( r1_struct_0(D,C) => r1_struct_0(D,k4_algstr_0(B,C)) ) ) ) ) ) )).
fof(t22_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( 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 ) ) ) ) )).
fof(t22_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_4(C,A,B) => m2_rmod_4(C,A,B,k2_rmod_4(A,B,C)) ) ) ) )).
fof(t22_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t22_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t22_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_robbins3(A) & l3_robbins3(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_orders_2(A,B,C) <=> r1_lattices(A,B,C) ) ) ) ) )).
fof(t22_robbins4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k2_robbins4)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_robbins4)) => ( ( A = k6_subset_1(3,2) & B = 2 ) => k3_lattices(k2_robbins4,A,B) = 3 ) ) ) )).
fof(t22_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t22_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( k1_rpr_1(A,B) = k6_xcmplx_0(1,k1_rpr_1(A,k3_subset_1(A,B))) & k1_rpr_1(A,k3_subset_1(A,B)) = k6_xcmplx_0(1,k1_rpr_1(A,B)) ) ) ) )).
fof(t22_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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)) ) ) ) )).
fof(t22_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ( r1_tarski(u1_struct_0(B),u1_struct_0(C)) => m1_rusub_1(B,C) ) ) ) ) )).
fof(t22_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => m1_rusub_1(k2_rusub_2(A,B,C),k1_rusub_2(A,B,C)) ) ) ) )).
fof(t22_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t22_rusub_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ( v2_rusub_4(k2_struct_0(A),A) & v2_rusub_4(k1_struct_0(A),A) ) ) )).
fof(t22_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => k2_rusub_5(A,k1_rusub_1(A)) = k2_rusub_1(A) ) )).
fof(t22_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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(k4_ordinal1,A,k5_numbers) ) ) )).
fof(t22_rvsum_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k9_rvsum_2(k2_finseq_2(A,C),B) = k2_finseq_2(A,k3_xcmplx_0(B,C)) ) ) ) )).
fof(t22_scm_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( r1_tarski(k1_ordinal4(k5_afinsq_1(k9_ami_3(1,k10_ami_3(k5_numbers))),k5_afinsq_1(k2_compos_1(k1_ami_3))),A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( ( v5_memstr_0(D,k7_card_1(2),k1_ami_3,k5_numbers) & m1_scm_1(D,k6_afinsq_1(B,C)) ) => ( r1_extpro_1(k7_card_1(2),k1_ami_3,A,D) & k8_extpro_1(k7_card_1(2),k1_ami_3,A,D) = 1 & ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_ami_3)) ) => k1_funct_1(k6_extpro_1(k7_card_1(2),k1_ami_3,A,D),E) = k1_funct_1(D,E) ) ) ) ) ) ) ) )).
fof(t22_scm_halt,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( m1_scmfsa_2(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2,E,k1_scmfsa6b(D,A,C)),B) ) ) ) ) ) )).
fof(t22_scmfsa10,axiom,( ! [A] : ( 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) ) ) )).
fof(t22_scmfsa6a,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => ! [C] : ( m1_subset_1(C,u1_compos_1(k1_scmfsa_2)) => k5_scmfsa6a(k6_scmfsa6a(A,B),C) = k4_scmfsa6a(A,k6_scmfsa6a(B,C)) ) ) ) )).
fof(t22_scmfsa7b,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( v1_int_1(B) => r1_tarski(k10_xtuple_0(k2_scmfsa_7(A,B)),k1_enumset1(k6_scmfsa_2(A,k4_scmfsa_2(k5_numbers)),k7_scmfsa_2(A,k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(A,k4_scmfsa_2(k5_numbers)))) ) ) )).
fof(t22_scmfsa8a,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( v7_ordinal1(D) => ( r1_xxreal_0(D,k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))))) => ( r8_pboole(u1_struct_0(k1_scmfsa_2),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),D),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k2_scmfsa6a(C)),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),D)) & k3_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k2_scmfsa6a(C)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k2_scmfsa6a(C)),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),D)) != k2_compos_1(k1_scmfsa_2) ) ) ) ) ) ) ) )).
fof(t22_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [E] : ( ( 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),k7_card_1(3),k1_scmfsa_2) & ( ~ r1_xxreal_0(k1_funct_1(B,E),k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),3)))) ) & ( r1_xxreal_0(k1_funct_1(B,E),k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),3)))) ) ) ) ) ) ) ) )).
fof(t22_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(C,k4_compos_1(k1_scmfsa_2))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B)) = k2_scmfsa8a(B,A,k2_scmfsa6a(C)) & ! [D] : ( v7_ordinal1(D) => ( ~ r1_xxreal_0(k2_scmfsa8a(B,A,k2_scmfsa6a(C)),D) => k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),D)) = k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(C,k4_compos_1(k1_scmfsa_2))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),D)) ) ) & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(D,k2_scmfsa8a(B,A,k2_scmfsa6a(C))) => k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),D)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(C,k4_compos_1(k1_scmfsa_2))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),D)) ) ) ) ) ) ) ) )).
fof(t22_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ( k1_funct_1(B,k4_scmfsa_2(k5_numbers)) = 1 => ( k1_funct_1(B,C) = k5_numbers | k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(k1_scmfsa_9(C,D),B,A)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,B) ) ) ) ) ) ) )).
fof(t22_scmfsa_1,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k4_scmfsa_1,k5_scmfsa_1))) => k9_xtuple_0(A) = k1_scmfsa_1 ) )).
fof(t22_scmfsa_2,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( ( 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 ) ) )).
fof(t22_scmfsa_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( ( k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(D,B,C,A),E)) = k5_numbers & r6_pboole(u1_struct_0(k1_scmfsa_2),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(D,B,C,A),E),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa_9(C,B)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D),F)) ) => ( r6_pboole(u1_struct_0(k1_scmfsa_2),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(D,B,C,A),E),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(D,B,C,A),E))) & r6_pboole(u1_struct_0(k1_scmfsa_2),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(D,B,C,A),k1_nat_1(E,1)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa_9(C,B)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D),k1_nat_1(F,k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(k1_funct_4(A,k1_scmfsa_9(C,B)),B),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(D,B,C,A),E))),3)))) ) ) ) ) ) ) ) ) )).
fof(t22_scmfsa_m,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_scmfsa_2)) ) => ( ~ r2_hidden(k5_numbers,k9_nat_1(k1_zfmisc_1(k4_ordinal1),k8_scmfsa_m(B),A)) & ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(C,k9_nat_1(k1_zfmisc_1(k4_ordinal1),k8_scmfsa_m(B),A)) & r2_hidden(k4_scmfsa_2(C),B) ) ) ) ) ) )).
fof(t22_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmpds_2)) ) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t22_scmpds_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) & v3_scmpds_4(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ( r1_xxreal_0(k5_numbers,k2_xcmplx_0(k5_card_1(A),C)) => v3_scmpds_4(k3_scmpds_4(A,k7_scmpds_2(D,B,C))) ) ) ) ) ) )).
fof(t22_scmpds_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) & v2_scmpds_4(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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)) ) ) ) ) )).
fof(t22_scmpds_6,axiom,( ! [A] : ( ( 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] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [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_partfun1(D,u1_struct_0(k1_scmpds_2)) & v5_memstr_0(D,2,k1_scmpds_2,k5_numbers) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(E) & 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] : ( v7_ordinal1(F) => ( ( 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] : ( v7_ordinal1(G) => ( k2_xcmplx_0(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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t22_scmpds_7,axiom,( ! [A] : ( ( 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] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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) ) ) ) ) ) ) )).
fof(t22_scmpds_8,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ! [F] : ( v1_int_1(F) => ! [G] : ! [H] : ! [I] : ( ( v1_funct_1(I) & v1_funct_2(I,k4_card_3(k2_memstr_0(2,k1_scmpds_2)),k4_ordinal1) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k4_card_3(k2_memstr_0(2,k1_scmpds_2)),k4_ordinal1))) ) => ( ( ! [J] : ( ( 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,k5_numbers) ) => ( k1_recdef_1(I,J) = k5_numbers => r1_xxreal_0(k1_funct_1(J,k2_scmpds_2(k1_funct_1(B,D),E)),k5_numbers) ) ) & ! [J] : ( ( 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] : ( ( 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,k5_numbers) ) => ! [K] : ( ( v1_relat_1(K) & v4_relat_1(K,k4_ordinal1) & v5_relat_1(K,u1_compos_1(k1_scmpds_2)) & v1_funct_1(K) & v1_partfun1(K,k4_ordinal1) ) => ( ( ! [L] : ( ( 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] : ( ( 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)),k5_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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t22_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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) ) )).
fof(t22_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t22_scmyciel,axiom,( v4_scmyciel(k1_tarski(k1_xboole_0)) )).
fof(t22_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t22_seq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k26_valued_1(k4_ordinal1,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C),A),k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k26_valued_1(k4_ordinal1,k1_numbers,B,A),k26_valued_1(k4_ordinal1,k1_numbers,C,A))) ) ) ) )).
fof(t22_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(A) & v9_ordinal1(A) ) => ( k1_seq_2(A) = k5_numbers | k1_seq_2(k37_valued_1(k4_ordinal1,k1_numbers,A)) = k5_xcmplx_0(k1_seq_2(A)) ) ) ) )).
fof(t22_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(k1_valued_0(k1_numbers,B,A)) => k1_seq_2(B) = k1_seq_2(k1_valued_0(k1_numbers,B,A)) ) ) ) )).
fof(t22_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ! [D] : ( ( r1_tarski(D,C) & r1_seqfunc(A,k1_numbers,B,C) ) => ( D = k1_xboole_0 | r1_seqfunc(A,k1_numbers,B,D) ) ) ) ) )).
fof(t22_series_3,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(t22_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => r1_xxreal_0(3,k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(B,C),A),A),k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(C,A),B),B)),k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),C),C))) ) ) ) )).
fof(t22_setfam_1,axiom,( ! [A] : r1_setfam_1(k4_setfam_1(A,A),A) )).
fof(t22_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( v7_ordinal1(C) => k1_funct_1(k4_setlim_1(A,B),C) = k2_xboole_0(k3_funct_2(k4_ordinal1,k9_setfam_1(A),k4_setlim_1(A,B),k1_nat_1(C,1)),k1_funct_1(B,C)) ) ) )).
fof(t22_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(C) => v3_prob_1(k5_setlim_2(A,C,B)) ) ) ) )).
fof(t22_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,k5_finsub_1(A)) => ! [E] : ( ( 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] : ( m1_subset_1(F,B) => ( k7_relset_1(A,B,E,D) = k1_tarski(F) => k7_setwiseo(A,B,C,D,E) = F ) ) ) ) ) ) ) ) )).
fof(t22_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => k2_partfun1(k4_ordinal1,A,k1_setwop_2(A,k8_finseq_1(A,C,D),B),k4_finseq_1(C)) = C ) ) ) ) )).
fof(t22_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( v7_ordinal1(B) => k2_sf_mastr(A) = k2_sf_mastr(k61_valued_1(A,B)) ) ) )).
fof(t22_sfmastr3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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))) ) ) ) ) )).
fof(t22_sgraph1,axiom,( ! [A] : ! [B] : ( m1_sgraph1(B,A) => ~ ( B != g1_sgraph1(k1_xboole_0,k1_subset_1(k2_sgraph1(k1_xboole_0))) & ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_sgraph1(C))) => ~ ( ~ v1_xboole_0(C) & B = g1_sgraph1(C,D) ) ) ) ) )).
fof(t22_sheffer1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_sheffer1(A,B,C) <=> r2_lattices(A,B,C) ) ) ) ) )).
fof(t22_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t22_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ( k6_simplex0(A) = k2_xxreal_3(1) <=> v4_simplex0(A) ) ) )).
fof(t22_simplex1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( ~ 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),k5_numbers) ) => ( r1_xxreal_0(A,k5_numbers) | g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = k5_simplex1(A,B,C) ) ) ) ) ) )).
fof(t22_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k1_funct_1(k5_sin_cos2,k2_xcmplx_0(A,B)) = k7_xcmplx_0(k2_xcmplx_0(k1_funct_1(k5_sin_cos2,A),k1_funct_1(k5_sin_cos2,B)),k2_xcmplx_0(1,k3_xcmplx_0(k1_funct_1(k5_sin_cos2,A),k1_funct_1(k5_sin_cos2,B)))) & k1_funct_1(k5_sin_cos2,k6_xcmplx_0(A,B)) = k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(k5_sin_cos2,A),k1_funct_1(k5_sin_cos2,B)),k6_xcmplx_0(1,k3_xcmplx_0(k1_funct_1(k5_sin_cos2,A),k1_funct_1(k5_sin_cos2,B)))) ) ) ) )).
fof(t22_sin_cos3,axiom,( k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,k5_complex1) = k5_numbers )).
fof(t22_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( k19_sin_cos(A) != k5_numbers & k17_sin_cos(B) != k5_numbers & k6_xcmplx_0(k1_sin_cos4(A),k2_sin_cos4(B)) != k4_xcmplx_0(k7_xcmplx_0(k19_sin_cos(k2_xcmplx_0(A,B)),k3_xcmplx_0(k19_sin_cos(A),k17_sin_cos(B)))) ) ) ) )).
fof(t22_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => k1_newton(k17_sin_cos(A),3) = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(3,k17_sin_cos(A)),k17_sin_cos(k3_xcmplx_0(3,A))),4) ) )).
fof(t22_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ~ ( r1_xxreal_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B),A) & ~ r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)),A) & k19_sin_cos(A) = k5_numbers & A != k2_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)) & A != k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)) ) ) ) )).
fof(t22_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(A,1) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(k5_numbers,k6_xcmplx_0(1,k1_square_1(A))) ) ) ) )).
fof(t22_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k4_sin_cos2(k3_xcmplx_0(2,A)),k4_sin_cos2(k3_xcmplx_0(2,B))),k4_sin_cos2(k3_xcmplx_0(2,C))),k4_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,k4_sin_cos2(k2_xcmplx_0(B,C))),k4_sin_cos2(k2_xcmplx_0(C,A))),k4_sin_cos2(k2_xcmplx_0(A,B))) ) ) ) )).
fof(t22_sin_cos9,axiom,( k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k27_sin_cos,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos)))) = k1_rcomp_1(k4_xcmplx_0(1),1) )).
fof(t22_sincos10,axiom,( v2_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k4_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos))) )).
fof(t22_sppol_1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => v1_finset_1(a_1_0_sppol_1(A)) ) )).
fof(t22_sppol_2,axiom,( ! [A] : ( 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)) ) )).
fof(t22_sprect_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t22_sprect_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r1_sprect_2(A,B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( 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)) ) ) ) ) ) ) )).
fof(t22_sprect_3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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) ) ) ) )).
fof(t22_sprect_5,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t22_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k5_numbers,A) => k3_square_1(k1_square_1(A)) = A ) ) )).
fof(t22_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ( B = k5_numbers => A = k5_numbers ) & ( A = k5_numbers => B = k5_numbers ) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k7_card_1(B),k7_card_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(B),k7_card_1(A)))) ) => ~ v1_stirl2_1(C,B,A) ) ) ) ) )).
fof(t22_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_funct_2(C,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [D] : ( m2_subset_1(D,k16_substut1(A),k38_substut1(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t22_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( 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))) ) ) )).
fof(t22_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( m1_subset_1(D,k5_finsub_1(k4_partfun1(A,B))) => ! [E] : ( 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)) ) ) ) )).
fof(t22_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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))))) ) ) ) )).
fof(t22_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t22_supinf_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t22_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( ~ r1_orders_2(B,D,C) => k1_symsp_1(A,B,C,D,D) = k1_group_1(A) ) ) ) ) ) )).
fof(t22_sysrel,axiom,( ! [A] : ( 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) ) ) ) )).
fof(t22_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),k1_numbers))) ) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t22_taylor_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r1_fdiff_1(C,B) => ( r1_xxreal_0(k1_funct_1(C,B),k5_numbers) | ( r1_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(A)),B) & k1_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(A)),B) = k3_xcmplx_0(k3_xcmplx_0(A,k6_prepower(k1_funct_1(C,B),k6_xcmplx_0(A,1))),k1_fdiff_1(C,B)) ) ) ) ) ) ) )).
fof(t22_taylor_2,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k5_numbers,C) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( r2_hidden(E,k2_rcomp_1(k4_xcmplx_0(A),A)) => ( r1_xxreal_0(F,k5_numbers) | r1_xxreal_0(1,F) | ( r1_xxreal_0(k9_complex1(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k16_sin_cos,k2_rcomp_1(k4_xcmplx_0(A),A)),D),k3_xcmplx_0(F,E)),k1_newton(E,D)),k2_newton(D))),k7_xcmplx_0(k3_xcmplx_0(B,k1_newton(C,D)),k2_newton(D))) & r1_xxreal_0(k9_complex1(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k18_sin_cos,k2_rcomp_1(k4_xcmplx_0(A),A)),D),k3_xcmplx_0(F,E)),k1_newton(E,D)),k2_newton(D))),k7_xcmplx_0(k3_xcmplx_0(B,k1_newton(C,D)),k2_newton(D))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t22_tbsp_1,axiom,( ! [A] : ( ( ~ 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] : ( 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) = k5_numbers & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B != k6_domain_1(u1_struct_0(A),C) ) ) ) ) )).
fof(t22_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => v5_tops_1(k2_pre_topc(A,k1_tops_1(A,B)),A) ) ) )).
fof(t22_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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))) ) ) ) )).
fof(t22_tdlat_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v3_tdlat_3(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(B,A) => v3_pre_topc(B,A) ) ) ) ) )).
fof(t22_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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) ) ) ) ) ) )).
fof(t22_tex_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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))) ) ) ) ) ) ) )).
fof(t22_tex_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t22_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t22_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t22_tietze,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t22_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ v2_struct_0(E) & m1_pre_topc(E,A) ) => ( ( m1_pre_topc(D,B) & m1_pre_topc(E,C) ) => m1_pre_topc(k1_tsep_1(A,D,E),k1_tsep_1(A,B,C)) ) ) ) ) ) ) )).
fof(t22_toler_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(t22_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t22_topalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_borsuk_2(C,A,B,B) => ( k1_funct_1(C,k5_numbers) = B & k1_funct_1(C,1) = B ) ) ) ) )).
fof(t22_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_borsuk_2(G,k2_borsuk_1(A,B),k4_borsuk_1(A,B,C,E),k4_borsuk_1(A,B,D,F)) => ! [H] : ( m1_borsuk_2(H,k2_borsuk_1(A,B),k4_borsuk_1(A,B,C,E),k4_borsuk_1(A,B,D,F)) => ! [I] : ( m1_borsuk_2(I,A,C,D) => ! [J] : ( m1_borsuk_2(J,A,C,D) => ! [K] : ( m1_borsuk_2(K,B,E,F) => ! [L] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t22_topalg_6,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t22_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t22_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_topgen_1(A,B,C) <=> ? [D] : ( 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) ) ) ) ) ) )).
fof(t22_topgen_2,axiom,( ! [A] : ! [B] : ! [C] : ( 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)))) ) ) ) )).
fof(t22_topgen_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) & k4_series_1(k8_nat_1(k1_numbers,k1_prepower(A),B)) != k7_xcmplx_0(k1_newton(A,B),k6_xcmplx_0(1,A)) ) ) ) )).
fof(t22_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t22_topgen_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( ( v1_xreal_0(D) & v2_xxreal_0(D) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t22_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( v3_pre_topc(E,A) & m1_connsp_2(E,A,D) ) => ? [F] : ( 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) ) ) ) ) )).
fof(t22_topmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t22_topreal1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(A))) => ( ( k3_finseq_1(B) = k5_numbers | k3_finseq_1(B) = 1 ) <=> k3_topreal1(A,B) = k1_xboole_0 ) ) ) )).
fof(t22_topreal4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(2))) => ~ ( ~ r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),B,1),k8_metric_1(k14_euclid(2),D,C)) & r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B)),k8_metric_1(k14_euclid(2),D,C)) & r2_hidden(A,k8_metric_1(k14_euclid(2),D,C)) & v4_topreal1(B) & ~ r2_hidden(A,k3_topreal1(2,B)) & ! [E] : ( 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),k8_metric_1(k14_euclid(2),D,C))) ) ) ) ) ) ) ) )).
fof(t22_topreal6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k14_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( ( A = k4_struct_0(k15_euclid(2)) & A = B ) => ( B = k2_finseq_4(k4_ordinal1,k5_numbers,k5_numbers) & k17_euclid(B) = k5_numbers & k18_euclid(B) = k5_numbers ) ) ) ) )).
fof(t22_topreal7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v9_metric_1(B) & l1_metric_1(B) ) => v9_metric_1(k1_topreal7(A,B)) ) ) )).
fof(t22_topreal8,axiom,( ! [A] : ( ( v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ 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)) ) ) ) )).
fof(t22_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(A))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(A))) => ( ( k2_xcmplx_0(B,C) = 1 & k2_xcmplx_0(k9_complex1(B),k9_complex1(C)) = 1 & r2_hidden(E,k2_topreal9(A,G,D)) & r2_hidden(F,k1_topreal9(A,G,D)) ) => ( C = k5_numbers | r2_hidden(k3_rlvect_1(k15_euclid(A),k1_rlvect_1(k15_euclid(A),E,B),k1_rlvect_1(k15_euclid(A),F,C)),k1_topreal9(A,G,D)) ) ) ) ) ) ) ) ) ) )).
fof(t22_topreala,axiom,( ! [A] : ( ( 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] : ( ( 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) ) ) ) )).
fof(t22_toprealb,axiom,( ! [A] : ( 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))) ) )).
fof(t22_toprealc,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( v13_struct_0(B,1) & l1_struct_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t22_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ( v1_toprns_1(B,A) => v1_toprns_1(k3_toprns_1(A,B),A) ) ) ) )).
fof(t22_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k1_tops_1(A,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D,A) & r1_tarski(D,C) & r2_hidden(B,D) ) ) ) ) )).
fof(t22_tops_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t22_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => v3_tops_1(k1_struct_0(A),A) ) )).
fof(t22_tops_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k3_topmetr)) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t22_transgeo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t22_treal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => ! [C] : ( ( 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] : ( 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 ) ) ) ) ) )).
fof(t22_trees_1,axiom,( ~ v1_xboole_0(k1_tarski(k1_xboole_0)) & v1_trees_1(k1_tarski(k1_xboole_0)) )).
fof(t22_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( m1_trees_2(E,A) => ~ ( r2_hidden(C,E) & r2_hidden(D,E) & r1_tarski(B,D) & ~ r2_hidden(C,k1_trees_1(B)) & ~ r1_tarski(B,C) ) ) ) ) ) ) )).
fof(t22_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v4_trees_3(A) <=> ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => ( ~ v1_xboole_0(k1_funct_1(A,B)) & v1_trees_1(k1_funct_1(A,B)) ) ) ) ) )).
fof(t22_trees_4,axiom,( ! [A] : ! [B] : ( ( 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),k14_trees_3(k5_numbers),B) ) )).
fof(t22_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => k9_trees_9(k1_tarski(A)) = k3_trees_9(A) ) )).
fof(t22_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => m1_pre_topc(B,k1_tsep_1(A,B,C)) ) ) ) )).
fof(t22_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t22_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ? [C] : ( 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) ) ) ) )).
fof(t22_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( m2_funct_2(B,k4_numbers,u1_turing_1(A),k9_funct_2(k4_numbers,u1_turing_1(A))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( r1_xxreal_0(1,k3_finseq_1(D)) & r2_turing_1(k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,C),D),A,B) ) => r1_turing_1(A,B,C,k1_nat_1(k1_nat_1(C,k7_partfun1(k4_ordinal1,D,1)),2)) ) ) ) ) ) )).
fof(t22_twoscomp,axiom,( k1_funct_1(k25_twoscomp,k11_finseq_1(k5_numbers,k5_numbers,k5_numbers)) = k5_numbers & k1_funct_1(k25_twoscomp,k11_finseq_1(k5_numbers,k5_numbers,1)) = 1 & k1_funct_1(k25_twoscomp,k11_finseq_1(k5_numbers,1,k5_numbers)) = 1 & k1_funct_1(k25_twoscomp,k11_finseq_1(k5_numbers,1,1)) = 1 & k1_funct_1(k25_twoscomp,k11_finseq_1(1,k5_numbers,k5_numbers)) = 1 & k1_funct_1(k25_twoscomp,k11_finseq_1(1,k5_numbers,1)) = 1 & k1_funct_1(k25_twoscomp,k11_finseq_1(1,1,k5_numbers)) = 1 & k1_funct_1(k25_twoscomp,k11_finseq_1(1,1,1)) = 1 )).
fof(t22_unialg_2,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_unialg_1(B) & m1_unialg_2(B,A) ) => ! [C] : ( ( v1_unialg_1(C) & m1_unialg_2(C,A) ) => k5_unialg_2(A,B,k8_unialg_2(A,B,C)) = B ) ) ) )).
fof(t22_unialg_3,axiom,( ! [A] : ( ( ~ 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 ) )).
fof(t22_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => r2_hidden(k1_group_1(k1_complfld),k2_uniroots(A)) ) )).
fof(t22_uproots,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_polynom3(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t22_urysohn1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ( v10_pre_topc(A) & v7_pre_topc(A) ) => ! [B] : ( ( v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( B != k1_xboole_0 & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( C != k1_xboole_0 & r1_tarski(k2_pre_topc(A,C),B) ) ) ) ) ) ) )).
fof(t22_urysohn2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(k6_xcmplx_0(B,A),1) & ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(C,A) & ~ r1_xxreal_0(B,C) ) ) ) ) ) )).
fof(t22_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t22_valued_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ! [E] : ( ( 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(k4_ordinal1,B,A,D,E),B,k8_funct_2(k4_ordinal1,B,A,C,E)) ) ) ) ) ) ) )).
fof(t22_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( v7_ordinal1(C) => k61_valued_1(k3_relat_1(A,B),C) = k3_relat_1(k61_valued_1(A,C),B) ) ) ) )).
fof(t22_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t22_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(k6_vectsp10(A,B,C))) => ( m2_vectsp_4(D,A,B,C) & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & D = k3_vectsp_4(A,B,E,C) ) ) ) ) ) ) )).
fof(t22_vectsp11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m1_vectsp_4(D,B,C) => ! [E] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t22_vectsp_1,axiom,( k3_rlvect_1(k2_vectsp_1,k5_struct_0(k2_vectsp_1),k5_struct_0(k2_vectsp_1)) != k4_struct_0(k2_vectsp_1) )).
fof(t22_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C != k4_struct_0(A) => k6_algstr_0(A,k1_vectsp_2(A,B,C),C) = B ) ) ) ) )).
fof(t22_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_vectsp_4(D,A,B) => ( r1_struct_0(D,C) => r1_struct_0(D,k4_algstr_0(B,C)) ) ) ) ) ) )).
fof(t22_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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 ) ) )).
fof(t22_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_vectsp_6(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t22_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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] : ( m1_vectsp_7(C,A,B) => ! [D] : ( m1_vectsp_7(D,A,B) => k1_card_1(C) = k1_card_1(D) ) ) ) ) ) )).
fof(t22_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( v1_xreal_0(D) => r2_relset_1(A,k1_numbers,k4_normsp_0(A,B,k4_vfunct_1(A,B,C,D)),k26_valued_1(A,k1_numbers,k4_normsp_0(A,B,C),k9_complex1(D))) ) ) ) ) )).
fof(t22_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( v1_xcmplx_0(D) => r2_relset_1(A,k1_numbers,k4_normsp_0(A,B,k2_vfunct_2(A,B,C,D)),k26_valued_1(A,k1_numbers,k4_normsp_0(A,B,C),k9_complex1(D))) ) ) ) ) )).
fof(t22_waybel10,axiom,( ! [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) ) => r5_waybel_1(k2_waybel10(A),k1_waybel10(k3_waybel10(A),k4_waybel10(A))) ) )).
fof(t22_waybel11,axiom,( ! [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] : ( ( ~ 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) ) ) )).
fof(t22_waybel12,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( 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 ) ) )).
fof(t22_waybel13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t22_waybel14,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( ! [C] : ( 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) ) ) ) )).
fof(t22_waybel15,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t22_waybel16,axiom,( ! [A] : ( ( 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)) ) )).
fof(t22_waybel17,axiom,( ! [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] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t22_waybel19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ! [C] : ( ( 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)))) ) ) ) ) ) )).
fof(t22_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t22_waybel21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v4_yellow_0(C,A) & m1_yellow_0(C,A) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(t22_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_waybel23(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t22_waybel24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [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) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ( E = k1_yellow_0(k5_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))) ) ) ) ) ) ) ) )).
fof(t22_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) )).
fof(t22_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v6_pre_topc(B) & v1_waybel25(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t22_waybel27,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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))) ) ) )).
fof(t22_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => r1_tarski(k3_waybel28(A),k2_waybel11(A)) ) )).
fof(t22_waybel29,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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(k4_yellow_1(A,k2_funcop_1(A,k1_waybel25(B)))) ) ) )).
fof(t22_waybel30,axiom,( ! [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_waybel_2(A) & l1_waybel_9(A) ) => ( v3_waybel_3(k1_yellow_1(k5_waybel11(A))) => v2_yellow13(A) ) ) )).
fof(t22_waybel31,axiom,( ! [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] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => ! [C] : ( ( 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)))) ) ) ) ) )).
fof(t22_waybel32,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ! [C] : ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(C,A) => v12_waybel_0(C,A) ) ) ) ) ) )).
fof(t22_waybel33,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ( ( m2_yellow_9(C,A) & m2_yellow_9(C,B) ) => ! [D] : ( m3_yellow_9(D,A,B) => m2_yellow_9(C,D) ) ) ) ) ) )).
fof(t22_waybel34,axiom,( ! [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] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t22_waybel35,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( m1_waybel35(C,A,B) => ( ! [D] : ( 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) ) ) ) ) )).
fof(t22_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t22_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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] : ( 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))) ) ) ) ) ) ) )).
fof(t22_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) <=> m1_subset_1(D,u1_struct_0(k3_waybel_2(A,C,B))) ) ) ) ) )).
fof(t22_waybel_3,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_waybel_3(A,B,C) <=> ! [D] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(t22_waybel_4,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) )).
fof(t22_waybel_5,axiom,( ! [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] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( 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)))) ) ) ) ) ) ) )).
fof(t22_waybel_6,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v5_waybel_6(B,A) <=> ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & r1_orders_2(A,D,B) ) ) ) ) ) ) ) )).
fof(t22_waybel_7,axiom,( ! [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] : ( ( ~ 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) ) ) ) )).
fof(t22_waybel_8,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v4_waybel_7(B,A) => v5_waybel_6(B,A) ) ) => v3_waybel_8(A) ) ) )).
fof(t22_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_yellow_6(A,B))) => ! [D] : ( 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))) ) ) ) ) )).
fof(t22_weddwitt,axiom,( ! [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) & 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))) ) )).
fof(t22_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(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)))),k3_metric_1(A,C,D)) ) ) ) ) ) ) )).
fof(t22_wellord1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r1_tarski(B,A) => k2_wellord1(k2_wellord1(C,A),B) = k2_wellord1(C,B) ) ) )).
fof(t22_wsierp_1,axiom,( ! [A] : ( v1_rat_1(A) => r1_int_2(k2_rat_1(A),k1_rat_1(A)) ) )).
fof(t22_xboole_1,axiom,( ! [A] : ! [B] : k2_xboole_0(A,k3_xboole_0(A,B)) = A )).
fof(t22_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( 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)) ) ) ) )).
fof(t22_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k6_xcmplx_0(A,C) = k6_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(C,B)) ) ) ) )).
fof(t22_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t22_xtuple_0,axiom,( ! [A] : ( v3_xtuple_0(A) => ! [B] : ( 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 ) ) ) )).
fof(t22_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(A,k3_xxreal_0(B,C)) => r1_xxreal_0(A,B) ) ) ) ) )).
fof(t22_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => r1_tarski(k4_xxreal_1(A,B),k2_xxreal_1(A,B)) ) ) )).
fof(t22_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => m1_xxreal_2(B,k3_xxreal_1(A,B)) ) ) )).
fof(t22_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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 ) ) ) ) )).
fof(t22_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & l1_orders_2(B) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t22_yellow12,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(t22_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_yellow13(C,A,B) & m1_yellow13(C,A,B) ) => C = k1_tarski(u1_struct_0(A)) ) ) ) )).
fof(t22_yellow14,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( ( D = k1_tarski(B) & E = k1_tarski(C) & ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t22_yellow15,axiom,( ! [A] : ( ( 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) ) )).
fof(t22_yellow16,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) ) )).
fof(t22_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(B)) & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & E = C & F = D & ? [G] : ( m1_subset_1(G,k1_altcat_1(A,C,D)) & ? [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t22_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_pre_topc(A,B)) <=> ? [D] : ( ~ 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)) ) ) ) ) ) )).
fof(t22_yellow20,axiom,( ! [A] : ( ( v2_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( v2_altcat_1(B) & l2_altcat_1(B) ) => ( r1_yellow20(A,B) => v2_altcat_1(k2_yellow20(A,B)) ) ) ) )).
fof(t22_yellow_0,axiom,( ! [A] : ( ( v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t22_yellow_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_yellow_1(u1_pre_topc(A))))) => k1_yellow_0(k1_yellow_1(u1_pre_topc(A)),B) = k3_tarski(B) ) ) )).
fof(t22_yellow_2,axiom,( ! [A] : ! [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) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t22_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t22_yellow_4,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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 ) ) ) ) )).
fof(t22_yellow_5,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t22_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( r2_waybel_0(A,B,C) => m2_yellow_6(k5_yellow_6(A,B,C),A,B) ) ) ) )).
fof(t22_yellow_7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_lattice3(A))) => ! [C] : ( 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) ) ) ) )).
fof(t22_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v8_pre_topc(A) & l1_pre_topc(A) ) => v4_yellow_8(A) ) )).
fof(t22_yellow_9,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)))) ) ) ) ) )).
fof(t22_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ( ( v8_zf_fund1(B,A) & r2_hidden(C,B) ) => r2_hidden(k5_zf_fund1(D,C),B) ) ) ) ) ) )).
fof(t22_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v6_zf_lang(A) => k1_funct_1(A,1) = 4 ) ) )).
fof(t22_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,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) ) ) ) ) ) )).
fof(t22_zf_model,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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] : ( 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] : ( m2_subset_1(G,k4_ordinal1,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) ) ) ) ) ) ) ) )).
fof(t22_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ~ ( r1_tarski(k2_tarski(A,B),k2_tarski(C,D)) & A != C & A != D ) )).
fof(t22_zfmodel2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( ( 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(k5_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(k5_numbers),k8_zf_lang(k2_zf_lang(4),k12_zf_lang(C,k4_zf_lang(k2_zf_lang(4),k2_zf_lang(k5_numbers))))))) & r1_xboole_0(k1_enumset1(k2_zf_lang(k5_numbers),k2_zf_lang(1),k2_zf_lang(2)),k2_zf_model(D)) & r1_zf_model(A,E,k8_zf_lang(k2_zf_lang(3),k13_zf_lang(k2_zf_lang(k5_numbers),k8_zf_lang(k2_zf_lang(4),k12_zf_lang(D,k4_zf_lang(k2_zf_lang(4),k2_zf_lang(k5_numbers))))))) & r1_xboole_0(k1_enumset1(k2_zf_lang(k5_numbers),k2_zf_lang(1),k2_zf_lang(2)),k2_zf_model(B)) ) => ( r2_hidden(k2_zf_lang(4),k2_zf_model(B)) | ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ( ( k9_xtuple_0(F) = A & ! [G] : ( m1_subset_1(G,A) => ( ( r1_zf_model(A,k2_zf_lang1(A,E,k2_zf_lang(3),G),B) => k1_funct_1(F,G) = k3_funct_2(A,A,k1_zfmodel1(C,A,E),G) ) & ( r1_zf_model(A,k2_zf_lang1(A,E,k2_zf_lang(3),G),k6_zf_lang(B)) => k1_funct_1(F,G) = k3_funct_2(A,A,k1_zfmodel1(D,A,E),G) ) ) ) ) => r2_zfmodel1(F,A) ) ) ) ) ) ) ) ) ) )).
fof(t22_zfrefle1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(t22_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t22_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( B != C => ! [D] : ( m2_zmodul02(D,A,k7_domain_1(u1_struct_0(A),B,C)) => k21_zmodul02(A,D) = k3_rlvect_1(A,k1_zmodul01(A,B,k3_funct_2(u1_struct_0(A),k4_numbers,D,B)),k1_zmodul01(A,C,k3_funct_2(u1_struct_0(A),k4_numbers,D,C))) ) ) ) ) ) )).
fof(t22_zmodul03,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v8_vectsp_1(C,k9_int_3(A)) & v9_vectsp_1(C,k9_int_3(A)) & v10_vectsp_1(C,k9_int_3(A)) & v11_vectsp_1(C,k9_int_3(A)) & v2_rlvect_1(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l1_vectsp_1(C,k9_int_3(A)) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ~ ( C = k12_zmodul02(A,B) & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => D != k13_zmodul02(A,B,E) ) ) ) ) ) ) )).
fof(t230_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ( k27_member_1(A,C) = k27_member_1(B,C) => ( C = k5_numbers | A = B ) ) ) ) ) )).
fof(t230_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k6_xcmplx_0(k6_xcmplx_0(A,B),A) = k4_xcmplx_0(B) ) ) )).
fof(t230_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(B,C) ) => r1_xxreal_0(k6_xcmplx_0(B,A),C) ) ) ) ) )).
fof(t230_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => k4_xxreal_1(A,k1_xxreal_0) = a_1_1_xxreal_1(A) ) )).
fof(t231_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ( C != k5_numbers => k27_member_1(k3_xboole_0(A,B),C) = k3_xboole_0(k27_member_1(A,C),k27_member_1(B,C)) ) ) ) ) )).
fof(t231_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),A) = k4_xcmplx_0(B) ) ) )).
fof(t231_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(B,C) & r1_xxreal_0(C,k6_xcmplx_0(B,A)) ) ) ) ) )).
fof(t231_xxreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => k3_xxreal_1(k2_xxreal_0,A) = a_1_2_xxreal_1(A) ) )).
fof(t232_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ( C != k5_numbers => k27_member_1(k6_subset_1(A,B),C) = k6_subset_1(k27_member_1(A,C),k27_member_1(B,C)) ) ) ) ) )).
fof(t232_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( B != k5_numbers & ! [C] : ( v1_xcmplx_0(C) => A != k7_xcmplx_0(B,C) ) ) ) ) )).
fof(t232_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => k1_xreal_0(A,A) = k5_numbers ) )).
fof(t232_xxreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => k2_xxreal_1(A,k1_xxreal_0) = a_1_3_xxreal_1(A) ) )).
fof(t233_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ( C != k5_numbers => k27_member_1(k5_xboole_0(A,B),C) = k5_xboole_0(k27_member_1(A,C),k27_member_1(B,C)) ) ) ) ) )).
fof(t233_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t233_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(B,A) => k1_xreal_0(A,B) = k6_xcmplx_0(A,B) ) ) ) )).
fof(t233_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,k4_xxreal_1(k2_xxreal_0,A)) <=> ~ r1_xxreal_0(A,B) ) ) ) )).
fof(t234_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t234_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(D,C),B),A),C) = k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(1,k7_xcmplx_0(A,B)),C),k3_xcmplx_0(k7_xcmplx_0(A,B),D)) ) ) ) ) )).
fof(t234_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(C,A) & r1_xxreal_0(C,B) & k1_xreal_0(A,C) = k1_xreal_0(B,C) ) => A = B ) ) ) ) )).
fof(t234_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,k3_xxreal_1(k2_xxreal_0,A)) <=> r1_xxreal_0(B,A) ) ) ) )).
fof(t235_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t235_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( A != k5_numbers => k2_xcmplx_0(k3_xcmplx_0(A,B),C) = k3_xcmplx_0(A,k2_xcmplx_0(B,k7_xcmplx_0(C,A))) ) ) ) ) )).
fof(t235_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(B,A) => k2_xcmplx_0(k1_xreal_0(A,B),B) = A ) ) ) )).
fof(t235_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,k4_xxreal_1(A,k1_xxreal_0)) <=> ~ r1_xxreal_0(B,A) ) ) ) )).
fof(t236_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t236_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,k2_xxreal_1(A,k1_xxreal_0)) <=> r1_xxreal_0(A,B) ) ) ) )).
fof(t237_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( r1_xxreal_0(1,A) & r1_xxreal_0(A,k1_xreal_0(A,1)) ) ) )).
fof(t237_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(A,B) => r1_tarski(k1_xxreal_1(B,C),k1_xxreal_1(A,k1_xxreal_0)) ) ) ) ) )).
fof(t238_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(A,B) => r1_tarski(k2_xxreal_1(B,C),k1_xxreal_1(A,k1_xxreal_0)) ) ) ) ) )).
fof(t239_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(A,B) => r1_tarski(k3_xxreal_1(B,C),k1_xxreal_1(A,k1_xxreal_0)) ) ) ) ) )).
fof(t23_abcmiz_0,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_abcmiz_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t23_abcmiz_1,axiom,( r1_tarski(k2_abcmiz_1,k4_classes1(k4_ordinal1)) )).
fof(t23_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & v1_abcmiz_a(A) & l1_msualg_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t23_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => k2_absvalue(A) = k2_absvalue(k7_xcmplx_0(1,A)) ) )).
fof(t23_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t23_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_4(E,A) & r2_hidden(B,E) & r1_tarski(C,E) & r2_hidden(B,D) ) => ( ( ~ r5_aff_1(A,C,D) & ~ r5_aff_1(A,D,C) ) | r1_tarski(D,E) ) ) ) ) ) ) ) )).
fof(t23_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ( r2_hidden(A,k2_afinsq_1(C)) => r2_hidden(k2_xcmplx_0(k1_afinsq_1(B),A),k2_afinsq_1(k1_ordinal4(B,C))) ) ) ) ) )).
fof(t23_afinsq_2,axiom,( ! [A] : ! [B] : ( r1_afinsq_2(A,B) => k3_xboole_0(k3_xboole_0(A,B),k4_ordinal1) = k1_xboole_0 ) )).
fof(t23_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(k13_afproj(A))) <=> ~ ! [C] : ( 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) ) ) ) ) ) )).
fof(t23_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t23_algspec1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( m1_algspec1(B,A) => r1_tarski(k10_xtuple_0(B),k9_xtuple_0(A)) ) ) )).
fof(t23_algstr_4,axiom,( ! [A] : ! [B] : ! [C] : ( v7_ordinal1(C) => ( r1_tarski(A,B) => r1_tarski(k11_algstr_4(A,C),k11_algstr_4(B,C)) ) ) )).
fof(t23_altcat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k6_altcat_2(A,B))) => C = B ) ) ) )).
fof(t23_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v16_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t23_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( v7_ordinal1(B) => ~ v2_extpro_1(k9_ami_3(B,A),k7_card_1(2),k1_ami_3) ) ) )).
fof(t23_ami_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( ~ 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(k7_card_1(2),k1_ami_3)) & v1_finset_1(B) & v4_extpro_1(B,k7_card_1(2),k1_ami_3,A) ) => ! [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(C,u1_struct_0(k1_ami_3)) ) => ! [D] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ( ( r1_tarski(B,C) & r1_tarski(B,D) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_ami_3)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_ami_3)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( ( r1_tarski(A,E) & r1_tarski(A,F) ) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v1_ami_2(H) & m1_subset_1(H,u1_struct_0(k1_ami_3)) ) => ! [I] : ( v7_ordinal1(I) => ! [J] : ( m1_subset_1(J,u1_compos_1(k1_ami_3)) => ( ( J = k3_extpro_1(k7_card_1(2),k1_ami_3,E,k5_extpro_1(k7_card_1(2),k1_ami_3,E,C,G)) & J = k9_ami_3(I,H) ) => ( I = k1_ordinal1(k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,E,C,G))) | ( ~ ( ~ r1_xxreal_0(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,E,C,G),H),k5_numbers) & r1_xxreal_0(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,F,D,G),H),k5_numbers) ) & ~ ( ~ r1_xxreal_0(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,F,D,G),H),k5_numbers) & r1_xxreal_0(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,E,C,G),H),k5_numbers) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t23_ami_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) )).
fof(t23_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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,k5_numbers),k1_relset_1(k4_ordinal1,C)) ) => v4_ami_wstd(C,A,B) ) ) ) ) )).
fof(t23_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_analmetr(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k2_analmetr(A,B,C))) => ( r4_analmetr(k2_analmetr(A,B,C),D,F,E,G) => r4_analmetr(k2_analmetr(A,B,C),E,G,D,F) ) ) ) ) ) ) ) ) )).
fof(t23_analoaf,axiom,( ! [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) ) => ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( k3_rlvect_1(A,k1_rlvect_1(A,B,D),k1_rlvect_1(A,C,E)) = k4_struct_0(A) => ( D = k5_numbers & E = k5_numbers ) ) ) ) ) ) => ( ~ ! [B] : ( m1_subset_1(B,u1_struct_0(k2_analoaf(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_analoaf(A))) => B = C ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(k2_analoaf(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_analoaf(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_analoaf(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_analoaf(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_analoaf(A))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k2_analoaf(A))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k2_analoaf(A))) => ! [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] : ( m1_subset_1(B,u1_struct_0(k2_analoaf(A))) & ? [C] : ( m1_subset_1(C,u1_struct_0(k2_analoaf(A))) & ? [D] : ( m1_subset_1(D,u1_struct_0(k2_analoaf(A))) & ? [E] : ( 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] : ( m1_subset_1(B,u1_struct_0(k2_analoaf(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_analoaf(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_analoaf(A))) => ? [E] : ( 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] : ( m1_subset_1(B,u1_struct_0(k2_analoaf(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_analoaf(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_analoaf(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_analoaf(A))) => ~ ( B != D & r2_analoaf(k2_analoaf(A),D,B,B,E) & ! [F] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t23_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => r2_analort(A,E,F,B,C,D,D) ) ) ) ) ) ) )).
fof(t23_anproj_1,axiom,( ! [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) & 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) ) ) )).
fof(t23_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_anproj_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_anproj_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_anproj_1(A))) => ( r1_collsp(k5_anproj_1(A),B,C,D) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t23_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : k10_xtuple_0(k7_aofa_a00(A,B,C,D,E,F,G)) = k5_enumset1(A,B,C,D,E,F,G) )).
fof(t23_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ( k1_msualg_1(A,D) = k2_finseq_4(u1_struct_0(A),B,C) => ! [E] : ( l3_msualg_1(E,A) => k3_msualg_1(A,D,E) = k4_card_3(k2_finseq_4(k10_xtuple_0(u3_msualg_1(A,E)),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,E),B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,E),C))) ) ) ) ) ) ) )).
fof(t23_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m2_aofa_i00(E,A,B,C,D) => ! [F] : ( m3_aofa_i00(F,A,B,C,D) => r2_hidden(k44_aofa_i00(A,B,C,D,E,F),k18_aofa_000(A)) ) ) ) ) ) ) )).
fof(t23_armstrng,axiom,( ! [A] : ( l1_armstrng(A) => v6_armstrng(k5_armstrng(A),u1_armstrng(A)) ) )).
fof(t23_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => k1_arytm_0(A,k1_arytm_0(B,C)) = k1_arytm_0(k1_arytm_0(A,B),C) ) ) ) )).
fof(t23_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ~ ( ~ r1_arytm_2(B,A) & ~ r1_arytm_2(B,C) & k2_arytm_1(A,k1_arytm_1(B,C)) != k2_arytm_1(C,k1_arytm_1(B,A)) ) ) ) ) )).
fof(t23_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ( r1_arytm_3(A,B) => k4_arytm_3(A,B) = A ) ) ) )).
fof(t23_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v4_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v4_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) & k1_seq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) = k5_numbers ) => ( r2_hidden(B,k7_asympt_0(A)) & ~ r2_hidden(A,k7_asympt_0(B)) ) ) ) ) )).
fof(t23_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(B,1) => k9_nat_1(k1_numbers,A,B) = k7_xcmplx_0(k5_series_1(B,2),k3_power(2,B)) ) ) & ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v4_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( r2_funct_2(k4_ordinal1,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)) ) ) ) ) )).
fof(t23_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t23_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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 ) ) )).
fof(t23_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) )).
fof(t23_bcialg_1,axiom,( ! [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) ) => r2_hidden(k4_struct_0(A),k5_bcialg_1(A)) ) )).
fof(t23_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v10_bcialg_1(B,A) <=> ! [C] : ( 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)) ) ) ) ) )).
fof(t23_bcialg_3,axiom,( ! [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) & v6_bcialg_3(A) & l2_bcialg_1(A) ) => ( v7_bcialg_3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v2_bcialg_3(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t23_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) )).
fof(t23_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( 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 ) ) ) ) ) )).
fof(t23_bcialg_6,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => k3_bcialg_6(A,D,k3_bcialg_6(A,C,B)) = k3_bcialg_6(A,k3_xcmplx_0(C,D),B) ) ) ) ) )).
fof(t23_bciideal,axiom,( ! [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) ) => ( v3_bciideal(k4_bcialg_1(A),A) & m2_bcialg_1(k4_bcialg_1(A),A) ) ) )).
fof(t23_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_bhsp_1(A,B,k4_struct_0(A)) ) ) )).
fof(t23_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_bhsp_2(C,A) & k1_bhsp_2(A,C) = B ) => v2_comseq_2(k3_bhsp_2(A,C,B)) ) ) ) ) )).
fof(t23_bhsp_4,axiom,( ! [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_bhsp_1(A) & v3_bhsp_3(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_bhsp_4(B,A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & ? [F] : ( v7_ordinal1(F) & 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)))) ) ) ) ) ) ) ) ) )).
fof(t23_bilinear,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t23_binari_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t23_binari_4,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => k1_binari_4(A,1) = A ) ) )).
fof(t23_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k1_funct_1(k8_binom(A,B,C,D),1) = k2_binom(A,B,D) ) ) ) ) )).
fof(t23_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree2(A) ) => k1_funct_1(k2_bintree2(A,1),2) = k10_binarith(k4_ordinal1,1) ) )).
fof(t23_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t23_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t23_borsuk_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)))) ) ) ) ) ) ) )).
fof(t23_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ! [C] : ( v1_xreal_0(C) => ( ( r2_hidden(C,B) & B = A ) => ( r1_xxreal_0(k3_seq_4(B),C) & r1_xxreal_0(C,k2_seq_4(B)) ) ) ) ) ) )).
fof(t23_borsuk_5,axiom,( ! [A] : ( v1_rat_1(A) => ! [B] : ( ( v1_xreal_0(B) & ~ v1_rat_1(B) ) => ~ ( A != k5_numbers & v1_rat_1(k7_xcmplx_0(A,B)) ) ) ) )).
fof(t23_borsuk_6,axiom,( 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)))) )).
fof(t23_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k1_borsuk_7(A,A,B,C,D,E) = k4_funct_4(A,B,D,E) )).
fof(t23_bspace,axiom,( ! [A] : v4_rlvect_1(k7_bspace(A)) )).
fof(t23_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(t23_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t23_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t23_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t23_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t23_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t23_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(E,A) => ( r3_bvfunc_2(A,D,B,E) => r2_funct_2(A,k6_margrel1,k6_bvfunc_2(A,k5_bvfunc_1(A,C,D),B,E),k5_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),D)) ) ) ) ) ) ) )).
fof(t23_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t23_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t23_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t23_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t23_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t23_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t23_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t23_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k11_c0sp1(A))) => k1_binop_1(k5_c0sp1(k12_funcsdom(A),k6_c0sp1(A)),1,B) = B ) ) )).
fof(t23_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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))) ) ) ) )).
fof(t23_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_valuat_1(D,A,C) => ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t23_calcul_2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t23_card_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r1_tarski(A,B) & r1_tarski(B,C) & r2_wellord2(A,C) ) => ( r2_wellord2(A,B) & r2_wellord2(B,C) ) ) )).
fof(t23_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(A,B) => r1_tarski(k2_card_3(A),k2_card_3(B)) ) ) ) )).
fof(t23_card_5,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => k1_card_5(k2_card_1(A)) = k2_card_1(A) ) )).
fof(t23_card_fil,axiom,( ! [A] : ( ~ v1_finset_1(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t23_card_fin,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( k5_relat_1(A,k8_relat_1(B,k1_tarski(C))) = k7_funcop_1(k8_relat_1(B,k1_tarski(C)),k3_tarski(k10_xtuple_0(A))) => k2_card_fin(A,B,C) = k3_tarski(k10_xtuple_0(A)) ) ) ) )).
fof(t23_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t23_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( m1_subset_1(E,u4_struct_0(B)) => ! [F] : ( 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(k6_cat_2(A,B),k8_cat_2(A,B,C,E),k8_cat_2(A,B,D,F)) = k8_cat_2(A,B,k1_cat_1(A,C,D),k1_cat_1(B,E,F)) ) ) ) ) ) ) ) )).
fof(t23_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_cat_1(D,A,B,C) => ( v2_cat_3(D,A,B,C) => v7_cat_1(D,A,B,C) ) ) ) ) ) )).
fof(t23_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( k2_cat_1(A,D,B) != k1_xboole_0 & k2_cat_1(A,D,C) != k1_xboole_0 & k2_cat_1(A,D,k2_cat_4(A,B,C)) = k1_xboole_0 ) ) ) ) ) )).
fof(t23_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( r2_hidden(C,k9_cat_5(A,B)) <=> k4_graph_1(A,C) = B ) ) ) ) )).
fof(t23_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => k2_catalan2(A,k5_numbers) = k6_domain_1(k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1)),k8_funcop_1(k4_ordinal1,A,k5_numbers)) ) )).
fof(t23_catalg_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t23_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v3_algstr_0(k5_cayldick(A,B,C),k4_cayldick(A)) => ( v3_algstr_0(B,A) & v3_algstr_0(C,A) ) ) ) ) ) )).
fof(t23_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k7_cc0sp1(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k7_cc0sp1(A))) => ( ( C = E & D = F ) => ( F = k1_clvect_1(k7_cc0sp1(A),E,B) <=> ! [G] : ( m1_subset_1(G,A) => k3_funct_2(A,k2_numbers,D,G) = k3_xcmplx_0(B,k3_funct_2(A,k2_numbers,C,G)) ) ) ) ) ) ) ) ) ) )).
fof(t23_cc0sp2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v1_compts_1(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k5_cc0sp2(B))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k5_cc0sp2(B))) => ( ( C = E & D = F ) => ( F = k1_clvect_1(k5_cc0sp2(B),E,A) <=> ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t23_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v2_comseq_2(A) => ( ! [C] : ( v7_ordinal1(C) => ~ r2_relset_1(k4_ordinal1,k2_numbers,A,k1_valued_0(k2_numbers,B,C)) ) | k3_comseq_2(B) = k3_comseq_2(A) ) ) ) ) )).
fof(t23_cfdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [C] : ( v1_xcmplx_0(C) => ( ( 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) = k2_xcmplx_0(k2_cfdiff_1(A,C),k2_cfdiff_1(B,C)) ) ) ) ) ) )).
fof(t23_cfuncdom,axiom,( ? [A] : ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => ( k3_rlvect_1(A,k1_clvect_1(A,B,D),k1_clvect_1(A,C,E)) = k4_struct_0(A) => ( D = k5_numbers & E = k5_numbers ) ) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( v1_xcmplx_0(E) & ? [F] : ( v1_xcmplx_0(F) & D = k3_rlvect_1(A,k1_clvect_1(A,B,E),k1_clvect_1(A,C,F)) ) ) ) ) ) ) )).
fof(t23_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( v1_xcmplx_0(D) => 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))) ) ) ) ) )).
fof(t23_cgames_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t23_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ( ~ ! [E] : ( m2_subset_1(E,k4_ordinal1,k2_finseq_1(A)) => r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) => ( r2_hidden(D,k3_chain_1(A,B,C)) <=> ? [E] : ( m2_subset_1(E,k4_ordinal1,k2_finseq_1(A)) & ~ r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(C,E)) & ( r1_xxreal_0(k1_funct_1(D,E),k1_funct_1(C,E)) | r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(D,E)) ) ) ) ) ) ) ) ) )).
fof(t23_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) ) => ! [C] : ( m2_glib_000(C,A,B,k21_glib_000(A,B)) => ! [D] : ( m3_glib_001(D,A) => ( r1_tarski(k13_glib_001(A,D),B) => m3_glib_001(D,C) ) ) ) ) ) )).
fof(t23_circcmb2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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] : ( v7_ordinal1(G) => ! [H] : ( m1_subset_1(H,k4_card_3(u3_msualg_1(C,F))) => ! [I] : ( m1_subset_1(I,k4_card_3(u3_msualg_1(A,D))) => ( I = k5_relat_1(H,u1_struct_0(A)) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t23_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => m1_subset_1(C,u1_struct_0(k2_circcomb(A,B))) ) ) ) )).
fof(t23_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_msualg_1(C) ) => ! [D] : ( ( v4_msualg_1(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t23_circled1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 | ( k3_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(k5_numbers,k3_funct_2(u1_struct_0(A),k1_numbers,D,B)) & r1_xxreal_0(k5_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))) ) ) ) ) ) ) ) )).
fof(t23_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t23_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_pdiff_7(C,A) & m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) ) => k4_struct_0(k2_ckspace1(A,B,C)) = k8_funcop_1(k4_ordinal1,C,k5_numbers) ) ) ) )).
fof(t23_classes1,axiom,( ! [A] : ( v1_ordinal1(A) => v1_ordinal1(k1_classes1(A)) ) )).
fof(t23_classes2,axiom,( ! [A] : ! [B] : ( ~ ( ~ ( 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)) ) )).
fof(t23_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k9_clopban1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_clopban1(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_clopban1(A,B))) => ( E = k3_rlvect_1(k9_clopban1(A,B),C,D) <=> ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t23_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => k5_struct_0(k9_clopban2(A)) = k6_clopban2(A) ) )).
fof(t23_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_seq_2(k3_series_1(k5_normsp_0(A,B))) <=> v2_clopban3(B,A) ) ) ) )).
fof(t23_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v7_ordinal1(D) => k1_normsp_1(A,k1_clopban4(A,C),D) = k1_normsp_1(A,k3_clopban4(D,A,C,B),D) ) ) ) ) )).
fof(t23_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m2_pboole(C,A,k5_mssubfam(A,B),k5_mssubfam(A,B)) => ! [D] : ( 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) ) ) ) ) )).
fof(t23_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) => ! [D] : ( m1_closure2(D,A,B,k2_closure2(A,B)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t23_clvect_1,axiom,( ! [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) ) => v6_clvect_1(k6_domain_1(u1_struct_0(A),k4_struct_0(A)),A) ) )).
fof(t23_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_clvect_2(C,A) & k1_clvect_2(A,C) = B ) => v2_comseq_2(k3_clvect_2(A,C,B)) ) ) ) ) )).
fof(t23_clvect_3,axiom,( ! [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) & v2_csspace(A) & v4_clvect_2(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clvect_3(B,A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & ? [F] : ( v7_ordinal1(F) & 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)))) ) ) ) ) ) ) ) ) )).
fof(t23_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_coh_sp(A)) => ! [C] : ( m1_subset_1(C,k5_coh_sp(A)) => ! [D] : ( m1_subset_1(D,k5_coh_sp(A)) => ( ( k6_coh_sp(A,C) = k7_coh_sp(A,B) & k6_coh_sp(A,D) = k7_coh_sp(A,C) ) => k9_coh_sp(A,k9_coh_sp(A,B,C),D) = k9_coh_sp(A,B,k9_coh_sp(A,C,D)) ) ) ) ) )).
fof(t23_cohsp_1,axiom,( ! [A] : ( ( 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] : ! [C] : ~ ( r2_hidden(B,k9_xtuple_0(A)) & r2_hidden(C,k1_funct_1(A,B)) & ! [D] : ~ ( r2_hidden(D,B) & r2_hidden(C,k1_funct_1(A,k1_tarski(D))) & ! [E] : ( ( r1_tarski(E,B) & r2_hidden(C,k1_funct_1(A,E)) ) => r2_hidden(D,E) ) ) ) ) ) ) ) )).
fof(t23_combgras,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ( ( r1_xxreal_0(2,A) & r1_ordinal1(k1_nat_1(A,2),k1_card_1(B)) ) => ! [C] : ( l1_combgras(C,k1_combgras(A,B),k1_combgras(A,B)) => ( v7_combgras(C,k1_combgras(A,B)) => ! [D] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t23_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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] : ( ( v2_relat_1(D) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & v5_compl_sp(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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] : ( v7_ordinal1(E) => ? [F] : ( m1_subset_1(F,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & k9_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) ) ) ) ) ) ) ) ) )).
fof(t23_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k3_complex1(A) = k5_numbers => ( k4_complex1(A) = k5_numbers | ( k3_complex1(k5_xcmplx_0(A)) = k5_numbers & k4_complex1(k5_xcmplx_0(A)) = k1_real_1(k2_real_1(k4_complex1(A))) ) ) ) ) )).
fof(t23_complex2,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ( A != k5_numbers => ( k19_sin_cos(k1_comptrig(k4_xcmplx_0(A))) = k4_xcmplx_0(k19_sin_cos(k1_comptrig(A))) & k17_sin_cos(k1_comptrig(k4_xcmplx_0(A))) = k4_xcmplx_0(k17_sin_cos(k1_comptrig(A))) ) ) ) )).
fof(t23_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => k3_vectsp_1(k1_complfld,A,k5_struct_0(k1_complfld)) = A ) )).
fof(t23_complsp2,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,k8_complex1(A)) = k3_xcmplx_0(k3_xcmplx_0(2,k4_complex1(A)),k7_complex1) ) )).
fof(t23_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) ) ) )).
fof(t23_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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)) ) ) ) )).
fof(t23_comptrig,axiom,( v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k16_sin_cos,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(t23_compts_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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))))) ) ) ) )).
fof(t23_comput_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k4_ordinal1) => ( r1_tarski(k1_relset_1(k3_finseq_2(A),B),k4_finseq_2(C,A)) => k19_margrel1(B) = C ) ) ) ) )).
fof(t23_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,k31_valued_1(k4_ordinal1,k2_numbers,B)),k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)) ) ) )).
fof(t23_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v9_ordinal1(A) => ( k3_comseq_2(A) = k5_complex1 | v2_comseq_2(k36_valued_1(k4_ordinal1,k2_numbers,A)) ) ) ) )).
fof(t23_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( v7_ordinal1(B) => ( r2_funct_2(k4_ordinal1,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(k4_ordinal1,k1_numbers,k1_valued_0(k1_numbers,k8_comseq_3(A),B),k8_comseq_3(k1_valued_0(k2_numbers,A,B))) ) ) ) )).
fof(t23_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(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) ) ) )).
fof(t23_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => ( v2_connsp_1(C,A) <=> v2_connsp_1(D,B) ) ) ) ) ) ) )).
fof(t23_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_hidden(B,k1_connsp_2(A,B)) ) ) )).
fof(t23_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ! [C] : ( 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) ) ) ) )).
fof(t23_convex1,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ~ ( v2_convex1(B,A) & B = k4_rlvect_2(A) ) ) ) )).
fof(t23_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_convex4(B,A) => r1_convex4(A,k5_convex4(A,B,k2_convex4(A)),B) ) ) )).
fof(t23_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t23_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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) ) ) )).
fof(t23_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ! [D] : ( m2_finseq_1(D,k2_zfmisc_1(k3_cqc_lang(A),k2_cqc_the1)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t23_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t23_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => r4_cqc_the3(A,B,k1_cqc_the1(A,B)) ) ) )).
fof(t23_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t23_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t23_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(t23_descip_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,A) => ! [I] : ( m1_subset_1(I,A) => ! [J] : ( m1_subset_1(J,A) => ! [K] : ( m1_subset_1(K,A) => ! [L] : ( m1_subset_1(L,A) => ! [M] : ( m1_subset_1(M,A) => ! [N] : ( m1_subset_1(N,A) => ! [O] : ( m1_subset_1(O,A) => ! [P] : ( m1_subset_1(P,A) => ! [Q] : ( m1_subset_1(Q,A) => ! [R] : ( m1_subset_1(R,A) => ! [S] : ( m1_subset_1(S,A) => ! [T] : ( m1_subset_1(T,A) => ! [U] : ( m1_subset_1(U,A) => ! [V] : ( m1_subset_1(V,A) => ! [W] : ( m1_subset_1(W,A) => ! [X] : ( m1_subset_1(X,A) => ! [Y] : ( m1_subset_1(Y,A) => ! [Z] : ( m1_subset_1(Z,A) => ! [A1] : ( m1_subset_1(A1,A) => ! [B1] : ( m1_subset_1(B1,A) => ! [C1] : ( m1_subset_1(C1,A) => ! [D1] : ( m1_subset_1(D1,A) => ! [E1] : ( m1_subset_1(E1,A) => ! [F1] : ( m1_subset_1(F1,A) => ! [G1] : ( m1_subset_1(G1,A) => ! [H1] : ( m1_subset_1(H1,A) => ! [I1] : ( m1_subset_1(I1,A) => ! [J1] : ( m1_subset_1(J1,A) => ! [K1] : ( m1_subset_1(K1,A) => ! [L1] : ( m1_subset_1(L1,A) => ! [M1] : ( m1_subset_1(M1,A) => ! [N1] : ( m1_subset_1(N1,A) => ! [O1] : ( m1_subset_1(O1,A) => ! [P1] : ( m1_subset_1(P1,A) => ! [Q1] : ( m1_subset_1(Q1,A) => ! [R1] : ( m1_subset_1(R1,A) => ! [S1] : ( m1_subset_1(S1,A) => ! [T1] : ( m1_subset_1(T1,A) => ! [U1] : ( m1_subset_1(U1,A) => ! [V1] : ( m1_subset_1(V1,A) => ! [W1] : ( m1_subset_1(W1,A) => ? [X1] : ( m2_finseq_1(X1,A) & v3_card_1(X1,48) & k1_funct_1(X1,1) = B & k1_funct_1(X1,2) = C & k1_funct_1(X1,3) = D & k1_funct_1(X1,4) = E & k1_funct_1(X1,5) = F & k1_funct_1(X1,6) = G & k1_funct_1(X1,7) = H & k1_funct_1(X1,8) = I & k1_funct_1(X1,9) = J & k1_funct_1(X1,10) = K & k1_funct_1(X1,11) = L & k1_funct_1(X1,12) = M & k1_funct_1(X1,13) = N & k1_funct_1(X1,14) = O & k1_funct_1(X1,15) = P & k1_funct_1(X1,16) = Q & k1_funct_1(X1,17) = R & k1_funct_1(X1,18) = S & k1_funct_1(X1,19) = T & k1_funct_1(X1,20) = U & k1_funct_1(X1,21) = V & k1_funct_1(X1,22) = W & k1_funct_1(X1,23) = X & k1_funct_1(X1,24) = Y & k1_funct_1(X1,25) = Z & k1_funct_1(X1,26) = A1 & k1_funct_1(X1,27) = B1 & k1_funct_1(X1,28) = C1 & k1_funct_1(X1,29) = D1 & k1_funct_1(X1,30) = E1 & k1_funct_1(X1,31) = F1 & k1_funct_1(X1,32) = G1 & k1_funct_1(X1,33) = H1 & k1_funct_1(X1,34) = I1 & k1_funct_1(X1,35) = J1 & k1_funct_1(X1,36) = K1 & k1_funct_1(X1,37) = L1 & k1_funct_1(X1,38) = M1 & k1_funct_1(X1,39) = N1 & k1_funct_1(X1,40) = O1 & k1_funct_1(X1,41) = P1 & k1_funct_1(X1,42) = Q1 & k1_funct_1(X1,43) = R1 & k1_funct_1(X1,44) = S1 & k1_funct_1(X1,45) = T1 & k1_funct_1(X1,46) = U1 & k1_funct_1(X1,47) = V1 & k1_funct_1(X1,48) = W1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t23_dickson,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v3_dickson(A) => ( ( v16_waybel_0(A) & v1_wellfnd1(k5_dickson(A)) ) <=> ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => k1_card_1(k6_dickson(A,B)) = 1 ) ) ) ) )).
fof(t23_diff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( ( 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_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,D,E),B),k1_nat_1(A,1)),C) = k6_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(D,B),k1_nat_1(A,1)),C),k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(E,B),k1_nat_1(A,1)),C)) ) ) ) ) ) )).
fof(t23_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( r2_zfmisc_1(A,B,C,D) => k11_diff_1(k1_fcont_1(E,F),A,B,C,D) = k5_numbers ) ) ) ) ) ) ) )).
fof(t23_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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,k6_xcmplx_0(B,k7_xcmplx_0(A,2)),k2_xcmplx_0(B,k7_xcmplx_0(A,2))) = k7_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(C,A),1),B),A) ) ) ) )).
fof(t23_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(B,k1_relset_1(k1_numbers,k26_sin_cos)) & r2_hidden(k2_xcmplx_0(B,A),k1_relset_1(k1_numbers,k26_sin_cos)) ) => k1_funct_1(k3_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k26_sin_cos),k18_sin_cos),A),B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k16_sin_cos),k2_xcmplx_0(B,A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k16_sin_cos),B)) ) ) ) )).
fof(t23_dilworth,axiom,( ! [A] : ( ( v4_dilworth(A) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t23_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t23_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m2_finseq_2(B,A,k3_finseq_2(A)) => ! [C] : ( ( 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_relat_1(k1_partfun1(k4_ordinal1,A,A,k6_margrel1,B,k1_bvfunc_1(A,C)),k8_margrel1) = k7_subset_1(k4_ordinal1,k4_finseq_1(B),k10_relat_1(k1_partfun1(k4_ordinal1,A,A,k6_margrel1,B,C),k8_margrel1)) ) ) ) )).
fof(t23_domain_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) => k8_mcart_1(A,B,C,D) = a_4_1_domain_1(A,B,C,D) ) ) ) ) )).
fof(t23_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v2_finsub_1(B) => v2_finsub_1(k5_dynkin(A,B)) ) ) ) )).
fof(t23_e_siec,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t23_ec_pf_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(C))) => ( D = k4_nat_d(B,C) => k2_binom(k9_int_3(C),D,A) = k4_nat_d(k1_newton(B,A),C) ) ) ) ) ) )).
fof(t23_ec_pf_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k9_int_3(C))) => ( ( D = k5_int_1(A,C) & E = k5_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) ) ) ) ) ) ) ) )).
fof(t23_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k2_ens_1(A)) => m1_subset_1(B,u4_struct_0(k11_ens_1(A))) ) ) )).
fof(t23_entropy1,axiom,( ! [A] : ( ( v1_matrprob(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( ( v1_matrprob(B) & m2_finseq_1(B,k1_numbers) ) => v4_matrprob(k6_matrixr1(k9_matrixr1(A),k10_matrixr1(B))) ) ) )).
fof(t23_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : 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)) )).
fof(t23_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( 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) ) ) ) )).
fof(t23_equation,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v3_msualg_1(C,A) & v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m1_msafree(D,A,B) => ! [E] : ( ( v2_relat_1(E) & m1_msafree(E,A,C) ) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t23_euclid,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ? [B] : ( m1_subset_1(B,k1_numbers) & ? [C] : ( m1_subset_1(C,k1_numbers) & A = k10_finseq_1(B,C) ) ) ) )).
fof(t23_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(A))) => k22_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) = k2_xcmplx_0(k3_xcmplx_0(B,k22_rvsum_1(D,F)),k3_xcmplx_0(C,k22_rvsum_1(E,F))) ) ) ) ) ) ) )).
fof(t23_euclid_3,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( ( k3_finseq_1(A) = 2 & B = A ) => k12_euclid(B) = k12_euclid(A) ) ) ) )).
fof(t23_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => k22_rvsum_1(k6_euclid(A,B),C) = k4_xcmplx_0(k22_rvsum_1(B,C)) ) ) ) )).
fof(t23_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(3))) => ! [C] : ( 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)) ) ) ) )).
fof(t23_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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),k28_sin_cos) ) => ( r1_xxreal_0(k4_euclid_3(B,C,A),k28_sin_cos) & r1_xxreal_0(k4_euclid_3(C,A,B),k28_sin_cos) ) ) ) ) ) )).
fof(t23_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k1_euclid(A)) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k1_euclid(A)) => ( ( v2_funct_1(C) & r1_tarski(k2_relset_1(k4_ordinal1,C),k4_finseq_1(B)) & r2_relset_1(k4_ordinal1,k1_euclid(A),D,k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k1_euclid(A),C,B)) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k4_finseq_1(B)) => ( r2_hidden(E,k2_relset_1(k4_ordinal1,C)) | k1_funct_1(B,E) = k5_euclid(A) ) ) ) ) => k5_euclid_7(A,B) = k5_euclid_7(A,D) ) ) ) ) ) )).
fof(t23_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => k9_euclid(3,k4_euclid_8,A) = k1_euclid_8(k5_numbers,k5_numbers,A) ) )).
fof(t23_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(k14_euclid(A))) => ~ ( r2_hidden(C,B) & ! [D] : ( ( ~ v8_ordinal1(D) & m1_subset_1(D,k4_ordinal1) ) => ~ r1_tarski(k4_euclid_9(A,C,k7_xcmplx_0(1,D)),B) ) ) ) ) ) ) )).
fof(t23_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(E)) => ! [G] : ( 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,k2_xcmplx_0(A,C)),k9_euclid(E,G,k2_xcmplx_0(B,D))) ) ) ) ) ) ) ) )).
fof(t23_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t23_exchsort,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( ( 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 ) ) ) ) ) ) )).
fof(t23_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t23_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( ( v1_xreal_0(A) | v1_xreal_0(B) ) => r1_xxreal_0(k3_extreal1(k4_supinf_2(k3_extreal1(A),k3_extreal1(B))),k3_extreal1(k3_xxreal_3(A,B))) ) ) ) )).
fof(t23_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_circcomb(A) & v2_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_circcomb(B) & v2_circcomb(B) & l1_msualg_1(B) ) => k2_circcomb(A,B) = k2_circcomb(B,A) ) ) )).
fof(t23_facirc_2,axiom,( ! [A] : ! [B] : ! [C] : 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))) )).
fof(t23_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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(k5_numbers)) = k1_xboole_0 ) => v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k6_rfunct_1(k1_numbers,k1_numbers,B),A)) ) ) )).
fof(t23_fcont_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(k2_rcomp_1(B,A),k1_relset_1(k1_numbers,C)) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,k2_rcomp_1(B,A))) ) => ( ( ~ v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,C,k2_rcomp_1(B,A))) & ~ v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,C,k2_rcomp_1(B,A))) ) | v3_rcomp_1(k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,C,k2_rcomp_1(B,A)))) ) ) ) ) ) )).
fof(t23_fdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(D,E) = k2_xcmplx_0(k3_xcmplx_0(A,E),B) ) ) ) => ( r2_fdiff_1(D,C) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(k2_fdiff_1(D,C),E) = A ) ) ) ) ) ) ) ) )).
fof(t23_fdiff_10,axiom,( ! [A] : ( ( 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,k26_sin_cos,k18_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k18_sin_cos),A),B) = k4_xcmplx_0(k7_xcmplx_0(k17_sin_cos(k1_funct_1(k26_sin_cos,B)),k1_square_1(k1_funct_1(k18_sin_cos,B)))) ) ) ) ) ) )).
fof(t23_fdiff_11,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_fdiff_9),A),B) = k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k18_sin_cos,k1_funct_1(k1_sin_cos9,B)),k3_xcmplx_0(k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k1_sin_cos9,B))),k2_xcmplx_0(1,k1_square_1(B))))) ) ) ) ) ) )).
fof(t23_fdiff_2,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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))) ) ) ) ) ) )).
fof(t23_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k22_sin_cos,k1_taylor_1(2)),B))) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_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,k22_sin_cos,k1_taylor_1(2)),B),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(k2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_taylor_1(2)),B),A),C) = k3_xcmplx_0(2,k23_sin_cos(k3_xcmplx_0(2,C))) ) ) ) ) ) ) )).
fof(t23_fdiff_7,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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(k7_xcmplx_0(1,2)))))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) & B = k47_valued_1(k1_numbers,k1_numbers,k1_numbers,C,D) & D = k1_taylor_1(2) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,A) => ( k1_funct_1(C,E) = 1 & ~ r1_xxreal_0(k1_funct_1(B,E),k5_numbers) & E != k5_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(k7_xcmplx_0(1,2)))),A) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,A) => k1_funct_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(k7_xcmplx_0(1,2)))),A),E) = k1_funct_1(k1_sin_cos6,E) ) ) ) ) ) ) ) ) )).
fof(t23_fdiff_8,axiom,( ! [A] : ( ( 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,k26_sin_cos,k6_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos)))) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( k6_xcmplx_0(1,k1_funct_1(k16_sin_cos,B)) != k5_numbers & k2_xcmplx_0(1,k1_funct_1(k16_sin_cos,B)) != k5_numbers ) ) ) ) => ( r2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k6_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k6_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos)),A),B) = k7_xcmplx_0(1,k2_xcmplx_0(1,k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t23_fdiff_9,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(k18_sin_cos,B),k1_square_1(k1_funct_1(k16_sin_cos,B))),k1_square_1(k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t23_ff_siec,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t23_fib_num2,axiom,( k1_pre_ff(4) = 3 )).
fof(t23_fib_num4,axiom,( ! [A] : ( 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)) ) ) ) )).
fof(t23_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ! [D] : ( m1_finseq_1(D,A) => ! [E] : ( m1_finseq_1(E,A) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t23_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t23_filter_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t23_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v18_lattices(B,A) & v21_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r2_hidden(C,B) ) ) ) )).
fof(t23_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t23_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(k1_nat_1(k3_finseq_1(A),1),C) & r1_xxreal_0(C,k1_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))) ) ) ) ) )).
fof(t23_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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) ) ) ) )).
fof(t23_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_hidden(B,k1_relset_1(k4_ordinal1,A)) => m1_subset_1(B,k4_ordinal1) ) ) )).
fof(t23_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_hidden(B,k10_xtuple_0(A)) => r2_hidden(k4_finseq_4(A,B),k8_relat_1(A,k1_tarski(B))) ) ) )).
fof(t23_finseq_5,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => k17_finseq_1(A,k3_finseq_1(B),k8_finseq_1(A,B,C)) = B ) ) )).
fof(t23_finseq_6,axiom,( ! [A] : ! [B] : ! [C] : ~ ( A != C & B != C & k4_finseq_4(k11_finseq_1(A,B,C),C) != 3 ) )).
fof(t23_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => k2_finseq_7(A,k2_finseq_4(A,B,C),1,2) = k2_finseq_4(A,C,B) ) ) ) )).
fof(t23_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r4_finseq_8(A,B,C) => r1_xxreal_0(k3_finseq_1(C),k3_finseq_1(B)) ) ) ) ) )).
fof(t23_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( ( 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))) ) => ! [G] : ( ( v3_card_1(G,E) & m2_finseq_1(G,A) ) => k4_funcop_1(F,G,D) = k3_relat_1(G,k4_funcop_1(F,k6_partfun1(A),D)) ) ) ) ) ) ) ) )).
fof(t23_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k12_fintopo2(A,C)) <=> ( r2_hidden(B,C) & ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t23_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t23_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( v7_ordinal1(C) => k7_flang_1(A,B,k1_nat_1(C,1)) = k6_flang_1(A,k7_flang_1(A,B,C),B) ) ) )).
fof(t23_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( ( r1_xxreal_0(E,C) & r1_xxreal_0(D,F) ) => r1_tarski(k1_flang_2(A,B,C,D),k1_flang_2(A,B,E,F)) ) ) ) ) ) ) )).
fof(t23_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( 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) ) ) )).
fof(t23_fomodel0,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( 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)) ) ) )).
fof(t23_fomodel2,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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] : ( ( 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 = k37_fomodel2(B,D) & C = k38_fomodel2(B,D) ) ) ) ) ) ) ) )).
fof(t23_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v4_frechet(A) => ( v3_frechet(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) ) )).
fof(t23_fscirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ~ v1_facirc_1(k2_msafree2(k8_fscirc_1(A,B,C))) ) ) ) )).
fof(t23_fscirc_2,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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] : ( 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)) ) ) )).
fof(t23_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t23_fsm_2,axiom,( ! [A] : ( ( ~ 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] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(C,B) => k1_funct_1(u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(B,C))) = B ) ) ) & ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,B) => k1_funct_1(u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(B,C))) = C ) ) ) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( 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),k4_xxreal_0(B,C)) ) ) ) ) )).
fof(t23_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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) ) ) ) ) ) )).
fof(t23_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t23_funcsdom,axiom,( ? [A] : ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( k3_rlvect_1(A,k1_rlvect_1(A,B,D),k1_rlvect_1(A,C,E)) = k4_struct_0(A) => ( D = k5_numbers & E = k5_numbers ) ) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & D = k3_rlvect_1(A,k1_rlvect_1(A,B,E),k1_rlvect_1(A,C,F)) ) ) ) ) ) ) )).
fof(t23_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t23_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t23_funct_3,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(t23_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => k5_relat_1(k1_funct_4(A,B),k9_xtuple_0(B)) = B ) ) )).
fof(t23_funct_5,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) ) )).
fof(t23_funct_6,axiom,( ! [A] : ! [B] : ( A != k1_xboole_0 => ( k3_card_3(k7_funcop_1(A,B)) = B & k3_funct_6(k7_funcop_1(A,B)) = B ) ) )).
fof(t23_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t23_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t23_funct_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & v1_int_1(A) ) => v1_funct_9(k1_fdiff_9,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A)) ) )).
fof(t23_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_altcat_1(B) ) => ! [C] : ( ( v11_functor0(C,A,B) & l2_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t23_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t23_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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(C,B) & r1_fuzzy_1(C,D) ) => r1_fuzzy_1(C,k1_fuzzy_1(A,B,D)) ) ) ) ) ) )).
fof(t23_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D,C)),k1_fuzzy_1(A,k1_fuzzy_1(A,B,D),C)),k1_fuzzy_2(A,B,k6_fuzzy_1(A,D,C))) ) ) ) ) )).
fof(t23_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,k3_fuzzy_4(A,B,C,D,k4_fuzzy_2(B,C)),k4_fuzzy_2(A,C)) ) ) ) ) )).
fof(t23_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_fvaluat1(D,A) => ( v3_fvaluat1(A) => ( B = k4_struct_0(A) | C = k4_struct_0(A) | k3_funct_2(u1_struct_0(A),k6_numbers,D,k1_vectsp_2(A,B,C)) = k2_supinf_2(k3_funct_2(u1_struct_0(A),k6_numbers,D,k1_vectsp_2(A,C,B))) ) ) ) ) ) ) )).
fof(t23_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_algstr_0(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(A,u1_struct_0(C))) => ( ( r2_hidden(B,k2_finseq_1(A)) & D = k1_funct_1(E,B) ) => k1_funct_1(k6_fvsum_1(A,C,E),B) = k4_algstr_0(C,D) ) ) ) ) ) ) )).
fof(t23_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ 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) ) ) )).
fof(t23_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v4_vectsp_1(A) & l4_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),B) => ! [D] : ( m2_subset_1(D,u1_struct_0(A),B) => ( r4_gcd_1(A,C,D) => C = D ) ) ) ) ) )).
fof(t23_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v2_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( m1_genealg1(E,D) => ! [F] : ( m1_genealg1(F,D) => ( ( r1_xxreal_0(k3_finseq_1(E),B) & r1_xxreal_0(k3_finseq_1(E),C) ) => k9_genealg1(D,E,F,A,B,C) = k7_genealg1(D,E,F,A) ) ) ) ) ) ) ) )).
fof(t23_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r1_analmetr(A,E,F) & r2_geomtrap(A,E,F,D,B,D,C) ) => B = C ) ) ) ) ) ) ) )).
fof(t23_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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] : ( 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)) ) ) )).
fof(t23_gfacirc2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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)))) ) ) ) )).
fof(t23_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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 ) )).
fof(t23_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k1_relset_1(k4_ordinal1,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(k4_ordinal1,k6_glib_001(A,B))) ) ) ) ) ) )).
fof(t23_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(t23_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( m3_glib_001(B,A) => k10_glib_003(A,B) = k10_glib_003(A,k6_glib_001(A,B)) ) ) )).
fof(t23_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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] : ( 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_funct_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) ) ) ) ) ) ) ) )).
fof(t23_goboard1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( 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] : ( v7_ordinal1(D) => ~ ( r2_hidden(D,k2_finseq_1(k1_matrix_0(B))) & r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),C,A),k10_xtuple_0(k8_matrix_0(u1_struct_0(k15_euclid(2)),B,D))) ) ) ) ) ) ) )).
fof(t23_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_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_0(B),A) | k1_tops_1(k15_euclid(2),k3_goboard5(B,k3_finseq_1(B),A)) = a_2_3_goboard6(A,B) ) ) ) ) )).
fof(t23_goboard7,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k3_finseq_1(A)) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(A)) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(A)) & r1_xxreal_0(1,E) & r1_xxreal_0(E,k1_matrix_0(A)) & ~ r1_xboole_0(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1),C)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,D,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,k1_nat_1(D,1),E))) & ~ ( B = D & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1),C)) = k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,D,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,k1_nat_1(D,1),E)) ) & ~ ( B = k1_nat_1(D,1) & k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1),C)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,D,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,k1_nat_1(D,1),E))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,C)) ) & ~ ( k1_nat_1(B,1) = D & k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1),C)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,D,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,k1_nat_1(D,1),E))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),A,D,E)) ) ) ) ) ) ) ) )).
fof(t23_goboard9,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k3_finseq_1(A)) ) => r1_tarski(k1_tops_1(k15_euclid(2),k4_goboard5(A,B)),k3_goboard9(A)) ) ) ) )).
fof(t23_gobrd11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(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(k1_matrix_0(B),A) | k2_goboard5(B,A) = a_2_1_gobrd11(A,B) ) ) ) ) )).
fof(t23_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_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)) ) ) ) ) )).
fof(t23_gobrd14,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t23_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => r1_henmodel(A,B,k5_cqc_lang(A)) ) ) )).
fof(t23_gr_cy_1,axiom,( 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))) )).
fof(t23_gr_cy_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & v1_gr_cy_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( A = k5_group_4(A,k6_domain_1(u1_struct_0(A),B)) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & l3_algstr_0(C) ) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t23_gr_cy_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ( A != 2 => k4_nat_d(k1_gr_cy_3(A),k3_xcmplx_0(2,A)) = 1 ) ) )).
fof(t23_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ 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 ) ) ) ) )).
fof(t23_graph_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( A != B & ~ r1_xxreal_0(C,1) & ! [D] : ( ( 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 ) ) ) ) )).
fof(t23_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_card_1(k6_graph_3(A,B)) = k9_graph_1(A,B) ) ) )).
fof(t23_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t23_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t23_graphsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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(k5_numbers,k11_graphsp(A,B,C,D)) <=> ? [E] : ( r2_hidden(E,u4_struct_0(A)) & r1_graph_4(A,B,C,E) ) ) ) ) ) ) )).
fof(t23_grcat_1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( ( 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 ) ) ) ) )).
fof(t23_grfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( r1_tarski(B,A) & v2_funct_1(A) ) => k6_relat_1(k10_xtuple_0(B),A) = B ) ) ) )).
fof(t23_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v15_algstr_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( v15_algstr_0(D) & m1_group_2(D,A) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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))) ) ) ) ) ) ) ) )).
fof(t23_groeb_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ( r1_groeb_1(A,B,C,E) => ( r2_hidden(D,k7_ideal_1(k12_polynom1(A,C),E)) <=> r1_rewrite1(k3_polyred(A,B,C,E),D,k8_polynom1(A,C)) ) ) ) ) ) ) ) )).
fof(t23_groeb_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( r1_groeb_1(A,B,C,D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(G,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,k8_polynom1(A,C)) ) ) ) ) ) ) ) ) ) )).
fof(t23_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,k5_card_1(k3_polynom1(k15_pre_poly(A),C,D))) ) => r2_hidden(k3_termord(A,B,C,D),k3_groeb_3(A,B,C,D,E)) ) ) ) ) ) ) )).
fof(t23_group_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t23_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(t23_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ! [C] : ( 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 ) ) ) )).
fof(t23_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t23_group_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & l3_algstr_0(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t23_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t23_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ! [C] : ( ( v1_group_3(C,A) & m1_group_2(C,A) ) => ( r1_struct_0(k5_group_6(A,C),B) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & B = k13_group_2(A,C,D) & B = k14_group_2(A,C,D) ) ) ) ) )).
fof(t23_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t23_group_8,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => B = k1_group_1(A) ) ) ) )).
fof(t23_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v2_group_9(C,A) & v4_group_9(C,A,B) & m1_group_9(C,A,B) ) => ! [D] : ( ( v2_group_9(D,A) & v4_group_9(D,A,B) & m1_group_9(D,A,B) ) => ? [E] : ( 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)) ) ) ) ) )).
fof(t23_groupp_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v8_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_group_2(C,B) => ( v2_group_10(B,A) => r1_xxreal_0(k2_groupp_1(A,C),k2_groupp_1(A,B)) ) ) ) ) )).
fof(t23_hahnban,axiom,( ! [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) & 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))) ) ) )).
fof(t23_hahnban1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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))) ) ) ) )).
fof(t23_hallmar1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m2_finseq_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m3_hallmar1(D,A,B,C) => ~ ( r2_hidden(C,k4_finseq_1(B)) & k1_funct_1(D,C) = k1_xboole_0 ) ) ) ) ) )).
fof(t23_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t23_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ( k3_glib_001(A,B) = k3_glib_001(A,C) => ( r1_tarski(B,C) | r1_xxreal_0(k1_nat_1(k3_finseq_1(k1_helly(B,C)),2),k3_finseq_1(B)) ) ) ) ) ) )).
fof(t23_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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)) ) ) )).
fof(t23_heyting1,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(t23_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( ( 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)) ) ) )).
fof(t23_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_tarski(k2_heyting3(A,B),k2_heyting3(C,B)) => A = C ) ) ) ) )).
fof(t23_hfdiff_1,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t23_hilbasis,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t23_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) ) )).
fof(t23_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => k4_hilbert1(A,B) != k2_hilbert1 ) ) )).
fof(t23_hilbert3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ ( C = k1_xboole_0 & B != k1_xboole_0 & A != k1_xboole_0 ) => ! [D] : ( ( 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)))) ) ) ) )).
fof(t23_hurwitz,axiom,( ! [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) & v3_rlvect_1(A) & v4_rlvect_1(A) & v1_vectsp_2(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) )).
fof(t23_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( v1_int_2(k1_nat_1(k5_series_1(2,D),1)) & r1_idea_1(D,A) & r1_idea_1(D,B) & r1_idea_1(D,C) ) => k9_idea_1(D,k9_idea_1(D,A,B),C) = k9_idea_1(D,A,k9_idea_1(D,B,C)) ) ) ) ) ) )).
fof(t23_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_ideal_1(D,A,B) => m1_ideal_1(k9_fvsum_1(A,D,C),A,B) ) ) ) ) )).
fof(t23_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ~ ( ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & r1_incsp_1(A,D,B) & r1_incsp_1(A,D,C) ) & ! [D] : ( m1_subset_1(D,u4_incsp_1(A)) => ~ ( r3_incsp_1(A,B,D) & r3_incsp_1(A,C,D) ) ) ) ) ) ) )).
fof(t23_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( 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] : ( 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))) ) ) ) ) ) )).
fof(t23_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r3_pua2mss1(A,B,C,D) => ! [E] : ( l3_msualg_1(E,B) => ! [F] : ( m1_subset_1(F,u4_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t23_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( r1_xxreal_0(B,A) & r1_xxreal_0(C,A) ) => ( r1_xxreal_0(B,k6_xcmplx_0(A,1)) | r1_xxreal_0(C,k6_xcmplx_0(A,1)) | B = C ) ) ) ) ) )).
fof(t23_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ~ ( ~ ( A = k5_numbers & B = k5_numbers ) & ! [C] : ( v1_int_1(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t23_int_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(C,k5_numbers) => ( k4_nat_d(A,C) = k4_nat_d(B,C) <=> r1_int_1(C,k6_xcmplx_0(A,B)) ) ) ) ) ) )).
fof(t23_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t23_int_6,axiom,( ! [A] : ( ( 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) = k5_numbers ) )).
fof(t23_int_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => k7_group_1(k3_int_7(A)) = k6_xcmplx_0(A,1) ) )).
fof(t23_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r2_hidden(B,k1_relset_1(k4_ordinal1,k14_finseq_1(k2_int_8(A)))) & r2_hidden(C,k1_relset_1(k4_ordinal1,k14_finseq_1(k2_int_8(A)))) & B != C & r2_int_1(k1_funct_1(k14_finseq_1(k2_int_8(A)),B),k1_funct_1(k14_finseq_1(k2_int_8(A)),C),A) ) ) ) ) )).
fof(t23_integr11,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( B = k1_rcomp_1(k5_numbers,k3_xcmplx_0(2,k28_sin_cos)) => k2_integra5(B,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(A)),k16_sin_cos)) = k5_numbers ) ) ) )).
fof(t23_integr12,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( v3_rcomp_1(G) & m1_subset_1(G,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(C,G) & r1_tarski(G,k2_rcomp_1(k4_xcmplx_0(1),1)) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,G) => ( k1_funct_1(E,H) = k2_xcmplx_0(k3_xcmplx_0(A,H),B) & k1_funct_1(F,H) = 1 ) ) ) & G = k1_relset_1(k1_numbers,D) & r2_relset_1(k1_numbers,k1_numbers,D,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,E,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,F,k1_taylor_1(2)),k4_taylor_1(k7_xcmplx_0(1,2)))))) ) => k2_integra5(C,D) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,E,k1_sin_cos6),k2_seq_4(C)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,E,k1_sin_cos6),k3_seq_4(C))) ) ) ) ) ) ) ) ) )).
fof(t23_integr13,axiom,( ! [A] : ( ( 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,k27_sin_cos,k22_sin_cos))) => ( r2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k22_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k22_sin_cos)),A),B) = k7_xcmplx_0(k1_funct_1(k22_sin_cos,k1_funct_1(k27_sin_cos,B)),k1_square_1(k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t23_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k26_sin_cos) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k26_sin_cos,A)) ) => k2_integra5(A,k26_sin_cos) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fdiff_9,k3_taylor_1),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fdiff_9,k3_taylor_1),k3_seq_4(A))) ) ) ) )).
fof(t23_integr15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k1_euclid(A)))) ) => ! [E] : ( 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) ) ) ) ) )).
fof(t23_integr16,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k2_numbers))) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( B = k1_rcomp_1(D,C) => k4_xcmplx_0(k7_integr16(B,A)) = k8_integr16(C,D,A) ) ) ) ) ) )).
fof(t23_integr19,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( ~ v8_ordinal1(E) & m1_subset_1(E,k4_ordinal1) ) => ! [F] : ( ( 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))) ) ) ) ) ) ) ) ) )).
fof(t23_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [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))) ) => ( v2_seq_2(k2_partfun1(A,k1_numbers,C,A)) => r1_xxreal_0(k3_xcmplx_0(k3_seq_4(k1_rvsum_1(C)),k3_integra1(A)),k7_integra1(A,C,B)) ) ) ) ) )).
fof(t23_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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] : ( m1_integra1(E,C) => ( ( r2_hidden(B,k4_finseq_1(E)) & v1_seq_2(k2_partfun1(C,k1_numbers,D,C)) & r1_xxreal_0(k5_numbers,A) ) => k1_funct_1(k4_integra1(C,k26_valued_1(C,k1_numbers,D,A),E),B) = k3_xcmplx_0(A,k1_funct_1(k4_integra1(C,D,E),B)) ) ) ) ) ) ) )).
fof(t23_integra4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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_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(k9_complex1(k12_integra1(A,B)),k12_integra1(A,k56_valued_1(A,k1_numbers,B))) ) ) ) ) )).
fof(t23_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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] : ( v1_xreal_0(G) => ( r2_hidden(G,k3_integra5(C,D)) => r1_xxreal_0(k9_complex1(k1_funct_1(F,G)),E) ) ) ) => ( r1_xxreal_0(k9_complex1(k4_integra5(C,D,F)),k3_xcmplx_0(E,k6_xcmplx_0(D,C))) & r1_xxreal_0(k9_complex1(k4_integra5(D,C,F)),k3_xcmplx_0(E,k6_xcmplx_0(D,C))) ) ) ) ) ) ) ) ) )).
fof(t23_integra7,axiom,( r1_integra7(k1_numbers,k16_sin_cos,k18_sin_cos) )).
fof(t23_integra8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => k1_funct_1(k2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,A),B),C) = k4_xcmplx_0(k1_fdiff_1(A,C)) ) ) ) ) ) ) )).
fof(t23_integra9,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( ~ 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))) ) ) ) ) )).
fof(t23_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_interva1(C,A) ) => ! [D] : ( ( ~ 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))) ) ) ) ) )).
fof(t23_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) ) )).
fof(t23_irrat_1,axiom,( v1_series_1(k5_irrat_1) & k4_series_1(k5_irrat_1) = k23_sin_cos(1) )).
fof(t23_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ( r2_nattra_1(A,B,C,D) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t23_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(t23_jgraph_1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t23_jgraph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ~ ( v5_pre_topc(B,A,k3_topmetr) & ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t23_jgraph_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( 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 ) ) ) )).
fof(t23_jgraph_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r1_xxreal_0(k5_numbers,k17_euclid(B)) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) | r1_xxreal_0(1,A) | r1_xxreal_0(A,k7_xcmplx_0(k18_euclid(B),k12_euclid(B))) | k12_euclid(B) = k5_numbers | ! [C] : ( 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(k5_numbers,k17_euclid(C)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(C)) ) ) ) ) ) ) ) )).
fof(t23_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t23_jordan,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( ( ~ v8_ordinal1(C) & v1_xreal_0(C) ) => k2_pre_topc(k15_euclid(A),k1_topreal9(A,B,C)) = k2_topreal9(A,B,C) ) ) ) )).
fof(t23_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => m1_subset_1(a_4_2_jordan1(A,B,C,D),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ) ) ) )).
fof(t23_jordan12,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(D,k1_rltopsp1(k15_euclid(2),A,B)) & ? [E] : 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)) ) ) ) ) ) )).
fof(t23_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( 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_0(k1_jordan8(A,E))) & k7_partfun1(u1_struct_0(k15_euclid(2)),k1_jordan13(A,E),D) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,E),B,C) & r1_xxreal_0(k3_finseq_1(k1_jordan8(A,E)),B) ) ) ) ) ) ) )).
fof(t23_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & ~ r1_xxreal_0(A,k5_numbers) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E),k8_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k9_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k9_jordan6(B)) ) ) ) ) ) ) )).
fof(t23_jordan16,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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] : ( ( ~ 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)) ) ) ) ) ) ) ) ) )).
fof(t23_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t23_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( ~ 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_0(B)) ) => r1_xxreal_0(k8_pscomp_1(k3_topreal1(2,C)),k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B),A))) ) ) ) ) )).
fof(t23_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(k1_jordan8(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,k1_matrix_0(k1_jordan8(B,A))),k10_xtuple_0(k2_jordan9(B,A))) ) ) ) )).
fof(t23_jordan1g,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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)))) ) => r1_xxreal_0(k4_finseq_4(k1_jordan1e(B,A),k21_pscomp_1(k3_topreal1(2,k2_jordan9(B,A)))),k4_finseq_4(k1_jordan1e(B,A),k22_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))))) ) ) )).
fof(t23_jordan1h,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(B)) ) => k2_gobrd13(B,k2_goboard2(B),A) = k4_goboard5(B,A) ) ) ) )).
fof(t23_jordan1j,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) ) )).
fof(t23_jordan1k,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => k1_topreal6(2,k5_algstr_0(k15_euclid(2),B,A),k5_algstr_0(k15_euclid(2),C,A)) = k1_topreal6(2,B,C) ) ) ) )).
fof(t23_jordan20,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t23_jordan21,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [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) & 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) ) ) ) )).
fof(t23_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(k18_euclid(k1_jordan21(k8_jordan6(k3_topreal1(2,k2_jordan9(A,B))))),k18_euclid(k1_jordan21(A))) ) ) ) )).
fof(t23_jordan23,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t23_jordan2b,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k1_jordan2b(A) = k1_jordan2b(B) => A = B ) ) ) )).
fof(t23_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => k2_jordan2c(A,k1_struct_0(k15_euclid(A))) = k1_euclid(A) ) ) )).
fof(t23_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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] : ( v7_ordinal1(C) => ( r1_xxreal_0(C,k3_finseq_1(k2_jordan3(A,B))) => ( r1_xxreal_0(C,1) | ( ( B = k1_funct_1(A,k1_nat_1(k1_jordan3(A,B),1)) => k1_funct_1(k2_jordan3(A,B),C) = k1_funct_1(A,k2_xcmplx_0(k1_jordan3(A,B),C)) ) & ( B != k1_funct_1(A,k1_nat_1(k1_jordan3(A,B),1)) => k1_funct_1(k2_jordan3(A,B),C) = k1_funct_1(A,k6_xcmplx_0(k2_xcmplx_0(k1_jordan3(A,B),C),1)) ) ) ) ) ) ) ) ) ) )).
fof(t23_jordan4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( k1_jordan4(A,B) = k1_jordan4(k1_nat_1(A,k7_nat_d(k3_finseq_1(B),1)),B) & k1_jordan4(A,B) = k1_jordan4(k2_xcmplx_0(k7_nat_d(k3_finseq_1(B),1),A),B) ) ) ) )).
fof(t23_jordan5a,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ( A = B => ( v2_rcomp_1(A) <=> v4_pre_topc(B,k3_topmetr) ) ) ) ) )).
fof(t23_jordan5b,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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))) ) ) ) ) )).
fof(t23_jordan5c,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ( ( v4_topreal1(A) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_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,k1_nat_1(B,1))) ) ) ) )).
fof(t23_jordan5d,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( B = a_1_4_jordan5d(A) => k3_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))) ) ) ) )).
fof(t23_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) )).
fof(t23_jordan9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ~ ( r1_xxreal_0(2,k3_finseq_1(B)) & r1_xxreal_0(2,k1_matrix_0(B)) & r1_goboard1(u1_struct_0(k15_euclid(2)),C,B) & r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) & r2_hidden(D,k9_matrix_0(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,k1_nat_1(A,1)) ) ) ) ) ) )).
fof(t23_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_jordan_a(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(C,A) & ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(D,k4_finseq_1(B)) & r2_hidden(C,k2_jordan_a(A,D,B)) ) ) ) ) ) ) )).
fof(t23_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( 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] : ( v3_ordinal1(D) => r3_lattices(A,k6_knaster(A,B,C,D),C) ) ) ) ) ) )).
fof(t23_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & v3_kurato_0(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( r2_hidden(C,k4_kurato_0(A,B)) <=> ? [D] : ( v7_ordinal1(D) & ! [E] : ( v7_ordinal1(E) => r2_hidden(C,k1_funct_1(B,k2_xcmplx_0(D,E))) ) ) ) ) )).
fof(t23_kurato_1,axiom,( 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)) )).
fof(t23_kurato_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ! [D] : ( v7_ordinal1(D) => k2_kurato_2(A,B,D) = C ) => k1_kurato_2(A,B) = k2_pre_topc(A,C) ) ) ) ) )).
fof(t23_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(k11_group_4(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t23_latsum_1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t23_lattice2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t23_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t23_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v8_lattice6(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => C = k15_lattice3(A,a_3_0_lattice6(A,B,C)) ) ) ) ) )).
fof(t23_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m1_lattice5(D,A,B,C) => ! [E] : ( v3_ordinal1(E) => r1_relset_1(k2_zfmisc_1(A,A),u1_struct_0(B),C,k6_lattice8(A,B,C,D,E)) ) ) ) ) ) )).
fof(t23_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k4_lattices(A,C,B) = k5_lattices(A) <=> r3_lattices(A,C,k7_lattices(A,B)) ) ) ) ) )).
fof(t23_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( ( v4_lexbfs(B,A) & m1_lexbfs(B,A) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ! [E] : ( ( 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))))) ) ) ) ) ) )).
fof(t23_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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,k3_fuzzy_4(A,A,A,B,k4_fuzzy_4(A,A)),B) ) ) )).
fof(t23_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_limfunc1(A) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(C,k1_funct_1(B,D)) ) ) ) | v2_limfunc1(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).
fof(t23_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t23_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,C) & ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ~ ( ~ 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] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(k6_xcmplx_0(A,C),A))) & v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(A,k2_xcmplx_0(A,C)))) & ~ v2_seq_2(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(k6_xcmplx_0(A,C),A))) & ~ v2_seq_2(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(A,k2_xcmplx_0(A,C)))) ) ) | r3_limfunc3(B,A) ) ) ) ) )).
fof(t23_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(A,k2_xcmplx_0(A,D)))) & r1_xxreal_0(k1_funct_1(B,E),k2_limfunc2(B,A)) ) ) ) ) | r5_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t23_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t23_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t23_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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),k9_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k7_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B)),k8_rsspace(k8_lopban_1(A,B),k10_lopban_1(A,B))),k8_lopban_1(A,B)) ) ) )).
fof(t23_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => k5_struct_0(k9_lopban_2(A)) = k6_lopban_2(A) ) )).
fof(t23_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_seq_2(k3_series_1(k5_normsp_0(A,B))) <=> v2_lopban_3(B,A) ) ) ) )).
fof(t23_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v7_ordinal1(D) => k9_nat_1(u1_struct_0(A),k1_bhsp_4(A,k7_lopban_4(k1_nat_1(D,1),A,C,B)),D) = k3_rlvect_1(A,k9_nat_1(u1_struct_0(A),k1_bhsp_4(A,k7_lopban_4(D,A,C,B)),D),k9_nat_1(u1_struct_0(A),k1_bhsp_4(A,k6_lopban_4(k1_nat_1(D,1),A,C,B)),D)) ) ) ) ) )).
fof(t23_lopclset,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v7_struct_0(B) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B) ) => ( r2_hidden(A,k10_lopclset(B)) <=> ? [C] : ( 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 ) ) ) )).
fof(t23_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( r1_lpspacc1(A,B,C,D,E) => r1_lpspacc1(A,B,C,E,D) ) ) ) ) ) ) )).
fof(t23_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t23_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v2_xxreal_0(D) & v1_xreal_0(D) ) => ( v1_funct_1(k8_lpspace1(A,k5_numbers)) & m1_subset_1(k8_lpspace1(A,k5_numbers),k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) & r2_hidden(k8_lpspace1(A,k5_numbers),k1_lpspace2(A,B,C,D)) ) ) ) ) ) )).
fof(t23_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => ( r1_ltlaxio1(B,A) <=> r2_ltlaxio1(B,k6_domain_1(k1_hilbert1,A)) ) ) ) )).
fof(t23_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(k1_ltlaxio1(k3_ltlaxio1),A)) ) )).
fof(t23_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_hilbert1)) => ( r2_hidden(A,k5_ltlaxio3(B)) => r1_tarski(k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,A),k5_ltlaxio3(B)) ) ) ) )).
fof(t23_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ( ( r2_hidden(C,k9_ltlaxio4(B)) & r1_tarski(k10_ltlaxio3(B),k5_setfam_1(k1_hilbert1,k7_ltlaxio3(k10_ltlaxio3(A)))) ) => r1_tarski(k10_ltlaxio3(C),k5_setfam_1(k1_hilbert1,k7_ltlaxio3(k10_ltlaxio3(A)))) ) ) ) ) )).
fof(t23_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) )).
fof(t23_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) )).
fof(t23_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,B,B) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( v2_matrix10(C) => ( r1_xxreal_0(A,k5_numbers) | v2_matrix10(k6_matrix10(B,A,C)) ) ) ) ) ) )).
fof(t23_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_matrix_2(B,k3_matrix_2(k1_nat_1(A,2))) => ! [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,k2_matrix_2(k3_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,k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))) ) & ( ~ v5_matrix_2(B,k2_matrix_2(k3_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,k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))) ) ) ) ) ) )).
fof(t23_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( m1_subset_1(D,u1_struct_0(C)) => ( r2_hidden(A,k4_finseq_1(k3_matrix_1(C,B))) => ( D = k4_struct_0(C) | r1_xxreal_0(B,k5_numbers) | k1_matrix_6(B,C,k5_matrix12(B,B,C,k3_matrix_1(C,B),A,D)) = k5_matrix12(B,B,C,k3_matrix_1(C,B),A,k11_algstr_0(C,D)) ) ) ) ) ) ) )).
fof(t23_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(A)) ) => ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(C,k4_ordinal1)) => ! [F] : ( m2_finseq_2(F,k4_ordinal1,k4_finseq_2(B,k4_ordinal1)) => ( ( C = 2 & B = 2 ) => k1_matrix13(A,D,C,B,E,F) = k15_matrix_0(A,k3_matrix_0(A,D,k1_funct_1(E,1),k1_funct_1(F,1)),k3_matrix_0(A,D,k1_funct_1(E,1),k1_funct_1(F,2)),k3_matrix_0(A,D,k1_funct_1(E,2),k1_funct_1(F,1)),k3_matrix_0(A,D,k1_funct_1(E,2),k1_funct_1(F,2))) ) ) ) ) ) ) ) )).
fof(t23_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k3_finseq_1(k3_matrix14(A,B,C)) = B ) ) ) )).
fof(t23_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(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)) ) ) ) ) ) )).
fof(t23_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(B),A,A) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(B))) ) => ( ( v3_matrix16(E,u1_struct_0(B)) & v3_matrix16(F,u1_struct_0(B)) ) => v3_matrix16(k3_matrix_3(B,k2_matrix13(A,A,B,E,C),k2_matrix13(A,A,B,F,D)),u1_struct_0(B)) ) ) ) ) ) ) ) )).
fof(t23_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ( ~ r1_xxreal_0(A,k5_numbers) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,C,A,B) & m2_finseq_1(D,k3_finseq_2(C)) ) => ( k3_finseq_1(D) = A & k1_matrix_0(D) = B & k2_matrix_0(D) = k2_zfmisc_1(k2_finseq_1(A),k2_finseq_1(B)) ) ) ) ) ) ) )).
fof(t23_matrix_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( ( 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] : ( ( v1_funct_1(F) & v1_funct_2(F,A,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,B,C) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ! [H] : ( m1_subset_1(H,k5_finsub_1(A)) => ! [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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t23_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(D) ) => k3_matrix_3(A,B,D) = k3_matrix_3(A,k3_matrix_3(A,B,C),k1_matrix_4(A,D,C)) ) ) ) ) ) )).
fof(t23_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k2_numbers)) ) => ( k1_matrix_0(A) = k3_finseq_1(B) => ( r1_xxreal_0(k3_finseq_1(A),k5_numbers) | r1_xxreal_0(k3_finseq_1(B),k5_numbers) | k6_matrix_5(k8_matrix_5(k3_finseq_1(A),k1_matrix_0(A)),B) = k8_matrix_5(k3_finseq_1(A),k1_matrix_0(B)) ) ) ) ) )).
fof(t23_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => k4_matrix_0(u1_struct_0(B),k3_matrix_3(B,C,D)) = k3_matrix_3(B,k4_matrix_0(u1_struct_0(B),C),k4_matrix_0(u1_struct_0(B),D)) ) ) ) ) )).
fof(t23_matrix_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) )).
fof(t23_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v2_matrix_8(C,A,B) & r1_matrix_6(A,B,C,D) ) => ( r1_xxreal_0(A,k5_numbers) | v2_matrix_8(k4_matrix_3(B,C,D),A,B) ) ) ) ) ) ) )).
fof(t23_matrix_9,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( ( v1_matrix_0(K) & v2_matrix_0(K,u1_struct_0(A),3,3) & m2_finseq_1(K,k3_finseq_2(u1_struct_0(A))) ) => ( K = k3_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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] : ( m1_matrix_2(L,k3_matrix_2(3)) => ( L = k3_finseq_4(k4_ordinal1,2,3,1) => k10_matrix_3(3,A,K,L) = k3_finseq_4(u1_struct_0(A),C,G,H) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t23_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( m1_subset_1(C,k2_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => k5_matrixc1(A,k10_seq_4(B,C)) = k10_seq_4(k5_matrixc1(A,B),C) ) ) ) ) )).
fof(t23_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(A)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,A,k2_wsierp_1(k10_matrixj1(A,k5_matrixj1(A,C,D))),k2_wsierp_1(k11_matrixj1(A,k5_matrixj1(A,C,D)))) & m2_finseq_1(E,k3_finseq_2(A)) ) => ( E = k13_matrixj1(A,B,k5_matrixj1(A,C,D)) <=> ! [F] : ( v7_ordinal1(F) => ( ( r2_hidden(F,k4_finseq_1(C)) => k7_matrix_0(A,E,F) = k8_finseq_1(A,k7_matrix_0(A,C,F),k5_finseq_2(A,k1_matrix_0(D),B)) ) & ( r2_hidden(F,k4_finseq_1(D)) => k7_matrix_0(A,E,k1_nat_1(F,k3_finseq_1(C))) = k8_finseq_1(A,k5_finseq_2(A,k1_matrix_0(C),B),k7_matrix_0(A,D,F)) ) ) ) ) ) ) ) ) ) )).
fof(t23_matrixj2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( ~ 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] : ( ( ~ 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] : ( m1_matrlin(F,B,D) => ! [G] : ( m2_finseq_1(G,u1_struct_0(E)) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(B),k3_finseq_1(F),k3_finseq_1(G)) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(B))) ) => ( H = k2_matrixj2(B,C,A) => ! [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))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t23_matrixr1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(B)) ) => ( C = D => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( r2_hidden(k4_tarski(E,F),k2_matrix_0(C)) => k3_matrix_0(A,C,E,F) = k3_matrix_0(B,D,E,F) ) ) ) ) ) ) )).
fof(t23_matrixr2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( 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)) ) ) ) )).
fof(t23_matrlin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,E,D,A) & m2_finseq_1(F,k3_finseq_2(E)) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,E,C,A) & m2_finseq_1(G,k3_finseq_2(E)) ) => ( r2_hidden(B,k9_xtuple_0(F)) => k7_matrix_0(E,k8_matrlin(E,D,C,A,F,G),B) = k7_matrix_0(E,F,B) ) ) ) ) ) ) ) ) )).
fof(t23_matrlin2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( ~ 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] : ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t23_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( ( v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : ( m1_matroid0(C,A) & r1_tarski(B,C) ) ) ) )).
fof(t23_matrprob,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( k3_finseq_1(A) = k5_numbers => k5_matrprob(A) = k5_numbers ) ) )).
fof(t23_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_card_1(D,A) & v1_finseq_1(D) & v3_valued_0(D) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => 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) ) ) ) ) ) )).
fof(t23_matrtop2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ! [D] : ( ( 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) = A => v1_rlvect_3(k2_ranknull(k15_euclid(A),k15_euclid(B),k3_matrtop1(A,B,C),D),k15_euclid(B)) ) ) ) ) ) )).
fof(t23_matrtop3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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),k9_finseq_1(k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(E,B),k19_sin_cos(A)),k3_xcmplx_0(k1_funct_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))),k9_finseq_1(k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(E,B),k17_sin_cos(A)),k3_xcmplx_0(k1_funct_1(E,C),k19_sin_cos(A))))),k1_rfinseq(C,E)) ) ) ) ) ) ) ) )).
fof(t23_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(t23_mboolean,axiom,( ! [A] : ! [B] : r6_pboole(B,k2_mboolean(B,k7_funcop_1(B,k1_tarski(A))),k7_funcop_1(B,A)) )).
fof(t23_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( 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 ) ) ) )).
fof(t23_measure1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) ) ) ) )).
fof(t23_measure2,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ( ! [E] : ( m1_subset_1(E,k4_ordinal1) => r1_tarski(k9_nat_1(B,D,E),k9_nat_1(B,D,k1_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(k4_ordinal1,B,B,k6_numbers,D,C))) ) ) ) ) )).
fof(t23_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( v1_xreal_0(B) => k1_measure6(k1_measure6(A,B),k4_xcmplx_0(B)) = A ) ) )).
fof(t23_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => k6_member_1(k2_xboole_0(A,B)) = k2_xboole_0(k6_member_1(A),k6_member_1(B)) ) ) )).
fof(t23_membered,axiom,( ! [A] : ! [B] : ( v5_membered(B) => ( r1_tarski(A,B) => v5_membered(A) ) ) )).
fof(t23_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) & v4_memstr_0(C,A,B) ) => ! [D] : ( v7_ordinal1(D) => r1_partfun1(C,k7_memstr_0(A,B,D)) ) ) ) ) )).
fof(t23_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t23_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k2_numbers)) & v1_mesfunc8(B,A,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ! [C] : ( m1_subset_1(C,A) => ( r2_hidden(C,k1_relset_1(A,k4_mesfunc5(A,k2_numbers,B,k5_numbers))) => ( r2_funct_2(k4_ordinal1,k1_numbers,k10_seqfunc(A,k11_mesfun7c(A,B),C),k7_comseq_3(k9_mesfun7c(A,B,C))) & r2_funct_2(k4_ordinal1,k1_numbers,k10_seqfunc(A,k12_mesfun7c(A,B),C),k8_comseq_3(k9_mesfun7c(A,B,C))) ) ) ) ) ) )).
fof(t23_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ( ( v1_mesfunc8(D,A,k2_numbers) & r1_tarski(C,k1_relset_1(A,k4_mesfunc5(A,k2_numbers,D,k5_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)) ) ) ) ) )).
fof(t23_mesfunc1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ! [F] : ( m1_subset_1(F,k4_ordinal1) => k9_nat_1(B,C,F) = k9_subset_1(A,E,k17_mesfunc1(A,D,F)) ) => k9_subset_1(A,E,k19_mesfunc1(A,D,k1_supinf_1)) = k1_measure2(A,B,k1_measure3(A,B,C)) ) ) ) ) )).
fof(t23_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => r2_relset_1(A,k6_numbers,B,k4_mesfunc1(A,k1_mesfunc2(A,B),k2_mesfunc2(A,B))) ) ) )).
fof(t23_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t23_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( r2_relset_1(A,k6_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,k6_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)) ) ) ) ) )).
fof(t23_mesfunc7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : k1_mesfunc2(A,k3_mesfunc2(B,A)) = k3_mesfunc2(B,A) ) )).
fof(t23_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k6_numbers)) & v1_mesfunc8(C,A,k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( ( k1_relset_1(A,k4_mesfunc5(A,k6_numbers,C,k5_numbers)) = D & ! [E] : ( v7_ordinal1(E) => r1_mesfunc1(A,B,k4_mesfunc5(A,k6_numbers,C,E),D) ) ) => r1_mesfunc1(A,B,k6_mesfunc8(A,C),D) ) ) ) ) ) )).
fof(t23_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ~ ( r2_hidden(D,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,k4_mesfunc9(A,B),C))) & k1_mesfunc9(k4_mesfunc5(A,k6_numbers,k4_mesfunc9(A,B),C),D) = k1_supinf_1 & ! [E] : ( v7_ordinal1(E) => ~ ( r1_xxreal_0(E,C) & k1_mesfunc9(k4_mesfunc5(A,k6_numbers,B,E),D) = k1_supinf_1 ) ) ) ) ) ) )).
fof(t23_metric_1,axiom,( ! [A] : ( m1_subset_1(A,1) => ! [B] : ( m1_subset_1(B,1) => ! [C] : ( m1_subset_1(C,1) => r1_xxreal_0(k1_binop_1(k2_metric_1,A,C),k2_xcmplx_0(k1_binop_1(k2_metric_1,A,B),k1_binop_1(k2_metric_1,B,C))) ) ) ) )).
fof(t23_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k2_metric_2(A)) => ! [C] : ( m1_subset_1(C,k2_metric_2(A)) => ! [D] : ( m1_subset_1(D,k1_numbers) => ( r2_hidden(D,k3_metric_2(A,B,C)) <=> r4_metric_2(A,B,C,D) ) ) ) ) ) )).
fof(t23_metric_3,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers)) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k1_numbers,k1_numbers)) => k2_binop_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers,k18_metric_3,A,B) = k2_binop_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers,k18_metric_3,B,A) ) ) )).
fof(t23_metric_6,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_funct_1(B) => v2_tbsp_1(B,A) ) ) ) )).
fof(t23_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_finset_1(B) & v1_card_1(B) ) => ! [C] : ( ( 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] : ( 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] : ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t23_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => m1_rlvect_3(k8_euclid_7(A),k15_euclid(A)) ) )).
fof(t23_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t23_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t23_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_midsp_3(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(B))) => ! [F] : ( ( v4_midsp_2(F,B) & l1_midsp_2(F,B) ) => ! [G] : ( m1_subset_1(G,u1_struct_0(u1_midsp_2(B,F))) => ! [H] : ( m2_finseq_2(H,u1_struct_0(u1_midsp_2(B,F)),k4_finseq_2(k1_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 ) ) ) ) ) ) ) ) ) )).
fof(t23_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,k2_mmlquery(A,C,B)) <=> ? [E] : ( m1_subset_1(E,A) & r2_hidden(D,k1_mmlquery(A,C,E)) & r2_hidden(E,B) ) ) ) ) ) )).
fof(t23_mod_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k18_mod_2)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k18_mod_2)) => ! [C] : ( m1_subset_1(C,k1_enumset1(k5_numbers,1,2)) => ! [D] : ( m1_subset_1(D,k1_enumset1(k5_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) ) ) ) ) ) ) )).
fof(t23_mod_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t23_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k6_modal_1) => m1_subset_1(k7_trees_2(k8_funcop_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k2_trees_1(1),k1_domain_1(k4_ordinal1,k4_ordinal1,1,1)),k14_trees_3(k5_numbers),A),k6_modal_1) ) )).
fof(t23_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_partfun1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(k30_modelc_1(B))) ) => ! [F] : ( ( 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] : ( m1_modelc_1(G,B,C) & k3_funct_2(k4_ordinal1,B,G,k5_numbers) = D & ! [H] : ( m1_subset_1(H,k4_ordinal1) => r4_modelc_1(B,C,E,F,k3_funct_2(k4_ordinal1,B,G,H),A) ) ) ) ) ) ) ) ) ) )).
fof(t23_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( v5_modelc_2(A) => ( r1_modelc_2(B,A) <=> ( B = k11_modelc_2(A) | B = k12_modelc_2(A) ) ) ) ) ) )).
fof(t23_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_3(B,A) & l1_modelc_3(B,A) ) => ~ ( ~ r1_xxreal_0(k21_modelc_3(A,B),k5_numbers) & u2_modelc_3(A,B) = k7_modelc_3(A) ) ) ) )).
fof(t23_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ~ v1_moebius1(A) ) )).
fof(t23_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m2_monoid_0(B,A) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t23_monoid_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t23_morph_01,axiom,( ! [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) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t23_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [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] : ( m1_dtconstr(C,u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),B,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_numbers))))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),B,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_numbers)))))),k1_msaterm(A,k2_pboole(u1_struct_0(A),B,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_numbers))))) => ! [D] : ( 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(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_numbers))),B),D)) => r2_hidden(C,k1_funct_1(u3_msualg_1(A,k1_msafree3(A,B)),D)) ) ) ) ) ) )).
fof(t23_msafree4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r1_pzfmisc1(A,B,C) => ! [D] : ( m2_pboole(D,A,B,C) => ~ ( v2_msualg_3(D,A,B,C) & ! [E] : ( m2_pboole(E,A,C,B) => ~ r6_pboole(A,k8_pboole(E,D),k2_msualg_3(A,C)) ) ) ) ) ) ) )).
fof(t23_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m1_msaterm(D,A,B,k2_msaterm(A,B,C)) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(D)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t23_msscyc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t23_mssubfam,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t23_mssublat,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v13_struct_0(A,1) & v5_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ( u1_struct_0(A) = k1_tarski(k5_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)) ) ) ) )).
fof(t23_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(t23_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) ) => ~ ( r1_msualg_6(A,E,F,B,G) & ! [H] : ( ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t23_msualg_7,axiom,( ? [A] : ( m2_nat_lat(A,k1_msualg_7(k10_subset_1(k5_numbers,k1_numbers),k10_subset_1(1,k1_numbers))) & v1_msualg_7(A,k1_msualg_7(k10_subset_1(k5_numbers,k1_numbers),k10_subset_1(1,k1_numbers))) & ~ v2_msualg_7(A,k1_msualg_7(k10_subset_1(k5_numbers,k1_numbers),k10_subset_1(1,k1_numbers))) ) )).
fof(t23_msualg_9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v2_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( v1_relat_1(E) & v2_relat_1(E) & v4_relat_1(E,A) & v1_funct_1(E) & v1_partfun1(E,A) ) => ! [F] : ( m2_pboole(F,A,B,k6_pboole(A,D,E)) => ( r1_pboole(A,C,k1_funct_6(F)) => ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(t23_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t23_mycielsk,axiom,( ! [A] : ( ( v1_necklace(A) & v3_dilworth(A) & l1_orders_2(A) ) => k1_dilworth(A) = k2_dilworth(k3_necklace(A)) ) )).
fof(t23_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t23_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( ~ r1_xxreal_0(2,A) & A != k5_numbers & A != 1 ) ) )).
fof(t23_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(A,B) & r1_nat_d(k3_xcmplx_0(2,C),A) ) => ( v1_abian(k3_nat_d(B,C)) <=> v1_abian(k3_nat_d(k7_nat_d(B,A),C)) ) ) ) ) ) )).
fof(t23_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( B != k5_numbers & ~ r1_xxreal_0(A,B) & A != 1 & k11_nat_3(B,A) != k5_numbers ) ) ) )).
fof(t23_nat_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ~ ( k6_xcmplx_0(A,1) = k2_nat_1(B,k11_newton(C,E)) & ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(E,k5_numbers) & v1_int_2(C) & k4_nat_d(k11_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(k11_newton(G,k3_nat_d(k7_nat_d(A,1),C)),1)) & k4_nat_d(F,k11_newton(C,E)) != 1 ) ) ) ) ) ) ) ) )).
fof(t23_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k4_nat_d(k2_xcmplx_0(A,C),B) = k4_nat_d(k1_nat_1(A,k4_nat_d(C,B)),B) ) ) ) )).
fof(t23_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_nattra_1(E,A,B,C,D) => ( ( r2_nattra_1(A,B,C,D) & v1_nattra_1(E,A,B,C,D) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => k2_nattra_1(A,B,D,C,k7_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),k2_nattra_1(A,B,C,D,E,F)) ) ) ) ) ) ) ) )).
fof(t23_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),k8_funct_2(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,C),k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,D))) & r2_funct_2(k4_ordinal1,u1_struct_0(B),k8_funct_2(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,C),k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,D))) ) ) ) ) ) ) ) )).
fof(t23_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( 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) ) ) ) )).
fof(t23_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( F != k4_struct_0(A) & ~ r1_xxreal_0(E,k2_normsp_0(A,F)) & r1_xxreal_0(D,k3_xcmplx_0(k5_xcmplx_0(k2_normsp_0(A,F)),k2_normsp_0(B,k7_partfun1(u1_struct_0(B),C,F)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t23_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ! [C] : ( ( 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) ) ) ) )).
fof(t23_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( E != k5_numbers & ~ r1_xxreal_0(D,k9_complex1(E)) & r1_xxreal_0(C,k3_xcmplx_0(k5_xcmplx_0(k9_complex1(E)),k2_normsp_0(k4_real_ns1(A),k7_partfun1(u1_struct_0(k4_real_ns1(A)),B,E)))) ) ) ) ) ) ) ) ) ) ) )).
fof(t23_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_prvect_2(A))) => ! [D] : ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t23_neckla_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ( v1_neckla_2(A) => v1_neckla_2(B) ) ) ) )).
fof(t23_necklace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t23_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : ! [C] : ( r1_tarski(C,k2_net_1(A)) => ( r2_hidden(B,k12_net_1(A,C)) <=> ? [D] : ( m1_subset_1(D,k2_net_1(A)) & r2_hidden(D,C) & r2_hidden(B,k5_net_1(A,D)) ) ) ) ) )).
fof(t23_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => k3_newton(1,A) = A ) ) )).
fof(t23_nfcont_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t23_nfcont_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( 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] : ( 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) ) ) ) ) )).
fof(t23_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t23_normform,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(t23_normsp_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_normsp_1(B,A) => v2_comseq_2(k5_normsp_0(A,B)) ) ) ) )).
fof(t23_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t23_numbers,axiom,( k3_numbers != k2_numbers )).
fof(t23_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t23_openlatt,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(t23_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t23_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k5_ordeq_01(A,B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k5_ordeq_01(A,B))))) ) => ( ( v3_lopban_1(B) & v1_rsspace3(C,k5_ordeq_01(A,B)) ) => v3_normsp_1(C,k5_ordeq_01(A,B)) ) ) ) ) )).
fof(t23_orders_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t23_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t23_ordinal1,axiom,( ! [A] : ? [B] : ( v3_ordinal1(B) & ~ r2_hidden(B,A) & ! [C] : ( v3_ordinal1(C) => ( ~ r2_hidden(C,A) => r1_ordinal1(B,C) ) ) ) )).
fof(t23_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => k3_ordinal2(k1_tarski(A)) = k1_ordinal1(A) ) )).
fof(t23_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r1_ordinal1(k10_ordinal2(A,B),k10_ordinal2(A,C)) => r1_ordinal1(B,C) ) ) ) ) )).
fof(t23_ordinal4,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r2_hidden(1,B) => r2_hidden(k12_ordinal2(B,A),k12_ordinal2(B,k1_ordinal1(A))) ) ) ) )).
fof(t23_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( ( r2_hidden(k5_numbers,A) & r2_hidden(k5_numbers,B) ) => r1_ordinal1(A,k1_ordinal5(A,B)) ) ) ) )).
fof(t23_ordinal6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) ) )).
fof(t23_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r1_orders_2(B,D,k3_rlvect_1(B,E,C)) => ( r1_orders_2(B,D,C) | k1_ortsp_1(A,B,C,D,E) = k4_algstr_0(A,k1_ortsp_1(A,B,E,D,C)) ) ) ) ) ) ) ) )).
fof(t23_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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] : ! [D] : ! [E] : ( 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)) ) ) ) ) )).
fof(t23_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t23_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_osalg_2(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t23_osalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & v13_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v2_msualg_4(C,A,B) & v3_msualg_4(C,A,B) & m1_osalg_4(C,A,B) ) => v3_osalg_4(C,A,B) ) ) ) )).
fof(t23_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t23_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_parsp_2(A,G,B,C) & r1_parsp_2(A,G,D,E) & r1_parsp_2(A,G,D,F) & r1_parsp_1(A,B,D,C,E) & r1_parsp_1(A,B,D,C,F) ) => ( r1_parsp_2(A,G,B,D) | E = F ) ) ) ) ) ) ) ) ) )).
fof(t23_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t23_partfun2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( ( 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] : ( m1_subset_1(F,B) & r2_hidden(F,k1_relset_1(B,E)) & r2_hidden(F,A) & D = k7_partfun1(C,E,F) ) ) ) ) ) ) )).
fof(t23_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(t23_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) => ( v3_relat_2(C) => r3_relat_2(C,A) ) ) ) ) )).
fof(t23_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_analoaf(A,B,C,D,E) & ~ r3_diraf(A,B,C,D) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_diraf(A,B,F,E) & r1_diraf(A,C,F,D) ) ) ) ) ) ) ) ) )).
fof(t23_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t23_pcomps_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v2_pcomps_1(A) & v4_pre_topc(C,A) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v3_pre_topc(E,A) & v3_pre_topc(F,A) & r1_tarski(B,E) & r2_hidden(D,F) & r1_xboole_0(E,F) ) ) ) ) ) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t23_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k20_pcs_0(A,B))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k20_pcs_0(A,B))) => ( ( C = E & D = F & r1_orders_2(A,C,D) ) => r1_orders_2(k20_pcs_0(A,B),E,F) ) ) ) ) ) ) )).
fof(t23_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( 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] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [G] : ( m1_subset_1(G,u1_struct_0(k4_real_ns1(A))) => ! [H] : ( m2_finseq_2(H,k1_numbers,k1_euclid(A)) => ( ( E = F & G = H ) => ( r5_pdiff_1(A,B,C,D,E,G) <=> r6_pdiff_1(A,B,C,D,F,H) ) ) ) ) ) ) ) ) ) ) )).
fof(t23_pdiff_3,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(2)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [C] : ( ( 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) & k10_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) = k2_xcmplx_0(k4_pdiff_3(B,A),k4_pdiff_3(C,A)) ) ) ) ) ) )).
fof(t23_pdiff_4,axiom,( ! [A] : ! [B] : ( ( 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] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => ( r2_hidden(C,A) => r3_pdiff_1(3,2,B,C) ) ) ) ) ) )).
fof(t23_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( 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) ) ) ) )).
fof(t23_pdiff_6,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(A))) => ! [D] : ( v1_xreal_0(D) => ( B = C => a_3_0_pdiff_6(A,B,D) = a_3_1_pdiff_6(A,C,D) ) ) ) ) ) )).
fof(t23_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( 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) & 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),k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_1(B,A),D)) & k10_pdiff_1(A,B,C,D) = k1_funct_1(k1_pdiff_7(A,C,D),k1_funct_1(k6_pdiff_1(A,B,k5_euclid(A)),1)) ) ) ) ) ) ) )).
fof(t23_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [E] : ( ( 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] : ( m1_subset_1(F,k1_zfmisc_1(k1_euclid(A))) => ! [G] : ( 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)),k14_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)),k14_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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t23_pencil_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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] : ( E != k3_pencil_1(A,B) => k1_funct_1(C,E) = k1_funct_1(D,E) ) ) ) ) ) ) )).
fof(t23_pencil_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v15_pencil_1(B) ) => ( ! [C] : ( m1_subset_1(C,A) => v10_pencil_1(k2_pencil_1(A,B,C)) ) => ! [C] : ( m1_pencil_2(C,A,B) <=> ? [D] : ( 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)) ) ) ) ) ) )).
fof(t23_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( v7_ordinal1(D) => k2_vectsp_9(A,B,D) = k2_vectsp_9(A,C,D) ) ) ) ) ) )).
fof(t23_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( v1_abian(k3_xcmplx_0(A,B)) & ~ v1_abian(A) & ~ v1_abian(B) ) ) ) )).
fof(t23_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m3_pnproc_1(C,A,B) => k8_pnproc_1(A,B,k3_pre_poly(B,C)) = k7_pnproc_1(A,C) ) ) )).
fof(t23_polyalg1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t23_polyeq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( k1_square_1(B) = A & B != k2_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(A),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A))))),2)),k3_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(A)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A))))),2)),k7_complex1)) & B != k2_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(A),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A))))),2))),k3_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(A)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A))))),2))),k7_complex1)) & B != k2_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(A),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A))))),2)),k3_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(A)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A))))),2))),k7_complex1)) & B != k2_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(A),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A))))),2))),k3_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(A)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A))))),2)),k7_complex1)) ) ) ) )).
fof(t23_polyeq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k2_power(A,B) = A => ( r1_xxreal_0(A,k5_numbers) | A = 1 | B = 1 ) ) ) ) )).
fof(t23_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( v1_xcmplx_0(F) => ! [G] : ( 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 = k4_xcmplx_0(k7_xcmplx_0(D,k3_xcmplx_0(B,C))) ) => ( D = k5_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)) = k5_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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t23_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(t23_polynom1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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),k5_polynom1(A,B,C,k8_polynom1(A,B)),C) ) ) )).
fof(t23_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_xxreal_0(k1_algseq_1(A,B),C) <=> r1_algseq_1(A,B,C) ) ) ) ) )).
fof(t23_polynom5,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( k1_algseq_1(A,B) != k5_numbers => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k1_algseq_1(A,k2_polynom5(A,B,C)) = k2_xcmplx_0(k6_xcmplx_0(k2_nat_1(C,k1_algseq_1(A,B)),C),1) ) ) ) ) )).
fof(t23_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( 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 ) ) ) )).
fof(t23_polynom8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B != k4_struct_0(A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t23_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(D,A,C) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( 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),k3_polynom1(k15_pre_poly(A),C,E)) => r2_hidden(k3_termord(A,B,C,k10_polynom1(A,C,F,D)),k3_polynom1(k15_pre_poly(A),C,k10_polynom1(A,C,F,E))) ) ) ) ) ) ) ) )).
fof(t23_power,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_xxreal_0(1,C) => k9_nat_1(k1_numbers,A,C) = k1_power(C,B) ) ) => ( r1_xxreal_0(B,k5_numbers) | ( v2_comseq_2(A) & k1_seq_2(A) = 1 ) ) ) ) ) )).
fof(t23_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ! [E] : ( m1_subset_1(E,k3_msualg_1(B,D,k14_pralg_2(A,B,C))) => ( k1_msualg_1(B,D) != k1_xboole_0 => ! [F] : ( 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(k9_funct_6(E),F) ) ) ) ) ) ) ) )).
fof(t23_pre_circ,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( k5_card_1(A) = k1_nat_1(B,1) & ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ~ ( A = k2_xboole_0(D,k1_tarski(C)) & k5_card_1(D) = B ) ) ) ) ) ) )).
fof(t23_pre_poly,axiom,( ! [A] : k1_card_3(k9_finseq_1(A)) = k9_finseq_1(k1_card_1(A)) )).
fof(t23_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t23_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t23_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(1,B) => ( r1_xxreal_0(A,k5_numbers) | k2_prepower(B,k7_xcmplx_0(1,A)) = k7_xcmplx_0(1,k2_prepower(B,A)) ) ) ) ) )).
fof(t23_prob_1,axiom,( ! [A] : ! [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))) ) => m1_prob_1(A,A,B) ) )).
fof(t23_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m2_prob_1(D,A,B) => ! [E] : ( m1_prob_1(E,A,B) => ( E = k1_xboole_0 => r1_prob_2(A,B,D,C,E) ) ) ) ) ) ) )).
fof(t23_prob_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( ~ 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] : ( ( v5_relat_1(D,C) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => r1_tarski(k1_prob_2(B,C,k1_prob_3(B,D),A),k1_prob_2(B,C,D,A)) ) ) ) )).
fof(t23_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t23_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t23_projpl_1,axiom,( ! [A] : ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ? [D] : ( m1_subset_1(D,u2_incsp_1(A)) & r4_incsp_1(A,k7_domain_1(u1_incsp_1(A),B,C),D) ) ) ) & ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & r2_projpl_1(A,D,B,C) ) ) ) & ? [B] : ( m1_subset_1(B,u1_incsp_1(A)) & ? [C] : ( m1_subset_1(C,u1_incsp_1(A)) & ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & ? [E] : ( m1_subset_1(E,u1_incsp_1(A)) & r5_projpl_1(A,B,C,D,E) ) ) ) ) ) ) ) )).
fof(t23_projred1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u1_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u1_incsp_1(A)) => ! [H] : ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(t23_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u2_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u2_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u2_incsp_1(A)) => ! [H] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t23_prvect_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ? [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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(k4_ordinal1,u1_struct_0(B))),D,k12_finseq_1(u1_struct_0(B),E)) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(k7_prvect_3(A,B))) => ! [E] : ( 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] : ( m1_subset_1(D,u1_struct_0(k7_prvect_3(A,B))) => ! [E] : ( 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] : ( m1_subset_1(D,u1_struct_0(k7_prvect_3(A,B))) => k2_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)) = k2_normsp_0(k7_prvect_3(A,B),D) ) ) ) ) )).
fof(t23_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(B,A) => k1_funct_1(k3_pscomp_1(k15_euclid(2),k5_pscomp_1,A),B) = k18_euclid(B) ) ) ) )).
fof(t23_pua2mss1,axiom,( ! [A] : ( ( v2_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( 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))) ) ) )).
fof(t23_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t23_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k1_qc_lang1(A)) => ( ( r1_qc_lang1(A,B,C) & r1_qc_lang1(A,C,B) ) => C = B ) ) ) ) )).
fof(t23_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( m1_subset_1(E,k9_qc_lang1(A)) => ! [F] : ( m1_subset_1(F,k9_qc_lang1(A)) => ! [G] : ( m2_subset_1(G,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [H] : ( m2_subset_1(H,k2_qc_lang1(A),k3_qc_lang1(A)) => ( k8_qc_lang2(A,B,C,D,E) = k6_qc_lang2(A,H,G,F) => ( B = H & C = G & k15_qc_lang1(A,D,E) = F ) ) ) ) ) ) ) ) ) ) )).
fof(t23_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t23_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m1_trees_1(D,k9_xtuple_0(k2_qc_lang4(A,C))) => ! [E] : ( m1_trees_1(E,k9_xtuple_0(k2_qc_lang4(A,C))) => ( ( E = k7_finseq_1(D,k9_finseq_1(B)) & v5_qc_lang1(k3_trees_2(k9_qc_lang1(A),k2_qc_lang4(A,C),D),A) ) => ( k3_trees_2(k9_qc_lang1(A),k2_qc_lang4(A,C),E) = k22_qc_lang1(A,k3_trees_2(k9_qc_lang1(A),k2_qc_lang4(A,C),D)) & B = k5_numbers ) ) ) ) ) ) ) )).
fof(t23_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_henmodel(B,A) & m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) ) => ! [C] : ( ( v1_qc_trans(C,A) & m1_qc_lang1(C) ) => v2_qc_trans(B,A,C) ) ) ) )).
fof(t23_quantal1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_lattices(A,B,C) => r3_lattices(A,k5_quantal1(A,C),k5_quantal1(A,B)) ) ) ) ) )).
fof(t23_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k23_quaterni(k25_quaterni(A,B),C) = k25_quaterni(k23_quaterni(A,C),k23_quaterni(B,C)) ) ) ) )).
fof(t23_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k22_quaterni(k23_quaterni(k12_quaterni,A),k23_quaterni(A,k12_quaterni)) = k6_quaterni(k4_xcmplx_0(k3_xcmplx_0(2,k16_quaterni(A))),k5_numbers,k5_numbers,k3_xcmplx_0(2,k13_quaterni(A))) ) )).
fof(t23_quaterni,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( k13_quaterni(k6_quaterni(A,B,C,D)) = A & k14_quaterni(k6_quaterni(A,B,C,D)) = B & k15_quaterni(k6_quaterni(A,B,C,D)) = C & k16_quaterni(k6_quaterni(A,B,C,D)) = D ) ) ) ) ) )).
fof(t23_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(k6_xcmplx_0(k1_square_1(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,B),A),C)),k1_quin_1(B,C,D)),k5_numbers) & r1_xxreal_0(k5_numbers,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(A)),k3_xcmplx_0(C,A)),D)) ) ) ) ) ) )).
fof(t23_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t23_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_radix_1(k2_xcmplx_0(C,1),B,A) => k4_radix_1(k2_xcmplx_0(C,1),A,k2_xcmplx_0(C,1),k10_radix_1(A,k2_xcmplx_0(C,1),B)) = k3_nat_d(B,k1_newton(k1_radix_1(A),C)) ) ) ) ) )).
fof(t23_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_random_1(C,A,B) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(k5_numbers,D) & v6_supinf_2(C) ) => m1_random_1(k2_mesfun6c(D,A,C),A,B) ) ) ) ) ) )).
fof(t23_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m2_vectsp_6(D,A,B,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => m2_vectsp_6(k14_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))) ) ) ) ) ) ) )).
fof(t23_rat_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_rat_1(B) => ( A != k5_numbers => B = k7_xcmplx_0(k3_xcmplx_0(k2_rat_1(B),A),k3_xcmplx_0(k1_rat_1(B),A)) ) ) ) )).
fof(t23_ratfunc1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t23_rcomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ~ ( v3_rcomp_1(A) & v5_xxreal_2(A) & ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r1_tarski(k1_rcomp_1(B,C),A) ) ) ) & ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => A != k2_rcomp_1(B,C) ) ) ) ) )).
fof(t23_rcomp_3,axiom,( ! [A] : ( ( ~ 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(k2_seq_4(A),A) | A = k10_prob_1(k2_seq_4(A)) ) ) ) )).
fof(t23_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k6_real_lat(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k6_real_lat(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t23_realset2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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)) ) ) )).
fof(t23_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(A),k8_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t23_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [D] : ( ( v1_rearran1(D) & v2_rearran1(D) & v3_rearran1(D,k1_zfmisc_1(A)) & m2_finseq_1(D,k1_zfmisc_1(A)) ) => ( ( v1_partfun1(C,B) & k5_card_1(A) = k5_card_1(B) ) => r2_classes1(k4_rearran1(B,A,D,C),k20_rfunct_3(B,C,B)) ) ) ) ) ) )).
fof(t23_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => ( r1_tarski(A,C) => r1_tarski(k3_relat_1(B,A),k3_relat_1(B,C)) ) ) ) ) )).
fof(t23_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ( k7_relset_1(A,B,C,k8_relset_1(A,B,C,B)) = k2_relset_1(B,C) & k8_relset_1(A,B,C,k7_relset_1(A,B,C,A)) = k1_relset_1(A,C) ) ) )).
fof(t23_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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 ) ) ) )).
fof(t23_revrot_1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t23_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ! [D] : ( r1_rewrite1(A,C,D) <=> r1_rewrite1(k2_xboole_0(A,k4_relat_1(B)),C,D) ) ) )).
fof(t23_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t23_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_afinsq_1(D))) => ! [F] : ( l1_rewrite3(F,E) => ( r1_rewrite3(E,F,A,B,C) <=> r2_rewrite3(D,E,F,A,B,C,k2_flang_1(D)) ) ) ) ) )).
fof(t23_rfinseq,axiom,( ! [A] : ( ( v8_valued_0(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( ( v8_valued_0(B) & m2_finseq_1(B,k1_numbers) ) => ( r2_classes1(A,B) => A = B ) ) ) )).
fof(t23_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( v1_integra2(A) => v8_valued_0(k6_rvsum_1(A)) ) ) )).
fof(t23_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t23_rfunct_2,axiom,( ! [A] : ! [B] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( 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_funct_1(B,D),k1_funct_1(B,C)) ) ) ) ) ) ) )).
fof(t23_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_rfunct_3(B,A,k1_numbers,k3_rfunct_3(A,k1_numbers)) => ! [C] : ( 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)) ) ) ) )).
fof(t23_rfunct_4,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(t23_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v8_valued_0(A) & v2_seq_2(A) ) => v1_comseq_2(A) ) ) )).
fof(t23_rinfsup2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( r1_xxreal_0(k2_rinfsup2(B),k12_supinf_2(B,A)) & r1_xxreal_0(k12_supinf_2(B,A),k1_rinfsup2(B)) ) ) ) )).
fof(t23_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(k17_ringcat1(A))) => ! [C] : ( m1_subset_1(C,u4_struct_0(k17_ringcat1(A))) => ! [D] : ( m3_ringcat1(D,k10_ringcat1(k9_ringcat1(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t23_rlaffin1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ 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] : ( m1_rlvect_2(C,B) => ( A != k5_numbers => k3_rlvect_2(B,k2_rlaffin1(B,C,A)) = k1_convex1(B,k3_rlvect_2(B,C),A) ) ) ) ) )).
fof(t23_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t23_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( ( v1_rlvect_1(C) & m1_rlsub_1(C,A) ) => k1_rlsub_2(A,k2_rlsub_2(A,B,C),C) = C ) ) ) )).
fof(t23_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t23_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k5_algstr_0(A,B,C) = k5_algstr_0(A,B,D) => C = D ) ) ) ) ) )).
fof(t23_rlvect_2,axiom,( ! [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) ) => ! [B] : ( 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)) ) ) )).
fof(t23_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t23_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( v1_rlvect_3(k8_domain_1(u1_struct_0(A),B,D,C),A) => ( B = C | B = D | C = D | v1_rlvect_3(k8_domain_1(u1_struct_0(A),B,D,k5_algstr_0(A,C,B)),A) ) ) ) ) ) ) )).
fof(t23_rlvect_5,axiom,( ! [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) ) => ( v1_rlvect_5(A) => ! [B] : ( m1_rlvect_3(B,A) => v1_finset_1(B) ) ) ) )).
fof(t23_rlvect_x,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t23_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t23_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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 ) ) )).
fof(t23_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(B)) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t23_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t23_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_robbins1(A,k3_robbins1(A,B)) = B ) ) )).
fof(t23_robbins3,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t23_robbins4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k2_robbins4)) => ( ( A = k5_numbers => k3_robbins1(k2_robbins4,A) = 3 ) & ( A = 3 => k3_robbins1(k2_robbins4,A) = k5_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 ) ) ) )).
fof(t23_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t23_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k1_rpr_1(A,k7_subset_1(A,B,C)) = k6_xcmplx_0(k1_rpr_1(A,B),k1_rpr_1(A,k9_subset_1(A,B,C))) ) ) ) )).
fof(t23_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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)) ) ) ) )).
fof(t23_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_struct_0(B,D) => r1_struct_0(C,D) ) ) => m1_rusub_1(B,C) ) ) ) ) )).
fof(t23_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( ( v1_bhsp_1(C) & m1_rusub_1(C,A) ) => k1_rusub_2(A,k2_rusub_2(A,B,C),C) = C ) ) ) )).
fof(t23_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t23_rusub_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => v2_rusub_4(k6_domain_1(u1_struct_0(A),B),A) ) ) )).
fof(t23_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => k2_rusub_5(A,k2_rusub_1(A)) = k1_rusub_1(A) ) )).
fof(t23_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => ( k5_rvsum_1(A,B,C) = k5_finseq_2(k4_ordinal1,A,k5_numbers) => B = k7_rvsum_1(A,C) ) ) ) ) )).
fof(t23_rvsum_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v1_valued_0(C) ) => k9_rvsum_2(C,k2_xcmplx_0(A,B)) = k3_rvsum_2(k9_rvsum_2(C,A),k9_rvsum_2(C,B)) ) ) ) )).
fof(t23_scm_1,axiom,( ! [A] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(A,u1_struct_0(k1_ami_3)) ) => m1_scm_1(A,k6_finseq_1(k4_numbers)) ) )).
fof(t23_scm_halt,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => r1_scm_halt(A,B,C) ) ) ) ) )).
fof(t23_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( 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),k1_nat_1(k5_card_1(A),C)) = k5_compos_0(u1_compos_1(k1_scmfsa_2),D,k5_card_1(A)) ) ) ) ) ) ) )).
fof(t23_scmfsa10,axiom,( ! [A] : ( 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) ) ) )).
fof(t23_scmfsa6a,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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)) = k1_nat_1(k5_card_1(B),2) ) ) )).
fof(t23_scmfsa7b,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( 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(k5_numbers)),k7_scmfsa_2(A,k4_scmfsa_2(k5_numbers)),k8_scmfsa_2(A,k4_scmfsa_2(k5_numbers)))) ) ) )).
fof(t23_scmfsa8a,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k2_scmfsa6a(C)),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))),1))) = k5_card_1(C) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k2_scmfsa6a(C)),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),k1_funct_4(A,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))),1))) ) ) ) ) ) )).
fof(t23_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,k6_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(C,k4_compos_1(k1_scmfsa_2))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),k2_scmfsa8a(B,A,k2_scmfsa6a(C)))) ) ) ) ) )).
fof(t23_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ( r2_scmfsa9a(A,k1_scmfsa_m(B),C,D) => ( ( ~ r1_scmfsa9a(A,k1_scmfsa_m(B),C,D) & ~ v7_amistd_1(D,k7_card_1(3),k1_scmfsa_2) ) | k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(k1_scmfsa_9(C,D),B,A)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(k1_scmfsa_m(B),D,C,A),k1_scmfsa9a(A,k1_scmfsa_m(B),C,D))) ) ) ) ) ) ) )).
fof(t23_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ~ ( k2_compos_0(u1_compos_1(k1_scmfsa_2),A) = 1 & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => A != k6_scmfsa_2(B,C) ) ) ) ) )).
fof(t23_scmfsa_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ( ! [E] : ( v7_ordinal1(E) => ( r5_scmfsa7b(B,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(D,B,C,A),E),k1_funct_4(A,k1_scmfsa_9(C,B))) & r6_scmfsa7b(B,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(D,B,C,A),E),k1_funct_4(A,k1_scmfsa_9(C,B))) ) ) => ( ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1))) ) => ~ ! [F] : ( v7_ordinal1(F) => ( ~ ( r1_xxreal_0(k3_funct_2(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(D,B,C,A),F)),k3_funct_2(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(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(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(D,B,C,A),F)) != k5_numbers ) & ~ ( k3_funct_2(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(D,B,C,A),F)) = k5_numbers & k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(D,B,C,A),F),C) = k5_numbers ) & ( k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(D,B,C,A),F),C) != k5_numbers => k3_funct_2(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(D,B,C,A),F)) = k5_numbers ) ) ) ) | ( r6_scmfsa7b(k1_scmfsa_9(C,B),D,A) & r5_scmfsa7b(k1_scmfsa_9(C,B),D,A) ) ) ) ) ) ) ) )).
fof(t23_scmfsa_m,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ r1_xxreal_0(k4_seq_4(k3_funct_2(k4_ordinal1,k1_zfmisc_1(k4_ordinal1),k8_scmfsa_m(A),k1_nat_1(B,1))),k4_seq_4(k3_funct_2(k4_ordinal1,k1_zfmisc_1(k4_ordinal1),k8_scmfsa_m(A),B))) ) ) )).
fof(t23_scmisort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( 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),k5_numbers) | k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(k2_scmfsa_9(D,C),B,A)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(k2_scmfsa_9(D,C),k1_scmfsa6b(C,B,A),A)) ) ) ) ) ) ) )).
fof(t23_scmpds_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ~ ( k2_compos_0(u1_compos_1(k1_scmpds_2),A) = 14 & ! [B] : ( v1_int_1(B) => A != k3_scmpds_2(B) ) ) ) )).
fof(t23_scmpds_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) & v3_scmpds_4(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ( r1_xxreal_0(k5_numbers,k2_xcmplx_0(k5_card_1(A),C)) => v3_scmpds_4(k3_scmpds_4(A,k8_scmpds_2(D,B,C))) ) ) ) ) ) )).
fof(t23_scmpds_5,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( 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,k5_numbers) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v2_compos_1(D,k1_scmpds_2) & v2_scmpds_4(D) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(E) & 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) ) ) ) ) ) )).
fof(t23_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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(k1_nat_1(k5_card_1(D),1))),D),B,A)) = k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),1) ) ) ) ) ) )).
fof(t23_scmpds_7,axiom,( ! [A] : ( ( 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] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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) ) ) ) ) ) )).
fof(t23_scmpds_8,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ! [F] : ( v1_int_1(F) => ! [G] : ! [H] : ! [I] : ( ( v1_funct_1(I) & v1_funct_2(I,k4_card_3(k2_memstr_0(2,k1_scmpds_2)),k4_ordinal1) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k4_card_3(k2_memstr_0(2,k1_scmpds_2)),k4_ordinal1))) ) => ( ( ! [J] : ( ( 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,k5_numbers) ) => ( k1_recdef_1(I,J) = k5_numbers => r1_xxreal_0(k1_funct_1(J,k2_scmpds_2(k1_funct_1(B,D),E)),k5_numbers) ) ) & ! [J] : ( ( 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] : ( ( 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,k5_numbers) ) => ! [K] : ( ( v1_relat_1(K) & v4_relat_1(K,k4_ordinal1) & v5_relat_1(K,u1_compos_1(k1_scmpds_2)) & v1_funct_1(K) & v1_partfun1(K,k4_ordinal1) ) => ( ( ! [L] : ( ( 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] : ( ( 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)),k5_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] : ( ( 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] : ( ( 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)),k5_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) ) ) ) ) ) ) ) ) ) )).
fof(t23_scmring2,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(t23_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t23_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ( v1_finset_1(k3_tarski(A)) => v1_finset_1(A) ) ) )).
fof(t23_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t23_seq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k26_valued_1(k4_ordinal1,k1_numbers,C,k3_xcmplx_0(A,B)),k26_valued_1(k4_ordinal1,k1_numbers,k26_valued_1(k4_ordinal1,k1_numbers,C,B),A)) ) ) ) )).
fof(t23_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(B) & v2_comseq_2(A) & v9_ordinal1(A) ) => ( k1_seq_2(A) = k5_numbers | v2_comseq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,A)) ) ) ) ) )).
fof(t23_seq_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( v2_comseq_2(A) & k1_seq_2(A) != k5_numbers & ! [B] : ( v7_ordinal1(B) => ~ v9_ordinal1(k1_valued_0(k1_numbers,A,B)) ) ) ) )).
fof(t23_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ! [D] : ( ( r1_tarski(D,C) & r2_seqfunc(A,B,C) ) => ( D = k1_xboole_0 | ( r2_seqfunc(A,B,D) & r2_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,k11_seqfunc(A,B,C),D),k11_seqfunc(A,B,D)) ) ) ) ) ) )).
fof(t23_series_3,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ( k2_xcmplx_0(A,B) = 1 => r1_xxreal_0(k7_xcmplx_0(25,4),k3_xcmplx_0(k2_xcmplx_0(A,k7_xcmplx_0(1,A)),k2_xcmplx_0(B,k7_xcmplx_0(1,B)))) ) ) ) )).
fof(t23_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => r1_xxreal_0(k1_square_1(k2_xcmplx_0(k3_square_1(k3_xcmplx_0(A,B)),k7_xcmplx_0(1,k3_square_1(k3_xcmplx_0(A,B))))),k3_xcmplx_0(k2_xcmplx_0(A,k7_xcmplx_0(1,A)),k2_xcmplx_0(B,k7_xcmplx_0(1,B)))) ) ) )).
fof(t23_setfam_1,axiom,( ! [A] : ! [B] : ( ~ r1_xboole_0(A,B) => k3_xboole_0(k1_setfam_1(A),k1_setfam_1(B)) = k1_setfam_1(k3_setfam_1(A,B)) ) )).
fof(t23_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => v3_prob_1(k2_setlim_1(A,B)) ) )).
fof(t23_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_setlim_1(C,A) => v1_setlim_1(k5_setlim_2(A,C,B),A) ) ) ) )).
fof(t23_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( m1_subset_1(F,k5_finsub_1(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t23_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => k10_xtuple_0(k1_setwop_2(A,C,B)) = k2_xboole_0(k10_xtuple_0(C),k1_tarski(B)) ) ) ) )).
fof(t23_sf_mastr,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( v7_ordinal1(B) => k1_sf_mastr(A) = k1_sf_mastr(k5_compos_0(u1_compos_1(k1_scmfsa_2),A,B)) ) ) )).
fof(t23_sfmastr2,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( 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),k5_numbers) => k1_funct_1(k1_scmfsa6b(k4_sfmastr2(C),A,B),C) = k1_funct_1(A,C) ) ) ) ) )).
fof(t23_sfmastr3,axiom,( ! [A] : ( ( v1_ami_2(A) & ~ v1_scmfsa_m(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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) ) ) ) ) ) ) )).
fof(t23_sgraph1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_sgraph1(B))) => ! [D] : ! [E] : ( ( 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)) ) ) ) ) )).
fof(t23_sheffer1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t23_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t23_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => r1_xxreal_0(k2_xxreal_3(1),k6_simplex0(A)) ) )).
fof(t23_simplex1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( ~ v3_pencil_1(C) & v1_matroid0(C) & v3_matroid0(C) & m1_simplex0(C,u1_struct_0(B)) ) => ! [D] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t23_simplex2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_rlaffin1(B,k15_euclid(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ( k5_card_1(B) = k2_xcmplx_0(A,1) => ! [C] : ( ( 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] : ( 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 ) ) ) ) ) )).
fof(t23_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k15_sin_cos(k2_xcmplx_0(A,B)) = k3_xcmplx_0(k15_sin_cos(A),k15_sin_cos(B)) ) ) )).
fof(t23_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_funct_1(k1_sin_cos2,k3_xcmplx_0(2,A)) = k3_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k1_sin_cos2,A)),k1_funct_1(k3_sin_cos2,A)) & k1_funct_1(k3_sin_cos2,k3_xcmplx_0(2,A)) = k6_xcmplx_0(k3_xcmplx_0(2,k1_square_1(k1_funct_1(k3_sin_cos2,A))),1) & k1_funct_1(k5_sin_cos2,k3_xcmplx_0(2,A)) = k7_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k5_sin_cos2,A)),k2_xcmplx_0(1,k1_square_1(k1_funct_1(k5_sin_cos2,A)))) ) ) )).
fof(t23_sin_cos3,axiom,( k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,k5_complex1) = 1 )).
fof(t23_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( k17_sin_cos(A) != k5_numbers & k17_sin_cos(B) != k5_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))) ) ) ) )).
fof(t23_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => k1_newton(k19_sin_cos(A),3) = k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(3,k19_sin_cos(A)),k19_sin_cos(k3_xcmplx_0(3,A))),4) ) )).
fof(t23_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( k17_sin_cos(A) = k4_xcmplx_0(1) => A = k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k1_int_1(k7_xcmplx_0(A,k3_xcmplx_0(2,k28_sin_cos))))) ) ) )).
fof(t23_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( r1_xxreal_0(1,A) & r1_xxreal_0(k2_xcmplx_0(A,k3_square_1(k6_xcmplx_0(k1_square_1(A),1))),k5_numbers) ) ) )).
fof(t23_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k2_sin_cos2(A),k2_sin_cos2(B)),k2_sin_cos2(k6_xcmplx_0(B,A))),k3_xcmplx_0(k3_xcmplx_0(k2_sin_cos2(B),k2_sin_cos2(C)),k2_sin_cos2(k6_xcmplx_0(C,B)))),k3_xcmplx_0(k3_xcmplx_0(k2_sin_cos2(C),k2_sin_cos2(A)),k2_sin_cos2(k6_xcmplx_0(A,C)))),k3_xcmplx_0(k3_xcmplx_0(k2_sin_cos2(k6_xcmplx_0(B,A)),k2_sin_cos2(k6_xcmplx_0(C,B))),k2_sin_cos2(k6_xcmplx_0(A,C)))) = k5_numbers ) ) ) )).
fof(t23_sin_cos9,axiom,( r1_tarski(k1_rcomp_1(k4_xcmplx_0(1),1),k1_relset_1(k1_numbers,k1_sin_cos9)) )).
fof(t23_sincos10,axiom,( v2_funct_1(k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers))) )).
fof(t23_sppol_1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => v1_finset_1(a_1_1_sppol_1(A)) ) )).
fof(t23_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t23_sprect_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t23_sprect_2,axiom,( ! [A] : ( ( ~ v1_zfmisc_1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( 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)) ) ) ) ) )).
fof(t23_sprect_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v4_topreal1(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t23_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t23_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(A,k5_numbers) => k3_square_1(k1_square_1(A)) = k4_xcmplx_0(A) ) ) )).
fof(t23_stacks_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( m1_rewrite1(C,B) => ( r2_hidden(k1_funct_1(C,1),A) <=> v5_relat_1(C,A) ) ) ) ) )).
fof(t23_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ( B = k5_numbers => A = k5_numbers ) & ( A = k5_numbers => B = k5_numbers ) & r1_xxreal_0(A,B) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k7_card_1(B),k7_card_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(B),k7_card_1(A)))) ) => ~ ( v2_funct_2(C,k7_card_1(A)) & v1_stirl2_1(C,B,A) ) ) ) ) ) )).
fof(t23_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k16_substut1(A),k38_substut1(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t23_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_xboole_0(B,C) <=> r1_tarski(B,k3_subset_1(A,C)) ) ) ) )).
fof(t23_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => r1_tarski(C,k4_substlat(A,B,C,C)) ) )).
fof(t23_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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))))) ) ) ) ) )).
fof(t23_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ( ! [D] : ( 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] : ( 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))) ) ) ) ) ) )).
fof(t23_supinf_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t23_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( ~ r1_orders_2(B,D,C) => ( r1_orders_2(B,E,C) <=> k1_symsp_1(A,B,C,D,E) = k4_struct_0(A) ) ) ) ) ) ) ) )).
fof(t23_sysrel,axiom,( ! [A] : ( 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)) ) ) ) )).
fof(t23_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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,k5_numbers)),k1_taxonom1(A,B,k5_numbers)) ) ) ) )).
fof(t23_taylor_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ! [C] : ( v7_ordinal1(C) => ( r1_taylor_1(A,C,B) => ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(D,C) => r1_taylor_1(A,D,B) ) ) ) ) ) ) )).
fof(t23_taylor_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & r2_hidden(E,k2_rcomp_1(k4_xcmplx_0(A),A)) & ~ r1_xxreal_0(F,k5_numbers) & ~ r1_xxreal_0(1,F) & ~ ( ~ r1_xxreal_0(B,k9_complex1(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k16_sin_cos,k2_rcomp_1(k4_xcmplx_0(A),A)),D),k3_xcmplx_0(F,E)),k1_newton(E,D)),k2_newton(D)))) & ~ r1_xxreal_0(B,k9_complex1(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k18_sin_cos,k2_rcomp_1(k4_xcmplx_0(A),A)),D),k3_xcmplx_0(F,E)),k1_newton(E,D)),k2_newton(D)))) ) ) ) ) ) ) ) ) )).
fof(t23_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_numbers) => r1_xxreal_0(k3_tbsp_1(A,k8_metric_1(A,B,C)),k3_xcmplx_0(2,C)) ) ) ) ) )).
fof(t23_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => v6_tops_1(k1_tops_1(A,k2_pre_topc(A,B)),A) ) ) )).
fof(t23_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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))) ) ) ) )).
fof(t23_tdlat_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v3_tdlat_3(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) => k2_pre_topc(A,B) = B ) ) ) ) )).
fof(t23_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t23_tex_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ( ~ v1_xboole_0(k6_subset_1(A,k6_domain_1(A,B))) => ! [C] : ( 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)) ) ) ) ) ) ) ) )).
fof(t23_tex_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t23_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) )).
fof(t23_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t23_tietze,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v10_pre_topc(A) => ! [B] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k1_pre_topc(A,B)),u1_struct_0(k4_topmetr(k4_xcmplx_0(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(k4_xcmplx_0(1),1))))) ) => ~ ( v5_pre_topc(C,k1_pre_topc(A,B),k4_topmetr(k4_xcmplx_0(1),1)) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k4_topmetr(k4_xcmplx_0(1),1))) & v5_pre_topc(D,A,k4_topmetr(k4_xcmplx_0(1),1)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k4_topmetr(k4_xcmplx_0(1),1))))) ) => k2_partfun1(u1_struct_0(A),u1_struct_0(k4_topmetr(k4_xcmplx_0(1),1)),D,B) != C ) ) ) ) ) ) )).
fof(t23_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ v2_struct_0(E) & m1_pre_topc(E,A) ) => ( ( m1_pre_topc(D,B) & m1_pre_topc(E,C) ) => ( r1_tsep_1(D,E) | m1_pre_topc(k2_tsep_1(A,D,E),k2_tsep_1(A,B,C)) ) ) ) ) ) ) ) )).
fof(t23_toler_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t23_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r1_borsuk_6(A,B,C) & r1_borsuk_6(A,D,B) ) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t23_topalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t23_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ! [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] : ( m1_borsuk_2(J,k2_borsuk_1(A,B),k4_borsuk_1(A,B,D,G),k4_borsuk_1(A,B,E,H)) => ! [K] : ( m1_borsuk_2(K,A,C,D) => ! [L] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t23_topalg_6,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)))) ) ) ) )).
fof(t23_topdim_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v4_pre_topc(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ~ ( ~ r2_hidden(D,C) & ! [E] : ( 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),k6_xcmplx_0(A,1)) ) ) ) ) ) ) ) ) ) )).
fof(t23_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t23_topgen_2,axiom,( ! [A] : ! [B] : ( ~ v1_finset_1(A) => ! [C] : ( 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)) ) ) ) )).
fof(t23_topgen_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k4_series_1(k8_nat_1(k1_numbers,k1_prepower(k7_xcmplx_0(1,2)),k1_nat_1(A,1))) = k1_newton(k7_xcmplx_0(1,2),A) ) )).
fof(t23_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t23_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) ) ) )).
fof(t23_topmetr,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t23_topreal1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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 ) ) ) )).
fof(t23_topreal4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( m1_subset_1(G,u1_struct_0(k14_euclid(2))) => ~ ( B != C & r1_topreal4(E,C,D) & r1_tarski(E,A) & r2_hidden(B,k8_metric_1(k14_euclid(2),G,F)) & r2_hidden(D,k8_metric_1(k14_euclid(2),G,F)) & r1_tarski(k8_metric_1(k14_euclid(2),G,F),A) & ! [H] : ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ~ ( r1_topreal4(H,C,B) & r1_tarski(H,A) ) ) ) ) ) ) ) ) ) ) )).
fof(t23_topreal7,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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)) ) ) )).
fof(t23_topreal8,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ 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) ) ) ) ) ) )).
fof(t23_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(t23_topreala,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(D,B) ) => ( v4_pre_topc(k1_rcomp_1(C,D),k4_topmetr(A,B)) & m1_subset_1(k1_rcomp_1(C,D),k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B)))) ) ) ) ) ) ) )).
fof(t23_toprealb,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k8_toprealb(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k8_toprealb(2))) => ( A != B => m1_subset_1(B,u1_struct_0(k11_toprealb(A))) ) ) ) )).
fof(t23_toprealc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t23_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => k12_euclid(k4_struct_0(k15_euclid(A))) = k5_numbers ) )).
fof(t23_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t23_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( 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)))) ) ) ) )).
fof(t23_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v3_tops_1(B,A) & B = u1_struct_0(A) ) ) ) )).
fof(t23_tops_4,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(k3_topmetr)) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => ? [D] : ( 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))) ) ) ) ) ) )).
fof(t23_transgeo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_transgeo(A) & l1_analoaf(A) ) => r3_transgeo(A,k6_partfun1(u1_struct_0(A))) ) )).
fof(t23_treal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & m1_pre_topc(A,k3_topmetr) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,k3_topmetr) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & 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] : ( m1_subset_1(D,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,D) != D ) ) ) ) ) )).
fof(t23_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ( ~ v1_xboole_0(k2_xboole_0(A,B)) & v1_trees_1(k2_xboole_0(A,B)) ) ) ) )).
fof(t23_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v5_trees_3(A) <=> ! [B] : ( 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)) ) ) ) ) )).
fof(t23_trees_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ! [C] : ( ~ ( r2_hidden(C,k10_xtuple_0(A)) & r2_hidden(C,k4_trees_2(A)) ) => k9_trees_4(A,B,C) = A ) ) ) )).
fof(t23_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) ) => k9_trees_9(A) = k3_tarski(a_1_3_trees_9(A)) ) )).
fof(t23_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t23_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) ) )).
fof(t23_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => r1_borsuk_1(A,B) ) ) )).
fof(t23_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( m2_funct_2(B,k4_numbers,u1_turing_1(A),k9_funct_2(k4_numbers,u1_turing_1(A))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( r1_xxreal_0(3,k3_finseq_1(D)) & r2_turing_1(k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,C),D),A,B) ) => ( r1_turing_1(A,B,C,k1_nat_1(k1_nat_1(C,k7_partfun1(k4_ordinal1,D,1)),2)) & r1_turing_1(A,B,k1_nat_1(k1_nat_1(C,k7_partfun1(k4_ordinal1,D,1)),2),k1_nat_1(k1_nat_1(k1_nat_1(C,k7_partfun1(k4_ordinal1,D,1)),k7_partfun1(k4_ordinal1,D,2)),4)) & r1_turing_1(A,B,k1_nat_1(k1_nat_1(k1_nat_1(C,k7_partfun1(k4_ordinal1,D,1)),k7_partfun1(k4_ordinal1,D,2)),4),k1_nat_1(k1_nat_1(k1_nat_1(k1_nat_1(C,k7_partfun1(k4_ordinal1,D,1)),k7_partfun1(k4_ordinal1,D,2)),k7_partfun1(k4_ordinal1,D,3)),6)) ) ) ) ) ) ) )).
fof(t23_twoscomp,axiom,( k1_funct_1(k26_twoscomp,k11_finseq_1(k5_numbers,k5_numbers,k5_numbers)) = 1 & k1_funct_1(k26_twoscomp,k11_finseq_1(k5_numbers,k5_numbers,1)) = 1 & k1_funct_1(k26_twoscomp,k11_finseq_1(k5_numbers,1,k5_numbers)) = 1 & k1_funct_1(k26_twoscomp,k11_finseq_1(k5_numbers,1,1)) = 1 & k1_funct_1(k26_twoscomp,k11_finseq_1(1,k5_numbers,k5_numbers)) = k5_numbers & k1_funct_1(k26_twoscomp,k11_finseq_1(1,k5_numbers,1)) = 1 & k1_funct_1(k26_twoscomp,k11_finseq_1(1,1,k5_numbers)) = 1 & k1_funct_1(k26_twoscomp,k11_finseq_1(1,1,1)) = 1 )).
fof(t23_unialg_2,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_unialg_1(B) & m1_unialg_2(B,A) ) => ! [C] : ( ( v1_unialg_1(C) & m1_unialg_2(C,A) ) => k8_unialg_2(A,k5_unialg_2(A,B,C),C) = C ) ) ) )).
fof(t23_unialg_3,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t23_uproots,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,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))) ) ) ) ) )).
fof(t23_urysohn1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v10_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t23_urysohn2,axiom,( ! [A] : ( v7_ordinal1(A) => r1_tarski(k1_urysohn1(A),k2_urysohn1) ) )).
fof(t23_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_funct_2(C,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t23_valued_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ( ( v1_funct_1(D) & v3_funct_1(D) & v1_funct_2(D,k4_ordinal1,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,C))) ) => k9_nat_1(C,D,A) = k9_nat_1(C,D,B) ) ) ) )).
fof(t23_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(t23_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t23_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t23_vectsp11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( ~ 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] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t23_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k5_algstr_0(A,B,C) = k4_struct_0(A) => B = C ) ) ) ) )).
fof(t23_vectsp_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_vectsp_2(A))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t23_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t23_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => m1_vectsp_4(k2_vectsp_5(A,B,C,D),A,k1_vectsp_5(A,B,C,D)) ) ) ) ) )).
fof(t23_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => ! [D] : ( 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))) ) ) ) ) )).
fof(t23_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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) ) ) )).
fof(t23_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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,k4_xcmplx_0(1))) ) ) ) )).
fof(t23_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( 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,k4_xcmplx_0(k6_complex1))) ) ) ) )).
fof(t23_waybel10,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t23_waybel11,axiom,( ! [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] : ( ( ~ 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) ) ) )).
fof(t23_waybel12,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ v1_xboole_0(a_2_0_waybel12(A,B)) ) ) )).
fof(t23_waybel13,axiom,( ! [A] : ( ( 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(k1_yellow_1(k7_waybel_0(k1_waybel_8(A)))) & v4_yellow_0(k1_yellow_1(k7_waybel_0(k1_waybel_8(A))),k2_yellow_1(u1_struct_0(k1_waybel_8(A)))) & v7_yellow_0(k1_yellow_1(k7_waybel_0(k1_waybel_8(A))),k2_yellow_1(u1_struct_0(k1_waybel_8(A)))) & v4_waybel_0(k1_yellow_1(k7_waybel_0(k1_waybel_8(A))),k2_yellow_1(u1_struct_0(k1_waybel_8(A)))) & m1_yellow_0(k1_yellow_1(k7_waybel_0(k1_waybel_8(A))),k2_yellow_1(u1_struct_0(k1_waybel_8(A)))) ) ) )).
fof(t23_waybel14,axiom,( ! [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) ) => k5_waybel11(A) = u1_pre_topc(A) ) )).
fof(t23_waybel15,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t23_waybel16,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_waybel16(B,A) => v2_waybel_6(B,A) ) ) ) )).
fof(t23_waybel17,axiom,( ! [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) & v4_waybel11(A) & l1_waybel_9(A) ) => ! [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) & v3_waybel_3(B) & v4_waybel11(B) & l1_waybel_9(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t23_waybel19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( u1_struct_0(A) = u1_struct_0(B) => ! [C] : ( m3_yellow_9(C,A,B) => ! [D] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) )).
fof(t23_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t23_waybel21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v4_yellow_0(C,A) & m1_yellow_0(C,A) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(t23_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_waybel23(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),B) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t23_waybel24,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_yellow_1(A,B)))) => ! [D] : ( m1_subset_1(D,A) => k4_waybel_3(A,B,k2_yellow_0(k4_yellow_1(A,B),C),D) = k2_yellow_0(k3_waybel_3(A,B,D),k5_waybel_3(A,B,D,C)) ) ) ) ) ) )).
fof(t23_waybel25,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t23_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v6_pre_topc(B) & v1_waybel25(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t23_waybel27,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_waybel27(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_waybel27(A,B))) => ( r3_orders_2(k2_waybel27(A,B),C,D) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => r3_orders_2(B,k3_waybel27(A,B,C,E),k3_waybel27(A,B,D,E)) ) ) ) ) ) ) )).
fof(t23_waybel28,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r2_hidden(A,k1_yellow_6(B)) ) )).
fof(t23_waybel29,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v4_waybel11(C) & m1_yellow_9(C,k1_yellow_1(u1_pre_topc(B))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_waybel24(A,C))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t23_waybel30,axiom,( ! [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_waybel_2(A) & l1_waybel_9(A) ) => ( v3_waybel_3(k1_yellow_1(k5_waybel11(A))) => ( v8_pre_topc(A) <=> ! [B] : ( 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)) ) ) ) ) ) )).
fof(t23_waybel32,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t23_waybel33,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m2_yellow_9(B,A) => ! [C] : ( 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))) ) ) ) ) ) ) )).
fof(t23_waybel34,axiom,( ! [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] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t23_waybel35,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ! [D] : ( 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) ) ) ) ) )).
fof(t23_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v12_waybel_0(B,A) <=> r1_tarski(k3_waybel_0(A,B),B) ) ) ) )).
fof(t23_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t23_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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))) ) ) ) )).
fof(t23_waybel_4,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t23_waybel_5,axiom,( ! [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) ) => ( v3_waybel_3(A) <=> ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t23_waybel_6,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v6_waybel_6(B,A) <=> ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & r3_orders_2(A,B,D) ) ) ) ) ) ) ) )).
fof(t23_waybel_7,axiom,( ! [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] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t23_waybel_8,axiom,( ! [A] : ( ( 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] : ( ( 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)))) ) ) ) )).
fof(t23_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_yellow_6(A,B))) => ! [D] : ( 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))) ) ) ) ) )).
fof(t23_weddwitt,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_tarski(u1_struct_0(k5_weddwitt(A,B)),u1_struct_0(A)) ) ) )).
fof(t23_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( ( E = k1_funct_1(k6_weierstr(A,B),C) & F = k1_funct_1(k6_weierstr(A,B),D) ) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(E,F)),k3_metric_1(A,C,D)) ) ) ) ) ) ) ) ) ) )).
fof(t23_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => k2_wellord1(A,k1_relat_1(A)) = A ) )).
fof(t23_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_rat_1(C) => ( ( C = k7_xcmplx_0(B,A) & r1_int_2(B,A) ) => ( A = k5_numbers | ( B = k2_rat_1(C) & A = k1_rat_1(C) ) ) ) ) ) ) )).
fof(t23_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : k3_xboole_0(A,k2_xboole_0(B,C)) = k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)) )).
fof(t23_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( 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)) ) ) ) )).
fof(t23_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k6_xcmplx_0(k6_xcmplx_0(C,A),k6_xcmplx_0(C,B)) = k6_xcmplx_0(B,A) ) ) ) )).
fof(t23_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t23_xtuple_0,axiom,( ! [A] : ! [B] : k9_xtuple_0(k2_xboole_0(A,B)) = k2_xboole_0(k9_xtuple_0(A),k9_xtuple_0(B)) )).
fof(t23_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ~ ( ~ r1_xxreal_0(k3_xxreal_0(B,C),A) & r1_xxreal_0(B,A) ) ) ) ) )).
fof(t23_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => r1_tarski(k3_xxreal_1(A,B),k1_xxreal_1(A,B)) ) ) )).
fof(t23_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => m1_xxreal_2(B,k2_xxreal_1(A,B)) ) ) )).
fof(t23_xxreal_3,axiom,( ! [A] : ( 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 ) ) ) )).
fof(t23_yellow10,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(t23_yellow12,axiom,( ! [A] : ( ( 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))) ) )).
fof(t23_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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) ) ) ) )).
fof(t23_yellow14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v3_yellow_8(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t23_yellow15,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t23_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t23_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(B)) & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & E = C & F = D & ? [G] : ( m1_subset_1(G,k1_altcat_1(A,C,D)) & ? [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t23_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(B,A) <=> ! [C] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ( r1_waybel_0(A,C,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r3_waybel_9(A,C,D) => r2_hidden(D,B) ) ) ) ) ) ) ) )).
fof(t23_yellow20,axiom,( ! [A] : ( l2_altcat_1(A) => ! [B] : ( l2_altcat_1(B) => ( r1_yellow20(A,B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(k2_yellow20(A,B))) => ! [H] : ( 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] : ( m1_subset_1(I,k1_altcat_1(A,C,D)) => ! [J] : ( m1_subset_1(J,k1_altcat_1(B,E,F)) => ( I = J => r2_hidden(I,k1_altcat_1(k2_yellow20(A,B),G,H)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t23_yellow_0,axiom,( ! [A] : ( ( v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t23_yellow_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => k3_yellow_0(k1_yellow_1(u1_pre_topc(A))) = k1_xboole_0 ) )).
fof(t23_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( ! [B] : r1_yellow_0(A,B) <=> ! [B] : r2_yellow_0(A,B) ) ) )).
fof(t23_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t23_yellow_4,axiom,( ! [A] : ( ( v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(t23_yellow_5,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_yellow_5(A,k3_yellow_0(A),B) = k3_yellow_0(A) ) ) )).
fof(t23_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ! [D] : ( m2_yellow_6(D,A,B) => ( D = k5_yellow_6(A,B,C) => r1_waybel_0(A,D,C) ) ) ) ) )).
fof(t23_yellow_7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t23_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v6_pre_topc(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) ) )).
fof(t23_yellow_9,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)))) ) ) ) ) )).
fof(t23_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t23_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ~ ( ~ ( v2_zf_lang(A) & k1_funct_1(A,1) = k5_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 ) ) ) )).
fof(t23_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v8_zf_lang(A) => k21_zf_lang(A) = k20_zf_lang(k21_zf_lang(k20_zf_lang(A))) ) ) )).
fof(t23_zf_model,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ~ v1_xboole_0(C) => ( r2_zf_model(C,k8_zf_lang(B,A)) <=> r2_zf_model(C,A) ) ) ) ) )).
fof(t23_zfmisc_1,axiom,( ! [A] : ! [B] : ( A != B => k5_xboole_0(k1_tarski(A),k1_tarski(B)) = k2_tarski(A,B) ) )).
fof(t23_zfmodel2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => r1_zfmodel1(k6_partfun1(A),A) ) )).
fof(t23_zfrefle1,axiom,( ! [A] : ( v3_ordinal1(A) => r2_ordinal2(k1_ordinal1(A),1) ) )).
fof(t23_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( m1_zmodul01(D,A) => ( ( r1_struct_0(C,B) & m1_zmodul01(C,D) ) => r1_struct_0(D,B) ) ) ) ) )).
fof(t23_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ( k18_zmodul02(A,B) = k1_xboole_0 => k21_zmodul02(A,B) = k4_struct_0(A) ) ) ) )).
fof(t23_zmodul03,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_vectsp_6(D,k9_int_3(A),k12_zmodul02(A,B)) => ? [E] : ( m2_zmodul02(E,B,C) & ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ~ ( r2_hidden(F,C) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ~ ( r2_hidden(G,C) & r2_hidden(G,k13_zmodul02(A,B,F)) & k3_funct_2(u1_struct_0(B),k4_numbers,E,G) = k1_zmodul03(k9_int_3(A),k12_zmodul02(A,B),D,k13_zmodul02(A,B,F)) ) ) ) ) ) ) ) ) ) )).
fof(t240_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(A,B) => r1_tarski(k4_xxreal_1(B,C),k1_xxreal_1(A,k1_xxreal_0)) ) ) ) ) )).
fof(t241_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(A,B) => r1_tarski(k2_xxreal_1(B,C),k2_xxreal_1(A,k1_xxreal_0)) ) ) ) ) )).
fof(t242_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ~ r1_xxreal_0(B,A) => r1_tarski(k1_xxreal_1(B,C),k3_xxreal_1(A,k1_xxreal_0)) ) ) ) ) )).
fof(t243_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ~ r1_xxreal_0(B,A) => r1_tarski(k2_xxreal_1(B,C),k3_xxreal_1(A,k1_xxreal_0)) ) ) ) ) )).
fof(t244_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(A,B) => r1_tarski(k4_xxreal_1(B,C),k3_xxreal_1(A,k1_xxreal_0)) ) ) ) ) )).
fof(t245_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(A,B) => r1_tarski(k3_xxreal_1(B,C),k3_xxreal_1(A,k1_xxreal_0)) ) ) ) ) )).
fof(t246_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(A,B) => r1_tarski(k4_xxreal_1(B,C),k2_xxreal_1(A,k1_xxreal_0)) ) ) ) ) )).
fof(t247_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(A,B) => r1_tarski(k4_xxreal_1(B,C),k4_xxreal_1(A,k1_xxreal_0)) ) ) ) ) )).
fof(t248_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ~ r1_xxreal_0(B,A) => r1_tarski(k2_xxreal_1(B,C),k4_xxreal_1(A,k1_xxreal_0)) ) ) ) ) )).
fof(t249_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(B,A) => r1_tarski(k1_xxreal_1(B,C),k4_xxreal_1(A,k1_xxreal_0)) ) ) ) ) )).
fof(t24_abcmiz_0,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) ) )).
fof(t24_abcmiz_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t24_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & v1_abcmiz_a(A) & l1_msualg_1(A) ) => ! [B] : ( 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 ) ) ) ) )).
fof(t24_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t24_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t24_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t24_afinsq_2,axiom,( ! [A] : ( ( v1_finset_1(A) & v6_membered(A) ) => ! [B] : ( ( v1_finset_1(B) & v6_membered(B) ) => ( r1_afinsq_2(A,B) => r1_xboole_0(A,B) ) ) ) )).
fof(t24_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(k14_afproj(A))) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & B = k6_afproj(A,C) & v1_aff_4(C,A) ) ) ) )).
fof(t24_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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 ) ) ) ) ) ) ) )).
fof(t24_algspec1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( m1_algspec1(B,A) => ! [C] : ( 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 ) ) ) ) )).
fof(t24_altcat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & m1_altcat_2(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t24_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v16_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t24_ami_3,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) <=> ~ ( A != k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0) & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_ami_3)) ) => A != k2_ami_3(B,C) ) ) & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_ami_3)) ) => A != k3_ami_3(B,C) ) ) & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_ami_3)) ) => A != k4_ami_3(B,C) ) ) & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_ami_3)) ) => A != k5_ami_3(B,C) ) ) & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_ami_3)) ) => A != k6_ami_3(B,C) ) ) & ! [B] : ( v7_ordinal1(B) => A != k7_ami_3(B) ) & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [C] : ( v7_ordinal1(C) => A != k8_ami_3(C,B) ) ) & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [C] : ( v7_ordinal1(C) => A != k9_ami_3(C,B) ) ) ) ) )).
fof(t24_ami_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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) ) ) ) )).
fof(t24_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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,k5_numbers),k2_compos_1(B)),A,B) ) ) )).
fof(t24_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_analmetr(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k2_analmetr(A,B,C))) => ( r4_analmetr(k2_analmetr(A,B,C),D,F,E,G) => r4_analmetr(k2_analmetr(A,B,C),D,F,G,E) ) ) ) ) ) ) ) ) )).
fof(t24_analoaf,axiom,( ! [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) ) => ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & k3_rlvect_1(A,k1_rlvect_1(A,B,E),k1_rlvect_1(A,C,F)) = D ) ) ) ) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_analoaf(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_analoaf(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_analoaf(A))) => ! [E] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_analmetr(A,D,E) => r3_analmetr(A,B,C,k2_analort(A,D,E,B),k2_analort(A,D,E,C),D,E) ) ) ) ) ) ) )).
fof(t24_anproj_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ! [G] : ( 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) ) ) ) ) ) ) )).
fof(t24_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_anproj_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_anproj_1(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t24_aofa_000,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ? [C] : ( 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) ) ) ) )).
fof(t24_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ( ( v1_relat_1(I) & v1_funct_1(I) & v1_finseq_1(I) ) => ( I = k9_aofa_a00(A,B,C,D,E,F,G,H) <=> ( k3_finseq_1(I) = 8 & k1_funct_1(I,1) = A & k1_funct_1(I,2) = B & k1_funct_1(I,3) = C & k1_funct_1(I,4) = D & k1_funct_1(I,5) = E & k1_funct_1(I,6) = F & k1_funct_1(I,7) = G & k1_funct_1(I,8) = H ) ) ) )).
fof(t24_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ( k1_msualg_1(A,E) = k3_finseq_4(u1_struct_0(A),B,C,D) => ! [F] : ( l3_msualg_1(F,A) => k3_msualg_1(A,E,F) = k4_card_3(k3_finseq_4(k10_xtuple_0(u3_msualg_1(A,F)),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,F),B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,F),C),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,F),D))) ) ) ) ) ) ) ) )).
fof(t24_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [E] : ( ( v1_aofa_i00(E,A,B,D) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),D) ) => ! [F] : ( m2_aofa_i00(F,A,B,D,E) => ! [G] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_armstrng,axiom,( ! [A] : ! [B] : ( 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)))) ) ) )).
fof(t24_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ( r2_hidden(k5_arytm_0(A,B),k1_numbers) => B = k5_numbers ) ) ) )).
fof(t24_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( r1_arytm_2(B,A) => k2_arytm_1(A,k7_arytm_2(B,C)) = k2_arytm_1(k1_arytm_1(A,B),C) ) ) ) ) )).
fof(t24_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ( k4_arytm_3(A,1) = A & k4_arytm_3(1,A) = 1 ) ) )).
fof(t24_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v4_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v4_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_limfunc1(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) => ( ~ r2_hidden(B,k7_asympt_0(A)) & r2_hidden(A,k7_asympt_0(B)) ) ) ) ) )).
fof(t24_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => k9_nat_1(k1_numbers,A,B) = k2_power(k2_xcmplx_0(k6_xcmplx_0(k1_square_1(B),B),1),4) ) & ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v4_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( r2_funct_2(k4_ordinal1,k1_numbers,B,A) & k6_asympt_0(k3_asympt_1(8)) = k6_asympt_0(B) ) ) ) ) )).
fof(t24_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t24_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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))) ) ) )).
fof(t24_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => v2_bagorder(k6_bagorder(A),A) ) )).
fof(t24_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( r2_hidden(B,k5_bcialg_1(A)) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_1(A,C,k1_bcialg_1(A,C,B)) = B ) ) ) ) )).
fof(t24_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v10_bcialg_1(k2_bcialg_1(A,B),A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_bcialg_1(A,C,B) => k2_bcialg_1(A,B) = k2_bcialg_1(A,C) ) ) ) ) ) )).
fof(t24_bcialg_3,axiom,( ! [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) & v6_bcialg_3(A) & l2_bcialg_1(A) ) => ( v7_bcialg_3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v2_bcialg_3(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(t24_bcialg_4,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t24_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( 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 ) ) ) ) ) )).
fof(t24_bcialg_6,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => k3_bcialg_6(A,k2_xcmplx_0(C,D),B) = k1_bcialg_1(A,k3_bcialg_6(A,C,B),k2_bcialg_1(A,k3_bcialg_6(A,D,B))) ) ) ) ) )).
fof(t24_bciideal,axiom,( ! [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) ) => ( ( ~ 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) ) ) ) )).
fof(t24_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) = k2_xcmplx_0(k2_bhsp_1(A,B,B),k2_bhsp_1(A,C,C)) ) ) ) ) )).
fof(t24_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_bhsp_2(C,A) & k1_bhsp_2(A,C) = B ) => ( v2_comseq_2(k3_bhsp_2(A,C,B)) & k1_seq_2(k3_bhsp_2(A,C,B)) = k5_numbers ) ) ) ) ) )).
fof(t24_bhsp_4,axiom,( ! [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_bhsp_1(A) & v3_bhsp_3(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_bhsp_4(B,A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & ? [F] : ( v7_ordinal1(F) & 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))) ) ) ) ) ) ) ) ) )).
fof(t24_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t24_binari_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( 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 ) ) ) )).
fof(t24_binari_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(A,k5_series_1(2,B)) => k1_binari_4(B,A) = B ) ) ) )).
fof(t24_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k1_funct_1(k8_binom(A,B,C,D),k1_nat_1(D,1)) = k2_binom(A,C,D) ) ) ) ) )).
fof(t24_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ( r1_xxreal_0(C,k5_series_1(2,k1_nat_1(B,1))) => ! [D] : ( m2_finseq_2(D,k6_margrel1,k4_finseq_2(B,k6_margrel1)) => ( D = k1_funct_1(k2_bintree2(A,B),k3_nat_d(k1_nat_1(C,1),2)) => k1_funct_1(k2_bintree2(A,k1_nat_1(B,1)),C) = k7_finseq_1(D,k10_binarith(k4_ordinal1,k4_nat_d(k1_nat_1(C,1),2))) ) ) ) ) ) ) )).
fof(t24_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t24_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t24_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_topmetr))) => ( A = B => ( v2_rcomp_1(A) <=> v4_pre_topc(B,k5_topmetr) ) ) ) ) )).
fof(t24_borsuk_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v1_rat_1(A) ) => ~ v1_rat_1(k3_int_1(A)) ) )).
fof(t24_borsuk_6,axiom,( ~ 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)))) )).
fof(t24_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( A != B => k1_borsuk_7(A,B,A,C,D,E) = k4_funct_4(A,B,E,D) ) )).
fof(t24_bspace,axiom,( ! [A] : v13_algstr_0(k7_bspace(A)) )).
fof(t24_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t24_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t24_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t24_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t24_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(t24_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t24_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(E,A) => ( r3_bvfunc_2(A,D,B,E) => 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),D)) ) ) ) ) ) ) )).
fof(t24_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t24_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t24_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t24_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t24_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t24_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t24_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) ) ) )).
fof(t24_c0sp1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(t24_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(t24_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_valuat_1(F,A,E) => ! [G] : ( 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] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(t24_calcul_2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t24_card_1,axiom,( ! [A] : ! [B] : ( r1_tarski(k1_zfmisc_1(B),A) => ( r2_hidden(k1_card_1(B),k1_card_1(A)) & ~ r2_wellord2(B,A) ) ) )).
fof(t24_card_2,axiom,( ! [A] : ( v1_card_1(A) => k3_card_2(A,k5_numbers) = 1 ) )).
fof(t24_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(A,B) => r1_tarski(k3_card_3(A),k3_card_3(B)) ) ) ) )).
fof(t24_card_5,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => r1_tarski(k4_ordinal1,k1_card_5(A)) ) )).
fof(t24_card_fil,axiom,( ! [A] : ( v1_card_1(A) => r1_ordinal1(k2_card_1(A),k3_card_2(2,A)) ) )).
fof(t24_card_fin,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t24_card_lar,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) & ~ v4_card_3(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ( r2_hidden(k4_ordinal1,k1_card_5(A)) & v1_card_lar(B,A) ) => ! [C] : ( v3_ordinal1(C) => ~ ( r2_hidden(C,A) & ! [D] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t24_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t24_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( m1_subset_1(E,u4_struct_0(B)) => ! [F] : ( m1_subset_1(F,u4_struct_0(B)) => ( k3_graph_1(k6_cat_2(A,B),k8_cat_2(A,B,D,F)) = k4_graph_1(k6_cat_2(A,B),k8_cat_2(A,B,C,E)) => k1_cat_1(k6_cat_2(A,B),k8_cat_2(A,B,C,E),k8_cat_2(A,B,D,F)) = k8_cat_2(A,B,k1_cat_1(A,C,D),k1_cat_1(B,E,F)) ) ) ) ) ) ) ) )).
fof(t24_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,B,C) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t24_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t24_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( r2_hidden(C,k10_cat_5(A,B)) <=> k3_graph_1(A,C) = B ) ) ) ) )).
fof(t24_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => k5_card_1(k2_catalan2(A,k5_numbers)) = 1 ) )).
fof(t24_catalg_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(t24_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v4_algstr_0(B,A) & v4_algstr_0(C,A) ) => v4_algstr_0(k5_cayldick(A,B,C),k4_cayldick(A)) ) ) ) ) )).
fof(t24_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k7_cc0sp1(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k7_cc0sp1(A))) => ! [G] : ( 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] : ( m1_subset_1(H,A) => k3_funct_2(A,k2_numbers,D,H) = k3_xcmplx_0(k3_funct_2(A,k2_numbers,B,H),k3_funct_2(A,k2_numbers,C,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k5_cc0sp2(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k5_cc0sp2(A))) => ! [G] : ( 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] : ( m1_subset_1(H,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k2_numbers,D,H) = k3_xcmplx_0(k3_funct_2(u1_struct_0(A),k2_numbers,B,H),k3_funct_2(u1_struct_0(A),k2_numbers,C,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ~ ( v2_comseq_2(A) & k3_comseq_2(A) != k5_numbers & ! [B] : ( v7_ordinal1(B) => ~ v9_ordinal1(k1_valued_0(k2_numbers,A,B)) ) ) ) )).
fof(t24_cfdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [C] : ( v1_xcmplx_0(C) => ( ( 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) = k6_xcmplx_0(k2_cfdiff_1(A,C),k2_cfdiff_1(B,C)) ) ) ) ) ) )).
fof(t24_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_cfuncdom(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_cfuncdom(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t24_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( 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),k4_xcmplx_0(k6_complex1))) ) ) ) )).
fof(t24_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => r2_hidden(A,k10_cgames_1(A)) ) )).
fof(t24_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t24_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ( r5_glib_000(A,B) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m3_glib_001(D,B) => ( ( C = D & v8_glib_001(C,A) ) => v8_glib_001(D,B) ) ) ) ) ) ) )).
fof(t24_circcmb2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ( ( ! [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] : ( m1_subset_1(I,k4_card_3(u3_msualg_1(B,E))) => v1_circuit2(k5_facirc_1(B,E,I,H),B,E) ) ) => ! [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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => m1_subset_1(C,u1_struct_0(k2_circcomb(A,B))) ) ) ) )).
fof(t24_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v4_msualg_1(C,A) & v4_msafree2(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t24_circled1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t24_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t24_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_pdiff_7(C,A) & m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) ) => k1_group_1(k2_ckspace1(A,B,C)) = k8_funcop_1(k4_ordinal1,C,1) ) ) ) )).
fof(t24_classes1,axiom,( ! [A] : ! [B] : ( r2_hidden(B,k1_classes1(A)) => r2_hidden(k1_card_1(B),k1_card_1(k1_classes1(A))) ) )).
fof(t24_classes2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) ) => ( ( v4_ordinal1(k9_xtuple_0(A)) & ! [B] : ( 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) ) ) )).
fof(t24_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k9_clopban1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_clopban1(A,B))) => ! [E] : ( v1_xcmplx_0(E) => ( D = k1_clvect_1(k9_clopban1(A,B),C,E) <=> ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t24_clopban3,axiom,( ! [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_clopban1(A) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clopban3(B,A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(D,E) & r1_xxreal_0(C,k2_normsp_0(A,k5_algstr_0(A,k1_normsp_0(A,k1_bhsp_4(A,B),E),k1_normsp_0(A,k1_bhsp_4(A,B),D)))) ) ) ) ) ) ) ) )).
fof(t24_clopban4,axiom,( ! [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) & 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] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t24_closure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( 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] : ( 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)) ) ) ) ) ) )).
fof(t24_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) => ! [D] : ( m3_pboole(D,A,B) => ( ! [E] : ( ( 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))) ) ) ) ) )).
fof(t24_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( u1_struct_0(A) = B => v6_clvect_1(B,A) ) ) ) )).
fof(t24_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_clvect_2(C,A) & k1_clvect_2(A,C) = B ) => ( v2_comseq_2(k3_clvect_2(A,C,B)) & k1_seq_2(k3_clvect_2(A,C,B)) = k5_numbers ) ) ) ) ) )).
fof(t24_clvect_3,axiom,( ! [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) & v2_csspace(A) & v4_clvect_2(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clvect_3(B,A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(D,E) & r1_xxreal_0(D,F) & r1_xxreal_0(C,k13_csspace(A,k3_clvect_3(A,B,E,F))) ) ) ) ) ) ) ) ) )).
fof(t24_coh_sp,axiom,( ! [A] : ! [B] : ( 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 ) ) )).
fof(t24_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( 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)) ) ) ) )).
fof(t24_combgras,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ( ( A = 1 & r1_ordinal1(k1_nat_1(A,1),k1_card_1(B)) ) => ! [C] : ( l1_combgras(C,k1_combgras(A,B),k1_combgras(A,B)) => ~ ( v7_combgras(C,k1_combgras(A,B)) & ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t24_compl_sp,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v2_prob_1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ~ ( ! [D] : ( v7_ordinal1(D) => r2_hidden(k9_nat_1(A,C,D),k9_nat_1(k9_setfam_1(A),B,D)) ) & v1_finset_1(k2_relset_1(A,C)) & v1_xboole_0(k2_kurato_0(A,B)) ) ) ) ) ) )).
fof(t24_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k3_complex1(k7_xcmplx_0(A,B)) = k7_xcmplx_0(k3_real_1(k4_real_1(k3_complex1(A),k3_complex1(B)),k4_real_1(k4_complex1(A),k4_complex1(B))),k2_xcmplx_0(k1_square_1(k3_complex1(B)),k1_square_1(k4_complex1(B)))) & k4_complex1(k7_xcmplx_0(A,B)) = k7_xcmplx_0(k5_real_1(k4_real_1(k3_complex1(B),k4_complex1(A)),k4_real_1(k3_complex1(A),k4_complex1(B))),k2_xcmplx_0(k1_square_1(k3_complex1(B)),k1_square_1(k4_complex1(B)))) ) ) ) )).
fof(t24_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( A != k5_numbers => ( k19_sin_cos(k1_comptrig(A)) = k7_xcmplx_0(k3_complex1(A),k9_complex1(A)) & k17_sin_cos(k1_comptrig(A)) = k7_xcmplx_0(k4_complex1(A),k9_complex1(A)) ) ) ) )).
fof(t24_complfld,axiom,( ! [A] : ( 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) ) ) )).
fof(t24_complsp2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t24_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) ) ) ) )).
fof(t24_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( r1_tarski(B,C) => r1_compos_2(B,C) ) ) ) )).
fof(t24_comptrig,axiom,( v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k16_sin_cos,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos)))) )).
fof(t24_comput_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v2_margrel1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k3_finseq_2(A),A))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( k1_relset_1(k3_finseq_2(A),B) = k4_finseq_2(C,A) => k19_margrel1(B) = C ) ) ) ) )).
fof(t24_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,C)),k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B),C)) ) ) ) )).
fof(t24_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v2_comseq_2(A) & v9_ordinal1(A) ) => ( k3_comseq_2(A) = k5_complex1 | k3_comseq_2(k36_valued_1(k4_ordinal1,k2_numbers,A)) = k5_xcmplx_0(k3_comseq_2(A)) ) ) ) )).
fof(t24_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) & l2_conlat_1(B,A) ) => ( ( u2_conlat_1(A,B) = k1_xboole_0 => v8_conlat_1(B,A) ) & ( u3_conlat_1(A,B) = k1_xboole_0 => v7_conlat_1(B,A) ) ) ) ) )).
fof(t24_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t24_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t24_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ! [C] : ( 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) ) ) ) )).
fof(t24_convex1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t24_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( m1_convex4(C,A) => ( B != k5_complex1 => k1_convex4(A,k7_convex4(A,B,C)) = k1_convex4(A,C) ) ) ) ) )).
fof(t24_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( 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) ) ) ) )).
fof(t24_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t24_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ! [D] : ( m2_finseq_1(D,k2_zfmisc_1(k3_cqc_lang(A),k2_cqc_the1)) => ! [E] : ( 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(E)) & r1_cqc_the1(A,E,B,C) ) => r1_cqc_the1(A,k8_finseq_1(k2_zfmisc_1(k3_cqc_lang(A),k2_cqc_the1),D,E),k1_nat_1(B,k3_finseq_1(D)),C) ) ) ) ) ) ) )).
fof(t24_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t24_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t24_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t24_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t24_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(t24_descip_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,A) => ! [I] : ( m1_subset_1(I,A) => ! [J] : ( m1_subset_1(J,A) => ! [K] : ( m1_subset_1(K,A) => ! [L] : ( m1_subset_1(L,A) => ! [M] : ( m1_subset_1(M,A) => ! [N] : ( m1_subset_1(N,A) => ! [O] : ( m1_subset_1(O,A) => ! [P] : ( m1_subset_1(P,A) => ! [Q] : ( m1_subset_1(Q,A) => ! [R] : ( m1_subset_1(R,A) => ! [S] : ( m1_subset_1(S,A) => ! [T] : ( m1_subset_1(T,A) => ! [U] : ( m1_subset_1(U,A) => ! [V] : ( m1_subset_1(V,A) => ! [W] : ( m1_subset_1(W,A) => ! [X] : ( m1_subset_1(X,A) => ! [Y] : ( m1_subset_1(Y,A) => ! [Z] : ( m1_subset_1(Z,A) => ! [A1] : ( m1_subset_1(A1,A) => ! [B1] : ( m1_subset_1(B1,A) => ! [C1] : ( m1_subset_1(C1,A) => ! [D1] : ( m1_subset_1(D1,A) => ! [E1] : ( m1_subset_1(E1,A) => ! [F1] : ( m1_subset_1(F1,A) => ! [G1] : ( m1_subset_1(G1,A) => ! [H1] : ( m1_subset_1(H1,A) => ! [I1] : ( m1_subset_1(I1,A) => ! [J1] : ( m1_subset_1(J1,A) => ! [K1] : ( m1_subset_1(K1,A) => ! [L1] : ( m1_subset_1(L1,A) => ! [M1] : ( m1_subset_1(M1,A) => ! [N1] : ( m1_subset_1(N1,A) => ! [O1] : ( m1_subset_1(O1,A) => ! [P1] : ( m1_subset_1(P1,A) => ! [Q1] : ( m1_subset_1(Q1,A) => ! [R1] : ( m1_subset_1(R1,A) => ! [S1] : ( m1_subset_1(S1,A) => ! [T1] : ( m1_subset_1(T1,A) => ! [U1] : ( m1_subset_1(U1,A) => ! [V1] : ( m1_subset_1(V1,A) => ! [W1] : ( m1_subset_1(W1,A) => ! [X1] : ( m1_subset_1(X1,A) => ! [Y1] : ( m1_subset_1(Y1,A) => ! [Z1] : ( m1_subset_1(Z1,A) => ! [A2] : ( m1_subset_1(A2,A) => ! [B2] : ( m1_subset_1(B2,A) => ! [C2] : ( m1_subset_1(C2,A) => ! [D2] : ( m1_subset_1(D2,A) => ! [E2] : ( m1_subset_1(E2,A) => ? [F2] : ( m2_finseq_1(F2,A) & v3_card_1(F2,56) & k1_funct_1(F2,1) = B & k1_funct_1(F2,2) = C & k1_funct_1(F2,3) = D & k1_funct_1(F2,4) = E & k1_funct_1(F2,5) = F & k1_funct_1(F2,6) = G & k1_funct_1(F2,7) = H & k1_funct_1(F2,8) = I & k1_funct_1(F2,9) = J & k1_funct_1(F2,10) = K & k1_funct_1(F2,11) = L & k1_funct_1(F2,12) = M & k1_funct_1(F2,13) = N & k1_funct_1(F2,14) = O & k1_funct_1(F2,15) = P & k1_funct_1(F2,16) = Q & k1_funct_1(F2,17) = R & k1_funct_1(F2,18) = S & k1_funct_1(F2,19) = T & k1_funct_1(F2,20) = U & k1_funct_1(F2,21) = V & k1_funct_1(F2,22) = W & k1_funct_1(F2,23) = X & k1_funct_1(F2,24) = Y & k1_funct_1(F2,25) = Z & k1_funct_1(F2,26) = A1 & k1_funct_1(F2,27) = B1 & k1_funct_1(F2,28) = C1 & k1_funct_1(F2,29) = D1 & k1_funct_1(F2,30) = E1 & k1_funct_1(F2,31) = F1 & k1_funct_1(F2,32) = G1 & k1_funct_1(F2,33) = H1 & k1_funct_1(F2,34) = I1 & k1_funct_1(F2,35) = J1 & k1_funct_1(F2,36) = K1 & k1_funct_1(F2,37) = L1 & k1_funct_1(F2,38) = M1 & k1_funct_1(F2,39) = N1 & k1_funct_1(F2,40) = O1 & k1_funct_1(F2,41) = P1 & k1_funct_1(F2,42) = Q1 & k1_funct_1(F2,43) = R1 & k1_funct_1(F2,44) = S1 & k1_funct_1(F2,45) = T1 & k1_funct_1(F2,46) = U1 & k1_funct_1(F2,47) = V1 & k1_funct_1(F2,48) = W1 & k1_funct_1(F2,49) = X1 & k1_funct_1(F2,50) = Y1 & k1_funct_1(F2,51) = Z1 & k1_funct_1(F2,52) = A2 & k1_funct_1(F2,53) = B2 & k1_funct_1(F2,54) = C2 & k1_funct_1(F2,55) = D2 & k1_funct_1(F2,56) = E2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_dickson,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => k1_card_1(k6_dickson(A,B)) = 1 ) ) ) )).
fof(t24_diff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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] : ( ( 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_funct_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,C),k26_valued_1(k1_numbers,k1_numbers,G,D)),B),k1_nat_1(A,1)),E) = k2_xcmplx_0(k3_xcmplx_0(C,k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(F,B),k1_nat_1(A,1)),E)),k3_xcmplx_0(D,k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(G,B),k1_nat_1(A,1)),E))) ) ) ) ) ) ) ) )).
fof(t24_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k1_funct_1(k3_diff_1(k1_fcont_1(B,C),A),D) = k3_xcmplx_0(B,A) ) ) ) ) )).
fof(t24_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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 != k5_numbers => k10_diff_1(C,k6_xcmplx_0(B,A),B,k2_xcmplx_0(B,A)) = k7_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(C,A),2),B),k3_xcmplx_0(k3_xcmplx_0(2,A),A)) ) ) ) ) )).
fof(t24_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(B,k1_relset_1(k1_numbers,k26_sin_cos)) & r2_hidden(k6_xcmplx_0(B,A),k1_relset_1(k1_numbers,k26_sin_cos)) ) => k1_funct_1(k4_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k26_sin_cos),k18_sin_cos),A),B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k16_sin_cos),B),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k16_sin_cos),k6_xcmplx_0(B,A))) ) ) ) )).
fof(t24_dilworth,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t24_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ~ ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_diraf(A,B,C,B,D) ) ) ) ) )).
fof(t24_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => ! [C] : ( m1_dist_2(C,A,B) => ! [D] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,A,k6_margrel1) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => k4_dist_2(A,B,C,k5_bvfunc_1(A,D,E)) = k7_xcmplx_0(k5_card_1(k2_xboole_0(k3_dist_2(k1_partfun1(k4_ordinal1,A,A,k6_margrel1,C,D)),k3_dist_2(k1_partfun1(k4_ordinal1,A,A,k6_margrel1,C,E)))),k3_finseq_1(C)) ) ) ) ) ) )).
fof(t24_domain_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(B)) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t24_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v2_finsub_1(B) => ! [C] : ( m1_dynkin(C,A) => ( r1_tarski(B,C) => r1_tarski(k9_prob_1(A,B),C) ) ) ) ) ) )).
fof(t24_e_siec,axiom,( ! [A] : ( ( 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 ) ) )).
fof(t24_ec_pf_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => k2_binom(A,B,k1_nat_1(C,1)) = k6_algstr_0(A,k2_binom(A,B,C),B) ) ) ) )).
fof(t24_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ( B = k5_int_1(2,A) => k5_algstr_0(k9_int_3(A),k8_group_1(k9_int_3(A),B,C),C) = C ) ) ) ) )).
fof(t24_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u4_struct_0(k11_ens_1(A))) => m1_subset_1(B,k2_ens_1(A)) ) ) )).
fof(t24_entropy1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( v1_entropy1(B,A) <=> ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => r1_entropy1(k7_matrix_0(k1_numbers,B,C),C) ) ) ) ) ) )).
fof(t24_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : 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)) )).
fof(t24_eqrel_1,axiom,( ! [A] : ! [B] : ( ( 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] : ! [D] : ~ ( 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)) ) ) )).
fof(t24_equation,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v3_msualg_1(D,A) & v4_msualg_1(D,A) & v2_msafree(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_euclid,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k17_euclid(k19_euclid(A,B)) = A & k18_euclid(k19_euclid(A,B)) = B ) ) ) )).
fof(t24_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => k22_rvsum_1(B,k3_rlvect_1(k15_euclid(A),C,D)) = k2_xcmplx_0(k22_rvsum_1(B,C),k22_rvsum_1(B,D)) ) ) ) ) )).
fof(t24_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => k22_rvsum_1(B,k6_euclid(A,C)) = k4_xcmplx_0(k22_rvsum_1(B,C)) ) ) ) )).
fof(t24_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(3))) => ! [C] : ( 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)) ) ) ) )).
fof(t24_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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),k28_sin_cos) | ( ~ r1_xxreal_0(k4_euclid_3(B,C,A),k28_sin_cos) & ~ r1_xxreal_0(k4_euclid_3(C,A,B),k28_sin_cos) ) ) ) ) ) ) )).
fof(t24_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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 ) ) ) ) )).
fof(t24_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => k9_euclid(3,A,1) = A ) )).
fof(t24_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(k14_euclid(A))))) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(A))) => ~ ( r2_hidden(C,B) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k4_euclid_9(A,C,D),B) ) ) ) ) => v3_pre_topc(B,k3_pcomps_1(k14_euclid(A))) ) ) ) )).
fof(t24_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ! [H] : ( m2_finseq_2(H,k1_numbers,k1_euclid(G)) => ! [I] : ( m2_finseq_2(I,k1_numbers,k1_euclid(G)) => ! [J] : ( 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,k2_xcmplx_0(A,D)),k9_euclid(G,I,k2_xcmplx_0(B,E))),k9_euclid(G,J,k2_xcmplx_0(C,F))) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) ) => ( k1_exchsort(A) = k5_numbers & k2_exchsort(A) = k9_xtuple_0(A) & k3_exchsort(A) = k9_xtuple_0(A) ) ) )).
fof(t24_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ( 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) ) ) ) ) ) ) )).
fof(t24_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( r1_xxreal_0(k5_numbers,k4_xxreal_3(A,B)) => k3_extreal1(k1_xxreal_3(A,B)) = k3_supinf_2(k3_extreal1(A),k3_extreal1(B)) ) ) ) )).
fof(t24_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_circcomb(A) & v2_circcomb(A) & v3_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v1_circcomb(B) & v2_circcomb(B) & v3_circcomb(B) & l1_msualg_1(B) ) => ! [C] : ( ( v4_msafree2(C,A) & v4_circcomb(C,A) & v6_circcomb(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t24_facirc_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( 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(k5_numbers,k6_margrel1),k7_margrel1) & k9_xtuple_0(k2_xtuple_0(k5_facirc_2(C,A,B))) = k4_finseq_2(k5_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) ) ) ) ) ) )).
fof(t24_fcont_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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(k5_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)) ) ) ) )).
fof(t24_fcont_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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)))) ) ) ) ) )).
fof(t24_fdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r1_fdiff_1(A,B) => r1_fcont_1(A,B) ) ) ) )).
fof(t24_fdiff_10,axiom,( ! [A] : ( ( 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,k27_sin_cos,k18_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k18_sin_cos),A),B) = k7_xcmplx_0(k17_sin_cos(k1_funct_1(k27_sin_cos,B)),k1_square_1(k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t24_fdiff_11,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k2_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k2_fdiff_9),A),B) = k7_xcmplx_0(k1_funct_1(k18_sin_cos,k1_funct_1(k2_sin_cos9,B)),k3_xcmplx_0(k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k2_sin_cos9,B))),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t24_fdiff_2,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r2_hidden(C,A) & r2_hidden(D,A) ) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k1_funct_1(B,C),k1_funct_1(B,D))),k1_square_1(k6_xcmplx_0(C,D))) ) ) ) ) => ( r2_fdiff_1(B,A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_fdiff_1(B,C) = k5_numbers ) ) ) ) ) ) )).
fof(t24_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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] : ( v1_xreal_0(F) => ( r2_hidden(F,C) => ( k1_funct_1(D,F) = k6_xcmplx_0(F,A) & ~ r1_xxreal_0(k1_funct_1(D,F),k5_numbers) & k1_funct_1(E,F) = k6_xcmplx_0(F,B) & ~ r1_xxreal_0(k1_funct_1(E,F),k5_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] : ( v1_xreal_0(F) => ( r2_hidden(F,C) => k1_funct_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) = k7_xcmplx_0(k6_xcmplx_0(A,B),k3_xcmplx_0(k6_xcmplx_0(F,A),k6_xcmplx_0(F,B))) ) ) ) ) ) ) ) ) ) )).
fof(t24_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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),k7_xcmplx_0(1,2)))) & B = k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_taylor_1(2)),C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_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),k7_xcmplx_0(1,2)),A) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_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),k7_xcmplx_0(1,2)),A),D) = k7_xcmplx_0(k23_sin_cos(D),k2_xcmplx_0(k23_sin_cos(D),k23_sin_cos(k4_xcmplx_0(D)))) ) ) ) ) ) ) ) )).
fof(t24_fdiff_7,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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),k3_sin_cos6),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k4_taylor_1(k7_xcmplx_0(1,2)))))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) & B = k47_valued_1(k1_numbers,k1_numbers,k1_numbers,C,D) & D = k1_taylor_1(2) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,A) => ( k1_funct_1(C,E) = 1 & ~ r1_xxreal_0(k1_funct_1(B,E),k5_numbers) & E != k5_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),k3_sin_cos6),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k4_taylor_1(k7_xcmplx_0(1,2)))),A) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,A) => k1_funct_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),k3_sin_cos6),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k4_taylor_1(k7_xcmplx_0(1,2)))),A),E) = k1_funct_1(k3_sin_cos6,E) ) ) ) ) ) ) ) ) )).
fof(t24_fdiff_8,axiom,( ! [A] : ( ( 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,k26_sin_cos,k1_partfun2(k1_numbers,A)))) => ( r2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_partfun2(k1_numbers,A)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_partfun2(k1_numbers,A)),A),B) = k7_xcmplx_0(k1_square_1(k1_funct_1(k16_sin_cos,B)),k1_square_1(k1_funct_1(k18_sin_cos,B))) ) ) ) ) ) )).
fof(t24_fdiff_9,axiom,( ! [A] : ( ( 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,k22_sin_cos,k1_fdiff_9))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_fdiff_9),A),B) = k2_xcmplx_0(k7_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_funct_1(k18_sin_cos,B)),k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_funct_1(k16_sin_cos,B)),k1_square_1(k1_funct_1(k18_sin_cos,B)))) ) ) ) ) ) )).
fof(t24_ff_siec,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t24_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => k1_pre_ff(k1_nat_1(A,2)) = k1_nat_1(k1_pre_ff(A),k1_pre_ff(k1_nat_1(A,1))) ) )).
fof(t24_fib_num3,axiom,( ! [A] : ( v7_ordinal1(A) => k1_nat_1(k1_fib_num3(A),k1_pre_ff(A)) = k2_nat_1(2,k1_pre_ff(k1_nat_1(A,1))) ) )).
fof(t24_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(2,A) => k1_pre_ff(k2_xcmplx_0(A,1)) = k1_int_1(k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_pre_ff(A),k3_xcmplx_0(k3_square_1(5),k1_pre_ff(A))),1),2)) ) ) )).
fof(t24_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_finseq_1(B,A) => ! [C] : ( m1_finseq_1(C,A) => r1_tarski(B,k1_finseq_8(A,B,C)) ) ) ) )).
fof(t24_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t24_filter_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t24_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t24_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t24_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t24_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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))) ) ) ) )).
fof(t24_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ~ ( r2_hidden(B,k1_relset_1(k4_ordinal1,A)) & B = k5_numbers ) ) )).
fof(t24_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : ( 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 ) ) ) )).
fof(t24_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ! [D] : ( 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) ) ) ) ) )).
fof(t24_finseq_6,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(t24_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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) ) ) ) ) )).
fof(t24_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r4_finseq_8(A,B,C) => ( r1_xxreal_0(k3_finseq_1(C),k5_numbers) | ( r1_xxreal_0(k3_finseq_1(C),k3_finseq_1(B)) & k3_finseq_6(A,B,k7_nat_d(k1_nat_1(k3_finseq_1(B),1),k3_finseq_1(C)),k3_finseq_1(B)) = C ) ) ) ) ) ) )).
fof(t24_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t24_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t24_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v4_fin_topo(k6_domain_1(u1_struct_0(A),B),A) ) ) )).
fof(t24_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => k7_flang_1(A,B,k5_numbers) = k4_flang_1(A,k2_flang_1(A)) ) )).
fof(t24_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(D,C) & r1_xxreal_0(C,E) ) => k1_flang_2(A,B,D,E) = k4_subset_1(k8_afinsq_1(A),k1_flang_2(A,B,D,C),k1_flang_2(A,B,C,E)) ) ) ) ) ) )).
fof(t24_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) )).
fof(t24_fomodel0,axiom,( ! [A] : ! [B] : ( k8_relset_1(B,k6_margrel1,k10_fomodel0(A,B),k6_domain_1(k4_ordinal1,k5_numbers)) = k6_subset_1(B,A) & k8_relset_1(B,k6_margrel1,k10_fomodel0(A,B),k6_domain_1(k4_ordinal1,1)) = k3_xboole_0(A,B) ) )).
fof(t24_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_subset_1(D,k9_funct_2(k37_fomodel1(B),k3_rfunct_3(k3_finseq_2(C),k2_xboole_0(C,k6_margrel1))),k15_fomodel2(B,C)) => r2_hidden(k23_fomodel2(B,C,A,D),k9_funct_2(k24_fomodel2(B,A),k6_margrel1)) ) ) ) ) )).
fof(t24_frechet,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(B,A) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r1_tarski(k2_relset_1(u1_struct_0(A),C),B) => r1_tarski(k2_frechet(A,C),B) ) ) ) ) ) )).
fof(t24_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v8_pre_topc(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( v2_frechet(B,A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_frechet(A,B) != k6_domain_1(u1_struct_0(A),C) ) ) ) ) ) )).
fof(t24_fscirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k8_fscirc_1(A,B,C),k9_fscirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t24_fscirc_2,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k8_fscirc_1(A,B,C),k9_fscirc_1(A,B,C)))) & ? [E] : ( m1_subset_1(E,k6_margrel1) & ? [F] : ( m1_subset_1(F,k6_margrel1) & ? [G] : ( 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)) ) ) ) ) ) ) )).
fof(t24_fsm_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ v2_struct_0(D) & l2_fsm_1(D,B,C) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t24_fsm_2,axiom,( ! [A] : ( ( ~ 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] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,B) => k1_funct_1(u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(B,C))) = B ) ) ) & ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(C,B) => k1_funct_1(u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(B,C))) = C ) ) ) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( 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),k3_xxreal_0(B,C)) ) ) ) ) )).
fof(t24_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( ( ~ 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] : ( 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] : ( v7_ordinal1(F) => ~ ( r2_hidden(F,k4_finseq_1(E)) & k2_xtuple_0(k1_funct_1(E,F)) = C ) ) ) ) ) ) ) ) )).
fof(t24_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( 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))) ) )).
fof(t24_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t24_funcsdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k5_struct_0(k11_funcsdom(A)) = k9_funcsdom(A) ) )).
fof(t24_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( v2_funct_1(A) & v2_funct_1(B) ) => v2_funct_1(k3_relat_1(A,B)) ) ) ) )).
fof(t24_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t24_funct_3,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(t24_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t24_funct_5,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t24_funct_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( ( r2_hidden(A,C) & r2_hidden(B,k9_xtuple_0(D)) ) => k4_funct_6(k7_funcop_1(C,D),A,B) = k1_funct_1(D,B) ) ) )).
fof(t24_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : r1_funct_7(A,A,B) ) )).
fof(t24_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t24_funct_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & v1_int_1(A) ) => v1_funct_9(k2_fdiff_9,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A)) ) )).
fof(t24_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_altcat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( k1_altcat_1(B,C,C) != k1_xboole_0 => ! [D] : ( m1_subset_1(D,k1_altcat_1(B,C,C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t24_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( m1_functor2(E,A,B,C,D) => ( r1_functor2(A,B,C,D) => r8_pboole(u1_struct_0(A),k7_functor3(A,A,B,k12_functor0(A),k12_functor0(A),C,D,k4_functor2(A,A,k12_functor0(A)),E),E) ) ) ) ) ) ) )).
fof(t24_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D) => r1_fuzzy_1(k1_fuzzy_1(A,B,C),k1_fuzzy_1(A,D,C)) ) ) ) ) ) )).
fof(t24_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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) ) ) ) ) )).
fof(t24_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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,k3_fuzzy_4(A,A,A,B,k4_fuzzy_2(A,A)),k3_fuzzy_4(A,A,A,k4_fuzzy_2(A,A),B)) ) ) )).
fof(t24_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_fvaluat1(D,A) => ( ( v3_fvaluat1(A) & r1_xxreal_0(k5_numbers,k3_funct_2(u1_struct_0(A),k6_numbers,D,k1_vectsp_2(A,B,C))) ) => ( C = k4_struct_0(A) | r1_xxreal_0(k3_funct_2(u1_struct_0(A),k6_numbers,D,C),k3_funct_2(u1_struct_0(A),k6_numbers,D,B)) ) ) ) ) ) ) )).
fof(t24_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_fvsum_1(A,k12_finseq_1(u1_struct_0(A),B)) = k12_finseq_1(u1_struct_0(A),k4_algstr_0(A,B)) ) ) )).
fof(t24_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ~ 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) ) ) )).
fof(t24_gcd_1,axiom,( ! [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) & v1_vectsp_2(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => m2_subset_1(k4_struct_0(A),u1_struct_0(A),B) ) ) )).
fof(t24_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v2_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( m1_genealg1(E,D) => ! [F] : ( 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 ) ) ) ) ) ) ) )).
fof(t24_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ~ ( r1_analmetr(A,G,H) & r2_geomtrap(A,G,H,B,D,C,E) & r2_geomtrap(A,G,H,B,D,C,F) & B != D & E != F ) ) ) ) ) ) ) ) ) )).
fof(t24_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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))) )).
fof(t24_gfacirc2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(A,B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t24_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ( k7_glib_000(A) = k1_xboole_0 => v7_glib_000(A) ) ) )).
fof(t24_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k1_relset_1(k4_ordinal1,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(k4_ordinal1,B)) ) ) ) ) ) )).
fof(t24_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(t24_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t24_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,k6_glib_000(A)) => v13_glib_000(k10_glib_004(A,B)) ) ) )).
fof(t24_goboard1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ~ ( r1_goboard1(u1_struct_0(k15_euclid(2)),D,C) & r2_hidden(B,k4_finseq_1(D)) & r2_hidden(k1_nat_1(B,1),k4_finseq_1(D)) & r2_hidden(A,k2_finseq_1(k1_matrix_0(C))) & r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),D,B),k10_xtuple_0(k8_matrix_0(u1_struct_0(k15_euclid(2)),C,A))) & ~ r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(B,1)),k10_xtuple_0(k8_matrix_0(u1_struct_0(k15_euclid(2)),C,A))) & ? [E] : ( v7_ordinal1(E) & r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(B,1)),k10_xtuple_0(k8_matrix_0(u1_struct_0(k15_euclid(2)),C,E))) & r2_hidden(E,k2_finseq_1(k1_matrix_0(C))) & k9_complex1(k6_xcmplx_0(A,E)) != 1 ) ) ) ) ) ) )).
fof(t24_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_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,k5_numbers)) = a_2_4_goboard6(A,B) ) ) ) ) )).
fof(t24_goboard7,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(A)) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k1_matrix_0(A)) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(A)) & r1_xxreal_0(1,E) & r1_xxreal_0(E,k1_matrix_0(A)) & ~ r1_xboole_0(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,k1_nat_1(C,1))),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,D,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,k1_nat_1(D,1),E))) & ~ ( C = E & k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,k1_nat_1(C,1))),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,D,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,k1_nat_1(D,1),E))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,C)) ) & ~ ( k1_nat_1(C,1) = E & k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,k1_nat_1(C,1))),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,D,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,k1_nat_1(D,1),E))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,k1_nat_1(C,1))) ) ) ) ) ) ) ) )).
fof(t24_gobrd11,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => k3_goboard5(A,k5_numbers,k5_numbers) = a_1_13_gobrd11(A) ) )).
fof(t24_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( ( ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) & r1_goboard1(u1_struct_0(k15_euclid(2)),C,D) & r1_xxreal_0(k1_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) ) ) ) ) ) ) )).
fof(t24_gobrd14,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t24_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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) ) ) ) )).
fof(t24_gr_cy_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k4_ordinal1) & k7_group_1(A) = k3_xcmplx_0(2,B) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ( k6_group_1(A,B) = 2 & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k6_group_1(A,C) = 2 => B = C ) ) ) ) ) ) )).
fof(t24_gr_cy_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ( A != 2 => k4_nat_d(k1_gr_cy_3(A),8) = 7 ) ) )).
fof(t24_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t24_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ( ( r1_tarski(k10_xtuple_0(B),k1_relset_1(k4_ordinal1,A)) & r1_tarski(k10_xtuple_0(C),k1_relset_1(k4_ordinal1,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) ) ) ) ) ) ) ) )).
fof(t24_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k10_graph_1(A,B) = k7_graph_3(A,B,u4_struct_0(A)) ) ) )).
fof(t24_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( 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) ) ) ) ) ) )).
fof(t24_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u4_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t24_graphsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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))) ) => ( k11_graphsp(A,B,C,D) = k4_xcmplx_0(1) <=> ! [E] : ~ ( r2_hidden(E,u4_struct_0(A)) & r1_graph_4(A,B,C,E) ) ) ) ) ) ) )).
fof(t24_grcat_1,axiom,( ! [A] : ( ( v1_grcat_1(A) & v2_grcat_1(A) & l1_grcat_1(A) ) => ( ~ v1_xboole_0(k1_tarski(A)) & v4_grcat_1(k1_tarski(A)) ) ) )).
fof(t24_grfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(B,k8_relat_1(C,A)) <=> ( r2_hidden(k4_tarski(B,k1_funct_1(C,B)),C) & r2_hidden(k1_funct_1(C,B),A) ) ) ) )).
fof(t24_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v15_algstr_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( v15_algstr_0(D) & m1_group_2(D,A) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_group_6(G,B,k10_group_6(A,B,C)) => ! [H] : ( m1_subset_1(H,u1_struct_0(k10_group_6(A,B,C))) => ! [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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_groeb_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ( r2_groeb_1(A,B,C,E,D) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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,k8_polynom1(A,C)) ) ) ) ) ) ) ) ) )).
fof(t24_groeb_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(G,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,k8_polynom1(A,C)) ) ) ) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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),k8_polynom1(A,C)) ) ) ) ) ) ) ) ) )).
fof(t24_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(E,k5_card_1(k3_polynom1(k15_pre_poly(A),C,D))) => ( r1_tarski(k4_groeb_3(A,B,C,D,E),k3_polynom1(k15_pre_poly(A),C,D)) & k5_card_1(k4_groeb_3(A,B,C,D,E)) = k6_xcmplx_0(k5_card_1(k3_polynom1(k15_pre_poly(A),C,D)),E) & ! [F] : ( ( 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] : ( ( 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,k3_polynom1(k15_pre_poly(A),C,D)) & r1_termord(A,B,G,F) ) => r2_hidden(G,k4_groeb_3(A,B,C,D,E)) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_group_1(A,k5_numbers,B) = k1_group_1(A) ) ) )).
fof(t24_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(t24_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) )).
fof(t24_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t24_group_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( ( ~ v2_struct_0(D) & v2_group_1(D) & v3_group_1(D) & l3_algstr_0(D) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(t24_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t24_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => k1_group_1(k5_group_6(A,B)) = k8_group_2(A,B) ) ) )).
fof(t24_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t24_group_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( A = k5_group_4(A,k6_domain_1(u1_struct_0(A),B)) => ! [C] : ( ( v15_algstr_0(C) & m1_group_2(C,A) ) => ~ ( C != k6_group_2(A) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_struct_0(C,k5_group_1(A,D,B)) ) ) ) ) ) ) ) )).
fof(t24_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r1_struct_0(k18_group_9(A,B,C),D) <=> ? [E] : ( m2_finseq_1(E,u1_struct_0(B)) & ? [F] : ( m2_finseq_1(F,k4_numbers) & ? [G] : ( 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 ) ) ) ) ) ) ) )).
fof(t24_groupp_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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) = k5_numbers ) => B = k6_group_2(B) ) ) ) )).
fof(t24_hahnban,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( D = E => r1_xxreal_0(k3_funct_2(u1_struct_0(B),k1_numbers,C,D),k2_normsp_0(A,E)) ) ) ) & ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => r1_xxreal_0(k3_funct_2(u1_struct_0(A),k1_numbers,D,E),k2_normsp_0(A,E)) ) ) ) ) ) ) ) )).
fof(t24_hahnban1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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))) ) ) ) )).
fof(t24_hallmar1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v2_relat_1(B) & m2_finseq_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m3_hallmar1(E,A,B,C) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t24_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t24_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v5_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( 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,k1_nat_1(k3_finseq_1(k1_helly(B,C)),2)) = k1_funct_1(C,k1_nat_1(k3_finseq_1(k1_helly(B,C)),2)) ) ) ) ) )).
fof(t24_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( 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) ) ) )).
fof(t24_heyting1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k12_normform(A))) => ! [C] : ( 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) ) ) )).
fof(t24_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m1_subset_1(C,k4_partfun1(A,B)) => ! [D] : ( m2_subset_1(D,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B)) => ! [E] : ( m2_subset_1(E,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B)) => ~ ( ! [F] : ~ ( r2_hidden(F,D) & ! [G] : ~ ( r2_hidden(G,E) & r1_tarski(G,k2_xboole_0(F,C)) ) ) & ! [F] : ~ ( r2_hidden(F,k3_heyting2(A,B,D,E)) & r1_tarski(F,C) ) ) ) ) ) ) )).
fof(t24_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_tarski(k3_heyting3(A,B),k2_heyting3(C,B)) <=> ~ r1_xxreal_0(C,A) ) ) ) ) )).
fof(t24_hfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t24_hilbasis,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ! [E] : ( ( 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] : ( m1_ideal_1(F,A,C) => ! [G] : ( m1_ideal_1(G,B,D) => ! [H] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t24_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( 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) ) ) ) ) )).
fof(t24_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => k4_hilbert1(B,C) != k1_hilbert2(A) ) ) ) )).
fof(t24_hilbert3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( ( 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)) ) ) )).
fof(t24_hurwitz,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( k2_hurwitz(A,B) = k5_numbers & v1_polynom5(B,A) ) ) ) )).
fof(t24_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => r1_idea_1(C,k9_idea_1(C,A,B)) ) ) ) )).
fof(t24_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_ideal_1(D,A,B) => m1_ideal_1(k1_polynom1(A,D,C),A,B) ) ) ) ) )).
fof(t24_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ~ ! [E] : ( m1_subset_1(E,u2_incsp_1(A)) => ( r4_incsp_1(A,k7_domain_1(u1_incsp_1(A),B,C),E) <=> E = D ) ) ) ) ) ) ) )).
fof(t24_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( 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] : ( 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)) ) ) ) ) ) )).
fof(t24_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r3_pua2mss1(A,B,C,D) => ! [E] : ( l3_msualg_1(E,B) => ! [F] : ( m1_subset_1(F,u4_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(A,C) ) => ( r1_xxreal_0(k2_xcmplx_0(A,1),B) | r1_xxreal_0(k2_xcmplx_0(A,1),C) | B = C ) ) ) ) ) )).
fof(t24_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t24_int_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( v1_int_2(A) & r1_int_2(A,B) ) => ( r1_xxreal_0(C,k5_numbers) | ! [D] : ( v1_int_1(D) => k5_int_1(k6_xcmplx_0(k3_xcmplx_0(A,k1_square_1(D)),B),k1_newton(A,C)) != k5_numbers ) ) ) ) ) ) )).
fof(t24_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t24_int_6,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ( r1_xxreal_0(B,k3_finseq_1(A)) => ( r1_xxreal_0(B,k5_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)) ) ) ) ) ) )).
fof(t24_int_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_int_1(C) => ~ ( ~ v4_group_1(B,A) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( k5_group_1(A,C,B) = k5_group_1(A,D,B) & D = k2_xcmplx_0(k2_nat_1(E,k6_group_1(A,B)),C) ) ) ) ) ) ) ) )).
fof(t24_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_finset_1(B) => ( r1_int_8(B,A) => ( k5_card_1(B) = k1_euler_1(A) & ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & C != D & r2_int_1(C,D,A) ) ) ) & ! [C] : ( v1_int_1(C) => ( r2_hidden(C,B) => r1_int_2(C,A) ) ) ) ) ) ) )).
fof(t24_integr11,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( B = k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_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,k18_sin_cos,k1_taylor_1(A)),k16_sin_cos)) = k5_numbers ) ) ) )).
fof(t24_integr12,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( v3_rcomp_1(G) & m1_subset_1(G,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(C,G) & r1_tarski(G,k2_rcomp_1(k4_xcmplx_0(1),1)) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,G) => ( k1_funct_1(E,H) = k2_xcmplx_0(k3_xcmplx_0(A,H),B) & k1_funct_1(F,H) = 1 ) ) ) & G = k1_relset_1(k1_numbers,D) & r2_relset_1(k1_numbers,k1_numbers,D,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_valued_1(k1_numbers,k1_numbers,k3_sin_cos6,A),k3_rfunct_1(k1_numbers,k1_numbers,E,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,F,k1_taylor_1(2)),k4_taylor_1(k7_xcmplx_0(1,2)))))) ) => k2_integra5(C,D) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,E,k3_sin_cos6),k2_seq_4(C)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,E,k3_sin_cos6),k3_seq_4(C))) ) ) ) ) ) ) ) ) )).
fof(t24_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k27_sin_cos,k22_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) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k22_sin_cos)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k22_sin_cos)),k3_seq_4(A))) ) ) ) ) )).
fof(t24_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k27_sin_cos) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k27_sin_cos),A)) ) => k2_integra5(A,k32_valued_1(k1_numbers,k1_numbers,k27_sin_cos)) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k3_taylor_1),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k3_taylor_1),k3_seq_4(A))) ) ) ) )).
fof(t24_integr19,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( ~ v8_ordinal1(F) & m1_subset_1(F,k4_ordinal1) ) => ! [G] : ( ( 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] : ( 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)),k3_xcmplx_0(E,k6_xcmplx_0(D,C))) & r1_xxreal_0(k12_euclid(k12_integr15(D,C,F,G)),k3_xcmplx_0(E,k6_xcmplx_0(D,C))) ) ) ) ) ) ) ) ) ) )).
fof(t24_integra1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( m1_integra1(C,B) => ! [D] : ( ( 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(k3_xcmplx_0(k2_seq_4(k1_rvsum_1(k2_partfun1(B,k1_numbers,D,k2_integra1(B,C,A)))),k3_integra1(k2_integra1(B,C,A))),k3_xcmplx_0(k2_seq_4(k1_rvsum_1(D)),k3_integra1(k2_integra1(B,C,A)))) ) ) ) ) ) )).
fof(t24_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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] : ( 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,k5_numbers) ) => k1_funct_1(k5_integra1(C,k26_valued_1(C,k1_numbers,D,A),E),B) = k3_xcmplx_0(A,k1_funct_1(k4_integra1(C,D,E),B)) ) ) ) ) ) ) )).
fof(t24_integra4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( r2_hidden(D,B) & r2_hidden(E,B) ) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k1_funct_1(C,D),k1_funct_1(C,E))),A) ) ) ) => r1_xxreal_0(k6_xcmplx_0(k2_seq_4(k1_rvsum_1(C)),k3_seq_4(k1_rvsum_1(C))),A) ) ) ) ) )).
fof(t24_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( 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)) = k2_xcmplx_0(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)) = k6_xcmplx_0(k4_integra5(C,D,E),k4_integra5(C,D,F)) ) ) ) ) ) ) ) ) )).
fof(t24_integra7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k6_xcmplx_0(k1_funct_1(k16_sin_cos,B),k1_funct_1(k16_sin_cos,A)) = k4_integra5(A,B,k18_sin_cos) ) ) )).
fof(t24_integra8,axiom,( r2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k16_sin_cos),k1_numbers) )).
fof(t24_integra9,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( ~ 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) ) ) ) )).
fof(t24_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_interva1(C,A) ) => ! [D] : ( ( ~ 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))) ) ) ) ) )).
fof(t24_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(t24_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ( r2_nattra_1(A,B,C,D) => ! [E] : ( m2_nattra_1(E,A,B,C,D) => ! [F] : ( m2_nattra_1(F,A,B,C,D) => ( ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => k2_nattra_1(A,B,C,D,E,G) = k2_nattra_1(A,B,C,D,F,G) ) => r2_funct_2(u1_struct_0(A),u4_struct_0(B),E,F) ) ) ) ) ) ) ) ) )).
fof(t24_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(t24_jgraph_1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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) ) ) ) )).
fof(t24_jgraph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ~ ( v5_pre_topc(B,A,k3_topmetr) & ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t24_jgraph_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r1_xxreal_0(k5_numbers,k17_euclid(B)) & r1_xxreal_0(k5_numbers,k17_euclid(C)) ) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) | r1_xxreal_0(1,A) | k12_euclid(B) = k5_numbers | k12_euclid(C) = k5_numbers | r1_xxreal_0(k7_xcmplx_0(k18_euclid(C),k12_euclid(C)),k7_xcmplx_0(k18_euclid(B),k12_euclid(B))) | ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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(k7_xcmplx_0(k18_euclid(E),k12_euclid(E)),k7_xcmplx_0(k18_euclid(D),k12_euclid(D))) ) ) ) ) ) ) ) ) )).
fof(t24_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ( k6_jgraph_6(k5_numbers,k5_numbers,A) = a_1_0_jgraph_6(A) & ( ~ r1_xxreal_0(A,k5_numbers) => k5_jgraph_6(k5_numbers,k5_numbers,A) = a_1_1_jgraph_6(A) ) & k8_jgraph_6(k5_numbers,k5_numbers,A) = a_1_2_jgraph_6(A) & k7_jgraph_6(k5_numbers,k5_numbers,A) = a_1_3_jgraph_6(A) & k9_jgraph_6(k5_numbers,k5_numbers,A) = a_1_4_jgraph_6(A) ) ) )).
fof(t24_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_jordan,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( ( ~ v8_ordinal1(C) & v1_xreal_0(C) ) => k2_tops_1(k15_euclid(A),k1_topreal9(A,B,C)) = k3_topreal9(A,B,C) ) ) ) )).
fof(t24_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => m1_subset_1(a_4_4_jordan1(A,B,C,D),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ) ) ) )).
fof(t24_jordan12,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t24_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( 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_0(k1_jordan8(A,E))) & k7_partfun1(u1_struct_0(k15_euclid(2)),k1_jordan13(A,E),D) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,E),B,C) & r1_xxreal_0(C,1) ) ) ) ) ) ) )).
fof(t24_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & ~ r1_xxreal_0(A,k5_numbers) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E),k8_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k9_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k8_jordan6(B)) ) ) ) ) ) ) )).
fof(t24_jordan16,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t24_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ( ( r1_jordan17(A,B,C,D,E) & r1_jordan17(A,B,D,C,E) ) => ( B = D | B = E | C = E | C = D ) ) ) ) ) ) ) )).
fof(t24_jordan18,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => r1_jordan18(A,B,E,E,C,D) ) ) ) ) ) )).
fof(t24_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_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_0(C)) & v1_xboole_0(k3_goboard5(C,A,B)) ) ) ) ) )).
fof(t24_jordan1c,axiom,( ! [A] : ( 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)) ) ) )).
fof(t24_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(k1_jordan8(B,A))) & k23_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),k3_finseq_1(k1_jordan8(B,A)),C) ) ) ) )).
fof(t24_jordan1g,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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)))) ) => k4_finseq_4(k1_jordan1e(B,A),k22_pscomp_1(k3_topreal1(2,k2_jordan9(B,A)))) = k3_finseq_1(k1_jordan1e(B,A)) ) ) )).
fof(t24_jordan1h,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t24_jordan1j,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) ) )).
fof(t24_jordan1k,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) )).
fof(t24_jordan20,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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 ) ) ) ) )).
fof(t24_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(k18_euclid(k2_jordan21(A)),k18_euclid(k2_jordan21(k9_jordan6(k3_topreal1(2,k2_jordan9(A,B)))))) ) ) ) )).
fof(t24_jordan23,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t24_jordan2b,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ( A = a_1_0_jordan2b(B) => v3_pre_topc(A,k3_topmetr) ) ) ) )).
fof(t24_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [F] : ( ( 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] : ( ( 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,k5_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,k5_numbers) & D = k1_funct_1(G,1) & ! [H] : ( ( 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,k5_numbers) & D = k1_funct_1(H,1) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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] : ( m1_subset_1(C,k4_ordinal1) => ( ( 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) ) ) ) ) ) ) )).
fof(t24_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r3_jordan4(A,B,C,D) => ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(A)) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_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] : ( 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_xcmplx_0(C,E),1),A)) ) ) | ! [E] : ( 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_xcmplx_0(k3_finseq_1(A),C),E),A)) ) ) ) ) ) ) ) ) ) )).
fof(t24_jordan5a,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ( A = B => k5_measure6(A) = k2_pre_topc(k3_topmetr,B) ) ) ) )).
fof(t24_jordan5b,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t24_jordan5c,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( 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)) ) ) ) ) )).
fof(t24_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( B = a_1_3_jordan5d(A) => k3_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)))) ) ) ) )).
fof(t24_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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 ) ) ) ) )).
fof(t24_jordan9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r2_hidden(k4_tarski(A,B),k2_matrix_0(D)) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(D)) ) => r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,A,B)),k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,k3_finseq_1(D),C))) ) ) ) ) ) )).
fof(t24_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_jordan_a(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( 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)) ) ) ) ) ) ) )).
fof(t24_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( 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] : ( v3_ordinal1(D) => ! [E] : ( v3_ordinal1(E) => ( r1_ordinal1(D,E) => r3_lattices(A,k5_knaster(A,B,C,D),k5_knaster(A,B,C,E)) ) ) ) ) ) ) ) )).
fof(t24_kurato_1,axiom,( k2_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)) = k3_rcomp_1(4,k1_xxreal_0) )).
fof(t24_kurato_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ! [C] : ( ( v4_pre_topc(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( ! [D] : ( v7_ordinal1(D) => k2_kurato_2(A,B,D) = C ) => k1_kurato_2(A,B) = C ) ) ) ) )).
fof(t24_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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,k4_matrix_0(u1_struct_0(B),C)) ) ) ) ) ) ) )).
fof(t24_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k11_group_4(A))) => ! [C] : ( m1_group_2(C,A) => ( B = C => ( v15_algstr_0(C) & m1_group_2(C,A) ) ) ) ) ) )).
fof(t24_latsum_1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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)) ) ) ) )).
fof(t24_lattice2,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t24_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k5_finsub_1(u1_struct_0(A))) => ( r1_tarski(C,B) => r2_hidden(k2_lattice4(A,C),B) ) ) ) ) ) )).
fof(t24_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v3_ordinal1(B) => r1_tarski(A,k8_lattice5(A,B)) ) ) )).
fof(t24_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v9_lattice6(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => C = k16_lattice3(A,a_3_1_lattice6(A,B,C)) ) ) ) ) )).
fof(t24_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( v3_ordinal1(D) => ! [E] : ( v3_ordinal1(E) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t24_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_lattices(A,B,C) => r3_lattices(A,k7_lattices(A,C),k7_lattices(A,B)) ) ) ) ) )).
fof(t24_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( ( v4_lexbfs(B,A) & m1_lexbfs(B,A) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ! [E] : ~ ( 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))))) ) ) ) ) )).
fof(t24_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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,k5_numbers),k4_fuzzy_4(A,A)) ) ) )).
fof(t24_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_limfunc1(A) & v2_limfunc1(B) ) => v1_limfunc1(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) ) ) )).
fof(t24_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t24_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r2_limfunc3(C,A) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ r1_xxreal_0(F,D) & ~ r1_xxreal_0(A,F) & r2_hidden(F,k9_xtuple_0(B)) & ~ r1_xxreal_0(E,G) & ~ r1_xxreal_0(G,A) & r2_hidden(G,k9_xtuple_0(B)) ) ) ) ) ) ) ) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k9_subset_1(k1_numbers,k9_xtuple_0(B),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,D),A),k2_rcomp_1(A,k2_xcmplx_0(A,D)))),k9_subset_1(k1_numbers,k9_xtuple_0(C),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,D),A),k2_rcomp_1(A,k2_xcmplx_0(A,D))))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k9_subset_1(k1_numbers,k9_xtuple_0(B),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,D),A),k2_rcomp_1(A,k2_xcmplx_0(A,D))))) => r1_xxreal_0(k1_funct_1(C,E),k1_funct_1(B,E)) ) ) ) ) | r2_limfunc3(B,A) ) ) ) ) ) )).
fof(t24_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(A,k2_xcmplx_0(A,D)))) & r1_xxreal_0(k1_funct_1(B,E),k2_limfunc2(B,A)) ) ) ) ) | r6_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t24_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t24_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k11_lopban_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k11_lopban_1(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k11_lopban_1(A,B))) => ( E = k3_rlvect_1(k11_lopban_1(A,B),C,D) <=> ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t24_lopban_3,axiom,( ! [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) & v3_lopban_1(A) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_lopban_3(B,A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(D,E) & r1_xxreal_0(C,k2_normsp_0(A,k5_algstr_0(A,k5_rsspace3(A,k1_bhsp_4(A,B),E),k5_rsspace3(A,k1_bhsp_4(A,B),D)))) ) ) ) ) ) ) ) )).
fof(t24_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v7_ordinal1(D) => k9_nat_1(u1_struct_0(A),k1_lopban_4(A,C),D) = k9_nat_1(u1_struct_0(A),k6_lopban_4(D,A,C,B),D) ) ) ) ) )).
fof(t24_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t24_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( ( r1_lpspacc1(A,B,C,D,E) & r1_lpspacc1(A,B,C,E,F) ) => r1_lpspacc1(A,B,C,D,F) ) ) ) ) ) ) ) )).
fof(t24_lpspace1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,C,k6_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,k6_numbers))) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t24_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,k5_numbers) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( 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_funct_1(k2_mesfun6c(B,A,k56_valued_1(A,k1_numbers,k3_valued_1(A,k1_numbers,k1_numbers,C,D))),E),k1_funct_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))),k2_power(2,B)),E)) ) ) ) ) ) ) ) )).
fof(t24_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_hilbert1)) => ( ( r3_ltlaxio1(C,A) & r3_ltlaxio1(C,k3_hilbert1(A,B)) ) => r3_ltlaxio1(C,B) ) ) ) ) )).
fof(t24_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(A,A)) ) )).
fof(t24_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => r2_hidden(k4_hilbert1(A,B),k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k6_ltlaxio3,k4_hilbert1(A,B))) ) ) )).
fof(t24_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( ( ~ v2_ltlaxio3(C) & v3_ltlaxio3(C) & m1_subset_1(C,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) ) => ! [D] : ( m2_subset_1(D,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)),k9_ltlaxio4(C)) => ( r2_hidden(k4_hilbert1(A,B),k2_relset_1(k1_hilbert1,k9_ltlaxio3(C))) => ( r2_hidden(B,k2_relset_1(k1_hilbert1,k9_ltlaxio3(D))) & ( r2_hidden(A,k2_relset_1(k1_hilbert1,k9_ltlaxio3(D))) | r2_hidden(k4_hilbert1(A,B),k2_relset_1(k1_hilbert1,k9_ltlaxio3(D))) ) ) ) ) ) ) ) )).
fof(t24_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t24_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) )).
fof(t24_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( v4_matrix10(B) => v3_matrix10(k2_matrix10(A,B)) ) ) ) )).
fof(t24_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_matrix_2(C,k3_matrix_2(k1_nat_1(A,2))) => ! [D] : ( m1_matrix_2(D,k3_matrix_2(k1_nat_1(A,2))) => ! [E] : ( m1_matrix_2(E,k3_matrix_2(k1_nat_1(A,2))) => ( r2_funct_2(k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),E,k1_partfun1(k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),k2_finseq_1(k2_matrix_2(k3_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)) ) ) ) ) ) ) )).
fof(t24_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(A)) ) => ! [F] : ( m2_finseq_2(F,k4_ordinal1,k4_finseq_2(D,k4_ordinal1)) => ! [G] : ( m2_finseq_2(G,k4_ordinal1,k4_finseq_2(C,k4_ordinal1)) => ( ( r2_hidden(B,k2_finseq_1(D)) & r1_tarski(k10_xtuple_0(G),k2_finseq_1(k1_matrix_0(E))) ) => k7_matrix_0(A,k1_matrix13(A,E,D,C,F,G),B) = k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,A,G,k7_matrix_0(A,E,k1_funct_1(F,B))) ) ) ) ) ) ) ) ) )).
fof(t24_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t24_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(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] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ( ( r1_tarski(D,k4_finseq_1(B)) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,D) => k7_matrix_0(u1_struct_0(A),B,E) = k5_finseq_2(u1_struct_0(A),k1_matrix_0(B),k4_struct_0(A)) ) ) ) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,D) => k7_matrix_0(u1_struct_0(A),C,E) = k5_finseq_2(u1_struct_0(A),k1_matrix_0(C),k4_struct_0(A)) ) ) ) ) ) ) ) ) )).
fof(t24_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(B),A,A) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(B))) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(B),A,A) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(B))) ) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(B),A,A) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(B))) ) => ( ( 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_3(B,k3_matrix_3(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)) ) ) ) ) ) ) ) ) ) )).
fof(t24_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,B,A,A) & m2_finseq_1(C,k3_finseq_2(B)) ) => ( k3_finseq_1(C) = A & k1_matrix_0(C) = A & k2_matrix_0(C) = k2_zfmisc_1(k2_finseq_1(A),k2_finseq_1(A)) ) ) ) ) )).
fof(t24_matrix_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( ( 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] : ( ( v1_funct_1(F) & v1_funct_2(F,B,A) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [G] : ( ( 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] : ( m1_subset_1(H,B) => ! [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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(D) ) => k1_matrix_4(A,k3_matrix_3(A,B,C),D) = k3_matrix_3(A,k1_matrix_4(A,B,D),C) ) ) ) ) ) )).
fof(t24_matrix_5,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ( ~ r1_xxreal_0(k3_finseq_1(B),k5_numbers) => k6_matrix_3(A,B,k4_struct_0(A)) = k1_matrix_3(A,k3_finseq_1(B),k1_matrix_0(B)) ) ) ) )).
fof(t24_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v2_matrix_6(C,A,B) & v2_matrix_6(D,A,B) ) => v2_matrix_6(k3_matrix_3(B,C,D),A,B) ) ) ) ) ) )).
fof(t24_matrix_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) )).
fof(t24_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v2_matrix_8(C,A,B) & v2_matrix_8(D,A,B) & r1_matrix_6(A,B,C,D) & k4_matrix_3(B,C,D) = k2_matrix_1(B,A) ) => ( r1_xxreal_0(A,k5_numbers) | v2_matrix_8(k3_matrix_3(B,C,D),A,B) ) ) ) ) ) ) )).
fof(t24_matrix_9,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( ( v1_matrix_0(K) & v2_matrix_0(K,u1_struct_0(A),3,3) & m2_finseq_1(K,k3_finseq_2(u1_struct_0(A))) ) => ( K = k3_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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] : ( m1_matrix_2(L,k3_matrix_2(3)) => ( L = k3_finseq_4(k4_ordinal1,2,1,3) => k10_matrix_3(3,A,K,L) = k3_finseq_4(u1_struct_0(A),C,E,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( m1_subset_1(C,k2_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => k5_matrixc1(k10_seq_4(A,C),B) = k10_seq_4(k5_matrixc1(A,B),C) ) ) ) ) )).
fof(t24_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(A)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,A,k2_wsierp_1(k10_matrixj1(A,k5_matrixj1(A,C,D))),k2_wsierp_1(k11_matrixj1(A,k5_matrixj1(A,C,D)))) & m2_finseq_1(E,k3_finseq_2(A)) ) => ( E = k13_matrixj1(A,B,k5_matrixj1(A,C,D)) <=> ! [F] : ( v7_ordinal1(F) => ( ( r2_hidden(F,k2_finseq_1(k1_matrix_0(C))) => k8_matrix_0(A,E,F) = k8_finseq_1(A,k8_matrix_0(A,C,F),k5_finseq_2(A,k3_finseq_1(D),B)) ) & ( r2_hidden(F,k2_finseq_1(k1_matrix_0(D))) => k8_matrix_0(A,E,k2_xcmplx_0(F,k1_matrix_0(C))) = k8_finseq_1(A,k5_finseq_2(A,k3_finseq_1(C),B),k8_matrix_0(A,D,F)) ) ) ) ) ) ) ) ) ) )).
fof(t24_matrixj2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( m1_matrlin(E,A,C) => ! [F] : ( m2_finseq_1(F,u1_struct_0(D)) => ! [G] : ( m1_matrixj2(G,A,B) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(A),k3_finseq_1(E),k3_finseq_1(F)) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(A))) ) => ( H = k20_matrixj1(u1_struct_0(A),k4_struct_0(A),G) => ! [I] : ( v7_ordinal1(I) => ! [J] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_matrixr1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => k2_matrix_0(k3_matrix_3(A,B,C)) = k2_matrix_0(B) ) ) ) )).
fof(t24_matrixr2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => ( r1_xxreal_0(k3_finseq_1(A),k5_numbers) | k9_matrixr1(k8_rvsum_1(A,B)) = k5_matrixr1(k9_matrixr1(A),k9_matrixr1(B)) ) ) ) ) )).
fof(t24_matrlin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,D,C,A) & m2_finseq_1(E,k3_finseq_2(D)) ) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,D,B,A) & m2_finseq_1(F,k3_finseq_2(D)) ) => ( k1_matrix_0(E) = k1_matrix_0(F) => k1_matrix_0(k8_matrlin(D,C,B,A,E,F)) = k1_matrix_0(E) ) ) ) ) ) ) ) )).
fof(t24_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( k2_vectsp_5(A,B,C,D) = k1_vectsp_4(A,B) => ! [E] : ( m1_matrlin(E,A,C) => ! [F] : ( m1_matrlin(F,A,D) => ! [G] : ( m1_matrlin(G,A,k1_vectsp_5(A,B,C,D)) => ( G = k7_finseq_1(E,F) => ! [H] : ( m1_subset_1(H,u1_struct_0(k1_vectsp_5(A,B,C,D))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k1_vectsp_5(A,B,C,D))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k1_vectsp_5(A,B,C,D))) => ! [K] : ( m1_subset_1(K,u1_struct_0(C)) => ! [L] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t24_matrprob,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,k5_numbers) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => k5_matrprob(B) = k5_numbers ) ) )).
fof(t24_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & v3_valued_0(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_card_1(D,A) & v1_finseq_1(D) & v3_valued_0(D) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => 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)) ) ) ) ) ) )).
fof(t24_matrtop2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ! [D] : ( ( 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) = A => v1_rlaffin1(k2_ranknull(k15_euclid(A),k15_euclid(B),k3_matrtop1(A,B,C),D),k15_euclid(B)) ) ) ) ) ) )).
fof(t24_matrtop3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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(k1_square_1(A),k2_xcmplx_0(k1_square_1(k1_funct_1(E,B)),k1_square_1(k1_funct_1(E,C)))) & ! [F] : ( v1_xreal_0(F) => k1_funct_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 ) ) ) ) ) ) ) )).
fof(t24_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(t24_mboolean,axiom,( ! [A] : ! [B] : ! [C] : r6_pboole(C,k2_mboolean(C,k7_funcop_1(C,k2_tarski(k1_tarski(A),k1_tarski(B)))),k7_funcop_1(C,k2_tarski(A,B))) )).
fof(t24_mcart_1,axiom,( ! [A] : ! [B] : ( k3_zfmisc_1(A,A,A) = k3_zfmisc_1(B,B,B) => A = B ) )).
fof(t24_measure6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( B = k1_numbers => k1_measure6(B,A) = B ) ) ) )).
fof(t24_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => r1_tarski(k6_member_1(k3_xboole_0(A,B)),k3_xboole_0(k6_member_1(A),k6_member_1(B))) ) ) )).
fof(t24_membered,axiom,( ! [A] : ! [B] : ( v6_membered(B) => ( r1_tarski(A,B) => v6_membered(A) ) ) )).
fof(t24_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_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))) ) ) ) ) )).
fof(t24_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( 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))) ) ) ) ) ) ) ) )).
fof(t24_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ! [C] : ( 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))) ) ) ) ) )).
fof(t24_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ( v1_mesfunc8(B,A,k2_numbers) <=> v1_mesfunc8(k11_mesfun7c(A,B),A,k1_numbers) ) ) ) )).
fof(t24_mesfunc1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ! [F] : ( m1_subset_1(F,k4_ordinal1) => k9_nat_1(B,C,F) = k9_subset_1(A,E,k15_mesfunc1(A,D,F)) ) => k9_subset_1(A,E,k15_mesfunc1(A,D,k1_supinf_1)) = k2_measure2(A,B,k1_measure3(A,B,C)) ) ) ) ) )).
fof(t24_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => r2_relset_1(A,k6_numbers,k10_mesfunc1(A,B),k3_mesfunc1(A,k1_mesfunc2(A,B),k2_mesfunc2(A,B))) ) ) )).
fof(t24_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_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))) ) ) ) ) ) )).
fof(t24_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( ( 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] : ( 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,k6_xcmplx_0(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)) ) ) ) ) ) ) ) ) )).
fof(t24_mesfunc7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( 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,k6_numbers,k3_mesfunc2(D,A),D)) = k12_supinf_2(C,D) ) ) ) ) ) ) )).
fof(t24_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k6_numbers)) & v1_mesfunc8(C,A,k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( ( k1_relset_1(A,k4_mesfunc5(A,k6_numbers,C,k5_numbers)) = D & ! [E] : ( v7_ordinal1(E) => r1_mesfunc1(A,B,k4_mesfunc5(A,k6_numbers,C,E),D) ) ) => r1_mesfunc1(A,B,k5_mesfunc8(A,C),D) ) ) ) ) ) )).
fof(t24_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ~ ( v2_mesfunc9(B,A) & r2_hidden(E,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,k4_mesfunc9(A,B),C))) & k1_mesfunc9(k4_mesfunc5(A,k6_numbers,k4_mesfunc9(A,B),C),E) = k1_supinf_1 & r1_xxreal_0(D,C) & k1_mesfunc9(k4_mesfunc5(A,k6_numbers,B,D),E) = k2_supinf_1 ) ) ) ) ) )).
fof(t24_metric_1,axiom,( ! [A] : ( m1_subset_1(A,1) => ! [B] : ( m1_subset_1(B,1) => ! [C] : ( m1_subset_1(C,1) => r1_xxreal_0(k1_binop_1(k2_metric_1,A,C),k4_xxreal_0(k1_binop_1(k2_metric_1,A,B),k1_binop_1(k2_metric_1,B,C))) ) ) ) )).
fof(t24_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(k2_metric_2(A),k2_metric_2(A))) => ( r2_hidden(C,k4_metric_2(A,B)) <=> ? [D] : ( m1_subset_1(D,k2_metric_2(A)) & ? [E] : ( 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) ) ) ) ) ) ) )).
fof(t24_metric_3,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers)) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k1_numbers,k1_numbers)) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(k1_numbers,k1_numbers)) => r1_xxreal_0(k2_binop_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers,k18_metric_3,A,C),k3_real_1(k2_binop_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers,k18_metric_3,A,B),k2_binop_1(k2_zfmisc_1(k1_numbers,k1_numbers),k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers,k18_metric_3,B,C))) ) ) ) )).
fof(t24_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [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)))) ) => ~ ( v1_metrizts(A) & ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t24_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t24_midsp_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t24_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_midsp_3(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_2(E,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(B))) => ! [F] : ( ( v4_midsp_2(F,B) & l1_midsp_2(F,B) ) => ! [G] : ( m1_subset_1(G,u1_struct_0(u1_midsp_2(B,F))) => ! [H] : ( m2_finseq_2(H,u1_struct_0(u1_midsp_2(B,F)),k4_finseq_2(k1_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 ) ) ) ) ) ) ) ) ) )).
fof(t24_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t24_mod_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k18_mod_2)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k18_mod_2)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k18_mod_2)) => ! [D] : ( m1_subset_1(D,k1_enumset1(k5_numbers,1,2)) => ! [E] : ( m1_subset_1(E,k1_enumset1(k5_numbers,1,2)) => ! [F] : ( m1_subset_1(F,k1_enumset1(k5_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)) ) ) ) ) ) ) ) ) )).
fof(t24_mod_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t24_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k6_modal_1) => ! [B] : ( m1_subset_1(B,k6_modal_1) => m1_subset_1(k7_trees_2(k7_trees_2(k8_funcop_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k2_trees_1(2),k1_domain_1(k4_ordinal1,k4_ordinal1,2,k5_numbers)),k14_trees_3(k5_numbers),A),k14_trees_3(1),B),k6_modal_1) ) ) )).
fof(t24_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_1(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_partfun1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,C))) ) => ! [E] : ( m1_subset_1(E,C) => ! [F] : ( ( ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(k30_modelc_1(C))) ) => ! [G] : ( ( 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] : ( m1_modelc_1(H,C,D) & k3_funct_2(k4_ordinal1,C,H,k5_numbers) = E & ? [I] : ( m1_subset_1(I,k4_ordinal1) & ! [J] : ( m1_subset_1(J,k4_ordinal1) => ( ~ r1_xxreal_0(I,J) => r4_modelc_1(C,D,F,G,k3_funct_2(k4_ordinal1,C,H,J),A) ) ) & r4_modelc_1(C,D,F,G,k3_funct_2(k4_ordinal1,C,H,I),B) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( v7_modelc_2(A) => ( r1_modelc_2(B,A) <=> ( B = k11_modelc_2(A) | B = k12_modelc_2(A) ) ) ) ) ) )).
fof(t24_moebius1,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ v1_moebius1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => r1_xxreal_0(k11_nat_3(A,B),1) ) ) ) )).
fof(t24_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m2_monoid_0(B,A) ) => u2_algstr_0(B) = k1_realset1(u2_algstr_0(A),u1_struct_0(B)) ) ) )).
fof(t24_monoid_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m2_monoid_0(C,B) ) => m2_monoid_0(k9_monoid_1(C,A),k9_monoid_1(B,A)) ) ) )).
fof(t24_morph_01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(t24_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_numbers))),B)) ) ) )).
fof(t24_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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] : ( m3_pboole(D,u1_struct_0(A),u3_msualg_1(A,B)) => ! [E] : ( m3_pboole(E,u1_struct_0(A),u3_msualg_1(A,C)) => ( r8_pboole(u1_struct_0(A),D,E) => ! [F] : ( m1_subset_1(F,u4_struct_0(A)) => ( r1_msualg_2(A,B,F,D) => r1_msualg_2(A,C,F,E) ) ) ) ) ) ) ) ) ) )).
fof(t24_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ~ ( r2_hidden(E,k4_finseq_1(D)) & ! [F] : ( 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] : ( v7_ordinal1(E) => ~ ( r2_hidden(E,k4_finseq_1(D)) & ! [F] : ( 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)) ) ) ) ) ) )).
fof(t24_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_funcop_1(B) ) => ( v2_finset_1(k1_funct_6(B)) => v2_finset_1(k2_funct_6(B)) ) ) )).
fof(t24_mssublat,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v13_struct_0(A,1) & v5_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t24_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msualg_2(C,A,B) => ! [D] : ( m3_pboole(D,u1_struct_0(A),u3_msualg_1(A,B)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t24_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( m2_pboole(E,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [F] : ( m1_subset_1(F,k3_msualg_1(A,D,B)) => ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) ) => ! [H] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msualg_6(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ~ ( r1_msualg_6(A,D,E,B,F) & ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t24_msualg_7,axiom,( ? [A] : ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) & ? [B] : ( m2_nat_lat(B,A) & v1_msualg_7(B,A) & ~ v2_msualg_7(B,A) ) ) )).
fof(t24_msualg_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_pboole(C,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,k7_msafree2(A))) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( 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)) = k5_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)) = k5_numbers ) ) ) ) ) ) )).
fof(t24_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t24_mycielsk,axiom,( ! [A] : ( ( v1_necklace(A) & v4_dilworth(A) & l1_orders_2(A) ) => k2_dilworth(A) = k1_dilworth(k3_necklace(A)) ) )).
fof(t24_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t24_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( A = k3_xcmplx_0(C,B) => ( B = k5_numbers | r1_xxreal_0(C,A) ) ) ) ) ) )).
fof(t24_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(C,B) => r1_xxreal_0(k3_nat_d(C,A),k3_nat_d(B,A)) ) ) ) ) )).
fof(t24_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ~ ( A != 1 & A != B & k11_nat_3(B,A) != k5_numbers ) ) ) )).
fof(t24_nat_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( k6_xcmplx_0(A,1) = k2_nat_1(B,C) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( r1_nat_d(D,B) & v1_int_2(D) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( k4_nat_d(k11_newton(E,k7_nat_d(A,1)),A) = 1 & k6_nat_d(k7_nat_d(k11_newton(E,k3_nat_d(k7_nat_d(A,1),D)),1),A) = 1 ) ) ) ) ) => ( r1_xxreal_0(B,C) | r1_xxreal_0(C,k5_numbers) | v1_int_2(A) ) ) ) ) ) )).
fof(t24_nat_5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ( r1_funct_2(k4_ordinal1,k4_ordinal1,k4_ordinal1,k1_numbers,A,B) => ( ! [D] : ( v7_ordinal1(D) => ~ r1_tarski(C,k2_finseq_1(D)) ) | k2_uproots(C,k1_nat_5(k4_ordinal1,A,C)) = k18_rvsum_1(k4_bhsp_5(k1_numbers,k4_ordinal1,B,k14_finseq_1(C))) ) ) ) ) ) )).
fof(t24_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,A) => k4_nat_d(A,B) = A ) ) ) )).
fof(t24_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ( r3_nattra_1(A,B,C,D) => r3_nattra_1(A,B,D,C) ) ) ) ) ) )).
fof(t24_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),k8_funct_2(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,C),k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,D))) & r2_funct_2(k4_ordinal1,u1_struct_0(B),k8_funct_2(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,C),k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,D))) ) ) ) ) ) ) ) )).
fof(t24_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t24_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_ndiff_1(D,A,k4_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v12_struct_0(D,k4_ordinal1,A) => ( v3_normsp_1(k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),D,C),B) & k6_normsp_1(B,k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),D,C)) = k4_struct_0(B) ) ) ) ) ) ) )).
fof(t24_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t24_ndiff_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(B))))) ) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t24_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( 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] : ( 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] : ( m1_subset_1(F,u1_struct_0(k14_prvect_2(A))) => ( r2_hidden(F,E) => r1_ndiff_5(A,B,C,D,F) ) ) ) ) ) ) ) ) ) )).
fof(t24_neckla_3,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t24_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : ! [C] : ( r1_tarski(C,k2_net_1(A)) => ( r2_hidden(B,k13_net_1(A,C)) <=> ? [D] : ( m1_subset_1(D,k2_net_1(A)) & r2_hidden(D,C) & r2_hidden(B,k6_net_1(A,D)) ) ) ) ) )).
fof(t24_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,A) & B = k6_xcmplx_0(A,1) ) => k3_newton(B,A) = A ) ) ) )).
fof(t24_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,k1_relset_1(u1_struct_0(A),C)) => r3_nfcont_1(A,B,C,k1_tarski(D)) ) ) ) ) ) )).
fof(t24_nfcont_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t24_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(D,B) & ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( v1_xreal_0(G) => ~ ( r2_hidden(G,B) & ~ r1_xxreal_0(F,k9_complex1(k6_xcmplx_0(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)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))) => ( ( r2_hidden(C,k7_normform(A)) & r2_hidden(B,k7_normform(A)) ) => ( r2_hidden(k1_normform(k5_finsub_1(A),k5_finsub_1(A),C,B),k7_normform(A)) <=> k5_setwiseo(A,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)),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))) = k1_xboole_0 ) ) ) ) )).
fof(t24_normsp_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v3_normsp_1(C,A) & k6_normsp_1(A,C) = B ) => ( v2_comseq_2(k5_normsp_0(A,k4_normsp_1(A,C,B))) & k1_seq_2(k5_normsp_0(A,k4_normsp_1(A,C,B))) = k5_numbers ) ) ) ) ) )).
fof(t24_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t24_numbers,axiom,( k4_numbers != k3_numbers )).
fof(t24_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t24_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => u1_struct_0(k15_openlatt(A)) = k9_openlatt(A) ) )).
fof(t24_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t24_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_ordeq_01(A,B))) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ( D = C => ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,A) => r1_xxreal_0(k2_normsp_0(B,k7_partfun1(u1_struct_0(B),D,E)),k2_normsp_0(k5_ordeq_01(A,B),C)) ) ) ) ) ) ) ) )).
fof(t24_orders_1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(t24_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t24_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => ( v4_ordinal1(A) <=> ! [B] : ( v3_ordinal1(B) => ( r2_hidden(B,A) => r2_hidden(k1_ordinal1(B),A) ) ) ) ) )).
fof(t24_ordinal2,axiom,( ! [A] : r1_ordinal1(k2_ordinal2(A),k3_ordinal2(A)) )).
fof(t24_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r1_ordinal1(A,k10_ordinal2(A,B)) & r1_ordinal1(B,k10_ordinal2(A,B)) ) ) ) )).
fof(t24_ordinal4,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( ( r2_hidden(1,C) & r2_hidden(A,B) ) => r2_hidden(k12_ordinal2(C,A),k12_ordinal2(C,B)) ) ) ) ) )).
fof(t24_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(1,A) => ( r1_xxreal_0(C,B) | r2_hidden(k1_ordinal5(A,B),k1_ordinal5(A,C)) ) ) ) ) ) )).
fof(t24_ordinal6,axiom,( ! [A] : ( v1_ordinal6(A) => ! [B] : ( v1_ordinal6(B) => ( ! [C] : ! [D] : ( ( 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))) ) ) ) )).
fof(t24_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t24_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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] : ( m2_subset_1(C,k1_zfmisc_1(u1_struct_0(A)),k2_osalg_4(A)) => ! [D] : ! [E] : ( r2_hidden(k4_tarski(D,E),k5_osalg_4(A,k8_osafree(A,B),k20_osafree(A,B),C)) <=> ? [F] : ( 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)) ) ) ) ) ) )).
fof(t24_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t24_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(t24_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & v12_osalg_1(C,A) & v13_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t24_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t24_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t24_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) ) )).
fof(t24_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t24_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(t24_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) => ( v4_relat_2(C) => r4_relat_2(C,A) ) ) ) ) )).
fof(t24_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => v6_pasch(A) ) )).
fof(t24_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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)) ) ) ) )).
fof(t24_pcomps_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ( v8_pre_topc(A) & v2_pcomps_1(A) ) => v9_pre_topc(A) ) ) )).
fof(t24_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k20_pcs_0(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k20_pcs_0(A,B))) => ( ( C = D & r1_orders_2(k20_pcs_0(A,B),D,E) ) => ( C = B | r2_hidden(B,u1_struct_0(A)) | ( r2_hidden(E,u1_struct_0(A)) & E != B ) ) ) ) ) ) ) )).
fof(t24_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( 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] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [G] : ( m1_subset_1(G,u1_struct_0(k4_real_ns1(A))) => ! [H] : ( m2_finseq_2(H,k1_numbers,k1_euclid(A)) => ( ( E = F & G = H & r5_pdiff_1(A,B,C,D,E,G) ) => k1_funct_1(k12_pdiff_1(A,B,C,D,E,G),k12_finseq_1(k4_ordinal1,1)) = k9_finseq_1(k13_pdiff_1(A,B,C,D,F,H)) ) ) ) ) ) ) ) ) ) )).
fof(t24_pdiff_3,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(2)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [C] : ( ( 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) & k10_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) = k2_xcmplx_0(k5_pdiff_3(B,A),k5_pdiff_3(C,A)) ) ) ) ) ) )).
fof(t24_pdiff_4,axiom,( ! [A] : ! [B] : ( ( 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] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => ( r2_hidden(C,A) => r3_pdiff_1(3,3,B,C) ) ) ) ) ) )).
fof(t24_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( 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) ) ) ) )).
fof(t24_pdiff_6,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( ( 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] : ( ( 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] : ( v1_xreal_0(G) => ~ ( ~ r1_xxreal_0(G,k5_numbers) & r1_tarski(a_3_2_pdiff_6(A,D,G),k1_relset_1(k1_euclid(A),C)) & ! [H] : ( v1_xreal_0(H) => ~ ( ~ r1_xxreal_0(H,k5_numbers) & ! [I] : ( v1_xreal_0(I) => ~ ( ~ r1_xxreal_0(I,k5_numbers) & ! [J] : ( m2_finseq_2(J,k1_numbers,k1_euclid(A)) => ! [K] : ( 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,k3_xcmplx_0(k5_xcmplx_0(k12_euclid(J)),k12_euclid(K))) ) ) ) ) ) ) ) & ! [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t24_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_1(B,k1_euclid(A)) => ! [C] : ( m2_finseq_1(C,k1_euclid(A)) => ! [D] : ( m2_finseq_1(D,k1_euclid(A)) => ( ( k4_finseq_1(B) = k4_finseq_1(C) & r2_relset_1(k4_ordinal1,k1_euclid(A),D,k7_integr15(A,k4_ordinal1,B,C)) ) => k5_euclid_7(A,D) = k7_euclid(A,k5_euclid_7(A,B),k5_euclid_7(A,C)) ) ) ) ) ) )).
fof(t24_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(k1_euclid(A))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k4_real_ns1(A)))) => ( ( E = F & v1_pdiff_7(E,A) & C = D ) => ( ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t24_pencil_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v15_pencil_1(B) ) => ! [C] : ( m1_subset_1(C,u1_pre_topc(k5_pencil_1(A,B))) <=> ? [D] : ( ~ 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)))) ) ) ) ) )).
fof(t24_pencil_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v15_pencil_1(B) ) => ( ! [C] : ( m1_subset_1(C,A) => v10_pencil_1(k2_pencil_1(A,B,C)) ) => ! [C] : ( m1_pencil_2(C,A,B) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t24_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t24_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => k1_newton(A,2) = k1_square_1(A) ) )).
fof(t24_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m3_pnproc_1(C,A,B) => k3_relat_1(k6_partfun1(k9_funct_2(A,k4_ordinal1)),k7_pnproc_1(A,C)) = k7_pnproc_1(A,C) ) ) )).
fof(t24_polyalg1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t24_polyeq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ~ ( B != k5_numbers & k2_polyeq_1(B,C,k5_numbers,A) = k5_numbers & A != k4_xcmplx_0(k7_xcmplx_0(C,B)) & A != k5_numbers ) ) ) ) )).
fof(t24_polyeq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( k3_power(A,C) = k5_numbers => ( r1_xxreal_0(A,k5_numbers) | A = 1 | r1_xxreal_0(C,k5_numbers) | C = 1 ) ) ) ) ) )).
fof(t24_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( v1_xcmplx_0(F) => ! [G] : ( v1_xcmplx_0(G) => ! [H] : ( v1_xcmplx_0(H) => ! [I] : ( v1_xcmplx_0(I) => ! [J] : ( v1_xcmplx_0(J) => ! [K] : ( v1_xcmplx_0(K) => ( ( K = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(8,D),k3_xcmplx_0(3,k1_newton(G,2))),32) & H = k7_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(8,C),k3_xcmplx_0(k3_xcmplx_0(4,D),G)),k1_newton(G,3)),64) & I = k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(256,B),k3_xcmplx_0(k3_xcmplx_0(64,G),C)),k3_xcmplx_0(k3_xcmplx_0(16,k1_newton(G,2)),D)),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 = k4_xcmplx_0(k7_xcmplx_0(H,k3_xcmplx_0(E,F))) ) => ( H = k5_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(D,k1_newton(A,2))),k3_xcmplx_0(C,A)),B) = k5_numbers <=> ~ ( A != k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(E,F),J),k7_xcmplx_0(G,4)) & A != k6_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(E,F),J),k7_xcmplx_0(G,4)) & A != k6_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(E),F),J),k7_xcmplx_0(G,4)) & A != k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(E),F),J),k7_xcmplx_0(G,4)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(t24_polynom1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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),k7_polynom1(A,B,C,C),k8_polynom1(A,B)) ) ) )).
fof(t24_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_algseq_1(A,B,D) & r1_algseq_1(A,C,D) ) => r1_algseq_1(A,k2_normsp_1(A,B,C),D) ) ) ) ) ) )).
fof(t24_polynom4,axiom,( ! [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) & v5_vectsp_1(A) & v6_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(t24_polynom5,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k1_algseq_1(A,k3_polynom5(A,B,k4_struct_0(A))) = k5_numbers ) ) )).
fof(t24_polynom7,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( 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] : ( ( 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_polynom2(A,B,C,D) = k3_polynom7(A,B,C) ) ) ) ) )).
fof(t24_polynom8,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k3_polynom8(A,B,k2_nat_1(C,D)) = k3_polynom8(A,k3_polynom8(A,B,C),D) ) ) ) ) )).
fof(t24_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(D,A,C) & v1_polynom1(D,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) ) ) ) ) )).
fof(t24_power,axiom,( ! [A] : ( v1_xreal_0(A) => k2_power(A,k5_numbers) = 1 ) )).
fof(t24_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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)) ) ) ) ) )).
fof(t24_pre_circ,axiom,( ! [A] : ( v1_finset_1(A) => ~ ( k5_card_1(A) = 1 & ! [B] : ( m1_subset_1(B,A) => A != k1_tarski(B) ) ) ) )).
fof(t24_pre_poly,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t24_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_pre_topc(A,B)) <=> ( ~ v2_struct_0(A) & ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t24_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t24_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(1,C) ) => ( r1_xxreal_0(B,k5_numbers) | k2_prepower(C,k7_xcmplx_0(A,B)) = k7_xcmplx_0(k2_prepower(C,A),k2_prepower(C,B)) ) ) ) ) ) )).
fof(t24_prob_1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => m1_prob_1(k7_subset_1(A,C,D),A,B) ) ) ) )).
fof(t24_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m2_prob_1(D,A,B) => r1_prob_2(A,B,D,C,k4_prob_1(A,B)) ) ) ) ) )).
fof(t24_prob_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( ~ 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] : ( ( v5_relat_1(D,C) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => r1_tarski(k1_prob_2(B,C,D,A),k1_prob_2(B,C,k2_prob_3(B,D),A)) ) ) ) )).
fof(t24_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => m1_prob_4(k1_xboole_0,A,B,C) ) ) ) )).
fof(t24_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t24_projpl_1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & v5_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t24_projred1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t24_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u2_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u2_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u2_incsp_1(A)) => ! [H] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_prvect_3,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ? [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(k14_prvect_2(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ? [F] : ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) & ? [G] : ( 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] : ( m1_subset_1(D,u1_struct_0(k7_prvect_3(k14_prvect_2(A),B))) => ! [E] : ( 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] : ( m1_subset_1(D,u1_struct_0(k7_prvect_3(k14_prvect_2(A),B))) => ! [E] : ( 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] : ( m1_subset_1(D,u1_struct_0(k7_prvect_3(k14_prvect_2(A),B))) => k2_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)) = k2_normsp_0(k7_prvect_3(k14_prvect_2(A),B),D) ) ) ) ) )).
fof(t24_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ 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)) ) ) ) ) )).
fof(t24_pua2mss1,axiom,( ! [A] : ( ( 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) ) )).
fof(t24_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) )).
fof(t24_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k1_qc_lang1(A)) => ( r1_qc_lang1(A,B,C) | r1_qc_lang1(A,C,B) ) ) ) ) )).
fof(t24_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( m2_subset_1(E,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [F] : ( m2_subset_1(F,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [G] : ( m2_subset_1(G,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [H] : ( m2_subset_1(H,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [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 ) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( v6_qc_lang1(C,A) => v6_qc_lang1(k15_qc_lang1(A,B,C),A) ) ) ) ) )).
fof(t24_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,k5_numbers)),k9_xtuple_0(k2_qc_lang4(A,B))) & k1_funct_1(k2_qc_lang4(A,B),k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,k5_numbers))) = k18_qc_lang1(A,k3_trees_2(k9_qc_lang1(A),k2_qc_lang4(A,B),C)) ) ) ) ) ) )).
fof(t24_quantal1,axiom,( ! [A] : ( ( ~ 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] : k5_quantal1(A,k15_lattice3(A,B)) = k16_lattice3(A,a_2_0_quantal1(A,B)) ) )).
fof(t24_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k23_quaterni(A,k25_quaterni(B,C)) = k25_quaterni(k23_quaterni(A,B),k23_quaterni(A,C)) ) ) ) )).
fof(t24_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k13_quaterni(k21_quaterni(k7_xcmplx_0(1,k1_square_1(k28_quaterni(A))),k27_quaterni(A))) = k3_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k28_quaterni(A))),k13_quaterni(A)) ) )).
fof(t24_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => A = k6_quaterni(k13_quaterni(A),k14_quaterni(A),k15_quaterni(A),k16_quaterni(A)) ) )).
fof(t24_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( k1_quin_1(B,C,D) = k5_numbers => ( r1_xxreal_0(k5_numbers,B) | ( ~ ( ~ r1_xxreal_0(k5_numbers,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(A)),k3_xcmplx_0(C,A)),D)) & A = k4_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(2,B))) ) & ~ ( A != k4_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(2,B))) & r1_xxreal_0(k5_numbers,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(A)),k3_xcmplx_0(C,A)),D)) ) ) ) ) ) ) ) ) )).
fof(t24_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [C] : ( 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) ) ) ) )).
fof(t24_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t24_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_random_1(C,A,B) => m1_random_1(k56_valued_1(A,k1_numbers,C),A,B) ) ) ) )).
fof(t24_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_6(C,A,B) => r1_vectsp_6(A,B,C,k6_ranknull(A,B,C,k1_vectsp_6(A,B,C))) ) ) ) )).
fof(t24_rat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_rat_1(C) => ~ ( A != k5_numbers & C = k7_xcmplx_0(B,A) & ! [D] : ( v7_ordinal1(D) => ~ ( B = k3_xcmplx_0(k2_rat_1(C),D) & A = k3_xcmplx_0(k1_rat_1(C),D) ) ) ) ) ) ) )).
fof(t24_ratfunc1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t24_rcomp_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v3_xxreal_2(A) => r1_tarski(A,k2_limfunc1(k3_seq_4(A))) ) ) )).
fof(t24_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k6_real_lat(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k6_real_lat(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t24_realset2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(A),k8_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t24_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(A),k8_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t24_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [D] : ( ( v1_rearran1(D) & v2_rearran1(D) & v3_rearran1(D,k1_zfmisc_1(A)) & m2_finseq_1(D,k1_zfmisc_1(A)) ) => ( ( v1_partfun1(C,B) & k5_card_1(A) = k5_card_1(B) ) => k20_rfunct_3(A,k4_rearran1(B,A,D,C),A) = k20_rfunct_3(B,C,B) ) ) ) ) ) )).
fof(t24_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => ( r1_tarski(A,B) => r1_tarski(k3_relat_1(A,C),k3_relat_1(B,C)) ) ) ) ) )).
fof(t24_relset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,k1_relset_1(A,C)) <=> ? [E] : ( m1_subset_1(E,B) & r2_hidden(k4_tarski(D,E),C) ) ) ) ) ) ) )).
fof(t24_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C))) => ( r2_hidden(A,k6_relset_2(B,C,D,E)) => ! [F] : ( r2_hidden(F,D) => r2_hidden(A,k1_relset_2(B,C,E,F)) ) ) ) ) )).
fof(t24_revrot_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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,k1_nat_1(k7_nat_d(A,1),k4_finseq_4(C,B))) ) ) ) ) ) )).
fof(t24_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r1_rewrite1(A,B,C) => r1_rewrite1(k2_relat_1(A),C,B) ) ) )).
fof(t24_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t24_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(C))) => ! [G] : ( 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) ) ) ) ) ) ) )).
fof(t24_rfinseq,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( B != k5_numbers => k8_relset_1(k4_ordinal1,k1_numbers,A,k1_tarski(k7_xcmplx_0(C,B))) = k8_relset_1(k4_ordinal1,k1_numbers,k10_rvsum_1(A,B),k1_tarski(C)) ) ) ) ) )).
fof(t24_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t24_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t24_rfunct_2,axiom,( ! [A] : ! [B] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( 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_funct_1(B,C),k1_funct_1(B,D)) ) ) ) ) ) )).
fof(t24_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_rfunct_3(B,A,k1_numbers,k3_rfunct_3(A,k1_numbers)) => ! [C] : ( m2_rfunct_3(C,A,k1_numbers,k3_rfunct_3(A,k1_numbers)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t24_rfunct_4,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(t24_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v7_valued_0(A) & v1_seq_2(A) ) => k1_seq_2(A) = k1_rinfsup1(A) ) ) )).
fof(t24_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => r1_xxreal_0(k2_rinfsup2(A),k1_rinfsup2(A)) ) )).
fof(t24_ringcat1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k17_ringcat1(A))) => ! [C] : ( m2_ringcat1(C,k9_ringcat1(A)) => ( B = C => k4_cat_1(k17_ringcat1(A),B) = k13_ringcat1(k9_ringcat1(A),C) ) ) ) ) )).
fof(t24_rlaffin1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ 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] : ( m1_rlvect_2(C,B) => ! [D] : ( 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))) ) ) ) ) )).
fof(t24_rlaffin2,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_rlvect_2(C,A) => ~ ( k6_rlvect_2(A,B) != k6_rlvect_2(A,C) & k3_rlaffin1(A,B) = k3_rlaffin1(A,C) & ! [D] : ( 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)) ) ) ) ) ) )).
fof(t24_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t24_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( ( v1_rlvect_1(C) & m1_rlsub_1(C,A) ) => k2_rlsub_2(A,C,k1_rlsub_2(A,C,B)) = C ) ) ) )).
fof(t24_rltopsp1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t24_rlvect_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( 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)) ) ) ) )).
fof(t24_rlvect_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( ( 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(k4_ordinal1,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)) ) ) ) ) ) ) )).
fof(t24_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_rlvect_3(B,A) & ! [C] : ( 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)) ) ) ) ) ) )).
fof(t24_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( v1_rlvect_3(k8_domain_1(u1_struct_0(A),B,D,C),A) => ( B = C | B = D | C = D | v1_rlvect_3(k8_domain_1(u1_struct_0(A),B,k5_algstr_0(A,D,B),k5_algstr_0(A,C,B)),A) ) ) ) ) ) ) )).
fof(t24_rlvect_5,axiom,( ! [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) ) => ( v1_rlvect_5(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_rlvect_3(B,A) => v1_finset_1(B) ) ) ) ) )).
fof(t24_rlvect_x,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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] : ( v1_int_1(G) & ? [H] : ( v1_int_1(H) & ? [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)) ) ) ) ) ) ) ) ) ) )).
fof(t24_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t24_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => m1_rmod_2(k2_rmod_3(A,B,C,D),A,k1_rmod_3(A,B,C,D)) ) ) ) ) )).
fof(t24_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( 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)) ) ) ) )).
fof(t24_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t24_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t24_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_lattice3(A) & v2_lattice3(A) & v6_oposet_1(A) & l2_qmax_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t24_robbins4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k2_robbins4)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_robbins4)) => ( r3_lattices(k2_robbins4,A,B) <=> r1_tarski(A,B) ) ) ) )).
fof(t24_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t24_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_tarski(C,B) => k1_rpr_1(A,k7_subset_1(A,B,C)) = k6_xcmplx_0(k1_rpr_1(A,B),k1_rpr_1(A,C)) ) ) ) ) )).
fof(t24_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_rsspace4(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_rsspace4(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_rsspace4(A,B))) => ! [F] : ( ( 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] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_bhsp_1(B) & m1_rusub_1(B,A) ) => ! [C] : ( ( v1_bhsp_1(C) & m1_rusub_1(C,A) ) => ( u1_struct_0(B) = u1_struct_0(C) => B = C ) ) ) ) )).
fof(t24_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( ( v1_bhsp_1(C) & m1_rusub_1(C,A) ) => k2_rusub_2(A,C,k1_rusub_2(A,C,B)) = C ) ) ) )).
fof(t24_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_3(C,B) => ? [D] : ( m1_rusub_3(D,A) & r1_tarski(C,D) ) ) ) ) )).
fof(t24_rusub_4,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ( v2_rusub_4(k3_rusub_4(A,B),A) & r2_hidden(k4_struct_0(A),u1_struct_0(B)) ) ) ) )).
fof(t24_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t24_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ( k30_valued_1(A) = k30_valued_1(B) => A = B ) ) ) )).
fof(t24_rvsum_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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) ) ) )).
fof(t24_scm_halt,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => r2_scm_halt(A,B,C) ) ) ) ) )).
fof(t24_scmfsa10,axiom,( ! [A] : ( 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) ) ) )).
fof(t24_scmfsa6a,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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)) = k1_nat_1(k5_card_1(B),2) ) ) )).
fof(t24_scmfsa8a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [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(k7_card_1(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) ) ) ) ) ) )).
fof(t24_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( 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(k5_numbers,k1_funct_1(B,E)) | ( r5_scmfsa7b(k3_scmfsa8b(E,C,D),B,A) & r6_scmfsa7b(k3_scmfsa8b(E,C,D),B,A) ) ) ) ) ) ) ) ) )).
fof(t24_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k5_numbers)) = 1 & r1_scmfsa8a(B,A,k2_scmfsa6a(C)) ) => k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(k3_scmfsa6a(C,k4_compos_1(k1_scmfsa_2)),B,A)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),k2_scmfsa8a(B,A,k2_scmfsa6a(C)))) ) ) ) ) )).
fof(t24_scmfsa9a,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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_sf_mastr(k2_scmfsa_9(A,B)) = k4_subset_1(k2_scmfsa_2,k4_scmfsa_m(A),k2_sf_mastr(B)) ) ) )).
fof(t24_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ~ ( k2_compos_0(u1_compos_1(k1_scmfsa_2),A) = 2 & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => A != k7_scmfsa_2(B,C) ) ) ) ) )).
fof(t24_scmfsa_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ( ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1))) & ! [F] : ( v7_ordinal1(F) => ( ~ ( r1_xxreal_0(k3_funct_2(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(D,B,C,A),F)),k3_funct_2(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(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(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(D,B,C,A),F)) != k5_numbers ) & ~ ( k3_funct_2(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(D,B,C,A),F)) = k5_numbers & k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(D,B,C,A),F),C) = k5_numbers ) & ( k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(D,B,C,A),F),C) != k5_numbers => k3_funct_2(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(D,B,C,A),F)) = k5_numbers ) ) ) ) => ( r6_scmfsa7b(k1_scmfsa_9(C,B),D,A) & r5_scmfsa7b(k1_scmfsa_9(C,B),D,A) ) ) ) ) ) ) )).
fof(t24_scmfsa_m,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( ~ r1_xxreal_0(C,B) & r1_xxreal_0(k4_seq_4(k3_funct_2(k4_ordinal1,k1_zfmisc_1(k4_ordinal1),k8_scmfsa_m(A),C)),k4_seq_4(k3_funct_2(k4_ordinal1,k1_zfmisc_1(k4_ordinal1),k8_scmfsa_m(A),B))) ) ) ) ) )).
fof(t24_scmpds_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) & v3_scmpds_4(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ( r1_xxreal_0(k5_numbers,k2_xcmplx_0(k5_card_1(A),C)) => v3_scmpds_4(k3_scmpds_4(A,k9_scmpds_2(D,B,C))) ) ) ) ) ) )).
fof(t24_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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(k1_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,k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),1))) ) ) ) ) ) )).
fof(t24_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( 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] : ( v7_ordinal1(D) => ~ ( 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) ) ) ) ) ) )).
fof(t24_scmpds_8,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ! [F] : ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k4_card_3(k2_memstr_0(2,k1_scmpds_2)),k4_ordinal1) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_card_3(k2_memstr_0(2,k1_scmpds_2)),k4_ordinal1))) ) => ( ( ! [H] : ( ( 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,k5_numbers) ) => ( k1_recdef_1(G,H) = k5_numbers => r1_xxreal_0(k1_funct_1(H,k2_scmpds_2(k1_funct_1(B,D),E)),k5_numbers) ) ) & ! [H] : ( ( 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,k5_numbers) ) => ! [I] : ( ( v1_relat_1(I) & v4_relat_1(I,k4_ordinal1) & v5_relat_1(I,u1_compos_1(k1_scmpds_2)) & v1_funct_1(I) & v1_partfun1(I,k4_ordinal1) ) => ( ( ! [J] : ( ( 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)),k5_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] : ( ( 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)),k5_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) ) ) ) ) ) ) ) ) ) )).
fof(t24_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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(k7_card_1(2),k1_scmring2(A)) = k3_relat_1(k3_ami_2,k1_scmring1(A)) ) )).
fof(t24_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t24_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( r2_hidden(B,k3_tarski(A)) <=> r2_hidden(k1_tarski(B),A) ) ) )).
fof(t24_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ~ ( B != C & C != D & D != B ) => r1_semi_af1(A,B,C,D) ) ) ) ) ) )).
fof(t24_seq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k26_valued_1(k4_ordinal1,k1_numbers,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C),A),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k26_valued_1(k4_ordinal1,k1_numbers,B,A),k26_valued_1(k4_ordinal1,k1_numbers,C,A))) ) ) ) )).
fof(t24_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(B) & v2_comseq_2(A) & v9_ordinal1(A) ) => ( k1_seq_2(A) = k5_numbers | k1_seq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,A)) = k7_xcmplx_0(k1_seq_2(B),k1_seq_2(A)) ) ) ) ) )).
fof(t24_seq_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( v2_comseq_2(A) & k1_seq_2(A) != k5_numbers & ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( m2_valued_0(B,k1_numbers,A) & v9_ordinal1(B) ) ) ) ) )).
fof(t24_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ! [D] : ( ( r1_tarski(D,C) & r3_seqfunc(A,B,C) ) => ( D = k1_xboole_0 | r3_seqfunc(A,B,D) ) ) ) ) )).
fof(t24_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v7_valued_0(A) & m2_valued_0(B,k1_numbers,A) ) => v7_valued_0(B) ) ) ) )).
fof(t24_series_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(1,k9_complex1(A)) => ( v1_series_1(k1_prepower(A)) & k4_series_1(k1_prepower(A)) = k7_xcmplx_0(1,k6_xcmplx_0(1,A)) ) ) ) )).
fof(t24_series_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k9_complex1(A),B) => r1_xxreal_0(k1_square_1(A),k1_square_1(B)) ) ) ) )).
fof(t24_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( 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(k7_xcmplx_0(k3_xcmplx_0(B,C),A),k7_xcmplx_0(k3_xcmplx_0(A,C),B)),k7_xcmplx_0(k3_xcmplx_0(A,B),C))) ) ) ) )).
fof(t24_setfam_1,axiom,( ! [A] : ! [B] : ( B != k1_xboole_0 => k2_xboole_0(A,k1_setfam_1(B)) = k1_setfam_1(k2_setfam_1(k1_tarski(A),B)) ) )).
fof(t24_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => v2_prob_1(k4_setlim_1(A,B)) ) )).
fof(t24_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v2_prob_1(C) => v2_prob_1(k6_setlim_2(A,C,B)) ) ) ) )).
fof(t24_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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))) ) => ( ( v3_binop_1(C,B) & v1_binop_1(C,B) & v2_binop_1(C,B) & r6_binop_1(B,D,C) ) => ! [E] : ( m1_subset_1(E,k5_finsub_1(A)) => ( E != k1_xboole_0 => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,A,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [G] : ( m1_subset_1(G,B) => k5_binop_1(B,D,G,k7_setwiseo(A,B,C,E,F)) = k7_setwiseo(A,B,C,E,k10_funcop_1(B,A,D,G,F)) ) ) ) ) ) ) ) ) ) )).
fof(t24_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( m2_finseq_1(E,A) => r2_funct_2(k4_ordinal1,B,k1_partfun1(k4_ordinal1,A,A,B,k1_setwop_2(A,E,C),D),k1_setwop_2(B,k4_finseqop(A,B,E,D),k3_funct_2(A,B,D,C))) ) ) ) ) ) )).
fof(t24_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( v7_ordinal1(B) => k2_sf_mastr(A) = k2_sf_mastr(k5_compos_1(k1_scmfsa_2,A,B)) ) ) )).
fof(t24_sfmastr3,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & ~ v1_scmfsa_m(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( k1_funct_1(A,k4_scmfsa_2(k5_numbers)) = 1 => ( r1_xxreal_0(k1_funct_1(A,C),k1_funct_1(A,D)) | ( ! [G] : ( ( 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] : ( m1_scmfsa_2(G) => k18_scmfsa_2(k1_scmfsa6b(k2_sfmastr3(B,C,D,E),A,F),G) = k18_scmfsa_2(A,G) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_sgraph1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_sgraph1(B))) => ! [D] : ! [E] : ~ ( r2_hidden(D,B) & r2_hidden(E,B) & D != E & r2_hidden(g1_sgraph1(B,C),k3_sgraph1(A)) & ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t24_sheffer1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t24_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t24_simplex0,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t24_simplex1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( ~ 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))) ) ) ) ) )).
fof(t24_simplex2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_rlaffin1(B,k15_euclid(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ( k5_card_1(B) = k2_xcmplx_0(A,1) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t24_sin_cos,axiom,( k1_relset_1(k1_numbers,k16_sin_cos) = k1_numbers & k1_relset_1(k1_numbers,k18_sin_cos) = k1_numbers )).
fof(t24_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k6_xcmplx_0(k1_square_1(k1_funct_1(k1_sin_cos2,A)),k1_square_1(k1_funct_1(k1_sin_cos2,B))) = k3_xcmplx_0(k1_funct_1(k1_sin_cos2,k2_xcmplx_0(A,B)),k1_funct_1(k1_sin_cos2,k6_xcmplx_0(A,B))) & k3_xcmplx_0(k1_funct_1(k1_sin_cos2,k2_xcmplx_0(A,B)),k1_funct_1(k1_sin_cos2,k6_xcmplx_0(A,B))) = k6_xcmplx_0(k1_square_1(k1_funct_1(k3_sin_cos2,A)),k1_square_1(k1_funct_1(k3_sin_cos2,B))) & k6_xcmplx_0(k1_square_1(k1_funct_1(k1_sin_cos2,A)),k1_square_1(k1_funct_1(k1_sin_cos2,B))) = k6_xcmplx_0(k1_square_1(k1_funct_1(k3_sin_cos2,A)),k1_square_1(k1_funct_1(k3_sin_cos2,B))) ) ) ) )).
fof(t24_sin_cos3,axiom,( k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,k5_complex1) = 1 )).
fof(t24_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( k17_sin_cos(A) != k5_numbers & k17_sin_cos(B) != k5_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)))) ) ) ) )).
fof(t24_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => k1_newton(k17_sin_cos(A),4) = k7_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(3,k3_xcmplx_0(4,k19_sin_cos(k3_xcmplx_0(2,A)))),k19_sin_cos(k3_xcmplx_0(4,A))),8) ) )).
fof(t24_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( k17_sin_cos(A) = 1 => A = k2_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k1_int_1(k7_xcmplx_0(A,k3_xcmplx_0(2,k28_sin_cos))))) ) ) )).
fof(t24_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(1,B) ) => r1_xxreal_0(k5_numbers,k2_xcmplx_0(k3_xcmplx_0(A,k3_square_1(k6_xcmplx_0(k1_square_1(B),1))),k3_xcmplx_0(B,k3_square_1(k6_xcmplx_0(k1_square_1(A),1))))) ) ) ) )).
fof(t24_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k5_numbers,A) => k2_sin_cos2(k7_xcmplx_0(A,2)) = k3_square_1(k7_xcmplx_0(k6_xcmplx_0(k4_sin_cos2(A),1),2)) ) ) )).
fof(t24_sin_cos9,axiom,( r1_tarski(k1_rcomp_1(k4_xcmplx_0(1),1),k1_relset_1(k1_numbers,k2_sin_cos9)) )).
fof(t24_sincos10,axiom,( v2_funct_1(k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k4_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(t24_sppol_1,axiom,( ! [A] : ( 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))))) ) )).
fof(t24_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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))) ) ) ) )).
fof(t24_sprect_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t24_sprect_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t24_sprect_3,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t24_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t24_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k5_numbers,A) & k3_square_1(A) = k5_numbers ) => A = k5_numbers ) ) )).
fof(t24_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_rewrite1(C,k12_stacks_1(A)) => ( B = k1_funct_1(C,1) => r1_tarski(k10_xtuple_0(C),k11_stacks_1(A,B)) ) ) ) ) )).
fof(t24_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => v1_finset_1(a_2_0_stirl2_1(A,B)) ) ) )).
fof(t24_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_valuat_1(C,A,B) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [E] : ( m2_subset_1(E,k16_substut1(A),k38_substut1(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t24_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_xboole_0(B,k3_subset_1(A,C)) <=> r1_tarski(B,C) ) ) ) )).
fof(t24_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) )).
fof(t24_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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))))) ) ) ) )).
fof(t24_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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))) ) ) )).
fof(t24_supinf_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t24_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ~ ( ~ r1_orders_2(B,D,C) & ~ r1_orders_2(B,F,C) & k8_group_1(A,k1_symsp_1(A,B,C,D,E),k11_algstr_0(A,k1_symsp_1(A,B,C,D,F))) != k1_symsp_1(A,B,C,F,E) ) ) ) ) ) ) ) )).
fof(t24_sysrel,axiom,( ! [A] : ! [B] : ( 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 ) ) ) )).
fof(t24_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),k1_numbers))) ) => ! [C] : ( ( 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,k5_numbers))) & v1_taxonom1(B,A) & v2_metric_1(B,A) & v3_metric_1(B,A) ) => C = k4_relat_1(A) ) ) ) ) )).
fof(t24_taylor_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & ? [E] : ( v1_xreal_0(E) & r2_hidden(E,k2_rcomp_1(k4_xcmplx_0(A),A)) & ~ ( ~ r1_xxreal_0(B,k9_complex1(k6_xcmplx_0(k1_funct_1(k16_sin_cos,E),k9_nat_1(k1_numbers,k3_series_1(k1_taylor_2(k16_sin_cos,k2_rcomp_1(k4_xcmplx_0(A),A),E)),D)))) & ~ r1_xxreal_0(B,k9_complex1(k6_xcmplx_0(k1_funct_1(k18_sin_cos,E),k9_nat_1(k1_numbers,k3_series_1(k1_taylor_2(k18_sin_cos,k2_rcomp_1(k4_xcmplx_0(A),A),E)),D)))) ) ) ) ) ) ) ) )).
fof(t24_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t24_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t24_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t24_tdlat_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v3_tdlat_3(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(B,A) => k1_tops_1(A,B) = B ) ) ) ) )).
fof(t24_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( 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) = k4_polynom1(A,C,D,k16_pre_poly(A)) ) ) ) ) ) )).
fof(t24_tex_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t24_tex_2,axiom,( ! [A] : ( l1_pre_topc(A) => ( ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t24_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v2_tex_3(B,A) <=> ? [C] : ( v1_pre_topc(C) & v1_tsep_1(C,A) & v1_tex_3(C,A) & m1_pre_topc(C,A) & m1_pre_topc(C,B) ) ) ) ) )).
fof(t24_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t24_tietze,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( ( ~ v1_xboole_0(B) & v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k1_pre_topc(A,B)),u1_struct_0(k4_topmetr(k4_xcmplx_0(1),1))) & v5_pre_topc(C,k1_pre_topc(A,B),k4_topmetr(k4_xcmplx_0(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(k4_xcmplx_0(1),1))))) ) => ? [D] : ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k4_topmetr(k4_xcmplx_0(1),1))) & v5_pre_topc(D,A,k4_topmetr(k4_xcmplx_0(1),1)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k4_topmetr(k4_xcmplx_0(1),1))))) & k2_partfun1(u1_struct_0(A),u1_struct_0(k4_topmetr(k4_xcmplx_0(1),1)),D,B) = C ) ) ) => v10_pre_topc(A) ) ) )).
fof(t24_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( ( m1_pre_topc(C,B) & m1_pre_topc(D,B) ) => m1_pre_topc(k1_tsep_1(A,C,D),B) ) ) ) ) ) )).
fof(t24_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t24_topalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t24_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v1_borsuk_2(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ! [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] : ( 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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_topalg_6,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)) ) ) ) )).
fof(t24_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r1_borsuk_3(A,B) => ( v3_topdim_1(A) <=> v3_topdim_1(B) ) ) ) ) )).
fof(t24_topdim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v2_pre_topc(B) & v3_pcomps_1(B) & l1_pre_topc(B) ) => ( v3_topdim_1(B) => ! [C] : ( 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] : ( ( v4_pre_topc(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ! [E] : ( ( 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] : ( ( v4_pre_topc(F,B) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B))) ) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t24_topgen_2,axiom,( ! [A] : ! [B] : ! [C] : ( 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 ) ) )).
fof(t24_topgen_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) & ~ r1_xxreal_0(k4_series_1(k4_topgen_3(B,A)),k4_series_1(k1_prepower(A))) ) ) )).
fof(t24_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t24_topgen_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_topgen_2(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t24_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) ) ) )).
fof(t24_topmetr,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_topmetr))) => ( ( r1_xxreal_0(k5_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) ) ) ) ) )).
fof(t24_topreal1,axiom,( ? [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) & ? [B] : ( 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(k5_numbers,k5_numbers),k19_euclid(1,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,1) = k19_euclid(k5_numbers,k5_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(k5_numbers,k5_numbers) & k7_partfun1(u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B)) = k19_euclid(1,1) ) ) )).
fof(t24_topreal4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( v2_topreal4(B,k15_euclid(2)) & A = a_2_0_topreal4(B,C) ) => v3_pre_topc(A,k15_euclid(2)) ) ) ) ) )).
fof(t24_topreal7,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & C = D & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & r1_tarski(k8_metric_1(B,D,F),k8_metric_1(A,C,E)) ) ) ) ) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & C = D & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & r1_tarski(k8_metric_1(A,C,F),k8_metric_1(B,D,E)) ) ) ) ) ) ) ) => k3_pcomps_1(A) = k3_pcomps_1(B) ) ) ) )).
fof(t24_topreal8,axiom,( ! [A] : ( ( v1_finseq_6(A,u1_struct_0(k15_euclid(2))) & v1_goboard5(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( v7_ordinal1(B) => ( 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)) ) ) ) ) )).
fof(t24_topreal9,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( r2_hidden(D,k4_topreal9(A,B,C)) <=> ? [E] : ( v1_xreal_0(E) & D = k3_rlvect_1(A,k1_rlvect_1(A,B,k6_xcmplx_0(1,E)),k1_rlvect_1(A,C,E)) & r1_xxreal_0(k5_numbers,E) ) ) ) ) ) )).
fof(t24_topreala,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(D,B) ) => ( v3_pre_topc(k2_rcomp_1(C,D),k4_topmetr(A,B)) & m1_subset_1(k2_rcomp_1(C,D),k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B)))) ) ) ) ) ) ) )).
fof(t24_toprealc,axiom,( ! [A] : ( v1_valued_2(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t24_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ( k12_euclid(B) = k5_numbers => B = k4_struct_0(k15_euclid(A)) ) ) ) )).
fof(t24_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t24_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v3_pre_topc(C,B) <=> ? [D] : ( 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 ) ) ) ) ) )).
fof(t24_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t24_transgeo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_transgeo(A) & l1_analoaf(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t24_treal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & m1_pre_topc(A,k3_topmetr) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,k3_topmetr) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & 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] : ( m1_subset_1(D,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,D) != D ) ) ) ) ) )).
fof(t24_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ( ~ v1_xboole_0(k3_xboole_0(A,B)) & v1_trees_1(k3_xboole_0(A,B)) ) ) ) )).
fof(t24_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_2(B,A) => m1_trees_2(a_2_2_trees_2(A,B),A) ) ) )).
fof(t24_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v6_trees_3(A) <=> ! [B] : ( 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)) ) ) ) ) )).
fof(t24_trees_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t24_trees_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(C) & v3_trees_3(C) ) => ( r2_hidden(A,k12_trees_9(C,B)) <=> ? [D] : ( m1_subset_1(D,C) & ? [E] : ( 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) ) ) ) ) ) )).
fof(t24_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t24_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t24_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t24_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( m2_funct_2(B,k4_numbers,u1_turing_1(A),k9_funct_2(k4_numbers,u1_turing_1(A))) => ! [C] : ( v1_int_1(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t24_twoscomp,axiom,( k1_funct_1(k27_twoscomp,k11_finseq_1(k5_numbers,k5_numbers,k5_numbers)) = 1 & k1_funct_1(k27_twoscomp,k11_finseq_1(k5_numbers,k5_numbers,1)) = 1 & k1_funct_1(k27_twoscomp,k11_finseq_1(k5_numbers,1,k5_numbers)) = 1 & k1_funct_1(k27_twoscomp,k11_finseq_1(k5_numbers,1,1)) = 1 & k1_funct_1(k27_twoscomp,k11_finseq_1(1,k5_numbers,k5_numbers)) = 1 & k1_funct_1(k27_twoscomp,k11_finseq_1(1,k5_numbers,1)) = 1 & k1_funct_1(k27_twoscomp,k11_finseq_1(1,1,k5_numbers)) = k5_numbers & k1_funct_1(k27_twoscomp,k11_finseq_1(1,1,1)) = 1 )).
fof(t24_unialg_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t24_unialg_3,axiom,( ! [A] : ( ( ~ 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] : ( ( 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))) ) ) ) )).
fof(t24_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ( r2_hidden(B,k2_uniroots(A)) <=> ? [C] : ( m1_subset_1(C,k4_ordinal1) & B = k1_hahnban1(k19_sin_cos(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C),A)),k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C),A))) ) ) ) ) )).
fof(t24_uproots,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_normsp_1(A,B,C),k9_polynom3(A)) => r2_funct_2(k4_ordinal1,u1_struct_0(A),B,C) ) ) ) ) )).
fof(t24_urysohn1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v10_pre_topc(A) => ! [B] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v4_pre_topc(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( B != k1_xboole_0 => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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,k5_numbers)) & C = k7_subset_1(u1_struct_0(A),k2_struct_0(A),k1_funct_1(E,1)) & ! [F] : ( m2_subset_1(F,k1_numbers,k1_urysohn1(D)) => ! [G] : ( 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] : ( ( v1_funct_1(F) & v1_funct_2(F,k1_urysohn1(k1_nat_1(D,1)),k1_zfmisc_1(u1_struct_0(A))) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_urysohn1(k1_nat_1(D,1)),k1_zfmisc_1(u1_struct_0(A))))) ) => ~ ( r1_tarski(B,k1_funct_1(F,k5_numbers)) & C = k7_subset_1(u1_struct_0(A),k2_struct_0(A),k1_funct_1(F,1)) & ! [G] : ( m2_subset_1(G,k1_numbers,k1_urysohn1(k1_nat_1(D,1))) => ! [H] : ( m2_subset_1(H,k1_numbers,k1_urysohn1(k1_nat_1(D,1))) => ! [I] : ( m2_subset_1(I,k1_numbers,k1_urysohn1(k1_nat_1(D,1))) => ( ~ r1_xxreal_0(H,G) => ( v3_pre_topc(k4_urysohn1(A,k1_urysohn1(k1_nat_1(D,1)),F,G),A) & v3_pre_topc(k4_urysohn1(A,k1_urysohn1(k1_nat_1(D,1)),F,H),A) & r1_tarski(k2_pre_topc(A,k4_urysohn1(A,k1_urysohn1(k1_nat_1(D,1)),F,G)),k4_urysohn1(A,k1_urysohn1(k1_nat_1(D,1)),F,H)) & ( r2_hidden(I,k1_urysohn1(D)) => k4_urysohn1(A,k1_urysohn1(k1_nat_1(D,1)),F,I) = k1_funct_1(E,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_urysohn2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,A) & r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(B,1) & ! [C] : ( v1_xreal_0(C) => ~ ( r2_hidden(C,k2_urysohn1) & ~ r1_xxreal_0(C,A) & ~ r1_xxreal_0(B,C) ) ) ) ) ) )).
fof(t24_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_funct_2(C,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t24_valued_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ( ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k9_nat_1(A,B,C) = k9_nat_1(A,B,D) ) ) => v3_funct_1(B) ) ) ) )).
fof(t24_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k9_xtuple_0(A)) => r2_hidden(k2_xcmplx_0(C,B),k1_relset_1(k4_ordinal1,k61_valued_1(A,B))) ) ) ) ) )).
fof(t24_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t24_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m2_vectsp_4(D,A,B,C) => m1_subset_1(D,u1_struct_0(k6_vectsp10(A,B,C))) ) ) ) ) )).
fof(t24_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ( r1_struct_0(k2_vectsp11(A,B,C),D) <=> ? [E] : ( v7_ordinal1(E) & k3_funct_2(u1_struct_0(B),u1_struct_0(B),k1_vectsp11(B,C,E),D) = k4_struct_0(B) ) ) ) ) ) ) )).
fof(t24_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( k4_algstr_0(A,B) = k4_struct_0(A) => B = k4_struct_0(A) ) ) ) )).
fof(t24_vectsp_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_vectsp_2(A))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t24_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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) ) ) )).
fof(t24_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t24_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_vectsp_6(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t24_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ( v1_matrlin(B,A) => v1_matrlin(C,A) ) ) ) ) )).
fof(t24_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t24_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( 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) ) ) ) )).
fof(t24_waybel10,axiom,( ! [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] : ( ( 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) ) ) ) )).
fof(t24_waybel11,axiom,( ! [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] : ( ( ~ 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)) ) ) )).
fof(t24_waybel12,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(t24_waybel13,axiom,( ! [A] : ( ( 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] : ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k2_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(k2_yellow_1(u1_struct_0(k1_waybel_8(A))))))) & v17_waybel_0(B,A,k2_yellow_1(u1_struct_0(k1_waybel_8(A)))) & v22_waybel_0(B,A,k2_yellow_1(u1_struct_0(k1_waybel_8(A)))) & v2_funct_1(B) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k2_yellow_1(u1_struct_0(k1_waybel_8(A)))),B,C) = k2_waybel_8(A,C) ) ) ) )).
fof(t24_waybel14,axiom,( ! [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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k5_waybel11(A)) <=> v3_pre_topc(B,A) ) ) ) )).
fof(t24_waybel15,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v2_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t24_waybel16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_waybel16(B,A) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t24_waybel17,axiom,( ! [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) & v4_waybel11(A) & l1_waybel_9(A) ) => ! [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) & v3_waybel_3(B) & v4_waybel11(B) & l1_waybel_9(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) )).
fof(t24_waybel19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v2_pre_topc(D) & l1_pre_topc(D) ) => ! [E] : ( m3_yellow_9(E,A,B) => ! [F] : ( m3_yellow_9(F,C,D) => ! [G] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t24_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) ) )).
fof(t24_waybel21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t24_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_waybel23(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),B) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t24_waybel24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [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) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ( E = k2_yellow_0(k5_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))) ) ) ) ) ) ) ) )).
fof(t24_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t24_waybel26,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t24_waybel27,axiom,( ! [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] : ( ( 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) ) ) )).
fof(t24_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t24_waybel29,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( ( v4_waybel11(D) & m1_yellow_9(D,k3_waybel24(A,C)) ) => ? [E] : ( 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] : ( 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] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( ( v4_waybel11(D) & m1_yellow_9(D,k3_waybel24(A,C)) ) => ? [E] : ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t24_waybel30,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t24_waybel31,axiom,( ! [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] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => k1_waybel31(A) = k2_waybel23(B) ) ) )).
fof(t24_waybel32,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t24_waybel33,axiom,( ! [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) ) => r1_tarski(k2_waybel19(A),k4_waybel28(A)) ) )).
fof(t24_waybel34,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(t24_waybel35,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_waybel35(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ( ( v3_waybel35(C,A,B) & m1_waybel35(C,A,B) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t24_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v13_waybel_0(B,A) <=> r1_tarski(k4_waybel_0(A,B),B) ) ) ) )).
fof(t24_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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) ) ) ) ) ) ) )).
fof(t24_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ! [C] : ( ( 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] : 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))) ) ) ) )).
fof(t24_waybel_3,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ( ! [B] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( ~ r3_orders_2(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r1_waybel_3(A,D,B) & ~ r3_orders_2(A,D,C) ) ) ) ) ) ) ) ) )).
fof(t24_waybel_4,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t24_waybel_5,axiom,( ! [A] : ( ( 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) ) )).
fof(t24_waybel_6,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v5_waybel_6(B,A) => v2_waybel_6(B,A) ) ) ) )).
fof(t24_waybel_7,axiom,( ! [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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( ~ r2_hidden(C,B) & ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t24_waybel_8,axiom,( ! [A] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t24_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( 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)) ) ) ) ) ) ) )).
fof(t24_weddwitt,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t24_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(t24_wellord1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( v1_wellord1(B) => v1_wellord1(k2_wellord1(B,A)) ) ) )).
fof(t24_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ? [C] : ( v1_rat_1(C) & A = k1_newton(C,B) ) & ! [C] : ( v1_int_1(C) => A != k1_newton(C,B) ) ) ) ) )).
fof(t24_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : k2_xboole_0(A,k3_xboole_0(B,C)) = k3_xboole_0(k2_xboole_0(A,B),k2_xboole_0(A,C)) )).
fof(t24_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( 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)) ) ) )).
fof(t24_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( k6_xcmplx_0(A,B) = k6_xcmplx_0(C,D) => k6_xcmplx_0(A,C) = k6_xcmplx_0(B,D) ) ) ) ) ) )).
fof(t24_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) <=> r1_xxreal_0(k4_xcmplx_0(B),k4_xcmplx_0(A)) ) ) ) )).
fof(t24_xtuple_0,axiom,( ! [A] : ! [B] : r1_tarski(k9_xtuple_0(k3_xboole_0(A,B)),k3_xboole_0(k9_xtuple_0(A),k9_xtuple_0(B))) )).
fof(t24_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r1_xxreal_0(C,A) & r1_xxreal_0(C,B) & ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(D,A) & r1_xxreal_0(D,B) ) => r1_xxreal_0(D,C) ) ) ) => C = k3_xxreal_0(A,B) ) ) ) ) )).
fof(t24_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => r1_tarski(k2_xxreal_1(A,B),k1_xxreal_1(A,B)) ) ) )).
fof(t24_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => m1_xxreal_2(B,k4_xxreal_1(A,B)) ) ) )).
fof(t24_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( v1_xreal_0(B) => A = k3_xxreal_3(k1_xxreal_3(A,B),B) ) ) ) )).
fof(t24_yellow10,axiom,( ! [A] : ( ( v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t24_yellow12,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & v2_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t24_yellow13,axiom,( ! [A] : ( l1_pre_topc(A) => m2_yellow13(k9_setfam_1(u1_struct_0(A)),A) ) )).
fof(t24_yellow14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t24_yellow16,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t24_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v11_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( ~ 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] : ( ( v15_functor0(E,B,C) & m2_functor0(E,B,C) ) => ! [F] : ( ( 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)))) ) ) ) ) ) ) ) ) )).
fof(t24_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(B,A) <=> ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,k10_yellow_6(A,C)) => r2_hidden(D,B) ) ) ) ) ) ) ) )).
fof(t24_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ( r1_yellow20(A,B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t24_yellow_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( B = k13_lattice3(A,B,C) <=> r1_orders_2(A,C,B) ) ) ) ) )).
fof(t24_yellow_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => k4_yellow_0(k1_yellow_1(u1_pre_topc(A))) = u1_struct_0(A) ) )).
fof(t24_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( ! [B] : r1_yellow_0(A,B) => v3_lattice3(A) ) ) )).
fof(t24_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t24_yellow_4,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) ) )).
fof(t24_yellow_5,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t24_yellow_6,axiom,( ! [A] : ! [B] : ( l1_struct_0(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( m3_yellow_6(C,A,B) <=> ! [D] : ( 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) ) ) ) ) ) )).
fof(t24_yellow_7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_lattice3(A))) => ! [C] : ( 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) ) ) ) )).
fof(t24_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v4_yellow_8(A) & l1_pre_topc(A) ) => v6_pre_topc(A) ) )).
fof(t24_yellow_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)))) ) ) ) ) )).
fof(t24_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(t24_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( k1_funct_1(A,1) = k5_numbers => v2_zf_lang(A) ) ) )).
fof(t24_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v8_zf_lang(A) => k22_zf_lang(A) = k20_zf_lang(k22_zf_lang(k20_zf_lang(A))) ) ) )).
fof(t24_zfmisc_1,axiom,( ! [A] : k1_zfmisc_1(k1_tarski(A)) = k2_tarski(k1_xboole_0,k1_tarski(A)) )).
fof(t24_zfmodel2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => r2_zfmodel1(k6_partfun1(A),A) ) )).
fof(t24_zfrefle1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ~ ( r2_ordinal2(A,k1_ordinal1(B)) & ! [C] : ( v3_ordinal1(C) => A != k1_ordinal1(C) ) ) ) ) )).
fof(t24_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( r1_struct_0(B,C) => r1_struct_0(A,C) ) ) ) )).
fof(t24_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_zmodul02(C,A) => ( k18_zmodul02(A,C) = k6_domain_1(u1_struct_0(A),B) => k21_zmodul02(A,C) = k1_zmodul01(A,B,k3_funct_2(u1_struct_0(A),k4_numbers,C,B)) ) ) ) ) )).
fof(t24_zmodul03,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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) & v1_zmodul03(B) & l1_zmodul01(B) ) => ! [C] : ( m1_zmodul03(C,B) => ! [D] : ( m1_vectsp_6(D,k9_int_3(A),k12_zmodul02(A,B)) => ? [E] : ( m2_zmodul02(E,B,C) & ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( r2_hidden(F,C) => k3_funct_2(u1_struct_0(B),k4_numbers,E,F) = k1_zmodul03(k9_int_3(A),k12_zmodul02(A,B),D,k13_zmodul02(A,B,F)) ) ) ) ) ) ) ) )).
fof(t250_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(A,B) => r1_tarski(k3_xxreal_1(B,C),k4_xxreal_1(A,k1_xxreal_0)) ) ) ) ) )).
fof(t251_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(A,B) => r1_tarski(k1_xxreal_1(B,C),k2_xxreal_1(A,k1_xxreal_0)) ) ) ) ) )).
fof(t252_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(A,B) => r1_tarski(k3_xxreal_1(B,C),k2_xxreal_1(A,k1_xxreal_0)) ) ) ) ) )).
fof(t253_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(C,A) => r1_tarski(k1_xxreal_1(B,C),k1_xxreal_1(k2_xxreal_0,A)) ) ) ) ) )).
fof(t254_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(C,A) => r1_tarski(k2_xxreal_1(B,C),k1_xxreal_1(k2_xxreal_0,A)) ) ) ) ) )).
fof(t255_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(C,A) => r1_tarski(k3_xxreal_1(B,C),k1_xxreal_1(k2_xxreal_0,A)) ) ) ) ) )).
fof(t256_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(C,A) => r1_tarski(k4_xxreal_1(B,C),k1_xxreal_1(k2_xxreal_0,A)) ) ) ) ) )).
fof(t257_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(C,A) => r1_tarski(k2_xxreal_1(B,C),k2_xxreal_1(k2_xxreal_0,A)) ) ) ) ) )).
fof(t258_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(C,A) => r1_tarski(k4_xxreal_1(B,C),k3_xxreal_1(k2_xxreal_0,A)) ) ) ) ) )).
fof(t259_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(C,A) => r1_tarski(k3_xxreal_1(B,C),k3_xxreal_1(k2_xxreal_0,A)) ) ) ) ) )).
fof(t25_abcmiz_0,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_abcmiz_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t25_abcmiz_1,axiom,( ! [A] : ( v7_ordinal1(A) => r2_hidden(k4_tarski(k1_xboole_0,A),k2_abcmiz_1) ) )).
fof(t25_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & v1_abcmiz_a(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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 ) ) ) )).
fof(t25_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => r1_xxreal_0(k5_numbers,k2_xcmplx_0(A,k9_complex1(A))) ) )).
fof(t25_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r2_aff_1(A,C,D,B) ) ) => v1_aff_1(B,A) ) ) ) )).
fof(t25_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ! [F] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t25_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => r1_tarski(k10_xtuple_0(B),k10_xtuple_0(k1_ordinal4(A,B))) ) ) )).
fof(t25_afinsq_2,axiom,( ! [A] : ! [B] : ! [C] : ( r1_afinsq_2(B,C) => r1_afinsq_2(k3_xboole_0(A,B),k3_xboole_0(A,C)) ) )).
fof(t25_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(k14_afproj(A))) => m1_subset_1(k4_tarski(B,2),u2_incsp_1(k13_afproj(A))) ) ) )).
fof(t25_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r2_afvect0(A,B,F,D) & r2_afvect0(A,C,F,E) ) => r2_analoaf(A,B,C,E,D) ) ) ) ) ) ) ) )).
fof(t25_algspec1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) => m1_algspec1(k2_funct_1(A),A) ) ) )).
fof(t25_algstr_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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)))) ) ) )).
fof(t25_altcat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t25_altcat_3,axiom,( ! [A] : ( l1_altcat_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v6_altcat_3(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,k1_altcat_1(A,B,C)) & r2_hidden(D,k1_altcat_1(A,B,C)) & ! [E] : ( m1_subset_1(E,k1_altcat_1(A,B,C)) => ( r2_hidden(E,k1_altcat_1(A,B,C)) => D = E ) ) ) ) ) ) ) )).
fof(t25_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v16_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t25_ami_3,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => ( v2_extpro_1(A,k7_card_1(2),k1_ami_3) => A = k2_compos_1(k1_ami_3) ) ) )).
fof(t25_ami_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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) ) ) ) )).
fof(t25_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_compos_1(B)) => v5_ami_wstd(k16_funcop_1(k1_ami_wstd(A,B,k5_numbers),C),A,B) ) ) ) )).
fof(t25_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_analmetr(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C))) => r4_analmetr(k2_analmetr(A,B,C),D,E,F,F) ) ) ) ) ) ) ) )).
fof(t25_analoaf,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ( ( ~ ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = C ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ~ r2_analoaf(A,B,C,D,E) & ~ r2_analoaf(A,B,C,E,D) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( B != D & r2_analoaf(A,D,B,B,E) & ! [F] : ( 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) ) ) ) )).
fof(t25_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t25_anproj_1,axiom,( ! [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) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t25_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( k3_rlvect_1(A,k1_rlvect_1(A,B,D),k1_rlvect_1(A,C,E)) = k4_struct_0(A) => ( D = k5_numbers & E = k5_numbers ) ) ) ) ) ) => v3_anproj_2(k5_anproj_1(A)) ) ) )).
fof(t25_aofa_000,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t25_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : k10_xtuple_0(k9_aofa_a00(A,B,C,D,E,F,G,H)) = k6_enumset1(A,B,C,D,E,F,G,H) )).
fof(t25_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,B),D)) => ! [F] : ( m2_pboole(F,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [G] : ( m1_subset_1(G,u4_struct_0(A)) => ( k1_msualg_1(A,G) = k12_finseq_1(u1_struct_0(A),D) => ! [H] : ( m1_subset_1(H,k3_msualg_1(A,G,B)) => ( H = k12_finseq_1(k1_funct_1(u3_msualg_1(A,B),D),E) => k5_msualg_3(A,B,C,G,F,H) = k12_finseq_1(k1_funct_1(u3_msualg_1(A,C),D),k3_funct_2(k1_funct_1(u3_msualg_1(A,B),D),k1_funct_1(u3_msualg_1(A,C),D),k2_msafree4(u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C),F,D),E)) ) ) ) ) ) ) ) ) ) ) )).
fof(t25_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [E] : ( ( v1_aofa_i00(E,A,B,D) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),D) ) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),E) => ! [G] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t25_armstrng,axiom,( ! [A] : ! [B] : ( 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) ) )).
fof(t25_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( 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)) ) ) )).
fof(t25_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( 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) ) ) ) ) )).
fof(t25_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ~ ( B != k1_xboole_0 & k4_arytm_3(B,A) = k1_xboole_0 ) ) ) )).
fof(t25_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) & ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v4_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( r2_funct_2(k4_ordinal1,k1_numbers,B,k1_asympt_1(k2_xcmplx_0(1,A),1,k5_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) ) ) ) ) )).
fof(t25_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(t25_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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))) ) ) )).
fof(t25_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( r2_hidden(B,k5_bcialg_1(A)) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t25_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v10_bcialg_1(k2_bcialg_1(A,B),A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t25_bcialg_3,axiom,( ! [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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( m1_bcialg_3(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t25_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( A = k2_bcialg_5(A,B,C,D) => ( r1_xxreal_0(A,B) & r1_xxreal_0(A,C) & r1_xxreal_0(A,D) ) ) ) ) ) ) )).
fof(t25_bcialg_6,axiom,( ! [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] : ( 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) ) ) ) )).
fof(t25_bciideal,axiom,( ! [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) ) => k4_bcialg_1(A) = u1_struct_0(A) ) )).
fof(t25_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) = k2_xcmplx_0(k2_bhsp_1(A,B,B),k2_bhsp_1(A,C,C)) ) ) ) ) )).
fof(t25_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) & k1_seq_2(k2_bhsp_2(A,k2_normsp_1(A,D,E))) = k3_bhsp_1(A,k3_rlvect_1(A,B,C)) ) ) ) ) ) ) ) )).
fof(t25_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v2_bhsp_4(B,A) & v2_bhsp_4(C,A) ) => v2_bhsp_4(k6_bhsp_1(A,B,C),A) ) ) ) ) )).
fof(t25_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t25_binari_3,axiom,( ! [A] : ( v7_ordinal1(A) => k1_binari_3(A,k5_numbers) = k5_euclid(A) ) )).
fof(t25_binari_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(A,k5_series_1(2,B)) & r1_xxreal_0(k1_binari_4(B,A),B) ) ) ) )).
fof(t25_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r3_lattices(A,k7_lattices(A,B),k7_lattices(A,k4_lattices(A,B,C))) ) ) ) )).
fof(t25_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( v2_compts_1(D,A) => ! [E] : ( m2_connsp_2(E,k2_borsuk_1(A,B),k3_borsuk_1(A,B,D,k6_domain_1(u1_struct_0(B),C))) => ? [F] : ( m2_connsp_2(F,A,D) & ? [G] : ( m1_connsp_2(G,B,C) & r1_tarski(k6_borsuk_1(A,B,D,C,F,G),E) ) ) ) ) ) ) ) ) )).
fof(t25_borsuk_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => r1_xxreal_0(k3_seq_4(A),k2_seq_4(A)) ) )).
fof(t25_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,A) & ! [C] : ( v1_rat_1(C) => ! [D] : ( v1_rat_1(D) => ~ ( ~ r1_xxreal_0(C,A) & ~ r1_xxreal_0(D,C) & ~ r1_xxreal_0(B,D) ) ) ) ) ) ) )).
fof(t25_borsuk_6,axiom,( ~ 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)))) )).
fof(t25_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k1_borsuk_7(A,B,B,C,D,E) = k4_funct_4(A,B,C,E) )).
fof(t25_bspace,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k2_bspace)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_bspace(A))) => ! [D] : ( 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)) ) ) ) )).
fof(t25_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(t25_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t25_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t25_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t25_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t25_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( 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)) ) ) ) )).
fof(t25_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(E,A) => ( r3_bvfunc_2(A,D,B,E) => r2_funct_2(A,k6_margrel1,k6_bvfunc_2(A,k2_bvfunc_1(A,D,C),B,E),k2_bvfunc_1(A,D,k6_bvfunc_2(A,C,B,E))) ) ) ) ) ) ) )).
fof(t25_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t25_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t25_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t25_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t25_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t25_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t25_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t25_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k8_funcop_1(k4_ordinal1,A,k5_numbers) = k4_struct_0(k11_c0sp1(A)) ) )).
fof(t25_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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))) ) ) ) )).
fof(t25_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t25_calcul_2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t25_card_1,axiom,( ! [A] : ( r2_wellord2(A,k1_xboole_0) => A = k1_xboole_0 ) )).
fof(t25_card_2,axiom,( ! [A] : ( v1_card_1(A) => ( A != k5_numbers => k3_card_2(k5_numbers,A) = k5_numbers ) ) )).
fof(t25_card_3,axiom,( ! [A] : ! [B] : k3_card_3(k2_card_3(k7_funcop_1(B,A))) = k2_zfmisc_1(A,B) )).
fof(t25_card_5,axiom,( ! [A] : ( v7_ordinal1(A) => ( k1_card_5(k5_numbers) = k5_numbers & k1_card_5(k5_card_1(k1_nat_1(A,1))) = 1 ) ) )).
fof(t25_card_fil,axiom,( v4_card_fil(k4_ordinal1) )).
fof(t25_card_fin,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : k2_card_fin(A,k1_xboole_0,B) = k3_tarski(k10_xtuple_0(A)) ) )).
fof(t25_card_lar,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) & ~ v4_card_3(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t25_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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) ) ) )).
fof(t25_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k4_cat_1(k6_cat_2(A,B),k7_cat_2(A,B,C,D)) = k8_cat_2(A,B,k4_cat_1(A,C),k4_cat_1(B,D)) ) ) ) ) )).
fof(t25_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,B,C) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t25_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_cat_1(F,A,D,B) => ! [G] : ( m1_cat_1(G,A,D,C) => ! [H] : ( m1_cat_1(H,A,E,D) => ~ ( k2_cat_1(A,D,B) != k1_xboole_0 & k2_cat_1(A,D,C) != k1_xboole_0 & k2_cat_1(A,E,D) != k1_xboole_0 & k9_cat_4(A,B,C,E,k5_cat_1(A,E,D,B,H,F),k5_cat_1(A,E,D,C,H,G)) != k5_cat_1(A,E,D,k2_cat_4(A,B,C),H,k9_cat_4(A,B,C,D,F,G)) ) ) ) ) ) ) ) ) ) )).
fof(t25_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t25_catalg_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( l3_msualg_1(B,k3_catalg_1(A)) => ! [C] : ( m1_subset_1(C,A) => k3_msualg_1(k3_catalg_1(A),k8_catalg_1(A,C),B) = k1_tarski(k1_xboole_0) ) ) ) )).
fof(t25_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v4_algstr_0(k5_cayldick(A,B,C),k4_cayldick(A)) => ( v4_algstr_0(B,A) & v4_algstr_0(C,A) ) ) ) ) ) )).
fof(t25_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_cc0sp1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_cc0sp1(A))) => ( ( k2_normsp_0(k7_cc0sp1(A),C) = k5_numbers => C = k4_struct_0(k7_cc0sp1(A)) ) & ( C = k4_struct_0(k7_cc0sp1(A)) => k2_normsp_0(k7_cc0sp1(A),C) = k5_numbers ) & k2_normsp_0(k7_cc0sp1(A),k1_clvect_1(k7_cc0sp1(A),C,B)) = k3_xcmplx_0(k9_complex1(B),k2_normsp_0(k7_cc0sp1(A),C)) & r1_xxreal_0(k2_normsp_0(k7_cc0sp1(A),k1_algstr_0(k7_cc0sp1(A),C,D)),k2_xcmplx_0(k2_normsp_0(k7_cc0sp1(A),C),k2_normsp_0(k7_cc0sp1(A),D))) ) ) ) ) ) )).
fof(t25_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => k2_normsp_0(k5_cc0sp2(A),k4_struct_0(k5_cc0sp2(A))) = k5_numbers ) )).
fof(t25_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ~ ( v2_comseq_2(A) & k3_comseq_2(A) != k5_numbers & ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ~ ( m2_valued_0(B,k2_numbers,A) & v9_ordinal1(B) ) ) ) ) )).
fof(t25_cfdiff_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [C] : ( v1_xcmplx_0(C) => ( 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) = k3_xcmplx_0(A,k2_cfdiff_1(B,C)) ) ) ) ) ) )).
fof(t25_cfuncdom,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(t25_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t25_cgames_1,axiom,( ! [A] : ( ( 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] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(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)) ) ) ) )).
fof(t25_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => k3_chain_1(A,B,B) = k6_domain_1(k1_euclid(A),B) ) ) )).
fof(t25_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v5_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ( ( v7_ordinal1(C) & ~ v1_abian(C) ) => ! [D] : ( ( 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 ) ) ) ) ) ) )).
fof(t25_circcmb3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( 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] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_card_1(D,A) & v1_finseq_1(D) ) => m1_circcmb3(k5_circcomb(C,D),B) ) ) ) ) )).
fof(t25_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(A,C))) => ! [E] : ( ( v4_msualg_1(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( 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)))) ) ) ) ) ) ) ) )).
fof(t25_circled1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_rlvect_2(D,A,k7_domain_1(u1_struct_0(A),B,C)) => ( v1_circled1(D,A) => ( B = C | ( k3_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(k5_numbers,k3_funct_2(u1_struct_0(A),k1_numbers,D,B)) & r1_xxreal_0(k5_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))) ) ) ) ) ) ) ) )).
fof(t25_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => r1_circtrm1(A,A,k6_partfun1(u1_struct_0(A)),k6_partfun1(u4_struct_0(A))) ) )).
fof(t25_classes1,axiom,( ! [A] : ! [B] : ~ ( r2_hidden(B,k1_classes1(A)) & r2_tarski(B,k1_classes1(A)) ) )).
fof(t25_classes2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t25_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t25_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => r1_xxreal_0(k2_normsp_0(A,k5_algstr_0(A,k1_normsp_0(A,k1_bhsp_4(A,B),D),k1_normsp_0(A,k1_bhsp_4(A,B),C))),k9_complex1(k5_real_1(k9_nat_1(k1_numbers,k3_series_1(k5_normsp_0(A,B)),D),k9_nat_1(k1_numbers,k3_series_1(k5_normsp_0(A,B)),C)))) ) ) ) ) ) )).
fof(t25_clopban4,axiom,( ! [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) & 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] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t25_closure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( 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] : ( m2_subset_1(F,k1_zfmisc_1(k1_funct_1(C,A)),k9_setfam_1(k1_funct_1(C,A))) => ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(t25_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t25_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) & k1_seq_2(k2_clvect_2(A,k16_csspace(A,D,E))) = k13_csspace(A,k3_rlvect_1(A,B,C)) ) ) ) ) ) ) ) )).
fof(t25_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v2_clvect_3(B,A) & v2_clvect_3(C,A) ) => v2_clvect_3(k16_csspace(A,B,C),A) ) ) ) ) )).
fof(t25_coh_sp,axiom,( ! [A] : ! [B] : ( 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 ) ) )).
fof(t25_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v6_cohsp_1(A) ) => ! [B] : ! [C] : ( ( r2_hidden(C,k9_xtuple_0(A)) & r1_tarski(B,C) & v1_finset_1(C) ) => ! [D] : ( r2_hidden(k4_tarski(B,D),k5_cohsp_1(A)) => r2_hidden(k4_tarski(C,D),k5_cohsp_1(A)) ) ) ) )).
fof(t25_combgras,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ( k1_card_1(B) = k1_nat_1(A,1) => ( r1_xxreal_0(A,1) | ! [C] : ( l1_combgras(C,k1_combgras(A,B),k1_combgras(A,B)) => ~ ( v7_combgras(C,k1_combgras(A,B)) & ! [D] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t25_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v8_compl_sp(A) <=> ! [B] : ( 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) ) ) ) ) )).
fof(t25_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,k5_numbers) => k1_comptrig(k3_xcmplx_0(A,B)) = k1_comptrig(A) ) ) ) )).
fof(t25_complfld,axiom,( ! [A] : ( 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) ) ) )).
fof(t25_complsp2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( m2_finseq_1(C,k2_numbers) => ( k3_finseq_1(B) = k3_finseq_1(C) => k10_seq_4(k7_seq_4(B,C),A) = k7_seq_4(k10_seq_4(B,A),k10_seq_4(C,A)) ) ) ) ) )).
fof(t25_compos_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( l1_compos_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t25_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( r1_tarski(C,D) => r1_compos_2(B,D) ) ) ) ) ) )).
fof(t25_comptrig,axiom,( v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k5_numbers,k28_sin_cos))) )).
fof(t25_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_comput_1(A) ) => ( k3_finseq_1(A) = k5_numbers => k1_comput_1(A) = k5_numbers ) ) )).
fof(t25_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,C)),k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B),C)) ) ) ) )).
fof(t25_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v2_comseq_2(A) & v9_ordinal1(A) ) => ( k3_comseq_2(A) = k5_complex1 | k3_comseq_2(k2_comseq_2(k4_ordinal1,k36_valued_1(k4_ordinal1,k2_numbers,A))) = k5_xcmplx_0(k8_complex1(k3_comseq_2(A))) ) ) ) )).
fof(t25_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => k9_nat_1(k2_numbers,A,B) = k5_complex1 ) => ! [B] : ( v7_ordinal1(B) => k9_nat_1(k1_numbers,k3_series_1(k55_valued_1(k4_ordinal1,k2_numbers,A)),B) = k5_numbers ) ) ) )).
fof(t25_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( v3_conlat_1(B,A) & ~ v4_conlat_1(B,A) & v6_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) ) ) ) ) )).
fof(t25_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => v2_connsp_1(C,A) ) ) => ( ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( C != k1_struct_0(A) & r2_hidden(C,B) & ! [D] : ( 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) ) ) ) ) )).
fof(t25_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v4_pre_topc(k1_connsp_2(A,B),A) ) ) )).
fof(t25_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t25_convex1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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(k5_numbers,k1_funct_1(D,B)) & r1_xxreal_0(k5_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))) ) ) ) ) ) ) ) )).
fof(t25_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_convex4(B,A) => r1_convex4(A,k7_convex4(A,k5_complex1,B),k2_convex4(A)) ) ) )).
fof(t25_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t25_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => k14_cqc_sim1(A,k5_cqc_lang(A)) = k5_cqc_lang(A) ) )).
fof(t25_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_finseq_1(C,k2_zfmisc_1(k3_cqc_lang(A),k2_cqc_the1)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t25_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ! [E] : ( m2_subset_1(E,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t25_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_cqc_lang(A))) => ( r4_cqc_the3(A,C,D) => r4_cqc_the3(A,k4_subset_1(k3_cqc_lang(A),C,B),k4_subset_1(k3_cqc_lang(A),D,B)) ) ) ) ) ) )).
fof(t25_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t25_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k9_csspace4(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_csspace4(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_csspace4(A,B))) => ! [F] : ( ( 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] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t25_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(t25_descip_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,A) => ! [I] : ( m1_subset_1(I,A) => ! [J] : ( m1_subset_1(J,A) => ! [K] : ( m1_subset_1(K,A) => ! [L] : ( m1_subset_1(L,A) => ! [M] : ( m1_subset_1(M,A) => ! [N] : ( m1_subset_1(N,A) => ! [O] : ( m1_subset_1(O,A) => ! [P] : ( m1_subset_1(P,A) => ! [Q] : ( m1_subset_1(Q,A) => ! [R] : ( m1_subset_1(R,A) => ! [S] : ( m1_subset_1(S,A) => ! [T] : ( m1_subset_1(T,A) => ! [U] : ( m1_subset_1(U,A) => ! [V] : ( m1_subset_1(V,A) => ! [W] : ( m1_subset_1(W,A) => ! [X] : ( m1_subset_1(X,A) => ! [Y] : ( m1_subset_1(Y,A) => ! [Z] : ( m1_subset_1(Z,A) => ! [A1] : ( m1_subset_1(A1,A) => ! [B1] : ( m1_subset_1(B1,A) => ! [C1] : ( m1_subset_1(C1,A) => ! [D1] : ( m1_subset_1(D1,A) => ! [E1] : ( m1_subset_1(E1,A) => ! [F1] : ( m1_subset_1(F1,A) => ! [G1] : ( m1_subset_1(G1,A) => ! [H1] : ( m1_subset_1(H1,A) => ! [I1] : ( m1_subset_1(I1,A) => ! [J1] : ( m1_subset_1(J1,A) => ! [K1] : ( m1_subset_1(K1,A) => ! [L1] : ( m1_subset_1(L1,A) => ! [M1] : ( m1_subset_1(M1,A) => ! [N1] : ( m1_subset_1(N1,A) => ! [O1] : ( m1_subset_1(O1,A) => ! [P1] : ( m1_subset_1(P1,A) => ! [Q1] : ( m1_subset_1(Q1,A) => ! [R1] : ( m1_subset_1(R1,A) => ! [S1] : ( m1_subset_1(S1,A) => ! [T1] : ( m1_subset_1(T1,A) => ! [U1] : ( m1_subset_1(U1,A) => ! [V1] : ( m1_subset_1(V1,A) => ! [W1] : ( m1_subset_1(W1,A) => ! [X1] : ( m1_subset_1(X1,A) => ! [Y1] : ( m1_subset_1(Y1,A) => ! [Z1] : ( m1_subset_1(Z1,A) => ! [A2] : ( m1_subset_1(A2,A) => ! [B2] : ( m1_subset_1(B2,A) => ! [C2] : ( m1_subset_1(C2,A) => ! [D2] : ( m1_subset_1(D2,A) => ! [E2] : ( m1_subset_1(E2,A) => ! [F2] : ( m1_subset_1(F2,A) => ! [G2] : ( m1_subset_1(G2,A) => ! [H2] : ( m1_subset_1(H2,A) => ! [I2] : ( m1_subset_1(I2,A) => ! [J2] : ( m1_subset_1(J2,A) => ! [K2] : ( m1_subset_1(K2,A) => ! [L2] : ( m1_subset_1(L2,A) => ! [M2] : ( m1_subset_1(M2,A) => ? [N2] : ( m2_finseq_1(N2,A) & v3_card_1(N2,64) & k1_funct_1(N2,1) = B & k1_funct_1(N2,2) = C & k1_funct_1(N2,3) = D & k1_funct_1(N2,4) = E & k1_funct_1(N2,5) = F & k1_funct_1(N2,6) = G & k1_funct_1(N2,7) = H & k1_funct_1(N2,8) = I & k1_funct_1(N2,9) = J & k1_funct_1(N2,10) = K & k1_funct_1(N2,11) = L & k1_funct_1(N2,12) = M & k1_funct_1(N2,13) = N & k1_funct_1(N2,14) = O & k1_funct_1(N2,15) = P & k1_funct_1(N2,16) = Q & k1_funct_1(N2,17) = R & k1_funct_1(N2,18) = S & k1_funct_1(N2,19) = T & k1_funct_1(N2,20) = U & k1_funct_1(N2,21) = V & k1_funct_1(N2,22) = W & k1_funct_1(N2,23) = X & k1_funct_1(N2,24) = Y & k1_funct_1(N2,25) = Z & k1_funct_1(N2,26) = A1 & k1_funct_1(N2,27) = B1 & k1_funct_1(N2,28) = C1 & k1_funct_1(N2,29) = D1 & k1_funct_1(N2,30) = E1 & k1_funct_1(N2,31) = F1 & k1_funct_1(N2,32) = G1 & k1_funct_1(N2,33) = H1 & k1_funct_1(N2,34) = I1 & k1_funct_1(N2,35) = J1 & k1_funct_1(N2,36) = K1 & k1_funct_1(N2,37) = L1 & k1_funct_1(N2,38) = M1 & k1_funct_1(N2,39) = N1 & k1_funct_1(N2,40) = O1 & k1_funct_1(N2,41) = P1 & k1_funct_1(N2,42) = Q1 & k1_funct_1(N2,43) = R1 & k1_funct_1(N2,44) = S1 & k1_funct_1(N2,45) = T1 & k1_funct_1(N2,46) = U1 & k1_funct_1(N2,47) = V1 & k1_funct_1(N2,48) = W1 & k1_funct_1(N2,49) = X1 & k1_funct_1(N2,50) = Y1 & k1_funct_1(N2,51) = Z1 & k1_funct_1(N2,52) = A2 & k1_funct_1(N2,53) = B2 & k1_funct_1(N2,54) = C2 & k1_funct_1(N2,55) = D2 & k1_funct_1(N2,56) = E2 & k1_funct_1(N2,57) = F2 & k1_funct_1(N2,58) = G2 & k1_funct_1(N2,59) = H2 & k1_funct_1(N2,60) = I2 & k1_funct_1(N2,61) = J2 & k1_funct_1(N2,62) = K2 & k1_funct_1(N2,63) = L2 & k1_funct_1(N2,64) = M2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t25_dickson,axiom,( ! [A] : ( l1_orders_2(A) => r1_dickson(A,k1_subset_1(u1_struct_0(A)),k1_xboole_0) ) )).
fof(t25_diff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(C,A),1),B) = k6_xcmplx_0(k1_funct_1(k2_diff_1(C,k7_xcmplx_0(A,2)),B),k1_funct_1(k2_diff_1(C,k4_xcmplx_0(k7_xcmplx_0(A,2))),B)) ) ) ) )).
fof(t25_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k1_funct_1(k4_diff_1(k1_fcont_1(B,C),A),D) = k3_xcmplx_0(B,A) ) ) ) ) )).
fof(t25_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( ( 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) = k6_xcmplx_0(k9_diff_1(C,A,B),k9_diff_1(D,A,B)) ) ) ) ) )).
fof(t25_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(k2_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k26_sin_cos)) & r2_hidden(k6_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k26_sin_cos)) ) => k1_funct_1(k5_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k26_sin_cos),k18_sin_cos),A),B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k16_sin_cos),k2_xcmplx_0(B,k7_xcmplx_0(A,2))),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k16_sin_cos),k6_xcmplx_0(B,k7_xcmplx_0(A,2)))) ) ) ) )).
fof(t25_dilworth,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t25_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_diraf(A,B,D,C,E) & C != E ) ) ) ) ) )).
fof(t25_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => ! [C] : ( m1_dist_2(C,A,B) => ! [D] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,A,k6_margrel1) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => k4_dist_2(A,B,C,k2_bvfunc_1(A,D,E)) = k7_xcmplx_0(k5_card_1(k9_subset_1(k9_xtuple_0(k1_partfun1(k4_ordinal1,A,A,k6_margrel1,C,E)),k3_dist_2(k1_partfun1(k4_ordinal1,A,A,k6_margrel1,C,D)),k3_dist_2(k1_partfun1(k4_ordinal1,A,A,k6_margrel1,C,E)))),k3_finseq_1(C)) ) ) ) ) ) )).
fof(t25_e_siec,axiom,( ! [A] : ( ( 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 ) ) )).
fof(t25_ec_pf_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(B))) => ~ ( C != k5_numbers & k2_binom(k9_int_3(B),C,A) = k5_numbers ) ) ) ) )).
fof(t25_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(A))) => ( B = k5_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)) ) ) ) ) ) )).
fof(t25_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t25_entropy1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( B = k1_entropy1(A) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & k1_matrix_0(B) = k3_finseq_1(A) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => ( r1_entropy1(k7_matrix_0(k1_numbers,B,C),C) & k1_funct_1(k7_matrix_0(k1_numbers,B,C),C) = k1_funct_1(A,C) ) ) ) ) ) ) ) )).
fof(t25_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : 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)) )).
fof(t25_eqrel_1,axiom,( ! [A] : ! [B] : ( r2_hidden(B,A) => k6_eqrel_1(A,A,k6_partfun1(A),B) = k1_tarski(B) ) )).
fof(t25_euclid,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => A = k19_euclid(k17_euclid(A),k18_euclid(A)) ) )).
fof(t25_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => k22_rvsum_1(B,k5_algstr_0(k15_euclid(A),C,D)) = k6_xcmplx_0(k22_rvsum_1(B,C),k22_rvsum_1(B,D)) ) ) ) ) )).
fof(t25_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => k9_complex1(k2_euclid_3(A)) = k12_euclid(A) ) )).
fof(t25_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => k22_rvsum_1(k6_euclid(A,B),k6_euclid(A,C)) = k22_rvsum_1(B,C) ) ) ) )).
fof(t25_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => k5_euclid_5(A,A) = k4_struct_0(k15_euclid(3)) ) )).
fof(t25_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k11_euclid(B,k6_euclid_7(B,A)) = k6_euclid_7(B,A) ) ) )).
fof(t25_euclid_8,axiom,( k6_euclid(3,k2_euclid_8) = k1_euclid_8(k4_xcmplx_0(1),k5_numbers,k5_numbers) )).
fof(t25_euclid_9,axiom,( ! [A] : ( 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))) ) )).
fof(t25_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(E)) => ! [G] : ( 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,k6_xcmplx_0(A,C)),k9_euclid(E,G,k6_xcmplx_0(B,D))) ) ) ) ) ) ) ) )).
fof(t25_extpro_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & ~ v1_setfam_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(C)) & v1_funct_1(D) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t25_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( 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(k3_xxreal_3(k1_xxreal_3(A,B),k3_extreal1(k3_xxreal_3(A,B))),2) ) ) ) )).
fof(t25_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_circcomb(A) & v2_circcomb(A) & v3_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v1_circcomb(B) & v2_circcomb(B) & v3_circcomb(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & ~ v11_struct_0(C) & v1_circcomb(C) & v2_circcomb(C) & v3_circcomb(C) & l1_msualg_1(C) ) => ! [D] : ( ( v4_msafree2(D,A) & v6_circcomb(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msafree2(E,B) & v6_circcomb(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) )).
fof(t25_facirc_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( k5_facirc_2(A,B,C) != k4_tarski(D,k3_facirc_1) & k5_facirc_2(A,B,C) != k4_tarski(D,k1_facirc_1) ) ) ) ) )).
fof(t25_fcont_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t25_fcont_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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)))) ) ) ) ) )).
fof(t25_fdiff_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t25_fdiff_10,axiom,( ! [A] : ( ( 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,k26_sin_cos,k27_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,k26_sin_cos,k27_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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,k26_sin_cos,k27_sin_cos)),A),B) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,B),k2_xcmplx_0(k1_funct_1(k26_sin_cos,B),k1_funct_1(k27_sin_cos,B))),k3_xcmplx_0(k1_funct_1(k16_sin_cos,B),k6_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B)))))) ) ) ) ) ) )).
fof(t25_fdiff_11,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k1_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k1_sin_cos9),A),B) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,B),k1_funct_1(k1_sin_cos9,B)),k7_xcmplx_0(k1_funct_1(k16_sin_cos,B),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t25_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( r2_hidden(D,k2_rcomp_1(B,A)) & r2_hidden(E,k2_rcomp_1(B,A)) ) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k1_funct_1(C,D),k1_funct_1(C,E))),k1_square_1(k6_xcmplx_0(D,E))) ) ) ) & r1_tarski(k2_rcomp_1(B,A),k1_relset_1(k1_numbers,C)) ) => ( r2_fdiff_1(C,k2_rcomp_1(B,A)) & v3_funct_1(k2_partfun1(k1_numbers,k1_numbers,C,k2_rcomp_1(B,A))) ) ) ) ) ) )).
fof(t25_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( 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,k7_xcmplx_0(1,k6_xcmplx_0(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] : ( v1_xreal_0(G) => ( r2_hidden(G,C) => ( k1_funct_1(E,G) = k6_xcmplx_0(G,A) & ~ r1_xxreal_0(k1_funct_1(E,G),k5_numbers) & k1_funct_1(F,G) = k6_xcmplx_0(G,B) & ~ r1_xxreal_0(k1_funct_1(F,G),k5_numbers) & k6_xcmplx_0(A,B) != k5_numbers ) ) ) ) => ( r2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,D,k7_xcmplx_0(1,k6_xcmplx_0(A,B))),C) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,C) => k1_funct_1(k2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,D,k7_xcmplx_0(1,k6_xcmplx_0(A,B))),C),G) = k7_xcmplx_0(1,k3_xcmplx_0(k6_xcmplx_0(G,A),k6_xcmplx_0(G,B))) ) ) ) ) ) ) ) ) ) ) )).
fof(t25_fdiff_5,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & k1_funct_1(k3_taylor_1,B) = k5_numbers ) ) ) => ( r2_fdiff_1(k6_rfunct_1(k1_numbers,k1_numbers,k3_taylor_1),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k6_rfunct_1(k1_numbers,k1_numbers,k3_taylor_1),A),B) = k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(B,k1_square_1(k1_funct_1(k3_taylor_1,B))))) ) ) ) ) ) )).
fof(t25_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k22_sin_cos,k1_taylor_1(2)),B))) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_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,k22_sin_cos,k1_taylor_1(2)),B),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(k2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_taylor_1(2)),B),A),C) = k3_xcmplx_0(2,k23_sin_cos(k3_xcmplx_0(2,C))) ) ) ) ) ) ) )).
fof(t25_fdiff_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k1_funct_1(C,D) = k7_xcmplx_0(D,A) & ~ r1_xxreal_0(k1_funct_1(C,D),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_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] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_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) = k2_xcmplx_0(k1_funct_1(k1_sin_cos6,k7_xcmplx_0(D,A)),k7_xcmplx_0(D,k3_xcmplx_0(A,k3_square_1(k6_xcmplx_0(1,k1_square_1(k7_xcmplx_0(D,A))))))) ) ) ) ) ) ) ) )).
fof(t25_fdiff_8,axiom,( ! [A] : ( ( 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,k27_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,k27_sin_cos),k1_partfun2(k1_numbers,A)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k27_sin_cos),k1_partfun2(k1_numbers,A)),A),B) = k7_xcmplx_0(k1_square_1(k1_funct_1(k18_sin_cos,B)),k1_square_1(k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t25_fdiff_9,axiom,( ! [A] : ( ( 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,k22_sin_cos,k2_fdiff_9))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k2_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k2_fdiff_9),A),B) = k6_xcmplx_0(k7_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_funct_1(k16_sin_cos,B)),k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_funct_1(k18_sin_cos,B)),k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t25_ff_siec,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t25_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => k1_pre_ff(k1_nat_1(A,3)) = k1_nat_1(k1_pre_ff(k1_nat_1(A,2)),k1_pre_ff(k1_nat_1(A,1))) ) )).
fof(t25_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(2,A) => k1_pre_ff(k2_xcmplx_0(A,1)) = k2_int_1(k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k1_pre_ff(A),k3_xcmplx_0(k3_square_1(5),k1_pre_ff(A))),1),2)) ) ) )).
fof(t25_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_finseq_1(B,A) => ! [C] : ( m1_finseq_1(C,A) => r1_tarski(B,k9_finseq_8(A,B,C)) ) ) ) )).
fof(t25_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t25_filter_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t25_filter_2,axiom,( ! [A] : ( ( ~ 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))) ) ) ) )).
fof(t25_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(C,k4_finseq_1(k7_finseq_1(A,B))) & ~ r2_hidden(C,k4_finseq_1(A)) & ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(D,k4_finseq_1(B)) & C = k2_xcmplx_0(k3_finseq_1(A),D) ) ) ) ) ) ) )).
fof(t25_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => m2_finseq_1(k17_funct_3(k4_ordinal1,B,C,k2_finseq_1(A)),B) ) ) ) )).
fof(t25_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k1_relset_1(k4_ordinal1,A)) <=> ( r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(A)) ) ) ) ) )).
fof(t25_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_finseq_4(A,B) => k1_finseq_4(A,B) = k4_finseq_4(A,B) ) ) )).
fof(t25_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => r1_xxreal_0(k3_finseq_1(k2_rfinseq(B,A,C)),k3_finseq_1(C)) ) ) ) )).
fof(t25_finseq_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_5(k3_finseq_5(A)) = A ) )).
fof(t25_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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) ) ) ) ) )).
fof(t25_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( ( ~ r1_xxreal_0(k3_finseq_1(C),k5_numbers) => ( r1_xxreal_0(k3_finseq_1(C),k3_finseq_1(B)) & k3_finseq_6(A,B,k7_nat_d(k1_nat_1(k3_finseq_1(B),1),k3_finseq_1(C)),k3_finseq_1(B)) = C ) ) => r4_finseq_8(A,B,C) ) ) ) ) )).
fof(t25_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( 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)))) ) ) ) ) ) ) ) )).
fof(t25_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t25_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_orders_2(A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_tarski(k3_fintopo3(A,B,C),k3_fintopo3(A,B,k1_nat_1(C,1))) ) ) ) ) )).
fof(t25_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r1_fintopo6(A,B) & B = k1_struct_0(A) ) ) ) )).
fof(t25_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => k7_flang_1(A,B,1) = B ) )).
fof(t25_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(D,C) & r1_xxreal_0(C,E) ) => k1_flang_2(A,B,D,E) = k4_subset_1(k8_afinsq_1(A),k1_flang_2(A,B,D,C),k1_flang_2(A,B,k2_xcmplx_0(C,1),E)) ) ) ) ) ) )).
fof(t25_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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)) ) ) ) ) )).
fof(t25_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ~ v1_xboole_0(C) => ( C = k1_funct_1(B,A) <=> r2_hidden(A,k8_relat_1(B,k1_tarski(C))) ) ) ) )).
fof(t25_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v4_fomodel1(E,A) & m1_subset_1(E,k1_fomodel1(A)) ) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) & v1_fomodel2(F,A,B) ) => ( ~ r2_hidden(E,k10_xtuple_0(C)) => k1_funct_1(k9_fomodel2(A,B,k5_fomodel2(F,E,D)),C) = k1_funct_1(k9_fomodel2(A,B,F),C) ) ) ) ) ) ) ) )).
fof(t25_frechet,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) )).
fof(t25_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v8_pre_topc(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_frechet(A,B,C) <=> ( v2_frechet(B,A) & C = k2_frechet2(A,B) ) ) ) ) ) ) )).
fof(t25_fscirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t25_fscirc_2,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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] : ( 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)) ) ) )).
fof(t25_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => r6_fsm_1(A,B,C,D,E,k5_numbers) ) ) ) ) ) )).
fof(t25_fsm_2,axiom,( ! [A] : ( ( ~ 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] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k1_funct_1(u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(B,C))) = k2_xcmplx_0(B,C) ) ) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( 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),k3_real_1(B,C)) ) ) ) ) )).
fof(t25_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k8_afinsq_1(C)) => ! [G] : ( ( ~ 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] : ( 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,F)) & k1_funct_1(H,k3_finseq_1(H)) = k4_tarski(B,k1_flang_1(C,E,F)) & ! [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,E) ) ) ) ) ) ) ) ) ) )).
fof(t25_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( 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))) ) )).
fof(t25_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t25_funcsdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k11_funcsdom(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k11_funcsdom(A))) => ! [D] : ( 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] : ( 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)) ) ) ) ) ) )).
fof(t25_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( v2_funct_1(k3_relat_1(A,B)) & r1_tarski(k10_xtuple_0(A),k9_xtuple_0(B)) ) => v2_funct_1(A) ) ) ) )).
fof(t25_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) ) )).
fof(t25_funct_3,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(t25_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => r1_tarski(B,k1_funct_4(A,B)) ) ) )).
fof(t25_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ( ( 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] : ( r2_hidden(F,A) => k1_funct_1(E,F) = k1_binop_1(D,F,C) ) ) ) ) ) )).
fof(t25_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ( k9_xtuple_0(k5_funct_6(A)) = k3_funct_6(k1_funct_6(A)) & r1_tarski(k10_xtuple_0(k5_funct_6(A)),k4_card_3(k2_funct_6(A))) ) ) )).
fof(t25_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( r1_funct_7(A,B,C) => r1_funct_7(B,A,C) ) ) ) )).
fof(t25_funct_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_8(B) & m1_subset_1(B,k1_zfmisc_1(k2_numbers)) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t25_funct_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & v1_int_1(A) ) => v1_funct_9(k26_sin_cos,k3_xcmplx_0(k28_sin_cos,A)) ) )).
fof(t25_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l1_altcat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,k1_altcat_1(B,C,C)) => ! [E] : ( ( v8_functor0(E,A,B) & v10_functor0(E,A,B) & l2_functor0(E,A,B) ) => ( E = k9_functor0(A,B,C,D) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(t25_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ! [F] : ( ( v15_functor0(F,B,C) & m2_functor0(F,B,C) ) => ! [G] : ( m1_functor2(G,A,B,D,E) => ( r1_functor2(A,B,D,E) => r8_pboole(u1_struct_0(A),k5_functor3(A,B,C,D,E,G,F),k7_functor3(A,B,C,D,E,F,F,G,k4_functor2(B,C,F))) ) ) ) ) ) ) ) ) )).
fof(t25_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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,D) & r1_fuzzy_1(C,E) ) => r1_fuzzy_1(k1_fuzzy_1(A,B,C),k1_fuzzy_1(A,D,E)) ) ) ) ) ) ) )).
fof(t25_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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)) ) ) ) )).
fof(t25_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,B) => ( ( C = D => k2_binop_1(A,B,k1_numbers,k4_fuzzy_4(A,B),C,D) = 1 ) & ( C != D => k2_binop_1(A,B,k1_numbers,k4_fuzzy_4(A,B),C,D) = k5_numbers ) ) ) ) ) ) )).
fof(t25_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_fvaluat1(D,A) => ( ( v3_fvaluat1(A) & r1_xxreal_0(k3_funct_2(u1_struct_0(A),k6_numbers,D,k1_vectsp_2(A,B,C)),k5_numbers) ) => ( B = k4_struct_0(A) | C = k4_struct_0(A) | r1_xxreal_0(k5_numbers,k3_funct_2(u1_struct_0(A),k6_numbers,D,k1_vectsp_2(A,C,B))) ) ) ) ) ) ) )).
fof(t25_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(t25_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ~ ( ~ 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)) ) ) )).
fof(t25_gcd_1,axiom,( ! [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) & v1_vectsp_2(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t25_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v2_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( m1_genealg1(E,D) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t25_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( ( r1_analmetr(A,G,H) & r2_geomtrap(A,G,H,B,C,D,E) ) => ( B = C | ( ~ r2_geomtrap(A,G,H,B,C,D,F) & ~ r2_geomtrap(A,G,H,B,C,F,D) ) | E = F ) ) ) ) ) ) ) ) ) ) )).
fof(t25_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t25_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => r1_xxreal_0(1,k15_glib_000(A)) ) )).
fof(t25_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m3_glib_001(D,B) => ( C = D => k6_glib_001(A,C) = k6_glib_001(B,D) ) ) ) ) ) )).
fof(t25_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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) ) ) ) )).
fof(t25_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( 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_funct_1(k5_glib_003(A),C)) ) ) ) )).
fof(t25_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,k6_glib_000(A)) => k1_nat_1(k39_glib_000(k10_glib_004(A,B)),1) = k5_card_1(k2_glib_002(A,B)) ) ) )).
fof(t25_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_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_0(C),B) | k9_subset_1(u1_struct_0(k15_euclid(2)),k3_goboard5(C,A,B),k3_goboard5(C,k1_nat_1(A,1),B)) = k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),k1_nat_1(B,1))) ) ) ) ) ) )).
fof(t25_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_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_0(B))) = a_2_5_goboard6(A,B) ) ) ) ) )).
fof(t25_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_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,C) & r1_xxreal_0(k1_nat_1(C,1),k1_matrix_0(E)) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(E)) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k1_matrix_0(E)) & r2_hidden(k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,k1_nat_1(C,1))),k7_xcmplx_0(1,2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),E,B,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),E,B,k1_nat_1(D,1)))) ) => ( A = B & C = D ) ) ) ) ) ) ) )).
fof(t25_gobrd11,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => k3_goboard5(A,k5_numbers,k1_matrix_0(A)) = a_1_14_gobrd11(A) ) )).
fof(t25_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( ( ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_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_xcmplx_0(A,B)) = k3_gobrd13(k2_rfinseq(u1_struct_0(k15_euclid(2)),B,C),D,A) & k2_gobrd13(C,D,k2_xcmplx_0(A,B)) = k2_gobrd13(k2_rfinseq(u1_struct_0(k15_euclid(2)),B,C),D,A) ) ) ) ) ) ) )).
fof(t25_gobrd14,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t25_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => ! [D] : ( 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),k5_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))) ) ) ) ) ) ) )).
fof(t25_gr_cy_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k4_ordinal1) & k7_group_1(A) = k3_xcmplx_0(2,B) ) & ! [B] : ( 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) ) ) ) ) )).
fof(t25_gr_cy_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v2_gr_cy_3(A) ) => ~ ( ~ r1_xxreal_0(A,2) & k4_nat_d(A,4) = 3 & ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) & v1_gr_cy_3(B) ) => ~ r1_nat_d(B,k1_gr_cy_3(A)) ) ) ) )).
fof(t25_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_graph_1(B) & l1_graph_1(B) ) => ( r4_graph_1(A,B) => v2_graph_1(A) ) ) ) )).
fof(t25_graph_2,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ( r1_tarski(k1_relset_1(k4_ordinal1,C),k4_finseq_1(B)) & r1_tarski(k10_xtuple_0(C),k10_xtuple_0(B)) ) ) ) )).
fof(t25_graph_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v6_graph_1(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ~ ( k7_graph_3(B,C,A) != k5_numbers & v1_xboole_0(k4_graph_3(B,C,A)) ) ) ) )).
fof(t25_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u4_struct_0(A)) => ! [C] : ( ( v7_graph_1(C,A) & m2_graph_1(C,A) ) => ! [D] : ( ( 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)))) ) ) ) ) ) )).
fof(t25_graphsp,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_graph_1(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( 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) ) => k11_graphsp(B,C,D,E) = k1_funct_1(E,A) ) ) ) ) ) )).
fof(t25_grcat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,A) => ( v1_grcat_1(D) & m1_grcat_1(D,B,C) ) ) ) ) ) ) )).
fof(t25_grfunc_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t25_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v15_algstr_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( v15_algstr_0(D) & m1_group_2(D,A) ) => ! [E] : ( ( v15_algstr_0(E) & v1_group_3(E,A) & m1_group_2(E,A) ) => ! [F] : ( ( v15_algstr_0(F) & m1_group_6(F,B,k10_group_6(A,B,C)) ) => ! [G] : ( ( 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))) ) ) ) ) ) ) ) ) )).
fof(t25_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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,k8_polynom1(A,C)) ) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(F,A,C) & v1_polynom1(F,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) ) ) ) ) ) ) ) ) )).
fof(t25_groeb_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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),k8_polynom1(A,C)) ) ) ) => ( r2_hidden(k8_polynom1(A,C),D) | r1_groeb_1(A,B,C,D) ) ) ) ) ) ) )).
fof(t25_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(E,k5_card_1(k3_polynom1(k15_pre_poly(A),C,D))) => ( k3_polynom1(k15_pre_poly(A),C,k5_groeb_3(A,B,C,D,E)) = k3_groeb_3(A,B,C,D,E) & k3_polynom1(k15_pre_poly(A),C,k6_groeb_3(A,B,C,D,E)) = k4_groeb_3(A,B,C,D,E) ) ) ) ) ) ) ) )).
fof(t25_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_group_1(A,1,B) = B ) ) )).
fof(t25_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,A) => ( m1_group_2(C,D) => r1_tarski(k1_group_11(A,B,D),k1_group_11(A,B,C)) ) ) ) ) ) )).
fof(t25_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t25_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t25_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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 ) ) )).
fof(t25_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t25_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_group_3(C,A) & m1_group_2(C,A) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t25_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t25_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v2_group_9(C,A) & m1_group_9(C,A,B) ) => k18_group_9(A,B,k15_group_9(A,B,C)) = C ) ) )).
fof(t25_groupp_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t25_hahnban1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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)))) ) ) ) )).
fof(t25_hallmar1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => m1_hallmar1(B,A,B,C) ) ) )).
fof(t25_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t25_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( ( v5_glib_001(B,A) & m3_glib_001(B,A) ) => ~ ( ~ v3_glib_001(B,A) & v1_glib_001(B,A) ) ) ) )).
fof(t25_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( m1_vectsp_4(B,k1_complfld,A) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t25_heyting1,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t25_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_substlat(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_substlat(A,B))) => ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,k4_partfun1(A,B)) ) => ( ( ! [F] : ( 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)) ) ) ) ) ) )).
fof(t25_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => m1_subset_1(k4_heyting3(A,B),u1_struct_0(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,B)))) ) ) )).
fof(t25_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(A,D) => k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k26_valued_1(k1_numbers,k1_numbers,k16_sin_cos,B),D),C),A) = k3_xcmplx_0(B,k1_funct_1(k16_sin_cos,k2_xcmplx_0(A,k7_xcmplx_0(k3_xcmplx_0(C,k28_sin_cos),2)))) ) ) ) ) ) )).
fof(t25_hilbasis,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t25_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => r2_hidden(k3_hilbert1(k3_hilbert1(k3_hilbert1(A,B),C),k3_hilbert1(B,C)),k6_hilbert1) ) ) ) )).
fof(t25_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => k3_hilbert1(A,B) != k2_hilbert1 ) ) )).
fof(t25_hilbert3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) )).
fof(t25_hurwitz,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( C != k5_numbers => ( k1_normsp_1(A,k3_hurwitz(A,B,C),k5_numbers) = k4_algstr_0(A,k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k4_group_1(A),B,C)) & k1_normsp_1(A,k3_hurwitz(A,B,C),C) = k1_group_1(A) ) ) ) ) ) )).
fof(t25_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k8_idea_1(B,A) = 1 => A = 1 ) ) ) )).
fof(t25_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_vectsp_1(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_ideal_1(C,A,B) => m1_ideal_1(C,A,B) ) ) ) )).
fof(t25_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ~ ( ~ v3_incsp_1(k8_domain_1(u1_incsp_1(A),B,C,D),A) & ! [E] : ( m1_subset_1(E,u4_incsp_1(A)) => ~ ! [F] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t25_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( 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] : ( 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) ) ) ) ) ) )).
fof(t25_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(t25_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_int_1(A) = A <=> v1_int_1(A) ) ) )).
fof(t25_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( r1_int_1(C,k3_xcmplx_0(A,B)) & r1_int_2(A,C) ) => r1_int_1(C,B) ) ) ) ) )).
fof(t25_int_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( v1_int_2(A) & r1_int_2(A,B) ) => ( r1_xxreal_0(C,k5_numbers) | ! [D] : ( v1_int_1(D) => k5_int_1(k6_xcmplx_0(k3_xcmplx_0(A,D),B),k1_newton(A,C)) != k5_numbers ) ) ) ) ) ) )).
fof(t25_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ~ ( k2_int_5(A,B) != 1 & k2_int_5(A,B) != k5_numbers & k2_int_5(A,B) != k4_xcmplx_0(1) ) ) ) )).
fof(t25_int_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & v5_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t25_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_int_8(k1_xboole_0,A) <=> A = k5_numbers ) ) )).
fof(t25_integr11,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ~ ( k2_xcmplx_0(B,A) != k5_numbers & k6_xcmplx_0(B,A) != k5_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(B,k5_numbers),k18_sin_cos),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,k5_numbers),k18_sin_cos))) != k6_xcmplx_0(k1_funct_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(k2_xcmplx_0(B,A),k5_numbers),k16_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k2_xcmplx_0(B,A)))),k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k6_xcmplx_0(B,A),k5_numbers),k16_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k6_xcmplx_0(B,A))))),k2_seq_4(C)),k1_funct_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(k2_xcmplx_0(B,A),k5_numbers),k16_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k2_xcmplx_0(B,A)))),k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k6_xcmplx_0(B,A),k5_numbers),k16_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k6_xcmplx_0(B,A))))),k3_seq_4(C))) ) ) ) ) )).
fof(t25_integr12,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v3_rcomp_1(F) & m1_subset_1(F,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,F) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,F) => ( k1_funct_1(D,G) = 1 & k1_funct_1(E,G) = k7_xcmplx_0(G,A) & ~ r1_xxreal_0(k1_funct_1(E,G),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(E,G)) ) ) ) & F = k1_relset_1(k1_numbers,C) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,B)) & 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,E,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,D,k41_valued_1(k1_numbers,k1_numbers,E)),k4_taylor_1(k7_xcmplx_0(1,2))),A)))) ) => k2_integra5(B,C) = k6_xcmplx_0(k1_funct_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,E,k1_sin_cos6)),k2_seq_4(B)),k1_funct_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,E,k1_sin_cos6)),k3_seq_4(B))) ) ) ) ) ) ) ) )).
fof(t25_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k18_sin_cos))))) & r1_tarski(C,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k26_sin_cos))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k26_sin_cos),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k26_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t25_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k27_sin_cos) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k27_sin_cos,A)) ) => k2_integra5(A,k27_sin_cos) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k3_taylor_1)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k3_taylor_1)),k3_seq_4(A))) ) ) ) )).
fof(t25_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t25_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [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_seq_2(k2_partfun1(A,k1_numbers,C,A)) => r1_xxreal_0(k6_integra1(A,C,B),k3_xcmplx_0(k2_seq_4(k1_rvsum_1(C)),k3_integra1(A))) ) ) ) ) )).
fof(t25_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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] : ( m1_integra1(E,C) => ( ( r2_hidden(B,k4_finseq_1(E)) & v2_seq_2(k2_partfun1(C,k1_numbers,D,C)) & r1_xxreal_0(k5_numbers,A) ) => k1_funct_1(k5_integra1(C,k26_valued_1(C,k1_numbers,D,A),E),B) = k3_xcmplx_0(A,k1_funct_1(k5_integra1(C,D,E),B)) ) ) ) ) ) ) )).
fof(t25_integra4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( ( 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(k5_numbers,A) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( ( r2_hidden(E,B) & r2_hidden(F,B) ) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k1_funct_1(D,E),k1_funct_1(D,F))),k3_xcmplx_0(A,k9_complex1(k6_xcmplx_0(k1_funct_1(C,E),k1_funct_1(C,F))))) ) ) ) ) => r1_xxreal_0(k6_xcmplx_0(k2_seq_4(k1_rvsum_1(D)),k3_seq_4(k1_rvsum_1(D))),k3_xcmplx_0(A,k6_xcmplx_0(k2_seq_4(k1_rvsum_1(C)),k3_seq_4(k1_rvsum_1(C))))) ) ) ) ) ) )).
fof(t25_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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)) = k3_xcmplx_0(E,k4_integra5(C,D,F)) ) ) ) ) ) ) ) )).
fof(t25_integra7,axiom,( r1_integra7(k1_numbers,k26_valued_1(k1_numbers,k1_numbers,k18_sin_cos,k4_xcmplx_0(1)),k16_sin_cos) )).
fof(t25_integra8,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k18_sin_cos),A) & k1_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k18_sin_cos),A) = k1_funct_1(k16_sin_cos,A) ) ) )).
fof(t25_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t25_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) ) )).
fof(t25_irrat_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(B) & k1_seq_2(B) = A ) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(D,E) & r1_xxreal_0(k1_funct_1(B,E),k6_xcmplx_0(A,C)) ) ) ) ) ) ) ) )).
fof(t25_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,A,B) => ! [G] : ( m2_cat_1(G,B,C) => ! [H] : ( m2_nattra_1(H,A,B,D,E) => ! [I] : ( m2_nattra_1(I,A,B,E,F) => ( ( r2_nattra_1(A,B,D,E) & r2_nattra_1(A,B,E,F) ) => r2_funct_2(u1_struct_0(A),u4_struct_0(C),k4_isocat_1(A,B,C,D,F,k5_nattra_1(A,B,D,E,F,H,I),G),k5_nattra_1(A,C,k9_cat_1(A,B,C,D,G),k9_cat_1(A,B,C,E,G),k9_cat_1(A,B,C,F,G),k4_isocat_1(A,B,C,D,E,H,G),k4_isocat_1(A,B,C,E,F,I,G))) ) ) ) ) ) ) ) ) ) ) )).
fof(t25_isomichi,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( 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) ) ) ) )).
fof(t25_jgraph_1,axiom,( ! [A] : ( 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] : ( 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)) ) ) ) ) )).
fof(t25_jgraph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( 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) ) ) ) ) ) ) )).
fof(t25_jgraph_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ~ r1_xxreal_0(k5_numbers,k18_euclid(B)) & ? [C] : ( 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(k5_numbers,k18_euclid(C)) ) ) ) ) )).
fof(t25_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t25_jordan,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v4_pre_topc(B,k15_euclid(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ~ ( ~ r2_hidden(C,B) & ! [D] : ( ( v1_xreal_0(D) & v2_xxreal_0(D) ) => ~ r1_xboole_0(k1_topreal9(A,C,D),B) ) ) ) ) ) )).
fof(t25_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t25_jordan12,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t25_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( 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_0(k1_jordan8(A,E))) & k7_partfun1(u1_struct_0(k15_euclid(2)),k1_jordan13(A,E),D) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,E),B,C) & r1_xxreal_0(k1_matrix_0(k1_jordan8(A,E)),C) ) ) ) ) ) ) )).
fof(t25_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(C,D) & r1_xxreal_0(D,k1_matrix_0(k1_jordan8(B,k1_nat_1(A,1)))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),D),k8_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),C),k9_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),D)),k9_jordan6(B)) ) ) ) ) ) )).
fof(t25_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t25_jordan18,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t25_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_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_0(C)) ) => v2_connsp_1(k3_goboard5(C,A,B),k15_euclid(2)) ) ) ) ) )).
fof(t25_jordan1b,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ 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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,k3_finseq_1(k1_jordan8(B,A)))),k8_jordan6(B)) ) ) ) ) )).
fof(t25_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(k1_jordan8(B,A))) & k22_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),k3_finseq_1(k1_jordan8(B,A)),C) ) ) ) )).
fof(t25_jordan1g,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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)))) ) => k4_finseq_4(k2_jordan1e(B,A),k22_pscomp_1(k3_topreal1(2,k2_jordan9(B,A)))) = 1 ) ) )).
fof(t25_jordan1h,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( ~ 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] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_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)) ) ) ) ) ) ) )).
fof(t25_jordan1j,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) ) )).
fof(t25_jordan1k,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) )).
fof(t25_jordan20,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t25_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => r1_xxreal_0(k18_euclid(k1_jordan21(k3_topreal1(2,k2_jordan9(A,C)))),k18_euclid(k1_jordan21(k3_topreal1(2,k2_jordan9(A,B))))) ) ) ) ) )).
fof(t25_jordan23,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v3_funct_1(k3_graph_2(A,B)) => v3_funct_1(A) ) ) ) )).
fof(t25_jordan2b,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ( A = a_1_1_jordan2b(B) => v3_pre_topc(A,k3_topmetr) ) ) ) )).
fof(t25_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( 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] : ( ( 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,k5_numbers) & E = k1_funct_1(F,1) ) ) ) ) ) ) ) ) )).
fof(t25_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) = k1_nat_1(k1_jordan3(A,B),1) ) & ( B = k1_funct_1(A,1) => k3_finseq_1(k3_jordan3(A,B)) = k1_jordan3(A,B) ) ) ) ) ) )).
fof(t25_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_jordan4(A,B,C,D) & r1_xxreal_0(C,D) ) => ( k3_finseq_1(B) = k1_nat_1(k7_nat_d(D,C),1) & B = k3_finseq_6(u1_struct_0(k15_euclid(2)),A,C,D) ) ) ) ) ) ) )).
fof(t25_jordan5a,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ( A = B => ( v1_rcomp_1(A) <=> v2_compts_1(B,k3_topmetr) ) ) ) ) )).
fof(t25_jordan5b,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( 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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,k1_matrix_0(k2_goboard2(A))),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),B,k1_matrix_0(k2_goboard2(A)))),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,k1_matrix_0(k2_goboard2(A))),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k3_finseq_1(k2_goboard2(A)),k1_matrix_0(k2_goboard2(A))))) = k1_xboole_0 ) ) ) ) ) )).
fof(t25_jordan5c,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ( ( v4_topreal1(A) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_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) ) ) ) ) )).
fof(t25_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( B = a_1_3_jordan5d(A) => k2_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)))) ) ) ) )).
fof(t25_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t25_jordan9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r2_hidden(k4_tarski(A,B),k2_matrix_0(D)) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(D)) ) => r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,A,B)),k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,C,k1_matrix_0(D)))) ) ) ) ) ) )).
fof(t25_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_jordan_a(B,A) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ 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)) ) ) ) ) )).
fof(t25_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( 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] : ( v3_ordinal1(D) => ! [E] : ( v3_ordinal1(E) => ( r1_ordinal1(D,E) => r3_lattices(A,k6_knaster(A,B,C,E),k6_knaster(A,B,C,D)) ) ) ) ) ) ) ) )).
fof(t25_kurato_1,axiom,( 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) )).
fof(t25_kurato_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(A)))))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( ( v9_rltopsp1(C,k15_euclid(A)) & ! [D] : ( v7_ordinal1(D) => r1_tarski(k2_kurato_2(k15_euclid(A),B,D),C) ) ) => v9_rltopsp1(k1_kurato_2(k15_euclid(A),B),k15_euclid(A)) ) ) ) ) )).
fof(t25_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r2_hidden(C,k2_finseq_1(A)) => k12_matrix_3(A,B,D) = k4_rlvect_1(B,k8_laplace(A,C,B,D)) ) ) ) ) ) )).
fof(t25_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(k11_group_4(A))) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t25_latsum_1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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)) ) ) ) )).
fof(t25_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => r6_binop_1(u1_struct_0(A),u1_lattices(A),u1_lattices(A)) ) )).
fof(t25_lattice3,axiom,( ! [A] : v4_lattice3(k1_lattice3(A)) )).
fof(t25_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & v14_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t25_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( v3_ordinal1(C) => ! [D] : ( ( 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] : ( m1_lattice5(E,A,B,D) => ( r2_hidden(C,k7_lattice5(A,B,D)) <=> r2_hidden(C,k9_xtuple_0(E)) ) ) ) ) ) ) )).
fof(t25_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t25_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m1_lattice5(D,A,B,C) => ! [E] : ( v3_ordinal1(E) => v2_lattice5(k6_lattice8(A,B,C,D,E),k3_lattice8(A,E),B) ) ) ) ) ) ) )).
fof(t25_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t25_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)))) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ! [E] : ( 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),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),B),D) = k1_funct_1(k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),k11_lexbfs(A,B,C,E)),D) ) ) ) ) ) )).
fof(t25_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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) ) ) )).
fof(t25_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_limfunc1(A) | v2_limfunc1(A) ) => v1_limfunc1(k56_valued_1(k4_ordinal1,k1_numbers,A)) ) ) )).
fof(t25_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,C) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,C) & ~ r1_xxreal_0(A,D) & r2_hidden(D,k1_relset_1(k1_numbers,B)) ) ) ) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(k6_xcmplx_0(A,C),A))) & ~ v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(k6_xcmplx_0(A,C),A))) ) ) | r2_limfunc2(B,A) ) ) ) ) )).
fof(t25_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r3_limfunc3(C,A) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ r1_xxreal_0(F,D) & ~ r1_xxreal_0(A,F) & r2_hidden(F,k9_xtuple_0(B)) & ~ r1_xxreal_0(E,G) & ~ r1_xxreal_0(G,A) & r2_hidden(G,k9_xtuple_0(B)) ) ) ) ) ) ) ) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k9_subset_1(k1_numbers,k9_xtuple_0(B),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,D),A),k2_rcomp_1(A,k2_xcmplx_0(A,D)))),k9_subset_1(k1_numbers,k9_xtuple_0(C),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,D),A),k2_rcomp_1(A,k2_xcmplx_0(A,D))))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k9_subset_1(k1_numbers,k9_xtuple_0(B),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,D),A),k2_rcomp_1(A,k2_xcmplx_0(A,D))))) => r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) | r3_limfunc3(B,A) ) ) ) ) ) )).
fof(t25_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(A,k2_xcmplx_0(A,D)))) & r1_xxreal_0(k2_limfunc2(B,A),k1_funct_1(B,E)) ) ) ) ) | r5_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t25_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m1_vectsp_4(E,A,B) => ( r1_lmod_6(A,C,E) => r1_lmod_6(A,k2_vectsp_5(A,B,C,D),E) ) ) ) ) ) ) )).
fof(t25_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k11_lopban_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k11_lopban_1(A,B))) => ! [E] : ( v1_xreal_0(E) => ( D = k1_rlvect_1(k11_lopban_1(A,B),C,E) <=> ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t25_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => r1_xxreal_0(k2_normsp_0(A,k5_algstr_0(A,k5_rsspace3(A,k1_bhsp_4(A,B),D),k5_rsspace3(A,k1_bhsp_4(A,B),C))),k9_complex1(k5_real_1(k9_nat_1(k1_numbers,k3_series_1(k5_normsp_0(A,B)),D),k9_nat_1(k1_numbers,k3_series_1(k5_normsp_0(A,B)),C)))) ) ) ) ) ) )).
fof(t25_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_lopban_4(A,C,D) => k9_nat_1(u1_struct_0(A),k1_bhsp_4(A,k1_lopban_4(A,k3_rlvect_1(A,C,D))),B) = k9_nat_1(u1_struct_0(A),k1_bhsp_4(A,k7_lopban_4(B,A,C,D)),B) ) ) ) ) ) )).
fof(t25_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( 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)) ) ) )).
fof(t25_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( ( r1_lpspacc1(A,B,C,D,F) & r1_lpspacc1(A,B,C,E,G) ) => r1_lpspacc1(A,B,C,k2_valued_1(A,k2_numbers,k2_numbers,D,E),k2_valued_1(A,k2_numbers,k2_numbers,F,G)) ) ) ) ) ) ) ) ) )).
fof(t25_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(k10_lpspace1(A,B,C))) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t25_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( v2_xxreal_0(F) & v1_xreal_0(F) ) => ( ( 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)) ) ) ) ) ) ) ) )).
fof(t25_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_hilbert1)) => ( r3_ltlaxio1(B,A) => r3_ltlaxio1(B,k2_ltlaxio1(A)) ) ) ) )).
fof(t25_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(k1_ltlaxio1(k1_ltlaxio1(A)),A)) ) )).
fof(t25_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => r1_tarski(k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,A),k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k6_ltlaxio3,A)) ) )).
fof(t25_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( ( ~ v2_ltlaxio3(C) & v3_ltlaxio3(C) & m1_subset_1(C,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) ) => ! [D] : ( m2_subset_1(D,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)),k9_ltlaxio4(C)) => ~ ( r2_hidden(k4_hilbert1(A,B),k2_relset_1(k1_hilbert1,k8_ltlaxio3(C))) & ~ r2_hidden(B,k2_relset_1(k1_hilbert1,k8_ltlaxio3(D))) & ~ ( r2_hidden(A,k2_relset_1(k1_hilbert1,k8_ltlaxio3(D))) & r2_hidden(k4_hilbert1(A,B),k2_relset_1(k1_hilbert1,k8_ltlaxio3(D))) ) ) ) ) ) ) )).
fof(t25_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) )).
fof(t25_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t25_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( v2_matrix10(B) => v3_matrix10(B) ) ) ) )).
fof(t25_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_matrix_2(B,k3_matrix_2(A)) => ! [C] : ( m1_matrix_2(C,k3_matrix_2(A)) => ( ( ( v5_matrix_2(B,k2_matrix_2(k3_matrix_2(A))) & v5_matrix_2(C,k2_matrix_2(k3_matrix_2(A))) ) | ( ~ v5_matrix_2(B,k2_matrix_2(k3_matrix_2(A))) & ~ v5_matrix_2(C,k2_matrix_2(k3_matrix_2(A))) ) ) <=> v5_matrix_2(k1_partfun1(k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),C,B),k2_matrix_2(k3_matrix_2(A))) ) ) ) ) )).
fof(t25_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( ( v1_matrix_0(F) & m2_finseq_1(F,k3_finseq_2(A)) ) => ! [G] : ( m2_finseq_2(G,k4_ordinal1,k4_finseq_2(E,k4_ordinal1)) => ! [H] : ( m2_finseq_2(H,k4_ordinal1,k4_finseq_2(D,k4_ordinal1)) => ( ( r2_hidden(B,k2_finseq_1(E)) & r2_hidden(C,k2_finseq_1(E)) & k1_funct_1(G,B) = k1_funct_1(G,C) ) => k7_matrix_0(A,k1_matrix13(A,F,E,D,G,H),B) = k7_matrix_0(A,k1_matrix13(A,F,E,D,G,H),C) ) ) ) ) ) ) ) ) ) )).
fof(t25_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t25_matrix15,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ( C = k2_matrix15(A,B) <=> ( k7_matrix_0(A,C,1) = B & k3_finseq_1(C) = 1 ) ) ) ) ) )).
fof(t25_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v3_matrix16(C,u1_struct_0(B)) => v3_matrix16(k2_matrix_3(B,C),u1_struct_0(B)) ) ) ) ) )).
fof(t25_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,C,A,B) & m2_finseq_1(D,k3_finseq_2(C)) ) => ( k3_finseq_1(D) = A & k2_matrix_0(D) = k2_zfmisc_1(k2_finseq_1(A),k2_finseq_1(k1_matrix_0(D))) ) ) ) ) ) )).
fof(t25_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(D) ) => k3_matrix_3(A,k1_matrix_4(A,B,C),D) = k3_matrix_3(A,k1_matrix_4(A,D,C),B) ) ) ) ) ) )).
fof(t25_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ( ~ r1_xxreal_0(k3_finseq_1(A),k5_numbers) => k7_matrix_5(k5_numbers,A) = k8_matrix_5(k3_finseq_1(A),k1_matrix_0(A)) ) ) )).
fof(t25_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & v1_matrix_2(C,A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) & v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & v2_matrix_2(C,A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => v2_matrix_6(C,A,B) ) ) ) ) )).
fof(t25_matrix_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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))) ) ) )).
fof(t25_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v2_matrix_8(C,A,B) & v2_matrix_8(D,A,B) & k4_matrix_3(B,C,D) = k2_matrix_3(B,k4_matrix_3(B,D,C)) ) => ( r1_xxreal_0(A,k5_numbers) | v2_matrix_8(k3_matrix_3(B,C,D),A,B) ) ) ) ) ) ) )).
fof(t25_matrix_9,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( ( v1_matrix_0(K) & v2_matrix_0(K,u1_struct_0(A),3,3) & m2_finseq_1(K,k3_finseq_2(u1_struct_0(A))) ) => ( K = k3_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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] : ( m1_matrix_2(L,k3_matrix_2(3)) => ( L = k3_finseq_4(k4_ordinal1,3,1,2) => k10_matrix_3(3,A,K,L) = k3_finseq_4(u1_struct_0(A),D,E,I) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t25_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( 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)) ) ) ) )).
fof(t25_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( v1_matrixj1(D,A) & m2_finseq_1(D,k3_finseq_2(k3_finseq_2(A))) ) => ! [E] : ( ( v1_matrixj1(E,A) & m2_finseq_1(E,k3_finseq_2(k3_finseq_2(A))) ) => m1_subset_1(k2_matrix_0(k13_matrixj1(A,B,D)),k1_zfmisc_1(k2_matrix_0(k13_matrixj1(A,C,k3_matrixj1(A,D,E))))) ) ) ) ) ) )).
fof(t25_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( k3_finseq_1(k3_matrixr1(A,B)) = k3_finseq_1(A) & k1_matrix_0(k3_matrixr1(A,B)) = k1_matrix_0(A) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k4_tarski(C,D),k2_matrix_0(A)) => k3_matrix_0(k1_numbers,k3_matrixr1(A,B),C,D) = k3_real_1(k3_matrix_0(k1_numbers,A,C,D),k3_matrix_0(k1_numbers,B,C,D)) ) ) ) ) ) ) )).
fof(t25_matrixr2,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k1_matrix_0(A) = k1_matrix_0(B) ) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(A)) ) => k7_matrix_0(k1_numbers,k5_matrixr1(A,B),C) = k8_rvsum_1(k7_matrix_0(k1_numbers,A,C),k7_matrix_0(k1_numbers,B,C)) ) ) ) ) ) )).
fof(t25_matrlin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( ~ v1_xboole_0(F) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,F,B,A) & m2_finseq_1(G,k3_finseq_2(F)) ) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,F,D,A) & m2_finseq_1(H,k3_finseq_2(F)) ) => ( ( r2_hidden(E,k9_xtuple_0(H)) & C = k2_xcmplx_0(k3_finseq_1(G),E) ) => k7_matrix_0(F,k8_matrlin(F,B,D,A,G,H),C) = k7_matrix_0(F,H,E) ) ) ) ) ) ) ) ) ) )).
fof(t25_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_matrlin(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( D = k2_vectsp_4(A,B) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_matrlin(G,A,D) => ( ( F = E & C = G ) => k9_matrlin(A,B,C,F) = k9_matrlin(A,D,G,E) ) ) ) ) ) ) ) ) ) )).
fof(t25_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t25_matrprob,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,B,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,k1_numbers,C,A) & m2_finseq_1(E,k3_finseq_2(k1_numbers)) ) => k3_matrprob(k8_matrlin(k1_numbers,B,C,A,D,E)) = k8_finseq_1(k1_numbers,k3_matrprob(D),k3_matrprob(E)) ) ) ) ) ) )).
fof(t25_matrtop2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ! [D] : ( ( 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) = A => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ( r2_hidden(E,k4_rlaffin1(k15_euclid(A),D)) => ( r2_hidden(k3_funct_2(u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(B)),k3_matrtop1(A,B,C),E),k4_rlaffin1(k15_euclid(B),k2_ranknull(k15_euclid(A),k15_euclid(B),k3_matrtop1(A,B,C),D))) & ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) & v3_card_1(F,A) & v1_finseq_1(F) & v3_valued_0(F) ) => k1_funct_1(k5_rlaffin1(k15_euclid(A),D,E),F) = k1_funct_1(k5_rlaffin1(k15_euclid(B),k2_ranknull(k15_euclid(A),k15_euclid(B),k3_matrtop1(A,B,C),D),k3_funct_2(u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(B)),k3_matrtop1(A,B,C),E)),k1_funct_1(k3_matrtop1(A,B,C),F)) ) ) ) ) ) ) ) ) ) )).
fof(t25_matrtop3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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(k1_square_1(A),k2_xcmplx_0(k1_square_1(k1_funct_1(E,B)),k1_square_1(k1_funct_1(E,C)))) & ! [F] : ( v1_xreal_0(F) => k1_funct_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 ) ) ) ) ) ) ) )).
fof(t25_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r1_pboole(A,C,B) => r2_pboole(A,C,k2_mboolean(A,B)) ) ) ) )).
fof(t25_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : k3_zfmisc_1(k1_tarski(A),k1_tarski(B),k1_tarski(C)) = k1_tarski(k3_xtuple_0(A,B,C)) )).
fof(t25_measure1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,k6_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( v6_supinf_2(D) => v6_supinf_2(k1_partfun1(A,B,B,k6_numbers,C,D)) ) ) ) ) ) )).
fof(t25_measure6,axiom,( ! [A] : ( v1_xreal_0(A) => k1_measure6(k1_xboole_0,A) = k1_xboole_0 ) )).
fof(t25_member_1,axiom,( ! [A] : ( v2_membered(A) => k4_member_1(k6_member_1(A)) = k6_member_1(k4_member_1(A)) ) )).
fof(t25_membered,axiom,( ! [A] : ( ! [B] : ( r2_hidden(B,A) => v1_membered(B) ) => v1_membered(k3_tarski(A)) ) )).
fof(t25_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_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))) ) ) ) )).
fof(t25_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ( ( r2_mesfun6c(A,B,C,D) & F = k7_subset_1(A,k1_relset_1(A,D),E) ) => ( r2_mesfun6c(A,B,C,k2_partfun1(A,k2_numbers,D,E)) & k1_mesfun6c(A,B,C,D) = 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))) ) ) ) ) ) ) ) ) )).
fof(t25_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k2_numbers)) & v1_mesfunc8(B,A,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ( ! [C] : ( m1_subset_1(C,A) => ( r2_hidden(C,k1_relset_1(A,k4_mesfunc5(A,k2_numbers,B,k5_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)) ) ) ) ) )).
fof(t25_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ( v1_mesfunc8(k11_mesfun7c(A,B),A,k1_numbers) <=> v1_mesfunc8(k12_mesfun7c(A,B),A,k1_numbers) ) ) ) )).
fof(t25_mesfunc1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ! [F] : ( m1_subset_1(F,k4_ordinal1) => k9_nat_1(B,C,F) = k9_subset_1(A,E,k15_mesfunc1(A,D,k4_xcmplx_0(F))) ) => k9_subset_1(A,E,k19_mesfunc1(A,D,k2_supinf_1)) = k1_measure2(A,B,k1_measure3(A,B,C)) ) ) ) ) )).
fof(t25_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,C) => ( r1_mesfunc1(A,C,B,D) => r1_mesfunc1(A,C,k1_mesfunc2(A,B),D) ) ) ) ) ) )).
fof(t25_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( v3_mesfunc5(B) & v4_mesfunc5(B) & v3_mesfunc5(C) & v4_mesfunc5(C) ) => r2_relset_1(A,k6_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))) ) ) ) ) )).
fof(t25_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( v1_xreal_0(F) => ~ ( r1_mesfunc6(A,B,C,E) & r1_mesfunc6(A,B,D,E) & ! [G] : ( ( 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] : ( 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,k6_xcmplx_0(F,H)))) ) ) ) ) ) ) ) ) ) )).
fof(t25_mesfunc7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( 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,k6_numbers,k3_mesfunc2(D,A),E)) = k12_supinf_2(C,k5_prob_1(A,B,D,E)) ) ) ) ) ) ) )).
fof(t25_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k6_numbers)) & v1_mesfunc8(C,A,k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( ( k1_relset_1(A,k4_mesfunc5(A,k6_numbers,C,k5_numbers)) = D & ! [E] : ( v7_ordinal1(E) => r1_mesfunc1(A,B,k4_mesfunc5(A,k6_numbers,C,E),D) ) & ! [E] : ( 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) ) ) ) ) ) )).
fof(t25_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ~ ( r2_hidden(D,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,k4_mesfunc9(A,B),C))) & k1_mesfunc9(k4_mesfunc5(A,k6_numbers,k4_mesfunc9(A,B),C),D) = k2_supinf_1 & ! [E] : ( v7_ordinal1(E) => ~ ( r1_xxreal_0(E,C) & k1_mesfunc9(k4_mesfunc5(A,k6_numbers,B,E),D) = k2_supinf_1 ) ) ) ) ) ) )).
fof(t25_metric_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & r1_xxreal_0(k1_metric_1(A,B,C),k5_numbers) ) ) ) <=> v11_metric_1(A) ) ) )).
fof(t25_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => ( r2_hidden(B,k5_metric_2(A)) <=> ? [C] : ( m1_subset_1(C,k2_metric_2(A)) & ? [D] : ( m1_subset_1(D,k2_metric_2(A)) & r4_metric_2(A,C,D,B) ) ) ) ) ) )).
fof(t25_metric_3,axiom,( ! [A] : ( m1_subset_1(A,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)) => ! [B] : ( m1_subset_1(B,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)) => ( k2_binop_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k1_numbers,k20_metric_3,A,B) = k5_numbers <=> A = B ) ) ) )).
fof(t25_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r1_connsp_1(A,B,C) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ r2_metrizts(A,B,C,D) ) ) ) ) ) )).
fof(t25_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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),C),k2_mfold_2(A,B,D)) = k2_mfold_2(A,B,k3_rlvect_1(k15_euclid(A),C,D)) ) ) ) ) )).
fof(t25_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( 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)))) ) ) ) )).
fof(t25_midsp_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t25_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_midsp_3(B,A) => ! [C] : ( m2_midsp_3(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m2_finseq_2(F,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(C))) => ! [G] : ( ( v4_midsp_2(G,C) & l1_midsp_2(G,C) ) => ! [H] : ( m1_subset_1(H,u1_struct_0(u1_midsp_2(C,G))) => ! [I] : ( m2_finseq_2(I,u1_struct_0(u1_midsp_2(C,G)),k4_finseq_2(k1_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)),k1_nat_1(A,1),I,B,H) ) ) ) ) ) ) ) ) ) ) )).
fof(t25_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t25_mod_2,axiom,( ! [A] : ( m1_subset_1(A,k1_enumset1(k5_numbers,1,2)) => ! [B] : ( m1_subset_1(B,k1_enumset1(k5_numbers,1,2)) => ! [C] : ( m1_subset_1(C,k1_enumset1(k5_numbers,1,2)) => ! [D] : ( m1_subset_1(D,k1_enumset1(k5_numbers,1,2)) => ! [E] : ( m1_subset_1(E,k1_enumset1(k5_numbers,1,2)) => ( ( D = k5_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] : ( m1_subset_1(F,k1_enumset1(k5_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)) ) ) ) ) ) ) ) )).
fof(t25_mod_4,axiom,( ! [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) & 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) ) ) ) )).
fof(t25_modal_1,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k7_funcop_1(k2_trees_1(k5_numbers),k4_tarski(3,A)),k6_modal_1) ) )).
fof(t25_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m1_subset_1(C,A) => ? [D] : ( m1_modelc_1(D,A,B) & k3_funct_2(k4_ordinal1,A,D,k5_numbers) = C ) ) ) ) )).
fof(t25_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( v8_modelc_2(A) => ( r1_modelc_2(B,A) <=> ( B = k11_modelc_2(A) | B = k12_modelc_2(A) ) ) ) ) ) )).
fof(t25_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_3(B,A) & l1_modelc_3(B,A) ) => ! [C] : ( ( v1_modelc_3(C,A) & l1_modelc_3(C,A) ) => ( r4_modelc_3(A,B,C) => ( r1_tarski(u1_modelc_3(A,B),u1_modelc_3(A,C)) & r1_tarski(u3_modelc_3(A,B),u3_modelc_3(A,C)) ) ) ) ) ) )).
fof(t25_moebius1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ v1_moebius1(k3_xcmplx_0(A,B)) & v1_moebius1(A) ) ) ) )).
fof(t25_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m2_monoid_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( C = E & D = F ) => k6_algstr_0(B,C,D) = k6_algstr_0(A,E,F) ) ) ) ) ) ) ) )).
fof(t25_monoid_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v1_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t25_morph_01,axiom,( ! [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) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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)) ) ) ) ) )).
fof(t25_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_numbers)))),k5_msafree3(A,k2_pboole(u1_struct_0(A),B,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_numbers))),B)) = k1_msafree3(A,B) ) ) )).
fof(t25_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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] : ( m3_pboole(D,u1_struct_0(A),u3_msualg_1(A,B)) => ! [E] : ( m3_pboole(E,u1_struct_0(A),u3_msualg_1(A,C)) => ( r8_pboole(u1_struct_0(A),D,E) => ! [F] : ( m1_subset_1(F,u4_struct_0(A)) => ( r1_msualg_2(A,B,F,D) => k3_msualg_2(A,C,F,E) = k3_msualg_2(A,B,F,D) ) ) ) ) ) ) ) ) ) )).
fof(t25_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(D)) => ! [F] : ( 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] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(D)) => ! [F] : ( 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)) ) ) ) ) ) )).
fof(t25_msscyc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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)) ) ) ) )).
fof(t25_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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,k2_funct_6(C)) & ! [D] : ! [E] : ( ( 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) ) ) ) )).
fof(t25_mssublat,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v13_struct_0(A,1) & v5_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ( u1_struct_0(A) = k1_tarski(k5_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))) ) ) ) )).
fof(t25_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msualg_2(C,A,B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t25_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( r1_rewrite1(k3_msualg_6(A),E,F) => ! [G] : ( m2_msualg_6(G,A,B,E,F) => ? [H] : ( 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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t25_msualg_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(t25_msuhom_1,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(t25_mycielsk,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( 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))) ) ) ) )).
fof(t25_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( r1_xxreal_0(A,1) & A != k5_numbers & A != 1 ) ) )).
fof(t25_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(A,k3_xcmplx_0(2,B)) => r1_xxreal_0(k3_nat_d(k1_nat_1(A,1),2),B) ) ) ) )).
fof(t25_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,1) => k11_nat_3(k1_newton(B,A),B) = A ) ) ) )).
fof(t25_nat_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ( k6_xcmplx_0(A,1) = k2_nat_1(k11_newton(F,D),C) & v1_int_2(F) & k4_nat_d(k11_newton(E,k7_nat_d(A,1)),A) = 1 & k6_nat_d(k7_nat_d(k11_newton(E,k3_nat_d(k7_nat_d(A,1),F)),1),A) = 1 ) => ( r1_xxreal_0(k11_newton(F,D),C) | r1_xxreal_0(C,k5_numbers) | v1_int_2(A) ) ) ) ) ) ) ) ) )).
fof(t25_nat_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ( C = B => k2_uproots(D,k1_nat_5(A,C,D)) = k21_rfunct_3(A,B,D) ) ) ) ) ) )).
fof(t25_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => k4_nat_d(A,A) = k5_numbers ) )).
fof(t25_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t25_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,u1_struct_0(A),k8_funct_2(k4_ordinal1,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(k4_ordinal1,u1_struct_0(A),u1_struct_0(B),E,C),k8_funct_2(k4_ordinal1,u1_struct_0(A),u1_struct_0(B),E,D))) & r2_funct_2(k4_ordinal1,u1_struct_0(A),k8_funct_2(k4_ordinal1,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(k4_ordinal1,u1_struct_0(A),u1_struct_0(B),E,C),k8_funct_2(k4_ordinal1,u1_struct_0(A),u1_struct_0(B),E,D))) ) ) ) ) ) ) ) )).
fof(t25_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t25_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_partfun1(C,u1_struct_0(A)) & v1_partfun1(D,u1_struct_0(A)) ) => ( r2_funct_2(k4_ordinal1,u1_struct_0(B),k8_funct_2(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,C),k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,D))) & r2_funct_2(k4_ordinal1,u1_struct_0(B),k8_funct_2(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,C),k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,D))) ) ) ) ) ) ) ) )).
fof(t25_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [C] : ( v1_xreal_0(C) => ( r1_ndiff_3(k4_real_ns1(A),B,C) <=> ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( 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) ) ) ) ) ) ) )).
fof(t25_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ! [E] : ( ( 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)))) ) ) ) ) )).
fof(t25_neckla_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_necklace(A) & l1_orders_2(A) ) => ( v1_neckla_2(A) <=> v1_neckla_2(k3_necklace(A)) ) ) )).
fof(t25_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_net_1(A))) => ! [C] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t25_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ( ( r3_nfcont_1(A,B,D,C) & r3_nfcont_1(A,B,E,C) ) => ( r3_nfcont_1(A,B,k6_vfunct_1(u1_struct_0(A),B,D,E),C) & r3_nfcont_1(A,B,k2_vfunct_1(u1_struct_0(A),B,D,E),C) ) ) ) ) ) ) )).
fof(t25_nfcont_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t25_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ! [D] : ( ( 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) ) ) ) )).
fof(t25_normform,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(t25_normsp_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) )).
fof(t25_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_normsp_2(A))))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k4_normsp_2(A))))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_normsp_2(A))) => ! [E] : ( 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))))) ) ) ) ) ) ) ) ) )).
fof(t25_numbers,axiom,( k4_numbers != k1_numbers )).
fof(t25_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t25_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_openlatt(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t25_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u4_struct_0(k2_oppcat_1(B)),u4_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(k2_oppcat_1(B)),u4_struct_0(A)))) ) => ! [D] : ( m1_subset_1(D,u4_struct_0(k2_oppcat_1(B))) => k3_funct_2(u4_struct_0(B),u4_struct_0(A),k9_oppcat_1(B,A,C),k6_oppcat_1(B,D)) = k3_funct_2(u4_struct_0(k2_oppcat_1(B)),u4_struct_0(A),C,D) ) ) ) ) )).
fof(t25_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_ordeq_01(A,B))) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ( ( E = D & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,A) => r1_xxreal_0(k2_normsp_0(B,k7_partfun1(u1_struct_0(B),E,F)),C) ) ) ) => r1_xxreal_0(k2_normsp_0(k5_ordeq_01(A,B),D),C) ) ) ) ) ) ) )).
fof(t25_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_orders_1(A) => v1_orders_1(k2_wellord1(A,B)) ) ) )).
fof(t25_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_orders_2(A,k1_struct_0(A),B) = k1_xboole_0 ) ) )).
fof(t25_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => ( ~ ( ~ v4_ordinal1(A) & ! [B] : ( v3_ordinal1(B) => A != k1_ordinal1(B) ) ) & ~ ( ? [B] : ( v3_ordinal1(B) & A = k1_ordinal1(B) ) & v4_ordinal1(A) ) ) ) )).
fof(t25_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_ordinal2(B) ) => ( r2_hidden(A,k9_xtuple_0(B)) => v3_ordinal1(k1_funct_1(B,A)) ) ) ) )).
fof(t25_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r2_hidden(A,B) => ( r2_hidden(A,k10_ordinal2(B,C)) & r2_hidden(A,k10_ordinal2(C,B)) ) ) ) ) ) )).
fof(t25_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( v3_ordinal1(B) => ( ( r2_hidden(1,B) & ! [C] : ( v3_ordinal1(C) => ( r2_hidden(C,k9_xtuple_0(A)) => k1_funct_1(A,C) = k12_ordinal2(B,C) ) ) ) => v2_ordinal2(A) ) ) ) )).
fof(t25_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( v3_ordinal1(C) => ( r2_hidden(C,k9_xtuple_0(B)) => k1_funct_1(B,C) = k1_ordinal5(A,C) ) ) ) => v2_ordinal2(B) ) ) ) )).
fof(t25_ordinal6,axiom,( ! [A] : ( v1_ordinal6(A) => ! [B] : ( v1_ordinal6(B) => ( ! [C] : ! [D] : ( ( 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)) ) ) ) )).
fof(t25_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ~ ( ~ r1_orders_2(B,D,C) & ~ r1_orders_2(B,D,F) & ~ r1_orders_2(B,E,C) & ~ r1_orders_2(B,E,F) & k8_group_1(A,k1_ortsp_1(A,B,C,E,D),k1_ortsp_1(A,B,D,C,F)) != k8_group_1(A,k1_ortsp_1(A,B,E,C,F),k1_ortsp_1(A,B,F,E,D)) ) ) ) ) ) ) ) )).
fof(t25_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t25_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t25_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t25_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t25_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t25_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t25_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(t25_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t25_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ( k4_partit1(A,B) = k4_partit1(A,C) => B = C ) ) ) ) )).
fof(t25_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( r4_relat_2(B,A) => v4_relat_2(B) ) ) ) )).
fof(t25_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r3_diraf(A,F,B,E) & r3_diraf(A,F,C,D) ) ) ) ) ) ) ) ) )).
fof(t25_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( r2_pboole(A,B,D) => r6_pboole(A,k2_pboole(A,B,k3_pboole(A,C,D)),k3_pboole(A,k2_pboole(A,B,C),D)) ) ) ) ) )).
fof(t25_pcomps_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ( v8_pre_topc(A) & v2_pcomps_1(A) ) => v10_pre_topc(A) ) ) )).
fof(t25_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k20_pcs_0(A,B))) => ( C != B => r2_hidden(C,u1_struct_0(A)) ) ) ) )).
fof(t25_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ! [E] : ( ( 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))))) ) => ( r7_pdiff_1(A,B,C,E,D) => m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k4_real_ns1(A)))) ) ) ) ) ) )).
fof(t25_pdiff_3,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(2)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [C] : ( ( 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) & k10_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) = k6_xcmplx_0(k2_pdiff_3(B,A),k2_pdiff_3(C,A)) ) ) ) ) ) )).
fof(t25_pdiff_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m1_rcomp_1(C,k3_funct_2(k1_euclid(3),k1_numbers,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] : ( ( v9_ordinal1(D) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k1_rvsum_1(E) = k1_tarski(k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(1,3),B)) & r1_tarski(k1_rvsum_1(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),C) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,1,A,B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,1,A,B))))) & k10_pdiff_1(3,1,A,B) = k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,1,A,B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,1,A,B))))) ) ) ) ) ) ) ) ) )).
fof(t25_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( 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) ) ) ) )).
fof(t25_pdiff_6,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ( r1_pdiff_1(A,B,C,D) <=> ? [E] : ( v1_xreal_0(E) & ~ r1_xxreal_0(E,k5_numbers) & r1_tarski(a_3_2_pdiff_6(A,D,E),k1_relset_1(k1_euclid(A),C)) & ? [F] : ( 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] : ( 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] : ( v1_xreal_0(H) => ~ ( ~ r1_xxreal_0(H,k5_numbers) & ! [I] : ( v1_xreal_0(I) => ~ ( ~ r1_xxreal_0(I,k5_numbers) & ! [J] : ( m2_finseq_2(J,k1_numbers,k1_euclid(A)) => ! [K] : ( 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,k3_xcmplx_0(k5_xcmplx_0(k12_euclid(J)),k12_euclid(K))) ) ) ) ) ) ) ) & ! [H] : ( 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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t25_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(k1_euclid(A))) => ! [F] : ( 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] : ( m2_finseq_2(G,k1_numbers,k1_euclid(A)) => ! [H] : ( v1_xreal_0(H) => ~ ( r2_hidden(G,E) & ~ r1_xxreal_0(H,k5_numbers) & ! [I] : ( v1_xreal_0(I) => ~ ( ~ r1_xxreal_0(I,k5_numbers) & ! [J] : ( 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] : ( 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))),k3_xcmplx_0(H,k12_euclid(K))) ) ) ) ) ) ) ) ) ) ) ) & ( ( r1_pdiff_6(E,B,A,C) & ! [G] : ( m2_finseq_2(G,k1_numbers,k1_euclid(A)) => ! [H] : ( v1_xreal_0(H) => ~ ( r2_hidden(G,E) & ~ r1_xxreal_0(H,k5_numbers) & ! [I] : ( v1_xreal_0(I) => ~ ( ~ r1_xxreal_0(I,k5_numbers) & ! [J] : ( 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] : ( 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))),k3_xcmplx_0(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) ) ) ) ) ) ) ) ) ) ) )).
fof(t25_pencil_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v15_pencil_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_pencil_1(A,B,D))) => m1_subset_1(k1_funct_7(C,D,E),u1_struct_0(k5_pencil_1(A,B))) ) ) ) ) ) ) )).
fof(t25_pencil_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v15_pencil_1(B) ) => ( ! [C] : ( m1_subset_1(C,A) => v10_pencil_1(k2_pencil_1(A,B,C)) ) => ! [C] : ( m1_pencil_2(C,A,B) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t25_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(D,k1_vectsp_9(A,B)) & v3_pencil_1(k7_pencil_4(A,B,C,D)) ) ) ) ) ) )).
fof(t25_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(A,1) & ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(k1_newton(A,B),1) ) ) ) )).
fof(t25_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m3_pnproc_1(C,A,B) => ! [D] : ( 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)) ) ) ) )).
fof(t25_polyeq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( k2_polyeq_1(B,k5_numbers,C,A) = k5_numbers => ( B = k5_numbers | ! [D] : ( v1_xcmplx_0(D) => ~ ( D = k4_xcmplx_0(k7_xcmplx_0(C,B)) & A != k2_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(D),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(D)),k1_square_1(k4_complex1(D))))),2)),k3_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(D)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(D)),k1_square_1(k4_complex1(D))))),2)),k7_complex1)) & A != k2_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(D),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(D)),k1_square_1(k4_complex1(D))))),2))),k3_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(D)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(D)),k1_square_1(k4_complex1(D))))),2))),k7_complex1)) & A != k2_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(D),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(D)),k1_square_1(k4_complex1(D))))),2)),k3_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(D)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(D)),k1_square_1(k4_complex1(D))))),2))),k7_complex1)) & A != k2_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(D),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(D)),k1_square_1(k4_complex1(D))))),2))),k3_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(D)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(D)),k1_square_1(k4_complex1(D))))),2)),k7_complex1)) ) ) ) ) ) ) ) )).
fof(t25_polyeq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( k3_power(A,C) = 1 => ( r1_xxreal_0(A,k5_numbers) | A = 1 | r1_xxreal_0(C,k5_numbers) | C = A ) ) ) ) ) )).
fof(t25_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( v1_xcmplx_0(F) => ! [G] : ( v1_xcmplx_0(G) => ! [H] : ( v1_xcmplx_0(H) => ! [I] : ( v1_xcmplx_0(I) => ( ( I = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(8,D),k3_xcmplx_0(3,k1_newton(F,2))),32) & G = k7_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(8,C),k3_xcmplx_0(k3_xcmplx_0(4,D),F)),k1_newton(F,3)),64) & G = k5_numbers & H = k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(256,B),k3_xcmplx_0(k3_xcmplx_0(64,F),C)),k3_xcmplx_0(k3_xcmplx_0(16,k1_newton(F,2)),D)),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(D,k1_newton(A,2))),k3_xcmplx_0(C,A)),B) = k5_numbers <=> ~ ( A != k6_xcmplx_0(k1_polyeq_5(2,k4_xcmplx_0(k3_xcmplx_0(2,k6_xcmplx_0(I,E)))),k7_xcmplx_0(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))))),k7_xcmplx_0(F,4)) & A != k6_xcmplx_0(k1_polyeq_5(2,k4_xcmplx_0(k3_xcmplx_0(2,k2_xcmplx_0(I,E)))),k7_xcmplx_0(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))))),k7_xcmplx_0(F,4)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t25_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ~ ( ~ r1_xxreal_0(k7_polyform(A),B) & r1_xxreal_0(k7_polyform(A),k6_xcmplx_0(B,1)) ) ) ) )).
fof(t25_polynom1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_vectsp_1(B) & l5_algstr_0(B) ) => ( k4_polynom1(A,B,k9_polynom1(A,B),k16_pre_poly(A)) = k5_struct_0(B) & ! [C] : ( ( 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) => k4_polynom1(A,B,k9_polynom1(A,B),C) = k4_struct_0(B) ) ) ) ) )).
fof(t25_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,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))) ) ) ) ) )).
fof(t25_polynom5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t25_polynom7,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( 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_polynom2(A,B,k4_polynom7(A,B,C),D) = C ) ) ) ) )).
fof(t25_polynom8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B != k4_struct_0(A) => ! [C] : ( v1_int_1(C) => k3_polynom8(A,k11_algstr_0(A,B),C) = k11_algstr_0(A,k3_polynom8(A,B,C)) ) ) ) ) )).
fof(t25_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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) ) ) ) ) )).
fof(t25_power,axiom,( ! [A] : ( v1_xreal_0(A) => k2_power(A,1) = A ) )).
fof(t25_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_pralg_2(D,A,B) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( ( v4_msualg_1(F,B) & l3_msualg_1(F,B) ) => ! [G] : ( ( v1_relat_1(G) & v4_relat_1(G,A) & v1_funct_1(G) & v1_partfun1(G,A) & v1_funcop_1(G) ) => ( ! [H] : ( m1_subset_1(H,A) => ? [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(k9_funct_6(G),E),C) = k1_funct_1(k1_funct_1(G,C),E) ) ) ) ) ) ) ) ) ) )).
fof(t25_pre_poly,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_pre_poly(A) <=> ! [B] : ( r2_hidden(B,k10_xtuple_0(A)) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ) ) )).
fof(t25_pre_topc,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => m1_subset_1(C,u1_struct_0(A)) ) ) ) )).
fof(t25_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t25_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(1,C) & r1_xxreal_0(1,B) ) => k2_prepower(C,k2_prepower(B,A)) = k2_prepower(k3_xcmplx_0(C,B),A) ) ) ) ) )).
fof(t25_prob_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( ~ 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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) <=> ! [D] : ( v7_ordinal1(D) => m1_prob_1(k9_nat_1(k9_setfam_1(A),B,D),A,C) ) ) ) ) )).
fof(t25_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t25_prob_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( ~ 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] : ( ( v5_relat_1(D,C) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ! [E] : ( r2_hidden(E,k1_prob_2(B,C,k1_prob_3(B,D),A)) <=> ! [F] : ( v7_ordinal1(F) => ( r1_xxreal_0(F,A) => r2_hidden(E,k1_prob_2(B,C,D,F)) ) ) ) ) ) ) )).
fof(t25_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ! [E] : ( ( r2_hidden(D,B) & r2_hidden(E,B) ) => ! [F] : ( m1_prob_4(F,A,B,C) => ! [G] : ( 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) ) ) ) ) ) ) ) )).
fof(t25_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t25_projpl_1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & v5_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t25_projred1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u2_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u2_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u2_incsp_1(A)) => ~ ( ~ r1_incsp_1(A,C,E) & ~ r1_incsp_1(A,C,F) & ~ r1_incsp_1(A,D,F) & ~ r1_incsp_1(A,D,G) & r1_incsp_1(A,B,E) & r1_incsp_1(A,B,F) & r1_incsp_1(A,B,G) & E != G & ! [H] : ( 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,C),k1_projred1(A,F,G,D)) = k1_projred1(A,E,G,H) ) ) ) ) ) ) ) ) ) ) )).
fof(t25_pua2mss1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m2_finseq_1(C,B) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ! [F] : ! [G] : ( r2_hidden(k7_finseq_1(k7_finseq_1(D,k9_finseq_1(F)),E),k4_card_3(C)) => ( ! [H] : ( 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)) ) ) ) ) ) ) ) )).
fof(t25_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t25_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k1_qc_lang1(A)) => ( r2_qc_lang1(A,B,C) <=> ~ r1_qc_lang1(A,C,B) ) ) ) ) )).
fof(t25_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( m1_subset_1(E,k9_qc_lang1(A)) => ! [F] : ( m1_subset_1(F,k9_qc_lang1(A)) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t25_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t25_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,k5_numbers)),k9_xtuple_0(k2_qc_lang4(A,B))) & k1_funct_1(k2_qc_lang4(A,B),k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,k5_numbers))) = k19_qc_lang1(A,k3_trees_2(k9_qc_lang1(A),k2_qc_lang4(A,B),C)) & r2_hidden(k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,1)),k9_xtuple_0(k2_qc_lang4(A,B))) & k1_funct_1(k2_qc_lang4(A,B),k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,1))) = k20_qc_lang1(A,k3_trees_2(k9_qc_lang1(A),k2_qc_lang4(A,B),C)) ) ) ) ) ) )).
fof(t25_quantal1,axiom,( ! [A] : ( ( ~ 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] : k5_quantal1(A,k16_lattice3(A,B)) = k15_lattice3(A,a_2_0_quantal1(A,B)) ) )).
fof(t25_quatern2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k27_quaterni(k6_quaterni(A,B,C,D)) = k6_quaterni(A,k4_xcmplx_0(B),k4_xcmplx_0(C),k4_xcmplx_0(D)) ) ) ) ) )).
fof(t25_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k14_quaterni(k21_quaterni(k7_xcmplx_0(1,k1_square_1(k28_quaterni(A))),k27_quaterni(A))) = k4_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k28_quaterni(A))),k14_quaterni(A))) ) )).
fof(t25_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ( ( k13_quaterni(A) = k13_quaterni(B) & k14_quaterni(A) = k14_quaterni(B) & k15_quaterni(A) = k15_quaterni(B) & k16_quaterni(A) = k16_quaterni(B) ) => A = B ) ) ) )).
fof(t25_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(k1_quin_1(A,B,C),k5_numbers) & r1_xxreal_0(k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A)),k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A))) ) ) ) ) )).
fof(t25_quofield,axiom,( ! [A] : ( ( ~ 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] : ( 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 ) ) ) )).
fof(t25_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_random_1(C,A,B) => ! [D] : ( v1_xreal_0(D) => ( r1_xxreal_0(k5_numbers,D) => m1_random_1(k2_mesfun6c(D,A,k7_random_1(A,B,C)),A,B) ) ) ) ) ) )).
fof(t25_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_6(C,A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t25_rat_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_rat_1(C) => ~ ( C = k7_xcmplx_0(A,B) & B != k5_numbers & ! [D] : ( v1_int_1(D) => ~ ( A = k3_xcmplx_0(k2_rat_1(C),D) & B = k3_xcmplx_0(k1_rat_1(C),D) ) ) ) ) ) ) )).
fof(t25_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v4_ratfunc1(B,A) & v5_ratfunc1(B,A) & m1_ratfunc1(B,A) ) => k11_ratfunc1(A,B) = k6_ratfunc1(A,B) ) ) )).
fof(t25_rcomp_3,axiom,( ! [A] : ( ( v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( ( v3_xxreal_2(A) & r2_hidden(k3_seq_4(A),A) ) => ( v4_xxreal_2(A) | A = k2_limfunc1(k3_seq_4(A)) ) ) ) )).
fof(t25_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ? [C] : ( v7_ordinal1(C) & k9_nat_1(k4_ordinal1,k2_real_3(B,A),C) = k5_numbers & k9_nat_1(k4_ordinal1,k1_real_3(B,A),C) = k5_numbers ) ) ) )).
fof(t25_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k6_real_lat(A))) => ! [C] : ( 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 ) ) ) ) )).
fof(t25_realset2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k3_rlvect_1(A,B,C) = k3_rlvect_1(A,B,D) => C = D ) ) ) ) ) )).
fof(t25_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_subset_1(D,u1_struct_0(A),k8_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t25_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [D] : ( ( v1_rearran1(D) & v2_rearran1(D) & v3_rearran1(D,k1_zfmisc_1(A)) & m2_finseq_1(D,k1_zfmisc_1(A)) ) => ( ( v1_partfun1(C,B) & k5_card_1(A) = k5_card_1(B) ) => k21_rfunct_3(A,k4_rearran1(B,A,D,C),A) = k21_rfunct_3(B,C,B) ) ) ) ) ) )).
fof(t25_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => ! [D] : ( v1_relat_1(D) => ( ( r1_tarski(A,C) & r1_tarski(B,D) ) => r1_tarski(k3_relat_1(A,B),k3_relat_1(C,D)) ) ) ) ) ) )).
fof(t25_relset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ! [D] : ( r2_hidden(D,k2_relset_1(B,C)) <=> ? [E] : ( m1_subset_1(E,A) & r2_hidden(k4_tarski(E,D),C) ) ) ) ) ) )).
fof(t25_relset_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,A))) => ( r2_hidden(D,k6_relset_2(B,A,C,E)) <=> ! [F] : ( r2_hidden(F,C) => r2_hidden(D,k1_relset_2(B,A,E,F)) ) ) ) ) ) ) )).
fof(t25_revrot_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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),k1_nat_1(k7_nat_d(A,k4_finseq_4(C,B)),1)) ) ) ) ) ) )).
fof(t25_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r1_rewrite1(A,B,C) => ( r2_rewrite1(A,B,C) & r2_rewrite1(A,C,B) ) ) ) )).
fof(t25_rewrite2,axiom,( ! [A] : ! [B] : ( 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))) ) ) )).
fof(t25_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k8_afinsq_1(C)) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k8_afinsq_1(C))) => ! [H] : ( 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)) ) ) ) ) ) ) ) )).
fof(t25_rfinseq,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => k8_relset_1(k4_ordinal1,k1_numbers,k10_rvsum_1(A,k5_numbers),k1_tarski(k5_numbers)) = k4_finseq_1(A) ) )).
fof(t25_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( r2_classes1(A,B) => r2_classes1(k6_rvsum_1(A),k6_rvsum_1(B)) ) ) ) )).
fof(t25_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( v1_xcmplx_0(B) => k54_valued_1(k24_valued_1(A,B)) = k24_valued_1(k54_valued_1(A),k9_complex1(B)) ) ) )).
fof(t25_rfunct_2,axiom,( ! [A] : ! [B] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( 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_funct_1(B,D),k1_funct_1(B,C)) ) ) ) ) ) )).
fof(t25_rfunct_4,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(t25_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v8_valued_0(A) & v2_seq_2(A) ) => k1_seq_2(A) = k2_rinfsup1(A) ) ) )).
fof(t25_rinfsup2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v8_valued_0(B) => ( v8_valued_0(k1_valued_0(k6_numbers,B,A)) & k2_rinfsup2(B) = k2_rinfsup2(k1_valued_0(k6_numbers,B,A)) ) ) ) ) )).
fof(t25_rlaffin1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(t25_rlaffin2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_rlvect_2(E,C) => ! [F] : ( m1_rlvect_2(F,C) => ! [G] : ( v1_xreal_0(G) => ~ ( 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,k6_xcmplx_0(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,k6_xcmplx_0(1,B),F)),D)) & ! [H] : ( v1_xreal_0(H) => ~ ( k3_funct_2(u1_struct_0(C),k1_numbers,k7_rlvect_2(C,k8_rlvect_2(C,H,E),k8_rlvect_2(C,k6_xcmplx_0(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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t25_rlaffin3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_rlaffin1(C,k15_euclid(A)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) => ! [E] : ( m2_rlaffin3(E,k15_euclid(A),C) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( ( r1_xxreal_0(B,A) & k5_card_1(C) = k2_xcmplx_0(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)) ) ) ) ) ) ) ) ) )).
fof(t25_rlsub_1,axiom,( ! [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) ) => m1_rlsub_1(A,A) ) )).
fof(t25_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( 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))) ) ) ) ) )).
fof(t25_rltopsp1,axiom,( ! [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) ) => ! [B] : ( ( v2_rltopsp1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => r2_hidden(k4_algstr_0(A,C),B) ) ) ) ) )).
fof(t25_rlvect_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( 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)) ) ) ) )).
fof(t25_rlvect_2,axiom,( ! [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) ) => ! [B] : ( ( 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(k4_ordinal1,u1_struct_0(A),k5_rlvect_2(A,k2_pre_poly(u1_struct_0(A)),B),k2_pre_poly(u1_struct_0(A))) ) ) )).
fof(t25_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( k1_rlvect_3(A,B) = A & ! [C] : ( 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 ) ) ) ) ) )).
fof(t25_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( v1_rlvect_3(k8_domain_1(u1_struct_0(A),B,D,C),A) => ( B = C | B = D | C = D | v1_rlvect_3(k8_domain_1(u1_struct_0(A),B,D,k3_rlvect_1(A,C,B)),A) ) ) ) ) ) ) )).
fof(t25_rlvect_5,axiom,( ! [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) ) => ( v1_rlvect_5(A) => ! [B] : ( m1_rlvect_3(B,A) => ! [C] : ( m1_rlvect_3(C,A) => k1_card_1(B) = k1_card_1(C) ) ) ) ) )).
fof(t25_rlvect_x,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( r2_hidden(C,k2_rlvect_x(A,B)) <=> ? [D] : ( m2_finseq_1(D,u1_struct_0(A)) & ? [E] : ( m2_finseq_1(E,u1_struct_0(A)) & ? [F] : ( 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] : ( 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_funct_1(F,G)) ) ) ) ) ) ) ) ) )).
fof(t25_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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 ) ) ) ) )).
fof(t25_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t25_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t25_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t25_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_robbins1(A,k3_robbins1(A,k1_lattices(A,B,C))) = k1_lattices(A,C,B) ) ) ) )).
fof(t25_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v1_lattice3(A) & v2_lattice3(A) & v10_robbins3(A) & l4_robbins3(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k10_lattice3(A,B,C) = k5_robbins3(A,B,C) ) ) ) )).
fof(t25_robbins4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k2_robbins4)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_robbins4)) => ( A = k5_numbers => k4_lattices(k2_robbins4,A,B) = A ) ) ) )).
fof(t25_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t25_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => r1_xxreal_0(k1_rpr_1(A,k4_subset_1(A,B,C)),k2_xcmplx_0(k1_rpr_1(A,B),k1_rpr_1(A,C))) ) ) ) )).
fof(t25_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k9_rsspace4(A,B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k9_rsspace4(A,B))))) ) => ( v1_rsspace3(C,k9_rsspace4(A,B)) => v3_normsp_1(C,k9_rsspace4(A,B)) ) ) ) ) ) )).
fof(t25_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_bhsp_1(B) & m1_rusub_1(B,A) ) => ! [C] : ( ( v1_bhsp_1(C) & m1_rusub_1(C,A) ) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_struct_0(B,D) <=> r1_struct_0(C,D) ) ) => B = C ) ) ) ) )).
fof(t25_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( 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))) ) ) ) ) )).
fof(t25_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_rlvect_3(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t25_rusub_4,axiom,( ! [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) ) => ! [B] : ( ( v2_rusub_4(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( r2_hidden(k4_struct_0(A),B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(C,B) => r2_hidden(k1_rlvect_1(A,C,D),B) ) ) ) ) ) ) )).
fof(t25_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( ~ 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)))) ) ) )).
fof(t25_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k4_finseq_2(A,k1_numbers)) => ( k5_rvsum_1(A,C,B) = k5_rvsum_1(A,D,B) => C = D ) ) ) ) ) )).
fof(t25_rvsum_2,axiom,( ! [A] : ( ( 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) ) )).
fof(t25_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_3(k4_scmfsa_2(k5_numbers),1)),B) & r1_tarski(C,A) ) => ( r4_scmfsa7b(C,D) | ! [E] : ( v7_ordinal1(E) => k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B,E),D) = k1_funct_1(B,D) ) ) ) ) ) ) ) )).
fof(t25_scmfsa10,axiom,( ! [A] : ( 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) ) ) )).
fof(t25_scmfsa6a,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => k5_card_1(k6_scmfsa6a(A,B)) = 4 ) ) )).
fof(t25_scmfsa8a,axiom,( ! [A] : ( v7_ordinal1(A) => ( r2_hidden(k5_numbers,k2_afinsq_1(k1_scmfsa8a(A))) & k1_funct_1(k1_scmfsa8a(A),k5_numbers) = k11_scmfsa_2(A) ) ) )).
fof(t25_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( 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(k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),k5_card_1(D)),7)))) ) ) ) ) ) ) ) )).
fof(t25_scmfsa8c,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => k1_funct_1(k1_scmfsa8b(C,A,B),k1_nat_1(k1_nat_1(k5_card_1(A),k5_card_1(B)),3)) = k2_compos_1(k1_scmfsa_2) ) ) ) )).
fof(t25_scmfsa9a,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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_sf_mastr(k2_scmfsa_9(A,B)) = k4_sf_mastr(B) ) ) )).
fof(t25_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ~ ( k2_compos_0(u1_compos_1(k1_scmfsa_2),A) = 3 & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => A != k8_scmfsa_2(B,C) ) ) ) ) )).
fof(t25_scmfsa_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [B] : ( ( v1_ami_2(B) & ~ v1_scmfsa_m(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ( ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1))) & ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ( ~ ( r1_xxreal_0(k1_funct_1(C,D),k3_funct_2(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,C,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_scmfsa_9(D,A,B,E),1))) & k1_funct_1(C,D) != k5_numbers ) & ~ ( k1_funct_1(C,D) = k5_numbers & k1_funct_1(D,B) = k5_numbers ) & ( k1_funct_1(D,B) != k5_numbers => k1_funct_1(C,D) = k5_numbers ) ) ) ) ) => v7_amistd_1(k1_scmfsa_9(B,A),k7_card_1(3),k1_scmfsa_2) ) ) ) )).
fof(t25_scmfsa_m,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ r2_hidden(k9_scmfsa_m(B,A),A) ) ) )).
fof(t25_scmpds_5,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t25_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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) ) ) ) ) )).
fof(t25_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [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_partfun1(D,u1_struct_0(k1_scmpds_2)) & v5_memstr_0(D,2,k1_scmpds_2,k5_numbers) ) => ! [E] : ( v7_ordinal1(E) => ~ ( 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) ) ) ) ) ) ) )).
fof(t25_scmpds_8,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ! [F] : ( v1_int_1(F) => ! [G] : ! [H] : ( ( ! [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] : ( ( 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,k5_numbers) ) => ! [J] : ( ( v1_relat_1(J) & v4_relat_1(J,k4_ordinal1) & v5_relat_1(J,u1_compos_1(k1_scmpds_2)) & v1_funct_1(J) & v1_partfun1(J,k4_ordinal1) ) => ( ( ! [K] : ( ( 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] : ( ( 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)),k5_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] : ( ( 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] : ( ( 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)),k5_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) ) ) ) ) ) ) ) ) ) )).
fof(t25_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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(k4_ordinal1)) = k2_ami_2 ) )).
fof(t25_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t25_scmyciel,axiom,( ! [A] : v4_scmyciel(k2_tarski(k1_xboole_0,k1_tarski(A))) )).
fof(t25_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_semi_af1(A,B,C,D) ) ) ) ) ) )).
fof(t25_seq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k26_valued_1(k4_ordinal1,k1_numbers,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,B),A),k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k26_valued_1(k4_ordinal1,k1_numbers,C,A),B)) ) ) ) )).
fof(t25_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(A) & v1_comseq_2(B) & k1_seq_2(A) = k5_numbers ) => v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) ) ) )).
fof(t25_seq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v3_funct_1(B) => ( ( ~ r2_hidden(A,k1_rvsum_1(B)) & ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,B,C) != A ) ) | k1_seq_2(B) = A ) ) ) ) )).
fof(t25_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( r1_seqfunc(A,k1_numbers,B,C) => ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,C) => r1_seqfunc(A,k1_numbers,B,k1_tarski(D)) ) ) ) ) ) )).
fof(t25_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v8_valued_0(A) & m2_valued_0(B,k1_numbers,A) ) => v8_valued_0(B) ) ) ) )).
fof(t25_series_3,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,k9_complex1(B)) => r1_xxreal_0(k1_square_1(A),k1_square_1(B)) ) ) ) )).
fof(t25_series_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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(k1_square_1(A),B),k3_xcmplx_0(k1_square_1(B),C)),k3_xcmplx_0(k1_square_1(C),A)),k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k1_square_1(B)),k3_xcmplx_0(B,k1_square_1(C))),k3_xcmplx_0(C,k1_square_1(A)))) ) ) ) ) )).
fof(t25_setfam_1,axiom,( ! [A] : ! [B] : k3_xboole_0(A,k3_tarski(B)) = k3_tarski(k3_setfam_1(k1_tarski(A),B)) )).
fof(t25_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_setlim_1(k2_setlim_1(A,B),A) & v1_setlim_1(k4_setlim_1(A,B),A) ) ) )).
fof(t25_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(C) => v3_prob_1(k6_setlim_2(A,C,B)) ) ) ) )).
fof(t25_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t25_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( v7_ordinal1(B) => k2_sf_mastr(A) = k2_sf_mastr(k6_compos_1(k1_scmfsa_2,A,B)) ) ) )).
fof(t25_sfmastr3,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & ~ v1_scmfsa_m(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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] : ( v7_ordinal1(F) => ! [G] : ( ( v1_relat_1(G) & v4_relat_1(G,k4_ordinal1) & v5_relat_1(G,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(G) & v1_partfun1(G,k4_ordinal1) ) => ( ( k1_funct_1(A,k4_scmfsa_2(k5_numbers)) = 1 & F = k2_xcmplx_0(k6_xcmplx_0(k1_funct_1(A,D),k1_funct_1(A,C)),1) ) => ( ( ~ r1_sfmastr3(G,B,C,D,E,A) & ~ v7_amistd_1(E,k7_card_1(3),k1_scmfsa_2) ) | k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(k2_sfmastr3(B,C,D,E),A,G)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k1_sfmastr3(G,B,C,D,E,A),F)) ) ) ) ) ) ) ) ) ) )).
fof(t25_sgraph1,axiom,( ! [A] : r2_sgraph1(A,k3_sgraph1(A)) )).
fof(t25_sheffer1,axiom,( ! [A] : ( ( ~ 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) ) ) ) )).
fof(t25_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t25_simplex0,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t25_simplex1,axiom,( ! [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) ) => ! [B] : ( ( v1_matroid0(B) & m1_simplex0(B,u1_struct_0(A)) ) => ( v2_simplex1(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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 ) ) ) ) ) ) ) )).
fof(t25_simplex2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_rlaffin1(B,k15_euclid(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ( k5_card_1(B) = k2_xcmplx_0(A,1) => k2_topdim_1(k15_euclid(A),k3_convex1(k15_euclid(A),B)) = A ) ) ) )).
fof(t25_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => k15_sin_cos(k3_xcmplx_0(A,k7_complex1)) = k2_xcmplx_0(k19_sin_cos(A),k3_xcmplx_0(k17_sin_cos(A),k7_complex1)) ) )).
fof(t25_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k2_xcmplx_0(k1_square_1(k1_funct_1(k1_sin_cos2,A)),k1_square_1(k1_funct_1(k3_sin_cos2,B))) = k3_xcmplx_0(k1_funct_1(k3_sin_cos2,k2_xcmplx_0(A,B)),k1_funct_1(k3_sin_cos2,k6_xcmplx_0(A,B))) & k3_xcmplx_0(k1_funct_1(k3_sin_cos2,k2_xcmplx_0(A,B)),k1_funct_1(k3_sin_cos2,k6_xcmplx_0(A,B))) = k2_xcmplx_0(k1_square_1(k1_funct_1(k3_sin_cos2,A)),k1_square_1(k1_funct_1(k1_sin_cos2,B))) & k2_xcmplx_0(k1_square_1(k1_funct_1(k1_sin_cos2,A)),k1_square_1(k1_funct_1(k3_sin_cos2,B))) = k2_xcmplx_0(k1_square_1(k1_funct_1(k3_sin_cos2,A)),k1_square_1(k1_funct_1(k1_sin_cos2,B))) ) ) ) )).
fof(t25_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k15_sin_cos(A) = k2_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A)) ) )).
fof(t25_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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),k19_sin_cos(B))) ) ) )).
fof(t25_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => k1_newton(k19_sin_cos(A),4) = k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(3,k3_xcmplx_0(4,k19_sin_cos(k3_xcmplx_0(2,A)))),k19_sin_cos(k3_xcmplx_0(4,A))),8) ) )).
fof(t25_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( k19_sin_cos(A) = k4_xcmplx_0(1) => A = k2_xcmplx_0(k28_sin_cos,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k1_int_1(k7_xcmplx_0(A,k3_xcmplx_0(2,k28_sin_cos))))) ) ) )).
fof(t25_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( r1_xxreal_0(1,A) & r1_xxreal_0(k6_xcmplx_0(A,k3_square_1(k6_xcmplx_0(k1_square_1(A),1))),k5_numbers) ) ) )).
fof(t25_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(k5_numbers,A) => k2_sin_cos2(k7_xcmplx_0(A,2)) = k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k6_xcmplx_0(k4_sin_cos2(A),1),2))) ) ) )).
fof(t25_sin_cos9,axiom,( k2_partfun1(k1_numbers,k1_numbers,k1_sin_cos9,k1_rcomp_1(k4_xcmplx_0(1),1)) = k2_partfun2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k26_sin_cos,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)),k7_xcmplx_0(k28_sin_cos,4)))) )).
fof(t25_sincos10,axiom,( k2_relset_1(k1_numbers,k1_sincos10) = k3_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)) )).
fof(t25_sppol_1,axiom,( ! [A] : ( 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))))) ) )).
fof(t25_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ( 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)) ) ) ) ) )).
fof(t25_sprect_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t25_sprect_3,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t25_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t25_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k3_square_1(A),k5_numbers) ) ) )).
fof(t25_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => k11_stacks_1(A,B) = a_2_0_stacks_1(A,B) ) ) )).
fof(t25_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => m1_subset_1(k1_card_1(a_2_0_stirl2_1(A,B)),k4_ordinal1) ) ) )).
fof(t25_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_valuat_1(C,A,B) => ! [D] : ( m2_subset_1(D,k16_substut1(A),k38_substut1(A)) => ! [E] : ( m2_subset_1(E,k16_substut1(A),k38_substut1(A)) => ( ( k19_substut1(A,D) = k19_substut1(A,E) & ! [F] : ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t25_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( 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) ) ) ) )).
fof(t25_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( 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 ) )).
fof(t25_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) = k5_numbers ) & ~ ( v4_substut1(B,A) & ! [C] : ( v7_ordinal1(C) => ~ 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 ) ) ) ) )).
fof(t25_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m1_subset_1(C,k1_substut1(A)) => k7_cqc_sim1(A,B) = k7_cqc_sim1(A,k39_substut1(A,k2_substut2(A,B,C))) ) ) ) )).
fof(t25_supinf_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t25_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ~ ( ~ r1_orders_2(B,D,C) & ~ r1_orders_2(B,E,C) & k1_symsp_1(A,B,C,D,E) != k11_algstr_0(A,k1_symsp_1(A,B,C,E,D)) ) ) ) ) ) ) )).
fof(t25_sysrel,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r2_hidden(k4_tarski(B,C),k1_sysrel(A)) => ( r2_hidden(B,k9_xtuple_0(k1_sysrel(A))) & B = C ) ) ) )).
fof(t25_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),k1_numbers))) ) => ! [C] : ( ( 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,k5_numbers))) & v1_taxonom1(B,A) & v2_metric_1(B,A) & v3_metric_1(B,A) ) => k8_eqrel_1(A,C) = k10_eqrel_1(A) ) ) ) ) )).
fof(t25_taylor_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( 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,k1_nat_1(A,1),k2_rcomp_1(D,E)) ) => ( r1_xxreal_0(E,D) | ! [F] : ( v1_xreal_0(F) => ! [G] : ( ( 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] : ( v1_xreal_0(H) => k1_funct_1(G,H) = k6_xcmplx_0(k6_xcmplx_0(k1_funct_1(B,E),k9_nat_1(k1_numbers,k3_series_1(k6_taylor_1(B,C,H,E)),A)),k7_xcmplx_0(k3_xcmplx_0(F,k1_newton(k6_xcmplx_0(E,H),k1_nat_1(A,1))),k2_newton(k1_nat_1(A,1)))) ) & k6_xcmplx_0(k6_xcmplx_0(k1_funct_1(B,E),k9_nat_1(k1_numbers,k3_series_1(k6_taylor_1(B,C,D,E)),A)),k7_xcmplx_0(k3_xcmplx_0(F,k1_newton(k6_xcmplx_0(E,D),k1_nat_1(A,1))),k2_newton(k1_nat_1(A,1)))) = k5_numbers ) => ( r2_fdiff_1(G,k2_rcomp_1(D,E)) & k1_funct_1(G,D) = k5_numbers & k1_funct_1(G,E) = k5_numbers & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,G,k1_rcomp_1(D,E))) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,k2_rcomp_1(D,E)) => k1_fdiff_1(G,H) = k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(B,k2_rcomp_1(D,E)),k1_nat_1(A,1)),H),k1_newton(k6_xcmplx_0(E,H),A)),k2_newton(A))),k7_xcmplx_0(k3_xcmplx_0(F,k1_newton(k6_xcmplx_0(E,H),A)),k2_newton(A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t25_taylor_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ r1_xxreal_0(A,k5_numbers) => ( k3_funct_2(k4_ordinal1,k1_numbers,k3_series_1(k1_taylor_2(k16_sin_cos,k2_rcomp_1(k4_xcmplx_0(A),A),B)),k1_nat_1(k2_nat_1(2,C),1)) = k3_funct_2(k4_ordinal1,k1_numbers,k3_series_1(k20_sin_cos(B)),C) & k3_funct_2(k4_ordinal1,k1_numbers,k3_series_1(k1_taylor_2(k18_sin_cos,k2_rcomp_1(k4_xcmplx_0(A),A),B)),k1_nat_1(k2_nat_1(2,C),1)) = k3_funct_2(k4_ordinal1,k1_numbers,k3_series_1(k21_sin_cos(B)),C) ) ) ) ) ) )).
fof(t25_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)),k2_xcmplx_0(k3_tbsp_1(A,B),k3_tbsp_1(A,C))) ) ) ) ) ) )).
fof(t25_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t25_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) )).
fof(t25_tdlat_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) )).
fof(t25_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t25_tex_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ 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] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(t25_tex_2,axiom,( ! [A] : ( l1_pre_topc(A) => ( ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t25_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t25_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(t25_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( ( m1_pre_topc(C,B) & m1_pre_topc(D,B) ) => ( r1_tsep_1(C,D) | m1_pre_topc(k2_tsep_1(A,C,D),B) ) ) ) ) ) ) )).
fof(t25_toler_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : ! [E] : ( r2_hidden(k4_tarski(D,E),B) <=> ? [F] : ( r2_hidden(F,A) & r2_hidden(D,F) & r2_hidden(E,F) ) ) & ! [D] : ! [E] : ( r2_hidden(k4_tarski(D,E),C) <=> ? [F] : ( r2_hidden(F,A) & r2_hidden(D,F) & r2_hidden(E,F) ) ) ) => r2_relset_1(k3_tarski(A),k3_tarski(A),B,C) ) ) ) )).
fof(t25_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r1_borsuk_6(A,B,C) & r1_borsuk_6(A,B,D) ) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t25_topalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t25_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ! [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] : ( m1_borsuk_2(J,k2_borsuk_1(A,B),k4_borsuk_1(A,B,D,G),k4_borsuk_1(A,B,E,H)) => ! [K] : ( m1_borsuk_2(K,B,F,G) => ! [L] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t25_topalg_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( m1_borsuk_2(B,k2_topalg_2,k4_toprealb(k5_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)) ) ) )).
fof(t25_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t25_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t25_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t25_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ~ v4_pre_topc(B,A) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t25_topgen_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => r1_xxreal_0(k4_series_1(k8_nat_1(k1_numbers,k4_topgen_3(A,k7_xcmplx_0(1,2)),k1_nat_1(B,1))),k1_newton(k7_xcmplx_0(1,2),B)) ) )).
fof(t25_topgen_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( 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))) ) ) )).
fof(t25_topgen_5,axiom,( 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))) )).
fof(t25_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) ) ) )).
fof(t25_topreal1,axiom,( ! [A] : ( 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)) ) ) )).
fof(t25_topreal4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( v2_topreal4(C,k15_euclid(2)) & r2_hidden(A,C) & B = a_2_1_topreal4(A,C) ) => v3_pre_topc(B,k15_euclid(2)) ) ) ) ) )).
fof(t25_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ~ ( D = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),B,k6_xcmplx_0(1,A)),k1_rlvect_1(k15_euclid(2),C,A)) & D != B & r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,k5_numbers) ) ) ) ) ) )).
fof(t25_topreal7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => r1_t_0topsp(k2_borsuk_1(k3_pcomps_1(k14_euclid(A)),k3_pcomps_1(k14_euclid(B))),k3_pcomps_1(k14_euclid(k1_nat_1(A,B)))) ) ) )).
fof(t25_topreal8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t25_topreal9,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_hidden(B,k4_topreal9(A,B,C)) ) ) ) )).
fof(t25_topreala,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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)))) ) ) ) ) ) )).
fof(t25_toprealc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => k2_rltopsp1(k15_euclid(A),B) = k2_toprealc(B) ) ) )).
fof(t25_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => r1_xxreal_0(k5_numbers,k12_euclid(B)) ) ) )).
fof(t25_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) <=> ! [C] : ( r2_hidden(C,B) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D,A) & r1_tarski(D,B) & r2_hidden(C,D) ) ) ) ) ) )).
fof(t25_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_pre_topc(C,A) => ( v3_pre_topc(B,A) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) => ( D = B => v3_pre_topc(D,C) ) ) ) ) ) ) )).
fof(t25_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v3_tops_1(B,A) & v1_tops_1(B,A) ) ) ) )).
fof(t25_transgeo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_transgeo(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t25_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t25_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( ( v2_trees_2(D,A) & m1_trees_2(D,A) ) => ( ( r1_tarski(B,C) & r2_hidden(C,D) ) => r2_hidden(B,D) ) ) ) ) ) )).
fof(t25_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t25_trees_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t25_trees_9,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v3_trees_3(B) ) => ( v1_xboole_0(k12_trees_9(B,A)) <=> ! [C] : ( m1_subset_1(C,B) => ( v1_zfmisc_1(C) & ~ r2_hidden(k1_funct_1(C,k1_xboole_0),A) ) ) ) ) )).
fof(t25_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_tsep_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t25_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(D))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t25_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t25_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k9_funct_2(k4_numbers,u1_turing_1(A)))) => ! [C] : ! [D] : ! [E] : ( 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),k1_enumset1(k4_xcmplx_0(1),k5_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),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),k8_turing_1(A,B)))) ) ) ) ) )).
fof(t25_twoscomp,axiom,( k1_funct_1(k28_twoscomp,k11_finseq_1(k5_numbers,k5_numbers,k5_numbers)) = 1 & k1_funct_1(k28_twoscomp,k11_finseq_1(k5_numbers,k5_numbers,1)) = 1 & k1_funct_1(k28_twoscomp,k11_finseq_1(k5_numbers,1,k5_numbers)) = 1 & k1_funct_1(k28_twoscomp,k11_finseq_1(k5_numbers,1,1)) = 1 & k1_funct_1(k28_twoscomp,k11_finseq_1(1,k5_numbers,k5_numbers)) = 1 & k1_funct_1(k28_twoscomp,k11_finseq_1(1,k5_numbers,1)) = 1 & k1_funct_1(k28_twoscomp,k11_finseq_1(1,1,k5_numbers)) = 1 & k1_funct_1(k28_twoscomp,k11_finseq_1(1,1,1)) = k5_numbers )).
fof(t25_unialg_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t25_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k2_numbers) => ! [C] : ( m1_subset_1(C,k2_numbers) => ( ( r2_hidden(B,k2_uniroots(A)) & r2_hidden(C,k2_uniroots(A)) ) => r2_hidden(k3_xcmplx_0(B,C),k2_uniroots(A)) ) ) ) ) )).
fof(t25_uproots,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r2_funct_2(k4_ordinal1,u1_struct_0(A),k11_polynom3(A,B,C),k11_polynom3(A,B,D)) => ( B = k9_polynom3(A) | r2_funct_2(k4_ordinal1,u1_struct_0(A),C,D) ) ) ) ) ) ) )).
fof(t25_urysohn2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,A) & ! [C] : ( v1_xreal_0(C) => ~ ( r2_hidden(C,k3_urysohn1) & ~ r1_xxreal_0(C,A) & ~ r1_xxreal_0(B,C) ) ) ) ) ) )).
fof(t25_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t25_valued_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ( ! [C] : ( v7_ordinal1(C) => k9_nat_1(A,B,C) = k9_nat_1(A,B,k1_nat_1(C,1)) ) => v3_funct_1(B) ) ) ) )).
fof(t25_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( v7_ordinal1(B) => r1_tarski(k10_xtuple_0(k61_valued_1(A,B)),k10_xtuple_0(A)) ) ) )).
fof(t25_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t25_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(k6_vectsp10(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t25_vectsp11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( ~ 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] : ( ( 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)) ) ) ) ) )).
fof(t25_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t25_vectsp_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ v2_struct_0(C) & l2_vectsp_2(C,A,B) ) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(C)) => ! [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) ) ) ) ) ) )).
fof(t25_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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 ) ) ) ) )).
fof(t25_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t25_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t25_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_vectsp_4(C,A,B) => r1_xxreal_0(k1_vectsp_9(A,C),k1_vectsp_9(A,B)) ) ) ) )).
fof(t25_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t25_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t25_waybel10,axiom,( ! [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] : ( ( 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) ) ) ) )).
fof(t25_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_waybel11(A,B))) => C = B ) ) ) )).
fof(t25_waybel12,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(t25_waybel14,axiom,( ! [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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_yellow_1(k5_waybel11(A))))) => ! [C] : ( ( 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,k1_yellow_1(k5_waybel11(A))) ) ) ) ) )).
fof(t25_waybel15,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(t25_waybel16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_waybel_6(B,A) => r1_tarski(k1_waybel16(A),B) ) ) ) )).
fof(t25_waybel17,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [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) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) )).
fof(t25_waybel19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ! [E] : ( 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)) ) ) ) ) ) )).
fof(t25_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t25_waybel21,axiom,( ! [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] : ( ( ~ 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))) ) ) ) )).
fof(t25_waybel23,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t25_waybel24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [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) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_yellow_1(u1_struct_0(A),B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_funct_1(k1_yellow_0(k5_yellow_1(u1_struct_0(A),B),C),D) = k1_yellow_0(B,a_4_1_waybel24(A,B,C,D)) ) ) ) ) )).
fof(t25_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(t25_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t25_waybel27,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(t25_waybel28,axiom,( ! [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] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_yellow_6(C,A,k4_waybel17(A,B)) => k1_waybel11(A,C) = k1_yellow_0(A,B) ) ) ) )).
fof(t25_waybel29,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & l1_pre_topc(A) ) => ( v3_waybel_3(k1_yellow_1(u1_pre_topc(A))) <=> ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => v23_waybel_0(k3_waybel29(B,A),k1_yellow_1(u1_pre_topc(k2_borsuk_1(B,A))),k3_waybel24(B,k1_waybel29(k1_yellow_1(u1_pre_topc(A))))) ) ) ) )).
fof(t25_waybel30,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_waybel30(A,k6_waybel_0(A,B)) = k2_waybel_3(A,B) ) ) )).
fof(t25_waybel31,axiom,( ! [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] : ( ( v2_pre_topc(B) & v2_waybel19(B) & m1_yellow_9(B,A) ) => k1_waybel31(A) = k2_waybel23(B) ) ) )).
fof(t25_waybel32,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(t25_waybel33,axiom,( ! [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] : ( ( v1_waybel33(B) & m1_yellow_9(B,A) ) => ! [C] : ( ( v2_pre_topc(C) & v2_waybel19(C) & m1_yellow_9(C,A) ) => m2_yellow_9(B,C) ) ) ) )).
fof(t25_waybel34,axiom,( ! [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] : ( ( 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] : ( ( 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] : ( ( v4_waybel11(D) & m1_yellow_9(D,B) ) => ! [E] : ( ( v4_waybel11(E) & m1_yellow_9(E,A) ) => ! [F] : ( ( 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))) ) ) ) ) ) ) )).
fof(t25_waybel35,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_waybel35(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ( ( v3_waybel35(C,A,B) & m1_waybel35(C,A,B) ) => r1_waybel35(A,k6_waybel35(A,B,C),B) ) ) ) )).
fof(t25_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t25_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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] : ( 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))) ) ) ) ) ) ) )).
fof(t25_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ! [C] : ( ( 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)))) ) ) )).
fof(t25_waybel_3,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t25_waybel_4,axiom,( ! [A] : ( ( 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(k1_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(k1_yellow_1(k7_waybel_0(A)))))) ) ) )).
fof(t25_waybel_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t25_waybel_6,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v5_waybel_6(B,A) <=> ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k2_yellow_1(k1_tarski(C)))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k2_yellow_1(k1_tarski(C)))))) ) => ( ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k3_funct_2(u1_struct_0(A),u1_struct_0(k2_yellow_1(k1_tarski(C))),D,E) = k1_xboole_0 <=> r3_orders_2(A,E,B) ) ) => ( v19_waybel_0(D,A,k2_yellow_1(k1_tarski(C))) & v20_waybel_0(D,A,k2_yellow_1(k1_tarski(C))) ) ) ) ) ) ) )).
fof(t25_waybel_7,axiom,( ! [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] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t25_waybel_8,axiom,( ! [A] : ( ( 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] : ( ( 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))) ) ) ) )).
fof(t25_waybel_9,axiom,( ! [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) & l1_waybel_9(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & v3_yellow_6(B,A) & l1_waybel_0(B,A) ) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t25_weddwitt,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_tarski(u1_struct_0(k4_weddwitt(A)),u1_struct_0(k5_weddwitt(A,B))) ) ) )).
fof(t25_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [C] : ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t25_wellord1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( v2_wellord1(B) => v2_wellord1(k2_wellord1(B,A)) ) ) )).
fof(t25_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ? [C] : ( v1_rat_1(C) & A = k1_newton(C,B) ) & ! [C] : ( v7_ordinal1(C) => A != k1_newton(C,B) ) ) ) ) )).
fof(t25_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(t25_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( 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)) ) ) ) )).
fof(t25_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => A = k2_xcmplx_0(A,k6_xcmplx_0(B,B)) ) ) )).
fof(t25_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,k4_xcmplx_0(B)) => r1_xxreal_0(B,k4_xcmplx_0(A)) ) ) ) )).
fof(t25_xtuple_0,axiom,( ! [A] : ! [B] : r1_tarski(k4_xboole_0(k9_xtuple_0(A),k9_xtuple_0(B)),k9_xtuple_0(k4_xboole_0(A,B))) )).
fof(t25_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => r1_xxreal_0(A,k4_xxreal_0(A,B)) ) ) )).
fof(t25_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => r1_tarski(k4_xxreal_1(A,B),k1_xxreal_1(A,B)) ) ) )).
fof(t25_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( r1_xxreal_0(A,B) => k2_xxreal_2(k1_xxreal_1(A,B)) = A ) ) ) )).
fof(t25_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k2_xxreal_3(k1_xxreal_3(A,B)) = k3_xxreal_3(k2_xxreal_3(B),A) ) ) )).
fof(t25_yellow10,axiom,( ! [A] : ( ( v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t25_yellow12,axiom,( ! [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] : ( 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) ) ) ) )).
fof(t25_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m2_yellow13(B,A) => ~ v1_xboole_0(B) ) ) )).
fof(t25_yellow14,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t25_yellow15,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t25_yellow16,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( m1_yellow_0(C,B) => ( v4_yellow_0(C,B) <=> ( v4_yellow_0(C,A) & m1_yellow_0(C,A) ) ) ) ) ) )).
fof(t25_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v11_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(t25_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_pre_topc(A,B)) <=> ? [D] : ( ~ v1_xboole_0(D) & v1_subset_1(D,u1_struct_0(k2_yellow_1(k2_struct_0(A)))) & v2_waybel_0(D,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(D,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))))) & r2_hidden(B,D) & r1_waybel_7(A,D,C) ) ) ) ) ) )).
fof(t25_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t25_yellow_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( B = k12_lattice3(A,B,C) <=> r3_orders_2(A,B,C) ) ) ) ) )).
fof(t25_yellow_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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(k1_yellow_1(u1_pre_topc(A))))) ) ) ) )).
fof(t25_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( ! [B] : r2_yellow_0(A,B) => v3_lattice3(A) ) ) )).
fof(t25_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t25_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( ~ 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))) ) ) ) )).
fof(t25_yellow_5,axiom,( ! [A] : ( ( v5_orders_2(A) & v2_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k12_lattice3(A,B,k3_yellow_0(A)) = k3_yellow_0(A) ) ) )).
fof(t25_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m3_yellow_6(C,u1_struct_0(B),A) => ( ( r2_hidden(B,k6_yellow_6(A)) & ! [D] : ( 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)) ) ) ) ) )).
fof(t25_yellow_7,axiom,( ! [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) <=> v2_waybel_1(k7_lattice3(A)) ) ) )).
fof(t25_yellow_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t25_yellow_9,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t25_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( B != D => k3_relat_1(k2_tarski(k4_tarski(A,B),k4_tarski(C,D)),k2_tarski(k4_tarski(B,E),k4_tarski(D,F))) = k2_tarski(k4_tarski(A,E),k4_tarski(C,F)) ) )).
fof(t25_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( k1_funct_1(A,1) = 1 => v3_zf_lang(A) ) ) )).
fof(t25_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v9_zf_lang(A) => k25_zf_lang(A) = k21_zf_lang(k20_zf_lang(A)) ) ) )).
fof(t25_zfmisc_1,axiom,( ! [A] : k3_tarski(k1_tarski(A)) = A )).
fof(t25_zfrefle1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r2_ordinal2(A,B) => ( v4_ordinal1(A) <=> v4_ordinal1(B) ) ) ) ) )).
fof(t25_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => m1_subset_1(C,u1_struct_0(A)) ) ) ) )).
fof(t25_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k18_zmodul02(A,B) = k7_domain_1(u1_struct_0(A),C,D) => ( C = D | k21_zmodul02(A,B) = k3_rlvect_1(A,k1_zmodul01(A,C,k3_funct_2(u1_struct_0(A),k4_numbers,B,C)),k1_zmodul01(A,D,k3_funct_2(u1_struct_0(A),k4_numbers,B,D))) ) ) ) ) ) ) )).
fof(t25_zmodul03,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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) & v1_zmodul03(B) & l1_zmodul01(B) ) => ! [C] : ( m1_zmodul03(C,B) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_zmodul02(A,B)))) ) => ~ ( D = a_3_0_zmodul03(A,B,C) & ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,D,u1_struct_0(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(D,u1_struct_0(B)))) ) => ~ ( ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( r2_hidden(F,C) => k1_funct_1(E,k13_zmodul02(A,B,F)) = F ) ) & v2_funct_1(E) & k1_relset_1(D,E) = D & k2_relset_1(u1_struct_0(B),E) = C ) ) ) ) ) ) ) )).
fof(t260_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ~ r1_xxreal_0(A,C) => r1_tarski(k1_xxreal_1(B,C),k2_xxreal_1(k2_xxreal_0,A)) ) ) ) ) )).
fof(t261_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ~ r1_xxreal_0(A,C) => r1_tarski(k3_xxreal_1(B,C),k2_xxreal_1(k2_xxreal_0,A)) ) ) ) ) )).
fof(t262_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(C,A) => r1_tarski(k4_xxreal_1(B,C),k2_xxreal_1(k2_xxreal_0,A)) ) ) ) ) )).
fof(t263_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(C,A) => r1_tarski(k4_xxreal_1(B,C),k4_xxreal_1(k2_xxreal_0,A)) ) ) ) ) )).
fof(t264_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ~ r1_xxreal_0(A,C) => r1_tarski(k3_xxreal_1(B,C),k4_xxreal_1(k2_xxreal_0,A)) ) ) ) ) )).
fof(t265_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(B,A) => r1_tarski(k1_xxreal_1(C,B),k3_xxreal_1(k2_xxreal_0,A)) ) ) ) ) )).
fof(t266_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(B,A) => r1_tarski(k2_xxreal_1(C,B),k3_xxreal_1(k2_xxreal_0,A)) ) ) ) ) )).
fof(t267_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(A,B) => r1_tarski(k1_xxreal_1(C,B),k4_xxreal_1(k2_xxreal_0,A)) ) ) ) ) )).
fof(t268_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(B,A) => r1_tarski(k2_xxreal_1(C,B),k4_xxreal_1(k2_xxreal_0,A)) ) ) ) ) )).
fof(t269_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) )).
fof(t26_abcmiz_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v9_abcmiz_0(A) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_abcmiz_0(A))) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t26_abcmiz_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( 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))) ) ) )).
fof(t26_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & v1_abcmiz_a(A) & l1_msualg_1(A) ) => ! [B] : ( 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 ) ) ) ) )).
fof(t26_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => r1_xxreal_0(k5_numbers,k2_xcmplx_0(k4_xcmplx_0(A),k9_complex1(A))) ) )).
fof(t26_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ( ( r2_hidden(D,F) & r2_hidden(E,F) & v1_aff_1(F,A) ) => ( D = E | ( r2_aff_1(A,B,C,F) <=> r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) ) ) )).
fof(t26_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_4(D,A) & v1_aff_4(E,A) & v1_aff_1(B,A) & v1_aff_1(C,A) & r1_tarski(B,D) & r1_tarski(C,D) & r1_tarski(B,E) & r1_tarski(C,E) ) => ( B = C | D = E ) ) ) ) ) ) ) )).
fof(t26_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t26_afinsq_2,axiom,( ! [A] : ( ( v1_finset_1(A) & v6_membered(A) ) => ! [B] : ( ( v1_finset_1(B) & v6_membered(B) ) => ~ ( B != k1_xboole_0 & ? [C] : ( r2_hidden(C,A) & r2_afinsq_2(k1_tarski(C),B) ) & ~ r1_xxreal_0(k1_recdef_1(k4_afinsq_2(A),k5_numbers),k1_recdef_1(k4_afinsq_2(B),k5_numbers)) ) ) ) )).
fof(t26_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k13_afproj(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t26_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r2_afvect0(A,B,F,D) & r2_afvect0(A,C,G,E) & r1_afvect0(A,F,G) ) => r2_analoaf(A,B,C,E,D) ) ) ) ) ) ) ) ) )).
fof(t26_algspec1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) => ! [B] : ( m1_algspec1(B,A) => B = k2_funct_1(A) ) ) ) )).
fof(t26_algstr_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k12_algstr_4(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t26_altcat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & m1_altcat_2(B,A) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t26_altcat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v6_altcat_3(B,A) & v6_altcat_3(C,A) ) => r2_altcat_3(A,B,C) ) ) ) ) )).
fof(t26_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t26_ami_3,axiom,( k2_compos_1(k1_ami_3) = k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0) )).
fof(t26_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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,k5_numbers),k1_relset_1(k4_ordinal1,C)) ) ) ) )).
fof(t26_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_analmetr(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k2_analmetr(A,B,C))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k2_analmetr(A,B,C))) => ! [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) ) ) ) ) ) ) ) ) ) ) )).
fof(t26_analoaf,axiom,( ! [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) ) => ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( k3_rlvect_1(A,k1_rlvect_1(A,B,D),k1_rlvect_1(A,C,E)) = k4_struct_0(A) => ( D = k5_numbers & E = k5_numbers ) ) ) ) ) ) => ( ~ v7_struct_0(k2_analoaf(A)) & v2_analoaf(k2_analoaf(A)) & l1_analoaf(k2_analoaf(A)) ) ) ) )).
fof(t26_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t26_anproj_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) & ~ v9_struct_0(C,B) & A = k2_anproj_1(B,C) ) ) ) )).
fof(t26_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_anproj_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_anproj_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_anproj_1(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_anproj_1(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k5_anproj_1(A))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k5_anproj_1(A))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k5_anproj_1(A))) => ~ ( r1_collsp(k5_anproj_1(A),C,H,D) & r1_collsp(k5_anproj_1(A),G,E,D) & r1_collsp(k5_anproj_1(A),C,G,B) & r1_collsp(k5_anproj_1(A),H,E,B) & r1_collsp(k5_anproj_1(A),C,E,F) & r1_collsp(k5_anproj_1(A),H,G,F) & r1_collsp(k5_anproj_1(A),B,D,F) & ~ r1_collsp(k5_anproj_1(A),C,H,E) & ~ r1_collsp(k5_anproj_1(A),C,H,G) & ~ r1_collsp(k5_anproj_1(A),C,G,E) & ~ r1_collsp(k5_anproj_1(A),H,G,E) ) ) ) ) ) ) ) ) ) )).
fof(t26_aofa_000,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r2_hidden(B,k10_aofa_000(A)) <=> ! [C] : ( m5_margrel1(C,u1_struct_0(A),k1_unialg_2(A)) => ~ r2_hidden(B,k2_relset_1(u1_struct_0(A),C)) ) ) ) ) )).
fof(t26_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : k10_xtuple_0(k7_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H),k9_finseq_1(I))) = k7_enumset1(A,B,C,D,E,F,G,H,I) )).
fof(t26_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,B),D)) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,B),E)) => ! [H] : ( m2_pboole(H,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [I] : ( m1_subset_1(I,u4_struct_0(A)) => ( k1_msualg_1(A,I) = k2_finseq_4(u1_struct_0(A),D,E) => ! [J] : ( m1_subset_1(J,k3_msualg_1(A,I,B)) => ( J = k10_finseq_1(F,G) => k5_msualg_3(A,B,C,I,H,J) = k10_finseq_1(k3_funct_2(k1_funct_1(u3_msualg_1(A,B),D),k1_funct_1(u3_msualg_1(A,C),D),k2_msafree4(u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C),H,D),F),k3_funct_2(k1_funct_1(u3_msualg_1(A,B),E),k1_funct_1(u3_msualg_1(A,C),E),k2_msafree4(u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C),H,E),G)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t26_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [E] : ( ( v1_aofa_i00(E,A,B,D) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),D) ) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),E) => ! [G] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t26_armstrng,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k4_armstrng(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ~ ( r2_hidden(B,C) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t26_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( r1_arytm_2(C,B) => k8_arytm_2(A,k1_arytm_1(B,C)) = k2_arytm_1(k8_arytm_2(A,B),k8_arytm_2(A,C)) ) ) ) ) )).
fof(t26_arytm_3,axiom,( ! [A] : ( ( 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 ) ) ) )).
fof(t26_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k7_asympt_0(k1_asympt_0(A,B)) = k7_asympt_0(k5_asympt_0(A,B)) ) ) )).
fof(t26_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ r1_xxreal_0(C,k5_numbers) => k9_nat_1(k1_numbers,A,C) = k2_power(C,k3_power(2,C)) ) ) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ r1_xxreal_0(C,k5_numbers) => k9_nat_1(k1_numbers,B,C) = k2_power(C,k3_square_1(C)) ) ) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & v4_asympt_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v4_asympt_0(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( r2_funct_2(k4_ordinal1,k1_numbers,C,A) & r2_funct_2(k4_ordinal1,k1_numbers,D,B) & r1_tarski(k6_asympt_0(C),k6_asympt_0(D)) & k6_asympt_0(C) != k6_asympt_0(D) ) ) ) ) ) ) )).
fof(t26_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_autalg_1(C,u1_struct_0(A),u3_msualg_1(A,B),k5_autalg_1(A,B)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t26_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_autgroup(A,k2_group_1(A,B)) = k2_funct_1(k6_autgroup(A,B)) ) ) )).
fof(t26_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => v2_bagorder(k7_bagorder(A),A) ) )).
fof(t26_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( r2_hidden(B,k5_bcialg_1(A)) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t26_bcialg_2,axiom,( ! [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) ) => ( v3_bcialg_2(k4_struct_0(A),A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v10_bcialg_1(B,A) ) ) ) )).
fof(t26_bcialg_3,axiom,( ! [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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [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) ) => ( m1_bcialg_3(B,C) => m2_bcialg_1(B,C) ) ) ) ) )).
fof(t26_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t26_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( 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)) ) ) ) ) ) )).
fof(t26_bcialg_6,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( v7_ordinal1(C) => ( ( v1_bcialg_6(B,A) & k4_bcialg_6(A,B) = C ) => k3_bcialg_6(A,C,B) = k4_struct_0(A) ) ) ) ) )).
fof(t26_bciideal,axiom,( ! [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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) )).
fof(t26_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( k3_bhsp_1(A,B) = k5_numbers <=> B = k4_struct_0(A) ) ) ) )).
fof(t26_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)))) & k1_seq_2(k2_bhsp_2(A,k4_normsp_1(A,k2_normsp_1(A,D,E),k3_rlvect_1(A,B,C)))) = k5_numbers ) ) ) ) ) ) ) )).
fof(t26_bhsp_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( v2_bhsp_4(C,B) => v2_bhsp_4(k5_normsp_1(B,C,A),B) ) ) ) ) )).
fof(t26_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t26_binari_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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 ) ) ) )).
fof(t26_binari_4,axiom,( ! [A] : ( v7_ordinal1(A) => k2_binari_4(A,k5_numbers) = k5_euclid(A) ) )).
fof(t26_binom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( 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] : ( v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(k4_ordinal1,A),B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A),B))) & ! [F] : ( m1_subset_1(F,A) => ( k2_binop_1(k4_ordinal1,A,B,E,k5_numbers,F) = C & ! [G] : ( m1_subset_1(G,k4_ordinal1) => k2_binop_1(k4_ordinal1,A,B,E,k1_nat_1(G,1),F) = k2_binop_1(A,B,B,D,F,k2_binop_1(k4_ordinal1,A,B,E,G,F)) ) ) ) ) ) ) ) ) )).
fof(t26_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r3_lattices(A,k7_lattices(A,k3_lattices(A,B,C)),k7_lattices(A,B)) ) ) ) )).
fof(t26_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(B,k10_borsuk_1(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B != k6_domain_1(u1_struct_0(A),C) ) ) ) ) )).
fof(t26_borsuk_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( ( A = B & r1_tarski(k1_rcomp_1(k3_seq_4(B),k2_seq_4(B)),B) ) => k1_rcomp_1(k3_seq_4(B),k2_seq_4(B)) = B ) ) ) )).
fof(t26_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,A) & ! [C] : ( ( v1_xreal_0(C) & ~ v1_rat_1(C) ) => ~ ( ~ r1_xxreal_0(C,A) & ~ r1_xxreal_0(B,C) ) ) ) ) ) )).
fof(t26_borsuk_6,axiom,( ~ 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)))) )).
fof(t26_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ~ ( A != B & A != C & k1_funct_1(k1_borsuk_7(A,B,C,D,E,F),A) != D ) )).
fof(t26_bspace,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k2_bspace)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_bspace)) => ! [D] : ( 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)) ) ) ) )).
fof(t26_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(t26_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t26_bvfunc14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ( 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 ) ) ) ) )).
fof(t26_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t26_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t26_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( 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)) ) ) ) )).
fof(t26_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(E,A) => ( r3_bvfunc_2(A,D,B,E) => r2_funct_2(A,k6_margrel1,k6_bvfunc_2(A,k2_bvfunc_1(A,C,D),B,E),k2_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),D)) ) ) ) ) ) ) )).
fof(t26_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t26_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t26_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t26_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t26_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t26_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t26_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) )).
fof(t26_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [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))) ) => ! [D] : ( 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(k9_complex1(k3_funct_2(A,k1_numbers,C,B)),k2_normsp_0(k11_c0sp1(A),D)) ) ) ) ) ) )).
fof(t26_c0sp2,axiom,( ! [A] : ( ( ~ 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))))) ) ) )).
fof(t26_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [E] : ( m1_subset_1(E,C) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t26_calcul_2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t26_card_1,axiom,( k1_card_1(k1_xboole_0) = k5_ordinal1 )).
fof(t26_card_2,axiom,( ! [A] : ( v1_card_1(A) => ( k3_card_2(A,1) = A & k3_card_2(1,A) = 1 ) ) )).
fof(t26_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( k4_card_3(A) = k1_xboole_0 <=> r2_hidden(k1_xboole_0,k10_xtuple_0(A)) ) ) )).
fof(t26_card_5,axiom,( ! [A] : ! [B] : ( 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) ) ) ) )).
fof(t26_card_fil,axiom,( v5_card_fil(k4_ordinal1) )).
fof(t26_card_fin,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : r1_tarski(k2_card_fin(B,C,D),k2_card_fin(B,k5_relat_1(C,A),D)) ) ) )).
fof(t26_card_lar,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) & ~ v4_card_3(A) ) => ( v5_card_lar(A) => v4_card_lar(A) ) ) )).
fof(t26_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_cat_1(D,A,B,C) => ( k2_cat_1(A,B,C) != k1_xboole_0 => ( v7_cat_1(D,A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_cat_1(F,A,E,B) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) ) ) )).
fof(t26_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => k2_cat_1(k6_cat_2(A,B),k7_cat_2(A,B,C,E),k7_cat_2(A,B,D,F)) = k2_zfmisc_1(k2_cat_1(A,C,D),k2_cat_1(B,E,F)) ) ) ) ) ) ) )).
fof(t26_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,B,C) => ! [F] : ( m1_cat_1(F,A,C,D) => ( v1_cat_3(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,B) = k1_xboole_0 | v1_cat_3(F,A,C,D) ) ) ) ) ) ) ) ) )).
fof(t26_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,D,B) => ! [F] : ( m1_cat_1(F,A,D,B) => ! [G] : ( m1_cat_1(G,A,D,C) => ! [H] : ( m1_cat_1(H,A,D,C) => ( k9_cat_4(A,B,C,D,E,G) = k9_cat_4(A,B,C,D,F,H) => ( k2_cat_1(A,D,B) = k1_xboole_0 | k2_cat_1(A,D,C) = k1_xboole_0 | ( E = F & G = H ) ) ) ) ) ) ) ) ) ) ) )).
fof(t26_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(t26_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(A,B) & r1_xxreal_0(k4_newton(A,B),k5_numbers) ) ) ) )).
fof(t26_catalg_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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) ) ) )).
fof(t26_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v9_algstr_0(k5_cayldick(A,B,C),k4_cayldick(A)) & v3_algstr_0(k5_cayldick(A,B,C),k4_cayldick(A)) ) => k4_algstr_0(k4_cayldick(A),k5_cayldick(A,B,C)) = k5_cayldick(A,k4_algstr_0(A,B),k4_algstr_0(A,C)) ) ) ) ) )).
fof(t26_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k7_cc0sp1(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k7_cc0sp1(A))) => ! [G] : ( 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] : ( m1_subset_1(H,A) => k3_funct_2(A,k2_numbers,D,H) = k6_xcmplx_0(k3_funct_2(A,k2_numbers,B,H),k3_funct_2(A,k2_numbers,C,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t26_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_cc0sp2(A))) => ( k2_normsp_0(k5_cc0sp2(A),B) = k5_numbers => B = k4_struct_0(k5_cc0sp2(A)) ) ) ) )).
fof(t26_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v3_funct_1(A) => v2_comseq_2(A) ) ) )).
fof(t26_cfdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [C] : ( v1_xcmplx_0(C) => ( ( 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) = k2_xcmplx_0(k3_xcmplx_0(k7_partfun1(k2_numbers,B,C),k2_cfdiff_1(A,C)),k3_xcmplx_0(k7_partfun1(k2_numbers,A,C),k2_cfdiff_1(B,C))) ) ) ) ) ) )).
fof(t26_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k8_cfuncdom(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k8_cfuncdom(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k8_cfuncdom(A))) => ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( v1_xcmplx_0(F) => ( 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,k2_xcmplx_0(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,k3_xcmplx_0(E,F)) = k1_clvect_1(k8_cfuncdom(A),k1_clvect_1(k8_cfuncdom(A),B,F),E) ) ) ) ) ) ) ) )).
fof(t26_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) )).
fof(t26_cgames_1,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(t26_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ( ! [F] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(A)) => r1_xxreal_0(k1_funct_1(D,F),k1_funct_1(E,F)) ) => ( r1_tarski(k3_chain_1(A,B,C),k3_chain_1(A,D,E)) <=> ! [F] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(A)) => ( r1_xxreal_0(k1_funct_1(D,F),k1_funct_1(B,F)) & r1_xxreal_0(k1_funct_1(B,F),k1_funct_1(C,F)) & r1_xxreal_0(k1_funct_1(C,F),k1_funct_1(E,F)) ) ) ) ) ) ) ) ) ) )).
fof(t26_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v5_glib_001(B,A) & m3_glib_001(B,A) ) => ( ~ v1_glib_001(B,A) => ! [C] : ! [D] : ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t26_circcmb3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t26_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msualg_1(D,B) & l3_msualg_1(D,B) ) => ( r1_partfun1(u3_msualg_1(A,C),u3_msualg_1(B,D)) => ! [E] : ( 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))) ) ) ) ) ) ) ) )).
fof(t26_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t26_classes1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t26_classes2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t26_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( 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)) ) ) ) )).
fof(t26_clopban3,axiom,( ! [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_clopban1(A) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v2_clopban3(B,A) => v1_clopban3(B,A) ) ) ) )).
fof(t26_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,k4_sin_cos(k2_normsp_0(A,B)),C)) ) ) ) )).
fof(t26_closure1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( 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] : ( 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)) ) ) ) ) ) )).
fof(t26_closure2,axiom,( ! [A] : ! [B] : ( ( 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)))) ) ) )).
fof(t26_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t26_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)))) & k1_seq_2(k2_clvect_2(A,k4_normsp_1(A,k16_csspace(A,D,E),k3_rlvect_1(A,B,C)))) = k5_numbers ) ) ) ) ) ) ) )).
fof(t26_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v1_xcmplx_0(C) => ( v2_clvect_3(B,A) => v2_clvect_3(k6_clvect_1(A,B,C),A) ) ) ) ) )).
fof(t26_coh_sp,axiom,( ! [A] : ! [B] : ( r2_hidden(A,k15_coh_sp(B)) <=> ? [C] : ( 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))) ) ) )).
fof(t26_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ! [F] : ( ( 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) ) ) ) ) ) )).
fof(t26_combgras,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ( r1_ordinal1(k1_nat_1(A,1),k1_card_1(B)) => ( r1_xxreal_0(A,k5_numbers) | ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_incsp_1(k1_combgras(A,B)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) => ( ( k1_card_1(D) = k6_xcmplx_0(A,1) & C = a_3_0_combgras(A,B,D) ) => D = k1_setfam_1(C) ) ) ) ) ) ) ) )).
fof(t26_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v8_compl_sp(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ( v1_pcomps_1(B,A) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => k1_card_1(C) = 1 ) ) ) => v1_finset_1(B) ) ) ) ) )).
fof(t26_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(k5_numbers,B) => k1_comptrig(k3_xcmplx_0(A,B)) = k1_comptrig(k4_xcmplx_0(A)) ) ) ) )).
fof(t26_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ( k3_vectsp_1(k1_complfld,A,B) = k4_struct_0(k1_complfld) => ( B = k4_struct_0(k1_complfld) | A = k4_struct_0(k1_complfld) ) ) ) ) )).
fof(t26_complsp2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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) = k15_seq_4(k3_finseq_1(A)) ) => ( A = k30_valued_1(B) & B = k30_valued_1(A) ) ) ) ) )).
fof(t26_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => r2_hidden(k5_numbers,k2_afinsq_1(k10_compos_1(A,B))) ) ) )).
fof(t26_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(k62_valued_1(B),C) <=> r2_hidden(C,k9_xtuple_0(k63_valued_1(B))) ) ) ) ) )).
fof(t26_comptrig,axiom,( v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k28_sin_cos,k3_xcmplx_0(2,k28_sin_cos)))) )).
fof(t26_comput_1,axiom,( ! [A] : r2_hidden(k1_xboole_0,k2_comput_1(A)) )).
fof(t26_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( r2_relset_1(k4_ordinal1,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k31_valued_1(k4_ordinal1,k2_numbers,A),B),k31_valued_1(k4_ordinal1,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B))) & r2_relset_1(k4_ordinal1,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,k31_valued_1(k4_ordinal1,k2_numbers,B)),k31_valued_1(k4_ordinal1,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B))) ) ) ) )).
fof(t26_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v2_comseq_2(B) & v2_comseq_2(A) & v9_ordinal1(A) ) => ( k3_comseq_2(A) = k5_complex1 | v2_comseq_2(k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,A)) ) ) ) ) )).
fof(t26_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( r2_funct_2(k4_ordinal1,k1_numbers,k3_series_1(k7_comseq_3(A)),k7_comseq_3(k10_comseq_3(A))) & r2_funct_2(k4_ordinal1,k1_numbers,k3_series_1(k8_comseq_3(A)),k8_comseq_3(k10_comseq_3(A))) ) ) )).
fof(t26_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( v5_conlat_1(B,A) & l2_conlat_1(B,A) ) => ~ ( ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) & l2_conlat_1(B,A) & ~ v7_conlat_1(B,A) & ~ v8_conlat_1(B,A) ) ) ) )).
fof(t26_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ! [C] : ( 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) ) ) ) ) )).
fof(t26_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_tarski(k1_connsp_1(A,B),k1_connsp_2(A,B)) ) ) )).
fof(t26_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => r2_hidden(C,k6_connsp_3(A,B,C)) ) ) ) ) )).
fof(t26_convex1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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(k5_numbers,k1_funct_1(E,B)) & r1_xxreal_0(k5_numbers,k1_funct_1(E,C)) & r1_xxreal_0(k5_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))) ) ) ) ) ) ) ) ) )).
fof(t26_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( m1_convex4(D,A) => ( m2_convex4(D,A,B) => m2_convex4(k7_convex4(A,C,D),A,B) ) ) ) ) ) )).
fof(t26_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( k5_qc_lang3(A,C) = k1_xboole_0 => k13_cqc_lang(A,C,B) = C ) ) ) ) )).
fof(t26_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v5_relat_1(C,k3_qc_lang1(A)) & v3_card_1(C,B) & m2_finseq_1(C,k2_qc_lang1(A)) ) => ! [D] : ( 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) ) ) ) ) )).
fof(t26_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t26_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_cqc_lang(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k3_cqc_lang(A))) => ( ( r4_cqc_the3(A,D,E) & r2_cqc_the3(A,k4_subset_1(k3_cqc_lang(A),D,B),C) ) => r2_cqc_the3(A,k4_subset_1(k3_cqc_lang(A),E,B),C) ) ) ) ) ) ) )).
fof(t26_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t26_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k9_csspace4(A,B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k9_csspace4(A,B))))) ) => ( v1_csspace3(C,k9_csspace4(A,B)) => v9_clvect_1(C,k9_csspace4(A,B)) ) ) ) ) ) )).
fof(t26_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(t26_descip_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t26_dickson,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ~ ( r1_dickson(A,B,C) & v1_xboole_0(C) ) ) ) )).
fof(t26_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k1_funct_1(k5_diff_1(k1_fcont_1(B,C),A),D) = k3_xcmplx_0(B,A) ) ) ) ) )).
fof(t26_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( ( 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) = k2_xcmplx_0(k3_xcmplx_0(A,k9_diff_1(D,B,C)),k9_diff_1(E,B,C)) ) ) ) ) ) )).
fof(t26_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(A,k1_relset_1(k1_numbers,k27_sin_cos)) & r2_hidden(B,k1_relset_1(k1_numbers,k27_sin_cos)) ) => k9_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k27_sin_cos),k16_sin_cos),A,B) = k9_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k18_sin_cos),A,B) ) ) ) )).
fof(t26_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t26_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_diraf(A,B,C,D,E) & r2_diraf(A,B,D,C,E) ) ) ) ) ) )).
fof(t26_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => ! [C] : ( m1_dist_2(C,A,B) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,k6_margrel1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => k4_dist_2(A,B,C,k1_bvfunc_1(A,D)) = k6_xcmplx_0(1,k4_dist_2(A,B,C,D)) ) ) ) ) )).
fof(t26_domain_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k1_subset_1(A) = a_1_1_domain_1(A) ) )).
fof(t26_e_siec,axiom,( ! [A] : ( ( 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)))) ) ) )).
fof(t26_ec_pf_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t26_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(A))) => ( B = k5_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)) ) ) ) ) ) )).
fof(t26_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k11_ens_1(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t26_entropy1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(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_0(C) = k1_matrix_0(B) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(D,E),k2_matrix_0(C)) => k3_matrix_0(k1_numbers,C,D,E) = k3_xcmplx_0(k1_funct_1(A,D),k3_matrix_0(k1_numbers,B,D,E)) ) ) ) ) ) ) ) ) ) )).
fof(t26_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : 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)) )).
fof(t26_eqrel_1,axiom,( ! [A] : ! [B] : ( r2_hidden(B,A) => k6_eqrel_1(A,A,k1_eqrel_1(A),B) = A ) )).
fof(t26_euclid,axiom,( k4_struct_0(k15_euclid(2)) = k19_euclid(k5_numbers,k5_numbers) )).
fof(t26_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => k22_rvsum_1(k3_rlvect_1(k15_euclid(A),B,C),k3_rlvect_1(k15_euclid(A),D,E)) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k22_rvsum_1(B,D),k22_rvsum_1(B,E)),k22_rvsum_1(C,D)),k22_rvsum_1(C,E)) ) ) ) ) ) )).
fof(t26_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( 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) ) ) ) )).
fof(t26_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => k22_rvsum_1(k8_euclid(A,B,C),D) = k6_xcmplx_0(k22_rvsum_1(B,D),k22_rvsum_1(C,D)) ) ) ) ) )).
fof(t26_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(3))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(3))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t26_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,B) ) => k18_rvsum_1(k6_euclid_7(B,A)) = 1 ) ) ) )).
fof(t26_euclid_8,axiom,( k6_euclid(3,k3_euclid_8) = k1_euclid_8(k5_numbers,k4_xcmplx_0(1),k5_numbers) )).
fof(t26_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ( A != k5_numbers => ! [B] : ( 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))) ) ) ) ) )).
fof(t26_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ! [H] : ( m2_finseq_2(H,k1_numbers,k1_euclid(G)) => ! [I] : ( m2_finseq_2(I,k1_numbers,k1_euclid(G)) => ! [J] : ( 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,k6_xcmplx_0(A,D)),k9_euclid(G,I,k6_xcmplx_0(B,E))),k9_euclid(G,J,k6_xcmplx_0(C,F))) ) ) ) ) ) ) ) ) ) ) )).
fof(t26_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,u1_compos_1(B)) => ! [E] : ( ( 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] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(B)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( r1_tarski(k16_funcop_1(C,D),F) => k4_extpro_1(A,B,E,F) = k2_extpro_1(A,B,D,E) ) ) ) ) ) ) ) )).
fof(t26_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( 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(k1_xxreal_3(k1_xxreal_3(A,B),k3_extreal1(k3_xxreal_3(A,B))),2) ) ) ) )).
fof(t26_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_circcomb(A) & v2_circcomb(A) & v3_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v1_circcomb(B) & v2_circcomb(B) & v3_circcomb(B) & l1_msualg_1(B) ) => ! [C] : ( ( v4_msualg_1(C,A) & v4_msafree2(C,A) & v4_circcomb(C,A) & v6_circcomb(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msualg_1(D,B) & v4_msafree2(D,B) & v4_circcomb(D,B) & v6_circcomb(D,B) & l3_msualg_1(D,B) ) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t26_fcont_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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)))) ) ) ) )).
fof(t26_fcont_3,axiom,( ! [A] : ( ( 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)) ) ) ) )).
fof(t26_fdiff_1,axiom,( ! [A] : ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t26_fdiff_10,axiom,( ! [A] : ( ( 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,k18_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos)))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos)),A),B) = k2_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,B),k2_xcmplx_0(k1_funct_1(k26_sin_cos,B),k1_funct_1(k27_sin_cos,B)))),k3_xcmplx_0(k1_funct_1(k18_sin_cos,B),k6_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B)))))) ) ) ) ) ) )).
fof(t26_fdiff_11,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k2_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k2_sin_cos9),A),B) = k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,B),k1_funct_1(k2_sin_cos9,B)),k7_xcmplx_0(k1_funct_1(k16_sin_cos,B),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t26_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r2_hidden(C,k10_prob_1(A)) & r2_hidden(D,k10_prob_1(A)) ) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k1_funct_1(B,C),k1_funct_1(B,D))),k1_square_1(k6_xcmplx_0(C,D))) ) ) ) ) => ( r2_fdiff_1(B,k10_prob_1(A)) & v3_funct_1(k2_partfun1(k1_numbers,k1_numbers,B,k10_prob_1(A))) ) ) ) ) )).
fof(t26_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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),k7_xcmplx_0(1,2)))) & B = k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_taylor_1(2)),C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => ( k1_funct_1(C,D) = 1 & ~ r1_xxreal_0(k1_funct_1(B,D),k5_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),k7_xcmplx_0(1,2)),A) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_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),k7_xcmplx_0(1,2)),A),D) = k7_xcmplx_0(k23_sin_cos(D),k6_xcmplx_0(k23_sin_cos(D),k23_sin_cos(k4_xcmplx_0(D)))) ) ) ) ) ) ) ) )).
fof(t26_fdiff_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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,k3_sin_cos6)))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k1_funct_1(C,D) = k7_xcmplx_0(D,A) & ~ r1_xxreal_0(k1_funct_1(C,D),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_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,k3_sin_cos6)),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_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,k3_sin_cos6)),B),D) = k6_xcmplx_0(k1_funct_1(k3_sin_cos6,k7_xcmplx_0(D,A)),k7_xcmplx_0(D,k3_xcmplx_0(A,k3_square_1(k6_xcmplx_0(1,k1_square_1(k7_xcmplx_0(D,A))))))) ) ) ) ) ) ) ) )).
fof(t26_fdiff_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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,k26_sin_cos),k7_xcmplx_0(1,A)),k1_partfun2(k1_numbers,B)))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k1_funct_1(C,D) = k3_xcmplx_0(A,D) & A != k5_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,k26_sin_cos),k7_xcmplx_0(1,A)),k1_partfun2(k1_numbers,B)),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_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,k26_sin_cos),k7_xcmplx_0(1,A)),k1_partfun2(k1_numbers,B)),B),D) = k7_xcmplx_0(k1_square_1(k1_funct_1(k16_sin_cos,k3_xcmplx_0(A,D))),k1_square_1(k1_funct_1(k18_sin_cos,k3_xcmplx_0(A,D)))) ) ) ) ) ) ) ) )).
fof(t26_fdiff_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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),k7_xcmplx_0(1,A)),k1_partfun2(k1_numbers,B)))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k1_funct_1(C,D) = k3_xcmplx_0(A,D) & A != k5_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),k7_xcmplx_0(1,A)),k1_partfun2(k1_numbers,B)),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_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),k7_xcmplx_0(1,A)),k1_partfun2(k1_numbers,B)),B),D) = k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(k16_sin_cos,k3_xcmplx_0(A,D)),k1_square_1(k1_funct_1(k18_sin_cos,k3_xcmplx_0(A,D)))),k1_square_1(k1_funct_1(k18_sin_cos,k3_xcmplx_0(A,D)))) ) ) ) ) ) ) ) )).
fof(t26_ff_siec,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t26_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => k1_pre_ff(k1_nat_1(A,4)) = k1_nat_1(k1_pre_ff(k1_nat_1(A,2)),k1_pre_ff(k1_nat_1(A,3))) ) )).
fof(t26_fib_num3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k2_nat_1(2,k1_fib_num3(k1_nat_1(A,B))) = k1_nat_1(k2_nat_1(k1_fib_num3(A),k1_fib_num3(B)),k2_nat_1(k2_nat_1(5,k1_pre_ff(A)),k1_pre_ff(B))) ) ) )).
fof(t26_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => k1_pre_ff(k2_xcmplx_0(A,1)) = k7_xcmplx_0(k2_xcmplx_0(k1_pre_ff(A),k3_square_1(k2_xcmplx_0(k3_xcmplx_0(5,k1_pepin(k1_pre_ff(A))),k3_xcmplx_0(4,k2_power(k4_xcmplx_0(1),A))))),2) ) )).
fof(t26_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_finseq_1(B,A) => ! [C] : ( m1_finseq_1(C,A) => ( r4_finseq_8(A,B,C) => r1_xxreal_0(k5_numbers,k6_xcmplx_0(k3_finseq_1(B),k3_finseq_1(C))) ) ) ) ) )).
fof(t26_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t26_filter_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t26_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t26_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t26_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ( C = k17_funct_3(k4_ordinal1,B,D,k2_finseq_1(A)) => k3_finseq_1(C) = A ) ) ) ) ) )).
fof(t26_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k1_relset_1(k4_ordinal1,A)) <=> ( m1_subset_1(k6_xcmplx_0(B,1),k4_ordinal1) & m1_subset_1(k6_xcmplx_0(k3_finseq_1(A),B),k4_ordinal1) ) ) ) ) )).
fof(t26_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_finseq_4(A,B) => ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(C,k4_finseq_1(A)) & C != k4_finseq_4(A,B) & k1_funct_1(A,C) = B ) ) ) ) )).
fof(t26_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ( 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)) ) ) ) ) )).
fof(t26_finseq_6,axiom,( ! [A] : ! [B] : ( A != B => k5_finseq_4(k10_finseq_1(A,B),B) = k9_finseq_1(A) ) )).
fof(t26_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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) ) ) ) ) )).
fof(t26_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( ( r1_xxreal_0(1,k3_finseq_1(B)) & r1_tarski(C,B) ) => r2_finseq_8(A,B,C,1) ) ) ) ) )).
fof(t26_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v3_card_1(D,C) & m2_finseq_1(D,A) ) => ! [E] : ( ( v3_card_1(E,C) & m2_finseq_1(E,A) ) => ! [F] : ( ( 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(k4_ordinal1,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)) ) ) ) ) ) ) ) )).
fof(t26_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t26_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_orders_2(A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_tarski(k5_fintopo3(A,B,k1_nat_1(C,1)),k5_fintopo3(A,B,C)) ) ) ) ) )).
fof(t26_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t26_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => k7_flang_1(A,B,2) = k6_flang_1(A,B,B) ) )).
fof(t26_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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))) ) ) ) ) )).
fof(t26_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k2_flang_1(A),C) => ( r1_tarski(B,k6_flang_1(A,B,k1_flang_3(A,C,D))) & r1_tarski(B,k6_flang_1(A,k1_flang_3(A,C,D),B)) ) ) ) ) ) )).
fof(t26_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( v5_relat_1(B,A) & v1_finseq_1(B) ) => m2_finseq_1(B,A) ) ) )).
fof(t26_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v4_fomodel1(C,A) & m1_subset_1(C,k1_fomodel1(A)) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_fomodel2(D,A,B) ) => ? [E] : ( m1_subset_1(E,B) & E = k1_funct_1(k4_fomodel2(A,B,D,C),k1_xboole_0) & k5_fomodel2(D,C,E) = D ) ) ) ) ) )).
fof(t26_frechet,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v3_frechet(A) => v4_frechet(A) ) ) )).
fof(t26_frechet2,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k3_pcomps_1(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k3_pcomps_1(A))))) ) ) ) )).
fof(t26_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t26_fsm_2,axiom,( ! [A] : ( ( ~ 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] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ ( r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(C,k5_numbers) ) => k1_funct_1(u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(B,C))) = 1 ) ) ) & ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(C,k5_numbers) ) => ( ( B != k5_numbers & C != k5_numbers ) | k1_funct_1(u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(B,C))) = k5_numbers ) ) ) ) & ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(k5_numbers,C) & k1_funct_1(u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(B,C))) != k4_xcmplx_0(1) ) ) ) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( 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),k4_xxreal_0(k2_absvalue(B),k2_absvalue(C))) ) ) ) ) )).
fof(t26_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k8_afinsq_1(C)) => ! [G] : ( ( ~ 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,F)),k4_tarski(B,k1_flang_1(C,E,F))) => 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,E)) ) ) ) ) ) ) )).
fof(t26_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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))) ) ) ) ) ) ) )).
fof(t26_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : k4_funcop_1(B,A,C) = k3_funcop_1(B,A,k2_funcop_1(k9_xtuple_0(A),C)) ) ) )).
fof(t26_funcsdom,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(t26_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( v2_funct_1(k3_relat_1(A,B)) & k10_xtuple_0(A) = k9_xtuple_0(B) ) => ( v2_funct_1(A) & v2_funct_1(B) ) ) ) ) )).
fof(t26_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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 ) ) ) )).
fof(t26_funct_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t26_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t26_funct_5,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) ) )).
fof(t26_funct_6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_funcop_1(C) ) => ( ( r2_hidden(A,k9_xtuple_0(k5_funct_6(C))) & B = k1_funct_1(k5_funct_6(C),A) ) => ( k9_xtuple_0(B) = k9_xtuple_0(C) & ! [D] : ( r2_hidden(D,k9_xtuple_0(B)) => ( r2_hidden(k4_tarski(D,A),k9_xtuple_0(k2_funct_5(C))) & k1_funct_1(B,D) = k1_binop_1(k2_funct_5(C),D,A) ) ) ) ) ) ) )).
fof(t26_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( r1_funct_7(A,B,D) & r1_funct_7(B,C,D) ) => r1_funct_7(A,C,D) ) ) ) ) )).
fof(t26_funct_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_8(B) & m1_subset_1(B,k1_zfmisc_1(k2_numbers)) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t26_funct_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & v1_int_1(A) ) => v1_funct_9(k27_sin_cos,k3_xcmplx_0(k28_sin_cos,A)) ) )).
fof(t26_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l1_altcat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,k1_altcat_1(B,C,C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t26_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,B,C) & m2_functor0(E,B,C) ) => ! [F] : ( ( v15_functor0(F,B,C) & m2_functor0(F,B,C) ) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t26_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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) ) ) ) ) )).
fof(t26_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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) ) ) ) ) )).
fof(t26_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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))) ) => k2_binop_1(B,A,k1_numbers,k1_fuzzy_4(B,A,E),D,C) = k2_binop_1(A,B,k1_numbers,E,C,D) ) ) ) ) ) )).
fof(t26_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_fvaluat1(D,A) => ( ( v3_fvaluat1(A) & r1_xxreal_0(k3_funct_2(u1_struct_0(A),k6_numbers,D,k1_vectsp_2(A,B,C)),k5_numbers) ) => ( C = k4_struct_0(A) | r1_xxreal_0(k3_funct_2(u1_struct_0(A),k6_numbers,D,B),k3_funct_2(u1_struct_0(A),k6_numbers,D,C)) ) ) ) ) ) ) )).
fof(t26_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(t26_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ~ ( ~ 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)) ) ) )).
fof(t26_gcd_1,axiom,( ! [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) & v1_vectsp_2(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) <=> C = k4_gcd_1(A,B,C) ) ) ) ) )).
fof(t26_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v2_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( m1_genealg1(E,D) => ! [F] : ( m1_genealg1(F,D) => k9_genealg1(D,E,F,A,B,C) = k9_genealg1(D,E,F,C,A,B) ) ) ) ) ) ) )).
fof(t26_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_analmetr(A,F,G) & r2_geomtrap(A,F,G,B,D,C,E) ) => r2_geomtrap(A,F,G,B,D,k1_geomtrap(A,B,C),k1_geomtrap(A,D,E)) ) ) ) ) ) ) ) ) )).
fof(t26_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t26_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) ) )).
fof(t26_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ( k4_glib_001(A,B) = k3_glib_001(A,C) => k1_nat_1(k3_finseq_1(k7_glib_001(A,B,C)),1) = k1_nat_1(k3_finseq_1(B),k3_finseq_1(C)) ) ) ) ) )).
fof(t26_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( r2_hidden(B,k3_glib_002(A)) => ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) ) ) ) )).
fof(t26_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) & v1_glib_003(B) & v7_glib_003(B) ) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t26_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( 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) ) ) )).
fof(t26_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( r1_xxreal_0(1,A) => ( r1_xxreal_0(k1_matrix_0(C),B) | r1_xxreal_0(k3_finseq_1(C),A) | k9_subset_1(u1_struct_0(k15_euclid(2)),k3_goboard5(C,A,B),k3_goboard5(C,A,k1_nat_1(B,1))) = k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),k1_nat_1(B,1))) ) ) ) ) ) )).
fof(t26_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_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_0(C),B) | k1_tops_1(k15_euclid(2),k3_goboard5(C,A,B)) = a_3_0_goboard6(A,B,C) ) ) ) ) ) )).
fof(t26_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(E)) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(E)) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k3_finseq_1(E)) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k1_matrix_0(E)) & r2_hidden(k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),E,k1_nat_1(A,1),C)),k7_xcmplx_0(1,2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),E,B,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),E,k1_nat_1(B,1),D))) ) => ( A = B & C = D ) ) ) ) ) ) ) )).
fof(t26_gobrd11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_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_0(B),A) | k3_goboard5(B,k5_numbers,A) = a_2_2_gobrd11(A,B) ) ) ) ) )).
fof(t26_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [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_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)) ) ) ) ) ) )).
fof(t26_gobrd14,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t26_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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) ) ) )).
fof(t26_gr_cy_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v15_algstr_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t26_gr_cy_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v2_gr_cy_3(A) ) => ~ ( ~ r1_xxreal_0(A,2) & k4_nat_d(A,4) = 1 & ! [B] : ( ( 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) ) ) ) )).
fof(t26_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_graph_1(B) & l1_graph_1(B) ) => ( r4_graph_1(A,B) => v3_graph_1(A) ) ) ) )).
fof(t26_graph_2,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => m1_subset_1(B,k1_zfmisc_1(B)) ) )).
fof(t26_graph_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(C) & v6_graph_1(C) & l1_graph_1(C) ) => ! [D] : ( 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) ) ) ) )).
fof(t26_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( m1_subset_1(D,k4_ordinal1) => ~ ( 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)) ) ) ) ) ) ) )).
fof(t26_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) => r1_tarski(k12_graphsp(B,A),k2_finseq_1(A)) ) ) )).
fof(t26_grcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( v1_grcat_1(C) & m1_grcat_1(C,A,B) ) => m4_grcat_1(k1_tarski(C),A,B) ) ) ) )).
fof(t26_grfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => k5_relat_1(A,k1_tarski(B)) = k1_tarski(k4_tarski(B,k1_funct_1(A,B))) ) ) )).
fof(t26_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v15_algstr_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t26_groeb_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_ideal_1(D,k12_polynom1(A,C)) & v2_ideal_1(D,k12_polynom1(A,C)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( ( r1_tarski(E,D) & ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(F,A,C) & v1_polynom1(F,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] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(F,A,C) & v1_polynom1(F,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) ) ) ) ) ) ) ) ) )).
fof(t26_groeb_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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(k8_polynom1(A,C),D) | r1_groeb_1(A,B,C,D) ) ) ) ) ) ) )).
fof(t26_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(E,k5_card_1(k3_polynom1(k15_pre_poly(A),C,D))) => ( r1_tarski(k3_polynom1(k15_pre_poly(A),C,k5_groeb_3(A,B,C,D,E)),k3_polynom1(k15_pre_poly(A),C,D)) & r1_tarski(k3_polynom1(k15_pre_poly(A),C,k6_groeb_3(A,B,C,D,E)),k3_polynom1(k15_pre_poly(A),C,D)) ) ) ) ) ) ) ) )).
fof(t26_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_group_1(A,2,B) = k6_algstr_0(A,B,B) ) ) )).
fof(t26_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,A) => ( m1_group_2(C,D) => r1_tarski(k2_group_11(A,B,C),k2_group_11(A,B,D)) ) ) ) ) ) )).
fof(t26_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & v5_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t26_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t26_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t26_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => k7_struct_0(k5_group_6(A,B)) = k17_group_2(A,B) ) ) )).
fof(t26_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t26_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t26_groupp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t26_hahnban1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( m1_vectsp_4(C,k1_complfld,A) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( F = E => r1_xxreal_0(k9_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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => r1_xxreal_0(k9_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)) ) ) ) ) ) ) ) ) )).
fof(t26_hallmar1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => m2_hallmar1(B,A,B) ) )).
fof(t26_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t26_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( ( v5_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ( ( v7_ordinal1(C) & ~ v1_abian(C) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t26_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k6_vectsp10(k1_complfld,A,k9_vectsp10(k1_complfld,A,k1_hermitan(A,B))))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t26_heyting1,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k12_normform(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k12_normform(A))) => ( ( ! [E] : ( 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)) ) ) ) ) )).
fof(t26_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( 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)) ) ) )).
fof(t26_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k4_heyting3(1,A) = k7_domain_1(k4_partfun1(k4_ordinal1,k6_domain_1(k4_ordinal1,A)),k2_heyting3(1,A),k3_heyting3(1,A)) ) )).
fof(t26_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(A,D) => k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k26_valued_1(k1_numbers,k1_numbers,k18_sin_cos,B),D),C),A) = k3_xcmplx_0(B,k1_funct_1(k18_sin_cos,k2_xcmplx_0(A,k7_xcmplx_0(k3_xcmplx_0(C,k28_sin_cos),2)))) ) ) ) ) ) )).
fof(t26_hilbasis,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t26_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(t26_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => k3_hilbert1(B,C) != k1_hilbert2(A) ) ) ) )).
fof(t26_hilbert3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t26_hurwitz,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( C != k5_numbers & C != D & k1_normsp_1(A,k3_hurwitz(A,B,D),C) != k4_struct_0(A) ) ) ) ) ) )).
fof(t26_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( 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)) ) ) ) ) ) )).
fof(t26_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_ideal_1(D,A,B) => m2_ideal_1(k9_fvsum_1(A,D,C),A,B) ) ) ) ) )).
fof(t26_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ~ ( ~ r1_incsp_1(A,B,C) & ! [D] : ( m1_subset_1(D,u4_incsp_1(A)) => ~ ! [E] : ( m1_subset_1(E,u4_incsp_1(A)) => ( ( r2_incsp_1(A,B,E) & r3_incsp_1(A,C,E) ) <=> D = E ) ) ) ) ) ) ) )).
fof(t26_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,B,C) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t26_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => k2_instalg1(A,A,B) = g3_msualg_1(A,u3_msualg_1(A,B),u4_msualg_1(A,B)) ) ) )).
fof(t26_int_1,axiom,( ! [A] : ( 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)) ) ) ) )).
fof(t26_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( r1_int_2(A,C) & r1_int_2(B,C) ) => r1_int_2(k3_xcmplx_0(A,B),C) ) ) ) ) )).
fof(t26_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ( k5_int_1(k6_xcmplx_0(k3_xcmplx_0(A,D),B),C) = k5_numbers => ( C = k5_numbers | ! [E] : ( v1_int_1(E) => ( ( ( r1_int_2(A,C) & k5_int_1(k6_xcmplx_0(k3_xcmplx_0(A,E),B),C) = k5_numbers ) => r2_hidden(E,k6_eqrel_1(k4_numbers,k4_numbers,k1_int_4(C),D)) ) & ( r2_hidden(E,k6_eqrel_1(k4_numbers,k4_numbers,k1_int_4(C),D)) => k5_int_1(k6_xcmplx_0(k3_xcmplx_0(A,E),B),C) = k5_numbers ) ) ) ) ) ) ) ) ) )).
fof(t26_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ( k5_int_1(A,B) != k5_numbers => k2_int_5(k1_pepin(A),B) = 1 ) ) ) )).
fof(t26_int_6,axiom,( ! [A] : ( ( 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] : ( m1_int_6(B,A) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => r2_int_1(k1_funct_1(B,C),1,k1_funct_1(A,C)) ) ) ) ) )).
fof(t26_int_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r1_xxreal_0(k5_numbers,k2_hurwitz(A,B)) => v1_uproots(B,A) ) ) ) )).
fof(t26_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k4_numbers)) ) => ( ( k5_card_1(B) = k1_euler_1(A) & ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & C != D & r2_int_1(C,D,A) ) ) ) & ! [C] : ( v1_int_1(C) => ( r2_hidden(C,B) => r1_int_2(C,A) ) ) ) => ( r1_xxreal_0(A,1) | r1_int_8(B,A) ) ) ) ) )).
fof(t26_integr11,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ~ ( k2_xcmplx_0(B,A) != k5_numbers & k6_xcmplx_0(B,A) != k5_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(B,k5_numbers),k16_sin_cos),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,k5_numbers),k16_sin_cos))) != k6_xcmplx_0(k1_funct_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(k6_xcmplx_0(B,A),k5_numbers),k16_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k6_xcmplx_0(B,A)))),k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k2_xcmplx_0(B,A),k5_numbers),k16_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k2_xcmplx_0(B,A))))),k2_seq_4(C)),k1_funct_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(k6_xcmplx_0(B,A),k5_numbers),k16_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k6_xcmplx_0(B,A)))),k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k2_xcmplx_0(B,A),k5_numbers),k16_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k2_xcmplx_0(B,A))))),k3_seq_4(C))) ) ) ) ) )).
fof(t26_integr12,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v3_rcomp_1(F) & m1_subset_1(F,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,F) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,F) => ( k1_funct_1(D,G) = 1 & k1_funct_1(E,G) = k7_xcmplx_0(G,A) & ~ r1_xxreal_0(k1_funct_1(E,G),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(E,G)) ) ) ) & F = k1_relset_1(k1_numbers,C) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,B)) & 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,E,k3_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,D,k41_valued_1(k1_numbers,k1_numbers,E)),k4_taylor_1(k7_xcmplx_0(1,2))),A)))) ) => k2_integra5(B,C) = k6_xcmplx_0(k1_funct_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,E,k3_sin_cos6)),k2_seq_4(B)),k1_funct_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,E,k3_sin_cos6)),k3_seq_4(B))) ) ) ) ) ) ) ) )).
fof(t26_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k27_sin_cos))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k27_sin_cos),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k27_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t26_integr14,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,D) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => k1_funct_1(C,E) = k7_xcmplx_0(k3_xcmplx_0(A,k1_funct_1(k16_sin_cos,E)),k3_prepower(k1_funct_1(k18_sin_cos,E),k2_xcmplx_0(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) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fdiff_9,k1_taylor_1(A)),k2_seq_4(B)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fdiff_9,k1_taylor_1(A)),k3_seq_4(B))) ) ) ) ) ) )).
fof(t26_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t26_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [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_comseq_2(k2_partfun1(A,k1_numbers,C,A)) => r1_xxreal_0(k7_integra1(A,C,B),k6_integra1(A,C,B)) ) ) ) ) )).
fof(t26_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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] : ( 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,k5_numbers) ) => k1_funct_1(k4_integra1(C,k26_valued_1(C,k1_numbers,D,A),E),B) = k3_xcmplx_0(A,k1_funct_1(k5_integra1(C,D,E),B)) ) ) ) ) ) ) )).
fof(t26_integra4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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(k5_numbers,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( ( r2_hidden(F,B) & r2_hidden(G,B) ) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k1_funct_1(E,F),k1_funct_1(E,G))),k3_xcmplx_0(A,k2_xcmplx_0(k9_complex1(k6_xcmplx_0(k1_funct_1(C,F),k1_funct_1(C,G))),k9_complex1(k6_xcmplx_0(k1_funct_1(D,F),k1_funct_1(D,G)))))) ) ) ) ) => r1_xxreal_0(k6_xcmplx_0(k2_seq_4(k1_rvsum_1(E)),k3_seq_4(k1_rvsum_1(E))),k3_xcmplx_0(A,k2_xcmplx_0(k6_xcmplx_0(k2_seq_4(k1_rvsum_1(C)),k3_seq_4(k1_rvsum_1(C))),k6_xcmplx_0(k2_seq_4(k1_rvsum_1(D)),k3_seq_4(k1_rvsum_1(D)))))) ) ) ) ) ) ) )).
fof(t26_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,k3_integra5(A,B)) => k1_funct_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)) ) ) ) ) ) ) )).
fof(t26_integra7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k6_xcmplx_0(k1_funct_1(k18_sin_cos,A),k1_funct_1(k18_sin_cos,B)) = k4_integra5(A,B,k16_sin_cos) ) ) )).
fof(t26_integra8,axiom,( r2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k18_sin_cos),k1_numbers) & ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k1_numbers) => k1_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k18_sin_cos),A) = k1_funct_1(k16_sin_cos,A) ) ) )).
fof(t26_integra9,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( ~ 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) = k6_xcmplx_0(k1_integra9(D,A,C),k1_integra9(D,B,C)) ) ) ) ) ) )).
fof(t26_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t26_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) ) )).
fof(t26_irrat_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(D,E) & r1_xxreal_0(k1_funct_1(B,E),k6_xcmplx_0(A,C)) ) ) ) ) => ( ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & ~ r1_xxreal_0(k1_funct_1(B,D),A) ) ) | ( v2_comseq_2(B) & k1_seq_2(B) = A ) ) ) ) ) )).
fof(t26_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,B,C) => ! [F] : ( m2_cat_1(F,B,C) => ! [G] : ( m2_cat_1(G,B,C) => ! [H] : ( m2_nattra_1(H,B,C,E,F) => ! [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,k5_nattra_1(B,C,E,F,G,H,I)),k5_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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t26_isomichi,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( 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) ) ) ) )).
fof(t26_jgraph_1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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_funct_1(k1_goboard1(A),1),k1_funct_1(k1_goboard1(A),k3_finseq_1(A))) & r1_goboard4(k1_goboard1(B),k1_funct_1(k1_goboard1(A),1),k1_funct_1(k1_goboard1(A),k3_finseq_1(A))) & r1_goboard4(k2_goboard1(A),k1_funct_1(k2_goboard1(B),1),k1_funct_1(k2_goboard1(B),k3_finseq_1(B))) & r1_goboard4(k2_goboard1(B),k1_funct_1(k2_goboard1(B),1),k1_funct_1(k2_goboard1(B),k3_finseq_1(B))) & r1_xboole_0(k3_topreal1(2,A),k3_topreal1(2,B)) ) ) ) )).
fof(t26_jgraph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,C) != k5_numbers ) & ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) = k7_xcmplx_0(1,E) ) ) ) & v5_pre_topc(C,A,k3_topmetr) ) ) ) ) ) )).
fof(t26_jgraph_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( A = a_0_3_jgraph_3 => v1_topreal2(A) ) ) )).
fof(t26_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t26_jordan,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v9_rltopsp1(B,k15_euclid(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ? [D] : ( v1_xreal_0(D) & v2_xxreal_0(D) & r1_tarski(B,k1_topreal9(A,C,D)) ) ) ) ) )).
fof(t26_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t26_jordan12,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t26_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ~ ( r1_jordan1h(A,B) & r1_xxreal_0(k1_matrix_0(k1_jordan8(A,B)),k5_jordan11(A,B)) ) ) ) )).
fof(t26_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(C,D) & r1_xxreal_0(D,k1_matrix_0(k1_jordan8(B,k1_nat_1(A,1)))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),D),k8_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),C),k9_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),D)),k8_jordan6(B)) ) ) ) ) ) )).
fof(t26_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t26_jordan18,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t26_jordan19,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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)) ) ) ) )).
fof(t26_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_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,k5_numbers),k15_euclid(2)) ) ) ) )).
fof(t26_jordan1b,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ 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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,k3_finseq_1(k1_jordan8(B,A)))),k9_jordan6(B)) ) ) ) ) )).
fof(t26_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(k1_jordan8(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),k3_finseq_1(k1_jordan8(B,A)),C),k10_xtuple_0(k2_jordan9(B,A))) ) ) ) )).
fof(t26_jordan1g,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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,k2_jordan9(B,A)))),k4_finseq_4(k2_jordan1e(B,A),k22_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))))) ) ) )).
fof(t26_jordan1h,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r2_hidden(k4_tarski(A,B),k2_matrix_0(E)) & r2_hidden(k4_tarski(C,D),k2_matrix_0(E)) & k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,C,D) ) => ( A = C & B = D ) ) ) ) ) ) ) )).
fof(t26_jordan1j,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) ) )).
fof(t26_jordan1k,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v1_xreal_0(C) => k1_topreal6(2,k1_rlvect_1(k15_euclid(2),A,C),k1_rlvect_1(k15_euclid(2),B,C)) = k3_xcmplx_0(k9_complex1(C),k1_topreal6(2,A,B)) ) ) ) )).
fof(t26_jordan20,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( v1_xreal_0(G) => ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t26_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => r1_xxreal_0(k18_euclid(k2_jordan21(k3_topreal1(2,k2_jordan9(A,B)))),k18_euclid(k2_jordan21(k3_topreal1(2,k2_jordan9(A,C))))) ) ) ) ) )).
fof(t26_jordan23,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t26_jordan2b,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( A = a_2_0_jordan2b(B,C) => v3_pre_topc(A,k3_topmetr) ) ) ) ) )).
fof(t26_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ! [F] : ( 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] : ( ( 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,k5_numbers) & F = k1_funct_1(G,1) ) ) ) ) ) ) ) ) ) )).
fof(t26_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(B,k3_topreal1(2,A)) => ( ( B = k1_funct_1(A,k1_nat_1(k1_jordan3(A,B),1)) => k3_finseq_1(k2_jordan3(A,B)) = k6_xcmplx_0(k3_finseq_1(A),k1_jordan3(A,B)) ) & ( B != k1_funct_1(A,k1_nat_1(k1_jordan3(A,B),1)) => k3_finseq_1(k2_jordan3(A,B)) = k2_xcmplx_0(k6_xcmplx_0(k3_finseq_1(A),k1_jordan3(A,B)),1) ) ) ) ) ) )).
fof(t26_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r1_jordan4(A,B,C,D) => ( r1_xxreal_0(C,D) | ( k3_finseq_1(B) = k7_nat_d(k2_xcmplx_0(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)) ) ) ) ) ) ) ) )).
fof(t26_jordan5a,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( A != B <=> k5_measure6(k2_rcomp_1(A,B)) = k1_rcomp_1(A,B) ) ) ) )).
fof(t26_jordan5b,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(C,k1_matrix_0(k2_goboard2(A))) ) => ( r1_xxreal_0(C,B) | k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k3_finseq_1(k2_goboard2(A)),1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k3_finseq_1(k2_goboard2(A)),B)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k3_finseq_1(k2_goboard2(A)),C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k3_finseq_1(k2_goboard2(A)),k1_matrix_0(k2_goboard2(A))))) = k1_xboole_0 ) ) ) ) ) )).
fof(t26_jordan5c,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ( ( v4_topreal1(A) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_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,k1_nat_1(C,1))) ) ) ) ) )).
fof(t26_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( B = a_1_2_jordan5d(A) => k3_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)))) ) ) ) )).
fof(t26_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t26_jordan9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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(k1_nat_1(A,1),k3_finseq_1(C)) ) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t26_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_jordan_a(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( 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,k1_nat_1(C,1))) ) ) ) ) ) ) )).
fof(t26_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( 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] : ( v3_ordinal1(D) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t26_kurato_1,axiom,( k1_tops_1(k3_topmetr,k2_pre_topc(k3_topmetr,k6_kurato_1)) = k2_rcomp_1(2,k1_xxreal_0) )).
fof(t26_kurato_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( v9_rltopsp1(B,k15_euclid(2)) & ! [C] : ( v7_ordinal1(C) => r1_tarski(k2_kurato_2(k15_euclid(2),A,C),B) ) ) => v2_compts_1(k1_kurato_2(k15_euclid(2),A),k15_euclid(2)) ) ) ) )).
fof(t26_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k2_finseq_1(A)) => k9_laplace(A,D,B,C) = k8_laplace(A,D,B,k4_matrix_0(u1_struct_0(B),C)) ) ) ) ) ) )).
fof(t26_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(k11_group_4(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t26_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => r1_lattice2(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ) )).
fof(t26_lattice3,axiom,( ! [A] : v5_lattice3(k1_lattice3(A)) )).
fof(t26_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v3_filter_0(B) & l3_lattices(B) ) => ! [C] : ( m1_lattice4(C,B,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t26_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v8_lattice6(B,A) => r1_tarski(k6_lattice6(A),B) ) ) ) )).
fof(t26_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m1_lattice5(D,A,B,C) => ! [E] : ( v3_ordinal1(E) => v1_lattice5(k6_lattice8(A,B,C,D,E),k3_lattice8(A,E),B) ) ) ) ) ) ) )).
fof(t26_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)))) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ! [E] : ( v7_ordinal1(E) => ( r2_hidden(D,k1_relset_1(k6_glib_000(A),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),B))) => k1_funct_1(k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),k11_lexbfs(A,B,C,E)),D) = k1_funct_1(k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),B),D) ) ) ) ) ) )).
fof(t26_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( v7_ordinal1(C) => r2_relset_1(k2_zfmisc_1(A,A),k1_numbers,k4_lfuzzy_1(A,B,k1_nat_1(C,1)),k3_fuzzy_4(A,A,A,k4_lfuzzy_1(A,B,C),B)) ) ) ) )).
fof(t26_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_limfunc1(A) & m2_valued_0(B,k1_numbers,A) ) => v1_limfunc1(B) ) ) ) )).
fof(t26_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,C) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,C) & ~ r1_xxreal_0(A,D) & r2_hidden(D,k1_relset_1(k1_numbers,B)) ) ) ) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(k6_xcmplx_0(A,C),A))) & ~ v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(k6_xcmplx_0(A,C),A))) ) ) | r2_limfunc2(B,A) ) ) ) ) )).
fof(t26_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r2_limfunc3(C,A) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,D),A),k2_rcomp_1(A,k2_xcmplx_0(A,D))),k3_xboole_0(k9_xtuple_0(B),k9_xtuple_0(C))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,D),A),k2_rcomp_1(A,k2_xcmplx_0(A,D)))) => r1_xxreal_0(k1_funct_1(C,E),k1_funct_1(B,E)) ) ) ) ) | r2_limfunc3(B,A) ) ) ) ) ) )).
fof(t26_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(A,k2_xcmplx_0(A,D)))) & r1_xxreal_0(k2_limfunc2(B,A),k1_funct_1(B,E)) ) ) ) ) | r6_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t26_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t26_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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)) ) ) )).
fof(t26_lopban_3,axiom,( ! [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) & v3_lopban_1(A) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v2_lopban_3(B,A) => v1_lopban_3(B,A) ) ) ) )).
fof(t26_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_lopban_4(A,C,D) => k5_algstr_0(A,k6_algstr_0(A,k9_nat_1(u1_struct_0(A),k1_bhsp_4(A,k1_lopban_4(A,C)),B),k9_nat_1(u1_struct_0(A),k1_bhsp_4(A,k1_lopban_4(A,D)),B)),k9_nat_1(u1_struct_0(A),k1_bhsp_4(A,k1_lopban_4(A,k3_rlvect_1(A,C,D))),B)) = k9_nat_1(u1_struct_0(A),k1_bhsp_4(A,k8_lopban_4(A,C,D,B)),B) ) ) ) ) ) )).
fof(t26_lopclset,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t26_lpspacc1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,C,k6_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,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => ( r1_lpspacc1(B,C,D,E,F) => r1_lpspacc1(B,C,D,k25_valued_1(B,k2_numbers,E,A),k25_valued_1(B,k2_numbers,F,A)) ) ) ) ) ) ) ) )).
fof(t26_lpspace1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,C,k6_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,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t26_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( v2_xxreal_0(F) & v1_xreal_0(F) ) => ( 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)) ) ) ) ) ) ) ) )).
fof(t26_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_hilbert1)) => ( r3_ltlaxio1(B,A) => r3_ltlaxio1(B,k6_ltlaxio1(A)) ) ) ) )).
fof(t26_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(A,k1_ltlaxio1(k1_ltlaxio1(A)))) ) )).
fof(t26_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( m1_subset_1(D,k1_hilbert1) => ( ( r2_hidden(C,k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k6_ltlaxio3,k4_hilbert1(A,B))) & r2_hidden(k4_hilbert1(A,B),k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k6_ltlaxio3,D)) ) => r2_hidden(C,k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k6_ltlaxio3,D)) ) ) ) ) ) )).
fof(t26_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ! [B] : ( m3_ltlaxio4(B,A) => ! [C] : ( m1_trees_1(C,k9_xtuple_0(B)) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k7_finseq_1(C,k9_finseq_1(D)),k9_xtuple_0(B)) => r2_hidden(k1_funct_1(B,k7_finseq_1(C,k9_finseq_1(D))),k9_ltlaxio4(k3_trees_2(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)),B,C))) ) ) ) ) ) )).
fof(t26_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t26_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) )).
fof(t26_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( v3_matrix10(B) & v3_matrix10(C) ) => v3_matrix10(k4_matrix10(A,B,C)) ) ) ) ) )).
fof(t26_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_matrix_2(D,k3_matrix_2(k1_nat_1(A,2))) => k5_matrix_2(B,k1_nat_1(A,2),C,D) = k8_group_1(B,k2_matrix11(A,B,D),C) ) ) ) ) )).
fof(t26_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(C,k4_ordinal1)) => ! [F] : ( m2_finseq_2(F,k4_ordinal1,k4_finseq_2(C,k4_ordinal1)) => ! [G] : ( ( v1_matrix_0(G) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(D))) ) => ( ( r2_hidden(A,k2_finseq_1(C)) & r2_hidden(B,k2_finseq_1(C)) & k1_funct_1(E,A) = k1_funct_1(E,B) ) => ( A = B | k12_matrix_3(C,D,k1_matrix13(u1_struct_0(D),G,C,C,E,F)) = k4_struct_0(D) ) ) ) ) ) ) ) ) ) )).
fof(t26_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(B,C) ) => k1_funct_1(k3_matrix_1(A,C),B) = k3_matrix14(A,C,B) ) ) ) ) )).
fof(t26_matrix15,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ( ~ ( k3_finseq_1(C) = k5_numbers & k3_finseq_1(B) = k5_numbers ) => ( C = k3_matrix15(A,B) <=> ( k8_matrix_0(A,C,1) = B & k1_matrix_0(C) = 1 ) ) ) ) ) ) )).
fof(t26_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v3_matrix16(C,u1_struct_0(B)) & v3_matrix16(D,u1_struct_0(B)) ) => v3_matrix16(k1_matrix_4(B,C,D),u1_struct_0(B)) ) ) ) ) ) )).
fof(t26_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,C,A,B) & m2_finseq_1(D,k3_finseq_2(C)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,C,A,B) & m2_finseq_1(E,k3_finseq_2(C)) ) => k2_matrix_0(D) = k2_matrix_0(E) ) ) ) ) ) )).
fof(t26_matrix_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( ( 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] : ( ( v1_funct_1(F) & v1_funct_2(F,B,A) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,C,A) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(C,A))) ) => ! [H] : ( m1_subset_1(H,k5_finsub_1(B)) => ! [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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t26_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(D) ) => k3_matrix_3(A,B,D) = k1_matrix_4(A,k3_matrix_3(A,B,C),k1_matrix_4(A,C,D)) ) ) ) ) ) )).
fof(t26_matrix_6,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(A),B,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => k4_matrix_0(u1_struct_0(A),k2_matrix_3(A,C)) = k2_matrix_3(A,k4_matrix_0(u1_struct_0(A),C)) ) ) ) )).
fof(t26_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v2_matrix_8(C,A,B) => ( r1_xxreal_0(A,k5_numbers) | v2_matrix_8(k4_matrix_0(u1_struct_0(B),C),A,B) ) ) ) ) ) )).
fof(t26_matrix_9,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t26_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m1_subset_1(B,k2_numbers) => k17_rvsum_1(k10_seq_4(A,B)) = k3_xcmplx_0(B,k17_rvsum_1(A)) ) ) )).
fof(t26_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( ( v1_matrixj1(E,C) & m2_finseq_1(E,k3_finseq_2(k3_finseq_2(C))) ) => ! [F] : ( ( v1_matrixj1(F,C) & m2_finseq_1(F,k3_finseq_2(k3_finseq_2(C))) ) => ( r2_hidden(k4_tarski(A,B),k2_matrix_0(k13_matrixj1(C,D,E))) => k3_matrix_0(C,k13_matrixj1(C,D,E),A,B) = k3_matrix_0(C,k13_matrixj1(C,D,k3_matrixj1(C,E,F)),A,B) ) ) ) ) ) ) ) )).
fof(t26_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(C) = k3_finseq_1(A) & k1_matrix_0(C) = k1_matrix_0(A) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(D,E),k2_matrix_0(A)) => k3_matrix_0(k1_numbers,C,D,E) = k3_real_1(k3_matrix_0(k1_numbers,A,D,E),k3_matrix_0(k1_numbers,B,D,E)) ) ) ) ) => C = k3_matrixr1(A,B) ) ) ) ) )).
fof(t26_matrixr2,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k1_matrix_0(A) = k1_matrix_0(B) ) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(A)) ) => k8_matrix_0(k1_numbers,k5_matrixr1(A,B),C) = k8_rvsum_1(k8_matrix_0(k1_numbers,A,C),k8_matrix_0(k1_numbers,B,C)) ) ) ) ) ) )).
fof(t26_matrlin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,D,C,A) & m2_finseq_1(E,k3_finseq_2(D)) ) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,D,B,A) & m2_finseq_1(F,k3_finseq_2(D)) ) => ( k1_matrix_0(E) = k1_matrix_0(F) => ! [G] : ( v7_ordinal1(G) => ( r2_hidden(G,k2_finseq_1(k1_matrix_0(E))) => k8_matrix_0(D,k8_matrlin(D,C,B,A,E,F),G) = k8_finseq_1(D,k8_matrix_0(D,E,G),k8_matrix_0(D,F,G)) ) ) ) ) ) ) ) ) ) )).
fof(t26_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( k2_vectsp_5(A,B,C,D) = k1_vectsp_4(A,B) => ! [E] : ( m1_matrlin(E,A,C) => ! [F] : ( m1_matrlin(F,A,D) => m1_matrlin(k7_finseq_1(E,F),A,k1_vectsp_5(A,B,C,D)) ) ) ) ) ) ) ) )).
fof(t26_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t26_matrprob,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(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)) ) ) )).
fof(t26_matrtop2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ! [D] : ( ( 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) = A => v1_rlvect_3(k7_ranknull(k15_euclid(A),k15_euclid(B),k3_matrtop1(A,B,C),D),k15_euclid(A)) ) ) ) ) ) )).
fof(t26_matrtop3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t26_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t26_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k3_zfmisc_1(k2_tarski(A,D),k1_tarski(B),k1_tarski(C)) = k2_tarski(k3_xtuple_0(A,B,C),k3_xtuple_0(D,B,C)) )).
fof(t26_measure1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( m1_subset_1(C,k6_numbers) => ! [D] : ( m1_subset_1(D,k6_numbers) => ? [E] : ( v1_funct_1(E) & v1_funct_2(E,B,k6_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & ! [F] : ( 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 ) ) ) ) ) ) ) )).
fof(t26_measure6,axiom,( ! [A] : ( ( v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ( v1_measure5(A) <=> v1_measure5(k1_measure6(A,B)) ) ) ) )).
fof(t26_member_1,axiom,( ! [A] : ( v1_xxreal_0(A) => k6_member_1(k1_tarski(A)) = k1_tarski(k5_xxreal_3(A)) ) )).
fof(t26_membered,axiom,( ! [A] : ( ! [B] : ( r2_hidden(B,A) => v2_membered(B) ) => v2_membered(k3_tarski(A)) ) )).
fof(t26_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_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))) ) ) ) ) )).
fof(t26_mesfun6c,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( m2_subset_1(D,k1_zfmisc_1(B),C) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ( ( v6_supinf_2(E) & r1_xxreal_0(k5_numbers,A) ) => v6_supinf_2(k2_mesfun6c(A,B,E)) ) ) ) ) ) ) )).
fof(t26_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k2_numbers)) & v1_mesfunc8(C,A,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( ( k1_relset_1(A,k4_mesfunc5(A,k2_numbers,C,k5_numbers)) = D & ! [E] : ( v7_ordinal1(E) => r1_mesfun6c(A,B,k4_mesfunc5(A,k2_numbers,C,E),D) ) & ! [E] : ( 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) ) ) ) ) ) )).
fof(t26_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ( ( v1_mesfunc8(C,A,k2_numbers) & B = k1_relset_1(A,k4_mesfunc5(A,k2_numbers,C,k5_numbers)) & ! [D] : ( 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))) ) ) ) )).
fof(t26_mesfunc1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ! [F] : ( m1_subset_1(F,k4_ordinal1) => k9_nat_1(B,C,F) = k9_subset_1(A,E,k17_mesfunc1(A,D,k4_xcmplx_0(F))) ) => k9_subset_1(A,E,k17_mesfunc1(A,D,k2_supinf_1)) = k2_measure2(A,B,k1_measure3(A,B,C)) ) ) ) ) )).
fof(t26_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( ~ 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] : ( 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) ) ) ) ) ) )).
fof(t26_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k5_numbers,C) => ( r2_relset_1(A,k6_numbers,k1_mesfunc2(A,k6_mesfunc1(A,B,C)),k6_mesfunc1(A,k1_mesfunc2(A,B),C)) & r2_relset_1(A,k6_numbers,k2_mesfunc2(A,k6_mesfunc1(A,B,C)),k6_mesfunc1(A,k2_mesfunc2(A,B),C)) ) ) ) ) ) )).
fof(t26_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t26_mesfunc7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( ( r1_mesfunc5(A,B,C,D) & r1_tarski(E,k1_relset_1(A,D)) & ! [H] : ( 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(k4_xxreal_3(F,k12_supinf_2(C,E)),k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,E))) & r1_xxreal_0(k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,E)),k4_xxreal_3(G,k12_supinf_2(C,E))) ) ) ) ) ) ) ) ) ) ) )).
fof(t26_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k6_numbers)) & v1_mesfunc8(C,A,k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( ( k1_relset_1(A,k4_mesfunc5(A,k6_numbers,C,k5_numbers)) = E & ! [F] : ( v7_ordinal1(F) => r1_mesfunc1(A,B,k4_mesfunc5(A,k6_numbers,C,F),E) ) & k1_relset_1(A,D) = E & ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t26_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ~ ( v2_mesfunc9(B,A) & r2_hidden(E,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,k4_mesfunc9(A,B),C))) & k1_mesfunc9(k4_mesfunc5(A,k6_numbers,k4_mesfunc9(A,B),C),E) = k2_supinf_1 & r1_xxreal_0(D,C) & k1_mesfunc9(k4_mesfunc5(A,k6_numbers,B,D),E) = k1_supinf_1 ) ) ) ) ) )).
fof(t26_metric_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v11_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k5_numbers,k1_metric_1(A,B,C)) ) ) ) )).
fof(t26_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k2_metric_2(A)) => ( r2_hidden(B,k6_metric_2(A)) <=> ? [C] : ( m1_subset_1(C,k2_metric_2(A)) & ? [D] : ( m1_subset_1(D,k1_numbers) & r4_metric_2(A,B,C,D) ) ) ) ) ) )).
fof(t26_metric_3,axiom,( ! [A] : ( m1_subset_1(A,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)) => ! [B] : ( m1_subset_1(B,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)) => k2_binop_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k1_numbers,k20_metric_3,A,B) = k2_binop_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k1_numbers,k20_metric_3,B,A) ) ) )).
fof(t26_metric_6,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_funct_1(B) => v3_tbsp_1(B,A) ) ) ) )).
fof(t26_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v4_pre_topc(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( v4_pre_topc(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ! [E] : ( ( v3_pre_topc(E,A) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k1_pre_topc(A,B)))) => ! [H] : ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(k1_pre_topc(A,B)))) => ! [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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t26_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ~ ( B != k4_struct_0(k15_euclid(A)) & ! [C] : ( ( v1_rlvect_3(C,k15_euclid(A)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ~ ( k1_card_1(C) = k6_xcmplx_0(A,1) & k2_struct_0(k1_rlvect_3(k15_euclid(A),C)) = k2_mfold_2(A,B,k4_struct_0(k15_euclid(A))) ) ) ) ) ) )).
fof(t26_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t26_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_midsp_1(A) ) => ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) <=> ? [B] : ( ~ 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] : ( 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) ) ) ) ) )).
fof(t26_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_midsp_3(B,A) => ! [C] : ( m2_midsp_3(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m2_finseq_2(F,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(C))) => ! [G] : ( ( v4_midsp_2(G,C) & l1_midsp_2(G,C) ) => ! [H] : ( m1_subset_1(H,u1_struct_0(u1_midsp_2(C,G))) => ! [I] : ( m2_finseq_2(I,u1_struct_0(u1_midsp_2(C,G)),k4_finseq_2(k1_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)),k1_nat_1(A,1),I,B,H)) = k6_midsp_3(A,C,F,B,E) ) ) ) ) ) ) ) ) ) ) )).
fof(t26_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t26_mod_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( 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)) ) ) ) ) => ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) ) ) )).
fof(t26_mod_4,axiom,( ! [A] : ( ( ~ 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) <=> ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) ) ) )).
fof(t26_modal_1,axiom,( m1_subset_1(k8_funcop_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k2_trees_1(k5_numbers),k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers)),k6_modal_1) )).
fof(t26_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( v1_partfun1(B,A) <=> ! [C] : ~ ( r2_hidden(C,A) & ! [D] : ~ ( r2_hidden(D,A) & r2_hidden(k4_tarski(C,D),B) ) ) ) ) ) )).
fof(t26_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ~ ( r1_modelc_2(B,A) & ~ v3_modelc_2(A) & ~ v6_modelc_2(A) & ~ v4_modelc_2(A) & ~ v5_modelc_2(A) & ~ v7_modelc_2(A) & ~ v8_modelc_2(A) ) ) ) )).
fof(t26_modelc_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_modelc_2(D) & m2_finseq_1(D,k4_ordinal1) ) => ( ( 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) ) ) ) ) ) )).
fof(t26_moebius1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ v1_moebius1(A) & r1_nat_d(B,A) & v1_moebius1(B) ) ) ) )).
fof(t26_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m2_monoid_0(B,A) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t26_monoid_1,axiom,( ! [A] : ( u1_struct_0(k13_monoid_1(A)) = k9_funct_2(A,k4_ordinal1) & 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,k4_ordinal1),k9_funct_2(A,k4_ordinal1)),k9_funct_2(A,k4_ordinal1),u2_algstr_0(k13_monoid_1(A)),k8_monoid_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k23_binop_2,A)) & k5_struct_0(k13_monoid_1(A)) = k5_monoid_1(k4_ordinal1,A,k5_numbers) ) )).
fof(t26_morph_01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t26_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( 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] : ( m1_msualg_2(D,A,k11_msafree(A,B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t26_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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] : ( m3_pboole(D,u1_struct_0(A),u3_msualg_1(A,B)) => ! [E] : ( m3_pboole(E,u1_struct_0(A),u3_msualg_1(A,C)) => ( ( r8_pboole(u1_struct_0(A),D,E) & v3_msualg_2(D,A,B) ) => r8_pboole(u4_struct_0(A),k4_msualg_2(A,C,E),k4_msualg_2(A,B,D)) ) ) ) ) ) ) ) )).
fof(t26_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t26_msscyc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,k11_msafree(A,B)),C)) => ! [G] : ( m1_msaterm(G,A,B,k2_msaterm(A,B,E)) => ! [H] : ( m1_subset_1(H,k4_ordinal1) => ! [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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t26_mssublat,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v13_struct_0(A,1) & v5_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ( u1_struct_0(A) = k1_tarski(k5_numbers) => k9_msualg_1(k12_msualg_1(A,B)) = g3_msualg_1(A,u3_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ) )).
fof(t26_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msualg_2(C,A,B) => ! [D] : ( m1_msualg_2(D,A,B) => k13_msualg_2(A,B,C,D) = k13_msualg_2(A,B,D,C) ) ) ) ) )).
fof(t26_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msualg_6(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_rewrite1(k3_msualg_6(A),D,E) => ! [F] : ( m2_msualg_6(F,A,B,D,E) => ? [G] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t26_msualg_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( ? [C] : ( 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)) ) ) ) )).
fof(t26_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(t26_mycielsk,axiom,( ! [A] : ( ( v1_necklace(A) & l1_orders_2(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t26_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( 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] : ( ( 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] : ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) )).
fof(t26_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => k4_card_1(A) = k1_nat_1(A,1) ) )).
fof(t26_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_abian(A) => k3_nat_d(A,2) = k3_nat_d(k1_nat_1(A,1),2) ) ) )).
fof(t26_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_nat_d(B,k1_newton(B,k11_nat_3(A,B))) => ( B = 1 | A = k5_numbers | r1_nat_d(B,A) ) ) ) ) )).
fof(t26_nat_4,axiom,( v1_int_2(7) )).
fof(t26_nat_5,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ( r1_xboole_0(C,D) => k2_uproots(k4_subset_1(A,C,D),k1_nat_5(A,B,k4_subset_1(A,C,D))) = k2_xcmplx_0(k2_uproots(C,k1_nat_5(A,B,C)),k2_uproots(D,k1_nat_5(A,B,D))) ) ) ) ) )).
fof(t26_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => k5_numbers = k4_nat_d(k5_numbers,A) ) )).
fof(t26_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => m3_nattra_1(k4_nattra_1(A,B,C),A,B,C,C) ) ) ) )).
fof(t26_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( 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(k4_ordinal1,u1_struct_0(B),k8_funct_2(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),D,C),E)) ) ) ) ) ) ) )).
fof(t26_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t26_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( v1_xreal_0(E) => ( v1_partfun1(C,u1_struct_0(A)) => r2_funct_2(k4_ordinal1,u1_struct_0(B),k8_funct_2(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),D,C),E)) ) ) ) ) ) ) )).
fof(t26_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t26_ndiff_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(B)))) ) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t26_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k14_prvect_2(A))) => ! [F] : ( 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))) ) ) ) ) ) ) ) )).
fof(t26_necklace,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k5_card_1(u1_orders_2(k4_necklace(A))) = k3_xcmplx_0(2,k6_xcmplx_0(A,1)) ) ) )).
fof(t26_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_net_1(A))) => ! [C] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t26_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ( ( r3_nfcont_1(A,B,E,C) & r3_nfcont_1(A,B,F,D) ) => ( r3_nfcont_1(A,B,k6_vfunct_1(u1_struct_0(A),B,E,F),k3_xboole_0(C,D)) & r3_nfcont_1(A,B,k2_vfunct_1(u1_struct_0(A),B,E,F),k3_xboole_0(C,D)) ) ) ) ) ) ) )).
fof(t26_nfcont_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) & ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( 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(k2_normsp_0(B,k5_algstr_0(B,k7_partfun1(u1_struct_0(B),C,E),k7_partfun1(u1_struct_0(B),C,F))),k3_xcmplx_0(D,k9_complex1(k6_xcmplx_0(E,F)))) ) ) ) ) ) ) ) )).
fof(t26_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t26_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t26_normsp_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) )).
fof(t26_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k3_normsp_2(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k3_normsp_2(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k4_normsp_2(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k4_normsp_2(A))))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_normsp_2(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k4_normsp_2(A))) => ( ( r1_funct_2(k4_ordinal1,u1_struct_0(k3_normsp_2(A)),k4_ordinal1,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) ) ) ) ) ) ) ) )).
fof(t26_numbers,axiom,( k4_numbers != k2_numbers )).
fof(t26_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t26_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_openlatt(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_openlatt(A))) => ( r3_lattices(k15_openlatt(A),B,C) <=> r1_tarski(B,C) ) ) ) ) )).
fof(t26_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,k2_oppcat_1(B),A) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k3_funct_2(u1_struct_0(B),u1_struct_0(A),k7_cat_1(B,A,k9_oppcat_1(B,A,C)),D) = k3_funct_2(u1_struct_0(k2_oppcat_1(B)),u1_struct_0(A),k7_cat_1(k2_oppcat_1(B),A,C),k3_oppcat_1(B,D)) ) ) ) ) )).
fof(t26_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_ordeq_01(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_ordeq_01(A,B))) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ( ( E = C & F = D ) => ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,A) => r1_xxreal_0(k2_normsp_0(B,k5_algstr_0(B,k7_partfun1(u1_struct_0(B),E,G),k7_partfun1(u1_struct_0(B),F,G))),k2_normsp_0(k5_ordeq_01(A,B),k5_algstr_0(k5_ordeq_01(A,B),C,D))) ) ) ) ) ) ) ) ) ) )).
fof(t26_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v2_orders_1(A) => v2_orders_1(k2_wellord1(A,B)) ) ) )).
fof(t26_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ r2_hidden(B,k3_orders_2(A,C,B)) ) ) ) )).
fof(t26_ordinal2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) ) => ( k4_ordinal2(A) = k3_ordinal2(k10_xtuple_0(A)) & k5_ordinal2(A) = k2_ordinal2(k10_xtuple_0(A)) ) ) )).
fof(t26_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( k10_ordinal2(A,B) = k1_xboole_0 => ( A = k1_xboole_0 & B = k1_xboole_0 ) ) ) ) )).
fof(t26_ordinal4,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( ( r2_hidden(1,B) & v4_ordinal1(A) ) => ( A = k1_xboole_0 | ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_ordinal2(C) ) => ( ( k9_xtuple_0(C) = A & ! [D] : ( v3_ordinal1(D) => ( r2_hidden(D,A) => k1_funct_1(C,D) = k12_ordinal2(B,D) ) ) ) => k12_ordinal2(B,A) = k4_ordinal2(C) ) ) ) ) ) ) )).
fof(t26_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( ( r2_hidden(1,A) & r2_hidden(1,B) ) => r2_hidden(A,k1_ordinal5(A,B)) ) ) ) )).
fof(t26_ordinal6,axiom,( ! [A] : ( v1_ordinal6(A) => ! [B] : ( v1_ordinal6(B) => ( ! [C] : ! [D] : ( ( 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)) ) ) ) )).
fof(t26_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ~ ( ~ r1_orders_2(B,E,C) & ~ r1_orders_2(B,E,G) & ~ r1_orders_2(B,F,C) & ~ r1_orders_2(B,F,G) & ~ r1_orders_2(B,D,C) & k8_group_1(A,k8_group_1(A,k1_ortsp_1(A,B,C,D,E),k1_ortsp_1(A,B,E,C,G)),k1_ortsp_1(A,B,G,E,H)) != k8_group_1(A,k8_group_1(A,k1_ortsp_1(A,B,C,D,F),k1_ortsp_1(A,B,F,C,G)),k1_ortsp_1(A,B,G,F,H)) ) ) ) ) ) ) ) ) ) )).
fof(t26_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( ( 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] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( m1_subset_1(F,k3_msualg_1(A,D,k8_osafree(A,B))) => ! [G] : ( m1_subset_1(G,k3_msualg_1(A,E,k8_osafree(A,B))) => ! [H] : ( 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] : ( m2_finseq_2(I,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) & k4_finseq_1(I) = k4_finseq_1(F) & ! [J] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t26_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t26_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m2_osalg_2(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t26_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t26_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t26_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(t26_partfun2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ( D = k8_relset_1(B,C,E,A) <=> ! [F] : ( m1_subset_1(F,B) => ( r2_hidden(F,D) <=> ( r2_hidden(F,k1_relset_1(B,E)) & r2_hidden(k7_partfun1(C,E,F),A) ) ) ) ) ) ) ) ) )).
fof(t26_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => k3_partit1(A,k3_partit1(A,B,C),D) = k3_partit1(A,B,k3_partit1(A,C,D)) ) ) ) ) )).
fof(t26_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) => ( v8_relat_2(C) => r8_relat_2(C,A) ) ) ) ) )).
fof(t26_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t26_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t26_pcomps_1,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,k5_numbers) & r1_tarski(k8_metric_1(A,B,C),u1_struct_0(A)) ) ) ) )).
fof(t26_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k20_pcs_0(A,B))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k20_pcs_0(A,B))) => ( ( C = E & D = F & r1_orders_2(k20_pcs_0(A,B),E,F) ) => ( C = B | r1_orders_2(A,C,D) ) ) ) ) ) ) ) )).
fof(t26_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k4_real_ns1(A))) => ( r2_relset_1(u1_struct_0(k4_real_ns1(1)),u1_struct_0(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,F),k6_vfunct_1(u1_struct_0(k4_real_ns1(A)),k4_real_ns1(B),D,E)),k6_vfunct_1(u1_struct_0(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,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(B)),k7_pdiff_1(A,C,F),E))) & r2_relset_1(u1_struct_0(k4_real_ns1(1)),u1_struct_0(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,F),k2_vfunct_1(u1_struct_0(k4_real_ns1(A)),k4_real_ns1(B),D,E)),k2_vfunct_1(u1_struct_0(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,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(B)),k7_pdiff_1(A,C,F),E))) ) ) ) ) ) ) ) )).
fof(t26_pdiff_3,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(2)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [C] : ( ( 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) & k10_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) = k6_xcmplx_0(k3_pdiff_3(B,A),k3_pdiff_3(C,A)) ) ) ) ) ) )).
fof(t26_pdiff_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m1_rcomp_1(C,k3_funct_2(k1_euclid(3),k1_numbers,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] : ( ( v9_ordinal1(D) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k1_rvsum_1(E) = k1_tarski(k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(2,3),B)) & r1_tarski(k1_rvsum_1(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),C) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,2,A,B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,2,A,B))))) & k10_pdiff_1(3,2,A,B) = k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,2,A,B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,2,A,B))))) ) ) ) ) ) ) ) ) )).
fof(t26_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( 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) ) ) ) )).
fof(t26_pdiff_6,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(B))) => ! [D] : ( 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)),k4_pdiff_1(A,B),k3_rlvect_1(k4_real_ns1(B),C,D)) = k3_rlvect_1(k4_real_ns1(1),k3_funct_2(u1_struct_0(k4_real_ns1(B)),u1_struct_0(k4_real_ns1(1)),k4_pdiff_1(A,B),C),k3_funct_2(u1_struct_0(k4_real_ns1(B)),u1_struct_0(k4_real_ns1(1)),k4_pdiff_1(A,B),D)) ) ) ) ) )).
fof(t26_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) => ! [D] : ( ( 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] : ( m1_subset_1(E,k4_ordinal1) => ( ( 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] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( v1_xreal_0(F) => ~ ( r2_hidden(E,C) & ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( v1_xreal_0(G) => ~ ( ~ r1_xxreal_0(G,k5_numbers) & ! [H] : ( 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] : ( 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))),k3_xcmplx_0(F,k12_euclid(I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t26_pencil_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( D != k3_pencil_1(A,B) => k1_funct_1(B,D) = k1_funct_1(C,D) ) ) ) ) ) ) )).
fof(t26_pencil_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v15_pencil_1(B) ) => ( ! [C] : ( m1_subset_1(C,A) => v10_pencil_1(k2_pencil_1(A,B,C)) ) => ! [C] : ( ( 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] : ( m1_pencil_2(D,A,B) => ! [E] : ( m1_pencil_2(E,A,B) => ( ( r1_xboole_0(D,E) & r1_pencil_3(A,B,D,E) ) => ! [F] : ( ( ~ v13_pencil_1(F) & v16_pencil_1(F,A) & m3_pboole(F,A,k12_pralg_1(A,B)) ) => ! [G] : ( ( ~ 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t26_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t26_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( A != k5_numbers & B != k5_numbers & k1_newton(A,B) != k3_xcmplx_0(A,k1_newton(A,k7_nat_d(B,1))) ) ) ) )).
fof(t26_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m2_finseq_2(C,B,k3_finseq_2(B)) => ( k9_xtuple_0(k8_pnproc_1(A,B,C)) = k9_funct_2(A,k4_ordinal1) & r1_tarski(k10_xtuple_0(k8_pnproc_1(A,B,C)),k9_funct_2(A,k4_ordinal1)) ) ) ) )).
fof(t26_polyeq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( k2_polyeq_1(B,C,D,A) = k5_numbers => ( B = k5_numbers | ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( v1_xcmplx_0(F) => ~ ( E = k6_xcmplx_0(k1_square_1(k7_xcmplx_0(C,k3_xcmplx_0(2,B))),k7_xcmplx_0(D,B)) & F = k7_xcmplx_0(C,k3_xcmplx_0(2,B)) & A != k6_xcmplx_0(k2_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(E),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(E)),k1_square_1(k4_complex1(E))))),2)),k3_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(E)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(E)),k1_square_1(k4_complex1(E))))),2)),k7_complex1)),F) & A != k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(E),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(E)),k1_square_1(k4_complex1(E))))),2))),k3_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(E)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(E)),k1_square_1(k4_complex1(E))))),2))),k7_complex1)),F) & A != k6_xcmplx_0(k2_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(E),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(E)),k1_square_1(k4_complex1(E))))),2)),k3_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(E)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(E)),k1_square_1(k4_complex1(E))))),2))),k7_complex1)),F) & A != k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(E),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(E)),k1_square_1(k4_complex1(E))))),2))),k3_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(E)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(E)),k1_square_1(k4_complex1(E))))),2)),k7_complex1)),F) ) ) ) ) ) ) ) ) ) )).
fof(t26_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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) ) ) ) ) )).
fof(t26_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => k4_finseq_1(k10_polyform(A,B)) = k2_finseq_1(k11_polyform(A,B)) ) ) )).
fof(t26_polynom1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( ( 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),k10_polynom1(A,B,C,k6_polynom1(A,B,D,E)),k6_polynom1(A,B,k10_polynom1(A,B,C,D),k10_polynom1(A,B,C,E))) ) ) ) ) ) )).
fof(t26_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => 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)) ) ) ) ) )).
fof(t26_polynom5,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_polynom5(A,B,k4_struct_0(A)),k9_polynom3(A)) ) ) )).
fof(t26_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v5_group_1(B) & l5_algstr_0(B) ) => ! [C] : ( ( 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] : ( 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)) ) ) ) )).
fof(t26_polynom8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B != k4_struct_0(A) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => k3_polynom8(A,B,k3_xcmplx_0(C,D)) = k3_polynom8(A,k3_polynom8(A,B,C),D) ) ) ) ) ) )).
fof(t26_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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) ) <=> k3_polynom1(k15_pre_poly(A),C,D) = k3_polynom1(k15_pre_poly(A),C,E) ) ) ) ) ) ) )).
fof(t26_power,axiom,( ! [A] : ( v1_xreal_0(A) => k2_power(1,A) = 1 ) )).
fof(t26_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v4_msualg_1(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,A) & v1_funct_1(F) & v1_partfun1(F,A) & v1_funcop_1(F) ) => ( ! [G] : ( m1_subset_1(G,A) => ? [H] : ( 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(k9_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))))) ) ) ) ) ) ) ) )).
fof(t26_pre_poly,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k3_finseq_2(A)) => k3_finseq_1(k5_pre_poly(A,B)) = k2_wsierp_1(k10_pre_poly(A,B)) ) )).
fof(t26_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t26_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r3_prelamb(A,k2_prelamb(A,B,k3_prelamb(A,D,C)),k2_prelamb(A,k2_prelamb(A,B,C),D)) ) ) ) ) )).
fof(t26_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(1,C) & r1_xxreal_0(1,B) ) => k3_xcmplx_0(k2_prepower(C,A),k2_prepower(B,A)) = k2_prepower(k3_xcmplx_0(C,B),k1_newton(A,k2_xcmplx_0(C,B))) ) ) ) ) )).
fof(t26_prob_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( ~ 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,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => m1_prob_1(k1_prob_1(A,B),A,C) ) ) ) )).
fof(t26_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t26_prob_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( ( v5_relat_1(E,D) & v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k9_setfam_1(C)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(C)))) ) => ( r2_hidden(B,k1_prob_2(C,D,k2_prob_3(C,E),A)) <=> ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(F,A) & r2_hidden(B,k1_prob_2(C,D,E,F)) ) ) ) ) ) )).
fof(t26_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_prob_4(D,A,B,C) => r2_hidden(D,k4_prob_4(A,B,C)) ) ) ) ) )).
fof(t26_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t26_projpl_1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ( ~ r4_projpl_1(A,B,C,D) => r1_zfmisc_1(B,C,D) ) ) ) ) ) )).
fof(t26_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t26_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k1_qc_lang1(A)) => ~ ( ~ r2_qc_lang1(A,B,C) & B != C & ~ r2_qc_lang1(A,C,B) ) ) ) ) )).
fof(t26_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( m1_subset_1(E,k9_qc_lang1(A)) => ! [F] : ( m1_subset_1(F,k9_qc_lang1(A)) => ! [G] : ( m2_subset_1(G,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [H] : ( m2_subset_1(H,k2_qc_lang1(A),k3_qc_lang1(A)) => ( k9_qc_lang2(A,B,C,D,E) = k7_qc_lang2(A,H,G,F) => ( B = H & C = G & k5_qc_lang2(A,D,E) = F ) ) ) ) ) ) ) ) ) ) )).
fof(t26_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t26_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,k5_numbers)),k9_xtuple_0(k2_qc_lang4(A,B))) & k1_funct_1(k2_qc_lang4(A,B),k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,k5_numbers))) = k22_qc_lang1(A,k3_trees_2(k9_qc_lang1(A),k2_qc_lang4(A,B),C)) ) ) ) ) ) )).
fof(t26_quantal1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t26_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => k27_quaterni(k27_quaterni(A)) = A ) )).
fof(t26_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k15_quaterni(k21_quaterni(k7_xcmplx_0(1,k1_square_1(k28_quaterni(A))),k27_quaterni(A))) = k4_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k28_quaterni(A))),k15_quaterni(A))) ) )).
fof(t26_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ( ( k13_quaterni(A) = k5_numbers & k14_quaterni(A) = k5_numbers & k15_quaterni(A) = k5_numbers & k16_quaterni(A) = k5_numbers ) => A = k17_quaterni ) ) )).
fof(t26_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(k1_quin_1(B,C,D),k5_numbers) & ~ ( ~ r1_xxreal_0(k5_numbers,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(A)),k3_xcmplx_0(C,A)),D)) <=> ( ~ r1_xxreal_0(A,k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B))) & ~ r1_xxreal_0(k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B)),A) ) ) ) ) ) ) ) )).
fof(t26_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t26_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_random_1(D,A,B) => ! [E] : ( 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)) = k2_xcmplx_0(k8_random_1(A,B,C,D),k8_random_1(A,B,C,E)) ) ) ) ) ) ) )).
fof(t26_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_6(C,A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t26_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(B,1) & ? [C] : ( v1_int_1(C) & ? [D] : ( v7_ordinal1(D) & k2_rat_1(A) = k3_xcmplx_0(C,B) & k1_rat_1(A) = k3_xcmplx_0(D,B) ) ) ) ) ) )).
fof(t26_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( m1_ratfunc1(B,A) => ! [C] : ( 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) ) ) ) )).
fof(t26_rcomp_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v3_xxreal_2(A) => ( r2_hidden(k3_seq_4(A),A) | r1_tarski(A,k3_limfunc1(k3_seq_4(A))) ) ) ) )).
fof(t26_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => k9_nat_1(k1_numbers,k3_real_3(B),k1_nat_1(A,1)) = k7_xcmplx_0(1,k5_real_1(k9_nat_1(k1_numbers,k3_real_3(B),A),k9_nat_1(k1_numbers,k4_real_3(B),A))) ) ) )).
fof(t26_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k6_real_lat(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k6_real_lat(A))) => ( k1_binop_1(k5_real_lat(A),C,k1_binop_1(k4_real_lat(A),C,B)) = C & k1_binop_1(k5_real_lat(A),k1_binop_1(k4_real_lat(A),B,C),C) = C & k1_binop_1(k5_real_lat(A),C,k1_binop_1(k4_real_lat(A),B,C)) = C & k1_binop_1(k5_real_lat(A),k1_binop_1(k4_real_lat(A),C,B),C) = C ) ) ) ) )).
fof(t26_realset2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(A),k8_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k8_group_1(A,B,C) = k8_group_1(A,B,D) => C = D ) ) ) ) ) )).
fof(t26_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) )).
fof(t26_rearran1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,k1_numbers))) ) => ! [E] : ( ( v1_rearran1(E) & v2_rearran1(E) & v3_rearran1(E,k1_zfmisc_1(B)) & m2_finseq_1(E,k1_zfmisc_1(B)) ) => ( ( v1_partfun1(D,C) & k5_card_1(B) = k5_card_1(C) ) => ( k20_rfunct_3(B,k15_valued_1(B,k1_numbers,k4_rearran1(C,B,E,D),A),B) = k20_rfunct_3(C,k15_valued_1(C,k1_numbers,D,A),C) & k21_rfunct_3(B,k15_valued_1(B,k1_numbers,k4_rearran1(C,B,E,D),A),B) = k21_rfunct_3(C,k15_valued_1(C,k1_numbers,D,A),C) ) ) ) ) ) ) ) )).
fof(t26_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => k3_relat_1(A,k2_xboole_0(C,B)) = k2_xboole_0(k3_relat_1(A,C),k3_relat_1(A,B)) ) ) ) )).
fof(t26_relset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ~ ( k1_relset_1(A,C) != k1_xboole_0 & ! [D] : ( m1_subset_1(D,B) => ~ r2_hidden(D,k2_relset_1(B,C)) ) ) ) ) ) )).
fof(t26_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( 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) ) ) ) ) )).
fof(t26_revrot_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => k26_seq_4(k1_goboard1(B)) = k26_seq_4(k1_goboard1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A))) ) ) )).
fof(t26_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : r2_rewrite1(A,B,B) ) )).
fof(t26_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( 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)) ) ) ) )).
fof(t26_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(C))) => ! [G] : ( l1_rewrite3(G,F) => ( r2_rewrite3(C,F,G,A,D,B,E) => r1_xxreal_0(k1_afinsq_1(E),k1_afinsq_1(D)) ) ) ) ) ) ) )).
fof(t26_rfinseq,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t26_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => k5_rfinseq2(k6_rvsum_1(A)) = k6_rvsum_1(k6_rfinseq2(A)) ) )).
fof(t26_rfunct_1,axiom,( ! [A] : ( ( 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))) ) )).
fof(t26_rfunct_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) ) )).
fof(t26_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,k3_rfunct_3(A,B)) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_rfunct_3(A,B,C,D) => ( E = k5_numbers | r1_rfunct_3(A,B,k17_finseq_1(k3_rfunct_3(A,B),E,C),D) ) ) ) ) ) ) ) )).
fof(t26_rfunct_4,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(t26_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_seq_2(B) => v1_seq_2(k1_valued_0(k1_numbers,B,A)) ) ) ) )).
fof(t26_rinfsup2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v7_valued_0(B) => ( v7_valued_0(k1_valued_0(k6_numbers,B,A)) & k1_rinfsup2(B) = k1_rinfsup2(k1_valued_0(k6_numbers,B,A)) ) ) ) ) )).
fof(t26_rlaffin1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t26_rlaffin3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( ( v1_rlaffin1(D,k15_euclid(A)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) => ! [F] : ( m2_rlaffin3(F,k15_euclid(A),D) => ( ( r1_xxreal_0(B,A) & k5_card_1(D) = k2_xcmplx_0(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)) ) ) ) ) ) ) ) ) )).
fof(t26_rlsub_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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 ) ) ) )).
fof(t26_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t26_rltopsp1,axiom,( ! [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) ) => v3_rltopsp1(k6_domain_1(u1_struct_0(A),k4_struct_0(A)),A) ) )).
fof(t26_rlvect_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( 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) ) ) ) )).
fof(t26_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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(k4_ordinal1,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)))) ) ) ) )).
fof(t26_rlvect_3,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_rlvect_3(B,A) & ! [C] : ( m1_rlvect_3(C,A) => ~ r1_tarski(B,C) ) ) ) ) )).
fof(t26_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( v1_rlvect_3(k8_domain_1(u1_struct_0(A),B,D,C),A) => ( B = C | B = D | C = D | v1_rlvect_3(k8_domain_1(u1_struct_0(A),B,k3_rlvect_1(A,D,B),k3_rlvect_1(A,C,B)),A) ) ) ) ) ) ) )).
fof(t26_rlvect_5,axiom,( ! [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) ) => v1_rlvect_5(k1_rlsub_1(A)) ) )).
fof(t26_rlvect_x,axiom,( ! [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) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( r2_hidden(C,k3_rlvect_x(A,B)) <=> ? [D] : ( v3_card_1(D,k3_finseq_1(B)) & m2_finseq_1(D,u1_struct_0(A)) & ? [E] : ( 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] : ( 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_funct_1(E,F)) ) ) ) ) ) ) ) )).
fof(t26_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) )).
fof(t26_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t26_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t26_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t26_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t26_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v1_lattice3(A) & v2_lattice3(A) & v10_robbins3(A) & l4_robbins3(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k11_lattice3(A,B,C) = k4_robbins3(A,B,C) ) ) ) )).
fof(t26_robbins4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k2_robbins4)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_robbins4)) => ( A = k5_numbers => k3_lattices(k2_robbins4,A,B) = B ) ) ) )).
fof(t26_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t26_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k1_rpr_1(A,B) = k2_xcmplx_0(k1_rpr_1(A,k9_subset_1(A,B,C)),k1_rpr_1(A,k9_subset_1(A,B,k3_subset_1(A,C)))) ) ) ) )).
fof(t26_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & 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)) ) ) ) )).
fof(t26_rusub_1,axiom,( ! [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_bhsp_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_bhsp_1(B) & m1_rusub_1(B,A) ) => ( u1_struct_0(B) = u1_struct_0(A) => B = A ) ) ) )).
fof(t26_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t26_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_3(B,A) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( r1_xboole_0(C,B) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t26_rusub_4,axiom,( ! [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) ) => ! [B] : ( ( ~ 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)) ) ) ) ) )).
fof(t26_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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))) ) ) ) ) )).
fof(t26_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t26_rvsum_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k11_rvsum_2(k9_finseq_1(A),k9_finseq_1(B)) = k9_finseq_1(k3_xcmplx_0(A,B)) ) ) )).
fof(t26_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_scmfsa6c(C) & v2_scmfsa6c(C) & m1_subset_1(C,u1_compos_1(k1_scmfsa_2)) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2,C,k1_scmfsa_m(B)),A),E) ) ) ) ) ) )).
fof(t26_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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(k7_card_1(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)) ) ) )).
fof(t26_scmfsa10,axiom,( ! [A] : ( 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) ) ) )).
fof(t26_scmfsa8a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( ( r5_scmfsa7b(A,k1_scmfsa_m(B),C) & r6_scmfsa7b(A,k1_scmfsa_m(B),C) ) => k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_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(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(C,A),k1_funct_4(B,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))),1))) = k5_card_1(A) ) ) ) ) )).
fof(t26_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( v1_ami_2(E) & ~ v1_scmfsa_m(E) & m1_subset_1(E,u1_struct_0(k1_scmfsa_2)) ) => ( ( k1_funct_1(B,E) = k5_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) ) ) ) ) ) ) ) )).
fof(t26_scmfsa8c,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => k1_funct_1(k2_scmfsa8b(C,A,B),k1_nat_1(k1_nat_1(k5_card_1(A),k5_card_1(B)),3)) = k2_compos_1(k1_scmfsa_2) ) ) ) )).
fof(t26_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => r3_scmfsa9a(A,B,C,D) ) ) ) ) )).
fof(t26_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ~ ( k2_compos_0(u1_compos_1(k1_scmfsa_2),A) = 4 & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => A != k9_scmfsa_2(B,C) ) ) ) ) )).
fof(t26_scmfsa_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( 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) ) ) ) )).
fof(t26_scmfsa_m,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( B != C & k9_scmfsa_m(B,A) = k9_scmfsa_m(C,A) ) ) ) ) )).
fof(t26_scmpds_5,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t26_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => k5_card_1(k2_scmpds_6(A,B,C,D)) = k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),2) ) ) ) ) )).
fof(t26_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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_xcmplx_0(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)))) ) ) ) ) ) )).
fof(t26_scmpds_8,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ! [F] : ( ! [G] : ( ( 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,k5_numbers) ) => ! [H] : ( ( v1_relat_1(H) & v4_relat_1(H,k4_ordinal1) & v5_relat_1(H,u1_compos_1(k1_scmpds_2)) & v1_funct_1(H) & v1_partfun1(H,k4_ordinal1) ) => ( ( ! [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)),k5_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] : ( ( 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)),k5_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) ) ) ) ) ) ) ) ) )).
fof(t26_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t26_scmyciel,axiom,( ! [A] : ( ( v1_finset_1(A) & v4_scmyciel(A) ) => r1_xxreal_0(k2_scmyciel(A),k5_card_1(A)) ) )).
fof(t26_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t26_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C)),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B),C)) ) ) ) )).
fof(t26_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(A) & v1_comseq_2(B) & k1_seq_2(A) = k5_numbers ) => k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) = k5_numbers ) ) ) )).
fof(t26_seq_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v3_funct_1(A) => ! [B] : ( v7_ordinal1(B) => k1_seq_2(A) = k9_nat_1(k1_numbers,A,B) ) ) ) )).
fof(t26_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( r2_seqfunc(A,B,C) => ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,C) => r1_seqfunc(A,k1_numbers,B,k1_tarski(D)) ) ) ) ) ) )).
fof(t26_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_seqm_3(A) & m2_valued_0(B,k1_numbers,A) ) => v1_seqm_3(B) ) ) ) )).
fof(t26_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(k9_nat_1(k1_numbers,A,C),k5_numbers) & k9_nat_1(k1_numbers,B,C) = k6_real_1(k3_funct_2(k4_ordinal1,k1_numbers,A,k1_nat_1(C,1)),k9_nat_1(k1_numbers,A,C)) ) ) & v2_comseq_2(B) ) => ( r1_xxreal_0(1,k1_seq_2(B)) | v1_series_1(A) ) ) ) ) )).
fof(t26_series_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k9_complex1(A),k9_complex1(B))),k2_xcmplx_0(k9_complex1(A),k9_complex1(B))) ) ) )).
fof(t26_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => ~ ( ~ r1_xxreal_0(A,B) & ~ r1_xxreal_0(B,C) & r1_xxreal_0(k7_xcmplx_0(B,k6_xcmplx_0(A,B)),k7_xcmplx_0(C,k6_xcmplx_0(A,C))) ) ) ) ) )).
fof(t26_setfam_1,axiom,( ! [A] : ! [B] : ( B != k1_xboole_0 => k6_subset_1(A,k3_tarski(B)) = k1_setfam_1(k4_setfam_1(k1_tarski(A),B)) ) )).
fof(t26_setlim_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => r1_tarski(k3_prob_1(B,C),k1_funct_1(k2_setlim_1(B,C),A)) ) ) )).
fof(t26_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_setlim_1(C,A) => v1_setlim_1(k6_setlim_2(A,C,B),A) ) ) ) )).
fof(t26_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( m1_subset_1(E,k5_finsub_1(B)) => ( E != k1_xboole_0 => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,B,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t26_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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] : ( v7_ordinal1(D) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t26_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(t26_sfmastr3,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & ~ v1_scmfsa_m(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( k1_funct_1(A,k4_scmfsa_2(k5_numbers)) = 1 => ( ( ~ r1_sfmastr3(F,B,C,D,E,A) & ~ v7_amistd_1(E,k7_card_1(3),k1_scmfsa_2) ) | ( r5_scmfsa7b(k2_sfmastr3(B,C,D,E),A,F) & r6_scmfsa7b(k2_sfmastr3(B,C,D,E),A,F) ) ) ) ) ) ) ) ) ) )).
fof(t26_sgraph1,axiom,( ! [A] : ! [B] : ( r2_sgraph1(A,B) => r1_tarski(k3_sgraph1(A),B) ) )).
fof(t26_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & v8_robbins1(A) & v9_sheffer1(A) & l3_sheffer1(A) ) => v10_sheffer1(A) ) )).
fof(t26_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t26_simplex0,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t26_simplex1,axiom,( ! [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) ) => ! [B] : ( ( v1_matroid0(B) & v3_matroid0(B) & v2_simplex1(B,A) & m1_simplex0(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t26_simplex2,axiom,( ! [A] : ( v7_ordinal1(A) => k4_topdim_1(k15_euclid(A)) = A ) )).
fof(t26_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => k8_complex1(k15_sin_cos(k3_xcmplx_0(A,k7_complex1))) = k15_sin_cos(k4_xcmplx_0(k3_xcmplx_0(A,k7_complex1))) ) )).
fof(t26_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k2_xcmplx_0(k1_funct_1(k1_sin_cos2,A),k1_funct_1(k1_sin_cos2,B)) = k3_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k1_sin_cos2,k2_xcmplx_0(k7_xcmplx_0(A,2),k7_xcmplx_0(B,2)))),k1_funct_1(k3_sin_cos2,k6_xcmplx_0(k7_xcmplx_0(A,2),k7_xcmplx_0(B,2)))) & k6_xcmplx_0(k1_funct_1(k1_sin_cos2,A),k1_funct_1(k1_sin_cos2,B)) = k3_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k1_sin_cos2,k6_xcmplx_0(k7_xcmplx_0(A,2),k7_xcmplx_0(B,2)))),k1_funct_1(k3_sin_cos2,k2_xcmplx_0(k7_xcmplx_0(A,2),k7_xcmplx_0(B,2)))) ) ) ) )).
fof(t26_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k15_sin_cos(k4_xcmplx_0(A)) = k6_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A)) ) )).
fof(t26_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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(k19_sin_cos(A),k17_sin_cos(B))) ) ) )).
fof(t26_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k17_sin_cos(k7_xcmplx_0(A,2)) = k3_square_1(k7_xcmplx_0(k6_xcmplx_0(1,k19_sin_cos(A)),2)) | k17_sin_cos(k7_xcmplx_0(A,2)) = k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k6_xcmplx_0(1,k19_sin_cos(A)),2))) ) ) )).
fof(t26_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( k19_sin_cos(A) = 1 => A = k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k1_int_1(k7_xcmplx_0(A,k3_xcmplx_0(2,k28_sin_cos)))) ) ) )).
fof(t26_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(1,B) & r1_xxreal_0(k9_complex1(B),k9_complex1(A)) ) => r1_xxreal_0(k5_numbers,k6_xcmplx_0(k3_xcmplx_0(B,k3_square_1(k6_xcmplx_0(k1_square_1(A),1))),k3_xcmplx_0(A,k3_square_1(k6_xcmplx_0(k1_square_1(B),1))))) ) ) ) )).
fof(t26_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ( k2_sin_cos2(k3_xcmplx_0(2,A)) = k3_xcmplx_0(k3_xcmplx_0(2,k2_sin_cos2(A)),k4_sin_cos2(A)) & k4_sin_cos2(k3_xcmplx_0(2,A)) = k6_xcmplx_0(k3_xcmplx_0(2,k1_square_1(k4_sin_cos2(A))),1) & k6_sin_cos2(k3_xcmplx_0(2,A)) = k7_xcmplx_0(k3_xcmplx_0(2,k6_sin_cos2(A)),k2_xcmplx_0(1,k1_square_1(k6_sin_cos2(A)))) ) ) )).
fof(t26_sin_cos9,axiom,( k2_partfun1(k1_numbers,k1_numbers,k2_sin_cos9,k1_rcomp_1(k4_xcmplx_0(1),1)) = k2_partfun2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k27_sin_cos,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos)))) )).
fof(t26_sincos10,axiom,( k2_relset_1(k1_numbers,k2_sincos10) = k4_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos) )).
fof(t26_sppol_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( 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)) ) ) ) )).
fof(t26_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( r1_xxreal_0(k3_finseq_1(A),2) => v2_topreal1(A) ) ) )).
fof(t26_sprect_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t26_sprect_3,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t26_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t26_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,B) ) => r1_xxreal_0(k3_square_1(A),k3_square_1(B)) ) ) ) )).
fof(t26_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ( r1_stacks_1(A,B) => k13_stacks_1(A,B) = B ) ) ) )).
fof(t26_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => k3_stirl2_1(A,A) = 1 ) )).
fof(t26_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k16_substut1(A),k3_qc_lang1(A))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(t26_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t26_substlat,axiom,( ! [A] : ! [B] : k5_lattices(k5_substlat(A,B)) = k1_xboole_0 )).
fof(t26_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) != k5_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 ) ) ) ) )).
fof(t26_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ~ ( v2_qc_lang1(B,A) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_subset_1(D,k6_qc_lang1(A),k8_qc_lang1(A,C)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t26_supinf_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( m1_subset_1(D,A) => ( r1_xxreal_0(k11_supinf_2(k6_numbers,A,B,C),k12_supinf_2(C,D)) & r1_xxreal_0(k12_supinf_2(C,D),k10_supinf_2(k6_numbers,A,B,C)) ) ) ) ) ) )).
fof(t26_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r1_orders_2(B,D,k3_rlvect_1(B,E,C)) => ( r1_orders_2(B,D,C) | k1_symsp_1(A,B,C,D,E) = k1_symsp_1(A,B,E,D,C) ) ) ) ) ) ) ) )).
fof(t26_sysrel,axiom,( ! [A] : ( v1_relat_1(A) => k9_xtuple_0(k1_sysrel(A)) = k10_xtuple_0(k1_sysrel(A)) ) )).
fof(t26_taxonom1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( v1_xreal_0(D) => ( ( C = k2_relset_1(k1_numbers,B) & r1_xxreal_0(k1_xxreal_2(C),D) ) => ! [E] : ( m2_subset_1(E,k1_numbers,A) => ! [F] : ( m2_subset_1(F,k1_numbers,A) => r1_xxreal_0(k2_binop_1(A,A,k1_numbers,B,E,F),D) ) ) ) ) ) ) ) )).
fof(t26_taylor_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_numbers)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ? [F] : ( 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] : ( v1_xreal_0(G) => k1_funct_1(F,G) = k6_xcmplx_0(k6_xcmplx_0(k1_funct_1(B,D),k9_nat_1(k1_numbers,k3_series_1(k6_taylor_1(B,C,G,D)),A)),k7_xcmplx_0(k3_xcmplx_0(E,k1_newton(k6_xcmplx_0(D,G),k1_nat_1(A,1))),k2_newton(k1_nat_1(A,1)))) ) ) ) ) ) ) ) )).
fof(t26_taylor_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(C,k5_numbers) & ~ ( k3_funct_2(k4_ordinal1,k1_numbers,k3_series_1(k1_taylor_2(k16_sin_cos,k2_rcomp_1(k4_xcmplx_0(A),A),B)),k2_nat_1(2,C)) = k1_funct_1(k3_series_1(k20_sin_cos(B)),k6_xcmplx_0(C,1)) & k3_funct_2(k4_ordinal1,k1_numbers,k3_series_1(k1_taylor_2(k18_sin_cos,k2_rcomp_1(k4_xcmplx_0(A),A),B)),k2_nat_1(2,C)) = k3_funct_2(k4_ordinal1,k1_numbers,k3_series_1(k21_sin_cos(B)),C) ) ) ) ) ) )).
fof(t26_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t26_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) )).
fof(t26_tdlat_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_tdlat_3(A) <=> ( v3_tdlat_3(A) & ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( B = k1_tarski(C) => v4_pre_topc(B,A) ) ) ) ) ) ) )).
fof(t26_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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)) ) ) ) ) )).
fof(t26_tex_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ 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] : ( ( ~ 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)) ) ) ) ) ) ) )).
fof(t26_tex_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_tex_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t26_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t26_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(t26_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( ~ ( ( r1_tsep_1(C,B) | r1_tsep_1(B,C) ) & ~ ( r1_tsep_1(D,B) & r1_tsep_1(B,D) ) & ~ ( k2_tsep_1(A,k1_tsep_1(A,C,D),B) = k2_tsep_1(A,D,B) & k2_tsep_1(A,B,k1_tsep_1(A,C,D)) = k2_tsep_1(A,B,D) ) ) & ~ ( ~ ( r1_tsep_1(C,B) & r1_tsep_1(B,C) ) & ( r1_tsep_1(D,B) | r1_tsep_1(B,D) ) & ~ ( k2_tsep_1(A,k1_tsep_1(A,C,D),B) = k2_tsep_1(A,C,B) & k2_tsep_1(A,B,k1_tsep_1(A,C,D)) = k2_tsep_1(A,B,C) ) ) ) ) ) ) ) )).
fof(t26_toler_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) )).
fof(t26_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t26_topalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t26_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v1_borsuk_2(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ! [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] : ( 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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t26_topalg_5,axiom,( v3_funct_2(k7_topalg_5,u1_struct_0(k2_gr_cy_1),u1_struct_0(k5_topalg_1(k8_toprealb(2),k9_toprealb))) )).
fof(t26_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m2_subset_1(B,k4_partfun1(k1_numbers,k2_struct_0(A)),k1_topalg_6(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t26_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t26_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t26_topgen_2,axiom,( ! [A] : ! [B] : ( r2_hidden(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(t26_topgen_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( 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))) ) ) )).
fof(t26_topgen_5,axiom,( v4_pre_topc(k1_topgen_5,k3_topgen_5) & m1_subset_1(k1_topgen_5,k1_zfmisc_1(u1_struct_0(k3_topgen_5))) )).
fof(t26_topgrp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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))) ) ) ) ) ) )).
fof(t26_topreal1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ~ ( v5_topreal1(A) & A = k1_xboole_0 ) ) )).
fof(t26_topreal3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(2))) => ! [D] : ( v7_ordinal1(D) => ~ ( ~ r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),A,1),k8_metric_1(k14_euclid(2),C,B)) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k6_xcmplx_0(k3_finseq_1(A),1)) & ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,k6_xcmplx_0(k3_finseq_1(A),1)) ) => ( k9_subset_1(u1_struct_0(k14_euclid(2)),k2_topreal1(2,A,E),k8_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),k8_metric_1(k14_euclid(2),C,B)) ) ) ) ) ) )).
fof(t26_topreal4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( r2_hidden(A,C) & B = a_2_1_topreal4(A,C) ) => r1_tarski(B,C) ) ) ) ) )).
fof(t26_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ~ ( D = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),B,k6_xcmplx_0(1,A)),k1_rlvect_1(k15_euclid(2),C,A)) & D != C & r1_xxreal_0(A,1) & r1_xxreal_0(1,A) ) ) ) ) ) )).
fof(t26_topreal7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ? [C] : ( 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(k1_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(k1_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(k1_nat_1(A,B)))) & ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t26_topreal8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_topreal1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t26_topreal9,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_hidden(C,k4_topreal9(A,B,C)) ) ) ) )).
fof(t26_topreala,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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)))) ) ) ) ) ) )).
fof(t26_toprealb,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k8_toprealb(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( m1_subset_1(B,u1_struct_0(k11_toprealb(A))) => ( r1_xxreal_0(k4_xcmplx_0(1),k17_euclid(B)) & r1_xxreal_0(k17_euclid(B),1) & r1_xxreal_0(k4_xcmplx_0(1),k18_euclid(B)) & r1_xxreal_0(k18_euclid(B),1) ) ) ) ) )).
fof(t26_toprealc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ~ ( A != k5_numbers & r2_hidden(C,k1_topreal9(A,D,B)) & r1_xxreal_0(k3_xcmplx_0(A,B),k9_complex1(k16_rvsum_1(k5_algstr_0(k15_euclid(A),C,D)))) ) ) ) ) ) )).
fof(t26_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => k12_euclid(k4_algstr_0(k15_euclid(A),B)) = k12_euclid(B) ) ) )).
fof(t26_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)))) ) ) )).
fof(t26_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_pre_topc(C,A) => ( v4_pre_topc(B,A) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) => ( D = B => v4_pre_topc(D,C) ) ) ) ) ) ) )).
fof(t26_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v3_tops_1(C,A) & r1_tarski(B,C) ) => v3_tops_1(B,A) ) ) ) ) )).
fof(t26_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => v1_transgeo(A) ) )).
fof(t26_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t26_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( v2_trees_2(B,A) & m1_trees_2(B,A) ) => r2_hidden(k1_xboole_0,B) ) ) )).
fof(t26_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t26_trees_4,axiom,( ! [A] : ! [B] : k13_funct_3(k1_trees_4(A),k1_trees_4(B)) = k1_trees_4(k4_tarski(A,B)) )).
fof(t26_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : k12_trees_9(k1_tarski(A),B) = k7_trees_9(A,B) ) )).
fof(t26_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ 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)) ) ) ) ) ) ) )).
fof(t26_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(D))) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t26_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t26_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( m2_funct_2(B,k4_numbers,u1_turing_1(A),k9_funct_2(k4_numbers,u1_turing_1(A))) => ! [C] : ( v1_int_1(C) => ! [D] : ( m1_subset_1(D,u1_turing_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t26_twoscomp,axiom,( k1_funct_1(k33_twoscomp,k11_finseq_1(k5_numbers,k5_numbers,k5_numbers)) = k5_numbers & k1_funct_1(k33_twoscomp,k11_finseq_1(k5_numbers,k5_numbers,1)) = 1 & k1_funct_1(k33_twoscomp,k11_finseq_1(k5_numbers,1,k5_numbers)) = 1 & k1_funct_1(k33_twoscomp,k11_finseq_1(k5_numbers,1,1)) = k5_numbers & k1_funct_1(k33_twoscomp,k11_finseq_1(1,k5_numbers,k5_numbers)) = 1 & k1_funct_1(k33_twoscomp,k11_finseq_1(1,k5_numbers,1)) = k5_numbers & k1_funct_1(k33_twoscomp,k11_finseq_1(1,1,k5_numbers)) = k5_numbers & k1_funct_1(k33_twoscomp,k11_finseq_1(1,1,1)) = 1 )).
fof(t26_unialg_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t26_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => k2_uniroots(A) = a_1_1_uniroots(A) ) )).
fof(t26_uproots,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( C != k9_polynom3(A) & k2_polynom5(A,C,B) = k9_polynom3(A) ) ) ) ) )).
fof(t26_urysohn2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( m1_subset_1(B,k6_numbers) => ! [C] : ( m1_subset_1(C,k6_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) ) ) ) ) ) )).
fof(t26_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [F] : ( m2_funct_2(F,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ? [G] : ( m2_funct_2(G,k3_qc_lang1(A),B,k2_valuat_1(A,B)) & ! [H] : ( 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) ) ) ) ) ) ) ) )).
fof(t26_valued_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ( ( v3_funct_1(B) & m2_valued_0(C,A,B) ) => r2_funct_2(k4_ordinal1,A,B,C) ) ) ) ) )).
fof(t26_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( r1_tarski(k9_xtuple_0(A),k4_ordinal1) => ! [B] : ( v7_ordinal1(B) => k10_xtuple_0(k61_valued_1(A,B)) = k10_xtuple_0(A) ) ) ) )).
fof(t26_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t26_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(k6_vectsp10(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k6_vectsp10(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t26_vectsp11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( ~ 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] : ( ( 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)))) ) ) ) ) ) )).
fof(t26_vectsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(t26_vectsp_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t26_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) )).
fof(t26_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t26_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => ! [D] : ( m1_vectsp_6(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t26_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( 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)) ) ) ) ) )).
fof(t26_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t26_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t26_waybel10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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)))) ) ) ) )).
fof(t26_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_waybel11(A,B))) => k2_waybel_0(A,k4_waybel11(A,B),C) = B ) ) ) )).
fof(t26_waybel12,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t26_waybel13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t26_waybel14,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t26_waybel15,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t26_waybel16,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( ? [C] : ( 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) ) ) ) )).
fof(t26_waybel17,axiom,( ! [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] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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] : ( 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)) ) ) ) ) ) )).
fof(t26_waybel19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t26_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t26_waybel21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t26_waybel23,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t26_waybel24,axiom,( ! [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) & l1_waybel_9(A) ) => ! [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) & l1_waybel_9(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_waybel24(A,B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_funct_1(k1_yellow_0(k5_yellow_1(u1_struct_0(A),B),C),D) = k1_yellow_0(B,a_4_2_waybel24(A,B,C,D)) ) ) ) ) )).
fof(t26_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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(k1_yellow_1(u1_pre_topc(A))) ) ) ) )).
fof(t26_waybel27,axiom,( ! [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] : ( ( 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),k5_yellow_1(u1_struct_0(A),B)) & m1_yellow_0(k2_waybel27(A,B),k5_yellow_1(u1_struct_0(A),B)) ) ) ) )).
fof(t26_waybel28,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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)) ) ) )).
fof(t26_waybel29,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & l1_pre_topc(A) ) => ( v3_waybel_3(k1_yellow_1(u1_pre_topc(A))) <=> ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(B),u1_struct_0(k1_waybel29(k1_yellow_1(u1_pre_topc(A))))) & v5_pre_topc(C,B,k1_waybel29(k1_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(k1_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)))) ) ) ) ) ) )).
fof(t26_waybel30,axiom,( ! [A] : ( ( 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] : ( ( 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)) ) ) )).
fof(t26_waybel31,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t26_waybel33,axiom,( ! [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) & v1_waybel33(A) & l1_waybel_9(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v3_waybel_7(B,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))))) ) => r2_waybel_7(A,B,k1_waybel33(A,k2_struct_0(A),B)) ) ) )).
fof(t26_waybel34,axiom,( ! [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] : ( ( 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] : ( ( 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] : ( ( v4_waybel11(D) & m1_yellow_9(D,B) ) => ! [E] : ( ( v4_waybel11(E) & m1_yellow_9(E,A) ) => ( ! [F] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t26_waybel35,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_waybel35(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ( ( v3_waybel35(C,A,B) & m1_waybel35(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & r2_hidden(E,C) & r2_orders_2(A,D,E) & ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t26_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ! [C] : ( 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))) ) ) ) ) )).
fof(t26_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t26_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ! [C] : ( ( 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] : ( 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)) ) ) ) )).
fof(t26_waybel_3,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => v1_waybel_3(B,A) ) => v2_waybel_3(A) ) ) )).
fof(t26_waybel_4,axiom,( ! [A] : ( ( 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))) ) )).
fof(t26_waybel_5,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t26_waybel_6,axiom,( ! [A] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t26_waybel_7,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ~ 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) ) ) ) )).
fof(t26_waybel_8,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k2_yellow_1(A))) <=> r1_tarski(B,A) ) )).
fof(t26_waybel_9,axiom,( ! [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) & l1_waybel_9(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & v3_yellow_6(B,A) & l1_waybel_0(B,A) ) => ! [C] : ( 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))) ) ) ) ) )).
fof(t26_weddwitt,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t26_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [C] : ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t26_wellord1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( v2_wellord1(C) => r3_xboole_0(k1_wellord1(C,A),k1_wellord1(C,B)) ) ) )).
fof(t26_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_nat_d(k1_newton(A,C),k1_newton(B,C)) => ( r1_xxreal_0(C,k5_numbers) | r1_nat_d(A,B) ) ) ) ) ) )).
fof(t26_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(A,B) => r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,C)) ) )).
fof(t26_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k6_xboolean(A,k7_xboolean(A,B)) = k6_xboolean(A,B) ) ) )).
fof(t26_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => A = k6_xcmplx_0(k2_xcmplx_0(A,B),B) ) ) )).
fof(t26_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k4_xcmplx_0(B),A) => r1_xxreal_0(k4_xcmplx_0(A),B) ) ) ) )).
fof(t26_xtuple_0,axiom,( ! [A] : ! [B] : r1_tarski(k5_xboole_0(k9_xtuple_0(A),k9_xtuple_0(B)),k9_xtuple_0(k5_xboole_0(A,B))) )).
fof(t26_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t26_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( r1_xxreal_0(A,B) => k3_xxreal_1(B,A) = k1_xboole_0 ) ) ) )).
fof(t26_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( ~ r1_xxreal_0(B,A) => k2_xxreal_2(k2_xxreal_1(A,B)) = A ) ) ) )).
fof(t26_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t26_yellow10,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( 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)))) ) ) ) )).
fof(t26_yellow12,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t26_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m2_yellow13(B,A) => r1_tarski(u1_pre_topc(A),k1_cantor_1(u1_struct_0(A),k1_tdlat_2(A,B))) ) ) )).
fof(t26_yellow14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t26_yellow15,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) => ! [C] : ( ( 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] : ~ ( r2_hidden(D,k2_yellow15(u1_struct_0(A),C)) & ~ r1_xboole_0(B,D) & ~ r1_tarski(D,B) ) ) ) ) ) ) )).
fof(t26_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & v4_waybel_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v4_waybel_0(C,B) & m1_yellow_0(C,B) ) => ( v4_waybel_0(C,A) & m1_yellow_0(C,A) ) ) ) ) )).
fof(t26_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t26_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_pre_topc(A,B)) <=> ? [D] : ( ~ v1_xboole_0(D) & v2_waybel_0(D,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(D,k2_yellow_1(k2_struct_0(A))) & v3_waybel_7(D,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))))) & r2_hidden(B,D) & r2_waybel_7(A,D,C) ) ) ) ) ) )).
fof(t26_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_altcat_2(B,A) ) => ( v2_altcat_2(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( E = C & F = D ) => k1_altcat_1(B,E,F) = k1_altcat_1(A,C,D) ) ) ) ) ) ) ) ) )).
fof(t26_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [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] : ( r1_yellow_0(A,C) => k1_yellow_0(A,C) = k1_yellow_0(B,C) ) ) ) ) )).
fof(t26_yellow_1,axiom,( ! [A] : ( ( 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) ) => k4_yellow_1(k1_xboole_0,A) = g1_orders_2(k1_tarski(k1_xboole_0),k6_partfun1(k1_tarski(k1_xboole_0))) ) )).
fof(t26_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r2_yellow_0(A,B) ) => ! [B] : ( r2_yellow_0(A,B) & k2_yellow_0(A,B) = k2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) ) ) ) )).
fof(t26_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t26_yellow_4,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t26_yellow_5,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_yellow_5(A,B,k12_lattice3(A,C,D)) => r2_yellow_5(A,B,C) ) ) ) ) ) )).
fof(t26_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( 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))) ) ) ) )).
fof(t26_yellow_7,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( 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)))) ) ) ) )).
fof(t26_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v7_pre_topc(A) => ! [B] : ( 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) ) ) ) )).
fof(t26_yellow_9,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t26_zf_fund1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ( k4_zf_fund1(k6_domain_1(k1_zf_lang,A)) = k6_domain_1(k4_ordinal1,k3_zf_fund1(A)) & k4_zf_fund1(k7_domain_1(k1_zf_lang,A,B)) = k7_domain_1(k4_ordinal1,k3_zf_fund1(A),k3_zf_fund1(B)) ) ) ) )).
fof(t26_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( k1_funct_1(A,1) = 2 => v4_zf_lang(A) ) ) )).
fof(t26_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v9_zf_lang(A) => k26_zf_lang(A) = k20_zf_lang(k22_zf_lang(k20_zf_lang(A))) ) ) )).
fof(t26_zfmisc_1,axiom,( ! [A] : ! [B] : k3_tarski(k2_tarski(k1_tarski(A),k1_tarski(B))) = k2_tarski(A,B) )).
fof(t26_zfrefle1,axiom,( ! [A] : ( v3_ordinal1(A) => ( r2_ordinal2(A,k1_xboole_0) => A = k1_xboole_0 ) ) )).
fof(t26_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => k4_struct_0(B) = k4_struct_0(A) ) ) )).
fof(t26_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( m1_zmodul02(C,A) => r1_tarski(k18_zmodul02(A,k22_zmodul02(A,B,C)),k4_subset_1(u1_struct_0(A),k18_zmodul02(A,B),k18_zmodul02(A,C))) ) ) ) )).
fof(t26_zmodul03,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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) & v1_zmodul03(B) & l1_zmodul01(B) ) => ! [C] : ( m1_zmodul03(C,B) => k1_card_1(a_3_0_zmodul03(A,B,C)) = k1_card_1(C) ) ) ) )).
fof(t270_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) )).
fof(t271_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) )).
fof(t272_xxreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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) ) ) )).
fof(t273_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(D,A) => r1_xboole_0(k2_xxreal_1(C,D),k4_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t274_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(D,A) => r1_xboole_0(k2_xxreal_1(C,D),k3_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t275_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(D,A) => r1_xboole_0(k4_xxreal_1(C,D),k4_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t276_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(D,A) => r1_xboole_0(k4_xxreal_1(C,D),k3_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t277_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ~ r1_xxreal_0(A,D) => r1_xboole_0(k1_xxreal_1(C,D),k2_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t278_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ~ r1_xxreal_0(A,D) => r1_xboole_0(k1_xxreal_1(C,D),k1_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t279_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ~ r1_xxreal_0(A,D) => r1_xboole_0(k3_xxreal_1(C,D),k2_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t27_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_abcmiz_0(A,B,k1_subset_1(u1_abcmiz_0(A))) = B ) ) )).
fof(t27_abcmiz_1,axiom,( ! [A] : ( 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)) ) )).
fof(t27_abcmiz_a,axiom,( k23_abcmiz_1(k8_abcmiz_a) = k6_abcmiz_1 & k25_abcmiz_1(k8_abcmiz_a) = k1_xboole_0 & k26_abcmiz_1(k8_abcmiz_a) = k5_numbers )).
fof(t27_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( k9_complex1(A) = k9_complex1(B) & A != B & A != k4_xcmplx_0(B) ) ) ) )).
fof(t27_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_aff_1(A,B,C,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t27_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t27_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t27_afinsq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_finset_1(B) & v6_membered(B) ) => ! [C] : ( ( 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) ) ) ) ) ) ) )).
fof(t27_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k13_afproj(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t27_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k1_afvect0(A,D,B) = C <=> r2_analoaf(A,B,D,D,C) ) ) ) ) ) )).
fof(t27_algspec1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_partfun1(A,B) => ! [C] : ( m1_algspec1(C,A) => ! [D] : ( m1_algspec1(D,B) => m1_algspec1(k1_funct_4(C,D),k1_funct_4(A,B)) ) ) ) ) ) )).
fof(t27_algstr_4,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_tarski(k12_algstr_4(A),k12_algstr_4(B)) ) )).
fof(t27_altcat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t27_altcat_3,axiom,( ! [A] : ( l1_altcat_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v7_altcat_3(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,k1_altcat_1(A,C,B)) & r2_hidden(D,k1_altcat_1(A,C,B)) & ! [E] : ( m1_subset_1(E,k1_altcat_1(A,C,B)) => ( r2_hidden(E,k1_altcat_1(A,C,B)) => D = E ) ) ) ) ) ) ) )).
fof(t27_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t27_ami_3,axiom,( k8_struct_0(k1_ami_3) = k2_ami_2 )).
fof(t27_ami_wstd,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_setfam_1(B) => ! [C] : ( ( ~ 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] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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(k4_ordinal1,D)) ) ) ) ) ) )).
fof(t27_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_analmetr(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C))) => ? [G] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t27_analoaf,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ( ( ~ ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = C ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ~ r2_analoaf(A,B,C,D,E) & ~ r2_analoaf(A,B,C,E,D) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( B != D & r2_analoaf(A,D,B,B,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_analoaf(A,C,B,B,F) & r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( ~ r2_analoaf(A,B,C,D,E) & ~ r2_analoaf(A,B,C,E,D) & ! [F] : ( 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) ) ) ) )).
fof(t27_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( r1_analmetr(A,F,G) => ( r1_analoaf(A,B,D,C,E) <=> ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & ? [I] : ( m1_subset_1(I,u1_struct_0(A)) & H != I & r1_analort(A,F,G,H,I,B,D) & r1_analort(A,F,G,H,I,C,E) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t27_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => ~ ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( 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 = k5_numbers & F = k5_numbers & G = k5_numbers ) ) ) ) ) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ? [F] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & 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] : ( m1_subset_1(B,u1_struct_0(k5_anproj_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_anproj_1(A))) => ~ ( B != C & ! [D] : ( m1_subset_1(D,u1_struct_0(k5_anproj_1(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_anproj_1(A))) => ? [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t27_aofa_a00,axiom,( k2_finseq_1(9) = k7_enumset1(1,2,3,4,5,6,7,8,9) )).
fof(t27_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,B),D)) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,B),E)) => ! [I] : ( m1_subset_1(I,k1_funct_1(u3_msualg_1(A,B),F)) => ! [J] : ( m2_pboole(J,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [K] : ( m1_subset_1(K,u4_struct_0(A)) => ( k1_msualg_1(A,K) = k3_finseq_4(u1_struct_0(A),D,E,F) => ! [L] : ( m1_subset_1(L,k3_msualg_1(A,K,B)) => ( L = k11_finseq_1(G,H,I) => k5_msualg_3(A,B,C,K,J,L) = k11_finseq_1(k3_funct_2(k1_funct_1(u3_msualg_1(A,B),D),k1_funct_1(u3_msualg_1(A,C),D),k2_msafree4(u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C),J,D),G),k3_funct_2(k1_funct_1(u3_msualg_1(A,B),E),k1_funct_1(u3_msualg_1(A,C),E),k2_msafree4(u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C),J,E),H),k3_funct_2(k1_funct_1(u3_msualg_1(A,B),F),k1_funct_1(u3_msualg_1(A,C),F),k2_msafree4(u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C),J,F),I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t27_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [E] : ( ( v1_aofa_i00(E,A,B,D) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),D) ) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),E) => ! [G] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t27_armstrng,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( r4_armstrng(A,B,C,D) <=> ( r2_hidden(k6_armstrng(A,C,D),B) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t27_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ~ ( ~ r1_arytm_2(C,B) & A != k11_arytm_3 & k4_tarski(k11_arytm_3,k8_arytm_2(A,k1_arytm_1(C,B))) != k2_arytm_1(k8_arytm_2(A,B),k8_arytm_2(A,C)) ) ) ) ) )).
fof(t27_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ( A != k1_xboole_0 => k4_arytm_3(A,A) = 1 ) ) )).
fof(t27_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k8_asympt_0(A) = a_1_2_asympt_0(A) ) )).
fof(t27_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(B,k5_numbers) => k9_nat_1(k1_numbers,A,B) = k2_power(B,k3_square_1(B)) ) ) & ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v4_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & v4_asympt_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( r2_funct_2(k4_ordinal1,k1_numbers,B,A) & r2_funct_2(k4_ordinal1,k1_numbers,C,k1_asympt_1(2,1,k5_numbers)) & r1_tarski(k6_asympt_0(B),k6_asympt_0(C)) & k6_asympt_0(B) != k6_asympt_0(C) ) ) ) ) ) )).
fof(t27_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( 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] : ( m2_funct_2(C,u1_struct_0(A),u1_struct_0(A),k1_autalg_1(A)) => ( B = k16_funcop_1(k5_numbers,C) => r2_hidden(B,k5_autalg_1(k6_msualg_1(A),k9_msualg_1(A))) ) ) ) ) )).
fof(t27_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t27_bagorder,axiom,( ! [A] : ( v3_ordinal1(A) => v2_wellord1(k7_bagorder(A)) ) )).
fof(t27_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( r2_hidden(B,k5_bcialg_1(A)) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t27_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) & v4_bcialg_2(B,A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v1_bcialg_2(B,A) ) ) ) )).
fof(t27_bcialg_3,axiom,( ! [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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( m1_bcialg_3(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t27_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t27_bcialg_6,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_bcialg_6(B,A) & k4_bcialg_6(A,B) = 1 ) ) ) ) )).
fof(t27_bciideal,axiom,( ! [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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) )).
fof(t27_bhsp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => k3_bhsp_1(B,k1_rlvect_1(B,C,A)) = k3_xcmplx_0(k9_complex1(A),k3_bhsp_1(B,C)) ) ) ) )).
fof(t27_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) & k1_seq_2(k2_bhsp_2(A,k3_normsp_1(A,D,E))) = k3_bhsp_1(A,k5_algstr_0(A,B,C)) ) ) ) ) ) ) ) )).
fof(t27_bhsp_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( ( ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k9_nat_1(k1_numbers,k2_bhsp_2(B,C),D),k9_nat_1(k1_numbers,A,D)) ) & v1_series_1(A) ) => v2_bhsp_4(C,B) ) ) ) ) )).
fof(t27_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t27_binari_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t27_binari_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v1_int_1(B) => ( ( r1_xxreal_0(B,k6_xcmplx_0(k5_series_1(2,k7_nat_d(A,1)),1)) & r1_xxreal_0(k4_xcmplx_0(k5_series_1(2,k7_nat_d(A,1))),B) ) => k3_binari_2(A,k2_binari_4(A,B)) = B ) ) ) )).
fof(t27_binom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( 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] : ( v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(A,k4_ordinal1),B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1),B))) & ! [F] : ( m1_subset_1(F,A) => ( k2_binop_1(A,k4_ordinal1,B,E,F,k5_numbers) = C & ! [G] : ( m1_subset_1(G,k4_ordinal1) => k2_binop_1(A,k4_ordinal1,B,E,F,k1_nat_1(G,1)) = k2_binop_1(B,A,B,D,k2_binop_1(A,k4_ordinal1,B,E,F,G),F) ) ) ) ) ) ) ) ) )).
fof(t27_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_lattices(A,B,k1_boolealg(A,C,B)) => r1_boolealg(A,B,k5_lattices(A)) ) ) ) ) )).
fof(t27_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) ) => ! [C] : ( 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))) ) ) ) ) )).
fof(t27_borsuk_4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t27_borsuk_5,axiom,( ! [A] : ( 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) ) ) )).
fof(t27_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t27_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( r1_zfmisc_1(A,B,C) => ( k1_funct_1(k1_borsuk_7(A,B,C,D,E,F),A) = D & k1_funct_1(k1_borsuk_7(A,B,C,D,E,F),B) = E & k1_funct_1(k1_borsuk_7(A,B,C,D,E,F),C) = F ) ) )).
fof(t27_bspace,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k2_bspace)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_bspace)) => ! [D] : ( 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)) ) ) ) )).
fof(t27_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))))) ) ) ) ) )).
fof(t27_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t27_bvfunc14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ( 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) ) ) )).
fof(t27_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t27_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t27_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t27_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t27_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t27_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t27_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t27_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t27_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t27_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t27_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t27_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k11_c0sp1(A))) => r1_xxreal_0(k5_numbers,k2_normsp_0(k11_c0sp1(A),B)) ) ) )).
fof(t27_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t27_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_valuat_1(C,A,B) => ! [D] : ( m2_finseq_1(D,k3_cqc_lang(A)) => ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t27_calcul_2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)))) ) ) ) ) ) )).
fof(t27_card_1,axiom,( ! [A] : ! [B] : ( r2_wellord2(A,k1_tarski(B)) <=> ? [C] : A = k1_tarski(C) ) )).
fof(t27_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ! [C] : ( 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)) ) ) ) )).
fof(t27_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( k9_xtuple_0(A) = k9_xtuple_0(B) & ! [C] : ( 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)) ) ) ) )).
fof(t27_card_5,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t27_card_fil,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ( v5_card_fil(A) => v2_card_1(A) ) ) )).
fof(t27_card_fin,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( k8_relat_1(D,k1_tarski(A)) = k8_relat_1(k5_relat_1(D,B),k1_tarski(A)) => k2_card_fin(C,D,A) = k2_card_fin(C,k5_relat_1(D,B),A) ) ) ) )).
fof(t27_card_lar,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) & ~ v4_card_3(A) ) => ( v4_card_lar(A) => v1_card_5(A) ) ) )).
fof(t27_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,B,C) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t27_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,C,D) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( 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(k8_cat_2(A,B,E,H),k6_cat_2(A,B),k7_cat_2(A,B,C,F),k7_cat_2(A,B,D,G)) ) ) ) ) ) ) ) ) ) )).
fof(t27_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,B,C) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t27_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,D,B) => ! [F] : ( 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 & ( v7_cat_1(E,A,D,B) | v7_cat_1(F,A,D,C) ) & ~ v7_cat_1(k9_cat_4(A,B,C,D,E,F),A,D,k2_cat_4(A,B,C)) ) ) ) ) ) ) ) )).
fof(t27_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t27_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(k2_nat_1(2,k1_nat_1(A,1)),B) => k5_card_1(k7_subset_1(k9_funct_2(B,k2_tarski(1,k5_numbers)),k1_card_fin(B,k1_nat_1(A,1),1,k5_numbers),k2_catalan2(B,k1_nat_1(A,1)))) = k5_card_1(k1_card_fin(B,A,1,k5_numbers)) ) ) ) )).
fof(t27_catalg_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t27_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v3_rlvect_1(A) & v4_rlvect_1(A) & v13_algstr_0(A) ) => k4_algstr_0(k4_cayldick(A),k5_cayldick(A,B,C)) = k5_cayldick(A,k4_algstr_0(A,B),k4_algstr_0(A,C)) ) ) ) ) )).
fof(t27_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k7_cc0sp1(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k7_cc0sp1(A))))) ) => ( v1_csspace3(B,k7_cc0sp1(A)) => v9_clvect_1(B,k7_cc0sp1(A)) ) ) ) )).
fof(t27_cc0sp2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v1_compts_1(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_cc0sp2(B))) => k2_normsp_0(k5_cc0sp2(B),k1_clvect_1(k5_cc0sp2(B),C,A)) = k3_xcmplx_0(k9_complex1(A),k2_normsp_0(k5_cc0sp2(B),C)) ) ) ) )).
fof(t27_cfcont_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( ( v3_funct_1(B) & r2_hidden(A,k2_relset_1(k2_numbers,B)) ) | ( v3_funct_1(B) & ? [C] : ( v7_ordinal1(C) & k9_nat_1(k2_numbers,B,C) = A ) ) ) => k3_comseq_2(B) = A ) ) ) )).
fof(t27_cfuncdom,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(t27_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t27_cgames_1,axiom,( ! [A] : ! [B] : ( v2_cgames_1(B) => ( r2_hidden(A,k10_cgames_1(B)) <=> ~ ( A != B & ! [C] : ( v2_cgames_1(C) => ~ ( r2_hidden(C,k8_cgames_1(B)) & r2_hidden(A,k10_cgames_1(C)) ) ) ) ) ) )).
fof(t27_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ( ! [F] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(A)) => ~ r1_xxreal_0(k1_funct_1(B,F),k1_funct_1(C,F)) ) => ( r1_tarski(k3_chain_1(A,B,C),k3_chain_1(A,D,E)) <=> ! [F] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(A)) => ( r1_xxreal_0(k1_funct_1(C,F),k1_funct_1(E,F)) & ~ r1_xxreal_0(k1_funct_1(D,F),k1_funct_1(E,F)) & r1_xxreal_0(k1_funct_1(D,F),k1_funct_1(B,F)) ) ) ) ) ) ) ) ) ) )).
fof(t27_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v5_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t27_circcmb3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_circcmb3(B,A) => ! [C] : ( m1_circcmb3(C,A) => ! [D] : ( m2_circcmb3(D,A,B) => ! [E] : ( m2_circcmb3(E,A,C) => r2_circcomb(B,C,D,E) ) ) ) ) ) )).
fof(t27_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msualg_1(D,B) & l3_msualg_1(D,B) ) => ( r1_partfun1(u3_msualg_1(A,C),u3_msualg_1(B,D)) => ! [E] : ( m1_subset_1(E,u4_struct_0(k2_circcomb(A,B))) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t27_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_msualg_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t27_classes1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r2_hidden(B,k1_classes1(A)) & r2_hidden(C,k1_classes1(A)) ) => r2_hidden(k4_tarski(B,C),k1_classes1(A)) ) )).
fof(t27_classes2,axiom,( ! [A] : ( v2_classes1(A) => r1_tarski(k4_classes1(k1_card_1(A)),A) ) )).
fof(t27_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_series_1(B) => ( ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(D,E) & ~ r1_xxreal_0(k2_normsp_0(A,k1_normsp_0(A,C,E)),k9_nat_1(k1_numbers,B,E)) ) ) | v2_clopban3(C,A) ) ) ) ) ) )).
fof(t27_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k2_normsp_0(A,k1_normsp_1(A,k1_bhsp_4(A,k1_clopban4(A,B)),C)),k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k2_normsp_0(A,B))),C)) & r1_xxreal_0(k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k2_normsp_0(A,B))),C),k4_series_1(k4_sin_cos(k2_normsp_0(A,B)))) & r1_xxreal_0(k2_normsp_0(A,k1_normsp_1(A,k1_bhsp_4(A,k1_clopban4(A,B)),C)),k4_series_1(k4_sin_cos(k2_normsp_0(A,B)))) ) ) ) ) )).
fof(t27_closure2,axiom,( ! [A] : ! [B] : ( ( 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)))) ) ) )).
fof(t27_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_clvect_1(B,A) => ! [C] : ( m1_clvect_1(C,A) => ! [D] : ( ( r1_struct_0(B,D) & m1_clvect_1(B,C) ) => r1_struct_0(C,D) ) ) ) ) )).
fof(t27_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) & k1_seq_2(k2_clvect_2(A,k3_normsp_1(A,D,E))) = k13_csspace(A,k5_algstr_0(A,B,C)) ) ) ) ) ) ) ) )).
fof(t27_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k9_nat_1(k1_numbers,k2_clvect_2(A,B),D),k9_nat_1(k1_numbers,C,D)) ) & v1_series_1(C) ) => v2_clvect_3(B,A) ) ) ) ) )).
fof(t27_coh_sp,axiom,( ! [A] : r2_hidden(k1_eqrel_1(A),k14_coh_sp(A)) )).
fof(t27_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(k2_xboole_0(D,E),A) => ! [F] : ! [G] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t27_combgras,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ( r1_ordinal1(k1_nat_1(A,1),k1_card_1(B)) => ( r1_xxreal_0(A,k5_numbers) | ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_incsp_1(k1_combgras(A,B)))) => ( v3_combgras(C,A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) => ( D = k1_setfam_1(C) => ( k1_card_1(D) = k6_xcmplx_0(A,1) & C = a_3_0_combgras(A,B,D) ) ) ) ) ) ) ) ) ) )).
fof(t27_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v7_pre_topc(A) & l1_pre_topc(A) ) => ( v8_compl_sp(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( ~ v1_finset_1(B) & v1_xboole_0(k2_topgen_1(A,B)) ) ) ) ) )).
fof(t27_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k3_complex1(k8_complex1(A)) = k3_complex1(A) & k4_complex1(k8_complex1(A)) = k1_real_1(k4_complex1(A)) ) ) )).
fof(t27_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k1_complex2(A,B) = k2_xcmplx_0(k3_real_1(k4_real_1(k3_complex1(A),k3_complex1(B)),k4_real_1(k4_complex1(A),k4_complex1(B))),k3_xcmplx_0(k3_real_1(k1_real_1(k4_real_1(k3_complex1(A),k4_complex1(B))),k4_real_1(k4_complex1(A),k3_complex1(B))),k7_complex1)) ) ) )).
fof(t27_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_complfld)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_complfld)) => ~ ( B != k4_struct_0(k1_complfld) & D != k4_struct_0(k1_complfld) & k8_group_1(k1_complfld,k3_vectsp_1(k1_complfld,A,B),k3_vectsp_1(k1_complfld,C,D)) != k3_vectsp_1(k1_complfld,k8_group_1(k1_complfld,A,C),k8_group_1(k1_complfld,B,D)) ) ) ) ) ) )).
fof(t27_complsp2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => k1_valued_1(A,k15_seq_4(k3_finseq_1(A))) = A ) )).
fof(t27_compos_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( l1_compos_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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)) ) ) ) ) )).
fof(t27_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(k62_valued_1(B),C) => k1_funct_1(k63_valued_1(B),C) = k1_funct_1(B,C) ) ) ) ) )).
fof(t27_comptrig,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_hidden(k1_funct_1(k16_sin_cos,A),k1_rcomp_1(k4_xcmplx_0(1),1)) & r2_hidden(k1_funct_1(k18_sin_cos,A),k1_rcomp_1(k4_xcmplx_0(1),1)) ) ) )).
fof(t27_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v4_valued_0(A) & v2_margrel1(A) ) => m2_rfunct_3(A,k3_finseq_2(k4_ordinal1),k4_ordinal1,k2_comput_1(k4_ordinal1)) ) )).
fof(t27_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v9_ordinal1(A) => v9_ordinal1(k36_valued_1(k4_ordinal1,k2_numbers,A)) ) ) )).
fof(t27_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v2_comseq_2(B) & v2_comseq_2(A) & v9_ordinal1(A) ) => ( k3_comseq_2(A) = k5_complex1 | k3_comseq_2(k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,A)) = k7_xcmplx_0(k3_comseq_2(B),k3_comseq_2(A)) ) ) ) ) )).
fof(t27_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_funct_2(k4_ordinal1,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))) ) ) )).
fof(t27_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( v5_conlat_1(B,A) & l2_conlat_1(B,A) ) => ~ ( v3_conlat_1(B,A) & ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) & l2_conlat_1(B,A) & B != k5_conlat_1(A) & B != k6_conlat_1(A) ) ) ) )).
fof(t27_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v2_connsp_1(k2_struct_0(A),A) <=> v1_connsp_1(A) ) ) )).
fof(t27_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_pre_topc(A,B)) <=> ! [D] : ( m1_connsp_2(D,A,C) => ~ r1_xboole_0(D,B) ) ) ) ) ) )).
fof(t27_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t27_convex1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t27_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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))) ) ) ) ) )).
fof(t27_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => k13_cqc_lang(A,C,B) = C ) ) ) )).
fof(t27_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ( v2_qc_lang1(B,A) => k14_cqc_sim1(A,B) = B ) ) ) )).
fof(t27_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t27_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ! [E] : ( m2_subset_1(E,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t27_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_cqc_lang(A))) => ( ( r4_cqc_the3(A,C,D) & r2_cqc_the3(A,B,C) ) => r2_cqc_the3(A,B,D) ) ) ) ) ) )).
fof(t27_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t27_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t27_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(t27_descip_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,A) => ! [I] : ( m1_subset_1(I,A) => ! [J] : ( m1_subset_1(J,A) => ! [K] : ( m1_subset_1(K,A) => ! [L] : ( m1_subset_1(L,A) => ! [M] : ( m1_subset_1(M,A) => ! [N] : ( m1_subset_1(N,A) => ! [O] : ( m1_subset_1(O,A) => ! [P] : ( m1_subset_1(P,A) => ! [Q] : ( m1_subset_1(Q,A) => ! [R] : ( m1_subset_1(R,A) => ! [S] : ( m1_subset_1(S,A) => ! [T] : ( m1_subset_1(T,A) => ! [U] : ( m1_subset_1(U,A) => ! [V] : ( m1_subset_1(V,A) => ! [W] : ( m1_subset_1(W,A) => ! [X] : ( m1_subset_1(X,A) => ! [Y] : ( m1_subset_1(Y,A) => ! [Z] : ( m1_subset_1(Z,A) => ! [A1] : ( m1_subset_1(A1,A) => ! [B1] : ( m1_subset_1(B1,A) => ! [C1] : ( m1_subset_1(C1,A) => ! [D1] : ( m1_subset_1(D1,A) => ! [E1] : ( m1_subset_1(E1,A) => ! [F1] : ( m1_subset_1(F1,A) => ! [G1] : ( m1_subset_1(G1,A) => ! [H1] : ( m1_subset_1(H1,A) => ! [I1] : ( m1_subset_1(I1,A) => ! [J1] : ( m1_subset_1(J1,A) => ! [K1] : ( m1_subset_1(K1,A) => ! [L1] : ( m1_subset_1(L1,A) => ! [M1] : ( m1_subset_1(M1,A) => ! [N1] : ( m1_subset_1(N1,A) => ! [O1] : ( m1_subset_1(O1,A) => ! [P1] : ( m1_subset_1(P1,A) => ! [Q1] : ( m1_subset_1(Q1,A) => ! [R1] : ( m1_subset_1(R1,A) => ! [S1] : ( m1_subset_1(S1,A) => ! [T1] : ( m1_subset_1(T1,A) => ! [U1] : ( m1_subset_1(U1,A) => ! [V1] : ( m1_subset_1(V1,A) => ! [W1] : ( m1_subset_1(W1,A) => ! [X1] : ( m1_subset_1(X1,A) => ! [Y1] : ( m1_subset_1(Y1,A) => ! [Z1] : ( m1_subset_1(Z1,A) => ! [A2] : ( m1_subset_1(A2,A) => ! [B2] : ( m1_subset_1(B2,A) => ! [C2] : ( m1_subset_1(C2,A) => ! [D2] : ( m1_subset_1(D2,A) => ! [E2] : ( m1_subset_1(E2,A) => ! [F2] : ( m1_subset_1(F2,A) => ! [G2] : ( m1_subset_1(G2,A) => ! [H2] : ( m1_subset_1(H2,A) => ! [I2] : ( m1_subset_1(I2,A) => ! [J2] : ( m1_subset_1(J2,A) => ! [K2] : ( m1_subset_1(K2,A) => ! [L2] : ( m1_subset_1(L2,A) => ! [M2] : ( m1_subset_1(M2,A) => ? [N2] : ( v1_funct_1(N2) & v1_funct_2(N2,64,A) & m1_subset_1(N2,k1_zfmisc_1(k2_zfmisc_1(64,A))) & k1_funct_1(N2,k5_numbers) = B & k1_funct_1(N2,1) = C & k1_funct_1(N2,2) = D & k1_funct_1(N2,3) = E & k1_funct_1(N2,4) = F & k1_funct_1(N2,5) = G & k1_funct_1(N2,6) = H & k1_funct_1(N2,7) = I & k1_funct_1(N2,8) = J & k1_funct_1(N2,9) = K & k1_funct_1(N2,10) = L & k1_funct_1(N2,11) = M & k1_funct_1(N2,12) = N & k1_funct_1(N2,13) = O & k1_funct_1(N2,14) = P & k1_funct_1(N2,15) = Q & k1_funct_1(N2,16) = R & k1_funct_1(N2,17) = S & k1_funct_1(N2,18) = T & k1_funct_1(N2,19) = U & k1_funct_1(N2,20) = V & k1_funct_1(N2,21) = W & k1_funct_1(N2,22) = X & k1_funct_1(N2,23) = Y & k1_funct_1(N2,24) = Z & k1_funct_1(N2,25) = A1 & k1_funct_1(N2,26) = B1 & k1_funct_1(N2,27) = C1 & k1_funct_1(N2,28) = D1 & k1_funct_1(N2,29) = E1 & k1_funct_1(N2,30) = F1 & k1_funct_1(N2,31) = G1 & k1_funct_1(N2,32) = H1 & k1_funct_1(N2,33) = I1 & k1_funct_1(N2,34) = J1 & k1_funct_1(N2,35) = K1 & k1_funct_1(N2,36) = L1 & k1_funct_1(N2,37) = M1 & k1_funct_1(N2,38) = N1 & k1_funct_1(N2,39) = O1 & k1_funct_1(N2,40) = P1 & k1_funct_1(N2,41) = Q1 & k1_funct_1(N2,42) = R1 & k1_funct_1(N2,43) = S1 & k1_funct_1(N2,44) = T1 & k1_funct_1(N2,45) = U1 & k1_funct_1(N2,46) = V1 & k1_funct_1(N2,47) = W1 & k1_funct_1(N2,48) = X1 & k1_funct_1(N2,49) = Y1 & k1_funct_1(N2,50) = Z1 & k1_funct_1(N2,51) = A2 & k1_funct_1(N2,52) = B2 & k1_funct_1(N2,53) = C2 & k1_funct_1(N2,54) = D2 & k1_funct_1(N2,55) = E2 & k1_funct_1(N2,56) = F2 & k1_funct_1(N2,57) = G2 & k1_funct_1(N2,58) = H2 & k1_funct_1(N2,59) = I2 & k1_funct_1(N2,60) = J2 & k1_funct_1(N2,61) = K2 & k1_funct_1(N2,62) = L2 & k1_funct_1(N2,63) = M2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t27_dickson,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( ( v1_wellfnd1(k5_dickson(A)) & v16_waybel_0(A) ) => v4_dickson(A) ) ) )).
fof(t27_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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] : ( v1_xreal_0(G) => k1_funct_1(F,G) = k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(C,k1_square_1(G)),k3_xcmplx_0(D,G)),E) ) => ( A = B | k9_diff_1(F,A,B) = k2_xcmplx_0(k3_xcmplx_0(C,k2_xcmplx_0(A,B)),D) ) ) ) ) ) ) ) ) )).
fof(t27_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( ( 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) = k6_xcmplx_0(k3_xcmplx_0(A,k9_diff_1(D,B,C)),k9_diff_1(E,B,C)) ) ) ) ) ) )).
fof(t27_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(B,k1_relset_1(k1_numbers,k27_sin_cos)) & r2_hidden(k2_xcmplx_0(B,A),k1_relset_1(k1_numbers,k27_sin_cos)) ) => k1_funct_1(k3_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k27_sin_cos),k16_sin_cos),A),B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k18_sin_cos),k2_xcmplx_0(B,A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k18_sin_cos),B)) ) ) ) )).
fof(t27_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t27_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_diraf(A,D,B,B,E) & B != D & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_diraf(A,C,B,B,F) & r2_diraf(A,C,D,E,F) ) ) ) ) ) ) ) ) )).
fof(t27_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,A,k6_margrel1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => k6_dist_2(A,B,k5_bvfunc_1(A,C,D)) = k6_xcmplx_0(k2_xcmplx_0(k6_dist_2(A,B,C),k6_dist_2(A,B,D)),k6_dist_2(A,B,k2_bvfunc_1(A,C,D))) ) ) ) ) )).
fof(t27_domain_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k3_subset_1(A,B) = a_2_2_domain_1(A,B) ) ) )).
fof(t27_e_siec,axiom,( ! [A] : ( ( 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 ) ) )).
fof(t27_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(t27_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k9_int_3(A))) => ( B = k5_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))) ) ) ) ) ) ) ) )).
fof(t27_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u4_struct_0(k11_ens_1(A))) => ! [C] : ( m1_subset_1(C,u4_struct_0(k11_ens_1(A))) => ( k3_graph_1(k11_ens_1(A),C) = k4_graph_1(k11_ens_1(A),B) => k1_cat_1(k11_ens_1(A),B,C) = k6_ens_1(A,k15_ens_1(A,B),k15_ens_1(A,C)) ) ) ) ) )).
fof(t27_entropy1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(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_0(C) = k1_matrix_0(B) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(C)) => k7_matrix_0(k1_numbers,C,D) = k11_rvsum_1(k1_matrix_0(B),k7_matrix_0(k1_numbers,B,D),k1_funct_1(A,D)) ) ) ) ) ) ) ) ) )).
fof(t27_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : 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)) )).
fof(t27_eqrel_1,axiom,( ! [A] : ! [B] : ( ( 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] : k6_eqrel_1(A,A,B,C) = A => r2_relset_1(A,A,B,k1_eqrel_1(A)) ) ) )).
fof(t27_euclid,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => k3_rlvect_1(k15_euclid(2),A,B) = k19_euclid(k2_xcmplx_0(k17_euclid(A),k17_euclid(B)),k2_xcmplx_0(k18_euclid(A),k18_euclid(B))) ) ) )).
fof(t27_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => k22_rvsum_1(k5_algstr_0(k15_euclid(A),B,C),k5_algstr_0(k15_euclid(A),D,E)) = k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k22_rvsum_1(B,D),k22_rvsum_1(B,E)),k22_rvsum_1(C,D)),k22_rvsum_1(C,E)) ) ) ) ) ) )).
fof(t27_euclid_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( A = k3_xcmplx_0(k12_euclid(C),k19_sin_cos(k3_euclid_3(C))) & B = k3_xcmplx_0(k12_euclid(C),k17_sin_cos(k3_euclid_3(C))) ) => C = k19_euclid(A,B) ) ) ) ) )).
fof(t27_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(A)) => k22_rvsum_1(k7_euclid(A,k9_euclid(A,D,B),k9_euclid(A,E,C)),F) = k2_xcmplx_0(k3_xcmplx_0(B,k22_rvsum_1(D,F)),k3_xcmplx_0(C,k22_rvsum_1(E,F))) ) ) ) ) ) ) )).
fof(t27_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => A = k11_finseq_1(k1_euclid_5(A),k2_euclid_5(A),k3_euclid_5(A)) ) )).
fof(t27_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,B) ) => k12_euclid(k6_euclid_7(B,A)) = 1 ) ) ) )).
fof(t27_euclid_8,axiom,( k6_euclid(3,k4_euclid_8) = k1_euclid_8(k5_numbers,k5_numbers,k4_xcmplx_0(1)) )).
fof(t27_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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))) ) ) ) )).
fof(t27_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(D)) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(D)) => ! [G] : ( m2_finseq_2(G,k1_numbers,k1_euclid(D)) => ( k2_xcmplx_0(k2_xcmplx_0(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)) ) ) ) ) ) ) ) ) )).
fof(t27_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) ) => ( ( v4_exchsort(A) & v1_finset_1(k1_funct_1(A,k5_numbers)) ) => v1_finset_1(A) ) ) )).
fof(t27_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k1_xxreal_3(k3_xxreal_0(A,B),k4_xxreal_0(A,B)) = k1_xxreal_3(A,B) ) ) )).
fof(t27_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_circcomb(A) & v2_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t27_fcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v1_partfun1(A,k1_numbers) & ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k1_funct_1(A,k2_xcmplx_0(B,C)) = k2_xcmplx_0(k1_funct_1(A,B),k1_funct_1(A,C)) ) ) ) => ( ! [B] : ( v1_xreal_0(B) => ~ r1_fcont_1(A,B) ) | v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,A,k1_numbers)) ) ) ) )).
fof(t27_fdiff_10,axiom,( ! [A] : ( ( 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,k26_sin_cos,k27_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,k26_sin_cos,k27_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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,k26_sin_cos,k27_sin_cos)),A),B) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,B),k6_xcmplx_0(k1_funct_1(k26_sin_cos,B),k1_funct_1(k27_sin_cos,B))),k3_xcmplx_0(k1_funct_1(k16_sin_cos,B),k2_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B)))))) ) ) ) ) ) )).
fof(t27_fdiff_11,axiom,( ! [A] : ( ( 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,k18_sin_cos,k1_sin_cos9))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_sin_cos9),A),B) = k2_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,B),k1_funct_1(k1_sin_cos9,B))),k7_xcmplx_0(k1_funct_1(k18_sin_cos,B),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t27_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r2_hidden(C,k3_limfunc1(A)) & r2_hidden(D,k3_limfunc1(A)) ) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k1_funct_1(B,C),k1_funct_1(B,D))),k1_square_1(k6_xcmplx_0(C,D))) ) ) ) ) => ( r2_fdiff_1(B,k3_limfunc1(A)) & v3_funct_1(k2_partfun1(k1_numbers,k1_numbers,B,k3_limfunc1(A))) ) ) ) ) )).
fof(t27_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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(k7_xcmplx_0(3,2))))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k1_funct_1(C,D) = k2_xcmplx_0(A,D) & ~ r1_xxreal_0(k1_funct_1(C,D),k5_numbers) ) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(k7_xcmplx_0(3,2))),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(k7_xcmplx_0(3,2))),B),D) = k3_xcmplx_0(k7_xcmplx_0(3,2),k6_prepower(k2_xcmplx_0(A,D),k7_xcmplx_0(1,2))) ) ) ) ) ) ) ) )).
fof(t27_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k22_sin_cos,B),k1_taylor_1(2)))) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_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,k22_sin_cos,B),k1_taylor_1(2)),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,B),k1_taylor_1(2)),A),C) = k3_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k22_sin_cos,C)),k6_xcmplx_0(k1_funct_1(k22_sin_cos,C),1)) ) ) ) ) ) ) )).
fof(t27_fdiff_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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(k7_xcmplx_0(1,2))))) & C = k47_valued_1(k1_numbers,k1_numbers,k1_numbers,D,E) & E = k1_taylor_1(2) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => ( k1_funct_1(D,F) = k1_square_1(A) & ~ r1_xxreal_0(k1_funct_1(C,F),k5_numbers) ) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(k7_xcmplx_0(1,2))),B) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(k7_xcmplx_0(1,2))),B),F) = k4_xcmplx_0(k3_xcmplx_0(F,k6_prepower(k6_xcmplx_0(k1_square_1(A),k3_prepower(F,2)),k4_xcmplx_0(k7_xcmplx_0(1,2))))) ) ) ) ) ) ) ) ) ) )).
fof(t27_fdiff_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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,k27_sin_cos),k4_xcmplx_0(k7_xcmplx_0(1,A))),k1_partfun2(k1_numbers,B)))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k1_funct_1(C,D) = k3_xcmplx_0(A,D) & A != k5_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,k27_sin_cos),k4_xcmplx_0(k7_xcmplx_0(1,A))),k1_partfun2(k1_numbers,B)),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_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,k27_sin_cos),k4_xcmplx_0(k7_xcmplx_0(1,A))),k1_partfun2(k1_numbers,B)),B),D) = k7_xcmplx_0(k1_square_1(k1_funct_1(k18_sin_cos,k3_xcmplx_0(A,D))),k1_square_1(k1_funct_1(k16_sin_cos,k3_xcmplx_0(A,D)))) ) ) ) ) ) ) ) )).
fof(t27_fdiff_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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),k4_xcmplx_0(k7_xcmplx_0(1,A))),k1_partfun2(k1_numbers,B)))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k1_funct_1(C,D) = k3_xcmplx_0(A,D) & A != k5_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),k4_xcmplx_0(k7_xcmplx_0(1,A))),k1_partfun2(k1_numbers,B)),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_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),k4_xcmplx_0(k7_xcmplx_0(1,A))),k1_partfun2(k1_numbers,B)),B),D) = k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(k18_sin_cos,k3_xcmplx_0(A,D)),k1_square_1(k1_funct_1(k16_sin_cos,k3_xcmplx_0(A,D)))),k1_square_1(k1_funct_1(k16_sin_cos,k3_xcmplx_0(A,D)))) ) ) ) ) ) ) ) )).
fof(t27_ff_siec,axiom,( ! [A] : ( ( 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 ) ) )).
fof(t27_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => k1_pre_ff(k1_nat_1(A,5)) = k1_nat_1(k1_pre_ff(k1_nat_1(A,3)),k1_pre_ff(k1_nat_1(A,4))) ) )).
fof(t27_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(2,A) => k1_pre_ff(k2_xcmplx_0(A,1)) = k1_int_1(k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_pre_ff(A),1),k3_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)) ) ) )).
fof(t27_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_finseq_1(B,A) => ! [C] : ( m1_finseq_1(C,A) => ( r4_finseq_8(A,C,B) => C = k9_finseq_8(A,C,B) ) ) ) ) )).
fof(t27_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t27_filter_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t27_filter_2,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(t27_finseq_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ~ ( r2_hidden(A,k4_finseq_1(C)) & ! [D] : ( v7_ordinal1(D) => ~ ( D = A & r2_hidden(k2_xcmplx_0(k3_finseq_1(B),D),k4_finseq_1(k7_finseq_1(B,C))) ) ) ) ) ) )).
fof(t27_finseq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t27_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( k3_finseq_1(A) = k3_finseq_1(B) <=> k1_relset_1(k4_ordinal1,A) = k1_relset_1(k4_ordinal1,B) ) ) ) )).
fof(t27_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( r2_hidden(B,k10_xtuple_0(A)) & ! [C] : ( 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) ) ) )).
fof(t27_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ( 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)) ) ) ) ) )).
fof(t27_finseq_6,axiom,( ! [A] : ! [B] : ! [C] : ( A != B => k5_finseq_4(k11_finseq_1(A,B,C),B) = k9_finseq_1(A) ) )).
fof(t27_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t27_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ~ r2_finseq_8(A,B,C,D) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( r1_xxreal_0(D,E) & ~ r1_xxreal_0(E,k5_numbers) & k3_finseq_6(A,B,E,k1_nat_1(k7_nat_d(E,1),k3_finseq_1(C))) = C ) ) ) ) ) ) ) )).
fof(t27_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v3_card_1(D,C) & m2_finseq_1(D,A) ) => ! [E] : ( ( v3_card_1(E,C) & m2_finseq_1(E,A) ) => ! [F] : ( ( 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(k4_ordinal1,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)))) ) ) ) ) ) ) ) )).
fof(t27_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t27_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k3_subset_1(u1_struct_0(A),k5_fintopo3(A,k3_subset_1(u1_struct_0(A),B),C)) = k3_fintopo3(A,B,C) ) ) ) )).
fof(t27_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t27_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( v7_ordinal1(C) => ( k7_flang_1(A,B,C) = k1_xboole_0 <=> ( ~ r1_xxreal_0(C,k5_numbers) & B = k1_xboole_0 ) ) ) ) )).
fof(t27_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t27_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) )).
fof(t27_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_funct_2(E,B,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ! [F] : ( ( v1_funct_2(F,B,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,D))) ) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ( v1_funct_1(k4_relset_1(A,B,B,D,k4_relset_1(A,C,C,B,k4_relset_1(A,B,B,C,G,E),k3_relset_1(B,C,E)),F)) => r2_relset_1(A,D,k4_relset_1(A,B,B,D,k4_relset_1(A,C,C,B,k4_relset_1(A,B,B,C,G,E),k3_relset_1(B,C,E)),F),k4_relset_1(A,B,B,D,G,F)) ) ) ) ) ) ) )).
fof(t27_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m2_subset_1(D,k9_funct_2(k37_fomodel1(A),k3_rfunct_3(k3_finseq_2(B),k2_xboole_0(B,k6_margrel1))),k15_fomodel2(A,B)) => ( k25_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) ) ) ) ) ) )).
fof(t27_frechet,axiom,( m1_subset_1(k1_numbers,u1_struct_0(k3_frechet)) )).
fof(t27_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k3_pcomps_1(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k3_pcomps_1(A))))) ) => ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) ) ) )).
fof(t27_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( v7_ordinal1(F) => ( r1_xxreal_0(1,F) => ( r6_fsm_1(A,B,C,D,E,F) <=> ( r6_fsm_1(A,B,C,D,E,1) & ! [G] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,k4_ordinal1) => ( H = k6_xcmplx_0(F,1) => r6_fsm_1(A,B,C,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,G)),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,E,G)),H) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t27_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k7_domain_1(k4_ordinal1,k5_numbers,1),B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k7_domain_1(k4_ordinal1,k5_numbers,1),B))) ) => k2_fsm_2(A,B,k1_fsm_2(A,B,k5_numbers,1,D),C) = k1_funct_1(D,1) ) ) ) ) )).
fof(t27_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k8_afinsq_1(C)) => ! [G] : ( ( ~ 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,F),B,k1_flang_1(C,E,F)) => 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,E) ) ) ) ) ) ) )).
fof(t27_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ! [E] : ! [F] : ( 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] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( m1_subset_1(H,k6_margrel1) => ! [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)) ) ) ) ) ) ) ) ) ) )).
fof(t27_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( 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) ) ) ) )).
fof(t27_funcsdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k5_struct_0(k12_funcsdom(A)) = k9_funcsdom(A) ) )).
fof(t27_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) <=> ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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 ) ) ) ) ) )).
fof(t27_funct_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t27_funct_3,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(t27_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r1_partfun1(A,k1_funct_4(B,C)) => r1_partfun1(A,C) ) ) ) ) )).
fof(t27_funct_5,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t27_funct_6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) ) => ( r2_hidden(A,k9_xtuple_0(k5_funct_6(B))) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(C,k10_xtuple_0(B)) => r2_hidden(A,k9_xtuple_0(C)) ) ) ) ) )).
fof(t27_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( r1_funct_7(A,B,C) => k6_subset_1(k9_xtuple_0(A),C) = k6_subset_1(k9_xtuple_0(B),C) ) ) ) )).
fof(t27_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t27_funct_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & v1_int_1(A) ) => v1_funct_9(k55_valued_1(k1_numbers,k1_numbers,k16_sin_cos),k3_xcmplx_0(k28_sin_cos,A)) ) )).
fof(t27_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_altcat_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k3_functor0(B,A,k10_functor0(A,B),C) = C ) ) ) )).
fof(t27_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v11_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v2_altcat_1(D) & v11_altcat_1(D) & v12_altcat_1(D) & l2_altcat_1(D) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ! [F] : ( ( v15_functor0(F,A,B) & m2_functor0(F,A,B) ) => ! [G] : ( ( v15_functor0(G,B,C) & m2_functor0(G,B,C) ) => ! [H] : ( ( v15_functor0(H,B,C) & m2_functor0(H,B,C) ) => ! [I] : ( ( v15_functor0(I,C,D) & m2_functor0(I,C,D) ) => ! [J] : ( ( v15_functor0(J,C,D) & m2_functor0(J,C,D) ) => ! [K] : ( m1_functor2(K,A,B,E,F) => ! [L] : ( m1_functor2(L,B,C,G,H) => ! [M] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t27_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D) & r1_fuzzy_1(B,C) & r2_funct_2(A,k1_numbers,k1_fuzzy_1(A,D,C),k4_fuzzy_1(A)) ) => r2_funct_2(A,k1_numbers,B,k4_fuzzy_1(A)) ) ) ) ) ) )).
fof(t27_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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) ) ) ) ) )).
fof(t27_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_fvaluat1(D,A) => ( v3_fvaluat1(A) => r1_xxreal_0(k3_xxreal_0(k3_funct_2(u1_struct_0(A),k6_numbers,D,B),k3_funct_2(u1_struct_0(A),k6_numbers,D,C)),k3_funct_2(u1_struct_0(A),k6_numbers,D,k3_rlvect_1(A,B,C))) ) ) ) ) ) )).
fof(t27_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t27_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ~ 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) ) ) )).
fof(t27_gcd_1,axiom,( ! [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) & v1_vectsp_2(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ( v2_gcd_1(B,A) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),B) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t27_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v2_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( m1_genealg1(E,D) => ! [F] : ( m1_genealg1(F,D) => ( k9_genealg1(D,E,F,A,A,C) = k7_genealg1(D,E,F,C) & k9_genealg1(D,E,F,A,B,A) = k7_genealg1(D,E,F,B) & k9_genealg1(D,E,F,A,B,B) = k7_genealg1(D,E,F,A) ) ) ) ) ) ) ) )).
fof(t27_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( r1_analmetr(A,F,G) & r2_geomtrap(A,F,G,B,D,C,E) & ~ r2_geomtrap(A,F,G,B,D,k1_geomtrap(A,B,E),k1_geomtrap(A,D,C)) & ~ r2_geomtrap(A,F,G,B,D,k1_geomtrap(A,D,C),k1_geomtrap(A,B,E)) ) ) ) ) ) ) ) ) )).
fof(t27_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) ) )).
fof(t27_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ( k15_glib_000(A) = 1 <=> ? [B] : ( m1_subset_1(B,k6_glib_000(A)) & k6_glib_000(A) = k6_domain_1(k6_glib_000(A),B) ) ) ) )).
fof(t27_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t27_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ( v1_glib_002(A) <=> k4_glib_002(A) = 1 ) ) )).
fof(t27_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( ( v1_glib_003(B) & v4_glib_003(B,A) & m1_glib_000(B,A) ) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m3_glib_001(D,B) => ( C = D => k10_glib_003(A,C) = k10_glib_003(B,D) ) ) ) ) ) )).
fof(t27_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( ( 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] : ( 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_funct_1(k5_glib_004(k6_glib_000(A),k1_numbers,k1_zfmisc_1(k7_glib_000(A)),k11_glib_004(A,B)),D) ) ) ) ) ) ) ) )).
fof(t27_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(D)) & r2_hidden(k4_tarski(k1_nat_1(A,1),B),k2_matrix_0(k2_goboard2(D))) & r2_hidden(k4_tarski(k1_nat_1(A,1),k1_nat_1(B,1)),k2_matrix_0(k2_goboard2(D))) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1)) ) => ( k5_goboard5(D,C) = k3_goboard5(k2_goboard2(D),A,B) & k4_goboard5(D,C) = k3_goboard5(k2_goboard2(D),k1_nat_1(A,1),B) ) ) ) ) ) ) )).
fof(t27_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_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_0(C)) & r2_hidden(B,k1_tops_1(k15_euclid(2),k2_goboard5(C,A))) & r1_xxreal_0(k18_euclid(B),k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,A))) ) ) ) ) )).
fof(t27_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k1_matrix_0(C)) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(C)) & r1_xxreal_0(1,E) & r1_xxreal_0(k1_nat_1(E,1),k1_matrix_0(C)) & r2_hidden(k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),B)),k7_xcmplx_0(1,2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,D,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,D,k1_nat_1(E,1)))) ) ) ) ) ) ) ) )).
fof(t27_gobrd11,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => k3_goboard5(A,k3_finseq_1(A),k5_numbers) = a_1_15_gobrd11(A) ) )).
fof(t27_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(D)) & r1_goboard1(u1_struct_0(k15_euclid(2)),D,E) & r2_hidden(k4_tarski(A,B),k2_matrix_0(E)) & r2_hidden(k4_tarski(A,k1_nat_1(B,1)),k2_matrix_0(E)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,k1_nat_1(B,1)) ) => k5_gobrd13(D,E,C) = k3_goboard5(E,k7_nat_d(A,1),k1_nat_1(B,1)) ) ) ) ) ) ) )).
fof(t27_gobrd14,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t27_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t27_gr_cy_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t27_gr_cy_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(A,1) => r1_int_1(k6_xcmplx_0(A,1),k6_xcmplx_0(k1_newton(A,B),1)) ) ) ) )).
fof(t27_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_graph_1(B) & l1_graph_1(B) ) => ( r4_graph_1(A,B) => v4_graph_1(A) ) ) ) )).
fof(t27_graph_2,axiom,( ! [A] : ! [B] : ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(C)) => m1_subset_1(k5_relat_1(D,B),k1_zfmisc_1(C)) ) ) )).
fof(t27_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ! [D] : ( r1_tarski(D,C) => k5_card_1(k2_graph_3(A,B,k6_subset_1(C,D))) = k6_xcmplx_0(k5_card_1(k2_graph_3(A,B,C)),k5_card_1(k2_graph_3(A,B,D))) ) ) ) )).
fof(t27_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t27_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) => r1_tarski(k7_graphsp(B,A),k12_graphsp(B,A)) ) ) )).
fof(t27_grcat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r1_grcat_1(A,B) & r1_grcat_1(A,C) ) => B = C ) )).
fof(t27_grfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t27_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ( ? [B] : ( m2_finseq_1(B,k2_grnilp_1(A)) & ~ r1_xxreal_0(k3_finseq_1(B),k5_numbers) & k1_funct_1(B,1) = k7_group_2(A) & k1_funct_1(B,k3_finseq_1(B)) = k6_group_2(A) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(k2_xcmplx_0(C,1),k4_finseq_1(B)) ) => ! [D] : ( ( 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) ) ) )).
fof(t27_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(F,A,C) & v1_polynom1(F,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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t27_groeb_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_ideal_1(C,A,B) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => m2_ideal_1(k17_finseq_1(u1_struct_0(A),D,C),A,B) ) ) ) ) )).
fof(t27_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,k5_card_1(k3_polynom1(k15_pre_poly(A),C,D))) ) => r1_tarski(k3_polynom1(k15_pre_poly(A),C,k6_groeb_3(A,B,C,D,E)),k3_polynom1(k15_pre_poly(A),C,k6_termord(A,B,C,D))) ) ) ) ) ) ) )).
fof(t27_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) )).
fof(t27_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t27_group_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r2_hidden(A,k4_group_2(B,D,C)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k6_algstr_0(B,D,E) & r2_hidden(E,C) ) ) ) ) ) )).
fof(t27_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t27_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t27_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t27_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & v5_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v5_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t27_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( 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)) ) ) )).
fof(t27_groupp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => v2_groupp_1(k6_group_2(A),B) ) ) )).
fof(t27_hallmar1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v2_relat_1(B) & ~ v1_xboole_0(B) & m2_finseq_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( m4_hallmar1(C,A,B) <=> ( k9_xtuple_0(C) = k4_finseq_1(B) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k4_finseq_1(B)) => m3_hallmar1(C,A,B,D) ) ) ) ) ) ) ) )).
fof(t27_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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(k5_numbers) ) ) )).
fof(t27_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( ( v5_glib_001(D,A) & m3_glib_001(D,A) ) => ! [E] : ( ( 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 ) ) ) ) ) ) )).
fof(t27_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,k1_complfld) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k1_complfld)) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t27_heyting1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k12_normform(A))) => ! [C] : ( 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))) ) ) )).
fof(t27_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_substlat(A,B))) => ! [D] : ( 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) ) ) ) )).
fof(t27_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k4_heyting3(1,A) != k1_tarski(k1_xboole_0) ) )).
fof(t27_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(A,D) => k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k26_valued_1(k1_numbers,k1_numbers,k22_sin_cos,B),D),C),A) = k3_xcmplx_0(B,k1_funct_1(k22_sin_cos,A)) ) ) ) ) ) )).
fof(t27_hilbasis,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t27_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => r2_hidden(k3_hilbert1(k3_hilbert1(A,k3_hilbert1(A,B)),k3_hilbert1(A,B)),k6_hilbert1) ) ) )).
fof(t27_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ( k4_hilbert1(A,B) != A & k4_hilbert1(A,B) != B ) ) ) )).
fof(t27_hilbert3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t27_hurwitz,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v6_struct_0(A) & v4_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k2_hurwitz(A,k3_hurwitz(A,B,C)) = C ) ) ) )).
fof(t27_idea_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ( 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)) ) ) ) ) ) )).
fof(t27_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_ideal_1(D,A,B) => m1_ideal_1(k1_polynom1(A,D,C),A,B) ) ) ) ) )).
fof(t27_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ~ ( B != C & ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & r1_incsp_1(A,D,B) & r1_incsp_1(A,D,C) ) & ! [D] : ( m1_subset_1(D,u4_incsp_1(A)) => ~ ! [E] : ( m1_subset_1(E,u4_incsp_1(A)) => ( ( r3_incsp_1(A,B,E) & r3_incsp_1(A,C,E) ) <=> D = E ) ) ) ) ) ) ) )).
fof(t27_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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] : ( m4_index_1(C,u1_struct_0(A),u4_struct_0(A),u1_graph_1(A),u2_graph_1(A),B) => ! [D] : ( ( ~ 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] : ( ( ~ 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] : ( m2_cat_1(F,C,D) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t27_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_msualg_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r3_pua2mss1(A,B,D,E) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) ) => ( r3_pua2mss1(B,C,F,G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t27_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k6_xcmplx_0(k1_int_1(A),1)) & ~ r1_xxreal_0(k2_xcmplx_0(A,1),k1_int_1(A)) ) ) )).
fof(t27_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r1_int_1(A,B) => ( r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(A,B) ) ) ) ) )).
fof(t27_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ~ ( C != k5_numbers & r1_int_2(A,C) & k5_int_1(k6_xcmplx_0(k3_xcmplx_0(A,D),B),C) = k5_numbers & ! [E] : ( v1_int_1(E) => ~ r2_hidden(k4_tarski(D,k3_xcmplx_0(B,E)),k1_int_4(C)) ) ) ) ) ) ) )).
fof(t27_int_5,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => k2_int_5(1,A) = 1 ) )).
fof(t27_int_6,axiom,( ! [A] : ( ( 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] : ( m1_int_6(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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),k5_numbers,k1_funct_1(A,D)) ) ) ) ) ) ) )).
fof(t27_int_7,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r1_xxreal_0(k5_numbers,k2_hurwitz(A,B)) => ( v1_finset_1(k6_polynom5(A,B)) & ? [C] : ( m1_subset_1(C,k4_ordinal1) & ? [D] : ( m1_subset_1(D,k4_ordinal1) & D = k2_hurwitz(A,B) & C = k1_card_1(k6_polynom5(A,B)) & r1_xxreal_0(C,D) ) ) ) ) ) ) )).
fof(t27_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k4_numbers)) ) => ! [C] : ( v1_int_1(C) => ( ( r1_int_2(C,A) & r1_int_8(B,A) ) => ( r1_xxreal_0(A,1) | r1_int_8(k23_member_1(B,C),A) ) ) ) ) ) )).
fof(t27_integr11,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ~ ( k2_xcmplx_0(B,A) != k5_numbers & k6_xcmplx_0(B,A) != k5_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(B,k5_numbers),k16_sin_cos),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,k5_numbers),k18_sin_cos))) != k6_xcmplx_0(k1_funct_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(k2_xcmplx_0(B,A),k5_numbers),k18_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k2_xcmplx_0(B,A))))),k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k6_xcmplx_0(B,A),k5_numbers),k18_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k6_xcmplx_0(B,A))))),k2_seq_4(C)),k1_funct_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(k2_xcmplx_0(B,A),k5_numbers),k18_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k2_xcmplx_0(B,A))))),k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k6_xcmplx_0(B,A),k5_numbers),k18_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k6_xcmplx_0(B,A))))),k3_seq_4(C))) ) ) ) ) )).
fof(t27_integr12,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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(k6_xcmplx_0(A,1))),A),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(k1_nat_1(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,k26_sin_cos,k1_taylor_1(A)))) & D = k1_relset_1(k1_numbers,C) ) => k2_integra5(B,C) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_taylor_1(A)),k2_seq_4(B)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_taylor_1(A)),k3_seq_4(B))) ) ) ) ) ) )).
fof(t27_integr13,axiom,( ! [A] : ( ( 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,k27_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,k27_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k27_sin_cos)),A),B) = k7_xcmplx_0(1,k3_xcmplx_0(B,k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k3_taylor_1,B))))) ) ) ) ) ) )).
fof(t27_integr14,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,D) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => k1_funct_1(C,E) = k7_xcmplx_0(k3_xcmplx_0(A,k1_funct_1(k18_sin_cos,E)),k3_prepower(k1_funct_1(k16_sin_cos,E),k2_xcmplx_0(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) = k6_xcmplx_0(k1_funct_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))),k2_seq_4(B)),k1_funct_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))),k3_seq_4(B))) ) ) ) ) ) )).
fof(t27_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t27_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [C] : ( m1_integra1(C,A) => ( k3_finseq_1(B) = 1 => r1_integra1(B,C) ) ) ) ) )).
fof(t27_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( m1_integra1(D,B) => ( ( v1_seq_2(k2_partfun1(B,k1_numbers,C,B)) & r1_xxreal_0(k5_numbers,A) ) => k6_integra1(B,k26_valued_1(B,k1_numbers,C,A),D) = k3_xcmplx_0(A,k6_integra1(B,C,D)) ) ) ) ) ) )).
fof(t27_integra4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( ( 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] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( ( r2_hidden(E,B) & r2_hidden(F,B) ) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k1_funct_1(D,E),k1_funct_1(D,F))),k3_xcmplx_0(A,k9_complex1(k6_xcmplx_0(k1_funct_1(C,E),k1_funct_1(C,F))))) ) ) ) ) => ( r1_xxreal_0(A,k5_numbers) | v3_integra1(D,B) ) ) ) ) ) ) )).
fof(t27_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_xxreal_0(A,B) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,k3_integra5(A,B)) => k1_funct_1(F,G) = 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,F) = k3_xcmplx_0(E,k6_xcmplx_0(D,C)) ) ) ) ) ) ) ) )).
fof(t27_integra7,axiom,( r1_integra7(k1_numbers,k22_sin_cos,k22_sin_cos) )).
fof(t27_integra8,axiom,( k2_fdiff_1(k16_sin_cos,k1_numbers) = k18_sin_cos )).
fof(t27_integra9,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( ~ 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) = k4_xcmplx_0(k1_integra9(C,A,B)) ) ) ) ) )).
fof(t27_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( ( ~ 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 ) ) ) ) ) ) )).
fof(t27_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => ! [D] : ( 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) ) ) ) ) )).
fof(t27_irrat_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_series_1(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k1_funct_1(k3_series_1(A),C),k6_xcmplx_0(k4_series_1(A),B)) ) ) ) ) ) )).
fof(t27_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,B,C) => ! [G] : ( m2_cat_1(G,C,D) => ! [H] : ( m2_cat_1(H,C,D) => ! [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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t27_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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(k9_nattra_1(k6_cat_2(A,B),C),k9_nattra_1(A,k9_nattra_1(B,C))) ) ) ) )).
fof(t27_isomichi,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t27_jgraph_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(C,B) & r1_xxreal_0(A,D) & r1_xxreal_0(D,B) ) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(C,D)),k6_xcmplx_0(B,A)) ) ) ) ) ) )).
fof(t27_jgraph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) != k5_numbers ) & ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( 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) ) ) ) ) ) ) )).
fof(t27_jgraph_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r1_xxreal_0(k18_euclid(B),k5_numbers) & r1_xxreal_0(k18_euclid(C),k5_numbers) ) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) | r1_xxreal_0(1,A) | k12_euclid(B) = k5_numbers | k12_euclid(C) = k5_numbers | r1_xxreal_0(k7_xcmplx_0(k17_euclid(C),k12_euclid(C)),k7_xcmplx_0(k17_euclid(B),k12_euclid(B))) | ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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(k7_xcmplx_0(k17_euclid(E),k12_euclid(E)),k7_xcmplx_0(k17_euclid(D),k12_euclid(D))) ) ) ) ) ) ) ) ) )).
fof(t27_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t27_jordan,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(t27_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t27_jordan12,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t27_jordan14,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(B,C) & r1_xxreal_0(1,B) ) => k3_jordan1h(A,C) = k2_xcmplx_0(k3_xcmplx_0(k11_newton(2,k7_nat_d(C,B)),k6_xcmplx_0(k3_jordan1h(A,B),2)),2) ) ) ) ) )).
fof(t27_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t27_jordan18,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => r1_jordan18(A,B,C,D,C,E) ) ) ) ) ) )).
fof(t27_jordan19,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( k17_euclid(B) = k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)),2) & r2_hidden(B,k3_jordan19(A)) & r2_hidden(B,k4_jordan19(A)) ) ) ) )).
fof(t27_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_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_0(B)),k15_euclid(2)) ) ) ) )).
fof(t27_jordan1b,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),1),k3_matrix_0(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)) ) ) )).
fof(t27_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(k1_jordan8(B,A))) & k25_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,1) ) ) ) )).
fof(t27_jordan1g,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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,k2_jordan9(B,A)))),k4_finseq_4(k2_jordan1e(B,A),k24_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))))) ) ) )).
fof(t27_jordan1h,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( ( ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_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) ) ) ) ) ) )).
fof(t27_jordan1k,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v1_xreal_0(C) => ( 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,k6_xcmplx_0(1,C)))) = k3_xcmplx_0(k6_xcmplx_0(1,C),k1_topreal6(2,A,B)) ) ) ) ) )).
fof(t27_jordan20,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( v1_xreal_0(G) => ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t27_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => ( r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(k18_euclid(k1_jordan21(k8_jordan6(k3_topreal1(2,k2_jordan9(A,C))))),k18_euclid(k1_jordan21(k8_jordan6(k3_topreal1(2,k2_jordan9(A,B)))))) ) ) ) ) ) )).
fof(t27_jordan23,axiom,( ! [A] : ( ( v1_topreal1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => v1_topreal1(k3_finseq_6(u1_struct_0(k15_euclid(2)),A,B,C)) ) ) ) )).
fof(t27_jordan2b,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k14_euclid(1))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( k9_finseq_1(C) = A => k8_metric_1(k14_euclid(1),A,B) = a_2_2_jordan2b(B,C) ) ) ) ) )).
fof(t27_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(A))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(A))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k15_euclid(A))) => ! [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] : ( ( 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,k5_numbers) & I = k1_funct_1(J,1) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t27_jordan3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( ( r2_jordan3(A,B,C,D) & r2_jordan3(A,B,D,C) ) => C = D ) ) ) ) ) )).
fof(t27_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_jordan4(A,B,C,D) & r1_xxreal_0(D,C) ) => ( k3_finseq_1(B) = k1_nat_1(k7_nat_d(C,D),1) & B = k3_finseq_6(u1_struct_0(k15_euclid(2)),A,C,D) ) ) ) ) ) ) )).
fof(t27_jordan5a,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t27_jordan5b,axiom,( ! [A] : ( 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 ) ) )).
fof(t27_jordan5c,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( 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(k1_nat_1(D,1),k3_finseq_1(A)) & r2_hidden(C,k2_topreal1(2,A,E)) & r1_xxreal_0(1,E) & r1_xxreal_0(k1_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,k1_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) ) ) ) ) ) ) ) ) ) )).
fof(t27_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( B = a_1_2_jordan5d(A) => k2_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)))) ) ) ) )).
fof(t27_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t27_jordan9,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( ~ 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] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_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)) ) ) ) ) ) ) )).
fof(t27_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_jordan_a(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( 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)) ) ) ) ) ) )).
fof(t27_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( 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] : ( v3_ordinal1(D) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t27_kurato_1,axiom,( 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) )).
fof(t27_kurato_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(A)))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(A)))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(A)))))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,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(k4_ordinal1,k9_setfam_1(u1_struct_0(k2_borsuk_1(k15_euclid(A),k15_euclid(A))))))) ) => ( ! [E] : ( v7_ordinal1(E) => k2_kurato_2(k2_borsuk_1(k15_euclid(A),k15_euclid(A)),D,E) = k3_borsuk_1(k15_euclid(A),k15_euclid(A),k2_kurato_2(k15_euclid(A),B,E),k2_kurato_2(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) ) ) ) ) ) )).
fof(t27_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r2_hidden(C,k2_finseq_1(A)) => k12_matrix_3(A,B,D) = k4_rlvect_1(B,k9_laplace(A,C,B,D)) ) ) ) ) ) )).
fof(t27_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => v4_lattice3(k11_group_4(A)) ) )).
fof(t27_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => r1_lattice2(u1_struct_0(A),u1_lattices(A),u2_lattices(A)) ) )).
fof(t27_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v3_filter_0(B) & l3_lattices(B) ) => ! [C] : ( m1_lattice4(C,B,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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,F)),k3_funct_2(u1_struct_0(B),u1_struct_0(A),C,E)) ) => r3_lattices(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),C,k4_filter_0(B,D,E))) ) ) ) ) ) ) ) )).
fof(t27_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( v3_ordinal1(C) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t27_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v9_lattice6(B,A) => r1_tarski(k5_lattice6(A),B) ) ) ) )).
fof(t27_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( v3_ordinal1(D) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t27_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)))) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ! [E] : ( 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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),B))) | k1_funct_1(k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),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),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),B),D),k6_domain_1(k4_ordinal1,k7_nat_d(k15_glib_000(A),E))) ) ) ) ) ) ) )).
fof(t27_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_limfunc1(A) & m2_valued_0(B,k1_numbers,A) ) => v2_limfunc1(B) ) ) ) )).
fof(t27_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,C) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,C) & ~ r1_xxreal_0(A,D) & r2_hidden(D,k1_relset_1(k1_numbers,B)) ) ) ) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( v8_valued_0(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(k6_xcmplx_0(A,C),A))) & ~ v2_seq_2(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(k6_xcmplx_0(A,C),A))) ) ) | r3_limfunc2(B,A) ) ) ) ) )).
fof(t27_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r3_limfunc3(C,A) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,D),A),k2_rcomp_1(A,k2_xcmplx_0(A,D))),k3_xboole_0(k9_xtuple_0(B),k9_xtuple_0(C))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,D),A),k2_rcomp_1(A,k2_xcmplx_0(A,D)))) => r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) | r3_limfunc3(B,A) ) ) ) ) ) )).
fof(t27_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k3_limfunc1(C))) & r1_xxreal_0(k4_limfunc1(A),k1_funct_1(A,D)) ) ) | v4_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).
fof(t27_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => r1_lmod_6(A,k2_vectsp_5(A,B,C,D),k1_vectsp_5(A,B,C,D)) ) ) ) ) )).
fof(t27_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t27_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_series_1(B) => ( ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(D,E) & ~ r1_xxreal_0(k2_normsp_0(A,k5_rsspace3(A,C,E)),k9_nat_1(k1_numbers,B,E)) ) ) | v2_lopban_3(C,A) ) ) ) ) ) )).
fof(t27_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,k4_sin_cos(k2_normsp_0(A,B)),C)) ) ) ) )).
fof(t27_lopclset,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ ! [B] : ( m1_subset_1(B,k5_finsub_1(A)) => v1_xboole_0(B) ) ) )).
fof(t27_lpspacc1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ( r2_relset_1(B,k2_numbers,k2_valued_1(B,k2_numbers,k2_numbers,k8_funcop_1(k2_numbers,B,k5_complex1),k8_funcop_1(k2_numbers,B,k5_complex1)),k8_funcop_1(k2_numbers,B,k5_complex1)) & r2_relset_1(B,k2_numbers,k25_valued_1(B,k2_numbers,k8_funcop_1(k2_numbers,B,k5_complex1),A),k8_funcop_1(k2_numbers,B,k5_complex1)) ) ) ) )).
fof(t27_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( 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,k4_xcmplx_0(1))) = k2_partfun1(A,k1_numbers,k8_lpspace1(A,k5_numbers),k1_relset_1(A,D)) & ? [F] : ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) & ? [G] : ( 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,k4_xcmplx_0(1))) & r2_relset_1(A,k1_numbers,G,k8_lpspace1(A,k5_numbers)) & r1_lpspace1(A,B,C,F,G) ) ) ) ) ) ) ) ) ) )).
fof(t27_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( v2_xxreal_0(F) & v1_xreal_0(F) ) => ( ( 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)) ) ) ) ) ) ) ) )).
fof(t27_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(k4_ltlaxio1(A,B),A)) ) ) )).
fof(t27_ltlaxio3,axiom,( k12_ltlaxio3(k11_ltlaxio3(k6_finseq_1(k1_hilbert1),k6_finseq_1(k1_hilbert1))) = k4_ltlaxio1(k3_ltlaxio1,k3_ltlaxio1) )).
fof(t27_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) )).
fof(t27_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t27_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( r2_matrix10(B,k2_matrix10(A,C)) => v3_matrix10(k4_matrix10(A,B,C)) ) ) ) ) )).
fof(t27_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_matrix_2(B,k3_matrix_2(k1_nat_1(A,2))) => ~ ( v4_matrix_2(B,k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))) & v5_matrix_2(B,k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))) ) ) ) )).
fof(t27_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m2_finseq_2(C,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [D] : ( m2_finseq_2(D,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [E] : ( ( v1_matrix_0(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) ) ) ) ) ) ) )).
fof(t27_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,A) & r1_xxreal_0(1,D) & r1_xxreal_0(D,A) ) => k3_matrix_0(u1_struct_0(B),k3_matrix_1(B,A),C,D) = k1_funct_1(k3_matrix14(B,A,C),D) ) ) ) ) ) )).
fof(t27_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t27_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(B),A,A) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(B))) ) => ( ( v3_matrix16(E,u1_struct_0(B)) & v3_matrix16(F,u1_struct_0(B)) ) => v3_matrix16(k1_matrix_4(B,k2_matrix13(A,A,B,E,C),k2_matrix13(A,A,B,F,D)),u1_struct_0(B)) ) ) ) ) ) ) ) )).
fof(t27_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,C,A,B) & m2_finseq_1(D,k3_finseq_2(C)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,C,A,B) & m2_finseq_1(E,k3_finseq_2(C)) ) => ( ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ( r2_hidden(k4_tarski(F,G),k2_matrix_0(D)) => k3_matrix_0(C,D,F,G) = k3_matrix_0(C,E,F,G) ) ) ) => D = E ) ) ) ) ) ) )).
fof(t27_matrix_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( ( 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] : ( ( v1_funct_1(F) & v1_funct_2(F,B,A) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [G] : ( ( 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] : ( m1_subset_1(H,B) => ! [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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t27_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(D) ) => k1_matrix_4(A,B,D) = k1_matrix_4(A,k3_matrix_3(A,B,C),k3_matrix_3(A,D,C)) ) ) ) ) ) )).
fof(t27_matrix_6,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(A),B,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( v2_matrix_6(C,B,A) => v2_matrix_6(k2_matrix_3(A,C),B,A) ) ) ) ) )).
fof(t27_matrix_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_matrix_2(B,k3_matrix_2(A)) => ( r1_xxreal_0(1,A) => ( v5_matrix_2(B,k2_matrix_2(k3_matrix_2(A))) <=> v5_matrix_2(k3_matrix_7(A,B),k2_matrix_2(k3_matrix_2(A))) ) ) ) ) )).
fof(t27_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( ( v2_matrix_8(C,A,B) & v1_matrix_8(C,A,B) ) => C = k2_matrix_1(B,A) ) ) ) ) )).
fof(t27_matrix_9,axiom,( r2_hidden(k3_finseq_4(k4_ordinal1,1,3,2),k3_matrix_2(3)) & r2_hidden(k3_finseq_4(k4_ordinal1,2,3,1),k3_matrix_2(3)) & r2_hidden(k3_finseq_4(k4_ordinal1,2,1,3),k3_matrix_2(3)) & r2_hidden(k3_finseq_4(k4_ordinal1,3,1,2),k3_matrix_2(3)) & r2_hidden(k3_finseq_4(k4_ordinal1,1,2,3),k3_matrix_2(3)) & r2_hidden(k3_finseq_4(k4_ordinal1,3,2,1),k3_matrix_2(3)) )).
fof(t27_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( m1_subset_1(E,C) => ! [F] : ( ( v1_matrixj1(F,C) & m2_finseq_1(F,k3_finseq_2(k3_finseq_2(C))) ) => ! [G] : ( ( v1_matrixj1(G,C) & m2_finseq_1(G,k3_finseq_2(k3_finseq_2(C))) ) => ( r2_hidden(k4_tarski(A,B),k2_matrix_0(k13_matrixj1(C,D,G))) <=> ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & r2_hidden(k4_tarski(k1_nat_1(A,k2_wsierp_1(k10_matrixj1(C,F))),k1_nat_1(B,k2_wsierp_1(k11_matrixj1(C,F)))),k2_matrix_0(k13_matrixj1(C,E,k3_matrixj1(C,F,G)))) ) ) ) ) ) ) ) ) ) )).
fof(t27_matrixr1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( k3_finseq_1(k7_matrixr1(A,B)) = k3_finseq_1(B) & k1_matrix_0(k7_matrixr1(A,B)) = k1_matrix_0(B) ) ) ) )).
fof(t27_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,k1_numbers,B,A) & m2_finseq_1(E,k3_finseq_2(k1_numbers)) ) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,k1_numbers,A,C) & m2_finseq_1(F,k3_finseq_2(k1_numbers)) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,k1_numbers,C,D) & m2_finseq_1(G,k3_finseq_2(k1_numbers)) ) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(C,k5_numbers) & k6_matrixr1(k6_matrixr1(E,F),G) != k6_matrixr1(E,k6_matrixr1(F,G)) ) ) ) ) ) ) ) ) )).
fof(t27_matrlin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( ( ~ 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] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(E),C,A) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(E))) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(E),B,A) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(E))) ) => k6_matrlin(E,k8_matrlin(u1_struct_0(E),C,B,A,F,G)) = k8_finseq_1(u1_struct_0(E),k6_matrlin(E,F),k6_matrlin(E,G)) ) ) ) ) ) ) ) )).
fof(t27_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( m1_matrlin(D,A,B) => ! [E] : ( m1_matrlin(E,A,C) => ! [F] : ( ( 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] : ( m1_vectsp_4(G,A,B) => ! [H] : ( m1_vectsp_4(H,A,B) => ! [I] : ( m1_vectsp_4(I,A,C) => ! [J] : ( m1_vectsp_4(J,A,C) => ( r1_vectsp_5(A,C,I,J) => ( ( k1_vectsp_9(A,G) = k5_numbers & k1_vectsp_9(A,I) != k5_numbers ) | ( k1_vectsp_9(A,H) = k5_numbers & k1_vectsp_9(A,J) != k5_numbers ) | ! [K] : ( ( 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] : ( ( 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] : ( m1_matrlin(M,A,G) => ! [N] : ( m1_matrlin(N,A,H) => ! [O] : ( m1_matrlin(O,A,I) => ! [P] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t27_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t27_matrprob,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( k3_finseq_1(A) = k3_finseq_1(B) => k2_xcmplx_0(k5_matrprob(A),k5_matrprob(B)) = k5_matrprob(k7_matrlin(k1_numbers,A,B)) ) ) ) )).
fof(t27_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => 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)) ) ) ) ) ) )).
fof(t27_matrtop2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ! [D] : ( ( 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) = A => v1_rlaffin1(k7_ranknull(k15_euclid(A),k15_euclid(B),k3_matrtop1(A,B,C),D),k15_euclid(A)) ) ) ) ) ) )).
fof(t27_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,k2_finseq_1(B)) => v2_matrtop3(k3_matrtop1(B,B,k1_matrtop3(B,A)),B) ) ) ) )).
fof(t27_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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))) ) ) )).
fof(t27_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k3_zfmisc_1(k1_tarski(A),k2_tarski(B,D),k1_tarski(C)) = k2_tarski(k3_xtuple_0(A,B,C),k3_xtuple_0(A,D,C)) )).
fof(t27_measure1,axiom,( ! [A] : ! [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))) ) => ? [C] : ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & ! [D] : ( 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 ) ) ) ) ) )).
fof(t27_measure6,axiom,( ! [A] : ( ( v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ( v2_measure5(A) <=> v2_measure5(k1_measure6(A,B)) ) ) ) )).
fof(t27_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ! [D] : ( m2_measure8(D,A,B) => ( v3_prob_1(D) => v7_valued_0(k10_measure8(A,B,D,C)) ) ) ) ) )).
fof(t27_member_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k6_member_1(k2_tarski(A,B)) = k2_tarski(k5_xxreal_3(A),k5_xxreal_3(B)) ) ) )).
fof(t27_membered,axiom,( ! [A] : ( ! [B] : ( r2_hidden(B,A) => v3_membered(B) ) => v3_membered(k3_tarski(A)) ) )).
fof(t27_memstr_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_setfam_1(B) => ! [C] : ( ( ~ v2_struct_0(C) & v2_memstr_0(C,B) & v3_memstr_0(C,B) & l1_memstr_0(C,B) ) => ! [D] : ( ( 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)))) ) ) ) ) )).
fof(t27_mesfun6c,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( m2_subset_1(D,k1_zfmisc_1(B),C) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ( v6_supinf_2(E) => k2_power(k1_funct_1(E,A),k2_extreal1(1,2)) = k3_square_1(k1_funct_1(E,A)) ) ) ) ) ) )).
fof(t27_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k2_numbers)) & v1_mesfunc8(C,A,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( ( k1_relset_1(A,k4_mesfunc5(A,k2_numbers,C,k5_numbers)) = E & ! [F] : ( v7_ordinal1(F) => r1_mesfun6c(A,B,k4_mesfunc5(A,k2_numbers,C,F),E) ) & k1_relset_1(A,D) = E & ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t27_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ( ( v1_mesfunc8(E,A,k2_numbers) & r1_tarski(C,k1_relset_1(A,k4_mesfunc5(A,k2_numbers,E,k5_numbers))) & ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t27_mesfunc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( r1_tarski(D,k9_xtuple_0(C)) => ( r1_mesfunc1(A,B,C,D) <=> ! [E] : ( v1_xreal_0(E) => r2_hidden(k9_subset_1(A,D,k18_mesfunc1(A,C,E)),B) ) ) ) ) ) ) ) )).
fof(t27_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t27_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k5_numbers,C) => ( r2_relset_1(A,k6_numbers,k1_mesfunc2(A,k6_mesfunc1(A,B,k2_xxreal_3(C))),k6_mesfunc1(A,k2_mesfunc2(A,B),C)) & r2_relset_1(A,k6_numbers,k2_mesfunc2(A,k6_mesfunc1(A,B,k2_xxreal_3(C))),k6_mesfunc1(A,k1_mesfunc2(A,B),C)) ) ) ) ) ) )).
fof(t27_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => r2_relset_1(A,k6_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)))) ) ) ) )).
fof(t27_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ! [D] : ( 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) ) ) ) ) )).
fof(t27_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( v7_ordinal1(C) => ( v2_mesfunc9(B,A) => ( k9_subset_1(A,k8_relset_1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,k4_mesfunc9(A,B),C),k1_tarski(k2_supinf_1)),k8_relset_1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,B,k1_nat_1(C,1)),k1_tarski(k1_supinf_1))) = k1_xboole_0 & k9_subset_1(A,k8_relset_1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,k4_mesfunc9(A,B),C),k1_tarski(k1_supinf_1)),k8_relset_1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,B,k1_nat_1(C,1)),k1_tarski(k2_supinf_1))) = k1_xboole_0 ) ) ) ) ) )).
fof(t27_metric_1,axiom,( ! [A] : ( m1_subset_1(A,2) => ! [B] : ( m1_subset_1(B,2) => k1_binop_1(k11_metric_1,A,B) = k5_numbers ) ) )).
fof(t27_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k2_metric_2(A)) => ( r2_hidden(B,k7_metric_2(A)) <=> ? [C] : ( m1_subset_1(C,k2_metric_2(A)) & ? [D] : ( m1_subset_1(D,k1_numbers) & r4_metric_2(A,C,B,D) ) ) ) ) ) )).
fof(t27_metric_3,axiom,( ! [A] : ( m1_subset_1(A,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)) => ! [B] : ( m1_subset_1(B,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)) => ! [C] : ( m1_subset_1(C,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)) => r1_xxreal_0(k2_binop_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k1_numbers,k20_metric_3,A,C),k3_real_1(k2_binop_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k1_numbers,k20_metric_3,A,B),k2_binop_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k1_numbers,k20_metric_3,B,C))) ) ) ) )).
fof(t27_metric_6,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v2_tbsp_1(B,A) => v1_metric_6(B,A) ) ) ) )).
fof(t27_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( 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] : ( ( 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))) ) ) ) ) ) ) )).
fof(t27_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t27_midsp_2,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & l1_midsp_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( 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,G) = k1_midsp_1(B,E,F) <=> k2_binop_1(u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),C,D,G) = k3_rlvect_1(A,k2_binop_1(u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),C,D,E),k2_binop_1(u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),C,D,F)) ) ) ) ) ) ) ) ) ) )).
fof(t27_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [D] : ( 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)) ) ) ) )).
fof(t27_mod_2,axiom,( ~ 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) )).
fof(t27_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(t27_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k3_modal_1) => ! [B] : ( m1_subset_1(B,k3_modal_1) => ( k16_modal_1(A) = k16_modal_1(B) => A = B ) ) ) )).
fof(t27_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ~ ( r2_hidden(k4_tarski(C,D),B) & ! [E] : ( m1_modelc_1(E,A,B) => ~ ( k3_funct_2(k4_ordinal1,A,E,k5_numbers) = C & k3_funct_2(k4_ordinal1,A,E,1) = D ) ) ) ) ) ) ) )).
fof(t27_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => r2_modelc_2(A,A) ) )).
fof(t27_modelc_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_modelc_2(D) & m2_finseq_1(D,k4_ordinal1) ) => ~ ( 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(t27_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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) ) ) ) ) ) ) )).
fof(t27_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m3_monoid_0(B,A) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t27_monoid_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(A,u1_struct_0(k13_monoid_1(B))) <=> ( v1_funct_1(A) & v1_funct_2(A,B,k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,k4_ordinal1))) ) ) )).
fof(t27_morph_01,axiom,( ! [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) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t27_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) ) => ! [D] : ( 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) ) ) ) ) )).
fof(t27_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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] : ( m3_pboole(D,u1_struct_0(A),u3_msualg_1(A,B)) => ! [E] : ( m3_pboole(E,u1_struct_0(A),u3_msualg_1(A,C)) => ( ( r8_pboole(u1_struct_0(A),D,E) & v3_msualg_2(D,A,B) ) => v3_msualg_2(E,A,C) ) ) ) ) ) ) ) )).
fof(t27_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( ( 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] : ( 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))) ) ) ) ) )).
fof(t27_mssublat,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( 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(k5_numbers) => m1_unialg_2(k12_msualg_1(k6_msualg_1(A),B),A) ) ) ) )).
fof(t27_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msualg_2(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t27_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(t27_msualg_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t27_mycielsk,axiom,( ! [A] : ( ( v1_necklace(A) & l1_orders_2(A) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(t27_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t27_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(B,A) <=> r1_ordinal1(B,A) ) ) ) )).
fof(t27_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k3_nat_d(k3_nat_d(C,B),A) = k3_nat_d(C,k3_xcmplx_0(B,A)) ) ) ) )).
fof(t27_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( B != 1 => ( ( A != k5_numbers & k11_nat_3(A,B) = k5_numbers ) <=> ~ r1_nat_d(B,A) ) ) ) ) )).
fof(t27_nat_4,axiom,( v1_int_2(11) )).
fof(t27_nat_5,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ! [D] : ( C = k1_tarski(D) => k2_uproots(C,k1_nat_5(A,B,C)) = k1_funct_1(B,D) ) ) ) )).
fof(t27_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,A) => k3_nat_d(A,B) = k5_numbers ) ) ) )).
fof(t27_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ( ( r3_nattra_1(A,B,C,D) & r3_nattra_1(A,B,D,E) ) => ! [F] : ( m3_nattra_1(F,A,B,C,D) => ! [G] : ( m3_nattra_1(G,A,B,D,E) => m3_nattra_1(k5_nattra_1(A,B,C,D,E,F,G),A,B,C,E) ) ) ) ) ) ) ) ) )).
fof(t27_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( v1_xreal_0(E) => ( r1_tarski(k2_relset_1(u1_struct_0(A),D),k1_relset_1(u1_struct_0(A),C)) => r2_funct_2(k4_ordinal1,u1_struct_0(B),k8_funct_2(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),D,C),E)) ) ) ) ) ) ) )).
fof(t27_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t27_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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 & ! [F] : ( m1_subset_1(F,k4_ordinal1) => k1_normsp_1(A,E,F) != D ) ) => ( v3_normsp_1(k8_funct_2(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,C)) ) ) ) ) ) ) ) ) ) )).
fof(t27_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [C] : ( v1_xreal_0(C) => ( r1_ndiff_4(A,B,C) <=> ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( 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) ) ) ) ) ) ) )).
fof(t27_ndiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finseq_1(B) & v2_prvect_2(B) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k14_prvect_2(B))) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(t27_newton,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k5_newton(A,B,k5_numbers) = k12_finseq_1(k4_ordinal1,1) ) ) )).
fof(t27_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ( r3_nfcont_1(A,B,E,D) => r3_nfcont_1(A,B,k4_vfunct_1(u1_struct_0(A),B,E,C),D) ) ) ) ) ) )).
fof(t27_nfcont_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( 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) ) ) ) )).
fof(t27_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t27_normform,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [C] : ~ ( 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)) ) ) )).
fof(t27_normsp_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(t27_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k3_normsp_2(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k3_normsp_2(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k4_normsp_2(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k4_normsp_2(A))))) ) => ( r1_funct_2(k4_ordinal1,u1_struct_0(k3_normsp_2(A)),k4_ordinal1,u1_struct_0(k4_normsp_2(A)),B,C) => ( v2_frechet(C,k4_normsp_2(A)) <=> v2_frechet(B,k3_normsp_2(A)) ) ) ) ) ) )).
fof(t27_numbers,axiom,( k4_ordinal1 != k4_numbers )).
fof(t27_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t27_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => r1_filter_1(A,k15_openlatt(A)) ) )).
fof(t27_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,k2_oppcat_1(B),A) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_oppcat_1(B))) => k3_funct_2(u1_struct_0(B),u1_struct_0(A),k7_cat_1(B,A,k9_oppcat_1(B,A,C)),k4_oppcat_1(B,D)) = k3_funct_2(u1_struct_0(k2_oppcat_1(B)),u1_struct_0(A),k7_cat_1(k2_oppcat_1(B),A,C),D) ) ) ) ) )).
fof(t27_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_ordeq_01(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_ordeq_01(A,B))) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ( ( F = D & G = E & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,A) => r1_xxreal_0(k2_normsp_0(B,k5_algstr_0(B,k7_partfun1(u1_struct_0(B),F,H),k7_partfun1(u1_struct_0(B),G,H))),C) ) ) ) => r1_xxreal_0(k2_normsp_0(k5_ordeq_01(A,B),k5_algstr_0(k5_ordeq_01(A,B),D,E)),C) ) ) ) ) ) ) ) ) )).
fof(t27_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v3_orders_1(A) => v3_orders_1(k2_wellord1(A,B)) ) ) )).
fof(t27_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t27_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => k10_ordinal2(A,k5_ordinal1) = A ) )).
fof(t27_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ~ ( r1_ordinal1(A,B) & ! [C] : ( v3_ordinal1(C) => B != k10_ordinal2(A,C) ) ) ) ) )).
fof(t27_ordinal4,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r1_ordinal1(A,B) => ( C = k1_xboole_0 | r1_ordinal1(k12_ordinal2(C,A),k12_ordinal2(C,B)) ) ) ) ) ) )).
fof(t27_ordinal6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_abian(A,B) => r2_hidden(A,k10_xtuple_0(B)) ) ) )).
fof(t27_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t27_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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)) ) ) )).
fof(t27_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ( v13_osalg_1(B,A) <=> ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t27_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m2_osalg_2(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t27_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ~ r1_parsp_1(A,B,C,B,D) => ( B != C & C != D & D != B ) ) ) ) ) ) )).
fof(t27_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t27_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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)) ) ) ) )).
fof(t27_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ? [D] : ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) & ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,k1_relset_1(A,C)) => k3_funct_2(A,B,D,E) = k7_partfun1(B,C,E) ) ) ) ) ) ) )).
fof(t27_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => k2_partit1(A,B,k3_partit1(A,B,C)) = B ) ) ) )).
fof(t27_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( r8_relat_2(B,A) => v8_relat_2(B) ) ) ) )).
fof(t27_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_diraf(A,B,C,E) & r1_diraf(A,C,F,D) & ~ r3_diraf(A,B,C,D) & ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( r1_diraf(A,B,G,D) & r1_diraf(A,G,F,E) ) ) ) ) ) ) ) ) ) )).
fof(t27_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t27_pcomps_1,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ~ ( v9_metric_1(A) & r2_hidden(C,k8_metric_1(A,B,D)) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & r1_tarski(k8_metric_1(A,C,E),k8_metric_1(A,B,D)) ) ) ) ) ) ) ) )).
fof(t27_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k20_pcs_0(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k20_pcs_0(A,B))) => ( C = B => ( r1_pcs_0(k20_pcs_0(A,B),C,D) & r1_pcs_0(k20_pcs_0(A,B),D,C) ) ) ) ) ) )).
fof(t27_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k4_real_ns1(A))) => r2_relset_1(u1_struct_0(k4_real_ns1(1)),u1_struct_0(k4_real_ns1(B)),k4_vfunct_1(u1_struct_0(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,F),E),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(B)),k7_pdiff_1(A,C,F),k4_vfunct_1(u1_struct_0(k4_real_ns1(A)),k4_real_ns1(B),E,D))) ) ) ) ) ) ) )).
fof(t27_pdiff_3,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(2)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [C] : ( ( 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) & k10_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) = k6_xcmplx_0(k4_pdiff_3(B,A),k4_pdiff_3(C,A)) ) ) ) ) ) )).
fof(t27_pdiff_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m1_rcomp_1(C,k3_funct_2(k1_euclid(3),k1_numbers,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] : ( ( v9_ordinal1(D) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k1_rvsum_1(E) = k1_tarski(k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(3,3),B)) & r1_tarski(k1_rvsum_1(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),C) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,3,A,B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,3,A,B))))) & k10_pdiff_1(3,3,A,B) = k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,3,A,B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,3,A,B))))) ) ) ) ) ) ) ) ) )).
fof(t27_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( 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) ) ) ) )).
fof(t27_pdiff_6,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(B))) => ! [D] : ( v1_xreal_0(D) => k3_funct_2(u1_struct_0(k4_real_ns1(B)),u1_struct_0(k4_real_ns1(1)),k4_pdiff_1(A,B),k1_rlvect_1(k4_real_ns1(B),C,D)) = k1_rlvect_1(k4_real_ns1(1),k3_funct_2(u1_struct_0(k4_real_ns1(B)),u1_struct_0(k4_real_ns1(1)),k4_pdiff_1(A,B),C),D) ) ) ) ) )).
fof(t27_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_1(B,k1_euclid(A)) => ! [C] : ( m2_finseq_1(C,k1_euclid(A)) => ! [D] : ( m2_finseq_1(D,k1_euclid(A)) => ( ( k3_finseq_1(B) = k3_finseq_1(D) & k3_finseq_1(C) = k3_finseq_1(D) & ! [E] : ( 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)) ) ) ) ) ) )).
fof(t27_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t27_pencil_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ~ v1_zfmisc_1(C) => ( v16_pencil_1(k1_funct_7(B,k3_pencil_1(A,B),C),A) & ~ v13_pencil_1(k1_funct_7(B,k3_pencil_1(A,B),C)) ) ) ) ) )).
fof(t27_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t27_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k4_nat_d(B,2) = k5_numbers => k1_square_1(k1_newton(A,k3_nat_d(B,2))) = k1_newton(A,B) ) ) ) )).
fof(t27_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m2_finseq_2(C,B,k3_finseq_2(B)) => ! [D] : ( 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)) ) ) ) )).
fof(t27_polyeq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k1_newton(A,3) = k3_xcmplx_0(k3_xcmplx_0(A,A),A) & k1_newton(A,3) = k3_xcmplx_0(k1_square_1(A),A) & k1_newton(A,3) = k3_polyeq_3(A) ) ) )).
fof(t27_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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 ) ) ) ) )).
fof(t27_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => k3_finseq_1(k10_polyform(A,B)) = k11_polyform(A,B) ) ) )).
fof(t27_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k2_normsp_1(A,B,k9_polynom3(A)),B) ) ) )).
fof(t27_polynom5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_vectsp_1(A) & l4_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_polynom5(A,B,k5_struct_0(A)),B) ) ) )).
fof(t27_polynom7,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( 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] : ( 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),k10_polynom1(A,B,k4_polynom7(A,B,D),C)) ) ) ) ) )).
fof(t27_polynom8,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( 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)) ) ) ) ) ) )).
fof(t27_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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) ) ) ) ) ) ) ) )).
fof(t27_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(A,k5_numbers) => k2_power(A,k2_xcmplx_0(B,C)) = k3_xcmplx_0(k2_power(A,B),k2_power(A,C)) ) ) ) ) )).
fof(t27_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_pralg_2(D,A,B) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( ( v4_msualg_1(F,B) & l3_msualg_1(F,B) ) => ! [G] : ( ( v1_relat_1(G) & v4_relat_1(G,A) & v1_funct_1(G) & v1_partfun1(G,A) & v1_funcop_1(G) ) => ( ! [H] : ( m1_subset_1(H,A) => ? [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] : ( 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] : ( r2_hidden(I,k1_funct_1(u3_msualg_1(B,F),E)) => ! [J] : ( ( v1_relat_1(J) & v1_funct_1(J) ) => ( J = k1_funct_1(k9_funct_6(k1_funct_1(k9_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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t27_pre_poly,axiom,( ! [A] : ! [B] : ! [C] : ( m2_finseq_1(C,k3_finseq_2(A)) => ! [D] : ( 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)) ) ) ) )).
fof(t27_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_pre_topc(D,B) => ( v5_pre_topc(C,A,B) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t27_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t27_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,B) & r1_xxreal_0(1,C) ) => r1_xxreal_0(k2_prepower(C,A),k2_prepower(C,B)) ) ) ) ) )).
fof(t27_prob_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( v1_relat_1(D) & v1_funct_1(D) & k9_xtuple_0(D) = C & ! [E] : ( 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) = k5_numbers ) ) ) ) ) ) )).
fof(t27_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m1_prob_1(E,A,B) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t27_prob_3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => v2_prob_1(k1_prob_3(A,C)) ) ) )).
fof(t27_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => k4_prob_4(A,B,C) = k2_measure3(A,B,k2_prob_4(A,B,C)) ) ) ) )).
fof(t27_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t27_projpl_1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ( r5_projpl_1(A,B,C,D,E) => r2_zfmisc_1(B,C,D,E) ) ) ) ) ) ) )).
fof(t27_pua2mss1,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t27_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t27_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_qc_lang1(A)) => r2_qc_lang1(A,B,k28_qc_lang1(A,B)) ) ) )).
fof(t27_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t27_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t27_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ! [E] : ( m1_trees_1(E,k9_xtuple_0(k2_qc_lang4(A,B))) => ! [F] : ( 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(k4_ordinal1,E,F),k3_qc_lang4(A,B,D)) ) ) ) ) ) ) ) )).
fof(t27_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k5_quatern2(A,B) = k22_quaterni(k22_quaterni(k19_quaterni(k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(B),k13_quaterni(A)),k3_xcmplx_0(k14_quaterni(A),k14_quaterni(B))),k3_xcmplx_0(k15_quaterni(B),k15_quaterni(A))),k3_xcmplx_0(k16_quaterni(B),k16_quaterni(A))),k1_square_1(k28_quaterni(B))),k21_quaterni(k7_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k13_quaterni(B),k14_quaterni(A)),k3_xcmplx_0(k14_quaterni(B),k13_quaterni(A))),k3_xcmplx_0(k15_quaterni(B),k16_quaterni(A))),k3_xcmplx_0(k16_quaterni(B),k15_quaterni(A))),k1_square_1(k28_quaterni(B))),k3_quatern2)),k21_quaterni(k7_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(B),k15_quaterni(A)),k3_xcmplx_0(k14_quaterni(B),k16_quaterni(A))),k3_xcmplx_0(k15_quaterni(B),k13_quaterni(A))),k3_xcmplx_0(k16_quaterni(B),k14_quaterni(A))),k1_square_1(k28_quaterni(B))),k11_quaterni)),k21_quaterni(k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k13_quaterni(B),k16_quaterni(A)),k3_xcmplx_0(k14_quaterni(B),k15_quaterni(A))),k3_xcmplx_0(k15_quaterni(B),k14_quaterni(A))),k3_xcmplx_0(k16_quaterni(B),k13_quaterni(A))),k1_square_1(k28_quaterni(B))),k12_quaterni)) ) ) )).
fof(t27_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k16_quaterni(k21_quaterni(k7_xcmplx_0(1,k1_square_1(k28_quaterni(A))),k27_quaterni(A))) = k4_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k28_quaterni(A))),k16_quaterni(A))) ) )).
fof(t27_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ( A = k5_numbers => k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k13_quaterni(A)),k1_square_1(k14_quaterni(A))),k1_square_1(k15_quaterni(A))),k1_square_1(k16_quaterni(A))) = k5_numbers ) ) )).
fof(t27_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(k1_quin_1(B,C,D),k5_numbers) & ~ ( ~ ( ~ r1_xxreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(A)),k3_xcmplx_0(C,A)),D),k5_numbers) & r1_xxreal_0(k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B)),A) & r1_xxreal_0(A,k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B))) ) & ~ ( ~ ( r1_xxreal_0(k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B)),A) & r1_xxreal_0(A,k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B))) ) & r1_xxreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(A)),k3_xcmplx_0(C,A)),D),k5_numbers) ) ) ) ) ) ) ) )).
fof(t27_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t27_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_random_1(D,A,B) => ! [E] : ( v1_xreal_0(E) => ( r1_random_1(A,B,D,C) => k8_random_1(A,B,C,k5_random_1(A,B,D,E)) = k3_xcmplx_0(E,k8_random_1(A,B,C,D)) ) ) ) ) ) ) )).
fof(t27_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( 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)))) ) ) ) ) ) ) )).
fof(t27_rat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_rat_1(C) => ( ( C = k7_xcmplx_0(B,A) & ! [D] : ( v7_ordinal1(D) => ~ ( ~ r1_xxreal_0(D,1) & ? [E] : ( v1_int_1(E) & ? [F] : ( v7_ordinal1(F) & B = k3_xcmplx_0(E,D) & A = k3_xcmplx_0(F,D) ) ) ) ) ) => ( A = k5_numbers | ( A = k1_rat_1(C) & B = k2_rat_1(C) ) ) ) ) ) ) )).
fof(t27_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( m1_ratfunc1(B,A) => k11_ratfunc1(A,k11_ratfunc1(A,B)) = k11_ratfunc1(A,B) ) ) )).
fof(t27_rcomp_3,axiom,( ! [A] : ( ( ~ 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(k3_seq_4(A),A) | A = k3_limfunc1(k3_seq_4(A)) ) ) ) )).
fof(t27_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => ( ( k9_nat_1(k1_numbers,k3_real_3(C),A) = k5_numbers & r1_xxreal_0(A,B) ) => k9_nat_1(k1_numbers,k3_real_3(C),B) = k5_numbers ) ) ) ) )).
fof(t27_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k6_real_lat(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k6_real_lat(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k6_real_lat(A))) => k1_binop_1(k5_real_lat(A),C,k1_binop_1(k4_real_lat(A),B,D)) = k1_binop_1(k4_real_lat(A),k1_binop_1(k5_real_lat(A),C,B),k1_binop_1(k5_real_lat(A),C,D)) ) ) ) ) )).
fof(t27_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_binop_1(k2_realset3(A),B,k5_struct_0(A)) = B ) ) )).
fof(t27_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [D] : ( ( v1_rearran1(D) & v2_rearran1(D) & v3_rearran1(D,k1_zfmisc_1(A)) & m2_finseq_1(D,k1_zfmisc_1(A)) ) => ( ( v1_partfun1(C,B) & k5_card_1(A) = k5_card_1(B) ) => ( r2_classes1(k4_rearran1(B,A,D,C),k3_rearran1(B,A,D,C)) & k20_rfunct_3(A,k4_rearran1(B,A,D,C),A) = k20_rfunct_3(A,k3_rearran1(B,A,D,C),A) & k21_rfunct_3(A,k4_rearran1(B,A,D,C),A) = k21_rfunct_3(A,k3_rearran1(B,A,D,C),A) ) ) ) ) ) ) )).
fof(t27_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => r1_tarski(k3_relat_1(A,k3_xboole_0(C,B)),k3_xboole_0(k3_relat_1(A,C),k3_relat_1(A,B))) ) ) ) )).
fof(t27_relset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ~ ( k2_relset_1(B,C) != k1_xboole_0 & ! [D] : ( m1_subset_1(D,A) => ~ r2_hidden(D,k1_relset_1(A,C)) ) ) ) ) ) )).
fof(t27_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( 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)) ) ) ) )).
fof(t27_revrot_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => k26_seq_4(k2_goboard1(B)) = k26_seq_4(k2_goboard1(k1_finseq_6(u1_struct_0(k15_euclid(2)),B,A))) ) ) )).
fof(t27_rewrite1,axiom,( ! [A] : ! [B] : ( r2_rewrite1(k1_xboole_0,A,B) => A = B ) )).
fof(t27_rewrite2,axiom,( ! [A] : 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))) )).
fof(t27_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ~ v1_xboole_0(F) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k8_afinsq_1(F))) => ! [H] : ( 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,E) & r2_rewrite3(F,G,H,A,B,D,E) ) => C = D ) ) ) ) )).
fof(t27_rfinseq,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => k2_rfinseq(A,k3_finseq_1(B),B) = k1_xboole_0 ) )).
fof(t27_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => k6_rfinseq2(k6_rvsum_1(A)) = k6_rvsum_1(k5_rfinseq2(A)) ) )).
fof(t27_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t27_rfunct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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,B)) & v8_valued_0(k2_partfun1(k1_numbers,k1_numbers,C,A)) ) => v3_funct_1(k2_partfun1(k1_numbers,k1_numbers,C,k3_xboole_0(B,A))) ) ) )).
fof(t27_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,k3_rfunct_3(A,B)) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_rfunct_3(A,B,C,D) => r1_rfunct_3(A,B,k2_rfinseq(k3_rfunct_3(A,B),E,C),D) ) ) ) ) ) ) )).
fof(t27_rfunct_4,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(t27_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_seq_2(B) => v2_seq_2(k1_valued_0(k1_numbers,B,A)) ) ) ) )).
fof(t27_rinfsup2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( k12_supinf_2(k4_rinfsup2(B),A) = k1_rinfsup2(k1_valued_0(k6_numbers,B,A)) & k12_supinf_2(k3_rinfsup2(B),A) = k2_rinfsup2(k1_valued_0(k6_numbers,B,A)) ) ) ) )).
fof(t27_rlaffin1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( m1_rlvect_2(D,C) => r1_rlvect_2(C,k2_rlaffin1(C,k2_rlaffin1(C,D,B),A),k2_rlaffin1(C,D,k3_xcmplx_0(A,B))) ) ) ) ) )).
fof(t27_rlaffin2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(t27_rlaffin3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_rlaffin1(C,k15_euclid(A)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) => ! [E] : ( m2_rlaffin3(E,k15_euclid(A),C) => ! [F] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(t27_rlsub_1,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( ~ 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) ) ) ) ) )).
fof(t27_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( m1_rlsub_1(D,A) => m1_rlsub_1(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))) ) ) ) ) )).
fof(t27_rltopsp1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t27_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t27_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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(k4_ordinal1,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)))) ) ) ) ) )).
fof(t27_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( k1_rlvect_3(A,B) = A & ! [C] : ( m1_rlvect_3(C,A) => ~ r1_tarski(C,B) ) ) ) ) )).
fof(t27_rlvect_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( v1_rlvect_3(k8_domain_1(u1_struct_0(B),C,E,D),B) => ( C = D | C = E | D = E | A = k5_numbers | v1_rlvect_3(k8_domain_1(u1_struct_0(B),C,E,k1_rlvect_1(B,D,A)),B) ) ) ) ) ) ) ) )).
fof(t27_rlvect_5,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ( v1_rlvect_5(A) => v1_rlvect_5(B) ) ) ) )).
fof(t27_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ( r1_tarski(u1_struct_0(C),u1_struct_0(D)) => m1_rmod_2(C,A,D) ) ) ) ) ) )).
fof(t27_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t27_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( ( 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)) ) ) ) ) ) ) )).
fof(t27_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t27_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_lattices(A,B,C) = k1_lattices(A,C,B) ) ) ) )).
fof(t27_robbins3,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t27_robbins4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k2_robbins4)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_robbins4)) => ( A = 3 => k3_lattices(k2_robbins4,A,B) = A ) ) ) )).
fof(t27_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t27_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k1_rpr_1(A,B) = k6_xcmplx_0(k1_rpr_1(A,k4_subset_1(A,B,C)),k1_rpr_1(A,k7_subset_1(A,C,B))) ) ) ) )).
fof(t27_rusub_1,axiom,( ! [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_bhsp_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_bhsp_1(B) & m1_rusub_1(B,A) ) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_struct_0(B,C) <=> r1_struct_0(A,C) ) ) => B = A ) ) ) )).
fof(t27_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( 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))) ) ) ) ) )).
fof(t27_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t27_rusub_4,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => v3_rusub_4(k3_rusub_4(A,B),A) ) ) )).
fof(t27_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t27_rvsum_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(B,k1_numbers)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k4_finseq_2(B,k1_numbers)) => k1_funct_1(k9_rvsum_1(B,C,D),A) = k6_xcmplx_0(k1_funct_1(C,A),k1_funct_1(D,A)) ) ) ) )).
fof(t27_rvsum_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( 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) ) ) ) )).
fof(t27_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_scmfsa6c(C) & v2_scmfsa6c(C) & m1_subset_1(C,u1_compos_1(k1_scmfsa_2)) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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] : ( 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(k7_card_1(3),k1_scmfsa_2,C,k1_scmfsa_m(B)),A),E) ) ) ) ) ) )).
fof(t27_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( m1_scmfsa_2(D) => k18_scmfsa_2(k6_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(B)),D) = k18_scmfsa_2(k1_scmfsa6b(C,B,A),D) ) ) ) ) )).
fof(t27_scmfsa10,axiom,( ! [A] : ( 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) ) ) )).
fof(t27_scmfsa8a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( ( r5_scmfsa7b(A,k1_scmfsa_m(B),C) & r6_scmfsa7b(A,k1_scmfsa_m(B),C) ) => k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(C,A),k1_funct_4(B,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(C,A),k1_funct_4(B,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_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(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(C,A),k1_funct_4(B,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))),1))) ) ) ) ) )).
fof(t27_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( v1_ami_2(E) & ~ v1_scmfsa_m(E) & m1_subset_1(E,u1_struct_0(k1_scmfsa_2)) ) => ( ( k1_funct_1(B,E) = k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),k5_card_1(D)),7)))) ) ) ) ) ) ) )).
fof(t27_scmfsa8c,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => k1_funct_1(k1_scmfsa8b(C,A,B),k1_nat_1(k5_card_1(B),2)) = k11_scmfsa_2(k1_nat_1(k1_nat_1(k5_card_1(A),k5_card_1(B)),3)) ) ) ) )).
fof(t27_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ( ( 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) ) ) ) ) ) ) )).
fof(t27_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ~ ( k2_compos_0(u1_compos_1(k1_scmfsa_2),A) = 5 & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => A != k10_scmfsa_2(B,C) ) ) ) ) )).
fof(t27_scmfsa_m,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_scmfsa_2)) => ! [D] : ( 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] : ( ( 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] : ( m1_scmfsa_2(E) => ( r2_hidden(E,D) => k18_scmfsa_2(A,E) = k18_scmfsa_2(B,E) ) ) ) ) ) ) ) ) )).
fof(t27_scmpds_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t27_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ( r2_hidden(k5_numbers,k9_xtuple_0(k2_scmpds_6(A,B,C,D))) & r2_hidden(1,k9_xtuple_0(k2_scmpds_6(A,B,C,D))) ) ) ) ) ) )).
fof(t27_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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)) ) ) ) ) ) )).
fof(t27_scmpds_8,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ! [F] : ( v1_int_1(F) => ! [G] : ( ( ! [H] : ( ( 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] : ( ( 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,k5_numbers) ) => ! [I] : ( ( v1_relat_1(I) & v4_relat_1(I,k4_ordinal1) & v5_relat_1(I,u1_compos_1(k1_scmpds_2)) & v1_funct_1(I) & v1_partfun1(I,k4_ordinal1) ) => ( ( ! [J] : ( ( 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)),k5_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] : ( ( 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)),k5_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) ) ) ) ) ) ) ) ) ) )).
fof(t27_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => 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) = k4_ordinal1 ) ) )).
fof(t27_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => A = k2_xboole_0(k2_xboole_0(k1_tarski(k1_xboole_0),k9_bspace(k3_tarski(A))),k1_scmyciel(A)) ) )).
fof(t27_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t27_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k26_valued_1(k4_ordinal1,k1_numbers,A,1),A) ) )).
fof(t27_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v2_comseq_2(A) => k1_seq_2(k55_valued_1(k4_ordinal1,k2_numbers,A)) = k9_complex1(k3_comseq_2(A)) ) ) )).
fof(t27_seq_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(A) => ( k1_seq_2(A) = k5_numbers | ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( m2_valued_0(B,k1_numbers,A) & v9_ordinal1(B) ) => k1_seq_2(k37_valued_1(k4_ordinal1,k1_numbers,B)) = k5_xcmplx_0(k1_seq_2(A)) ) ) ) ) ) )).
fof(t27_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( 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(k4_ordinal1,k1_numbers,k3_valued_1(k4_ordinal1,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(k4_ordinal1,k1_numbers,k47_valued_1(k4_ordinal1,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(k4_ordinal1,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k10_seqfunc(A,B,D),k10_seqfunc(A,C,D)),k10_seqfunc(A,k8_seqfunc(A,B,C),D)) ) ) ) ) ) ) )).
fof(t27_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_seq_2(A) & m2_valued_0(B,k1_numbers,A) ) => v1_seq_2(B) ) ) ) )).
fof(t27_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k5_numbers) ) & ? [B] : ( v7_ordinal1(B) & ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => r1_xxreal_0(1,k6_real_1(k3_funct_2(k4_ordinal1,k1_numbers,A,k1_nat_1(C,1)),k9_nat_1(k1_numbers,A,C))) ) ) ) & v1_series_1(A) ) ) )).
fof(t27_series_3,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( 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(k3_square_1(A),k3_square_1(B)),k3_square_1(C)),k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(1,A),k7_xcmplx_0(1,B)),k7_xcmplx_0(1,C))) ) ) ) ) )).
fof(t27_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => ! [D] : ( ( v1_xreal_0(D) & v2_xxreal_0(D) ) => ~ ( ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(C,D) & r1_xxreal_0(k7_xcmplx_0(C,k2_xcmplx_0(C,A)),k7_xcmplx_0(D,k2_xcmplx_0(D,B))) ) ) ) ) ) )).
fof(t27_setfam_1,axiom,( ! [A] : ! [B] : ( B != k1_xboole_0 => k6_subset_1(A,k1_setfam_1(B)) = k3_tarski(k4_setfam_1(k1_tarski(A),B)) ) )).
fof(t27_setlim_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => r1_tarski(k1_funct_1(k4_setlim_1(B,C),A),k1_kurato_0(B,C)) ) ) )).
fof(t27_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v2_prob_1(C) => v3_prob_1(k7_setlim_2(A,C,B)) ) ) ) )).
fof(t27_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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] : ( ( v1_funct_1(F) & v1_funct_2(F,A,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,B,D) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(B,D))) ) => ( ! [H] : ( m1_subset_1(H,B) => ! [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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t27_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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] : ( v7_ordinal1(D) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t27_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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)) ) ) )).
fof(t27_sfmastr3,axiom,( ! [A] : ( ( v1_ami_2(A) & ~ v1_scmfsa_m(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( m1_scmfsa_2(D) => ~ ( A != B & r4_scmfsa7b(k3_sfmastr3(B,C,A,D),B) ) ) ) ) ) )).
fof(t27_sgraph1,axiom,( ! [A] : ( r2_sgraph1(A,k3_sgraph1(A)) & ! [B] : ( r2_sgraph1(A,B) => r1_tarski(k3_sgraph1(A),B) ) ) )).
fof(t27_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & v8_robbins1(A) & v9_sheffer1(A) & l3_sheffer1(A) ) => v11_sheffer1(A) ) )).
fof(t27_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t27_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ! [C] : ( m2_simplex0(C,A,B) => ! [D] : ( m2_simplex0(D,A,C) => m2_simplex0(D,A,B) ) ) ) )).
fof(t27_simplex1,axiom,( ! [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) ) => ! [B] : ( ( v1_matroid0(B) & v3_matroid0(B) & v2_simplex1(B,A) & m1_simplex0(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t27_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( k9_complex1(k15_sin_cos(k3_xcmplx_0(A,k7_complex1))) = 1 & ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k9_complex1(k17_sin_cos(B)),1) & r1_xxreal_0(k9_complex1(k19_sin_cos(B)),1) ) ) ) ) )).
fof(t27_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k2_xcmplx_0(k1_funct_1(k3_sin_cos2,A),k1_funct_1(k3_sin_cos2,B)) = k3_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k3_sin_cos2,k2_xcmplx_0(k7_xcmplx_0(A,2),k7_xcmplx_0(B,2)))),k1_funct_1(k3_sin_cos2,k6_xcmplx_0(k7_xcmplx_0(A,2),k7_xcmplx_0(B,2)))) & k6_xcmplx_0(k1_funct_1(k3_sin_cos2,A),k1_funct_1(k3_sin_cos2,B)) = k3_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k1_sin_cos2,k6_xcmplx_0(k7_xcmplx_0(A,2),k7_xcmplx_0(B,2)))),k1_funct_1(k1_sin_cos2,k2_xcmplx_0(k7_xcmplx_0(A,2),k7_xcmplx_0(B,2)))) ) ) ) )).
fof(t27_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k15_sin_cos(k2_xcmplx_0(A,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k7_complex1))) = k15_sin_cos(A) ) )).
fof(t27_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k19_sin_cos(k7_xcmplx_0(A,2)) = k3_square_1(k7_xcmplx_0(k2_xcmplx_0(1,k19_sin_cos(A)),2)) | k19_sin_cos(k7_xcmplx_0(A,2)) = k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(1,k19_sin_cos(A)),2))) ) ) )).
fof(t27_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,k3_xcmplx_0(2,k28_sin_cos)) & k17_sin_cos(A) = k4_xcmplx_0(1) ) => A = k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos) ) ) )).
fof(t27_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(1,k1_square_1(A)) & ~ r1_xxreal_0(1,k1_square_1(B)) & k3_xcmplx_0(A,B) = k4_xcmplx_0(1) ) ) ) )).
fof(t27_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ( k2_sin_cos2(k3_xcmplx_0(2,A)) = k7_xcmplx_0(k3_xcmplx_0(2,k6_sin_cos2(A)),k6_xcmplx_0(1,k1_square_1(k6_sin_cos2(A)))) & k2_sin_cos2(k3_xcmplx_0(3,A)) = k3_xcmplx_0(k2_sin_cos2(A),k6_xcmplx_0(k3_xcmplx_0(4,k1_square_1(k4_sin_cos2(A))),1)) & k2_sin_cos2(k3_xcmplx_0(3,A)) = k6_xcmplx_0(k3_xcmplx_0(3,k2_sin_cos2(A)),k3_xcmplx_0(k3_xcmplx_0(2,k2_sin_cos2(A)),k6_xcmplx_0(1,k4_sin_cos2(k3_xcmplx_0(2,A))))) & k4_sin_cos2(k3_xcmplx_0(2,A)) = k2_xcmplx_0(1,k3_xcmplx_0(2,k1_square_1(k2_sin_cos2(A)))) & k4_sin_cos2(k3_xcmplx_0(2,A)) = k2_xcmplx_0(k1_square_1(k4_sin_cos2(A)),k1_square_1(k2_sin_cos2(A))) & k4_sin_cos2(k3_xcmplx_0(2,A)) = k7_xcmplx_0(k2_xcmplx_0(1,k1_square_1(k6_sin_cos2(A))),k6_xcmplx_0(1,k1_square_1(k6_sin_cos2(A)))) & k4_sin_cos2(k3_xcmplx_0(3,A)) = k3_xcmplx_0(k4_sin_cos2(A),k2_xcmplx_0(k3_xcmplx_0(4,k1_square_1(k2_sin_cos2(A))),1)) & k6_sin_cos2(k3_xcmplx_0(3,A)) = k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(3,k6_sin_cos2(A)),k1_newton(k6_sin_cos2(A),3)),k2_xcmplx_0(1,k3_xcmplx_0(3,k1_square_1(k6_sin_cos2(A))))) ) ) )).
fof(t27_sin_cos9,axiom,( k3_relat_1(k2_partfun1(k1_numbers,k1_numbers,k1_sin_cos9,k1_rcomp_1(k4_xcmplx_0(1),1)),k2_partfun1(k1_numbers,k1_numbers,k26_sin_cos,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)),k7_xcmplx_0(k28_sin_cos,4)))) = k1_partfun2(k1_numbers,k1_rcomp_1(k4_xcmplx_0(1),1)) )).
fof(t27_sincos10,axiom,( k2_relset_1(k1_numbers,k3_sincos10) = k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers) )).
fof(t27_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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(k1_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,k1_nat_1(A,1))) ) => k18_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),B,k1_nat_1(A,1))) = k18_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),B,k1_nat_1(A,2))) ) ) ) )).
fof(t27_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t27_sprect_3,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t27_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t27_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(k3_square_1(B),k3_square_1(A)) ) ) ) )).
fof(t27_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k13_stacks_1(A,k7_stacks_1(A,B,C)) = k13_stacks_1(A,B) ) ) ) )).
fof(t27_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( A != k5_numbers => k3_stirl2_1(k5_numbers,A) = k5_numbers ) ) )).
fof(t27_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_sublemma(B,A) & m1_subset_1(B,k2_zfmisc_1(k16_substut1(A),k3_qc_lang1(A))) ) => ! [C] : ( m1_substut1(C,A,B) => ( v3_substut1(B,A) => v7_substut1(k9_sublemma(A,B,C),A) ) ) ) ) )).
fof(t27_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( ! [D] : ( m1_subset_1(D,B) => r2_hidden(D,C) ) => r1_tarski(B,C) ) ) ) )).
fof(t27_substlat,axiom,( ! [A] : ! [B] : k6_lattices(k5_substlat(A,B)) = k1_tarski(k1_xboole_0) )).
fof(t27_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t27_supinf_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => ! [C] : ( ( 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(k6_numbers,A,B,C),k1_numbers) ) ) ) ) ) )).
fof(t27_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t27_sysrel,axiom,( ! [A] : ! [B] : ( 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))) ) ) ) )).
fof(t27_taxonom1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( v1_xreal_0(D) => ( ( C = k2_relset_1(k1_numbers,B) & r1_xxreal_0(k1_xxreal_2(C),D) ) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t27_taylor_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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,k1_nat_1(A,1),k2_rcomp_1(D,E)) & ! [F] : ( v1_xreal_0(F) => ~ ( r2_hidden(F,k2_rcomp_1(D,E)) & k1_funct_1(B,E) = k2_xcmplx_0(k9_nat_1(k1_numbers,k3_series_1(k6_taylor_1(B,C,D,E)),A),k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(B,k2_rcomp_1(D,E)),k1_nat_1(A,1)),F),k1_newton(k6_xcmplx_0(E,D),k1_nat_1(A,1))),k2_newton(k1_nat_1(A,1)))) ) ) ) ) ) ) ) ) ) )).
fof(t27_taylor_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ r1_xxreal_0(A,k5_numbers) => k3_funct_2(k4_ordinal1,k1_numbers,k3_series_1(k1_taylor_2(k18_sin_cos,k2_rcomp_1(k4_xcmplx_0(A),A),B)),k2_nat_1(2,C)) = k3_funct_2(k4_ordinal1,k1_numbers,k3_series_1(k21_sin_cos(B)),C) ) ) ) ) )).
fof(t27_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t27_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(t27_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v4_tdlat_3(A) <=> ! [B] : ( 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) ) ) ) ) )).
fof(t27_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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) ) ) ) ) )).
fof(t27_tex_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t27_tex_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_tex_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t27_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t27_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( r2_hidden(C,B) & v3_tex_4(B,A) ) => B = k2_tex_4(A,C) ) ) ) ) )).
fof(t27_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( ~ r1_tsep_1(C,D) => ( ( m1_pre_topc(C,B) => m1_pre_topc(k2_tsep_1(A,C,D),k2_tsep_1(A,B,D)) ) & ( m1_pre_topc(D,B) => m1_pre_topc(k2_tsep_1(A,C,D),k2_tsep_1(A,C,B)) ) ) ) ) ) ) ) )).
fof(t27_toler_1,axiom,( ! [A] : ! [B] : ( ( 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] : ! [D] : ( r2_hidden(D,k9_relat_1(B,C)) <=> r2_hidden(k4_tarski(C,D),B) ) ) )).
fof(t27_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r1_borsuk_6(A,B,C) & r1_borsuk_6(A,D,C) ) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t27_topalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_borsuk_2(F,A,D,E) => ! [G] : ( m1_borsuk_2(G,A,D,E) => ! [H] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t27_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_topalg_1(k2_borsuk_1(A,B),k4_borsuk_1(A,B,C,D)))) => ! [F] : ( 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))) ) ) ) ) ) ) ) )).
fof(t27_topalg_5,axiom,( ! [A] : ( ( v1_toprealb(A) & m1_pre_topc(A,k15_euclid(2)) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_group_6(k2_gr_cy_1,k5_topalg_1(A,B)) ) ) )).
fof(t27_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t27_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t27_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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)) ) ) ) )).
fof(t27_topgen_2,axiom,( ! [A] : ! [B] : ! [C] : ( 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 ) ) )).
fof(t27_topgen_4,axiom,( ! [A] : ! [B] : r1_tarski(k3_tarski(k2_setfam_1(A,B)),k2_xboole_0(k3_tarski(A),k3_tarski(B))) )).
fof(t27_topgen_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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,k5_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,k5_numbers))),k1_zfmisc_1(u1_struct_0(k3_topgen_5))) ) ) ) )).
fof(t27_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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) ) ) ) ) ) )).
fof(t27_topreal1,axiom,( ? [A] : ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ? [B] : ( ~ 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(k5_numbers,k5_numbers),k19_euclid(1,1)) ) ) )).
fof(t27_topreal4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( v2_topreal4(C,k15_euclid(2)) & r2_hidden(A,C) & B = a_2_1_topreal4(A,C) ) => r1_tarski(C,B) ) ) ) ) )).
fof(t27_topreal8,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t27_topreal9,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k4_topreal9(A,B,B) = k1_tarski(B) ) ) )).
fof(t27_topreala,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t27_toprealc,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_algstr_0(A,k1_algstr_0(A,B,C),C) = B ) ) ) )).
fof(t27_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t27_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) )).
fof(t27_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( m1_pre_topc(C,A) => ( v1_tops_2(B,A) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C)))) => ( D = B => v1_tops_2(D,C) ) ) ) ) ) ) )).
fof(t27_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_tops_1(B,A) <=> ? [C] : ( 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) ) ) ) ) )).
fof(t27_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t27_trees_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,A) => r2_hidden(k9_finseq_1(A),k2_trees_1(B)) ) ) ) )).
fof(t27_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t27_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t27_trees_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_trees_3(E,k2_zfmisc_1(A,B)) ) => ! [F] : ( ( ~ v1_xboole_0(F) & m1_trees_3(F,A) ) => ! [G] : ( m2_finseq_1(G,E) => ! [H] : ( m2_finseq_1(H,F) => ( ( k4_finseq_1(H) = k4_finseq_1(G) & ! [I] : ( v7_ordinal1(I) => ( r2_hidden(I,k4_finseq_1(G)) => ! [J] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t27_trees_9,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v3_trees_3(B) ) => k12_trees_9(B,A) = k3_tarski(a_2_2_trees_9(A,B)) ) )).
fof(t27_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t27_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(D))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t27_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(t27_turing_1,axiom,( ! [A] : ( 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] : ( m2_funct_2(B,k4_numbers,u1_turing_1(k14_turing_1),k9_funct_2(k4_numbers,u1_turing_1(k14_turing_1))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( A = k4_domain_1(k4_ordinal1,k4_ordinal1,k9_funct_2(k4_numbers,u1_turing_1(k14_turing_1)),k5_numbers,C,B) & r2_turing_1(k3_finseq_4(k4_ordinal1,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)) = k1_nat_1(1,C) & r2_turing_1(k2_finseq_4(k4_ordinal1,k1_nat_1(1,C),k1_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))) ) ) ) ) ) ) ) )).
fof(t27_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ 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))) ) ) )).
fof(t27_unialg_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t27_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => k1_card_1(k2_uniroots(A)) = A ) )).
fof(t27_uproots,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k13_polynom3(A,k2_polynom5(A,D,B),k2_polynom5(A,D,C)),k2_polynom5(A,D,k1_nat_1(B,C))) ) ) ) ) )).
fof(t27_urysohn2,axiom,( r2_hidden(k5_numbers,k2_urysohn1) & r2_hidden(1,k2_urysohn1) )).
fof(t27_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m1_valuat_1(E,A,B) => ( ~ r2_hidden(C,k24_qc_lang1(A,D)) => ! [F] : ( m2_funct_2(F,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [G] : ( m2_funct_2(G,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ( ! [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t27_valued_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( v7_ordinal1(E) => ( r1_tarski(k2_relset_1(A,C),k1_relset_1(A,D)) => r2_funct_2(k4_ordinal1,B,k1_valued_0(B,k8_funct_2(k4_ordinal1,B,A,C,D),E),k8_funct_2(k4_ordinal1,B,A,k1_valued_0(A,C,E),D)) ) ) ) ) ) ) )).
fof(t27_valued_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) ) => r2_tarski(k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,k61_valued_1(B,A))) ) ) )).
fof(t27_valued_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t27_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t27_vectsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ( v4_vectsp_1(A) => k5_struct_0(A) = k1_group_1(A) ) ) )).
fof(t27_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( r1_tarski(u1_struct_0(C),u1_struct_0(D)) => m1_vectsp_4(C,A,D) ) ) ) ) ) )).
fof(t27_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t27_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t27_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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)) ) ) )).
fof(t27_vfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,u1_struct_0(C)))) ) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t27_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [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),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))) ) ) ) ) ) )).
fof(t27_waybel10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t27_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( r1_waybel_0(A,k4_waybel11(A,B),C) <=> r2_hidden(B,C) ) ) ) )).
fof(t27_waybel13,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t27_waybel14,axiom,( ! [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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(k5_waybel11(A)))) => ( C = B => ( v6_waybel_6(C,k1_yellow_1(k5_waybel11(A))) <=> ( v2_waybel_0(B,A) & v13_waybel_0(B,A) ) ) ) ) ) ) )).
fof(t27_waybel15,axiom,( ! [A] : ( ( 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] : r5_waybel_1(A,k2_yellow_1(B)) ) ) )).
fof(t27_waybel16,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_orders_2(A,B,C) & ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t27_waybel17,axiom,( ! [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] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t27_waybel19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t27_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t27_waybel21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( r1_tarski(k2_relset_1(u1_struct_0(A),u1_waybel_0(A,B)),C) => r1_waybel_0(A,B,C) ) ) ) )).
fof(t27_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v3_waybel23(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => k2_yellow_0(k5_yellow_0(A,B),C) = k2_yellow_0(A,C) ) ) ) )).
fof(t27_waybel24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [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) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_yellow_1(u1_struct_0(A),B)))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => k7_relat_1(k1_yellow_0(k5_yellow_1(u1_struct_0(A),B),C),D) = a_4_3_waybel24(A,B,C,D) ) ) ) ) )).
fof(t27_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t27_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & v6_pre_topc(C) & v1_waybel25(C) & l1_pre_topc(C) ) => ? [D] : ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t27_waybel27,axiom,( ! [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] : ( ( 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] : ( 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(k5_yellow_1(u1_struct_0(A),B),C) ) ) ) )).
fof(t27_waybel28,axiom,( ! [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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k4_waybel28(A)) => v3_waybel11(B,A) ) ) ) )).
fof(t27_waybel29,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & l1_pre_topc(A) ) => ( v3_waybel_3(k1_yellow_1(u1_pre_topc(A))) <=> ( v3_pre_topc(a_1_0_waybel29(A),k2_borsuk_1(k1_waybel29(k1_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(k1_yellow_1(u1_pre_topc(A))),A)))) ) ) ) )).
fof(t27_waybel30,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t27_waybel31,axiom,( ! [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] : ( ( v6_waybel23(B,A) & m1_waybel23(B,A) ) => ( k1_card_1(B) = k1_waybel31(A) => k1_waybel31(A) = k1_waybel31(k1_yellow_1(k7_waybel_0(k5_yellow_0(A,B)))) ) ) ) )).
fof(t27_waybel33,axiom,( ! [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) & v1_waybel33(A) & l1_waybel_9(A) ) => ( v1_compts_1(A) & v7_pre_topc(A) ) ) )).
fof(t27_waybel34,axiom,( ! [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] : ( ( 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] : ( ( 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] : ( ( v4_waybel11(D) & m1_yellow_9(D,B) ) => ! [E] : ( ( v4_waybel11(E) & m1_yellow_9(E,A) ) => ! [F] : ( ( v4_waybel11(F) & m1_yellow_9(F,k1_yellow_2(B,A,k1_waybel34(A,B,C))) ) => ! [G] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t27_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t27_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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)) ) ) ) ) ) ) )).
fof(t27_waybel_2,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v10_waybel_0(B,A) => v10_waybel_0(k3_waybel_2(A,C,B),A) ) ) ) ) )).
fof(t27_waybel_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( m1_subset_1(C,u1_struct_0(k4_yellow_1(A,B))) <=> ( k9_xtuple_0(C) = A & ! [D] : ( m1_subset_1(D,A) => m1_subset_1(k1_funct_1(C,D),u1_struct_0(k3_waybel_3(A,B,D))) ) ) ) ) ) ) )).
fof(t27_waybel_4,axiom,( ! [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] : ( ( 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(k1_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))) ) ) )).
fof(t27_waybel_5,axiom,( ! [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] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) ) => ! [D] : ( m2_pboole(D,B,C,k7_funcop_1(B,u1_struct_0(A))) => ( ! [E] : ( 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) ) ) ) ) ) )).
fof(t27_waybel_6,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v5_waybel_6(B,A) <=> v2_waybel_6(B,A) ) ) ) )).
fof(t27_waybel_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_waybel_0(B,k2_yellow_1(u1_struct_0(A))) & v13_waybel_0(B,k2_yellow_1(u1_struct_0(A))) & v3_waybel_7(B,k2_yellow_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(u1_struct_0(A))))) ) => ! [C] : ( r1_waybel_7(A,B,C) <=> r2_waybel_7(A,B,C) ) ) ) )).
fof(t27_waybel_8,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k2_yellow_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_yellow_1(A))) => ( r1_waybel_3(k2_yellow_1(A),B,C) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) => ~ ( r1_tarski(C,k5_setfam_1(A,D)) & ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(D)) ) => ~ r1_tarski(B,k3_tarski(E)) ) ) ) ) ) ) )).
fof(t27_waybel_9,axiom,( ! [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) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ! [C] : ( 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) ) ) ) )).
fof(t27_weddwitt,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(t27_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(t27_wellord1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( ( v2_wellord1(C) & r2_hidden(B,k1_wellord1(C,A)) ) => k1_wellord1(k2_wellord1(C,k1_wellord1(C,A)),B) = k1_wellord1(C,B) ) ) )).
fof(t27_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ? [C] : ( v1_int_1(C) & ? [D] : ( v1_int_1(D) & k3_int_2(A,B) = k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D)) ) ) ) ) )).
fof(t27_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( r1_tarski(A,B) & r1_tarski(C,D) ) => r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,D)) ) )).
fof(t27_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k6_xboolean(A,k7_xboolean(A,B)) = k6_xboolean(A,k6_xboolean(A,B)) ) ) )).
fof(t27_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => A = k2_xcmplx_0(k6_xcmplx_0(A,B),B) ) ) )).
fof(t27_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) & k2_xcmplx_0(A,B) = k5_numbers ) => A = k5_numbers ) ) ) )).
fof(t27_xtuple_0,axiom,( ! [A] : ! [B] : k10_xtuple_0(k2_xboole_0(A,B)) = k2_xboole_0(k10_xtuple_0(A),k10_xtuple_0(B)) )).
fof(t27_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t27_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( r1_xxreal_0(A,B) => k2_xxreal_1(B,A) = k1_xboole_0 ) ) ) )).
fof(t27_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( ~ r1_xxreal_0(B,A) => k2_xxreal_2(k3_xxreal_1(A,B)) = A ) ) ) )).
fof(t27_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t27_yellow10,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t27_yellow12,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t27_yellow13,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [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)))) ) => m2_yellow13(B,A) ) ) )).
fof(t27_yellow14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t27_yellow15,axiom,( ! [A] : ( ( v2_pre_topc(A) & v6_pre_topc(A) & l1_pre_topc(A) ) => ( ~ v8_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)))) ) => ~ v1_finset_1(B) ) ) ) )).
fof(t27_yellow16,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & v4_waybel_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t27_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t27_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(B,A) <=> ! [C] : ( ( ~ v1_xboole_0(C) & v1_subset_1(C,u1_struct_0(k2_yellow_1(k2_struct_0(A)))) & v2_waybel_0(C,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(C,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))))) ) => ( r2_hidden(B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_waybel_7(A,C,D) => r2_hidden(D,B) ) ) ) ) ) ) ) )).
fof(t27_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v3_altcat_2(B,A) & m1_altcat_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( k1_altcat_1(B,C,D) != k1_xboole_0 => ! [E] : ( m1_subset_1(E,k1_altcat_1(B,C,D)) => k6_functor0(B,A,k10_functor0(A,B),C,D,E) = E ) ) ) ) ) ) )).
fof(t27_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [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] : ( r2_yellow_0(A,C) => k2_yellow_0(A,C) = k2_yellow_0(B,C) ) ) ) ) )).
fof(t27_yellow_1,axiom,( ! [A] : ( l1_orders_2(A) => k5_yellow_1(k1_xboole_0,A) = g1_orders_2(k1_tarski(k1_xboole_0),k6_partfun1(k1_tarski(k1_xboole_0))) ) )).
fof(t27_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_yellow_0(A,B) ) => ! [B] : ( r1_yellow_0(A,B) & k1_yellow_0(A,B) = k1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) ) ) ) )).
fof(t27_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t27_yellow_4,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t27_yellow_5,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t27_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m3_yellow_6(C,u1_struct_0(B),A) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k4_yellow_1(u1_struct_0(B),C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k8_yellow_6(A,B,C))) => ( F = k7_yellow_3(B,k4_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)) ) ) ) ) ) ) ) )).
fof(t27_yellow_7,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( 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))) ) ) ) )).
fof(t27_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v9_pre_topc(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(B,k1_tops_1(A,C)) & ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(t27_yellow_9,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(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)))) ) => ( 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)))) ) ) ) )).
fof(t27_zf_fund1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) )).
fof(t27_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( k1_funct_1(A,1) = 3 => v5_zf_lang(A) ) ) )).
fof(t27_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( 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)) ) ) ) )).
fof(t27_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r2_hidden(k4_tarski(A,C),k2_zfmisc_1(k1_tarski(B),k1_tarski(D))) <=> ( A = B & C = D ) ) )).
fof(t27_zfrefle1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( v3_ordinal1(B) & m1_subset_1(B,A) ) => ~ r2_ordinal2(k2_ordinal1(A),B) ) ) )).
fof(t27_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => k4_struct_0(B) = k4_struct_0(C) ) ) ) )).
fof(t27_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( m1_zmodul02(C,A) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( m2_zmodul02(B,A,D) & m2_zmodul02(C,A,D) ) => m2_zmodul02(k22_zmodul02(A,B,C),A,D) ) ) ) ) ) )).
fof(t27_zmodul03,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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) & v1_zmodul03(B) & l1_zmodul01(B) ) => k13_zmodul02(A,B,k4_struct_0(B)) = k4_struct_0(k12_zmodul02(A,B)) ) ) )).
fof(t280_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ~ r1_xxreal_0(A,D) => r1_xboole_0(k3_xxreal_1(C,D),k1_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t281_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k6_subset_1(k1_xxreal_1(k2_xxreal_0,B),k1_xxreal_1(k2_xxreal_0,A)) = k3_xxreal_1(A,B) ) ) )).
fof(t282_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k6_subset_1(k2_xxreal_1(k2_xxreal_0,B),k1_xxreal_1(k2_xxreal_0,A)) = k4_xxreal_1(A,B) ) ) )).
fof(t283_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k6_subset_1(k1_xxreal_1(k2_xxreal_0,B),k1_xxreal_1(k2_xxreal_0,A)) = k3_xxreal_1(A,B) ) ) )).
fof(t284_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) )).
fof(t285_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) )).
fof(t286_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) )).
fof(t287_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) )).
fof(t288_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) )).
fof(t289_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) )).
fof(t28_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l2_abcmiz_0(A) ) => ! [B] : ( 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) ) ) )).
fof(t28_abcmiz_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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) ) ) )).
fof(t28_abcmiz_a,axiom,( k20_abcmiz_1 = k2_zfmisc_1(k1_enumset1(k6_abcmiz_1,k7_abcmiz_1,k8_abcmiz_1),k2_zfmisc_1(k4_abcmiz_1,k4_ordinal1)) )).
fof(t28_absvalue,axiom,( ! [A] : ( v7_ordinal1(A) => A = k9_complex1(A) ) )).
fof(t28_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( B != C => r2_aff_1(A,B,C,k2_aff_1(A,B,C)) ) ) ) ) )).
fof(t28_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_4(D,A) & v1_aff_1(C,A) & r2_hidden(B,D) & r1_tarski(C,D) ) => r1_tarski(k2_aff_4(A,B,C),D) ) ) ) ) ) )).
fof(t28_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ( ( k1_ordinal4(A,C) = k1_ordinal4(B,C) | k1_ordinal4(C,A) = k1_ordinal4(C,B) ) => A = B ) ) ) ) )).
fof(t28_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k13_afproj(A))) => ! [E] : ( m1_subset_1(E,u2_incsp_1(k13_afproj(A))) => ( ( D = k5_afproj(A,C) & k4_tarski(B,1) = E & v1_aff_1(C,A) & v1_aff_1(B,A) ) => ( r1_incsp_1(k13_afproj(A),D,E) <=> r1_aff_4(A,C,B) ) ) ) ) ) ) ) )).
fof(t28_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_afvect0(A,C,B) = B <=> ( B = C | r1_afvect0(A,B,C) ) ) ) ) ) )).
fof(t28_algspec1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(A,B) => ! [C] : ( m1_algspec1(C,A) => ? [D] : ( m1_algspec1(D,B) & r1_tarski(C,D) ) ) ) ) ) )).
fof(t28_algstr_4,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,k5_numbers) => r1_tarski(k2_zfmisc_1(k11_algstr_4(A,B),k1_tarski(B)),k12_algstr_4(A)) ) ) )).
fof(t28_altcat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_2(B,A) & m1_altcat_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( C = E & D = F ) => k1_altcat_1(A,C,D) = k1_altcat_1(B,E,F) ) ) ) ) ) ) ) )).
fof(t28_altcat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v7_altcat_3(B,A) & v7_altcat_3(C,A) ) => r2_altcat_3(A,B,C) ) ) ) ) )).
fof(t28_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t28_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k4_ordinal1,C)) ) ) ) )).
fof(t28_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_analmetr(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k2_analmetr(A,B,C))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k2_analmetr(A,B,C))) => ! [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) ) ) ) ) ) ) ) ) ) ) )).
fof(t28_analoaf,axiom,( ! [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) ) => ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( k3_rlvect_1(A,k1_rlvect_1(A,B,D),k1_rlvect_1(A,C,E)) = k4_struct_0(A) => ( D = k5_numbers & E = k5_numbers ) ) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & 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)) ) ) ) )).
fof(t28_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( r1_analmetr(A,F,G) => ( r1_analoaf(A,B,D,C,E) <=> ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & ? [I] : ( m1_subset_1(I,u1_struct_0(A)) & H != I & r2_analort(A,F,G,H,I,B,D) & r2_analort(A,F,G,H,I,C,E) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t28_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => ( ? [B] : ( m1_subset_1(B,u1_struct_0(k5_anproj_1(A))) & ? [C] : ( m1_subset_1(C,u1_struct_0(k5_anproj_1(A))) & B != C & ! [D] : ( m1_subset_1(D,u1_struct_0(k5_anproj_1(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_anproj_1(A))) => ? [F] : ( 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] : ( m1_subset_1(B,u1_struct_0(k5_anproj_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_anproj_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_anproj_1(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_anproj_1(A))) => ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t28_aofa_000,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t28_aofa_a00,axiom,( k2_finseq_1(10) = k8_enumset1(1,2,3,4,5,6,7,8,9,10) )).
fof(t28_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),F)) => k15_aofa_a00(A,B,C,D,F,G,k1_msafree(u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D),k1_aofa_a01(A,B,C),E)) = k3_funct_2(k1_funct_1(u3_msualg_1(A,C),F),k1_funct_1(u3_msualg_1(A,D),F),k2_msafree4(u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D),E,F),G) ) ) ) ) ) ) ) ) )).
fof(t28_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [E] : ( ( v1_aofa_i00(E,A,B,D) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),D) ) => ! [F] : ( v1_int_1(F) => ! [G] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t28_armstrng,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t28_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( r1_arytm_2(C,B) => ( k1_arytm_1(B,C) = k11_arytm_3 | A = k11_arytm_3 | k2_arytm_1(k8_arytm_2(A,C),k8_arytm_2(A,B)) = k4_tarski(k11_arytm_3,k8_arytm_2(A,k1_arytm_1(B,C))) ) ) ) ) ) )).
fof(t28_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ! [C] : ( ( v3_ordinal1(C) & v7_ordinal1(C) ) => ( C != k1_xboole_0 => k4_arytm_3(k9_ordinal3(A,C),k9_ordinal3(B,C)) = k4_arytm_3(A,B) ) ) ) ) )).
fof(t28_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_hidden(A,k8_asympt_0(A)) ) )).
fof(t28_asympt_1,axiom,( ? [A] : ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v4_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & ? [B] : ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v4_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & r2_funct_2(k4_ordinal1,k1_numbers,A,k1_asympt_1(2,1,k5_numbers)) & r2_funct_2(k4_ordinal1,k1_numbers,B,k1_asympt_1(2,1,1)) & k6_asympt_0(A) = k6_asympt_0(B) ) ) )).
fof(t28_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_autalg_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_autalg_1(A,B))) => ! [E] : ( m1_autalg_1(E,u1_struct_0(A),u3_msualg_1(A,B),k5_autalg_1(A,B)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t28_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t28_bagorder,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t28_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( r2_hidden(B,k5_bcialg_1(A)) <=> ! [C] : ( 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) ) ) ) ) )).
fof(t28_bcialg_2,axiom,( ! [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] : ( 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)) ) ) ) )).
fof(t28_bcialg_3,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t28_bcialg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_bcialg_4(A) ) => ! [B] : ( 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 ) ) )).
fof(t28_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( 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,k1_nat_1(A,1),A,k1_nat_1(A,1)) ) ) ) ) ) ) ) ) )).
fof(t28_bcialg_6,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t28_bciideal,axiom,( ! [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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) )).
fof(t28_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_xxreal_0(k5_numbers,k3_bhsp_1(A,B)) ) ) )).
fof(t28_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)))) & k1_seq_2(k2_bhsp_2(A,k4_normsp_1(A,k3_normsp_1(A,D,E),k5_algstr_0(A,B,C)))) = k5_numbers ) ) ) ) ) ) ) )).
fof(t28_bhsp_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( ( ! [D] : ( v7_ordinal1(D) => ( k1_normsp_1(B,C,D) != k4_struct_0(B) & k9_nat_1(k1_numbers,A,D) = k7_xcmplx_0(k3_bhsp_1(B,k1_normsp_1(B,C,k1_nat_1(D,1))),k3_bhsp_1(B,k1_normsp_1(B,C,D))) ) ) & v2_comseq_2(A) ) => ( r1_xxreal_0(1,k1_seq_2(A)) | v2_bhsp_4(C,B) ) ) ) ) ) )).
fof(t28_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ! [H] : ( ( 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))) ) ) ) ) ) ) ) ) )).
fof(t28_binari_3,axiom,( ! [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(k4_ordinal1,1)) ) )).
fof(t28_binari_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( k5_int_1(B,k5_series_1(2,A)) = k5_int_1(C,k5_series_1(2,A)) => ( ( ~ ( r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k5_numbers,C) ) & ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(k5_numbers,C) ) ) | k2_binari_4(A,B) = k2_binari_4(A,C) ) ) ) ) ) )).
fof(t28_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t28_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) ) => ! [C] : ( 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)) ) ) ) )).
fof(t28_borsuk_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k5_topmetr)) & ? [C] : ( m1_subset_1(C,u1_struct_0(k5_topmetr)) & r1_xxreal_0(B,C) & A = k1_rcomp_1(B,C) ) ) ) )).
fof(t28_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t28_borsuk_6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))) => ! [B] : ( 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(k5_numbers,k7_xcmplx_0(1,2)),k1_rcomp_1(k5_numbers,1)) & B = k8_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(k7_xcmplx_0(1,2),1),k1_rcomp_1(k5_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)) ) ) ) )).
fof(t28_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) ) => ( ( k9_xtuple_0(G) = k1_enumset1(A,B,C) & k1_funct_1(G,A) = D & k1_funct_1(G,B) = E & k1_funct_1(G,C) = F ) => G = k1_borsuk_7(A,B,C,D,E,F) ) ) )).
fof(t28_bspace,axiom,( ! [A] : ! [B] : ( 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 ) )).
fof(t28_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t28_bvfunc14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ( 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)) ) ) )).
fof(t28_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t28_bvfunc26,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(t28_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t28_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(E,A) => ( r3_bvfunc_2(A,D,B,E) => r1_bvfunc_1(A,k6_bvfunc_2(A,k6_bvfunc_1(A,D,C),B,E),k6_bvfunc_1(A,D,k6_bvfunc_2(A,C,B,E))) ) ) ) ) ) ) )).
fof(t28_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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)))) ) ) ) ) ) )).
fof(t28_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t28_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t28_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t28_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t28_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k11_c0sp1(A))) => ( B = k4_struct_0(k11_c0sp1(A)) => k5_numbers = k2_normsp_0(k11_c0sp1(A),B) ) ) ) )).
fof(t28_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => v1_rlsub_1(k6_c0sp2(A),k10_funcsdom(u1_struct_0(A))) ) )).
fof(t28_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m2_funct_2(F,k3_qc_lang1(A),E,k2_valuat_1(A,E)) => ! [G] : ( m1_subset_1(G,E) => ( ~ r2_hidden(D,k24_qc_lang1(A,k11_cqc_lang(A,C,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,D,G)),k12_sublemma(A,E,C,G)),k24_qc_lang1(A,B)),k2_partfun1(k3_qc_lang1(A),E,k1_sublemma(A,E,F,k12_sublemma(A,E,C,G)),k24_qc_lang1(A,B))) ) ) ) ) ) ) ) ) )).
fof(t28_calcul_2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => ( ( r1_xxreal_0(1,k3_finseq_1(C)) & r4_calcul_1(A,k8_finseq_1(k3_cqc_lang(A),B,C)) ) => r4_calcul_1(A,k8_finseq_1(k3_cqc_lang(A),B,k12_finseq_1(k3_cqc_lang(A),k5_calcul_2(A,k4_finseq_5(k3_cqc_lang(A),C))))) ) ) ) ) )).
fof(t28_card_1,axiom,( ! [A] : ! [B] : ( k1_card_1(A) = k1_card_1(k1_tarski(B)) <=> ? [C] : A = k1_tarski(C) ) )).
fof(t28_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ! [C] : ( 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)) ) ) ) )).
fof(t28_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) ) => ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => k1_card_1(k1_funct_1(A,B)) = k1_funct_1(A,B) ) ) )).
fof(t28_card_5,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ( r2_hidden(k1_card_5(A),A) => v2_card_1(A) ) ) )).
fof(t28_card_fil,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ( ( r3_card_fil & v2_card_1(A) ) => v5_card_fil(A) ) ) )).
fof(t28_card_fin,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => r1_tarski(k2_card_fin(k5_relat_1(C,B),D,A),k2_card_fin(C,D,A)) ) ) )).
fof(t28_card_lar,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) & ~ v4_card_3(A) ) => ( v4_card_lar(A) => v2_card_1(A) ) ) )).
fof(t28_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,B,C) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t28_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,k6_cat_2(A,C),B) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => m2_cat_1(k1_funct_1(k1_funct_5(D),k4_cat_1(A,E)),C,B) ) ) ) ) ) )).
fof(t28_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t28_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t28_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t28_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(k2_nat_1(2,k1_nat_1(A,1)),B) => k5_card_1(k2_catalan2(B,k1_nat_1(A,1))) = k6_xcmplx_0(k4_newton(k1_nat_1(A,1),B),k4_newton(A,B)) ) ) ) )).
fof(t28_catalg_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( 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)))) ) ) ) )).
fof(t28_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( v3_rlvect_1(A) & v4_rlvect_1(A) & v13_algstr_0(A) ) => k5_algstr_0(k4_cayldick(A),k5_cayldick(A,B,D),k5_cayldick(A,C,E)) = k5_cayldick(A,k5_algstr_0(A,B,C),k5_algstr_0(A,D,E)) ) ) ) ) ) ) )).
fof(t28_cc0sp1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(t28_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_cc0sp2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_cc0sp2(A))) => r1_xxreal_0(k2_normsp_0(k5_cc0sp2(A),k3_rlvect_1(k5_cc0sp2(A),B,C)),k2_xcmplx_0(k2_normsp_0(k5_cc0sp2(A),B),k2_normsp_0(k5_cc0sp2(A),C))) ) ) ) )).
fof(t28_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v3_funct_1(A) => ! [B] : ( v7_ordinal1(B) => k3_comseq_2(A) = k9_nat_1(k2_numbers,A,B) ) ) ) )).
fof(t28_cfdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [C] : ( ( 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] : ( v1_xcmplx_0(D) => ( r2_hidden(D,C) => k7_partfun1(k2_numbers,k3_cfdiff_1(k2_valued_1(k2_numbers,k2_numbers,k2_numbers,A,B),C),D) = k2_xcmplx_0(k2_cfdiff_1(A,D),k2_cfdiff_1(B,D)) ) ) ) ) ) ) ) )).
fof(t28_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k5_struct_0(k7_cfuncdom(A)) = k5_cfuncdom(A) ) )).
fof(t28_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t28_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ! [B] : ( v2_cgames_1(B) => ~ ( r2_hidden(B,k10_cgames_1(A)) & B != A & ~ r2_hidden(k9_cgames_1(B),k9_cgames_1(A)) ) ) ) )).
fof(t28_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( 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)) = k1_nat_1(k15_glib_001(A,B),k15_glib_001(A,C)) ) ) ) ) )).
fof(t28_circcmb3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_circcmb3(B,A) => ! [C] : ( m1_circcmb3(C,A) => ! [D] : ( m2_circcmb3(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t28_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u4_struct_0(k2_circcomb(A,B))) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t28_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t28_classes1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r1_tarski(B,k1_classes1(A)) & r1_tarski(C,k1_classes1(A)) ) => r1_tarski(k2_zfmisc_1(B,C),k1_classes1(A)) ) )).
fof(t28_classes2,axiom,( ! [A] : r1_tarski(k4_classes1(k1_card_1(k1_classes1(A))),k1_classes1(A)) )).
fof(t28_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( 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) ) ) ) )).
fof(t28_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,k5_normsp_0(A,B),D)) & r1_xxreal_0(k9_nat_1(k1_numbers,k5_normsp_0(A,B),D),k9_nat_1(k1_numbers,k5_normsp_0(A,C),D)) ) ) & v2_clopban3(C,A) ) => ( v2_clopban3(B,A) & r1_xxreal_0(k4_series_1(k5_normsp_0(A,B)),k4_series_1(k5_normsp_0(A,C))) ) ) ) ) ) )).
fof(t28_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => r1_xxreal_0(1,k4_series_1(k4_sin_cos(k2_normsp_0(A,B)))) ) ) )).
fof(t28_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,C,C) => ( ( r1_pboole(A,B,C) & r6_pboole(A,k16_pralg_1(A,D,B),B) ) <=> r1_pboole(A,B,k5_closure1(A,C,D)) ) ) ) ) )).
fof(t28_closure2,axiom,( ! [A] : ! [B] : ( ( 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)))) ) ) )).
fof(t28_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_clvect_1(B,A) => ! [C] : ( r1_struct_0(B,C) => r1_struct_0(A,C) ) ) ) )).
fof(t28_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)))) & k1_seq_2(k2_clvect_2(A,k4_normsp_1(A,k3_normsp_1(A,D,E),k5_algstr_0(A,B,C)))) = k5_numbers ) ) ) ) ) ) ) )).
fof(t28_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [D] : ( v7_ordinal1(D) => ( k1_normsp_0(A,B,D) != k4_struct_0(A) & k9_nat_1(k1_numbers,C,D) = k7_xcmplx_0(k13_csspace(A,k1_normsp_0(A,B,k1_nat_1(D,1))),k13_csspace(A,k1_normsp_0(A,B,D))) ) ) & v2_comseq_2(C) ) => ( r1_xxreal_0(1,k1_seq_2(C)) | v2_clvect_3(B,A) ) ) ) ) ) )).
fof(t28_coh_sp,axiom,( ! [A] : r2_hidden(k1_xboole_0,k15_coh_sp(A)) )).
fof(t28_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t28_combgras,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ( r1_ordinal1(k1_nat_1(A,1),k1_card_1(B)) => ( r1_xxreal_0(A,k5_numbers) | ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_incsp_1(k1_combgras(A,B)))) => ! [D] : ( 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 ) ) ) ) ) ) ) )).
fof(t28_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v7_pre_topc(A) & l1_pre_topc(A) ) => ( v8_compl_sp(A) <=> ! [B] : ( 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)) ) ) ) ) )).
fof(t28_complex1,axiom,( k8_complex1(k5_numbers) = k5_numbers )).
fof(t28_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k1_complex2(A,A) = k3_real_1(k4_real_1(k3_complex1(A),k3_complex1(A)),k4_real_1(k4_complex1(A),k4_complex1(A))) & k1_complex2(A,A) = k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A))) ) ) )).
fof(t28_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_complfld)) => ( C != k4_struct_0(k1_complfld) => k8_group_1(k1_complfld,A,k3_vectsp_1(k1_complfld,B,C)) = k3_vectsp_1(k1_complfld,k8_group_1(k1_complfld,A,B),C) ) ) ) ) )).
fof(t28_complsp2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => k1_valued_1(A,k30_valued_1(A)) = k15_seq_4(k3_finseq_1(A)) ) )).
fof(t28_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(A)) & v1_funct_1(C) & v1_finset_1(C) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(t28_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( 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) ) ) ) ) ) ) )).
fof(t28_comptrig,axiom,( k10_xtuple_0(k16_sin_cos) = k1_rcomp_1(k4_xcmplx_0(1),1) )).
fof(t28_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v4_valued_0(A) & v2_margrel1(A) & v2_comput_1(A) ) => ( v3_margrel1(A,k4_ordinal1) & m2_rfunct_3(A,k3_finseq_2(k4_ordinal1),k4_ordinal1,k2_comput_1(k4_ordinal1)) ) ) )).
fof(t28_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v9_ordinal1(A) & v9_ordinal1(B) ) <=> v9_ordinal1(k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)) ) ) ) )).
fof(t28_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v2_comseq_2(B) & v2_comseq_2(A) & v9_ordinal1(A) ) => ( k3_comseq_2(A) = k5_complex1 | k3_comseq_2(k2_comseq_2(k4_ordinal1,k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,A))) = k7_xcmplx_0(k8_complex1(k3_comseq_2(B)),k8_complex1(k3_comseq_2(A))) ) ) ) ) )).
fof(t28_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_funct_2(k4_ordinal1,k2_numbers,k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k10_comseq_3(A),k10_comseq_3(B)),k10_comseq_3(k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B))) ) ) )).
fof(t28_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) & l2_conlat_1(B,A) ) => ! [C] : ( ( ~ v4_conlat_1(C,A) & v6_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)) ) ) ) ) )).
fof(t28_connsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_connsp_1(A,B,C) ) ) => v1_connsp_1(A) ) ) )).
fof(t28_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => m2_connsp_2(k2_struct_0(A),A,B) ) ) )).
fof(t28_connsp_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t28_convex1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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(k5_numbers,k1_funct_1(D,B)) & r1_xxreal_0(k5_numbers,k1_funct_1(D,C)) ) ) ) ) ) ) ) )).
fof(t28_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( m1_convex4(C,A) => ! [D] : ( 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))) ) ) ) ) )).
fof(t28_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) )).
fof(t28_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t28_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t28_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t28_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t28_csspace4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v1_comseq_2(A) & v1_comseq_2(B) ) => v1_comseq_2(k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)) ) ) ) )).
fof(t28_decomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(t28_descip_1,axiom,( 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)) )).
fof(t28_dickson,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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) ) ) ) )).
fof(t28_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( ( 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] : ( v1_xreal_0(H) => k1_funct_1(G,H) = k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(D,k1_square_1(H)),k3_xcmplx_0(E,H)),F) ) & r1_zfmisc_1(A,B,C) ) => k10_diff_1(G,A,B,C) = D ) ) ) ) ) ) ) ) )).
fof(t28_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( ( 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) = k2_xcmplx_0(k9_diff_1(D,B,C),k3_xcmplx_0(A,k9_diff_1(E,B,C))) ) ) ) ) ) )).
fof(t28_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(B,k1_relset_1(k1_numbers,k27_sin_cos)) & r2_hidden(k6_xcmplx_0(B,A),k1_relset_1(k1_numbers,k27_sin_cos)) ) => k1_funct_1(k4_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k27_sin_cos),k16_sin_cos),A),B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k18_sin_cos),B),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k18_sin_cos),k6_xcmplx_0(B,A))) ) ) ) )).
fof(t28_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t28_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_diraf(A,B,C,D) => r3_diraf(A,B,C,D) ) ) ) ) ) )).
fof(t28_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => ! [C] : ( ( 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_dist_2(A,B,k1_bvfunc_1(A,C)) = k6_xcmplx_0(1,k6_dist_2(A,B,C)) ) ) ) )).
fof(t28_domain_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k9_subset_1(A,B,C) = a_3_1_domain_1(A,B,C) ) ) ) )).
fof(t28_e_siec,axiom,( ! [A] : ( ( 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 ) ) )).
fof(t28_ec_pf_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(B))) => ( C != k5_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)) ) ) ) ) )).
fof(t28_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ( C = k5_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)) ) ) ) ) ) ) )).
fof(t28_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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)) ) ) )).
fof(t28_entropy1,axiom,( ! [A] : ( ( v1_matrprob(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(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)) ) ) ) )).
fof(t28_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : 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)) )).
fof(t28_equation,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_msafree(B,A) & v1_msualg_6(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v1_msafree(C,A,B) & m1_msafree(C,A,B) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t28_euclid,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k3_rlvect_1(k15_euclid(2),k19_euclid(A,C),k19_euclid(B,D)) = k19_euclid(k2_xcmplx_0(A,B),k2_xcmplx_0(C,D)) ) ) ) ) )).
fof(t28_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => k22_rvsum_1(k3_rlvect_1(k15_euclid(A),B,C),k3_rlvect_1(k15_euclid(A),B,C)) = k2_xcmplx_0(k2_xcmplx_0(k22_rvsum_1(B,B),k3_xcmplx_0(2,k22_rvsum_1(B,C))),k22_rvsum_1(C,C)) ) ) ) )).
fof(t28_euclid_3,axiom,( k3_euclid_3(k4_struct_0(k15_euclid(2))) = k5_numbers )).
fof(t28_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => k22_rvsum_1(B,k7_euclid(A,C,D)) = k2_xcmplx_0(k22_rvsum_1(B,C),k22_rvsum_1(B,D)) ) ) ) ) )).
fof(t28_euclid_5,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( ( k3_finseq_1(A) = 3 & k3_finseq_1(B) = 3 ) => k14_rvsum_1(A,B) = k11_finseq_1(k3_xcmplx_0(k1_funct_1(A,1),k1_funct_1(B,1)),k3_xcmplx_0(k1_funct_1(A,2),k1_funct_1(B,2)),k3_xcmplx_0(k1_funct_1(A,3),k1_funct_1(B,3))) ) ) ) )).
fof(t28_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,C) ) => ( A = B | k22_rvsum_1(k6_euclid_7(C,A),k6_euclid_7(C,B)) = k5_numbers ) ) ) ) ) )).
fof(t28_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => k9_euclid(3,A,k5_numbers) = k1_euclid_8(k5_numbers,k5_numbers,k5_numbers) ) )).
fof(t28_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => k3_pcomps_1(k14_euclid(A)) = k3_waybel18(k2_finseq_1(A),k7_funcop_1(k2_finseq_1(A),k3_topmetr)) ) )).
fof(t28_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(C)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(C)) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(C)) => ! [G] : ( 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] : ( v1_xreal_0(H) => ~ ( D = k7_euclid(C,k7_euclid(C,k9_euclid(C,E,H),k9_euclid(C,F,A)),k9_euclid(C,G,B)) & k2_xcmplx_0(k2_xcmplx_0(H,A),B) = 1 ) ) ) ) ) ) ) ) ) ) )).
fof(t28_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) ) => ( ( v4_exchsort(A) & v1_finset_1(k1_funct_1(A,k5_numbers)) & ! [B] : ( 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 ) ) )).
fof(t28_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t28_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ~ ( k3_extreal1(A) = k1_supinf_1 & A != k1_supinf_1 & A != k2_supinf_1 ) ) )).
fof(t28_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_circcomb(A) & v2_circcomb(A) & v3_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v4_msafree2(C,A) & v4_circcomb(C,A) & v6_circcomb(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msafree2(D,B) & v4_circcomb(D,B) & v6_circcomb(D,B) & l3_msualg_1(D,B) ) => ! [E] : ( m1_subset_1(E,k4_card_3(u3_msualg_1(k2_circcomb(A,B),k3_circcomb(A,B,C,D)))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t28_facirc_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k15_facirc_1(A,B,C),k18_facirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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) ) ) ) ) ) )).
fof(t28_fcont_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t28_fdiff_1,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t28_fdiff_10,axiom,( ! [A] : ( ( 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,k18_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos)))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos)),A),B) = k2_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,B),k6_xcmplx_0(k1_funct_1(k26_sin_cos,B),k1_funct_1(k27_sin_cos,B)))),k3_xcmplx_0(k1_funct_1(k18_sin_cos,B),k2_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B)))))) ) ) ) ) ) )).
fof(t28_fdiff_11,axiom,( ! [A] : ( ( 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,k18_sin_cos,k2_sin_cos9))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k2_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k2_sin_cos9),A),B) = k6_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,B),k1_funct_1(k2_sin_cos9,B))),k7_xcmplx_0(k1_funct_1(k18_sin_cos,B),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t28_fdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v1_partfun1(A,k1_numbers) & ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k1_funct_1(A,B),k1_funct_1(A,C))),k1_square_1(k6_xcmplx_0(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))) ) ) ) )).
fof(t28_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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(k7_xcmplx_0(3,2))),k7_xcmplx_0(2,3)))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k1_funct_1(C,D) = k2_xcmplx_0(A,D) & ~ r1_xxreal_0(k1_funct_1(C,D),k5_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(k7_xcmplx_0(3,2))),k7_xcmplx_0(2,3)),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_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(k7_xcmplx_0(3,2))),k7_xcmplx_0(2,3)),B),D) = k6_prepower(k2_xcmplx_0(A,D),k7_xcmplx_0(1,2)) ) ) ) ) ) ) ) )).
fof(t28_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k22_sin_cos,C),k1_taylor_1(2)),k22_sin_cos),k3_taylor_1) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => ( k1_funct_1(C,D) = 1 & ~ r1_xxreal_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,C),D),k5_numbers) ) ) ) ) => ( r2_fdiff_1(B,A) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_1(k2_fdiff_1(B,A),D) = k7_xcmplx_0(k2_xcmplx_0(k1_funct_1(k22_sin_cos,D),1),k6_xcmplx_0(k1_funct_1(k22_sin_cos,D),1)) ) ) ) ) ) ) ) )).
fof(t28_fdiff_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( 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,F,k1_sin_cos6)),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(k7_xcmplx_0(1,2)))))) & C = k47_valued_1(k1_numbers,k1_numbers,k1_numbers,D,E) & E = k1_taylor_1(2) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,B) => ( k1_funct_1(D,G) = k1_square_1(A) & ~ r1_xxreal_0(k1_funct_1(C,G),k5_numbers) & k1_funct_1(F,G) = k7_xcmplx_0(G,A) & ~ r1_xxreal_0(k1_funct_1(F,G),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(F,G)) & G != k5_numbers & ~ r1_xxreal_0(A,k5_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,F,k1_sin_cos6)),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(k7_xcmplx_0(1,2)))),B) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,B) => k1_funct_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,F,k1_sin_cos6)),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(k7_xcmplx_0(1,2)))),B),G) = k1_funct_1(k1_sin_cos6,k7_xcmplx_0(G,A)) ) ) ) ) ) ) ) ) ) ) )).
fof(t28_fdiff_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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,k26_sin_cos))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(D,E) = k2_xcmplx_0(k3_xcmplx_0(A,E),B) ) ) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k26_sin_cos),C) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k26_sin_cos),C),E) = k2_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(A,k1_funct_1(k16_sin_cos,E)),k1_funct_1(k18_sin_cos,E)),k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,E),B),k1_square_1(k1_funct_1(k18_sin_cos,E)))) ) ) ) ) ) ) ) ) )).
fof(t28_fdiff_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(D,E) = k2_xcmplx_0(k3_xcmplx_0(A,E),B) ) ) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k1_fdiff_9),C) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k1_fdiff_9),C),E) = k2_xcmplx_0(k7_xcmplx_0(A,k1_funct_1(k18_sin_cos,E)),k7_xcmplx_0(k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,E),B),k1_funct_1(k16_sin_cos,E)),k1_square_1(k1_funct_1(k18_sin_cos,E)))) ) ) ) ) ) ) ) ) )).
fof(t28_ff_siec,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t28_fib_num2,axiom,( ! [A] : ( 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))) ) )).
fof(t28_fib_num3,axiom,( ! [A] : ( v7_ordinal1(A) => k1_pre_ff(k3_xcmplx_0(2,A)) = k2_nat_1(k1_pre_ff(A),k1_fib_num3(A)) ) )).
fof(t28_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(2,A) => k1_pre_ff(A) = k1_int_1(k3_xcmplx_0(k7_xcmplx_0(1,k1_fib_num),k2_xcmplx_0(k1_pre_ff(k2_xcmplx_0(A,1)),k7_xcmplx_0(1,2)))) ) ) )).
fof(t28_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_finseq_1(B,A) => ! [C] : ( m1_finseq_1(C,A) => ( r5_finseq_8(A,C,B) => C = k9_finseq_8(A,C,B) ) ) ) ) )).
fof(t28_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k4_filter_0(A,B,B) = k6_lattices(A) ) ) )).
fof(t28_filter_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t28_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k6_filter_2(A,B)) <=> r3_lattices(A,C,B) ) ) ) ) )).
fof(t28_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(A,k4_finseq_1(C)) => r2_hidden(k2_xcmplx_0(k3_finseq_1(B),A),k4_finseq_1(k7_finseq_1(B,C))) ) ) ) ) )).
fof(t28_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ( B = k2_finseq_1(A) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(t28_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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(k4_ordinal1,A),k1_relset_1(k4_ordinal1,B)) ) ) ) )).
fof(t28_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t28_finseq_5,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => k2_rfinseq(A,k5_numbers,B) = B ) )).
fof(t28_finseq_6,axiom,( ! [A] : ! [B] : ! [C] : ~ ( A != C & B != C & k5_finseq_4(k11_finseq_1(A,B,C),C) != k10_finseq_1(A,B) ) )).
fof(t28_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t28_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => r5_finseq_8(A,B,B) ) ) )).
fof(t28_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,B) & m2_finseq_1(C,A) ) => ! [D] : ( ( v3_card_1(D,B) & m2_finseq_1(D,A) ) => ! [E] : ( ( v3_card_1(E,B) & m2_finseq_1(E,A) ) => ! [F] : ( ( 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(k4_ordinal1,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))) ) ) ) ) ) ) ) )).
fof(t28_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t28_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k3_subset_1(u1_struct_0(A),k3_fintopo3(A,k3_subset_1(u1_struct_0(A),B),C)) = k5_fintopo3(A,B,C) ) ) ) )).
fof(t28_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t28_flang_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => k7_flang_1(A,k4_flang_1(A,k2_flang_1(A)),B) = k4_flang_1(A,k2_flang_1(A)) ) )).
fof(t28_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( 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))) ) ) )).
fof(t28_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r1_tarski(B,k1_flang_3(A,C,D)) => ( r1_xxreal_0(E,k5_numbers) | r1_tarski(k7_flang_1(A,B,E),k1_flang_3(A,C,D)) ) ) ) ) ) ) )).
fof(t28_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t28_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m1_subset_1(B,k1_fomodel1(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t28_frechet,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_frechet))) => ( ( v3_pre_topc(A,k3_frechet) & r2_hidden(k1_numbers,A) ) <=> ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_topmetr))) & v3_pre_topc(B,k3_topmetr) & r1_tarski(k4_ordinal1,B) & A = k2_xboole_0(k7_subset_1(u1_struct_0(k3_topmetr),B,k4_ordinal1),k1_tarski(k1_numbers)) ) ) ) )).
fof(t28_frechet2,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(k3_pcomps_1(A))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k3_pcomps_1(A))))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k3_pcomps_1(A))) => ( ( r1_funct_2(k4_ordinal1,u1_struct_0(A),k4_ordinal1,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) ) ) ) ) ) ) ) )).
fof(t28_fsm_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ v2_struct_0(D) & l2_fsm_1(D,B,C) ) => r1_setfam_1(k7_fsm_1(B,C,D,k1_nat_1(A,1)),k7_fsm_1(B,C,D,A)) ) ) ) ) )).
fof(t28_fsm_2,axiom,( ! [A] : ( ( ~ 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] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(C,B) => k1_funct_1(u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(B,C))) = B ) ) ) & ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,B) => k1_funct_1(u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(B,C))) = C ) ) ) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( 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)) = k4_xxreal_0(B,C) ) ) ) ) )).
fof(t28_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( ( ~ 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] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t28_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t28_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( 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) ) ) ) ) )).
fof(t28_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t28_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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] : ! [F] : ( ( ( 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) ) ) ) ) )).
fof(t28_funct_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t28_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_partfun1(A,B) <=> r1_tarski(A,k1_funct_4(A,B)) ) ) ) )).
fof(t28_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) ) )).
fof(t28_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_funcop_1(C) ) => ( ( r2_hidden(A,k10_xtuple_0(C)) & ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r2_hidden(D,k10_xtuple_0(C)) => r2_hidden(B,k9_xtuple_0(D)) ) ) ) => r2_hidden(B,k9_xtuple_0(k5_funct_6(C))) ) ) ) )).
fof(t28_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( r1_tarski(k9_xtuple_0(B),C) => r1_funct_7(A,k1_funct_4(A,B),C) ) ) ) )).
fof(t28_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t28_funct_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & v1_int_1(A) ) => v1_funct_9(k55_valued_1(k1_numbers,k1_numbers,k18_sin_cos),k3_xcmplx_0(k28_sin_cos,A)) ) )).
fof(t28_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_altcat_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t28_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v11_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ! [F] : ( ( v15_functor0(F,B,C) & m2_functor0(F,B,C) ) => ! [G] : ( m2_functor2(G,A,B,D,E) => ( r2_functor2(A,B,D,E) => m2_functor2(k5_functor3(A,B,C,D,E,G,F),A,C,k1_functor3(A,B,C,D,F),k1_functor3(A,B,C,E,F)) ) ) ) ) ) ) ) ) )).
fof(t28_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D),k1_fuzzy_1(A,B,C)),B) => r1_fuzzy_1(B,k2_fuzzy_1(A,D,C)) ) ) ) ) ) )).
fof(t28_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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)) ) ) ) )).
fof(t28_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_fvaluat1(D,A) => ( v3_fvaluat1(A) => ( r1_xxreal_0(k3_funct_2(u1_struct_0(A),k6_numbers,D,C),k3_funct_2(u1_struct_0(A),k6_numbers,D,B)) | k3_funct_2(u1_struct_0(A),k6_numbers,D,B) = k3_funct_2(u1_struct_0(A),k6_numbers,D,k3_rlvect_1(A,B,C)) ) ) ) ) ) ) )).
fof(t28_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( 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 ) ) ) )).
fof(t28_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ~ 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) ) ) )).
fof(t28_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t28_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v2_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ! [F] : ( m1_genealg1(F,E) => ! [G] : ( m1_genealg1(G,E) => m1_genealg1(k4_genealg1(E,F,G,A,B,C,D),E) ) ) ) ) ) ) ) )).
fof(t28_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ! [L] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t28_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( C != k4_tarski(k10_finseq_1(A,B),k14_twoscomp) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k10_gfacirc1(A,B,C),k11_gfacirc1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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 ) ) ) ) ) ) ) )).
fof(t28_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t28_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t28_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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) ) ) ) )).
fof(t28_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v8_glib_003(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k4_finseq_1(k9_glib_003(A,B))) => r1_xxreal_0(k5_numbers,k1_funct_1(k9_glib_003(A,B),C)) ) ) ) ) )).
fof(t28_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( 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] : ( 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(o_2_1_glib_004(A,B)))) ) ) ) ) ) )).
fof(t28_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(D)) & r2_hidden(k4_tarski(A,k1_nat_1(B,1)),k2_matrix_0(k2_goboard2(D))) & r2_hidden(k4_tarski(k1_nat_1(A,1),k1_nat_1(B,1)),k2_matrix_0(k2_goboard2(D))) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1)) ) => ( k5_goboard5(D,C) = k3_goboard5(k2_goboard2(D),A,k1_nat_1(B,1)) & k4_goboard5(D,C) = k3_goboard5(k2_goboard2(D),A,B) ) ) ) ) ) ) )).
fof(t28_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ~ ( ~ r1_xxreal_0(k1_matrix_0(C),A) & r2_hidden(B,k1_tops_1(k15_euclid(2),k2_goboard5(C,A))) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,k1_nat_1(A,1))),k18_euclid(B)) ) ) ) ) )).
fof(t28_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_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_nat_1(B,1),k1_matrix_0(C)) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(C)) & r1_xxreal_0(1,E) & r1_xxreal_0(E,k1_matrix_0(C)) & r2_hidden(k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_nat_1(B,1))),k7_xcmplx_0(1,2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,D,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(D,1),E))) ) ) ) ) ) ) ) )).
fof(t28_gobrd11,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => k3_goboard5(A,k3_finseq_1(A),k1_matrix_0(A)) = a_1_16_gobrd11(A) ) )).
fof(t28_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(D)) & r1_goboard1(u1_struct_0(k15_euclid(2)),D,E) & r2_hidden(k4_tarski(A,B),k2_matrix_0(E)) & r2_hidden(k4_tarski(A,k1_nat_1(B,1)),k2_matrix_0(E)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,k1_nat_1(B,1)) ) => k4_gobrd13(D,E,C) = k3_goboard5(E,A,k1_nat_1(B,1)) ) ) ) ) ) ) )).
fof(t28_gobrd14,axiom,( ! [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)))) ) => 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)))))) ) )).
fof(t28_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_qc_lang1(A))) => ~ ( v1_finset_1(B) & ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => r2_hidden(C,B) ) ) ) ) )).
fof(t28_gr_cy_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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) ) ) ) ) ) )).
fof(t28_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_graph_1(B) & l1_graph_1(B) ) => ( r2_hidden(B,k11_graph_1(A)) <=> r4_graph_1(B,A) ) ) ) )).
fof(t28_graph_2,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(B)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(B)) => ! [G] : ( 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(k4_ordinal1,k4_ordinal1,k14_finseq_1(k1_relset_1(k4_ordinal1,E)),k1_relset_1(k4_ordinal1,G)))) ) => k15_finseq_1(F) = D ) ) ) ) ) ) ) )).
fof(t28_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ! [D] : ( r1_tarski(D,C) => k5_card_1(k3_graph_3(A,B,k6_subset_1(C,D))) = k6_xcmplx_0(k5_card_1(k3_graph_3(A,B,C)),k5_card_1(k3_graph_3(A,B,D))) ) ) ) )).
fof(t28_graph_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r2_hidden(A,k3_graph_5(B,C,D)) <=> ? [E] : ( v7_graph_1(E,B) & m2_graph_1(E,B) & E = A & r1_graph_5(B,E,C,D) ) ) ) ) ) )).
fof(t28_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) => r1_tarski(k7_graphsp(B,A),k2_finseq_1(A)) ) ) )).
fof(t28_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ? [B] : ( r2_hidden(B,A) & r1_grcat_1(B,k3_algstr_0) ) ) )).
fof(t28_grfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( ( 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)) ) ) ) )).
fof(t28_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ( ? [B] : ( m2_finseq_1(B,k2_grnilp_1(A)) & ~ r1_xxreal_0(k3_finseq_1(B),k5_numbers) & k1_funct_1(B,1) = k7_group_2(A) & k1_funct_1(B,k3_finseq_1(B)) = k6_group_2(A) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(k2_xcmplx_0(C,1),k4_finseq_1(B)) ) => ! [D] : ( ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) ) => ! [E] : ( ( 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) ) ) )).
fof(t28_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( ! [F] : ( ( 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] : ( ( 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))) ) ) ) ) ) ) )).
fof(t28_groeb_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_ideal_1(C,A,B) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => m2_ideal_1(k2_rfinseq(u1_struct_0(A),D,C),A,B) ) ) ) ) )).
fof(t28_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(E,k5_card_1(k3_polynom1(k15_pre_poly(A),C,D))) => ! [F] : ( ( 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,k3_polynom1(k15_pre_poly(A),C,D)) => ( ( r2_hidden(F,k3_polynom1(k15_pre_poly(A),C,k5_groeb_3(A,B,C,D,E))) | r2_hidden(F,k3_polynom1(k15_pre_poly(A),C,k6_groeb_3(A,B,C,D,E))) ) & ~ r2_hidden(F,k3_xboole_0(k3_polynom1(k15_pre_poly(A),C,k5_groeb_3(A,B,C,D,E)),k3_polynom1(k15_pre_poly(A),C,k6_groeb_3(A,B,C,D,E)))) ) ) ) ) ) ) ) ) ) )).
fof(t28_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( k5_group_1(A,2,B) = k1_group_1(A) <=> k2_group_1(A,B) = B ) ) ) )).
fof(t28_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( m1_group_2(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t28_group_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r2_hidden(A,k5_group_2(B,D,C)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k6_algstr_0(B,E,D) & r2_hidden(E,C) ) ) ) ) ) )).
fof(t28_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t28_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_struct_0(k5_group_4(A,C),B) <=> ? [D] : ( m2_finseq_1(D,u1_struct_0(A)) & ? [E] : ( 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 ) ) ) ) ) ) )).
fof(t28_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t28_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t28_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t28_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v2_group_9(C,A) & v4_group_9(C,A,B) & m1_group_9(C,A,B) ) => ! [D] : ( ( 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) ) ) ) )).
fof(t28_groupp_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t28_hallmar1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,k1_zfmisc_1(A)) ) => ! [C] : ! [D] : ( m2_hallmar1(D,A,B) => ( r1_hallmar1(A,D,C) => r1_hallmar1(A,B,C) ) ) ) ) )).
fof(t28_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( ( ~ 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(k5_numbers,k8_weierstr(A,B,C)) ) ) ) ) )).
fof(t28_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t28_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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] : ( 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) = k1_square_1(k9_complex1(k3_funct_2(u1_struct_0(A),u1_struct_0(k1_complfld),B,C))) ) ) ) )).
fof(t28_heyting1,axiom,( ! [A] : k6_lattices(k12_normform(A)) = k1_tarski(k4_tarski(k1_xboole_0,k1_xboole_0)) )).
fof(t28_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_substlat(A,B))) => ! [D] : ( 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))) ) ) ) )).
fof(t28_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => m1_subset_1(k6_domain_1(k4_partfun1(k4_ordinal1,k6_domain_1(k4_ordinal1,B)),k2_heyting3(A,B)),u1_struct_0(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,B)))) ) ) )).
fof(t28_hfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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(k6_xcmplx_0(A,1)),A),B)) ) ) )).
fof(t28_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => r2_hidden(k3_hilbert1(B,k3_hilbert1(k3_hilbert1(B,A),A)),k6_hilbert1) ) ) )).
fof(t28_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ( k3_hilbert1(A,B) != A & k3_hilbert1(A,B) != B ) ) ) )).
fof(t28_hilbert3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => k3_hilbert3(A,k2_hilbert1) = 1 ) )).
fof(t28_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ( ( 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)) ) ) ) ) )).
fof(t28_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_vectsp_1(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m3_ideal_1(C,A,B) => m1_ideal_1(C,A,B) ) ) ) )).
fof(t28_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ( B != C => k1_incsp_1(A,B,C) = k1_incsp_1(A,C,B) ) ) ) ) )).
fof(t28_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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] : ( m4_index_1(C,u1_struct_0(A),u4_struct_0(A),u1_graph_1(A),u2_graph_1(A),B) => ! [D] : ( ( ~ 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] : ( 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)) ) ) ) ) ) )).
fof(t28_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_instalg1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_instalg1(C,B) ) => ! [D] : ( l3_msualg_1(D,A) => k2_instalg1(A,C,D) = k2_instalg1(B,C,k2_instalg1(A,B,D)) ) ) ) ) )).
fof(t28_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => k2_xcmplx_0(k1_int_1(A),B) = k1_int_1(k2_xcmplx_0(A,B)) ) ) )).
fof(t28_int_2,axiom,( v1_int_2(2) )).
fof(t28_int_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r1_int_2(A,B) => ( A = k5_numbers | r1_xxreal_0(B,1) | ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ( k5_int_1(k6_xcmplx_0(k3_xcmplx_0(A,D),C),B) = k5_numbers => r2_hidden(k4_tarski(D,k3_xcmplx_0(C,k11_newton(A,k7_nat_d(k1_euler_1(B),1)))),k1_int_4(B)) ) ) ) ) ) ) ) )).
fof(t28_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t28_int_6,axiom,( ! [A] : ( ( 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] : ( m1_int_6(B,A) => ! [C] : ( m1_int_6(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t28_int_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_int_7(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ( B = C => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k2_binop_1(u1_struct_0(k3_int_7(A)),k4_ordinal1,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)),k4_ordinal1,u1_struct_0(k9_int_3(A)),k4_group_1(k9_int_3(A)),C,D) ) ) ) ) ) )).
fof(t28_integr11,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( A != k5_numbers => k2_integra5(B,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(1,k5_numbers),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,k5_numbers),k16_sin_cos))) = k6_xcmplx_0(k1_funct_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,k5_numbers),k16_sin_cos),k7_xcmplx_0(1,k1_square_1(A))),k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,A),k5_numbers),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,k5_numbers),k18_sin_cos))),k2_seq_4(B)),k1_funct_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,k5_numbers),k16_sin_cos),k7_xcmplx_0(1,k1_square_1(A))),k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,A),k5_numbers),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,k5_numbers),k18_sin_cos))),k3_seq_4(B))) ) ) ) )).
fof(t28_integr12,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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,k18_sin_cos,k1_taylor_1(k6_xcmplx_0(A,1))),A),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k1_taylor_1(k1_nat_1(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,k27_sin_cos,k1_taylor_1(A)))) & D = k1_relset_1(k1_numbers,C) ) => k2_integra5(B,C) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k1_taylor_1(A))),k2_seq_4(B)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k1_taylor_1(A))),k3_seq_4(B))) ) ) ) ) ) )).
fof(t28_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k27_sin_cos))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k27_sin_cos)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k27_sin_cos)),k3_seq_4(A))) ) ) ) ) )).
fof(t28_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k2_xcmplx_0(k7_xcmplx_0(k1_funct_1(k22_sin_cos,D),k1_funct_1(k18_sin_cos,D)),k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k22_sin_cos,D),k1_funct_1(k16_sin_cos,D)),k1_square_1(k1_funct_1(k18_sin_cos,D)))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_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) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_fdiff_9),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_fdiff_9),k3_seq_4(A))) ) ) ) ) )).
fof(t28_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t28_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [C] : ( m1_integra1(C,A) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t28_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( m1_integra1(D,B) => ( ( v1_seq_2(k2_partfun1(B,k1_numbers,C,B)) & r1_xxreal_0(A,k5_numbers) ) => k7_integra1(B,k26_valued_1(B,k1_numbers,C,A),D) = k3_xcmplx_0(A,k6_integra1(B,C,D)) ) ) ) ) ) )).
fof(t28_integra4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( ( r2_hidden(F,B) & r2_hidden(G,B) ) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k1_funct_1(E,F),k1_funct_1(E,G))),k3_xcmplx_0(A,k2_xcmplx_0(k9_complex1(k6_xcmplx_0(k1_funct_1(C,F),k1_funct_1(C,G))),k9_complex1(k6_xcmplx_0(k1_funct_1(D,F),k1_funct_1(D,G)))))) ) ) ) ) => ( r1_xxreal_0(A,k5_numbers) | v3_integra1(E,B) ) ) ) ) ) ) ) )).
fof(t28_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( v1_xreal_0(F) => ( r2_hidden(F,k2_rcomp_1(A,B)) => k1_funct_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_funct_1(C,D) ) ) ) ) ) ) ) )).
fof(t28_integra7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k6_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_funct_1(k22_sin_cos,A)) = k4_integra5(A,B,k22_sin_cos) ) ) )).
fof(t28_integra8,axiom,( k2_fdiff_1(k18_sin_cos,k1_numbers) = k32_valued_1(k1_numbers,k1_numbers,k16_sin_cos) )).
fof(t28_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( ~ 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) = k3_xcmplx_0(A,k1_integra9(D,B,C)) ) ) ) ) ) )).
fof(t28_interva1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t28_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(t28_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => r1_xxreal_0(k1_funct_1(k4_irrat_1,A),k4_series_1(k5_irrat_1)) ) ) )).
fof(t28_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,B,C) => ! [G] : ( m2_cat_1(G,B,C) => ! [H] : ( m2_cat_1(H,C,D) => ! [I] : ( m2_nattra_1(I,B,C,F,G) => ( r2_nattra_1(B,C,F,G) => r2_funct_2(u1_struct_0(A),u4_struct_0(D),k5_isocat_1(A,B,D,k9_cat_1(B,C,D,F,H),k9_cat_1(B,C,D,G,H),E,k4_isocat_1(B,C,D,F,G,I,H)),k4_isocat_1(A,C,D,k9_cat_1(A,B,C,E,F),k9_cat_1(A,B,C,E,G),k5_isocat_1(A,B,C,F,G,E,I),H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t28_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,B,C) => ( r2_nattra_1(A,B,D,E) => ! [G] : ( m2_nattra_1(G,A,B,D,E) => k4_isocat_1(A,B,C,D,E,G,F) = k3_relat_1(G,F) ) ) ) ) ) ) ) ) )).
fof(t28_isomichi,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( A = k2_borsuk_5(B,C) => k1_tops_1(k3_topmetr,A) = k1_xboole_0 ) ) ) ) )).
fof(t28_jgraph_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(A))) => ( ( D = B & E = C ) => k12_euclid(k5_algstr_0(k15_euclid(A),B,C)) = k3_metric_1(k14_euclid(A),D,E) ) ) ) ) ) ) )).
fof(t28_jgraph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) != k5_numbers ) & ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( 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) ) ) ) ) ) ) )).
fof(t28_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [D] : ( ( 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,k4_xcmplx_0(1)) | r1_xxreal_0(1,A) | v5_pre_topc(D,k1_pre_topc(k15_euclid(2),B),k1_pre_topc(k15_euclid(2),C)) ) ) ) ) ) ) )).
fof(t28_jgraph_5,axiom,( ! [A] : ( ( ~ 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) = k4_xcmplx_0(1) & k8_pscomp_1(A) = 1 & k9_pscomp_1(A) = k4_xcmplx_0(1) & k7_pscomp_1(A) = 1 ) ) ) )).
fof(t28_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t28_jordan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t28_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t28_jordan12,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t28_jordan14,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(B,C) & r1_jordan1h(A,B) ) => r1_jordan1h(A,C) ) ) ) ) )).
fof(t28_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C)),k3_topreal1(2,k1_jordan1e(B,A))) = k1_tarski(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C)),k3_topreal1(2,k2_jordan1e(B,A))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C)) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C)),k9_jordan6(B)) ) ) ) ) ) ) )).
fof(t28_jordan18,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => r1_jordan18(A,B,D,C,E,C) ) ) ) ) ) )).
fof(t28_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => k1_matrix_0(k1_jordan8(B,A)) = k1_nat_1(k1_newton(2,A),3) ) ) )).
fof(t28_jordan1b,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),1),k3_matrix_0(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)) ) ) )).
fof(t28_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(k1_jordan8(B,A))) & k24_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,1) ) ) ) )).
fof(t28_jordan1g,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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,k2_jordan9(B,A)))),k4_finseq_4(k2_jordan1e(B,A),k24_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))))) ) ) )).
fof(t28_jordan1i,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ~ ( k17_euclid(D) = k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(C),k8_pscomp_1(C)),2) & ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k1_matrix_0(k1_jordan8(C,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(C,A),k1_jordan1a(k1_jordan8(C,A)),B),k8_jordan6(k3_topreal1(2,k2_jordan9(C,A)))) & k18_euclid(D) = k2_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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(C,1),k1_jordan1a(k1_jordan8(C,1)),1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(C,A),k1_jordan1a(k1_jordan8(C,A)),B)),k9_jordan6(k3_topreal1(2,k2_jordan9(C,A)))))) & ! [E] : ( v7_ordinal1(E) => ~ ( r1_xxreal_0(1,E) & r1_xxreal_0(E,k1_matrix_0(k1_jordan8(C,A))) & D = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(C,A),k1_jordan1a(k1_jordan8(C,A)),E) ) ) ) ) ) ) ) )).
fof(t28_jordan1k,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k5_numbers,C) => k1_topreal6(2,B,k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),A,C),k1_rlvect_1(k15_euclid(2),B,k6_xcmplx_0(1,C)))) = k3_xcmplx_0(C,k1_topreal6(2,A,B)) ) ) ) ) )).
fof(t28_jordan20,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( v1_xreal_0(G) => ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t28_jordan21,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( 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(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(B),k8_pscomp_1(B)),2)))) => r1_xxreal_0(k18_euclid(A),k18_euclid(k1_jordan21(B))) ) ) ) )).
fof(t28_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => ( r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(k18_euclid(k2_jordan21(k9_jordan6(k3_topreal1(2,k2_jordan9(A,B))))),k18_euclid(k2_jordan21(k9_jordan6(k3_topreal1(2,k2_jordan9(A,C)))))) ) ) ) ) ) )).
fof(t28_jordan23,axiom,( ! [A] : ( ( v2_topreal1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => v2_topreal1(k3_finseq_6(u1_struct_0(k15_euclid(2)),A,B,C)) ) ) ) )).
fof(t28_jordan2b,axiom,( ! [A] : ( ( 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] : ( 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) ) ) )).
fof(t28_jordan3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t28_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_jordan4(A,B,C,D) => ( r1_xxreal_0(D,C) | ( k3_finseq_1(B) = k7_nat_d(k2_xcmplx_0(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)) ) ) ) ) ) ) ) )).
fof(t28_jordan5b,axiom,( ! [A] : ( 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 ) ) )).
fof(t28_jordan5c,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( 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(k1_nat_1(D,1),k3_finseq_1(A)) & r2_hidden(C,k2_topreal1(2,A,E)) & r1_xxreal_0(1,E) & r1_xxreal_0(k1_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,k1_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)))) ) ) ) ) ) ) ) ) ) )).
fof(t28_jordan5d,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( B = a_1_5_jordan5d(A) => k3_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))) ) ) ) )).
fof(t28_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t28_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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)) ) ) )).
fof(t28_knaster,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) ) => ! [C] : ( ( 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] : ( 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] : ( v3_ordinal1(E) => ( r1_ordinal1(A,E) => k5_knaster(B,C,D,A) = k5_knaster(B,C,D,E) ) ) ) ) ) ) ) )).
fof(t28_kurato_1,axiom,( 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)) )).
fof(t28_kurato_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) )).
fof(t28_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( m1_matrix_2(E,k3_matrix_2(A)) => ! [F] : ( v7_ordinal1(F) => ( ( k3_finseq_1(C) = A & r2_hidden(F,k2_finseq_1(A)) ) => k11_fvsum_1(B,k7_matrix_0(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)) ) ) ) ) ) ) ) )).
fof(t28_latsubgr,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(t28_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m1_subset_1(D,k5_finsub_1(B)) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t28_lattice3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( r3_lattice3(B,C,A) <=> r1_lattice3(k3_lattice3(B),A,k4_lattice3(B,C)) ) ) ) )).
fof(t28_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v3_filter_0(B) & l3_lattices(B) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t28_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( v3_ordinal1(D) => ! [E] : ( 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)))) ) ) ) ) ) ) ) )).
fof(t28_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => v2_lexbfs(k16_lexbfs(A)) ) )).
fof(t28_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_limfunc1(A) & v2_comseq_2(B) ) => ( r1_xxreal_0(k1_seq_2(B),k5_numbers) | v1_limfunc1(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).
fof(t28_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,C) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,C) & ~ r1_xxreal_0(A,D) & r2_hidden(D,k1_relset_1(k1_numbers,B)) ) ) ) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(k6_xcmplx_0(A,C),A))) & ~ v2_seq_2(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(k6_xcmplx_0(A,C),A))) ) ) | r3_limfunc2(B,A) ) ) ) ) )).
fof(t28_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k3_limfunc1(C))) & r1_xxreal_0(k4_limfunc1(A),k1_funct_1(A,D)) ) ) | v5_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).
fof(t28_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t28_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,k5_normsp_0(A,B),D)) & r1_xxreal_0(k9_nat_1(k1_numbers,k5_normsp_0(A,B),D),k9_nat_1(k1_numbers,k5_normsp_0(A,C),D)) ) ) & v2_lopban_3(C,A) ) => ( v2_lopban_3(B,A) & r1_xxreal_0(k4_series_1(k5_normsp_0(A,B)),k4_series_1(k5_normsp_0(A,C))) ) ) ) ) ) )).
fof(t28_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k2_normsp_0(A,k9_nat_1(u1_struct_0(A),k1_bhsp_4(A,k1_lopban_4(A,B)),C)),k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k2_normsp_0(A,B))),C)) & r1_xxreal_0(k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k2_normsp_0(A,B))),C),k4_series_1(k4_sin_cos(k2_normsp_0(A,B)))) & r1_xxreal_0(k2_normsp_0(A,k9_nat_1(u1_struct_0(A),k1_bhsp_4(A,k1_lopban_4(A,B)),C)),k4_series_1(k4_sin_cos(k2_normsp_0(A,B)))) ) ) ) ) )).
fof(t28_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) )).
fof(t28_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => r1_lpspace1(A,B,C,D,D) ) ) ) ) )).
fof(t28_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v2_xxreal_0(E) & v1_xreal_0(E) ) => ( r2_hidden(D,k1_lpspace2(A,B,C,E)) => r2_hidden(k56_valued_1(A,k1_numbers,D),k1_lpspace2(A,B,C,E)) ) ) ) ) ) ) )).
fof(t28_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(k8_nat_1(k1_zfmisc_1(k10_ltlaxio1),D,B)),k1_domain_1(k4_ordinal1,k1_hilbert1,C,A)) = k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(D),k1_domain_1(k4_ordinal1,k1_hilbert1,k1_nat_1(B,C),A)) ) ) ) ) )).
fof(t28_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(k4_ltlaxio1(A,B),B)) ) ) )).
fof(t28_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ( r2_hidden(A,k2_relset_1(k1_hilbert1,k8_ltlaxio3(B))) => r8_ltlaxio1(k1_subset_1(k1_hilbert1),k3_hilbert1(k12_ltlaxio3(B),A)) ) ) ) )).
fof(t28_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ! [D] : ( m3_ltlaxio4(D,A) => ( ( r2_hidden(C,k2_relset_1(k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)),D)) & r2_hidden(B,k8_ltlaxio4(C)) ) => r1_relset_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1),k5_ltlaxio4(B),k11_ltlaxio4(A,D)) ) ) ) ) ) )).
fof(t28_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t28_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t28_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( r2_matrix10(B,C) => v3_matrix10(k5_matrix10(A,B,C)) ) ) ) ) )).
fof(t28_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,C,A,B) & m2_finseq_1(E,k3_finseq_2(C)) ) => ! [F] : ( m2_finseq_1(F,C) => ! [G] : ( v7_ordinal1(G) => ( r2_hidden(G,k2_finseq_1(A)) => ( ( ( G = D & k3_finseq_1(F) = k1_matrix_0(E) ) => k7_matrix_0(C,k3_matrix11(D,A,B,C,E,F),G) = F ) & ( G != D => k7_matrix_0(C,k3_matrix11(D,A,B,C,E,F),G) = k7_matrix_0(C,E,G) ) ) ) ) ) ) ) ) ) ) )).
fof(t28_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(A)) ) => ! [F] : ( m2_finseq_2(F,k4_ordinal1,k4_finseq_2(D,k4_ordinal1)) => ! [G] : ( m2_finseq_2(G,k4_ordinal1,k4_finseq_2(C,k4_ordinal1)) => ( ( r2_hidden(B,k2_finseq_1(C)) & r1_tarski(k10_xtuple_0(F),k2_finseq_1(k3_finseq_1(E))) ) => k8_matrix_0(A,k1_matrix13(A,E,D,C,F,G),B) = k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,A,F,k8_matrix_0(A,E,k1_funct_1(G,B))) ) ) ) ) ) ) ) ) )).
fof(t28_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( C = k2_matrix_1(B,A) <=> ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,A) & r1_xxreal_0(1,E) & r1_xxreal_0(E,A) ) => k3_matrix_0(u1_struct_0(B),C,D,E) = k4_struct_0(B) ) ) ) ) ) ) ) )).
fof(t28_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t28_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(B),A,A) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(B))) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(B),A,A) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(B))) ) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(B),A,A) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(B))) ) => ( ( v3_matrix16(F,u1_struct_0(B)) & v3_matrix16(G,u1_struct_0(B)) & v3_matrix16(H,u1_struct_0(B)) ) => v3_matrix16(k1_matrix_4(B,k3_matrix_3(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)) ) ) ) ) ) ) ) ) ) )).
fof(t28_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,B,A,A) & m2_finseq_1(C,k3_finseq_2(B)) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(D,E),k2_matrix_0(C)) => r2_hidden(k4_tarski(E,D),k2_matrix_0(C)) ) ) ) ) ) ) )).
fof(t28_matrix_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( ( 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] : ( ( v1_funct_1(F) & v1_funct_2(F,B,A) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,C,A) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(C,A))) ) => ! [H] : ( m1_subset_1(H,k5_finsub_1(B)) => ! [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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t28_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ! [E] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(D) & k1_matrix_0(D) = k1_matrix_0(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) ) ) ) ) ) ) )).
fof(t28_matrix_6,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(A),B,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(A),B,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ( ( v2_matrix_6(C,B,A) & v2_matrix_6(D,B,A) ) => v2_matrix_6(k1_matrix_4(A,C,D),B,A) ) ) ) ) ) )).
fof(t28_matrix_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_matrix_2(C,k3_matrix_2(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r1_xxreal_0(1,A) => k5_matrix_2(B,A,D,C) = k5_matrix_2(B,A,D,k3_matrix_7(A,C)) ) ) ) ) ) )).
fof(t28_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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,k5_numbers) & k2_matrix_1(B,A) = k3_matrix_1(B,A) ) ) ) )).
fof(t28_matrix_9,axiom,( k2_funct_1(k3_finseq_4(k4_ordinal1,2,3,1)) = k3_finseq_4(k4_ordinal1,3,1,2) )).
fof(t28_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ( ( A = B & r1_xxreal_0(1,k3_finseq_1(A)) ) => k18_rvsum_1(A) = k17_rvsum_1(B) ) ) ) )).
fof(t28_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( ( v1_matrixj1(E,C) & m2_finseq_1(E,k3_finseq_2(k3_finseq_2(C))) ) => ! [F] : ( ( v1_matrixj1(F,C) & m2_finseq_1(F,k3_finseq_2(k3_finseq_2(C))) ) => ( r2_hidden(k4_tarski(A,B),k2_matrix_0(k13_matrixj1(C,D,F))) => k3_matrix_0(C,k13_matrixj1(C,D,F),A,B) = k3_matrix_0(C,k13_matrixj1(C,D,k3_matrixj1(C,E,F)),k1_nat_1(A,k2_wsierp_1(k10_matrixj1(C,E))),k1_nat_1(B,k2_wsierp_1(k11_matrixj1(C,E)))) ) ) ) ) ) ) ) )).
fof(t28_matrixr1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => k2_matrix_0(k7_matrixr1(A,B)) = k2_matrix_0(B) ) ) )).
fof(t28_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => k1_matrixr2(A,k1_matrixr2(A,B,C),D) = k1_matrixr2(A,B,k1_matrixr2(A,C,D)) ) ) ) ) )).
fof(t28_matrlin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,D,C,A) & m2_finseq_1(E,k3_finseq_2(D)) ) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,D,B,A) & m2_finseq_1(F,k3_finseq_2(D)) ) => ( k1_matrix_0(E) = k1_matrix_0(F) => k4_matrix_0(D,k8_matrlin(D,C,B,A,E,F)) = k7_matrlin(D,k4_matrix_0(D,E),k4_matrix_0(D,F)) ) ) ) ) ) ) ) )).
fof(t28_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_matrlin(C,A,B) => k1_matrlin2(A,B,B,k3_struct_0(B),C,C) = k3_matrix_1(A,k3_finseq_1(C)) ) ) ) )).
fof(t28_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => r2_matroid0(A,C,B) ) ) ) ) )).
fof(t28_matrprob,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => k5_matrprob(A) = k5_matrprob(k4_matrix_0(k1_numbers,A)) ) )).
fof(t28_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => 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)) ) ) ) ) ) )).
fof(t28_matrtop3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t28_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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))) ) ) )).
fof(t28_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : 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)) )).
fof(t28_measure1,axiom,( ! [A] : ! [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))) ) => ? [C] : ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) & ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => k12_supinf_2(C,D) = k1_supinf_2 ) ) ) )).
fof(t28_measure6,axiom,( ! [A] : ( ( v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ( v3_measure5(A) <=> v3_measure5(k1_measure6(A,B)) ) ) ) )).
fof(t28_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ! [D] : ( m2_measure8(D,A,B) => ( v2_prob_1(D) => v8_valued_0(k10_measure8(A,B,D,C)) ) ) ) ) )).
fof(t28_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => ( r2_hidden(B,A) <=> r2_hidden(k5_xcmplx_0(B),k7_member_1(A)) ) ) ) )).
fof(t28_membered,axiom,( ! [A] : ( ! [B] : ( r2_hidden(B,A) => v4_membered(B) ) => v4_membered(k3_tarski(A)) ) )).
fof(t28_memstr_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_setfam_1(B) => ! [C] : ( ( ~ v2_struct_0(C) & v2_memstr_0(C,B) & v3_memstr_0(C,B) & l1_memstr_0(C,B) ) => ! [D] : ( ( 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] : ( ( 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 ) ) ) ) ) ) )).
fof(t28_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(A),B) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ( 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))) ) ) ) ) ) ) )).
fof(t28_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( v1_xreal_0(D) => 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)) ) ) ) )).
fof(t28_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ( ( r1_tarski(C,k1_relset_1(A,k4_mesfunc5(A,k2_numbers,D,k5_numbers))) & v1_mesfunc8(D,A,k2_numbers) & ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,C) => v1_comseq_3(k9_mesfun7c(A,D,E)) ) ) ) => ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,C) => v1_comseq_3(k9_mesfun7c(A,k1_mesfun9c(A,k2_numbers,D,C),E)) ) ) ) ) ) ) ) )).
fof(t28_mesfunc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( r1_mesfunc1(A,B,C,D) <=> ! [E] : ( v1_xreal_0(E) => r2_hidden(k9_subset_1(A,D,k16_mesfunc1(A,C,E)),B) ) ) ) ) ) ) )).
fof(t28_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_subset_1(C,B) => v3_valued_0(k3_mesfunc2(C,A)) ) ) ) )).
fof(t28_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( r2_relset_1(A,k6_numbers,k1_mesfunc2(A,k2_partfun1(A,k6_numbers,B,C)),k2_partfun1(A,k6_numbers,k1_mesfunc2(A,B),C)) & r2_relset_1(A,k6_numbers,k2_mesfunc2(A,k2_partfun1(A,k6_numbers,B,C)),k2_partfun1(A,k6_numbers,k2_mesfunc2(A,B),C)) ) ) ) )).
fof(t28_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( r2_relset_1(A,k6_numbers,k7_mesfunc1(A,k1_mesfunc5(A,B)),k1_mesfunc5(A,k26_valued_1(A,k1_numbers,B,k4_xcmplx_0(1)))) & r2_relset_1(A,k6_numbers,k7_mesfunc1(A,k1_mesfunc5(A,B)),k1_mesfunc5(A,k32_valued_1(A,k1_numbers,B))) ) ) ) )).
fof(t28_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( v7_ordinal1(C) => ( v2_mesfunc9(B,A) => k1_relset_1(A,k4_mesfunc5(A,k6_numbers,k4_mesfunc9(A,B),C)) = k1_setfam_1(a_3_0_mesfunc9(A,B,C)) ) ) ) ) )).
fof(t28_metric_1,axiom,( ! [A] : ( m1_subset_1(A,2) => ! [B] : ( m1_subset_1(B,2) => k1_binop_1(k11_metric_1,A,B) = k1_binop_1(k11_metric_1,B,A) ) ) )).
fof(t28_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k2_metric_2(A),k2_metric_2(A))) => ( r2_hidden(B,k8_metric_2(A)) <=> ? [C] : ( m1_subset_1(C,k2_metric_2(A)) & ? [D] : ( m1_subset_1(D,k2_metric_2(A)) & ? [E] : ( 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) ) ) ) ) ) ) )).
fof(t28_metric_3,axiom,( ! [A] : ( m1_subset_1(A,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)) => ! [B] : ( m1_subset_1(B,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)) => ( k2_binop_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k1_numbers,k22_metric_3,A,B) = k5_numbers <=> A = B ) ) ) )).
fof(t28_metric_6,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_tbsp_1(B,A) => v1_metric_6(B,A) ) ) ) )).
fof(t28_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t28_midsp_2,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & l1_midsp_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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,F) = E <=> k2_binop_1(u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),C,D,F) = k1_midsp_2(A,k2_binop_1(u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),C,D,E)) ) ) ) ) ) ) ) ) )).
fof(t28_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_midsp_3(B,A) => ! [C] : ( m2_midsp_3(C,A) => ! [D] : ( ( v4_midsp_2(D,C) & l1_midsp_2(D,C) ) => ( r2_midsp_3(A,B,C) <=> ! [E] : ( m2_finseq_2(E,u1_struct_0(u1_midsp_2(C,D)),k4_finseq_2(k1_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)),k1_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)) ) ) ) ) ) ) )).
fof(t28_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t28_mod_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_classes2(C) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t28_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(t28_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k6_modal_1) => ! [B] : ( m1_subset_1(B,k6_modal_1) => ( k10_modal_1(A) = k10_modal_1(B) => A = B ) ) ) )).
fof(t28_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [E] : ( 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] : ( m1_subset_1(F,A) & r2_hidden(k4_tarski(C,F),B) & r3_modelc_1(A,B,D,F,E) ) ) ) ) ) ) ) )).
fof(t28_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ~ ( r1_modelc_2(B,A) & r1_xxreal_0(k3_finseq_1(A),k3_finseq_1(B)) ) ) ) )).
fof(t28_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_3(C,B) & l1_modelc_3(C,B) ) => ! [D] : ( ( v1_modelc_3(D,B) & l1_modelc_3(D,B) ) => ( ( r4_modelc_3(B,C,D) & r2_hidden(A,u1_modelc_3(B,D)) ) => ( r2_hidden(A,u1_modelc_3(B,C)) | r1_modelc_3(B,C,D,A) ) ) ) ) ) ) )).
fof(t28_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t28_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m2_monoid_0(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t28_monoid_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k13_monoid_1(A))) => ( k9_xtuple_0(B) = A & r1_tarski(k10_xtuple_0(B),k4_ordinal1) ) ) )).
fof(t28_morph_01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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,D),k5_rusub_4(A,C,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,D),C),B) ) ) ) ) )).
fof(t28_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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) ) ) ) )).
fof(t28_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( l3_msualg_1(D,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)) => ! [E] : ( m1_msualg_2(E,A,B) => ( 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)) => m1_msualg_2(D,A,C) ) ) ) ) ) ) ) )).
fof(t28_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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) ) ) ) ) )).
fof(t28_mssublat,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( v1_unialg_1(B) & m1_unialg_2(B,A) ) => ! [C] : ( ( v1_unialg_1(C) & m1_unialg_2(C,A) ) => ! [D] : ( ( 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] : ( ( 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(k5_numbers,k2_xboole_0(u1_struct_0(B),u1_struct_0(C))) ) ) ) ) ) ) )).
fof(t28_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msualg_2(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t28_msualg_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_msualg_5(A,B)))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t28_mycielsk,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t28_nagata_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ( k1_binop_1(B,C,C) = k5_numbers & r1_xxreal_0(k1_binop_1(B,C,E),k2_xcmplx_0(k1_binop_1(B,C,D),k1_binop_1(B,E,D))) ) ) ) ) ) ) )).
fof(t28_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_ordinal1(k5_card_1(B),k5_card_1(A)) <=> r1_xxreal_0(B,A) ) ) ) )).
fof(t28_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ v1_zfmisc_1(A) <=> ( ~ v1_xboole_0(A) & A != 1 ) ) ) )).
fof(t28_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => k11_nat_3(k3_xcmplx_0(B,C),A) = k2_xcmplx_0(k11_nat_3(B,A),k11_nat_3(C,A)) ) ) ) )).
fof(t28_nat_4,axiom,( v1_int_2(13) )).
fof(t28_nat_5,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(A)) ) => k2_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(k4_ordinal1,k4_ordinal1),k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1,k16_funct_3(A,A,k4_ordinal1,k4_ordinal1,B,C),k24_binop_2),k8_mcart_1(A,A,D,E))) = k3_xcmplx_0(k2_uproots(D,k1_nat_5(A,B,D)),k2_uproots(E,k1_nat_5(A,C,E))) ) ) ) ) )).
fof(t28_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(A,k5_numbers) => k6_nat_d(B,A) = k6_nat_d(A,k4_nat_d(B,A)) ) ) ) )).
fof(t28_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_nattra_1(E,A,B,C,D) => ( r2_nattra_1(A,B,C,D) <=> r2_hidden(k4_tarski(k4_tarski(C,D),E),k8_nattra_1(A,B)) ) ) ) ) ) ) )).
fof(t28_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ! [E] : ( 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(k4_ordinal1,u1_struct_0(A),k8_funct_2(k4_ordinal1,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(k4_ordinal1,u1_struct_0(A),u1_struct_0(B),D,C),E)) ) ) ) ) ) ) )).
fof(t28_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( ( 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)))) ) => ( v1_funct_1(k6_vfunct_1(u1_struct_0(A),B,C,D)) & v2_ndiff_1(k6_vfunct_1(u1_struct_0(A),B,C,D),A,B) & m1_subset_1(k6_vfunct_1(u1_struct_0(A),B,C,D),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & v1_funct_1(k2_vfunct_1(u1_struct_0(A),B,C,D)) & v2_ndiff_1(k2_vfunct_1(u1_struct_0(A),B,C,D),A,B) & m1_subset_1(k2_vfunct_1(u1_struct_0(A),B,C,D),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) ) ) ) ) )).
fof(t28_ndiff_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t28_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k14_prvect_2(A))) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t28_neckla_3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t28_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k1_funct_1(k5_newton(B,C,A),1) = k1_newton(B,A) ) ) ) )).
fof(t28_nfcont_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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,k4_normsp_0(u1_struct_0(B),C,D),A) & r3_nfcont_1(B,C,k5_vfunct_1(u1_struct_0(B),C,D),A) ) ) ) ) ) )).
fof(t28_nfcont_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(C)))) ) => ! [E] : ( ( 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) ) ) ) ) )).
fof(t28_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t28_normform,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [C] : ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t28_normsp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(t28_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k3_normsp_2(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k3_normsp_2(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k4_normsp_2(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k4_normsp_2(A))))) ) => ( ( r1_funct_2(k4_ordinal1,u1_struct_0(k3_normsp_2(A)),k4_ordinal1,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) ) ) ) ) ) )).
fof(t28_numbers,axiom,( k4_ordinal1 != k3_numbers )).
fof(t28_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t28_openlatt,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t28_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_oppcat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t28_ordeq_01,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [D] : ( m1_subset_1(D,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,D),k1_pdiff_1(B,A)),k2_partfun1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_euclid(A),k1_euclid(A),k1_numbers,C,k1_pdiff_1(B,A)),D)) ) ) ) ) )).
fof(t28_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r2_wellord1(A,B) => ( r1_orders_1(A,B) & r2_orders_1(A,B) & r3_orders_1(A,B) ) ) ) )).
fof(t28_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t28_ordinal1,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => ! [C] : ( ( 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) ) ) ) )).
fof(t28_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => k10_ordinal2(A,k1_ordinal1(B)) = k1_ordinal1(k10_ordinal2(A,B)) ) ) )).
fof(t28_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ~ ( r2_hidden(A,B) & ! [C] : ( v3_ordinal1(C) => ~ ( B = k10_ordinal2(A,C) & C != k1_xboole_0 ) ) ) ) ) )).
fof(t28_ordinal6,axiom,( ! [A] : ( ( 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) ) )).
fof(t28_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( E = k4_struct_0(B) => ( r1_orders_2(B,D,C) | k2_ortsp_1(A,B,E,F,C,D) = k4_struct_0(A) ) ) ) ) ) ) ) ) )).
fof(t28_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => k21_osafree(A,B,C) = a_3_3_osafree(A,B,C) ) ) ) )).
fof(t28_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ( ( v1_orders_3(A) | v6_osalg_1(A) ) => v13_osalg_1(B,A) ) ) ) )).
fof(t28_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t28_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ~ r1_parsp_1(A,B,C,D,E) => ( B != C & D != E ) ) ) ) ) ) ) )).
fof(t28_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t28_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r1_tarski(C,A) => r1_relset_1(C,B,k3_partfun1(D,C,B),k3_partfun1(D,A,B)) ) ) )).
fof(t28_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( r1_partfun1(C,D) <=> ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,k9_subset_1(A,k1_relset_1(A,C),k1_relset_1(A,D))) => k7_partfun1(B,C,E) = k7_partfun1(B,D,E) ) ) ) ) ) ) ) )).
fof(t28_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => k3_partit1(A,B,k2_partit1(A,B,C)) = B ) ) ) )).
fof(t28_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) => ( v5_relat_2(C) => r5_relat_2(C,A) ) ) ) ) )).
fof(t28_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => v4_pasch(A) ) )).
fof(t28_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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))) ) ) ) )).
fof(t28_pcomps_1,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( v9_metric_1(A) & r2_hidden(E,k9_subset_1(u1_struct_0(A),k8_metric_1(A,D,B),k8_metric_1(A,F,C))) & ! [G] : ( v1_xreal_0(G) => ~ ( r1_tarski(k8_metric_1(A,E,G),k8_metric_1(A,D,B)) & r1_tarski(k8_metric_1(A,E,G),k8_metric_1(A,F,C)) ) ) ) ) ) ) ) ) ) )).
fof(t28_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k20_pcs_0(A,B))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k20_pcs_0(A,B))) => ( ( C = E & D = F & r1_pcs_0(A,C,D) ) => r1_pcs_0(k20_pcs_0(A,B),E,F) ) ) ) ) ) ) )).
fof(t28_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k4_real_ns1(A))) => ( ( r2_pdiff_1(B,A,C,D,F) & r2_pdiff_1(B,A,C,E,F) ) => ( r2_pdiff_1(B,A,C,k6_vfunct_1(u1_struct_0(k4_real_ns1(A)),k4_real_ns1(B),D,E),F) & k9_pdiff_1(A,B,C,k6_vfunct_1(u1_struct_0(k4_real_ns1(A)),k4_real_ns1(B),D,E),F) = k3_rlvect_1(k16_lopban_1(k4_real_ns1(1),k4_real_ns1(B)),k9_pdiff_1(A,B,C,D,F),k9_pdiff_1(A,B,C,E,F)) ) ) ) ) ) ) ) ) )).
fof(t28_pdiff_3,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(2)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [C] : ( ( 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) & k10_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) = k6_xcmplx_0(k5_pdiff_3(B,A),k5_pdiff_3(C,A)) ) ) ) ) ) )).
fof(t28_pdiff_4,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t28_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( 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) = k10_pdiff_1(3,1,k1_pdiff_3(1,3,B),A) ) ) ) )).
fof(t28_pdiff_6,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(k4_real_ns1(A))) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( 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) ) ) ) ) ) ) ) )).
fof(t28_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(k1_euclid(A))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k4_real_ns1(A)))) => ( ( E = F & v1_pdiff_7(E,A) & C = D ) => ( ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t28_pencil_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t28_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( 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))) ) ) ) ) )).
fof(t28_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(1,A) => ( B = k5_numbers | k3_nat_d(k1_newton(B,A),B) = k1_newton(B,k7_nat_d(A,1)) ) ) ) ) )).
fof(t28_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m3_pnproc_1(C,A,B) => ! [D] : ( 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)) ) ) ) )).
fof(t28_polyeq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ~ ( B != k5_numbers & k4_polyeq_1(B,C,k5_numbers,k5_numbers,A) = k5_numbers & A != k4_xcmplx_0(k7_xcmplx_0(C,B)) & A != k5_numbers ) ) ) ) )).
fof(t28_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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) ) ) ) ) )).
fof(t28_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => k10_xtuple_0(k10_polyform(A,B)) = k8_polyform(A,B) ) ) )).
fof(t28_polynom1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( 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),k10_polynom1(A,B,C,k8_polynom1(A,B)),k8_polynom1(A,B)) ) ) ) )).
fof(t28_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_normsp_1(A,B,B),k9_polynom3(A)) ) ) )).
fof(t28_polynom5,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_polynom5(A,k9_polynom3(A),B),k9_polynom3(A)) ) ) )).
fof(t28_polynom7,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( 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] : ( 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),k10_polynom1(A,B,C,k4_polynom7(A,B,D))) ) ) ) ) )).
fof(t28_polynom8,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( k3_finseq_1(k4_polynom8(A,B,C)) = A & k1_matrix_0(k4_polynom8(A,B,C)) = 1 & ! [D] : ( v7_ordinal1(D) => ( ~ r1_xxreal_0(A,D) => k3_matrix_0(u1_struct_0(B),k4_polynom8(A,B,C),k1_nat_1(D,1),1) = k9_nat_1(u1_struct_0(B),C,D) ) ) ) ) ) ) ) )).
fof(t28_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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) ) ) ) ) ) ) )).
fof(t28_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(A,k5_numbers) => k2_power(A,k4_xcmplx_0(B)) = k7_xcmplx_0(1,k2_power(A,B)) ) ) ) )).
fof(t28_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v4_msualg_1(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,A) & v1_funct_1(F) & v1_partfun1(F,A) & v1_funcop_1(F) ) => ( ! [G] : ( m1_subset_1(G,A) => ? [H] : ( 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] : ( r2_hidden(G,k1_funct_1(u3_msualg_1(B,E),D)) => r2_hidden(k1_funct_1(k9_funct_6(k1_funct_1(k9_funct_6(F),D)),G),k4_card_3(k9_pralg_2(A,B,D,C))) ) ) ) ) ) ) ) ) )).
fof(t28_pre_poly,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k3_finseq_2(A)) => ! [C] : ~ ( r2_hidden(C,k4_finseq_1(k5_pre_poly(A,B))) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( r2_hidden(D,k4_finseq_1(B)) & r2_hidden(E,k4_finseq_1(k1_funct_1(B,D))) & C = k1_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) ) ) ) ) ) )).
fof(t28_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ( v2_pre_topc(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) => v2_pre_topc(A) ) ) )).
fof(t28_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t28_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(1,C) & r1_xxreal_0(k2_prepower(C,B),k2_prepower(C,A)) ) ) ) ) )).
fof(t28_prob_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( 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] : ( 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) = k5_numbers ) ) ) ) ) ) )).
fof(t28_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m1_prob_1(E,A,B) => ~ ( r1_prob_2(A,B,C,D,E) & ~ r1_xxreal_0(1,k3_funct_2(B,k1_numbers,C,D)) & ~ r1_xxreal_0(1,k3_funct_2(B,k1_numbers,C,E)) & r1_xxreal_0(1,k3_funct_2(B,k1_numbers,C,k6_prob_1(A,B,D,E))) ) ) ) ) ) ) )).
fof(t28_prob_3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => v3_prob_1(k2_prob_3(A,C)) ) ) )).
fof(t28_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => r1_tarski(B,k4_prob_4(A,B,C)) ) ) ) )).
fof(t28_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t28_projpl_1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & v5_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t28_pua2mss1,axiom,( ! [A] : ( l1_msualg_1(A) => ! [B] : ( l1_msualg_1(B) => ! [C] : ( l1_msualg_1(C) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t28_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(t28_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_qc_lang1(A))) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t28_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t28_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t28_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ! [E] : ( m1_trees_1(E,k9_xtuple_0(k2_qc_lang4(A,B))) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t28_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => k7_quatern2(A) = k25_quaterni(k25_quaterni(k20_quaterni(k7_xcmplx_0(k13_quaterni(A),k1_square_1(k28_quaterni(A))),k21_quaterni(k7_xcmplx_0(k14_quaterni(A),k1_square_1(k28_quaterni(A))),k3_quatern2)),k21_quaterni(k7_xcmplx_0(k15_quaterni(A),k1_square_1(k28_quaterni(A))),k11_quaterni)),k21_quaterni(k7_xcmplx_0(k16_quaterni(A),k1_square_1(k28_quaterni(A))),k12_quaterni)) ) )).
fof(t28_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k21_quaterni(k7_xcmplx_0(1,k1_square_1(k28_quaterni(A))),k27_quaterni(A)) = k6_quaterni(k3_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k28_quaterni(A))),k13_quaterni(A)),k4_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k28_quaterni(A))),k14_quaterni(A))),k4_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k28_quaterni(A))),k15_quaterni(A))),k4_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k28_quaterni(A))),k16_quaterni(A)))) ) )).
fof(t28_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ( k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k13_quaterni(A)),k1_square_1(k14_quaterni(A))),k1_square_1(k15_quaterni(A))),k1_square_1(k16_quaterni(A))) = k5_numbers => A = k17_quaterni ) ) )).
fof(t28_quofield,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(t28_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_random_1(D,A,B) => ! [E] : ( 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)) = k6_xcmplx_0(k8_random_1(A,B,C,D),k8_random_1(A,B,C,E)) ) ) ) ) ) ) )).
fof(t28_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_6(C,A,B) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t28_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ( ~ ( ~ r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(k4_xcmplx_0(k1_rat_1(A)),k2_rat_1(A)) ) & ~ ( ~ r1_xxreal_0(k4_xcmplx_0(k1_rat_1(A)),k2_rat_1(A)) & r1_xxreal_0(k4_xcmplx_0(1),A) ) ) ) )).
fof(t28_ratfunc1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & 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] : ( ( ~ v4_ratfunc1(B,A) & m1_ratfunc1(B,A) ) => ( v5_ratfunc1(B,A) <=> ? [C] : ( 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) ) ) ) ) )).
fof(t28_rcomp_3,axiom,( ! [A] : ( ( v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ~ ( ~ v4_xxreal_2(A) & ~ v3_xxreal_2(A) & A != k1_numbers ) ) )).
fof(t28_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => ( ( k9_nat_1(k1_numbers,k3_real_3(C),A) = k5_numbers & r1_xxreal_0(A,B) ) => k9_nat_1(k1_numbers,k4_real_3(C),B) = k5_numbers ) ) ) ) )).
fof(t28_real_lat,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(t28_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(A),k8_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t28_rearran1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,k1_numbers))) ) => ! [E] : ( ( v1_rearran1(E) & v2_rearran1(E) & v3_rearran1(E,k1_zfmisc_1(B)) & m2_finseq_1(E,k1_zfmisc_1(B)) ) => ( ( v1_partfun1(D,C) & k5_card_1(B) = k5_card_1(C) ) => ( r2_classes1(k18_rfunct_3(B,k15_valued_1(B,k1_numbers,k3_rearran1(C,B,E,D),A)),k18_rfunct_3(C,k15_valued_1(C,k1_numbers,D,A))) & k20_rfunct_3(B,k18_rfunct_3(B,k15_valued_1(B,k1_numbers,k3_rearran1(C,B,E,D),A)),B) = k20_rfunct_3(C,k18_rfunct_3(C,k15_valued_1(C,k1_numbers,D,A)),C) & k21_rfunct_3(B,k18_rfunct_3(B,k15_valued_1(B,k1_numbers,k3_rearran1(C,B,E,D),A)),B) = k21_rfunct_3(C,k18_rfunct_3(C,k15_valued_1(C,k1_numbers,D,A)),C) ) ) ) ) ) ) ) )).
fof(t28_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => r1_tarski(k6_subset_1(k3_relat_1(A,C),k3_relat_1(A,B)),k3_relat_1(A,k6_subset_1(C,B))) ) ) ) )).
fof(t28_relset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C))) => ! [F] : ! [G] : ( r2_hidden(k4_tarski(F,G),k4_relset_1(A,B,B,C,D,E)) <=> ? [H] : ( m1_subset_1(H,B) & r2_hidden(k4_tarski(F,H),D) & r2_hidden(k4_tarski(H,G),E) ) ) ) ) ) ) ) )).
fof(t28_revrot_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ 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) ) ) )).
fof(t28_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r2_rewrite1(A,B,C) => ( r2_hidden(B,k1_relat_1(A)) | B = C ) ) ) )).
fof(t28_rewrite2,axiom,( ! [A] : ! [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,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)))) ) )).
fof(t28_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_afinsq_1(D))) => ! [F] : ( 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,C,B,C) ) ) ) ) )).
fof(t28_rfinseq,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( ( 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] : ( 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) ) ) ) )).
fof(t28_rfinseq2,axiom,( ! [A] : ( 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) ) ) )).
fof(t28_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( v1_xcmplx_0(B) => ( B != k5_numbers => k4_rfunct_1(k24_valued_1(A,B)) = k24_valued_1(k4_rfunct_1(A),k5_xcmplx_0(B)) ) ) ) )).
fof(t28_rfunct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t28_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,k3_rfunct_3(A,k1_numbers)) => ( k3_finseq_1(C) != k5_numbers => ( r1_rfunct_3(A,k1_numbers,C,B) <=> r2_hidden(B,k1_relset_1(A,k14_rfunct_3(A,C))) ) ) ) ) ) )).
fof(t28_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_comseq_2(B) => v1_comseq_2(k1_valued_0(k1_numbers,B,A)) ) ) ) )).
fof(t28_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_funct_2(k4_ordinal1,k6_numbers,k4_rinfsup2(k1_valued_0(k6_numbers,A,B)),k1_valued_0(k6_numbers,k4_rinfsup2(A),B)) & k5_rinfsup2(k1_valued_0(k6_numbers,A,B)) = k5_rinfsup2(A) ) ) ) )).
fof(t28_rlaffin1,axiom,( ! [A] : ( ( ~ 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] : ( m1_rlvect_2(B,A) => r1_rlvect_2(A,k2_rlaffin1(A,B,1),B) ) ) )).
fof(t28_rlaffin2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( 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))) ) ) ) ) ) ) )).
fof(t28_rlaffin3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_rlaffin1(C,k15_euclid(A)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) => ! [E] : ( m2_rlaffin3(E,k15_euclid(A),C) => ! [F] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(t28_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ( r1_tarski(u1_struct_0(B),u1_struct_0(C)) => m1_rlsub_1(B,C) ) ) ) ) )).
fof(t28_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t28_rltopsp1,axiom,( ! [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) ) => ! [B] : ( ( v3_rltopsp1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( v1_xreal_0(C) => ( k9_complex1(C) = 1 => k1_convex1(A,B,C) = B ) ) ) ) )).
fof(t28_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t28_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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(k4_ordinal1,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)))) ) ) ) ) ) )).
fof(t28_rlvect_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_orders_1(B,A,k6_partfun1(A)) => ( ~ r2_hidden(k1_xboole_0,A) => k9_xtuple_0(B) = A ) ) ) )).
fof(t28_rlvect_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ( v1_rlvect_3(k8_domain_1(u1_struct_0(C),D,F,E),C) => ( D = E | D = F | E = F | A = k5_numbers | B = k5_numbers | v1_rlvect_3(k8_domain_1(u1_struct_0(C),D,k1_rlvect_1(C,F,A),k1_rlvect_1(C,E,B)),C) ) ) ) ) ) ) ) ) )).
fof(t28_rlvect_5,axiom,( ! [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_rlvect_5(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_rlsub_1(B,A) => r1_xxreal_0(k1_rlvect_5(B),k1_rlvect_5(A)) ) ) )).
fof(t28_rlvect_x,axiom,( ! [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) ) => ! [B] : ( 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) ) ) ) )).
fof(t28_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ( ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r1_struct_0(C,E) => r1_struct_0(D,E) ) ) => m1_rmod_2(C,A,D) ) ) ) ) ) )).
fof(t28_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t28_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t28_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t28_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) )).
fof(t28_robbins3,axiom,( ! [A] : ( ( ~ 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) ) ) ) )).
fof(t28_robbins4,axiom,( k6_lattices(k2_robbins4) = 3 )).
fof(t28_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) )).
fof(t28_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k2_xcmplx_0(k1_rpr_1(A,B),k1_rpr_1(A,k9_subset_1(A,k3_subset_1(A,B),C))) = k2_xcmplx_0(k1_rpr_1(A,C),k1_rpr_1(A,k9_subset_1(A,k3_subset_1(A,C),B))) ) ) ) )).
fof(t28_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( u1_struct_0(B) = C => v1_rlsub_1(C,A) ) ) ) ) )).
fof(t28_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t28_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => k1_rusub_3(A,C) = k1_rusub_3(B,D) ) ) ) ) ) )).
fof(t28_rusub_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t28_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( ~ 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))) ) ) )).
fof(t28_rvsum_1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t28_rvsum_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k11_rvsum_2(k2_finseq_2(A,B),k2_finseq_2(A,C)) = k2_finseq_2(A,k3_xcmplx_0(B,C)) ) ) ) )).
fof(t28_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) ) ) ) )).
fof(t28_scmbsort,axiom,( ! [A] : ( m1_scmfsa_2(A) => k2_sf_mastr(k1_scmbsort(A)) = k5_enumset1(k4_scmfsa_2(k5_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)) ) )).
fof(t28_scmfsa10,axiom,( ! [A] : ( 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) ) ) )).
fof(t28_scmfsa8a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( ( r5_scmfsa7b(A,k1_scmfsa_m(B),C) & r6_scmfsa7b(A,k1_scmfsa_m(B),C) ) => r1_extpro_1(k7_card_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(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))) ) ) ) ) )).
fof(t28_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( 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),k5_numbers) | ( r5_scmfsa7b(k3_scmfsa8b(E,C,D),B,A) & r6_scmfsa7b(k3_scmfsa8b(E,C,D),B,A) ) ) ) ) ) ) ) ) )).
fof(t28_scmfsa8c,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => k1_funct_1(k2_scmfsa8b(C,A,B),k1_nat_1(k5_card_1(B),2)) = k11_scmfsa_2(k1_nat_1(k1_nat_1(k5_card_1(A),k5_card_1(B)),3)) ) ) ) )).
fof(t28_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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,k7_card_1(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) ) ) ) ) ) ) )).
fof(t28_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ~ ( k2_compos_0(u1_compos_1(k1_scmfsa_2),A) = 6 & ! [B] : ( v7_ordinal1(B) => A != k11_scmfsa_2(B) ) ) ) )).
fof(t28_scmfsa_9,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(6,C) => r2_hidden(C,k2_afinsq_1(k2_scmfsa_9(A,B))) ) ) ) ) )).
fof(t28_scmfsa_m,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( 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] : ( ( 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] : ( m1_scmfsa_2(D) => k18_scmfsa_2(A,D) = k18_scmfsa_2(B,D) ) ) ) ) ) ) )).
fof(t28_scmisort,axiom,( ! [A] : ( m1_scmfsa_2(A) => k2_sf_mastr(k2_scmisort(A)) = k5_enumset1(k4_scmfsa_2(k5_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)) ) )).
fof(t28_scmpds_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ~ ( k2_compos_0(u1_compos_1(k1_scmpds_2),A) = 5 & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => A != k8_scmpds_2(B,C,D) ) ) ) ) ) )).
fof(t28_scmpds_5,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( 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,k5_numbers) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v2_compos_1(D,k1_scmpds_2) & v2_scmpds_4(D) ) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t28_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => k1_funct_1(k2_scmpds_6(A,B,C,D),k5_numbers) = k7_scmpds_2(A,B,k1_nat_1(k5_card_1(C),2)) ) ) ) ) )).
fof(t28_scmpds_7,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( 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,k5_numbers) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v2_compos_1(D,k1_scmpds_2) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(E) & 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) ) ) ) ) ) ) )).
fof(t28_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( v7_ordinal1(C) => 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) = k4_ordinal1 ) ) ) )).
fof(t28_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ( k3_tarski(A) = k1_xboole_0 => v1_scmyciel(A) ) ) )).
fof(t28_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t28_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,k32_valued_1(k4_ordinal1,k1_numbers,B)),k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) ) )).
fof(t28_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & v2_comseq_2(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => k1_seq_2(k55_valued_1(k4_ordinal1,k2_numbers,k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B))) = k9_complex1(k2_xcmplx_0(k3_comseq_2(A),k3_comseq_2(B))) ) ) )).
fof(t28_seq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( r1_xxreal_0(k5_numbers,A) & ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,B,C) = k7_xcmplx_0(1,k2_xcmplx_0(C,A)) ) ) => v2_comseq_2(B) ) ) ) )).
fof(t28_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( m1_subset_1(C,A) => ( r2_relset_1(k4_ordinal1,k1_numbers,k10_seqfunc(A,k5_seqfunc(A,B),C),k56_valued_1(k4_ordinal1,k1_numbers,k10_seqfunc(A,B,C))) & r2_relset_1(k4_ordinal1,k1_numbers,k10_seqfunc(A,k4_seqfunc(A,B),C),k32_valued_1(k4_ordinal1,k1_numbers,k10_seqfunc(A,B,C))) ) ) ) ) )).
fof(t28_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_seq_2(A) & m2_valued_0(B,k1_numbers,A) ) => v2_seq_2(B) ) ) ) )).
fof(t28_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,A,C)) & k9_nat_1(k1_numbers,B,C) = k1_power(C,k9_nat_1(k1_numbers,A,C)) ) ) & v2_comseq_2(B) ) => ( r1_xxreal_0(1,k1_seq_2(B)) | v1_series_1(A) ) ) ) ) )).
fof(t28_series_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( k2_xcmplx_0(k2_xcmplx_0(A,B),C) = k5_numbers => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(k5_numbers,C) | r1_xxreal_0(k3_xcmplx_0(6,k1_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)) ) ) ) ) ) )).
fof(t28_series_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(D,C)),k3_xcmplx_0(k3_square_1(k2_xcmplx_0(k1_square_1(A),k1_square_1(D))),k3_square_1(k2_xcmplx_0(k1_square_1(B),k1_square_1(C))))) ) ) ) ) )).
fof(t28_setfam_1,axiom,( ! [A] : ! [B] : k3_tarski(k3_setfam_1(A,B)) = k3_xboole_0(k3_tarski(A),k3_tarski(B)) )).
fof(t28_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( v7_ordinal1(C) => m1_subset_1(a_3_3_setlim_1(A,B,C),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) )).
fof(t28_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(C) => v2_prob_1(k7_setlim_2(A,C,B)) ) ) ) )).
fof(t28_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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) & v1_setwiseo(C,B) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => k7_setwiseo(A,B,C,k1_setwiseo(A),D) = k4_binop_1(B,C) ) ) ) ) ) )).
fof(t28_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( m2_finseq_1(F,A) => ( ( v1_setwiseo(C,A) & v1_setwiseo(D,B) & k3_funct_2(A,B,E,k4_binop_1(A,C)) = k4_binop_1(B,D) & ! [G] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,A) => k3_funct_2(A,B,E,k5_binop_1(A,C,G,H)) = k5_binop_1(B,D,k3_funct_2(A,B,E,G),k3_funct_2(A,B,E,H)) ) ) ) => k3_funct_2(A,B,E,k1_finsop_1(A,F,C)) = k1_finsop_1(B,k4_finseqop(A,B,F,E),D) ) ) ) ) ) ) ) )).
fof(t28_sf_mastr,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => k2_sf_mastr(k11_compos_1(k1_scmfsa_2,A)) = k1_sf_mastr(A) ) )).
fof(t28_sfmastr3,axiom,( ! [A] : ( ( v1_ami_2(A) & ~ v1_scmfsa_m(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( m1_scmfsa_2(D) => r1_tarski(k6_scmfsa_m(B,C,A),k2_sf_mastr(k3_sfmastr3(B,C,A,D))) ) ) ) ) )).
fof(t28_sgraph1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_sgraph1(B,A) => ! [C] : ? [D] : ( v1_finset_1(D) & D = a_3_0_sgraph1(A,B,C) & k4_sgraph1(A,B,C) = k5_card_1(D) ) ) ) )).
fof(t28_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & v8_robbins1(A) & v9_sheffer1(A) & l3_sheffer1(A) ) => v12_sheffer1(A) ) )).
fof(t28_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t28_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t28_simplex1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t28_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( k2_xcmplx_0(k1_square_1(k1_funct_1(k18_sin_cos,A)),k1_square_1(k1_funct_1(k16_sin_cos,A))) = 1 & k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,A),k1_funct_1(k18_sin_cos,A)),k3_xcmplx_0(k1_funct_1(k16_sin_cos,A),k1_funct_1(k16_sin_cos,A))) = 1 ) ) )).
fof(t28_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k2_xcmplx_0(k1_funct_1(k5_sin_cos2,A),k1_funct_1(k5_sin_cos2,B)) = k7_xcmplx_0(k1_funct_1(k1_sin_cos2,k2_xcmplx_0(A,B)),k3_xcmplx_0(k1_funct_1(k3_sin_cos2,A),k1_funct_1(k3_sin_cos2,B))) & k6_xcmplx_0(k1_funct_1(k5_sin_cos2,A),k1_funct_1(k5_sin_cos2,B)) = k7_xcmplx_0(k1_funct_1(k1_sin_cos2,k6_xcmplx_0(A,B)),k3_xcmplx_0(k1_funct_1(k3_sin_cos2,A),k1_funct_1(k3_sin_cos2,B))) ) ) ) )).
fof(t28_sin_cos3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k15_sin_cos(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A),k7_complex1)) = 1 ) )).
fof(t28_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k17_sin_cos(k7_xcmplx_0(A,2)) != k5_numbers => k1_sin_cos4(k7_xcmplx_0(A,2)) = k7_xcmplx_0(k6_xcmplx_0(1,k19_sin_cos(A)),k17_sin_cos(A)) ) ) )).
fof(t28_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,k3_xcmplx_0(2,k28_sin_cos)) & k17_sin_cos(A) = 1 ) => A = k7_xcmplx_0(k28_sin_cos,2) ) ) )).
fof(t28_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(1,k1_square_1(A)) & ~ r1_xxreal_0(1,k1_square_1(B)) & k3_xcmplx_0(A,B) = 1 ) ) ) )).
fof(t28_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_sin_cos2(k3_xcmplx_0(5,A)),k3_xcmplx_0(2,k2_sin_cos2(k3_xcmplx_0(3,A)))),k2_sin_cos2(A)),k2_xcmplx_0(k2_xcmplx_0(k2_sin_cos2(k3_xcmplx_0(7,A)),k3_xcmplx_0(2,k2_sin_cos2(k3_xcmplx_0(5,A)))),k2_sin_cos2(k3_xcmplx_0(3,A)))) = k7_xcmplx_0(k2_sin_cos2(k3_xcmplx_0(3,A)),k2_sin_cos2(k3_xcmplx_0(5,A))) ) )).
fof(t28_sin_cos9,axiom,( k3_relat_1(k2_partfun1(k1_numbers,k1_numbers,k2_sin_cos9,k1_rcomp_1(k4_xcmplx_0(1),1)),k2_partfun1(k1_numbers,k1_numbers,k27_sin_cos,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos)))) = k1_partfun2(k1_numbers,k1_rcomp_1(k4_xcmplx_0(1),1)) )).
fof(t28_sincos10,axiom,( k2_relset_1(k1_numbers,k4_sincos10) = k4_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)) )).
fof(t28_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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(k1_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,k1_nat_1(A,1))) ) => k17_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),B,k1_nat_1(A,1))) = k17_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),B,k1_nat_1(A,2))) ) ) ) )).
fof(t28_sppol_2,axiom,( ! [A] : ( 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)) ) ) )).
fof(t28_sprect_3,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) & r1_xxreal_0(1,B) & ~ r1_xxreal_0(k3_finseq_1(k2_goboard2(A)),B) & k20_pscomp_1(k3_topreal1(2,A)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),B,k1_matrix_0(k2_goboard2(A))) ) ) )).
fof(t28_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t28_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) & k3_square_1(A) = k3_square_1(B) ) => A = B ) ) ) )).
fof(t28_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(t28_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( k3_stirl2_1(k5_numbers,A) = 1 <=> A = k5_numbers ) ) )).
fof(t28_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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))) ) ) ) )).
fof(t28_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ! [C] : ( m1_subset_1(C,A) => r2_hidden(C,B) ) => A = B ) ) )).
fof(t28_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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))) ) ) ) )).
fof(t28_supinf_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => ! [C] : ( ( 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(k6_numbers,A,B,C),k1_numbers) ) ) ) ) ) )).
fof(t28_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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,E) & ~ r1_orders_2(B,C,F) & ~ r1_orders_2(B,D,F) & k8_group_1(A,k1_symsp_1(A,B,C,E,F),k1_symsp_1(A,B,D,F,E)) != k8_group_1(A,k1_symsp_1(A,B,E,C,D),k1_symsp_1(A,B,F,D,C)) ) ) ) ) ) ) ) )).
fof(t28_sysrel,axiom,( ! [A] : ( v1_relat_1(A) => k1_sysrel(A) = k4_relat_1(k9_xtuple_0(k1_sysrel(A))) ) )).
fof(t28_taxonom1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t28_taylor_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( 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,k1_nat_1(A,1),k2_rcomp_1(D,E)) ) => ( r1_xxreal_0(E,D) | ! [F] : ( v1_xreal_0(F) => ! [G] : ( ( 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] : ( v1_xreal_0(H) => k1_funct_1(G,H) = k6_xcmplx_0(k6_xcmplx_0(k1_funct_1(B,D),k9_nat_1(k1_numbers,k3_series_1(k6_taylor_1(B,C,H,D)),A)),k7_xcmplx_0(k3_xcmplx_0(F,k1_newton(k6_xcmplx_0(D,H),k1_nat_1(A,1))),k2_newton(k1_nat_1(A,1)))) ) & k6_xcmplx_0(k6_xcmplx_0(k1_funct_1(B,D),k9_nat_1(k1_numbers,k3_series_1(k6_taylor_1(B,C,E,D)),A)),k7_xcmplx_0(k3_xcmplx_0(F,k1_newton(k6_xcmplx_0(D,E),k1_nat_1(A,1))),k2_newton(k1_nat_1(A,1)))) = k5_numbers ) => ( r2_fdiff_1(G,k2_rcomp_1(D,E)) & k1_funct_1(G,E) = k5_numbers & k1_funct_1(G,D) = k5_numbers & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,G,k1_rcomp_1(D,E))) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,k2_rcomp_1(D,E)) => k1_fdiff_1(G,H) = k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(B,k2_rcomp_1(D,E)),k1_nat_1(A,1)),H),k1_newton(k6_xcmplx_0(D,H),A)),k2_newton(A))),k7_xcmplx_0(k3_xcmplx_0(F,k1_newton(k6_xcmplx_0(D,H),A)),k2_newton(A))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t28_taylor_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(A,k5_numbers) => ( v2_comseq_2(k3_series_1(k1_taylor_2(k16_sin_cos,k2_rcomp_1(k4_xcmplx_0(A),A),B))) & k1_funct_1(k16_sin_cos,B) = k4_series_1(k1_taylor_2(k16_sin_cos,k2_rcomp_1(k4_xcmplx_0(A),A),B)) & v2_comseq_2(k3_series_1(k1_taylor_2(k18_sin_cos,k2_rcomp_1(k4_xcmplx_0(A),A),B))) & k1_funct_1(k18_sin_cos,B) = k4_series_1(k1_taylor_2(k18_sin_cos,k2_rcomp_1(k4_xcmplx_0(A),A),B)) ) ) ) ) )).
fof(t28_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t28_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(t28_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v4_tdlat_3(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t28_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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)) ) ) ) ) )).
fof(t28_tex_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ( k3_tex_1(A,B) = k2_tex_1(A) <=> A = k6_domain_1(A,B) ) ) ) )).
fof(t28_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( v2_tex_2(B,A) & ! [C] : ( ( ~ v2_struct_0(C) & v1_pre_topc(C) & v1_tdlat_3(C) & m1_pre_topc(C,A) ) => B != u1_struct_0(C) ) ) ) ) )).
fof(t28_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t28_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) )).
fof(t28_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( m1_pre_topc(C,B) => ( ( ~ r1_tsep_1(B,D) & ~ r1_tsep_1(D,B) ) | ( k2_tsep_1(A,B,k1_tsep_1(A,C,D)) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) & k2_tsep_1(A,B,k1_tsep_1(A,D,C)) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) ) ) ) ) ) ) ) )).
fof(t28_toler_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( ! [E] : ( 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) ) ) )).
fof(t28_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t28_topalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_borsuk_2(F,A,D,E) => ! [G] : ( m1_borsuk_2(G,A,D,E) => ! [H] : ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t28_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t28_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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(k5_numbers,1) => m1_borsuk_2(B,A,k2_topalg_6(A,B),k3_topalg_6(A,B)) ) ) ) )).
fof(t28_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(t28_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k2_topgen_1(A,B),k2_pre_topc(A,B)) ) ) )).
fof(t28_topgen_2,axiom,( ! [A] : ! [B] : ( r2_hidden(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(t28_topgen_4,axiom,( ! [A] : ! [B] : ~ ( A != k1_xboole_0 & B != k1_xboole_0 & k2_xboole_0(k3_tarski(A),k3_tarski(B)) != k3_tarski(k2_setfam_1(A,B)) ) )).
fof(t28_topgen_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t28_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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) ) ) ) ) ) )).
fof(t28_topreal1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ~ ( v5_topreal1(A) & ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ r1_topreal1(k15_euclid(2),B,C,A) ) ) ) ) )).
fof(t28_topreal4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( v2_topreal4(C,k15_euclid(2)) & r2_hidden(A,C) & B = a_2_1_topreal4(A,C) ) => C = B ) ) ) ) )).
fof(t28_topreal8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) )).
fof(t28_topreal9,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,k4_topreal9(A,B,C)) => r1_tarski(k4_topreal9(A,B,D),k4_topreal9(A,B,C)) ) ) ) ) ) )).
fof(t28_topreala,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k19_euclid(A,B) = k4_funct_4(1,2,A,B) ) ) )).
fof(t28_toprealc,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_rlvect_1(A,k5_algstr_0(A,B,C),C) = B ) ) ) )).
fof(t28_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ( k12_euclid(k5_algstr_0(k15_euclid(A),B,C)) = k5_numbers <=> B = C ) ) ) ) )).
fof(t28_tops_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_tops_1(A,B)) <=> ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t28_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( m1_pre_topc(C,A) => ( v2_tops_2(B,A) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(C)))) => ( D = B => v2_tops_2(D,C) ) ) ) ) ) ) )).
fof(t28_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_tops_1(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( C != k1_xboole_0 & v3_pre_topc(C,A) & ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t28_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => v2_transgeo(k6_partfun1(u1_struct_0(A)),A) ) )).
fof(t28_trees_1,axiom,( k2_trees_1(k5_numbers) = k1_tarski(k1_xboole_0) )).
fof(t28_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_2(B,A) => ? [C] : ( v2_trees_2(C,A) & m1_trees_2(C,A) & r1_tarski(B,C) ) ) ) )).
fof(t28_trees_3,axiom,( ! [A] : ( v4_trees_3(k9_finseq_1(A)) <=> ( ~ v1_xboole_0(A) & v1_trees_1(A) ) ) )).
fof(t28_trees_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_trees_3(E,k2_zfmisc_1(A,B)) ) => ! [F] : ( ( ~ v1_xboole_0(F) & m1_trees_3(F,B) ) => ! [G] : ( m2_finseq_1(G,E) => ! [H] : ( m2_finseq_1(H,F) => ( ( k4_finseq_1(H) = k4_finseq_1(G) & ! [I] : ( v7_ordinal1(I) => ( r2_hidden(I,k4_finseq_1(G)) => ! [J] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t28_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t28_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t28_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(D))) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t28_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(t28_turing_1,axiom,( r1_tarski(k9_xtuple_0(k15_comput_1),k4_finseq_2(2,k4_ordinal1)) )).
fof(t28_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => r2_hidden(k4_tarski(k10_finseq_1(A,B),k15_twoscomp),k3_msafree2(k34_twoscomp(A,B))) ) ) )).
fof(t28_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ( r1_nat_d(B,A) => r1_tarski(k2_uniroots(B),k2_uniroots(A)) ) ) ) )).
fof(t28_uproots,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l5_algstr_0(A) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k10_polynom3(A),k2_algseq_1(A,k5_struct_0(A))) ) )).
fof(t28_urysohn2,axiom,( r1_tarski(k2_urysohn1,k1_xxreal_1(k5_numbers,1)) )).
fof(t28_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( m1_valuat_1(F,A,B) => ( r1_valuat_1(A,B,E,F,D) => ( r2_hidden(C,k24_qc_lang1(A,E)) | ! [G] : ( m2_funct_2(G,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ( ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t28_valued_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ! [C] : ( v7_ordinal1(C) => r2_hidden(k9_nat_1(A,B,C),k2_relset_1(A,B)) ) ) ) )).
fof(t28_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) ) => k61_valued_1(A,k5_numbers) = A ) )).
fof(t28_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => k9_xtuple_0(k14_valued_2(B,A)) = k9_xtuple_0(B) ) ) )).
fof(t28_vectsp10,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t28_vectsp11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( ~ 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] : ( ( 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)))))) ) ) ) ) ) )).
fof(t28_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t28_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) )).
fof(t28_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r1_struct_0(C,E) => r1_struct_0(D,E) ) ) => m1_vectsp_4(C,A,D) ) ) ) ) ) )).
fof(t28_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m1_vectsp_4(E,A,B) => m1_vectsp_4(k1_vectsp_5(A,B,D,k2_vectsp_5(A,B,C,E)),A,k2_vectsp_5(A,B,k1_vectsp_5(A,B,C,D),k1_vectsp_5(A,B,D,E))) ) ) ) ) ) )).
fof(t28_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t28_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( 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) ) ) ) ) )).
fof(t28_vfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,u1_struct_0(C)))) ) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t28_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t28_waybel10,axiom,( ! [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) ) => 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)) ) )).
fof(t28_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => B = k1_waybel11(A,k4_waybel11(A,B)) ) ) )).
fof(t28_waybel13,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) ) )).
fof(t28_waybel14,axiom,( ! [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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(k5_waybel11(A)))) => ( C = B => ( ! [D] : ( 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,k1_yellow_1(k5_waybel11(A))) & C != u1_struct_0(A) ) ) ) ) ) ) )).
fof(t28_waybel15,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t28_waybel16,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_orders_2(A,B,C) & ! [E] : ( 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) ) ) ) ) ) )).
fof(t28_waybel17,axiom,( ! [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] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) ) )).
fof(t28_waybel19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) )).
fof(t28_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t28_waybel21,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) )).
fof(t28_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_waybel23(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => k1_yellow_0(k5_yellow_0(A,B),C) = k1_yellow_0(A,C) ) ) ) )).
fof(t28_waybel24,axiom,( ! [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] : ( ( 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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_waybel24(A,B)))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => k7_relat_1(k1_yellow_0(k5_yellow_1(u1_struct_0(A),B),C),D) = a_4_4_waybel24(A,B,C,D) ) ) ) ) )).
fof(t28_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & v1_waybel25(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v6_pre_topc(B) & l1_pre_topc(B) ) => ( r2_borsuk_3(A,B) => v1_waybel25(B) ) ) ) )).
fof(t28_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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)) ) ) ) ) )).
fof(t28_waybel27,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v3_orders_2(D) & v4_orders_2(D) & v5_orders_2(D) & l1_orders_2(D) ) => ! [E] : ( ( ~ v2_struct_0(E) & v3_orders_2(E) & v4_orders_2(E) & v5_orders_2(E) & l1_orders_2(E) ) => ! [F] : ( ( ~ v2_struct_0(F) & v3_orders_2(F) & v4_orders_2(F) & v5_orders_2(F) & l1_orders_2(F) ) => ! [G] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t28_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k5_waybel11(A)) => r2_hidden(B,k4_waybel28(A)) ) ) ) )).
fof(t28_waybel29,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & l1_pre_topc(A) ) => ( v3_waybel_3(k1_yellow_1(u1_pre_topc(A))) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v3_pre_topc(C,A) & m1_connsp_2(C,A,B) ) => ? [D] : ( v3_pre_topc(D,k1_waybel29(k1_yellow_1(u1_pre_topc(A)))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k1_waybel29(k1_yellow_1(u1_pre_topc(A)))))) & r2_hidden(C,D) & m1_connsp_2(k1_setfam_1(D),A,B) ) ) ) ) ) )).
fof(t28_waybel30,axiom,( ! [A] : ( ( 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] : ( ( v13_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t28_waybel31,axiom,( ! [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) ) => r1_ordinal1(k1_waybel31(A),k1_waybel31(k1_yellow_1(k5_waybel11(A)))) ) )).
fof(t28_waybel34,axiom,( ! [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] : ( ( 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] : ( ( 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] : ( ( v4_waybel11(D) & m1_yellow_9(D,B) ) => ! [E] : ( ( v4_waybel11(E) & m1_yellow_9(E,A) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t28_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ! [C] : ( 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))) ) ) ) ) )).
fof(t28_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(t28_waybel_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & v2_lattice3(A) & l1_orders_2(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t28_waybel_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k4_yellow_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_yellow_1(A,B))) => ( r1_orders_2(k4_yellow_1(A,B),C,D) <=> ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t28_waybel_4,axiom,( ! [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] : ( ( v5_waybel_4(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ( ( 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),k1_yellow_1(k7_waybel_0(A)),k7_waybel_4(A,B),k7_waybel_4(A,C)) ) ) ) ) )).
fof(t28_waybel_5,axiom,( ! [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) ) => ( v3_waybel_3(A) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t28_waybel_6,axiom,( ! [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) ) => k4_waybel_6(A) = k3_waybel_6(A) ) )).
fof(t28_waybel_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ( r1_waybel_3(k1_yellow_1(u1_pre_topc(A)),B,C) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_subset_1(D,u1_struct_0(k2_yellow_1(u1_struct_0(A)))) & v2_waybel_0(D,k2_yellow_1(u1_struct_0(A))) & v13_waybel_0(D,k2_yellow_1(u1_struct_0(A))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k2_yellow_1(u1_struct_0(A))))) ) => ~ ( r2_hidden(B,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,C) & r1_waybel_7(A,D,E) ) ) ) ) ) ) ) ) )).
fof(t28_waybel_8,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k2_yellow_1(A))) => ( v1_finset_1(B) <=> v1_waybel_3(B,k2_yellow_1(A)) ) ) )).
fof(t28_waybel_9,axiom,( ! [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) & v1_compts_1(A) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ! [C] : ( 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) ) ) ) )).
fof(t28_weddwitt,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ~ r1_xxreal_0(k5_card_1(u1_struct_0(k5_weddwitt(A,B))),1) ) ) )).
fof(t28_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [C] : ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t28_wellord1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( ( v2_wellord1(B) & r1_tarski(A,k1_relat_1(B)) ) => ( ~ ( A != k1_relat_1(B) & ! [C] : ~ ( r2_hidden(C,k1_relat_1(B)) & A = k1_wellord1(B,C) ) ) <=> ! [C] : ( r2_hidden(C,A) => ! [D] : ( r2_hidden(k4_tarski(D,C),B) => r2_hidden(D,A) ) ) ) ) ) )).
fof(t28_wsierp_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ? [C] : ( v1_int_1(C) & ? [D] : ( v1_int_1(D) & k3_int_2(A,B) = k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D)) ) ) ) ) )).
fof(t28_xboole_1,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => k3_xboole_0(A,B) = A ) )).
fof(t28_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k5_xboolean(A,k7_xboolean(A,B)) = k6_xboolean(B,A) ) ) )).
fof(t28_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k2_xcmplx_0(A,C) = k2_xcmplx_0(k2_xcmplx_0(A,B),k6_xcmplx_0(C,B)) ) ) ) )).
fof(t28_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(B,k5_numbers) & k2_xcmplx_0(A,B) = k5_numbers ) => A = k5_numbers ) ) ) )).
fof(t28_xtuple_0,axiom,( ! [A] : ! [B] : r1_tarski(k10_xtuple_0(k3_xboole_0(A,B)),k3_xboole_0(k10_xtuple_0(A),k10_xtuple_0(B))) )).
fof(t28_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r1_xxreal_0(B,A) & r1_xxreal_0(C,A) ) => r1_xxreal_0(k4_xxreal_0(B,C),A) ) ) ) ) )).
fof(t28_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( r1_xxreal_0(A,B) => k4_xxreal_1(B,A) = k1_xboole_0 ) ) ) )).
fof(t28_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( ~ r1_xxreal_0(B,A) => k2_xxreal_2(k4_xxreal_1(A,B)) = A ) ) ) )).
fof(t28_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( r1_xxreal_0(k5_numbers,A) => ( r1_xxreal_0(k1_xxreal_0,A) | B = k3_xxreal_3(k1_xxreal_3(B,A),A) ) ) ) ) )).
fof(t28_yellow10,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( 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))) ) ) ) ) )).
fof(t28_yellow12,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t28_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v2_yellow13(A) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v5_pre_topc(k4_waybel_1(A,B),A,A) ) ) )).
fof(t28_yellow14,axiom,( ! [A] : ( l1_pre_topc(A) => ! [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_compts_1(A) ) => v1_compts_1(B) ) ) ) )).
fof(t28_yellow15,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v8_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)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_hidden(k1_setfam_1(a_2_1_yellow15(A,C)),B) ) ) ) ) )).
fof(t28_yellow16,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k4_yellow_1(A,B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k4_yellow_1(A,B)))) => ( r2_lattice3(k4_yellow_1(A,B),D,C) <=> ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t28_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t28_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(B,A) <=> ! [C] : ( ( ~ v1_xboole_0(C) & v2_waybel_0(C,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(C,k2_yellow_1(k2_struct_0(A))) & v3_waybel_7(C,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))))) ) => ( r2_hidden(B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_waybel_7(A,C,D) => r2_hidden(D,B) ) ) ) ) ) ) ) )).
fof(t28_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v3_altcat_2(C,A) & m1_altcat_2(C,A) ) => ! [D] : ( l2_functor0(D,A,B) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t28_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( k1_yellow_0(A,B) = k15_lattice3(k14_lattice3(A),B) & k2_yellow_0(A,B) = k16_lattice3(k14_lattice3(A),B) ) ) )).
fof(t28_yellow_1,axiom,( ! [A] : ! [B] : ( l1_orders_2(B) => k1_funct_2(A,u1_struct_0(B)) = u1_struct_0(k5_yellow_1(A,B)) ) )).
fof(t28_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r2_yellow_0(A,B) ) => v3_lattice3(A) ) ) )).
fof(t28_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t28_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t28_yellow_5,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ~ r1_yellow_5(A,B,k3_yellow_0(A)) ) ) )).
fof(t28_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( 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))) ) ) ) )).
fof(t28_yellow_7,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( 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)))) ) ) ) )).
fof(t28_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v9_pre_topc(A) => ( v6_waybel_3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(B,k1_tops_1(A,C)) & v2_compts_1(C,A) ) ) ) ) ) )).
fof(t28_yellow_9,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t28_zf_fund1,axiom,( 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 )).
fof(t28_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( k1_funct_1(A,1) = 4 => v6_zf_lang(A) ) ) )).
fof(t28_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( 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)) ) ) ) )).
fof(t28_zfmisc_1,axiom,( ! [A] : ! [B] : k2_zfmisc_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k4_tarski(A,B)) )).
fof(t28_zfrefle1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( v3_ordinal1(B) & m1_subset_1(B,A) ) => ! [C] : ( ( 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] : ( ( v3_ordinal1(D) & m1_subset_1(D,A) ) => ~ ( r2_hidden(B,D) & k4_ordinal4(A,C,D) = D ) ) ) ) ) ) )).
fof(t28_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_zmodul01(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ( ( E = C & F = B ) => k3_rlvect_1(D,E,F) = k3_rlvect_1(A,C,B) ) ) ) ) ) ) ) )).
fof(t28_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( m1_zmodul02(C,A) => ! [D] : ( m1_zmodul02(D,A) => r1_zmodul02(A,k22_zmodul02(A,B,k22_zmodul02(A,C,D)),k22_zmodul02(A,k22_zmodul02(A,B,C),D)) ) ) ) ) )).
fof(t28_zmodul03,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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) & v1_zmodul03(B) & l1_zmodul01(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k3_rlvect_1(k12_zmodul02(A,B),k13_zmodul02(A,B,C),k13_zmodul02(A,B,D)) = k13_zmodul02(A,B,k3_rlvect_1(B,C,D)) ) ) ) ) )).
fof(t290_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) )).
fof(t291_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) )).
fof(t292_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) )).
fof(t293_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) )).
fof(t294_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) )).
fof(t295_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) )).
fof(t296_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) )).
fof(t297_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(D,C) & ~ r1_xxreal_0(B,A) & k6_subset_1(k4_xxreal_1(C,B),k4_xxreal_1(A,D)) != k2_xboole_0(k3_xxreal_1(C,A),k2_xxreal_1(D,B)) ) ) ) ) ) )).
fof(t298_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(C,D) => ( r1_xxreal_0(B,A) | k6_subset_1(k2_xxreal_1(C,B),k4_xxreal_1(A,D)) = k2_xboole_0(k1_xxreal_1(C,A),k2_xxreal_1(D,B)) ) ) ) ) ) ) )).
fof(t299_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(A,B) => ( r1_xxreal_0(D,C) | k6_subset_1(k3_xxreal_1(C,B),k4_xxreal_1(A,D)) = k2_xboole_0(k3_xxreal_1(C,A),k1_xxreal_1(D,B)) ) ) ) ) ) ) )).
fof(t29_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t29_abcmiz_1,axiom,( r2_hidden(k2_pre_poly(k2_abcmiz_1),k4_abcmiz_1) )).
fof(t29_abcmiz_a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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) ) ) ) )).
fof(t29_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(A,k5_numbers) => k9_complex1(A) = k4_xcmplx_0(A) ) ) )).
fof(t29_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_aff_1(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ( r2_aff_1(A,B,C,D) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t29_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t29_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( 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 ) ) ) ) )).
fof(t29_afinsq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_finset_1(B) & v6_membered(B) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t29_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k13_afproj(A))) => ! [E] : ( m1_subset_1(E,u2_incsp_1(k13_afproj(A))) => ( ( D = k5_afproj(A,C) & E = k4_tarski(k6_afproj(A,B),2) & v1_aff_1(C,A) & v1_aff_4(B,A) ) => ( r1_incsp_1(k13_afproj(A),D,E) <=> r1_aff_4(A,C,B) ) ) ) ) ) ) ) )).
fof(t29_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_afvect0(A,C,k1_afvect0(A,C,B)) = B ) ) ) )).
fof(t29_algspec1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r1_algspec1(A,B,C) <=> ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t29_algstr_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => m1_algstr_4(k14_algstr_4(B),k14_algstr_4(A)) ) )).
fof(t29_altcat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_altcat_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => m1_subset_1(C,u1_struct_0(A)) ) ) ) )).
fof(t29_altcat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v8_altcat_3(B,A) & v8_altcat_3(C,A) ) => r2_altcat_3(A,B,C) ) ) ) ) )).
fof(t29_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t29_ami_3,axiom,( ! [A] : ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(A,u1_struct_0(k1_ami_3)) ) ) )).
fof(t29_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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)) ) ) ) ) ) )).
fof(t29_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_analmetr(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k2_analmetr(A,B,C))) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t29_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( r1_analmetr(A,F,G) => ( r3_analmetr(A,B,D,C,E,F,G) <=> ( r1_analort(A,F,G,B,D,C,E) | r1_analort(A,F,G,B,D,E,C) ) ) ) ) ) ) ) ) ) ) )).
fof(t29_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => ~ ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( 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 = k5_numbers & F = k5_numbers & G = k5_numbers ) ) ) ) ) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ? [F] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & 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] : ( ( ~ 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) ) ) ) ) )).
fof(t29_aofa_000,axiom,( ! [A] : ( ( ~ 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] : ( m1_freealg(B,A) => B != k1_xboole_0 ) ) ) )).
fof(t29_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ( k4_finseq_1(k7_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H),k9_finseq_1(I))) = k2_finseq_1(9) & k1_funct_1(k7_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H),k9_finseq_1(I)),1) = A & k1_funct_1(k7_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H),k9_finseq_1(I)),2) = B & k1_funct_1(k7_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H),k9_finseq_1(I)),3) = C & k1_funct_1(k7_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H),k9_finseq_1(I)),4) = D & k1_funct_1(k7_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H),k9_finseq_1(I)),5) = E & k1_funct_1(k7_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H),k9_finseq_1(I)),6) = F & k1_funct_1(k7_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H),k9_finseq_1(I)),7) = G & k1_funct_1(k7_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H),k9_finseq_1(I)),8) = H & k1_funct_1(k7_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H),k9_finseq_1(I)),9) = I ) )).
fof(t29_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( m2_subset_1(F,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => ! [G] : ( m2_pboole(G,u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D)) => ( ( r1_msualg_3(A,C,D,G) & r8_pboole(u1_struct_0(A),F,k1_msafree(u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D),u4_aofa_a00(A,B,C,E),G)) ) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,k1_funct_1(u3_msualg_1(A,C),H)) => k15_aofa_a00(A,B,C,D,H,I,F) = k3_funct_2(k1_funct_1(u3_msualg_1(A,C),H),k1_funct_1(u3_msualg_1(A,D),H),k2_msafree4(u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D),G,H),I) ) ) ) ) ) ) ) ) ) ) )).
fof(t29_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [E] : ( ( v1_aofa_i00(E,A,B,D) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),D) ) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),E) => ! [G] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t29_armstrng,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ! [C] : ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t29_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ~ ( ~ r2_hidden(A,k4_ordinal1) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( A = k4_tarski(B,C) & r1_arytm_3(B,C) & C != k1_xboole_0 & C != 1 ) ) ) ) ) )).
fof(t29_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(A,k8_asympt_0(B)) => r2_hidden(B,k8_asympt_0(A)) ) ) ) )).
fof(t29_asympt_1,axiom,( ? [A] : ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v4_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & ? [B] : ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v4_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & r2_funct_2(k4_ordinal1,k1_numbers,A,k1_asympt_1(2,1,k5_numbers)) & r2_funct_2(k4_ordinal1,k1_numbers,B,k1_asympt_1(2,2,k5_numbers)) & r1_tarski(k6_asympt_0(A),k6_asympt_0(B)) & k6_asympt_0(A) != k6_asympt_0(B) ) ) )).
fof(t29_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t29_bagorder,axiom,( ! [A] : ( v7_ordinal1(A) => u1_struct_0(k4_yellow_1(A,k7_funcop_1(A,k11_dickson))) = k15_pre_poly(A) ) )).
fof(t29_bcialg_1,axiom,( ! [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] : ( 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 ) ) ) )).
fof(t29_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v10_bcialg_1(B,A) <=> k2_bcialg_1(A,k2_bcialg_1(A,B)) = B ) ) ) )).
fof(t29_bcialg_3,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)))) ) ) ) ) )).
fof(t29_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t29_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t29_bcialg_6,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( v1_bcialg_6(B,A) & k4_bcialg_6(A,B) = D ) => ( r2_hidden(k3_bcialg_6(A,C,B),k4_bcialg_1(A)) <=> r1_int_1(D,C) ) ) ) ) ) ) )).
fof(t29_bciideal,axiom,( ! [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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) )).
fof(t29_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k9_complex1(k2_bhsp_1(A,B,C)),k3_xcmplx_0(k3_bhsp_1(A,B),k3_bhsp_1(A,C))) ) ) ) )).
fof(t29_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) & k1_seq_2(k2_bhsp_2(A,k5_normsp_1(A,D,C))) = k3_bhsp_1(A,k1_rlvect_1(A,B,C)) ) ) ) ) ) ) )).
fof(t29_bhsp_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ? [D] : ( v7_ordinal1(D) & ! [E] : ( v7_ordinal1(E) => ( 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) ) ) ) ) )).
fof(t29_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v4_rlvect_1(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t29_binari_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( 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 ) ) ) ) )).
fof(t29_binari_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( r2_int_1(B,C,k5_series_1(2,A)) => ( ( ~ ( r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k5_numbers,C) ) & ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(k5_numbers,C) ) ) | k2_binari_4(A,B) = k2_binari_4(A,C) ) ) ) ) ) )).
fof(t29_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_boolealg(A,k1_boolealg(A,B,C),k5_lattices(A)) <=> r3_lattices(A,B,C) ) ) ) ) )).
fof(t29_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k11_borsuk_1(A,B))) => ? [D] : ( 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 ) ) ) ) )).
fof(t29_borsuk_4,axiom,( ! [A] : ( 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) ) ) )).
fof(t29_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t29_borsuk_6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)))) => ! [B] : ( 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(k5_numbers,k7_xcmplx_0(1,2)),k1_rcomp_1(k5_numbers,1)) & B = k8_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(k7_xcmplx_0(1,2),1),k1_rcomp_1(k5_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(k7_xcmplx_0(1,2)),k1_rcomp_1(k5_numbers,1)) ) ) ) )).
fof(t29_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : k11_finseq_1(A,B,C) = k1_borsuk_7(1,2,3,A,B,C) )).
fof(t29_bspace,axiom,( ! [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) ) )).
fof(t29_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t29_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_subset_1(H,A) => ! [I] : ( m1_subset_1(I,A) => ! [J] : ( ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t29_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t29_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t29_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_eqrel_1(C,A) => r2_bvfunc_1(A,k16_bvfunc_1(A,B,C),C) ) ) ) )).
fof(t29_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(E,A) => ( r3_bvfunc_2(A,D,B,E) => r1_bvfunc_1(A,k6_bvfunc_2(A,k6_bvfunc_1(A,C,D),B,E),k6_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),D)) ) ) ) ) ) ) )).
fof(t29_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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))))) ) ) ) ) ) )).
fof(t29_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t29_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t29_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t29_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t29_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [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))) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k11_c0sp1(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k11_c0sp1(A))) => ! [G] : ( 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] : ( m1_subset_1(H,A) => k3_funct_2(A,k1_numbers,D,H) = k3_real_1(k3_funct_2(A,k1_numbers,B,H),k3_funct_2(A,k1_numbers,C,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t29_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => m1_rlsub_1(k7_c0sp2(A),k10_funcsdom(u1_struct_0(A))) ) )).
fof(t29_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t29_calcul_2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k1_relset_1(k4_ordinal1,C),k1_relset_1(k4_ordinal1,C)) & v3_funct_2(D,k1_relset_1(k4_ordinal1,C),k1_relset_1(k4_ordinal1,C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_relset_1(k4_ordinal1,C),k1_relset_1(k4_ordinal1,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))) ) ) ) ) ) )).
fof(t29_card_1,axiom,( ! [A] : k1_card_1(k1_tarski(A)) = 1 )).
fof(t29_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ! [C] : ( v1_card_1(C) => k3_card_2(A,k2_card_2(B,C)) = k3_card_2(k3_card_2(A,B),C) ) ) ) )).
fof(t29_card_5,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ~ ( r2_hidden(k1_card_5(A),A) & ! [B] : ( ( 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(k5_numbers,k10_xtuple_0(B)) ) ) ) ) )).
fof(t29_card_fil,axiom,( v6_card_fil(k4_ordinal1) )).
fof(t29_card_fin,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( ( r2_hidden(A,k10_xtuple_0(D)) & r1_tarski(k8_relat_1(D,k1_tarski(A)),B) ) => k2_card_fin(k5_relat_1(C,B),D,A) = k2_card_fin(C,D,A) ) ) ) )).
fof(t29_card_lar,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) & ~ v4_card_3(A) ) => ( v4_card_lar(A) => v4_card_fil(A) ) ) )).
fof(t29_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_cat_1(D,A,B,C) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t29_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,k6_cat_2(A,C),B) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => m2_cat_1(k1_funct_1(k3_funct_5(D),k4_cat_1(C,E)),A,B) ) ) ) ) ) )).
fof(t29_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t29_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(t29_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(k3_xcmplx_0(2,A),B) => k5_card_1(k2_catalan2(B,A)) = k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k1_nat_1(B,1),k3_xcmplx_0(2,A)),k6_xcmplx_0(k1_nat_1(B,1),A)),k4_newton(A,B)) ) ) ) )).
fof(t29_catalg_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_subset_1(F,u4_struct_0(A)) & ? [G] : ( 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 ) ) ) ) ) ) ) )).
fof(t29_cayldick,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v31_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_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) & v4_vectsp_1(A) & v5_vectsp_1(A) & v3_lopban_2(A) & v4_lopban_2(A) & v3_cayldick(A) & v4_cayldick(A) & l1_cayldick(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v17_algstr_0(k5_cayldick(A,B,C),k4_cayldick(A)) & v23_algstr_0(k5_cayldick(A,B,C),k4_cayldick(A)) ) => ( ( v9_struct_0(B,A) & v9_struct_0(C,A) ) | k11_algstr_0(k4_cayldick(A),k5_cayldick(A,B,C)) = k5_cayldick(A,k1_rlvect_1(A,k2_cayldick(A,B),k7_xcmplx_0(1,k2_xcmplx_0(k1_square_1(k2_normsp_0(A,B)),k1_square_1(k2_normsp_0(A,C))))),k1_rlvect_1(A,k4_algstr_0(A,C),k7_xcmplx_0(1,k2_xcmplx_0(k1_square_1(k2_normsp_0(A,B)),k1_square_1(k2_normsp_0(A,C)))))) ) ) ) ) ) )).
fof(t29_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k5_cc0sp2(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k5_cc0sp2(A))) => ! [G] : ( 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] : ( m1_subset_1(H,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k2_numbers,D,H) = k6_xcmplx_0(k3_funct_2(u1_struct_0(A),k2_numbers,B,H),k3_funct_2(u1_struct_0(A),k2_numbers,C,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t29_cfdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [C] : ( ( 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] : ( v1_xcmplx_0(D) => ( r2_hidden(D,C) => k7_partfun1(k2_numbers,k3_cfdiff_1(k46_valued_1(k2_numbers,k2_numbers,k2_numbers,A,B),C),D) = k6_xcmplx_0(k2_cfdiff_1(A,D),k2_cfdiff_1(B,D)) ) ) ) ) ) ) ) )).
fof(t29_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k5_struct_0(k8_cfuncdom(A)) = k5_cfuncdom(A) ) )).
fof(t29_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t29_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ! [B] : ( v2_cgames_1(B) => ( r2_hidden(B,k10_cgames_1(A)) => r1_ordinal1(k9_cgames_1(B),k9_cgames_1(A)) ) ) ) )).
fof(t29_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ( ( ! [F] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(A)) => r1_xxreal_0(k1_funct_1(B,F),k1_funct_1(C,F)) ) | ! [F] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(A)) => ~ r1_xxreal_0(k1_funct_1(B,F),k1_funct_1(C,F)) ) ) => ( k3_chain_1(A,B,C) = k3_chain_1(A,D,E) <=> ( B = D & C = E ) ) ) ) ) ) ) ) )).
fof(t29_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k6_glib_000(A))) ) => ( r1_tarski(C,B) => ! [D] : ( m2_glib_000(D,A,B,k21_glib_000(A,B)) => ! [E] : ( m2_glib_000(E,D,C,k21_glib_000(D,C)) => m2_glib_000(E,A,C,k21_glib_000(A,C)) ) ) ) ) ) ) )).
fof(t29_circcmb3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_circcmb3(B,A) => ! [C] : ( m1_circcmb3(C,A) => ! [D] : ( m2_circcmb3(D,A,B) => ! [E] : ( m2_circcmb3(E,A,C) => v4_circcomb(k3_circcomb(B,C,D,E),k2_circcomb(B,C)) ) ) ) ) ) )).
fof(t29_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & ~ v11_struct_0(C) & v2_msafree2(C) & l1_msualg_1(C) ) => ( C = k2_circcomb(A,B) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( v4_msualg_1(F,C) & v4_msafree2(F,C) & l3_msualg_1(F,C) ) => ! [G] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(C,F))) => ! [H] : ( 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] : ( m1_subset_1(I,u4_struct_0(C)) => ! [J] : ( m1_subset_1(J,u4_struct_0(B)) => ( I = J => k3_circuit1(C,F,G,I) = k3_circuit1(B,E,H,J) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t29_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_msualg_1(C) ) => ( ( r2_circtrm1(A,B) & r2_circtrm1(B,C) ) => r2_circtrm1(A,C) ) ) ) ) )).
fof(t29_classes1,axiom,( k4_classes1(k1_xboole_0) = k1_xboole_0 )).
fof(t29_classes2,axiom,( ! [A] : ! [B] : ( ( v2_classes1(B) & v1_ordinal1(B) & r2_hidden(A,B) ) => r2_hidden(k6_classes1(A),B) ) )).
fof(t29_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( 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_funct_1(k13_clopban1(A,B),C) = k2_seq_4(k12_clopban1(A,B,C)) ) ) ) )).
fof(t29_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( ! [C] : ( v7_ordinal1(C) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,k5_normsp_0(A,B),C),k5_numbers) ) & ? [C] : ( v7_ordinal1(C) & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => r1_xxreal_0(1,k6_real_1(k9_nat_1(k1_numbers,k5_normsp_0(A,B),k1_nat_1(D,1)),k9_nat_1(k1_numbers,k5_normsp_0(A,B),D))) ) ) ) & v2_clopban3(B,A) ) ) ) )).
fof(t29_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( k9_complex1(k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k2_normsp_0(A,B))),D)) = k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k2_normsp_0(A,B))),D) & ( r1_xxreal_0(D,C) => k9_complex1(k5_real_1(k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k2_normsp_0(A,B))),C),k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k2_normsp_0(A,B))),D))) = k5_real_1(k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k2_normsp_0(A,B))),C),k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k2_normsp_0(A,B))),D)) ) ) ) ) ) ) )).
fof(t29_closure1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t29_closure2,axiom,( ! [A] : ! [B] : ( ( 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)))) ) ) )).
fof(t29_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_clvect_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => m1_subset_1(C,u1_struct_0(A)) ) ) ) )).
fof(t29_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) & k1_seq_2(k2_clvect_2(A,k6_clvect_1(A,D,C))) = k13_csspace(A,k1_clvect_1(A,B,C)) ) ) ) ) ) ) )).
fof(t29_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ? [D] : ( v7_ordinal1(D) & ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(D,E) => r1_xxreal_0(C,k13_csspace(A,k1_normsp_0(A,B,E))) ) ) ) & v1_clvect_2(B,A) & k1_clvect_2(A,B) = k4_struct_0(A) ) ) ) ) )).
fof(t29_coh_sp,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r2_hidden(k1_eqrel_1(A),k15_coh_sp(B)) ) )).
fof(t29_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k3_tarski(B)))) => ~ ( ! [D] : ( r2_hidden(D,C) => v1_finset_1(k1_xtuple_0(D)) ) & ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,A) ) => ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,A) ) => ( r1_tarski(D,E) => ! [F] : ( r2_hidden(k4_tarski(D,F),C) => r2_hidden(k4_tarski(E,F),C) ) ) ) ) & ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,A) ) => ! [E] : ! [F] : ( ( r2_hidden(k4_tarski(D,E),C) & r2_hidden(k4_tarski(D,F),C) ) => r2_hidden(k2_tarski(E,F),B) ) ) & ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t29_combgras,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ( r1_ordinal1(k1_nat_1(A,1),k1_card_1(B)) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ( k5_card_1(C) = k6_xcmplx_0(A,1) => v3_combgras(k7_combgras(A,B,C),A,B) ) ) ) ) ) )).
fof(t29_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k8_complex1(A) = k5_numbers => A = k5_numbers ) ) )).
fof(t29_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k1_complex2(A,A) = k1_square_1(k9_complex1(A)) & k1_square_1(k9_complex1(A)) = k3_complex1(k1_complex2(A,A)) ) ) )).
fof(t29_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ( k3_vectsp_1(k1_complfld,A,B) = k5_struct_0(k1_complfld) => ( B = k4_struct_0(k1_complfld) | A = B ) ) ) ) )).
fof(t29_complsp2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t29_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k6_compos_1(A,k6_compos_1(A,B,C),D) = k6_compos_1(A,B,k2_xcmplx_0(C,D)) ) ) ) ) )).
fof(t29_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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) ) ) )).
fof(t29_comptrig,axiom,( k10_xtuple_0(k18_sin_cos) = k1_rcomp_1(k4_xcmplx_0(1),1) )).
fof(t29_comput_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_relat_1(B) => ( ( r1_tarski(k10_xtuple_0(B),k2_comput_1(A)) & ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_margrel1(C) ) => ! [D] : ( ( 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) ) ) ) )).
fof(t29_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k36_valued_1(k4_ordinal1,k2_numbers,A),k36_valued_1(k4_ordinal1,k2_numbers,B)),k36_valued_1(k4_ordinal1,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B))) ) ) )).
fof(t29_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v2_comseq_2(A) & v1_comseq_2(B) & k3_comseq_2(A) = k5_complex1 ) => v2_comseq_2(k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)) ) ) ) )).
fof(t29_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( v1_xcmplx_0(B) => r2_funct_2(k4_ordinal1,k2_numbers,k10_comseq_3(k25_valued_1(k4_ordinal1,k2_numbers,A,B)),k25_valued_1(k4_ordinal1,k2_numbers,k10_comseq_3(A),B)) ) ) )).
fof(t29_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) & l2_conlat_1(B,A) ) => ! [C] : ( ( ~ v4_conlat_1(C,A) & v6_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)) ) ) ) ) )).
fof(t29_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_connsp_1(A,B,C) ) ) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_connsp_1(A,B,C) ) ) ) ) )).
fof(t29_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m2_connsp_2(C,A,B) => r1_tarski(B,C) ) ) ) )).
fof(t29_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t29_convex1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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(k5_numbers,k1_funct_1(E,B)) & r1_xxreal_0(k5_numbers,k1_funct_1(E,C)) & r1_xxreal_0(k5_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))) ) ) ) ) ) ) ) ) )).
fof(t29_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t29_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t29_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => r1_tarski(B,a_2_0_cqc_the1(A,B)) ) ) )).
fof(t29_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ! [E] : ( m2_subset_1(E,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t29_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t29_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k12_csspace(A,k4_struct_0(A),B) = k5_numbers ) ) )).
fof(t29_csspace4,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_comseq_2(B) => v1_comseq_2(k25_valued_1(k4_ordinal1,k2_numbers,B,A)) ) ) ) )).
fof(t29_descip_1,axiom,( ! [A] : ( m2_finseq_2(A,k6_margrel1,k4_finseq_2(48,k6_margrel1)) => ? [B] : ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(6,k6_margrel1)) & ? [C] : ( m2_finseq_2(C,k6_margrel1,k4_finseq_2(6,k6_margrel1)) & ? [D] : ( m2_finseq_2(D,k6_margrel1,k4_finseq_2(6,k6_margrel1)) & ? [E] : ( m2_finseq_2(E,k6_margrel1,k4_finseq_2(6,k6_margrel1)) & ? [F] : ( m2_finseq_2(F,k6_margrel1,k4_finseq_2(6,k6_margrel1)) & ? [G] : ( m2_finseq_2(G,k6_margrel1,k4_finseq_2(6,k6_margrel1)) & ? [H] : ( m2_finseq_2(H,k6_margrel1,k4_finseq_2(6,k6_margrel1)) & ? [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(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(6,6),6),6),6),6),6),6,k6_margrel1,k9_binarith(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(6,6),6),6),6),6),6,k6_margrel1,k9_binarith(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(6,6),6),6),6),6,k6_margrel1,k9_binarith(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(6,6),6),6),6,k6_margrel1,k9_binarith(k2_xcmplx_0(k2_xcmplx_0(6,6),6),6,k6_margrel1,k9_binarith(k2_xcmplx_0(6,6),6,k6_margrel1,k9_binarith(6,6,k6_margrel1,B,C),D),E),F),G),H),I) ) ) ) ) ) ) ) ) ) )).
fof(t29_dickson,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v4_dickson(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ? [C] : ( m1_subset_1(C,k4_ordinal1) & ? [D] : ( m1_subset_1(D,k4_ordinal1) & ~ r1_xxreal_0(D,C) & r1_orders_2(A,k9_nat_1(u1_struct_0(A),B,C),k9_nat_1(u1_struct_0(A),B,D)) ) ) ) ) ) )).
fof(t29_diff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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) ) ) ) )).
fof(t29_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( ( 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] : ( v1_xreal_0(I) => k1_funct_1(H,I) = k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(E,k1_square_1(I)),k3_xcmplx_0(F,I)),G) ) & r2_zfmisc_1(A,B,C,D) ) => k11_diff_1(H,A,B,C,D) = k5_numbers ) ) ) ) ) ) ) ) ) )).
fof(t29_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( ( 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) = k6_xcmplx_0(k9_diff_1(D,B,C),k3_xcmplx_0(A,k9_diff_1(E,B,C))) ) ) ) ) ) )).
fof(t29_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(k2_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k27_sin_cos)) & r2_hidden(k6_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k27_sin_cos)) ) => k1_funct_1(k5_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k27_sin_cos),k16_sin_cos),A),B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k18_sin_cos),k2_xcmplx_0(B,k7_xcmplx_0(A,2))),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k18_sin_cos),k6_xcmplx_0(B,k7_xcmplx_0(A,2)))) ) ) ) )).
fof(t29_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( 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)))) ) ) ) ) )).
fof(t29_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t29_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => ! [C] : ( ( 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_funct_2(A,k6_margrel1,A,k2_tarski(k1_xboole_0,1),C,k5_funct_3(A,A)) => k6_dist_2(A,B,C) = 1 ) ) ) ) )).
fof(t29_domain_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k4_subset_1(A,B,C) = a_3_2_domain_1(A,B,C) ) ) ) )).
fof(t29_e_siec,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t29_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_uniroots(k9_int_3(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( v7_ordinal1(D) => ( B = C => k5_group_1(k1_uniroots(k9_int_3(A)),D,B) = k2_binom(k9_int_3(A),C,D) ) ) ) ) ) )).
fof(t29_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(A))) => ( D = k5_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)) ) ) ) ) ) ) ) )).
fof(t29_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k11_ens_1(A))) => ( B = k1_xboole_0 => v11_cat_1(B,k11_ens_1(A)) ) ) ) )).
fof(t29_entropy1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( 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] : ( v7_ordinal1(D) => ( r1_xxreal_0(1,D) => ( r1_xxreal_0(k3_finseq_1(B),D) | k1_matrprob(A,C,k1_nat_1(D,1)) = k8_finseq_1(A,k1_matrprob(A,C,D),k1_matrprob(A,B,k1_nat_1(D,1))) ) ) ) ) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(C)) => k3_finseq_1(k1_matrprob(A,C,D)) = k3_xcmplx_0(D,k1_matrix_0(B)) ) ) ) ) ) ) )).
fof(t29_enumset1,axiom,( ! [A] : k2_tarski(A,A) = k1_tarski(A) )).
fof(t29_eqrel_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ~ ( 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) ) ) ) ) ) )).
fof(t29_equation,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t29_euclid,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => k1_rlvect_1(k15_euclid(2),B,A) = k19_euclid(k3_xcmplx_0(A,k17_euclid(B)),k3_xcmplx_0(A,k18_euclid(B))) ) ) )).
fof(t29_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => k22_rvsum_1(k5_algstr_0(k15_euclid(A),B,C),k5_algstr_0(k15_euclid(A),B,C)) = k2_xcmplx_0(k6_xcmplx_0(k22_rvsum_1(B,B),k3_xcmplx_0(2,k22_rvsum_1(B,C))),k22_rvsum_1(C,C)) ) ) ) )).
fof(t29_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( A != k4_struct_0(k15_euclid(2)) => ( ( ~ r1_xxreal_0(k28_sin_cos,k3_euclid_3(A)) => k3_euclid_3(k4_algstr_0(k15_euclid(2),A)) = k2_xcmplx_0(k3_euclid_3(A),k28_sin_cos) ) & ( r1_xxreal_0(k28_sin_cos,k3_euclid_3(A)) => k3_euclid_3(k4_algstr_0(k15_euclid(2),A)) = k6_xcmplx_0(k3_euclid_3(A),k28_sin_cos) ) ) ) ) )).
fof(t29_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => k22_rvsum_1(B,k8_euclid(A,C,D)) = k6_xcmplx_0(k22_rvsum_1(B,C),k22_rvsum_1(B,D)) ) ) ) ) )).
fof(t29_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(3))) => k22_rvsum_1(A,B) = k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k1_euclid_5(A),k1_euclid_5(B)),k3_xcmplx_0(k2_euclid_5(A),k2_euclid_5(B))),k3_xcmplx_0(k3_euclid_5(A),k3_euclid_5(B))) ) ) )).
fof(t29_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(A,k6_jgraph_6(C,D,E)) & r2_hidden(B,k8_jgraph_6(C,D,E)) & ! [F] : ( 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))) ) ) ) ) ) ) ) )).
fof(t29_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(B)) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,B) ) => k22_rvsum_1(C,k6_euclid_7(B,A)) = k1_funct_1(C,A) ) ) ) ) )).
fof(t29_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => A = k7_euclid(3,k7_euclid(3,k9_euclid(3,k2_euclid_8,k1_funct_1(A,1)),k9_euclid(3,k3_euclid_8,k1_funct_1(A,2))),k9_euclid(3,k4_euclid_8,k1_funct_1(A,3))) ) )).
fof(t29_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(1,A) & k21_euclid(A) = k5_euclid(A) ) ) )).
fof(t29_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(k9_funct_7(C,A,B),A) = k1_funct_1(C,B) ) ) )).
fof(t29_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) & k3_extpro_1(A,B,C,k5_extpro_1(A,B,C,D,E)) = k2_compos_1(B) ) ) ) ) ) ) )).
fof(t29_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ( ~ r1_xxreal_0(k1_supinf_1,k3_extreal1(A)) <=> r2_hidden(A,k1_numbers) ) ) )).
fof(t29_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_circcomb(A) & v2_circcomb(A) & v3_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v4_msafree2(C,A) & v4_circcomb(C,A) & v6_circcomb(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msafree2(D,B) & v4_circcomb(D,B) & v6_circcomb(D,B) & l3_msualg_1(D,B) ) => ! [E] : ( m1_subset_1(E,k4_card_3(u3_msualg_1(k2_circcomb(A,B),k3_circcomb(A,B,C,D)))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t29_facirc_2,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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] : ( 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)) ) ) )).
fof(t29_fcont_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( ( 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)) ) ) ) )).
fof(t29_fdiff_10,axiom,( ! [A] : ( ( 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,k22_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos)))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos)),A),B) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(k22_sin_cos,B),k2_xcmplx_0(k1_funct_1(k26_sin_cos,B),k1_funct_1(k27_sin_cos,B))),k3_xcmplx_0(k1_funct_1(k22_sin_cos,B),k6_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B)))))) ) ) ) ) ) )).
fof(t29_fdiff_11,axiom,( ! [A] : ( ( 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,k26_sin_cos,k1_sin_cos9))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_sin_cos9),A),B) = k2_xcmplx_0(k7_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k1_square_1(k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(k1_funct_1(k26_sin_cos,B),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t29_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ~ ( r2_hidden(C,k10_prob_1(A)) & r1_xxreal_0(k1_fdiff_1(B,C),k5_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))) ) ) ) ) )).
fof(t29_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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(k7_xcmplx_0(3,2))),k4_xcmplx_0(k7_xcmplx_0(2,3))))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k1_funct_1(C,D) = k6_xcmplx_0(A,D) & ~ r1_xxreal_0(k1_funct_1(C,D),k5_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(k7_xcmplx_0(3,2))),k4_xcmplx_0(k7_xcmplx_0(2,3))),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_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(k7_xcmplx_0(3,2))),k4_xcmplx_0(k7_xcmplx_0(2,3))),B),D) = k6_prepower(k6_xcmplx_0(A,D),k7_xcmplx_0(1,2)) ) ) ) ) ) ) ) )).
fof(t29_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k22_sin_cos,B),k1_taylor_1(2)))) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_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,k22_sin_cos,B),k1_taylor_1(2)),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,B),k1_taylor_1(2)),A),C) = k3_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k22_sin_cos,C)),k2_xcmplx_0(k1_funct_1(k22_sin_cos,C),1)) ) ) ) ) ) ) )).
fof(t29_fdiff_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( 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,F,k3_sin_cos6)),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(k7_xcmplx_0(1,2)))))) & C = k47_valued_1(k1_numbers,k1_numbers,k1_numbers,D,E) & E = k1_taylor_1(2) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,B) => ( k1_funct_1(D,G) = k1_square_1(A) & ~ r1_xxreal_0(k1_funct_1(C,G),k5_numbers) & k1_funct_1(F,G) = k7_xcmplx_0(G,A) & ~ r1_xxreal_0(k1_funct_1(F,G),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(F,G)) & G != k5_numbers & ~ r1_xxreal_0(A,k5_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,F,k3_sin_cos6)),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(k7_xcmplx_0(1,2)))),B) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,B) => k1_funct_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,F,k3_sin_cos6)),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(k7_xcmplx_0(1,2)))),B),G) = k1_funct_1(k3_sin_cos6,k7_xcmplx_0(G,A)) ) ) ) ) ) ) ) ) ) ) )).
fof(t29_fdiff_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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,k27_sin_cos))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(D,E) = k2_xcmplx_0(k3_xcmplx_0(A,E),B) ) ) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k27_sin_cos),C) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k27_sin_cos),C),E) = k6_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(A,k1_funct_1(k18_sin_cos,E)),k1_funct_1(k16_sin_cos,E)),k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,E),B),k1_square_1(k1_funct_1(k16_sin_cos,E)))) ) ) ) ) ) ) ) ) )).
fof(t29_fdiff_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(D,E) = k2_xcmplx_0(k3_xcmplx_0(A,E),B) ) ) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k2_fdiff_9),C) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k2_fdiff_9),C),E) = k6_xcmplx_0(k7_xcmplx_0(A,k1_funct_1(k16_sin_cos,E)),k7_xcmplx_0(k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,E),B),k1_funct_1(k18_sin_cos,E)),k1_square_1(k1_funct_1(k16_sin_cos,E)))) ) ) ) ) ) ) ) ) )).
fof(t29_fib_num2,axiom,( ! [A] : ( 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)) ) )).
fof(t29_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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(k2_power(k1_fib_num,B),k1_pre_ff(A)),k7_xcmplx_0(1,2))) = k1_pre_ff(k2_xcmplx_0(A,B)) ) ) ) )).
fof(t29_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_finseq_1(B,A) => ! [C] : ( m1_finseq_1(C,A) => ( r5_finseq_8(A,B,C) => r1_xxreal_0(k3_finseq_1(C),k3_finseq_1(B)) ) ) ) ) )).
fof(t29_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(t29_filter_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t29_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t29_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t29_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ( B = k2_finseq_1(A) => ! [D] : ( m2_finseq_1(D,C) => ! [E] : ( m2_finseq_1(E,B) => ( r1_xxreal_0(A,k3_finseq_1(D)) => m2_finseq_1(k1_partfun1(k4_ordinal1,B,k4_ordinal1,C,E,D),C) ) ) ) ) ) ) ) )).
fof(t29_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_hidden(B,k10_xtuple_0(A)) => r2_hidden(1,k1_relset_1(k4_ordinal1,A)) ) ) )).
fof(t29_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t29_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t29_finseq_6,axiom,( ! [A] : ! [B] : k6_finseq_4(k10_finseq_1(A,B),A) = k9_finseq_1(B) )).
fof(t29_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t29_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v3_card_1(E,D) & m2_finseq_1(E,A) ) => ! [F] : ( ( 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(k4_ordinal1,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))) ) ) ) ) ) ) ) )).
fof(t29_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t29_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => 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)) ) ) ) ) )).
fof(t29_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t29_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( v7_ordinal1(C) => ( k7_flang_1(A,B,C) = k4_flang_1(A,k2_flang_1(A)) <=> ( C = k5_numbers | B = k4_flang_1(A,k2_flang_1(A)) ) ) ) ) )).
fof(t29_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r1_tarski(B,C) => r1_tarski(k1_flang_2(A,B,D,E),k1_flang_2(A,C,D,E)) ) ) ) ) ) )).
fof(t29_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r1_tarski(B,k1_flang_3(A,C,D)) => ( r1_xxreal_0(E,k5_numbers) | r1_tarski(k1_flang_3(A,B,E),k1_flang_3(A,C,D)) ) ) ) ) ) ) )).
fof(t29_fomodel0,axiom,( ! [A] : ! [B] : ( ( k5_xboole_0(B,A) = k1_xboole_0 => B = A ) & ( B = A => k5_xboole_0(B,A) = k1_xboole_0 ) & ( k6_subset_1(B,A) = k1_xboole_0 => r1_tarski(B,A) ) & ( r1_tarski(B,A) => k6_subset_1(B,A) = k1_xboole_0 ) & ! [C] : ( k6_subset_1(k1_tarski(C),A) = k1_xboole_0 <=> r2_hidden(C,A) ) ) )).
fof(t29_frechet,axiom,( ! [A] : ( ( 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))) & k3_xboole_0(k4_ordinal1,A) = k1_xboole_0 ) ) ) & ( ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) & k3_xboole_0(k4_ordinal1,A) = k1_xboole_0 ) => ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_frechet))) & ~ r2_hidden(k1_numbers,A) ) ) ) )).
fof(t29_frechet2,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k3_pcomps_1(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k3_pcomps_1(A))))) ) => ( r1_funct_2(k4_ordinal1,u1_struct_0(A),k4_ordinal1,u1_struct_0(k3_pcomps_1(A)),B,C) => ( v2_tbsp_1(B,A) <=> v2_frechet(C,k3_pcomps_1(A)) ) ) ) ) ) )).
fof(t29_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t29_fsm_2,axiom,( ! [A] : ( ( ~ 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] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,B) => k1_funct_1(u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(B,C))) = B ) ) ) & ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(C,B) => k1_funct_1(u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(B,C))) = C ) ) ) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( 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)) = k3_xxreal_0(B,C) ) ) ) ) )).
fof(t29_fsm_3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(B)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(B)) => ! [E] : ( ( ~ 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,D,C),A) = k3_rewrite3(B,k4_subset_1(k3_catalan2(B),k9_flang_1(B),k4_flang_1(B,k2_flang_1(B))),E,C,k3_rewrite3(B,k4_subset_1(k3_catalan2(B),k9_flang_1(B),k4_flang_1(B,k2_flang_1(B))),E,D,A)) ) ) ) ) )).
fof(t29_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t29_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : k3_relat_1(B,k4_funcop_1(C,A,D)) = k4_funcop_1(C,k3_relat_1(B,A),D) ) ) ) )).
fof(t29_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( k10_xtuple_0(k3_relat_1(A,B)) = k10_xtuple_0(B) & v2_funct_1(B) ) => r1_tarski(k9_xtuple_0(B),k10_xtuple_0(A)) ) ) ) )).
fof(t29_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) ) ) )).
fof(t29_funct_3,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(t29_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => r1_tarski(k1_funct_4(A,B),k2_xboole_0(A,B)) ) ) )).
fof(t29_funct_5,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t29_funct_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_funcop_1(E) ) => ( ( r2_hidden(A,k9_xtuple_0(E)) & C = k1_funct_1(E,A) & r2_hidden(B,k9_xtuple_0(k5_funct_6(E))) & D = k1_funct_1(k5_funct_6(E),B) ) => k1_funct_1(C,B) = k1_funct_1(D,A) ) ) ) ) )).
fof(t29_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : k9_xtuple_0(k1_funct_7(A,C,B)) = k9_xtuple_0(A) ) )).
fof(t29_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t29_funct_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(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,k18_sin_cos)),k3_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),A)) ) )).
fof(t29_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_functor0(A,A,k11_functor0(A),B) = B ) ) )).
fof(t29_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v11_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,B,C) & m2_functor0(E,B,C) ) => ! [F] : ( ( v15_functor0(F,B,C) & m2_functor0(F,B,C) ) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t29_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D) & r2_funct_2(A,k1_numbers,k1_fuzzy_1(A,D,C),k4_fuzzy_1(A)) ) => r2_funct_2(A,k1_numbers,k1_fuzzy_1(A,B,C),k4_fuzzy_1(A)) ) ) ) ) ) )).
fof(t29_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D),C),k2_fuzzy_2(A,B,k2_fuzzy_2(A,D,C))) ) ) ) ) )).
fof(t29_fvaluat1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_fvaluat1(D,B) => ( v3_fvaluat1(B) => ( C = k4_struct_0(B) | k3_funct_2(u1_struct_0(B),k6_numbers,D,k3_fvaluat1(B,C,A)) = k4_xxreal_3(A,k3_funct_2(u1_struct_0(B),k6_numbers,D,C)) ) ) ) ) ) ) )).
fof(t29_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t29_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ~ ( ~ 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)) ) ) )).
fof(t29_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k5_gcd_1(A,B,C,D) = k5_gcd_1(A,B,D,C) ) ) ) ) )).
fof(t29_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v2_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ! [F] : ( m1_genealg1(F,E) => ! [G] : ( m1_genealg1(G,E) => ( k10_genealg1(E,F,G,k5_numbers,B,C,D) = k9_genealg1(E,G,F,B,C,D) & k10_genealg1(E,F,G,A,k5_numbers,C,D) = k9_genealg1(E,G,F,A,C,D) & k10_genealg1(E,F,G,A,B,k5_numbers,D) = k9_genealg1(E,G,F,A,B,D) & k10_genealg1(E,F,G,A,B,C,k5_numbers) = k9_genealg1(E,G,F,A,B,C) ) ) ) ) ) ) ) ) )).
fof(t29_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k4_geomtrap(A,B,C,D,E) = k4_geomtrap(A,B,C,E,D) ) ) ) ) ) )).
fof(t29_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( C != k4_tarski(k10_finseq_1(A,B),k14_twoscomp) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k10_gfacirc1(A,B,C),k11_gfacirc1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( 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) ) ) ) ) ) ) ) )).
fof(t29_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( r1_tarski(k18_glib_000(A,B),k20_glib_000(A,B)) & r1_tarski(k19_glib_000(A,B),k20_glib_000(A,B)) ) ) )).
fof(t29_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ! [E] : ! [F] : ( ( 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)) ) ) ) ) )).
fof(t29_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) ) )).
fof(t29_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v8_glib_003(A) ) => ! [B] : ( m3_glib_001(B,A) => r1_xxreal_0(k5_numbers,k10_glib_003(A,B)) ) ) )).
fof(t29_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(t29_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(D)) & r2_hidden(k4_tarski(A,k1_nat_1(B,1)),k2_matrix_0(k2_goboard2(D))) & r2_hidden(k4_tarski(k1_nat_1(A,1),k1_nat_1(B,1)),k2_matrix_0(k2_goboard2(D))) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,1)) ) => ( k5_goboard5(D,C) = k3_goboard5(k2_goboard2(D),A,B) & k4_goboard5(D,C) = k3_goboard5(k2_goboard2(D),A,k1_nat_1(B,1)) ) ) ) ) ) ) )).
fof(t29_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_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_0(u1_struct_0(k15_euclid(2)),C,A,1))) ) ) ) ) )).
fof(t29_gobrd11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_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_0(B),A) | k3_goboard5(B,k3_finseq_1(B),A) = a_2_3_gobrd11(A,B) ) ) ) ) )).
fof(t29_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(D)) & r1_goboard1(u1_struct_0(k15_euclid(2)),D,E) & r2_hidden(k4_tarski(A,B),k2_matrix_0(E)) & r2_hidden(k4_tarski(k1_nat_1(A,1),B),k2_matrix_0(E)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,k1_nat_1(A,1),B) ) => k5_gobrd13(D,E,C) = k3_goboard5(E,k1_nat_1(A,1),B) ) ) ) ) ) ) )).
fof(t29_gobrd14,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t29_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t29_gr_cy_3,axiom,( ! [A] : ( 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) ) ) ) ) )).
fof(t29_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_graph_1(A) & l1_graph_1(A) ) => r2_hidden(A,k11_graph_1(A)) ) )).
fof(t29_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( r2_graph_1(A,B,C,D) => r2_graph_1(A,C,B,D) ) ) ) ) )).
fof(t29_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ! [D] : ( r1_tarski(D,C) => k7_graph_3(A,B,k6_subset_1(C,D)) = k6_xcmplx_0(k7_graph_3(A,B,C),k7_graph_3(A,B,D)) ) ) ) )).
fof(t29_graph_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v7_graph_1(E,B) & m2_graph_1(E,B) ) => ( r2_graph_5(B,C,D,E,A) => ( C = D | r2_hidden(C,A) ) ) ) ) ) ) )).
fof(t29_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => ( A = k14_graphsp(k7_graphsp(C,B),C,B) => ( k7_graphsp(C,B) = k1_xboole_0 | ( r2_hidden(A,k4_finseq_1(C)) & r1_xxreal_0(1,A) & r1_xxreal_0(A,B) & k1_funct_1(C,A) != k4_xcmplx_0(1) & k1_funct_1(C,k1_nat_1(B,A)) != k4_xcmplx_0(1) ) ) ) ) ) ) )).
fof(t29_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => r2_hidden(k3_algstr_0,k17_grcat_1(A)) ) )).
fof(t29_grfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ! [E] : ( ( 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)) ) ) ) )).
fof(t29_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ( ? [B] : ( m2_finseq_1(B,k2_grnilp_1(A)) & ~ r1_xxreal_0(k3_finseq_1(B),k5_numbers) & k1_funct_1(B,1) = k7_group_2(A) & k1_funct_1(B,k3_finseq_1(B)) = k6_group_2(A) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(k2_xcmplx_0(C,1),k4_finseq_1(B)) ) => ! [D] : ( ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) ) => ! [E] : ( ( 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) ) ) )).
fof(t29_groeb_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( ~ v1_xboole_0(D) & v1_ideal_1(D,k12_polynom1(A,C)) & v2_ideal_1(D,k12_polynom1(A,C)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_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) ) ) ) ) ) ) )).
fof(t29_groeb_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( m2_ideal_1(D,A,B) => ( r1_tarski(B,C) => m2_ideal_1(D,A,C) ) ) ) ) ) )).
fof(t29_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(E,k5_card_1(k3_polynom1(k15_pre_poly(A),C,D))) => ! [F] : ( ( 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] : ( ( 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_polynom1(k15_pre_poly(A),C,k6_groeb_3(A,B,C,D,E))) & r2_hidden(G,k3_polynom1(k15_pre_poly(A),C,k5_groeb_3(A,B,C,D,E))) ) => r2_termord(A,B,F,G) ) ) ) ) ) ) ) ) ) )).
fof(t29_group_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( r1_xxreal_0(A,k5_numbers) => k5_group_1(B,A,C) = k2_group_1(B,k5_group_1(B,k1_int_2(A),C)) ) ) ) ) )).
fof(t29_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t29_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t29_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t29_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,C) => r1_struct_0(k5_group_4(A,C),B) ) ) ) ) )).
fof(t29_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t29_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(t29_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t29_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( 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)) ) ) ) )).
fof(t29_hallmar1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ( v1_hallmar1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r1_xxreal_0(2,k5_card_1(k1_funct_1(B,C))) & ! [D] : ~ ( r2_hidden(D,k1_funct_1(B,C)) & v1_hallmar1(k2_hallmar1(A,B,C,D),A) ) ) ) ) ) ) )).
fof(t29_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => k8_weierstr(A,B,B) = k5_numbers ) ) )).
fof(t29_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t29_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,k1_complfld) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t29_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,u1_struct_0(k1_heyting3(B,k6_domain_1(k4_ordinal1,A)))) => ( r2_hidden(C,D) => ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_domain_1(k4_ordinal1,A)))) ) ) ) ) )).
fof(t29_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( A != k5_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) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(B,k3_prepower(A,k6_xcmplx_0(B,1))),k1_square_1(k3_prepower(A,B)))) ) ) ) ) )).
fof(t29_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ( ( r2_hidden(k3_hilbert1(C,k3_hilbert1(B,A)),k6_hilbert1) & r2_hidden(B,k6_hilbert1) ) => r2_hidden(k3_hilbert1(C,A),k6_hilbert1) ) ) ) ) )).
fof(t29_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k2_hilbert1 != k1_hilbert2(A) ) )).
fof(t29_hilbert3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => k3_hilbert3(B,k1_hilbert2(A)) = k1_funct_1(B,A) ) ) )).
fof(t29_hurwitz,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_polynom4(A,k3_hurwitz(A,C,1),B) = k5_algstr_0(A,B,C) ) ) ) )).
fof(t29_idea_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( v1_int_2(k1_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 ) ) ) ) ) )).
fof(t29_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m3_ideal_1(D,A,B) => m3_ideal_1(k1_polynom1(A,D,C),A,B) ) ) ) ) )).
fof(t29_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t29_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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] : ( m4_index_1(C,u1_struct_0(A),u4_struct_0(A),u1_graph_1(A),u2_graph_1(A),B) => ! [D] : ( ( ~ 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] : ( 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)) ) ) ) ) ) )).
fof(t29_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r3_pua2mss1(A,B,C,D) => ! [E] : ( l3_msualg_1(E,B) => ! [F] : ( l3_msualg_1(F,B) => ! [G] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t29_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ r1_xxreal_0(k2_xcmplx_0(k1_int_1(A),1),A) ) )).
fof(t29_int_2,axiom,( ~ v1_int_2(4) )).
fof(t29_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t29_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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] : ( m1_int_6(C,B) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t29_int_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_int_7(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_int_7(A))) => ! [D] : ( 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,k5_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)))) ) ) ) ) ) ) )).
fof(t29_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ( ( r1_int_2(A,B) & r2_int_8(A,B) ) => ( r1_xxreal_0(B,2) | ! [C] : ( v7_ordinal1(C) => ~ r1_int_5(k1_newton(A,k1_nat_1(k3_xcmplx_0(2,C),1)),B) ) ) ) ) ) )).
fof(t29_integr11,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( A != k5_numbers => k2_integra5(B,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(1,k5_numbers),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,k5_numbers),k18_sin_cos))) = k6_xcmplx_0(k1_funct_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,k5_numbers),k18_sin_cos),k7_xcmplx_0(1,k1_square_1(A))),k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,A),k5_numbers),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,k5_numbers),k16_sin_cos))),k2_seq_4(B)),k1_funct_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,k5_numbers),k18_sin_cos),k7_xcmplx_0(1,k1_square_1(A))),k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,A),k5_numbers),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,k5_numbers),k16_sin_cos))),k3_seq_4(B))) ) ) ) )).
fof(t29_integr12,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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,D,k26_sin_cos))) & r2_relset_1(k1_numbers,k1_numbers,C,k3_rfunct_1(k1_numbers,k1_numbers,k41_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k16_sin_cos)),k41_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k18_sin_cos)))) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => ( k1_funct_1(D,F) = k3_xcmplx_0(A,F) & A != k5_numbers ) ) ) & E = k1_relset_1(k1_numbers,C) ) => k2_integra5(B,C) = k6_xcmplx_0(k1_funct_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,k26_sin_cos),k7_xcmplx_0(1,A)),k1_partfun2(k1_numbers,E)),k2_seq_4(B)),k1_funct_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,k26_sin_cos),k7_xcmplx_0(1,A)),k1_partfun2(k1_numbers,E)),k3_seq_4(B))) ) ) ) ) ) ) )).
fof(t29_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k22_sin_cos,k41_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k18_sin_cos)))) & r1_tarski(C,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k26_sin_cos))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k26_sin_cos),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k26_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t29_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k6_xcmplx_0(k7_xcmplx_0(k1_funct_1(k22_sin_cos,D),k1_funct_1(k16_sin_cos,D)),k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k22_sin_cos,D),k1_funct_1(k18_sin_cos,D)),k1_square_1(k1_funct_1(k16_sin_cos,D)))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_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) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k2_fdiff_9),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k2_fdiff_9),k3_seq_4(A))) ) ) ) ) )).
fof(t29_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [E] : ( 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] : ( 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,k6_xcmplx_0(C,B)) ) ) ) ) ) ) ) )).
fof(t29_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [C] : ( m1_integra1(C,A) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t29_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( m1_integra1(D,B) => ( ( v2_seq_2(k2_partfun1(B,k1_numbers,C,B)) & r1_xxreal_0(k5_numbers,A) ) => k7_integra1(B,k26_valued_1(B,k1_numbers,C,A),D) = k3_xcmplx_0(A,k7_integra1(B,C,D)) ) ) ) ) ) )).
fof(t29_integra4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => ! [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_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) ) ) ) ) )).
fof(t29_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( 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] : ( ( 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] : ( v1_xreal_0(F) => ( r2_hidden(F,k2_rcomp_1(A,B)) => k1_funct_1(E,F) = k4_integra5(A,F,C) ) ) & r1_fdiff_1(E,D) & k1_fdiff_1(E,D) = k1_funct_1(C,D) ) ) ) ) ) ) ) )).
fof(t29_integra7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => r1_integra7(k1_numbers,k1_taylor_1(k1_nat_1(A,1)),k26_valued_1(k1_numbers,k1_numbers,k1_taylor_1(A),k1_nat_1(A,1))) ) )).
fof(t29_integra8,axiom,( k2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k18_sin_cos),k1_numbers) = k16_sin_cos )).
fof(t29_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( ~ 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)) = k3_xcmplx_0(k3_xcmplx_0(A,B),k1_integra9(E,C,D)) ) ) ) ) ) ) )).
fof(t29_interva1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_interva1(B,A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_interva1(C,A) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ! [D] : ( ( ~ 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)) ) ) ) )).
fof(t29_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(t29_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_series_1(B) & ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k5_numbers,k1_funct_1(B,C)) ) ) => r1_xxreal_0(k1_funct_1(k3_series_1(B),A),k4_series_1(B)) ) ) ) )).
fof(t29_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,A,B) => ! [G] : ( m2_cat_1(G,B,C) => ! [H] : ( m2_cat_1(H,C,D) => ! [I] : ( m2_nattra_1(I,A,B,E,F) => ( r2_nattra_1(A,B,E,F) => r2_funct_2(u1_struct_0(A),u4_struct_0(D),k4_isocat_1(A,B,D,E,F,I,k9_cat_1(B,C,D,G,H)),k4_isocat_1(A,C,D,k9_cat_1(A,B,C,E,G),k9_cat_1(A,B,C,F,G),k4_isocat_1(A,B,C,E,F,I,G),H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t29_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t29_isomichi,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( A = k3_borsuk_5(B,C) => k1_tops_1(k3_topmetr,A) = k1_xboole_0 ) ) ) ) )).
fof(t29_jgraph_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => k1_square_1(k12_euclid(A)) = k2_xcmplx_0(k1_square_1(k17_euclid(A)),k1_square_1(k18_euclid(A))) ) )).
fof(t29_jgraph_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( ( 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] : ( 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) ) ) ) )).
fof(t29_jgraph_5,axiom,( ! [A] : ( ( ~ 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(k4_xcmplx_0(1),k5_numbers) ) ) )).
fof(t29_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t29_jordan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t29_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t29_jordan12,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t29_jordan14,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( 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_0(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)) ) ) ) ) ) )).
fof(t29_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C)),k3_topreal1(2,k1_jordan1e(B,A))) = k1_tarski(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C)),k3_topreal1(2,k2_jordan1e(B,A))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C)) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C)),k8_jordan6(B)) ) ) ) ) ) ) )).
fof(t29_jordan18,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => r1_jordan18(A,B,D,C,C,E) ) ) ) ) ) )).
fof(t29_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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))) ) ) ) ) )).
fof(t29_jordan1b,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ~ ( 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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,k3_finseq_1(k1_jordan8(B,A)))),k8_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) ) ) ) ) )).
fof(t29_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(k1_jordan8(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,1),k10_xtuple_0(k2_jordan9(B,A))) ) ) ) )).
fof(t29_jordan1g,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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,k2_jordan9(B,A)))),k4_finseq_4(k2_jordan1e(B,A),k18_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))))) ) ) )).
fof(t29_jordan1k,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,k1_rltopsp1(k15_euclid(2),B,C)) => k2_xcmplx_0(k1_topreal6(2,B,A),k1_topreal6(2,A,C)) = k1_topreal6(2,B,C) ) ) ) ) )).
fof(t29_jordan20,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( v1_xreal_0(G) => ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t29_jordan21,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( 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(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(B),k8_pscomp_1(B)),2)))) => r1_xxreal_0(k18_euclid(k2_jordan21(B)),k18_euclid(A)) ) ) ) )).
fof(t29_jordan22,axiom,( ! [A] : ( ( 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)) ) )).
fof(t29_jordan23,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v1_topreal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(B,k3_topreal1(2,A)) => v1_topreal1(k2_jordan3(A,B)) ) ) ) ) )).
fof(t29_jordan2b,axiom,( ! [A] : ( 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) ) ) )).
fof(t29_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( 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] : ( v1_xreal_0(F) => ( D != k1_rlvect_1(k15_euclid(A),E,F) & E != k1_rlvect_1(k15_euclid(A),D,F) ) ) & ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(A))) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t29_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t29_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r1_jordan4(A,B,C,D) => r2_jordan4(A,k4_finseq_5(u1_struct_0(k15_euclid(2)),B),D,C) ) ) ) ) ) )).
fof(t29_jordan5b,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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,k1_nat_1(k1_jordan3(A,B),1)))) ) ) ) )).
fof(t29_jordan5c,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v7_ordinal1(D) => ( ( 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(k1_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,k1_nat_1(D,1)),B,C) ) ) ) ) ) )).
fof(t29_jordan5d,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( B = a_1_4_jordan5d(A) => k2_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))) ) ) ) )).
fof(t29_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t29_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_jordan_a(B,A) => ~ r2_subset_1(k2_jordan_a(A,k3_finseq_1(B),B),k2_jordan_a(A,1,B)) ) ) )).
fof(t29_knaster,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v4_lattice3(B) & l3_lattices(B) ) => ! [C] : ( ( 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] : ( 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] : ( v3_ordinal1(E) => ( r1_ordinal1(A,E) => k6_knaster(B,C,D,A) = k6_knaster(B,C,D,E) ) ) ) ) ) ) ) )).
fof(t29_kurato_1,axiom,( 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) )).
fof(t29_kurato_2,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => k2_tops_1(k15_euclid(2),k3_subset_1(u1_struct_0(k15_euclid(2)),k2_jordan2c(2,k3_topreal1(2,k2_jordan9(A,B))))) = k3_topreal1(2,k2_jordan9(A,B)) ) ) )).
fof(t29_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(D),C,C) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(D))) ) => ( r2_hidden(A,k2_finseq_1(C)) => k13_fvsum_1(D,k7_matrix_0(u1_struct_0(D),E,B),k8_matrix_0(u1_struct_0(D),k4_matrix_0(u1_struct_0(D),k7_laplace(C,D,E)),A)) = k12_matrix_3(C,D,k3_matrix11(A,C,C,u1_struct_0(D),E,k7_matrix_0(u1_struct_0(D),E,B))) ) ) ) ) ) ) )).
fof(t29_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t29_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k5_finsub_1(C)) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t29_lattice3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( 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) ) ) ) )).
fof(t29_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => k7_lattices(A,k6_lattices(A)) = k5_lattices(A) ) )).
fof(t29_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r1_ordinal1(B,C) => r1_tarski(k8_lattice5(A,B),k8_lattice5(A,C)) ) ) ) ) )).
fof(t29_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ! [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] : ( m1_subset_1(J,D) => ! [K] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t29_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)))) => ! [C] : ~ ( ~ r2_hidden(C,k1_relset_1(k6_glib_000(A),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),B))) & k1_relset_1(k6_glib_000(A),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),B)) != k6_glib_000(A) & ~ r1_termord(k4_ordinal1,k4_bagorder(k4_ordinal1),k1_uproots(k4_ordinal1,k17_lexbfs(k6_glib_000(A),k4_ordinal1,k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),B),C),1),k1_uproots(k4_ordinal1,k17_lexbfs(k6_glib_000(A),k4_ordinal1,k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),B),k10_lexbfs(A,B)),1)) ) ) ) )).
fof(t29_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( m1_subset_1(C,A) => ! [D] : ( 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(k5_numbers,1)),k5_card_3(k1_domain_1(A,A,C,D),a_2_0_lfuzzy_1(A,B))) ) ) ) ) )).
fof(t29_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v7_valued_0(A) => ( v1_seq_2(A) | v1_limfunc1(A) ) ) ) )).
fof(t29_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,A) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(C,D) & ~ r1_xxreal_0(D,A) & r2_hidden(D,k1_relset_1(k1_numbers,B)) ) ) ) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( v8_valued_0(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(A,k2_xcmplx_0(A,C)))) & ~ v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(A,k2_xcmplx_0(A,C)))) ) ) | r5_limfunc2(B,A) ) ) ) ) )).
fof(t29_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t29_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k3_limfunc1(C))) & r1_xxreal_0(k1_funct_1(A,D),k4_limfunc1(A)) ) ) | v4_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).
fof(t29_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t29_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t29_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( ! [C] : ( v7_ordinal1(C) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,k5_normsp_0(A,B),C),k5_numbers) ) & ? [C] : ( v7_ordinal1(C) & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => r1_xxreal_0(1,k6_real_1(k9_nat_1(k1_numbers,k5_normsp_0(A,B),k1_nat_1(D,1)),k9_nat_1(k1_numbers,k5_normsp_0(A,B),D))) ) ) ) & v2_lopban_3(B,A) ) ) ) )).
fof(t29_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_xxreal_0(1,k4_series_1(k4_sin_cos(k2_normsp_0(A,B)))) ) ) )).
fof(t29_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t29_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(k16_lpspacc1(A,B,C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k16_lpspacc1(A,B,C))) => ( ( D = F & E = G ) => k2_valued_1(A,k2_numbers,k2_numbers,D,E) = k1_algstr_0(k16_lpspacc1(A,B,C),F,G) ) ) ) ) ) ) ) ) )).
fof(t29_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t29_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( v2_xxreal_0(F) & v1_xreal_0(F) ) => ! [G] : ( m1_subset_1(G,u1_struct_0(k2_lpspace2(A,B,C,F))) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t29_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => ( r2_ltlaxio1(C,A) => r2_ltlaxio1(k8_nat_1(k1_zfmisc_1(k10_ltlaxio1),C,B),A) ) ) ) ) )).
fof(t29_ltlaxio2,axiom,( ! [A] : ( m2_finseq_1(A,k1_hilbert1) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => v1_ltlaxio1(k3_hilbert1(k7_partfun1(k1_hilbert1,A,B),k1_ltlaxio1(k7_partfun1(k1_hilbert1,k2_ltlaxio2(k4_ltlaxio2(A)),k3_finseq_1(k2_ltlaxio2(k4_ltlaxio2(A))))))) ) ) ) )).
fof(t29_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => ( r2_hidden(A,k2_relset_1(k1_hilbert1,k9_ltlaxio3(B))) => r8_ltlaxio1(k1_subset_1(k1_hilbert1),k3_hilbert1(k12_ltlaxio3(B),k1_ltlaxio1(A))) ) ) ) )).
fof(t29_ltlaxio4,axiom,( ! [A] : ( ( ~ v2_ltlaxio3(A) & v3_ltlaxio3(A) & m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) ) => ! [B] : ( m3_ltlaxio4(B,A) => ! [C] : ( m2_finseq_1(C,k1_hilbert1) => ( k2_relset_1(k1_hilbert1,C) = k3_ltlaxio4(k11_ltlaxio4(A,B)) => r8_ltlaxio1(k1_subset_1(k1_hilbert1),k3_hilbert1(k1_ltlaxio1(k7_partfun1(k1_hilbert1,k2_ltlaxio2(k4_ltlaxio2(C)),k3_finseq_1(k2_ltlaxio2(k4_ltlaxio2(C))))),k2_ltlaxio1(k1_ltlaxio1(k7_partfun1(k1_hilbert1,k2_ltlaxio2(k4_ltlaxio2(C)),k3_finseq_1(k2_ltlaxio2(k4_ltlaxio2(C)))))))) ) ) ) ) )).
fof(t29_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t29_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t29_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,B,B) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( r1_xxreal_0(A,k5_numbers) & v1_matrix10(C) ) => v3_matrix10(k6_matrix10(B,A,C)) ) ) ) ) )).
fof(t29_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,D,B,C) & m2_finseq_1(E,k3_finseq_2(D)) ) => ! [F] : ( m2_finseq_1(F,D) => ( k3_finseq_1(F) = k1_matrix_0(E) => ! [G] : ( m2_finseq_2(G,D,k3_finseq_2(D)) => ( F = G => k3_matrix11(A,B,C,D,E,F) = k1_finseq_7(k3_finseq_2(D),E,A,G) ) ) ) ) ) ) ) ) ) )).
fof(t29_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( ( v1_matrix_0(F) & m2_finseq_1(F,k3_finseq_2(A)) ) => ! [G] : ( m2_finseq_2(G,k4_ordinal1,k4_finseq_2(E,k4_ordinal1)) => ! [H] : ( m2_finseq_2(H,k4_ordinal1,k4_finseq_2(D,k4_ordinal1)) => ( ( r2_hidden(B,k2_finseq_1(D)) & r2_hidden(C,k2_finseq_1(D)) & k1_funct_1(H,B) = k1_funct_1(H,C) ) => k8_matrix_0(A,k1_matrix13(A,F,E,D,G,H),B) = k8_matrix_0(A,k1_matrix13(A,F,E,D,G,H),C) ) ) ) ) ) ) ) ) ) )).
fof(t29_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( C = k3_matrix_1(B,A) <=> ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,A) & r1_xxreal_0(1,E) & r1_xxreal_0(E,A) ) => k3_matrix_0(u1_struct_0(B),C,D,E) = k15_funcop_1(u1_struct_0(B),D,E,k5_struct_0(B),k4_struct_0(B)) ) ) ) ) ) ) ) )).
fof(t29_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t29_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(B),A,A) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(B))) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(B),A,A) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(B))) ) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(B),A,A) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(B))) ) => ( ( v3_matrix16(F,u1_struct_0(B)) & v3_matrix16(G,u1_struct_0(B)) & v3_matrix16(H,u1_struct_0(B)) ) => v3_matrix16(k1_matrix_4(B,k1_matrix_4(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)) ) ) ) ) ) ) ) ) ) )).
fof(t29_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ( ~ r1_xxreal_0(k1_matrix_0(B),k5_numbers) => ( k3_finseq_1(k4_matrix_0(A,B)) = k1_matrix_0(B) & k1_matrix_0(k4_matrix_0(A,B)) = k3_finseq_1(B) ) ) ) ) )).
fof(t29_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ! [E] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(D) & k1_matrix_0(D) = k1_matrix_0(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) ) ) ) ) ) ) )).
fof(t29_matrix_6,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(A),B,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( v2_matrix_6(C,B,A) & v3_matrix_6(C,B,A) ) => C = k1_matrix_3(A,B,B) ) ) ) ) )).
fof(t29_matrix_7,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t29_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & v2_matrix_8(C,A,B) & v1_matrix_6(C,A,B) ) ) ) ) )).
fof(t29_matrix_9,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k4_matrix_2(3))) => ( A = k3_finseq_4(k4_ordinal1,2,3,1) => k2_group_1(k4_matrix_2(3),A) = k3_finseq_4(k4_ordinal1,3,1,2) ) ) )).
fof(t29_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => k17_rvsum_1(k8_seq_4(A,B)) = k6_xcmplx_0(k17_rvsum_1(A),k17_rvsum_1(B)) ) ) ) )).
fof(t29_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( ( v1_matrixj1(E,C) & m2_finseq_1(E,k3_finseq_2(k3_finseq_2(C))) ) => ! [F] : ( ( v1_matrixj1(F,C) & m2_finseq_1(F,k3_finseq_2(k3_finseq_2(C))) ) => ( r2_hidden(k4_tarski(A,B),k2_matrix_0(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_0(C,k13_matrixj1(C,D,k3_matrixj1(C,E,F)),A,B) = D ) ) ) ) ) ) ) ) )).
fof(t29_matrixj2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( 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] : ( v2_relat_1(D) & m1_matrixj2(D,A,k4_struct_0(A)) & ? [E] : ( m1_matrlin(E,A,B) & k1_matrlin2(A,B,B,C,E,E) = k20_matrixj1(u1_struct_0(A),k4_struct_0(A),D) ) ) ) ) ) )).
fof(t29_matrixr1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k4_tarski(C,D),k2_matrix_0(B)) => k3_matrix_0(k1_numbers,k7_matrixr1(A,B),C,D) = k3_xcmplx_0(A,k3_matrix_0(k1_numbers,B,C,D)) ) ) ) ) ) )).
fof(t29_matrixr2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,A,B,B) & m2_finseq_1(C,k3_finseq_2(A)) ) => k4_matrix_0(A,k4_matrix_0(A,C)) = C ) ) ) )).
fof(t29_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(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)) ) ) ) ) )).
fof(t29_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_matrlin(C,A,B) => ! [D] : ( 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) = k1_matrix_6(k3_finseq_1(C),A,k3_matrlin2(A,B,B,k3_struct_0(B),C,D)) ) ) ) ) ) )).
fof(t29_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r1_tarski(B,C) & r2_matroid0(A,D,B) ) => r2_matroid0(A,D,C) ) ) ) ) ) )).
fof(t29_matrprob,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => k5_matrprob(A) = k18_rvsum_1(k4_matrprob(A)) ) )).
fof(t29_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => 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)) ) ) ) )).
fof(t29_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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_3(k2_vectsp_1,k3_matrtop3(A,C),k3_matrtop3(A,B)) ) ) ) )).
fof(t29_mboolean,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t29_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k3_zfmisc_1(k2_tarski(A,D),k2_tarski(B,E),k1_tarski(C)) = k2_enumset1(k3_xtuple_0(A,B,C),k3_xtuple_0(D,B,C),k3_xtuple_0(A,E,C),k3_xtuple_0(D,E,C)) )).
fof(t29_measure1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) ) ) )).
fof(t29_measure6,axiom,( ! [A] : ( ( v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ( v4_measure5(A) <=> v4_measure5(k1_measure6(A,B)) ) ) ) )).
fof(t29_measure8,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(D) => v7_valued_0(k11_measure8(A,B,D,C)) ) ) ) ) )).
fof(t29_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_xcmplx_0(B) => ( r2_hidden(k5_xcmplx_0(B),A) <=> r2_hidden(B,k7_member_1(A)) ) ) ) )).
fof(t29_membered,axiom,( ! [A] : ( ! [B] : ( r2_hidden(B,A) => v5_membered(B) ) => v5_membered(k3_tarski(A)) ) )).
fof(t29_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t29_mesfun6c,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( m2_subset_1(D,k1_zfmisc_1(B),C) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ( ( v6_supinf_2(E) & r1_xxreal_0(k5_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) ) ) ) ) ) ) )).
fof(t29_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( ( r1_xxreal_0(k5_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) ) ) ) ) ) ) )).
fof(t29_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ( r2_funct_2(k4_ordinal1,k4_partfun1(A,k1_numbers),k2_mesfun9c(A,k11_mesfun7c(A,B)),k11_mesfun7c(A,k3_mesfun9c(A,B))) & r2_funct_2(k4_ordinal1,k4_partfun1(A,k1_numbers),k2_mesfun9c(A,k12_mesfun7c(A,B)),k12_mesfun7c(A,k3_mesfun9c(A,B))) ) ) ) )).
fof(t29_mesfunc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( r1_tarski(D,k9_xtuple_0(C)) => ( r1_mesfunc1(A,B,C,D) <=> ! [E] : ( v1_xreal_0(E) => r2_hidden(k9_subset_1(A,D,k17_mesfunc1(A,C,E)),B) ) ) ) ) ) ) ) )).
fof(t29_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m1_subset_1(D,B) => r1_mesfunc1(A,B,k3_mesfunc2(C,A),D) ) ) ) ) )).
fof(t29_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( r1_tarski(D,k1_relset_1(A,k3_mesfunc1(A,B,C))) => ( k1_relset_1(A,k2_partfun1(A,k6_numbers,k3_mesfunc1(A,B,C),D)) = D & k1_relset_1(A,k3_mesfunc1(A,k2_partfun1(A,k6_numbers,B,D),k2_partfun1(A,k6_numbers,C,D))) = D & r2_relset_1(A,k6_numbers,k2_partfun1(A,k6_numbers,k3_mesfunc1(A,B,C),D),k3_mesfunc1(A,k2_partfun1(A,k6_numbers,B,D),k2_partfun1(A,k6_numbers,C,D))) ) ) ) ) ) )).
fof(t29_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t29_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ! [F] : ( 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))) ) ) ) ) ) )).
fof(t29_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( v7_ordinal1(C) => ( ( v2_mesfunc9(B,A) & v1_mesfunc8(B,A,k6_numbers) ) => k1_relset_1(A,k4_mesfunc5(A,k6_numbers,k4_mesfunc9(A,B),C)) = k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers)) ) ) ) ) )).
fof(t29_metric_1,axiom,( ! [A] : ( m1_subset_1(A,2) => ! [B] : ( m1_subset_1(B,2) => ! [C] : ( m1_subset_1(C,2) => r1_xxreal_0(k1_binop_1(k11_metric_1,A,C),k2_xcmplx_0(k1_binop_1(k11_metric_1,A,B),k1_binop_1(k11_metric_1,B,C))) ) ) ) )).
fof(t29_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( 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] : ( m1_subset_1(C,k2_metric_2(A)) & ? [D] : ( m1_subset_1(D,k2_metric_2(A)) & ? [E] : ( 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) ) ) ) ) ) ) )).
fof(t29_metric_3,axiom,( ! [A] : ( m1_subset_1(A,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)) => ! [B] : ( m1_subset_1(B,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)) => k2_binop_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k1_numbers,k22_metric_3,A,B) = k2_binop_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k1_numbers,k22_metric_3,B,A) ) ) )).
fof(t29_metric_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( ( v6_tbsp_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( v1_xreal_0(D) & ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(B,k8_metric_1(A,C,D)) ) ) ) ) )).
fof(t29_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(k2_xcmplx_0(A,1)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(k2_xcmplx_0(A,1)))) => ( B != k4_struct_0(k15_euclid(k2_xcmplx_0(A,1))) => r1_mfold_2(k15_euclid(A),k3_mfold_2(k2_xcmplx_0(A,1),B,C)) ) ) ) ) )).
fof(t29_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t29_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( ( v4_midsp_2(B,A) & l1_midsp_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( k3_midsp_1(A,C,F) = k3_midsp_1(A,D,E) <=> k9_midsp_2(A,B,C,F) = k1_algstr_0(u1_midsp_2(A,B),k9_midsp_2(A,B,C,D),k9_midsp_2(A,B,C,E)) ) ) ) ) ) ) ) )).
fof(t29_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_midsp_3(B,A) => ! [C] : ( m2_midsp_3(C,A) => ( ( r1_midsp_3(A,B,C) & r3_midsp_3(A,B,C) ) => r2_midsp_3(A,B,C) ) ) ) ) )).
fof(t29_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( ! [D] : ( m1_subset_1(D,A) => k1_mmlquery(A,B,D) = k1_mmlquery(A,C,D) ) => r2_relset_1(A,A,B,C) ) ) ) )).
fof(t29_mod_2,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t29_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(t29_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k6_modal_1) => ! [B] : ( m1_subset_1(B,k6_modal_1) => ( k11_modal_1(A) = k11_modal_1(B) => A = B ) ) ) )).
fof(t29_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t29_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r1_modelc_2(B,A) => r3_modelc_2(B,A) ) ) ) )).
fof(t29_modelc_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_modelc_2(D) & m2_finseq_1(D,k4_ordinal1) ) => ~ ( 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(t29_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( v7_ordinal1(B) => ( r1_nat_d(A,B) => ( v1_moebius1(B) | a_2_2_moebius1(A,B) = a_2_3_moebius1(A,B) ) ) ) ) )).
fof(t29_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m3_monoid_0(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t29_monoid_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k13_monoid_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k13_monoid_1(A))) => ! [D] : ( m1_subset_1(D,A) => k15_monoid_1(A,k6_algstr_0(k13_monoid_1(A),B,C),D) = k1_nat_1(k15_monoid_1(A,B,D),k15_monoid_1(A,C,D)) ) ) ) ) )).
fof(t29_morph_01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t29_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( 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] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t29_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ( v1_catalg_1(C,A) => ! [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => r1_msualg_3(A,B,C,D) ) ) ) ) ) )).
fof(t29_mssublat,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( v1_unialg_1(B) & v4_unialg_1(B) & m1_unialg_2(B,A) ) => ! [C] : ( ( v1_unialg_1(C) & v4_unialg_1(C) & m1_unialg_2(C,A) ) => ! [D] : ( ( 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] : ( ( 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(k5_numbers,k3_xboole_0(u1_struct_0(B),u1_struct_0(C))) ) ) ) ) ) ) )).
fof(t29_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => v1_binop_1(k15_msualg_2(A,B),k14_msualg_2(A,B)) ) ) )).
fof(t29_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msualg_4(C,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,B),D)) => ! [F] : ( 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] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,B),G)) & ? [I] : ( m1_subset_1(I,k1_funct_1(u3_msualg_1(A,B),G)) & ? [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t29_msualg_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t29_mycielsk,axiom,( ! [A] : ( ( v1_necklace(A) & v1_mycielsk(A) & l1_orders_2(A) ) => k2_mycielsk(A) = k3_mycielsk(k3_necklace(A)) ) )).
fof(t29_nagata_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => r1_xxreal_0(k5_numbers,k1_binop_1(B,C,D)) ) ) ) ) )).
fof(t29_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(k5_card_1(B),k5_card_1(A)) <=> ~ r1_xxreal_0(A,B) ) ) ) )).
fof(t29_nat_2,axiom,( ! [A] : ( ( ~ v1_zfmisc_1(A) & v7_ordinal1(A) ) => r1_xxreal_0(2,A) ) )).
fof(t29_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => k1_newton(A,k11_nat_3(k3_xcmplx_0(B,C),A)) = k3_xcmplx_0(k1_newton(A,k11_nat_3(B,A)),k1_newton(A,k11_nat_3(C,A))) ) ) ) )).
fof(t29_nat_4,axiom,( v1_int_2(19) )).
fof(t29_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => k3_nat_5(A,1) = 1 ) )).
fof(t29_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k3_xcmplx_0(A,B) = k2_nat_1(k5_nat_d(A,B),k6_nat_d(A,B)) ) ) )).
fof(t29_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_nattra_1(E,A,B,C,D) => ! [F] : ( m1_subset_1(F,u4_struct_0(k9_nattra_1(A,B))) => ( F = k4_tarski(k4_tarski(C,D),E) => ( k3_graph_1(k9_nattra_1(A,B),F) = C & k4_graph_1(k9_nattra_1(A,B),F) = D ) ) ) ) ) ) ) ) )).
fof(t29_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,k1_numbers,k5_normsp_0(B,k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),D,C)),k8_funct_2(k4_ordinal1,k1_numbers,u1_struct_0(A),D,k4_normsp_0(u1_struct_0(A),B,C))) & r2_funct_2(k4_ordinal1,u1_struct_0(B),k5_vfunct_1(k4_ordinal1,B,k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),D,C)),k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),D,k5_vfunct_1(u1_struct_0(A),B,C))) ) ) ) ) ) ) )).
fof(t29_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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)))) ) => ( v1_funct_1(k4_vfunct_1(u1_struct_0(A),B,D,C)) & v2_ndiff_1(k4_vfunct_1(u1_struct_0(A),B,D,C),A,B) & m1_subset_1(k4_vfunct_1(u1_struct_0(A),B,D,C),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) ) ) ) ) )).
fof(t29_ndiff_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t29_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k14_prvect_2(A))) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t29_neckla_3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( C = k1_neckla_3(A,B) <=> ! [D] : ( r2_hidden(D,C) <=> r2_hidden(k4_tarski(B,D),k1_msualg_5(u1_struct_0(A),u1_orders_2(A))) ) ) ) ) )).
fof(t29_necklace,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( r5_waybel_1(k4_necklace(A),k3_necklace(k4_necklace(A))) & A != k5_numbers & A != 1 & A != 4 ) ) )).
fof(t29_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k1_funct_1(k5_newton(B,C,A),k1_nat_1(A,1)) = k1_newton(C,A) ) ) ) )).
fof(t29_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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)) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k7_partfun1(u1_struct_0(B),C,k3_rlvect_1(A,D,E)) = k3_rlvect_1(B,k7_partfun1(u1_struct_0(B),C,D),k7_partfun1(u1_struct_0(B),C,E)) ) ) ) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ r1_nfcont_1(A,B,C,D) ) | r3_nfcont_1(A,B,C,u1_struct_0(A)) ) ) ) ) ) )).
fof(t29_nfcont_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(C)))) ) => ! [E] : ( ( 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) ) ) ) ) )).
fof(t29_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ( ( 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) ) ) ) ) )).
fof(t29_normform,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(t29_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k4_normsp_2(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k4_normsp_2(A))))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k4_normsp_2(A))) => ( ( r1_funct_2(k4_ordinal1,u1_struct_0(A),k4_ordinal1,u1_struct_0(k4_normsp_2(A)),B,C) & D = E ) => ( r1_frechet(k4_normsp_2(A),C,E) <=> ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( v7_ordinal1(G) => ? [H] : ( v7_ordinal1(H) & r1_xxreal_0(G,H) & r1_xxreal_0(F,k2_normsp_0(A,k5_algstr_0(A,k1_normsp_1(A,B,H),D))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t29_numbers,axiom,( k4_ordinal1 != k1_numbers )).
fof(t29_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t29_openlatt,axiom,( ! [A] : ( ( ~ 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 ) )).
fof(t29_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_oppcat_1(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t29_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_nfcont_4(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ( k1_relset_1(k1_numbers,D) = k3_integra5(B,C) => v3_integr15(k2_partfun1(k1_numbers,k1_euclid(A),D,k3_integra5(B,C)),A) ) ) ) ) ) )).
fof(t29_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r3_orders_1(A,B) => ( r1_orders_1(A,B) & r2_orders_1(A,B) ) ) ) )).
fof(t29_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_orders_2(C,A,B) => r1_tarski(C,B) ) ) ) )).
fof(t29_ordinal1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) & v5_ordinal1(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(t29_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( v4_ordinal1(A) => ( A = k1_xboole_0 | v4_ordinal1(k10_ordinal2(B,A)) ) ) ) ) )).
fof(t29_ordinal4,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r2_hidden(1,B) => ( A = k1_xboole_0 | r2_hidden(1,k12_ordinal2(B,A)) ) ) ) ) )).
fof(t29_ordinal6,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(t29_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ~ r1_orders_2(B,D,C) => ( k2_ortsp_1(A,B,E,F,C,D) = k4_struct_0(A) <=> r1_orders_2(B,F,E) ) ) ) ) ) ) ) ) )).
fof(t29_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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)) ) ) )).
fof(t29_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t29_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t29_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t29_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t29_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r1_tarski(C,B) => r1_relset_1(A,C,k3_partfun1(D,A,C),k3_partfun1(D,A,B)) ) ) )).
fof(t29_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,B) => ( r2_hidden(D,C) => k7_partfun1(B,k4_partfun2(A,B,C,E),D) = E ) ) ) ) ) ) )).
fof(t29_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ( ( r1_setfam_1(B,D) & r1_setfam_1(C,D) ) => r1_setfam_1(k3_partit1(A,B,C),D) ) ) ) ) ) )).
fof(t29_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( r5_relat_2(B,A) => v5_relat_2(B) ) ) ) )).
fof(t29_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_diraf(A,B,C,E) & r1_diraf(A,B,F,D) & ~ r3_diraf(A,B,C,D) & ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( r1_diraf(A,C,G,D) & r1_diraf(A,F,G,E) ) ) ) ) ) ) ) ) ) )).
fof(t29_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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))) ) ) ) )).
fof(t29_pcomps_1,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ( v9_metric_1(A) => r2_hidden(k8_metric_1(A,B,C),k2_pcomps_1(A)) ) ) ) ) )).
fof(t29_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k20_pcs_0(A,B))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k20_pcs_0(A,B))) => ( ( C = E & D = F & r1_pcs_0(k20_pcs_0(A,B),E,F) ) => ( C = B | D = B | r1_pcs_0(A,C,D) ) ) ) ) ) ) ) )).
fof(t29_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( 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) & k10_pdiff_1(A,B,k3_valued_1(k1_euclid(A),k1_numbers,k1_numbers,C,D),E) = k2_xcmplx_0(k10_pdiff_1(A,B,C,E),k10_pdiff_1(A,B,D,E)) ) ) ) ) ) ) ) )).
fof(t29_pdiff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(2)) => ! [C] : ( ( 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) & k10_pdiff_1(2,1,k26_valued_1(k1_euclid(2),k1_numbers,k1_pdiff_3(1,2,C),A),B) = k3_xcmplx_0(A,k2_pdiff_3(C,B)) ) ) ) ) ) )).
fof(t29_pdiff_4,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t29_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( 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) = k10_pdiff_1(3,2,k1_pdiff_3(1,3,B),A) ) ) ) )).
fof(t29_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t29_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( 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))) ) ) ) ) ) ) )).
fof(t29_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(B))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k3_finseq_2(B))) => k10_pnproc_1(A,B,k4_subset_1(k3_finseq_2(B),D,E),C) = k4_subset_1(k3_finseq_2(B),k10_pnproc_1(A,B,D,C),k10_pnproc_1(A,B,E,C)) ) ) ) ) )).
fof(t29_polyeq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( k4_polyeq_1(B,k5_numbers,C,k5_numbers,A) = k5_numbers => ( B = k5_numbers | ! [D] : ( v1_xcmplx_0(D) => ~ ( D = k4_xcmplx_0(k7_xcmplx_0(C,B)) & A != k5_numbers & A != k2_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(D),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(D)),k1_square_1(k4_complex1(D))))),2)),k3_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(D)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(D)),k1_square_1(k4_complex1(D))))),2)),k7_complex1)) & A != k2_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(D),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(D)),k1_square_1(k4_complex1(D))))),2))),k3_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(D)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(D)),k1_square_1(k4_complex1(D))))),2))),k7_complex1)) & A != k2_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(D),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(D)),k1_square_1(k4_complex1(D))))),2)),k3_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(D)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(D)),k1_square_1(k4_complex1(D))))),2))),k7_complex1)) & A != k2_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(D),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(D)),k1_square_1(k4_complex1(D))))),2))),k3_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(D)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(D)),k1_square_1(k4_complex1(D))))),2)),k7_complex1)) ) ) ) ) ) ) ) )).
fof(t29_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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 ) ) ) ) )).
fof(t29_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => k11_polyform(A,k4_xcmplx_0(1)) = 1 ) )).
fof(t29_polynom1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( 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),k10_polynom1(A,B,C,k9_polynom1(A,B)),C) ) ) ) )).
fof(t29_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l5_algstr_0(A) ) => ( k1_normsp_1(A,k10_polynom3(A),k5_numbers) = k5_struct_0(A) & ! [B] : ( v7_ordinal1(B) => ( B != k5_numbers => k1_normsp_1(A,k10_polynom3(A),B) = k4_struct_0(A) ) ) ) ) )).
fof(t29_polynom5,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_polynom5(A,k10_polynom3(A),B),k2_algseq_1(A,B)) ) ) )).
fof(t29_polynom7,axiom,( ! [A] : ( v3_ordinal1(A) => ! [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) & v5_group_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & v1_algstr_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( 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)))) ) => k2_polynom2(A,B,k5_polynom7(A,B,C,D),E) = k8_group_1(B,D,k2_polynom2(A,B,C,E)) ) ) ) ) ) )).
fof(t29_polynom8,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,1) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ! [E] : ( v7_ordinal1(E) => ( ~ r1_xxreal_0(A,E) => k3_matrix_0(u1_struct_0(B),D,k1_nat_1(E,1),1) = k9_nat_1(u1_struct_0(B),C,E) ) ) => k4_polynom8(A,B,C) = D ) ) ) ) ) ) )).
fof(t29_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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) ) ) ) ) ) ) )).
fof(t29_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(A,k5_numbers) => k2_power(A,k6_xcmplx_0(B,C)) = k7_xcmplx_0(k2_power(A,B),k2_power(A,C)) ) ) ) ) )).
fof(t29_pre_poly,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k3_finseq_2(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(D,k4_finseq_1(k1_funct_1(B,C))) ) => ( r2_hidden(k1_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),k1_nat_1(k2_wsierp_1(k10_pre_poly(A,k17_finseq_1(k3_finseq_2(A),k7_nat_d(C,1),B))),D)) ) ) ) ) ) )).
fof(t29_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) => m1_pre_topc(B,A) ) ) )).
fof(t29_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_prelamb(A) & l2_prelamb(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t29_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ( ( 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) ) ) ) ) )).
fof(t29_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m1_prob_1(E,A,B) => ( ~ r1_xxreal_0(k3_funct_2(B,k1_numbers,C,D),k5_numbers) => k3_funct_2(B,k1_numbers,C,k5_prob_1(A,B,E,D)) = k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,C,D),E),k3_funct_2(B,k1_numbers,C,D)) ) ) ) ) ) ) )).
fof(t29_prob_3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k3_prob_1(A,k1_prob_3(A,C)) = k3_prob_1(A,C) ) ) )).
fof(t29_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t29_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t29_projpl_1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & v5_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t29_pscomp_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(t29_pua2mss1,axiom,( ! [A] : ( l1_msualg_1(A) => ! [B] : ( l1_msualg_1(B) => ! [C] : ( l1_msualg_1(C) => ( ( r4_pua2mss1(A,B) & r4_pua2mss1(B,C) ) => r4_pua2mss1(A,C) ) ) ) ) )).
fof(t29_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(t29_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k1_qc_lang1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t29_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t29_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( v6_qc_lang1(C,A) => v6_qc_lang1(k5_qc_lang2(A,B,C),A) ) ) ) ) )).
fof(t29_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t29_quantal1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t29_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ( k13_quaterni(k7_quatern2(A)) = k7_xcmplx_0(k13_quaterni(A),k1_square_1(k28_quaterni(A))) & k14_quaterni(k7_quatern2(A)) = k4_xcmplx_0(k7_xcmplx_0(k14_quaterni(A),k1_square_1(k28_quaterni(A)))) & k15_quaterni(k7_quatern2(A)) = k4_xcmplx_0(k7_xcmplx_0(k15_quaterni(A),k1_square_1(k28_quaterni(A)))) & k16_quaterni(k7_quatern2(A)) = k4_xcmplx_0(k7_xcmplx_0(k16_quaterni(A),k1_square_1(k28_quaterni(A)))) ) ) )).
fof(t29_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k23_quaterni(A,k21_quaterni(k7_xcmplx_0(1,k1_square_1(k28_quaterni(A))),k27_quaterni(A))) = k6_quaterni(k7_xcmplx_0(k1_square_1(k28_quaterni(A)),k1_square_1(k28_quaterni(A))),k5_numbers,k5_numbers,k5_numbers) ) )).
fof(t29_quaterni,axiom,( k13_quaterni(k18_quaterni) = 1 & k14_quaterni(k18_quaterni) = k5_numbers & k15_quaterni(k18_quaterni) = k5_numbers & k16_quaterni(k18_quaterni) = k5_numbers )).
fof(t29_quofield,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(t29_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [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))) ) => m1_random_1(B,A,k1_random_1(A)) ) ) )).
fof(t29_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_vectsp_6(E,A,B) => m2_vectsp_6(k8_ranknull(A,B,C,E,D),A,C,k2_ranknull(B,C,D,k1_vectsp_6(A,B,E))) ) ) ) ) ) )).
fof(t29_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) <=> r1_xxreal_0(k2_rat_1(A),k4_xcmplx_0(k1_rat_1(A))) ) ) )).
fof(t29_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( 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)))) ) ) )).
fof(t29_rcomp_3,axiom,( ! [A] : ( ( v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ~ ( ~ v1_xboole_0(A) & A != k1_numbers & ! [B] : ( v1_xreal_0(B) => A != k1_limfunc1(B) ) & ! [B] : ( v1_xreal_0(B) => A != k10_prob_1(B) ) & ! [B] : ( v1_xreal_0(B) => A != k2_limfunc1(B) ) & ! [B] : ( v1_xreal_0(B) => A != k3_limfunc1(B) ) & ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( r1_xxreal_0(B,C) & A = k1_rcomp_1(B,C) ) ) ) & ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,B) & A = k3_rcomp_1(B,C) ) ) ) & ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,B) & A = k4_rcomp_1(B,C) ) ) ) & ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,B) & A = k2_rcomp_1(B,C) ) ) ) ) ) )).
fof(t29_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t29_rearran1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,k1_numbers))) ) => ! [E] : ( ( v1_rearran1(E) & v2_rearran1(E) & v3_rearran1(E,k1_zfmisc_1(B)) & m2_finseq_1(E,k1_zfmisc_1(B)) ) => ( ( v1_partfun1(D,C) & k5_card_1(B) = k5_card_1(C) ) => ( r2_classes1(k19_rfunct_3(B,k15_valued_1(B,k1_numbers,k3_rearran1(C,B,E,D),A)),k19_rfunct_3(C,k15_valued_1(C,k1_numbers,D,A))) & k20_rfunct_3(B,k19_rfunct_3(B,k15_valued_1(B,k1_numbers,k3_rearran1(C,B,E,D),A)),B) = k20_rfunct_3(C,k19_rfunct_3(C,k15_valued_1(C,k1_numbers,D,A)),C) & k21_rfunct_3(B,k19_rfunct_3(B,k15_valued_1(B,k1_numbers,k3_rearran1(C,B,E,D),A)),B) = k21_rfunct_3(C,k19_rfunct_3(C,k15_valued_1(C,k1_numbers,D,A)),C) ) ) ) ) ) ) ) )).
fof(t29_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => k2_relat_1(k3_relat_1(A,B)) = k3_relat_1(k2_relat_1(B),k2_relat_1(A)) ) ) )).
fof(t29_relset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,C))) => ! [E] : ( m1_subset_1(E,C) => ( r2_hidden(E,k7_relset_1(A,C,D,B)) <=> ? [F] : ( m1_subset_1(F,A) & r2_hidden(k4_tarski(F,E),D) & r2_hidden(F,B) ) ) ) ) ) ) ) )).
fof(t29_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ( C = k1_xboole_0 => k6_relset_2(A,B,C,D) = B ) ) ) )).
fof(t29_revrot_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ 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) ) ) )).
fof(t29_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r2_hidden(k4_tarski(B,C),A) => r2_rewrite1(A,B,C) ) ) )).
fof(t29_rewrite2,axiom,( ! [A] : 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))) )).
fof(t29_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(C))) => ! [G] : ( 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)) ) ) ) ) ) ) )).
fof(t29_rfinseq,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => k3_finseq_1(k2_rfinseq(A,C,B)) = k1_xreal_0(k3_finseq_1(B),C) ) ) ) )).
fof(t29_rfinseq2,axiom,( ! [A] : ( 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) ) ) )).
fof(t29_rfunct_1,axiom,( ! [A] : ( ( 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),k4_xcmplx_0(1)) ) )).
fof(t29_rfunct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t29_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,k3_rfunct_3(A,k1_numbers)) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => 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)) ) ) ) ) )).
fof(t29_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v7_ordinal1(B) => m1_subset_1(a_2_0_rinfsup1(A,B),k1_zfmisc_1(k1_numbers)) ) ) )).
fof(t29_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_funct_2(k4_ordinal1,k6_numbers,k3_rinfsup2(k1_valued_0(k6_numbers,A,B)),k1_valued_0(k6_numbers,k3_rinfsup2(A),B)) & k6_rinfsup2(k1_valued_0(k6_numbers,A,B)) = k6_rinfsup2(A) ) ) ) )).
fof(t29_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( 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)) = k5_numbers ) ) ) ) )).
fof(t29_rlaffin2,axiom,( ! [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) ) => ! [B] : ( ( 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))) ) ) ) ) )).
fof(t29_rlaffin3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( 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),k4_ordinal1,k2_rlaffin3(B,C,A),k8_funcop_1(k4_ordinal1,k2_struct_0(B),k5_numbers)) ) ) ) )).
fof(t29_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_struct_0(B,D) => r1_struct_0(C,D) ) ) => m1_rlsub_1(B,C) ) ) ) ) )).
fof(t29_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( m1_rlsub_1(D,A) => ( ( v1_rlvect_1(B) & m1_rlsub_1(B,D) ) => k1_rlsub_2(A,B,k2_rlsub_2(A,C,D)) = k2_rlsub_2(A,k1_rlsub_2(A,B,C),D) ) ) ) ) ) )).
fof(t29_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t29_rlvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t29_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( B != k1_xboole_0 & v1_rlsub_1(B,A) ) <=> ! [C] : ( m2_rlvect_2(C,A,B) => r2_hidden(k6_rlvect_2(A,C),B) ) ) ) ) )).
fof(t29_rlvect_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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) ) ) )).
fof(t29_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( v1_rlvect_3(k8_domain_1(u1_struct_0(A),B,D,C),A) => ( B = C | B = D | C = D | v1_rlvect_3(k8_domain_1(u1_struct_0(A),B,D,k4_algstr_0(A,C)),A) ) ) ) ) ) ) )).
fof(t29_rlvect_5,axiom,( ! [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_rlvect_5(A) & l1_rlvect_1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t29_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v2_vectsp_2(C,A) & m1_rmod_2(C,A,B) ) => ! [D] : ( ( v2_vectsp_2(D,A) & m1_rmod_2(D,A,B) ) => ( u1_struct_0(C) = u1_struct_0(D) => C = D ) ) ) ) ) )).
fof(t29_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( m1_rmod_2(E,A,B) => m1_rmod_2(k1_rmod_3(A,B,D,k2_rmod_3(A,B,C,E)),A,k2_rmod_3(A,B,k1_rmod_3(A,B,C,D),k1_rmod_3(A,B,D,E))) ) ) ) ) ) )).
fof(t29_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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] : ( m2_rmod_4(D,A,B,C) => r2_hidden(k5_rmod_4(A,B,D),C) ) ) ) ) ) ) )).
fof(t29_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t29_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) )).
fof(t29_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v10_robbins1(A) & v8_robbins3(A) & v9_robbins3(A) & l4_robbins1(A) ) => ! [B] : ( ( v10_robbins3(B) & m3_robbins3(B,A) ) => v12_oposet_1(B) ) ) )).
fof(t29_robbins4,axiom,( k5_lattices(k2_robbins4) = k5_numbers )).
fof(t29_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) )).
fof(t29_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => k1_rpr_1(A,k4_subset_1(A,k4_subset_1(A,B,C),D)) = k2_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_rpr_1(A,B),k1_rpr_1(A,C)),k1_rpr_1(A,D)),k2_xcmplx_0(k2_xcmplx_0(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))) ) ) ) ) )).
fof(t29_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( B != k1_xboole_0 & v1_rlsub_1(B,A) & ! [C] : ( ( v1_bhsp_1(C) & m1_rusub_1(C,A) ) => B != u1_struct_0(C) ) ) ) ) )).
fof(t29_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t29_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( r1_struct_0(k1_rusub_3(A,k6_domain_1(u1_struct_0(A),B)),C) <=> ? [D] : ( v1_xreal_0(D) & C = k1_rlvect_1(A,B,D) ) ) ) ) )).
fof(t29_rusub_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => v3_rusub_4(k4_rusub_4(A,B),A) ) ) )).
fof(t29_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_square_1(k3_bhsp_1(A,k3_rlvect_1(A,B,C))) = k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k3_bhsp_1(A,B)),k3_xcmplx_0(2,k2_bhsp_1(A,B,C))),k1_square_1(k3_bhsp_1(A,C))) & k1_square_1(k3_bhsp_1(A,k5_algstr_0(A,B,C))) = k2_xcmplx_0(k6_xcmplx_0(k1_square_1(k3_bhsp_1(A,B)),k3_xcmplx_0(2,k2_bhsp_1(A,B,C))),k1_square_1(k3_bhsp_1(A,C))) ) ) ) ) )).
fof(t29_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k8_rvsum_1(k9_finseq_1(A),k9_finseq_1(B)) = k9_finseq_1(k6_xcmplx_0(A,B)) ) ) )).
fof(t29_rvsum_2,axiom,( k17_rvsum_1(k6_finseq_1(k2_numbers)) = k5_complex1 )).
fof(t29_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) ) ) ) )).
fof(t29_scmbsort,axiom,( ! [A] : ( m1_scmfsa_2(A) => k4_sf_mastr(k1_scmbsort(A)) = k1_tarski(A) ) )).
fof(t29_scmfsa10,axiom,( ! [A] : ( 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) ) ) )).
fof(t29_scmfsa8a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( ( r5_scmfsa7b(A,k1_scmfsa_m(B),C) & r6_scmfsa7b(A,k1_scmfsa_m(B),C) ) => k8_extpro_1(k7_card_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(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))) = k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(C,A),k1_funct_4(B,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))),1) ) ) ) ) )).
fof(t29_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( 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),k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),k5_card_1(D)),7)))) ) ) ) ) ) ) ) )).
fof(t29_scmfsa8c,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => k1_funct_1(k1_scmfsa8b(B,k1_scmfsa8a(2),A),k1_nat_1(k5_card_1(A),3)) = k11_scmfsa_2(k1_nat_1(k5_card_1(A),5)) ) ) )).
fof(t29_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_ami_2(B) & ~ v1_scmfsa_m(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(D,k7_card_1(3),k1_scmfsa_2,k5_numbers) ) => ( ( r1_tarski(k2_scmfsa_9(B,C),A) & r1_xxreal_0(k1_funct_1(D,B),k5_numbers) ) => ( k8_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D) = 4 & ! [E] : ( v7_ordinal1(E) => k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D,E)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,D) ) ) ) ) ) ) ) )).
fof(t29_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ~ ( k2_compos_0(u1_compos_1(k1_scmfsa_2),A) = 7 & ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => A != k12_scmfsa_2(B,C) ) ) ) ) )).
fof(t29_scmfsa_9,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(6,C) => r2_hidden(k2_xcmplx_0(k5_card_1(B),C),k2_afinsq_1(k2_scmfsa_9(A,B))) ) ) ) ) )).
fof(t29_scmfsa_m,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(A,k9_xtuple_0(k1_funct_4(k16_funcop_1(k4_scmfsa_2(B),C),k7_memstr_0(k7_card_1(3),k1_scmfsa_2,D)))) & A != k4_scmfsa_2(B) & A != k4_struct_0(k1_scmfsa_2) ) ) ) ) )).
fof(t29_scmisort,axiom,( ! [A] : ( m1_scmfsa_2(A) => k4_sf_mastr(k2_scmisort(A)) = k1_tarski(A) ) )).
fof(t29_scmpds_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ~ ( k2_compos_0(u1_compos_1(k1_scmpds_2),A) = 6 & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => A != k9_scmpds_2(B,C,D) ) ) ) ) ) )).
fof(t29_scmpds_5,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( 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,k5_numbers) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t29_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v3_scmpds_4(D) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( ( k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,E),F)) = k5_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) ) ) ) ) ) ) ) ) )).
fof(t29_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k1_amistd_1(k7_card_1(2),k1_scmring2(A),B,k8_scmring2(A,C)) = k1_tarski(C) ) ) ) )).
fof(t29_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ~ ( r2_hidden(B,A) & B != k1_xboole_0 & ! [C] : ~ ( B = k1_tarski(C) & r2_hidden(C,k3_tarski(A)) ) & ~ r2_hidden(B,k1_scmyciel(A)) ) ) )).
fof(t29_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r1_semi_af1(A,D,B,E) & r1_semi_af1(A,D,C,E) ) => ( r1_semi_af1(A,D,B,C) | D = E ) ) ) ) ) ) ) )).
fof(t29_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C)),k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B),C)) ) ) ) )).
fof(t29_seq_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & v2_comseq_2(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => k1_seq_2(k55_valued_1(k4_ordinal1,k2_numbers,k25_valued_1(k4_ordinal1,k2_numbers,B,A))) = k3_xcmplx_0(k9_complex1(A),k9_complex1(k3_comseq_2(B))) ) ) )).
fof(t29_seq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( r1_xxreal_0(k5_numbers,A) & ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,B,C) = k7_xcmplx_0(1,k2_xcmplx_0(C,A)) ) ) => k1_seq_2(B) = k5_numbers ) ) ) )).
fof(t29_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( m1_subset_1(D,A) => ( r1_seqfunc(A,k1_numbers,C,k1_tarski(D)) => r2_relset_1(k4_ordinal1,k1_numbers,k10_seqfunc(A,k2_seqfunc(A,C,B),D),k26_valued_1(k4_ordinal1,k1_numbers,k10_seqfunc(A,C,D),B)) ) ) ) ) ) )).
fof(t29_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_comseq_2(A) & m2_valued_0(B,k1_numbers,A) ) => v1_comseq_2(B) ) ) ) )).
fof(t29_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,A,C)) & k9_nat_1(k1_numbers,B,C) = k1_power(C,k9_nat_1(k1_numbers,A,C)) ) ) & ? [C] : ( v7_ordinal1(C) & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => r1_xxreal_0(1,k9_nat_1(k1_numbers,B,D)) ) ) ) & v1_series_1(A) ) ) ) )).
fof(t29_series_3,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => ( r1_xxreal_0(1,A) => r1_xxreal_0(k3_xcmplx_0(2,k2_power(A,k3_square_1(k3_xcmplx_0(B,C)))),k2_xcmplx_0(k2_power(A,B),k2_power(A,C))) ) ) ) ) )).
fof(t29_series_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => r1_xxreal_0(k1_square_1(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,E)),k3_xcmplx_0(C,F))),k3_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(C)),k2_xcmplx_0(k2_xcmplx_0(k1_square_1(D),k1_square_1(E)),k1_square_1(F)))) ) ) ) ) ) ) )).
fof(t29_setfam_1,axiom,( ! [A] : ! [B] : ~ ( 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))) ) )).
fof(t29_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k1_kurato_0(A,B) = k3_subset_1(A,k3_prob_1(A,k2_prob_1(A,B))) ) )).
fof(t29_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_setlim_1(C,A) => v1_setlim_1(k7_setlim_2(A,C,B),A) ) ) ) )).
fof(t29_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,k5_finsub_1(A)) => ! [E] : ( ( 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) & v1_setwiseo(C,B) ) => ! [F] : ( m1_subset_1(F,A) => k7_setwiseo(A,B,C,k5_setwiseo(A,D,k2_setwiseo(A,F)),E) = k5_binop_1(B,C,k7_setwiseo(A,B,C,D,E),k3_funct_2(A,B,E,F)) ) ) ) ) ) ) ) )).
fof(t29_sf_mastr,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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)) ) ) )).
fof(t29_sfmastr3,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & ~ v1_scmfsa_m(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( m1_scmfsa_2(E) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( k1_funct_1(A,k4_scmfsa_2(k5_numbers)) = 1 => ( r5_scmfsa7b(k3_sfmastr3(C,D,B,E),A,F) & r6_scmfsa7b(k3_sfmastr3(C,D,B,E),A,F) ) ) ) ) ) ) ) ) )).
fof(t29_sgraph1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_sgraph1(B,A) => ! [C] : ~ ( r2_hidden(C,u1_struct_0(B)) & ! [D] : ( v1_finset_1(D) => ~ ( D = u1_struct_0(B) & ~ r1_xxreal_0(k5_card_1(D),k4_sgraph1(A,B,C)) ) ) ) ) ) )).
fof(t29_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v12_sheffer1(A) & l3_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t29_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t29_simplex0,axiom,( ! [A] : ! [B] : ( ( v1_matroid0(B) & m1_simplex0(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t29_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( k2_xcmplx_0(k1_square_1(k19_sin_cos(A)),k1_square_1(k17_sin_cos(A))) = 1 & k2_xcmplx_0(k3_xcmplx_0(k19_sin_cos(A),k19_sin_cos(A)),k3_xcmplx_0(k17_sin_cos(A),k17_sin_cos(A))) = 1 ) ) )).
fof(t29_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k1_newton(k2_xcmplx_0(k1_funct_1(k3_sin_cos2,A),k1_funct_1(k1_sin_cos2,A)),B) = k2_xcmplx_0(k1_funct_1(k3_sin_cos2,k3_xcmplx_0(B,A)),k1_funct_1(k1_sin_cos2,k3_xcmplx_0(B,A))) ) ) )).
fof(t29_sin_cos3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k15_sin_cos(k3_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A)),k7_complex1)) = 1 ) )).
fof(t29_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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(k19_sin_cos(k2_xcmplx_0(A,B)),k19_sin_cos(k6_xcmplx_0(A,B))))) ) ) )).
fof(t29_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k19_sin_cos(k7_xcmplx_0(A,2)) != k5_numbers => k1_sin_cos4(k7_xcmplx_0(A,2)) = k7_xcmplx_0(k17_sin_cos(A),k2_xcmplx_0(1,k19_sin_cos(A))) ) ) )).
fof(t29_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,k3_xcmplx_0(2,k28_sin_cos)) & k19_sin_cos(A) = k4_xcmplx_0(1) ) => A = k28_sin_cos ) ) )).
fof(t29_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( A != k5_numbers & k23_sin_cos(A) = 1 ) ) )).
fof(t29_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k5_numbers,A) => k6_sin_cos2(k7_xcmplx_0(A,2)) = k3_square_1(k7_xcmplx_0(k6_xcmplx_0(k4_sin_cos2(A),1),k2_xcmplx_0(k4_sin_cos2(A),1))) ) ) )).
fof(t29_sin_cos9,axiom,( k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_sin_cos9,k1_rcomp_1(k4_xcmplx_0(1),1)),k2_partfun1(k1_numbers,k1_numbers,k26_sin_cos,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)),k7_xcmplx_0(k28_sin_cos,4)))) = k1_partfun2(k1_numbers,k1_rcomp_1(k4_xcmplx_0(1),1)) )).
fof(t29_sincos10,axiom,( k1_funct_1(k16_sin_cos,k7_xcmplx_0(k28_sin_cos,4)) = k7_xcmplx_0(1,k3_square_1(2)) & k1_funct_1(k18_sin_cos,k7_xcmplx_0(k28_sin_cos,4)) = k7_xcmplx_0(1,k3_square_1(2)) )).
fof(t29_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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(k1_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,k1_nat_1(A,1)) & E = k7_partfun1(u1_struct_0(k15_euclid(2)),B,k1_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) ) ) ) ) ) ) ) )).
fof(t29_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t29_sprect_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( v2_funct_1(B) & v1_topreal1(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t29_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t29_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => k3_square_1(k3_xcmplx_0(A,B)) = k3_xcmplx_0(k3_square_1(A),k3_square_1(B)) ) ) ) )).
fof(t29_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => r2_hidden(k13_stacks_1(A,B),k11_stacks_1(A,B)) ) ) )).
fof(t29_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(A,B) => k3_stirl2_1(B,A) = k5_numbers ) ) ) )).
fof(t29_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_sublemma(B,A) & m1_subset_1(B,k2_zfmisc_1(k16_substut1(A),k3_qc_lang1(A))) ) => ! [C] : ( m1_substut1(C,A,B) => ( v3_substut1(B,A) => k10_sublemma(A,k9_sublemma(A,B,C)) = k8_sublemma(A,B) ) ) ) ) )).
fof(t29_subset_1,axiom,( ! [A] : ( A != k1_xboole_0 => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,A) => ( ~ r2_hidden(C,B) => r2_hidden(C,k3_subset_1(A,B)) ) ) ) ) )).
fof(t29_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => k37_substut1(A,k20_substut1(A,B)) = k13_qc_lang1(A,k37_substut1(A,B)) ) ) )).
fof(t29_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( m1_substut2(F,A,E,D) => ~ ( r1_xxreal_0(k7_cqc_sim1(A,D),C) & r2_qc_lang2(A,E,D) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(F)) & ! [G] : ( m2_subset_1(G,k9_qc_lang1(A),k3_cqc_lang(A)) => ~ ( G = k1_funct_1(F,B) & r1_xxreal_0(k7_cqc_sim1(A,G),C) ) ) ) ) ) ) ) ) ) )).
fof(t29_supinf_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => ! [C] : ( ( 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(k6_numbers,A,B,C),k1_numbers) & r2_hidden(k10_supinf_2(k6_numbers,A,B,C),k1_numbers) ) ) ) ) ) ) )).
fof(t29_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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,D,C) & ~ r1_orders_2(B,D,F) & ~ r1_orders_2(B,E,C) & ~ r1_orders_2(B,E,F) & k8_group_1(A,k1_symsp_1(A,B,C,E,D),k1_symsp_1(A,B,D,C,F)) != k8_group_1(A,k1_symsp_1(A,B,F,E,D),k1_symsp_1(A,B,E,C,F)) ) ) ) ) ) ) ) )).
fof(t29_sysrel,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) ) ) ) ) )).
fof(t29_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),k1_numbers))) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t29_taylor_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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,k1_nat_1(A,1),k2_rcomp_1(D,E)) & ! [F] : ( v1_xreal_0(F) => ~ ( r2_hidden(F,k2_rcomp_1(D,E)) & k1_funct_1(B,D) = k2_xcmplx_0(k9_nat_1(k1_numbers,k3_series_1(k6_taylor_1(B,C,E,D)),A),k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(B,k2_rcomp_1(D,E)),k1_nat_1(A,1)),F),k1_newton(k6_xcmplx_0(D,E),k1_nat_1(A,1))),k2_newton(k1_nat_1(A,1)))) ) ) ) ) ) ) ) ) ) )).
fof(t29_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t29_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v4_tdlat_3(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t29_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(D,A,C) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(E,A,C) & v1_polynom1(E,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)),k3_polynom1(k15_pre_poly(A),C,k10_polynom1(A,C,D,E))) ) ) ) ) ) )).
fof(t29_tex_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ( k3_tex_1(A,B) = k1_compts_1(A) <=> A = k6_domain_1(A,B) ) ) ) )).
fof(t29_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v2_tex_2(B,A) ) ) )).
fof(t29_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t29_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t29_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( ~ r1_tsep_1(C,D) => ( ( m1_pre_topc(C,B) => ( ~ r1_tsep_1(k2_tsep_1(A,B,D),C) & ~ r1_tsep_1(k2_tsep_1(A,D,B),C) ) ) & ( m1_pre_topc(D,B) => ( ~ r1_tsep_1(k2_tsep_1(A,C,B),D) & ~ r1_tsep_1(k2_tsep_1(A,B,C),D) ) ) ) ) ) ) ) ) )).
fof(t29_toler_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( ! [E] : ( r2_hidden(E,D) <=> ( r2_hidden(B,E) & m1_toler_1(E,A,C) ) ) => k9_relat_1(C,B) = k3_tarski(D) ) ) )).
fof(t29_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r1_borsuk_6(A,B,C) & r1_borsuk_6(A,B,D) ) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t29_topalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_borsuk_2(G,A,D,E) => ! [H] : ( m1_borsuk_2(H,A,E,F) => ! [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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t29_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))))) ) ) ) ) )).
fof(t29_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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(k5_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)) ) ) )).
fof(t29_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t29_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) )).
fof(t29_topgen_2,axiom,( ! [A] : ! [B] : ? [C] : ( 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)) ) )).
fof(t29_topgen_3,axiom,( k3_topgen_3 = k3_card_2(2,k4_ordinal1) )).
fof(t29_topgen_4,axiom,( ! [A] : k2_setfam_1(k1_xboole_0,A) = k1_xboole_0 )).
fof(t29_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m3_topgrp_1(B,A) => m3_topgrp_1(k2_tops_2(u1_struct_0(A),u1_struct_0(A),B),A) ) ) )).
fof(t29_topreal1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ~ ( v5_topreal1(A) & ! [B] : ( ( 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)) ) ) ) )).
fof(t29_topreal4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ~ ( r1_topreal4(D,A,B) & r1_tarski(D,C) ) ) ) ) ) ) )).
fof(t29_topreal8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ! [C] : ( ( ~ 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),k1_nat_1(A,1)) | k2_topreal1(2,k4_graph_2(u1_struct_0(k15_euclid(2)),B,C),k2_xcmplx_0(k3_finseq_1(B),A)) = k2_topreal1(2,C,k1_nat_1(A,1)) ) ) ) ) ) )).
fof(t29_topreal9,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,k4_topreal9(A,B,C)) => ( D = B | k4_topreal9(A,B,C) = k4_topreal9(A,B,D) ) ) ) ) ) ) )).
fof(t29_topreala,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k1_funct_1(k19_euclid(A,B),1) = A & k1_funct_1(k19_euclid(A,B),2) = B ) ) ) )).
fof(t29_toprealc,axiom,( ! [A] : ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_valued_2(C) => ! [D] : ( ( 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)) ) ) ) )).
fof(t29_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => r1_xxreal_0(k12_euclid(k3_rlvect_1(k15_euclid(A),B,C)),k2_xcmplx_0(k12_euclid(B),k12_euclid(C))) ) ) ) )).
fof(t29_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)) ) ) )).
fof(t29_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)))) ) ) ) )).
fof(t29_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t29_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t29_trees_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ~ ( r2_hidden(B,k2_trees_1(A)) & B != k1_xboole_0 & ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(A,C) & B = k9_finseq_1(C) ) ) ) ) ) )).
fof(t29_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ~ ( ! [B] : ( v7_ordinal1(B) => ? [C] : ( v1_finset_1(C) & m1_trees_2(C,A) & k5_card_1(C) = B ) ) & ! [B] : ( m1_trees_1(B,A) => v1_finset_1(k1_trees_2(A,B)) ) & ! [B] : ( m1_trees_2(B,A) => v1_finset_1(B) ) ) ) )).
fof(t29_trees_3,axiom,( ! [A] : ( v5_trees_3(k9_finseq_1(A)) <=> ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) ) )).
fof(t29_trees_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_trees_3(E,k2_zfmisc_1(A,B)) ) => ! [F] : ( m2_finseq_1(F,E) => ? [G] : ( m2_finseq_1(G,k4_trees_3(A)) & k4_finseq_1(G) = k4_finseq_1(F) & ! [H] : ( v7_ordinal1(H) => ~ ( r2_hidden(H,k4_finseq_1(F)) & ! [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) ) ) ) ) ) ) ) )).
fof(t29_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v5_trees_3(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t29_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t29_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t29_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(t29_turing_1,axiom,( r3_turing_1(k14_turing_1,k15_comput_1) )).
fof(t29_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ( r2_hidden(A,k2_msafree2(k34_twoscomp(A,B))) & r2_hidden(B,k2_msafree2(k34_twoscomp(A,B))) ) ) ) )).
fof(t29_uniroots,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k1_uniroots(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C = B => ! [D] : ( v7_ordinal1(D) => k1_binop_1(k4_group_1(k1_uniroots(A)),B,D) = k1_binop_1(k4_group_1(A),C,D) ) ) ) ) ) )).
fof(t29_uproots,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k11_polynom3(A,B,k2_algseq_1(A,k5_struct_0(A))),B) ) ) )).
fof(t29_urysohn2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(A,B) => r1_tarski(k1_urysohn1(A),k1_urysohn1(B)) ) ) ) )).
fof(t29_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( m1_valuat_1(F,A,B) => ( r1_valuat_1(A,B,k11_cqc_lang(A,C,E),F,D) <=> ! [G] : ( m2_funct_2(G,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ( ! [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t29_valued_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( v7_ordinal1(E) => ( v1_partfun1(D,A) => r2_funct_2(k4_ordinal1,B,k8_funct_2(k4_ordinal1,B,A,k1_valued_0(A,C,E),D),k1_valued_0(B,k8_funct_2(k4_ordinal1,B,A,C,D),E)) ) ) ) ) ) ) )).
fof(t29_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & r2_hidden(k5_numbers,k1_relset_1(k4_ordinal1,k61_valued_1(A,B))) ) ) ) )).
fof(t29_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : k1_funct_1(k14_valued_2(B,A),C) = k7_xcmplx_0(k1_funct_1(B,C),A) ) ) )).
fof(t29_vectsp10,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t29_vectsp11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( ~ 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] : ( ( 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] : ( 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)))))) ) ) ) ) ) ) )).
fof(t29_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t29_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) )).
fof(t29_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( v7_vectsp_1(C,A) & m1_vectsp_4(C,A,B) ) => ! [D] : ( ( v7_vectsp_1(D,A) & m1_vectsp_4(D,A,B) ) => ( u1_struct_0(C) = u1_struct_0(D) => C = D ) ) ) ) ) )).
fof(t29_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t29_vectsp_6,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t29_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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) = k5_numbers <=> k2_vectsp_4(A,B) = k1_vectsp_4(A,B) ) ) ) )).
fof(t29_vfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( 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,k4_normsp_0(B,C,D),A),k4_normsp_0(B,C,k2_partfun1(B,u1_struct_0(C),D,A))) ) ) ) ) )).
fof(t29_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( 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,k4_normsp_0(A,B,C),D),k4_normsp_0(A,B,k2_partfun1(A,u1_struct_0(B),C,D))) ) ) ) ) )).
fof(t29_waybel10,axiom,( ! [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) ) => r5_waybel_1(k7_waybel10(A),k1_waybel10(k4_waybel10(A),k8_waybel10(A))) ) )).
fof(t29_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_hidden(k4_waybel11(A,B),k6_yellow_6(A)) ) ) )).
fof(t29_waybel12,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t29_waybel13,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) )).
fof(t29_waybel14,axiom,( ! [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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(k5_waybel11(A)))) => ~ ( C = B & v1_waybel14(k5_waybel_2(A),A) & v5_waybel_6(C,k1_yellow_1(k5_waybel11(A))) & C != u1_struct_0(A) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => B != k3_subset_1(u1_struct_0(A),k5_waybel_0(A,D)) ) ) ) ) ) )).
fof(t29_waybel15,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t29_waybel16,axiom,( ! [A] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t29_waybel17,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t29_waybel19,axiom,( ! [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] : ( ( v2_pre_topc(B) & v1_waybel19(B) & m1_yellow_9(B,A) ) => ! [C] : ( ( v4_waybel11(C) & m1_yellow_9(C,A) ) => ! [D] : ( ( v2_pre_topc(D) & m1_yellow_9(D,A) ) => ( v2_waybel19(D) <=> m3_yellow_9(D,C,B) ) ) ) ) ) )).
fof(t29_waybel23,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_waybel23(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v2_waybel_0(B,A) ) ) )).
fof(t29_waybel24,axiom,( ! [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] : ( ( 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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_waybel24(A,B)))) ) => ( v1_funct_1(k1_yellow_0(k5_yellow_1(u1_struct_0(A),B),C)) & v1_funct_2(k1_yellow_0(k5_yellow_1(u1_struct_0(A),B),C),u1_struct_0(A),u1_struct_0(B)) & v5_orders_3(k1_yellow_0(k5_yellow_1(u1_struct_0(A),B),C),A,B) & m1_subset_1(k1_yellow_0(k5_yellow_1(u1_struct_0(A),B),C),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) ) ) ) )).
fof(t29_waybel25,axiom,( ! [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) ) => v1_waybel25(A) ) )).
fof(t29_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,B) => k1_funct_1(k9_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)) ) ) ) ) ) )).
fof(t29_waybel27,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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))) ) ) )).
fof(t29_waybel28,axiom,( ! [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] : ( 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)) ) ) ) )).
fof(t29_waybel29,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t29_waybel30,axiom,( ! [A] : ( ( 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] : ( ( 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))) ) ) )).
fof(t29_waybel31,axiom,( ! [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) ) => ( ~ v8_struct_0(A) => k1_waybel31(A) = k1_waybel31(k1_yellow_1(k5_waybel11(A))) ) ) )).
fof(t29_waybel34,axiom,( ! [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] : ( ( 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)) ) ) ) )).
fof(t29_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t29_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(t29_waybel_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ( ! [B] : ( ( v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t29_waybel_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => v4_orders_2(k3_waybel_3(A,B,C)) ) => v4_orders_2(k4_yellow_1(A,B)) ) ) ) )).
fof(t29_waybel_4,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t29_waybel_5,axiom,( ! [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] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ( ? [C] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t29_waybel_6,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( B != k4_yellow_0(A) => ( v5_waybel_6(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_orders_2(A,B,C) => C = k4_yellow_0(A) ) ) ) ) ) ) )).
fof(t29_waybel_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ( r1_waybel_3(k1_yellow_1(u1_pre_topc(A)),B,C) => ! [D] : ( ( ~ v1_xboole_0(D) & v2_waybel_0(D,k2_yellow_1(u1_struct_0(A))) & v13_waybel_0(D,k2_yellow_1(u1_struct_0(A))) & v3_waybel_7(D,k2_yellow_1(u1_struct_0(A))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k2_yellow_1(u1_struct_0(A))))) ) => ~ ( r2_hidden(B,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,C) & r2_waybel_7(A,D,E) ) ) ) ) ) ) ) ) )).
fof(t29_waybel_8,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k2_yellow_1(A))) => k2_waybel_8(k2_yellow_1(A),B) = a_2_1_waybel_8(A,B) ) )).
fof(t29_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k10_yellow_6(A,B)) => r3_waybel_9(A,B,C) ) ) ) ) )).
fof(t29_weddwitt,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t29_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [C] : ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t29_wellord1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) ) ) )).
fof(t29_wsierp_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( r1_int_1(B,k3_xcmplx_0(C,A)) & k3_int_2(B,C) = 1 ) => r1_int_1(B,A) ) ) ) ) )).
fof(t29_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : r1_tarski(k3_xboole_0(A,B),k2_xboole_0(A,C)) )).
fof(t29_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k5_xboolean(k3_xboolean(A),k7_xboolean(A,B)) = k6_xboolean(A,B) ) ) )).
fof(t29_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k6_xcmplx_0(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(k6_xcmplx_0(A,C),B) ) ) ) )).
fof(t29_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k2_xcmplx_0(B,A),B) ) ) ) )).
fof(t29_xtuple_0,axiom,( ! [A] : ! [B] : r1_tarski(k4_xboole_0(k10_xtuple_0(A),k10_xtuple_0(B)),k10_xtuple_0(k4_xboole_0(A,B))) )).
fof(t29_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ~ ( ~ r1_xxreal_0(A,B) & ~ r1_xxreal_0(A,C) & r1_xxreal_0(A,k4_xxreal_0(B,C)) ) ) ) ) )).
fof(t29_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( ~ r1_xxreal_0(B,A) => k1_xxreal_1(B,A) = k1_xboole_0 ) ) ) )).
fof(t29_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( r1_xxreal_0(A,B) => k1_xxreal_2(k1_xxreal_1(A,B)) = B ) ) ) )).
fof(t29_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t29_yellow10,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(t29_yellow12,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t29_yellow14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k3_waybel18(A,B))) => ! [D] : ( 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] : ( 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)))) ) ) ) ) ) ) )).
fof(t29_yellow16,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k4_yellow_1(A,B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k4_yellow_1(A,B)))) => ( r1_lattice3(k4_yellow_1(A,B),D,C) <=> ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t29_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t29_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_waybel_9(A,B,C) <=> ! [D] : ( m1_yellow19(D,A,B) => r2_hidden(C,k2_pre_topc(A,D)) ) ) ) ) ) )).
fof(t29_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v3_altcat_2(C,A) & m1_altcat_2(C,A) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ! [H] : ( m1_subset_1(H,u1_struct_0(C)) => ( ( G = E & H = F ) => ( k1_altcat_1(C,G,H) = k1_xboole_0 | ! [I] : ( m1_subset_1(I,k1_altcat_1(A,E,F)) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t29_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( k15_lattice3(A,B) = k1_yellow_0(k3_lattice3(A),B) & k16_lattice3(A,B) = k2_yellow_0(k3_lattice3(A),B) ) ) )).
fof(t29_yellow_2,axiom,( ! [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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t29_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t29_yellow_4,axiom,( ! [A] : ( ( v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( ~ 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))) ) ) ) )).
fof(t29_yellow_5,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t29_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_yellow_6(A,B))) => ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & D = C & r2_hidden(B,D) & v3_pre_topc(D,A) ) ) ) ) )).
fof(t29_yellow_7,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( 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))) ) ) ) )).
fof(t29_yellow_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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)))) ) ) ) )).
fof(t29_zf_fund1,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_zf_lang)) ) => r2_tarski(A,k4_zf_fund1(A)) ) )).
fof(t29_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( B = k7_finseq_1(A,C) => B = A ) ) ) ) )).
fof(t29_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( 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))) ) ) ) )).
fof(t29_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(t29_zfrefle1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( v3_ordinal1(B) & m1_subset_1(B,A) ) => ! [C] : ( ( 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] : ( ( v3_ordinal1(D) & m1_subset_1(D,A) ) => ~ ( r2_hidden(B,D) & k4_ordinal4(A,C,D) = D & r2_ordinal2(D,k4_ordinal1) ) ) ) ) ) ) )).
fof(t29_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_int_1(C) => ! [D] : ( m1_zmodul01(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ( E = B => k1_zmodul01(D,E,C) = k1_zmodul01(A,B,C) ) ) ) ) ) ) )).
fof(t29_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( v1_int_1(C) => ( C != k5_numbers => k18_zmodul02(A,k23_zmodul02(A,C,B)) = k18_zmodul02(A,B) ) ) ) ) )).
fof(t29_zmodul03,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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) & v1_zmodul03(B) & l1_zmodul01(B) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k12_zmodul02(A,B))) => ( ( k3_finseq_1(C) = k3_finseq_1(D) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( r2_hidden(E,k4_finseq_1(C)) & ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ~ ( F = k1_funct_1(C,E) & k1_funct_1(D,E) = k13_zmodul02(A,B,F) ) ) ) ) ) => k4_rlvect_1(k12_zmodul02(A,B),D) = k13_zmodul02(A,B,k4_rlvect_1(B,C)) ) ) ) ) ) )).
fof(t2_abcmiz_0,axiom,( ! [A] : ( l1_abcmiz_0(A) => ! [B] : ( l1_abcmiz_0(B) => ( ( u1_abcmiz_0(A) = u1_abcmiz_0(B) & v4_abcmiz_0(A) ) => v4_abcmiz_0(B) ) ) ) )).
fof(t2_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( k3_card_3(B) = k1_xboole_0 => k1_funct_1(B,A) = k1_xboole_0 ) ) )).
fof(t2_abcmiz_a,axiom,( ! [A] : ( m1_subset_1(A,k2_abcmiz_1) => k1_abcmiz_1(k3_abcmiz_1(A)) = k3_abcmiz_1(A) ) )).
fof(t2_abian,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) ) => ( r2_hidden(k5_numbers,A) => k4_seq_4(A) = k5_numbers ) ) )).
fof(t2_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ( A = k5_numbers <=> k9_complex1(A) = k5_numbers ) ) )).
fof(t2_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,D) & r2_analoaf(A,D,D,B,C) ) ) ) ) ) )).
fof(t2_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v4_aff_2(A) <=> v5_aff_2(A) ) ) )).
fof(t2_aff_3,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v2_aff_3(A) => v1_aff_3(A) ) ) )).
fof(t2_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t2_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => k2_xboole_0(A,k1_tarski(A)) = k1_nat_1(A,1) ) )).
fof(t2_afinsq_2,axiom,( ! [A] : ( ( v1_finset_1(A) & v6_membered(A) ) => ? [B] : ( v7_ordinal1(B) & r1_tarski(A,B) ) ) )).
fof(t2_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t2_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_analoaf(A,B,B,B,B) ) ) )).
fof(t2_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect01(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,E) => r2_analoaf(A,D,E,B,C) ) ) ) ) ) ) )).
fof(t2_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) )).
fof(t2_algseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( ! [D] : ( v7_ordinal1(D) => ~ ( ~ r1_xxreal_0(A,D) & k1_funct_1(C,D) = k4_struct_0(B) ) ) => r1_xxreal_0(A,k1_algseq_1(B,C)) ) ) ) ) )).
fof(t2_algspec1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t2_algstr_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_algstr_0(A,C,k4_struct_0(A)) = C ) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & k1_algstr_0(A,C,D) = k4_struct_0(A) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) )).
fof(t2_algstr_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t2_algstr_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_3)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_algstr_3)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_algstr_3)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( ( A = D & B = E & C = F ) => k1_algstr_3(k3_algstr_3,A,B,C) = k2_xcmplx_0(k3_xcmplx_0(D,E),F) ) ) ) ) ) ) ) )).
fof(t2_algstr_4,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t2_altcat_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k2_zfmisc_1(A,B)) & v1_funct_1(D) & v1_partfun1(D,k2_zfmisc_1(A,B)) ) => ( ! [E] : ! [F] : ( ( r2_hidden(E,A) & r2_hidden(F,B) ) => k1_binop_1(C,E,F) = k1_binop_1(D,E,F) ) => r6_pboole(k2_zfmisc_1(A,B),D,C) ) ) ) )).
fof(t2_altcat_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => k2_funct_4(k3_relat_1(A,B)) = k3_relat_1(k2_funct_4(A),B) ) ) )).
fof(t2_altcat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t2_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_altcat_1(A,C,D)) => ! [F] : ( m1_subset_1(F,k1_altcat_1(A,B,D)) => ! [G] : ( m1_subset_1(G,k1_altcat_1(A,B,C)) => ( ( F = k5_altcat_1(A,B,C,D,G,E) & k5_altcat_1(A,C,B,C,k1_altcat_3(A,B,C,G),G) = k8_altcat_1(A,C) ) => ( 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 | E = k5_altcat_1(A,C,B,D,k1_altcat_3(A,B,C,G),F) ) ) ) ) ) ) ) ) ) )).
fof(t2_altcat_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k1_xboole_0,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_xboole_0,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( v7_altcat_3(C,A) & ! [D] : ( m1_altcat_5(D,A,C,k1_xboole_0,B) => ~ ( v1_xboole_0(D) & v3_altcat_5(D,A,k1_xboole_0,B,C) ) ) ) ) ) ) )).
fof(t2_ami_2,axiom,( ! [A] : ( m1_subset_1(A,k1_ami_2) => ( r2_hidden(A,k2_ami_2) => k1_funct_1(k3_relat_1(k3_ami_2,k4_ami_2),A) = k4_numbers ) ) )).
fof(t2_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(C,u1_struct_0(k1_ami_3)) ) => ( k1_funct_1(k2_extpro_1(k7_card_1(2),k1_ami_3,k2_ami_3(A,B),C),k4_struct_0(k1_ami_3)) = k4_card_1(k5_memstr_0(k7_card_1(2),k1_ami_3,C)) & k1_funct_1(k2_extpro_1(k7_card_1(2),k1_ami_3,k2_ami_3(A,B),C),A) = k1_funct_1(C,B) & ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_ami_3)) ) => ( D != A => k1_funct_1(k2_extpro_1(k7_card_1(2),k1_ami_3,k2_ami_3(A,B),C),D) = k1_funct_1(C,D) ) ) ) ) ) ) )).
fof(t2_ami_4,axiom,( ! [A] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_ami_3)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ( r1_tarski(k1_ami_4,B) => ! [C] : ( v7_ordinal1(C) => ( k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,C)) = k5_numbers => ( k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,k1_nat_1(C,1))) = 1 & k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,k1_nat_1(C,1)),k10_ami_3(k5_numbers)) = k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,C),k10_ami_3(k5_numbers)) & k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,k1_nat_1(C,1)),k10_ami_3(1)) = k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,C),k10_ami_3(1)) & k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,k1_nat_1(C,1)),k10_ami_3(2)) = k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,C),k10_ami_3(1)) ) ) ) ) ) ) )).
fof(t2_ami_5,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => A != k4_struct_0(k1_ami_3) ) )).
fof(t2_ami_6,axiom,( k5_xtuple_0(k2_compos_1(k1_ami_3)) = k1_xboole_0 )).
fof(t2_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_ordinal1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ( ( v3_funct_2(C,k4_ordinal1,k4_ordinal1) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(E,F) <=> r1_ami_wstd(A,B,k3_funct_2(k4_ordinal1,k4_ordinal1,C,E),k3_funct_2(k4_ordinal1,k4_ordinal1,C,F)) ) ) ) & v3_funct_2(D,k4_ordinal1,k4_ordinal1) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(E,F) <=> r1_ami_wstd(A,B,k3_funct_2(k4_ordinal1,k4_ordinal1,D,E),k3_funct_2(k4_ordinal1,k4_ordinal1,D,F)) ) ) ) ) => r2_funct_2(k4_ordinal1,k4_ordinal1,C,D) ) ) ) ) ) )).
fof(t2_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,u1_compos_1(B)) => ( v2_extpro_1(D,A,B) => k1_amistd_1(A,B,C,D) = k1_tarski(C) ) ) ) ) ) )).
fof(t2_amistd_2,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_compos_1(B)) => ( ! [D] : ( m1_subset_1(D,k4_ordinal1) => k1_amistd_1(A,B,D,C) = k1_tarski(k1_ordinal1(D)) ) => v1_xboole_0(k2_amistd_1(A,B,C)) ) ) ) ) )).
fof(t2_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_compos_1(B)) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t2_amistd_5,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(k4_amistd_1(A))) => ! [C] : ( ( 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] : ( v7_ordinal1(D) => r6_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)) ) ) ) ) )).
fof(t2_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_analmetr(A,B,C,B,C) ) ) ) )).
fof(t2_analoaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k3_rlvect_1(A,E,B) = k3_rlvect_1(A,C,D) => k5_algstr_0(A,E,D) = k5_algstr_0(A,C,B) ) ) ) ) ) ) )).
fof(t2_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ( r1_analmetr(A,C,D) => k1_analort(A,C,D,k1_rlvect_1(A,B,E)) = k1_rlvect_1(A,k1_analort(A,C,D,B),E) ) ) ) ) ) ) )).
fof(t2_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r1_anproj_1(A,B,D) & r1_anproj_1(A,D,C) ) => r1_anproj_1(A,B,C) ) ) ) ) ) )).
fof(t2_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( 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 = k5_numbers & G = k5_numbers & H = k5_numbers & I = k5_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) ) ) ) ) ) ) ) )).
fof(t2_aofa_000,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( v7_ordinal1(C) => k19_margrel1(k1_aofa_000(A,A,k4_finseq_2(C,A),B)) = C ) ) ) )).
fof(t2_aofa_a00,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r2_pboole(A,B,C) => r2_pboole(k3_finseq_2(A),k6_finseq_2(A,B),k6_finseq_2(A,C)) ) ) ) )).
fof(t2_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_msualg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( r2_hidden(E,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,C),D)) => r2_hidden(E,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),D)) ) ) ) ) ) )).
fof(t2_aofa_i00,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,k1_aofa_i00(A,B,C)) <=> k1_funct_1(D,B) != C ) ) ) )).
fof(t2_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,k5_numbers) = k5_numbers ) )).
fof(t2_armstrng,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_2(A) & v8_relat_2(A) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_relat_1(A))) ) => ~ ( B != k1_xboole_0 & ! [C] : ( m1_subset_1(C,B) => ~ r2_waybel_4(B,C,A) ) ) ) ) )).
fof(t2_arrow,axiom,( ! [A] : ( v1_finset_1(A) => ( r1_xxreal_0(3,k5_card_1(A)) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ? [D] : ( m1_subset_1(D,A) & D != B & D != C ) ) ) ) ) )).
fof(t2_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ( A != k11_arytm_3 => r2_hidden(k4_tarski(k11_arytm_3,A),k1_numbers) ) ) )).
fof(t2_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ~ ( k8_arytm_2(A,B) = k11_arytm_3 & A != k11_arytm_3 & B != k11_arytm_3 ) ) ) )).
fof(t2_arytm_2,axiom,( r1_tarski(k4_ordinal1,k2_arytm_2) )).
fof(t2_arytm_3,axiom,( ! [A] : ( v3_ordinal1(A) => r1_arytm_3(1,A) ) )).
fof(t2_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v4_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v4_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) => ( k1_seq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) = k5_numbers | ( v2_comseq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,A)) & k1_seq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,A)) = k5_xcmplx_0(k1_seq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B))) ) ) ) ) ) )).
fof(t2_asympt_1,axiom,( ! [A] : ( ( v1_xreal_0(A) & v1_asympt_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v1_asympt_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ~ r1_xxreal_0(A,1) & ~ r1_xxreal_0(B,1) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ~ r1_xxreal_0(E,k5_numbers) => k9_nat_1(k1_numbers,C,E) = k3_power(A,E) ) ) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ~ r1_xxreal_0(E,k5_numbers) => k9_nat_1(k1_numbers,D,E) = k3_power(B,E) ) ) & ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & v4_asympt_0(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k1_numbers) & v4_asympt_0(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( r2_funct_2(k4_ordinal1,k1_numbers,E,C) & r2_funct_2(k4_ordinal1,k1_numbers,F,D) & k6_asympt_0(E) = k6_asympt_0(F) ) ) ) ) ) ) ) ) )).
fof(t2_autalg_1,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t2_autgroup,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t2_axioms,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(A,k4_ordinal1) & r2_hidden(B,k4_ordinal1) ) => r2_hidden(k2_xcmplx_0(A,B),k4_ordinal1) ) ) ) )).
fof(t2_bagorder,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(B,k2_finseq_1(A)) <=> ( m1_subset_1(k6_xcmplx_0(B,1),k4_ordinal1) & ~ r1_xxreal_0(A,k6_xcmplx_0(B,1)) ) ) ) ) )).
fof(t2_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => k1_bcialg_1(A,B,k4_struct_0(A)) = B ) ) )).
fof(t2_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_2(A,B,C,1) = k1_bcialg_1(A,B,C) ) ) ) )).
fof(t2_bcialg_3,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t2_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m2_subset_1(D,u1_struct_0(A),k3_bcialg_4(A,B,C)) & ! [E] : ( m2_subset_1(E,u1_struct_0(A),k3_bcialg_4(A,B,C)) => r1_bcialg_1(A,E,D) ) ) ) ) ) )).
fof(t2_bcialg_5,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( r1_bcialg_1(A,B,C) & r1_bcialg_1(A,C,B) ) => B = C ) ) ) ) )).
fof(t2_bcialg_6,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => k3_bcialg_6(A,k1_nat_1(C,1),B) = k1_bcialg_1(A,B,k2_bcialg_1(A,k3_bcialg_6(A,C,B))) ) ) ) )).
fof(t2_bciideal,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t2_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k2_bhsp_1(A,B,k3_rlvect_1(A,C,D)) = k2_xcmplx_0(k2_bhsp_1(A,B,C),k2_bhsp_1(A,B,D)) ) ) ) ) )).
fof(t2_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_bhsp_2(B,A) => ( ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(D,E) & k1_normsp_1(A,C,E) != k1_normsp_1(A,B,E) ) ) | v1_bhsp_2(C,A) ) ) ) ) ) )).
fof(t2_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( r1_bhsp_3(A,B,C) & r1_bhsp_3(A,C,D) ) => r1_bhsp_3(A,B,D) ) ) ) ) ) )).
fof(t2_bhsp_4,axiom,( ! [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) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,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))) ) ) ) )).
fof(t2_bhsp_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => m1_bhsp_5(k1_xboole_0,A) ) )).
fof(t2_bhsp_6,axiom,( ! [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_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] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( r1_xboole_0(B,C) => ! [D] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t2_bhsp_7,axiom,( ! [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_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] : ( ( v1_finset_1(B) & m1_bhsp_5(B,A) ) => ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( 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] : ( ( 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] : ( 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),k9_binop_2,B,D) ) ) ) ) ) ) ) ) )).
fof(t2_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) ) )).
fof(t2_binari_2,axiom,( ! [A] : ( ( 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 ) ) )).
fof(t2_binari_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k6_margrel1) ) => ( k6_binarith(A,B) = k6_binarith(A,C) => B = C ) ) ) ) )).
fof(t2_binarith,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t2_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_algstr_0(A) & v1_algstr_1(A) & v1_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_algstr_0(A,B,k4_struct_0(A)) = k4_struct_0(A) ) ) )).
fof(t2_binop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,A) => ! [G] : ( 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) ) ) ) )).
fof(t2_binop_2,axiom,( k4_binop_1(k1_numbers,k9_binop_2) = k5_numbers )).
fof(t2_bintree1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) & v3_trees_2(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,A) & v1_funct_1(C) & v3_trees_2(C) ) => k15_trees_3(k10_finseq_1(B,C)) = k4_pre_poly(A,k1_bintree1(A,B),k1_bintree1(A,C)) ) ) ) )).
fof(t2_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree1(A) ) => ! [B] : ( m1_trees_1(B,A) => m2_finseq_1(B,k6_margrel1) ) ) )).
fof(t2_boole,axiom,( ! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 )).
fof(t2_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r3_lattices(A,k4_lattices(A,B,C),k3_lattices(A,B,D)) ) ) ) ) )).
fof(t2_boolmark,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t2_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( 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))) ) ) ) ) )).
fof(t2_borsuk_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t2_borsuk_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( 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)))))) ) ) ) ) )).
fof(t2_borsuk_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t2_borsuk_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( r4_zfmisc_1(A,B,C,D,E,F) => k5_card_1(k4_enumset1(A,B,C,D,E,F)) = 6 ) )).
fof(t2_borsuk_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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(k5_numbers,1))) ) ) ) ) )).
fof(t2_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k3_int_1(B),k3_int_1(A)) => k3_int_1(k6_xcmplx_0(A,B)) = k6_xcmplx_0(k3_int_1(A),k3_int_1(B)) ) ) ) )).
fof(t2_brouwer,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => k2_topreal9(A,B,k5_numbers) = k1_tarski(B) ) ) )).
fof(t2_brouwer2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ( ( r2_hidden(D,k4_topreal9(k15_euclid(A),B,C)) & r2_hidden(E,k4_topreal9(k15_euclid(A),B,C)) & k12_euclid(k5_algstr_0(k15_euclid(A),D,B)) = k12_euclid(k5_algstr_0(k15_euclid(A),E,B)) ) => D = E ) ) ) ) ) ) )).
fof(t2_bspace,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ! [C] : ( 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)) ) ) ) )).
fof(t2_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(t2_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => r1_tarski(k15_bvfunc_1(A,B,C),k15_bvfunc_1(A,B,k3_partit1(A,C,D))) ) ) ) ) )).
fof(t2_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ( B = k2_tarski(C,D) => ( C = D | k2_bvfunc_2(A,B) = k2_partit1(A,C,D) ) ) ) ) ) ) )).
fof(t2_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t2_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t2_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t2_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t2_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t2_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t2_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t2_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t2_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) )).
fof(t2_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t2_c0sp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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))) ) ) ) ) ) )).
fof(t2_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => m2_c0sp1(k3_c0sp2(A),k12_funcsdom(u1_struct_0(A))) ) )).
fof(t2_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ( ~ r1_xxreal_0(k3_finseq_1(B),k5_numbers) => ( k1_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))) ) ) ) ) )).
fof(t2_calcul_2,axiom,( ! [A] : ( v7_ordinal1(A) => k2_calcul_2(A,k5_numbers) = k1_xboole_0 ) )).
fof(t2_cantor_1,axiom,( ! [A] : ( 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)))) ) ) )).
fof(t2_card_1,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ( r2_hidden(A,B) <=> ( r1_ordinal1(A,B) & A != B ) ) ) ) )).
fof(t2_card_3,axiom,( ! [A] : ! [B] : k1_card_3(k7_funcop_1(A,B)) = k7_funcop_1(A,k1_card_1(B)) )).
fof(t2_card_4,axiom,( v4_card_3(k4_ordinal1) )).
fof(t2_card_5,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(A,k3_card_3(B)) <=> ? [C] : ( r2_hidden(C,k9_xtuple_0(B)) & r2_hidden(A,k1_funct_1(B,C)) ) ) ) )).
fof(t2_card_fil,axiom,( ! [A] : ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(t2_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ! [C] : ! [D] : ( 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)) ) ) ) ) )).
fof(t2_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => r1_tarski(B,k3_ordinal2(B)) ) ) )).
fof(t2_cardfin2,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(1,k23_sin_cos(A)) ) ) )).
fof(t2_cat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_cat_1(A) ) => ! [B] : ( 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 ) ) )).
fof(t2_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m3_cat_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => m1_subset_1(C,u1_struct_0(A)) ) ) ) )).
fof(t2_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ( r2_hidden(B,A) => k7_partfun1(C,k8_funcop_1(C,A,D),B) = D ) ) ) )).
fof(t2_cat_4,axiom,( ! [A] : ! [B] : 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) )).
fof(t2_catalan1,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => r1_xxreal_0(k7_nat_d(A,1),k7_nat_d(k3_xcmplx_0(2,A),2)) ) ) )).
fof(t2_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ( v1_catalan2(B) => r1_xxreal_0(k3_xcmplx_0(2,k7_afinsq_2(k5_relat_1(B,A))),A) ) ) ) )).
fof(t2_catalg_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r2_pboole(A,k2_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)) ) ) ) ) ) )).
fof(t2_cayldick,axiom,( ! [A] : ! [B] : ( k5_afinsq_1(A) = k5_afinsq_1(B) => A = B ) )).
fof(t2_cayley,axiom,( ! [A] : r1_tarski(k1_cayley(A),k1_funct_2(A,A)) )).
fof(t2_cc0sp1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) )).
fof(t2_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t2_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_ordinal1) & v5_valued_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ( r2_relset_1(k4_ordinal1,k2_numbers,k9_comseq_3(C,k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)),k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k9_comseq_3(C,A),k9_comseq_3(C,B))) & r2_relset_1(k4_ordinal1,k2_numbers,k9_comseq_3(C,k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)),k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k9_comseq_3(C,A),k9_comseq_3(C,B))) & r2_relset_1(k4_ordinal1,k2_numbers,k9_comseq_3(C,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)),k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k9_comseq_3(C,A),k9_comseq_3(C,B))) ) ) ) ) )).
fof(t2_cfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => v2_comseq_2(k1_cfdiff_1(A)) ) ) )).
fof(t2_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ! [C] : ( m2_funct_2(C,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ! [D] : ( m2_funct_2(D,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ( r2_funct_2(A,k2_numbers,D,k1_funcsdom(A,k2_numbers,k2_cfuncdom(A),B,C)) <=> ! [E] : ( m1_subset_1(E,A) => k3_funct_2(A,k2_numbers,D,E) = k3_xcmplx_0(k3_funct_2(A,k2_numbers,B,E),k3_funct_2(A,k2_numbers,C,E)) ) ) ) ) ) ) )).
fof(t2_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( 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] : ( 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) = k6_xcmplx_0(k7_partfun1(k2_numbers,B,D),k7_partfun1(k2_numbers,C,D)) ) ) ) ) ) ) )).
fof(t2_cgames_1,axiom,( k2_cgames_1(k5_ordinal1) = k1_tarski(k1_cgames_1) )).
fof(t2_chain_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ? [C] : ( m1_subset_1(C,k1_numbers) & ~ r1_xxreal_0(C,A) & ~ r1_xxreal_0(C,B) ) ) ) )).
fof(t2_chord,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v1_abian(A) ) => ( v7_ordinal1(k6_xcmplx_0(A,1)) & r1_xxreal_0(1,A) ) ) )).
fof(t2_circcmb2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,B) & v1_finseq_1(C) ) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t2_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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))) ) ) ) ) )).
fof(t2_circcomb,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( 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) ) ) )).
fof(t2_circled1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v1_xreal_0(C) => ( v3_rltopsp1(B,A) => v3_rltopsp1(k1_convex1(A,B,C),A) ) ) ) ) )).
fof(t2_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) => ( v11_struct_0(k1_circtrm1(A,B,C)) <=> ! [D] : ( 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)))) ) ) ) ) ) ) )).
fof(t2_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_pboole(C,k2_msafree2(A),k7_funcop_1(k2_msafree2(A),k4_ordinal1),k5_relat_1(u3_msualg_1(A,B),k2_msafree2(A))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( v1_msafree2(A) => m1_msafree2(k1_funct_1(k9_funct_6(C),D),A,B) ) ) ) ) ) )).
fof(t2_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msafree2(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,k5_msafree2(A,B)),D)) => ! [F] : ( ( 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 ) ) ) ) ) ) )).
fof(t2_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) ) => ! [D] : ( ( 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_tarski(C,k1_relset_1(k1_euclid(A),D)) ) => ( r1_ckspace1(A,D,1,C) <=> ( r2_pdiff_9(C,A,D) & ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( v1_xreal_0(F) => ~ ( r2_hidden(E,C) & ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( v1_xreal_0(G) => ~ ( ~ r1_xxreal_0(G,k5_numbers) & ! [H] : ( 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] : ( m2_finseq_2(I,k1_numbers,k1_euclid(A)) => r1_xxreal_0(k9_complex1(k5_real_1(k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_7(A,D,H),I),k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_7(A,D,E),I))),k3_xcmplx_0(F,k12_euclid(I))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t2_classes1,axiom,( ! [A] : r2_hidden(A,k1_classes1(A)) )).
fof(t2_classes2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_classes1(C) & r2_hidden(A,C) & r2_hidden(B,C) ) => ( r2_hidden(k1_tarski(A),C) & r2_hidden(k2_tarski(A,B),C) ) ) )).
fof(t2_clopban1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m2_funct_2(C,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => ! [D] : ( m2_funct_2(D,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => ! [E] : ( v1_xcmplx_0(E) => ( D = k1_funct_1(k2_clopban1(A,B),k4_tarski(E,C)) <=> ! [F] : ( m1_subset_1(F,A) => k3_funct_2(A,u1_struct_0(B),D,F) = k1_clvect_1(B,k3_funct_2(A,u1_struct_0(B),C,F),E) ) ) ) ) ) ) ) )).
fof(t2_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ( r1_xxreal_0(k2_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)),k3_xcmplx_0(k3_xcmplx_0(k1_funct_1(k13_clopban1(B,C),E),k1_funct_1(k13_clopban1(A,B),D)),k2_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))) ) ) ) ) ) ) ) ) )).
fof(t2_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,k5_normsp_0(A,B),C)) ) ) ) )).
fof(t2_clopban4,axiom,( ! [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) & 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ! [D] : ( v7_ordinal1(D) => k1_normsp_1(A,B,D) = C ) => k7_clvect_1(A,B) = C ) ) ) ) )).
fof(t2_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ( ? [C] : ( 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) ) ) )).
fof(t2_closure2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,B) => r1_tarski(k10_xtuple_0(C),k3_tarski(k10_xtuple_0(k5_mssubfam(A,B)))) ) ) ) )).
fof(t2_closure3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( 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) ) ) ) ) )).
fof(t2_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xcmplx_0(C) => ~ ( k1_clvect_1(A,B,C) = k4_struct_0(A) & C != k5_numbers & B != k4_struct_0(A) ) ) ) ) )).
fof(t2_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clvect_2(B,A) => ( ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(D,E) & k1_normsp_1(A,C,E) != k1_normsp_1(A,B,E) ) ) | v1_clvect_2(C,A) ) ) ) ) ) )).
fof(t2_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) )).
fof(t2_coh_sp,axiom,( ! [A] : ( ~ v1_xboole_0(k9_setfam_1(A)) & v1_classes1(k9_setfam_1(A)) & v1_coh_sp(k9_setfam_1(A)) ) )).
fof(t2_cohsp_1,axiom,( ! [A] : k3_tarski(k1_cohsp_1(A)) = A )).
fof(t2_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ~ ( B != C & B != D & C != D ) => r1_collsp(A,B,C,D) ) ) ) ) ) )).
fof(t2_combgras,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ( ( k1_card_1(C) = k2_xcmplx_0(B,A) & k1_card_1(D) = k2_xcmplx_0(B,A) ) => ( k1_card_1(k3_xboole_0(C,D)) = B <=> k1_card_1(k2_xboole_0(C,D)) = k2_xcmplx_0(B,k3_xcmplx_0(2,A)) ) ) ) ) )).
fof(t2_compact1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( 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 ) ) ) ) )).
fof(t2_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & v1_compl_sp(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) )).
fof(t2_complex1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k1_numbers) & ? [C] : ( m1_subset_1(C,k1_numbers) & r1_funct_2(2,k1_numbers,k2_tarski(k5_numbers,1),k1_numbers,A,k5_funct_4(k1_numbers,k5_numbers,1,B,C)) ) ) ) )).
fof(t2_complex2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k5_numbers,C) ) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(A,B) | r1_xxreal_0(A,C) | ! [D] : ( v1_int_1(D) => ( B = k2_xcmplx_0(C,k3_xcmplx_0(A,D)) => B = C ) ) ) ) ) ) ) )).
fof(t2_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( v1_xcmplx_0(B) => ( A = B => k4_algstr_0(k1_complfld,A) = k4_xcmplx_0(B) ) ) ) )).
fof(t2_complsp1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => u1_struct_0(k1_complsp1(A)) = k12_seq_4(A) ) )).
fof(t2_complsp2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( m2_finseq_1(C,k2_numbers) => ( r2_hidden(A,k4_finseq_1(k8_seq_4(B,C))) => k9_matrix_5(k8_seq_4(B,C),A) = k6_xcmplx_0(k9_matrix_5(B,A),k9_matrix_5(C,A)) ) ) ) ) )).
fof(t2_compos_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_compos_0(A) & v2_compos_0(A) & v3_compos_0(A) ) => ! [B] : ( m1_subset_1(B,A) => k5_compos_0(A,B,k5_numbers) = B ) ) )).
fof(t2_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => r2_hidden(k5_numbers,k2_afinsq_1(k4_compos_1(A))) ) )).
fof(t2_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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)) ) ) ) ) )).
fof(t2_comptrig,axiom,( ! [A] : ( v1_xcmplx_0(A) => r1_xxreal_0(k4_xcmplx_0(k9_complex1(A)),k4_complex1(A)) ) )).
fof(t2_compts_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(C,k2_struct_0(B)) => ( v2_compts_1(C,A) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( D = C => v2_compts_1(D,B) ) ) ) ) ) ) ) )).
fof(t2_comput_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ( k1_funct_7(E,A,B) = k1_funct_7(F,A,C) => k1_funct_7(E,A,D) = k1_funct_7(F,A,D) ) ) ) )).
fof(t2_comseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) <=> ( k9_xtuple_0(A) = k4_ordinal1 & ! [B] : ( m1_subset_1(B,k4_ordinal1) => m1_subset_1(k1_funct_1(A,B),k2_numbers) ) ) ) ) )).
fof(t2_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => k9_nat_1(k1_numbers,A,B) = k5_numbers ) => ! [B] : ( v7_ordinal1(B) => k9_nat_1(k1_numbers,k3_series_1(k56_valued_1(k4_ordinal1,k1_numbers,A)),B) = k5_numbers ) ) ) )).
fof(t2_conaffm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v4_conaffm(A) => v2_conaffm(A) ) ) )).
fof(t2_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( 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) ) ) )).
fof(t2_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t2_conmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r5_analmetr(A,B,C,D) & B != D & C != D ) ) ) ) )).
fof(t2_conmetr1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v3_conmetr1(A) <=> ( v1_conmetr1(A) & v2_conmetr1(A) ) ) ) )).
fof(t2_connsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t2_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t2_connsp_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ! [C] : ( 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 ) ) ) )).
fof(t2_convex1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t2_convex2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ( B = a_3_0_convex2(A,C,D) => v1_convex1(B,A) ) ) ) ) ) )).
fof(t2_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k2_numbers,k2_convex4(A),B) = k5_complex1 ) ) )).
fof(t2_convfun1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_rlvect_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(k3_convfun1(A,B))) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t2_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( 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)))) ) ) ) ) )).
fof(t2_cqc_sim1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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))) ) )).
fof(t2_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => r2_hidden(k5_cqc_lang(A),k1_cqc_the1(A,B)) ) ) )).
fof(t2_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t2_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t2_csspace,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace))) => ! [B] : ( 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)) ) ) )).
fof(t2_csspace2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k18_csspace)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k18_csspace)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k18_csspace)) => ! [D] : ( v1_xcmplx_0(D) => ( ( k12_csspace(k18_csspace,A,A) = k5_numbers => A = k4_struct_0(k18_csspace) ) & ( A = k4_struct_0(k18_csspace) => k12_csspace(k18_csspace,A,A) = k5_numbers ) & r1_xxreal_0(k5_numbers,k3_complex1(k12_csspace(k18_csspace,A,A))) & k4_complex1(k12_csspace(k18_csspace,A,A)) = k5_numbers & k12_csspace(k18_csspace,A,B) = k8_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)) ) ) ) ) ) )).
fof(t2_csspace3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(t2_csspace4,axiom,( u1_struct_0(k3_csspace4) = k1_csspace4 & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_csspace4)) <=> ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & v1_comseq_2(k2_csspace(A)) ) ) & k4_struct_0(k3_csspace4) = k6_csspace & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_csspace4)) => A = k2_csspace(A) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_csspace4)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_csspace4)) => k1_algstr_0(k3_csspace4,A,B) = k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k2_csspace(A),k2_csspace(B)) ) ) & ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_csspace4)) => k1_clvect_1(k3_csspace4,B,A) = k25_valued_1(k4_ordinal1,k2_numbers,k2_csspace(B),A) ) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_csspace4)) => ( k4_algstr_0(k3_csspace4,A) = k31_valued_1(k4_ordinal1,k2_numbers,k2_csspace(A)) & r2_funct_2(k4_ordinal1,k2_numbers,k2_csspace(k4_algstr_0(k3_csspace4,A)),k31_valued_1(k4_ordinal1,k2_numbers,k2_csspace(A))) ) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_csspace4)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_csspace4)) => k5_algstr_0(k3_csspace4,A,B) = k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k2_csspace(A),k2_csspace(B)) ) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_csspace4)) => v1_comseq_2(k2_csspace(A)) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_csspace4)) => k2_normsp_0(k3_csspace4,A) = k2_seq_4(k2_relset_1(k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,k2_csspace(A)))) ) )).
fof(t2_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( m1_decomp_1(B,A) <=> B = k3_decomp_1(A,B) ) ) ) )).
fof(t2_descip_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v8_ordinal1(D) & m1_subset_1(D,k4_ordinal1) ) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t2_dickson,axiom,( ! [A] : ( v7_ordinal1(A) => r1_ordinal1(A,k1_nat_1(A,1)) ) )).
fof(t2_diff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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] : ( 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))) ) ) ) ) )).
fof(t2_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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 != k5_numbers => k10_diff_1(C,B,k2_xcmplx_0(B,A),k2_xcmplx_0(B,k3_xcmplx_0(2,A))) = k7_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(C,A),2),B),k3_xcmplx_0(2,k1_square_1(A))) ) ) ) ) )).
fof(t2_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k3_diff_1(C,k4_xcmplx_0(k7_xcmplx_0(A,2))),B) = k4_xcmplx_0(k1_funct_1(k4_diff_1(C,k7_xcmplx_0(A,2)),B)) ) ) ) )).
fof(t2_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & k2_xcmplx_0(k3_power(k4_power,A),k3_power(k4_power,B)) != k3_power(k4_power,k3_xcmplx_0(A,B)) ) ) ) )).
fof(t2_dilworth,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [D] : ( 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)))) ) ) )).
fof(t2_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t2_dirort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(k6_analort(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k6_analort(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k6_analort(A,B,C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k6_analort(A,B,C))) => ! [H] : ( 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] : ( m1_subset_1(D,u1_struct_0(k6_analort(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k6_analort(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k6_analort(A,B,C))) => ? [G] : ( 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] : ( m1_subset_1(D,u1_struct_0(k6_analort(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k6_analort(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k6_analort(A,B,C))) => ? [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t2_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : k2_dist_1(A,B,C) = k3_xcmplx_0(k3_finseq_1(B),k3_dist_1(A,B,C)) ) ) )).
fof(t2_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_dist_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( k4_dist_1(A,C) = B => ( k8_dist_1(A,B) = k5_dist_1(A,C) & r2_hidden(C,k8_dist_1(A,B)) ) ) ) ) ) )).
fof(t2_domain_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t2_dtconstr,axiom,( ! [A] : ! [B] : ! [C] : ( m2_finseq_1(C,A) => ( r2_hidden(B,k4_finseq_1(C)) => r2_hidden(k1_funct_1(C,B),A) ) ) )).
fof(t2_e_siec,axiom,( ! [A] : ( 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)) ) )).
fof(t2_ec_pf_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t2_ec_pf_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) )).
fof(t2_endalg,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t2_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => r1_tarski(k1_funct_2(B,C),k1_ens_1(A)) ) ) ) )).
fof(t2_entropy1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ( r1_xxreal_0(k1_funct_1(k3_taylor_1,A),k6_xcmplx_0(A,1)) & ( A = 1 => k1_funct_1(k3_taylor_1,A) = k6_xcmplx_0(A,1) ) & ( k1_funct_1(k3_taylor_1,A) = k6_xcmplx_0(A,1) => A = 1 ) & ~ ( A != 1 & r1_xxreal_0(k6_xcmplx_0(A,1),k1_funct_1(k3_taylor_1,A)) ) & ~ ( ~ r1_xxreal_0(k6_xcmplx_0(A,1),k1_funct_1(k3_taylor_1,A)) & A = 1 ) ) ) ) )).
fof(t2_enumset1,axiom,( ! [A] : ! [B] : ! [C] : k1_enumset1(A,B,C) = k2_xboole_0(k1_tarski(A),k2_tarski(B,C)) )).
fof(t2_eqrel_1,axiom,( ! [A] : ( r1_relat_2(k6_partfun1(A),A) & r3_relat_2(k6_partfun1(A),A) & r8_relat_2(k6_partfun1(A),A) ) )).
fof(t2_equation,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v2_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( m2_pboole(E,A,B,C) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t2_euclid,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => k54_valued_1(k30_valued_1(A)) = k54_valued_1(A) ) )).
fof(t2_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => k14_rvsum_1(B,k5_euclid(A)) = k5_euclid(A) ) ) )).
fof(t2_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => k1_euclid_3(k2_euclid_3(A)) = A ) )).
fof(t2_euclid_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => k9_euclid(B,k5_euclid(B),A) = k5_euclid(B) ) ) )).
fof(t2_euclid_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( 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 ) ) ) ) )).
fof(t2_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => k17_sin_cos(k4_euclid_3(A,B,C)) = k4_xcmplx_0(k17_sin_cos(k4_euclid_3(C,B,A))) ) ) ) )).
fof(t2_euclid_7,axiom,( ! [A] : k3_relat_1(k12_finseq_1(k4_ordinal1,1),k9_finseq_1(A)) = k9_finseq_1(A) )).
fof(t2_euclid_8,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( k3_finseq_1(A) = 3 => m2_finseq_2(A,k1_numbers,k1_euclid(3)) ) ) )).
fof(t2_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) & v3_valued_0(B) ) => r2_hidden(B,k1_euclid(A)) ) ) )).
fof(t2_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( 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) ) ) ) )).
fof(t2_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t2_euler_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( v1_int_2(B) => ( A = k5_numbers | r1_xxreal_0(B,A) | r1_int_2(A,B) ) ) ) ) )).
fof(t2_euler_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_int_1(B) => ( r1_xxreal_0(1,k3_xcmplx_0(A,B)) => r1_xxreal_0(1,B) ) ) ) )).
fof(t2_exchsort,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t2_extens_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m3_pboole(D,A,B) => ! [E] : ( m2_pboole(E,A,B,C) => r2_pboole(A,k9_pboole(A,D,E),k9_pboole(A,B,E)) ) ) ) ) )).
fof(t2_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) ) => ! [D] : ( ( 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,k5_numbers) = D ) ) ) ) )).
fof(t2_extreal1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( A = C & B = D ) => k2_extreal1(A,B) = k2_extreal1(C,D) ) ) ) ) ) )).
fof(t2_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ( k3_extreal1(A) = A | k3_extreal1(A) = k2_xxreal_3(A) ) ) )).
fof(t2_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t2_facirc_2,axiom,( ! [A] : ! [B] : ! [C] : ( A != k4_tarski(k10_finseq_1(A,B),C) & B != k4_tarski(k10_finseq_1(A,B),C) ) )).
fof(t2_fcont_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t2_fcont_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r2_hidden(B,k2_rcomp_1(k6_xcmplx_0(A,C),k2_xcmplx_0(A,C))) => r2_hidden(k6_xcmplx_0(B,A),k2_rcomp_1(k4_xcmplx_0(C),C)) ) ) ) ) )).
fof(t2_fdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v3_fdiff_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(t2_fdiff_10,axiom,( ! [A] : ( ( 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,k26_sin_cos,k26_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k26_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k26_sin_cos),A),B) = k3_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,k1_funct_1(k26_sin_cos,B)))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,B)))) ) ) ) ) ) )).
fof(t2_fdiff_11,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k16_sin_cos,B),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k2_sin_cos9),A),B) = k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k18_sin_cos,B),k2_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B))))) ) ) ) ) ) )).
fof(t2_fdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => k3_funct_2(k4_ordinal1,k1_numbers,A,B) = k2_nat_1(2,B) ) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_ordinal1) & v5_valued_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) ) ) )).
fof(t2_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k1_funct_1(C,D) = k6_xcmplx_0(D,A) & ~ r1_xxreal_0(k1_funct_1(C,D),k5_numbers) ) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1),B),D) = k7_xcmplx_0(1,k6_xcmplx_0(D,A)) ) ) ) ) ) ) ) )).
fof(t2_fdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => ( k1_funct_1(C,E) = k6_xcmplx_0(E,A) & k1_funct_1(D,E) = k2_xcmplx_0(E,A) & k1_funct_1(D,E) != k5_numbers ) ) ) ) => ( r2_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,C,D),B) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_1(k2_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,C,D),B),E) = k7_xcmplx_0(k3_xcmplx_0(2,A),k1_square_1(k2_xcmplx_0(E,A))) ) ) ) ) ) ) ) ) )).
fof(t2_fdiff_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,k5_numbers) => k1_funct_1(k22_sin_cos,k4_xcmplx_0(k3_xcmplx_0(A,k3_power(k4_power,B)))) = k6_prepower(B,k4_xcmplx_0(A)) ) ) ) )).
fof(t2_fdiff_7,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k6_prepower(A,k7_xcmplx_0(1,2)) = k3_square_1(A) ) ) )).
fof(t2_fdiff_8,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( r2_hidden(A,k1_relset_1(k1_numbers,k27_sin_cos)) & k1_funct_1(k16_sin_cos,A) = k5_numbers ) ) )).
fof(t2_fdiff_9,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_funct_1(k16_sin_cos,A) != k5_numbers => ( r1_fdiff_1(k2_fdiff_9,A) & k1_fdiff_1(k2_fdiff_9,A) = k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k18_sin_cos,A),k1_square_1(k1_funct_1(k16_sin_cos,A)))) ) ) ) )).
fof(t2_ff_siec,axiom,( ! [A] : ( 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 ) )).
fof(t2_fib_num2,axiom,( ! [A] : ( ( v1_int_1(A) & ~ v1_abian(A) ) => k2_power(k4_xcmplx_0(1),A) = k4_xcmplx_0(1) ) )).
fof(t2_fib_num3,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xxreal_0(A) ) => k3_xcmplx_0(k3_square_1(A),k3_square_1(A)) = A ) )).
fof(t2_fib_num4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( A != k5_numbers => k2_power(A,k2_xcmplx_0(B,C)) = k3_xcmplx_0(k2_power(A,B),k2_power(A,C)) ) ) ) ) )).
fof(t2_filerec1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => k17_finseq_1(A,k3_finseq_1(B),B) = B ) )).
fof(t2_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r3_lattices(A,B,D) => r3_lattices(A,k4_lattices(A,B,C),D) ) ) ) ) ) )).
fof(t2_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_filter_0(A,B) = k2_filter_0(A,C) => B = C ) ) ) ) )).
fof(t2_filter_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,A) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t2_finance1,axiom,( ! [A] : ( v1_xreal_0(A) => k6_subset_1(k1_numbers,k2_rcomp_1(k2_xxreal_0,A)) = k3_rcomp_1(A,k1_xxreal_0) ) )).
fof(t2_finseq_1,axiom,( k2_finseq_1(1) = k1_tarski(1) & k2_finseq_1(2) = k2_tarski(1,2) )).
fof(t2_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(A,B) => k4_xxreal_0(k5_numbers,k6_xcmplx_0(A,B)) = k5_numbers ) ) ) )).
fof(t2_finseq_3,axiom,( k2_finseq_1(4) = k2_enumset1(1,2,3,4) )).
fof(t2_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t2_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t2_finseq_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ( r2_hidden(A,k4_finseq_1(B)) & ! [C] : ( 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 ) ) ) )).
fof(t2_finseq_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t2_finseq_8,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_xxreal_0(k3_finseq_1(B),C) => k2_rfinseq(A,C,B) = k6_finseq_1(A) ) ) ) )).
fof(t2_finseqop,axiom,( ! [A] : ( ( 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 ) ) )).
fof(t2_finset_1,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k2_xboole_0(A,B)) ) )).
fof(t2_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ~ ( k9_nat_1(A,E,1) = k1_funct_1(C,1) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( k5_numbers != F & ~ r1_xxreal_0(k3_finseq_1(C),F) & k9_nat_1(A,E,k1_nat_1(F,1)) != k1_binop_1(D,k9_nat_1(A,E,F),k1_funct_1(C,k1_nat_1(F,1))) ) ) & B = k9_nat_1(A,E,k3_finseq_1(C)) ) ) | B = k1_finsop_1(A,C,D) ) ) ) ) ) ) )).
fof(t2_finsub_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(t2_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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))) ) ) )).
fof(t2_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k1_fintopo3(A,B)) <=> ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t2_fintopo5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( ~ ( ~ r1_xxreal_0(A,k5_numbers) & k2_finseq_1(A) = k1_xboole_0 ) & ~ ( k2_finseq_1(A) != k1_xboole_0 & r1_xxreal_0(A,k5_numbers) ) ) ) )).
fof(t2_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) )).
fof(t2_flang_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k2_xcmplx_0(B,A),k1_nat_1(C,1)) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(B,C) ) ) ) ) ) )).
fof(t2_flang_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( r1_xxreal_0(D,E) & r1_xxreal_0(B,C) & r1_xxreal_0(k2_xcmplx_0(D,B),A) & r1_xxreal_0(A,k2_xcmplx_0(E,C)) & ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ~ ( k2_xcmplx_0(F,G) = A & r1_xxreal_0(D,F) & r1_xxreal_0(F,E) & r1_xxreal_0(B,G) & r1_xxreal_0(G,C) ) ) ) ) ) ) ) ) ) )).
fof(t2_flang_3,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(B,k1_flang_3(A,C,D)) <=> ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(D,E) & r2_hidden(B,k7_flang_1(A,C,E)) ) ) ) ) )).
fof(t2_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( v7_ordinal1(C) => k3_xboole_0(k4_finseq_2(C,A),k3_finseq_2(B)) = k4_finseq_2(C,k3_xboole_0(A,B)) ) )).
fof(t2_fomodel1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => r1_tarski(k1_funct_1(k25_fomodel1(B),A),k27_fomodel1(B)) ) ) )).
fof(t2_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_fomodel2(C,A,B) ) => r2_hidden(k5_relat_1(C,k37_fomodel1(A)),k15_fomodel2(A,B)) ) ) ) )).
fof(t2_fomodel3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( m2_subset_1(B,k3_finseq_2(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k35_fomodel1(A))) => ? [C] : ( m1_subset_1(C,k4_ordinal1) & m2_subset_1(B,k3_finseq_2(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0)),k9_nat_1(k9_setfam_1(k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))),k39_fomodel1(A),C))) ) ) ) )).
fof(t2_fomodel4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(D) & v11_fomodel1(D) & l1_fomodel1(D) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(D)),k9_setfam_1(k1_fomodel4(D))))) => ! [F] : ( 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) & v5_fomodel4(C,A,D,E,B) ) => ( ( ~ v7_fomodel4(F,D) & ~ v7_fomodel4(E,D) ) | v5_fomodel4(C,A,D,F,B) ) ) ) ) ) ) )).
fof(t2_fraenkel,axiom,( ! [A] : ! [B] : r1_tarski(k1_funct_2(A,B),k1_zfmisc_1(k2_zfmisc_1(A,B))) )).
fof(t2_frechet,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( l1_struct_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) ) ) ) ) )).
fof(t2_frechet2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r1_funct_2(k4_ordinal1,k1_numbers,k4_ordinal1,k4_ordinal1,A,k6_partfun1(k4_ordinal1)) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_ordinal1) & v5_valued_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) ) ) )).
fof(t2_freealg,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( r1_tarski(k1_lang1(k3_freealg(A,B)),B) & k2_lang1(k3_freealg(A,B)) = k4_finseq_1(A) ) ) )).
fof(t2_friends1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( v3_relat_2(B) => k7_relat_1(B,A) = k8_relat_1(B,A) ) ) )).
fof(t2_fscirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ~ v1_facirc_1(k2_msafree2(k4_fscirc_1(A,B,C))) ) ) ) )).
fof(t2_fscirc_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( k1_fscirc_2(k5_numbers,A,B) = k5_circcomb(k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k8_margrel1),k1_xboole_0) & k2_fscirc_2(k5_numbers,A,B) = k7_circcomb(k5_ordinal1,k6_margrel1,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k8_margrel1),k1_xboole_0) & k3_fscirc_2(k5_numbers,A,B) = k4_tarski(k1_xboole_0,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k8_margrel1)) ) ) ) )).
fof(t2_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => r1_fsm_1(A,B,k6_finseq_1(A),C,C) ) ) ) )).
fof(t2_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( ~ v2_struct_0(D) & l1_fsm_1(D,A) ) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t2_fsm_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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 ) ) ) )).
fof(t2_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : v1_relat_1(k3_msafree2(k1_ftacell1(A,B,C,D,E))) )).
fof(t2_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => k13_funct_3(A,B) = k1_funcop_1(k13_funct_3(B,A)) ) ) )).
fof(t2_funcsdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( m2_funct_2(C,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [D] : ( m2_funct_2(D,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ( r2_funct_2(A,k1_numbers,D,k1_funcsdom(A,k1_numbers,k6_funcsdom(A),B,C)) <=> ! [E] : ( m1_subset_1(E,A) => k3_funct_2(A,k1_numbers,D,E) = k4_real_1(k3_funct_2(A,k1_numbers,B,E),k3_funct_2(A,k1_numbers,C,E)) ) ) ) ) ) ) )).
fof(t2_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( k9_xtuple_0(A) = k9_xtuple_0(B) & ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) => A = B ) ) ) )).
fof(t2_funct_2,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) ) )).
fof(t2_funct_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t2_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => k3_relat_1(A,B) = k3_relat_1(A,k5_relat_1(B,k10_xtuple_0(A))) ) ) )).
fof(t2_funct_5,axiom,( k9_xtuple_0(k1_xboole_0) = k1_xboole_0 & k10_xtuple_0(k1_xboole_0) = k1_xboole_0 )).
fof(t2_funct_6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ~ ( r2_hidden(A,k9_xtuple_0(k2_funct_4(B))) & ! [C] : ! [D] : A != k4_tarski(C,D) ) ) )).
fof(t2_funct_7,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t2_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k6_xcmplx_0(k1_funct_1(B,C),k1_funct_1(B,k4_xcmplx_0(C))) = k5_numbers ) ) ) ) ) ) )).
fof(t2_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t2_functor0,axiom,( ! [A] : ! [B] : ( ( 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 ) )).
fof(t2_functor1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) ) )).
fof(t2_functor2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( m2_functor0(C,A,B) => ! [D] : ( m2_functor0(D,A,B) => ! [E] : ( m2_functor0(E,A,B) => ( ( r1_functor2(A,B,C,D) & r1_functor2(A,B,D,E) ) => r1_functor2(A,B,C,E) ) ) ) ) ) ) )).
fof(t2_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v8_functor0(D,A,B) & v10_functor0(D,A,B) & l2_functor0(D,A,B) ) => ! [E] : ( l2_functor0(E,B,C) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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))) ) ) ) ) ) ) ) )).
fof(t2_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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) ) ) ) ) ) )).
fof(t2_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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)) ) ) ) ) ) )).
fof(t2_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( r2_hidden(D,A) => r1_xxreal_0(k1_funct_1(B,D),k1_funct_1(C,D)) ) => r1_xxreal_0(k2_seq_4(k2_relset_1(k1_numbers,B)),k2_seq_4(k2_relset_1(k1_numbers,C))) ) ) ) ) )).
fof(t2_fvaluat1,axiom,( ! [A] : ( v1_xxreal_0(A) => ( k1_xxreal_3(A,A) = k5_numbers => A = k5_numbers ) ) )).
fof(t2_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_rlvect_1(A) & l2_algstr_0(A) ) => v2_binop_1(u1_algstr_0(A),u1_struct_0(A)) ) )).
fof(t2_gate_1,axiom,( ! [A] : ( ~ v1_xboole_0(k1_gate_1(A)) <=> v1_xboole_0(A) ) )).
fof(t2_gate_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ ( ~ v1_xboole_0(k8_gate_1(k2_gate_1(A,D),k2_gate_1(B,D),k2_gate_1(C,D))) & v1_xboole_0(k2_gate_1(k8_gate_1(A,B,C),D)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(k8_gate_1(A,B,C),D)) & v1_xboole_0(k8_gate_1(k2_gate_1(A,D),k2_gate_1(B,D),k2_gate_1(C,D))) ) ) )).
fof(t2_gate_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ~ ( ~ ( ~ 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) ) ) ) )).
fof(t2_gate_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ! [Q] : ! [R] : ! [S] : ! [T] : ! [U] : ! [V] : ! [W] : ! [X] : ! [Y] : ! [Z] : ! [A1] : ! [B1] : ! [C1] : ! [D1] : ! [E1] : ! [F1] : ! [G1] : ! [H1] : ! [I1] : ! [J1] : ! [K1] : ! [L1] : ! [M1] : ! [N1] : ! [O1] : ! [P1] : ! [Q1] : ! [R1] : ! [S1] : ! [T1] : ! [U1] : ! [V1] : ! [W1] : ! [X1] : ~ ( ~ v1_xboole_0(Q) & ~ ( ~ v1_xboole_0(H1) & v1_xboole_0(k4_gate_1(X1,k2_gate_1(A,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(X1,k2_gate_1(A,G1))) & v1_xboole_0(H1) ) & ~ ( ~ v1_xboole_0(I1) & v1_xboole_0(k4_gate_1(R,k2_gate_1(B,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(R,k2_gate_1(B,G1))) & v1_xboole_0(I1) ) & ~ ( ~ v1_xboole_0(J1) & v1_xboole_0(k4_gate_1(S,k2_gate_1(C,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(S,k2_gate_1(C,G1))) & v1_xboole_0(J1) ) & ~ ( ~ v1_xboole_0(K1) & v1_xboole_0(k4_gate_1(T,k2_gate_1(D,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(T,k2_gate_1(D,G1))) & v1_xboole_0(K1) ) & ~ ( ~ v1_xboole_0(L1) & v1_xboole_0(k4_gate_1(U,k2_gate_1(E,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(U,k2_gate_1(E,G1))) & v1_xboole_0(L1) ) & ~ ( ~ v1_xboole_0(M1) & v1_xboole_0(k4_gate_1(V,k2_gate_1(F,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(V,k2_gate_1(F,G1))) & v1_xboole_0(M1) ) & ~ ( ~ v1_xboole_0(N1) & v1_xboole_0(k4_gate_1(W,k2_gate_1(G,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(W,k2_gate_1(G,G1))) & v1_xboole_0(N1) ) & ~ ( ~ v1_xboole_0(O1) & v1_xboole_0(k4_gate_1(X,k2_gate_1(H,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(X,k2_gate_1(H,G1))) & v1_xboole_0(O1) ) & ~ ( ~ v1_xboole_0(P1) & v1_xboole_0(k4_gate_1(Y,k2_gate_1(I,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(Y,k2_gate_1(I,G1))) & v1_xboole_0(P1) ) & ~ ( ~ v1_xboole_0(Q1) & v1_xboole_0(k4_gate_1(Z,k2_gate_1(J,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(Z,k2_gate_1(J,G1))) & v1_xboole_0(Q1) ) & ~ ( ~ v1_xboole_0(R1) & v1_xboole_0(k4_gate_1(A1,k2_gate_1(K,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(A1,k2_gate_1(K,G1))) & v1_xboole_0(R1) ) & ~ ( ~ v1_xboole_0(S1) & v1_xboole_0(k4_gate_1(B1,k2_gate_1(L,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(B1,k2_gate_1(L,G1))) & v1_xboole_0(S1) ) & ~ ( ~ v1_xboole_0(T1) & v1_xboole_0(k4_gate_1(C1,k2_gate_1(M,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(C1,k2_gate_1(M,G1))) & v1_xboole_0(T1) ) & ~ ( ~ v1_xboole_0(U1) & v1_xboole_0(k4_gate_1(D1,k2_gate_1(N,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(D1,k2_gate_1(N,G1))) & v1_xboole_0(U1) ) & ~ ( ~ v1_xboole_0(V1) & v1_xboole_0(k4_gate_1(E1,k2_gate_1(O,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(E1,k2_gate_1(O,G1))) & v1_xboole_0(V1) ) & ~ ( ~ v1_xboole_0(W1) & v1_xboole_0(k4_gate_1(F1,k2_gate_1(P,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(F1,k2_gate_1(P,G1))) & v1_xboole_0(W1) ) & ~ ( ~ ( ~ v1_xboole_0(G1) & v1_xboole_0(k2_gate_1(Q,G1)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(Q,G1)) & v1_xboole_0(G1) ) & ~ ( ~ v1_xboole_0(F1) & v1_xboole_0(k4_gate_1(W1,k2_gate_1(P,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(W1,k2_gate_1(P,G1))) & v1_xboole_0(F1) ) & ~ ( ~ v1_xboole_0(E1) & v1_xboole_0(k4_gate_1(V1,k2_gate_1(O,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(V1,k2_gate_1(O,G1))) & v1_xboole_0(E1) ) & ~ ( ~ v1_xboole_0(D1) & v1_xboole_0(k4_gate_1(U1,k2_gate_1(N,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(U1,k2_gate_1(N,G1))) & v1_xboole_0(D1) ) & ~ ( ~ v1_xboole_0(C1) & v1_xboole_0(k4_gate_1(T1,k2_gate_1(M,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(T1,k2_gate_1(M,G1))) & v1_xboole_0(C1) ) & ~ ( ~ v1_xboole_0(B1) & v1_xboole_0(k4_gate_1(S1,k2_gate_1(L,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(S1,k2_gate_1(L,G1))) & v1_xboole_0(B1) ) & ~ ( ~ v1_xboole_0(A1) & v1_xboole_0(k4_gate_1(R1,k2_gate_1(K,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(R1,k2_gate_1(K,G1))) & v1_xboole_0(A1) ) & ~ ( ~ v1_xboole_0(Z) & v1_xboole_0(k4_gate_1(Q1,k2_gate_1(J,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(Q1,k2_gate_1(J,G1))) & v1_xboole_0(Z) ) & ~ ( ~ v1_xboole_0(Y) & v1_xboole_0(k4_gate_1(P1,k2_gate_1(I,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(P1,k2_gate_1(I,G1))) & v1_xboole_0(Y) ) & ~ ( ~ v1_xboole_0(X) & v1_xboole_0(k4_gate_1(O1,k2_gate_1(H,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(O1,k2_gate_1(H,G1))) & v1_xboole_0(X) ) & ~ ( ~ v1_xboole_0(W) & v1_xboole_0(k4_gate_1(N1,k2_gate_1(G,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(N1,k2_gate_1(G,G1))) & v1_xboole_0(W) ) & ~ ( ~ v1_xboole_0(V) & v1_xboole_0(k4_gate_1(M1,k2_gate_1(F,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(M1,k2_gate_1(F,G1))) & v1_xboole_0(V) ) & ~ ( ~ v1_xboole_0(U) & v1_xboole_0(k4_gate_1(L1,k2_gate_1(E,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(L1,k2_gate_1(E,G1))) & v1_xboole_0(U) ) & ~ ( ~ v1_xboole_0(T) & v1_xboole_0(k4_gate_1(K1,k2_gate_1(D,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(K1,k2_gate_1(D,G1))) & v1_xboole_0(T) ) & ~ ( ~ v1_xboole_0(S) & v1_xboole_0(k4_gate_1(J1,k2_gate_1(C,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(J1,k2_gate_1(C,G1))) & v1_xboole_0(S) ) & ~ ( ~ v1_xboole_0(R) & v1_xboole_0(k4_gate_1(I1,k2_gate_1(B,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(I1,k2_gate_1(B,G1))) & v1_xboole_0(R) ) & ~ ( ~ v1_xboole_0(X1) & v1_xboole_0(k4_gate_1(H1,k2_gate_1(A,G1))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(H1,k2_gate_1(A,G1))) & v1_xboole_0(X1) ) ) ) )).
fof(t2_gate_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ! [Q] : ! [R] : ! [S] : ! [T] : ! [U] : ! [V] : ! [W] : ! [X] : ! [Y] : ~ ( ~ ( ~ 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) ) ) ) )).
fof(t2_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & l4_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t2_genealg1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k17_finseq_1(A,k1_nat_1(k3_finseq_1(B),D),k8_finseq_1(A,B,C)) = k8_finseq_1(A,B,k17_finseq_1(A,D,C)) ) ) ) ) )).
fof(t2_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_analoaf(A))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k2_analoaf(A))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k2_analoaf(A))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k2_analoaf(A))) => ( ( F = B & G = D & H = C & I = E ) => ( r2_analoaf(k2_analoaf(A),F,G,H,I) <=> r1_analoaf(A,B,D,C,E) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t2_gfacirc1,axiom,( ! [A] : ( 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(k4_ordinal1,k5_numbers)) = k5_numbers & k1_funct_1(k2_gfacirc1,k10_binarith(k4_ordinal1,1)) = 1 ) ) )).
fof(t2_gfacirc2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( k1_gfacirc2(k5_numbers,A,B) = k5_circcomb(k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1),k1_xboole_0) & k2_gfacirc2(k5_numbers,A,B) = k7_circcomb(k5_ordinal1,k6_margrel1,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1),k1_xboole_0) & k3_gfacirc2(k5_numbers,A,B) = k4_tarski(k1_xboole_0,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1)) ) ) ) )).
fof(t2_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => r1_tarski(k5_glib_000,k1_relset_1(k4_ordinal1,A)) ) )).
fof(t2_glib_001,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => r1_xxreal_0(k3_finseq_1(k15_finseq_1(C)),k3_finseq_1(B)) ) ) )).
fof(t2_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & ~ v4_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( 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] : ~ ( r2_hidden(D,k28_glib_000(A,B)) & ~ r1_glib_000(A,B,B,D) ) | v1_glib_002(A) ) ) ) ) ) )).
fof(t2_glib_003,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k4_finseq_1(A)) => r1_xxreal_0(k5_numbers,k1_funct_1(A,C)) ) ) => r1_xxreal_0(k18_rvsum_1(k1_glib_003(k1_numbers,A,B)),k18_rvsum_1(A)) ) ) ) )).
fof(t2_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : r1_tarski(k13_pre_poly(k1_funct_4(A,k16_funcop_1(B,C))),k2_xboole_0(k13_pre_poly(A),k1_tarski(B))) ) )).
fof(t2_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( ( 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] : ( m3_glib_001(C,A) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r5_glib_005(A,B,C) => r5_glib_005(A,B,k8_glib_001(A,C,D,E)) ) ) ) ) ) ) )).
fof(t2_goboard1,axiom,( ! [A] : ( ( v1_matrix_0(A) & v1_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(B,k10_xtuple_0(k7_matrix_0(u1_struct_0(k15_euclid(2)),A,C))) & r2_hidden(B,k10_xtuple_0(k7_matrix_0(u1_struct_0(k15_euclid(2)),A,D))) & r2_hidden(C,k4_finseq_1(A)) & r2_hidden(D,k4_finseq_1(A)) ) => C = D ) ) ) ) )).
fof(t2_goboard2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ( ( 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(k1_nat_1(B,1),k4_finseq_1(A)) ) => k1_nat_1(B,1) = k3_finseq_1(A) ) ) ) )).
fof(t2_goboard3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ~ ( ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(C,k4_finseq_1(A)) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( r2_hidden(k4_tarski(D,E),k2_matrix_0(B)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),B,D,E) ) ) ) ) ) & v4_topreal1(A) & ! [C] : ( 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)) ) ) ) ) ) )).
fof(t2_goboard4,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [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)) & 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(k7_matrix_0(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(k7_matrix_0(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(k8_matrix_0(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(k8_matrix_0(u1_struct_0(k15_euclid(2)),A,k1_matrix_0(A)))) & r1_xboole_0(k3_topreal1(2,B),k3_topreal1(2,C)) ) ) ) ) )).
fof(t2_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( v1_goboard1(C) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k1_matrix_0(C)) & r1_xxreal_0(1,A) & r1_xxreal_0(A,k3_finseq_1(C)) ) => k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B)) = k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,1)) ) ) ) ) )).
fof(t2_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( v1_xreal_0(D) => ( B = C => ( r1_xxreal_0(D,k5_numbers) | m1_connsp_2(k8_metric_1(k14_euclid(A),B,D),k15_euclid(A),C) ) ) ) ) ) ) )).
fof(t2_goboard7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k9_complex1(k6_xcmplx_0(A,B)) = k5_numbers <=> A = B ) ) ) )).
fof(t2_goboard8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,2),k3_finseq_1(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,2),k3_finseq_1(k2_goboard2(A))) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,2),k1_matrix_0(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_nat_1(D,1)) ) => ( ( ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,2),k1_nat_1(D,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_nat_1(D,2)) ) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,2),k1_nat_1(D,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_nat_1(D,1))),k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,k1_nat_1(D,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_nat_1(D,2))),k7_xcmplx_0(1,2))),k3_topreal1(2,A)) ) ) ) ) ) ) ) )).
fof(t2_goboard9,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t2_gobrd10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( 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)) ) ) ) )).
fof(t2_gobrd11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t2_gobrd12,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(B,k3_finseq_1(k2_goboard2(A))) & r1_xxreal_0(C,k1_matrix_0(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))) ) ) ) ) )).
fof(t2_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_tarski(k9_matrix_0(D),k9_matrix_0(E)) & r2_hidden(k4_tarski(A,B),k2_matrix_0(D)) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(E)) & k3_matrix_0(u1_struct_0(k15_euclid(2)),D,A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,1,C) ) => A = 1 ) ) ) ) ) ) )).
fof(t2_gobrd14,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t2_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t2_gr_cy_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_struct_0(k5_group_4(A,k6_domain_1(u1_struct_0(A),B)),B) ) ) )).
fof(t2_gr_cy_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_gr_cy_3(A) ) => r1_xxreal_0(5,A) ) )).
fof(t2_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_hidden(B,u1_struct_0(A)) ) ) )).
fof(t2_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( B = k5_relat_1(A,k2_finseq_1(C)) => ( r1_xxreal_0(k3_finseq_1(B),k3_finseq_1(A)) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(B)) ) => k1_funct_1(A,D) = k1_funct_1(B,D) ) ) ) ) ) ) ) )).
fof(t2_graph_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( r2_hidden(D,k4_finseq_1(k1_graph_2(A,B,C))) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( r2_hidden(E,k4_finseq_1(A)) & k1_funct_1(A,E) = k1_funct_1(k1_graph_2(A,B,C),D) & k1_nat_1(E,1) = k1_nat_1(B,D) & r1_xxreal_0(B,E) & r1_xxreal_0(E,C) ) ) ) ) ) ) ) )).
fof(t2_graph_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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 ) ) ) ) ) ) ) )).
fof(t2_graph_5,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( C = a_2_0_graph_5(A,B) => v1_finset_1(C) ) ) ) )).
fof(t2_graphsp,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( 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) ) ) ) )).
fof(t2_grcat_1,axiom,( 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 )).
fof(t2_grfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(A,B) <=> ( r1_tarski(k9_xtuple_0(A),k9_xtuple_0(B)) & ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) ) )).
fof(t2_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t2_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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] : ( ( 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 = k7_polynom1(A,C,D,k11_polynom1(A,C,G,E)) & ~ r2_hidden(k3_termord(A,B,C,k11_polynom1(A,C,G,E)),k3_polynom1(k15_pre_poly(A),C,F)) & r1_termord(A,B,k3_termord(A,B,C,k11_polynom1(A,C,G,E)),k3_termord(A,B,C,D)) ) ) ) ) ) ) ) ) ) )).
fof(t2_groeb_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k4_rlvect_1(A,k2_finseq_7(u1_struct_0(A),B,C,D)) = k4_rlvect_1(A,B) ) ) ) ) )).
fof(t2_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(t2_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & k6_algstr_0(A,B,D) = C ) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & k6_algstr_0(A,D,B) = C ) ) ) ) ) => ( v3_group_1(A) & v2_group_1(A) ) ) ) )).
fof(t2_group_10,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ! [D] : ( C != D => k1_card_1(k1_card_fin(A,B,C,D)) = k5_card_1(k3_group_10(A,B)) ) ) ) )).
fof(t2_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t2_group_12,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( r2_hidden(D,k1_group_12(A,B,C)) <=> ? [E] : ( v1_relat_1(E) & v1_funct_1(E) & ? [F] : ( 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] : ( m1_subset_1(G,A) => ( G != C => k1_funct_1(E,G) = k1_group_1(k1_group_7(A,B,G)) ) ) ) ) ) ) ) ) )).
fof(t2_group_14,axiom,( ! [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) ) => ! [B] : ( ( ~ 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] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k4_prvect_3(A,B)),u1_struct_0(k20_prvect_1(k10_finseq_1(A,B)))) & v13_vectsp_1(C,k4_prvect_3(A,B),k20_prvect_1(k10_finseq_1(A,B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_prvect_3(A,B)),u1_struct_0(k20_prvect_1(k10_finseq_1(A,B)))))) & v3_funct_2(C,u1_struct_0(k4_prvect_3(A,B)),u1_struct_0(k20_prvect_1(k10_finseq_1(A,B)))) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => k1_binop_1(C,D,E) = k10_finseq_1(D,E) ) ) ) ) ) )).
fof(t2_group_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( r2_hidden(A,k1_group_2(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k2_group_1(B,D) & r2_hidden(D,C) ) ) ) ) )).
fof(t2_group_3,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t2_group_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_group_2(D,B) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ( C = E => k5_group_1(B,A,C) = k5_group_1(D,A,E) ) ) ) ) ) ) )).
fof(t2_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t2_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_group_6(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t2_group_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( C = E & D = F ) => k6_algstr_0(B,C,D) = k6_algstr_0(A,E,F) ) ) ) ) ) ) ) )).
fof(t2_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => m1_subset_1(D,u1_struct_0(B)) ) ) ) )).
fof(t2_groupp_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( r1_int_1(B,k1_newton(A,C)) & ! [D] : ( v7_ordinal1(D) => ~ ( B = k1_newton(A,D) & r1_xxreal_0(D,C) ) ) ) ) ) ) )).
fof(t2_grsolv_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ! [C] : ( ( v15_algstr_0(C) & v1_group_3(C,B) & m1_group_6(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t2_hahnban,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ( r1_rlsub_2(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t2_hahnban1,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => k2_xcmplx_0(k9_complex1(A),k3_xcmplx_0(k5_numbers,k7_complex1)) = k3_xcmplx_0(k7_xcmplx_0(k8_complex1(A),k2_xcmplx_0(k9_complex1(A),k3_xcmplx_0(k5_numbers,k7_complex1))),A) ) )).
fof(t2_hallmar1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v2_relat_1(B) & m2_finseq_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r2_hidden(C,k4_finseq_1(B)) & k1_funct_1(B,C) = k1_xboole_0 ) ) ) ) )).
fof(t2_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k1_funct_1(k4_weierstr(A,B),B) = k5_numbers ) ) )).
fof(t2_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( r1_tarski(A,B) <=> k1_helly(A,B) = A ) ) ) )).
fof(t2_henmodel,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) ) => ( r2_hidden(k3_tarski(A),A) & ! [B] : ~ ( r2_hidden(B,A) & ~ r2_hidden(B,k3_tarski(A)) & B != k3_tarski(A) ) ) ) )).
fof(t2_hermitan,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( A != k5_complex1 => ( k9_complex1(k2_xcmplx_0(k7_xcmplx_0(k3_complex1(A),k9_complex1(A)),k3_xcmplx_0(k7_xcmplx_0(k1_real_1(k4_complex1(A)),k9_complex1(A)),k7_complex1))) = 1 & k3_complex1(k3_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(k3_complex1(A),k9_complex1(A)),k3_xcmplx_0(k7_xcmplx_0(k1_real_1(k4_complex1(A)),k9_complex1(A)),k7_complex1)),A)) = k9_complex1(A) & k4_complex1(k3_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(k3_complex1(A),k9_complex1(A)),k3_xcmplx_0(k7_xcmplx_0(k1_real_1(k4_complex1(A)),k9_complex1(A)),k7_complex1)),A)) = k5_numbers ) ) ) )).
fof(t2_hessenbe,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t2_heyting1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(k7_normform(A))) => ( B = k1_xboole_0 => k9_normform(A,B) = k1_xboole_0 ) ) )).
fof(t2_heyting2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k4_partfun1(A,B)) ) => r2_hidden(k1_tarski(C),k1_substlat(A,B)) ) )).
fof(t2_heyting3,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) ) => ~ ! [B] : ( ( ~ v1_abian(B) & m1_subset_1(B,k4_ordinal1) ) => r2_hidden(B,A) ) ) )).
fof(t2_hfdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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)) ) ) )).
fof(t2_hilbasis,axiom,( ! [A] : ( ( 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) ) => k21_pre_poly(k1_xboole_0,A) = k9_finseq_1(k10_finseq_1(k1_xboole_0,k1_xboole_0)) ) )).
fof(t2_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => r2_hidden(k3_hilbert1(B,k3_hilbert1(C,k4_hilbert1(B,C))),k5_hilbert1(A)) ) ) ) )).
fof(t2_hilbert2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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 ) ) ) )).
fof(t2_hilbert3,axiom,( ! [A] : ( v1_int_1(A) => ( ~ v1_abian(A) <=> v1_abian(k6_xcmplx_0(A,1)) ) ) )).
fof(t2_holder_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & ? [C] : ( v1_xreal_0(C) & r1_xxreal_0(k5_numbers,C) & k2_power(k2_power(C,A),B) != k2_power(C,k3_xcmplx_0(A,B)) ) ) ) ) )).
fof(t2_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( B != C & B != D & r1_aff_1(A,B,C,D) & ! [E] : ( ( 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) ) ) )).
fof(t2_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( A != k5_numbers & k4_nat_d(B,A) = k4_nat_d(C,A) & r1_xxreal_0(B,C) & ! [D] : ( v7_ordinal1(D) => k6_xcmplx_0(C,B) != k3_xcmplx_0(A,D) ) ) ) ) ) )).
fof(t2_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_algstr_0(A) & v4_rlvect_1(A) & v2_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t2_incproj,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t2_incsp_1,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t2_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ 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] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t2_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ( r1_pzfmisc1(u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t2_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( v1_int_1(A) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( A != B & A != k4_xcmplx_0(B) ) ) ) ) )).
fof(t2_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( r1_int_1(A,B) => r1_int_1(A,k3_xcmplx_0(B,C)) ) ) ) ) )).
fof(t2_int_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_int_3)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_int_3)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_int_3)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_int_3)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k1_int_3)) => ! [F] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t2_int_4,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( v1_xreal_0(B) => k1_card_1(A) = k1_card_1(k1_measure6(A,B)) ) ) )).
fof(t2_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( r1_int_1(A,B) & r1_int_1(A,k6_xcmplx_0(B,C)) ) => r1_int_1(A,C) ) ) ) ) )).
fof(t2_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_valued_0(B) ) => k3_finseq_1(k45_valued_1(A,B)) = k4_nat_1(k3_finseq_1(A),k3_finseq_1(B)) ) ) )).
fof(t2_int_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v3_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v3_valued_0(C) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t2_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( r1_xxreal_0(1,A) & k2_int_8(A) = k1_xboole_0 ) ) )).
fof(t2_integr10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,A) & ~ r1_xxreal_0(B,E) & ~ r1_xxreal_0(C,k3_xcmplx_0(k6_xcmplx_0(E,A),D)) ) ) ) ) ) ) ) )).
fof(t2_integr11,axiom,( r2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,2),k5_numbers),k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(2,k5_numbers),k16_sin_cos),k7_xcmplx_0(1,4))),k1_numbers) & ! [A] : ( v1_xreal_0(A) => k1_funct_1(k2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,2),k5_numbers),k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(2,k5_numbers),k16_sin_cos),k7_xcmplx_0(1,4))),k1_numbers),A) = k1_square_1(k1_funct_1(k18_sin_cos,A)) ) )).
fof(t2_integr12,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( 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,D,E)),C)) & r2_relset_1(k1_numbers,k1_numbers,C,k2_sin_cos9) & r1_tarski(F,k2_rcomp_1(k4_xcmplx_0(1),1)) & r2_relset_1(k1_numbers,k1_numbers,E,k1_taylor_1(2)) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,F) => ( k1_funct_1(D,G) = 1 & ~ r1_xxreal_0(k1_funct_1(C,G),k5_numbers) ) ) ) & F = k1_relset_1(k1_numbers,B) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k3_taylor_1)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k3_taylor_1)),k3_seq_4(A))) ) ) ) ) ) ) ) )).
fof(t2_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k18_sin_cos)))) & r1_tarski(C,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_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) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k3_taylor_1),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k3_taylor_1),k3_seq_4(A))) ) ) ) ) )).
fof(t2_integr14,axiom,( ! [A] : ( ( 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,k22_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,k22_sin_cos,k2_fdiff_9)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k2_fdiff_9)),A),B) = k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_funct_1(k18_sin_cos,k1_funct_1(k22_sin_cos,B))),k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k22_sin_cos,B)))) ) ) ) ) ) )).
fof(t2_integr15,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => ! [C] : ( m1_integra1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t2_integr16,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k2_numbers))) ) => ! [B] : ( 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)) ) ) )).
fof(t2_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & r2_relset_1(k4_ordinal1,u1_struct_0(A),D,k2_vfunct_1(k4_ordinal1,A,B,C)) ) => k4_rlvect_1(A,D) = k5_algstr_0(A,k4_rlvect_1(A,B),k4_rlvect_1(A,C)) ) ) ) ) ) )).
fof(t2_integr19,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( r1_xxreal_0(B,D) & r1_xxreal_0(D,E) & r1_xxreal_0(E,C) & r1_tarski(k3_integra5(B,C),A) ) => r1_tarski(k3_integra5(D,E),A) ) ) ) ) ) )).
fof(t2_integr1c,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => k3_integr1c(k25_valued_1(k2_numbers,k2_numbers,A,C),B) = k3_xcmplx_0(C,k3_integr1c(A,B)) ) ) ) ) )).
fof(t2_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => A = k1_rcomp_1(k3_seq_4(A),k2_seq_4(A)) ) )).
fof(t2_integra3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ~ ( k3_integra1(A) != k5_numbers & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r2_hidden(C,k4_finseq_1(B)) & ~ r1_xxreal_0(k3_integra1(k2_integra1(A,B,C)),k5_numbers) ) ) ) ) ) )).
fof(t2_integra4,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t2_integra5,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( 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)) = k2_xcmplx_0(k18_rvsum_1(A),k18_rvsum_1(B)) & k18_rvsum_1(k8_rvsum_1(A,B)) = k6_xcmplx_0(k18_rvsum_1(A),k18_rvsum_1(B)) ) ) ) ) )).
fof(t2_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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))) ) ) ) ) )).
fof(t2_integra7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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] : ( r2_hidden(E,B) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k1_funct_1(C,E),k1_funct_1(D,E))),A) ) ) => ( r1_xxreal_0(k6_xcmplx_0(k3_seq_4(k1_rvsum_1(C)),k3_seq_4(k1_rvsum_1(D))),A) & r1_xxreal_0(k6_xcmplx_0(k3_seq_4(k1_rvsum_1(D)),k3_seq_4(k1_rvsum_1(C))),A) ) ) ) ) ) ) )).
fof(t2_integra8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k17_sin_cos(k2_xcmplx_0(A,k3_xcmplx_0(k1_nat_1(k2_nat_1(2,B),1),k28_sin_cos))) = k4_xcmplx_0(k17_sin_cos(A)) ) ) )).
fof(t2_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ( A != k5_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,k5_numbers),k22_sin_cos),k7_xcmplx_0(1,A)),k1_numbers) & ! [B] : ( v1_xreal_0(B) => k1_funct_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,k5_numbers),k22_sin_cos),k7_xcmplx_0(1,A)),k1_numbers),B) = k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,k5_numbers),k22_sin_cos),B) ) ) ) ) )).
fof(t2_interva1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t2_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => ! [D] : ( 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)) ) ) ) ) )).
fof(t2_irrat_1,axiom,( ? [A] : ( v1_xreal_0(A) & ? [B] : ( v1_xreal_0(B) & ~ v1_rat_1(A) & ~ v1_rat_1(B) & v1_rat_1(k2_power(A,B)) ) ) )).
fof(t2_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ( r1_nattra_1(A,B,C,D) => ! [E] : ( m1_nattra_1(E,A,B,C,D) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => r2_hidden(k2_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))) ) ) ) ) ) ) ) )).
fof(t2_isocat_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( m1_subset_1(E,A) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t2_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)))) ) ) ) )).
fof(t2_jct_misc,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k9_complex1(k6_xcmplx_0(C,D)),k9_complex1(k6_xcmplx_0(A,B)))),k2_xcmplx_0(k9_complex1(k6_xcmplx_0(C,A)),k9_complex1(k6_xcmplx_0(D,B)))) ) ) ) ) )).
fof(t2_jgraph_1,axiom,( ! [A] : u1_struct_0(k1_jgraph_1(A)) = A )).
fof(t2_jgraph_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( v1_xreal_0(D) => ( C = B => k8_metric_1(k14_euclid(A),B,D) = a_3_0_jgraph_2(A,C,D) ) ) ) ) ) )).
fof(t2_jgraph_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : k7_relat_1(k5_relat_1(A,B),C) = k7_relat_1(A,k3_xboole_0(C,B)) ) )).
fof(t2_jgraph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( v1_xreal_0(D) => ( ( v5_pre_topc(B,A,k3_topmetr) & C = a_3_1_jgraph_4(A,B,D) ) => v3_pre_topc(C,A) ) ) ) ) ) )).
fof(t2_jgraph_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( r1_xxreal_0(k12_euclid(A),1) => ( k17_euclid(A) = k5_numbers | k18_euclid(A) = k5_numbers | ( ~ r1_xxreal_0(k17_euclid(A),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k17_euclid(A)) & ~ r1_xxreal_0(k18_euclid(A),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k18_euclid(A)) ) ) ) ) )).
fof(t2_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t2_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ~ ( r1_topreal1(k15_euclid(A),C,D,B) & ! [E] : ( ( 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,k5_numbers) = C & k1_funct_1(E,1) = D ) ) ) ) ) ) ) )).
fof(t2_jgraph_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t2_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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),k7_xcmplx_0(1,2))),k18_euclid(A)) ) ) ) )).
fof(t2_jordan1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & C != D & ! [E] : ( ( 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,k5_numbers) & D = k1_funct_1(E,1) ) ) ) ) ) => v2_connsp_1(B,A) ) ) ) )).
fof(t2_jordan10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(k2_jordan9(E,D))) & r2_hidden(k4_tarski(A,B),k2_matrix_0(k1_jordan8(E,D))) & r2_hidden(k4_tarski(A,k1_nat_1(B,1)),k2_matrix_0(k1_jordan8(E,D))) & k7_partfun1(u1_struct_0(k15_euclid(2)),k2_jordan9(E,D),C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,D),A,k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),k2_jordan9(E,D),k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,D),A,B) & r1_xxreal_0(A,1) ) ) ) ) ) ) )).
fof(t2_jordan11,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ r1_xxreal_0(k4_jordan11(A),1) ) )).
fof(t2_jordan12,axiom,( ~ v1_abian(1) )).
fof(t2_jordan14,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t2_jordan16,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => r1_tarski(k5_jordan6(A,B,C,D,E),A) ) ) ) ) ) )).
fof(t2_jordan17,axiom,( ! [A] : ( ( 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)) ) )).
fof(t2_jordan18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) )).
fof(t2_jordan19,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,A) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k1_matrix_0(k1_jordan8(B,A))) ) => r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),k1_matrix_0(k1_jordan8(B,A))),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),D)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,C),k1_jordan1a(k1_jordan8(B,C)),k1_matrix_0(k1_jordan8(B,C))),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),D))) ) ) ) ) ) )).
fof(t2_jordan1a,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_abian(k3_finseq_1(A)) => k3_finseq_1(A) = k6_xcmplx_0(k3_xcmplx_0(2,k1_jordan1a(A)),2) ) ) )).
fof(t2_jordan1b,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) & v1_xboole_0(k3_finseq_6(A,B,C,D)) ) ) ) ) ) )).
fof(t2_jordan1c,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(k4_tarski(B,C),k2_matrix_0(k1_jordan8(A,D))) & r2_hidden(k4_tarski(B,k2_xcmplx_0(C,1)),k2_matrix_0(k1_jordan8(A,D))) ) => k1_topreal6(2,k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,D),1,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,D),1,2)) = k6_xcmplx_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,D),B,k2_xcmplx_0(C,1))),k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,D),B,C))) ) ) ) ) ) )).
fof(t2_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ( B != k5_numbers => k3_xcmplx_0(k7_xcmplx_0(1,B),k1_newton(B,k1_nat_1(A,1))) = k1_newton(B,A) ) ) ) )).
fof(t2_jordan1e,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r1_sprect_2(B,A) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t2_jordan1f,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_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_0(u1_struct_0(k15_euclid(2)),E,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,C)),k3_topreal1(2,D)) & r2_hidden(k4_tarski(A,B),k2_matrix_0(E)) & r2_hidden(k4_tarski(A,C),k2_matrix_0(E)) & r1_xxreal_0(B,C) & ! [F] : ( v7_ordinal1(F) => ~ ( r1_xxreal_0(B,F) & r1_xxreal_0(F,C) & k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,F)) = k2_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_0(u1_struct_0(k15_euclid(2)),E,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,C)),k3_topreal1(2,D)))) ) ) ) ) ) ) ) ) )).
fof(t2_jordan1g,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ! [D] : ( r1_goboard1(A,B,C) => r1_goboard1(A,k1_finseq_5(A,B,D),C) ) ) ) ) )).
fof(t2_jordan1h,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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) ) ) ) )).
fof(t2_jordan1i,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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_jordan9(B,A),k22_pscomp_1(k3_topreal1(2,k2_jordan9(B,A)))),1) ) ) )).
fof(t2_jordan1j,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( 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_0(A)) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),A,C,E)),k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,D))) ) ) ) ) ) ) )).
fof(t2_jordan1k,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,B) => ? [E] : ( m1_subset_1(E,A) & D = k1_funct_1(C,E) ) ) ) ) ) )).
fof(t2_jordan20,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v1_xreal_0(D) => ( ( 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) ) ) ) ) ) )).
fof(t2_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => r1_tarski(k2_kurato_2(k15_euclid(2),k2_jordan19(A),B),k2_pre_topc(k15_euclid(2),k3_goboard9(k2_jordan9(A,k5_numbers)))) ) ) )).
fof(t2_jordan23,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => r1_xxreal_0(1,k3_finseq_1(k3_jordan3(A,B))) ) ) )).
fof(t2_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => k9_complex1(k12_euclid(B)) = k12_euclid(B) ) ) )).
fof(t2_jordan3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t2_jordan4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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) ) ) ) ) ) )).
fof(t2_jordan5a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( k3_rlvect_1(k15_euclid(A),k1_rlvect_1(k15_euclid(A),B,k6_xcmplx_0(1,D)),k1_rlvect_1(k15_euclid(A),C,D)) = k3_rlvect_1(k15_euclid(A),k1_rlvect_1(k15_euclid(A),B,k6_xcmplx_0(1,E)),k1_rlvect_1(k15_euclid(A),C,E)) & D != E & B != C ) ) ) ) ) ) )).
fof(t2_jordan5b,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(k1_nat_1(A,1),B) => r1_xxreal_0(1,k7_nat_d(B,A)) ) ) ) )).
fof(t2_jordan5c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t2_jordan5d,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(3,A) => k4_nat_d(A,k7_nat_d(A,1)) = 1 ) ) )).
fof(t2_jordan6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_pre_topc(A,B)))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t2_jordan7,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(t2_jordan8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(B)) ) => ( r1_goboard1(B,C,D) => r1_goboard1(B,k2_rfinseq(B,A,C),D) ) ) ) ) ) )).
fof(t2_jordan9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( ! [D] : ( v7_ordinal1(D) => k17_finseq_1(A,D,B) = k17_finseq_1(A,D,C) ) => B = C ) ) ) ) )).
fof(t2_jordan_a,axiom,( ! [A] : ( ( v1_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(B,A) => r2_hidden(k3_seq_4(B),A) ) ) ) )).
fof(t2_knaster,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) => ( r1_abian(A,k1_abian(B,D,C)) => r1_abian(k1_funct_1(D,A),k1_abian(B,D,C)) ) ) ) )).
fof(t2_kolmog01,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( k3_xcmplx_0(A,A) = A & A != k5_numbers & A != 1 ) ) )).
fof(t2_kurato_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ~ ( ~ r1_xboole_0(A,B) & ~ r1_xboole_0(C,D) & r1_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ) )).
fof(t2_kurato_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(t2_kurato_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( v1_xreal_0(E) => ~ ( B = D & r2_hidden(C,k8_metric_1(k14_euclid(A),B,E)) & r1_xxreal_0(E,k12_euclid(k5_algstr_0(k15_euclid(A),C,D))) ) ) ) ) ) ) )).
fof(t2_l_hospit,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( ( r4_limfunc2(A,B) & k2_limfunc2(A,B) = C ) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,B) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(D,E) & ~ r1_xxreal_0(E,B) & r2_hidden(E,k1_relset_1(k1_numbers,A)) ) ) ) ) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(D) & k1_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(k4_ordinal1,k1_numbers,k1_numbers,D,A)) & k1_seq_2(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,D,A)) = C ) ) ) ) ) & ( ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,B) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(D,E) & ~ r1_xxreal_0(E,B) & r2_hidden(E,k1_relset_1(k1_numbers,A)) ) ) ) ) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(D) & k1_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(k4_ordinal1,k1_numbers,k1_numbers,D,A)) & k1_seq_2(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,D,A)) = C ) ) ) ) => ( r4_limfunc2(A,B) & k2_limfunc2(A,B) = C ) ) ) ) ) ) )).
fof(t2_lang1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ! [D] : ( m2_finseq_2(D,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t2_laplace,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(A),D,D) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(A))) ) => ( r2_hidden(B,k4_finseq_1(E)) => k3_finseq_1(k18_matrix_0(B,C,D,u1_struct_0(A),E)) = k7_nat_d(D,1) ) ) ) ) ) ) )).
fof(t2_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( r2_hidden(B,k1_group_3(A)) <=> ? [C] : ( v15_algstr_0(C) & m1_group_2(C,A) & B = C ) ) ) )).
fof(t2_latsum_1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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))) ) ) ) )).
fof(t2_lattice2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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] : ( m1_subset_1(F,A) => ( r2_hidden(F,C) => k1_funct_1(E,F) = k1_funct_1(D,F) ) ) ) ) ) ) ) )).
fof(t2_lattice3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k1_lattice3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_lattice3(A))) => ( r1_lattices(k1_lattice3(A),B,C) <=> r1_tarski(B,C) ) ) ) )).
fof(t2_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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))) ) ) ) ) )).
fof(t2_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => k2_zfmisc_1(k3_tarski(A),k3_tarski(B)) = k3_tarski(a_2_0_lattice5(A,B)) ) ) )).
fof(t2_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t2_lattice7,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t2_lattice8,axiom,( ! [A] : ( ( 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) ) )).
fof(t2_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_lattices(A,B,C) <=> k2_lattices(A,B,C) = B ) ) ) ) )).
fof(t2_lexbfs,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t2_lfuzzy_0,axiom,( ! [A] : ( ( v1_lfuzzy_0(A) & l1_orders_2(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t2_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( m1_subset_1(E,A) => ! [F] : ( 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) ) ) ) ) ) )).
fof(t2_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v9_ordinal1(A) & v2_comseq_2(A) & k1_seq_2(A) = k5_numbers & v7_valued_0(A) ) => ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k5_numbers,k1_funct_1(A,B)) ) ) ) )).
fof(t2_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( v2_comseq_2(B) & ~ r1_xxreal_0(A,k1_seq_2(B)) & ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & r1_xxreal_0(A,k1_funct_1(B,D)) ) ) ) ) ) )).
fof(t2_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ~ r1_xxreal_0(k9_complex1(k6_xcmplx_0(A,k3_funct_2(k4_ordinal1,k1_numbers,B,D))),k5_numbers) & ~ r1_xxreal_0(k7_xcmplx_0(1,k1_nat_1(D,1)),k9_complex1(k6_xcmplx_0(A,k3_funct_2(k4_ordinal1,k1_numbers,B,D)))) & r2_hidden(k3_funct_2(k4_ordinal1,k1_numbers,B,D),k9_xtuple_0(C)) ) ) => ( v2_comseq_2(B) & k1_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))) ) ) ) ) ) )).
fof(t2_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( r1_tarski(k10_xtuple_0(C),k7_subset_1(k1_numbers,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)),D)) => ( r1_tarski(k10_xtuple_0(C),k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B))) & r1_tarski(k10_xtuple_0(C),k1_relset_1(k1_numbers,A)) & r1_tarski(k10_xtuple_0(C),k7_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),D)) & r1_tarski(k10_xtuple_0(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,C,A)),k1_relset_1(k1_numbers,B)) ) ) ) ) ) )).
fof(t2_lmod_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t2_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t2_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t2_lopban_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m2_funct_2(C,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => ! [D] : ( m2_funct_2(D,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => ! [E] : ( v1_xreal_0(E) => ( D = k1_funct_1(k3_lopban_1(A,B),k4_tarski(E,C)) <=> ! [F] : ( m1_subset_1(F,A) => k3_funct_2(A,u1_struct_0(B),D,F) = k1_rlvect_1(B,k3_funct_2(A,u1_struct_0(B),C,F),E) ) ) ) ) ) ) ) )).
fof(t2_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ( r1_xxreal_0(k2_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)),k3_xcmplx_0(k3_xcmplx_0(k1_funct_1(k15_lopban_1(B,C),E),k1_funct_1(k15_lopban_1(A,B),D)),k2_normsp_0(A,F))) & r1_xxreal_0(k1_funct_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)),k3_xcmplx_0(k1_funct_1(k15_lopban_1(B,C),E),k1_funct_1(k15_lopban_1(A,B),D))) ) ) ) ) ) ) ) ) )).
fof(t2_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,k5_normsp_0(A,B),C)) ) ) ) )).
fof(t2_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ! [D] : ( v7_ordinal1(D) => k9_nat_1(u1_struct_0(A),B,D) = C ) => k6_normsp_1(A,B) = C ) ) ) ) )).
fof(t2_lopban_5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( ( v1_comseq_2(A) & r1_xxreal_0(k5_numbers,B) ) => k5_rinfsup1(k26_valued_1(k4_ordinal1,k1_numbers,A,B)) = k3_xcmplx_0(B,k5_rinfsup1(A)) ) ) ) )).
fof(t2_lopban_6,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => k1_lopban_5(A,B,C) = k5_rusub_4(A,k1_lopban_5(A,k4_struct_0(A),C),B) ) ) ) )).
fof(t2_lopban_7,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v6_rltopsp1(B) & v7_rltopsp1(B) & l1_rltopsp1(B) ) => ! [C] : ( ( 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] : ( ( 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_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & v1_t_0topsp(C,A,B) & D = k2_funct_1(C) ) => ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A)) & v13_vectsp_1(D,B,A) & v1_lopban_1(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) & v2_funct_2(D,u1_struct_0(A)) & v5_pre_topc(D,B,A) ) ) ) ) ) ) )).
fof(t2_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k1_lopclset(A)) => v4_pre_topc(B,A) ) ) ) )).
fof(t2_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k2_power(k9_nat_1(k1_numbers,k3_series_1(k1_lp_space(k1_series_1(k1_numbers,B,C),A)),D),k7_xcmplx_0(1,A)),k2_xcmplx_0(k2_power(k9_nat_1(k1_numbers,k3_series_1(k1_lp_space(B,A)),D),k7_xcmplx_0(1,A)),k2_power(k9_nat_1(k1_numbers,k3_series_1(k1_lp_space(C,A)),D),k7_xcmplx_0(1,A)))) ) ) ) ) ) )).
fof(t2_lpspacc1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),B) => ! [D] : ( ( 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] : ( ( 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))) ) => ( ( C = k4_struct_0(A) & D = k1_realset1(u1_algstr_0(A),B) & E = 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)) ) => ( v2_rlvect_1(g1_clvect_1(B,C,D,E)) & v3_rlvect_1(g1_clvect_1(B,C,D,E)) & v4_rlvect_1(g1_clvect_1(B,C,D,E)) & v2_clvect_1(g1_clvect_1(B,C,D,E)) & v3_clvect_1(g1_clvect_1(B,C,D,E)) & v4_clvect_1(g1_clvect_1(B,C,D,E)) & v5_clvect_1(g1_clvect_1(B,C,D,E)) ) ) ) ) ) ) ) )).
fof(t2_lpspace1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),B) => ! [D] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t2_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_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) ) ) ) ) ) ) ) )).
fof(t2_ltlaxio1,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k6_xboolean(k6_xboolean(A,k6_xboolean(B,C)),k6_xboolean(k4_xboolean(A,B),C)) = 1 ) ) ) )).
fof(t2_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( k3_finseq_1(B) = k5_numbers => k1_rfinseq(A,B) = B ) ) ) )).
fof(t2_ltlaxio3,axiom,( v1_funct_1(k7_funcop_1(k4_ordinal1,k1_xboole_0)) & v1_funct_2(k7_funcop_1(k4_ordinal1,k1_xboole_0),k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(k7_funcop_1(k4_ordinal1,k1_xboole_0),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) )).
fof(t2_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => m2_finseq_1(A,k4_ordinal1) ) )).
fof(t2_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t2_margrel1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v3_finseq_1(k1_tarski(A)) & v2_card_3(k1_tarski(A)) ) ) )).
fof(t2_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) )).
fof(t2_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( r2_hidden(k4_tarski(A,B),k2_matrix_0(C)) => k3_matrix_0(k1_numbers,k4_matrixr1(C),A,B) = k1_real_1(k3_matrix_0(k1_numbers,C,A,B)) ) ) ) ) )).
fof(t2_matrix11,axiom,( k2_sgraph1(k2_finseq_1(k5_numbers)) = k1_xboole_0 & k2_sgraph1(k2_finseq_1(1)) = k1_xboole_0 )).
fof(t2_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [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] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(E),C,D) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(E))) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(E),C,D) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(E))) ) => ! [H] : ( v7_ordinal1(H) => ( ( r2_hidden(B,k4_finseq_1(F)) & r2_hidden(A,k4_finseq_1(F)) & r2_hidden(H,k4_finseq_1(F)) & G = k1_matrix12(C,D,E,F,B,A) ) => ( ( H = B => k7_matrix_0(u1_struct_0(E),G,H) = k7_matrix_0(u1_struct_0(E),F,A) ) & ( H = A => k7_matrix_0(u1_struct_0(E),G,H) = k7_matrix_0(u1_struct_0(E),F,B) ) & ~ ( H != B & H != A & k7_matrix_0(u1_struct_0(E),G,H) != k7_matrix_0(u1_struct_0(E),F,H) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t2_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & v2_matrix_2(C,A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) <=> ( v1_matrix_0(k4_matrix_0(u1_struct_0(B),C)) & v2_matrix_0(k4_matrix_0(u1_struct_0(B),C),u1_struct_0(B),A,A) & v1_matrix_2(k4_matrix_0(u1_struct_0(B),C),A,B) & m2_finseq_1(k4_matrix_0(u1_struct_0(B),C),k3_finseq_2(u1_struct_0(B))) ) ) ) ) ) )).
fof(t2_matrix14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t2_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_matrix_0(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)) ) ) ) ) ) )).
fof(t2_matrix16,axiom,( ! [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] : ( 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) ) ) )).
fof(t2_matrix17,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => r1_matrix17(u1_struct_0(B),k11_matrix_0(u1_struct_0(B),A,A,C),k5_finseq_2(u1_struct_0(B),A,C)) ) ) ) )).
fof(t2_matrix_0,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => v1_matrix_0(k2_finseq_2(C,k2_finseq_2(B,A))) ) ) )).
fof(t2_matrix_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v2_struct_0(C) & l6_algstr_0(C) ) => ( m1_subset_1(A,k1_matrix_1(C,B)) <=> ( v1_matrix_0(A) & v2_matrix_0(A,u1_struct_0(C),B,B) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(C))) ) ) ) ) )).
fof(t2_matrix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( ~ v1_xboole_0(B) & v3_matrix_2(B) & k2_matrix_2(B) = A ) ) )).
fof(t2_matrix_3,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) ) => k3_matrix_3(A,B,C) = k3_matrix_3(A,C,B) ) ) ) ) )).
fof(t2_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(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_0(B)) ) ) )).
fof(t2_matrix_5,axiom,( k4_struct_0(k1_complfld) = k5_numbers )).
fof(t2_matrix_6,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ( ~ r1_xxreal_0(k1_matrix_0(B),k5_numbers) => k4_matrix_3(A,B,k1_matrix_3(A,k1_matrix_0(B),k1_matrix_0(B))) = k1_matrix_3(A,k3_finseq_1(B),k1_matrix_0(B)) ) ) ) )).
fof(t2_matrix_7,axiom,( ! [A] : ( ( 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)))) ) ) ) )).
fof(t2_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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(k2_matrix_1(B,A),A,B) & v2_matrix_8(k2_matrix_1(B,A),A,B) ) ) ) )).
fof(t2_matrix_9,axiom,( k1_funct_1(k3_finseq_5(k1_finseq_2(2)),1) = 2 & k1_funct_1(k3_finseq_5(k1_finseq_2(2)),2) = 1 )).
fof(t2_matrixc1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k2_numbers)) ) => ( k3_finseq_1(k7_matrix_5(A,B)) = k3_finseq_1(B) & k1_matrix_0(k7_matrix_5(A,B)) = k1_matrix_0(B) ) ) ) )).
fof(t2_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t2_matrixj2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( 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) ) ) ) )).
fof(t2_matrixr1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_vectsp_1)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_vectsp_1)) => ( ( A = C & B = D ) => k3_xcmplx_0(A,B) = k8_group_1(k2_vectsp_1,C,D) ) ) ) ) ) )).
fof(t2_matrixr2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(A)) ) => ! [E] : ( 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_0(D)) & k3_finseq_1(E) = k1_matrix_0(D) ) => k3_matrix_0(A,D,B,C) = k1_funct_1(E,C) ) ) ) ) ) ) )).
fof(t2_matrlin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,C,k1_nat_1(B,1),A) & m2_finseq_1(D,k3_finseq_2(C)) ) => ! [E] : ( ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(C)) ) => ( ( ~ r1_xxreal_0(B,k5_numbers) => k1_matrix_0(D) = k1_matrix_0(k1_matrlin(C,k1_nat_1(B,1),D)) ) & ( E = k9_finseq_1(k1_funct_1(D,k1_nat_1(B,1))) => k1_matrix_0(D) = k1_matrix_0(E) ) ) ) ) ) ) ) )).
fof(t2_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( k2_vectsp_5(A,B,C,D) = k1_vectsp_4(A,B) => ! [E] : ( ( v1_vectsp_7(E,A,C) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) ) => ! [F] : ( ( 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)))) ) ) ) ) ) ) ) ) )).
fof(t2_matroid0,axiom,( ! [A] : ( ( v1_matroid0(A) & l1_pre_topc(A) ) => ( ~ v3_pencil_1(A) <=> r2_hidden(k1_xboole_0,k1_matroid0(A)) ) ) )).
fof(t2_matrprob,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ? [F] : ( m2_finseq_1(F,A) & k3_finseq_1(F) = C & ! [G] : ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(t2_matrtop1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t2_matrtop2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_vectsp_6(B,k2_vectsp_1,k6_prvect_1(k2_vectsp_1,A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t2_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & v1_matrix_1(C,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => k4_matrix_0(u1_struct_0(B),C) = C ) ) ) )).
fof(t2_mazurulm,axiom,( k5_measure6(k2_urysohn1) = k1_xxreal_1(k5_numbers,1) )).
fof(t2_mboolean,axiom,( ! [A] : r6_pboole(A,k1_mboolean(A,k1_pboole(A)),k7_funcop_1(A,k1_tarski(k1_xboole_0))) )).
fof(t2_mcart_1,axiom,( ! [A] : ( v1_xtuple_0(A) => k4_tarski(k1_xtuple_0(A),k2_xtuple_0(A)) = A ) )).
fof(t2_measure1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => m1_subset_1(k2_tarski(B,C),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) )).
fof(t2_measure2,axiom,( ! [A] : ! [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))) ) => ! [C] : ( m1_measure2(C,A,B) => ( r2_hidden(k6_setfam_1(A,C),B) & r2_hidden(k5_setfam_1(A,C),B) ) ) ) )).
fof(t2_measure3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => k12_supinf_2(k18_supinf_2(A),C) = k12_supinf_2(k18_supinf_2(B),C) ) => k19_supinf_2(A) = k19_supinf_2(B) ) ) ) )).
fof(t2_measure5,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ! [B] : ( m1_subset_1(B,k6_numbers) => ~ ( ~ r1_xxreal_0(B,A) & ! [C] : ( m1_subset_1(C,k6_numbers) => ~ ( ~ r1_xxreal_0(C,A) & ~ r1_xxreal_0(B,C) & r2_hidden(C,k1_numbers) ) ) ) ) ) )).
fof(t2_measure6,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v6_supinf_2(A) => r1_xxreal_0(k1_supinf_2,k19_supinf_2(A)) ) ) )).
fof(t2_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v6_supinf_2(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => r1_xxreal_0(k12_supinf_2(A,B),k12_supinf_2(k18_supinf_2(A),B)) ) ) ) )).
fof(t2_measure8,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v6_supinf_2(A) => ( v1_mesfunc9(A) & k19_supinf_2(A) = k3_mesfunc9(A) ) ) ) )).
fof(t2_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => ( r2_hidden(k2_xxreal_3(B),A) <=> r2_hidden(B,k4_member_1(A)) ) ) ) )).
fof(t2_membered,axiom,( ! [A] : ( v2_membered(A) => r1_tarski(A,k6_numbers) ) )).
fof(t2_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_partfun1(C,u1_struct_0(B)) ) => r2_hidden(k4_struct_0(B),k9_xtuple_0(C)) ) ) ) )).
fof(t2_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v1_xreal_0(B) => ( k17_euclid(k1_rlvect_1(k15_euclid(2),A,B)) = k3_xcmplx_0(B,k17_euclid(A)) & k18_euclid(k1_rlvect_1(k15_euclid(2),A,B)) = k3_xcmplx_0(B,k18_euclid(A)) ) ) ) )).
fof(t2_mesfun10,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [C] : ( v7_ordinal1(C) => ( ! [D] : ( 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)) ) ) ) ) ) )).
fof(t2_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( 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))) ) ) ) ) )).
fof(t2_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( 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(k4_ordinal1,k10_seqfunc(A,B,C)))) ) ) ) ) )).
fof(t2_mesfun9c,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,B)))) ) => ( v1_mesfunc8(D,A,B) => v1_mesfunc8(k1_mesfun9c(A,B,D,C),A,B) ) ) )).
fof(t2_mesfunc1,axiom,( k4_numbers = k2_xboole_0(k1_mesfunc1,k4_ordinal1) )).
fof(t2_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_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)) ) ) ) ) ) )).
fof(t2_mesfunc3,axiom,( ! [A] : ( m2_finseq_1(A,k6_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( A = B => k4_extreal1(A) = k18_rvsum_1(B) ) ) ) )).
fof(t2_mesfunc4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [F] : ( ( v1_prob_2(F) & m2_finseq_1(F,B) ) => ! [G] : ( m2_finseq_1(G,k6_numbers) => ! [H] : ( m2_finseq_1(H,k6_numbers) => ( ( r1_mesfunc2(A,B,E) & ! [I] : ( r2_hidden(I,k9_xtuple_0(E)) => r1_xxreal_0(k1_supinf_2,k1_funct_1(E,I)) ) & r1_mesfunc3(A,B,E,F,G) & k4_finseq_1(H) = k4_finseq_1(F) & ! [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(k4_ordinal1,B,B,k6_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) ) ) ) ) ) ) ) ) ) ) )).
fof(t2_mesfunc5,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ! [B] : ( m1_subset_1(B,k6_numbers) => r1_xxreal_0(k4_supinf_2(B,A),k3_extreal1(k4_supinf_2(A,B))) ) ) )).
fof(t2_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ( ( r2_hidden(k1_relset_1(A,D),B) & ! [F] : ( r2_hidden(F,k1_relset_1(A,D)) => k1_funct_1(D,F) = E ) ) => r1_mesfunc2(A,B,D) ) ) ) ) ) ) )).
fof(t2_mesfunc7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( v1_xreal_0(D) => k2_partfun1(A,k6_numbers,k6_mesfunc1(A,C,D),B) = k6_mesfunc1(A,k2_partfun1(A,k6_numbers,C,B),D) ) ) ) )).
fof(t2_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( k9_nat_1(k9_setfam_1(A),k4_setlim_1(A,B),C) = k5_setfam_1(A,k2_relset_1(k9_setfam_1(A),k8_nat_1(k9_setfam_1(A),B,C))) & k9_nat_1(k9_setfam_1(A),k2_setlim_1(A,B),C) = k6_setfam_1(A,k2_relset_1(k9_setfam_1(A),k8_nat_1(k9_setfam_1(A),B,C))) ) ) ) ) )).
fof(t2_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_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)) ) ) ) ) )).
fof(t2_metric_1,axiom,( ! [A] : ( l1_metric_1(A) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_metric_1(A,B,C) = k5_numbers => B = C ) ) ) <=> v7_metric_1(A) ) ) )).
fof(t2_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k1_metric_2(A,B)) <=> r3_metric_2(A,C,B) ) ) ) ) )).
fof(t2_metric_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))) => k2_binop_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,k1_metric_3(A,B),C,D) = k2_binop_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,k1_metric_3(A,B),D,C) ) ) ) ) )).
fof(t2_metric_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => r1_xxreal_0(k5_numbers,k2_binop_1(A,A,k1_numbers,B,C,D)) ) ) ) ) ) )).
fof(t2_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( 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] : ( ( 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))) ) ) ) ) ) ) ) )).
fof(t2_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,k15_euclid(A)) ) => ! [C] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(A))) => ! [G] : ( 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)) ) ) ) ) ) ) )).
fof(t2_mfold_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( r1_tarski(C,B) => k8_relat_1(k6_relat_1(B,A),C) = k8_relat_1(A,C) ) ) )).
fof(t2_midsp_1,axiom,( 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(k1_tarski(k5_ordinal1),k1_tarski(k5_ordinal1)),k1_tarski(k5_ordinal1),u1_midsp_1(k2_midsp_1),k9_funct_5) )).
fof(t2_midsp_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t2_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( r2_hidden(B,k2_finseq_1(A)) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( A = k1_nat_1(k1_nat_1(C,1),D) & B = k1_nat_1(C,1) ) ) ) ) ) ) )).
fof(t2_mmlquer2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( r1_mmlquery(B,C,D) => ( r2_hidden(B,A) & r2_hidden(C,A) ) ) ) )).
fof(t2_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [D] : ( m1_subset_1(D,A) => ( r1_mmlquery(B,D,C) <=> r2_hidden(D,k1_mmlquery(A,C,B)) ) ) ) ) )).
fof(t2_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & l1_vectsp_1(D,A) ) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t2_mod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t2_mod_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k2_mod_4(A))) <=> m1_subset_1(B,u1_struct_0(A)) ) ) ) )).
fof(t2_modal_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ~ ( A != B & r2_xboole_0(k14_trees_3(A),k8_finseq_1(k4_ordinal1,k14_trees_3(B),C)) ) ) ) ) )).
fof(t2_modcat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(E,A) => ( v2_mod_2(E,B) & m1_mod_2(E,B,C,D) ) ) ) ) ) ) ) )).
fof(t2_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ~ ( ~ v2_modelc_1(A) & ~ v3_modelc_1(A) & ~ v4_modelc_1(A) & ~ v5_modelc_1(A) & ~ v6_modelc_1(A) & ~ v7_modelc_1(A) ) ) )).
fof(t2_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ~ ( ~ 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) ) ) )).
fof(t2_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_3(C,B) & l1_modelc_3(C,B) ) => ! [D] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t2_moebius1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(1,A) => ( r2_hidden(C,k2_finseq_1(B)) <=> r2_hidden(k3_xcmplx_0(A,C),k2_finseq_1(k3_xcmplx_0(A,B))) ) ) ) ) ) )).
fof(t2_monoid_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t2_monoid_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,E,A) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(E,A))) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,E,B) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(E,B))) ) => ! [H] : ( 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)) ) ) ) ) ) ) ) )).
fof(t2_morph_01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(t2_msafree,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( 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 ) ) ) ) )).
fof(t2_msafree1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [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] : ! [D] : ( 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))))) ) ) ) ) )).
fof(t2_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r2_hidden(B,k2_msafree2(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => k2_msualg_1(A,C) != B ) ) ) ) )).
fof(t2_msafree3,axiom,( ! [A] : ! [B] : ( ( ~ v11_struct_0(B) & v1_instalg1(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(B)) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(t2_msafree4,axiom,( ! [A] : k3_trees_9(k1_trees_4(A)) = k1_tarski(k1_trees_4(A)) )).
fof(t2_msalimit,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_msalimit(C,A,B) => ! [D] : ( m2_msalimit(D,A,B,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( r1_orders_2(A,F,E) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t2_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)))) ) ) ) ) )).
fof(t2_msinst_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( 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(k4_ordinal1,A),A))) ) ) ) ) ) )).
fof(t2_msscyc_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t2_msscyc_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(1,D) => ( ~ ( ? [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,k11_msafree(A,B)),C)) & k8_msafree2(A,B,C,E) = D ) & ! [E] : ( ( 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),k1_nat_1(k3_finseq_1(E),1)) = C ) ) ) & ~ ( ? [E] : ( 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),k1_nat_1(k3_finseq_1(E),1)) = C ) & ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,k11_msafree(A,B)),C)) => k8_msafree2(A,B,C,E) != D ) ) ) ) ) ) ) ) )).
fof(t2_mssubfam,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ( r2_hidden(B,C) => r1_tarski(k8_setfam_1(A,C),B) ) ) )).
fof(t2_mssublat,axiom,( ! [A] : k3_funct_2(k4_ordinal1,k3_finseq_2(k1_tarski(A)),k7_finseq_2(A),1) = k9_finseq_1(A) )).
fof(t2_msualg_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t2_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( m3_pboole(D,u1_struct_0(A),u3_msualg_1(A,C)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t2_msualg_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( m2_pboole(E,A,B,C) => ! [F] : ( m2_pboole(F,A,C,D) => ( k9_xtuple_0(k8_pboole(E,F)) = A & ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(t2_msualg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( 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] : ~ ( 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] : ( m1_subset_1(F,k3_msualg_1(A,B,C)) => E != k6_msualg_4(A,B,C,D,F) ) ) ) ) ) ) )).
fof(t2_msualg_5,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t2_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( ( 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(t2_msualg_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t2_msualg_8,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k2_msualg_5(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_msualg_5(A))) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t2_msualg_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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) ) ) )).
fof(t2_msuhom_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => r1_tarski(k3_finseq_2(B),k3_finseq_2(A)) ) )).
fof(t2_multop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,B) => ! [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) ) ) ) ) ) ) ) )).
fof(t2_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(A,k6_subset_1(B,C)) <=> ( r1_xxreal_0(C,A) & ~ r1_xxreal_0(B,A) ) ) ) ) ) )).
fof(t2_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t2_nagata_2,axiom,( v3_funct_2(k1_nagata_2,k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1) )).
fof(t2_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => r1_xxreal_0(k5_numbers,A) ) )).
fof(t2_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => k3_nat_d(k5_numbers,A) = k5_numbers ) )).
fof(t2_nat_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,1) & r1_xxreal_0(k3_xcmplx_0(A,A),B) & r1_xxreal_0(B,A) ) ) ) )).
fof(t2_nat_5,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ~ ( v1_abian(A) & ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ v1_abian(C) & ~ r1_xxreal_0(B,k5_numbers) & A = k3_xcmplx_0(k1_newton(2,B),C) ) ) ) ) ) )).
fof(t2_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(A,k5_numbers) => B = k1_nat_1(k2_nat_1(A,k3_nat_d(B,A)),k4_nat_d(B,A)) ) ) ) )).
fof(t2_nat_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_nat_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_nat_lat)) => k2_lattices(k3_nat_lat,A,B) = k6_nat_d(A,B) ) ) )).
fof(t2_nattra_1,axiom,( ! [A] : ! [B] : u1_cat_1(k3_cat_1(B,A)) = k1_tarski(k4_tarski(k4_tarski(A,A),A)) )).
fof(t2_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_numbers) => m1_ncfcont1(a_3_0_ncfcont1(A,B,C),A,B) ) ) ) ) )).
fof(t2_ncfcont2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t2_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_nfcont_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & ! [D] : ( m1_nfcont_1(D,A,C) => ~ r1_tarski(D,B) ) ) ) ) ) ) )).
fof(t2_ndiff_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_ndiff_1(A,B,C,D) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( ( v9_ordinal1(F) & v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k1_numbers) & v1_fdiff_1(F,k5_numbers) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [G] : ( ( v1_funct_1(G) & v3_funct_1(G) & v1_funct_2(G,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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,k2_ndiff_1(A,E,F),G)),k1_relset_1(u1_struct_0(A),C)) ) => ( v3_normsp_1(k1_ndiff_1(B,k3_normsp_1(B,k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),k2_normsp_1(A,k2_ndiff_1(A,E,F),G),C),k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),G,C)),k37_valued_1(k4_ordinal1,k1_numbers,F)),B) & k17_lopban_1(A,B,k3_ndiff_1(A,B,C,D),E) = k6_normsp_1(B,k1_ndiff_1(B,k3_normsp_1(B,k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),k2_normsp_1(A,k2_ndiff_1(A,E,F),G),C),k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),G,C)),k37_valued_1(k4_ordinal1,k1_numbers,F))) ) ) ) ) ) ) ) ) ) ) )).
fof(t2_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,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)) ) ) ) ) )).
fof(t2_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [D] : ( v1_xreal_0(D) => ( C = B => ( r1_ndiff_4(A,B,D) <=> r1_ndiff_3(k4_real_ns1(A),C,D) ) ) ) ) ) ) )).
fof(t2_ndiff_5,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( 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,k5_numbers) = k4_struct_0(A) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ( ~ r1_xxreal_0(D,k9_complex1(E)) => r1_xxreal_0(k2_normsp_0(A,k7_partfun1(u1_struct_0(A),B,E)),k3_xcmplx_0(C,k9_complex1(E))) ) ) ) ) ) ) ) ) ) )).
fof(t2_neckla_2,axiom,( u1_orders_2(k4_necklace(4)) = k4_enumset1(k4_tarski(k5_numbers,1),k4_tarski(1,k5_numbers),k4_tarski(1,2),k4_tarski(2,1),k4_tarski(2,3),k4_tarski(3,2)) )).
fof(t2_neckla_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : 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)) )).
fof(t2_necklace,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : 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)) )).
fof(t2_net_1,axiom,( ! [A] : ! [B] : ( 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)) ) ) ) )).
fof(t2_newton,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_1(B,k1_numbers) => k3_finseq_1(k10_rvsum_1(B,A)) = k3_finseq_1(B) ) ) )).
fof(t2_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k5_vfunct_1(k4_ordinal1,A,B),k5_normsp_1(A,B,k4_xcmplx_0(1))) ) ) )).
fof(t2_nfcont_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)))) ) => ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t2_nfcont_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,u1_struct_0(A),k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,D,k6_vfunct_1(k1_numbers,A,B,C)),k2_normsp_1(A,k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,D,B),k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,D,C))) & r2_funct_2(k4_ordinal1,u1_struct_0(A),k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,D,k2_vfunct_1(k1_numbers,A,B,C)),k3_normsp_1(A,k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,D,B),k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,D,C))) ) ) ) ) ) ) )).
fof(t2_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t2_normform,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_finsub_1(B) ) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(A,B)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t2_normsp_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_normsp_0(A,k4_algstr_0(A,B)) = k2_normsp_0(A,B) ) ) )).
fof(t2_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_normsp_2(A))) => ! [C] : ( v1_xreal_0(C) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & D = B & k8_metric_1(k2_normsp_2(A),B,C) = a_3_0_normsp_2(A,C,D) ) ) ) ) )).
fof(t2_ntalgo_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => ! [B] : ( m1_subset_1(B,k4_numbers) => k1_ntalgo_1(A,B) = k3_int_2(A,B) ) ) )).
fof(t2_numbers,axiom,( r2_xboole_0(k3_numbers,k1_numbers) )).
fof(t2_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t2_openlatt,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t2_oposet_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v3_orders_2(A) => v2_oposet_1(A) ) ) )).
fof(t2_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k4_oppcat_1(A,k3_oppcat_1(A,B)) = B ) ) )).
fof(t2_ordeq_01,axiom,( ! [A] : ! [B] : ! [C] : ( r1_abian(A,k1_tarski(k4_tarski(B,C))) => A = B ) )).
fof(t2_orders_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r1_tarski(B,A) <=> r2_hidden(B,k1_orders_1(A)) ) ) )).
fof(t2_orders_2,axiom,( ! [A] : ( ( v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( r1_orders_2(A,B,C) & r1_orders_2(A,C,B) ) => B = C ) ) ) ) )).
fof(t2_orders_3,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ( 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)) ) ) )).
fof(t2_orders_4,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ! [C] : ( r1_orders_4(A,B,C) => r1_xboole_0(B,C) ) ) )).
fof(t2_ordinal1,axiom,( ! [A] : r2_hidden(A,k1_ordinal1(A)) )).
fof(t2_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => k3_tarski(k1_ordinal1(A)) = A ) )).
fof(t2_ordinal3,axiom,( ! [A] : ! [B] : ( r1_tarski(k1_ordinal1(A),B) => r1_tarski(A,B) ) )).
fof(t2_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t2_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) ) => ~ ( k9_xtuple_0(C) = k10_ordinal2(A,B) & ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v5_ordinal1(D) ) => ! [E] : ( ( 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 ) ) ) ) ) ) ) )).
fof(t2_ordinal6,axiom,( ! [A] : ( v1_ordinal6(A) <=> k2_ordinal1(A) = A ) )).
fof(t2_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r1_orders_2(B,C,D) => r1_orders_2(B,D,C) ) ) ) ) ) )).
fof(t2_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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] : ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t2_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t2_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t2_osalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( m2_pboole(D,u1_struct_0(A),B,C) => ( v1_osalg_3(D,A) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( r3_orders_2(A,E,F) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t2_osalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_orders_2(A,B,C) => r2_hidden(k4_tarski(B,C),k1_osalg_4(A)) ) ) ) ) )).
fof(t2_papdesaf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_diraf(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_diraf(A))) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t2_pardepap,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v4_aff_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t2_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(t2_parsp_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_parsp_1(A))) => ( r1_parsp_1(k9_parsp_1(A),B,C,D,E) <=> ? [F] : ( m1_subset_1(F,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) & ? [G] : ( m1_subset_1(G,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) & ? [H] : ( m1_subset_1(H,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) & ? [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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t2_partfun1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( k2_xboole_0(A,B) = C => ! [D] : ( r2_hidden(D,k3_xboole_0(k9_xtuple_0(A),k9_xtuple_0(B))) => k1_funct_1(A,D) = k1_funct_1(B,D) ) ) ) ) ) )).
fof(t2_partfun2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ( r2_hidden(A,k2_relset_1(C,D)) <=> ? [E] : ( m1_subset_1(E,B) & r2_hidden(E,k1_relset_1(B,D)) & A = k7_partfun1(C,D,E) ) ) ) ) ) )).
fof(t2_partfun3,axiom,( ! [A] : ( ( 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) ) )).
fof(t2_partit1,axiom,( ! [A] : k3_tarski(k6_subset_1(A,k1_tarski(k1_xboole_0))) = k3_tarski(A) )).
fof(t2_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(t2_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_analoaf(A,E,C,E,D) & E != D & C != E & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_analoaf(A,E,B,E,F) & r2_diraf(A,B,C,D,F) & D != F ) ) ) ) ) ) ) ) )).
fof(t2_pboole,axiom,( ! [A] : ( ( 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) ) ) ) )).
fof(t2_pcomps_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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 ) ) ) ) )).
fof(t2_pcomps_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v9_pre_topc(A) => ! [B] : ( 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] : ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(D,C) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(E,B) & r1_tarski(k2_pre_topc(A,D),E) ) ) ) ) ) ) ) ) ) ) )).
fof(t2_pcs_0,axiom,( ! [A] : ( l1_pcs_0(A) => ( v2_struct_0(A) => g1_pcs_0(u1_struct_0(A),u1_pcs_0(A)) = k5_pcs_0 ) ) )).
fof(t2_pdiff_1,axiom,( 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] : ( 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 ) )).
fof(t2_pdiff_2,axiom,( 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] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k1_pdiff_1(2,2),k10_finseq_1(A,B)) = B ) ) )).
fof(t2_pdiff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(2)) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t2_pdiff_4,axiom,( 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] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k1_funct_1(k1_pdiff_1(2,3),k11_finseq_1(A,B,C)) = B ) ) ) )).
fof(t2_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t2_pdiff_6,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(B),k1_euclid(A)))) ) => ! [D] : ( ( 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] : ( m2_finseq_2(E,k1_numbers,k1_euclid(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t2_pdiff_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( 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)) ) ) ) )).
fof(t2_pdiff_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(1))) => ( B = k9_finseq_1(A) => k2_normsp_0(k4_real_ns1(1),B) = k9_complex1(A) ) ) ) )).
fof(t2_pdiff_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,k1_numbers,u1_struct_0(B),D,C)) & k7_partfun1(k1_numbers,C,k6_normsp_1(B,D)) = k1_seq_2(k8_funct_2(k4_ordinal1,k1_numbers,u1_struct_0(B),D,C)) ) ) ) ) ) ) ) )).
fof(t2_pencil_1,axiom,( ! [A] : ( r1_ordinal1(2,k1_card_1(A)) <=> ? [B] : ? [C] : ( r2_hidden(B,A) & r2_hidden(C,A) & B != C ) ) )).
fof(t2_pencil_2,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( 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) ) ) ) ) )).
fof(t2_pencil_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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)) ) ) ) )).
fof(t2_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => m1_vectsp_4(C,A,k2_vectsp_4(A,B)) ) ) ) )).
fof(t2_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( v1_int_2(B) & ~ r1_int_2(A,B) & k6_nat_d(A,B) != B ) ) ) )).
fof(t2_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( r2_hidden(C,k6_petri(A,B)) <=> ? [D] : ( m1_petri(D,u4_struct_0(A),u1_struct_0(A),u2_petri(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_hidden(E,B) & D = k4_tarski(C,E) ) ) ) ) ) )).
fof(t2_petri_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ! [D] : ( m1_petri_2(D,A,C) => ~ ( r1_tarski(A,B) & ! [E] : ( m1_petri_2(E,B,C) => ~ r1_tarski(D,E) ) ) ) ) ) )).
fof(t2_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,k4_ordinal1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ( ( r2_pnproc_1(A,B,C) & r2_pnproc_1(A,C,D) ) => r2_pnproc_1(A,B,D) ) ) ) ) )).
fof(t2_polyalg1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(t2_polyeq_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k1_polyeq_1(k5_numbers,k5_numbers,A) = k5_numbers ) )).
fof(t2_polyeq_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( E = k2_xcmplx_0(D,k7_xcmplx_0(1,D)) & k1_polyeq_2(A,B,C,B,A,D) = k5_numbers ) => ( A = k5_numbers | ( D != k5_numbers & k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k1_square_1(E)),k3_xcmplx_0(B,E)),C),k3_xcmplx_0(2,A)) = k5_numbers ) ) ) ) ) ) ) ) )).
fof(t2_polyeq_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xcmplx_0(D) => ~ ( A != k5_numbers & ~ r1_xxreal_0(k5_numbers,k1_quin_1(A,B,C)) & k2_polyeq_3(A,B,C,D) = k5_numbers & D != k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,k3_xcmplx_0(2,A))),k3_xcmplx_0(k7_xcmplx_0(k3_square_1(k4_xcmplx_0(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A)),k7_complex1)) & D != k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,k3_xcmplx_0(2,A))),k3_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k3_square_1(k4_xcmplx_0(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A))),k7_complex1)) ) ) ) ) ) )).
fof(t2_polyeq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k5_numbers,k1_quin_1(A,B,C)) => ( r1_xxreal_0(k7_xcmplx_0(B,A),k5_numbers) | r1_xxreal_0(k7_xcmplx_0(C,A),k5_numbers) | ( ~ r1_xxreal_0(k5_numbers,k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A))) & ~ r1_xxreal_0(k5_numbers,k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A))) ) ) ) ) ) ) )).
fof(t2_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(k3_xcmplx_0(A,A),A) = k1_newton(A,3) ) )).
fof(t2_polyform,axiom,( ! [A] : ( v1_int_1(A) => ( r1_xxreal_0(1,A) => v7_ordinal1(A) ) ) )).
fof(t2_polynom1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) => k4_finseq_1(k6_matrlin(A,B)) = k4_finseq_1(B) ) ) )).
fof(t2_polynom2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_rlvect_1(A) & v1_algstr_1(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r2_hidden(C,k4_finseq_1(B)) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( 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) ) ) ) ) )).
fof(t2_polynom4,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k11_polynom3(A,k9_polynom3(A),B),k9_polynom3(A)) ) ) )).
fof(t2_polynom5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,k5_numbers) => r1_xxreal_0(k7_xcmplx_0(k3_xxreal_0(A,B),k4_xxreal_0(A,B)),1) ) ) ) )).
fof(t2_polynom6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( v3_ordinal1(D) => ~ ( r2_hidden(D,A) & ~ r1_xxreal_0(k1_funct_1(C,D),k1_funct_1(B,D)) & ! [E] : ( v3_ordinal1(E) => ( r2_hidden(E,D) => k1_funct_1(B,E) = k1_funct_1(C,E) ) ) ) ) ) ) ) ) )).
fof(t2_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ( ~ ( ~ v7_struct_0(B) & ! [C] : ( ( 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)))) ) => k3_polynom1(k15_pre_poly(A),B,C) = k1_xboole_0 ) ) & ~ ( ~ ! [C] : ( ( 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)))) ) => k3_polynom1(k15_pre_poly(A),B,C) = k1_xboole_0 ) & v7_struct_0(B) ) ) ) )).
fof(t2_polynom8,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t2_polyred,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v1_algstr_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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),k5_polynom1(A,B,k8_polynom1(A,B),C),C) ) ) )).
fof(t2_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ v1_xboole_0(C) & v6_orders_2(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t2_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ v1_abian(B) => k1_newton(k4_xcmplx_0(A),B) = k4_xcmplx_0(k1_newton(A,B)) ) ) ) )).
fof(t2_pralg_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => k11_funcop_1(k2_zfmisc_1(A,B),B,A,k6_pralg_1(A,B)) = k2_zfmisc_1(B,A) ) ) )).
fof(t2_pralg_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( 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))) ) ) ) ) )).
fof(t2_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(A)) ) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t2_pre_circ,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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))) ) ) )).
fof(t2_pre_ff,axiom,( ! [A] : ( v1_int_1(A) => k4_int_1(A,1) = A ) )).
fof(t2_pre_poly,axiom,( ! [A] : k5_pre_poly(A,k2_pre_poly(k3_finseq_2(A))) = k2_pre_poly(A) )).
fof(t2_pre_topc,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( 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) ) ) )).
fof(t2_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_prelamb(A) ) => ! [B] : ( m1_prelamb(B,A) => ! [C] : ( m1_trees_1(C,k9_xtuple_0(B)) => ( k8_trees_2(k9_xtuple_0(B),C) = 2 => ( r2_hidden(k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,k5_numbers)),k9_xtuple_0(B)) & r2_hidden(k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,1)),k9_xtuple_0(B)) ) ) ) ) ) )).
fof(t2_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(B) & ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k1_funct_1(B,C),A) ) ) => r1_xxreal_0(k1_seq_2(B),A) ) ) ) )).
fof(t2_prgcor_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r1_xxreal_0(B,k4_nat_d(A,k2_nat_1(2,B))) => ( r1_xxreal_0(B,k5_numbers) | ( k6_xcmplx_0(k4_nat_d(A,k2_nat_1(2,B)),B) = k4_nat_d(A,B) & k1_nat_1(k4_nat_d(A,B),B) = k4_nat_d(A,k2_nat_1(2,B)) ) ) ) ) ) )).
fof(t2_prgcor_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ~ ( r1_tarski(k4_ordinal1,A) & ~ r1_xxreal_0(C,k3_finseq_1(B)) & ! [D] : ( ( v1_relat_1(D) & v5_relat_1(D,A) & v5_ordinal1(D) & v1_funct_1(D) & v1_finset_1(D) ) => ~ ( k1_afinsq_1(D) = C & r1_prgcor_2(A,D,B) ) ) ) ) ) ) )).
fof(t2_prob_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => m1_subset_1(k2_tarski(B,C),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) )).
fof(t2_prob_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(B) & ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k6_xcmplx_0(A,k9_nat_1(k1_numbers,B,D)) ) ) => ( v2_comseq_2(C) & k1_seq_2(C) = k6_xcmplx_0(A,k1_seq_2(B)) ) ) ) ) ) )).
fof(t2_prob_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( r2_hidden(A,k9_xtuple_0(B)) <=> ( A != k5_numbers & r1_xxreal_0(A,k3_finseq_1(B)) ) ) ) ) )).
fof(t2_prob_4,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) <=> ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) ) ) ) )).
fof(t2_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) )).
fof(t2_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_collsp(A,B,C,D) ) ) ) ) )).
fof(t2_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ( v1_projpl_1(A) <=> ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t2_projred1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ~ ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => r1_incsp_1(A,B,C) ) ) ) )).
fof(t2_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t2_prvect_1,axiom,( ! [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) ) => r1_finseqop(u1_struct_0(A),k5_vectsp_1(A),u1_algstr_0(A)) ) )).
fof(t2_prvect_2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k2_finseq_1(k3_finseq_1(A))) => ( r1_xxreal_0(k5_numbers,k1_funct_1(A,C)) & r1_xxreal_0(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) ) => r1_xxreal_0(k12_euclid(A),k12_euclid(B)) ) ) ) )).
fof(t2_prvect_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ~ ( k9_xtuple_0(B) = k6_domain_1(k4_ordinal1,1) & k1_funct_1(B,1) = A & ! [C] : ( ( 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] : ( r2_hidden(D,A) => k1_funct_1(C,D) = k9_finseq_1(D) ) ) ) ) ) ) )).
fof(t2_pscomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_xxreal_0(C,k3_funct_2(u1_struct_0(A),k1_numbers,B,D)) ) => r1_xxreal_0(C,k1_pscomp_1(A,B)) ) ) ) ) )).
fof(t2_pua2mss1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) ) => ( k4_card_3(A) = k4_card_3(B) => A = B ) ) ) )).
fof(t2_pythtrip,axiom,( ! [A] : ( v1_int_1(A) => ( v1_abian(A) <=> v1_abian(k1_pepin(A)) ) ) )).
fof(t2_qc_lang1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => r1_tarski(k2_zfmisc_1(k1_enumset1(C,D,E),B),k2_zfmisc_1(A,B)) ) ) ) ) )).
fof(t2_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ! [E] : ( m1_subset_1(E,k9_qc_lang1(A)) => ( k14_qc_lang1(A,B,C) = k14_qc_lang1(A,D,E) => ( B = D & C = E ) ) ) ) ) ) ) )).
fof(t2_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k2_qc_lang1(A)) => k23_qc_lang1(A,B) = k1_qc_lang3(A,B,k3_qc_lang1(A)) ) ) )).
fof(t2_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t2_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_qc_trans(B,A) & m1_qc_lang1(B) ) => r1_tarski(k1_qc_lang1(A),k1_qc_lang1(B)) ) ) )).
fof(t2_qmax_1,axiom,( ! [A] : ( ( v2_qmax_1(A) & l1_qmax_1(A) ) => ! [B] : ( m1_subset_1(B,k5_qmax_1(A)) => ! [C] : ( m1_subset_1(C,k5_qmax_1(A)) => ( r4_qmax_1(A,B,C) <=> ! [D] : ( 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)) ) ) ) ) ) )).
fof(t2_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t2_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k22_quaterni(k22_quaterni(A,B),C) = k22_quaterni(A,k22_quaterni(B,C)) ) ) ) )).
fof(t2_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ( v1_xreal_0(B) => k22_quaterni(B,A) = k22_quaterni(k22_quaterni(k19_quaterni(k2_xcmplx_0(k13_quaterni(B),k13_quaterni(A)),k21_quaterni(k14_quaterni(A),k3_quatern2)),k21_quaterni(k15_quaterni(A),k11_quaterni)),k21_quaterni(k16_quaterni(A),k12_quaterni)) ) ) ) )).
fof(t2_quaterni,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : r1_tarski(k10_xtuple_0(k2_quaterni(E,F,G,H,A,B,C,D)),k2_enumset1(A,B,C,D)) )).
fof(t2_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r1_xxreal_0(k1_quin_1(B,C,D),k5_numbers) => ( r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(k5_numbers,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(A)),k3_xcmplx_0(C,A)),D)) ) ) ) ) ) ) )).
fof(t2_quofield,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v6_struct_0(A) & l5_algstr_0(A) ) => ! [B] : ( 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) ) ) )).
fof(t2_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(k6_xcmplx_0(A,1),k4_nat_d(B,A)) => k4_nat_d(k2_xcmplx_0(B,1),A) = k2_xcmplx_0(k4_nat_d(B,A),1) ) ) ) )).
fof(t2_radix_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(C,k5_numbers) => k5_int_1(k2_xcmplx_0(k5_int_1(A,C),k5_int_1(B,C)),C) = k5_int_1(k2_xcmplx_0(A,k5_int_1(B,C)),C) ) ) ) ) )).
fof(t2_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => r1_tarski(k1_radix_3(A),k2_radix_3(A)) ) )).
fof(t2_radix_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( 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) = k5_numbers ) ) ) ) )).
fof(t2_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) ) ) )).
fof(t2_ramsey_1,axiom,( ! [A] : ( r1_tarski(A,k4_ordinal1) => ( v1_finset_1(A) | k1_card_1(A) = k4_ordinal1 ) ) )).
fof(t2_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( v1_xreal_0(F) => ( ( r3_mesfunc6(A,B,C,D) & r1_tarski(E,k1_relset_1(A,D)) & ! [G] : ( m1_subset_1(G,A) => ( r2_hidden(G,E) => r1_xxreal_0(F,k12_supinf_2(D,G)) ) ) ) => ( r1_xxreal_0(k1_xxreal_0,k3_funct_2(B,k6_numbers,C,E)) | r1_xxreal_0(k4_xxreal_3(F,k3_funct_2(B,k6_numbers,C,E)),k1_mesfunc6(A,B,C,k2_partfun1(A,k1_numbers,D,E))) ) ) ) ) ) ) ) ) )).
fof(t2_random_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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)))) ) ) )).
fof(t2_random_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ! [F] : ( m1_subset_1(F,k4_ordinal1) => k1_prob_4(A,k9_setfam_1(A),E,F) = k8_relset_1(A,B,C,k1_prob_4(B,k9_setfam_1(B),D,F)) ) => k8_relset_1(A,B,C,k1_prob_1(B,D)) = k1_prob_1(A,E) ) ) ) ) ) ) )).
fof(t2_ranknull,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( ( r1_tarski(B,C) & v2_funct_1(k5_relat_1(A,C)) ) => v2_funct_1(k5_relat_1(A,B)) ) ) )).
fof(t2_rat_1,axiom,( ! [A] : ~ ( v1_rat_1(A) & ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ~ ( C != k5_numbers & A = k7_xcmplx_0(B,C) ) ) ) ) )).
fof(t2_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( 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 ) ) ) ) ) )).
fof(t2_rcomp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r2_hidden(B,k1_rcomp_1(C,A)) <=> r1_xxreal_0(k9_complex1(k6_xcmplx_0(k2_xcmplx_0(C,A),k3_xcmplx_0(2,B))),k6_xcmplx_0(A,C)) ) ) ) ) )).
fof(t2_rcomp_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_membered(A) & v4_xxreal_2(A) ) => ! [B] : ( ( v2_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,B) => r2_hidden(k2_seq_4(A),B) ) ) ) )).
fof(t2_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(A,B) & v3_xxreal_0(B) ) => v3_xxreal_0(A) ) ) ) )).
fof(t2_real_3,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => ( r1_xxreal_0(k2_xcmplx_0(A,1),B) | k1_int_1(B) = A ) ) ) ) )).
fof(t2_real_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_real_lat)) => ! [B] : ( 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) ) ) )).
fof(t2_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(A))) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t2_realset1,axiom,( ! [A] : ! [B] : ( ( 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] : ( 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))) ) ) ) )).
fof(t2_realset2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t2_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(A),k8_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t2_rearran1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v2_rearran1(A) <=> ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( 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)) ) ) ) ) ) )).
fof(t2_recdef_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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) ) ) )).
fof(t2_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => k3_xboole_0(A,k2_zfmisc_1(k9_xtuple_0(A),k10_xtuple_0(A))) = A ) )).
fof(t2_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ( v2_relat_2(A) <=> r1_xboole_0(k4_relat_1(k1_relat_1(A)),A) ) ) )).
fof(t2_reloc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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) ) ) ) )).
fof(t2_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ~ ( r2_hidden(C,D) & ! [E] : ! [F] : ~ ( C = k4_tarski(E,F) & r2_hidden(E,A) & r2_hidden(F,B) ) ) ) )).
fof(t2_relset_2,axiom,( ! [A] : ( A = k1_xboole_0 <=> k10_eqrel_1(A) = k1_xboole_0 ) )).
fof(t2_revrot_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => k2_rfinseq(A,k3_finseq_1(B),B) = k1_xboole_0 ) ) )).
fof(t2_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( B != k1_xboole_0 => k1_rewrite1(k7_finseq_1(A,k9_finseq_1(C)),B) = k7_finseq_1(A,B) ) ) ) )).
fof(t2_rewrite2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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] : ( v7_ordinal1(D) => ~ ( A = k2_xcmplx_0(k3_finseq_1(B),D) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(C)) ) ) ) ) ) ) )).
fof(t2_rewrite3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ~ ( A != k1_xboole_0 & ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ~ ( A = k7_finseq_1(B,k9_finseq_1(C)) & k3_finseq_1(A) = k2_xcmplx_0(k3_finseq_1(B),1) ) ) ) ) )).
fof(t2_rfinseq,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => r2_classes1(k7_finseq_1(A,B),k7_finseq_1(B,A)) ) ) )).
fof(t2_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(A)) ) => ( r1_xxreal_0(k1_funct_1(A,k2_rfinseq2(A)),k1_funct_1(A,B)) & r1_xxreal_0(k4_rfinseq2(A),k1_funct_1(A,B)) ) ) ) ) )).
fof(t2_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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(k5_numbers))) = k9_subset_1(k9_xtuple_0(B),k6_subset_1(k9_xtuple_0(A),k8_relat_1(A,k1_tarski(k5_numbers))),k6_subset_1(k9_xtuple_0(B),k8_relat_1(B,k1_tarski(k5_numbers)))) ) ) )).
fof(t2_rfunct_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_ordinal1) & v5_valued_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ( r2_relset_1(k4_ordinal1,k1_numbers,k2_valued_0(k1_numbers,C,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)),k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k2_valued_0(k1_numbers,C,A),k2_valued_0(k1_numbers,C,B))) & r2_relset_1(k4_ordinal1,k1_numbers,k2_valued_0(k1_numbers,C,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k2_valued_0(k1_numbers,C,A),k2_valued_0(k1_numbers,C,B))) & r2_relset_1(k4_ordinal1,k1_numbers,k2_valued_0(k1_numbers,C,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)),k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k2_valued_0(k1_numbers,C,A),k2_valued_0(k1_numbers,C,B))) ) ) ) ) )).
fof(t2_rfunct_3,axiom,( ! [A] : ( v1_xreal_0(A) => k9_complex1(A) = k2_xcmplx_0(k1_rfunct_3(A),k2_rfunct_3(A)) ) )).
fof(t2_rfunct_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => k14_rvsum_1(k7_finseq_1(B,k9_finseq_1(D)),k7_finseq_1(C,k9_finseq_1(E))) = k7_finseq_1(k15_rvsum_1(A,B,C),k9_finseq_1(k3_xcmplx_0(D,E))) ) ) ) ) ) )).
fof(t2_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B),B),A) ) ) )).
fof(t2_rinfsup2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( ( ~ 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) = k2_seq_4(B) ) ) ) ) )).
fof(t2_ring_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => C = k5_algstr_0(A,B,k5_algstr_0(A,B,C)) ) ) ) )).
fof(t2_ringcat1,axiom,( ! [A] : ( ( v3_ringcat1(A) & l1_ringcat1(A) ) => ! [B] : ( ( v3_ringcat1(B) & l1_ringcat1(B) ) => ~ ( k1_ringcat1(A) = k2_ringcat1(B) & ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(t2_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(B,k3_convex1(A,B)) ) ) )).
fof(t2_rlaffin2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( ( v1_rlaffin1(F,C) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(C))) ) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ! [H] : ( m1_subset_1(H,u1_struct_0(C)) => ! [I] : ( m1_subset_1(I,u1_struct_0(C)) => ! [J] : ( 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,k6_xcmplx_0(1,A))) = D & k3_rlvect_1(C,k1_rlvect_1(C,E,B),k1_rlvect_1(C,J,k6_xcmplx_0(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 ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t2_rlaffin3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(A,k4_card_3(k7_finseq_1(B,C))) <=> ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) & ? [E] : ( 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)) ) ) ) ) ) )).
fof(t2_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_rlsub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => r2_hidden(k4_algstr_0(A,C),B) ) ) ) ) ) )).
fof(t2_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t2_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( m1_setfam_1(C,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,B) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(D,E) & r2_hidden(E,C) ) ) ) ) ) ) ) ) )).
fof(t2_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t2_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k1_relset_1(k4_ordinal1,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)) ) ) ) ) ) )).
fof(t2_rlvect_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( 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) ) ) ) )).
fof(t2_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k5_algstr_0(A,B,D) = k5_algstr_0(A,C,D) => B = C ) ) ) ) ) )).
fof(t2_rlvect_5,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_rlvect_3(B,A) & ! [C] : ( m1_rlvect_3(C,A) => ~ r1_tarski(B,C) ) ) ) ) )).
fof(t2_rlvect_x,axiom,( ! [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) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & r2_relset_1(k4_ordinal1,u1_struct_0(A),D,k2_vfunct_1(k4_ordinal1,A,B,C)) ) => k4_rlvect_1(A,D) = k5_algstr_0(A,k4_rlvect_1(A,B),k4_rlvect_1(A,C)) ) ) ) ) ) )).
fof(t2_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v1_rmod_2(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r2_hidden(D,C) => r2_hidden(k4_algstr_0(B,D),C) ) ) ) ) ) ) )).
fof(t2_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t2_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(t2_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( 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))) ) ) )).
fof(t2_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) )).
fof(t2_robbins3,axiom,( ! [A] : ( ( ~ 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) ) ) ) )).
fof(t2_robbins4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v10_robbins1(A) & v8_robbins3(A) & v9_robbins3(A) & l4_robbins1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t2_rolle,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,k5_numbers) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ~ ( r1_tarski(k1_rcomp_1(A,k2_xcmplx_0(A,B)),k1_relset_1(k1_numbers,C)) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,k1_rcomp_1(A,k2_xcmplx_0(A,B)))) & k1_funct_1(C,A) = k1_funct_1(C,k2_xcmplx_0(A,B)) & r2_fdiff_1(C,k2_rcomp_1(A,k2_xcmplx_0(A,B))) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(1,D) & k1_fdiff_1(C,k2_xcmplx_0(A,k3_xcmplx_0(D,B))) = k5_numbers ) ) ) ) ) ) ) )).
fof(t2_roughs_1,axiom,( ! [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)),u1_orders_2(A)) ) )).
fof(t2_rpr_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( ( 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 ) ) ) ) ) ) )).
fof(t2_rsspace,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace))) => ! [B] : ( m1_subset_1(B,u1_struct_0(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace))) => k1_algstr_0(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace),A,B) = k1_series_1(k1_numbers,k2_rsspace(A),k2_rsspace(B)) ) ) )).
fof(t2_rsspace3,axiom,( ! [A] : ( 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) ) ) ) )).
fof(t2_rsspace4,axiom,( u1_struct_0(k3_rsspace4) = k1_rsspace4 & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_rsspace4)) <=> ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v1_comseq_2(k2_rsspace(A)) ) ) & k4_struct_0(k3_rsspace4) = k5_rsspace & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_rsspace4)) => A = k2_rsspace(A) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_rsspace4)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_rsspace4)) => k1_algstr_0(k3_rsspace4,A,B) = k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k2_rsspace(A),k2_rsspace(B)) ) ) & ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_rsspace4)) => k1_rlvect_1(k3_rsspace4,B,A) = k26_valued_1(k4_ordinal1,k1_numbers,k2_rsspace(B),A) ) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_rsspace4)) => ( k4_algstr_0(k3_rsspace4,A) = k32_valued_1(k4_ordinal1,k1_numbers,k2_rsspace(A)) & r2_funct_2(k4_ordinal1,k1_numbers,k2_rsspace(k4_algstr_0(k3_rsspace4,A)),k32_valued_1(k4_ordinal1,k1_numbers,k2_rsspace(A))) ) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_rsspace4)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_rsspace4)) => k5_algstr_0(k3_rsspace4,A,B) = k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k2_rsspace(A),k2_rsspace(B)) ) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_rsspace4)) => v1_comseq_2(k2_rsspace(A)) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_rsspace4)) => k2_normsp_0(k3_rsspace4,A) = k2_seq_4(k2_relset_1(k1_numbers,k56_valued_1(k4_ordinal1,k1_numbers,k2_rsspace(A)))) ) )).
fof(t2_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( r1_struct_0(B,C) => r1_struct_0(A,C) ) ) ) )).
fof(t2_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t2_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( r2_hidden(C,B) => r1_struct_0(k1_rusub_3(A,B),C) ) ) ) )).
fof(t2_rusub_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t2_rusub_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l1_rlvect_1(A) ) => ! [B] : ( ( v2_rusub_4(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t2_rvsum_1,axiom,( r3_binop_1(k1_numbers,1,k11_binop_2) )).
fof(t2_rvsum_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => r7_binop_1(k2_numbers,k5_seq_4(A),k3_binop_2) ) )).
fof(t2_scheme1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( A != k2_nat_1(3,B) & A != k1_nat_1(k2_nat_1(3,B),1) & A != k1_nat_1(k2_nat_1(3,B),2) ) ) ) )).
fof(t2_scm_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v5_memstr_0(D,k7_card_1(2),k1_ami_3,C) & m1_scm_1(D,k6_afinsq_1(A,B)) ) => ( k1_funct_1(D,k10_ami_3(k5_numbers)) = A & k1_funct_1(D,k10_ami_3(1)) = B ) ) ) ) ) )).
fof(t2_scm_comp,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,4) & ~ m2_subset_1(k4_tarski(k5_numbers,A),u1_struct_0(k1_scm_comp),k7_dtconstr(k1_scm_comp)) ) ) )).
fof(t2_scm_halt,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( 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) ) ) ) ) ) )).
fof(t2_scm_inst,axiom,( ! [A] : ( v7_ordinal1(A) => r2_hidden(k3_xtuple_0(6,k9_finseq_1(A),k1_xboole_0),k3_scm_inst) ) )).
fof(t2_scmbsort,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( m1_scmfsa_2(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k14_scmfsa_2(D,C,B),A),D) = k7_partfun1(k4_numbers,k18_scmfsa_2(A,B),k9_complex1(k1_funct_1(A,C))) ) ) ) ) )).
fof(t2_scmfsa10,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( 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)) ) ) )).
fof(t2_scmfsa6b,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ( r1_tarski(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)),A) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( r1_tarski(B,C) => r1_extpro_1(k7_card_1(3),k1_scmfsa_2,C,A) ) ) ) ) ) )).
fof(t2_scmfsa6c,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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,k7_card_1(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) ) ) ) ) ) )).
fof(t2_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,C) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,D) & r5_scmfsa7b(E,C,A) ) => r5_scmfsa7b(E,D,B) ) ) ) ) ) ) )).
fof(t2_scmfsa8c,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k5_card_1(A),C) => ( r1_xxreal_0(k1_nat_1(k5_card_1(A),k5_card_1(B)),C) | ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(t2_scmfsa9a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => k4_sf_mastr(k16_funcop_1(A,B)) = k3_sf_mastr(B) ) ) )).
fof(t2_scmfsa_1,axiom,( r2_hidden(k4_ordinal1,k1_scmfsa_1) )).
fof(t2_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( A != B & k5_scmfsa_2(A) = k5_scmfsa_2(B) ) ) ) )).
fof(t2_scmfsa_3,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_scmfsa_2(C) => k18_scmfsa_2(A,C) = k18_scmfsa_2(k1_funct_4(A,k7_memstr_0(k7_card_1(3),k1_scmfsa_2,B)),C) ) ) ) )).
fof(t2_scmfsa_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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_xcmplx_0(B,A),C) ) ) ) )).
fof(t2_scmfsa_7,axiom,( ! [A] : ( ( 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(k5_numbers))),k5_afinsq_1(k2_compos_1(k1_scmfsa_2))) ) )).
fof(t2_scmfsa_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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(k5_numbers)),k4_compos_1(k1_scmfsa_2))) = k1_nat_1(k5_card_1(A),6) ) ) )).
fof(t2_scmfsa_i,axiom,( ! [A] : ( m1_subset_1(A,k2_scmfsa_i) => ( r1_xxreal_0(k4_xtuple_0(A),8) => r2_hidden(A,k3_scm_inst) ) ) )).
fof(t2_scmfsa_m,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ( ( ! [C] : ( ( 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] : ( m1_scmfsa_2(C) => k18_scmfsa_2(A,C) = k18_scmfsa_2(B,C) ) ) <=> k6_memstr_0(k7_card_1(3),k1_scmfsa_2,A) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,B) ) ) ) )).
fof(t2_scmp_gcd,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( k5_memstr_0(2,k1_scmpds_2,A) = k2_xcmplx_0(B,C) => k17_scmpds_2(A,k4_xcmplx_0(C)) = B ) ) ) ) )).
fof(t2_scmpds_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => k4_memstr_0(2,k1_scmpds_2,A) = k4_numbers ) )).
fof(t2_scmpds_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & 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)))) ) ) )).
fof(t2_scmpds_6,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => k1_funct_1(k2_scmpds_4(A,B),k5_numbers) = A ) ) )).
fof(t2_scmpds_7,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmpds_2)) => ! [C] : ( m1_subset_1(C,u1_compos_1(k1_scmpds_2)) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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)) ) ) ) ) )).
fof(t2_scmpds_8,axiom,( ! [A] : ( ( 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] : ( 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(k4_ordinal1,k5_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)) ) ) ) )).
fof(t2_scmpds_9,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => 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)) ) ) )).
fof(t2_scmpds_i,axiom,( r2_hidden(k3_xtuple_0(14,k1_xboole_0,k12_finseq_1(k4_ordinal1,k5_numbers)),k1_scmpds_i) )).
fof(t2_scmring1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t2_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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(k5_numbers,k1_xboole_0,k1_xboole_0),u1_compos_1(k1_scmring2(A))) ) )).
fof(t2_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => B != k4_struct_0(k1_scmring2(A)) ) ) )).
fof(t2_scmringi,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k7_card_1(8)) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( m1_subset_1(C,k1_scmringi(B)) => ! [D] : ( v7_ordinal1(D) => ( C = k3_xtuple_0(A,k9_finseq_1(D),k1_xboole_0) => k4_scmringi(B,C) = D ) ) ) ) ) )).
fof(t2_scmyciel,axiom,( ! [A] : ! [B] : k4_tarski(A,B) != B )).
fof(t2_scpisort,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ? [D] : ( m2_finseq_1(D,k4_numbers) & k3_finseq_1(D) = B & r1_scpisort(D,A,C) ) ) ) ) )).
fof(t2_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( 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] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v2_compos_1(D,k1_scmpds_2) & v3_scmpds_4(D) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ! [G] : ( v7_ordinal1(G) => ( ( r1_scmpds_6(D,B,A) & r2_scmpds_6(D,B,A) & G = k1_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)),k5_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) ) ) ) ) ) ) ) ) ) ) )).
fof(t2_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,E) => r2_analoaf(A,D,E,B,C) ) ) ) ) ) ) )).
fof(t2_seq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) <=> ( k9_xtuple_0(A) = k4_ordinal1 & ! [B] : ( v7_ordinal1(B) => v1_xreal_0(k1_funct_1(A,B)) ) ) ) ) )).
fof(t2_seq_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( B != k5_numbers & A != k5_numbers & k9_complex1(k6_xcmplx_0(k5_xcmplx_0(B),k5_xcmplx_0(A))) != k7_xcmplx_0(k9_complex1(k6_xcmplx_0(B,A)),k3_xcmplx_0(k9_complex1(B),k9_complex1(A))) ) ) ) )).
fof(t2_seq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => r2_hidden(k2_xcmplx_0(C,A),B) ) ) => ( r1_xxreal_0(A,k5_numbers) | ! [C] : ( v1_xreal_0(C) => ~ r2_hidden(C,B) ) | ! [C] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & r2_hidden(D,B) & ~ r1_xxreal_0(D,C) ) ) ) ) ) ) )).
fof(t2_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( r2_relset_1(k4_ordinal1,k4_partfun1(A,k1_numbers),D,k9_seqfunc(A,C,B)) <=> ! [E] : ( v7_ordinal1(E) => r2_relset_1(A,k1_numbers,k1_seqfunc(A,k1_numbers,D,E),k3_rfunct_1(A,k1_numbers,k1_seqfunc(A,k1_numbers,B,E),k1_seqfunc(A,k1_numbers,C,E))) ) ) ) ) ) ) )).
fof(t2_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v5_valued_0(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,A,k2_xcmplx_0(k1_nat_1(B,1),C)),k9_nat_1(k1_numbers,A,B)) ) ) ) ) )).
fof(t2_series_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => k2_power(k9_complex1(A),B) = k9_complex1(k2_power(A,B)) ) ) )).
fof(t2_series_2,axiom,( ! [A] : ( 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) ) ) )).
fof(t2_series_3,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => r1_xxreal_0(k3_square_1(k3_xcmplx_0(A,B)),k7_xcmplx_0(k2_xcmplx_0(A,B),2)) ) ) )).
fof(t2_series_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t2_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t2_setfam_1,axiom,( ! [A] : r1_tarski(k1_setfam_1(A),k3_tarski(A)) )).
fof(t2_setlim_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => a_3_0_setlim_1(A,B,C) = k2_xboole_0(a_3_1_setlim_1(A,B,C),k1_tarski(k1_funct_1(C,A))) ) ) )).
fof(t2_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => k9_nat_1(k9_setfam_1(B),k4_setlim_1(B,C),A) = k1_prob_1(B,k8_nat_1(k9_setfam_1(B),C,A)) ) ) )).
fof(t2_setwiseo,axiom,( ! [A] : ! [B] : ! [C] : r1_tarski(k2_tarski(A,B),k1_enumset1(A,B,C)) )).
fof(t2_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,k5_finsub_1(A)) => ! [E] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t2_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ( k7_scmfsa_2(A,C) = k7_scmfsa_2(B,D) => ( A = B & C = D ) ) ) ) ) ) )).
fof(t2_sfmastr1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) ) ) ) ) )).
fof(t2_sfmastr2,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( m1_scmfsa_2(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ( ( 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) ) ) ) ) ) ) )).
fof(t2_sfmastr3,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ( k1_funct_1(A,k4_scmfsa_2(k5_numbers)) = 1 => k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(k4_compos_1(k1_scmfsa_2),A,B)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,A) ) ) ) )).
fof(t2_sgraph1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k1_sgraph1(A,B)) <=> ( r1_xxreal_0(A,C) & r1_xxreal_0(C,B) ) ) ) ) ) )).
fof(t2_sheffer1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k3_lattices(A,B,k3_sheffer1(A,B)) = k1_sheffer1(A) ) ) )).
fof(t2_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t2_simplex0,axiom,( ! [A] : ! [B] : ( r2_hidden(A,k1_simplex0(B)) <=> ? [C] : ( r1_tarski(A,C) & r2_hidden(C,B) ) ) )).
fof(t2_simplex1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ( k1_card_1(A) = k2_xcmplx_0(k5_card_1(B),1) => ! [C] : ( ( 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] : ~ ( r2_hidden(D,B) & k1_card_1(k8_relset_1(A,B,C,k1_tarski(D))) = 2 & ! [E] : ( r2_hidden(E,B) => ( E = D | k1_card_1(k8_relset_1(A,B,C,k1_tarski(E))) = 1 ) ) ) ) ) ) ) )).
fof(t2_simplex2,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t2_sin_cos,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( ~ r1_xxreal_0(A,k5_numbers) => k3_xcmplx_0(k2_newton(k7_nat_d(A,1)),A) = k2_newton(A) ) & ( r1_xxreal_0(A,B) => k3_xcmplx_0(k2_newton(k7_nat_d(B,A)),k6_xcmplx_0(k1_nat_1(B,1),A)) = k2_newton(k7_nat_d(k1_nat_1(B,1),A)) ) ) ) ) )).
fof(t2_sin_cos2,axiom,( v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k16_sin_cos,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(t2_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k4_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,A)) = k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,k4_xcmplx_0(A)) ) )).
fof(t2_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => k3_sin_cos4(k4_xcmplx_0(A)) = k4_xcmplx_0(k7_xcmplx_0(1,k17_sin_cos(A))) ) )).
fof(t2_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k17_sin_cos(A) != k5_numbers => k19_sin_cos(A) = k3_xcmplx_0(k17_sin_cos(A),k2_sin_cos4(A)) ) ) )).
fof(t2_sin_cos6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( ( v2_funct_1(k5_relat_1(A,B)) & r1_tarski(C,B) ) => v2_funct_1(k5_relat_1(A,C)) ) ) )).
fof(t2_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,1) & r1_xxreal_0(1,k1_square_1(k7_xcmplx_0(k3_square_1(k6_xcmplx_0(k1_square_1(A),1)),A))) ) ) )).
fof(t2_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ( k2_sin_cos2(A) = k7_xcmplx_0(1,k3_sin_cos5(A)) & k4_sin_cos2(A) = k7_xcmplx_0(1,k2_sin_cos5(A)) & k6_sin_cos2(A) = k7_xcmplx_0(1,k1_sin_cos5(A)) ) ) )).
fof(t2_sin_cos9,axiom,( r1_tarski(k2_rcomp_1(k5_numbers,k28_sin_cos),k1_relset_1(k1_numbers,k27_sin_cos)) )).
fof(t2_sincos10,axiom,( r1_tarski(k4_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos),k1_relset_1(k1_numbers,k1_fdiff_9)) )).
fof(t2_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,k6_xcmplx_0(B,C)) & r1_xxreal_0(k6_xcmplx_0(B,C),A) ) => ( r2_hidden(k6_xcmplx_0(B,C),k2_finseq_1(A)) & m1_subset_1(k6_xcmplx_0(B,C),k4_ordinal1) ) ) ) ) ) )).
fof(t2_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t2_sprect_1,axiom,( ! [A] : ! [B] : ( v3_funct_1(k10_finseq_1(A,B)) => A = B ) )).
fof(t2_sprect_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( 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(k1_nat_1(k7_nat_d(A,C),1),k4_finseq_1(E)) ) ) ) ) ) ) ) )).
fof(t2_sprect_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_matrix_0(k12_matrix_0(A,B,C,D)) = k2_enumset1(k4_tarski(1,1),k4_tarski(1,2),k4_tarski(2,1),k4_tarski(2,2)) )).
fof(t2_sprect_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( 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 ) ) ) )).
fof(t2_sprect_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t2_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => r1_xxreal_0(k4_xxreal_0(A,B),k2_xcmplx_0(A,B)) ) ) ) )).
fof(t2_stacks_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_stacks_1(A) ) => ~ ( v2_stacks_1(A) & ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ~ r1_stacks_1(A,B) ) ) ) )).
fof(t2_stirl2_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k4_ordinal1)) ) => k4_nat_1(k4_seq_4(A),k4_seq_4(B)) = k4_seq_4(k4_subset_1(k4_ordinal1,A,B)) ) ) )).
fof(t2_struct_0,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & l4_struct_0(A) ) => r2_hidden(k5_struct_0(A),k8_struct_0(A)) ) )).
fof(t2_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( ( 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 ) ) ) ) )).
fof(t2_subset,axiom,( ! [A] : ! [B] : ( m1_subset_1(A,B) => ( v1_xboole_0(B) | r2_hidden(A,B) ) ) )).
fof(t2_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,B) => r2_hidden(D,C) ) ) => r1_tarski(B,C) ) ) ) )).
fof(t2_substlat,axiom,( ! [A] : ! [B] : r2_hidden(k1_tarski(k1_xboole_0),k1_substlat(A,B)) )).
fof(t2_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => k9_substut1(A,k5_cqc_lang(A)) = k1_xboole_0 ) )).
fof(t2_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [D] : ( ( v5_relat_1(D,k3_qc_lang1(A)) & v3_card_1(D,B) & m2_finseq_1(D,k2_qc_lang1(A)) ) => ! [E] : ( m1_subset_1(E,k1_substut1(A)) => ? [F] : ( 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 ) ) ) ) ) ) )).
fof(t2_supinf_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ( r1_tarski(A,B) => ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(C,k4_supinf_1(B)) => r2_hidden(C,k4_supinf_1(A)) ) ) ) ) ) )).
fof(t2_supinf_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( A = B => k2_xxreal_3(A) = k4_xcmplx_0(B) ) ) ) )).
fof(t2_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r1_orders_2(B,C,D) => r1_orders_2(B,D,C) ) ) ) ) ) )).
fof(t2_sysrel,axiom,( ! [A] : ! [B] : ! [C] : ( 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)))) ) ) )).
fof(t2_t_0topsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t2_t_1topsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_eqrel_1(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k11_borsuk_1(A,B)))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t2_tarski,axiom,( ! [A] : ! [B] : ( ! [C] : ( r2_hidden(C,A) <=> r2_hidden(C,B) ) => A = B ) )).
fof(t2_taxonom1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r2_hidden(B,k4_finseq_1(A)) & r2_hidden(C,k4_finseq_1(A)) & ! [D] : ( 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) ) ) ) ) )).
fof(t2_taxonom2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ! [D] : ! [E] : ( ( 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) ) ) ) )).
fof(t2_taylor_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ( r1_fdiff_1(k1_taylor_1(A),B) & k1_fdiff_1(k1_taylor_1(A),B) = k3_xcmplx_0(A,k3_prepower(B,k6_xcmplx_0(A,1))) ) ) ) )).
fof(t2_taylor_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( r1_tarski(k2_rcomp_1(k4_xcmplx_0(C),C),k9_xtuple_0(B)) & r1_taylor_1(B,k1_nat_1(A,1),k2_rcomp_1(k4_xcmplx_0(C),C)) ) => ( r1_xxreal_0(C,k5_numbers) | ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,k2_rcomp_1(k4_xcmplx_0(C),C)) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ~ r1_xxreal_0(1,E) & k1_funct_1(B,D) = k2_xcmplx_0(k9_nat_1(k1_numbers,k3_series_1(k1_taylor_2(B,k2_rcomp_1(k4_xcmplx_0(C),C),D)),A),k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(B,k2_rcomp_1(k4_xcmplx_0(C),C)),k1_nat_1(A,1)),k3_xcmplx_0(E,D)),k1_newton(D,k1_nat_1(A,1))),k2_newton(k1_nat_1(A,1)))) ) ) ) ) ) ) ) ) ) )).
fof(t2_tdgroup,axiom,( ! [A] : ( 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) ) ) )).
fof(t2_tdlat_1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t2_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)))) ) ) ) )).
fof(t2_tdlat_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) )).
fof(t2_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( 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),k10_polynom1(A,B,k8_polynom1(A,B),C),k8_polynom1(A,B)) ) ) ) )).
fof(t2_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t2_tex_2,axiom,( ! [A] : ( v3_card_1(A,1) => ! [B] : ( ~ v1_xboole_0(k3_xboole_0(A,B)) => r1_tarski(A,B) ) ) )).
fof(t2_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t2_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) )).
fof(t2_tietze,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t2_tmap_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ! [E] : ( ( 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] : ( ( v1_funct_1(F) & v1_funct_2(F,C,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(C,B))) ) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t2_toler_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r2_hidden(k4_tarski(B,C),k1_eqrel_1(A)) ) )).
fof(t2_topalg_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k17_borsuk_1))) => ! [B] : ( 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(k5_numbers,B) ) ) ) )).
fof(t2_topalg_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v1_topalg_2(B,A) & m1_pre_topc(B,k15_euclid(A)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_borsuk_2(E,B,C,D) => ! [F] : ( m1_borsuk_2(F,B,C,D) => r4_borsuk_2(B,C,D,E,F) ) ) ) ) ) ) )).
fof(t2_topalg_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( ( 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 ) ) )).
fof(t2_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l3_algstr_0(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & l3_algstr_0(D) ) => ! [E] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t2_topalg_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(A,B) & ! [C] : ( ( 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] : ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t2_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v10_pre_topc(A) <=> ! [B] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v4_pre_topc(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( r1_xboole_0(B,C) & ! [D] : ( ( v3_pre_topc(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t2_topdim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) => ( r1_xxreal_0(k1_topdim_2(B,C),A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t2_topgen_1,axiom,( ! [A] : ( l1_struct_0(A) => ( v1_orders_4(A) <=> r1_ordinal1(k1_card_1(k2_struct_0(A)),k4_ordinal1) ) ) )).
fof(t2_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [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] : ( 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)))) ) ) ) ) )).
fof(t2_topgen_3,axiom,( ! [A] : ! [B] : ( 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] : ( 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)))) ) ) ) ) ) )).
fof(t2_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k2_topgen_1(A,B) = a_2_0_topgen_4(A,B) ) ) )).
fof(t2_topgen_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_xboole_0(k9_xtuple_0(A),k9_xtuple_0(B)) => ! [C] : k8_relat_1(k1_funct_4(A,B),C) = k2_xboole_0(k8_relat_1(A,C),k8_relat_1(B,C)) ) ) ) )).
fof(t2_topgrp_1,axiom,( ! [A] : ( 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)) ) )).
fof(t2_topmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ( v8_pre_topc(A) => v8_pre_topc(B) ) ) ) )).
fof(t2_topmetr2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t2_topmetr3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_funct_1(k1_partfun1(k4_ordinal1,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(k4_ordinal1,u1_struct_0(A),u1_struct_0(k3_pcomps_1(A)),u1_struct_0(k3_pcomps_1(B)),D,C),k4_ordinal1,u1_struct_0(B)) & m1_subset_1(k1_partfun1(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B)))) ) ) ) ) ) )).
fof(t2_topreal1,axiom,( ! [A] : ( ( v2_pre_topc(A) & v8_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t2_topreal2,axiom,( v2_compts_1(k1_topreal1,k15_euclid(2)) )).
fof(t2_topreal3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( k17_euclid(k3_rlvect_1(k15_euclid(2),A,B)) = k2_xcmplx_0(k17_euclid(A),k17_euclid(B)) & k18_euclid(k3_rlvect_1(k15_euclid(2),A,B)) = k2_xcmplx_0(k18_euclid(A),k18_euclid(B)) ) ) ) )).
fof(t2_topreal4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( r1_topreal4(A,B,C) => r1_topreal1(k15_euclid(2),B,C,A) ) ) ) ) )).
fof(t2_topreal5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => v2_connsp_1(k2_struct_0(k4_topmetr(A,B)),k4_topmetr(A,B)) ) ) ) )).
fof(t2_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(B,A) & r1_xxreal_0(A,k5_numbers) ) => r1_xxreal_0(k9_complex1(A),k9_complex1(B)) ) ) ) )).
fof(t2_topreal7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( ( r1_xxreal_0(A,k2_xcmplx_0(B,C)) & r1_xxreal_0(D,k2_xcmplx_0(E,F)) ) => r1_xxreal_0(k4_xxreal_0(A,D),k2_xcmplx_0(k4_xxreal_0(B,E),k4_xxreal_0(C,F))) ) ) ) ) ) ) ) )).
fof(t2_topreal8,axiom,( ! [A] : ( ( ~ v1_zfmisc_1(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ~ r1_xxreal_0(k3_finseq_1(A),1) ) )).
fof(t2_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( E = k3_rlvect_1(B,k1_rlvect_1(B,C,k6_xcmplx_0(1,A)),k1_rlvect_1(B,D,A)) => ( ~ ( E = C & A != k5_numbers & C != D ) & ( ( A = k5_numbers | C = D ) => E = C ) & ~ ( E = D & A != 1 & C != D ) & ( ( A = 1 | C = D ) => E = D ) ) ) ) ) ) ) )).
fof(t2_topreala,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ~ ( r2_hidden(k2_xcmplx_0(B,1),k4_finseq_1(A)) & ~ r2_hidden(B,k4_finseq_1(A)) & B != k5_numbers ) ) ) )).
fof(t2_toprealb,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k19_sin_cos(k2_xcmplx_0(k3_xcmplx_0(A,C),B)) = k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,B),k18_sin_cos),C) ) ) ) )).
fof(t2_toprealc,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(t2_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ( v1_toprns_1(B,A) <=> ! [C] : ~ ( r2_hidden(C,k4_ordinal1) & k1_funct_1(B,C) = k4_struct_0(k15_euclid(A)) ) ) ) ) )).
fof(t2_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => k2_pre_topc(A,k2_struct_0(A)) = k2_struct_0(A) ) )).
fof(t2_tops_2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( r1_tarski(C,B) => m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) ) )).
fof(t2_tops_3,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t2_tops_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( v3_pre_topc(B,k15_euclid(A)) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ~ ( r2_hidden(C,B) & ! [D] : ( ( v1_xreal_0(D) & v2_xxreal_0(D) ) => ~ r1_tarski(k1_topreal9(A,C,D),B) ) ) ) ) ) ) )).
fof(t2_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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 ) ) ) ) ) )).
fof(t2_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_aff_1(A,C,D,F) & r1_aff_1(A,B,E,F) ) ) ) ) ) ) ) ) )).
fof(t2_treal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => v1_borsuk_1(k4_topmetr(A,B),k3_topmetr) ) ) ) )).
fof(t2_trees_1,axiom,( ! [A] : ! [B] : ( r1_tarski(k9_finseq_1(A),k9_finseq_1(B)) => A = B ) )).
fof(t2_trees_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t2_trees_3,axiom,( ! [A] : ( v2_trees_3(A) <=> r1_tarski(A,k2_trees_3) ) )).
fof(t2_trees_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k2_trees_1(A) = k2_trees_1(B) => A = B ) ) ) )).
fof(t2_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( r2_hidden(k8_finseq_1(k4_ordinal1,B,C),A) => k4_trees_1(A,k8_finseq_1(k4_ordinal1,B,C)) = k4_trees_1(k4_trees_1(A,B),C) ) ) ) ) )).
fof(t2_trees_a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t2_tsep_1,axiom,( ! [A] : ( l1_pre_topc(A) => m1_pre_topc(A,A) ) )).
fof(t2_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t2_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v4_pre_topc(C,A) & ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t2_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tsp_2(B,A) => v1_tops_1(B,A) ) ) ) )).
fof(t2_turing_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( 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)) ) ) )).
fof(t2_twoscomp,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( 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))) ) ) ) )).
fof(t2_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t2_unialg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m5_margrel1(C,u1_struct_0(A),k1_unialg_2(A)) => ( k19_margrel1(C) = k5_numbers => ( r2_unialg_2(A,B,C) <=> r2_hidden(k1_funct_1(C,k1_xboole_0),B) ) ) ) ) ) )).
fof(t2_uniform1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(B)))) => ( F = k8_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) ) ) ) ) ) ) ) ) )).
fof(t2_uproots,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ( ( r1_xxreal_0(2,k3_finseq_1(B)) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( 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)) ) ) ) )).
fof(t2_urysohn1,axiom,( k1_urysohn1(k5_numbers) = k7_domain_1(k4_ordinal1,k5_numbers,1) )).
fof(t2_urysohn2,axiom,( ! [A] : ( v1_xreal_0(A) => ( A != k5_numbers => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( B = k1_numbers => k1_integra2(B,A) = B ) ) ) ) )).
fof(t2_urysohn3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v10_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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] : ( v7_ordinal1(D) => ! [E] : ( m1_urysohn3(E,A,B,C,D) => ? [F] : ( m1_urysohn3(F,A,B,C,k1_nat_1(D,1)) & ! [G] : ( m2_subset_1(G,k1_numbers,k1_urysohn1(k1_nat_1(D,1))) => ( r2_hidden(G,k1_urysohn1(D)) => k4_urysohn1(A,k1_urysohn1(k1_nat_1(D,1)),F,G) = k1_funct_1(E,G) ) ) ) ) ) ) ) ) ) ) )).
fof(t2_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [E] : ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t2_valued_0,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ( v1_relat_1(B) & v2_valued_0(B) ) => ( r1_tarski(A,B) => v2_valued_0(A) ) ) ) )).
fof(t2_valued_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_membered(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t2_valued_2,axiom,( ! [A] : m1_subset_1(k5_valued_2(A),k1_zfmisc_1(k4_valued_2(A))) )).
fof(t2_vectmetr,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t2_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t2_vectsp11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ( r1_tarski(C,k2_finseq_1(A)) => k6_matrix13(u1_struct_0(B),k3_matrix_1(B,A),C,C) = k3_matrix_1(B,k5_card_1(C)) ) ) ) ) )).
fof(t2_vectsp_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k6_algstr_0(A,B,k4_struct_0(A)) = k4_struct_0(A) ) ) )).
fof(t2_vectsp_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t2_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v1_vectsp_4(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r2_hidden(D,C) => r2_hidden(k4_algstr_0(B,D),C) ) ) ) ) ) ) )).
fof(t2_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t2_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t2_vectsp_7,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ~ ( v1_vectsp_7(C,A,B) & r2_hidden(k4_struct_0(B),C) ) ) ) ) )).
fof(t2_vectsp_8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( 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)) ) ) ) )).
fof(t2_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t2_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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,k4_normsp_0(A,B,C),k1_tarski(k5_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))) ) ) ) ) )).
fof(t2_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( 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,k4_normsp_0(A,B,C),k1_tarski(k5_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))) ) ) ) ) )).
fof(t2_waybel10,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t2_waybel11,axiom,( ! [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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t2_waybel12,axiom,( ! [A] : ( v5_card_3(A) => r2_tarski(k4_ordinal1,A) ) )).
fof(t2_waybel13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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)))) ) ) )).
fof(t2_waybel14,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t2_waybel15,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k2_yellow_1(A))) => k6_waybel_0(k2_yellow_1(A),B) = a_2_0_waybel15(A,B) ) )).
fof(t2_waybel16,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t2_waybel17,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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) ) ) ) ) ) )).
fof(t2_waybel18,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)))) ) ) ) ) )).
fof(t2_waybel19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_waybel19(A) & l1_waybel_9(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t2_waybel20,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t2_waybel21,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ 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) ) ) ) ) ) )).
fof(t2_waybel22,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v3_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & v3_lattice3(C) & l1_orders_2(C) ) => ! [D] : ( m1_waybel16(D,A,B) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t2_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t2_waybel24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & l1_orders_2(B) ) => k3_yellow_0(k6_yellow_1(A,B)) = k6_struct_0(A,B,k3_yellow_0(B)) ) ) )).
fof(t2_waybel25,axiom,( ! [A] : ( 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) ) ) )).
fof(t2_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( 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)))) ) ) ) ) )).
fof(t2_waybel28,axiom,( ! [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] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ! [D] : ( m2_yellow_6(D,A,B) => C = k1_waybel11(A,D) ) => ( C = k1_waybel11(A,B) & ! [D] : ( m2_yellow_6(D,A,B) => r1_orders_2(A,k1_waybel_9(A,D),C) ) ) ) ) ) ) )).
fof(t2_waybel29,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_yellow_0(D,k5_yellow_1(k2_zfmisc_1(A,B),C)) ) => ! [E] : ( ( ~ v2_struct_0(E) & m1_yellow_0(E,k5_yellow_1(A,k5_yellow_1(B,C))) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t2_waybel30,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,k1_yellow_1(k7_waybel_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_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))) ) ) ) )).
fof(t2_waybel31,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v3_waybel_3(A) & l1_orders_2(A) ) => ? [B] : ( v6_waybel23(B,A) & m1_waybel23(B,A) & k1_card_1(B) = k1_waybel31(A) ) ) )).
fof(t2_waybel33,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ( u1_struct_0(A) = u1_struct_0(B) => ! [C] : ( l1_waybel_0(C,A) => ? [D] : ( 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)) ) ) ) ) ) )).
fof(t2_waybel34,axiom,( ! [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] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) )).
fof(t2_waybel35,axiom,( ! [A] : ( ( v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_waybel_4(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ( m1_waybel35(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t2_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( ~ v1_xboole_0(B) & v2_waybel_0(B,A) ) <=> ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r2_hidden(D,B) & r1_lattice3(A,C,D) ) ) ) ) ) )).
fof(t2_waybel_1,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t2_waybel_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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)) ) ) ) )).
fof(t2_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t2_waybel_4,axiom,( ! [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] : ( ( 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)) ) ) )).
fof(t2_waybel_5,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( ~ 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] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t2_waybel_6,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t2_waybel_7,axiom,( ! [A] : u1_struct_0(k2_yellow_1(A)) = k9_setfam_1(A) )).
fof(t2_waybel_8,axiom,( ! [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] : ( 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) ) ) ) )).
fof(t2_waybel_9,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & l1_orders_2(D) ) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t2_weddwitt,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,1) & ~ r1_xxreal_0(B,k5_numbers) & k1_newton(D,k2_xcmplx_0(k3_xcmplx_0(A,B),C)) != k3_xcmplx_0(k1_newton(D,A),k1_newton(D,k2_xcmplx_0(k2_nat_1(A,k7_nat_d(B,1)),C))) ) ) ) ) ) )).
fof(t2_weierstr,axiom,( ! [A] : ( ( v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [D] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ~ ( v1_finset_1(E) & v1_topmetr(E,A) & ? [F] : ( 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] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( v1_xreal_0(H) & 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),k8_metric_1(A,G,H))) ) ) ) ) ) ) ) ) ) ) )).
fof(t2_wellfnd1,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) & v1_card_5(A) ) => ! [B] : ( ( r1_tarski(B,A) & r2_hidden(k1_card_1(B),A) ) => r2_hidden(k3_ordinal2(B),A) ) ) )).
fof(t2_wellord1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( r2_hidden(A,k1_relat_1(B)) | k1_wellord1(B,A) = k1_xboole_0 ) ) )).
fof(t2_wellord2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( r1_tarski(B,A) => v2_wellord1(k1_wellord2(B)) ) ) )).
fof(t2_wellset1,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) ) ) )).
fof(t2_wsierp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ( k1_newton(k4_xcmplx_0(A),k3_xcmplx_0(2,B)) = k1_newton(A,k3_xcmplx_0(2,B)) & k1_newton(k4_xcmplx_0(A),k1_nat_1(k3_xcmplx_0(2,B),1)) = k4_xcmplx_0(k1_newton(A,k1_nat_1(k3_xcmplx_0(2,B),1))) ) ) ) )).
fof(t2_xboole_0,axiom,( ! [A] : ! [B] : ! [C] : ( ! [D] : ( ~ r2_hidden(D,A) <=> ( r2_hidden(D,B) <=> r2_hidden(D,C) ) ) => A = k5_xboole_0(B,C) ) )).
fof(t2_xboole_1,axiom,( ! [A] : r1_tarski(k1_xboole_0,A) )).
fof(t2_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k4_xboolean(A,k4_xboolean(A,B)) = k4_xboolean(A,B) ) ) )).
fof(t2_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( k2_xcmplx_0(A,C) = k2_xcmplx_0(B,C) => A = B ) ) ) ) )).
fof(t2_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(A,B) ) ) )).
fof(t2_xregular,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( r2_hidden(B,A) & ! [C] : ( r2_hidden(C,B) => r1_xboole_0(C,A) ) ) ) )).
fof(t2_xtuple_0,axiom,( ! [A] : ( v1_xtuple_0(A) => ! [B] : ( v1_xtuple_0(B) => ( ( k1_xtuple_0(A) = k1_xtuple_0(B) & k2_xtuple_0(A) = k2_xtuple_0(B) ) => A = B ) ) ) )).
fof(t2_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(B,C) ) => r1_xxreal_0(A,C) ) ) ) ) )).
fof(t2_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(C,k3_xxreal_1(A,B)) <=> ( ~ r1_xxreal_0(C,A) & r1_xxreal_0(C,B) ) ) ) ) ) )).
fof(t2_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( m2_xxreal_2(B,k1_tarski(A)) <=> r1_xxreal_0(B,A) ) ) ) )).
fof(t2_xxreal_3,axiom,( ! [A] : ( ( v1_xxreal_0(A) & v3_xxreal_0(A) & ~ v1_xreal_0(A) ) => A = k2_xxreal_0 ) )).
fof(t2_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ( v1_yellow_0(k3_yellow_3(A,B)) => ( v1_yellow_0(A) & v1_yellow_0(B) ) ) ) ) )).
fof(t2_yellow11,axiom,( k6_subset_1(2,1) = k6_domain_1(k4_ordinal1,1) )).
fof(t2_yellow12,axiom,( ! [A] : ! [B] : r1_tarski(k8_relset_1(B,k2_zfmisc_1(B,B),k12_funct_3(B),k2_zfmisc_1(A,A)),A) )).
fof(t2_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => v10_pre_topc(A) ) )).
fof(t2_yellow14,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k2_relset_1(A,k2_partfun1(A,A,k6_partfun1(A),B)) = B ) )).
fof(t2_yellow15,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k9_setfam_1(A)) => ! [C] : ( m2_finseq_1(C,k6_margrel1) => ! [D] : ( v7_ordinal1(D) => ( k1_funct_1(C,D) = k8_margrel1 => k1_funct_1(k1_yellow15(A,B,C),D) = k1_funct_1(B,D) ) ) ) ) )).
fof(t2_yellow16,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v4_yellow_0(C,B) & m1_yellow_0(C,B) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t2_yellow17,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( ( r2_hidden(D,k1_funct_1(A,C)) & r2_hidden(B,k4_card_3(A)) ) => r2_hidden(k1_funct_7(B,C,D),k4_card_3(A)) ) ) ) )).
fof(t2_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v16_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( v16_functor0(D,A,B) & m2_functor0(D,A,B) ) => ( ( ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k3_functor0(A,B,C,E) = k3_functor0(A,B,D,E) ) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( k1_altcat_1(A,E,F) != k1_xboole_0 => ! [G] : ( 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)) ) ) ) ) ) )).
fof(t2_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( r2_hidden(C,k1_yellow19(A,B)) <=> m1_connsp_2(C,A,B) ) ) ) )).
fof(t2_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v8_functor0(C,A,B) & v10_functor0(C,A,B) & l2_functor0(C,A,B) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( k1_altcat_1(A,E,F) != k1_xboole_0 => ! [G] : ( m1_subset_1(G,k1_altcat_1(A,E,F)) => ! [H] : ( 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 ) ) ) ) ) ) ) ) ) ) ) )).
fof(t2_yellow21,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k8_altcat_1(A,B) = k3_struct_0(k1_yellow21(B)) ) ) )).
fof(t2_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [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] : ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t2_yellow_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k2_yellow_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_yellow_1(A))) => ( r3_orders_2(k2_yellow_1(A),B,C) <=> r1_tarski(B,C) ) ) ) )).
fof(t2_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(C,k6_waybel_0(A,B)) <=> r1_lattice3(A,C,B) ) ) ) ) )).
fof(t2_yellow_3,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t2_yellow_4,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ! [C] : ( 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) ) ) ) )).
fof(t2_yellow_5,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k12_lattice3(A,B,B) = B ) ) )).
fof(t2_yellow_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v2_pralg_1(B) ) => ! [C] : ( m1_subset_1(C,A) => k1_funct_1(k12_pralg_1(A,B),C) = u1_struct_0(k10_pralg_1(A,B,C)) ) ) ) )).
fof(t2_yellow_7,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t2_yellow_8,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(t2_yellow_9,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) )).
fof(t2_yoneda_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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))) ) ) )).
fof(t2_zf_colla,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ( ! [C] : ( m1_subset_1(C,A) => ~ r2_hidden(C,B) ) <=> r2_hidden(B,k1_zf_colla(A,k1_xboole_0)) ) ) ) )).
fof(t2_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ! [D] : ( 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) ) ) ) ) ) )).
fof(t2_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ( k5_zf_lang(A,B) = k5_zf_lang(C,D) => ( A = C & B = D ) ) ) ) ) ) )).
fof(t2_zf_lang1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ( k18_zf_lang(k5_zf_lang(A,B)) = A & k19_zf_lang(k5_zf_lang(A,B)) = B ) ) ) )).
fof(t2_zf_model,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t2_zf_refle,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => r2_zf_model(A,k8_zf_model) ) )).
fof(t2_zfmisc_1,axiom,( k3_tarski(k1_xboole_0) = k1_xboole_0 )).
fof(t2_zfmodel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_ordinal1(A) => ( r2_zf_model(A,k7_zf_model) <=> ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => r2_hidden(k2_tarski(B,C),A) ) ) ) ) ) )).
fof(t2_zfmodel2,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ( ~ r2_hidden(B,k4_zf_lang1(C)) => ( ( r2_hidden(A,k2_zf_model(C)) => 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)) ) & ( ~ r2_hidden(A,k2_zf_model(C)) => k2_zf_model(k6_zf_lang1(C,A,B)) = k2_zf_model(C) ) ) ) ) ) ) )).
fof(t2_zfrefle1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_zf_lang)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_zf_lang)) => ( ( r1_tarski(B,C) & r1_zfrefle1(A,C) ) => r1_zfrefle1(A,B) ) ) ) ) )).
fof(t2_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k4_algstr_0(A,B) = k1_zmodul01(A,B,k4_xcmplx_0(1)) ) ) )).
fof(t2_zmodul02,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( ~ 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] : ( m1_zmodul01(D,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(k10_zmodul02(C,D))) => ( D = k5_zmodul02(C,A) => ( A = k5_numbers | k1_zmodul01(k10_zmodul02(C,D),E,B) = k1_zmodul01(k10_zmodul02(C,D),E,k5_int_1(B,A)) ) ) ) ) ) ) ) )).
fof(t2_zmodul03,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k4_numbers) => ! [C] : ( m1_subset_1(C,k4_numbers) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( A = g1_zmodul01(u1_struct_0(k1_int_3),u2_struct_0(k1_int_3),u1_algstr_0(k1_int_3),k12_zmodul01(k1_int_3)) & D = C ) => k1_zmodul01(A,D,B) = k3_xcmplx_0(B,C) ) ) ) ) ) )).
fof(t300_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(C,D) & r1_xxreal_0(A,B) ) => k6_subset_1(k1_xxreal_1(C,B),k4_xxreal_1(A,D)) = k2_xboole_0(k1_xxreal_1(C,A),k1_xxreal_1(D,B)) ) ) ) ) ) )).
fof(t301_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(A,B) => ( r1_xxreal_0(D,C) | k6_subset_1(k4_xxreal_1(C,B),k2_xxreal_1(A,D)) = k2_xboole_0(k4_xxreal_1(C,A),k2_xxreal_1(D,B)) ) ) ) ) ) ) )).
fof(t302_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(C,D) & r1_xxreal_0(A,B) ) => k6_subset_1(k2_xxreal_1(C,B),k2_xxreal_1(A,D)) = k2_xboole_0(k2_xxreal_1(C,A),k2_xxreal_1(D,B)) ) ) ) ) ) )).
fof(t303_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(A,B) => ( r1_xxreal_0(D,C) | k6_subset_1(k3_xxreal_1(C,B),k2_xxreal_1(A,D)) = k2_xboole_0(k4_xxreal_1(C,A),k1_xxreal_1(D,B)) ) ) ) ) ) ) )).
fof(t304_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(C,D) & r1_xxreal_0(A,B) ) => k6_subset_1(k1_xxreal_1(C,B),k2_xxreal_1(A,D)) = k2_xboole_0(k2_xxreal_1(C,A),k1_xxreal_1(D,B)) ) ) ) ) ) )).
fof(t305_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(D,C) & ~ r1_xxreal_0(B,A) & k6_subset_1(k4_xxreal_1(C,B),k3_xxreal_1(A,D)) != k2_xboole_0(k3_xxreal_1(C,A),k4_xxreal_1(D,B)) ) ) ) ) ) )).
fof(t306_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(C,D) => ( r1_xxreal_0(B,A) | k6_subset_1(k2_xxreal_1(C,B),k3_xxreal_1(A,D)) = k2_xboole_0(k1_xxreal_1(C,A),k4_xxreal_1(D,B)) ) ) ) ) ) ) )).
fof(t307_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(A,B) => ( r1_xxreal_0(D,C) | k6_subset_1(k3_xxreal_1(C,B),k3_xxreal_1(A,D)) = k2_xboole_0(k3_xxreal_1(C,A),k3_xxreal_1(D,B)) ) ) ) ) ) ) )).
fof(t308_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(C,D) & r1_xxreal_0(A,B) ) => k6_subset_1(k1_xxreal_1(C,B),k3_xxreal_1(A,D)) = k2_xboole_0(k1_xxreal_1(C,A),k3_xxreal_1(D,B)) ) ) ) ) ) )).
fof(t309_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(C,D) & r1_xxreal_0(A,B) ) => k6_subset_1(k4_xxreal_1(C,B),k1_xxreal_1(A,D)) = k2_xboole_0(k4_xxreal_1(C,A),k4_xxreal_1(D,B)) ) ) ) ) ) )).
fof(t30_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k8_abcmiz_0(A,B,k6_finseq_1(u1_abcmiz_0(A))) = B ) ) )).
fof(t30_abcmiz_1,axiom,( ! [A] : ( ( v2_funct_1(A) & m2_finseq_1(A,k2_abcmiz_1) ) => ( m2_finseq_2(A,k2_abcmiz_1,k4_abcmiz_1) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k2_abcmiz_1) => ( ( r2_hidden(B,k4_finseq_1(A)) & C = k1_funct_1(A,B) ) => ! [D] : ( m1_subset_1(D,k2_abcmiz_1) => ~ ( r2_hidden(D,k3_abcmiz_1(C)) & ! [E] : ( v7_ordinal1(E) => ~ ( r2_hidden(E,k4_finseq_1(A)) & ~ r1_xxreal_0(B,E) & D = k1_funct_1(A,E) ) ) ) ) ) ) ) ) ) )).
fof(t30_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t30_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) ) )).
fof(t30_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t30_afinsq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_finset_1(B) & v6_membered(B) ) => ! [C] : ( ( v1_finset_1(C) & v6_membered(C) ) => ( r1_afinsq_2(B,C) => ( r1_xxreal_0(k5_card_1(C),A) | ( k2_relset_1(k4_ordinal1,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)),k1_nat_1(A,k5_card_1(B))) ) ) ) ) ) ) )).
fof(t30_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t30_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k1_afvect0(A,D,B) = k1_afvect0(A,D,C) => B = C ) ) ) ) ) )).
fof(t30_algspec1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t30_algstr_4,axiom,( ! [A] : A = a_1_0_algstr_4(A) )).
fof(t30_altcat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_2(B,A) & m1_altcat_2(B,A) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t30_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v16_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t30_ami_3,axiom,( ! [A] : ( m1_subset_1(A,k3_scm_inst) => r1_xxreal_0(k2_compos_0(k3_scm_inst,A),8) ) )).
fof(t30_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,C)) => r1_ami_wstd(A,B,D,k6_ami_wstd(A,B,C)) ) ) ) ) ) )).
fof(t30_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_analmetr(A,B,C))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t30_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( r1_analmetr(A,F,G) & r1_analort(A,F,G,B,D,C,E) & r1_analort(A,F,G,B,D,E,C) & B != D & C != E ) ) ) ) ) ) ) ) )).
fof(t30_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => ~ ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & ? [I] : ( v1_xreal_0(I) & ? [J] : ( v1_xreal_0(J) & 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] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( 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 = k5_numbers & G = k5_numbers & H = k5_numbers & I = k5_numbers ) ) ) ) ) ) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(k5_anproj_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_anproj_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_anproj_1(A))) => ~ ( ~ r1_collsp(k5_anproj_1(A),B,C,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(k5_anproj_1(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k5_anproj_1(A))) => ? [G] : ( m1_subset_1(G,u1_struct_0(k5_anproj_1(A))) & ? [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t30_aofa_000,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( m1_freealg(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( v7_ordinal1(D) & r2_hidden(C,k9_aofa_000(A,B,D)) ) ) ) ) ) )).
fof(t30_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ( k4_finseq_1(k7_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H),k10_finseq_1(I,J))) = k2_finseq_1(10) & k1_funct_1(k7_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H),k10_finseq_1(I,J)),1) = A & k1_funct_1(k7_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H),k10_finseq_1(I,J)),2) = B & k1_funct_1(k7_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H),k10_finseq_1(I,J)),3) = C & k1_funct_1(k7_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H),k10_finseq_1(I,J)),4) = D & k1_funct_1(k7_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H),k10_finseq_1(I,J)),5) = E & k1_funct_1(k7_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H),k10_finseq_1(I,J)),6) = F & k1_funct_1(k7_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H),k10_finseq_1(I,J)),7) = G & k1_funct_1(k7_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H),k10_finseq_1(I,J)),8) = H & k1_funct_1(k7_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H),k10_finseq_1(I,J)),9) = I & k1_funct_1(k7_finseq_1(k9_aofa_a00(A,B,C,D,E,F,G,H),k10_finseq_1(I,J)),10) = J ) )).
fof(t30_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( m2_subset_1(F,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => k15_aofa_a00(A,B,C,D,u8_aofa_a00(A),k21_aofa_a00(A,C),F) = k8_margrel1 ) ) ) ) ) ) )).
fof(t30_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [E] : ( ( v1_aofa_i00(E,A,B,D) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),D) ) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),E) => ! [G] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t30_armstrng,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t30_arytm_3,axiom,( ! [A] : ! [B] : ~ v3_ordinal1(k4_tarski(A,B)) )).
fof(t30_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & v2_asympt_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( r2_hidden(A,k8_asympt_0(B)) & r2_hidden(B,k8_asympt_0(C)) ) => r2_hidden(A,k8_asympt_0(C)) ) ) ) ) )).
fof(t30_asympt_1,axiom,( ? [A] : ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v4_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & r2_funct_2(k4_ordinal1,k1_numbers,A,k1_asympt_1(2,2,k5_numbers)) & r1_tarski(k6_asympt_0(A),k6_asympt_0(k4_asympt_1(k5_numbers))) & k6_asympt_0(A) != k6_asympt_0(k4_asympt_1(k5_numbers)) ) )).
fof(t30_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_autalg_1(C,u1_struct_0(A),u3_msualg_1(A,B),k5_autalg_1(A,B)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t30_autgroup,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k5_autgroup(A))) => B = k1_group_1(k5_autgroup(A)) ) ) ) )).
fof(t30_bagorder,axiom,( ! [A] : ( v7_ordinal1(A) => k9_bagorder(A) = k4_yellow_1(A,k7_funcop_1(A,k11_dickson)) ) )).
fof(t30_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( r2_hidden(B,k5_bcialg_1(A)) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_bcialg_1(A,k1_bcialg_1(A,C,B)) = k1_bcialg_1(A,B,C) ) ) ) ) )).
fof(t30_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v10_bcialg_1(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & B = k2_bcialg_1(A,C) ) ) ) ) )).
fof(t30_bcialg_3,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t30_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t30_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( 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,k1_nat_1(C,1),C,A) ) ) ) ) ) ) ) ) )).
fof(t30_bcialg_6,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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,k5_numbers) | k4_bcialg_6(A,k3_bcialg_6(A,C,B)) = k4_int_1(D,k6_nat_d(C,D)) ) ) ) ) ) ) )).
fof(t30_bciideal,axiom,( ! [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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) )).
fof(t30_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k3_bhsp_1(A,k3_rlvect_1(A,B,C)),k2_xcmplx_0(k3_bhsp_1(A,B),k3_bhsp_1(A,C))) ) ) ) )).
fof(t30_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)))) & k1_seq_2(k2_bhsp_2(A,k4_normsp_1(A,k5_normsp_1(A,D,C),k1_rlvect_1(A,B,C)))) = k5_numbers ) ) ) ) ) ) )).
fof(t30_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( ! [C] : ( v7_ordinal1(C) => k1_normsp_1(A,B,C) != k4_struct_0(A) ) & ? [C] : ( v7_ordinal1(C) & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => r1_xxreal_0(1,k7_xcmplx_0(k3_bhsp_1(A,k1_normsp_1(A,B,k1_nat_1(D,1))),k3_bhsp_1(A,k1_normsp_1(A,B,D)))) ) ) ) & v1_bhsp_4(B,A) ) ) ) )).
fof(t30_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v4_rlvect_1(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t30_binari_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(t30_binari_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t30_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t30_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t30_borsuk_4,axiom,( u1_struct_0(k1_borsuk_4) = k6_subset_1(u1_struct_0(k5_topmetr),k7_domain_1(k4_ordinal1,k5_numbers,1)) )).
fof(t30_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t30_borsuk_6,axiom,( ! [A] : ( 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))) ) ) )).
fof(t30_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( r1_zfmisc_1(A,B,C) => k4_card_3(k1_borsuk_7(A,B,C,k1_tarski(D),k1_tarski(E),k1_tarski(F))) = k1_tarski(k1_borsuk_7(A,B,C,D,E,F)) ) )).
fof(t30_bspace,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t30_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t30_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_subset_1(H,A) => ! [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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t30_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t30_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t30_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_eqrel_1(C,A) => r2_bvfunc_1(A,k17_bvfunc_1(A,B,C),C) ) ) ) )).
fof(t30_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(E,A) => ( r3_bvfunc_2(A,D,B,E) => r1_bvfunc_1(A,k6_bvfunc_2(A,k10_bvfunc_1(A,D,C),B,E),k10_bvfunc_1(A,D,k6_bvfunc_2(A,C,B,E))) ) ) ) ) ) ) )).
fof(t30_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t30_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(t30_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t30_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t30_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_xreal_0(B) => ! [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))) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k11_c0sp1(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k11_c0sp1(A))) => ( ( C = E & D = F ) => ( F = k1_rlvect_1(k11_c0sp1(A),E,B) <=> ! [G] : ( m1_subset_1(G,A) => k3_funct_2(A,k1_numbers,D,G) = k3_xcmplx_0(B,k3_funct_2(A,k1_numbers,C,G)) ) ) ) ) ) ) ) ) ) )).
fof(t30_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( r2_hidden(B,k6_c0sp2(A)) => r2_hidden(B,k6_c0sp1(u1_struct_0(A))) ) ) )).
fof(t30_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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))))) ) ) )).
fof(t30_calcul_2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k1_relset_1(k4_ordinal1,C),k1_relset_1(k4_ordinal1,C)) & v3_funct_2(D,k1_relset_1(k4_ordinal1,C),k1_relset_1(k4_ordinal1,C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_relset_1(k4_ordinal1,C),k1_relset_1(k4_ordinal1,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))) ) ) ) ) ) )).
fof(t30_card_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(t30_card_2,axiom,( ! [A] : k3_card_2(2,k1_card_1(A)) = k1_card_1(k1_zfmisc_1(A)) )).
fof(t30_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_card_3(B) ) => ( ( k9_xtuple_0(A) = k9_xtuple_0(B) & ! [C] : ( 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)) ) ) ) )).
fof(t30_card_5,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ( v1_card_5(k4_ordinal1) & v1_card_5(k2_card_1(A)) ) ) )).
fof(t30_card_fil,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ( v6_card_fil(A) => v4_card_fil(A) ) ) )).
fof(t30_card_fin,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( r2_hidden(C,k8_relat_1(B,k1_tarski(D))) => r1_tarski(k2_card_fin(A,B,D),k1_funct_1(A,C)) ) ) ) )).
fof(t30_card_lar,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) & ~ v4_card_3(A) ) => ( v5_card_lar(A) => v5_card_fil(A) ) ) )).
fof(t30_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v7_cat_1(k4_cat_1(A,B),A,B,B) ) ) )).
fof(t30_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t30_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t30_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => k5_card_1(k2_catalan2(k2_xcmplx_0(2,A),1)) = k1_nat_1(A,1) ) )).
fof(t30_catalg_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u4_struct_0(A)) => ! [H] : ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t30_cayldick,axiom,( k6_algstr_0(k4_cayldick(k4_cayldick(k3_cayldick)),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k5_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick))),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k5_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)))) = k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k5_struct_0(k3_cayldick))) )).
fof(t30_cc0sp2,axiom,( ! [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_clopban1(A) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) ) )).
fof(t30_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v3_funct_1(A) & v2_comseq_2(B) ) => ( k3_comseq_2(k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)) = k2_xcmplx_0(k3_funct_2(k4_ordinal1,k2_numbers,A,k5_numbers),k3_comseq_2(B)) & k3_comseq_2(k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)) = k6_xcmplx_0(k3_funct_2(k4_ordinal1,k2_numbers,A,k5_numbers),k3_comseq_2(B)) & k3_comseq_2(k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,A)) = k6_xcmplx_0(k3_comseq_2(B),k3_funct_2(k4_ordinal1,k2_numbers,A,k5_numbers)) & k3_comseq_2(k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)) = k3_xcmplx_0(k3_funct_2(k4_ordinal1,k2_numbers,A,k5_numbers),k3_comseq_2(B)) ) ) ) ) )).
fof(t30_cfdiff_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [C] : ( ( 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] : ( v1_xcmplx_0(D) => ( r2_hidden(D,C) => k7_partfun1(k2_numbers,k3_cfdiff_1(k25_valued_1(k2_numbers,k2_numbers,B,A),C),D) = k3_xcmplx_0(A,k2_cfdiff_1(B,D)) ) ) ) ) ) ) ) )).
fof(t30_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( v1_xcmplx_0(C) => 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),k9_complex1(C))) ) ) ) )).
fof(t30_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_chain_1(C,B) => ( r1_xxreal_0(A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_euclid(B))) => ( r2_hidden(D,k4_chain_1(B,C,A)) <=> ? [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(B)) & ? [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(B)) & D = k3_chain_1(B,E,F) & ~ ( ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k2_finseq_1(B))) => ~ ( k5_card_1(G) = A & ! [H] : ( m2_subset_1(H,k4_ordinal1,k2_finseq_1(B)) => ( ( r2_hidden(H,G) & ~ r1_xxreal_0(k1_funct_1(F,H),k1_funct_1(E,H)) & m2_chain_1(k4_tarski(k1_funct_1(E,H),k1_funct_1(F,H)),k2_chain_1(B,C,H)) ) | ( ~ r2_hidden(H,G) & k1_funct_1(E,H) = k1_funct_1(F,H) & r2_hidden(k1_funct_1(E,H),k2_chain_1(B,C,H)) ) ) ) ) ) & ~ ( A = B & ! [G] : ( m2_subset_1(G,k4_ordinal1,k2_finseq_1(B)) => ( ~ r1_xxreal_0(k1_funct_1(E,G),k1_funct_1(F,G)) & m2_chain_1(k4_tarski(k1_funct_1(E,G),k1_funct_1(F,G)),k2_chain_1(B,C,G)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t30_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k6_glib_000(A))) ) => ( r1_tarski(C,B) => ! [D] : ( m2_glib_000(D,A,B,k21_glib_000(A,B)) => ! [E] : ( m2_glib_000(E,A,C,k21_glib_000(A,C)) => m2_glib_000(E,D,C,k21_glib_000(D,C)) ) ) ) ) ) ) )).
fof(t30_circcmb3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_circcmb3(B,A) => ! [C] : ( m1_circcmb3(C,A) => ! [D] : ( m2_circcmb3(D,A,B) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t30_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( v4_msualg_1(F,C) & v4_msafree2(F,C) & l3_msualg_1(F,C) ) => ! [G] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(C,F))) => ! [H] : ( 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] : ( m1_subset_1(I,u4_struct_0(C)) => ! [J] : ( m1_subset_1(J,u4_struct_0(A)) => ( I = J => k3_circuit1(C,F,G,I) = k3_circuit1(A,D,H,J) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t30_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r3_pua2mss1(A,B,C,D) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => m1_subset_1(k1_funct_1(C,E),u1_struct_0(B)) ) ) ) ) ) ) )).
fof(t30_classes1,axiom,( ! [A] : ( v3_ordinal1(A) => k4_classes1(k1_ordinal1(A)) = k9_setfam_1(k4_classes1(A)) ) )).
fof(t30_classes2,axiom,( ! [A] : ( ( v2_classes1(A) & v1_ordinal1(A) ) => r1_tarski(A,k4_classes1(k1_card_1(A))) ) )).
fof(t30_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t30_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k1_power(D,k9_nat_1(k1_numbers,k5_normsp_0(A,B),D)) ) & v2_comseq_2(C) ) => ( r1_xxreal_0(1,k1_seq_2(C)) | v2_clopban3(B,A) ) ) ) ) ) )).
fof(t30_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => k9_complex1(k9_nat_1(k1_numbers,k3_series_1(k5_normsp_0(A,k5_clopban4(A,C,B,D))),E)) = k9_nat_1(k1_numbers,k3_series_1(k5_normsp_0(A,k5_clopban4(A,C,B,D))),E) ) ) ) ) ) )).
fof(t30_closure1,axiom,( ! [A] : ( l1_struct_0(A) => ! [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] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t30_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_closure2(C,A,B,k2_closure2(A,B)) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t30_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_clvect_1(B,A) => k4_struct_0(B) = k4_struct_0(A) ) ) )).
fof(t30_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)))) & k1_seq_2(k2_clvect_2(A,k4_normsp_1(A,k6_clvect_1(A,D,C),k1_clvect_1(A,B,C)))) = k5_numbers ) ) ) ) ) ) )).
fof(t30_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( ! [C] : ( v7_ordinal1(C) => k1_normsp_0(A,B,C) != k4_struct_0(A) ) & ? [C] : ( v7_ordinal1(C) & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => r1_xxreal_0(1,k7_xcmplx_0(k13_csspace(A,k1_normsp_0(A,B,k1_nat_1(D,1))),k13_csspace(A,k1_normsp_0(A,B,D)))) ) ) ) & v1_clvect_3(B,A) ) ) ) )).
fof(t30_coh_sp,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r2_hidden(k6_partfun1(A),k15_coh_sp(B)) ) )).
fof(t30_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(t30_combgras,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ( r1_ordinal1(k1_nat_1(A,1),k1_card_1(B)) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ( k5_card_1(C) = k6_xcmplx_0(A,1) => k1_setfam_1(k7_combgras(A,B,C)) = C ) ) ) ) ) )).
fof(t30_complex1,axiom,( k8_complex1(k6_complex1) = k6_complex1 )).
fof(t30_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k9_complex1(k1_complex2(A,B)) = k3_xcmplx_0(k9_complex1(A),k9_complex1(B)) ) ) )).
fof(t30_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( 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) ) ) ) )).
fof(t30_complsp2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t30_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(A)) & v1_funct_1(C) & v1_finset_1(C) ) => ! [D] : ( v7_ordinal1(D) => ( r1_tarski(B,C) => r1_tarski(k6_compos_1(A,B,D),k6_compos_1(A,C,D)) ) ) ) ) ) )).
fof(t30_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( 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 ) ) )).
fof(t30_comptrig,axiom,( k10_xtuple_0(k2_partfun1(k1_numbers,k1_numbers,k16_sin_cos,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2)))) = k1_rcomp_1(k4_xcmplx_0(1),1) )).
fof(t30_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => r2_hidden(k3_comput_1(B,A),k2_comput_1(k4_ordinal1)) ) ) )).
fof(t30_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v9_ordinal1(A) => r2_relset_1(k4_ordinal1,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,A),A),B) ) ) ) )).
fof(t30_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v2_comseq_2(A) & v1_comseq_2(B) & k3_comseq_2(A) = k5_complex1 ) => k3_comseq_2(k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)) = k5_complex1 ) ) ) )).
fof(t30_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_complex1(k9_nat_1(k2_numbers,k10_comseq_3(A),B)),k9_nat_1(k1_numbers,k3_series_1(k55_valued_1(k4_ordinal1,k2_numbers,A)),B)) ) ) )).
fof(t30_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( ~ v4_conlat_1(B,A) & v6_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) ) ) ) )).
fof(t30_connsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_connsp_1(A,B,C) ) ) => v1_connsp_1(A) ) ) )).
fof(t30_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(t30_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t30_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_convex4(B,A) => r1_convex4(A,k7_convex4(A,k6_complex1,B),B) ) ) )).
fof(t30_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) )).
fof(t30_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ( B = a_2_0_cqc_the1(A,C) => v1_cqc_the1(B,A) ) ) ) ) )).
fof(t30_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t30_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t30_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k12_csspace(A,B,k4_struct_0(A)) = k5_numbers ) ) )).
fof(t30_csspace4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_comseq_2(A) <=> v1_comseq_2(k55_valued_1(k4_ordinal1,k2_numbers,A)) ) ) )).
fof(t30_descip_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( m2_finseq_2(D,k4_finseq_2(B,k6_margrel1),k4_finseq_2(C,k4_finseq_2(B,k6_margrel1))) => ! [E] : ( ( 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] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_finseq_2(k2_nat_1(2,A),k6_margrel1),k4_finseq_2(k2_nat_1(2,A),k6_margrel1)) & v3_funct_2(F,k4_finseq_2(k2_nat_1(2,A),k6_margrel1),k4_finseq_2(k2_nat_1(2,A),k6_margrel1)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(k2_nat_1(2,A),k6_margrel1),k4_finseq_2(k2_nat_1(2,A),k6_margrel1)))) ) => ! [G] : ( m2_finseq_2(G,k6_margrel1,k4_finseq_2(k2_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 ) ) ) ) ) ) ) )).
fof(t30_dickson,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) ) )).
fof(t30_diff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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) = k5_numbers ) ) ) ) )).
fof(t30_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( v1_xreal_0(J) => k1_funct_1(I,J) = k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(F,k1_square_1(J)),k3_xcmplx_0(G,J)),H) ) & r3_zfmisc_1(A,B,C,D,E) ) => k1_diff_2(I,A,B,C,D,E) = k5_numbers ) ) ) ) ) ) ) ) ) ) )).
fof(t30_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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) = k6_xcmplx_0(k3_xcmplx_0(A,k9_diff_1(E,C,D)),k3_xcmplx_0(B,k9_diff_1(F,C,D))) ) ) ) ) ) ) )).
fof(t30_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & k9_diff_1(k3_taylor_1,A,B) != k7_xcmplx_0(k1_funct_1(k3_taylor_1,k7_xcmplx_0(A,B)),k6_xcmplx_0(A,B)) ) ) ) )).
fof(t30_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t30_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t30_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => ! [C] : ( ( 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_xxreal_0(k5_numbers,k6_dist_2(A,B,C)) ) ) ) )).
fof(t30_domain_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k7_subset_1(A,B,C) = a_3_3_domain_1(A,B,C) ) ) ) )).
fof(t30_e_siec,axiom,( ! [A] : ( ( 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 ) ) )).
fof(t30_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ? [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) & ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ~ ( C != k4_struct_0(k9_int_3(A)) & ! [D] : ( v7_ordinal1(D) => C != k2_binom(k9_int_3(A),B,D) ) ) ) ) ) )).
fof(t30_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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)) ) ) ) )).
fof(t30_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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 ) ) ) )).
fof(t30_entropy1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( 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] : ( v7_ordinal1(D) => ( r1_xxreal_0(1,D) => ( r1_xxreal_0(k3_finseq_1(B),D) | k1_matrprob(A,C,k1_nat_1(D,1)) = k8_finseq_1(A,k1_matrprob(A,C,D),k1_matrprob(A,B,k1_nat_1(D,1))) ) ) ) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( 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))) ) ) ) ) ) ) ) )).
fof(t30_enumset1,axiom,( ! [A] : ! [B] : k1_enumset1(A,A,B) = k2_tarski(A,B) )).
fof(t30_eqrel_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(t30_equation,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t30_euclid,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k1_rlvect_1(k15_euclid(2),k19_euclid(B,C),A) = k19_euclid(k3_xcmplx_0(A,B),k3_xcmplx_0(A,C)) ) ) ) )).
fof(t30_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => k22_rvsum_1(B,k4_struct_0(k15_euclid(A))) = k5_numbers ) ) )).
fof(t30_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( k3_euclid_3(A) = k5_numbers => ( A = k19_euclid(k12_euclid(A),k5_numbers) & k18_euclid(A) = k5_numbers ) ) ) )).
fof(t30_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => k22_rvsum_1(k7_euclid(A,B,C),k7_euclid(A,D,E)) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k22_rvsum_1(B,D),k22_rvsum_1(B,E)),k22_rvsum_1(C,D)),k22_rvsum_1(C,E)) ) ) ) ) ) )).
fof(t30_euclid_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => k22_rvsum_1(k4_euclid_5(C,D,A),k4_euclid_5(E,F,B)) = k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(C,E),k3_xcmplx_0(D,F)),k3_xcmplx_0(A,B)) ) ) ) ) ) ) )).
fof(t30_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t30_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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,k3_xcmplx_0(A,k1_funct_1(B,1))),k9_euclid(3,k3_euclid_8,k3_xcmplx_0(A,k1_funct_1(B,2)))),k9_euclid(3,k4_euclid_8,k3_xcmplx_0(A,k1_funct_1(B,3)))) ) ) )).
fof(t30_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t30_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(D) & v5_relat_1(D,C) & v1_funct_1(D) & v1_exchsort(D) ) => ( ( r2_hidden(A,k9_xtuple_0(D)) & r2_hidden(B,k9_xtuple_0(D)) ) => k7_partfun1(C,k9_funct_7(D,A,B),A) = k7_partfun1(C,D,B) ) ) )).
fof(t30_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) & 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) ) ) ) ) ) )).
fof(t30_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_circcomb(A) & v2_circcomb(A) & v3_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v4_msafree2(C,A) & v4_circcomb(C,A) & v6_circcomb(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msafree2(D,B) & v4_circcomb(D,B) & v6_circcomb(D,B) & l3_msualg_1(D,B) ) => ! [E] : ( m1_subset_1(E,k4_card_3(u3_msualg_1(k2_circcomb(A,B),k3_circcomb(A,B,C,D)))) => ! [F] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t30_facirc_2,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k19_facirc_1(A,B,C),k20_facirc_1(A,B,C)))) & ? [E] : ( m1_subset_1(E,k6_margrel1) & ? [F] : ( m1_subset_1(F,k6_margrel1) & ? [G] : ( 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)) ) ) ) ) ) ) )).
fof(t30_fcont_1,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( r2_hidden(B,k1_relset_1(k1_numbers,A)) & r2_hidden(C,k1_relset_1(k1_numbers,A)) & k1_funct_1(A,B) = k2_seq_4(k2_relset_1(k1_numbers,A)) & k1_funct_1(A,C) = k3_seq_4(k2_relset_1(k1_numbers,A)) ) ) ) ) ) )).
fof(t30_fdiff_10,axiom,( ! [A] : ( ( 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,k22_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos)))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos)),A),B) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(k22_sin_cos,B),k6_xcmplx_0(k1_funct_1(k26_sin_cos,B),k1_funct_1(k27_sin_cos,B))),k3_xcmplx_0(k1_funct_1(k22_sin_cos,B),k2_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B)))))) ) ) ) ) ) )).
fof(t30_fdiff_11,axiom,( ! [A] : ( ( 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,k26_sin_cos,k2_sin_cos9))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k2_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k2_sin_cos9),A),B) = k6_xcmplx_0(k7_xcmplx_0(k1_funct_1(k2_sin_cos9,B),k1_square_1(k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(k1_funct_1(k26_sin_cos,B),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t30_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ~ ( r2_hidden(C,k10_prob_1(A)) & r1_xxreal_0(k5_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))) ) ) ) ) )).
fof(t30_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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(k7_xcmplx_0(1,2))),2))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k1_funct_1(C,D) = k2_xcmplx_0(A,D) & ~ r1_xxreal_0(k1_funct_1(C,D),k5_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(k7_xcmplx_0(1,2))),2),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_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(k7_xcmplx_0(1,2))),2),B),D) = k6_prepower(k2_xcmplx_0(A,D),k4_xcmplx_0(k7_xcmplx_0(1,2))) ) ) ) ) ) ) ) )).
fof(t30_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k22_sin_cos,C),k1_taylor_1(2)),k22_sin_cos),k3_taylor_1) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_1(C,D) = 1 ) ) ) => ( r2_fdiff_1(B,A) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_1(k2_fdiff_1(B,A),D) = k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(k22_sin_cos,D),1),k2_xcmplx_0(k1_funct_1(k22_sin_cos,D),1)) ) ) ) ) ) ) ) )).
fof(t30_fdiff_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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)),k4_xcmplx_0(k7_xcmplx_0(1,A))))) & ! [C] : ( v1_xreal_0(C) => ~ ( r2_hidden(C,B) & k1_funct_1(k16_sin_cos,C) = k5_numbers ) ) ) => ( r1_xxreal_0(A,k5_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)),k4_xcmplx_0(k7_xcmplx_0(1,A))),B) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => k1_funct_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)),k4_xcmplx_0(k7_xcmplx_0(1,A))),B),C) = k7_xcmplx_0(k1_funct_1(k18_sin_cos,C),k3_prepower(k1_funct_1(k16_sin_cos,C),k2_xcmplx_0(A,1))) ) ) ) ) ) ) ) )).
fof(t30_fdiff_8,axiom,( ! [A] : ( ( 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,k22_sin_cos,k26_sin_cos))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k26_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k26_sin_cos),A),B) = k2_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_funct_1(k16_sin_cos,B)),k1_funct_1(k18_sin_cos,B)),k7_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_square_1(k1_funct_1(k18_sin_cos,B)))) ) ) ) ) ) )).
fof(t30_fdiff_9,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k1_fdiff_9),A),B) = k2_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(1,k1_funct_1(k18_sin_cos,B)),B),k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k3_taylor_1,B),k1_funct_1(k16_sin_cos,B)),k1_square_1(k1_funct_1(k18_sin_cos,B)))) ) ) ) ) ) )).
fof(t30_fib_num2,axiom,( ! [A] : ( 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))) ) )).
fof(t30_fib_num3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k6_xcmplx_0(k2_nat_1(5,k11_newton(k1_pre_ff(A),2)),k11_newton(k1_fib_num3(A),2)) = k3_xcmplx_0(4,k2_power(k4_xcmplx_0(1),k1_nat_1(A,1))) ) )).
fof(t30_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(2,A) => k1_fib_num3(A) = k1_int_1(k2_xcmplx_0(k2_power(k1_fib_num,A),k7_xcmplx_0(1,2))) ) ) )).
fof(t30_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_finseq_1(B,A) => ! [C] : ( 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))) ) ) ) ) )).
fof(t30_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ 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(C,D) => r2_hidden(k4_filter_0(A,B,C),D) ) ) ) ) ) )).
fof(t30_filter_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t30_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t30_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => r1_tarski(k10_xtuple_0(B),k10_xtuple_0(k7_finseq_1(A,B))) ) ) )).
fof(t30_finseq_2,axiom,( ! [A] : ! [B] : ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( 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(k4_ordinal1,A,A,B,C,D),B) ) ) )).
fof(t30_finseq_3,axiom,( ! [A] : ( ( 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(k4_ordinal1,A)) ) ) )).
fof(t30_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_finseq_4(A,B) <=> k3_finseq_1(k1_finseq_3(A,k1_tarski(B))) = k6_xcmplx_0(k3_finseq_1(A),1) ) ) )).
fof(t30_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( 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))) ) ) ) ) )).
fof(t30_finseq_6,axiom,( ! [A] : ! [B] : ! [C] : ( A != B => k6_finseq_4(k11_finseq_1(A,B,C),B) = k9_finseq_1(C) ) )).
fof(t30_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,k3_finseq_1(B)) ) => ( C = E | D = E | k7_partfun1(A,k2_finseq_7(A,B,C,D),E) = k7_partfun1(A,B,E) ) ) ) ) ) ) ) )).
fof(t30_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v3_card_1(D,C) & m2_finseq_1(D,A) ) => ! [E] : ( ( v3_card_1(E,C) & m2_finseq_1(E,A) ) => ! [F] : ( ( 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(k4_ordinal1,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))) ) ) ) ) ) ) ) )).
fof(t30_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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] : ( 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t30_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => 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)) ) ) ) ) )).
fof(t30_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( ( v3_orders_2(A) & v1_fin_topo(A) & ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) )).
fof(t30_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k2_flang_1(A),B) => r2_hidden(k2_flang_1(A),k7_flang_1(A,B,C)) ) ) ) )).
fof(t30_flang_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( r2_hidden(B,C) & B != k2_flang_1(A) & ~ ( r1_xxreal_0(D,k5_numbers) & r1_xxreal_0(E,k5_numbers) ) & k1_flang_2(A,C,D,E) = k4_flang_1(A,k2_flang_1(A)) ) ) ) ) )).
fof(t30_flang_3,axiom,( ! [A] : ! [B] : ( 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) ) )).
fof(t30_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ( r2_hidden(A,k6_subset_1(k3_finseq_2(B),k1_tarski(k1_xboole_0))) <=> ( v1_relat_1(A) & v5_relat_1(A,B) & v1_funct_1(A) & v1_finseq_1(A) & ~ v1_xboole_0(A) ) ) ) )).
fof(t30_frechet,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_frechet))) => ( A = B => ( ( ( k9_subset_1(u1_struct_0(k3_topmetr),k4_ordinal1,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),k4_ordinal1,A) = k1_xboole_0 & v3_pre_topc(A,k3_topmetr) ) ) ) ) ) ) ) )).
fof(t30_frechet2,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k3_pcomps_1(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k3_pcomps_1(A))))) ) => ( ( r1_funct_2(k4_ordinal1,u1_struct_0(A),k4_ordinal1,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) ) ) ) ) )).
fof(t30_fsm_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ v2_struct_0(D) & l2_fsm_1(D,B,C) ) => ( k7_fsm_1(B,C,D,A) = k7_fsm_1(B,C,D,k1_nat_1(A,1)) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => k7_fsm_1(B,C,D,k1_nat_1(A,E)) = k7_fsm_1(B,C,D,A) ) ) ) ) ) ) )).
fof(t30_fsm_2,axiom,( ! [A] : ( ( ~ 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] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k1_funct_1(u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(B,C))) = k2_xcmplx_0(B,C) ) ) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( 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)) = k3_real_1(B,C) ) ) ) ) )).
fof(t30_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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)))) ) ) ) )).
fof(t30_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ( E != k4_tarski(k10_finseq_1(D,k36_gfacirc1(A,B,C)),k2_twoscomp) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t30_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : k3_relat_1(k6_partfun1(B),k4_funcop_1(C,A,D)) = k4_funcop_1(C,k5_relat_1(A,B),D) ) ) )).
fof(t30_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ? [B] : ( v1_relat_1(B) & v1_funct_1(B) & k3_relat_1(A,B) = k4_relat_1(k9_xtuple_0(A)) ) => v2_funct_1(A) ) ) )).
fof(t30_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t30_funct_3,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(t30_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_partfun1(A,B) <=> k2_xboole_0(A,B) = k1_funct_4(A,B) ) ) ) )).
fof(t30_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) ) )).
fof(t30_funct_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_funcop_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(k5_funct_6(C))) ) => k4_funct_6(C,A,B) = k4_funct_6(k5_funct_6(C),B,A) ) ) )).
fof(t30_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => k1_funct_1(k1_funct_7(A,C,B),C) = B ) ) )).
fof(t30_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t30_funct_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & v1_int_1(A) ) => v1_funct_9(k41_valued_1(k1_numbers,k1_numbers,k16_sin_cos),k3_xcmplx_0(k28_sin_cos,A)) ) )).
fof(t30_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_altcat_1(A,B,C) != k1_xboole_0 => ! [D] : ( m1_subset_1(D,k1_altcat_1(A,B,C)) => k1_funct_1(k4_functor0(A,A,k11_functor0(A),B,C),D) = D ) ) ) ) ) )).
fof(t30_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v11_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ! [F] : ( ( v15_functor0(F,B,C) & m2_functor0(F,B,C) ) => ! [G] : ( ( v15_functor0(G,B,C) & m2_functor0(G,B,C) ) => ! [H] : ( m2_functor2(H,A,B,D,E) => ! [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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t30_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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)) ) ) ) )).
fof(t30_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D),C),k3_fuzzy_2(A,B,k3_fuzzy_2(A,D,C))) ) ) ) ) )).
fof(t30_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_fvaluat1(C,A) => ( ( v3_fvaluat1(A) & r1_xxreal_0(k5_numbers,k3_funct_2(u1_struct_0(A),k6_numbers,C,k3_rlvect_1(A,k5_struct_0(A),B))) ) => r1_xxreal_0(k5_numbers,k3_funct_2(u1_struct_0(A),k6_numbers,C,B)) ) ) ) ) )).
fof(t30_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [D] : ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t30_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ~ ( ~ 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)) ) ) )).
fof(t30_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t30_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v2_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ! [F] : ( m1_genealg1(F,E) => ! [G] : ( m1_genealg1(G,E) => ( k10_genealg1(E,F,G,k5_numbers,k5_numbers,C,D) = k8_genealg1(E,F,G,C,D) & k10_genealg1(E,F,G,k5_numbers,B,k5_numbers,D) = k8_genealg1(E,F,G,B,D) & k10_genealg1(E,F,G,k5_numbers,B,C,k5_numbers) = k8_genealg1(E,F,G,B,C) & k10_genealg1(E,F,G,A,k5_numbers,C,k5_numbers) = k8_genealg1(E,F,G,A,C) & k10_genealg1(E,F,G,A,k5_numbers,k5_numbers,D) = k8_genealg1(E,F,G,A,D) & k10_genealg1(E,F,G,A,B,k5_numbers,k5_numbers) = k8_genealg1(E,F,G,A,B) ) ) ) ) ) ) ) ) )).
fof(t30_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( k4_geomtrap(A,B,C,D,k3_rlvect_1(A,E,F)) = k2_xcmplx_0(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)) = k6_xcmplx_0(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) = k6_xcmplx_0(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) = k2_xcmplx_0(k4_geomtrap(A,B,C,E,D),k4_geomtrap(A,B,C,F,D)) ) ) ) ) ) ) ) ) )).
fof(t30_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( C != k4_tarski(k10_finseq_1(A,B),k14_twoscomp) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k10_gfacirc1(A,B,C),k11_gfacirc1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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 ) ) ) ) ) ) ) )).
fof(t30_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => k7_glib_000(A) = k20_glib_000(A,k6_glib_000(A)) ) )).
fof(t30_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,B)) => ( k1_funct_1(k7_glib_001(A,B,C),D) = k1_funct_1(B,D) & r2_hidden(D,k1_relset_1(k4_ordinal1,k7_glib_001(A,B,C))) ) ) ) ) ) ) )).
fof(t30_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v4_glib_002(B,A) & m1_glib_000(B,A) ) => k25_glib_000(A,B) = k21_glib_000(A,k24_glib_000(A,B)) ) ) )).
fof(t30_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v8_glib_003(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m4_glib_001(C,A,B) => r1_xxreal_0(k10_glib_003(A,C),k10_glib_003(A,B)) ) ) ) )).
fof(t30_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( 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)))) ) ) ) )).
fof(t30_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(D)) & r2_hidden(k4_tarski(k1_nat_1(A,1),k1_nat_1(B,1)),k2_matrix_0(k2_goboard2(D))) & r2_hidden(k4_tarski(k1_nat_1(A,1),B),k2_matrix_0(k2_goboard2(D))) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),B) ) => ( k5_goboard5(D,C) = k3_goboard5(k2_goboard2(D),k1_nat_1(A,1),B) & k4_goboard5(D,C) = k3_goboard5(k2_goboard2(D),A,B) ) ) ) ) ) ) )).
fof(t30_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_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_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),1)),k17_euclid(B)) ) ) ) ) )).
fof(t30_goboard7,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) & 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)) ) ) )).
fof(t30_gobrd11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_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,k5_numbers) = a_2_4_gobrd11(A,B) ) ) ) ) )).
fof(t30_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(D)) & r1_goboard1(u1_struct_0(k15_euclid(2)),D,E) & r2_hidden(k4_tarski(A,B),k2_matrix_0(E)) & r2_hidden(k4_tarski(k1_nat_1(A,1),B),k2_matrix_0(E)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,k1_nat_1(A,1),B) ) => k4_gobrd13(D,E,C) = k3_goboard5(E,k1_nat_1(A,1),k7_nat_d(B,1)) ) ) ) ) ) ) )).
fof(t30_gobrd14,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t30_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => k6_goedelcp(A,k2_relset_1(k3_cqc_lang(A),B)) = k3_calcul_1(A,B) ) ) )).
fof(t30_gr_cy_3,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k5_int_1(k1_newton(A,B),C) = k5_int_1(k1_newton(k5_int_1(A,C),B),C) ) ) ) )).
fof(t30_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t30_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ~ ( r2_graph_1(A,B,C,F) & r2_graph_1(A,D,E,F) & ~ ( B = D & C = E ) & ~ ( B = E & C = D ) ) ) ) ) ) ) )).
fof(t30_graph_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v6_graph_1(B) & l1_graph_1(B) ) => ! [C] : ( 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))) ) ) ) )).
fof(t30_graph_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(C) & l1_graph_1(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( ( 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) ) ) ) ) ) )).
fof(t30_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) => r1_xxreal_0(k14_graphsp(k7_graphsp(B,A),B,A),A) ) ) )).
fof(t30_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t30_grfunc_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t30_groeb_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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,k8_polynom1(A,C)),k1_groeb_1(A,C,k8_polynom1(A,C))) ) ) ) )).
fof(t30_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,k5_card_1(k3_polynom1(k15_pre_poly(A),C,D))) ) => r2_hidden(k3_termord(A,B,C,D),k3_polynom1(k15_pre_poly(A),C,k5_groeb_3(A,B,C,D,E))) ) ) ) ) ) ) )).
fof(t30_group_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ 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) ) ) )).
fof(t30_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t30_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t30_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_group_3(A,B,C) = B ) ) => v5_group_1(A) ) ) )).
fof(t30_group_4,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t30_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t30_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t30_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l3_algstr_0(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(C)) => ! [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)) ) ) ) ) ) ) ) ) ) )).
fof(t30_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( 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) ) ) ) ) )).
fof(t30_groupp_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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] : ( m1_group_2(C,B) => ! [D] : ( m1_group_2(D,B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t30_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( ( ~ 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(k5_numbers,k9_weierstr(A,B,C)) ) ) ) ) )).
fof(t30_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => k13_glib_001(A,k2_helly(A,B,B)) = k1_tarski(B) ) ) )).
fof(t30_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t30_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A)))) => ( r1_lattice3(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A)),k5_heyting3(A),B) => ! [C] : ( ~ v1_xboole_0(C) => ~ ( r2_hidden(C,B) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( r2_hidden(k1_domain_1(k4_ordinal1,k4_ordinal1,D,A),C) & v1_abian(D) ) ) ) ) ) ) ) )).
fof(t30_hfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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(k6_xcmplx_0(A,2)),k3_xcmplx_0(A,k6_xcmplx_0(A,1))),B)) ) ) ) )).
fof(t30_hilbasis,axiom,( ! [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) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,u1_struct_0(k12_polynom1(k1_nat_1(B,1),A))) => k3_funct_2(u1_struct_0(k14_polynom3(k12_polynom1(B,A))),u1_struct_0(k12_polynom1(k1_nat_1(B,1),A)),k6_hilbasis(A,B),k3_funct_2(u1_struct_0(k12_polynom1(k1_nat_1(B,1),A)),u1_struct_0(k14_polynom3(k12_polynom1(B,A))),k7_hilbasis(A,B),C)) = C ) ) ) )).
fof(t30_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => r2_hidden(k3_hilbert1(A,k4_hilbert1(A,A)),k6_hilbert1) ) )).
fof(t30_hilbert2,axiom,( k3_hilbert2(k2_hilbert1) = k2_trees_4(k1_hilbert1,k2_hilbert1) )).
fof(t30_hilbert3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => k3_hilbert3(C,k4_hilbert1(A,B)) = k2_zfmisc_1(k3_hilbert3(C,A),k3_hilbert3(C,B)) ) ) ) )).
fof(t30_hurwitz,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => r1_polynom5(A,k3_hurwitz(A,B,1),B) ) ) )).
fof(t30_idea_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( v1_int_2(k1_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 ) ) ) ) ) )).
fof(t30_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m3_ideal_1(D,A,B) => m1_ideal_1(k9_fvsum_1(A,D,C),A,B) ) ) ) ) )).
fof(t30_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t30_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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] : ( m4_index_1(C,u1_struct_0(A),u4_struct_0(A),u1_graph_1(A),u2_graph_1(A),B) => ! [D] : ( ( ~ 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] : ( 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)) ) ) ) ) ) )).
fof(t30_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_instalg1(B,A) ) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( l3_msualg_1(D,A) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t30_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( k2_int_1(A) = A <=> v1_int_1(A) ) ) )).
fof(t30_int_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( v1_int_2(A) & v1_int_2(B) & ~ r1_int_2(A,B) & A != B ) ) ) )).
fof(t30_int_4,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r2_hidden(C,k1_relset_1(k4_ordinal1,A)) & k3_finseq_1(A) = k2_xcmplx_0(D,1) ) => r2_relset_1(k4_ordinal1,k4_ordinal1,k4_wsierp_1(k4_ordinal1,C,k8_finseq_1(k4_ordinal1,A,k3_pre_poly(k4_ordinal1,B))),k8_finseq_1(k4_ordinal1,k4_wsierp_1(k4_ordinal1,C,A),k3_pre_poly(k4_ordinal1,B))) ) ) ) ) ) )).
fof(t30_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t30_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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] : ( m1_int_6(C,B) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t30_int_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( v8_struct_0(A) & k6_group_1(A,B) = k2_nat_1(C,D) ) => k6_group_1(A,k5_group_1(A,C,B)) = D ) ) ) ) ) )).
fof(t30_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(3,A) => ! [B] : ( v7_ordinal1(B) => ~ ( r1_int_2(B,k1_newton(2,A)) & r2_int_8(B,k1_newton(2,A)) ) ) ) ) )).
fof(t30_integr11,axiom,( ! [A] : ( ( ~ 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,k5_numbers),k1_sin_cos2)) = k6_xcmplx_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(1,k5_numbers),k3_sin_cos2),k1_sin_cos2),k2_seq_4(A)),k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(1,k5_numbers),k3_sin_cos2),k1_sin_cos2),k3_seq_4(A))) ) )).
fof(t30_integr12,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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,D,k27_sin_cos))) & r2_relset_1(k1_numbers,k1_numbers,C,k3_rfunct_1(k1_numbers,k1_numbers,k41_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k18_sin_cos)),k41_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k16_sin_cos)))) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => ( k1_funct_1(D,F) = k3_xcmplx_0(A,F) & A != k5_numbers ) ) ) & E = k1_relset_1(k1_numbers,C) ) => k2_integra5(B,C) = k6_xcmplx_0(k1_funct_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,k27_sin_cos),k4_xcmplx_0(k7_xcmplx_0(1,A))),k1_partfun2(k1_numbers,E)),k2_seq_4(B)),k1_funct_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,k27_sin_cos),k4_xcmplx_0(k7_xcmplx_0(1,A))),k1_partfun2(k1_numbers,E)),k3_seq_4(B))) ) ) ) ) ) ) )).
fof(t30_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k22_sin_cos,k41_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k16_sin_cos))))) & r1_tarski(C,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k27_sin_cos))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k27_sin_cos),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k27_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t30_integr14,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v3_rcomp_1(E) & m1_subset_1(E,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,E) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => k1_funct_1(C,F) = k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(k16_sin_cos,k3_xcmplx_0(A,F)),k1_square_1(k1_funct_1(k18_sin_cos,k3_xcmplx_0(A,F)))),k1_square_1(k1_funct_1(k18_sin_cos,k3_xcmplx_0(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),k7_xcmplx_0(1,A)),k1_partfun2(k1_numbers,E)))) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => ( k1_funct_1(D,F) = k3_xcmplx_0(A,F) & A != k5_numbers ) ) ) & E = k1_relset_1(k1_numbers,C) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,B)) ) => k2_integra5(B,C) = k6_xcmplx_0(k1_funct_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),k7_xcmplx_0(1,A)),k1_partfun2(k1_numbers,E)),k2_seq_4(B)),k1_funct_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),k7_xcmplx_0(1,A)),k1_partfun2(k1_numbers,E)),k3_seq_4(B))) ) ) ) ) ) ) )).
fof(t30_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [G] : ( m2_finseq_2(G,k1_numbers,k1_euclid(A)) => ( ( r1_xxreal_0(B,C) & ! [H] : ( 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,k6_xcmplx_0(E,D)) ) ) ) ) ) ) ) ) )).
fof(t30_integra1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( m1_integra1(C,B) => ~ ( r2_hidden(A,k4_finseq_1(C)) & ! [D] : ( ( ~ v1_xboole_0(D) & v2_measure5(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v2_measure5(E) & m1_subset_1(E,k1_zfmisc_1(k1_numbers)) ) => ~ ( D = k1_rcomp_1(k3_seq_4(B),k1_funct_1(C,A)) & E = k1_rcomp_1(k1_funct_1(C,A),k2_seq_4(B)) & B = k4_subset_1(k1_numbers,D,E) ) ) ) ) ) ) ) )).
fof(t30_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( m1_integra1(D,B) => ( ( v2_seq_2(k2_partfun1(B,k1_numbers,C,B)) & r1_xxreal_0(A,k5_numbers) ) => k6_integra1(B,k26_valued_1(B,k1_numbers,C,A),D) = k3_xcmplx_0(A,k7_integra1(B,C,D)) ) ) ) ) ) )).
fof(t30_integra7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k6_xcmplx_0(k1_funct_1(k1_taylor_1(k1_nat_1(C,1)),B),k1_funct_1(k1_taylor_1(k1_nat_1(C,1)),A)) = k4_integra5(A,B,k26_valued_1(k1_numbers,k1_numbers,k1_taylor_1(C),k1_nat_1(C,1))) ) ) ) )).
fof(t30_integra8,axiom,( k2_fdiff_1(k1_sin_cos2,k1_numbers) = k3_sin_cos2 )).
fof(t30_integra9,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( ~ 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)) ) ) ) ) )).
fof(t30_interva1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_interva1(B,A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_interva1(C,A) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ! [D] : ( ( ~ 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)) ) ) ) )).
fof(t30_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( 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) ) ) )).
fof(t30_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( 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,k4_nattra_1(B,C,E)),k4_nattra_1(A,C,k9_cat_1(A,B,C,D,E))) ) ) ) ) ) )).
fof(t30_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,k6_cat_2(B,C)) => ! [E] : ( m2_cat_1(E,A,k6_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(k6_cat_2(B,C)),D,E) ) ) ) ) ) ) )).
fof(t30_isomichi,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(B,A) => k3_borsuk_5(A,B) = k1_xboole_0 ) ) ) )).
fof(t30_jgraph_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => k12_euclid(A) = k3_square_1(k2_xcmplx_0(k1_square_1(k17_euclid(A)),k1_square_1(k18_euclid(A)))) ) )).
fof(t30_jgraph_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( ( 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] : ( 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) ) ) ) )).
fof(t30_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t30_jordan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t30_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [G] : ( 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] : ( 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] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t30_jordan12,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( ( ~ 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] : ( 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] : ( v7_ordinal1(F) & r1_xxreal_0(1,F) & r1_xxreal_0(k1_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] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t30_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_jordan1h(A,B) & r1_xxreal_0(k5_jordan11(A,B),C) & r1_xxreal_0(C,k1_nat_1(k2_nat_1(k11_newton(2,k7_nat_d(B,k3_jordan11(A))),k7_nat_d(k4_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)))) ) ) ) ) )).
fof(t30_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C),k3_topreal1(2,k1_jordan1e(B,A))) & r2_hidden(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C)),k9_jordan6(B)) ) ) ) ) ) ) )).
fof(t30_jordan18,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => r1_jordan18(A,B,C,D,E,C) ) ) ) ) ) )).
fof(t30_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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))) ) ) ) ) )).
fof(t30_jordan1b,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ~ ( 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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,k3_finseq_1(k1_jordan8(B,A)))),k9_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) ) ) ) ) )).
fof(t30_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(k1_jordan8(B,A))) & k18_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),1,C) ) ) ) )).
fof(t30_jordan1g,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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,k2_jordan9(B,A)))) = k3_finseq_1(k2_jordan1e(B,A)) ) ) )).
fof(t30_jordan1h,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_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] : ( v7_ordinal1(C) => ~ ( r2_hidden(k4_tarski(1,C),k2_matrix_0(B)) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,C),k2_relset_1(u1_struct_0(k15_euclid(2)),A)) ) ) | ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(k4_tarski(k3_finseq_1(B),C),k2_matrix_0(B)) & r2_hidden(k3_matrix_0(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)) ) ) ) ) )).
fof(t30_jordan1k,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(B,k1_rltopsp1(k15_euclid(2),C,A)) & B != C & r1_xxreal_0(k1_topreal6(2,C,A),k1_topreal6(2,B,A)) ) ) ) ) )).
fof(t30_jordan21,axiom,( ! [A] : ( ( 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) ) )).
fof(t30_jordan22,axiom,( ! [A] : ( ( 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)) ) )).
fof(t30_jordan23,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v1_topreal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(B,k3_topreal1(2,A)) => v1_topreal1(k3_jordan3(A,B)) ) ) ) ) )).
fof(t30_jordan2b,axiom,( ! [A] : ( 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) ) ) )).
fof(t30_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( 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] : ( v1_xreal_0(F) => ( D != k1_rlvect_1(k15_euclid(A),E,F) & E != k1_rlvect_1(k15_euclid(A),D,F) ) ) & ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(A))) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t30_jordan3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t30_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_jordan4(A,B,C,D) => r1_jordan4(A,k4_finseq_5(u1_struct_0(k15_euclid(2)),B),D,C) ) ) ) ) ) )).
fof(t30_jordan5b,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ( ( 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 ) ) ) )).
fof(t30_jordan5c,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(B,k2_topreal1(2,A,D)) & r2_hidden(C,k2_topreal1(2,A,E)) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(A)) & r1_xxreal_0(1,E) & r1_xxreal_0(k1_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,k1_nat_1(D,1)),B,C) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t30_jordan5d,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( B = a_1_5_jordan5d(A) => k2_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))) ) ) ) )).
fof(t30_jordan6,axiom,( ! [A] : ( v1_xreal_0(A) => ( v4_pre_topc(k6_jordan6(A),k15_euclid(2)) & v4_pre_topc(k7_jordan6(A),k15_euclid(2)) ) ) )).
fof(t30_jordan9,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(k1_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] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,1) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),D,k1_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,2) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k1_nat_1(D,1),k1_matrix_0(k1_jordan8(A,B))) & r2_hidden(k20_pscomp_1(A),k3_goboard5(k1_jordan8(A,B),D,k7_nat_d(k1_matrix_0(k1_jordan8(A,B)),1))) & k20_pscomp_1(A) != k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),D,k7_nat_d(k1_matrix_0(k1_jordan8(A,B)),1)) ) ) | k20_pscomp_1(k3_topreal1(2,C)) = k7_partfun1(u1_struct_0(k15_euclid(2)),C,1) ) ) ) ) ) )).
fof(t30_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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))) ) ) )).
fof(t30_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t30_kurato_1,axiom,( 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))) )).
fof(t30_kurato_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => ( C = D => ( r1_frechet2(k15_euclid(A),B,C) <=> ! [E] : ( v1_xreal_0(E) => ! [F] : ( v7_ordinal1(F) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [G] : ( v7_ordinal1(G) => ~ ( r1_xxreal_0(F,G) & r2_hidden(k1_jordan11(A,B,G),k8_metric_1(k14_euclid(A),D,E)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t30_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( k12_matrix_3(A,B,C) != k4_struct_0(B) => k4_matrix_3(B,C,k1_matrix_7(A,B,k4_matrix_0(u1_struct_0(B),k7_laplace(A,B,C)),k11_algstr_0(B,k12_matrix_3(A,B,C)))) = k3_matrix_1(B,A) ) ) ) ) )).
fof(t30_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t30_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k5_finsub_1(C)) => ! [E] : ( ( 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] : ( 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 ) ) ) ) ) ) ) )).
fof(t30_lattice3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( r4_lattice3(B,C,A) <=> r2_lattice3(k3_lattice3(B),A,k4_lattice3(B,C)) ) ) ) )).
fof(t30_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => k7_lattices(A,k5_lattices(A)) = k6_lattices(A) ) )).
fof(t30_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m1_lattice8(D,A,B,C) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(E,F) => r1_tarski(k1_xtuple_0(k1_funct_1(D,E)),k1_xtuple_0(k1_funct_1(D,F))) ) ) ) ) ) ) ) )).
fof(t30_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)))) => ~ ( k1_relset_1(k6_glib_000(A),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),B)) != k6_glib_000(A) & r2_hidden(k10_lexbfs(A,B),k1_relset_1(k6_glib_000(A),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),B))) ) ) ) )).
fof(t30_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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)) ) ) )).
fof(t30_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v8_valued_0(A) => ( v2_seq_2(A) | v2_limfunc1(A) ) ) ) )).
fof(t30_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,A) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(C,D) & ~ r1_xxreal_0(D,A) & r2_hidden(D,k1_relset_1(k1_numbers,B)) ) ) ) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(A,k2_xcmplx_0(A,C)))) & ~ v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(A,k2_xcmplx_0(A,C)))) ) ) | r5_limfunc2(B,A) ) ) ) ) )).
fof(t30_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k3_limfunc1(C))) & r1_xxreal_0(k1_funct_1(A,D),k4_limfunc1(A)) ) ) | v5_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).
fof(t30_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m1_vectsp_4(E,A,B) => r1_lmod_6(A,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))) ) ) ) ) ) )).
fof(t30_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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_funct_1(k15_lopban_1(A,B),C) = k2_seq_4(k14_lopban_1(A,B,C)) ) ) ) )).
fof(t30_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k1_power(D,k9_nat_1(k1_numbers,k5_normsp_0(A,B),D)) ) & v2_comseq_2(C) ) => ( r1_xxreal_0(1,k1_seq_2(C)) | v2_lopban_3(B,A) ) ) ) ) ) )).
fof(t30_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( k9_complex1(k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k2_normsp_0(A,B))),D)) = k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k2_normsp_0(A,B))),D) & ( r1_xxreal_0(D,C) => k9_complex1(k5_real_1(k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k2_normsp_0(A,B))),C),k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k2_normsp_0(A,B))),D))) = k5_real_1(k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k2_normsp_0(A,B))),C),k9_nat_1(k1_numbers,k3_series_1(k4_sin_cos(k2_normsp_0(A,B))),D)) ) ) ) ) ) ) )).
fof(t30_lopclset,axiom,( ! [A] : ( ( ~ 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 ) )).
fof(t30_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( ( r2_hidden(D,k13_lpspacc1(A,B,C)) & r2_hidden(E,k13_lpspacc1(A,B,C)) ) => ( r1_lpspacc1(A,B,C,E,D) <=> r2_hidden(E,k17_lpspacc1(A,B,C,D)) ) ) ) ) ) ) ) )).
fof(t30_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t30_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( v2_xxreal_0(F) & v1_xreal_0(F) ) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t30_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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)) ) ) ) ) )).
fof(t30_ltlaxio2,axiom,( ! [A] : ( m2_finseq_1(A,k1_hilbert1) => ! [B] : ( m2_finseq_1(B,k1_hilbert1) => ( r1_tarski(k2_relset_1(k1_hilbert1,A),k2_relset_1(k1_hilbert1,B)) => v1_ltlaxio1(k3_hilbert1(k1_ltlaxio1(k7_partfun1(k1_hilbert1,k2_ltlaxio2(k4_ltlaxio2(A)),k3_finseq_1(k2_ltlaxio2(k4_ltlaxio2(A))))),k1_ltlaxio1(k7_partfun1(k1_hilbert1,k2_ltlaxio2(k4_ltlaxio2(B)),k3_finseq_1(k2_ltlaxio2(k4_ltlaxio2(B))))))) ) ) ) )).
fof(t30_ltlaxio3,axiom,( ! [A] : ( ( ~ v2_ltlaxio3(A) & m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) ) => r1_xboole_0(k2_relset_1(k1_hilbert1,k8_ltlaxio3(A)),k2_relset_1(k1_hilbert1,k9_ltlaxio3(A))) ) )).
fof(t30_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t30_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t30_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,B,B) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( r1_xxreal_0(k5_numbers,A) & v2_matrix10(C) ) => v3_matrix10(k6_matrix10(B,A,C)) ) ) ) ) )).
fof(t30_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,D,B,C) & m2_finseq_1(E,k3_finseq_2(D)) ) => E = k3_matrix11(A,B,C,D,E,k7_matrix_0(D,E,A)) ) ) ) ) ) )).
fof(t30_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(C,k4_ordinal1)) => ! [F] : ( m2_finseq_2(F,k4_ordinal1,k4_finseq_2(C,k4_ordinal1)) => ! [G] : ( ( v1_matrix_0(G) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(D))) ) => ( ( r2_hidden(A,k2_finseq_1(C)) & r2_hidden(B,k2_finseq_1(C)) & k1_funct_1(E,A) = k1_funct_1(E,B) ) => ( A = B | k12_matrix_3(C,D,k1_matrix13(u1_struct_0(D),G,C,C,F,E)) = k4_struct_0(D) ) ) ) ) ) ) ) ) ) )).
fof(t30_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => k4_matrix_0(u1_struct_0(B),k4_matrix_3(B,C,D)) = k4_matrix_3(B,k4_matrix_0(u1_struct_0(B),D),k4_matrix_0(u1_struct_0(B),C)) ) ) ) ) )).
fof(t30_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t30_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(B),A,A) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(B))) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(B),A,A) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(B))) ) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(B),A,A) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(B))) ) => ( ( 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_3(B,k1_matrix_4(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)) ) ) ) ) ) ) ) ) ) )).
fof(t30_matrix_0,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(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_0(D)) ) => r2_hidden(k4_tarski(B,C),k2_matrix_0(D)) ) ) ) ) )).
fof(t30_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ! [E] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(D) & k1_matrix_0(D) = k1_matrix_0(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) ) ) ) ) ) ) )).
fof(t30_matrix_6,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(A),B,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ( ( v3_matrix_6(D,B,A) & r2_hidden(C,k2_finseq_1(B)) ) => k3_matrix_0(u1_struct_0(A),D,C,C) = k4_struct_0(A) ) ) ) ) ) )).
fof(t30_matrix_7,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t30_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v4_matrix_8(C,A,B) => v3_matrix_8(C,A,B) ) ) ) ) )).
fof(t30_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( m2_finseq_1(C,k2_numbers) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k3_finseq_1(B) = k3_finseq_1(C) ) => k5_matrixc1(k8_seq_4(A,B),C) = k8_seq_4(k5_matrixc1(A,C),k5_matrixc1(B,C)) ) ) ) ) )).
fof(t30_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_matrixj1(C,A) & m2_finseq_1(C,k3_finseq_2(k3_finseq_2(A))) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( ( r2_hidden(D,k4_finseq_1(C)) & r2_hidden(k4_tarski(E,F),k2_matrix_0(k2_matrixj1(A,C,D))) ) => ( r2_hidden(k4_tarski(k1_nat_1(E,k2_wsierp_1(k17_finseq_1(k4_ordinal1,k7_nat_d(D,1),k10_matrixj1(A,C)))),k1_nat_1(F,k2_wsierp_1(k17_finseq_1(k4_ordinal1,k7_nat_d(D,1),k11_matrixj1(A,C))))),k2_matrix_0(k13_matrixj1(A,B,C))) & k3_matrix_0(A,k2_matrixj1(A,C,D),E,F) = k3_matrix_0(A,k13_matrixj1(A,B,C),k1_nat_1(E,k2_wsierp_1(k17_finseq_1(k4_ordinal1,k7_nat_d(D,1),k10_matrixj1(A,C)))),k1_nat_1(F,k2_wsierp_1(k17_finseq_1(k4_ordinal1,k7_nat_d(D,1),k11_matrixj1(A,C))))) ) ) ) ) ) ) ) ) )).
fof(t30_matrixj2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( ~ 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] : ( ( 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] : ( ( v1_matrlin(F,B) & m1_vectsp_4(F,B,D) ) => ! [G] : ( ( 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] : ( ( v2_relat_1(H) & m1_matrixj2(H,B,C) ) => ! [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) ) ) ) ) ) ) ) ) ) ) )).
fof(t30_matrixr1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( ~ r1_xxreal_0(k1_matrix_0(B),k5_numbers) => k4_matrix_0(k1_numbers,k7_matrixr1(A,B)) = k7_matrixr1(A,k4_matrix_0(k1_numbers,B)) ) ) ) )).
fof(t30_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => k4_matrix_0(k1_numbers,k1_matrixr2(A,B,C)) = k1_matrixr2(A,k4_matrix_0(k1_numbers,C),k4_matrix_0(k1_numbers,B)) ) ) ) )).
fof(t30_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t30_matrlin2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( ~ 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] : ( m1_matrlin(D,B,C) => ! [E] : ( m2_finseq_1(E,u1_struct_0(C)) => ! [F] : ( m2_finseq_1(F,u1_struct_0(B)) => ! [G] : ( 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] : ( 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),k5_numbers) | 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) ) ) ) ) ) ) ) ) ) )).
fof(t30_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t30_matrprob,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( 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) ) ) ) )).
fof(t30_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => k2_ranknull(k15_euclid(A),k15_euclid(B),k3_matrtop1(A,B,D),k5_rusub_4(k15_euclid(A),E,C)) = k5_rusub_4(k15_euclid(B),k2_ranknull(k15_euclid(A),k15_euclid(B),k3_matrtop1(A,B,D),E),k3_funct_2(u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(B)),k3_matrtop1(A,B,D),C)) ) ) ) ) ) )).
fof(t30_mboolean,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(t30_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k3_zfmisc_1(k2_tarski(A,D),k1_tarski(B),k2_tarski(C,E)) = k2_enumset1(k3_xtuple_0(A,B,C),k3_xtuple_0(D,B,C),k3_xtuple_0(A,B,E),k3_xtuple_0(D,B,E)) )).
fof(t30_measure1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t30_measure6,axiom,( ! [A] : ( ( v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ( v6_xxreal_2(k1_measure6(A,B)) & m1_subset_1(k1_measure6(A,B),k1_zfmisc_1(k1_numbers)) ) ) ) )).
fof(t30_measure8,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v2_prob_1(D) => v8_valued_0(k11_measure8(A,B,D,C)) ) ) ) ) )).
fof(t30_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ( r1_tarski(A,B) <=> r1_tarski(k7_member_1(A),k7_member_1(B)) ) ) ) )).
fof(t30_membered,axiom,( ! [A] : ( ! [B] : ( r2_hidden(B,A) => v6_membered(B) ) => v6_membered(k3_tarski(A)) ) )).
fof(t30_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_partfun1(C,u1_struct_0(B)) ) => r1_tarski(k7_memstr_0(A,B,k5_memstr_0(A,B,C)),C) ) ) ) )).
fof(t30_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t30_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => r2_relset_1(A,k6_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))) ) ) ) )).
fof(t30_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) ) ) ) ) ) ) )).
fof(t30_mesfunc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t30_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ~ ( v1_prob_2(C) & m2_finseq_1(C,B) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & v1_prob_2(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ~ ( k3_tarski(k10_xtuple_0(C)) = k2_measure2(A,B,k1_measure3(A,B,D)) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k9_xtuple_0(C)) => k1_funct_1(C,E) = k9_nat_1(B,D,E) ) ) & ! [E] : ( v7_ordinal1(E) => ( ~ r2_hidden(E,k9_xtuple_0(C)) => k9_nat_1(B,D,E) = k1_xboole_0 ) ) ) ) ) ) ) ) )).
fof(t30_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( m1_subset_1(C,k6_numbers) => k19_mesfunc1(A,B,C) = k8_relset_1(A,k6_numbers,B,k1_tarski(C)) ) ) ) )).
fof(t30_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t30_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ( ! [C] : ( v7_ordinal1(C) => v6_supinf_2(k4_mesfunc5(A,k6_numbers,B,C)) ) => v2_mesfunc9(B,A) ) ) ) )).
fof(t30_metric_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_metric_1(A,B,C,D) => r1_metric_1(A,D,C,B) ) ) ) ) ) )).
fof(t30_metric_2,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t30_metric_3,axiom,( ! [A] : ( m1_subset_1(A,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)) => ! [B] : ( m1_subset_1(B,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)) => ! [C] : ( m1_subset_1(C,k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers)) => r1_xxreal_0(k2_binop_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k1_numbers,k22_metric_3,A,C),k3_real_1(k2_binop_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k1_numbers,k22_metric_3,A,B),k2_binop_1(k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k3_zfmisc_1(k1_numbers,k1_numbers,k1_numbers),k1_numbers,k22_metric_3,B,C))) ) ) ) )).
fof(t30_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(k2_xcmplx_0(A,1)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(k2_xcmplx_0(A,1)))) => ( B != k4_struct_0(k15_euclid(k2_xcmplx_0(A,1))) => v3_mfold_1(k3_mfold_2(k2_xcmplx_0(A,1),B,C),A) ) ) ) ) )).
fof(t30_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) => r2_hidden(B,k4_midsp_1(A,B)) ) ) )).
fof(t30_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( ( v4_midsp_2(B,A) & l1_midsp_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k3_midsp_1(A,C,E) = D <=> k9_midsp_2(A,B,C,E) = k1_midsp_2(u1_midsp_2(A,B),k9_midsp_2(A,B,C,D)) ) ) ) ) ) ) )).
fof(t30_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_midsp_3(B,A) => ! [C] : ( m2_midsp_3(C,A) => ! [D] : ( ( v4_midsp_2(D,C) & l1_midsp_2(D,C) ) => ( r1_midsp_3(A,B,C) => ( r3_midsp_3(A,B,C) <=> ! [E] : ( m2_finseq_2(E,u1_struct_0(u1_midsp_2(C,D)),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(u1_midsp_2(C,D)))) => ! [F] : ( 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)),k1_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)),k1_nat_1(A,1),E,B,F))) ) ) ) ) ) ) ) ) )).
fof(t30_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( ! [D] : ( 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) ) ) ) )).
fof(t30_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(t30_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k6_modal_1) => ! [B] : ( m1_subset_1(B,k6_modal_1) => ! [C] : ( m1_subset_1(C,k6_modal_1) => ! [D] : ( m1_subset_1(D,k6_modal_1) => ( k12_modal_1(A,C) = k12_modal_1(B,D) => ( A = B & C = D ) ) ) ) ) ) )).
fof(t30_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ( k52_modelc_1(A,B,C,D) = k52_modelc_1(A,B,C,E) => D = E ) ) ) ) ) ) )).
fof(t30_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ( v3_modelc_2(A) | v6_modelc_2(A) ) => r2_modelc_2(k10_modelc_2(A),A) ) ) )).
fof(t30_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_3(C,B) & l1_modelc_3(C,B) ) => ! [D] : ( ( v1_modelc_3(D,B) & l1_modelc_3(D,B) ) => ( ( r4_modelc_3(B,C,D) & r2_hidden(A,u2_modelc_3(B,C)) ) => ( r2_hidden(A,u2_modelc_3(B,D)) | r1_modelc_3(B,C,D,A) ) ) ) ) ) ) )).
fof(t30_moebius1,axiom,( k2_moebius1(1) = 1 )).
fof(t30_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) ) ) )).
fof(t30_monoid_1,axiom,( ! [A] : ! [B] : m1_subset_1(k5_funct_3(B,A),u1_struct_0(k13_monoid_1(A))) )).
fof(t30_morph_01,axiom,( ! [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) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t30_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t30_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( l3_msualg_1(D,A) => ! [E] : ( ( v4_msualg_1(E,A) & 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,C),u4_msualg_1(A,C)) & 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)) ) => ! [F] : ( m2_pboole(F,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,D)) => ! [G] : ( m2_pboole(G,u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,E)) => ( ( r8_pboole(u1_struct_0(A),F,G) & r1_msualg_3(A,B,D,F) ) => r1_msualg_3(A,C,E,G) ) ) ) ) ) ) ) ) ) )).
fof(t30_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( r2_hidden(E,k1_funct_1(u3_msualg_1(A,B),D)) => ! [F] : ( m1_subset_1(F,k1_funct_1(C,D)) => E != F ) ) ) ) ) ) )).
fof(t30_mssublat,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_unialg_1(B) & v4_unialg_1(B) & m1_unialg_2(B,A) ) => ! [C] : ( ( v1_unialg_1(C) & v4_unialg_1(C) & m1_unialg_2(C,A) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t30_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => v2_binop_1(k15_msualg_2(A,B),k14_msualg_2(A,B)) ) ) )).
fof(t30_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t30_msualg_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t30_mycielsk,axiom,( ! [A] : ( ( v1_necklace(A) & v2_mycielsk(A) & l1_orders_2(A) ) => k3_mycielsk(A) = k2_mycielsk(k3_necklace(A)) ) )).
fof(t30_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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,k5_numbers) | r1_nagata_1(u1_struct_0(A),k5_nagata_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),B,C)) ) ) ) ) ) )).
fof(t30_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => k2_card_1(k5_card_1(A)) = k5_card_1(k1_nat_1(A,1)) ) )).
fof(t30_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k7_nat_d(k7_nat_d(A,B),C) = k7_nat_d(A,k2_xcmplx_0(B,C)) ) ) ) )).
fof(t30_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ( r1_nat_d(C,B) => r1_xxreal_0(k11_nat_3(C,A),k11_nat_3(B,A)) ) ) ) ) )).
fof(t30_nat_4,axiom,( v1_int_2(23) )).
fof(t30_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( v1_int_2(B) => k5_nat_5(k1_newton(B,A)) = k7_xcmplx_0(k6_xcmplx_0(k1_newton(B,k1_nat_1(A,1)),1),k6_xcmplx_0(B,1)) ) ) ) )).
fof(t30_nat_d,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r1_xxreal_0(k5_numbers,A) => ( r1_xxreal_0(B,k5_numbers) | k3_int_2(A,B) = k3_int_2(B,k5_int_1(A,B)) ) ) ) ) )).
fof(t30_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_nattra_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_nattra_1(A,B))) => ! [E] : ( m1_cat_1(E,k9_nattra_1(A,B),C,D) => ~ ( k2_cat_1(k9_nattra_1(A,B),C,D) != k1_xboole_0 & ! [F] : ( m2_cat_1(F,A,B) => ! [G] : ( m2_cat_1(G,A,B) => ! [H] : ( m2_nattra_1(H,A,B,F,G) => ~ ( C = F & D = G & E = k4_tarski(k4_tarski(F,G),H) ) ) ) ) ) ) ) ) ) ) )).
fof(t30_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,k1_numbers,k5_normsp_0(B,k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),D,C)),k8_funct_2(k4_ordinal1,k1_numbers,u1_struct_0(A),D,k4_normsp_0(u1_struct_0(A),B,C))) & r2_funct_2(k4_ordinal1,u1_struct_0(B),k5_vfunct_1(k4_ordinal1,B,k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),D,C)),k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),D,k5_vfunct_1(u1_struct_0(A),B,C))) ) ) ) ) ) ) )).
fof(t30_ndiff_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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))) ) ) ) ) )).
fof(t30_ndiff_4,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k4_ordinal1) => ( ( 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) ) ) ) ) ) )).
fof(t30_ndiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finseq_1(B) & v2_prvect_2(B) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k14_prvect_2(B))) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t30_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k1_newton(k2_xcmplx_0(B,C),A) = k18_rvsum_1(k5_newton(B,C,A)) ) ) ) )).
fof(t30_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ( ( v1_nfcont_1(k1_relset_1(u1_struct_0(A),C),A) & r3_nfcont_1(A,B,C,k1_relset_1(u1_struct_0(A),C)) ) => v1_nfcont_1(k2_relset_1(u1_struct_0(B),C),B) ) ) ) ) )).
fof(t30_nfcont_3,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t30_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k7_partfun1(k1_euclid(A),B,k2_xcmplx_0(C,D)) = k7_euclid(A,k7_partfun1(k1_euclid(A),B,C),k7_partfun1(k1_euclid(A),B,D)) ) ) ) => ( ! [C] : ( v1_xreal_0(C) => ~ r1_nfcont_4(A,B,C) ) | v1_nfcont_4(k2_partfun1(k1_numbers,k1_euclid(A),B,k1_numbers),A) ) ) ) ) )).
fof(t30_normform,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [C] : ! [D] : ( ( 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)) ) ) )).
fof(t30_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k4_normsp_2(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k4_normsp_2(A))))) ) => ( r1_funct_2(k4_ordinal1,u1_struct_0(A),k4_ordinal1,u1_struct_0(k4_normsp_2(A)),B,C) => ( v2_frechet(C,k4_normsp_2(A)) <=> v3_normsp_1(B,A) ) ) ) ) ) )).
fof(t30_numbers,axiom,( k4_ordinal1 != k2_numbers )).
fof(t30_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t30_openlatt,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t30_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_oppcat_1(C,A,B) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t30_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_nfcont_4(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ( k1_relset_1(k1_numbers,D) = k3_integra5(B,C) => r1_integr15(A,k3_integra5(B,C),D) ) ) ) ) ) )).
fof(t30_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r2_orders_1(A,B) => r1_orders_1(A,B) ) ) )).
fof(t30_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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 ) ) ) ) )).
fof(t30_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => k10_ordinal2(k5_ordinal1,A) = A ) )).
fof(t30_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => k10_ordinal2(k10_ordinal2(A,B),C) = k10_ordinal2(A,k10_ordinal2(B,C)) ) ) ) )).
fof(t30_ordinal4,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => k12_ordinal2(C,k10_ordinal2(A,B)) = k11_ordinal2(k12_ordinal2(C,B),k12_ordinal2(C,A)) ) ) ) )).
fof(t30_ordinal6,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t30_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ~ r1_orders_2(B,D,C) => k2_ortsp_1(A,B,E,F,C,D) = k2_ortsp_1(A,B,F,E,C,D) ) ) ) ) ) ) ) )).
fof(t30_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => k23_osafree(A,B,C) = a_3_4_osafree(A,B,C) ) ) ) )).
fof(t30_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t30_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t30_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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) ) ) ) ) ) ) ) ) ) ) )).
fof(t30_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_parsp_2(A,B,C,D,E) => r2_parsp_2(A,B,D,C,E) ) ) ) ) ) ) )).
fof(t30_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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)) ) ) )).
fof(t30_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,k1_relset_1(A,D)) => k7_partfun1(B,D,E) = C ) ) => r2_relset_1(A,B,D,k4_partfun2(A,B,k1_relset_1(A,D),C)) ) ) ) ) ) )).
fof(t30_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ( ( r1_setfam_1(D,B) & r1_setfam_1(D,C) ) => r1_setfam_1(D,k2_partit1(A,B,C)) ) ) ) ) ) )).
fof(t30_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) => ( ( v2_relat_2(C) & r1_tarski(k1_relat_1(C),A) ) => r2_relat_2(C,A) ) ) ) ) )).
fof(t30_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => v5_pasch(A) ) )).
fof(t30_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) )).
fof(t30_pcomps_1,axiom,( ! [A] : ( l1_metric_1(A) => r2_hidden(u1_struct_0(A),k2_pcomps_1(A)) ) )).
fof(t30_pcs_0,axiom,( ! [A] : ( ( v4_orders_2(A) & l2_pcs_0(A) ) => ! [B] : ( ~ r2_hidden(B,u1_struct_0(A)) => v4_orders_2(k20_pcs_0(A,B)) ) ) )).
fof(t30_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k4_real_ns1(A))) => ( ( r2_pdiff_1(B,A,C,D,F) & r2_pdiff_1(B,A,C,E,F) ) => ( r2_pdiff_1(B,A,C,k2_vfunct_1(u1_struct_0(k4_real_ns1(A)),k4_real_ns1(B),D,E),F) & k9_pdiff_1(A,B,C,k2_vfunct_1(u1_struct_0(k4_real_ns1(A)),k4_real_ns1(B),D,E),F) = k5_algstr_0(k16_lopban_1(k4_real_ns1(1),k4_real_ns1(B)),k9_pdiff_1(A,B,C,D,F),k9_pdiff_1(A,B,C,E,F)) ) ) ) ) ) ) ) ) )).
fof(t30_pdiff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(2)) => ! [C] : ( ( 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) & k10_pdiff_1(2,2,k26_valued_1(k1_euclid(2),k1_numbers,k1_pdiff_3(1,2,C),A),B) = k3_xcmplx_0(A,k3_pdiff_3(C,B)) ) ) ) ) ) )).
fof(t30_pdiff_4,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t30_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( 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) = k10_pdiff_1(3,3,k1_pdiff_3(1,3,B),A) ) ) ) )).
fof(t30_pdiff_6,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(B),k1_euclid(C)))) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t30_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [D] : ( ( 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] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t30_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( v1_xreal_0(E) => ( r3_pdiff_7(A,B,C,D) => r3_pdiff_7(A,B,k9_integr15(B,E,k1_euclid(A),C),D) ) ) ) ) ) ) )).
fof(t30_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( k1_newton(A,C) = k1_newton(A,B) => ( r1_xxreal_0(A,1) | C = B ) ) ) ) ) )).
fof(t30_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(B))) => ! [E] : ( 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)) ) ) ) ) )).
fof(t30_polyeq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( k4_polyeq_1(B,C,D,k5_numbers,A) = k5_numbers => ( B = k5_numbers | ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( v1_xcmplx_0(F) => ! [G] : ( v1_xcmplx_0(G) => ~ ( F = k6_xcmplx_0(k1_square_1(k7_xcmplx_0(C,k3_xcmplx_0(2,B))),k7_xcmplx_0(D,B)) & G = k7_xcmplx_0(C,k3_xcmplx_0(2,B)) & A != k5_numbers & A != k6_xcmplx_0(k2_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(F),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(F)),k1_square_1(k4_complex1(F))))),2)),k3_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(F)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(F)),k1_square_1(k4_complex1(F))))),2)),k7_complex1)),G) & A != k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(F),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(F)),k1_square_1(k4_complex1(F))))),2))),k3_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(F)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(F)),k1_square_1(k4_complex1(F))))),2))),k7_complex1)),G) & A != k6_xcmplx_0(k2_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(F),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(F)),k1_square_1(k4_complex1(F))))),2)),k3_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(F)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(F)),k1_square_1(k4_complex1(F))))),2))),k7_complex1)),G) & A != k6_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k3_complex1(F),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(F)),k1_square_1(k4_complex1(F))))),2))),k3_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_real_1(k3_complex1(F)),k3_square_1(k2_xcmplx_0(k1_square_1(k3_complex1(F)),k1_square_1(k4_complex1(F))))),2)),k7_complex1)),G) ) ) ) ) ) ) ) ) ) ) )).
fof(t30_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( v1_xcmplx_0(F) => ( F != k5_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(D,k1_newton(A,2))),k3_xcmplx_0(C,A)),B) = k5_numbers <=> ~ ( A != k5_polyeq_5(k7_xcmplx_0(B,F),k7_xcmplx_0(C,F),k7_xcmplx_0(D,F),k7_xcmplx_0(E,F)) & A != k6_polyeq_5(k7_xcmplx_0(B,F),k7_xcmplx_0(C,F),k7_xcmplx_0(D,F),k7_xcmplx_0(E,F)) & A != k7_polyeq_5(k7_xcmplx_0(B,F),k7_xcmplx_0(C,F),k7_xcmplx_0(D,F),k7_xcmplx_0(E,F)) & A != k8_polyeq_5(k7_xcmplx_0(B,F),k7_xcmplx_0(C,F),k7_xcmplx_0(D,F),k7_xcmplx_0(E,F)) ) ) ) ) ) ) ) ) ) )).
fof(t30_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => k11_polyform(A,k7_polyform(A)) = 1 ) )).
fof(t30_polynom1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( 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),k10_polynom1(A,B,k9_polynom1(A,B),C),C) ) ) ) )).
fof(t30_polynom3,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,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))) ) ) ) ) )).
fof(t30_polynom5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t30_polynom8,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k4_ordinal1) => ~ r1_polynom8(A,k4_struct_0(A),B) ) ) )).
fof(t30_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & l2_struct_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => r1_polyred(A,B,C,k8_polynom1(A,C),D) ) ) ) ) )).
fof(t30_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & k2_power(k3_xcmplx_0(A,B),C) != k3_xcmplx_0(k2_power(A,C),k2_power(B,C)) ) ) ) ) )).
fof(t30_pre_poly,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,k3_finseq_2(A)) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t30_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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))))) ) ) ) )).
fof(t30_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(k5_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)) ) ) ) ) ) )).
fof(t30_prob_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => k3_funct_2(B,k1_numbers,C,k4_prob_1(A,B)) = 1 ) ) ) )).
fof(t30_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m1_prob_1(E,A,B) => ! [F] : ( m1_prob_1(F,A,B) => ( ~ r1_xxreal_0(k3_funct_2(B,k1_numbers,C,k5_prob_1(A,B,D,E)),k5_numbers) => k3_funct_2(B,k1_numbers,C,k5_prob_1(A,B,k5_prob_1(A,B,D,E),F)) = k4_real_1(k4_real_1(k3_funct_2(B,k1_numbers,C,D),k3_funct_2(B,k1_numbers,k3_prob_2(A,B,C,D),E)),k3_funct_2(B,k1_numbers,k3_prob_2(A,B,C,k5_prob_1(A,B,D,E)),F)) ) ) ) ) ) ) ) )).
fof(t30_prob_3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k1_kurato_0(A,k2_prob_3(A,C)) = k1_kurato_0(A,C) ) ) )).
fof(t30_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),k4_prob_4(A,B,C)) => ! [E] : ! [F] : ( ( 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) ) ) ) ) ) )).
fof(t30_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t30_projpl_1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & v5_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t30_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t30_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k1_qc_lang1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t30_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t30_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ? [C] : ( m1_subset_1(C,k1_qc_lang1(A)) & k2_qc_lang3(A,C) = B ) ) ) )).
fof(t30_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t30_quantal1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r3_lattices(A,B,D) & r3_lattices(A,C,E) ) => r3_lattices(A,k9_quantal1(A,B,C),k9_quantal1(A,D,E)) ) ) ) ) ) ) )).
fof(t30_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ( k13_quaterni(k5_quatern2(A,B)) = k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(B),k13_quaterni(A)),k3_xcmplx_0(k14_quaterni(A),k14_quaterni(B))),k3_xcmplx_0(k15_quaterni(B),k15_quaterni(A))),k3_xcmplx_0(k16_quaterni(B),k16_quaterni(A))),k1_square_1(k28_quaterni(B))) & k14_quaterni(k5_quatern2(A,B)) = k7_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k13_quaterni(B),k14_quaterni(A)),k3_xcmplx_0(k14_quaterni(B),k13_quaterni(A))),k3_xcmplx_0(k15_quaterni(B),k16_quaterni(A))),k3_xcmplx_0(k16_quaterni(B),k15_quaterni(A))),k1_square_1(k28_quaterni(B))) & k15_quaterni(k5_quatern2(A,B)) = k7_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(B),k15_quaterni(A)),k3_xcmplx_0(k14_quaterni(B),k16_quaterni(A))),k3_xcmplx_0(k15_quaterni(B),k13_quaterni(A))),k3_xcmplx_0(k16_quaterni(B),k14_quaterni(A))),k1_square_1(k28_quaterni(B))) & k16_quaterni(k5_quatern2(A,B)) = k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k13_quaterni(B),k16_quaterni(A)),k3_xcmplx_0(k14_quaterni(B),k15_quaterni(A))),k3_xcmplx_0(k15_quaterni(B),k14_quaterni(A))),k3_xcmplx_0(k16_quaterni(B),k13_quaterni(A))),k1_square_1(k28_quaterni(B))) ) ) ) )).
fof(t30_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k1_square_1(k28_quaterni(k23_quaterni(k23_quaterni(A,B),C))) = k3_xcmplx_0(k3_xcmplx_0(k1_square_1(k28_quaterni(A)),k1_square_1(k28_quaterni(B))),k1_square_1(k28_quaterni(C))) ) ) ) )).
fof(t30_quaterni,axiom,( k13_quaterni(k1_xcmplx_0) = k5_numbers & k14_quaterni(k1_xcmplx_0) = 1 & k15_quaterni(k1_xcmplx_0) = k5_numbers & k16_quaterni(k1_xcmplx_0) = k5_numbers )).
fof(t30_quofield,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t30_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m2_prob_1(B,A,k1_random_1(A)) => ! [C] : ( m1_random_1(C,A,k1_random_1(A)) => r1_random_1(A,k1_random_1(A),C,B) ) ) ) )).
fof(t30_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_vectsp_6(E,A,B) => r1_tarski(k1_vectsp_6(A,C,k8_ranknull(A,B,C,E,D)),k2_ranknull(B,C,D,k1_vectsp_6(A,B,E))) ) ) ) ) ) )).
fof(t30_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ( ~ ( ~ r1_xxreal_0(k4_xcmplx_0(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(k4_xcmplx_0(1),A) ) ) ) )).
fof(t30_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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))) ) ) ) )).
fof(t30_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ 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,k3_seq_4(B)) & ~ r1_xxreal_0(k2_seq_4(B),A) ) ) ) )).
fof(t30_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k8_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t30_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [D] : ( ( v1_rearran1(D) & v2_rearran1(D) & v3_rearran1(D,k1_zfmisc_1(A)) & m2_finseq_1(D,k1_zfmisc_1(A)) ) => ( ( v1_partfun1(C,B) & k5_card_1(B) = k5_card_1(A) ) => ( k3_finseq_1(k20_rfunct_3(A,k3_rearran1(B,A,D,C),A)) = k5_card_1(A) & r1_xxreal_0(1,k3_finseq_1(k20_rfunct_3(A,k3_rearran1(B,A,D,C),A))) ) ) ) ) ) ) )).
fof(t30_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => k3_relat_1(k3_relat_1(A,C),B) = k3_relat_1(A,k3_relat_1(C,B)) ) ) ) )).
fof(t30_relset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,C))) => ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,k8_relset_1(A,C,D,B)) <=> ? [F] : ( m1_subset_1(F,C) & r2_hidden(k4_tarski(E,F),D) & r2_hidden(F,B) ) ) ) ) ) ) ) )).
fof(t30_relset_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t30_revrot_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t30_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ! [D] : ( ( r2_rewrite1(A,B,C) & r2_rewrite1(A,C,D) ) => r2_rewrite1(A,B,D) ) ) )).
fof(t30_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ( r2_rewrite2(A,k7_rewrite2(A,B),C,D) => r2_rewrite2(A,B,C,D) ) ) ) ) )).
fof(t30_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ~ v1_xboole_0(G) => ! [H] : ( m1_subset_1(H,k1_zfmisc_1(k8_afinsq_1(G))) => ! [I] : ( ( v2_rewrite3(I,G,H) & l1_rewrite3(I,H) ) => ( ( r2_rewrite3(G,H,I,A,B,C,E) & r2_rewrite3(G,H,I,A,B,D,F) ) => ( C = D & E = F ) ) ) ) ) )).
fof(t30_rfinseq,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ~ ( r2_hidden(C,k4_finseq_1(B)) & r2_classes1(A,B) & ! [D] : ~ ( r2_hidden(D,k4_finseq_1(B)) & k1_funct_1(A,C) = k1_funct_1(B,D) ) ) ) ) )).
fof(t30_rfinseq2,axiom,( ! [A] : ( 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_funct_1(k5_rfinseq2(A),1) = k3_rfinseq2(A) & k1_funct_1(k6_rfinseq2(A),1) = k4_rfinseq2(A) ) ) ) )).
fof(t30_rfunct_1,axiom,( ! [A] : ( ( 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)) ) )).
fof(t30_rfunct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t30_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( m1_subset_1(C,A) => r1_rfunct_3(A,k1_numbers,k15_rfunct_3(A,B),C) ) ) ) )).
fof(t30_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k2_relset_1(k1_numbers,k1_valued_0(k1_numbers,B,A)) = a_2_1_rinfsup1(A,B) ) ) )).
fof(t30_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( 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(k6_numbers,A,B)) & k1_rinfsup2(k1_valued_0(k6_numbers,A,B)) = k12_supinf_2(A,B) ) ) ) ) ) )).
fof(t30_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t30_rlaffin2,axiom,( ! [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) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(t30_rlaffin3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( 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),k4_ordinal1,k2_rlaffin3(B,C,A),k8_funcop_1(k4_ordinal1,k2_struct_0(B),k5_numbers)) & r2_hidden(A,C) ) ) ) )).
fof(t30_rlsub_1,axiom,( ! [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) ) => ! [B] : ( ( v1_rlvect_1(B) & m1_rlsub_1(B,A) ) => ! [C] : ( ( v1_rlvect_1(C) & m1_rlsub_1(C,A) ) => ( u1_struct_0(B) = u1_struct_0(C) => B = C ) ) ) ) )).
fof(t30_rlsub_2,axiom,( ! [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) ) => ! [B] : ( ( v1_rlvect_1(B) & m1_rlsub_1(B,A) ) => ! [C] : ( ( v1_rlvect_1(C) & m1_rlsub_1(C,A) ) => ( k1_rlsub_2(A,B,C) = C <=> k2_rlsub_2(A,B,C) = B ) ) ) ) )).
fof(t30_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t30_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t30_rlvect_2,axiom,( ! [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) ) => k6_rlvect_2(A,k4_rlvect_2(A)) = k4_struct_0(A) ) )).
fof(t30_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( m1_rlsub_1(D,A) => ( m1_rlsub_1(B,D) => m1_rlsub_1(k2_rlsub_2(A,B,C),D) ) ) ) ) ) )).
fof(t30_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( v1_rlvect_3(k8_domain_1(u1_struct_0(A),B,D,C),A) => ( B = C | B = D | C = D | v1_rlvect_3(k8_domain_1(u1_struct_0(A),B,k4_algstr_0(A,D),k4_algstr_0(A,C)),A) ) ) ) ) ) ) )).
fof(t30_rlvect_5,axiom,( ! [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_rlvect_5(A) & l1_rlvect_1(A) ) => k1_rlvect_5(A) = k1_rlvect_5(k2_rlsub_1(A)) ) )).
fof(t30_rlvect_x,axiom,( ! [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) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t30_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v2_vectsp_2(C,A) & m1_rmod_2(C,A,B) ) => ! [D] : ( ( v2_vectsp_2(D,A) & m1_rmod_2(D,A,B) ) => ( ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r1_struct_0(C,E) <=> r1_struct_0(D,E) ) ) => C = D ) ) ) ) ) )).
fof(t30_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t30_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t30_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t30_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) )).
fof(t30_robbins3,axiom,( ! [A] : ( ( ~ 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) ) ) ) )).
fof(t30_robbins4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v10_robbins1(A) & v8_robbins3(A) & v9_robbins3(A) & l4_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r1_robbins4(A,B,B) <=> B = k5_lattices(A) ) ) ) )).
fof(t30_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) )).
fof(t30_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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)) = k2_xcmplx_0(k2_xcmplx_0(k1_rpr_1(A,B),k1_rpr_1(A,C)),k1_rpr_1(A,D)) ) ) ) ) ) )).
fof(t30_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => k1_rusub_1(B) = k1_rusub_1(A) ) ) )).
fof(t30_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_bhsp_1(B) & m1_rusub_1(B,A) ) => ! [C] : ( ( v1_bhsp_1(C) & m1_rusub_1(C,A) ) => ( k1_rusub_2(A,B,C) = C <=> k2_rusub_2(A,B,C) = B ) ) ) ) )).
fof(t30_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_struct_0(k1_rusub_3(A,k6_domain_1(u1_struct_0(A),B)),B) ) ) )).
fof(t30_rusub_4,axiom,( ! [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) ) => ! [B] : ( ( v1_rlvect_1(B) & m1_rlsub_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t30_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_bhsp_1(A,B,C) => k1_square_1(k3_bhsp_1(A,k3_rlvect_1(A,B,C))) = k2_xcmplx_0(k1_square_1(k3_bhsp_1(A,B)),k1_square_1(k3_bhsp_1(A,C))) ) ) ) ) )).
fof(t30_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k8_rvsum_1(k2_finseq_2(A,B),k2_finseq_2(A,C)) = k2_finseq_2(A,k6_xcmplx_0(B,C)) ) ) ) )).
fof(t30_rvsum_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => k16_rvsum_1(k9_finseq_1(A)) = A ) )).
fof(t30_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [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(k7_card_1(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)) ) ) ) )).
fof(t30_scmbsort,axiom,( ! [A] : ( m1_scmfsa_2(A) => k5_card_1(k1_scmbsort(A)) = 63 ) )).
fof(t30_scmfsa10,axiom,( ! [A] : ( v7_ordinal1(A) => 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) = k4_ordinal1 ) )).
fof(t30_scmfsa8a,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,k5_card_1(C)))) ) ) ) ) )).
fof(t30_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [E] : ( ( 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),k7_card_1(3),k1_scmfsa_2) & ( ~ r1_xxreal_0(k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),k5_card_1(D)),7)))) ) & ( r1_xxreal_0(k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),k5_card_1(D)),7)))) ) ) ) ) ) ) ) )).
fof(t30_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( v1_ami_2(E) & ~ v1_scmfsa_m(E) & m1_subset_1(E,u1_struct_0(k1_scmfsa_2)) ) => ( ( k1_funct_1(B,E) = k5_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(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8b(E,C,D)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B)) = k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(C,k4_compos_1(k1_scmfsa_2))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B)),1) ) ) ) ) ) ) ) )).
fof(t30_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ( ( r5_scmfsa7b(D,B,A) & r6_scmfsa7b(D,B,A) ) => ( r1_xxreal_0(k1_funct_1(B,C),k5_numbers) | k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa_9(C,D)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,D),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B)),3))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,D),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,D),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B)))) ) ) ) ) ) ) )).
fof(t30_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ~ ( k2_compos_0(u1_compos_1(k1_scmfsa_2),A) = 8 & ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => A != k13_scmfsa_2(B,C) ) ) ) ) )).
fof(t30_scmfsa_m,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ( r1_tarski(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)),A) => k1_funct_1(A,k4_scmfsa_2(k5_numbers)) = 1 ) ) )).
fof(t30_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v3_scmpds_4(D) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( 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)) = k5_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) ) ) ) ) ) ) ) ) ) )).
fof(t30_scmpds_7,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => k5_card_1(k1_scmpds_7(A,B,C,D)) = k1_nat_1(k5_card_1(D),3) ) ) ) ) )).
fof(t30_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => k2_amistd_1(k7_card_1(2),k1_scmring2(A),k8_scmring2(A,B)) = k1_tarski(B) ) ) )).
fof(t30_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( k3_tarski(A) = k1_tarski(B) => A = k2_tarski(k1_xboole_0,k1_tarski(B)) ) ) )).
fof(t30_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r1_semi_af1(A,F,B,D) & r1_semi_af1(A,F,B,C) & r1_semi_af1(A,F,D,E) ) => ( F = B | F = D | r2_analoaf(A,B,D,C,E) ) ) ) ) ) ) ) ) )).
fof(t30_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C)),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B),C)) ) ) ) )).
fof(t30_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => k1_seq_2(k55_valued_1(k4_ordinal1,k2_numbers,k31_valued_1(k4_ordinal1,k2_numbers,A))) = k9_complex1(k3_comseq_2(A)) ) )).
fof(t30_seq_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => k9_nat_1(k1_numbers,A,B) = k7_xcmplx_0(1,k1_nat_1(B,1)) ) => ( v2_comseq_2(A) & k1_seq_2(A) = k5_numbers ) ) ) )).
fof(t30_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( ( r1_seqfunc(A,k1_numbers,B,D) & r1_seqfunc(A,k1_numbers,C,D) ) => ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,D) => ( r2_relset_1(k4_ordinal1,k1_numbers,k3_valued_1(k4_ordinal1,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(k4_ordinal1,k1_numbers,k47_valued_1(k4_ordinal1,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(k4_ordinal1,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k10_seqfunc(A,B,E),k10_seqfunc(A,C,E)),k10_seqfunc(A,k8_seqfunc(A,B,C),E)) ) ) ) ) ) ) ) )).
fof(t30_seqm_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v5_valued_0(B) => ( r1_xxreal_0(A,k5_numbers) | v5_valued_0(k26_valued_1(k4_ordinal1,k1_numbers,B,A)) ) ) & ( k5_numbers = A => v3_funct_1(k26_valued_1(k4_ordinal1,k1_numbers,B,A)) ) & ( v5_valued_0(B) => ( r1_xxreal_0(k5_numbers,A) | v6_valued_0(k26_valued_1(k4_ordinal1,k1_numbers,B,A)) ) ) ) ) ) )).
fof(t30_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,A,C)) & k9_nat_1(k1_numbers,B,C) = k1_power(C,k9_nat_1(k1_numbers,A,C)) ) ) & v2_comseq_2(B) & ~ r1_xxreal_0(k1_seq_2(B),1) & v1_series_1(A) ) ) ) )).
fof(t30_series_3,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => ( ( r1_xxreal_0(B,A) & r1_xxreal_0(C,B) ) => r1_xxreal_0(k2_power(k3_xcmplx_0(k3_xcmplx_0(A,B),C),k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C),3)),k3_xcmplx_0(k3_xcmplx_0(k2_power(A,A),k2_power(B,B)),k2_power(C,C))) ) ) ) ) )).
fof(t30_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => r1_xxreal_0(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(9,A),B),C),k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(C))),k2_xcmplx_0(k2_xcmplx_0(A,B),C)) ) ) ) )).
fof(t30_setfam_1,axiom,( ! [A] : ! [B] : r1_tarski(k1_setfam_1(k4_setfam_1(A,B)),k6_subset_1(k1_setfam_1(A),k1_setfam_1(B))) )).
fof(t30_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k3_funct_2(k4_ordinal1,k9_setfam_1(A),k2_setlim_1(A,B),C) = k3_subset_1(A,k3_funct_2(k4_ordinal1,k9_setfam_1(A),k4_setlim_1(A,k2_prob_1(A,B)),C)) ) ) )).
fof(t30_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v2_prob_1(C) => v2_prob_1(k8_setlim_2(A,C,B)) ) ) ) )).
fof(t30_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ( v3_binop_1(C,B) & v1_binop_1(C,B) & v2_binop_1(C,B) & v1_setwiseo(C,B) ) => ! [E] : ( m1_subset_1(E,k5_finsub_1(A)) => ! [F] : ( m1_subset_1(F,k5_finsub_1(A)) => k7_setwiseo(A,B,C,k5_setwiseo(A,E,F),D) = k5_binop_1(B,C,k7_setwiseo(A,B,C,E,D),k7_setwiseo(A,B,C,F,D)) ) ) ) ) ) ) ) )).
fof(t30_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t30_sf_mastr,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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)) ) ) )).
fof(t30_sgraph1,axiom,( ! [A] : ! [B] : ( m1_sgraph1(B,A) => ! [C] : ! [D] : ~ ( r2_hidden(D,u1_sgraph1(B)) & k4_sgraph1(A,B,C) = k5_numbers & r2_hidden(C,D) ) ) )).
fof(t30_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & l3_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => B = k6_sheffer1(A,k6_sheffer1(A,B)) ) ) )).
fof(t30_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t30_simplex0,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t30_simplex1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(C,k6_simplex0(B)) & ! [D] : ( ( v3_pre_topc(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ~ ( k5_card_1(D) = k2_xcmplx_0(C,1) & v1_rlaffin1(k1_simplex1(A,B,D),A) ) ) ) ) ) => k6_simplex0(B) = k6_simplex0(k4_simplex1(A,B)) ) ) ) )).
fof(t30_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_funct_1(k18_sin_cos,k5_numbers) = 1 & k1_funct_1(k16_sin_cos,k5_numbers) = k5_numbers & k1_funct_1(k18_sin_cos,k4_xcmplx_0(A)) = k1_funct_1(k18_sin_cos,A) & k1_funct_1(k16_sin_cos,k4_xcmplx_0(A)) = k4_xcmplx_0(k1_funct_1(k16_sin_cos,A)) ) ) )).
fof(t30_sin_cos2,axiom,( k1_relset_1(k1_numbers,k1_sin_cos2) = k1_numbers & k1_relset_1(k1_numbers,k3_sin_cos2) = k1_numbers & k1_relset_1(k1_numbers,k5_sin_cos2) = k1_numbers )).
fof(t30_sin_cos3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k15_sin_cos(k3_xcmplx_0(k3_xcmplx_0(k1_nat_1(k2_nat_1(2,A),1),k28_sin_cos),k7_complex1)) = k4_xcmplx_0(1) ) )).
fof(t30_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k3_xcmplx_0(k17_sin_cos(A),k19_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)))) ) ) )).
fof(t30_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_sin_cos4(k7_xcmplx_0(A,2)) = k3_square_1(k7_xcmplx_0(k6_xcmplx_0(1,k19_sin_cos(A)),k2_xcmplx_0(1,k19_sin_cos(A)))) | k1_sin_cos4(k7_xcmplx_0(A,2)) = k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k6_xcmplx_0(1,k19_sin_cos(A)),k2_xcmplx_0(1,k19_sin_cos(A))))) ) ) )).
fof(t30_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(k7_xcmplx_0(k28_sin_cos,2),A) & r1_xxreal_0(1,k17_sin_cos(A)) ) ) )).
fof(t30_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( k5_numbers != A & k6_xcmplx_0(k1_square_1(k23_sin_cos(A)),1) = k5_numbers ) ) )).
fof(t30_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(k5_numbers,A) => k6_sin_cos2(k7_xcmplx_0(A,2)) = k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k6_xcmplx_0(k4_sin_cos2(A),1),k2_xcmplx_0(k4_sin_cos2(A),1)))) ) ) )).
fof(t30_sin_cos9,axiom,( k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_sin_cos9,k1_rcomp_1(k4_xcmplx_0(1),1)),k2_partfun1(k1_numbers,k1_numbers,k27_sin_cos,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos)))) = k1_partfun2(k1_numbers,k1_rcomp_1(k4_xcmplx_0(1),1)) )).
fof(t30_sincos10,axiom,( k1_funct_1(k16_sin_cos,k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4))) = k4_xcmplx_0(k7_xcmplx_0(1,k3_square_1(2))) & k1_funct_1(k18_sin_cos,k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4))) = k7_xcmplx_0(1,k3_square_1(2)) & k1_funct_1(k16_sin_cos,k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos)) = k7_xcmplx_0(1,k3_square_1(2)) & k1_funct_1(k18_sin_cos,k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos)) = k4_xcmplx_0(k7_xcmplx_0(1,k3_square_1(2))) )).
fof(t30_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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(k1_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,k1_nat_1(A,1)) & E = k7_partfun1(u1_struct_0(k15_euclid(2)),B,k1_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) ) ) ) ) ) ) ) )).
fof(t30_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ( ( v2_topreal1(A) & k1_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))) ) ) ) ) )).
fof(t30_sprect_2,axiom,( ! [A] : ( ( ~ 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))) ) ) ) )).
fof(t30_sprect_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t30_sprect_5,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t30_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => k3_square_1(k7_xcmplx_0(A,B)) = k7_xcmplx_0(k3_square_1(A),k3_square_1(B)) ) ) ) )).
fof(t30_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ? [D] : ( m1_subset_1(D,u4_struct_0(A)) & k9_stacks_1(A,D) = C & r2_hidden(D,k11_stacks_1(A,B)) ) ) ) ) )).
fof(t30_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( k3_stirl2_1(A,k5_numbers) = 1 <=> A = k5_numbers ) ) )).
fof(t30_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k16_substut1(A),k38_substut1(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t30_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,B) <=> ~ r2_hidden(D,C) ) ) => B = k3_subset_1(A,C) ) ) ) )).
fof(t30_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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))) ) ) ) )).
fof(t30_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t30_supinf_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k6_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t30_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( 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,E,C) & ~ r1_orders_2(B,E,G) & ~ r1_orders_2(B,F,C) & ~ r1_orders_2(B,F,G) & ~ r1_orders_2(B,D,C) & k8_group_1(A,k8_group_1(A,k1_symsp_1(A,B,C,D,E),k1_symsp_1(A,B,E,C,G)),k1_symsp_1(A,B,G,E,H)) != k8_group_1(A,k8_group_1(A,k1_symsp_1(A,B,C,D,F),k1_symsp_1(A,B,F,C,G)),k1_symsp_1(A,B,G,F,H)) ) ) ) ) ) ) ) ) ) )).
fof(t30_sysrel,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) ) ) ) ) )).
fof(t30_taxonom1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t30_taylor_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(C,B) => ! [D] : ( v7_ordinal1(D) => ( 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)) ) ) ) ) ) ) )).
fof(t30_tdlat_1,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t30_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) )).
fof(t30_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v4_tdlat_3(A) <=> ! [B] : ( 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)) ) ) ) ) )).
fof(t30_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(D,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => r1_tarski(k3_polynom1(k15_pre_poly(A),B,k10_polynom1(A,B,C,D)),a_4_0_termord(A,B,C,D)) ) ) ) ) )).
fof(t30_tex_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t30_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v2_tex_2(k6_domain_1(u1_struct_0(A),B),A) ) ) )).
fof(t30_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( v2_tops_1(B,A) & ! [C] : ( ( v1_pre_topc(C) & m1_pre_topc(C,A) ) => ~ ( v3_tex_3(C,A) & B = u1_struct_0(C) ) ) ) ) ) )).
fof(t30_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t30_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ v2_struct_0(E) & m1_pre_topc(E,A) ) => ( ( m1_pre_topc(B,D) & m1_pre_topc(C,E) ) => ( ( ~ r1_tsep_1(D,E) & ~ r1_tsep_1(k2_tsep_1(A,D,E),k1_tsep_1(A,B,C)) ) | ( r1_tsep_1(D,C) & r1_tsep_1(E,B) ) ) ) ) ) ) ) ) )).
fof(t30_toler_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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,C),k4_toler_1(A,B)) => r1_relset_1(A,A,C,B) ) ) ) )).
fof(t30_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t30_topalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t30_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)))) ) ) ) ) )).
fof(t30_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( v7_topalg_6(B,A) & m2_subset_1(B,k4_partfun1(k1_numbers,k2_struct_0(A)),k1_topalg_6(A)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( m1_borsuk_2(k3_relat_1(k1_borsuk_6(k5_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) ) ) ) ) ) ) )).
fof(t30_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t30_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t30_topgen_3,axiom,( r2_hidden(k4_ordinal1,k3_topgen_3) )).
fof(t30_topgen_4,axiom,( ! [A] : ! [B] : ~ ( k2_setfam_1(A,B) = k1_xboole_0 & A != k1_xboole_0 & B != k1_xboole_0 ) )).
fof(t30_topgen_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_topgen_5)) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & ? [D] : ( 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] : ( 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))) ) ) ) ) ) ) )).
fof(t30_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m3_topgrp_1(B,A) => ! [C] : ( 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) ) ) ) )).
fof(t30_topreal1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => k4_topreal1(A) = a_1_0_topreal1(A) ) )).
fof(t30_topreal8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t30_topreal9,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_tarski(k1_rltopsp1(A,B,C),k4_topreal9(A,B,C)) ) ) ) )).
fof(t30_topreala,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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))) ) ) ) ) )).
fof(t30_toprealc,axiom,( ! [A] : ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_valued_2(C) => ! [D] : ( ( 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)) ) ) ) )).
fof(t30_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => r1_xxreal_0(k12_euclid(k5_algstr_0(k15_euclid(A),B,C)),k2_xcmplx_0(k12_euclid(B),k12_euclid(C))) ) ) ) )).
fof(t30_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)) ) ) )).
fof(t30_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t30_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t30_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t30_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => k4_trees_1(A,k6_finseq_1(k4_ordinal1)) = A ) )).
fof(t30_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_trees_2(A) ) => ~ ( ! [B] : ( v7_ordinal1(B) => ? [C] : ( v1_finset_1(C) & m1_trees_2(C,A) & k5_card_1(C) = B ) ) & ! [B] : ( m1_trees_2(B,A) => v1_finset_1(B) ) ) ) )).
fof(t30_trees_3,axiom,( ! [A] : ( v6_trees_3(k9_finseq_1(A)) <=> ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) ) )).
fof(t30_trees_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_trees_3(E,k2_zfmisc_1(A,B)) ) => ! [F] : ( m2_finseq_1(F,E) => ? [G] : ( m2_finseq_1(G,k4_trees_3(B)) & k4_finseq_1(G) = k4_finseq_1(F) & ! [H] : ( v7_ordinal1(H) => ~ ( r2_hidden(H,k4_finseq_1(F)) & ! [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) ) ) ) ) ) ) ) )).
fof(t30_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) ) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v6_trees_3(C) ) => ( A = k4_trees_4(B,C) => ! [D] : ( ( v1_xboole_0(D) & m1_trees_1(D,k9_xtuple_0(A)) ) => k2_trees_9(A,D) = k15_trees_3(C) ) ) ) ) )).
fof(t30_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_tsep_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t30_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ~ r3_tsep_2(A,B,B) ) ) )).
fof(t30_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(t30_turing_1,axiom,( k1_funct_1(k15_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers)) = k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,1,k5_numbers,1) & k1_funct_1(k15_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,1,1)) = k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,1,1,1) & k1_funct_1(k15_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,1,k5_numbers)) = k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,2,1,1) & k1_funct_1(k15_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,2,k5_numbers)) = k3_xtuple_0(3,k5_numbers,k4_xcmplx_0(1)) & k1_funct_1(k15_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,2,1)) = k3_xtuple_0(3,k5_numbers,k4_xcmplx_0(1)) & k1_funct_1(k15_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,3,1)) = k3_xtuple_0(3,1,k4_xcmplx_0(1)) & k1_funct_1(k15_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,3,k5_numbers)) = k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,4,k5_numbers,k5_numbers) )).
fof(t30_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ~ v1_facirc_1(k2_msafree2(k34_twoscomp(A,B))) ) ) )).
fof(t30_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( 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)) ) ) ) )).
fof(t30_uproots,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( k1_algseq_1(A,B) = k5_numbers | k1_algseq_1(A,C) = k5_numbers ) => k1_algseq_1(A,k11_polynom3(A,B,C)) = k5_numbers ) ) ) ) )).
fof(t30_urysohn2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(C,A) & ~ r1_xxreal_0(B,C) & ~ r1_xxreal_0(D,A) & ~ r1_xxreal_0(B,D) & r1_xxreal_0(k6_xcmplx_0(B,A),k9_complex1(k6_xcmplx_0(D,C))) ) ) ) ) ) )).
fof(t30_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( m2_subset_1(F,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [G] : ( m1_valuat_1(G,A,B) => ! [H] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t30_valued_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ! [D] : ( ( 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(k4_ordinal1,B,A,C,D)) ) ) ) ) ) )).
fof(t30_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) ) => r2_hidden(k62_valued_1(A),k1_relset_1(k4_ordinal1,A)) ) )).
fof(t30_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t30_vectsp10,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t30_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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))))) ) ) ) ) )).
fof(t30_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t30_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( 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) ) ) ) ) ) ) )).
fof(t30_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( v7_vectsp_1(C,A) & m1_vectsp_4(C,A,B) ) => ! [D] : ( ( v7_vectsp_1(D,A) & m1_vectsp_4(D,A,B) ) => ( ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r1_struct_0(C,E) <=> r1_struct_0(D,E) ) ) => C = D ) ) ) ) ) )).
fof(t30_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( ( v7_vectsp_1(E,A) & m1_vectsp_4(E,A,B) ) => ( m1_vectsp_4(E,A,D) => k1_vectsp_5(A,B,E,k2_vectsp_5(A,B,C,D)) = k2_vectsp_5(A,B,k1_vectsp_5(A,B,E,C),D) ) ) ) ) ) ) )).
fof(t30_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(t30_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( 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)) ) ) ) ) )).
fof(t30_vfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,u1_struct_0(C)))) ) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t30_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [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),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))) ) ) ) ) ) )).
fof(t30_waybel11,axiom,( ! [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] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t30_waybel12,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( m1_waybel12(C,A,B) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(t30_waybel13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t30_waybel14,axiom,( ! [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) ) => ( v3_waybel_3(A) => v1_waybel14(k5_waybel_2(A),A) ) ) )).
fof(t30_waybel15,axiom,( ! [A] : ( ( 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)) ) ) ) )).
fof(t30_waybel16,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ( v1_waybel16(B,A) & ! [C] : ( 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) ) ) ) ) ) ) )).
fof(t30_waybel19,axiom,( ! [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) & 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)))) ) ) )).
fof(t30_waybel21,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ v1_xboole_0(C) & v2_waybel_0(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( 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] : ( ( ~ 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)) ) ) ) ) ) ) )).
fof(t30_waybel23,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v2_waybel23(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v1_waybel_0(B,A) ) ) )).
fof(t30_waybel25,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t30_waybel26,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : r6_pboole(B,k12_pralg_1(B,k7_funcop_1(B,A)),k7_funcop_1(B,u1_struct_0(A))) ) )).
fof(t30_waybel27,axiom,( ! [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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(t30_waybel28,axiom,( ! [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] : ( 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) ) ) ) ) )).
fof(t30_waybel29,axiom,( ! [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) ) => ( v3_waybel_3(k1_yellow_1(k5_waybel11(A))) <=> ! [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) ) => k5_waybel11(k3_yellow_3(B,A)) = u1_pre_topc(k2_borsuk_1(k1_waybel29(B),k1_waybel29(A))) ) ) ) )).
fof(t30_waybel30,axiom,( ! [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) & l1_waybel_9(A) ) => ( v3_waybel_3(A) <=> ( v2_waybel_2(A) & v8_pre_topc(A) ) ) ) )).
fof(t30_waybel34,axiom,( ! [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] : ( ( 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)) ) ) ) )).
fof(t30_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t30_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) )).
fof(t30_waybel_2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t30_waybel_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => v5_orders_2(k3_waybel_3(A,B,C)) ) => v5_orders_2(k4_yellow_1(A,B)) ) ) ) )).
fof(t30_waybel_4,axiom,( ! [A] : ( ( 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(k1_yellow_1(k3_waybel_4(A))),u1_struct_0(k1_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(k1_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A)),u1_struct_0(k8_waybel_4(A)),u1_struct_0(k1_yellow_1(k3_waybel_4(A))),k9_waybel_4(A),k10_waybel_4(A)),k6_partfun1(k9_xtuple_0(k9_waybel_4(A)))) ) )).
fof(t30_waybel_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ! [E] : ( ( 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)) ) ) ) ) )).
fof(t30_waybel_6,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( B != k4_yellow_0(A) => ( v5_waybel_6(B,A) <=> ? [C] : ( ~ 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) ) ) ) ) ) )).
fof(t30_waybel_8,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( r2_hidden(B,u1_struct_0(k1_waybel_8(k2_yellow_1(A)))) <=> v1_finset_1(B) ) ) )).
fof(t30_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v8_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r3_waybel_9(A,B,C) ) ) ) )).
fof(t30_weddwitt,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t30_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(D,B) & r2_hidden(E,C) & k3_metric_1(A,D,E) = k7_weierstr(A,B,C) ) ) ) ) ) ) ) )).
fof(t30_wellord1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) ) ) ) )).
fof(t30_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( k3_int_2(A,B) = 1 & r1_nat_d(A,k3_xcmplx_0(B,C)) ) => r1_nat_d(A,C) ) ) ) ) )).
fof(t30_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(A,C) => k2_xboole_0(A,k3_xboole_0(B,C)) = k3_xboole_0(k2_xboole_0(A,B),C) ) )).
fof(t30_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( 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))) ) ) ) )).
fof(t30_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k2_xcmplx_0(k6_xcmplx_0(A,B),C) = k2_xcmplx_0(k6_xcmplx_0(C,B),A) ) ) ) )).
fof(t30_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(B,k2_xcmplx_0(A,B)) ) ) ) )).
fof(t30_xtuple_0,axiom,( ! [A] : ! [B] : r1_tarski(k5_xboole_0(k10_xtuple_0(A),k10_xtuple_0(B)),k10_xtuple_0(k5_xboole_0(A,B))) )).
fof(t30_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(k4_xxreal_0(B,C),A) => r1_xxreal_0(B,A) ) ) ) ) )).
fof(t30_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( r1_xxreal_0(A,B) & v1_xboole_0(k1_xxreal_1(A,B)) ) ) ) )).
fof(t30_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( ~ r1_xxreal_0(B,A) => k1_xxreal_2(k3_xxreal_1(A,B)) = B ) ) ) )).
fof(t30_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t30_yellow10,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( l1_orders_2(B) => ! [C] : ( 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)) ) ) ) )).
fof(t30_yellow12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t30_yellow14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_waybel18(A,k7_funcop_1(A,B)))) => ! [D] : ( 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] : ( 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)))) ) ) ) ) ) ) )).
fof(t30_yellow16,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_yellow_1(A,B)))) => ( r1_yellow_0(k4_yellow_1(A,B),C) <=> ! [D] : ( m1_subset_1(D,A) => r1_yellow_0(k2_yellow16(A,B,D),k5_waybel_3(A,B,D,C)) ) ) ) ) ) )).
fof(t30_yellow18,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) ) )).
fof(t30_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t30_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v3_altcat_2(C,A) & m1_altcat_2(C,A) ) => ! [D] : ( ( v16_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ! [H] : ( m1_subset_1(H,u1_struct_0(C)) => ( ( G = E & H = F ) => ( k1_altcat_1(C,G,H) = k1_xboole_0 | ! [I] : ( m1_subset_1(I,k1_altcat_1(A,E,F)) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t30_yellow_0,axiom,( ! [A] : ( ( v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ( B = k1_yellow_0(A,C) & r1_yellow_0(A,C) ) => ( r2_lattice3(A,C,B) & ! [D] : ( 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] : ( 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) ) ) ) ) ) )).
fof(t30_yellow_2,axiom,( ! [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] : ( ( ~ 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) ) ) ) )).
fof(t30_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t30_yellow_4,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( ( B = D & C = E ) => k13_lattice3(k1_yellow_1(k7_waybel_0(A)),B,C) = k3_waybel_0(A,k2_yellow_4(A,D,E)) ) ) ) ) ) ) )).
fof(t30_yellow_5,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t30_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t30_yellow_7,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_yellow_0(A) <=> v2_yellow_0(k7_lattice3(A)) ) ) )).
fof(t30_yellow_9,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(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)))) ) => ( 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)))) ) ) ) )).
fof(t30_zf_fund1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => A = k3_zf_fund1(k2_zf_lang(k5_card_1(A))) ) )).
fof(t30_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ( k7_zf_lang(C,A) = k7_zf_lang(D,B) => ( C = D & A = B ) ) ) ) ) ) )).
fof(t30_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( 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 ) ) ) )).
fof(t30_zfmisc_1,axiom,( ! [A] : ! [B] : ( r1_tarski(k1_tarski(A),B) <=> r2_hidden(A,B) ) )).
fof(t30_zfrefle1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( 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] : ( ( v3_ordinal1(C) & m1_subset_1(C,A) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t30_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ( D = B => k4_algstr_0(A,B) = k4_algstr_0(C,D) ) ) ) ) ) )).
fof(t30_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => r1_zmodul02(A,k23_zmodul02(A,k5_numbers,B),k19_zmodul02(A)) ) ) )).
fof(t30_zmodul03,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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) & v1_zmodul03(B) & l1_zmodul01(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( v1_int_1(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(A))) => ( D = E => k4_vectsp_1(k9_int_3(A),k12_zmodul02(A,B),E,k13_zmodul02(A,B,C)) = k13_zmodul02(A,B,k1_zmodul01(B,C,D)) ) ) ) ) ) ) )).
fof(t310_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(C,D) & r1_xxreal_0(A,B) ) => k6_subset_1(k2_xxreal_1(C,B),k1_xxreal_1(A,D)) = k2_xboole_0(k2_xxreal_1(C,A),k4_xxreal_1(D,B)) ) ) ) ) ) )).
fof(t311_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(A,B) => ( r1_xxreal_0(D,C) | k6_subset_1(k3_xxreal_1(C,B),k1_xxreal_1(A,D)) = k2_xboole_0(k4_xxreal_1(C,A),k3_xxreal_1(D,B)) ) ) ) ) ) ) )).
fof(t312_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(C,D) & r1_xxreal_0(A,B) ) => k6_subset_1(k1_xxreal_1(C,B),k1_xxreal_1(A,D)) = k2_xboole_0(k2_xxreal_1(C,A),k3_xxreal_1(D,B)) ) ) ) ) ) )).
fof(t313_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r1_xxreal_0(C,A) & r1_xxreal_0(A,B) ) => k6_subset_1(k4_xxreal_1(C,B),k1_tarski(A)) = k2_xboole_0(k4_xxreal_1(C,A),k4_xxreal_1(A,B)) ) ) ) ) )).
fof(t314_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r1_xxreal_0(C,A) & r1_xxreal_0(A,B) ) => k6_subset_1(k2_xxreal_1(C,B),k1_tarski(A)) = k2_xboole_0(k2_xxreal_1(C,A),k4_xxreal_1(A,B)) ) ) ) ) )).
fof(t315_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(A,B) => ( r1_xxreal_0(A,C) | k6_subset_1(k3_xxreal_1(C,B),k1_tarski(A)) = k2_xboole_0(k4_xxreal_1(C,A),k3_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t316_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r1_xxreal_0(C,A) & r1_xxreal_0(A,B) ) => k6_subset_1(k1_xxreal_1(C,B),k1_tarski(A)) = k2_xboole_0(k2_xxreal_1(C,A),k3_xxreal_1(A,B)) ) ) ) ) )).
fof(t317_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(A,B) => ( r1_xxreal_0(B,C) | k6_subset_1(k3_xxreal_1(C,B),k4_xxreal_1(A,B)) = k2_xboole_0(k3_xxreal_1(C,A),k1_tarski(B)) ) ) ) ) ) )).
fof(t318_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r1_xxreal_0(C,B) & r1_xxreal_0(A,B) ) => k6_subset_1(k1_xxreal_1(C,B),k4_xxreal_1(A,B)) = k2_xboole_0(k1_xxreal_1(C,A),k1_tarski(B)) ) ) ) ) )).
fof(t319_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(A,B) => ( r1_xxreal_0(B,C) | k6_subset_1(k3_xxreal_1(C,B),k2_xxreal_1(A,B)) = k2_xboole_0(k4_xxreal_1(C,A),k1_tarski(B)) ) ) ) ) ) )).
fof(t31_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t31_abcmiz_1,axiom,( ! [A] : ( m2_finseq_2(A,k2_abcmiz_1,k4_abcmiz_1) => ! [B] : ( 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)) ) ) ) ) )).
fof(t31_abcmiz_a,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_abcmiz_1)) ) => ? [B] : ( m2_finseq_2(B,k2_abcmiz_1,k4_abcmiz_1) & k2_relset_1(k2_abcmiz_1,B) = k1_abcmiz_1(A) ) ) )).
fof(t31_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t31_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t31_afinsq_1,axiom,( ! [A] : k5_afinsq_1(A) = k1_tarski(k4_tarski(k5_numbers,A)) )).
fof(t31_afinsq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_finset_1(B) & v6_membered(B) ) => ! [C] : ( ( 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)),k1_nat_1(A,k1_afinsq_1(k4_afinsq_2(B)))) ) ) ) ) ) )).
fof(t31_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k13_afproj(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t31_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & k1_afvect0(A,C,D) = B ) ) ) ) )).
fof(t31_algspec1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v11_struct_0(B) & v1_instalg1(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r3_pua2mss1(A,B,C,D) => r1_algspec1(A,C,D) ) ) ) ) ) )).
fof(t31_algstr_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k14_algstr_4(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t31_altcat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_altcat_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t31_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v16_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t31_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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 ) ) ) ) ) )).
fof(t31_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_analmetr(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C))) => ! [G] : ( 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,G,E,F) & r4_analmetr(k2_analmetr(A,B,C),E,G,F,D) ) => r4_analmetr(k2_analmetr(A,B,C),F,G,D,E) ) ) ) ) ) ) ) ) )).
fof(t31_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( r1_analmetr(A,F,G) & r2_analort(A,F,G,B,D,C,E) & r2_analort(A,F,G,B,D,E,C) & B != D & C != E ) ) ) ) ) ) ) ) )).
fof(t31_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => ~ ( v4_collsp(k5_anproj_1(A)) & v3_anproj_2(k5_anproj_1(A)) & ? [B] : ( m1_subset_1(B,u1_struct_0(k5_anproj_1(A))) & ? [C] : ( m1_subset_1(C,u1_struct_0(k5_anproj_1(A))) & ? [D] : ( m1_subset_1(D,u1_struct_0(k5_anproj_1(A))) & ~ r1_collsp(k5_anproj_1(A),B,C,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(k5_anproj_1(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k5_anproj_1(A))) => ? [G] : ( m1_subset_1(G,u1_struct_0(k5_anproj_1(A))) & ? [H] : ( 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] : ( ( ~ 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) ) ) ) ) )).
fof(t31_aofa_000,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_freealg(C,A) => ( r1_tarski(C,B) => m1_freealg(B,A) ) ) ) ) )).
fof(t31_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( m2_subset_1(F,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),u8_aofa_a00(A))) => k15_aofa_a00(A,B,C,D,u8_aofa_a00(A),k22_aofa_a00(A,C,G),F) = k22_aofa_a00(A,D,k15_aofa_a00(A,B,C,D,u8_aofa_a00(A),G,F)) ) ) ) ) ) ) ) )).
fof(t31_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [E] : ( ( v1_aofa_i00(E,A,B,D) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),D) ) => ! [F] : ( v1_int_1(F) => ! [G] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t31_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( 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] : ( m1_subset_1(D,k1_zfmisc_1(A)) & ? [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) & B = D & r4_armstrng(A,C,E,D) ) ) ) ) )).
fof(t31_arytm_3,axiom,( ! [A] : ( v3_ordinal1(A) => ( r2_hidden(A,k5_arytm_3) => r2_hidden(A,k4_ordinal1) ) ) )).
fof(t31_asympt_1,axiom,( r1_tarski(k6_asympt_0(k4_asympt_1(k5_numbers)),k6_asympt_0(k4_asympt_1(1))) & k6_asympt_0(k4_asympt_1(k5_numbers)) != k6_asympt_0(k4_asympt_1(1)) )).
fof(t31_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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] : ( 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,k5_numbers)) & v1_funct_2(k1_funct_1(C,k5_numbers),u1_struct_0(A),u1_struct_0(B)) & m1_subset_1(k1_funct_1(C,k5_numbers),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) ) ) ) ) )).
fof(t31_bagorder,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t31_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( r2_hidden(B,k5_bcialg_1(A)) <=> ! [C] : ( 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) ) ) ) ) )).
fof(t31_bcialg_2,axiom,( ! [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] : ( 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 ) ) ) ) )).
fof(t31_bcialg_3,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t31_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t31_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t31_bcialg_6,axiom,( ! [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] : ( 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)) ) ) ) )).
fof(t31_bciideal,axiom,( ! [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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) )).
fof(t31_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_bhsp_1(A,k4_algstr_0(A,B)) = k3_bhsp_1(A,B) ) ) )).
fof(t31_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,A,C))) & k1_seq_2(k2_bhsp_2(A,k5_vfunct_1(k4_ordinal1,A,C))) = k3_bhsp_1(A,k4_algstr_0(A,B)) ) ) ) ) ) )).
fof(t31_bhsp_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ~ ( ! [D] : ( v7_ordinal1(D) => k1_normsp_1(B,C,D) != k4_struct_0(B) ) & ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,A,D) = k7_xcmplx_0(k3_bhsp_1(B,k1_normsp_1(B,C,k1_nat_1(D,1))),k3_bhsp_1(B,k1_normsp_1(B,C,D))) ) & v2_comseq_2(A) & ~ r1_xxreal_0(k1_seq_2(A),1) & v1_bhsp_4(C,B) ) ) ) ) )).
fof(t31_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t31_binari_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(k5_series_1(2,A),B) => ! [C] : ( ( 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) ) ) ) ) ) ) )).
fof(t31_binari_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_int_1(B,C,k5_series_1(2,A)) => k1_binari_3(A,B) = k1_binari_3(A,C) ) ) ) ) )).
fof(t31_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t31_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) ) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( ~ r2_hidden(E,k2_struct_0(B)) & D = k6_domain_1(u1_struct_0(A),E) ) ) ) ) ) ) ) )).
fof(t31_borsuk_4,axiom,( v1_tsep_1(k1_borsuk_4,k5_topmetr) )).
fof(t31_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t31_borsuk_6,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t31_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [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))) ) )).
fof(t31_bspace,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => k11_bspace(A,k1_bspace(k7_bspace(A)),B) = k1_bspace(k2_bspace) ) ) )).
fof(t31_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t31_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t31_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t31_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t31_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_eqrel_1(C,A) => r1_bvfunc_1(A,k16_bvfunc_1(A,B,C),B) ) ) ) )).
fof(t31_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(E,A) => ( r3_bvfunc_2(A,D,B,E) => r1_bvfunc_1(A,k6_bvfunc_2(A,k10_bvfunc_1(A,C,D),B,E),k10_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),D)) ) ) ) ) ) ) )).
fof(t31_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t31_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t31_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t31_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t31_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [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))) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k11_c0sp1(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k11_c0sp1(A))) => ! [G] : ( 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] : ( m1_subset_1(H,A) => k3_funct_2(A,k1_numbers,D,H) = k4_real_1(k3_funct_2(A,k1_numbers,B,H),k3_funct_2(A,k1_numbers,C,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t31_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( r2_hidden(B,k6_c0sp2(A)) => r2_hidden(B,k2_c0sp2(A)) ) ) )).
fof(t31_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k2_zfmisc_1(k4_calcul_1(A),k2_cqc_the1)) => ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(B)) & ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(k5_numbers,D) & r1_xxreal_0(D,9) & k2_xtuple_0(k1_funct_1(B,C)) = D ) ) ) ) ) ) )).
fof(t31_calcul_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( r1_xxreal_0(1,A) => k10_xtuple_0(k2_finseq_2(A,B)) = k10_xtuple_0(k9_finseq_1(B)) ) ) )).
fof(t31_card_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r2_wellord2(k6_subset_1(A,k1_tarski(B)),k6_subset_1(A,k1_tarski(C))) ) )).
fof(t31_card_2,axiom,( ! [A] : ( v1_card_1(A) => k3_card_2(A,2) = k2_card_2(A,A) ) )).
fof(t31_card_3,axiom,( ! [A] : ( ( 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) = k5_ordinal1 ) ) )).
fof(t31_card_5,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ! [B] : ( ( ~ v1_finset_1(B) & v1_card_1(B) ) => ( r1_ordinal1(A,B) => k3_card_2(A,B) = k3_card_2(2,B) ) ) ) )).
fof(t31_card_fil,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ( ( r3_card_fil & v4_card_fil(A) ) => v6_card_fil(A) ) ) )).
fof(t31_card_fin,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( r2_hidden(C,k8_relat_1(B,k1_tarski(D))) => k8_subset_1(k3_tarski(k10_xtuple_0(A)),k2_card_fin(A,k5_relat_1(B,k6_subset_1(k9_xtuple_0(B),k1_tarski(C))),D),k1_funct_1(A,C)) = k2_card_fin(A,B,D) ) ) ) )).
fof(t31_card_lar,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) & ~ v4_card_3(A) ) => ( v5_card_lar(A) => v6_card_fil(A) ) ) )).
fof(t31_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_cat_1(D,A,B,C) => ( k2_cat_1(A,B,C) != k1_xboole_0 => ( v8_cat_1(D,A,B,C) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_cat_1(F,A,C,E) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) ) ) )).
fof(t31_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,k6_cat_2(A,C),B) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => k3_funct_2(u1_struct_0(C),u1_struct_0(B),k7_cat_1(C,B,k10_cat_2(A,C,B,D,E)),F) = k1_binop_1(k7_cat_1(k6_cat_2(A,C),B,D),E,F) ) ) ) ) ) ) )).
fof(t31_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,C,D) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t31_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) )).
fof(t31_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => k5_card_1(k2_catalan2(k2_xcmplx_0(4,A),2)) = k7_xcmplx_0(k2_nat_1(k1_nat_1(A,1),k1_nat_1(A,4)),2) ) )).
fof(t31_catalg_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t31_cayldick,axiom,( k6_algstr_0(k4_cayldick(k4_cayldick(k3_cayldick)),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k5_struct_0(k3_cayldick),k4_struct_0(k3_cayldick))),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k5_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)))) = k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_algstr_0(k3_cayldick,k5_struct_0(k3_cayldick)))) )).
fof(t31_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(t31_cfcont_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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] : ( v7_ordinal1(D) => k9_nat_1(k2_numbers,C,D) != A ) ) => ( v2_comseq_2(k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,C,B)) & k7_partfun1(k2_numbers,B,A) = k3_comseq_2(k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,C,B)) ) ) ) ) ) ) ) )).
fof(t31_cfdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [C] : ( ( 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] : ( v1_xcmplx_0(D) => ( r2_hidden(D,C) => k7_partfun1(k2_numbers,k3_cfdiff_1(k19_valued_1(k2_numbers,k2_numbers,k2_numbers,A,B),C),D) = k2_xcmplx_0(k3_xcmplx_0(k7_partfun1(k2_numbers,B,D),k2_cfdiff_1(A,D)),k3_xcmplx_0(k7_partfun1(k2_numbers,A,D),k2_cfdiff_1(B,D))) ) ) ) ) ) ) ) )).
fof(t31_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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,k4_xcmplx_0(k6_complex1))) ) ) )).
fof(t31_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ! [B] : ( v2_cgames_1(B) => ( r2_hidden(A,k10_cgames_1(B)) => r1_tarski(k10_cgames_1(A),k10_cgames_1(B)) ) ) ) )).
fof(t31_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(B)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(B)) => ! [E] : ( 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] : ( m1_subset_1(F,k1_zfmisc_1(k2_finseq_1(B))) => ~ ( k5_card_1(F) = A & ! [G] : ( m2_subset_1(G,k4_ordinal1,k2_finseq_1(B)) => ( ( r2_hidden(G,F) & ~ r1_xxreal_0(k1_funct_1(D,G),k1_funct_1(C,G)) & m2_chain_1(k4_tarski(k1_funct_1(C,G),k1_funct_1(D,G)),k2_chain_1(B,E,G)) ) | ( ~ r2_hidden(G,F) & k1_funct_1(C,G) = k1_funct_1(D,G) & r2_hidden(k1_funct_1(C,G),k2_chain_1(B,E,G)) ) ) ) ) ) & ~ ( A = B & ! [F] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(B)) => ( ~ r1_xxreal_0(k1_funct_1(C,F),k1_funct_1(D,F)) & m2_chain_1(k4_tarski(k1_funct_1(C,F),k1_funct_1(D,F)),k2_chain_1(B,E,F)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t31_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k6_glib_000(A))) ) => ( r1_tarski(C,B) => ! [D] : ( m2_glib_000(D,A,B,k21_glib_000(A,B)) => k21_glib_000(D,C) = k21_glib_000(A,C) ) ) ) ) ) )).
fof(t31_circcmb3,axiom,( ! [A] : ! [B] : ( r2_hidden(k6_classes1(A),k6_classes1(k4_tarski(A,B))) & r2_hidden(k6_classes1(B),k6_classes1(k4_tarski(A,B))) ) )).
fof(t31_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & ~ v11_struct_0(C) & v2_msafree2(C) & l1_msualg_1(C) ) => ( C = k2_circcomb(A,B) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(C,F))) => ! [H] : ( m1_subset_1(H,u1_struct_0(C)) => ( ! [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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t31_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r3_pua2mss1(A,B,C,D) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => m1_subset_1(k1_funct_1(D,E),u4_struct_0(B)) ) ) ) ) ) ) )).
fof(t31_classes1,axiom,( ! [A] : ( v3_ordinal1(A) => ( v4_ordinal1(A) => ( A = k1_xboole_0 | ! [B] : ( r2_hidden(B,k4_classes1(A)) <=> ? [C] : ( v3_ordinal1(C) & r2_hidden(C,A) & r2_hidden(B,k4_classes1(C)) ) ) ) ) ) )).
fof(t31_classes2,axiom,( ! [A] : ( ( v2_classes1(A) & v1_ordinal1(A) ) => k4_classes1(k1_card_1(A)) = A ) )).
fof(t31_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k14_clopban1(A,B))) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => r1_xxreal_0(k2_normsp_0(B,k3_funct_2(u1_struct_0(A),u1_struct_0(B),D,E)),k3_xcmplx_0(k2_normsp_0(k14_clopban1(A,B),C),k2_normsp_0(A,E))) ) ) ) ) ) ) )).
fof(t31_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k1_power(D,k9_nat_1(k1_numbers,k5_normsp_0(A,B),D)) ) & ? [D] : ( v7_ordinal1(D) & ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(D,E) => r1_xxreal_0(1,k9_nat_1(k1_numbers,C,E)) ) ) ) & v1_series_1(k5_normsp_0(A,B)) ) ) ) ) )).
fof(t31_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v5_mssubfam(C,A,B) & m3_pboole(C,A,k1_mboolean(A,B)) ) => ! [D] : ( m1_pboole(D,A,k5_mssubfam(A,B)) => ? [E] : ( v2_relat_1(E) & m3_pboole(E,A,k1_mboolean(A,B)) & ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t31_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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] : ( m1_closure2(D,A,B,k6_closure2(A,B)) => r2_pboole(A,k7_closure2(A,B,C,D),D) ) ) => v9_closure2(C,A,B) ) ) ) )).
fof(t31_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_clvect_1(B,A) => ! [C] : ( m1_clvect_1(C,A) => k4_struct_0(B) = k4_struct_0(C) ) ) ) )).
fof(t31_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,A,C))) & k1_seq_2(k2_clvect_2(A,k5_vfunct_1(k4_ordinal1,A,C))) = k13_csspace(A,k4_algstr_0(A,B)) ) ) ) ) ) )).
fof(t31_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [D] : ( v7_ordinal1(D) => k1_normsp_0(A,B,D) != k4_struct_0(A) ) & ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k7_xcmplx_0(k13_csspace(A,k1_normsp_0(A,B,k1_nat_1(D,1))),k13_csspace(A,k1_normsp_0(A,B,D))) ) & v2_comseq_2(C) & ~ r1_xxreal_0(k1_seq_2(C),1) & v1_clvect_3(B,A) ) ) ) ) )).
fof(t31_coh_sp,axiom,( ! [A] : r2_hidden(k1_eqrel_1(A),k15_coh_sp(A)) )).
fof(t31_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( 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] : ( ( r2_hidden(D,k9_xtuple_0(A)) & r1_tarski(D,B) & r2_hidden(C,k1_funct_1(A,D)) ) => B = D ) ) ) ) )).
fof(t31_compl_sp,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t31_complex1,axiom,( k8_complex1(k7_complex1) = k4_xcmplx_0(k7_complex1) )).
fof(t31_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k1_complex2(A,A) = k5_numbers => A = k5_numbers ) ) )).
fof(t31_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( 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) ) ) ) )).
fof(t31_complsp2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t31_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) ) => k6_compos_1(A,B,k5_numbers) = B ) ) )).
fof(t31_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( 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 ) ) ) )).
fof(t31_comptrig,axiom,( k10_xtuple_0(k2_partfun1(k1_numbers,k1_numbers,k16_sin_cos,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos)))) = k1_rcomp_1(k4_xcmplx_0(1),1) )).
fof(t31_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k19_margrel1(k3_comput_1(B,A)) = B ) ) )).
fof(t31_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k2_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,C,A),k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,D,B)),k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,C,D),k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B))) ) ) ) ) )).
fof(t31_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v2_comseq_2(A) & v1_comseq_2(B) & k3_comseq_2(A) = k5_complex1 ) => k3_comseq_2(k2_comseq_2(k4_ordinal1,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B))) = k5_complex1 ) ) ) )).
fof(t31_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k9_nat_1(k2_numbers,k10_comseq_3(A),C),k9_nat_1(k2_numbers,k10_comseq_3(A),B))),k9_complex1(k5_real_1(k9_nat_1(k1_numbers,k3_series_1(k55_valued_1(k4_ordinal1,k2_numbers,A)),C),k9_nat_1(k1_numbers,k3_series_1(k55_valued_1(k4_ordinal1,k2_numbers,A)),B)))) ) ) ) )).
fof(t31_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( r2_hidden(B,k8_conlat_1(A)) <=> ( v3_conlat_1(B,A) & ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) & l2_conlat_1(B,A) ) ) ) )).
fof(t31_connsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ~ ( ! [D] : ( 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 ) ) ) ) )).
fof(t31_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t31_convex1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : ! [D] : ~ ( 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) ) ) )).
fof(t31_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_convex4(C,A) => k3_funct_2(u1_struct_0(A),k2_numbers,k8_convex4(A,C),B) = k4_xcmplx_0(k3_funct_2(u1_struct_0(A),k2_numbers,C,B)) ) ) ) )).
fof(t31_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m1_subset_1(D,k1_qc_lang1(A)) => ! [E] : ( m1_subset_1(E,k5_finsub_1(k3_qc_lang1(A))) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t31_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => a_2_0_cqc_the1(A,B) = k1_cqc_the1(A,B) ) ) )).
fof(t31_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t31_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t31_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t31_csspace4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( r2_funct_2(k4_ordinal1,k2_numbers,A,k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,C)) <=> ! [D] : ( v7_ordinal1(D) => k1_funct_1(A,D) = k6_xcmplx_0(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) ) )).
fof(t31_descip_1,axiom,( ! [A] : ( m2_finseq_2(A,k4_finseq_2(48,k6_margrel1),k4_finseq_2(16,k4_finseq_2(48,k6_margrel1))) => ! [B] : ( ( 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] : ( ( 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] : ( 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 ) ) ) ) )).
fof(t31_dickson,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( ( v3_dickson(A) & ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ? [C] : ( m1_subset_1(C,k4_ordinal1) & ? [D] : ( m1_subset_1(D,k4_ordinal1) & ~ r1_xxreal_0(D,C) & r1_orders_2(A,k9_nat_1(u1_struct_0(A),B,C),k9_nat_1(u1_struct_0(A),B,D)) ) ) ) ) => ! [B] : ( ( ~ 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)) ) ) ) ) )).
fof(t31_diff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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) = k3_xcmplx_0(A,k9_diff_1(D,B,C)) ) ) ) ) )).
fof(t31_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( v1_xreal_0(F) => k1_funct_1(E,F) = k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(F)),k3_xcmplx_0(C,F)),D) ) => ! [F] : ( v1_xreal_0(F) => k1_funct_1(k3_diff_1(E,A),F) = k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,B),A),F),k3_xcmplx_0(B,k1_square_1(A))),k3_xcmplx_0(C,A)) ) ) ) ) ) ) ) )).
fof(t31_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( ( 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_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,C,D),A),1),B) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(C,B),k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(D,A),1),B)),k3_xcmplx_0(k1_funct_1(D,k6_xcmplx_0(B,A)),k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(C,A),1),B))) ) ) ) ) )).
fof(t31_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(k2_xcmplx_0(B,A),k5_numbers) & k1_funct_1(k3_diff_1(k3_taylor_1,A),B) != k1_funct_1(k3_taylor_1,k2_xcmplx_0(1,k7_xcmplx_0(A,B))) ) ) ) )).
fof(t31_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( 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)))) ) ) ) ) )).
fof(t31_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t31_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ! [C] : ! [D] : ( ( 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] : ( ( 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_tarski(B,A) & r1_tarski(C,A) & r1_funct_2(A,k6_margrel1,A,k2_tarski(k1_xboole_0,1),D,k5_funct_3(B,A)) & r1_funct_2(A,k6_margrel1,A,k2_tarski(k1_xboole_0,1),E,k5_funct_3(C,A)) ) => r1_funct_2(A,k2_tarski(k1_xboole_0,1),A,k6_margrel1,k5_funct_3(k2_xboole_0(B,C),A),k5_bvfunc_1(A,D,E)) ) ) ) ) )).
fof(t31_domain_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k5_subset_1(A,B,C) = a_3_4_domain_1(A,B,C) ) ) ) )).
fof(t31_e_siec,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t31_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ( B != k5_numbers => v2_ec_pf_1(k2_binom(k9_int_3(A),B,2),A) ) ) ) )).
fof(t31_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t31_ens_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k11_ens_1(A))) => ( v11_cat_1(B,k11_ens_1(A)) => B = k1_xboole_0 ) ) ) )).
fof(t31_entropy1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( 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] : ( v7_ordinal1(D) => ( r1_xxreal_0(1,D) => ( r1_xxreal_0(k3_finseq_1(B),D) | k1_matrprob(A,C,k1_nat_1(D,1)) = k8_finseq_1(A,k1_matrprob(A,C,D),k1_matrprob(A,B,k1_nat_1(D,1))) ) ) ) ) => ( k3_finseq_1(k1_matrprob(A,C,1)) = k1_matrix_0(B) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k4_tarski(1,D),k2_matrix_0(B)) => ( r2_hidden(D,k4_finseq_1(k1_matrprob(A,C,1))) & k1_funct_1(k1_matrprob(A,C,1),D) = k3_matrix_0(A,B,1,D) ) ) ) ) ) ) ) ) )).
fof(t31_enumset1,axiom,( ! [A] : ! [B] : ! [C] : k2_enumset1(A,A,B,C) = k1_enumset1(A,B,C) )).
fof(t31_eqrel_1,axiom,( ! [A] : ! [B] : ( ( 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 ) ) )).
fof(t31_equation,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_funct_1(k4_equation(A),C)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t31_euclid,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => k4_algstr_0(k15_euclid(2),A) = k19_euclid(k4_xcmplx_0(k17_euclid(A)),k4_xcmplx_0(k18_euclid(A))) ) )).
fof(t31_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => k22_rvsum_1(k4_struct_0(k15_euclid(A)),B) = k5_numbers ) ) )).
fof(t31_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( A != k4_struct_0(k15_euclid(2)) => ( ~ r1_xxreal_0(k28_sin_cos,k3_euclid_3(A)) <=> r1_xxreal_0(k28_sin_cos,k3_euclid_3(k4_algstr_0(k15_euclid(2),A))) ) ) ) )).
fof(t31_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => k22_rvsum_1(k8_euclid(A,B,C),k8_euclid(A,D,E)) = k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k22_rvsum_1(B,D),k22_rvsum_1(B,E)),k22_rvsum_1(C,D)),k22_rvsum_1(C,E)) ) ) ) ) ) )).
fof(t31_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(3))) => ( k6_euclid_5(A,A,B) = k5_numbers & k6_euclid_5(B,A,B) = k5_numbers ) ) ) )).
fof(t31_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( 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 & k3_xcmplx_0(2,k4_euclid_3(A,C,B)) != k4_euclid_3(A,D,B) & k3_xcmplx_0(2,k6_xcmplx_0(k4_euclid_3(A,C,B),k28_sin_cos)) != k4_euclid_3(A,D,B) ) ) ) ) ) ) ) ) )).
fof(t31_euclid_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => k8_euclid_7(A) != k1_xboole_0 ) )).
fof(t31_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => 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)) ) ) ) )).
fof(t31_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( 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] : ( v1_xreal_0(F) => k8_euclid(A,C,B) != k9_euclid(A,k8_euclid(A,E,D),F) ) ) ) ) ) ) ) )).
fof(t31_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(k9_funct_7(C,A,B),B) = k1_funct_1(C,A) ) ) )).
fof(t31_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ( ( k3_compos_1(B,C,k5_memstr_0(A,B,k5_extpro_1(A,B,C,D,k1_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) = k1_nat_1(E,1) & r1_extpro_1(A,B,C,D) ) ) ) & ( ( k8_extpro_1(A,B,C,D) = k1_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,k1_nat_1(E,1)))) = k2_compos_1(B) ) ) ) ) ) ) ) ) )).
fof(t31_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_circcomb(A) & v2_circcomb(A) & v3_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v4_msafree2(C,A) & v4_circcomb(C,A) & v6_circcomb(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msafree2(D,B) & v4_circcomb(D,B) & v6_circcomb(D,B) & l3_msualg_1(D,B) ) => ! [E] : ( m1_subset_1(E,k4_card_3(u3_msualg_1(k2_circcomb(A,B),k3_circcomb(A,B,C,D)))) => ! [F] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t31_facirc_2,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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] : ( 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)) ) ) )).
fof(t31_fcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( 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] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & k1_funct_1(A,C) = k2_seq_4(k7_relset_1(k1_numbers,k1_numbers,A,B)) & k1_funct_1(A,D) = k3_seq_4(k7_relset_1(k1_numbers,k1_numbers,A,B)) ) ) ) ) ) ) )).
fof(t31_fdiff_10,axiom,( ! [A] : ( ( 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,k18_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,k18_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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,k18_sin_cos)),A),B) = k6_xcmplx_0(k2_xcmplx_0(k1_square_1(k1_funct_1(k18_sin_cos,B)),k3_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k16_sin_cos,B)),k1_funct_1(k18_sin_cos,B))),k1_square_1(k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t31_fdiff_11,axiom,( ! [A] : ( ( 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,k27_sin_cos,k1_sin_cos9))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k1_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k1_sin_cos9),A),B) = k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k1_square_1(k1_funct_1(k16_sin_cos,B)))),k7_xcmplx_0(k1_funct_1(k27_sin_cos,B),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t31_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ( r2_hidden(C,k10_prob_1(A)) => r1_xxreal_0(k5_numbers,k1_fdiff_1(B,C)) ) ) ) => v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,B,k10_prob_1(A))) ) ) ) )).
fof(t31_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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(k7_xcmplx_0(1,2))),k4_xcmplx_0(2)))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k1_funct_1(C,D) = k6_xcmplx_0(A,D) & ~ r1_xxreal_0(k1_funct_1(C,D),k5_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(k7_xcmplx_0(1,2))),k4_xcmplx_0(2)),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_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(k7_xcmplx_0(1,2))),k4_xcmplx_0(2)),B),D) = k6_prepower(k6_xcmplx_0(A,D),k4_xcmplx_0(k7_xcmplx_0(1,2))) ) ) ) ) ) ) ) )).
fof(t31_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k22_sin_cos),k1_taylor_1(2)))) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_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,k22_sin_cos),k1_taylor_1(2)),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,B,k22_sin_cos),k1_taylor_1(2)),A),C) = k4_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k22_sin_cos,C)),k6_xcmplx_0(1,k1_funct_1(k22_sin_cos,C)))) ) ) ) ) ) ) )).
fof(t31_fdiff_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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,k18_sin_cos),k1_taylor_1(A)),k7_xcmplx_0(1,A)))) & ! [C] : ( v1_xreal_0(C) => ~ ( r2_hidden(C,B) & k1_funct_1(k18_sin_cos,C) = k5_numbers ) ) ) => ( r1_xxreal_0(A,k5_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,k18_sin_cos),k1_taylor_1(A)),k7_xcmplx_0(1,A)),B) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => k1_funct_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,k18_sin_cos),k1_taylor_1(A)),k7_xcmplx_0(1,A)),B),C) = k7_xcmplx_0(k1_funct_1(k16_sin_cos,C),k3_prepower(k1_funct_1(k18_sin_cos,C),k2_xcmplx_0(A,1))) ) ) ) ) ) ) ) )).
fof(t31_fdiff_8,axiom,( ! [A] : ( ( 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,k22_sin_cos,k27_sin_cos))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k27_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k27_sin_cos),A),B) = k6_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_funct_1(k18_sin_cos,B)),k1_funct_1(k16_sin_cos,B)),k7_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t31_fdiff_9,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k2_fdiff_9),A),B) = k6_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(1,k1_funct_1(k16_sin_cos,B)),B),k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k3_taylor_1,B),k1_funct_1(k18_sin_cos,B)),k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t31_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => k6_xcmplx_0(k2_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)) ) )).
fof(t31_fib_num3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k1_pre_ff(k1_nat_1(k2_nat_1(2,A),1)) = k6_xcmplx_0(k2_nat_1(k1_pre_ff(k1_nat_1(A,1)),k1_fib_num3(k1_nat_1(A,1))),k2_nat_1(k1_pre_ff(A),k1_fib_num3(A))) ) )).
fof(t31_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(2,A) => k1_fib_num3(A) = k2_int_1(k6_xcmplx_0(k2_power(k1_fib_num,A),k7_xcmplx_0(1,2))) ) ) )).
fof(t31_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => C = k1_finseq_8(A,k4_finseq_8(A,B,C),k7_finseq_8(A,B,C)) ) ) ) )).
fof(t31_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ! [E] : ( ( ~ 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)) ) ) ) ) ) ) ) )).
fof(t31_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t31_filter_2,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(t31_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t31_finseq_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( ( 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(k4_ordinal1,A,A,B,D,E) => k3_finseq_1(C) = k3_finseq_1(D) ) ) ) ) ) )).
fof(t31_finseq_3,axiom,( ! [A] : ! [B] : k1_xboole_0 != k10_finseq_1(A,B) )).
fof(t31_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_finseq_4(A,B) => ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(t31_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_finseq_1(D,C) => ( ( k1_nat_1(B,1) = A & r2_hidden(A,k4_finseq_1(D)) ) => k8_finseq_1(C,k12_finseq_1(C,k7_partfun1(C,D,A)),k2_rfinseq(C,A,D)) = k2_rfinseq(C,B,D) ) ) ) ) ) )).
fof(t31_finseq_6,axiom,( ! [A] : ! [B] : ! [C] : k6_finseq_4(k11_finseq_1(A,B,C),A) = k10_finseq_1(B,C) )).
fof(t31_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t31_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v3_card_1(E,D) & m2_finseq_1(E,A) ) => ! [F] : ( ( 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(k4_ordinal1,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))) ) ) ) ) ) ) ) )).
fof(t31_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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] : ( 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t31_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k7_fintopo3(A,B,k1_nat_1(C,1)) = k12_fin_topo(A,k7_fintopo3(A,B,C)) ) ) ) )).
fof(t31_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v1_fintopo6(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t31_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k2_flang_1(A),k7_flang_1(A,B,C)) => ( r1_xxreal_0(C,k5_numbers) | r2_hidden(k2_flang_1(A),B) ) ) ) ) )).
fof(t31_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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 = k5_numbers & D = k5_numbers ) & ~ ( C = k5_numbers & B = k1_xboole_0 ) ) ) ) ) ) )).
fof(t31_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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(k6_fomodel0(A,C),k12_finseq_1(A,B)) = B & ! [D] : ( ( v1_relat_1(D) & v5_relat_1(D,A) & v1_funct_1(D) & v1_finseq_1(D) ) => ( ~ v1_xboole_0(D) => k1_funct_1(k6_fomodel0(A,C),k7_finseq_1(D,k12_finseq_1(A,B))) = k1_binop_1(C,k1_funct_1(k6_fomodel0(A,C),D),B) ) ) ) ) ) ) )).
fof(t31_frechet,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_frechet))) => ( A = k1_tarski(k1_numbers) => v4_pre_topc(A,k3_frechet) ) ) )).
fof(t31_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ? [D] : ( m2_valued_0(D,u1_struct_0(A),B) & r1_frechet(A,D,C) ) => r1_frechet2(A,B,C) ) ) ) ) )).
fof(t31_fsm_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ v2_struct_0(D) & l2_fsm_1(D,B,C) ) => ( k7_fsm_1(B,C,D,k1_nat_1(A,1)) != k7_fsm_1(B,C,D,A) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( r1_xxreal_0(E,A) & k7_fsm_1(B,C,D,k1_nat_1(E,1)) = k7_fsm_1(B,C,D,E) ) ) ) ) ) ) ) )).
fof(t31_fsm_2,axiom,( ! [A] : ( ( ~ 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] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ ( r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(C,k5_numbers) ) => k1_funct_1(u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(B,C))) = 1 ) ) ) & ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(C,k5_numbers) ) => ( ( B != k5_numbers & C != k5_numbers ) | k1_funct_1(u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(B,C))) = k5_numbers ) ) ) ) & ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(k5_numbers,C) & k1_funct_1(u1_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(u2_fsm_1(k2_zfmisc_1(k1_numbers,k1_numbers),A),k4_tarski(B,C))) != k4_xcmplx_0(1) ) ) ) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( 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)) = k4_xxreal_0(k2_absvalue(B),k2_absvalue(C)) ) ) ) ) )).
fof(t31_fsm_3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(B)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(B)) => ! [E] : ( ( ~ 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),D,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,C,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,C,D),A)) ) ) ) ) )).
fof(t31_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : 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))) )).
fof(t31_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : k5_funcop_1(B,C,A) = k3_funcop_1(B,k2_funcop_1(k9_xtuple_0(A),C),A) ) ) )).
fof(t31_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( B = k2_funct_1(A) <=> ( k9_xtuple_0(B) = k10_xtuple_0(A) & ! [C] : ! [D] : ( ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t31_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( 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) ) ) )).
fof(t31_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(t31_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t31_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t31_funct_6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_funcop_1(C) ) => ( ( r2_hidden(B,k4_card_3(k1_funct_6(C))) & r2_hidden(A,k9_xtuple_0(B)) ) => k4_funct_6(k6_funct_6(C),B,A) = k4_funct_6(C,A,k1_funct_1(B,A)) ) ) ) )).
fof(t31_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ( C != D => k1_funct_1(k1_funct_7(A,C,B),D) = k1_funct_1(A,D) ) ) )).
fof(t31_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t31_funct_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & v1_int_1(A) ) => v1_funct_9(k41_valued_1(k1_numbers,k1_numbers,k18_sin_cos),k3_xcmplx_0(k28_sin_cos,A)) ) )).
fof(t31_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_altcat_1(A,B,C) != k1_xboole_0 => ! [D] : ( ( v8_functor0(D,A,A) & v10_functor0(D,A,A) & l2_functor0(D,A,A) ) => ( D = k11_functor0(A) => ! [E] : ( m1_subset_1(E,k1_altcat_1(A,B,C)) => k6_functor0(A,A,D,B,C,E) = E ) ) ) ) ) ) ) )).
fof(t31_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v11_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ! [F] : ( ( v15_functor0(F,A,B) & m2_functor0(F,A,B) ) => ! [G] : ( ( v15_functor0(G,B,C) & m2_functor0(G,B,C) ) => ! [H] : ( ( v15_functor0(H,B,C) & m2_functor0(H,B,C) ) => ! [I] : ( ( v15_functor0(I,B,C) & m2_functor0(I,B,C) ) => ! [J] : ( m2_functor2(J,B,C,G,H) => ! [K] : ( m2_functor2(K,B,C,H,I) => ! [L] : ( m1_functor2(L,A,B,D,E) => ! [M] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t31_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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)) ) ) ) ) ) )).
fof(t31_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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))) ) ) ) ) )).
fof(t31_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_fvaluat1(C,A) => ( ( v3_fvaluat1(A) & r1_xxreal_0(k5_numbers,k3_funct_2(u1_struct_0(A),k6_numbers,C,k5_algstr_0(A,k5_struct_0(A),B))) ) => r1_xxreal_0(k5_numbers,k3_funct_2(u1_struct_0(A),k6_numbers,C,B)) ) ) ) ) )).
fof(t31_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t31_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ~ 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) ) ) )).
fof(t31_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => k5_gcd_1(A,B,k4_struct_0(A),k4_struct_0(A)) = k4_struct_0(A) ) ) )).
fof(t31_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v2_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ! [F] : ( m1_genealg1(F,E) => ! [G] : ( m1_genealg1(G,E) => ( k10_genealg1(E,F,G,A,k5_numbers,k5_numbers,k5_numbers) = k7_genealg1(E,G,F,A) & k10_genealg1(E,F,G,k5_numbers,B,k5_numbers,k5_numbers) = k7_genealg1(E,G,F,B) & k10_genealg1(E,F,G,k5_numbers,k5_numbers,C,k5_numbers) = k7_genealg1(E,G,F,C) & k10_genealg1(E,F,G,k5_numbers,k5_numbers,k5_numbers,D) = k7_genealg1(E,G,F,D) ) ) ) ) ) ) ) ) )).
fof(t31_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ( k4_geomtrap(A,B,C,k1_rlvect_1(A,D,F),E) = k3_xcmplx_0(F,k4_geomtrap(A,B,C,D,E)) & k4_geomtrap(A,B,C,D,k1_rlvect_1(A,E,F)) = k3_xcmplx_0(F,k4_geomtrap(A,B,C,D,E)) & k4_geomtrap(A,B,C,k1_rlvect_1(A,D,F),E) = k3_xcmplx_0(k4_geomtrap(A,B,C,D,E),F) & k4_geomtrap(A,B,C,D,k1_rlvect_1(A,E,F)) = k3_xcmplx_0(k4_geomtrap(A,B,C,D,E),F) ) ) ) ) ) ) ) ) )).
fof(t31_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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))) )).
fof(t31_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t31_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ( k4_glib_001(A,B) = k3_glib_001(A,C) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ~ r1_xxreal_0(k3_finseq_1(C),D) => ( k1_funct_1(k7_glib_001(A,B,C),k1_nat_1(k3_finseq_1(B),D)) = k1_funct_1(C,k1_nat_1(D,1)) & r2_hidden(k1_nat_1(k3_finseq_1(B),D),k1_relset_1(k4_ordinal1,k7_glib_001(A,B,C))) ) ) ) ) ) ) ) )).
fof(t31_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v4_glib_002(B,A) & m1_glib_000(B,A) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t31_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v8_glib_003(A) ) => ! [B] : ( r2_hidden(B,k7_glib_000(A)) => r1_xxreal_0(k5_numbers,k1_funct_1(k5_glib_003(A),B)) ) ) )).
fof(t31_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( v7_ordinal1(B) => ! [C] : ( 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) ) ) ) )).
fof(t31_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_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) ) ) ) )).
fof(t31_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(C)) ) => r2_hidden(k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),k1_nat_1(B,1))),k7_xcmplx_0(1,2)),k1_tops_1(k15_euclid(2),k3_goboard5(C,A,B))) ) ) ) ) )).
fof(t31_goboard7,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) & 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)) ) ) )).
fof(t31_gobrd11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_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_0(B)) = a_2_5_gobrd11(A,B) ) ) ) ) )).
fof(t31_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(D)) & r1_goboard1(u1_struct_0(k15_euclid(2)),D,E) & r2_hidden(k4_tarski(A,B),k2_matrix_0(E)) & r2_hidden(k4_tarski(k1_nat_1(A,1),B),k2_matrix_0(E)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,k1_nat_1(A,1),B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,B) ) => k5_gobrd13(D,E,C) = k3_goboard5(E,k7_nat_d(A,1),k7_nat_d(B,1)) ) ) ) ) ) ) )).
fof(t31_gobrd14,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(t31_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( 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] : ( ( v1_henmodel(C,A) & m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) ) => ~ ( r1_tarski(B,C) & v2_goedelcp(C,A) ) ) ) ) ) )).
fof(t31_gr_cy_3,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( r1_int_2(A,C) & r2_int_1(A,B,C) ) => r1_int_2(B,C) ) ) ) ) )).
fof(t31_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_graph_1(A) & l1_graph_1(A) ) => r1_tarski(k1_tarski(A),k11_graph_1(A)) ) )).
fof(t31_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t31_graph_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v6_graph_1(B) & l1_graph_1(B) ) => ! [C] : ( 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))) ) ) )).
fof(t31_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t31_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => ~ ( ~ r1_xxreal_0(A,B) & A != k1_nat_1(k1_nat_1(k2_nat_1(B,B),k2_nat_1(3,B)),1) & k1_funct_1(k6_graphsp(k15_graphsp(B),C),A) != k1_funct_1(C,A) ) ) ) ) )).
fof(t31_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_grcat_1(A) ) => ! [B] : ( m3_grcat_1(B,k18_grcat_1(A)) => ! [C] : ( m3_grcat_1(C,k18_grcat_1(A)) => ~ ( k19_grcat_1(A,B) = k20_grcat_1(A,C) & ! [D] : ( ( v8_algstr_0(D) & m2_grcat_1(D,A) ) => ! [E] : ( ( v8_algstr_0(E) & m2_grcat_1(E,A) ) => ! [F] : ( ( v8_algstr_0(F) & m2_grcat_1(F,A) ) => ~ ( m1_grcat_1(B,E,F) & m1_grcat_1(C,D,E) ) ) ) ) ) ) ) ) )).
fof(t31_grfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t31_groeb_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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(k12_polynom1(A,C),k1_groeb_1(A,C,D))) ) ) ) ) )).
fof(t31_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [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] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(D,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,B)))) ) => ! [F] : ( m2_ideal_1(F,k12_polynom1(A,B),E) => ! [G] : ( m2_ideal_1(G,k12_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,k5_polynom1(A,B,C,D),E,k5_groeb_2(A,B,E,F,G)) ) ) ) ) ) ) ) ) )).
fof(t31_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(E,k5_card_1(k3_polynom1(k15_pre_poly(A),C,D))) => ! [F] : ( ( 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,k3_polynom1(k15_pre_poly(A),C,k6_groeb_3(A,B,C,D,E))) => ( k4_polynom1(A,C,k6_groeb_3(A,B,C,D,E),F) = k4_polynom1(A,C,D,F) & k4_polynom1(A,C,k5_groeb_3(A,B,C,D,E),F) = k4_struct_0(C) ) ) ) ) ) ) ) ) ) )).
fof(t31_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_group_1(A,k4_xcmplx_0(1),B) = k2_group_1(A,B) ) ) )).
fof(t31_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t31_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t31_group_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( r2_hidden(A,k3_group_3(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k2_group_3(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) ) ) ) )).
fof(t31_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => r1_group_2(A,k5_group_4(A,k8_group_2(A,B)),B) ) ) )).
fof(t31_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t31_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t31_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v2_group_9(C,A) & v4_group_9(C,A,B) & m1_group_9(C,A,B) ) => ! [D] : ( ( 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) ) ) ) )).
fof(t31_groupp_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v8_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_group_2(C,B) => ! [D] : ( ( 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] : ( ( v15_algstr_0(E) & m1_group_2(E,B) ) => ~ ( u1_struct_0(E) = k7_group_4(B,C,D) & v3_groupp_1(E,A) ) ) ) ) ) ) ) )).
fof(t31_hallmar1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,k1_zfmisc_1(A)) ) => ~ ( v1_hallmar1(B,A) & ! [C] : ( m4_hallmar1(C,A,B) => ~ v1_hallmar1(C,A) ) ) ) ) )).
fof(t31_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t31_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => k6_glib_001(A,k2_helly(A,B,C)) = k2_helly(A,C,B) ) ) ) )).
fof(t31_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,k1_complfld) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t31_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A))))) => ( ( r1_lattice3(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A)),D,B) & r1_lattice3(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A)),D,C) ) => r1_lattice3(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A)),D,k13_lattice3(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A)),B,C)) ) ) ) ) ) )).
fof(t31_hfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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(k6_xcmplx_0(A,3)),k3_xcmplx_0(k3_xcmplx_0(A,k6_xcmplx_0(A,1)),k6_xcmplx_0(A,2))),B)) ) ) ) )).
fof(t31_hilbasis,axiom,( ! [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) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ? [C] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k14_polynom3(k12_polynom1(B,A))),u1_struct_0(k12_polynom1(k1_nat_1(B,1),A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k14_polynom3(k12_polynom1(B,A))),u1_struct_0(k12_polynom1(k1_nat_1(B,1),A))))) & v4_quofield(C,k14_polynom3(k12_polynom1(B,A)),k12_polynom1(k1_nat_1(B,1),A)) ) ) ) )).
fof(t31_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ( r2_hidden(k4_hilbert1(A,B),k6_hilbert1) <=> ( r2_hidden(A,k6_hilbert1) & r2_hidden(B,k6_hilbert1) ) ) ) ) )).
fof(t31_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k3_hilbert2(k1_hilbert2(A)) = k2_trees_4(k1_hilbert1,k1_hilbert2(A)) ) )).
fof(t31_hilbert3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => k3_hilbert3(C,k3_hilbert1(A,B)) = k9_funct_2(k3_hilbert3(C,A),k3_hilbert3(C,B)) ) ) ) )).
fof(t31_hurwitz,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v6_struct_0(A) & v4_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_xxreal_0(1,C) => k2_hurwitz(A,k4_hurwitz(A,B,C)) = k6_xcmplx_0(C,1) ) ) ) ) )).
fof(t31_idea_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( 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 ) ) ) ) ) )).
fof(t31_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v5_group_1(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_ideal_1(C,A,B) => ( m2_ideal_1(C,A,B) & m3_ideal_1(C,A,B) ) ) ) ) )).
fof(t31_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t31_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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] : ( m4_index_1(C,u1_struct_0(A),u4_struct_0(A),u1_graph_1(A),u2_graph_1(A),B) => ! [D] : ( ( ~ 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] : ( ( ~ 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] : ( m2_cat_1(F,C,D) => ! [G] : ( 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) ) ) ) ) ) ) ) )).
fof(t31_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r3_pua2mss1(A,B,C,D) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t31_int_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(t31_int_2,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( r1_xxreal_0(2,A) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( v1_int_2(B) & r1_int_1(B,A) ) ) ) ) )).
fof(t31_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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(k5_numbers,k2_int_6(A,B)) & ~ r1_xxreal_0(k19_rvsum_1(B),k2_int_6(A,B)) ) ) ) ) )).
fof(t31_int_7,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t31_integr11,axiom,( ! [A] : ( ( ~ 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,k5_numbers),k3_sin_cos2)) = k6_xcmplx_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(1,k5_numbers),k1_sin_cos2),k3_sin_cos2),k2_seq_4(A)),k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(1,k5_numbers),k1_sin_cos2),k3_sin_cos2),k3_seq_4(A))) ) )).
fof(t31_integr12,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v3_rcomp_1(F) & m1_subset_1(F,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(C,F) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,F) => k1_funct_1(E,G) = k2_xcmplx_0(k3_xcmplx_0(A,G),B) ) ) & F = k1_relset_1(k1_numbers,D) & r2_relset_1(k1_numbers,k1_numbers,D,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,k18_sin_cos),A),k3_rfunct_1(k1_numbers,k1_numbers,E,k41_valued_1(k1_numbers,k1_numbers,k18_sin_cos)))) ) => k2_integra5(C,D) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,E,k26_sin_cos),k2_seq_4(C)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,E,k26_sin_cos),k3_seq_4(C))) ) ) ) ) ) ) ) )).
fof(t31_integr13,axiom,( ! [A] : ( ( 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,k22_sin_cos,k27_sin_cos))) => ( r2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k27_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k27_sin_cos)),A),B) = k7_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k22_sin_cos,B)))) ) ) ) ) ) )).
fof(t31_integr14,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v3_rcomp_1(E) & m1_subset_1(E,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,E) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => k1_funct_1(C,F) = k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(k18_sin_cos,k3_xcmplx_0(A,F)),k1_square_1(k1_funct_1(k16_sin_cos,k3_xcmplx_0(A,F)))),k1_square_1(k1_funct_1(k16_sin_cos,k3_xcmplx_0(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),k4_xcmplx_0(k7_xcmplx_0(1,A))),k1_partfun2(k1_numbers,E)))) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => ( k1_funct_1(D,F) = k3_xcmplx_0(A,F) & A != k5_numbers ) ) ) & E = k1_relset_1(k1_numbers,C) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,B)) ) => k2_integra5(B,C) = k6_xcmplx_0(k1_funct_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),k4_xcmplx_0(k7_xcmplx_0(1,A))),k1_partfun2(k1_numbers,E)),k2_seq_4(B)),k1_funct_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),k4_xcmplx_0(k7_xcmplx_0(1,A))),k1_partfun2(k1_numbers,E)),k3_seq_4(B))) ) ) ) ) ) ) )).
fof(t31_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t31_integra1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( m1_integra1(C,B) => ! [D] : ( m1_integra1(D,B) => ~ ( r2_hidden(A,k4_finseq_1(C)) & r1_integra1(C,D) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( r2_hidden(E,k4_finseq_1(D)) & k1_funct_1(C,A) = k1_funct_1(D,E) ) ) ) ) ) ) ) )).
fof(t31_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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)) = k3_xcmplx_0(A,k12_integra1(B,C)) ) ) ) ) ) )).
fof(t31_integra7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( 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_funct_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) & k1_seq_2(D) = k4_integra5(A,B,k11_seqfunc(k1_numbers,C,k3_integra5(A,B))) ) ) ) ) ) ) ) )).
fof(t31_integra8,axiom,( k2_fdiff_1(k3_sin_cos2,k1_numbers) = k1_sin_cos2 )).
fof(t31_integra9,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( ~ 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)) = k2_xcmplx_0(k2_xcmplx_0(k1_integra9(C,A,A),k3_xcmplx_0(2,k1_integra9(C,A,B))),k1_integra9(C,B,B)) ) ) ) ) )).
fof(t31_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_interva1(C,A) ) => ! [D] : ( ( ~ 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))) ) ) ) ) )).
fof(t31_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => r2_hidden(k3_intpro_1(B,k3_intpro_1(k3_intpro_1(B,A),A)),k8_intpro_1) ) ) )).
fof(t31_irrat_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( v1_rat_1(A) & ! [B] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(2,B) & v1_int_1(k3_xcmplx_0(k7_newton(B),A)) ) ) ) ) )).
fof(t31_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( 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,k4_nattra_1(A,B,D),E),k4_nattra_1(A,C,k9_cat_1(A,B,C,D,E))) ) ) ) ) ) )).
fof(t31_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,k6_cat_2(B,C)) => ! [E] : ( m2_cat_1(E,A,k6_cat_2(B,C)) => ! [F] : ( m2_cat_1(F,A,k6_cat_2(B,C)) => ! [G] : ( m2_cat_1(G,A,k6_cat_2(B,C)) => ( ( r2_nattra_1(A,k6_cat_2(B,C),D,E) & r2_nattra_1(A,k6_cat_2(B,C),F,G) ) => ! [H] : ( m2_nattra_1(H,A,k6_cat_2(B,C),D,E) => ! [I] : ( m2_nattra_1(I,A,k6_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(k6_cat_2(B,C)),H,I) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t31_isomichi,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_tarski(k3_borsuk_5(A,B),k3_rcomp_1(A,k1_xxreal_0)) ) ) )).
fof(t31_jgraph_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => r1_xxreal_0(k12_euclid(A),k2_xcmplx_0(k9_complex1(k17_euclid(A)),k9_complex1(k18_euclid(A)))) ) )).
fof(t31_jgraph_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( 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] : ( 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) = k7_xcmplx_0(1,k17_euclid(C)) ) ) & ! [C] : ( 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) = k5_numbers ) ) ) => v5_pre_topc(B,k1_pre_topc(k15_euclid(2),A),k3_topmetr) ) ) ) )).
fof(t31_jgraph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) != k5_numbers ) & ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( 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,k3_square_1(k2_xcmplx_0(1,k1_square_1(k7_xcmplx_0(F,G))))) ) ) ) ) & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).
fof(t31_jgraph_5,axiom,( ! [A] : ( ( 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] : ( 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) ) ) )).
fof(t31_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t31_jordan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t31_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t31_jordan12,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( 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] : ( v7_ordinal1(G) & r1_xxreal_0(1,G) & r1_xxreal_0(k1_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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t31_jordan14,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(C,B) & ~ r1_xxreal_0(D,1) & ~ r1_xxreal_0(k3_finseq_1(k1_jordan8(A,C)),k1_nat_1(D,1)) & r1_xxreal_0(k3_finseq_1(k1_jordan8(A,B)),k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k11_newton(2,k7_nat_d(B,C)),k6_xcmplx_0(D,2)),2),1)) ) ) ) ) ) )).
fof(t31_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C),k3_topreal1(2,k1_jordan1e(B,A))) & r2_hidden(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C)),k8_jordan6(B)) ) ) ) ) ) ) )).
fof(t31_jordan18,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t31_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_xxreal_0(B,C) => ( r1_xxreal_0(A,1) | r1_xxreal_0(k3_finseq_1(k1_jordan8(D,B)),A) | ( ~ r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(k11_newton(2,k7_nat_d(C,B)),k6_xcmplx_0(A,2)),2),1) & ~ r1_xxreal_0(k3_finseq_1(k1_jordan8(D,C)),k2_xcmplx_0(k3_xcmplx_0(k11_newton(2,k7_nat_d(C,B)),k6_xcmplx_0(A,2)),2)) ) ) ) ) ) ) ) )).
fof(t31_jordan1b,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),1),k3_matrix_0(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,k2_jordan9(B,A)))) ) ) )).
fof(t31_jordan1h,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_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] : ( v7_ordinal1(C) => ~ ( r2_hidden(k4_tarski(C,1),k2_matrix_0(B)) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,C,1),k2_relset_1(u1_struct_0(k15_euclid(2)),A)) ) ) | ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(k4_tarski(C,k1_matrix_0(B)),k2_matrix_0(B)) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,C,k1_matrix_0(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)) ) ) ) ) )).
fof(t31_jordan1k,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(2))) => ( B = k19_euclid(k5_numbers,k5_numbers) => k8_metric_1(k14_euclid(2),B,A) = a_1_0_jordan1k(A) ) ) ) )).
fof(t31_jordan21,axiom,( ! [A] : ( ( 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) ) )).
fof(t31_jordan22,axiom,( ! [A] : ( ( 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)) ) )).
fof(t31_jordan23,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( ( v1_topreal1(A) & v2_jordan23(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t31_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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,k1_nat_1(k1_jordan3(A,B),1)),B,C) ) => ( B = C | r2_hidden(C,k3_topreal1(2,k2_jordan3(A,B))) ) ) ) ) ) )).
fof(t31_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( 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) ) ) ) ) ) )).
fof(t31_jordan5d,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ 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] : ( v7_ordinal1(C) => ( ( r2_hidden(A,k3_topreal1(2,B)) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(k2_goboard2(B))) ) => r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(B),1,C)),k17_euclid(A)) ) ) ) ) )).
fof(t31_jordan6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(B,k6_jordan6(A)) <=> k17_euclid(B) = A ) ) ) )).
fof(t31_jordan9,axiom,( ! [A] : ( ( ~ 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)))) ) => ( v2_connsp_1(A,k15_euclid(2)) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(k2_jordan9(A,B))) ) => ( r1_xboole_0(k3_gobrd13(k2_jordan9(A,B),k1_jordan8(A,B),C),A) & ~ r1_xboole_0(k2_gobrd13(k2_jordan9(A,B),k1_jordan8(A,B),C),A) ) ) ) ) ) ) )).
fof(t31_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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)) ) ) )).
fof(t31_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t31_kurato_1,axiom,( 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)) )).
fof(t31_kurato_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => r1_tarski(k1_kurato_2(A,B),k3_kurato_2(A,B)) ) ) )).
fof(t31_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( v7_ordinal1(E) => ( ( k3_finseq_1(D) = A & r2_hidden(E,k2_finseq_1(A)) ) => k11_fvsum_1(B,k8_matrix_0(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),k4_matrix_0(u1_struct_0(B),C),D)) ) ) ) ) ) ) )).
fof(t31_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t31_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k5_finsub_1(C)) => ! [E] : ( ( 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] : ( m1_subset_1(F,C) => ( r2_hidden(F,D) => r3_lattices(A,k3_funct_2(C,u1_struct_0(A),E,F),B) ) ) ) ) ) ) ) ) )).
fof(t31_lattice3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( 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) ) ) ) )).
fof(t31_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B) ) => ! [C] : ( m1_lattice4(C,B,A) => ( v2_funct_2(C,u1_struct_0(A)) => ( v17_lattices(A) & r4_lattice4(B,A,C) ) ) ) ) ) )).
fof(t31_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( 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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),k13_lexbfs(A,k16_lexbfs(A),B))))) => k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),k13_lexbfs(A,k16_lexbfs(A),k1_nat_1(B,1))) = k1_funct_4(k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),k13_lexbfs(A,k16_lexbfs(A),B))))))) ) ) ) )).
fof(t31_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(C,k5_numbers) => r1_fuzzy_1(k4_lfuzzy_1(A,B,C),k5_lfuzzy_1(A,B)) ) ) ) ) )).
fof(t31_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v5_valued_0(A) => ( v1_seq_2(A) | v1_limfunc1(A) ) ) ) )).
fof(t31_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,A) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(C,D) & ~ r1_xxreal_0(D,A) & r2_hidden(D,k1_relset_1(k1_numbers,B)) ) ) ) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(A,k2_xcmplx_0(A,C)))) & ~ v2_seq_2(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(A,k2_xcmplx_0(A,C)))) ) ) | r6_limfunc2(B,A) ) ) ) ) )).
fof(t31_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r1_limfunc3(C,B) => ( r1_limfunc3(k26_valued_1(k1_numbers,k1_numbers,C,A),B) & k1_limfunc3(k26_valued_1(k1_numbers,k1_numbers,C,A),B) = k3_xcmplx_0(A,k1_limfunc3(C,B)) ) ) ) ) ) )).
fof(t31_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & 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_funct_1(A,D)) ) ) | v7_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).
fof(t31_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t31_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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)) ) ) )).
fof(t31_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k1_power(D,k9_nat_1(k1_numbers,k5_normsp_0(A,B),D)) ) & ? [D] : ( v7_ordinal1(D) & ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(D,E) => r1_xxreal_0(1,k9_nat_1(k1_numbers,C,E)) ) ) ) & v1_series_1(k5_normsp_0(A,B)) ) ) ) ) )).
fof(t31_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => k9_complex1(k9_nat_1(k1_numbers,k3_series_1(k5_normsp_0(A,k8_lopban_4(A,C,B,D))),E)) = k9_nat_1(k1_numbers,k3_series_1(k5_normsp_0(A,k8_lopban_4(A,C,B,D))),E) ) ) ) ) ) )).
fof(t31_lopclset,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t31_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( r2_hidden(D,k13_lpspacc1(A,B,C)) => r2_hidden(D,k17_lpspacc1(A,B,C,D)) ) ) ) ) ) )).
fof(t31_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( ( r1_lpspace1(A,B,C,D,F) & r1_lpspace1(A,B,C,E,G) ) => r1_lpspace1(A,B,C,k3_valued_1(A,k1_numbers,k1_numbers,D,E),k3_valued_1(A,k1_numbers,k1_numbers,F,G)) ) ) ) ) ) ) ) ) )).
fof(t31_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v2_xxreal_0(E) & v1_xreal_0(E) ) => ! [F] : ( 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,k4_xcmplx_0(1))) = k2_partfun1(A,k1_numbers,k8_lpspace1(A,k5_numbers),k1_relset_1(A,D)) & ? [G] : ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) & ? [H] : ( 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,k4_xcmplx_0(1))) & r2_relset_1(A,k1_numbers,H,k8_lpspace1(A,k5_numbers)) & r1_lpspace1(A,B,C,G,H) ) ) ) ) ) ) ) ) ) ) )).
fof(t31_ltlaxio1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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)) ) ) ) )).
fof(t31_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(k1_ltlaxio1(k3_hilbert1(A,B)),A)) ) ) )).
fof(t31_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( ( ~ v2_ltlaxio3(B) & m1_subset_1(B,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) ) => ~ ( ~ r2_hidden(A,k10_ltlaxio3(B)) & v2_ltlaxio3(k11_ltlaxio3(k3_ltlaxio3(k1_hilbert1,k8_ltlaxio3(B),k12_finseq_1(k1_hilbert1,A)),k9_ltlaxio3(B))) & v2_ltlaxio3(k11_ltlaxio3(k8_ltlaxio3(B),k3_ltlaxio3(k1_hilbert1,k9_ltlaxio3(B),k12_finseq_1(k1_hilbert1,A)))) ) ) ) )).
fof(t31_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( ( ~ v2_ltlaxio3(C) & v3_ltlaxio3(C) & m1_subset_1(C,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) ) => ! [D] : ( m3_ltlaxio4(D,C) => ( ( r2_hidden(k4_hilbert1(A,B),k2_relset_1(k1_hilbert1,k8_ltlaxio3(C))) & ! [E] : ( m2_subset_1(E,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)),k11_ltlaxio4(C,D)) => ~ r2_hidden(B,k2_relset_1(k1_hilbert1,k8_ltlaxio3(E))) ) ) => ! [E] : ( m2_subset_1(E,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)),k11_ltlaxio4(C,D)) => ( r2_hidden(B,k2_relset_1(k1_hilbert1,k9_ltlaxio3(E))) & r2_hidden(k4_hilbert1(A,B),k2_relset_1(k1_hilbert1,k8_ltlaxio3(E))) ) ) ) ) ) ) ) )).
fof(t31_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t31_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k4_subset_1(u1_struct_0(A),k3_mathmorp(A,B,D),k3_mathmorp(A,C,D)),k3_mathmorp(A,k4_subset_1(u1_struct_0(A),B,C),D)) ) ) ) ) )).
fof(t31_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,B,B) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( r1_xxreal_0(k5_numbers,A) & v3_matrix10(C) ) => v3_matrix10(k6_matrix10(B,A,C)) ) ) ) ) )).
fof(t31_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m2_finseq_2(C,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [D] : ( m2_finseq_2(D,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [E] : ( ( v1_matrix_0(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) ) ) ) ) ) ) )).
fof(t31_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v1_matrix_6(C,A,B) => ( v1_matrix_6(k4_matrix_0(u1_struct_0(B),C),A,B) & k1_matrix_6(A,B,k4_matrix_0(u1_struct_0(B),C)) = k4_matrix_0(u1_struct_0(B),k1_matrix_6(A,B,C)) ) ) ) ) ) )).
fof(t31_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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) ) ) )).
fof(t31_matrix16,axiom,( ! [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] : ( 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)) ) ) ) )).
fof(t31_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,E,C,D) & m2_finseq_1(F,k3_finseq_2(E)) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,C) & r1_xxreal_0(1,B) & r1_xxreal_0(B,D) ) => r2_hidden(k4_tarski(A,B),k2_matrix_0(F)) ) ) ) ) ) ) ) )).
fof(t31_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(D) ) => k1_matrix_4(A,B,k3_matrix_3(A,C,D)) = k1_matrix_4(A,k1_matrix_4(A,B,C),D) ) ) ) ) ) )).
fof(t31_matrix_6,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(A),B,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(A),B,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ( ( v3_matrix_6(C,B,A) & v3_matrix_6(D,B,A) ) => v3_matrix_6(k3_matrix_3(A,C,D),B,A) ) ) ) ) ) )).
fof(t31_matrix_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_matrix_2(C,k3_matrix_2(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(B)) => ( ( k3_finseq_1(D) = A & E = k1_partfun1(k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k4_ordinal1,u1_struct_0(B),C,D) ) => r2_classes1(D,E) ) ) ) ) ) ) )).
fof(t31_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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(k3_matrix_1(B,A),A,B) ) ) )).
fof(t31_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( 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,k8_seq_4(B,C)) = k8_seq_4(k5_matrixc1(A,B),k5_matrixc1(A,C)) ) ) ) ) )).
fof(t31_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( 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(k4_ordinal1,k2_finseq_1(k2_wsierp_1(k17_finseq_1(k4_ordinal1,A,k10_matrixj1(B,D)))),k2_finseq_1(k2_wsierp_1(k17_finseq_1(k4_ordinal1,k7_nat_d(A,1),k10_matrixj1(B,D))))),k7_subset_1(k4_ordinal1,k2_finseq_1(k2_wsierp_1(k17_finseq_1(k4_ordinal1,A,k11_matrixj1(B,D)))),k2_finseq_1(k2_wsierp_1(k17_finseq_1(k4_ordinal1,k7_nat_d(A,1),k11_matrixj1(B,D)))))) ) ) ) ) ) )).
fof(t31_matrixr1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( r2_hidden(B,k4_finseq_1(C)) => ( r1_xxreal_0(k3_finseq_1(C),k5_numbers) | ( ? [D] : ( m2_finseq_1(D,k1_numbers) & D = k1_funct_1(C,B) ) & ! [D] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t31_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(C) = A & k1_matrix_0(C) = B ) => k3_matrixr1(k4_matrixr1(C),C) = k8_matrixr1(A,B) ) ) ) ) )).
fof(t31_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(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))) ) ) ) ) ) )).
fof(t31_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( ( 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] : ( m1_matrlin(E,A,B) => ! [F] : ( m1_matrlin(F,A,C) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ( ( v13_vectsp_1(D,B,C) & v1_mod_2(D,A,B,C) ) => ( r1_xxreal_0(k3_finseq_1(E),k5_numbers) | k4_matrix_3(A,k2_matrix15(u1_struct_0(A),k9_matrlin(A,B,E,G)),k1_matrlin2(A,B,C,D,E,F)) = k2_matrix15(u1_struct_0(A),k9_matrlin(A,C,F,k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,G))) ) ) ) ) ) ) ) ) ) )).
fof(t31_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(B,k6_matroid0(A,B)) ) ) )).
fof(t31_matrprob,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => k14_rvsum_1(k5_finseq_2(k4_ordinal1,A,1),B) = B ) ) )).
fof(t31_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t31_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( 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))) ) ) ) ) )).
fof(t31_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( ( r2_pboole(A,k2_mboolean(A,D),B) & r1_pboole(A,C,D) ) => r2_pboole(A,C,B) ) ) ) ) )).
fof(t31_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k3_zfmisc_1(k1_tarski(A),k2_tarski(B,D),k2_tarski(C,E)) = k2_enumset1(k3_xtuple_0(A,B,C),k3_xtuple_0(A,D,C),k3_xtuple_0(A,B,E),k3_xtuple_0(A,D,E)) )).
fof(t31_measure1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t31_measure6,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k6_numbers) => ( B = C => k8_supinf_2(k1_measure6(A,B)) = k3_supinf_2(C,k8_supinf_2(A)) ) ) ) ) )).
fof(t31_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ( k7_member_1(A) = k7_member_1(B) => A = B ) ) ) )).
fof(t31_membered,axiom,( ! [A] : ! [B] : ( ( r2_hidden(B,A) & v1_membered(B) ) => v1_membered(k1_setfam_1(A)) ) )).
fof(t31_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_partfun1(C,u1_struct_0(B)) ) => k1_funct_4(C,k7_memstr_0(A,B,k5_memstr_0(A,B,C))) = C ) ) ) )).
fof(t31_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( ? [E] : ( 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)) ) ) ) ) ) ) )).
fof(t31_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(A),B) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t31_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) )).
fof(t31_mesfunc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t31_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t31_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t31_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,A) => r1_xxreal_0(k5_numbers,k12_supinf_2(k18_rfunct_3(A,B),C)) ) ) ) )).
fof(t31_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [D] : ( ( v2_mesfunc9(B,A) & ! [E] : ( v7_ordinal1(E) => r2_relset_1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,C,E),k2_partfun1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,B,E),D)) ) ) => v2_mesfunc9(C,A) ) ) ) ) )).
fof(t31_metric_1,axiom,( ! [A] : ( ( v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t31_metric_2,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t31_mfold_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( 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)))) ) ) ) ) )).
fof(t31_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ? [B] : ( m1_midsp_1(B,A) & ! [C] : ( 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) ) ) ) ) )).
fof(t31_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( ( v4_midsp_2(B,A) & l1_midsp_2(B,A) ) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(u1_midsp_2(A,B))) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & k9_midsp_2(A,B,C,E) = D ) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t31_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_midsp_3(B,A) => ! [C] : ( m2_midsp_3(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(C))) => ! [F] : ( ( v4_midsp_2(F,C) & l1_midsp_2(F,C) ) => ! [G] : ( m2_finseq_2(G,u1_struct_0(u1_midsp_2(C,F)),k4_finseq_2(k1_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,k1_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)),k1_nat_1(A,1),G,k1_nat_1(B,1),k5_midsp_3(A,u1_struct_0(u1_midsp_2(C,F)),G,B)) ) ) ) ) ) ) ) ) )).
fof(t31_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [D] : ( 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)) ) ) ) )).
fof(t31_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(t31_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k6_modal_1) => ~ ( k5_card_1(k9_xtuple_0(A)) = 1 & A != k17_modal_1 & ! [B] : ( m1_subset_1(B,k3_modal_1) => A != k16_modal_1(B) ) ) ) )).
fof(t31_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( 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 ) ) ) ) )).
fof(t31_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ~ ( ~ 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) ) ) ) )).
fof(t31_modelc_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_modelc_2(D) & m2_finseq_1(D,k4_ordinal1) ) => ( ( r5_modelc_3(D,C) & r1_xxreal_0(1,B) & r1_xxreal_0(B,A) & r1_xxreal_0(A,k3_finseq_1(C)) ) => ( r1_tarski(u1_modelc_3(D,k10_modelc_3(k1_funct_1(C,B),D)),u1_modelc_3(D,k10_modelc_3(k1_funct_1(C,A),D))) & r1_tarski(u3_modelc_3(D,k10_modelc_3(k1_funct_1(C,B),D)),u3_modelc_3(D,k10_modelc_3(k1_funct_1(C,A),D))) ) ) ) ) ) ) )).
fof(t31_moebius1,axiom,( k2_moebius1(2) = k4_xcmplx_0(1) )).
fof(t31_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_vectsp_1(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m3_monoid_0(B,A) ) => v4_vectsp_1(B) ) ) )).
fof(t31_monoid_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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) = k5_numbers ) ) ) ) ) )).
fof(t31_morph_01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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,D),k5_rusub_4(A,C,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,D),C),B) ) ) ) ) )).
fof(t31_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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) ) ) )).
fof(t31_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v3_msafree4(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_msafree4(D,u1_struct_0(A),k4_equation(A),k1_msafree4(u1_struct_0(A),k4_equation(A),C)) => r1_equation(A,B,C,D) ) ) ) ) )).
fof(t31_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( 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] : ( m2_pboole(E,u1_struct_0(A),C,u3_msualg_1(A,B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t31_mssubfam,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t31_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => v1_binop_1(k16_msualg_2(A,B),k14_msualg_2(A,B)) ) ) )).
fof(t31_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msualg_4(C,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,B),D)) => ! [F] : ( 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] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,B),D)) & ? [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,B),D)) & ? [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) ) ) ) ) ) ) ) ) ) ) )).
fof(t31_msualg_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,k13_msualg_4(A,B,C)),D)) => ? [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,B),D)) & E = k3_msualg_4(A,B,C,D,F) ) ) ) ) ) ) )).
fof(t31_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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,k5_numbers) | r1_pcomps_1(u1_struct_0(A),k5_nagata_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),B,C)) ) ) ) ) ) )).
fof(t31_nat_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ( r1_tarski(A,B) => r1_xxreal_0(k5_card_1(A),k5_card_1(B)) ) ) ) )).
fof(t31_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_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)) ) ) ) ) )).
fof(t31_nat_4,axiom,( v1_int_2(37) )).
fof(t31_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( r1_nat_d(A,B) => ( B = A | A = 1 | r1_xxreal_0(k2_xcmplx_0(k2_xcmplx_0(1,A),B),k5_nat_5(B)) ) ) ) ) )).
fof(t31_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => k5_nat_d(A,A) = A ) )).
fof(t31_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,A,B) => ! [G] : ( m2_nattra_1(G,A,B,C,D) => ! [H] : ( m2_nattra_1(H,A,B,E,F) => ! [I] : ( m1_subset_1(I,u4_struct_0(k9_nattra_1(A,B))) => ! [J] : ( m1_subset_1(J,u4_struct_0(k9_nattra_1(A,B))) => ( ( I = k4_tarski(k4_tarski(C,D),G) & J = k4_tarski(k4_tarski(E,F),H) ) => ( r2_hidden(k8_cat_2(k9_nattra_1(A,B),k9_nattra_1(A,B),J,I),k9_xtuple_0(u1_cat_1(k9_nattra_1(A,B)))) <=> r2_funct_2(u4_struct_0(A),u4_struct_0(B),D,E) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t31_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,k1_numbers,k5_normsp_0(A,k8_funct_2(k4_ordinal1,u1_struct_0(A),u1_struct_0(B),D,C)),k8_funct_2(k4_ordinal1,k1_numbers,u1_struct_0(B),D,k4_normsp_0(u1_struct_0(B),A,C))) & r2_funct_2(k4_ordinal1,u1_struct_0(A),k5_vfunct_1(k4_ordinal1,A,k8_funct_2(k4_ordinal1,u1_struct_0(A),u1_struct_0(B),D,C)),k8_funct_2(k4_ordinal1,u1_struct_0(A),u1_struct_0(B),D,k5_vfunct_1(u1_struct_0(B),A,C))) ) ) ) ) ) ) )).
fof(t31_ncfcont2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t31_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(E,D) => r1_ndiff_1(A,B,C,E) ) ) ) ) ) ) ) ) ) )).
fof(t31_ndiff_4,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k4_ordinal1) => ( ( 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) ) ) ) ) ) )).
fof(t31_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_prvect_2(A))) => r1_xxreal_0(k2_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)),k2_normsp_0(k14_prvect_2(A),C)) ) ) ) )).
fof(t31_newton,axiom,( ! [A] : ( v7_ordinal1(A) => k6_newton(A) = k5_newton(1,1,A) ) )).
fof(t31_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t31_nfcont_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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,k4_normsp_0(k1_numbers,B,C),A)) ) ) ) ) )).
fof(t31_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t31_normform,axiom,( ! [A] : r2_hidden(k1_xboole_0,k8_normform(A)) )).
fof(t31_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k4_normsp_2(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k4_normsp_2(A))))) ) => ( ( r1_funct_2(k4_ordinal1,u1_struct_0(A),k4_ordinal1,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) ) ) ) ) ) )).
fof(t31_numbers,axiom,( r1_tarski(k1_numbers,k6_numbers) )).
fof(t31_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t31_openlatt,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t31_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_oppcat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t31_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ( ( r1_xxreal_0(B,C) & k1_relset_1(k1_numbers,D) = k3_integra5(B,C) & k1_relset_1(k1_numbers,E) = k3_integra5(B,C) & v1_nfcont_4(D,A) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,k1_rcomp_1(B,C)) => k1_funct_1(E,F) = k12_integr15(B,F,A,D) ) ) ) => ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,k1_rcomp_1(B,C)) => r1_nfcont_4(A,E,F) ) ) ) ) ) ) ) ) )).
fof(t31_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_orders_1(A) => r1_orders_1(A,k1_relat_1(A)) ) ) )).
fof(t31_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t31_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ~ ( ~ r2_xboole_0(A,B) & A != B & ~ r2_xboole_0(B,A) ) ) ) )).
fof(t31_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => k10_ordinal2(A,1) = k1_ordinal1(A) ) )).
fof(t31_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ~ ( k11_ordinal2(A,B) = k1_xboole_0 & A != k1_xboole_0 & B != k1_xboole_0 ) ) ) )).
fof(t31_ordinal4,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => k12_ordinal2(k12_ordinal2(C,A),B) = k12_ordinal2(C,k11_ordinal2(B,A)) ) ) ) )).
fof(t31_ordinal6,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t31_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ~ r1_orders_2(B,D,C) => k2_ortsp_1(A,B,E,k4_vectsp_1(A,B,G,F),C,D) = k8_group_1(A,G,k2_ortsp_1(A,B,E,F,C,D)) ) ) ) ) ) ) ) ) )).
fof(t31_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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)) ) ) )).
fof(t31_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( r1_osalg_1(A,B,C) <=> k8_osalg_1(A,B) = k8_osalg_1(A,C) ) ) ) ) )).
fof(t31_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t31_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t31_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_parsp_2(A,B,C,D,E) => r2_parsp_2(A,D,E,B,C) ) ) ) ) ) ) )).
fof(t31_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(t31_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(C)) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( r2_hidden(E,k1_relset_1(A,F)) => r2_relset_1(C,B,k1_partfun1(C,A,A,B,k4_partfun2(C,A,D,E),F),k4_partfun2(C,B,D,k7_partfun1(B,F,E))) ) ) ) ) ) ) ) )).
fof(t31_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k10_eqrel_1(A) = a_1_0_partit1(A) ) )).
fof(t31_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( r2_relat_2(B,A) => v2_relat_2(B) ) ) ) )).
fof(t31_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_diraf(A,F,B,D) & r2_analoaf(A,F,B,G,C) & r3_diraf(A,G,C,E) & r2_analoaf(A,F,G,B,C) & r2_analoaf(A,F,G,D,E) ) => ( r3_diraf(A,F,B,G) | r1_diraf(A,G,C,E) ) ) ) ) ) ) ) ) ) )).
fof(t31_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) )).
fof(t31_pcomps_1,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t31_pcs_0,axiom,( ! [A] : ( ( v13_pcs_0(A) & l2_pcs_0(A) ) => ! [B] : ( ~ r2_hidden(B,u1_struct_0(A)) => v13_pcs_0(k20_pcs_0(A,B)) ) ) )).
fof(t31_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( 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) & k10_pdiff_1(A,B,k47_valued_1(k1_euclid(A),k1_numbers,k1_numbers,C,D),E) = k6_xcmplx_0(k10_pdiff_1(A,B,C,E),k10_pdiff_1(A,B,D,E)) ) ) ) ) ) ) ) )).
fof(t31_pdiff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(2)) => ! [C] : ( ( 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) & k10_pdiff_1(2,1,k26_valued_1(k1_euclid(2),k1_numbers,k1_pdiff_3(2,2,C),A),B) = k3_xcmplx_0(A,k4_pdiff_3(C,B)) ) ) ) ) ) )).
fof(t31_pdiff_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( 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),k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(1,3),B)) ) ) ) )).
fof(t31_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( 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) = k10_pdiff_1(3,1,k1_pdiff_3(2,3,B),A) ) ) ) )).
fof(t31_pdiff_6,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t31_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ( v1_pdiff_7(B,A) <=> ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ~ ( r2_hidden(C,B) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(a_3_0_pdiff_7(A,C,D),B) ) ) ) ) ) ) ) )).
fof(t31_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t31_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(A,B) <=> r1_nat_d(k1_newton(2,A),k1_newton(2,B)) ) ) ) )).
fof(t31_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m2_finseq_2(C,B,k3_finseq_2(B)) => ! [D] : ( 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)) ) ) ) )).
fof(t31_polyeq_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k1_newton(k2_xcmplx_0(k19_sin_cos(A),k3_xcmplx_0(k17_sin_cos(A),k7_complex1)),B) = k2_xcmplx_0(k19_sin_cos(k3_xcmplx_0(B,A)),k3_xcmplx_0(k17_sin_cos(k3_xcmplx_0(B,A)),k7_complex1)) ) ) )).
fof(t31_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ( ( r1_xxreal_0(k4_xcmplx_0(1),B) & r1_xxreal_0(B,k7_polyform(A)) ) => ! [C] : ( m1_subset_1(C,k8_polyform(A,B)) => ? [D] : ( v7_ordinal1(D) & C = k15_polyform(A,B,D) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k11_polyform(A,B)) ) ) ) ) ) )).
fof(t31_polynom1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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(k12_polynom1(A,B)) = k9_polynom1(A,B) ) ) )).
fof(t31_polynom3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v2_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,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))) ) ) ) ) )).
fof(t31_polynom7,axiom,( ! [A] : ( v3_ordinal1(A) => ! [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) & v5_group_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & v1_algstr_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( 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)))) ) => k2_polynom2(A,B,k6_polynom7(A,B,C,D),E) = k8_group_1(B,k2_polynom2(A,B,C,E),D) ) ) ) ) ) )).
fof(t31_polynom8,axiom,( ! [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) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_polynom8(A,C,B) => r1_polynom8(A,k11_algstr_0(A,C),B) ) ) ) ) )).
fof(t31_polyred,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) & r2_hidden(E,D) & ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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) ) ) ) ) ) ) ) )).
fof(t31_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & k2_power(k7_xcmplx_0(A,B),C) != k7_xcmplx_0(k2_power(A,C),k2_power(B,C)) ) ) ) ) )).
fof(t31_pre_poly,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,k3_finseq_2(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ? [E] : ( 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) ) ) ) ) ) )).
fof(t31_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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))))) ) ) ) )).
fof(t31_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(1,B) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(k6_xcmplx_0(k2_prepower(B,A),1),k7_xcmplx_0(k6_xcmplx_0(A,1),B)) ) ) ) ) )).
fof(t31_prob_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m2_prob_1(D,A,B) => k3_real_1(k3_funct_2(B,k1_numbers,D,k7_prob_1(A,B,k4_prob_1(A,B),C)),k3_funct_2(B,k1_numbers,D,C)) = 1 ) ) ) ) )).
fof(t31_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m1_prob_1(E,A,B) => ! [F] : ( m1_prob_1(F,A,B) => ( F = k3_subset_1(A,E) => ( r1_xxreal_0(k3_funct_2(B,k1_numbers,C,E),k5_numbers) | r1_xxreal_0(k3_funct_2(B,k1_numbers,C,F),k5_numbers) | k3_funct_2(B,k1_numbers,C,D) = k3_real_1(k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,C,E),D),k3_funct_2(B,k1_numbers,C,E)),k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,C,F),D),k3_funct_2(B,k1_numbers,C,F))) ) ) ) ) ) ) ) ) )).
fof(t31_prob_3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( r2_funct_2(k4_ordinal1,k9_setfam_1(A),D,k3_prob_3(A,C)) => ( k1_prob_2(A,B,D,k5_numbers) = k1_prob_2(A,B,C,k5_numbers) & ! [E] : ( v7_ordinal1(E) => k1_prob_2(A,B,D,k1_nat_1(E,1)) = k7_prob_1(A,B,k1_prob_2(A,B,C,k1_nat_1(E,1)),k1_prob_2(A,B,k2_prob_3(A,C),E)) ) ) ) ) ) ) )).
fof(t31_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t31_projpl_1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & v5_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t31_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ 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))) ) ) ) ) ) ) )).
fof(t31_pua2mss1,axiom,( ! [A] : ( ( v2_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( l3_msualg_1(C,B) => ! [D] : ( m2_pua2mss1(D,u4_struct_0(B)) => ( r6_pua2mss1(A,B,C,D) => ! [E] : ( m2_subset_1(E,k4_ordinal1,k4_finseq_1(u1_unialg_1(A))) => ! [F] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t31_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) )).
fof(t31_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t31_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k5_qc_lang1(A)) => ? [C] : ( v7_ordinal1(C) & k3_qc_lang3(A,C) = B ) ) ) )).
fof(t31_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t31_quantal1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t31_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ( A != k5_numbers => k23_quaterni(A,k7_quatern2(A)) = 1 ) ) )).
fof(t31_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k13_quaterni(k23_quaterni(k23_quaterni(A,B),C)) = k13_quaterni(k23_quaterni(k23_quaterni(C,A),B)) ) ) ) )).
fof(t31_quaterni,axiom,( k13_quaterni(k11_quaterni) = k5_numbers & k14_quaterni(k11_quaterni) = k5_numbers & k15_quaterni(k11_quaterni) = 1 & k16_quaterni(k11_quaterni) = k5_numbers & k13_quaterni(k12_quaterni) = k5_numbers & k14_quaterni(k12_quaterni) = k5_numbers & k15_quaterni(k12_quaterni) = k5_numbers & k16_quaterni(k12_quaterni) = 1 )).
fof(t31_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k19_quofield(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t31_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m2_prob_1(B,A,k1_random_1(A)) => ! [C] : ( m1_random_1(C,A,k1_random_1(A)) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ! [E] : ( 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] : ( v7_ordinal1(F) => ( r2_hidden(F,k4_finseq_1(D)) => k12_supinf_2(D,F) = k1_extreal1(k12_supinf_2(C,k1_funct_1(E,F)),k12_supinf_2(B,k1_tarski(k1_funct_1(E,F)))) ) ) ) => k8_random_1(A,k1_random_1(A),B,C) = k18_rvsum_1(D) ) ) ) ) ) ) )).
fof(t31_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_6(C,A,B) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t31_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) <=> r1_xxreal_0(k1_rat_1(A),k4_xcmplx_0(k2_rat_1(A))) ) ) )).
fof(t31_ratfunc1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k13_ratfunc1(A,k7_ratfunc1(A),B) = k4_struct_0(A) ) ) )).
fof(t31_rcomp_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v5_xxreal_2(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v5_xxreal_2(B) & v6_xxreal_2(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_xxreal_0(k3_seq_4(A),k3_seq_4(B)) & r1_xxreal_0(k2_seq_4(B),k2_seq_4(A)) ) => ( ( k3_seq_4(A) = k3_seq_4(B) & r2_hidden(k3_seq_4(B),B) & ~ r2_hidden(k3_seq_4(A),A) ) | ( k2_seq_4(A) = k2_seq_4(B) & r2_hidden(k2_seq_4(B),B) & ~ r2_hidden(k2_seq_4(A),A) ) | r1_tarski(B,A) ) ) ) ) )).
fof(t31_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_int_1(B) => ( ~ r1_xxreal_0(B,1) => ( k9_nat_1(k1_numbers,k3_real_3(k7_xcmplx_0(1,B)),1) = B & k9_nat_1(k1_numbers,k3_real_3(k7_xcmplx_0(1,B)),k1_nat_1(A,2)) = k5_numbers ) ) ) ) )).
fof(t31_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k8_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t31_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ( ! [B] : ! [C] : ~ r2_hidden(k4_tarski(B,C),A) => A = k1_xboole_0 ) ) )).
fof(t31_relset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( ! [D] : ( r2_hidden(D,A) => k9_relat_1(B,D) = k9_relat_1(C,D) ) => r2_relset_1(A,A,B,C) ) ) ) )).
fof(t31_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( 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)) ) ) ) ) )).
fof(t31_revrot_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( 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(k1_nat_1(A,k4_finseq_4(C,B)),k3_finseq_1(C))) ) ) ) ) ) )).
fof(t31_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r2_rewrite1(A,B,C) => r2_rewrite1(A,C,B) ) ) )).
fof(t31_rewrite2,axiom,( ! [A] : ! [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,k7_rewrite2(A,B)),k7_rewrite2(A,B)) ) )).
fof(t31_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k8_afinsq_1(C))) => ! [E] : ( ( ~ v2_struct_0(E) & l1_rewrite3(E,D) ) => ~ ( r2_hidden(k4_tarski(A,B),k1_rewrite3(C,D,E)) & ! [F] : ( m1_subset_1(F,u1_struct_0(E)) => ! [G] : ( m1_subset_1(G,k8_afinsq_1(C)) => ! [H] : ( m1_subset_1(H,u1_struct_0(E)) => ! [I] : ( m1_subset_1(I,k8_afinsq_1(C)) => ~ ( A = k4_tarski(F,G) & B = k4_tarski(H,I) ) ) ) ) ) ) ) ) ) )).
fof(t31_rfinseq,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t31_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t31_rfunct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t31_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,k3_rfunct_3(A,k1_numbers)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t31_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_seq_2(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_numbers)) => ( C = a_2_0_rinfsup1(A,B) => v4_xxreal_2(C) ) ) ) ) ) )).
fof(t31_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( 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(k6_numbers,A,B)) & k2_rinfsup2(k1_valued_0(k6_numbers,A,B)) = k12_supinf_2(A,B) ) ) ) ) ) )).
fof(t31_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => k3_rlaffin1(A,k4_rlvect_2(A)) = k5_numbers ) )).
fof(t31_rlaffin3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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)))) ) ) ) )).
fof(t31_rlsub_1,axiom,( ! [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) ) => ! [B] : ( ( v1_rlvect_1(B) & m1_rlsub_1(B,A) ) => ! [C] : ( ( v1_rlvect_1(C) & m1_rlsub_1(C,A) ) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_struct_0(B,D) <=> r1_struct_0(C,D) ) ) => B = C ) ) ) ) )).
fof(t31_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( ( v1_rlvect_1(C) & m1_rlsub_1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t31_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_connsp_2(D,A,k3_rlvect_1(A,B,C)) => ? [E] : ( m1_connsp_2(E,A,B) & ? [F] : ( m1_connsp_2(F,A,C) & r1_tarski(k7_rusub_4(A,E,F),D) ) ) ) ) ) ) )).
fof(t31_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t31_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m2_rlvect_2(B,A,k1_subset_1(u1_struct_0(A))) => k6_rlvect_2(A,B) = k4_struct_0(A) ) ) )).
fof(t31_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t31_rlvect_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t31_rlvect_5,axiom,( ! [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_rlvect_5(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_rlsub_1(B,A) => ( k1_rlvect_5(A) = k1_rlvect_5(B) <=> k2_rlsub_1(A) = k2_rlsub_1(B) ) ) ) )).
fof(t31_rlvect_x,axiom,( ! [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) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => r1_tarski(k2_relset_1(u1_struct_0(A),B),k3_rlvect_x(A,B)) ) ) )).
fof(t31_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v2_vectsp_2(C,A) & m1_rmod_2(C,A,B) ) => ( u1_struct_0(C) = u1_struct_0(B) => C = B ) ) ) ) )).
fof(t31_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( ( v2_vectsp_2(E,A) & m1_rmod_2(E,A,B) ) => ( m1_rmod_2(E,A,D) => k1_rmod_3(A,B,E,k2_rmod_3(A,B,C,D)) = k2_rmod_3(A,B,k1_rmod_3(A,B,E,C),D) ) ) ) ) ) ) )).
fof(t31_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m2_rmod_4(C,A,B,k1_subset_1(u1_struct_0(B))) => k5_rmod_4(A,B,C) = k4_struct_0(B) ) ) ) )).
fof(t31_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t31_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t31_robbins4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v10_robbins1(A) & v8_robbins3(A) & v9_robbins3(A) & l4_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t31_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) )).
fof(t31_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => r1_xxreal_0(k6_xcmplx_0(k1_rpr_1(A,B),k1_rpr_1(A,C)),k1_rpr_1(A,k7_subset_1(A,B,C))) ) ) ) )).
fof(t31_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => k1_rusub_1(B) = k1_rusub_1(C) ) ) ) )).
fof(t31_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( ( v1_bhsp_1(C) & m1_rusub_1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t31_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( r2_hidden(D,k3_rusub_1(A,B,k1_rusub_3(A,k6_domain_1(u1_struct_0(A),C)))) <=> ? [E] : ( v1_xreal_0(E) & D = k3_rlvect_1(A,B,k1_rlvect_1(A,C,E)) ) ) ) ) ) )).
fof(t31_rusub_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v2_rusub_4(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => v2_rusub_4(k5_rusub_4(A,B,C),A) ) ) ) )).
fof(t31_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_xcmplx_0(k1_square_1(k3_bhsp_1(A,k3_rlvect_1(A,B,C))),k1_square_1(k3_bhsp_1(A,k5_algstr_0(A,B,C)))) = k2_xcmplx_0(k3_xcmplx_0(2,k1_square_1(k3_bhsp_1(A,B))),k3_xcmplx_0(2,k1_square_1(k3_bhsp_1(A,C)))) ) ) ) )).
fof(t31_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t31_rvsum_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( 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))) = k2_xcmplx_0(k16_rvsum_1(B),A) ) ) )).
fof(t31_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( v1_ami_2(E) & ~ v1_scmfsa_m(E) & m1_subset_1(E,u1_struct_0(k1_scmfsa_2)) ) => ( ( k1_funct_1(B,E) = k5_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) ) ) ) ) ) ) ) )).
fof(t31_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( r1_tarski(k2_scmbsort,A) => ! [B] : ( m1_scmfsa_2(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ r1_xxreal_0(63,C) => k1_funct_1(k2_scmbsort,C) = k3_compos_1(k1_scmfsa_2,A,C) ) ) ) ) ) )).
fof(t31_scmfsa10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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) = k4_ordinal1 ) ) )).
fof(t31_scmfsa8a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( 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(k7_card_1(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(k1_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(k1_nat_1(k5_card_1(C),1))),C),k4_compos_1(k1_scmfsa_2)),D,A) ) ) ) ) ) ) )).
fof(t31_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,k6_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(B))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(C,B,A)) ) ) ) )).
fof(t31_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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] : ( v7_ordinal1(E) => ( r1_xxreal_0(k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(B,D,C,A),E),C),k5_numbers) => k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(B,D,C,A),k1_nat_1(E,1))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(B,D,C,A),E)) ) ) ) ) ) ) )).
fof(t31_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ~ ( k2_compos_0(u1_compos_1(k1_scmfsa_2),A) = 9 & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( m1_scmfsa_2(D) => A != k14_scmfsa_2(C,B,D) ) ) ) ) ) )).
fof(t31_scmfsa_m,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ! [B] : ( 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(k5_numbers),k4_struct_0(k1_scmfsa_2),B) ) ) )).
fof(t31_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v3_scmpds_4(D) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( ( k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,E),F)) = k5_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,k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),2))) ) ) ) ) ) ) ) )).
fof(t31_scmpds_7,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(E) & v1_funct_1(E) & v1_finset_1(E) & v1_afinsq_1(E) ) => ( ~ r1_xxreal_0(k1_nat_1(k5_card_1(E),3),D) <=> r2_hidden(D,k2_afinsq_1(k1_scmpds_7(A,B,C,E))) ) ) ) ) ) ) )).
fof(t31_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k1_amistd_1(k7_card_1(2),k1_scmring2(A),C,k9_scmring2(A,D,B))) & r1_tarski(k1_amistd_1(k7_card_1(2),k1_scmring2(A),C,k9_scmring2(A,D,B)),k2_tarski(D,k1_ordinal1(C))) ) ) ) ) ) )).
fof(t31_scmyciel,axiom,( ! [A] : ? [B] : ( v4_scmyciel(B) & v2_scmyciel(B) & k3_tarski(B) = A ) )).
fof(t31_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t31_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_funct_2(k4_ordinal1,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k32_valued_1(k4_ordinal1,k1_numbers,A),B),k32_valued_1(k4_ordinal1,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B))) & r2_funct_2(k4_ordinal1,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,k32_valued_1(k4_ordinal1,k1_numbers,B)),k32_valued_1(k4_ordinal1,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B))) ) ) ) )).
fof(t31_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & v2_comseq_2(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => k1_seq_2(k55_valued_1(k4_ordinal1,k2_numbers,k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B))) = k9_complex1(k6_xcmplx_0(k3_comseq_2(A),k3_comseq_2(B))) ) ) )).
fof(t31_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( m1_subset_1(C,A) => ( r2_relset_1(k4_ordinal1,k1_numbers,k10_seqfunc(A,k5_seqfunc(A,B),C),k56_valued_1(k4_ordinal1,k1_numbers,k10_seqfunc(A,B,C))) & r2_relset_1(k4_ordinal1,k1_numbers,k10_seqfunc(A,k4_seqfunc(A,B),C),k32_valued_1(k4_ordinal1,k1_numbers,k10_seqfunc(A,B,C))) ) ) ) ) )).
fof(t31_seqm_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v6_valued_0(B) => ( r1_xxreal_0(A,k5_numbers) | v6_valued_0(k26_valued_1(k4_ordinal1,k1_numbers,B,A)) ) ) & ( v6_valued_0(B) => ( r1_xxreal_0(k5_numbers,A) | v5_valued_0(k26_valued_1(k4_ordinal1,k1_numbers,B,A)) ) ) ) ) ) )).
fof(t31_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v8_valued_0(A) & ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,A,C)) & k9_nat_1(k1_numbers,B,C) = k3_xcmplx_0(k5_series_1(2,C),k3_funct_2(k4_ordinal1,k1_numbers,A,k5_series_1(2,C))) ) ) ) => ( v1_series_1(A) <=> v1_series_1(B) ) ) ) ) )).
fof(t31_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( 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(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k3_xcmplx_0(A,B)),k1_square_1(B)),3)),k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(B),k3_xcmplx_0(B,C)),k1_square_1(C)),3))),k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(C),k3_xcmplx_0(C,A)),k1_square_1(A)),3)))) ) ) ) )).
fof(t31_setfam_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ( ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( r2_hidden(D,B) <=> r2_hidden(D,C) ) ) => B = C ) ) ) )).
fof(t31_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k3_funct_2(k4_ordinal1,k9_setfam_1(A),k4_setlim_1(A,B),C) = k3_subset_1(A,k3_funct_2(k4_ordinal1,k9_setfam_1(A),k2_setlim_1(A,k2_prob_1(A,B)),C)) ) ) )).
fof(t31_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(C) => v3_prob_1(k8_setlim_2(A,C,B)) ) ) ) )).
fof(t31_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( m1_subset_1(F,k5_finsub_1(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t31_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t31_sf_mastr,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( 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)) ) ) )).
fof(t31_sgraph1,axiom,( ! [A] : ! [B] : ( m1_sgraph1(B,A) => ! [C] : ! [D] : ( v1_finset_1(D) => ( ( D = u1_struct_0(B) & r2_hidden(C,D) & k1_nat_1(1,k4_sgraph1(A,B,C)) = k5_card_1(D) ) => ! [E] : ( m1_subset_1(E,D) => ~ ( C != E & ! [F] : ~ ( r2_hidden(F,u1_sgraph1(B)) & F = k2_tarski(C,E) ) ) ) ) ) ) )).
fof(t31_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v9_sheffer1(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l3_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,B,C) = k5_sheffer1(A,C,B) ) ) ) )).
fof(t31_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) )).
fof(t31_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ! [C] : ( m2_simplex0(C,A,B) => r1_tarski(k4_simplex0(C),k4_simplex0(B)) ) ) )).
fof(t31_simplex1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t31_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( k19_sin_cos(k5_numbers) = 1 & k17_sin_cos(k5_numbers) = k5_numbers & k19_sin_cos(k4_xcmplx_0(A)) = k19_sin_cos(A) & k17_sin_cos(k4_xcmplx_0(A)) = k4_xcmplx_0(k17_sin_cos(A)) ) ) )).
fof(t31_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_fdiff_1(k1_sin_cos2,A) & k1_fdiff_1(k1_sin_cos2,A) = k1_funct_1(k3_sin_cos2,A) ) ) )).
fof(t31_sin_cos3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k15_sin_cos(k3_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(k1_nat_1(k2_nat_1(2,A),1),k28_sin_cos)),k7_complex1)) = k4_xcmplx_0(1) ) )).
fof(t31_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k3_xcmplx_0(k19_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)))) ) ) )).
fof(t31_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k19_sin_cos(k7_xcmplx_0(A,2)) != k5_numbers => k2_sin_cos4(k7_xcmplx_0(A,2)) = k7_xcmplx_0(k2_xcmplx_0(1,k19_sin_cos(A)),k17_sin_cos(A)) ) ) )).
fof(t31_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),A) & r1_xxreal_0(k17_sin_cos(A),k4_xcmplx_0(1)) ) ) )).
fof(t31_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ r1_xxreal_0(1,k7_xcmplx_0(k6_xcmplx_0(k1_square_1(A),1),k2_xcmplx_0(k1_square_1(A),1))) ) )).
fof(t31_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_newton(k2_sin_cos2(A),3) = k7_xcmplx_0(k6_xcmplx_0(k2_sin_cos2(k3_xcmplx_0(3,A)),k3_xcmplx_0(3,k2_sin_cos2(A))),4) & k1_newton(k2_sin_cos2(A),4) = k7_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k4_sin_cos2(k3_xcmplx_0(4,A)),k3_xcmplx_0(4,k4_sin_cos2(k3_xcmplx_0(2,A)))),3),8) & k1_newton(k2_sin_cos2(A),5) = k7_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k2_sin_cos2(k3_xcmplx_0(5,A)),k3_xcmplx_0(5,k2_sin_cos2(k3_xcmplx_0(3,A)))),k3_xcmplx_0(10,k2_sin_cos2(A))),16) & k1_newton(k2_sin_cos2(A),6) = k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k4_sin_cos2(k3_xcmplx_0(6,A)),k3_xcmplx_0(6,k4_sin_cos2(k3_xcmplx_0(4,A)))),k3_xcmplx_0(15,k4_sin_cos2(k3_xcmplx_0(2,A)))),10),32) & k1_newton(k2_sin_cos2(A),7) = k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k2_sin_cos2(k3_xcmplx_0(7,A)),k3_xcmplx_0(7,k2_sin_cos2(k3_xcmplx_0(5,A)))),k3_xcmplx_0(21,k2_sin_cos2(k3_xcmplx_0(3,A)))),k3_xcmplx_0(35,k2_sin_cos2(A))),64) & k1_newton(k2_sin_cos2(A),8) = k7_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k4_sin_cos2(k3_xcmplx_0(8,A)),k3_xcmplx_0(8,k4_sin_cos2(k3_xcmplx_0(6,A)))),k3_xcmplx_0(28,k4_sin_cos2(k3_xcmplx_0(4,A)))),k3_xcmplx_0(56,k4_sin_cos2(k3_xcmplx_0(2,A)))),35),128) ) ) )).
fof(t31_sin_cos9,axiom,( k3_relat_1(k2_partfun1(k1_numbers,k1_numbers,k26_sin_cos,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))),k1_sin_cos9) = k1_partfun2(k1_numbers,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))) )).
fof(t31_sincos10,axiom,( k1_funct_1(k1_fdiff_9,k5_numbers) = 1 & k1_funct_1(k1_fdiff_9,k7_xcmplx_0(k28_sin_cos,4)) = k3_square_1(2) & k1_funct_1(k1_fdiff_9,k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos)) = k4_xcmplx_0(k3_square_1(2)) & k1_funct_1(k1_fdiff_9,k28_sin_cos) = k4_xcmplx_0(1) )).
fof(t31_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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(k1_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,k1_nat_1(A,2))),k4_subset_1(u1_struct_0(k15_euclid(2)),k2_topreal1(2,B,A),k2_topreal1(2,B,k1_nat_1(A,1)))) ) ) ) )).
fof(t31_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ( ( v2_topreal1(A) & v2_topreal1(B) & k1_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)) ) ) ) ) )).
fof(t31_sprect_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t31_sprect_2,axiom,( k7_pscomp_1(k1_topreal1) = 1 )).
fof(t31_sprect_3,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t31_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t31_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => ( k3_square_1(k2_xcmplx_0(A,B)) = k5_numbers <=> ( A = k5_numbers & B = k5_numbers ) ) ) ) ) )).
fof(t31_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( A != k5_numbers => k3_stirl2_1(A,k5_numbers) = k5_numbers ) ) )).
fof(t31_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k16_substut1(A),k38_substut1(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t31_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( ! [D] : ( m1_subset_1(D,A) => ( ~ r2_hidden(D,B) <=> r2_hidden(D,C) ) ) => B = k3_subset_1(A,C) ) ) ) )).
fof(t31_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t31_supinf_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k6_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t31_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t31_sysrel,axiom,( ! [A] : ( 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) ) ) ) ) )).
fof(t31_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) )).
fof(t31_taylor_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(C,B) => ! [D] : ( v7_ordinal1(D) => ( r1_taylor_1(A,k1_nat_1(D,1),B) => r1_taylor_1(A,k1_nat_1(D,1),C) ) ) ) ) ) ) )).
fof(t31_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => r1_tarski(k5_tdlat_1(A),k1_tdlat_1(A)) ) )).
fof(t31_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) )).
fof(t31_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v4_tdlat_3(A) <=> ! [B] : ( 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)) ) ) ) ) )).
fof(t31_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(D,A,C) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(E,A,C) & v1_polynom1(E,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,k10_polynom1(A,C,D,E)),k11_pre_poly(A,k3_termord(A,B,C,D),k3_termord(A,B,C,E))) ) ) ) ) ) )).
fof(t31_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_tdlat_3(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( B != u1_struct_0(A) & v1_tops_1(B,A) ) ) ) ) )).
fof(t31_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & ! [D] : ( 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) ) ) ) )).
fof(t31_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_pre_topc(C,A) => ( r3_tsep_2(A,B,C) => ( v1_tex_3(B,A) <=> v3_tex_3(C,A) ) ) ) ) ) )).
fof(t31_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t31_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ 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)) ) ) ) ) ) ) ) ) )).
fof(t31_toler_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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) ) ) ) )).
fof(t31_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_borsuk_2(G,A,B,C) => ! [H] : ( m1_borsuk_2(H,A,C,D) => ! [I] : ( m1_borsuk_2(I,A,D,E) => ! [J] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t31_topalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)))) ) ) ) ) ) )).
fof(t31_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( ( 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] : ( ( 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))))) ) ) ) ) ) ) ) ) ) )).
fof(t31_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t31_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( v7_ordinal1(B) => ( ( v3_topdim_1(A) & r1_xxreal_0(k4_topdim_1(A),B) ) <=> ? [C] : ( 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] : ( 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)),k6_xcmplx_0(B,1)) ) ) ) ) ) ) ) )).
fof(t31_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t31_topgen_2,axiom,( ! [A] : ( ~ v1_finset_1(A) => k1_card_1(a_1_2_topgen_2(A)) = k1_card_1(A) ) )).
fof(t31_topgen_3,axiom,( ! [A] : ( 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) ) ) )).
fof(t31_topgen_4,axiom,( ! [A] : ! [B] : ~ ( k3_setfam_1(A,B) = k1_xboole_0 & A != k1_xboole_0 & B != k1_xboole_0 ) )).
fof(t31_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m3_topgrp_1(B,A) => ! [C] : ( m3_topgrp_1(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_topgrp_1(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t31_topreal8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ! [C] : ( ( ~ 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),k1_nat_1(A,1)) | k2_topreal1(2,k4_graph_2(u1_struct_0(k15_euclid(2)),B,C),k2_xcmplx_0(k3_finseq_1(B),A)) = k2_topreal1(2,C,k1_nat_1(A,1)) ) ) ) ) ) )).
fof(t31_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ( ( r2_hidden(C,k3_topreal9(A,E,B)) & r2_hidden(D,k1_topreal9(A,E,B)) ) => k9_subset_1(u1_struct_0(k15_euclid(A)),k1_rltopsp1(k15_euclid(A),C,D),k3_topreal9(A,E,B)) = k1_tarski(C) ) ) ) ) ) ) )).
fof(t31_topreala,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t31_toprealb,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k12_toprealb,B) = k1_funct_1(k12_toprealb,k2_xcmplx_0(B,A)) ) ) )).
fof(t31_toprealc,axiom,( ! [A] : ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_valued_2(C) => ! [D] : ( ( 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)) ) ) ) )).
fof(t31_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => r1_xxreal_0(k6_xcmplx_0(k12_euclid(B),k12_euclid(C)),k12_euclid(k3_rlvect_1(k15_euclid(A),B,C))) ) ) ) )).
fof(t31_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)) ) ) )).
fof(t31_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t31_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => v1_tops_3(k2_struct_0(A),A) ) )).
fof(t31_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t31_trees_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t31_trees_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ( ( k9_xtuple_0(A) = k9_xtuple_0(B) & ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( r2_hidden(C,k9_xtuple_0(A)) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) => A = B ) ) ) )).
fof(t31_trees_3,axiom,( ! [A] : ! [B] : ( v4_trees_3(k10_finseq_1(A,B)) <=> ( ~ v1_xboole_0(A) & v1_trees_1(A) & ~ v1_xboole_0(B) & v1_trees_1(B) ) ) )).
fof(t31_trees_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( m2_finseq_1(E,k5_trees_3(k2_zfmisc_1(A,B))) => ? [F] : ( m2_finseq_1(F,k5_trees_3(A)) & k4_finseq_1(F) = k4_finseq_1(E) & ! [G] : ( v7_ordinal1(G) => ~ ( r2_hidden(G,k4_finseq_1(E)) & ! [H] : ( 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) ) ) ) ) ) ) )).
fof(t31_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v3_trees_9(A) ) => ! [B] : ( m1_trees_1(B,k9_xtuple_0(A)) => ! [C] : ( m1_trees_1(C,k9_xtuple_0(k5_trees_2(A,B))) => k2_trees_9(A,k8_finseq_1(k4_ordinal1,B,C)) = k2_trees_9(k5_trees_2(A,B),C) ) ) ) )).
fof(t31_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t31_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( ( r4_tsep_2(A,C,B) & r4_tsep_2(A,B,D) ) => g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = g1_pre_topc(u1_struct_0(D),u1_pre_topc(D)) ) ) ) ) ) )).
fof(t31_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t31_turing_1,axiom,( ! [A] : ( 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] : ( m2_funct_2(B,k4_numbers,u1_turing_1(k16_turing_1),k9_funct_2(k4_numbers,u1_turing_1(k16_turing_1))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( A = k4_domain_1(k4_ordinal1,k4_ordinal1,k9_funct_2(k4_numbers,u1_turing_1(k16_turing_1)),k5_numbers,C,B) & r2_turing_1(k2_finseq_4(k4_ordinal1,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(k4_ordinal1,C,k1_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))) ) ) ) ) ) ) )).
fof(t31_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ 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))) ) ) )).
fof(t31_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_uniroots(k1_complfld))) => ( C = k1_hahnban1(k19_sin_cos(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B),A)),k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B),A))) => k6_group_1(k1_uniroots(k1_complfld),C) = k3_nat_d(A,k6_nat_d(B,A)) ) ) ) ) )).
fof(t31_uproots,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_uproots(k11_polynom3(A,B,C),A) => ( v1_uproots(B,A) & v1_uproots(C,A) ) ) ) ) ) )).
fof(t31_urysohn2,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( 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,k5_numbers) & ~ r1_xxreal_0(B,C) & ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(A,k6_xcmplx_0(D,C)) ) ) ) ) ) ) ) )).
fof(t31_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t31_valued_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( 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(k4_ordinal1,C,k8_funct_2(k4_ordinal1,C,B,k8_funct_2(k4_ordinal1,B,A,D,E),F),k8_funct_2(k4_ordinal1,C,A,D,k1_partfun1(A,B,B,C,E,F))) ) ) ) ) ) ) )).
fof(t31_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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)) ) ) ) )).
fof(t31_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t31_vectsp10,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t31_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( 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))))))) ) ) ) ) ) )).
fof(t31_vectsp_1,axiom,( ! [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) ) => ( ~ 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))) ) ) )).
fof(t31_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( 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 ) ) ) ) ) )).
fof(t31_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v7_vectsp_1(C,A) & m1_vectsp_4(C,A,B) ) => ( u1_struct_0(C) = u1_struct_0(B) => C = B ) ) ) ) )).
fof(t31_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( v7_vectsp_1(C,A) & m1_vectsp_4(C,A,B) ) => ! [D] : ( ( 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 ) ) ) ) ) )).
fof(t31_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t31_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_subset_1(C,u1_struct_0(B)) & ? [D] : ( 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)) ) ) ) ) ) )).
fof(t31_vfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,u1_struct_0(C)))) ) => ! [E] : ( v1_xreal_0(E) => 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)) ) ) ) ) )).
fof(t31_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : 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)) ) ) ) ) )).
fof(t31_waybel11,axiom,( ! [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] : ( 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) ) ) ) ) )).
fof(t31_waybel12,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( k2_relset_1(u1_struct_0(A),C) = B & ! [E] : ( m1_subset_1(E,k4_ordinal1) => k3_funct_2(k4_ordinal1,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) ) ) ) ) ) )).
fof(t31_waybel13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t31_waybel14,axiom,( ! [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) ) => ( v1_waybel14(k5_waybel_2(A),A) => v4_yellow_8(A) ) ) )).
fof(t31_waybel15,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t31_waybel16,axiom,( ! [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_8(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( ~ r3_orders_2(A,C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( v1_waybel16(D,A) & r3_orders_2(A,B,D) & ~ r3_orders_2(A,C,D) ) ) ) ) ) ) )).
fof(t31_waybel19,axiom,( ! [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) & 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)))) ) ) )).
fof(t31_waybel21,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ v1_xboole_0(C) & v2_waybel_0(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( 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] : ( ( ~ 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)))) ) ) ) ) ) ) )).
fof(t31_waybel23,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t31_waybel24,axiom,( ! [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] : ( ( 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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_waybel24(A,B)))) ) => ! [D] : ( ( ~ 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(k5_yellow_1(u1_struct_0(A),B),C),D)) = k1_funct_1(k1_yellow_0(k5_yellow_1(u1_struct_0(A),B),C),k1_yellow_0(A,D)) ) ) ) ) )).
fof(t31_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_waybel25(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t31_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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(k9_funct_6(D)) & v1_funct_2(k9_funct_6(D),C,u1_struct_0(k1_waybel26(A,B))) & m1_subset_1(k9_funct_6(D),k1_zfmisc_1(k2_zfmisc_1(C,u1_struct_0(k1_waybel26(A,B))))) ) ) ) ) ) )).
fof(t31_waybel27,axiom,( v4_waybel11(k1_waybel25(k9_waybel18)) )).
fof(t31_waybel29,axiom,( ! [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] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(t31_waybel30,axiom,( ! [A] : ( ( 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] : ( 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) ) ) ) )).
fof(t31_waybel34,axiom,( ! [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] : ( ( 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] : ( ( v4_waybel11(C) & m1_yellow_9(C,k1_yellow_2(A,A,B)) ) => ! [D] : ( ( v4_waybel11(D) & m1_yellow_9(D,A) ) => ! [E] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t31_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_lattice3(A,B,C) <=> r2_lattice3(A,k3_waybel_0(A,B),C) ) ) ) ) )).
fof(t31_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(t31_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) )).
fof(t31_waybel_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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(k4_yellow_1(A,B)) & v4_orders_2(k4_yellow_1(A,B)) & v5_orders_2(k4_yellow_1(A,B)) & v1_lattice3(k4_yellow_1(A,B)) & v2_lattice3(k4_yellow_1(A,B)) & v3_lattice3(k4_yellow_1(A,B)) & l1_orders_2(k4_yellow_1(A,B)) ) ) ) ) )).
fof(t31_waybel_4,axiom,( ! [A] : ( ( 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(k1_yellow_1(k3_waybel_4(A))),u1_struct_0(k1_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)))) ) )).
fof(t31_waybel_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( m2_pboole(E,A,D,k7_funcop_1(A,B)) => ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t31_waybel_6,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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(k2_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(k2_yellow_1(k1_tarski(k1_xboole_0)))))) ) ) ) )).
fof(t31_waybel_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ( r1_tarski(C,D) => ( r1_waybel_3(k1_yellow_1(u1_pre_topc(A)),C,D) <=> ! [E] : ( m1_subset_1(E,k1_zfmisc_1(B)) => ~ ( r1_tarski(D,k3_tarski(E)) & ! [F] : ( ( v1_finset_1(F) & m1_subset_1(F,k1_zfmisc_1(E)) ) => ~ r1_tarski(C,k3_tarski(F)) ) ) ) ) ) ) ) ) ) )).
fof(t31_waybel_8,axiom,( ! [A] : v2_waybel_8(k2_yellow_1(A)) )).
fof(t31_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m2_yellow_6(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r3_waybel_9(A,C,D) => r3_waybel_9(A,B,D) ) ) ) ) ) )).
fof(t31_weddwitt,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t31_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(D,B) & r2_hidden(E,C) & k3_metric_1(A,D,E) = k9_weierstr(A,B,C) ) ) ) ) ) ) ) )).
fof(t31_wellord1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( ( v2_wellord1(B) & r1_tarski(A,k1_relat_1(B)) ) => k1_relat_1(k2_wellord1(B,A)) = A ) ) )).
fof(t31_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( A != k5_numbers & B != k5_numbers & ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k3_int_2(A,B) != k6_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D)) ) ) ) ) ) )).
fof(t31_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : r1_tarski(k2_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)),k2_xboole_0(B,C)) )).
fof(t31_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => k9_xboolean(A,A) = k3_xboolean(A) ) )).
fof(t31_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k2_xcmplx_0(A,C) = k6_xcmplx_0(k2_xcmplx_0(A,B),k6_xcmplx_0(B,C)) ) ) ) )).
fof(t31_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k5_numbers,A) => r1_xxreal_0(B,k2_xcmplx_0(A,B)) ) ) ) )).
fof(t31_xtuple_0,axiom,( ! [A] : ! [B] : k11_xtuple_0(k2_xboole_0(A,B)) = k2_xboole_0(k11_xtuple_0(A),k11_xtuple_0(B)) )).
fof(t31_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ~ ( ~ r1_xxreal_0(A,k4_xxreal_0(B,C)) & r1_xxreal_0(A,B) ) ) ) ) )).
fof(t31_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( ~ r1_xxreal_0(B,A) & v1_xboole_0(k2_xxreal_1(A,B)) ) ) ) )).
fof(t31_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( ~ r1_xxreal_0(B,A) => k1_xxreal_2(k2_xxreal_1(A,B)) = B ) ) ) )).
fof(t31_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t31_yellow10,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( 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)))) ) ) ) )).
fof(t31_yellow12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t31_yellow14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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] : ( 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))) ) ) ) ) )).
fof(t31_yellow16,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_yellow_1(A,B)))) => ( r2_yellow_0(k4_yellow_1(A,B),C) <=> ! [D] : ( m1_subset_1(D,A) => r2_yellow_0(k2_yellow16(A,B,D),k5_waybel_3(A,B,D,C)) ) ) ) ) ) )).
fof(t31_yellow18,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_altcat_1(A))) => k8_altcat_1(k7_altcat_1(A),B) = k6_partfun1(B) ) ) )).
fof(t31_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_compts_1(A) <=> ! [B] : ( ( ~ v1_xboole_0(B) & v2_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v3_waybel_7(B,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))))) ) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r2_waybel_7(A,B,C) ) ) ) ) )).
fof(t31_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_altcat_1(B) ) => ! [C] : ( l1_functor0(C,A,B) => ( ( v10_functor0(C,A,B) & v4_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k3_functor0(A,B,C,D) = k3_functor0(A,B,C,E) => D = E ) ) ) ) ) ) ) )).
fof(t31_yellow_0,axiom,( ! [A] : ( ( v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ( B = k2_yellow_0(A,C) & r2_yellow_0(A,C) ) => ( r1_lattice3(A,C,B) & ! [D] : ( 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] : ( 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) ) ) ) ) ) )).
fof(t31_yellow_2,axiom,( ! [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] : ( ( ~ 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) ) ) ) )).
fof(t31_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t31_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) )).
fof(t31_yellow_5,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t31_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_yellow_6(A,B))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t31_yellow_7,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_yellow_0(k7_lattice3(A)) <=> v2_yellow_0(A) ) ) )).
fof(t31_yellow_9,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(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)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(C,A) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(E,B) & r2_hidden(D,E) & r1_tarski(E,C) ) ) ) ) ) ) ) ) )).
fof(t31_zf_fund1,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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 ) ) ) ) )).
fof(t31_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ( k10_zf_lang(A,C) = k10_zf_lang(B,D) => ( A = B & C = D ) ) ) ) ) ) )).
fof(t31_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => k20_zf_lang(k11_zf_lang(A,B)) = k7_zf_lang(A,k6_zf_lang(B)) ) ) )).
fof(t31_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(k2_tarski(A,B),C) <=> ( r2_hidden(A,C) & r2_hidden(B,C) ) ) )).
fof(t31_zfrefle1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( v3_ordinal1(B) & m1_subset_1(B,A) ) => r2_hidden(k4_classes1(B),A) ) ) )).
fof(t31_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_zmodul01(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ( ( E = C & F = B ) => k5_algstr_0(D,E,F) = k5_algstr_0(A,C,B) ) ) ) ) ) ) ) )).
fof(t31_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( v1_int_1(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( m2_zmodul02(B,A,D) => m2_zmodul02(k23_zmodul02(A,C,B),A,D) ) ) ) ) ) )).
fof(t31_zmodul03,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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) & v1_zmodul03(B) & l1_zmodul01(B) ) => ! [C] : ( m1_zmodul03(C,B) => ! [D] : ( m2_zmodul02(D,B,C) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_zmodul02(A,B)))) => ! [F] : ( m2_vectsp_6(F,k9_int_3(A),k12_zmodul02(A,B),E) => ( ( E = a_3_0_zmodul03(A,B,C) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ( r2_hidden(G,C) => k3_funct_2(u1_struct_0(B),k4_numbers,D,G) = k1_zmodul03(k9_int_3(A),k12_zmodul02(A,B),F,k13_zmodul02(A,B,G)) ) ) ) => k4_vectsp_6(k9_int_3(A),k12_zmodul02(A,B),F) = k13_zmodul02(A,B,k21_zmodul02(B,D)) ) ) ) ) ) ) ) )).
fof(t320_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r1_xxreal_0(C,B) & r1_xxreal_0(A,B) ) => k6_subset_1(k1_xxreal_1(C,B),k2_xxreal_1(A,B)) = k2_xboole_0(k2_xxreal_1(C,A),k1_tarski(B)) ) ) ) ) )).
fof(t321_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(A,C) => ( r1_xxreal_0(B,A) | k6_subset_1(k2_xxreal_1(A,B),k4_xxreal_1(A,C)) = k2_xboole_0(k1_tarski(A),k2_xxreal_1(C,B)) ) ) ) ) ) )).
fof(t322_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(A,B) ) => k6_subset_1(k1_xxreal_1(A,B),k4_xxreal_1(A,C)) = k2_xboole_0(k1_tarski(A),k1_xxreal_1(C,B)) ) ) ) ) )).
fof(t323_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(A,C) => ( r1_xxreal_0(B,A) | k6_subset_1(k2_xxreal_1(A,B),k3_xxreal_1(A,C)) = k2_xboole_0(k1_tarski(A),k4_xxreal_1(C,B)) ) ) ) ) ) )).
fof(t324_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(A,B) ) => k6_subset_1(k1_xxreal_1(A,B),k3_xxreal_1(A,C)) = k2_xboole_0(k1_tarski(A),k3_xxreal_1(C,B)) ) ) ) ) )).
fof(t325_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t326_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t327_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t328_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t329_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t32_abcmiz_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t32_abcmiz_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t32_abcmiz_a,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( ( 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) ) ) ) )).
fof(t32_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_aff_1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => r2_aff_1(A,B,B,C) ) ) ) )).
fof(t32_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t32_afinsq_1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) ) )).
fof(t32_afinsq_2,axiom,( ! [A] : ( ( v1_finset_1(A) & v6_membered(A) ) => ! [B] : ( ( v1_finset_1(B) & v6_membered(B) ) => ( r1_afinsq_2(A,B) => ( B = k1_xboole_0 | k1_recdef_1(k4_afinsq_2(B),k5_numbers) = k1_recdef_1(k4_afinsq_2(k2_xboole_0(A,B)),k1_afinsq_1(k4_afinsq_2(A))) ) ) ) ) )).
fof(t32_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,u1_incsp_1(k13_afproj(A))) => ! [F] : ( m1_subset_1(F,u2_incsp_1(k13_afproj(A))) => ( ( v1_aff_4(C,A) & r1_tarski(B,C) & r5_aff_1(A,D,B) & E = k5_afproj(A,D) & F = k4_tarski(k6_afproj(A,C),2) ) => r1_incsp_1(k13_afproj(A),E,F) ) ) ) ) ) ) ) )).
fof(t32_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_analoaf(A,B,C,k1_afvect0(A,D,C),k1_afvect0(A,D,B)) ) ) ) ) )).
fof(t32_algspec1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => r1_algspec1(A,B,k1_xboole_0) ) ) )).
fof(t32_algstr_4,axiom,( ! [A] : ! [B] : ( 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)) ) ) ) )).
fof(t32_altcat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & m1_altcat_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & F = C & G = D & H = E & ? [I] : ( m1_subset_1(I,k1_altcat_1(A,F,G)) & ? [J] : ( m1_subset_1(J,k1_altcat_1(A,G,H)) & ? [K] : ( m1_subset_1(K,k1_altcat_1(B,C,D)) & ? [L] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t32_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v16_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t32_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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)) ) ) ) )).
fof(t32_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_analmetr(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_analmetr(A,B,C))) => ( r1_analmetr(A,B,C) => ( D = E | ! [F] : ( m1_subset_1(F,u1_struct_0(k2_analmetr(A,B,C))) => ? [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t32_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ~ ( r1_analmetr(A,G,H) & r1_analort(A,G,H,B,D,C,E) & r1_analort(A,G,H,B,D,C,F) & ~ r1_analort(A,G,H,B,D,E,F) & ~ r1_analort(A,G,H,B,D,F,E) ) ) ) ) ) ) ) ) ) )).
fof(t32_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => ~ ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & ? [I] : ( v1_xreal_0(I) & ? [J] : ( v1_xreal_0(J) & 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] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( 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 = k5_numbers & G = k5_numbers & H = k5_numbers & I = k5_numbers ) ) ) ) ) ) ) ) ) ) & ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t32_aofa_000,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_freealg(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ! [D] : ( 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) ) ) ) ) )).
fof(t32_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( m2_subset_1(F,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => ! [G] : ( v1_xboolean(G) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),u8_aofa_a00(A))) => ( k15_aofa_a00(A,B,C,D,u8_aofa_a00(A),k22_aofa_a00(A,C,H),F) = k3_xboolean(G) <=> k15_aofa_a00(A,B,C,D,u8_aofa_a00(A),H,F) = G ) ) ) ) ) ) ) ) ) )).
fof(t32_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [E] : ( ( v1_aofa_i00(E,A,B,D) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),D) ) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),E) => ! [G] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t32_armstrng,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t32_arytm_3,axiom,( ! [A] : ! [B] : ~ r2_hidden(k4_tarski(A,B),k4_ordinal1) )).
fof(t32_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k8_asympt_0(k1_asympt_0(A,B)) = k8_asympt_0(k5_asympt_0(A,B)) ) ) )).
fof(t32_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m2_funct_2(B,u1_struct_0(A),u1_struct_0(A),k1_autalg_1(A)) => m2_pboole(k16_funcop_1(k5_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))) ) ) )).
fof(t32_bagorder,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k5_finsub_1(u1_struct_0(A))) => ! [C] : ( 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)))) ) ) ) ) ) ) )).
fof(t32_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( r2_hidden(B,k5_bcialg_1(A)) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t32_bcialg_2,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( k2_bcialg_2(A,B) = 1 & v5_bcialg_2(B,A) ) ) ) ) )).
fof(t32_bcialg_3,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t32_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t32_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( ( v8_bcialg_1(G) & m1_bcialg_5(G,A,B,E,F) ) => ( ( r1_xxreal_0(B,D) & r1_xxreal_0(F,C) ) => ( v8_bcialg_1(G) & m1_bcialg_5(G,C,D,D,C) ) ) ) ) ) ) ) ) ) )).
fof(t32_bcialg_6,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t32_bciideal,axiom,( ! [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) ) => ( v3_bciideal(u1_struct_0(A),A) & m2_bcialg_1(u1_struct_0(A),A) ) ) )).
fof(t32_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k6_xcmplx_0(k3_bhsp_1(A,B),k3_bhsp_1(A,C)),k3_bhsp_1(A,k5_algstr_0(A,B,C))) ) ) ) )).
fof(t32_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,A,C),k4_algstr_0(A,B)))) & k1_seq_2(k2_bhsp_2(A,k4_normsp_1(A,k5_vfunct_1(k4_ordinal1,A,C),k4_algstr_0(A,B)))) = k5_numbers ) ) ) ) ) )).
fof(t32_bhsp_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( ( ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,A,D) = k1_power(D,k3_bhsp_1(B,k1_normsp_1(B,C,D))) ) & v2_comseq_2(A) ) => ( r1_xxreal_0(1,k1_seq_2(A)) | v2_bhsp_4(C,B) ) ) ) ) ) )).
fof(t32_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t32_binari_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t32_binari_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,A) ) => k7_partfun1(k6_margrel1,k2_binari_4(k2_xcmplx_0(A,1),B),C) = k7_partfun1(k6_margrel1,k2_binari_4(A,B),C) ) ) ) ) )).
fof(t32_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_boolealg(A,k1_boolealg(A,B,k3_lattices(A,B,C)),k5_lattices(A)) ) ) ) )).
fof(t32_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t32_borsuk_4,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,u1_struct_0(k1_borsuk_4)) <=> ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) ) ) ) )).
fof(t32_borsuk_5,axiom,( ! [A] : ( ( v2_pre_topc(A) & v1_connsp_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t32_borsuk_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_topmetr)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_topmetr)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_topmetr)) => ! [D] : ( 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)))) ) ) ) ) ) )).
fof(t32_borsuk_7,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ( ( r1_zfmisc_1(A,B,C) & r2_hidden(D,G) & r2_hidden(E,H) & r2_hidden(F,I) ) => r2_hidden(k1_borsuk_7(A,B,C,D,E,F),k4_card_3(k1_borsuk_7(A,B,C,G,H,I))) ) )).
fof(t32_bspace,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k7_bspace(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_bspace(A))) => ! [D] : ( 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)) ) ) ) )).
fof(t32_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t32_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t32_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t32_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t32_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_eqrel_1(C,A) => r1_bvfunc_1(A,B,k17_bvfunc_1(A,B,C)) ) ) ) )).
fof(t32_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(E,A) => ( r3_bvfunc_2(A,D,B,E) => r2_funct_2(A,k6_margrel1,k7_bvfunc_2(A,k5_bvfunc_1(A,D,C),B,E),k5_bvfunc_1(A,D,k7_bvfunc_2(A,C,B,E))) ) ) ) ) ) ) )).
fof(t32_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(F,A) => r1_bvfunc_1(A,k2_bvfunc_1(A,k6_bvfunc_2(A,k9_bvfunc_1(A,C,E),B,F),k6_bvfunc_2(A,k9_bvfunc_1(A,E,D),B,F)),k6_bvfunc_2(A,k9_bvfunc_1(A,C,D),B,F)) ) ) ) ) ) ) )).
fof(t32_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t32_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t32_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t32_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k11_c0sp1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k11_c0sp1(A))) => ( ( k2_normsp_0(k11_c0sp1(A),C) = k5_numbers => C = k4_struct_0(k11_c0sp1(A)) ) & ( C = k4_struct_0(k11_c0sp1(A)) => k2_normsp_0(k11_c0sp1(A),C) = k5_numbers ) & k2_normsp_0(k11_c0sp1(A),k1_rlvect_1(k11_c0sp1(A),C,B)) = k3_xcmplx_0(k9_complex1(B),k2_normsp_0(k11_c0sp1(A),C)) & r1_xxreal_0(k2_normsp_0(k11_c0sp1(A),k1_algstr_0(k11_c0sp1(A),C,D)),k2_xcmplx_0(k2_normsp_0(k11_c0sp1(A),C),k2_normsp_0(k11_c0sp1(A),D))) ) ) ) ) ) )).
fof(t32_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => k4_struct_0(k7_c0sp2(A)) = k1_c0sp2(A,k5_numbers) ) )).
fof(t32_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ( r5_calcul_1(A,B,C) => r7_calcul_1(A,C,B) ) ) ) ) )).
fof(t32_card_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t32_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_card_3(B) ) => ( ( k9_xtuple_0(A) = k9_xtuple_0(B) & ! [C] : ( 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)) ) ) ) )).
fof(t32_card_fil,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) ) => ! [B] : ( ( r1_tarski(B,A) & k3_ordinal2(B) = A ) => k3_tarski(B) = A ) ) )).
fof(t32_card_fin,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( k8_relat_1(D,k1_tarski(B)) = k8_relat_1(E,k1_tarski(C)) => k2_card_fin(A,D,B) = k2_card_fin(A,E,C) ) ) ) ) )).
fof(t32_card_lar,axiom,( ! [A] : ( ! [B] : ~ ( r2_hidden(B,A) & ! [C] : ~ ( r2_hidden(C,A) & r1_tarski(B,C) & v1_card_1(C) ) ) => v1_card_1(k3_tarski(A)) ) )).
fof(t32_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,B,C) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t32_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,k6_cat_2(A,C),B) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u4_struct_0(A)) => k3_funct_2(u4_struct_0(A),u4_struct_0(B),k11_cat_2(A,C,B,D,E),F) = k9_cat_2(A,C,B,D,F,k4_cat_1(C,E)) ) ) ) ) ) ) )).
fof(t32_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,C,D) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t32_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t32_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => k5_card_1(k2_catalan2(k2_xcmplx_0(6,A),3)) = k7_xcmplx_0(k2_nat_1(k2_nat_1(k1_nat_1(A,1),k1_nat_1(A,5)),k1_nat_1(A,6)),6) ) )).
fof(t32_catalg_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u4_struct_0(A)) => ! [G] : ( m1_subset_1(G,u4_struct_0(A)) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t32_cayldick,axiom,( k6_algstr_0(k4_cayldick(k4_cayldick(k4_cayldick(k3_cayldick))),k5_cayldick(k4_cayldick(k4_cayldick(k3_cayldick)),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k5_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick))),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)))),k5_cayldick(k4_cayldick(k4_cayldick(k3_cayldick)),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k5_struct_0(k3_cayldick),k4_struct_0(k3_cayldick))),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick))))) = k5_cayldick(k4_cayldick(k4_cayldick(k3_cayldick)),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k5_struct_0(k3_cayldick))),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)))) )).
fof(t32_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k5_cc0sp2(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k5_cc0sp2(A))))) ) => ( v1_csspace3(B,k5_cc0sp2(A)) => v9_clvect_1(B,k5_cc0sp2(A)) ) ) ) )).
fof(t32_cfcont_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xcmplx_0(E) => ~ ( r2_hidden(E,k1_relset_1(k2_numbers,B)) & ~ r1_xxreal_0(D,k9_complex1(k6_xcmplx_0(E,A))) & r1_xxreal_0(C,k9_complex1(k6_xcmplx_0(k7_partfun1(k2_numbers,B,E),k7_partfun1(k2_numbers,B,A)))) ) ) ) ) ) ) ) ) ) ) )).
fof(t32_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t32_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ! [B] : ( v2_cgames_1(B) => ( r2_hidden(A,k10_cgames_1(B)) => r1_tarski(k11_cgames_1(A),k11_cgames_1(B)) ) ) ) )).
fof(t32_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(B)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(B)) => ! [E] : ( 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] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(B)) & ~ ( ~ r1_xxreal_0(k1_funct_1(D,F),k1_funct_1(C,F)) & m2_chain_1(k4_tarski(k1_funct_1(C,F),k1_funct_1(D,F)),k2_chain_1(B,E,F)) ) & ~ ( k1_funct_1(C,F) = k1_funct_1(D,F) & r2_hidden(k1_funct_1(C,F),k2_chain_1(B,E,F)) ) ) & ~ ! [F] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(B)) => ( ~ r1_xxreal_0(k1_funct_1(C,F),k1_funct_1(D,F)) & m2_chain_1(k4_tarski(k1_funct_1(C,F),k1_funct_1(D,F)),k2_chain_1(B,E,F)) ) ) ) ) ) ) ) ) )).
fof(t32_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v5_glib_001(B,A) => ( v1_glib_001(B,A) | v6_glib_001(B,A) ) ) ) ) )).
fof(t32_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(C,F))) => ! [H] : ( m1_subset_1(H,k4_card_3(u3_msualg_1(A,D))) => ! [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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t32_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t32_classes1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => ( r1_tarski(A,k4_classes1(B)) <=> r2_hidden(A,k4_classes1(k1_ordinal1(B))) ) ) )).
fof(t32_classes2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v2_classes1(B) & r2_hidden(A,k2_ordinal1(B)) ) => r1_ordinal1(k1_card_1(k4_classes1(A)),k1_card_1(B)) ) ) )).
fof(t32_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k14_clopban1(A,B))) => r1_xxreal_0(k5_numbers,k2_normsp_0(k14_clopban1(A,B),C)) ) ) ) )).
fof(t32_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k1_power(D,k9_nat_1(k1_numbers,k5_normsp_0(A,B),D)) ) & v2_comseq_2(C) & ~ r1_xxreal_0(k1_seq_2(C),1) & v2_clopban3(B,A) ) ) ) ) )).
fof(t32_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v5_mssubfam(C,A,B) & m3_pboole(C,A,k1_mboolean(A,B)) ) => ! [D] : ( m1_pboole(D,A,k5_mssubfam(A,B)) => ! [E] : ( ( v2_relat_1(E) & m3_pboole(E,A,k1_mboolean(A,B)) ) => ( ! [F] : ( ( 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] : ! [G] : ( ~ 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) ) ) ) ) ) ) ) )).
fof(t32_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_closure2(C,A,B,k2_closure2(A,B)) => ! [D] : ( m1_closure2(D,A,B,k2_closure2(A,B)) => ! [E] : ( ( 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] : ( 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))) ) ) ) ) ) ) )).
fof(t32_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_clvect_1(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ( ( E = C & F = B ) => k3_rlvect_1(D,E,F) = k3_rlvect_1(A,C,B) ) ) ) ) ) ) ) )).
fof(t32_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,A,C),k4_algstr_0(A,B)))) & k1_seq_2(k2_clvect_2(A,k4_normsp_1(A,k5_vfunct_1(k4_ordinal1,A,C),k4_algstr_0(A,B)))) = k5_numbers ) ) ) ) ) )).
fof(t32_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k1_power(D,k13_csspace(A,k1_normsp_0(A,B,D))) ) & v2_comseq_2(C) ) => ( r1_xxreal_0(1,k1_seq_2(C)) | v2_clvect_3(B,A) ) ) ) ) ) )).
fof(t32_coh_sp,axiom,( ! [A] : r2_hidden(k6_partfun1(A),k15_coh_sp(A)) )).
fof(t32_cohsp_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t32_compl_sp,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t32_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k8_complex1(k2_xcmplx_0(A,B)) = k2_xcmplx_0(k8_complex1(A),k8_complex1(B)) ) ) )).
fof(t32_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k1_complex2(B,A) = k8_complex1(k1_complex2(A,B)) ) ) )).
fof(t32_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( 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) ) ) ) )).
fof(t32_complsp2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t32_compos_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( l1_compos_1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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))) ) ) ) ) ) )).
fof(t32_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t32_comptrig,axiom,( k10_xtuple_0(k2_partfun1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k5_numbers,k28_sin_cos))) = k1_rcomp_1(k4_xcmplx_0(1),1) )).
fof(t32_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => r2_hidden(k4_comput_1(B,A),k2_comput_1(k4_ordinal1)) ) ) )).
fof(t32_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v9_ordinal1(A) & v9_ordinal1(B) ) => v9_ordinal1(k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)) ) ) ) )).
fof(t32_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( v7_ordinal1(B) => ( r2_funct_2(k4_ordinal1,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(k4_ordinal1,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))) ) ) ) )).
fof(t32_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( v3_conlat_1(B,A) & ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) & l2_conlat_1(B,A) ) => ! [C] : ( ( v3_conlat_1(C,A) & ~ v4_conlat_1(C,A) & v6_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) ) ) ) )).
fof(t32_connsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v3_connsp_1(B,A) & B = k1_struct_0(A) ) ) ) )).
fof(t32_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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 ) ) ) ) )).
fof(t32_convex1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k1_convex1(A,B,1) = B ) ) )).
fof(t32_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_convex4(B,A) => ! [C] : ( m1_convex4(C,A) => ( r1_convex4(A,k5_convex4(A,B,C),k2_convex4(A)) => r1_convex4(A,C,k8_convex4(A,B)) ) ) ) ) )).
fof(t32_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m1_subset_1(E,k1_qc_lang1(A)) => ! [F] : ( m1_subset_1(F,k5_finsub_1(k3_qc_lang1(A))) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t32_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ( r2_hidden(C,k1_cqc_the1(A,B)) <=> ? [D] : ( 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 ) ) ) ) ) )).
fof(t32_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t32_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t32_descip_1,axiom,( ! [A] : ( m2_finseq_2(A,k6_margrel1,k4_finseq_2(64,k6_margrel1)) => ! [B] : ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(64,k6_margrel1)) => k43_descip_1(k42_descip_1(A,B),B) = A ) ) )).
fof(t32_diff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( ( 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) = k2_xcmplx_0(k9_diff_1(C,A,B),k9_diff_1(D,A,B)) ) ) ) ) )).
fof(t32_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( v1_xreal_0(F) => k1_funct_1(E,F) = k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(F)),k3_xcmplx_0(C,F)),D) ) => ! [F] : ( v1_xreal_0(F) => k1_funct_1(k4_diff_1(E,A),F) = k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,B),A),F),k3_xcmplx_0(B,k1_square_1(A))),k3_xcmplx_0(C,A)) ) ) ) ) ) ) ) )).
fof(t32_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t32_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(k6_xcmplx_0(B,A),k5_numbers) & k1_funct_1(k4_diff_1(k3_taylor_1,A),B) != k1_funct_1(k3_taylor_1,k2_xcmplx_0(1,k7_xcmplx_0(A,k6_xcmplx_0(B,A)))) ) ) ) )).
fof(t32_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_yellow_0(A,B)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_yellow_0(A,B))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t32_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t32_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => ! [C] : ! [D] : ! [E] : ( ( 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] : ( ( 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_tarski(C,A) & r1_tarski(D,A) & r1_xboole_0(C,D) & r1_funct_2(A,k6_margrel1,A,k2_tarski(k1_xboole_0,1),E,k5_funct_3(C,A)) & r1_funct_2(A,k6_margrel1,A,k2_tarski(k1_xboole_0,1),F,k5_funct_3(D,A)) ) => k6_dist_2(A,B,k2_bvfunc_1(A,E,F)) = k5_numbers ) ) ) ) ) )).
fof(t32_e_siec,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t32_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t32_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m2_subset_1(D,k3_ec_pf_1(k9_int_3(A)),k6_ec_pf_1(A,B,C)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t32_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k11_ens_1(A))) => ( ? [C] : B = k1_tarski(C) => v10_cat_1(B,k11_ens_1(A)) ) ) ) )).
fof(t32_entropy1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( m2_finseq_1(C,k3_finseq_2(A)) => ( ( k3_finseq_1(C) = k3_finseq_1(B) & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(1,D) => ( r1_xxreal_0(k3_finseq_1(B),D) | k1_matrprob(A,C,k1_nat_1(D,1)) = k8_finseq_1(A,k1_matrprob(A,C,D),k1_matrprob(A,B,k1_nat_1(D,1))) ) ) ) ) => ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(1,D) => ( r1_xxreal_0(k3_finseq_1(C),D) | ! [E] : ( v7_ordinal1(E) => ( 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,k1_nat_1(D,1)),E) ) ) ) ) ) ) ) ) ) )).
fof(t32_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k3_enumset1(A,A,B,C,D) = k2_enumset1(A,B,C,D) )).
fof(t32_eqrel_1,axiom,( ! [A] : ( m1_eqrel_1(A,k1_xboole_0) => A = k1_xboole_0 ) )).
fof(t32_equation,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m3_pboole(C,u1_struct_0(A),k4_equation(A)) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t32_euclid,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k4_algstr_0(k15_euclid(2),k19_euclid(A,B)) = k19_euclid(k4_xcmplx_0(A),k4_xcmplx_0(B)) ) ) )).
fof(t32_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => k22_rvsum_1(k4_struct_0(k15_euclid(A)),k4_struct_0(k15_euclid(A))) = k5_numbers ) )).
fof(t32_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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(k28_sin_cos,k3_euclid_3(k5_algstr_0(k15_euclid(2),A,B))) <=> r1_xxreal_0(k28_sin_cos,k3_euclid_3(k5_algstr_0(k15_euclid(2),B,A))) ) ) ) ) )).
fof(t32_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => k22_rvsum_1(k7_euclid(A,B,C),k7_euclid(A,B,C)) = k2_xcmplx_0(k2_xcmplx_0(k22_rvsum_1(B,B),k3_xcmplx_0(2,k22_rvsum_1(B,C))),k22_rvsum_1(C,C)) ) ) ) )).
fof(t32_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(3))) => ! [C] : ( 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,k22_rvsum_1(A,C)),k1_rlvect_1(k15_euclid(3),C,k22_rvsum_1(A,B))) ) ) ) )).
fof(t32_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(A,k5_jgraph_6(B,C,D)) & ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t32_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k9_euclid(3,k1_euclid_8(B,C,D),A) = k7_euclid(3,k7_euclid(3,k9_euclid(3,k2_euclid_8,k3_xcmplx_0(A,B)),k9_euclid(3,k3_euclid_8,k3_xcmplx_0(A,C))),k9_euclid(3,k4_euclid_8,k3_xcmplx_0(A,D))) ) ) ) ) )).
fof(t32_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ~ ( r1_euclidlp(A,B,C) & ! [D] : ( v1_xreal_0(D) => ~ ( D != k5_numbers & B = k9_euclid(A,C,D) ) ) ) ) ) ) )).
fof(t32_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(D) & v5_relat_1(D,C) & v1_funct_1(D) & v1_exchsort(D) ) => ( ( r2_hidden(A,k9_xtuple_0(D)) & r2_hidden(B,k9_xtuple_0(D)) ) => k7_partfun1(C,k9_funct_7(D,A,B),B) = k7_partfun1(C,D,A) ) ) )).
fof(t32_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ( k3_compos_1(B,C,k5_memstr_0(A,B,k5_extpro_1(A,B,C,D,k1_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,k1_nat_1(E,1))) | k8_extpro_1(A,B,C,D) = k1_nat_1(E,1) ) ) ) ) ) ) ) )).
fof(t32_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_circcomb(A) & v2_circcomb(A) & v3_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v4_msafree2(C,A) & v4_circcomb(C,A) & v6_circcomb(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msafree2(D,B) & v4_circcomb(D,B) & v6_circcomb(D,B) & l3_msualg_1(D,B) ) => ! [E] : ( m1_subset_1(E,k4_card_3(u3_msualg_1(k2_circcomb(A,B),k3_circcomb(A,B,C,D)))) => ! [F] : ( 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] : ( r2_hidden(G,u1_struct_0(A)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t32_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( 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(k9_complex1(k6_xcmplx_0(k1_funct_1(B,D),k1_funct_1(B,E))),k3_xcmplx_0(C,k9_complex1(k6_xcmplx_0(D,E)))) ) ) ) ) ) ) )).
fof(t32_fdiff_10,axiom,( ! [A] : ( ( 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,k18_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,k18_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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,k18_sin_cos)),A),B) = k6_xcmplx_0(k2_xcmplx_0(k1_square_1(k1_funct_1(k16_sin_cos,B)),k3_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k16_sin_cos,B)),k1_funct_1(k18_sin_cos,B))),k1_square_1(k1_funct_1(k18_sin_cos,B))) ) ) ) ) ) )).
fof(t32_fdiff_11,axiom,( ! [A] : ( ( 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,k27_sin_cos,k2_sin_cos9))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k2_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k2_sin_cos9),A),B) = k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k2_sin_cos9,B),k1_square_1(k1_funct_1(k16_sin_cos,B)))),k7_xcmplx_0(k1_funct_1(k27_sin_cos,B),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t32_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ( r2_hidden(C,k10_prob_1(A)) => r1_xxreal_0(k1_fdiff_1(B,C),k5_numbers) ) ) ) => v8_valued_0(k2_partfun1(k1_numbers,k1_numbers,B,k10_prob_1(A))) ) ) ) )).
fof(t32_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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(k7_xcmplx_0(3,2))),k7_xcmplx_0(2,k3_xcmplx_0(3,B))))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => ( k1_funct_1(D,E) = k2_xcmplx_0(A,k3_xcmplx_0(B,E)) & B != k5_numbers & ~ r1_xxreal_0(k1_funct_1(D,E),k5_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(k7_xcmplx_0(3,2))),k7_xcmplx_0(2,k3_xcmplx_0(3,B))),C) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_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(k7_xcmplx_0(3,2))),k7_xcmplx_0(2,k3_xcmplx_0(3,B))),C),E) = k6_prepower(k2_xcmplx_0(A,k3_xcmplx_0(B,E)),k7_xcmplx_0(1,2)) ) ) ) ) ) ) ) ) )).
fof(t32_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k22_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,C,k22_sin_cos),k1_taylor_1(2))),k3_taylor_1) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => ( k1_funct_1(C,D) = 1 & ~ r1_xxreal_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,C,k22_sin_cos),D),k5_numbers) ) ) ) ) => ( r2_fdiff_1(B,A) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_1(k2_fdiff_1(B,A),D) = k7_xcmplx_0(k2_xcmplx_0(1,k1_funct_1(k22_sin_cos,D)),k6_xcmplx_0(1,k1_funct_1(k22_sin_cos,D))) ) ) ) ) ) ) ) )).
fof(t32_fdiff_7,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & r1_xxreal_0(B,k5_numbers) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k16_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k16_sin_cos),A),B) = k7_xcmplx_0(k1_funct_1(k18_sin_cos,k1_funct_1(k3_taylor_1,B)),B) ) ) ) ) ) )).
fof(t32_fdiff_8,axiom,( ! [A] : ( ( 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,k26_sin_cos))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k26_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k26_sin_cos),A),B) = k2_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(k1_funct_1(k16_sin_cos,B),k1_funct_1(k18_sin_cos,B)),B),k7_xcmplx_0(k1_funct_1(k3_taylor_1,B),k1_square_1(k1_funct_1(k18_sin_cos,B)))) ) ) ) ) ) )).
fof(t32_fdiff_9,axiom,( ! [A] : ( ( 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(k5_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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(1,k1_funct_1(k18_sin_cos,B)),k1_square_1(B))),k7_xcmplx_0(k7_xcmplx_0(k1_funct_1(k16_sin_cos,B),B),k1_square_1(k1_funct_1(k18_sin_cos,B)))) ) ) ) ) ) ) )).
fof(t32_fib_num2,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => k6_xcmplx_0(k2_nat_1(k1_pre_ff(k7_nat_d(A,1)),k1_pre_ff(k1_nat_1(A,1))),k1_pepin(k1_pre_ff(A))) = k1_newton(k4_xcmplx_0(1),A) ) )).
fof(t32_fib_num3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k3_fib_num3(A,B,k5_numbers) = A & k3_fib_num3(A,B,1) = B & ! [C] : ( v7_ordinal1(C) => k3_fib_num3(A,B,k1_nat_1(k1_nat_1(C,1),1)) = k1_nat_1(k3_fib_num3(A,B,C),k3_fib_num3(A,B,k1_nat_1(C,1))) ) ) ) ) )).
fof(t32_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(2,A) => k1_fib_num3(k3_xcmplx_0(2,A)) = k2_int_1(k2_power(k1_fib_num,k3_xcmplx_0(2,A))) ) ) )).
fof(t32_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => k5_finseq_8(A,B,C) = k1_finseq_8(A,k6_finseq_8(A,B,C),C) ) ) ) )).
fof(t32_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( B = k4_lattices(A,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) ) ) ) ) )).
fof(t32_filter_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t32_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t32_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t32_finseq_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t32_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : k1_xboole_0 != k11_finseq_1(A,B,C) )).
fof(t32_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v2_funct_1(A) & r2_hidden(B,k10_xtuple_0(A)) ) => ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(t32_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m2_finseq_1(C,B) => ( r1_xxreal_0(k3_finseq_1(C),A) => v1_xboole_0(k2_rfinseq(B,A,C)) ) ) ) )).
fof(t32_finseq_6,axiom,( ! [A] : ( k6_finseq_4(k9_finseq_1(A),A) = k1_xboole_0 & k5_finseq_4(k9_finseq_1(A),A) = k1_xboole_0 ) )).
fof(t32_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t32_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v3_card_1(E,D) & m2_finseq_1(E,A) ) => ! [F] : ( ( 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(k4_ordinal1,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)) ) ) ) ) ) ) ) )).
fof(t32_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ! [F] : ( 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] : ( 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))) ) ) ) ) )).
fof(t32_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k7_fintopo3(A,B,k5_numbers) = B ) ) )).
fof(t32_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t32_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( 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)) ) ) )).
fof(t32_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => r1_tarski(k1_flang_2(A,B,C,D),k8_flang_1(A,B)) ) ) ) )).
fof(t32_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( 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)) ) ) )).
fof(t32_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => k1_funct_1(k9_fomodel0(B),A) = k1_funct_1(k6_fomodel0(k3_finseq_2(B),k11_monoid_0(B)),A) ) )).
fof(t32_frechet,axiom,( ~ v1_frechet(k3_frechet) )).
fof(t32_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_frechet(A,B,C) => r1_frechet2(A,B,C) ) ) ) ) )).
fof(t32_fsm_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ 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,k1_nat_1(A,1)) & r1_xxreal_0(k5_card_1(k7_fsm_1(B,C,D,k1_nat_1(A,1))),k5_card_1(k7_fsm_1(B,C,D,A))) ) ) ) ) ) )).
fof(t32_fsm_3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(B)) => ! [D] : ( ( ~ 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)) ) ) ) )).
fof(t32_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : v1_relat_1(k3_msafree2(k19_ftacell1(A,B,C,D,E))) )).
fof(t32_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( 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)) ) ) ) )).
fof(t32_funct_1,axiom,( ! [A] : ( ( 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)) ) ) ) )).
fof(t32_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) ) ) )).
fof(t32_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( v2_funct_1(A) => r1_tarski(k7_relat_1(k1_funct_3(A),B),k8_relat_1(k3_funct_3(A),B)) ) ) )).
fof(t32_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t32_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t32_funct_6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_funcop_1(E) ) => ( ( r2_hidden(A,k9_xtuple_0(E)) & B = k1_funct_1(E,A) & r2_hidden(C,k4_card_3(k1_funct_6(E))) & D = k1_funct_1(k6_funct_6(E),C) ) => ( r2_hidden(k1_funct_1(C,A),k9_xtuple_0(B)) & k1_funct_1(D,A) = k1_funct_1(B,k1_funct_1(C,A)) & r2_hidden(D,k4_card_3(k2_funct_6(E))) ) ) ) ) ) ) )).
fof(t32_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ( D != E => k1_funct_7(k1_funct_7(A,D,B),E,C) = k1_funct_7(k1_funct_7(A,E,C),D,B) ) ) )).
fof(t32_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t32_funct_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & v1_int_1(A) ) => v1_funct_9(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),k3_xcmplx_0(k28_sin_cos,A)) ) )).
fof(t32_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l1_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_altcat_2(C) & l1_altcat_1(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v1_altcat_2(D) & l1_altcat_1(D) ) => ! [E] : ( ( v8_functor0(E,A,B) & l2_functor0(E,A,B) ) => ! [F] : ( ( v8_functor0(F,B,C) & l2_functor0(F,B,C) ) => ! [G] : ( 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) ) ) ) ) ) ) ) )).
fof(t32_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D,C)) <=> ( r1_fuzzy_1(D,B) & r1_fuzzy_1(C,B) & ! [E] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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(D,E) & r1_fuzzy_1(C,E) ) => r1_fuzzy_1(B,E) ) ) ) ) ) ) ) ) )).
fof(t32_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D,C)),k3_fuzzy_2(A,k2_fuzzy_2(A,B,D),k2_fuzzy_2(A,B,C))) ) ) ) ) )).
fof(t32_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_fvaluat1(D,A) => ( ( v3_fvaluat1(A) & r1_xxreal_0(k3_funct_2(u1_struct_0(A),k6_numbers,D,B),k3_funct_2(u1_struct_0(A),k6_numbers,D,C)) ) => ( B = k4_struct_0(A) | r1_xxreal_0(k5_numbers,k3_funct_2(u1_struct_0(A),k6_numbers,D,k1_vectsp_2(A,C,B))) ) ) ) ) ) ) )).
fof(t32_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t32_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ~ 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) ) ) )).
fof(t32_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t32_genealg1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_genealg1(B,A) => ! [C] : ( m1_genealg1(C,A) => k10_genealg1(A,B,C,k5_numbers,k5_numbers,k5_numbers,k5_numbers) = B ) ) ) )).
fof(t32_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_analmetr(A,D,E,B,C) <=> k4_geomtrap(A,B,C,D,E) = k5_numbers ) ) ) ) ) ) ) )).
fof(t32_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : v1_relat_1(k3_msafree2(k13_gfacirc1(A,B,C))) )).
fof(t32_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ( ( r2_hidden(D,B) & r2_hidden(E,B) & r1_glib_000(A,D,E,C) ) => r2_hidden(C,k21_glib_000(A,B)) ) ) )).
fof(t32_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( r2_hidden(D,k1_relset_1(k4_ordinal1,k7_glib_001(A,B,C))) & ~ r2_hidden(D,k1_relset_1(k4_ordinal1,B)) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( ~ r1_xxreal_0(k3_finseq_1(C),E) & D = k1_nat_1(k3_finseq_1(B),E) ) ) ) ) ) ) ) )).
fof(t32_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v4_glib_002(B,A) & m1_glib_000(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t32_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_003(A) ) => ! [B] : ! [C] : ( 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)) ) ) )).
fof(t32_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( v7_ordinal1(B) => ! [C] : ( 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) ) ) ) )).
fof(t32_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_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_0(u1_struct_0(k15_euclid(2)),B,A,k1_matrix_0(B)),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k1_nat_1(A,1),k1_matrix_0(B))),k7_xcmplx_0(1,2)),k19_euclid(k5_numbers,1)),k1_tops_1(k15_euclid(2),k3_goboard5(B,A,k1_matrix_0(B)))) ) ) ) )).
fof(t32_goboard7,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t32_gobrd11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_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_0(C),B) | k3_goboard5(C,A,B) = a_3_0_gobrd11(A,B,C) ) ) ) ) ) )).
fof(t32_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(D)) & r1_goboard1(u1_struct_0(k15_euclid(2)),D,E) & r2_hidden(k4_tarski(A,B),k2_matrix_0(E)) & r2_hidden(k4_tarski(k1_nat_1(A,1),B),k2_matrix_0(E)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,k1_nat_1(A,1),B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,B) ) => k4_gobrd13(D,E,C) = k3_goboard5(E,k7_nat_d(A,1),B) ) ) ) ) ) ) )).
fof(t32_gobrd14,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t32_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t32_gr_cy_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t32_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t32_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_graph_2(A,k12_finseq_1(u1_struct_0(A),B),k1_xboole_0) ) ) )).
fof(t32_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_graph_1(C,A) => ! [D] : ( 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)) != k5_numbers ) ) ) ) ) ) ) )).
fof(t32_graph_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m2_finseq_1(C,u4_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( ( v7_graph_1(G,B) & m2_graph_1(G,B) ) => ! [H] : ( ( v7_graph_1(H,B) & m2_graph_1(H,B) ) => ( ( H = k8_finseq_1(u4_struct_0(B),G,C) & r1_xxreal_0(1,k3_finseq_1(G)) & k3_finseq_1(C) = 1 & r2_graph_5(B,D,E,G,A) & r1_graph_4(B,E,F,k1_funct_1(C,1)) ) => r2_graph_5(B,D,F,H,k2_xboole_0(A,k1_tarski(E))) ) ) ) ) ) ) ) ) )).
fof(t32_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => ( ( r2_hidden(A,k4_finseq_1(C)) & k1_funct_1(C,A) = k4_xcmplx_0(1) ) => ( A = k1_nat_1(k1_nat_1(k2_nat_1(B,B),k2_nat_1(3,B)),1) | k1_funct_1(k6_graphsp(k15_graphsp(B),C),A) = k4_xcmplx_0(1) ) ) ) ) ) )).
fof(t32_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_grcat_1(A) ) => ! [B] : ( m3_grcat_1(B,k18_grcat_1(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t32_grfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(B,A) => B = k5_relat_1(A,k9_xtuple_0(B)) ) ) ) )).
fof(t32_groeb_1,axiom,( ! [A] : ( ( 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] : ( ( ~ 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] : ( ( ~ v1_xboole_0(C) & v1_ideal_1(C,k12_polynom1(k1_xboole_0,B)) & v2_ideal_1(C,k12_polynom1(k1_xboole_0,B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k12_polynom1(k1_xboole_0,B)))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(k1_xboole_0,B)))) ) => ( r1_tarski(D,C) => ( D = k1_groeb_1(k1_xboole_0,B,k8_polynom1(k1_xboole_0,B)) | r2_groeb_1(k1_xboole_0,A,B,D,C) ) ) ) ) ) ) )).
fof(t32_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ! [F] : ( m2_ideal_1(F,k12_polynom1(A,C),E) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t32_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(E,k5_card_1(k3_polynom1(k15_pre_poly(A),C,D))) => ! [F] : ( ( 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,k3_polynom1(k15_pre_poly(A),C,k5_groeb_3(A,B,C,D,E))) => ( k4_polynom1(A,C,k5_groeb_3(A,B,C,D,E),F) = k4_polynom1(A,C,D,F) & k4_polynom1(A,C,k6_groeb_3(A,B,C,D,E),F) = k4_struct_0(C) ) ) ) ) ) ) ) ) ) )).
fof(t32_group_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & l3_algstr_0(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => k5_group_1(C,k2_xcmplx_0(A,B),D) = k6_algstr_0(C,k5_group_1(C,A,D),k5_group_1(C,B,D)) ) ) ) ) )).
fof(t32_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t32_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t32_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(t32_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t32_group_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t32_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t32_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v2_group_9(C,A) & v4_group_9(C,A,B) & m1_group_9(C,A,B) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t32_groupp_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v8_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( v1_group_3(C,B) & m1_group_2(C,B) ) => ! [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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t32_hallmar1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,k1_zfmisc_1(A)) ) => ( ? [C] : r1_hallmar1(A,B,C) <=> v1_hallmar1(B,A) ) ) ) )).
fof(t32_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t32_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t32_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,k1_complfld) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t32_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A)))) => ( r2_hidden(k1_xboole_0,B) => B = k1_tarski(k1_xboole_0) ) ) ) )).
fof(t32_hfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( 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(k6_xcmplx_0(A,B)),k3_xcmplx_0(k4_newton(B,A),k2_newton(B))),C)) ) ) ) ) )).
fof(t32_hilbasis,axiom,( ! [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) ) => ( v6_ideal_1(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => v6_ideal_1(k12_polynom1(B,A)) ) ) ) )).
fof(t32_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ( r2_hidden(k4_hilbert1(A,B),k6_hilbert1) => r2_hidden(k4_hilbert1(B,A),k6_hilbert1) ) ) ) )).
fof(t32_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( 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)) ) ) )).
fof(t32_hilbert3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( 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))) ) ) )).
fof(t32_hurwitz,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ r1_xxreal_0(C,1) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k11_polynom3(A,k3_hurwitz(A,B,1),k4_hurwitz(A,B,C)),k3_hurwitz(A,B,C)) ) ) ) ) )).
fof(t32_idea_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ( r1_xxreal_0(4,k3_finseq_1(A)) => k13_idea_1(k13_idea_1(A)) = A ) ) )).
fof(t32_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_ideal_1(C,A,B) ) => ? [D] : ( m1_ideal_1(D,A,B) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_relset_1(k4_ordinal1,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) ) ) ) ) ) )).
fof(t32_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t32_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ 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] : ( 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] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t32_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_instalg1(B,A) ) => ! [C] : ( 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))) ) ) ) )).
fof(t32_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(k2_int_1(A),k6_xcmplx_0(A,1)) & ~ r1_xxreal_0(k2_xcmplx_0(k2_int_1(A),1),A) ) ) )).
fof(t32_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => ( k5_int_1(k1_int_2(A),k1_int_2(B)) = k5_int_1(A,B) & k4_int_1(k1_int_2(A),k1_int_2(B)) = k4_int_1(A,B) ) ) ) ) )).
fof(t32_int_4,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k1_relset_1(k4_ordinal1,A)) => r1_nat_d(k1_recdef_1(A,B),k3_wsierp_1(A)) ) ) ) )).
fof(t32_int_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(t32_integr11,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v1_xboole_0(D) & v2_measure5(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( k3_xcmplx_0(A,k2_xcmplx_0(C,1)) != k5_numbers => k2_integra5(D,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,B),k1_taylor_1(C))) = k6_xcmplx_0(k1_funct_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(k2_xcmplx_0(C,1))),k7_xcmplx_0(1,k3_xcmplx_0(A,k2_xcmplx_0(C,1)))),k2_seq_4(D)),k1_funct_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(k2_xcmplx_0(C,1))),k7_xcmplx_0(1,k3_xcmplx_0(A,k2_xcmplx_0(C,1)))),k3_seq_4(D))) ) ) ) ) ) )).
fof(t32_integr12,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v3_rcomp_1(F) & m1_subset_1(F,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(C,F) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,F) => k1_funct_1(E,G) = k2_xcmplx_0(k3_xcmplx_0(A,G),B) ) ) & F = k1_relset_1(k1_numbers,D) & r2_relset_1(k1_numbers,k1_numbers,D,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_valued_1(k1_numbers,k1_numbers,k3_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos,k16_sin_cos),A),k3_rfunct_1(k1_numbers,k1_numbers,E,k41_valued_1(k1_numbers,k1_numbers,k16_sin_cos)))) ) => k2_integra5(C,D) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,E,k27_sin_cos),k2_seq_4(C)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,E,k27_sin_cos),k3_seq_4(C))) ) ) ) ) ) ) ) )).
fof(t32_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k22_sin_cos,k41_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k16_sin_cos)))) & r1_tarski(C,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k27_sin_cos))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k27_sin_cos)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k27_sin_cos)),k3_seq_4(A))) ) ) ) ) )).
fof(t32_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k2_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(1,k1_funct_1(k18_sin_cos,D)),D),k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k3_taylor_1,D),k1_funct_1(k16_sin_cos,D)),k1_square_1(k1_funct_1(k18_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) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k1_fdiff_9),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k1_fdiff_9),k3_seq_4(A))) ) ) ) ) )).
fof(t32_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( ( 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] : ( 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)),k3_xcmplx_0(k3_xcmplx_0(A,F),k9_complex1(k6_xcmplx_0(E,D)))) ) ) ) ) ) ) ) ) )).
fof(t32_integra1,axiom,( ! [A] : ( ( v5_valued_0(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( 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) ) ) ) ) )).
fof(t32_integra2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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_comseq_2(k2_partfun1(A,k1_numbers,B,A)) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => r1_xxreal_0(k5_numbers,k1_funct_1(B,C)) ) ) ) => r1_xxreal_0(k5_numbers,k12_integra1(A,B)) ) ) ) )).
fof(t32_integra8,axiom,( k2_fdiff_1(k22_sin_cos,k1_numbers) = k22_sin_cos )).
fof(t32_integra9,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( ~ 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)) = k2_xcmplx_0(k1_integra9(C,A,A),k1_integra9(C,B,B)) ) ) ) ) )).
fof(t32_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_interva1(C,A) ) => ! [D] : ( ( ~ 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))) ) ) ) ) )).
fof(t32_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => ( ( r2_hidden(k3_intpro_1(C,k3_intpro_1(B,A)),k8_intpro_1) & r2_hidden(B,k8_intpro_1) ) => r2_hidden(k3_intpro_1(C,A),k8_intpro_1) ) ) ) ) )).
fof(t32_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k3_xcmplx_0(k7_newton(B),k1_funct_1(k5_irrat_1,A)) = k7_xcmplx_0(k7_newton(B),k7_newton(A)) ) ) )).
fof(t32_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( 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),k5_isocat_1(A,A,B,C,D,k10_cat_1(A),E),E) ) ) ) ) ) ) )).
fof(t32_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,C) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( k2_cat_1(A,F,G) != k1_xboole_0 => ! [H] : ( m1_cat_1(H,A,F,G) => k3_funct_2(u4_struct_0(A),u4_struct_0(k6_cat_2(B,C)),k8_isocat_2(A,B,C,D,E),H) = k8_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)) ) ) ) ) ) ) ) ) ) )).
fof(t32_isomichi,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t32_jgraph_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => r1_xxreal_0(k12_euclid(k5_algstr_0(k15_euclid(2),A,B)),k2_xcmplx_0(k9_complex1(k6_xcmplx_0(k17_euclid(A),k17_euclid(B))),k9_complex1(k6_xcmplx_0(k18_euclid(A),k18_euclid(B))))) ) ) )).
fof(t32_jgraph_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( 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] : ( 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) = k7_xcmplx_0(1,k18_euclid(C)) ) ) & ! [C] : ( 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) = k5_numbers ) ) ) => v5_pre_topc(B,k1_pre_topc(k15_euclid(2),A),k3_topmetr) ) ) ) )).
fof(t32_jgraph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) != k5_numbers ) & ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( 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(G,k3_square_1(k2_xcmplx_0(1,k1_square_1(k7_xcmplx_0(F,G))))) ) ) ) ) & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).
fof(t32_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(2),B)))) => ! [D] : ( ( 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,k4_xcmplx_0(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)) ) ) ) ) ) ) )).
fof(t32_jgraph_5,axiom,( ! [A] : ( ( 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] : ( 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) ) ) )).
fof(t32_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t32_jordan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t32_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [F] : ( 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_2_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)))) ) ) ) ) ) ) ) )).
fof(t32_jordan12,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t32_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( r1_jordan1h(A,B) & r1_xxreal_0(B,C) & r1_xboole_0(k3_goboard9(k1_jordan13(A,B)),k3_goboard9(k1_jordan13(A,C))) ) ) ) ) )).
fof(t32_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & ~ r1_xxreal_0(A,k5_numbers) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C),k8_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k9_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C)),k9_jordan6(B)) ) ) ) ) ) ) )).
fof(t32_jordan18,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t32_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_xxreal_0(B,C) => ( r1_xxreal_0(A,1) | r1_xxreal_0(k1_matrix_0(k1_jordan8(D,B)),A) | ( ~ r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(k11_newton(2,k7_nat_d(C,B)),k6_xcmplx_0(A,2)),2),1) & ~ r1_xxreal_0(k1_matrix_0(k1_jordan8(D,C)),k2_xcmplx_0(k3_xcmplx_0(k11_newton(2,k7_nat_d(C,B)),k6_xcmplx_0(A,2)),2)) ) ) ) ) ) ) ) )).
fof(t32_jordan1b,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),k1_jordan1a(k1_jordan8(B,A)),1),k3_matrix_0(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,k2_jordan9(B,A)))) ) ) )).
fof(t32_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(k1_jordan8(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),1,C),k10_xtuple_0(k2_jordan9(B,A))) ) ) ) )).
fof(t32_jordan1h,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_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)) ) )).
fof(t32_jordan22,axiom,( ! [A] : ( ( 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)) ) )).
fof(t32_jordan23,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v2_topreal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(B,k3_topreal1(2,A)) => v2_topreal1(k2_jordan3(A,B)) ) ) ) ) )).
fof(t32_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ! [E] : ( v1_xreal_0(E) => ( ( C = B & D = k9_euclid(A,B,E) ) => ( k3_finseq_1(C) = k3_finseq_1(D) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ( r1_xxreal_0(1,F) & r1_xxreal_0(F,k3_finseq_1(C)) ) => k7_partfun1(k1_numbers,D,F) = k3_xcmplx_0(E,k7_partfun1(k1_numbers,C,F)) ) ) ) ) ) ) ) ) ) )).
fof(t32_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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) ) ) ) ) )).
fof(t32_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( 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) ) ) ) ) ) )).
fof(t32_jordan5d,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ 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] : ( v7_ordinal1(C) => ( ( r2_hidden(A,k3_topreal1(2,B)) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(k2_goboard2(B))) ) => r1_xxreal_0(k17_euclid(A),k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(B),k3_finseq_1(k2_goboard2(B)),C))) ) ) ) ) )).
fof(t32_jordan6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(B,k7_jordan6(A)) <=> k18_euclid(B) = A ) ) ) )).
fof(t32_jordan9,axiom,( ! [A] : ( ( ~ 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)))) ) => ( v2_connsp_1(A,k15_euclid(2)) => ! [B] : ( v7_ordinal1(B) => k20_pscomp_1(k3_topreal1(2,k2_jordan9(A,B))) = k7_partfun1(u1_struct_0(k15_euclid(2)),k2_jordan9(A,B),1) ) ) ) )).
fof(t32_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_jordan_a(B,A) => ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k3_jordan_a(2,k2_jordan_a(A,C,B)),k4_jordan_a(A,B)) ) ) ) )).
fof(t32_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t32_kurato_1,axiom,( 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) )).
fof(t32_kurato_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))))) ) => ~ ( ! [D] : ( v7_ordinal1(D) => r1_tarski(k2_kurato_2(k15_euclid(2),A,D),k2_kurato_2(k15_euclid(2),B,D)) ) & m2_valued_0(C,k9_setfam_1(u1_struct_0(k15_euclid(2))),A) & ! [D] : ( m2_valued_0(D,k9_setfam_1(u1_struct_0(k15_euclid(2))),B) => ~ ! [E] : ( v7_ordinal1(E) => r1_tarski(k2_kurato_2(k15_euclid(2),C,E),k2_kurato_2(k15_euclid(2),D,E)) ) ) ) ) ) ) )).
fof(t32_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(D),C,C) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(D))) ) => ( ( r2_hidden(A,k2_finseq_1(C)) & r2_hidden(B,k2_finseq_1(C)) ) => k13_fvsum_1(D,k7_matrix_0(u1_struct_0(D),k4_matrix_0(u1_struct_0(D),k7_laplace(C,D,E)),A),k8_matrix_0(u1_struct_0(D),E,B)) = k12_matrix_3(C,D,k3_matrix11(A,C,C,u1_struct_0(D),k4_matrix_0(u1_struct_0(D),E),k7_matrix_0(u1_struct_0(D),k4_matrix_0(u1_struct_0(D),E),B))) ) ) ) ) ) ) )).
fof(t32_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t32_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k5_finsub_1(C)) => ! [E] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t32_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : r3_lattices(A,k15_lattice3(A,a_3_2_lattice3(A,B,C)),k4_lattices(A,B,k15_lattice3(A,C))) ) ) )).
fof(t32_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_lattice4(D,A) => ( ( r2_hidden(B,D) & r2_hidden(C,D) ) => r2_hidden(k3_lattices(A,B,C),D) ) ) ) ) ) )).
fof(t32_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( v3_ordinal1(C) => ! [D] : ( v3_ordinal1(D) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t32_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( 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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),k13_lexbfs(A,k16_lexbfs(A),B)))) = B ) ) ) )).
fof(t32_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k4_lfuzzy_0(A)))) => ! [C] : ( 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(k5_numbers,1)),k5_card_3(C,B)) ) ) ) )).
fof(t32_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v6_valued_0(A) => ( v2_seq_2(A) | v2_limfunc1(A) ) ) ) )).
fof(t32_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,A) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(C,D) & ~ r1_xxreal_0(D,A) & r2_hidden(D,k1_relset_1(k1_numbers,B)) ) ) ) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(A,k2_xcmplx_0(A,C)))) & ~ v2_seq_2(k2_partfun1(k1_numbers,k1_numbers,B,k2_rcomp_1(A,k2_xcmplx_0(A,C)))) ) ) | r6_limfunc2(B,A) ) ) ) ) )).
fof(t32_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) = k4_xcmplx_0(k1_limfunc3(B,A)) ) ) ) ) )).
fof(t32_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & 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_funct_1(A,D)) ) ) | v8_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).
fof(t32_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m1_vectsp_4(E,A,B) => ( r1_lmod_6(A,C,D) => r1_lmod_6(A,C,k1_vectsp_5(A,B,D,E)) ) ) ) ) ) ) )).
fof(t32_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k16_lopban_1(A,B))) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => r1_xxreal_0(k2_normsp_0(B,k3_funct_2(u1_struct_0(A),u1_struct_0(B),D,E)),k3_xcmplx_0(k2_normsp_0(k16_lopban_1(A,B),C),k2_normsp_0(A,E))) ) ) ) ) ) ) )).
fof(t32_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k1_power(D,k9_nat_1(k1_numbers,k5_normsp_0(A,B),D)) ) & v2_comseq_2(C) & ~ r1_xxreal_0(k1_seq_2(C),1) & v2_lopban_3(B,A) ) ) ) ) )).
fof(t32_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( ( r2_hidden(D,k13_lpspacc1(A,B,C)) & r2_hidden(E,k13_lpspacc1(A,B,C)) ) => ( k17_lpspacc1(A,B,C,D) = k17_lpspacc1(A,B,C,E) <=> r1_lpspacc1(A,B,C,D,E) ) ) ) ) ) ) ) )).
fof(t32_lpspace1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,C,k6_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,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t32_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(k1_ltlaxio1(k3_hilbert1(A,B)),k1_ltlaxio1(B))) ) ) )).
fof(t32_ltlaxio3,axiom,( ! [A] : ( ( ~ v2_ltlaxio3(A) & m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) ) => ~ r2_hidden(k2_hilbert1,k2_relset_1(k1_hilbert1,k8_ltlaxio3(A))) ) )).
fof(t32_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( ( ~ v2_ltlaxio3(C) & v3_ltlaxio3(C) & m1_subset_1(C,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) ) => ! [D] : ( m3_ltlaxio4(D,C) => ~ ( r2_hidden(k4_hilbert1(A,B),k2_relset_1(k1_hilbert1,k8_ltlaxio3(C))) & ! [E] : ( m2_subset_1(E,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1)),k11_ltlaxio4(C,D)) => ~ r2_hidden(B,k2_relset_1(k1_hilbert1,k8_ltlaxio3(E))) ) ) ) ) ) ) )).
fof(t32_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) )).
fof(t32_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t32_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,B,B) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( r1_xxreal_0(A,k5_numbers) & v4_matrix10(C) ) => v3_matrix10(k6_matrix10(B,A,C)) ) ) ) ) )).
fof(t32_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [C] : ( m2_finseq_2(C,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ~ ( v2_funct_1(B) & v2_funct_1(C) & k10_xtuple_0(B) = k10_xtuple_0(C) & ! [D] : ( ( 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),k4_ordinal1,k4_ordinal1,D,B) ) ) ) ) ) )).
fof(t32_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ? [D] : ( m1_subset_1(D,k4_ordinal1) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(B)) & k1_funct_1(B,D) = C & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( 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 ) ) ) ) )).
fof(t32_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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) ) ) )).
fof(t32_matrix16,axiom,( ! [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] : ( 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)) = k2_matrix_3(A,k1_matrix16(u1_struct_0(A),B)) ) ) ) )).
fof(t32_matrix_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_matrix_0(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k4_tarski(B,C),k2_matrix_0(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_0(A)) ) ) ) ) ) )).
fof(t32_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(D) ) => k1_matrix_4(A,B,k1_matrix_4(A,C,D)) = k3_matrix_3(A,k1_matrix_4(A,B,C),D) ) ) ) ) ) )).
fof(t32_matrix_6,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(A),B,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( v3_matrix_6(C,B,A) => v3_matrix_6(k2_matrix_3(A,C),B,A) ) ) ) ) )).
fof(t32_matrix_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_matrix_2(C,k3_matrix_2(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(B)) => ( ( r1_xxreal_0(1,A) & k3_finseq_1(D) = A & E = k1_partfun1(k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k4_ordinal1,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)) ) ) ) ) ) ) )).
fof(t32_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( ( v4_matrix_8(C,A,B) & v1_matrix_8(C,A,B) ) => C = k3_matrix_1(B,A) ) ) ) ) )).
fof(t32_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( 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,k7_seq_4(B,C)) = k7_seq_4(k5_matrixc1(A,B),k5_matrixc1(A,C)) ) ) ) ) )).
fof(t32_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ! [D] : ( ( 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_0(C))) ) ) ) ) )).
fof(t32_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => k7_matrixr1(1,A) = A ) )).
fof(t32_matrixr2,axiom,( ! [A] : ( ( v1_matrix_0(A) & v2_matrix_0(A,k1_numbers,2,2) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => k3_matrixr2(2,A) = k5_real_1(k4_real_1(k3_matrix_0(k1_numbers,A,1,1),k3_matrix_0(k1_numbers,A,2,2)),k4_real_1(k3_matrix_0(k1_numbers,A,1,2),k3_matrix_0(k1_numbers,A,2,1))) ) )).
fof(t32_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( m1_matrlin(D,A,B) => ! [E] : ( m1_matrlin(E,A,C) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(A),k3_finseq_1(D),k3_finseq_1(E)) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(A))) ) => ( ~ r1_xxreal_0(k3_finseq_1(D),k5_numbers) => k2_matrix15(u1_struct_0(A),k9_matrlin(A,C,E,k3_funct_2(u1_struct_0(B),u1_struct_0(C),k4_matrlin2(A,B,C,D,E,G),F))) = k4_matrix_3(A,k2_matrix15(u1_struct_0(A),k9_matrlin(A,B,D,F)),G) ) ) ) ) ) ) ) ) )).
fof(t32_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t32_matrprob,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => k14_rvsum_1(k5_finseq_2(k4_ordinal1,k3_finseq_1(A),1),A) = A ) )).
fof(t32_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(k2_vectsp_1),k1_matrix_0(D),C) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ~ ( ( A = k5_numbers => B = k5_numbers ) & ( B = k5_numbers => C = k5_numbers ) & k1_partfun1(u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(B)),u1_struct_0(k15_euclid(k1_matrix_0(D))),u1_struct_0(k15_euclid(C)),k3_matrtop1(A,B,D),k3_matrtop1(k1_matrix_0(D),C,E)) != k3_matrtop1(k3_finseq_1(D),k1_matrix_0(E),k5_matrix_3(A,B,C,k2_vectsp_1,D,E)) ) ) ) ) ) ) )).
fof(t32_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( ( 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] : ( 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] : ( 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_funct_1(k3_funct_2(u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(A)),C,B),E) = k1_funct_1(B,E) ) ) ) ) ) ) ) )).
fof(t32_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : k3_zfmisc_1(k2_tarski(A,D),k2_tarski(B,E),k2_tarski(C,F)) = k6_enumset1(k3_xtuple_0(A,B,C),k3_xtuple_0(A,E,C),k3_xtuple_0(A,B,F),k3_xtuple_0(A,E,F),k3_xtuple_0(D,B,C),k3_xtuple_0(D,E,C),k3_xtuple_0(D,B,F),k3_xtuple_0(D,E,F)) )).
fof(t32_measure1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t32_measure6,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k6_numbers) => ( B = C => k7_supinf_2(k1_measure6(A,B)) = k3_supinf_2(C,k7_supinf_2(A)) ) ) ) ) )).
fof(t32_measure8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ( ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k9_prob_1(A,B),k6_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),k6_numbers))) & r1_measure8(A,B,k9_prob_1(A,B),C,D) ) => v1_measure8(C,A,B) ) ) ) ) )).
fof(t32_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => k7_member_1(k2_xboole_0(A,B)) = k2_xboole_0(k7_member_1(A),k7_member_1(B)) ) ) )).
fof(t32_membered,axiom,( ! [A] : ! [B] : ( ( r2_hidden(B,A) & v2_membered(B) ) => v2_membered(k1_setfam_1(A)) ) )).
fof(t32_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => 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)))) ) ) ) )).
fof(t32_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t32_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( 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)))) ) ) ) ) )).
fof(t32_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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,k5_numbers)) ) ) ) ) )).
fof(t32_mesfunc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( ( 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,E)),k15_mesfunc1(A,C,F)),B) ) ) ) ) ) ) ) )).
fof(t32_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( v3_valued_0(B) => m1_subset_1(k2_relset_1(k6_numbers,B),k1_zfmisc_1(k1_numbers)) ) ) ) )).
fof(t32_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,A) => r1_xxreal_0(k5_numbers,k12_supinf_2(k19_rfunct_3(A,B),C)) ) ) ) )).
fof(t32_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( ( v2_mesfunc9(B,A) & v1_mesfunc8(B,A,k6_numbers) & r1_tarski(E,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_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) ) ) ) ) ) )).
fof(t32_metric_1,axiom,( ! [A] : ( ( v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t32_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k2_metric_2(A)) => ! [C] : ( m1_subset_1(C,k2_metric_2(A)) => ! [D] : ( m1_subset_1(D,k1_numbers) => ! [E] : ( m1_subset_1(E,k1_numbers) => ( ( r4_metric_2(A,B,C,D) & r4_metric_2(A,B,C,E) ) => D = E ) ) ) ) ) ) )).
fof(t32_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(t32_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( ( v4_midsp_2(B,A) & l1_midsp_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(u1_midsp_2(A,B))) => ? [J] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t32_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_midsp_3(B,A) => ! [C] : ( m2_midsp_3(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(C))) => ! [F] : ( ( v4_midsp_2(F,C) & l1_midsp_2(F,C) ) => ! [G] : ( m2_finseq_2(G,u1_struct_0(u1_midsp_2(C,F)),k4_finseq_2(k1_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)),k1_nat_1(A,1),G,k1_nat_1(B,1),k5_midsp_3(A,u1_struct_0(u1_midsp_2(C,F)),G,B))) = k6_midsp_3(A,C,E,k1_nat_1(B,1),k5_midsp_3(A,u1_struct_0(C),E,B)) ) ) ) ) ) ) ) ) )).
fof(t32_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [D] : ( 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)) ) ) ) )).
fof(t32_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(t32_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k6_modal_1) => ~ ( r1_xxreal_0(2,k5_card_1(k9_xtuple_0(A))) & ! [B] : ( m1_subset_1(B,k6_modal_1) => ( A != k10_modal_1(B) & A != k11_modal_1(B) ) ) & ! [B] : ( m1_subset_1(B,k6_modal_1) => ! [C] : ( m1_subset_1(C,k6_modal_1) => A != k12_modal_1(B,C) ) ) ) ) )).
fof(t32_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => k51_modelc_1(A,B,C,k52_modelc_1(A,B,C,D)) = D ) ) ) ) )).
fof(t32_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ~ ( r3_modelc_2(B,A) & r1_xxreal_0(k3_finseq_1(A),k3_finseq_1(B)) ) ) ) )).
fof(t32_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_3(C,B) & l1_modelc_3(C,B) ) => ! [D] : ( ( v1_modelc_3(D,B) & l1_modelc_3(D,B) ) => ( r1_modelc_3(B,C,D,A) => r2_hidden(A,u1_modelc_3(B,D)) ) ) ) ) ) )).
fof(t32_moebius1,axiom,( k2_moebius1(3) = k4_xcmplx_0(1) )).
fof(t32_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m2_monoid_0(B,A) ) => ( v5_group_1(A) => v5_group_1(B) ) ) ) )).
fof(t32_monoid_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k13_monoid_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k13_monoid_1(A))) => ( ! [D] : ( m1_subset_1(D,A) => k15_monoid_1(A,B,D) = k15_monoid_1(A,C,D) ) => B = C ) ) ) ) )).
fof(t32_morph_01,axiom,( ! [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) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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),k6_subset_1(u1_struct_0(A),B)) = 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,C),B)) & k3_funct_2(k1_zfmisc_1(u1_struct_0(A)),k9_setfam_1(u1_struct_0(A)),k4_morph_01(A,C),k6_subset_1(u1_struct_0(A),B)) = 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,C),B)) ) ) ) ) )).
fof(t32_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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] : ( 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)) ) ) ) ) )).
fof(t32_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v3_msafree4(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m3_pboole(C,u1_struct_0(A),k4_equation(A)) => r2_equation(A,B,C) ) ) ) )).
fof(t32_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( 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] : ( m2_pboole(E,u1_struct_0(A),C,u3_msualg_1(A,B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t32_mssubfam,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m3_pboole(D,A,k1_mboolean(A,C)) => ( r2_hidden(B,A) => m1_subset_1(k1_funct_1(D,B),k1_zfmisc_1(k1_zfmisc_1(k1_funct_1(C,B)))) ) ) ) )).
fof(t32_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => v2_binop_1(k16_msualg_2(A,B),k14_msualg_2(A,B)) ) ) )).
fof(t32_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(t32_msualg_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,B),E)) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t32_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => ( r2_hidden(k4_tarski(B,C),u1_orders_2(k5_mycielsk(A))) <=> B != C ) ) ) )).
fof(t32_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,B) <=> ~ r1_xxreal_0(B,A) ) ) ) )).
fof(t32_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => k11_nat_3(k1_newton(C,A),B) = k3_xcmplx_0(A,k11_nat_3(C,B)) ) ) ) )).
fof(t32_nat_4,axiom,( v1_int_2(43) )).
fof(t32_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ( ( r1_nat_d(B,C) & r1_nat_d(A,C) ) => ( C = B | C = A | B = 1 | A = 1 | B = A | r1_xxreal_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(1,B),A),C),k5_nat_5(C)) ) ) ) ) ) )).
fof(t32_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => k6_nat_d(A,A) = A ) )).
fof(t32_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_nattra_1(F,A,B,C,D) => ! [G] : ( m2_nattra_1(G,A,B,D,E) => ! [H] : ( m1_subset_1(H,u4_struct_0(k9_nattra_1(A,B))) => ! [I] : ( m1_subset_1(I,u4_struct_0(k9_nattra_1(A,B))) => ( ( H = k4_tarski(k4_tarski(C,D),F) & I = k4_tarski(k4_tarski(D,E),G) ) => k1_cat_1(k9_nattra_1(A,B),H,I) = k4_tarski(k4_tarski(C,E),k5_nattra_1(A,B,C,D,E,F,G)) ) ) ) ) ) ) ) ) ) ) )).
fof(t32_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t32_ncfcont2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t32_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_ndiff_1(D,A,B,C) => v3_nfcont_1(D,A) ) ) ) ) ) )).
fof(t32_ndiff_4,axiom,( ! [A] : ( ( 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] : ( 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) ) ) ) )).
fof(t32_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k14_prvect_2(A)))) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k14_prvect_2(A))) => ( r2_hidden(F,D) => r1_ndiff_5(A,B,C,E,F) ) ) ) ) ) ) ) ) ) )).
fof(t32_newton,axiom,( ! [A] : ( v7_ordinal1(A) => k1_newton(2,A) = k18_rvsum_1(k6_newton(A)) ) )).
fof(t32_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( 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_nfcont_1(A,B,C,D) ) => v1_nfcont_1(k7_relset_1(u1_struct_0(A),u1_struct_0(B),C,D),B) ) ) ) ) ) )).
fof(t32_nfcont_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ( ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & k2_relset_1(u1_struct_0(A),B) = k1_tarski(C) ) => v1_nfcont_3(B,A) ) ) ) )).
fof(t32_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_numbers)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t32_normform,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [C] : ( m2_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t32_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t32_numbers,axiom,( k1_numbers != k6_numbers )).
fof(t32_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t32_openlatt,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(t32_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,k2_oppcat_1(B),A) => m1_oppcat_1(k9_oppcat_1(B,A,C),B,A) ) ) ) )).
fof(t32_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_nfcont_3(D,k4_real_ns1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ( k1_relset_1(k1_numbers,D) = k3_integra5(B,C) => v1_integr19(k2_partfun1(k1_numbers,u1_struct_0(k4_real_ns1(A)),D,k3_integra5(B,C)),k4_real_ns1(A),k1_numbers) ) ) ) ) ) )).
fof(t32_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( ( r1_orders_1(A,C) & r1_tarski(B,C) ) => r1_orders_1(A,B) ) ) )).
fof(t32_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t32_ordinal1,axiom,( ! [A] : ( v3_ordinal1(A) => ? [B] : ( v3_ordinal1(B) & r2_hidden(A,B) & v4_ordinal1(B) ) ) )).
fof(t32_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r2_hidden(A,B) => r2_hidden(k10_ordinal2(C,A),k10_ordinal2(C,B)) ) ) ) ) )).
fof(t32_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(t32_ordinal4,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r2_hidden(1,B) => r1_ordinal1(A,k12_ordinal2(B,A)) ) ) ) )).
fof(t32_ordinal6,axiom,( ! [A] : ( ( 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)) ) )).
fof(t32_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ( ~ r1_orders_2(B,D,C) => k2_ortsp_1(A,B,E,k3_rlvect_1(B,F,G),C,D) = k3_rlvect_1(A,k2_ortsp_1(A,B,E,F,C,D),k2_ortsp_1(A,B,E,G,C,D)) ) ) ) ) ) ) ) ) )).
fof(t32_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(t32_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(u4_struct_0(A)),k7_osalg_1(A)) <=> ? [C] : ( m1_subset_1(C,u4_struct_0(A)) & B = k8_osalg_1(A,C) ) ) ) )).
fof(t32_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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))) ) ) ) )).
fof(t32_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t32_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_parsp_2(A,B,C,D,E) => r2_parsp_2(A,C,B,E,D) ) ) ) ) ) ) )).
fof(t32_partfun1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => A = k3_partfun1(A,k9_xtuple_0(A),k10_xtuple_0(A)) ) )).
fof(t32_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_partfun1(k1_partfun2(A,B),A) <=> B = A ) ) ) )).
fof(t32_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ( r1_setfam_1(B,k6_partit1(A)) & r1_setfam_1(k10_eqrel_1(A),B) ) ) ) )).
fof(t32_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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))) ) ) ) )).
fof(t32_pcomps_1,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t32_pcs_0,axiom,( ! [A] : ( ( v14_pcs_0(A) & l2_pcs_0(A) ) => ! [B] : ( ~ r2_hidden(B,u1_struct_0(A)) => ( v14_pcs_0(k20_pcs_0(A,B)) & l2_pcs_0(k20_pcs_0(A,B)) ) ) ) )).
fof(t32_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k4_real_ns1(A))) => ( r2_pdiff_1(B,A,C,E,F) => ( r2_pdiff_1(B,A,C,k4_vfunct_1(u1_struct_0(k4_real_ns1(A)),k4_real_ns1(B),E,D),F) & k9_pdiff_1(A,B,C,k4_vfunct_1(u1_struct_0(k4_real_ns1(A)),k4_real_ns1(B),E,D),F) = k1_rlvect_1(k16_lopban_1(k4_real_ns1(1),k4_real_ns1(B)),k9_pdiff_1(A,B,C,E,F),D) ) ) ) ) ) ) ) ) )).
fof(t32_pdiff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(2)) => ! [C] : ( ( 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) & k10_pdiff_1(2,2,k26_valued_1(k1_euclid(2),k1_numbers,k1_pdiff_3(2,2,C),A),B) = k3_xcmplx_0(A,k5_pdiff_3(C,B)) ) ) ) ) ) )).
fof(t32_pdiff_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( 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),k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(2,3),B)) ) ) ) )).
fof(t32_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( 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) = k10_pdiff_1(3,2,k1_pdiff_3(2,3,B),A) ) ) ) )).
fof(t32_pdiff_6,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_euclid(A))) => ( ? [E] : ( 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] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ( r2_hidden(E,D) => r1_pdiff_1(A,B,C,E) ) ) ) ) ) ) ) ) ) )).
fof(t32_pdiff_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ( ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v8_ordinal1(D) & m1_subset_1(D,k4_ordinal1) ) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t32_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t32_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( v1_int_2(C) & r1_nat_d(A,k1_newton(C,B)) & A != 1 & ! [D] : ( m1_subset_1(D,k4_ordinal1) => A != k2_nat_1(C,D) ) ) ) ) ) )).
fof(t32_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m2_finseq_2(C,B,k3_finseq_2(B)) => ! [D] : ( m2_finseq_2(D,B,k3_finseq_2(B)) => ! [E] : ( m2_finseq_2(E,B,k3_finseq_2(B)) => k10_pnproc_1(A,B,k7_domain_1(k3_finseq_2(B),D,E),k6_domain_1(k3_finseq_2(B),C)) = k7_domain_1(k3_finseq_2(B),k1_pre_poly(B,D,C),k1_pre_poly(B,E,C)) ) ) ) ) )).
fof(t32_polyeq_3,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k1_newton(A,B) = k2_xcmplx_0(k3_xcmplx_0(k2_power(k9_complex1(A),B),k19_sin_cos(k3_xcmplx_0(B,k1_comptrig(A)))),k3_xcmplx_0(k3_xcmplx_0(k2_power(k9_complex1(A),B),k17_sin_cos(k3_xcmplx_0(B,k1_comptrig(A)))),k7_complex1)) ) ) )).
fof(t32_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => v2_funct_1(k10_polyform(A,B)) ) ) )).
fof(t32_polynom8,axiom,( ! [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) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_polynom8(A,C,B) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t32_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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,k8_polynom1(A,C)) & E != k8_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)) ) ) ) ) ) ) ) ) )).
fof(t32_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(A,k5_numbers) => k2_power(k7_xcmplx_0(1,A),B) = k2_power(A,k4_xcmplx_0(B)) ) ) ) )).
fof(t32_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v3_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v3_valued_0(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) & v3_valued_0(D) ) => ( ! [E] : ( r2_hidden(E,A) => k1_funct_1(B,E) = k2_xcmplx_0(k1_funct_1(C,E),k1_funct_1(D,E)) ) => r6_pboole(A,B,k11_pre_poly(A,C,D)) ) ) ) ) )).
fof(t32_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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) ) ) ) ) ) ) )).
fof(t32_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k5_numbers,A) => k2_prepower(2,A) = k3_square_1(A) ) ) )).
fof(t32_prob_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m2_prob_1(D,A,B) => k3_funct_2(B,k1_numbers,D,k7_prob_1(A,B,k4_prob_1(A,B),C)) = k6_xcmplx_0(1,k3_funct_2(B,k1_numbers,D,C)) ) ) ) ) )).
fof(t32_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m1_prob_1(E,A,B) => ! [F] : ( m1_prob_1(F,A,B) => ! [G] : ( 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(k3_funct_2(B,k1_numbers,C,E),k5_numbers) | r1_xxreal_0(k3_funct_2(B,k1_numbers,C,F),k5_numbers) | r1_xxreal_0(k3_funct_2(B,k1_numbers,C,G),k5_numbers) | k3_funct_2(B,k1_numbers,C,D) = k3_real_1(k3_real_1(k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,C,E),D),k3_funct_2(B,k1_numbers,C,E)),k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,C,F),D),k3_funct_2(B,k1_numbers,C,F))),k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,C,G),D),k3_funct_2(B,k1_numbers,C,G))) ) ) ) ) ) ) ) ) ) )).
fof(t32_prob_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( ( v5_relat_1(E,D) & v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k9_setfam_1(C)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(C)))) ) => ( r2_hidden(B,k1_prob_2(C,D,k3_prob_3(C,E),A)) <=> ( r2_hidden(B,k1_prob_2(C,D,E,A)) & ! [F] : ( v7_ordinal1(F) => ~ ( ~ r1_xxreal_0(A,F) & r2_hidden(B,k1_prob_2(C,D,E,F)) ) ) ) ) ) ) ) )).
fof(t32_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t32_projpl_1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t32_pscomp_1,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t32_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) )).
fof(t32_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t32_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k4_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k5_qc_lang1(A)) => B != C ) ) ) )).
fof(t32_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => k3_qc_lang4(A,B,C) = a_3_1_qc_lang4(A,B,C) ) ) ) )).
fof(t32_quantal1,axiom,( ! [A] : ( ( ~ 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] : ( 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 ) ) ) )).
fof(t32_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ( A != k5_numbers => k23_quaterni(k7_quatern2(A),A) = 1 ) ) )).
fof(t32_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k28_quaterni(k23_quaterni(A,A)) = k28_quaterni(k23_quaterni(k27_quaterni(A),k27_quaterni(A))) ) )).
fof(t32_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => ! [D] : ( v1_quaterni(D) => ( k13_quaterni(k7_quaterni(k7_quaterni(k7_quaterni(A,B),C),D)) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k13_quaterni(A),k13_quaterni(B)),k13_quaterni(C)),k13_quaterni(D)) & k14_quaterni(k7_quaterni(k7_quaterni(k7_quaterni(A,B),C),D)) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k14_quaterni(A),k14_quaterni(B)),k14_quaterni(C)),k14_quaterni(D)) & k15_quaterni(k7_quaterni(k7_quaterni(k7_quaterni(A,B),C),D)) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k15_quaterni(A),k15_quaterni(B)),k15_quaterni(C)),k15_quaterni(D)) & k16_quaterni(k7_quaterni(k7_quaterni(k7_quaterni(A,B),C),D)) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k16_quaterni(A),k16_quaterni(B)),k16_quaterni(C)),k16_quaterni(D)) ) ) ) ) ) )).
fof(t32_quofield,axiom,( ! [A] : ( ( ~ 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] : ( 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))) ) ) )).
fof(t32_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m2_prob_1(B,A,k1_random_1(A)) => ! [C] : ( m1_random_1(C,A,k1_random_1(A)) => ? [D] : ( m2_finseq_1(D,k1_numbers) & ? [E] : ( 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] : ( v7_ordinal1(F) => ( r2_hidden(F,k4_finseq_1(D)) => k12_supinf_2(D,F) = k1_extreal1(k12_supinf_2(C,k1_funct_1(E,F)),k12_supinf_2(B,k1_tarski(k1_funct_1(E,F)))) ) ) & k8_random_1(A,k1_random_1(A),B,C) = k18_rvsum_1(D) ) ) ) ) ) )).
fof(t32_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_6(C,A,B) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t32_rat_1,axiom,( ! [A] : ( 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) ) ) ) )).
fof(t32_ratfunc1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k13_ratfunc1(A,k8_ratfunc1(A),B) = k5_struct_0(A) ) ) )).
fof(t32_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t32_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_int_1(B) => ( ~ r1_xxreal_0(B,1) => ( k9_nat_1(k1_numbers,k4_real_3(k7_xcmplx_0(1,B)),k5_numbers) = k5_numbers & k9_nat_1(k1_numbers,k4_real_3(k7_xcmplx_0(1,B)),1) = B & k9_nat_1(k1_numbers,k4_real_3(k7_xcmplx_0(1,B)),k1_nat_1(A,2)) = k5_numbers ) ) ) ) )).
fof(t32_relat_1,axiom,( k9_xtuple_0(k1_xboole_0) = k1_xboole_0 & k10_xtuple_0(k1_xboole_0) = k1_xboole_0 )).
fof(t32_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) => ( r1_xboole_0(A,B) => k5_relset_1(B,C,D,A) = k1_xboole_0 ) ) )).
fof(t32_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( 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)) ) ) ) )).
fof(t32_revrot_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( 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(k1_nat_1(A,k3_finseq_1(C)),k4_finseq_4(C,B))) ) ) ) ) ) )).
fof(t32_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r2_rewrite1(A,B,C) => ( B = C | ( r2_hidden(B,k1_relat_1(A)) & r2_hidden(C,k1_relat_1(A)) ) ) ) ) )).
fof(t32_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => r3_rewrite2(A,B,C,C) ) ) )).
fof(t32_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(E))) => ! [G] : ( ( ~ 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))) ) ) ) ) ) )).
fof(t32_rfinseq,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( r2_classes1(A,B) & r1_xxreal_0(C,D) & r1_xxreal_0(D,k3_finseq_1(A)) & ! [F] : ( v7_ordinal1(F) => ( ( r1_xxreal_0(1,F) & r1_xxreal_0(F,C) ) => k1_funct_1(A,F) = k1_funct_1(B,F) ) ) & ! [F] : ( v7_ordinal1(F) => ( 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] : ( v7_ordinal1(F) => ~ ( ~ r1_xxreal_0(F,C) & r1_xxreal_0(F,D) & k1_funct_1(A,E) = k1_funct_1(B,F) ) ) ) ) ) ) ) ) )).
fof(t32_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( v1_xcmplx_0(C) => k24_valued_1(k1_rfunct_1(B,A),C) = k1_rfunct_1(k24_valued_1(B,C),A) ) ) ) )).
fof(t32_rfunct_2,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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,k5_numbers) | v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k26_valued_1(k1_numbers,k1_numbers,C,B),A)) ) ) & ( B = k5_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(k5_numbers,B) | v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k26_valued_1(k1_numbers,k1_numbers,C,B),A)) ) ) ) ) ) )).
fof(t32_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,A) => r1_rfunct_3(A,k1_numbers,k16_rfunct_3(A,k15_rfunct_3(A,B),C),D) ) ) ) ) )).
fof(t32_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_seq_2(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_numbers)) => ( C = a_2_0_rinfsup1(A,B) => v3_xxreal_2(C) ) ) ) ) ) )).
fof(t32_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => r1_xxreal_0(k1_supinf_1,k12_supinf_2(A,B)) ) => v8_mesfunc5(A) ) ) )).
fof(t32_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( 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) = k3_funct_2(u1_struct_0(A),k1_numbers,B,C) ) ) ) ) )).
fof(t32_rlaffin3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_rlaffin1(C,k15_euclid(B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) ) => ( k5_card_1(C) = k2_xcmplx_0(B,1) => v5_pre_topc(k2_rlaffin3(k15_euclid(B),C,A),k15_euclid(B),k3_topmetr) ) ) ) )).
fof(t32_rlsub_1,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_rlvect_1(B) & m1_rlsub_1(B,A) ) => ( u1_struct_0(B) = u1_struct_0(A) => B = A ) ) ) )).
fof(t32_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ( ~ ( ? [D] : ( 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] : ( m1_rlsub_1(D,A) => u1_struct_0(D) != k2_xboole_0(u1_struct_0(B),u1_struct_0(C)) ) ) ) ) ) ) )).
fof(t32_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_connsp_2(D,A,k1_rlvect_1(A,C,B)) => ? [E] : ( v2_xxreal_0(E) & v1_xreal_0(E) & ? [F] : ( m1_connsp_2(F,A,C) & ! [G] : ( v1_xreal_0(G) => ( ~ r1_xxreal_0(E,k9_complex1(k6_xcmplx_0(G,B))) => r1_tarski(k1_convex1(A,F,G),D) ) ) ) ) ) ) ) ) )).
fof(t32_rlvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t32_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t32_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( m1_rlsub_1(D,A) => ( ( m1_rlsub_1(B,D) & m1_rlsub_1(C,D) ) => m1_rlsub_1(k1_rlsub_2(A,B,C),D) ) ) ) ) ) )).
fof(t32_rlvect_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t32_rlvect_5,axiom,( ! [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_rlvect_5(A) & l1_rlvect_1(A) ) => ( k1_rlvect_5(A) = k5_numbers <=> k2_rlsub_1(A) = k1_rlsub_1(A) ) ) )).
fof(t32_rlvect_x,axiom,( ! [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) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,u1_struct_0(A)) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( ( 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] : ( 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_funct_1(E,F)) ) ) ) => r2_hidden(k4_rlvect_1(A,D),k3_rlvect_x(A,B)) ) ) ) ) ) ) )).
fof(t32_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v2_vectsp_2(C,A) & m1_rmod_2(C,A,B) ) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => r1_struct_0(C,D) ) => C = B ) ) ) ) )).
fof(t32_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v2_vectsp_2(C,A) & m1_rmod_2(C,A,B) ) => ! [D] : ( ( 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 ) ) ) ) ) )).
fof(t32_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) )).
fof(t32_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & v8_robbins1(A) & l4_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_robbins1(A,k3_robbins1(A,B)) = B ) ) )).
fof(t32_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t32_robbins4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v10_robbins1(A) & v8_robbins3(A) & v9_robbins3(A) & l4_robbins1(A) ) => ( v1_robbins4(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t32_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) )).
fof(t32_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k2_rpr_1(A,k2_subset_1(A),B) = k1_rpr_1(A,B) ) ) )).
fof(t32_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => m1_rusub_1(k1_rusub_1(B),A) ) ) )).
fof(t32_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ( ~ ( ? [D] : ( 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] : ( m1_rusub_1(D,A) => u1_struct_0(D) != k2_xboole_0(u1_struct_0(B),u1_struct_0(C)) ) ) ) ) ) ) )).
fof(t32_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( r1_struct_0(k1_rusub_3(A,k7_domain_1(u1_struct_0(A),B,C)),D) <=> ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & D = k3_rlvect_1(A,k1_rlvect_1(A,B,E),k1_rlvect_1(A,C,F)) ) ) ) ) ) ) )).
fof(t32_rusub_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_bhsp_1(B) & m1_rusub_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t32_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_rusub_1(C,A) & u1_struct_0(C) = a_2_3_rusub_5(A,B) ) ) ) )).
fof(t32_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => k8_rvsum_1(B,k2_finseq_2(A,k5_numbers)) = B ) ) )).
fof(t32_rvsum_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_valued_0(B) ) => k16_rvsum_1(k7_finseq_1(A,B)) = k2_xcmplx_0(k16_rvsum_1(A),k16_rvsum_1(B)) ) ) )).
fof(t32_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( v1_ami_2(E) & ~ v1_scmfsa_m(E) & m1_subset_1(E,u1_struct_0(k1_scmfsa_2)) ) => ( ( k1_funct_1(B,E) = k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),3)))) ) ) ) ) ) ) )).
fof(t32_scmbsort,axiom,( v3_scm_halt(k1_scmbsort(k5_scmfsa_2(k5_numbers))) & v2_scm_halt(k1_scmbsort(k5_scmfsa_2(k5_numbers))) )).
fof(t32_scmfsa10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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) = k4_ordinal1 ) ) )).
fof(t32_scmfsa8a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ( ( r5_scmfsa7b(A,C,D) & r6_scmfsa7b(A,C,D) ) => r1_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(D,k3_scmfsa6a(k3_scmfsa6a(k3_scmfsa6a(A,k1_scmfsa8a(k1_nat_1(k5_card_1(B),1))),B),k4_compos_1(k1_scmfsa_2))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,C)) ) ) ) ) ) )).
fof(t32_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(B)),k1_scmfsa6b(C,B,A)) ) ) ) )).
fof(t32_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( 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),k5_numbers) | ( r6_scmfsa7b(k2_scmfsa8b(E,C,D),B,A) & r5_scmfsa7b(k2_scmfsa8b(E,C,D),B,A) & k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa8b(E,C,D)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B)) = k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(C,k4_compos_1(k1_scmfsa_2))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B)),1) ) ) ) ) ) ) ) ) )).
fof(t32_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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] : ( v7_ordinal1(E) => ( k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(B,D,C,A),E),k4_scmfsa_2(k5_numbers)) = 1 => ( ( ~ ( r6_scmfsa7b(D,k1_scmfsa_m(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(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(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(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,k7_card_1(3),k1_scmfsa_2) ) | r1_xxreal_0(k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(B,D,C,A),E),C),k5_numbers) | k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(B,D,C,A),k1_nat_1(E,1))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(D,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(B,D,C,A),E),k1_funct_4(A,k2_scmfsa_9(C,D)))) ) ) ) ) ) ) ) )).
fof(t32_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ~ ( k2_compos_0(u1_compos_1(k1_scmfsa_2),A) = 10 & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( m1_scmfsa_2(D) => A != k15_scmfsa_2(C,B,D) ) ) ) ) ) )).
fof(t32_scmfsa_m,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ! [B] : ( m1_scmfsa_2(B) => r1_xboole_0(k9_xtuple_0(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),k9_xtuple_0(k16_funcop_1(B,A))) ) ) )).
fof(t32_scmisort,axiom,( ! [A] : ( m1_scmfsa_2(A) => k5_card_1(k2_scmisort(A)) = 82 ) )).
fof(t32_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v2_compos_1(D,k1_scmpds_2) & v3_scmpds_4(D) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( 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)) = k5_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,k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),2))) ) ) ) ) ) ) ) ) )).
fof(t32_scmpds_7,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ( k1_funct_1(k1_scmpds_7(A,B,C,D),k5_numbers) = k9_scmpds_2(A,B,k1_nat_1(k5_card_1(D),3)) & k1_funct_1(k1_scmpds_7(A,B,C,D),k1_nat_1(k5_card_1(D),1)) = k11_scmpds_2(A,B,C) & k1_funct_1(k1_scmpds_7(A,B,C,D),k1_nat_1(k5_card_1(D),2)) = k3_scmpds_2(k4_xcmplx_0(k1_nat_1(k5_card_1(D),2))) ) ) ) ) ) )).
fof(t32_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ( ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t32_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t32_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v9_ordinal1(A) => v9_ordinal1(k37_valued_1(k4_ordinal1,k1_numbers,A)) ) ) )).
fof(t32_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & v2_comseq_2(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => k1_seq_2(k55_valued_1(k4_ordinal1,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B))) = k3_xcmplx_0(k9_complex1(k3_comseq_2(A)),k9_complex1(k3_comseq_2(B))) ) ) )).
fof(t32_seq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( r1_xxreal_0(k5_numbers,A) & ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,B,C) = k7_xcmplx_0(1,k2_xcmplx_0(k3_xcmplx_0(C,C),A)) ) ) => v2_comseq_2(B) ) ) ) )).
fof(t32_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( r1_seqfunc(A,k1_numbers,C,D) => ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,D) => r2_relset_1(k4_ordinal1,k1_numbers,k10_seqfunc(A,k2_seqfunc(A,C,B),E),k26_valued_1(k4_ordinal1,k1_numbers,k10_seqfunc(A,C,E),B)) ) ) ) ) ) ) )).
fof(t32_seqm_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ( v7_valued_0(B) & r1_xxreal_0(k5_numbers,A) ) => v7_valued_0(k26_valued_1(k4_ordinal1,k1_numbers,B,A)) ) & ( ( v7_valued_0(B) & r1_xxreal_0(A,k5_numbers) ) => v8_valued_0(k26_valued_1(k4_ordinal1,k1_numbers,B,A)) ) ) ) ) )).
fof(t32_series_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(1,C) => k9_nat_1(k1_numbers,B,C) = k7_xcmplx_0(1,k2_power(C,A)) ) ) => ( r1_xxreal_0(A,1) | v1_series_1(B) ) ) ) ) )).
fof(t32_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => r1_xxreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k3_xcmplx_0(A,B)),k1_square_1(B)),3)),k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(B),k3_xcmplx_0(B,C)),k1_square_1(C)),3))),k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(C),k3_xcmplx_0(C,A)),k1_square_1(A)),3))),k2_xcmplx_0(k2_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),2)),k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_square_1(B),k1_square_1(C)),2))),k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_square_1(C),k1_square_1(A)),2)))) ) ) ) )).
fof(t32_setfam_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ~ ( B != k1_xboole_0 & k7_setfam_1(A,B) = k1_xboole_0 ) ) )).
fof(t32_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => r2_funct_2(k4_ordinal1,k9_setfam_1(A),k2_prob_1(A,k2_setlim_1(A,B)),k4_setlim_1(A,k2_prob_1(A,B))) ) )).
fof(t32_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_setlim_1(C,A) => v1_setlim_1(k8_setlim_2(A,C,B),A) ) ) ) )).
fof(t32_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( m1_subset_1(E,k5_finsub_1(B)) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,B,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t32_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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] : ( ( 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] : ( m2_finseq_1(E,A) => ! [F] : ( 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] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,A) => ! [I] : ( m1_subset_1(I,A) => ! [J] : ( 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) ) ) ) ) ) ) ) )).
fof(t32_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t32_sfmastr3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( m1_scmfsa_2(D) => ~ ( C != k9_scmfsa_m(1,k5_scmfsa_m(A,B)) & C != k9_scmfsa_m(2,k5_scmfsa_m(A,B)) & r4_scmfsa7b(k4_sfmastr3(D,A,B),C) ) ) ) ) ) )).
fof(t32_sgraph1,axiom,( ! [A] : ! [B] : ( m1_sgraph1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( r2_hidden(E,k5_sgraph1(A,B,C,D)) <=> ? [F] : ( m2_finseq_2(F,u1_struct_0(B),k3_finseq_2(u1_struct_0(B))) & E = F & r3_sgraph1(A,B,C,D,F) ) ) ) ) ) )).
fof(t32_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v9_sheffer1(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l3_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t32_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t32_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ! [C] : ( m2_simplex0(C,A,B) => r1_xxreal_0(k6_simplex0(C),k6_simplex0(B)) ) ) )).
fof(t32_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_fdiff_1(k3_sin_cos2,A) & k1_fdiff_1(k3_sin_cos2,A) = k1_funct_1(k1_sin_cos2,A) ) ) )).
fof(t32_sin_cos3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k15_sin_cos(k3_xcmplx_0(k3_xcmplx_0(k2_xcmplx_0(k2_nat_1(2,A),k7_xcmplx_0(1,2)),k28_sin_cos),k7_complex1)) = k7_complex1 ) )).
fof(t32_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k3_xcmplx_0(k19_sin_cos(A),k19_sin_cos(B)) = k3_xcmplx_0(k7_xcmplx_0(1,2),k2_xcmplx_0(k19_sin_cos(k2_xcmplx_0(A,B)),k19_sin_cos(k6_xcmplx_0(A,B)))) ) ) )).
fof(t32_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k17_sin_cos(k7_xcmplx_0(A,2)) != k5_numbers => k2_sin_cos4(k7_xcmplx_0(A,2)) = k7_xcmplx_0(k17_sin_cos(A),k6_xcmplx_0(1,k19_sin_cos(A))) ) ) )).
fof(t32_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos)) & r1_xxreal_0(A,k3_xcmplx_0(2,k28_sin_cos)) & r1_xxreal_0(k17_sin_cos(A),k4_xcmplx_0(1)) ) ) )).
fof(t32_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & r1_xxreal_0(k7_xcmplx_0(k2_xcmplx_0(A,1),k6_xcmplx_0(1,A)),k5_numbers) ) ) )).
fof(t32_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_newton(k4_sin_cos2(A),3) = k7_xcmplx_0(k2_xcmplx_0(k4_sin_cos2(k3_xcmplx_0(3,A)),k3_xcmplx_0(3,k4_sin_cos2(A))),4) & k1_newton(k4_sin_cos2(A),4) = k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k4_sin_cos2(k3_xcmplx_0(4,A)),k3_xcmplx_0(4,k4_sin_cos2(k3_xcmplx_0(2,A)))),3),8) & k1_newton(k4_sin_cos2(A),5) = k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k4_sin_cos2(k3_xcmplx_0(5,A)),k3_xcmplx_0(5,k4_sin_cos2(k3_xcmplx_0(3,A)))),k3_xcmplx_0(10,k4_sin_cos2(A))),16) & k1_newton(k4_sin_cos2(A),6) = k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k4_sin_cos2(k3_xcmplx_0(6,A)),k3_xcmplx_0(6,k4_sin_cos2(k3_xcmplx_0(4,A)))),k3_xcmplx_0(15,k4_sin_cos2(k3_xcmplx_0(2,A)))),10),32) & k1_newton(k4_sin_cos2(A),7) = k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k4_sin_cos2(k3_xcmplx_0(7,A)),k3_xcmplx_0(7,k4_sin_cos2(k3_xcmplx_0(5,A)))),k3_xcmplx_0(21,k4_sin_cos2(k3_xcmplx_0(3,A)))),k3_xcmplx_0(35,k4_sin_cos2(A))),64) & k1_newton(k4_sin_cos2(A),8) = k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k4_sin_cos2(k3_xcmplx_0(8,A)),k3_xcmplx_0(8,k4_sin_cos2(k3_xcmplx_0(6,A)))),k3_xcmplx_0(28,k4_sin_cos2(k3_xcmplx_0(4,A)))),k3_xcmplx_0(56,k4_sin_cos2(k3_xcmplx_0(2,A)))),35),128) ) ) )).
fof(t32_sin_cos9,axiom,( k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k27_sin_cos,k2_rcomp_1(k5_numbers,k28_sin_cos)),k2_sin_cos9) = k1_partfun2(k1_numbers,k2_rcomp_1(k5_numbers,k28_sin_cos)) )).
fof(t32_sincos10,axiom,( k1_funct_1(k2_fdiff_9,k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2))) = k4_xcmplx_0(1) & k1_funct_1(k2_fdiff_9,k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4))) = k4_xcmplx_0(k3_square_1(2)) & k1_funct_1(k2_fdiff_9,k7_xcmplx_0(k28_sin_cos,4)) = k3_square_1(2) & k1_funct_1(k2_fdiff_9,k7_xcmplx_0(k28_sin_cos,2)) = 1 )).
fof(t32_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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(k1_nat_1(A,2),k3_finseq_1(B)) & v2_sppol_1(k2_topreal1(2,B,A)) ) => v1_sppol_1(k2_topreal1(2,B,k1_nat_1(A,1))) ) ) ) )).
fof(t32_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ( ( 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)) ) ) ) ) )).
fof(t32_sprect_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t32_sprect_2,axiom,( k6_pscomp_1(k1_topreal1) = k5_numbers )).
fof(t32_sprect_3,axiom,( ! [A] : ( ( v1_sprect_1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( 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)) ) ) ) )).
fof(t32_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t32_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k3_square_1(k7_xcmplx_0(1,A)) = k7_xcmplx_0(1,k3_square_1(A)) ) ) )).
fof(t32_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ( ( r2_hidden(C,k11_stacks_1(A,B)) & r2_hidden(D,k11_stacks_1(A,B)) & k9_stacks_1(A,C) = k9_stacks_1(A,D) ) => C = D ) ) ) ) ) )).
fof(t32_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( A != k5_numbers => k3_stirl2_1(A,1) = 1 ) ) )).
fof(t32_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t32_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( ! [D] : ( m1_subset_1(D,A) => ~ ( r2_hidden(D,B) <=> r2_hidden(D,C) ) ) => B = k3_subset_1(A,C) ) ) ) )).
fof(t32_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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))) ) ) ) )).
fof(t32_supinf_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k6_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t32_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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,D,C) | k2_symsp_1(A,B,E,F,C,D) = k4_struct_0(A) ) ) ) ) ) ) ) ) )).
fof(t32_sysrel,axiom,( ! [A] : ( 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)) ) ) )).
fof(t32_taxonom1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t32_taylor_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => ! [D] : ( v7_ordinal1(D) => k1_funct_1(A,C) = k9_nat_1(k1_numbers,k3_series_1(k6_taylor_1(A,B,C,C)),D) ) ) ) ) ) )).
fof(t32_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(u1_struct_0(A)),k5_tdlat_1(A)) => ! [C] : ( 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) ) ) ) )).
fof(t32_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) )).
fof(t32_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v4_tdlat_3(A) <=> ! [B] : ( 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) ) ) ) ) ) )).
fof(t32_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(D,A,C) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(E,A,C) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => k4_termord(A,B,C,k10_polynom1(A,C,D,E)) = k6_algstr_0(C,k4_termord(A,B,C,D),k4_termord(A,B,C,E)) ) ) ) ) ) )).
fof(t32_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v3_tdlat_3(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( B != u1_struct_0(A) & v1_tops_3(B,A) ) ) ) ) )).
fof(t32_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t32_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t32_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(B,k3_tex_4(A,B)) ) ) )).
fof(t32_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ v2_struct_0(E) & m1_pre_topc(E,A) ) => ! [F] : ( ( ~ 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,E,F),B) & m1_pre_topc(k2_tsep_1(A,E,k1_tsep_1(A,C,D)),C) & m1_pre_topc(k2_tsep_1(A,F,k1_tsep_1(A,C,D)),D) & m1_pre_topc(k2_tsep_1(A,B,k1_tsep_1(A,C,D)),k2_tsep_1(A,C,D)) ) => ( r1_tsep_1(C,D) | m1_pre_topc(C,D) | m1_pre_topc(D,C) | ( ~ r1_tsep_1(E,k1_tsep_1(A,C,D)) & ~ r1_tsep_1(F,k1_tsep_1(A,C,D)) ) ) ) ) ) ) ) ) ) )).
fof(t32_toler_1,axiom,( ! [A] : ! [B] : ( ( 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 ) )).
fof(t32_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_borsuk_2(G,A,B,C) => ! [H] : ( m1_borsuk_2(H,A,C,D) => ! [I] : ( m1_borsuk_2(I,A,D,E) => ! [J] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t32_topalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( 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] : ( m1_borsuk_2(F,B,D,k3_funct_2(u1_struct_0(A),u1_struct_0(B),E,C)) => ! [G] : ( ( 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))) ) ) ) ) ) ) ) ) )).
fof(t32_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v1_borsuk_2(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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)))) ) ) ) ) ) ) )).
fof(t32_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( ( v7_pre_topc(A) & ! [B] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v4_pre_topc(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( r1_xboole_0(B,C) & ! [D] : ( ( v4_pre_topc(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ! [E] : ( ( 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),k5_numbers) ) ) ) )).
fof(t32_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t32_topgen_2,axiom,( ! [A] : ( ~ v1_finset_1(A) => ! [B] : ! [C] : ( ( 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) ) ) ) )).
fof(t32_topgen_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k1_numbers))) => ~ ( r2_hidden(k1_card_1(A),k3_topgen_3) & ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_rat_1(C) => ~ ( ~ r1_xxreal_0(C,B) & ~ r2_hidden(k3_rcomp_1(B,C),k1_cantor_1(k1_numbers,A)) ) ) ) ) ) )).
fof(t32_topgen_4,axiom,( ! [A] : ! [B] : r1_tarski(k1_setfam_1(k2_setfam_1(A,B)),k2_xboole_0(k1_setfam_1(A),k1_setfam_1(B))) )).
fof(t32_topgen_5,axiom,( ! [A] : ( 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] : 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) ) ) )).
fof(t32_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => k4_topgrp_1(A) = k1_group_1(k5_topgrp_1(A)) ) )).
fof(t32_topreal1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => k5_topreal1(A) = a_1_2_topreal1(A) ) )).
fof(t32_topreal8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_topreal1(A) & v3_topreal1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( v7_ordinal1(B) => ( 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,k1_nat_1(B,1))) ) ) ) ) )).
fof(t32_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ( ( r2_hidden(C,k3_topreal9(A,E,B)) & r2_hidden(D,k3_topreal9(A,E,B)) ) => r1_tarski(k7_subset_1(u1_struct_0(k15_euclid(A)),k1_rltopsp1(k15_euclid(A),C,D),k2_tarski(C,D)),k1_topreal9(A,E,B)) ) ) ) ) ) ) )).
fof(t32_topreala,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( r1_xxreal_0(A,B) & r1_xxreal_0(C,D) & v2_struct_0(k1_topreala(A,B,C,D)) ) ) ) ) ) )).
fof(t32_toprealb,axiom,( ! [A] : ( v1_int_1(A) => k1_funct_1(k12_toprealb,A) = k9_toprealb ) )).
fof(t32_toprealc,axiom,( ! [A] : ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_valued_2(C) => ! [D] : ( ( 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)) ) ) ) )).
fof(t32_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => r1_xxreal_0(k6_xcmplx_0(k12_euclid(B),k12_euclid(C)),k12_euclid(k5_algstr_0(k15_euclid(A),B,C))) ) ) ) )).
fof(t32_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t32_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t32_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t32_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t32_trees_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_trees_1(C) ) => ( r2_hidden(A,B) => C = k4_trees_1(k5_trees_1(B,A,C),A) ) ) ) ) )).
fof(t32_trees_2,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( ( 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)) ) ) ) )).
fof(t32_trees_3,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(t32_trees_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( m2_finseq_1(E,k5_trees_3(k2_zfmisc_1(A,B))) => ? [F] : ( m2_finseq_1(F,k5_trees_3(B)) & k4_finseq_1(F) = k4_finseq_1(E) & ! [G] : ( v7_ordinal1(G) => ~ ( r2_hidden(G,k4_finseq_1(E)) & ! [H] : ( 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) ) ) ) ) ) ) )).
fof(t32_trees_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ? [C] : ( 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) ) ) ) )).
fof(t32_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ 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)) ) ) ) ) ) ) )).
fof(t32_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(t32_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t32_turing_1,axiom,( r3_turing_1(k16_turing_1,k4_comput_1(1,1)) )).
fof(t32_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => r2_hidden(k4_tarski(k10_finseq_1(A,B),k3_twoscomp),k3_msafree2(k37_twoscomp(A,B))) ) ) )).
fof(t32_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => r1_tarski(k2_uniroots(A),u1_struct_0(k1_uniroots(k1_complfld))) ) )).
fof(t32_uproots,axiom,( ! [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) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)),k5_numbers) ) ) ) ) )).
fof(t32_urysohn2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ( v4_xxreal_2(k1_integra2(A,B)) => ( r1_xxreal_0(B,k5_numbers) | v4_xxreal_2(A) ) ) ) ) )).
fof(t32_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_funct_2(C,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [D] : ( m1_valuat_1(D,A,B) => r1_valuat_1(A,B,k5_cqc_lang(A),D,C) ) ) ) ) )).
fof(t32_valued_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( m1_valued_0(C,B) => r1_tarski(k10_xtuple_0(C),k10_xtuple_0(B)) ) ) ) )).
fof(t32_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(B,k1_relset_1(k4_ordinal1,A)) => r1_xxreal_0(B,k62_valued_1(A)) ) ) ) )).
fof(t32_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( 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) ) ) )).
fof(t32_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t32_vectsp11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( ~ 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] : ( ( 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)))))) ) ) ) ) ) )).
fof(t32_vectsp_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(B,k5_numbers) => k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k4_group_1(A),k4_struct_0(A),B) = k4_struct_0(A) ) ) ) )).
fof(t32_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t32_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v7_vectsp_1(C,A) & m1_vectsp_4(C,A,B) ) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => r1_struct_0(C,D) ) => C = B ) ) ) ) )).
fof(t32_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( ( v7_vectsp_1(D,A) & m1_vectsp_4(D,A,B) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t32_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t32_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t32_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t32_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t32_waybel11,axiom,( ! [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) ) => g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = k13_yellow_6(A,k2_waybel11(A)) ) )).
fof(t32_waybel12,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( m1_waybel12(C,A,B) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( k2_relset_1(u1_struct_0(A),D) = C & ! [F] : ( m1_subset_1(F,k4_ordinal1) => k3_funct_2(k4_ordinal1,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) ) ) ) ) ) ) )).
fof(t32_waybel13,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t32_waybel14,axiom,( ! [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) ) => ( v3_waybel_3(A) => ( v1_compts_1(A) & v6_waybel_3(A) & v4_yellow_8(A) & v2_yellow_8(A) ) ) ) )).
fof(t32_waybel15,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & r1_tarski(C,k1_waybel15(A)) & B = k1_yellow_0(A,C) ) ) ) ) ) )).
fof(t32_waybel16,axiom,( ! [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_8(A) & l1_orders_2(A) ) => ( v4_waybel_6(k1_waybel16(A),A) & ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_waybel_6(B,A) => r1_tarski(k1_waybel16(A),B) ) ) ) ) )).
fof(t32_waybel19,axiom,( ! [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) & 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)))) ) ) )).
fof(t32_waybel21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t32_waybel23,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t32_waybel24,axiom,( ! [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] : ( ( 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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_waybel24(A,B)))) ) => r2_hidden(k1_yellow_0(k5_yellow_1(u1_struct_0(A),B),C),u1_struct_0(k3_waybel24(A,B))) ) ) ) )).
fof(t32_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_waybel25(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t32_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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))) ) ) )).
fof(t32_waybel27,axiom,( ! [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) ) => k1_waybel26(A,k9_waybel18) = k2_waybel27(A,k2_yellow_1(k1_tarski(k5_numbers))) ) )).
fof(t32_waybel29,axiom,( ! [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] : ( ( 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] : ( ( 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))) ) ) ) )).
fof(t32_waybel30,axiom,( ! [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_waybel_2(A) & l1_waybel_9(A) ) => ! [B] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ? [D] : ( 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] : ( 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) ) ) ) )).
fof(t32_waybel34,axiom,( ! [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] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & v8_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( E = C & F = D & r1_waybel_3(A,C,D) ) => r1_waybel_3(B,E,F) ) ) ) ) ) ) ) )).
fof(t32_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t32_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t32_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(t32_waybel_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_yellow_1(A,B)))) => ! [D] : ( m1_subset_1(D,A) => k4_waybel_3(A,B,k1_yellow_0(k4_yellow_1(A,B),C),D) = k1_yellow_0(k3_waybel_3(A,B,D),k5_waybel_3(A,B,D,C)) ) ) ) ) ) )).
fof(t32_waybel_4,axiom,( ! [A] : ( ( 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) ) )).
fof(t32_waybel_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( m2_pboole(E,A,D,k7_funcop_1(A,B)) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,B,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => k1_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))) = k1_funct_6(E) ) ) ) ) ) ) )).
fof(t32_waybel_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t32_waybel_7,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_waybel_3(A,B,C) <=> ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t32_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r3_waybel_9(A,B,C) & ! [D] : ( m2_yellow_6(D,A,B) => ~ r2_hidden(C,k10_yellow_6(A,D)) ) ) ) ) ) )).
fof(t32_weddwitt,axiom,( ! [A] : ( ( ~ 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)),k5_numbers) ) )).
fof(t32_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(D,B) & r2_hidden(E,C) & k3_metric_1(A,D,E) = k8_weierstr(A,B,C) ) ) ) ) ) ) ) )).
fof(t32_wellord1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( v2_wellord1(B) => k1_relat_1(k2_wellord1(B,k1_wellord1(B,A))) = k1_wellord1(B,A) ) ) )).
fof(t32_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(D,k5_numbers) & k3_int_2(C,D) = 1 & k1_newton(A,C) = k1_newton(B,D) & ! [E] : ( v7_ordinal1(E) => ~ ( A = k1_newton(E,D) & B = k1_newton(E,C) ) ) ) ) ) ) ) )).
fof(t32_xboole_1,axiom,( ! [A] : ! [B] : ( k4_xboole_0(A,B) = k4_xboole_0(B,A) => A = B ) )).
fof(t32_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k9_xboolean(A,k4_xboolean(A,B)) = k3_xboolean(A) ) ) )).
fof(t32_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k6_xcmplx_0(A,C) = k6_xcmplx_0(k2_xcmplx_0(A,B),k2_xcmplx_0(C,B)) ) ) ) )).
fof(t32_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,k5_numbers) => r1_xxreal_0(k2_xcmplx_0(A,B),B) ) ) ) )).
fof(t32_xtuple_0,axiom,( ! [A] : ! [B] : r1_tarski(k11_xtuple_0(k3_xboole_0(A,B)),k3_xboole_0(k11_xtuple_0(A),k11_xtuple_0(B))) )).
fof(t32_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(B,C) & ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(A,D) & r1_xxreal_0(B,D) ) => r1_xxreal_0(C,D) ) ) ) => C = k4_xxreal_0(A,B) ) ) ) ) )).
fof(t32_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( ~ r1_xxreal_0(B,A) & v1_xboole_0(k3_xxreal_1(A,B)) ) ) ) )).
fof(t32_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( ~ r1_xxreal_0(B,A) => k1_xxreal_2(k4_xxreal_1(A,B)) = B ) ) ) )).
fof(t32_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t32_yellow10,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t32_yellow12,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( ( 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)))) ) ) ) ) ) )).
fof(t32_yellow14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( 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))) ) ) ) ) )).
fof(t32_yellow16,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_yellow_1(A,B)))) => ( r1_yellow_0(k4_yellow_1(A,B),C) => ! [D] : ( m1_subset_1(D,A) => k4_waybel_3(A,B,k1_yellow_0(k4_yellow_1(A,B),C),D) = k1_yellow_0(k3_waybel_3(A,B,D),k5_waybel_3(A,B,D,C)) ) ) ) ) ) )).
fof(t32_yellow18,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_altcat_1(A))) => k3_yellow18(k7_altcat_1(A),B) = B ) ) )).
fof(t32_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_compts_1(A) <=> ! [B] : ( ( ~ v1_xboole_0(B) & v1_subset_1(B,u1_struct_0(k2_yellow_1(k2_struct_0(A)))) & v2_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(B,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))))) ) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r1_waybel_7(A,B,C) ) ) ) ) )).
fof(t32_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_altcat_2(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l1_altcat_1(B) ) => ! [C] : ( ( v8_functor0(C,A,B) & v10_functor0(C,A,B) & l2_functor0(C,A,B) ) => ( v17_functor0(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k1_altcat_1(A,D,E) != k1_xboole_0 => ! [F] : ( m1_subset_1(F,k1_altcat_1(A,D,E)) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(t32_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( B = k1_yellow_0(A,C) <=> ( r2_lattice3(A,C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_lattice3(A,C,D) => r1_orders_2(A,B,D) ) ) ) ) ) ) )).
fof(t32_yellow_2,axiom,( ! [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] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t32_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t32_yellow_4,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t32_yellow_5,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t32_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m2_yellow_6(C,A,B) => r1_tarski(k10_yellow_6(A,B),k10_yellow_6(A,C)) ) ) ) )).
fof(t32_yellow_7,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_yellow_0(A) <=> v3_yellow_0(k7_lattice3(A)) ) ) )).
fof(t32_yellow_9,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ( r1_tarski(B,u1_pre_topc(A)) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & ! [E] : ( 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)))) ) ) ) ) )).
fof(t32_zf_fund1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ( k3_funct_2(k4_ordinal1,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(k4_ordinal1,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) ) ) ) ) )).
fof(t32_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ( k11_zf_lang(A,C) = k11_zf_lang(B,D) => ( A = B & C = D ) ) ) ) ) ) )).
fof(t32_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( 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) ) ) ) )).
fof(t32_zfmisc_1,axiom,( ! [A] : ! [B] : ( r1_tarski(B,k1_tarski(A)) <=> ( B = k1_xboole_0 | B = k1_tarski(A) ) ) )).
fof(t32_zfrefle1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t32_zmodul01,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t32_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => r1_zmodul02(A,k23_zmodul02(A,k2_xcmplx_0(C,D),B),k22_zmodul02(A,k23_zmodul02(A,C,B),k23_zmodul02(A,D,B))) ) ) ) ) )).
fof(t32_zmodul03,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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) & v1_zmodul03(B) & l1_zmodul01(B) ) => ! [C] : ( m1_zmodul03(C,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_zmodul02(A,B)))) => ( D = a_3_0_zmodul03(A,B,C) => v1_vectsp_7(D,k9_int_3(A),k12_zmodul02(A,B)) ) ) ) ) ) )).
fof(t330_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t331_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t332_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t333_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t334_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t335_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t336_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t337_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t338_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t339_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t33_abcmiz_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(k3_finseq_1(B),C) => k1_funct_1(k1_rewrite1(A,B),k2_xcmplx_0(k3_finseq_1(A),C)) = k1_funct_1(B,k1_nat_1(C,1)) ) ) ) ) )).
fof(t33_abcmiz_1,axiom,( ! [A] : ( 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) ) )).
fof(t33_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => m1_abcmiz_a(B,A,B) ) ) )).
fof(t33_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t33_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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 ) ) ) ) ) )).
fof(t33_afinsq_1,axiom,( ! [A] : ! [B] : ( ( 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,k5_numbers) = A ) ) ) )).
fof(t33_afinsq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t33_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t33_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t33_algspec1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( v2_funct_1(C) & r1_tarski(k3_xboole_0(u4_struct_0(A),k10_xtuple_0(C)),k9_xtuple_0(C)) ) => r1_algspec1(A,B,C) ) ) ) ) )).
fof(t33_algstr_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k14_algstr_4(A))) => ! [C] : ( 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)) ) ) )).
fof(t33_altcat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_altcat_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( C = E & D = F ) => ( k1_altcat_1(B,E,F) = k1_xboole_0 | ! [G] : ( m1_subset_1(G,k1_altcat_1(B,E,F)) => m1_subset_1(G,k1_altcat_1(A,C,D)) ) ) ) ) ) ) ) ) ) )).
fof(t33_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v16_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t33_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t33_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ~ ( r1_analmetr(A,G,H) & r2_analort(A,G,H,B,D,C,E) & r2_analort(A,G,H,B,D,C,F) & ~ r2_analort(A,G,H,B,D,E,F) & ~ r2_analort(A,G,H,B,D,F,E) ) ) ) ) ) ) ) ) ) )).
fof(t33_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => ~ ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( 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 = k5_numbers & G = k5_numbers & H = k5_numbers & I = k5_numbers ) ) ) ) ) ) ) ) ) ) & ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t33_aofa_000,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_freealg(B,A) => r1_tarski(k10_aofa_000(A),B) ) ) )).
fof(t33_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,D),u8_aofa_a00(A))) => ! [F] : ( v1_xboolean(F) => ( k22_aofa_a00(A,D,E) = k3_xboolean(F) <=> E = F ) ) ) ) ) ) ) )).
fof(t33_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [E] : ( ( v1_aofa_i00(E,A,B,D) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),D) ) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),E) => ! [G] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t33_armstrng,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( 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) ) ) )).
fof(t33_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( 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 ) ) ) ) )).
fof(t33_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v4_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v4_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) => ( r1_xxreal_0(k1_seq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)),k5_numbers) | r2_hidden(A,k8_asympt_0(B)) ) ) ) ) )).
fof(t33_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( k9_xtuple_0(B) = k1_autalg_1(A) & ! [C] : ( r2_hidden(C,k1_autalg_1(A)) => k1_funct_1(B,C) = k16_funcop_1(k5_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)))))) ) ) ) ) )).
fof(t33_bagorder,axiom,( ! [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) ) => ! [B] : ( 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)))) ) ) ) )).
fof(t33_bcialg_1,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_hidden(k1_bcialg_1(A,B,C),k5_bcialg_1(A)) ) ) ) )).
fof(t33_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => v10_bcialg_1(k1_bcialg_2(A,k4_struct_0(A),k2_bcialg_1(A,B),C),A) ) ) ) )).
fof(t33_bcialg_3,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t33_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t33_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( ( v8_bcialg_1(F) & m1_bcialg_5(F,A,B,D,E) ) => ( r1_xxreal_0(k3_bcialg_5(A,B,D,E),C) => ( v8_bcialg_1(F) & m1_bcialg_5(F,C,C,C,C) ) ) ) ) ) ) ) ) )).
fof(t33_bcialg_6,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_subset_1(D,u1_struct_0(A),k5_bcialg_1(A)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t33_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( ( v3_bciideal(B,A) & m2_bcialg_1(B,A) ) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t33_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k3_bhsp_1(A,B),k3_bhsp_1(A,C))),k3_bhsp_1(A,k5_algstr_0(A,B,C))) ) ) ) )).
fof(t33_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_bhsp_2(D,A) & k1_bhsp_2(A,D) = C ) => ( v2_comseq_2(k2_bhsp_2(A,k4_normsp_1(A,k5_bhsp_1(A,D,B),k3_rlvect_1(A,C,B)))) & k1_seq_2(k2_bhsp_2(A,k4_normsp_1(A,k5_bhsp_1(A,D,B),k3_rlvect_1(A,C,B)))) = k5_numbers ) ) ) ) ) ) )).
fof(t33_bhsp_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ~ ( ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,A,D) = k1_power(D,k9_nat_1(k1_numbers,k2_bhsp_2(B,C),D)) ) & ? [D] : ( v7_ordinal1(D) & ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(D,E) => r1_xxreal_0(1,k9_nat_1(k1_numbers,A,E)) ) ) ) & v1_bhsp_4(C,B) ) ) ) ) )).
fof(t33_bilinear,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t33_binari_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_int_1(B) => ? [C] : ( m1_subset_1(C,k6_margrel1) & k2_binari_4(k2_xcmplx_0(A,1),B) = k8_finseq_1(k6_margrel1,k2_binari_4(A,B),k12_finseq_1(k6_margrel1,C)) ) ) ) )).
fof(t33_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t33_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t33_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_topmetr)) => ! [B] : ( 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))) ) ) ) ) )).
fof(t33_borsuk_5,axiom,( ! [A] : ( 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 ) ) )).
fof(t33_borsuk_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t33_borsuk_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => k11_toprealc(3,A) = k11_finseq_1(k1_square_1(k1_euclid_5(A)),k1_square_1(k2_euclid_5(A)),k1_square_1(k3_euclid_5(A))) ) )).
fof(t33_bspace,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k7_bspace(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_bspace(A))) => ! [D] : ( 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))) ) ) ) ) )).
fof(t33_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t33_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t33_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t33_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(t33_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( 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)) ) ) ) )).
fof(t33_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(E,A) => ( r3_bvfunc_2(A,D,B,E) => r2_funct_2(A,k6_margrel1,k7_bvfunc_2(A,k5_bvfunc_1(A,C,D),B,E),k5_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),D)) ) ) ) ) ) ) )).
fof(t33_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(F,A) => r1_bvfunc_1(A,k2_bvfunc_1(A,k6_bvfunc_2(A,k9_bvfunc_1(A,E,D),B,F),k7_bvfunc_2(A,k2_bvfunc_1(A,C,E),B,F)),k7_bvfunc_2(A,k2_bvfunc_1(A,C,D),B,F)) ) ) ) ) ) ) )).
fof(t33_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t33_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t33_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(t33_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v4_normsp_0(k11_c0sp1(A)) & v3_normsp_0(k11_c0sp1(A)) & v2_normsp_1(k11_c0sp1(A)) ) ) )).
fof(t33_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => k4_struct_0(k9_c0sp2(A)) = k1_c0sp2(A,k5_numbers) ) )).
fof(t33_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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) ) ) ) )).
fof(t33_card_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(t33_card_2,axiom,( ! [A] : ! [B] : r1_ordinal1(k1_card_1(k2_xboole_0(A,B)),k1_card_2(k1_card_1(A),k1_card_1(B))) )).
fof(t33_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_card_3(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t33_card_5,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ! [B] : ( ( ~ v1_finset_1(B) & v1_card_1(B) ) => r1_ordinal1(k6_card_3(k2_card_5(A,B)),k3_card_2(A,B)) ) ) )).
fof(t33_card_fil,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ( v7_card_fil(A) => v1_card_5(A) ) ) )).
fof(t33_card_fin,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( k8_relat_1(B,k1_tarski(C)) = k1_xboole_0 => k2_card_fin(A,B,C) = k3_tarski(k10_xtuple_0(A)) ) ) ) )).
fof(t33_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,B,C) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t33_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,k6_cat_2(A,C),B) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => k3_funct_2(u1_struct_0(A),u1_struct_0(B),k7_cat_1(A,B,k11_cat_2(A,C,B,D,F)),E) = k1_binop_1(k7_cat_1(k6_cat_2(A,C),B,D),E,F) ) ) ) ) ) ) )).
fof(t33_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_cat_1(A,k2_cat_4(A,B,C),k2_cat_4(A,C,B)) ) ) ) )).
fof(t33_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => k5_card_1(k2_catalan2(k3_xcmplx_0(2,A),A)) = k7_xcmplx_0(k4_newton(A,k3_xcmplx_0(2,A)),k1_nat_1(A,1)) ) )).
fof(t33_catalg_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t33_cayldick,axiom,( k6_algstr_0(k4_cayldick(k4_cayldick(k4_cayldick(k3_cayldick))),k5_cayldick(k4_cayldick(k4_cayldick(k3_cayldick)),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k5_struct_0(k3_cayldick),k4_struct_0(k3_cayldick))),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)))),k5_cayldick(k4_cayldick(k4_cayldick(k3_cayldick)),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k5_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick))),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick))))) = k5_cayldick(k4_cayldick(k4_cayldick(k3_cayldick)),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_algstr_0(k3_cayldick,k5_struct_0(k3_cayldick)))),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)))) )).
fof(t33_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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))) ) ) ) )).
fof(t33_cfcont_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t33_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)))) ) ) )).
fof(t33_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => r1_tarski(k8_cgames_1(A),k11_cgames_1(A)) ) )).
fof(t33_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(B)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(B)) => ! [E] : ( 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] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(B)) => ( r2_hidden(k1_funct_1(C,F),k2_chain_1(B,E,F)) & r2_hidden(k1_funct_1(D,F),k2_chain_1(B,E,F)) ) ) ) ) ) ) ) ) )).
fof(t33_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v5_glib_001(B,A) & m3_glib_001(B,A) ) => ~ ( ~ v1_glib_001(B,A) & ~ r1_xxreal_0(k3_finseq_1(B),3) & ? [C] : ( 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) ) ) ) ) )).
fof(t33_circcmb3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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)) ) ) )).
fof(t33_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(C,F))) => ! [H] : ( m1_subset_1(H,k4_card_3(u3_msualg_1(A,D))) => ! [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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t33_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r3_pua2mss1(A,B,C,D) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(E,k3_msafree2(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t33_classes1,axiom,( ! [A] : ( v3_ordinal1(A) => r1_tarski(k4_classes1(A),k4_classes1(k1_ordinal1(A))) ) )).
fof(t33_classes2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( r2_hidden(A,k2_ordinal1(k1_classes1(B))) => r1_ordinal1(k1_card_1(k4_classes1(A)),k1_card_1(k1_classes1(B))) ) ) )).
fof(t33_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k14_clopban1(A,B))) => ( C = k4_struct_0(k14_clopban1(A,B)) => k5_numbers = k2_normsp_0(k14_clopban1(A,B),C) ) ) ) ) )).
fof(t33_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v8_valued_0(k5_normsp_0(A,B)) & ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k3_xcmplx_0(k2_power(2,D),k1_funct_1(k5_normsp_0(A,B),k2_power(2,D))) ) ) => ( v2_clopban3(B,A) <=> v1_series_1(C) ) ) ) ) ) )).
fof(t33_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => k7_clopban4(A,B) = k1_clopban3(A,k1_clopban4(A,B)) ) ) )).
fof(t33_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_closure2(C,A,B,k2_closure2(A,B)) => ! [D] : ( m1_closure2(D,A,B,k2_closure2(A,B)) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t33_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( m1_clvect_1(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ( E = B => k1_clvect_1(D,E,C) = k1_clvect_1(A,B,C) ) ) ) ) ) ) )).
fof(t33_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_clvect_2(D,A) & k1_clvect_2(A,D) = C ) => ( v2_comseq_2(k2_clvect_2(A,k4_normsp_1(A,k5_bhsp_1(A,D,B),k3_rlvect_1(A,C,B)))) & k1_seq_2(k2_clvect_2(A,k4_normsp_1(A,k5_bhsp_1(A,D,B),k3_rlvect_1(A,C,B)))) = k5_numbers ) ) ) ) ) ) )).
fof(t33_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k1_power(D,k9_nat_1(k1_numbers,k2_clvect_2(A,B),D)) ) & ? [D] : ( v7_ordinal1(D) & ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(D,E) => r1_xxreal_0(1,k9_nat_1(k1_numbers,C,E)) ) ) ) & v1_clvect_3(B,A) ) ) ) ) )).
fof(t33_coh_sp,axiom,( ! [A] : r2_hidden(k4_tarski(k1_xboole_0,k1_xboole_0),k16_coh_sp(A)) )).
fof(t33_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v8_cohsp_1(A) ) => ( v1_classes1(k9_xtuple_0(A)) => ! [B] : ! [C] : ( r2_hidden(k4_tarski(B,C),k7_cohsp_1(A)) => v1_finset_1(B) ) ) ) )).
fof(t33_combgras,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ( ( r1_xxreal_0(2,A) & r1_ordinal1(k1_nat_1(A,2),k1_card_1(B)) ) => ! [C] : ( l1_combgras(C,k1_combgras(A,B),k1_combgras(A,B)) => ~ ( v7_combgras(C,k1_combgras(A,B)) & ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t33_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v5_waybel23(A) => ! [B] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t33_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k8_complex1(k4_xcmplx_0(A)) = k4_xcmplx_0(k8_complex1(A)) ) )).
fof(t33_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k1_complex2(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(k1_complex2(A,C),k1_complex2(B,C)) ) ) ) )).
fof(t33_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ( B != k4_struct_0(k1_complfld) => k3_vectsp_1(k1_complfld,A,k11_algstr_0(k1_complfld,B)) = k8_group_1(k1_complfld,A,B) ) ) ) )).
fof(t33_complsp2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t33_compos_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( l1_compos_1(B) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ! [D] : ( ( 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] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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)))) ) ) ) ) ) ) )).
fof(t33_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( v6_compos_0(D,u1_compos_1(A)) & m1_subset_1(D,u1_compos_1(A)) ) => ! [E] : ( ( 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 ) ) ) ) ) )).
fof(t33_comptrig,axiom,( k10_xtuple_0(k2_partfun1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k28_sin_cos,k3_xcmplx_0(2,k28_sin_cos)))) = k1_rcomp_1(k4_xcmplx_0(1),1) )).
fof(t33_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k19_margrel1(k4_comput_1(B,A)) = B ) ) )).
fof(t33_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k36_valued_1(k4_ordinal1,k2_numbers,k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)),k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,A)) ) ) )).
fof(t33_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ! [C] : ( v7_ordinal1(C) => k9_nat_1(k2_numbers,B,C) = k9_nat_1(k2_numbers,A,k5_numbers) ) => r2_funct_2(k4_ordinal1,k2_numbers,k10_comseq_3(k1_valued_0(k2_numbers,A,1)),k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k1_valued_0(k2_numbers,k10_comseq_3(A),1),B)) ) ) ) )).
fof(t33_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( v3_conlat_1(B,A) & ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) & l2_conlat_1(B,A) ) => ! [C] : ( ( v3_conlat_1(C,A) & ~ v4_conlat_1(C,A) & v6_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) ) ) ) )).
fof(t33_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_connsp_1(B,A) => v4_pre_topc(B,A) ) ) ) )).
fof(t33_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => v2_connsp_1(k6_connsp_3(A,B,C),A) ) ) ) ) )).
fof(t33_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( v1_xreal_0(C) => k1_convex1(A,B,C) = k1_xboole_0 ) ) ) )).
fof(t33_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_convex4(B,A) => r1_convex4(A,k8_convex4(A,k8_convex4(A,B)),B) ) ) )).
fof(t33_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( m1_subset_1(E,k1_qc_lang1(A)) => ! [F] : ( m1_subset_1(F,k5_finsub_1(k3_qc_lang1(A))) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t33_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ~ ( r2_hidden(C,k1_cqc_the1(A,B)) & ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t33_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t33_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t33_dickson,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( ( v3_dickson(A) & v4_dickson(A) ) => v1_wellfnd1(k5_dickson(A)) ) ) )).
fof(t33_diff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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) = k2_xcmplx_0(k3_xcmplx_0(A,k9_diff_1(E,C,D)),k3_xcmplx_0(B,k9_diff_1(F,C,D))) ) ) ) ) ) ) )).
fof(t33_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( v1_xreal_0(F) => k1_funct_1(E,F) = k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(F)),k3_xcmplx_0(C,F)),D) ) => ! [F] : ( v1_xreal_0(F) => k1_funct_1(k5_diff_1(E,A),F) = k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,B),A),F),k3_xcmplx_0(C,A)) ) ) ) ) ) ) ) )).
fof(t33_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)) & v1_diff_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)))) ) => ( ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ( r1_xxreal_0(G,F) => k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,E,F),G) = k3_xcmplx_0(k3_xcmplx_0(k4_newton(G,F),k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(C,A),G),B)),k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(D,A),k7_nat_d(F,G)),k6_xcmplx_0(B,k3_xcmplx_0(G,A)))) ) ) ) => ( k1_funct_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_funct_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) ) ) ) ) ) ) ) )).
fof(t33_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k2_xcmplx_0(B,k7_xcmplx_0(A,2)),k5_numbers) & ~ r1_xxreal_0(k6_xcmplx_0(B,k7_xcmplx_0(A,2)),k5_numbers) & k1_funct_1(k5_diff_1(k3_taylor_1,A),B) != k1_funct_1(k3_taylor_1,k2_xcmplx_0(1,k7_xcmplx_0(A,k6_xcmplx_0(B,k7_xcmplx_0(A,2))))) ) ) ) )).
fof(t33_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_yellow_0(A,B)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_yellow_0(A,B))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t33_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t33_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => ! [C] : ( m3_dist_2(C,A,B) => k9_dist_2(A,B,C) = k1_funct_1(k2_dist_2(A,B),k1_dist_2(A,C)) ) ) ) )).
fof(t33_e_siec,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t33_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ( v2_ec_pf_1(B,A) <=> k2_ec_pf_1(A,B) = 1 ) ) ) )).
fof(t33_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k9_int_3(A))) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t33_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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] : B != k1_tarski(C) ) ) ) )).
fof(t33_entropy1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( 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] : ( v7_ordinal1(D) => ( r1_xxreal_0(1,D) => ( r1_xxreal_0(k3_finseq_1(B),D) | k1_matrprob(A,C,k1_nat_1(D,1)) = k8_finseq_1(A,k1_matrprob(A,C,D),k1_matrprob(A,B,k1_nat_1(D,1))) ) ) ) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(D,k4_finseq_1(C)) & r2_hidden(E,k4_finseq_1(C)) & r1_xxreal_0(D,E) ) => ! [F] : ( v7_ordinal1(F) => ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t33_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k4_enumset1(A,A,B,C,D,E) = k3_enumset1(A,B,C,D,E) )).
fof(t33_eqrel_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t33_equation,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t33_euclid,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => k5_algstr_0(k15_euclid(2),A,B) = k19_euclid(k6_xcmplx_0(k17_euclid(A),k17_euclid(B)),k6_xcmplx_0(k18_euclid(A),k18_euclid(B))) ) ) )).
fof(t33_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => r1_xxreal_0(k5_numbers,k22_rvsum_1(B,B)) ) ) )).
fof(t33_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( r2_hidden(k3_euclid_3(A),k2_rcomp_1(k5_numbers,k28_sin_cos)) <=> ~ r1_xxreal_0(k18_euclid(A),k5_numbers) ) ) )).
fof(t33_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => k22_rvsum_1(k8_euclid(A,B,C),k8_euclid(A,B,C)) = k2_xcmplx_0(k6_xcmplx_0(k22_rvsum_1(B,B),k3_xcmplx_0(2,k22_rvsum_1(B,C))),k22_rvsum_1(C,C)) ) ) ) )).
fof(t33_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(3))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(3))) => k6_euclid_5(A,B,C) = k6_euclid_5(B,C,A) ) ) ) )).
fof(t33_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( 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 & k3_xcmplx_0(2,k4_euclid_3(A,C,B)) != k4_euclid_3(A,D,B) & k3_xcmplx_0(2,k6_xcmplx_0(k4_euclid_3(A,C,B),k28_sin_cos)) != k4_euclid_3(A,D,B) ) ) ) ) ) ) ) ) )).
fof(t33_euclid_8,axiom,( ! [A] : ( 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_funct_1(A,1))),k9_euclid(3,k3_euclid_8,k1_funct_1(A,2))),k9_euclid(3,k4_euclid_8,k1_funct_1(A,3))) ) )).
fof(t33_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ( ( r2_euclidlp(A,B,C) & r2_euclidlp(A,C,D) ) => r2_euclidlp(A,B,D) ) ) ) ) ) )).
fof(t33_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ~ ( D != B & D != C & k1_funct_1(k9_funct_7(A,B,C),D) != k1_funct_1(A,D) ) ) )).
fof(t33_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ( 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)),k5_numbers) | k8_extpro_1(A,B,C,D) = k2_xcmplx_0(E,k8_extpro_1(A,B,C,k5_extpro_1(A,B,C,D,E))) ) ) ) ) ) ) ) )).
fof(t33_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_circcomb(A) & v2_circcomb(A) & v3_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v4_msafree2(C,A) & v4_circcomb(C,A) & v6_circcomb(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msafree2(D,B) & v4_circcomb(D,B) & v6_circcomb(D,B) & l3_msualg_1(D,B) ) => ! [E] : ( m1_subset_1(E,k4_card_3(u3_msualg_1(k2_circcomb(A,B),k3_circcomb(A,B,C,D)))) => ! [F] : ( 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] : ( r2_hidden(G,u1_struct_0(B)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t33_facirc_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,k1_nat_1(A,1)) & v1_finseq_1(B) ) => ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & ? [D] : B = k7_finseq_1(C,k9_finseq_1(D)) ) ) ) )).
fof(t33_fcont_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t33_fdiff_10,axiom,( ! [A] : ( ( 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,k18_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)),A),B) = k6_xcmplx_0(k2_xcmplx_0(k1_square_1(k1_funct_1(k18_sin_cos,B)),k3_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k16_sin_cos,B)),k1_funct_1(k18_sin_cos,B))),k1_square_1(k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t33_fdiff_11,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fdiff_9,k1_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fdiff_9,k1_sin_cos9),A),B) = k2_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,B),k1_funct_1(k1_sin_cos9,B)),k1_square_1(k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(1,k3_xcmplx_0(k1_funct_1(k18_sin_cos,B),k2_xcmplx_0(1,k1_square_1(B))))) ) ) ) ) ) )).
fof(t33_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ~ ( r2_hidden(C,k3_limfunc1(A)) & r1_xxreal_0(k1_fdiff_1(B,C),k5_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))) ) ) ) ) )).
fof(t33_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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(k7_xcmplx_0(3,2))),k4_xcmplx_0(k7_xcmplx_0(2,k3_xcmplx_0(3,B)))))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => ( k1_funct_1(D,E) = k6_xcmplx_0(A,k3_xcmplx_0(B,E)) & B != k5_numbers & ~ r1_xxreal_0(k1_funct_1(D,E),k5_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(k7_xcmplx_0(3,2))),k4_xcmplx_0(k7_xcmplx_0(2,k3_xcmplx_0(3,B)))),C) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_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(k7_xcmplx_0(3,2))),k4_xcmplx_0(k7_xcmplx_0(2,k3_xcmplx_0(3,B)))),C),E) = k6_prepower(k6_xcmplx_0(A,k3_xcmplx_0(B,E)),k7_xcmplx_0(1,2)) ) ) ) ) ) ) ) ) )).
fof(t33_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k22_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,C,k22_sin_cos),k1_taylor_1(2))),k3_taylor_1) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_1(C,D) = 1 ) ) ) => ( r2_fdiff_1(B,A) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_1(k2_fdiff_1(B,A),D) = k7_xcmplx_0(k6_xcmplx_0(1,k1_funct_1(k22_sin_cos,D)),k2_xcmplx_0(1,k1_funct_1(k22_sin_cos,D))) ) ) ) ) ) ) ) )).
fof(t33_fdiff_7,axiom,( ! [A] : ( ( 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,k18_sin_cos))) & ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & r1_xxreal_0(B,k5_numbers) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k18_sin_cos),A),B) = k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k16_sin_cos,k1_funct_1(k3_taylor_1,B)),B)) ) ) ) ) ) )).
fof(t33_fdiff_8,axiom,( ! [A] : ( ( 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,k27_sin_cos))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k27_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k27_sin_cos),A),B) = k6_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(k1_funct_1(k18_sin_cos,B),k1_funct_1(k16_sin_cos,B)),B),k7_xcmplx_0(k1_funct_1(k3_taylor_1,B),k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t33_fdiff_9,axiom,( ! [A] : ( ( 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(k5_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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(1,k1_funct_1(k16_sin_cos,B)),k1_square_1(B))),k7_xcmplx_0(k7_xcmplx_0(k1_funct_1(k18_sin_cos,B),B),k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) ) )).
fof(t33_fib_num2,axiom,( ~ r1_xxreal_0(k1_fib_num,k5_numbers) )).
fof(t33_fib_num3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( v7_ordinal1(C) => k11_newton(k1_nat_1(k3_fib_num3(A,B,k1_nat_1(C,1)),k3_fib_num3(A,B,k1_nat_1(k1_nat_1(C,1),1))),2) = k1_nat_1(k1_nat_1(k11_newton(k3_fib_num3(A,B,k1_nat_1(C,1)),2),k2_nat_1(k2_nat_1(2,k3_fib_num3(A,B,k1_nat_1(C,1))),k3_fib_num3(A,B,k1_nat_1(k1_nat_1(C,1),1)))),k11_newton(k3_fib_num3(A,B,k1_nat_1(k1_nat_1(C,1),1)),2)) ) ) ) )).
fof(t33_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(2,A) => k1_fib_num3(k2_xcmplx_0(k3_xcmplx_0(2,A),1)) = k1_int_1(k2_power(k1_fib_num,k2_xcmplx_0(k3_xcmplx_0(2,A),1))) ) ) )).
fof(t33_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_finseq_1(B,A) => ! [C] : ( m1_finseq_1(C,A) => k9_finseq_8(A,C,B) = k1_finseq_8(A,k6_finseq_8(A,C,B),B) ) ) ) )).
fof(t33_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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) ) ) ) )).
fof(t33_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t33_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( v14_lattices(A) => ! [B] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t33_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( ( k7_finseq_1(A,C) = k7_finseq_1(B,C) | k7_finseq_1(C,A) = k7_finseq_1(C,B) ) => A = B ) ) ) ) )).
fof(t33_finseq_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_finseq_1(D,B) => ! [E] : ( ( 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(k4_ordinal1,B,B,C,D,E) = k9_finseq_1(k1_funct_1(E,A)) ) ) ) ) ) )).
fof(t33_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : k9_finseq_1(A) != k10_finseq_1(B,C) )).
fof(t33_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : ( 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) ) ) ) )).
fof(t33_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => r1_tarski(k10_xtuple_0(k2_rfinseq(B,A,C)),k10_xtuple_0(C)) ) ) ) )).
fof(t33_finseq_6,axiom,( ! [A] : ! [B] : ( A != B => k6_finseq_4(k10_finseq_1(A,B),B) = k1_xboole_0 ) )).
fof(t33_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( ( 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)) ) => ( D = F | E = F | k2_finseq_7(A,k1_finseq_7(A,B,F,C),D,E) = k1_finseq_7(A,k2_finseq_7(A,B,D,E),F,C) ) ) ) ) ) ) ) ) )).
fof(t33_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,B) & m2_finseq_1(C,A) ) => ! [D] : ( ( v3_card_1(D,B) & m2_finseq_1(D,A) ) => ! [E] : ( ( 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(k4_ordinal1,A,k1_finseqop(A,A,A,E,C,D),k1_finseqop(A,A,A,E,D,C)) ) ) ) ) ) ) )).
fof(t33_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ( ( v2_fintopo2(A) & ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t33_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k7_fintopo3(A,B,1) = k12_fin_topo(A,B) ) ) )).
fof(t33_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t33_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k7_flang_1(A,B,k2_xcmplx_0(D,C)) = k6_flang_1(A,k7_flang_1(A,B,D),k7_flang_1(A,B,C)) ) ) ) )).
fof(t33_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k2_flang_1(A),k1_flang_2(A,B,C,D)) <=> ( C = k5_numbers | ( r1_xxreal_0(C,D) & r2_hidden(k2_flang_1(A),B) ) ) ) ) ) ) )).
fof(t33_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t33_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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(k9_fomodel0(A),k7_finseq_1(B,k9_finseq_1(C))) = k7_finseq_1(k1_funct_1(k9_fomodel0(A),B),C) ) ) ) ) )).
fof(t33_frechet,axiom,( v3_frechet(k3_frechet) )).
fof(t33_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t33_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( 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,k5_numbers),D) = u1_struct_0(C) ) ) ) ) )).
fof(t33_fsm_3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( 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))) ) ) ) ) )).
fof(t33_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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) ) ) ) ) ) )).
fof(t33_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( 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) ) ) ) ) )).
fof(t33_funct_1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) ) )).
fof(t33_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(t33_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t33_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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 ) ) ) )).
fof(t33_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) ) )).
fof(t33_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => k10_xtuple_0(k6_funct_6(A)) = k4_card_3(k2_funct_6(A)) ) )).
fof(t33_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : k1_funct_7(k1_funct_7(A,D,B),D,C) = k1_funct_7(A,D,C) ) )).
fof(t33_funct_8,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t33_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ v8_ordinal1(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,A),B),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)) ) ) ) )).
fof(t33_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_altcat_2(C) & l2_altcat_1(C) ) => ! [D] : ( ( v6_functor0(D,A,B) & v8_functor0(D,A,B) & l2_functor0(D,A,B) ) => ! [E] : ( l2_functor0(E,B,C) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t33_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t33_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D,C)) <=> ( r1_fuzzy_1(B,D) & r1_fuzzy_1(B,C) & ! [E] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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,D) & r1_fuzzy_1(E,C) ) => r1_fuzzy_1(E,B) ) ) ) ) ) ) ) ) )).
fof(t33_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D),k3_fuzzy_2(A,B,C)),k3_fuzzy_2(A,B,k2_fuzzy_2(A,D,C))) ) ) ) ) )).
fof(t33_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => r2_hidden(k1_xxreal_0,k2_relset_1(k6_numbers,B)) ) ) ) )).
fof(t33_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_algstr_0(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m2_finseq_2(F,u1_struct_0(C),k4_finseq_2(A,u1_struct_0(C))) => ! [G] : ( 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(k8_fvsum_1(A,C,F,G),B) = k5_algstr_0(C,D,E) ) ) ) ) ) ) ) ) )).
fof(t33_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ~ ( ~ 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)) ) ) )).
fof(t33_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t33_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v2_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ! [F] : ( m1_genealg1(F,E) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t33_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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)) = k5_numbers ) ) ) ) ) ) ) ) ) )).
fof(t33_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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) ) )).
fof(t33_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : r1_tarski(k21_glib_000(A,B),k20_glib_000(A,B)) ) )).
fof(t33_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m3_glib_001(D,A) => ! [E] : ( m3_glib_001(E,B) => ! [F] : ( m3_glib_001(F,B) => ( ( C = E & D = F ) => k7_glib_001(A,C,D) = k7_glib_001(B,E,F) ) ) ) ) ) ) ) )).
fof(t33_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v4_glib_002(B,A) & m1_glib_000(B,A) ) => ! [C] : ( ( v4_glib_002(C,A) & m1_glib_000(C,A) ) => ! [D] : ( ( r2_hidden(D,k24_glib_000(A,B)) & r2_hidden(D,k24_glib_000(A,C)) ) => r5_glib_000(B,C) ) ) ) ) )).
fof(t33_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_003(A) ) => ! [B] : ! [C] : ( r2_hidden(B,k7_glib_000(A)) => k1_funct_1(k6_glib_003(k12_glib_003(A,B,C)),B) = C ) ) )).
fof(t33_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( 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,o_1_1_glib_004(A))) ) ) )).
fof(t33_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_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_0(u1_struct_0(k15_euclid(2)),B,A,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k1_nat_1(A,1),1)),k7_xcmplx_0(1,2)),k19_euclid(k5_numbers,1)),k1_tops_1(k15_euclid(2),k3_goboard5(B,A,k5_numbers))) ) ) ) )).
fof(t33_goboard7,axiom,( ! [A] : ( ( ~ 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_0(k2_goboard2(A)),1) ) )).
fof(t33_goboard8,axiom,( ! [A] : ( ( ~ 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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,k7_nat_d(k1_matrix_0(k2_goboard2(A)),1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,k1_matrix_0(k2_goboard2(A)))),k7_xcmplx_0(1,2)),k19_euclid(1,k5_numbers)),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,k1_matrix_0(k2_goboard2(A))),k19_euclid(k4_xcmplx_0(1),1))),k3_topreal1(2,A)) ) )).
fof(t33_gobrd11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(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)) ) ) ) )).
fof(t33_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(D)) & r1_goboard1(u1_struct_0(k15_euclid(2)),D,E) & r2_hidden(k4_tarski(A,k1_nat_1(B,1)),k2_matrix_0(E)) & r2_hidden(k4_tarski(A,B),k2_matrix_0(E)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,B) ) => k5_gobrd13(D,E,C) = k3_goboard5(E,A,k7_nat_d(B,1)) ) ) ) ) ) ) )).
fof(t33_gobrd14,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t33_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_henmodel(B,A) & m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) ) => ~ ( v4_card_3(A) & v2_goedelcp(B,A) & ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t33_gr_cy_3,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t33_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t33_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_graph_1(B,A) => ? [C] : ( m2_finseq_1(C,u1_struct_0(A)) & r1_graph_2(A,C,B) ) ) ) )).
fof(t33_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v5_graph_1(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k10_graph_1(A,B) != k5_numbers ) ) )).
fof(t33_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v7_graph_1(D,A) & m2_graph_1(D,A) ) => ~ ( D = k1_xboole_0 & r3_graph_5(A,D,B,C) ) ) ) ) ) )).
fof(t33_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) => k4_finseq_1(k6_graphsp(k15_graphsp(A),B)) = k4_finseq_1(B) ) ) )).
fof(t33_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(k25_grcat_1(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t33_grfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( ( r1_tarski(D,C) & r2_hidden(B,A) & r1_tarski(k3_xboole_0(A,k9_xtuple_0(C)),k9_xtuple_0(D)) ) => k1_funct_1(C,B) = k1_funct_1(D,B) ) ) ) )).
fof(t33_groeb_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_ordinal1(A) ) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => r1_groeb_1(A,B,C,D) ) ) ) ) )).
fof(t33_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ! [G] : ( m2_ideal_1(G,k12_polynom1(A,C),F) => ! [H] : ( m2_ideal_1(H,k12_polynom1(A,C),F) => ! [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,k5_polynom1(A,C,D,E),F,k5_groeb_2(A,C,F,G,H),I) ) ) ) ) ) ) ) ) ) ) )).
fof(t33_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(E,k5_card_1(k3_polynom1(k15_pre_poly(A),C,D))) => r2_funct_2(k15_pre_poly(A),u1_struct_0(C),k5_polynom1(A,C,k5_groeb_3(A,B,C,D,E),k6_groeb_3(A,B,C,D,E)),D) ) ) ) ) ) ) )).
fof(t33_group_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( k5_group_1(B,k2_xcmplx_0(A,1),C) = k6_algstr_0(B,k5_group_1(B,A,C),C) & k5_group_1(B,k2_xcmplx_0(A,1),C) = k6_algstr_0(B,C,k5_group_1(B,A,C)) ) ) ) ) )).
fof(t33_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t33_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t33_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t33_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t33_group_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t33_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t33_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( 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 ) ) ) )).
fof(t33_groupp_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t33_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [D] : ( ( ~ 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),k2_xcmplx_0(k1_hausdorf(A,B,C),k1_hausdorf(A,C,D))) ) ) ) ) ) )).
fof(t33_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( ( v3_glib_002(D) & m1_glib_000(D,A) ) => ! [E] : ( m1_subset_1(E,k6_glib_000(D)) => ! [F] : ( m1_subset_1(F,k6_glib_000(D)) => ( ( B = E & C = F ) => k2_helly(A,B,C) = k2_helly(D,E,F) ) ) ) ) ) ) ) )).
fof(t33_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,k1_complfld) ) => ! [C] : ( ( 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] : ( 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))) ) ) ) ) )).
fof(t33_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,u1_struct_0(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A)))) ) => ~ ( B != k1_tarski(k1_xboole_0) & ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ~ ( r2_hidden(C,B) & C != k1_xboole_0 ) ) ) ) ) )).
fof(t33_hfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t33_hilbasis,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & 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) ) )).
fof(t33_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(t33_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( 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)) ) ) )).
fof(t33_hilbert3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( m1_hilbert3(C,B) => k5_hilbert3(B,C,k1_hilbert2(A)) = k1_funct_1(C,A) ) ) ) )).
fof(t33_hurwitz,axiom,( ! [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) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r1_polynom5(A,B,C) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ r2_funct_2(k4_ordinal1,u1_struct_0(A),B,k13_polynom3(A,k3_hurwitz(A,C,1),D)) ) ) ) ) ) )).
fof(t33_idea_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( v1_int_2(k1_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 ) ) ) ) ) )).
fof(t33_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m2_ideal_1(C,A,B) ) => ? [D] : ( m2_ideal_1(D,A,B) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_relset_1(k4_ordinal1,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) ) ) ) ) ) )).
fof(t33_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t33_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ 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] : ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t33_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r3_pua2mss1(A,B,C,D) => ! [E] : ( l3_msualg_1(E,B) => ! [F] : ( l3_msualg_1(F,B) => ! [G] : ( m2_pboole(G,u1_struct_0(B),u3_msualg_1(B,E),u3_msualg_1(B,F)) => ! [H] : ( 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] : ( m1_subset_1(I,u4_struct_0(A)) => ! [J] : ( 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] : ( m1_subset_1(K,k3_msualg_1(B,J,E)) => ! [L] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t33_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => k2_xcmplx_0(k2_int_1(A),B) = k2_int_1(k2_xcmplx_0(A,B)) ) ) )).
fof(t33_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => k2_int_2(A,B) = k2_int_2(k1_int_2(A),k1_int_2(B)) ) ) )).
fof(t33_int_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( v7_ordinal1(C) => ( ( r2_hidden(C,k1_relset_1(k4_ordinal1,B)) & r1_nat_d(A,k1_recdef_1(B,C)) ) => r1_nat_d(A,k3_wsierp_1(B)) ) ) ) ) )).
fof(t33_int_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t33_integr11,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k7_xcmplx_0(1,2)))) & B = k1_taylor_1(2) ) => ( r2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,B,k7_xcmplx_0(1,2)),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(k2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,B,k7_xcmplx_0(1,2)),A),C) = C ) ) ) ) ) ) )).
fof(t33_integr12,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k7_xcmplx_0(k1_square_1(k1_funct_1(k16_sin_cos,D)),k1_square_1(k1_funct_1(k18_sin_cos,D))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_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) = k6_xcmplx_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_partfun2(k1_numbers,C)),k2_seq_4(A)),k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_partfun2(k1_numbers,C)),k3_seq_4(A))) ) ) ) ) )).
fof(t33_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(k1_square_1(D),k1_square_1(k1_funct_1(k18_sin_cos,k7_xcmplx_0(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)),k26_sin_cos))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,C)),k26_sin_cos),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,C)),k26_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t33_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k6_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(1,k1_funct_1(k16_sin_cos,D)),D),k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k3_taylor_1,D),k1_funct_1(k18_sin_cos,D)),k1_square_1(k1_funct_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) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k2_fdiff_9),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k2_fdiff_9),k3_seq_4(A))) ) ) ) ) )).
fof(t33_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => k12_integr15(C,B,A,D) = k6_euclid(A,k12_integr15(B,C,A,D)) ) ) ) ) )).
fof(t33_integra1,axiom,( ! [A] : ( ( v5_valued_0(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( 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) ) ) ) ) ) )).
fof(t33_integra2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => ! [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_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)) = k6_xcmplx_0(k12_integra1(A,B),k12_integra1(A,C)) ) ) ) ) ) )).
fof(t33_integra8,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k9_xtuple_0(k26_sin_cos)) => ( r2_fdiff_1(k26_sin_cos,A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k26_sin_cos,A),B) = k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,B))) ) ) ) ) ) )).
fof(t33_integra9,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( ~ 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] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => r1_xxreal_0(k5_numbers,k1_funct_1(k1_integra5(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,A,A),B),C)) ) ) ) => r1_xxreal_0(k5_numbers,k1_integra9(B,A,A)) ) ) ) )).
fof(t33_interva1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_interva1(B,A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ! [C] : ( ( ~ 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 ) ) )).
fof(t33_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => r2_hidden(k3_intpro_1(A,k4_intpro_1(A,A)),k8_intpro_1) ) )).
fof(t33_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k7_xcmplx_0(k7_newton(B),k7_newton(A)),k5_numbers) ) ) )).
fof(t33_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t33_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,C) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => k8_cat_1(A,k6_cat_2(B,C),k8_isocat_2(A,B,C,D,E),F) = k7_cat_2(B,C,k8_cat_1(A,B,D,F),k8_cat_1(A,C,E,F)) ) ) ) ) ) ) )).
fof(t33_isomichi,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t33_jgraph_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( r1_xxreal_0(k9_complex1(k17_euclid(A)),k12_euclid(A)) & r1_xxreal_0(k9_complex1(k18_euclid(A)),k12_euclid(A)) ) ) )).
fof(t33_jgraph_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( 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] : ( 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) = k7_xcmplx_0(k7_xcmplx_0(k18_euclid(C),k17_euclid(C)),k17_euclid(C)) ) ) & ! [C] : ( 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) = k5_numbers ) ) ) => v5_pre_topc(B,k1_pre_topc(k15_euclid(2),A),k3_topmetr) ) ) ) )).
fof(t33_jgraph_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( 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] : ( 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) = k3_xcmplx_0(k17_euclid(C),k3_square_1(k2_xcmplx_0(1,k1_square_1(k7_xcmplx_0(k18_euclid(C),k17_euclid(C)))))) ) ) & ! [C] : ( 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) = k5_numbers ) ) ) => v5_pre_topc(B,k1_pre_topc(k15_euclid(2),A),k3_topmetr) ) ) ) )).
fof(t33_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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) ) ) )).
fof(t33_jgraph_5,axiom,( ! [A] : ( ( ~ 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) ) ) ) )).
fof(t33_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t33_jordan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( 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))) ) ) ) ) ) ) ) )).
fof(t33_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [F] : ( 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_2_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))))) ) ) ) ) ) ) ) )).
fof(t33_jordan12,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_topreal1(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( r2_jordan12(2,A,B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_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))),k4_ordinal1) ) <=> ? [D] : ( 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,k1_nat_1(C,1)),D) ) ) ) ) ) ) ) )).
fof(t33_jordan14,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( ( r1_goboard1(u1_struct_0(k15_euclid(2)),B,A) & v1_topreal1(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(C,k3_finseq_1(A)) & r1_xxreal_0(D,k1_matrix_0(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))) ) ) ) ) ) ) )).
fof(t33_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & ~ r1_xxreal_0(A,k5_numbers) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C),k8_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k9_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C)),k8_jordan6(B)) ) ) ) ) ) ) )).
fof(t33_jordan18,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t33_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_xxreal_0(C,D) => ( r1_xxreal_0(A,1) | r1_xxreal_0(k3_finseq_1(k1_jordan8(E,C)),A) | r1_xxreal_0(B,1) | r1_xxreal_0(k1_matrix_0(k1_jordan8(E,C)),B) | ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ( ( F = k2_xcmplx_0(k3_xcmplx_0(k11_newton(2,k7_nat_d(D,C)),k6_xcmplx_0(A,2)),2) & G = k2_xcmplx_0(k3_xcmplx_0(k11_newton(2,k7_nat_d(D,C)),k6_xcmplx_0(B,2)),2) ) => k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,C),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,D),F,G) ) ) ) ) ) ) ) ) ) ) )).
fof(t33_jordan1b,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(B,k1_matrix_0(A)) & v9_rltopsp1(k3_goboard5(A,k5_numbers,B),k15_euclid(2)) ) ) ) )).
fof(t33_jordan1g,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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,k2_jordan9(B,A))),k8_pscomp_1(k3_topreal1(2,k2_jordan9(B,A)))) = k2_xcmplx_0(k6_pscomp_1(B),k8_pscomp_1(B)) ) ) )).
fof(t33_jordan1h,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_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) ) ) ) )).
fof(t33_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => r2_hidden(k1_jordan21(A),k3_jordan19(A)) ) )).
fof(t33_jordan23,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v2_topreal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(B,k3_topreal1(2,A)) => v2_topreal1(k3_jordan3(A,B)) ) ) ) ) )).
fof(t33_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ~ ( B != k5_euclid(A) & B = C & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( r1_xxreal_0(1,D) & r1_xxreal_0(D,A) & k1_funct_1(C,D) != k5_numbers ) ) ) ) ) ) )).
fof(t33_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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))) ) ) ) ) )).
fof(t33_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( 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) ) ) ) ) ) )).
fof(t33_jordan5b,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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,k1_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)) ) ) ) ) ) )).
fof(t33_jordan5d,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ 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] : ( v7_ordinal1(C) => ( ( 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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(B),C,1)),k18_euclid(A)) ) ) ) ) )).
fof(t33_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_jordan_a(B,A) => ! [C] : ( v1_xreal_0(C) => ~ ( ! [D] : ( v7_ordinal1(D) => ~ r1_xxreal_0(C,k3_jordan_a(2,k2_jordan_a(A,D,B))) ) & r1_xxreal_0(C,k4_jordan_a(A,B)) ) ) ) ) )).
fof(t33_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t33_kurato_1,axiom,( k1_tops_1(k3_topmetr,k2_pre_topc(k3_topmetr,k6_kurato_1)) != k2_pre_topc(k3_topmetr,k6_kurato_1) )).
fof(t33_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( k12_matrix_3(A,B,C) != k4_struct_0(B) => k4_matrix_3(B,k1_matrix_7(A,B,k4_matrix_0(u1_struct_0(B),k7_laplace(A,B,C)),k11_algstr_0(B,k12_matrix_3(A,B,C))),C) = k3_matrix_1(B,A) ) ) ) ) )).
fof(t33_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t33_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k5_finsub_1(B)) => ! [D] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t33_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ( v5_lattice3(A) <=> ! [B] : ! [C] : ( 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))) ) ) ) )).
fof(t33_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_lattice4(D,A) => ( ( r2_hidden(B,D) & r2_hidden(C,D) ) => r2_hidden(k4_filter_0(A,B,C),D) ) ) ) ) ) )).
fof(t33_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( v3_ordinal1(C) => ! [D] : ( ( 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] : ( m1_lattice5(E,A,B,D) => v2_lattice5(k12_lattice5(A,B,D,E,C),k8_lattice5(A,C),B) ) ) ) ) ) ) )).
fof(t33_lattice8,axiom,( ! [A] : ( ( 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] : ( m1_lattice8(B,u1_struct_0(A),A,k16_lattice5(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( m1_subset_1(E,C) => ! [F] : ( m1_subset_1(F,C) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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] : ( m1_subset_1(I,C) => ! [J] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t33_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t33_lfuzzy_1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t33_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( v1_seqm_3(A) & ~ v2_comseq_2(A) & ~ v1_limfunc1(A) & ~ v2_limfunc1(A) ) ) )).
fof(t33_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r2_limfunc2(C,A) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,D) & ~ r1_xxreal_0(A,E) & r2_hidden(E,k1_relset_1(k1_numbers,B)) ) ) ) ) ) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(k6_xcmplx_0(A,D),A)),k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,C),k2_rcomp_1(k6_xcmplx_0(A,D),A))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(k6_xcmplx_0(A,D),A))) => r1_xxreal_0(k1_funct_1(C,E),k1_funct_1(B,E)) ) ) ) ) | r2_limfunc2(B,A) ) ) ) ) ) )).
fof(t33_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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) = k2_xcmplx_0(k1_limfunc3(B,A),k1_limfunc3(C,A)) ) ) ) ) ) )).
fof(t33_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k10_prob_1(C))) & r1_xxreal_0(k1_funct_1(A,D),k5_limfunc1(A)) ) ) | v7_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).
fof(t33_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m1_vectsp_4(E,A,B) => ( ( r1_lmod_6(A,C,E) & r1_lmod_6(A,D,E) ) => r1_lmod_6(A,k1_vectsp_5(A,B,C,D),E) ) ) ) ) ) ) )).
fof(t33_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k16_lopban_1(A,B))) => r1_xxreal_0(k5_numbers,k2_normsp_0(k16_lopban_1(A,B),C)) ) ) ) )).
fof(t33_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v8_valued_0(k5_normsp_0(A,B)) & ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k3_xcmplx_0(k2_power(2,D),k1_funct_1(k5_normsp_0(A,B),k2_power(2,D))) ) ) => ( v2_lopban_3(B,A) <=> v1_series_1(C) ) ) ) ) ) )).
fof(t33_lopclset,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t33_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( ( r2_hidden(D,k13_lpspacc1(A,B,C)) & r2_hidden(E,k13_lpspacc1(A,B,C)) ) => ( k17_lpspacc1(A,B,C,D) = k17_lpspacc1(A,B,C,E) <=> r2_hidden(E,k17_lpspacc1(A,B,C,D)) ) ) ) ) ) ) ) )).
fof(t33_lpspace1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ( r2_relset_1(B,k1_numbers,k3_valued_1(B,k1_numbers,k1_numbers,k8_lpspace1(B,k5_numbers),k8_lpspace1(B,k5_numbers)),k8_lpspace1(B,k5_numbers)) & r2_relset_1(B,k1_numbers,k26_valued_1(B,k1_numbers,k8_lpspace1(B,k5_numbers),A),k8_lpspace1(B,k5_numbers)) ) ) ) )).
fof(t33_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( v2_xxreal_0(F) & v1_xreal_0(F) ) => ! [G] : ( m1_subset_1(G,u1_struct_0(k4_lpspace2(A,B,C,F))) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t33_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(A,k3_hilbert1(B,A))) ) ) )).
fof(t33_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( ( ~ v2_ltlaxio3(C) & m1_subset_1(C,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) ) => ( ( r2_hidden(A,k10_ltlaxio3(C)) & r2_hidden(B,k10_ltlaxio3(C)) & r2_hidden(k3_hilbert1(A,B),k10_ltlaxio3(C)) ) => ( r2_hidden(k3_hilbert1(A,B),k2_relset_1(k1_hilbert1,k8_ltlaxio3(C))) <=> ( r2_hidden(A,k2_relset_1(k1_hilbert1,k9_ltlaxio3(C))) | r2_hidden(B,k2_relset_1(k1_hilbert1,k8_ltlaxio3(C))) ) ) ) ) ) ) )).
fof(t33_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t33_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t33_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => v4_matrix10(k3_matrix10(A,B)) ) ) )).
fof(t33_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( m2_finseq_1(F,u1_struct_0(B)) => ! [G] : ( 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] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(B),A,A) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(B))) ) => 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)))) ) ) ) ) ) ) ) ) ) )).
fof(t33_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(A)) ) => ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(C,k4_ordinal1)) => ! [F] : ( m2_finseq_2(F,k4_ordinal1,k4_finseq_2(C,k4_ordinal1)) => ! [G] : ( m2_finseq_2(G,k4_ordinal1,k4_finseq_2(B,k4_ordinal1)) => ! [H] : ( ( 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),k4_ordinal1,k4_ordinal1,H,E) => k1_matrix13(A,D,C,B,F,G) = k4_matrix11(C,B,A,H,k1_matrix13(A,D,C,B,E,G)) ) ) ) ) ) ) ) ) ) )).
fof(t33_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( k4_finseq_1(k11_fvsum_1(A,B,C)) = k9_subset_1(k4_ordinal1,k4_finseq_1(B),k4_finseq_1(C)) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( 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)) ) ) ) ) ) ) )).
fof(t33_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(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) ) ) ) ) )).
fof(t33_matrix16,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t33_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,E,C,D) & m2_finseq_1(F,k3_finseq_2(E)) ) => ( r2_hidden(k4_tarski(A,B),k2_matrix_0(F)) => ( r1_xxreal_0(1,A) & r1_xxreal_0(A,C) & r1_xxreal_0(1,B) & r1_xxreal_0(B,D) ) ) ) ) ) ) ) ) )).
fof(t33_matrix_3,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ( ( k1_matrix_0(B) = k3_finseq_1(C) & k1_matrix_0(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)) ) ) ) ) ) )).
fof(t33_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(D) ) => k1_matrix_4(A,B,k1_matrix_4(A,C,D)) = k3_matrix_3(A,B,k1_matrix_4(A,D,C)) ) ) ) ) ) )).
fof(t33_matrix_6,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(A),B,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(A),B,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ( ( v3_matrix_6(C,B,A) & v3_matrix_6(D,B,A) ) => v3_matrix_6(k1_matrix_4(A,C,D),B,A) ) ) ) ) ) )).
fof(t33_matrix_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_matrix_2(C,k3_matrix_2(A)) => ! [D] : ( 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(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k4_ordinal1,u1_struct_0(B),C,D),u1_struct_0(B)) ) ) ) ) ) )).
fof(t33_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( ( v4_matrix_8(C,A,B) & v2_matrix_6(C,A,B) ) => v4_matrix_6(C,A,B) ) ) ) ) )).
fof(t33_matrix_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t33_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( m2_finseq_1(C,k2_numbers) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k3_finseq_1(B) = k3_finseq_1(C) ) => k5_matrixc1(k7_seq_4(A,B),C) = k7_seq_4(k5_matrixc1(A,C),k5_matrixc1(B,C)) ) ) ) ) )).
fof(t33_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ! [D] : ( ( 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(k4_ordinal1,k2_finseq_1(k1_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(k4_ordinal1,k2_finseq_1(k1_nat_1(k1_matrix_0(C),k2_wsierp_1(k11_matrixj1(A,D)))),k2_finseq_1(k2_wsierp_1(k11_matrixj1(A,D))))) ) ) ) ) )).
fof(t33_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => k3_matrixr1(A,A) = k7_matrixr1(2,A) ) )).
fof(t33_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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_0(k11_finseq_1(B,C,D)) ) ) ) ) ) )).
fof(t33_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( m1_matrlin(D,A,B) => ! [E] : ( m2_finseq_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(A),k3_finseq_1(D),k3_finseq_1(E)) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(A))) ) => ( k3_finseq_1(D) = k5_numbers => k3_funct_2(u1_struct_0(B),u1_struct_0(C),k4_matrlin2(A,B,C,D,E,G),F) = k4_struct_0(C) ) ) ) ) ) ) ) ) )).
fof(t33_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k4_matroid0(A,k6_matroid0(A,B)) = k4_matroid0(A,B) ) ) )).
fof(t33_matrprob,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( ( ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(A)) => r1_xxreal_0(k5_numbers,k1_funct_1(A,C)) ) ) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => r1_xxreal_0(k5_numbers,k1_funct_1(B,C)) ) ) ) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(k14_rvsum_1(A,B))) => r1_xxreal_0(k5_numbers,k1_funct_1(k14_rvsum_1(A,B),C)) ) ) ) ) ) )).
fof(t33_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => r2_funct_2(u1_struct_0(k15_euclid(A)),u1_struct_0(k15_euclid(A)),k3_matrtop1(A,A,k3_matrix_1(k2_vectsp_1,A)),k3_struct_0(k15_euclid(A))) ) )).
fof(t33_matrtop3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(B))) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ( r2_hidden(E,k9_subset_1(k4_ordinal1,A,k2_finseq_1(B))) => k1_funct_1(C,E) = k5_numbers ) ) ) => k3_funct_2(u1_struct_0(k15_euclid(B)),u1_struct_0(k15_euclid(B)),D,C) = C ) ) ) ) )).
fof(t33_mcart_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t33_measure1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( 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))) ) ) ) ) )).
fof(t33_measure6,axiom,( ! [A] : ( ( v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => k2_measure5(A) = k2_measure5(k1_measure6(A,B)) ) ) )).
fof(t33_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => k7_member_1(k3_xboole_0(A,B)) = k3_xboole_0(k7_member_1(A),k7_member_1(B)) ) ) )).
fof(t33_membered,axiom,( ! [A] : ! [B] : ( ( r2_hidden(B,A) & v3_membered(B) ) => v3_membered(k1_setfam_1(A)) ) )).
fof(t33_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_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)))) ) ) ) )).
fof(t33_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t33_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t33_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ( ( v1_mesfunc8(E,A,k2_numbers) & r1_tarski(D,k1_relset_1(A,k4_mesfunc5(A,k2_numbers,E,k5_numbers))) & r2_hidden(C,D) ) => k9_nat_1(k2_numbers,k10_comseq_3(k9_mesfun7c(A,E,C)),B) = k9_nat_1(k2_numbers,k9_mesfun7c(A,k3_mesfun9c(A,E),C),B) ) ) ) ) ) )).
fof(t33_mesfunc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t33_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t33_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( ( 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,E)),k15_mesfunc1(A,C,F)),B) ) ) ) ) ) ) ) )).
fof(t33_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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))) ) ) )).
fof(t33_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( v2_mesfunc9(B,A) & v1_mesfunc8(B,A,k6_numbers) & r1_tarski(D,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_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))) ) ) ) ) ) ) )).
fof(t33_metric_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,k13_metric_1(A,B,C)) <=> r1_metric_1(A,B,D,C) ) ) ) ) ) )).
fof(t33_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k2_metric_2(A)) => ! [C] : ( m1_subset_1(C,k2_metric_2(A)) => ? [D] : ( v1_xreal_0(D) & r4_metric_2(A,B,C,D) ) ) ) ) )).
fof(t33_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_midsp_1(B,A) => ! [C] : ( m1_midsp_1(C,A) => ! [D] : ( m1_midsp_1(D,A) => ! [E] : ( m1_midsp_1(E,A) => ~ ( ? [F] : ( m1_subset_1(F,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) & ? [G] : ( 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] : ( m1_subset_1(F,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) & ? [G] : ( 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 ) ) ) ) ) ) )).
fof(t33_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( ( v4_midsp_2(B,A) & l1_midsp_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k10_midsp_2(A,B,C,k11_midsp_2(A,B)) = C ) ) ) )).
fof(t33_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [D] : ( 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)) ) ) ) )).
fof(t33_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(t33_modal_1,axiom,( ! [A] : ( 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))) ) )).
fof(t33_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t33_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ~ ( r3_modelc_2(B,A) & ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ~ r1_modelc_2(C,A) ) ) ) ) )).
fof(t33_modelc_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( ( 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))) ) ) ) )).
fof(t33_moebius1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( ~ v1_moebius1(A) & k2_moebius1(A) = k5_numbers ) ) )).
fof(t33_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m2_monoid_0(B,A) ) => ( v3_group_1(A) => v3_group_1(B) ) ) ) )).
fof(t33_monoid_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => m1_subset_1(k18_monoid_1(A,B),u1_struct_0(k19_monoid_1(A))) ) ) )).
fof(t33_morph_01,axiom,( ! [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) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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,D),k3_funct_2(k1_zfmisc_1(u1_struct_0(A)),k9_setfam_1(u1_struct_0(A)),k3_morph_01(A,C),B)) = 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,D),C)),B) & k3_funct_2(k9_setfam_1(u1_struct_0(A)),k9_setfam_1(u1_struct_0(A)),k4_morph_01(A,D),k3_funct_2(k1_zfmisc_1(u1_struct_0(A)),k9_setfam_1(u1_struct_0(A)),k4_morph_01(A,C),B)) = 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,D),C)),B) ) ) ) ) ) )).
fof(t33_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k3_card_3(u3_msualg_1(A,k1_msafree3(A,B)))) => ! [D] : ( 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)))) ) ) ) ) )).
fof(t33_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & v3_msafree4(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => r1_msualg_3(A,B,C,D) ) ) ) ) )).
fof(t33_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( m2_pboole(D,u1_struct_0(A),C,u3_msualg_1(A,B)) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( 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] : ( ( 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] : ( v7_ordinal1(H) => ! [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] : ( ( 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] : ( ( 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),k15_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) ) ) ) ) ) ) ) ) ) ) )).
fof(t33_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m3_pboole(D,A,k1_mboolean(A,C)) => ( r1_pboole(A,B,D) => m3_pboole(B,A,C) ) ) ) ) )).
fof(t33_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => v15_lattices(k17_msualg_2(A,B)) ) ) )).
fof(t33_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t33_msualg_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,B),D)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t33_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => k1_dilworth(k5_mycielsk(A)) = A ) )).
fof(t33_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => r2_hidden(A,k1_nat_1(A,1)) ) )).
fof(t33_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( r2_hidden(B,k9_xtuple_0(k12_nat_3(A))) => ( v7_ordinal1(B) & v1_int_2(B) ) ) ) )).
fof(t33_nat_4,axiom,( v1_int_2(83) )).
fof(t33_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( ( k5_nat_5(B) = k2_xcmplx_0(B,A) & r1_nat_d(A,B) ) => ( B = A | ( A = 1 & v1_int_2(B) ) ) ) ) ) )).
fof(t33_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(B,A) & A != k5_numbers & v1_int_1(k7_xcmplx_0(A,B)) ) ) ) )).
fof(t33_nattra_1,axiom,( ! [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) & v4_nattra_1(A) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_cat_1(A,B,B) = k1_tarski(k4_cat_1(A,B)) ) ) )).
fof(t33_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t33_ncfcont2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t33_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t33_ndiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t33_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(A)) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k4_finseq_1(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k11_prvect_2(A,B))) => ! [E] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t33_neckla_3,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t33_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(1,B) => r1_xxreal_0(A,k3_xcmplx_0(A,B)) ) ) ) )).
fof(t33_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) = k2_seq_4(k2_relset_1(k1_numbers,B)) & k7_partfun1(k1_numbers,B,D) = k3_seq_4(k2_relset_1(k1_numbers,B)) ) ) ) ) ) ) )).
fof(t33_nfcont_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( ! [F] : ( 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) ) ) ) ) ) )).
fof(t33_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( 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))),k3_xcmplx_0(C,k9_complex1(k6_xcmplx_0(D,E)))) ) ) ) ) ) ) ) )).
fof(t33_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(k7_normform(A))) => ( ! [C] : ( m2_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [D] : ( 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)) ) ) )).
fof(t33_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t33_numbers,axiom,( r2_xboole_0(k1_numbers,k6_numbers) )).
fof(t33_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t33_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v1_lattice2(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t33_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m1_oppcat_1(D,B,A) => ! [E] : ( m1_oppcat_1(E,A,C) => m2_cat_1(k1_partfun1(u4_struct_0(B),u4_struct_0(A),u4_struct_0(A),u4_struct_0(C),D,E),B,C) ) ) ) ) ) )).
fof(t33_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_nfcont_3(D,k4_real_ns1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ( k1_relset_1(k1_numbers,D) = k3_integra5(B,C) => r1_integr18(k4_real_ns1(A),k3_integra5(B,C),D) ) ) ) ) ) )).
fof(t33_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r1_orders_1(A,B) => v1_orders_1(k2_wellord1(A,B)) ) ) )).
fof(t33_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t33_ordinal1,axiom,( ! [A] : k6_subset_1(k1_ordinal1(A),k1_tarski(A)) = A )).
fof(t33_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r1_ordinal1(A,B) => r1_ordinal1(k10_ordinal2(C,A),k10_ordinal2(C,B)) ) ) ) ) )).
fof(t33_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( k11_ordinal2(B,A) = k11_ordinal2(C,A) => ( A = k1_xboole_0 | B = C ) ) ) ) ) )).
fof(t33_ordinal4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ( k2_ordinal4(A) = k1_xboole_0 & k3_ordinal4(A) = 1 ) ) )).
fof(t33_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) ) => ~ ( r1_abian(A,B) & ! [C] : ( v3_ordinal1(C) => ~ ( r2_hidden(C,k9_xtuple_0(k3_ordinal6(B))) & A = k1_funct_1(k3_ordinal6(B),C) ) ) ) ) ) )).
fof(t33_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ! [F] : ( ( 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 ) ) ) ) ) ) )).
fof(t33_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(u4_struct_0(A)),k7_osalg_1(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( m1_osalg_1(C,A,B) <=> k8_osalg_1(A,C) = B ) ) ) ) )).
fof(t33_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_osalg_2(C,A,B) => m1_msualg_2(k12_msualg_2(A,B,C),A,k10_osalg_2(A,B,C)) ) ) ) )).
fof(t33_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t33_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t33_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => k3_partfun1(C,A,B) = C ) )).
fof(t33_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,B) => ~ ( v1_partfun1(k4_partfun2(A,B,C,D),A) & C = k1_xboole_0 ) ) ) ) ) )).
fof(t33_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k4_partit1(A,k6_partit1(A)) = k1_eqrel_1(A) ) )).
fof(t33_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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))) ) ) ) )).
fof(t33_pcomps_1,axiom,( ! [A] : ( 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))) ) ) )).
fof(t33_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k21_pcs_0(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k21_pcs_0(A))) => ( ( B = D & C = E ) => ( r1_orders_2(A,B,C) <=> r1_orders_2(k21_pcs_0(A),E,D) ) ) ) ) ) ) ) )).
fof(t33_pdiff_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( 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) & k10_pdiff_1(A,B,k26_valued_1(k1_euclid(A),k1_numbers,D,C),E) = k3_xcmplx_0(C,k10_pdiff_1(A,B,D,E)) ) ) ) ) ) ) ) )).
fof(t33_pdiff_3,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(2)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t33_pdiff_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( 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),k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(3,3),B)) ) ) ) )).
fof(t33_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( 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) = k10_pdiff_1(3,3,k1_pdiff_3(2,3,B),A) ) ) ) )).
fof(t33_pdiff_6,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_euclid(A))) => ~ ( r1_pdiff_6(D,B,A,C) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k4_real_ns1(A)))) => ~ ( D = E & v3_nfcont_1(E,k4_real_ns1(A)) ) ) ) ) ) ) ) )).
fof(t33_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [E] : ( ( 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] : ( D = E => ( r2_pdiff_7(A,B,C,D,F) <=> r7_pdiff_1(A,B,C,E,F) ) ) ) ) ) ) ) )).
fof(t33_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t33_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( v1_int_2(B) => ( r1_xxreal_0(k1_newton(B,k1_nat_1(A,1)),C) | ( r1_nat_d(C,k1_newton(B,k1_nat_1(A,1))) <=> r1_nat_d(C,k1_newton(B,A)) ) ) ) ) ) ) )).
fof(t33_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m2_finseq_2(C,B,k3_finseq_2(B)) => ! [D] : ( m2_finseq_2(D,B,k3_finseq_2(B)) => ! [E] : ( 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)) ) ) ) ) )).
fof(t33_polyeq_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( v1_xreal_0(C) => ( A != k5_numbers => k1_newton(k2_xcmplx_0(k19_sin_cos(k7_xcmplx_0(k2_xcmplx_0(C,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)),A)),k3_xcmplx_0(k17_sin_cos(k7_xcmplx_0(k2_xcmplx_0(C,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)),A)),k7_complex1)),A) = k2_xcmplx_0(k19_sin_cos(C),k3_xcmplx_0(k17_sin_cos(C),k7_complex1)) ) ) ) ) )).
fof(t33_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t33_polynom3,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k11_polynom3(A,B,k9_polynom3(A)),k9_polynom3(A)) ) ) )).
fof(t33_polynom7,axiom,( ! [A] : ( v3_ordinal1(A) => ! [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) & v5_group_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & v1_algstr_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( 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)))) ) => k2_polynom2(A,B,k11_polynom1(A,B,k4_polynom7(A,B,D),C),E) = k8_group_1(B,D,k2_polynom2(A,B,C,E)) ) ) ) ) ) )).
fof(t33_polynom8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v4_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => r2_funct_2(k4_ordinal1,u1_struct_0(B),k6_polynom8(A,B,k9_polynom3(B),C),k9_polynom3(B)) ) ) ) )).
fof(t33_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(D,A,C) & v1_polynom1(D,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)) ) ) ) ) )).
fof(t33_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(A,k5_numbers) => k2_power(k2_power(A,B),C) = k2_power(A,k3_xcmplx_0(B,C)) ) ) ) ) )).
fof(t33_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v4_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v4_valued_0(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) & v4_valued_0(D) ) => ( ! [E] : ( 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)) ) ) ) ) )).
fof(t33_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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))) ) ) ) ) ) ) )).
fof(t33_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(1,C) => k1_funct_1(B,C) = k2_prepower(C,A) ) ) => ( r1_xxreal_0(A,k5_numbers) | ( v2_comseq_2(B) & k1_seq_2(B) = 1 ) ) ) ) ) )).
fof(t33_prob_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m2_prob_1(E,A,B) => ( r1_tarski(C,D) => k3_funct_2(B,k1_numbers,E,k7_prob_1(A,B,D,C)) = k5_real_1(k3_funct_2(B,k1_numbers,E,D),k3_funct_2(B,k1_numbers,E,C)) ) ) ) ) ) ) )).
fof(t33_prob_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( ~ 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] : ( ( v5_relat_1(D,C) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => r1_tarski(k1_prob_2(B,C,k3_prob_3(B,D),A),k1_prob_2(B,C,D,A)) ) ) ) )).
fof(t33_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => r2_hidden(k8_cqc_lang(A,k8_cqc_lang(A,D,B),k8_cqc_lang(A,k8_cqc_lang(A,D,C),k8_cqc_lang(A,D,k7_cqc_lang(A,B,C)))),k4_cqc_the1(A)) ) ) ) ) )).
fof(t33_projpl_1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t33_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t33_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t33_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k4_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => B != C ) ) ) )).
fof(t33_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t33_quantal1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( k9_quantal1(A,B,k3_quantal1(A)) = B & k9_quantal1(A,k3_quantal1(A),B) = B ) ) ) )).
fof(t33_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ( A != k1_quatern2 => k5_quatern2(A,A) = k2_quatern2 ) ) )).
fof(t33_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k28_quaterni(k23_quaterni(k27_quaterni(A),k27_quaterni(A))) = k1_square_1(k28_quaterni(A)) ) )).
fof(t33_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_xreal_0(B) => ( A = B => ( k13_quaterni(k10_quaterni(A,k1_xcmplx_0)) = k5_numbers & k14_quaterni(k10_quaterni(A,k1_xcmplx_0)) = B & k15_quaterni(k10_quaterni(A,k1_xcmplx_0)) = k5_numbers & k16_quaterni(k10_quaterni(A,k1_xcmplx_0)) = k5_numbers ) ) ) ) )).
fof(t33_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k19_quofield(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t33_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m2_prob_1(B,A,k1_random_1(A)) => ! [C] : ( m1_random_1(C,A,k1_random_1(A)) => ? [D] : ( m2_finseq_1(D,k1_numbers) & ? [E] : ( 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] : ( v7_ordinal1(F) => ( r2_hidden(F,k4_finseq_1(D)) => k12_supinf_2(D,F) = k1_extreal1(k12_supinf_2(C,k1_funct_1(E,F)),k12_supinf_2(B,k1_tarski(k1_funct_1(E,F)))) ) ) & k8_random_1(A,k1_random_1(A),B,C) = k18_rvsum_1(D) ) ) ) ) ) )).
fof(t33_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t33_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ( r1_xxreal_0(A,1) <=> r1_xxreal_0(k2_rat_1(A),k1_rat_1(A)) ) ) )).
fof(t33_ratfunc1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_ratfunc1(B,A) => ! [C] : ( m1_ratfunc1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t33_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t33_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,k4_real_3(B),C) = k5_numbers ) => k9_nat_1(k1_numbers,k3_real_3(B),A) = k5_numbers ) ) ) )).
fof(t33_rearran1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,k1_numbers))) ) => ! [E] : ( ( v1_rearran1(E) & v2_rearran1(E) & v3_rearran1(E,k1_zfmisc_1(B)) & m2_finseq_1(E,k1_zfmisc_1(B)) ) => ( ( v1_partfun1(D,C) & k5_card_1(B) = k5_card_1(C) ) => ( r2_classes1(k18_rfunct_3(B,k15_valued_1(B,k1_numbers,k4_rearran1(C,B,E,D),A)),k18_rfunct_3(C,k15_valued_1(C,k1_numbers,D,A))) & k20_rfunct_3(B,k18_rfunct_3(B,k15_valued_1(B,k1_numbers,k4_rearran1(C,B,E,D),A)),B) = k20_rfunct_3(C,k18_rfunct_3(C,k15_valued_1(C,k1_numbers,D,A)),C) & k21_rfunct_3(B,k18_rfunct_3(B,k15_valued_1(B,k1_numbers,k4_rearran1(C,B,E,D),A)),B) = k21_rfunct_3(C,k18_rfunct_3(C,k15_valued_1(C,k1_numbers,D,A)),C) ) ) ) ) ) ) ) )).
fof(t33_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ( k3_relat_1(k1_xboole_0,A) = k1_xboole_0 & k3_relat_1(A,k1_xboole_0) = k1_xboole_0 ) ) )).
fof(t33_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ! [E] : ( 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)) ) ) ) )).
fof(t33_revrot_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( 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) ) ) )).
fof(t33_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( ( r3_rewrite1(A,B) & r1_rewrite1(A,B,C) ) => B = C ) ) )).
fof(t33_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ( r2_rewrite2(A,B,C,D) => r3_rewrite2(A,B,C,D) ) ) ) ) )).
fof(t33_rewrite3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(B))) => ! [D] : ( ( ~ v2_struct_0(D) & l1_rewrite3(D,C) ) => ~ ( r2_hidden(A,k1_rewrite3(B,C,D)) & ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ! [G] : ( m1_subset_1(G,k8_afinsq_1(B)) => ! [H] : ( m1_subset_1(H,k8_afinsq_1(B)) => A != k4_tarski(k4_tarski(E,G),k4_tarski(F,H)) ) ) ) ) ) ) ) ) )).
fof(t33_rfinseq,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ? [B] : ( m2_finseq_1(B,k1_numbers) & r2_classes1(A,B) & m2_finseq_1(B,k4_numbers) & v8_valued_0(B) ) ) )).
fof(t33_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t33_rfunct_2,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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,k5_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(k5_numbers,B) | v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k26_valued_1(k1_numbers,k1_numbers,C,B),A)) ) ) ) ) ) )).
fof(t33_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,k3_rfunct_3(A,k1_numbers)) => ( r1_rfunct_3(A,k1_numbers,C,B) => k1_funct_1(k14_rfunct_3(A,C),B) = k18_rvsum_1(k17_rfunct_3(A,C,B)) ) ) ) ) )).
fof(t33_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_comseq_2(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_numbers)) => ( C = a_2_0_rinfsup1(A,B) => v5_xxreal_2(C) ) ) ) ) ) )).
fof(t33_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => r1_xxreal_0(k12_supinf_2(A,B),k2_supinf_1) ) => v9_mesfunc5(A) ) ) )).
fof(t33_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) = k3_real_1(k3_funct_2(u1_struct_0(A),k1_numbers,B,C),k3_funct_2(u1_struct_0(A),k1_numbers,B,D)) ) ) ) ) ) ) )).
fof(t33_rlaffin3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_rlaffin1(B,k15_euclid(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ( k5_card_1(B) = k2_xcmplx_0(A,1) => v3_pre_topc(k1_rlaffin2(k15_euclid(A),B),k15_euclid(A)) ) ) ) )).
fof(t33_rlsub_1,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_rlvect_1(B) & m1_rlsub_1(B,A) ) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_struct_0(B,C) <=> r1_struct_0(A,C) ) ) => B = A ) ) ) )).
fof(t33_rlsub_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t33_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rltopsp1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t33_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t33_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( B != C => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t33_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( m1_rlsub_1(D,A) => ( m1_rlsub_1(B,C) => m1_rlsub_1(B,k1_rlsub_2(A,C,D)) ) ) ) ) ) )).
fof(t33_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t33_rlvect_5,axiom,( ! [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_rlvect_5(A) & l1_rlvect_1(A) ) => ( k1_rlvect_5(A) = 1 <=> ? [B] : ( 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)) ) ) ) )).
fof(t33_rlvect_x,axiom,( ! [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) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t33_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_rmod_2(D,A,B) => ( u1_struct_0(D) = C => v1_rmod_2(C,A,B) ) ) ) ) ) )).
fof(t33_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( ( v2_vectsp_2(D,A) & m1_rmod_2(D,A,B) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t33_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( C != D => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t33_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & v15_lattices(A) & v8_robbins1(A) & l4_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t33_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t33_robbins4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v10_robbins1(A) & v8_robbins3(A) & v9_robbins3(A) & l4_robbins1(A) ) => ( v1_robbins4(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t33_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) )).
fof(t33_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => k2_rpr_1(A,k2_subset_1(A),k2_subset_1(A)) = 1 ) )).
fof(t33_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => m1_rusub_1(k1_rusub_1(A),B) ) ) )).
fof(t33_rusub_2,axiom,( ! [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_bhsp_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => r2_hidden(A,k3_rusub_2(A)) ) )).
fof(t33_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t33_rusub_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(t33_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r1_xxreal_0(C,D) => r1_tarski(k4_bhsp_2(A,B,C),k4_bhsp_2(A,B,D)) ) ) ) ) ) )).
fof(t33_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => k8_rvsum_1(k2_finseq_2(A,k5_numbers),B) = k7_rvsum_1(A,B) ) ) )).
fof(t33_rvsum_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( 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)) = k2_xcmplx_0(A,k16_rvsum_1(B)) ) ) )).
fof(t33_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( 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) = k5_numbers | ( r1_scm_halt(k1_scmfsa8b(E,C,D),B,A) & r2_scm_halt(k1_scmfsa8b(E,C,D),B,A) ) ) ) ) ) ) ) ) )).
fof(t33_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ( r2_classes1(k18_scmfsa_2(B,k5_scmfsa_2(k5_numbers)),k18_scmfsa_2(k1_scmfsa6b(k1_scmbsort(k5_scmfsa_2(k5_numbers)),B,A),k5_scmfsa_2(k5_numbers))) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(D,k3_finseq_1(k18_scmfsa_2(B,k5_scmfsa_2(k5_numbers)))) ) => ( r1_xxreal_0(D,C) | ! [E] : ( v1_int_1(E) => ! [F] : ( v1_int_1(F) => ( ( E = k1_funct_1(k18_scmfsa_2(k1_scmfsa6b(k1_scmbsort(k5_scmfsa_2(k5_numbers)),B,A),k5_scmfsa_2(k5_numbers)),C) & F = k1_funct_1(k18_scmfsa_2(k1_scmfsa6b(k1_scmbsort(k5_scmfsa_2(k5_numbers)),B,A),k5_scmfsa_2(k5_numbers)),D) ) => r1_xxreal_0(F,E) ) ) ) ) ) ) ) ) ) ) )).
fof(t33_scmfsa10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k1_amistd_1(k7_card_1(3),k1_scmfsa_2,A,k11_scmfsa_2(B)) = k1_tarski(B) ) ) )).
fof(t33_scmfsa8a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( 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(k7_card_1(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(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(k3_scmfsa6a(k3_scmfsa6a(B,k1_scmfsa8a(k1_nat_1(k5_card_1(C),1))),C),k4_compos_1(k1_scmfsa_2))),k1_funct_4(D,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)))) ) ) ) ) ) )).
fof(t33_scmfsa8b,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(k1_scmfsa_2)) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ( ( ! [E] : ( ( 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] : ( m1_scmfsa_2(E) => k18_scmfsa_2(A,E) = k18_scmfsa_2(B,E) ) & k5_memstr_0(k7_card_1(3),k1_scmfsa_2,A) = k5_memstr_0(k7_card_1(3),k1_scmfsa_2,B) ) => ( r1_scmfsa7b(C,D) | ( ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmfsa_2)) ) => ( D != E => k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,C,A),E) = k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,C,B),E) ) ) & ! [E] : ( m1_scmfsa_2(E) => k18_scmfsa_2(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,C,A),E) = k18_scmfsa_2(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,C,B),E) ) & k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k2_extpro_1(k7_card_1(3),k1_scmfsa_2,C,A)) = k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k2_extpro_1(k7_card_1(3),k1_scmfsa_2,C,B)) ) ) ) ) ) ) ) )).
fof(t33_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ~ ( k2_compos_0(u1_compos_1(k1_scmfsa_2),A) = 11 & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_scmfsa_2(C) => A != k16_scmfsa_2(B,C) ) ) ) ) )).
fof(t33_scmfsa_9,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(k1_nat_1(k5_card_1(B),6),C) => r2_hidden(C,k2_afinsq_1(k2_scmfsa_9(A,B))) ) ) ) ) )).
fof(t33_scmfsa_m,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ! [B] : ( m1_scmfsa_2(B) => ! [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(k7_card_1(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(k5_numbers)) = 1 ) ) ) ) ) )).
fof(t33_scmisort,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(82,B) => r2_hidden(B,k9_xtuple_0(k2_scmisort(A))) ) ) ) )).
fof(t33_scmpds_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ~ ( k2_compos_0(u1_compos_1(k1_scmpds_2),A) = 10 & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmpds_2)) ) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => A != k13_scmpds_2(B,C,D,E) ) ) ) ) ) ) )).
fof(t33_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => k5_memstr_0(2,k1_scmpds_2,k6_scmpds_4(k2_scmpds_6(E,F,C,D),B,A)) = k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),2) ) ) ) ) ) ) )).
fof(t33_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( v7_ordinal1(C) => k2_amistd_1(k7_card_1(2),k1_scmring2(A),k9_scmring2(A,C,B)) = k1_tarski(C) ) ) ) )).
fof(t33_scmyciel,axiom,( ! [A] : ! [B] : ( r2_hidden(B,A) => r2_hidden(k1_tarski(B),k5_scmyciel(A)) ) )).
fof(t33_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t33_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v9_ordinal1(A) & v9_ordinal1(B) ) <=> v9_ordinal1(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) ) ) )).
fof(t33_seq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( r1_xxreal_0(k5_numbers,A) & ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,B,C) = k7_xcmplx_0(1,k2_xcmplx_0(k3_xcmplx_0(C,C),A)) ) ) => k1_seq_2(B) = k5_numbers ) ) ) )).
fof(t33_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( ( r2_seqfunc(A,B,D) & r2_seqfunc(A,C,D) ) => ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,D) => ( r2_relset_1(k4_ordinal1,k1_numbers,k3_valued_1(k4_ordinal1,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(k4_ordinal1,k1_numbers,k47_valued_1(k4_ordinal1,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(k4_ordinal1,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k10_seqfunc(A,B,E),k10_seqfunc(A,C,E)),k10_seqfunc(A,k8_seqfunc(A,B,C),E)) ) ) ) ) ) ) ) )).
fof(t33_seqm_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ( v8_valued_0(B) & r1_xxreal_0(k5_numbers,A) ) => v8_valued_0(k26_valued_1(k4_ordinal1,k1_numbers,B,A)) ) & ( ( v8_valued_0(B) & r1_xxreal_0(A,k5_numbers) ) => v7_valued_0(k26_valued_1(k4_ordinal1,k1_numbers,B,A)) ) ) ) ) )).
fof(t33_series_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( r1_xxreal_0(A,1) & ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(1,C) => k9_nat_1(k1_numbers,B,C) = k7_xcmplx_0(1,k2_power(C,A)) ) ) & v1_series_1(B) ) ) ) )).
fof(t33_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => r1_xxreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),2)),k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_square_1(B),k1_square_1(C)),2))),k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_square_1(C),k1_square_1(A)),2))),k3_square_1(k3_xcmplx_0(3,k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(C))))) ) ) ) )).
fof(t33_setfam_1,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(t33_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => r2_funct_2(k4_ordinal1,k9_setfam_1(A),k2_prob_1(A,k4_setlim_1(A,B)),k2_setlim_1(A,k2_prob_1(A,B))) ) )).
fof(t33_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k3_prob_1(A,k5_setlim_2(A,C,B)) = k9_subset_1(A,B,k3_prob_1(A,C)) ) ) )).
fof(t33_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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] : ( ( v1_funct_1(F) & v1_funct_2(F,A,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [G] : ( ( 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] : ( m1_subset_1(H,B) => ! [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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t33_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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] : ( ( 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] : ( v7_ordinal1(E) => ! [F] : ( m2_finseq_2(F,A,k4_finseq_2(E,A)) => ! [G] : ( 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] : ( m1_subset_1(H,A) => ! [I] : ( m1_subset_1(I,A) => ! [J] : ( m1_subset_1(J,A) => ! [K] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t33_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_scmfsa_2(C) => ! [D] : ( m1_subset_1(D,u1_compos_1(k1_scmfsa_2)) => ( ( D = k14_scmfsa_2(B,A,C) | D = k15_scmfsa_2(B,A,C) ) => k3_sf_mastr(D) = k1_tarski(C) ) ) ) ) ) )).
fof(t33_sfmastr3,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( m1_scmfsa_2(D) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ( ( 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(k5_numbers)) = 1 ) => k18_scmfsa_2(k1_scmfsa6b(k4_sfmastr3(D,B,C),A,E),D) = k1_funct_7(k1_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))) ) ) ) ) ) ) )).
fof(t33_sgraph1,axiom,( ! [A] : ! [B] : ( m1_sgraph1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t33_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v9_sheffer1(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l3_sheffer1(A) ) => v4_lattices(A) ) )).
fof(t33_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t33_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(t33_simplex1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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] : ( ( 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)) ) ) ) ) )).
fof(t33_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_fdiff_1(k5_sin_cos2,A) & k1_fdiff_1(k5_sin_cos2,A) = k7_xcmplx_0(1,k1_square_1(k1_funct_1(k3_sin_cos2,A))) ) ) )).
fof(t33_sin_cos3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k15_sin_cos(k3_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(k2_xcmplx_0(k2_nat_1(2,A),k7_xcmplx_0(1,2)),k28_sin_cos)),k7_complex1)) = k4_xcmplx_0(k3_xcmplx_0(1,k7_complex1)) ) )).
fof(t33_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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)))) ) ) ) )).
fof(t33_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k2_sin_cos4(k7_xcmplx_0(A,2)) = k3_square_1(k7_xcmplx_0(k2_xcmplx_0(1,k19_sin_cos(A)),k6_xcmplx_0(1,k19_sin_cos(A)))) | k2_sin_cos4(k7_xcmplx_0(A,2)) = k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(1,k19_sin_cos(A)),k6_xcmplx_0(1,k19_sin_cos(A))))) ) ) )).
fof(t33_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k7_xcmplx_0(k28_sin_cos,2)) & r1_xxreal_0(A,k3_xcmplx_0(2,k28_sin_cos)) & r1_xxreal_0(1,k17_sin_cos(A)) ) ) )).
fof(t33_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k5_numbers,A) => k1_sin_cos7(A) = k2_sin_cos7(k3_square_1(k2_xcmplx_0(k1_square_1(A),1))) ) ) )).
fof(t33_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k2_xcmplx_0(k4_sin_cos2(k3_xcmplx_0(2,A)),k19_sin_cos(k3_xcmplx_0(2,B))) = k2_xcmplx_0(2,k3_xcmplx_0(2,k6_xcmplx_0(k1_square_1(k2_sin_cos2(A)),k1_square_1(k17_sin_cos(B))))) & k6_xcmplx_0(k4_sin_cos2(k3_xcmplx_0(2,A)),k19_sin_cos(k3_xcmplx_0(2,B))) = k3_xcmplx_0(2,k2_xcmplx_0(k1_square_1(k2_sin_cos2(A)),k1_square_1(k17_sin_cos(B)))) ) ) ) )).
fof(t33_sin_cos9,axiom,( k3_relat_1(k2_partfun1(k1_numbers,k1_numbers,k26_sin_cos,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))),k1_sin_cos9) = k1_partfun2(k1_numbers,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))) )).
fof(t33_sincos10,axiom,( ! [A] : ( r2_hidden(A,k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,4))) => r2_hidden(k1_funct_1(k1_fdiff_9,A),k1_rcomp_1(1,k3_square_1(2))) ) )).
fof(t33_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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(k1_nat_1(A,2),k3_finseq_1(B)) & v1_sppol_1(k2_topreal1(2,B,A)) ) => v2_sppol_1(k2_topreal1(2,B,k1_nat_1(A,1))) ) ) ) )).
fof(t33_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( r1_xxreal_0(k3_finseq_1(A),2) => v3_topreal1(A) ) ) )).
fof(t33_sprect_1,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t33_sprect_2,axiom,( k8_pscomp_1(k1_topreal1) = 1 )).
fof(t33_sprect_3,axiom,( ! [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) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t33_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t33_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k7_xcmplx_0(k3_square_1(A),A) = k7_xcmplx_0(1,k3_square_1(A)) ) ) )).
fof(t33_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ? [D] : ( 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) ) ) ) ) )).
fof(t33_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ ( ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,B) ) | A = B ) & r1_xxreal_0(k3_stirl2_1(B,A),k5_numbers) ) & ~ ( ~ r1_xxreal_0(k3_stirl2_1(B,A),k5_numbers) & ~ ( r1_xxreal_0(1,A) & r1_xxreal_0(A,B) ) & A != B ) ) ) ) )).
fof(t33_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t33_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ( A != k1_xboole_0 => m1_subset_1(k1_tarski(B),k1_zfmisc_1(A)) ) ) )).
fof(t33_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t33_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ( ! [C] : ( 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) = k5_numbers ) ) ) )).
fof(t33_supinf_2,axiom,( v1_funct_1(k6_partfun1(k4_ordinal1)) & v1_funct_2(k6_partfun1(k4_ordinal1),k4_ordinal1,k6_numbers) & m1_subset_1(k6_partfun1(k4_ordinal1),k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) & v2_funct_1(k6_partfun1(k4_ordinal1)) & k4_ordinal1 = k2_relset_1(k4_ordinal1,k6_partfun1(k4_ordinal1)) & ~ v1_xboole_0(k2_relset_1(k4_ordinal1,k6_partfun1(k4_ordinal1))) & m1_subset_1(k2_relset_1(k4_ordinal1,k6_partfun1(k4_ordinal1)),k1_zfmisc_1(k6_numbers)) )).
fof(t33_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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,D,C) & ~ ( k2_symsp_1(A,B,E,F,C,D) = k4_struct_0(A) <=> r1_orders_2(B,F,E) ) ) ) ) ) ) ) ) )).
fof(t33_sysrel,axiom,( ! [A] : ( 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))) ) ) )).
fof(t33_taxonom1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(t33_taylor_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_tarski(k2_rcomp_1(k6_xcmplx_0(C,D),k2_xcmplx_0(C,D)),k1_relset_1(k1_numbers,B)) & r1_taylor_1(B,k1_nat_1(A,1),k2_rcomp_1(k6_xcmplx_0(C,D),k2_xcmplx_0(C,D))) ) => ( r1_xxreal_0(D,k5_numbers) | ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k2_rcomp_1(k6_xcmplx_0(C,D),k2_xcmplx_0(C,D))) & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ~ r1_xxreal_0(1,F) & k1_funct_1(B,E) = k2_xcmplx_0(k9_nat_1(k1_numbers,k3_series_1(k6_taylor_1(B,k2_rcomp_1(k6_xcmplx_0(C,D),k2_xcmplx_0(C,D)),C,E)),A),k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(B,k2_rcomp_1(k6_xcmplx_0(C,D),k2_xcmplx_0(C,D))),k1_nat_1(A,1)),k2_xcmplx_0(C,k3_xcmplx_0(F,k6_xcmplx_0(E,C)))),k1_newton(k6_xcmplx_0(E,C),k1_nat_1(A,1))),k2_newton(k1_nat_1(A,1)))) ) ) ) ) ) ) ) ) ) ) )).
fof(t33_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(u1_struct_0(A)),k5_tdlat_1(A)) => ! [C] : ( 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) ) ) ) )).
fof(t33_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) )).
fof(t33_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v4_tdlat_3(A) <=> ! [B] : ( 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) ) ) ) ) ) )).
fof(t33_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(D,A,C) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(E,A,C) & v1_polynom1(E,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,k10_polynom1(A,C,D,E)),k10_polynom1(A,C,k5_termord(A,B,C,D),k5_termord(A,B,C,E))) ) ) ) ) ) )).
fof(t33_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ~ ( ~ v3_tdlat_3(A) & ! [B] : ( ( ~ 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] : ( ~ 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) ) ) ) )).
fof(t33_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t33_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v3_tex_3(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(C,u1_struct_0(B)) => v2_tops_1(C,A) ) ) ) ) ) )).
fof(t33_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) )).
fof(t33_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ v2_struct_0(E) & m1_pre_topc(E,A) ) => ! [F] : ( ( ~ 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,E,F),B) & m1_pre_topc(k2_tsep_1(A,E,k1_tsep_1(A,C,D)),C) & m1_pre_topc(k2_tsep_1(A,F,k1_tsep_1(A,C,D)),D) & m1_pre_topc(k2_tsep_1(A,B,k1_tsep_1(A,C,D)),k2_tsep_1(A,C,D)) ) => ( r1_tsep_1(C,D) | m1_pre_topc(C,D) | m1_pre_topc(D,C) | m1_pre_topc(k1_tsep_1(A,C,D),k1_tsep_1(A,E,F)) | ( ~ r1_tsep_1(k1_tsep_1(A,E,F),k1_tsep_1(A,C,D)) & ~ r1_tsep_1(B,k1_tsep_1(A,C,D)) ) ) ) ) ) ) ) ) ) )).
fof(t33_toler_1,axiom,( ! [A] : ! [B] : ( ( 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 ) )).
fof(t33_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_borsuk_2(G,A,B,C) => ! [H] : ( m1_borsuk_2(H,A,C,D) => ! [I] : ( m1_borsuk_2(I,A,D,E) => ! [J] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t33_topalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v1_borsuk_2(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t33_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t33_topgen_2,axiom,( ! [A] : ( ~ v1_finset_1(A) => ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t33_topgen_3,axiom,( k2_waybel23(k2_topgen_3) = k3_topgen_3 )).
fof(t33_topgen_4,axiom,( ! [A] : ! [B] : ~ ( 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)) ) )).
fof(t33_topgen_5,axiom,( ! [A] : ( 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] : 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) ) ) )).
fof(t33_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m3_topgrp_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t33_topreal3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ( ( 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)) ) ) ) ) )).
fof(t33_topreal6,axiom,( ! [A] : ( 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))) ) )).
fof(t33_topreal8,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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)) ) ) ) )).
fof(t33_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ( ( r2_hidden(C,k3_topreal9(A,E,B)) & r2_hidden(D,k3_topreal9(A,E,B)) ) => k9_subset_1(u1_struct_0(k15_euclid(A)),k1_rltopsp1(k15_euclid(A),C,D),k3_topreal9(A,E,B)) = k2_tarski(C,D) ) ) ) ) ) ) )).
fof(t33_topreala,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( 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)) ) ) )).
fof(t33_toprealb,axiom,( 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 )).
fof(t33_toprealc,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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))))) ) ) ) )).
fof(t33_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( 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)),k5_numbers) ) ) ) ) )).
fof(t33_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t33_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t33_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tops_3(B,A) => v1_tops_1(B,A) ) ) ) )).
fof(t33_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t33_trees_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => r2_tarski(k1_trees_1(A),k4_finseq_1(A)) ) )).
fof(t33_trees_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ! [B] : ( r2_hidden(B,A) => ( ~ v1_xboole_0(B) & v1_trees_1(B) ) ) => ( ~ v1_xboole_0(k3_tarski(A)) & v1_trees_1(k3_tarski(A)) ) ) ) )).
fof(t33_trees_3,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(t33_trees_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( v7_ordinal1(E) => ~ ( r1_xxreal_0(k1_nat_1(E,1),k3_finseq_1(B)) & C = k5_relset_1(k4_ordinal1,A,B,k2_finseq_1(k1_nat_1(E,1))) & D = k5_relset_1(k4_ordinal1,A,B,k2_finseq_1(E)) & ! [F] : ( m1_subset_1(F,A) => C != k7_finseq_1(D,k12_finseq_1(A,F)) ) ) ) ) ) ) ) )).
fof(t33_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ 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)) ) ) ) ) ) ) )).
fof(t33_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t33_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t33_turing_1,axiom,( k1_funct_1(k17_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers)) = k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,1,k5_numbers,1) & k1_funct_1(k17_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,1,1)) = k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,2,1,1) & k1_funct_1(k17_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,2,k5_numbers)) = k3_xtuple_0(3,k5_numbers,k4_xcmplx_0(1)) & k1_funct_1(k17_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,2,1)) = k3_xtuple_0(3,k5_numbers,k4_xcmplx_0(1)) & k1_funct_1(k17_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,3,1)) = k3_xtuple_0(4,1,k4_xcmplx_0(1)) )).
fof(t33_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ( r2_hidden(A,k2_msafree2(k37_twoscomp(A,B))) & r2_hidden(B,k2_msafree2(k37_twoscomp(A,B))) ) ) ) )).
fof(t33_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ? [B] : ( m1_subset_1(B,u1_struct_0(k1_uniroots(k1_complfld))) & k6_group_1(k1_uniroots(k1_complfld),B) = A ) ) )).
fof(t33_uproots,axiom,( ! [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) & v3_rlvect_1(A) & v4_rlvect_1(A) & v1_vectsp_2(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) )).
fof(t33_urysohn2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ( v3_xxreal_2(k1_integra2(A,B)) => ( r1_xxreal_0(B,k5_numbers) | v3_xxreal_2(A) ) ) ) ) )).
fof(t33_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_funct_2(C,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t33_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) ) => r2_hidden(k64_valued_1(A),k1_relset_1(k4_ordinal1,A)) ) )).
fof(t33_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( 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 ) ) ) ) ) )).
fof(t33_vectsp10,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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) ) ) ) )).
fof(t33_vectsp11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( ~ 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] : ( ( 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] : ( 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)))))) ) ) ) ) ) ) )).
fof(t33_vectsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ( v4_vectsp_1(A) => k5_struct_0(A) = k1_group_1(A) ) ) )).
fof(t33_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t33_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( u1_struct_0(C) = D => v1_vectsp_4(D,A,B) ) ) ) ) ) )).
fof(t33_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m1_vectsp_4(E,A,B) => ( m1_vectsp_4(C,A,D) => m1_vectsp_4(C,A,k1_vectsp_5(A,B,D,E)) ) ) ) ) ) ) )).
fof(t33_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_vectsp_6(D,A,B) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t33_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( 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))) ) ) ) ) )).
fof(t33_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t33_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t33_waybel11,axiom,( ! [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) & l1_waybel_9(A) ) => ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = k13_yellow_6(A,k2_waybel11(A)) => ! [B] : ( 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) ) ) ) ) ) )).
fof(t33_waybel12,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( v13_waybel_0(B,A) & v1_waybel_6(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r1_tarski(k4_yellow_4(A,B,C),B) & r2_hidden(D,B) & ? [E] : ( ~ v1_xboole_0(E) & m1_waybel12(E,A,C) & v4_card_3(E) ) & ! [E] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(t33_waybel13,axiom,( ! [A] : ( ( 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),k1_yellow_1(k7_waybel_0(A)),A) & v18_waybel_0(k2_yellow_2(A),k1_yellow_1(k7_waybel_0(A)),A) ) ) )).
fof(t33_waybel14,axiom,( ! [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] : ( 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)) ) ) ) )).
fof(t33_waybel16,axiom,( ! [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_8(A) & l1_orders_2(A) ) => ! [B] : ( 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))) ) ) )).
fof(t33_waybel19,axiom,( ! [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) ) => 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)))) ) )).
fof(t33_waybel20,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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(k4_yellow_1(A,B)) ) ) ) )).
fof(t33_waybel21,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( ~ 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)) ) ) ) ) )).
fof(t33_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( v2_waybel23(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t33_waybel24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & v1_yellow_0(B) & l1_orders_2(B) ) => k3_yellow_0(k5_yellow_1(u1_struct_0(A),B)) = k6_struct_0(A,B,k3_yellow_0(B)) ) ) )).
fof(t33_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_waybel25(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t33_waybel27,axiom,( ! [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] : ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k2_waybel27(A,k2_yellow_1(k1_tarski(k5_numbers)))),u1_struct_0(k1_yellow_1(k5_waybel11(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_waybel27(A,k2_yellow_1(k1_tarski(k5_numbers)))),u1_struct_0(k1_yellow_1(k5_waybel11(A)))))) & v23_waybel_0(B,k2_waybel27(A,k2_yellow_1(k1_tarski(k5_numbers))),k1_yellow_1(k5_waybel11(A))) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k2_yellow_1(k1_tarski(k5_numbers)))) & v22_waybel_0(C,A,k2_yellow_1(k1_tarski(k5_numbers))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k2_yellow_1(k1_tarski(k5_numbers)))))) ) => k1_funct_1(B,C) = k8_relset_1(u1_struct_0(A),u1_struct_0(k2_yellow_1(k1_tarski(k5_numbers))),C,k1_tarski(1)) ) ) ) )).
fof(t33_waybel29,axiom,( ! [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) ) => ( v3_waybel_3(k1_yellow_1(k5_waybel11(A))) <=> ! [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) ) => k1_waybel29(k3_yellow_3(B,A)) = k1_waybel25(k2_borsuk_1(k1_waybel29(B),k1_waybel29(A))) ) ) ) )).
fof(t33_waybel30,axiom,( ! [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) & l1_waybel_9(A) ) => ! [B] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_tarski(a_3_2_waybel30(A,B,C),a_2_3_waybel30(A,C)) ) ) ) )).
fof(t33_waybel34,axiom,( ! [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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k1_yellow_2(A,A,B))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t33_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t33_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(t33_waybel_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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))) ) ) )).
fof(t33_waybel_4,axiom,( ! [A] : ( ( 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),k1_yellow_1(k3_waybel_4(A)),k8_waybel_4(A)) ) )).
fof(t33_waybel_5,axiom,( ! [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) ) => ( v3_waybel_3(A) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ( ? [C] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(t33_waybel_6,axiom,( ! [A] : ( ( 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] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k1_tarski(k1_xboole_0)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k2_yellow_1(k1_tarski(k1_xboole_0)))))) ) => ! [C] : ( ( 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(k2_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,k2_yellow_1(k1_tarski(k1_xboole_0))) & v20_waybel_0(B,A,k2_yellow_1(k1_tarski(k1_xboole_0))) ) ) ) ) ) )).
fof(t33_waybel_7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v5_waybel_6(B,A) => v1_waybel_7(k5_waybel_0(A,B),A) ) ) ) )).
fof(t33_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v8_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r3_waybel_9(A,B,C) & r3_waybel_9(A,B,D) ) => C = D ) ) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_waybel_9(A,B,C) => r2_hidden(C,k10_yellow_6(A,B)) ) ) ) ) ) )).
fof(t33_weddwitt,axiom,( ! [A] : ( ( ~ 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] : ( 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))) ) ) )).
fof(t33_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(D,B) & r2_hidden(E,C) & k3_metric_1(A,D,E) = k10_weierstr(A,B,C) ) ) ) ) ) ) ) )).
fof(t33_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ( v2_wellord1(A) => ! [B] : ( ! [C] : ( ( 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) ) ) ) )).
fof(t33_wsierp_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ? [D] : ( v1_int_1(D) & ? [E] : ( v1_int_1(E) & k2_xcmplx_0(k3_xcmplx_0(B,D),k3_xcmplx_0(C,E)) = A ) ) <=> r1_int_1(k3_int_2(B,C),A) ) ) ) ) )).
fof(t33_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(A,B) => r1_tarski(k4_xboole_0(A,C),k4_xboole_0(B,C)) ) )).
fof(t33_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k9_xboolean(A,k5_xboolean(A,B)) = k4_xboolean(k3_xboolean(A),k3_xboolean(B)) ) ) )).
fof(t33_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( k2_xcmplx_0(A,B) = k2_xcmplx_0(C,D) => k6_xcmplx_0(A,C) = k6_xcmplx_0(D,B) ) ) ) ) ) )).
fof(t33_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => r1_xxreal_0(k5_numbers,k2_xcmplx_0(A,B)) ) ) ) )).
fof(t33_xtuple_0,axiom,( ! [A] : ! [B] : r1_tarski(k4_xboole_0(k11_xtuple_0(A),k11_xtuple_0(B)),k11_xtuple_0(k4_xboole_0(A,B))) )).
fof(t33_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => k3_xxreal_0(k3_xxreal_0(A,B),C) = k3_xxreal_0(A,k3_xxreal_0(B,C)) ) ) ) )).
fof(t33_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( ~ r1_xxreal_0(B,A) & v1_xboole_0(k4_xxreal_1(A,B)) ) ) ) )).
fof(t33_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) ) ) )).
fof(t33_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( v1_xreal_0(C) => k3_xxreal_3(k1_xxreal_3(C,A),k1_xxreal_3(C,B)) = k3_xxreal_3(A,B) ) ) ) ) )).
fof(t33_yellow10,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( 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))) ) ) ) ) )).
fof(t33_yellow12,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( ( 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)))) ) ) ) ) ) )).
fof(t33_yellow14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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)) ) ) ) ) ) )).
fof(t33_yellow16,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_yellow_1(A,B)))) => ( r2_yellow_0(k4_yellow_1(A,B),C) => ! [D] : ( m1_subset_1(D,A) => k4_waybel_3(A,B,k2_yellow_0(k4_yellow_1(A,B),C),D) = k2_yellow_0(k3_waybel_3(A,B,D),k5_waybel_3(A,B,D,C)) ) ) ) ) ) )).
fof(t33_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ( v2_yellow18(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t33_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_compts_1(A) <=> ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r3_waybel_9(A,B,C) ) ) ) ) )).
fof(t33_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_altcat_1(B) ) => ! [C] : ( ( v10_functor0(C,A,B) & l2_functor0(C,A,B) ) => ( v20_functor0(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( k1_altcat_1(B,D,E) != k1_xboole_0 => ! [F] : ( m1_subset_1(F,k1_altcat_1(B,D,E)) => ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & ? [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t33_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( B = k2_yellow_0(A,C) <=> ( r1_lattice3(A,C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_lattice3(A,C,D) => r1_orders_2(A,D,B) ) ) ) ) ) ) )).
fof(t33_yellow_2,axiom,( ! [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] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t33_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t33_yellow_4,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t33_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t33_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t33_yellow_7,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t33_yellow_9,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t33_zf_fund1,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_zf_lang)) ) => ( r2_hidden(A,k4_zf_fund1(B)) <=> ? [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) & r2_hidden(C,B) & A = k3_zf_fund1(C) ) ) ) )).
fof(t33_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ( k12_zf_lang(A,C) = k12_zf_lang(B,D) => ( A = B & C = D ) ) ) ) ) ) )).
fof(t33_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => k20_zf_lang(k13_zf_lang(B,A)) = k8_zf_lang(B,k6_zf_lang(A)) ) ) )).
fof(t33_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(C,B) => ( r2_hidden(A,C) | r1_tarski(C,k4_xboole_0(B,k1_tarski(A))) ) ) )).
fof(t33_zfrefle1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ~ ( r2_hidden(k4_ordinal1,A) & ! [B] : ( ( 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] : ( ( v3_ordinal1(C) & m1_subset_1(C,A) ) => ! [D] : ( ~ v1_xboole_0(D) => ( ( k4_ordinal4(A,B,C) = C & D = k4_classes1(C) ) => ( k1_xboole_0 = C | r3_zfrefle1(D,A) ) ) ) ) ) ) ) ) )).
fof(t33_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => r1_struct_0(B,k4_struct_0(A)) ) ) )).
fof(t33_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( m1_zmodul02(C,A) => ! [D] : ( v1_int_1(D) => r1_zmodul02(A,k23_zmodul02(A,D,k22_zmodul02(A,B,C)),k22_zmodul02(A,k23_zmodul02(A,D,B),k23_zmodul02(A,D,C))) ) ) ) ) )).
fof(t33_zmodul03,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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) & v1_zmodul03(B) & l1_zmodul01(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_zmodul02(A,B)))) => ( D = a_3_1_zmodul03(A,B,C) => ! [E] : ( m2_finseq_1(E,u1_struct_0(B)) => ( ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( r2_hidden(F,k4_finseq_1(E)) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ~ ( G = k1_funct_1(E,F) & r1_struct_0(k1_vectsp_7(k9_int_3(A),k12_zmodul02(A,B),D),k13_zmodul02(A,B,G)) ) ) ) ) => r1_struct_0(k1_vectsp_7(k9_int_3(A),k12_zmodul02(A,B),D),k13_zmodul02(A,B,k4_rlvect_1(B,E))) ) ) ) ) ) ) ) )).
fof(t340_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t341_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t342_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t343_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t344_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t345_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t346_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t347_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t348_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t349_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t34_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_abcmiz_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t34_abcmiz_1,axiom,( ! [A] : ( 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 ) ) )).
fof(t34_abcmiz_a,axiom,( ! [A] : ( m1_subset_1(A,k2_abcmiz_1) => ! [B] : ( ( 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 ) ) )).
fof(t34_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t34_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_aff_4(B,A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t34_afinsq_1,axiom,( ! [A] : ! [B] : ( ( 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),k5_numbers) = A ) )).
fof(t34_afinsq_2,axiom,( ! [A] : ( ( v1_finset_1(A) & v6_membered(A) ) => ! [B] : ( ( v1_finset_1(B) & v6_membered(B) ) => ( r1_afinsq_2(A,B) => ( A = k1_xboole_0 | k1_recdef_1(k4_afinsq_2(A),k5_numbers) = k1_recdef_1(k4_afinsq_2(k2_xboole_0(A,B)),k5_numbers) ) ) ) ) )).
fof(t34_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t34_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t34_algspec1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( v2_funct_1(C) & r1_xboole_0(k10_xtuple_0(C),u4_struct_0(A)) ) => r1_algspec1(A,B,C) ) ) ) ) )).
fof(t34_algstr_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k14_algstr_4(A))) => ~ ( r1_xxreal_0(2,k15_algstr_4(A,B)) & ! [C] : ( m1_subset_1(C,u1_struct_0(k14_algstr_4(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t34_altcat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v3_altcat_2(B,A) & m1_altcat_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( C = D => k8_altcat_1(B,C) = k8_altcat_1(A,D) ) ) ) ) ) )).
fof(t34_altcat_4,axiom,( ! [A] : ( l2_altcat_1(A) => ! [B] : ( 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) ) ) ) )).
fof(t34_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k4_ordinal1) => k7_ami_wstd(A,B,C,k5_numbers) = C ) ) ) )).
fof(t34_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t34_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( r1_analort(A,F,G,B,D,C,E) => r1_analort(A,F,G,D,B,E,C) ) ) ) ) ) ) ) ) )).
fof(t34_anproj_2,axiom,( ! [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) & l1_rlvect_1(A) ) => ~ ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & ? [I] : ( v1_xreal_0(I) & ? [J] : ( v1_xreal_0(J) & 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] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( 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 = k5_numbers & G = k5_numbers & H = k5_numbers & I = k5_numbers ) ) ) ) ) ) ) ) ) ) & ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t34_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( m2_subset_1(F,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => k15_aofa_a00(A,B,C,D,u8_aofa_a00(A),k2_aofa_a01(A,C),F) = k7_margrel1 ) ) ) ) ) ) )).
fof(t34_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_aofa_i00(E,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) ) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),E) => ! [G] : ( 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) = k5_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) = k5_numbers ) & ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t34_armstrng,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => r1_tarski(B,k9_armstrng(A,k10_armstrng(A,B))) ) ) )).
fof(t34_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => r1_arytm_3(k6_arytm_3(A),k7_arytm_3(A)) ) )).
fof(t34_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v4_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v4_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) & k1_seq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) = k5_numbers ) => ( r2_hidden(A,k6_asympt_0(B)) & ~ r2_hidden(A,k8_asympt_0(B)) ) ) ) ) )).
fof(t34_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( 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] : ( r2_hidden(C,k1_autalg_1(A)) => k1_funct_1(B,C) = k16_funcop_1(k5_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)))) ) ) ) )).
fof(t34_bagorder,axiom,( ! [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) ) => ! [B] : ( 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))) ) ) )).
fof(t34_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => r2_hidden(k2_bcialg_1(A,B),k5_bcialg_1(A)) ) ) )).
fof(t34_bcialg_2,axiom,( ! [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] : ( 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)) ) ) ) )).
fof(t34_bcialg_3,axiom,( ! [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) ) => ( ( ~ 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) ) ) ) )).
fof(t34_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t34_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t34_bcialg_6,axiom,( ! [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] : ( m1_bcialg_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( C = E & D = F ) => k1_bcialg_1(A,C,D) = k1_bcialg_1(B,E,F) ) ) ) ) ) ) ) )).
fof(t34_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t34_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k4_bhsp_1(A,B,B) = k5_numbers ) ) )).
fof(t34_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_bhsp_2(D,A) & k1_bhsp_2(A,D) = C ) => ( v2_comseq_2(k2_bhsp_2(A,k4_normsp_1(A,D,B))) & k1_seq_2(k2_bhsp_2(A,k4_normsp_1(A,D,B))) = k3_bhsp_1(A,k5_algstr_0(A,C,B)) ) ) ) ) ) ) )).
fof(t34_bhsp_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ~ ( ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,A,D) = k1_power(D,k9_nat_1(k1_numbers,k2_bhsp_2(B,C),D)) ) & v2_comseq_2(A) & ~ r1_xxreal_0(k1_seq_2(A),1) & v1_bhsp_4(C,B) ) ) ) ) )).
fof(t34_bilinear,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t34_binari_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k1_binari_3(k2_xcmplx_0(A,1),B) = k7_finseq_1(k10_binarith(k4_ordinal1,k4_nat_d(B,2)),k1_binari_3(A,k3_nat_d(B,2))) ) ) )).
fof(t34_binari_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ? [C] : ( m1_subset_1(C,k6_margrel1) & k1_binari_3(k2_xcmplx_0(B,1),A) = k8_finseq_1(k6_margrel1,k1_binari_3(B,A),k12_finseq_1(k6_margrel1,C)) ) ) ) )).
fof(t34_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_boolealg(A,k4_lattices(A,k1_boolealg(A,B,C),C),k5_lattices(A)) ) ) ) )).
fof(t34_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t34_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_topmetr)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_topmetr)) => ~ ( ~ r1_xxreal_0(B,A) & A != k5_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))) ) ) ) ) )).
fof(t34_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( A = k3_rcomp_1(B,C) => ( B = C | k2_pre_topc(k3_topmetr,A) = k1_rcomp_1(B,C) ) ) ) ) ) )).
fof(t34_borsuk_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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))))) ) ) ) ) ) ) ) )).
fof(t34_borsuk_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => k16_rvsum_1(k11_toprealc(3,A)) = k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k1_euclid_5(A)),k1_square_1(k2_euclid_5(A))),k1_square_1(k3_euclid_5(A))) ) )).
fof(t34_bspace,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k7_bspace(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t34_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t34_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t34_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t34_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t34_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t34_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(E,A) => ( r3_bvfunc_2(A,D,B,E) => r2_funct_2(A,k6_margrel1,k7_bvfunc_2(A,k2_bvfunc_1(A,D,C),B,E),k2_bvfunc_1(A,D,k7_bvfunc_2(A,C,B,E))) ) ) ) ) ) ) )).
fof(t34_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(F,A) => r1_bvfunc_1(A,k2_bvfunc_1(A,k6_bvfunc_2(A,k9_bvfunc_1(A,D,k1_bvfunc_1(A,E)),B,F),k6_bvfunc_2(A,k9_bvfunc_1(A,C,E),B,F)),k6_bvfunc_2(A,k9_bvfunc_1(A,C,k1_bvfunc_1(A,D)),B,F)) ) ) ) ) ) ) )).
fof(t34_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t34_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t34_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t34_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [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))) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k11_c0sp1(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k11_c0sp1(A))) => ! [G] : ( 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] : ( m1_subset_1(H,A) => k3_funct_2(A,k1_numbers,D,H) = k5_real_1(k3_funct_2(A,k1_numbers,B,H),k3_funct_2(A,k1_numbers,C,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t34_c0sp2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_c0sp2(B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_c0sp2(B))) => ( ( k2_normsp_0(k9_c0sp2(B),C) = k5_numbers => C = k4_struct_0(k9_c0sp2(B)) ) & ( C = k4_struct_0(k9_c0sp2(B)) => k2_normsp_0(k9_c0sp2(B),C) = k5_numbers ) & k2_normsp_0(k9_c0sp2(B),k1_rlvect_1(k9_c0sp2(B),C,A)) = k3_xcmplx_0(k9_complex1(A),k2_normsp_0(k9_c0sp2(B),C)) & r1_xxreal_0(k2_normsp_0(k9_c0sp2(B),k1_algstr_0(k9_c0sp2(B),C,D)),k2_xcmplx_0(k2_normsp_0(k9_c0sp2(B),C),k2_normsp_0(k9_c0sp2(B),D))) ) ) ) ) ) )).
fof(t34_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k2_zfmisc_1(k4_calcul_1(A),k2_cqc_the1)) => ! [C] : ( m2_finseq_1(C,k2_zfmisc_1(k4_calcul_1(A),k2_cqc_the1)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t34_card_2,axiom,( ! [A] : ! [B] : ( r1_xboole_0(A,B) => k1_card_1(k2_xboole_0(A,B)) = k1_card_2(k1_card_1(A),k1_card_1(B)) ) )).
fof(t34_card_fin,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( k1_tarski(C) = k8_relat_1(B,k1_tarski(D)) => k2_card_fin(A,B,D) = k1_funct_1(A,C) ) ) ) )).
fof(t34_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_cat_1(D,A,B,C) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t34_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_cat_1(A,B,k2_cat_4(A,B,B)) != k1_xboole_0 ) ) )).
fof(t34_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => k5_card_1(k2_catalan2(k3_xcmplx_0(2,A),A)) = k1_catalan1(k1_nat_1(A,1)) ) )).
fof(t34_cayldick,axiom,( k6_algstr_0(k4_cayldick(k4_cayldick(k4_cayldick(k3_cayldick))),k6_algstr_0(k4_cayldick(k4_cayldick(k4_cayldick(k3_cayldick))),k5_cayldick(k4_cayldick(k4_cayldick(k3_cayldick)),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k5_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick))),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)))),k5_cayldick(k4_cayldick(k4_cayldick(k3_cayldick)),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k5_struct_0(k3_cayldick),k4_struct_0(k3_cayldick))),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick))))),k5_cayldick(k4_cayldick(k4_cayldick(k3_cayldick)),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick))),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k5_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick))))) = k5_cayldick(k4_cayldick(k4_cayldick(k3_cayldick)),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick))),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_algstr_0(k3_cayldick,k5_struct_0(k3_cayldick)),k4_struct_0(k3_cayldick)))) )).
fof(t34_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(t34_cfcont_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ( r1_cfcont_1(C,B) => r1_cfcont_1(k25_valued_1(k2_numbers,k2_numbers,C,A),B) ) ) ) ) )).
fof(t34_cfdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [B] : ( v1_xcmplx_0(B) => ( r1_cfdiff_1(A,B) => r1_cfcont_1(A,B) ) ) ) )).
fof(t34_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t34_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => r1_tarski(k8_cgames_1(A),k10_cgames_1(A)) ) )).
fof(t34_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(B)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(B)) => ! [E] : ( 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] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(B)) => r1_xxreal_0(k1_funct_1(C,F),k1_funct_1(D,F)) ) & ? [F] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(B)) & r1_xxreal_0(k1_funct_1(C,F),k1_funct_1(D,F)) ) ) ) ) ) ) ) )).
fof(t34_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( 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 ) ) ) ) )).
fof(t34_circcmb3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)) ) ) )).
fof(t34_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(C,F))) => ! [H] : ( m1_subset_1(H,k4_card_3(u3_msualg_1(A,D))) => ! [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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t34_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t34_classes1,axiom,( ! [A] : ( v3_ordinal1(A) => r1_tarski(k3_tarski(k4_classes1(A)),k4_classes1(A)) ) )).
fof(t34_classes2,axiom,( ! [A] : ( v2_classes1(A) => k1_card_1(A) = k1_card_1(k4_classes1(k1_card_1(A))) ) )).
fof(t34_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k14_clopban1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_clopban1(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_clopban1(A,B))) => ( E = k1_algstr_0(k14_clopban1(A,B),C,D) <=> ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t34_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v1_xreal_0(C) => ( ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(1,D) => k9_nat_1(k1_numbers,k5_normsp_0(A,B),D) = k7_xcmplx_0(1,k2_power(D,C)) ) ) => ( r1_xxreal_0(C,1) | v2_clopban3(B,A) ) ) ) ) ) )).
fof(t34_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t34_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v5_mssubfam(C,A,B) & m3_pboole(C,A,k1_mboolean(A,B)) ) => ! [D] : ( m1_pboole(D,A,k5_mssubfam(A,B)) => ! [E] : ( m2_pboole(E,A,k5_mssubfam(A,B),k5_mssubfam(A,B)) => ( ( r1_pboole(A,D,C) & ! [F] : ( m1_pboole(F,A,k5_mssubfam(A,B)) => ! [G] : ( ( v2_relat_1(G) & m3_pboole(G,A,k1_mboolean(A,B)) ) => ( ! [H] : ( ( 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) ) ) ) ) ) )).
fof(t34_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t34_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_clvect_1(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ( D = B => k4_algstr_0(A,B) = k4_algstr_0(C,D) ) ) ) ) ) )).
fof(t34_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_clvect_2(D,A) & k1_clvect_2(A,D) = C ) => ( v2_comseq_2(k2_clvect_2(A,k4_normsp_1(A,D,B))) & k1_seq_2(k2_clvect_2(A,k4_normsp_1(A,D,B))) = k13_csspace(A,k5_algstr_0(A,C,B)) ) ) ) ) ) ) )).
fof(t34_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k1_power(D,k9_nat_1(k1_numbers,k2_clvect_2(A,B),D)) ) & v2_comseq_2(C) & ~ r1_xxreal_0(k1_seq_2(C),1) & v1_clvect_3(B,A) ) ) ) ) )).
fof(t34_coh_sp,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r2_hidden(k4_tarski(k6_partfun1(A),A),k16_coh_sp(B)) ) )).
fof(t34_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( ( 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] : ! [E] : ( r2_hidden(k2_xboole_0(D,E),A) => ! [F] : ! [G] : ( ( 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) ) ) ) ) ) )).
fof(t34_combgras,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ( r1_ordinal1(k1_nat_1(A,1),k1_card_1(B)) => ( r1_xxreal_0(A,k5_numbers) | ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(t34_compl_sp,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t34_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k8_complex1(k6_xcmplx_0(A,B)) = k6_xcmplx_0(k8_complex1(A),k8_complex1(B)) ) ) )).
fof(t34_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k1_complex2(A,k2_xcmplx_0(B,C)) = k2_xcmplx_0(k1_complex2(A,B),k1_complex2(A,C)) ) ) ) )).
fof(t34_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( 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)) ) ) ) )).
fof(t34_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( v1_xcmplx_0(B) => k10_seq_4(k15_seq_4(k3_finseq_1(A)),B) = k15_seq_4(k3_finseq_1(A)) ) ) )).
fof(t34_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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)))) ) ) ) )).
fof(t34_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( v6_compos_0(D,u1_compos_1(A)) & m1_subset_1(D,u1_compos_1(A)) ) => ! [E] : ( ( v6_compos_0(E,u1_compos_1(A)) & m1_subset_1(E,u1_compos_1(A)) ) => ! [F] : ( ( 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 ) ) ) ) ) ) )).
fof(t34_comptrig,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( r1_xxreal_0(k5_numbers,k1_comptrig(A)) & ~ r1_xxreal_0(k3_xcmplx_0(2,k28_sin_cos),k1_comptrig(A)) ) ) )).
fof(t34_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => r2_hidden(k5_comput_1(B,A),k2_comput_1(k4_ordinal1)) ) ) )).
fof(t34_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,C,k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,A)),k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,C,B),A)) ) ) ) )).
fof(t34_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => v7_valued_0(k3_series_1(k55_valued_1(k4_ordinal1,k2_numbers,A))) ) )).
fof(t34_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( v3_conlat_1(B,A) & ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) & l2_conlat_1(B,A) ) => ! [C] : ( ( v3_conlat_1(C,A) & ~ v4_conlat_1(C,A) & v6_conlat_1(C,A) & l2_conlat_1(C,A) ) => ! [D] : ( ( v3_conlat_1(D,A) & ~ v4_conlat_1(D,A) & v6_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) ) ) ) ) )).
fof(t34_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t34_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_connsp_3(B,A) ) => ( v2_connsp_1(B,A) => v3_connsp_1(B,A) ) ) ) )).
fof(t34_convex1,axiom,( ! [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) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => k1_convex1(A,B,k5_numbers) = k6_domain_1(u1_struct_0(A),k4_struct_0(A)) ) ) )).
fof(t34_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_convex4(C,A) => ! [D] : ( m1_convex4(D,A) => k3_funct_2(u1_struct_0(A),k2_numbers,k9_convex4(A,C,D),B) = k6_xcmplx_0(k3_funct_2(u1_struct_0(A),k2_numbers,C,B),k3_funct_2(u1_struct_0(A),k2_numbers,D,B)) ) ) ) ) )).
fof(t34_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),k3_qc_lang1(A),k9_funct_2(k3_qc_lang1(A),k3_qc_lang1(A))) => ! [F] : ( 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)),D,B,F,E),k15_cqc_sim1(A,C)) & 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,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)),C,k13_cqc_sim1(A,C),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,D),B,F,E),k15_cqc_sim1(A,C)) & ! [G] : ( 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,D,G),B,F,E),k15_cqc_sim1(A,C)) ) & ! [G] : ( m2_subset_1(G,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [H] : ( 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,D),H,F,E),k15_cqc_sim1(A,C)) ) ) ) & ! [G] : ( m2_subset_1(G,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [H] : ( m1_subset_1(H,k1_qc_lang1(A)) => ! [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,D),H,F,I),k15_cqc_sim1(A,C)) | 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,D),H,k6_subset_1(F,k6_domain_1(k3_qc_lang1(A),G)),I),k15_cqc_sim1(A,C)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t34_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ( v1_cqc_the1(B,A) => r1_tarski(k4_cqc_the1(A),B) ) ) ) )).
fof(t34_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t34_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k9_complex1(k12_csspace(A,B,B)) = k3_complex1(k12_csspace(A,B,B)) ) ) )).
fof(t34_dickson,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( v4_dickson(A) & ! [C] : ~ ( r1_dickson(A,B,C) & ! [D] : ( r1_dickson(A,B,D) => r1_tarski(C,D) ) ) ) ) ) )).
fof(t34_diff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t34_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => k1_funct_1(D,E) = k7_xcmplx_0(C,E) ) => ( A = B | A = k5_numbers | B = k5_numbers | k9_diff_1(D,A,B) = k4_xcmplx_0(k7_xcmplx_0(C,k3_xcmplx_0(A,B))) ) ) ) ) ) ) )).
fof(t34_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( ( 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_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,C,D),A),1),B) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(C,k2_xcmplx_0(B,k7_xcmplx_0(A,2))),k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(D,A),1),B)),k3_xcmplx_0(k1_funct_1(D,k6_xcmplx_0(B,k7_xcmplx_0(A,2))),k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(C,A),1),B))) ) ) ) ) )).
fof(t34_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k23_sin_cos(k6_xcmplx_0(A,B)) = k7_xcmplx_0(k23_sin_cos(A),k23_sin_cos(B)) ) ) )).
fof(t34_dilworth,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v2_dilworth(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t34_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t34_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k4_finseq_1(C))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(B)) => ( ( E = k8_relset_1(k4_ordinal1,A,C,B) & D = k5_dist_2(A,C,E) ) => k5_card_1(k8_relset_1(k4_ordinal1,A,C,F)) = k5_card_1(k8_relset_1(k4_ordinal1,A,D,F)) ) ) ) ) ) ) ) )).
fof(t34_e_siec,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t34_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ( B = k5_numbers <=> k2_ec_pf_1(A,B) = k5_numbers ) ) ) )).
fof(t34_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t34_ens_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k11_ens_1(A))) => ~ ( v10_cat_1(B,k11_ens_1(A)) & ! [C] : B != k1_tarski(C) ) ) ) )).
fof(t34_entropy1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( 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] : ( v7_ordinal1(D) => ( r1_xxreal_0(1,D) => ( r1_xxreal_0(k3_finseq_1(B),D) | k1_matrprob(A,C,k1_nat_1(D,1)) = k8_finseq_1(A,k1_matrprob(A,C,D),k1_matrprob(A,B,k1_nat_1(D,1))) ) ) ) ) => ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(1,D) => ( r1_xxreal_0(k3_finseq_1(C),D) | ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k2_finseq_1(k1_matrix_0(B))) => ( r2_hidden(k2_xcmplx_0(k3_xcmplx_0(D,k1_matrix_0(B)),E),k4_finseq_1(k1_matrprob(A,C,k1_nat_1(D,1)))) & k1_funct_1(k1_matrprob(A,C,k1_nat_1(D,1)),k2_xcmplx_0(k3_xcmplx_0(D,k1_matrix_0(B)),E)) = k1_funct_1(k1_matrprob(A,B,k1_nat_1(D,1)),E) ) ) ) ) ) ) ) ) ) ) )).
fof(t34_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : k5_enumset1(A,A,B,C,D,E,F) = k4_enumset1(A,B,C,D,E,F) )).
fof(t34_eqrel_1,axiom,( ! [A] : ! [B] : ( m1_eqrel_1(B,A) => ? [C] : ( 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) ) ) )).
fof(t34_equation,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t34_euclid,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k5_algstr_0(k15_euclid(2),k19_euclid(A,C),k19_euclid(B,D)) = k19_euclid(k6_xcmplx_0(A,B),k6_xcmplx_0(C,D)) ) ) ) ) )).
fof(t34_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => k22_rvsum_1(B,B) = k1_square_1(k12_euclid(B)) ) ) )).
fof(t34_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xxreal_0(k28_sin_cos,k3_euclid_3(A)) & ~ r1_xxreal_0(k28_sin_cos,k3_euclid_3(B)) & r1_xxreal_0(k28_sin_cos,k3_euclid_3(k3_rlvect_1(k15_euclid(2),A,B))) ) ) ) )).
fof(t34_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => k1_square_1(k12_euclid(k7_euclid(A,B,C))) = k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k12_euclid(B)),k3_xcmplx_0(2,k22_rvsum_1(B,C))),k1_square_1(k12_euclid(C))) ) ) ) )).
fof(t34_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(3))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(3))) => k6_euclid_5(A,B,C) = k6_euclid_5(C,A,B) ) ) ) )).
fof(t34_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( 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) != k6_xcmplx_0(k4_euclid_3(A,D,B),k28_sin_cos) & k4_euclid_3(A,C,B) != k2_xcmplx_0(k4_euclid_3(A,D,B),k28_sin_cos) ) ) ) ) ) ) ) ) )).
fof(t34_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_rlsub_1(B,k10_funcsdom(k2_finseq_1(A))) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(C,u1_struct_0(B)) => r2_hidden(k9_euclid(A,C,D),u1_struct_0(B)) ) ) ) ) ) )).
fof(t34_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => 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)) ) ) ) )).
fof(t34_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ( r3_euclidlp(A,B,C) => ( B != k5_euclid(A) & C != k5_euclid(A) ) ) ) ) ) )).
fof(t34_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(E) & v5_relat_1(E,D) & v1_funct_1(E) & v1_exchsort(E) ) => ( r2_hidden(C,k9_xtuple_0(E)) => ( C = A | C = B | k7_partfun1(D,k9_funct_7(E,A,B),C) = k7_partfun1(D,E,C) ) ) ) )).
fof(t34_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ( 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) ) ) ) ) ) ) )).
fof(t34_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ( v4_circcomb(B,A) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t34_facirc_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,k1_nat_1(A,1)) & v1_finseq_1(B) & v2_facirc_1(B) ) => ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & v2_facirc_1(C) & ? [D] : ( ~ v1_xtuple_0(D) & B = k7_finseq_1(C,k9_finseq_1(D)) ) ) ) ) )).
fof(t34_fcont_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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))) ) ) ) )).
fof(t34_fdiff_10,axiom,( ! [A] : ( ( 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,k18_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)),A),B) = k6_xcmplx_0(k6_xcmplx_0(k1_square_1(k1_funct_1(k18_sin_cos,B)),k3_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k16_sin_cos,B)),k1_funct_1(k18_sin_cos,B))),k1_square_1(k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t34_fdiff_11,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fdiff_9,k2_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fdiff_9,k2_sin_cos9),A),B) = k6_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,B),k1_funct_1(k2_sin_cos9,B)),k1_square_1(k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(1,k3_xcmplx_0(k1_funct_1(k18_sin_cos,B),k2_xcmplx_0(1,k1_square_1(B))))) ) ) ) ) ) )).
fof(t34_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ~ ( r2_hidden(C,k3_limfunc1(A)) & r1_xxreal_0(k5_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))) ) ) ) ) )).
fof(t34_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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(k7_xcmplx_0(1,2))))) & C = k3_valued_1(k1_numbers,k1_numbers,k1_numbers,D,E) & E = k1_taylor_1(2) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => ( k1_funct_1(D,F) = k1_square_1(A) & ~ r1_xxreal_0(k1_funct_1(C,F),k5_numbers) ) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(k7_xcmplx_0(1,2))),B) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(k7_xcmplx_0(1,2))),B),F) = k3_xcmplx_0(F,k6_prepower(k2_xcmplx_0(k1_square_1(A),k1_newton(F,2)),k4_xcmplx_0(k7_xcmplx_0(1,2)))) ) ) ) ) ) ) ) ) ) )).
fof(t34_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k22_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k22_sin_cos)) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_1(C,D) = k4_xcmplx_0(D) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k3_taylor_1),A) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k3_taylor_1),A),D) = k7_xcmplx_0(k6_xcmplx_0(k23_sin_cos(D),k23_sin_cos(k4_xcmplx_0(D))),k2_xcmplx_0(k23_sin_cos(D),k23_sin_cos(k4_xcmplx_0(D)))) ) ) ) ) ) ) ) )).
fof(t34_fdiff_7,axiom,( ! [A] : ( ( 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,k22_sin_cos,k16_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k16_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k16_sin_cos),A),B) = k3_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_funct_1(k18_sin_cos,k1_funct_1(k22_sin_cos,B))) ) ) ) ) ) )).
fof(t34_fdiff_8,axiom,( ! [A] : ( ( 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)),k26_sin_cos))) => ( r2_hidden(k5_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)),k26_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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)),k26_sin_cos),A),B) = k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(k1_funct_1(k16_sin_cos,B),k1_funct_1(k18_sin_cos,B)),k1_square_1(B))),k7_xcmplx_0(k7_xcmplx_0(1,B),k1_square_1(k1_funct_1(k18_sin_cos,B)))) ) ) ) ) ) ) )).
fof(t34_fdiff_9,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k1_fdiff_9),A),B) = k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,B),k1_funct_1(k16_sin_cos,k1_funct_1(k16_sin_cos,B))),k1_square_1(k1_funct_1(k18_sin_cos,k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t34_fib_num2,axiom,( k2_fib_num = k2_power(k4_xcmplx_0(k1_fib_num),k4_xcmplx_0(1)) )).
fof(t34_fib_num3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k1_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)) ) ) ) )).
fof(t34_fib_num4,axiom,( ! [A] : ( 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)) ) ) ) )).
fof(t34_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_finseq_1(B,A) => ! [C] : ( m1_finseq_1(C,A) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t34_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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))) ) ) ) ) )).
fof(t34_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t34_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ( ~ ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_lattices(A,B,C) = B ) & k6_filter_2(A,B) = u1_struct_0(A) ) ) ) )).
fof(t34_finseq_1,axiom,( ! [A] : ( ( 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 ) ) )).
fof(t34_finseq_2,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m2_finseq_1(E,C) => ! [F] : ( ( 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(k4_ordinal1,C,C,D,E,F) = k10_finseq_1(k1_funct_1(F,A),k1_funct_1(F,B)) ) ) ) ) ) )).
fof(t34_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k9_finseq_1(A) != k11_finseq_1(B,C,D) )).
fof(t34_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_hidden(B,k10_xtuple_0(A)) => k3_finseq_1(k5_finseq_4(A,B)) = k6_xcmplx_0(k4_finseq_4(A,B),1) ) ) )).
fof(t34_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( 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))) ) ) ) ) )).
fof(t34_finseq_6,axiom,( ! [A] : ! [B] : ! [C] : ~ ( A != C & B != C & k6_finseq_4(k11_finseq_1(A,B,C),C) != k1_xboole_0 ) )).
fof(t34_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( 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)) & r1_xxreal_0(1,E) & r1_xxreal_0(E,k3_finseq_1(B)) ) => ( C = E | D = E | k2_finseq_7(A,k2_finseq_7(A,B,C,D),D,E) = k2_finseq_7(A,k2_finseq_7(A,B,C,E),C,D) ) ) ) ) ) ) ) )).
fof(t34_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v3_card_1(D,C) & m2_finseq_1(D,A) ) => ! [E] : ( ( 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(k4_ordinal1,A,k3_finseqop(A,A,A,E,B,D),k2_finseqop(A,A,A,E,D,B)) ) ) ) ) ) ) )).
fof(t34_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)))) ) ) ) ) ) )).
fof(t34_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) )).
fof(t34_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t34_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k7_flang_1(A,k7_flang_1(A,B,D),C) = k7_flang_1(A,B,k3_xcmplx_0(D,C)) ) ) ) )).
fof(t34_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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) ) ) ) ) )).
fof(t34_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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) ) ) ) ) )).
fof(t34_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t34_frechet,axiom,( ? [A] : ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) & v3_frechet(A) & ~ v1_frechet(A) ) )).
fof(t34_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( k9_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))) ) ) ) ) ) )).
fof(t34_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => k7_fsm_1(A,B,C,k5_numbers) = k1_tarski(u1_struct_0(C)) ) ) ) )).
fof(t34_fsm_3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t34_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( 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))) ) )).
fof(t34_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : k3_relat_1(B,k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k3_relat_1(B,A)) ) ) ) )).
fof(t34_funct_1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) ) )).
fof(t34_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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,A) & r2_hidden(k1_funct_1(E,D),C) ) => ( B = k1_xboole_0 | k1_funct_1(k6_relset_1(A,B,C,E),D) = k1_funct_1(E,D) ) ) ) )).
fof(t34_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t34_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_partfun1(A,B) <=> k1_funct_4(A,B) = k1_funct_4(B,A) ) ) ) )).
fof(t34_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) ) )).
fof(t34_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : k1_funct_7(A,B,k1_funct_1(A,B)) = A ) )).
fof(t34_funct_8,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t34_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ v8_ordinal1(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),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)) ) ) ) )).
fof(t34_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l1_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_altcat_2(C) & l1_altcat_1(C) ) => ! [D] : ( ( v6_functor0(D,A,B) & v8_functor0(D,A,B) & l2_functor0(D,A,B) ) => ! [E] : ( l2_functor0(E,B,C) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(t34_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ! [F] : ( m1_functor3(F,A,B,C,D) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t34_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D,C)) & r2_funct_2(A,k1_numbers,k1_fuzzy_1(A,B,C),k4_fuzzy_1(A)) ) => r1_fuzzy_1(B,D) ) ) ) ) ) )).
fof(t34_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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))) ) ) ) )).
fof(t34_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_fvaluat1(C,A) => ( k3_funct_2(u1_struct_0(A),k6_numbers,C,B) = 1 => k1_fvaluat1(k2_relset_1(k6_numbers,C)) = 1 ) ) ) ) )).
fof(t34_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k7_fvsum_1(A,k12_finseq_1(u1_struct_0(A),B),k12_finseq_1(u1_struct_0(A),C)) = k12_finseq_1(u1_struct_0(A),k5_algstr_0(A,B,C)) ) ) ) )).
fof(t34_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ~ ( ~ 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)) ) ) )).
fof(t34_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t34_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v2_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ! [F] : ( m1_genealg1(F,E) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t34_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => k3_xcmplx_0(2,k4_geomtrap(A,B,C,D,k1_geomtrap(A,E,F))) = k2_xcmplx_0(k4_geomtrap(A,B,C,D,E),k4_geomtrap(A,B,C,D,F)) ) ) ) ) ) ) ) )).
fof(t34_gfacirc1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => k2_msafree2(k13_gfacirc1(A,B,C)) = k1_enumset1(A,B,C) ) ) ) )).
fof(t34_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => k7_glib_000(A) = k21_glib_000(A,k6_glib_000(A)) ) )).
fof(t34_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( ( r1_xxreal_0(C,D) & r1_xxreal_0(D,k3_finseq_1(B)) ) => ( k1_nat_1(k3_finseq_1(k8_glib_001(A,B,C,D)),C) = k1_nat_1(D,1) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ~ r1_xxreal_0(k3_finseq_1(k8_glib_001(A,B,C,D)),E) => ( k1_funct_1(k8_glib_001(A,B,C,D),k1_nat_1(E,1)) = k1_funct_1(B,k1_nat_1(C,E)) & r2_hidden(k1_nat_1(C,E),k1_relset_1(k4_ordinal1,B)) ) ) ) ) ) ) ) ) ) )).
fof(t34_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ( ~ v5_glib_002(B,A) <=> ! [C] : ( 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)) ) ) ) ) )).
fof(t34_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_003(A) ) => ! [B] : ! [C] : r5_glib_000(A,k12_glib_003(A,B,C)) ) )).
fof(t34_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k1_matrix_0(B)) ) => r2_hidden(k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B),A),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B),k1_nat_1(A,1))),k7_xcmplx_0(1,2)),k19_euclid(1,k5_numbers)),k1_tops_1(k15_euclid(2),k3_goboard5(B,k3_finseq_1(B),A))) ) ) ) )).
fof(t34_goboard7,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t34_gobrd11,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(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_0(A)) ) ) )).
fof(t34_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(D)) & r1_goboard1(u1_struct_0(k15_euclid(2)),D,E) & r2_hidden(k4_tarski(A,k1_nat_1(B,1)),k2_matrix_0(E)) & r2_hidden(k4_tarski(A,B),k2_matrix_0(E)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,B) ) => k4_gobrd13(D,E,C) = k3_goboard5(E,k7_nat_d(A,1),k7_nat_d(B,1)) ) ) ) ) ) ) )).
fof(t34_gobrd14,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t34_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( 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] : ( ( v1_henmodel(C,A) & m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) ) => ! [D] : ( m1_henmodel(D,A,C) => ~ r6_calcul_1(A,B,k1_henmodel(A),D,k3_henmodel(A)) ) ) ) ) ) )).
fof(t34_gr_cy_3,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_int_1(A,B,C) => ( C = k5_numbers | r2_int_1(k1_newton(A,D),k1_newton(B,D),C) ) ) ) ) ) ) )).
fof(t34_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_graph_1(C) ) => ( ( r2_hidden(B,k11_graph_1(A)) & r2_hidden(C,k11_graph_1(A)) ) => r2_hidden(k5_graph_1(B,C),k11_graph_1(A)) ) ) ) ) )).
fof(t34_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t34_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v7_graph_1(D,A) & m2_graph_1(D,A) ) => ( r3_graph_5(A,D,B,C) => r1_graph_5(A,D,B,C) ) ) ) ) ) )).
fof(t34_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) => ~ ( k7_graphsp(B,A) != k1_xboole_0 & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r2_hidden(C,k7_graphsp(B,A)) & r1_xxreal_0(1,C) & r1_xxreal_0(C,A) & k1_funct_1(k6_graphsp(k15_graphsp(A),B),C) = k4_xcmplx_0(1) ) ) ) ) ) )).
fof(t34_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(k25_grcat_1(A))) => ! [C] : ( m3_grcat_1(C,k18_grcat_1(k17_grcat_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k25_grcat_1(A))) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t34_groeb_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(g1_orders_2(k15_pre_poly(A),k4_groeb_1(A))))) => ? [C] : ( 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) ) ) ) )).
fof(t34_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ! [G] : ( m2_ideal_1(G,k12_polynom1(A,C),F) => ! [H] : ( m2_ideal_1(H,k12_polynom1(A,C),F) => ! [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] : ( m1_subset_1(J,k4_ordinal1) => ( ( r3_groeb_2(A,B,C,D,F,G,I) & H = k17_finseq_1(u1_struct_0(k12_polynom1(A,C)),J,G) & E = k4_rlvect_1(k12_polynom1(A,C),k2_rfinseq(u1_struct_0(k12_polynom1(A,C)),J,G)) ) => r3_groeb_2(A,B,C,k7_polynom1(A,C,D,E),F,H,I) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t34_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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_numbers),k8_polynom1(A,C)) & r2_funct_2(k15_pre_poly(A),u1_struct_0(C),k6_groeb_3(A,B,C,D,k5_numbers),D) ) ) ) ) ) )).
fof(t34_group_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & l3_algstr_0(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => k5_group_1(C,k3_xcmplx_0(A,B),D) = k5_group_1(C,B,k5_group_1(C,A,D)) ) ) ) ) )).
fof(t34_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_group_2(C,A) => k1_group_11(A,k1_group_11(A,B,C),C) = k1_group_11(A,B,C) ) ) ) )).
fof(t34_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t34_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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))) ) ) ) ) )).
fof(t34_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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)) ) ) )).
fof(t34_group_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t34_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t34_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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)) ) ) )).
fof(t34_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(t34_groupp_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v15_algstr_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t34_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [D] : ( ( ~ 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),k2_xcmplx_0(k1_hausdorf(A,B,C),k1_hausdorf(A,C,D))) ) ) ) ) ) )).
fof(t34_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t34_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,k1_complfld) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t34_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,u1_struct_0(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A)))) ) => ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(k4_ordinal1,k6_domain_1(k4_ordinal1,A)))) => ( B = C => ( B = k1_tarski(k1_xboole_0) | ( ~ v1_xboole_0(k1_heyting2(k4_ordinal1,k6_domain_1(k4_ordinal1,A),C)) & v1_finset_1(k1_heyting2(k4_ordinal1,k6_domain_1(k4_ordinal1,A),C)) & m1_subset_1(k1_heyting2(k4_ordinal1,k6_domain_1(k4_ordinal1,A),C),k1_zfmisc_1(k4_ordinal1)) ) ) ) ) ) ) )).
fof(t34_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(B,D) => ( k9_nat_1(k1_numbers,k6_taylor_1(k16_sin_cos,D,B,A),C) = k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,k2_xcmplx_0(B,k7_xcmplx_0(k3_xcmplx_0(C,k28_sin_cos),2))),k1_newton(k6_xcmplx_0(A,B),C)),k2_newton(C)) & k9_nat_1(k1_numbers,k6_taylor_1(k18_sin_cos,D,B,A),C) = k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,k2_xcmplx_0(B,k7_xcmplx_0(k3_xcmplx_0(C,k28_sin_cos),2))),k1_newton(k6_xcmplx_0(A,B),C)),k2_newton(C)) ) ) ) ) ) ) )).
fof(t34_hilbasis,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => v6_ideal_1(k12_polynom1(B,A)) ) ) )).
fof(t34_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(t34_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => k1_funct_1(k3_hilbert2(A),k1_xboole_0) = A ) )).
fof(t34_hilbert3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( 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))) ) ) ) ) )).
fof(t34_hurwitz,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( C != k9_polynom3(A) => ( r1_hurwitz(A,B,C) <=> ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & r2_funct_2(k4_ordinal1,u1_struct_0(A),k13_polynom3(A,D,C),B) ) ) ) ) ) ) )).
fof(t34_idea_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( v1_int_2(k1_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 ) ) ) ) ) )).
fof(t34_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m3_ideal_1(C,A,B) ) => ? [D] : ( m3_ideal_1(D,A,B) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_relset_1(k4_ordinal1,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) ) ) ) ) ) )).
fof(t34_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ~ ( B != C & ? [D] : ( 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) ) ) ) ) )).
fof(t34_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( 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] : ( m4_index_1(E,u1_struct_0(B),u4_struct_0(B),u1_graph_1(B),u2_graph_1(B),D) => ! [F] : ( ( ~ 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t34_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( l3_msualg_1(D,A) => ( r1_pzfmisc1(u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D)) => ! [E] : ( 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] : ( ( 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] : ( ( v1_relat_1(G) & v1_funct_1(G) ) => ~ ( r3_pua2mss1(B,A,F,G) & ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t34_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_int_1(A) = k2_int_1(A) <=> v1_int_1(A) ) ) )).
fof(t34_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => k3_int_2(A,B) = k3_int_2(k1_int_2(A),k1_int_2(B)) ) ) )).
fof(t34_int_4,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( v7_ordinal1(C) => ( ( k3_finseq_1(A) = k2_xcmplx_0(B,1) & r1_xxreal_0(1,C) & r1_xxreal_0(C,B) ) => k1_recdef_1(k4_wsierp_1(k4_ordinal1,C,A),B) = k1_recdef_1(A,k3_finseq_1(A)) ) ) ) ) )).
fof(t34_int_5,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ~ ( ~ r1_xxreal_0(A,2) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => k3_int_2(k1_recdef_1(B,C),A) = 1 ) ) & ! [C] : ( m2_finseq_1(C,k4_numbers) => ~ ( k3_finseq_1(C) = k3_finseq_1(B) & ! [D] : ( 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) ) ) ) ) ) )).
fof(t34_int_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t34_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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,k7_xcmplx_0(1,2))) ) => k2_integra5(A,k1_partfun2(k1_numbers,B)) = k6_xcmplx_0(k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,C,k7_xcmplx_0(1,2)),k2_seq_4(A)),k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,C,k7_xcmplx_0(1,2)),k3_seq_4(A))) ) ) ) ) )).
fof(t34_integr12,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k7_xcmplx_0(k1_square_1(k1_funct_1(k18_sin_cos,D)),k1_square_1(k1_funct_1(k16_sin_cos,D))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k27_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) = k6_xcmplx_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k27_sin_cos),k1_partfun2(k1_numbers,C)),k2_seq_4(A)),k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k27_sin_cos),k1_partfun2(k1_numbers,C)),k3_seq_4(A))) ) ) ) ) )).
fof(t34_integr13,axiom,( ! [A] : ( ( 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)),k26_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)),k26_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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)),k26_sin_cos)),A),B) = k7_xcmplx_0(1,k3_xcmplx_0(k1_square_1(B),k1_square_1(k1_funct_1(k18_sin_cos,k7_xcmplx_0(1,B))))) ) ) ) ) ) )).
fof(t34_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k6_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(1,k1_funct_1(k18_sin_cos,D)),k1_square_1(D)),k7_xcmplx_0(k7_xcmplx_0(k1_funct_1(k16_sin_cos,D),D),k1_square_1(k1_funct_1(k18_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) = k6_xcmplx_0(k1_funct_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)),k2_seq_4(A)),k1_funct_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)),k3_seq_4(A))) ) ) ) ) )).
fof(t34_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t34_integra1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( m1_integra1(D,C) => ~ ( r2_hidden(A,k4_finseq_1(D)) & r2_hidden(B,k4_finseq_1(D)) & r1_xxreal_0(A,B) & ! [E] : ( ( ~ v1_xboole_0(E) & v2_measure5(E) & m1_subset_1(E,k1_zfmisc_1(k1_numbers)) ) => ~ ( k3_seq_4(E) = k1_funct_1(k3_finseq_6(k1_numbers,D,A,B),1) & k2_seq_4(E) = k1_funct_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) ) ) ) ) ) ) ) )).
fof(t34_integra2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => ! [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_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] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => r1_xxreal_0(k1_funct_1(C,D),k1_funct_1(B,D)) ) ) ) => r1_xxreal_0(k12_integra1(A,C),k12_integra1(A,B)) ) ) ) ) )).
fof(t34_integra8,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k9_xtuple_0(k27_sin_cos)) => ( r2_fdiff_1(k27_sin_cos,A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k27_sin_cos,A),B) = k4_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t34_integra9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k28_sin_cos) => r1_integra9(A,k16_sin_cos,k18_sin_cos) ) ) )).
fof(t34_interva1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_interva1(B,A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ! [C] : ( ( ~ 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 ) ) )).
fof(t34_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( 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) ) ) ) ) )).
fof(t34_irrat_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( v1_series_1(A) & ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k1_funct_1(A,B),k5_numbers) ) & r1_xxreal_0(k4_series_1(A),k5_numbers) ) ) )).
fof(t34_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,B,C) => ! [G] : ( m2_cat_1(G,B,C) => ! [H] : ( m2_nattra_1(H,A,B,D,E) => ! [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),k5_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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t34_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,A,C) => ! [G] : ( m2_cat_1(G,A,C) => ( ( r1_nattra_1(A,B,D,E) & r1_nattra_1(A,C,F,G) ) => r1_nattra_1(A,k6_cat_2(B,C),k8_isocat_2(A,B,C,D,F),k8_isocat_2(A,B,C,E,G)) ) ) ) ) ) ) ) ) )).
fof(t34_isomichi,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t34_jgraph_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r1_xxreal_0(k9_complex1(k6_xcmplx_0(k17_euclid(A),k17_euclid(B))),k12_euclid(k5_algstr_0(k15_euclid(2),A,B))) & r1_xxreal_0(k9_complex1(k6_xcmplx_0(k18_euclid(A),k18_euclid(B))),k12_euclid(k5_algstr_0(k15_euclid(2),A,B))) ) ) ) )).
fof(t34_jgraph_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( 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] : ( 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) = k7_xcmplx_0(k7_xcmplx_0(k17_euclid(C),k18_euclid(C)),k18_euclid(C)) ) ) & ! [C] : ( 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) = k5_numbers ) ) ) => v5_pre_topc(B,k1_pre_topc(k15_euclid(2),A),k3_topmetr) ) ) ) )).
fof(t34_jgraph_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( 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] : ( 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) = k3_xcmplx_0(k18_euclid(C),k3_square_1(k2_xcmplx_0(1,k1_square_1(k7_xcmplx_0(k18_euclid(C),k17_euclid(C)))))) ) ) & ! [C] : ( 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) = k5_numbers ) ) ) => v5_pre_topc(B,k1_pre_topc(k15_euclid(2),A),k3_topmetr) ) ) ) )).
fof(t34_jgraph_5,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t34_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t34_jordan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(t34_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [F] : ( 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_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)))) ) ) ) ) ) ) ) ) )).
fof(t34_jordan12,axiom,( ! [A] : ( ( v1_topreal1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( ( v1_topreal1(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ! [C] : ( ( 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))),k4_ordinal1) ) <=> ? [D] : ( 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) ) ) ) ) ) ) )).
fof(t34_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( 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)))) ) ) ) ) )).
fof(t34_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( ~ r1_xxreal_0(C,1) & r1_xxreal_0(C,D) & ~ r1_xxreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,1))),D) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),D,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1)))),k8_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1)))),k9_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1)))),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),D,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))))),k9_jordan6(B)) ) ) ) ) ) )).
fof(t34_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_xxreal_0(B,C) => ( r1_xxreal_0(A,1) | r1_xxreal_0(k3_finseq_1(k1_jordan8(D,B)),k1_nat_1(A,1)) | ( ~ r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(k11_newton(2,k7_nat_d(C,B)),k6_xcmplx_0(A,1)),2),1) & r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(k11_newton(2,k7_nat_d(C,B)),k6_xcmplx_0(A,1)),2),k3_finseq_1(k1_jordan8(D,C))) ) ) ) ) ) ) ) )).
fof(t34_jordan1b,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(B,k1_matrix_0(A)) & v9_rltopsp1(k3_goboard5(A,k3_finseq_1(A),B),k15_euclid(2)) ) ) ) )).
fof(t34_jordan1g,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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,k2_jordan9(B,A))),k7_pscomp_1(k3_topreal1(2,k2_jordan9(B,A)))) = k2_xcmplx_0(k9_pscomp_1(B),k7_pscomp_1(B)) ) ) )).
fof(t34_jordan1h,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_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] : ( v7_ordinal1(C) => ~ ( r2_hidden(k4_tarski(1,C),k2_matrix_0(B)) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,C),k2_relset_1(u1_struct_0(k15_euclid(2)),A)) ) ) | ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(k4_tarski(C,1),k2_matrix_0(B)) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,C,1),k2_relset_1(u1_struct_0(k15_euclid(2)),A)) ) ) | ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(k4_tarski(k3_finseq_1(B),C),k2_matrix_0(B)) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B),C),k2_relset_1(u1_struct_0(k15_euclid(2)),A)) ) ) | ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(k4_tarski(C,k1_matrix_0(B)),k2_matrix_0(B)) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),B,C,k1_matrix_0(B)),k2_relset_1(u1_struct_0(k15_euclid(2)),A)) ) ) | B = k2_goboard2(A) ) ) ) ) )).
fof(t34_jordan1k,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_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(k7_xcmplx_0(1,A),k4_xcmplx_0(k7_xcmplx_0(C,A)),k7_xcmplx_0(1,B),k4_xcmplx_0(k7_xcmplx_0(D,B))),k2_jgraph_2(A,C,B,D)),k6_partfun1(k1_euclid(2))) ) ) ) ) ) )).
fof(t34_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => r2_hidden(k2_jordan21(A),k4_jordan19(A)) ) )).
fof(t34_jordan23,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( ( v2_topreal1(A) & v2_jordan23(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t34_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ~ ( r1_xxreal_0(2,A) & B != k5_euclid(A) & ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ~ ! [D] : ( v1_xreal_0(D) => ( C != k9_euclid(A,B,D) & B != k9_euclid(A,C,D) ) ) ) ) ) ) )).
fof(t34_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) ) )).
fof(t34_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( 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) ) ) ) ) ) )).
fof(t34_jordan5d,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ 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] : ( v7_ordinal1(C) => ( ( 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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(B),C,k1_matrix_0(k2_goboard2(B))))) ) ) ) ) )).
fof(t34_jordan6,axiom,( ! [A] : ( 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(k5_numbers,1)) => v3_pre_topc(A,k17_borsuk_1) ) ) )).
fof(t34_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( m1_jordan_a(C,A) => r1_xxreal_0(B,k4_jordan_a(A,C)) ) ) ) ) )).
fof(t34_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r3_lattices(A,C,D) & r2_abian(u1_struct_0(A),D,B) ) => ! [E] : ( v3_ordinal1(E) => r3_lattices(A,k5_knaster(A,B,C,E),D) ) ) ) ) ) ) )).
fof(t34_kurato_1,axiom,( 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))) )).
fof(t34_kurato_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))))) ) => ( ! [C] : ( v7_ordinal1(C) => r1_tarski(k2_kurato_2(k15_euclid(2),A,C),k2_kurato_2(k15_euclid(2),B,C)) ) => r1_tarski(k3_kurato_2(k15_euclid(2),A),k3_kurato_2(k15_euclid(2),B)) ) ) ) )).
fof(t34_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v1_matrix_6(C,A,B) <=> k12_matrix_3(A,B,C) != k4_struct_0(B) ) ) ) ) )).
fof(t34_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k5_finsub_1(B)) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t34_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( B = k16_lattice3(A,C) <=> ( r3_lattice3(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r3_lattice3(A,D,C) => r3_lattices(A,D,B) ) ) ) ) ) ) )).
fof(t34_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => m2_lattice4(u1_struct_0(A),A) ) )).
fof(t34_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( v3_ordinal1(C) => ! [D] : ( ( 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] : ( m1_lattice5(E,A,B,D) => v1_lattice5(k12_lattice5(A,B,D,E,C),k8_lattice5(A,C),B) ) ) ) ) ) ) )).
fof(t34_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t34_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_lfuzzy_0(k2_zfmisc_1(A,A))))) => k3_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)) ) ) ) )).
fof(t34_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_limfunc1(A) | v2_limfunc1(A) ) => ( v2_comseq_2(k37_valued_1(k4_ordinal1,k1_numbers,A)) & k1_seq_2(k37_valued_1(k4_ordinal1,k1_numbers,A)) = k5_numbers ) ) ) )).
fof(t34_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r3_limfunc2(C,A) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,D) & ~ r1_xxreal_0(A,E) & r2_hidden(E,k1_relset_1(k1_numbers,B)) ) ) ) ) ) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(k6_xcmplx_0(A,D),A)),k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,C),k2_rcomp_1(k6_xcmplx_0(A,D),A))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(k6_xcmplx_0(A,D),A))) => r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) | r3_limfunc2(B,A) ) ) ) ) ) )).
fof(t34_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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) = k6_xcmplx_0(k1_limfunc3(B,A),k1_limfunc3(C,A)) ) ) ) ) ) )).
fof(t34_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k10_prob_1(C))) & r1_xxreal_0(k1_funct_1(A,D),k5_limfunc1(A)) ) ) | v8_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).
fof(t34_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t34_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k16_lopban_1(A,B))) => ( C = k4_struct_0(k16_lopban_1(A,B)) => k5_numbers = k2_normsp_0(k16_lopban_1(A,B),C) ) ) ) ) )).
fof(t34_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v1_xreal_0(C) => ( ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(1,D) => k9_nat_1(k1_numbers,k5_normsp_0(A,B),D) = k7_xcmplx_0(1,k2_power(D,C)) ) ) => ( r1_xxreal_0(C,1) | v2_lopban_3(B,A) ) ) ) ) ) )).
fof(t34_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k10_lopban_4(A,B) = k1_lopban_3(A,k1_lopban_4(A,B)) ) ) )).
fof(t34_lopclset,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t34_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( ( r2_hidden(D,k13_lpspacc1(A,B,C)) & r2_hidden(F,k13_lpspacc1(A,B,C)) & r2_hidden(E,k13_lpspacc1(A,B,C)) & r2_hidden(G,k13_lpspacc1(A,B,C)) & k17_lpspacc1(A,B,C,D) = k17_lpspacc1(A,B,C,F) & k17_lpspacc1(A,B,C,E) = k17_lpspacc1(A,B,C,G) ) => k17_lpspacc1(A,B,C,k2_valued_1(A,k2_numbers,k2_numbers,D,E)) = k17_lpspacc1(A,B,C,k2_valued_1(A,k2_numbers,k2_numbers,F,G)) ) ) ) ) ) ) ) ) )).
fof(t34_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( v2_xxreal_0(F) & v1_xreal_0(F) ) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t34_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => r2_hidden(k3_hilbert1(A,k3_hilbert1(B,A)),k13_ltlaxio1) ) ) )).
fof(t34_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(A,k3_hilbert1(B,k3_hilbert1(A,B)))) ) ) )).
fof(t34_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t34_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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))) ) ) ) ) )).
fof(t34_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( v1_matrix10(B) => v4_matrix10(B) ) ) ) )).
fof(t34_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(C)) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(C),B,B) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(C))) ) => ( ( 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))) ) ) ) ) ) ) ) )).
fof(t34_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(A)) ) => ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(C,k4_ordinal1)) => ! [F] : ( m2_finseq_2(F,k4_ordinal1,k4_finseq_2(B,k4_ordinal1)) => ! [G] : ( m2_finseq_2(G,k4_ordinal1,k4_finseq_2(B,k4_ordinal1)) => ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,k2_finseq_1(B),k2_finseq_1(B)) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(B),k2_finseq_1(B)))) ) => ( G = k1_partfun1(k2_finseq_1(B),k2_finseq_1(B),k4_ordinal1,k4_ordinal1,H,F) => k4_matrix_0(A,k1_matrix13(A,D,C,B,E,G)) = k1_partfun1(k2_finseq_1(B),k2_finseq_1(B),k4_ordinal1,k3_finseq_2(A),H,k4_matrix_0(A,k1_matrix13(A,D,C,B,E,F))) ) ) ) ) ) ) ) ) ) )).
fof(t34_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( 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] : ( m1_subset_1(F,k4_ordinal1) => ( ( r1_xxreal_0(1,F) & r1_xxreal_0(F,A) ) => ( F = E | k1_funct_1(D,F) = k4_struct_0(B) ) ) ) ) ) ) ) ) ) ) )).
fof(t34_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ( ( r2_hidden(E,k4_matrix15(B,C,D)) & r2_hidden(A,k2_finseq_1(k1_matrix_0(E))) & k8_matrix_0(u1_struct_0(B),E,A) = k5_finseq_2(u1_struct_0(B),k3_finseq_1(E),k4_struct_0(B)) ) => k8_matrix_0(u1_struct_0(B),D,A) = k5_finseq_2(u1_struct_0(B),k3_finseq_1(D),k4_struct_0(B)) ) ) ) ) ) ) )).
fof(t34_matrix16,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t34_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,k3_finseq_2(B)) => m2_finseq_1(k1_funct_1(C,A),B) ) ) ) )).
fof(t34_matrix_3,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => k12_matrix_3(1,A,k14_matrix_0(u1_struct_0(A),1,k13_matrix_0(u1_struct_0(A),B))) = B ) ) )).
fof(t34_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) ) => k1_matrix_4(A,B,D) = k3_matrix_3(A,k1_matrix_4(A,B,C),k1_matrix_4(A,C,D)) ) ) ) ) ) )).
fof(t34_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( ~ r1_xxreal_0(A,k5_numbers) => v3_matrix_6(k1_matrix_4(B,C,k4_matrix_0(u1_struct_0(B),C)),A,B) ) ) ) ) )).
fof(t34_matrix_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_matrix_2(C,k3_matrix_2(A)) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r1_xxreal_0(1,A) => k10_matrix_3(A,B,k4_matrix_0(u1_struct_0(B),D),k3_matrix_7(A,C)) = k1_partfun1(k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k4_ordinal1,u1_struct_0(B),k3_matrix_7(A,C),k10_matrix_3(A,B,D,C)) ) ) ) ) ) )).
fof(t34_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ( ( r1_matrix_8(A,B,C,D) & r1_matrix_8(A,B,D,E) ) => r1_matrix_8(A,B,C,E) ) ) ) ) ) ) )).
fof(t34_matrix_9,axiom,( ! [A] : ( ( 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(k4_ordinal1,3,1,2) & v4_matrix_2(A,3) ) ) )).
fof(t34_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => k17_rvsum_1(k7_seq_4(A,B)) = k2_xcmplx_0(k17_rvsum_1(A),k17_rvsum_1(B)) ) ) ) )).
fof(t34_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => k13_matrixj1(A,B,k4_matrixj1(A,C)) = C ) ) ) )).
fof(t34_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => k3_matrixr1(k3_matrixr1(A,A),A) = k7_matrixr1(3,A) ) )).
fof(t34_matrixr2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( m2_finseq_1(E,A) => ( ( k3_finseq_1(C) = B & k3_finseq_1(D) = B & k3_finseq_1(E) = B ) => ( v1_matrix_0(k3_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),C,D,E)) & v2_matrix_0(k3_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),C,D,E),A,3,B) & m2_finseq_1(k3_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),C,D,E),k3_finseq_2(A)) ) ) ) ) ) ) ) )).
fof(t34_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_matrlin(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( k9_matrlin(A,B,C,D) = k9_matrlin(A,B,C,E) => D = E ) ) ) ) ) ) )).
fof(t34_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( ( 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] : ( m1_matrlin(E,A,B) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t34_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_matroid0(A,C,k6_matroid0(A,B)) => r2_matroid0(A,C,B) ) ) ) ) )).
fof(t34_matrprob,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [D] : ( m2_finseq_2(D,u1_struct_0(k2_vectsp_1),k4_finseq_2(A,u1_struct_0(k2_vectsp_1))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t34_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( 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 ) ) ) ) ) )).
fof(t34_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(B))) => ~ ( r2_hidden(A,k2_finseq_1(B)) & r1_xxreal_0(2,B) & ! [D] : ( ( 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) = k1_funct_7(C,A,k4_xcmplx_0(k1_funct_1(C,A))) ) ) ) ) ) ) )).
fof(t34_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ ( ~ 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 ) )).
fof(t34_measure1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ( r2_hidden(k1_xboole_0,B) & r2_hidden(A,B) & ! [D] : ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t34_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => k7_member_1(k6_subset_1(A,B)) = k6_subset_1(k7_member_1(A),k7_member_1(B)) ) ) )).
fof(t34_membered,axiom,( ! [A] : ! [B] : ( ( r2_hidden(B,A) & v4_membered(B) ) => v4_membered(k1_setfam_1(A)) ) )).
fof(t34_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_partfun1(C,u1_struct_0(B)) ) => ! [D] : ( ( 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 ) ) ) ) ) )).
fof(t34_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t34_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( 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] : ( m1_subset_1(F,A) => ( r2_hidden(F,k1_relset_1(A,E)) => r1_xxreal_0(k12_supinf_2(E,F),k12_supinf_2(D,F)) ) ) ) => ( ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t34_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ( v1_mesfunc8(B,A,k2_numbers) => v1_mesfunc8(k3_mesfun9c(A,B),A,k2_numbers) ) ) ) )).
fof(t34_mesfunc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t34_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,C) => ( r1_mesfunc2(A,C,B) => r1_mesfunc1(A,C,B,D) ) ) ) ) ) )).
fof(t34_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( r1_mesfunc2(A,B,D) => r1_mesfunc2(A,B,k2_partfun1(A,k6_numbers,D,E)) ) ) ) ) ) ) )).
fof(t34_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( r2_hidden(C,k1_relset_1(A,B)) => ( r1_xxreal_0(k12_supinf_2(k18_rfunct_3(A,B),C),k5_numbers) | k12_supinf_2(k19_rfunct_3(A,B),C) = k5_numbers ) ) ) ) )).
fof(t34_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( m1_subset_1(D,A) => ( ( v2_mesfunc9(B,A) & v1_mesfunc8(B,A,k6_numbers) & r1_tarski(k1_relset_1(A,C),k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_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)) ) ) ) ) ) )).
fof(t34_metric_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,k14_metric_1(A,B,C)) <=> ~ ( ~ r1_metric_1(A,B,D,C) & D != B & D != C ) ) ) ) ) ) )).
fof(t34_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k2_metric_2(A)) => ! [C] : ( m1_subset_1(C,k2_metric_2(A)) => ( k2_binop_1(k2_metric_2(A),k2_metric_2(A),k1_numbers,k10_metric_2(A),B,C) = k5_numbers <=> B = C ) ) ) ) )).
fof(t34_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_midsp_1(C,A) => ? [D] : ( 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)) ) ) ) ) )).
fof(t34_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [D] : ( 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)) ) ) ) )).
fof(t34_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(t34_modal_1,axiom,( ! [A] : ( 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))) ) )).
fof(t34_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ( r1_tarski(D,E) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t34_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ( ( r3_modelc_2(A,B) & r3_modelc_2(B,C) ) => r3_modelc_2(A,C) ) ) ) ) )).
fof(t34_modelc_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ( ( 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))) ) ) ) ) )).
fof(t34_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => k2_moebius1(A) = k4_xcmplx_0(1) ) )).
fof(t34_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m2_monoid_0(B,A) ) => ( v10_monoid_0(A) => v10_monoid_0(B) ) ) ) )).
fof(t34_monoid_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => k1_relset_1(k4_ordinal1,k6_relat_1(k1_tarski(A),k7_finseq_1(C,k9_finseq_1(A)))) = k4_subset_1(k4_ordinal1,k1_relset_1(k4_ordinal1,k6_relset_1(k4_ordinal1,B,k1_tarski(A),C)),k6_domain_1(k4_ordinal1,k1_nat_1(k3_finseq_1(C),1))) ) ) )).
fof(t34_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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] : ( 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)) ) ) ) ) )).
fof(t34_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v3_msafree4(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & m1_msualg_2(C,A,B) ) => g3_msualg_1(A,u3_msualg_1(A,C),u4_msualg_1(A,C)) = g3_msualg_1(A,u3_msualg_1(A,B),u4_msualg_1(A,B)) ) ) ) )).
fof(t34_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( m2_pboole(D,u1_struct_0(A),C,u3_msualg_1(A,B)) => ! [E] : ( 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] : ( ( 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] : ( m1_trees_1(G,k9_xtuple_0(E)) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t34_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) => ! [D] : ( m3_pboole(D,A,k1_mboolean(A,B)) => m3_pboole(k2_pboole(A,C,D),A,k1_mboolean(A,B)) ) ) ) )).
fof(t34_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t34_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t34_msualg_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,k13_msualg_4(A,B,C)),F)) => ! [H] : ( 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)) ) ) ) ) ) ) )).
fof(t34_mycielsk,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => k2_dilworth(k5_mycielsk(A)) = 1 ) )).
fof(t34_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(A,B) => A = k3_xboole_0(A,B) ) ) ) )).
fof(t34_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( r2_hidden(B,k13_pre_poly(k12_nat_3(A))) => ( v7_ordinal1(B) & v1_int_2(B) ) ) ) )).
fof(t34_nat_4,axiom,( v1_int_2(139) )).
fof(t34_nat_5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_ordinal1) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ( ( v1_nat_5(A) & ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => k1_recdef_1(B,C) = k2_uproots(k3_moebius1(C),k1_nat_5(k4_ordinal1,A,k3_moebius1(C))) ) ) => v1_nat_5(B) ) ) ) )).
fof(t34_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k7_nat_d(k2_xcmplx_0(A,B),B) = A ) ) )).
fof(t34_nattra_1,axiom,( ! [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) & v4_nattra_1(A) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,B,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t34_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t34_ncfcont2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_numbers))) ) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & r2_hidden(E,C) & k7_partfun1(k1_numbers,B,D) = k2_seq_4(k7_relset_1(u1_struct_0(A),k1_numbers,B,C)) & k7_partfun1(k1_numbers,B,E) = k3_seq_4(k7_relset_1(u1_struct_0(A),k1_numbers,B,C)) ) ) ) ) ) ) ) )).
fof(t34_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,u1_struct_0(A)) & v1_ndiff_1(F,A,k4_struct_0(A)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v12_struct_0(F,k4_ordinal1,A) => ! [G] : ( ( v1_funct_1(G) & v3_funct_1(G) & v1_funct_2(G,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),k2_normsp_1(A,F,G),C),k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),G,C)),B) & k6_normsp_1(B,k3_normsp_1(B,k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),k2_normsp_1(A,F,G),C),k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),G,C))) = k4_struct_0(B) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t34_ndiff_4,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t34_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k11_prvect_2(A,B))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t34_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k3_xcmplx_0(A,C),B) ) => r1_xxreal_0(A,B) ) ) ) ) )).
fof(t34_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & 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) != k1_xboole_0 & v1_nfcont_1(k1_relset_1(u1_struct_0(A),C),A) & r3_nfcont_1(A,B,C,k1_relset_1(u1_struct_0(A),C)) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(D,k1_relset_1(u1_struct_0(A),C)) & r2_hidden(E,k1_relset_1(u1_struct_0(A),C)) & k7_partfun1(k1_numbers,k4_normsp_0(u1_struct_0(A),B,C),D) = k2_seq_4(k2_relset_1(k1_numbers,k4_normsp_0(u1_struct_0(A),B,C))) & k7_partfun1(k1_numbers,k4_normsp_0(u1_struct_0(A),B,C),E) = k3_seq_4(k2_relset_1(k1_numbers,k4_normsp_0(u1_struct_0(A),B,C))) ) ) ) ) ) ) ) )).
fof(t34_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(t34_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A))) => ! [C] : ( m1_subset_1(C,k5_finsub_1(k7_normform(A))) => ! [D] : ( m1_subset_1(D,k5_finsub_1(k7_normform(A))) => ~ ( r2_hidden(B,k10_normform(A,C,D)) & ! [E] : ( m2_subset_1(E,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t34_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_normsp_2(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_normsp_2(A)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_normsp_2(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t34_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t34_openlatt,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t34_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_oppcat_1(C,k2_oppcat_1(B),A) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k3_funct_2(u1_struct_0(B),u1_struct_0(A),k7_cat_1(B,A,k9_oppcat_1(B,A,C)),D) = k3_funct_2(u1_struct_0(k2_oppcat_1(B)),u1_struct_0(A),k7_cat_1(k2_oppcat_1(B),A,C),k3_oppcat_1(B,D)) ) ) ) ) )).
fof(t34_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_nfcont_3(D,k4_real_ns1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [E] : ( ( 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) & k1_relset_1(k1_numbers,D) = k3_integra5(B,C) & k1_relset_1(k1_numbers,E) = k3_integra5(B,C) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,k1_rcomp_1(B,C)) => k1_funct_1(E,F) = k6_integr18(k4_real_ns1(A),D,B,F) ) ) ) => ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,k1_rcomp_1(B,C)) => r1_nfcont_3(k4_real_ns1(A),E,F) ) ) ) ) ) ) ) ) )).
fof(t34_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v2_orders_1(A) => r2_orders_1(A,k1_relat_1(A)) ) ) )).
fof(t34_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r1_tarski(B,C) & r2_wellord1(u1_orders_2(A),C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) )).
fof(t34_ordinal1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,B) => v7_ordinal1(A) ) ) )).
fof(t34_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r1_ordinal1(A,B) => r1_ordinal1(k10_ordinal2(A,C),k10_ordinal2(B,C)) ) ) ) ) )).
fof(t34_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r2_hidden(k11_ordinal2(B,A),k11_ordinal2(C,A)) => r2_hidden(B,C) ) ) ) ) )).
fof(t34_ordinal4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( v3_ordinal1(B) & m1_subset_1(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t34_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r1_ordinal1(A,B) => r1_ordinal1(k2_ordinal5(A),k2_ordinal5(B)) ) ) ) )).
fof(t34_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t34_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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] : ( ( 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] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t34_osalg_1,axiom,( ! [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) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t34_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v3_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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 ) ) ) ) )).
fof(t34_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(t34_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( ~ r1_parsp_2(A,B,C,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ r2_parsp_2(A,B,C,D,E) ) ) ) ) ) ) )).
fof(t34_partfun1,axiom,( ! [A] : ! [B] : k3_partfun1(k1_xboole_0,A,B) = k1_xboole_0 )).
fof(t34_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,B) => ( v1_partfun1(k4_partfun2(A,B,C,D),A) <=> C = A ) ) ) ) ) )).
fof(t34_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k4_partit1(A,k10_eqrel_1(A)) = k4_relat_1(A) ) )).
fof(t34_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t34_pcomps_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t34_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k21_pcs_0(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k21_pcs_0(A))) => ~ ( B = D & C = E & r1_pcs_0(A,B,C) & r1_pcs_0(k21_pcs_0(A),D,E) ) ) ) ) ) ) )).
fof(t34_pdiff_3,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(2)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t34_pdiff_4,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( 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(k10_pdiff_1(3,1,B,A),k10_pdiff_1(3,2,B,A),k10_pdiff_1(3,3,B,A)) ) ) )).
fof(t34_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( 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) = k10_pdiff_1(3,1,k1_pdiff_3(3,3,B),A) ) ) ) )).
fof(t34_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [E] : ( 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] : ( m2_finseq_2(F,k1_numbers,k1_euclid(A)) => ( r2_hidden(F,E) => r4_pdiff_1(A,B,C,D,F) ) ) ) ) ) ) ) ) ) ) )).
fof(t34_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [F] : ( ( 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) ) ) ) ) ) ) )).
fof(t34_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( v1_int_2(B) & r1_nat_d(A,k1_newton(B,C)) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( A = k1_newton(B,D) & r1_xxreal_0(D,C) ) ) ) ) ) ) )).
fof(t34_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(B))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k3_finseq_2(B))) => k11_pnproc_1(A,B,k4_subset_1(k3_finseq_2(B),D,E),C) = k4_subset_1(k3_finseq_2(B),k11_pnproc_1(A,B,D,C),k11_pnproc_1(A,B,E,C)) ) ) ) ) )).
fof(t34_polyeq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( B != k5_numbers => A = k1_newton(k2_xcmplx_0(k3_xcmplx_0(k1_power(B,k9_complex1(A)),k19_sin_cos(k7_xcmplx_0(k2_xcmplx_0(k1_comptrig(A),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)),B))),k3_xcmplx_0(k3_xcmplx_0(k1_power(B,k9_complex1(A)),k17_sin_cos(k7_xcmplx_0(k2_xcmplx_0(k1_comptrig(A),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)),B))),k7_complex1)),B) ) ) ) ) )).
fof(t34_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,k8_polyform(A,B)) => k3_bspace(k4_struct_0(k17_polyform(A,B)),C) = k4_struct_0(k2_bspace) ) ) ) )).
fof(t34_polynom3,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k11_polynom3(A,B,k10_polynom3(A)),B) ) ) )).
fof(t34_polynom5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k2_algseq_1(A,k4_struct_0(A)),k9_polynom3(A)) ) )).
fof(t34_polynom8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(D,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => r2_funct_2(k4_ordinal1,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)) ) ) ) ) ) )).
fof(t34_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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) ) ) ) ) )).
fof(t34_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k2_power(A,B),k5_numbers) ) ) ) )).
fof(t34_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v3_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v3_valued_0(C) ) => ! [D] : ( ( 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))) ) ) ) )).
fof(t34_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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))) ) ) ) ) ) ) )).
fof(t34_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => k3_prepower(A,k5_numbers) = 1 ) )).
fof(t34_prob_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m2_prob_1(E,A,B) => ( r1_tarski(C,D) => r1_xxreal_0(k3_funct_2(B,k1_numbers,E,C),k3_funct_2(B,k1_numbers,E,D)) ) ) ) ) ) ) )).
fof(t34_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m1_prob_1(E,A,B) => ( k3_funct_2(B,k1_numbers,k3_prob_2(A,B,C,E),D) = k3_funct_2(B,k1_numbers,k3_prob_2(A,B,C,k7_prob_1(A,B,k4_prob_1(A,B),E)),D) => ( r1_xxreal_0(k3_funct_2(B,k1_numbers,C,E),k5_numbers) | r1_xxreal_0(1,k3_funct_2(B,k1_numbers,C,E)) | r1_prob_2(A,B,C,D,E) ) ) ) ) ) ) ) )).
fof(t34_prob_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( ~ 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] : ( ( v5_relat_1(D,C) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => r1_tarski(k1_prob_2(B,C,k3_prob_3(B,D),A),k1_prob_2(B,C,k2_prob_3(B,D),A)) ) ) ) )).
fof(t34_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t34_projpl_1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & v5_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t34_pscomp_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t34_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t34_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t34_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k5_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => B != C ) ) ) )).
fof(t34_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_qc_lang4(C,A,B) => ! [D] : ( m2_qc_lang4(D,A,B,C) => ! [E] : ( m2_qc_lang4(E,A,B,C) => ~ ( D != E & r3_xboole_0(D,E) ) ) ) ) ) ) )).
fof(t34_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => k7_quatern2(k24_quaterni(A)) = k24_quaterni(k7_quatern2(A)) ) )).
fof(t34_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k28_quaterni(k23_quaterni(k23_quaterni(A,B),C)) = k3_xcmplx_0(k3_xcmplx_0(k28_quaterni(A),k28_quaterni(B)),k28_quaterni(C)) ) ) ) )).
fof(t34_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_xreal_0(B) => ( A = B => ( k13_quaterni(k10_quaterni(A,k11_quaterni)) = k5_numbers & k14_quaterni(k10_quaterni(A,k11_quaterni)) = k5_numbers & k15_quaterni(k10_quaterni(A,k11_quaterni)) = B & k16_quaterni(k10_quaterni(A,k11_quaterni)) = k5_numbers ) ) ) ) )).
fof(t34_quofield,axiom,( ! [A] : ( ( ~ 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] : ( 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))) ) ) )).
fof(t34_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ! [F] : ( m2_vectsp_6(F,A,B,E) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ~ ( v2_funct_1(k2_partfun1(u1_struct_0(B),u1_struct_0(C),D,E)) & r2_hidden(G,E) & ! [H] : ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(B))) => ~ ( r1_xboole_0(H,E) & k7_ranknull(B,C,D,k6_domain_1(u1_struct_0(C),k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,G))) = k4_subset_1(u1_struct_0(B),k6_domain_1(u1_struct_0(B),G),H) ) ) ) ) ) ) ) ) ) ) )).
fof(t34_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ( ~ ( ~ r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,k2_rat_1(A)) ) & ~ ( ~ r1_xxreal_0(k5_numbers,k2_rat_1(A)) & r1_xxreal_0(k5_numbers,A) ) ) ) )).
fof(t34_ratfunc1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_ratfunc1(B,A) => ! [C] : ( m1_ratfunc1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t34_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t34_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ( ! [B] : ( v7_ordinal1(B) => k9_nat_1(k1_numbers,k4_real_3(A),B) = k5_numbers ) => A = k5_numbers ) ) )).
fof(t34_rearran1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,k1_numbers))) ) => ! [E] : ( ( v1_rearran1(E) & v2_rearran1(E) & v3_rearran1(E,k1_zfmisc_1(B)) & m2_finseq_1(E,k1_zfmisc_1(B)) ) => ( ( v1_partfun1(D,C) & k5_card_1(B) = k5_card_1(C) ) => ( r2_classes1(k19_rfunct_3(B,k15_valued_1(B,k1_numbers,k4_rearran1(C,B,E,D),A)),k19_rfunct_3(C,k15_valued_1(C,k1_numbers,D,A))) & k20_rfunct_3(B,k19_rfunct_3(B,k15_valued_1(B,k1_numbers,k4_rearran1(C,B,E,D),A)),B) = k20_rfunct_3(C,k19_rfunct_3(C,k15_valued_1(C,k1_numbers,D,A)),C) & k21_rfunct_3(B,k19_rfunct_3(B,k15_valued_1(B,k1_numbers,k4_rearran1(C,B,E,D),A)),B) = k21_rfunct_3(C,k19_rfunct_3(C,k15_valued_1(C,k1_numbers,D,A)),C) ) ) ) ) ) ) ) )).
fof(t34_relat_1,axiom,( k1_relat_1(k1_xboole_0) = k1_xboole_0 )).
fof(t34_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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)) ) ) )).
fof(t34_revrot_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( v1_finseq_6(B,u1_struct_0(k15_euclid(2))) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_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) ) ) ) ) )).
fof(t34_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ~ r2_hidden(B,k1_relat_1(A)) => r3_rewrite1(A,B) ) ) )).
fof(t34_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ( r1_rewrite2(A,B,C,D) => r3_rewrite2(A,B,C,D) ) ) ) ) )).
fof(t34_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( ( ~ v2_struct_0(D) & l1_rewrite3(D,B) ) => ! [E] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t34_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_valued_0(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_valued_0(D) ) => k18_valued_1(k1_rfunct_1(A,C),k1_rfunct_1(B,D)) = k1_rfunct_1(k18_valued_1(A,B),k18_valued_1(C,D)) ) ) ) ) )).
fof(t34_rfunct_2,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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(k5_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,k5_numbers) ) => v8_valued_0(k2_partfun1(k1_numbers,k1_numbers,k26_valued_1(k1_numbers,k1_numbers,C,B),A)) ) ) ) ) )).
fof(t34_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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))) ) ) ) )).
fof(t34_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v7_valued_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_numbers)) => ( C = a_2_0_rinfsup1(A,B) => k3_seq_4(C) = k1_funct_1(A,B) ) ) ) ) ) )).
fof(t34_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ( v8_valued_0(A) & k2_supinf_1 = k2_rinfsup2(A) ) => ( v9_mesfunc5(A) & k2_mesfunc5(A) = k2_supinf_1 ) ) ) )).
fof(t34_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_rlvect_2(C,A) => k3_rlaffin1(A,k7_rlvect_2(A,B,C)) = k2_xcmplx_0(k3_rlaffin1(A,B),k3_rlaffin1(A,C)) ) ) ) )).
fof(t34_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_rlsub_1(C,A) => ( u1_struct_0(C) = B => v1_rlsub_1(B,A) ) ) ) ) )).
fof(t34_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ( r1_rlsub_2(A,B,C) => m1_rlsub_2(C,A,B) ) ) ) ) )).
fof(t34_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k2_relset_1(u1_struct_0(A),k3_rltopsp1(A,B)) = k2_struct_0(A) ) ) )).
fof(t34_rlvect_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t34_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ( k3_rlvect_2(A,B) = k1_xboole_0 => k6_rlvect_2(A,B) = k4_struct_0(A) ) ) ) )).
fof(t34_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t34_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t34_rlvect_5,axiom,( ! [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_rlvect_5(A) & l1_rlvect_1(A) ) => ( k1_rlvect_5(A) = 2 <=> ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( 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)) ) ) ) ) )).
fof(t34_rlvect_x,axiom,( ! [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) ) => ! [B] : ( 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) ) ) )).
fof(t34_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ~ ( C != k1_xboole_0 & v1_rmod_2(C,A,B) & ! [D] : ( ( v2_vectsp_2(D,A) & m1_rmod_2(D,A,B) ) => C != u1_struct_0(D) ) ) ) ) ) )).
fof(t34_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( m1_rmod_2(E,A,B) => ( m1_rmod_2(C,A,D) => m1_rmod_2(C,A,k1_rmod_3(A,B,D,E)) ) ) ) ) ) ) )).
fof(t34_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(t34_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k8_robbins1(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t34_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t34_robbins4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v10_robbins1(A) & v8_robbins3(A) & v9_robbins3(A) & l4_robbins1(A) ) => ( v1_robbins4(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) ) )).
fof(t34_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) )).
fof(t34_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => m1_rusub_1(k1_rusub_1(B),C) ) ) ) )).
fof(t34_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ( r1_rusub_2(A,B,C) => m1_rusub_2(C,A,B) ) ) ) ) )).
fof(t34_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( r2_hidden(E,k3_rusub_1(A,B,k1_rusub_3(A,k7_domain_1(u1_struct_0(A),C,D)))) <=> ? [F] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & E = k3_rlvect_1(A,k3_rlvect_1(A,B,k1_rlvect_1(A,C,F)),k1_rlvect_1(A,D,G)) ) ) ) ) ) ) ) )).
fof(t34_rusub_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v2_rusub_4(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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) ) ) ) )).
fof(t34_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,k5_numbers) & r1_tarski(k4_bhsp_2(A,B,C),u1_struct_0(A)) ) ) ) )).
fof(t34_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t34_rvsum_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k16_rvsum_1(k10_finseq_1(A,B)) = k2_xcmplx_0(A,B) ) ) )).
fof(t34_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & ~ v1_scmfsa_m(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( 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(k7_card_1(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) = k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k5_card_1(B),k5_card_1(C)),3)))) ) ) ) ) ) ) ) )).
fof(t34_scmbsort,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( r1_tarski(k2_scmbsort,C) => ! [D] : ( m2_finseq_1(D,k4_numbers) => ( r1_tarski(k1_scmfsa_m(k16_funcop_1(k5_scmfsa_2(k5_numbers),D)),B) => r2_hidden(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,C,B,A)),k9_xtuple_0(k2_scmbsort)) ) ) ) ) ) ) )).
fof(t34_scmfsa10,axiom,( ! [A] : ( v7_ordinal1(A) => k2_amistd_1(k7_card_1(3),k1_scmfsa_2,k11_scmfsa_2(A)) = k1_tarski(A) ) )).
fof(t34_scmfsa8a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( 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(k7_card_1(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(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(k3_scmfsa6a(k3_scmfsa6a(k3_scmfsa6a(B,k1_scmfsa8a(k1_nat_1(k5_card_1(C),1))),C),k4_compos_1(k1_scmfsa_2)),D,A)) = k1_nat_1(k1_nat_1(k5_card_1(B),k5_card_1(C)),1) ) ) ) ) ) )).
fof(t34_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_finset_1(E) & v1_afinsq_1(E) ) => ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_scmfsa_2)) ) => ( ( ! [G] : ( ( 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] : ( m1_scmfsa_2(G) => k18_scmfsa_2(C,G) = k18_scmfsa_2(D,G) ) & r5_scmfsa7b(E,C,A) ) => ( r2_scmfsa7b(E,F) | ! [G] : ( v7_ordinal1(G) => ( ! [H] : ( ( v1_ami_2(H) & m1_subset_1(H,u1_struct_0(k1_scmfsa_2)) ) => ( F != H => k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,E),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,C),G),H) = k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,E),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D),G),H) ) ) & ! [H] : ( m1_scmfsa_2(H) => k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,E),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,C),G),H) = k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,E),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D),G),H) ) & k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,E),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,C),G)) = k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,E),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D),G)) & k3_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,E),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,E),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,C),G)) = k3_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,E),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,E),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D),G)) ) ) ) ) ) ) ) ) ) ) )).
fof(t34_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( 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) = k5_numbers | ( r6_scmfsa7b(k1_scmfsa8b(E,C,D),B,A) & r5_scmfsa7b(k1_scmfsa8b(E,C,D),B,A) & k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8b(E,C,D)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B)) = k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(D,k4_compos_1(k1_scmfsa_2))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B)),3) ) ) ) ) ) ) ) ) )).
fof(t34_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( v1_ami_2(E) & ~ v1_scmfsa_m(E) & m1_subset_1(E,u1_struct_0(k1_scmfsa_2)) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & ~ v1_xboole_0(F) & v1_funct_1(F) & v1_finset_1(F) & v1_afinsq_1(F) ) => ( ( r3_scmfsa9a(A,C,E,F) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,C) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,D) ) => ! [G] : ( v7_ordinal1(G) => k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(C,F,E,A),G)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(D,F,E,B),G)) ) ) ) ) ) ) ) ) )).
fof(t34_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ~ ( k2_compos_0(u1_compos_1(k1_scmfsa_2),A) = 12 & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_scmfsa_2(C) => A != k17_scmfsa_2(B,C) ) ) ) ) )).
fof(t34_scmfsa_m,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(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)) ) ) ) )).
fof(t34_scmisort,axiom,( v3_scm_halt(k2_scmisort(k5_scmfsa_2(k5_numbers))) & v2_scm_halt(k2_scmisort(k5_scmfsa_2(k5_numbers))) )).
fof(t34_scmpds_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ~ ( k2_compos_0(u1_compos_1(k1_scmpds_2),A) = 11 & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmpds_2)) ) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => A != k14_scmpds_2(B,C,D,E) ) ) ) ) ) ) )).
fof(t34_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v3_scmpds_4(D) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_scmpds_2)) ) => ! [G] : ( v1_int_1(G) => ( k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,E),G)) = k5_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) ) ) ) ) ) ) ) ) )).
fof(t34_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ! [G] : ( v7_ordinal1(G) => ( r1_xxreal_0(k5_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,k1_nat_1(k5_card_1(C),3))) ) ) ) ) ) ) ) ) )).
fof(t34_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => k3_amistd_1(k7_card_1(2),k1_scmring2(A),B) = k2_tarski(B,k1_ordinal1(B)) ) ) )).
fof(t34_scmyciel,axiom,( ! [A] : ! [B] : ! [C] : ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r2_hidden(k2_tarski(B,C),k5_scmyciel(A)) ) )).
fof(t34_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_semi_af1(A,G,B,C) & r1_semi_af1(A,G,D,E) & r1_semi_af1(A,G,D,F) & r2_analoaf(A,B,D,C,E) & r2_analoaf(A,B,D,C,F) ) => ( r1_semi_af1(A,G,B,D) | E = F ) ) ) ) ) ) ) ) ) )).
fof(t34_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,A),k37_valued_1(k4_ordinal1,k1_numbers,B)),k37_valued_1(k4_ordinal1,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B))) ) ) )).
fof(t34_seq_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => k9_nat_1(k1_numbers,A,B) = k7_xcmplx_0(1,k1_nat_1(k3_xcmplx_0(B,B),1)) ) => ( v2_comseq_2(A) & k1_seq_2(A) = k5_numbers ) ) ) )).
fof(t34_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( m1_subset_1(C,A) => ( r2_relset_1(k4_ordinal1,k1_numbers,k10_seqfunc(A,k5_seqfunc(A,B),C),k56_valued_1(k4_ordinal1,k1_numbers,k10_seqfunc(A,B,C))) & r2_relset_1(k4_ordinal1,k1_numbers,k10_seqfunc(A,k4_seqfunc(A,B),C),k32_valued_1(k4_ordinal1,k1_numbers,k10_seqfunc(A,B,C))) ) ) ) ) )).
fof(t34_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ( v5_valued_0(A) & v5_valued_0(B) ) => v5_valued_0(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) & ( ( v6_valued_0(A) & v6_valued_0(B) ) => v6_valued_0(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) & ( ( v7_valued_0(A) & v7_valued_0(B) ) => v7_valued_0(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) & ( ( v8_valued_0(A) & v8_valued_0(B) ) => v8_valued_0(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).
fof(t34_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => r1_xxreal_0(k9_complex1(k5_real_1(k9_nat_1(k1_numbers,k3_series_1(A),C),k9_nat_1(k1_numbers,k3_series_1(A),B))),k9_complex1(k5_real_1(k9_nat_1(k1_numbers,k3_series_1(k55_valued_1(k4_ordinal1,k1_numbers,A)),C),k9_nat_1(k1_numbers,k3_series_1(k55_valued_1(k4_ordinal1,k1_numbers,A)),B)))) ) ) ) ) )).
fof(t34_series_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,A,B)) ) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,k3_series_1(A),B)) ) ) ) )).
fof(t34_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => r1_xxreal_0(k3_square_1(k3_xcmplx_0(3,k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(C)))),k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(B,C),A),k7_xcmplx_0(k3_xcmplx_0(C,A),B)),k7_xcmplx_0(k3_xcmplx_0(A,B),C))) ) ) ) )).
fof(t34_setfam_1,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(t34_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ! [E] : ( v7_ordinal1(E) => k1_funct_1(D,E) = k2_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) => ! [E] : ( v7_ordinal1(E) => r1_tarski(k2_xboole_0(k1_funct_1(k2_setlim_1(A,B),E),k1_funct_1(k2_setlim_1(A,C),E)),k1_funct_1(k2_setlim_1(A,D),E)) ) ) ) ) ) )).
fof(t34_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k3_prob_1(A,k6_setlim_2(A,C,B)) = k4_subset_1(A,B,k3_prob_1(A,C)) ) ) )).
fof(t34_setwiseo,axiom,( ! [A] : v3_binop_1(k9_setwiseo(A),k5_finsub_1(A)) )).
fof(t34_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m2_finseq_1(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t34_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( m1_scmfsa_2(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t34_sfmastr3,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( m1_scmfsa_2(D) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ( ( 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(k5_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)) ) ) ) ) ) ) ) )).
fof(t34_sgraph1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_sgraph1(k2_finseq_1(3)))) & A = k4_setwiseo(k5_finsub_1(k4_ordinal1),k3_setwiseo(k4_ordinal1,1,2),k3_setwiseo(k4_ordinal1,2,3),k3_setwiseo(k4_ordinal1,3,1)) & k8_sgraph1 = g1_sgraph1(k2_finseq_1(3),A) ) )).
fof(t34_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v9_sheffer1(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l3_sheffer1(A) ) => v6_lattices(A) ) )).
fof(t34_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t34_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ! [C] : ( m2_simplex0(C,A,B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t34_simplex1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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] : ( ( v1_tops_2(C,B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t34_sin_cos,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ( k9_nat_1(k1_numbers,k3_series_1(k20_sin_cos(B)),A) = k9_nat_1(k1_numbers,k3_series_1(k8_comseq_3(k3_sin_cos(k3_xcmplx_0(B,k7_complex1)))),k1_nat_1(k3_xcmplx_0(2,A),1)) & k9_nat_1(k1_numbers,k3_series_1(k21_sin_cos(B)),A) = k9_nat_1(k1_numbers,k3_series_1(k7_comseq_3(k3_sin_cos(k3_xcmplx_0(B,k7_complex1)))),k3_xcmplx_0(2,A)) ) ) ) )).
fof(t34_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_fdiff_1(k1_sin_cos2,k1_numbers) & k1_fdiff_1(k1_sin_cos2,A) = k1_funct_1(k3_sin_cos2,A) ) ) )).
fof(t34_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,k2_xcmplx_0(A,k3_xcmplx_0(k2_nat_1(2,B),k28_sin_cos))) = k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,A) ) ) )).
fof(t34_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k3_xcmplx_0(k3_xcmplx_0(k17_sin_cos(A),k17_sin_cos(B)),k19_sin_cos(C)) = k3_xcmplx_0(k7_xcmplx_0(1,4),k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(k19_sin_cos(k6_xcmplx_0(k2_xcmplx_0(A,B),C))),k19_sin_cos(k6_xcmplx_0(k2_xcmplx_0(B,C),A))),k19_sin_cos(k6_xcmplx_0(k2_xcmplx_0(C,A),B))),k19_sin_cos(k2_xcmplx_0(k2_xcmplx_0(A,B),C)))) ) ) ) )).
fof(t34_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( k17_sin_cos(k7_xcmplx_0(A,2)) != k5_numbers & k19_sin_cos(k7_xcmplx_0(A,2)) != k5_numbers & k6_xcmplx_0(1,k1_square_1(k1_sin_cos4(k7_xcmplx_0(A,2)))) != k5_numbers & k4_sin_cos4(k7_xcmplx_0(A,2)) != k3_square_1(k7_xcmplx_0(k3_xcmplx_0(2,k4_sin_cos4(A)),k2_xcmplx_0(k4_sin_cos4(A),1))) & k4_sin_cos4(k7_xcmplx_0(A,2)) != k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k3_xcmplx_0(2,k4_sin_cos4(A)),k2_xcmplx_0(k4_sin_cos4(A),1)))) ) ) )).
fof(t34_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(k3_xcmplx_0(2,k28_sin_cos),A) & r1_xxreal_0(1,k19_sin_cos(A)) ) ) )).
fof(t34_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(k5_numbers,A) => k1_sin_cos7(A) = k3_sin_cos7(k3_square_1(k2_xcmplx_0(k1_square_1(A),1))) ) ) )).
fof(t34_sin_cos9,axiom,( k3_relat_1(k2_partfun1(k1_numbers,k1_numbers,k27_sin_cos,k2_rcomp_1(k5_numbers,k28_sin_cos)),k2_sin_cos9) = k1_partfun2(k1_numbers,k2_rcomp_1(k5_numbers,k28_sin_cos)) )).
fof(t34_sincos10,axiom,( ! [A] : ( r2_hidden(A,k1_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos),k28_sin_cos)) => r2_hidden(k1_funct_1(k1_fdiff_9,A),k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1))) ) )).
fof(t34_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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(k1_nat_1(A,2),k3_finseq_1(B)) & ~ ( v2_sppol_1(k2_topreal1(2,B,A)) & v1_sppol_1(k2_topreal1(2,B,k1_nat_1(A,1))) ) & ~ ( v1_sppol_1(k2_topreal1(2,B,A)) & v2_sppol_1(k2_topreal1(2,B,k1_nat_1(A,1))) ) ) ) ) )).
fof(t34_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t34_sprect_1,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t34_sprect_3,axiom,( ! [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) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => k1_sprect_1(k3_topreal1(2,A)) = A ) )).
fof(t34_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t34_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k7_xcmplx_0(A,k3_square_1(A)) = k3_square_1(A) ) ) )).
fof(t34_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(k14_stacks_1(A))) => ? [C] : ( 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) ) ) ) )).
fof(t34_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k7_card_1(k1_nat_1(B,1)),k7_card_1(k1_nat_1(A,1))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(k1_nat_1(B,1)),k7_card_1(k1_nat_1(A,1))))) ) => ( ( v2_funct_2(C,k7_card_1(k1_nat_1(A,1))) & v1_stirl2_1(C,k1_nat_1(B,1),k1_nat_1(A,1)) & k1_stirl2_1(k1_nat_1(B,1),k7_card_1(k1_nat_1(A,1)),C,k6_domain_1(k7_card_1(k1_nat_1(A,1)),k2_stirl2_1(k7_card_1(k1_nat_1(B,1)),k1_nat_1(A,1),C,B))) = k1_seq_4(B) ) => k2_stirl2_1(k7_card_1(k1_nat_1(B,1)),k1_nat_1(A,1),C,B) = A ) ) ) ) )).
fof(t34_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => r1_tarski(k2_zfmisc_1(k9_qc_lang1(A),k1_substut1(A)),k9_xtuple_0(k15_substut1(A))) ) )).
fof(t34_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ( A != k1_xboole_0 => m1_subset_1(k2_tarski(B,C),k1_zfmisc_1(A)) ) ) ) )).
fof(t34_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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 ) ) ) ) ) )).
fof(t34_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ~ ( r1_xxreal_0(1,k7_cqc_sim1(A,B)) & ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ~ ( r2_qc_lang2(A,C,B) & k7_cqc_sim1(A,C) = 1 ) ) ) ) ) )).
fof(t34_supinf_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_card_3(A) & v5_supinf_2(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( m1_supinf_2(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_xxreal_0(k1_supinf_2,k12_supinf_2(B,C)) ) ) ) )).
fof(t34_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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,D,C) & k2_symsp_1(A,B,E,F,C,D) != k4_algstr_0(A,k2_symsp_1(A,B,F,E,C,D)) ) ) ) ) ) ) ) )).
fof(t34_sysrel,axiom,( ! [A] : ( 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) ) ) )).
fof(t34_taxonom1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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(k5_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)))) ) ) ) ) ) )).
fof(t34_tdlat_1,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t34_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) )).
fof(t34_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v4_tdlat_3(A) <=> ! [B] : ( 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)) ) ) ) ) )).
fof(t34_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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,k5_polynom1(A,C,D,E)),k2_termord(A,B,k3_termord(A,B,C,D),k3_termord(A,B,C,E))) ) ) ) ) ) )).
fof(t34_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ~ ( ~ v3_tdlat_3(A) & ! [B] : ( 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] : ( 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) ) ) ) )).
fof(t34_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t34_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_pre_topc(C,A) => ( ( v3_tex_3(B,A) & m1_pre_topc(C,B) ) => v3_tex_3(C,A) ) ) ) ) )).
fof(t34_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t34_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( ~ ( ~ r1_tsep_1(k1_tsep_1(A,C,D),B) & r1_tsep_1(C,B) & r1_tsep_1(D,B) ) & ~ ( ~ ( r1_tsep_1(C,B) & r1_tsep_1(D,B) ) & r1_tsep_1(k1_tsep_1(A,C,D),B) ) & ~ ( ~ r1_tsep_1(B,k1_tsep_1(A,C,D)) & r1_tsep_1(B,C) & r1_tsep_1(B,D) ) & ~ ( ~ ( r1_tsep_1(B,C) & r1_tsep_1(B,D) ) & r1_tsep_1(B,k1_tsep_1(A,C,D)) ) ) ) ) ) ) )).
fof(t34_toler_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( r2_hidden(C,A) => m1_toler_1(k9_relat_1(B,C),A,B) ) => v8_relat_2(B) ) ) )).
fof(t34_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_borsuk_2(G,A,B,C) => ! [H] : ( m1_borsuk_2(H,A,C,D) => ! [I] : ( m1_borsuk_2(I,A,D,E) => ! [J] : ( 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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t34_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( v7_topalg_6(B,A) & m2_subset_1(B,k4_partfun1(k1_numbers,k2_struct_0(A)),k1_topalg_6(A)) ) => ! [C] : ( ( v7_topalg_6(C,A) & m2_subset_1(C,k4_partfun1(k1_numbers,k2_struct_0(A)),k1_topalg_6(A)) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_borsuk_2(F,A,D,E) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t34_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( ( v3_topdim_1(A) & r1_xxreal_0(k4_topdim_1(A),k5_numbers) & v1_metrizts(A) ) => ! [B] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v4_pre_topc(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( r1_xboole_0(B,C) & ! [D] : ( ( v4_pre_topc(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ! [E] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t34_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(t34_topgen_2,axiom,( ! [A] : ( ~ v1_finset_1(A) => ! [B] : k2_waybel23(k5_topgen_2(A,B)) = k1_card_1(A) ) )).
fof(t34_topgen_3,axiom,( ! [A] : ! [B] : ( 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)) ) ) ) )).
fof(t34_topgen_4,axiom,( ! [A] : ! [B] : ~ ( 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)) ) )).
fof(t34_topgen_5,axiom,( ! [A] : ( 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) ) ) )).
fof(t34_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_topgrp_1(A) & l1_pre_topc(A) ) => ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & v4_pre_topc(k6_domain_1(u1_struct_0(A),B),A) ) => v7_pre_topc(A) ) ) )).
fof(t34_topreal1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => k6_topreal1(A) = a_1_4_topreal1(A) ) )).
fof(t34_topreal3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) ) ) )).
fof(t34_topreal6,axiom,( ! [A] : ( 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))) ) )).
fof(t34_topreal8,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t34_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ( ( r2_hidden(C,k3_topreal9(A,E,B)) & r2_hidden(D,k3_topreal9(A,E,B)) ) => k9_subset_1(u1_struct_0(k15_euclid(A)),k4_topreal9(k15_euclid(A),C,D),k3_topreal9(A,E,B)) = k2_tarski(C,D) ) ) ) ) ) ) )).
fof(t34_topreala,axiom,( v3_tops_2(k2_topreala,k2_borsuk_1(k3_topmetr,k3_topmetr),k15_euclid(2)) )).
fof(t34_toprealb,axiom,( ! [A] : ( v1_xreal_0(A) => ( k3_int_1(A) = k7_xcmplx_0(1,2) => k1_funct_1(k12_toprealb,A) = k19_euclid(k4_xcmplx_0(1),k5_numbers) ) ) )).
fof(t34_toprealc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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))))) ) ) ) ) )).
fof(t34_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => r1_xxreal_0(k12_euclid(k5_algstr_0(k15_euclid(A),C,D)),k2_xcmplx_0(k12_euclid(k5_algstr_0(k15_euclid(A),C,B)),k12_euclid(k5_algstr_0(k15_euclid(A),B,D)))) ) ) ) ) )).
fof(t34_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)) ) ) )).
fof(t34_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t34_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_tops_3(B,A) & B = k1_xboole_0 ) ) ) )).
fof(t34_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t34_trees_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k5_card_1(k1_trees_1(A)) = k3_finseq_1(A) ) )).
fof(t34_trees_2,axiom,( ! [A] : ( ( ! [B] : ( 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)) ) ) )).
fof(t34_trees_3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( B != k5_numbers => ( v4_trees_3(k2_finseq_2(B,A)) <=> ( ~ v1_xboole_0(A) & v1_trees_1(A) ) ) ) ) )).
fof(t34_trees_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ~ ( r1_xxreal_0(1,k3_finseq_1(B)) & C = k5_relset_1(k4_ordinal1,A,B,k2_finseq_1(1)) & ! [D] : ( m1_subset_1(D,A) => C != k12_finseq_1(A,D) ) ) ) ) ) )).
fof(t34_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t34_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t34_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t34_turing_1,axiom,( ! [A] : ( 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] : ( m2_funct_2(B,k4_numbers,u1_turing_1(k18_turing_1),k9_funct_2(k4_numbers,u1_turing_1(k18_turing_1))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( r1_xxreal_0(1,k3_finseq_1(D)) & A = k4_domain_1(k4_ordinal1,k4_ordinal1,k9_funct_2(k4_numbers,u1_turing_1(k18_turing_1)),k5_numbers,C,B) & r2_turing_1(k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,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(k4_ordinal1,C,k5_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))) ) ) ) ) ) ) )).
fof(t34_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ~ v1_facirc_1(k2_msafree2(k37_twoscomp(A,B))) ) ) )).
fof(t34_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( 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)) ) ) ) )).
fof(t34_uproots,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( k1_normsp_1(A,k11_polynom3(A,k4_polynom5(A,B,C),D),k5_numbers) = k6_algstr_0(A,B,k1_normsp_1(A,D,k5_numbers)) & ! [E] : ( 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,k1_normsp_1(A,D,E))) ) ) ) ) ) ) )).
fof(t34_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_funct_2(C,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t34_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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)) ) ) ) )).
fof(t34_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(t34_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t34_vectsp11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( ~ 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] : ( ( 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) ) ) ) ) ) )).
fof(t34_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t34_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ~ ( C != k1_xboole_0 & v1_vectsp_4(C,A,B) & ! [D] : ( ( v7_vectsp_1(D,A) & m1_vectsp_4(D,A,B) ) => C != u1_struct_0(D) ) ) ) ) ) )).
fof(t34_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m1_vectsp_4(E,A,B) => ( ( m1_vectsp_4(C,A,E) & m1_vectsp_4(D,A,E) ) => m1_vectsp_4(k1_vectsp_5(A,B,C,D),A,E) ) ) ) ) ) ) )).
fof(t34_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t34_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t34_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( v1_xreal_0(D) => ( v1_partfun1(C,A) <=> v1_partfun1(k4_vfunct_1(A,B,C,D),A) ) ) ) ) ) )).
fof(t34_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( v1_xcmplx_0(D) => ( v1_partfun1(C,A) <=> v1_partfun1(k2_vfunct_2(A,B,C,D),A) ) ) ) ) ) )).
fof(t34_waybel11,axiom,( ! [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) & 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) ) ) )).
fof(t34_waybel12,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( v13_waybel_0(B,A) & v1_waybel_6(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v4_card_3(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r1_tarski(k4_yellow_4(A,B,C),B) & r2_hidden(D,B) & ! [E] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(t34_waybel13,axiom,( ! [A] : ( ( 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] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v4_yellow_0(C,k2_yellow_1(B)) & m1_yellow_0(C,k2_yellow_1(B)) ) => ~ ( v7_yellow_0(C,k2_yellow_1(B)) & v4_waybel_0(C,k2_yellow_1(B)) & r5_waybel_1(A,C) ) ) ) ) & ( ? [B] : ? [C] : ( v4_yellow_0(C,k2_yellow_1(B)) & m1_yellow_0(C,k2_yellow_1(B)) & v7_yellow_0(C,k2_yellow_1(B)) & v4_waybel_0(C,k2_yellow_1(B)) & r5_waybel_1(A,C) ) => v2_waybel_8(A) ) ) ) )).
fof(t34_waybel14,axiom,( ! [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] : ( 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) ) ) )).
fof(t34_waybel16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v1_waybel16(C,A) & C = k2_yellow_0(A,B) ) => r2_hidden(C,B) ) ) ) ) )).
fof(t34_waybel19,axiom,( ! [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] : ( ( v2_pre_topc(B) & v1_waybel19(B) & m1_yellow_9(B,A) ) => ! [C] : ( ( v2_pre_topc(C) & v4_waybel11(C) & m1_yellow_9(C,A) ) => ! [D] : ( m3_yellow_9(D,C,B) => k2_waybel19(A) = u1_pre_topc(D) ) ) ) ) )).
fof(t34_waybel20,axiom,( ! [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) & l1_orders_2(A) ) => ! [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) & l1_orders_2(B) ) => ! [C] : ( m1_waybel16(C,A,B) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t34_waybel21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_waybel17(A,B))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t34_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_waybel23(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t34_waybel24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & v2_yellow_0(B) & l1_orders_2(B) ) => k4_yellow_0(k5_yellow_1(u1_struct_0(A),B)) = k6_struct_0(A,B,k4_yellow_0(B)) ) ) )).
fof(t34_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( ( ~ 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) ) ) )).
fof(t34_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ? [C] : ( 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(k4_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(k4_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))),k4_yellow_1(B,k7_funcop_1(B,k1_waybel26(A,k9_waybel18)))) & ! [D] : ( ( 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) = k9_funct_6(D) ) ) ) ) )).
fof(t34_waybel27,axiom,( ! [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) ) => r5_waybel_1(k2_waybel27(A,k2_yellow_1(k1_tarski(k5_numbers))),k1_yellow_1(k5_waybel11(A))) ) )).
fof(t34_waybel30,axiom,( ! [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_waybel_2(A) & l1_waybel_9(A) ) => ! [B] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => a_3_3_waybel30(A,B,C) = a_2_4_waybel30(A,C) ) ) ) )).
fof(t34_waybel34,axiom,( ! [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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k1_yellow_2(A,A,B))) => ! [F] : ( 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) ) ) ) )).
fof(t34_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t34_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t34_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) )).
fof(t34_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ( r1_waybel_3(k1_yellow_1(u1_pre_topc(A)),B,C) => ! [D] : ( 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] : ( ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(D)) ) => ~ r1_tarski(B,k3_tarski(E)) ) ) ) ) ) ) ) )).
fof(t34_waybel_4,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => k1_setfam_1(a_2_0_waybel_4(A,B)) = k1_waybel_3(A,B) ) ) )).
fof(t34_waybel_6,axiom,( ! [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) ) => ( v4_waybel_6(k4_waybel_6(A),A) => ( v2_waybel_1(A) & v2_waybel_2(A) ) ) ) )).
fof(t34_waybel_7,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v5_waybel_6(B,A) => v4_waybel_7(B,A) ) ) ) )).
fof(t34_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t34_weddwitt,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ~ r1_xxreal_0(k1_vectsp_9(k4_weddwitt(A),k7_weddwitt(A,B)),k5_numbers) ) ) )).
fof(t34_weierstr,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [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)) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r2_hidden(D,B) & r2_hidden(E,C) ) => ( r1_xxreal_0(k7_weierstr(A,B,C),k3_metric_1(A,D,E)) & r1_xxreal_0(k3_metric_1(A,D,E),k10_weierstr(A,B,C)) ) ) ) ) ) ) ) ) )).
fof(t34_wellord1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( ( v2_wellord1(C) & r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k1_relat_1(C)) & ! [D] : ( r2_hidden(D,k1_wellord1(C,A)) => ( r2_hidden(k4_tarski(D,B),C) & D != B ) ) ) => r2_hidden(k4_tarski(A,B),C) ) ) )).
fof(t34_wsierp_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => ( k2_xcmplx_0(k3_xcmplx_0(B,D),k3_xcmplx_0(C,E)) = A => ( B = k5_numbers | C = k5_numbers | ! [F] : ( v1_int_1(F) => ! [G] : ( v1_int_1(G) => ~ ( k2_xcmplx_0(k3_xcmplx_0(B,F),k3_xcmplx_0(C,G)) = A & ! [H] : ( v1_int_1(H) => ~ ( F = k2_xcmplx_0(D,k3_xcmplx_0(H,k7_xcmplx_0(C,k3_int_2(B,C)))) & G = k6_xcmplx_0(E,k3_xcmplx_0(H,k7_xcmplx_0(B,k3_int_2(B,C)))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t34_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(A,B) => r1_tarski(k4_xboole_0(C,B),k4_xboole_0(C,A)) ) )).
fof(t34_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k9_xboolean(A,k9_xboolean(A,B)) = k4_xboolean(k3_xboolean(A),B) ) ) )).
fof(t34_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( k6_xcmplx_0(A,C) = k6_xcmplx_0(D,B) => k2_xcmplx_0(A,B) = k2_xcmplx_0(C,D) ) ) ) ) ) )).
fof(t34_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(k2_xcmplx_0(A,B),k5_numbers) ) ) ) )).
fof(t34_xtuple_0,axiom,( ! [A] : ! [B] : r1_tarski(k5_xboole_0(k11_xtuple_0(A),k11_xtuple_0(B)),k11_xtuple_0(k5_xboole_0(A,B))) )).
fof(t34_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => k4_xxreal_0(k4_xxreal_0(A,B),C) = k4_xxreal_0(A,k4_xxreal_0(B,C)) ) ) ) )).
fof(t34_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(D,B) ) => r1_tarski(k1_xxreal_1(C,D),k1_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t34_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( ~ r1_xxreal_0(B,A) => v1_xxreal_2(k2_xxreal_1(A,B)) ) ) ) )).
fof(t34_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( v1_xreal_0(B) => k1_xxreal_3(k3_xxreal_3(C,B),k3_xxreal_3(B,A)) = k3_xxreal_3(C,A) ) ) ) ) )).
fof(t34_yellow10,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(t34_yellow12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(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)))) ) => ~ v1_xboole_0(B) ) ) )).
fof(t34_yellow14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t34_yellow16,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( v1_waybel_0(C,k4_yellow_1(A,B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_yellow_1(A,B)))) ) => ! [D] : ( m1_subset_1(D,A) => v1_waybel_0(k5_waybel_3(A,B,D,C),k3_waybel_3(A,B,D)) ) ) ) ) )).
fof(t34_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & v2_yellow18(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_altcat_1(A,B,C) != k1_xboole_0 => ! [D] : ( 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)))) ) ) ) ) ) ) )).
fof(t34_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_compts_1(A) <=> ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ~ r3_waybel_9(A,B,C) ) ) ) ) ) )).
fof(t34_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_altcat_1(B) ) => ! [C] : ( l1_functor0(C,A,B) => ( ( v11_functor0(C,A,B) & v4_functor0(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k3_functor0(A,B,C,D) = k3_functor0(A,B,C,E) => D = E ) ) ) ) ) ) ) )).
fof(t34_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t34_yellow_2,axiom,( ! [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] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) ) )).
fof(t34_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t34_yellow_4,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t34_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t34_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k10_yellow_6(A,B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ? [E] : ( 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)) ) ) ) ) ) ) )).
fof(t34_yellow_7,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t34_yellow_9,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t34_zf_fund1,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_zf_lang)) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t34_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ( k13_zf_lang(A,D) = k13_zf_lang(B,C) => ( A = B & D = C ) ) ) ) ) ) )).
fof(t34_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( 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))) ) ) ) )).
fof(t34_zfmisc_1,axiom,( ! [A] : ! [B] : ~ ( B != k1_tarski(A) & B != k1_xboole_0 & ! [C] : ~ ( r2_hidden(C,B) & C != A ) ) )).
fof(t34_zfrefle1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( v3_ordinal1(B) & m1_subset_1(B,A) ) => ~ ( r2_hidden(k4_ordinal1,A) & ! [C] : ( ( v3_ordinal1(C) & m1_subset_1(C,A) ) => ! [D] : ( ~ v1_xboole_0(D) => ~ ( r2_hidden(B,C) & D = k4_classes1(C) & r3_zfrefle1(D,A) ) ) ) ) ) ) )).
fof(t34_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => r1_struct_0(C,k4_struct_0(B)) ) ) ) )).
fof(t34_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => r1_zmodul02(A,k23_zmodul02(A,C,k23_zmodul02(A,D,B)),k23_zmodul02(A,k3_xcmplx_0(C,D),B)) ) ) ) ) )).
fof(t34_zmodul03,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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) & v1_zmodul03(B) & l1_zmodul01(B) ) => ! [C] : ( m1_zmodul03(C,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_zmodul02(A,B)))) => ! [E] : ( m2_zmodul02(E,B,C) => ( D = a_3_0_zmodul03(A,B,C) => r1_struct_0(k1_vectsp_7(k9_int_3(A),k12_zmodul02(A,B),D),k13_zmodul02(A,B,k21_zmodul02(B,E))) ) ) ) ) ) ) )).
fof(t350_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t351_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t352_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t353_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ~ r1_xxreal_0(C,B) => k6_subset_1(k3_xxreal_1(B,k1_xxreal_0),k4_xxreal_1(A,C)) = k2_xboole_0(k3_xxreal_1(B,A),k1_xxreal_1(C,k1_xxreal_0)) ) ) ) ) )).
fof(t354_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(B,C) => k6_subset_1(k1_xxreal_1(B,k1_xxreal_0),k4_xxreal_1(A,C)) = k2_xboole_0(k1_xxreal_1(B,A),k1_xxreal_1(C,k1_xxreal_0)) ) ) ) ) )).
fof(t355_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ~ r1_xxreal_0(C,B) => k6_subset_1(k4_xxreal_1(B,k1_xxreal_0),k2_xxreal_1(A,C)) = k2_xboole_0(k4_xxreal_1(B,A),k2_xxreal_1(C,k1_xxreal_0)) ) ) ) ) )).
fof(t356_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(B,C) => k6_subset_1(k2_xxreal_1(B,k1_xxreal_0),k2_xxreal_1(A,C)) = k2_xboole_0(k2_xxreal_1(B,A),k2_xxreal_1(C,k1_xxreal_0)) ) ) ) ) )).
fof(t357_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ~ r1_xxreal_0(C,B) => k6_subset_1(k3_xxreal_1(B,k1_xxreal_0),k2_xxreal_1(A,C)) = k2_xboole_0(k4_xxreal_1(B,A),k1_xxreal_1(C,k1_xxreal_0)) ) ) ) ) )).
fof(t358_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(B,C) => k6_subset_1(k1_xxreal_1(B,k1_xxreal_0),k2_xxreal_1(A,C)) = k2_xboole_0(k2_xxreal_1(B,A),k1_xxreal_1(C,k1_xxreal_0)) ) ) ) ) )).
fof(t359_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ~ r1_xxreal_0(C,B) => k6_subset_1(k3_xxreal_1(B,k1_xxreal_0),k3_xxreal_1(A,C)) = k2_xboole_0(k3_xxreal_1(B,A),k3_xxreal_1(C,k1_xxreal_0)) ) ) ) ) )).
fof(t35_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_abcmiz_0(A)) => ! [D] : ( m2_finseq_1(D,u1_abcmiz_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t35_abcmiz_1,axiom,( ! [A] : ( m1_subset_1(A,k2_abcmiz_1) => ! [B] : ( 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)) ) ) ) ) )).
fof(t35_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_abcmiz_1(B,A) & m1_subset_1(B,u4_struct_0(A)) ) => ! [C] : ( 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 ) ) ) ) )).
fof(t35_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t35_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_aff_1(B,A) & v1_aff_4(C,A) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & ~ r2_hidden(D,B) ) ) ) ) ) ) )).
fof(t35_afinsq_1,axiom,( ! [A] : ! [B] : ( ( 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 ) )).
fof(t35_afinsq_2,axiom,( ! [A] : ( ( v1_finset_1(A) & v6_membered(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t35_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k13_afproj(A))) => ! [E] : ( 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),D,E) & r1_incsp_1(k13_afproj(A),C,E) ) => ( C = D | m1_subset_1(D,u1_struct_0(A)) | m1_subset_1(C,u1_struct_0(A)) ) ) ) ) ) ) ) )).
fof(t35_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t35_algspec1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v11_struct_0(B) & v1_instalg1(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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)) ) ) ) ) ) )).
fof(t35_algstr_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k14_algstr_4(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_algstr_4(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_algstr_4(A))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t35_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t35_ami_wstd,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_setfam_1(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,k4_ordinal1) => k7_ami_wstd(B,C,k4_ami_wstd(B,C,D,A),A) = D ) ) ) ) )).
fof(t35_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) <=> m1_subset_1(B,u1_struct_0(k3_analmetr(A))) ) ) )).
fof(t35_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( r2_analort(A,F,G,B,D,C,E) => r2_analort(A,F,G,D,B,E,C) ) ) ) ) ) ) ) ) )).
fof(t35_anproj_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & r1_collsp(A,B,C,F) & r1_collsp(A,D,E,F) ) ) ) ) ) ) ) ) )).
fof(t35_aofa_a00,axiom,( ! [A] : ( l1_msualg_1(A) => ! [B] : ( l1_msualg_1(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)) => ! [C] : ! [D] : ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( E = F & r1_aofa_a00(A,C,D,E) ) => r1_aofa_a00(B,C,D,F) ) ) ) ) ) ) )).
fof(t35_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( m2_subset_1(F,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),u8_aofa_a00(A))) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),u8_aofa_a00(A))) => k15_aofa_a00(A,B,C,D,u8_aofa_a00(A),k23_aofa_a00(A,C,G,H),F) = k23_aofa_a00(A,D,k15_aofa_a00(A,B,C,D,u8_aofa_a00(A),G,F),k15_aofa_a00(A,B,C,D,u8_aofa_a00(A),H,F)) ) ) ) ) ) ) ) ) )).
fof(t35_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_aofa_i00(E,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) ) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),E) => ! [G] : ( 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) = k5_numbers ) & ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t35_armstrng,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(t35_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => k7_arytm_3(A) != k1_xboole_0 ) )).
fof(t35_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v4_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v4_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_limfunc1(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) => ( r2_hidden(A,k7_asympt_0(B)) & ~ r2_hidden(A,k8_asympt_0(B)) ) ) ) ) )).
fof(t35_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & v6_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( k5_int_1(C,2) = k5_numbers => k9_nat_1(k1_numbers,B,C) = 1 ) & ( k5_int_1(C,2) = 1 => k9_nat_1(k1_numbers,B,C) = C ) ) ) & r2_hidden(B,k8_asympt_0(A)) ) ) ) )).
fof(t35_bagorder,axiom,( ! [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) ) => ( 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))))) ) ) )).
fof(t35_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m2_subset_1(C,u1_struct_0(A),k5_bcialg_1(A)) & r1_bcialg_1(A,C,B) ) ) ) )).
fof(t35_bcialg_2,axiom,( ! [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] : ( 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) ) ) ) )).
fof(t35_bcialg_3,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t35_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t35_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( 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,k1_nat_1(A,1)) ) ) ) ) ) ) ) ) )).
fof(t35_bcialg_6,axiom,( ! [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] : ( ( ~ 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] : ( ( 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) ) ) ) )).
fof(t35_bciideal,axiom,( ! [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] : ( 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) ) ) ) )).
fof(t35_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_xxreal_0(k4_bhsp_1(A,B,D),k2_xcmplx_0(k4_bhsp_1(A,B,C),k4_bhsp_1(A,C,D))) ) ) ) ) )).
fof(t35_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_bhsp_2(D,A) & k1_bhsp_2(A,D) = C ) => ( v2_comseq_2(k2_bhsp_2(A,k4_normsp_1(A,k4_normsp_1(A,D,B),k5_algstr_0(A,C,B)))) & k1_seq_2(k2_bhsp_2(A,k4_normsp_1(A,k4_normsp_1(A,D,B),k5_algstr_0(A,C,B)))) = k5_numbers ) ) ) ) ) ) )).
fof(t35_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => v7_valued_0(k3_series_1(k2_bhsp_2(A,B))) ) ) )).
fof(t35_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t35_binari_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(k5_series_1(2,A),B) => k6_binarith(A,k1_binari_3(A,B)) = B ) ) ) )).
fof(t35_binari_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ( ( r1_xxreal_0(k4_xcmplx_0(k5_series_1(2,C)),k2_xcmplx_0(A,B)) & r1_xxreal_0(k4_xcmplx_0(k5_series_1(2,k7_nat_d(C,1))),A) & r1_xxreal_0(k4_xcmplx_0(k5_series_1(2,k7_nat_d(C,1))),B) ) => ( r1_xxreal_0(k5_numbers,A) | r1_xxreal_0(k5_numbers,B) | k7_partfun1(k6_margrel1,k4_binarith(k2_xcmplx_0(C,1),k2_binari_4(k2_xcmplx_0(C,1),A),k2_binari_4(k2_xcmplx_0(C,1),B)),k2_xcmplx_0(C,1)) = k8_margrel1 ) ) ) ) ) )).
fof(t35_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t35_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t35_borsuk_4,axiom,( ! [A] : ( ( 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)) ) )).
fof(t35_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( A = k4_rcomp_1(B,C) => ( B = C | k2_pre_topc(k3_topmetr,A) = k1_rcomp_1(B,C) ) ) ) ) ) )).
fof(t35_borsuk_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r1_xxreal_0(C,D) => ( r1_xxreal_0(B,A) | ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t35_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)))) ) ) ) ) )).
fof(t35_bspace,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_vectsp_6(B,k2_bspace,k7_bspace(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t35_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t35_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t35_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)))) ) ) ) )).
fof(t35_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t35_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t35_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(E,A) => ( r3_bvfunc_2(A,D,B,E) => r2_funct_2(A,k6_margrel1,k7_bvfunc_2(A,k2_bvfunc_1(A,C,D),B,E),k2_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),D)) ) ) ) ) ) ) )).
fof(t35_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(F,A) => r1_bvfunc_1(A,k2_bvfunc_1(A,k6_bvfunc_2(A,k9_bvfunc_1(A,D,E),B,F),k6_bvfunc_2(A,k9_bvfunc_1(A,C,k1_bvfunc_1(A,E)),B,F)),k6_bvfunc_2(A,k9_bvfunc_1(A,C,k1_bvfunc_1(A,D)),B,F)) ) ) ) ) ) ) )).
fof(t35_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t35_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t35_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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,D),k9_bvfunc_1(A,C,D)),k5_bvfunc_1(A,B,C)),D) ) ) ) ) )).
fof(t35_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k11_c0sp1(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k11_c0sp1(A))))) ) => ( v1_rsspace3(B,k11_c0sp1(A)) => v3_normsp_1(B,k11_c0sp1(A)) ) ) ) )).
fof(t35_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => v2_normsp_1(k9_c0sp2(A)) ) )).
fof(t35_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k2_zfmisc_1(k4_calcul_1(A),k2_cqc_the1)) => ! [D] : ( 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(D)) & r3_calcul_1(A,D,B) ) => r3_calcul_1(A,k8_finseq_1(k2_zfmisc_1(k4_calcul_1(A),k2_cqc_the1),C,D),k1_nat_1(B,k3_finseq_1(C))) ) ) ) ) ) )).
fof(t35_card_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k2_xcmplx_0(B,A) = k8_ordinal3(B,A) ) ) )).
fof(t35_card_3,axiom,( ! [A] : ( v1_card_1(A) => k6_card_3(k7_funcop_1(k1_xboole_0,A)) = k5_ordinal1 ) )).
fof(t35_card_fil,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) & ~ v2_card_1(A) ) => ! [B] : ( m2_card_fil(B,A) => ~ ( r2_card_fil(A,A,B) & r1_tarski(k5_card_fil(A),B) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ~ ( k1_card_1(C) = A & ! [D] : ~ ( r2_hidden(D,C) & r2_hidden(D,B) ) & ! [D] : ! [E] : ( ( r2_hidden(D,C) & r2_hidden(E,C) ) => ( D = E | r1_xboole_0(D,E) ) ) ) ) ) ) ) )).
fof(t35_card_fin,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( k2_tarski(A,B) = k8_relat_1(E,k1_tarski(C)) => k2_card_fin(D,E,C) = k3_xboole_0(k1_funct_1(D,A),k1_funct_1(D,B)) ) ) ) )).
fof(t35_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v8_cat_1(k4_cat_1(A,B),A,B,B) ) ) )).
fof(t35_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v10_cat_1(C,A) => ( k3_graph_1(A,k10_cat_3(A,B,C)) = B & k4_graph_1(A,k10_cat_3(A,B,C)) = C ) ) ) ) ) )).
fof(t35_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t35_cayldick,axiom,( k6_algstr_0(k4_cayldick(k4_cayldick(k4_cayldick(k3_cayldick))),k5_cayldick(k4_cayldick(k4_cayldick(k3_cayldick)),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k5_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick))),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)))),k6_algstr_0(k4_cayldick(k4_cayldick(k4_cayldick(k3_cayldick))),k5_cayldick(k4_cayldick(k4_cayldick(k3_cayldick)),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k5_struct_0(k3_cayldick),k4_struct_0(k3_cayldick))),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)))),k5_cayldick(k4_cayldick(k4_cayldick(k3_cayldick)),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick))),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k5_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)))))) = k5_cayldick(k4_cayldick(k4_cayldick(k3_cayldick)),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick))),k5_cayldick(k4_cayldick(k3_cayldick),k5_cayldick(k3_cayldick,k4_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)),k5_cayldick(k3_cayldick,k5_struct_0(k3_cayldick),k4_struct_0(k3_cayldick)))) )).
fof(t35_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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))) ) ) ) )).
fof(t35_cfcont_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t35_cfdiff_1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(t35_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( v1_xcmplx_0(C) => ( C != k5_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),k5_xcmplx_0(C))) ) ) ) ) )).
fof(t35_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ! [B] : ( v2_cgames_1(B) => ( r2_hidden(A,k11_cgames_1(B)) => r1_tarski(k10_cgames_1(A),k11_cgames_1(B)) ) ) ) )).
fof(t35_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_chain_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) => ( r2_hidden(C,k4_chain_1(A,B,k5_numbers)) <=> ? [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) & C = k3_chain_1(A,D,D) & ! [E] : ( m2_subset_1(E,k4_ordinal1,k2_finseq_1(A)) => r2_hidden(k1_funct_1(D,E),k2_chain_1(A,B,E)) ) ) ) ) ) ) )).
fof(t35_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m4_glib_001(C,A,B) => ( k3_finseq_1(C) = k3_finseq_1(B) => C = B ) ) ) ) )).
fof(t35_circcmb3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( 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] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_card_1(D,A) & v1_finseq_1(D) ) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t35_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(C,F))) => ! [H] : ( m1_subset_1(H,k4_card_3(u3_msualg_1(A,D))) => ! [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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t35_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_msualg_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) ) => ! [H] : ( ( v4_msualg_1(H,A) & l3_msualg_1(H,A) ) => ! [I] : ( ( v4_msualg_1(I,B) & l3_msualg_1(I,B) ) => ! [J] : ( ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t35_classes1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => ( r2_hidden(A,k4_classes1(B)) => r2_hidden(k3_tarski(A),k4_classes1(B)) ) ) )).
fof(t35_classes2,axiom,( ! [A] : k1_card_1(k1_classes1(A)) = k1_card_1(k4_classes1(k1_card_1(k1_classes1(A)))) )).
fof(t35_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k14_clopban1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_clopban1(A,B))) => ! [E] : ( v1_xcmplx_0(E) => ( D = k1_clvect_1(k14_clopban1(A,B),C,E) <=> ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t35_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v1_xreal_0(C) => ~ ( r1_xxreal_0(C,1) & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(1,D) => k9_nat_1(k1_numbers,k5_normsp_0(A,B),D) = k7_xcmplx_0(1,k2_power(D,C)) ) ) & v2_clopban3(B,A) ) ) ) ) )).
fof(t35_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t35_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t35_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_clvect_1(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ( ( E = C & F = B ) => k5_algstr_0(D,E,F) = k5_algstr_0(A,C,B) ) ) ) ) ) ) ) )).
fof(t35_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_clvect_2(D,A) & k1_clvect_2(A,D) = C ) => ( v2_comseq_2(k2_clvect_2(A,k4_normsp_1(A,k4_normsp_1(A,D,B),k5_algstr_0(A,C,B)))) & k1_seq_2(k2_clvect_2(A,k4_normsp_1(A,k4_normsp_1(A,D,B),k5_algstr_0(A,C,B)))) = k5_numbers ) ) ) ) ) ) )).
fof(t35_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => v7_valued_0(k3_series_1(k2_clvect_2(A,B))) ) ) )).
fof(t35_coh_sp,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r2_hidden(k4_tarski(k1_eqrel_1(A),A),k16_coh_sp(B)) ) )).
fof(t35_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( ( 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] : ! [E] : ( r2_hidden(k2_xboole_0(D,E),A) => ! [F] : ( ( 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 ) ) ) ) ) )).
fof(t35_combgras,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ( r1_ordinal1(k1_nat_1(A,1),k1_card_1(B)) => ( r1_xxreal_0(A,k5_numbers) | ! [C] : ( l1_combgras(C,k1_combgras(A,B),k1_combgras(A,B)) => ( v7_combgras(C,k1_combgras(A,B)) <=> ? [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t35_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k8_complex1(k3_xcmplx_0(A,B)) = k3_xcmplx_0(k8_complex1(A),k8_complex1(B)) ) ) )).
fof(t35_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k1_complex2(k3_xcmplx_0(A,B),C) = k3_xcmplx_0(A,k1_complex2(B,C)) ) ) ) )).
fof(t35_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_complfld)) => ~ ( B != k4_struct_0(k1_complfld) & C != k4_struct_0(k1_complfld) & k8_group_1(k1_complfld,k11_algstr_0(k1_complfld,B),k3_vectsp_1(k1_complfld,A,C)) != k3_vectsp_1(k1_complfld,A,k8_group_1(k1_complfld,B,C)) ) ) ) ) )).
fof(t35_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( v1_xcmplx_0(B) => k9_seq_4(k10_seq_4(A,B)) = k10_seq_4(k9_seq_4(A),B) ) ) )).
fof(t35_compos_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( l1_compos_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) ) ) )).
fof(t35_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( v6_compos_0(D,u1_compos_1(A)) & m1_subset_1(D,u1_compos_1(A)) ) => ! [E] : ( ( v6_compos_0(E,u1_compos_1(A)) & m1_subset_1(E,u1_compos_1(A)) ) => ! [F] : ( ( v6_compos_0(F,u1_compos_1(A)) & m1_subset_1(F,u1_compos_1(A)) ) => ! [G] : ( ( 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 ) ) ) ) ) ) ) )).
fof(t35_comptrig,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k5_numbers,A) => k1_comptrig(A) = k5_numbers ) ) )).
fof(t35_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( k1_relset_1(k3_finseq_2(k4_ordinal1),k5_comput_1(B,A)) = k4_finseq_2(B,k4_ordinal1) & ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,B) ) => k10_xtuple_0(k5_comput_1(B,A)) = k4_ordinal1 ) ) ) ) )).
fof(t35_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,C,k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)),k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,C,B),A)) ) ) ) )).
fof(t35_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( v7_ordinal1(C) => ( ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(D,C) => k9_nat_1(k2_numbers,A,D) = k9_nat_1(k2_numbers,B,D) ) ) => k9_nat_1(k2_numbers,k10_comseq_3(A),C) = k9_nat_1(k2_numbers,k10_comseq_3(B),C) ) ) ) ) )).
fof(t35_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( v3_conlat_1(B,A) & ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) & l2_conlat_1(B,A) ) => ! [C] : ( ( v3_conlat_1(C,A) & ~ v4_conlat_1(C,A) & v6_conlat_1(C,A) & l2_conlat_1(C,A) ) => ! [D] : ( ( v3_conlat_1(D,A) & ~ v4_conlat_1(D,A) & v6_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) ) ) ) ) )).
fof(t35_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t35_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( 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 ) ) )).
fof(t35_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_convex4(B,A) => ! [C] : ( 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))) ) ) ) )).
fof(t35_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m1_subset_1(D,k1_qc_lang1(A)) => ! [E] : ( m1_subset_1(E,k5_finsub_1(k3_qc_lang1(A))) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t35_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => r1_tarski(k4_cqc_the1(A),k1_cqc_the1(A,B)) ) ) )).
fof(t35_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t35_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t35_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k9_complex1(k12_csspace(A,B,C)),k3_xcmplx_0(k3_square_1(k9_complex1(k12_csspace(A,B,B))),k3_square_1(k9_complex1(k12_csspace(A,C,C))))) ) ) ) )).
fof(t35_diff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t35_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( v1_xreal_0(F) => k1_funct_1(E,F) = k7_xcmplx_0(D,F) ) & r1_zfmisc_1(A,B,C) ) => ( A = k5_numbers | B = k5_numbers | C = k5_numbers | k10_diff_1(E,A,B,C) = k7_xcmplx_0(D,k3_xcmplx_0(k3_xcmplx_0(A,B),C)) ) ) ) ) ) ) ) )).
fof(t35_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)) & v1_diff_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)))) ) => ( ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ( r1_xxreal_0(G,F) => k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,E,F),G) = k3_xcmplx_0(k3_xcmplx_0(k4_newton(G,F),k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(C,A),G),k2_xcmplx_0(B,k3_xcmplx_0(k7_nat_d(F,G),k7_xcmplx_0(A,2))))),k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(D,A),k7_nat_d(F,G)),k6_xcmplx_0(B,k3_xcmplx_0(G,k7_xcmplx_0(A,2))))) ) ) ) => ( k1_funct_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_funct_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) ) ) ) ) ) ) ) )).
fof(t35_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k3_diff_1(C,A),B) = k6_xcmplx_0(k1_funct_1(k2_diff_1(C,A),B),k1_funct_1(C,B)) ) ) ) )).
fof(t35_dilworth,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v2_dilworth(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t35_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r3_diraf(A,B,C,E) & r3_diraf(A,B,C,D) & r3_diraf(A,E,D,F) ) => ( E = D | r3_diraf(A,B,C,F) ) ) ) ) ) ) ) ) )).
fof(t35_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k4_finseq_1(C))) => ! [F] : ( ( E = k8_relset_1(k4_ordinal1,A,C,B) & D = k5_dist_2(A,C,E) & r2_hidden(F,B) ) => k2_dist_1(A,C,F) = k2_dist_1(A,D,F) ) ) ) ) ) ) )).
fof(t35_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ( B != k5_numbers => k2_ec_pf_1(A,k2_binom(k9_int_3(A),B,2)) = 1 ) ) ) )).
fof(t35_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t35_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k11_ens_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k11_ens_1(A))) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t35_entropy1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( 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] : ( v7_ordinal1(D) => ( r1_xxreal_0(1,D) => ( r1_xxreal_0(k3_finseq_1(B),D) | k1_matrprob(A,C,k1_nat_1(D,1)) = k8_finseq_1(A,k1_matrprob(A,C,D),k1_matrprob(A,B,k1_nat_1(D,1))) ) ) ) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(D,E),k2_matrix_0(B)) => ( r2_hidden(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(D,1),k1_matrix_0(B)),E),k4_finseq_1(k1_matrprob(A,C,D))) & k3_matrix_0(A,B,D,E) = k1_funct_1(k1_matrprob(A,C,D),k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(D,1),k1_matrix_0(B)),E)) ) ) ) ) ) ) ) ) )).
fof(t35_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : k6_enumset1(A,A,B,C,D,E,F,G) = k5_enumset1(A,B,C,D,E,F,G) )).
fof(t35_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( 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) ) ) ) )).
fof(t35_equation,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_funct_1(k4_equation(A),C)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t35_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t35_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => k12_euclid(B) = k3_square_1(k22_rvsum_1(B,B)) ) ) )).
fof(t35_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) )).
fof(t35_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => k1_square_1(k12_euclid(k8_euclid(A,B,C))) = k2_xcmplx_0(k6_xcmplx_0(k1_square_1(k12_euclid(B)),k3_xcmplx_0(2,k22_rvsum_1(B,C))),k1_square_1(k12_euclid(C))) ) ) ) )).
fof(t35_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(3))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(3))) => k6_euclid_5(A,B,C) = k22_rvsum_1(k5_euclid_5(A,B),C) ) ) ) )).
fof(t35_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( 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) = k28_sin_cos ) ) ) ) ) ) ) )).
fof(t35_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_rlsub_1(B,k10_funcsdom(k2_finseq_1(A))) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t35_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( 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,k2_xcmplx_0(k1_funct_1(A,1),k1_funct_1(B,1))),k9_euclid(3,k3_euclid_8,k2_xcmplx_0(k1_funct_1(A,2),k1_funct_1(B,2)))),k9_euclid(3,k4_euclid_8,k2_xcmplx_0(k1_funct_1(A,3),k1_funct_1(B,3)))) ) ) )).
fof(t35_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(E)) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t35_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r2_hidden(A,k9_xtuple_0(C)) & r2_hidden(B,k9_xtuple_0(C)) ) => k9_funct_7(C,A,B) = k9_funct_7(C,B,A) ) ) )).
fof(t35_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ( 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) ) ) ) ) ) ) ) )).
fof(t35_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_circcomb(A) & v2_circcomb(A) & v3_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & v4_circcomb(B,A) & v6_circcomb(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t35_facirc_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ? [B] : ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) & k3_funct_2(k4_ordinal1,k4_ordinal1,B,k5_numbers) = 1 & k3_funct_2(k4_ordinal1,k4_ordinal1,B,1) = 2 & k3_funct_2(k4_ordinal1,k4_ordinal1,B,2) = A ) ) )).
fof(t35_fcont_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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))) ) ) ) )).
fof(t35_fdiff_10,axiom,( ! [A] : ( ( 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,k26_sin_cos,k27_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,k26_sin_cos,k27_sin_cos),k16_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),k16_sin_cos),A),B) = k3_xcmplx_0(k1_funct_1(k18_sin_cos,k2_xcmplx_0(k1_funct_1(k26_sin_cos,B),k1_funct_1(k27_sin_cos,B))),k6_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B))))) ) ) ) ) ) )).
fof(t35_fdiff_11,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k1_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k1_sin_cos9),A),B) = k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,B),k1_funct_1(k1_sin_cos9,B)),k1_square_1(k1_funct_1(k16_sin_cos,B)))),k7_xcmplx_0(1,k3_xcmplx_0(k1_funct_1(k16_sin_cos,B),k2_xcmplx_0(1,k1_square_1(B))))) ) ) ) ) ) )).
fof(t35_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ( r2_hidden(C,k3_limfunc1(A)) => r1_xxreal_0(k5_numbers,k1_fdiff_1(B,C)) ) ) ) => v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,B,k3_limfunc1(A))) ) ) ) )).
fof(t35_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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(k7_xcmplx_0(1,2)))))) & C = k47_valued_1(k1_numbers,k1_numbers,k1_numbers,D,E) & E = k1_taylor_1(2) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => ( k1_funct_1(D,F) = k1_square_1(A) & ~ r1_xxreal_0(k1_funct_1(C,F),k5_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(k7_xcmplx_0(1,2)))),B) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => k1_funct_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(k7_xcmplx_0(1,2)))),B),F) = k3_xcmplx_0(F,k6_prepower(k6_xcmplx_0(k1_square_1(A),k1_newton(F,2)),k4_xcmplx_0(k7_xcmplx_0(1,2)))) ) ) ) ) ) ) ) ) ) )).
fof(t35_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k22_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k22_sin_cos)) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => ( k1_funct_1(C,D) = k4_xcmplx_0(D) & ~ r1_xxreal_0(k1_funct_1(B,D),k5_numbers) ) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k3_taylor_1),A) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k3_taylor_1),A),D) = k7_xcmplx_0(k2_xcmplx_0(k23_sin_cos(D),k23_sin_cos(k4_xcmplx_0(D))),k6_xcmplx_0(k23_sin_cos(D),k23_sin_cos(k4_xcmplx_0(D)))) ) ) ) ) ) ) ) )).
fof(t35_fdiff_7,axiom,( ! [A] : ( ( 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,k22_sin_cos,k18_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k18_sin_cos),A),B) = k4_xcmplx_0(k3_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_funct_1(k16_sin_cos,k1_funct_1(k22_sin_cos,B)))) ) ) ) ) ) )).
fof(t35_fdiff_8,axiom,( ! [A] : ( ( 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)),k27_sin_cos))) => ( r2_hidden(k5_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)),k27_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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)),k27_sin_cos),A),B) = k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(k1_funct_1(k18_sin_cos,B),k1_funct_1(k16_sin_cos,B)),k1_square_1(B))),k7_xcmplx_0(k7_xcmplx_0(1,B),k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) ) )).
fof(t35_fdiff_9,axiom,( ! [A] : ( ( 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,k18_sin_cos,k1_fdiff_9))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_fdiff_9),A),B) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,B),k1_funct_1(k16_sin_cos,k1_funct_1(k18_sin_cos,B))),k1_square_1(k1_funct_1(k18_sin_cos,k1_funct_1(k18_sin_cos,B))))) ) ) ) ) ) )).
fof(t35_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => k2_power(k4_xcmplx_0(k1_fib_num),k3_xcmplx_0(k4_xcmplx_0(1),A)) = k2_power(k2_power(k4_xcmplx_0(k1_fib_num),k4_xcmplx_0(1)),A) ) )).
fof(t35_fib_num3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k1_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)) ) ) ) )).
fof(t35_fib_num4,axiom,( ! [A] : ( 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)) ) ) )).
fof(t35_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_finseq_1(B,A) => ! [C] : ( m1_finseq_1(C,A) => ! [D] : ( m1_finseq_1(D,A) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t35_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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),C,B)) = a_3_1_filter_0(A,B,C) ) ) ) )).
fof(t35_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t35_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ( v14_lattices(A) & B != k6_lattices(A) & ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t35_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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 ) ) ) ) )).
fof(t35_finseq_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m2_finseq_1(F,D) => ! [G] : ( ( 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(k4_ordinal1,D,D,E,F,G) = k11_finseq_1(k1_funct_1(G,A),k1_funct_1(G,B),k1_funct_1(G,C)) ) ) ) ) ) )).
fof(t35_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k10_finseq_1(A,B) != k11_finseq_1(C,D,E) )).
fof(t35_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : ( 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) ) ) ) )).
fof(t35_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t35_finseq_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(t35_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( ( 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)) & r1_xxreal_0(1,E) & r1_xxreal_0(E,k3_finseq_1(B)) & r1_xxreal_0(1,F) & r1_xxreal_0(F,k3_finseq_1(B)) ) => ( C = E | D = E | F = C | F = D | k2_finseq_7(A,k2_finseq_7(A,B,C,D),E,F) = k2_finseq_7(A,k2_finseq_7(A,B,E,F),C,D) ) ) ) ) ) ) ) ) )).
fof(t35_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( 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] : ( ( 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))) ) ) ) ) ) ) ) ) )).
fof(t35_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ( v2_fintopo2(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(B,k9_fintopo2(A,B)) ) ) ) )).
fof(t35_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t35_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k2_flang_1(A),B) => ( r1_xxreal_0(C,k5_numbers) | r1_tarski(B,k7_flang_1(A,B,C)) ) ) ) ) )).
fof(t35_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => k6_flang_1(A,k1_flang_2(A,B,D,E),k7_flang_1(A,B,C)) = k6_flang_1(A,k7_flang_1(A,B,C),k1_flang_2(A,B,D,E)) ) ) ) ) )).
fof(t35_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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))) ) ) ) )).
fof(t35_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t35_frechet,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t35_fsm_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ v2_struct_0(D) & v8_struct_0(D) & l2_fsm_1(D,B,C) ) => ( k1_nat_1(A,1) = k5_card_1(u1_struct_0(D)) => k7_fsm_1(B,C,D,k1_nat_1(A,1)) = k7_fsm_1(B,C,D,A) ) ) ) ) ) )).
fof(t35_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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))) ) ) )).
fof(t35_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( 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))) ) )).
fof(t35_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : k3_relat_1(k6_partfun1(B),k5_funcop_1(C,D,A)) = k5_funcop_1(C,D,k5_relat_1(A,B)) ) ) )).
fof(t35_funct_1,axiom,( ! [A] : ( ( 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) ) ) ) )).
fof(t35_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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 => ! [E] : ( ? [F] : ( r2_hidden(F,B) & r2_hidden(F,A) & E = k1_funct_1(D,F) ) => r2_hidden(E,k7_relset_1(B,C,D,A)) ) ) ) )).
fof(t35_funct_3,axiom,( ! [A] : ( ( 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))))) ) ) )).
fof(t35_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t35_funct_5,axiom,( k1_funct_5(k1_xboole_0) = k1_xboole_0 & k3_funct_5(k1_xboole_0) = k1_xboole_0 )).
fof(t35_funct_6,axiom,( k5_funct_6(k1_xboole_0) = k1_xboole_0 & k6_funct_6(k1_xboole_0) = k16_funcop_1(k1_xboole_0,k1_xboole_0) )).
fof(t35_funct_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(B)) => k7_partfun1(A,k2_funct_7(A,B,D,C),D) = C ) ) ) ) ) )).
fof(t35_funct_8,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t35_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ v8_ordinal1(C) & v1_int_1(C) ) => v1_funct_9(k9_valued_1(k1_numbers,k1_numbers,k26_valued_1(k1_numbers,k1_numbers,k18_sin_cos,A),B),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)) ) ) ) )).
fof(t35_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t35_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v11_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ! [F] : ( ( v15_functor0(F,B,C) & m2_functor0(F,B,C) ) => ! [G] : ( m1_functor3(G,A,B,D,E) => ( r1_functor3(A,B,D,E) => ( r1_functor3(A,C,k1_functor3(A,B,C,D,F),k1_functor3(A,B,C,E,F)) & m1_functor3(k5_functor3(A,B,C,D,E,G,F),A,C,k1_functor3(A,B,C,D,F),k1_functor3(A,B,C,E,F)) ) ) ) ) ) ) ) ) ) )).
fof(t35_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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)) ) ) ) ) )).
fof(t35_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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))) ) ) ) )).
fof(t35_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => v1_int_1(k1_fvaluat1(k2_relset_1(k6_numbers,B))) ) ) ) )).
fof(t35_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t35_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ~ 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) ) ) )).
fof(t35_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t35_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v2_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ! [F] : ( m1_genealg1(F,E) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t35_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) = k5_numbers ) ) ) ) ) ) ) )).
fof(t35_gfacirc1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ~ v1_facirc_1(k2_msafree2(k13_gfacirc1(A,B,C))) ) ) ) )).
fof(t35_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : k6_subset_1(k7_glib_000(A),k20_glib_000(A,B)) = k21_glib_000(A,k6_subset_1(k6_glib_000(A),B)) ) )).
fof(t35_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( ( 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)) ) ) ) ) ) ) )).
fof(t35_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t35_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v2_glib_003(A) ) => ! [B] : ! [C] : k5_glib_003(A) = k5_glib_003(k12_glib_003(A,B,C)) ) )).
fof(t35_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k1_matrix_0(B)) ) => r2_hidden(k5_algstr_0(k15_euclid(2),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,A),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,k1_nat_1(A,1))),k7_xcmplx_0(1,2)),k19_euclid(1,k5_numbers)),k1_tops_1(k15_euclid(2),k3_goboard5(B,k5_numbers,A))) ) ) ) )).
fof(t35_goboard7,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( 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) ) ) ) ) ) )).
fof(t35_gobrd11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_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_0(C)) ) => k3_goboard5(C,A,B) = k2_pre_topc(k15_euclid(2),k1_tops_1(k15_euclid(2),k3_goboard5(C,A,B))) ) ) ) ) )).
fof(t35_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( ( ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) & r1_goboard1(u1_struct_0(k15_euclid(2)),C,D) & r1_xxreal_0(k1_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) ) ) ) ) ) ) )).
fof(t35_gobrd14,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t35_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_valuat_1(E,A,D) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t35_gr_cy_3,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ~ ( k5_int_1(k3_xcmplx_0(A,A),B) = 1 & ~ r2_int_1(A,1,B) & ~ r2_int_1(A,k4_xcmplx_0(1),B) ) ) ) )).
fof(t35_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_graph_1(C,A) => ( ( r2_graph_2(A,C) & r1_graph_2(A,B,C) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( r2_hidden(D,k4_finseq_1(C)) & k1_funct_1(B,D) = k1_funct_1(B,k1_nat_1(D,1)) ) ) ) ) ) ) )).
fof(t35_graph_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t35_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_tarski(k4_graph_5(A,B,C),k3_graph_5(A,B,C)) ) ) ) )).
fof(t35_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) => k4_finseq_1(k6_graphsp(k18_graphsp(A),B)) = k4_finseq_1(B) ) ) )).
fof(t35_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(k25_grcat_1(A))) => ! [C] : ( m1_subset_1(C,u4_struct_0(k25_grcat_1(A))) => ! [D] : ( m3_grcat_1(D,k18_grcat_1(k17_grcat_1(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t35_groeb_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( ~ v1_xboole_0(D) & v1_ideal_1(D,k12_polynom1(A,C)) & v2_ideal_1(D,k12_polynom1(A,C)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ? [E] : ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) & r2_groeb_1(A,B,C,E,D) ) ) ) ) ) )).
fof(t35_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ! [G] : ( m2_ideal_1(G,k12_polynom1(A,C),F) => ! [H] : ( m2_ideal_1(H,k12_polynom1(A,C),F) => ! [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] : ( m1_subset_1(J,k4_ordinal1) => ( ( r3_groeb_2(A,B,C,D,F,G,I) & H = k2_rfinseq(u1_struct_0(k12_polynom1(A,C)),J,G) & E = k4_rlvect_1(k12_polynom1(A,C),k17_finseq_1(u1_struct_0(k12_polynom1(A,C)),J,G)) & r1_xxreal_0(J,k3_finseq_1(G)) ) => r3_groeb_2(A,B,C,k7_polynom1(A,C,D,E),F,H,I) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t35_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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(k3_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(k3_polynom1(k15_pre_poly(A),C,D))),k8_polynom1(A,C)) ) ) ) ) ) )).
fof(t35_group_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k5_group_1(B,k4_xcmplx_0(A),C) = k2_group_1(B,k5_group_1(B,A,C)) ) ) ) )).
fof(t35_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_group_2(C,A) => k2_group_11(A,B,C) = k2_group_11(A,k2_group_11(A,B,C),C) ) ) ) )).
fof(t35_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t35_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t35_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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))))) ) ) )).
fof(t35_group_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t35_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( ( 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)) ) ) ) ) ) ) )).
fof(t35_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t35_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t35_groupp_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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) = k5_numbers ) => v3_groupp_1(B,A) ) ) ) )).
fof(t35_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( ( ~ 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(k5_numbers,k1_hausdorf(A,B,C)) ) ) ) ) )).
fof(t35_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( ( v5_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => ! [E] : ( ( v7_ordinal1(E) & ~ v1_abian(E) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t35_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( ( 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)) ) ) ) ) ) ) )).
fof(t35_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A)))) => ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(k4_ordinal1,k6_domain_1(k4_ordinal1,A)))) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ( ( D = k1_heyting2(k4_ordinal1,k6_domain_1(k4_ordinal1,A),C) & C = B ) => ! [E] : ( r2_hidden(E,B) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( ~ r1_xxreal_0(F,k1_nat_1(k1_xxreal_2(D),1)) & r2_hidden(k1_domain_1(k4_ordinal1,k4_ordinal1,F,A),E) ) ) ) ) ) ) ) ) )).
fof(t35_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ r1_xxreal_0(B,k5_numbers) => ( k9_nat_1(k1_numbers,k1_taylor_2(k16_sin_cos,k2_rcomp_1(k4_xcmplx_0(B),B),A),C) = k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,k7_xcmplx_0(k3_xcmplx_0(C,k28_sin_cos),2)),k1_newton(A,C)),k2_newton(C)) & k9_nat_1(k1_numbers,k1_taylor_2(k18_sin_cos,k2_rcomp_1(k4_xcmplx_0(B),B),A),C) = k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,k7_xcmplx_0(k3_xcmplx_0(C,k28_sin_cos),2)),k1_newton(A,C)),k2_newton(C)) ) ) ) ) ) )).
fof(t35_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => r2_hidden(k3_hilbert1(k3_hilbert1(C,A),k3_hilbert1(k3_hilbert1(C,B),k3_hilbert1(C,k4_hilbert1(A,B)))),k6_hilbert1) ) ) ) )).
fof(t35_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( 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)) ) ) )).
fof(t35_hilbert3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( m1_hilbert3(D,C) => ! [E] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t35_hurwitz,axiom,( ! [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) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_polynom5(A,B,C) => r1_hurwitz(A,B,k3_hurwitz(A,C,1)) ) ) ) ) )).
fof(t35_idea_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( v1_int_2(k1_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 ) ) ) ) ) )).
fof(t35_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_ideal_1(C,A,B) => ? [D] : ( 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) ) ) ) ) )).
fof(t35_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t35_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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] : ( m4_index_1(C,u1_struct_0(A),u4_struct_0(A),u1_graph_1(A),u2_graph_1(A),B) => ! [D] : ( ( ~ 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] : ( m2_cat_1(E,C,D) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t35_instalg1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v11_struct_0(B) & m1_instalg1(B,A) ) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( l3_msualg_1(D,A) => ( r1_pzfmisc1(u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D)) => ! [E] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t35_int_1,axiom,( ! [A] : ( 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)) ) ) ) )).
fof(t35_int_4,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r2_hidden(B,k1_relset_1(k4_ordinal1,A)) & r2_hidden(C,k1_relset_1(k4_ordinal1,A)) & r1_xxreal_0(1,k3_finseq_1(A)) ) => ( B = C | r1_nat_d(k1_recdef_1(A,C),k3_wsierp_1(k4_wsierp_1(k4_ordinal1,B,A))) ) ) ) ) ) )).
fof(t35_int_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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(k3_xcmplx_0(k1_pepin(A),B),C) = k2_int_5(B,C) ) ) ) ) ) )).
fof(t35_int_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t35_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(A,B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( D != k5_numbers & k1_funct_1(C,D) = k4_xcmplx_0(k7_xcmplx_0(1,k1_square_1(D))) ) ) ) & k9_xtuple_0(C) = B & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,A)) ) => ( r2_hidden(k5_numbers,B) | k2_integra5(A,C) = k6_xcmplx_0(k1_funct_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B)),k2_seq_4(A)),k1_funct_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B)),k3_seq_4(A))) ) ) ) ) ) )).
fof(t35_integr12,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => ( k1_funct_1(B,D) = k7_xcmplx_0(1,k3_xcmplx_0(D,k2_xcmplx_0(1,k1_square_1(k1_funct_1(k3_taylor_1,D))))) & ~ r1_xxreal_0(k1_funct_1(k3_taylor_1,D),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_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) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k1_sin_cos9),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k1_sin_cos9),k3_seq_4(A))) ) ) ) ) )).
fof(t35_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k7_xcmplx_0(1,k3_xcmplx_0(k1_square_1(D),k1_square_1(k1_funct_1(k18_sin_cos,k7_xcmplx_0(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)),k26_sin_cos))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_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)),k26_sin_cos)),k2_seq_4(A)),k1_funct_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)),k26_sin_cos)),k3_seq_4(A))) ) ) ) ) )).
fof(t35_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k2_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(1,k1_funct_1(k16_sin_cos,D)),k1_square_1(D)),k7_xcmplx_0(k7_xcmplx_0(k1_funct_1(k18_sin_cos,D),D),k1_square_1(k1_funct_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) = k6_xcmplx_0(k1_funct_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)),k2_seq_4(A)),k1_funct_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)),k3_seq_4(A))) ) ) ) ) )).
fof(t35_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t35_integra1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v2_measure5(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ! [E] : ( 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(k3_seq_4(D),k1_funct_1(E,A)) & k1_funct_1(E,B) = k2_seq_4(D) ) => m1_integra1(k3_finseq_6(k1_numbers,E,A,B),D) ) ) ) ) ) ) )).
fof(t35_integra2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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_comseq_2(k2_partfun1(A,k1_numbers,B,A)) => v3_xxreal_2(k1_rvsum_1(k8_integra1(A,B))) ) ) ) )).
fof(t35_integra8,axiom,( ! [A] : ( v1_xreal_0(A) => r1_tarski(k10_xtuple_0(k7_funcop_1(k1_numbers,A)),k1_numbers) ) )).
fof(t35_integra9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k3_xcmplx_0(k28_sin_cos,2)) => r1_integra9(A,k16_sin_cos,k18_sin_cos) ) ) )).
fof(t35_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_interva1(C,A) ) => r1_interva1(A,k3_interva1(A,B,k4_interva1(A,B,C)),B) ) ) ) )).
fof(t35_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( 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) ) ) ) )).
fof(t35_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ r1_xxreal_0(k3_xcmplx_0(k7_newton(A),k4_series_1(k1_valued_0(k1_numbers,k5_irrat_1,k1_nat_1(A,1)))),k5_numbers) ) )).
fof(t35_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( 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,k4_nattra_1(B,B,k10_cat_1(B))),E) ) ) ) ) ) ) )).
fof(t35_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,A,C) => ! [G] : ( m2_cat_1(G,A,C) => ( ( r1_nattra_1(A,B,D,E) & r1_nattra_1(A,C,F,G) ) => ! [H] : ( m1_nattra_1(H,A,B,D,E) => ! [I] : ( m1_nattra_1(I,A,C,F,G) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => k2_nattra_1(A,k6_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) = k8_cat_2(B,C,k2_nattra_1(A,B,D,E,H,J),k2_nattra_1(A,C,F,G,I,J)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t35_isomichi,axiom,( ! [A] : ! [B] : ~ ( r3_xboole_0(A,B) & ~ r1_tarski(A,B) & ~ r2_xboole_0(B,A) ) )).
fof(t35_jgraph_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t35_jgraph_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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)) ) ) ) ) ) ) ) )).
fof(t35_jgraph_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( 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] : ( 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) = k3_xcmplx_0(k18_euclid(C),k3_square_1(k2_xcmplx_0(1,k1_square_1(k7_xcmplx_0(k17_euclid(C),k18_euclid(C)))))) ) ) & ! [C] : ( 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) = k5_numbers ) ) ) => v5_pre_topc(B,k1_pre_topc(k15_euclid(2),A),k3_topmetr) ) ) ) )).
fof(t35_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ! [C] : ( ( r2_hidden(B,C) & C = a_0_1_jgraph_4 ) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) | r1_xxreal_0(1,A) | r2_hidden(k1_funct_1(k3_jgraph_4(A),B),C) ) ) ) )).
fof(t35_jgraph_6,axiom,( a_0_13_jgraph_6 = a_0_14_jgraph_6 )).
fof(t35_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t35_jordan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_borsuk_2(E,A,C,D) => ! [F] : ( 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))) ) ) ) ) ) ) ) )).
fof(t35_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [F] : ( 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_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))))) ) ) ) ) ) ) ) ) )).
fof(t35_jordan12,axiom,( ! [A] : ( ( v1_topreal1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( ( v1_topreal1(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ! [C] : ( ( v1_topreal1(C) & m2_finseq_1(C,u1_struct_0(k15_euclid(2))) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(2))) => ! [H] : ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t35_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_jordan1h(A,B) & r1_xxreal_0(B,C) ) => r1_tarski(k3_goboard9(k1_jordan13(A,B)),k3_goboard9(k1_jordan13(A,C))) ) ) ) ) )).
fof(t35_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( ~ r1_xxreal_0(C,1) & r1_xxreal_0(C,D) & ~ r1_xxreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,1))),D) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),D,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1)))),k8_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1)))),k9_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1)))),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),D,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))))),k8_jordan6(B)) ) ) ) ) ) )).
fof(t35_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_xxreal_0(B,C) => ( r1_xxreal_0(A,1) | r1_xxreal_0(k1_matrix_0(k1_jordan8(D,B)),k1_nat_1(A,1)) | ( ~ r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(k11_newton(2,k7_nat_d(C,B)),k6_xcmplx_0(A,1)),2),1) & r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(k11_newton(2,k7_nat_d(C,B)),k6_xcmplx_0(A,1)),2),k1_matrix_0(k1_jordan8(D,C))) ) ) ) ) ) ) ) )).
fof(t35_jordan1b,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,k1_matrix_0(k1_jordan8(A,C))) => r1_tarski(k3_goboard5(k1_jordan8(A,C),k5_numbers,B),k2_jordan2c(2,A)) ) ) ) ) )).
fof(t35_jordan1g,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(k1_jordan8(A,B))) ) => ( r1_xxreal_0(B,k5_numbers) | k17_euclid(k3_matrix_0(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) ) ) ) ) ) )).
fof(t35_jordan1h,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(1,B) => m1_subset_1(k1_int_1(k2_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(B,2),k11_newton(2,k7_nat_d(C,A))),2)),k4_ordinal1) ) ) ) ) )).
fof(t35_jordan1j,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t35_jordan1k,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(2))) => ( ( D = k19_euclid(k5_numbers,k5_numbers) & C = A ) => ( r1_xxreal_0(B,k5_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)),k8_metric_1(k14_euclid(2),D,1)) = k8_metric_1(k14_euclid(2),C,B) ) ) ) ) ) ) )).
fof(t35_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => r1_tarski(k3_jordan19(A),A) ) )).
fof(t35_jordan23,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)),k13_matrix_0(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) ) ) ) ) ) )).
fof(t35_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( 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] : ( v1_xreal_0(F) => ( D != k1_rlvect_1(k15_euclid(A),E,F) & E != k1_rlvect_1(k15_euclid(A),D,F) ) ) & ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(A))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(A))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k15_euclid(A))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k15_euclid(A))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t35_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) ) )).
fof(t35_jordan4,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( 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)) ) ) ) ) )).
fof(t35_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( 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_0(k2_goboard2(A))) & ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ~ ( k17_euclid(D) = k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),B,C)) & r2_hidden(D,k3_topreal1(2,A)) ) ) ) ) ) ) )).
fof(t35_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( A = k2_rcomp_1(B,C) => v3_pre_topc(A,k3_topmetr) ) ) ) ) )).
fof(t35_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_jordan_a(B,A) => ? [C] : ( ~ 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) ) ) ) )).
fof(t35_kurato_1,axiom,( 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)) )).
fof(t35_kurato_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))))) ) => ( ! [D] : ( v7_ordinal1(D) => k2_kurato_2(k15_euclid(2),C,D) = k4_subset_1(u1_struct_0(k15_euclid(2)),k2_kurato_2(k15_euclid(2),A,D),k2_kurato_2(k15_euclid(2),B,D)) ) => r1_tarski(k4_subset_1(u1_struct_0(k15_euclid(2)),k3_kurato_2(k15_euclid(2),A),k3_kurato_2(k15_euclid(2),B)),k3_kurato_2(k15_euclid(2),C)) ) ) ) ) )).
fof(t35_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( k12_matrix_3(A,B,C) != k4_struct_0(B) => k1_matrix_6(A,B,C) = k1_matrix_7(A,B,k4_matrix_0(u1_struct_0(B),k7_laplace(A,B,C)),k11_algstr_0(B,k12_matrix_3(A,B,C))) ) ) ) ) )).
fof(t35_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k5_finsub_1(C)) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t35_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : r3_lattices(A,k3_lattices(A,B,k16_lattice3(A,C)),k16_lattice3(A,a_3_4_lattice3(A,B,C))) ) ) )).
fof(t35_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m2_lattice4(B,A) => ( v20_lattices(B,A) & v21_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).
fof(t35_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( v3_ordinal1(C) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t35_lattice8,axiom,( ! [A] : ( ( 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) ) )).
fof(t35_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => v3_lexbfs(k16_lexbfs(A)) ) )).
fof(t35_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(A) & k1_seq_2(A) = k5_numbers ) => ( ! [B] : ( v7_ordinal1(B) => ? [C] : ( v7_ordinal1(C) & r1_xxreal_0(B,C) & r1_xxreal_0(k1_funct_1(A,C),k5_numbers) ) ) | v1_limfunc1(k37_valued_1(k4_ordinal1,k1_numbers,A)) ) ) ) )).
fof(t35_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r5_limfunc2(C,A) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(D,E) & ~ r1_xxreal_0(E,A) & r2_hidden(E,k1_relset_1(k1_numbers,B)) ) ) ) ) ) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(A,k2_xcmplx_0(A,D))),k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,C),k2_rcomp_1(A,k2_xcmplx_0(A,D)))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(A,k2_xcmplx_0(A,D)))) => r1_xxreal_0(k1_funct_1(C,E),k1_funct_1(B,E)) ) ) ) ) | r5_limfunc2(B,A) ) ) ) ) ) )).
fof(t35_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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(k5_numbers)) = k1_xboole_0 ) => ( k1_limfunc3(B,A) = k5_numbers | ( r1_limfunc3(k6_rfunct_1(k1_numbers,k1_numbers,B),A) & k1_limfunc3(k6_rfunct_1(k1_numbers,k1_numbers,B),A) = k5_xcmplx_0(k1_limfunc3(B,A)) ) ) ) ) ) )).
fof(t35_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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) ) ) ) ) )).
fof(t35_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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))) ) ) ) ) )).
fof(t35_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k16_lopban_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k16_lopban_1(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k16_lopban_1(A,B))) => ( E = k1_algstr_0(k16_lopban_1(A,B),C,D) <=> ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t35_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v1_xreal_0(C) => ~ ( r1_xxreal_0(C,1) & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(1,D) => k9_nat_1(k1_numbers,k5_normsp_0(A,B),D) = k7_xcmplx_0(1,k2_power(D,C)) ) ) & v2_lopban_3(B,A) ) ) ) ) )).
fof(t35_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t35_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => r1_filter_1(A,k12_lopclset(A)) ) )).
fof(t35_lpspacc1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,C,k6_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,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => ( ( r2_hidden(E,k13_lpspacc1(B,C,D)) & r2_hidden(F,k13_lpspacc1(B,C,D)) & k17_lpspacc1(B,C,D,E) = k17_lpspacc1(B,C,D,F) ) => k17_lpspacc1(B,C,D,k25_valued_1(B,k2_numbers,E,A)) = k17_lpspacc1(B,C,D,k25_valued_1(B,k2_numbers,F,A)) ) ) ) ) ) ) ) )).
fof(t35_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(k12_lpspace1(A,B,C))) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t35_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v2_xxreal_0(E) & v1_xreal_0(E) ) => ~ ( r2_hidden(D,k1_lpspace2(A,B,C,E)) & ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ~ ( k1_funct_1(C,k3_subset_1(A,F)) = k5_numbers & k1_relset_1(A,D) = F & r1_mesfunc6(A,B,D,F) ) ) ) ) ) ) ) ) )).
fof(t35_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(t35_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(k1_ltlaxio1(k4_ltlaxio1(A,B)),k5_ltlaxio1(k1_ltlaxio1(A),k1_ltlaxio1(B)))) ) ) )).
fof(t35_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t35_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k6_rusub_4(A,D,k9_subset_1(u1_struct_0(A),B,C)),k9_subset_1(u1_struct_0(A),k6_rusub_4(A,D,B),k6_rusub_4(A,D,C))) ) ) ) ) )).
fof(t35_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( v3_matrix10(B) => v4_matrix10(k2_matrix10(A,B)) ) ) ) )).
fof(t35_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(C),B,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(C))) ) => ( 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_0(E),C,k7_matrix_0(u1_struct_0(C),E,A),D))) = k8_group_1(C,D,k12_matrix_3(B,C,E)) ) ) ) ) ) ) )).
fof(t35_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m2_finseq_2(C,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [D] : ( m2_finseq_2(D,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [F] : ( ( v1_matrix_0(F) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(B))) ) => ! [G] : ( m1_matrix_2(G,k3_matrix_2(A)) => ( D = k1_partfun1(k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k4_ordinal1,k4_ordinal1,G,E) => ( k12_matrix_3(A,B,k1_matrix13(u1_struct_0(B),F,A,A,D,C)) = k5_matrix_2(B,A,k12_matrix_3(A,B,k1_matrix13(u1_struct_0(B),F,A,A,E,C)),G) & k12_matrix_3(A,B,k1_matrix13(u1_struct_0(B),F,A,A,C,D)) = k5_matrix_2(B,A,k12_matrix_3(A,B,k1_matrix13(u1_struct_0(B),F,A,A,C,E)),G) ) ) ) ) ) ) ) ) ) )).
fof(t35_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [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] : ( 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) ) ) ) ) ) ) )).
fof(t35_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ! [E] : ( ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(A))) ) => ( r2_hidden(E,k4_matrix15(A,C,D)) => ( r2_hidden(k6_matrix_3(A,E,B),k4_matrix15(A,C,k6_matrix_3(A,D,B))) & r2_hidden(E,k4_matrix15(A,k6_matrix_3(A,C,B),k6_matrix_3(A,D,B))) ) ) ) ) ) ) ) )).
fof(t35_matrix16,axiom,( ! [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] : ( 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)) ) ) ) )).
fof(t35_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,k3_finseq_2(A)) => k9_matrix_0(B) = k3_tarski(a_2_0_matrix_0(A,B)) ) ) )).
fof(t35_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ( k2_matrix_3(A,B) = k2_matrix_3(A,C) => B = C ) ) ) ) ) )).
fof(t35_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ~ r1_xxreal_0(A,k5_numbers) => ( r1_matrix_6(A,B,C,D) <=> k4_matrix_3(B,k3_matrix_3(B,C,D),k3_matrix_3(B,C,D)) = k3_matrix_3(B,k3_matrix_3(B,k3_matrix_3(B,k4_matrix_3(B,C,C),k4_matrix_3(B,C,D)),k4_matrix_3(B,C,D)),k4_matrix_3(B,D,D)) ) ) ) ) ) ) )).
fof(t35_matrix_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_matrix_2(C,k3_matrix_2(A)) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r1_xxreal_0(1,A) => k3_funct_2(k3_matrix_2(A),u1_struct_0(B),k11_matrix_3(A,B,k4_matrix_0(u1_struct_0(B),D)),k3_matrix_7(A,C)) = k3_funct_2(k3_matrix_2(A),u1_struct_0(B),k11_matrix_3(A,B,D),C) ) ) ) ) ) )).
fof(t35_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( r1_matrix_8(A,B,C,D) & v1_matrix_8(D,A,B) ) => v1_matrix_8(C,A,B) ) ) ) ) ) )).
fof(t35_matrix_9,axiom,( ! [A] : ( ( 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(k4_ordinal1,2,3,1) & v4_matrix_2(A,3) ) ) )).
fof(t35_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ! [D] : ( 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,k5_binop_2,A,B) = k1_finseqop(k1_numbers,k1_numbers,k1_numbers,k11_binop_2,C,D) ) ) ) ) ) )).
fof(t35_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_matrixj1(C,A) & m2_finseq_1(C,k3_finseq_2(k3_finseq_2(A))) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t35_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => k5_matrixr1(A,k4_matrixr1(B)) = k3_matrixr1(A,B) ) ) )).
fof(t35_matrixr2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,A) => ! [I] : ( m1_subset_1(I,A) => ! [J] : ( m1_subset_1(J,A) => ( v1_matrix_0(k3_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),k3_finseq_4(A,B,C,D),k3_finseq_4(A,E,F,G),k3_finseq_4(A,H,I,J))) & v2_matrix_0(k3_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),k3_finseq_4(A,B,C,D),k3_finseq_4(A,E,F,G),k3_finseq_4(A,H,I,J)),A,3,3) & m2_finseq_1(k3_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),k3_finseq_4(A,B,C,D),k3_finseq_4(A,E,F,G),k3_finseq_4(A,H,I,J)),k3_finseq_2(A)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t35_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_matrlin(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => D = k4_rlvect_1(B,k5_matrlin(A,B,k9_matrlin(A,B,C,D),C)) ) ) ) ) )).
fof(t35_matrlin2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( r2_hidden(A,k4_finseq_1(C)) & k1_matrix_0(C) = k3_finseq_1(D) ) => k4_matrix_3(B,k2_matrix15(u1_struct_0(B),k7_matrix_0(u1_struct_0(B),C,A)),D) = k2_matrix15(u1_struct_0(B),k7_matrix_0(u1_struct_0(B),k4_matrix_3(B,C,D),A)) ) ) ) ) ) )).
fof(t35_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k6_matroid0(A,k6_matroid0(A,B)) = k6_matroid0(A,B) ) ) )).
fof(t35_matrprob,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k2_vectsp_1)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t35_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_card_1(D,A) & v1_finseq_1(D) & v3_valued_0(D) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(k2_vectsp_1),C,B) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( 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(k4_ordinal1,C,k5_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(k4_ordinal1,C,k5_numbers),D)) = k1_funct_1(k3_matrtop1(A,B,E),D) ) ) ) ) ) ) ) )).
fof(t35_mcart_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t35_measure1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v4_card_3(D) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ( ! [E] : ( r2_hidden(E,D) => r2_hidden(E,B) ) => ( r2_hidden(k5_setfam_1(A,D),B) & r2_hidden(k6_setfam_1(A,D),B) ) ) ) ) ) )).
fof(t35_measure6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(B))) => ! [E] : ( ( 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),k2_measure6(A,B,E),D))) => r2_hidden(k1_funct_1(E,C),k6_setfam_1(B,D)) ) ) ) )).
fof(t35_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => k7_member_1(k5_xboole_0(A,B)) = k5_xboole_0(k7_member_1(A),k7_member_1(B)) ) ) )).
fof(t35_membered,axiom,( ! [A] : ! [B] : ( ( r2_hidden(B,A) & v5_membered(B) ) => v5_membered(k1_setfam_1(A)) ) )).
fof(t35_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_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)) ) ) ) ) )).
fof(t35_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t35_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( r2_mesfun6c(A,B,C,D) => ( ? [E] : ( 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)) ) ) ) ) ) ) )).
fof(t35_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ( ( v1_mesfunc8(D,A,k2_numbers) & r1_tarski(C,k1_relset_1(A,k4_mesfunc5(A,k2_numbers,D,k5_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)) ) ) ) ) ) )).
fof(t35_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(A),B) => ! [D] : ( ( v1_prob_2(D) & m2_finseq_1(D,B) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ( ( k1_relset_1(k4_ordinal1,D) = k1_relset_1(k4_ordinal1,E) & ! [F] : ( v7_ordinal1(F) => ( r2_hidden(F,k1_relset_1(k4_ordinal1,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) ) ) ) ) ) ) ) )).
fof(t35_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( r2_hidden(C,k1_relset_1(A,B)) => ( r1_xxreal_0(k12_supinf_2(k19_rfunct_3(A,B),C),k5_numbers) | k12_supinf_2(k18_rfunct_3(A,B),C) = k5_numbers ) ) ) ) )).
fof(t35_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [D] : ( v7_ordinal1(D) => ( ! [E] : ( v7_ordinal1(E) => r1_mesfunc2(A,B,k4_mesfunc5(A,k6_numbers,C,E)) ) => ( v2_mesfunc9(C,A) & r1_mesfunc2(A,B,k4_mesfunc5(A,k6_numbers,k4_mesfunc9(A,C),D)) ) ) ) ) ) ) )).
fof(t35_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k2_metric_2(A)) => ! [C] : ( m1_subset_1(C,k2_metric_2(A)) => k2_binop_1(k2_metric_2(A),k2_metric_2(A),k1_numbers,k10_metric_2(A),B,C) = k2_binop_1(k2_metric_2(A),k2_metric_2(A),k1_numbers,k10_metric_2(A),C,B) ) ) ) )).
fof(t35_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_midsp_1(C,A) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & C = k8_midsp_1(A,B,D) ) ) ) ) )).
fof(t35_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [D] : ( 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)) ) ) ) )).
fof(t35_mod_4,axiom,( ! [A] : ( ( ~ 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] : ( ( 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)) ) ) ) )).
fof(t35_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k6_modal_1) => ! [B] : ( 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))) ) ) ) )).
fof(t35_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k48_modelc_1(A,B,C))) => ( ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t35_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ( ( r2_modelc_2(A,B) & r2_modelc_2(B,C) ) => r2_modelc_2(A,C) ) ) ) ) )).
fof(t35_modelc_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ( ( 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)) ) ) ) ) ) )).
fof(t35_moebius1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ( r1_int_2(A,B) => k2_moebius1(k2_nat_1(A,B)) = k3_xcmplx_0(k2_moebius1(A),k2_moebius1(B)) ) ) ) )).
fof(t35_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m2_monoid_0(B,A) ) => ( v16_monoid_0(A) => v16_monoid_0(B) ) ) ) )).
fof(t35_monoid_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_finseq_1(D,C) => ( A != B => k1_relset_1(k4_ordinal1,k6_relat_1(k1_tarski(A),k7_finseq_1(D,k9_finseq_1(B)))) = k1_relset_1(k4_ordinal1,k6_relset_1(k4_ordinal1,C,k1_tarski(A),D)) ) ) ) )).
fof(t35_msafree3,axiom,( ! [A] : ! [B] : ( ( ~ v11_struct_0(B) & v1_instalg1(B) & l1_msualg_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k3_card_3(u3_msualg_1(B,k1_msafree3(B,C)))) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t35_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_msafree4(E,u1_struct_0(A),k4_equation(A),k1_msafree4(u1_struct_0(A),k4_equation(A),D)) => ( r1_equation(A,B,D,E) => r1_equation(A,C,D,E) ) ) ) ) ) ) )).
fof(t35_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( m2_pboole(D,u1_struct_0(A),C,u3_msualg_1(A,B)) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( 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] : ( ( 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] : ( ( 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),k15_trees_3(H)),H) & ! [I] : ( v7_ordinal1(I) => ! [J] : ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t35_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) => ! [D] : ( m3_pboole(D,A,k1_mboolean(A,B)) => m3_pboole(k3_pboole(A,C,D),A,k1_mboolean(A,B)) ) ) ) )).
fof(t35_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t35_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t35_msualg_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,k13_msualg_4(A,B,C)),F)) => ! [H] : ( 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) ) ) ) ) ) ) )).
fof(t35_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => k2_mycielsk(k5_mycielsk(A)) = A ) )).
fof(t35_nat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => r2_funct_2(k4_ordinal1,A,k8_nat_1(A,B,k5_numbers),B) ) ) )).
fof(t35_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(A,B) & B != k5_numbers & k1_funct_1(k12_nat_3(B),A) != k5_numbers ) ) ) )).
fof(t35_nat_4,axiom,( v1_int_2(163) )).
fof(t35_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => v1_nat_5(k2_nat_5(A)) ) )).
fof(t35_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k7_nat_d(A,B),A) ) ) )).
fof(t35_nattra_1,axiom,( ! [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) & v4_nattra_1(A) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,B,A) => ! [D] : ( m1_nattra_1(D,B,A,C,C) => r2_funct_2(u1_struct_0(B),u4_struct_0(A),D,k4_nattra_1(B,A,C)) ) ) ) ) )).
fof(t35_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t35_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t35_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r1_ndiff_1(A,B,C,E) & r1_ndiff_1(A,B,D,E) ) => ( r1_ndiff_1(A,B,k6_vfunct_1(u1_struct_0(A),B,C,D),E) & k3_ndiff_1(A,B,k6_vfunct_1(u1_struct_0(A),B,C,D),E) = k3_rlvect_1(k16_lopban_1(A,B),k3_ndiff_1(A,B,C,E),k3_ndiff_1(A,B,D,E)) ) ) ) ) ) ) ) )).
fof(t35_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(1))) => ! [D] : ( m1_subset_1(D,k1_numbers) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t35_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_prvect_2(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t35_neckla_3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t35_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ( A != k5_numbers => r1_nat_d(A,k7_newton(A)) ) ) )).
fof(t35_nfcont_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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,k4_normsp_0(u1_struct_0(B),C,D),A),k4_normsp_0(u1_struct_0(B),C,k2_partfun1(u1_struct_0(B),u1_struct_0(C),D,A))) ) ) ) )).
fof(t35_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ( ( 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] : ( v1_xreal_0(D) & ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( 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))),k3_xcmplx_0(D,k9_complex1(k6_xcmplx_0(E,F)))) ) ) ) ) ) ) ) )).
fof(t35_normform,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [C] : ( m2_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [D] : ( m1_subset_1(D,k5_finsub_1(k7_normform(A))) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t35_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k3_normsp_2(A))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t35_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t35_openlatt,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t35_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_oppcat_1(C,k2_oppcat_1(B),A) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_oppcat_1(B))) => k3_funct_2(u1_struct_0(B),u1_struct_0(A),k7_cat_1(B,A,k9_oppcat_1(B,A,C)),k4_oppcat_1(B,D)) = k3_funct_2(u1_struct_0(k2_oppcat_1(B)),u1_struct_0(A),k7_cat_1(k2_oppcat_1(B),A,C),D) ) ) ) ) )).
fof(t35_ordeq_01,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v1_partfun1(A,k1_numbers) => ( v2_fdiff_1(A) <=> ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ~ ( D != k5_numbers & ~ r1_xxreal_0(C,k9_complex1(D)) & r1_xxreal_0(B,k3_xcmplx_0(k5_xcmplx_0(k9_complex1(D)),k9_complex1(k7_partfun1(k1_numbers,A,D)))) ) ) ) ) ) ) ) ) ) )).
fof(t35_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( ( r2_orders_1(A,C) & r1_tarski(B,C) ) => r2_orders_1(A,B) ) ) )).
fof(t35_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r1_tarski(B,C) & r2_wellord1(u1_orders_2(A),C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) )).
fof(t35_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => k11_ordinal2(k5_ordinal1,A) = k5_ordinal1 ) )).
fof(t35_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r1_ordinal1(k11_ordinal2(B,A),k11_ordinal2(C,A)) => ( A = k1_xboole_0 | r1_ordinal1(B,C) ) ) ) ) ) )).
fof(t35_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t35_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( ( r2_hidden(A,B) & r2_hidden(B,k2_ordinal5(A)) ) => k2_ordinal5(B) = k2_ordinal5(A) ) ) ) )).
fof(t35_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t35_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t35_osalg_1,axiom,( ! [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) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t35_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v3_msualg_1(C,A) & v12_osalg_1(C,A) & m1_msualg_2(C,A,B) ) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t35_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t35_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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 ) ) ) ) ) ) ) )).
fof(t35_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => r1_relset_1(A,C,k1_partfun1(A,B,B,C,k3_partfun1(D,A,B),k3_partfun1(E,B,C)),k3_partfun1(k3_relat_1(D,E),A,C)) ) ) )).
fof(t35_partfun2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ( v3_funct_1(k2_partfun1(B,C,D,A)) <=> ? [E] : ( m1_subset_1(E,C) & ! [F] : ( m1_subset_1(F,B) => ( r2_hidden(F,k9_subset_1(B,A,k1_relset_1(B,D))) => k7_partfun1(C,D,F) = E ) ) ) ) ) ) ) )).
fof(t35_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => r1_setfam_1(k10_eqrel_1(A),k6_partit1(A)) ) )).
fof(t35_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t35_pcomps_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) ) )).
fof(t35_pcs_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_pcs_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k21_pcs_0(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k21_pcs_0(A))) => ( ( B = D & C = E ) => ( r1_pcs_0(k21_pcs_0(A),D,E) | r1_pcs_0(A,B,C) ) ) ) ) ) ) ) )).
fof(t35_pdiff_3,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(2)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t35_pdiff_4,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t35_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( 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) = k10_pdiff_1(3,2,k1_pdiff_3(3,3,B),A) ) ) ) )).
fof(t35_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [D] : ( ( 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] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t35_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t35_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( k4_nat_d(A,C) = 1 => ( r1_xxreal_0(C,1) | k4_nat_d(k1_newton(A,B),C) = 1 ) ) ) ) ) )).
fof(t35_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m3_pnproc_1(C,A,B) => ! [D] : ( 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)) ) ) ) )).
fof(t35_polyeq_3,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => m1_comptrig(k2_xcmplx_0(k3_xcmplx_0(k1_power(B,k9_complex1(A)),k19_sin_cos(k7_xcmplx_0(k2_xcmplx_0(k1_comptrig(A),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)),B))),k3_xcmplx_0(k3_xcmplx_0(k1_power(B,k9_complex1(A)),k17_sin_cos(k7_xcmplx_0(k2_xcmplx_0(k1_comptrig(A),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)),B))),k7_complex1)),A,B) ) ) ) )).
fof(t35_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => k11_polyform(A,B) = k1_vectsp_9(k2_bspace,k17_polyform(A,B)) ) ) )).
fof(t35_polynom3,axiom,( ! [A] : ( ( ~ 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) ) => k5_struct_0(k14_polynom3(A)) = k10_polynom3(A) ) )).
fof(t35_polynom8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(B,k5_numbers) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(A),B,C) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => k4_matrix_3(A,k3_matrix_1(A,B),D) = D ) ) ) ) ) )).
fof(t35_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(D,A,C) & v1_polynom1(D,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) ) ) ) ) )).
fof(t35_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,1) & ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(k2_power(A,B),1) ) ) ) )).
fof(t35_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v4_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v4_valued_0(C) ) => ! [D] : ( ( 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))) ) ) ) )).
fof(t35_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ( m1_pre_topc(A,B) <=> m1_pre_topc(A,g1_pre_topc(u1_struct_0(B),u1_pre_topc(B))) ) ) ) )).
fof(t35_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => k3_prepower(A,1) = A ) )).
fof(t35_prob_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m2_prob_1(D,A,B) => r1_xxreal_0(k3_funct_2(B,k1_numbers,D,C),1) ) ) ) ) )).
fof(t35_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m1_prob_1(E,A,B) => ( ~ r1_xxreal_0(k3_funct_2(B,k1_numbers,C,E),k5_numbers) => r1_xxreal_0(k7_xcmplx_0(k6_xcmplx_0(k3_real_1(k3_funct_2(B,k1_numbers,C,D),k3_funct_2(B,k1_numbers,C,E)),1),k3_funct_2(B,k1_numbers,C,E)),k3_funct_2(B,k1_numbers,k3_prob_2(A,B,C,E),D)) ) ) ) ) ) ) )).
fof(t35_prob_3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => r2_funct_2(k4_ordinal1,k9_setfam_1(A),k2_prob_3(A,k3_prob_3(A,C)),k2_prob_3(A,C)) ) ) )).
fof(t35_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( r2_hidden(D,k4_prob_4(A,B,C)) <=> ? [E] : ? [F] : ( 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)) = k5_numbers ) ) ) ) ) )).
fof(t35_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => r2_hidden(k8_cqc_lang(A,k8_cqc_lang(A,B,D),k8_cqc_lang(A,k8_cqc_lang(A,C,D),k8_cqc_lang(A,k9_cqc_lang(A,B,C),D))),k4_cqc_the1(A)) ) ) ) ) )).
fof(t35_projpl_1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & v5_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t35_pscomp_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t35_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( ~ ( ~ r6_pboole(A,D,k1_pboole(A)) & ~ r6_pboole(A,D,k1_pzfmisc1(A,B)) & ~ r6_pboole(A,D,k1_pzfmisc1(A,C)) & ~ r6_pboole(A,D,k2_pzfmisc1(A,B,C)) ) => r2_pboole(A,D,k2_pzfmisc1(A,B,C)) ) ) ) ) )).
fof(t35_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t35_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( ~ 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 ) ) )).
fof(t35_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_qc_lang4(C,A,B) => ! [D] : ( m2_qc_lang4(D,A,B,C) => r2_hidden(D,k4_qc_lang4(A,B,C)) ) ) ) ) )).
fof(t35_quatern2,axiom,( k4_struct_0(k14_quatern2) = k1_quatern2 )).
fof(t35_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => r1_xxreal_0(k28_quaterni(k22_quaterni(k22_quaterni(A,B),C)),k2_xcmplx_0(k2_xcmplx_0(k28_quaterni(A),k28_quaterni(B)),k28_quaterni(C))) ) ) ) )).
fof(t35_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_xreal_0(B) => ( A = B => ( k13_quaterni(k10_quaterni(A,k12_quaterni)) = k5_numbers & k14_quaterni(k10_quaterni(A,k12_quaterni)) = k5_numbers & k15_quaterni(k10_quaterni(A,k12_quaterni)) = k5_numbers & k16_quaterni(k10_quaterni(A,k12_quaterni)) = B ) ) ) ) )).
fof(t35_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k19_quofield(A))) => ! [C] : ( 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) ) ) ) )).
fof(t35_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_6(C,A,B) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t35_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ( r1_xxreal_0(A,k5_numbers) <=> r1_xxreal_0(k2_rat_1(A),k5_numbers) ) ) )).
fof(t35_ratfunc1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_ratfunc1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t35_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t35_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => k3_int_1(A) = k6_xcmplx_0(A,k9_nat_1(k1_numbers,k4_real_3(A),k5_numbers)) ) )).
fof(t35_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [D] : ( ( v1_rearran1(D) & v2_rearran1(D) & v3_rearran1(D,k1_zfmisc_1(A)) & m2_finseq_1(D,k1_zfmisc_1(A)) ) => ( ( v1_partfun1(C,B) & k5_card_1(B) = k5_card_1(A) ) => ( k3_finseq_1(k20_rfunct_3(A,k4_rearran1(B,A,D,C),A)) = k5_card_1(A) & r1_xxreal_0(1,k3_finseq_1(k20_rfunct_3(A,k4_rearran1(B,A,D,C),A))) ) ) ) ) ) ) )).
fof(t35_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ( ( k9_xtuple_0(A) = k1_xboole_0 | k10_xtuple_0(A) = k1_xboole_0 ) => A = k1_xboole_0 ) ) )).
fof(t35_revrot_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ( ( 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(k1_nat_1(C,k3_finseq_1(A)),k4_finseq_4(A,B))) ) ) ) ) ) )).
fof(t35_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ~ r2_hidden(B,k1_relat_1(A)) => r4_rewrite1(A,B,B) ) ) )).
fof(t35_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t35_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(E))) => ! [G] : ( ( ~ 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] : ( m1_subset_1(H,k8_afinsq_1(E)) => ! [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) ) ) ) ) ) ) ) )).
fof(t35_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t35_rfunct_2,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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(k5_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,k5_numbers) ) => v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,k26_valued_1(k1_numbers,k1_numbers,C,B),A)) ) ) ) ) )).
fof(t35_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_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)) ) ) ) ) )).
fof(t35_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v8_valued_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_numbers)) => ( C = a_2_0_rinfsup1(A,B) => k2_seq_4(C) = k1_funct_1(A,B) ) ) ) ) ) )).
fof(t35_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ( v7_valued_0(A) & k1_supinf_1 = k1_rinfsup2(A) ) => ( v8_mesfunc5(A) & k2_mesfunc5(A) = k1_supinf_1 ) ) ) )).
fof(t35_rlaffin1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_rlvect_2(C,B) => k3_rlaffin1(B,k8_rlvect_2(B,A,C)) = k3_xcmplx_0(A,k3_rlaffin1(B,C)) ) ) ) )).
fof(t35_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( B != k1_xboole_0 & v1_rlsub_1(B,A) & ! [C] : ( ( v1_rlvect_1(C) & m1_rlsub_1(C,A) ) => B != u1_struct_0(C) ) ) ) ) )).
fof(t35_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_2(C,A,B) => ( r1_rlsub_2(A,C,B) & r1_rlsub_2(A,B,C) ) ) ) ) )).
fof(t35_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( 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))) ) ) )).
fof(t35_rlvect_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(t35_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t35_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( C != k4_struct_0(A) & ~ v1_rlvect_3(k7_domain_1(u1_struct_0(A),B,C),A) & ! [D] : ( v1_xreal_0(D) => B != k1_rlvect_1(A,C,D) ) ) ) ) ) )).
fof(t35_rlvect_5,axiom,( ! [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_rlvect_5(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => k1_nat_1(k1_rlvect_5(k1_rlsub_2(A,B,C)),k1_rlvect_5(k2_rlsub_2(A,B,C))) = k1_nat_1(k1_rlvect_5(B),k1_rlvect_5(C)) ) ) ) )).
fof(t35_rlvect_x,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(A)) => ! [F] : ( ( 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] : ( 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_funct_1(F,G)) ) ) ) => r2_hidden(C,k2_rlvect_x(A,B)) ) ) ) ) ) ) )).
fof(t35_rmod_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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) ) ) ) )).
fof(t35_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( m1_rmod_2(E,A,B) => ( ( m1_rmod_2(C,A,E) & m1_rmod_2(D,A,E) ) => m1_rmod_2(k1_rmod_3(A,B,C,D),A,E) ) ) ) ) ) ) )).
fof(t35_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t35_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => k7_robbins1(A) = k5_lattices(k8_robbins1(A)) ) )).
fof(t35_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t35_robbins4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v10_robbins1(A) & v8_robbins3(A) & v9_robbins3(A) & l4_robbins1(A) ) => ( v1_robbins4(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t35_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) )).
fof(t35_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( ~ r1_xxreal_0(k1_rpr_1(A,C),k5_numbers) => r1_xxreal_0(k5_numbers,k2_rpr_1(A,C,B)) ) ) ) ) )).
fof(t35_rusub_1,axiom,( ! [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_bhsp_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => m1_rusub_1(A,k2_rusub_1(A)) ) )).
fof(t35_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_2(C,A,B) => ( r1_rusub_2(A,C,B) & r1_rusub_2(A,B,C) ) ) ) ) )).
fof(t35_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( r1_struct_0(k1_rusub_3(A,k8_domain_1(u1_struct_0(A),B,C,D)),E) <=> ? [F] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & 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)) ) ) ) ) ) ) ) ) )).
fof(t35_rusub_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( v2_rusub_4(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t35_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(C,k4_bhsp_2(A,B,D)) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & r1_tarski(k4_bhsp_2(A,C,E),k4_bhsp_2(A,B,D)) ) ) ) ) ) ) ) )).
fof(t35_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t35_rvsum_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k16_rvsum_1(k11_finseq_1(A,B,C)) = k2_xcmplx_0(k2_xcmplx_0(A,B),C) ) ) ) )).
fof(t35_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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] : ( ( 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) = k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),3)))) ) & ( k1_funct_1(B,E) != k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),3)))) ) ) ) ) ) ) ) )).
fof(t35_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m2_finseq_1(C,k4_numbers) => ~ ( r1_tarski(k1_funct_4(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)),k16_funcop_1(k5_scmfsa_2(k5_numbers),C)),B) & r1_tarski(k2_scmbsort,A) & ! [D] : ( 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(k7_card_1(3),k1_scmfsa_2,A,B),k5_scmfsa_2(k5_numbers)) = D ) ) ) ) ) ) )).
fof(t35_scmfsa10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => k1_amistd_1(k7_card_1(3),k1_scmfsa_2,A,k12_scmfsa_2(B,C)) = k2_tarski(B,k1_ordinal1(A)) ) ) ) )).
fof(t35_scmfsa8a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( 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(k7_card_1(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(k1_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k5_card_1(B),k5_card_1(C)),1)))) ) ) ) ) ) )).
fof(t35_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( v7_ordinal1(E) => ( ( ( r5_scmfsa7b(C,B,A) & r6_scmfsa7b(C,B,A) ) => ( r5_scmfsa7b(C,k1_funct_4(B,k7_memstr_0(k7_card_1(3),k1_scmfsa_2,E)),k1_funct_4(A,C)) & r6_scmfsa7b(C,k1_funct_4(B,k7_memstr_0(k7_card_1(3),k1_scmfsa_2,E)),k1_funct_4(A,C)) ) ) & ( ( r5_scmfsa7b(C,k1_funct_4(B,k7_memstr_0(k7_card_1(3),k1_scmfsa_2,E)),k1_funct_4(A,C)) & r6_scmfsa7b(C,k1_funct_4(B,k7_memstr_0(k7_card_1(3),k1_scmfsa_2,E)),k1_funct_4(A,C)) ) => ( r5_scmfsa7b(C,B,A) & r6_scmfsa7b(C,B,A) ) ) ) ) ) ) ) ) )).
fof(t35_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ( ( k1_funct_1(B,k4_scmfsa_2(k5_numbers)) = 1 & r1_xxreal_0(k1_funct_1(B,C),k5_numbers) ) => k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(k2_scmfsa_9(C,D),B,A)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,B) ) ) ) ) ) )).
fof(t35_scmfsa_2,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( 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)) ) ) )).
fof(t35_scmfsa_m,axiom,( ! [A] : ( r2_hidden(A,k9_xtuple_0(k10_scmfsa_m)) <=> ? [B] : ( m2_finseq_1(B,k4_numbers) & A = k16_funcop_1(k5_scmfsa_2(k5_numbers),B) ) ) )).
fof(t35_scmisort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ( r2_classes1(k18_scmfsa_2(B,k5_scmfsa_2(k5_numbers)),k18_scmfsa_2(k1_scmfsa6b(k2_scmisort(k5_scmfsa_2(k5_numbers)),B,A),k5_scmfsa_2(k5_numbers))) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(D,k3_finseq_1(k18_scmfsa_2(B,k5_scmfsa_2(k5_numbers)))) ) => ( r1_xxreal_0(D,C) | ! [E] : ( v1_int_1(E) => ! [F] : ( v1_int_1(F) => ( ( E = k1_funct_1(k18_scmfsa_2(k1_scmfsa6b(k2_scmisort(k5_scmfsa_2(k5_numbers)),B,A),k5_scmfsa_2(k5_numbers)),C) & F = k1_funct_1(k18_scmfsa_2(k1_scmfsa6b(k2_scmisort(k5_scmfsa_2(k5_numbers)),B,A),k5_scmfsa_2(k5_numbers)),D) ) => r1_xxreal_0(F,E) ) ) ) ) ) ) ) ) ) ) )).
fof(t35_scmpds_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ~ ( k2_compos_0(u1_compos_1(k1_scmpds_2),A) = 12 & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmpds_2)) ) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => A != k15_scmpds_2(B,C,D,E) ) ) ) ) ) ) )).
fof(t35_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_scmpds_2)) ) => ! [G] : ( v1_int_1(G) => ( k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,E),G)) != k5_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) ) ) ) ) ) ) ) ) )).
fof(t35_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ! [F] : ( v7_ordinal1(F) => ( r1_xxreal_0(k5_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)) = k1_nat_1(k5_card_1(C),3) ) ) ) ) ) ) ) )).
fof(t35_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(k1_nat_1(B,1),k3_amistd_1(k7_card_1(2),k1_scmring2(A),B)) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k3_amistd_1(k7_card_1(2),k1_scmring2(A),B)) => r1_xxreal_0(B,C) ) ) ) ) ) )).
fof(t35_scmyciel,axiom,( k5_scmyciel(k1_xboole_0) = k1_tarski(k1_xboole_0) )).
fof(t35_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t35_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v9_ordinal1(A) => r2_funct_2(k4_ordinal1,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,A),A),B) ) ) ) )).
fof(t35_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( r2_seqfunc(A,C,D) => ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,D) => r2_relset_1(k4_ordinal1,k1_numbers,k10_seqfunc(A,k2_seqfunc(A,C,B),E),k26_valued_1(k4_ordinal1,k1_numbers,k10_seqfunc(A,C,E),B)) ) ) ) ) ) ) )).
fof(t35_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_series_1(A) => v1_series_1(A) ) ) )).
fof(t35_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ( k2_xcmplx_0(A,B) = 1 => r1_xxreal_0(9,k3_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(1,k1_square_1(A)),1),k6_xcmplx_0(k7_xcmplx_0(1,k1_square_1(B)),1))) ) ) ) )).
fof(t35_setfam_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r2_hidden(k3_subset_1(A,C),k7_setfam_1(A,B)) <=> r2_hidden(C,B) ) ) ) )).
fof(t35_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ! [E] : ( v7_ordinal1(E) => k1_funct_1(D,E) = k3_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) => ! [E] : ( v7_ordinal1(E) => k1_funct_1(k2_setlim_1(A,D),E) = k3_xboole_0(k1_funct_1(k2_setlim_1(A,B),E),k1_funct_1(k2_setlim_1(A,C),E)) ) ) ) ) ) )).
fof(t35_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) ) ) )).
fof(t35_setwiseo,axiom,( ! [A] : v1_binop_1(k9_setwiseo(A),k5_finsub_1(A)) )).
fof(t35_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_2(D,A,k4_finseq_2(C,A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t35_sf_mastr,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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)) ) ) ) )).
fof(t35_sfmastr3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_scmfsa_2(C) => r1_tarski(k5_scmfsa_m(A,B),k2_sf_mastr(k4_sfmastr3(C,A,B))) ) ) ) )).
fof(t35_sgraph1,axiom,( u1_struct_0(k8_sgraph1) = k2_finseq_1(3) & u1_sgraph1(k8_sgraph1) = k4_setwiseo(k5_finsub_1(k4_ordinal1),k3_setwiseo(k4_ordinal1,1,2),k3_setwiseo(k4_ordinal1,2,3),k3_setwiseo(k4_ordinal1,3,1)) )).
fof(t35_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v9_sheffer1(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l3_sheffer1(A) ) => v11_lattices(A) ) )).
fof(t35_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t35_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ! [C] : ( m2_simplex0(C,A,B) => ! [D] : ( m2_simplex0(D,A,C) => ( ( v7_simplex0(D,A,B) & m2_simplex0(D,A,B) ) => v7_simplex0(D,A,C) ) ) ) ) )).
fof(t35_simplex1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_finset_1(C) & v1_rlaffin1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ! [E] : ( ( 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(k2_xcmplx_0(k2_xcmplx_0(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))),k2_xcmplx_0(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] : ( 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) = k2_xcmplx_0(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)) ) ) ) ) ) ) ) ) )).
fof(t35_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( v2_comseq_2(k3_series_1(k20_sin_cos(A))) & k4_series_1(k20_sin_cos(A)) = k4_complex1(k11_comseq_3(k3_sin_cos(k3_xcmplx_0(A,k7_complex1)))) & v2_comseq_2(k3_series_1(k21_sin_cos(A))) & k4_series_1(k21_sin_cos(A)) = k3_complex1(k11_comseq_3(k3_sin_cos(k3_xcmplx_0(A,k7_complex1)))) ) ) )).
fof(t35_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_fdiff_1(k3_sin_cos2,k1_numbers) & k1_fdiff_1(k3_sin_cos2,A) = k1_funct_1(k1_sin_cos2,A) ) ) )).
fof(t35_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,k2_xcmplx_0(A,k3_xcmplx_0(k2_nat_1(2,B),k28_sin_cos))) = k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,A) ) ) )).
fof(t35_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k3_xcmplx_0(k3_xcmplx_0(k17_sin_cos(A),k19_sin_cos(B)),k19_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)))) ) ) ) )).
fof(t35_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( k17_sin_cos(k7_xcmplx_0(A,2)) != k5_numbers & k19_sin_cos(k7_xcmplx_0(A,2)) != k5_numbers & k6_xcmplx_0(1,k1_square_1(k1_sin_cos4(k7_xcmplx_0(A,2)))) != k5_numbers & k3_sin_cos4(k7_xcmplx_0(A,2)) != k3_square_1(k7_xcmplx_0(k3_xcmplx_0(2,k4_sin_cos4(A)),k6_xcmplx_0(k4_sin_cos4(A),1))) & k3_sin_cos4(k7_xcmplx_0(A,2)) != k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k3_xcmplx_0(2,k4_sin_cos4(A)),k6_xcmplx_0(k4_sin_cos4(A),1)))) ) ) )).
fof(t35_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(k28_sin_cos,A) & r1_xxreal_0(k19_sin_cos(A),k4_xcmplx_0(1)) ) ) )).
fof(t35_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => k1_sin_cos7(A) = k4_sin_cos7(k7_xcmplx_0(A,k3_square_1(k2_xcmplx_0(k1_square_1(A),1)))) ) )).
fof(t35_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2))) & ~ r1_xxreal_0(k7_xcmplx_0(k28_sin_cos,2),A) & ~ ( k3_sin_cos9(k1_funct_1(k26_sin_cos,A)) = A & k3_sin_cos9(k1_sin_cos4(A)) = A ) ) ) )).
fof(t35_sincos10,axiom,( ! [A] : ( r2_hidden(A,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)))) => r2_hidden(k1_funct_1(k2_fdiff_9,A),k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1))) ) )).
fof(t35_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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(k1_nat_1(A,2),k3_finseq_1(B)) & r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),B,k1_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,k1_nat_1(A,1)))) & k7_partfun1(u1_struct_0(k15_euclid(2)),B,k1_nat_1(A,1)) != C & k7_partfun1(u1_struct_0(k15_euclid(2)),B,k1_nat_1(A,1)) != D ) ) ) ) ) )).
fof(t35_sppol_2,axiom,( ! [A] : ( 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)) ) ) )).
fof(t35_sprect_1,axiom,( ! [A] : ( 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) ) )).
fof(t35_sprect_2,axiom,( k15_pscomp_1(k1_topreal1) = k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,1),k19_euclid(1,1)) )).
fof(t35_sprect_3,axiom,( ! [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) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => k3_topreal1(2,A) = a_1_0_sprect_3(A) ) )).
fof(t35_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t35_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => k3_xcmplx_0(k6_xcmplx_0(k3_square_1(A),k3_square_1(B)),k2_xcmplx_0(k3_square_1(A),k3_square_1(B))) = k6_xcmplx_0(A,B) ) ) ) )).
fof(t35_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( 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))) ) ) )).
fof(t35_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k1_nat_1(B,1),A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_nat_1(B,1),A))) ) => ~ ( A != k5_numbers & k8_relset_1(k1_nat_1(B,1),A,C,k1_seq_4(k1_funct_1(C,B))) != k1_seq_4(B) & ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(D,k8_relset_1(k1_nat_1(B,1),A,C,k1_seq_4(k1_funct_1(C,B)))) & D != B ) ) ) ) ) ) )).
fof(t35_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_sublemma(B,A) & m1_subset_1(B,k2_zfmisc_1(k16_substut1(A),k3_qc_lang1(A))) ) => ! [C] : ( m1_substut1(C,A,B) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(k16_substut1(A),k3_qc_lang1(A))) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t35_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ( A != k1_xboole_0 => m1_subset_1(k1_enumset1(B,C,D),k1_zfmisc_1(A)) ) ) ) ) )).
fof(t35_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [D] : ( ( v5_relat_1(D,k3_qc_lang1(A)) & v3_card_1(D,B) & m2_finseq_1(D,k2_qc_lang1(A)) ) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t35_supinf_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_card_3(A) & v5_supinf_2(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( m1_supinf_2(B,A) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k12_supinf_2(k15_supinf_2(A,B),C),k12_supinf_2(k15_supinf_2(A,B),k1_nat_1(C,1))) & r1_xxreal_0(k1_supinf_2,k12_supinf_2(k15_supinf_2(A,B),C)) ) ) ) ) )).
fof(t35_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( 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,D,C) & k2_symsp_1(A,B,E,k4_vectsp_1(A,B,G,F),C,D) != k8_group_1(A,G,k2_symsp_1(A,B,E,F,C,D)) ) ) ) ) ) ) ) ) )).
fof(t35_sysrel,axiom,( ! [A] : ! [B] : ( 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) ) ) ) )).
fof(t35_taxonom1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t35_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => r1_tarski(k9_tdlat_1(A),k1_tdlat_1(A)) ) )).
fof(t35_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) )).
fof(t35_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v4_tdlat_3(A) <=> ! [B] : ( 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) ) ) ) ) )).
fof(t35_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => r1_tarski(k3_polynom1(k15_pre_poly(A),C,k6_termord(A,B,C,D)),k3_polynom1(k15_pre_poly(A),C,D)) ) ) ) ) )).
fof(t35_tex_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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))) ) ) ) ) )).
fof(t35_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_tex_2(B,A) <=> ! [C] : ( 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 ) ) ) ) ) )).
fof(t35_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t35_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t35_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( ( r1_tsep_1(k1_tsep_1(A,C,D),B) => ( r1_tsep_1(C,B) & r1_tsep_1(D,B) ) ) & ( ( r1_tsep_1(C,B) & r1_tsep_1(D,B) ) => r1_tsep_1(k1_tsep_1(A,C,D),B) ) & ( r1_tsep_1(B,k1_tsep_1(A,C,D)) => ( r1_tsep_1(B,C) & r1_tsep_1(B,D) ) ) & ( ( r1_tsep_1(B,C) & r1_tsep_1(B,D) ) => r1_tsep_1(B,k1_tsep_1(A,C,D)) ) ) ) ) ) ) )).
fof(t35_toler_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( r2_hidden(C,A) => ( v1_toler_1(k9_relat_1(B,C),A,B) & m1_toler_1(k9_relat_1(B,C),A,B) ) ) ) ) )).
fof(t35_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_borsuk_2(G,A,B,C) => ! [H] : ( m1_borsuk_2(H,A,C,D) => ! [I] : ( m1_borsuk_2(I,A,D,E) => ! [J] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t35_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( v7_topalg_6(B,A) & m2_subset_1(B,k4_partfun1(k1_numbers,k2_struct_0(A)),k1_topalg_6(A)) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t35_topdim_1,axiom,( ! [A] : ( ( 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),k5_numbers) ) <=> ! [B] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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)) ) ) ) ) ) ) )).
fof(t35_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( r1_tarski(B,C) & r1_topgen_1(A,B,D) ) => r1_topgen_1(A,C,D) ) ) ) ) )).
fof(t35_topgen_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ? [C] : ( 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)) ) ) )).
fof(t35_topgen_3,axiom,( ! [A] : ( ~ v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ~ ( v1_finset_1(B) & v1_finset_1(k3_subset_1(A,B)) ) ) ) )).
fof(t35_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => v5_topgen_4(k2_struct_0(A),A) ) )).
fof(t35_topgen_5,axiom,( ! [A] : ( 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 ) ) ) )).
fof(t35_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_topgrp_1(A) & l1_pre_topc(A) ) => ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v3_pre_topc(C,A) & r2_hidden(B,C) & ! [D] : ( 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) ) ) )).
fof(t35_topreal3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) ) ) )).
fof(t35_topreal6,axiom,( ! [A] : ( 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))) ) )).
fof(t35_topreal8,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [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_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)) ) ) ) ) )).
fof(t35_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(A))) => ! [G] : ( m2_finseq_2(G,k1_numbers,k1_euclid(A)) => ! [H] : ( m2_finseq_2(H,k1_numbers,k1_euclid(A)) => ! [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,C)) & B = k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(2,k22_rvsum_1(k5_algstr_0(k15_euclid(A),E,D),k5_algstr_0(k15_euclid(A),D,F)))),k3_square_1(k1_quin_1(k18_rvsum_1(k11_euclid(A,k8_euclid(A,H,G))),k3_xcmplx_0(2,k22_rvsum_1(k5_algstr_0(k15_euclid(A),E,D),k5_algstr_0(k15_euclid(A),D,F))),k6_xcmplx_0(k18_rvsum_1(k11_euclid(A,k8_euclid(A,G,I))),k1_square_1(C))))),k3_xcmplx_0(2,k18_rvsum_1(k11_euclid(A,k8_euclid(A,H,G))))) & ! [J] : ( m1_subset_1(J,u1_struct_0(k15_euclid(A))) => ~ ( k1_tarski(J) = k9_subset_1(u1_struct_0(k15_euclid(A)),k4_topreal9(k15_euclid(A),D,E),k3_topreal9(A,F,C)) & J = k3_rlvect_1(k15_euclid(A),k1_rlvect_1(k15_euclid(A),D,k6_xcmplx_0(1,B)),k1_rlvect_1(k15_euclid(A),E,B)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t35_topreala,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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))))) ) ) ) ) ) ) )).
fof(t35_toprealb,axiom,( ! [A] : ( v1_xreal_0(A) => ( k3_int_1(A) = k7_xcmplx_0(1,4) => k1_funct_1(k12_toprealb,A) = k19_euclid(k5_numbers,1) ) ) )).
fof(t35_toprealc,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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))))) ) ) ) ) )).
fof(t35_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ! [C] : ( v7_ordinal1(C) => ? [D] : ( v1_xreal_0(D) & ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ~ ( r1_xxreal_0(E,C) & r1_xxreal_0(D,k12_euclid(k9_nat_1(u1_struct_0(k15_euclid(A)),B,E))) ) ) ) ) ) ) )).
fof(t35_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(B,A) => r1_tarski(k2_tops_1(A,B),B) ) ) ) )).
fof(t35_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t35_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t35_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t35_trees_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => v2_trees_1(k1_tarski(A)) ) )).
fof(t35_trees_3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( B != k5_numbers => ( v5_trees_3(k2_finseq_2(B,A)) <=> ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) ) ) ) )).
fof(t35_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => k1_funct_1(A,B) = k1_funct_1(k5_trees_2(A,B),k1_xboole_0) ) ) )).
fof(t35_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t35_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ v2_struct_0(E) & m1_pre_topc(E,A) ) => ( ( r4_tsep_2(A,B,C) & r4_tsep_2(A,D,E) ) => ( r1_tsep_1(B,D) | r4_tsep_2(A,k2_tsep_1(A,B,D),k1_tsep_1(A,C,E)) ) ) ) ) ) ) ) )).
fof(t35_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tsp_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t35_turing_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( r1_xxreal_0(1,A) => r3_turing_1(k18_turing_1,k3_comput_1(A,k5_numbers)) ) ) )).
fof(t35_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => v1_relat_1(k3_msafree2(k40_twoscomp(A,B))) ) ) )).
fof(t35_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => k2_uniroots(A) = a_1_2_uniroots(A) ) )).
fof(t35_uproots,axiom,( ! [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) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & v1_uproots(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k1_algseq_1(A,k11_polynom3(A,k4_polynom5(A,B,k5_struct_0(A)),C)) = k1_nat_1(k1_algseq_1(A,C),1) ) ) ) )).
fof(t35_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_funct_2(C,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t35_valued_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_finset_1(B) ) => ( r2_hidden(A,k1_relset_1(k4_ordinal1,B)) => r1_xxreal_0(k64_valued_1(B),A) ) ) ) )).
fof(t35_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( 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) ) ) ) )).
fof(t35_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(k6_vectsp10(A,B,k9_vectsp10(A,B,C)))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t35_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t35_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t35_vectsp_4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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) ) ) ) )).
fof(t35_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( ~ ( ? [E] : ( 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] : ( m1_vectsp_4(E,A,B) => u1_struct_0(E) != k2_xboole_0(u1_struct_0(C),u1_struct_0(D)) ) ) ) ) ) ) ) )).
fof(t35_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => r1_vectsp_6(A,B,k6_vectsp_6(A,B,k5_struct_0(A),C),C) ) ) ) )).
fof(t35_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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] : ( v7_vectsp_1(D,A) & m1_vectsp_4(D,A,C) & k1_vectsp_9(A,D) = B ) ) ) ) ) )).
fof(t35_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t35_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t35_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ! [D] : ( m2_yellow_6(D,A,B) => ( D = k5_yellow_6(A,B,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => r2_hidden(k2_waybel_0(A,D,E),C) ) ) ) ) ) )).
fof(t35_waybel12,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( v13_waybel_0(B,A) & v1_waybel_6(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v4_card_3(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( ( 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))) ) ) ) ) ) ) ) ) )).
fof(t35_waybel13,axiom,( ! [A] : ( ( 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] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k2_yellow_1(B)),u1_struct_0(k2_yellow_1(B))) & v7_waybel_1(C,k2_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_yellow_1(B)),u1_struct_0(k2_yellow_1(B))))) ) => ~ ( v22_waybel_0(C,k2_yellow_1(B),k2_yellow_1(B)) & r5_waybel_1(A,k1_yellow_2(k2_yellow_1(B),k2_yellow_1(B),C)) ) ) ) ) & ( ? [B] : ? [C] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k2_yellow_1(B)),u1_struct_0(k2_yellow_1(B))) & v7_waybel_1(C,k2_yellow_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_yellow_1(B)),u1_struct_0(k2_yellow_1(B))))) & v22_waybel_0(C,k2_yellow_1(B),k2_yellow_1(B)) & r5_waybel_1(A,k1_yellow_2(k2_yellow_1(B),k2_yellow_1(B),C)) ) => v2_waybel_8(A) ) ) ) )).
fof(t35_waybel14,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ( v3_waybel_3(A) & ! [C] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t35_waybel16,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_waybel16(B,A) => B = k2_yellow_0(A,a_2_0_waybel16(A,B)) ) ) ) )).
fof(t35_waybel20,axiom,( ! [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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) ) => ( v1_waybel20(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t35_waybel21,axiom,( ! [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) & l1_waybel_9(A) ) => ! [B] : ( ( ~ 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))) ) ) )).
fof(t35_waybel23,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v2_waybel23(k5_waybel_0(A,B),A) ) ) )).
fof(t35_waybel24,axiom,( ! [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] : ( ( 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),k5_yellow_1(u1_struct_0(A),B)) & m1_yellow_0(k3_waybel24(A,B),k5_yellow_1(u1_struct_0(A),B)) ) ) ) )).
fof(t35_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_waybel25(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v6_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t35_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ~ v1_xboole_0(B) => r5_waybel_1(k1_waybel26(A,k3_waybel18(B,k7_funcop_1(B,k9_waybel18))),k4_yellow_1(B,k7_funcop_1(B,k1_waybel26(A,k9_waybel18)))) ) ) )).
fof(t35_waybel27,axiom,( ! [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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t35_waybel30,axiom,( ! [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_waybel_2(A) & l1_waybel_9(A) ) => ( v3_waybel_3(A) <=> ( v3_waybel30(A) & v3_waybel_3(k1_yellow_1(k5_waybel11(A))) ) ) ) )).
fof(t35_waybel34,axiom,( ! [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] : ( ( 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)) ) ) ) )).
fof(t35_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t35_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) & ? [D] : ( 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] : ( 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) ) ) ) )).
fof(t35_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(t35_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ( ! [D] : ( 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] : ( ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(D)) ) => ~ r1_tarski(B,k3_tarski(E)) ) ) ) => r1_waybel_3(k1_yellow_1(u1_pre_topc(A)),B,C) ) ) ) ) )).
fof(t35_waybel_4,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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))) ) ) )).
fof(t35_waybel_6,axiom,( ! [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) & l1_orders_2(A) ) => ( v2_waybel_1(A) <=> v4_waybel_6(k4_waybel_6(A),A) ) ) )).
fof(t35_waybel_7,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v4_waybel_7(B,A) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & r3_orders_2(A,D,B) ) ) ) ) ) ) ) )).
fof(t35_waybel_9,axiom,( ! [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) & v1_compts_1(A) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ( ( ! [D] : ( 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) ) ) ) ) )).
fof(t35_weddwitt,axiom,( ! [A] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(t35_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ( 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] : ! [D] : ( 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] : ( r2_hidden(C,k1_relat_1(A)) => r2_hidden(k4_tarski(C,k1_funct_1(B,C)),A) ) ) ) ) )).
fof(t35_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( k3_int_2(A,B) = 1 & k3_xcmplx_0(A,B) = k1_newton(C,D) & ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ~ ( A = k1_newton(E,D) & B = k1_newton(F,D) ) ) ) ) ) ) ) ) )).
fof(t35_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( r1_tarski(A,B) & r1_tarski(C,D) ) => r1_tarski(k4_xboole_0(A,D),k4_xboole_0(B,C)) ) )).
fof(t35_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k9_xboolean(A,k4_xboolean(A,B)) = k3_xboolean(A) ) ) )).
fof(t35_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( k2_xcmplx_0(A,B) = k6_xcmplx_0(C,D) => k2_xcmplx_0(A,D) = k6_xcmplx_0(C,B) ) ) ) ) ) )).
fof(t35_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(C,B) ) => r1_xxreal_0(k2_xcmplx_0(C,A),B) ) ) ) ) )).
fof(t35_xtuple_0,axiom,( ! [A] : ! [B] : k12_xtuple_0(k2_xboole_0(A,B)) = k2_xboole_0(k12_xtuple_0(A),k12_xtuple_0(B)) )).
fof(t35_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k3_xxreal_0(k4_xxreal_0(A,B),B) = B ) ) )).
fof(t35_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(D,B) ) => r1_tarski(k2_xxreal_1(C,D),k1_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t35_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( ~ r1_xxreal_0(B,A) => v2_xxreal_2(k3_xxreal_1(A,B)) ) ) ) )).
fof(t35_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(A,B) => r1_xxreal_0(k1_xxreal_3(A,C),k1_xxreal_3(B,C)) ) ) ) ) )).
fof(t35_yellow10,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( l1_orders_2(B) => ! [C] : ( 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)) ) ) ) )).
fof(t35_yellow12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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) ) ) ) )).
fof(t35_yellow14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(t35_yellow16,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,A) => m1_yellow_0(k3_waybel_3(A,C,D),k3_waybel_3(A,B,D)) ) => m1_yellow_0(k4_yellow_1(A,C),k4_yellow_1(A,B)) ) ) ) ) )).
fof(t35_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & v2_yellow18(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_altcat_1(A,B,C) != k1_xboole_0 => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t35_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_compts_1(A) <=> ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ? [C] : ( m2_yellow_6(C,A,B) & v3_yellow_6(C,A) ) ) ) ) )).
fof(t35_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_altcat_2(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l1_altcat_1(B) ) => ! [C] : ( ( v8_functor0(C,A,B) & v11_functor0(C,A,B) & l2_functor0(C,A,B) ) => ( v17_functor0(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k1_altcat_1(A,D,E) != k1_xboole_0 => ! [F] : ( m1_subset_1(F,k1_altcat_1(A,D,E)) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(t35_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t35_yellow_2,axiom,( ! [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] : ( ( 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)) ) ) ) ) )).
fof(t35_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( r1_yellow_0(A,C) & r1_yellow_0(B,D) & ! [G] : ( 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] : ( m1_subset_1(G,u1_struct_0(A)) => ( r2_lattice3(A,C,G) => r1_orders_2(A,E,G) ) ) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ( r2_lattice3(B,D,G) => r1_orders_2(B,F,G) ) ) ) ) ) ) ) ) ) ) )).
fof(t35_yellow_4,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t35_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t35_yellow_7,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t35_yellow_9,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t35_zf_fund1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ( 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) ) ) ) ) ) )).
fof(t35_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v7_zf_lang(A) => ( k18_zf_lang(A) = k1_funct_1(A,2) & k19_zf_lang(A) = k1_funct_1(A,3) ) ) ) )).
fof(t35_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( 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))) ) ) ) )).
fof(t35_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(C,k2_tarski(A,B)) <=> ~ ( C != k1_xboole_0 & C != k1_tarski(A) & C != k1_tarski(B) & C != k2_tarski(A,B) ) ) )).
fof(t35_zfrefle1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ~ ( r2_hidden(k4_ordinal1,A) & ! [B] : ( ( v3_ordinal1(B) & m1_subset_1(B,A) ) => ! [C] : ( ~ v1_xboole_0(C) => ~ ( r2_ordinal2(B,k4_ordinal1) & C = k4_classes1(B) & r3_zfrefle1(C,A) ) ) ) ) ) )).
fof(t35_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => r1_struct_0(A,k4_struct_0(B)) ) ) )).
fof(t35_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_zmodul02(C,A) => k3_funct_2(u1_struct_0(A),k4_numbers,k24_zmodul02(A,C),B) = k4_xcmplx_0(k3_funct_2(u1_struct_0(A),k4_numbers,C,B)) ) ) ) )).
fof(t35_zmodul03,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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) & v1_zmodul03(B) & l1_zmodul01(B) ) => ! [C] : ( m1_zmodul03(C,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_zmodul02(A,B)))) => ( D = a_3_0_zmodul03(A,B,C) => m1_vectsp_7(D,k9_int_3(A),k12_zmodul02(A,B)) ) ) ) ) ) )).
fof(t360_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(B,C) => k6_subset_1(k1_xxreal_1(B,k1_xxreal_0),k3_xxreal_1(A,C)) = k2_xboole_0(k1_xxreal_1(B,A),k3_xxreal_1(C,k1_xxreal_0)) ) ) ) ) )).
fof(t361_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(B,C) => k6_subset_1(k4_xxreal_1(B,k1_xxreal_0),k1_xxreal_1(A,C)) = k2_xboole_0(k4_xxreal_1(B,A),k4_xxreal_1(C,k1_xxreal_0)) ) ) ) ) )).
fof(t362_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(B,C) => k6_subset_1(k2_xxreal_1(B,k1_xxreal_0),k1_xxreal_1(A,C)) = k2_xboole_0(k2_xxreal_1(B,A),k4_xxreal_1(C,k1_xxreal_0)) ) ) ) ) )).
fof(t363_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ~ r1_xxreal_0(C,B) => k6_subset_1(k3_xxreal_1(B,k1_xxreal_0),k1_xxreal_1(A,C)) = k2_xboole_0(k4_xxreal_1(B,A),k3_xxreal_1(C,k1_xxreal_0)) ) ) ) ) )).
fof(t364_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(B,C) => k6_subset_1(k1_xxreal_1(B,k1_xxreal_0),k1_xxreal_1(A,C)) = k2_xboole_0(k2_xxreal_1(B,A),k3_xxreal_1(C,k1_xxreal_0)) ) ) ) ) )).
fof(t365_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( r1_xxreal_0(B,A) => k6_subset_1(k4_xxreal_1(B,k1_xxreal_0),k1_tarski(A)) = k2_xboole_0(k4_xxreal_1(B,A),k4_xxreal_1(A,k1_xxreal_0)) ) ) ) )).
fof(t366_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( r1_xxreal_0(B,A) => k6_subset_1(k2_xxreal_1(B,k1_xxreal_0),k1_tarski(A)) = k2_xboole_0(k2_xxreal_1(B,A),k4_xxreal_1(A,k1_xxreal_0)) ) ) ) )).
fof(t367_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( ~ r1_xxreal_0(A,B) => k6_subset_1(k3_xxreal_1(B,k1_xxreal_0),k1_tarski(A)) = k2_xboole_0(k4_xxreal_1(B,A),k3_xxreal_1(A,k1_xxreal_0)) ) ) ) )).
fof(t368_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( r1_xxreal_0(B,A) => k6_subset_1(k1_xxreal_1(B,k1_xxreal_0),k1_tarski(A)) = k2_xboole_0(k2_xxreal_1(B,A),k3_xxreal_1(A,k1_xxreal_0)) ) ) ) )).
fof(t369_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k6_subset_1(k1_xxreal_1(B,k1_xxreal_0),k4_xxreal_1(A,k1_xxreal_0)) = k2_xboole_0(k1_xxreal_1(B,A),k1_tarski(k1_xxreal_0)) ) ) )).
fof(t36_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_abcmiz_0(A)) => ! [D] : ( 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)),k1_nat_1(k3_finseq_1(C),1)) = k8_abcmiz_0(A,B,C) ) ) ) ) )).
fof(t36_abcmiz_1,axiom,( ! [A] : ( m1_subset_1(A,k2_abcmiz_1) => ! [B] : ( m1_subset_1(B,k2_abcmiz_1) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t36_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r3_aff_1(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t36_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_aff_1(C,A) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(B,D) & r1_tarski(C,D) & v1_aff_4(D,A) ) ) ) ) ) ) )).
fof(t36_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(t36_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ! [B] : ( k1_afinsq_1(k5_afinsq_2(A,B)) = k5_card_1(k3_xboole_0(B,k1_afinsq_1(A))) & ! [C] : ( 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)) ) ) ) ) )).
fof(t36_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k14_afproj(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t36_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k1_afvect0(A,C,B) = k1_afvect0(A,D,B) <=> ( C = D | r1_afvect0(A,C,D) ) ) ) ) ) ) )).
fof(t36_algspec1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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))))) ) ) ) ) ) )).
fof(t36_algstr_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t36_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v3_altcat_2(B,A) & m1_altcat_2(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t36_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(k3_analmetr(A))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k3_analmetr(A))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k3_analmetr(A))) => ! [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t36_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( ( r1_analmetr(A,G,H) & r1_analort(A,G,H,B,D,C,E) & r1_analort(A,G,H,B,D,E,F) ) => r1_analort(A,G,H,B,D,C,F) ) ) ) ) ) ) ) ) ) )).
fof(t36_aofa_000,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & v3_freealg(A) & l1_unialg_1(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(u1_unialg_1(A))) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k4_finseq_1(u1_unialg_1(A))) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( 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 ) ) ) ) ) ) ) )).
fof(t36_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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] : ( m3_pboole(D,u1_struct_0(A),u3_msualg_1(A,B)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t36_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( ( v19_aofa_a00(F,A) & m1_subset_1(F,u1_struct_0(A)) ) => ! [G] : ( m2_subset_1(G,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => k15_aofa_a00(A,B,C,D,F,k27_aofa_a00(A,C,F),G) = k5_numbers ) ) ) ) ) ) ) )).
fof(t36_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_aofa_i00(E,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) ) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),E) => ! [G] : ( 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,k5_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,k5_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,k5_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,k5_numbers)) => r1_xxreal_0(G,k21_aofa_i00(B,k4_numbers,C,F)) ) ) ) ) ) ) ) ) ) )).
fof(t36_armstrng,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t36_arytm_3,axiom,( ! [A] : ( 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 ) ) ) )).
fof(t36_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : k11_asympt_0(A,B) = k3_xboole_0(k9_asympt_0(A,B),k10_asympt_0(A,B)) ) )).
fof(t36_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( r2_hidden(B,k5_asympt_1) => k9_nat_1(k1_numbers,A,B) = B ) & ( ~ r2_hidden(B,k5_asympt_1) => k9_nat_1(k1_numbers,A,B) = k5_series_1(2,B) ) ) ) => ( r2_hidden(A,k11_asympt_0(k3_asympt_1(1),k5_asympt_1)) & ~ r2_hidden(A,k8_asympt_0(k3_asympt_1(1))) & v7_asympt_0(k3_asympt_1(1)) & ~ v6_asympt_0(A) ) ) ) )).
fof(t36_bagorder,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_bagorder(A))) => ! [C] : ( 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] : ( m1_subset_1(D,k5_finsub_1(u1_struct_0(A))) & ? [E] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t36_bcialg_1,axiom,( ! [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) ) => v11_bcialg_1(A) ) )).
fof(t36_bcialg_2,axiom,( ! [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] : ( ( 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) ) ) ) ) )).
fof(t36_bcialg_3,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t36_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k5_bcialg_1(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( ! [E] : ( m2_subset_1(E,u1_struct_0(A),k7_bcialg_1(A,B)) => r1_bcialg_1(A,E,D) ) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ! [F] : ( m2_subset_1(F,u1_struct_0(A),k7_bcialg_1(A,C)) => r1_bcialg_1(A,F,E) ) ) ) ) ) ) ) )).
fof(t36_bcialg_5,axiom,( ! [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] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( m1_bcialg_5(A,B,C,k1_nat_1(C,D),k1_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) ) ) ) ) ) ) )).
fof(t36_bcialg_6,axiom,( ! [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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t36_bciideal,axiom,( ! [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) ) => ( ( 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) ) ) ) )).
fof(t36_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ~ ( B != C & k4_bhsp_1(A,B,C) = k5_numbers ) & ~ ( k4_bhsp_1(A,B,C) != k5_numbers & B = C ) ) ) ) ) )).
fof(t36_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) & k1_seq_2(k3_bhsp_2(A,k2_normsp_1(A,D,E),k3_rlvect_1(A,B,C))) = k5_numbers ) ) ) ) ) ) ) )).
fof(t36_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,k3_series_1(k2_bhsp_2(A,B)),C)) ) ) ) )).
fof(t36_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t36_binari_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => k1_binari_3(A,k6_binarith(A,B)) = B ) ) )).
fof(t36_binari_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ( ( r1_xxreal_0(k2_xcmplx_0(A,B),k6_xcmplx_0(k5_series_1(2,k7_nat_d(C,1)),1)) & r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => k3_binari_2(C,k7_binarith(C,k2_binari_4(C,A),k2_binari_4(C,B))) = k2_xcmplx_0(A,B) ) ) ) ) )).
fof(t36_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t36_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t36_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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)))) ) ) ) ) ) )).
fof(t36_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t36_borsuk_6,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( 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) ) ) ) ) ) )).
fof(t36_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)))) ) ) ) ) )).
fof(t36_bspace,axiom,( ! [A] : v1_vectsp_7(k9_bspace(A),k2_bspace,k7_bspace(A)) )).
fof(t36_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t36_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t36_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t36_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t36_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) )).
fof(t36_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(E,A) => r1_bvfunc_1(A,k9_bvfunc_1(A,D,k7_bvfunc_2(A,C,B,E)),k7_bvfunc_2(A,k9_bvfunc_1(A,D,C),B,E)) ) ) ) ) ) )).
fof(t36_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(F,A) => r1_bvfunc_1(A,k2_bvfunc_1(A,k6_bvfunc_2(A,k9_bvfunc_1(A,D,k1_bvfunc_1(A,E)),B,F),k7_bvfunc_2(A,k2_bvfunc_1(A,C,E),B,F)),k7_bvfunc_2(A,k2_bvfunc_1(A,C,k1_bvfunc_1(A,D)),B,F)) ) ) ) ) ) ) )).
fof(t36_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t36_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t36_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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,D),k9_bvfunc_1(A,C,D)),k2_bvfunc_1(A,B,C)),D) ) ) ) ) )).
fof(t36_c0sp1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(t36_c0sp2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t36_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t36_card_1,axiom,( ! [A] : ( r2_hidden(A,k4_ordinal1) => v1_card_1(A) ) )).
fof(t36_card_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k3_xcmplx_0(B,A) = k9_ordinal3(B,A) ) ) )).
fof(t36_card_3,axiom,( ! [A] : ( v1_card_1(A) => k7_card_3(k7_funcop_1(k1_xboole_0,A)) = 1 ) )).
fof(t36_card_5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v1_finset_1(B) => ( r1_tarski(B,A) => k2_wellord2(k1_wellord2(B)) = k5_card_1(B) ) ) ) )).
fof(t36_card_fil,axiom,( ! [A] : ! [B] : ( v1_card_1(B) => ~ ( r1_ordinal1(B,k1_card_1(A)) & ! [C] : ~ ( r1_tarski(C,A) & k1_card_1(C) = B ) ) ) )).
fof(t36_card_fin,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ~ v1_xboole_0(C) => ( r2_hidden(B,k2_card_fin(C,k7_funcop_1(k9_xtuple_0(C),A),A)) <=> ! [D] : ( r2_hidden(D,k9_xtuple_0(C)) => r2_hidden(B,k1_funct_1(C,D)) ) ) ) ) )).
fof(t36_card_lar,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) & ~ v4_card_3(A) ) => ( v6_card_fil(A) => v2_classes1(k4_classes1(A)) ) ) )).
fof(t36_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t36_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k1_binop_1(k7_cat_1(k6_cat_2(A,B),A,k12_cat_2(A,B)),C,D) = C ) ) ) ) )).
fof(t36_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ( ( v10_cat_1(C,A) & k3_graph_1(A,D) = B & k4_graph_1(A,D) = C ) => k10_cat_3(A,B,C) = D ) ) ) ) ) )).
fof(t36_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t36_cc0sp2,axiom,( ! [A] : ( ( ~ 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))))) ) ) )).
fof(t36_cfcont_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( 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) = k5_numbers | r1_cfcont_1(k2_cfunct_1(k2_numbers,B),A) ) ) ) ) )).
fof(t36_cfdiff_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t36_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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),k4_xcmplx_0(k6_complex1))) ) ) )).
fof(t36_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ! [B] : ( v2_cgames_1(B) => ( r2_hidden(B,k8_cgames_1(A)) => r1_tarski(k10_cgames_1(B),k11_cgames_1(A)) ) ) ) )).
fof(t36_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m1_chain_1(D,A) => ( r2_hidden(k3_chain_1(A,B,C),k4_chain_1(A,D,k5_numbers)) <=> ( B = C & ! [E] : ( m2_subset_1(E,k4_ordinal1,k2_finseq_1(A)) => r2_hidden(k1_funct_1(B,E),k2_chain_1(A,D,E)) ) ) ) ) ) ) ) )).
fof(t36_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v1_chord(B,A) => v5_glib_001(B,A) ) ) ) )).
fof(t36_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( 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] : ( ( v1_relat_1(F) & v1_funct_1(F) & v3_card_1(F,D) & v1_finseq_1(F) ) => ! [G] : ( 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) ) ) ) ) ) ) ) )).
fof(t36_circcomb,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(t36_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v4_msualg_1(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( ( v4_msualg_1(F,B) & l3_msualg_1(F,B) ) => ( r5_circtrm1(A,B,C,D,E,F) => r1_circtrm1(A,B,C,D) ) ) ) ) ) ) ) )).
fof(t36_classes1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r2_hidden(A,B) <=> r2_hidden(k4_classes1(A),k4_classes1(B)) ) ) ) )).
fof(t36_classes2,axiom,( ! [A] : ! [B] : ~ ( v2_classes1(B) & r1_tarski(A,k4_classes1(k1_card_1(B))) & ~ r2_tarski(A,k4_classes1(k1_card_1(B))) & ~ r2_hidden(A,k4_classes1(k1_card_1(B))) ) )).
fof(t36_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k14_clopban1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_clopban1(A,B))) => ! [E] : ( v1_xcmplx_0(E) => ( ( k2_normsp_0(k14_clopban1(A,B),C) = k5_numbers => C = k4_struct_0(k14_clopban1(A,B)) ) & ( C = k4_struct_0(k14_clopban1(A,B)) => k2_normsp_0(k14_clopban1(A,B),C) = k5_numbers ) & k2_normsp_0(k14_clopban1(A,B),k1_clvect_1(k14_clopban1(A,B),C,E)) = k3_xcmplx_0(k9_complex1(E),k2_normsp_0(k14_clopban1(A,B),C)) & r1_xxreal_0(k2_normsp_0(k14_clopban1(A,B),k1_algstr_0(k14_clopban1(A,B),C,D)),k2_xcmplx_0(k2_normsp_0(k14_clopban1(A,B),C),k2_normsp_0(k14_clopban1(A,B),D))) ) ) ) ) ) ) )).
fof(t36_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [D] : ( v7_ordinal1(D) => ( k1_normsp_0(A,B,D) != k4_struct_0(A) & k9_nat_1(k1_numbers,C,D) = k6_real_1(k9_nat_1(k1_numbers,k5_normsp_0(A,B),k1_nat_1(D,1)),k9_nat_1(k1_numbers,k5_normsp_0(A,B),D)) ) ) & v2_comseq_2(C) ) => ( r1_xxreal_0(1,k1_seq_2(C)) | v2_clopban3(B,A) ) ) ) ) ) )).
fof(t36_clopban4,axiom,( ! [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) & 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) ) )).
fof(t36_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v5_mssubfam(C,A,B) & m3_pboole(C,A,k1_mboolean(A,B)) ) => ! [D] : ( m2_pboole(D,A,k5_mssubfam(A,B),k5_mssubfam(A,B)) => ( ! [E] : ( m1_pboole(E,A,k5_mssubfam(A,B)) => ! [F] : ( ( v2_relat_1(F) & m3_pboole(F,A,k1_mboolean(A,B)) ) => ( ! [G] : ( ( 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) ) ) ) ) ) )).
fof(t36_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t36_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_clvect_1(B,A) => r1_struct_0(B,k4_struct_0(A)) ) ) )).
fof(t36_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) & k1_seq_2(k3_clvect_2(A,k16_csspace(A,D,E),k3_rlvect_1(A,B,C))) = k5_numbers ) ) ) ) ) ) ) )).
fof(t36_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,k3_series_1(k2_clvect_2(A,B)),C)) ) ) ) )).
fof(t36_coh_sp,axiom,( ! [A] : r2_hidden(k4_tarski(k6_partfun1(A),A),k16_coh_sp(A)) )).
fof(t36_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,A) => r1_tarski(k3_funct_2(A,B,C,E),k3_funct_2(A,B,D,E)) ) ) ) ) ) ) )).
fof(t36_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k8_complex1(k5_xcmplx_0(A)) = k5_xcmplx_0(k8_complex1(A)) ) )).
fof(t36_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k1_complex2(B,k3_xcmplx_0(A,C)) = k3_xcmplx_0(k8_complex1(A),k1_complex2(B,C)) ) ) ) )).
fof(t36_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_complfld)) => ~ ( A != k4_struct_0(k1_complfld) & C != k4_struct_0(k1_complfld) & ~ ( k3_vectsp_1(k1_complfld,B,C) = k3_vectsp_1(k1_complfld,k8_group_1(k1_complfld,B,A),k8_group_1(k1_complfld,C,A)) & k3_vectsp_1(k1_complfld,B,C) = k3_vectsp_1(k1_complfld,k8_group_1(k1_complfld,A,B),k8_group_1(k1_complfld,A,C)) ) ) ) ) ) )).
fof(t36_complsp2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( m2_finseq_1(C,k2_numbers) => ( k3_finseq_1(B) = k3_finseq_1(C) => k10_seq_4(k8_seq_4(B,C),A) = k8_seq_4(k10_seq_4(B,A),k10_seq_4(C,A)) ) ) ) ) )).
fof(t36_compos_1,axiom,( ! [A] : ! [B] : ( l1_compos_1(B) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ( r2_hidden(A,k2_afinsq_1(k9_compos_1(B,C))) <=> A = k5_numbers ) ) ) )).
fof(t36_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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),k5_numbers) = B ) ) ) )).
fof(t36_comptrig,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(k5_numbers,A) => k1_comptrig(A) = k28_sin_cos ) ) )).
fof(t36_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k19_margrel1(k5_comput_1(B,A)) = B ) ) )).
fof(t36_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v9_ordinal1(B) => r2_relset_1(k4_ordinal1,k2_numbers,k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,C,A),k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,C,B),k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B))) ) ) ) ) )).
fof(t36_comseq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k6_complex1 != A => ! [B] : ( v7_ordinal1(B) => k9_nat_1(k2_numbers,k10_comseq_3(k1_comseq_3(A)),B) = k7_xcmplx_0(k6_xcmplx_0(k6_complex1,k2_comseq_3(A,k1_nat_1(B,1))),k6_xcmplx_0(k6_complex1,A)) ) ) ) )).
fof(t36_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( v3_conlat_1(B,A) & ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) & l2_conlat_1(B,A) ) => ! [C] : ( ( v3_conlat_1(C,A) & ~ v4_conlat_1(C,A) & v6_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 ) ) ) )).
fof(t36_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_connsp_1(B,A) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t36_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t36_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_convex4(C,A) => ! [D] : ( m1_convex4(D,A) => ( ( m2_convex4(C,A,B) & m2_convex4(D,A,B) ) => m2_convex4(k9_convex4(A,C,D),A,B) ) ) ) ) ) )).
fof(t36_cqc_sim1,axiom,( ! [A] : ( 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)))) ) )).
fof(t36_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => v1_cqc_the1(k4_cqc_the1(A),A) ) )).
fof(t36_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t36_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => r5_cqc_the3(A,k11_cqc_lang(A,C,B),B) ) ) ) )).
fof(t36_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_csspace(A,B,C) => r1_csspace(A,B,k4_algstr_0(A,C)) ) ) ) ) )).
fof(t36_dickson,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_struct_0(A) => v4_dickson(A) ) ) )).
fof(t36_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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] : ( v1_xreal_0(G) => k1_funct_1(F,G) = k7_xcmplx_0(E,G) ) & r2_zfmisc_1(A,B,C,D) ) => ( A = k5_numbers | B = k5_numbers | C = k5_numbers | D = k5_numbers | k11_diff_1(F,A,B,C,D) = k4_xcmplx_0(k7_xcmplx_0(E,k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(A,B),C),D))) ) ) ) ) ) ) ) ) )).
fof(t36_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k3_square_1(D) ) => ( A = B | r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(B,k5_numbers) | k9_diff_1(C,A,B) = k7_xcmplx_0(1,k2_xcmplx_0(k3_square_1(A),k3_square_1(B))) ) ) ) ) ) )).
fof(t36_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( ( 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] : ( v1_xreal_0(F) => k1_funct_1(D,F) = k1_funct_1(k3_diff_1(E,A),F) ) => k9_diff_1(D,B,C) = k6_xcmplx_0(k9_diff_1(E,k2_xcmplx_0(B,A),k2_xcmplx_0(C,A)),k9_diff_1(E,B,C)) ) ) ) ) ) ) )).
fof(t36_dilworth,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & v5_orders_2(A) & v3_dilworth(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( 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) ) ) ) ) )).
fof(t36_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ~ ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r3_diraf(A,B,C,D) ) ) ) ) )).
fof(t36_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) => ! [C] : ( m2_finseq_1(C,A) => ( r2_hidden(C,B) => B = k5_dist_1(A,C) ) ) ) ) )).
fof(t36_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t36_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( 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))) ) ) ) ) )).
fof(t36_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k11_ens_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k11_ens_1(A))) => ! [D] : ( 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] : ( m1_subset_1(E,A) => ! [F] : ! [G] : ~ ( r2_hidden(F,E) & r2_hidden(G,E) & F != G ) ) | v1_ens_1(k15_ens_1(A,D),A) ) ) ) ) ) ) )).
fof(t36_entropy1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( 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] : ( v7_ordinal1(D) => ( r1_xxreal_0(1,D) => ( r1_xxreal_0(k3_finseq_1(B),D) | k1_matrprob(A,C,k1_nat_1(D,1)) = k8_finseq_1(A,k1_matrprob(A,C,D),k1_matrprob(A,B,k1_nat_1(D,1))) ) ) ) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(D,E),k2_matrix_0(B)) => ( r2_hidden(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(D,1),k1_matrix_0(B)),E),k4_finseq_1(k1_matrprob(A,C,k3_finseq_1(B)))) & k3_matrix_0(A,B,D,E) = k1_funct_1(k1_matrprob(A,C,k3_finseq_1(B)),k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(D,1),k1_matrix_0(B)),E)) ) ) ) ) ) ) ) ) )).
fof(t36_enumset1,axiom,( ! [A] : k1_enumset1(A,A,A) = k1_tarski(A) )).
fof(t36_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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_hidden(B,k7_eqrel_1(A,C)) & ! [D] : ( m1_subset_1(D,A) => B != k6_eqrel_1(A,A,C,D) ) ) ) )).
fof(t36_equation,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m3_pboole(C,u1_struct_0(A),k4_equation(A)) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t36_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_valued_0(D) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t36_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => r1_xxreal_0(k5_numbers,k12_euclid(B)) ) ) )).
fof(t36_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( k4_euclid_3(A,B,C) = k5_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) = k5_numbers ) ) ) ) ) )).
fof(t36_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => k2_xcmplx_0(k1_square_1(k12_euclid(k7_euclid(A,B,C))),k1_square_1(k12_euclid(k8_euclid(A,B,C)))) = k3_xcmplx_0(2,k2_xcmplx_0(k1_square_1(k12_euclid(B)),k1_square_1(k12_euclid(C)))) ) ) ) )).
fof(t36_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t36_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_rlsub_1(B,k10_funcsdom(k2_finseq_1(A))) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( ( 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)) ) ) ) ) ) ) ) )).
fof(t36_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( 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,k6_xcmplx_0(k1_funct_1(A,1),k1_funct_1(B,1))),k9_euclid(3,k3_euclid_8,k6_xcmplx_0(k1_funct_1(A,2),k1_funct_1(B,2)))),k9_euclid(3,k4_euclid_8,k6_xcmplx_0(k1_funct_1(A,3),k1_funct_1(B,3)))) ) ) )).
fof(t36_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(E)) => ! [G] : ( m2_finseq_2(G,k1_numbers,k1_euclid(E)) => ! [H] : ( m2_finseq_2(H,k1_numbers,k1_euclid(E)) => ! [I] : ( m2_finseq_2(I,k1_numbers,k1_euclid(E)) => ! [J] : ( 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] : ( v1_xreal_0(K) => ! [L] : ( v1_xreal_0(L) => ! [M] : ( v1_xreal_0(M) => ! [N] : ( v1_xreal_0(N) => ~ ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t36_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) => k9_funct_7(k9_funct_7(C,A,B),A,B) = C ) ) )).
fof(t36_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_circcomb(A) & v2_circcomb(A) & v3_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & v4_circcomb(B,A) & v6_circcomb(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( ( r2_hidden(k4_tarski(D,E),u4_struct_0(A)) & ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t36_fcont_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( 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))) ) ) ) )).
fof(t36_fdiff_10,axiom,( ! [A] : ( ( 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,k26_sin_cos,k27_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,k26_sin_cos,k27_sin_cos),k16_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),k16_sin_cos),A),B) = k3_xcmplx_0(k1_funct_1(k18_sin_cos,k6_xcmplx_0(k1_funct_1(k26_sin_cos,B),k1_funct_1(k27_sin_cos,B))),k2_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B))))) ) ) ) ) ) )).
fof(t36_fdiff_11,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k2_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k2_sin_cos9),A),B) = k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,B),k1_funct_1(k2_sin_cos9,B)),k1_square_1(k1_funct_1(k16_sin_cos,B)))),k7_xcmplx_0(1,k3_xcmplx_0(k1_funct_1(k16_sin_cos,B),k2_xcmplx_0(1,k1_square_1(B))))) ) ) ) ) ) )).
fof(t36_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ( r2_hidden(C,k3_limfunc1(A)) => r1_xxreal_0(k1_fdiff_1(B,C),k5_numbers) ) ) ) => v8_valued_0(k2_partfun1(k1_numbers,k1_numbers,B,k3_limfunc1(A))) ) ) ) )).
fof(t36_fdiff_4,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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(k7_xcmplx_0(1,2))),2))) & B = k3_valued_1(k1_numbers,k1_numbers,k1_numbers,C,D) & D = k1_taylor_1(2) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,A) => ( k1_funct_1(C,E) = E & ~ r1_xxreal_0(k1_funct_1(B,E),k5_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(k7_xcmplx_0(1,2))),2),A) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,A) => k1_funct_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(k7_xcmplx_0(1,2))),2),A),E) = k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(2,E),1),k6_prepower(k2_xcmplx_0(k1_newton(E,2),E),k4_xcmplx_0(k7_xcmplx_0(1,2)))) ) ) ) ) ) ) ) ) )).
fof(t36_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k22_sin_cos),k4_taylor_1(k7_xcmplx_0(3,2))),k7_xcmplx_0(2,3)))) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_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,k22_sin_cos),k4_taylor_1(k7_xcmplx_0(3,2))),k7_xcmplx_0(2,3)),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_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,k22_sin_cos),k4_taylor_1(k7_xcmplx_0(3,2))),k7_xcmplx_0(2,3)),A),C) = k3_xcmplx_0(k1_funct_1(k22_sin_cos,C),k6_prepower(k2_xcmplx_0(1,k1_funct_1(k22_sin_cos,C)),k7_xcmplx_0(1,2))) ) ) ) ) ) ) )).
fof(t36_fdiff_7,axiom,( ! [A] : ( ( 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,k18_sin_cos,k22_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k22_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k22_sin_cos),A),B) = k4_xcmplx_0(k3_xcmplx_0(k1_funct_1(k22_sin_cos,k1_funct_1(k18_sin_cos,B)),k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t36_fdiff_9,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k2_fdiff_9),A),B) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,B),k1_funct_1(k18_sin_cos,k1_funct_1(k16_sin_cos,B))),k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k16_sin_cos,B))))) ) ) ) ) ) )).
fof(t36_fib_num2,axiom,( k4_xcmplx_0(k7_xcmplx_0(1,k1_fib_num)) = k2_fib_num )).
fof(t36_fib_num3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k1_nat_1(k3_fib_num3(A,B,k1_nat_1(C,2)),k3_fib_num3(A,B,k1_nat_1(C,3))) = k3_fib_num3(A,B,k1_nat_1(C,4)) ) ) ) )).
fof(t36_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ( A != 1 => k1_fib_num3(k2_xcmplx_0(A,1)) = k7_xcmplx_0(k2_xcmplx_0(k1_fib_num3(A),k3_square_1(k3_xcmplx_0(5,k6_xcmplx_0(k1_pepin(k1_fib_num3(A)),k3_xcmplx_0(4,k2_power(k4_xcmplx_0(1),A)))))),2) ) ) )).
fof(t36_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_finseq_1(B,A) => ! [C] : ( m1_finseq_1(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t36_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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(C,k5_filter_0(A,C,B)) & r1_tarski(B,k5_filter_0(A,C,B)) ) ) ) ) )).
fof(t36_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t36_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t36_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( m2_finseq_1(k7_finseq_1(A,B),C) => ( m2_finseq_1(A,C) & m2_finseq_1(B,C) ) ) ) ) )).
fof(t36_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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 = k5_numbers & A != k5_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)) ) ) ) ) ) ) ) )).
fof(t36_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( ( k3_finseq_1(C) = k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,A)) => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,B)) => k1_funct_1(C,k1_nat_1(k3_finseq_1(A),D)) = k1_funct_1(B,D) ) ) ) => C = k7_finseq_1(A,B) ) ) ) ) )).
fof(t36_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : ( 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) ) ) ) )).
fof(t36_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ! [D] : ( m2_finseq_1(D,B) => k2_rfinseq(B,k2_xcmplx_0(k3_finseq_1(C),A),k8_finseq_1(B,C,D)) = k2_rfinseq(B,A,D) ) ) ) ) )).
fof(t36_finseq_6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) = k1_nat_1(k3_finseq_1(B),1) ) ) ) )).
fof(t36_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( 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] : ( ( 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))) ) ) ) ) ) ) ) ) )).
fof(t36_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ( v2_fintopo2(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k10_fintopo2(A,B),B) ) ) ) )).
fof(t36_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_orders_2(A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_tarski(B,k7_fintopo3(A,B,C)) ) ) ) ) )).
fof(t36_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t36_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k2_flang_1(A),B) => ( r1_xxreal_0(D,C) | r1_tarski(k7_flang_1(A,B,C),k7_flang_1(A,B,D)) ) ) ) ) ) )).
fof(t36_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) )).
fof(t36_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) )).
fof(t36_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_relat_1(D) & v5_relat_1(D,B) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( 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)) ) ) ) ) )).
fof(t36_frechet,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(A,k7_xcmplx_0(1,B)) & ~ r1_xxreal_0(B,k5_numbers) ) ) ) ) )).
fof(t36_fsm_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ 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,k1_nat_1(A,1)) = k6_fsm_1(B,C,D,A) ) ) ) ) ) )).
fof(t36_fsm_3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(B)) => ! [D] : ( ( ~ 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)) ) ) ) )).
fof(t36_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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))) ) ) ) ) ) ) )).
fof(t36_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t36_funct_1,axiom,( ! [A] : ( ( 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) ) ) ) )).
fof(t36_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => r1_tarski(k7_relset_1(B,C,D,A),C) ) )).
fof(t36_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ( k1_funct_1(k4_funct_3(A,B),C) = 1 => r2_hidden(C,A) ) )).
fof(t36_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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 ) ) ) )).
fof(t36_funct_5,axiom,( k2_funct_5(k1_xboole_0) = k1_xboole_0 & k4_funct_5(k1_xboole_0) = k1_xboole_0 )).
fof(t36_funct_6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( A != k1_xboole_0 => ( k9_xtuple_0(k5_funct_6(k7_funcop_1(A,B))) = k9_xtuple_0(B) & ! [C] : ( r2_hidden(C,k9_xtuple_0(B)) => k1_funct_1(k5_funct_6(k7_funcop_1(A,B)),C) = k7_funcop_1(A,k1_funct_1(B,C)) ) ) ) ) )).
fof(t36_funct_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(B)) => ( D = E | k7_partfun1(A,k2_funct_7(A,B,D,C),E) = k7_partfun1(A,B,E) ) ) ) ) ) ) ) )).
fof(t36_funct_8,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t36_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ v8_ordinal1(C) & v1_int_1(C) ) => v1_funct_9(k15_valued_1(k1_numbers,k1_numbers,k26_valued_1(k1_numbers,k1_numbers,k18_sin_cos,A),B),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)) ) ) ) )).
fof(t36_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t36_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v11_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,B,C) & m2_functor0(E,B,C) ) => ! [F] : ( ( v15_functor0(F,B,C) & m2_functor0(F,B,C) ) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t36_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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)) ) ) ) ) )).
fof(t36_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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)))) ) ) ) )).
fof(t36_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( C != k4_struct_0(A) & ! [D] : ( v1_int_1(D) => k3_funct_2(u1_struct_0(A),k6_numbers,B,C) != k4_xxreal_3(D,k1_fvaluat1(k2_relset_1(k6_numbers,B))) ) ) ) ) ) ) )).
fof(t36_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( 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 ) ) ) )).
fof(t36_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ~ 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) ) ) )).
fof(t36_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t36_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v2_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ! [F] : ( m1_genealg1(F,E) => ! [G] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t36_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( v1_xreal_0(I) => ( ( r2_geomtrap(A,B,C,D,E,F,G) & I = k3_xcmplx_0(k6_xcmplx_0(k4_geomtrap(A,B,C,k5_algstr_0(A,D,E),k3_rlvect_1(A,D,E)),k3_xcmplx_0(2,k4_geomtrap(A,B,C,k5_algstr_0(A,D,E),F))),k5_xcmplx_0(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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t36_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t36_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( r1_tarski(B,C) => r1_tarski(k21_glib_000(A,B),k21_glib_000(A,C)) ) ) )).
fof(t36_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ! [E] : ( ( ~ v1_abian(E) & m1_subset_1(E,k4_ordinal1) ) => ( ( r1_xxreal_0(C,D) & r1_xxreal_0(D,E) & r1_xxreal_0(E,k3_finseq_1(B)) ) => r2_relset_1(k4_ordinal1,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)) ) ) ) ) ) ) )).
fof(t36_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,k6_glib_000(A)) & ? [C] : ( m1_subset_1(C,k6_glib_000(A)) & B != C & ~ v5_glib_002(B,A) & ~ v5_glib_002(C,A) ) ) ) )).
fof(t36_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_003(A) & v3_glib_003(A) ) => ! [B] : ! [C] : k7_glib_003(A) = k7_glib_003(k12_glib_003(A,B,C)) ) )).
fof(t36_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( 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))) = k4_nat_1(k1_nat_1(B,1),k5_card_1(k1_glib_002(A,o_1_1_glib_004(A)))) ) ) )).
fof(t36_goboard6,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_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_0(u1_struct_0(k15_euclid(2)),A,1,1),k19_euclid(1,1)),k1_tops_1(k15_euclid(2),k3_goboard5(A,k5_numbers,k5_numbers))) ) )).
fof(t36_goboard7,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( 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) ) ) ) ) )).
fof(t36_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ( m2_finseq_1(D,C) => ! [E] : ( ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(C)) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,2),B) & r1_gobrd13(C,k17_finseq_1(C,B,D),E,A) ) => r1_gobrd13(C,D,E,A) ) ) ) ) ) )).
fof(t36_gobrd14,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t36_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( 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)))) ) ) ) ) )).
fof(t36_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t36_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_graph_1(D,A) => ! [E] : ( m2_finseq_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t36_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v7_graph_1(B,A) & m2_graph_1(B,A) ) => r1_tarski(k6_graph_5(A,B),k7_graph_5(A)) ) ) )).
fof(t36_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( 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,k2_nat_1(3,B)) ) | k1_funct_1(k6_graphsp(k18_graphsp(B),C),A) = k1_funct_1(C,A) ) ) ) ) ) )).
fof(t36_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => r2_hidden(k3_algstr_0,k26_grcat_1(A)) ) )).
fof(t36_groeb_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( ~ v1_xboole_0(D) & v1_ideal_1(D,k12_polynom1(A,C)) & v2_ideal_1(D,k12_polynom1(A,C)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ~ ( D != k1_groeb_1(A,C,k8_polynom1(A,C)) & ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ~ ( r2_groeb_1(A,B,C,E,D) & ~ r2_hidden(k8_polynom1(A,C),E) ) ) ) ) ) ) ) )).
fof(t36_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(D,A,C) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ! [F] : ( m2_ideal_1(F,k12_polynom1(A,C),E) => ~ ( r2_groeb_2(A,C,D,E,F) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ! [H] : ( ( 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] : ( ( v1_funct_1(I) & v1_funct_2(I,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(I,A,C) & v1_polynom1(I,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) = k10_polynom1(A,C,H,I) & r1_termord(A,B,k3_termord(A,B,C,D),k3_termord(A,B,C,k10_polynom1(A,C,H,I))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t36_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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)) ) ) ) ) ) )).
fof(t36_group_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(t36_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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)) ) ) ) )).
fof(t36_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t36_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t36_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ~ v1_group_4(k1_group_1(A),A) ) )).
fof(t36_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t36_group_6,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & l3_algstr_0(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t36_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & l3_algstr_0(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t36_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t36_groupp_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t36_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => k1_hausdorf(A,B,B) = k5_numbers ) ) )).
fof(t36_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t36_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( ( 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))) ) ) ) ) ) ) ) )).
fof(t36_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k4_yellow_0(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A))) = k1_tarski(k1_xboole_0) ) )).
fof(t36_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(A,D) => ( r1_xxreal_0(B,C) | k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k1_taylor_1(B),D),C),A) = k3_xcmplx_0(k3_xcmplx_0(k4_newton(C,B),k2_newton(C)),k3_prepower(A,k6_xcmplx_0(B,C))) ) ) ) ) ) ) )).
fof(t36_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => r2_hidden(k3_hilbert1(k4_hilbert1(k3_hilbert1(A,B),A),B),k6_hilbert1) ) ) )).
fof(t36_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ~ ( r2_hidden(A,k6_trees_2(k1_hilbert1,k3_hilbert2(B))) & A != k2_hilbert1 & ~ v3_hilbert2(A) ) ) ) )).
fof(t36_hilbert3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( m1_hilbert3(D,C) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t36_hurwitz,axiom,( ! [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) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t36_idea_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k4_ordinal1,B,6) & m2_finseq_1(C,k3_finseq_2(k4_ordinal1)) ) => ! [D] : ( v7_ordinal1(D) => k17_idea_1(k1_nat_1(D,1),B,A,C) = k7_finseq_1(k17_idea_1(D,B,A,C),k9_finseq_1(k15_idea_1(A,k7_matrix_0(k4_ordinal1,C,k1_nat_1(D,1))))) ) ) ) ) )).
fof(t36_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l4_algstr_0(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( m1_ideal_1(D,A,C) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) ) => ! [F] : ( ( 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] : ( 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] : ( m1_ideal_1(H,B,E) => ~ ( k3_finseq_1(D) = k3_finseq_1(H) & ! [I] : ( r2_hidden(I,k1_relset_1(k4_ordinal1,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)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t36_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t36_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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] : ( m4_index_1(C,u1_struct_0(A),u4_struct_0(A),u1_graph_1(A),u2_graph_1(A),B) => ! [D] : ( 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] : ( m4_index_1(E,u1_struct_0(C),u4_struct_0(C),u1_graph_1(C),u2_graph_1(C),D) => ! [F] : ( ( ~ 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t36_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( 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] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r3_pua2mss1(B,A,D,E) => ! [F] : ( ( v4_msualg_1(F,B) & l3_msualg_1(F,B) ) => ( F = k1_instalg1(B,A,C,D,E) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ! [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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t36_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => r1_xxreal_0(k1_int_1(A),k2_int_1(A)) ) )).
fof(t36_int_5,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t36_int_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t36_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(A,B) & D = k1_taylor_1(2) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => ( k1_funct_1(E,F) = 1 & F != k5_numbers & k1_funct_1(C,F) = k7_xcmplx_0(k3_xcmplx_0(2,F),k1_square_1(k2_xcmplx_0(1,k1_square_1(F)))) ) ) ) & k9_xtuple_0(k3_rfunct_1(k1_numbers,k1_numbers,D,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,E,D))) = B & B = k9_xtuple_0(C) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,A)) ) => k2_integra5(A,C) = k6_xcmplx_0(k1_funct_1(k3_rfunct_1(k1_numbers,k1_numbers,D,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,E,D)),k2_seq_4(A)),k1_funct_1(k3_rfunct_1(k1_numbers,k1_numbers,D,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,E,D)),k3_seq_4(A))) ) ) ) ) ) ) )).
fof(t36_integr12,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => ( k1_funct_1(B,D) = k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(D,k2_xcmplx_0(1,k1_square_1(k1_funct_1(k3_taylor_1,D)))))) & ~ r1_xxreal_0(k1_funct_1(k3_taylor_1,D),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_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) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k2_sin_cos9),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k2_sin_cos9),k3_seq_4(A))) ) ) ) ) )).
fof(t36_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k7_xcmplx_0(1,k3_xcmplx_0(k1_square_1(D),k1_square_1(k1_funct_1(k16_sin_cos,k7_xcmplx_0(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)),k27_sin_cos))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,C)),k27_sin_cos),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,C)),k27_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t36_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,D),k1_funct_1(k16_sin_cos,k1_funct_1(k16_sin_cos,D))),k1_square_1(k1_funct_1(k18_sin_cos,k1_funct_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) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k1_fdiff_9),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k1_fdiff_9),k3_seq_4(A))) ) ) ) ) )).
fof(t36_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( ( 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] : ( m1_integra1(E,B) => ! [F] : ( m2_finseq_1(F,k1_euclid(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t36_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [C] : ( m1_integra1(C,A) => ! [D] : ( ( 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] : ( ( ~ v8_ordinal1(E) & m1_subset_1(E,k4_ordinal1) ) => ( 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)))) ) ) ) ) ) ) ) )).
fof(t36_integra2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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_comseq_2(k2_partfun1(A,k1_numbers,B,A)) => v4_xxreal_2(k1_rvsum_1(k9_integra1(A,B))) ) ) ) )).
fof(t36_integra8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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) ) ) ) )).
fof(t36_integra9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( B = k1_rcomp_1(k3_xcmplx_0(k3_xcmplx_0(2,A),k28_sin_cos),k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(2,A),1),k28_sin_cos)) => r1_integra9(B,k16_sin_cos,k18_sin_cos) ) ) ) )).
fof(t36_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_interva1(C,A) ) => r1_interva1(A,k4_interva1(A,k3_interva1(A,B,C),C),C) ) ) ) )).
fof(t36_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(t36_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(A,B) => v1_int_1(k7_xcmplx_0(k7_newton(B),k7_newton(A))) ) ) ) )).
fof(t36_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ! [E] : ( 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,A,B,k10_cat_1(A),k10_cat_1(A),C,D,k4_nattra_1(A,A,k10_cat_1(A)),E),E) ) ) ) ) ) ) )).
fof(t36_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,A,C) => ! [G] : ( m2_cat_1(G,A,C) => ( ( r2_nattra_1(A,B,D,E) & r2_nattra_1(A,C,F,G) ) => r2_nattra_1(A,k6_cat_2(B,C),k8_isocat_2(A,B,C,D,F),k8_isocat_2(A,B,C,E,G)) ) ) ) ) ) ) ) ) )).
fof(t36_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( ~ v3_isomichi(B,A) & ~ v4_isomichi(B,A) & ~ v5_isomichi(B,A) ) ) ) )).
fof(t36_jgraph_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [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)) ) => ( B = k1_xboole_0 | C = k1_xboole_0 | r1_xxreal_0(k5_numbers,k7_weierstr(A,B,C)) ) ) ) ) ) )).
fof(t36_jgraph_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( 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] : ( 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) = k3_xcmplx_0(k17_euclid(C),k3_square_1(k2_xcmplx_0(1,k1_square_1(k7_xcmplx_0(k17_euclid(C),k18_euclid(C)))))) ) ) & ! [C] : ( 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) = k5_numbers ) ) ) => v5_pre_topc(B,k1_pre_topc(k15_euclid(2),A),k3_topmetr) ) ) ) )).
fof(t36_jgraph_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( r1_xxreal_0(A,B) & ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(k2_xcmplx_0(k3_xcmplx_0(D,A),C),k2_xcmplx_0(k3_xcmplx_0(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(k2_xcmplx_0(k3_xcmplx_0(D,A),C),k2_xcmplx_0(k3_xcmplx_0(D,B),C)))))) ) => ~ ( v3_tops_2(E,k4_topmetr(A,B),k4_topmetr(k2_xcmplx_0(k3_xcmplx_0(D,A),C),k2_xcmplx_0(k3_xcmplx_0(D,B),C))) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,k1_rcomp_1(A,B)) => k1_funct_1(E,F) = k2_xcmplx_0(k3_xcmplx_0(D,F),C) ) ) ) ) ) ) ) ) ) )).
fof(t36_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t36_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t36_jordan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_borsuk_2(E,A,C,D) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(t36_jordan1,axiom,( ! [A] : ( 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ? [D] : ( 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] : ( 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] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t36_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_jordan1h(A,B) & r1_xxreal_0(B,C) ) => r1_tarski(k2_goboard9(k1_jordan13(A,C)),k2_goboard9(k1_jordan13(A,B))) ) ) ) ) )).
fof(t36_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C)),k3_topreal1(2,k1_jordan1e(B,A))) = k1_tarski(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C)),k3_topreal1(2,k2_jordan1e(B,A))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C)) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C)),k9_jordan6(B)) ) ) ) ) ) ) )).
fof(t36_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ 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,D))) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(k1_jordan8(E,C))) ) => ( ( ~ ( ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(C,k5_numbers) ) & ~ ( D = k5_numbers & C = k5_numbers ) ) | k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,D),k1_jordan1a(k1_jordan8(E,D)),A)) = k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,C),k1_jordan1a(k1_jordan8(E,C)),B)) ) ) ) ) ) ) ) )).
fof(t36_jordan1b,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( 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)) ) ) ) ) )).
fof(t36_jordan1g,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(k1_jordan8(A,B))) ) => ( r1_xxreal_0(B,k5_numbers) | k18_euclid(k3_matrix_0(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) ) ) ) ) ) )).
fof(t36_jordan1h,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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,C) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k3_finseq_1(k1_jordan8(D,C))) ) => ( r1_xxreal_0(1,k1_int_1(k2_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(B,2),k11_newton(2,k7_nat_d(C,A))),2))) & r1_xxreal_0(k2_xcmplx_0(k1_int_1(k2_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(B,2),k11_newton(2,k7_nat_d(C,A))),2)),1),k3_finseq_1(k1_jordan8(D,A))) ) ) ) ) ) ) )).
fof(t36_jordan1j,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t36_jordan1k,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(C,k5_numbers) & ~ v2_funct_2(k2_jgraph_2(A,B,C,D),u1_struct_0(k15_euclid(2))) ) ) ) ) ) )).
fof(t36_jordan21,axiom,( ! [A] : ( ( 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))) ) )).
fof(t36_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => r1_tarski(k4_jordan19(A),A) ) )).
fof(t36_jordan23,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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,k1_nat_1(k1_jordan3(A,B),1)) ) => ( B = k1_funct_1(A,k3_finseq_1(A)) | k1_nat_1(k1_nat_1(k1_jordan3(k4_finseq_5(u1_struct_0(k15_euclid(2)),A),B),k1_jordan3(A,B)),1) = k3_finseq_1(A) ) ) ) ) )).
fof(t36_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( 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] : ( v1_xreal_0(F) => ( D != k1_rlvect_1(k15_euclid(A),E,F) & E != k1_rlvect_1(k15_euclid(A),D,F) ) ) & ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(A))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(A))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k15_euclid(A))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k15_euclid(A))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t36_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t36_jordan4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( v2_funct_1(B) <=> ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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(B,C) != k1_funct_1(B,D) & k7_partfun1(A,B,C) != k7_partfun1(A,B,D) ) | C = D ) ) ) ) ) ) ) )).
fof(t36_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( 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_0(k2_goboard2(A))) & ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ~ ( k18_euclid(D) = k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),B,C)) & r2_hidden(D,k3_topreal1(2,A)) ) ) ) ) ) ) )).
fof(t36_jordan6,axiom,( ! [A] : ( 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(k5_numbers,1)) => ( A != k1_xboole_0 & v2_connsp_1(A,k17_borsuk_1) ) ) ) )).
fof(t36_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_jordan_a(B,A) => ~ r1_xxreal_0(k5_jordan_a(A,B),k5_numbers) ) ) )).
fof(t36_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t36_kurato_1,axiom,( k1_tops_1(k3_topmetr,k2_pre_topc(k3_topmetr,k6_kurato_1)) != k1_tops_1(k3_topmetr,k6_kurato_1) )).
fof(t36_kurato_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))))) ) => ( ! [D] : ( v7_ordinal1(D) => k2_kurato_2(k15_euclid(2),C,D) = k9_subset_1(u1_struct_0(k15_euclid(2)),k2_kurato_2(k15_euclid(2),A,D),k2_kurato_2(k15_euclid(2),B,D)) ) => r1_tarski(k3_kurato_2(k15_euclid(2),C),k9_subset_1(u1_struct_0(k15_euclid(2)),k3_kurato_2(k15_euclid(2),A),k3_kurato_2(k15_euclid(2),B))) ) ) ) ) )).
fof(t36_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v1_matrix_6(C,A,B) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(D,E),k2_matrix_0(k1_matrix_6(A,B,C))) => k3_matrix_0(u1_struct_0(B),k1_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)) ) ) ) ) ) ) ) )).
fof(t36_lattice2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( m1_subset_1(C,k5_finsub_1(A)) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t36_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ( v6_lattice3(A) <=> ! [B] : ! [C] : ( 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))) ) ) ) )).
fof(t36_lattice4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v17_lattices(B) & l3_lattices(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,k4_lattice4(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k4_filter_0(B,D,E) & r2_hidden(D,C) & r2_hidden(E,C) ) ) ) ) ) )).
fof(t36_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( v3_ordinal1(C) => ! [D] : ( ( 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] : ( 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)))) ) ) ) ) ) ) ) )).
fof(t36_lattice8,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t36_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( v7_ordinal1(B) => ( k1_relset_1(k6_glib_000(A),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),k13_lexbfs(A,k16_lexbfs(A),B))) = k6_glib_000(A) <=> r1_xxreal_0(k15_glib_000(A),B) ) ) ) )).
fof(t36_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(A) & k1_seq_2(A) = k5_numbers ) => ( ! [B] : ( v7_ordinal1(B) => ? [C] : ( v7_ordinal1(C) & r1_xxreal_0(B,C) & r1_xxreal_0(k5_numbers,k1_funct_1(A,C)) ) ) | v2_limfunc1(k37_valued_1(k4_ordinal1,k1_numbers,A)) ) ) ) )).
fof(t36_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r6_limfunc2(C,A) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(D,E) & ~ r1_xxreal_0(E,A) & r2_hidden(E,k1_relset_1(k1_numbers,B)) ) ) ) ) ) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(A,k2_xcmplx_0(A,D))),k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,C),k2_rcomp_1(A,k2_xcmplx_0(A,D)))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(A,k2_xcmplx_0(A,D)))) => r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) | r6_limfunc2(B,A) ) ) ) ) ) )).
fof(t36_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) = k9_complex1(k1_limfunc3(B,A)) ) ) ) ) )).
fof(t36_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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) ) ) ) ) )).
fof(t36_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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)) ) ) ) ) )).
fof(t36_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k16_lopban_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k16_lopban_1(A,B))) => ! [E] : ( v1_xreal_0(E) => ( D = k1_rlvect_1(k16_lopban_1(A,B),C,E) <=> ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t36_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [D] : ( v7_ordinal1(D) => ( k5_rsspace3(A,B,D) != k4_struct_0(A) & k9_nat_1(k1_numbers,C,D) = k6_real_1(k9_nat_1(k1_numbers,k5_normsp_0(A,B),k1_nat_1(D,1)),k9_nat_1(k1_numbers,k5_normsp_0(A,B),D)) ) ) & v2_comseq_2(C) ) => ( r1_xxreal_0(1,k1_seq_2(C)) | v2_lopban_3(B,A) ) ) ) ) ) )).
fof(t36_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t36_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v7_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ? [B] : ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) & r1_filter_1(A,k6_lopclset(B)) ) ) )).
fof(t36_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( ( r2_hidden(D,k13_lpspacc1(A,B,C)) & r2_hidden(E,k13_lpspacc1(A,B,C)) & r1_lpspacc1(A,B,C,D,E) ) => k1_mesfun6c(A,B,C,D) = k1_mesfun6c(A,B,C,E) ) ) ) ) ) ) )).
fof(t36_lpspace1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,C,k6_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,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t36_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( v2_xxreal_0(F) & v1_xreal_0(F) ) => ( ( r2_hidden(E,k1_lpspace2(A,B,C,F)) & r1_lpspace1(A,B,C,E,D) ) => r2_hidden(E,k5_lpspace2(A,B,C,D,F)) ) ) ) ) ) ) ) )).
fof(t36_ltlaxio1,axiom,( ! [A] : ( 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) ) ) )).
fof(t36_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(k1_ltlaxio1(k5_ltlaxio1(A,B)),k4_ltlaxio1(k1_ltlaxio1(A),k1_ltlaxio1(B)))) ) ) )).
fof(t36_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t36_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k4_subset_1(u1_struct_0(A),k3_mathmorp(A,D,B),k3_mathmorp(A,D,C)),k3_mathmorp(A,D,k9_subset_1(u1_struct_0(A),B,C))) ) ) ) ) )).
fof(t36_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( v4_matrix10(B) & v4_matrix10(C) ) => v4_matrix10(k4_matrix10(A,B,C)) ) ) ) ) )).
fof(t36_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( m2_finseq_1(D,u1_struct_0(C)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(C)) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(C),B,B) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(C))) ) => ( ( 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))) ) ) ) ) ) ) ) )).
fof(t36_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( m2_finseq_2(D,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [F] : ( m2_finseq_2(F,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [G] : ( m2_finseq_2(G,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ~ ( 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))) ) ) ) ) ) ) ) ) )).
fof(t36_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( 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) ) ) ) ) )).
fof(t36_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(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)) ) ) ) ) ) )).
fof(t36_matrix16,axiom,( ! [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] : ( 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)) = k2_matrix_3(A,k2_matrix16(u1_struct_0(A),B)) ) ) ) )).
fof(t36_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ! [D] : ( ( v1_matrix_0(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_0(D) ) ) ) ) ) )).
fof(t36_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(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_0(B)) => B = k1_matrix_3(A,k3_finseq_1(B),k1_matrix_0(B)) ) ) ) )).
fof(t36_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_6(C,A,B) & v1_matrix_6(D,A,B) ) => ( v1_matrix_6(k4_matrix_3(B,C,D),A,B) & k1_matrix_6(A,B,k4_matrix_3(B,C,D)) = k4_matrix_3(B,k1_matrix_6(A,B,D),k1_matrix_6(A,B,C)) ) ) ) ) ) ) )).
fof(t36_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( r1_matrix_8(A,B,C,D) & v2_matrix_8(D,A,B) ) => ( r1_xxreal_0(A,k5_numbers) | v2_matrix_8(C,A,B) ) ) ) ) ) ) )).
fof(t36_matrix_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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)) ) ) )).
fof(t36_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( 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)) ) ) ) )).
fof(t36_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_matrixj1(C,A) & m2_finseq_1(C,k3_finseq_2(k3_finseq_2(A))) ) => ! [D] : ( ( 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)))) ) ) ) ) )).
fof(t36_matrixr1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(C) = A & k1_matrix_0(C) = B ) => ( r1_xxreal_0(A,k5_numbers) | ( k3_matrixr1(C,k8_matrixr1(A,B)) = C & k3_matrixr1(k8_matrixr1(A,B),C) = C ) ) ) ) ) ) )).
fof(t36_matrixr2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,A,B,B) & m2_finseq_1(C,k3_finseq_2(A)) ) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( v7_ordinal1(E) => ( ( D = k1_funct_1(C,E) & r2_hidden(E,k2_finseq_1(B)) ) => k3_finseq_1(D) = B ) ) ) ) ) ) )).
fof(t36_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_matrlin(C,A,B) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t36_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( m1_matrlin(D,A,B) => ! [E] : ( m1_matrlin(E,A,C) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(A),k3_finseq_1(D),k3_finseq_1(E)) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(A))) ) => k1_matrlin2(A,B,C,k4_matrlin2(A,B,C,D,E,F),D,E) = F ) ) ) ) ) ) )).
fof(t36_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,k6_matroid0(A,k4_subset_1(u1_struct_0(A),B,k6_domain_1(u1_struct_0(A),C)))) => ( r2_hidden(D,k6_matroid0(A,B)) | r2_hidden(C,k6_matroid0(A,k4_subset_1(u1_struct_0(A),B,k6_domain_1(u1_struct_0(A),D)))) ) ) ) ) ) ) )).
fof(t36_matrprob,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k2_vectsp_1)) => ( A = B => k18_rvsum_1(A) = k4_rlvect_1(k2_vectsp_1,B) ) ) ) )).
fof(t36_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_card_1(D,A) & v1_finseq_1(D) & v3_valued_0(D) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(k2_vectsp_1),C,B) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t36_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ~ 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) ) ) )).
fof(t36_measure1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( m2_measure1(E,A,B,C) => ( r1_tarski(D,E) => m2_measure1(D,A,B,C) ) ) ) ) ) )).
fof(t36_measure6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k2_xcmplx_0(k9_complex1(A),k9_complex1(B)) = k5_numbers => A = k5_numbers ) ) ) )).
fof(t36_member_1,axiom,( ! [A] : ( v1_membered(A) => k5_member_1(k7_member_1(A)) = k7_member_1(k5_member_1(A)) ) )).
fof(t36_membered,axiom,( ! [A] : ! [B] : ( ( r2_hidden(B,A) & v6_membered(B) ) => v6_membered(k1_setfam_1(A)) ) )).
fof(t36_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t36_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( 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] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t36_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ! [D] : ( ( 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,k5_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)) ) ) ) ) ) )).
fof(t36_mesfunc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( v1_xreal_0(F) => ( ( 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,F)),k17_mesfunc1(A,D,F)),B) ) ) ) ) ) ) ) )).
fof(t36_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( ( v1_prob_2(E) & m2_finseq_1(E,B) ) => ! [F] : ( ( v1_prob_2(F) & m2_finseq_1(F,B) ) => ! [G] : ( m2_finseq_1(G,k6_numbers) => ( ( k1_relset_1(k4_ordinal1,E) = k1_relset_1(k4_ordinal1,F) & ! [H] : ( v7_ordinal1(H) => ( r2_hidden(H,k1_relset_1(k4_ordinal1,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,k6_numbers,C,D),F,G) ) ) ) ) ) ) ) ) )).
fof(t36_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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))) ) ) ) )).
fof(t36_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k2_metric_2(A)) => ! [C] : ( m1_subset_1(C,k2_metric_2(A)) => ! [D] : ( m1_subset_1(D,k2_metric_2(A)) => r1_xxreal_0(k2_binop_1(k2_metric_2(A),k2_metric_2(A),k1_numbers,k10_metric_2(A),B,D),k2_xcmplx_0(k2_binop_1(k2_metric_2(A),k2_metric_2(A),k1_numbers,k10_metric_2(A),B,C),k2_binop_1(k2_metric_2(A),k2_metric_2(A),k1_numbers,k10_metric_2(A),C,D))) ) ) ) ) )).
fof(t36_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t36_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ! [D] : ( r2_hidden(k4_tarski(C,D),k18_mmlquery(A,B)) <=> ( C = D & r2_hidden(C,A) & ~ r2_hidden(C,k1_relset_1(A,B)) ) ) ) )).
fof(t36_mod_4,axiom,( ! [A] : ( ( ~ 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] : ( ( 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)) ) ) ) )).
fof(t36_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k48_modelc_1(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k48_modelc_1(A,B,C))) => ( ! [G] : ( m1_subset_1(G,A) => ( r3_modelc_1(A,B,C,G,E) => r3_modelc_1(A,B,C,G,F) ) ) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t36_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( ( r2_modelc_2(A,B) & r2_modelc_2(B,A) ) => A = B ) ) ) )).
fof(t36_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r1_xxreal_0(1,B) => ( v1_moebius1(k3_xcmplx_0(B,A)) | k2_moebius1(k3_xcmplx_0(B,A)) = k4_xcmplx_0(k2_moebius1(B)) ) ) ) ) )).
fof(t36_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t36_monoid_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => k15_monoid_1(A,k20_monoid_1(A,k6_finseq_1(A)),B) = k5_numbers ) ) )).
fof(t36_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [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] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( k1_funct_1(B,C) = k1_xboole_0 & ! [D] : ( 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) ) ) ) )).
fof(t36_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( m3_pboole(D,u1_struct_0(A),k4_equation(A)) => ( r2_equation(A,B,D) => r2_equation(A,C,D) ) ) ) ) ) )).
fof(t36_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( 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] : ( m2_pboole(E,u1_struct_0(A),C,u3_msualg_1(A,B)) => ? [F] : ( v1_relat_1(F) & v1_funct_1(F) & v1_finset_1(F) & v3_trees_2(F) & r1_msaterm(A,B,C,D,E,F) ) ) ) ) ) ) )).
fof(t36_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m3_pboole(D,A,k1_mboolean(A,C)) => m3_pboole(k4_pboole(A,D,B),A,k1_mboolean(A,C)) ) ) ) )).
fof(t36_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t36_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t36_mycielsk,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => k3_mycielsk(k5_mycielsk(A)) = 1 ) )).
fof(t36_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,C))) ) => r2_funct_2(k4_ordinal1,C,k8_nat_1(C,k8_nat_1(C,D,A),B),k8_nat_1(C,D,k2_xcmplx_0(A,B))) ) ) ) ) )).
fof(t36_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,k13_pre_poly(k12_nat_3(B))) => r1_nat_d(A,B) ) ) ) )).
fof(t36_nat_4,axiom,( v1_int_2(317) )).
fof(t36_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => v1_nat_5(k4_nat_5(A)) ) )).
fof(t36_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k7_nat_d(A,B) = k5_numbers => r1_xxreal_0(A,B) ) ) ) )).
fof(t36_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => k10_nattra_1(k6_cat_2(A,B)) = k6_cat_2(k10_nattra_1(A),k10_nattra_1(B)) ) ) )).
fof(t36_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ( r2_ncfcont1(A,B,C,D) => r2_ncfcont1(A,B,k4_vfunct_1(u1_struct_0(A),B,C,E),D) ) ) ) ) ) ) )).
fof(t36_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t36_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r1_ndiff_1(A,B,C,E) & r1_ndiff_1(A,B,D,E) ) => ( r1_ndiff_1(A,B,k2_vfunct_1(u1_struct_0(A),B,C,D),E) & k3_ndiff_1(A,B,k2_vfunct_1(u1_struct_0(A),B,C,D),E) = k5_algstr_0(k16_lopban_1(A,B),k3_ndiff_1(A,B,C,E),k3_ndiff_1(A,B,D,E)) ) ) ) ) ) ) ) )).
fof(t36_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(1))) => ! [D] : ( m1_subset_1(D,k1_numbers) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t36_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k11_prvect_2(A,B))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t36_neckla_3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t36_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( A != k5_numbers & r1_xxreal_0(k7_xcmplx_0(k1_nat_1(A,1),A),1) ) ) )).
fof(t36_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( D != k1_xboole_0 & r1_tarski(D,k1_relset_1(u1_struct_0(A),C)) & v1_nfcont_1(D,A) & r3_nfcont_1(A,B,C,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_hidden(E,D) & r2_hidden(F,D) & k7_partfun1(k1_numbers,k4_normsp_0(u1_struct_0(A),B,C),E) = k2_seq_4(k7_relset_1(u1_struct_0(A),k1_numbers,k4_normsp_0(u1_struct_0(A),B,C),D)) & k7_partfun1(k1_numbers,k4_normsp_0(u1_struct_0(A),B,C),F) = k3_seq_4(k7_relset_1(u1_struct_0(A),k1_numbers,k4_normsp_0(u1_struct_0(A),B,C),D)) ) ) ) ) ) ) ) ) )).
fof(t36_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ! [D] : ( ( 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) ) ) ) )).
fof(t36_normform,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [C] : ( m2_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t36_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(t36_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t36_openlatt,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t36_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_oppcat_1(C,k2_oppcat_1(B),A) => m2_cat_1(k9_oppcat_1(B,A,C),B,A) ) ) ) )).
fof(t36_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(A))) => ! [F] : ( ( v1_funct_1(F) & v1_nfcont_3(F,k4_real_ns1(A)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [G] : ( ( 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) & k1_relset_1(k1_numbers,F) = k3_integra5(B,C) & k1_relset_1(k1_numbers,G) = k3_integra5(B,C) & D = k2_rcomp_1(B,C) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,k3_integra5(B,C)) => k1_funct_1(G,H) = k3_rlvect_1(k4_real_ns1(A),E,k6_integr18(k4_real_ns1(A),F,B,H)) ) ) ) => ( v1_nfcont_3(G,k4_real_ns1(A)) & k7_partfun1(u1_struct_0(k4_real_ns1(A)),G,B) = E & r2_ndiff_3(k4_real_ns1(A),G,D) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,D) => k1_ndiff_3(k4_real_ns1(A),G,H) = k7_partfun1(u1_struct_0(k4_real_ns1(A)),F,H) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t36_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r2_orders_1(A,B) => v2_orders_1(k2_wellord1(A,B)) ) ) )).
fof(t36_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m2_orders_1(B,k1_orders_1(u1_struct_0(A)),k6_partfun1(k1_orders_1(u1_struct_0(A)))) => m2_orders_2(k1_tarski(k1_funct_1(B,u1_struct_0(A))),A,B) ) ) )).
fof(t36_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => k11_ordinal2(k1_ordinal1(B),A) = k10_ordinal2(k11_ordinal2(B,A),A) ) ) )).
fof(t36_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( B != k1_xboole_0 => ( r1_ordinal1(A,k11_ordinal2(A,B)) & r1_ordinal1(A,k11_ordinal2(B,A)) ) ) ) ) )).
fof(t36_ordinal6,axiom,( ! [A] : ! [B] : ( ( 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] : ~ ( r2_hidden(C,A) & ! [D] : ~ ( 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)) ) ) ) )).
fof(t36_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ! [F] : ( ( 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 ) ) ) ) ) ) )).
fof(t36_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t36_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & l1_parsp_1(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = C ) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => r1_parsp_1(A,B,C,D,E) ) ) ) ) ) ) )).
fof(t36_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_parsp_2(A,B,C,D,E) & r1_parsp_1(A,B,E,C,D) ) ) ) ) ) ) )).
fof(t36_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r1_tarski(k3_xboole_0(k10_xtuple_0(D),k9_xtuple_0(E)),B) => k1_partfun1(A,B,B,C,k3_partfun1(D,A,B),k3_partfun1(E,B,C)) = k3_partfun1(k3_relat_1(D,E),A,C) ) ) ) )).
fof(t36_partfun2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ( v3_funct_1(k2_partfun1(B,C,D,A)) <=> ! [E] : ( m1_subset_1(E,B) => ! [F] : ( m1_subset_1(F,B) => ( ( r2_hidden(E,k9_subset_1(B,A,k1_relset_1(B,D))) & r2_hidden(F,k9_subset_1(B,A,k1_relset_1(B,D))) ) => k7_partfun1(C,D,E) = k7_partfun1(C,D,F) ) ) ) ) ) ) ) )).
fof(t36_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ( k3_partit1(A,k6_partit1(A),B) = k6_partit1(A) & k2_partit1(A,k6_partit1(A),B) = B ) ) ) )).
fof(t36_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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))) ) ) ) )).
fof(t36_pcomps_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t36_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ( l2_pcs_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k22_pcs_0(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k22_pcs_0(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( 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,E,F) & r1_orders_2(B,G,H) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t36_pdiff_3,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(2)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t36_pdiff_4,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t36_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( 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) = k10_pdiff_1(3,3,k1_pdiff_3(3,3,B),A) ) ) ) )).
fof(t36_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [D] : ( 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] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( 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)))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t36_pdiff_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( 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,k9_complex1(k5_real_1(k7_partfun1(k1_numbers,B,F),k7_partfun1(k1_numbers,B,C)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t36_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(A,k5_numbers) => k4_nat_d(k1_newton(B,A),B) = k5_numbers ) ) ) )).
fof(t36_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m3_pnproc_1(C,A,B) => ! [D] : ( m3_pnproc_1(D,A,B) => ! [E] : ( m3_pnproc_1(E,A,B) => k11_pnproc_1(A,B,k7_domain_1(k3_finseq_2(B),k3_pre_poly(B,D),k3_pre_poly(B,E)),k6_domain_1(k3_finseq_2(B),k3_pre_poly(B,C))) = k9_domain_1(k3_finseq_2(B),k4_pre_poly(B,D,C),k4_pre_poly(B,E,C),k4_pre_poly(B,C,D),k4_pre_poly(B,C,E)) ) ) ) ) )).
fof(t36_polyeq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( m1_comptrig(B,A,1) => B = A ) ) )).
fof(t36_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k17_polyform(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k17_polyform(A,B))) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t36_polynom8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(B,k5_numbers) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(A),B,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(A),B,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(A),B,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(A))) ) => ( ! [F] : ( v7_ordinal1(F) => ! [G] : ( 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_0(u1_struct_0(A),k4_matrix_3(A,C,D),F,G) = k8_group_1(A,k1_polynom8(A,B),k3_matrix_0(u1_struct_0(A),E,F,G)) ) ) ) => k4_matrix_3(A,C,D) = k6_matrix_3(A,E,k1_polynom8(A,B)) ) ) ) ) ) ) ) )).
fof(t36_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(E,A,C) & v1_polynom1(E,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] : ( 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,k3_polynom1(k15_pre_poly(A),C,D)) & r3_pre_poly(A,k3_termord(A,B,C,E),F) ) ) ) ) ) ) ) )).
fof(t36_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,1) & ~ r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(1,k2_power(A,B)) ) ) ) )).
fof(t36_pre_poly,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => r1_tarski(k13_pre_poly(A),k9_xtuple_0(A)) ) )).
fof(t36_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t36_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => k3_prepower(A,B) = k1_newton(A,B) ) ) )).
fof(t36_prob_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m2_prob_1(E,A,B) => k3_funct_2(B,k1_numbers,E,k6_prob_1(A,B,C,D)) = k3_real_1(k3_funct_2(B,k1_numbers,E,C),k3_funct_2(B,k1_numbers,E,k7_prob_1(A,B,D,C))) ) ) ) ) ) )).
fof(t36_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m2_prob_1(E,A,B) => ~ ( ~ r1_xxreal_0(k3_funct_2(B,k1_numbers,E,C),k5_numbers) & ~ r1_xxreal_0(k3_funct_2(B,k1_numbers,E,D),k5_numbers) & k3_funct_2(B,k1_numbers,k3_prob_2(A,B,E,D),C) != k6_real_1(k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,E,C),D),k3_funct_2(B,k1_numbers,E,C)),k3_funct_2(B,k1_numbers,E,D)) ) ) ) ) ) ) )).
fof(t36_prob_3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k1_kurato_0(A,k3_prob_3(A,C)) = k1_kurato_0(A,C) ) ) )).
fof(t36_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ( ! [E] : ( r2_hidden(E,D) <=> ? [F] : ? [G] : ( 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)) = k5_numbers ) ) => D = k4_prob_4(A,B,C) ) ) ) ) ) )).
fof(t36_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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,D),k8_cqc_lang(A,C,D)),k8_cqc_lang(A,k9_cqc_lang(A,B,C),D)),k4_cqc_the1(A)) ) ) ) ) )).
fof(t36_projpl_1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & v5_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t36_pscomp_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t36_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t36_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t36_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t36_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_qc_lang4(C,A,B) => k4_qc_lang4(A,B,C) = a_3_3_qc_lang4(A,B,C) ) ) ) )).
fof(t36_quatern2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k14_quatern2)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_quatern2)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_quatern2)) => ( k3_rlvect_1(k14_quatern2,A,B) = k3_rlvect_1(k14_quatern2,B,A) & k3_rlvect_1(k14_quatern2,k3_rlvect_1(k14_quatern2,A,B),C) = k3_rlvect_1(k14_quatern2,A,k3_rlvect_1(k14_quatern2,B,C)) & k3_rlvect_1(k14_quatern2,A,k4_struct_0(k14_quatern2)) = A ) ) ) ) )).
fof(t36_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => r1_xxreal_0(k28_quaterni(k25_quaterni(k22_quaterni(A,B),C)),k2_xcmplx_0(k2_xcmplx_0(k28_quaterni(A),k28_quaterni(B)),k28_quaterni(C))) ) ) ) )).
fof(t36_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ( k13_quaterni(k22_quaterni(A,B)) = k2_xcmplx_0(k13_quaterni(A),k13_quaterni(B)) & k14_quaterni(k22_quaterni(A,B)) = k2_xcmplx_0(k14_quaterni(A),k14_quaterni(B)) & k15_quaterni(k22_quaterni(A,B)) = k2_xcmplx_0(k15_quaterni(A),k15_quaterni(B)) & k16_quaterni(k22_quaterni(A,B)) = k2_xcmplx_0(k16_quaterni(A),k16_quaterni(B)) ) ) ) )).
fof(t36_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k19_quofield(A))) => k4_algstr_0(k19_quofield(A),B) = k1_funct_1(k17_quofield(A),B) ) ) )).
fof(t36_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( m2_prob_1(D,A,C) => ! [E] : ( m1_random_1(E,A,C) => ( ( v6_supinf_2(E) & r1_random_1(A,C,E,D) ) => ( r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(k12_supinf_2(D,a_4_0_random_1(A,B,C,E)),k2_extreal1(k8_random_1(A,C,D,E),B)) ) ) ) ) ) ) ) )).
fof(t36_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_vectsp_6(E,A,B) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t36_rat_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => ( ~ ( ~ r1_xxreal_0(B,A) & r1_xxreal_0(k2_rat_1(B),k3_xcmplx_0(A,k1_rat_1(B))) ) & ~ ( ~ r1_xxreal_0(k2_rat_1(B),k3_xcmplx_0(A,k1_rat_1(B))) & r1_xxreal_0(B,A) ) ) ) ) )).
fof(t36_ratfunc1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_ratfunc1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t36_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t36_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => k9_nat_1(k1_numbers,k3_real_3(B),k1_nat_1(A,1)) = k9_nat_1(k1_numbers,k3_real_3(k7_xcmplx_0(1,k3_int_1(B))),A) ) ) )).
fof(t36_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ( k9_xtuple_0(A) = k1_xboole_0 <=> k10_xtuple_0(A) = k1_xboole_0 ) ) )).
fof(t36_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t36_revrot_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ 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) ) ) )).
fof(t36_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( 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) ) ) ) )).
fof(t36_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t36_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(C))) => ! [G] : ( ( ~ 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] : ( m1_subset_1(H,k8_afinsq_1(C)) => ~ ( r1_rewrite3(F,G,A,H,B) & D = k1_flang_1(C,H,E) ) ) ) ) ) ) ) ) )).
fof(t36_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_valued_0(C) ) => k18_valued_1(C,k1_rfunct_1(A,B)) = k1_rfunct_1(k18_valued_1(C,A),B) ) ) ) )).
fof(t36_rfunct_2,axiom,( ! [A] : ! [B] : ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t36_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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(k5_numbers)) = k8_relset_1(A,k1_numbers,k18_rfunct_3(A,B),k1_tarski(k5_numbers)) ) ) )).
fof(t36_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k1_funct_1(k3_rinfsup1(B),A) = k2_rinfsup1(k1_valued_0(k1_numbers,B,A)) ) ) )).
fof(t36_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v8_valued_0(A) => ( v10_mesfunc5(A) & k2_mesfunc5(A) = k2_rinfsup2(A) ) ) ) )).
fof(t36_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_rlvect_2(C,A) => k3_rlaffin1(A,k10_rlvect_2(A,B,C)) = k6_xcmplx_0(k3_rlaffin1(A,B),k3_rlaffin1(A,C)) ) ) ) )).
fof(t36_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => k1_rlsub_1(B) = k1_rlsub_1(A) ) ) )).
fof(t36_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t36_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t36_rlvect_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( k1_rlvect_1(B,C,A) = k1_rlvect_1(B,D,A) => ( A = k5_numbers | C = D ) ) ) ) ) ) )).
fof(t36_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t36_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( C != D & v1_rlvect_3(k7_domain_1(u1_struct_0(A),C,D),A) & ~ v1_rlvect_3(k8_domain_1(u1_struct_0(A),B,C,D),A) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => B != k3_rlvect_1(A,k1_rlvect_1(A,C,E),k1_rlvect_1(A,D,F)) ) ) ) ) ) ) ) )).
fof(t36_rlvect_5,axiom,( ! [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_rlvect_5(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => r1_xxreal_0(k6_xcmplx_0(k1_nat_1(k1_rlvect_5(B),k1_rlvect_5(C)),k1_rlvect_5(A)),k1_rlvect_5(k2_rlsub_2(A,B,C))) ) ) ) )).
fof(t36_rlvect_x,axiom,( ! [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) ) => ! [B] : ( 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) ) ) )).
fof(t36_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => k1_rmod_2(A,C) = k1_rmod_2(A,B) ) ) ) )).
fof(t36_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ( ~ ( ? [E] : ( 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] : ( m1_rmod_2(E,A,B) => u1_struct_0(E) != k2_xboole_0(u1_struct_0(C),u1_struct_0(D)) ) ) ) ) ) ) ) )).
fof(t36_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t36_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k9_robbins1(A,k5_robbins1(A,B,C),k9_robbins1(A,B,C)) = C ) ) ) )).
fof(t36_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t36_robbins4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v10_robbins1(A) & v8_robbins3(A) & v9_robbins3(A) & l4_robbins1(A) ) => ( v1_robbins4(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t36_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) )).
fof(t36_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( ~ r1_xxreal_0(k1_rpr_1(A,C),k5_numbers) => k2_rpr_1(A,C,B) = k6_xcmplx_0(1,k7_xcmplx_0(k1_rpr_1(A,k7_subset_1(A,C,B)),k1_rpr_1(A,C))) ) ) ) ) )).
fof(t36_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t36_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t36_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t36_rusub_4,axiom,( ! [A] : ( ( ~ 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] : ( ( v2_rusub_4(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t36_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ~ ( r2_hidden(C,k9_subset_1(u1_struct_0(A),k4_bhsp_2(A,B,E),k4_bhsp_2(A,D,F))) & ! [G] : ( v1_xreal_0(G) => ~ ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t36_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t36_rvsum_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xcmplx_0(B) => k16_rvsum_1(k2_finseq_2(A,B)) = k3_xcmplx_0(A,B) ) ) )).
fof(t36_scmbsort,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => v4_extpro_1(k1_scmfsa_m(k16_funcop_1(k5_scmfsa_2(k5_numbers),A)),k7_card_1(3),k1_scmfsa_2,k2_scmbsort) ) )).
fof(t36_scmfsa10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => k2_amistd_1(k7_card_1(3),k1_scmfsa_2,k12_scmfsa_2(A,B)) = k1_tarski(A) ) ) )).
fof(t36_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_finset_1(E) & v1_afinsq_1(E) ) => ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_scmfsa_2)) ) => ( ( ! [G] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t36_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( 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),k5_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(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa8b(E,C,D)),k1_funct_4(B,k7_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_numbers))) = k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(D,k4_compos_1(k1_scmfsa_2))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B)),3) ) ) ) ) ) ) ) )).
fof(t36_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ( r4_scmfsa9a(A,k1_scmfsa_m(B),C,D) => ( ( ~ r3_scmfsa9a(A,k1_scmfsa_m(B),C,D) & ~ v7_amistd_1(D,k7_card_1(3),k1_scmfsa_2) ) | k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(k2_scmfsa_9(C,D),B,A)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(k1_scmfsa_m(B),D,C,A),k2_scmfsa9a(A,k1_scmfsa_m(B),C,D))) ) ) ) ) ) ) )).
fof(t36_scmfsa_2,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [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(k7_card_1(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)) ) ) )).
fof(t36_scmfsa_m,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ? [B] : ( 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(k5_numbers),A)) = k16_funcop_1(k5_scmfsa_2(k5_numbers),B) ) ) )).
fof(t36_scmisort,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( r1_tarski(k3_scmisort,C) => ! [D] : ( m2_finseq_1(D,k4_numbers) => ( r1_tarski(k1_scmfsa_m(k16_funcop_1(k5_scmfsa_2(k5_numbers),D)),B) => r2_hidden(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,C,B,A)),k9_xtuple_0(k3_scmisort)) ) ) ) ) ) ) )).
fof(t36_scmpds_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ~ ( k2_compos_0(u1_compos_1(k1_scmpds_2),A) = 13 & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmpds_2)) ) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => A != k16_scmpds_2(B,C,D,E) ) ) ) ) ) ) )).
fof(t36_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => k5_card_1(k5_scmpds_6(A,B,C)) = k1_nat_1(k5_card_1(C),1) ) ) ) )).
fof(t36_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ! [G] : ( v7_ordinal1(G) => ( r1_xxreal_0(k5_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) ) ) ) ) ) ) ) ) )).
fof(t36_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k5_compos_0(u1_compos_1(k1_scmring2(A)),k8_scmring2(A,B),C) = k8_scmring2(A,k2_xcmplx_0(B,C)) ) ) ) )).
fof(t36_scmyciel,axiom,( ! [A] : k5_scmyciel(k1_tarski(A)) = k2_tarski(k1_xboole_0,k1_tarski(A)) )).
fof(t36_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t36_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,A),k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,B)),k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,D),k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B))) ) ) ) ) )).
fof(t36_seq_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_seqm_3(A) & v1_comseq_2(A) ) => v2_comseq_2(A) ) ) )).
fof(t36_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t36_seqm_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_seq_2(B) => ( r1_xxreal_0(A,k5_numbers) | v1_seq_2(k26_valued_1(k4_ordinal1,k1_numbers,B,A)) ) ) & ( k5_numbers = A => v1_comseq_2(k26_valued_1(k4_ordinal1,k1_numbers,B,A)) ) & ( v1_seq_2(B) => ( r1_xxreal_0(k5_numbers,A) | v2_seq_2(k26_valued_1(k4_ordinal1,k1_numbers,B,A)) ) ) ) ) ) )).
fof(t36_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,A,B)) ) & v1_series_1(A) ) => v2_series_1(A) ) ) )).
fof(t36_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ( k2_xcmplx_0(A,B) = 1 => r1_xxreal_0(k7_xcmplx_0(17,4),k2_xcmplx_0(k3_xcmplx_0(A,B),k7_xcmplx_0(1,k3_xcmplx_0(A,B)))) ) ) ) )).
fof(t36_setfam_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( 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) ) ) ) )).
fof(t36_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ! [E] : ( v7_ordinal1(E) => k1_funct_1(D,E) = k2_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) => ! [E] : ( v7_ordinal1(E) => k1_funct_1(k4_setlim_1(A,D),E) = k2_xboole_0(k1_funct_1(k4_setlim_1(A,B),E),k1_funct_1(k4_setlim_1(A,C),E)) ) ) ) ) ) )).
fof(t36_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k3_prob_1(A,k8_setlim_2(A,C,B)) = k7_subset_1(A,k3_prob_1(A,C),B) ) ) )).
fof(t36_setwiseo,axiom,( ! [A] : v2_binop_1(k9_setwiseo(A),k5_finsub_1(A)) )).
fof(t36_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t36_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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))) ) ) )).
fof(t36_sfmastr3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_scmfsa_2(C) => k4_sf_mastr(k4_sfmastr3(C,A,B)) = k1_tarski(C) ) ) ) )).
fof(t36_sgraph1,axiom,( 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)) )).
fof(t36_sheffer1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v9_sheffer1(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l3_sheffer1(A) ) => v3_sheffer1(A) ) )).
fof(t36_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t36_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ! [C] : ( ( v7_simplex0(C,A,B) & m2_simplex0(C,A,B) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t36_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_funct_1(k18_sin_cos,A) = k4_series_1(k21_sin_cos(A)) & k1_funct_1(k16_sin_cos,A) = k4_series_1(k20_sin_cos(A)) ) ) )).
fof(t36_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_fdiff_1(k5_sin_cos2,k1_numbers) & k1_fdiff_1(k5_sin_cos2,A) = k7_xcmplx_0(1,k1_square_1(k1_funct_1(k3_sin_cos2,A))) ) ) )).
fof(t36_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k15_sin_cos(k3_xcmplx_0(k7_complex1,A)) = k2_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,A),k3_xcmplx_0(k7_complex1,k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,A))) ) )).
fof(t36_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k3_xcmplx_0(k3_xcmplx_0(k19_sin_cos(A),k19_sin_cos(B)),k19_sin_cos(C)) = k3_xcmplx_0(k7_xcmplx_0(1,4),k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k19_sin_cos(k6_xcmplx_0(k2_xcmplx_0(A,B),C)),k19_sin_cos(k6_xcmplx_0(k2_xcmplx_0(B,C),A))),k19_sin_cos(k6_xcmplx_0(k2_xcmplx_0(C,A),B))),k19_sin_cos(k2_xcmplx_0(k2_xcmplx_0(A,B),C)))) ) ) ) )).
fof(t36_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_sin_cos5(A) = k7_xcmplx_0(k2_xcmplx_0(k23_sin_cos(A),k23_sin_cos(k4_xcmplx_0(A))),k6_xcmplx_0(k23_sin_cos(A),k23_sin_cos(k4_xcmplx_0(A)))) & k2_sin_cos5(A) = k7_xcmplx_0(2,k2_xcmplx_0(k23_sin_cos(A),k23_sin_cos(k4_xcmplx_0(A)))) & k3_sin_cos5(A) = k7_xcmplx_0(2,k6_xcmplx_0(k23_sin_cos(A),k23_sin_cos(k4_xcmplx_0(A)))) ) ) )).
fof(t36_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k28_sin_cos) & r1_xxreal_0(A,k3_xcmplx_0(2,k28_sin_cos)) & r1_xxreal_0(k19_sin_cos(A),k4_xcmplx_0(1)) ) ) )).
fof(t36_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => k2_sin_cos7(A) = k1_sin_cos7(k3_square_1(k6_xcmplx_0(k1_square_1(A),1))) ) ) )).
fof(t36_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(k28_sin_cos,A) & ~ ( k4_sin_cos9(k1_funct_1(k27_sin_cos,A)) = A & k4_sin_cos9(k2_sin_cos4(A)) = A ) ) ) )).
fof(t36_sincos10,axiom,( ! [A] : ( r2_hidden(A,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k7_xcmplx_0(k28_sin_cos,2))) => r2_hidden(k1_funct_1(k2_fdiff_9,A),k1_rcomp_1(1,k3_square_1(2))) ) )).
fof(t36_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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(k1_nat_1(A,2),k3_finseq_1(B)) ) => r1_sppol_1(2,k7_partfun1(u1_struct_0(k15_euclid(2)),B,k1_nat_1(A,1)),k4_subset_1(u1_struct_0(k15_euclid(2)),k2_topreal1(2,B,A),k2_topreal1(2,B,k1_nat_1(A,1)))) ) ) ) )).
fof(t36_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_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] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(2,C) & r1_xxreal_0(k1_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)) ) ) ) )).
fof(t36_sprect_1,axiom,( ! [A] : ( 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) ) )).
fof(t36_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t36_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => ( A = B | k7_xcmplx_0(1,k2_xcmplx_0(k3_square_1(A),k3_square_1(B))) = k7_xcmplx_0(k6_xcmplx_0(k3_square_1(A),k3_square_1(B)),k6_xcmplx_0(A,B)) ) ) ) ) )).
fof(t36_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t36_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k7_card_1(D),k7_card_1(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(D),k7_card_1(A)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k7_card_1(k2_xcmplx_0(D,C)),k7_card_1(k2_xcmplx_0(A,B))) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(k2_xcmplx_0(D,C)),k7_card_1(k2_xcmplx_0(A,B))))) ) => ( ( v1_stirl2_1(F,k2_xcmplx_0(D,C),k2_xcmplx_0(A,B)) & E = k2_partfun1(k7_card_1(k2_xcmplx_0(D,C)),k7_card_1(k2_xcmplx_0(A,B)),F,D) ) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ~ ( r2_hidden(G,k2_relset_1(k7_card_1(A),E)) & r2_hidden(H,k2_relset_1(k7_card_1(A),E)) & ~ r1_xxreal_0(H,G) & r1_xxreal_0(k3_nat_1(k1_stirl2_1(D,k7_card_1(A),E,k1_seq_4(H))),k3_nat_1(k1_stirl2_1(D,k7_card_1(A),E,k1_seq_4(G)))) ) ) ) ) ) ) ) ) ) ) )).
fof(t36_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_sublemma(B,A) & m1_subset_1(B,k2_zfmisc_1(k16_substut1(A),k3_qc_lang1(A))) ) => ! [C] : ( m1_substut1(C,A,B) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(k16_substut1(A),k3_qc_lang1(A))) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t36_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ( A != k1_xboole_0 => m1_subset_1(k2_enumset1(B,C,D,E),k1_zfmisc_1(A)) ) ) ) ) ) )).
fof(t36_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t36_supinf_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_card_3(A) & v5_supinf_2(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( m1_supinf_2(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => r1_xxreal_0(k12_supinf_2(k15_supinf_2(A,B),C),k12_supinf_2(k15_supinf_2(A,B),k1_nat_1(C,D))) ) ) ) ) )).
fof(t36_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( 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,D,C) & k2_symsp_1(A,B,E,k3_rlvect_1(B,F,G),C,D) != k3_rlvect_1(A,k2_symsp_1(A,B,E,F,C,D),k2_symsp_1(A,B,E,G,C,D)) ) ) ) ) ) ) ) ) )).
fof(t36_sysrel,axiom,( ! [A] : ( 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))) ) ) ) ) )).
fof(t36_taxonom1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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,k5_numbers))) => k8_eqrel_1(u1_struct_0(A),B) = k10_eqrel_1(u1_struct_0(A)) ) ) ) )).
fof(t36_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(u1_struct_0(A)),k9_tdlat_1(A)) => ! [C] : ( 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) ) ) ) )).
fof(t36_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))))) ) ) )).
fof(t36_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v4_tdlat_3(A) <=> ! [B] : ( 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) ) ) ) ) ) )).
fof(t36_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => k3_polynom1(k15_pre_poly(A),C,k6_termord(A,B,C,D)) = k7_subset_1(k15_pre_poly(A),k3_polynom1(k15_pre_poly(A),C,D),k1_tarski(k3_termord(A,B,C,D))) ) ) ) ) )).
fof(t36_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t36_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_tex_2(B,A) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t36_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( v3_tops_1(B,A) & ! [C] : ( ( v1_pre_topc(C) & m1_pre_topc(C,A) ) => ~ ( v4_tex_3(C,A) & B = u1_struct_0(C) ) ) ) ) ) )).
fof(t36_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t36_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( ~ r1_tsep_1(C,D) => ( ( ~ r1_tsep_1(k2_tsep_1(A,C,D),B) => ( ~ r1_tsep_1(C,B) & ~ r1_tsep_1(D,B) ) ) & ( ~ r1_tsep_1(B,k2_tsep_1(A,C,D)) => ( ~ r1_tsep_1(B,C) & ~ r1_tsep_1(B,D) ) ) ) ) ) ) ) ) )).
fof(t36_toler_1,axiom,( ! [A] : ! [B] : ( ( 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] : ! [D] : ( ( v1_toler_1(D,A,B) & m1_toler_1(D,A,B) ) => ( r2_hidden(C,D) => r1_tarski(D,k9_relat_1(B,C)) ) ) ) )).
fof(t36_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_borsuk_2(G,A,B,C) => ! [H] : ( m1_borsuk_2(H,A,C,D) => ! [I] : ( m1_borsuk_2(I,A,D,E) => ! [J] : ( 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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t36_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v7_topalg_6(B,A) & m2_subset_1(B,k4_partfun1(k1_numbers,k2_struct_0(A)),k1_topalg_6(A)) ) => ! [C] : ( ( v7_topalg_6(C,A) & m2_subset_1(C,k4_partfun1(k1_numbers,k2_struct_0(A)),k1_topalg_6(A)) ) => ! [D] : ( 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] : ( 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] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( 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] : ( m1_subset_1(H,u1_struct_0(k1_pre_topc(k2_topalg_2,D))) => ( k1_binop_1(E,H,k5_numbers) = k1_funct_1(B,H) & k1_binop_1(E,H,1) = k1_funct_1(C,H) ) ) & ! [H] : ( 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 ) ) ) ) ) ) ) ) ) ) ) )).
fof(t36_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t36_topgen_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) ) => ( ! [D] : ( 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))) ) ) ) ) )).
fof(t36_topgen_3,axiom,( ! [A] : ( ~ v1_finset_1(A) => ! [B] : ( ( ~ 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] : ( ( ~ 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) ) ) ) )).
fof(t36_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => v6_topgen_4(k2_struct_0(A),A) ) )).
fof(t36_topgen_5,axiom,( 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))) )).
fof(t36_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v4_topgrp_1(A) & l1_topgrp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_connsp_2(D,A,k6_algstr_0(A,B,C)) => ? [E] : ( v3_pre_topc(E,A) & m1_connsp_2(E,A,B) & ? [F] : ( v3_pre_topc(F,A) & m1_connsp_2(F,A,C) & r1_tarski(k2_group_2(A,E,F),D) ) ) ) ) ) ) )).
fof(t36_topreal1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => k7_topreal1(A) = a_1_6_topreal1(A) ) )).
fof(t36_topreal3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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),k7_xcmplx_0(k2_xcmplx_0(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) ) ) ) ) ) ) )).
fof(t36_topreal8,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ~ ( ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(C,k4_finseq_1(B)) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( r2_hidden(k4_tarski(D,E),k2_matrix_0(A)) & k7_partfun1(u1_struct_0(k15_euclid(2)),B,C) = k3_matrix_0(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] : ( 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)) ) ) ) ) ) )).
fof(t36_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(A))) => ! [G] : ( m2_finseq_2(G,k1_numbers,k1_euclid(A)) => ! [H] : ( m2_finseq_2(H,k1_numbers,k1_euclid(A)) => ! [I] : ( m2_finseq_2(I,k1_numbers,k1_euclid(A)) => ~ ( G = k3_rlvect_1(k15_euclid(A),k1_rlvect_1(k15_euclid(A),D,k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(A),E,k7_xcmplx_0(1,2))) & H = E & I = F & D != E & r2_hidden(D,k3_topreal9(A,F,C)) & r2_hidden(E,k2_topreal9(A,F,C)) & ! [J] : ( 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(k15_euclid(A),D,E),k3_topreal9(A,F,C)) & ( r2_hidden(E,k3_topreal9(A,F,C)) => J = E ) & ( B = k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(2,k22_rvsum_1(k5_algstr_0(k15_euclid(A),E,k3_rlvect_1(k15_euclid(A),k1_rlvect_1(k15_euclid(A),D,k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(A),E,k7_xcmplx_0(1,2)))),k5_algstr_0(k15_euclid(A),k3_rlvect_1(k15_euclid(A),k1_rlvect_1(k15_euclid(A),D,k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(A),E,k7_xcmplx_0(1,2))),F)))),k3_square_1(k1_quin_1(k18_rvsum_1(k11_euclid(A,k8_euclid(A,H,G))),k3_xcmplx_0(2,k22_rvsum_1(k5_algstr_0(k15_euclid(A),E,k3_rlvect_1(k15_euclid(A),k1_rlvect_1(k15_euclid(A),D,k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(A),E,k7_xcmplx_0(1,2)))),k5_algstr_0(k15_euclid(A),k3_rlvect_1(k15_euclid(A),k1_rlvect_1(k15_euclid(A),D,k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(A),E,k7_xcmplx_0(1,2))),F))),k6_xcmplx_0(k18_rvsum_1(k11_euclid(A,k8_euclid(A,G,I))),k1_square_1(C))))),k3_xcmplx_0(2,k18_rvsum_1(k11_euclid(A,k8_euclid(A,H,G))))) => ( r2_hidden(E,k3_topreal9(A,F,C)) | 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,k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(A),E,k7_xcmplx_0(1,2))),k6_xcmplx_0(1,B)),k1_rlvect_1(k15_euclid(A),E,B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t36_topreala,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(C,D) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t36_toprealb,axiom,( ! [A] : ( v1_xreal_0(A) => ( k3_int_1(A) = k7_xcmplx_0(3,4) => k1_funct_1(k12_toprealb,A) = k19_euclid(k5_numbers,k4_xcmplx_0(1)) ) ) )).
fof(t36_toprealc,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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))))) ) ) ) ) )).
fof(t36_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(t36_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t36_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t36_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t36_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t36_trees_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ r3_xboole_0(A,B) => v2_trees_1(k2_tarski(A,B)) ) ) ) )).
fof(t36_trees_3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( B != k5_numbers => ( v6_trees_3(k2_finseq_2(B,A)) <=> ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) ) ) ) )).
fof(t36_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v3_trees_9(A) ) => ! [B] : ( 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) ) ) )).
fof(t36_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t36_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ v2_struct_0(E) & m1_pre_topc(E,A) ) => ( ( r4_tsep_2(A,B,C) & r4_tsep_2(A,D,E) ) => ( r1_tsep_1(C,E) | r4_tsep_2(A,k1_tsep_1(A,B,D),k2_tsep_1(A,C,E)) ) ) ) ) ) ) ) )).
fof(t36_turing_1,axiom,( k1_funct_1(k19_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers)) = k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,1,k5_numbers,1) & k1_funct_1(k19_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,1,1)) = k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,1,k5_numbers,1) & k1_funct_1(k19_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,1,k5_numbers)) = k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,2,k5_numbers,1) & k1_funct_1(k19_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,2,1)) = k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,2,k5_numbers,1) & k1_funct_1(k19_turing_1,k1_domain_1(k4_ordinal1,k4_ordinal1,2,k5_numbers)) = k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,3,k5_numbers,k5_numbers) )).
fof(t36_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ 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))) ) ) ) )).
fof(t36_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( r2_hidden(B,k2_uniroots(A)) <=> ? [C] : ( 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) ) ) ) )).
fof(t36_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_funct_2(C,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( m2_subset_1(F,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) )).
fof(t36_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) ) => k1_relset_1(k4_ordinal1,k63_valued_1(A)) = k7_subset_1(k4_ordinal1,k1_relset_1(k4_ordinal1,A),k1_tarski(k62_valued_1(A))) ) )).
fof(t36_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(t36_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( m1_vectsp_5(D,A,B,k2_vectsp11(A,B,C)) => v2_funct_1(k8_matrlin2(A,B,B,D,C)) ) ) ) ) )).
fof(t36_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( 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) ) ) ) ) ) ) )).
fof(t36_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => k1_vectsp_4(A,C) = k1_vectsp_4(A,B) ) ) ) )).
fof(t36_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t36_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t36_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t36_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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(k4_normsp_0(A,B,C),A) ) ) ) ) )).
fof(t36_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( 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(k4_normsp_0(A,B,C),A) ) ) ) ) )).
fof(t36_waybel11,axiom,( ! [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) & v4_waybel11(A) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v3_pre_topc(k2_waybel_3(A,B),A) ) ) )).
fof(t36_waybel12,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ v1_xboole_0(C) & v4_card_3(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( ~ r3_orders_2(A,D,B) & ! [E] : ( ( 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))) ) ) ) ) ) ) ) ) )).
fof(t36_waybel14,axiom,( ! [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) ) => ( v3_waybel_3(A) => v3_waybel_3(k1_yellow_1(k5_waybel11(A))) ) ) )).
fof(t36_waybel19,axiom,( ! [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) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) => v3_waybel11(B,A) ) ) ) )).
fof(t36_waybel20,axiom,( ! [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] : ( ( ~ 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))) ) ) ) ) )).
fof(t36_waybel21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m2_yellow_6(C,A,B) => ! [D] : ( m2_waybel21(D,A,B,C) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t36_waybel23,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v1_waybel23(k5_waybel_0(A,B),A) ) ) )).
fof(t36_waybel24,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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)) ) ) )).
fof(t36_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & v1_waybel25(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v6_pre_topc(B) & l1_pre_topc(B) ) => ( r1_waybel18(B,A) => v1_waybel25(B) ) ) ) )).
fof(t36_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v3_waybel_3(k1_yellow_1(u1_pre_topc(A))) => ! [B] : ( ( ~ 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)) ) ) ) ) )).
fof(t36_waybel27,axiom,( ! [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] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t36_waybel30,axiom,( ! [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) & l1_waybel_9(A) ) => ( v1_compts_1(A) & v8_pre_topc(A) & v2_yellow13(A) & v3_waybel30(A) ) ) )).
fof(t36_waybel34,axiom,( ! [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] : ( ( 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) ) ) ) )).
fof(t36_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_lattice3(A,B,C) <=> r1_lattice3(A,k4_waybel_0(A,B),C) ) ) ) ) )).
fof(t36_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t36_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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))) ) ) )).
fof(t36_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( B = C => ( v1_waybel_3(B,k1_yellow_1(u1_pre_topc(A))) <=> v2_compts_1(C,A) ) ) ) ) ) )).
fof(t36_waybel_4,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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) ) ) ) )).
fof(t36_waybel_6,axiom,( ! [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) & l1_orders_2(A) ) => ( v2_waybel_1(A) <=> v9_waybel_1(A) ) ) )).
fof(t36_waybel_7,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( ! [C] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(t36_waybel_9,axiom,( ! [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) & v1_compts_1(A) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ( ( ! [D] : ( 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) ) ) ) ) )).
fof(t36_weddwitt,axiom,( ! [A] : ( ( ~ 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] : ( 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))) ) ) ) )).
fof(t36_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r3_wellord1(A,B,C) => ! [D] : ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t36_xboole_1,axiom,( ! [A] : ! [B] : r1_tarski(k4_xboole_0(A,B),A) )).
fof(t36_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k9_xboolean(A,k5_xboolean(A,B)) = k9_xboolean(A,B) ) ) )).
fof(t36_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k6_xcmplx_0(A,k2_xcmplx_0(B,C)) = k6_xcmplx_0(k6_xcmplx_0(A,B),C) ) ) ) )).
fof(t36_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,C) & r1_xxreal_0(B,k2_xcmplx_0(C,A)) ) ) ) ) )).
fof(t36_xtuple_0,axiom,( ! [A] : ! [B] : r1_tarski(k12_xtuple_0(k3_xboole_0(A,B)),k3_xboole_0(k12_xtuple_0(A),k12_xtuple_0(B))) )).
fof(t36_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k4_xxreal_0(k3_xxreal_0(A,B),B) = B ) ) )).
fof(t36_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(D,B) ) => r1_tarski(k3_xxreal_1(C,D),k1_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t36_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => m2_xxreal_2(A,k1_xboole_0) ) )).
fof(t36_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t36_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t36_yellow12,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( v2_pre_topc(D) & l1_pre_topc(D) ) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t36_yellow14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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))) ) ) )).
fof(t36_yellow16,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( 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(k4_yellow_1(A,C),k4_yellow_1(A,B)) & m1_yellow_0(k4_yellow_1(A,C),k4_yellow_1(A,B)) ) ) ) ) ) )).
fof(t36_yellow18,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(E,k1_altcat_1(A,B,C)) => ! [F] : ( m1_subset_1(F,k1_altcat_1(A,C,D)) => k5_altcat_1(A,B,C,D,E,F) = k3_relat_1(E,F) ) ) ) ) ) ) ) )).
fof(t36_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_compts_1(A) <=> ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t36_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_altcat_1(B) ) => ! [C] : ( ( v11_functor0(C,A,B) & l2_functor0(C,A,B) ) => ( v20_functor0(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( k1_altcat_1(B,D,E) != k1_xboole_0 => ! [F] : ( m1_subset_1(F,k1_altcat_1(B,D,E)) => ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( m1_subset_1(H,u1_struct_0(A)) & ? [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t36_yellow_0,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t36_yellow_2,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ! [C] : ( 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))) ) ) ) ) )).
fof(t36_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( r2_yellow_0(A,C) & r2_yellow_0(B,D) & ! [G] : ( 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] : ( m1_subset_1(G,u1_struct_0(A)) => ( r1_lattice3(A,C,G) => r1_orders_2(A,G,E) ) ) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ( r1_lattice3(B,D,G) => r1_orders_2(B,G,F) ) ) ) ) ) ) ) ) ) ) )).
fof(t36_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k3_yellow_4(A,B,k1_struct_0(A)) = k1_xboole_0 ) ) )).
fof(t36_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t36_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v8_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t36_yellow_7,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t36_yellow_9,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t36_zf_fund1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t36_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v2_zf_lang(A) => A = k4_zf_lang(k18_zf_lang(A),k19_zf_lang(A)) ) ) )).
fof(t36_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v10_zf_lang(A) => ( v5_zf_lang(A) & v9_zf_lang(k21_zf_lang(A)) & v9_zf_lang(k22_zf_lang(A)) ) ) ) )).
fof(t36_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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 ) ) )).
fof(t36_zfrefle1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( 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] : ( ( v3_ordinal1(C) & m1_subset_1(C,A) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t36_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_zmodul01(D,A) => ( ( r1_struct_0(D,B) & r1_struct_0(D,C) ) => r1_struct_0(D,k3_rlvect_1(A,B,C)) ) ) ) ) ) )).
fof(t36_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( m1_zmodul02(C,A) => ( r1_zmodul02(A,k22_zmodul02(A,B,C),k19_zmodul02(A)) => r1_zmodul02(A,C,k24_zmodul02(A,B)) ) ) ) ) )).
fof(t36_zmodul03,axiom,( ! [A] : ( ( ~ 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) & v1_zmodul03(A) & v2_zmodul03(A) & l1_zmodul01(A) ) => ! [B] : ( m1_zmodul03(B,A) => ! [C] : ( m1_zmodul03(C,A) => k5_card_1(B) = k5_card_1(C) ) ) ) )).
fof(t370_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k6_subset_1(k1_xxreal_1(B,k1_xxreal_0),k2_xxreal_1(A,k1_xxreal_0)) = k2_xboole_0(k2_xxreal_1(B,A),k1_tarski(k1_xxreal_0)) ) ) )).
fof(t371_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t372_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t373_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t374_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t375_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t376_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t377_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t378_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t379_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t37_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_abcmiz_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t37_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t37_abcmiz_a,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t37_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( ( v1_aff_1(F,A) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t37_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( 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) ) ) ) ) ) )).
fof(t37_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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,k5_numbers) = A & k1_funct_1(C,1) = B ) ) ) )).
fof(t37_afinsq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => k6_afinsq_2(A,k5_afinsq_1(C),B) = C ) ) ) )).
fof(t37_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k14_afproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k13_afproj(A))) => ! [D] : ( m1_subset_1(D,u2_incsp_1(k14_afproj(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t37_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_afvect0(A,D,k1_afvect0(A,C,k1_afvect0(A,D,B))) = k1_afvect0(A,k1_afvect0(A,D,C),B) ) ) ) ) )).
fof(t37_algspec1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r1_algspec1(A,B,C) => ! [D] : ( ( 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(t37_algstr_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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))) ) ) )).
fof(t37_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & m1_altcat_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,k1_altcat_1(A,C,D)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t37_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( ( r1_analmetr(A,G,H) & r2_analort(A,G,H,B,D,C,E) & r2_analort(A,G,H,B,D,E,F) ) => r2_analort(A,G,H,B,D,C,F) ) ) ) ) ) ) ) ) ) )).
fof(t37_aofa_000,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & v3_freealg(A) & l1_unialg_1(A) ) => ! [B] : ( m5_margrel1(B,u1_struct_0(A),k1_unialg_2(A)) => ! [C] : ( m5_margrel1(C,u1_struct_0(A),k1_unialg_2(A)) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( 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 ) ) ) ) ) ) ) )).
fof(t37_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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] : ( m1_msafree(D,A,B) => m1_msafree(D,A,C) ) ) ) ) ) )).
fof(t37_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( ( v19_aofa_a00(F,A) & m1_subset_1(F,u1_struct_0(A)) ) => ! [G] : ( m2_subset_1(G,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => k15_aofa_a00(A,B,C,D,F,k28_aofa_a00(A,C,F),G) = 1 ) ) ) ) ) ) ) )).
fof(t37_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_aofa_i00(E,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) ) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),E) => ! [G] : ( 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,k5_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,k5_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,k5_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,k5_numbers)) => r1_xxreal_0(k21_aofa_i00(B,k4_numbers,C,G),k21_aofa_i00(B,k4_numbers,C,F)) ) ) ) ) ) ) ) ) ) )).
fof(t37_armstrng,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( 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] : ( 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) ) ) ) ) ) )).
fof(t37_arytm_3,axiom,( ! [A] : ( 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 ) ) ) )).
fof(t37_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ? [B] : ( m1_subset_1(B,k4_ordinal1) & r1_xxreal_0(2,B) & r2_asympt_0(A,B) ) => v7_asympt_0(A) ) ) )).
fof(t37_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ r1_xxreal_0(C,k5_numbers) => k9_nat_1(k1_numbers,A,C) = k2_power(C,k2_power(2,k1_int_1(k3_power(2,C)))) ) ) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ r1_xxreal_0(C,k5_numbers) => k9_nat_1(k1_numbers,B,C) = k5_series_1(C,C) ) ) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & v4_asympt_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( r2_funct_2(k4_ordinal1,k1_numbers,C,B) & r2_hidden(A,k11_asympt_0(C,k5_asympt_1)) & ~ r2_hidden(A,k8_asympt_0(C)) & v6_asympt_0(A) & v6_asympt_0(C) & ~ r2_asympt_0(C,2) ) ) ) ) ) )).
fof(t37_bagorder,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => ( v3_wellfnd1(B,A) => v3_wellfnd1(k8_nat_1(u1_struct_0(A),B,C),A) ) ) ) ) )).
fof(t37_bcialg_1,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k5_bcialg_1(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t37_bcialg_2,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ! [C] : ( m4_bcialg_2(C,A,B) => m1_bcialg_2(C,A) ) ) ) )).
fof(t37_bcialg_3,axiom,( ! [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) & v6_bcialg_3(A) & l2_bcialg_1(A) ) => ! [B] : ( 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) ) ) ) ) ) )).
fof(t37_bcialg_4,axiom,( ! [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) & l1_bcialg_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t37_bcialg_5,axiom,( ! [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) ) => ( m1_bcialg_5(A,k5_numbers,k5_numbers,k5_numbers,k5_numbers) <=> ( v8_bcialg_1(A) & m1_bcialg_5(A,k5_numbers,k5_numbers,k5_numbers,k5_numbers) ) ) ) )).
fof(t37_bcialg_6,axiom,( ! [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] : ( ( ~ 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] : ( ( 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)))) ) => ( v2_funct_1(C) <=> k5_bcialg_6(A,B,C) = k1_tarski(k4_struct_0(A)) ) ) ) ) )).
fof(t37_bciideal,axiom,( ! [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) ) => ( ( ~ 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] : ( m2_bcialg_1(B,A) => ( v3_bciideal(B,A) & m2_bcialg_1(B,A) ) ) ) ) )).
fof(t37_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k5_numbers,k4_bhsp_1(A,B,C)) ) ) ) )).
fof(t37_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) & k1_seq_2(k3_bhsp_2(A,k3_normsp_1(A,D,E),k5_algstr_0(A,B,C))) = k5_numbers ) ) ) ) ) ) ) )).
fof(t37_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k3_bhsp_1(A,k1_normsp_1(A,k1_bhsp_4(A,B),C)),k9_nat_1(k1_numbers,k3_series_1(k2_bhsp_2(A,B)),C)) ) ) ) )).
fof(t37_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ! [H] : ( ( 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))) ) ) ) ) ) ) ) ) )).
fof(t37_binari_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ( ( r1_xxreal_0(k4_xcmplx_0(k5_series_1(2,k7_nat_d(k2_xcmplx_0(C,1),1))),k2_xcmplx_0(A,B)) & r1_xxreal_0(k4_xcmplx_0(k5_series_1(2,k7_nat_d(C,1))),A) & r1_xxreal_0(k4_xcmplx_0(k5_series_1(2,k7_nat_d(C,1))),B) ) => ( r1_xxreal_0(k5_numbers,A) | r1_xxreal_0(k5_numbers,B) | k3_binari_2(k2_xcmplx_0(C,1),k7_binarith(k2_xcmplx_0(C,1),k2_binari_4(k2_xcmplx_0(C,1),A),k2_binari_4(k2_xcmplx_0(C,1),B))) = k2_xcmplx_0(A,B) ) ) ) ) ) )).
fof(t37_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t37_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_eqrel_1(C,u1_struct_0(B)) ) => ! [D] : ( 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))) ) ) ) ) )).
fof(t37_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t37_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ( A = k1_seq_4(B) => k2_pre_topc(k3_topmetr,A) = k1_seq_4(B) ) ) ) )).
fof(t37_borsuk_6,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( 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) ) ) ) ) ) )).
fof(t37_borsuk_7,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ( A = k3_numbers => ! [B] : ( ( v2_pre_topc(B) & v1_connsp_1(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t37_bspace,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k7_bspace(A))) => ( ? [C] : ( r2_hidden(C,A) & B = k1_tarski(C) ) => r2_hidden(B,k9_bspace(A)) ) ) )).
fof(t37_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t37_bvfunc14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) ) => ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ( 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 ) ) ) ) )).
fof(t37_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t37_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t37_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) )).
fof(t37_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t37_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(F,A) => r1_bvfunc_1(A,k2_bvfunc_1(A,k6_bvfunc_2(A,k9_bvfunc_1(A,D,E),B,F),k7_bvfunc_2(A,k2_bvfunc_1(A,C,k1_bvfunc_1(A,E)),B,F)),k7_bvfunc_2(A,k2_bvfunc_1(A,C,k1_bvfunc_1(A,D)),B,F)) ) ) ) ) ) ) )).
fof(t37_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t37_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t37_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(t37_c0sp1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(t37_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => ( ( r2_relset_1(k4_ordinal1,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)))) ) ) ) ) ) )).
fof(t37_card_1,axiom,( ! [A] : ! [B] : ( ( r2_wellord2(A,B) & v1_finset_1(A) ) => v1_finset_1(B) ) )).
fof(t37_card_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k5_card_1(k2_xcmplx_0(B,A)) = k1_card_2(k5_card_1(B),k5_card_1(A)) ) ) )).
fof(t37_card_5,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => ( r1_tarski(k1_tarski(A),B) => k2_wellord2(k1_wellord2(k1_tarski(A))) = 1 ) ) )).
fof(t37_card_fil,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) & ~ v2_card_1(A) ) => ! [B] : ( m1_card_fil(B,A) => ~ ( v1_card_fil(B,A) & v3_card_fil(B,A) & r1_card_fil(A,A,B) ) ) ) )).
fof(t37_card_fin,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t37_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & ~ v1_xboole_0(A) ) => ~ v1_xboole_0(k4_classes1(A)) ) )).
fof(t37_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_cat_1(E,A,C,B) & ? [F] : ( 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 ) ) ) ) ) ) ) )).
fof(t37_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k1_binop_1(k7_cat_1(k6_cat_2(A,B),B,k13_cat_2(A,B)),C,D) = D ) ) ) ) )).
fof(t37_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_cat_1(D,A,B,C) => ( v10_cat_1(C,A) => k10_cat_3(A,B,C) = D ) ) ) ) ) )).
fof(t37_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t37_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(k3_xcmplx_0(2,B),A) & ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v5_ordinal1(C) & v1_finset_1(C) ) => ~ ( k1_card_1(a_2_0_catalan2(A,B)) = k7_afinsq_2(C) & k1_relset_1(k4_ordinal1,C) = B & ! [D] : ( v7_ordinal1(D) => ( ~ r1_xxreal_0(B,D) => k1_recdef_1(C,D) = k2_nat_1(k5_card_1(k2_catalan2(k3_xcmplx_0(2,D),D)),k5_card_1(k2_catalan2(k7_nat_d(A,k2_nat_1(2,k1_nat_1(D,1))),k7_nat_d(B,k1_nat_1(D,1))))) ) ) ) ) ) ) ) )).
fof(t37_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t37_cfcont_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [C] : ( ( 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) = k5_numbers | r1_cfcont_1(k1_cfunct_1(k2_numbers,C,B),A) ) ) ) ) ) )).
fof(t37_cfdiff_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ~ ( r1_cfdiff_1(B,A) & ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t37_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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))) ) ) )).
fof(t37_cgames_1,axiom,( k12_cgames_1(k5_ordinal1,k3_cgames_1) = k1_tarski(k3_cgames_1) )).
fof(t37_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_chain_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) => ( r2_hidden(C,k4_chain_1(A,B,A)) <=> ? [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) & ? [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) & C = k3_chain_1(A,D,E) & ! [F] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(A)) => m2_chain_1(k4_tarski(k1_funct_1(D,F),k1_funct_1(E,F)),k2_chain_1(A,B,F)) ) & ( ! [F] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(A)) => ~ r1_xxreal_0(k1_funct_1(E,F),k1_funct_1(D,F)) ) | ! [F] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(A)) => ~ r1_xxreal_0(k1_funct_1(D,F),k1_funct_1(E,F)) ) ) ) ) ) ) ) ) )).
fof(t37_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( ! [C] : ( ( 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) ) ) ) )).
fof(t37_circcmb3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t37_circcomb,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( 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 ) ) ) )).
fof(t37_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v4_msualg_1(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t37_classes1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r1_ordinal1(A,B) <=> r1_tarski(k4_classes1(A),k4_classes1(B)) ) ) ) )).
fof(t37_classes2,axiom,( ! [A] : ! [B] : ~ ( 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)))) ) )).
fof(t37_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t37_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( ! [C] : ( v7_ordinal1(C) => k1_normsp_0(A,B,C) != k4_struct_0(A) ) & ? [C] : ( v7_ordinal1(C) & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => r1_xxreal_0(1,k6_real_1(k9_nat_1(k1_numbers,k5_normsp_0(A,B),k1_nat_1(D,1)),k9_nat_1(k1_numbers,k5_normsp_0(A,B),D))) ) ) ) & v2_clopban3(B,A) ) ) ) )).
fof(t37_clopban4,axiom,( ! [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) & 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] : ( 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) ) ) ) )).
fof(t37_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v4_mssubfam(C,A,B) & m3_pboole(C,A,k1_mboolean(A,B)) ) => ! [D] : ( m2_pboole(D,A,k5_mssubfam(A,B),k5_mssubfam(A,B)) => ( ! [E] : ( m1_pboole(E,A,k5_mssubfam(A,B)) => ! [F] : ( ( v2_relat_1(F) & m3_pboole(F,A,k1_mboolean(A,B)) ) => ( ! [G] : ( ( 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) ) ) ) ) )).
fof(t37_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t37_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_clvect_1(B,A) => ! [C] : ( m1_clvect_1(C,A) => r1_struct_0(C,k4_struct_0(B)) ) ) ) )).
fof(t37_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) & k1_seq_2(k3_clvect_2(A,k3_normsp_1(A,D,E),k5_algstr_0(A,B,C))) = k5_numbers ) ) ) ) ) ) ) )).
fof(t37_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k13_csspace(A,k1_normsp_0(A,k1_bhsp_4(A,B),C)),k9_nat_1(k1_numbers,k3_series_1(k2_clvect_2(A,B)),C)) ) ) ) )).
fof(t37_coh_sp,axiom,( ! [A] : r2_hidden(k4_tarski(k1_eqrel_1(A),A),k16_coh_sp(A)) )).
fof(t37_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t37_compl_sp,axiom,( ! [A] : ! [B] : ( l1_metric_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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] : ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & D = k4_tarski(E,F) & ( ( r2_hidden(E,A) & F != C ) | ( E = A & F = C ) ) ) ) ) ) )).
fof(t37_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k8_complex1(k7_xcmplx_0(A,B)) = k7_xcmplx_0(k8_complex1(A),k8_complex1(B)) ) ) )).
fof(t37_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k1_complex2(k3_xcmplx_0(A,B),C) = k1_complex2(B,k3_xcmplx_0(k8_complex1(A),C)) ) ) ) )).
fof(t37_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_complfld)) => ~ ( B != k4_struct_0(k1_complfld) & C != k4_struct_0(k1_complfld) & k3_vectsp_1(k1_complfld,A,k8_group_1(k1_complfld,B,C)) != k3_vectsp_1(k1_complfld,k3_vectsp_1(k1_complfld,A,B),C) ) ) ) ) )).
fof(t37_complsp2,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m1_subset_1(B,k2_numbers) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( A = C & B = D ) => k5_binop_1(k2_numbers,k3_binop_2,A,B) = k1_binop_1(k9_binop_2,C,D) ) ) ) ) ) )).
fof(t37_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t37_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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),k5_numbers) = B ) ) ) ) )).
fof(t37_comptrig,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k1_comptrig(k3_xcmplx_0(A,k7_complex1)) = k7_xcmplx_0(k28_sin_cos,2) ) ) )).
fof(t37_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k4_ordinal1,k4_finseq_2(B,k4_ordinal1)) => k1_recdef_1(k5_comput_1(B,A),C) = k1_recdef_1(C,A) ) ) ) )).
fof(t37_comseq_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v9_ordinal1(B) => ( A = k5_complex1 | v9_ordinal1(k25_valued_1(k4_ordinal1,k2_numbers,B,A)) ) ) ) ) )).
fof(t37_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( v1_xcmplx_0(B) => ( ! [C] : ( v7_ordinal1(C) => k9_nat_1(k2_numbers,A,k1_nat_1(C,1)) = k3_xcmplx_0(B,k9_nat_1(k2_numbers,A,C)) ) => ( B = k6_complex1 | ! [C] : ( v7_ordinal1(C) => k9_nat_1(k2_numbers,k10_comseq_3(A),C) = k3_xcmplx_0(k9_nat_1(k2_numbers,A,k5_numbers),k7_xcmplx_0(k6_xcmplx_0(k6_complex1,k2_comseq_3(B,k1_nat_1(C,1))),k6_xcmplx_0(k6_complex1,B))) ) ) ) ) ) )).
fof(t37_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( v3_conlat_1(B,A) & ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) & l2_conlat_1(B,A) ) => ! [C] : ( ( v3_conlat_1(C,A) & ~ v4_conlat_1(C,A) & v6_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 ) ) ) )).
fof(t37_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t37_convex1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k1_convex1(A,k1_convex1(A,B,D),C) = k1_convex1(A,B,k3_xcmplx_0(C,D)) ) ) ) ) )).
fof(t37_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_convex4(B,A) => r1_convex4(A,k9_convex4(A,B,B),k2_convex4(A)) ) ) )).
fof(t37_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v5_relat_1(C,k3_qc_lang1(A)) & v3_card_1(C,B) & m2_finseq_1(C,k2_qc_lang1(A)) ) => ! [D] : ( 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)))) ) ) ) ) )).
fof(t37_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => r2_hidden(k5_cqc_lang(A),k4_cqc_the1(A)) ) )).
fof(t37_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t37_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t37_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_csspace(A,B,C) => r1_csspace(A,k4_algstr_0(A,B),C) ) ) ) ) )).
fof(t37_dickson,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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)) ) ) ) ) )).
fof(t37_diff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)) & v1_diff_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)))) ) => ( ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( r1_xxreal_0(G,F) => k3_funct_2(k4_ordinal1,k1_numbers,k12_diff_1(E,F),G) = k3_xcmplx_0(k3_xcmplx_0(k4_newton(G,F),k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(C,A),G),B)),k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(D,A),k7_nat_d(F,G)),k2_xcmplx_0(B,k3_xcmplx_0(G,A)))) ) ) ) => ( k1_funct_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_funct_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) ) ) ) ) ) ) ) )).
fof(t37_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( ( 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] : ( v1_xreal_0(H) => k1_funct_1(G,H) = k7_xcmplx_0(F,H) ) & r3_zfmisc_1(A,B,C,D,E) ) => ( A = k5_numbers | B = k5_numbers | C = k5_numbers | D = k5_numbers | E = k5_numbers | k1_diff_2(G,A,B,C,D,E) = k7_xcmplx_0(F,k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(A,B),C),D),E)) ) ) ) ) ) ) ) ) ) )).
fof(t37_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => k1_funct_1(D,E) = k3_square_1(E) ) & r1_zfmisc_1(A,B,C) ) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(C,k5_numbers) | k10_diff_1(D,A,B,C) = k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(k3_xcmplx_0(k2_xcmplx_0(k3_square_1(A),k3_square_1(B)),k2_xcmplx_0(k3_square_1(A),k3_square_1(C))),k2_xcmplx_0(k3_square_1(B),k3_square_1(C))))) ) ) ) ) ) ) )).
fof(t37_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k3_diff_1(k3_diff_1(C,A),A),B) = k6_xcmplx_0(k1_funct_1(k3_diff_1(C,k3_xcmplx_0(2,A)),B),k3_xcmplx_0(2,k1_funct_1(k3_diff_1(C,A),B))) ) ) ) )).
fof(t37_dilworth,axiom,( ! [A] : ( ( 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) ) )).
fof(t37_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r3_diraf(A,B,C,D) ) ) ) ) ) )).
fof(t37_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m2_finseq_1(C,A) => k8_relset_1(k4_ordinal1,A,C,B) = k3_dist_2(k1_partfun1(k4_ordinal1,A,A,k6_margrel1,C,k7_dist_2(A,B))) ) ) ) )).
fof(t37_ec_pf_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(B))) => ( k4_nat_d(A,2) = k5_numbers => ( C = k5_numbers | k2_ec_pf_1(B,k2_binom(k9_int_3(B),C,A)) = 1 ) ) ) ) ) )).
fof(t37_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( 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)) = k5_numbers => ( k7_ec_pf_2(A,D) = k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k5_numbers,1,k5_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) = k5_numbers ) ) ) ) ) ) )).
fof(t37_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k11_ens_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k11_ens_1(A))) => ( k2_cat_1(k11_ens_1(A),B,C) != k1_xboole_0 => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t37_entropy1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( m2_finseq_1(B,k3_finseq_2(k1_numbers)) => ( ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(1,C) => ( r1_xxreal_0(k3_finseq_1(A),C) | k1_matrprob(k1_numbers,B,k1_nat_1(C,1)) = k8_finseq_1(k1_numbers,k1_matrprob(k1_numbers,B,C),k1_matrprob(k1_numbers,A,k1_nat_1(C,1))) ) ) ) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(1,C) => ( r1_xxreal_0(k3_finseq_1(A),C) | k18_rvsum_1(k1_matrprob(k1_numbers,B,k1_nat_1(C,1))) = k2_xcmplx_0(k18_rvsum_1(k1_matrprob(k1_numbers,B,C)),k18_rvsum_1(k1_matrprob(k1_numbers,A,k1_nat_1(C,1)))) ) ) ) ) ) ) )).
fof(t37_enumset1,axiom,( ! [A] : ! [B] : k2_enumset1(A,A,A,B) = k2_tarski(A,B) )).
fof(t37_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k10_eqrel_1(A) = a_1_0_eqrel_1(A) ) )).
fof(t37_equation,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,k1_funct_1(k4_equation(B),C)) => ! [E] : ( m1_pralg_2(E,A,B) => ( ! [F] : ~ ( r2_hidden(F,A) & ! [G] : ( 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) ) ) ) ) ) )).
fof(t37_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t37_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => k12_euclid(k4_struct_0(k15_euclid(A))) = k5_numbers ) )).
fof(t37_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( k4_euclid_3(A,B,C) != k5_numbers => k4_euclid_3(C,B,A) = k6_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k4_euclid_3(A,B,C)) ) ) ) ) )).
fof(t37_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => k6_xcmplx_0(k1_square_1(k12_euclid(k7_euclid(A,B,C))),k1_square_1(k12_euclid(k8_euclid(A,B,C)))) = k3_xcmplx_0(4,k22_rvsum_1(B,C)) ) ) ) )).
fof(t37_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( 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) = k22_rvsum_1(B,C) ) ) ) )).
fof(t37_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => 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,k2_xcmplx_0(A,D)),k9_euclid(3,k3_euclid_8,k2_xcmplx_0(B,E))),k9_euclid(3,k4_euclid_8,k2_xcmplx_0(C,F))) ) ) ) ) ) ) )).
fof(t37_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ~ ( r3_euclidlp(A,B,C) & B = C ) ) ) ) )).
fof(t37_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_exchsort(A) ) => ! [B] : ( m1_exchsort(B,A) => ( k9_xtuple_0(B) = k9_xtuple_0(A) & k10_xtuple_0(B) = k10_xtuple_0(A) ) ) ) )).
fof(t37_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_circcomb(A) & l1_msualg_1(A) ) => k3_msafree2(A) = u4_struct_0(A) ) )).
fof(t37_fcont_1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(t37_fdiff_10,axiom,( ! [A] : ( ( 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,k26_sin_cos,k27_sin_cos),k18_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),k18_sin_cos),A),B) = k4_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,k6_xcmplx_0(k1_funct_1(k26_sin_cos,B),k1_funct_1(k27_sin_cos,B))),k2_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B)))))) ) ) ) ) ) )).
fof(t37_fdiff_11,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) => ( r2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_sin_cos9),A),B) = k5_numbers ) ) ) ) ) )).
fof(t37_fdiff_2,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ~ r1_xxreal_0(k1_fdiff_1(A,B),k5_numbers) ) ) => ( v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,A,k2_subset_1(k1_numbers))) & v2_funct_1(A) ) ) ) )).
fof(t37_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(D,E) = k2_xcmplx_0(k3_xcmplx_0(A,E),B) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k16_sin_cos),C) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k16_sin_cos),C),E) = k3_xcmplx_0(A,k1_funct_1(k18_sin_cos,k2_xcmplx_0(k3_xcmplx_0(A,E),B))) ) ) ) ) ) ) ) ) )).
fof(t37_fdiff_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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,k22_sin_cos)),k4_taylor_1(k7_xcmplx_0(3,2))),k7_xcmplx_0(2,k3_xcmplx_0(3,k3_power(k4_power,A)))))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => ( k1_funct_1(C,E) = 1 & k1_funct_1(D,E) = k3_xcmplx_0(E,k3_power(k4_power,A)) ) ) ) ) => ( r1_xxreal_0(A,k5_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,k22_sin_cos)),k4_taylor_1(k7_xcmplx_0(3,2))),k7_xcmplx_0(2,k3_xcmplx_0(3,k3_power(k4_power,A)))),B) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_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,k22_sin_cos)),k4_taylor_1(k7_xcmplx_0(3,2))),k7_xcmplx_0(2,k3_xcmplx_0(3,k3_power(k4_power,A)))),B),E) = k3_xcmplx_0(k6_prepower(A,E),k6_prepower(k2_xcmplx_0(1,k6_prepower(A,E)),k7_xcmplx_0(1,2))) ) ) ) ) ) ) ) ) ) )).
fof(t37_fdiff_7,axiom,( ! [A] : ( ( 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,k22_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k22_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k22_sin_cos),A),B) = k3_xcmplx_0(k1_funct_1(k22_sin_cos,k1_funct_1(k16_sin_cos,B)),k1_funct_1(k18_sin_cos,B)) ) ) ) ) ) )).
fof(t37_fdiff_9,axiom,( ! [A] : ( ( 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,k18_sin_cos,k2_fdiff_9))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k2_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k2_fdiff_9),A),B) = k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,B),k1_funct_1(k18_sin_cos,k1_funct_1(k18_sin_cos,B))),k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k18_sin_cos,B)))) ) ) ) ) ) )).
fof(t37_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => k2_xcmplx_0(k6_xcmplx_0(k1_square_1(k2_power(k1_fib_num,A)),k3_xcmplx_0(2,k2_power(k4_xcmplx_0(1),A))),k1_square_1(k2_power(k1_fib_num,k4_xcmplx_0(A)))) = k1_square_1(k6_xcmplx_0(k2_power(k1_fib_num,A),k2_power(k2_fib_num,A))) ) )).
fof(t37_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(4,A) => k1_fib_num3(k2_xcmplx_0(A,1)) = k1_int_1(k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_fib_num3(A),1),k3_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)) ) ) )).
fof(t37_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_finseq_1(B,A) => ! [C] : ( m1_finseq_1(C,A) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( C = k1_xboole_0 => ( r1_xxreal_0(D,k5_numbers) | k8_finseq_8(A,B,C,D) = D ) ) ) ) ) ) )).
fof(t37_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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),C,B)) = k3_filter_0(A,k5_filter_0(A,C,B)) ) ) ) )).
fof(t37_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ( ( v12_lattices(A) & v12_lattices(B) ) <=> v12_lattices(k7_filter_1(A,B)) ) ) ) )).
fof(t37_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t37_finseq_1,axiom,( ! [A] : k9_finseq_1(A) = k1_tarski(k4_tarski(1,A)) )).
fof(t37_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(t37_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_finset_1(B) => ( r1_tarski(B,k2_finseq_1(A)) => k3_finseq_1(k14_finseq_1(B)) = k5_card_1(B) ) ) ) )).
fof(t37_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ~ ( r2_hidden(B,k10_xtuple_0(A)) & r2_hidden(B,k10_xtuple_0(k5_finseq_4(A,B))) ) ) )).
fof(t37_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => k2_rfinseq(A,k3_finseq_1(B),k8_finseq_1(A,B,C)) = C ) ) ) )).
fof(t37_finseq_6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( r2_finseq_4(B,A) => k1_nat_1(k4_finseq_4(B,A),k4_finseq_4(k3_finseq_5(B),A)) = k1_nat_1(k3_finseq_1(B),1) ) ) )).
fof(t37_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,B,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ! [G] : ( ( 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] : ( ( v1_funct_1(H) & v1_funct_2(H,k2_zfmisc_1(C,C),C) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(C,C),C))) ) => ( ! [I] : ( m1_subset_1(I,B) => ! [J] : ( m1_subset_1(J,B) => k3_funct_2(B,C,F,k5_binop_1(B,G,I,J)) = k5_binop_1(C,H,k3_funct_2(B,C,F,I),k3_funct_2(B,C,F,J)) ) ) => r2_funct_2(A,C,k1_partfun1(A,B,B,C,k6_funcop_1(B,A,G,D,E),F),k6_funcop_1(C,A,H,k1_partfun1(A,B,B,C,D,F),k1_partfun1(A,B,B,C,E,F))) ) ) ) ) ) ) ) ) ) )).
fof(t37_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( 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) ) ) )).
fof(t37_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_orders_2(A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_tarski(k7_fintopo3(A,B,C),k7_fintopo3(A,B,k1_nat_1(C,1))) ) ) ) ) )).
fof(t37_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_fintopo6(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => ( v4_fin_topo(C,A) <=> v4_fin_topo(D,B) ) ) ) ) ) ) )).
fof(t37_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_catalan2(A))) => ! [D] : ( v7_ordinal1(D) => ( r1_tarski(B,C) => r1_tarski(k7_flang_1(A,B,D),k7_flang_1(A,C,D)) ) ) ) ) )).
fof(t37_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( ( r1_xxreal_0(E,F) & r1_xxreal_0(C,D) ) => k6_flang_1(A,k1_flang_2(A,B,E,F),k1_flang_2(A,B,C,D)) = k1_flang_2(A,B,k2_xcmplx_0(E,C),k2_xcmplx_0(F,D)) ) ) ) ) ) ) )).
fof(t37_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(t37_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( 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(k9_fomodel0(B),D)) = k1_funct_1(k9_fomodel0(B),k3_relat_1(D,k20_fomodel0(B,A,C))) ) ) ) ) )).
fof(t37_fsm_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ v2_struct_0(D) & l2_fsm_1(D,B,C) ) => ( k7_fsm_1(B,C,D,A) = k7_fsm_1(B,C,D,k1_nat_1(A,1)) => v4_fsm_1(k7_fsm_1(B,C,D,A),B,C,D) ) ) ) ) ) )).
fof(t37_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => ! [C] : ( ( ~ 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))) ) ) ) )).
fof(t37_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ! [E] : ! [F] : ( 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] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( m1_subset_1(H,k6_margrel1) => ! [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))) ) ) ) ) ) ) ) ) ) )).
fof(t37_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,B,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t37_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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] : ! [D] : ( ( 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) ) ) ) )).
fof(t37_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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 => ! [E] : ( r2_hidden(E,k8_relset_1(B,C,D,A)) <=> ( r2_hidden(E,B) & r2_hidden(k1_funct_1(D,E),A) ) ) ) ) )).
fof(t37_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(A,k6_subset_1(C,B)) => k1_funct_1(k4_funct_3(B,C),A) = k1_xboole_0 ) )).
fof(t37_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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 ) ) ) )).
fof(t37_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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 ) ) ) )).
fof(t37_funct_6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( k9_xtuple_0(k6_funct_6(k7_funcop_1(A,B))) = k1_funct_2(A,k9_xtuple_0(B)) & k10_xtuple_0(k6_funct_6(k7_funcop_1(A,B))) = k1_funct_2(A,k10_xtuple_0(B)) & ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(C,k1_funct_2(A,k9_xtuple_0(B))) => k1_funct_1(k6_funct_6(k7_funcop_1(A,B)),C) = k3_relat_1(C,B) ) ) ) ) )).
fof(t37_funct_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( v7_ordinal1(E) => k2_funct_7(A,B,E,k7_partfun1(A,B,E)) = B ) ) ) ) ) )).
fof(t37_funct_8,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t37_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( A != k5_numbers => v1_funct_9(k7_funcop_1(k1_numbers,B),A) ) ) ) )).
fof(t37_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t37_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v11_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ! [F] : ( ( v15_functor0(F,B,C) & m2_functor0(F,B,C) ) => ! [G] : ( ( v15_functor0(G,B,C) & m2_functor0(G,B,C) ) => ! [H] : ( m1_functor3(H,A,B,D,E) => ! [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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t37_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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)) ) ) ) )).
fof(t37_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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) ) ) ) )).
fof(t37_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_fvaluat1(C,A) => ( v3_fvaluat1(A) => ( k3_funct_2(u1_struct_0(A),k6_numbers,C,B) = k5_numbers <=> k3_funct_2(u1_struct_0(A),k6_numbers,k5_fvaluat1(A,C),B) = k5_numbers ) ) ) ) ) )).
fof(t37_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v1_algstr_1(B) & v2_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( 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) ) ) ) )).
fof(t37_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ~ ( ~ 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)) ) ) )).
fof(t37_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t37_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v2_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ! [F] : ( m1_genealg1(F,E) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t37_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ! [L] : ( m1_subset_1(L,u1_struct_0(A)) => ! [M] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t37_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t37_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ( ( r1_tarski(B,C) & r1_tarski(D,E) ) => r1_tarski(k22_glib_000(A,B,D),k22_glib_000(A,C,E)) ) ) )).
fof(t37_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => r2_relset_1(k4_ordinal1,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),k8_glib_001(A,B,1,k3_finseq_1(B)),B) ) ) )).
fof(t37_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ~ ( v5_glib_002(B,A) & v4_glib_000(A) ) ) ) )).
fof(t37_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_003(A) ) => ! [B] : ! [C] : ! [D] : ( B != C => k1_funct_1(k6_glib_003(k12_glib_003(A,B,D)),C) = k1_funct_1(k6_glib_003(A),C) ) ) )).
fof(t37_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) & k1_nat_1(k39_glib_000(k16_glib_004(A)),1) = k5_card_1(k1_glib_002(A,o_1_1_glib_004(A))) ) ) )).
fof(t37_goboard6,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_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_0(u1_struct_0(k15_euclid(2)),A,k3_finseq_1(A),k1_matrix_0(A)),k19_euclid(1,1)),k1_tops_1(k15_euclid(2),k3_goboard5(A,k3_finseq_1(A),k1_matrix_0(A)))) ) )).
fof(t37_goboard7,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ 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) ) ) ) ) )).
fof(t37_goboard8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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(k1_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)) ) ) ) )).
fof(t37_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ( m2_finseq_1(D,C) => ! [E] : ( ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(C)) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,2),B) & r2_gobrd13(C,k17_finseq_1(C,B,D),E,A) ) => r2_gobrd13(C,D,E,A) ) ) ) ) ) )).
fof(t37_gobrd14,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t37_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_valuat_1(E,A,D) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t37_gr_cy_3,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(k1_uniroots(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( B = C => k2_group_1(k1_uniroots(A),B) = k11_algstr_0(A,C) ) ) ) ) )).
fof(t37_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t37_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_graph_1(D,A) => m1_graph_1(D,k8_graph_3(A,B,C)) ) ) ) ) )).
fof(t37_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_tarski(k4_graph_5(A,B,C),k7_graph_5(A)) ) ) ) )).
fof(t37_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => k4_finseq_1(k6_graphsp(k9_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),k15_graphsp(B),k18_graphsp(B))),A),C)) = k4_finseq_1(k6_graphsp(k9_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),k15_graphsp(B),k18_graphsp(B))),k1_nat_1(A,1)),C)) ) ) ) )).
fof(t37_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => u1_struct_0(k27_grcat_1(A)) = k26_grcat_1(A) ) )).
fof(t37_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_ideal_1(D,k12_polynom1(A,C)) & v2_ideal_1(D,k12_polynom1(A,C)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ! [E] : ( ( 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] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(G,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] : ( ( v1_funct_1(H) & v1_funct_2(H,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(H,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] : ( ( v1_funct_1(H) & v1_funct_2(H,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(H,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 ) ) ) ) ) ) ) ) )).
fof(t37_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(D,A,C) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ! [F] : ( m2_ideal_1(F,k12_polynom1(A,C),E) => ~ ( r4_groeb_2(A,B,C,D,E,F) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ! [H] : ( ( 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] : ( ( v1_funct_1(I) & v1_funct_2(I,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(I,A,C) & v1_polynom1(I,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(k12_polynom1(A,C)),F,G) = k10_polynom1(A,C,H,I) & r6_pboole(A,k3_termord(A,B,C,D),k3_termord(A,B,C,k10_polynom1(A,C,H,I))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t37_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( E = k6_xcmplx_0(k5_card_1(k3_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)))) ) ) ) ) ) ) ) )).
fof(t37_group_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t37_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_group_2(C,A) => r1_tarski(k2_group_11(A,k1_group_11(A,B,C),C),B) ) ) ) )).
fof(t37_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t37_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t37_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ! [C] : ( 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 ) ) ) ) ) )).
fof(t37_group_5,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_group_5(A,B,C) = k1_group_1(A) ) ) ) ) )).
fof(t37_group_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & l3_algstr_0(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t37_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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] : ( 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)))))) ) ) ) ) )).
fof(t37_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( m1_group_9(D,A,B) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t37_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( ( ~ 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) = k5_numbers ) => B = C ) ) ) ) )).
fof(t37_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t37_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(k1_complfld)) => ! [H] : ( m1_subset_1(H,u1_struct_0(k1_complfld)) => ! [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))))) ) ) ) ) ) ) ) ) ) )).
fof(t37_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k3_yellow_0(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A))) = k1_xboole_0 ) )).
fof(t37_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(A,C) => k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k1_taylor_1(B),C),B),A) = k2_newton(B) ) ) ) ) )).
fof(t37_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => r2_hidden(k3_hilbert1(k4_hilbert1(k4_hilbert1(k3_hilbert1(A,B),A),C),B),k6_hilbert1) ) ) ) )).
fof(t37_hilbert3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( m1_hilbert3(D,C) => ! [E] : ( ( 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)))) ) ) ) ) ) )).
fof(t37_hurwitz,axiom,( ~ v1_hurwitz(k9_polynom3(k1_complfld)) )).
fof(t37_idea_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k4_ordinal1,B,6) & m2_finseq_1(C,k3_finseq_2(k4_ordinal1)) ) => ! [D] : ( v7_ordinal1(D) => k18_idea_1(k1_nat_1(D,1),B,A,C) = k7_finseq_1(k9_finseq_1(k16_idea_1(A,k7_matrix_0(k4_ordinal1,C,k1_nat_1(D,1)))),k18_idea_1(D,B,A,C)) ) ) ) ) )).
fof(t37_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t37_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( 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] : ( m4_index_1(E,u1_struct_0(B),u4_struct_0(B),u1_graph_1(B),u2_graph_1(B),D) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t37_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( 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] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r3_pua2mss1(B,A,C,D) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t37_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => k1_int_1(k2_int_1(A)) = k2_int_1(A) ) )).
fof(t37_int_5,axiom,( ! [A] : ( ( 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) ) ) ) )).
fof(t37_int_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t37_integr11,axiom,( ! [A] : ( ( 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,k26_sin_cos,k1_fdiff_9))) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( k2_xcmplx_0(1,k1_funct_1(k16_sin_cos,B)) != k5_numbers & k6_xcmplx_0(1,k1_funct_1(k16_sin_cos,B)) != k5_numbers ) ) ) ) => ( r2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_fdiff_9),A),B) = k7_xcmplx_0(1,k6_xcmplx_0(1,k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t37_integr12,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v3_rcomp_1(F) & m1_subset_1(F,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(C,F) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,F) => ( k1_funct_1(D,G) = k7_xcmplx_0(A,k3_square_1(k6_xcmplx_0(1,k1_square_1(k2_xcmplx_0(k3_xcmplx_0(A,G),B))))) & k1_funct_1(E,G) = k2_xcmplx_0(k3_xcmplx_0(A,G),B) & ~ r1_xxreal_0(k1_funct_1(E,G),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_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) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,E,k1_sin_cos6),k2_seq_4(C)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,E,k1_sin_cos6),k3_seq_4(C))) ) ) ) ) ) ) ) )).
fof(t37_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,D) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => ( k1_funct_1(C,E) = 1 & ~ r1_xxreal_0(k1_funct_1(k1_sin_cos9,E),k5_numbers) ) ) ) & r2_relset_1(k1_numbers,k1_numbers,B,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,C,k1_taylor_1(2)),k1_sin_cos9))) & r1_tarski(D,k2_rcomp_1(k4_xcmplx_0(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,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k3_taylor_1),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k3_taylor_1),k3_seq_4(A))) ) ) ) ) ) )).
fof(t37_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,D),k1_funct_1(k16_sin_cos,k1_funct_1(k18_sin_cos,D))),k1_square_1(k1_funct_1(k18_sin_cos,k1_funct_1(k18_sin_cos,D)))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_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) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_fdiff_9)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_fdiff_9)),k3_seq_4(A))) ) ) ) ) )).
fof(t37_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( ( 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] : ( m1_integra1(E,B) => ! [F] : ( m3_integr15(F,A,B,C,E) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t37_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [C] : ( m1_integra1(C,A) => ! [D] : ( ( 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] : ( ( ~ v8_ordinal1(E) & m1_subset_1(E,k4_ordinal1) ) => ( 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)))) ) ) ) ) ) ) ) )).
fof(t37_integra2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [C] : ( m1_integra1(C,A) => ( r1_integra1(B,C) => ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(D,k4_finseq_1(C)) & ! [E] : ( v7_ordinal1(E) => ~ ( r2_hidden(E,k4_finseq_1(B)) & r1_tarski(k2_integra1(A,C,D),k2_integra1(A,B,E)) ) ) ) ) ) ) ) ) )).
fof(t37_integra8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( C = k1_rcomp_1(A,B) => ( k2_seq_4(C) = B & k3_seq_4(C) = A ) ) ) ) ) )).
fof(t37_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( C = k1_rcomp_1(k2_xcmplx_0(A,k3_xcmplx_0(k3_xcmplx_0(2,B),k28_sin_cos)),k2_xcmplx_0(A,k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(2,B),1),k28_sin_cos))) => r1_integra9(C,k16_sin_cos,k18_sin_cos) ) ) ) ) )).
fof(t37_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t37_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(t37_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => v1_int_1(k3_xcmplx_0(k7_newton(A),k1_funct_1(k3_series_1(k5_irrat_1),A))) ) )).
fof(t37_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,A,B) => ! [G] : ( m2_cat_1(G,B,C) => ! [H] : ( m2_cat_1(H,B,C) => ! [I] : ( m2_cat_1(I,C,D) => ! [J] : ( m2_cat_1(J,C,D) => ! [K] : ( m2_nattra_1(K,A,B,E,F) => ! [L] : ( m2_nattra_1(L,B,C,G,H) => ! [M] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t37_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,A,C) => ! [G] : ( m2_cat_1(G,A,C) => ( ( r2_nattra_1(A,B,D,E) & r2_nattra_1(A,C,F,G) ) => ! [H] : ( m2_nattra_1(H,A,B,D,E) => ! [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t37_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_isomichi(B,A) <=> v1_xboole_0(k1_isomichi(A,B)) ) ) ) )).
fof(t37_jgraph_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [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)) ) => ( B = k1_xboole_0 | C = k1_xboole_0 | ( r1_xboole_0(B,C) <=> ~ r1_xxreal_0(k7_weierstr(A,B,C),k5_numbers) ) ) ) ) ) ) )).
fof(t37_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ! [B] : ( ( 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)) ) ) ) ) )).
fof(t37_jgraph_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( r1_xxreal_0(A,B) & ~ r1_xxreal_0(k5_numbers,D) & ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k4_topmetr(k2_xcmplx_0(k3_xcmplx_0(D,B),C),k2_xcmplx_0(k3_xcmplx_0(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(k2_xcmplx_0(k3_xcmplx_0(D,B),C),k2_xcmplx_0(k3_xcmplx_0(D,A),C)))))) ) => ~ ( v3_tops_2(E,k4_topmetr(A,B),k4_topmetr(k2_xcmplx_0(k3_xcmplx_0(D,B),C),k2_xcmplx_0(k3_xcmplx_0(D,A),C))) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,k1_rcomp_1(A,B)) => k1_funct_1(E,F) = k2_xcmplx_0(k3_xcmplx_0(D,F),C) ) ) ) ) ) ) ) ) ) )).
fof(t37_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t37_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t37_jordan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t37_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t37_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C)),k3_topreal1(2,k1_jordan1e(B,A))) = k1_tarski(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C)),k3_topreal1(2,k2_jordan1e(B,A))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C)) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C)),k8_jordan6(B)) ) ) ) ) ) ) )).
fof(t37_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ 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,D))) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(k1_jordan8(E,C))) ) => ( ( ~ ( ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(C,k5_numbers) ) & ~ ( D = k5_numbers & C = k5_numbers ) ) | k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,D),A,k1_jordan1a(k1_jordan8(E,D)))) = k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,C),B,k1_jordan1a(k1_jordan8(E,C)))) ) ) ) ) ) ) ) )).
fof(t37_jordan1b,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(B,k3_finseq_1(k1_jordan8(A,D))) & r1_xxreal_0(C,k1_matrix_0(k1_jordan8(A,D))) & r1_tarski(k3_goboard5(k1_jordan8(A,D),B,C),k1_jordan2c(2,A)) & r1_xxreal_0(C,1) ) ) ) ) ) )).
fof(t37_jordan1g,axiom,( ! [A] : ( ( v4_topreal1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( 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 ) ) ) ) )).
fof(t37_jordan1h,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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,D) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(k1_jordan8(E,D))) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(k1_jordan8(E,D))) & ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ~ ( F = k1_int_1(k2_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(C,2),k11_newton(2,k7_nat_d(D,A))),2)) & G = k1_int_1(k2_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(B,2),k11_newton(2,k7_nat_d(D,A))),2)) & r1_tarski(k3_goboard5(k1_jordan8(E,D),C,B),k3_goboard5(k1_jordan8(E,A),F,G)) ) ) ) ) ) ) ) ) ) )).
fof(t37_jordan1j,axiom,( ! [A] : ( ( v4_topreal1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( 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)) ) ) ) )).
fof(t37_jordan1k,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(2))) => ( v2_connsp_1(k3_subset_1(u1_struct_0(k14_euclid(2)),k8_metric_1(k14_euclid(2),B,A)),k15_euclid(2)) & m1_subset_1(k3_subset_1(u1_struct_0(k14_euclid(2)),k8_metric_1(k14_euclid(2),B,A)),k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) ) ) )).
fof(t37_jordan21,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => k1_jordan21(A) != k2_jordan21(A) ) )).
fof(t37_jordan22,axiom,( ! [A] : ( ( 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)) ) ) ) )).
fof(t37_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(1,A) & a_2_2_jordan2c(A,B) = k1_xboole_0 ) ) ) )).
fof(t37_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t37_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( r1_xxreal_0(k1_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)) ) ) ) ) )).
fof(t37_jordan5d,axiom,( ! [A] : ( ( ~ 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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,1)) ) )).
fof(t37_jordan6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ~ ( r1_topreal1(k15_euclid(A),C,D,B) & C = D ) ) ) ) ) )).
fof(t37_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t37_kurato_1,axiom,( 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) )).
fof(t37_kurato_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,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(k4_ordinal1,k9_setfam_1(u1_struct_0(k2_borsuk_1(k15_euclid(2),k15_euclid(2))))))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,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(k4_ordinal1,k9_setfam_1(u1_struct_0(k2_borsuk_1(k15_euclid(2),k15_euclid(2))))))) ) => ~ ( ! [E] : ( v7_ordinal1(E) => k2_kurato_2(k2_borsuk_1(k15_euclid(2),k15_euclid(2)),C,E) = k3_borsuk_1(k15_euclid(2),k15_euclid(2),k2_kurato_2(k15_euclid(2),A,E),k2_kurato_2(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] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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] : ( v7_ordinal1(G) => k2_kurato_2(k2_borsuk_1(k15_euclid(2),k15_euclid(2)),D,G) = k3_borsuk_1(k15_euclid(2),k15_euclid(2),k2_kurato_2(k15_euclid(2),E,G),k2_kurato_2(k15_euclid(2),F,G)) ) ) ) ) ) ) ) ) ) )).
fof(t37_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( k12_matrix_3(A,B,C) != k4_struct_0(B) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(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,k1_matrix_6(A,B,C),E) & ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ( r2_hidden(k4_tarski(F,G),k2_matrix_0(D)) => k3_matrix_0(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,k8_matrix_0(u1_struct_0(B),E,G)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t37_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_lattice2(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t37_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : k15_lattice3(A,B) = k16_lattice3(A,a_2_2_lattice3(A,B)) ) )).
fof(t37_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k4_lattice4(A,B)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( 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) ) ) ) ) ) ) )).
fof(t37_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ! [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] : ( m1_subset_1(J,D) => ! [K] : ( m1_subset_1(K,D) => ! [L] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t37_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(t37_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( v7_ordinal1(C) => ( v3_lfuzzy_1(B,A) => ( r1_xxreal_0(C,k5_numbers) | r1_fuzzy_1(k4_lfuzzy_1(A,B,C),B) ) ) ) ) ) )).
fof(t37_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v9_ordinal1(A) & v2_comseq_2(A) & k1_seq_2(A) = k5_numbers & v7_valued_0(A) ) => v2_limfunc1(k37_valued_1(k4_ordinal1,k1_numbers,A)) ) ) )).
fof(t37_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r2_limfunc2(C,A) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k2_rcomp_1(k6_xcmplx_0(A,D),A),k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k1_relset_1(k1_numbers,C))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k2_rcomp_1(k6_xcmplx_0(A,D),A)) => r1_xxreal_0(k1_funct_1(C,E),k1_funct_1(B,E)) ) ) ) ) | r2_limfunc2(B,A) ) ) ) ) ) )).
fof(t37_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_limfunc3(B,A) & ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,C) & ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ~ ( ~ 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_funct_1(B,E) != k5_numbers & k1_funct_1(B,F) != k5_numbers ) ) ) ) ) ) ) => ( k1_limfunc3(B,A) = k5_numbers | ( r1_limfunc3(k6_rfunct_1(k1_numbers,k1_numbers,B),A) & k1_limfunc3(k6_rfunct_1(k1_numbers,k1_numbers,B),A) = k5_xcmplx_0(k1_limfunc3(B,A)) ) ) ) ) ) )).
fof(t37_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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) ) ) ) ) )).
fof(t37_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( r1_lmod_6(A,C,D) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r1_struct_0(C,E) => r1_struct_0(D,E) ) ) ) ) ) ) ) )).
fof(t37_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k16_lopban_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k16_lopban_1(A,B))) => ! [E] : ( v1_xreal_0(E) => ( ( k2_normsp_0(k16_lopban_1(A,B),C) = k5_numbers => C = k4_struct_0(k16_lopban_1(A,B)) ) & ( C = k4_struct_0(k16_lopban_1(A,B)) => k2_normsp_0(k16_lopban_1(A,B),C) = k5_numbers ) & k2_normsp_0(k16_lopban_1(A,B),k1_rlvect_1(k16_lopban_1(A,B),C,E)) = k3_xcmplx_0(k9_complex1(E),k2_normsp_0(k16_lopban_1(A,B),C)) & r1_xxreal_0(k2_normsp_0(k16_lopban_1(A,B),k1_algstr_0(k16_lopban_1(A,B),C,D)),k2_xcmplx_0(k2_normsp_0(k16_lopban_1(A,B),C),k2_normsp_0(k16_lopban_1(A,B),D))) ) ) ) ) ) ) )).
fof(t37_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( ! [C] : ( v7_ordinal1(C) => k5_rsspace3(A,B,C) != k4_struct_0(A) ) & ? [C] : ( v7_ordinal1(C) & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => r1_xxreal_0(1,k6_real_1(k9_nat_1(k1_numbers,k5_normsp_0(A,B),k1_nat_1(D,1)),k9_nat_1(k1_numbers,k5_normsp_0(A,B),D))) ) ) ) & v2_lopban_3(B,A) ) ) ) )).
fof(t37_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => k10_lopban_4(A,k4_struct_0(A)) = k5_struct_0(A) ) )).
fof(t37_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( r2_mesfun6c(A,B,C,D) => ( r2_hidden(k1_mesfun6c(A,B,C,D),k2_numbers) & r2_hidden(k1_mesfunc6(A,B,C,k55_valued_1(A,k2_numbers,D)),k1_numbers) & r3_mesfunc6(A,B,C,k55_valued_1(A,k2_numbers,D)) ) ) ) ) ) ) )).
fof(t37_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t37_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( v2_xxreal_0(F) & v1_xreal_0(F) ) => ( r2_hidden(E,k5_lpspace2(A,B,C,D,F)) => ( ! [G] : ( m2_subset_1(G,k1_zfmisc_1(A),B) => ~ ( k1_funct_1(C,k3_subset_1(A,G)) = k5_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)) ) ) ) ) ) ) ) ) ) )).
fof(t37_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( 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) ) ) ) )).
fof(t37_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(k1_ltlaxio1(k4_ltlaxio1(A,B)),k3_hilbert1(A,k1_ltlaxio1(B)))) ) ) )).
fof(t37_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t37_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t37_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( r2_matrix10(k2_matrix10(A,B),C) => v4_matrix10(k4_matrix10(A,B,C)) ) ) ) ) )).
fof(t37_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( ( v1_matrix_0(E) & v2_matrix_0(E,C,A,B) & m2_finseq_1(E,k3_finseq_2(C)) ) => ( k2_matrix_0(E) = k2_matrix_0(k4_matrix11(A,B,C,D,E)) & ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ~ ( r2_hidden(k4_tarski(F,G),k2_matrix_0(E)) & ! [H] : ( v7_ordinal1(H) => ~ ( k1_funct_1(D,F) = H & r2_hidden(k4_tarski(H,G),k2_matrix_0(E)) & k3_matrix_0(C,k4_matrix11(A,B,C,D,E),F,G) = k3_matrix_0(C,E,H,G) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t37_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,A,E,D) & m2_finseq_1(F,k3_finseq_2(A)) ) => ! [G] : ( m2_finseq_1(G,A) => ! [H] : ( m2_finseq_1(H,A) => ! [I] : ( m2_finseq_2(I,k4_ordinal1,k4_finseq_2(C,k4_ordinal1)) => ! [J] : ( m2_finseq_2(J,k4_ordinal1,k4_finseq_2(B,k4_ordinal1)) => ( ( k3_finseq_1(G) = k1_matrix_0(F) & H = k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,A,J,G) & r1_tarski(k2_zfmisc_1(k10_xtuple_0(I),k10_xtuple_0(J)),k2_matrix_0(F)) ) => ! [K] : ( v7_ordinal1(K) => ! [L] : ( v7_ordinal1(L) => ( k8_relat_1(I,k1_tarski(L)) = k1_tarski(K) => k3_matrix11(K,C,B,A,k1_matrix13(A,F,C,B,I,J),H) = k1_matrix13(A,k3_matrix11(L,E,D,A,F,G),C,B,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t37_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ( ( k3_matrix_0(u1_struct_0(B),D,1,1) = k11_algstr_0(B,C) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(F,A) => ( r1_xxreal_0(F,1) | k1_funct_1(D,F) = k3_matrix14(B,A,F) ) ) ) & k3_matrix_0(u1_struct_0(B),E,1,1) = C & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(F,A) => ( r1_xxreal_0(F,1) | k3_matrix_0(u1_struct_0(B),E,1,F) = k4_algstr_0(B,k8_group_1(B,C,k3_matrix_0(u1_struct_0(B),D,1,F))) ) ) ) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(F,A) => ( r1_xxreal_0(F,1) | k1_funct_1(E,F) = k3_matrix14(B,A,F) ) ) ) ) => ( r1_xxreal_0(A,k5_numbers) | C = k4_struct_0(B) | ( v1_matrix_6(D,A,B) & E = k1_matrix_6(A,B,D) ) ) ) ) ) ) ) ) )).
fof(t37_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ! [E] : ( ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(A))) ) => ! [F] : ( ( v1_matrix_0(F) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(A))) ) => ( ( r2_hidden(E,k4_matrix15(A,B,C)) & r2_hidden(F,k4_matrix15(A,B,D)) & k1_matrix_0(C) = k1_matrix_0(D) ) => r2_hidden(k3_matrix_3(A,E,F),k4_matrix15(A,B,k3_matrix_3(A,C,D))) ) ) ) ) ) ) ) )).
fof(t37_matrix16,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t37_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_finseq_1(D,C) => ! [E] : ( ( v1_matrix_0(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_0(E)) ) ) ) ) ) ) )).
fof(t37_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) & k3_matrix_3(A,B,k2_matrix_3(A,C)) = k1_matrix_3(A,k3_finseq_1(B),k1_matrix_0(B)) ) => B = C ) ) ) ) )).
fof(t37_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_6(C,A,B) & v1_matrix_6(D,A,B) & r1_matrix_6(A,B,C,D) ) => ( v1_matrix_6(k4_matrix_3(B,C,D),A,B) & k1_matrix_6(A,B,k4_matrix_3(B,C,D)) = k4_matrix_3(B,k1_matrix_6(A,B,C),k1_matrix_6(A,B,D)) ) ) ) ) ) ) )).
fof(t37_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( r1_matrix_8(A,B,C,D) & v3_matrix_8(D,A,B) ) => v3_matrix_8(C,A,B) ) ) ) ) ) )).
fof(t37_matrix_9,axiom,( k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k4_ordinal1,k3_finseq_4(k4_ordinal1,1,3,2),k3_finseq_4(k4_ordinal1,2,1,3)) = k3_finseq_4(k4_ordinal1,2,3,1) & k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k4_ordinal1,k3_finseq_4(k4_ordinal1,2,1,3),k3_finseq_4(k4_ordinal1,1,3,2)) = k3_finseq_4(k4_ordinal1,3,1,2) & k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k4_ordinal1,k3_finseq_4(k4_ordinal1,3,2,1),k3_finseq_4(k4_ordinal1,2,1,3)) = k3_finseq_4(k4_ordinal1,3,1,2) & k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k4_ordinal1,k3_finseq_4(k4_ordinal1,2,1,3),k3_finseq_4(k4_ordinal1,3,2,1)) = k3_finseq_4(k4_ordinal1,2,3,1) & k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k4_ordinal1,k3_finseq_4(k4_ordinal1,3,2,1),k3_finseq_4(k4_ordinal1,3,2,1)) = k3_finseq_4(k4_ordinal1,1,2,3) & k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k4_ordinal1,k3_finseq_4(k4_ordinal1,2,1,3),k3_finseq_4(k4_ordinal1,2,1,3)) = k3_finseq_4(k4_ordinal1,1,2,3) & k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k4_ordinal1,k3_finseq_4(k4_ordinal1,1,3,2),k3_finseq_4(k4_ordinal1,1,3,2)) = k3_finseq_4(k4_ordinal1,1,2,3) & k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k4_ordinal1,k3_finseq_4(k4_ordinal1,2,3,1),k3_finseq_4(k4_ordinal1,1,3,2)) = k3_finseq_4(k4_ordinal1,3,2,1) & k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k4_ordinal1,k3_finseq_4(k4_ordinal1,2,3,1),k3_finseq_4(k4_ordinal1,2,3,1)) = k3_finseq_4(k4_ordinal1,3,1,2) & k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k4_ordinal1,k3_finseq_4(k4_ordinal1,3,1,2),k3_finseq_4(k4_ordinal1,2,3,1)) = k3_finseq_4(k4_ordinal1,1,2,3) & k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k4_ordinal1,k3_finseq_4(k4_ordinal1,2,3,1),k3_finseq_4(k4_ordinal1,3,1,2)) = k3_finseq_4(k4_ordinal1,1,2,3) & k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k4_ordinal1,k3_finseq_4(k4_ordinal1,3,1,2),k3_finseq_4(k4_ordinal1,3,1,2)) = k3_finseq_4(k4_ordinal1,2,3,1) & k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k4_ordinal1,k3_finseq_4(k4_ordinal1,3,2,1),k3_finseq_4(k4_ordinal1,1,3,2)) = k3_finseq_4(k4_ordinal1,2,3,1) & k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k4_ordinal1,k3_finseq_4(k4_ordinal1,1,3,2),k3_finseq_4(k4_ordinal1,3,2,1)) = k3_finseq_4(k4_ordinal1,3,1,2) )).
fof(t37_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( 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))) ) ) ) )).
fof(t37_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( ( 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) ) => k7_matrix_0(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),k7_matrix_0(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)) ) ) ) ) ) ) )).
fof(t37_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k1_matrix_0(A) = k1_matrix_0(B) & A = k3_matrixr1(A,B) ) => B = k8_matrixr1(k3_finseq_1(A),k1_matrix_0(A)) ) ) ) )).
fof(t37_matrixr2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,A,3,3) & m2_finseq_1(B,k3_finseq_2(A)) ) => B = k3_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),k3_finseq_4(A,k3_matrix_0(A,B,1,1),k3_matrix_0(A,B,1,2),k3_matrix_0(A,B,1,3)),k3_finseq_4(A,k3_matrix_0(A,B,2,1),k3_matrix_0(A,B,2,2),k3_matrix_0(A,B,2,3)),k3_finseq_4(A,k3_matrix_0(A,B,3,1),k3_matrix_0(A,B,3,2),k3_matrix_0(A,B,3,3))) ) ) )).
fof(t37_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( m1_matrlin(D,A,B) => ! [E] : ( m2_finseq_1(E,u1_struct_0(C)) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(A),k3_finseq_1(D),k3_finseq_1(E)) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(A))) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(A),k3_finseq_1(D),k3_finseq_1(E)) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(A))) ) => 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))) ) ) ) ) ) ) ) )).
fof(t37_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v5_matroid0(B,A) => ( ~ v1_xboole_0(B) & v1_finset_1(B) ) ) ) ) )).
fof(t37_matrprob,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [D] : ( m2_finseq_2(D,u1_struct_0(k2_vectsp_1),k4_finseq_2(A,u1_struct_0(k2_vectsp_1))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t37_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_card_1(D,A) & v1_finseq_1(D) & v3_valued_0(D) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(k2_vectsp_1),A,C) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( ( A = k5_numbers => k2_xcmplx_0(C,B) = k5_numbers ) => k1_funct_1(k3_matrtop1(A,k2_xcmplx_0(k1_matrix_0(E),k1_matrix_0(F)),k1_matrix15(u1_struct_0(k2_vectsp_1),A,C,B,E,F)),D) = k7_finseq_1(k1_funct_1(k3_matrtop1(A,C,E),D),k1_funct_1(k3_matrtop1(A,B,F),D)) ) ) ) ) ) ) ) )).
fof(t37_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t37_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k4_zfmisc_1(A,B,C,D) = k2_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C),D) )).
fof(t37_measure1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m2_measure1(D,A,B,C) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t37_measure6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(C,B) & r1_xxreal_0(k2_xcmplx_0(k9_complex1(A),k9_complex1(C)),k9_complex1(B)) ) ) ) ) )).
fof(t37_member_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_member_1(k1_tarski(A)) = k1_tarski(k5_xcmplx_0(A)) ) )).
fof(t37_membered,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( v3_membered(B) => ~ ( A != k1_xboole_0 & B != k1_xboole_0 & ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r2_hidden(C,A) & r2_hidden(D,B) ) => r1_xxreal_0(C,D) ) ) ) & ! [C] : ( v1_xreal_0(C) => ~ ( ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => r1_xxreal_0(D,C) ) ) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => r1_xxreal_0(C,D) ) ) ) ) ) ) ) )).
fof(t37_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_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 ) ) ) ) )).
fof(t37_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( 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] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t37_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : 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))) ) ) )).
fof(t37_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ( ! [E] : ( 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)) ) ) ) ) ) )).
fof(t37_mesfunc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( v1_xreal_0(E) => ( ( r1_mesfunc1(A,B,C,D) & r1_tarski(D,k9_xtuple_0(C)) ) => r1_mesfunc1(A,B,k6_mesfunc1(A,C,E),D) ) ) ) ) ) ) )).
fof(t37_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( r1_mesfunc2(A,B,D) => m2_subset_1(k1_relset_1(A,D),k1_zfmisc_1(A),B) ) ) ) ) ) )).
fof(t37_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( r2_hidden(C,k1_relset_1(A,B)) => ( ( k12_supinf_2(k18_rfunct_3(A,B),C) = k12_supinf_2(B,C) | k12_supinf_2(k18_rfunct_3(A,B),C) = k5_numbers ) & ( k12_supinf_2(k19_rfunct_3(A,B),C) = k2_supinf_2(k12_supinf_2(B,C)) | k12_supinf_2(k19_rfunct_3(A,B),C) = k5_numbers ) ) ) ) ) )).
fof(t37_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( m1_subset_1(E,A) => ( ( v1_mesfunc8(B,A,k6_numbers) & r2_hidden(E,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers))) & ! [F] : ( v7_ordinal1(F) => v6_supinf_2(k4_mesfunc5(A,k6_numbers,B,F)) ) & r1_xxreal_0(C,D) ) => r1_xxreal_0(k1_mesfunc9(k4_mesfunc5(A,k6_numbers,k4_mesfunc9(A,B),C),E),k1_mesfunc9(k4_mesfunc5(A,k6_numbers,k4_mesfunc9(A,B),D),E)) ) ) ) ) ) ) )).
fof(t37_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t37_mmlquery,axiom,( ! [A] : ! [B] : ( 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))) ) )).
fof(t37_mod_4,axiom,( ! [A] : ( ( ~ 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] : ( ( 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)) ) ) ) )).
fof(t37_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k6_modal_1) => ~ ( A != k17_modal_1 & ! [B] : ( m1_subset_1(B,k3_modal_1) => A != k16_modal_1(B) ) & ! [B] : ( m1_subset_1(B,k6_modal_1) => A != k10_modal_1(B) ) & ! [B] : ( m1_subset_1(B,k6_modal_1) => A != k11_modal_1(B) ) & ! [B] : ( m1_subset_1(B,k6_modal_1) => ! [C] : ( m1_subset_1(C,k6_modal_1) => A != k12_modal_1(B,C) ) ) ) ) )).
fof(t37_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t37_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r3_modelc_2(A,B) => ( ( ~ v3_modelc_2(B) & ~ v6_modelc_2(B) ) | r2_modelc_2(A,k10_modelc_2(B)) ) ) ) ) )).
fof(t37_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_3(B,A) & v3_modelc_3(B,A) & l1_modelc_3(B,A) ) => ! [C] : ( ( v1_modelc_3(C,A) & v3_modelc_3(C,A) & l1_modelc_3(C,A) ) => ( r6_modelc_3(A,B,C) => r1_tarski(u3_modelc_3(A,B),u1_modelc_3(A,C)) ) ) ) ) )).
fof(t37_moebius1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ( ~ r1_int_2(A,B) => k2_moebius1(k2_nat_1(A,B)) = k5_numbers ) ) ) )).
fof(t37_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_vectsp_1(A) & v17_monoid_0(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m3_monoid_0(B,A) ) => v17_monoid_0(B) ) ) )).
fof(t37_monoid_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k20_monoid_1(A,k6_finseq_1(A)) = k17_monoid_1(A,k5_numbers) ) )).
fof(t37_msafree3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_msualg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => r1_tarski(k3_msualg_1(A,D,C),k3_msualg_1(A,D,B)) ) ) ) ) )).
fof(t37_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & l3_msualg_1(D,A) ) => ( ( g3_msualg_1(A,u3_msualg_1(A,C),u4_msualg_1(A,C)) = g3_msualg_1(A,u3_msualg_1(A,D),u4_msualg_1(A,D)) & v5_msafree4(C,A,B) ) => v5_msafree4(D,A,B) ) ) ) ) ) )).
fof(t37_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( 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] : ( m2_pboole(E,u1_struct_0(A),C,u3_msualg_1(A,B)) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) & v1_finset_1(F) & v3_trees_2(F) ) => ! [G] : ( ( 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 ) ) ) ) ) ) ) ) )).
fof(t37_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) => ! [D] : ( m3_pboole(D,A,k1_mboolean(A,B)) => m3_pboole(k5_pboole(A,C,D),A,k1_mboolean(A,B)) ) ) ) )).
fof(t37_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => m1_msualg_2(g3_msualg_1(A,u3_msualg_1(A,B),u4_msualg_1(A,B)),A,B) ) ) )).
fof(t37_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(t37_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_mycielsk(B,A) => r1_tarski(u1_struct_0(B),u1_struct_0(k6_mycielsk(A,B))) ) ) )).
fof(t37_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,C))) ) => r2_funct_2(k4_ordinal1,C,k8_nat_1(C,k8_nat_1(C,D,A),B),k8_nat_1(C,k8_nat_1(C,D,B),A)) ) ) ) ) )).
fof(t37_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( v7_ordinal1(A) & v1_int_2(A) & r1_nat_d(A,B) ) => ( v1_xboole_0(B) | r2_hidden(A,k13_pre_poly(k12_nat_3(B))) ) ) ) ) )).
fof(t37_nat_4,axiom,( v1_int_2(631) )).
fof(t37_nat_5,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( r1_int_2(A,B) => k5_nat_5(k3_xcmplx_0(A,B)) = k2_nat_1(k5_nat_5(A),k5_nat_5(B)) ) ) ) )).
fof(t37_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t37_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t37_ncfcont2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t37_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_ndiff_1(A,B,D,E) => ( r1_ndiff_1(A,B,k4_vfunct_1(u1_struct_0(A),B,D,C),E) & k3_ndiff_1(A,B,k4_vfunct_1(u1_struct_0(A),B,D,C),E) = k1_rlvect_1(k16_lopban_1(A,B),k3_ndiff_1(A,B,D,E),C) ) ) ) ) ) ) ) )).
fof(t37_ndiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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(k4_ordinal1,1) ) ) ) ) )).
fof(t37_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_prvect_2(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t37_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ~ r1_xxreal_0(1,k7_xcmplx_0(A,k1_nat_1(A,1))) ) )).
fof(t37_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_numbers))) ) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & r2_hidden(E,C) & k7_partfun1(k1_numbers,B,D) = k2_seq_4(k7_relset_1(u1_struct_0(A),k1_numbers,B,C)) & k7_partfun1(k1_numbers,B,E) = k3_seq_4(k7_relset_1(u1_struct_0(A),k1_numbers,B,C)) ) ) ) ) ) ) ) )).
fof(t37_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [E] : ( ( 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) ) ) ) ) )).
fof(t37_normform,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [C] : ( m1_subset_1(C,k5_finsub_1(k7_normform(A))) => ( r2_hidden(B,k9_normform(A,C)) => r2_hidden(B,C) ) ) ) )).
fof(t37_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t37_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( 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)))) ) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => k3_funct_2(u4_struct_0(k2_oppcat_1(B)),u4_struct_0(A),k10_oppcat_1(B,A,C),k5_oppcat_1(B,D)) = k3_funct_2(u4_struct_0(B),u4_struct_0(A),C,D) ) ) ) ) )).
fof(t37_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_real_ns1(A))) => k1_funct_1(k1_pdiff_1(B,A),k3_rlvect_1(k4_real_ns1(A),C,D)) = k2_xcmplx_0(k1_funct_1(k1_pdiff_1(B,A),C),k1_funct_1(k1_pdiff_1(B,A),D)) ) ) ) ) )).
fof(t37_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v3_orders_1(A) => r3_orders_1(A,k1_relat_1(A)) ) ) )).
fof(t37_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m2_orders_1(B,k1_orders_1(u1_struct_0(A)),k6_partfun1(k1_orders_1(u1_struct_0(A)))) => ! [C] : ( m2_orders_2(C,A,B) => r2_hidden(k1_funct_1(B,u1_struct_0(A)),C) ) ) ) )).
fof(t37_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( v4_ordinal1(B) => ( B = k5_ordinal1 | ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_ordinal2(C) ) => ( ( k9_xtuple_0(C) = B & ! [D] : ( v3_ordinal1(D) => ( r2_hidden(D,B) => k1_funct_1(C,D) = k11_ordinal2(D,A) ) ) ) => k11_ordinal2(B,A) = k3_tarski(k4_ordinal2(C)) ) ) ) ) ) ) )).
fof(t37_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( k11_ordinal2(A,B) = 1 => ( A = 1 & B = 1 ) ) ) ) )).
fof(t37_ordinal4,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( ( r2_ordinal2(A,B) & r2_ordinal2(B,C) ) => r2_ordinal2(A,C) ) ) ) ) )).
fof(t37_ordinal5,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal5(A) ) => r2_hidden(k4_ordinal1,A) ) )).
fof(t37_ordinal6,axiom,( ! [A] : ! [B] : ( ( 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] : ( r2_hidden(C,A) => r1_abian(C,B) ) ) => ( v1_xboole_0(A) | k3_tarski(A) = k1_funct_1(B,k3_tarski(A)) ) ) ) )).
fof(t37_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v12_osalg_1(C,A) & m1_msualg_2(C,A,B) ) => ! [D] : ( m2_osalg_2(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t37_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & l1_parsp_1(A) ) => ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & B != C & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_parsp_1(A,B,C,B,D) ) ) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => r1_parsp_1(A,B,C,D,E) ) ) ) ) ) ) )).
fof(t37_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_parsp_2(A,B,C,D,E) & r2_parsp_2(A,B,C,E,D) ) ) ) ) ) ) )).
fof(t37_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( v2_funct_1(C) => v2_funct_1(k3_partfun1(C,A,B)) ) ) )).
fof(t37_partfun2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( m1_subset_1(E,C) & k2_relset_1(C,k2_partfun1(B,C,D,A)) = k1_tarski(E) ) ) ) ) ) ) )).
fof(t37_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t37_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t37_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ( l2_pcs_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k22_pcs_0(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k22_pcs_0(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t37_pdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( 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),k3_funct_2(k1_euclid(2),k1_numbers,k1_pdiff_1(1,2),B)) ) ) ) )).
fof(t37_pdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t37_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m1_rcomp_1(C,k3_funct_2(k1_euclid(3),k1_numbers,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] : ( ( v9_ordinal1(D) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,E) = k1_tarski(k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(1,3),B)) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),C) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,1,k1_pdiff_3(1,3,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,1,k1_pdiff_3(1,3,A),B))))) & k1_pdiff_5(A,B) = k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,1,k1_pdiff_3(1,3,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,1,k1_pdiff_3(1,3,A),B))))) ) ) ) ) ) ) ) ) )).
fof(t37_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [D] : ( ( 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] : ( C = D => ( r4_pdiff_7(A,B,C,E) <=> r3_nfcont_1(k4_real_ns1(A),k4_real_ns1(B),D,E) ) ) ) ) ) ) )).
fof(t37_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t37_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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 ) ) ) )).
fof(t37_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(B))) => ! [E] : ( 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)) ) ) ) ) )).
fof(t37_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k17_polyform(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k17_polyform(A,B))) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t37_polynom5,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_polynom4(A,k2_algseq_1(A,B),C) = B ) ) ) )).
fof(t37_polynom8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ( 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] : ( 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_0(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) ) ) ) ) ) ) ) )).
fof(t37_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ~ r6_polyred(A,B,C,k8_polynom1(A,C),D) ) ) ) ) )).
fof(t37_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(C,k5_numbers) & r1_xxreal_0(k2_power(B,C),k2_power(A,C)) ) ) ) ) )).
fof(t37_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v4_valued_0(B) ) => ! [C] : ( ( 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)) ) ) )).
fof(t37_prepower,axiom,( ! [A] : ( v1_int_1(A) => k3_prepower(1,A) = 1 ) )).
fof(t37_prob_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m2_prob_1(E,A,B) => k3_funct_2(B,k1_numbers,E,k6_prob_1(A,B,C,D)) = k3_real_1(k3_funct_2(B,k1_numbers,E,C),k3_funct_2(B,k1_numbers,E,k7_prob_1(A,B,D,k5_prob_1(A,B,C,D)))) ) ) ) ) ) )).
fof(t37_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m1_prob_1(E,A,B) => ! [F] : ( m2_prob_1(F,A,B) => ( E = k3_subset_1(A,D) => ( r1_xxreal_0(k3_funct_2(B,k1_numbers,F,C),k5_numbers) | r1_xxreal_0(k3_funct_2(B,k1_numbers,F,D),k5_numbers) | r1_xxreal_0(k3_funct_2(B,k1_numbers,F,E),k5_numbers) | ( k3_funct_2(B,k1_numbers,k3_prob_2(A,B,F,C),D) = k6_real_1(k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,F,D),C),k3_funct_2(B,k1_numbers,F,D)),k3_real_1(k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,F,D),C),k3_funct_2(B,k1_numbers,F,D)),k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,F,E),C),k3_funct_2(B,k1_numbers,F,E)))) & k3_funct_2(B,k1_numbers,k3_prob_2(A,B,F,C),E) = k6_real_1(k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,F,E),C),k3_funct_2(B,k1_numbers,F,E)),k3_real_1(k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,F,D),C),k3_funct_2(B,k1_numbers,F,D)),k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,F,E),C),k3_funct_2(B,k1_numbers,F,E)))) ) ) ) ) ) ) ) ) ) )).
fof(t37_prob_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( m2_prob_1(D,A,B) => v7_valued_0(k8_prob_1(A,B,k2_prob_3(A,C),D)) ) ) ) ) )).
fof(t37_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( 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)),k6_numbers,k7_prob_4(A,B,C),k4_measure3(A,B,k2_prob_4(A,B,C))) ) ) ) )).
fof(t37_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t37_projpl_1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & v5_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u1_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u2_incsp_1(A)) => ! [H] : ( 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] : ( 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 ) ) ) ) ) ) ) ) ) ) ) )).
fof(t37_pscomp_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(t37_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( r2_pboole(A,k2_pboole(A,C,k1_pzfmisc1(A,B)),D) <=> ( r1_pboole(A,B,D) & r2_pboole(A,C,D) ) ) ) ) ) )).
fof(t37_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t37_qc_lang3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_qc_lang1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_qc_lang1(B))) ) => ! [D] : ( m2_subset_1(D,k6_qc_lang1(B),k8_qc_lang1(B,A)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t37_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_qc_lang4(C,A,B) => ! [D] : ( m1_qc_lang4(D,A,B) => ! [E] : ( m2_qc_lang4(E,A,B,C) => ! [F] : ( 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(k4_ordinal1,E,F),A,B,D) ) ) ) ) ) ) ) )).
fof(t37_quatern2,axiom,( k5_struct_0(k15_quatern2) = k2_quatern2 )).
fof(t37_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => r1_xxreal_0(k28_quaterni(k25_quaterni(k25_quaterni(A,B),C)),k2_xcmplx_0(k2_xcmplx_0(k28_quaterni(A),k28_quaterni(B)),k28_quaterni(C))) ) ) ) )).
fof(t37_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => A = k22_quaterni(k22_quaterni(k19_quaterni(k13_quaterni(A),k21_quaterni(k14_quaterni(A),k1_xcmplx_0)),k21_quaterni(k15_quaterni(A),k11_quaterni)),k21_quaterni(k16_quaterni(A),k12_quaterni)) ) )).
fof(t37_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k19_quofield(A))) => ! [C] : ( 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) ) ) ) )).
fof(t37_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_vectsp_6(E,A,B) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( v2_funct_1(k2_partfun1(u1_struct_0(B),u1_struct_0(C),D,k1_vectsp_6(A,B,E))) & r2_hidden(F,k1_vectsp_6(A,B,E)) ) => k3_funct_2(u1_struct_0(C),u1_struct_0(A),k8_ranknull(A,B,C,E,D),k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,F)) = k3_funct_2(u1_struct_0(B),u1_struct_0(A),E,F) ) ) ) ) ) ) ) )).
fof(t37_rat_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => ( r1_xxreal_0(A,B) <=> r1_xxreal_0(k3_xcmplx_0(A,k1_rat_1(B)),k2_rat_1(B)) ) ) ) )).
fof(t37_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t37_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => k9_nat_1(k1_numbers,k4_real_3(B),k1_nat_1(A,1)) = k9_nat_1(k1_numbers,k4_real_3(k7_xcmplx_0(1,k3_int_1(B))),A) ) ) )).
fof(t37_relat_1,axiom,( k2_relat_1(k1_xboole_0) = k1_xboole_0 )).
fof(t37_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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 ) ) ) )).
fof(t37_revrot_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ 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) ) ) )).
fof(t37_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( ( r5_rewrite1(A,B,C) | r6_rewrite1(A,B,C) ) => r2_rewrite1(A,B,C) ) ) )).
fof(t37_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(A)) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t37_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_afinsq_1(D))) => ! [F] : ( ( ~ 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)) ) ) ) ) )).
fof(t37_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_valued_0(C) ) => k1_rfunct_1(C,k1_rfunct_1(A,B)) = k1_rfunct_1(k18_valued_1(C,k5_relat_1(B,k9_xtuple_0(k4_rfunct_1(B)))),A) ) ) ) )).
fof(t37_rfunct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t37_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,A) => r1_xxreal_0(k5_numbers,k1_funct_1(k18_rfunct_3(A,B),C)) ) ) ) )).
fof(t37_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k1_funct_1(k4_rinfsup1(B),A) = k1_rinfsup1(k1_valued_0(k1_numbers,B,A)) ) ) )).
fof(t37_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v7_valued_0(A) => ( v10_mesfunc5(A) & k2_mesfunc5(A) = k1_rinfsup2(A) ) ) ) )).
fof(t37_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_rlaffin1(A,B) = k3_rlaffin1(A,k1_rlaffin1(A,B,C)) ) ) ) )).
fof(t37_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => k1_rlsub_1(B) = k1_rlsub_1(C) ) ) ) )).
fof(t37_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t37_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t37_rlvect_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( 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 ) ) ) ) ) ) )).
fof(t37_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( 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))) ) ) ) )).
fof(t37_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ? [D] : ( 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 ) ) ) ) )).
fof(t37_rlvect_5,axiom,( ! [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_rlvect_5(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ( r1_rlsub_2(A,B,C) => k1_rlvect_5(A) = k1_nat_1(k1_rlvect_5(B),k1_rlvect_5(C)) ) ) ) ) )).
fof(t37_rlvect_x,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t37_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => k1_rmod_2(A,C) = k1_rmod_2(A,D) ) ) ) ) )).
fof(t37_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t37_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_4(C,A,B) => ! [D] : ( 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))) ) ) ) ) )).
fof(t37_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k10_robbins1(A,B,C) = C ) ) ) )).
fof(t37_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t37_robbins4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v10_robbins1(A) & v8_robbins3(A) & v9_robbins3(A) & l4_robbins1(A) ) => ( v1_robbins4(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t37_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ! [D] : ( ( 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)) ) ) ) )).
fof(t37_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_tarski(B,C) => ( r1_xxreal_0(k1_rpr_1(A,C),k5_numbers) | k2_rpr_1(A,C,B) = k7_xcmplx_0(k1_rpr_1(A,B),k1_rpr_1(A,C)) ) ) ) ) ) )).
fof(t37_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_hidden(C,k3_rusub_1(A,C,B)) ) ) ) )).
fof(t37_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t37_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( r2_hidden(F,k3_rusub_1(A,B,k1_rusub_3(A,k8_domain_1(u1_struct_0(A),C,D,E)))) <=> ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & ? [I] : ( v1_xreal_0(I) & 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)) ) ) ) ) ) ) ) ) ) )).
fof(t37_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => r2_hidden(k4_bhsp_2(A,B,C),k4_rusub_5(A)) ) ) ) )).
fof(t37_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => k9_rvsum_1(A,B,B) = k5_finseq_2(k4_ordinal1,A,k5_numbers) ) ) )).
fof(t37_rvsum_2,axiom,( ! [A] : ( v7_ordinal1(A) => k17_rvsum_1(k5_finseq_2(k2_numbers,A,k5_complex1)) = k5_complex1 ) )).
fof(t37_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( 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),k5_numbers) | ( r1_scm_halt(k2_scmfsa8b(E,C,D),B,A) & r2_scm_halt(k2_scmfsa8b(E,C,D),B,A) ) ) ) ) ) ) ) ) )).
fof(t37_scmbsort,axiom,( r2_extpro_1(k7_card_1(3),k1_scmfsa_2,k2_scmbsort,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)),k10_scmfsa_m) )).
fof(t37_scmfsa10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => k1_amistd_1(k7_card_1(3),k1_scmfsa_2,A,k13_scmfsa_2(B,C)) = k2_tarski(B,k1_ordinal1(A)) ) ) ) )).
fof(t37_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_finset_1(E) & v1_afinsq_1(E) ) => ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_scmfsa_2)) ) => ( ( ! [G] : ( ( 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] : ( 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] : ( ( 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] : ( 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(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(E,C,A)) = k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(E,D,B)) ) ) ) ) ) ) ) ) ) )).
fof(t37_scmfsa_2,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [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(k7_card_1(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)) ) ) )).
fof(t37_scmfsa_9,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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),k1_nat_1(k5_card_1(B),4)) = k11_scmfsa_2(k5_numbers) ) ) )).
fof(t37_scmfsa_m,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ( ! [B] : ( ( 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] : ( m1_scmfsa_2(B) => k18_scmfsa_2(k1_scmfsa_m(A),B) = k18_scmfsa_2(A,B) ) ) ) )).
fof(t37_scmisort,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( m2_finseq_1(B,k4_numbers) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ~ ( r1_tarski(k1_funct_4(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)),k16_funcop_1(k5_scmfsa_2(k5_numbers),B)),A) & r1_tarski(k3_scmisort,C) & ! [D] : ( 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(k7_card_1(3),k1_scmfsa_2,C,A),k5_scmfsa_2(k5_numbers)) = D ) ) ) ) ) ) )).
fof(t37_scmpds_2,axiom,( ! [A] : ( ( 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] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => r2_hidden(B,k9_xtuple_0(A)) ) ) )).
fof(t37_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => r2_hidden(k5_numbers,k9_xtuple_0(k5_scmpds_6(A,B,C))) ) ) ) )).
fof(t37_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k5_compos_0(u1_compos_1(k1_scmring2(A)),k9_scmring2(A,C,B),D) = k9_scmring2(A,k2_xcmplx_0(C,D),B) ) ) ) ) )).
fof(t37_scmyciel,axiom,( ! [A] : ! [B] : k5_scmyciel(k2_tarski(A,B)) = k2_enumset1(k1_xboole_0,k1_tarski(A),k1_tarski(B),k2_tarski(A,B)) )).
fof(t37_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t37_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v9_ordinal1(A) & v9_ordinal1(B) ) => v9_ordinal1(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) ) ) )).
fof(t37_seq_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_seq_2(A) & v7_valued_0(A) ) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k1_seq_2(A)) ) ) ) )).
fof(t37_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t37_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_comseq_2(A) => ! [B] : ( v1_xreal_0(B) => v1_comseq_2(k26_valued_1(k4_ordinal1,k1_numbers,A,B)) ) ) & ( v1_comseq_2(A) => v1_comseq_2(k32_valued_1(k4_ordinal1,k1_numbers,A)) ) & ( v1_comseq_2(A) => v1_comseq_2(k56_valued_1(k4_ordinal1,k1_numbers,A)) ) & ( v1_comseq_2(k56_valued_1(k4_ordinal1,k1_numbers,A)) => v1_comseq_2(A) ) ) ) )).
fof(t37_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [C] : ( v7_ordinal1(C) => ( k9_nat_1(k1_numbers,A,C) != k5_numbers & k9_nat_1(k1_numbers,B,C) = k6_real_1(k3_funct_2(k4_ordinal1,k1_numbers,k56_valued_1(k4_ordinal1,k1_numbers,A),k1_nat_1(C,1)),k9_nat_1(k1_numbers,k56_valued_1(k4_ordinal1,k1_numbers,A),C)) ) ) & v2_comseq_2(B) ) => ( r1_xxreal_0(1,k1_seq_2(B)) | v2_series_1(A) ) ) ) ) )).
fof(t37_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => ( k2_xcmplx_0(k2_xcmplx_0(A,B),C) = 1 => r1_xxreal_0(9,k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(1,A),k7_xcmplx_0(1,B)),k7_xcmplx_0(1,C))) ) ) ) ) )).
fof(t37_setfam_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t37_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ! [E] : ( v7_ordinal1(E) => k1_funct_1(D,E) = k3_xboole_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) => ! [E] : ( v7_ordinal1(E) => r1_tarski(k1_funct_1(k4_setlim_1(A,D),E),k3_xboole_0(k1_funct_1(k4_setlim_1(A,B),E),k1_funct_1(k4_setlim_1(A,C),E))) ) ) ) ) ) )).
fof(t37_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) ) ) )).
fof(t37_setwiseo,axiom,( ! [A] : r3_binop_1(k5_finsub_1(A),k1_setwiseo(A),k9_setwiseo(A)) )).
fof(t37_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( v7_ordinal1(D) => ! [E] : ( m2_finseq_2(E,A,k4_finseq_2(D,A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t37_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) ) => ( r1_xboole_0(k1_relset_1(k4_ordinal1,A),k1_relset_1(k4_ordinal1,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)) ) ) ) )).
fof(t37_sgraph1,axiom,( r4_sgraph1(k4_ordinal1,k8_sgraph1,k8_finseq_1(k4_ordinal1,k8_finseq_1(k4_ordinal1,k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,1),k12_finseq_1(k4_ordinal1,2)),k12_finseq_1(k4_ordinal1,3)),k12_finseq_1(k4_ordinal1,1))) )).
fof(t37_sheffer1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t37_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t37_simplex0,axiom,( ! [A] : ! [B] : ( ( v1_matroid0(B) & v3_matroid0(B) & m1_simplex0(B,A) ) => ! [C] : ( 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)) ) ) )).
fof(t37_simplex1,axiom,( ! [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) ) => ! [B] : ( ( 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] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t37_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(C) & k1_seq_2(C) = B & ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(A,k9_nat_1(k1_numbers,C,D)) ) ) => r1_xxreal_0(A,B) ) ) ) ) )).
fof(t37_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => r1_xxreal_0(1,k1_funct_1(k3_sin_cos2,A)) ) )).
fof(t37_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k15_sin_cos(k4_xcmplx_0(k3_xcmplx_0(k7_complex1,A))) = k6_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,A),k3_xcmplx_0(k7_complex1,k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,A))) ) )).
fof(t37_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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))) ) ) )).
fof(t37_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k6_xcmplx_0(k23_sin_cos(A),k23_sin_cos(k4_xcmplx_0(A))) != k5_numbers => k3_xcmplx_0(k6_sin_cos2(A),k1_sin_cos5(A)) = 1 ) ) )).
fof(t37_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ~ ( r1_xxreal_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B),A) & ~ r1_xxreal_0(k2_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)),A) & r1_xxreal_0(1,k17_sin_cos(A)) ) ) ) )).
fof(t37_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,1) => k2_sin_cos7(A) = k4_sin_cos7(k7_xcmplx_0(k3_square_1(k6_xcmplx_0(k1_square_1(A),1)),A)) ) ) )).
fof(t37_sin_cos9,axiom,( k3_sin_cos9(k4_xcmplx_0(1)) = k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)) & k1_funct_1(k1_sin_cos9,k4_xcmplx_0(1)) = k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)) )).
fof(t37_sincos10,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k3_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(t37_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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(k1_nat_1(A,2),k3_finseq_1(B)) & E = k7_partfun1(u1_struct_0(k15_euclid(2)),B,k1_nat_1(A,1)) & r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),B,k1_nat_1(A,1)),k1_rltopsp1(k15_euclid(2),C,D)) ) => ( k7_partfun1(u1_struct_0(k15_euclid(2)),B,k1_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,k1_nat_1(A,1)))) | ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( 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,k1_nat_1(A,1)))) & r2_hidden(G,k1_rltopsp1(k15_euclid(2),C,D)) & r2_hidden(G,k8_metric_1(k14_euclid(2),E,F)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t37_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ( ( 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)) ) ) ) ) ) )).
fof(t37_sprect_1,axiom,( ! [A] : ( 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) ) )).
fof(t37_sprect_2,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ 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))) ) ) ) ) ) )).
fof(t37_sprect_3,axiom,( ! [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) & 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) ) ) )).
fof(t37_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t37_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k5_numbers,B) => ( r1_xxreal_0(A,B) | k7_xcmplx_0(1,k2_xcmplx_0(k3_square_1(A),k3_square_1(B))) = k7_xcmplx_0(k6_xcmplx_0(k3_square_1(A),k3_square_1(B)),k6_xcmplx_0(A,B)) ) ) ) ) )).
fof(t37_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(k14_stacks_1(A))) => ( r1_stacks_1(k14_stacks_1(A),B) <=> B = u1_stacks_1(A) ) ) ) )).
fof(t37_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k7_card_1(k1_nat_1(B,1)),k7_card_1(k1_nat_1(A,1))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(k1_nat_1(B,1)),k7_card_1(k1_nat_1(A,1))))) ) => ( ( v2_funct_2(C,k7_card_1(k1_nat_1(A,1))) & v1_stirl2_1(C,k1_nat_1(B,1),k1_nat_1(A,1)) & k1_stirl2_1(k1_nat_1(B,1),k7_card_1(k1_nat_1(A,1)),C,k6_domain_1(k7_card_1(k1_nat_1(A,1)),k2_stirl2_1(k7_card_1(k1_nat_1(B,1)),k1_nat_1(A,1),C,B))) = k1_seq_4(B) ) => ( r1_tarski(k2_relset_1(k3_numbers,k2_partfun1(k7_card_1(k1_nat_1(B,1)),k7_card_1(k1_nat_1(A,1)),C,B)),A) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k7_card_1(B),k7_card_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(B),k7_card_1(A)))) ) => ( D = k2_partfun1(k7_card_1(k1_nat_1(B,1)),k7_card_1(k1_nat_1(A,1)),C,B) => ( v2_funct_2(D,k7_card_1(A)) & v1_stirl2_1(D,B,A) ) ) ) ) ) ) ) ) )).
fof(t37_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k16_substut1(A),k38_substut1(A)) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t37_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ( A != k1_xboole_0 => m1_subset_1(k3_enumset1(B,C,D,E,F),k1_zfmisc_1(A)) ) ) ) ) ) ) )).
fof(t37_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t37_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ~ v1_xboole_0(k2_relset_1(k6_numbers,A)) & v4_card_3(k2_relset_1(k6_numbers,A)) & m1_subset_1(k2_relset_1(k6_numbers,A),k1_zfmisc_1(k6_numbers)) ) ) )).
fof(t37_sysrel,axiom,( ! [A] : ( 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 ) ) ) )).
fof(t37_taxonom1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t37_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(u1_struct_0(A)),k9_tdlat_1(A)) => ! [C] : ( 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) ) ) ) )).
fof(t37_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))))) ) ) )).
fof(t37_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v4_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t37_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => k3_polynom1(k15_pre_poly(A),C,k5_polynom1(A,C,k5_termord(A,B,C,D),k6_termord(A,B,C,D))) = k3_polynom1(k15_pre_poly(A),C,D) ) ) ) ) )).
fof(t37_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t37_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => v2_tex_2(B,A) ) ) )).
fof(t37_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_pre_topc(C,A) => ( r3_tsep_2(A,B,C) => ( v2_tex_3(B,A) <=> v4_tex_3(C,A) ) ) ) ) ) )).
fof(t37_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t37_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( ~ r1_tsep_1(C,D) => ( ( ( r1_tsep_1(C,B) | r1_tsep_1(D,B) ) => r1_tsep_1(k2_tsep_1(A,C,D),B) ) & ( ( r1_tsep_1(B,C) | r1_tsep_1(B,D) ) => r1_tsep_1(B,k2_tsep_1(A,C,D)) ) ) ) ) ) ) ) )).
fof(t37_toler_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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,C),k3_toler_1(A,B)) <=> r1_relset_1(A,A,C,B) ) ) ) )).
fof(t37_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( m1_borsuk_2(G,A,E,C) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t37_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( v7_topalg_6(B,A) & m2_subset_1(B,k4_partfun1(k1_numbers,k2_struct_0(A)),k1_topalg_6(A)) ) => ! [C] : ( v1_xreal_0(C) => ? [D] : ( m2_subset_1(D,k4_partfun1(k1_numbers,k2_struct_0(A)),k1_topalg_6(A)) & ? [E] : ( 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)))) ) ) ) ) ) )).
fof(t37_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v4_pre_topc(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( r1_xboole_0(B,C) => ! [D] : ( ( v1_topdim_1(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( r1_xxreal_0(k2_topdim_1(A,D),k5_numbers) & v5_waybel23(k1_pre_topc(A,D)) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_metrizts(A,B,C,E) & r1_xboole_0(E,D) ) ) ) ) ) ) ) ) )).
fof(t37_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(t37_topgen_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(t37_topgen_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t37_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t37_topgen_5,axiom,( 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))) )).
fof(t37_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_topgrp_1(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_connsp_2(D,A,k6_algstr_0(A,B,C)) => ? [E] : ( m1_connsp_2(E,A,B) & ? [F] : ( m1_connsp_2(F,A,C) & r1_tarski(k2_group_2(A,E,F),D) ) ) ) ) ) => v4_topgrp_1(A) ) ) )).
fof(t37_topreal3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(2))) => ( ( k18_euclid(A) = k18_euclid(B) & C = k11_finseq_1(A,k19_euclid(k7_xcmplx_0(k2_xcmplx_0(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) ) ) ) ) ) ) )).
fof(t37_topreal6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(2))) => ! [D] : ( v1_xreal_0(D) => ( ( C = B & r2_hidden(A,k8_metric_1(k14_euclid(2),C,D)) ) => ( ~ r1_xxreal_0(k17_euclid(A),k6_xcmplx_0(k17_euclid(B),D)) & ~ r1_xxreal_0(k2_xcmplx_0(k17_euclid(B),D),k17_euclid(A)) ) ) ) ) ) ) )).
fof(t37_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ( ~ v1_xboole_0(k3_topreal9(A,C,B)) => r1_xxreal_0(k5_numbers,B) ) ) ) ) )).
fof(t37_topreala,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t37_toprealb,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( 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(k3_xcmplx_0(2,k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)),k18_sin_cos),A),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k3_xcmplx_0(2,k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)),k16_sin_cos),A)) ) ) ) )).
fof(t37_toprealc,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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))))) ) ) ) ) )).
fof(t37_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) )).
fof(t37_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)) ) ) )).
fof(t37_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t37_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_tops_3(B,A) & v2_tops_1(B,A) ) ) ) )).
fof(t37_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t37_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ( m4_trees_1(k1_xboole_0,A) & m4_trees_1(k1_tarski(k1_xboole_0),A) ) ) )).
fof(t37_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( r2_hidden(C,A) => ! [D] : ( m1_trees_1(D,k5_trees_1(A,C,B)) => ! [E] : ( m1_trees_1(E,B) => ( r2_relset_1(k4_ordinal1,k4_ordinal1,D,k8_finseq_1(k4_ordinal1,C,E)) => r2_tarski(k1_trees_2(k5_trees_1(A,C,B),D),k1_trees_2(B,E)) ) ) ) ) ) ) ) )).
fof(t37_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v6_trees_3(A) ) => ( k9_xtuple_0(k1_funct_6(A)) = k9_xtuple_0(A) & v4_trees_3(k1_funct_6(A)) ) ) )).
fof(t37_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v3_trees_9(A) ) => ! [B] : ( m1_trees_1(B,k9_xtuple_0(A)) => k1_relset_1(k4_ordinal1,k3_relat_1(k1_trees_9(k9_xtuple_0(A),B),A)) = k4_finseq_1(k1_trees_9(k9_xtuple_0(A),B)) ) ) )).
fof(t37_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t37_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_pre_topc(C,A) => ! [D] : ( m1_pre_topc(D,A) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t37_turing_1,axiom,( ! [A] : ( 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] : ( m2_funct_2(B,k4_numbers,u1_turing_1(k20_turing_1),k9_funct_2(k4_numbers,u1_turing_1(k20_turing_1))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( r1_xxreal_0(3,k3_finseq_1(D)) & A = k4_domain_1(k4_ordinal1,k4_ordinal1,k9_funct_2(k4_numbers,u1_turing_1(k20_turing_1)),k5_numbers,C,B) & r2_turing_1(k8_finseq_1(k4_ordinal1,k12_finseq_1(k4_ordinal1,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)) = k1_nat_1(k1_nat_1(k1_nat_1(C,k7_partfun1(k4_ordinal1,D,1)),k7_partfun1(k4_ordinal1,D,2)),4) & r2_turing_1(k2_finseq_4(k4_ordinal1,k1_nat_1(k1_nat_1(k1_nat_1(C,k7_partfun1(k4_ordinal1,D,1)),k7_partfun1(k4_ordinal1,D,2)),4),k7_partfun1(k4_ordinal1,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))) ) ) ) ) ) ) )).
fof(t37_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ 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))) ) ) )).
fof(t37_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => m1_group_2(k3_uniroots(A),k1_uniroots(k1_complfld)) ) )).
fof(t37_uproots,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & v1_uproots(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k1_algseq_1(A,k13_polynom3(A,k2_polynom5(A,k4_polynom5(A,B,k5_struct_0(A)),D),C)) = k1_nat_1(D,k1_algseq_1(A,C)) ) ) ) ) )).
fof(t37_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_funct_2(C,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t37_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) ) => k1_relset_1(k4_ordinal1,A) = k2_xboole_0(k1_relset_1(k4_ordinal1,k63_valued_1(A)),k1_tarski(k62_valued_1(A))) ) )).
fof(t37_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t37_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t37_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( 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 ) ) ) ) ) )).
fof(t37_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => k1_vectsp_4(A,C) = k1_vectsp_4(A,D) ) ) ) ) )).
fof(t37_vectsp_5,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( r1_vectsp_5(A,B,C,D) => m1_vectsp_5(D,A,B,C) ) ) ) ) ) )).
fof(t37_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t37_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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 ) ) ) ) )).
fof(t37_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(C)))) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t37_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t37_waybel11,axiom,( ! [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) & l1_waybel_9(A) ) => ( u1_pre_topc(A) = k5_waybel11(A) => v4_waybel11(A) ) ) )).
fof(t37_waybel12,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ( v2_waybel12(B,A) & B = k3_yellow_0(A) ) ) ) )).
fof(t37_waybel14,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( 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] : ( 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(k1_yellow_1(k5_waybel11(A))) ) => B = k1_yellow_0(A,a_2_4_waybel14(A,B)) ) ) ) )).
fof(t37_waybel19,axiom,( ! [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] : ( ( v2_pre_topc(B) & v2_waybel19(B) & m1_yellow_9(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(C,A) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( D = C => v3_pre_topc(D,B) ) ) ) ) ) ) )).
fof(t37_waybel20,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t37_waybel21,axiom,( ! [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] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m2_yellow_6(C,A,B) => r3_orders_2(A,k1_waybel11(A,B),k1_waybel11(A,C)) ) ) ) )).
fof(t37_waybel23,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v2_waybel23(k6_waybel_0(A,B),A) ) ) )).
fof(t37_waybel24,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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)) ) ) )).
fof(t37_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & v2_waybel18(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t37_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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(k1_yellow_1(u1_pre_topc(A))) & v3_waybel_3(B) ) ) & ( ( v3_waybel_3(k1_yellow_1(u1_pre_topc(A))) & v3_waybel_3(B) ) => ( v3_lattice3(k1_waybel26(A,B)) & v3_waybel_3(k1_waybel26(A,B)) ) ) ) ) ) )).
fof(t37_waybel27,axiom,( ! [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] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(t37_waybel30,axiom,( ! [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_yellow13(A) & v3_waybel30(A) & l1_waybel_9(A) ) => v2_waybel30(A) ) )).
fof(t37_waybel34,axiom,( ! [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] : ( ( 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] : ( ( v4_waybel11(C) & m1_yellow_9(C,k1_yellow_2(A,A,B)) ) => ! [D] : ( ( v4_waybel11(D) & m1_yellow_9(D,A) ) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t37_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t37_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t37_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ( ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) )).
fof(t37_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ( B = u1_struct_0(A) => ( v1_waybel_3(B,k1_yellow_1(u1_pre_topc(A))) <=> v1_compts_1(A) ) ) ) ) )).
fof(t37_waybel_4,axiom,( ! [A] : ( ( 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] : ( ( ~ 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) ) ) )).
fof(t37_waybel_7,axiom,( ! [A] : ( ( 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] : ( ( ~ 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] : ( 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))) ) ) ) )).
fof(t37_waybel_9,axiom,( ! [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) & l1_waybel_9(A) ) => ( ( ! [B] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => v5_pre_topc(k4_waybel_1(A,B),A,A) ) ) => v2_waybel_2(A) ) ) )).
fof(t37_weddwitt,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t37_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => r3_wellord1(A,A,k4_relat_1(k1_relat_1(A))) ) )).
fof(t37_xboole_1,axiom,( ! [A] : ! [B] : ( k4_xboole_0(A,B) = k1_xboole_0 <=> r1_tarski(A,B) ) )).
fof(t37_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k4_xboolean(k3_xboolean(A),k9_xboolean(A,B)) = k9_xboolean(A,B) ) ) )).
fof(t37_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k6_xcmplx_0(A,k6_xcmplx_0(B,C)) = k2_xcmplx_0(k6_xcmplx_0(A,B),C) ) ) ) )).
fof(t37_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(C,B) & r1_xxreal_0(B,k2_xcmplx_0(C,A)) ) ) ) ) )).
fof(t37_xtuple_0,axiom,( ! [A] : ! [B] : r1_tarski(k4_xboole_0(k12_xtuple_0(A),k12_xtuple_0(B)),k12_xtuple_0(k4_xboole_0(A,B))) )).
fof(t37_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(A,C) => k4_xxreal_0(A,k3_xxreal_0(B,C)) = k3_xxreal_0(k4_xxreal_0(A,B),C) ) ) ) ) )).
fof(t37_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(D,B) ) => r1_tarski(k4_xxreal_1(C,D),k1_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t37_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => m1_xxreal_2(A,k1_xboole_0) ) )).
fof(t37_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t37_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( 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))) ) ) ) ) )).
fof(t37_yellow12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => k6_partfun1(u1_struct_0(A)) = a_1_0_yellow12(A) ) )).
fof(t37_yellow14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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)) ) ) ) )).
fof(t37_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_yellow_0(B,A) ) => ! [C] : m1_yellow_0(k5_yellow_1(C,B),k5_yellow_1(C,A)) ) ) )).
fof(t37_yellow18,axiom,( ! [A] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(t37_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v11_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v2_altcat_1(D) & v11_altcat_1(D) & v12_altcat_1(D) & l2_altcat_1(D) ) => ! [E] : ( l2_functor0(E,A,B) => ( r2_yellow20(A,B,E,C,D) => r1_functor0(C,D) ) ) ) ) ) ) )).
fof(t37_yellow_0,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t37_yellow_2,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ! [C] : ( 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))) ) ) ) ) )).
fof(t37_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( r2_lattice3(A,C,G) => r1_orders_2(A,E,G) ) ) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ( r2_lattice3(B,D,G) => r1_orders_2(B,F,G) ) ) ) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t37_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t37_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t37_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( ~ r2_hidden(C,k10_yellow_6(A,B)) & ! [D] : ( m2_yellow_6(D,A,B) => ? [E] : ( m2_yellow_6(E,A,D) & r2_hidden(C,k10_yellow_6(A,E)) ) ) ) ) ) ) )).
fof(t37_yellow_7,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => k7_waybel_1(k7_lattice3(A),k8_lattice3(A,B)) = k7_waybel_1(A,B) ) ) )).
fof(t37_yellow_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t37_zf_fund1,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k4_ordinal1)) ) => ! [C] : ( ~ v1_xboole_0(C) => ~ ( r2_hidden(A,k9_funct_2(B,C)) & ! [D] : ( ( 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) ) ) ) ) )).
fof(t37_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v3_zf_lang(A) => A = k5_zf_lang(k18_zf_lang(A),k19_zf_lang(A)) ) ) )).
fof(t37_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( 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))) ) ) ) )).
fof(t37_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( k1_tarski(A) = k2_xboole_0(B,C) & B != C & B != k1_xboole_0 & C != k1_xboole_0 ) )).
fof(t37_zfrefle1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ~ ( r2_hidden(k4_ordinal1,A) & ! [B] : ( ( 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] : ( ( v3_ordinal1(C) & m1_subset_1(C,A) ) => ! [D] : ( ~ v1_xboole_0(D) => ( ( k4_ordinal4(A,B,C) = C & D = k4_classes1(C) ) => ( k1_xboole_0 = C | r2_zfrefle1(D,A) ) ) ) ) ) ) ) ) )).
fof(t37_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_int_1(C) => ! [D] : ( m1_zmodul01(D,A) => ( r1_struct_0(D,B) => r1_struct_0(D,k1_zmodul01(A,B,C)) ) ) ) ) ) )).
fof(t37_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => k18_zmodul02(A,k24_zmodul02(A,B)) = k18_zmodul02(A,B) ) ) )).
fof(t37_zmodul03,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ 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) & v1_zmodul03(B) & v2_zmodul03(B) & l1_zmodul01(B) ) => k2_zmodul03(B) = k1_vectsp_9(k9_int_3(A),k12_zmodul02(A,B)) ) ) )).
fof(t380_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t381_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t382_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t383_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t384_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t385_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t386_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t387_xxreal_1,axiom,( ! [A] : ( 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)) ) )).
fof(t388_xxreal_1,axiom,( ! [A] : ( 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)) ) )).
fof(t389_xxreal_1,axiom,( ! [A] : ( 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)) ) )).
fof(t38_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r3_abcmiz_0(A,B,k6_finseq_1(u1_abcmiz_0(A))) ) ) )).
fof(t38_abcmiz_1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t38_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => ( v3_abcmiz_1(A) <=> ? [B] : ( m2_abcmiz_1(B,A,k12_abcmiz_1(A)) & ? [C] : ( m2_abcmiz_1(C,A,k13_abcmiz_1(A)) & v4_abcmiz_a(B,A) & v4_abcmiz_a(C,A) ) ) ) ) )).
fof(t38_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t38_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r1_tarski(C,E) & r1_tarski(D,E) & v1_aff_4(E,A) ) ) ) ) ) ) ) )).
fof(t38_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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,k5_numbers) = A & k1_funct_1(D,1) = B & k1_funct_1(D,2) = C ) ) ) )).
fof(t38_afinsq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => k6_afinsq_2(A,k6_afinsq_1(C,D),B) = k5_binop_1(A,B,C,D) ) ) ) ) )).
fof(t38_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k14_afproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k14_afproj(A))) => ! [D] : ( m1_subset_1(D,u2_incsp_1(k14_afproj(A))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t38_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k1_afvect0(A,C,k1_afvect0(A,D,B)) = k1_afvect0(A,D,k1_afvect0(A,C,B)) <=> ~ ( C != D & ~ r1_afvect0(A,C,D) & ~ r1_afvect0(A,D,k1_afvect0(A,C,D)) ) ) ) ) ) ) )).
fof(t38_algspec1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r1_algspec1(A,B,C) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t38_algstr_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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))))) ) ) ) ) )).
fof(t38_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v3_altcat_2(B,A) & m1_altcat_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,k1_altcat_1(A,C,D)) => ! [H] : ( m1_subset_1(H,k1_altcat_1(A,D,C)) => ! [I] : ( m1_subset_1(I,k1_altcat_1(B,E,F)) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t38_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & F != G & r1_analort(A,B,C,F,G,D,E) ) ) ) ) ) ) ) ) )).
fof(t38_aofa_000,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & v3_freealg(A) & l1_unialg_1(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(u1_unialg_1(A))) => ! [C] : ( ( 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] : ~ ( r2_hidden(D,k10_xtuple_0(C)) & D = k1_funct_1(k2_pua2mss1(A,B),C) ) ) ) ) ) )).
fof(t38_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & 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] : ( m1_msafree(D,A,B) => ! [E] : ( m1_msafree(E,A,C) => ( ( r8_pboole(u1_struct_0(A),D,E) & v1_msafree(D,A,B) ) => v1_msafree(E,A,C) ) ) ) ) ) ) ) )).
fof(t38_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( ( v19_aofa_a00(F,A) & m1_subset_1(F,u1_struct_0(A)) ) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),F)) => ! [H] : ( m2_subset_1(H,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => k15_aofa_a00(A,B,C,D,F,k29_aofa_a00(A,C,F,G),H) = k29_aofa_a00(A,D,F,k15_aofa_a00(A,B,C,D,F,G,H)) ) ) ) ) ) ) ) ) )).
fof(t38_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_aofa_i00(E,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) ) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),E) => ! [G] : ( 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) = k5_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) = k5_numbers ) & ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t38_armstrng,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( 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))) ) ) )).
fof(t38_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ( r2_hidden(A,k4_ordinal1) <=> k7_arytm_3(A) = 1 ) ) )).
fof(t38_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & v6_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( v7_ordinal1(C) => ( ( 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)) ) ) ) ) )).
fof(t38_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( r2_hidden(B,k5_asympt_1) => k9_nat_1(k1_numbers,A,B) = B ) & ( ~ r2_hidden(B,k5_asympt_1) => k9_nat_1(k1_numbers,A,B) = k5_series_1(B,2) ) ) ) & ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v4_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( r2_funct_2(k4_ordinal1,k1_numbers,B,A) & r2_hidden(k3_asympt_1(1),k11_asympt_0(B,k5_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) ) ) ) ) )).
fof(t38_bcialg_1,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k4_bcialg_1(A)) => k1_bcialg_1(A,B,C) = B ) ) ) )).
fof(t38_bcialg_2,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ! [C] : ( 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) ) ) ) )).
fof(t38_bcialg_3,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t38_bcialg_4,axiom,( ! [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) & l1_bcialg_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t38_bcialg_5,axiom,( ! [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) ) => ( ( ~ 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,k5_numbers,k5_numbers,k5_numbers,k5_numbers) ) ) )).
fof(t38_bcialg_6,axiom,( ! [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] : ( ( ~ 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] : ( ( 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] : ( ( 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)))) ) => ( ( v3_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & D = k2_funct_1(C) ) => v3_funct_2(D,u1_struct_0(B),u1_struct_0(A)) ) ) ) ) ) )).
fof(t38_bciideal,axiom,( ! [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) ) => ( ( v3_bciideal(k1_tarski(k4_struct_0(A)),A) & m2_bcialg_1(k1_tarski(k4_struct_0(A)),A) ) <=> ! [B] : ( m2_bcialg_1(B,A) => ( v3_bciideal(B,A) & m2_bcialg_1(B,A) ) ) ) ) )).
fof(t38_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ~ ( B != C & r1_xxreal_0(k4_bhsp_1(A,B,C),k5_numbers) ) & ~ ( ~ r1_xxreal_0(k4_bhsp_1(A,B,C),k5_numbers) & B = C ) ) ) ) ) )).
fof(t38_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) & k1_seq_2(k3_bhsp_2(A,k5_normsp_1(A,D,C),k1_rlvect_1(A,B,C))) = k5_numbers ) ) ) ) ) ) )).
fof(t38_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k3_bhsp_1(A,k3_bhsp_4(A,B,C)),k6_series_1(k2_bhsp_2(A,B),C)) ) ) ) )).
fof(t38_bilinear,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( ( 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))))) ) ) ) ) ) ) ) ) ) ) )).
fof(t38_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t38_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_borsuk_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(k11_borsuk_1(A,B))) => ! [D] : ( 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) ) ) ) ) )).
fof(t38_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( 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))) ) ) ) ) )).
fof(t38_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ( A = B => ( v3_rcomp_1(A) <=> v3_pre_topc(B,k3_topmetr) ) ) ) ) )).
fof(t38_borsuk_6,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( 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) ) ) ) ) ) )).
fof(t38_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t38_bspace,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ? [C] : ( m2_vectsp_6(C,k2_bspace,k7_bspace(A),k9_bspace(A)) & k4_vectsp_6(k2_bspace,k7_bspace(A),C) = B ) ) ) )).
fof(t38_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t38_bvfunc14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) ) => ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ( 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) ) ) )).
fof(t38_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t38_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t38_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( 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))) ) ) ) ) )).
fof(t38_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(E,A) => ( r3_bvfunc_2(A,D,B,E) => r1_bvfunc_1(A,k6_bvfunc_1(A,D,k7_bvfunc_2(A,C,B,E)),k7_bvfunc_2(A,k6_bvfunc_1(A,D,C),B,E)) ) ) ) ) ) ) )).
fof(t38_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(F,A) => r1_bvfunc_1(A,k2_bvfunc_1(A,k2_bvfunc_1(A,k7_bvfunc_2(A,E,B,F),k6_bvfunc_2(A,k9_bvfunc_1(A,E,D),B,F)),k6_bvfunc_2(A,k9_bvfunc_1(A,E,C),B,F)),k7_bvfunc_2(A,k2_bvfunc_1(A,C,D),B,F)) ) ) ) ) ) ) )).
fof(t38_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t38_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t38_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t38_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => ! [D] : ( m2_finseq_1(D,k3_cqc_lang(A)) => ( ( r2_relset_1(k4_ordinal1,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))) ) ) ) ) ) ) )).
fof(t38_card_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_finset_1(A) & v1_finset_1(k1_card_1(A)) ) ) )).
fof(t38_card_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k5_card_1(k3_xcmplx_0(B,A)) = k2_card_2(k5_card_1(B),k5_card_1(A)) ) ) )).
fof(t38_card_3,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : k7_card_3(k16_funcop_1(B,A)) = A ) )).
fof(t38_card_5,axiom,( ! [A] : ! [B] : ( 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(k5_numbers,A) ) ) )).
fof(t38_card_fil,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ( v7_card_fil(A) => v2_card_1(A) ) ) )).
fof(t38_card_fin,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t38_card_lar,axiom,( ! [A] : ( ( ~ 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)) ) ) ) )).
fof(t38_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t38_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,C) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k6_cat_2(B,C)),k7_cat_1(A,k6_cat_2(B,C),k14_cat_2(A,B,C,D,E)),F) = k7_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)) ) ) ) ) ) ) )).
fof(t38_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) ) )).
fof(t38_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t38_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k2_catalan2(k3_xcmplx_0(2,A),A) = a_1_5_catalan2(A) ) ) )).
fof(t38_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => v1_ideal_1(k6_cc0sp2(A),k6_cfuncdom(u1_struct_0(A))) ) )).
fof(t38_cfcont_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,k2_numbers,k2_numbers,C,B)) & k7_partfun1(k2_numbers,B,k3_comseq_2(C)) = k3_comseq_2(k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,C,B)) ) ) ) ) ) ) )).
fof(t38_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t38_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m1_chain_1(D,A) => ( r2_hidden(k3_chain_1(A,B,C),k4_chain_1(A,D,A)) <=> ( ! [E] : ( m2_subset_1(E,k4_ordinal1,k2_finseq_1(A)) => m2_chain_1(k4_tarski(k1_funct_1(B,E),k1_funct_1(C,E)),k2_chain_1(A,D,E)) ) & ( ! [E] : ( m2_subset_1(E,k4_ordinal1,k2_finseq_1(A)) => ~ r1_xxreal_0(k1_funct_1(C,E),k1_funct_1(B,E)) ) | ! [E] : ( m2_subset_1(E,k4_ordinal1,k2_finseq_1(A)) => ~ r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) ) ) )).
fof(t38_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ? [C] : ( 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) ) ) ) )).
fof(t38_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) ) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t38_circcomb,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(t38_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t38_classes1,axiom,( ! [A] : ( v3_ordinal1(A) => r1_tarski(A,k4_classes1(A)) ) )).
fof(t38_classes2,axiom,( ! [A] : ( v2_classes1(A) => v2_classes1(k4_classes1(k1_card_1(A))) ) )).
fof(t38_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t38_clopban3,axiom,( ! [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) & l1_clopban2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( v1_xcmplx_0(F) => ( 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,k2_xcmplx_0(E,F)) = k3_rlvect_1(A,k1_clvect_1(A,B,E),k1_clvect_1(A,B,F)) & k1_clvect_1(A,B,k3_xcmplx_0(E,F)) = k1_clvect_1(A,k1_clvect_1(A,B,F),E) & k1_clvect_1(A,k6_algstr_0(A,B,C),k3_xcmplx_0(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)) & ( k2_normsp_0(A,B) = k5_numbers => B = k4_struct_0(A) ) & ( B = k4_struct_0(A) => k2_normsp_0(A,B) = k5_numbers ) & k2_normsp_0(A,k1_clvect_1(A,B,E)) = k3_xcmplx_0(k9_complex1(E),k2_normsp_0(A,B)) & r1_xxreal_0(k2_normsp_0(A,k3_rlvect_1(A,B,C)),k2_xcmplx_0(k2_normsp_0(A,B),k2_normsp_0(A,C))) & r1_xxreal_0(k2_normsp_0(A,k6_algstr_0(A,B,C)),k3_xcmplx_0(k2_normsp_0(A,B),k2_normsp_0(A,C))) & k2_normsp_0(A,k5_struct_0(A)) = 1 ) ) ) ) ) ) ) )).
fof(t38_clopban4,axiom,( ! [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) & 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] : ( 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) ) ) ) )).
fof(t38_closure1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( v9_closure1(B,A) & l1_closure1(B,A) ) => ! [C] : ( 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] : ( m1_pboole(D,u1_struct_0(A),k5_mssubfam(u1_struct_0(A),u3_msualg_1(A,B))) => ! [E] : ( ( v2_relat_1(E) & m3_pboole(E,u1_struct_0(A),k1_mboolean(u1_struct_0(A),u3_msualg_1(A,B))) ) => ( ! [F] : ( ( 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))) ) ) ) ) ) )).
fof(t38_closure2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( v15_closure2(B,A) & l1_closure2(B,A) ) => ! [C] : ( m1_closure2(C,u1_struct_0(A),u3_msualg_1(A,B),k6_closure2(u1_struct_0(A),u3_msualg_1(A,B))) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t38_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_clvect_1(B,A) => r1_struct_0(A,k4_struct_0(B)) ) ) )).
fof(t38_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) & k1_seq_2(k3_clvect_2(A,k6_clvect_1(A,D,C),k1_clvect_1(A,B,C))) = k5_numbers ) ) ) ) ) ) )).
fof(t38_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k13_csspace(A,k2_clvect_3(A,B,C)),k6_series_1(k2_clvect_2(A,B),C)) ) ) ) )).
fof(t38_coh_sp,axiom,( ! [A] : ! [B] : ( r2_hidden(A,k19_coh_sp(B)) <=> ? [C] : ( m1_subset_1(C,k16_coh_sp(B)) & ? [D] : ( 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)))) ) ) ) )).
fof(t38_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k3_tarski(B)))) => ~ ( ! [D] : ( r2_hidden(D,C) => v1_finset_1(k1_xtuple_0(D)) ) & ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(k2_xboole_0(D,E),A) => ! [F] : ! [G] : ( ( r2_hidden(k4_tarski(D,F),C) & r2_hidden(k4_tarski(E,G),C) ) => r2_hidden(k2_tarski(F,G),B) ) ) ) ) & ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(k2_xboole_0(D,E),A) => ! [F] : ( ( r2_hidden(k4_tarski(D,F),C) & r2_hidden(k4_tarski(E,F),C) ) => D = E ) ) ) ) & ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t38_compl_sp,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ~ 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) ) ) ) ) ) )).
fof(t38_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k4_complex1(A) = k5_numbers => k8_complex1(A) = A ) ) )).
fof(t38_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => k1_complex2(k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D)),E) = k2_xcmplx_0(k3_xcmplx_0(A,k1_complex2(C,E)),k3_xcmplx_0(B,k1_complex2(D,E))) ) ) ) ) ) )).
fof(t38_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_complfld)) => ~ ( B != k4_struct_0(k1_complfld) & C != k4_struct_0(k1_complfld) & k3_vectsp_1(k1_complfld,k8_group_1(k1_complfld,A,C),B) != k3_vectsp_1(k1_complfld,A,k3_vectsp_1(k1_complfld,B,C)) ) ) ) ) )).
fof(t38_complsp2,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( m2_finseq_1(C,k2_numbers) => ! [D] : ( m2_finseq_1(D,k2_numbers) => ! [E] : ( m2_finseq_1(E,k1_numbers) => ! [F] : ( m2_finseq_1(F,k1_numbers) => ( ( C = E & D = F & k3_finseq_1(C) = k3_finseq_1(F) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( r2_hidden(G,k4_finseq_1(C)) => k5_binop_1(k2_numbers,A,k9_matrix_5(C,G),k9_matrix_5(D,G)) = k1_binop_1(B,k9_matrix_5(E,G),k9_matrix_5(F,G)) ) ) ) => k1_finseqop(k2_numbers,k2_numbers,k2_numbers,A,C,D) = k1_finseqop(k1_numbers,k1_numbers,k1_numbers,B,E,F) ) ) ) ) ) ) ) )).
fof(t38_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(A)) => ( k2_afinsq_1(k9_compos_1(A,B)) = k6_domain_1(k4_ordinal1,k5_numbers) & k1_funct_1(k9_compos_1(A,B),k5_numbers) = B ) ) ) )).
fof(t38_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( v6_compos_0(D,u1_compos_1(A)) & m1_subset_1(D,u1_compos_1(A)) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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),k5_numbers) = B ) ) ) ) ) )).
fof(t38_comptrig,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(k5_numbers,A) => k1_comptrig(k3_xcmplx_0(A,k7_complex1)) = k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos) ) ) )).
fof(t38_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t38_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v9_ordinal1(A) => v9_ordinal1(k31_valued_1(k4_ordinal1,k2_numbers,A)) ) ) )).
fof(t38_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ! [D] : ( v7_ordinal1(D) => ( k3_complex1(k9_nat_1(k2_numbers,C,D)) = k9_nat_1(k1_numbers,A,D) & k4_complex1(k9_nat_1(k2_numbers,C,D)) = k9_nat_1(k1_numbers,B,D) ) ) => ( ( v2_comseq_2(A) & v2_comseq_2(B) ) <=> v2_comseq_2(C) ) ) ) ) ) )).
fof(t38_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( v3_conlat_1(B,A) & ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) & l2_conlat_1(B,A) ) => k1_binop_1(k9_conlat_1(A),B,k5_conlat_1(A)) = B ) ) )).
fof(t38_connsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_hidden(B,k1_connsp_1(A,B)) ) ) )).
fof(t38_convex1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( v1_xreal_0(D) => k1_convex1(A,k6_rusub_4(A,B,C),D) = k6_rusub_4(A,k1_convex1(A,B,D),k1_convex1(A,C,D)) ) ) ) ) )).
fof(t38_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_convex4(B,A) => ! [C] : ( 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) ) ) ) )).
fof(t38_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m1_subset_1(D,k1_qc_lang1(A)) => ! [E] : ( m1_subset_1(E,k5_finsub_1(k3_qc_lang1(A))) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t38_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) )).
fof(t38_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t38_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ( r6_cqc_the3(A,B,C) => r5_cqc_the3(A,B,C) ) ) ) ) )).
fof(t38_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t38_diff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r2_hidden(B,k1_relset_1(k1_numbers,C)) & r2_hidden(k6_xcmplx_0(B,A),k1_relset_1(k1_numbers,C)) ) => k1_funct_1(k4_diff_1(C,A),B) = k6_xcmplx_0(k1_funct_1(C,B),k1_funct_1(C,k6_xcmplx_0(B,A))) ) ) ) ) )).
fof(t38_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( k1_funct_1(C,D) = k7_xcmplx_0(B,D) & D != k5_numbers & k2_xcmplx_0(D,A) != k5_numbers ) ) => ! [D] : ( v1_xreal_0(D) => k1_funct_1(k3_diff_1(C,A),D) = k7_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(B,A)),k3_xcmplx_0(k2_xcmplx_0(D,A),D)) ) ) ) ) ) )).
fof(t38_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( v1_xreal_0(F) => k1_funct_1(E,F) = k3_square_1(F) ) & r2_zfmisc_1(A,B,C,D) ) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(C,k5_numbers) | r1_xxreal_0(D,k5_numbers) | k11_diff_1(E,A,B,C,D) = k7_xcmplx_0(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)),k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k2_xcmplx_0(k3_square_1(A),k3_square_1(B)),k2_xcmplx_0(k3_square_1(A),k3_square_1(C))),k2_xcmplx_0(k3_square_1(A),k3_square_1(D))),k2_xcmplx_0(k3_square_1(B),k3_square_1(C))),k2_xcmplx_0(k3_square_1(B),k3_square_1(D))),k2_xcmplx_0(k3_square_1(C),k3_square_1(D)))) ) ) ) ) ) ) ) )).
fof(t38_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k4_diff_1(k3_diff_1(C,A),A),B) = k6_xcmplx_0(k1_funct_1(k3_diff_1(C,A),B),k1_funct_1(k4_diff_1(C,A),B)) ) ) ) )).
fof(t38_dilworth,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & v5_orders_2(A) & v3_dilworth(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( 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) ) ) ) ) )).
fof(t38_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_analoaf(B) ) => ( B = k2_diraf(A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ! [I] : ( m1_subset_1(I,u1_struct_0(B)) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t38_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( v1_setfam_1(C) & m2_subset_1(C,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => ! [D] : ( m1_dist_2(D,A,C) => ! [E] : ( m1_dist_2(E,A,C) => ! [F] : ( m2_finseq_1(F,A) => ! [G] : ( m2_finseq_1(G,A) => ! [H] : ( m1_subset_1(H,k1_zfmisc_1(k4_finseq_1(D))) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(k4_finseq_1(E))) => ( ( H = k8_relset_1(k4_ordinal1,A,D,B) & F = k5_dist_2(A,D,H) & I = k8_relset_1(k4_ordinal1,A,E,B) & G = k5_dist_2(A,E,I) ) => r1_dist_1(A,F,G) ) ) ) ) ) ) ) ) ) ) )).
fof(t38_ec_pf_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t38_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( 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)) != k5_numbers => ( k7_ec_pf_2(A,D) = k4_domain_1(u1_struct_0(k9_int_3(A)),u1_struct_0(k9_int_3(A)),k4_ordinal1,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) != k5_numbers ) ) ) ) ) ) )).
fof(t38_ens_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k11_ens_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k11_ens_1(A))) => ( k2_cat_1(k11_ens_1(A),B,C) != k1_xboole_0 => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t38_entropy1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( 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] : ( v7_ordinal1(C) => ( r1_xxreal_0(1,C) => ( r1_xxreal_0(k3_finseq_1(A),C) | k1_matrprob(k1_numbers,B,k1_nat_1(C,1)) = k8_finseq_1(k1_numbers,k1_matrprob(k1_numbers,B,C),k1_matrprob(k1_numbers,A,k1_nat_1(C,1))) ) ) ) ) => k5_matrprob(A) = k18_rvsum_1(k1_matrprob(k1_numbers,B,k3_finseq_1(A))) ) ) ) )).
fof(t38_enumset1,axiom,( ! [A] : ! [B] : ! [C] : k3_enumset1(A,A,A,B,C) = k1_enumset1(A,B,C) )).
fof(t38_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ( ! [D] : ( m1_subset_1(D,A) => k11_eqrel_1(A,D,B) = k11_eqrel_1(A,D,C) ) => B = C ) ) ) ) )).
fof(t38_equation,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m3_pboole(C,u1_struct_0(B),k4_equation(B)) => ! [D] : ( m1_pralg_2(D,A,B) => ( ! [E] : ~ ( r2_hidden(E,A) & ! [F] : ( 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) ) ) ) ) )).
fof(t38_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => k16_euclid(A) = k4_struct_0(k15_euclid(A)) ) )).
fof(t38_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ( k22_rvsum_1(B,B) = k5_numbers <=> k12_euclid(B) = k5_numbers ) ) ) )).
fof(t38_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( k4_euclid_3(C,B,A) != k5_numbers => k4_euclid_3(C,B,A) = k6_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k4_euclid_3(A,B,C)) ) ) ) ) )).
fof(t38_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => r1_xxreal_0(k9_complex1(k22_rvsum_1(B,C)),k3_xcmplx_0(k12_euclid(B),k12_euclid(C))) ) ) ) )).
fof(t38_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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)) ) => k3_xcmplx_0(k12_euclid(k5_algstr_0(k15_euclid(2),A,E)),k12_euclid(k5_algstr_0(k15_euclid(2),E,C))) = k3_xcmplx_0(k12_euclid(k5_algstr_0(k15_euclid(2),B,E)),k12_euclid(k5_algstr_0(k15_euclid(2),E,D))) ) ) ) ) ) ) ) ) ) )).
fof(t38_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => 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,k6_xcmplx_0(A,D)),k9_euclid(3,k3_euclid_8,k6_xcmplx_0(B,E))),k9_euclid(3,k4_euclid_8,k6_xcmplx_0(C,F))) ) ) ) ) ) ) )).
fof(t38_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ~ ( r3_euclidlp(A,k8_euclid(A,C,B),k8_euclid(A,D,B)) & C = D ) ) ) ) ) )).
fof(t38_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_exchsort(A) ) => m1_exchsort(A,A) ) )).
fof(t38_facirc_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => v1_relat_1(k3_msafree2(k5_circcomb(A,B))) ) )).
fof(t38_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) ) )).
fof(t38_fdiff_10,axiom,( ! [A] : ( ( 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,k26_sin_cos,k27_sin_cos),k18_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),k18_sin_cos),A),B) = k4_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,k2_xcmplx_0(k1_funct_1(k26_sin_cos,B),k1_funct_1(k27_sin_cos,B))),k6_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B)))))) ) ) ) ) ) )).
fof(t38_fdiff_11,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) => ( r2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_sin_cos9),A),B) = k7_xcmplx_0(2,k2_xcmplx_0(1,k1_square_1(B))) ) ) ) ) ) )).
fof(t38_fdiff_2,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ~ r1_xxreal_0(k5_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) ) ) ) )).
fof(t38_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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,k18_sin_cos))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(D,E) = k2_xcmplx_0(k3_xcmplx_0(A,E),B) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k18_sin_cos),C) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k18_sin_cos),C),E) = k4_xcmplx_0(k3_xcmplx_0(A,k1_funct_1(k16_sin_cos,k2_xcmplx_0(k3_xcmplx_0(A,E),B)))) ) ) ) ) ) ) ) ) )).
fof(t38_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k18_sin_cos),k4_xcmplx_0(k7_xcmplx_0(1,2))))) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(B,C) = k3_xcmplx_0(2,C) ) ) ) => ( r2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k18_sin_cos),k4_xcmplx_0(k7_xcmplx_0(1,2))),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(k2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k18_sin_cos),k4_xcmplx_0(k7_xcmplx_0(1,2))),A),C) = k17_sin_cos(k3_xcmplx_0(2,C)) ) ) ) ) ) ) )).
fof(t38_fdiff_7,axiom,( ! [A] : ( ( 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,k18_sin_cos))) => ( r2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),A),B) = k6_xcmplx_0(k1_funct_1(k18_sin_cos,B),k1_funct_1(k16_sin_cos,B)) ) ) ) ) ) )).
fof(t38_fdiff_9,axiom,( ! [A] : ( ( 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,k26_sin_cos,k1_fdiff_9))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_fdiff_9),A),B) = k7_xcmplx_0(k7_xcmplx_0(k1_funct_1(k16_sin_cos,k1_funct_1(k26_sin_cos,B)),k1_square_1(k1_funct_1(k18_sin_cos,B))),k1_square_1(k1_funct_1(k18_sin_cos,k1_funct_1(k26_sin_cos,B)))) ) ) ) ) ) )).
fof(t38_fib_num2,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ( r1_xxreal_0(B,A) => k6_xcmplx_0(k1_pepin(k1_pre_ff(A)),k2_nat_1(k1_pre_ff(k1_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))) ) ) ) )).
fof(t38_fib_num3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k3_fib_num3(2,1,A) = k1_fib_num3(A) ) )).
fof(t38_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,2) => k1_fib_num3(A) = k1_int_1(k3_xcmplx_0(k7_xcmplx_0(1,k1_fib_num),k2_xcmplx_0(k1_fib_num3(k2_xcmplx_0(A,1)),k7_xcmplx_0(1,2)))) ) ) )).
fof(t38_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_finseq_1(B,A) => ! [C] : ( m1_finseq_1(C,A) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r1_xxreal_0(D,k3_finseq_1(B)) => ( r1_xxreal_0(D,k5_numbers) | r1_xxreal_0(k8_finseq_8(A,B,C,D),k3_finseq_1(B)) ) ) ) ) ) ) )).
fof(t38_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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) ) ) ) )).
fof(t38_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) ) ) ) ) )).
fof(t38_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t38_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( A = k9_finseq_1(B) <=> ( k4_finseq_1(A) = k2_finseq_1(1) & k10_xtuple_0(A) = k1_tarski(B) ) ) ) )).
fof(t38_finseq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t38_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_finset_1(B) => ( r1_tarski(B,k2_finseq_1(A)) => k1_relset_1(k4_ordinal1,k14_finseq_1(B)) = k2_finseq_1(k5_card_1(B)) ) ) ) )).
fof(t38_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_hidden(B,k10_xtuple_0(A)) => r1_xboole_0(k10_xtuple_0(k5_finseq_4(A,B)),k1_tarski(B)) ) ) )).
fof(t38_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r2_hidden(B,k10_xtuple_0(C)) => k7_partfun1(A,C,k4_finseq_4(C,B)) = B ) ) ) ) )).
fof(t38_finseq_6,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(t38_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,B,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ! [G] : ( ( 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] : ( ( v1_funct_1(H) & v1_funct_2(H,k2_zfmisc_1(C,C),C) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(C,C),C))) ) => ( ! [I] : ( m1_subset_1(I,B) => ! [J] : ( m1_subset_1(J,B) => k3_funct_2(B,C,F,k5_binop_1(B,G,I,J)) = k5_binop_1(C,H,k3_funct_2(B,C,F,I),k3_funct_2(B,C,F,J)) ) ) => r2_funct_2(A,C,k1_partfun1(A,B,B,C,k10_funcop_1(B,A,G,D,E),F),k10_funcop_1(C,A,H,k3_funct_2(B,C,F,D),k1_partfun1(A,B,B,C,E,F))) ) ) ) ) ) ) ) ) ) )).
fof(t38_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( 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) ) ) )).
fof(t38_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k9_fintopo3(A,B,k1_nat_1(C,1)) = k1_fintopo3(A,k9_fintopo3(A,B,C)) ) ) ) )).
fof(t38_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t38_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_catalan2(A))) => ! [D] : ( 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)) ) ) ) )).
fof(t38_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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) ) ) ) )).
fof(t38_flang_3,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ( k1_flang_3(A,C,D) = k1_tarski(B) => B = k2_flang_1(A) ) ) ) )).
fof(t38_fomodel0,axiom,( ! [A] : ( ~ 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) ) )).
fof(t38_fsm_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ v2_struct_0(D) & v8_struct_0(D) & l2_fsm_1(D,B,C) ) => ~ ( k1_nat_1(A,1) = k5_card_1(u1_struct_0(D)) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( r1_xxreal_0(E,A) & v4_fsm_1(k7_fsm_1(B,C,D,E),B,C,D) ) ) ) ) ) ) ) )).
fof(t38_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t38_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t38_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,B,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,B,A) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ( ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(t38_funct_1,axiom,( ! [A] : ( ( 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)) ) ) ) )).
fof(t38_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => r1_tarski(k8_relset_1(B,C,D,A),B) ) )).
fof(t38_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( r1_tarski(A,C) & r1_tarski(B,C) & k4_funct_3(A,C) = k4_funct_3(B,C) ) => A = B ) )).
fof(t38_funct_4,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( 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 ) ) )).
fof(t38_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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 ) ) ) )).
fof(t38_funct_6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( k9_xtuple_0(B) = A & k9_xtuple_0(C) = A & ! [D] : ( 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)) ) ) ) )).
fof(t38_funct_7,axiom,( ! [A] : k3_funct_7(A,k1_xboole_0) = k6_partfun1(A) )).
fof(t38_funct_8,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t38_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t38_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( m1_functor3(E,A,B,C,D) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( r1_functor3(A,B,C,D) => k2_functor2(A,B,D,C,k8_functor3(A,B,C,D,E),F) = k1_altcat_3(B,k3_functor0(A,B,C,F),k3_functor0(A,B,D,F),k2_functor2(A,B,C,D,E,F)) ) ) ) ) ) ) ) )).
fof(t38_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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))) ) ) ) )).
fof(t38_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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)) ) ) ) )).
fof(t38_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_fvaluat1(C,A) => ( v3_fvaluat1(A) => ( k3_funct_2(u1_struct_0(A),k6_numbers,C,B) = k1_xxreal_0 <=> k3_funct_2(u1_struct_0(A),k6_numbers,k5_fvaluat1(A,C),B) = k1_xxreal_0 ) ) ) ) ) )).
fof(t38_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [D] : ( 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) ) ) ) ) )).
fof(t38_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ~ ( ~ 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)) ) ) )).
fof(t38_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t38_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v2_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ! [F] : ( m1_genealg1(F,E) => ! [G] : ( m1_genealg1(G,E) => ( k10_genealg1(E,F,G,A,A,C,D) = k8_genealg1(E,F,G,C,D) & k10_genealg1(E,F,G,A,B,A,D) = k8_genealg1(E,F,G,B,D) & k10_genealg1(E,F,G,A,B,C,A) = k8_genealg1(E,F,G,B,C) & k10_genealg1(E,F,G,A,B,B,D) = k8_genealg1(E,F,G,A,D) & k10_genealg1(E,F,G,A,B,C,B) = k8_genealg1(E,F,G,A,C) & k10_genealg1(E,F,G,A,B,C,C) = k8_genealg1(E,F,G,A,B) ) ) ) ) ) ) ) ) )).
fof(t38_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t38_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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))) ) ) )).
fof(t38_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ( ( r1_tarski(B,C) & r1_tarski(D,E) ) => r1_tarski(k23_glib_000(A,B,D),k23_glib_000(A,C,E)) ) ) )).
fof(t38_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( ~ r1_xxreal_0(k3_finseq_1(B),C) => r2_relset_1(k4_ordinal1,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),k2_glib_001(A,k1_funct_1(B,C),k1_funct_1(B,k1_nat_1(C,2)),k1_funct_1(B,k1_nat_1(C,1))),k8_glib_001(A,B,C,k1_nat_1(C,2))) ) ) ) ) )).
fof(t38_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t38_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_003(A) ) => ! [B] : ! [C] : ( 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)) ) ) )).
fof(t38_goboard6,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_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_0(u1_struct_0(k15_euclid(2)),A,1,k1_matrix_0(A)),k19_euclid(k4_xcmplx_0(1),1)),k1_tops_1(k15_euclid(2),k3_goboard5(A,k5_numbers,k1_matrix_0(A)))) ) )).
fof(t38_goboard7,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( 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) ) ) ) ) )).
fof(t38_goboard8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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(k1_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)) ) ) ) )).
fof(t38_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ( m2_finseq_1(D,C) => ! [E] : ( ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(C)) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,2),B) & r3_gobrd13(C,k17_finseq_1(C,B,D),E,A) ) => r3_gobrd13(C,D,E,A) ) ) ) ) ) )).
fof(t38_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t38_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_graph_1(B,A) => ~ ( r2_graph_2(A,B) & ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ~ ( C != D & r1_graph_2(A,C,B) & r1_graph_2(A,D,B) & ! [E] : ( m2_finseq_1(E,u1_struct_0(A)) => ~ ( r1_graph_2(A,E,B) & E != C & E != D ) ) ) ) ) ) ) ) )).
fof(t38_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v2_funct_1(D) & m2_graph_1(D,A) ) => ( v2_funct_1(D) & m2_graph_1(D,k8_graph_3(A,B,C)) ) ) ) ) ) )).
fof(t38_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t38_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => ( k7_graphsp(k6_graphsp(k9_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),k15_graphsp(B),k18_graphsp(B))),A),C),B) != k1_xboole_0 => r2_xboole_0(k12_graphsp(k6_graphsp(k9_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),k15_graphsp(B),k18_graphsp(B))),k1_nat_1(A,1)),C),B),k12_graphsp(k6_graphsp(k9_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),k15_graphsp(B),k18_graphsp(B))),A),C),B)) ) ) ) ) )).
fof(t38_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => u1_struct_0(k29_grcat_1(A)) = k28_grcat_1(A) ) )).
fof(t38_groeb_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( ~ v1_xboole_0(D) & v1_ideal_1(D,k12_polynom1(A,C)) & v2_ideal_1(D,k12_polynom1(A,C)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(G,A,C) & v1_polynom1(G,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(k12_polynom1(A,C)),E,k1_groeb_1(A,C,F)),D) ) ) ) ) ) ) ) ) ) )).
fof(t38_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ( r1_rewrite1(k3_polyred(A,B,C,E),D,k8_polynom1(A,C)) => r6_groeb_2(A,B,C,D,E) ) ) ) ) ) ) )).
fof(t38_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ~ r1_xxreal_0(k5_card_1(k3_polynom1(k15_pre_poly(A),C,D)),E) => r1_termord(A,B,k3_termord(A,B,C,k6_groeb_3(A,B,C,D,k1_nat_1(E,1))),k3_termord(A,B,C,k6_groeb_3(A,B,C,D,E))) ) ) ) ) ) ) )).
fof(t38_group_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & l3_algstr_0(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t38_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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) ) ) ) )).
fof(t38_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t38_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t38_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & l3_algstr_0(C) ) => ( ? [D] : ( v15_algstr_0(D) & m1_group_2(D,C) & v2_group_4(D,C) ) => ( r1_struct_0(k6_group_4(C),B) <=> ! [D] : ( ( v15_algstr_0(D) & m1_group_2(D,C) ) => ( v2_group_4(D,C) => r1_struct_0(D,B) ) ) ) ) ) ) ) )).
fof(t38_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t38_group_6,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t38_group_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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] : ( 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)))) ) ) ) )).
fof(t38_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( ( v2_group_9(D,A) & m1_group_9(D,A,B) ) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t38_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [D] : ( ( ~ 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),k2_xcmplx_0(k1_hausdorf(A,B,C),k1_hausdorf(A,C,D))) ) ) ) ) ) )).
fof(t38_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( ( v5_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t38_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(k1_complfld)) => ! [H] : ( m1_subset_1(H,u1_struct_0(k1_complfld)) => ! [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))))) ) ) ) ) ) ) ) ) ) )).
fof(t38_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A)))) => ( ( r3_orders_2(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A)),B,C) & B = k1_tarski(k1_xboole_0) ) => C = k1_tarski(k1_xboole_0) ) ) ) ) )).
fof(t38_hfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => r1_taylor_1(k1_taylor_1(A),A,B) ) ) )).
fof(t38_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => r2_hidden(k3_hilbert1(k3_hilbert1(B,C),k3_hilbert1(k4_hilbert1(A,B),C)),k6_hilbert1) ) ) ) )).
fof(t38_hilbert3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( m1_hilbert3(D,C) => ! [E] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t38_hurwitz,axiom,( ! [A] : ( 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)) ) ) )).
fof(t38_idea_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k4_ordinal1,B,6) & m2_finseq_1(C,k3_finseq_2(k4_ordinal1)) ) => ! [D] : ( v7_ordinal1(D) => ( 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)) ) ) ) ) ) )).
fof(t38_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t38_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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] : ( m4_index_1(C,u1_struct_0(A),u4_struct_0(A),u1_graph_1(A),u2_graph_1(A),B) => ! [D] : ( 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] : ( m4_index_1(E,u1_struct_0(C),u4_struct_0(C),u1_graph_1(C),u2_graph_1(C),D) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t38_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( 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] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r3_pua2mss1(B,A,D,E) => ! [F] : ( ( v4_msualg_1(F,B) & l3_msualg_1(F,B) ) => ( F = k1_instalg1(B,A,C,D,E) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ( r1_rewrite1(k3_msualg_6(B),G,H) => ! [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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t38_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => k2_int_1(k1_int_1(A)) = k1_int_1(A) ) )).
fof(t38_int_4,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( v7_ordinal1(B) => ( ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r2_hidden(C,k1_relset_1(k4_ordinal1,A)) & r2_hidden(D,k1_relset_1(k4_ordinal1,A)) ) => ( C = D | k6_nat_d(k1_recdef_1(A,C),k1_recdef_1(A,D)) = 1 ) ) ) ) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k1_relset_1(k4_ordinal1,A)) => r1_nat_d(k1_recdef_1(A,C),B) ) ) ) => r1_nat_d(k3_wsierp_1(A),B) ) ) ) )).
fof(t38_int_5,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t38_int_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( 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(k5_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) ) ) ) ) ) )).
fof(t38_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(A,B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k2_xcmplx_0(1,k1_funct_1(k16_sin_cos,D)) != k5_numbers & k6_xcmplx_0(1,k1_funct_1(k16_sin_cos,D)) != k5_numbers & k1_funct_1(C,D) = k7_xcmplx_0(1,k6_xcmplx_0(1,k1_funct_1(k16_sin_cos,D))) ) ) ) & k9_xtuple_0(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_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) = k6_xcmplx_0(k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_fdiff_9),k2_seq_4(A)),k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_fdiff_9),k3_seq_4(A))) ) ) ) ) )).
fof(t38_integr12,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v3_rcomp_1(F) & m1_subset_1(F,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(C,F) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,F) => ( k1_funct_1(D,G) = k7_xcmplx_0(A,k3_square_1(k6_xcmplx_0(1,k1_square_1(k2_xcmplx_0(k3_xcmplx_0(A,G),B))))) & k1_funct_1(E,G) = k2_xcmplx_0(k3_xcmplx_0(A,G),B) & ~ r1_xxreal_0(k1_funct_1(E,G),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(E,G)) ) ) ) & r1_tarski(F,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,E,k3_sin_cos6))) & F = k1_relset_1(k1_numbers,D) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,D,C)) ) => k2_integra5(C,D) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,E,k3_sin_cos6)),k2_seq_4(C)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,E,k3_sin_cos6)),k3_seq_4(C))) ) ) ) ) ) ) ) )).
fof(t38_integr13,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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(k6_xcmplx_0(A,1))),k3_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k1_taylor_1(2))),A)) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => k1_funct_1(D,F) = 1 ) ) & r1_tarski(E,k2_rcomp_1(k4_xcmplx_0(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) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k1_taylor_1(A)),k2_seq_4(B)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k1_taylor_1(A)),k3_seq_4(B))) ) ) ) ) ) ) )).
fof(t38_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,D),k1_funct_1(k18_sin_cos,k1_funct_1(k16_sin_cos,D))),k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_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) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k2_fdiff_9)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k2_fdiff_9)),k3_seq_4(A))) ) ) ) ) )).
fof(t38_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_integra1(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(B)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k3_finseq_2(k1_euclid(A))) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k3_finseq_2(k1_euclid(A))))) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k4_ordinal1,k3_finseq_2(u1_struct_0(k4_real_ns1(A)))) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,k3_finseq_2(k1_euclid(A)),k4_ordinal1,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) ) ) ) ) ) ) ) ) ) )).
fof(t38_integra1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( m1_integra1(C,B) => ! [D] : ( m1_integra1(D,B) => ! [E] : ( ( 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_funct_1(k14_integra1(k4_integra1(B,E,D)),k13_integra1(B,C,D,A)),k1_funct_1(k14_integra1(k4_integra1(B,E,C)),A)) ) ) ) ) ) ) )).
fof(t38_integra2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t38_integra8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => k4_integra5(A,B,k1_integra8(1)) = k6_xcmplx_0(B,A) ) ) ) )).
fof(t38_integra9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k4_xcmplx_0(k28_sin_cos),k28_sin_cos) => r1_integra9(A,k16_sin_cos,k18_sin_cos) ) ) )).
fof(t38_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_interva1(B,A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ! [C] : ( ( ~ 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) ) ) ) )).
fof(t38_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => r2_hidden(k3_intpro_1(k3_intpro_1(C,A),k3_intpro_1(k3_intpro_1(C,B),k3_intpro_1(C,k4_intpro_1(A,B)))),k8_intpro_1) ) ) ) )).
fof(t38_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,B,C) => ! [F] : ( m2_cat_1(F,B,C) => ! [G] : ( 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,k4_nattra_1(A,B,D),G)) ) ) ) ) ) ) ) ) )).
fof(t38_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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(k9_nattra_1(A,k6_cat_2(B,C)),k6_cat_2(k9_nattra_1(A,B),k9_nattra_1(A,C))) ) ) ) )).
fof(t38_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t38_jgraph_1,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( r1_xxreal_0(1,k3_finseq_1(A)) & r1_goboard4(k1_goboard1(A),k1_funct_1(k1_goboard1(A),1),k1_funct_1(k1_goboard1(A),k3_finseq_1(A))) & r1_goboard4(k2_goboard1(A),C,D) & ~ r1_xxreal_0(B,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ~ ( r1_xxreal_0(1,E) & r1_xxreal_0(k1_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,k1_nat_1(E,1))))) ) ) & ! [E] : ( 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_funct_1(k1_goboard1(A),1),k1_funct_1(k1_goboard1(A),k3_finseq_1(A))) & r1_goboard4(k2_goboard1(E),C,D) & ! [F] : ( v7_ordinal1(F) => ~ ( r2_hidden(F,k4_finseq_1(E)) & ! [G] : ( v7_ordinal1(G) => ~ ( 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] : ( v7_ordinal1(F) => ~ ( r1_xxreal_0(1,F) & r1_xxreal_0(k1_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,k1_nat_1(F,1))))) ) ) ) ) ) ) ) ) ) )).
fof(t38_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ~ v2_funct_1(k3_jgraph_4(A)) ) ) )).
fof(t38_jgraph_5,axiom,( ? [A] : ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k4_topmetr(k4_xcmplx_0(1),1))) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k4_topmetr(k4_xcmplx_0(1),1))))) & v3_tops_2(A,k5_topmetr,k4_topmetr(k4_xcmplx_0(1),1)) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,k1_rcomp_1(k5_numbers,1)) => k1_funct_1(A,B) = k2_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2),B),1) ) ) & k1_funct_1(A,k5_numbers) = 1 & k1_funct_1(A,1) = k4_xcmplx_0(1) ) )).
fof(t38_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t38_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t38_jordan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t38_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t38_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_topreal1(2,k1_jordan1e(B,A))) & r2_hidden(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C)),k9_jordan6(B)) ) ) ) ) ) ) )).
fof(t38_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,1),k1_jordan1a(k1_jordan8(B,1)),A)) = k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(B),k8_pscomp_1(B)),2) ) ) ) )).
fof(t38_jordan1b,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(B,k3_finseq_1(k1_jordan8(A,D))) & r1_xxreal_0(C,k1_matrix_0(k1_jordan8(A,D))) & r1_tarski(k3_goboard5(k1_jordan8(A,D),B,C),k1_jordan2c(2,A)) & r1_xxreal_0(B,1) ) ) ) ) ) )).
fof(t38_jordan1g,axiom,( ! [A] : ( ( v4_topreal1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( 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) ) ) ) ) )).
fof(t38_jordan1h,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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,D) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(k1_jordan8(E,D))) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(k1_jordan8(E,D))) & ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ~ ( r1_xxreal_0(1,F) & r1_xxreal_0(k1_nat_1(F,1),k3_finseq_1(k1_jordan8(E,A))) & r1_xxreal_0(1,G) & r1_xxreal_0(k1_nat_1(G,1),k1_matrix_0(k1_jordan8(E,A))) & r1_tarski(k3_goboard5(k1_jordan8(E,D),C,B),k3_goboard5(k1_jordan8(E,A),F,G)) ) ) ) ) ) ) ) ) ) )).
fof(t38_jordan1j,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( v4_topreal1(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( r1_goboard1(u1_struct_0(k15_euclid(2)),B,A) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t38_jordan1k,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => r1_xxreal_0(k5_numbers,k1_jordan1k(A,B,C)) ) ) ) )).
fof(t38_jordan21,axiom,( ! [A] : ( ( 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)) ) )).
fof(t38_jordan22,axiom,( ! [A] : ( ( 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)) ) )).
fof(t38_jordan23,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(t38_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t38_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)))) ) ) ) )).
fof(t38_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( r1_xxreal_0(1,B) => ( r1_xxreal_0(k3_finseq_1(A),k1_nat_1(B,1)) | v4_topreal1(k2_rfinseq(u1_struct_0(k15_euclid(2)),B,A)) ) ) ) ) )).
fof(t38_jordan5d,axiom,( ! [A] : ( ( ~ 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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,1)) ) )).
fof(t38_jordan6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(A),B)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t38_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t38_kurato_1,axiom,( k2_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)) != k2_pre_topc(k3_topmetr,k6_kurato_1) )).
fof(t38_kurato_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,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(k4_ordinal1,k9_setfam_1(u1_struct_0(k2_borsuk_1(k15_euclid(2),k15_euclid(2))))))) ) => ( ! [D] : ( v7_ordinal1(D) => k2_kurato_2(k2_borsuk_1(k15_euclid(2),k15_euclid(2)),C,D) = k3_borsuk_1(k15_euclid(2),k15_euclid(2),k2_kurato_2(k15_euclid(2),A,D),k2_kurato_2(k15_euclid(2),B,D)) ) => r1_tarski(k3_kurato_2(k2_borsuk_1(k15_euclid(2),k15_euclid(2)),C),k3_borsuk_1(k15_euclid(2),k15_euclid(2),k3_kurato_2(k15_euclid(2),A),k3_kurato_2(k15_euclid(2),B))) ) ) ) ) )).
fof(t38_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( k12_matrix_3(A,B,C) != k4_struct_0(B) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ( ( k1_matrix_0(D) = A & k4_matrix_3(B,D,C) = E ) => ( D = k4_matrix_3(B,E,k1_matrix_6(A,B,C)) & ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ( r2_hidden(k4_tarski(F,G),k2_matrix_0(D)) => k3_matrix_0(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,k7_matrix_0(u1_struct_0(B),E,F)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t38_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_lattices(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_lattice2(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k1_lattice2(A))) => ( ( B = D & C = E ) => r3_lattices(k1_lattice2(A),E,D) ) ) ) ) ) ) ) )).
fof(t38_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( r2_hidden(B,C) => ( r3_lattices(A,B,k15_lattice3(A,C)) & r3_lattices(A,k16_lattice3(A,C),B) ) ) ) ) )).
fof(t38_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t38_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( m2_lattice5(D,A,B,C) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(E,F) => r1_tarski(k1_xtuple_0(k1_funct_1(D,E)),k1_xtuple_0(k1_funct_1(D,F))) ) ) ) ) ) ) ) )).
fof(t38_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => v3_lexbfs(k15_lexbfs(A,k16_lexbfs(A))) ) )).
fof(t38_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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)) ) ) ) )).
fof(t38_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v9_ordinal1(A) & v2_comseq_2(A) & k1_seq_2(A) = k5_numbers & v8_valued_0(A) ) => v1_limfunc1(k37_valued_1(k4_ordinal1,k1_numbers,A)) ) ) )).
fof(t38_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r3_limfunc2(C,A) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k2_rcomp_1(k6_xcmplx_0(A,D),A),k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k1_relset_1(k1_numbers,C))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k2_rcomp_1(k6_xcmplx_0(A,D),A)) => r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) | r3_limfunc2(B,A) ) ) ) ) ) )).
fof(t38_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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) = k3_xcmplx_0(k1_limfunc3(B,A),k1_limfunc3(C,A)) ) ) ) ) ) )).
fof(t38_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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) ) ) ) ) )).
fof(t38_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( r1_lmod_6(A,C,D) <=> r1_tarski(k2_struct_0(C),k2_struct_0(D)) ) ) ) ) ) )).
fof(t38_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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)) ) ) ) )).
fof(t38_lopban_3,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( 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] : ( 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,k5_numbers) = k4_struct_0(A) & k1_rlvect_1(A,k4_struct_0(A),E) = k4_struct_0(A) & k1_rlvect_1(A,B,k4_xcmplx_0(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,k2_xcmplx_0(E,F)) = k3_rlvect_1(A,k1_rlvect_1(A,B,E),k1_rlvect_1(A,B,F)) & k1_rlvect_1(A,B,k3_xcmplx_0(E,F)) = k1_rlvect_1(A,k1_rlvect_1(A,B,F),E) & k1_rlvect_1(A,k6_algstr_0(A,B,C),k3_xcmplx_0(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)) & ( k2_normsp_0(A,B) = k5_numbers => B = k4_struct_0(A) ) & ( B = k4_struct_0(A) => k2_normsp_0(A,B) = k5_numbers ) & k2_normsp_0(A,k1_rlvect_1(A,B,E)) = k3_xcmplx_0(k9_complex1(E),k2_normsp_0(A,B)) & r1_xxreal_0(k2_normsp_0(A,k3_rlvect_1(A,B,C)),k2_xcmplx_0(k2_normsp_0(A,B),k2_normsp_0(A,C))) & r1_xxreal_0(k2_normsp_0(A,k6_algstr_0(A,B,C)),k3_xcmplx_0(k2_normsp_0(A,B),k2_normsp_0(A,C))) & k2_normsp_0(A,k5_struct_0(A)) = 1 & v3_lopban_1(A) ) ) ) ) ) ) ) )).
fof(t38_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t38_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( ( r2_hidden(D,k13_lpspacc1(A,B,C)) & r2_hidden(E,k13_lpspacc1(A,B,C)) & r1_lpspacc1(A,B,C,D,E) ) => ( r1_lpspace1(A,B,C,k55_valued_1(A,k2_numbers,D),k55_valued_1(A,k2_numbers,E)) & k1_mesfunc6(A,B,C,k55_valued_1(A,k2_numbers,D)) = k1_mesfunc6(A,B,C,k55_valued_1(A,k2_numbers,E)) ) ) ) ) ) ) ) )).
fof(t38_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t38_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v2_xxreal_0(E) & v1_xreal_0(E) ) => ( r2_hidden(D,k1_lpspace2(A,B,C,E)) => r2_hidden(D,k5_lpspace2(A,B,C,D,E)) ) ) ) ) ) ) )).
fof(t38_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => ! [B] : ( m2_finseq_1(B,k1_hilbert1) => ! [C] : ( m2_finseq_1(C,k1_hilbert1) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(k1_nat_1(E,k3_finseq_1(B)),k3_finseq_1(C)) & ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t38_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(k1_ltlaxio1(k4_ltlaxio1(k3_ltlaxio1,k1_ltlaxio1(A))),A)) ) )).
fof(t38_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t38_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t38_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( r2_matrix10(C,B) => v4_matrix10(k5_matrix10(A,B,C)) ) ) ) ) )).
fof(t38_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,C,A,B) & m2_finseq_1(D,k3_finseq_2(C)) ) => ! [E] : ( ( 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] : ( v7_ordinal1(F) => ( r2_hidden(F,k2_finseq_1(A)) => k7_matrix_0(C,k4_matrix11(A,B,C,E,D),F) = k1_funct_1(D,k1_funct_1(E,F)) ) ) ) ) ) ) ) )).
fof(t38_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,A,E,D) & m2_finseq_1(F,k3_finseq_2(A)) ) => ! [G] : ( m2_finseq_2(G,k4_ordinal1,k4_finseq_2(B,k4_ordinal1)) => ! [H] : ( m2_finseq_1(H,A) => ! [I] : ( v7_ordinal1(I) => ! [J] : ( m2_finseq_2(J,k4_ordinal1,k4_finseq_2(C,k4_ordinal1)) => ( r1_tarski(k2_zfmisc_1(k10_xtuple_0(J),k10_xtuple_0(G)),k2_matrix_0(F)) => ( r2_hidden(I,k10_xtuple_0(J)) | k1_matrix13(A,F,C,B,J,G) = k1_matrix13(A,k3_matrix11(I,E,D,A,F,H),C,B,J,G) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t38_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [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] : ( m1_subset_1(F,u1_struct_0(E)) => ! [G] : ( ( v1_matrix_0(G) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(E))) ) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(E),C,D) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(E))) ) => ! [I] : ( ( v1_matrix_0(I) & v2_matrix_0(I,u1_struct_0(E),C,B) & m2_finseq_1(I,k3_finseq_2(u1_struct_0(E))) ) => ( r2_hidden(G,k4_matrix15(E,H,I)) => r2_hidden(G,k4_matrix15(E,k3_matrix11(A,C,D,u1_struct_0(E),H,k10_fvsum_1(k1_matrix_0(H),E,k7_matrix_0(u1_struct_0(E),H,A),F)),k3_matrix11(A,C,B,u1_struct_0(E),I,k10_fvsum_1(k1_matrix_0(I),E,k7_matrix_0(u1_struct_0(E),I,A),F)))) ) ) ) ) ) ) ) ) ) ) )).
fof(t38_matrix16,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t38_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_finseq_1(D,C) => ! [E] : ( ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(C)) ) => ( ( r2_hidden(k4_tarski(A,B),k2_matrix_0(E)) & k1_funct_1(E,A) = D ) => ( k3_finseq_1(D) = k1_matrix_0(E) & r2_hidden(B,k4_finseq_1(D)) ) ) ) ) ) ) ) )).
fof(t38_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) ) => B = k3_matrix_3(A,k3_matrix_3(A,B,C),k2_matrix_3(A,C)) ) ) ) ) )).
fof(t38_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_6(C,A,B) & k4_matrix_3(B,C,D) = k3_matrix_1(B,A) ) => r2_matrix_6(A,B,C,D) ) ) ) ) ) )).
fof(t38_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r1_matrix_8(A,B,C,D) => ( r1_xxreal_0(A,k5_numbers) | r1_matrix_8(A,B,k3_matrix_3(B,C,k3_matrix_1(B,A)),k3_matrix_3(B,D,k3_matrix_1(B,A))) ) ) ) ) ) ) )).
fof(t38_matrix_9,axiom,( ! [A] : ( ( 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(k4_ordinal1,2,1,3) & A != k3_finseq_4(k4_ordinal1,1,3,2) & A != k3_finseq_4(k4_ordinal1,3,2,1) ) ) )).
fof(t38_matrixc1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k2_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(k2_numbers)) ) => ( ( k1_matrix_0(C) = k1_matrix_0(D) & r2_hidden(B,k2_finseq_1(k3_finseq_1(C))) ) => k7_matrix_0(k2_numbers,k3_matrix_5(C,D),B) = k7_seq_4(k7_matrix_0(k2_numbers,C,B),k7_matrix_0(k2_numbers,D,B)) ) ) ) ) ) )).
fof(t38_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( ( 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) ) => k8_matrix_0(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),k8_matrix_0(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)) ) ) ) ) ) ) )).
fof(t38_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k1_matrix_0(A) = k1_matrix_0(B) & k3_matrixr1(A,B) = k8_matrixr1(k3_finseq_1(A),k1_matrix_0(A)) ) => B = k4_matrixr1(A) ) ) ) )).
fof(t38_matrixr2,axiom,( ! [A] : ( ( v1_matrix_0(A) & v2_matrix_0(A,k1_numbers,3,3) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => k3_matrixr2(3,A) = k3_real_1(k5_real_1(k3_real_1(k5_real_1(k5_real_1(k4_real_1(k4_real_1(k3_matrix_0(k1_numbers,A,1,1),k3_matrix_0(k1_numbers,A,2,2)),k3_matrix_0(k1_numbers,A,3,3)),k4_real_1(k4_real_1(k3_matrix_0(k1_numbers,A,1,3),k3_matrix_0(k1_numbers,A,2,2)),k3_matrix_0(k1_numbers,A,3,1))),k4_real_1(k4_real_1(k3_matrix_0(k1_numbers,A,1,1),k3_matrix_0(k1_numbers,A,2,3)),k3_matrix_0(k1_numbers,A,3,2))),k4_real_1(k4_real_1(k3_matrix_0(k1_numbers,A,1,2),k3_matrix_0(k1_numbers,A,2,3)),k3_matrix_0(k1_numbers,A,3,1))),k4_real_1(k4_real_1(k3_matrix_0(k1_numbers,A,1,2),k3_matrix_0(k1_numbers,A,2,1)),k3_matrix_0(k1_numbers,A,3,3))),k4_real_1(k4_real_1(k3_matrix_0(k1_numbers,A,1,3),k3_matrix_0(k1_numbers,A,2,1)),k3_matrix_0(k1_numbers,A,3,2))) ) )).
fof(t38_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( ( 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] : ( m1_matrlin(E,A,B) => ! [F] : ( m1_matrlin(F,A,C) => ( k3_finseq_1(E) = k5_numbers => k10_matrlin(A,B,C,D,E,F) = k1_xboole_0 ) ) ) ) ) ) ) )).
fof(t38_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( m1_matrlin(E,A,C) => ! [F] : ( m2_finseq_1(F,u1_struct_0(D)) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(A),k3_finseq_1(E),k3_finseq_1(F)) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(A))) ) => 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))) ) ) ) ) ) ) ) )).
fof(t38_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v5_matroid0(B,A) <=> ( ~ v1_xboole_0(B) & ! [C] : ( 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) ) ) ) ) ) ) )).
fof(t38_matrprob,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k2_vectsp_1)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t38_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & v3_valued_0(C) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( D = k17_finseq_1(k3_finseq_2(u1_struct_0(k2_vectsp_1)),A,k3_matrix_1(k2_vectsp_1,B)) => k16_finseq_1(A,k1_funct_1(k3_matrtop1(A,B,D),C)) = C ) ) ) ) ) )).
fof(t38_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k3_zfmisc_1(k2_zfmisc_1(A,B),C,D) = k4_zfmisc_1(A,B,C,D) )).
fof(t38_measure1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t38_measure6,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( v2_comseq_2(A) & v9_ordinal1(A) & k1_seq_2(A) = k5_numbers & v1_comseq_2(k37_valued_1(k4_ordinal1,k1_numbers,A)) ) ) )).
fof(t38_member_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k7_member_1(k2_tarski(A,B)) = k2_tarski(k5_xcmplx_0(A),k5_xcmplx_0(B)) ) ) )).
fof(t38_memstr_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_setfam_1(B) => ! [C] : ( ( ~ v2_struct_0(C) & v2_memstr_0(C,B) & v3_memstr_0(C,B) & l1_memstr_0(C,B) ) => ! [D] : ( ( 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] : ( ( 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 ) ) ) ) ) ) )).
fof(t38_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( v1_xreal_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)) ) ) ) ) ) ) ) )).
fof(t38_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t38_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ( ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t38_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( r1_mesfunc2(A,B,C) & r1_mesfunc2(A,B,D) ) => r1_mesfunc2(A,B,k3_mesfunc1(A,C,D)) ) ) ) ) ) )).
fof(t38_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( r2_hidden(C,k1_relset_1(A,B)) & k12_supinf_2(k18_rfunct_3(A,B),C) = k12_supinf_2(B,C) ) => k12_supinf_2(k19_rfunct_3(A,B),C) = k5_numbers ) ) ) )).
fof(t38_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( m1_subset_1(C,A) => ( ( v1_mesfunc8(B,A,k6_numbers) & r2_hidden(C,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers))) & ! [D] : ( v7_ordinal1(D) => v6_supinf_2(k4_mesfunc5(A,k6_numbers,B,D)) ) ) => ( v7_valued_0(k3_mesfunc5(A,k4_mesfunc9(A,B),C)) & v10_mesfunc5(k3_mesfunc5(A,k4_mesfunc9(A,B),C)) ) ) ) ) ) )).
fof(t38_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_midsp_1(A) = k8_midsp_1(A,B,B) ) ) )).
fof(t38_mmlquery,axiom,( ! [A] : ! [B] : ( 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) ) )).
fof(t38_mod_4,axiom,( ! [A] : ( ( ~ 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] : ( ( 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)) ) ) ) )).
fof(t38_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k3_modal_1) => ! [B] : ( m1_subset_1(B,k6_modal_1) => ! [C] : ( 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) ) ) ) ) )).
fof(t38_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m1_modelc_1(C,A,B) => ! [D] : ( m1_modelc_1(D,A,B) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( k3_funct_2(k4_ordinal1,A,C,E) = k3_funct_2(k4_ordinal1,A,D,k5_numbers) => m1_modelc_1(k57_modelc_1(A,B,C,D,E),A,B) ) ) ) ) ) ) )).
fof(t38_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ~ ( ~ ( ~ v4_modelc_2(B) & ~ v5_modelc_2(B) & ~ v7_modelc_2(B) & ~ v8_modelc_2(B) ) & r3_modelc_2(A,B) & ~ r2_modelc_2(A,k11_modelc_2(B)) & ~ r2_modelc_2(A,k12_modelc_2(B)) ) ) ) )).
fof(t38_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_3(C,B) & v3_modelc_3(C,B) & l1_modelc_3(C,B) ) => ! [D] : ( ( v1_modelc_3(D,B) & v3_modelc_3(D,B) & l1_modelc_3(D,B) ) => ~ ( r6_modelc_3(B,C,D) & r2_hidden(A,u1_modelc_3(B,D)) & ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ! [F] : ( 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,C) & k1_funct_1(E,k3_finseq_1(E)) = D & 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) ) ) ) ) ) ) ) ) )).
fof(t38_moebius1,axiom,( ! [A] : ( v7_ordinal1(A) => ( r2_hidden(A,k1_moebius1) <=> k2_moebius1(A) != k5_numbers ) ) )).
fof(t38_monoid_0,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k2_monoid_0)) <=> m1_subset_1(A,k1_numbers) ) )).
fof(t38_monoid_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => k20_monoid_1(A,k12_finseq_1(A,B)) = k18_monoid_1(A,B) ) ) )).
fof(t38_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_msualg_6(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msualg_2(C,A,B) => v1_msualg_6(C,A) ) ) ) )).
fof(t38_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ( ! [D] : ( m1_subset_1(D,k3_card_3(u3_msualg_1(A,C))) => m1_subset_1(D,k3_card_3(u3_msualg_1(A,k1_msafree3(A,B)))) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,C),D)) => m1_subset_1(E,k1_funct_1(u3_msualg_1(A,k1_msafree3(A,B)),D)) ) ) ) ) ) ) )).
fof(t38_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t38_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(t38_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msualg_4(C,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,B),D)) => ! [F] : ( 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] : ( m1_subset_1(G,u1_struct_0(A)) & r1_rewrite1(k3_msualg_6(A),G,D) & ? [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,B),G)) & ? [I] : ( m1_subset_1(I,k1_funct_1(u3_msualg_1(A,B),G)) & ? [J] : ( m1_msualg_6(J,A,B) & ? [K] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t38_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_mycielsk(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t38_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_ordinal1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => r2_funct_2(k4_ordinal1,B,k8_nat_1(B,k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,B,D,C),A),k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,B,k8_nat_1(k4_ordinal1,D,A),C)) ) ) ) ) )).
fof(t38_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ~ ( r1_nat_d(A,B) & k1_funct_1(k12_nat_3(B),A) = k5_numbers ) ) ) )).
fof(t38_nat_4,axiom,( v1_int_2(1259) )).
fof(t38_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( ( v1_int_2(k7_nat_d(k1_newton(2,A),1)) & B = k2_nat_1(k11_newton(2,k7_nat_d(A,1)),k7_nat_d(k1_newton(2,A),1)) ) => v2_nat_5(B) ) ) ) )).
fof(t38_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(A,B) => k7_nat_d(k2_xcmplx_0(B,C),A) = k2_xcmplx_0(k7_nat_d(B,A),C) ) ) ) ) )).
fof(t38_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_ncfcont1(A,B,C,D) => ( r5_ncfcont1(A,k4_normsp_0(u1_struct_0(A),B,C),D) & r1_ncfcont1(A,B,k5_vfunct_1(u1_struct_0(A),B,C),D) ) ) ) ) ) ) )).
fof(t38_ncfcont2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ~ ( ~ r1_xxreal_0(k2_normsp_0(A,k5_algstr_0(A,B,C)),k5_numbers) & B = C ) & ~ ( B != C & r1_xxreal_0(k2_normsp_0(A,k5_algstr_0(A,B,C)),k5_numbers) ) ) ) ) ) )).
fof(t38_ndiff_4,axiom,( ! [A] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t38_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t38_neckla_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_necklace(A) & v3_necklace(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t38_newton,axiom,( ! [A] : ( v7_ordinal1(A) => r1_xxreal_0(A,k7_newton(A)) ) )).
fof(t38_nfcont_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t38_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [E] : ( ( 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) ) ) ) ) )).
fof(t38_normform,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [C] : ( m2_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t38_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t38_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,B,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_oppcat_1(B))) => k3_funct_2(u1_struct_0(k2_oppcat_1(B)),u1_struct_0(A),k7_cat_1(k2_oppcat_1(B),A,k10_oppcat_1(B,A,C)),D) = k3_funct_2(u1_struct_0(B),u1_struct_0(A),k7_cat_1(B,A,C),k4_oppcat_1(B,D)) ) ) ) ) )).
fof(t38_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(A))) => ! [D] : ( v1_xreal_0(D) => k1_funct_1(k1_pdiff_1(B,A),k1_rlvect_1(k4_real_ns1(A),C,D)) = k3_xcmplx_0(D,k1_funct_1(k1_pdiff_1(B,A),C)) ) ) ) ) )).
fof(t38_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( ( r3_orders_1(A,C) & r1_tarski(B,C) ) => r3_orders_1(A,B) ) ) )).
fof(t38_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_orders_1(D,k1_orders_1(u1_struct_0(A)),k6_partfun1(k1_orders_1(u1_struct_0(A)))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t38_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => k11_ordinal2(A,k5_ordinal1) = k5_ordinal1 ) )).
fof(t38_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ~ ( r2_hidden(A,k10_ordinal2(B,C)) & ~ r2_hidden(A,B) & ! [D] : ( v3_ordinal1(D) => ~ ( r2_hidden(D,C) & A = k10_ordinal2(B,D) ) ) ) ) ) ) )).
fof(t38_ordinal4,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r2_ordinal2(A,B) => ( v4_ordinal1(A) <=> v4_ordinal1(B) ) ) ) ) )).
fof(t38_ordinal5,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal5(A) ) => k12_ordinal2(k4_ordinal1,k12_ordinal2(A,k4_ordinal1)) = k12_ordinal2(A,k12_ordinal2(A,k4_ordinal1)) ) )).
fof(t38_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v3_ordinal1(B) & v4_ordinal1(B) & ~ v1_xboole_0(B) ) => ! [C] : ( ( 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] : ( r2_hidden(D,B) => r2_hidden(k1_funct_1(k3_ordinal6(C),D),A) ) ) => r2_hidden(B,k9_xtuple_0(k3_ordinal6(C))) ) ) ) ) )).
fof(t38_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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)) ) ) )).
fof(t38_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v12_osalg_1(C,A) & m1_msualg_2(C,A,B) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t38_parsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t38_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r1_parsp_2(A,B,C,D) & D != B & D != C ) ) ) ) ) ) )).
fof(t38_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(t38_partfun2,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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)) ) ) ) ) )).
fof(t38_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t38_pcs_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_pcs_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l2_pcs_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k22_pcs_0(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k22_pcs_0(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t38_pdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( 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),k3_funct_2(k1_euclid(2),k1_numbers,k1_pdiff_1(2,2),B)) ) ) ) )).
fof(t38_pdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t38_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m1_rcomp_1(C,k3_funct_2(k1_euclid(3),k1_numbers,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] : ( ( v9_ordinal1(D) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,E) = k1_tarski(k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(2,3),B)) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),C) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,2,k1_pdiff_3(1,3,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,2,k1_pdiff_3(1,3,A),B))))) & k2_pdiff_5(A,B) = k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,2,k1_pdiff_3(1,3,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,2,k1_pdiff_3(1,3,A),B))))) ) ) ) ) ) ) ) ) )).
fof(t38_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [D] : ( r4_pdiff_7(A,B,C,D) <=> ( r1_tarski(D,k1_relset_1(k1_euclid(A),C)) & ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( v1_xreal_0(F) => ~ ( r2_hidden(E,D) & ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( v1_xreal_0(G) => ~ ( ~ r1_xxreal_0(G,k5_numbers) & ! [H] : ( 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)))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t38_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t38_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( v1_int_2(C) & r1_nat_d(A,k1_newton(C,B)) ) => ( r1_xxreal_0(A,1) | r1_nat_d(A,k3_nat_d(k1_newton(C,B),C)) | A = k1_newton(C,B) ) ) ) ) ) )).
fof(t38_polyeq_3,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( m1_comptrig(C,B,A) => ( C = k5_numbers => B = k5_numbers ) ) ) ) )).
fof(t38_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k17_polyform(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k17_polyform(A,B))) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t38_polynom5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k3_funct_2(k4_ordinal1,u1_struct_0(A),k4_polynom5(A,B,C),k5_numbers) = B & k3_funct_2(k4_ordinal1,u1_struct_0(A),k4_polynom5(A,B,C),1) = C & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(2,D) => k1_funct_1(k4_polynom5(A,B,C),D) = k4_struct_0(A) ) ) ) ) ) ) )).
fof(t38_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( 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,k7_polynom1(A,C,D,k11_polynom1(A,C,F,E))) => r2_hidden(k3_termord(A,B,C,k11_polynom1(A,C,F,E)),k3_polynom1(k15_pre_poly(A),C,D)) ) ) ) ) ) ) ) )).
fof(t38_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(k2_power(A,C),k2_power(B,C)) ) ) ) ) )).
fof(t38_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v4_valued_0(B) ) => ! [C] : ( ( 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)) ) ) )).
fof(t38_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ~ ( A != k5_numbers & k3_prepower(A,B) = k5_numbers ) ) ) )).
fof(t38_prob_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m2_prob_1(E,A,B) => k3_funct_2(B,k1_numbers,E,k6_prob_1(A,B,C,D)) = k5_real_1(k3_real_1(k3_funct_2(B,k1_numbers,E,C),k3_funct_2(B,k1_numbers,E,D)),k3_funct_2(B,k1_numbers,E,k5_prob_1(A,B,C,D))) ) ) ) ) ) )).
fof(t38_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m1_prob_1(E,A,B) => ! [F] : ( m1_prob_1(F,A,B) => ! [G] : ( 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(k3_funct_2(B,k1_numbers,G,C),k5_numbers) | r1_xxreal_0(k3_funct_2(B,k1_numbers,G,D),k5_numbers) | r1_xxreal_0(k3_funct_2(B,k1_numbers,G,E),k5_numbers) | r1_xxreal_0(k3_funct_2(B,k1_numbers,G,F),k5_numbers) | ( k3_funct_2(B,k1_numbers,k3_prob_2(A,B,G,C),D) = k6_real_1(k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,G,D),C),k3_funct_2(B,k1_numbers,G,D)),k3_real_1(k3_real_1(k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,G,D),C),k3_funct_2(B,k1_numbers,G,D)),k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,G,E),C),k3_funct_2(B,k1_numbers,G,E))),k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,G,F),C),k3_funct_2(B,k1_numbers,G,F)))) & k3_funct_2(B,k1_numbers,k3_prob_2(A,B,G,C),E) = k6_real_1(k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,G,E),C),k3_funct_2(B,k1_numbers,G,E)),k3_real_1(k3_real_1(k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,G,D),C),k3_funct_2(B,k1_numbers,G,D)),k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,G,E),C),k3_funct_2(B,k1_numbers,G,E))),k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,G,F),C),k3_funct_2(B,k1_numbers,G,F)))) & k3_funct_2(B,k1_numbers,k3_prob_2(A,B,G,C),F) = k6_real_1(k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,G,F),C),k3_funct_2(B,k1_numbers,G,F)),k3_real_1(k3_real_1(k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,G,D),C),k3_funct_2(B,k1_numbers,G,D)),k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,G,E),C),k3_funct_2(B,k1_numbers,G,E))),k4_real_1(k3_funct_2(B,k1_numbers,k3_prob_2(A,B,G,F),C),k3_funct_2(B,k1_numbers,G,F)))) ) ) ) ) ) ) ) ) ) ) )).
fof(t38_prob_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( m2_prob_1(D,A,B) => v8_valued_0(k8_prob_1(A,B,k1_prob_3(A,C),D)) ) ) ) ) )).
fof(t38_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => r1_prob_4(A,k4_prob_4(A,B,C),k7_prob_4(A,B,C)) ) ) ) )).
fof(t38_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t38_pscomp_1,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(t38_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t38_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t38_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t38_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_qc_lang4(C,A,B) => ! [D] : ( m1_qc_lang4(D,A,B) => ! [E] : ( m2_qc_lang4(E,A,B,C) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ( m2_qc_lang4(k7_finseq_1(E,F),A,B,D) => r2_hidden(F,k3_qc_lang4(A,C,D)) ) ) ) ) ) ) ) )).
fof(t38_quatern2,axiom,( k1_group_1(k15_quatern2) = k2_quatern2 )).
fof(t38_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => r1_xxreal_0(k6_xcmplx_0(k28_quaterni(A),k28_quaterni(B)),k7_xcmplx_0(k2_xcmplx_0(k28_quaterni(k22_quaterni(A,B)),k28_quaterni(k25_quaterni(A,B))),2)) ) ) )).
fof(t38_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ( ( k14_quaterni(A) = k5_numbers & k14_quaterni(B) = k5_numbers & k15_quaterni(A) = k5_numbers & k15_quaterni(B) = k5_numbers & k16_quaterni(A) = k5_numbers & k16_quaterni(B) = k5_numbers ) => ( k13_quaterni(k23_quaterni(A,B)) = k3_xcmplx_0(k13_quaterni(A),k13_quaterni(B)) & k14_quaterni(k23_quaterni(A,B)) = k6_xcmplx_0(k3_xcmplx_0(k15_quaterni(A),k16_quaterni(B)),k3_xcmplx_0(k16_quaterni(A),k15_quaterni(B))) & k15_quaterni(k23_quaterni(A,B)) = k6_xcmplx_0(k3_xcmplx_0(k16_quaterni(A),k14_quaterni(B)),k3_xcmplx_0(k14_quaterni(A),k16_quaterni(B))) & k16_quaterni(k23_quaterni(A,B)) = k6_xcmplx_0(k3_xcmplx_0(k14_quaterni(A),k15_quaterni(B)),k3_xcmplx_0(k15_quaterni(A),k14_quaterni(B))) ) ) ) ) )).
fof(t38_quofield,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t38_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_vectsp_6(E,A,B) => ! [F] : ( m2_finseq_1(F,u1_struct_0(B)) => ( ( k10_xtuple_0(F) = k1_vectsp_6(A,B,E) & v2_funct_1(k2_partfun1(u1_struct_0(B),u1_struct_0(C),D,k1_vectsp_6(A,B,E))) ) => k4_finseqop(u1_struct_0(B),u1_struct_0(C),k3_vectsp_6(A,B,F,E),D) = k3_vectsp_6(A,C,k4_finseqop(u1_struct_0(B),u1_struct_0(C),F,D),k8_ranknull(A,B,C,E,D)) ) ) ) ) ) ) ) )).
fof(t38_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ! [B] : ( v1_rat_1(B) => ( ( k1_rat_1(A) = k1_rat_1(B) & k2_rat_1(A) = k2_rat_1(B) ) => A = B ) ) ) )).
fof(t38_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t38_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(1,A) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,k4_real_3(B),A)) ) ) ) )).
fof(t38_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [D] : ( ( v1_rearran1(D) & v2_rearran1(D) & v3_rearran1(D,k1_zfmisc_1(A)) & m2_finseq_1(D,k1_zfmisc_1(A)) ) => ( ( v1_partfun1(C,B) & k5_card_1(B) = k5_card_1(A) ) => ( r2_classes1(k3_rearran1(B,A,D,C),C) & r2_classes1(k4_rearran1(B,A,D,C),C) & k1_rvsum_1(k3_rearran1(B,A,D,C)) = k1_rvsum_1(C) & k1_rvsum_1(k4_rearran1(B,A,D,C)) = k1_rvsum_1(C) ) ) ) ) ) ) )).
fof(t38_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r1_xboole_0(k10_xtuple_0(B),k9_xtuple_0(A)) => k3_relat_1(B,A) = k1_xboole_0 ) ) ) )).
fof(t38_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,B)))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(B))) => ( E = a_4_5_relset_2(A,B,C,D) => k6_relset_2(A,B,C,k8_setfam_1(k2_zfmisc_1(A,B),D)) = k8_setfam_1(B,E) ) ) ) ) )).
fof(t38_revrot_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t38_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r5_rewrite1(A,B,B) & r6_rewrite1(A,B,B) ) ) )).
fof(t38_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t38_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(C))) => ! [G] : ( ( ~ 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)) ) ) ) ) ) ) )).
fof(t38_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t38_rfunct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t38_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_numbers) => k8_relset_1(A,k1_numbers,B,k1_tarski(k4_xcmplx_0(C))) = k8_relset_1(A,k1_numbers,k19_rfunct_3(A,B),k1_tarski(C)) ) ) ) ) )).
fof(t38_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_seq_2(A) => k3_funct_2(k4_ordinal1,k1_numbers,k3_rinfsup1(A),k5_numbers) = k2_rinfsup1(A) ) ) )).
fof(t38_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ( v10_mesfunc5(A) & v10_mesfunc5(B) & ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k12_supinf_2(A,C),k12_supinf_2(B,C)) ) ) => r1_xxreal_0(k2_mesfunc5(A),k2_mesfunc5(B)) ) ) ) )).
fof(t38_rlaffin1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ 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] : ( m1_rlvect_2(C,B) => ( A != k5_numbers => k3_rlaffin1(B,C) = k3_rlaffin1(B,k2_rlaffin1(B,C,A)) ) ) ) ) )).
fof(t38_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => m1_rlsub_1(k1_rlsub_1(B),A) ) ) )).
fof(t38_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ( r1_rlsub_2(A,B,C) => r1_rlsub_2(A,C,B) ) ) ) ) )).
fof(t38_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t38_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ( ( k3_finseq_1(C) = k1_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) ) ) ) ) ) )).
fof(t38_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_rlvect_2(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t38_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( B != C & ! [F] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t38_rlvect_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( v1_rlvect_1(C) & m1_rlsub_1(C,B) & k1_rlvect_5(C) = A ) ) ) ) )).
fof(t38_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => m1_rmod_2(k1_rmod_2(A,C),A,B) ) ) ) )).
fof(t38_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ( r1_rmod_3(A,B,C,D) => r1_rmod_3(A,B,D,C) ) ) ) ) ) )).
fof(t38_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_rmod_4(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t38_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t38_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t38_robbins4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = k1_lattices(A,B,k2_lattices(A,C,k3_robbins1(A,C))) ) ) ) ) ) )).
fof(t38_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_xxreal_0(k5_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) ) ) ) ) )).
fof(t38_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_xboole_0(B,C) => k2_rpr_1(A,C,B) = k5_numbers ) ) ) ) )).
fof(t38_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => k3_rusub_1(A,k4_struct_0(A),B) = u1_struct_0(B) ) ) )).
fof(t38_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ( r1_rusub_2(A,B,C) => r1_rusub_2(A,C,B) ) ) ) ) )).
fof(t38_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t38_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => r2_hidden(u1_struct_0(A),k4_rusub_5(A)) ) )).
fof(t38_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => ( k9_rvsum_1(A,B,C) = k5_finseq_2(k4_ordinal1,A,k5_numbers) => B = C ) ) ) ) )).
fof(t38_rvsum_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_valued_0(B) ) => k17_rvsum_1(k9_rvsum_2(B,A)) = k3_xcmplx_0(A,k16_rvsum_1(B)) ) ) )).
fof(t38_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( 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),k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),3)))) ) ) ) ) ) ) ) )).
fof(t38_scmfsa10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => k2_amistd_1(k7_card_1(3),k1_scmfsa_2,k13_scmfsa_2(A,B)) = k1_tarski(A) ) ) )).
fof(t38_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t38_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( v1_ami_2(E) & ~ v1_scmfsa_m(E) & m1_subset_1(E,u1_struct_0(k1_scmfsa_2)) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & ~ v1_xboole_0(F) & v1_funct_1(F) & v1_finset_1(F) & v1_afinsq_1(F) ) => ( ( k6_memstr_0(k7_card_1(3),k1_scmfsa_2,C) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,D) & r3_scmfsa9a(A,C,E,F) ) => r3_scmfsa9a(B,D,E,F) ) ) ) ) ) ) ) )).
fof(t38_scmfsa_2,axiom,( ! [A] : ( ( 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(k7_card_1(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)) ) )).
fof(t38_scmfsa_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( 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),k5_numbers) | ( k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa_9(D,C)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B)),3))) = k5_numbers & ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(E,k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B)),3)) => r2_hidden(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa_9(D,C)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),E)),k2_afinsq_1(k2_scmfsa_9(D,C))) ) ) ) ) ) ) ) ) ) )).
fof(t38_scmisort,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => v4_extpro_1(k1_scmfsa_m(k16_funcop_1(k5_scmfsa_2(k5_numbers),A)),k7_card_1(3),k1_scmfsa_2,k3_scmisort) ) )).
fof(t38_scmpds_2,axiom,( ! [A] : ( ( 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)) ) )).
fof(t38_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => k1_funct_1(k5_scmpds_6(A,B,C),k5_numbers) = k7_scmpds_2(A,B,k1_nat_1(k5_card_1(C),1)) ) ) ) )).
fof(t38_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmring2(A))) => r1_xxreal_0(k2_compos_0(u1_compos_1(k1_scmring2(A)),B),7) ) ) )).
fof(t38_scmyciel,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_tarski(k5_scmyciel(A),k5_scmyciel(B)) ) )).
fof(t38_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t38_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)),k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,A)) ) ) )).
fof(t38_seq_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_seq_2(A) & v8_valued_0(A) ) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k1_seq_2(A),k9_nat_1(k1_numbers,A,B)) ) ) ) )).
fof(t38_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( r1_seqfunc(A,k1_numbers,C,D) => r1_seqfunc(A,k1_numbers,k2_seqfunc(A,C,B),D) ) ) ) ) )).
fof(t38_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_seq_2(A) & v8_valued_0(B) ) => v1_seq_2(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) ) ) )).
fof(t38_series_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ? [C] : ( v7_ordinal1(C) & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => r1_xxreal_0(A,k9_complex1(k9_nat_1(k1_numbers,B,D))) ) ) ) & v2_comseq_2(B) & k1_seq_2(B) = k5_numbers ) ) ) )).
fof(t38_series_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(k9_nat_1(k1_numbers,B,C),k5_numbers) & r1_xxreal_0(k1_funct_1(B,k6_xcmplx_0(C,1)),k9_nat_1(k1_numbers,B,C)) ) ) => r1_xxreal_0(k9_nat_1(k1_numbers,k3_series_1(B),A),k3_xcmplx_0(k1_nat_1(A,1),k3_funct_2(k4_ordinal1,k1_numbers,B,k1_nat_1(A,1)))) ) ) ) )).
fof(t38_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( 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(k7_xcmplx_0(1,A),1),k6_xcmplx_0(k7_xcmplx_0(1,B),1)),k6_xcmplx_0(k7_xcmplx_0(1,C),1))) ) ) ) ) )).
fof(t38_setfam_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ( k7_setfam_1(A,B) = k7_setfam_1(A,C) => B = C ) ) ) )).
fof(t38_setlim_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ( v3_funct_1(C) & k3_funct_1(C) = B ) => ! [D] : ( v7_ordinal1(D) => k1_funct_1(k2_setlim_1(A,C),D) = B ) ) ) ) )).
fof(t38_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k1_prob_1(A,k5_setlim_2(A,C,B)) = k9_subset_1(A,B,k1_prob_1(A,C)) ) ) )).
fof(t38_setwiseo,axiom,( ! [A] : v1_setwiseo(k9_setwiseo(A),k5_finsub_1(A)) )).
fof(t38_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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] : ( ( 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] : ( m2_finseq_1(F,A) => ( ( v1_binop_1(D,A) & v2_binop_1(D,A) & v1_setwiseo(D,A) & C = k4_binop_1(A,D) & r6_binop_1(A,E,D) & k5_binop_1(A,E,B,C) = C ) => k5_binop_1(A,E,B,k1_finsop_1(A,F,D)) = k1_finsop_1(A,k3_finseqop(A,A,A,E,B,F),D) ) ) ) ) ) ) ) )).
fof(t38_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( v7_ordinal1(B) => k4_sf_mastr(A) = k4_sf_mastr(k61_valued_1(A,B)) ) ) )).
fof(t38_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t38_simplex0,axiom,( ! [A] : ! [B] : ( ( v1_matroid0(B) & v3_matroid0(B) & m1_simplex0(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t38_simplex1,axiom,( ! [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) ) => ! [B] : ( ( 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] : ( 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)))))) ) ) ) ) ) ) )).
fof(t38_sin_cos,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(B,A) => r1_xxreal_0(k2_newton(B),k2_newton(A)) ) ) ) )).
fof(t38_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => r1_fcont_1(k1_sin_cos2,A) ) )).
fof(t38_sin_cos3,axiom,( ! [A] : ( v1_xreal_0(A) => k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,A) = k1_funct_1(k16_sin_cos,A) ) )).
fof(t38_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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(k19_sin_cos(B),k19_sin_cos(B)),k3_xcmplx_0(k19_sin_cos(A),k19_sin_cos(A))) ) ) )).
fof(t38_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => k2_xcmplx_0(k1_square_1(k2_sin_cos5(A)),k1_square_1(k6_sin_cos2(A))) = 1 ) )).
fof(t38_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ~ ( r1_xxreal_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B),A) & ~ r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)),A) & r1_xxreal_0(k17_sin_cos(A),k4_xcmplx_0(1)) ) ) ) )).
fof(t38_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => k2_sin_cos7(A) = k3_xcmplx_0(2,k2_sin_cos7(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(A,1),2)))) ) ) )).
fof(t38_sin_cos9,axiom,( k4_sin_cos9(k4_xcmplx_0(1)) = k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos) & k1_funct_1(k2_sin_cos9,k4_xcmplx_0(1)) = k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos) )).
fof(t38_sincos10,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k4_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos))) )).
fof(t38_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t38_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t38_sprect_1,axiom,( ! [A] : ( 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) ) )).
fof(t38_sprect_2,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ 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))) ) ) ) ) ) )).
fof(t38_sprect_5,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t38_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => k7_xcmplx_0(1,k6_xcmplx_0(k3_square_1(A),k3_square_1(B))) = k7_xcmplx_0(k2_xcmplx_0(k3_square_1(A),k3_square_1(B)),k6_xcmplx_0(A,B)) ) ) ) )).
fof(t38_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(k14_stacks_1(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t38_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k7_card_1(k1_nat_1(B,1)),k7_card_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(k1_nat_1(B,1)),k7_card_1(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k7_card_1(B),k7_card_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(B),k7_card_1(A)))) ) => ( ( v2_funct_2(C,k7_card_1(A)) & v1_stirl2_1(C,k1_nat_1(B,1),A) & k2_partfun1(k7_card_1(k1_nat_1(B,1)),k7_card_1(A),C,B) = D ) => ( k1_stirl2_1(k1_nat_1(B,1),k7_card_1(A),C,k1_seq_4(k2_stirl2_1(k7_card_1(k1_nat_1(B,1)),A,C,B))) = k1_seq_4(B) | ( v2_funct_2(D,k7_card_1(A)) & v1_stirl2_1(D,B,A) ) ) ) ) ) ) ) )).
fof(t38_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k16_substut1(A),k38_substut1(A)) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t38_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ( A != k1_xboole_0 => m1_subset_1(k4_enumset1(B,C,D,E,F,G),k1_zfmisc_1(A)) ) ) ) ) ) ) ) )).
fof(t38_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k16_substut1(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t38_supinf_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( v6_supinf_2(B) <=> ! [C] : ( m1_subset_1(C,A) => r1_xxreal_0(k1_supinf_2,k12_supinf_2(B,C)) ) ) ) )).
fof(t38_sysrel,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( ( ( k3_relat_1(B,A) = B & k3_relat_1(A,k6_subset_1(A,k4_relat_1(k9_xtuple_0(A)))) = k1_xboole_0 ) => k3_relat_1(B,k6_subset_1(A,k4_relat_1(k9_xtuple_0(A)))) = 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 ) => k3_relat_1(k6_subset_1(A,k4_relat_1(k9_xtuple_0(A))),B) = k1_xboole_0 ) ) ) ) )).
fof(t38_taxonom1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t38_tdlat_1,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t38_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))))) ) ) )).
fof(t38_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( ( ~ v2_struct_0(B) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) ) => v4_tdlat_3(B) ) => v5_tdlat_3(A) ) ) )).
fof(t38_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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_polynom1(A,C,k5_termord(A,B,C,D),k6_termord(A,B,C,D)),D) ) ) ) ) )).
fof(t38_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v2_tex_2(B,A) <=> v1_zfmisc_1(B) ) ) ) )).
fof(t38_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t38_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t38_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t38_toler_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(t38_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( m1_borsuk_2(G,A,E,C) => ! [H] : ( m1_borsuk_2(H,A,C,D) => r4_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)) ) ) ) ) ) ) ) ) )).
fof(t38_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v7_topalg_6(B,A) & m2_subset_1(B,k4_partfun1(k1_numbers,k2_struct_0(A)),k1_topalg_6(A)) ) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t38_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( 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),k5_numbers) ) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v3_pre_topc(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( r2_hidden(C,D) & ! [E] : ( ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t38_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t38_topgen_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(k9_setfam_1(A)))) => ~ ( ! [C] : ( 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] : ( 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] : ( 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] : ( ( v2_pre_topc(D) & l1_pre_topc(D) ) => ( ( u1_struct_0(D) = A & ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t38_topgen_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t38_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t38_topgen_5,axiom,( 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))) )).
fof(t38_topgrp_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_connsp_2(C,A,k2_group_1(A,B)) => ? [D] : ( v3_pre_topc(D,A) & m1_connsp_2(D,A,B) & r1_tarski(k1_group_2(A,D),C) ) ) ) ) )).
fof(t38_topreal1,axiom,( ! [A] : ( 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)) ) ) )).
fof(t38_topreal3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ( ( r2_hidden(B,k4_finseq_1(A)) & r2_hidden(k1_nat_1(B,1),k4_finseq_1(A)) ) => k3_topreal1(2,k17_finseq_1(u1_struct_0(k15_euclid(2)),k1_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,k1_nat_1(B,1)))) ) ) ) )).
fof(t38_topreal6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(2))) => ! [D] : ( v1_xreal_0(D) => ( ( C = B & r2_hidden(A,k8_metric_1(k14_euclid(2),C,D)) ) => ( ~ r1_xxreal_0(k18_euclid(A),k6_xcmplx_0(k18_euclid(B),D)) & ~ r1_xxreal_0(k2_xcmplx_0(k18_euclid(B),D),k18_euclid(A)) ) ) ) ) ) ) )).
fof(t38_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ~ ( ~ v8_ordinal1(A) & v1_xboole_0(k3_topreal9(A,C,B)) & r1_xxreal_0(k5_numbers,B) ) ) ) ) )).
fof(t38_topreala,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(C,D) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B)))) => ! [F] : ( 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)))) ) ) ) ) ) ) ) )).
fof(t38_toprealb,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k2_topalg_2))) => ! [B] : ( ( 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(k5_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))) ) ) ) )).
fof(t38_toprealc,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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))))) ) ) ) ) )).
fof(t38_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ( v3_toprns_1(C,A) => v3_toprns_1(k2_toprns_1(B,A,C),A) ) ) ) ) )).
fof(t38_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)) ) ) )).
fof(t38_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t38_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t38_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => v4_transgeo(k6_partfun1(u1_struct_0(A)),A) ) )).
fof(t38_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => m4_trees_1(k1_tarski(B),A) ) ) )).
fof(t38_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ( ! [C] : ( v7_ordinal1(C) => k2_trees_2(A,C) = k2_trees_2(B,C) ) => A = B ) ) ) )).
fof(t38_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v6_trees_3(A) ) => k3_finseq_1(k1_funct_6(A)) = k3_finseq_1(A) ) )).
fof(t38_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v3_trees_9(A) ) => ! [B] : ( 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)) ) ) )).
fof(t38_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t38_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t38_turing_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( r1_xxreal_0(3,A) => r3_turing_1(k20_turing_1,k5_comput_1(A,3)) ) ) )).
fof(t38_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ 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)) ) ) )).
fof(t38_uniroots,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ( k3_funct_2(k4_ordinal1,u1_struct_0(A),k4_uniroots(B,A),k5_numbers) = k4_algstr_0(A,k1_group_1(A)) & k3_funct_2(k4_ordinal1,u1_struct_0(A),k4_uniroots(B,A),B) = k1_group_1(A) ) ) ) )).
fof(t38_uproots,axiom,( ! [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) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( r2_funct_2(k4_ordinal1,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) ) ) ) ) ) )).
fof(t38_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( m1_valuat_1(F,A,B) => r1_valuat_1(A,B,k8_cqc_lang(A,k11_cqc_lang(A,C,E),E),F,D) ) ) ) ) ) ) )).
fof(t38_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(t38_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t38_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => m1_vectsp_4(k1_vectsp_4(A,C),A,B) ) ) ) )).
fof(t38_vectsp_5,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_5(D,A,B,C) => ( r1_vectsp_5(A,B,D,C) & r1_vectsp_5(A,B,C,D) ) ) ) ) ) )).
fof(t38_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => k1_vectsp_6(A,B,k7_vectsp_6(A,B,C)) = k1_vectsp_6(A,B,C) ) ) ) )).
fof(t38_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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] : ( m1_vectsp_4(D,A,C) => r1_tarski(k2_vectsp_9(A,D,B),k2_vectsp_9(A,C,B)) ) ) ) ) )).
fof(t38_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(C)))) ) => ! [E] : ( ( 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_funct_1(E,B)) ) ) ) ) ) ) )).
fof(t38_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t38_waybel11,axiom,( ! [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) & v4_waybel11(A) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t38_waybel12,axiom,( ! [A] : ( ( 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) ) )).
fof(t38_waybel14,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => B = k1_yellow_0(A,a_2_4_waybel14(A,B)) ) => v3_waybel_3(A) ) ) )).
fof(t38_waybel19,axiom,( ! [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) & l1_waybel_9(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t38_waybel20,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( 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] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t38_waybel21,axiom,( ! [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] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m2_yellow_6(C,A,B) => ! [D] : ( m2_waybel21(D,A,B,C) => ( ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ~ ( r1_orders_2(B,k2_yellow_6(u1_struct_0(C),B,D,F),E) & ! [G] : ( 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) ) ) ) ) ) )).
fof(t38_waybel23,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v1_waybel23(k6_waybel_0(A,B),A) ) ) )).
fof(t38_waybel24,axiom,( ! [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] : ( ( 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) ) ) )).
fof(t38_waybel25,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t38_waybel26,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) ) )).
fof(t38_waybel27,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(k5_yellow_1(A,C))) & v22_waybel_0(D,B,k5_yellow_1(A,C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(k5_yellow_1(A,C))))) ) => ! [E] : ( m1_subset_1(E,A) => ( v1_funct_1(k1_funct_1(k9_funct_6(D),E)) & v1_funct_2(k1_funct_1(k9_funct_6(D),E),u1_struct_0(B),u1_struct_0(C)) & v22_waybel_0(k1_funct_1(k9_funct_6(D),E),B,C) & m1_subset_1(k1_funct_1(k9_funct_6(D),E),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)))) ) ) ) ) ) ) )).
fof(t38_waybel30,axiom,( ! [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) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => B = k1_yellow_0(A,a_2_5_waybel30(A,B)) ) ) )).
fof(t38_waybel34,axiom,( ! [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] : ( ( 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)) ) ) ) )).
fof(t38_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t38_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t38_waybel_2,axiom,( ! [A] : ( ( 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),k1_yellow_1(k7_waybel_0(A)),A) => ! [B] : ( ( ~ 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] : ( ( ~ 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)) ) ) ) ) )).
fof(t38_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ( ? [D] : ( 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(k1_yellow_1(u1_pre_topc(A)),B,C) ) ) ) ) )).
fof(t38_waybel_4,axiom,( ! [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) & l1_orders_2(A) ) => v2_waybel_2(A) ) )).
fof(t38_waybel_6,axiom,( ! [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) ) => ( v1_waybel_5(A) <=> ( v3_waybel_3(A) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & B = k1_yellow_0(A,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,C) => v6_waybel_6(D,A) ) ) ) ) ) ) ) )).
fof(t38_waybel_7,axiom,( ! [A] : ( ( 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] : ( 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] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & r3_orders_2(A,D,B) ) ) ) ) ) ) ) )).
fof(t38_waybel_9,axiom,( ! [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) & v1_compts_1(A) & l1_waybel_9(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v5_pre_topc(k4_waybel_1(A,B),A,A) ) => ! [B] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t38_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => r4_wellord1(A,A) ) )).
fof(t38_xboole_1,axiom,( ! [A] : ! [B] : ( r1_tarski(A,k4_xboole_0(B,A)) => A = k1_xboole_0 ) )).
fof(t38_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k5_xboolean(A,k9_xboolean(B,C)) = k4_xboolean(k5_xboolean(A,k3_xboolean(B)),k5_xboolean(A,k3_xboolean(C))) ) ) ) )).
fof(t38_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k6_xcmplx_0(A,k6_xcmplx_0(B,C)) = k2_xcmplx_0(A,k6_xcmplx_0(C,B)) ) ) ) )).
fof(t38_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(B,C) ) => r1_xxreal_0(B,k2_xcmplx_0(A,C)) ) ) ) ) )).
fof(t38_xtuple_0,axiom,( ! [A] : ! [B] : r1_tarski(k5_xboole_0(k12_xtuple_0(A),k12_xtuple_0(B)),k12_xtuple_0(k5_xboole_0(A,B))) )).
fof(t38_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) )).
fof(t38_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(D,B) ) => r1_tarski(k2_xxreal_1(C,D),k2_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t38_xxreal_2,axiom,( k2_xxreal_2(k1_xboole_0) = k1_xxreal_0 )).
fof(t38_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( r1_xxreal_0(A,B) <=> r1_xxreal_0(k2_xxreal_3(B),k2_xxreal_3(A)) ) ) ) )).
fof(t38_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(t38_yellow12,axiom,( ! [A] : ( ( ~ 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))))) ) ) )).
fof(t38_yellow14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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)) ) ) ) )).
fof(t38_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( v4_yellow_0(k5_yellow_1(C,B),k5_yellow_1(C,A)) & m1_yellow_0(k5_yellow_1(C,B),k5_yellow_1(C,A)) ) ) ) )).
fof(t38_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & v4_yellow18(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( 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) ) ) ) ) ) )).
fof(t38_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v11_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v2_altcat_1(D) & v11_altcat_1(D) & v12_altcat_1(D) & l2_altcat_1(D) ) => ! [E] : ( l2_functor0(E,A,B) => ( r3_yellow20(A,B,E,C,D) => r2_functor0(C,D) ) ) ) ) ) ) )).
fof(t38_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t38_yellow_2,axiom,( ! [A] : ( ( v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ! [C] : ( 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))) ) ) ) ) )).
fof(t38_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( r2_lattice3(A,C,G) => r1_orders_2(A,G,E) ) ) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ( r2_lattice3(B,D,G) => r1_orders_2(B,G,F) ) ) ) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t38_yellow_4,axiom,( ! [A] : ( ( v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( ~ 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) ) ) ) )).
fof(t38_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t38_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( ~ r2_hidden(C,k10_yellow_6(A,B)) & ! [D] : ( m2_yellow_6(D,A,B) => ~ ( r2_hidden(D,k6_yellow_6(A)) & ! [E] : ( m2_yellow_6(E,A,D) => ~ r2_hidden(C,k10_yellow_6(A,E)) ) ) ) ) ) ) ) ) )).
fof(t38_yellow_7,axiom,( ! [A] : ( ( 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)) ) )).
fof(t38_yellow_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t38_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( v5_zf_lang(B) => ( ~ ( A = k21_zf_lang(B) & ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => k7_zf_lang(A,C) != B ) ) & ( ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & k7_zf_lang(A,C) = B ) => A = k21_zf_lang(B) ) & ~ ( A = k22_zf_lang(B) & ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => k7_zf_lang(C,A) != B ) ) & ( ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & k7_zf_lang(C,A) = B ) => A = k22_zf_lang(B) ) ) ) ) ) )).
fof(t38_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ~ ( 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) ) ) ) )).
fof(t38_zfmisc_1,axiom,( ! [A] : ! [B] : ( r1_tarski(k2_xboole_0(k1_tarski(A),B),B) => r2_hidden(A,B) ) )).
fof(t38_zfrefle1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( v3_ordinal1(B) & m1_subset_1(B,A) ) => ~ ( r2_hidden(k4_ordinal1,A) & ! [C] : ( ( v3_ordinal1(C) & m1_subset_1(C,A) ) => ! [D] : ( ~ v1_xboole_0(D) => ~ ( r2_hidden(B,C) & D = k4_classes1(C) & r2_zfrefle1(D,A) ) ) ) ) ) ) )).
fof(t38_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_zmodul01(C,A) => ( r1_struct_0(C,B) => r1_struct_0(C,k4_algstr_0(A,B)) ) ) ) ) )).
fof(t38_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( m2_zmodul02(B,A,C) => m2_zmodul02(k24_zmodul02(A,B),A,C) ) ) ) ) )).
fof(t390_xxreal_1,axiom,( ! [A] : ( 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)) ) )).
fof(t391_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t392_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t393_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t394_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t395_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t396_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t397_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t398_xxreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t399_xxreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t39_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t39_abcmiz_1,axiom,( r1_subset_1(k2_tarski(k9_abcmiz_1,k10_abcmiz_1),k20_abcmiz_1) )).
fof(t39_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t39_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t39_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r5_aff_1(A,B,C) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r1_tarski(B,D) & r1_tarski(C,D) & v1_aff_4(D,A) ) ) ) ) ) ) )).
fof(t39_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ~ ( A != k1_xboole_0 & ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : A != k1_ordinal4(B,k5_afinsq_1(C)) ) ) ) )).
fof(t39_afinsq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t39_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(k14_afproj(A))) => ? [C] : ( m1_subset_1(C,u1_incsp_1(k14_afproj(A))) & ? [D] : ( m1_subset_1(D,u1_incsp_1(k14_afproj(A))) & ? [E] : ( 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 ) ) ) ) ) )).
fof(t39_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k1_afvect0(A,C,k1_afvect0(A,D,k1_afvect0(A,E,B))) = k1_afvect0(A,E,k1_afvect0(A,D,k1_afvect0(A,C,B))) ) ) ) ) ) )).
fof(t39_algspec1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v11_struct_0(B) & v1_instalg1(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r3_pua2mss1(A,B,C,D) => m1_instalg1(k2_algspec1(A,C,D),B) ) ) ) ) ) )).
fof(t39_algstr_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(t39_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v2_altcat_2(B,A) & v3_altcat_2(B,A) & m1_altcat_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,k1_altcat_1(A,C,D)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t39_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analmetr(A) ) => ( v3_analmetr(A) <=> ( ~ ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = C ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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] : ( m1_subset_1(J,u1_struct_0(A)) & r2_analoaf(A,B,C,D,J) & r2_analoaf(A,B,D,C,J) ) & ~ ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ! [L] : ( m1_subset_1(L,u1_struct_0(A)) => r2_analoaf(A,J,K,J,L) ) ) ) & ? [J] : ( 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] : ( 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] : ( 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] : ( m1_subset_1(J,u1_struct_0(A)) => ~ ( r2_analoaf(A,B,C,B,J) & r2_analoaf(A,D,E,D,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t39_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & F != G & r2_analort(A,B,C,F,G,D,E) ) ) ) ) ) ) ) ) )).
fof(t39_aofa_000,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & v3_freealg(A) & l1_unialg_1(A) ) => ! [B] : ( m1_freealg(B,A) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k4_finseq_1(u1_unialg_1(A))) => ( ! [D] : ( m2_subset_1(D,k4_ordinal1,k4_finseq_1(u1_unialg_1(A))) => ! [E] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t39_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( ( v19_aofa_a00(F,A) & m1_subset_1(F,u1_struct_0(A)) ) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),F)) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),F)) => ! [I] : ( m2_subset_1(I,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => k15_aofa_a00(A,B,C,D,F,k30_aofa_a00(A,C,F,G,H),I) = k30_aofa_a00(A,D,F,k15_aofa_a00(A,B,C,D,F,G,I),k15_aofa_a00(A,B,C,D,F,H,I)) ) ) ) ) ) ) ) ) ) )).
fof(t39_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_aofa_i00(E,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) ) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),E) => ! [G] : ( 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) = k5_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) = k5_numbers ) & ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t39_armstrng,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t39_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => k8_arytm_3(k6_arytm_3(A),k7_arytm_3(A)) = A ) )).
fof(t39_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & v6_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( v7_asympt_0(A) & r1_xxreal_0(2,C) & r2_hidden(B,k10_asympt_0(A,a_1_4_asympt_0(C))) ) => r2_hidden(B,k7_asympt_0(A)) ) ) ) ) )).
fof(t39_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => k9_nat_1(k1_numbers,A,B) = k6_asympt_1(B) ) & ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v4_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( r2_funct_2(k4_ordinal1,k1_numbers,B,A) & ~ v7_asympt_0(B) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_xxreal_0(k9_nat_1(k1_numbers,A,C),k9_nat_1(k1_numbers,k3_asympt_1(1),C)) ) & v6_asympt_0(A) ) ) ) ) )).
fof(t39_bcialg_1,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k5_bcialg_1(A)) => ! [D] : ( m2_subset_1(D,u1_struct_0(A),k7_bcialg_1(A,B)) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t39_bcialg_2,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t39_bcialg_3,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)))) ) ) ) ) )).
fof(t39_bcialg_4,axiom,( ! [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) & l1_bcialg_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t39_bcialg_5,axiom,( ! [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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t39_bcialg_6,axiom,( ! [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] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & v2_bcialg_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(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)) & v2_bcialg_6(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)))) ) ) ) ) ) ) )).
fof(t39_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t39_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k4_bhsp_1(A,B,C) = k3_square_1(k2_bhsp_1(A,k5_algstr_0(A,B,C),k5_algstr_0(A,B,C))) ) ) ) )).
fof(t39_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_bhsp_2(D,A) & k1_bhsp_2(A,D) = C ) => ( v2_comseq_2(k3_bhsp_2(A,k5_bhsp_1(A,D,B),k3_rlvect_1(A,C,B))) & k1_seq_2(k3_bhsp_2(A,k5_bhsp_1(A,D,B),k3_rlvect_1(A,C,B))) = k5_numbers ) ) ) ) ) ) )).
fof(t39_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => 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))),k9_complex1(k5_real_1(k9_nat_1(k1_numbers,k3_series_1(k2_bhsp_2(A,B)),D),k9_nat_1(k1_numbers,k3_series_1(k2_bhsp_2(A,B)),C)))) ) ) ) ) )).
fof(t39_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( ( 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))))) ) ) ) ) ) ) ) ) ) ) )).
fof(t39_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t39_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => m1_borsuk_1(k10_borsuk_1(A),A) ) )).
fof(t39_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k1_borsuk_4))) => ( ? [B] : ( m1_subset_1(B,u1_struct_0(k5_topmetr)) & ? [C] : ( 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)) ) ) )).
fof(t39_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( A = k2_rcomp_1(B,C) => v3_pre_topc(A,k3_topmetr) ) ) ) ) )).
fof(t39_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ( v5_pre_topc(D,k5_topmetr,A) => ( v1_funct_1(k1_partfun1(u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k5_topmetr),u1_struct_0(A),k3_treal_1(k5_numbers,1,k2_treal_1(k5_numbers,1),k1_treal_1(k5_numbers,1)),D)) & v1_funct_2(k1_partfun1(u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k5_topmetr),u1_struct_0(A),k3_treal_1(k5_numbers,1,k2_treal_1(k5_numbers,1),k1_treal_1(k5_numbers,1)),D),u1_struct_0(k5_topmetr),u1_struct_0(A)) & v5_pre_topc(k1_partfun1(u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k5_topmetr),u1_struct_0(A),k3_treal_1(k5_numbers,1,k2_treal_1(k5_numbers,1),k1_treal_1(k5_numbers,1)),D),k5_topmetr,A) & m1_subset_1(k1_partfun1(u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k5_topmetr),u1_struct_0(A),k3_treal_1(k5_numbers,1,k2_treal_1(k5_numbers,1),k1_treal_1(k5_numbers,1)),D),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(A)))) ) ) ) ) ) ) )).
fof(t39_borsuk_7,axiom,( k30_valued_1(k8_borsuk_7) = k9_borsuk_7 )).
fof(t39_bspace,axiom,( ! [A] : ( v1_finset_1(A) => k1_vectsp_7(k2_bspace,k7_bspace(A),k9_bspace(A)) = k7_bspace(A) ) )).
fof(t39_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t39_bvfunc14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) ) => ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ( 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)) ) ) )).
fof(t39_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t39_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)))) ) ) ) )).
fof(t39_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( 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))) ) ) ) ) )).
fof(t39_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(E,A) => ( r3_bvfunc_2(A,D,B,E) => r1_bvfunc_1(A,k6_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),D),k7_bvfunc_2(A,k6_bvfunc_1(A,C,D),B,E)) ) ) ) ) ) ) )).
fof(t39_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(F,A) => r1_bvfunc_1(A,k2_bvfunc_1(A,k6_bvfunc_2(A,k9_bvfunc_1(A,D,E),B,F),k6_bvfunc_2(A,k9_bvfunc_1(A,E,k1_bvfunc_1(A,C)),B,F)),k6_bvfunc_2(A,k9_bvfunc_1(A,C,k1_bvfunc_1(A,D)),B,F)) ) ) ) ) ) ) )).
fof(t39_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) )).
fof(t39_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t39_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t39_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => ( ( r2_relset_1(k4_ordinal1,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))))) ) ) ) ) )).
fof(t39_card_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k1_card_1(B) = k1_card_1(A) => B = A ) ) ) )).
fof(t39_card_2,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ( r1_xboole_0(A,B) => k5_card_1(k2_xboole_0(A,B)) = k1_nat_1(k5_card_1(A),k5_card_1(B)) ) ) ) )).
fof(t39_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => r1_ordinal1(k1_card_1(k3_card_3(A)),k6_card_3(k1_card_3(A))) ) )).
fof(t39_card_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) => r1_ordinal1(k1_card_1(A),k2_wellord2(k1_wellord2(A))) ) )).
fof(t39_card_fil,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ( v7_card_fil(A) => v4_card_fil(A) ) ) )).
fof(t39_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v9_cat_1(k4_cat_1(A,B),A,B,B) ) ) )).
fof(t39_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( m2_cat_1(E,A,B) => ! [F] : ( 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(k6_cat_2(A,C)),u4_struct_0(k6_cat_2(B,D)),k16_funct_3(u4_struct_0(A),u4_struct_0(C),u4_struct_0(B),u4_struct_0(D),E,F),k14_cat_2(k6_cat_2(A,C),B,D,k9_cat_1(k6_cat_2(A,C),A,B,k12_cat_2(A,C),E),k9_cat_1(k6_cat_2(A,C),C,D,k13_cat_2(A,C),F))) ) ) ) ) ) ) )).
fof(t39_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t39_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( k2_cat_1(A,B,D) != k1_xboole_0 & k2_cat_1(A,C,E) != k1_xboole_0 & k2_cat_1(A,k2_cat_4(A,B,C),k2_cat_4(A,D,E)) = k1_xboole_0 ) ) ) ) ) ) )).
fof(t39_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ~ ( k7_afinsq_2(B) = k1_catalan1(k1_nat_1(A,1)) & k1_relset_1(k4_ordinal1,B) = A & ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(A,C) => k1_recdef_1(B,C) = k3_xcmplx_0(k1_catalan1(k1_nat_1(C,1)),k1_catalan1(k7_nat_d(A,C))) ) ) ) ) ) ) )).
fof(t39_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => v6_clvect_1(k6_cc0sp2(A),k6_cfuncdom(u1_struct_0(A))) ) )).
fof(t39_cfcont_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(C,A) & ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xcmplx_0(F) => ~ ( r2_hidden(F,A) & ~ r1_xxreal_0(E,k9_complex1(k6_xcmplx_0(F,C))) & r1_xxreal_0(D,k9_complex1(k6_xcmplx_0(k7_partfun1(k2_numbers,B,F),k7_partfun1(k2_numbers,B,C)))) ) ) ) ) ) ) ) ) ) ) )).
fof(t39_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( v1_xcmplx_0(D) => r2_relset_1(A,k2_numbers,k25_valued_1(A,k2_numbers,k1_cfunct_1(A,C,B),D),k1_cfunct_1(A,k25_valued_1(A,k2_numbers,C,D),B)) ) ) ) ) )).
fof(t39_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ( ! [B] : ( r2_hidden(B,k6_cgames_1(k13_cgames_1(A))) <=> ? [C] : ( v2_cgames_1(C) & r2_hidden(C,k7_cgames_1(A)) & B = k13_cgames_1(C) ) ) & ! [B] : ( r2_hidden(B,k7_cgames_1(k13_cgames_1(A))) <=> ? [C] : ( v2_cgames_1(C) & r2_hidden(C,k6_cgames_1(A)) & B = k13_cgames_1(C) ) ) ) ) )).
fof(t39_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_chain_1(C,B) => ( B = k1_nat_1(A,1) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_euclid(B))) => ( r2_hidden(D,k4_chain_1(B,C,A)) <=> ? [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(B)) & ? [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(B)) & ? [G] : ( m2_subset_1(G,k4_ordinal1,k2_finseq_1(B)) & D = k3_chain_1(B,E,F) & k1_funct_1(E,G) = k1_funct_1(F,G) & r2_hidden(k1_funct_1(E,G),k2_chain_1(B,C,G)) & ! [H] : ( m2_subset_1(H,k4_ordinal1,k2_finseq_1(B)) => ( H != G => ( ~ r1_xxreal_0(k1_funct_1(F,H),k1_funct_1(E,H)) & m2_chain_1(k4_tarski(k1_funct_1(E,H),k1_funct_1(F,H)),k2_chain_1(B,C,H)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t39_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v1_chord(B,A) => ! [C] : ( ( v7_ordinal1(C) & ~ v1_abian(C) ) => ! [D] : ( ( v7_ordinal1(D) & ~ v1_abian(D) ) => ( r1_xxreal_0(D,k3_finseq_1(B)) => ( r1_xxreal_0(D,k1_nat_1(C,2)) | ! [E] : ~ r1_glib_000(A,k1_funct_1(B,C),k1_funct_1(B,D),E) ) ) ) ) ) ) ) )).
fof(t39_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) ) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t39_circcomb,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => k5_circcomb(A,B) = k4_circcomb(A,B,k4_tarski(B,A)) ) )).
fof(t39_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v4_msualg_1(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t39_classes2,axiom,( ! [A] : v2_classes1(k4_classes1(k1_card_1(k1_classes1(A)))) )).
fof(t39_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k14_clopban1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_clopban1(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_clopban1(A,B))) => ( E = k5_algstr_0(k14_clopban1(A,B),C,D) <=> ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t39_clopban3,axiom,( ! [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) & l1_clopban2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_clopban3(A,B,k5_numbers) = k5_struct_0(A) ) ) )).
fof(t39_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => r1_lopban_4(A,k1_clvect_1(A,B,C),k1_clvect_1(A,B,D)) ) ) ) ) )).
fof(t39_closure1,axiom,( ! [A] : ( l1_struct_0(A) => ! [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] : ( ( 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) ) ) ) )).
fof(t39_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t39_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_clvect_2(D,A) & k1_clvect_2(A,D) = C ) => ( v2_comseq_2(k3_clvect_2(A,k5_bhsp_1(A,D,B),k3_rlvect_1(A,C,B))) & k1_seq_2(k3_clvect_2(A,k5_bhsp_1(A,D,B),k3_rlvect_1(A,C,B))) = k5_numbers ) ) ) ) ) ) )).
fof(t39_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k13_csspace(A,k5_algstr_0(A,k1_normsp_0(A,k1_bhsp_4(A,B),D),k1_normsp_0(A,k1_bhsp_4(A,B),C))),k9_complex1(k5_real_1(k9_nat_1(k1_numbers,k3_series_1(k2_clvect_2(A,B)),D),k9_nat_1(k1_numbers,k3_series_1(k2_clvect_2(A,B)),C)))) ) ) ) ) )).
fof(t39_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k20_coh_sp(A)) => ? [C] : ( m1_subset_1(C,k19_coh_sp(A)) & ? [D] : ( m1_subset_1(D,k16_coh_sp(A)) & ? [E] : ( 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] : ! [G] : ( 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)) ) ) ) ) ) )).
fof(t39_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(t39_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k3_complex1(A) = k5_numbers => k8_complex1(A) = k4_xcmplx_0(A) ) ) )).
fof(t39_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => k1_complex2(C,k2_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,E))) = k2_xcmplx_0(k3_xcmplx_0(k8_complex1(A),k1_complex2(C,D)),k3_xcmplx_0(k8_complex1(B),k1_complex2(C,E))) ) ) ) ) ) )).
fof(t39_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_complfld)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_complfld)) => ~ ( B != k4_struct_0(k1_complfld) & C != k4_struct_0(k1_complfld) & D != k4_struct_0(k1_complfld) & k3_vectsp_1(k1_complfld,k3_vectsp_1(k1_complfld,A,B),k3_vectsp_1(k1_complfld,C,D)) != k3_vectsp_1(k1_complfld,k8_group_1(k1_complfld,A,D),k8_group_1(k1_complfld,B,C)) ) ) ) ) ) )).
fof(t39_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ! [D] : ( 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,k3_binop_2,A,B) = k1_finseqop(k1_numbers,k1_numbers,k1_numbers,k9_binop_2,C,D) ) ) ) ) ) )).
fof(t39_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(A)) => r2_hidden(k5_numbers,k2_afinsq_1(k9_compos_1(A,B))) ) ) )).
fof(t39_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( v6_compos_0(D,u1_compos_1(A)) & m1_subset_1(D,u1_compos_1(A)) ) => ! [E] : ( ( v6_compos_0(E,u1_compos_1(A)) & m1_subset_1(E,u1_compos_1(A)) ) => ! [F] : ( ( 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),k5_numbers) = C ) ) ) ) ) ) )).
fof(t39_comptrig,axiom,( k1_comptrig(1) = k5_numbers )).
fof(t39_comseq_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k36_valued_1(k4_ordinal1,k2_numbers,k25_valued_1(k4_ordinal1,k2_numbers,B,A)),k25_valued_1(k4_ordinal1,k2_numbers,k36_valued_1(k4_ordinal1,k2_numbers,B),k5_xcmplx_0(A))) ) ) )).
fof(t39_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_comseq_2(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ! [D] : ( v7_ordinal1(D) => ( k3_complex1(k9_nat_1(k2_numbers,C,D)) = k9_nat_1(k1_numbers,A,D) & k4_complex1(k9_nat_1(k2_numbers,C,D)) = k9_nat_1(k1_numbers,B,D) ) ) => ( v2_comseq_2(C) & k3_comseq_2(C) = k2_xcmplx_0(k1_seq_2(A),k3_xcmplx_0(k1_seq_2(B),k7_complex1)) ) ) ) ) ) )).
fof(t39_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( v3_conlat_1(B,A) & ~ v4_conlat_1(B,A) & v6_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) ) ) )).
fof(t39_connsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t39_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( v1_xreal_0(D) => ( r1_tarski(B,C) => r1_tarski(k1_convex1(A,B,D),k1_convex1(A,C,D)) ) ) ) ) ) )).
fof(t39_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( m1_convex4(C,A) => k1_clvect_1(k15_convex4(A),k1_rlvect_2(k15_convex4(A),C),B) = k7_convex4(A,B,C) ) ) ) )).
fof(t39_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k1_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( m2_funct_2(F,k3_qc_lang1(A),k3_qc_lang1(A),k9_funct_2(k3_qc_lang1(A),k3_qc_lang1(A))) => ! [G] : ( 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)),E,B,G,F),k15_cqc_sim1(A,D)) & 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) ) ) ) ) ) ) ) ) )).
fof(t39_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t39_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t39_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_csspace(A,B,k4_struct_0(A)) ) ) )).
fof(t39_diff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r2_hidden(k2_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,C)) & r2_hidden(k6_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,C)) ) => k1_funct_1(k5_diff_1(C,A),B) = k6_xcmplx_0(k1_funct_1(C,k2_xcmplx_0(B,k7_xcmplx_0(A,2))),k1_funct_1(C,k6_xcmplx_0(B,k7_xcmplx_0(A,2)))) ) ) ) ) )).
fof(t39_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( k1_funct_1(C,D) = k7_xcmplx_0(B,D) & D != k5_numbers & k6_xcmplx_0(D,A) != k5_numbers ) ) => ! [D] : ( v1_xreal_0(D) => k1_funct_1(k4_diff_1(C,A),D) = k7_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(B,A)),k3_xcmplx_0(k6_xcmplx_0(D,A),D)) ) ) ) ) ) )).
fof(t39_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k3_square_1(D) ) => ( r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(k2_xcmplx_0(B,A),k5_numbers) | k1_funct_1(k3_diff_1(C,A),B) = k6_xcmplx_0(k3_square_1(k2_xcmplx_0(B,A)),k3_square_1(B)) ) ) ) ) ) )).
fof(t39_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k5_diff_1(k3_diff_1(C,A),A),B) = k6_xcmplx_0(k1_funct_1(k3_diff_1(C,A),k2_xcmplx_0(B,k7_xcmplx_0(A,2))),k1_funct_1(k5_diff_1(C,A),B)) ) ) ) )).
fof(t39_dilworth,axiom,( ! [A] : ( ( 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) ) )).
fof(t39_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_analoaf(B) ) => ( B = k2_diraf(A) => ( ~ ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => C = D ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => r2_analoaf(B,C,D,C,E) ) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r2_analoaf(B,C,E,D,F) & D != F ) ) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r2_analoaf(B,C,D,E,F) & r2_analoaf(B,C,E,D,F) ) ) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ~ ( r2_analoaf(B,E,C,C,F) & C != E & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ~ ( r2_analoaf(B,D,C,C,G) & r2_analoaf(B,D,E,F,G) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t39_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => ! [C] : ( m4_dist_2(C,A,B) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,k6_margrel1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => k3_xcmplx_0(k12_dist_2(A,B,C,D),k10_dist_2(A,B,C)) = k6_dist_2(A,B,k2_bvfunc_1(A,D,k7_dist_2(A,C))) ) ) ) ) )).
fof(t39_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t39_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( 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] : ( 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) ) ) ) ) ) )).
fof(t39_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t39_entropy1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => k3_finseq_1(k2_entropy1(A,B)) = k3_xcmplx_0(k3_finseq_1(B),k1_matrix_0(B)) ) ) )).
fof(t39_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k4_enumset1(A,A,A,B,C,D) = k2_enumset1(A,B,C,D) )).
fof(t39_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_eqrel_1(k1_tarski(A),A) ) )).
fof(t39_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => u1_struct_0(k14_euclid(A)) = u1_struct_0(k15_euclid(A)) ) )).
fof(t39_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ( k22_rvsum_1(B,B) = k5_numbers <=> B = k4_struct_0(k15_euclid(A)) ) ) ) )).
fof(t39_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m1_subset_1(B,k2_numbers) => k3_complex1(k1_complex2(A,B)) = k3_real_1(k4_real_1(k3_complex1(A),k3_complex1(B)),k4_real_1(k4_complex1(A),k4_complex1(B))) ) ) )).
fof(t39_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ~ ( B = a_4_0_euclid_4(A,C,D,E) & ! [F] : ( 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)) = k3_seq_4(B) & r1_rvsum_1(k8_euclid(A,C,D),k8_euclid(A,E,F)) ) ) ) ) ) ) ) ) )).
fof(t39_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( ( D = k12_euclid(k5_algstr_0(k15_euclid(2),B,A)) & E = k12_euclid(k5_algstr_0(k15_euclid(2),C,B)) & F = k12_euclid(k5_algstr_0(k15_euclid(2),A,C)) & G = k7_xcmplx_0(k2_euclid_6(A,B,C),2) ) => k9_complex1(k1_euclid_6(A,B,C)) = k3_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))) ) ) ) ) ) ) ) ) )).
fof(t39_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k10_funcsdom(k2_finseq_1(A))))) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( v1_xreal_0(E) => ( ( 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 ) ) ) ) ) ) )).
fof(t39_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => ( k7_euclid(3,k7_euclid(3,k9_euclid(3,k2_euclid_8,k1_funct_1(A,1)),k9_euclid(3,k3_euclid_8,k1_funct_1(A,2))),k9_euclid(3,k4_euclid_8,k1_funct_1(A,3))) = k7_euclid(3,k7_euclid(3,k9_euclid(3,k2_euclid_8,k2_xcmplx_0(k1_funct_1(B,1),k1_funct_1(C,1))),k9_euclid(3,k3_euclid_8,k2_xcmplx_0(k1_funct_1(B,2),k1_funct_1(C,2)))),k9_euclid(3,k4_euclid_8,k2_xcmplx_0(k1_funct_1(B,3),k1_funct_1(C,3)))) <=> k7_euclid(3,k7_euclid(3,k9_euclid(3,k2_euclid_8,k1_funct_1(B,1)),k9_euclid(3,k3_euclid_8,k1_funct_1(B,2))),k9_euclid(3,k4_euclid_8,k1_funct_1(B,3))) = k7_euclid(3,k7_euclid(3,k9_euclid(3,k2_euclid_8,k6_xcmplx_0(k1_funct_1(A,1),k1_funct_1(C,1))),k9_euclid(3,k3_euclid_8,k6_xcmplx_0(k1_funct_1(A,2),k1_funct_1(C,2)))),k9_euclid(3,k4_euclid_8,k6_xcmplx_0(k1_funct_1(A,3),k1_funct_1(C,3)))) ) ) ) ) )).
fof(t39_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(B)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t39_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_exchsort(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_exchsort(B) ) => ( m1_exchsort(A,B) => m1_exchsort(B,A) ) ) ) )).
fof(t39_facirc_1,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(t39_fcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ? [B] : ( v1_xreal_0(B) & k2_relset_1(k1_numbers,A) = k1_seq_4(B) ) => v1_fcont_1(A) ) ) )).
fof(t39_fdiff_10,axiom,( ! [A] : ( ( 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,k26_sin_cos,k27_sin_cos),k22_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),k22_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),k22_sin_cos),A),B) = k3_xcmplx_0(k1_funct_1(k22_sin_cos,k2_xcmplx_0(k1_funct_1(k26_sin_cos,B),k1_funct_1(k27_sin_cos,B))),k6_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B))))) ) ) ) ) ) )).
fof(t39_fdiff_11,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k3_xcmplx_0(k1_funct_1(k18_sin_cos,B),k2_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k1_funct_1(k2_sin_cos9,B))) ) ) ) ) ) )).
fof(t39_fdiff_2,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => r1_xxreal_0(k5_numbers,k1_fdiff_1(A,B)) ) ) => v7_valued_0(k2_partfun1(k1_numbers,k1_numbers,A,k2_subset_1(k1_numbers))) ) ) )).
fof(t39_fdiff_4,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & k1_funct_1(k18_sin_cos,B) = k5_numbers ) ) => ( r2_fdiff_1(k6_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k6_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos),A),B) = k7_xcmplx_0(k1_funct_1(k16_sin_cos,B),k1_square_1(k1_funct_1(k18_sin_cos,B))) ) ) ) ) ) )).
fof(t39_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k18_sin_cos),k4_taylor_1(k7_xcmplx_0(1,2))),2))) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => ( k1_funct_1(B,C) = 1 & ~ r1_xxreal_0(k1_funct_1(k16_sin_cos,C),k5_numbers) & ~ r1_xxreal_0(1,k1_funct_1(k18_sin_cos,C)) & ~ r1_xxreal_0(k1_funct_1(k18_sin_cos,C),k4_xcmplx_0(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,k18_sin_cos),k4_taylor_1(k7_xcmplx_0(1,2))),2),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_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,k18_sin_cos),k4_taylor_1(k7_xcmplx_0(1,2))),2),A),C) = k6_prepower(k2_xcmplx_0(1,k1_funct_1(k18_sin_cos,C)),k7_xcmplx_0(1,2)) ) ) ) ) ) ) )).
fof(t39_fdiff_7,axiom,( ! [A] : ( ( 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,k18_sin_cos))) => ( r2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),A),B) = k2_xcmplx_0(k1_funct_1(k18_sin_cos,B),k1_funct_1(k16_sin_cos,B)) ) ) ) ) ) )).
fof(t39_fdiff_9,axiom,( ! [A] : ( ( 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,k27_sin_cos,k1_fdiff_9))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k1_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k1_fdiff_9),A),B) = k4_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(k1_funct_1(k16_sin_cos,k1_funct_1(k27_sin_cos,B)),k1_square_1(k1_funct_1(k16_sin_cos,B))),k1_square_1(k1_funct_1(k18_sin_cos,k1_funct_1(k27_sin_cos,B))))) ) ) ) ) ) )).
fof(t39_fib_num3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k1_nat_1(k3_fib_num3(A,B,C),k3_fib_num3(A,B,k1_nat_1(C,3))) = k2_nat_1(2,k3_fib_num3(A,B,k1_nat_1(C,2))) ) ) ) )).
fof(t39_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_finseq_1(B,A) => ! [C] : ( m1_finseq_1(C,A) => r2_finseq_8(A,k5_finseq_8(A,B,C),C,1) ) ) ) )).
fof(t39_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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) ) ) ) )).
fof(t39_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ( ( v13_lattices(A) & v13_lattices(B) ) <=> v13_lattices(k7_filter_1(A,B)) ) ) ) )).
fof(t39_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t39_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( A = k9_finseq_1(B) <=> ( k3_finseq_1(A) = 1 & k10_xtuple_0(A) = k1_tarski(B) ) ) ) )).
fof(t39_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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 ) ) ) ) ) )).
fof(t39_finseq_3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ~ ( r1_tarski(A,k2_finseq_1(B)) & ~ r1_xxreal_0(D,C) & r1_xxreal_0(1,F) & r1_xxreal_0(E,k3_finseq_1(k14_finseq_1(A))) & k1_funct_1(k14_finseq_1(A),E) = C & k1_funct_1(k14_finseq_1(A),F) = D & r1_xxreal_0(F,E) ) ) ) ) ) ) )).
fof(t39_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_hidden(B,k10_xtuple_0(A)) => r1_tarski(k10_xtuple_0(k5_finseq_4(A,B)),k10_xtuple_0(A)) ) ) )).
fof(t39_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t39_finseq_6,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(t39_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,B,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ! [G] : ( ( 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] : ( ( v1_funct_1(H) & v1_funct_2(H,k2_zfmisc_1(C,C),C) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(C,C),C))) ) => ( ! [I] : ( m1_subset_1(I,B) => ! [J] : ( m1_subset_1(J,B) => k3_funct_2(B,C,F,k5_binop_1(B,G,I,J)) = k5_binop_1(C,H,k3_funct_2(B,C,F,I),k3_funct_2(B,C,F,J)) ) ) => r2_funct_2(A,C,k1_partfun1(A,B,B,C,k9_funcop_1(B,A,G,E,D),F),k9_funcop_1(C,A,H,k1_partfun1(A,B,B,C,E,F),k3_funct_2(B,C,F,D))) ) ) ) ) ) ) ) ) ) )).
fof(t39_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( 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))) ) ) )).
fof(t39_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k9_fintopo3(A,B,k5_numbers) = B ) ) )).
fof(t39_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t39_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_catalan2(A))) => ! [D] : ( 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))) ) ) ) )).
fof(t39_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => k6_flang_1(A,k1_flang_2(A,B,E,F),k1_flang_2(A,B,C,D)) = k6_flang_1(A,k1_flang_2(A,B,C,D),k1_flang_2(A,B,E,F)) ) ) ) ) ) )).
fof(t39_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ( r1_tarski(B,k8_flang_1(A,C)) => r1_tarski(k1_flang_3(A,B,D),k8_flang_1(A,C)) ) ) ) ) )).
fof(t39_fomodel0,axiom,( ! [A] : ( v1_xboolean(A) => ( A = 1 <=> A != k5_numbers ) ) )).
fof(t39_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v7_ordinal1(D) => ( r1_frechet2(A,B,C) => r1_frechet2(A,k1_valued_0(u1_struct_0(A),B,D),C) ) ) ) ) ) )).
fof(t39_fsm_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ v2_struct_0(D) & v8_struct_0(D) & l2_fsm_1(D,B,C) ) => ( k1_nat_1(A,1) = k5_card_1(u1_struct_0(D)) => k8_fsm_1(B,C,D) = k7_fsm_1(B,C,D,A) ) ) ) ) ) )).
fof(t39_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ~ 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) ) ) ) )).
fof(t39_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t39_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t39_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) => v2_funct_1(k2_funct_1(A)) ) ) )).
fof(t39_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) ) )).
fof(t39_funct_3,axiom,( ! [A] : ! [B] : r1_tarski(k10_xtuple_0(k4_funct_3(A,B)),k2_tarski(k1_xboole_0,1)) )).
fof(t39_funct_4,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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 ) ) ) )).
fof(t39_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t39_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( k9_xtuple_0(A) = k9_xtuple_0(C) & k9_xtuple_0(B) = k10_xtuple_0(C) & v2_funct_1(C) & ! [D] : ( r2_hidden(D,k9_xtuple_0(C)) => r2_wellord2(k1_funct_1(A,D),k1_funct_1(B,k1_funct_1(C,D))) ) ) => r2_wellord2(k4_card_3(A),k4_card_3(B)) ) ) ) ) )).
fof(t39_funct_7,axiom,( ! [A] : k4_funct_7(k1_xboole_0,A) = k9_finseq_1(A) )).
fof(t39_funct_8,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t39_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t39_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t39_fuzzy_1,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(t39_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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)) ) ) ) )).
fof(t39_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_fvaluat1(D,A) => ( v3_fvaluat1(A) => ( k3_funct_2(u1_struct_0(A),k6_numbers,D,B) = k3_funct_2(u1_struct_0(A),k6_numbers,D,C) <=> k3_funct_2(u1_struct_0(A),k6_numbers,k5_fvaluat1(A,D),B) = k3_funct_2(u1_struct_0(A),k6_numbers,k5_fvaluat1(A,D),C) ) ) ) ) ) ) )).
fof(t39_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [D] : ( 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) ) ) ) ) )).
fof(t39_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ~ 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) ) ) )).
fof(t39_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t39_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v2_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( m1_genealg1(E,D) => ! [F] : ( m1_genealg1(F,D) => ( k10_genealg1(D,E,F,A,A,C,C) = E & k10_genealg1(D,E,F,A,B,A,B) = E & k10_genealg1(D,E,F,A,B,B,A) = E ) ) ) ) ) ) ) )).
fof(t39_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t39_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k13_gfacirc1(A,B,C),k14_gfacirc1(A,B,C)))) & ? [E] : ( m1_subset_1(E,k6_margrel1) & ? [F] : ( m1_subset_1(F,k6_margrel1) & ? [G] : ( 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)) ) ) ) ) ) ) )).
fof(t39_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t39_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( r1_xxreal_0(C,D) => ( r1_xxreal_0(k3_finseq_1(B),D) | r2_relset_1(k4_ordinal1,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,k1_nat_1(D,1))),k8_glib_001(A,B,C,k1_nat_1(D,2))) ) ) ) ) ) ) )).
fof(t39_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k1_nat_1(k17_glib_000(A),1)) ) )).
fof(t39_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_003(A) ) => ! [B] : ! [C] : ( r2_hidden(B,k6_glib_000(A)) => k1_funct_1(k7_glib_003(k13_glib_003(A,B,C)),B) = C ) ) )).
fof(t39_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(t39_goboard6,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_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_0(u1_struct_0(k15_euclid(2)),A,k3_finseq_1(A),1),k19_euclid(1,k4_xcmplx_0(1))),k1_tops_1(k15_euclid(2),k3_goboard5(A,k3_finseq_1(A),k5_numbers))) ) )).
fof(t39_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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_nat_1(B,1),k1_matrix_0(k2_goboard2(C))) & r2_hidden(k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1))),k7_xcmplx_0(1,2)),k3_topreal1(2,C)) & ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(C)) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1))) = k2_topreal1(2,C,D) ) ) ) ) ) ) )).
fof(t39_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m2_finseq_1(C,B) => ! [D] : ( m2_finseq_1(D,B) => ! [E] : ( ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(B)) ) => ( ( r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) & r1_xxreal_0(k1_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,k1_nat_1(A,1),C) = k17_finseq_1(B,k1_nat_1(A,1),D) ) ) ) ) ) ) )).
fof(t39_gobrd14,axiom,( ! [A] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(t39_graph_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t39_graph_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t39_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_2(D,k1_numbers,k3_finseq_2(k1_numbers)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k3_finseq_2(k1_numbers)) => ! [F] : ( m2_finseq_2(F,k1_numbers,k3_finseq_2(k1_numbers)) => ( ( E = k6_graphsp(k9_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),k15_graphsp(C),k18_graphsp(C))),A),D) & F = k6_graphsp(k9_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),k15_graphsp(C),k18_graphsp(C))),k1_nat_1(A,1)),D) & B = k14_graphsp(k7_graphsp(E,C),E,C) ) => ( k7_graphsp(E,C) = k1_xboole_0 | ( k13_graphsp(F,C) = k4_subset_1(k4_ordinal1,k13_graphsp(E,C),k6_domain_1(k4_ordinal1,B)) & ~ r2_hidden(B,k13_graphsp(E,C)) ) ) ) ) ) ) ) ) ) )).
fof(t39_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => r2_hidden(k3_algstr_0,k28_grcat_1(A)) ) )).
fof(t39_groeb_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(D,A,C) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ( r6_groeb_2(A,B,C,D,E) => r10_polyred(A,B,C,D,E) ) ) ) ) ) ) )).
fof(t39_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ~ r1_xxreal_0(k5_card_1(k3_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)) ) ) ) ) ) ) )).
fof(t39_group_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t39_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t39_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ( v8_struct_0(A) => v8_struct_0(B) ) ) ) )).
fof(t39_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t39_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ! [C] : ( ( v15_algstr_0(C) & m1_group_2(C,A) ) => ~ v2_group_4(C,A) ) => r1_struct_0(k6_group_4(A),B) ) ) ) )).
fof(t39_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t39_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & l3_algstr_0(C) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t39_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( m1_group_9(D,A,C) => ! [E] : ( m1_group_9(E,A,C) => ! [F] : ( m1_group_9(F,A,B) => ! [G] : ( m1_group_9(G,A,B) => ( ( D = F & E = G ) => k17_group_9(A,B,F,G) = k17_group_9(A,C,D,E) ) ) ) ) ) ) ) )).
fof(t39_hausdorf,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [C] : ( ( ~ 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(k5_numbers,k3_hausdorf(A,B,C)) ) ) ) ) )).
fof(t39_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t39_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( 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) ) ) ) )).
fof(t39_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A)))) => ( ( r3_orders_2(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A)),B,C) & C = k1_xboole_0 ) => B = k1_xboole_0 ) ) ) ) )).
fof(t39_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( v3_rcomp_1(E) & m1_subset_1(E,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(A,E) => ( r1_xxreal_0(C,D) | k1_funct_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) = k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(B,k4_newton(D,C)),k2_newton(D)),k3_prepower(A,k6_xcmplx_0(C,D))) ) ) ) ) ) ) ) )).
fof(t39_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => r2_hidden(k3_hilbert1(k3_hilbert1(B,C),k3_hilbert1(k4_hilbert1(B,A),C)),k6_hilbert1) ) ) ) )).
fof(t39_hilbert3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( m1_hilbert3(D,C) => ! [E] : ( r1_abian(E,k5_hilbert3(C,D,A)) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t39_hurwitz,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( 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(k5_numbers,k3_complex1(B)) ) ) ) ) )).
fof(t39_idea_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k4_ordinal1,B,6) & m2_finseq_1(C,k3_finseq_2(k4_ordinal1)) ) => ! [D] : ( v7_ordinal1(D) => ( 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)) ) ) ) ) ) )).
fof(t39_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u2_incsp_1(A)) => ( r4_incsp_1(A,k7_domain_1(u1_incsp_1(A),B,C),E) => ( r1_incsp_1(A,D,E) | B = C | k3_incsp_1(A,D,E) = k2_incsp_1(A,B,C,D) ) ) ) ) ) ) ) )).
fof(t39_index_1,axiom,( ! [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) & 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))) ) )).
fof(t39_instalg1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m3_pboole(D,A,B) => ! [E] : ( m2_pboole(E,A,B,C) => ! [F] : ( r2_hidden(F,A) => ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) ) => ! [H] : ( ( 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] : ( r2_hidden(I,k1_funct_1(D,F)) => k1_funct_1(H,I) = k1_funct_1(G,I) ) ) ) ) ) ) ) ) ) )).
fof(t39_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_int_1(A) = k2_int_1(A) <=> k2_xcmplx_0(k1_int_1(A),1) != k2_int_1(A) ) ) )).
fof(t39_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( ( ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r2_hidden(D,k1_relset_1(k4_ordinal1,C)) & r2_hidden(E,k1_relset_1(k4_ordinal1,C)) ) => ( D = E | k6_nat_d(k1_recdef_1(C,D),k1_recdef_1(C,E)) = 1 ) ) ) ) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( r2_hidden(D,k1_relset_1(k4_ordinal1,C)) & r1_xxreal_0(k1_recdef_1(C,D),k5_numbers) ) ) ) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k1_relset_1(k4_ordinal1,C)) => ( k5_int_1(k6_xcmplx_0(A,k1_recdef_1(D,E)),k1_recdef_1(C,E)) = k5_numbers & k5_int_1(k6_xcmplx_0(B,k1_recdef_1(D,E)),k1_recdef_1(C,E)) = k5_numbers ) ) ) => r2_int_1(A,B,k3_wsierp_1(C)) ) ) ) ) ) ) )).
fof(t39_int_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( v2_funct_1(B) <=> v2_funct_1(k2_finseq_7(A,B,C,D)) ) ) ) ) ) )).
fof(t39_int_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( 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(k5_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) ) ) ) ) ) )).
fof(t39_integr11,axiom,( ! [A] : ( ( 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_sin_cos,k1_fdiff_9))) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( k2_xcmplx_0(1,k1_funct_1(k16_sin_cos,B)) != k5_numbers & k6_xcmplx_0(1,k1_funct_1(k16_sin_cos,B)) != k5_numbers ) ) ) ) => ( r2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_fdiff_9),A),B) = k7_xcmplx_0(1,k2_xcmplx_0(1,k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t39_integr12,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v3_rcomp_1(F) & m1_subset_1(F,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,F) & r2_relset_1(k1_numbers,k1_numbers,D,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,C,E)) & r2_relset_1(k1_numbers,k1_numbers,E,k1_taylor_1(2)) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,F) => ( k1_funct_1(B,G) = k3_xcmplx_0(G,k6_prepower(k6_xcmplx_0(1,k3_prepower(G,2)),k4_xcmplx_0(k7_xcmplx_0(1,2)))) & k1_funct_1(C,G) = 1 & ~ r1_xxreal_0(k1_funct_1(D,G),k5_numbers) ) ) ) & r1_tarski(F,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k4_taylor_1(k7_xcmplx_0(1,2))))) & F = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k4_taylor_1(k7_xcmplx_0(1,2)))),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k4_taylor_1(k7_xcmplx_0(1,2)))),k3_seq_4(A))) ) ) ) ) ) ) ) )).
fof(t39_integr13,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v3_rcomp_1(E) & m1_subset_1(E,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,E) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => k1_funct_1(D,F) = 1 ) ) & r2_relset_1(k1_numbers,k1_numbers,C,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(k6_xcmplx_0(A,1))),k3_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k1_taylor_1(2))),A))) & r1_tarski(E,k2_rcomp_1(k4_xcmplx_0(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,C) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,B)) ) => k2_integra5(B,C) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k1_taylor_1(A)),k2_seq_4(B)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k1_taylor_1(A)),k3_seq_4(B))) ) ) ) ) ) ) )).
fof(t39_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,D),k1_funct_1(k18_sin_cos,k1_funct_1(k18_sin_cos,D))),k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k18_sin_cos,D)))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_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) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k2_fdiff_9),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k2_fdiff_9),k3_seq_4(A))) ) ) ) ) )).
fof(t39_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_integra1(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(B)))) ) => ! [F] : ( m4_integr15(F,A,B,C,E) => ! [G] : ( 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(k4_ordinal1,k3_finseq_2(k1_euclid(A)),k4_ordinal1,k3_finseq_2(u1_struct_0(k4_real_ns1(A))),F,G) ) => r2_funct_2(k4_ordinal1,u1_struct_0(k4_real_ns1(A)),k6_integr15(A,B,C,E,F),k3_integr18(k4_real_ns1(A),B,D,E,G)) ) ) ) ) ) ) ) ) )).
fof(t39_integra1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( m1_integra1(C,B) => ! [D] : ( m1_integra1(D,B) => ! [E] : ( ( 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_funct_1(k14_integra1(k5_integra1(B,E,C)),A),k1_funct_1(k14_integra1(k5_integra1(B,E,D)),k13_integra1(B,C,D,A))) ) ) ) ) ) ) )).
fof(t39_integra2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( r2_hidden(C,k1_integra2(A,B)) & ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,A) & C = k3_xcmplx_0(B,D) ) ) ) ) ) ) )).
fof(t39_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => k2_integra5(A,k18_sin_cos) = k6_xcmplx_0(k1_funct_1(k16_sin_cos,k2_seq_4(A)),k1_funct_1(k16_sin_cos,k3_seq_4(A))) ) )).
fof(t39_integra9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2)) => r1_integra9(A,k16_sin_cos,k18_sin_cos) ) ) )).
fof(t39_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t39_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( 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) ) ) )).
fof(t39_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ( B = k7_xcmplx_0(1,k1_nat_1(A,1)) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(k3_xcmplx_0(k7_newton(A),k4_series_1(k1_valued_0(k1_numbers,k5_irrat_1,k1_nat_1(A,1)))),k7_xcmplx_0(B,k6_xcmplx_0(1,B))) ) ) ) ) )).
fof(t39_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,B,C) => ! [G] : ( m2_nattra_1(G,A,B,D,E) => ( r2_nattra_1(A,B,D,E) => r2_funct_2(u1_struct_0(A),u4_struct_0(C),k4_isocat_1(A,B,C,D,E,G,F),k6_isocat_1(A,B,C,D,E,F,F,G,k4_nattra_1(B,C,F))) ) ) ) ) ) ) ) ) )).
fof(t39_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t39_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(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)) ) ) ) )).
fof(t39_jgraph_5,axiom,( ? [A] : ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k4_topmetr(k4_xcmplx_0(1),1))) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k4_topmetr(k4_xcmplx_0(1),1))))) & v3_tops_2(A,k5_topmetr,k4_topmetr(k4_xcmplx_0(1),1)) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,k1_rcomp_1(k5_numbers,1)) => k1_funct_1(A,B) = k6_xcmplx_0(k3_xcmplx_0(2,B),1) ) ) & k1_funct_1(A,k5_numbers) = k4_xcmplx_0(1) & k1_funct_1(A,1) = 1 ) )).
fof(t39_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t39_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t39_jordan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( m1_borsuk_2(G,A,C,D) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t39_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t39_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_topreal1(2,k1_jordan1e(B,A))) & r2_hidden(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C)),k8_jordan6(B)) ) ) ) ) ) ) )).
fof(t39_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,1),A,k1_jordan1a(k1_jordan8(B,1)))) = k7_xcmplx_0(k2_xcmplx_0(k9_pscomp_1(B),k7_pscomp_1(B)),2) ) ) ) )).
fof(t39_jordan1b,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(B,k3_finseq_1(k1_jordan8(A,D))) & r1_xxreal_0(C,k1_matrix_0(k1_jordan8(A,D))) & r1_tarski(k3_goboard5(k1_jordan8(A,D),B,C),k1_jordan2c(2,A)) & r1_xxreal_0(k1_matrix_0(k1_jordan8(A,D)),k1_nat_1(C,1)) ) ) ) ) ) )).
fof(t39_jordan1g,axiom,( ! [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] : ( v7_ordinal1(B) => ( r1_tarski(k10_xtuple_0(k1_jordan1e(A,B)),k10_xtuple_0(k2_jordan9(A,B))) & r1_tarski(k10_xtuple_0(k2_jordan1e(A,B)),k10_xtuple_0(k2_jordan9(A,B))) ) ) ) )).
fof(t39_jordan1h,axiom,( ! [A] : ( 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)) ) ) )).
fof(t39_jordan1j,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( v4_topreal1(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ( r1_goboard1(u1_struct_0(k15_euclid(2)),B,A) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t39_jordan1k,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v2_compts_1(B,k15_euclid(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [C] : ( ( 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) = k5_numbers ) ) ) ) )).
fof(t39_jordan21,axiom,( ! [A] : ( ( 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)) ) )).
fof(t39_jordan22,axiom,( ! [A] : ( ( 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)) ) )).
fof(t39_jordan23,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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) ) ) ) ) )).
fof(t39_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(1,A) & k6_subset_1(k1_euclid(A),a_2_3_jordan2c(A,B)) = k1_xboole_0 ) ) ) )).
fof(t39_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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))) ) ) ) )).
fof(t39_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_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)) ) ) ) ) ) )).
fof(t39_jordan5d,axiom,( ! [A] : ( ( ~ 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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k3_finseq_1(k2_goboard2(A)),1)) ) )).
fof(t39_jordan6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(A),B)))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(A))) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t39_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k8_knaster(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k8_knaster(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t39_kurato_1,axiom,( k1_tops_1(k3_topmetr,k6_kurato_1) != k2_pre_topc(k3_topmetr,k6_kurato_1) )).
fof(t39_kurato_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ! [D] : ( v7_ordinal1(D) => k2_kurato_2(A,B,D) = C ) => k1_kurato_2(A,B) = k3_kurato_2(A,B) ) ) ) ) )).
fof(t39_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( k12_matrix_3(A,B,C) != k4_struct_0(B) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(B)) => ( ( k3_finseq_1(D) = A & k11_laplace(B,C,D) = k4_matrix_0(u1_struct_0(B),k10_laplace(u1_struct_0(B),E)) ) => ( k4_matrix_0(u1_struct_0(B),k10_laplace(u1_struct_0(B),D)) = k11_laplace(B,k1_matrix_6(A,B,C),E) & ! [F] : ( 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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t39_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_lattice2(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t39_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( r3_lattice3(A,B,C) => r3_lattices(A,B,k16_lattice3(A,C)) ) ) ) )).
fof(t39_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( 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)) ) ) )).
fof(t39_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(t39_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( v7_ordinal1(D) => ( r1_fuzzy_1(B,C) => r1_fuzzy_1(k4_lfuzzy_1(A,B,D),k4_lfuzzy_1(A,C,D)) ) ) ) ) ) )).
fof(t39_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v9_ordinal1(A) & v2_comseq_2(A) & k1_seq_2(A) = k5_numbers & v5_valued_0(A) ) => v2_limfunc1(k37_valued_1(k4_ordinal1,k1_numbers,A)) ) ) )).
fof(t39_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r5_limfunc2(C,A) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k2_rcomp_1(A,k2_xcmplx_0(A,D)),k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k1_relset_1(k1_numbers,C))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k2_rcomp_1(A,k2_xcmplx_0(A,D))) => r1_xxreal_0(k1_funct_1(C,E),k1_funct_1(B,E)) ) ) ) ) | r5_limfunc2(B,A) ) ) ) ) ) )).
fof(t39_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,D),A),k2_rcomp_1(A,k2_xcmplx_0(A,D))))) & k1_funct_1(B,E) = k1_limfunc3(B,A) ) ) ) ) | r2_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t39_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t39_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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)) ) ) ) )).
fof(t39_lopban_3,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_lopban_3(A,B,k5_numbers) = k5_struct_0(A) ) ) )).
fof(t39_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t39_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( ? [F] : ( m1_subset_1(F,u1_struct_0(k22_lpspacc1(A,B,C))) & r2_hidden(D,F) & r2_hidden(E,F) ) => ( r1_lpspacc1(A,B,C,D,E) & r2_hidden(D,k13_lpspacc1(A,B,C)) & r2_hidden(E,k13_lpspacc1(A,B,C)) ) ) ) ) ) ) ) )).
fof(t39_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t39_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( v2_xxreal_0(F) & v1_xreal_0(F) ) => ( k5_lpspace2(A,B,C,D,F) = k5_lpspace2(A,B,C,E,F) => ( ! [G] : ( m2_subset_1(G,k1_zfmisc_1(A),B) => ~ ( k1_funct_1(C,k3_subset_1(A,G)) = k5_numbers & G = k1_relset_1(A,E) & r1_mesfunc6(A,B,E,G) ) ) | k5_lpspace2(A,B,C,D,F) = k1_xboole_0 | r1_lpspace1(A,B,C,D,E) ) ) ) ) ) ) ) ) )).
fof(t39_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => ! [B] : ( m2_finseq_1(B,k1_hilbert1) => ! [C] : ( m2_finseq_1(C,k1_hilbert1) => ! [D] : ( m2_finseq_1(D,k1_hilbert1) => ( ( D = k8_finseq_1(k1_hilbert1,B,C) & r1_xxreal_0(1,k3_finseq_1(B)) & r1_xxreal_0(1,k3_finseq_1(C)) & ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,k3_finseq_1(B)) ) => r7_ltlaxio1(E,B,A) ) ) & ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,k3_finseq_1(C)) ) => r7_ltlaxio1(E,C,A) ) ) ) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,k3_finseq_1(D)) ) => r7_ltlaxio1(E,D,A) ) ) ) ) ) ) ) )).
fof(t39_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(k1_ltlaxio1(k4_ltlaxio1(C,B)),k3_hilbert1(k3_hilbert1(A,B),k3_hilbert1(A,k1_ltlaxio1(C))))) ) ) ) )).
fof(t39_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t39_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(t39_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,B,B) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( r1_xxreal_0(k5_numbers,A) & v1_matrix10(C) ) => v4_matrix10(k6_matrix10(B,A,C)) ) ) ) ) )).
fof(t39_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,C,A,B) & m2_finseq_1(D,k3_finseq_2(C)) ) => k3_relat_1(k1_finseq_2(A),D) = D ) ) ) ) )).
fof(t39_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,A,G,F) & m2_finseq_1(H,k3_finseq_2(A)) ) => ! [I] : ( m2_finseq_2(I,k4_ordinal1,k4_finseq_2(E,k4_ordinal1)) => ! [J] : ( m2_finseq_2(J,k4_ordinal1,k4_finseq_2(D,k4_ordinal1)) => ~ ( r2_hidden(B,k10_xtuple_0(I)) & r1_tarski(k2_zfmisc_1(k10_xtuple_0(I),k10_xtuple_0(J)),k2_matrix_0(H)) & ! [K] : ( m2_finseq_2(K,k4_ordinal1,k4_finseq_2(E,k4_ordinal1)) => ~ ( k10_xtuple_0(K) = k2_xboole_0(k6_subset_1(k10_xtuple_0(I),k1_tarski(B)),k1_tarski(C)) & k1_matrix13(A,k3_matrix11(B,G,F,A,H,k7_matrix_0(A,H,C)),E,D,I,J) = k1_matrix13(A,H,E,D,K,J) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t39_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & k3_matrix_0(u1_struct_0(B),C,1,1) != k4_struct_0(B) & ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ~ ( v1_matrix_6(D,A,B) & k3_matrix_0(u1_struct_0(B),k4_matrix_3(B,C,D),1,1) = k5_struct_0(B) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(E,A) => ( r1_xxreal_0(E,1) | k3_matrix_0(u1_struct_0(B),k4_matrix_3(B,C,D),1,E) = k4_struct_0(B) ) ) ) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(E,A) & k3_matrix_0(u1_struct_0(B),C,E,1) = k4_struct_0(B) ) => ( r1_xxreal_0(E,1) | k3_matrix_0(u1_struct_0(B),k4_matrix_3(B,C,D),E,1) = k4_struct_0(B) ) ) ) ) ) ) ) ) ) )).
fof(t39_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [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] : ( m1_subset_1(G,u1_struct_0(F)) => ! [H] : ( ( v1_matrix_0(H) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(F))) ) => ! [I] : ( ( v1_matrix_0(I) & v2_matrix_0(I,u1_struct_0(F),D,E) & m2_finseq_1(I,k3_finseq_2(u1_struct_0(F))) ) => ! [J] : ( ( v1_matrix_0(J) & v2_matrix_0(J,u1_struct_0(F),D,C) & m2_finseq_1(J,k3_finseq_2(u1_struct_0(F))) ) => ( ( r2_hidden(H,k4_matrix15(F,I,J)) & r2_hidden(B,k2_finseq_1(D)) ) => r2_hidden(H,k4_matrix15(F,k3_matrix11(A,D,E,u1_struct_0(F),I,k4_fvsum_1(k1_matrix_0(I),F,k7_matrix_0(u1_struct_0(F),I,A),k10_fvsum_1(k1_matrix_0(I),F,k7_matrix_0(u1_struct_0(F),I,B),G))),k3_matrix11(A,D,C,u1_struct_0(F),J,k4_fvsum_1(k1_matrix_0(J),F,k7_matrix_0(u1_struct_0(F),J,A),k10_fvsum_1(k1_matrix_0(J),F,k7_matrix_0(u1_struct_0(F),J,B),G))))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t39_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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,k5_numbers) => v3_matrix16(k3_matrix_1(B,A),u1_struct_0(B)) ) ) ) )).
fof(t39_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => k9_matrix_0(B) = a_2_1_matrix_0(A,B) ) ) )).
fof(t39_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) ) => B = k3_matrix_3(A,B,k3_matrix_3(A,C,k2_matrix_3(A,C))) ) ) ) ) )).
fof(t39_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_6(D,A,B) & k4_matrix_3(B,D,C) = k3_matrix_1(B,A) ) => r2_matrix_6(A,B,C,D) ) ) ) ) ) )).
fof(t39_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r1_matrix_8(A,B,C,D) => ( r1_xxreal_0(A,k5_numbers) | r1_matrix_8(A,B,k3_matrix_3(B,C,C),k3_matrix_3(B,D,D)) ) ) ) ) ) ) )).
fof(t39_matrix_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_matrix_2(B,k3_matrix_2(A)) => ! [C] : ( m1_matrix_2(C,k3_matrix_2(A)) => r2_hidden(k1_partfun1(k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),C,B),k3_matrix_2(A)) ) ) ) )).
fof(t39_matrixc1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k2_numbers)) ) => ( r2_hidden(A,k2_finseq_1(k3_finseq_1(B))) => k7_matrix_0(k2_numbers,B,A) = k1_complsp2(k7_matrix_0(k2_numbers,k1_matrixc1(B),A)) ) ) ) )).
fof(t39_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(A)) ) => ! [E] : ( ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(A)) ) => ! [F] : ( ( v1_matrix_0(F) & m2_finseq_1(F,k3_finseq_2(A)) ) => ! [G] : ( ( v1_matrix_0(G) & m2_finseq_1(G,k3_finseq_2(A)) ) => ( ( k3_finseq_1(D) = k3_finseq_1(F) & k1_matrix_0(D) = k1_matrix_0(F) & k3_finseq_1(E) = k3_finseq_1(G) & k1_matrix_0(E) = k1_matrix_0(G) & k13_matrixj1(A,B,k5_matrixj1(A,D,E)) = k13_matrixj1(A,C,k5_matrixj1(A,F,G)) ) => ( D = F & E = G ) ) ) ) ) ) ) ) ) )).
fof(t39_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k1_matrix_0(A) = k1_matrix_0(B) & k5_matrixr1(B,A) = B ) => A = k8_matrixr1(k3_finseq_1(A),k1_matrix_0(A)) ) ) ) )).
fof(t39_matrixr2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k2_finseq_1(k5_numbers),k2_finseq_1(k5_numbers)) & v3_funct_2(A,k2_finseq_1(k5_numbers),k2_finseq_1(k5_numbers)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_finseq_1(k5_numbers),k2_finseq_1(k5_numbers)))) ) => A = k6_finseq_1(k4_ordinal1) ) )).
fof(t39_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( ( 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] : ( m1_matrlin(E,A,B) => ! [F] : ( m1_matrlin(F,A,C) => ( ~ r1_xxreal_0(k3_finseq_1(E),k5_numbers) => k1_matrix_0(k10_matrlin(A,B,C,D,E,F)) = k3_finseq_1(F) ) ) ) ) ) ) ) )).
fof(t39_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( m1_matrlin(D,A,B) => ! [E] : ( m1_matrlin(E,A,C) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(A),k3_finseq_1(D),k3_finseq_1(E)) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(A))) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(A),k3_finseq_1(D),k3_finseq_1(E)) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(A))) ) => ( 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 ) ) ) ) ) ) ) ) )).
fof(t39_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t39_matrprob,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( k1_matrix_0(B) = k3_finseq_1(C) => ( A = k6_matrixr1(B,C) <=> ( k3_finseq_1(A) = k3_finseq_1(B) & k1_matrix_0(A) = k1_matrix_0(C) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(D,E),k2_matrix_0(A)) => k3_matrix_0(k1_numbers,A,D,E) = k22_rvsum_1(k7_matrix_0(k1_numbers,B,D),k8_matrix_0(k1_numbers,C,E)) ) ) ) ) ) ) ) ) ) )).
fof(t39_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( v2_funct_1(k3_matrtop1(A,B,C)) <=> k8_matrix13(k2_vectsp_1,C) = A ) ) ) ) )).
fof(t39_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t39_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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 ) )).
fof(t39_measure6,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v5_xxreal_2(k2_relset_1(k1_numbers,A)) <=> v1_comseq_2(A) ) ) )).
fof(t39_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r2_hidden(C,A) & r2_hidden(D,B) ) => r2_hidden(k1_xxreal_3(C,D),k8_member_1(A,B)) ) ) ) ) ) )).
fof(t39_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ( r1_tarski(k7_memstr_0(A,B,k5_numbers),C) => k5_memstr_0(A,B,C) = k5_numbers ) ) ) ) )).
fof(t39_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t39_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( 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))))) ) ) ) )).
fof(t39_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ( ( k1_relset_1(A,k4_mesfunc5(A,k2_numbers,D,k5_numbers)) = C & v1_mesfunc8(D,A,k2_numbers) & ! [E] : ( v7_ordinal1(E) => r1_mesfun6c(A,B,k4_mesfunc5(A,k2_numbers,k3_mesfun9c(A,D),E),C) ) & ! [E] : ( 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) ) ) ) ) ) )).
fof(t39_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ( r1_mesfunc2(A,B,D) => r1_mesfunc2(A,B,k6_mesfunc1(A,D,E)) ) ) ) ) ) ) )).
fof(t39_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( r2_hidden(C,k1_relset_1(A,B)) & k12_supinf_2(k18_rfunct_3(A,B),C) = k5_numbers ) => k12_supinf_2(k19_rfunct_3(A,B),C) = k2_supinf_2(k12_supinf_2(B,C)) ) ) ) )).
fof(t39_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k8_midsp_1(A,B,C) = k8_midsp_1(A,B,D) => C = D ) ) ) ) ) )).
fof(t39_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( 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) ) ) )).
fof(t39_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t39_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k6_modal_1) => ! [B] : ( m1_subset_1(B,k6_modal_1) => ! [C] : ( m1_subset_1(C,k6_modal_1) => ( k10_modal_1(A) != k11_modal_1(B) & k10_modal_1(A) != k12_modal_1(B,C) ) ) ) ) )).
fof(t39_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t39_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r3_modelc_2(A,k3_modelc_2(B)) => r2_modelc_2(A,B) ) ) ) )).
fof(t39_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_3(C,B) & v3_modelc_3(C,B) & l1_modelc_3(C,B) ) => ! [D] : ( ( v1_modelc_3(D,B) & v3_modelc_3(D,B) & l1_modelc_3(D,B) ) => ( ( r6_modelc_3(B,C,D) & v8_modelc_2(A) & r2_hidden(A,u1_modelc_3(B,D)) ) => ( r2_hidden(k11_modelc_2(A),u1_modelc_3(B,D)) | ( r2_hidden(k12_modelc_2(A),u1_modelc_3(B,D)) & r2_hidden(A,u3_modelc_3(B,D)) ) ) ) ) ) ) ) )).
fof(t39_moebius1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k3_moebius1(A)) <=> ( ~ r1_xxreal_0(B,k5_numbers) & r1_nat_d(B,A) ) ) ) ) )).
fof(t39_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & m2_monoid_0(A,k2_monoid_0) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( B = D & C = E ) => k6_algstr_0(A,B,C) = k2_xcmplx_0(D,E) ) ) ) ) ) ) )).
fof(t39_monoid_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(t39_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t39_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_msafree4(E,u1_struct_0(A),B,k1_msafree4(u1_struct_0(A),B,D)) => m1_subset_1(k1_trees_4(k4_tarski(E,D)),k1_funct_1(u3_msualg_1(A,C),D)) ) ) ) ) ) )).
fof(t39_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( m2_pboole(D,u1_struct_0(A),C,u3_msualg_1(A,B)) => ! [E] : ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t39_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( ( r2_pboole(A,B,D) & r2_pboole(A,C,D) ) => m3_pboole(k2_pzfmisc1(A,B,C),A,k1_mboolean(A,D)) ) ) ) ) )).
fof(t39_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(t39_msualg_6,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( ! [D] : ! [E] : ( ( 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) ) ) ) ) )).
fof(t39_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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))) ) ) )).
fof(t39_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => r2_hidden(k6_nat_1(B,C,A),k10_xtuple_0(C)) ) ) ) )).
fof(t39_nat_3,axiom,( r8_pboole(k8_newton,k12_nat_3(1),k16_pre_poly(k8_newton)) )).
fof(t39_nat_4,axiom,( v1_int_2(2503) )).
fof(t39_nat_5,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ~ ( v1_abian(A) & v2_nat_5(A) & ! [B] : ( v7_ordinal1(B) => ~ ( v1_int_2(k7_nat_d(k1_newton(2,B),1)) & A = k2_nat_1(k11_newton(2,k7_nat_d(B,1)),k7_nat_d(k1_newton(2,B),1)) ) ) ) ) )).
fof(t39_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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) ) ) ) )).
fof(t39_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_ncfcont1(A,B,C,D) => ( r5_ncfcont1(A,k4_normsp_0(u1_struct_0(A),B,C),D) & r2_ncfcont1(A,B,k5_vfunct_1(u1_struct_0(A),B,C),D) ) ) ) ) ) ) )).
fof(t39_ncfcont2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_normsp_0(A,k5_algstr_0(A,B,C)) = k2_normsp_0(A,k5_algstr_0(A,C,B)) ) ) ) )).
fof(t39_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v3_nfcont_1(C,A) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t39_ndiff_4,axiom,( ! [A] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t39_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k11_prvect_2(A,B))) => ! [D] : ( v1_xreal_0(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))),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) ) ) ) ) )).
fof(t39_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( B != 1 & r1_nat_d(B,A) & r1_nat_d(B,k1_nat_1(A,1)) ) ) ) )).
fof(t39_nfcont_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)))) ) => ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t39_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t39_normform,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [C] : ( m1_subset_1(C,k5_finsub_1(k7_normform(A))) => ( ( r2_hidden(B,C) & ! [D] : ( 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)) ) ) ) )).
fof(t39_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t39_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,B,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k3_funct_2(u1_struct_0(k2_oppcat_1(B)),u1_struct_0(A),k7_cat_1(k2_oppcat_1(B),A,k10_oppcat_1(B,A,C)),k3_oppcat_1(B,D)) = k3_funct_2(u1_struct_0(B),u1_struct_0(A),k7_cat_1(B,A,C),D) ) ) ) ) )).
fof(t39_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,A) & r1_ndiff_3(k4_real_ns1(A),B,C) ) => ( r1_fdiff_1(k1_partfun1(k1_numbers,u1_struct_0(k4_real_ns1(A)),k1_euclid(A),k1_numbers,B,k1_pdiff_1(D,A)),C) & k1_funct_1(k1_pdiff_1(D,A),k1_ndiff_3(k4_real_ns1(A),B,C)) = k1_fdiff_1(k1_partfun1(k1_numbers,u1_struct_0(k4_real_ns1(A)),k1_euclid(A),k1_numbers,B,k1_pdiff_1(D,A)),C) ) ) ) ) ) ) )).
fof(t39_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r3_orders_1(A,B) => v3_orders_1(k2_wellord1(A,B)) ) ) )).
fof(t39_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_orders_1(C,k1_orders_1(u1_struct_0(A)),k6_partfun1(k1_orders_1(u1_struct_0(A)))) => ! [D] : ( m2_orders_2(D,A,C) => ( B = k1_funct_1(C,u1_struct_0(A)) => k3_orders_2(A,D,B) = k1_xboole_0 ) ) ) ) ) )).
fof(t39_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ( k11_ordinal2(1,A) = A & k11_ordinal2(A,1) = A ) ) )).
fof(t39_ordinal3,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_ordinal2(B) ) => ! [C] : ( v3_ordinal1(C) => ( ( k9_xtuple_0(A) = k9_xtuple_0(B) & ! [D] : ( v3_ordinal1(D) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t39_ordinal5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v3_ordinal1(B) & v4_ordinal5(B) ) => ( r2_hidden(k5_numbers,A) => k1_ordinal5(B,k1_nat_1(A,2)) = k12_ordinal2(k4_ordinal1,k1_ordinal5(B,k1_nat_1(A,1))) ) ) ) )).
fof(t39_ordinal6,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_xboole_0(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t39_osafree,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_relat_1(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) ) ) )).
fof(t39_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v12_osalg_1(C,A) & m1_msualg_2(C,A,B) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t39_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r2_parsp_2(A,B,E,C,F) & r2_parsp_2(A,B,E,D,G) ) => r1_parsp_1(A,C,D,F,G) ) ) ) ) ) ) ) ) )).
fof(t39_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => k6_relset_1(A,B,C,k3_partfun1(D,A,B)) = k3_partfun1(D,A,k3_xboole_0(C,B)) ) )).
fof(t39_partfun2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t39_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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))) ) ) ) )).
fof(t39_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ( l2_pcs_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k23_pcs_0(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k23_pcs_0(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ( ( C = k4_tarski(E,G) & D = k4_tarski(F,H) ) => ( r1_orders_2(k23_pcs_0(A,B),C,D) <=> ( r1_orders_2(A,F,E) & r1_orders_2(B,G,H) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t39_pdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( 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),k3_funct_2(k1_euclid(2),k1_numbers,k1_pdiff_1(1,2),B)) ) ) ) )).
fof(t39_pdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t39_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m1_rcomp_1(C,k3_funct_2(k1_euclid(3),k1_numbers,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] : ( ( v9_ordinal1(D) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,E) = k1_tarski(k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(3,3),B)) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),C) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,3,k1_pdiff_3(1,3,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,3,k1_pdiff_3(1,3,A),B))))) & k3_pdiff_5(A,B) = k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,3,k1_pdiff_3(1,3,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,3,k1_pdiff_3(1,3,A),B))))) ) ) ) ) ) ) ) ) )).
fof(t39_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( v1_xreal_0(E) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,A) & C = k1_funct_1(k6_pdiff_1(A,D,B),E) ) => k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_1(D,A),C) = E ) ) ) ) ) ) )).
fof(t39_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_nfcont_4(A,B,C) => r2_nfcont_4(A,k26_valued_1(k1_euclid(A),k1_numbers,B,D),C) ) ) ) ) ) )).
fof(t39_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,1) => ( k4_nat_d(A,B) = 1 <=> r2_int_1(A,1,B) ) ) ) ) )).
fof(t39_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B))) => ! [D] : ( 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)) ) ) ) )).
fof(t39_polyeq_3,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => m1_comptrig(k2_xcmplx_0(k19_sin_cos(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B),A)),k3_xcmplx_0(k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B),A)),k7_complex1)),1,A) ) ) )).
fof(t39_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k17_polyform(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k17_polyform(A,B))) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t39_polynom5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k1_algseq_1(A,k4_polynom5(A,B,C)),2) ) ) ) )).
fof(t39_polynom8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(B,k5_numbers) => ! [C] : ( 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,k3_matrix_1(A,B),k1_polynom8(A,B)) ) ) ) ) ) )).
fof(t39_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [G] : ( ( 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,k3_polynom1(k15_pre_poly(A),C,F)) ) ) ) ) ) ) ) ) )).
fof(t39_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(C,1) & r1_xxreal_0(k2_power(C,B),k2_power(C,A)) ) ) ) ) )).
fof(t39_pre_poly,axiom,( ! [A] : ( v1_relat_1(k8_funcop_1(k4_ordinal1,A,k5_numbers)) & v4_relat_1(k8_funcop_1(k4_ordinal1,A,k5_numbers),A) & v1_funct_1(k8_funcop_1(k4_ordinal1,A,k5_numbers)) & v1_partfun1(k8_funcop_1(k4_ordinal1,A,k5_numbers),A) & v4_valued_0(k8_funcop_1(k4_ordinal1,A,k5_numbers)) & v2_pre_poly(k8_funcop_1(k4_ordinal1,A,k5_numbers)) ) )).
fof(t39_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k3_prepower(A,B),k5_numbers) ) ) ) )).
fof(t39_prob_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m2_prob_1(E,A,B) => r1_xxreal_0(k3_funct_2(B,k1_numbers,E,k6_prob_1(A,B,C,D)),k3_real_1(k3_funct_2(B,k1_numbers,E,C),k3_funct_2(B,k1_numbers,E,D))) ) ) ) ) ) )).
fof(t39_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m2_prob_1(E,A,B) => ( ~ r1_xxreal_0(k3_funct_2(B,k1_numbers,E,D),k5_numbers) => r1_xxreal_0(k6_xcmplx_0(1,k6_real_1(k3_funct_2(B,k1_numbers,E,k7_prob_1(A,B,k4_prob_1(A,B),C)),k3_funct_2(B,k1_numbers,E,D))),k3_funct_2(B,k1_numbers,k3_prob_2(A,B,E,D),C)) ) ) ) ) ) ) )).
fof(t39_prob_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( m2_prob_1(D,A,B) => v7_valued_0(k3_series_1(k8_prob_1(A,B,C,D))) ) ) ) ) )).
fof(t39_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => k3_funct_2(B,k1_numbers,C,D) = k1_funct_1(k7_prob_4(A,B,C),D) ) ) ) ) )).
fof(t39_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t39_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ 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))) ) ) ) ) ) ) )).
fof(t39_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t39_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t39_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( ( ~ 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) ) ) ) )).
fof(t39_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_qc_lang4(C,A,B) => ! [D] : ( m1_qc_lang4(D,A,B) => a_4_1_qc_lang4(A,B,C,D) = a_4_2_qc_lang4(A,B,C,D) ) ) ) ) )).
fof(t39_quatern2,axiom,( k4_struct_0(k15_quatern2) = k1_quatern2 )).
fof(t39_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => r1_xxreal_0(k6_xcmplx_0(k28_quaterni(A),k28_quaterni(B)),k7_xcmplx_0(k2_xcmplx_0(k28_quaterni(k22_quaterni(A,B)),k28_quaterni(k25_quaterni(B,A))),2)) ) ) )).
fof(t39_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ( ( k13_quaterni(A) = k5_numbers & k13_quaterni(B) = k5_numbers ) => ( k13_quaterni(k23_quaterni(A,B)) = k6_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(k14_quaterni(A),k14_quaterni(B))),k3_xcmplx_0(k15_quaterni(A),k15_quaterni(B))),k3_xcmplx_0(k16_quaterni(A),k16_quaterni(B))) & k14_quaterni(k23_quaterni(A,B)) = k6_xcmplx_0(k3_xcmplx_0(k15_quaterni(A),k16_quaterni(B)),k3_xcmplx_0(k16_quaterni(A),k15_quaterni(B))) & k15_quaterni(k23_quaterni(A,B)) = k6_xcmplx_0(k3_xcmplx_0(k16_quaterni(A),k14_quaterni(B)),k3_xcmplx_0(k14_quaterni(A),k16_quaterni(B))) & k16_quaterni(k23_quaterni(A,B)) = k6_xcmplx_0(k3_xcmplx_0(k14_quaterni(A),k15_quaterni(B)),k3_xcmplx_0(k15_quaterni(A),k14_quaterni(B))) ) ) ) ) )).
fof(t39_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k19_quofield(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k19_quofield(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t39_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_vectsp_6(E,A,B) => ( v2_funct_1(k2_partfun1(u1_struct_0(B),u1_struct_0(C),D,k1_vectsp_6(A,B,E))) => k2_ranknull(B,C,D,k1_vectsp_6(A,B,E)) = k1_vectsp_6(A,C,k8_ranknull(A,B,C,E,D)) ) ) ) ) ) ) )).
fof(t39_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ! [B] : ( v1_rat_1(B) => ( ~ ( ~ r1_xxreal_0(B,A) & r1_xxreal_0(k3_xcmplx_0(k2_rat_1(B),k1_rat_1(A)),k3_xcmplx_0(k2_rat_1(A),k1_rat_1(B))) ) & ~ ( ~ r1_xxreal_0(k3_xcmplx_0(k2_rat_1(B),k1_rat_1(A)),k3_xcmplx_0(k2_rat_1(A),k1_rat_1(B))) & r1_xxreal_0(B,A) ) ) ) ) )).
fof(t39_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t39_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(1,A) => r2_hidden(k9_nat_1(k1_numbers,k4_real_3(B),A),k4_ordinal1) ) ) ) )).
fof(t39_relat_1,axiom,( ! [A] : ( k9_xtuple_0(k4_relat_1(A)) = A & k10_xtuple_0(k4_relat_1(A)) = A ) )).
fof(t39_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ! [E] : ( 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)) ) ) ) ) )).
fof(t39_rewrite1,axiom,( ! [A] : ! [B] : ( ( r5_rewrite1(k1_xboole_0,A,B) | r6_rewrite1(k1_xboole_0,A,B) ) => A = B ) )).
fof(t39_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t39_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k8_afinsq_1(C)) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k8_afinsq_1(C))) => ! [H] : ( ( ~ 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)) ) ) ) ) ) ) ) )).
fof(t39_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_valued_0(C) ) => ( k1_valued_1(k1_rfunct_1(B,A),k1_rfunct_1(C,A)) = k1_rfunct_1(k1_valued_1(B,C),A) & k45_valued_1(k1_rfunct_1(B,A),k1_rfunct_1(C,A)) = k1_rfunct_1(k45_valued_1(B,C),A) ) ) ) ) )).
fof(t39_rfunct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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))) ) ) ) )).
fof(t39_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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(k5_numbers)) = k8_relset_1(A,k1_numbers,k19_rfunct_3(A,B),k1_tarski(k5_numbers)) ) ) )).
fof(t39_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_seq_2(A) => k3_funct_2(k4_ordinal1,k1_numbers,k4_rinfsup1(A),k5_numbers) = k1_rinfsup1(A) ) ) )).
fof(t39_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => r1_xxreal_0(k6_rinfsup2(A),k5_rinfsup2(A)) ) )).
fof(t39_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t39_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => m1_rlsub_1(k1_rlsub_1(A),B) ) ) )).
fof(t39_rlsub_2,axiom,( ! [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) ) => ( r1_rlsub_2(A,k1_rlsub_1(A),k2_rlsub_1(A)) & r1_rlsub_2(A,k2_rlsub_1(A),k1_rlsub_1(A)) ) ) )).
fof(t39_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_connsp_2(D,A,B) => m1_connsp_2(k5_rusub_4(A,D,C),A,k3_rlvect_1(A,C,B)) ) ) ) ) )).
fof(t39_rlvect_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ( ( k3_finseq_1(C) = k3_finseq_1(D) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( 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) ) ) ) ) ) )).
fof(t39_rlvect_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_rlvect_2(C,A) => r1_rlvect_2(A,k7_rlvect_2(A,B,C),k7_rlvect_2(A,C,B)) ) ) ) )).
fof(t39_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( B != C & B != D & C != D & ! [H] : ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(t39_rlvect_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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)) ) ) ) )).
fof(t39_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => m1_rmod_2(k1_rmod_2(A,B),A,C) ) ) ) )).
fof(t39_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t39_rmod_4,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_rmod_4(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t39_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k9_robbins1(A,B,B) = k11_robbins1(A,B) ) ) )).
fof(t39_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t39_robbins4,axiom,( ! [A] : ( ( ~ 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) ) ) ) )).
fof(t39_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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(k5_numbers,1)) ) ) ) )).
fof(t39_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ~ ( ~ r1_xxreal_0(k1_rpr_1(A,B),k5_numbers) & ~ r1_xxreal_0(k1_rpr_1(A,C),k5_numbers) & k3_xcmplx_0(k1_rpr_1(A,B),k2_rpr_1(A,B,C)) != k3_xcmplx_0(k1_rpr_1(A,C),k2_rpr_1(A,C,B)) ) ) ) ) )).
fof(t39_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( 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) ) ) )).
fof(t39_rusub_2,axiom,( ! [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_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)) ) ) )).
fof(t39_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t39_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t39_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t39_rvsum_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => k17_rvsum_1(k5_rvsum_2(A)) = k4_xcmplx_0(k16_rvsum_1(A)) ) )).
fof(t39_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( 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),k5_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) ) ) ) ) ) ) ) )).
fof(t39_scmfsa10,axiom,( ! [A] : ( v7_ordinal1(A) => k3_amistd_1(k7_card_1(3),k1_scmfsa_2,A) = k2_tarski(A,k1_ordinal1(A)) ) )).
fof(t39_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t39_scmfsa_2,axiom,( ! [A] : ( ( 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(k7_card_1(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)) ) )).
fof(t39_scmfsa_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( v7_ordinal1(B) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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] : ( ( 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),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(C,D,E,A),k1_nat_1(B,1)),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(C,D,E,A),B),D,E,A),1)) ) ) ) ) ) )).
fof(t39_scmisort,axiom,( r2_extpro_1(k7_card_1(3),k1_scmfsa_2,k3_scmisort,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)),k10_scmfsa_m) )).
fof(t39_scmpds_2,axiom,( ! [A] : ( ( 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 ) )).
fof(t39_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ( ( k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),E)) = k5_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) ) ) ) ) ) ) ) )).
fof(t39_scmpds_7,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => k5_card_1(k2_scmpds_7(A,B,C,D)) = k1_nat_1(k5_card_1(D),3) ) ) ) ) )).
fof(t39_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( r2_hidden(B,k3_tarski(A)) => r1_tarski(k5_scmyciel(k1_tarski(B)),A) ) ) )).
fof(t39_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t39_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,A)),k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,B),A)) ) ) ) )).
fof(t39_seq_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ? [B] : ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_ordinal1) & v5_valued_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) & v1_seqm_3(k2_valued_0(k1_numbers,B,A)) ) ) )).
fof(t39_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t39_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_seq_2(A) & v7_valued_0(B) ) => v2_seq_2(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) ) ) )).
fof(t39_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [B] : ( v7_ordinal1(B) => k9_nat_1(k1_numbers,A,B) != k5_numbers ) & ? [B] : ( v7_ordinal1(B) & ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => r1_xxreal_0(1,k6_real_1(k3_funct_2(k4_ordinal1,k1_numbers,k56_valued_1(k4_ordinal1,k1_numbers,A),k1_nat_1(C,1)),k9_nat_1(k1_numbers,k56_valued_1(k4_ordinal1,k1_numbers,A),C))) ) ) ) & v1_series_1(A) ) ) )).
fof(t39_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( 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,k7_xcmplx_0(1,A)),k2_xcmplx_0(1,k7_xcmplx_0(1,B))),k2_xcmplx_0(1,k7_xcmplx_0(1,C)))) ) ) ) ) )).
fof(t39_setfam_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( 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)) ) ) )).
fof(t39_setlim_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ( v3_funct_1(C) & k3_funct_1(C) = B ) => ! [D] : ( v7_ordinal1(D) => k1_funct_1(k4_setlim_1(A,C),D) = B ) ) ) ) )).
fof(t39_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k1_prob_1(A,k6_setlim_2(A,C,B)) = k4_subset_1(A,B,k1_prob_1(A,C)) ) ) )).
fof(t39_setwiseo,axiom,( ! [A] : r3_binop_1(k5_finsub_1(A),k4_binop_1(k5_finsub_1(A),k9_setwiseo(A)),k9_setwiseo(A)) )).
fof(t39_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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] : ( ( 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] : ( m2_finseq_1(F,A) => ( ( v1_binop_1(D,A) & v2_binop_1(D,A) & v1_setwiseo(D,A) & C = k4_binop_1(A,D) & r6_binop_1(A,E,D) & k5_binop_1(A,E,C,B) = C ) => k5_binop_1(A,E,k1_finsop_1(A,F,D),B) = k1_finsop_1(A,k2_finseqop(A,A,A,E,F,B),D) ) ) ) ) ) ) ) )).
fof(t39_sf_mastr,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( v7_ordinal1(B) => k3_sf_mastr(A) = k3_sf_mastr(k5_compos_0(u1_compos_1(k1_scmfsa_2),A,B)) ) ) )).
fof(t39_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t39_simplex0,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(t39_simplex1,axiom,( ! [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) ) => ! [B] : ( ( 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) & k2_xcmplx_0(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 ) ) ) )).
fof(t39_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => r1_fcont_1(k3_sin_cos2,A) ) )).
fof(t39_sin_cos3,axiom,( ! [A] : ( v1_xreal_0(A) => k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,A) = k1_funct_1(k18_sin_cos,A) ) )).
fof(t39_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k3_xcmplx_0(k17_sin_cos(k2_xcmplx_0(A,B)),k19_sin_cos(k6_xcmplx_0(A,B))) = k2_xcmplx_0(k3_xcmplx_0(k17_sin_cos(A),k19_sin_cos(A)),k3_xcmplx_0(k17_sin_cos(B),k19_sin_cos(B))) ) ) )).
fof(t39_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k2_sin_cos2(A) != k5_numbers => k6_xcmplx_0(k1_square_1(k1_sin_cos5(A)),k1_square_1(k3_sin_cos5(A))) = 1 ) ) )).
fof(t39_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ~ ( ~ r1_xxreal_0(A,k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B))) & r1_xxreal_0(A,k2_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B))) & r1_xxreal_0(k17_sin_cos(A),k4_xcmplx_0(1)) ) ) ) )).
fof(t39_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => k3_sin_cos7(A) = k3_xcmplx_0(2,k3_sin_cos7(k3_square_1(k7_xcmplx_0(k2_xcmplx_0(A,1),2)))) ) ) )).
fof(t39_sin_cos9,axiom,( k3_sin_cos9(1) = k7_xcmplx_0(k28_sin_cos,4) & k1_funct_1(k1_sin_cos9,1) = k7_xcmplx_0(k28_sin_cos,4) )).
fof(t39_sincos10,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers))) )).
fof(t39_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(A))) => ( ( B = D & C = E ) => k3_metric_1(k14_euclid(A),D,E) = k12_euclid(k5_algstr_0(k15_euclid(A),B,C)) ) ) ) ) ) ) )).
fof(t39_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t39_sprect_1,axiom,( ! [A] : ( 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) ) )).
fof(t39_sprect_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t39_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t39_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k5_numbers,B) => ( r1_xxreal_0(A,B) | k7_xcmplx_0(1,k6_xcmplx_0(k3_square_1(A),k3_square_1(B))) = k7_xcmplx_0(k2_xcmplx_0(k3_square_1(A),k3_square_1(B)),k6_xcmplx_0(A,B)) ) ) ) ) )).
fof(t39_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) ) )).
fof(t39_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k7_card_1(C),k7_card_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(C),k7_card_1(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k7_card_1(k1_nat_1(C,1)),k7_card_1(k2_xcmplx_0(A,B))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(k1_nat_1(C,1)),k7_card_1(k2_xcmplx_0(A,B))))) ) => ( ( v2_funct_2(D,k7_card_1(A)) & v1_stirl2_1(D,C,A) & D = k2_partfun1(k7_card_1(k1_nat_1(C,1)),k7_card_1(k2_xcmplx_0(A,B)),E,C) ) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ~ ( r2_hidden(F,k2_relset_1(k7_card_1(k2_xcmplx_0(A,B)),E)) & r2_hidden(G,k2_relset_1(k7_card_1(k2_xcmplx_0(A,B)),E)) & ~ r1_xxreal_0(G,F) & r1_xxreal_0(k3_nat_1(k1_stirl2_1(k1_nat_1(C,1),k7_card_1(k2_xcmplx_0(A,B)),E,k1_seq_4(G))),k3_nat_1(k1_stirl2_1(k1_nat_1(C,1),k7_card_1(k2_xcmplx_0(A,B)),E,k1_seq_4(F)))) ) ) ) ) ) ) ) ) ) )).
fof(t39_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k16_substut1(A),k38_substut1(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t39_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t39_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_substut1(A)) => r1_tarski(k2_relset_1(k3_qc_lang1(A),k2_substut1(A,B)),k3_qc_lang1(A)) ) ) )).
fof(t39_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( v6_supinf_2(A) => ( r1_xxreal_0(k12_supinf_2(k18_supinf_2(A),B),k12_supinf_2(k18_supinf_2(A),k1_nat_1(B,1))) & r1_xxreal_0(k1_supinf_2,k12_supinf_2(k18_supinf_2(A),B)) ) ) ) ) )).
fof(t39_sysrel,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( ( ( k3_relat_1(B,A) = B & k3_relat_1(A,k6_subset_1(A,k4_relat_1(k9_xtuple_0(A)))) = k1_xboole_0 ) => r1_tarski(k1_sysrel(B),k1_sysrel(A)) ) & ( ( k3_relat_1(A,B) = B & k3_relat_1(k6_subset_1(A,k4_relat_1(k9_xtuple_0(A))),A) = k1_xboole_0 ) => r1_tarski(k1_sysrel(B),k1_sysrel(A)) ) ) ) ) )).
fof(t39_taxonom1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t39_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k6_tdlat_1(A) = k1_realset1(k2_tdlat_1(A),k5_tdlat_1(A)) ) )).
fof(t39_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))))) ) ) )).
fof(t39_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v4_tdlat_3(A) & l1_pre_topc(A) ) => k1_tdlat_1(A) = k5_tdlat_1(A) ) )).
fof(t39_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => k4_polynom1(A,C,k6_termord(A,B,C,D),k3_termord(A,B,C,D)) = k4_struct_0(C) ) ) ) ) )).
fof(t39_tex_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t39_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v4_tex_3(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(C,u1_struct_0(B)) => v3_tops_1(C,A) ) ) ) ) ) )).
fof(t39_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(t39_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t39_toler_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : ( r2_hidden(D,A) => r1_tarski(k9_relat_1(C,D),k9_relat_1(B,D)) ) => r1_relset_1(A,A,C,B) ) ) ) )).
fof(t39_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( m1_borsuk_2(G,A,D,E) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t39_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v7_topalg_6(B,A) & m2_subset_1(B,k4_partfun1(k1_numbers,k2_struct_0(A)),k1_topalg_6(A)) ) => ! [C] : ( ( v7_topalg_6(C,A) & m2_subset_1(C,k4_partfun1(k1_numbers,k2_struct_0(A)),k1_topalg_6(A)) ) => ! [D] : ( ( v7_topalg_6(D,A) & m2_subset_1(D,k4_partfun1(k1_numbers,k2_struct_0(A)),k1_topalg_6(A)) ) => ! [E] : ( ( v7_topalg_6(E,A) & m2_subset_1(E,k4_partfun1(k1_numbers,k2_struct_0(A)),k1_topalg_6(A)) ) => ! [F] : ( ( v7_topalg_6(F,A) & m2_subset_1(F,k4_partfun1(k1_numbers,k2_struct_0(A)),k1_topalg_6(A)) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t39_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( 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),k5_numbers) ) <=> ? [C] : ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(D,C) => r1_xboole_0(B,k2_tops_1(A,D)) ) ) ) ) ) ) ) )).
fof(t39_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => k2_tops_1(A,k1_struct_0(A)) = k1_xboole_0 ) )).
fof(t39_topgen_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(k9_setfam_1(A)))) => ? [C] : ( 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] : ( 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] : ( ( v2_pre_topc(D) & l1_pre_topc(D) ) => ( ( u1_struct_0(D) = A & ! [E] : ( 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)) ) ) ) ) )).
fof(t39_topgen_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t39_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t39_topgen_5,axiom,( 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))) )).
fof(t39_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v2_group_1(A) & v3_group_1(A) & l1_topgrp_1(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_connsp_2(C,A,k2_group_1(A,B)) => ? [D] : ( m1_connsp_2(D,A,B) & r1_tarski(k1_group_2(A,D),C) ) ) ) => v3_topgrp_1(A) ) ) )).
fof(t39_topreal3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(B)) & k7_partfun1(u1_struct_0(k15_euclid(2)),B,C) = A ) ) ) ) ) ) )).
fof(t39_topreal6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(2))) => ! [C] : ( v1_xreal_0(C) => ( A = B => r1_tarski(k4_card_3(k5_funct_4(k1_zfmisc_1(k1_numbers),1,2,k2_rcomp_1(k6_xcmplx_0(k17_euclid(A),k7_xcmplx_0(C,k3_square_1(2))),k2_xcmplx_0(k17_euclid(A),k7_xcmplx_0(C,k3_square_1(2)))),k2_rcomp_1(k6_xcmplx_0(k18_euclid(A),k7_xcmplx_0(C,k3_square_1(2))),k2_xcmplx_0(k18_euclid(A),k7_xcmplx_0(C,k3_square_1(2)))))),k8_metric_1(k14_euclid(2),B,C)) ) ) ) ) )).
fof(t39_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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))) = k2_xcmplx_0(k3_xcmplx_0(A,k17_euclid(C)),k3_xcmplx_0(B,k17_euclid(D))) ) ) ) ) )).
fof(t39_topreala,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(C,D) ) => ! [E] : ( ( v3_pre_topc(E,k4_topmetr(A,B)) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B)))) ) => ! [F] : ( ( 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)))) ) ) ) ) ) ) ) ) )).
fof(t39_toprealb,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k6_xcmplx_0(B,A),1) => ! [C] : ( r2_hidden(C,k3_toprealb(A,B)) => v2_funct_1(k2_partfun1(u1_struct_0(k2_topalg_2),u1_struct_0(k8_toprealb(2)),k12_toprealb,C)) ) ) ) ) )).
fof(t39_toprealc,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( ( 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))))) ) ) ) ) )).
fof(t39_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(t39_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_xboole_0(k1_tops_1(A,B),k2_tops_1(A,B)) ) ) )).
fof(t39_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) => ~ ( v1_tops_2(C,B) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ~ ( v1_tops_2(D,A) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( E = k2_struct_0(B) => C = k1_tops_2(A,E,D) ) ) ) ) ) ) ) ) )).
fof(t39_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t39_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t39_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => ! [C] : ( m1_trees_1(C,A) => ( ~ r3_xboole_0(B,C) => m4_trees_1(k2_tarski(B,C),A) ) ) ) ) )).
fof(t39_trees_2,axiom,( ! [A] : ( v7_ordinal1(A) => k2_trees_2(k8_trees_1,A) = k1_tarski(k5_finseq_2(k4_ordinal1,A,k5_numbers)) ) )).
fof(t39_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,k2_zfmisc_1(A,B)) & v1_funct_1(C) & v3_trees_2(C) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t39_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v3_trees_9(A) ) => ! [B] : ( m1_trees_1(B,k9_xtuple_0(A)) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k8_finseq_1(k4_ordinal1,B,k14_trees_3(C)),k9_xtuple_0(A)) <=> r2_hidden(k1_nat_1(C,1),k4_finseq_1(k1_trees_9(k9_xtuple_0(A),B))) ) ) ) ) )).
fof(t39_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t39_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t39_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t39_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ 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))) ) ) ) )).
fof(t39_uniroots,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( v7_ordinal1(C) => ~ ( C != k5_numbers & C != B & k1_funct_1(k4_uniroots(B,A),C) != k4_struct_0(A) ) ) ) ) )).
fof(t39_uproots,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k4_uproots(A,B,k5_numbers),B) ) ) )).
fof(t39_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_valuat_1(C,A,B) => r2_valuat_1(A,B,C,k5_cqc_lang(A)) ) ) ) )).
fof(t39_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(B,k1_relset_1(k4_ordinal1,k61_valued_1(A,C))) & ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(D,k9_xtuple_0(A)) & B = k2_xcmplx_0(D,C) ) ) ) ) ) ) )).
fof(t39_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t39_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => m1_vectsp_4(k1_vectsp_4(A,B),A,C) ) ) ) )).
fof(t39_vectsp_5,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t39_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t39_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(C)))) ) => ! [E] : ( v1_xreal_0(E) => ( 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) ) ) ) ) ) ) )).
fof(t39_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t39_waybel11,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t39_waybel12,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) & v3_waybel12(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( C != k3_yellow_0(A) & ! [D] : ( ( 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))) ) ) ) ) ) ) )).
fof(t39_waybel14,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( 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] : ( 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] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(k5_waybel11(A)))) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_yellow_1(k5_waybel11(A))))) & B = k1_yellow_0(k1_yellow_1(k5_waybel11(A)),C) & ! [D] : ( m1_subset_1(D,u1_struct_0(k1_yellow_1(k5_waybel11(A)))) => ( r2_hidden(D,C) => v6_waybel_6(D,k1_yellow_1(k5_waybel11(A))) ) ) ) ) ) ) )).
fof(t39_waybel19,axiom,( ! [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) & l1_waybel_9(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t39_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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)))) ) ) ) )).
fof(t39_waybel21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_yellow_6(C,A,B) & m1_yellow_6(C,A,B) ) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ? [E] : ( 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) ) ) ) ) ) )).
fof(t39_waybel23,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v2_waybel23(k1_waybel_3(A,B),A) ) ) )).
fof(t39_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & v2_waybel18(A) & l1_pre_topc(A) ) => v1_waybel25(A) ) )).
fof(t39_waybel27,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(B),u1_struct_0(k5_yellow_1(A,C))) & v22_waybel_0(D,B,k5_yellow_1(A,C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(k5_yellow_1(A,C))))) ) => ( v1_funct_1(k9_funct_6(D)) & v1_funct_2(k9_funct_6(D),A,u1_struct_0(k2_waybel27(B,C))) & m1_subset_1(k9_funct_6(D),k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(k2_waybel27(B,C))))) ) ) ) ) ) )).
fof(t39_waybel30,axiom,( ! [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_waybel_2(A) & l1_waybel_9(A) ) => ( v3_waybel_3(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => B = k1_yellow_0(A,a_2_4_waybel30(A,B)) ) ) ) )).
fof(t39_waybel34,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t39_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t39_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t39_waybel_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & v2_lattice3(A) & l1_orders_2(A) ) => ( ! [B] : ( ( ~ 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] : ( ( ~ 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),k1_yellow_1(k7_waybel_0(A)),A) ) ) )).
fof(t39_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v6_waybel_3(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ~ ( r1_waybel_3(k1_yellow_1(u1_pre_topc(A)),B,C) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r1_tarski(B,D) & r1_tarski(D,C) & v2_compts_1(D,A) ) ) ) ) ) ) ) )).
fof(t39_waybel_4,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t39_waybel_6,axiom,( ! [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) ) => ( v1_waybel_5(A) <=> ( v2_waybel_1(A) & v3_waybel_3(A) & v3_waybel_3(k7_lattice3(A)) ) ) ) )).
fof(t39_waybel_7,axiom,( ! [A] : ( ( 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] : ( 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) ) ) ) )).
fof(t39_waybel_9,axiom,( ! [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) & v1_compts_1(A) & l1_waybel_9(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v5_pre_topc(k4_waybel_1(A,B),A,A) ) => ! [B] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t39_weddwitt,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => k5_struct_0(k4_weddwitt(A)) = k5_struct_0(A) ) )).
fof(t39_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r3_wellord1(A,B,C) => r3_wellord1(B,A,k2_funct_1(C)) ) ) ) ) )).
fof(t39_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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)) ) ) )).
fof(t39_xboole_1,axiom,( ! [A] : ! [B] : k2_xboole_0(A,k4_xboole_0(B,A)) = k2_xboole_0(A,B) )).
fof(t39_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k9_xboolean(A,k9_xboolean(B,C)) = k5_xboolean(k4_xboolean(k3_xboolean(A),B),k4_xboolean(k3_xboolean(A),C)) ) ) ) )).
fof(t39_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k6_xcmplx_0(A,C) = k2_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(B,C)) ) ) ) )).
fof(t39_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(B,C) & r1_xxreal_0(k2_xcmplx_0(A,C),B) ) ) ) ) )).
fof(t39_xtuple_0,axiom,( ! [A] : ! [B] : k13_xtuple_0(k2_xboole_0(A,B)) = k2_xboole_0(k13_xtuple_0(A),k13_xtuple_0(B)) )).
fof(t39_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) )).
fof(t39_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(D,B) => ( r1_xxreal_0(C,A) | r1_tarski(k1_xxreal_1(C,D),k3_xxreal_1(A,B)) ) ) ) ) ) ) )).
fof(t39_xxreal_2,axiom,( k1_xxreal_2(k1_xboole_0) = k2_xxreal_0 )).
fof(t39_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( r1_xxreal_0(k5_numbers,B) => r1_xxreal_0(A,k1_xxreal_3(A,B)) ) ) ) )).
fof(t39_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(t39_yellow12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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)))) ) ) ) )).
fof(t39_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( 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) ) ) ) ) ) ) )).
fof(t39_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & v4_yellow18(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( m1_subset_1(D,k1_altcat_1(A,B,C)) & v2_altcat_3(D,A,B,C) & ~ v2_funct_1(D) ) ) ) ) ) )).
fof(t39_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ( r2_yellow20(A,B,C,A,B) => v21_functor0(C,A,B) ) ) ) ) )).
fof(t39_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t39_yellow_2,axiom,( ! [A] : ( ( v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ! [C] : ( 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))) ) ) ) ) )).
fof(t39_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t39_yellow_4,axiom,( ! [A] : ( ( v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => r1_yellow_4(A,k4_yellow_4(A,B,C),B) ) ) ) )).
fof(t39_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t39_yellow_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)))) ) ) ) ) ) )).
fof(t39_yellow_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ v2_struct_0(D) & v4_orders_2(D) & v7_waybel_0(D) & l1_waybel_0(D,A) ) => ( ! [E] : ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t39_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( v8_zf_lang(B) => ( ~ ( A = k21_zf_lang(B) & ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => k10_zf_lang(A,C) != B ) ) & ( ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & k10_zf_lang(A,C) = B ) => A = k21_zf_lang(B) ) & ~ ( A = k22_zf_lang(B) & ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => k10_zf_lang(C,A) != B ) ) & ( ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & k10_zf_lang(C,A) = B ) => A = k22_zf_lang(B) ) ) ) ) ) )).
fof(t39_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r2_zf_lang(A,B) => r1_xxreal_0(k3_finseq_1(A),k3_finseq_1(B)) ) ) ) )).
fof(t39_zfmisc_1,axiom,( ! [A] : ! [B] : ( r2_hidden(A,B) => k2_xboole_0(k1_tarski(A),B) = B ) )).
fof(t39_zfrefle1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ~ ( r2_hidden(k4_ordinal1,A) & ! [B] : ( ( v3_ordinal1(B) & m1_subset_1(B,A) ) => ! [C] : ( ~ v1_xboole_0(C) => ~ ( r2_ordinal2(B,k4_ordinal1) & C = k4_classes1(B) & r2_zfrefle1(C,A) ) ) ) ) ) )).
fof(t39_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_zmodul01(D,A) => ( ( r1_struct_0(D,B) & r1_struct_0(D,C) ) => r1_struct_0(D,k5_algstr_0(A,B,C)) ) ) ) ) ) )).
fof(t39_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_zmodul02(C,A) => ! [D] : ( m1_zmodul02(D,A) => k3_funct_2(u1_struct_0(A),k4_numbers,k25_zmodul02(A,C,D),B) = k6_xcmplx_0(k3_funct_2(u1_struct_0(A),k4_numbers,C,B),k3_funct_2(u1_struct_0(A),k4_numbers,D,B)) ) ) ) ) )).
fof(t3_abcmiz_0,axiom,( ! [A] : ( l1_abcmiz_0(A) => ! [B] : ( 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] : ( m1_subset_1(C,u1_abcmiz_0(A)) => ! [D] : ( m1_subset_1(D,u1_abcmiz_0(B)) => ( C = D => k1_abcmiz_0(A,C) = k1_abcmiz_0(B,D) ) ) ) ) ) ) )).
fof(t3_abcmiz_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( A = k4_tarski(B,C) => B = C ) ) )).
fof(t3_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( 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] : ( m1_subset_1(C,k2_abcmiz_1) => B != k35_abcmiz_1(C,A) ) ) ) ) )).
fof(t3_abian,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m1_subset_1(C,A) => k3_funct_2(A,A,k1_abian(A,B,k5_numbers),C) = C ) ) ) )).
fof(t3_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( k9_complex1(A) = k4_xcmplx_0(A) & A != k5_numbers & r1_xxreal_0(k5_numbers,A) ) ) )).
fof(t3_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t3_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v7_aff_2(A) => v8_aff_2(A) ) ) )).
fof(t3_aff_3,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v4_aff_2(A) => v1_aff_3(A) ) ) )).
fof(t3_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t3_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => r1_tarski(k2_finseq_1(A),k1_nat_1(A,1)) ) )).
fof(t3_afinsq_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ~ ( r2_hidden(A,k10_xtuple_0(B)) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r2_hidden(C,k1_relset_1(k4_ordinal1,B)) & k1_funct_1(B,C) = A ) ) ) ) )).
fof(t3_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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 ) ) ) ) )).
fof(t3_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,E) => r2_analoaf(A,D,E,B,C) ) ) ) ) ) ) )).
fof(t3_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect01(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,E) => r2_analoaf(A,B,C,E,D) ) ) ) ) ) ) )).
fof(t3_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( 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 ) ) )).
fof(t3_algseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ~ ( k1_algseq_1(B,C) = k1_nat_1(A,1) & k1_funct_1(C,A) = k4_struct_0(B) ) ) ) ) )).
fof(t3_algspec1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t3_algstr_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ( ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_algstr_0(A,B,k4_struct_0(A)) = B ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & k1_algstr_0(A,B,C) = k4_struct_0(A) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & k1_algstr_0(A,C,B) = k4_struct_0(A) ) ) ) ) )).
fof(t3_algstr_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_algstr_0(A) & v3_algstr_1(A) & v2_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_algstr_2(A,k1_algstr_2(A,B)) = B ) ) )).
fof(t3_algstr_3,axiom,( 1 = k5_struct_0(k3_algstr_3) )).
fof(t3_algstr_4,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) & v1_funct_1(B) ) => ! [C] : ( ( 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] : ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) )).
fof(t3_altcat_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k2_zfmisc_1(A,B)) & v1_funct_1(D) & v1_partfun1(D,k2_zfmisc_1(A,B)) ) => ( ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,B) => k1_binop_1(C,E,F) = k1_binop_1(D,E,F) ) ) => r8_pboole(k2_zfmisc_1(A,B),D,C) ) ) ) ) ) )).
fof(t3_altcat_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t3_altcat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( 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 ) ) ) ) ) )).
fof(t3_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t3_altcat_5,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,u1_struct_0(k7_altcat_1(k1_tarski(k1_xboole_0)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(k7_altcat_1(k1_tarski(k1_xboole_0)))))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_altcat_1(k1_tarski(k1_xboole_0)))) => m1_altcat_5(k7_funcop_1(A,k1_xboole_0),k7_altcat_1(k1_tarski(k1_xboole_0)),C,A,B) ) ) )).
fof(t3_ami_2,axiom,( ! [A] : ( m2_subset_1(A,k1_ami_2,k2_ami_2) => k1_funct_1(k3_relat_1(k3_ami_2,k4_ami_2),A) = k4_numbers ) )).
fof(t3_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(C,u1_struct_0(k1_ami_3)) ) => ( k1_funct_1(k2_extpro_1(k7_card_1(2),k1_ami_3,k3_ami_3(A,B),C),k4_struct_0(k1_ami_3)) = k4_card_1(k5_memstr_0(k7_card_1(2),k1_ami_3,C)) & k1_funct_1(k2_extpro_1(k7_card_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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_ami_3)) ) => ( D != A => k1_funct_1(k2_extpro_1(k7_card_1(2),k1_ami_3,k3_ami_3(A,B),C),D) = k1_funct_1(C,D) ) ) ) ) ) ) )).
fof(t3_ami_4,axiom,( ! [A] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_ami_3)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ( r1_tarski(k1_ami_4,B) => ! [C] : ( v7_ordinal1(C) => ( k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,C)) = 1 => ( k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,k1_nat_1(C,1))) = 2 & k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,k1_nat_1(C,1)),k10_ami_3(k5_numbers)) = k4_int_1(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,C),k10_ami_3(k5_numbers)),k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,C),k10_ami_3(1))) & k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,k1_nat_1(C,1)),k10_ami_3(1)) = k5_int_1(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,C),k10_ami_3(k5_numbers)),k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,C),k10_ami_3(1))) & k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,k1_nat_1(C,1)),k10_ami_3(2)) = k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,C),k10_ami_3(2)) ) ) ) ) ) ) )).
fof(t3_ami_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => A != B ) ) )).
fof(t3_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ( v3_funct_2(C,k4_ordinal1,k4_ordinal1) => ( ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(D,E) <=> r1_ami_wstd(A,B,k3_funct_2(k4_ordinal1,k4_ordinal1,C,D),k3_funct_2(k4_ordinal1,k4_ordinal1,C,E)) ) ) ) <=> ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(k3_funct_2(k4_ordinal1,k4_ordinal1,C,k1_nat_1(D,1)),k3_amistd_1(A,B,k3_funct_2(k4_ordinal1,k4_ordinal1,C,D))) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(k3_funct_2(k4_ordinal1,k4_ordinal1,C,E),k3_amistd_1(A,B,k3_funct_2(k4_ordinal1,k4_ordinal1,C,D))) => r1_xxreal_0(D,E) ) ) ) ) ) ) ) ) ) )).
fof(t3_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_compos_1(B)) => r1_tarski(k3_amistd_4(A,B,C),k2_amistd_4(A,B,C)) ) ) ) )).
fof(t3_amistd_5,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) & ~ v2_compos_1(C,B) ) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t3_analmetr,axiom,( ? [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) & ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r1_analmetr(A,B,C) ) ) ) )).
fof(t3_analoaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => 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)) ) ) ) ) )).
fof(t3_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t3_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r1_anproj_1(A,B,k4_struct_0(A)) <=> B = k4_struct_0(A) ) ) ) )).
fof(t3_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ? [F] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & 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] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( 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 = k5_numbers & F = k5_numbers & G = k5_numbers ) ) ) ) ) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ? [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t3_aofa_000,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,k5_trees_3(A)) => ! [C] : ! [D] : ~ ( r2_hidden(D,k2_relset_1(k5_trees_3(A),B)) & D = k4_trees_4(C,B) ) ) ) )).
fof(t3_aofa_a00,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( r2_pboole(A,C,D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,B,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => r2_pboole(B,k3_msafree4(A,B,E,C),k3_msafree4(A,B,E,D)) ) ) ) ) ) )).
fof(t3_aofa_a01,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ! [D] : ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(D,k1_funct_1(k2_aofa_a00(A,E,B),C)) <=> ( C = E & D = B ) ) ) ) )).
fof(t3_aofa_i00,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t3_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(1,A) = A ) )).
fof(t3_armstrng,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,A) => ? [C] : ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(A)) & B = k1_setfam_1(C) & ! [D] : ( r2_hidden(D,C) => r1_armstrng(D,A) ) ) ) ) )).
fof(t3_arrow,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,k2_arrow(A)) => r1_arrow(C,B,B) ) ) ) )).
fof(t3_arytm_0,axiom,( ! [A] : ~ ( r2_hidden(k4_tarski(k11_arytm_3,A),k1_numbers) & A = k11_arytm_3 ) )).
fof(t3_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( ( r1_arytm_2(A,B) & r1_arytm_2(B,C) ) => r1_arytm_2(A,C) ) ) ) ) )).
fof(t3_arytm_2,axiom,( ! [A] : ~ r2_hidden(k4_tarski(k11_arytm_3,A),k2_arytm_2) )).
fof(t3_arytm_3,axiom,( ! [A] : ( v3_ordinal1(A) => ( r1_arytm_3(k1_xboole_0,A) => A = 1 ) ) )).
fof(t3_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(A) => r1_xxreal_0(k5_numbers,k1_seq_2(A)) ) ) )).
fof(t3_asympt_1,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ~ ( ~ r1_xxreal_0(B,A) & r2_hidden(k1_asympt_1(B,1,k5_numbers),k6_asympt_0(k1_asympt_1(A,1,k5_numbers))) ) ) ) )).
fof(t3_autalg_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t3_autgroup,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t3_axioms,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( ( r2_hidden(k5_numbers,A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => r2_hidden(k2_xcmplx_0(B,1),A) ) ) ) => r1_tarski(k4_ordinal1,A) ) ) )).
fof(t3_bagorder,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ( k2_wsierp_1(A) = k5_numbers <=> A = k5_finseq_2(k4_ordinal1,k3_finseq_1(A),k5_numbers) ) ) )).
fof(t3_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t3_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t3_bcialg_3,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t3_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( 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) ) ) ) )).
fof(t3_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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,k1_nat_1(A,1)),k1_bcialg_2(B,C,D,A)) ) ) ) ) ) )).
fof(t3_bcialg_6,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => k3_bcialg_6(A,k5_numbers,B) = k4_struct_0(A) ) ) )).
fof(t3_bciideal,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t3_bhsp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k2_bhsp_1(B,C,k1_rlvect_1(B,D,A)) = k3_xcmplx_0(A,k2_bhsp_1(B,C,D)) ) ) ) ) )).
fof(t3_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_bhsp_2(B,A) & v1_bhsp_2(C,A) ) => v1_bhsp_2(k2_normsp_1(A,B,C),A) ) ) ) ) )).
fof(t3_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r1_bhsp_3(A,B,C) <=> ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & 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)))) ) ) ) ) ) ) ) ) )).
fof(t3_bhsp_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(B),k1_bhsp_4(B,k5_normsp_1(B,C,A)),k5_normsp_1(B,k1_bhsp_4(B,C),A)) ) ) ) )).
fof(t3_bhsp_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => m2_bhsp_5(k1_xboole_0,A) ) )).
fof(t3_bhsp_6,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_bhsp_6(B,A) => v3_bhsp_6(B,A) ) ) ) )).
fof(t3_bhsp_7,axiom,( ! [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_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] : ( ( v1_finset_1(B) & m1_bhsp_5(B,A) ) => ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( 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),k9_binop_2,B,C) ) ) ) ) ) ) )).
fof(t3_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t3_binari_2,axiom,( ! [A] : ( ( 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) = k4_xcmplx_0(2) ) ) )).
fof(t3_binari_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( k3_finseq_5(A) = k3_finseq_5(B) => A = B ) ) ) )).
fof(t3_binari_4,axiom,( ! [A] : ( v7_ordinal1(A) => k7_euclid(A,k5_euclid(A),k5_euclid(A)) = k5_euclid(A) ) )).
fof(t3_binarith,axiom,( ! [A] : ( v1_xboolean(A) => k5_xboolean(A,k7_margrel1) = A ) )).
fof(t3_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_algstr_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k4_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)) = B ) ) )).
fof(t3_binop_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ( r3_binop_1(A,C,B) <=> ! [D] : ( m1_subset_1(D,A) => ( k3_binop_1(A,B,C,D) = D & k3_binop_1(A,B,D,C) = D ) ) ) ) ) )).
fof(t3_binop_2,axiom,( k4_binop_1(k3_numbers,k15_binop_2) = k5_numbers )).
fof(t3_bintree1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => ( k1_trees_2(A,B) = k1_xboole_0 <=> r2_hidden(B,k3_trees_1(A)) ) ) ) )).
fof(t3_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ( A = k3_finseq_2(k7_domain_1(k4_ordinal1,k5_numbers,1)) => v1_bintree1(A) ) ) )).
fof(t3_boole,axiom,( ! [A] : k4_xboole_0(A,k1_xboole_0) = A )).
fof(t3_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r3_lattices(A,B,D) => r3_lattices(A,k1_boolealg(A,B,C),D) ) ) ) ) ) )).
fof(t3_boolmark,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( r1_xboole_0(A,B) => k7_relat_1(k1_funct_4(C,k7_funcop_1(A,D)),B) = k7_relat_1(C,B) ) ) )).
fof(t3_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( 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] : ( m1_connsp_2(E,B,C) => m2_connsp_2(k8_relset_1(u1_struct_0(A),u1_struct_0(B),D,E),A,k8_relset_1(u1_struct_0(A),u1_struct_0(B),D,k6_domain_1(u1_struct_0(B),C))) ) ) ) ) ) )).
fof(t3_borsuk_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( 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,k5_numbers) = B & k1_funct_1(C,1) = B ) ) ) )).
fof(t3_borsuk_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t3_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ~ ( r1_topreal1(k15_euclid(A),C,D,B) & v1_xboole_0(k7_subset_1(u1_struct_0(k15_euclid(A)),B,k6_domain_1(u1_struct_0(k15_euclid(A)),C))) ) ) ) ) ) )).
fof(t3_borsuk_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( r5_zfmisc_1(A,B,C,D,E,F,G) => k5_card_1(k5_enumset1(A,B,C,D,E,F,G)) = 7 ) )).
fof(t3_borsuk_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_topmetr)) => ( r1_xxreal_0(A,k7_xcmplx_0(1,2)) => m1_subset_1(k3_xcmplx_0(2,A),u1_struct_0(k5_topmetr)) ) ) )).
fof(t3_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(k3_int_1(B),k3_int_1(A)) => k3_int_1(k6_xcmplx_0(A,B)) = k2_xcmplx_0(k6_xcmplx_0(k3_int_1(A),k3_int_1(B)),1) ) ) ) )).
fof(t3_brouwer,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => u1_struct_0(k2_brouwer(A,C,B)) = k2_topreal9(A,C,B) ) ) ) )).
fof(t3_bspace,axiom,( k2_struct_0(k2_bspace) = k7_domain_1(k4_ordinal1,k5_numbers,1) )).
fof(t3_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(t3_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => r1_tarski(k15_bvfunc_1(A,B,k2_partit1(A,C,D)),k15_bvfunc_1(A,B,C)) ) ) ) ) )).
fof(t3_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t3_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t3_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t3_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t3_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ( r2_hidden(C,B) => r1_setfam_1(k2_bvfunc_2(A,B),C) ) ) ) ) )).
fof(t3_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t3_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t3_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t3_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t3_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t3_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) )).
fof(t3_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t3_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(F))) => ! [H] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t3_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_c0sp2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_c0sp2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_c0sp2(A))) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(H,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k1_numbers,G,H) = k3_real_1(k3_funct_2(u1_struct_0(A),k1_numbers,E,H),k3_funct_2(u1_struct_0(A),k1_numbers,F,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t3_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ( ~ r1_xxreal_0(k3_finseq_1(B),k5_numbers) => ( r2_relset_1(k4_ordinal1,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))) ) ) ) ) )).
fof(t3_calcul_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( B = k5_numbers | r2_hidden(k2_xcmplx_0(B,A),k2_calcul_2(A,B)) ) ) ) )).
fof(t3_cantor_1,axiom,( ! [A] : ( l1_pre_topc(A) => v1_tops_2(u1_pre_topc(A),A) ) )).
fof(t3_card_1,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ( r2_hidden(A,B) <=> ~ r1_ordinal1(B,A) ) ) ) )).
fof(t3_card_2,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(C,k1_funct_2(A,B)) => ( r2_wellord2(C,A) & k1_card_1(C) = k1_card_1(A) ) ) )).
fof(t3_card_3,axiom,( k2_card_3(k1_xboole_0) = k1_xboole_0 )).
fof(t3_card_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ( ~ ( ~ ( B = k5_numbers & A != k5_numbers ) & k1_newton(B,A) = k5_numbers ) & ~ ( k1_newton(B,A) != k5_numbers & B = k5_numbers & A != k5_numbers ) ) ) ) )).
fof(t3_card_5,axiom,( ! [A] : ( v3_ordinal1(A) => ~ v1_finset_1(k3_card_1(A)) ) )).
fof(t3_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t3_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ! [C] : ( v3_ordinal1(C) => ~ ( r2_hidden(C,B) & ! [D] : ( 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)) ) ) ) ) ) )).
fof(t3_cardfin2,axiom,( ! [A] : ( v1_int_1(A) => k1_cardfin2(A) = A ) )).
fof(t3_cat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => m1_cat_1(B,A,k3_graph_1(A,B),k4_graph_1(A,B)) ) ) )).
fof(t3_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m3_cat_2(B,A) => r1_tarski(u4_struct_0(B),u4_struct_0(A)) ) ) )).
fof(t3_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ( A != B => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( 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 ) ) ) ) ) )).
fof(t3_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k5_cat_4(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_cat_4(A,B))) => C = D ) ) )).
fof(t3_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t3_catalan1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( ~ r1_xxreal_0(A,1) & r1_xxreal_0(k7_nat_d(k3_xcmplx_0(2,A),1),A) ) ) )).
fof(t3_catalan2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ( v1_catalan2(A) => k1_recdef_1(A,k5_numbers) = k5_numbers ) ) )).
fof(t3_catalg_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,B) & v1_funct_1(D) & v1_partfun1(D,B) ) => ( ! [E] : ( 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) ) ) ) ) )).
fof(t3_cayldick,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( k6_afinsq_1(A,B) = k6_afinsq_1(C,D) => ( A = C & B = D ) ) )).
fof(t3_cayley,axiom,( ! [A] : ( v7_ordinal1(A) => k1_cayley(k2_finseq_1(A)) = k3_matrix_2(A) ) )).
fof(t3_cc0sp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_cc0sp1(B,A) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) )).
fof(t3_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t3_cfcont_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_ordinal1) & v5_valued_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k9_comseq_3(C,k25_valued_1(k4_ordinal1,k2_numbers,B,A)),k25_valued_1(k4_ordinal1,k2_numbers,k9_comseq_3(C,B),A)) ) ) ) )).
fof(t3_cfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k3_comseq_2(k1_cfdiff_1(A)) = k5_numbers ) ) )).
fof(t3_cfdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ( v2_comseq_2(A) & k1_seq_2(A) = k5_numbers ) => ( v2_comseq_2(k56_valued_1(k4_ordinal1,k1_numbers,A)) & k1_seq_2(k56_valued_1(k4_ordinal1,k1_numbers,A)) = k5_numbers ) ) & ( ( v2_comseq_2(k56_valued_1(k4_ordinal1,k1_numbers,A)) & k1_seq_2(k56_valued_1(k4_ordinal1,k1_numbers,A)) = k5_numbers ) => ( v2_comseq_2(A) & k1_seq_2(A) = k5_numbers ) ) ) ) )).
fof(t3_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k4_cfuncdom(A) != k5_cfuncdom(A) ) )).
fof(t3_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( 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] : ( 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) = k3_xcmplx_0(k7_partfun1(k2_numbers,B,D),k7_partfun1(k2_numbers,C,D)) ) ) ) ) ) ) )).
fof(t3_cgames_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r1_ordinal1(A,B) => r1_tarski(k2_cgames_1(A),k2_cgames_1(B)) ) ) ) )).
fof(t3_chain_1,axiom,( ! [A] : ! [B] : ( v1_zfmisc_1(k2_tarski(A,B)) <=> A = B ) )).
fof(t3_chord,axiom,( ! [A] : ( ( v1_int_1(A) & ~ v1_abian(A) ) => ! [B] : ( ( v1_int_1(B) & ~ v1_abian(B) ) => ( ~ r1_xxreal_0(B,A) => r1_xxreal_0(A,k6_xcmplx_0(B,2)) ) ) ) )).
fof(t3_circcmb2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ( v1_circuit2(C,A,B) => ! [D] : ( v7_ordinal1(D) => k5_facirc_1(A,B,C,D) = C ) ) ) ) ) )).
fof(t3_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( v1_circuit2(k5_facirc_1(A,B,C,D),A,B) => r1_xxreal_0(k2_circcmb3(A,B,C),D) ) ) ) ) ) )).
fof(t3_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t3_circled1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( 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) ) ) ) ) ) ) )).
fof(t3_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( ~ 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)) ) ) ) ) )).
fof(t3_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => k1_relset_1(u1_struct_0(A),C) = u1_struct_0(A) ) ) ) )).
fof(t3_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msafree2(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t3_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) ) => ! [C] : ( ( 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)) & r1_ckspace1(A,C,1,B) ) => r1_pdiff_9(A,B,C) ) ) ) ) )).
fof(t3_classes1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r2_hidden(B,k1_classes1(A)) & r1_tarski(C,B) ) => r2_hidden(C,k1_classes1(A)) ) )).
fof(t3_classes2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v2_classes1(C) & r2_hidden(A,C) & r2_hidden(B,C) ) => r2_hidden(k4_tarski(A,B),C) ) )).
fof(t3_clopban1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m2_funct_2(C,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t3_clopban2,axiom,( ! [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) & 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)))) ) ) )).
fof(t3_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k2_normsp_0(A,k5_algstr_0(A,B,C)) = k2_normsp_0(A,k3_rlvect_1(A,k5_algstr_0(A,B,D),k5_algstr_0(A,D,C))) ) ) ) ) )).
fof(t3_clopban4,axiom,( ! [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) & 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v9_clvect_1(B,A) & v9_clvect_1(C,A) ) => v9_clvect_1(k4_clopban3(A,B,C),A) ) ) ) ) )).
fof(t3_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v2_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( m2_pboole(E,A,B,D) => ( r1_pboole(A,C,B) => r1_pboole(A,k16_pralg_1(A,E,C),D) ) ) ) ) ) )).
fof(t3_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) => ! [D] : ( 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))) ) ) ) )).
fof(t3_closure3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v3_msualg_1(B,A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t3_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k4_algstr_0(A,B) = k1_clvect_1(A,B,k4_xcmplx_0(k6_complex1)) ) ) )).
fof(t3_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_clvect_2(B,A) & v1_clvect_2(C,A) ) => v1_clvect_2(k16_csspace(A,B,C),A) ) ) ) ) )).
fof(t3_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v1_xcmplx_0(C) => k1_bhsp_4(A,k6_clvect_1(A,B,C)) = k6_clvect_1(A,k1_bhsp_4(A,B),C) ) ) ) )).
fof(t3_coh_sp,axiom,( ~ v1_xboole_0(k1_tarski(k1_xboole_0)) & v1_classes1(k1_tarski(k1_xboole_0)) & v1_coh_sp(k1_tarski(k1_xboole_0)) )).
fof(t3_cohsp_1,axiom,( ! [A] : ( ( v1_finset_1(A) & v1_classes1(A) ) => k2_cohsp_1(A) = A ) )).
fof(t3_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t3_combgras,axiom,( ! [A] : ! [B] : ( r1_ordinal1(k1_card_1(A),k1_card_1(B)) <=> ? [C] : ( 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) ) ) )).
fof(t3_commacat,axiom,( ! [A] : ! [B] : ( u1_struct_0(k3_cat_1(B,A)) = k1_tarski(B) & u4_struct_0(k3_cat_1(B,A)) = k1_tarski(A) ) )).
fof(t3_compact1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r1_tarski(k2_struct_0(A),k2_struct_0(B)) => ( ! [C] : ( 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) ) ) ) ) )).
fof(t3_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & v1_compl_sp(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ( v3_prob_1(B) => v7_valued_0(k1_compl_sp(A,B)) ) ) ) )).
fof(t3_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( ( k3_complex1(A) = k3_complex1(B) & k4_complex1(A) = k4_complex1(B) ) => A = B ) ) ) )).
fof(t3_complex2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k17_sin_cos(k6_xcmplx_0(A,B)) = k6_xcmplx_0(k3_xcmplx_0(k17_sin_cos(A),k19_sin_cos(B)),k3_xcmplx_0(k19_sin_cos(A),k17_sin_cos(B))) & k19_sin_cos(k6_xcmplx_0(A,B)) = k2_xcmplx_0(k3_xcmplx_0(k19_sin_cos(A),k19_sin_cos(B)),k3_xcmplx_0(k17_sin_cos(A),k17_sin_cos(B))) ) ) ) )).
fof(t3_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( ( A = C & B = D ) => k5_algstr_0(k1_complfld,A,B) = k6_xcmplx_0(C,D) ) ) ) ) ) )).
fof(t3_complsp1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complsp1(A))) => m2_finseq_2(B,k2_numbers,k12_seq_4(A)) ) ) )).
fof(t3_complsp2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( m2_finseq_1(B,k2_numbers) => k3_finseq_1(k10_seq_4(B,A)) = k3_finseq_1(B) ) ) )).
fof(t3_compos_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_compos_0(B) & v2_compos_0(B) & v3_compos_0(B) ) => ! [C] : ( m1_subset_1(C,B) => ( v4_compos_0(C,B) => k5_compos_0(B,C,A) = C ) ) ) ) )).
fof(t3_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => k5_card_1(k4_compos_1(A)) = 1 ) )).
fof(t3_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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)) ) ) ) ) )).
fof(t3_comptrig,axiom,( ! [A] : ( v1_xcmplx_0(A) => k1_square_1(k9_complex1(A)) = k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A))) ) )).
fof(t3_compts_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)) ) ) ) ) ) ) )).
fof(t3_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => k2_finseq_3(A,k1_funct_7(C,A,B)) = k2_finseq_3(A,C) ) ) )).
fof(t3_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v9_ordinal1(A) <=> ! [B] : ~ ( r2_hidden(B,k4_ordinal1) & k1_funct_1(A,B) = k5_complex1 ) ) ) )).
fof(t3_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v9_ordinal1(A) => v9_ordinal1(k2_comseq_2(k4_ordinal1,A)) ) ) )).
fof(t3_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => k9_nat_1(k1_numbers,A,B) = k5_numbers ) => v2_series_1(A) ) ) )).
fof(t3_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t3_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t3_conmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( v4_analmetr(B,A) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(C,D) & r10_analmetr(A,B,D) ) ) ) ) ) ) )).
fof(t3_conmetr1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v5_conmetr1(A) => v1_conmetr1(A) ) ) )).
fof(t3_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t3_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v3_pre_topc(B,A) & r2_hidden(C,B) ) => m1_connsp_2(B,A,C) ) ) ) ) )).
fof(t3_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => k1_connsp_3(A,k1_struct_0(A)) = u1_struct_0(A) ) )).
fof(t3_convex1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t3_convex2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ( B = a_3_1_convex2(A,C,D) => v1_convex1(B,A) ) ) ) ) ) )).
fof(t3_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m2_convex4(D,A,B) => ( r1_tarski(B,C) => m2_convex4(D,A,C) ) ) ) ) ) )).
fof(t3_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k5_qc_lang1(A),k2_qc_lang1(A)))) ) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( m2_subset_1(E,k2_qc_lang1(A),k5_qc_lang1(A)) => ! [F] : ( m2_finseq_1(F,k2_qc_lang1(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t3_cqc_sim1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : 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))) ) )).
fof(t3_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( 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,C),C),C),k1_cqc_the1(A,B)) ) ) ) )).
fof(t3_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t3_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t3_csspace,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( 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(k4_ordinal1,k2_numbers,k2_csspace(B),A) ) ) )).
fof(t3_csspace2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( ( k3_xcmplx_0(k3_complex1(A),k4_complex1(B)) = k3_xcmplx_0(k3_complex1(B),k4_complex1(A)) & r1_xxreal_0(k5_numbers,k2_xcmplx_0(k3_xcmplx_0(k3_complex1(A),k3_complex1(B)),k3_xcmplx_0(k4_complex1(A),k4_complex1(B)))) ) => k9_complex1(k2_xcmplx_0(A,B)) = k2_xcmplx_0(k9_complex1(A),k9_complex1(B)) ) ) ) )).
fof(t3_csspace3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => k1_funct_1(A,B) = k5_complex1 ) => ( v2_comseq_3(A) & k4_series_1(k55_valued_1(k4_ordinal1,k2_numbers,A)) = k5_numbers ) ) ) )).
fof(t3_csspace4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_csspace4)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_csspace4)) => ! [C] : ( v1_xcmplx_0(C) => ( ( k2_normsp_0(k3_csspace4,A) = k5_numbers => A = k4_struct_0(k3_csspace4) ) & ( A = k4_struct_0(k3_csspace4) => k2_normsp_0(k3_csspace4,A) = k5_numbers ) & r1_xxreal_0(k5_numbers,k2_normsp_0(k3_csspace4,A)) & r1_xxreal_0(k2_normsp_0(k3_csspace4,k1_algstr_0(k3_csspace4,A,B)),k2_xcmplx_0(k2_normsp_0(k3_csspace4,A),k2_normsp_0(k3_csspace4,B))) & k2_normsp_0(k3_csspace4,k1_clvect_1(k3_csspace4,A,C)) = k3_xcmplx_0(k9_complex1(C),k2_normsp_0(k3_csspace4,A)) ) ) ) ) )).
fof(t3_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_decomp_1(B,A) <=> B = k1_decomp_1(A,B) ) ) ) )).
fof(t3_descip_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m2_finseq_2(C,A,k4_finseq_2(k2_nat_1(2,B),A)) => k9_binarith(B,B,A,k4_descip_1(A,B,C),k5_descip_1(A,B,C)) = C ) ) ) )).
fof(t3_dickson,axiom,( ! [A] : ( ~ v1_finset_1(A) => ? [B] : ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) & v2_funct_1(B) ) ) )).
fof(t3_diff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k3_diff_1(C,A),B) = k6_xcmplx_0(k1_funct_1(C,k2_xcmplx_0(B,A)),k1_funct_1(C,B)) ) ) ) )).
fof(t3_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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,k6_xcmplx_0(B,A),B) = k7_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(C,A),1),B),A) ) ) ) )).
fof(t3_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k5_diff_1(C,A),B) = k6_xcmplx_0(k1_funct_1(k4_diff_1(C,k7_xcmplx_0(A,2)),B),k1_funct_1(k4_diff_1(C,k4_xcmplx_0(k7_xcmplx_0(A,2))),B)) ) ) ) )).
fof(t3_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k3_power(k4_power,A) = k1_funct_1(k3_taylor_1,A) ) ) )).
fof(t3_dilworth,axiom,( ! [A] : ! [B] : ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,B) => ( r1_xboole_0(A,B) => m1_eqrel_1(k2_xboole_0(C,D),k2_xboole_0(A,B)) ) ) ) )).
fof(t3_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r2_analoaf(A,B,C,D,E) & r2_analoaf(A,D,E,F,G) ) => ( D = E | r2_analoaf(A,B,C,F,G) ) ) ) ) ) ) ) ) ) )).
fof(t3_dirort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t3_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : k3_dist_1(A,B,C) = k1_rpr_1(k9_xtuple_0(B),k1_dist_1(A,B,C)) ) ) )).
fof(t3_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,A) => ( r2_hidden(B,k2_relset_1(A,k19_finseq_1(A))) & ? [C] : ( v7_ordinal1(C) & r2_hidden(C,k4_finseq_1(k19_finseq_1(A))) & B = k1_funct_1(k19_finseq_1(A),C) & r2_hidden(C,k2_finseq_1(k5_card_1(A))) ) ) ) ) )).
fof(t3_domain_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ( r2_hidden(A,k3_zfmisc_1(B,C,D)) <=> ? [E] : ( m1_subset_1(E,B) & ? [F] : ( m1_subset_1(F,C) & ? [G] : ( m1_subset_1(G,D) & A = k3_xtuple_0(E,F,G) ) ) ) ) ) ) ) )).
fof(t3_dtconstr,axiom,( k15_trees_3(k1_xboole_0) = k1_xboole_0 )).
fof(t3_dynkin,axiom,( ! [A] : ! [B] : k3_card_3(k12_funct_7(A,B,k1_xboole_0)) = k2_xboole_0(A,B) )).
fof(t3_e_siec,axiom,( ! [A] : ( 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))) ) )).
fof(t3_ec_pf_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [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] : ( r1_struct_0(A,C) => r1_struct_0(B,C) ) ) ) ) )).
fof(t3_ec_pf_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k8_group_1(A,B,k11_algstr_0(A,C)) = k8_group_1(A,D,k11_algstr_0(A,E)) => ( C = k4_struct_0(A) | E = k4_struct_0(A) | k8_group_1(A,B,E) = k8_group_1(A,C,D) ) ) ) ) ) ) ) )).
fof(t3_endalg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m2_funct_2(B,u1_struct_0(A),u1_struct_0(A),k1_endalg(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t3_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => r1_tarski(k1_ens_1(B),k1_ens_1(A)) ) ) )).
fof(t3_entropy1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ( r1_xxreal_0(k3_power(k4_power,A),k6_xcmplx_0(A,1)) & ( A = 1 => k3_power(k4_power,A) = k6_xcmplx_0(A,1) ) & ( k3_power(k4_power,A) = k6_xcmplx_0(A,1) => A = 1 ) & ~ ( A != 1 & r1_xxreal_0(k6_xcmplx_0(A,1),k3_power(k4_power,A)) ) & ~ ( ~ r1_xxreal_0(k6_xcmplx_0(A,1),k3_power(k4_power,A)) & A = 1 ) ) ) ) )).
fof(t3_enumset1,axiom,( ! [A] : ! [B] : ! [C] : k1_enumset1(A,B,C) = k2_xboole_0(k2_tarski(A,B),k1_tarski(C)) )).
fof(t3_eqrel_1,axiom,( ! [A] : ( 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))) ) )).
fof(t3_equation,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ! [D] : ! [E] : ( ( 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(k9_funct_6(E),D)) = A & r1_tarski(k10_xtuple_0(k1_funct_1(k9_funct_6(E),D)),C) ) ) ) ) ) )).
fof(t3_euclid,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v3_valued_0(B) ) => k3_euclid(k10_rvsum_1(B,A)) = k10_rvsum_1(k3_euclid(B),k9_complex1(A)) ) ) )).
fof(t3_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v3_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v3_valued_0(C) ) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ( ( D = B & E = C ) => k22_rvsum_1(B,C) = k3_xcmplx_0(k7_xcmplx_0(1,4),k6_xcmplx_0(k1_square_1(k12_euclid(k7_euclid(A,D,E))),k1_square_1(k12_euclid(k8_euclid(A,D,E))))) ) ) ) ) ) ) )).
fof(t3_euclid_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k1_euclid_3(A) = k1_euclid_3(B) => A = B ) ) ) )).
fof(t3_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ( k9_euclid(A,B,1) = B & k9_euclid(A,B,k5_numbers) = k5_euclid(A) ) ) ) )).
fof(t3_euclid_5,axiom,( ! [A] : ( 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)) ) )).
fof(t3_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => k19_sin_cos(k4_euclid_3(A,B,C)) = k19_sin_cos(k4_euclid_3(C,B,A)) ) ) ) )).
fof(t3_euclid_7,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(k5_numbers)) => A = k6_finseq_1(k1_numbers) ) )).
fof(t3_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( ~ r3_euclidlp(3,A,B) => k5_euclid_8(A,B) = k16_euclid(3) ) ) ) )).
fof(t3_euclid_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t3_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(B)) => ( k6_euclid(B,k9_euclid(B,C,A)) = k9_euclid(B,C,k4_xcmplx_0(A)) & k6_euclid(B,k9_euclid(B,C,A)) = k9_euclid(B,k6_euclid(B,C),A) ) ) ) ) )).
fof(t3_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t3_euler_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( ( v1_int_2(B) & r2_hidden(A,a_1_0_euler_1(B)) ) => ( v1_int_2(B) & r2_hidden(A,B) & ~ r2_hidden(A,k1_tarski(k5_numbers)) ) ) & ( ( v1_int_2(B) & r2_hidden(A,B) ) => ( r2_hidden(A,k1_tarski(k5_numbers)) | ( v1_int_2(B) & r2_hidden(A,a_1_0_euler_1(B)) ) ) ) ) ) ) )).
fof(t3_euler_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_int_2(A,C) & r1_int_2(B,C) ) => ( A = k5_numbers | B = k5_numbers | C = k5_numbers | r1_int_2(C,k4_nat_d(k3_xcmplx_0(A,B),C)) ) ) ) ) ) )).
fof(t3_exchsort,axiom,( ! [A] : ! [B] : ( ~ r2_hidden(A,B) => k6_subset_1(k2_xboole_0(B,k1_tarski(A)),B) = k1_tarski(A) ) )).
fof(t3_extens_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,C) => ! [E] : ( m3_pboole(E,A,B) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t3_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) ) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t3_extreal1,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ( r1_xxreal_0(k5_numbers,A) => k3_extreal1(A) = A ) ) )).
fof(t3_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => r1_xxreal_0(k5_numbers,k3_extreal1(A)) ) )).
fof(t3_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_circcomb(A) & v2_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t3_facirc_2,axiom,( ! [A] : ! [B] : ( l1_msualg_1(B) => r1_circcomb(k1_facirc_2(A),B) ) )).
fof(t3_fcont_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r1_fcont_1(B,A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k1_relset_1(k1_numbers,B)) & ~ r1_xxreal_0(D,k9_complex1(k6_xcmplx_0(E,A))) & r1_xxreal_0(C,k9_complex1(k6_xcmplx_0(k1_funct_1(B,E),k1_funct_1(B,A)))) ) ) ) ) ) ) ) ) ) )).
fof(t3_fcont_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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))) ) ) ) )).
fof(t3_fcont_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( C = k2_xcmplx_0(A,B) => ( r1_xxreal_0(D,k9_complex1(B)) | ( ~ r1_xxreal_0(D,k5_numbers) & r2_hidden(C,k2_rcomp_1(k6_xcmplx_0(A,D),k2_xcmplx_0(A,D))) ) ) ) ) ) ) ) )).
fof(t3_fdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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))) ) ) ) )).
fof(t3_fdiff_10,axiom,( ! [A] : ( ( 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,k27_sin_cos,k27_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k27_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k27_sin_cos),A),B) = k3_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k27_sin_cos,B)))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t3_fdiff_11,axiom,( ! [A] : ( ( 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,k18_sin_cos,k1_sin_cos9))) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k18_sin_cos,B),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(k18_sin_cos,B)) ) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_sin_cos9),A),B) = k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k16_sin_cos,B),k2_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,B))))) ) ) ) ) ) )).
fof(t3_fdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => k3_funct_2(k4_ordinal1,k1_numbers,A,B) = k1_nat_1(k2_nat_1(2,B),1) ) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k4_ordinal1) & v5_valued_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) ) ) )).
fof(t3_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k1_funct_1(C,D) = k6_xcmplx_0(A,D) & ~ r1_xxreal_0(k1_funct_1(C,D),k5_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] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_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) = k7_xcmplx_0(1,k6_xcmplx_0(A,D)) ) ) ) ) ) ) ) )).
fof(t3_fdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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] : ( v1_xreal_0(F) => ( r2_hidden(F,C) => ( k1_funct_1(D,F) = k6_xcmplx_0(F,A) & k1_funct_1(E,F) = k6_xcmplx_0(F,B) & k1_funct_1(E,F) != k5_numbers ) ) ) ) => ( r2_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,D,E),C) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,C) => k1_funct_1(k2_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,D,E),C),F) = k7_xcmplx_0(k6_xcmplx_0(A,B),k1_square_1(k6_xcmplx_0(F,B))) ) ) ) ) ) ) ) ) ) )).
fof(t3_fdiff_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_1(C,E) = k1_square_1(A) ) ) & D = k1_taylor_1(2) ) => ( r2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,C,D),B) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_1(k2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,C,D),B),E) = k4_xcmplx_0(k3_xcmplx_0(2,E)) ) ) ) ) ) ) ) ) )).
fof(t3_fdiff_7,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k6_prepower(A,k4_xcmplx_0(k7_xcmplx_0(1,2))) = k7_xcmplx_0(1,k3_square_1(A)) ) ) )).
fof(t3_fdiff_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k3_prepower(k1_funct_1(k3_rfunct_1(k1_numbers,k1_numbers,C,D),E),A) = k7_xcmplx_0(k3_prepower(k1_funct_1(C,E),A),k3_prepower(k1_funct_1(D,E),A)) ) ) ) ) ) ) ) )).
fof(t3_fdiff_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => k3_prepower(k7_xcmplx_0(1,A),B) = k7_xcmplx_0(1,k3_prepower(A,B)) ) ) )).
fof(t3_ff_siec,axiom,( ! [A] : ( 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 ) )).
fof(t3_fib_num,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(k7_xcmplx_0(1,B),k5_numbers) & r1_xxreal_0(k7_xcmplx_0(1,B),A) ) ) ) ) )).
fof(t3_fib_num2,axiom,( ! [A] : ( ( v1_int_1(A) & v1_abian(A) ) => k2_power(k4_xcmplx_0(1),A) = 1 ) )).
fof(t3_fib_num3,axiom,( ! [A] : ( v1_xreal_0(A) => k2_power(A,2) = k2_power(k4_xcmplx_0(A),2) ) )).
fof(t3_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ( v1_abian(A) => ( B = k5_numbers | k2_power(k4_xcmplx_0(B),A) = k2_power(B,A) ) ) ) ) )).
fof(t3_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( k3_finseq_1(B) = k5_numbers => C = k1_finseq_8(A,B,C) ) ) ) ) )).
fof(t3_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r3_lattices(A,B,D) => r3_lattices(A,B,k3_lattices(A,C,D)) ) ) ) ) ) )).
fof(t3_filter_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t3_filter_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t3_fin_topo,axiom,( v3_orders_2(k4_fin_topo) )).
fof(t3_finance1,axiom,( ! [A] : ( 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) ) ) )).
fof(t3_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( A = k5_numbers | r2_hidden(A,k2_finseq_1(A)) ) ) )).
fof(t3_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(B,A) => k4_xxreal_0(k5_numbers,k6_xcmplx_0(A,B)) = k6_xcmplx_0(A,B) ) ) ) )).
fof(t3_finseq_3,axiom,( k2_finseq_1(5) = k3_enumset1(1,2,3,4,5) )).
fof(t3_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r1_finseq_4(A,B) <=> ( r2_hidden(B,k9_xtuple_0(A)) & ! [C] : ~ ( r2_hidden(C,k9_xtuple_0(A)) & B != C & k1_funct_1(A,B) = k1_funct_1(A,C) ) ) ) ) )).
fof(t3_finseq_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( 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 ) ) ) )).
fof(t3_finseq_6,axiom,( ! [A] : ! [B] : k5_relat_1(k10_finseq_1(A,B),k2_finseq_1(1)) = k9_finseq_1(A) )).
fof(t3_finseq_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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_xcmplx_0(k3_finseq_1(C),A)) ) ) ) ) )).
fof(t3_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k3_finseq_6(A,k6_finseq_1(A),B,C) = k6_finseq_1(A) ) ) ) )).
fof(t3_finseqop,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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 ) ) ) )).
fof(t3_finset_1,axiom,( ! [A] : ! [B] : ( v1_finset_1(A) => v1_finset_1(k3_xboole_0(A,B)) ) )).
fof(t3_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( 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(k4_ordinal1,A,C,k3_finsop_1(B),k2_finsop_1(A,k8_funcop_1(A,k4_ordinal1,k4_binop_1(A,C)),B)) ) ) ) ) ) )).
fof(t3_finsub_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) )).
fof(t3_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) )).
fof(t3_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_orders_2(A) => r1_tarski(k1_fintopo3(A,B),B) ) ) ) )).
fof(t3_fintopo5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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) ) ) ) ) ) ) )).
fof(t3_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_fin_topo(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t3_flang_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k2_xcmplx_0(A,B) = 1 <=> ( ( A = 1 & B = k5_numbers ) | ( A = k5_numbers & B = 1 ) ) ) ) ) )).
fof(t3_flang_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(B,A) & ! [C] : ( v7_ordinal1(C) => ~ ( k2_xcmplx_0(A,C) = B & ~ r1_xxreal_0(C,k5_numbers) ) ) ) ) ) )).
fof(t3_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(D,C) => r1_tarski(k7_flang_1(A,B,C),k1_flang_3(A,B,D)) ) ) ) ) )).
fof(t3_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(t3_fomodel1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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] : ( m2_subset_1(D,k3_finseq_2(k3_finseq_2(k15_fomodel1(B))),k3_fomodel0(k3_finseq_2(k15_fomodel1(B)),k3_funct_2(k4_ordinal1,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(k12_finseq_1(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)) ) ) ) ) )).
fof(t3_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( ( 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] : ( ( v1_relat_1(F) & v1_funct_1(F) & v1_fomodel2(F,B,C) ) => ( k1_funct_1(k10_funct_5(k4_ordinal1,k35_fomodel1(B),C,k9_funct_2(k35_fomodel1(B),C),k7_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),k9_nat_1(k9_funct_2(k35_fomodel1(B),C),k7_fomodel2(B,C,D,F),A))) & ( v14_fomodel1(E,k5_numbers,B) => k1_funct_1(k10_funct_5(k4_ordinal1,k35_fomodel1(B),C,k9_funct_2(k35_fomodel1(B),C),k7_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) ) ) ) ) ) ) ) ) )).
fof(t3_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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] : ( ( 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),k9_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),k9_fomodel2(B,A,D),k17_fomodel3(A,C))) ) ) ) ) )).
fof(t3_fomodel4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => ! [B] : ( v2_fomodel4(B,A) => ! [C] : ( v1_fomodel4(C,A) => ! [D] : ( 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(k23_fomodel4(A,D),B)) ) ) ) ) ) )).
fof(t3_fraenkel,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ! [D] : ( ( r1_tarski(C,B) & r1_tarski(D,A) ) => ( k1_funct_2(C,D) = k1_xboole_0 | ! [E] : ( 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))) ) ) ) ) ) )).
fof(t3_frechet,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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 ) ) ) )).
fof(t3_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( ! [D] : ( m2_valued_0(D,u1_struct_0(A),B) => ~ r1_tarski(k2_relset_1(u1_struct_0(A),D),C) ) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ? [E] : ( m1_subset_1(E,k4_ordinal1) & r1_xxreal_0(D,E) & r2_hidden(k9_nat_1(u1_struct_0(A),B,E),C) ) ) ) ) ) ) )).
fof(t3_freealg,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( v1_freealg(B) => k1_lang1(k3_freealg(A,B)) = B ) ) )).
fof(t3_friends1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ( ( k7_finseq_1(k1_rfinseq(A,C),k16_finseq_1(A,C)) = k7_finseq_1(k1_rfinseq(B,D),k16_finseq_1(B,D)) & r1_xxreal_0(A,B) & r1_xxreal_0(B,k3_finseq_1(C)) ) => C = k7_finseq_1(k1_rfinseq(k7_nat_d(B,A),D),k16_finseq_1(k7_nat_d(B,A),D)) ) ) ) ) ) )).
fof(t3_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k3_fscirc_1(A,B,C),k5_fscirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( 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) ) ) ) ) )).
fof(t3_fscirc_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( C = k4_tarski(k1_xboole_0,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k8_margrel1)) => ( k1_fscirc_2(1,A,B) = k2_circcomb(k5_circcomb(k1_margrel1(k6_margrel1,k4_finseq_2(k5_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(k5_numbers,k6_margrel1),k8_margrel1),k1_xboole_0),k8_fscirc_1(k1_funct_1(A,1),k1_funct_1(B,1),C),k7_circcomb(k5_ordinal1,k6_margrel1,k1_margrel1(k6_margrel1,k4_finseq_2(k5_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) ) ) ) ) )).
fof(t3_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(t3_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( ( ~ v2_struct_0(E) & l1_fsm_1(E,A) ) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(t3_fsm_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t3_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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) ) ) ) ) ) )).
fof(t3_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : k1_funcop_1(k5_relat_1(A,B)) = k5_relat_1(k1_funcop_1(A),B) ) )).
fof(t3_funcsdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k8_funcsdom(A) != k9_funcsdom(A) ) )).
fof(t3_funct_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t3_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( k9_xtuple_0(C) = A & ! [D] : ( 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))) ) ) ) )).
fof(t3_funct_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t3_funct_4,axiom,( ! [A] : ! [B] : ( r1_relset_1(A,A,k6_partfun1(A),k6_partfun1(B)) <=> r1_tarski(A,B) ) )).
fof(t3_funct_5,axiom,( ! [A] : ! [B] : ( ~ ( B = k1_xboole_0 & k2_zfmisc_1(A,B) = k1_xboole_0 & k2_zfmisc_1(B,A) = k1_xboole_0 ) => ( k9_xtuple_0(k2_zfmisc_1(A,B)) = A & k10_xtuple_0(k2_zfmisc_1(B,A)) = A ) ) )).
fof(t3_funct_6,axiom,( ! [A] : ! [B] : ! [C] : k2_funct_4(k7_funcop_1(k2_zfmisc_1(B,C),A)) = k7_funcop_1(k2_zfmisc_1(C,B),A) )).
fof(t3_funct_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t3_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ~ ( r2_hidden(C,A) & k1_funct_1(B,C) = k5_numbers ) ) ) => ( r1_tarski(A,k1_relset_1(k1_numbers,B)) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k7_xcmplx_0(k1_funct_1(B,C),k1_funct_1(B,k4_xcmplx_0(C))) = k4_xcmplx_0(1) ) ) ) ) ) ) )).
fof(t3_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t3_functor0,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(t3_functor1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t3_functor2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( m2_functor0(C,A,B) => ! [D] : ( m2_functor0(D,A,B) => ( r1_functor2(A,B,C,D) => ! [E] : ( m1_functor2(E,A,B,C,D) => ! [F] : ( m1_functor2(F,A,B,C,D) => ( ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t3_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v8_functor0(D,A,B) & v11_functor0(D,A,B) & l2_functor0(D,A,B) ) => ! [E] : ( l2_functor0(E,B,C) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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))) ) ) ) ) ) ) ) )).
fof(t3_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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) ) ) )).
fof(t3_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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)) ) ) ) )).
fof(t3_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( r1_xxreal_0(k5_numbers,k1_funct_1(C,D)) & r1_xxreal_0(k1_funct_1(C,D),1) ) ) ) ) )).
fof(t3_fvaluat1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,B) & r1_xxreal_0(k5_numbers,D) & r1_xxreal_0(D,C) ) => r1_xxreal_0(k4_xxreal_3(A,D),k4_xxreal_3(B,C)) ) ) ) ) ) )).
fof(t3_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_group_1(A) & l3_algstr_0(A) ) => v1_binop_1(u2_algstr_0(A),u1_struct_0(A)) ) )).
fof(t3_gate_1,axiom,( ~ v1_xboole_0(k1_gate_1(k1_xboole_0)) )).
fof(t3_gate_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ ( 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)) ) ) )).
fof(t3_gate_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ! [Q] : ! [R] : ! [S] : ! [T] : ! [U] : ! [V] : ~ ( ~ ( ~ 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) ) ) ) )).
fof(t3_gate_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ! [Q] : ! [R] : ! [S] : ! [T] : ! [U] : ! [V] : ! [W] : ! [X] : ! [Y] : ! [Z] : ! [A1] : ! [B1] : ! [C1] : ! [D1] : ! [E1] : ! [F1] : ! [G1] : ! [H1] : ! [I1] : ! [J1] : ! [K1] : ! [L1] : ! [M1] : ( v1_xboole_0(L1) => ( v1_xboole_0(A) | ( ~ v1_xboole_0(Z) & v1_xboole_0(k4_gate_1(M1,Y)) ) | ( ~ v1_xboole_0(k4_gate_1(M1,Y)) & v1_xboole_0(Z) ) | ( ~ v1_xboole_0(A1) & v1_xboole_0(k4_gate_1(N,k2_gate_1(B,Z))) ) | ( ~ v1_xboole_0(k4_gate_1(N,k2_gate_1(B,Z))) & v1_xboole_0(A1) ) | ( ~ v1_xboole_0(B1) & v1_xboole_0(k4_gate_1(O,k2_gate_1(C,Z))) ) | ( ~ v1_xboole_0(k4_gate_1(O,k2_gate_1(C,Z))) & v1_xboole_0(B1) ) | ( ~ v1_xboole_0(C1) & v1_xboole_0(k4_gate_1(P,k2_gate_1(D,Z))) ) | ( ~ v1_xboole_0(k4_gate_1(P,k2_gate_1(D,Z))) & v1_xboole_0(C1) ) | ( ~ v1_xboole_0(D1) & v1_xboole_0(k4_gate_1(Q,k2_gate_1(E,Z))) ) | ( ~ v1_xboole_0(k4_gate_1(Q,k2_gate_1(E,Z))) & v1_xboole_0(D1) ) | ( ~ v1_xboole_0(E1) & v1_xboole_0(k4_gate_1(R,k2_gate_1(F,Z))) ) | ( ~ v1_xboole_0(k4_gate_1(R,k2_gate_1(F,Z))) & v1_xboole_0(E1) ) | ( ~ v1_xboole_0(F1) & v1_xboole_0(k4_gate_1(S,k2_gate_1(G,Z))) ) | ( ~ v1_xboole_0(k4_gate_1(S,k2_gate_1(G,Z))) & v1_xboole_0(F1) ) | ( ~ v1_xboole_0(G1) & v1_xboole_0(k4_gate_1(T,k2_gate_1(H,Z))) ) | ( ~ v1_xboole_0(k4_gate_1(T,k2_gate_1(H,Z))) & v1_xboole_0(G1) ) | ( ~ v1_xboole_0(H1) & v1_xboole_0(k4_gate_1(U,k2_gate_1(I,Z))) ) | ( ~ v1_xboole_0(k4_gate_1(U,k2_gate_1(I,Z))) & v1_xboole_0(H1) ) | ( ~ v1_xboole_0(I1) & v1_xboole_0(k4_gate_1(V,k2_gate_1(J,Z))) ) | ( ~ v1_xboole_0(k4_gate_1(V,k2_gate_1(J,Z))) & v1_xboole_0(I1) ) | ( ~ v1_xboole_0(J1) & v1_xboole_0(k4_gate_1(W,k2_gate_1(K,Z))) ) | ( ~ v1_xboole_0(k4_gate_1(W,k2_gate_1(K,Z))) & v1_xboole_0(J1) ) | ( ~ v1_xboole_0(K1) & v1_xboole_0(k4_gate_1(X,k2_gate_1(L,Z))) ) | ( ~ v1_xboole_0(k4_gate_1(X,k2_gate_1(L,Z))) & v1_xboole_0(K1) ) | ( ~ ( ~ v1_xboole_0(K1) & v1_xboole_0(k4_gate_1(k4_gate_1(X,k2_gate_1(L,Y)),k4_gate_1(L1,k2_gate_1(L,M1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(X,k2_gate_1(L,Y)),k4_gate_1(L1,k2_gate_1(L,M1)))) & v1_xboole_0(K1) ) & ~ ( ~ v1_xboole_0(J1) & v1_xboole_0(k4_gate_1(k4_gate_1(W,k2_gate_1(K,Y)),k4_gate_1(L1,k2_gate_1(K,M1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(W,k2_gate_1(K,Y)),k4_gate_1(L1,k2_gate_1(K,M1)))) & v1_xboole_0(J1) ) & ~ ( ~ v1_xboole_0(I1) & v1_xboole_0(k4_gate_1(k4_gate_1(V,k2_gate_1(J,Y)),k4_gate_1(L1,k2_gate_1(J,M1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(V,k2_gate_1(J,Y)),k4_gate_1(L1,k2_gate_1(J,M1)))) & v1_xboole_0(I1) ) & ~ ( ~ v1_xboole_0(H1) & v1_xboole_0(k4_gate_1(k4_gate_1(U,k2_gate_1(I,Y)),k4_gate_1(L1,k2_gate_1(I,M1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(U,k2_gate_1(I,Y)),k4_gate_1(L1,k2_gate_1(I,M1)))) & v1_xboole_0(H1) ) & ~ ( ~ v1_xboole_0(G1) & v1_xboole_0(k4_gate_1(k4_gate_1(T,k2_gate_1(H,Y)),k4_gate_1(L1,k2_gate_1(H,M1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(T,k2_gate_1(H,Y)),k4_gate_1(L1,k2_gate_1(H,M1)))) & v1_xboole_0(G1) ) & ~ ( ~ v1_xboole_0(F1) & v1_xboole_0(k4_gate_1(k4_gate_1(S,k2_gate_1(G,Y)),k4_gate_1(L1,k2_gate_1(G,M1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(S,k2_gate_1(G,Y)),k4_gate_1(L1,k2_gate_1(G,M1)))) & v1_xboole_0(F1) ) & ~ ( ~ v1_xboole_0(E1) & v1_xboole_0(k4_gate_1(k4_gate_1(R,k2_gate_1(F,Y)),k4_gate_1(L1,k2_gate_1(F,M1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(R,k2_gate_1(F,Y)),k4_gate_1(L1,k2_gate_1(F,M1)))) & v1_xboole_0(E1) ) & ~ ( ~ v1_xboole_0(D1) & v1_xboole_0(k4_gate_1(k4_gate_1(Q,k2_gate_1(E,Y)),k4_gate_1(L1,k2_gate_1(E,M1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(Q,k2_gate_1(E,Y)),k4_gate_1(L1,k2_gate_1(E,M1)))) & v1_xboole_0(D1) ) & ~ ( ~ v1_xboole_0(C1) & v1_xboole_0(k4_gate_1(k4_gate_1(P,k2_gate_1(D,Y)),k4_gate_1(L1,k2_gate_1(D,M1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(P,k2_gate_1(D,Y)),k4_gate_1(L1,k2_gate_1(D,M1)))) & v1_xboole_0(C1) ) & ~ ( ~ v1_xboole_0(B1) & v1_xboole_0(k4_gate_1(k4_gate_1(O,k2_gate_1(C,Y)),k4_gate_1(L1,k2_gate_1(C,M1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(O,k2_gate_1(C,Y)),k4_gate_1(L1,k2_gate_1(C,M1)))) & v1_xboole_0(B1) ) & ~ ( ~ v1_xboole_0(A1) & v1_xboole_0(k4_gate_1(k4_gate_1(N,k2_gate_1(B,Y)),k4_gate_1(L1,k2_gate_1(B,M1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(N,k2_gate_1(B,Y)),k4_gate_1(L1,k2_gate_1(B,M1)))) & v1_xboole_0(A1) ) & ~ ( ~ v1_xboole_0(Z) & v1_xboole_0(k4_gate_1(k4_gate_1(L1,k2_gate_1(A,Y)),k4_gate_1(L1,k2_gate_1(A,M1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(L1,k2_gate_1(A,Y)),k4_gate_1(L1,k2_gate_1(A,M1)))) & v1_xboole_0(Z) ) ) ) ) )).
fof(t3_gate_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ! [Q] : ! [R] : ! [S] : ! [T] : ! [U] : ! [V] : ! [W] : ! [X] : ! [Y] : ~ ( ~ ( ~ 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) ) ) ) )).
fof(t3_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v5_group_1(A) & l4_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t3_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( m1_genealg1(C,B) => ! [D] : ( m1_genealg1(D,B) => m1_genealg1(k1_genealg1(B,C,D,A),B) ) ) ) ) )).
fof(t3_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( r1_analmetr(A,F,G) => ! [H] : ( m1_subset_1(H,u1_struct_0(k2_diraf(k2_analoaf(A)))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k2_diraf(k2_analoaf(A)))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k2_diraf(k2_analoaf(A)))) => ! [K] : ( m1_subset_1(K,u1_struct_0(k2_diraf(k2_analoaf(A)))) => ( ( H = B & I = D & J = C & K = E ) => ( r2_analoaf(k2_diraf(k2_analoaf(A)),H,I,J,K) <=> r1_geomtrap(A,B,D,C,E) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t3_gfacirc1,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( 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(k5_numbers,k5_numbers)) = k5_numbers & k1_funct_1(k3_gfacirc1,k10_finseq_1(k5_numbers,1)) = k5_numbers & k1_funct_1(k3_gfacirc1,k10_finseq_1(1,k5_numbers)) = 1 & k1_funct_1(k3_gfacirc1,k10_finseq_1(1,1)) = k5_numbers ) ) ) )).
fof(t3_gfacirc2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( C = k4_tarski(k1_xboole_0,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1)) => ( k1_gfacirc2(1,A,B) = k2_circcomb(k5_circcomb(k1_margrel1(k6_margrel1,k4_finseq_2(k5_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(k5_numbers,k6_margrel1),k7_margrel1),k1_xboole_0),k13_gfacirc1(k1_funct_1(A,1),k1_funct_1(B,1),C),k7_circcomb(k5_ordinal1,k6_margrel1,k1_margrel1(k6_margrel1,k4_finseq_2(k5_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) ) ) ) ) )).
fof(t3_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) ) )).
fof(t3_glib_001,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( r2_hidden(D,k1_relset_1(k4_ordinal1,k15_finseq_1(C))) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( r2_hidden(E,k1_relset_1(k4_ordinal1,B)) & r1_xxreal_0(D,E) & k1_funct_1(k15_finseq_1(C),D) = k1_funct_1(B,E) ) ) ) ) ) ) )).
fof(t3_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & ~ v4_glib_000(A) & v1_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t3_glib_003,axiom,( k2_glib_003 = 5 & k3_glib_003 = 6 & k4_glib_003 = 7 )).
fof(t3_glib_004,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( ( 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] : ( ( 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) => k2_uproots(A,C) = k2_xcmplx_0(k2_uproots(B,D),k2_uproots(k6_subset_1(A,B),E)) ) ) ) ) )).
fof(t3_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( ( 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] : ( m3_glib_001(C,A) => ! [D] : ! [E] : ( 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),k5_numbers) ) ) | r5_glib_005(A,B,k10_glib_001(A,C,D)) ) ) ) ) ) )).
fof(t3_goboard1,axiom,( ! [A] : ( ( v1_matrix_0(A) & v2_goboard1(A) & v3_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(B,k10_xtuple_0(k8_matrix_0(u1_struct_0(k15_euclid(2)),A,C))) & r2_hidden(B,k10_xtuple_0(k8_matrix_0(u1_struct_0(k15_euclid(2)),A,D))) & r2_hidden(C,k2_finseq_1(k1_matrix_0(A))) & r2_hidden(D,k2_finseq_1(k1_matrix_0(A))) ) => C = D ) ) ) ) )).
fof(t3_goboard2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ( k3_finseq_1(A) = k1_nat_1(B,1) => ( B = k5_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)) ) ) ) ) )).
fof(t3_goboard4,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [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)) & 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(k7_matrix_0(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(k7_matrix_0(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(k8_matrix_0(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(k8_matrix_0(u1_struct_0(k15_euclid(2)),A,k1_matrix_0(A)))) & r1_xboole_0(k3_topreal1(2,B),k3_topreal1(2,C)) ) ) ) ) )).
fof(t3_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ~ ( v4_goboard1(D) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(D)) & r1_xxreal_0(1,A) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(B,k3_finseq_1(D)) & r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,B,C)),k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,A,C))) ) ) ) ) ) )).
fof(t3_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => ( C = k8_metric_1(k14_euclid(A),D,B) => v3_pre_topc(C,k15_euclid(A)) ) ) ) ) ) )).
fof(t3_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t3_goboard8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,2),k3_finseq_1(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,2),k3_finseq_1(k2_goboard2(A))) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,2),k1_matrix_0(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_nat_1(D,1)) ) => ( ( ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,2),k1_nat_1(D,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),D) ) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,2),k1_nat_1(D,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_nat_1(D,1))),k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,k1_nat_1(D,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_nat_1(D,2))),k7_xcmplx_0(1,2))),k3_topreal1(2,A)) ) ) ) ) ) ) ) )).
fof(t3_goboard9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r3_connsp_1(A,C,D) & r1_tarski(B,D) ) ) ) ) ) ) )).
fof(t3_gobrd10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_gobrd10(A,C,B,D) => r2_gobrd10(k1_nat_1(A,1),k1_nat_1(C,1),k1_nat_1(B,1),k1_nat_1(D,1)) ) ) ) ) ) )).
fof(t3_gobrd11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t3_gobrd12,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(B,k3_finseq_1(k2_goboard2(A))) & r1_xxreal_0(C,k1_matrix_0(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)) ) ) ) ) ) )).
fof(t3_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_tarski(k9_matrix_0(D),k9_matrix_0(E)) & r2_hidden(k4_tarski(A,B),k2_matrix_0(D)) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(E)) & k3_matrix_0(u1_struct_0(k15_euclid(2)),D,A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,k3_finseq_1(E),C) ) => A = k3_finseq_1(D) ) ) ) ) ) ) )).
fof(t3_gobrd14,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_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_0(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_0(u1_struct_0(k15_euclid(2)),C,A,1)),k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),1))),k1_rcomp_1(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,B)),k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,k1_nat_1(B,1)))))) ) ) ) ) ) )).
fof(t3_goedcpuc,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_goedcpuc(C,A,B) => m1_qc_lang1(k1_funct_1(C,k1_nat_1(B,1))) ) ) ) )).
fof(t3_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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] : ( m2_subset_1(E,k2_qc_lang1(A),k3_qc_lang1(A)) & r1_henmodel(A,B,k4_substut2(A,C,D,E)) ) ) ) ) ) ) ) )).
fof(t3_gr_cy_1,axiom,( k1_gr_cy_1(k6_finseq_1(k4_numbers)) = k5_numbers )).
fof(t3_gr_cy_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t3_gr_cy_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_gr_cy_3(A) ) => k4_nat_d(A,2) = 1 ) )).
fof(t3_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t3_graph_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r1_tarski(A,k2_finseq_1(C)) & r1_tarski(B,k4_finseq_1(k14_finseq_1(A))) ) => k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k4_ordinal1,k14_finseq_1(B),k14_finseq_1(A)) = k14_finseq_1(k10_xtuple_0(k2_partfun1(k4_ordinal1,k4_ordinal1,k14_finseq_1(A),B))) ) ) )).
fof(t3_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ~ ( r1_graph_2(A,C,B) & v1_xboole_0(C) ) ) ) ) )).
fof(t3_graph_4,axiom,( ! [A] : ( ( ~ 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 ) ) )).
fof(t3_graph_5,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( C = a_2_1_graph_5(A,B) => v1_finset_1(C) ) ) ) )).
fof(t3_graphsp,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( 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) ) ) ) )).
fof(t3_grcat_1,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t3_grfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( k9_xtuple_0(A) = k9_xtuple_0(B) & r1_tarski(A,B) ) => A = B ) ) ) )).
fof(t3_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t3_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( ( r1_tarski(F,G) & r5_polyred(A,B,C,D,E,F) ) => r5_polyred(A,B,C,D,E,G) ) ) ) ) ) ) ) ) )).
fof(t3_groeb_2,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(t3_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t3_group_1,axiom,( v3_group_1(g3_algstr_0(k1_numbers,k9_binop_2)) & v2_group_1(g3_algstr_0(k1_numbers,k9_binop_2)) )).
fof(t3_group_10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t3_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( ~ r1_xboole_0(k13_group_2(A,B,D),k8_group_2(A,C)) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,k13_group_2(A,B,D)) & r1_struct_0(C,E) ) ) ) ) ) ) ) )).
fof(t3_group_12,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_group_7(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_group_7(A,B))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k1_group_7(A,B,C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k1_group_7(A,B,C))) => ( ( D = k1_funct_7(k1_group_1(k2_group_7(A,B)),C,F) & E = k1_funct_7(k1_group_1(k2_group_7(A,B)),C,G) ) => k6_algstr_0(k2_group_7(A,B),D,E) = k1_funct_7(k1_group_1(k2_group_7(A,B)),C,k6_algstr_0(k1_group_7(A,B,C),F,G)) ) ) ) ) ) ) ) ) )).
fof(t3_group_14,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v1_prvect_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_finseq_1(B) & v1_prvect_1(B) ) => ? [C] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k4_prvect_3(k20_prvect_1(A),k20_prvect_1(B))),u1_struct_0(k20_prvect_1(k7_finseq_1(A,B)))) & v13_vectsp_1(C,k4_prvect_3(k20_prvect_1(A),k20_prvect_1(B)),k20_prvect_1(k7_finseq_1(A,B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_prvect_3(k20_prvect_1(A),k20_prvect_1(B))),u1_struct_0(k20_prvect_1(k7_finseq_1(A,B)))))) & v3_funct_2(C,u1_struct_0(k4_prvect_3(k20_prvect_1(A),k20_prvect_1(B))),u1_struct_0(k20_prvect_1(k7_finseq_1(A,B)))) & ! [D] : ( m1_subset_1(D,u1_struct_0(k20_prvect_1(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k20_prvect_1(B))) => ? [F] : ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) & ? [G] : ( 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) ) ) ) ) ) ) ) )).
fof(t3_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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)) ) ) )).
fof(t3_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => v5_group_1(k6_group_2(A)) ) )).
fof(t3_group_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_group_2(D,B) => ( r1_struct_0(D,C) => r1_struct_0(D,k5_group_1(B,A,C)) ) ) ) ) ) )).
fof(t3_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t3_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_6(C,A,B) => ! [D] : ( m1_group_6(D,A,B) => k10_group_2(A,C,D) = k10_group_2(B,C,D) ) ) ) ) )).
fof(t3_group_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( C = D => ! [E] : ( m1_subset_1(E,k4_ordinal1) => k5_group_1(B,E,C) = k5_group_1(A,E,D) ) ) ) ) ) ) )).
fof(t3_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ( ( F = D & G = E ) => k6_algstr_0(C,F,G) = k6_algstr_0(B,D,E) ) ) ) ) ) ) ) )).
fof(t3_groupp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t3_grsolv_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ! [C] : ( ( v15_algstr_0(C) & m1_group_2(C,A) ) => ! [D] : ( ( v15_algstr_0(D) & v1_group_3(D,C) & m1_group_6(D,A,C) ) => ! [E] : ( ( v15_algstr_0(E) & m1_group_2(E,A) ) => ( r1_group_2(A,E,k10_group_2(A,B,C)) => ! [F] : ( ( v1_group_3(F,E) & m1_group_6(F,A,E) ) => ~ ( F = k10_group_2(A,B,D) & ! [G] : ( m1_group_2(G,k5_group_6(C,D)) => ~ r1_group_6(k5_group_6(E,F),G) ) ) ) ) ) ) ) ) ) )).
fof(t3_hahnban,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ( r1_rlsub_2(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t3_hahnban1,axiom,( k8_group_1(k1_complfld,k2_hahnban1,k2_hahnban1) = k4_algstr_0(k1_complfld,k1_group_1(k1_complfld)) )).
fof(t3_hallmar1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ! [C] : r1_tarski(k1_hallmar1(A,B,C),A) ) )).
fof(t3_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => r2_hidden(k5_numbers,k7_relset_1(u1_struct_0(k3_pcomps_1(A)),u1_struct_0(k3_topmetr),k4_weierstr(A,C),B)) ) ) ) ) )).
fof(t3_heine,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_limfunc1(A) => v1_limfunc1(k1_heine(A,2)) ) ) )).
fof(t3_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t3_henmodel,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ! [C] : ( v1_finset_1(C) => ~ ( ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(E,k1_relset_1(k4_ordinal1,B)) & r2_hidden(D,k1_relset_1(k4_ordinal1,B)) ) => ( r1_xxreal_0(E,D) | r1_tarski(k9_nat_1(A,B,D),k9_nat_1(A,B,E)) ) ) ) ) & r1_tarski(C,k3_tarski(k2_relset_1(A,B))) & ! [D] : ( v7_ordinal1(D) => ~ r1_tarski(C,k9_nat_1(A,B,D)) ) ) ) ) ) )).
fof(t3_hermitan,axiom,( ! [A] : ( v1_xcmplx_0(A) => ? [B] : ( v1_xcmplx_0(B) & k9_complex1(B) = 1 & k3_complex1(k3_xcmplx_0(B,A)) = k9_complex1(A) & k4_complex1(k3_xcmplx_0(B,A)) = k5_numbers ) ) )).
fof(t3_hessenbe,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r1_collsp(A,B,C,D) & r1_collsp(A,B,C,F) & r1_collsp(A,D,F,E) ) => ( D = F | r1_collsp(A,B,C,E) ) ) ) ) ) ) ) ) )).
fof(t3_heyting1,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A)) => k9_normform(A,k10_normform(A,B,B)) = B ) )).
fof(t3_heyting2,axiom,( ! [A] : ! [B] : ! [C] : ( m2_subset_1(C,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B)) => ! [D] : ( m2_subset_1(D,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B)) => ( k4_substlat(A,B,C,D) = C => ! [E] : ~ ( r2_hidden(E,C) & ! [F] : ~ ( r2_hidden(F,D) & r1_tarski(F,E) ) ) ) ) ) )).
fof(t3_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_domain_1(k4_ordinal1,A)))) ) => ? [C] : ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) & r1_tarski(B,k8_mcart_1(k4_ordinal1,k4_ordinal1,k1_finsub_1(k1_zfmisc_1(k4_ordinal1),k2_finseq_1(C),k6_domain_1(k4_ordinal1,k5_numbers)),k6_domain_1(k4_ordinal1,A))) ) ) ) )).
fof(t3_hfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( 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(k5_numbers)) & k8_relset_1(k1_numbers,k1_numbers,k1_taylor_1(A),k1_tarski(k5_numbers)) = k1_tarski(k5_numbers) ) ) ) )).
fof(t3_hilbasis,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t3_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( 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)) ) ) ) ) )).
fof(t3_hilbert2,axiom,( ! [A] : ! [B] : ( m2_finseq_1(k9_finseq_1(B),A) => r2_hidden(B,A) ) )).
fof(t3_holder_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(B,C) ) => r1_xxreal_0(k2_power(B,A),k2_power(C,A)) ) ) ) ) ) )).
fof(t3_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v4_aff_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( B != C & B != D & r1_aff_1(A,B,C,D) & ! [E] : ( ( 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 ) ) ) ) ) ) ) ) )).
fof(t3_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k6_xcmplx_0(A,B),A) ) ) )).
fof(t3_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_algstr_0(A) & v1_vectsp_1(A) & v1_algstr_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t3_incproj,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) <=> m1_subset_1(B,u1_incsp_1(k3_incproj(A))) ) ) )).
fof(t3_incsp_1,axiom,( ! [A] : ( l2_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t3_index_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & 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)) ) ) )).
fof(t3_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t3_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( r1_xxreal_0(k5_numbers,A) => r2_hidden(A,k4_ordinal1) ) ) )).
fof(t3_int_2,axiom,( ! [A] : ( v1_int_1(A) => ( r1_int_1(k5_numbers,A) <=> A = k5_numbers ) ) )).
fof(t3_int_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_int_3)) => ! [B] : ( 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)) ) ) ) )).
fof(t3_int_4,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( v1_xreal_0(B) => ( B != k5_numbers => r2_tarski(A,k1_integra2(A,B)) ) ) ) )).
fof(t3_int_5,axiom,( ! [A] : ( 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)) ) ) )).
fof(t3_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_valued_0(B) ) => k3_finseq_1(k18_valued_1(A,B)) = k4_nat_1(k3_finseq_1(A),k3_finseq_1(B)) ) ) )).
fof(t3_int_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t3_int_8,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k4_numbers)) => ! [C] : ( v1_int_1(C) => ( r2_hidden(A,k23_member_1(B,C)) <=> ? [D] : ( v1_int_1(D) & r2_hidden(D,B) & A = k3_xcmplx_0(C,D) ) ) ) ) ) )).
fof(t3_integr10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k6_xcmplx_0(k1_funct_1(k22_sin_cos,B),k1_funct_1(k22_sin_cos,A)) = k4_integra5(A,B,k22_sin_cos) ) ) )).
fof(t3_integr11,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( 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(k2_xcmplx_0(A,1))),k7_xcmplx_0(1,k2_xcmplx_0(A,1))),k1_numbers) & ! [B] : ( v1_xreal_0(B) => k1_funct_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(k2_xcmplx_0(A,1))),k7_xcmplx_0(1,k2_xcmplx_0(A,1))),k1_numbers),B) = k3_xcmplx_0(k3_prepower(k1_funct_1(k16_sin_cos,B),A),k1_funct_1(k18_sin_cos,B)) ) ) ) )).
fof(t3_integr12,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,D) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => ( ~ r1_xxreal_0(1,k1_funct_1(k22_sin_cos,E)) & k1_funct_1(C,E) = 1 ) ) ) & r1_tarski(D,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_sin_cos9))) & D = k1_relset_1(k1_numbers,B) & r2_relset_1(k1_numbers,k1_numbers,B,k3_rfunct_1(k1_numbers,k1_numbers,k22_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,C,k41_valued_1(k1_numbers,k1_numbers,k22_sin_cos)))) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_sin_cos9),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_sin_cos9),k3_seq_4(A))) ) ) ) ) ) )).
fof(t3_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k22_sin_cos,k16_sin_cos),2)) & r1_tarski(C,k1_relset_1(k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)),k3_seq_4(A))) ) ) ) ) )).
fof(t3_integr14,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k7_xcmplx_0(k1_funct_1(k18_sin_cos,k1_funct_1(k3_taylor_1,B)),k3_xcmplx_0(B,k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k3_taylor_1,B))))) ) ) ) ) ) )).
fof(t3_integr15,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => ! [C] : ( m1_integra1(C,A) => ! [D] : ( v1_xreal_0(D) => ~ ( v2_seq_2(k2_partfun1(A,k1_numbers,B,A)) & ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( m1_integr15(E,A,B,C) => ~ r1_xxreal_0(k1_integr15(A,B,C,E),k2_xcmplx_0(k7_integra1(A,B,C),D)) ) ) ) ) ) ) )).
fof(t3_integr16,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k2_numbers))) ) => ! [B] : ( 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)) ) ) )).
fof(t3_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_relset_1(k4_ordinal1,u1_struct_0(A),C,k4_vfunct_1(k4_ordinal1,A,B,D)) => k4_rlvect_1(A,C) = k1_rlvect_1(A,k4_rlvect_1(A,B),D) ) ) ) ) ) )).
fof(t3_integr19,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t3_integr1c,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_integr1c(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_integr1c(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k2_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_integr1c(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k2_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( ( 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] : ( v1_xreal_0(H) => ( r2_hidden(H,k1_relset_1(k1_numbers,C)) => k1_funct_1(B,H) = k1_funct_1(C,H) ) ) & ! [H] : ( v1_xreal_0(H) => ( 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)) ) ) ) ) ) ) ) ) )).
fof(t3_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( A = k1_rcomp_1(B,D) & A = k1_rcomp_1(C,E) ) => ( B = C & D = E ) ) ) ) ) ) ) )).
fof(t3_integra4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( 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)) ) ) ) ) )).
fof(t3_integra5,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k4_finseq_1(A)) => r1_xxreal_0(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) ) => r1_xxreal_0(k18_rvsum_1(A),k18_rvsum_1(B)) ) ) ) )).
fof(t3_integra6,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(t3_integra7,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t3_integra8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k19_sin_cos(k2_xcmplx_0(A,k3_xcmplx_0(k2_nat_1(2,B),k28_sin_cos))) = k19_sin_cos(A) ) ) )).
fof(t3_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( A != k5_numbers => k2_integra5(B,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,k5_numbers),k22_sin_cos)) = k6_xcmplx_0(k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,k5_numbers),k22_sin_cos),k7_xcmplx_0(1,A)),k2_seq_4(B)),k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,k5_numbers),k22_sin_cos),k7_xcmplx_0(1,A)),k3_seq_4(B))) ) ) ) )).
fof(t3_interva1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( ~ r1_tarski(B,C) => k1_interva1(A,B,C) = k1_xboole_0 ) ) ) )).
fof(t3_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => r2_hidden(k3_intpro_1(k4_intpro_1(B,C),B),k7_intpro_1(A)) ) ) ) )).
fof(t3_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k1_funct_1(k3_irrat_1(B),A) = k1_funct_1(k2_irrat_1(A),B) ) ) )).
fof(t3_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,B,C) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t3_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => k1_cat_1(A,B,k4_cat_1(A,k4_graph_1(A,B))) = B ) ) )).
fof(t3_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(B,A) => v1_isomichi(B,A) ) ) ) )).
fof(t3_jct_misc,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( r2_hidden(C,k2_rcomp_1(A,B)) & r1_xxreal_0(k4_xxreal_0(k9_complex1(A),k9_complex1(B)),k9_complex1(C)) ) ) ) ) )).
fof(t3_jgraph_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => m2_finseq_1(B,u1_struct_0(k1_jgraph_1(A))) ) ) )).
fof(t3_jgraph_2,axiom,( k17_euclid(k4_struct_0(k15_euclid(2))) = k5_numbers & k18_euclid(k4_struct_0(k15_euclid(2))) = k5_numbers )).
fof(t3_jgraph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) ) => ! [F] : ( ( 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] : ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t3_jgraph_4,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ? [C] : ( ~ 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] : ( 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)) ) ) )).
fof(t3_jgraph_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( ~ v2_struct_0(F) & l1_metric_1(F) ) => ! [G] : ( ( ~ v2_struct_0(G) & l1_metric_1(G) ) => ! [H] : ( m1_subset_1(H,u1_struct_0(F)) => ! [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(k8_metric_1(F,H,E),k8_metric_1(G,I,E)) ) ) ) ) ) ) ) ) ) ) )).
fof(t3_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t3_jgraph_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t3_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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),k7_xcmplx_0(1,2)))) ) ) ) )).
fof(t3_jordan1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t3_jordan10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(k2_jordan9(E,D))) & r2_hidden(k4_tarski(A,B),k2_matrix_0(k1_jordan8(E,D))) & r2_hidden(k4_tarski(k1_nat_1(A,1),B),k2_matrix_0(k1_jordan8(E,D))) & k7_partfun1(u1_struct_0(k15_euclid(2)),k2_jordan9(E,D),C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,D),A,B) & k7_partfun1(u1_struct_0(k15_euclid(2)),k2_jordan9(E,D),k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,D),k1_nat_1(A,1),B) & r1_xxreal_0(B,1) ) ) ) ) ) ) )).
fof(t3_jordan11,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ r1_xxreal_0(k1_matrix_0(k1_jordan8(A,k3_jordan11(A))),k1_nat_1(k4_jordan11(A),1)) ) )).
fof(t3_jordan12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_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,k1_nat_1(C,1)),k10_xtuple_0(B)) ) ) ) ) ) )).
fof(t3_jordan14,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_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)) ) ) ) ) )).
fof(t3_jordan15,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t3_jordan16,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( r2_hidden(D,A) => r2_hidden(D,k3_jordan6(A,B,C,D)) ) ) ) ) ) )).
fof(t3_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r1_jordan6(A,B,k22_pscomp_1(A)) => r2_hidden(B,k8_jordan6(A)) ) ) ) )).
fof(t3_jordan18,axiom,( ! [A] : ( 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))) ) )).
fof(t3_jordan19,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( 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_0(k1_jordan8(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_topreal1(2,k2_jordan9(B,A))) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,k1_matrix_0(k1_jordan8(B,A))),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D)),k3_topreal1(2,k1_jordan1e(B,A))) ) ) ) ) ) )).
fof(t3_jordan1b,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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) ) ) ) )).
fof(t3_jordan1c,axiom,( ! [A] : ( 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)) ) ) )).
fof(t3_jordan1e,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(B,k3_topreal1(2,A)) & k2_jordan3(A,B) = k1_xboole_0 ) ) ) )).
fof(t3_jordan1g,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t3_jordan1h,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t3_jordan1i,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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_jordan9(B,A),k24_pscomp_1(k3_topreal1(2,k2_jordan9(B,A)))),1) ) ) )).
fof(t3_jordan1k,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( 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))) ) ) ) ) )).
fof(t3_jordan20,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v1_xreal_0(D) => ( ( 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)) ) ) ) ) ) )).
fof(t3_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( v2_compts_1(k2_kurato_2(k15_euclid(2),k1_jordan19(A),B),k15_euclid(2)) & v2_connsp_1(k2_kurato_2(k15_euclid(2),k1_jordan19(A),B),k15_euclid(2)) ) ) ) )).
fof(t3_jordan23,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => k4_jordan3(A,B,C) != k1_xboole_0 ) ) ) )).
fof(t3_jordan2b,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k2_finseq_1(A)) => k7_partfun1(k1_numbers,k1_rlvect_1(k15_euclid(A),C,B),D) = k3_xcmplx_0(B,k7_partfun1(k1_numbers,C,D)) ) ) ) ) ) )).
fof(t3_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k12_euclid(B),k12_euclid(C))),k12_euclid(k5_algstr_0(k15_euclid(A),B,C))) ) ) ) )).
fof(t3_jordan3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t3_jordan4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k4_nat_d(k2_xcmplx_0(B,B),B) = k5_numbers ) ) )).
fof(t3_jordan5a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ~ ( B != C & ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,k1_rcomp_1(k5_numbers,1)) => k1_funct_1(D,E) = k3_rlvect_1(k15_euclid(A),k1_rlvect_1(k15_euclid(A),B,k6_xcmplx_0(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,k5_numbers) = B & k1_funct_1(D,1) = C ) ) ) ) ) ) )).
fof(t3_jordan5b,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(1,B) ) => r1_xxreal_0(k1_nat_1(k7_nat_d(B,A),1),B) ) ) ) )).
fof(t3_jordan5c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t3_jordan5d,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ 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] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(B)) & k1_funct_1(B,C) = A ) ) ) ) ) )).
fof(t3_jordan6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t3_jordan7,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(t3_jordan8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m2_finseq_1(C,B) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(B)) ) => ~ ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) & r1_goboard1(B,C,D) & ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ~ ( r2_hidden(k4_tarski(E,F),k2_matrix_0(D)) & k7_partfun1(B,C,A) = k3_matrix_0(B,D,E,F) & r2_hidden(k4_tarski(G,H),k2_matrix_0(D)) & k7_partfun1(B,C,k1_nat_1(A,1)) = k3_matrix_0(B,D,G,H) & ~ ( ~ ( E = G & k1_nat_1(F,1) = H ) & ~ ( k1_nat_1(E,1) = G & F = H ) & ~ ( E = k1_nat_1(G,1) & F = H ) & ~ ( E = G & F = k1_nat_1(H,1) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t3_jordan9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ~ ( r2_hidden(A,k4_finseq_1(C)) & ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(D,k4_finseq_1(k4_finseq_5(B,C))) & k2_xcmplx_0(A,D) = k1_nat_1(k3_finseq_1(C),1) & k7_partfun1(B,C,A) = k7_partfun1(B,k4_finseq_5(B,C),D) ) ) ) ) ) ) )).
fof(t3_jordan_a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k15_euclid(A))) => ? [G] : ( 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) = k3_seq_4(G) ) ) => k3_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))) = k3_seq_4(k7_relset_1(u1_struct_0(k15_euclid(A)),k1_numbers,E,B)) ) ) ) ) ) ) )).
fof(t3_knaster,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) => ( ? [D] : ( m1_subset_1(D,k4_ordinal1) & r1_abian(A,k1_abian(B,C,D)) & ! [E] : ( r1_abian(E,k1_abian(B,C,D)) => A = E ) ) => r1_abian(A,C) ) ) )).
fof(t3_kolmog01,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t3_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( r2_hidden(C,k2_kurato_0(A,B)) <=> ! [D] : ( v7_ordinal1(D) => r2_hidden(C,k1_funct_1(B,D)) ) ) ) )).
fof(t3_kurato_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t3_kurato_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( v1_xreal_0(E) => ( B = D => ( r1_xxreal_0(E,k12_euclid(k5_algstr_0(k15_euclid(A),C,D))) | r2_hidden(C,k8_metric_1(k14_euclid(A),B,E)) ) ) ) ) ) ) ) )).
fof(t3_l_hospit,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( ( r1_limfunc2(A,B) & k1_limfunc2(A,B) = C ) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(B,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,D) & ~ r1_xxreal_0(B,E) & r2_hidden(E,k1_relset_1(k1_numbers,A)) ) ) ) ) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(D) & k1_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(k4_ordinal1,k1_numbers,k1_numbers,D,A)) & k1_seq_2(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,D,A)) = C ) ) ) ) ) & ( ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(B,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,D) & ~ r1_xxreal_0(B,E) & r2_hidden(E,k1_relset_1(k1_numbers,A)) ) ) ) ) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(D) & k1_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(k4_ordinal1,k1_numbers,k1_numbers,D,A)) & k1_seq_2(k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,D,A)) = C ) ) ) ) => ( r1_limfunc2(A,B) & k1_limfunc2(A,B) = C ) ) ) ) ) ) )).
fof(t3_lang1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t3_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( r2_hidden(A,k2_finseq_1(k1_matrix_0(C))) => k1_matrix_0(k16_matrix_0(A,u1_struct_0(B),C)) = k7_nat_d(k1_matrix_0(C),1) ) ) ) ) )).
fof(t3_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v15_algstr_0(C) & m1_group_2(C,A) ) => ( B = u1_struct_0(C) => r1_group_2(A,k5_group_4(A,B),C) ) ) ) ) )).
fof(t3_latsum_1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ( ( v3_orders_2(A) & v3_orders_2(B) ) => v3_orders_2(k1_latsum_1(A,B)) ) ) ) )).
fof(t3_lattice2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( 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))) ) ) ) ) )).
fof(t3_lattice3,axiom,( ! [A] : ( v13_lattices(k1_lattice3(A)) & k5_lattices(k1_lattice3(A)) = k1_xboole_0 ) )).
fof(t3_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,B) & r3_lattices(A,k4_lattices(A,D,E),C) ) ) ) ) ) ) ) )).
fof(t3_lattice5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v6_ordinal1(A) => k2_zfmisc_1(k3_tarski(A),k3_tarski(A)) = k3_tarski(a_1_0_lattice5(A)) ) ) )).
fof(t3_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v1_lattice6(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r3_lattices(A,B,C) & B != C & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r3_lattices(A,D,C) & r1_lattice6(A,D,B) ) ) ) ) ) ) )).
fof(t3_lattice7,axiom,( ! [A] : ( ( 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] : ( ( v6_orders_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t3_lattice8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( 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) ) ) ) ) ) )).
fof(t3_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_lattices(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_lattices(A,B,k1_lattices(A,B,C)) ) ) ) )).
fof(t3_lexbfs,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(A,k2_finsub_1(k1_zfmisc_1(k4_ordinal1),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) ) ) ) ) ) )).
fof(t3_lfuzzy_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_lfuzzy_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_xxreal_0(B,C) <=> r1_orders_2(A,B,C) ) ) ) ) )).
fof(t3_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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) ) ) ) ) ) )).
fof(t3_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v9_ordinal1(A) & v2_comseq_2(A) & k1_seq_2(A) = k5_numbers & v8_valued_0(A) ) => ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k1_funct_1(A,B),k5_numbers) ) ) ) )).
fof(t3_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r1_tarski(k2_rcomp_1(k6_xcmplx_0(A,B),A),k1_relset_1(k1_numbers,C)) => ( r1_xxreal_0(B,k5_numbers) | ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,D) & ~ r1_xxreal_0(A,E) & r2_hidden(E,k1_relset_1(k1_numbers,C)) ) ) ) ) ) ) ) ) ) )).
fof(t3_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v2_comseq_2(B) & k1_seq_2(B) = A & r1_tarski(k10_xtuple_0(B),k6_subset_1(k9_xtuple_0(C),k1_tarski(A))) ) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ? [F] : ( m1_subset_1(F,k4_ordinal1) & r1_xxreal_0(E,F) & ~ ( ~ r1_xxreal_0(k9_complex1(k6_xcmplx_0(A,k3_funct_2(k4_ordinal1,k1_numbers,B,F))),k5_numbers) & ~ r1_xxreal_0(D,k9_complex1(k6_xcmplx_0(A,k3_funct_2(k4_ordinal1,k1_numbers,B,F)))) & r2_hidden(k3_funct_2(k4_ordinal1,k1_numbers,B,F),k9_xtuple_0(C)) ) ) ) ) ) ) ) ) ) )).
fof(t3_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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)) ) ) ) )).
fof(t3_lmod_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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) ) ) )).
fof(t3_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t3_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v7_struct_0(A) => ( ! [D] : ( 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)) ) ) ) ) ) )).
fof(t3_lopban_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m2_funct_2(C,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t3_lopban_2,axiom,( ! [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) & 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)))) ) ) )).
fof(t3_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k2_normsp_0(A,k5_algstr_0(A,B,C)) = k2_normsp_0(A,k3_rlvect_1(A,k5_algstr_0(A,B,D),k5_algstr_0(A,D,C))) ) ) ) ) )).
fof(t3_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v3_normsp_1(B,A) & v3_normsp_1(C,A) ) => v3_normsp_1(k4_lopban_3(A,B,C),A) ) ) ) ) )).
fof(t3_lopban_5,axiom,( ! [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) & v3_lopban_1(A) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ~ ( k3_tarski(k10_xtuple_0(B)) = u1_struct_0(A) & ! [C] : ( v7_ordinal1(C) => v2_nfcont_1(k9_nat_1(k9_setfam_1(u1_struct_0(A)),B,C),A) ) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k1_lopban_5(A,E,D),k9_nat_1(k9_setfam_1(u1_struct_0(A)),B,C)) ) ) ) ) ) ) ) )).
fof(t3_lopban_6,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_numbers) => k1_lopban_5(A,k4_struct_0(A),k3_xcmplx_0(C,B)) = k1_convex1(A,k1_lopban_5(A,k4_struct_0(A),B),C) ) ) ) ) )).
fof(t3_lopban_7,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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)))) ) => k4_struct_0(B) = k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,k4_struct_0(A)) ) ) ) )).
fof(t3_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t3_lp_space,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( 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(k2_power(k4_series_1(k1_lp_space(k1_series_1(k1_numbers,A,B),C)),k7_xcmplx_0(1,C)),k2_xcmplx_0(k2_power(k4_series_1(k1_lp_space(A,C)),k7_xcmplx_0(1,C)),k2_power(k4_series_1(k1_lp_space(B,C)),k7_xcmplx_0(1,C)))) ) ) ) ) ) )).
fof(t3_lpspace1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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,k10_subset_1(k4_struct_0(A),B),k1_ideal_1(A,B),k1_lpspace1(A,B))) & v3_rlvect_1(g1_rlvect_1(B,k10_subset_1(k4_struct_0(A),B),k1_ideal_1(A,B),k1_lpspace1(A,B))) & v4_rlvect_1(g1_rlvect_1(B,k10_subset_1(k4_struct_0(A),B),k1_ideal_1(A,B),k1_lpspace1(A,B))) & v5_rlvect_1(g1_rlvect_1(B,k10_subset_1(k4_struct_0(A),B),k1_ideal_1(A,B),k1_lpspace1(A,B))) & v6_rlvect_1(g1_rlvect_1(B,k10_subset_1(k4_struct_0(A),B),k1_ideal_1(A,B),k1_lpspace1(A,B))) & v7_rlvect_1(g1_rlvect_1(B,k10_subset_1(k4_struct_0(A),B),k1_ideal_1(A,B),k1_lpspace1(A,B))) & v8_rlvect_1(g1_rlvect_1(B,k10_subset_1(k4_struct_0(A),B),k1_ideal_1(A,B),k1_lpspace1(A,B))) ) ) ) ) )).
fof(t3_lpspace2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(k2_power(B,C),k2_power(A,C)) ) ) ) ) )).
fof(t3_ltlaxio1,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k6_xboolean(k6_xboolean(k4_xboolean(A,B),C),k6_xboolean(A,k6_xboolean(B,C))) = 1 ) ) ) )).
fof(t3_ltlaxio2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( k10_xtuple_0(A) = k10_xtuple_0(B) => ( k3_finseq_1(A) = k5_numbers <=> k3_finseq_1(B) = k5_numbers ) ) ) ) )).
fof(t3_ltlaxio3,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_tarski(k1_ltlaxio3(A),k1_ltlaxio3(B)) ) )).
fof(t3_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( r3_ltlaxio1(k1_subset_1(k1_hilbert1),A) <=> ~ v1_ltlaxio4(k1_ltlaxio1(A)) ) ) )).
fof(t3_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t3_margrel1,axiom,( ! [A] : ( ( v3_finseq_1(A) & v2_card_3(A) ) => ( ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ r2_hidden(B,A) ) => A = k1_xboole_0 ) ) )).
fof(t3_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_tarski(B,C) => r1_tarski(k1_mathmorp(A,D,B),k1_mathmorp(A,D,C)) ) ) ) ) ) )).
fof(t3_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(C) = k3_finseq_1(D) & k1_matrix_0(C) = k1_matrix_0(D) & r2_hidden(k4_tarski(A,B),k2_matrix_0(C)) ) => k3_matrix_0(k1_numbers,k5_matrixr1(C,D),A,B) = k5_real_1(k3_matrix_0(k1_numbers,C,A,B),k3_matrix_0(k1_numbers,D,A,B)) ) ) ) ) ) )).
fof(t3_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(2,A) => r2_hidden(k2_tarski(1,2),k2_sgraph1(k2_finseq_1(A))) ) ) )).
fof(t3_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(C),A,B) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(C))) ) => ( ( r2_hidden(E,k4_finseq_1(G)) & r2_hidden(F,k2_finseq_1(k1_matrix_0(G))) ) => k1_funct_1(k10_fvsum_1(k1_matrix_0(G),C,k7_matrix_0(u1_struct_0(C),G,E),D),F) = k8_group_1(C,D,k3_matrix_0(u1_struct_0(C),G,E,F)) ) ) ) ) ) ) ) ) )).
fof(t3_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => k13_matrix_3(A,B,C) = k13_matrix_3(A,B,k4_matrix_0(u1_struct_0(B),C)) ) ) ) )).
fof(t3_matrix14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t3_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,B,A,A) & m2_finseq_1(C,k3_finseq_2(B)) ) => ( v1_matrix16(C,B) => ( r1_xxreal_0(A,k5_numbers) | v3_matrix16(k4_matrix_0(B,C),B) ) ) ) ) ) )).
fof(t3_matrix17,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ( 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)) ) ) ) ) ) ) )).
fof(t3_matrix_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => v1_matrix_0(k9_finseq_1(A)) ) )).
fof(t3_matrix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => k5_matrix_1(B,A,C,D) = k5_matrix_1(B,A,D,C) ) ) ) ) )).
fof(t3_matrix_2,axiom,( ! [A] : ( v7_ordinal1(A) => k2_matrix_2(k3_matrix_2(A)) = A ) )).
fof(t3_matrix_3,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) ) => k3_matrix_3(A,k3_matrix_3(A,B,C),D) = k3_matrix_3(A,B,k3_matrix_3(A,C,D)) ) ) ) ) ) )).
fof(t3_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(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_0(B)) ) ) )).
fof(t3_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k2_numbers)) ) => ( k1_matrix_5(A) = k1_matrix_5(B) => A = B ) ) ) )).
fof(t3_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => r1_matrix_6(A,B,C,k1_matrix_3(B,A,A)) ) ) ) )).
fof(t3_matrix_7,axiom,( k3_matrix_2(2) = k2_tarski(k10_finseq_1(1,2),k10_finseq_1(2,1)) )).
fof(t3_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( ~ r1_xxreal_0(A,k5_numbers) => ( v1_matrix_8(C,A,B) <=> v1_matrix_8(k4_matrix_0(u1_struct_0(B),C),A,B) ) ) ) ) ) )).
fof(t3_matrix_9,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t3_matrixc1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(k2_numbers)) ) => ( r2_hidden(k4_tarski(A,B),k2_matrix_0(D)) => k3_matrix_0(k2_numbers,k7_matrix_5(C,D),A,B) = k3_xcmplx_0(C,k3_matrix_0(k2_numbers,D,A,B)) ) ) ) ) ) )).
fof(t3_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t3_matrixj2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( m1_subset_1(C,u1_struct_0(B)) => ( v1_matrix_6(k2_matrixj2(B,C,A),A,B) <=> ~ ( A != k5_numbers & C = k4_struct_0(B) ) ) ) ) ) )).
fof(t3_matrixr1,axiom,( ! [A] : ( 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)) ) ) )).
fof(t3_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( r2_hidden(k4_tarski(A,B),k2_matrix_0(D)) => k3_matrix_0(k1_numbers,k7_matrixr1(C,D),A,B) = k3_xcmplx_0(C,k3_matrix_0(k1_numbers,D,A,B)) ) ) ) ) ) )).
fof(t3_matrlin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,C,k1_nat_1(B,1),A) & m2_finseq_1(D,k3_finseq_2(C)) ) => ( v1_matrix_0(k1_matrlin(C,k1_nat_1(B,1),D)) & v2_matrix_0(k1_matrlin(C,k1_nat_1(B,1),D),C,B,A) & m2_finseq_1(k1_matrlin(C,k1_nat_1(B,1),D),k3_finseq_2(C)) ) ) ) ) ) )).
fof(t3_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( k2_vectsp_5(A,B,C,D) = k1_vectsp_4(A,B) => ! [E] : ( m1_vectsp_7(E,A,C) => ! [F] : ( m1_vectsp_7(F,A,D) => m1_vectsp_7(k2_xboole_0(E,F),A,k1_vectsp_5(A,B,C,D)) ) ) ) ) ) ) ) )).
fof(t3_matroid0,axiom,( ! [A] : ( ( ~ v3_pencil_1(A) & l1_pre_topc(A) ) => ( v1_matroid0(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t3_matrprob,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => r1_xxreal_0(k5_numbers,k1_funct_1(A,B)) ) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [C] : ( v7_ordinal1(C) => ~ ( k5_numbers != C & ~ r1_xxreal_0(k3_finseq_1(A),C) & k9_nat_1(k1_numbers,B,k1_nat_1(C,1)) != k2_xcmplx_0(k9_nat_1(k1_numbers,B,C),k1_funct_1(A,k1_nat_1(C,1))) ) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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(k9_nat_1(k1_numbers,B,C),k9_nat_1(k1_numbers,B,D)) ) ) ) ) ) ) ) )).
fof(t3_matrtop1,axiom,( ! [A] : ( v1_xreal_0(A) => k1_partfun3(k9_finseq_1(A)) = k9_finseq_1(k3_square_1(A)) ) )).
fof(t3_matrtop2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( ( 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] : ( m2_finseq_1(D,u1_struct_0(k6_prvect_1(k2_vectsp_1,A))) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t3_matrtop3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v3_valued_0(B) ) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => k18_rvsum_1(k12_rvsum_1(k1_funct_7(B,C,A))) = k2_xcmplx_0(k6_xcmplx_0(k18_rvsum_1(k12_rvsum_1(B)),k1_square_1(k1_funct_1(B,C))),k1_square_1(A)) ) ) ) ) )).
fof(t3_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_rlvect_1(A,B,B) = k1_rlvect_1(A,B,2) ) ) )).
fof(t3_mboolean,axiom,( ! [A] : ! [B] : r6_pboole(A,k1_mboolean(A,k7_funcop_1(A,B)),k7_funcop_1(A,k1_zfmisc_1(B))) )).
fof(t3_mcart_1,axiom,( ! [A] : ~ ( A != k1_xboole_0 & ! [B] : ~ ( r2_hidden(B,A) & ! [C] : ! [D] : ~ ( ( r2_hidden(C,A) | r2_hidden(D,A) ) & B = k4_tarski(C,D) ) ) ) )).
fof(t3_measure1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => m1_subset_1(k1_enumset1(B,C,D),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ) )).
fof(t3_measure3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( ( r1_tarski(k1_measure2(A,B,k1_measure3(A,B,D)),E) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => r1_tarski(E,k9_nat_1(B,D,F)) ) ) => k12_supinf_2(C,E) = k12_supinf_2(C,k1_measure2(A,B,k1_measure3(A,B,D))) ) ) ) ) ) )).
fof(t3_measure4,axiom,( ! [A] : ( ~ 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))) ) )).
fof(t3_measure5,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ! [B] : ( m1_subset_1(B,k6_numbers) => ! [C] : ( m1_subset_1(C,k6_numbers) => ~ ( ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(C,A) & ! [D] : ( m1_subset_1(D,k6_numbers) => ~ ( ~ r1_xxreal_0(D,A) & ~ r1_xxreal_0(B,D) & ~ r1_xxreal_0(C,D) & r2_hidden(D,k1_numbers) ) ) ) ) ) ) )).
fof(t3_measure6,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( m1_subset_1(B,k6_numbers) => ( v6_supinf_2(A) => ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ r1_xxreal_0(B,k12_supinf_2(A,C)) ) | r1_xxreal_0(B,k19_supinf_2(A)) ) ) ) ) )).
fof(t3_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ( r1_tarski(A,B) <=> r1_tarski(k4_member_1(A),k4_member_1(B)) ) ) ) )).
fof(t3_membered,axiom,( ! [A] : ( v3_membered(A) => r1_tarski(A,k1_numbers) ) )).
fof(t3_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( l1_memstr_0(B,A) => ! [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_hidden(k4_struct_0(B),k9_xtuple_0(k6_memstr_0(A,B,C))) ) ) ) )).
fof(t3_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( k17_euclid(k4_algstr_0(k15_euclid(2),A)) = k4_xcmplx_0(k17_euclid(A)) & k18_euclid(k4_algstr_0(k15_euclid(2),A)) = k4_xcmplx_0(k18_euclid(A)) ) ) )).
fof(t3_mesfun10,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ! [C] : ( 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)) ) ) ) ) )).
fof(t3_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( 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)))) ) ) ) ) )).
fof(t3_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( 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(k4_ordinal1,k10_seqfunc(A,B,C)))) ) ) ) ) )).
fof(t3_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( r1_tarski(C,k1_relset_1(A,k4_mesfunc5(A,k1_numbers,B,k5_numbers))) & ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,C) => v2_comseq_2(k10_seqfunc(A,B,D)) ) ) ) => r2_relset_1(A,k6_numbers,k2_partfun1(A,k6_numbers,k8_mesfun7c(A,B),C),k8_mesfun7c(A,k1_mesfun9c(A,k1_numbers,B,C))) ) ) ) )).
fof(t3_mesfunc1,axiom,( r2_tarski(k4_ordinal1,k4_numbers) )).
fof(t3_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( 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] : ( v1_xreal_0(F) => ! [G] : ( m1_subset_1(G,B) => ( ( v3_valued_0(C) & v3_valued_0(D) & ! [H] : ( v1_rat_1(H) => k1_funct_1(E,H) = k9_subset_1(A,k9_subset_1(A,G,k15_mesfunc1(A,C,H)),k9_subset_1(A,G,k15_mesfunc1(A,D,k6_xcmplx_0(F,H)))) ) ) => k9_subset_1(A,G,k15_mesfunc1(A,k3_mesfunc1(A,C,D),F)) = k3_tarski(k2_relset_1(B,E)) ) ) ) ) ) ) ) ) )).
fof(t3_mesfunc3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ~ ( r1_mesfunc2(A,B,C) & ! [D] : ( ( v1_prob_2(D) & m2_finseq_1(D,B) ) => ! [E] : ( m2_finseq_1(E,k6_numbers) => ~ ( k1_relset_1(A,C) = k3_tarski(k2_relset_1(B,D)) & k4_finseq_1(D) = k4_finseq_1(E) & ! [F] : ( v7_ordinal1(F) => ( r2_hidden(F,k4_finseq_1(D)) => ! [G] : ( r2_hidden(G,k1_funct_1(D,F)) => k1_funct_1(C,G) = k12_supinf_2(E,F) ) ) ) & ! [F] : ~ ( r2_hidden(F,k1_relset_1(A,C)) & ! [G] : ( m2_finseq_1(G,k6_numbers) => ~ ( k4_finseq_1(G) = k4_finseq_1(E) & ! [H] : ( v7_ordinal1(H) => ( r2_hidden(H,k4_finseq_1(G)) => k12_supinf_2(G,H) = k4_xxreal_3(k12_supinf_2(E,H),k1_funct_1(k3_mesfunc2(k1_funct_1(D,H),A),F)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t3_mesfunc4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,k6_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,k6_numbers))) ) => ! [E] : ( ( v1_prob_2(E) & m2_finseq_1(E,B) ) => ! [F] : ( m2_finseq_1(F,k6_numbers) => ! [G] : ( m2_finseq_1(G,k6_numbers) => ( ( r1_mesfunc2(A,B,C) & ! [H] : ( r2_hidden(H,k9_xtuple_0(C)) => r1_xxreal_0(k1_supinf_2,k1_funct_1(C,H)) ) & r1_mesfunc3(A,B,C,E,F) & k4_finseq_1(G) = k4_finseq_1(E) & ! [H] : ( 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(k4_ordinal1,B,B,k6_numbers,E,D),H)) ) ) ) => ( k9_xtuple_0(C) = k1_xboole_0 | k1_mesfunc3(A,B,D,C) = k4_extreal1(G) ) ) ) ) ) ) ) ) ) )).
fof(t3_mesfunc5,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ! [B] : ( m1_subset_1(B,k6_numbers) => ! [C] : ( 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 ) ) ) ) ) )).
fof(t3_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( r2_hidden(D,k11_mesfunc1(B,C)) <=> ( r2_hidden(D,k1_relset_1(A,B)) & ? [E] : ( v1_xreal_0(E) & E = k12_supinf_2(B,D) & ~ r1_xxreal_0(C,E) ) ) ) ) ) ) )).
fof(t3_mesfunc7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ~ ( r1_mesfunc5(A,B,C,D) & r1_mesfunc5(A,B,C,E) & v6_supinf_2(k4_mesfunc1(A,E,D)) & ! [F] : ( 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,k6_numbers,D,F)),k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,E,F))) ) ) ) ) ) ) ) ) )).
fof(t3_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) & r1_funct_2(k4_ordinal1,B,k4_ordinal1,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(k4_ordinal1,B,B,k6_numbers,E,C))) ) ) ) ) ) )).
fof(t3_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( v3_mesfunc5(B) & v3_mesfunc5(C) ) => v3_mesfunc5(k3_mesfunc1(A,B,C)) ) ) ) ) )).
fof(t3_metric_1,axiom,( ! [A] : ( l1_metric_1(A) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_metric_1(A,B,C) = k1_metric_1(A,C,B) ) ) => v8_metric_1(A) ) ) )).
fof(t3_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t3_metric_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))) => ! [E] : ( m1_subset_1(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B))) => r1_xxreal_0(k2_binop_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,k1_metric_3(A,B),C,E),k3_real_1(k2_binop_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,k1_metric_3(A,B),C,D),k2_binop_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,k1_metric_3(A,B),D,E))) ) ) ) ) ) )).
fof(t3_metric_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t3_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t3_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t3_mfold_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t3_midsp_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k2_midsp_1)) => ! [B] : ( 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) ) ) )).
fof(t3_midsp_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( ~ v2_struct_0(D) & v13_algstr_0(D) & v3_rlvect_1(D) & v4_rlvect_1(D) & l2_algstr_0(D) ) => ! [E] : ( ( 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 ) ) ) ) ) ) )).
fof(t3_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m2_finseq_1(D,B) => ! [E] : ( m2_finseq_1(E,B) => ! [F] : ( m2_finseq_1(F,B) => ( ( D = k8_finseq_1(B,k8_finseq_1(B,E,k12_finseq_1(B,C)),F) & A = k1_nat_1(k3_finseq_1(E),1) ) => ( ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( ( 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] : ( m1_subset_1(G,k4_ordinal1) => ( ( r1_xxreal_0(k1_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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t3_mmlquer2,axiom,( ! [A] : ! [B] : k7_relset_1(A,A,k6_partfun1(A),B) = k3_xboole_0(A,B) )).
fof(t3_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t3_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ 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] : ( l1_mod_2(D,A) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t3_mod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t3_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l6_algstr_0(A) ) => k5_struct_0(A) = k5_struct_0(k2_mod_4(A)) ) & ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_mod_4(A))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k2_mod_4(A))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k2_mod_4(A))) => ! [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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t3_modal_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(B,C) & r2_hidden(k14_trees_3(C),A) ) => r2_hidden(k14_trees_3(B),A) ) ) ) ) )).
fof(t3_modcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( v2_mod_2(D,A) & m1_mod_2(D,A,B,C) ) => m5_modcat_1(k1_tarski(D),A,B,C) ) ) ) ) )).
fof(t3_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => r1_xxreal_0(1,k3_finseq_1(A)) ) )).
fof(t3_moebius1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( r1_int_2(A,B) & r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(B,k5_numbers) ) ) ) )).
fof(t3_monoid_0,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t3_monoid_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t3_morph_01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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 ) ) ) ) ) ) )).
fof(t3_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v3_msualg_1(B,A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m3_pboole(C,u1_struct_0(A),u3_msualg_1(A,B)) => ( m1_msafree(C,A,B) <=> k12_msualg_2(A,B,C) = B ) ) ) ) )).
fof(t3_msafree1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( ( 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] : ( 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] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(t3_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => r1_tarski(k1_msafree2(A),k3_msafree2(A)) ) )).
fof(t3_msafree3,axiom,( ! [A] : ! [B] : ( ( ~ v11_struct_0(B) & v1_instalg1(B) & l1_msualg_1(B) ) => ! [C] : ( ( 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] : ( ( v1_relat_1(D) & v4_relat_1(D,u1_struct_0(B)) & v1_funct_1(D) & v1_partfun1(D,u1_struct_0(B)) ) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t3_msafree4,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v6_trees_3(B) ) => k3_trees_9(k4_trees_4(A,B)) = k2_xboole_0(k1_tarski(k4_trees_4(A,B)),k9_trees_9(k10_xtuple_0(B))) ) )).
fof(t3_msalimit,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_msalimit(C,A,B) => ! [D] : ( m2_msalimit(D,A,B,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t3_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( l3_msualg_1(C,A) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ~ ( r2_hidden(F,k1_funct_1(u3_msualg_1(A,C),E)) & k1_funct_1(D,k1_xboole_0) = k4_tarski(F,E) ) ) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)))) ) ) ) ) ) )).
fof(t3_msinst_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t3_msscyc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t3_msscyc_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_struct_0(A) & l1_msualg_1(A) ) => ( v5_msafree2(A) <=> v3_msscyc_1(k4_msscyc_2(A)) ) ) )).
fof(t3_mssubfam,axiom,( ! [A] : ! [B] : ( 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 ) ) )).
fof(t3_mssublat,axiom,( ! [A] : k3_funct_2(k4_ordinal1,k3_finseq_2(k1_tarski(A)),k7_finseq_2(A),2) = k10_finseq_1(A,A) )).
fof(t3_msualg_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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) ) ) )).
fof(t3_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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] : ( m1_subset_1(D,u4_struct_0(A)) => k3_msualg_2(A,B,D,C) = k5_msualg_1(A,D,B) ) ) ) ) ) ) )).
fof(t3_msualg_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,C) => k8_pboole(k2_msualg_3(A,B),D) = D ) ) ) )).
fof(t3_msualg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t3_msualg_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_msualg_4(C,A,B) & m1_msualg_4(C,A,B,B) ) => r8_pboole(A,k3_msualg_5(A,B,C),C) ) ) ) )).
fof(t3_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( l3_msualg_1(C,A) => ( k3_msualg_1(A,B,C) != k1_xboole_0 <=> ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( 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 ) ) ) ) ) ) )).
fof(t3_msualg_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) )).
fof(t3_msualg_8,axiom,( ! [A] : k5_lattices(k2_msualg_5(A)) = k6_partfun1(A) )).
fof(t3_msualg_9,axiom,( ! [A] : r1_tarski(k8_eqrel_1(A,k1_eqrel_1(A)),k1_tarski(A)) )).
fof(t3_msuhom_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( v1_funcop_1(A) => v1_funcop_1(k5_relat_1(A,B)) ) ) )).
fof(t3_multop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,B) => ! [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) ) ) ) ) ) ) ) )).
fof(t3_mycielsk,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ~ ( ~ 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)) ) )).
fof(t3_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t3_nagata_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t3_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( k5_numbers != A & r1_xxreal_0(A,k5_numbers) ) ) )).
fof(t3_nat_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => k3_nat_d(A,A) = 1 ) )).
fof(t3_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( A != k5_numbers => r1_nat_d(B,k1_newton(B,A)) ) ) ) )).
fof(t3_nat_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(A,1) & r1_xxreal_0(k1_newton(A,B),B) ) ) ) )).
fof(t3_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( B = k1_newton(2,A) => ( v1_abian(C) | r1_int_2(B,C) ) ) ) ) ) )).
fof(t3_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_nat_d(B,A) <=> A = k2_nat_1(B,k3_nat_d(A,B)) ) ) ) )).
fof(t3_nat_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_nat_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_nat_lat)) => ( r1_lattices(k3_nat_lat,A,B) => r1_nat_d(A,B) ) ) ) )).
fof(t3_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => m3_cat_2(k3_cat_1(B,k4_cat_1(A,B)),A) ) ) )).
fof(t3_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_ncfcont1(C,A,B) => r2_hidden(B,C) ) ) ) )).
fof(t3_ncfcont2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t3_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_nfcont_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(a_3_0_ndiff_1(A,C,D),B) ) ) ) ) ) ) ) )).
fof(t3_ndiff_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_nfcont_1(E,A,D) => ( r1_tarski(E,k1_relset_1(u1_struct_0(A),C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ( ! [H] : ( ( v9_ordinal1(H) & v1_funct_1(H) & v1_funct_2(H,k4_ordinal1,k1_numbers) & v1_fdiff_1(H,k5_numbers) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [I] : ( ( v1_funct_1(I) & v3_funct_1(I) & v1_funct_2(I,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),k2_normsp_1(A,k2_ndiff_1(A,F,H),I),C),k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),I,C)),k37_valued_1(k4_ordinal1,k1_numbers,H)),B) & G = k6_normsp_1(B,k1_ndiff_1(B,k3_normsp_1(B,k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),k2_normsp_1(A,k2_ndiff_1(A,F,H),I),C),k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),I,C)),k37_valued_1(k4_ordinal1,k1_numbers,H))) ) ) ) ) <=> ! [H] : ( v1_xreal_0(H) => ~ ( ~ r1_xxreal_0(H,k5_numbers) & ! [I] : ( v1_xreal_0(I) => ~ ( ~ r1_xxreal_0(I,k5_numbers) & ! [J] : ( v1_xreal_0(J) => ~ ( ~ r1_xxreal_0(I,k9_complex1(J)) & J != k5_numbers & r2_hidden(k3_rlvect_1(A,k1_rlvect_1(A,F,J),D),E) & r1_xxreal_0(H,k2_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)),k5_xcmplx_0(J)),G))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t3_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(t3_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [D] : ( v1_xreal_0(D) => ( C = B => k1_ndiff_4(A,B,D) = k1_ndiff_3(k4_real_ns1(A),C,D) ) ) ) ) ) )).
fof(t3_ndiff_5,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( ( 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)))) ) ) ) ) ) )).
fof(t3_neckla_2,axiom,( ! [A] : ( r2_hidden(A,k13_classes2) => v1_finset_1(A) ) )).
fof(t3_neckla_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : 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))) )).
fof(t3_necklace,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => r2_hidden(k5_numbers,A) ) )).
fof(t3_net_1,axiom,( ! [A] : ! [B] : ( 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)) ) ) ) )).
fof(t3_newton,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_1(B,k1_numbers) => k4_finseq_1(B) = k4_finseq_1(k10_rvsum_1(B,A)) ) ) )).
fof(t3_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_numbers) => m1_nfcont_1(a_3_0_nfcont_1(A,B,C),A,B) ) ) ) ) )).
fof(t3_nfcont_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)))) ) => ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t3_nfcont_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v1_xreal_0(C) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k4_vfunct_1(k4_ordinal1,A,B,C),k5_normsp_1(A,B,C)) ) ) ) )).
fof(t3_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ~ ( r2_hidden(F,k1_relset_1(k1_numbers,C)) & ~ r1_xxreal_0(E,k9_complex1(k6_xcmplx_0(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)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t3_normform,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_finsub_1(B) ) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(A,B)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t3_normsp_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k2_normsp_0(A,k5_algstr_0(A,B,C)),k2_xcmplx_0(k2_normsp_0(A,B),k2_normsp_0(A,C))) ) ) ) )).
fof(t3_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_normsp_2(A))) => ! [C] : ( v1_xreal_0(C) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & D = B & k9_metric_1(k2_normsp_2(A),B,C) = a_3_1_normsp_2(A,C,D) ) ) ) ) )).
fof(t3_ntalgo_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r1_xxreal_0(A,k5_numbers) => r1_xxreal_0(k5_int_1(B,A),k5_numbers) ) ) ) )).
fof(t3_numbers,axiom,( r2_xboole_0(k3_numbers,k2_numbers) )).
fof(t3_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t3_openlatt,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(t3_oposet_1,axiom,( v3_orders_2(k1_oposet_1) )).
fof(t3_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_oppcat_1(A))) => k3_oppcat_1(A,k4_oppcat_1(A,B)) = B ) ) )).
fof(t3_ordeq_01,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & r1_xxreal_0(C,k2_normsp_0(A,B)) ) ) => B = k4_struct_0(A) ) ) ) )).
fof(t3_orders_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(t3_orders_2,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t3_orders_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t3_orders_4,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t3_ordinal1,axiom,( ! [A] : ! [B] : ( k1_ordinal1(A) = k1_ordinal1(B) => A = B ) )).
fof(t3_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => r1_tarski(k1_ordinal1(A),k9_setfam_1(A)) ) )).
fof(t3_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r2_hidden(A,B) <=> r2_hidden(k1_ordinal1(A),k1_ordinal1(B)) ) ) ) )).
fof(t3_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_ordinal2(B) ) => ! [C] : ( v3_ordinal1(C) => ( r1_ordinal2(C,B) => r1_ordinal2(C,k1_ordinal4(A,B)) ) ) ) ) )).
fof(t3_ordinal5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(t3_ordinal6,axiom,( ! [A] : ( v1_ordinal6(A) => r1_tarski(A,k3_ordinal2(A)) ) )).
fof(t3_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t3_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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)) ) ) ) )).
fof(t3_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_osalg_1(A) ) => ( v6_osalg_1(A) <=> ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( r1_osalg_1(A,B,C) => B = C ) ) ) ) ) )).
fof(t3_osalg_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t3_osalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t3_osalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t3_papdesaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_analoaf(A))) <=> m1_subset_1(B,u1_struct_0(A)) ) ) )).
fof(t3_pardepap,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v11_aff_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t3_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( 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))) ) ) )).
fof(t3_parsp_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A))) => ! [E] : ( m1_subset_1(E,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) => ! [F] : ( m1_subset_1(F,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(t3_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ~ ( r2_hidden(A,k10_xtuple_0(D)) & ! [E] : ( m1_subset_1(E,B) => ~ ( r2_hidden(E,k1_relset_1(B,D)) & A = k1_funct_1(D,E) ) ) ) ) )).
fof(t3_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ( r2_relset_1(A,C,F,k1_partfun1(A,B,B,C,D,E)) <=> ( ! [G] : ( m1_subset_1(G,A) => ( r2_hidden(G,k1_relset_1(A,F)) <=> ( r2_hidden(G,k1_relset_1(A,D)) & r2_hidden(k7_partfun1(B,D,G),k1_relset_1(B,E)) ) ) ) & ! [G] : ( m1_subset_1(G,A) => ( r2_hidden(G,k1_relset_1(A,F)) => k7_partfun1(C,F,G) = k7_partfun1(C,E,k7_partfun1(B,D,G)) ) ) ) ) ) ) ) ) ) ) )).
fof(t3_partfun3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t3_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ( ( r1_setfam_1(C,B) & r1_setfam_1(B,C) ) => r1_tarski(C,B) ) ) ) ) )).
fof(t3_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => r1_relset_1(A,A,B,k1_eqrel_1(A)) ) ) )).
fof(t3_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_diraf(A,E,C,E,D) & E != C & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_diraf(A,E,B,E,F) & r2_diraf(A,B,C,D,F) ) ) ) ) ) ) ) ) )).
fof(t3_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( ! [D] : ( r2_hidden(D,A) => k1_funct_1(B,D) = k1_funct_1(C,D) ) => B = C ) ) ) )).
fof(t3_pcomps_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( m1_setfam_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(C,D) & r2_hidden(D,B) ) ) ) ) ) )).
fof(t3_pcomps_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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] : ( 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) ) ) ) ) ) )).
fof(t3_pcs_0,axiom,( ! [A] : ( l1_pcs_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t3_pdiff_1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(1))) => ! [C] : ( v1_xreal_0(C) => ( B = k1_funct_1(A,C) => k2_normsp_0(k4_real_ns1(1),B) = k9_complex1(C) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(1))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(1))) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( B = k1_funct_1(A,D) & C = k1_funct_1(A,E) ) => k3_rlvect_1(k4_real_ns1(1),B,C) = k1_funct_1(A,k2_xcmplx_0(D,E)) ) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(1))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( B = k1_funct_1(A,C) => k1_rlvect_1(k4_real_ns1(1),B,D) = k1_funct_1(A,k3_xcmplx_0(D,C)) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(1))) => ! [C] : ( v1_xreal_0(C) => ( B = k1_funct_1(A,C) => k4_algstr_0(k4_real_ns1(1),B) = k1_funct_1(A,k4_xcmplx_0(C)) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(1))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(1))) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( B = k1_funct_1(A,D) & C = k1_funct_1(A,E) ) => k5_algstr_0(k4_real_ns1(1),B,C) = k1_funct_1(A,k6_xcmplx_0(D,E)) ) ) ) ) ) ) ) ) )).
fof(t3_pdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(2)) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t3_pdiff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(2)) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t3_pdiff_4,axiom,( 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] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k1_funct_1(k1_pdiff_1(3,3),k11_finseq_1(A,B,C)) = C ) ) ) )).
fof(t3_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t3_pdiff_6,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(B),k1_euclid(A)))) ) => ! [D] : ( ( 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] : ( m2_finseq_2(E,k1_numbers,k1_euclid(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t3_pdiff_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k2_rfinseq(k1_numbers,A,k5_euclid(B)) = k5_euclid(k7_nat_d(B,A)) ) ) )).
fof(t3_pdiff_8,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(A))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,A) ) => r1_xxreal_0(k2_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)),k2_normsp_0(k4_real_ns1(A),B)) ) ) ) ) )).
fof(t3_pdiff_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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) ) ) )).
fof(t3_pencil_1,axiom,( ! [A] : ( r1_ordinal1(2,k1_card_1(A)) => ! [B] : ? [C] : ( r2_hidden(C,A) & B != C ) ) )).
fof(t3_pencil_2,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(D,k4_finseq_1(B)) & k3_finseq_1(k1_pencil_2(A,B,C,D)) = k5_numbers ) => ( C = 1 & D = k3_finseq_1(B) ) ) ) ) ) )).
fof(t3_pencil_3,axiom,( ! [A] : ( ( ~ v3_pencil_1(A) & v6_pencil_1(A) & l1_pre_topc(A) ) => ( v10_pencil_1(A) => v8_pencil_1(A) ) ) )).
fof(t3_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,k2_vectsp_4(A,B)) => m1_vectsp_4(C,A,B) ) ) ) )).
fof(t3_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_nat_d(A,k3_xcmplx_0(C,B)) & r1_int_2(C,A) ) => r1_nat_d(A,B) ) ) ) ) )).
fof(t3_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k7_petri(A,B) = a_2_3_petri(A,B) ) ) )).
fof(t3_petri_2,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,C,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,A))) ) => ! [E] : ! [F] : ( ( 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) ) ) ) ) ) )).
fof(t3_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => r1_pnproc_1(A,k2_pnproc_1(A,B,k1_pnproc_1(A)),B) ) )).
fof(t3_polyalg1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,A) ) => k2_rfinseq(A,1,B) = k1_polynom3(A,1,B) ) ) )).
fof(t3_polyeq_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( A != k5_numbers => ! [B] : ( v1_xcmplx_0(B) => k1_polyeq_1(k5_numbers,A,B) != k5_numbers ) ) ) )).
fof(t3_polyeq_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( E = k2_xcmplx_0(D,k7_xcmplx_0(1,D)) & k1_polyeq_2(A,B,C,B,A,D) = k5_numbers ) => ( A = k5_numbers | r1_xxreal_0(k2_xcmplx_0(k6_xcmplx_0(k1_square_1(B),k3_xcmplx_0(k3_xcmplx_0(4,A),C)),k3_xcmplx_0(8,k1_square_1(A))),k5_numbers) | ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( ( F = k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k2_xcmplx_0(k6_xcmplx_0(k1_square_1(B),k3_xcmplx_0(k3_xcmplx_0(4,A),C)),k3_xcmplx_0(8,k1_square_1(A))))),k3_xcmplx_0(2,A)) & G = k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k2_xcmplx_0(k6_xcmplx_0(k1_square_1(B),k3_xcmplx_0(k3_xcmplx_0(4,A),C)),k3_xcmplx_0(8,k1_square_1(A))))),k3_xcmplx_0(2,A)) ) => ( D != k5_numbers & ~ ( D != k7_xcmplx_0(k2_xcmplx_0(F,k3_square_1(k1_quin_1(1,k4_xcmplx_0(F),1))),2) & D != k7_xcmplx_0(k2_xcmplx_0(G,k3_square_1(k1_quin_1(1,k4_xcmplx_0(G),1))),2) & D != k7_xcmplx_0(k6_xcmplx_0(F,k3_square_1(k1_quin_1(1,k4_xcmplx_0(F),1))),2) & D != k7_xcmplx_0(k6_xcmplx_0(G,k3_square_1(k1_quin_1(1,k4_xcmplx_0(G),1))),2) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t3_polyeq_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( ! [D] : ( v1_xcmplx_0(D) => k2_polyeq_3(k5_numbers,A,B,D) = k5_numbers ) => ( A = k5_numbers | C = k4_xcmplx_0(k7_xcmplx_0(B,A)) ) ) ) ) ) )).
fof(t3_polyeq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(k5_numbers,k7_xcmplx_0(C,A)) & ~ ( ~ r1_xxreal_0(k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A)),k5_numbers) & ~ r1_xxreal_0(k5_numbers,k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A))) ) & ~ ( ~ r1_xxreal_0(k5_numbers,k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k3_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),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A)),k5_numbers) ) ) ) ) ) )).
fof(t3_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(A,A),A),A) = k1_newton(A,4) ) )).
fof(t3_polyform,axiom,( ~ v1_abian(1) )).
fof(t3_polynom1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( 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)) ) ) )).
fof(t3_polynom2,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(A)) => ( ? [C] : ( m1_subset_1(C,k4_ordinal1) & 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) ) ) ) )).
fof(t3_polynom3,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => k18_rvsum_1(A) = k18_rvsum_1(k4_finseq_5(k1_numbers,A)) ) )).
fof(t3_polynom4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => k1_algseq_1(A,k9_polynom3(A)) = k5_numbers ) )).
fof(t3_polynom5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(1,C) & ~ r1_xxreal_0(B,k3_xcmplx_0(C,A)) ) ) => r1_xxreal_0(B,k5_numbers) ) ) ) )).
fof(t3_polynom6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( m2_subset_1(C,k14_pre_poly(A),k15_pre_poly(A)) => ! [D] : ( m2_subset_1(D,k14_pre_poly(B),k15_pre_poly(B)) => ( B = k1_xboole_0 => k1_polynom6(A,B,C,D) = C ) ) ) ) ) )).
fof(t3_polynom7,axiom,( ! [A] : ( ( 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) ) )).
fof(t3_polynom8,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t3_polyred,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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),k5_polynom1(A,B,k5_vfunct_1(k15_pre_poly(A),B,C),C),k8_polynom1(A,B)) & r2_funct_2(k15_pre_poly(A),u1_struct_0(B),k5_polynom1(A,B,C,k5_vfunct_1(k15_pre_poly(A),B,C)),k8_polynom1(A,B)) ) ) ) )).
fof(t3_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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))) ) ) ) )).
fof(t3_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( r1_xxreal_0(k5_numbers,A) | v1_abian(B) ) => r1_xxreal_0(k5_numbers,k1_newton(A,B)) ) ) ) )).
fof(t3_pralg_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => v2_funct_1(k6_pralg_1(A,B)) ) ) )).
fof(t3_pralg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t3_pralg_3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m2_subset_1(D,k1_zfmisc_1(B),k8_eqrel_1(B,C)) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(B),k8_eqrel_1(B,C)) => ( ( r2_hidden(A,D) & r2_hidden(A,E) ) => D = E ) ) ) ) ) )).
fof(t3_pre_circ,axiom,( ! [A] : k2_funct_5(k7_funcop_1(A,k1_xboole_0)) = k1_xboole_0 )).
fof(t3_pre_ff,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & k4_int_1(A,B) = k5_numbers & r1_xxreal_0(B,A) ) ) ) )).
fof(t3_pre_poly,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k3_finseq_2(A)) => ! [C] : ( 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)) ) ) )).
fof(t3_pre_topc,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( 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 ) ) )).
fof(t3_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_prelamb(A) ) => ! [B] : ( m1_prelamb(B,A) => ! [C] : ( 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)),k4_ordinal1),B,C)) = k5_numbers & ! [D] : ( 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)),k4_ordinal1),B,C)) != k6_prelamb(A,k12_finseq_1(u1_struct_0(A),D),D) ) ) ) ) ) )).
fof(t3_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( B = k1_prepower(A) <=> ( k1_funct_1(B,k5_numbers) = 1 & ! [C] : ( v7_ordinal1(C) => k1_funct_1(B,k1_nat_1(C,1)) = k3_xcmplx_0(k1_funct_1(B,C),A) ) ) ) ) ) )).
fof(t3_prgcor_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r1_xxreal_0(B,k4_nat_d(A,k2_nat_1(2,B))) => ( r1_xxreal_0(B,k5_numbers) | k3_nat_d(A,B) = k1_nat_1(k2_nat_1(k3_nat_d(A,k2_nat_1(2,B)),2),1) ) ) ) ) )).
fof(t3_prgcor_2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k1_numbers) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ( ( k1_funct_1(B,k5_numbers) = k5_numbers & ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(k3_finseq_1(A),C) => k1_funct_1(B,k1_nat_1(C,1)) = k2_xcmplx_0(k1_funct_1(B,C),k1_funct_1(A,k1_nat_1(C,1))) ) ) ) => k18_rvsum_1(A) = k1_funct_1(B,k3_finseq_1(A)) ) ) ) )).
fof(t3_prob_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ! [D] : ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k2_xboole_0(C,D),B) ) ) )).
fof(t3_prob_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ? [C] : ( v7_ordinal1(C) & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => k1_funct_1(B,D) = A ) ) ) => ( v2_comseq_2(B) & k1_seq_2(B) = A ) ) ) ) )).
fof(t3_prob_4,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_xboole_0(B,C) => v1_prob_2(k12_funct_7(B,C,k1_xboole_0)) ) ) ) )).
fof(t3_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t3_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( ~ r1_collsp(A,B,C,E) & r1_collsp(A,B,C,D) & B != D & r1_collsp(A,B,D,E) ) ) ) ) ) ) )).
fof(t3_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ( v1_projpl_1(A) <=> ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t3_projred1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t3_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( 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] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t3_prvect_1,axiom,( ! [A] : ( ( ~ 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) ) ) ) )).
fof(t3_prvect_2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(B,k4_finseq_1(A)) => k1_funct_1(A,B) = k5_numbers ) ) => k18_rvsum_1(A) = k5_numbers ) ) )).
fof(t3_prvect_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ~ ( k9_xtuple_0(C) = k7_domain_1(k4_ordinal1,1,2) & k1_funct_1(C,1) = A & k1_funct_1(C,2) = B & ! [D] : ( ( 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] : ! [F] : ( ( r2_hidden(E,A) & r2_hidden(F,B) ) => k1_binop_1(D,E,F) = k10_finseq_1(E,F) ) ) ) ) ) ) ) )).
fof(t3_pscomp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => r1_xxreal_0(A,k3_funct_2(u1_struct_0(B),k1_numbers,C,D)) ) & ! [D] : ( v1_xreal_0(D) => ( ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => r1_xxreal_0(D,k3_funct_2(u1_struct_0(B),k1_numbers,C,E)) ) => r1_xxreal_0(D,A) ) ) ) => A = k1_pscomp_1(B,C) ) ) ) ) )).
fof(t3_pythtrip,axiom,( ! [A] : ( v1_int_1(A) => ( v1_abian(A) => k4_nat_d(k1_pepin(A),4) = k5_numbers ) ) )).
fof(t3_pzfmisc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t3_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ( r1_tarski(k4_ordinal1,k1_qc_lang1(A)) & r2_hidden(k5_numbers,k1_qc_lang1(A)) ) ) )).
fof(t3_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t3_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => k24_qc_lang1(A,k12_qc_lang1(A)) = k1_xboole_0 ) )).
fof(t3_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t3_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_qc_trans(B,A) & m1_qc_lang1(B) ) => r1_tarski(k6_qc_lang1(A),k6_qc_lang1(B)) ) ) )).
fof(t3_qmax_1,axiom,( ! [A] : ( ( v2_qmax_1(A) & l1_qmax_1(A) ) => ! [B] : ( m1_subset_1(B,k5_qmax_1(A)) => r3_qmax_1(A,B,B) ) ) )).
fof(t3_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_quantal1(B,A) & v1_xboole_0(B) ) ) ) )).
fof(t3_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => k22_quaterni(A,k1_quatern2) = A ) )).
fof(t3_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ( v1_xreal_0(B) => k25_quaterni(B,A) = k6_quaterni(k6_xcmplx_0(k13_quaterni(B),k13_quaterni(A)),k4_xcmplx_0(k14_quaterni(A)),k4_xcmplx_0(k15_quaterni(A)),k4_xcmplx_0(k16_quaterni(A))) ) ) ) )).
fof(t3_quaterni,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( r2_zfmisc_1(E,F,G,H) => ( k1_funct_1(k2_quaterni(E,F,G,H,A,B,C,D),E) = A & k1_funct_1(k2_quaterni(E,F,G,H,A,B,C,D),F) = B & k1_funct_1(k2_quaterni(E,F,G,H,A,B,C,D),G) = C & k1_funct_1(k2_quaterni(E,F,G,H,A,B,C,D),H) = D ) ) )).
fof(t3_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(k5_numbers,k1_quin_1(B,C,D)) & r1_xxreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(A)),k3_xcmplx_0(C,A)),D),k5_numbers) ) ) ) ) ) )).
fof(t3_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A)) => ! [C] : ( m2_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t3_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( B != k5_numbers => k4_nat_d(k4_nat_d(A,k3_xcmplx_0(B,C)),C) = k4_nat_d(A,C) ) ) ) ) )).
fof(t3_radix_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(C,k5_numbers) => k5_int_1(k3_xcmplx_0(A,B),C) = k5_int_1(k3_xcmplx_0(A,k5_int_1(B,C)),C) ) ) ) ) )).
fof(t3_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => r1_tarski(k1_radix_3(A),k1_radix_3(k2_xcmplx_0(A,1))) ) )).
fof(t3_radix_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(2,C) => k7_radix_3(k2_xcmplx_0(A,1),C,k2_xcmplx_0(A,1),k10_radix_3(A,C,k10_radix_1(C,A,B))) = k5_radix_3(k4_radix_1(A,C,A,k10_radix_1(C,A,B)),C) ) ) ) ) )).
fof(t3_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(2,A) => r1_xxreal_0(4,k1_radix_1(A)) ) ) )).
fof(t3_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(2,B) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t3_ramsey_1,axiom,( ! [A] : ! [B] : ~ ( ~ v1_finset_1(A) & v1_finset_1(k2_xboole_0(A,B)) ) )).
fof(t3_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( v1_xreal_0(F) => ( ( r1_mesfunc5(A,B,C,D) & r1_tarski(E,k1_relset_1(A,D)) & ! [G] : ( m1_subset_1(G,A) => ( r2_hidden(G,E) => r1_xxreal_0(k12_supinf_2(D,G),F) ) ) ) => ( r1_xxreal_0(k1_xxreal_0,k3_funct_2(B,k6_numbers,C,E)) | r1_xxreal_0(k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,E)),k4_xxreal_3(F,k3_funct_2(B,k6_numbers,C,E))) ) ) ) ) ) ) ) ) )).
fof(t3_random_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k8_funcop_1(k4_ordinal1,A,1) = k3_mesfunc2(A,A) ) )).
fof(t3_random_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ! [F] : ( m1_subset_1(F,k4_ordinal1) => k1_prob_4(A,k9_setfam_1(A),E,F) = k8_relset_1(A,B,C,k1_prob_4(B,k9_setfam_1(B),D,F)) ) => k8_relset_1(A,B,C,k3_prob_1(B,D)) = k3_prob_1(A,E) ) ) ) ) ) ) )).
fof(t3_ranknull,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ~ ( ~ r1_xboole_0(B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,B) & r2_hidden(D,C) ) ) ) & ~ ( ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r2_hidden(D,B) & r2_hidden(D,C) ) & r1_xboole_0(B,C) ) ) ) ) ) )).
fof(t3_rat_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => v1_rat_1(k7_xcmplx_0(A,B)) ) ) )).
fof(t3_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( 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))) ) ) ) ) )).
fof(t3_rcomp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r2_hidden(B,k2_rcomp_1(C,A)) <=> ~ r1_xxreal_0(k6_xcmplx_0(A,C),k9_complex1(k6_xcmplx_0(k2_xcmplx_0(C,A),k3_xcmplx_0(2,B)))) ) ) ) ) )).
fof(t3_rcomp_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => k5_measure6(k4_subset_1(k1_numbers,A,B)) = k4_subset_1(k1_numbers,k5_measure6(A),k5_measure6(B)) ) ) )).
fof(t3_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(A,B) & ~ v3_xxreal_0(A) & v3_xxreal_0(B) ) ) ) )).
fof(t3_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k1_int_1(k7_xcmplx_0(B,A)) = k3_nat_d(B,A) ) ) )).
fof(t3_real_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_real_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_real_lat)) => ! [C] : ( 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) ) ) ) ) )).
fof(t3_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(A))) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( v1_xreal_0(D) => ( B = C => k1_rlvect_1(k4_real_ns1(A),B,D) = k9_euclid(A,C,D) ) ) ) ) ) )).
fof(t3_realset1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ? [C] : ( 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] : ( r2_hidden(D,k2_zfmisc_1(B,B)) => r2_hidden(k1_funct_1(C,D),B) ) ) ) )).
fof(t3_realset2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( 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) ) ) ) )).
fof(t3_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(A),k8_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t3_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( 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 ) ) )).
fof(t3_recdef_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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)) ) )).
fof(t3_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( C = k1_tarski(k4_tarski(A,B)) => ( k9_xtuple_0(C) = k1_tarski(A) & k10_xtuple_0(C) = k1_tarski(B) ) ) ) )).
fof(t3_relat_2,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( r4_relat_2(B,A) <=> r5_relat_2(k4_xboole_0(B,k4_relat_1(A)),A) ) ) )).
fof(t3_reloc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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) ) ) ) )).
fof(t3_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( r2_hidden(C,A) & r2_hidden(D,B) ) => m1_subset_1(k1_tarski(k4_tarski(C,D)),k1_zfmisc_1(k2_zfmisc_1(A,B))) ) )).
fof(t3_relset_2,axiom,( ! [A] : ! [B] : k10_eqrel_1(k2_xboole_0(A,B)) = k2_xboole_0(k10_eqrel_1(A),k10_eqrel_1(B)) )).
fof(t3_revrot_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,A) ) => r2_hidden(k7_partfun1(A,B,k3_finseq_1(B)),k10_xtuple_0(B)) ) ) )).
fof(t3_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ! [D] : 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) ) ) )).
fof(t3_rewrite2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( m1_rewrite1(C,B) => ( r1_xxreal_0(1,A) => m1_rewrite1(k16_finseq_1(A,C),B) ) ) ) ) )).
fof(t3_rewrite3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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 ) ) ) ) )).
fof(t3_rfinseq,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t3_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( v1_xreal_0(B) => ( A = k9_finseq_1(B) => ( k1_rfinseq2(A) = 1 & k3_rfinseq2(A) = B ) ) ) ) )).
fof(t3_rfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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) = k5_numbers ) ) ) ) )).
fof(t3_rfunct_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_ordinal1) & v5_valued_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => r2_relset_1(k4_ordinal1,k1_numbers,k2_valued_0(k1_numbers,C,k26_valued_1(k4_ordinal1,k1_numbers,B,A)),k26_valued_1(k4_ordinal1,k1_numbers,k2_valued_0(k1_numbers,C,B),A)) ) ) ) )).
fof(t3_rfunct_3,axiom,( ! [A] : ( v1_xreal_0(A) => k3_xcmplx_0(2,k1_rfunct_3(A)) = k2_xcmplx_0(A,k9_complex1(A)) ) )).
fof(t3_rfunct_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ( ( k18_rvsum_1(B) = k5_numbers & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k4_finseq_1(B)) => r1_xxreal_0(k5_numbers,k1_funct_1(B,C)) ) ) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k4_finseq_1(B)) => k1_funct_1(B,C) = k5_numbers ) ) ) ) ) )).
fof(t3_rinfsup1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,k1_numbers,B))) ) ) ) )).
fof(t3_rinfsup2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( ( ~ 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) = k3_seq_4(B) ) ) ) ) )).
fof(t3_ring_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t3_ringcat1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t3_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t3_rlaffin3,axiom,( ! [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) ) => ( v1_rlvect_5(A) <=> v1_rlvect_5(k2_rlsub_1(A)) ) ) )).
fof(t3_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_rlsub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t3_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( r1_struct_0(k2_rlsub_2(A,B,C),D) <=> ( r1_struct_0(B,D) & r1_struct_0(C,D) ) ) ) ) ) )).
fof(t3_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t3_rlvect_1,axiom,( ! [A] : ( ( v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => v6_algstr_0(A) ) )).
fof(t3_rlvect_2,axiom,( ! [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) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ( ( k3_finseq_1(C) = k3_finseq_1(D) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k1_relset_1(k4_ordinal1,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) ) ) ) ) ) )).
fof(t3_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => k6_rlvect_2(A,k9_rlvect_2(A,B)) = k4_algstr_0(A,k6_rlvect_2(A,B)) ) ) )).
fof(t3_rlvect_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => k4_algstr_0(B,k1_rlvect_1(B,C,A)) = k1_rlvect_1(B,C,k4_xcmplx_0(A)) ) ) ) )).
fof(t3_rlvect_5,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k3_rlvect_2(A,B)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & C = D & k3_funct_2(u1_struct_0(A),k1_numbers,B,D) != k5_numbers ) ) ) ) ) )).
fof(t3_rlvect_x,axiom,( ! [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) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_numbers) => ( r2_relset_1(k4_ordinal1,u1_struct_0(A),C,k4_vfunct_1(k4_ordinal1,A,B,D)) => k4_rlvect_1(A,C) = k1_rlvect_1(A,k4_rlvect_1(A,B),D) ) ) ) ) ) )).
fof(t3_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v1_rmod_2(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t3_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( r1_struct_0(k2_rmod_3(A,B,C,D),E) <=> ( r1_struct_0(C,E) & r1_struct_0(D,E) ) ) ) ) ) ) )).
fof(t3_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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),E,D))) = k3_rlvect_1(B,k5_vectsp_2(A,B,C,E),k5_vectsp_2(A,B,C,D)) ) ) ) ) ) )).
fof(t3_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_robbins1(A,k3_robbins1(A,B)) = B ) ) )).
fof(t3_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( 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) ) ) )).
fof(t3_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( ( v2_robbins3(A) & v1_robbins3(A) & v3_robbins3(A) & v9_lattices(A) ) => v8_lattices(A) ) ) )).
fof(t3_robbins4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = k2_lattices(A,B,k1_lattices(A,B,C)) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = k1_lattices(A,B,k2_lattices(A,C,k3_robbins1(A,C))) ) ) ) ) ) )).
fof(t3_rolle,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,A) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,k2_rcomp_1(A,B)) & k1_fdiff_1(C,D) = k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(C,B),k1_funct_1(C,A)),k6_xcmplx_0(B,A)) ) ) ) ) ) ) ) )).
fof(t3_roughs_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t3_rpr_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( ( 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 ) ) ) ) ) ) )).
fof(t3_rsspace,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace))) => k1_rlvect_1(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace),B,A) = k26_valued_1(k4_ordinal1,k1_numbers,k2_rsspace(B),A) ) ) )).
fof(t3_rsspace2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,A,B)) ) => ( ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,k3_series_1(A),B)) ) & ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,k3_series_1(A),B)) ) & ( v1_series_1(A) => ( ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_nat_1(k1_numbers,k3_series_1(A),B),k4_series_1(A)) ) & ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k4_series_1(A)) ) ) ) ) ) ) )).
fof(t3_rsspace3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => k1_funct_1(A,B) = k5_numbers ) => ( v2_series_1(A) & k4_series_1(k56_valued_1(k4_ordinal1,k1_numbers,A)) = k5_numbers ) ) ) )).
fof(t3_rsspace4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_rsspace4)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_rsspace4)) => ! [C] : ( v1_xreal_0(C) => ( ( k2_normsp_0(k3_rsspace4,A) = k5_numbers => A = k4_struct_0(k3_rsspace4) ) & ( A = k4_struct_0(k3_rsspace4) => k2_normsp_0(k3_rsspace4,A) = k5_numbers ) & r1_xxreal_0(k5_numbers,k2_normsp_0(k3_rsspace4,A)) & r1_xxreal_0(k2_normsp_0(k3_rsspace4,k1_algstr_0(k3_rsspace4,A,B)),k2_xcmplx_0(k2_normsp_0(k3_rsspace4,A),k2_normsp_0(k3_rsspace4,B))) & k2_normsp_0(k3_rsspace4,k1_rlvect_1(k3_rsspace4,A,C)) = k3_xcmplx_0(k9_complex1(C),k2_normsp_0(k3_rsspace4,A)) ) ) ) ) )).
fof(t3_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => m1_subset_1(C,u1_struct_0(A)) ) ) ) )).
fof(t3_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( r1_struct_0(k2_rusub_2(A,B,C),D) <=> ( r1_struct_0(B,D) & r1_struct_0(C,D) ) ) ) ) ) )).
fof(t3_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => k1_rusub_3(A,k1_subset_1(u1_struct_0(A))) = k1_rusub_1(A) ) )).
fof(t3_rusub_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ( v1_rusub_4(A) => ! [B] : ( m1_rusub_3(B,A) => v1_finset_1(B) ) ) ) )).
fof(t3_rusub_5,axiom,( ! [A] : ( ( ~ 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] : ( ( v2_rusub_4(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v2_rusub_4(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t3_rvsum_1,axiom,( r6_binop_1(k1_numbers,k11_binop_2,k9_binop_2) )).
fof(t3_rvsum_2,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,B) & m2_finseq_1(C,k2_numbers) ) => ! [D] : ( ( v3_card_1(D,B) & m2_finseq_1(D,k2_numbers) ) => k1_funct_1(k4_rvsum_2(B,C,D),A) = k2_xcmplx_0(k1_funct_1(C,A),k1_funct_1(D,A)) ) ) ) )).
fof(t3_scheme1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( A != k2_nat_1(4,B) & A != k1_nat_1(k2_nat_1(4,B),1) & A != k1_nat_1(k2_nat_1(4,B),2) & A != k1_nat_1(k2_nat_1(4,B),3) ) ) ) )).
fof(t3_scm_1,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_ami_3)) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_ami_3)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ( r1_tarski(k1_ordinal4(k5_afinsq_1(A),k5_afinsq_1(B)),C) => ( k3_compos_1(k1_ami_3,C,k5_numbers) = A & k3_compos_1(k1_ami_3,C,1) = B ) ) ) ) ) )).
fof(t3_scm_comp,axiom,( ! [A] : ( m1_dtconstr(A,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ~ ( ! [B] : ( m2_subset_1(B,u1_struct_0(k1_scm_comp),k6_dtconstr(k1_scm_comp)) => A != k3_scm_comp(B) ) & ! [B] : ( m1_dtconstr(B,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t3_scm_halt,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( 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) ) ) ) ) ) )).
fof(t3_scm_inst,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k2_scm_inst) => ( r2_hidden(A,k7_domain_1(k4_ordinal1,7,8)) => r2_hidden(k3_xtuple_0(A,k9_finseq_1(B),k12_finseq_1(k2_scm_inst,C)),k3_scm_inst) ) ) ) )).
fof(t3_scmbsort,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( m1_scmfsa_2(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => k18_scmfsa_2(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k15_scmfsa_2(D,C,B),A),B) = k1_funct_7(k18_scmfsa_2(A,B),k9_complex1(k1_funct_1(A,C)),k1_funct_1(A,D)) ) ) ) ) )).
fof(t3_scmfsa10,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( 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)) ) ) )).
fof(t3_scmfsa6a,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [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(k7_card_1(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(k4_ordinal1,k5_numbers,6,7,8)) | k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B),k4_struct_0(k1_scmfsa_2)) = k1_ordinal1(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,B)) ) ) ) )).
fof(t3_scmfsa7b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( v1_int_1(D) => ( k1_funct_1(k1_scmfsa6b(k1_scmfsa_7(C,D),B,A),C) = D & ! [E] : ( ( 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] : ( m1_scmfsa_2(E) => k18_scmfsa_2(k1_scmfsa6b(k1_scmfsa_7(C,D),B,A),E) = k18_scmfsa_2(B,E) ) ) ) ) ) ) )).
fof(t3_scmfsa8a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ~ ( ~ r4_scmfsa7b(A,C) & r4_scmfsa7b(k6_compos_1(k1_scmfsa_2,A,B),C) ) ) ) ) )).
fof(t3_scmfsa8b,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,A) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,B) => r8_pboole(u1_struct_0(k1_scmfsa_2),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,A),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B)) ) ) ) ) ) )).
fof(t3_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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)) ) ) ) )).
fof(t3_scmfsa9a,axiom,( k2_sf_mastr(k4_compos_1(k1_scmfsa_2)) = k1_xboole_0 )).
fof(t3_scmfsa_1,axiom,( k1_scmfsa_1 = k2_xboole_0(k2_xboole_0(k1_tarski(k4_ordinal1),k2_scmfsa_1),k3_scmfsa_1) )).
fof(t3_scmfsa_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( ~ 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(k7_card_1(3),k1_scmfsa_2)) & v1_finset_1(B) & v4_extpro_1(B,k7_card_1(3),k1_scmfsa_2,A) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ( ( r1_tarski(B,C) & r1_tarski(B,D) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( ( r1_tarski(A,E) & r1_tarski(A,F) ) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v1_ami_2(H) & m1_subset_1(H,u1_struct_0(k1_scmfsa_2)) ) => ! [I] : ( ( v1_ami_2(I) & m1_subset_1(I,u1_struct_0(k1_scmfsa_2)) ) => ( ( k3_extpro_1(k7_card_1(3),k1_scmfsa_2,E,k5_extpro_1(k7_card_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(k7_card_1(3),k1_scmfsa_2,E,C,G),I) = k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,D,G),I) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t3_scmfsa_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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_xcmplx_0(B,A),C) ) ) ) )).
fof(t3_scmfsa_7,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => k1_scmfsa_7(A,k5_numbers) = k1_ordinal4(k1_ordinal4(k5_afinsq_1(k6_scmfsa_2(A,k4_scmfsa_2(k5_numbers))),k5_afinsq_1(k8_scmfsa_2(A,k4_scmfsa_2(k5_numbers)))),k5_afinsq_1(k2_compos_1(k1_scmfsa_2))) ) )).
fof(t3_scmfsa_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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(k5_numbers))))) = k1_nat_1(k5_card_1(A),11) ) ) )).
fof(t3_scmfsa_i,axiom,( r2_hidden(k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0),k2_scmfsa_i) )).
fof(t3_scmfsa_m,axiom,( ! [A] : ( ( 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(k7_card_1(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(k5_numbers))),k6_domain_1(u1_struct_0(k1_scmfsa_2),k4_struct_0(k1_scmfsa_2))) ) )).
fof(t3_scmp_gcd,axiom,( k2_scmp_gcd != k3_scmp_gcd )).
fof(t3_scmpds_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => r1_xxreal_0(k2_compos_0(u1_compos_1(k1_scmpds_2),A),14) ) )).
fof(t3_scmpds_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( A != B & k2_scmpds_2(A,k5_numbers) = k2_scmpds_2(B,k5_numbers) ) ) ) )).
fof(t3_scmpds_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & 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)) ) ) )).
fof(t3_scmpds_6,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => 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 ) ) ) ) )).
fof(t3_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => r1_tarski(k61_valued_1(B,k5_card_1(A)),k1_scmpds_4(k1_scmpds_4(A,B),C)) ) ) ) )).
fof(t3_scmpds_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( 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))) ) ) )).
fof(t3_scmpds_i,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k7_card_1(15)) => ! [B] : ( m1_subset_1(B,k1_scmpds_i) => ! [C] : ( 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 ) ) ) ) )).
fof(t3_scmring1,axiom,( ! [A] : ( m2_subset_1(A,k1_ami_2,k2_ami_2) => ! [B] : ( ( ~ 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) ) ) )).
fof(t3_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ! [C] : ( ( ~ 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmring2(C))) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmring2(C))) ) => ( r2_hidden(B,k9_domain_1(k4_ordinal1,1,2,3,4)) => r2_hidden(k3_xtuple_0(B,k1_xboole_0,k10_finseq_1(D,E)),k1_scmringi(A)) ) ) ) ) ) )).
fof(t3_scmring4,axiom,( ! [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) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( B != C & k2_scmring3(A,B) = k2_scmring3(A,C) ) ) ) ) )).
fof(t3_scmringi,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k7_card_1(8)) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( m1_subset_1(C,k1_scmringi(B)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k2_scm_inst) => ( C = k3_xtuple_0(A,k12_finseq_1(k4_ordinal1,D),k12_finseq_1(k2_scm_inst,E)) => ( k5_scmringi(B,C) = D & k6_scmringi(B,C) = E ) ) ) ) ) ) ) )).
fof(t3_scmyciel,axiom,( ! [A] : ! [B] : k4_tarski(A,B) != A )).
fof(t3_scpisort,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ! [B] : ( m2_finseq_1(B,k4_numbers) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( 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] : ( v7_ordinal1(E) => ( ( 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) ) ) ) ) ) )).
fof(t3_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ( ! [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_partfun1(D,u1_struct_0(k1_scmpds_2)) & v5_memstr_0(D,2,k1_scmpds_2,k5_numbers) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmpds_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ( 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) ) ) ) ) )).
fof(t3_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_analoaf(A,B,B,C,D) ) ) ) ) )).
fof(t3_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v9_ordinal1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r1_tarski(k2_relset_1(k1_numbers,A),k6_subset_1(k1_numbers,k1_tarski(k5_numbers))) ) )).
fof(t3_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_comseq_2(A) <=> ? [B] : ( v1_xreal_0(B) & ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v7_ordinal1(C) => ~ r1_xxreal_0(B,k9_complex1(k1_funct_1(A,C))) ) ) ) ) )).
fof(t3_seq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(B,A) ) ) )).
fof(t3_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( r2_relset_1(k4_ordinal1,k4_partfun1(A,k1_numbers),D,k7_seqfunc(A,B,C)) <=> ! [E] : ( v7_ordinal1(E) => r2_relset_1(A,k1_numbers,k1_seqfunc(A,k1_numbers,D,E),k47_valued_1(A,k1_numbers,k1_numbers,k1_seqfunc(A,k1_numbers,B,E),k1_seqfunc(A,k1_numbers,C,E))) ) ) ) ) ) ) )).
fof(t3_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v6_valued_0(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,A,k2_xcmplx_0(k1_nat_1(B,1),C))) ) ) ) ) )).
fof(t3_series_3,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => r1_xxreal_0(2,k2_xcmplx_0(k7_xcmplx_0(B,A),k7_xcmplx_0(A,B))) ) ) )).
fof(t3_series_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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)) ) ) ) )).
fof(t3_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => ~ ( ~ r1_xxreal_0(B,A) & r1_xxreal_0(k7_xcmplx_0(k2_xcmplx_0(B,C),k2_xcmplx_0(A,C)),1) ) ) ) ) )).
fof(t3_setfam_1,axiom,( ! [A] : ! [B] : ( r2_hidden(B,A) => r1_tarski(k1_setfam_1(A),B) ) )).
fof(t3_setlim_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,C))) ) => ( ! [E] : ( v7_ordinal1(E) => r2_hidden(B,k1_funct_1(D,k2_xcmplx_0(A,E))) ) <=> ! [E] : ( r2_hidden(E,a_3_0_setlim_1(A,C,D)) => r2_hidden(B,E) ) ) ) ) )).
fof(t3_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) )).
fof(t3_setwiseo,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => k7_relat_1(C,k6_subset_1(B,k8_relat_1(C,A))) = k6_subset_1(k7_relat_1(C,B),A) ) )).
fof(t3_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t3_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ( k8_scmfsa_2(A,C) = k8_scmfsa_2(B,D) => ( A = B & C = D ) ) ) ) ) ) )).
fof(t3_sfmastr1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) ) ) ) ) )).
fof(t3_sfmastr2,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ~ ( ( ( r5_scmfsa7b(D,k1_scmfsa_m(A),B) & r6_scmfsa7b(D,k1_scmfsa_m(A),B) ) | v7_amistd_1(D,k7_card_1(3),k1_scmfsa_2) ) & ~ ( k1_funct_1(A,k4_scmfsa_2(k5_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) ) ) ) ) ) )).
fof(t3_sfmastr3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ~ r2_scmfsa7b(k4_compos_1(k1_scmfsa_2),A) ) )).
fof(t3_sgraph1,axiom,( ! [A] : ( v7_ordinal1(A) => k1_sgraph1(1,A) = k2_finseq_1(A) ) )).
fof(t3_sheffer1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k4_lattices(A,B,k3_sheffer1(A,B)) = k2_sheffer1(A) ) ) )).
fof(t3_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t3_simplex0,axiom,( ! [A] : ! [B] : ( ( r1_tarski(A,B) & v1_classes1(B) ) => r1_tarski(k1_simplex0(A),B) ) )).
fof(t3_simplex1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( v1_matroid0(B) & m1_simplex0(B,u1_struct_0(A)) ) => ( v6_simplex0(B,u1_struct_0(A)) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t3_simplex2,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( m1_simplex2(C,A,B) => ! [D] : ( ( v1_xreal_0(D) & v2_xxreal_0(D) ) => ( ( 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) ) ) ) ) ) )).
fof(t3_sin_cos,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xcmplx_0(B) => ( k9_nat_1(k2_numbers,k3_sin_cos(B),k1_nat_1(A,1)) = k7_xcmplx_0(k3_xcmplx_0(k9_nat_1(k2_numbers,k3_sin_cos(B),A),B),k2_xcmplx_0(k1_nat_1(A,1),k3_xcmplx_0(k5_numbers,k7_complex1))) & k9_nat_1(k2_numbers,k3_sin_cos(B),k5_numbers) = 1 & k9_complex1(k9_nat_1(k2_numbers,k3_sin_cos(B),A)) = k9_nat_1(k1_numbers,k4_sin_cos(k9_complex1(B)),A) ) ) ) )).
fof(t3_sin_cos2,axiom,( v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k16_sin_cos,k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos))) )).
fof(t3_sin_cos3,axiom,( ! [A] : ( 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,k4_xcmplx_0(A)) ) )).
fof(t3_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => k2_sin_cos4(k4_xcmplx_0(A)) = k4_xcmplx_0(k2_sin_cos4(A)) ) )).
fof(t3_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( k17_sin_cos(A) != k5_numbers & k17_sin_cos(B) != k5_numbers & k17_sin_cos(C) != k5_numbers & k17_sin_cos(k2_xcmplx_0(k2_xcmplx_0(A,B),C)) != k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k17_sin_cos(A),k17_sin_cos(B)),k17_sin_cos(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(A),k2_sin_cos4(C))),k3_xcmplx_0(k2_sin_cos4(A),k2_sin_cos4(B))),1)) ) ) ) ) )).
fof(t3_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => r1_xxreal_0(k4_xcmplx_0(1),k17_sin_cos(A)) ) )).
fof(t3_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ r1_xxreal_0(1,k1_square_1(k7_xcmplx_0(A,k3_square_1(k2_xcmplx_0(k1_square_1(A),1))))) ) )).
fof(t3_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k2_sin_cos5(A),1) & ~ r1_xxreal_0(k2_sin_cos5(A),k5_numbers) & k2_sin_cos5(k5_numbers) = 1 ) ) )).
fof(t3_sin_cos9,axiom,( r2_fdiff_1(k26_sin_cos,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))) & ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))) => k1_fdiff_1(k26_sin_cos,A) = k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,A))) ) ) )).
fof(t3_sincos10,axiom,( r1_tarski(k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers),k1_relset_1(k1_numbers,k2_fdiff_9)) )).
fof(t3_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_euclid(A)) => ! [C] : ( m1_subset_1(C,k1_euclid(A)) => ! [D] : ( m1_subset_1(D,k1_euclid(A)) => r1_xxreal_0(k6_xcmplx_0(k12_euclid(k8_euclid(A,B,C)),k12_euclid(k8_euclid(A,C,D))),k12_euclid(k8_euclid(A,B,D))) ) ) ) ) )).
fof(t3_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t3_sprect_1,axiom,( ! [A] : ! [B] : ! [C] : ( v3_funct_1(k11_finseq_1(A,B,C)) => ( A = B & B = C & C = A ) ) )).
fof(t3_sprect_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( 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_xcmplx_0(C,A),1)) ) ) ) ) ) ) )).
fof(t3_sprect_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( v1_xreal_0(D) => ( B = k3_rlvect_1(k15_euclid(A),k1_rlvect_1(k15_euclid(A),B,k6_xcmplx_0(1,D)),k1_rlvect_1(k15_euclid(A),C,D)) => ( r1_xxreal_0(D,k5_numbers) | B = C ) ) ) ) ) ) )).
fof(t3_sprect_4,axiom,( ! [A] : ( ( v4_topreal1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ( ( 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) ) ) ) ) ) )).
fof(t3_sprect_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t3_square_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k1_square_1(A) = k1_square_1(k4_xcmplx_0(A)) ) )).
fof(t3_stacks_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_stacks_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t3_stirl2_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k4_ordinal1)) => r1_xxreal_0(k4_nat_1(k3_nat_1(A),k3_nat_1(B)),k3_nat_1(k4_subset_1(k4_ordinal1,A,B))) ) ) )).
fof(t3_struct_0,axiom,( ! [A] : ( l2_struct_0(A) => ~ r2_hidden(k4_struct_0(A),k8_struct_0(A)) ) )).
fof(t3_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k16_substut1(A),k38_substut1(A)) => ( v2_substut1(B,A) => k39_substut1(A,B) = k5_cqc_lang(A) ) ) ) )).
fof(t3_subset,axiom,( ! [A] : ! [B] : ( m1_subset_1(A,k1_zfmisc_1(B)) <=> r1_tarski(A,B) ) )).
fof(t3_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,B) <=> r2_hidden(D,C) ) ) => B = C ) ) ) )).
fof(t3_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( m1_subset_1(D,k5_finsub_1(k4_partfun1(A,B))) => k4_substlat(A,B,C,D) = k4_substlat(A,B,D,C) ) ) )).
fof(t3_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t3_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( 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 ) ) ) ) ) ) )).
fof(t3_supinf_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t3_supinf_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( A = C & B = D ) => k3_xxreal_3(A,B) = k6_xcmplx_0(C,D) ) ) ) ) ) )).
fof(t3_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t3_sysrel,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) ) ) )).
fof(t3_t_0topsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_t_0topsp(A))) <=> ? [C] : ( 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) ) ) ) )).
fof(t3_t_1topsp,axiom,( ! [A] : ( ( ~ 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))))) ) ) )).
fof(t3_tarski,axiom,( ! [A] : ! [B] : ~ ( r2_hidden(A,B) & ! [C] : ~ ( r2_hidden(C,B) & ! [D] : ~ ( r2_hidden(D,B) & r2_hidden(D,C) ) ) ) )).
fof(t3_taxonom1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( r1_relat_2(B,A) => k1_relset_1(A,B) = A ) ) )).
fof(t3_taxonom2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( m1_taxonom1(B,A) & r2_hidden(C,k3_tarski(B)) ) => r1_tarski(C,A) ) ) )).
fof(t3_taylor_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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) = k3_xcmplx_0(k3_xcmplx_0(A,k3_prepower(k1_funct_1(C,B),k6_xcmplx_0(A,1))),k1_fdiff_1(C,B)) ) ) ) ) ) )).
fof(t3_taylor_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_tarski(k2_rcomp_1(k6_xcmplx_0(C,D),k2_xcmplx_0(C,D)),k9_xtuple_0(B)) & r1_taylor_1(B,k1_nat_1(A,1),k2_rcomp_1(k6_xcmplx_0(C,D),k2_xcmplx_0(C,D))) ) => ( r1_xxreal_0(D,k5_numbers) | ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k2_rcomp_1(k6_xcmplx_0(C,D),k2_xcmplx_0(C,D))) & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ~ r1_xxreal_0(1,F) & k9_complex1(k6_xcmplx_0(k1_funct_1(B,E),k9_nat_1(k1_numbers,k3_series_1(k6_taylor_1(B,k2_rcomp_1(k6_xcmplx_0(C,D),k2_xcmplx_0(C,D)),C,E)),A))) = k9_complex1(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(B,k2_rcomp_1(k6_xcmplx_0(C,D),k2_xcmplx_0(C,D))),k1_nat_1(A,1)),k2_xcmplx_0(C,k3_xcmplx_0(F,k6_xcmplx_0(E,C)))),k1_newton(k6_xcmplx_0(E,C),k1_nat_1(A,1))),k2_newton(k1_nat_1(A,1)))) ) ) ) ) ) ) ) ) ) ) )).
fof(t3_tbsp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) & ? [B] : ( v1_xreal_0(B) & ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(B,k2_power(A,C)) ) ) ) ) )).
fof(t3_tdgroup,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & k3_rlvect_1(A,C,C) = B ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( k3_rlvect_1(A,B,B) = k4_struct_0(A) => B = k4_struct_0(A) ) ) ) ) ) )).
fof(t3_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) )).
fof(t3_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t3_tdlat_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) )).
fof(t3_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [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) & v1_vectsp_2(B) & l6_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( ~ v9_struct_0(E,B) & m1_subset_1(E,u1_struct_0(B)) ) => ! [F] : ( ( ~ 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)),k10_polynom1(A,B,k1_polynom7(A,B,E,C),k1_polynom7(A,B,F,D))) ) ) ) ) ) ) )).
fof(t3_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) ) )).
fof(t3_tex_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ~ ( v1_subset_1(k6_domain_1(A,B),A) & v1_zfmisc_1(A) ) ) ) )).
fof(t3_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t3_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) )).
fof(t3_tietze,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t3_tmap_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,C,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,B))) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t3_toler_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(t3_topalg_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k17_borsuk_1))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k17_borsuk_1)) => ( A = k3_rcomp_1(k5_numbers,B) => k3_subset_1(u1_struct_0(k17_borsuk_1),A) = k1_rcomp_1(B,1) ) ) ) )).
fof(t3_topalg_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v1_topalg_2(B,A) & m1_pre_topc(B,k15_euclid(A)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t3_topalg_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(t3_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l3_algstr_0(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & l3_algstr_0(D) ) => ! [E] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t3_topalg_5,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => r1_tarski(k6_connsp_3(A,B,C),B) ) ) ) ) )).
fof(t3_topalg_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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))) ) ) ) )).
fof(t3_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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)),k4_ordinal1,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),k4_ordinal1,k9_setfam_1(u1_struct_0(A)),k1_topdim_1(A),D)) ) ) ) ) ) ) ) )).
fof(t3_topdim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(B))) => ( ! [D] : ( ( 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) ) ) ) )).
fof(t3_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(t3_topgen_2,axiom,( ! [A] : ( ! [B] : ( r2_hidden(B,A) => v1_card_1(B) ) => v1_card_1(k3_tarski(A)) ) )).
fof(t3_topgen_3,axiom,( ! [A] : ! [B] : ( ( 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] : ! [D] : ( ( r2_hidden(C,A) & r2_hidden(D,k1_funct_1(B,C)) ) => r2_hidden(C,D) ) & ! [C] : ! [D] : ! [E] : ~ ( r2_hidden(C,E) & r2_hidden(E,k1_funct_1(B,D)) & r2_hidden(D,A) & ! [F] : ~ ( r2_hidden(F,k1_funct_1(B,C)) & r1_tarski(F,E) ) ) & ! [C] : ! [D] : ! [E] : ~ ( r2_hidden(C,A) & r2_hidden(D,k1_funct_1(B,C)) & r2_hidden(E,k1_funct_1(B,C)) & ! [F] : ~ ( r2_hidden(F,k1_funct_1(B,C)) & r1_tarski(F,k3_xboole_0(D,E)) ) ) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ~ ( C = k3_card_3(B) & ! [D] : ( 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] : ( ( ~ v2_struct_0(E) & v2_pre_topc(E) & l1_pre_topc(E) ) => ( E = D => m1_topgen_2(B,E) ) ) ) ) ) ) ) ) ) )).
fof(t3_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(B,A) <=> r1_tarski(k2_topgen_1(A,B),B) ) ) ) )).
fof(t3_topgrp_1,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( 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 ) ) )).
fof(t3_topmetr,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_pre_topc(C,A) => ( r1_tarski(u1_struct_0(B),u1_struct_0(C)) => m1_pre_topc(B,C) ) ) ) ) )).
fof(t3_topmetr2,axiom,( ! [A] : ( ( v2_pre_topc(A) & v8_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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] : ( ( 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,k5_numbers) = D & ! [G] : ( ( 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,k5_numbers) = k1_funct_1(E,k5_numbers) & k1_funct_1(G,1) = k1_funct_1(F,1) ) ) ) ) ) ) ) ) ) )).
fof(t3_topmetr3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( ( v2_tbsp_1(D,A) & E = k1_partfun1(k4_ordinal1,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) ) ) ) ) ) ) )).
fof(t3_topreal1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r1_xxreal_0(k17_euclid(B),k17_euclid(C)) & r2_hidden(A,k1_rltopsp1(k15_euclid(2),B,C)) ) => ( r1_xxreal_0(k17_euclid(B),k17_euclid(A)) & r1_xxreal_0(k17_euclid(A),k17_euclid(C)) ) ) ) ) ) )).
fof(t3_topreal2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t3_topreal3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( k17_euclid(k5_algstr_0(k15_euclid(2),A,B)) = k6_xcmplx_0(k17_euclid(A),k17_euclid(B)) & k18_euclid(k5_algstr_0(k15_euclid(2),A,B)) = k6_xcmplx_0(k18_euclid(A),k18_euclid(B)) ) ) ) )).
fof(t3_topreal4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( r1_topreal4(A,B,C) => ( r2_hidden(B,A) & r2_hidden(C,A) ) ) ) ) ) )).
fof(t3_topreal5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r2_hidden(B,A) & ? [C] : ( v1_xreal_0(C) & ? [D] : ( 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) ) ) ) )).
fof(t3_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => k19_rvsum_1(k2_finseq_2(k5_numbers,A)) = 1 ) )).
fof(t3_topreal7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t3_topreal8,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ! [B] : ( ( ~ v3_funct_1(B) & v1_finseq_6(B,A) & m2_finseq_1(B,A) ) => ~ r1_xxreal_0(k3_finseq_1(B),2) ) ) )).
fof(t3_topreal9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => k1_square_1(k12_euclid(A)) = k18_rvsum_1(k12_rvsum_1(A)) ) )).
fof(t3_topreala,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) ) ) ) )).
fof(t3_toprealb,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( r2_hidden(C,k1_toprealb(A,B)) <=> ? [D] : ( m1_subset_1(D,k4_numbers) & C = k2_rcomp_1(k2_xcmplx_0(A,D),k2_xcmplx_0(B,D)) ) ) ) ) )).
fof(t3_toprealc,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(t3_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ( v1_toprns_1(B,A) <=> ! [C] : ( v7_ordinal1(C) => k9_nat_1(u1_struct_0(k15_euclid(A)),B,C) != k4_struct_0(k15_euclid(A)) ) ) ) ) )).
fof(t3_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) )).
fof(t3_tops_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t3_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t3_tops_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( v3_pre_topc(E,A) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( r2_hidden(D,E) & ! [F] : ( ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t3_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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 ) ) ) ) )).
fof(t3_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t3_treal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(D,B) & r1_xxreal_0(C,D) ) => ( v1_borsuk_1(k4_topmetr(C,D),k4_topmetr(A,B)) & m1_pre_topc(k4_topmetr(C,D),k4_topmetr(A,B)) ) ) ) ) ) ) )).
fof(t3_trees_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ( ( r3_xboole_0(A,B) & k5_card_1(A) = k5_card_1(B) ) => A = B ) ) ) )).
fof(t3_trees_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ ( k3_finseq_1(B) = k1_nat_1(A,1) & ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ~ ( B = k7_finseq_1(C,k9_finseq_1(D)) & k3_finseq_1(C) = A ) ) ) ) ) )).
fof(t3_trees_3,axiom,( ! [A] : ! [B] : ( ( v1_trees_3(A) & v1_trees_3(B) ) <=> v1_trees_3(k2_xboole_0(A,B)) ) )).
fof(t3_trees_4,axiom,( ! [A] : ( k9_xtuple_0(k1_trees_4(A)) = k2_trees_1(k5_numbers) & k1_funct_1(k1_trees_4(A),k1_xboole_0) = A ) )).
fof(t3_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( r2_hidden(k8_finseq_1(k4_ordinal1,B,C),k9_xtuple_0(A)) => k5_trees_2(A,k8_finseq_1(k4_ordinal1,B,C)) = k5_trees_2(k5_trees_2(A,B),C) ) ) ) ) )).
fof(t3_trees_a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m4_trees_1(B,A) => r1_tarski(a_2_1_trees_a(A,B),a_2_0_trees_a(A,B)) ) ) )).
fof(t3_triang_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_hidden(k6_domain_1(u1_struct_0(A),B),k1_triang_1(A)) ) ) )).
fof(t3_tsep_1,axiom,( ! [A] : ( ( v1_pre_topc(A) & l1_pre_topc(A) ) => k1_pre_topc(A,k2_struct_0(A)) = A ) )).
fof(t3_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t3_tsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t3_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t3_turing_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( 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)) ) ) )).
fof(t3_twoscomp,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( 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)) ) ) ) )).
fof(t3_unialg_2,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t3_unialg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_unialg_2(B,A) => r1_tarski(u1_struct_0(B),u1_struct_0(A)) ) ) )).
fof(t3_uniform1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & F = k1_funct_1(C,E) & ! [G] : ( v1_xreal_0(G) => ~ ( ~ r1_xxreal_0(G,k5_numbers) & ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(B)) => ~ ( I = k1_funct_1(C,H) & ~ r1_xxreal_0(G,k3_metric_1(A,E,H)) & r1_xxreal_0(D,k3_metric_1(B,F,I)) ) ) ) ) ) ) ) ) ) => v5_pre_topc(C,k3_pcomps_1(A),k3_pcomps_1(B)) ) ) ) ) )).
fof(t3_uproots,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ~ r2_hidden(D,B) => k1_funct_1(k1_uproots(A,B,C),D) = k5_numbers ) ) ) )).
fof(t3_urysohn1,axiom,( k1_urysohn1(1) = k1_enumset1(k5_numbers,k7_xcmplx_0(1,2),1) )).
fof(t3_urysohn2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( A != k1_xboole_0 => k1_integra2(A,k5_numbers) = k1_seq_4(k5_numbers) ) ) )).
fof(t3_urysohn3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( m1_urysohn3(E,A,B,C,D) => m1_subset_1(E,k4_partfun1(k2_urysohn1,k9_setfam_1(u1_struct_0(A)))) ) ) ) ) ) )).
fof(t3_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [E] : ( 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] : ( m2_funct_2(F,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ( ! [G] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t3_valued_0,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ( v1_relat_1(B) & v3_valued_0(B) ) => ( r1_tarski(A,B) => v3_valued_0(A) ) ) ) )).
fof(t3_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( v1_xcmplx_0(B) => ( k9_xtuple_0(k13_valued_1(A,B)) = k9_xtuple_0(A) & ! [C] : ( 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) ) ) ) ) )).
fof(t3_valued_2,axiom,( ! [A] : m1_subset_1(k7_valued_2(A),k1_zfmisc_1(k6_valued_2(A))) )).
fof(t3_vectmetr,axiom,( ! [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) & v5_vectmetr(A) & l1_vectmetr(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_vectmetr(A,k1_rlvect_1(A,C,B)) = k3_xcmplx_0(k9_complex1(B),k3_vectmetr(A,C)) ) ) ) )).
fof(t3_vectsp10,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(A)) & C = k4_vectsp_1(A,B,E,D) ) ) ) ) ) )).
fof(t3_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ! [E] : ( ( v1_finset_1(E) & v1_setfam_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ( r1_tarski(k2_zfmisc_1(D,E),k2_matrix_0(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)) ) ) ) ) ) ) )).
fof(t3_vectsp_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k6_algstr_0(A,k4_struct_0(A),B) = k4_struct_0(A) ) ) )).
fof(t3_vectsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B = k4_struct_0(A) <=> k4_algstr_0(A,B) = k4_struct_0(A) ) ) ) )).
fof(t3_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v1_vectsp_4(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t3_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( r1_struct_0(k2_vectsp_5(A,B,C,D),E) <=> ( r1_struct_0(C,E) & r1_struct_0(D,E) ) ) ) ) ) ) )).
fof(t3_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(t3_vectsp_7,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t3_vectsp_8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t3_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(B)) => ( v2_funct_1(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t3_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( v1_xreal_0(D) => ( D != k5_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))) ) ) ) ) ) )).
fof(t3_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( v1_xcmplx_0(D) => ( 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))) ) ) ) ) ) )).
fof(t3_waybel10,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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) ) ) ) ) ) )).
fof(t3_waybel11,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v13_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t3_waybel12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t3_waybel13,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_yellow_0(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).
fof(t3_waybel14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t3_waybel15,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v2_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r1_orders_2(A,k4_yellow_0(A),B) => B = k4_yellow_0(A) ) ) ) )).
fof(t3_waybel16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t3_waybel17,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t3_waybel18,axiom,( ! [A] : ! [B] : ( 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)))) ) )).
fof(t3_waybel19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t3_waybel20,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( 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))) ) ) ) )).
fof(t3_waybel21,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_yellow_0(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_yellow_0(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t3_waybel22,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => v17_waybel_0(k3_struct_0(A),A,A) ) )).
fof(t3_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & v8_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t3_waybel24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & v2_yellow_0(B) & l1_orders_2(B) ) => k4_yellow_0(k6_yellow_1(A,B)) = k6_struct_0(A,B,k4_yellow_0(B)) ) ) )).
fof(t3_waybel25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v4_waybel11(B) & m1_yellow_9(B,k4_yellow_1(A,k7_funcop_1(A,k2_yellow_1(k1_tarski(k5_numbers))))) ) => u1_struct_0(B) = u1_struct_0(k3_waybel18(A,k7_funcop_1(A,k9_waybel18))) ) ) )).
fof(t3_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_waybel26(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_waybel26(A,B))) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t3_waybel28,axiom,( ! [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] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( r2_hidden(B,k6_yellow_6(A)) & ! [D] : ( m2_yellow_6(D,A,B) => ( r2_hidden(D,k6_yellow_6(A)) => C = k1_waybel11(A,D) ) ) ) => ( C = k1_waybel11(A,B) & ! [D] : ( m2_yellow_6(D,A,B) => ( r2_hidden(D,k6_yellow_6(A)) => r1_orders_2(A,k1_waybel_9(A,D),C) ) ) ) ) ) ) ) )).
fof(t3_waybel29,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v4_yellow_0(D,k5_yellow_1(k2_zfmisc_1(A,B),C)) & m1_yellow_0(D,k5_yellow_1(k2_zfmisc_1(A,B),C)) ) => ! [E] : ( ( ~ v2_struct_0(E) & v4_yellow_0(E,k5_yellow_1(A,k5_yellow_1(B,C))) & m1_yellow_0(E,k5_yellow_1(A,k5_yellow_1(B,C))) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t3_waybel30,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,k1_yellow_1(k7_waybel_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_yellow_1(k7_waybel_0(A))))) ) => k1_yellow_0(k1_yellow_1(k7_waybel_0(A)),B) = k3_tarski(B) ) ) )).
fof(t3_waybel31,axiom,( ! [A] : ( ( 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))) ) )).
fof(t3_waybel32,axiom,( ! [A] : ( ( ~ 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] : ( m1_yellow_9(B,A) & v4_waybel11(B) ) ) )).
fof(t3_waybel33,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ( u1_struct_0(A) = u1_struct_0(B) => ! [C] : ( l1_waybel_0(C,A) => ~ ( r2_hidden(C,k6_yellow_6(A)) & ! [D] : ( ( ~ 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)) ) ) ) ) ) ) ) )).
fof(t3_waybel34,axiom,( ! [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] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) )).
fof(t3_waybel35,axiom,( ! [A] : ( ( v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_waybel_4(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(k4_tarski(C,D),B) & r2_hidden(k4_tarski(D,C),B) ) => C = D ) ) ) ) ) )).
fof(t3_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( ( C = D & v1_waybel_0(C,A) ) => v1_waybel_0(D,B) ) ) ) ) ) ) )).
fof(t3_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( 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 ) ) ) ) )).
fof(t3_waybel_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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))) ) ) ) )).
fof(t3_waybel_3,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t3_waybel_4,axiom,( ! [A] : ( ( 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(k1_yellow_1(k3_waybel_4(A))) = k2_waybel_4(A) ) )).
fof(t3_waybel_5,axiom,( ! [A] : ( ( 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),k1_yellow_1(k7_waybel_0(A)),A) ) )).
fof(t3_waybel_6,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t3_waybel_7,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t3_waybel_8,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(t3_waybel_9,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t3_weddwitt,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_nat_d(k7_nat_d(k11_newton(A,B),1),k7_nat_d(k11_newton(A,C),1)) => ( r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(A,1) | r1_nat_d(B,C) ) ) ) ) ) )).
fof(t3_wellfnd1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : r1_tarski(k1_wellord1(u1_orders_2(A),B),u1_struct_0(A)) ) )).
fof(t3_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_wellord1(A) <=> r1_wellord1(A,k1_relat_1(A)) ) ) )).
fof(t3_wellord2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r2_hidden(A,B) => A = k1_wellord1(k1_wellord2(B),A) ) ) ) )).
fof(t3_wellset1,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) ) ) )).
fof(t3_wsierp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) & k1_newton(A,C) = k1_newton(B,C) ) => ( r1_xxreal_0(C,k5_numbers) | A = B ) ) ) ) ) )).
fof(t3_xboole_0,axiom,( ! [A] : ! [B] : ( ~ ( ~ r1_xboole_0(A,B) & ! [C] : ~ ( r2_hidden(C,A) & r2_hidden(C,B) ) ) & ~ ( ? [C] : ( r2_hidden(C,A) & r2_hidden(C,B) ) & r1_xboole_0(A,B) ) ) )).
fof(t3_xboole_1,axiom,( ! [A] : ( r1_tarski(A,k1_xboole_0) => A = k1_xboole_0 ) )).
fof(t3_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => k5_xboolean(A,A) = A ) )).
fof(t3_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( A = k2_xcmplx_0(A,B) => B = k5_numbers ) ) ) )).
fof(t3_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,A) & ~ r1_xxreal_0(C,B) ) ) ) )).
fof(t3_xtuple_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( k3_xtuple_0(A,B,C) = k3_xtuple_0(D,E,F) => ( A = D & B = E & C = F ) ) )).
fof(t3_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => r1_xxreal_0(A,k1_xxreal_0) ) )).
fof(t3_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(C,k2_xxreal_1(A,B)) <=> ( r1_xxreal_0(A,C) & ~ r1_xxreal_0(B,C) ) ) ) ) ) )).
fof(t3_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v2_membered(B) => ( r2_hidden(A,B) => r1_xxreal_0(k2_xxreal_2(B),A) ) ) ) )).
fof(t3_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( ~ r1_xxreal_0(B,A) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,A) & ~ r1_xxreal_0(B,C) ) ) ) ) ) )).
fof(t3_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v2_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t3_yellow11,axiom,( k6_subset_1(3,1) = k7_domain_1(k4_ordinal1,1,2) )).
fof(t3_yellow12,axiom,( ! [A] : ! [B] : ( 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 ) )).
fof(t3_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => v9_pre_topc(A) ) )).
fof(t3_yellow14,axiom,( ! [A] : ( ( v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( l1_struct_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t3_yellow15,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k9_setfam_1(A)) => ! [C] : ( m2_finseq_1(C,k6_margrel1) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(D,k4_finseq_1(B)) & k1_funct_1(C,D) = k7_margrel1 ) => k1_funct_1(k1_yellow15(A,B,C),D) = k6_subset_1(A,k1_funct_1(B,D)) ) ) ) ) )).
fof(t3_yellow16,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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 ) ) ) )).
fof(t3_yellow17,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t3_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_altcat_2(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l1_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_altcat_2(C) & l1_altcat_1(C) ) => ! [D] : ( ( v8_functor0(D,A,B) & l2_functor0(D,A,B) ) => ! [E] : ( ( v8_functor0(E,A,B) & l2_functor0(E,A,B) ) => ! [F] : ( l2_functor0(F,B,C) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t3_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v13_waybel_0(C,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))))) ) => ( r2_waybel_7(A,C,B) <=> r1_tarski(k1_yellow19(A,B),C) ) ) ) ) )).
fof(t3_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v8_functor0(C,A,B) & v11_functor0(C,A,B) & l2_functor0(C,A,B) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( k1_altcat_1(A,E,F) != k1_xboole_0 => ! [G] : ( m1_subset_1(G,k1_altcat_1(A,E,F)) => ! [H] : ( 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 ) ) ) ) ) ) ) ) ) ) ) )).
fof(t3_yellow21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & v2_yellow21(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(E,k1_altcat_1(A,B,C)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t3_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [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) ) ) ) )).
fof(t3_yellow_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(A))) => ( r3_orders_2(k1_yellow_1(A),B,C) <=> r1_tarski(B,C) ) ) ) ) )).
fof(t3_yellow_2,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ! [C] : ( ( 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)) ) ) ) )).
fof(t3_yellow_3,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t3_yellow_4,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_yellow_4(A,k1_struct_0(A),B) ) ) )).
fof(t3_yellow_5,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_orders_2(A,k13_lattice3(A,B,C),D) => r1_orders_2(A,B,D) ) ) ) ) ) )).
fof(t3_yellow_6,axiom,( ! [A] : ( l1_orders_2(A) => u1_struct_0(A) = u1_struct_0(k7_lattice3(A)) ) )).
fof(t3_yellow_7,axiom,( ! [A] : ( l1_orders_2(A) => ( v2_struct_0(A) <=> v2_struct_0(k7_lattice3(A)) ) ) )).
fof(t3_yellow_8,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => r2_tarski(B,k7_setfam_1(A,B)) ) )).
fof(t3_yellow_9,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( 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) ) ) )).
fof(t3_yoneda_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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(k9_nattra_1(A,k1_yoneda_1(A)))) ) ) )).
fof(t3_zf_colla,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( 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))) ) ) ) ) )).
fof(t3_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ( v8_zf_fund1(B,A) => r2_hidden(k1_xboole_0,B) ) ) ) )).
fof(t3_zf_lang,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ( k8_zf_lang(C,A) = k8_zf_lang(D,B) => ( C = D & A = B ) ) ) ) ) ) )).
fof(t3_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => k20_zf_lang(k6_zf_lang(A)) = A ) )).
fof(t3_zf_model,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t3_zf_refle,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ( r2_hidden(k4_ordinal1,A) => r2_zf_model(A,k9_zf_model) ) ) )).
fof(t3_zfmisc_1,axiom,( ! [A] : ! [B] : ( r1_tarski(k1_tarski(A),k1_tarski(B)) => A = B ) )).
fof(t3_zfmodel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_ordinal1(A) => ( r2_zf_model(A,k7_zf_model) <=> ! [B] : ! [C] : ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r2_hidden(k2_tarski(B,C),A) ) ) ) ) )).
fof(t3_zfmodel2,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ? [B] : ( m1_subset_1(B,k4_ordinal1) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r2_hidden(k2_zf_lang(C),k4_zf_lang1(A)) & r1_xxreal_0(B,C) ) ) ) & ~ ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => r2_hidden(B,k4_zf_lang1(A)) ) ) ) )).
fof(t3_zfrefle1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_zf_lang)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t3_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( ( v6_zmodul01(A) & B = k4_algstr_0(A,B) ) => B = k4_struct_0(A) ) ) ) )).
fof(t3_zmodul02,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( ~ 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] : ( m1_zmodul01(D,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ( ( D = k5_zmodul02(C,A) & r1_int_2(A,B) & k1_zmodul01(C,E,B) = k4_struct_0(C) ) => ( r1_xxreal_0(A,1) | r1_xxreal_0(B,1) | k5_zmodul01(C,E,D) = k4_struct_0(k10_zmodul02(C,D)) ) ) ) ) ) ) ) )).
fof(t3_zmodul03,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( m1_zmodul02(C,A) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_zmodul02(D,A) & r1_tarski(k18_zmodul02(A,B),D) & r1_tarski(k18_zmodul02(A,C),D) & k21_zmodul02(A,B) = k21_zmodul02(A,C) ) => r1_zmodul02(A,B,C) ) ) ) ) ) )).
fof(t400_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t401_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t402_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t403_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t404_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t405_xxreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => k6_subset_1(k1_xxreal_1(k2_xxreal_0,A),k2_xxreal_1(k2_xxreal_0,A)) = k1_tarski(A) ) )).
fof(t406_xxreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => k6_subset_1(k3_xxreal_1(k2_xxreal_0,A),k4_xxreal_1(k2_xxreal_0,A)) = k1_tarski(A) ) )).
fof(t407_xxreal_1,axiom,( ! [A] : ( 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) ) )).
fof(t408_xxreal_1,axiom,( ! [A] : ( 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) ) )).
fof(t409_xxreal_1,axiom,( ! [A] : ( 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) ) )).
fof(t40_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_abcmiz_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t40_abcmiz_1,axiom,( ! [A] : ( 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 ) ) ) )).
fof(t40_abcmiz_a,axiom,( k1_msualg_1(k27_abcmiz_1,k14_abcmiz_a(k8_abcmiz_a)) = k1_xboole_0 )).
fof(t40_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( v1_aff_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => r3_aff_1(A,B,B) ) ) )).
fof(t40_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t40_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ! [D] : ( ( 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] : ( ( v1_relat_1(E) & v5_ordinal1(E) & v1_funct_1(E) & v1_finset_1(E) ) => k1_ordinal4(A,E) != C ) ) ) ) ) ) )).
fof(t40_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k14_afproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k14_afproj(A))) => ? [D] : ( 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) ) ) ) ) )).
fof(t40_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ? [F] : ( 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) ) ) ) ) ) ) )).
fof(t40_algspec1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t40_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v3_altcat_2(B,A) & m1_altcat_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,k1_altcat_1(A,C,D)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t40_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k3_analmetr(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k3_analmetr(A))) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t40_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & F != G & r1_analort(A,B,C,D,E,F,G) ) ) ) ) ) ) ) ) )).
fof(t40_aofa_000,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & v3_freealg(A) & l1_unialg_1(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(u1_unialg_1(A))) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t40_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & l1_aofa_a00(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,C),D)) => m3_pboole(k11_aofa_a00(A,C,D,E),u1_struct_0(A),k13_msafree(A,B)) ) ) ) ) ) )).
fof(t40_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( ( v19_aofa_a00(F,A) & m1_subset_1(F,u1_struct_0(A)) ) => ! [G] : ( m2_subset_1(G,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => k15_aofa_a00(A,B,C,D,F,k7_aofa_a01(A,B,C,F),G) = 2 ) ) ) ) ) ) ) )).
fof(t40_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_aofa_i00(E,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) ) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),E) => ! [G] : ( 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,k5_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,k5_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,k5_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,k5_numbers)) & r1_xxreal_0(G,k21_aofa_i00(B,k4_numbers,C,F)) ) ) ) ) ) ) ) ) ) )).
fof(t40_armstrng,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t40_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ( k8_arytm_3(k1_xboole_0,B) = k1_xboole_0 & k8_arytm_3(A,1) = A ) ) ) )).
fof(t40_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & v6_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( v7_asympt_0(A) & r1_xxreal_0(2,C) & r2_hidden(B,k11_asympt_0(A,a_1_4_asympt_0(C))) ) => r2_hidden(B,k8_asympt_0(A)) ) ) ) ) )).
fof(t40_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_funct_2(k4_ordinal1,k1_numbers,A,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k3_asympt_1(1),k1_seq_1(1))) => k13_asympt_0(k4_ordinal1,k8_asympt_0(A),k8_asympt_0(k3_asympt_1(1))) = k8_asympt_0(k3_asympt_1(1)) ) ) )).
fof(t40_bcialg_1,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k7_bcialg_1(A,B)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t40_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t40_bcialg_3,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t40_bcialg_4,axiom,( ! [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) & l1_bcialg_4(A) ) => ! [B] : ( 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 ) ) )).
fof(t40_bcialg_5,axiom,( ! [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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t40_bcialg_6,axiom,( ! [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] : ( ( ~ 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] : ( ( 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] : ( m1_bcialg_1(D,B) => ( u1_struct_0(D) = k2_relset_1(u1_struct_0(B),C) => ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(D)) & v2_bcialg_6(C,A,D) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(D)))) ) ) ) ) ) ) )).
fof(t40_bciideal,axiom,( ! [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) ) => ( ( v3_bciideal(k1_tarski(k4_struct_0(A)),A) & m2_bcialg_1(k1_tarski(k4_struct_0(A)),A) ) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t40_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)),k2_xcmplx_0(k4_bhsp_1(A,B,D),k4_bhsp_1(A,C,E))) ) ) ) ) ) )).
fof(t40_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(C,k4_bhsp_2(A,B,D)) <=> ~ r1_xxreal_0(D,k3_bhsp_1(A,k5_algstr_0(A,B,C))) ) ) ) ) ) )).
fof(t40_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k3_bhsp_1(A,k5_algstr_0(A,k3_bhsp_4(A,B,D),k3_bhsp_4(A,B,C))),k9_complex1(k6_xcmplx_0(k6_series_1(k2_bhsp_2(A,B),D),k6_series_1(k2_bhsp_2(A,B),C)))) ) ) ) ) )).
fof(t40_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v4_rlvect_1(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t40_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t40_borsuk_1,axiom,( u1_struct_0(k17_borsuk_1) = k1_rcomp_1(k5_numbers,1) )).
fof(t40_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_topmetr)) => ! [F] : ( m1_subset_1(F,u1_struct_0(k5_topmetr)) => ~ ( r1_topreal1(k15_euclid(A),C,D,B) & ~ r1_xxreal_0(F,E) & ! [G] : ( ( ~ v1_xboole_0(G) & m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k5_topmetr))) ) => ! [H] : ( ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(t40_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ( A = k4_rcomp_1(k2_xxreal_0,B) => v4_pre_topc(A,k3_topmetr) ) ) ) )).
fof(t40_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ( ( k1_funct_1(D,k5_numbers) = B & k1_funct_1(D,1) = C ) => ( k1_funct_1(k1_partfun1(u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k5_topmetr),u1_struct_0(A),k3_treal_1(k5_numbers,1,k2_treal_1(k5_numbers,1),k1_treal_1(k5_numbers,1)),D),k5_numbers) = C & k1_funct_1(k1_partfun1(u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k5_topmetr),u1_struct_0(A),k3_treal_1(k5_numbers,1,k2_treal_1(k5_numbers,1),k1_treal_1(k5_numbers,1)),D),1) = B ) ) ) ) ) ) )).
fof(t40_borsuk_7,axiom,( k30_valued_1(k9_borsuk_7) = k8_borsuk_7 )).
fof(t40_bspace,axiom,( ! [A] : ( v1_finset_1(A) => m1_vectsp_7(k9_bspace(A),k2_bspace,k7_bspace(A)) ) )).
fof(t40_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t40_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_subset_1(I,A) => ! [J] : ( m1_subset_1(J,A) => ! [K] : ( ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t40_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t40_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t40_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(F,A) => r1_bvfunc_1(A,k2_bvfunc_1(A,k2_bvfunc_1(A,k7_bvfunc_2(A,D,B,F),k6_bvfunc_2(A,k9_bvfunc_1(A,D,E),B,F)),k6_bvfunc_2(A,k9_bvfunc_1(A,E,C),B,F)),k7_bvfunc_2(A,k2_bvfunc_1(A,C,D),B,F)) ) ) ) ) ) ) )).
fof(t40_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) )).
fof(t40_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t40_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t40_card_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_ordinal1(k1_card_1(B),k1_card_1(A)) <=> r1_ordinal1(B,A) ) ) ) )).
fof(t40_card_2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ( ~ r2_hidden(A,B) => k5_card_1(k2_xboole_0(B,k1_tarski(A))) = k1_nat_1(k5_card_1(B),1) ) ) )).
fof(t40_card_3,axiom,( ! [A] : ( ( 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)) ) )).
fof(t40_card_fil,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ( v7_card_fil(A) => v5_card_fil(A) ) ) )).
fof(t40_card_fin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_finset_1(B) ) => ! [C] : ! [D] : ! [E] : ( v1_finset_1(E) => ! [F] : ( ( 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] : ( ( v1_relat_1(G) & v5_relat_1(G,k4_ordinal1) & v5_ordinal1(G) & v1_funct_1(G) & v1_finset_1(G) ) => ( ( k1_relset_1(k4_ordinal1,G) = k1_relset_1(k5_card_1(k1_card_fin(E,A,C,D)),F) & ! [H] : ! [I] : ( ( v1_relat_1(I) & v1_funct_1(I) ) => ( ( r2_hidden(H,k1_relset_1(k4_ordinal1,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) ) ) ) ) ) ) ) ) )).
fof(t40_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,B,C) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t40_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,C,D) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(C)) => k1_binop_1(k7_cat_1(k6_cat_2(A,C),k6_cat_2(B,D),k15_cat_2(A,C,B,D,E,F)),G,H) = k7_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)) ) ) ) ) ) ) ) ) )).
fof(t40_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_cat_1(D,A,B,C) => ( v11_cat_1(B,A) => k11_cat_3(A,B,C) = D ) ) ) ) ) )).
fof(t40_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t40_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k1_card_1(a_2_1_catalan2(A,B)) = k5_card_1(k2_catalan2(B,A)) ) ) )).
fof(t40_cc0sp2,axiom,( ! [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) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t40_cfcont_1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(t40_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( 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)))) ) ) ) )).
fof(t40_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => k13_cgames_1(k13_cgames_1(A)) = A ) )).
fof(t40_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(B)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(B)) => ! [E] : ( m1_chain_1(E,B) => ( B = k1_nat_1(A,1) => ( r2_hidden(k3_chain_1(B,C,D),k4_chain_1(B,E,A)) <=> ? [F] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(B)) & k1_funct_1(C,F) = k1_funct_1(D,F) & r2_hidden(k1_funct_1(C,F),k2_chain_1(B,E,F)) & ! [G] : ( m2_subset_1(G,k4_ordinal1,k2_finseq_1(B)) => ( G != F => ( ~ r1_xxreal_0(k1_funct_1(D,G),k1_funct_1(C,G)) & m2_chain_1(k4_tarski(k1_funct_1(C,G),k1_funct_1(D,G)),k2_chain_1(B,E,G)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t40_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) ) => ! [C] : ( m2_glib_000(C,A,B,k21_glib_000(A,B)) => ! [D] : ( m3_glib_001(D,C) => ( v1_chord(D,C) => ! [E] : ( ( v7_ordinal1(E) & ~ v1_abian(E) ) => ! [F] : ( ( v7_ordinal1(F) & ~ v1_abian(F) ) => ( r1_xxreal_0(F,k3_finseq_1(D)) => ( r1_xxreal_0(F,k1_nat_1(E,2)) | ! [G] : ~ r1_glib_000(A,k1_funct_1(D,E),k1_funct_1(D,F),G) ) ) ) ) ) ) ) ) ) )).
fof(t40_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) ) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t40_circcomb,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t40_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_msualg_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) ) => ! [H] : ( ( v4_msualg_1(H,A) & l3_msualg_1(H,A) ) => ! [I] : ( ( v4_msualg_1(I,B) & l3_msualg_1(I,B) ) => ! [J] : ( ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t40_classes1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => ( r1_tarski(A,k4_classes1(B)) <=> r1_tarski(k9_setfam_1(A),k4_classes1(k1_ordinal1(B))) ) ) )).
fof(t40_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v9_clvect_1(B,A) => ( v2_comseq_2(k5_normsp_0(A,B)) & k1_seq_2(k5_normsp_0(A,B)) = k2_normsp_0(A,k7_clvect_1(A,B)) ) ) ) ) )).
fof(t40_clopban3,axiom,( ! [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) & l1_clopban2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ~ r1_xxreal_0(1,k2_normsp_0(A,B)) => ( v1_clopban3(k5_clopban3(A,B),A) & v2_clopban3(k5_clopban3(A,B),A) ) ) ) ) )).
fof(t40_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t40_closure2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( v15_closure2(B,A) & l1_closure2(B,A) ) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t40_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( m1_clvect_1(D,A) => ( r1_struct_0(D,B) => r1_struct_0(D,k1_clvect_1(A,B,C)) ) ) ) ) ) )).
fof(t40_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(C,k4_clvect_2(A,B,D)) <=> ~ r1_xxreal_0(D,k13_csspace(A,k5_algstr_0(A,B,C))) ) ) ) ) ) )).
fof(t40_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k13_csspace(A,k5_algstr_0(A,k2_clvect_3(A,B,D),k2_clvect_3(A,B,C))),k9_complex1(k6_xcmplx_0(k6_series_1(k2_clvect_2(A,B),D),k6_series_1(k2_clvect_2(A,B),C)))) ) ) ) ) )).
fof(t40_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k16_coh_sp(A)) => ! [C] : ( m1_subset_1(C,k16_coh_sp(A)) => ! [D] : ( ( 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] : ! [F] : ( 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)) ) ) ) ) ) )).
fof(t40_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( r2_hidden(E,k3_funct_2(A,B,C,D)) <=> ? [F] : ( m1_subset_1(F,A) & r2_hidden(k4_tarski(F,E),k8_cohsp_1(A,B,C)) & r1_tarski(F,D) ) ) ) ) ) ) )).
fof(t40_compl_sp,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v6_metric_1(B) & v8_metric_1(B) & v9_metric_1(B) & l1_metric_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(k3_compl_sp(B,C,A))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k3_compl_sp(B,C,A))))) ) => ~ ( v3_tbsp_1(D,k3_compl_sp(B,C,A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(k3_compl_sp(B,C,A))) & E = k4_tarski(A,C) & ? [F] : ( v1_xreal_0(F) & ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( v7_ordinal1(G) => ? [H] : ( v7_ordinal1(H) & r1_xxreal_0(G,H) & r1_xxreal_0(F,k3_metric_1(k3_compl_sp(B,C,A),k2_tbsp_1(k3_compl_sp(B,C,A),D,H),E)) ) ) ) ) & ! [E] : ( v7_ordinal1(E) => ! [F] : ? [G] : ( v7_ordinal1(G) & r1_xxreal_0(E,G) & ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => k2_tbsp_1(k3_compl_sp(B,C,A),D,G) != k4_tarski(F,H) ) ) ) ) ) ) ) )).
fof(t40_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k3_complex1(k3_xcmplx_0(A,k8_complex1(A))) = k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A))) & k4_complex1(k3_xcmplx_0(A,k8_complex1(A))) = k5_numbers ) ) )).
fof(t40_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k1_complex2(k4_xcmplx_0(A),B) = k1_complex2(A,k4_xcmplx_0(B)) ) ) )).
fof(t40_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_complfld)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_complfld)) => ~ ( B != k4_struct_0(k1_complfld) & D != k4_struct_0(k1_complfld) & k3_rlvect_1(k1_complfld,k3_vectsp_1(k1_complfld,A,B),k3_vectsp_1(k1_complfld,C,D)) != k3_vectsp_1(k1_complfld,k3_rlvect_1(k1_complfld,k8_group_1(k1_complfld,A,D),k8_group_1(k1_complfld,C,B)),k8_group_1(k1_complfld,B,D)) ) ) ) ) ) )).
fof(t40_complsp2,axiom,( ! [A] : ( 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) ) ) )).
fof(t40_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(A)) => k5_card_1(k9_compos_1(A,B)) = 1 ) ) )).
fof(t40_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( v6_compos_0(D,u1_compos_1(A)) & m1_subset_1(D,u1_compos_1(A)) ) => ! [E] : ( ( v6_compos_0(E,u1_compos_1(A)) & m1_subset_1(E,u1_compos_1(A)) ) => ! [F] : ( ( v6_compos_0(F,u1_compos_1(A)) & m1_subset_1(F,u1_compos_1(A)) ) => ! [G] : ( ( 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),k5_numbers) = C ) ) ) ) ) ) ) )).
fof(t40_comptrig,axiom,( k1_comptrig(k7_complex1) = k7_xcmplx_0(k28_sin_cos,2) )).
fof(t40_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v9_ordinal1(A) => r2_relset_1(k4_ordinal1,k2_numbers,k36_valued_1(k4_ordinal1,k2_numbers,k31_valued_1(k4_ordinal1,k2_numbers,A)),k25_valued_1(k4_ordinal1,k2_numbers,k36_valued_1(k4_ordinal1,k2_numbers,A),k4_xcmplx_0(k6_complex1))) ) ) )).
fof(t40_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & v2_comseq_2(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ! [D] : ( v7_ordinal1(D) => ( k3_complex1(k9_nat_1(k2_numbers,C,D)) = k9_nat_1(k1_numbers,A,D) & k4_complex1(k9_nat_1(k2_numbers,C,D)) = k9_nat_1(k1_numbers,B,D) ) ) => ( v2_comseq_2(A) & v2_comseq_2(B) & k1_seq_2(A) = k3_complex1(k3_comseq_2(C)) & k1_seq_2(B) = k4_complex1(k3_comseq_2(C)) ) ) ) ) ) )).
fof(t40_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( v3_conlat_1(B,A) & ~ v4_conlat_1(B,A) & v6_conlat_1(B,A) & l2_conlat_1(B,A) ) => k1_binop_1(k10_conlat_1(A),B,k6_conlat_1(A)) = B ) ) )).
fof(t40_connsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_connsp_1(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & B = k1_connsp_1(A,C) ) ) ) ) )).
fof(t40_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => k6_rusub_4(A,B,C) = k1_xboole_0 ) ) ) )).
fof(t40_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_convex4(B,A) => k4_algstr_0(k15_convex4(A),k1_rlvect_2(k15_convex4(A),B)) = k8_convex4(A,B) ) ) )).
fof(t40_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),k3_qc_lang1(A),k9_funct_2(k3_qc_lang1(A),k3_qc_lang1(A))) => ! [F] : ( 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)),D,B,F,E),k15_cqc_sim1(A,C)) & r2_hidden(k2_qc_lang3(A,B),k8_setwiseo(k3_qc_lang1(A),k3_qc_lang1(A),E,F)) ) ) ) ) ) ) ) )).
fof(t40_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t40_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t40_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t40_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t40_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( k1_funct_1(C,D) = k7_xcmplx_0(B,D) & k2_xcmplx_0(D,k7_xcmplx_0(A,2)) != k5_numbers & k6_xcmplx_0(D,k7_xcmplx_0(A,2)) != k5_numbers ) ) => ! [D] : ( v1_xreal_0(D) => k1_funct_1(k5_diff_1(C,A),D) = k7_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(B,A)),k3_xcmplx_0(k6_xcmplx_0(D,k7_xcmplx_0(A,2)),k2_xcmplx_0(D,k7_xcmplx_0(A,2)))) ) ) ) ) ) )).
fof(t40_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k3_square_1(D) ) => ( r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(k6_xcmplx_0(B,A),k5_numbers) | k1_funct_1(k4_diff_1(C,A),B) = k6_xcmplx_0(k3_square_1(B),k3_square_1(k6_xcmplx_0(B,A))) ) ) ) ) ) )).
fof(t40_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(C,A),1),B) = k6_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(C,A),k5_numbers),k2_xcmplx_0(B,A)),k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(C,A),k5_numbers),B)) ) ) ) )).
fof(t40_dilworth,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v3_dilworth(A) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t40_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ( ~ ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = C ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_analoaf(A,B,C,B,D) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_analoaf(A,B,D,C,E) & C != E ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_analoaf(A,B,C,D,E) & r2_analoaf(A,B,D,C,E) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_analoaf(A,D,B,B,E) & B != D & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_analoaf(A,C,B,B,F) & r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) ) ) ) )).
fof(t40_ec_pf_1,axiom,( ! [A] : ( ( 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(k4_ordinal1,k4_ordinal1,k4_ordinal1),k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers,k5_numbers))) ) )).
fof(t40_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( 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(k4_ordinal1,k4_ordinal1,k4_ordinal1,k5_numbers,1,k5_numbers) => r1_ec_pf_1(A,k9_ec_pf_2(A,B,k8_ec_pf_2(A,B),C),C) ) ) ) ) )).
fof(t40_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_hidden(k2_cat_1(A,B,C),k16_ens_1(A)) ) ) ) )).
fof(t40_entropy1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k4_tarski(C,D),k2_matrix_0(B)) => ( r2_hidden(k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(C,1),k1_matrix_0(B)),D),k4_finseq_1(k2_entropy1(A,B))) & k3_matrix_0(A,B,C,D) = k1_funct_1(k2_entropy1(A,B),k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(C,1),k1_matrix_0(B)),D)) ) ) ) ) ) ) )).
fof(t40_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k5_enumset1(A,A,A,B,C,D,E) = k3_enumset1(A,B,C,D,E) )).
fof(t40_eqrel_1,axiom,( ! [A] : ! [B] : ( 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)))) ) ) )).
fof(t40_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t40_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ( k12_euclid(B) = k5_numbers <=> B = k4_struct_0(k15_euclid(A)) ) ) ) )).
fof(t40_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m1_subset_1(B,k2_numbers) => k4_complex1(k1_complex2(A,B)) = k3_real_1(k1_real_1(k4_real_1(k3_complex1(A),k4_complex1(B))),k4_real_1(k4_complex1(A),k3_complex1(B))) ) ) )).
fof(t40_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t40_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => k5_card_1(k8_euclid_7(A)) = A ) )).
fof(t40_euclid_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( v1_xreal_0(D) => k1_funct_1(k6_euclid_8(A,B,C),D) = k7_euclid(3,k7_euclid(3,k9_euclid(3,k2_euclid_8,k1_funct_1(A,D)),k9_euclid(3,k3_euclid_8,k1_funct_1(B,D))),k9_euclid(3,k4_euclid_8,k1_funct_1(C,D))) ) ) ) ) )).
fof(t40_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(A)) => ! [G] : ( m2_finseq_2(G,k1_numbers,k1_euclid(A)) => ! [H] : ( m2_finseq_2(H,k1_numbers,k1_euclid(A)) => ! [I] : ( m2_finseq_2(I,k1_numbers,k1_euclid(A)) => ( ( r3_euclidlp(A,k8_euclid(A,C,B),k8_euclid(A,E,D)) & r2_hidden(F,k2_euclid_4(A,B,C)) & r2_hidden(G,k2_euclid_4(A,B,C)) & r2_hidden(H,k2_euclid_4(A,D,E)) & r2_hidden(I,k2_euclid_4(A,D,E)) ) => ( F = G | H = I | r3_euclidlp(A,k8_euclid(A,G,F),k8_euclid(A,I,H)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t40_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_exchsort(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_exchsort(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_exchsort(C) ) => ( ( m1_exchsort(A,B) & m1_exchsort(B,C) ) => m1_exchsort(A,C) ) ) ) ) )).
fof(t40_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : k2_msafree2(k5_circcomb(A,k10_finseq_1(B,C))) = k2_tarski(B,C) )).
fof(t40_fcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,k1_relset_1(k1_numbers,A)) => k1_funct_1(A,B) = B ) ) => v1_fcont_1(A) ) ) )).
fof(t40_fdiff_10,axiom,( ! [A] : ( ( 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,k26_sin_cos,k27_sin_cos),k22_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),k22_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),k22_sin_cos),A),B) = k3_xcmplx_0(k1_funct_1(k22_sin_cos,k6_xcmplx_0(k1_funct_1(k26_sin_cos,B),k1_funct_1(k27_sin_cos,B))),k2_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B))))) ) ) ) ) ) )).
fof(t40_fdiff_11,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,B),k6_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k1_funct_1(k2_sin_cos9,B))),k7_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k16_sin_cos,B)),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t40_fdiff_2,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => r1_xxreal_0(k1_fdiff_1(A,B),k5_numbers) ) ) => v8_valued_0(k2_partfun1(k1_numbers,k1_numbers,A,k2_subset_1(k1_numbers))) ) ) )).
fof(t40_fdiff_4,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & k1_funct_1(k16_sin_cos,B) = k5_numbers ) ) => ( r2_fdiff_1(k6_rfunct_1(k1_numbers,k1_numbers,k16_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k6_rfunct_1(k1_numbers,k1_numbers,k16_sin_cos),A),B) = k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k18_sin_cos,B),k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t40_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k18_sin_cos),k4_taylor_1(k7_xcmplx_0(1,2))),k4_xcmplx_0(2)))) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => ( k1_funct_1(B,C) = 1 & ~ r1_xxreal_0(k1_funct_1(k16_sin_cos,C),k5_numbers) & ~ r1_xxreal_0(1,k1_funct_1(k18_sin_cos,C)) & ~ r1_xxreal_0(k1_funct_1(k18_sin_cos,C),k4_xcmplx_0(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,k18_sin_cos),k4_taylor_1(k7_xcmplx_0(1,2))),k4_xcmplx_0(2)),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_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,k18_sin_cos),k4_taylor_1(k7_xcmplx_0(1,2))),k4_xcmplx_0(2)),A),C) = k6_prepower(k6_xcmplx_0(1,k1_funct_1(k18_sin_cos,C)),k7_xcmplx_0(1,2)) ) ) ) ) ) ) )).
fof(t40_fdiff_7,axiom,( ! [A] : ( ( 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,k22_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)),A),B) = k3_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k22_sin_cos,B)),k1_funct_1(k16_sin_cos,B)) ) ) ) ) ) )).
fof(t40_fdiff_9,axiom,( ! [A] : ( ( 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,k26_sin_cos,k2_fdiff_9))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k2_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k2_fdiff_9),A),B) = k4_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(k1_funct_1(k18_sin_cos,k1_funct_1(k26_sin_cos,B)),k1_square_1(k1_funct_1(k18_sin_cos,B))),k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k26_sin_cos,B))))) ) ) ) ) ) )).
fof(t40_fib_num3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k1_nat_1(k3_fib_num3(A,B,C),k3_fib_num3(A,B,k1_nat_1(C,4))) = k2_nat_1(3,k3_fib_num3(A,B,k1_nat_1(C,2))) ) ) ) )).
fof(t40_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_finseq_1(B,A) => ! [C] : ( m1_finseq_1(C,A) => r2_finseq_8(A,k9_finseq_8(A,B,C),C,1) ) ) ) )).
fof(t40_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ( r2_hidden(C,k3_filter_0(A,k4_subset_1(u1_struct_0(A),D,k6_domain_1(u1_struct_0(A),B)))) => r2_hidden(k4_filter_0(A,B,C),k3_filter_0(A,D)) ) ) ) ) ) )).
fof(t40_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ( ( v14_lattices(A) & v14_lattices(B) ) <=> v14_lattices(k7_filter_1(A,B)) ) ) ) )).
fof(t40_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t40_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( A = k9_finseq_1(B) <=> ( k3_finseq_1(A) = 1 & k1_funct_1(A,1) = B ) ) ) )).
fof(t40_finseq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t40_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_tarski(A,k2_finseq_1(C)) & r1_tarski(B,k2_finseq_1(D)) ) => ( ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( r2_hidden(E,A) & r2_hidden(F,B) & r1_xxreal_0(F,E) ) ) ) <=> r2_relset_1(k4_ordinal1,k4_ordinal1,k14_finseq_1(k2_xboole_0(A,B)),k8_finseq_1(k4_ordinal1,k14_finseq_1(A),k14_finseq_1(B))) ) ) ) ) )).
fof(t40_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_hidden(B,k10_xtuple_0(A)) => ( k4_finseq_4(A,B) = 1 <=> k5_finseq_4(A,B) = k1_xboole_0 ) ) ) )).
fof(t40_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t40_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t40_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( 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))) ) ) )).
fof(t40_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k9_fintopo3(A,B,1) = k1_fintopo3(A,B) ) ) )).
fof(t40_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t40_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( m1_subset_1(C,k3_catalan2(A)) => ! [D] : ( m1_subset_1(D,k3_catalan2(A)) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( ( r2_hidden(C,k7_flang_1(A,B,F)) & r2_hidden(D,k7_flang_1(A,B,E)) ) => r2_hidden(k1_flang_1(A,C,D),k7_flang_1(A,B,k2_xcmplx_0(F,E))) ) ) ) ) ) ) )).
fof(t40_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => k7_flang_1(A,k1_flang_2(A,B,D,E),C) = k1_flang_2(A,B,k3_xcmplx_0(D,C),k3_xcmplx_0(E,C)) ) ) ) ) )).
fof(t40_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ( r1_tarski(k2_flang_2(A,B),k1_flang_3(A,B,C)) <=> ( C = k5_numbers | r2_hidden(k2_flang_1(A),B) ) ) ) ) )).
fof(t40_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( 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))) ) ) ) ) )).
fof(t40_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( ~ v2_struct_0(D) & v8_struct_0(D) & l2_fsm_1(D,A,B) ) => ! [E] : ( ( ~ v2_struct_0(E) & v8_struct_0(E) & l2_fsm_1(E,A,B) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ! [G] : ( m1_subset_1(G,u1_struct_0(E)) => ( ( E = k11_fsm_1(A,B,D) & r2_hidden(F,G) ) => ! [H] : ( m1_subset_1(H,k4_ordinal1) => ( r2_hidden(H,k2_finseq_1(k1_nat_1(k3_finseq_1(C),1))) => r2_hidden(k1_funct_1(k2_fsm_1(A,D,F,C),H),k1_funct_1(k2_fsm_1(A,E,G,C),H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t40_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ~ 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) ) ) ) )).
fof(t40_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ( E != k4_tarski(k10_finseq_1(D,k48_gfacirc1(A,B,C)),k4_twoscomp) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t40_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t40_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t40_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ! [D] : ~ ( r2_hidden(D,B) & k8_relset_1(A,B,C,k1_tarski(D)) = k1_xboole_0 ) <=> k2_relset_1(B,C) = B ) ) )).
fof(t40_funct_3,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t40_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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))) ) ) ) )).
fof(t40_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t40_funct_6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t40_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => k3_funct_7(A,k7_finseq_1(B,k9_finseq_1(C))) = k3_relat_1(k3_funct_7(A,B),C) ) ) )).
fof(t40_funct_8,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t40_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t40_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t40_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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) ) ) )).
fof(t40_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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)) ) ) ) )).
fof(t40_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_fvaluat1(C,A) => ( v3_fvaluat1(A) => ( v2_xxreal_0(k3_funct_2(u1_struct_0(A),k6_numbers,C,B)) <=> v2_xxreal_0(k3_funct_2(u1_struct_0(A),k6_numbers,k5_fvaluat1(A,C),B)) ) ) ) ) ) )).
fof(t40_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [D] : ( 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) ) ) ) ) )).
fof(t40_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ! [Q] : ! [R] : ! [S] : ~ ( ~ ( ~ 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) ) ) ) )).
fof(t40_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t40_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( ( ~ v1_xboole_0(F) & v1_relat_1(F) & v2_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ! [G] : ( m1_genealg1(G,F) => ! [H] : ( m1_genealg1(H,F) => m1_genealg1(k5_genealg1(F,G,H,A,B,C,D,E),F) ) ) ) ) ) ) ) ) )).
fof(t40_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ! [L] : ( m1_subset_1(L,u1_struct_0(A)) => ! [M] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t40_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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] : ( 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)) ) ) )).
fof(t40_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => m1_glib_000(A,A) ) )).
fof(t40_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( 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)) ) ) ) ) )).
fof(t40_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_002(A) ) => v7_glib_000(A) ) )).
fof(t40_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_003(A) ) => ! [B] : ! [C] : r5_glib_000(A,k13_glib_003(A,B,C)) ) )).
fof(t40_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( 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) ) ) ) ) ) )).
fof(t40_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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_nat_1(A,1),k3_finseq_1(k2_goboard2(C))) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k1_matrix_0(k2_goboard2(C))) & r2_hidden(k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B)),k7_xcmplx_0(1,2)),k3_topreal1(2,C)) & ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(C)) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B)) = k2_topreal1(2,C,D) ) ) ) ) ) ) )).
fof(t40_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m2_finseq_1(C,B) => ! [D] : ( m2_finseq_1(D,B) => ! [E] : ( ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(B)) ) => ( ( r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) & r1_xxreal_0(k1_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,k1_nat_1(A,1),C) = k17_finseq_1(B,k1_nat_1(A,1),D) ) ) ) ) ) ) )).
fof(t40_gobrd14,axiom,( ! [A] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(t40_graph_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( m2_graph_1(E,B) => ! [F] : ( m2_graph_1(F,B) => ( ( r1_graph_2(B,C,E) & F = k2_partfun1(k4_ordinal1,u4_struct_0(B),E,k2_finseq_1(A)) & D = k2_partfun1(k4_ordinal1,u1_struct_0(B),C,k2_finseq_1(k1_nat_1(A,1))) ) => r1_graph_2(B,D,F) ) ) ) ) ) ) ) )).
fof(t40_graph_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k8_graph_3(B,C,D))) => ( E = D => ( C = D | k3_graph_3(k8_graph_3(B,C,D),E,A) = k3_graph_3(B,D,A) ) ) ) ) ) ) )).
fof(t40_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v7_graph_1(B,A) & m2_graph_1(B,A) ) => ! [C] : ( ( v7_graph_1(C,A) & m2_graph_1(C,A) ) => ( r2_hidden(C,k6_graph_5(A,B)) => r1_xxreal_0(k3_finseq_1(C),k3_finseq_1(B)) ) ) ) ) )).
fof(t40_grcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) ) )).
fof(t40_groeb_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( ~ v1_xboole_0(D) & v1_ideal_1(D,k12_polynom1(A,C)) & v2_ideal_1(D,k12_polynom1(A,C)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ! [F] : ( ( ~ v1_xboole_0(F) & v1_finset_1(F) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k12_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 ) ) ) ) ) ) ) )).
fof(t40_groeb_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ( r1_groeb_1(A,B,C,D) <=> ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(E,A,C) & v1_polynom1(E,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(k12_polynom1(A,C),D)) => r6_groeb_2(A,B,C,E,D) ) ) ) ) ) ) ) )).
fof(t40_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( 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] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(F,k5_card_1(k3_polynom1(k15_pre_poly(A),C,D))) => ! [G] : ( ( 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),k3_polynom1(k15_pre_poly(A),C,k6_groeb_3(A,B,C,k10_polynom1(A,C,E,D),F))) <=> r2_hidden(G,k3_polynom1(k15_pre_poly(A),C,k6_groeb_3(A,B,C,D,F))) ) ) ) ) ) ) ) ) ) )).
fof(t40_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_group_1(A,k6_group_1(A,B),B) = k1_group_1(A) ) ) )).
fof(t40_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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) ) ) ) )).
fof(t40_group_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_group_2(C,B) => ( r1_struct_0(C,A) => r1_struct_0(B,A) ) ) ) )).
fof(t40_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t40_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ( v2_group_4(B,A) => m1_group_2(k6_group_4(A),B) ) ) ) )).
fof(t40_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_group_5(A,B,B,C) = k1_group_1(A) ) ) ) )).
fof(t40_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & l3_algstr_0(C) ) => ! [D] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(t40_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v4_group_9(C,A,B) & m1_group_9(C,A,B) ) => ! [D] : ( m1_group_9(D,A,B) => ( m1_group_9(C,A,D) => ( v4_group_9(C,A,D) & m1_group_9(C,A,D) ) ) ) ) ) )).
fof(t40_hausdorf,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => k3_hausdorf(A,B,B) = k5_numbers ) ) )).
fof(t40_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => ! [E] : ( m1_subset_1(E,k6_glib_000(A)) => ! [F] : ( ( v5_glib_001(F,A) & m3_glib_001(F,A) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t40_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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))))) ) ) ) ) )).
fof(t40_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A)))) => ~ ( r1_lattice3(k1_heyting3(k4_ordinal1,k6_domain_1(k4_ordinal1,A)),k5_heyting3(A),B) & B = k1_tarski(k1_xboole_0) ) ) ) )).
fof(t40_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(A,D) => k1_funct_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) = k3_xcmplx_0(B,k2_newton(C)) ) ) ) ) ) )).
fof(t40_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => r2_hidden(k3_hilbert1(k3_hilbert1(k4_hilbert1(A,C),B),k3_hilbert1(k4_hilbert1(A,C),k4_hilbert1(B,C))),k6_hilbert1) ) ) ) )).
fof(t40_hilbert3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ( ( v1_hilbert3(A) & v1_hilbert3(k3_hilbert1(A,B)) ) => v1_hilbert3(B) ) ) ) )).
fof(t40_hurwitz,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(A,k1_complfld) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(t40_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t40_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r3_pua2mss1(A,B,D,E) => ! [F] : ( m1_subset_1(F,u4_struct_0(A)) => ! [G] : ( m1_subset_1(G,k3_msualg_1(A,F,k11_msafree(A,k3_relat_1(D,C)))) => ! [H] : ( ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t40_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => A = k2_xcmplx_0(k1_int_1(A),k3_int_1(A)) ) )).
fof(t40_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ~ ( A != k5_numbers & B != k5_numbers & r1_int_2(A,B) & ! [E] : ( v1_int_1(E) => ~ ( ! [F] : ( v1_int_1(F) => ( ( k5_int_1(k6_xcmplx_0(F,C),A) = k5_numbers & k5_int_1(k6_xcmplx_0(F,D),B) = k5_numbers ) => r2_int_1(F,k2_xcmplx_0(C,k3_xcmplx_0(A,E)),k3_xcmplx_0(A,B)) ) ) & k5_int_1(k6_xcmplx_0(k3_xcmplx_0(A,E),k6_xcmplx_0(D,C)),B) = k5_numbers ) ) ) ) ) ) ) )).
fof(t40_int_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( 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(k5_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) ) ) ) ) ) )).
fof(t40_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(A,B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k2_xcmplx_0(1,k1_funct_1(k16_sin_cos,D)) != k5_numbers & k6_xcmplx_0(1,k1_funct_1(k16_sin_cos,D)) != k5_numbers & k1_funct_1(C,D) = k7_xcmplx_0(1,k2_xcmplx_0(1,k1_funct_1(k16_sin_cos,D))) ) ) ) & k9_xtuple_0(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_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) = k6_xcmplx_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_fdiff_9),k2_seq_4(A)),k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_fdiff_9),k3_seq_4(A))) ) ) ) ) )).
fof(t40_integr12,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( v3_rcomp_1(G) & m1_subset_1(G,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,G) & 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)) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,G) => ( k1_funct_1(C,H) = k3_xcmplx_0(H,k6_prepower(k6_xcmplx_0(k1_square_1(A),k3_prepower(H,2)),k4_xcmplx_0(k7_xcmplx_0(1,2)))) & k1_funct_1(E,H) = k1_square_1(A) & ~ r1_xxreal_0(k1_funct_1(D,H),k5_numbers) ) ) ) & r1_tarski(G,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k4_taylor_1(k7_xcmplx_0(1,2))))) & G = k1_relset_1(k1_numbers,C) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,B)) ) => k2_integra5(B,C) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k4_taylor_1(k7_xcmplx_0(1,2)))),k2_seq_4(B)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k4_taylor_1(k7_xcmplx_0(1,2)))),k3_seq_4(B))) ) ) ) ) ) ) ) ) )).
fof(t40_integr13,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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(k4_xcmplx_0(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] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => k1_funct_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) = k7_xcmplx_0(k3_xcmplx_0(A,k3_prepower(k1_funct_1(k2_sin_cos9,C),k6_xcmplx_0(A,1))),k2_xcmplx_0(1,k1_square_1(C))) ) ) ) ) ) ) )).
fof(t40_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k7_xcmplx_0(k7_xcmplx_0(k1_funct_1(k16_sin_cos,k1_funct_1(k26_sin_cos,D)),k1_square_1(k1_funct_1(k18_sin_cos,D))),k1_square_1(k1_funct_1(k18_sin_cos,k1_funct_1(k26_sin_cos,D)))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_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) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_fdiff_9),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_fdiff_9),k3_seq_4(A))) ) ) ) ) )).
fof(t40_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( ( 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] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( 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] : ( ( v1_funct_1(G) & v1_funct_2(G,k4_ordinal1,k1_integra1(B)) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(B)))) ) => ! [H] : ( m4_integr15(H,A,B,C,G) => ( ( v2_comseq_2(k2_integra3(B,G)) & k1_seq_2(k2_integra3(B,G)) = k5_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] : ( ( v1_funct_1(G) & v1_funct_2(G,k4_ordinal1,k1_integra1(B)) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(B)))) ) => ! [H] : ( m2_integr18(H,k4_real_ns1(A),B,D,G) => ( ( v2_comseq_2(k2_integra3(B,G)) & k1_seq_2(k2_integra3(B,G)) = k5_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 ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t40_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [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))) ) => k1_funct_1(k14_integra1(k4_integra1(A,C,B)),k3_finseq_1(B)) = k6_integra1(A,C,B) ) ) ) )).
fof(t40_integra2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_membered(A) ) => k22_member_1(A,k5_numbers) = k1_seq_4(k5_numbers) ) )).
fof(t40_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)) => k2_integra5(A,k18_sin_cos) = 1 ) ) )).
fof(t40_integra9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k4_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos)),k3_xcmplx_0(2,k28_sin_cos)) => r1_integra9(A,k16_sin_cos,k18_sin_cos) ) ) )).
fof(t40_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => ! [C] : ( ( ~ 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))) ) ) ) )).
fof(t40_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(t40_irrat_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(2,B) & A = k7_xcmplx_0(1,k2_xcmplx_0(B,1)) & r1_xxreal_0(1,k7_xcmplx_0(A,k6_xcmplx_0(1,A))) ) ) ) )).
fof(t40_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,A,B) => ! [G] : ( m2_cat_1(G,B,C) => ! [H] : ( m2_cat_1(H,B,C) => ! [I] : ( m2_cat_1(I,B,C) => ! [J] : ( m2_nattra_1(J,A,B,D,E) => ! [K] : ( m2_nattra_1(K,A,B,E,F) => ! [L] : ( m2_nattra_1(L,B,C,G,H) => ! [M] : ( 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,k5_nattra_1(A,B,D,E,F,J,K),k5_nattra_1(B,C,G,H,I,L,M)),k5_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))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t40_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t40_jgraph_1,axiom,( ! [A] : ( 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_funct_1(k1_goboard1(A),1) = k17_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),A,1)) & k1_funct_1(k1_goboard1(A),k3_finseq_1(A)) = k17_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),A,k3_finseq_1(A))) ) ) ) )).
fof(t40_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ! [C] : ( ( ~ 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] : ( 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) ) ) ) ) ) ) )).
fof(t40_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t40_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t40_jordan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( m1_borsuk_2(G,A,C,D) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t40_jordan1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) )).
fof(t40_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & ~ r1_xxreal_0(A,k5_numbers) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k8_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C),k9_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C)),k9_jordan6(B)) ) ) ) ) ) ) )).
fof(t40_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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,D))) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(k1_jordan8(E,C))) & r1_xxreal_0(C,D) ) => r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,D),A,k3_finseq_1(k1_jordan8(E,D)))),k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,C),B,k3_finseq_1(k1_jordan8(E,C))))) ) ) ) ) ) ) )).
fof(t40_jordan1b,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(B,k3_finseq_1(k1_jordan8(A,D))) & r1_xxreal_0(C,k1_matrix_0(k1_jordan8(A,D))) & r1_tarski(k3_goboard5(k1_jordan8(A,D),B,C),k1_jordan2c(2,A)) & r1_xxreal_0(k3_finseq_1(k1_jordan8(A,D)),k1_nat_1(B,1)) ) ) ) ) ) )).
fof(t40_jordan1h,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t40_jordan1j,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r1_goboard1(u1_struct_0(k15_euclid(2)),B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(A)) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k1_matrix_0(A)) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),A,C,D),k3_topreal1(2,B)) ) => r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),A,C,D),k10_xtuple_0(B)) ) ) ) ) ) ) )).
fof(t40_jordan1k,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ( ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ! [F] : ( 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)) ) ) ) ) ) )).
fof(t40_jordan21,axiom,( ! [A] : ( ( 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))) ) )).
fof(t40_jordan22,axiom,( ! [A] : ( ( 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)) ) )).
fof(t40_jordan23,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( 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))) ) ) ) ) )).
fof(t40_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t40_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => r1_tarski(k3_topreal1(2,k2_rfinseq(u1_struct_0(k15_euclid(2)),B,A)),k3_topreal1(2,A)) ) ) )).
fof(t40_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( 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)) ) ) ) ) ) )).
fof(t40_jordan5d,axiom,( ! [A] : ( ( ~ 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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,k1_matrix_0(k2_goboard2(A)))) ) )).
fof(t40_jordan6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(A),B)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t40_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t40_kurato_1,axiom,( k2_pre_topc(k3_topmetr,k6_kurato_1) != k6_kurato_1 )).
fof(t40_kurato_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k15_euclid(2)))))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ! [C] : ( v7_ordinal1(C) => k2_kurato_2(k15_euclid(2),A,C) = B ) => k3_kurato_2(k15_euclid(2),A) = k2_pre_topc(k15_euclid(2),B) ) ) ) )).
fof(t40_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( k12_matrix_3(A,B,C) != k4_struct_0(B) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( 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,k1_matrix_6(A,B,C),E) & ! [F] : ( 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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t40_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m1_subset_1(D,k5_finsub_1(B)) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t40_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( r2_hidden(B,C) & r4_lattice3(A,B,C) ) => k15_lattice3(A,C) = B ) ) ) )).
fof(t40_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t40_lattice5,axiom,( ! [A] : ( ( 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)) ) )).
fof(t40_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),k14_lexbfs(A,k16_lexbfs(A))) ) )).
fof(t40_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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) ) ) ) ) )).
fof(t40_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v9_ordinal1(A) & v2_comseq_2(A) & k1_seq_2(A) = k5_numbers & v6_valued_0(A) ) => v1_limfunc1(k37_valued_1(k4_ordinal1,k1_numbers,A)) ) ) )).
fof(t40_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r6_limfunc2(C,A) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k2_rcomp_1(A,k2_xcmplx_0(A,D)),k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k1_relset_1(k1_numbers,C))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k2_rcomp_1(A,k2_xcmplx_0(A,D))) => r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) | r6_limfunc2(B,A) ) ) ) ) ) )).
fof(t40_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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) = k5_numbers & ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & v1_comseq_2(k2_partfun1(k1_numbers,k1_numbers,C,k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,D),A),k2_rcomp_1(A,k2_xcmplx_0(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) = k5_numbers ) ) ) ) ) ) )).
fof(t40_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,D),A),k2_rcomp_1(A,k2_xcmplx_0(A,D))))) & k1_funct_1(B,E) = k1_limfunc3(B,A) ) ) ) ) | r3_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t40_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t40_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k16_lopban_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k16_lopban_1(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k16_lopban_1(A,B))) => ( E = k5_algstr_0(k16_lopban_1(A,B),C,D) <=> ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t40_lopban_3,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ~ r1_xxreal_0(1,k2_normsp_0(A,B)) => ( v1_lopban_3(k5_lopban_3(A,B),A) & v2_lopban_3(k5_lopban_3(A,B),A) ) ) ) ) )).
fof(t40_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => r1_lopban_4(A,k1_rlvect_1(A,B,C),k1_rlvect_1(A,B,D)) ) ) ) ) )).
fof(t40_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t40_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( v2_xxreal_0(F) & v1_xreal_0(F) ) => ( ( r2_hidden(D,k1_lpspace2(A,B,C,F)) & k5_lpspace2(A,B,C,D,F) = k5_lpspace2(A,B,C,E,F) ) => ( ! [G] : ( m2_subset_1(G,k1_zfmisc_1(A),B) => ~ ( k1_funct_1(C,k3_subset_1(A,G)) = k5_numbers & G = k1_relset_1(A,E) & r1_mesfunc6(A,B,E,G) ) ) | r1_lpspace1(A,B,C,D,E) ) ) ) ) ) ) ) ) )).
fof(t40_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_hilbert1)) => ! [C] : ( m2_finseq_1(C,k1_hilbert1) => ! [D] : ( 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] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t40_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(k3_hilbert1(A,B),k3_hilbert1(k3_hilbert1(A,C),k3_hilbert1(A,k4_ltlaxio1(B,C))))) ) ) ) )).
fof(t40_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t40_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(t40_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,B,B) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( r1_xxreal_0(A,k5_numbers) & v2_matrix10(C) ) => v4_matrix10(k6_matrix10(B,A,C)) ) ) ) ) )).
fof(t40_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( m1_matrix_2(D,k3_matrix_2(A)) => ! [E] : ( ( 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] : ( m1_matrix_2(F,k3_matrix_2(A)) => ( F = k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_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),k4_ordinal1,u1_struct_0(B),E,k10_matrix_3(A,B,C,F)) ) ) ) ) ) ) ) )).
fof(t40_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,A,D,C) & m2_finseq_1(E,k3_finseq_2(A)) ) => ! [F] : ( m2_finseq_1(F,A) => ( ~ r2_hidden(B,k2_finseq_1(k3_finseq_1(E))) => k3_matrix11(B,D,C,A,E,F) = E ) ) ) ) ) ) ) )).
fof(t40_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & k3_matrix_0(u1_struct_0(B),C,1,1) != k4_struct_0(B) & ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ~ ( v1_matrix_6(D,A,B) & k3_matrix_0(u1_struct_0(B),k4_matrix_3(B,D,C),1,1) = k5_struct_0(B) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(E,A) => ( r1_xxreal_0(E,1) | k3_matrix_0(u1_struct_0(B),k4_matrix_3(B,D,C),E,1) = k4_struct_0(B) ) ) ) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(E,A) & k3_matrix_0(u1_struct_0(B),C,1,E) = k4_struct_0(B) ) => ( r1_xxreal_0(E,1) | k3_matrix_0(u1_struct_0(B),k4_matrix_3(B,D,C),1,E) = k4_struct_0(B) ) ) ) ) ) ) ) ) ) )).
fof(t40_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [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] : ( m1_subset_1(G,u1_struct_0(F)) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(F),D,E) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(F))) ) => ! [I] : ( ( v1_matrix_0(I) & v2_matrix_0(I,u1_struct_0(F),D,C) & m2_finseq_1(I,k3_finseq_2(u1_struct_0(F))) ) => ( r2_hidden(B,k2_finseq_1(D)) => ( ( A = B & G = k4_algstr_0(F,k1_group_1(F)) ) | k4_matrix15(F,H,I) = k4_matrix15(F,k3_matrix11(A,D,E,u1_struct_0(F),H,k4_fvsum_1(k1_matrix_0(H),F,k7_matrix_0(u1_struct_0(F),H,A),k10_fvsum_1(k1_matrix_0(H),F,k7_matrix_0(u1_struct_0(F),H,B),G))),k3_matrix11(A,D,C,u1_struct_0(F),I,k4_fvsum_1(k1_matrix_0(I),F,k7_matrix_0(u1_struct_0(F),I,A),k10_fvsum_1(k1_matrix_0(I),F,k7_matrix_0(u1_struct_0(F),I,B),G)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t40_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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,k5_numbers) => v1_matrix16(k3_matrix_1(B,A),u1_struct_0(B)) ) ) ) )).
fof(t40_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) ) => B = k3_matrix_3(A,k3_matrix_3(A,k2_matrix_3(A,C),B),C) ) ) ) ) )).
fof(t40_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_6(C,A,B) & r1_matrix_6(A,B,C,D) ) => r1_matrix_6(A,B,k1_matrix_6(A,B,C),D) ) ) ) ) ) )).
fof(t40_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r1_matrix_8(A,B,C,D) => ( r1_xxreal_0(A,k5_numbers) | r1_matrix_8(A,B,k3_matrix_3(B,k3_matrix_3(B,C,C),C),k3_matrix_3(B,k3_matrix_3(B,D,D),D)) ) ) ) ) ) ) )).
fof(t40_matrixc1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k2_numbers)) ) => ( k3_finseq_1(B) = k1_matrix_0(C) => k5_matrixc1(B,k1_complsp2(k7_matrix_0(k2_numbers,k1_matrixc1(C),A))) = k1_complsp2(k5_matrixc1(k7_matrix_0(k2_numbers,k1_matrixc1(C),A),k1_complsp2(B))) ) ) ) ) )).
fof(t40_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t40_matrixr1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( k1_matrix_0(B) = k3_finseq_1(C) => k6_matrixr1(B,k7_matrixr1(A,C)) = k7_matrixr1(A,k6_matrixr1(B,C)) ) ) ) ) )).
fof(t40_matrixr2,axiom,( k3_matrix_2(k5_numbers) = k1_tarski(k6_finseq_1(k4_ordinal1)) )).
fof(t40_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( m1_matrlin(F,A,B) => ! [G] : ( 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),k5_numbers) | r2_funct_2(u1_struct_0(B),u1_struct_0(C),D,E) ) ) ) ) ) ) ) ) ) )).
fof(t40_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( ( ~ 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] : ( m1_matrlin(E,A,B) => ! [F] : ( m1_matrlin(F,A,C) => ! [G] : ( m2_finseq_1(G,u1_struct_0(D)) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(A),k3_finseq_1(E),k3_finseq_1(F)) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(A))) ) => ! [I] : ( ( v1_matrix_0(I) & v2_matrix_0(I,u1_struct_0(A),k3_finseq_1(F),k3_finseq_1(G)) & m2_finseq_1(I,k3_finseq_2(u1_struct_0(A))) ) => ( k1_matrix_0(H) = k3_finseq_1(I) => ! [J] : ( ( v1_matrix_0(J) & v2_matrix_0(J,u1_struct_0(A),k3_finseq_1(E),k3_finseq_1(G)) & m2_finseq_1(J,k3_finseq_2(u1_struct_0(A))) ) => ( 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))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t40_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) ) )).
fof(t40_matrprob,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k2_finseq_1(k3_finseq_1(k12_matrixr1(A,B)))) => k1_funct_1(k12_matrixr1(A,B),C) = k22_rvsum_1(B,k8_matrix_0(k1_numbers,A,C)) ) ) ) ) ) )).
fof(t40_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,u1_struct_0(k2_vectsp_1),A,A) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( v2_funct_1(k3_matrtop1(A,A,B)) <=> k12_matrix_3(A,k2_vectsp_1,B) != k4_struct_0(k2_vectsp_1) ) ) ) )).
fof(t40_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ~ ( A = 1 & k12_euclid(B) = k12_euclid(C) & ! [D] : ( ( 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) = k3_matrix_1(k2_vectsp_1,A) ) ) ) ) ) ) ) )).
fof(t40_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( 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 ) ) ) )).
fof(t40_measure6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( r2_hidden(A,B) <=> r2_hidden(k4_xcmplx_0(A),k3_measure6(B)) ) ) ) )).
fof(t40_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( v2_membered(C) => ! [D] : ( v2_membered(D) => ( ( r1_tarski(A,B) & r1_tarski(C,D) ) => r1_tarski(k8_member_1(A,C),k8_member_1(B,D)) ) ) ) ) ) )).
fof(t40_memstr_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_setfam_1(B) => ! [C] : ( ( ~ v2_struct_0(C) & v2_memstr_0(C,B) & v3_memstr_0(C,B) & l1_memstr_0(C,B) ) => ! [D] : ( ( 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 ) ) ) ) ) )).
fof(t40_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t40_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( 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(k12_supinf_2(k55_valued_1(A,k2_numbers,k2_valued_1(A,k2_numbers,k2_numbers,B,C)),D),k12_supinf_2(k3_valued_1(A,k1_numbers,k1_numbers,k55_valued_1(A,k2_numbers,B),k55_valued_1(A,k2_numbers,C)),D)) ) ) ) ) )).
fof(t40_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k2_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ( ! [E] : ( v7_ordinal1(E) => r2_mesfun6c(A,B,C,k4_mesfunc5(A,k2_numbers,D,E)) ) => ! [E] : ( v7_ordinal1(E) => r2_mesfun6c(A,B,C,k4_mesfunc5(A,k2_numbers,k3_mesfun9c(A,D),E)) ) ) ) ) ) ) )).
fof(t40_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( r1_mesfunc2(A,B,D) & r1_mesfunc2(A,B,E) & ! [F] : ( r2_hidden(F,k1_relset_1(A,k4_mesfunc1(A,D,E))) => r1_xxreal_0(k1_funct_1(E,F),k1_funct_1(D,F)) ) ) => v6_supinf_2(k4_mesfunc1(A,D,E)) ) ) ) ) ) ) )).
fof(t40_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( r2_hidden(C,k1_relset_1(A,B)) & k12_supinf_2(k19_rfunct_3(A,B),C) = k2_supinf_2(k12_supinf_2(B,C)) ) => k12_supinf_2(k18_rfunct_3(A,B),C) = k5_numbers ) ) ) )).
fof(t40_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t40_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => k10_mmlquery(A,B,C,k5_numbers) = k4_mmlquery(A,k18_mmlquery(A,C),B) ) ) )).
fof(t40_mod_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) )).
fof(t40_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k6_modal_1) => ! [B] : ( m1_subset_1(B,k6_modal_1) => ! [C] : ( m1_subset_1(C,k6_modal_1) => k11_modal_1(A) != k12_modal_1(B,C) ) ) ) )).
fof(t40_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( m1_subset_1(E,A) => ~ ( r3_modelc_1(A,B,C,E,D) & ! [F] : ( 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] : ( m1_modelc_1(F,A,B) => ~ ( k3_funct_2(k4_ordinal1,A,F,k5_numbers) = E & ! [G] : ( m1_subset_1(G,k4_ordinal1) => r3_modelc_1(A,B,C,k3_funct_2(k4_ordinal1,A,F,G),D) ) ) ) ) ) ) ) ) ) )).
fof(t40_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r3_modelc_2(A,k6_modelc_2(B)) => r2_modelc_2(A,B) ) ) ) )).
fof(t40_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_3(C,B) & v3_modelc_3(C,B) & l1_modelc_3(C,B) ) => ! [D] : ( ( v1_modelc_3(D,B) & v3_modelc_3(D,B) & l1_modelc_3(D,B) ) => ( ( r6_modelc_3(B,C,D) & v8_modelc_2(A) & r2_hidden(A,u3_modelc_3(B,C)) ) => ( r2_hidden(k12_modelc_2(A),u1_modelc_3(B,D)) & r2_hidden(A,u1_modelc_3(B,D)) ) ) ) ) ) ) )).
fof(t40_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => r1_tarski(k3_moebius1(A),k2_finseq_1(A)) ) )).
fof(t40_monoid_0,axiom,( ! [A] : ( ( ~ 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)) = k5_numbers ) )).
fof(t40_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => r1_tarski(k3_msualg_1(A,D,C),k3_msualg_1(A,D,k1_msafree3(A,B))) ) ) ) ) )).
fof(t40_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( m2_pboole(D,u1_struct_0(A),C,u3_msualg_1(A,B)) => ! [E] : ( 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] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t40_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) => r2_pboole(A,k2_mboolean(A,C),B) ) ) )).
fof(t40_msualg_6,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( ( 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] : ! [E] : ( ( r2_hidden(D,A) & r2_rewrite1(B,D,E) ) => r2_hidden(k4_tarski(D,E),C) ) ) ) ) )).
fof(t40_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_mycielsk(B,A) => ! [C] : ! [D] : ( ( 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)) ) ) ) )).
fof(t40_nat_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ( ! [D] : ( v7_ordinal1(D) => r2_hidden(k6_nat_1(B,C,D),A) ) => r1_tarski(k10_xtuple_0(C),A) ) ) ) )).
fof(t40_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => k1_funct_1(k12_nat_3(k1_newton(B,A)),B) = A ) ) )).
fof(t40_nat_4,axiom,( v1_int_2(4001) )).
fof(t40_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => k7_nat_d(A,k5_numbers) = A ) )).
fof(t40_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r3_ncfcont1(B,A,C,D) => ( r2_nfcont_1(B,k4_normsp_0(u1_struct_0(B),A,C),D) & r3_ncfcont1(B,A,k5_vfunct_1(u1_struct_0(B),A,C),D) ) ) ) ) ) ) )).
fof(t40_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v3_nfcont_1(C,A) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t40_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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))))) ) ) ) ) ) ) )).
fof(t40_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_prvect_2(A))) => ! [D] : ( v1_xreal_0(D) => 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) ) ) ) ) )).
fof(t40_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( A != k5_numbers => r1_nat_d(A,k7_newton(k2_xcmplx_0(A,B))) ) ) ) )).
fof(t40_nfcont_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)))) ) => ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t40_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ( ( 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) ) ) ) ) )).
fof(t40_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(k7_normform(A))) => r1_tarski(k9_normform(A,B),B) ) )).
fof(t40_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t40_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,B,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k3_funct_2(u1_struct_0(B),u1_struct_0(k2_oppcat_1(A)),k7_cat_1(B,k2_oppcat_1(A),k11_oppcat_1(B,A,C)),D) = k3_oppcat_1(A,k3_funct_2(u1_struct_0(B),u1_struct_0(A),k7_cat_1(B,A,C),D)) ) ) ) ) )).
fof(t40_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [C] : ( ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,A) ) => v3_funct_1(k2_partfun1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,u1_struct_0(k4_real_ns1(A)),k1_euclid(A),k1_numbers,B,k1_pdiff_1(D,A)),C)) ) ) => v3_funct_1(k2_partfun1(k1_numbers,u1_struct_0(k4_real_ns1(A)),B,C)) ) ) ) )).
fof(t40_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r1_orders_1(A,B) => r1_orders_1(k2_relat_1(A),B) ) ) )).
fof(t40_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m2_orders_1(B,k1_orders_1(u1_struct_0(A)),k6_partfun1(k1_orders_1(u1_struct_0(A)))) => ! [C] : ( m2_orders_2(C,A,B) => ! [D] : ( m2_orders_2(D,A,B) => ~ r1_xboole_0(C,D) ) ) ) ) )).
fof(t40_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r2_hidden(A,B) => ( C = k5_ordinal1 | r2_hidden(k11_ordinal2(A,C),k11_ordinal2(B,C)) ) ) ) ) ) )).
fof(t40_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( v4_ordinal1(A) => v4_ordinal1(k11_ordinal2(A,B)) ) ) ) )).
fof(t40_ordinal6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t40_osafree,axiom,( ! [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) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( 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),k15_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))))),k15_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))) ) ) ) ) ) ) ) ) )).
fof(t40_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v3_msualg_1(C,A) & v12_osalg_1(C,A) & m1_msualg_2(C,A,B) ) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t40_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r2_parsp_2(A,B,E,C,F) & r2_parsp_2(A,B,E,D,G) ) => ( r1_parsp_2(A,C,F,D) | r2_parsp_2(A,C,F,D,G) ) ) ) ) ) ) ) ) ) )).
fof(t40_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( v1_partfun1(k3_partfun1(C,A,B),A) => r1_tarski(A,k9_xtuple_0(C)) ) ) )).
fof(t40_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t40_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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))) ) ) ) )).
fof(t40_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ( l2_pcs_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k23_pcs_0(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k23_pcs_0(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ~ ( C = k4_tarski(E,G) & D = k4_tarski(F,H) & r1_pcs_0(k23_pcs_0(A,B),C,D) & r1_pcs_0(A,E,F) & ~ r1_pcs_0(B,G,H) ) ) ) ) ) ) ) ) ) )).
fof(t40_pdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( 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),k3_funct_2(k1_euclid(2),k1_numbers,k1_pdiff_1(2,2),B)) ) ) ) )).
fof(t40_pdiff_4,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( 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) ) ) ) )).
fof(t40_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m1_rcomp_1(C,k3_funct_2(k1_euclid(3),k1_numbers,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] : ( ( v9_ordinal1(D) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,E) = k1_tarski(k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(1,3),B)) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),C) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,1,k1_pdiff_3(2,3,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,1,k1_pdiff_3(2,3,A),B))))) & k4_pdiff_5(A,B) = k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,1,k1_pdiff_3(2,3,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,1,k1_pdiff_3(2,3,A),B))))) ) ) ) ) ) ) ) ) )).
fof(t40_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( v1_xreal_0(F) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,A) & D = k1_funct_1(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)) ) ) ) ) ) ) ) )).
fof(t40_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t40_pepin,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ( ( r2_int_1(A,B,D) & r2_int_1(A,C,D) ) => r2_int_1(B,C,D) ) ) ) ) ) )).
fof(t40_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(B))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k3_finseq_2(B))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k3_finseq_2(B))) => ( ( r1_tarski(C,E) & r1_tarski(D,F) ) => r1_tarski(k10_pnproc_1(A,B,C,D),k10_pnproc_1(A,B,E,F)) ) ) ) ) ) ) )).
fof(t40_polyeq_3,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m1_subset_1(B,k2_numbers) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r1_xxreal_0(1,C) & k1_newton(B,C) = k1_newton(A,C) ) => ( B = k5_numbers | A = k5_numbers | k9_complex1(B) = k9_complex1(A) ) ) ) ) ) )).
fof(t40_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k17_polyform(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_bspace)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t40_polynom5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C != k4_struct_0(A) => k1_algseq_1(A,k4_polynom5(A,B,C)) = 2 ) ) ) ) )).
fof(t40_polynom8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_polynom8(A,C,B) => ( r1_xxreal_0(B,k5_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)) ) ) ) ) ) )).
fof(t40_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [G] : ( ( 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] : ( ( 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,k3_polynom1(k15_pre_poly(A),C,F)) <=> r2_hidden(H,k3_polynom1(k15_pre_poly(A),C,D)) ) ) ) ) ) ) ) ) ) ) )).
fof(t40_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(1,C) & r1_xxreal_0(k2_power(C,A),k2_power(C,B)) ) ) ) ) )).
fof(t40_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t40_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_int_1(C) => k3_prepower(k3_xcmplx_0(A,B),C) = k3_xcmplx_0(k3_prepower(A,C),k3_prepower(B,C)) ) ) ) )).
fof(t40_prob_1,axiom,( ! [A] : ( ~ 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))) ) )).
fof(t40_prob_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( m2_prob_1(D,A,B) => k3_funct_2(k4_ordinal1,k1_numbers,k8_prob_1(A,B,k2_prob_3(A,C),D),k5_numbers) = k3_funct_2(k4_ordinal1,k1_numbers,k3_series_1(k8_prob_1(A,B,C,D)),k5_numbers) ) ) ) ) )).
fof(t40_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( 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) = k5_numbers ) ) ) ) )).
fof(t40_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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,D),k9_cqc_lang(A,C,D)),k9_cqc_lang(A,k7_cqc_lang(A,B,C),D)),k4_cqc_the1(A)) ) ) ) ) )).
fof(t40_pscomp_1,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t40_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t40_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)))) ) ) ) )).
fof(t40_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( ~ 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 ) ) )).
fof(t40_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_qc_lang4(C,A,B) => ! [D] : ( m1_qc_lang4(D,A,B) => r1_tarski(a_4_1_qc_lang4(A,B,C,D),k4_qc_lang4(A,B,D)) ) ) ) ) )).
fof(t40_quatern2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_quatern2)) => k4_algstr_0(k15_quatern2,A) = k6_algstr_0(k15_quatern2,k4_algstr_0(k15_quatern2,k1_group_1(k15_quatern2)),A) ) )).
fof(t40_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k28_quaterni(A),k28_quaterni(B))),k28_quaterni(k25_quaterni(B,A))) ) ) )).
fof(t40_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ( k13_quaterni(k23_quaterni(A,A)) = k6_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k1_square_1(k13_quaterni(A)),k1_square_1(k14_quaterni(A))),k1_square_1(k15_quaterni(A))),k1_square_1(k16_quaterni(A))) & k14_quaterni(k23_quaterni(A,A)) = k3_xcmplx_0(2,k3_xcmplx_0(k13_quaterni(A),k14_quaterni(A))) & k15_quaterni(k23_quaterni(A,A)) = k3_xcmplx_0(2,k3_xcmplx_0(k13_quaterni(A),k15_quaterni(A))) & k16_quaterni(k23_quaterni(A,A)) = k3_xcmplx_0(2,k3_xcmplx_0(k13_quaterni(A),k16_quaterni(A))) ) ) )).
fof(t40_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k19_quofield(A))) => ! [C] : ( 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) ) ) ) )).
fof(t40_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ! [F] : ( m1_vectsp_7(F,A,B) => ! [G] : ( m2_vectsp_6(G,A,B,k7_subset_1(u1_struct_0(B),F,E)) => ( ( m1_vectsp_7(E,A,k1_ranknull(A,B,C,D)) & r1_tarski(E,F) ) => k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,k4_vectsp_6(A,B,G)) = k4_vectsp_6(A,C,k8_ranknull(A,B,C,G,D)) ) ) ) ) ) ) ) ) )).
fof(t40_rat_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(t40_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t40_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(1,A) => ( k9_nat_1(k1_numbers,k4_real_3(B),A) = k5_numbers | r1_xxreal_0(1,k9_nat_1(k1_numbers,k4_real_3(B),A)) ) ) ) ) )).
fof(t40_relat_1,axiom,( ! [A] : k2_relat_1(k4_relat_1(A)) = k4_relat_1(A) )).
fof(t40_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ! [E] : ( 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))) ) ) ) )).
fof(t40_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r5_rewrite1(A,B,C) => r5_rewrite1(A,C,B) ) ) )).
fof(t40_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t40_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(C))) => ! [G] : ( ( ~ 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)) ) ) ) ) ) ) )).
fof(t40_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_valued_0(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_valued_0(D) ) => k1_valued_1(k1_rfunct_1(B,A),k1_rfunct_1(D,C)) = k1_rfunct_1(k1_valued_1(k18_valued_1(B,C),k18_valued_1(D,A)),k18_valued_1(A,C)) ) ) ) ) )).
fof(t40_rfunct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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))) ) ) ) )).
fof(t40_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,A) => r1_xxreal_0(k5_numbers,k1_funct_1(k19_rfunct_3(A,B),C)) ) ) ) )).
fof(t40_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_seq_2(C) => ( B = k1_funct_1(k3_rinfsup1(C),A) <=> ( ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(B,k1_funct_1(C,k2_xcmplx_0(A,D))) ) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => r1_xxreal_0(k2_xcmplx_0(B,D),k1_funct_1(C,k2_xcmplx_0(A,E))) ) ) ) ) ) ) ) ) ) )).
fof(t40_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v10_mesfunc5(A) <=> k6_rinfsup2(A) = k5_rinfsup2(A) ) ) )).
fof(t40_rlaffin1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_rlvect_2(C,B) => k6_rlvect_2(B,k2_rlaffin1(B,C,A)) = k1_rlvect_1(B,k6_rlvect_2(B,C),A) ) ) ) )).
fof(t40_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => m1_rlsub_1(k1_rlsub_1(B),C) ) ) ) )).
fof(t40_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_2(C,A,B) => m1_rlsub_2(B,A,C) ) ) ) )).
fof(t40_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_connsp_2(C,A,B) => m1_connsp_2(k5_rusub_4(A,C,k4_algstr_0(A,B)),A,k4_struct_0(A)) ) ) ) )).
fof(t40_rlvect_1,axiom,( ! [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) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( 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)) ) ) ) ) )).
fof(t40_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_rlvect_2(C,A) => ! [D] : ( 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)) ) ) ) ) )).
fof(t40_rlvect_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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 ) ) ) )).
fof(t40_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => m1_rmod_2(k1_rmod_2(A,C),A,D) ) ) ) ) )).
fof(t40_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( m2_rmod_2(E,A,B,C) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t40_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_4(C,A,B) => ! [D] : ( m1_rmod_4(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t40_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k9_robbins1(A,k12_robbins1(A,B),k11_robbins1(A,B)) = B ) ) )).
fof(t40_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t40_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t40_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( ~ r1_xxreal_0(k1_rpr_1(A,C),k5_numbers) => ( k2_rpr_1(A,C,B) = k6_xcmplx_0(1,k2_rpr_1(A,C,k3_subset_1(A,B))) & k2_rpr_1(A,C,k3_subset_1(A,B)) = k6_xcmplx_0(1,k2_rpr_1(A,C,B)) ) ) ) ) ) )).
fof(t40_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_rusub_1(A,B,k2_rusub_1(A)) = u1_struct_0(A) ) ) )).
fof(t40_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_2(C,A,B) => m1_rusub_2(B,A,C) ) ) ) )).
fof(t40_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( r1_struct_0(k1_rusub_1(A),B) <=> B = k4_struct_0(A) ) ) )).
fof(t40_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t40_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t40_rvsum_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k2_numbers) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k2_numbers) ) => k17_rvsum_1(k4_rvsum_2(A,B,C)) = k2_xcmplx_0(k17_rvsum_1(B),k17_rvsum_1(C)) ) ) ) )).
fof(t40_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & ~ v1_scmfsa_m(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(E,u1_struct_0(k1_scmfsa_2)) ) => ( ( r1_xxreal_0(k1_funct_1(E,D),k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k5_card_1(B),k5_card_1(C)),3)))) ) ) ) ) ) ) )).
fof(t40_scmfsa10,axiom,( ! [A] : ( v7_ordinal1(A) => ( r2_hidden(k1_nat_1(A,1),k3_amistd_1(k7_card_1(3),k1_scmfsa_2,A)) & ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k3_amistd_1(k7_card_1(3),k1_scmfsa_2,A)) => r1_xxreal_0(A,B) ) ) ) ) )).
fof(t40_scmfsa8c,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ~ ( ~ r4_scmfsa7b(A,B) & r4_scmfsa7b(k2_scmfsa6a(A),B) ) ) ) )).
fof(t40_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) & v1_scmfsa7b(D) ) => ~ ( k1_funct_1(B,k4_scmfsa_2(k5_numbers)) = 1 & r3_scmfsa9a(A,B,C,D) & r4_scmfsa9a(A,B,C,D) & ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1))) ) => ~ ( v7_memstr_0(E,k7_card_1(3),k1_scmfsa_2) & ! [F] : ( v7_ordinal1(F) => ~ ( r1_xxreal_0(k3_funct_2(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(B,D,C,A),F)),k3_funct_2(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(B,D,C,A),k1_nat_1(F,1)))) & ~ r1_xxreal_0(k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(B,D,C,A),F),C),k5_numbers) ) ) ) ) ) ) ) ) ) )).
fof(t40_scmfsa_2,axiom,( ! [A] : ( ( 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(k7_card_1(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 ) )).
fof(t40_scmfsa_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => r6_pboole(u1_struct_0(k1_scmfsa_2),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(D,B,C,A),k1_nat_1(k5_numbers,1)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa_9(C,B)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D),k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(k1_funct_4(A,k2_scmfsa_9(C,B)),B),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D)),3))) ) ) ) ) )).
fof(t40_scmpds_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => A != k4_struct_0(k1_scmpds_2) ) )).
fof(t40_scmpds_7,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(E) & v1_funct_1(E) & v1_finset_1(E) & v1_afinsq_1(E) ) => ( ~ r1_xxreal_0(k1_nat_1(k5_card_1(E),3),D) <=> r2_hidden(D,k2_afinsq_1(k2_scmpds_7(A,B,C,E))) ) ) ) ) ) ) )).
fof(t40_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => k3_tarski(A) = k3_tarski(k6_scmyciel(A)) ) )).
fof(t40_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_semi_af1(A,B,C,D,E) => r2_semi_af1(A,B,D,C,E) ) ) ) ) ) ) )).
fof(t40_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)),k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,B),A)) ) ) ) )).
fof(t40_seq_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( v1_comseq_2(A) & ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( m2_valued_0(B,k1_numbers,A) & v2_comseq_2(B) ) ) ) ) )).
fof(t40_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( 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),k55_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))) ) ) ) ) )).
fof(t40_seqm_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k9_complex1(k6_xcmplx_0(A,B)) = 1 <=> ( ( ~ r1_xxreal_0(A,B) & A = k2_xcmplx_0(B,1) ) | ( ~ r1_xxreal_0(B,A) & B = k2_xcmplx_0(A,1) ) ) ) ) ) )).
fof(t40_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,B,C) = k1_power(C,k9_nat_1(k1_numbers,k56_valued_1(k4_ordinal1,k1_numbers,A),C)) ) & v2_comseq_2(B) ) => ( r1_xxreal_0(1,k1_seq_2(B)) | v2_series_1(A) ) ) ) ) )).
fof(t40_series_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( k2_xcmplx_0(k2_xcmplx_0(A,B),C) = 1 => r1_xxreal_0(k7_xcmplx_0(1,3),k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(C))) ) ) ) ) )).
fof(t40_setfam_1,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(t40_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( v7_ordinal1(C) => ( v3_prob_1(B) => r1_tarski(k1_funct_1(B,C),k3_funct_2(k4_ordinal1,k9_setfam_1(A),k4_setlim_1(A,B),k1_nat_1(C,1))) ) ) ) )).
fof(t40_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) ) ) )).
fof(t40_setwiseo,axiom,( ! [A] : k4_binop_1(k5_finsub_1(A),k9_setwiseo(A)) = k1_xboole_0 )).
fof(t40_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t40_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( v7_ordinal1(B) => k4_sf_mastr(A) = k4_sf_mastr(k5_compos_1(k1_scmfsa_2,A,B)) ) ) )).
fof(t40_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t40_simplex0,axiom,( ! [A] : ! [B] : ( ( v1_matroid0(B) & v3_matroid0(B) & m1_simplex0(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t40_simplex1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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] : ( ( v1_finset_1(C) & v1_rlaffin1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(t40_sin_cos,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => k7_xcmplx_0(k1_newton(B,A),k2_newton(A)) = k7_xcmplx_0(k1_newton(B,A),k2_newton(A)) ) ) )).
fof(t40_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => r1_fcont_1(k5_sin_cos2,A) ) )).
fof(t40_sin_cos3,axiom,( ! [A] : ( v1_xreal_0(A) => k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A) = k1_funct_1(k1_sin_cos2,A) ) )).
fof(t40_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k3_xcmplx_0(k19_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),k19_sin_cos(A)),k3_xcmplx_0(k17_sin_cos(B),k19_sin_cos(B))) ) ) )).
fof(t40_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( k2_sin_cos2(A) != k5_numbers & k2_sin_cos2(B) != k5_numbers & k1_sin_cos5(k2_xcmplx_0(A,B)) != k7_xcmplx_0(k2_xcmplx_0(1,k3_xcmplx_0(k1_sin_cos5(A),k1_sin_cos5(B))),k2_xcmplx_0(k1_sin_cos5(A),k1_sin_cos5(B))) ) ) ) )).
fof(t40_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ~ ( ~ r1_xxreal_0(A,k2_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B))) & r1_xxreal_0(A,k2_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B))) & r1_xxreal_0(1,k17_sin_cos(A)) ) ) ) )).
fof(t40_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => k2_sin_cos7(A) = k3_xcmplx_0(2,k1_sin_cos7(k3_square_1(k7_xcmplx_0(k6_xcmplx_0(A,1),2)))) ) ) )).
fof(t40_sin_cos9,axiom,( k4_sin_cos9(1) = k7_xcmplx_0(k28_sin_cos,4) & k1_funct_1(k2_sin_cos9,1) = k7_xcmplx_0(k28_sin_cos,4) )).
fof(t40_sincos10,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k4_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(t40_sppol_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) )).
fof(t40_sppol_2,axiom,( ! [A] : ( 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)) ) ) )).
fof(t40_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k3_finseq_1(k1_sprect_1(A)) = 5 ) )).
fof(t40_sprect_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t40_sprect_3,axiom,( ! [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) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( 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)) ) ) ) )).
fof(t40_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t40_square_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( k1_square_1(A) = k1_square_1(B) & A != B & A != k4_xcmplx_0(B) ) ) ) )).
fof(t40_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t40_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k7_card_1(B),k7_card_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(B),k7_card_1(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k7_card_1(k1_nat_1(B,1)),k7_card_1(k1_nat_1(A,1))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(k1_nat_1(B,1)),k7_card_1(k1_nat_1(A,1))))) ) => ( ( v2_funct_2(C,k7_card_1(A)) & v1_stirl2_1(C,B,A) & C = k2_partfun1(k7_card_1(k1_nat_1(B,1)),k7_card_1(k1_nat_1(A,1)),D,k7_card_1(B)) & k2_stirl2_1(k7_card_1(k1_nat_1(B,1)),k1_nat_1(A,1),D,B) = A ) => ( v2_funct_2(D,k7_card_1(k1_nat_1(A,1))) & v1_stirl2_1(D,k1_nat_1(B,1),k1_nat_1(A,1)) & k1_stirl2_1(k1_nat_1(B,1),k7_card_1(k1_nat_1(A,1)),D,k6_domain_1(k7_card_1(k1_nat_1(A,1)),k2_stirl2_1(k7_card_1(k1_nat_1(B,1)),k1_nat_1(A,1),D,B))) = k1_seq_4(B) ) ) ) ) ) ) )).
fof(t40_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k16_substut1(A),k38_substut1(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t40_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,A) => ! [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)) ) ) ) ) ) ) ) ) ) )).
fof(t40_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v6_supinf_2(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_xxreal_0(k12_supinf_2(k18_supinf_2(A),B),k12_supinf_2(k18_supinf_2(A),k1_nat_1(B,C))) ) ) ) ) )).
fof(t40_sysrel,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( ( ( k3_relat_1(B,A) = B & k3_relat_1(A,k6_subset_1(A,k4_relat_1(k9_xtuple_0(A)))) = k1_xboole_0 & k3_relat_1(A,B) = A & k3_relat_1(B,k6_subset_1(B,k4_relat_1(k9_xtuple_0(B)))) = k1_xboole_0 ) => k1_sysrel(B) = k1_sysrel(A) ) & ( ( k3_relat_1(A,B) = B & k3_relat_1(k6_subset_1(A,k4_relat_1(k9_xtuple_0(A))),A) = 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 ) => k1_sysrel(B) = k1_sysrel(A) ) ) ) ) )).
fof(t40_taxonom1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v5_tbsp_1(A) & l1_metric_1(A) ) => ! [B] : ( ( 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] : ( ( ~ 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)) ) ) ) ) )).
fof(t40_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k7_tdlat_1(A) = k1_realset1(k3_tdlat_1(A),k5_tdlat_1(A)) ) )).
fof(t40_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)))) ) ) )).
fof(t40_tdlat_3,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t40_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( 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,k3_polynom1(k15_pre_poly(A),C,D)) => ( E = k3_termord(A,B,C,D) | k4_polynom1(A,C,k6_termord(A,B,C,D),E) = k4_polynom1(A,C,D,E) ) ) ) ) ) ) ) )).
fof(t40_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ v3_tex_2(B,A) ) ) )).
fof(t40_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_pre_topc(C,A) => ( ( v4_tex_3(B,A) & m1_pre_topc(C,B) ) => v4_tex_3(C,A) ) ) ) ) )).
fof(t40_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t40_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ 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)) ) ) ) ) ) ) )).
fof(t40_toler_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(t40_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( m1_borsuk_2(G,A,D,E) => ! [H] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t40_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( 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 ) ) )).
fof(t40_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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),k5_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)),k2_xcmplx_0(k2_topdim_1(A,C),1)) ) ) ) ) ) )).
fof(t40_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k2_topgen_1(A,k1_struct_0(A)) = k1_struct_0(A) ) )).
fof(t40_topgen_3,axiom,( ! [A] : ! [B] : ! [C] : ( 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 ) ) )).
fof(t40_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t40_topgen_5,axiom,( v3_tops_1(k1_topgen_5,k3_topgen_5) & m1_subset_1(k1_topgen_5,k1_zfmisc_1(u1_struct_0(k3_topgen_5))) )).
fof(t40_topgrp_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_connsp_2(D,A,k6_algstr_0(A,B,k2_group_1(A,C))) => ? [E] : ( v3_pre_topc(E,A) & m1_connsp_2(E,A,B) & ? [F] : ( v3_pre_topc(F,A) & m1_connsp_2(F,A,C) & r1_tarski(k2_group_2(A,E,k1_group_2(A,F)),D) ) ) ) ) ) ) )).
fof(t40_topreal3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(2))) => ~ ( B != A & k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),B,A),k3_topreal1(2,C)) = k1_tarski(B) & r2_hidden(A,k3_topreal1(2,C)) ) ) ) ) )).
fof(t40_topreal6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(2))) => ! [C] : ( v1_xreal_0(C) => ( A = B => r1_tarski(k8_metric_1(k14_euclid(2),B,C),k4_card_3(k5_funct_4(k1_zfmisc_1(k1_numbers),1,2,k2_rcomp_1(k6_xcmplx_0(k17_euclid(A),C),k2_xcmplx_0(k17_euclid(A),C)),k2_rcomp_1(k6_xcmplx_0(k18_euclid(A),C),k2_xcmplx_0(k18_euclid(A),C))))) ) ) ) ) )).
fof(t40_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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))) = k2_xcmplx_0(k3_xcmplx_0(A,k18_euclid(C)),k3_xcmplx_0(B,k18_euclid(D))) ) ) ) ) )).
fof(t40_topreala,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(C,D) ) => ! [E] : ( ( v4_pre_topc(E,k4_topmetr(A,B)) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B)))) ) => ! [F] : ( ( 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)))) ) ) ) ) ) ) ) ) )).
fof(t40_toprealb,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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))) ) ) ) )).
fof(t40_toprealc,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( ( 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))))) ) ) ) ) )).
fof(t40_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ( v3_toprns_1(B,A) => v3_toprns_1(k3_toprns_1(A,B),A) ) ) ) )).
fof(t40_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)) ) ) )).
fof(t40_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & k9_xtuple_0(D) = C & k10_xtuple_0(D) = k1_tops_2(A,B,C) & ! [E] : ( r2_hidden(E,C) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t40_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t40_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t40_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => r1_xxreal_0(1,k7_trees_1(A)) ) )).
fof(t40_trees_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v6_ordinal1(C) & m1_subset_1(C,k1_zfmisc_1(k4_partfun1(A,B))) ) => r2_hidden(k3_tarski(C),k4_partfun1(A,B)) ) )).
fof(t40_trees_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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 ) ) ) )).
fof(t40_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v3_trees_9(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k7_finseq_1(B,k14_trees_3(C)),k9_xtuple_0(A)) => k1_funct_1(A,k7_finseq_1(B,k14_trees_3(C))) = k1_funct_1(k2_trees_9(A,B),k1_nat_1(C,1)) ) ) ) ) )).
fof(t40_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t40_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t40_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( l1_turing_1(B) => ! [C] : ( 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)) ) ) ) )).
fof(t40_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => k2_msafree2(k40_twoscomp(A,B)) = k2_tarski(A,B) ) ) )).
fof(t40_uniroots,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v6_struct_0(A) & v4_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => k1_algseq_1(A,k4_uniroots(B,A)) = k2_xcmplx_0(B,1) ) ) )).
fof(t40_uproots,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r1_xxreal_0(k1_algseq_1(A,C),B) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k4_uproots(A,C,B),k9_polynom3(A)) ) ) ) ) )).
fof(t40_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t40_valued_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => k1_relset_1(k4_ordinal1,k61_valued_1(B,A)) = a_2_1_valued_1(A,B) ) ) )).
fof(t40_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t40_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => m1_vectsp_4(k1_vectsp_4(A,C),A,D) ) ) ) ) )).
fof(t40_vectsp_5,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t40_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_vectsp_6(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t40_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ 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] : ( ( 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_funct_1(k4_normsp_0(A,C,D),B) = k2_normsp_0(C,k7_partfun1(u1_struct_0(C),D,B)) ) ) ) ) ) ) )).
fof(t40_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( 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(k4_normsp_0(A,B,C),D) = k2_normsp_0(B,k7_partfun1(u1_struct_0(B),C,D)) ) ) ) ) ) ) )).
fof(t40_waybel11,axiom,( ! [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) ) => ( v3_waybel_3(A) <=> k12_yellow_6(A) = k2_waybel11(A) ) ) )).
fof(t40_waybel12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ! [C] : ( 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,k1_yellow_1(u1_pre_topc(A))) ) ) ) ) )).
fof(t40_waybel14,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(k5_waybel11(A)))) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_yellow_1(k5_waybel11(A))))) & B = k1_yellow_0(k1_yellow_1(k5_waybel11(A)),C) & ! [D] : ( m1_subset_1(D,u1_struct_0(k1_yellow_1(k5_waybel11(A)))) => ( r2_hidden(D,C) => v6_waybel_6(D,k1_yellow_1(k5_waybel11(A))) ) ) ) ) & v3_waybel_3(k1_yellow_1(k5_waybel11(A))) ) <=> v1_waybel_5(k1_yellow_1(k5_waybel11(A))) ) ) )).
fof(t40_waybel19,axiom,( ! [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) & l1_waybel_9(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t40_waybel20,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t40_waybel21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t40_waybel23,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v1_waybel23(k1_waybel_3(A,B),A) ) ) )).
fof(t40_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v6_pre_topc(B) & v1_waybel25(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) ) => ! [D] : ( ( 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] : ( ( 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(k5_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(k5_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) ) ) ) ) ) ) )).
fof(t40_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v4_waybel11(C) & m1_yellow_9(C,k1_yellow_1(u1_pre_topc(B))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t40_waybel30,axiom,( ! [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_waybel_2(A) & l1_waybel_9(A) ) => ( v2_waybel_8(A) <=> ( v3_waybel30(A) & v2_waybel_8(k1_yellow_1(k5_waybel11(A))) ) ) ) )).
fof(t40_waybel34,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(t40_waybel_0,axiom,( ! [A] : ( ( v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v12_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_waybel_0(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k13_lattice3(A,C,D),B) ) ) ) ) ) ) )).
fof(t40_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t40_waybel_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & v2_lattice3(A) & l1_orders_2(A) ) => ( ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t40_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ( v6_waybel_3(A) & v8_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ~ ( r1_waybel_3(k1_yellow_1(u1_pre_topc(A)),B,C) & ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t40_waybel_4,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => k5_waybel_4(A,B,k1_waybel_4(A)) = k1_waybel_3(A,B) ) ) )).
fof(t40_waybel_7,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => v2_waybel_0(k6_waybel_4(A,C,B),A) ) ) ) ) )).
fof(t40_waybel_9,axiom,( ! [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) & v1_compts_1(A) & l1_waybel_9(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v5_pre_topc(k4_waybel_1(A,B),A,A) ) => v3_yellow_0(A) ) ) )).
fof(t40_weddwitt,axiom,( ! [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) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_struct_0(k5_weddwitt(A,B)) = k5_struct_0(A) ) ) )).
fof(t40_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r4_wellord1(A,B) => r4_wellord1(B,A) ) ) ) )).
fof(t40_wsierp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( k2_finseq_3(1,k7_finseq_1(k9_finseq_1(B),A)) = A & k2_finseq_3(k1_nat_1(k3_finseq_1(A),1),k7_finseq_1(A,k9_finseq_1(B))) = A ) ) )).
fof(t40_xboole_1,axiom,( ! [A] : ! [B] : k4_xboole_0(k2_xboole_0(A,B),B) = k4_xboole_0(A,B) )).
fof(t40_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k9_xboolean(A,k4_xboolean(B,C)) = k5_xboolean(k3_xboolean(k5_xboolean(A,B)),k3_xboolean(k5_xboolean(A,C))) ) ) ) )).
fof(t40_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( 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)) ) ) ) )).
fof(t40_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(C,B) & r1_xxreal_0(k2_xcmplx_0(A,C),B) ) ) ) ) )).
fof(t40_xtuple_0,axiom,( ! [A] : ! [B] : r1_tarski(k13_xtuple_0(k3_xboole_0(A,B)),k3_xboole_0(k13_xtuple_0(A),k13_xtuple_0(B))) )).
fof(t40_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) )).
fof(t40_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(D,B) => ( r1_xxreal_0(C,A) | r1_tarski(k2_xxreal_1(C,D),k3_xxreal_1(A,B)) ) ) ) ) ) ) )).
fof(t40_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ( ~ v1_xboole_0(A) <=> r1_xxreal_0(k2_xxreal_2(A),k1_xxreal_2(A)) ) ) )).
fof(t40_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( r1_xxreal_0(A,B) => r1_xxreal_0(k5_numbers,k3_xxreal_3(B,A)) ) ) ) )).
fof(t40_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t40_yellow12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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)))) ) ) ) )).
fof(t40_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( 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) ) ) ) ) ) ) )).
fof(t40_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & v4_yellow18(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t40_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v16_functor0(C,A,B) & m2_functor0(C,A,B) ) => ( r3_yellow20(A,B,C,A,B) => v21_functor0(C,A,B) ) ) ) ) )).
fof(t40_yellow_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t40_yellow_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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))) ) ) ) ) )).
fof(t40_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t40_yellow_4,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(B,k4_yellow_4(A,B,B)) ) ) )).
fof(t40_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t40_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) => r1_tarski(B,k12_yellow_6(k13_yellow_6(A,B))) ) ) )).
fof(t40_yellow_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t40_yellow_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( ( 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))))) ) ) ) ) ) )).
fof(t40_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v5_zf_lang(A) => A = k7_zf_lang(k21_zf_lang(A),k22_zf_lang(A)) ) ) )).
fof(t40_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ( ~ ( ~ ( 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) ) ) ) ) )).
fof(t40_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(k2_xboole_0(k2_tarski(A,B),C),C) => r2_hidden(A,C) ) )).
fof(t40_zfrefle1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ~ ( r2_hidden(k4_ordinal1,A) & ! [B] : ( ( v3_ordinal1(B) & m1_subset_1(B,A) ) => ! [C] : ( ~ v1_xboole_0(C) => ~ ( r2_ordinal2(B,k4_ordinal1) & C = k4_classes1(B) & v1_zf_model(C) ) ) ) ) ) )).
fof(t40_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t40_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( m1_zmodul02(C,A) => r1_tarski(k18_zmodul02(A,k25_zmodul02(A,B,C)),k4_subset_1(u1_struct_0(A),k18_zmodul02(A,B),k18_zmodul02(A,C))) ) ) ) )).
fof(t410_xxreal_1,axiom,( ! [A] : ( 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) ) )).
fof(t411_xxreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => k6_subset_1(k1_xxreal_1(A,k1_xxreal_0),k3_xxreal_1(A,k1_xxreal_0)) = k1_tarski(A) ) )).
fof(t412_xxreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => k6_subset_1(k2_xxreal_1(A,k1_xxreal_0),k4_xxreal_1(A,k1_xxreal_0)) = k1_tarski(A) ) )).
fof(t413_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t414_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t415_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t416_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t417_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t418_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t419_xxreal_1,axiom,( ! [A] : ( 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)) ) )).
fof(t41_abcmiz_0,axiom,( ! [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) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_abcmiz_0(A)) => ( r3_abcmiz_0(A,B,C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,E) & r1_xxreal_0(E,k1_nat_1(k3_finseq_1(C),1)) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t41_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & l1_msualg_1(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(t41_abcmiz_a,axiom,( 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)) )).
fof(t41_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r3_aff_1(A,B,C) => r3_aff_1(A,C,B) ) ) ) ) )).
fof(t41_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t41_afinsq_1,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(t41_afinsq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,A) & v1_funct_1(C) & v5_ordinal1(C) & v1_finset_1(C) ) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t41_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k14_afproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k14_afproj(A))) => ! [D] : ( 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] : ( m1_subset_1(E,u2_incsp_1(k14_afproj(A))) => D != k4_tarski(E,2) ) ) ) ) ) ) )).
fof(t41_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & k1_afvect0(A,B,k1_afvect0(A,E,D)) = k1_afvect0(A,E,k1_afvect0(A,C,D)) ) ) ) ) ) )).
fof(t41_algspec1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t41_algstr_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ v2_struct_0(D) & m1_algstr_4(D,B) ) => ! [E] : ( ( v1_partfun1(E,u1_struct_0(A)) & v3_relat_2(E) & v8_relat_2(E) & v1_algstr_4(E,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ~ ( v1_group_6(C,A,B) & u1_struct_0(D) = k2_relset_1(u1_struct_0(B),C) & r2_relset_1(u1_struct_0(A),u1_struct_0(A),E,k7_algstr_4(u1_struct_0(A),u1_struct_0(B),C)) & ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(k4_algstr_4(A,E)),u1_struct_0(D)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_algstr_4(A,E)),u1_struct_0(D)))) ) => ~ ( r1_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),u1_struct_0(D),C,k1_partfun1(u1_struct_0(A),u1_struct_0(k4_algstr_4(A,E)),u1_struct_0(k4_algstr_4(A,E)),u1_struct_0(D),k5_algstr_4(A,E),F)) & v3_funct_2(F,u1_struct_0(k4_algstr_4(A,E)),u1_struct_0(D)) & v1_group_6(F,k4_algstr_4(A,E),D) ) ) ) ) ) ) ) ) )).
fof(t41_altcat_4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t41_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_analmetr(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t41_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & F != G & r2_analort(A,B,C,D,E,F,G) ) ) ) ) ) ) ) ) )).
fof(t41_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & l1_aofa_a00(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,C),D)) => ( r2_hidden(E,k1_msafree4(u1_struct_0(A),k13_msafree(A,B),D)) => r8_pboole(u1_struct_0(A),k11_aofa_a00(A,C,D,E),k2_aofa_a00(u1_struct_0(A),D,E)) ) ) ) ) ) ) )).
fof(t41_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( ( v19_aofa_a00(F,A) & m1_subset_1(F,u1_struct_0(A)) ) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),F)) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),F)) => ! [I] : ( m2_subset_1(I,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => k15_aofa_a00(A,B,C,D,F,k34_aofa_a00(A,C,F,G,H),I) = k34_aofa_a00(A,D,F,k15_aofa_a00(A,B,C,D,F,G,I),k15_aofa_a00(A,B,C,D,F,H,I)) ) ) ) ) ) ) ) ) ) )).
fof(t41_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_aofa_i00(E,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) ) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),E) => ! [G] : ( 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,k5_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,k5_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,k5_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,k5_numbers)) & r1_xxreal_0(k21_aofa_i00(B,k4_numbers,C,G),k21_aofa_i00(B,k4_numbers,C,F)) ) ) ) ) ) ) ) ) ) )).
fof(t41_armstrng,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t41_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ( A != k1_xboole_0 => k8_arytm_3(A,A) = 1 ) ) )).
fof(t41_asympt_1,axiom,( ? [A] : ( m1_funct_2(A,k4_ordinal1,k1_numbers) & A = k1_tarski(k3_asympt_1(1)) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => r1_xxreal_0(k9_nat_1(k1_numbers,k3_asympt_1(k4_xcmplx_0(1)),B),k9_nat_1(k1_numbers,k3_asympt_1(1),B)) ) & ~ r2_hidden(k3_asympt_1(k4_xcmplx_0(1)),k15_asympt_0(A,k6_asympt_0(k1_seq_1(1)))) ) )).
fof(t41_bcialg_1,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k5_bcialg_1(A)) => ! [D] : ( m2_subset_1(D,u1_struct_0(A),k7_bcialg_1(A,B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t41_bcialg_2,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ! [C] : ( m2_bcialg_1(C,A) => ! [D] : ( m5_bcialg_2(D,A,B) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t41_bcialg_3,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t41_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t41_bcialg_5,axiom,( ! [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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t41_bcialg_6,axiom,( ! [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] : ( ( ~ 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] : ( ( 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) & m2_bcialg_1(k5_bcialg_6(A,B,C),A) ) ) ) ) )).
fof(t41_bciideal,axiom,( ! [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) ) => ( ( v3_bciideal(k1_tarski(k4_struct_0(A)),A) & m2_bcialg_1(k1_tarski(k4_struct_0(A)),A) ) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t41_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)),k2_xcmplx_0(k4_bhsp_1(A,B,D),k4_bhsp_1(A,C,E))) ) ) ) ) ) )).
fof(t41_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(C,k4_bhsp_2(A,B,D)) <=> ~ r1_xxreal_0(D,k4_bhsp_1(A,B,C)) ) ) ) ) ) )).
fof(t41_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k3_bhsp_1(A,k4_bhsp_4(A,B,D,C)),k9_complex1(k7_series_1(k2_bhsp_2(A,B),D,C))) ) ) ) ) )).
fof(t41_bilinear,axiom,( ! [A] : ( l2_struct_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t41_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t41_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t41_borsuk_4,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( v2_pre_topc(D) & l1_pre_topc(D) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( ( v5_pre_topc(C,A,B) & m1_pre_topc(D,B) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t41_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ( A = k3_rcomp_1(B,k1_xxreal_0) => v4_pre_topc(A,k3_topmetr) ) ) ) )).
fof(t41_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ( ( v5_pre_topc(D,k5_topmetr,A) & k1_funct_1(D,k5_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),k5_numbers) = C & k1_funct_1(k2_borsuk_2(A,B,C,D),1) = B ) ) ) ) ) ) )).
fof(t41_borsuk_7,axiom,( k45_valued_1(k8_borsuk_7,k9_borsuk_7) = k4_euclid_5(2,k5_numbers,k5_numbers) )).
fof(t41_bspace,axiom,( ! [A] : k1_card_1(k9_bspace(A)) = k1_card_1(A) )).
fof(t41_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t41_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_subset_1(I,A) => ! [J] : ( m1_subset_1(J,A) => ! [K] : ( ( 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))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t41_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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,k2_bvfunc_1(A,B,C),D)),k12_bvfunc_1(A)) ) ) ) ) )).
fof(t41_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t41_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(F,A) => r1_bvfunc_1(A,k2_bvfunc_1(A,k2_bvfunc_1(A,k7_bvfunc_2(A,E,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,C),B,F)),k7_bvfunc_2(A,k2_bvfunc_1(A,C,k1_bvfunc_1(A,D)),B,F)) ) ) ) ) ) ) )).
fof(t41_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t41_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t41_card_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(k1_card_1(B),k1_card_1(A)) <=> r2_hidden(B,A) ) ) ) )).
fof(t41_card_2,axiom,( ! [A] : ( k1_card_1(A) = 1 <=> ? [B] : A = k1_tarski(B) ) )).
fof(t41_card_fil,axiom,( ! [A] : ( ( ~ v1_finset_1(A) & v1_card_1(A) ) => ( v7_card_fil(A) => v6_card_fil(A) ) ) )).
fof(t41_card_fin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_finset_1(B) ) => ( ( v1_finset_1(k9_xtuple_0(B)) & A = k5_numbers ) => k3_card_fin(A,B) = k1_card_1(k3_tarski(k10_xtuple_0(B))) ) ) ) )).
fof(t41_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t41_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_cat_3(E,C,D,A) => ( r2_hidden(B,A) => k3_graph_1(C,k7_partfun1(u4_struct_0(C),E,B)) = D ) ) ) ) )).
fof(t41_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_cat_1(G,A,B,C) => ! [H] : ( m1_cat_1(H,A,D,E) => ! [I] : ( m1_cat_1(I,A,F,B) => ! [J] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t41_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(k3_xcmplx_0(2,B),A) & ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v5_ordinal1(C) & v1_finset_1(C) ) => ~ ( k5_card_1(k2_catalan2(A,B)) = k1_nat_1(k7_afinsq_2(C),k5_card_1(k2_catalan2(k7_nat_d(A,1),B))) & k1_relset_1(k4_ordinal1,C) = B & ! [D] : ( v7_ordinal1(D) => ( ~ r1_xxreal_0(B,D) => k1_recdef_1(C,D) = k2_nat_1(k5_card_1(k2_catalan2(k3_xcmplx_0(2,D),D)),k5_card_1(k2_catalan2(k7_nat_d(A,k2_nat_1(2,k1_nat_1(D,1))),k7_nat_d(B,k1_nat_1(D,1))))) ) ) ) ) ) ) ) )).
fof(t41_cc0sp2,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t41_cfcont_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(t41_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( 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,D),k1_cfunct_1(A,C,E)),k1_cfunct_1(A,k19_valued_1(A,k2_numbers,k2_numbers,B,C),k19_valued_1(A,k2_numbers,k2_numbers,D,E))) ) ) ) ) ) )).
fof(t41_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ! [B] : ( v2_cgames_1(B) => ( ( r2_hidden(B,k6_cgames_1(k13_cgames_1(A))) => r2_hidden(k13_cgames_1(B),k7_cgames_1(A)) ) & ( r2_hidden(k13_cgames_1(B),k7_cgames_1(A)) => r2_hidden(B,k6_cgames_1(k13_cgames_1(A))) ) & ( r2_hidden(B,k6_cgames_1(A)) => r2_hidden(k13_cgames_1(B),k7_cgames_1(k13_cgames_1(A))) ) & ( r2_hidden(k13_cgames_1(B),k7_cgames_1(k13_cgames_1(A))) => r2_hidden(B,k6_cgames_1(A)) ) & ( r2_hidden(B,k7_cgames_1(k13_cgames_1(A))) => r2_hidden(k13_cgames_1(B),k6_cgames_1(A)) ) & ( r2_hidden(k13_cgames_1(B),k6_cgames_1(A)) => r2_hidden(B,k7_cgames_1(k13_cgames_1(A))) ) & ( r2_hidden(B,k7_cgames_1(A)) => r2_hidden(k13_cgames_1(B),k6_cgames_1(k13_cgames_1(A))) ) & ( r2_hidden(k13_cgames_1(B),k6_cgames_1(k13_cgames_1(A))) => r2_hidden(B,k7_cgames_1(A)) ) ) ) ) )).
fof(t41_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_chain_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) => ( r2_hidden(C,k4_chain_1(A,B,1)) <=> ? [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) & ? [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) & ? [F] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(A)) & C = k3_chain_1(A,D,E) & ~ ( r1_xxreal_0(k1_funct_1(E,F),k1_funct_1(D,F)) & ~ ( A = 1 & ~ r1_xxreal_0(k1_funct_1(D,F),k1_funct_1(E,F)) ) ) & m2_chain_1(k4_tarski(k1_funct_1(D,F),k1_funct_1(E,F)),k2_chain_1(A,B,F)) & ! [G] : ( m2_subset_1(G,k4_ordinal1,k2_finseq_1(A)) => ( G != F => ( k1_funct_1(D,G) = k1_funct_1(E,G) & r2_hidden(k1_funct_1(D,G),k2_chain_1(A,B,G)) ) ) ) ) ) ) ) ) ) ) )).
fof(t41_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v1_chord(B,A) => ! [C] : ( ( v7_ordinal1(C) & ~ v1_abian(C) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t41_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(D) & v1_finset_1(D) ) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t41_circcomb,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( 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 ) ) ) )).
fof(t41_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v4_msualg_1(E,A) & v4_msafree2(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t41_classes1,axiom,( ! [A] : ! [B] : ! [C] : ( v3_ordinal1(C) => ( ( r1_tarski(A,B) & r2_hidden(B,k4_classes1(C)) ) => r2_hidden(A,k4_classes1(C)) ) ) )).
fof(t41_classes2,axiom,( ! [A] : ( v1_ordinal1(A) => r1_ordinal1(k1_card_1(k6_classes1(A)),k1_card_1(A)) ) )).
fof(t41_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k14_clopban1(A,B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k14_clopban1(A,B))))) ) => ( v1_csspace3(C,k14_clopban1(A,B)) => v9_clvect_1(C,k14_clopban1(A,B)) ) ) ) ) ) )).
fof(t41_clopban3,axiom,( ! [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) & l1_clopban2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ~ r1_xxreal_0(1,k2_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) ) ) ) ) )).
fof(t41_closure2,axiom,( ! [A] : ( l1_struct_0(A) => ! [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] : ( ( 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) ) ) ) )).
fof(t41_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_clvect_1(C,A) => ( r1_struct_0(C,B) => r1_struct_0(C,k4_algstr_0(A,B)) ) ) ) ) )).
fof(t41_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(C,k4_clvect_2(A,B,D)) <=> ~ r1_xxreal_0(D,k15_csspace(A,B,C)) ) ) ) ) ) )).
fof(t41_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k13_csspace(A,k3_clvect_3(A,B,D,C)),k9_complex1(k7_series_1(k2_clvect_2(A,B),D,C))) ) ) ) ) )).
fof(t41_coh_sp,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(t41_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ? [C] : ( 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 ) ) ) )).
fof(t41_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k3_complex1(k2_xcmplx_0(A,k8_complex1(A))) = k3_xcmplx_0(2,k3_complex1(A)) & k4_complex1(k2_xcmplx_0(A,k8_complex1(A))) = k5_numbers ) ) )).
fof(t41_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k1_complex2(k4_xcmplx_0(A),B) = k4_xcmplx_0(k1_complex2(A,B)) ) ) )).
fof(t41_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ! [C] : ( 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) ) ) ) ) )).
fof(t41_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => ( k6_complsp2(k7_seq_4(A,B)) = k4_rvsum_1(k6_complsp2(A),k6_complsp2(B)) & k7_complsp2(k7_seq_4(A,B)) = k4_rvsum_1(k7_complsp2(A),k7_complsp2(B)) ) ) ) ) )).
fof(t41_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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)) = k1_nat_1(k5_card_1(B),1) ) ) )).
fof(t41_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( v6_compos_0(D,u1_compos_1(A)) & m1_subset_1(D,u1_compos_1(A)) ) => ! [E] : ( ( v6_compos_0(E,u1_compos_1(A)) & m1_subset_1(E,u1_compos_1(A)) ) => ! [F] : ( ( v6_compos_0(F,u1_compos_1(A)) & m1_subset_1(F,u1_compos_1(A)) ) => ! [G] : ( ( v6_compos_0(G,u1_compos_1(A)) & m1_subset_1(G,u1_compos_1(A)) ) => ! [H] : ( ( 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),k5_numbers) = C ) ) ) ) ) ) ) ) )).
fof(t41_comptrig,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( r2_hidden(k1_comptrig(A),k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) <=> ( ~ r1_xxreal_0(k3_complex1(A),k5_numbers) & ~ r1_xxreal_0(k4_complex1(A),k5_numbers) ) ) ) )).
fof(t41_comput_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_rfunct_3(B,k3_finseq_2(A),A,k2_comput_1(A)) => ! [C] : ( ( v3_comput_1(C) & m2_finseq_1(C,k2_comput_1(A)) ) => ( r1_tarski(k9_xtuple_0(k3_relat_1(k5_funct_6(C),B)),k4_finseq_2(k1_comput_1(C),A)) & r1_tarski(k10_xtuple_0(k3_relat_1(k5_funct_6(C),B)),A) & r2_hidden(k3_relat_1(k5_funct_6(C),B),k2_comput_1(A)) ) ) ) ) )).
fof(t41_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v9_ordinal1(A) => ( r2_relset_1(k4_ordinal1,k2_numbers,k31_valued_1(k4_ordinal1,k2_numbers,k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,A)),k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k31_valued_1(k4_ordinal1,k2_numbers,B),A)) & r2_relset_1(k4_ordinal1,k2_numbers,k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,k31_valued_1(k4_ordinal1,k2_numbers,A)),k31_valued_1(k4_ordinal1,k2_numbers,k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,A))) ) ) ) ) )).
fof(t41_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v2_comseq_2(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v2_comseq_2(k7_comseq_3(A)) & v2_comseq_2(k8_comseq_3(A)) & k1_seq_2(k7_comseq_3(A)) = k3_complex1(k3_comseq_2(A)) & k1_seq_2(k8_comseq_3(A)) = k4_complex1(k3_comseq_2(A)) ) ) )).
fof(t41_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( ( v3_conlat_1(B,A) & ~ v4_conlat_1(B,A) & v6_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) ) ) )).
fof(t41_connsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v3_connsp_1(B,A) & r2_hidden(C,B) ) => B = k1_connsp_1(A,C) ) ) ) ) )).
fof(t41_convex1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(B,k3_convex1(A,B)) ) ) )).
fof(t41_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_convex4(B,A) => ! [C] : ( 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) ) ) ) )).
fof(t41_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k1_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( m2_funct_2(F,k3_qc_lang1(A),k3_qc_lang1(A),k9_funct_2(k3_qc_lang1(A),k3_qc_lang1(A))) => ! [G] : ( 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)),E,B,G,F),k15_cqc_sim1(A,D)) & r2_hidden(k2_qc_lang3(A,C),k7_relat_1(F,k24_qc_lang1(A,D))) ) => r2_qc_lang1(A,C,B) ) ) ) ) ) ) ) ) )).
fof(t41_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t41_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t41_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t41_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t41_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k9_diff_1(k16_sin_cos,A,B) = k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k19_sin_cos(k7_xcmplx_0(k2_xcmplx_0(A,B),2))),k17_sin_cos(k7_xcmplx_0(k6_xcmplx_0(A,B),2))),k6_xcmplx_0(A,B)) ) ) )).
fof(t41_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k3_square_1(D) ) => ( r1_xxreal_0(k2_xcmplx_0(B,k7_xcmplx_0(A,2)),k5_numbers) | r1_xxreal_0(k6_xcmplx_0(B,k7_xcmplx_0(A,2)),k5_numbers) | k1_funct_1(k5_diff_1(C,A),B) = k6_xcmplx_0(k3_square_1(k2_xcmplx_0(B,k7_xcmplx_0(A,2))),k3_square_1(k6_xcmplx_0(B,k7_xcmplx_0(A,2)))) ) ) ) ) ) )).
fof(t41_dilworth,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v3_dilworth(A) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t41_diraf,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t41_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(A))) => ! [F] : ( 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)))) ) ) ) ) ) ) )).
fof(t41_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( 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 ) ) ) )).
fof(t41_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) ) )).
fof(t41_entropy1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(C,k4_finseq_1(k2_entropy1(A,B))) & D = k6_xcmplx_0(C,1) ) => ( r2_hidden(k4_tarski(k1_nat_1(k3_nat_d(D,k1_matrix_0(B)),1),k1_nat_1(k4_nat_d(D,k1_matrix_0(B)),1)),k2_matrix_0(B)) & k1_funct_1(k2_entropy1(A,B),C) = k3_matrix_0(A,B,k1_nat_1(k3_nat_d(D,k1_matrix_0(B)),1),k1_nat_1(k4_nat_d(D,k1_matrix_0(B)),1)) ) ) ) ) ) ) )).
fof(t41_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : k6_enumset1(A,A,A,B,C,D,E,F) = k4_enumset1(A,B,C,D,E,F) )).
fof(t41_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t41_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_valued_0(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v3_valued_0(E) ) => ( ( B = D & C = E ) => k5_algstr_0(k15_euclid(A),B,C) = k45_valued_1(D,E) ) ) ) ) ) ) )).
fof(t41_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ( ~ ( B != k4_struct_0(k15_euclid(A)) & r1_xxreal_0(k22_rvsum_1(B,B),k5_numbers) ) & ~ ( ~ r1_xxreal_0(k22_rvsum_1(B,B),k5_numbers) & B = k4_struct_0(k15_euclid(A)) ) ) ) ) )).
fof(t41_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => k22_rvsum_1(A,B) = k2_xcmplx_0(k3_xcmplx_0(k17_euclid(A),k17_euclid(B)),k3_xcmplx_0(k18_euclid(A),k18_euclid(B))) ) ) )).
fof(t41_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ( ( r2_hidden(D,k4_euclid_4(A,B,C)) & r2_hidden(E,k4_euclid_4(A,B,C)) ) => r1_tarski(k4_euclid_4(A,D,E),k4_euclid_4(A,B,C)) ) ) ) ) ) ) )).
fof(t41_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( k17_euclid(k5_algstr_0(k15_euclid(2),A,B)) = k6_xcmplx_0(k17_euclid(A),k17_euclid(B)) & k18_euclid(k5_algstr_0(k15_euclid(2),A,B)) = k6_xcmplx_0(k18_euclid(A),k18_euclid(B)) ) ) ) )).
fof(t41_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ( A = k1_funct_1(k6_euclid_8(B,C,D),E) <=> ( k1_funct_1(A,1) = k1_funct_1(B,E) & k1_funct_1(A,2) = k1_funct_1(C,E) & k1_funct_1(A,3) = k1_funct_1(D,E) ) ) ) ) ) ) ) )).
fof(t41_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t41_exchsort,axiom,( ! [A] : ! [B] : ! [C] : v2_funct_1(k9_funct_7(k6_partfun1(C),A,B)) )).
fof(t41_facirc_1,axiom,( ! [A] : ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ~ v1_facirc_1(k2_msafree2(k5_circcomb(A,k10_finseq_1(B,C)))) ) ) )).
fof(t41_fcont_1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,A) => k1_funct_1(D,E) = k2_xcmplx_0(k3_xcmplx_0(B,E),C) ) ) => v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,D,A)) ) ) ) ) )).
fof(t41_fdiff_10,axiom,( ! [A] : ( ( 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,k26_sin_cos,k27_sin_cos),k22_sin_cos))) => ( r2_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),k22_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),k22_sin_cos),A),B) = k7_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B)))),k1_funct_1(k26_sin_cos,B)),k1_funct_1(k27_sin_cos,B)),k1_funct_1(k22_sin_cos,B)) ) ) ) ) ) )).
fof(t41_fdiff_11,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_sin_cos9)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_sin_cos9)),A),B) = k4_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,B),k2_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k1_funct_1(k2_sin_cos9,B)))) ) ) ) ) ) )).
fof(t41_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(k2_rcomp_1(B,A),k1_relset_1(k1_numbers,C)) & r2_fdiff_1(C,k2_rcomp_1(B,A)) ) => ( ( ? [D] : ( v1_xreal_0(D) & r2_hidden(D,k2_rcomp_1(B,A)) & r1_xxreal_0(k1_fdiff_1(C,D),k5_numbers) ) & ? [D] : ( v1_xreal_0(D) & r2_hidden(D,k2_rcomp_1(B,A)) & r1_xxreal_0(k5_numbers,k1_fdiff_1(C,D)) ) ) | v3_rcomp_1(k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,C,k2_rcomp_1(B,A)))) ) ) ) ) ) )).
fof(t41_fdiff_4,axiom,( ! [A] : ( ( 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,k18_sin_cos))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),A),B) = k19_sin_cos(k3_xcmplx_0(2,B)) ) ) ) ) ) )).
fof(t41_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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),k7_xcmplx_0(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] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => ( k1_funct_1(C,D) = 1 & ~ r1_xxreal_0(k1_funct_1(B,D),k5_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),k7_xcmplx_0(1,2)),A) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_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),k7_xcmplx_0(1,2)),A),D) = k7_xcmplx_0(k1_funct_1(k18_sin_cos,D),k2_xcmplx_0(1,k3_xcmplx_0(2,k1_funct_1(k16_sin_cos,D)))) ) ) ) ) ) ) ) )).
fof(t41_fdiff_7,axiom,( ! [A] : ( ( 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,k22_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)),A),B) = k3_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k22_sin_cos,B)),k1_funct_1(k18_sin_cos,B)) ) ) ) ) ) )).
fof(t41_fdiff_9,axiom,( ! [A] : ( ( 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,k27_sin_cos,k2_fdiff_9))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k2_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k2_fdiff_9),A),B) = k7_xcmplx_0(k7_xcmplx_0(k1_funct_1(k18_sin_cos,k1_funct_1(k27_sin_cos,B)),k1_square_1(k1_funct_1(k16_sin_cos,B))),k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k27_sin_cos,B)))) ) ) ) ) ) )).
fof(t41_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => r1_nat_d(k1_pre_ff(B),k1_pre_ff(k3_xcmplx_0(B,A))) ) ) )).
fof(t41_fib_num3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k6_xcmplx_0(k3_fib_num3(A,B,k1_nat_1(C,3)),k3_fib_num3(A,B,C)) = k2_nat_1(2,k3_fib_num3(A,B,k1_nat_1(C,1))) ) ) ) )).
fof(t41_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_finseq_8(A,k17_finseq_1(A,D,B),C,1) => ( r1_xxreal_0(k3_finseq_1(C),k5_numbers) | r2_finseq_8(A,B,C,1) ) ) ) ) ) ) )).
fof(t41_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t41_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ( ( v15_lattices(A) & v15_lattices(B) ) <=> v15_lattices(k7_filter_1(A,B)) ) ) ) )).
fof(t41_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t41_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : k1_funct_1(k7_finseq_1(k9_finseq_1(B),A),1) = B ) )).
fof(t41_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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 ) ) ) ) ) )).
fof(t41_finseq_3,axiom,( k14_finseq_1(k1_xboole_0) = k1_xboole_0 )).
fof(t41_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : ( ~ 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) ) ) ) )).
fof(t41_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( 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 ) ) ) ) )).
fof(t41_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t41_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( 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)) ) ) )).
fof(t41_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k9_fintopo3(A,B,2) = k1_fintopo3(A,k1_fintopo3(A,B)) ) ) )).
fof(t41_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r1_fintopo6(A,C) & ~ r1_xboole_0(B,C) & ~ r1_tarski(B,C) ) ) ) ) ) )).
fof(t41_flang_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_catalan2(A))) => ( r2_hidden(B,k8_flang_1(A,C)) <=> ? [D] : ( v7_ordinal1(D) & r2_hidden(B,k7_flang_1(A,C,D)) ) ) ) )).
fof(t41_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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))) ) ) ) ) )).
fof(t41_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => k6_flang_1(A,k1_flang_3(A,B,C),k2_flang_2(A,B)) = k1_flang_3(A,B,C) ) ) )).
fof(t41_fomodel0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( 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 ) ) ) ) ) ) ) ) )).
fof(t41_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t41_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t41_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t41_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ( r1_tarski(A,B) => ( ( C = k1_xboole_0 & B != k1_xboole_0 ) | r1_tarski(A,k8_relset_1(B,C,D,k7_relset_1(B,C,D,A))) ) ) ) )).
fof(t41_funct_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k6_funct_3(A,B) = k5_relat_1(k4_relat_1(A),B) ) )).
fof(t41_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => r1_tarski(k10_xtuple_0(k2_funct_4(A)),k10_xtuple_0(A)) ) )).
fof(t41_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) ) ) ) )).
fof(t41_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ~ r2_hidden(k1_xboole_0,k10_xtuple_0(A)) => k7_funct_6(A,k1_xboole_0) = k7_funcop_1(k9_xtuple_0(A),k1_xboole_0) ) ) )).
fof(t41_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => k4_funct_7(k7_finseq_1(B,k9_finseq_1(C)),A) = k7_finseq_1(k4_funct_7(B,A),k9_finseq_1(k1_funct_1(C,k1_funct_1(k4_funct_7(B,A),k1_nat_1(k3_finseq_1(B),1))))) ) ) )).
fof(t41_funct_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t41_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t41_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t41_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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)) ) ) )).
fof(t41_fuzzy_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k5_numbers,C) => ( k3_xcmplx_0(C,k4_xxreal_0(A,B)) = k4_xxreal_0(k3_xcmplx_0(C,A),k3_xcmplx_0(C,B)) & k3_xcmplx_0(C,k3_xxreal_0(A,B)) = k3_xxreal_0(k3_xcmplx_0(C,A),k3_xcmplx_0(C,B)) ) ) ) ) ) )).
fof(t41_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_fvaluat1(C,A) => ( v3_fvaluat1(A) => ( r1_xxreal_0(k5_numbers,k3_funct_2(u1_struct_0(A),k6_numbers,C,B)) <=> r1_xxreal_0(k5_numbers,k3_funct_2(u1_struct_0(A),k6_numbers,k5_fvaluat1(A,C),B)) ) ) ) ) ) )).
fof(t41_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(t41_gate_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(k34_gate_1(A,B)) <=> ( ~ ( v1_xboole_0(A) & v1_xboole_0(B) ) & ~ ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) ) ) )).
fof(t41_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t41_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( ( ~ v1_xboole_0(F) & v1_relat_1(F) & v2_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ! [G] : ( m1_genealg1(G,F) => ! [H] : ( m1_genealg1(H,F) => ( k11_genealg1(F,G,H,k5_numbers,B,C,D,E) = k10_genealg1(F,H,G,B,C,D,E) & k11_genealg1(F,G,H,A,k5_numbers,C,D,E) = k10_genealg1(F,H,G,A,C,D,E) & k11_genealg1(F,G,H,A,B,k5_numbers,D,E) = k10_genealg1(F,H,G,A,B,D,E) & k11_genealg1(F,G,H,A,B,C,k5_numbers,E) = k10_genealg1(F,H,G,A,B,C,E) & k11_genealg1(F,G,H,A,B,C,D,k5_numbers) = k10_genealg1(F,H,G,A,B,C,D) ) ) ) ) ) ) ) ) ) )).
fof(t41_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ! [L] : ( m1_subset_1(L,u1_struct_0(A)) => ! [M] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t41_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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)) )).
fof(t41_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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) ) ) ) ) ) )).
fof(t41_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r1_xxreal_0(D,C) => ( v1_abian(D) | r2_relset_1(k4_ordinal1,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),k8_glib_001(A,k8_glib_001(A,B,1,C),1,D),k8_glib_001(A,B,1,D)) ) ) ) ) ) ) )).
fof(t41_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_002(A) ) => ! [B] : ( ( v5_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t41_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v3_glib_003(A) ) => ! [B] : ! [C] : k5_glib_003(A) = k5_glib_003(k13_glib_003(A,B,C)) ) )).
fof(t41_glib_004,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) ) ) ) ) )).
fof(t41_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ 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(k1_nat_1(A,1),k3_finseq_1(k2_goboard2(D))) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(k2_goboard2(D))) & r1_xxreal_0(1,C) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1))) = k2_topreal1(2,D,C) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1))) = k2_topreal1(2,D,k1_nat_1(C,1)) ) => ( r1_xxreal_0(k3_finseq_1(D),k1_nat_1(C,1)) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),B) ) ) ) ) ) ) ) )).
fof(t41_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m2_finseq_1(C,B) => ! [D] : ( m2_finseq_1(D,B) => ! [E] : ( ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(B)) ) => ( ( r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) & r1_xxreal_0(k1_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,k1_nat_1(A,1),C) = k17_finseq_1(B,k1_nat_1(A,1),D) ) ) ) ) ) ) )).
fof(t41_gobrd14,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t41_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v2_struct_0(D) & l1_graph_1(D) ) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t41_graph_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k8_graph_3(B,C,D))) => ( ( E = C & r2_hidden(u4_struct_0(B),A) ) => ( k3_graph_3(k8_graph_3(B,C,D),E,A) = k2_xboole_0(k3_graph_3(B,C,A),k1_tarski(u4_struct_0(B))) & r1_xboole_0(k3_graph_3(B,C,A),k1_tarski(u4_struct_0(B))) ) ) ) ) ) ) )).
fof(t41_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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 ) ) ) ) ) ) )).
fof(t41_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => k4_finseq_1(C) = k4_finseq_1(k6_graphsp(k9_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),k15_graphsp(B),k18_graphsp(B))),A),C)) ) ) ) )).
fof(t41_grcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k25_grcat_1(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t41_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ~ r1_xxreal_0(k5_card_1(k3_polynom1(k15_pre_poly(A),C,D)),E) => r1_tarski(k3_polynom1(k15_pre_poly(A),C,k6_groeb_3(A,B,C,D,k1_nat_1(E,1))),k3_polynom1(k15_pre_poly(A),C,k6_groeb_3(A,B,C,D,E))) ) ) ) ) ) ) )).
fof(t41_group_1,axiom,( ! [A] : ( ( ~ 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 ) )).
fof(t41_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t41_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => r1_struct_0(A,C) ) ) ) )).
fof(t41_group_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( r2_hidden(A,k4_group_3(B,D,C)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k2_group_3(B,E,C) & r2_hidden(E,D) ) ) ) ) ) )).
fof(t41_group_4,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t41_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t41_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t41_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v4_group_9(C,A,B) & m1_group_9(C,A,B) ) => ! [D] : ( 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) ) ) ) ) )).
fof(t41_hausdorf,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [C] : ( ( ~ 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) = k5_numbers ) => B = C ) ) ) ) )).
fof(t41_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => k3_helly(A,B,C,D) = k3_helly(A,B,D,C) ) ) ) ) )).
fof(t41_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ( k9_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) = k9_complex1(k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(k1_complfld),B,C,C)) ) ) ) ) )).
fof(t41_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( v3_rcomp_1(E) & m1_subset_1(E,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(B,E) => ( r1_xxreal_0(C,D) | ( k9_nat_1(k1_numbers,k6_taylor_1(k1_taylor_1(C),E,B,A),D) = k3_xcmplx_0(k3_xcmplx_0(k4_newton(D,C),k3_prepower(B,k6_xcmplx_0(C,D))),k1_newton(k6_xcmplx_0(A,B),D)) & k9_nat_1(k1_numbers,k6_taylor_1(k1_taylor_1(C),E,B,A),C) = k1_newton(k6_xcmplx_0(A,B),C) ) ) ) ) ) ) ) ) )).
fof(t41_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(t41_hilbert3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( r2_hidden(A,k6_hilbert1) => v1_hilbert3(A) ) ) )).
fof(t41_hurwitz,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(A,k1_complfld) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(B,k1_complfld) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => ( v1_hurwitz(k13_polynom3(k1_complfld,A,B)) <=> ( v1_hurwitz(A) & v1_hurwitz(B) ) ) ) ) )).
fof(t41_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_ideal_1(C,A,B) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => m1_ideal_1(k2_partfun1(k4_ordinal1,u1_struct_0(A),C,k2_finseq_1(D)),A,B) ) ) ) ) )).
fof(t41_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u4_incsp_1(A)) => ? [C] : ( m1_subset_1(C,u1_incsp_1(A)) & ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & ? [E] : ( 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) ) ) ) ) ) )).
fof(t41_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r3_pua2mss1(A,B,D,E) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t41_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(1,k3_int_1(A)) & r1_xxreal_0(k5_numbers,k3_int_1(A)) ) ) )).
fof(t41_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ~ ( A != k5_numbers & B != k5_numbers & ~ r1_int_1(k3_int_2(A,B),k6_xcmplx_0(C,D)) & ? [E] : ( v1_int_1(E) & k5_int_1(k6_xcmplx_0(E,C),A) = k5_numbers & k5_int_1(k6_xcmplx_0(E,D),B) = k5_numbers ) ) ) ) ) ) )).
fof(t41_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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] : ( v1_int_1(C) => ~ ( r1_xxreal_0(k5_numbers,C) & ~ r1_xxreal_0(k19_rvsum_1(B),C) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(A)) => r2_int_1(C,k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) ) )).
fof(t41_integr11,axiom,( ! [A] : ( ( 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,k27_sin_cos),k2_fdiff_9))) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( k2_xcmplx_0(1,k1_funct_1(k18_sin_cos,B)) != k5_numbers & k6_xcmplx_0(1,k1_funct_1(k18_sin_cos,B)) != k5_numbers ) ) ) ) => ( r2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k27_sin_cos),k2_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k27_sin_cos),k2_fdiff_9),A),B) = k7_xcmplx_0(1,k2_xcmplx_0(1,k1_funct_1(k18_sin_cos,B))) ) ) ) ) ) )).
fof(t41_integr12,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,D) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => ( k1_funct_1(C,E) = k7_xcmplx_0(k1_funct_1(k18_sin_cos,E),k3_prepower(k1_funct_1(k16_sin_cos,E),k1_nat_1(A,1))) & k1_funct_1(k16_sin_cos,E) != k5_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,k5_numbers) | k2_integra5(B,C) = k6_xcmplx_0(k1_funct_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)),k4_xcmplx_0(k7_xcmplx_0(1,A))),k2_seq_4(B)),k1_funct_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)),k4_xcmplx_0(k7_xcmplx_0(1,A))),k3_seq_4(B))) ) ) ) ) ) ) )).
fof(t41_integr13,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v3_rcomp_1(E) & m1_subset_1(E,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,E) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => k1_funct_1(D,F) = 1 ) ) & 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,k2_sin_cos9,k1_taylor_1(k6_xcmplx_0(A,1))),k3_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k1_taylor_1(2))),A)) & r1_tarski(E,k2_rcomp_1(k4_xcmplx_0(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,C) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,B)) ) => k2_integra5(B,C) = k6_xcmplx_0(k1_funct_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))),k2_seq_4(B)),k1_funct_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))),k3_seq_4(B))) ) ) ) ) ) ) )).
fof(t41_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k7_xcmplx_0(k7_xcmplx_0(k1_funct_1(k16_sin_cos,k1_funct_1(k27_sin_cos,D)),k1_square_1(k1_funct_1(k16_sin_cos,D))),k1_square_1(k1_funct_1(k18_sin_cos,k1_funct_1(k27_sin_cos,D)))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_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) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k1_fdiff_9)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k1_fdiff_9)),k3_seq_4(A))) ) ) ) ) )).
fof(t41_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t41_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [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))) ) => k1_funct_1(k14_integra1(k5_integra1(A,C,B)),k3_finseq_1(B)) = k7_integra1(A,C,B) ) ) ) )).
fof(t41_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k28_sin_cos) => k2_integra5(A,k18_sin_cos) = k5_numbers ) ) )).
fof(t41_integra9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( B = k1_rcomp_1(k4_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,A),k28_sin_cos)),k3_xcmplx_0(k3_xcmplx_0(2,A),k28_sin_cos)) => r1_integra9(B,k16_sin_cos,k18_sin_cos) ) ) ) )).
fof(t41_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_interva1(C,A) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t41_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => r2_hidden(k3_intpro_1(k3_intpro_1(B,C),k3_intpro_1(k4_intpro_1(A,B),C)),k8_intpro_1) ) ) ) )).
fof(t41_irrat_1,axiom,( ~ v1_rat_1(k4_power) )).
fof(t41_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( m2_cat_1(E,A,B) => ! [F] : ( m2_cat_1(F,C,D) => ! [G] : ( m2_cat_1(G,B,C) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t41_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) ) ) )).
fof(t41_jgraph_1,axiom,( ! [A] : ( 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_funct_1(k2_goboard1(A),1) = k18_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),A,1)) & k1_funct_1(k2_goboard1(A),k3_finseq_1(A)) = k18_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),A,k3_finseq_1(A))) ) ) ) )).
fof(t41_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ! [B] : ( ( 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)) ) ) ) ) )).
fof(t41_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t41_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t41_jordan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => m1_borsuk_2(k6_struct_0(k5_topmetr,A,B),A,B,B) ) ) )).
fof(t41_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & ~ r1_xxreal_0(A,k5_numbers) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k8_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C),k9_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),E,C)),k8_jordan6(B)) ) ) ) ) ) ) )).
fof(t41_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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,D))) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(k1_jordan8(E,C))) & r1_xxreal_0(C,D) ) => r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,D),k3_finseq_1(k1_jordan8(E,D)),A)),k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,C),k3_finseq_1(k1_jordan8(E,C)),B))) ) ) ) ) ) ) )).
fof(t41_jordan1b,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ( ? [C] : ( v7_ordinal1(C) & ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,k3_finseq_1(k1_jordan8(A,B))) & r1_xxreal_0(D,k1_matrix_0(k1_jordan8(A,B))) & r1_tarski(k3_goboard5(k1_jordan8(A,B),C,D),k1_jordan2c(2,A)) ) ) => r1_xxreal_0(1,B) ) ) ) )).
fof(t41_jordan1h,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t41_jordan1j,axiom,( ! [A] : ( ( v4_topreal1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( 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] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_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] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(2,C) & r1_xxreal_0(k1_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)) ) ) ) )).
fof(t41_jordan1k,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [D] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t41_jordan21,axiom,( ! [A] : ( ( 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))) ) )).
fof(t41_jordan22,axiom,( ! [A] : ( ( 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)) ) )).
fof(t41_jordan23,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) ) )).
fof(t41_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t41_jordan4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t41_jordan5d,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(A)) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(k2_goboard2(A))) & E = a_2_0_jordan5d(A,B) & k17_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),A,D)) = k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),B,1)) & C = k4_seq_4(E) ) => r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),B,C)),k18_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),A,D))) ) ) ) ) ) ) )).
fof(t41_jordan6,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k1_pre_topc(A,B)))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t41_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t41_kurato_1,axiom,( k6_kurato_1 != k1_tops_1(k3_topmetr,k6_kurato_1) )).
fof(t41_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k5_finsub_1(C)) => ! [E] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t41_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( r2_hidden(B,C) & r3_lattice3(A,B,C) ) => k16_lattice3(A,C) = B ) ) ) )).
fof(t41_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( 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)) ) ) )).
fof(t41_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t41_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_comseq_2(A) => ( ( ~ v1_limfunc1(B) & ~ v2_limfunc1(B) ) | ( v2_comseq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) & k1_seq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) = k5_numbers ) ) ) ) ) )).
fof(t41_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_limfunc3(C,A) & r1_limfunc3(D,A) & k1_limfunc3(C,A) = k1_limfunc3(D,A) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(A,E) & ~ r1_xxreal_0(F,A) & ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ~ ( ~ r1_xxreal_0(G,E) & ~ r1_xxreal_0(A,G) & r2_hidden(G,k9_xtuple_0(B)) & ~ r1_xxreal_0(F,H) & ~ r1_xxreal_0(H,A) & r2_hidden(H,k9_xtuple_0(B)) ) ) ) ) ) ) ) => ( ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,k9_subset_1(k1_numbers,k9_xtuple_0(B),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,E),A),k2_rcomp_1(A,k2_xcmplx_0(A,E))))) => ( r1_xxreal_0(k1_funct_1(C,F),k1_funct_1(B,F)) & r1_xxreal_0(k1_funct_1(B,F),k1_funct_1(D,F)) ) ) ) & ( ( r1_tarski(k9_subset_1(k1_numbers,k9_xtuple_0(C),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,E),A),k2_rcomp_1(A,k2_xcmplx_0(A,E)))),k9_subset_1(k1_numbers,k9_xtuple_0(D),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,E),A),k2_rcomp_1(A,k2_xcmplx_0(A,E))))) & r1_tarski(k9_subset_1(k1_numbers,k9_xtuple_0(B),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,E),A),k2_rcomp_1(A,k2_xcmplx_0(A,E)))),k9_subset_1(k1_numbers,k9_xtuple_0(C),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,E),A),k2_rcomp_1(A,k2_xcmplx_0(A,E))))) ) | ( r1_tarski(k9_subset_1(k1_numbers,k9_xtuple_0(D),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,E),A),k2_rcomp_1(A,k2_xcmplx_0(A,E)))),k9_subset_1(k1_numbers,k9_xtuple_0(C),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,E),A),k2_rcomp_1(A,k2_xcmplx_0(A,E))))) & r1_tarski(k9_subset_1(k1_numbers,k9_xtuple_0(B),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,E),A),k2_rcomp_1(A,k2_xcmplx_0(A,E)))),k9_subset_1(k1_numbers,k9_xtuple_0(D),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,E),A),k2_rcomp_1(A,k2_xcmplx_0(A,E))))) ) ) ) ) | ( r1_limfunc3(B,A) & k1_limfunc3(B,A) = k1_limfunc3(C,A) ) ) ) ) ) ) ) )).
fof(t41_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,D),A),k2_rcomp_1(A,k2_xcmplx_0(A,D))))) & r1_xxreal_0(k1_funct_1(B,E),k1_limfunc3(B,A)) ) ) ) ) | r2_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t41_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_normsp_1(B,A) => ( v2_comseq_2(k5_normsp_0(A,B)) & k1_seq_2(k5_normsp_0(A,B)) = k2_normsp_0(A,k6_normsp_1(A,B)) ) ) ) ) )).
fof(t41_lopban_3,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ~ r1_xxreal_0(1,k2_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) ) ) ) ) )).
fof(t41_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( 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,k2_xcmplx_0(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,k2_xcmplx_0(D,C))) & k10_lopban_4(A,k1_rlvect_1(A,B,k2_xcmplx_0(C,D))) = k10_lopban_4(A,k1_rlvect_1(A,B,k2_xcmplx_0(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))) ) ) ) ) ) )).
fof(t41_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k22_lpspacc1(A,B,C))) => ( r2_hidden(D,E) => ( r2_mesfun6c(A,B,C,D) & r2_hidden(D,k13_lpspacc1(A,B,C)) & r3_mesfunc6(A,B,C,k56_valued_1(A,k2_numbers,D)) ) ) ) ) ) ) ) )).
fof(t41_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [G] : ( ( 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(F,k9_lpspace1(A,B,C)) & r2_hidden(E,k9_lpspace1(A,B,C)) & r2_hidden(G,k9_lpspace1(A,B,C)) & k13_lpspace1(A,B,C,D) = k13_lpspace1(A,B,C,F) & k13_lpspace1(A,B,C,E) = k13_lpspace1(A,B,C,G) ) => k13_lpspace1(A,B,C,k3_valued_1(A,k1_numbers,k1_numbers,D,E)) = k13_lpspace1(A,B,C,k3_valued_1(A,k1_numbers,k1_numbers,F,G)) ) ) ) ) ) ) ) ) )).
fof(t41_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( v2_xxreal_0(F) & v1_xreal_0(F) ) => ( r1_lpspace1(A,B,C,D,E) => k5_lpspace2(A,B,C,D,F) = k5_lpspace2(A,B,C,E,F) ) ) ) ) ) ) ) )).
fof(t41_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( m1_subset_1(D,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(k1_ltlaxio1(k4_ltlaxio1(A,D)),k1_ltlaxio1(k4_ltlaxio1(k4_ltlaxio1(C,D),k4_ltlaxio1(A,B))))) ) ) ) ) )).
fof(t41_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t41_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,B,B) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( r1_xxreal_0(A,k5_numbers) & v3_matrix10(C) ) => v4_matrix10(k6_matrix10(B,A,C)) ) ) ) ) )).
fof(t41_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( m1_matrix_2(D,k3_matrix_2(A)) => ! [E] : ( ( 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] : ( m1_matrix_2(F,k3_matrix_2(A)) => ( F = k1_partfun1(k2_finseq_1(A),k2_finseq_1(A),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_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)) ) ) ) ) ) ) ) )).
fof(t41_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(B,k4_ordinal1)) => ! [F] : ( m2_finseq_2(F,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [G] : ( ( v1_matrix_0(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_0(G)) => k2_matrix13(B,A,C,k1_matrix13(u1_struct_0(C),G,B,A,E,F),D) = k1_matrix13(u1_struct_0(C),k6_matrix_3(C,G,D),B,A,E,F) ) ) ) ) ) ) ) ) )).
fof(t41_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & k3_matrix_0(u1_struct_0(B),C,1,1) != k4_struct_0(B) & ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ~ ( v1_matrix_6(D,A,B) & v1_matrix_6(E,A,B) & k3_matrix_0(u1_struct_0(B),k4_matrix_3(B,k4_matrix_3(B,D,C),E),1,1) = k5_struct_0(B) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(F,A) => ( r1_xxreal_0(F,1) | k3_matrix_0(u1_struct_0(B),k4_matrix_3(B,k4_matrix_3(B,D,C),E),F,1) = k4_struct_0(B) ) ) ) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(F,A) => ( r1_xxreal_0(F,1) | k3_matrix_0(u1_struct_0(B),k4_matrix_3(B,k4_matrix_3(B,D,C),E),1,F) = k4_struct_0(B) ) ) ) ) ) ) ) ) ) ) )).
fof(t41_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ( ( r2_hidden(E,k4_matrix15(B,C,D)) & r2_hidden(A,k4_finseq_1(C)) & k7_matrix_0(u1_struct_0(B),C,A) = k5_finseq_2(u1_struct_0(B),k1_matrix_0(C),k4_struct_0(B)) ) => k7_matrix_0(u1_struct_0(B),D,A) = k5_finseq_2(u1_struct_0(B),k1_matrix_0(D),k4_struct_0(B)) ) ) ) ) ) ) )).
fof(t41_matrix16,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t41_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(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_0(D)) ) => r2_hidden(k3_matrix_0(A,D,B,C),k9_matrix_0(D)) ) ) ) ) ) )).
fof(t41_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(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)) ) ) ) ) )).
fof(t41_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( ( k4_matrix_3(B,C,k4_matrix_0(u1_struct_0(B),C)) = k3_matrix_1(B,A) & v1_matrix_6(C,A,B) ) <=> v4_matrix_6(C,A,B) ) ) ) ) )).
fof(t41_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( v1_matrix_6(C,A,B) => r1_matrix_8(A,B,k4_matrix_3(B,D,C),k4_matrix_3(B,C,D)) ) ) ) ) ) )).
fof(t41_matrix_9,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k4_matrix_2(3))) => ~ ( k4_nat_d(k3_finseq_1(A),2) = k5_numbers & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( r2_hidden(B,k4_finseq_1(A)) & ! [C] : ( m1_matrix_2(C,k3_matrix_2(3)) => ~ ( k1_funct_1(A,B) = C & v4_matrix_2(C,k2_matrix_2(k3_matrix_2(3))) ) ) ) ) & k3_group_4(k4_matrix_2(3),A) != k3_finseq_4(k4_ordinal1,1,2,3) & k3_group_4(k4_matrix_2(3),A) != k3_finseq_4(k4_ordinal1,2,3,1) & k3_group_4(k4_matrix_2(3),A) != k3_finseq_4(k4_ordinal1,3,1,2) ) ) )).
fof(t41_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k2_numbers)) ) => ( ( k3_finseq_1(A) = k1_matrix_0(B) & r1_xxreal_0(1,k3_finseq_1(A)) ) => k1_complsp2(k6_matrixc1(B,A)) = k6_matrixc1(k1_matrixc1(B),k1_complsp2(A)) ) ) ) )).
fof(t41_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( 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_0(D) = k1_matrix_0(k17_matrix_0(u1_struct_0(B),A,D)) ) => k17_matrix_0(u1_struct_0(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),k17_matrix_0(u1_struct_0(B),A,D)),E)) ) ) ) ) ) ) )).
fof(t41_matrixr1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( k1_matrix_0(B) = k3_finseq_1(C) => ( r1_xxreal_0(k3_finseq_1(B),k5_numbers) | r1_xxreal_0(k3_finseq_1(C),k5_numbers) | r1_xxreal_0(k1_matrix_0(C),k5_numbers) | k6_matrixr1(k7_matrixr1(A,B),C) = k7_matrixr1(A,k6_matrixr1(B,C)) ) ) ) ) ) )).
fof(t41_matrixr2,axiom,( ! [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] : ( ( v1_matrix_0(B) & v2_matrix_0(B,u1_struct_0(A),k5_numbers,k5_numbers) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => k12_matrix_3(k5_numbers,A,B) = k5_struct_0(A) ) ) )).
fof(t41_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( m1_matrlin(G,A,B) => ! [H] : ( m1_matrlin(H,A,C) => ! [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),k5_numbers) | r1_xxreal_0(k3_finseq_1(H),k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t41_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( m1_matrlin(D,A,B) => ! [E] : ( m1_matrlin(E,A,C) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(A),k3_finseq_1(D),k3_finseq_1(E)) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(A))) ) => ~ ( ~ r1_xxreal_0(k3_finseq_1(D),k5_numbers) & ~ r1_xxreal_0(k3_finseq_1(E),k5_numbers) & ~ ( r1_struct_0(k1_ranknull(A,B,C,k4_matrlin2(A,B,C,D,E,G)),F) <=> r1_struct_0(k7_matrix15(A,k4_matrix_0(u1_struct_0(A),G)),k9_matrlin(A,B,D,F)) ) ) ) ) ) ) ) ) ) )).
fof(t41_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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 ) ) ) ) )).
fof(t41_matrprob,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( k1_matrix_0(A) = k3_finseq_1(B) => ( r1_xxreal_0(k1_matrix_0(A),k5_numbers) | ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k2_finseq_1(k3_finseq_1(k11_matrixr1(A,B)))) => k1_funct_1(k11_matrixr1(A,B),C) = k22_rvsum_1(k7_matrix_0(k1_numbers,A,C),B) ) ) ) ) ) ) )).
fof(t41_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( v2_funct_2(k3_matrtop1(A,B,C),u1_struct_0(k15_euclid(B))) <=> k8_matrix13(k2_vectsp_1,C) = B ) ) ) ) )).
fof(t41_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( 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 ) ) ) )).
fof(t41_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v4_xxreal_2(A) <=> v3_xxreal_2(k3_measure6(A)) ) ) )).
fof(t41_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t41_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [C] : ( ( ~ 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))) ) ) ) )).
fof(t41_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ! [D] : ( v1_xreal_0(D) => 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)) ) ) ) )).
fof(t41_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( ! [D] : ( r2_hidden(D,k1_relset_1(A,B)) => r1_xxreal_0(k12_supinf_2(B,D),k12_supinf_2(C,D)) ) => v6_supinf_2(k47_valued_1(A,k1_numbers,k1_numbers,C,B)) ) ) ) ) )).
fof(t41_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( m1_subset_1(D,B) => ( r1_mesfun7c(A,B,C) => r1_mesfun6c(A,B,C,D) ) ) ) ) ) )).
fof(t41_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( m1_subset_1(E,k6_numbers) => ~ ( E != k1_supinf_1 & E != k2_supinf_1 & ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ~ ( r1_mesfunc2(A,B,F) & k1_relset_1(A,F) = D & ! [G] : ( r2_hidden(G,D) => k1_funct_1(F,G) = E ) ) ) ) ) ) ) ) ) )).
fof(t41_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( r2_hidden(C,k1_relset_1(A,B)) & k12_supinf_2(k19_rfunct_3(A,B),C) = k5_numbers ) => k12_supinf_2(k18_rfunct_3(A,B),C) = k12_supinf_2(B,C) ) ) ) )).
fof(t41_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t41_mmlquery,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(t41_mod_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t41_modal_1,axiom,( ! [A] : ( m1_subset_1(A,k3_modal_1) => ! [B] : ( m1_subset_1(B,k6_modal_1) => ! [C] : ( 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) ) ) ) ) )).
fof(t41_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k48_modelc_1(A,B,C))) => ( ! [F] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t41_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ~ ( r3_modelc_2(A,k4_modelc_2(B,C)) & ~ r2_modelc_2(A,B) & ~ r2_modelc_2(A,C) ) ) ) ) )).
fof(t41_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_3(C,B) & v3_modelc_3(C,B) & l1_modelc_3(C,B) ) => ! [D] : ( ( v1_modelc_3(D,B) & v3_modelc_3(D,B) & l1_modelc_3(D,B) ) => ( ( r6_modelc_3(B,C,D) & r2_hidden(A,u1_modelc_3(B,D)) ) => ( ( v4_modelc_2(A) => ( r2_hidden(k11_modelc_2(A),u1_modelc_3(B,D)) & r2_hidden(k12_modelc_2(A),u1_modelc_3(B,D)) ) ) & ~ ( ( v5_modelc_2(A) | v7_modelc_2(A) ) & ~ r2_hidden(k11_modelc_2(A),u1_modelc_3(B,D)) & ~ r2_hidden(k12_modelc_2(A),u1_modelc_3(B,D)) ) & ( v6_modelc_2(A) => r2_hidden(k10_modelc_2(A),u3_modelc_3(B,D)) ) & ( v8_modelc_2(A) => r2_hidden(k12_modelc_2(A),u1_modelc_3(B,D)) ) ) ) ) ) ) ) )).
fof(t41_moebius1,axiom,( k3_moebius1(1) = k6_domain_1(k4_ordinal1,1) )).
fof(t41_monoid_0,axiom,( ! [A] : ( ( ~ 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 ) ) )).
fof(t41_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( m1_subset_1(D,k3_card_3(u3_msualg_1(A,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)) ) ) ) ) )).
fof(t41_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( m2_pboole(D,u1_struct_0(A),C,u3_msualg_1(A,B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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 ) ) ) ) ) ) )).
fof(t41_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) => ( r6_pboole(A,C,k1_pboole(A)) => r6_pboole(A,k4_mssubfam(A,B,C),B) ) ) ) )).
fof(t41_msualg_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(k4_tarski(C,D),k1_msualg_5(A,B)) <=> r2_rewrite1(B,C,D) ) ) ) ) ) )).
fof(t41_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_mycielsk(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t41_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( ~ v8_ordinal1(A) & A != 1 & r1_xxreal_0(A,1) ) ) )).
fof(t41_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => k1_funct_1(k12_nat_3(A),A) = 1 ) )).
fof(t41_nat_4,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( 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)) ) ) ) ) )).
fof(t41_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(A,B) => r1_xxreal_0(k7_nat_d(C,B),k7_nat_d(C,A)) ) ) ) ) )).
fof(t41_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ! [D] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,D)) ) ) ) ) ) ) ) ) )).
fof(t41_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v3_nfcont_1(C,A) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t41_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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))))) ) ) ) ) ) ) )).
fof(t41_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(k14_prvect_2(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t41_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(A,B) => ( A = k5_numbers | r1_nat_d(A,k7_newton(B)) ) ) ) ) )).
fof(t41_nfcont_1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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)) ) ) ) ) ) )).
fof(t41_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [D] : ( m1_subset_1(D,k1_euclid(A)) => ! [E] : ( m1_subset_1(E,k1_euclid(A)) => ( ! [F] : ( 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) ) ) ) ) ) )).
fof(t41_normform,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [C] : ( m1_subset_1(C,k5_finsub_1(k7_normform(A))) => ~ ( r2_hidden(B,C) & ! [D] : ( 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)) ) ) ) ) ) )).
fof(t41_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t41_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_oppcat_1(C,B,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_oppcat_1(B))) => k3_funct_2(u1_struct_0(k2_oppcat_1(B)),u1_struct_0(A),k7_cat_1(k2_oppcat_1(B),A,k10_oppcat_1(B,A,C)),D) = k3_funct_2(u1_struct_0(B),u1_struct_0(A),k7_cat_1(B,A,C),k4_oppcat_1(B,D)) ) ) ) ) )).
fof(t41_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,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,D)) & r2_ndiff_3(k4_real_ns1(A),D,k2_rcomp_1(B,C)) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k2_rcomp_1(B,C)) => k1_ndiff_3(k4_real_ns1(A),D,E) = k4_struct_0(k4_real_ns1(A)) ) ) ) => v3_funct_1(k2_partfun1(k1_numbers,u1_struct_0(k4_real_ns1(A)),D,k2_rcomp_1(B,C))) ) ) ) ) ) )).
fof(t41_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r2_orders_1(A,B) => r2_orders_1(k2_relat_1(A),B) ) ) )).
fof(t41_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m2_orders_1(B,k1_orders_1(u1_struct_0(A)),k6_partfun1(k1_orders_1(u1_struct_0(A)))) => ! [C] : ( m2_orders_2(C,A,B) => ! [D] : ( m2_orders_2(D,A,B) => ( C != D => ( m1_orders_2(C,A,D) <=> ~ m1_orders_2(D,A,C) ) ) ) ) ) ) )).
fof(t41_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r1_ordinal1(A,B) => r1_ordinal1(k11_ordinal2(A,C),k11_ordinal2(B,C)) ) ) ) ) )).
fof(t41_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ~ ( r2_hidden(A,k11_ordinal2(B,C)) & v4_ordinal1(B) & ! [D] : ( v3_ordinal1(D) => ~ ( r2_hidden(D,B) & r2_hidden(A,k11_ordinal2(D,C)) ) ) ) ) ) ) )).
fof(t41_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) ) => ( r2_hidden(A,B) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t41_osafree,axiom,( ! [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) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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] : ( 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) ) ) ) ) ) )).
fof(t41_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v3_msualg_1(C,A) & v12_osalg_1(C,A) & m1_msualg_2(C,A,B) ) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t41_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t41_partfun1,axiom,( ! [A] : ! [B] : ( v1_partfun1(k3_partfun1(k1_xboole_0,A,B),A) => A = k1_xboole_0 ) )).
fof(t41_partfun2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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))) ) ) ) )).
fof(t41_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) )).
fof(t41_pcs_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_pcs_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l2_pcs_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k23_pcs_0(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k23_pcs_0(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( 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(k23_pcs_0(A,B),C,D) ) ) ) ) ) ) ) ) ) ) )).
fof(t41_pdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(3)) => ! [F] : ( ( 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) => k6_pdiff_4(F,D,E) = k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k10_pdiff_1(3,1,F,D),A),k3_square_1(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(C)))),k7_xcmplx_0(k3_xcmplx_0(k10_pdiff_1(3,2,F,D),B),k3_square_1(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(C))))),k7_xcmplx_0(k3_xcmplx_0(k10_pdiff_1(3,3,F,D),C),k3_square_1(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(C))))) ) ) ) ) ) ) ) )).
fof(t41_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m1_rcomp_1(C,k3_funct_2(k1_euclid(3),k1_numbers,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] : ( ( v9_ordinal1(D) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,E) = k1_tarski(k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(2,3),B)) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),C) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,2,k1_pdiff_3(2,3,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,2,k1_pdiff_3(2,3,A),B))))) & k5_pdiff_5(A,B) = k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,2,k1_pdiff_3(2,3,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,2,k1_pdiff_3(2,3,A),B))))) ) ) ) ) ) ) ) ) )).
fof(t41_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( v1_xreal_0(G) => ( ( r1_xxreal_0(1,F) & r1_xxreal_0(F,A) & E = k1_funct_1(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) = k10_pdiff_1(A,F,B,E) ) ) ) ) ) ) ) ) )).
fof(t41_pdiff_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t41_pepin,axiom,( v1_int_2(3) )).
fof(t41_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(B))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k3_finseq_2(B))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k3_finseq_2(B))) => ( ( r1_tarski(C,E) & r1_tarski(D,F) ) => r1_tarski(k11_pnproc_1(A,B,C,D),k11_pnproc_1(A,B,E,F)) ) ) ) ) ) ) )).
fof(t41_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k17_polyform(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_bspace)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t41_polynom5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t41_polynom8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_xxreal_0(k1_algseq_1(A,B),C) => ( r1_xxreal_0(C,k5_numbers) | ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ~ r1_xxreal_0(C,E) => k9_nat_1(u1_struct_0(A),k6_polynom8(C,A,B,D),E) = k3_matrix_0(u1_struct_0(A),k4_matrix_3(A,k7_polynom8(A,C,D),k4_polynom8(C,A,B)),k1_nat_1(E,1),1) ) ) ) ) ) ) ) ) )).
fof(t41_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [G] : ( ( 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] : ( ( 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) ) => k4_polynom1(A,C,D,H) = k4_polynom1(A,C,F,H) ) ) ) ) ) ) ) ) ) )).
fof(t41_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => k2_power(A,B) = k1_newton(A,B) ) ) )).
fof(t41_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t41_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => k3_prepower(A,k4_xcmplx_0(B)) = k7_xcmplx_0(1,k3_prepower(A,B)) ) ) )).
fof(t41_prob_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => r2_funct_2(k4_ordinal1,k1_zfmisc_1(A),k2_prob_1(A,k11_funct_7(k1_zfmisc_1(A),B,C)),k11_funct_7(k1_zfmisc_1(A),k3_subset_1(A,B),k3_subset_1(A,C))) ) ) )).
fof(t41_prob_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( m2_prob_1(D,A,B) => ( v2_comseq_2(k8_prob_1(A,B,k2_prob_3(A,C),D)) & k1_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)) & k1_seq_2(k8_prob_1(A,B,k2_prob_3(A,C),D)) = k1_funct_1(D,k1_kurato_0(A,C)) ) ) ) ) ) )).
fof(t41_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),k4_prob_4(A,B,C)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t41_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t41_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t41_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ~ r1_qc_lang2(A,B,k12_qc_lang1(A)) ) ) )).
fof(t41_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( ( ~ 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))) ) ) ) ) )).
fof(t41_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_qc_lang4(C,A,B) => ! [D] : ( m1_qc_lang4(D,A,B) => ( ? [E] : ( m2_qc_lang4(E,A,B,C) & ? [F] : ( m2_qc_lang4(F,A,B,D) & r1_tarski(E,F) ) ) => r2_qc_lang2(A,D,C) ) ) ) ) ) )).
fof(t41_quatern2,axiom,( k16_quatern2(k4_struct_0(k15_quatern2)) = k4_struct_0(k15_quatern2) )).
fof(t41_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k28_quaterni(A),k28_quaterni(B))),k2_xcmplx_0(k28_quaterni(A),k28_quaterni(B))) ) ) )).
fof(t41_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ( k13_quaterni(k24_quaterni(A)) = k4_xcmplx_0(k13_quaterni(A)) & k14_quaterni(k24_quaterni(A)) = k4_xcmplx_0(k14_quaterni(A)) & k15_quaterni(k24_quaterni(A)) = k4_xcmplx_0(k15_quaterni(A)) & k16_quaterni(k24_quaterni(A)) = k4_xcmplx_0(k16_quaterni(A)) ) ) )).
fof(t41_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k19_quofield(A))) => k1_algstr_0(k19_quofield(A),B,k4_struct_0(k19_quofield(A))) = B ) ) )).
fof(t41_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ~ ( ~ v1_vectsp_7(C,A,B) & ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t41_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ! [B] : ( v1_rat_1(B) => ( ( B = k7_xcmplx_0(1,A) => ( r1_xxreal_0(A,k5_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,k5_numbers) & B = k7_xcmplx_0(1,A) ) ) ) ) ) )).
fof(t41_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r1_xxreal_0(C,D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k4_topmetr(C,D)))) => ( ( E = k3_rcomp_1(A,B) & r1_xxreal_0(B,D) ) => ( r1_xxreal_0(A,C) | k1_tops_1(k4_topmetr(C,D),E) = k2_rcomp_1(A,B) ) ) ) ) ) ) ) ) )).
fof(t41_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( ! [C] : ( r2_hidden(C,A) => r2_hidden(k4_tarski(C,C),B) ) => r1_tarski(k4_relat_1(A),B) ) ) )).
fof(t41_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,D))) => ( r2_hidden(B,k9_relat_1(k3_subset_1(k2_zfmisc_1(C,D),E),A)) <=> ( ~ r2_hidden(k4_tarski(A,B),E) & r2_hidden(A,C) & r2_hidden(B,D) ) ) ) )).
fof(t41_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r6_rewrite1(A,B,C) => r6_rewrite1(A,C,B) ) ) )).
fof(t41_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t41_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(E))) => ! [G] : ( ( ~ 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,D)),k1_rewrite3(E,F,G)) & r2_hidden(k4_tarski(A,k4_tarski(C,D)),k1_rewrite3(E,F,G)) ) => B = C ) ) ) ) )).
fof(t41_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_valued_0(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_valued_0(D) ) => k1_rfunct_1(k1_rfunct_1(A,C),k1_rfunct_1(B,D)) = k1_rfunct_1(k18_valued_1(A,k5_relat_1(D,k9_xtuple_0(k4_rfunct_1(D)))),k18_valued_1(C,B)) ) ) ) ) )).
fof(t41_rfunct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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))) ) ) ) )).
fof(t41_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t41_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_seq_2(C) => ( B = k1_funct_1(k4_rinfsup1(C),A) <=> ( ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k1_funct_1(C,k2_xcmplx_0(A,D)),B) ) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => r1_xxreal_0(k1_funct_1(C,k2_xcmplx_0(A,E)),k6_xcmplx_0(B,D)) ) ) ) ) ) ) ) ) ) )).
fof(t41_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v10_mesfunc5(A) => ( k2_mesfunc5(A) = k6_rinfsup2(A) & k2_mesfunc5(A) = k5_rinfsup2(A) ) ) ) )).
fof(t41_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_rlaffin1(B,A) <=> ! [C] : ( 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) ) ) ) ) ) )).
fof(t41_rlsub_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t41_rlsub_2,axiom,( ! [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) ) => ( m1_rlsub_2(k1_rlsub_1(A),A,k2_rlsub_1(A)) & m1_rlsub_2(k2_rlsub_1(A),A,k1_rlsub_1(A)) ) ) )).
fof(t41_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( ( v9_rltopsp1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t41_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t41_rlvect_2,axiom,( ! [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) ) => ! [B] : ( 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) ) ) ) )).
fof(t41_rlvect_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_rlsub_1(C,B) => r1_tarski(k2_rlvect_5(C,A),k2_rlvect_5(B,A)) ) ) ) )).
fof(t41_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t41_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ( r1_rmod_3(A,B,C,D) <=> ! [E] : ( m2_rmod_2(E,A,B,C) => ! [F] : ( m2_rmod_2(F,A,B,D) => ? [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t41_rmod_4,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(t41_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k9_robbins1(A,k14_robbins1(A,B),B) = k11_robbins1(A,B) ) ) )).
fof(t41_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t41_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k3_funct_2(u1_struct_0(A),k1_numbers,k6_roughs_1(A,B),C) = k5_numbers <=> r2_hidden(C,k3_subset_1(u1_struct_0(A),k4_roughs_1(A,B))) ) ) ) ) )).
fof(t41_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_tarski(C,B) => ( r1_xxreal_0(k1_rpr_1(A,C),k5_numbers) | k2_rpr_1(A,C,B) = 1 ) ) ) ) ) )).
fof(t41_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t41_rusub_2,axiom,( ! [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_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)) ) ) )).
fof(t41_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( m1_rusub_1(D,A) => ( m1_rusub_1(B,D) => m1_rusub_1(k2_rusub_2(A,B,C),D) ) ) ) ) ) )).
fof(t41_rusub_5,axiom,( ! [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_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))) ) ) )).
fof(t41_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t41_rvsum_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k2_numbers) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k2_numbers) ) => k17_rvsum_1(k8_rvsum_2(A,B,C)) = k6_xcmplx_0(k17_rvsum_1(B),k17_rvsum_1(C)) ) ) ) )).
fof(t41_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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] : ( ( 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),k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),3)))) ) & ( r1_xxreal_0(k1_funct_1(B,E),k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),3)))) ) ) ) ) ) ) ) )).
fof(t41_scmfsa10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k5_compos_0(u1_compos_1(k1_scmfsa_2),k11_scmfsa_2(A),B) = k11_scmfsa_2(k2_xcmplx_0(A,B)) ) ) )).
fof(t41_scmfsa8c,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( ( 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) ) ) ) )).
fof(t41_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( v1_ami_2(E) & ~ v1_scmfsa_m(E) & m1_subset_1(E,u1_struct_0(k1_scmfsa_2)) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & ~ v1_xboole_0(F) & v1_funct_1(F) & v1_finset_1(F) & v1_afinsq_1(F) & v1_scmfsa7b(F) ) => ( ( k1_funct_1(C,k4_scmfsa_2(k5_numbers)) = 1 & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,C) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,D) & r3_scmfsa9a(A,C,E,F) & r4_scmfsa9a(A,C,E,F) ) => r4_scmfsa9a(B,D,E,F) ) ) ) ) ) ) ) )).
fof(t41_scmfsa_2,axiom,( ! [A] : ( ( 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(k7_card_1(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 ) )).
fof(t41_scmfsa_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( ( k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(D,B,C,A),E)) = k5_numbers & r6_pboole(u1_struct_0(k1_scmfsa_2),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(D,B,C,A),E),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa_9(C,B)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D),F)) ) => ( r6_pboole(u1_struct_0(k1_scmfsa_2),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(D,B,C,A),E),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(D,B,C,A),E))) & r6_pboole(u1_struct_0(k1_scmfsa_2),k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(D,B,C,A),k1_nat_1(E,1)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa_9(C,B)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D),k1_nat_1(F,k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(k1_funct_4(A,k2_scmfsa_9(C,B)),B),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(D,B,C,A),E))),3)))) ) ) ) ) ) ) ) ) )).
fof(t41_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ( ( k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),E)) = k5_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,k1_nat_1(k5_card_1(C),1))) ) ) ) ) ) ) )).
fof(t41_scmpds_7,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ( k1_funct_1(k2_scmpds_7(A,B,C,D),k5_numbers) = k8_scmpds_2(A,B,k1_nat_1(k5_card_1(D),3)) & k1_funct_1(k2_scmpds_7(A,B,C,D),k1_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),k1_nat_1(k5_card_1(D),2)) = k3_scmpds_2(k4_xcmplx_0(k1_nat_1(k5_card_1(D),2))) ) ) ) ) ) )).
fof(t41_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ! [C] : ( ( 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))) ) ) ) ) )).
fof(t41_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_semi_af1(A,B,C,D,E) => r2_semi_af1(A,D,E,B,C) ) ) ) ) ) ) )).
fof(t41_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v9_ordinal1(B) => r2_funct_2(k4_ordinal1,k1_numbers,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,A),k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,B),k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B))) ) ) ) ) )).
fof(t41_seq_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(A) <=> ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & r1_xxreal_0(B,k9_complex1(k5_real_1(k9_nat_1(k1_numbers,A,D),k9_nat_1(k1_numbers,A,C)))) ) ) ) ) ) ) )).
fof(t41_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t41_seqm_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( k2_xcmplx_0(k9_complex1(k6_xcmplx_0(C,D)),k9_complex1(k6_xcmplx_0(A,B))) = 1 <=> ( ( k9_complex1(k6_xcmplx_0(C,D)) = 1 & A = B ) | ( k9_complex1(k6_xcmplx_0(A,B)) = 1 & C = D ) ) ) ) ) ) ) )).
fof(t41_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,B,C) = k1_power(C,k9_nat_1(k1_numbers,k56_valued_1(k4_ordinal1,k1_numbers,A),C)) ) & ? [C] : ( v7_ordinal1(C) & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => r1_xxreal_0(1,k9_nat_1(k1_numbers,B,D)) ) ) ) & v1_series_1(A) ) ) ) )).
fof(t41_series_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [D] : ( m1_subset_1(D,k4_ordinal1) => k9_nat_1(k1_numbers,C,D) = k2_xcmplx_0(k3_xcmplx_0(A,D),B) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k9_nat_1(k1_numbers,k3_series_1(C),D) = k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(A,k1_nat_1(D,1)),D),2),k3_xcmplx_0(D,B)),B) ) ) ) ) ) )).
fof(t41_series_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_complex1(k9_nat_1(k1_numbers,k3_series_1(A),B)),k9_nat_1(k1_numbers,k3_series_1(k56_valued_1(k4_ordinal1,k1_numbers,A)),B)) ) ) )).
fof(t41_series_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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)),k7_xcmplx_0(1,3)) ) ) ) ) )).
fof(t41_setfam_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r1_tarski(k3_tarski(B),C) & r2_hidden(A,B) ) => r1_tarski(A,C) ) )).
fof(t41_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( v7_ordinal1(C) => ( v3_prob_1(B) => k1_funct_1(k4_setlim_1(A,B),C) = k3_funct_2(k4_ordinal1,k9_setfam_1(A),k4_setlim_1(A,B),k1_nat_1(C,1)) ) ) ) )).
fof(t41_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k1_prob_1(A,k8_setlim_2(A,C,B)) = k7_subset_1(A,k1_prob_1(A,C),B) ) ) )).
fof(t41_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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] : ( m1_subset_1(D,A) => k10_setwiseo(A,B,k2_setwiseo(A,D),C) = k3_funct_2(A,k5_finsub_1(B),C,D) ) ) ) )).
fof(t41_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t41_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( v7_ordinal1(B) => k4_sf_mastr(A) = k4_sf_mastr(k6_compos_1(k1_scmfsa_2,A,B)) ) ) )).
fof(t41_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t41_simplex0,axiom,( ! [A] : ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t41_simplex1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( ~ 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] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ! [E] : ( ( 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(k2_xcmplx_0(k5_card_1(E),A),k6_simplex0(C)) ) => ( ( m3_simplex0(D,k4_simplex1(B,C),k2_xcmplx_0(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] : ( 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) = k2_xcmplx_0(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)) ) ) ) ) ) ) ) ) )).
fof(t41_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => k4_complex1(k11_comseq_3(k3_sin_cos(A))) = k5_numbers ) )).
fof(t41_sin_cos2,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k1_sin_cos2,k1_numbers)) )).
fof(t41_sin_cos3,axiom,( ! [A] : ( v1_xreal_0(A) => k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A) = k1_funct_1(k3_sin_cos2,A) ) )).
fof(t41_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k3_xcmplx_0(k19_sin_cos(k2_xcmplx_0(A,B)),k19_sin_cos(k6_xcmplx_0(A,B))) = k6_xcmplx_0(k3_xcmplx_0(k19_sin_cos(A),k19_sin_cos(A)),k3_xcmplx_0(k17_sin_cos(B),k17_sin_cos(B))) ) ) )).
fof(t41_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( k2_sin_cos2(A) != k5_numbers & k2_sin_cos2(B) != k5_numbers & k1_sin_cos5(k6_xcmplx_0(A,B)) != k7_xcmplx_0(k6_xcmplx_0(1,k3_xcmplx_0(k1_sin_cos5(A),k1_sin_cos5(B))),k6_xcmplx_0(k1_sin_cos5(A),k1_sin_cos5(B))) ) ) ) )).
fof(t41_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ~ ( ~ r1_xxreal_0(A,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)) & ~ r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)),A) & r1_xxreal_0(1,k19_sin_cos(A)) ) ) ) )).
fof(t41_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(1,k1_square_1(A)) => k4_sin_cos7(A) = k1_sin_cos7(k7_xcmplx_0(A,k3_square_1(k6_xcmplx_0(1,k1_square_1(A))))) ) ) )).
fof(t41_sin_cos9,axiom,( k1_funct_1(k26_sin_cos,k5_numbers) = k5_numbers & k1_sin_cos4(k5_numbers) = k5_numbers )).
fof(t41_sincos10,axiom,( k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,4)))) = k1_rcomp_1(1,k3_square_1(2)) )).
fof(t41_sppol_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) )).
fof(t41_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ( ( 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)) ) ) ) ) )).
fof(t41_sprect_1,axiom,( ! [A] : ( 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)))) ) )).
fof(t41_sprect_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t41_sprect_3,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t41_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t41_square_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ~ ( k1_square_1(A) = 1 & A != 1 & A != k4_xcmplx_0(1) ) ) )).
fof(t41_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k7_card_1(B),k7_card_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(B),k7_card_1(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k7_card_1(k1_nat_1(B,1)),k7_card_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k7_card_1(k1_nat_1(B,1)),k7_card_1(A)))) ) => ( ( v2_funct_2(C,k7_card_1(A)) & v1_stirl2_1(C,B,A) & C = k2_partfun1(k7_card_1(k1_nat_1(B,1)),k7_card_1(A),D,k7_card_1(B)) ) => ( r1_xxreal_0(A,k2_stirl2_1(k7_card_1(k1_nat_1(B,1)),A,D,B)) | ( v2_funct_2(D,k7_card_1(A)) & v1_stirl2_1(D,k1_nat_1(B,1),A) & k1_stirl2_1(k1_nat_1(B,1),k7_card_1(A),D,k1_seq_4(k2_stirl2_1(k7_card_1(k1_nat_1(B,1)),A,D,B))) != k1_seq_4(B) ) ) ) ) ) ) ) )).
fof(t41_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k16_substut1(A),k38_substut1(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t41_subset_1,axiom,( ! [A] : ! [B] : ( r2_hidden(B,A) => m1_subset_1(k1_tarski(B),k1_zfmisc_1(A)) ) )).
fof(t41_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_xxreal_0(k12_supinf_2(A,C),k12_supinf_2(B,C)) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_xxreal_0(k12_supinf_2(k18_supinf_2(A),C),k12_supinf_2(k18_supinf_2(B),C)) ) ) ) ) )).
fof(t41_taxonom1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t41_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => m2_nat_lat(k8_tdlat_1(A),k4_tdlat_1(A)) ) )).
fof(t41_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)))) ) ) )).
fof(t41_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v4_tdlat_3(A) & l1_pre_topc(A) ) => k4_tdlat_1(A) = k8_tdlat_1(A) ) )).
fof(t41_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t41_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) )).
fof(t41_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(t41_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ 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)) ) ) ) ) ) ) )).
fof(t41_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( m1_borsuk_2(G,A,D,E) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t41_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m2_subset_1(B,k4_partfun1(k1_numbers,k2_struct_0(A)),k1_topalg_6(A)) => ! [C] : ( 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) ) ) ) )).
fof(t41_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v5_topgen_1(B,A) <=> k2_topgen_1(A,B) = B ) ) ) )).
fof(t41_topgen_3,axiom,( ! [A] : ! [B] : ! [C] : ( 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 ) ) ) )).
fof(t41_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t41_topgen_5,axiom,( ! [A] : ( 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)) ) ) )).
fof(t41_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v2_group_1(A) & v3_group_1(A) & l1_topgrp_1(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_connsp_2(D,A,k6_algstr_0(A,B,k2_group_1(A,C))) => ? [E] : ( m1_connsp_2(E,A,B) & ? [F] : ( 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) ) ) ) )).
fof(t41_topreal3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ( ( 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(k1_nat_1(B,1),k3_finseq_1(A)) ) => k1_nat_1(B,1) = k3_finseq_1(A) ) ) ) )).
fof(t41_topreal6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(2))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [D] : ( v1_xreal_0(D) => ( ( C = k8_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(k6_xcmplx_0(k17_euclid(A),D),k2_xcmplx_0(k17_euclid(A),D)) ) ) ) ) ) )).
fof(t41_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t41_toprealb,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( 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),k2_xcmplx_0(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),k2_xcmplx_0(k2_xcmplx_0(B,A),1))),k13_toprealb(k4_toprealb(B))) ) ) )).
fof(t41_toprealc,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( ( 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))))) ) ) ) ) )).
fof(t41_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) )).
fof(t41_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) )).
fof(t41_tops_2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t41_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tops_3(B,A) <=> ? [C] : ( 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) ) ) ) ) )).
fof(t41_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t41_trees_1,axiom,( k6_trees_1(k2_trees_1(k5_numbers)) = k5_numbers )).
fof(t41_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => m4_trees_3(A,k2_trees_1(k5_numbers)) ) )).
fof(t41_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v3_trees_9(A) ) => ! [B] : ( m1_trees_1(B,k9_xtuple_0(A)) => ! [C] : ( m1_trees_1(C,k9_xtuple_0(A)) => ( r2_hidden(C,k1_trees_2(k9_xtuple_0(A),B)) => r2_hidden(k1_funct_1(A,C),k10_xtuple_0(k2_trees_9(A,B))) ) ) ) ) )).
fof(t41_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t41_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t41_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( l1_turing_1(B) => ! [C] : ( 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)) ) ) ) )).
fof(t41_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ( r2_hidden(A,k2_msafree2(k40_twoscomp(A,B))) & r2_hidden(B,k2_msafree2(k40_twoscomp(A,B))) ) ) ) )).
fof(t41_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => k2_polynom4(k1_complfld,k4_uniroots(A,k1_complfld),B) = k6_xcmplx_0(k2_binop_1(u1_struct_0(k1_complfld),k4_ordinal1,u1_struct_0(k1_complfld),k4_group_1(k1_complfld),B,A),1) ) ) )).
fof(t41_uproots,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v6_struct_0(A) & l5_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r1_xxreal_0(B,k1_algseq_1(A,C)) => k1_nat_1(k1_algseq_1(A,k4_uproots(A,C,B)),B) = k1_algseq_1(A,C) ) ) ) ) )).
fof(t41_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t41_valued_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_finseq_1(B) ) => ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) & k1_relset_1(k4_ordinal1,C) = k1_relset_1(k4_ordinal1,B) & k10_xtuple_0(C) = k1_relset_1(k4_ordinal1,k61_valued_1(B,A)) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,B)) => k1_funct_1(C,D) = k1_nat_1(A,D) ) ) & v2_funct_1(C) ) ) ) )).
fof(t41_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( ( 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 ) ) )).
fof(t41_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t41_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( r1_vectsp_5(A,B,C,D) => r1_vectsp_5(A,B,D,C) ) ) ) ) ) )).
fof(t41_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => ! [D] : ( 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))) ) ) ) ) )).
fof(t41_vfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ 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] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,u1_struct_0(D)))) ) => ( ( r1_tarski(B,A) & r1_vfunct_1(C,D,E,A) ) => r1_vfunct_1(C,D,E,B) ) ) ) ) )).
fof(t41_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ! [E] : ( ( r1_tarski(E,D) & r1_vfunct_2(A,B,C,D) ) => r1_vfunct_2(A,B,C,E) ) ) ) ) )).
fof(t41_waybel11,axiom,( ! [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] : ( ( 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) ) ) ) )).
fof(t41_waybel12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( B = C => ( B = k4_yellow_0(k1_yellow_1(u1_pre_topc(A))) | ( v2_waybel_6(B,k1_yellow_1(u1_pre_topc(A))) <=> v3_yellow_8(k3_subset_1(u1_struct_0(A),C),A) ) ) ) ) ) ) )).
fof(t41_waybel14,axiom,( ! [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) ) => ( v1_waybel_5(k1_yellow_1(k5_waybel11(A))) <=> ( v3_waybel_3(k1_yellow_1(k5_waybel11(A))) & v3_waybel_3(k7_lattice3(k1_yellow_1(k5_waybel11(A)))) ) ) ) )).
fof(t41_waybel19,axiom,( ! [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] : ( ( v2_pre_topc(B) & v2_waybel19(B) & m1_yellow_9(B,A) ) => ! [C] : ( ( v13_waybel_0(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( v3_pre_topc(C,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( D = C => v3_pre_topc(D,A) ) ) ) ) ) ) )).
fof(t41_waybel20,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,A)))) ) => ( v1_waybel20(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_waybel20(A,B))) <=> ? [D] : ( 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) ) ) ) ) ) )).
fof(t41_waybel21,axiom,( ! [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] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k1_waybel11(A,k5_waybel_9(A,B,C)) = k1_waybel11(A,B) ) ) ) )).
fof(t41_waybel23,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v2_waybel23(k2_waybel_3(A,B),A) ) ) )).
fof(t41_waybel26,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r1_tarski(k9_xtuple_0(A),B) => k5_waybel26(k6_waybel26(A,B)) = A ) ) )).
fof(t41_waybel27,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ? [D] : ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(k2_waybel27(B,k5_yellow_1(A,C))),u1_struct_0(k5_yellow_1(A,k2_waybel27(B,C)))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_waybel27(B,k5_yellow_1(A,C))),u1_struct_0(k5_yellow_1(A,k2_waybel27(B,C)))))) & v3_waybel27(D) & v23_waybel_0(D,k2_waybel27(B,k5_yellow_1(A,C)),k5_yellow_1(A,k2_waybel27(B,C))) ) ) ) ) )).
fof(t41_waybel34,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t41_waybel_0,axiom,( ! [A] : ( ( v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v13_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v2_waybel_0(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k12_lattice3(A,C,D),B) ) ) ) ) ) ) )).
fof(t41_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t41_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ( v1_waybel_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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)))) ) ) ) ) ) )).
fof(t41_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ( v9_pre_topc(A) & v3_waybel_3(k1_yellow_1(u1_pre_topc(A))) ) => v6_waybel_3(A) ) ) )).
fof(t41_waybel_4,axiom,( ! [A] : ( ( 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) ) )).
fof(t41_waybel_7,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t41_waybel_9,axiom,( ! [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) & v1_compts_1(A) & l1_waybel_9(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v5_pre_topc(k4_waybel_1(A,B),A,A) ) => v2_waybel_2(A) ) ) )).
fof(t41_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t41_wsierp_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & k5_int_1(A,B) != k5_numbers & k4_xcmplx_0(k4_int_1(A,B)) != k2_xcmplx_0(k4_int_1(k4_xcmplx_0(A),B),1) ) ) ) )).
fof(t41_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : k4_xboole_0(k4_xboole_0(A,B),C) = k4_xboole_0(A,k2_xboole_0(B,C)) )).
fof(t41_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k4_xboolean(A,k9_xboolean(B,C)) = k4_xboolean(k4_xboolean(A,k3_xboolean(B)),k3_xboolean(C)) ) ) ) )).
fof(t41_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t41_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_numbers) => r1_xxreal_0(B,k2_xcmplx_0(A,C)) ) ) => r1_xxreal_0(B,A) ) ) ) )).
fof(t41_xtuple_0,axiom,( ! [A] : ! [B] : r1_tarski(k4_xboole_0(k13_xtuple_0(A),k13_xtuple_0(B)),k13_xtuple_0(k4_xboole_0(A,B))) )).
fof(t41_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => k4_xxreal_0(A,k1_xxreal_0) = k1_xxreal_0 ) )).
fof(t41_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(D,B) ) => r1_tarski(k4_xxreal_1(C,D),k3_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t41_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => m1_xxreal_2(k1_xxreal_0,A) ) )).
fof(t41_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(k3_xxreal_3(A,B),C) => ( ( C = k2_xxreal_0 & B = k1_xxreal_0 & ~ r1_xxreal_0(A,k5_numbers) ) | ( C = k1_xxreal_0 & B = k2_xxreal_0 & ~ r1_xxreal_0(A,k5_numbers) ) | r1_xxreal_0(A,k1_xxreal_3(C,B)) ) ) ) ) ) )).
fof(t41_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( 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))) ) ) ) ) )).
fof(t41_yellow12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(C),u1_struct_0(B)) & v5_pre_topc(D,C,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(B)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(C),u1_struct_0(A)) & v5_pre_topc(E,C,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(A)))) ) => ( v1_funct_1(k14_funct_3(u1_struct_0(C),u1_struct_0(B),u1_struct_0(A),D,E)) & v1_funct_2(k14_funct_3(u1_struct_0(C),u1_struct_0(B),u1_struct_0(A),D,E),u1_struct_0(C),u1_struct_0(k2_borsuk_1(B,A))) & v5_pre_topc(k14_funct_3(u1_struct_0(C),u1_struct_0(B),u1_struct_0(A),D,E),C,k2_borsuk_1(B,A)) & m1_subset_1(k14_funct_3(u1_struct_0(C),u1_struct_0(B),u1_struct_0(A),D,E),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(k2_borsuk_1(B,A))))) ) ) ) ) ) ) )).
fof(t41_yellow18,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_altcat_1(A,B,C) != k1_xboole_0 => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t41_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ( v21_functor0(C,A,B) => r2_yellow20(A,B,C,A,B) ) ) ) ) )).
fof(t41_yellow_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t41_yellow_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ( m1_subset_1(A,u1_struct_0(k1_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))) ) ) ) )).
fof(t41_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t41_yellow_4,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t41_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t41_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( v8_yellow_6(B,A) & m4_yellow_6(B,A) ) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,C) => ! [E] : ( ( ~ 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) ) ) ) ) ) ) ) ) )).
fof(t41_yellow_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t41_yellow_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( ( 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))))) ) ) ) ) ) )).
fof(t41_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v8_zf_lang(A) => A = k10_zf_lang(k21_zf_lang(A),k22_zf_lang(A)) ) ) )).
fof(t41_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ~ r1_zf_lang(A,A) ) )).
fof(t41_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r2_hidden(A,C) & r2_hidden(B,C) ) => k2_xboole_0(k2_tarski(A,B),C) = C ) )).
fof(t41_zfrefle1,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) ) => ~ ( r2_hidden(k4_ordinal1,B) & r2_hidden(A,B) & ! [C] : ( ~ v1_xboole_0(C) => ~ ( r2_hidden(A,C) & r2_hidden(C,B) & v1_zf_model(C) ) ) ) ) )).
fof(t41_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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 ) ) ) )).
fof(t41_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( m1_zmodul02(C,A) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( m2_zmodul02(B,A,D) & m2_zmodul02(C,A,D) ) => m2_zmodul02(k25_zmodul02(A,B,C),A,D) ) ) ) ) ) )).
fof(t420_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => k1_xxreal_1(k2_xxreal_0,A) = k2_xboole_0(k2_xxreal_1(k2_xxreal_0,A),k1_tarski(A)) ) )).
fof(t421_xxreal_1,axiom,( ! [A] : ( 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)) ) )).
fof(t422_xxreal_1,axiom,( ! [A] : ( 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)) ) )).
fof(t423_xxreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => k3_xxreal_1(k2_xxreal_0,A) = k2_xboole_0(k4_xxreal_1(k2_xxreal_0,A),k1_tarski(A)) ) )).
fof(t424_xxreal_1,axiom,( ! [A] : ( 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)) ) )).
fof(t425_xxreal_1,axiom,( ! [A] : ( 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)) ) )).
fof(t426_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => k1_xxreal_1(A,k1_xxreal_0) = k2_xboole_0(k1_tarski(A),k3_xxreal_1(A,k1_xxreal_0)) ) )).
fof(t427_xxreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => k2_xxreal_1(A,k1_xxreal_0) = k2_xboole_0(k1_tarski(A),k4_xxreal_1(A,k1_xxreal_0)) ) )).
fof(t428_xxreal_1,axiom,( ! [A] : ( 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)) ) )).
fof(t42_abcmiz_0,axiom,( ! [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) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_abcmiz_0(A)) => ( r3_abcmiz_0(A,B,C) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t42_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ( k3_finseq_1(k1_msualg_1(A,B)) = 1 => ! [C] : ( m1_subset_1(C,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ( ? [D] : ( 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)) ) ) ) ) ) )).
fof(t42_abcmiz_a,axiom,( ! [A] : ( m1_subset_1(A,u4_struct_0(k27_abcmiz_1)) => ( v2_abcmiz_1(A,k27_abcmiz_1) <=> r2_hidden(A,k20_abcmiz_1) ) ) )).
fof(t42_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t42_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t42_afinsq_1,axiom,( ! [A] : r2_hidden(k1_xboole_0,k8_afinsq_1(A)) )).
fof(t42_afinsq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,B) & v1_funct_1(C) & v5_ordinal1(C) & v1_finset_1(C) ) => ! [D] : ( ( 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(k4_ordinal1,C)) => ( ( ~ v1_setwiseo(D,B) & A = k5_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,k1_nat_1(A,1)),D) ) ) ) ) ) ) )).
fof(t42_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k13_afproj(A))) => ! [C] : ( 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))) ) ) ) ) )).
fof(t42_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t42_algspec1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t42_algstr_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t42_altcat_4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t42_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) <=> m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_analmetr(A)))) ) ) )).
fof(t42_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ~ ( r1_analmetr(A,J,K) & r1_analort(A,J,K,B,C,E,F) & r1_analort(A,J,K,H,I,E,F) & r1_analort(A,J,K,H,I,D,G) & H != I & E != F & ~ r1_analort(A,J,K,B,C,D,G) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t42_aofa_000,axiom,( ! [A] : ( ( 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,k10_subset_1(1,k4_finseq_1(u1_unialg_1(A))))) = k1_tarski(k1_xboole_0) ) )).
fof(t42_aofa_a00,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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) & l1_unialg_1(B) ) => ( g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)) = g1_unialg_1(u1_struct_0(B),u1_unialg_1(B)) => ( k12_aofa_000(A) = k12_aofa_000(B) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( C = E & D = F ) => ( k13_aofa_000(A,C,D) = k13_aofa_000(B,E,F) & k16_aofa_000(A,C,D) = k16_aofa_000(B,E,F) & ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ( G = H => k14_aofa_000(A,G,C,D) = k14_aofa_000(B,H,E,F) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t42_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( ( v19_aofa_a00(F,A) & m1_subset_1(F,u1_struct_0(A)) ) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),F)) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),F)) => ! [I] : ( m2_subset_1(I,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => k15_aofa_a00(A,B,C,D,F,k31_aofa_a00(A,C,F,G,H),I) = k31_aofa_a00(A,D,F,k15_aofa_a00(A,B,C,D,F,G,I),k15_aofa_a00(A,B,C,D,F,H,I)) ) ) ) ) ) ) ) ) ) )).
fof(t42_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [E] : ( ( v1_aofa_i00(E,A,B,D) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),D) ) => ! [F] : ( v1_int_1(F) => ! [G] : ( 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) = k5_int_1(k21_aofa_i00(B,k4_numbers,C,G),F) & ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t42_armstrng,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => r5_armstrng(A,B,k9_armstrng(A,k10_armstrng(A,B))) ) ) )).
fof(t42_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ( B != k1_xboole_0 => ( k6_arytm_3(k8_arytm_3(A,B)) = k4_arytm_3(A,B) & k7_arytm_3(k8_arytm_3(A,B)) = k4_arytm_3(B,A) ) ) ) ) )).
fof(t42_asympt_1,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xxreal_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & v2_asympt_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(B,k6_asympt_0(k3_asympt_0(C,A))) => ( ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(E,F) => r1_xxreal_0(D,k9_nat_1(k1_numbers,C,F)) ) ) ) ) ) | r2_hidden(B,k6_asympt_0(C)) ) ) ) ) ) )).
fof(t42_bcialg_1,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t42_bcialg_3,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t42_bcialg_4,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v4_bcialg_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t42_bcialg_5,axiom,( ! [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) ) => ( ( ~ 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,k5_numbers,1,k5_numbers,k5_numbers) ) ) )).
fof(t42_bcialg_6,axiom,( ! [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] : ( ( ~ 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] : ( ( 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)))) ) => ( v2_funct_2(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & D = k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,E) ) ) ) ) ) ) )).
fof(t42_bciideal,axiom,( ! [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) ) => ( ( v3_bciideal(k1_tarski(k4_struct_0(A)),A) & m2_bcialg_1(k1_tarski(k4_struct_0(A)),A) ) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)))) ) ) ) ) )).
fof(t42_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k4_bhsp_1(A,k5_algstr_0(A,B,D),k5_algstr_0(A,C,D)) = k4_bhsp_1(A,B,C) ) ) ) ) )).
fof(t42_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_numbers) => r2_hidden(B,k4_bhsp_2(A,B,C)) ) ) ) ) )).
fof(t42_bhsp_4,axiom,( ! [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_bhsp_1(A) & v3_bhsp_3(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v2_bhsp_4(B,A) => v1_bhsp_4(B,A) ) ) ) )).
fof(t42_bilinear,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t42_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t42_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t42_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_topmetr)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_topmetr)) => ( A = k2_rcomp_1(B,C) => v3_pre_topc(A,k5_topmetr) ) ) ) ) )).
fof(t42_borsuk_5,axiom,( ! [A] : ( 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)) ) )).
fof(t42_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t42_borsuk_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ( k17_euclid(A) = k3_xcmplx_0(k12_euclid(A),k19_sin_cos(k3_euclid_3(A))) & k18_euclid(A) = k3_xcmplx_0(k12_euclid(A),k17_sin_cos(k3_euclid_3(A))) ) ) )).
fof(t42_bspace,axiom,( ! [A] : k1_card_1(k2_struct_0(k7_bspace(A))) = k3_card_2(2,k1_card_1(A)) )).
fof(t42_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t42_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t42_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t42_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t42_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => k8_xboolean(k8_margrel1,A) = k3_xboolean(A) ) )).
fof(t42_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t42_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( 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)))) ) ) ) ) ) ) )).
fof(t42_card_1,axiom,( ! [A] : ( v7_ordinal1(A) => k2_card_1(k1_card_1(A)) = k1_card_1(k1_ordinal1(A)) ) )).
fof(t42_card_2,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => r1_xxreal_0(k5_card_1(k2_xboole_0(A,B)),k1_nat_1(k5_card_1(A),k5_card_1(B))) ) ) )).
fof(t42_card_3,axiom,( ! [A] : ( v1_finset_1(A) => r2_hidden(k1_card_1(A),k1_card_1(k4_ordinal1)) ) )).
fof(t42_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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) = k5_numbers ) ) ) ) ) )).
fof(t42_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,B,C) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t42_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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) ) ) ) )).
fof(t42_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,D,B) => ! [F] : ( 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 & k9_cat_4(A,B,C,D,E,F) != k5_cat_1(A,D,k2_cat_4(A,D,D),k2_cat_4(A,B,C),k15_cat_4(A,D),k18_cat_4(A,D,B,D,C,E,F)) ) ) ) ) ) ) ) )).
fof(t42_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( r2_hidden(B,k6_cc0sp2(A)) => r2_hidden(B,k2_cc0sp1(u1_struct_0(A))) ) ) )).
fof(t42_cfcont_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t42_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t42_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ~ ( ~ v7_cgames_1(A) & ~ v9_cgames_1(A) & ~ v10_cgames_1(A) & ~ v8_cgames_1(A) ) ) )).
fof(t42_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m1_chain_1(D,A) => ( r2_hidden(k3_chain_1(A,B,C),k4_chain_1(A,D,1)) <=> ? [E] : ( m2_subset_1(E,k4_ordinal1,k2_finseq_1(A)) & ~ ( r1_xxreal_0(k1_funct_1(C,E),k1_funct_1(B,E)) & ~ ( A = 1 & ~ r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) & m2_chain_1(k4_tarski(k1_funct_1(B,E),k1_funct_1(C,E)),k2_chain_1(A,D,E)) & ! [F] : ( m2_subset_1(F,k4_ordinal1,k2_finseq_1(A)) => ( F != E => ( k1_funct_1(B,F) = k1_funct_1(C,F) & r2_hidden(k1_funct_1(B,F),k2_chain_1(A,D,F)) ) ) ) ) ) ) ) ) ) )).
fof(t42_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ( v1_glib_002(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k6_glib_000(A))) ) => ~ ( r1_subset_1(B,C) & ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t42_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(D) & v1_finset_1(D) ) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t42_circcomb,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t42_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v4_msualg_1(E,A) & v4_msafree2(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( ( v4_msualg_1(F,B) & v4_msafree2(F,B) & l3_msualg_1(F,B) ) => ( r4_circtrm1(A,B,C,D,E,F) => ! [G] : ( m1_subset_1(G,u4_struct_0(A)) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t42_classes1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => ( r2_hidden(A,k4_classes1(B)) <=> r2_hidden(k9_setfam_1(A),k4_classes1(k1_ordinal1(B))) ) ) )).
fof(t42_classes2,axiom,( ! [A] : ! [B] : ( ( v2_classes1(B) & v1_ordinal1(A) & r2_hidden(A,B) ) => r2_hidden(A,k4_classes1(k1_card_1(B))) ) )).
fof(t42_clopban1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t42_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t42_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_numbers) => r2_hidden(B,k4_clvect_2(A,B,C)) ) ) ) ) )).
fof(t42_clvect_3,axiom,( ! [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) & v2_csspace(A) & v4_clvect_2(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v2_clvect_3(B,A) => v1_clvect_3(B,A) ) ) ) )).
fof(t42_coh_sp,axiom,( ! [A] : ! [B] : ( 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] : ! [D] : ( 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))) ) ) ) )).
fof(t42_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,A) ) => ! [D] : ~ ( r2_hidden(D,k3_tarski(B)) & ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t42_compl_sp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( ~ ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_metric_1(A,B,C) = k5_numbers ) => ! [C] : ( ~ v1_finset_1(C) => ( v4_tbsp_1(k3_compl_sp(A,B,C)) & ? [D] : ( v2_relat_1(D) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,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(k4_ordinal1,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)) ) ) ) ) ) ) ) )).
fof(t42_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k3_complex1(k6_xcmplx_0(A,k8_complex1(A))) = k5_numbers & k4_complex1(k6_xcmplx_0(A,k8_complex1(A))) = k3_xcmplx_0(2,k4_complex1(A)) ) ) )).
fof(t42_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k4_xcmplx_0(k1_complex2(A,B)) = k1_complex2(A,k4_xcmplx_0(B)) ) ) )).
fof(t42_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ( B != k4_struct_0(k1_complfld) => ( k4_algstr_0(k1_complfld,k3_vectsp_1(k1_complfld,A,B)) = k3_vectsp_1(k1_complfld,k4_algstr_0(k1_complfld,A),B) & k4_algstr_0(k1_complfld,k3_vectsp_1(k1_complfld,A,B)) = k3_vectsp_1(k1_complfld,A,k4_algstr_0(k1_complfld,B)) ) ) ) ) )).
fof(t42_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ! [D] : ( 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,k4_binop_2,A,B) = k1_finseqop(k1_numbers,k1_numbers,k1_numbers,k10_binop_2,C,D) ) ) ) ) ) )).
fof(t42_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(A)) => k5_card_1(k11_compos_1(A,B)) = 2 ) ) )).
fof(t42_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( 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) ) ) ) ) ) )).
fof(t42_comptrig,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( r2_hidden(k1_comptrig(A),k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos)) <=> ( ~ r1_xxreal_0(k5_numbers,k3_complex1(A)) & ~ r1_xxreal_0(k4_complex1(A),k5_numbers) ) ) ) )).
fof(t42_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v4_valued_0(A) & v2_margrel1(A) ) => k1_comput_1(k9_finseq_1(A)) = k19_margrel1(A) ) )).
fof(t42_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( r2_relset_1(k4_ordinal1,k2_numbers,k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,A),k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,C,A)),k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,C),A)) & r2_relset_1(k4_ordinal1,k2_numbers,k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,A),k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,C,A)),k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,C),A)) ) ) ) ) )).
fof(t42_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) = k1_seq_2(k7_comseq_3(A)) & k4_complex1(k3_comseq_2(A)) = k1_seq_2(k8_comseq_3(A)) ) ) ) )).
fof(t42_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ( ~ v2_struct_0(k11_conlat_1(A)) & v10_lattices(k11_conlat_1(A)) & l3_lattices(k11_conlat_1(A)) ) ) )).
fof(t42_connsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t42_convex4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xcmplx_0(B) => k3_complex1(k3_xcmplx_0(A,B)) = k3_xcmplx_0(A,k3_complex1(B)) ) ) )).
fof(t42_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k1_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( m2_funct_2(F,k3_qc_lang1(A),k3_qc_lang1(A),k9_funct_2(k3_qc_lang1(A),k3_qc_lang1(A))) => ! [G] : ( 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)),E,B,G,F),k15_cqc_sim1(A,D)) & r2_hidden(k2_qc_lang3(A,C),k7_relat_1(F,k24_qc_lang1(A,E))) ) => r2_qc_lang1(A,C,B) ) ) ) ) ) ) ) ) )).
fof(t42_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t42_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t42_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k3_cqc_lang(A))) => ( r6_cqc_the3(A,D,B) => ( r3_cqc_the1(A,k4_subset_1(k3_cqc_lang(A),E,k6_domain_1(k3_cqc_lang(A),B)),C) <=> r3_cqc_the1(A,E,k8_cqc_lang(A,D,C)) ) ) ) ) ) ) ) )).
fof(t42_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( k13_csspace(A,B) = k5_numbers <=> B = k4_struct_0(A) ) ) ) )).
fof(t42_dickson,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k7_card_1(A)) & v1_funct_1(B) & v1_partfun1(B,k7_card_1(A)) & v1_yellow_1(B) ) => ( ! [C] : ( m2_subset_1(C,k4_ordinal1,k7_card_1(A)) => ( v4_dickson(k3_waybel_3(k7_card_1(A),B,C)) & v3_dickson(k3_waybel_3(k7_card_1(A),B,C)) ) ) => ( v3_dickson(k4_yellow_1(k7_card_1(A),B)) & v4_dickson(k4_yellow_1(k7_card_1(A),B)) ) ) ) ) )).
fof(t42_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k3_diff_1(k16_sin_cos,A),B) = k3_xcmplx_0(2,k3_xcmplx_0(k19_sin_cos(k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(2,B),A),2)),k17_sin_cos(k7_xcmplx_0(A,2)))) ) ) )).
fof(t42_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_square_1(D) ) => ( A = B | k9_diff_1(C,A,B) = k2_xcmplx_0(A,B) ) ) ) ) ) )).
fof(t42_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k4_diff_1(C,A),B) = k6_xcmplx_0(k1_funct_1(C,B),k1_funct_1(k2_diff_1(C,k4_xcmplx_0(A)),B)) ) ) ) )).
fof(t42_dilworth,axiom,( ! [A] : ( ( v3_dilworth(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_xxreal_0(k1_dilworth(k5_yellow_0(A,B)),k1_dilworth(A)) ) ) )).
fof(t42_diraf,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ( ( ~ ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = C ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_analoaf(A,B,C,B,D) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_analoaf(A,B,D,C,E) & C != E ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_analoaf(A,B,C,D,E) & r2_analoaf(A,B,D,C,E) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_analoaf(A,D,B,B,E) & B != D & ! [F] : ( 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) ) ) ) )).
fof(t42_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => m2_subset_1(k4_domain_1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k5_numbers,1,k5_numbers),k3_ec_pf_1(k9_int_3(A)),k6_ec_pf_1(A,B,C)) ) ) ) )).
fof(t42_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( 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) != k5_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)) ) ) ) ) )).
fof(t42_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t42_entropy1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => k5_matrprob(A) = k18_rvsum_1(k2_entropy1(k1_numbers,A)) ) )).
fof(t42_enumset1,axiom,( ! [A] : k2_enumset1(A,A,A,A) = k1_tarski(A) )).
fof(t42_eqrel_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_eqrel_1(C,B) => ~ ( r2_hidden(A,C) & ! [D] : ( m1_subset_1(D,B) => A != k11_eqrel_1(B,D,C) ) ) ) ) )).
fof(t42_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => k4_struct_0(k15_euclid(A)) = k5_euclid(A) ) )).
fof(t42_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ( ~ ( B != k4_struct_0(k15_euclid(A)) & r1_xxreal_0(k12_euclid(B),k5_numbers) ) & ~ ( ~ r1_xxreal_0(k12_euclid(B),k5_numbers) & B = k4_struct_0(k15_euclid(A)) ) ) ) ) )).
fof(t42_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => k22_rvsum_1(A,B) = k3_complex1(k1_complex2(k2_euclid_3(A),k2_euclid_3(B))) ) ) )).
fof(t42_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ( ( r2_hidden(D,k4_euclid_4(A,B,C)) & r2_hidden(E,k4_euclid_4(A,B,C)) ) => ( D = E | r1_tarski(k4_euclid_4(A,B,C),k4_euclid_4(A,D,E)) ) ) ) ) ) ) ) )).
fof(t42_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( k12_euclid(k5_algstr_0(k15_euclid(2),A,B)) = k5_numbers <=> A = B ) ) ) )).
fof(t42_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k10_funcsdom(k2_finseq_1(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k10_funcsdom(k2_finseq_1(A))))) => ~ ( C = k8_euclid_7(A) & ! [D] : ( m2_rlvect_2(D,k10_funcsdom(k2_finseq_1(A)),C) => B != k6_rlvect_2(k10_funcsdom(k2_finseq_1(A)),D) ) ) ) ) ) )).
fof(t42_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ( k3_finseq_1(A) = 3 & k4_finseq_1(A) = k2_finseq_1(3) ) ) )).
fof(t42_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t42_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_exchsort(E) ) => ( ( r2_hidden(A,C) & r2_hidden(B,C) & D = k9_funct_7(k6_partfun1(C),A,B) & C = k9_xtuple_0(E) ) => k9_funct_7(E,A,B) = k3_relat_1(D,E) ) ) ) )).
fof(t42_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_msafree2(k5_circcomb(A,k11_finseq_1(B,C,D))) = k1_enumset1(B,C,D) )).
fof(t42_fcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,k1_relset_1(k1_numbers,A)) => k1_funct_1(A,B) = k1_square_1(B) ) ) => v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,A,k1_relset_1(k1_numbers,A))) ) ) )).
fof(t42_fdiff_10,axiom,( ! [A] : ( ( 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,k26_sin_cos,k27_sin_cos),k22_sin_cos))) => ( r2_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),k22_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),k22_sin_cos),A),B) = k7_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B)))),k1_funct_1(k26_sin_cos,B)),k1_funct_1(k27_sin_cos,B)),k1_funct_1(k22_sin_cos,B)) ) ) ) ) ) )).
fof(t42_fdiff_11,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_sin_cos9)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_sin_cos9)),A),B) = k2_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,B),k6_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k1_funct_1(k2_sin_cos9,B)))),k7_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k18_sin_cos,B)),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t42_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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] : ( v1_xreal_0(C) & r2_hidden(C,k10_prob_1(A)) & r1_xxreal_0(k1_fdiff_1(B,C),k5_numbers) ) & ? [C] : ( v1_xreal_0(C) & r2_hidden(C,k10_prob_1(A)) & r1_xxreal_0(k5_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)))) ) ) ) ) )).
fof(t42_fdiff_4,axiom,( ! [A] : ( ( 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,k18_sin_cos,k3_taylor_1))) & ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & r1_xxreal_0(k1_funct_1(k18_sin_cos,B),k5_numbers) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k3_taylor_1),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k3_taylor_1),A),B) = k4_xcmplx_0(k1_sin_cos4(B)) ) ) ) ) ) )).
fof(t42_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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),k4_xcmplx_0(k7_xcmplx_0(1,2))))) & B = k3_valued_1(k1_numbers,k1_numbers,k1_numbers,C,k26_valued_1(k1_numbers,k1_numbers,k18_sin_cos,2)) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => ( k1_funct_1(C,D) = 1 & ~ r1_xxreal_0(k1_funct_1(B,D),k5_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),k4_xcmplx_0(k7_xcmplx_0(1,2))),A) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_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),k4_xcmplx_0(k7_xcmplx_0(1,2))),A),D) = k7_xcmplx_0(k1_funct_1(k16_sin_cos,D),k2_xcmplx_0(1,k3_xcmplx_0(2,k1_funct_1(k18_sin_cos,D)))) ) ) ) ) ) ) ) )).
fof(t42_fdiff_7,axiom,( ! [A] : ( ( 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,k18_sin_cos),k22_sin_cos))) => ( r2_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),k22_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),k22_sin_cos),A),B) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k16_sin_cos,B)),k1_funct_1(k22_sin_cos,B))) ) ) ) ) ) )).
fof(t42_fdiff_9,axiom,( ! [A] : ( ( 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,k26_sin_cos,k1_fdiff_9))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_fdiff_9),A),B) = k2_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,B))),k1_funct_1(k18_sin_cos,B)),k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k26_sin_cos,B),k1_funct_1(k16_sin_cos,B)),k1_square_1(k1_funct_1(k18_sin_cos,B)))) ) ) ) ) ) )).
fof(t42_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ( r1_nat_d(B,A) => r1_nat_d(k1_pre_ff(B),k1_pre_ff(A)) ) ) ) )).
fof(t42_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_finseq_1(B,A) => ! [C] : ( m1_finseq_1(C,A) => ? [D] : ( m1_finseq_1(D,A) & r1_filerec1(A,D,B,C) ) ) ) ) )).
fof(t42_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k4_filter_0(A,B,C) = k3_lattices(A,k7_lattices(A,B),C) ) ) ) )).
fof(t42_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t42_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t42_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : k1_funct_1(k7_finseq_1(A,k9_finseq_1(B)),k1_nat_1(k3_finseq_1(A),1)) = B ) )).
fof(t42_finseq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t42_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( k5_numbers != A => k14_finseq_1(k1_tarski(A)) = k9_finseq_1(A) ) ) )).
fof(t42_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : ( 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) ) ) ) )).
fof(t42_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t42_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( B != k1_xboole_0 => r2_hidden(k7_partfun1(A,B,1),k10_xtuple_0(B)) ) ) ) )).
fof(t42_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( 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)) ) ) )).
fof(t42_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => 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)) ) ) ) ) )).
fof(t42_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(t42_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( v7_ordinal1(C) => r1_tarski(k7_flang_1(A,B,C),k8_flang_1(A,B)) ) ) )).
fof(t42_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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))) ) ) ) ) )).
fof(t42_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( 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)) ) ) )).
fof(t42_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_frechet(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( 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] : ( v1_relat_1(D) & v1_funct_1(D) & k9_xtuple_0(D) = k4_ordinal1 & k10_xtuple_0(D) = C & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(E,F) => r1_tarski(k1_funct_1(D,F),k1_funct_1(D,E)) ) ) ) ) ) ) ) ) )).
fof(t42_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( ( ~ v2_struct_0(D) & l2_fsm_1(D,A,B) ) => ! [E] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t42_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t42_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) => k2_funct_1(k2_funct_1(A)) = A ) ) )).
fof(t42_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) ) )).
fof(t42_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ( r2_hidden(A,C) => r2_hidden(k1_funct_1(k6_funct_3(B,C),A),B) ) ) )).
fof(t42_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( r2_hidden(k4_tarski(B,C),k9_xtuple_0(A)) <=> r2_hidden(k4_tarski(C,B),k9_xtuple_0(k2_funct_4(A))) ) ) )).
fof(t42_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) ) ) )).
fof(t42_funct_6,axiom,( ! [A] : k7_funct_6(k1_xboole_0,A) = k1_xboole_0 )).
fof(t42_funct_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t42_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t42_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ! [F] : ( m1_functor3(F,A,B,C,D) => ! [G] : ( m1_functor3(G,A,B,D,E) => ! [H] : ( m1_functor3(H,A,B,C,E) => ( ( r8_pboole(u1_struct_0(A),H,k5_functor2(A,B,C,D,E,F,G)) & r1_functor3(A,B,C,D) & r1_functor3(A,B,D,E) ) => r8_pboole(u1_struct_0(A),k8_functor3(A,B,C,E,H),k5_functor2(A,B,E,D,C,k8_functor3(A,B,D,E,G),k8_functor3(A,B,C,D,F))) ) ) ) ) ) ) ) ) ) )).
fof(t42_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D),k2_fuzzy_1(A,D,C)),k2_fuzzy_1(A,C,B)),k2_fuzzy_1(A,k2_fuzzy_1(A,k1_fuzzy_1(A,B,D),k1_fuzzy_1(A,D,C)),k1_fuzzy_1(A,C,B))) ) ) ) ) )).
fof(t42_fuzzy_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( k2_xcmplx_0(C,k4_xxreal_0(A,B)) = k4_xxreal_0(k2_xcmplx_0(C,A),k2_xcmplx_0(C,B)) & k2_xcmplx_0(C,k3_xxreal_0(A,B)) = k3_xxreal_0(k2_xcmplx_0(C,A),k2_xcmplx_0(C,B)) ) ) ) ) )).
fof(t42_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_fvaluat1(C,A) => ( v3_fvaluat1(A) => ( ~ ( ~ v3_xxreal_0(k3_funct_2(u1_struct_0(A),k6_numbers,C,B)) & v3_xxreal_0(k3_funct_2(u1_struct_0(A),k6_numbers,k5_fvaluat1(A,C),B)) ) & ~ ( ~ v3_xxreal_0(k3_funct_2(u1_struct_0(A),k6_numbers,k5_fvaluat1(A,C),B)) & v3_xxreal_0(k3_funct_2(u1_struct_0(A),k6_numbers,C,B)) ) ) ) ) ) ) )).
fof(t42_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t42_gate_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ! [Q] : ! [R] : ! [S] : ! [T] : ! [U] : ! [V] : ! [W] : ! [X] : ! [Y] : ! [Z] : ! [A1] : ! [B1] : ! [C1] : ! [D1] : ! [E1] : ! [F1] : ! [G1] : ! [H1] : ! [I1] : ! [J1] : ! [K1] : ! [L1] : ! [M1] : ! [N1] : ! [O1] : ~ ( ~ ( ~ v1_xboole_0(K) & v1_xboole_0(k7_gate_1(B,C)) ) & ~ ( ~ v1_xboole_0(k7_gate_1(B,C)) & v1_xboole_0(K) ) & ~ ( ~ v1_xboole_0(L) & v1_xboole_0(k6_gate_1(B,C)) ) & ~ ( ~ v1_xboole_0(k6_gate_1(B,C)) & v1_xboole_0(L) ) & ~ ( ~ v1_xboole_0(M) & v1_xboole_0(k34_gate_1(B,C)) ) & ~ ( ~ v1_xboole_0(k34_gate_1(B,C)) & v1_xboole_0(M) ) & ~ ( ~ v1_xboole_0(N) & v1_xboole_0(k7_gate_1(D,E)) ) & ~ ( ~ v1_xboole_0(k7_gate_1(D,E)) & v1_xboole_0(N) ) & ~ ( ~ v1_xboole_0(O) & v1_xboole_0(k6_gate_1(D,E)) ) & ~ ( ~ v1_xboole_0(k6_gate_1(D,E)) & v1_xboole_0(O) ) & ~ ( ~ v1_xboole_0(P) & v1_xboole_0(k34_gate_1(D,E)) ) & ~ ( ~ v1_xboole_0(k34_gate_1(D,E)) & v1_xboole_0(P) ) & ~ ( ~ v1_xboole_0(Q) & v1_xboole_0(k7_gate_1(F,G)) ) & ~ ( ~ v1_xboole_0(k7_gate_1(F,G)) & v1_xboole_0(Q) ) & ~ ( ~ v1_xboole_0(R) & v1_xboole_0(k6_gate_1(F,G)) ) & ~ ( ~ v1_xboole_0(k6_gate_1(F,G)) & v1_xboole_0(R) ) & ~ ( ~ v1_xboole_0(S) & v1_xboole_0(k34_gate_1(F,G)) ) & ~ ( ~ v1_xboole_0(k34_gate_1(F,G)) & v1_xboole_0(S) ) & ~ ( ~ v1_xboole_0(T) & v1_xboole_0(k7_gate_1(H,I)) ) & ~ ( ~ v1_xboole_0(k7_gate_1(H,I)) & v1_xboole_0(T) ) & ~ ( ~ v1_xboole_0(U) & v1_xboole_0(k6_gate_1(H,I)) ) & ~ ( ~ v1_xboole_0(k6_gate_1(H,I)) & v1_xboole_0(U) ) & ~ ( ~ v1_xboole_0(V) & v1_xboole_0(k34_gate_1(H,I)) ) & ~ ( ~ v1_xboole_0(k34_gate_1(H,I)) & v1_xboole_0(V) ) & ~ ( ~ v1_xboole_0(W) & v1_xboole_0(k1_gate_1(A)) ) & ~ ( ~ v1_xboole_0(k1_gate_1(A)) & v1_xboole_0(W) ) & ~ ( ~ v1_xboole_0(X) & v1_xboole_0(k1_gate_1(W)) ) & ~ ( ~ v1_xboole_0(k1_gate_1(W)) & v1_xboole_0(X) ) & ~ ( ~ v1_xboole_0(L1) & v1_xboole_0(k4_gate_1(X,M)) ) & ~ ( ~ v1_xboole_0(k4_gate_1(X,M)) & v1_xboole_0(L1) ) & ~ ( ~ v1_xboole_0(Y) & v1_xboole_0(k2_gate_1(W,L)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(W,L)) & v1_xboole_0(Y) ) & ~ ( ~ v1_xboole_0(Z) & v1_xboole_0(k7_gate_1(Y,K)) ) & ~ ( ~ v1_xboole_0(k7_gate_1(Y,K)) & v1_xboole_0(Z) ) & ~ ( ~ v1_xboole_0(M1) & v1_xboole_0(k4_gate_1(Z,P)) ) & ~ ( ~ v1_xboole_0(k4_gate_1(Z,P)) & v1_xboole_0(M1) ) & ~ ( ~ v1_xboole_0(A1) & v1_xboole_0(k2_gate_1(K,O)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(K,O)) & v1_xboole_0(A1) ) & ~ ( ~ v1_xboole_0(B1) & v1_xboole_0(k8_gate_1(O,L,W)) ) & ~ ( ~ v1_xboole_0(k8_gate_1(O,L,W)) & v1_xboole_0(B1) ) & ~ ( ~ v1_xboole_0(C1) & v1_xboole_0(k13_gate_1(A1,B1,N)) ) & ~ ( ~ v1_xboole_0(k13_gate_1(A1,B1,N)) & v1_xboole_0(C1) ) & ~ ( ~ v1_xboole_0(N1) & v1_xboole_0(k4_gate_1(C1,S)) ) & ~ ( ~ v1_xboole_0(k4_gate_1(C1,S)) & v1_xboole_0(N1) ) & ~ ( ~ v1_xboole_0(D1) & v1_xboole_0(k2_gate_1(N,R)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(N,R)) & v1_xboole_0(D1) ) & ~ ( ~ v1_xboole_0(E1) & v1_xboole_0(k8_gate_1(K,R,O)) ) & ~ ( ~ v1_xboole_0(k8_gate_1(K,R,O)) & v1_xboole_0(E1) ) & ~ ( ~ v1_xboole_0(F1) & v1_xboole_0(k14_gate_1(R,O,L,W)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(R,O,L,W)) & v1_xboole_0(F1) ) & ~ ( ~ v1_xboole_0(G1) & v1_xboole_0(k17_gate_1(D1,E1,F1,Q)) ) & ~ ( ~ v1_xboole_0(k17_gate_1(D1,E1,F1,Q)) & v1_xboole_0(G1) ) & ~ ( ~ v1_xboole_0(O1) & v1_xboole_0(k4_gate_1(G1,V)) ) & ~ ( ~ v1_xboole_0(k4_gate_1(G1,V)) & v1_xboole_0(O1) ) & ~ ( ~ v1_xboole_0(H1) & v1_xboole_0(k2_gate_1(Q,U)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(Q,U)) & v1_xboole_0(H1) ) & ~ ( ~ v1_xboole_0(I1) & v1_xboole_0(k8_gate_1(N,U,R)) ) & ~ ( ~ v1_xboole_0(k8_gate_1(N,U,R)) & v1_xboole_0(I1) ) & ~ ( ~ v1_xboole_0(J1) & v1_xboole_0(k14_gate_1(K,U,R,O)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(K,U,R,O)) & v1_xboole_0(J1) ) & ~ ( ~ v1_xboole_0(K1) & v1_xboole_0(k18_gate_1(U,R,O,L,W)) ) & ~ ( ~ v1_xboole_0(k18_gate_1(U,R,O,L,W)) & v1_xboole_0(K1) ) & ~ ( ~ v1_xboole_0(J) & v1_xboole_0(k21_gate_1(T,H1,I1,J1,K1)) ) & ~ ( ~ v1_xboole_0(k21_gate_1(T,H1,I1,J1,K1)) & v1_xboole_0(J) ) & ~ ( ~ ( ~ v1_xboole_0(L1) & v1_xboole_0(k10_gate_1(B,C,A)) ) & ~ ( ~ v1_xboole_0(k10_gate_1(B,C,A)) & v1_xboole_0(L1) ) & ~ ( ~ v1_xboole_0(M1) & v1_xboole_0(k35_gate_1(B,C,D,E,A)) ) & ~ ( ~ v1_xboole_0(k35_gate_1(B,C,D,E,A)) & v1_xboole_0(M1) ) & ~ ( ~ v1_xboole_0(N1) & v1_xboole_0(k37_gate_1(B,C,D,E,F,G,A)) ) & ~ ( ~ v1_xboole_0(k37_gate_1(B,C,D,E,F,G,A)) & v1_xboole_0(N1) ) & ~ ( ~ v1_xboole_0(O1) & v1_xboole_0(k39_gate_1(B,C,D,E,F,G,H,I,A)) ) & ~ ( ~ v1_xboole_0(k39_gate_1(B,C,D,E,F,G,H,I,A)) & v1_xboole_0(O1) ) & ~ ( ~ v1_xboole_0(J) & v1_xboole_0(k40_gate_1(B,C,D,E,F,G,H,I,A)) ) & ~ ( ~ v1_xboole_0(k40_gate_1(B,C,D,E,F,G,H,I,A)) & v1_xboole_0(J) ) ) ) )).
fof(t42_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m2_gcd_1(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r5_gcd_1(A,B,D,E) => r5_gcd_1(A,C,D,E) ) ) ) ) ) ) )).
fof(t42_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( ( ~ v1_xboole_0(F) & v1_relat_1(F) & v2_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ! [G] : ( m1_genealg1(G,F) => ! [H] : ( m1_genealg1(H,F) => ( k11_genealg1(F,G,H,k5_numbers,k5_numbers,C,D,E) = k9_genealg1(F,G,H,C,D,E) & k11_genealg1(F,G,H,k5_numbers,B,k5_numbers,D,E) = k9_genealg1(F,G,H,B,D,E) & k11_genealg1(F,G,H,k5_numbers,B,C,k5_numbers,E) = k9_genealg1(F,G,H,B,C,E) & k11_genealg1(F,G,H,k5_numbers,B,C,D,k5_numbers) = k9_genealg1(F,G,H,B,C,D) & k11_genealg1(F,G,H,A,k5_numbers,k5_numbers,D,E) = k9_genealg1(F,G,H,A,D,E) & k11_genealg1(F,G,H,A,k5_numbers,C,k5_numbers,E) = k9_genealg1(F,G,H,A,C,E) & k11_genealg1(F,G,H,A,k5_numbers,C,D,k5_numbers) = k9_genealg1(F,G,H,A,C,D) & k11_genealg1(F,G,H,A,B,k5_numbers,k5_numbers,E) = k9_genealg1(F,G,H,A,B,E) & k11_genealg1(F,G,H,A,B,k5_numbers,D,k5_numbers) = k9_genealg1(F,G,H,A,B,D) & k11_genealg1(F,G,H,A,B,C,k5_numbers,k5_numbers) = k9_genealg1(F,G,H,A,B,C) ) ) ) ) ) ) ) ) ) )).
fof(t42_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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,D),k1_domain_1(u1_struct_0(A),u1_struct_0(A),C,E)),k5_geomtrap(A,F,G)) <=> r2_geomtrap(A,F,G,B,D,C,E) ) ) ) ) ) ) ) ) )).
fof(t42_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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))) )).
fof(t42_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t42_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ! [E] : ( ( ~ v1_abian(E) & m1_subset_1(E,k4_ordinal1) ) => ( ( 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(k4_ordinal1,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)) ) ) ) ) ) ) )).
fof(t42_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t42_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_003(A) & v3_glib_003(A) ) => ! [B] : ! [C] : k6_glib_003(A) = k6_glib_003(k13_glib_003(A,B,C)) ) )).
fof(t42_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ 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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,2))) = k2_topreal1(2,D,C) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,1))) = k2_topreal1(2,D,k1_nat_1(C,1)) ) => ( r1_xxreal_0(k1_matrix_0(k2_goboard2(D)),k1_nat_1(B,1)) | r1_xxreal_0(k3_finseq_1(D),k1_nat_1(C,1)) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,2)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,B) ) ) ) ) ) ) ) )).
fof(t42_gobrd14,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t42_graph_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v2_struct_0(C) & l1_graph_1(C) ) => ! [D] : ( m2_finseq_1(D,u1_struct_0(C)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(C)) => ! [F] : ( m2_graph_1(F,C) => ! [G] : ( 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,k1_nat_1(B,1)) ) => r1_graph_2(C,E,G) ) ) ) ) ) ) ) ) )).
fof(t42_graph_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t42_graph_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( 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 ) ) ) ) ) ) )).
fof(t42_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => r2_graphsp(C,C,A,B) ) ) ) )).
fof(t42_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ~ r1_xxreal_0(k5_card_1(k3_polynom1(k15_pre_poly(A),C,D)),E) => k4_xboole_0(k3_polynom1(k15_pre_poly(A),C,k6_groeb_3(A,B,C,D,E)),k3_polynom1(k15_pre_poly(A),C,k6_groeb_3(A,B,C,D,k1_nat_1(E,1)))) = k1_tarski(k3_termord(A,B,C,k6_groeb_3(A,B,C,D,E))) ) ) ) ) ) ) )).
fof(t42_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( k6_group_1(A,B) = 1 => B = k1_group_1(A) ) ) ) )).
fof(t42_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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) ) ) ) )).
fof(t42_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => m1_subset_1(C,u1_struct_0(A)) ) ) ) )).
fof(t42_group_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( r2_hidden(A,k5_group_3(B,D,C)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k2_group_3(B,C,E) & r2_hidden(E,D) ) ) ) ) ) )).
fof(t42_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r1_struct_0(k6_group_4(A),B) <=> ~ v1_group_4(B,A) ) ) ) )).
fof(t42_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_group_5(A,C,B,B) = k2_group_3(A,k6_algstr_0(A,k2_group_5(A,C,k2_group_1(A,B)),k2_group_5(A,C,B)),B) ) ) ) )).
fof(t42_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ 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 ) ) )).
fof(t42_group_9,axiom,( ! [A] : ! [B] : ( ( ~ 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 ) ) )).
fof(t42_hausdorf,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [D] : ( ( ~ 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),k2_xcmplx_0(k3_hausdorf(A,B,C),k3_hausdorf(A,C,D))) ) ) ) ) ) )).
fof(t42_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => k3_helly(A,B,C,D) = k3_helly(A,C,B,D) ) ) ) ) )).
fof(t42_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ! [F] : ( m1_subset_1(F,u1_struct_0(k1_complfld)) => ( k9_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,k5_numbers),F),C)),k5_algstr_0(A,B,k4_vectsp_1(k1_complfld,A,k8_group_1(k1_complfld,k1_hahnban1(E,k5_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,k5_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,k5_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(k1_square_1(E),k5_numbers),k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(k1_complfld),D,C,C))) ) ) ) ) ) ) ) )).
fof(t42_hfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,k1_numbers) => ~ ( ~ r1_xxreal_0(A,B) & ~ r1_xxreal_0(C,k5_numbers) & ~ ( k9_nat_1(k1_numbers,k1_taylor_2(k1_taylor_1(A),k2_rcomp_1(k1_real_1(C),C),D),B) = k5_numbers & k9_nat_1(k1_numbers,k1_taylor_2(k1_taylor_1(A),k2_rcomp_1(k1_real_1(C),C),D),A) = k1_newton(D,A) ) ) ) ) ) ) )).
fof(t42_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(t42_hilbert3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ( ( v2_hilbert3(A) & v2_hilbert3(k3_hilbert1(A,B)) ) => v2_hilbert3(B) ) ) ) )).
fof(t42_hurwitz,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(A,k1_complfld) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => k2_hurwitz(k1_complfld,k7_hurwitz(A)) = k2_hurwitz(k1_complfld,A) ) )).
fof(t42_idea_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( 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)) ) ) ) ) ) ) )).
fof(t42_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m2_ideal_1(C,A,B) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => m2_ideal_1(k2_partfun1(k4_ordinal1,u1_struct_0(A),C,k2_finseq_1(D)),A,B) ) ) ) ) )).
fof(t42_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u4_incsp_1(A)) => ? [C] : ( m1_subset_1(C,u1_incsp_1(A)) & ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & ? [E] : ( m1_subset_1(E,u1_incsp_1(A)) & ? [F] : ( 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) ) ) ) ) ) ) )).
fof(t42_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => k1_int_1(k3_int_1(A)) = k5_numbers ) )).
fof(t42_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ~ ( A != k5_numbers & B != k5_numbers & r1_int_1(k3_int_2(A,B),k6_xcmplx_0(D,C)) & ! [E] : ( v1_int_1(E) => ~ ( ! [F] : ( v1_int_1(F) => ( ( k5_int_1(k6_xcmplx_0(F,C),A) = k5_numbers & k5_int_1(k6_xcmplx_0(F,D),B) = k5_numbers ) => r2_int_1(F,k2_xcmplx_0(C,k3_xcmplx_0(A,E)),k2_int_2(A,B)) ) ) & k5_int_1(k6_xcmplx_0(k3_xcmplx_0(k4_int_1(A,k3_int_2(A,B)),E),k4_int_1(k6_xcmplx_0(D,C),k3_int_2(A,B))),k4_int_1(B,k3_int_2(A,B))) = k5_numbers ) ) ) ) ) ) ) )).
fof(t42_int_5,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t42_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ( ( r1_xxreal_0(k5_numbers,C) & ! [E] : ( 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(k5_numbers,D) & ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t42_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(A,B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k2_xcmplx_0(1,k1_funct_1(k18_sin_cos,D)) != k5_numbers & k6_xcmplx_0(1,k1_funct_1(k18_sin_cos,D)) != k5_numbers & k1_funct_1(C,D) = k7_xcmplx_0(1,k2_xcmplx_0(1,k1_funct_1(k18_sin_cos,D))) ) ) ) & k9_xtuple_0(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k27_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) = k6_xcmplx_0(k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k27_sin_cos),k2_fdiff_9),k2_seq_4(A)),k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k27_sin_cos),k2_fdiff_9),k3_seq_4(A))) ) ) ) ) )).
fof(t42_integr12,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,D) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => ( k1_funct_1(C,E) = k7_xcmplx_0(k1_funct_1(k16_sin_cos,E),k3_prepower(k1_funct_1(k18_sin_cos,E),k1_nat_1(A,1))) & k1_funct_1(k18_sin_cos,E) != k5_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,k18_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,k5_numbers) | k2_integra5(B,C) = k6_xcmplx_0(k1_funct_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,k18_sin_cos),k1_taylor_1(A)),k7_xcmplx_0(1,A)),k2_seq_4(B)),k1_funct_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,k18_sin_cos),k1_taylor_1(A)),k7_xcmplx_0(1,A)),k3_seq_4(B))) ) ) ) ) ) ) )).
fof(t42_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,D) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => k1_funct_1(C,E) = 1 ) ) & r2_relset_1(k1_numbers,k1_numbers,B,k3_rfunct_1(k1_numbers,k1_numbers,k1_sin_cos9,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,C,k1_taylor_1(2)))) & r1_tarski(D,k2_rcomp_1(k4_xcmplx_0(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,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_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)),k7_xcmplx_0(1,2)),k2_seq_4(A)),k1_funct_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)),k7_xcmplx_0(1,2)),k3_seq_4(A))) ) ) ) ) ) )).
fof(t42_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k7_xcmplx_0(k7_xcmplx_0(k1_funct_1(k18_sin_cos,k1_funct_1(k26_sin_cos,D)),k1_square_1(k1_funct_1(k18_sin_cos,D))),k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k26_sin_cos,D)))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_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) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k2_fdiff_9)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k2_fdiff_9)),k3_seq_4(A))) ) ) ) ) )).
fof(t42_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t42_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [C] : ( m1_integra1(C,A) => ( r1_integra1(B,C) => k13_integra1(A,B,C,k3_finseq_1(B)) = k3_finseq_1(C) ) ) ) ) )).
fof(t42_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k7_xcmplx_0(k3_xcmplx_0(k28_sin_cos,3),2)) => k2_integra5(A,k18_sin_cos) = k4_xcmplx_0(1) ) ) )).
fof(t42_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( C = k1_rcomp_1(k6_xcmplx_0(A,k3_xcmplx_0(k3_xcmplx_0(2,B),k28_sin_cos)),k2_xcmplx_0(A,k3_xcmplx_0(k3_xcmplx_0(2,B),k28_sin_cos))) => r1_integra9(C,k16_sin_cos,k18_sin_cos) ) ) ) ) )).
fof(t42_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_interva1(C,A) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(A)) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t42_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => r2_hidden(k3_intpro_1(k3_intpro_1(B,C),k3_intpro_1(k4_intpro_1(B,A),C)),k8_intpro_1) ) ) ) )).
fof(t42_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,B,A) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t42_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t42_jgraph_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(A,k4_finseq_1(B)) => ( k1_funct_1(k1_goboard1(B),A) = k17_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),B,A)) & k1_funct_1(k2_goboard1(B),A) = k18_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),B,A)) ) ) ) ) )).
fof(t42_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r1_xxreal_0(A,k7_xcmplx_0(k18_euclid(B),k12_euclid(B))) => ( r1_xxreal_0(1,A) | r1_xxreal_0(k5_numbers,k17_euclid(B)) | ! [C] : ( 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(k5_numbers,k17_euclid(C)) & r1_xxreal_0(k5_numbers,k18_euclid(C)) ) ) ) ) ) ) ) )).
fof(t42_jgraph_5,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( ( k1_funct_1(B,E) = C & k1_funct_1(B,F) = D & r2_hidden(E,k1_rcomp_1(k5_numbers,1)) & r2_hidden(F,k1_rcomp_1(k5_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,k5_numbers) = k22_pscomp_1(A) & k1_funct_1(B,1) = k18_pscomp_1(A) ) ) ) ) )).
fof(t42_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t42_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t42_jordan,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ~ ( r1_topreal1(k15_euclid(A),B,C,D) & ! [E] : ( m1_borsuk_2(E,k15_euclid(A),B,C) => ! [F] : ( ( 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 ) ) ) ) ) ) ) ) )).
fof(t42_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( ~ r1_xxreal_0(C,1) & r1_xxreal_0(C,D) & ~ r1_xxreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,1))),D) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1)))),k8_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),D,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1)))),k9_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1)))),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),D,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))))),k9_jordan6(B)) ) ) ) ) ) )).
fof(t42_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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,D))) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(k1_jordan8(E,C))) & r1_xxreal_0(C,D) ) => r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,C),1,B)),k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,D),1,A))) ) ) ) ) ) ) )).
fof(t42_jordan1g,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(C,1) & r1_xxreal_0(C,k3_finseq_1(k1_jordan8(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,1),k10_xtuple_0(k1_jordan1e(B,A))) ) ) ) ) )).
fof(t42_jordan1h,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t42_jordan1k,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) & ? [E] : ( 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) ) ) ) ) ) )).
fof(t42_jordan23,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(t42_jordan2c,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t42_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t42_jordan4,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t42_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(A)) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k1_matrix_0(k2_goboard2(A))) & E = a_2_1_jordan5d(A,B) & k18_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),A,D)) = k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,B)) & C = k4_seq_4(E) ) => r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,B)),k17_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),A,D))) ) ) ) ) ) ) )).
fof(t42_jordan6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ~ ( r1_topreal1(k15_euclid(A),C,D,B) & ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ~ ( r2_hidden(E,B) & E != C & E != D ) ) ) ) ) ) ) )).
fof(t42_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t42_kurato_1,axiom,( 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))) )).
fof(t42_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k5_finsub_1(C)) => ! [E] : ( ( 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] : ( 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 ) ) ) ) ) ) ) )).
fof(t42_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t42_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k5_finsub_1(u1_struct_0(A))) => ~ ( r1_tarski(C,k4_lattice4(A,B)) & ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t42_lattice5,axiom,( ! [A] : ( ( 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] : ( m2_lattice5(B,u1_struct_0(A),A,k16_lattice5(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( m1_subset_1(E,C) => ! [F] : ( m1_subset_1(F,C) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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] : ( m1_subset_1(I,C) => ! [J] : ( m1_subset_1(J,C) => ! [K] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t42_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(k15_glib_000(A),B) & ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ~ ( C = k10_lexbfs(A,k13_lexbfs(A,k16_lexbfs(A),B)) & ! [D] : ( ( 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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),k13_lexbfs(A,k16_lexbfs(A),B)))) | k17_lexbfs(k6_glib_000(A),k4_ordinal1,k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),k13_lexbfs(A,k16_lexbfs(A),k1_nat_1(B,1))),D) = k1_finsub_1(k1_zfmisc_1(k4_ordinal1),k17_lexbfs(k6_glib_000(A),k4_ordinal1,k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),k13_lexbfs(A,k16_lexbfs(A),B)),D),k6_domain_1(k4_ordinal1,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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),k13_lexbfs(A,k16_lexbfs(A),B)))) ) => k17_lexbfs(k6_glib_000(A),k4_ordinal1,k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),k13_lexbfs(A,k16_lexbfs(A),k1_nat_1(B,1))),D) = k17_lexbfs(k6_glib_000(A),k4_ordinal1,k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),k13_lexbfs(A,k16_lexbfs(A),B)),D) ) ) ) ) ) ) ) )).
fof(t42_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_limfunc1(A) & ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) => v1_limfunc1(B) ) ) ) )).
fof(t42_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_limfunc3(C,A) & r1_limfunc3(D,A) & k1_limfunc3(C,A) = k1_limfunc3(D,A) ) => ( ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & r1_tarski(k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,E),A),k2_rcomp_1(A,k2_xcmplx_0(A,E))),k3_xboole_0(k3_xboole_0(k9_xtuple_0(C),k9_xtuple_0(D)),k9_xtuple_0(B))) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,E),A),k2_rcomp_1(A,k2_xcmplx_0(A,E)))) => ( r1_xxreal_0(k1_funct_1(C,F),k1_funct_1(B,F)) & r1_xxreal_0(k1_funct_1(B,F),k1_funct_1(D,F)) ) ) ) ) ) | ( r1_limfunc3(B,A) & k1_limfunc3(B,A) = k1_limfunc3(C,A) ) ) ) ) ) ) ) )).
fof(t42_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,D),A),k2_rcomp_1(A,k2_xcmplx_0(A,D))))) & r1_xxreal_0(k1_funct_1(B,E),k1_limfunc3(B,A)) ) ) ) ) | r3_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t42_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k16_lopban_1(A,B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) ) )).
fof(t42_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(k22_lpspacc1(A,B,C))) => ( ( r2_hidden(D,F) & r2_hidden(E,F) ) => ( r1_lpspacc1(A,B,C,D,E) & k1_mesfun6c(A,B,C,D) = k1_mesfun6c(A,B,C,E) & k1_mesfunc6(A,B,C,k56_valued_1(A,k2_numbers,D)) = k1_mesfunc6(A,B,C,k56_valued_1(A,k2_numbers,E)) ) ) ) ) ) ) ) ) )).
fof(t42_lpspace1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,C,k6_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,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t42_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( v2_xxreal_0(F) & v1_xreal_0(F) ) => ( r1_lpspace1(A,B,C,D,E) => k5_lpspace2(A,B,C,D,F) = k5_lpspace2(A,B,C,E,F) ) ) ) ) ) ) ) )).
fof(t42_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_hilbert1)) => ( ( r2_hidden(A,k13_ltlaxio1) | r2_hidden(A,B) ) => r8_ltlaxio1(B,A) ) ) ) )).
fof(t42_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( m1_subset_1(D,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(k1_ltlaxio1(k4_ltlaxio1(A,D)),k1_ltlaxio1(k4_ltlaxio1(k4_ltlaxio1(A,B),k4_ltlaxio1(C,D))))) ) ) ) ) )).
fof(t42_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t42_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k4_mathmorp(A,B,B) = B ) ) )).
fof(t42_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,B,B) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( r1_xxreal_0(k5_numbers,A) & v4_matrix10(C) ) => v4_matrix10(k6_matrix10(B,A,C)) ) ) ) ) )).
fof(t42_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_matrix_2(C,k3_matrix_2(k1_nat_1(A,2))) => ! [D] : ( m1_matrix_2(D,k3_matrix_2(k1_nat_1(A,2))) => ( r2_funct_2(k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),D,k2_funct_2(k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),C)) => k2_matrix11(A,B,C) = k2_matrix11(A,B,D) ) ) ) ) ) )).
fof(t42_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(A)) ) => ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(C,k4_ordinal1)) => ! [F] : ( m2_finseq_2(F,k4_ordinal1,k4_finseq_2(B,k4_ordinal1)) => ( ( E = k1_finseq_2(k3_finseq_1(D)) & F = k1_finseq_2(k1_matrix_0(D)) ) => k1_matrix13(A,D,C,B,E,F) = D ) ) ) ) ) ) ) )).
fof(t42_matrix14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,A,B,C) & m2_finseq_1(F,k3_finseq_2(A)) ) => ( v1_matrix_0(k2_finseq_7(k3_finseq_2(A),F,D,E)) & v2_matrix_0(k2_finseq_7(k3_finseq_2(A),F,D,E),A,B,C) & m2_finseq_1(k2_finseq_7(k3_finseq_2(A),F,D,E),k3_finseq_2(A)) ) ) ) ) ) ) ) )).
fof(t42_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ( r1_tarski(k10_xtuple_0(E),k4_finseq_1(C)) => ( r1_xxreal_0(A,k5_numbers) | 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_0(C))),E,k5_matrix13(k2_finseq_1(k1_matrix_0(C)))),k1_matrix13(u1_struct_0(B),D,A,k5_card_1(k2_finseq_1(k1_matrix_0(D))),E,k5_matrix13(k2_finseq_1(k1_matrix_0(D)))))) ) ) ) ) ) ) ) )).
fof(t42_matrix16,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t42_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(D,k4_finseq_1(B)) & r2_hidden(C,k2_finseq_1(k1_matrix_0(B))) ) => k1_funct_1(k8_matrix_0(A,B,C),D) = k1_funct_1(k7_matrix_0(A,B,D),C) ) ) ) ) ) )).
fof(t42_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(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))) ) ) ) ) )).
fof(t42_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_6(C,A,B) & k4_matrix_3(B,k4_matrix_0(u1_struct_0(B),C),C) = k3_matrix_1(B,A) ) <=> v4_matrix_6(C,A,B) ) ) ) ) )).
fof(t42_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_6(D,A,B) & r1_matrix_8(A,B,C,D) ) => v1_matrix_6(C,A,B) ) ) ) ) ) )).
fof(t42_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( 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) ) ) ) ) )).
fof(t42_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( 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_0(D) = k1_matrix_0(k17_matrix_0(u1_struct_0(B),A,D)) ) => k17_matrix_0(u1_struct_0(B),k2_xcmplx_0(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),k17_matrix_0(u1_struct_0(B),A,D)))) ) ) ) ) ) ) )).
fof(t42_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => k3_matrixr1(A,k8_matrixr1(k3_finseq_1(A),k1_matrix_0(A))) = A ) )).
fof(t42_matrixr2,axiom,( ! [A] : ( ( v1_matrix_0(A) & v2_matrix_0(A,k1_numbers,k5_numbers,k5_numbers) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => k3_matrixr2(k5_numbers,A) = 1 ) )).
fof(t42_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( m1_matrlin(F,A,B) => ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(t42_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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) = k5_numbers ) ) ) )).
fof(t42_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r1_tarski(C,B) & v5_matroid0(C,A) ) ) => v3_pre_topc(B,A) ) ) ) )).
fof(t42_matrprob,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( k1_matrix_0(B) = k3_finseq_1(C) => ( A = k6_matrixr1(B,C) <=> ( k3_finseq_1(A) = k3_finseq_1(B) & k1_matrix_0(A) = k1_matrix_0(C) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k2_finseq_1(k3_finseq_1(A))) => k7_matrix_0(k1_numbers,A,D) = k12_matrixr1(C,k7_matrix_0(k1_numbers,B,D)) ) ) ) ) ) ) ) ) )).
fof(t42_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,u1_struct_0(k2_vectsp_1),A,A) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( 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) ) ) ) )).
fof(t42_mcart_1,axiom,( ! [A] : ! [B] : ( k4_zfmisc_1(A,A,A,A) = k4_zfmisc_1(B,B,B,B) => A = B ) )).
fof(t42_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v3_xxreal_2(A) <=> v4_xxreal_2(k3_measure6(A)) ) ) )).
fof(t42_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( 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))) ) ) ) )).
fof(t42_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => 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))) ) ) ) )).
fof(t42_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ~ ( ? [F] : ( 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] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t42_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( 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] : ( 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)))) ) ) ) ) ) ) ) ) )).
fof(t42_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( m1_subset_1(D,B) => ( r1_mesfun7c(A,B,C) => r1_mesfun7c(A,B,k2_partfun1(A,k2_numbers,C,D)) ) ) ) ) ) )).
fof(t42_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( 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,k6_numbers,D,E),F) ) ) ) ) ) ) ) )).
fof(t42_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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))) ) ) )).
fof(t42_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t42_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( 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))) ) ) )).
fof(t42_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k48_modelc_1(A,B,C))) => ( ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t42_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ~ ( r3_modelc_2(A,k5_modelc_2(B,C)) & ~ r2_modelc_2(A,B) & ~ r2_modelc_2(A,C) ) ) ) ) )).
fof(t42_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_3(C,B) & v3_modelc_3(C,B) & l1_modelc_3(C,B) ) => ! [D] : ( ( v1_modelc_3(D,B) & v3_modelc_3(D,B) & l1_modelc_3(D,B) ) => ! [E] : ( ( v1_modelc_3(E,B) & v3_modelc_3(E,B) & l1_modelc_3(E,B) ) => ~ ( r6_modelc_3(B,C,D) & r6_modelc_3(B,D,E) & r2_hidden(A,u1_modelc_3(B,D)) & v7_modelc_2(A) & ~ r2_hidden(k12_modelc_2(A),u1_modelc_3(B,D)) & ~ ( r2_hidden(k11_modelc_2(A),u1_modelc_3(B,D)) & r2_hidden(A,u1_modelc_3(B,E)) ) ) ) ) ) ) ) )).
fof(t42_moebius1,axiom,( k2_uproots(k4_ordinal1,k4_moebius1(k3_moebius1(1))) = 1 )).
fof(t42_monoid_0,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_monoid_0)) <=> v1_int_1(A) ) )).
fof(t42_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( m1_subset_1(D,k3_card_3(u3_msualg_1(A,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(D,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),E)) => r2_hidden(D,k1_msafree4(u1_struct_0(A),u3_msualg_1(A,C),E)) ) ) ) ) ) ) )).
fof(t42_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( m2_pboole(D,u1_struct_0(A),C,u3_msualg_1(A,B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t42_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v2_relat_1(C) & m3_pboole(C,A,k1_mboolean(A,B)) ) => r2_pboole(A,k4_mssubfam(A,B,C),k2_mboolean(A,C)) ) ) )).
fof(t42_msualg_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_msualg_4(C,A,B,B) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,k1_funct_1(B,D)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t42_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_mycielsk(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t42_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => k1_ordinal1(A) = a_1_0_nat_1(A) ) )).
fof(t42_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ( A != k5_numbers => k22_pre_poly(k8_newton,k12_nat_3(k1_newton(B,A))) = k1_tarski(B) ) ) ) )).
fof(t42_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(A,B) => r1_xxreal_0(k7_nat_d(A,C),k7_nat_d(B,C)) ) ) ) ) )).
fof(t42_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),E,D)) ) ) ) ) ) ) ) ) )).
fof(t42_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(1))) => ! [D] : ( m1_subset_1(D,k1_numbers) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [F] : ( ( 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(k4_ordinal1,1)) & ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t42_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( A != 1 & A != k5_numbers & r1_nat_d(A,k1_nat_1(k7_newton(B),1)) & r1_xxreal_0(A,B) ) ) ) )).
fof(t42_nfcont_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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,k4_normsp_0(u1_struct_0(B),C,D)) ) ) ) ) ) )).
fof(t42_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( 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) ) ) ) ) )).
fof(t42_normform,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A)) => k9_normform(A,B) = B ) )).
fof(t42_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t42_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_oppcat_1(C,B,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k3_funct_2(u1_struct_0(k2_oppcat_1(B)),u1_struct_0(A),k7_cat_1(k2_oppcat_1(B),A,k10_oppcat_1(B,A,C)),k3_oppcat_1(B,D)) = k3_funct_2(u1_struct_0(B),u1_struct_0(A),k7_cat_1(B,A,C),D) ) ) ) ) )).
fof(t42_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_nfcont_3(D,k4_real_ns1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ( ( k1_rcomp_1(B,C) = k1_relset_1(k1_numbers,D) & v3_funct_1(k2_partfun1(k1_numbers,u1_struct_0(k4_real_ns1(A)),D,k2_rcomp_1(B,C))) ) => ( r1_xxreal_0(C,B) | ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k1_rcomp_1(B,C)) => k1_funct_1(D,E) = k1_funct_1(D,B) ) ) ) ) ) ) ) ) )).
fof(t42_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r3_orders_1(A,B) => r3_orders_1(k2_relat_1(A),B) ) ) )).
fof(t42_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m2_orders_1(B,k1_orders_1(u1_struct_0(A)),k6_partfun1(k1_orders_1(u1_struct_0(A)))) => ! [C] : ( m2_orders_2(C,A,B) => ! [D] : ( m2_orders_2(D,A,B) => ( r2_xboole_0(C,D) <=> m1_orders_2(C,A,D) ) ) ) ) ) )).
fof(t42_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r1_ordinal1(A,B) => r1_ordinal1(k11_ordinal2(C,A),k11_ordinal2(C,B)) ) ) ) ) )).
fof(t42_ordinal3,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_ordinal2(B) ) => ! [C] : ( v3_ordinal1(C) => ( ( k9_xtuple_0(A) = k9_xtuple_0(B) & v4_ordinal1(k4_ordinal2(A)) & ! [D] : ( v3_ordinal1(D) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t42_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) ) => ( r2_hidden(A,B) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t42_osafree,axiom,( ! [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) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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] : ( 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) ) ) ) ) ) )).
fof(t42_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => r1_tarski(k12_osalg_2(A,B),k14_msualg_2(A,B)) ) ) )).
fof(t42_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ( ( r2_parsp_2(A,B,F,C,G) & r2_parsp_2(A,B,F,D,H) & r2_parsp_2(A,C,G,E,I) ) => r1_parsp_1(A,D,E,H,I) ) ) ) ) ) ) ) ) ) ) )).
fof(t42_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(t42_partfun2,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t42_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) )).
fof(t42_pcs_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ! [D] : ( r2_hidden(k4_tarski(C,D),k24_pcs_0(A,B)) <=> ( r2_hidden(C,B) & r2_hidden(D,B) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,C) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_hidden(F,D) & r1_orders_2(A,E,F) ) ) ) ) ) ) ) ) )).
fof(t42_pdiff_4,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( ( 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) = k22_rvsum_1(k4_pdiff_4(C,A),k5_pdiff_4(B)) ) ) ) )).
fof(t42_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m1_rcomp_1(C,k3_funct_2(k1_euclid(3),k1_numbers,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] : ( ( v9_ordinal1(D) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,E) = k1_tarski(k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(3,3),B)) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),C) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,3,k1_pdiff_3(2,3,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,3,k1_pdiff_3(2,3,A),B))))) & k6_pdiff_5(A,B) = k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,3,k1_pdiff_3(2,3,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,3,k1_pdiff_3(2,3,A),B))))) ) ) ) ) ) ) ) ) )).
fof(t42_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( r1_xxreal_0(1,F) & r1_xxreal_0(F,A) & ~ r1_xxreal_0(D,C) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,k1_rcomp_1(C,D)) => r2_hidden(k1_funct_1(k6_pdiff_1(A,F,E),G),k1_relset_1(k1_euclid(A),B)) ) ) & ! [G] : ( 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] : ( v1_xreal_0(G) => ! [H] : ( m2_finseq_2(H,k1_numbers,k1_euclid(A)) => ~ ( r2_hidden(G,k2_rcomp_1(C,D)) & H = k1_funct_1(k6_pdiff_1(A,F,E),G) & k5_real_1(k7_partfun1(k1_numbers,B,k1_funct_1(k6_pdiff_1(A,F,E),D)),k7_partfun1(k1_numbers,B,k1_funct_1(k6_pdiff_1(A,F,E),C))) = k3_xcmplx_0(k6_xcmplx_0(D,C),k10_pdiff_1(A,F,B,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t42_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t42_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( A != k5_numbers & k1_euler_1(A) = k5_numbers ) ) )).
fof(t42_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_finseq_2(B))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k3_finseq_2(B))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k3_finseq_2(B))) => r1_tarski(k10_pnproc_1(A,B,k11_pnproc_1(A,B,C,D),k11_pnproc_1(A,B,E,F)),k11_pnproc_1(A,B,k10_pnproc_1(A,B,C,E),k10_pnproc_1(A,B,D,F))) ) ) ) ) ) )).
fof(t42_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k17_polyform(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k17_polyform(A,B))) => ( C = D <=> ! [E] : ( m1_subset_1(E,k8_polyform(A,B)) => k3_bspace(C,E) = k3_bspace(D,E) ) ) ) ) ) ) )).
fof(t42_polynom5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k4_polynom5(A,k4_struct_0(A),k4_struct_0(A)),k9_polynom3(A)) ) )).
fof(t42_polynom8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k1_algseq_1(A,B),C) => ( r1_xxreal_0(C,k5_numbers) | ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_funct_2(k4_ordinal1,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)))) ) ) ) ) ) ) )).
fof(t42_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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] : ( ( 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,k3_polynom1(k15_pre_poly(A),C,F)) => r1_termord(A,B,G,k3_termord(A,B,C,D)) ) ) ) ) ) ) ) ) ) )).
fof(t42_power,axiom,( ! [A] : ( v1_int_1(A) => ( A != k5_numbers => k2_power(k5_numbers,A) = k5_numbers ) ) )).
fof(t42_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t42_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => k3_prepower(k7_xcmplx_0(1,A),B) = k7_xcmplx_0(1,k3_prepower(A,B)) ) ) )).
fof(t42_prob_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_prob_2(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ~ r1_xxreal_0(E,D) => r1_xboole_0(k1_prob_2(A,B,k2_prob_3(A,C),D),k1_prob_2(A,B,C,E)) ) ) ) ) ) ) ) )).
fof(t42_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t42_pscomp_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t42_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t42_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_subset_1(D,k6_qc_lang1(A),k8_qc_lang1(A,C)) => ! [E] : ( ( v3_card_1(E,C) & m2_finseq_1(E,k2_qc_lang1(A)) ) => ~ r1_qc_lang2(A,B,k10_qc_lang1(A,D,E)) ) ) ) ) ) )).
fof(t42_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( ( ~ 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)) ) ) ) ) )).
fof(t42_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_qc_lang4(C,A,B) => ! [D] : ( m1_qc_lang4(D,A,B) => ( r2_qc_lang2(A,D,C) => ! [E] : ( m2_qc_lang4(E,A,B,C) => ? [F] : ( m2_qc_lang4(F,A,B,D) & r1_tarski(E,F) ) ) ) ) ) ) ) )).
fof(t42_quatern2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_quatern2)) => ( k16_quatern2(A) = k4_struct_0(k15_quatern2) => A = k4_struct_0(k15_quatern2) ) ) )).
fof(t42_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => r1_xxreal_0(k6_xcmplx_0(k28_quaterni(A),k28_quaterni(B)),k2_xcmplx_0(k28_quaterni(k25_quaterni(A,C)),k28_quaterni(k25_quaterni(C,B)))) ) ) ) )).
fof(t42_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ( k13_quaterni(k25_quaterni(A,B)) = k6_xcmplx_0(k13_quaterni(A),k13_quaterni(B)) & k14_quaterni(k25_quaterni(A,B)) = k6_xcmplx_0(k14_quaterni(A),k14_quaterni(B)) & k15_quaterni(k25_quaterni(A,B)) = k6_xcmplx_0(k15_quaterni(A),k15_quaterni(B)) & k16_quaterni(k25_quaterni(A,B)) = k6_xcmplx_0(k16_quaterni(A),k16_quaterni(B)) ) ) ) )).
fof(t42_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k19_quofield(A))) => k8_group_1(k19_quofield(A),k5_struct_0(k19_quofield(A)),B) = B ) ) )).
fof(t42_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ! [F] : ( m2_vectsp_6(F,A,C,k2_ranknull(B,C,D,E)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ( ( r2_hidden(G,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(A),k9_ranknull(A,B,C,E,D,F),G) = k3_funct_2(u1_struct_0(C),u1_struct_0(A),F,k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,G)) ) ) ) ) ) ) ) ) )).
fof(t42_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ! [B] : ( v1_rat_1(B) => ( ( B = k7_xcmplx_0(1,A) => ( r1_xxreal_0(k5_numbers,A) | ( k2_rat_1(B) = k4_xcmplx_0(k1_rat_1(A)) & k1_rat_1(B) = k4_xcmplx_0(k2_rat_1(A)) ) ) ) & ( ( k2_rat_1(B) = k4_xcmplx_0(k1_rat_1(A)) & k1_rat_1(B) = k4_xcmplx_0(k2_rat_1(A)) ) => ( ~ r1_xxreal_0(k5_numbers,A) & B = k7_xcmplx_0(1,A) ) ) ) ) ) )).
fof(t42_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r1_xxreal_0(C,D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k4_topmetr(C,D)))) => ( ( E = k4_rcomp_1(A,B) & r1_xxreal_0(C,A) ) => ( r1_xxreal_0(D,B) | k1_tops_1(k4_topmetr(C,D),E) = k2_rcomp_1(A,B) ) ) ) ) ) ) ) ) )).
fof(t42_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_rat_1(A) <=> ? [B] : ( v7_ordinal1(B) & ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => k9_nat_1(k1_numbers,k4_real_3(A),C) = k5_numbers ) ) ) ) ) )).
fof(t42_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v1_relat_1(D) => ( r2_hidden(k4_tarski(B,C),k3_relat_1(k4_relat_1(A),D)) <=> ( r2_hidden(B,A) & r2_hidden(k4_tarski(B,C),D) ) ) ) )).
fof(t42_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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)) ) ) ) )).
fof(t42_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ! [D] : ( ( ( 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) ) ) )).
fof(t42_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => ! [C] : ( 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 ) ) ) )).
fof(t42_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(C))) => ! [G] : ( ( ~ 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)) ) ) ) ) ) ) )).
fof(t42_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_valued_0(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_valued_0(D) ) => k45_valued_1(k1_rfunct_1(B,A),k1_rfunct_1(D,C)) = k1_rfunct_1(k45_valued_1(k18_valued_1(B,C),k18_valued_1(D,A)),k18_valued_1(A,C)) ) ) ) ) )).
fof(t42_rfunct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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))) ) ) ) )).
fof(t42_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t42_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_seq_2(C) => ( ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(B,k1_funct_1(C,k2_xcmplx_0(A,D))) ) <=> r1_xxreal_0(B,k1_funct_1(k3_rinfsup1(C),A)) ) ) ) ) ) )).
fof(t42_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_rlaffin1(B,A) <=> ! [C] : ( m2_rlvect_2(C,A,B) => ( ( k6_rlvect_2(A,C) = k4_struct_0(A) & k3_rlaffin1(A,C) = k5_numbers ) => k3_rlvect_2(A,C) = k1_xboole_0 ) ) ) ) ) )).
fof(t42_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rlsub_1(C,A) => ( r2_hidden(k4_struct_0(A),k3_rlsub_1(A,B,C)) <=> r1_struct_0(C,B) ) ) ) ) )).
fof(t42_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( m2_rlsub_1(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t42_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( ( v9_rltopsp1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(C,B) => v9_rltopsp1(C,A) ) ) ) ) )).
fof(t42_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t42_rlvect_2,axiom,( ! [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) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_rlvect_2(C,A) => ( B != k5_numbers => k3_rlvect_2(A,k8_rlvect_2(A,B,C)) = k3_rlvect_2(A,C) ) ) ) ) )).
fof(t42_rmod_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_rmod_2(E,B,C) => ( r2_hidden(A,k3_rmod_2(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(C)) & r1_struct_0(E,F) & A = k3_rlvect_1(C,D,F) ) ) ) ) ) ) )).
fof(t42_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ( k1_rmod_3(A,B,C,D) = B <=> ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & ? [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t42_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t42_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( 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)) ) ) )).
fof(t42_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t42_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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),k5_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)) ) ) ) ) )).
fof(t42_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ~ r1_xxreal_0(k1_rpr_1(A,B),k5_numbers) => k2_rpr_1(A,B,k2_subset_1(A)) = 1 ) ) ) )).
fof(t42_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_struct_0(B,C) <=> k3_rusub_1(A,C,B) = u1_struct_0(B) ) ) ) ) )).
fof(t42_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( m2_rusub_1(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t42_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t42_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(t42_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => C = k9_rvsum_1(A,k5_rvsum_1(A,C,B),B) ) ) ) )).
fof(t42_rvsum_2,axiom,( k20_rvsum_1(k6_finseq_1(k2_numbers)) = 1 )).
fof(t42_scmfsa10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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_xcmplx_0(A,B),C) ) ) ) )).
fof(t42_scmfsa8c,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ~ r1_scmfsa7b(k2_compos_1(k1_scmfsa_2),A) ) )).
fof(t42_scmfsa_2,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(k5_relat_1(A,k1_ami_2),u1_struct_0(k1_ami_3)) ) ) ) )).
fof(t42_scmfsa_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ( ! [E] : ( v7_ordinal1(E) => ( r5_scmfsa7b(B,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(D,B,C,A),E),k1_funct_4(A,k2_scmfsa_9(C,B))) & r6_scmfsa7b(B,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(D,B,C,A),E),k1_funct_4(A,k2_scmfsa_9(C,B))) ) ) => ( ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1))) ) => ~ ! [F] : ( v7_ordinal1(F) => ( ~ ( r1_xxreal_0(k3_funct_2(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(D,B,C,A),F)),k3_funct_2(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(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(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(D,B,C,A),F)) != k5_numbers ) & ( k3_funct_2(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(D,B,C,A),F)) = k5_numbers => r1_xxreal_0(k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(D,B,C,A),F),C),k5_numbers) ) & ( r1_xxreal_0(k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(D,B,C,A),F),C),k5_numbers) => k3_funct_2(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(D,B,C,A),F)) = k5_numbers ) ) ) ) | ( r6_scmfsa7b(k2_scmfsa_9(C,B),D,A) & r5_scmfsa7b(k2_scmfsa_9(C,B),D,A) ) ) ) ) ) ) ) )).
fof(t42_scmpds_2,axiom,( ! [A] : ( ( 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] : ( v1_int_1(B) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t42_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ( k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),E)) != k5_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,k1_nat_1(k5_card_1(C),1))) ) ) ) ) ) ) )).
fof(t42_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => A = k7_scmyciel(A,k3_tarski(A)) ) )).
fof(t42_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_semi_af1(A,B,C,D,E) => r2_semi_af1(A,C,B,E,D) ) ) ) ) ) ) )).
fof(t42_seq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v9_ordinal1(B) => ( A = k5_numbers | v9_ordinal1(k26_valued_1(k4_ordinal1,k1_numbers,B,A)) ) ) ) ) )).
fof(t42_seq_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v3_funct_1(A) & v2_comseq_2(B) ) => ( k1_seq_2(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) = k2_xcmplx_0(k9_nat_1(k1_numbers,A,k5_numbers),k1_seq_2(B)) & k1_seq_2(k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) = k6_xcmplx_0(k9_nat_1(k1_numbers,A,k5_numbers),k1_seq_2(B)) & k1_seq_2(k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,A)) = k6_xcmplx_0(k1_seq_2(B),k9_nat_1(k1_numbers,A,k5_numbers)) & k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) = k3_xcmplx_0(k9_nat_1(k1_numbers,A,k5_numbers),k1_seq_2(B)) ) ) ) ) )).
fof(t42_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( r3_seqfunc(A,B,C) <=> ( r1_seqfunc(A,k1_numbers,B,C) & r2_seqfunc(A,B,C) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & ? [G] : ( m1_subset_1(G,A) & r1_xxreal_0(E,F) & r2_hidden(G,C) & r1_xxreal_0(D,k9_complex1(k6_xcmplx_0(k1_funct_1(k1_seqfunc(A,k1_numbers,B,F),G),k1_funct_1(k11_seqfunc(A,B,C),G)))) ) ) ) ) ) ) ) ) ) )).
fof(t42_seqm_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ ( ~ r1_xxreal_0(A,1) & ! [B] : ( v7_ordinal1(B) => ~ ( A = k1_nat_1(B,1) & ~ r1_xxreal_0(B,k5_numbers) ) ) ) & ~ ( ? [B] : ( v7_ordinal1(B) & A = k1_nat_1(B,1) & ~ r1_xxreal_0(B,k5_numbers) ) & r1_xxreal_0(A,1) ) ) ) )).
fof(t42_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,B,C) = k1_power(C,k9_nat_1(k1_numbers,k56_valued_1(k4_ordinal1,k1_numbers,A),C)) ) & v2_comseq_2(B) & ~ r1_xxreal_0(k1_seq_2(B),1) & v1_series_1(A) ) ) ) )).
fof(t42_series_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [D] : ( m1_subset_1(D,k4_ordinal1) => k9_nat_1(k1_numbers,C,D) = k2_xcmplx_0(k3_xcmplx_0(A,D),B) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k9_nat_1(k1_numbers,k3_series_1(C),D) = k7_xcmplx_0(k3_xcmplx_0(k1_nat_1(D,1),k2_xcmplx_0(k9_nat_1(k1_numbers,C,k5_numbers),k9_nat_1(k1_numbers,C,D))),2) ) ) ) ) ) )).
fof(t42_series_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r1_xxreal_0(k9_nat_1(k1_numbers,k3_series_1(B),A),k9_nat_1(k1_numbers,k3_series_1(k56_valued_1(k4_ordinal1,k1_numbers,B)),A)) ) ) )).
fof(t42_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( 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(k2_power(A,k3_xcmplx_0(2,A)),k2_power(B,k3_xcmplx_0(2,B))),k2_power(C,k3_xcmplx_0(2,C))),k3_xcmplx_0(k3_xcmplx_0(k2_power(A,k2_xcmplx_0(B,C)),k2_power(B,k2_xcmplx_0(A,C))),k2_power(C,k2_xcmplx_0(A,B)))) ) ) ) ) )).
fof(t42_setfam_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r1_tarski(C,k3_tarski(k2_xboole_0(A,B))) & ! [D] : ( r2_hidden(D,B) => r1_xboole_0(D,C) ) ) => r1_tarski(C,k3_tarski(A)) ) )).
fof(t42_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( v7_ordinal1(C) => ( v3_prob_1(B) => k1_funct_1(k4_setlim_1(A,B),C) = k1_kurato_0(A,B) ) ) ) )).
fof(t42_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) ) ) )).
fof(t42_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( 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)) ) ) ) ) )).
fof(t42_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(t42_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t42_simplex0,axiom,( ! [A] : ! [B] : ( v1_int_1(B) => ! [C] : ( m1_simplex0(C,A) => ~ ( v1_matroid0(C) & v4_simplex0(k8_simplex0(A,C,B)) & ~ v4_simplex0(C) & B != k2_xxreal_3(1) ) ) ) )).
fof(t42_simplex1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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] : ( ( v1_finset_1(C) & v1_tops_2(C,B) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) => ! [D] : ( ( 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) = k2_xcmplx_0(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)))) ) ) ) ) ) )).
fof(t42_sin_cos,axiom,( ~ r1_xxreal_0(k1_funct_1(k18_sin_cos,1),k5_numbers) & ~ r1_xxreal_0(k1_funct_1(k16_sin_cos,1),k5_numbers) & ~ r1_xxreal_0(k1_funct_1(k16_sin_cos,1),k1_funct_1(k18_sin_cos,1)) )).
fof(t42_sin_cos2,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k3_sin_cos2,k1_numbers)) )).
fof(t42_sin_cos3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1))) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,A),k1_funct_1(k3_sin_cos2,B)),k3_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,A),k1_funct_1(k1_sin_cos2,B)),k7_complex1)) ) ) )).
fof(t42_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k3_xcmplx_0(k19_sin_cos(k2_xcmplx_0(A,B)),k19_sin_cos(k6_xcmplx_0(A,B))) = k6_xcmplx_0(k3_xcmplx_0(k19_sin_cos(B),k19_sin_cos(B)),k3_xcmplx_0(k17_sin_cos(A),k17_sin_cos(A))) ) ) )).
fof(t42_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( k2_sin_cos2(A) != k5_numbers & k2_sin_cos2(B) != k5_numbers & ~ ( k2_xcmplx_0(k1_sin_cos5(A),k1_sin_cos5(B)) = k7_xcmplx_0(k2_sin_cos2(k2_xcmplx_0(A,B)),k3_xcmplx_0(k2_sin_cos2(A),k2_sin_cos2(B))) & k6_xcmplx_0(k1_sin_cos5(A),k1_sin_cos5(B)) = k4_xcmplx_0(k7_xcmplx_0(k2_sin_cos2(k6_xcmplx_0(A,B)),k3_xcmplx_0(k2_sin_cos2(A),k2_sin_cos2(B)))) ) ) ) ) )).
fof(t42_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ~ ( r1_xxreal_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B),A) & ~ r1_xxreal_0(k2_xcmplx_0(k28_sin_cos,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)),A) & r1_xxreal_0(k19_sin_cos(A),k4_xcmplx_0(1)) ) ) ) )).
fof(t42_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) & k4_sin_cos7(A) != k2_sin_cos7(k7_xcmplx_0(1,k3_square_1(k6_xcmplx_0(1,k1_square_1(A))))) ) ) )).
fof(t42_sin_cos9,axiom,( k1_funct_1(k27_sin_cos,k7_xcmplx_0(k28_sin_cos,2)) = k5_numbers & k2_sin_cos4(k7_xcmplx_0(k28_sin_cos,2)) = k5_numbers )).
fof(t42_sincos10,axiom,( k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos),k28_sin_cos))) = k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1)) )).
fof(t42_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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) ) ) ) ) )).
fof(t42_sprect_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t42_sprect_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t42_sprect_3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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,k13_matrix_0(u1_struct_0(k15_euclid(2)),B)) & r1_sprect_2(A,k13_matrix_0(u1_struct_0(k15_euclid(2)),C)) ) ) ) ) ) )).
fof(t42_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t42_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,1) ) => r1_xxreal_0(k1_square_1(A),A) ) ) )).
fof(t42_stacks_1,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t42_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k1_card_1(a_2_1_stirl2_1(A,B)) = k1_card_1(a_2_2_stirl2_1(A,B)) ) ) )).
fof(t42_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => r1_tarski(k24_qc_lang1(A,k5_cqc_lang(A)),k9_substut1(A,k5_cqc_lang(A))) ) )).
fof(t42_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( k3_subset_1(A,B) = k3_subset_1(A,C) => B = C ) ) ) )).
fof(t42_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_xxreal_0(k12_supinf_2(A,C),k12_supinf_2(B,C)) ) => r1_xxreal_0(k19_supinf_2(A),k19_supinf_2(B)) ) ) ) )).
fof(t42_taxonom1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t42_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k10_tdlat_1(A) = k1_realset1(k2_tdlat_1(A),k9_tdlat_1(A)) ) )).
fof(t42_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)))) ) ) )).
fof(t42_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v4_tdlat_3(A) & l1_pre_topc(A) ) => k1_tdlat_1(A) = k9_tdlat_1(A) ) )).
fof(t42_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t42_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ( v4_tex_3(B,A) <=> ? [C] : ( ~ 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) ) ) ) ) )).
fof(t42_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t42_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_tmap_1(A,B,C,D) <=> ! [E] : ( m1_connsp_2(E,B,k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,D)) => m1_connsp_2(k8_relset_1(u1_struct_0(A),u1_struct_0(B),C,E),A,D) ) ) ) ) ) ) )).
fof(t42_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( m1_borsuk_2(G,A,D,E) => ! [H] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t42_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => v5_topgen_1(k1_struct_0(A),A) ) )).
fof(t42_topgen_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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) ) ) )).
fof(t42_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t42_topgen_5,axiom,( ! [A] : ( 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))) ) ) )).
fof(t42_topgrp_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => m3_topgrp_1(k1_topgrp_1(A,B),A) ) ) )).
fof(t42_topreal6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(2))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [D] : ( v1_xreal_0(D) => ( ( C = k8_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(k6_xcmplx_0(k18_euclid(A),D),k2_xcmplx_0(k18_euclid(A),D)) ) ) ) ) ) )).
fof(t42_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t42_toprealb,axiom,( 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(k5_numbers)))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k4_toprealb(k5_numbers),k2_xcmplx_0(k4_toprealb(k5_numbers),1))))),u1_struct_0(k11_toprealb(k9_toprealb)),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k5_numbers,1)))),k2_tops_2(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k4_toprealb(k5_numbers),k2_xcmplx_0(k4_toprealb(k5_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(k5_numbers)))),k13_toprealb(k4_toprealb(k5_numbers))),k14_toprealb) )).
fof(t42_toprealc,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( ( 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))))) ) ) ) ) )).
fof(t42_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(t42_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t42_tops_2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)))) ) ) ) ) )).
fof(t42_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tops_3(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( C != u1_struct_0(A) & v4_pre_topc(C,A) & ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t42_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => v4_transgeo(k6_partfun1(u1_struct_0(A)),A) ) )).
fof(t42_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ( k6_trees_1(A) = k5_numbers => A = k2_trees_1(k5_numbers) ) ) )).
fof(t42_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ( ( r1_tarski(k2_trees_2(A,1),k2_trees_2(B,1)) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(k12_finseq_1(k4_ordinal1,C),A) => k4_trees_1(A,k12_finseq_1(k4_ordinal1,C)) = k4_trees_1(B,k12_finseq_1(k4_ordinal1,C)) ) ) ) => r1_tarski(A,B) ) ) ) )).
fof(t42_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v3_trees_9(A) ) => ! [B] : ( m1_trees_1(B,k9_xtuple_0(A)) => ! [C] : ~ ( r2_hidden(C,k10_xtuple_0(k2_trees_9(A,B))) & ! [D] : ( 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)) ) ) ) ) ) )).
fof(t42_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_connsp_1(A,B,C) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & ? [E] : ( 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) ) ) ) ) ) ) )).
fof(t42_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t42_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( l1_turing_1(B) => ! [C] : ( m1_subset_1(C,k21_turing_1(A,B)) => ? [D] : ( m1_subset_1(D,u2_turing_1(A)) & ? [E] : ( m1_subset_1(E,u2_turing_1(B)) & C = k1_domain_1(u2_turing_1(A),u2_turing_1(B),D,E) ) ) ) ) ) )).
fof(t42_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ~ v1_facirc_1(k2_msafree2(k40_twoscomp(A,B))) ) ) )).
fof(t42_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => k6_polynom5(k1_complfld,k4_uniroots(A,k1_complfld)) = k2_uniroots(A) ) )).
fof(t42_uproots,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ~ r1_xxreal_0(k1_algseq_1(A,D),C) => k2_polynom4(A,k4_uproots(A,D,C),B) = k3_rlvect_1(A,k8_group_1(A,B,k2_polynom4(A,k4_uproots(A,D,k1_nat_1(C,1)),B)),k1_normsp_1(A,D,C)) ) ) ) ) ) )).
fof(t42_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t42_valued_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_finseq_1(B) ) => k5_card_1(B) = k5_card_1(k61_valued_1(B,A)) ) ) )).
fof(t42_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( v1_valued_2(C) => ! [D] : ( v1_valued_2(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [F] : ( ( 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 ) ) ) ) ) )).
fof(t42_vectsp_4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_vectsp_4(E,B,C) => ( r2_hidden(A,k3_vectsp_4(B,C,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(C)) & r1_struct_0(E,F) & A = k3_rlvect_1(C,D,F) ) ) ) ) ) ) )).
fof(t42_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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)) ) ) ) )).
fof(t42_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_vectsp_6(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t42_vfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t42_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( r1_xboole_0(D,k1_relset_1(A,C)) => r1_vfunct_2(A,B,C,D) ) ) ) ) )).
fof(t42_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( v13_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => r1_tarski(k6_waybel_0(A,C),B) ) ) ) ) )).
fof(t42_waybel12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(u1_pre_topc(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( B = C => ( v2_waybel12(B,k1_yellow_1(u1_pre_topc(A))) <=> v1_tops_3(C,A) ) ) ) ) ) )).
fof(t42_waybel14,axiom,( ! [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) ) => ~ ( v2_waybel_8(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)))) ) => B != a_1_0_waybel14(A) ) ) ) )).
fof(t42_waybel19,axiom,( ! [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) & l1_waybel_9(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t42_waybel20,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t42_waybel21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ~ ( r1_waybel_0(A,B,C) & ! [D] : ( 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) ) ) ) ) ) )).
fof(t42_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( ( v6_waybel23(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v1_yellow_0(k5_yellow_0(A,B)) ) ) )).
fof(t42_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v6_pre_topc(B) & v1_waybel25(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,k3_waybel24(A,k1_waybel25(B))) ) => ( ! [D] : ( 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(k5_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(k5_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(k5_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(k5_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)))) ) ) ) ) ) )).
fof(t42_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t42_waybel27,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ 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,k5_yellow_1(A,C)),k5_yellow_1(A,k2_waybel27(B,C))) ) ) ) )).
fof(t42_waybel34,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t42_waybel_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ( C != k1_xboole_0 => r2_hidden(k1_yellow_0(A,C),B) ) ) ) ) ) )).
fof(t42_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t42_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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) ) ) )).
fof(t42_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v6_waybel_3(A) => v3_waybel_3(k1_yellow_1(u1_pre_topc(A))) ) ) )).
fof(t42_waybel_4,axiom,( ! [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] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A)))))) ) => ~ ( v7_waybel_4(B,A) & r2_hidden(B,u1_struct_0(k8_waybel_4(A))) & ! [C] : ( ( 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) ) ) ) ) )).
fof(t42_waybel_7,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t42_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => ( ( r4_wellord1(A,B) & r4_wellord1(B,C) ) => r4_wellord1(A,C) ) ) ) ) )).
fof(t42_wsierp_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v7_ordinal1(B) => ( k5_int_1(A,B) = k5_numbers => ( r1_xxreal_0(B,k5_numbers) | k4_xcmplx_0(k4_int_1(A,B)) = k4_int_1(k4_xcmplx_0(A),B) ) ) ) ) )).
fof(t42_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : k4_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(k4_xboole_0(A,C),k4_xboole_0(B,C)) )).
fof(t42_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k6_xboolean(A,k9_xboolean(A,B)) = k3_xboolean(A) ) ) )).
fof(t42_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t42_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(k5_numbers,C) => r1_xxreal_0(k2_xcmplx_0(A,C),B) ) ) => r1_xxreal_0(A,B) ) ) ) )).
fof(t42_xtuple_0,axiom,( ! [A] : ! [B] : r1_tarski(k5_xboole_0(k13_xtuple_0(A),k13_xtuple_0(B)),k13_xtuple_0(k5_xboole_0(A,B))) )).
fof(t42_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => k3_xxreal_0(A,k1_xxreal_0) = A ) )).
fof(t42_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(D,B) ) => r1_tarski(k3_xxreal_1(C,D),k3_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t42_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => m2_xxreal_2(k2_xxreal_0,A) ) )).
fof(t42_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(A,k1_xxreal_3(C,B)) => ( ( A = k1_xxreal_0 & B = k1_xxreal_0 & ~ r1_xxreal_0(k5_numbers,C) ) | ( A = k2_xxreal_0 & B = k2_xxreal_0 & ~ r1_xxreal_0(k5_numbers,C) ) | r1_xxreal_0(k3_xxreal_3(A,B),C) ) ) ) ) ) )).
fof(t42_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(t42_yellow12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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))))) ) ) ) )).
fof(t42_yellow16,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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(k5_yellow_1(A,B)) ) ) )).
fof(t42_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & v4_yellow18(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( 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) ) ) ) ) ) )).
fof(t42_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v16_functor0(C,A,B) & m2_functor0(C,A,B) ) => ( v21_functor0(C,A,B) => r3_yellow20(A,B,C,A,B) ) ) ) ) )).
fof(t42_yellow_0,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t42_yellow_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(k7_waybel_0(B)))) => ( r2_hidden(A,C) => m1_subset_1(A,u1_struct_0(B)) ) ) ) )).
fof(t42_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t42_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(t42_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t42_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( v8_yellow_6(B,A) & m4_yellow_6(B,A) ) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(t42_yellow_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t42_yellow_9,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,B)))) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ! [E] : ( ( ~ 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))) ) ) ) ) )).
fof(t42_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ( v6_zf_lang(B) => ( ~ ( A = k23_zf_lang(B) & ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => k8_zf_lang(A,D) != B ) ) & ( ? [D] : ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) & k8_zf_lang(A,D) = B ) => A = k23_zf_lang(B) ) & ~ ( C = k24_zf_lang(B) & ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => k8_zf_lang(D,C) != B ) ) & ( ? [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) & k8_zf_lang(D,C) = B ) => C = k24_zf_lang(B) ) ) ) ) ) ) )).
fof(t42_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ~ ( r3_zf_lang(A,B) & r2_zf_lang(B,A) ) ) ) )).
fof(t42_zfmisc_1,axiom,( ! [A] : ! [B] : k2_xboole_0(k1_tarski(A),B) != k1_xboole_0 )).
fof(t42_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) )).
fof(t42_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => r1_zmodul02(A,k25_zmodul02(A,B,B),k19_zmodul02(A)) ) ) )).
fof(t43_abcmiz_0,axiom,( ! [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) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t43_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t43_abcmiz_a,axiom,( ! [A] : ( ( 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 ) )).
fof(t43_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t43_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t43_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( k1_afinsq_1(k1_funct_7(A,B,C)) = k1_afinsq_1(A) & ( ~ r1_xxreal_0(k1_afinsq_1(A),B) => k1_funct_1(k1_funct_7(A,B,C),B) = C ) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( D != B => k1_funct_1(k1_funct_7(A,B,C),D) = k1_funct_1(A,D) ) ) ) ) ) )).
fof(t43_afinsq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t43_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,u2_incsp_1(k13_afproj(A))) => ! [F] : ( m1_subset_1(F,u2_incsp_1(k13_afproj(A))) => ~ ( v1_aff_4(C,A) & v1_aff_1(B,A) & v1_aff_1(D,A) & r1_tarski(B,C) & r1_tarski(D,C) & E = k4_tarski(B,1) & F = k4_tarski(D,1) & ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t43_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_afvect0(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_afvect0(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t43_algspec1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t43_algstr_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ? [B] : ( ~ v1_xboole_0(B) & ? [C] : ( 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] : ( 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) ) ) ) ) )).
fof(t43_altcat_4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t43_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t43_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ~ ( r1_analmetr(A,J,K) & r2_analort(A,J,K,B,C,E,F) & r2_analort(A,J,K,H,I,E,F) & r2_analort(A,J,K,H,I,D,G) & H != I & E != F & ~ r2_analort(A,J,K,B,C,D,G) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t43_aofa_000,axiom,( ! [A] : ( ( ~ 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] : ( 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,k10_subset_1(1,k4_finseq_1(u1_unialg_1(A))))) => ( k19_margrel1(B) = k5_numbers & r2_hidden(k12_aofa_000(A),k2_relset_1(u1_struct_0(A),B)) ) ) ) ) )).
fof(t43_aofa_a00,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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) & l1_unialg_1(B) ) => ( g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)) = g1_unialg_1(u1_struct_0(B),u1_unialg_1(B)) => k18_aofa_000(A) = k18_aofa_000(B) ) ) ) )).
fof(t43_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( ( v19_aofa_a00(F,A) & m1_subset_1(F,u1_struct_0(A)) ) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),F)) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),F)) => ! [I] : ( m2_subset_1(I,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => k15_aofa_a00(A,B,C,D,F,k32_aofa_a00(A,C,F,G,H),I) = k32_aofa_a00(A,D,F,k15_aofa_a00(A,B,C,D,F,G,I),k15_aofa_a00(A,B,C,D,F,H,I)) ) ) ) ) ) ) ) ) ) )).
fof(t43_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [E] : ( ( v1_aofa_i00(E,A,B,D) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),D) ) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),E) => ! [G] : ( 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) = 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t43_armstrng,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v6_armstrng(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) ) => ? [C] : ( 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)) ) ) ) )).
fof(t43_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( 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 ) ) ) ) ) )).
fof(t43_asympt_1,axiom,( k5_series_1(2,12) = 4096 )).
fof(t43_bcialg_1,axiom,( ! [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) ) => ( v12_bcialg_1(k1_tarski(k4_struct_0(A)),A) & m2_bcialg_1(k1_tarski(k4_struct_0(A)),A) ) ) )).
fof(t43_bcialg_3,axiom,( ! [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) & v6_bcialg_3(A) & l2_bcialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v2_bcialg_3(B,A) => ( v11_bcialg_3(A) <=> ! [C] : ( 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) ) ) ) ) ) )).
fof(t43_bcialg_4,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_tarski(k3_bcialg_4(A,B,C),k8_bcialg_4(A,D)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t43_bcialg_6,axiom,( ! [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] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ( v10_bcialg_1(D,A) => v10_bcialg_1(k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,D),B) ) ) ) ) ) )).
fof(t43_bciideal,axiom,( ! [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) ) => ( ( v3_bciideal(k1_tarski(k4_struct_0(A)),A) & m2_bcialg_1(k1_tarski(k4_struct_0(A)),A) ) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t43_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_xxreal_0(k4_bhsp_1(A,k5_algstr_0(A,B,D),k5_algstr_0(A,C,D)),k2_xcmplx_0(k4_bhsp_1(A,D,B),k4_bhsp_1(A,D,C))) ) ) ) ) )).
fof(t43_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(C,k4_bhsp_2(A,B,E)) & r2_hidden(D,k4_bhsp_2(A,B,E)) & r1_xxreal_0(k3_xcmplx_0(2,E),k4_bhsp_1(A,C,D)) ) ) ) ) ) ) )).
fof(t43_bhsp_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => r2_funct_2(k4_ordinal1,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))) ) ) ) ) )).
fof(t43_bilinear,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t43_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t43_borsuk_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,1) ) <=> r2_hidden(A,u1_struct_0(k17_borsuk_1)) ) ) )).
fof(t43_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k1_borsuk_4))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_topmetr)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_topmetr)) => ( A = k2_rcomp_1(B,C) => v3_pre_topc(A,k1_borsuk_4) ) ) ) ) )).
fof(t43_borsuk_5,axiom,( ! [A] : ( 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)) ) )).
fof(t43_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_borsuk_6(A,B,C) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t43_borsuk_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => A = k1_euclid_3(k2_xcmplx_0(k3_xcmplx_0(k12_euclid(A),k19_sin_cos(k3_euclid_3(A))),k3_xcmplx_0(k3_xcmplx_0(k12_euclid(A),k17_sin_cos(k3_euclid_3(A))),k7_complex1))) ) )).
fof(t43_bspace,axiom,( k1_vectsp_9(k2_bspace,k7_bspace(k1_xboole_0)) = k5_numbers )).
fof(t43_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t43_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t43_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t43_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t43_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => k8_xboolean(k7_margrel1,A) = k8_margrel1 ) )).
fof(t43_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t43_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( 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)))) ) ) ) ) ) ) ) )).
fof(t43_card_1,axiom,( ! [A] : ( v1_finset_1(A) => v1_finset_1(k2_card_1(A)) ) )).
fof(t43_card_2,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t43_card_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r2_hidden(k1_card_1(A),k1_card_1(B)) => r2_hidden(A,B) ) ) ) )).
fof(t43_card_fin,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_finset_1(A) ) => ! [B] : ( v1_finset_1(B) => ( k9_xtuple_0(A) = B => ! [C] : ( ( 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] : ( ( v1_relat_1(D) & v5_relat_1(D,k4_ordinal1) & v5_ordinal1(D) & v1_funct_1(D) & v1_finset_1(D) ) => ~ ( k1_relset_1(k4_ordinal1,D) = k5_card_1(B) & ! [E] : ( r2_hidden(E,k1_relset_1(k4_ordinal1,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) ) ) ) ) ) ) ) )).
fof(t43_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( m1_cat_1(D,A,B,C) & ? [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t43_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t43_cat_4,axiom,( ! [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_4(A) & l1_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_cat_1(H,A,B,C) => ! [I] : ( m1_cat_1(I,A,D,E) => ! [J] : ( m1_cat_1(J,A,F,B) => ! [K] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t43_catalan2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k1_numbers) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k1_numbers) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ( ( k1_relset_1(k4_ordinal1,A) = k1_relset_1(k4_ordinal1,B) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k1_afinsq_1(A)) => k1_funct_1(A,C) = k1_funct_1(B,k7_nat_d(k1_afinsq_1(A),k2_xcmplx_0(1,C))) ) ) ) => k7_afinsq_2(A) = k7_afinsq_2(B) ) ) ) )).
fof(t43_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( r2_hidden(B,k6_cc0sp2(A)) => r2_hidden(B,k2_cc0sp2(A)) ) ) )).
fof(t43_cfcont_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t43_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( 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,D,k1_cfunct_1(A,B,C)),k1_cfunct_1(A,k19_valued_1(A,k2_numbers,k2_numbers,D,B),C)) ) ) ) ) )).
fof(t43_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ( v5_cgames_1(A) <=> ! [B] : ( v2_cgames_1(B) => ~ ( r2_hidden(B,k7_cgames_1(A)) & ! [C] : ( v2_cgames_1(C) => ~ ( r2_hidden(C,k6_cgames_1(B)) & v5_cgames_1(C) ) ) ) ) ) ) )).
fof(t43_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(C)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(C)) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(C)) => ! [G] : ( m2_finseq_2(G,k1_numbers,k1_euclid(C)) => ! [H] : ( 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] : ( m2_subset_1(I,k4_ordinal1,k2_finseq_1(C)) => ~ ( ~ ( k1_funct_1(D,I) = k1_funct_1(F,I) & k1_funct_1(E,I) = k1_funct_1(G,I) ) & ~ ( k1_funct_1(D,I) = k1_funct_1(F,I) & k1_funct_1(E,I) = k1_funct_1(F,I) ) & ~ ( k1_funct_1(D,I) = k1_funct_1(G,I) & k1_funct_1(E,I) = k1_funct_1(G,I) ) & ~ ( r1_xxreal_0(k1_funct_1(D,I),k1_funct_1(E,I)) & ~ r1_xxreal_0(k1_funct_1(F,I),k1_funct_1(G,I)) & r1_xxreal_0(k1_funct_1(G,I),k1_funct_1(D,I)) & r1_xxreal_0(k1_funct_1(E,I),k1_funct_1(F,I)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t43_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ( r5_glib_000(A,B) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => ( r1_chord(A,C,D) => ! [E] : ( m1_subset_1(E,k6_glib_000(B)) => ! [F] : ( m1_subset_1(F,k6_glib_000(B)) => ( ( C = E & D = F ) => r1_chord(B,E,F) ) ) ) ) ) ) ) ) ) )).
fof(t43_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(D) & v1_finset_1(D) ) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t43_circcomb,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => r1_circcomb(k5_circcomb(A,B),k5_circcomb(A,C)) ) ) )).
fof(t43_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v4_msualg_1(E,A) & v4_msafree2(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( ( v4_msualg_1(F,B) & v4_msafree2(F,B) & l3_msualg_1(F,B) ) => ( r4_circtrm1(A,B,C,D,E,F) => ! [G] : ( m1_subset_1(G,u4_struct_0(A)) => ! [H] : ( m1_subset_1(H,u4_struct_0(B)) => ( H = k1_funct_1(D,G) => ! [I] : ( m1_subset_1(I,k4_card_3(u3_msualg_1(A,E))) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t43_classes1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => ( r2_hidden(A,k4_classes1(B)) <=> r2_hidden(k1_tarski(A),k4_classes1(k1_ordinal1(B))) ) ) )).
fof(t43_classes2,axiom,( ! [A] : ! [B] : ( ( v1_ordinal1(A) & r2_hidden(A,k1_classes1(B)) ) => r2_hidden(A,k4_classes1(k1_card_1(k1_classes1(B)))) ) )).
fof(t43_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t43_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(C,k4_clvect_2(A,B,E)) & r2_hidden(D,k4_clvect_2(A,B,E)) & r1_xxreal_0(k3_xcmplx_0(2,E),k15_csspace(A,C,D)) ) ) ) ) ) ) )).
fof(t43_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k2_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) )).
fof(t43_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k20_coh_sp(A)) => ! [C] : ( m1_subset_1(C,k20_coh_sp(A)) => ( k21_coh_sp(A,C) = k22_coh_sp(A,B) => ( k2_xtuple_0(k24_coh_sp(A,B,C)) = k3_relat_1(k2_xtuple_0(B),k2_xtuple_0(C)) & k21_coh_sp(A,k24_coh_sp(A,B,C)) = k21_coh_sp(A,B) & k22_coh_sp(A,k24_coh_sp(A,B,C)) = k22_coh_sp(A,C) ) ) ) ) )).
fof(t43_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ! [E] : ( ( 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] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t43_compl_sp,axiom,( ? [A] : ( ~ 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] : ( v2_relat_1(B) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & v1_compl_sp(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) )).
fof(t43_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k5_numbers,A) => k9_complex1(A) = A ) ) )).
fof(t43_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k1_complex2(k4_xcmplx_0(A),k4_xcmplx_0(B)) = k1_complex2(A,B) ) ) )).
fof(t43_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ( B != k4_struct_0(k1_complfld) => k3_vectsp_1(k1_complfld,A,B) = k3_vectsp_1(k1_complfld,k4_algstr_0(k1_complfld,A),k4_algstr_0(k1_complfld,B)) ) ) ) )).
fof(t43_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => ( k6_complsp2(k8_seq_4(A,B)) = k8_rvsum_1(k6_complsp2(A),k6_complsp2(B)) & k7_complsp2(k8_seq_4(A,B)) = k8_rvsum_1(k7_complsp2(A),k7_complsp2(B)) ) ) ) ) )).
fof(t43_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(A)) => ( r2_hidden(k5_numbers,k2_afinsq_1(k11_compos_1(A,B))) & r2_hidden(1,k2_afinsq_1(k11_compos_1(A,B))) ) ) ) )).
fof(t43_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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)) ) ) ) )).
fof(t43_comptrig,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( r2_hidden(k1_comptrig(A),k2_rcomp_1(k28_sin_cos,k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos))) <=> ( ~ r1_xxreal_0(k5_numbers,k3_complex1(A)) & ~ r1_xxreal_0(k5_numbers,k4_complex1(A)) ) ) ) )).
fof(t43_comput_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_rfunct_3(A,k3_finseq_2(k4_ordinal1),k4_ordinal1,k2_comput_1(k4_ordinal1)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_rfunct_3(B,k3_finseq_2(k4_ordinal1),k4_ordinal1,k2_comput_1(k4_ordinal1)) ) => ! [C] : ( ( v3_comput_1(C) & m2_finseq_1(C,k2_comput_1(k4_ordinal1)) ) => ( B = k3_relat_1(k5_funct_6(C),A) => k19_margrel1(B) = k1_comput_1(C) ) ) ) ) )).
fof(t43_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k2_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v9_ordinal1(A) & v9_ordinal1(C) ) => ( r2_relset_1(k4_ordinal1,k2_numbers,k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,A),k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,D,C)),k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,C),k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,D,A)),k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,C))) & r2_relset_1(k4_ordinal1,k2_numbers,k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,A),k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,D,C)),k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,C),k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,D,A)),k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,C))) ) ) ) ) ) ) )).
fof(t43_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( v1_xcmplx_0(B) => ( ( k9_nat_1(k2_numbers,A,k5_numbers) = B & ! [C] : ( v7_ordinal1(C) => k9_nat_1(k2_numbers,A,k1_nat_1(C,1)) = k3_xcmplx_0(k9_nat_1(k2_numbers,A,C),B) ) ) => ( r1_xxreal_0(k9_complex1(B),k5_numbers) | r1_xxreal_0(1,k9_complex1(B)) | ( v2_comseq_2(A) & k3_comseq_2(A) = k5_complex1 ) ) ) ) ) )).
fof(t43_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k11_conlat_1(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t43_connsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ! [C] : ( 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)) ) ) ) )).
fof(t43_convex4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xcmplx_0(B) => k4_complex1(k3_xcmplx_0(A,B)) = k3_xcmplx_0(A,k4_complex1(B)) ) ) )).
fof(t43_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),k3_qc_lang1(A),k9_funct_2(k3_qc_lang1(A),k3_qc_lang1(A))) => ! [F] : ( 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)),D,B,F,E),k15_cqc_sim1(A,C)) & r2_hidden(k2_qc_lang3(A,B),k7_relat_1(E,k24_qc_lang1(A,D))) ) ) ) ) ) ) ) )).
fof(t43_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t43_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t43_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t43_csspace,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => k13_csspace(B,k1_clvect_1(B,C,A)) = k3_xcmplx_0(k9_complex1(A),k13_csspace(B,C)) ) ) ) )).
fof(t43_dickson,axiom,( r1_relat_2(k10_dickson,k4_ordinal1) )).
fof(t43_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k4_diff_1(k16_sin_cos,A),B) = k3_xcmplx_0(2,k3_xcmplx_0(k19_sin_cos(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(2,B),A),2)),k17_sin_cos(k7_xcmplx_0(A,2)))) ) ) )).
fof(t43_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => k1_funct_1(D,E) = k1_square_1(E) ) & r1_zfmisc_1(A,B,C) ) => k10_diff_1(D,A,B,C) = 1 ) ) ) ) ) )).
fof(t43_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( ( 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] : ( v1_xreal_0(F) => k1_funct_1(D,F) = k1_funct_1(k4_diff_1(E,A),F) ) => k9_diff_1(D,B,C) = k6_xcmplx_0(k9_diff_1(E,B,C),k9_diff_1(E,k6_xcmplx_0(B,A),k6_xcmplx_0(C,A))) ) ) ) ) ) ) )).
fof(t43_dilworth,axiom,( ! [A] : ( ( v3_dilworth(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_dilworth(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t43_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & v3_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( ~ r2_diraf(A,B,C,D,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_diraf(A,B,C,B,F) & r2_diraf(A,D,E,D,F) ) ) ) ) ) ) ) ) )).
fof(t43_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(A))) => ! [E] : ( 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)),k4_ordinal1,D,E,1),k3_ec_pf_1(k9_int_3(A)),k6_ec_pf_1(A,B,C)) ) ) ) ) ) ) )).
fof(t43_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( 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] : ( 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) ) ) ) ) ) )).
fof(t43_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k18_ens_1(A,B,k4_cat_1(A,C)) = k6_partfun1(k2_cat_1(A,C,B)) ) ) ) )).
fof(t43_entropy1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( v2_matrprob(A) <=> v4_partfun3(k2_entropy1(k1_numbers,A)) ) ) )).
fof(t43_enumset1,axiom,( ! [A] : ! [B] : k3_enumset1(A,A,A,A,B) = k2_tarski(A,B) )).
fof(t43_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(t43_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => k12_euclid(k4_algstr_0(k15_euclid(A),B)) = k12_euclid(B) ) ) )).
fof(t43_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => k1_square_1(k12_euclid(k3_rlvect_1(k15_euclid(A),B,C))) = k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k12_euclid(B)),k3_xcmplx_0(2,k22_rvsum_1(C,B))),k1_square_1(k12_euclid(C))) ) ) ) )).
fof(t43_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( A != k4_struct_0(k15_euclid(2)) & B != k4_struct_0(k15_euclid(2)) & ~ ( k22_rvsum_1(A,B) = k5_numbers <=> ( k4_euclid_3(A,k4_struct_0(k15_euclid(2)),B) = k7_xcmplx_0(k28_sin_cos,2) | k4_euclid_3(A,k4_struct_0(k15_euclid(2)),B) = k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos) ) ) ) ) ) ) )).
fof(t43_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t43_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) )).
fof(t43_euclid_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_real_ns1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k7_real_ns1(A)))) => ~ ( C = k8_euclid_7(A) & ! [D] : ( m2_rlvect_2(D,k7_real_ns1(A),C) => B != k6_rlvect_2(k7_real_ns1(A),D) ) ) ) ) ) )).
fof(t43_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => k14_rvsum_1(A,B) = k11_finseq_1(k3_xcmplx_0(k1_funct_1(A,1),k1_funct_1(B,1)),k3_xcmplx_0(k1_funct_1(A,2),k1_funct_1(B,2)),k3_xcmplx_0(k1_funct_1(A,3),k1_funct_1(B,3))) ) ) )).
fof(t43_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ? [E] : ( 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)) ) ) ) ) ) )).
fof(t43_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(k9_funct_7(C,A,B),C) & m1_exchsort(C,k9_funct_7(C,A,B)) ) ) ) )).
fof(t43_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)))) ) )).
fof(t43_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(B,C) = k1_square_1(C) ) ) ) => v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) ) )).
fof(t43_fdiff_10,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fdiff_9,k16_sin_cos),A),B) = k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,k1_funct_1(k1_fdiff_9,B)),k1_funct_1(k16_sin_cos,B)),k1_square_1(k1_funct_1(k18_sin_cos,B))) ) ) ) ) ) )).
fof(t43_fdiff_11,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,k1_relset_1(k1_numbers,k26_sin_cos)) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_sin_cos9)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_sin_cos9)),A),B) = k7_xcmplx_0(k2_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k1_funct_1(k2_sin_cos9,B)),k1_square_1(k1_funct_1(k18_sin_cos,B))) ) ) ) ) ) )).
fof(t43_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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] : ( v1_xreal_0(C) & r2_hidden(C,k3_limfunc1(A)) & r1_xxreal_0(k1_fdiff_1(B,C),k5_numbers) ) & ? [C] : ( v1_xreal_0(C) & r2_hidden(C,k3_limfunc1(A)) & r1_xxreal_0(k5_numbers,k1_fdiff_1(B,C)) ) ) | v3_rcomp_1(k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,B,k3_limfunc1(A)))) ) ) ) ) )).
fof(t43_fdiff_4,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & r1_xxreal_0(k1_funct_1(k16_sin_cos,B),k5_numbers) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k3_taylor_1),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) ) ) ) ) ) )).
fof(t43_fdiff_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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),k7_xcmplx_0(1,k3_xcmplx_0(4,A))))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(C,D) = k3_xcmplx_0(k3_xcmplx_0(2,A),D) ) ) ) => ( A = k5_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),k7_xcmplx_0(1,k3_xcmplx_0(4,A))),B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_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),k7_xcmplx_0(1,k3_xcmplx_0(4,A))),B),D) = k3_xcmplx_0(k7_xcmplx_0(1,2),k19_sin_cos(k3_xcmplx_0(k3_xcmplx_0(2,A),D))) ) ) ) ) ) ) ) ) )).
fof(t43_fdiff_7,axiom,( ! [A] : ( ( 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,k18_sin_cos),k22_sin_cos))) => ( r2_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),k22_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),k22_sin_cos),A),B) = k7_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k18_sin_cos,B)),k1_funct_1(k22_sin_cos,B)) ) ) ) ) ) )).
fof(t43_fdiff_9,axiom,( ! [A] : ( ( 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,k27_sin_cos,k1_fdiff_9))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k1_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k1_fdiff_9),A),B) = k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B))),k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k27_sin_cos,B),k1_funct_1(k16_sin_cos,B)),k1_square_1(k1_funct_1(k18_sin_cos,B)))) ) ) ) ) ) )).
fof(t43_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_finseq_1(B,A) => ! [C] : ( m1_finseq_1(C,A) => ! [D] : ( m1_finseq_1(D,A) => ( r1_filerec1(A,D,B,C) => r1_filerec1(A,D,D,C) ) ) ) ) ) )).
fof(t43_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_lattices(A,B,C) <=> k4_lattices(A,B,k7_lattices(A,C)) = k5_lattices(A) ) ) ) ) )).
fof(t43_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t43_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t43_finseq_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(t43_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_finseq_1(D,C) => ! [E] : ( ( 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 = k5_numbers & A != k5_numbers ) | m2_finseq_1(k1_partfun1(k2_finseq_1(A),k2_finseq_1(B),k4_ordinal1,C,E,D),C) ) ) ) ) ) ) ) )).
fof(t43_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(A,B) & k14_finseq_1(k2_tarski(B,A)) != k10_finseq_1(B,A) ) ) ) )).
fof(t43_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : ( 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)) ) ) ) )).
fof(t43_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t43_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( B != k1_xboole_0 => k4_finseq_4(B,k7_partfun1(A,B,1)) = 1 ) ) ) )).
fof(t43_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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,k6_funcop_1(B,A,D,k8_funcop_1(B,A,k4_binop_1(B,D)),C),C) & r2_funct_2(A,B,k6_funcop_1(B,A,D,C,k8_funcop_1(B,A,k4_binop_1(B,D))),C) ) ) ) ) ) ) )).
fof(t43_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( 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)) ) ) )).
fof(t43_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t43_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => r1_tarski(B,k8_flang_1(A,B)) ) )).
fof(t43_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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)) ) ) ) ) )).
fof(t43_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ( r1_tarski(C,k8_flang_1(A,B)) => ( r1_tarski(k6_flang_1(A,k1_flang_3(A,B,D),C),k1_flang_3(A,B,D)) & r1_tarski(k6_flang_1(A,C,k1_flang_3(A,B,D)),k1_flang_3(A,B,D)) ) ) ) ) ) )).
fof(t43_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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)) ) ) ) )).
fof(t43_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( 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) ) ) )).
fof(t43_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( ~ v2_struct_0(D) & l2_fsm_1(D,A,B) ) => ! [E] : ( ( ~ v2_struct_0(E) & l2_fsm_1(E,A,B) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ! [G] : ( ( 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] : ( m1_subset_1(H,u1_struct_0(D)) => ! [I] : ( m1_subset_1(I,A) => k3_funct_2(u1_struct_0(D),u1_struct_0(E),G,k2_binop_1(u1_struct_0(D),A,u1_struct_0(D),u1_fsm_1(A,D),H,I)) = k2_binop_1(u1_struct_0(E),A,u1_struct_0(E),u1_fsm_1(A,E),k3_funct_2(u1_struct_0(D),u1_struct_0(E),G,H),I) ) ) => ! [H] : ( m1_subset_1(H,k4_ordinal1) => ( ( r1_xxreal_0(1,H) & r1_xxreal_0(H,k1_nat_1(k3_finseq_1(C),1)) ) => k1_funct_1(G,k1_funct_1(k2_fsm_1(A,D,F,C),H)) = k1_funct_1(k2_fsm_1(A,E,k3_funct_2(u1_struct_0(D),u1_struct_0(E),G,F),C),H) ) ) ) ) ) ) ) ) ) ) )).
fof(t43_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t43_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t43_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,B,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,C,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(C,D))) ) => ( ( D = k1_xboole_0 => C = k1_xboole_0 ) => r1_tarski(k8_relset_1(B,C,E,A),k8_relset_1(B,D,k1_partfun1(B,C,C,D,E,F),k7_relset_1(C,D,F,A))) ) ) ) )).
fof(t43_funct_3,axiom,( ! [A] : ! [B] : r1_tarski(k10_xtuple_0(k7_funct_3(A,B)),A) )).
fof(t43_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( r2_hidden(k4_tarski(C,B),k9_xtuple_0(k2_funct_4(A))) => k1_binop_1(k2_funct_4(A),C,B) = k1_binop_1(A,B,C) ) ) )).
fof(t43_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) ) ) )).
fof(t43_funct_6,axiom,( ! [A] : ! [B] : ! [C] : k7_funct_6(k7_funcop_1(A,B),C) = k7_funcop_1(A,k1_funct_2(B,C)) )).
fof(t43_funct_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t43_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t43_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t43_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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))) ) ) ) )).
fof(t43_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D,C)),k2_fuzzy_1(A,k2_fuzzy_2(A,B,D),k2_fuzzy_2(A,B,C))) ) ) ) ) )).
fof(t43_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => k3_funct_2(u1_struct_0(A),k6_numbers,k5_fvaluat1(A,B),k4_fvaluat1(A,B)) = 1 ) ) ) )).
fof(t43_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [D] : ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t43_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t43_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( ( ~ v1_xboole_0(F) & v1_relat_1(F) & v2_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ! [G] : ( m1_genealg1(G,F) => ! [H] : ( m1_genealg1(H,F) => ( k11_genealg1(F,G,H,k5_numbers,k5_numbers,k5_numbers,D,E) = k8_genealg1(F,H,G,D,E) & k11_genealg1(F,G,H,k5_numbers,k5_numbers,C,k5_numbers,E) = k8_genealg1(F,H,G,C,E) & k11_genealg1(F,G,H,k5_numbers,k5_numbers,C,D,k5_numbers) = k8_genealg1(F,H,G,C,D) & k11_genealg1(F,G,H,k5_numbers,B,k5_numbers,k5_numbers,E) = k8_genealg1(F,H,G,B,E) & k11_genealg1(F,G,H,k5_numbers,B,k5_numbers,D,k5_numbers) = k8_genealg1(F,H,G,B,D) & k11_genealg1(F,G,H,k5_numbers,B,C,k5_numbers,k5_numbers) = k8_genealg1(F,H,G,B,C) & k11_genealg1(F,G,H,A,k5_numbers,k5_numbers,k5_numbers,E) = k8_genealg1(F,H,G,A,E) & k11_genealg1(F,G,H,A,k5_numbers,k5_numbers,D,k5_numbers) = k8_genealg1(F,H,G,A,D) & k11_genealg1(F,G,H,A,k5_numbers,C,k5_numbers,k5_numbers) = k8_genealg1(F,H,G,A,C) & k11_genealg1(F,G,H,A,B,k5_numbers,k5_numbers,k5_numbers) = k8_genealg1(F,H,G,A,B) ) ) ) ) ) ) ) ) ) )).
fof(t43_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_geomtrap(A,B,C))) <=> m1_subset_1(D,u1_struct_0(A)) ) ) ) ) )).
fof(t43_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : v1_relat_1(k3_msafree2(k19_gfacirc1(A,B,C))) )).
fof(t43_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( m1_glib_000(C,B) => m1_glib_000(C,A) ) ) ) )).
fof(t43_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( r1_xxreal_0(C,k3_finseq_1(B)) => k3_finseq_1(k8_glib_001(A,B,1,C)) = C ) ) ) ) )).
fof(t43_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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) ) ) ) )).
fof(t43_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_003(A) ) => ! [B] : ! [C] : ! [D] : ( B != C => k1_funct_1(k7_glib_003(k13_glib_003(A,B,D)),C) = k1_funct_1(k7_glib_003(A),C) ) ) )).
fof(t43_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ 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(k1_nat_1(A,1),k3_finseq_1(k2_goboard2(D))) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(k2_goboard2(D))) & r1_xxreal_0(1,C) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1))) = k2_topreal1(2,D,C) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,1))) = k2_topreal1(2,D,k1_nat_1(C,1)) ) => ( r1_xxreal_0(k3_finseq_1(D),k1_nat_1(C,1)) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,B) ) ) ) ) ) ) ) )).
fof(t43_gobrd14,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t43_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_graph_1(D,A) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t43_graph_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(k8_graph_3(B,D,E))) => ( F = C => ( C = E | k2_graph_3(k8_graph_3(B,D,E),F,A) = k2_graph_3(B,C,A) ) ) ) ) ) ) ) )).
fof(t43_graph_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => r1_tarski(k5_graph_5(B,C,D,A),k7_graph_5(B)) ) ) ) )).
fof(t43_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k3_finseq_2(k1_numbers)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t43_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ v7_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ~ r1_xxreal_0(k5_card_1(k3_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,k1_nat_1(E,1)),k6_termord(A,B,C,k6_groeb_3(A,B,C,D,E))) ) ) ) ) ) ) )).
fof(t43_group_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t43_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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) ) ) ) )).
fof(t43_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_group_2(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ( ( E = B & F = C ) => k6_algstr_0(D,E,F) = k6_algstr_0(A,B,C) ) ) ) ) ) ) ) )).
fof(t43_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t43_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t43_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t43_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t43_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( 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) ) ) )).
fof(t43_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => k3_helly(A,B,C,D) = k3_helly(A,C,D,B) ) ) ) ) )).
fof(t43_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ! [F] : ( m1_subset_1(F,u1_struct_0(k1_complfld)) => ( ( k9_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))) = k9_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,k5_numbers),F),C)),k5_algstr_0(A,B,k4_vectsp_1(k1_complfld,A,k8_group_1(k1_complfld,k1_hahnban1(E,k5_numbers),F),C)))) = k2_xcmplx_0(k6_xcmplx_0(k4_hermitan(A,D,B),k3_xcmplx_0(k3_xcmplx_0(2,k9_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),k1_square_1(E))) & r1_xxreal_0(k5_numbers,k2_xcmplx_0(k6_xcmplx_0(k4_hermitan(A,D,B),k3_xcmplx_0(k3_xcmplx_0(2,k9_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),k1_square_1(E)))) ) ) ) ) ) ) ) ) )).
fof(t43_hfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( ~ r2_hidden(k5_numbers,B) => r2_fdiff_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_taylor_1(A)),B) ) ) ) )).
fof(t43_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => r2_hidden(k3_hilbert1(k4_hilbert1(A,B),k4_hilbert1(B,A)),k6_hilbert1) ) ) )).
fof(t43_hilbert3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( m1_hilbert3(D,C) => ~ ( ? [E] : r1_abian(E,k5_hilbert3(C,D,A)) & ! [E] : ~ r1_abian(E,k5_hilbert3(C,D,B)) & v2_hilbert3(k3_hilbert1(A,B)) ) ) ) ) ) )).
fof(t43_hurwitz,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(A,k1_complfld) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => r2_funct_2(k4_ordinal1,u1_struct_0(k1_complfld),k7_hurwitz(k3_polynom5(k1_complfld,A,B)),k3_polynom5(k1_complfld,k7_hurwitz(A),k2_complfld(B))) ) ) )).
fof(t43_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m3_ideal_1(C,A,B) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => m3_ideal_1(k2_partfun1(k4_ordinal1,u1_struct_0(A),C,k2_finseq_1(D)),A,B) ) ) ) ) )).
fof(t43_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & B != D & r1_incsp_1(A,D,C) ) ) ) ) )).
fof(t43_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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)))) ) ) )).
fof(t43_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( k3_int_1(A) = k5_numbers <=> v1_int_1(A) ) ) )).
fof(t43_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => ! [F] : ( v1_int_1(F) => ~ ( A != k5_numbers & B != k5_numbers & r1_int_1(k3_int_2(C,A),E) & r1_int_1(k3_int_2(D,B),F) & r1_int_2(A,B) & ! [G] : ( v1_int_1(G) => ! [H] : ( v1_int_1(H) => ! [I] : ( v1_int_1(I) => ~ ( ! [J] : ( v1_int_1(J) => ( ( k5_int_1(k6_xcmplx_0(k3_xcmplx_0(C,J),E),A) = k5_numbers & k5_int_1(k6_xcmplx_0(k3_xcmplx_0(D,J),F),B) = k5_numbers ) => r2_int_1(J,k2_xcmplx_0(H,k3_xcmplx_0(k4_int_1(A,k3_int_2(C,A)),G)),k3_xcmplx_0(k4_int_1(A,k3_int_2(C,A)),k4_int_1(B,k3_int_2(D,B)))) ) ) & k5_int_1(k6_xcmplx_0(k3_xcmplx_0(k4_int_1(C,k3_int_2(C,A)),H),k4_int_1(E,k3_int_2(C,A))),k4_int_1(A,k3_int_2(C,A))) = k5_numbers & k5_int_1(k6_xcmplx_0(k3_xcmplx_0(k4_int_1(D,k3_int_2(D,B)),I),k4_int_1(F,k3_int_2(D,B))),k4_int_1(B,k3_int_2(D,B))) = k5_numbers & k5_int_1(k6_xcmplx_0(k3_xcmplx_0(k4_int_1(A,k3_int_2(C,A)),G),k6_xcmplx_0(I,H)),k4_int_1(B,k3_int_2(D,B))) = k5_numbers ) ) ) ) ) ) ) ) ) ) ) )).
fof(t43_int_5,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t43_integr11,axiom,( ! [A] : ( ( 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,k27_sin_cos),k2_fdiff_9))) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( k2_xcmplx_0(1,k1_funct_1(k18_sin_cos,B)) != k5_numbers & k6_xcmplx_0(1,k1_funct_1(k18_sin_cos,B)) != k5_numbers ) ) ) ) => ( r2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k27_sin_cos),k2_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k27_sin_cos),k2_fdiff_9),A),B) = k7_xcmplx_0(1,k6_xcmplx_0(1,k1_funct_1(k18_sin_cos,B))) ) ) ) ) ) )).
fof(t43_integr12,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( 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,D,E)),C)) & r2_relset_1(k1_numbers,k1_numbers,C,k2_sin_cos9) & r1_tarski(F,k2_rcomp_1(k4_xcmplx_0(1),1)) & r2_relset_1(k1_numbers,k1_numbers,E,k1_taylor_1(2)) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,F) => ( k1_funct_1(B,G) = k7_xcmplx_0(1,k3_xcmplx_0(k2_xcmplx_0(1,k1_square_1(G)),k1_funct_1(k2_sin_cos9,G))) & k1_funct_1(D,G) = 1 & ~ r1_xxreal_0(k1_funct_1(C,G),k5_numbers) ) ) ) & F = k1_relset_1(k1_numbers,B) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k3_taylor_1)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k3_taylor_1)),k3_seq_4(A))) ) ) ) ) ) ) ) )).
fof(t43_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,D) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => k1_funct_1(C,E) = 1 ) ) & r2_relset_1(k1_numbers,k1_numbers,B,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,C,k1_taylor_1(2))))) & r1_tarski(D,k2_rcomp_1(k4_xcmplx_0(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,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_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)),k7_xcmplx_0(1,2)),k2_seq_4(A)),k1_funct_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)),k7_xcmplx_0(1,2)),k3_seq_4(A))) ) ) ) ) ) )).
fof(t43_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k7_xcmplx_0(k7_xcmplx_0(k1_funct_1(k18_sin_cos,k1_funct_1(k27_sin_cos,D)),k1_square_1(k1_funct_1(k16_sin_cos,D))),k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k27_sin_cos,D)))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_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) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k2_fdiff_9),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k2_fdiff_9),k3_seq_4(A))) ) ) ) ) )).
fof(t43_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t43_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [C] : ( m1_integra1(C,A) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t43_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k3_xcmplx_0(k28_sin_cos,2)) => k2_integra5(A,k18_sin_cos) = k5_numbers ) ) )).
fof(t43_integra9,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( ~ 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] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => r1_xxreal_0(k5_numbers,k1_funct_1(k1_integra5(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,A,A),B),C)) ) ) ) => r1_xxreal_0(k5_numbers,k2_integra9(B,A)) ) ) ) )).
fof(t43_interva1,axiom,( ! [A] : ( ~ 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) ) ) )).
fof(t43_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => r2_hidden(k3_intpro_1(k3_intpro_1(k4_intpro_1(A,C),B),k3_intpro_1(k4_intpro_1(A,C),k4_intpro_1(B,C))),k8_intpro_1) ) ) ) )).
fof(t43_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & 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) ) ) ) )).
fof(t43_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t43_jgraph_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( 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] : ( 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] : ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t43_jgraph_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( 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(k2_xcmplx_0(k3_xcmplx_0(A,k17_euclid(F)),B),k2_xcmplx_0(k3_xcmplx_0(C,k18_euclid(F)),D)) ) => v5_pre_topc(E,k15_euclid(2),k15_euclid(2)) ) ) ) ) ) ) )).
fof(t43_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(B)) & ~ r1_xxreal_0(A,k7_xcmplx_0(k18_euclid(B),k12_euclid(B))) & ? [C] : ( 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(k5_numbers,k17_euclid(C)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(C)) ) ) ) ) ) )).
fof(t43_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t43_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t43_jordan,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ? [D] : ( m1_borsuk_2(D,k15_euclid(A),B,C) & ? [E] : ( 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 ) ) ) ) ) )).
fof(t43_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( ~ r1_xxreal_0(C,1) & r1_xxreal_0(C,D) & ~ r1_xxreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,1))),D) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1)))),k8_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),D,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1)))),k9_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),C,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1)))),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),D,k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))))),k8_jordan6(B)) ) ) ) ) ) )).
fof(t43_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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,D))) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(k1_jordan8(E,C))) & r1_xxreal_0(C,D) ) => r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,C),B,1)),k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,D),A,1))) ) ) ) ) ) ) )).
fof(t43_jordan1g,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,C) & ~ r1_xxreal_0(k3_finseq_1(k1_jordan8(B,A)),C) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,k1_matrix_0(k1_jordan8(B,A))),k10_xtuple_0(k2_jordan1e(B,A))) ) ) ) ) )).
fof(t43_jordan1h,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t43_jordan1j,axiom,( ! [A] : ( ( v4_topreal1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( 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 ) ) ) )).
fof(t43_jordan1k,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( 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) ) ) ) )).
fof(t43_jordan21,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( r1_tarski(A,B) & k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)) = k2_xcmplx_0(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(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)),2))))) ) => ( v1_xboole_0(k9_subset_1(u1_struct_0(k15_euclid(2)),A,k6_jordan6(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)),2)))) | r1_xxreal_0(k18_euclid(k1_jordan21(A)),k18_euclid(k1_jordan21(B))) ) ) ) ) )).
fof(t43_jordan23,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t43_jordan2c,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t43_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t43_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t43_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(A)) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k1_matrix_0(k2_goboard2(A))) & E = a_2_1_jordan5d(A,B) & k18_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),A,D)) = k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,B)) & C = k1_xxreal_2(E) ) => r1_xxreal_0(k17_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),A,D)),k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,B))) ) ) ) ) ) ) )).
fof(t43_jordan6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t43_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t43_kurato_1,axiom,( 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) )).
fof(t43_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k5_finsub_1(C)) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t43_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t43_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t43_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : r1_tarski(k17_lexbfs(k6_glib_000(A),k4_ordinal1,k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),k13_lexbfs(A,k16_lexbfs(A),B)),C),k2_finsub_1(k1_zfmisc_1(k4_ordinal1),k2_finseq_1(k15_glib_000(A)),k2_finseq_1(k7_nat_d(k15_glib_000(A),B)))) ) ) )).
fof(t43_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_limfunc1(A) & ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k1_funct_1(B,C),k1_funct_1(A,C)) ) ) => v2_limfunc1(B) ) ) ) )).
fof(t43_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r1_limfunc2(C,B) => ( r1_limfunc2(k26_valued_1(k1_numbers,k1_numbers,C,A),B) & k1_limfunc2(k26_valued_1(k1_numbers,k1_numbers,C,A),B) = k3_xcmplx_0(A,k1_limfunc2(C,B)) ) ) ) ) ) )).
fof(t43_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(A,k2_xcmplx_0(A,D)))) & k1_funct_1(B,E) = k2_limfunc2(B,A) ) ) ) ) | r5_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t43_lopban_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & 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)) ) ) ) )).
fof(t43_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k24_lpspacc1(A,B,C))) => ( ? [E] : ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) & r2_hidden(E,k13_lpspacc1(A,B,C)) & D = k17_lpspacc1(A,B,C,E) & k2_normsp_0(k24_lpspacc1(A,B,C),D) = k1_mesfunc6(A,B,C,k56_valued_1(A,k2_numbers,E)) ) & ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( r2_hidden(E,D) => k1_mesfunc6(A,B,C,k56_valued_1(A,k2_numbers,E)) = k2_normsp_0(k24_lpspacc1(A,B,C),D) ) ) ) ) ) ) ) )).
fof(t43_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t43_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( v2_xxreal_0(F) & v1_xreal_0(F) ) => ( ( 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) ) ) ) ) ) ) ) )).
fof(t43_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_hilbert1)) => ( ( r8_ltlaxio1(C,A) & r8_ltlaxio1(C,k3_hilbert1(A,B)) ) => r8_ltlaxio1(C,B) ) ) ) ) )).
fof(t43_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(k3_hilbert1(A,k4_ltlaxio1(B,k1_ltlaxio1(B))),k1_ltlaxio1(A))) ) ) )).
fof(t43_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t43_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t43_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,C,C) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,k1_numbers,C,C) & m2_finseq_1(E,k3_finseq_2(k1_numbers)) ) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) & v4_matrix10(D) & v4_matrix10(E) ) => v4_matrix10(k4_matrix10(C,k6_matrix10(C,A,D),k6_matrix10(C,B,E))) ) ) ) ) ) ) )).
fof(t43_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),k1_nat_1(A,2),k1_nat_1(A,2)) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( m1_matrix_2(D,k3_matrix_2(k1_nat_1(A,2))) => ! [E] : ( ( 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] : ( m1_matrix_2(F,k3_matrix_2(k1_nat_1(A,2))) => ! [G] : ( m1_matrix_2(G,k3_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(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),k2_funct_2(k2_finseq_1(k1_nat_1(A,2)),E),F) => k3_funct_2(k3_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(k3_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)) ) ) ) ) ) ) ) ) ) )).
fof(t43_matrix13,axiom,( ! [A] : ( ( v1_finset_1(A) & v1_setfam_1(A) & m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) ) => ? [B] : ( v7_ordinal1(B) & r1_tarski(A,k2_finseq_1(B)) ) ) )).
fof(t43_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(A),B,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,B) & D = k4_matrix14(A,B,C) ) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( 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_0(u1_struct_0(A),D,E,F) = k5_struct_0(A) ) & ( ( E = C & F = 1 ) => k3_matrix_0(u1_struct_0(A),D,E,F) = k5_struct_0(A) ) & ( ( E = 1 & F = 1 ) => k3_matrix_0(u1_struct_0(A),D,E,F) = k4_struct_0(A) ) & ( ( E = C & F = C ) => k3_matrix_0(u1_struct_0(A),D,E,F) = k4_struct_0(A) ) & ( ~ ( ( E = 1 | E = C ) & ( F = 1 | F = C ) ) => ( ( E = F => k3_matrix_0(u1_struct_0(A),D,E,F) = k5_struct_0(A) ) & ( E != F => k3_matrix_0(u1_struct_0(A),D,E,F) = k4_struct_0(A) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t43_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ( ( r1_tarski(k10_xtuple_0(E),k4_finseq_1(C)) & k4_finseq_1(C) = k4_finseq_1(D) & ! [F] : ( v7_ordinal1(F) => ( r2_hidden(F,k7_subset_1(k4_ordinal1,k4_finseq_1(C),k10_xtuple_0(E))) => ( k7_matrix_0(u1_struct_0(B),C,F) = k5_finseq_2(u1_struct_0(B),k1_matrix_0(C),k4_struct_0(B)) & k7_matrix_0(u1_struct_0(B),D,F) = k5_finseq_2(u1_struct_0(B),k1_matrix_0(D),k4_struct_0(B)) ) ) ) ) => ( r1_xxreal_0(A,k5_numbers) | k4_matrix15(B,C,D) = k4_matrix15(B,k1_matrix13(u1_struct_0(B),C,A,k5_card_1(k2_finseq_1(k1_matrix_0(C))),E,k5_matrix13(k2_finseq_1(k1_matrix_0(C)))),k1_matrix13(u1_struct_0(B),D,A,k5_card_1(k2_finseq_1(k1_matrix_0(D))),E,k5_matrix13(k2_finseq_1(k1_matrix_0(D))))) ) ) ) ) ) ) ) )).
fof(t43_matrix16,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ( v2_matrix16(D,u1_struct_0(A)) => 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(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))) ) ) ) ) ) )).
fof(t43_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_finseq_1(D,C) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( ( v1_matrix_0(G) & m2_finseq_1(G,k3_finseq_2(C)) ) => ~ ( r1_xboole_0(k10_xtuple_0(D),k10_xtuple_0(k8_matrix_0(C,G,E))) & k7_partfun1(C,D,A) = k3_matrix_0(C,G,B,F) & r2_hidden(A,k4_finseq_1(D)) & r2_hidden(B,k4_finseq_1(G)) & E = F ) ) ) ) ) ) ) ) )).
fof(t43_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) ) => k2_matrix_3(A,k1_matrix_4(A,B,C)) = k1_matrix_4(A,C,B) ) ) ) ) )).
fof(t43_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v4_matrix_6(C,A,B) => k4_matrix_3(B,k4_matrix_0(u1_struct_0(B),C),C) = k4_matrix_3(B,C,k4_matrix_0(u1_struct_0(B),C)) ) ) ) ) )).
fof(t43_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_6(D,A,B) & r1_matrix_8(A,B,C,D) ) => r1_matrix_8(A,B,k1_matrix_6(A,B,C),k1_matrix_6(A,B,D)) ) ) ) ) ) )).
fof(t43_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => k17_rvsum_1(k9_seq_4(A)) = k4_xcmplx_0(k17_rvsum_1(A)) ) )).
fof(t43_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( 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_0(D))) => k16_matrix_0(A,u1_struct_0(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),k16_matrix_0(A,u1_struct_0(B),D)),E)) ) ) ) ) ) ) )).
fof(t43_matrixr1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) ) => k7_matrixr1(A,k3_matrixr1(B,C)) = k3_matrixr1(k7_matrixr1(A,B),k7_matrixr1(A,C)) ) ) ) ) )).
fof(t43_matrixr2,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(A),B,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => k12_matrix_3(B,A,C) = k12_matrix_3(B,A,k4_matrix_0(u1_struct_0(A),C)) ) ) ) )).
fof(t43_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_matrlin(F,A,C) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t43_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ 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] : ( ( 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) ) ) ) ) ) )).
fof(t43_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(t43_matrprob,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(C) & k3_finseq_1(B) = k1_matrix_0(C) ) => ( r1_xxreal_0(k3_finseq_1(B),k5_numbers) | k4_matrix_0(k1_numbers,k6_matrprob(A,B,C)) = k6_matrprob(B,A,k4_matrix_0(k1_numbers,C)) ) ) ) ) ) )).
fof(t43_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,u1_struct_0(k2_vectsp_1),A,A) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ( 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) <=> k1_matrix_6(A,k2_vectsp_1,B) = C ) ) ) ) ) )).
fof(t43_mcart_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t43_measure6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( v3_xxreal_2(A) => k3_seq_4(A) = k4_xcmplx_0(k2_seq_4(k3_measure6(A))) ) ) )).
fof(t43_member_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k8_member_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k1_xxreal_3(A,B)) ) ) )).
fof(t43_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ~ ( r2_hidden(D,k9_xtuple_0(k8_memstr_0(A,B,C))) & ~ r2_hidden(D,k9_xtuple_0(C)) & D != k4_struct_0(B) ) ) ) ) )).
fof(t43_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( r2_mesfun6c(A,B,C,D) => ( ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ~ ( E = k1_relset_1(A,D) & r1_mesfun6c(A,B,D,E) ) ) | r1_xxreal_0(k9_complex1(k1_mesfun6c(A,B,C,D)),k1_mesfunc6(A,B,C,k55_valued_1(A,k2_numbers,D))) ) ) ) ) ) ) )).
fof(t43_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(t43_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t43_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,k6_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) ) ) ) ) ) ) ) )).
fof(t43_mesfunc6,axiom,( ! [A] : ( v1_xreal_0(A) => k9_complex1(A) = k3_extreal1(A) ) )).
fof(t43_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ( ( v2_mesfunc9(B,A) & v1_mesfunc8(B,A,k6_numbers) ) => v1_mesfunc8(k4_mesfunc9(A,B),A,k6_numbers) ) ) ) )).
fof(t43_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_midsp_1(B,A) => ! [C] : ( m1_midsp_1(C,A) => ! [D] : ( 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)) ) ) ) ) )).
fof(t43_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( 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))) ) ) )).
fof(t43_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(t43_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ~ ( r3_modelc_2(A,k7_modelc_2(B,C)) & ~ r2_modelc_2(A,B) & ~ r2_modelc_2(A,C) ) ) ) ) )).
fof(t43_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => m1_subset_1(k11_modelc_3(A),k23_modelc_3(A)) ) )).
fof(t43_moebius1,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k4_ordinal1)) ) => ( 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(k4_ordinal1,k4_moebius1(A),k4_moebius1(B))) ) ) ) )).
fof(t43_monoid_0,axiom,( k4_monoid_0 = g3_algstr_0(k4_ordinal1,k23_binop_2) )).
fof(t43_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( m1_subset_1(D,k3_card_3(u3_msualg_1(A,C))) => ! [E] : ( m1_trees_1(E,k9_xtuple_0(D)) => m1_subset_1(k5_trees_2(D,E),k3_card_3(u3_msualg_1(A,C))) ) ) ) ) ) )).
fof(t43_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( m2_pboole(D,u1_struct_0(A),C,u3_msualg_1(A,B)) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( 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] : ( ( v1_relat_1(G) & v1_funct_1(G) & v1_finseq_1(G) ) => ( ( k3_finseq_1(G) = k3_finseq_1(F) & ! [H] : ( v7_ordinal1(H) => ( r2_hidden(H,k4_finseq_1(F)) => ! [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) ) ) ) ) ) ) ) ) )).
fof(t43_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m3_pboole(D,A,k1_mboolean(A,C)) => ( r1_pboole(A,B,D) => r2_pboole(A,k4_mssubfam(A,C,D),B) ) ) ) ) )).
fof(t43_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(t43_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_mycielsk(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t43_nat_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( v7_ordinal1(B) => r1_tarski(k10_xtuple_0(k7_nat_1(A,B)),k10_xtuple_0(A)) ) ) )).
fof(t43_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => k22_pre_poly(k8_newton,k12_nat_3(A)) = k1_tarski(A) ) )).
fof(t43_nat_4,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ( ( r1_tarski(A,B) & r1_tarski(B,k4_ordinal1) ) => ( r2_hidden(k1_xboole_0,B) | r1_xxreal_0(k3_wsierp_1(k14_finseq_1(A)),k3_wsierp_1(k14_finseq_1(B))) ) ) ) )).
fof(t43_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,k7_nat_d(A,B)) | r1_xxreal_0(1,k6_xcmplx_0(A,B)) ) => k2_xcmplx_0(k7_nat_d(A,B),B) = A ) ) ) )).
fof(t43_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,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(k4_ordinal1,u1_struct_0(A),u1_struct_0(B),E,D)) ) ) ) ) ) ) ) ) )).
fof(t43_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(1))) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [F] : ( ( 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 = k9_finseq_1(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) ) ) ) ) ) ) ) ) )).
fof(t43_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m1_subset_1(B,k4_card_3(k4_prvect_2(A))) => ! [C] : ( m1_subset_1(C,k4_card_3(k4_prvect_2(A))) => ! [D] : m1_subset_1(k1_funct_4(B,k11_card_3(k4_prvect_2(A),C,D)),k4_card_3(k4_prvect_2(A))) ) ) ) )).
fof(t43_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k5_nat_d(C,k5_nat_d(B,A)) = k5_nat_d(k5_nat_d(C,B),A) ) ) ) )).
fof(t43_nfcont_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t43_nfcont_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k4_ordinal1) => ( 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) ) ) ) ) ) ) ) )).
fof(t43_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(k7_normform(A))) => ! [C] : ( 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)) ) ) )).
fof(t43_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t43_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_oppcat_1(C,B,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k3_funct_2(u1_struct_0(B),u1_struct_0(k2_oppcat_1(A)),k7_cat_1(B,k2_oppcat_1(A),k11_oppcat_1(B,A,C)),D) = k3_oppcat_1(A,k3_funct_2(u1_struct_0(B),u1_struct_0(A),k7_cat_1(B,A,C),D)) ) ) ) ) )).
fof(t43_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(A))) => ! [F] : ( ( v1_funct_1(F) & v1_nfcont_3(F,k4_real_ns1(A)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [G] : ( ( v1_funct_1(G) & v1_nfcont_3(G,k4_real_ns1(A)) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ( ( D = k2_rcomp_1(B,C) & k1_relset_1(k1_numbers,F) = k3_integra5(B,C) & k1_relset_1(k1_numbers,H) = k3_integra5(B,C) & k1_relset_1(k1_numbers,G) = k3_integra5(B,C) & r2_ndiff_3(k4_real_ns1(A),F,D) & k7_partfun1(u1_struct_0(k4_real_ns1(A)),F,B) = E & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,D) => k1_ndiff_3(k4_real_ns1(A),F,I) = k7_partfun1(u1_struct_0(k4_real_ns1(A)),G,I) ) ) & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,k3_integra5(B,C)) => k1_funct_1(H,I) = k3_rlvect_1(k4_real_ns1(A),E,k6_integr18(k4_real_ns1(A),G,B,I)) ) ) ) => ( r1_xxreal_0(C,B) | r2_relset_1(k1_numbers,u1_struct_0(k4_real_ns1(A)),F,H) ) ) ) ) ) ) ) ) ) ) )).
fof(t43_orders_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t43_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m2_orders_1(B,k1_orders_1(u1_struct_0(A)),k6_partfun1(k1_orders_1(u1_struct_0(A)))) => k3_tarski(k4_orders_2(A,B)) != k1_xboole_0 ) ) )).
fof(t43_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => k12_ordinal2(A,k5_ordinal1) = 1 ) )).
fof(t43_ordinal3,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( v3_ordinal1(B) => ( k1_xboole_0 != k9_xtuple_0(A) => k4_ordinal2(k1_ordinal3(B,A)) = k10_ordinal2(B,k4_ordinal2(A)) ) ) ) )).
fof(t43_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ( v4_ordinal1(A) => ( A = k5_numbers | ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) ) => ( ( k9_xtuple_0(B) = A & ! [C] : ( v3_ordinal1(C) => ( r2_hidden(C,A) => k1_funct_1(B,C) = k3_ordinal5(C) ) ) ) => k3_ordinal5(A) = k8_ordinal2(B) ) ) ) ) ) )).
fof(t43_osafree,axiom,( ! [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) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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) ) ) ) )).
fof(t43_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m2_subset_1(C,k14_msualg_2(A,B),k13_osalg_2(A,B)) => ! [D] : ( 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) ) ) ) ) )).
fof(t43_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ r2_parsp_2(A,B,C,D,E) ) ) ) ) ) ) )).
fof(t43_partfun2,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,D))) ) => ( v3_funct_1(k2_partfun1(C,D,E,B)) => v3_funct_1(k2_partfun1(C,D,k2_partfun1(C,D,E,A),B)) ) ) ) ) )).
fof(t43_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => r2_pboole(A,k1_pboole(A),B) ) )).
fof(t43_pcs_0,axiom,( ! [A] : ( l1_pcs_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ! [D] : ( r2_hidden(k4_tarski(C,D),k25_pcs_0(A,B)) <=> ( r2_hidden(C,B) & r2_hidden(D,B) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r2_hidden(E,C) & r2_hidden(F,D) ) => r1_pcs_0(A,E,F) ) ) ) ) ) ) ) )).
fof(t43_pdiff_4,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [D] : ( ( 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(k6_xcmplx_0(k10_pdiff_1(3,2,D,A),k10_pdiff_1(3,3,C,A)),k6_xcmplx_0(k10_pdiff_1(3,3,B,A),k10_pdiff_1(3,1,D,A)),k6_xcmplx_0(k10_pdiff_1(3,1,C,A),k10_pdiff_1(3,2,B,A))) ) ) ) ) )).
fof(t43_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m1_rcomp_1(C,k3_funct_2(k1_euclid(3),k1_numbers,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] : ( ( v9_ordinal1(D) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,E) = k1_tarski(k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(1,3),B)) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),C) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,1,k1_pdiff_3(3,3,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,1,k1_pdiff_3(3,3,A),B))))) & k7_pdiff_5(A,B) = k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,1,k1_pdiff_3(3,3,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,1,k1_pdiff_3(3,3,A),B))))) ) ) ) ) ) ) ) ) )).
fof(t43_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( r1_xxreal_0(1,F) & r1_xxreal_0(F,A) & r1_xxreal_0(C,D) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,k1_rcomp_1(C,D)) => r2_hidden(k1_funct_1(k6_pdiff_1(A,F,E),G),k1_relset_1(k1_euclid(A),B)) ) ) & ! [G] : ( 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] : ( v1_xreal_0(G) => ! [H] : ( m2_finseq_2(H,k1_numbers,k1_euclid(A)) => ~ ( r2_hidden(G,k1_rcomp_1(C,D)) & H = k1_funct_1(k6_pdiff_1(A,F,E),G) & k5_real_1(k7_partfun1(k1_numbers,B,k1_funct_1(k6_pdiff_1(A,F,E),D)),k7_partfun1(k1_numbers,B,k1_funct_1(k6_pdiff_1(A,F,E),C))) = k3_xcmplx_0(k6_xcmplx_0(D,C),k10_pdiff_1(A,F,B,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t43_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(k4_real_ns1(A))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,k1_numbers,u1_struct_0(k4_real_ns1(A)),E,D)) & k7_partfun1(k1_numbers,D,k6_normsp_1(k4_real_ns1(A),E)) = k1_seq_2(k8_funct_2(k4_ordinal1,k1_numbers,u1_struct_0(k4_real_ns1(A)),E,D)) ) ) ) ) ) ) ) ) )).
fof(t43_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( A != k5_numbers & r1_xxreal_0(A,k4_xcmplx_0(A)) ) ) )).
fof(t43_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B))) => k10_pnproc_1(A,B,k12_pnproc_1(A,B),C) = C ) ) )).
fof(t43_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k17_polyform(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k17_polyform(A,B))) => ( C = D <=> ! [E] : ( m1_subset_1(E,k8_polyform(A,B)) => ( r2_hidden(E,C) <=> r2_hidden(E,D) ) ) ) ) ) ) ) )).
fof(t43_polynom8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(k1_algseq_1(A,B),D) & r1_xxreal_0(k1_algseq_1(A,C),D) ) => ( r1_xxreal_0(D,k5_numbers) | ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_polynom8(A,E,k2_nat_1(2,D)) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k6_polynom8(k2_nat_1(2,D),A,k6_polynom8(k2_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,k2_nat_1(2,D)))) ) ) ) ) ) ) ) ) )).
fof(t43_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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) ) ) ) ) ) ) ) )).
fof(t43_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => k2_power(A,B) = k3_prepower(A,B) ) ) )).
fof(t43_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t43_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( A != k5_numbers => k3_prepower(A,k6_xcmplx_0(B,C)) = k7_xcmplx_0(k1_newton(A,B),k1_newton(A,C)) ) ) ) ) )).
fof(t43_prob_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( v5_relat_1(D,C) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t43_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ( r2_hidden(C,k4_cqc_the1(A)) => r2_hidden(k9_cqc_lang(A,B,C),k4_cqc_the1(A)) ) ) ) ) )).
fof(t43_pscomp_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t43_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r6_pboole(A,k3_pboole(A,C,k1_pzfmisc1(A,B)),k1_pzfmisc1(A,B)) => r1_pboole(A,B,C) ) ) ) )).
fof(t43_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( r1_qc_lang2(A,B,k13_qc_lang1(A,C)) <=> B = C ) ) ) ) )).
fof(t43_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t43_quatern2,axiom,( k16_quatern2(k5_struct_0(k15_quatern2)) = k5_struct_0(k15_quatern2) )).
fof(t43_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ~ ( k6_xcmplx_0(k28_quaterni(A),k28_quaterni(B)) != k5_numbers & r1_xxreal_0(k6_xcmplx_0(k2_xcmplx_0(k1_square_1(k28_quaterni(A)),k1_square_1(k28_quaterni(B))),k3_xcmplx_0(k3_xcmplx_0(2,k28_quaterni(A)),k28_quaterni(B))),k5_numbers) ) ) ) )).
fof(t43_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => k27_quaterni(A) = k6_quaterni(k13_quaterni(A),k4_xcmplx_0(k14_quaterni(A)),k4_xcmplx_0(k15_quaterni(A)),k4_xcmplx_0(k16_quaterni(A))) ) )).
fof(t43_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k19_quofield(A))) => ! [C] : ( 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) ) ) ) )).
fof(t43_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ! [F] : ( m2_vectsp_6(F,A,C,k2_ranknull(B,C,D,E)) => ( v2_funct_1(k2_partfun1(u1_struct_0(B),u1_struct_0(C),D,E)) => r1_vectsp_6(A,C,k8_ranknull(A,B,C,k9_ranknull(A,B,C,E,D,F),D),F) ) ) ) ) ) ) ) )).
fof(t43_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_numbers)) => ( C = D => ( v2_connsp_1(C,k4_topmetr(A,B)) <=> v6_xxreal_2(D) ) ) ) ) ) ) )).
fof(t43_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ! [B] : ( v7_ordinal1(B) => k9_nat_1(k1_numbers,k4_real_3(A),B) != k5_numbers ) & v1_rat_1(A) ) ) )).
fof(t43_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v1_relat_1(D) => ( r2_hidden(k4_tarski(B,C),k3_relat_1(D,k4_relat_1(A))) <=> ( r2_hidden(C,A) & r2_hidden(k4_tarski(B,C),D) ) ) ) )).
fof(t43_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ! [D] : ! [E] : ( ~ ( ~ r1_xboole_0(D,k7_relset_1(B,A,k3_relset_1(A,B,C),E)) & ! [F] : ! [G] : ~ ( r2_hidden(F,D) & r2_hidden(G,E) & r2_hidden(F,k1_relset_2(B,A,k3_relset_1(A,B,C),G)) ) ) & ~ ( ? [F] : ? [G] : ( 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)) ) ) ) )).
fof(t43_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ! [D] : ( ( ( 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) ) ) )).
fof(t43_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ( r3_rewrite2(A,k7_rewrite2(A,B),C,D) => r3_rewrite2(A,B,C,D) ) ) ) ) )).
fof(t43_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_afinsq_1(D))) => ! [F] : ( ( ~ 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,C),k4_tarski(B,C)),k1_rewrite3(D,E,F)) ) ) ) ) )).
fof(t43_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t43_rfunct_2,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(t43_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t43_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_seq_2(C) => ( ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(A,D) => r1_xxreal_0(B,k1_funct_1(C,D)) ) ) <=> r1_xxreal_0(B,k1_funct_1(k3_rinfsup1(C),A)) ) ) ) ) ) )).
fof(t43_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_rlaffin1(B,A) & r1_tarski(C,B) ) => v1_rlaffin1(C,A) ) ) ) ) )).
fof(t43_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rlsub_1(C,A) => r2_hidden(B,k3_rlsub_1(A,B,C)) ) ) ) )).
fof(t43_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ( r1_rlsub_2(A,B,C) <=> ! [D] : ( m2_rlsub_1(D,A,B) => ! [E] : ( m2_rlsub_1(E,A,C) => ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t43_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => k4_rlvect_1(A,k6_finseq_1(u1_struct_0(A))) = k4_struct_0(A) ) )).
fof(t43_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => r1_rlvect_2(A,k8_rlvect_2(A,k5_numbers,B),k4_rlvect_2(A)) ) ) )).
fof(t43_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_rmod_2(D,A,B) => ( r2_hidden(k4_struct_0(B),k3_rmod_2(A,B,C,D)) <=> r1_struct_0(D,C) ) ) ) ) ) )).
fof(t43_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ! [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 ) ) ) ) ) ) ) ) ) ) ) )).
fof(t43_rmod_4,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_rmod_4(C,A,B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t43_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( 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)) ) ) )).
fof(t43_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t43_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_orders_3(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ v4_roughs_1(B,A) ) ) )).
fof(t43_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k2_rpr_1(A,B,k3_subset_1(A,B)) = k5_numbers ) ) )).
fof(t43_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r1_struct_0(B,C) => k3_rusub_1(A,k1_rlvect_1(A,C,D),B) = u1_struct_0(B) ) ) ) ) ) )).
fof(t43_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ( r1_rusub_2(A,B,C) <=> ! [D] : ( m2_rusub_1(D,A,B) => ! [E] : ( m2_rusub_1(E,A,C) => ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t43_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t43_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(t43_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => C = k5_rvsum_1(A,k9_rvsum_1(A,C,B),B) ) ) ) )).
fof(t43_rvsum_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( 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)) = k3_xcmplx_0(A,k19_rvsum_1(B)) ) ) )).
fof(t43_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( 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(k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),k5_card_1(D)),7)))) ) ) ) ) ) ) ) )).
fof(t43_scmfsa10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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_xcmplx_0(A,B),C) ) ) ) )).
fof(t43_scmfsa8c,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ~ ( A != B & r1_scmfsa7b(k7_scmfsa_2(C,B),A) ) ) ) ) )).
fof(t43_scmfsa_2,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(k1_funct_4(A,B),u1_struct_0(k1_scmfsa_2)) ) ) ) )).
fof(t43_scmfsa_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ( ? [E] : ( v1_funct_1(E) & v1_funct_2(E,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1))) & ! [F] : ( v7_ordinal1(F) => ( ~ ( r1_xxreal_0(k3_funct_2(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(D,B,C,A),F)),k3_funct_2(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(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(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(D,B,C,A),F)) != k5_numbers ) & ( k3_funct_2(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(D,B,C,A),F)) = k5_numbers => r1_xxreal_0(k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(D,B,C,A),F),C),k5_numbers) ) & ( r1_xxreal_0(k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(D,B,C,A),F),C),k5_numbers) => k3_funct_2(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,E,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(D,B,C,A),F)) = k5_numbers ) ) ) ) => ( r6_scmfsa7b(k2_scmfsa_9(C,B),D,A) & r5_scmfsa7b(k2_scmfsa_9(C,B),D,A) ) ) ) ) ) ) )).
fof(t43_scmpds_2,axiom,( ! [A] : ( ( 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] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t43_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => k5_memstr_0(2,k1_scmpds_2,k6_scmpds_4(k5_scmpds_6(D,E,C),B,A)) = k1_nat_1(k5_card_1(C),1) ) ) ) ) ) )).
fof(t43_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ! [G] : ( v7_ordinal1(G) => ( r1_xxreal_0(k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),F)),k5_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,k1_nat_1(k5_card_1(C),3))) ) ) ) ) ) ) ) ) )).
fof(t43_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : k7_scmyciel(A,B) = k7_scmyciel(A,k3_xboole_0(B,k3_tarski(A))) ) )).
fof(t43_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t43_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v9_ordinal1(A) => v9_ordinal1(k32_valued_1(k4_ordinal1,k1_numbers,A)) ) ) )).
fof(t43_seq_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_membered(A) ) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => r1_xxreal_0(B,C) ) ) => r1_xxreal_0(B,k3_seq_4(A)) ) ) ) )).
fof(t43_seqfunc,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(k1_numbers,k1_numbers)))) ) => ( ( r3_seqfunc(k1_numbers,B,A) & ! [C] : ( v7_ordinal1(C) => 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)) ) ) )).
fof(t43_seqm_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( k3_finseq_1(A) = k1_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,k1_nat_1(D,1)) ) ) ) ) ) )).
fof(t43_series_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [C] : ( v7_ordinal1(C) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,B,C),k5_numbers) ) & r1_xxreal_0(k9_nat_1(k1_numbers,k1_series_3(B),A),k5_numbers) ) ) ) )).
fof(t43_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( 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,k1_nat_1(C,1)),k1_newton(B,k1_nat_1(C,1)))) ) ) ) ) )).
fof(t43_setfam_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ( r2_hidden(B,A) => ( r2_hidden(B,k8_setfam_1(A,C)) <=> ! [D] : ( r2_hidden(D,C) => r2_hidden(B,D) ) ) ) ) )).
fof(t43_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(B) => k3_prob_1(A,k4_setlim_1(A,B)) = k1_kurato_0(A,B) ) ) )).
fof(t43_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => k9_nat_1(k9_setfam_1(B),k2_setlim_1(B,k1_setlim_2(B,C,D)),A) = k9_subset_1(B,k9_nat_1(k9_setfam_1(B),k2_setlim_1(B,C),A),k9_nat_1(k9_setfam_1(B),k2_setlim_1(B,D),A)) ) ) ) )).
fof(t43_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( 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)) ) ) ) ) ) )).
fof(t43_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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)) ) ) )).
fof(t43_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t43_simplex0,axiom,( ! [A] : ! [B] : ( v1_int_1(B) => ! [C] : ( m1_simplex0(C,A) => r1_xxreal_0(k6_simplex0(k8_simplex0(A,C,B)),k6_simplex0(C)) ) ) )).
fof(t43_simplex1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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] : ( ( 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) & k2_xcmplx_0(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 ) ) ) ) )).
fof(t43_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => r2_funct_2(k4_ordinal1,k1_numbers,k4_sin_cos(A),k7_comseq_3(k3_sin_cos(A))) ) )).
fof(t43_sin_cos2,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k5_sin_cos2,k1_numbers)) )).
fof(t43_sin_cos3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,k2_xcmplx_0(A,k3_xcmplx_0(k4_xcmplx_0(B),k7_complex1))) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,A),k1_funct_1(k3_sin_cos2,B)),k3_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,A),k1_funct_1(k1_sin_cos2,B))),k7_complex1)) ) ) )).
fof(t43_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( k19_sin_cos(A) != k5_numbers & k19_sin_cos(B) != k5_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))) ) ) ) )).
fof(t43_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => k2_sin_cos2(k3_xcmplx_0(3,A)) = k2_xcmplx_0(k3_xcmplx_0(3,k2_sin_cos2(A)),k3_xcmplx_0(4,k1_newton(k2_sin_cos2(A),3))) ) )).
fof(t43_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ~ ( ~ r1_xxreal_0(A,k2_xcmplx_0(k28_sin_cos,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B))) & r1_xxreal_0(A,k2_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B))) & r1_xxreal_0(k19_sin_cos(A),k4_xcmplx_0(1)) ) ) ) )).
fof(t43_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(1,k1_square_1(A)) => k4_sin_cos7(A) = k3_xcmplx_0(k7_xcmplx_0(1,2),k1_sin_cos7(k7_xcmplx_0(k3_xcmplx_0(2,A),k6_xcmplx_0(1,k1_square_1(A))))) ) ) )).
fof(t43_sin_cos9,axiom,( k3_sin_cos9(k5_numbers) = k5_numbers & k1_funct_1(k1_sin_cos9,k5_numbers) = k5_numbers )).
fof(t43_sincos10,axiom,( k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4))))) = k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1)) )).
fof(t43_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t43_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k6_pscomp_1(A) = k3_seq_4(k7_relset_1(u1_struct_0(k15_euclid(2)),k1_numbers,k4_pscomp_1,A)) ) )).
fof(t43_sprect_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t43_sprect_3,axiom,( ! [A] : ( ( v1_sprect_1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r1_sprect_2(A,k13_matrix_0(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)) ) ) ) ) )).
fof(t43_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t43_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k6_xcmplx_0(k1_square_1(A),1),k5_numbers) => ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) ) ) )).
fof(t43_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t43_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t43_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ~ ( r2_hidden(D,C) & r1_tarski(C,k2_zfmisc_1(A,B)) & ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,B) => D != k4_tarski(E,F) ) ) ) )).
fof(t43_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( k12_supinf_2(k18_supinf_2(A),k5_numbers) = k12_supinf_2(A,k5_numbers) & ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k6_numbers) => ( C = k12_supinf_2(k18_supinf_2(A),B) => k12_supinf_2(k18_supinf_2(A),k1_nat_1(B,1)) = k3_supinf_2(C,k12_supinf_2(A,k1_nat_1(B,1))) ) ) ) ) ) )).
fof(t43_taxonom1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t43_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k11_tdlat_1(A) = k1_realset1(k3_tdlat_1(A),k9_tdlat_1(A)) ) )).
fof(t43_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)))) ) ) )).
fof(t43_tdlat_3,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t43_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_tex_2(B,A) <=> ~ v1_subset_1(B,u1_struct_0(A)) ) ) ) )).
fof(t43_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t43_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_tex_4(B,A) & v4_pre_topc(B,A) ) <=> ! [C] : ( 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)) ) ) ) ) ) )).
fof(t43_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_tmap_1(A,B,C,D) <=> ! [E] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t43_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_borsuk_2(H,A,B,C) => ! [I] : ( m1_borsuk_2(I,A,C,D) => ! [J] : ( m1_borsuk_2(J,A,D,E) => ! [K] : ( m1_borsuk_2(K,A,E,F) => ! [L] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t43_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => v6_topgen_1(k1_struct_0(A),A) ) )).
fof(t43_topgen_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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) ) ) ) )).
fof(t43_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(B,A) => v5_topgen_4(B,A) ) ) ) )).
fof(t43_topgen_5,axiom,( v1_tops_1(k3_numbers,k2_topgen_3) & m1_subset_1(k3_numbers,k1_zfmisc_1(u1_struct_0(k2_topgen_3))) )).
fof(t43_topgrp_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => m3_topgrp_1(k2_topgrp_1(A,B),A) ) ) )).
fof(t43_topreal6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(2))) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [D] : ( v1_xreal_0(D) => ( ( C = k8_metric_1(k14_euclid(2),B,D) & A = B ) => k6_pscomp_1(C) = k6_xcmplx_0(k17_euclid(A),D) ) ) ) ) ) )).
fof(t43_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)))) ) ) ) ) ) )).
fof(t43_toprealb,axiom,( 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(k7_xcmplx_0(1,2))))),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k4_toprealb(k7_xcmplx_0(1,2)),k2_xcmplx_0(k4_toprealb(k7_xcmplx_0(1,2)),1))))),u1_struct_0(k11_toprealb(k10_toprealb)),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k7_xcmplx_0(1,2),k7_xcmplx_0(3,2))))),k2_tops_2(u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k4_toprealb(k7_xcmplx_0(1,2)),k2_xcmplx_0(k4_toprealb(k7_xcmplx_0(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(k7_xcmplx_0(1,2))))),k13_toprealb(k4_toprealb(k7_xcmplx_0(1,2)))),k15_toprealb) )).
fof(t43_toprealc,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( ( 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))))) ) ) ) ) )).
fof(t43_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) )).
fof(t43_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t43_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) ) ) )).
fof(t43_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t43_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t43_trees_1,axiom,( ! [A] : ( v7_ordinal1(A) => k6_trees_1(k2_trees_1(k1_nat_1(A,1))) = 1 ) )).
fof(t43_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( r2_hidden(C,k3_trees_1(A)) => r1_tarski(A,k5_trees_1(A,C,B)) ) ) ) ) )).
fof(t43_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => ( v1_finset_1(k1_trees_1(B)) & m1_trees_2(k1_trees_1(B),A) ) ) ) )).
fof(t43_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_connsp_1(A,B,C) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & ? [E] : ( 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) ) ) ) ) ) ) )).
fof(t43_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(t43_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( l1_turing_1(B) => ! [C] : ( m1_subset_1(C,k3_zfmisc_1(u2_turing_1(A),u1_turing_1(A),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1))) => ! [D] : ( m1_subset_1(D,u2_turing_1(A)) => ! [E] : ( 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),k1_enumset1(k4_xcmplx_0(1),k5_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),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),k1_domain_1(u2_turing_1(A),u2_turing_1(B),k1_mcart_1(u2_turing_1(A),u1_turing_1(A),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),C),u4_turing_1(B)),k2_mcart_1(u2_turing_1(A),u1_turing_1(A),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),C),k3_mcart_1(u2_turing_1(A),u1_turing_1(A),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),C)) ) ) ) ) ) ) ) )).
fof(t43_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t43_uniroots,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ~ ( v1_xreal_0(B) & ! [C] : ( v1_xreal_0(C) => ~ ( C = B & k2_binop_1(u1_struct_0(k1_complfld),k4_ordinal1,u1_struct_0(k1_complfld),k4_group_1(k1_complfld),B,A) = k1_newton(C,A) ) ) ) ) ) )).
fof(t43_uproots,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( k1_algseq_1(A,B) = 1 => k6_polynom5(A,B) = k1_xboole_0 ) ) ) )).
fof(t43_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( 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))))) ) ) ) ) ) ) )).
fof(t43_valued_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => k4_finseq_1(B) = k4_finseq_1(k15_finseq_1(k61_valued_1(B,A))) ) ) )).
fof(t43_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( ( 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 ) ) )).
fof(t43_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_vectsp_4(D,A,B) => ( r2_hidden(k4_struct_0(B),k3_vectsp_4(A,B,C,D)) <=> r1_struct_0(D,C) ) ) ) ) ) )).
fof(t43_vectsp_5,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_5(D,A,B,C) => m1_vectsp_5(C,A,B,D) ) ) ) ) )).
fof(t43_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => r1_vectsp_6(A,B,k8_vectsp_6(A,B,C,C),k2_vectsp_6(A,B)) ) ) ) )).
fof(t43_vfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( 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,k5_numbers),A) ) ) ) )).
fof(t43_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : r1_vfunct_2(A,B,k2_vfunct_2(A,B,C,k5_complex1),D) ) ) ) )).
fof(t43_waybel11,axiom,( ! [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) & v4_waybel11(A) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v3_pre_topc(C,A) & r2_hidden(B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r1_waybel_3(A,D,B) & r2_hidden(D,C) ) ) ) ) ) ) )).
fof(t43_waybel12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v6_waybel_3(A) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( v3_pre_topc(C,A) & ! [D] : ( ( v3_yellow_8(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ? [E] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t43_waybel14,axiom,( ! [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] : ( 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(k1_yellow_1(k5_waybel11(A))) & ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(k5_waybel11(A)))) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_yellow_1(k5_waybel11(A))))) & B = k1_yellow_0(k1_yellow_1(k5_waybel11(A)),C) & ! [D] : ( m1_subset_1(D,u1_struct_0(k1_yellow_1(k5_waybel11(A)))) => ( r2_hidden(D,C) => v6_waybel_6(D,k1_yellow_1(k5_waybel11(A))) ) ) ) ) ) ) ) )).
fof(t43_waybel19,axiom,( ! [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) & l1_waybel_9(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t43_waybel20,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t43_waybel21,axiom,( ! [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) & l1_waybel_9(A) ) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t43_waybel23,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t43_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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)),k5_yellow_1(u1_struct_0(A),k1_waybel25(B))) & m1_yellow_0(k3_waybel24(A,k1_waybel25(B)),k5_yellow_1(u1_struct_0(A),k1_waybel25(B))) ) ) ) )).
fof(t43_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v4_waybel11(C) & m1_yellow_9(C,k1_yellow_1(u1_pre_topc(B))) ) => ! [D] : ( ( 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)))) ) ) ) ) ) )).
fof(t43_waybel27,axiom,( ! [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) & l1_orders_2(A) ) => ! [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) & l1_orders_2(B) ) => v3_waybel_3(k2_waybel27(A,B)) ) ) )).
fof(t43_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t43_waybel_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(B)) ) => ( C != k1_xboole_0 => r2_hidden(k2_yellow_0(A,C),B) ) ) ) ) ) )).
fof(t43_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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))) ) ) ) ) )).
fof(t43_waybel_2,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t43_waybel_4,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => k1_setfam_1(a_2_1_waybel_4(A,B)) = k1_waybel_3(A,B) ) ) )).
fof(t43_waybel_7,axiom,( ! [A] : ( ( 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] : ( ( 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,k1_yellow_1(k7_waybel_0(A))) ) ) ) )).
fof(t43_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( ( 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) ) ) ) ) ) ) )).
fof(t43_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(A,k2_xboole_0(B,C)) => r1_tarski(k4_xboole_0(A,B),C) ) )).
fof(t43_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k6_xboolean(A,k9_xboolean(B,C)) = k4_xboolean(k6_xboolean(A,k3_xboolean(B)),k6_xboolean(A,k3_xboolean(C))) ) ) ) )).
fof(t43_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t43_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k5_numbers,A) => r1_xxreal_0(k6_xcmplx_0(B,A),B) ) ) ) )).
fof(t43_xtuple_0,axiom,( ! [A] : ! [B] : k14_xtuple_0(k2_xboole_0(A,B)) = k2_xboole_0(k14_xtuple_0(A),k14_xtuple_0(B)) )).
fof(t43_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => k4_xxreal_0(A,k2_xxreal_0) = A ) )).
fof(t43_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(A,C) => ( r1_xxreal_0(B,D) | r1_tarski(k1_xxreal_1(C,D),k2_xxreal_1(A,B)) ) ) ) ) ) ) )).
fof(t43_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ( ( r1_tarski(A,B) & v4_xxreal_2(B) ) => v4_xxreal_2(A) ) ) ) )).
fof(t43_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(C,k1_numbers) => ( r1_xxreal_0(B,A) | ( ~ r1_xxreal_0(k1_xxreal_3(B,C),k1_xxreal_3(A,C)) & ~ r1_xxreal_0(k3_xxreal_3(B,C),k3_xxreal_3(A,C)) ) ) ) ) ) ) )).
fof(t43_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(t43_yellow12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t43_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t43_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( r2_hidden(C,k3_yellow18(k4_yellow18(A),B)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( 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)) ) ) ) ) ) )).
fof(t43_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t43_yellow_0,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t43_yellow_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) => k11_lattice3(k1_yellow_1(k7_waybel_0(A)),B,C) = k3_xboole_0(B,C) ) ) ) )).
fof(t43_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t43_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t43_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_orders_2(A,B,k1_yellow_5(A,C,B)) => B = k3_yellow_0(A) ) ) ) ) )).
fof(t43_yellow_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t43_yellow_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( ( 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))))) ) ) ) ) ) ) )).
fof(t43_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ( v11_zf_lang(B) => ( ~ ( A = k23_zf_lang(B) & ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => k13_zf_lang(A,D) != B ) ) & ( ? [D] : ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) & k13_zf_lang(A,D) = B ) => A = k23_zf_lang(B) ) & ~ ( C = k24_zf_lang(B) & ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => k13_zf_lang(D,C) != B ) ) & ( ? [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) & k13_zf_lang(D,C) = B ) => C = k24_zf_lang(B) ) ) ) ) ) ) )).
fof(t43_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ~ ( r3_zf_lang(A,B) & r3_zf_lang(B,A) ) ) ) )).
fof(t43_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : k2_xboole_0(k2_tarski(A,B),C) != k1_xboole_0 )).
fof(t43_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ( r1_tarski(u1_struct_0(B),u1_struct_0(C)) => m1_zmodul01(B,C) ) ) ) ) )).
fof(t43_zmodul02,axiom,( ! [A] : ( ( ~ 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) ) => u1_struct_0(k31_zmodul02(A)) = k26_zmodul02(A) ) )).
fof(t44_abcmiz_0,axiom,( ! [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) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t44_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_abcmiz_1(B,A,k13_abcmiz_1(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t44_abcmiz_a,axiom,( ! [A] : ( ( 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] : ( 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 ) ) )).
fof(t44_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t44_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t44_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ( 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,k5_numbers) = B & k1_funct_1(A,1) = C & k1_funct_1(A,2) = D & k1_funct_1(A,3) = E ) ) ) )).
fof(t44_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k14_afproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k14_afproj(A))) => ! [D] : ( m1_subset_1(D,u1_incsp_1(k14_afproj(A))) => ! [E] : ( m1_subset_1(E,u1_incsp_1(k14_afproj(A))) => ! [F] : ( m1_subset_1(F,u1_incsp_1(k14_afproj(A))) => ! [G] : ( m1_subset_1(G,u2_incsp_1(k14_afproj(A))) => ! [H] : ( m1_subset_1(H,u2_incsp_1(k14_afproj(A))) => ! [I] : ( m1_subset_1(I,u2_incsp_1(k14_afproj(A))) => ! [J] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t44_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_afvect0(A,B))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t44_algspec1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t44_algstr_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t44_altcat_4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t44_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t44_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ~ ( r1_analmetr(A,J,K) & r1_analort(A,J,K,B,C,E,F) & r1_analort(A,J,K,E,F,H,I) & r1_analort(A,J,K,D,G,H,I) & ~ r1_analort(A,J,K,B,C,D,G) & E != F & H != I ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t44_aofa_000,axiom,( ! [A] : ( ( 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,k10_subset_1(2,k4_finseq_1(u1_unialg_1(A))))) = k4_finseq_2(2,u1_struct_0(A)) ) )).
fof(t44_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => ! [E] : ( m5_margrel1(E,u1_struct_0(A),k1_unialg_2(A)) => ! [F] : ( m5_margrel1(F,u1_struct_0(B),k1_unialg_2(B)) => ( ( E = F & r2_unialg_2(A,C,E) ) => r2_unialg_2(B,D,F) ) ) ) ) ) ) ) ) )).
fof(t44_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( ( v19_aofa_a00(F,A) & m1_subset_1(F,u1_struct_0(A)) ) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),F)) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),F)) => ! [I] : ( m2_subset_1(I,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => k15_aofa_a00(A,B,C,D,F,k35_aofa_a00(A,C,F,G,H),I) = k35_aofa_a00(A,D,F,k15_aofa_a00(A,B,C,D,F,G,I),k15_aofa_a00(A,B,C,D,F,H,I)) ) ) ) ) ) ) ) ) ) )).
fof(t44_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [E] : ( ( v1_aofa_i00(E,A,B,D) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),D) ) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),E) => ! [G] : ( 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) = k5_int_1(k21_aofa_i00(B,k4_numbers,C,F),k21_aofa_i00(B,k4_numbers,C,G)) & ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t44_armstrng,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) )).
fof(t44_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ! [C] : ( ( v3_ordinal1(C) & v7_ordinal1(C) ) => ( C != k1_xboole_0 => k8_arytm_3(k9_ordinal3(A,C),k9_ordinal3(B,C)) = k8_arytm_3(A,B) ) ) ) ) )).
fof(t44_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(3,A) & r1_xxreal_0(k1_square_1(A),k1_nat_1(k2_nat_1(2,A),1)) ) ) )).
fof(t44_bcialg_1,axiom,( ! [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) ) => ( v12_bcialg_1(u1_struct_0(A),A) & m2_bcialg_1(u1_struct_0(A),A) ) ) )).
fof(t44_bcialg_2,axiom,( ! [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) ) => r1_tarski(k3_bcialg_2(A),k4_bcialg_2(A)) ) )).
fof(t44_bcialg_3,axiom,( ! [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) & v6_bcialg_3(A) & l2_bcialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v2_bcialg_3(B,A) => ( v11_bcialg_3(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_1(A,C,k1_bcialg_1(A,B,C)) = C ) ) ) ) ) )).
fof(t44_bcialg_4,axiom,( ! [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) & l1_bcialg_4(A) ) => ( v4_bcialg_4(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_bcialg_4(A,B,B) = B ) ) ) )).
fof(t44_bcialg_5,axiom,( ! [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) ) => ( ( ~ 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,k5_numbers,1,k5_numbers,k5_numbers) & m1_bcialg_5(A,1,k5_numbers,k5_numbers,k5_numbers) ) ) ) )).
fof(t44_bcialg_6,axiom,( ! [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] : ( ( ~ 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] : ( ( 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] : ( m2_subset_1(D,u1_struct_0(A),k5_bcialg_1(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t44_bciideal,axiom,( ! [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) ) => ( ( v3_bciideal(k1_tarski(k4_struct_0(A)),A) & m2_bcialg_1(k1_tarski(k4_struct_0(A)),A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_bcialg_1(A,B,C) = B => k1_bcialg_1(A,C,B) = C ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(t44_bhsp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => k1_normsp_1(B,k5_vfunct_1(k4_ordinal1,B,C),A) = k4_algstr_0(B,k1_normsp_1(B,C,A)) ) ) ) )).
fof(t44_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ( r2_hidden(C,k4_bhsp_2(A,B,E)) => r2_hidden(k5_algstr_0(A,C,D),k4_bhsp_2(A,k5_algstr_0(A,B,D),E)) ) ) ) ) ) ) )).
fof(t44_bhsp_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(C)))) ) => r2_funct_2(k4_ordinal1,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))) ) ) ) ) )).
fof(t44_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t44_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t44_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k1_borsuk_4))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_topmetr)) => ( A = k4_rcomp_1(k5_numbers,B) => v4_pre_topc(A,k1_borsuk_4) ) ) ) )).
fof(t44_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => k2_rcomp_1(A,k1_xxreal_0) != k1_numbers ) )).
fof(t44_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t44_borsuk_7,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( k12_euclid(B) = k12_euclid(C) & k3_euclid_3(B) = k2_xcmplx_0(k3_euclid_3(C),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A)) ) => B = C ) ) ) ) )).
fof(t44_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t44_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t44_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t44_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t44_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ( k8_xboolean(A,A) = k3_xboolean(A) & k3_xboolean(k8_xboolean(A,A)) = A ) ) )).
fof(t44_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t44_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t44_card_1,axiom,( k3_card_1(k5_ordinal1) = k4_ordinal1 )).
fof(t44_card_2,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => k5_card_1(k2_xboole_0(A,B)) = k6_xcmplx_0(k1_nat_1(k5_card_1(A),k5_card_1(B)),k5_card_1(k3_xboole_0(A,B))) ) ) )).
fof(t44_card_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v1_card_1(B) => ( r2_hidden(k1_card_1(A),B) => r2_hidden(A,B) ) ) ) )).
fof(t44_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_finset_1(B) ) => ! [C] : ( k9_xtuple_0(B) = A => k3_card_fin(k5_card_1(A),B) = k1_card_1(k2_card_fin(B,k7_funcop_1(A,C),C)) ) ) ) )).
fof(t44_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v11_cat_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_cat_1(D,A,B,C) & k2_cat_1(A,B,C) = k1_tarski(D) ) ) ) ) ) )).
fof(t44_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u4_struct_0(C)) => ! [F] : ( 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)) ) ) ) ) ) )).
fof(t44_cat_4,axiom,( ! [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) & l1_cat_1(A) ) => ( v4_cat_4(A) <=> ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & v11_cat_1(B,A) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u4_struct_0(A)) & ? [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t44_catalan2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k1_numbers) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,k1_numbers) & v1_funct_1(C) & v5_ordinal1(C) & v1_finset_1(C) ) => ( ( k1_relset_1(k4_ordinal1,B) = k1_relset_1(k4_ordinal1,C) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k1_afinsq_1(B)) => k1_funct_1(B,D) = k3_xcmplx_0(A,k1_funct_1(C,D)) ) ) ) => k7_afinsq_2(B) = k3_xcmplx_0(A,k7_afinsq_2(C)) ) ) ) ) )).
fof(t44_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => k4_struct_0(k7_cc0sp2(A)) = k1_cc0sp2(A,k5_numbers) ) )).
fof(t44_cfcont_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t44_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( 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,D,k1_cfunct_1(A,B,C)),k1_cfunct_1(A,k19_valued_1(A,k2_numbers,k2_numbers,D,k2_partfun1(A,k2_numbers,C,k1_relset_1(A,k2_cfunct_1(A,C)))),B)) ) ) ) ) )).
fof(t44_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ( v6_cgames_1(A) <=> ! [B] : ( v2_cgames_1(B) => ~ ( r2_hidden(B,k6_cgames_1(A)) & ! [C] : ( v2_cgames_1(C) => ~ ( r2_hidden(C,k7_cgames_1(B)) & v6_cgames_1(C) ) ) ) ) ) ) )).
fof(t44_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) ) => ! [C] : ( m2_glib_000(C,A,B,k21_glib_000(A,B)) => ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => ! [E] : ( m1_subset_1(E,k6_glib_000(A)) => ! [F] : ( m1_subset_1(F,k6_glib_000(C)) => ! [G] : ( m1_subset_1(G,k6_glib_000(C)) => ( ( D = F & E = G ) => ( r1_chord(A,D,E) <=> r1_chord(C,F,G) ) ) ) ) ) ) ) ) ) )).
fof(t44_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(D) & v1_finset_1(D) ) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t44_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ( v1_circcomb(A) <=> ! [B] : ( r2_hidden(B,u4_struct_0(A)) => k1_funct_1(u2_msualg_1(A),B) = B ) ) ) )).
fof(t44_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v4_msualg_1(E,A) & v4_msafree2(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( ( v4_msualg_1(F,B) & v4_msafree2(F,B) & l3_msualg_1(F,B) ) => ( r4_circtrm1(A,B,C,D,E,F) => ! [G] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t44_classes1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) ) )).
fof(t44_classes2,axiom,( ! [A] : ( v1_ordinal1(A) => r1_classes1(A,k4_classes1(k1_card_1(k1_classes1(A)))) ) )).
fof(t44_clvect_1,axiom,( ! [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) ) => m1_clvect_1(A,A) ) )).
fof(t44_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ( r2_hidden(C,k4_clvect_2(A,B,E)) => r2_hidden(k5_algstr_0(A,C,D),k4_clvect_2(A,k5_algstr_0(A,B,D),E)) ) ) ) ) ) ) )).
fof(t44_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k2_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) )).
fof(t44_coh_sp,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k20_coh_sp(A)) => ! [C] : ( m1_subset_1(C,k20_coh_sp(A)) => ! [D] : ( m1_subset_1(D,k20_coh_sp(A)) => ( ( k21_coh_sp(A,C) = k22_coh_sp(A,B) & k21_coh_sp(A,D) = k22_coh_sp(A,C) ) => k24_coh_sp(A,k24_coh_sp(A,B,C),D) = k24_coh_sp(A,B,k24_coh_sp(A,C,D)) ) ) ) ) )).
fof(t44_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k8_cohsp_1(A,B,C))) => ? [E] : ( 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 ) ) ) ) ) )).
fof(t44_complex1,axiom,( k9_complex1(k5_numbers) = k5_numbers )).
fof(t44_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k1_complex2(k6_xcmplx_0(A,B),C) = k6_xcmplx_0(k1_complex2(A,C),k1_complex2(B,C)) ) ) ) )).
fof(t44_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_complfld)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_complfld)) => ~ ( B != k4_struct_0(k1_complfld) & D != k4_struct_0(k1_complfld) & k5_algstr_0(k1_complfld,k3_vectsp_1(k1_complfld,A,B),k3_vectsp_1(k1_complfld,C,D)) != k3_vectsp_1(k1_complfld,k5_algstr_0(k1_complfld,k8_group_1(k1_complfld,A,D),k8_group_1(k1_complfld,C,B)),k8_group_1(k1_complfld,B,D)) ) ) ) ) ) )).
fof(t44_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k10_seq_4(k10_seq_4(A,C),B) = k10_seq_4(A,k3_xcmplx_0(B,C)) ) ) ) )).
fof(t44_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(A)) => k1_funct_1(k11_compos_1(A,B),k5_numbers) = B ) ) )).
fof(t44_comptrig,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( r2_hidden(k1_comptrig(A),k2_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(2,k28_sin_cos))) <=> ( ~ r1_xxreal_0(k3_complex1(A),k5_numbers) & ~ r1_xxreal_0(k5_numbers,k4_complex1(A)) ) ) ) )).
fof(t44_comput_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v3_margrel1(B,A) & m2_rfunct_3(B,k3_finseq_2(A),A,k2_comput_1(A)) ) => ! [C] : ( ( v3_comput_1(C) & m2_finseq_1(C,k2_comput_1(A)) ) => ( ( k19_margrel1(B) = k3_finseq_1(C) & ! [D] : ( 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(k5_funct_6(C),B)) & v3_margrel1(k3_relat_1(k5_funct_6(C),B),A) & m2_rfunct_3(k3_relat_1(k5_funct_6(C),B),k3_finseq_2(A),A,k2_comput_1(A)) & k9_xtuple_0(k3_relat_1(k5_funct_6(C),B)) = k4_finseq_2(k1_comput_1(C),A) ) ) ) ) ) ) )).
fof(t44_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k2_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,D,A),k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,C,B)),k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,D,B),k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,C))) ) ) ) ) )).
fof(t44_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( v1_xcmplx_0(B) => ( ! [C] : ( v7_ordinal1(C) => k9_nat_1(k2_numbers,A,C) = k2_comseq_3(B,k1_nat_1(C,1)) ) => ( r1_xxreal_0(1,k9_complex1(B)) | ( v2_comseq_2(A) & k3_comseq_2(A) = k5_complex1 ) ) ) ) ) )).
fof(t44_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(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)) ) ) )).
fof(t44_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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))))) ) ) ) )).
fof(t44_convex4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,1) ) => ( k9_complex1(k3_xcmplx_0(A,B)) = k3_xcmplx_0(A,k9_complex1(B)) & k9_complex1(k3_xcmplx_0(k6_xcmplx_0(k6_complex1,A),B)) = k3_xcmplx_0(k6_xcmplx_0(k6_complex1,A),k9_complex1(B)) ) ) ) ) )).
fof(t44_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) )).
fof(t44_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t44_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t44_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_xxreal_0(k5_numbers,k13_csspace(A,B)) ) ) )).
fof(t44_dickson,axiom,( r4_relat_2(k10_dickson,k4_ordinal1) )).
fof(t44_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k5_diff_1(k16_sin_cos,A),B) = k3_xcmplx_0(2,k3_xcmplx_0(k19_sin_cos(B),k17_sin_cos(k7_xcmplx_0(A,2)))) ) ) )).
fof(t44_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( v1_xreal_0(F) => k1_funct_1(E,F) = k1_square_1(F) ) & r2_zfmisc_1(A,B,C,D) ) => k11_diff_1(E,A,B,C,D) = k5_numbers ) ) ) ) ) ) )).
fof(t44_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k3_diff_1(k4_diff_1(C,A),A),B) = k6_xcmplx_0(k1_funct_1(k3_diff_1(C,A),B),k1_funct_1(k4_diff_1(C,A),B)) ) ) ) )).
fof(t44_dilworth,axiom,( ! [A] : ( ( v4_dilworth(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_xxreal_0(k2_dilworth(k5_yellow_0(A,B)),k2_dilworth(A)) ) ) )).
fof(t44_diraf,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ! [B] : ( ( ~ v7_struct_0(B) & v2_analoaf(B) & v3_analoaf(B) & l1_analoaf(B) ) => ( A = k2_diraf(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( ~ r2_analoaf(A,C,D,E,F) & ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( r2_analoaf(A,C,D,C,G) & r2_analoaf(A,E,F,E,G) ) ) ) ) ) ) ) ) ) ) )).
fof(t44_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( 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] : ( 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] : ( 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) ) ) ) ) ) )).
fof(t44_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( 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) != k5_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) = k5_numbers ) ) ) ) ) )).
fof(t44_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ( k3_graph_1(A,D) = k4_graph_1(A,C) => k17_ens_1(A,B,k1_cat_1(A,C,D)) = k1_partfun1(k2_cat_1(A,B,k3_graph_1(A,C)),k2_cat_1(A,B,k4_graph_1(A,C)),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,C),k17_ens_1(A,B,D)) ) ) ) ) ) )).
fof(t44_entropy1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( v4_matrprob(A) <=> v1_matrprob(k2_entropy1(k1_numbers,A)) ) ) )).
fof(t44_enumset1,axiom,( ! [A] : ! [B] : ! [C] : k4_enumset1(A,A,A,A,B,C) = k1_enumset1(A,B,C) )).
fof(t44_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t44_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => k10_euclid(A,k21_euclid(A)) = k5_finseq_2(k4_ordinal1,A,1) ) )).
fof(t44_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => k1_square_1(k12_euclid(k5_algstr_0(k15_euclid(A),B,C))) = k2_xcmplx_0(k6_xcmplx_0(k1_square_1(k12_euclid(B)),k3_xcmplx_0(2,k22_rvsum_1(C,B))),k1_square_1(k12_euclid(C))) ) ) ) )).
fof(t44_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( A != k4_struct_0(k15_euclid(2)) & B != k4_struct_0(k15_euclid(2)) & ~ ( ~ ( ( k2_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(k17_euclid(A),k18_euclid(B))),k3_xcmplx_0(k18_euclid(A),k17_euclid(B))) = k3_xcmplx_0(k12_euclid(A),k12_euclid(B)) | k2_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(k17_euclid(A),k18_euclid(B))),k3_xcmplx_0(k18_euclid(A),k17_euclid(B))) = k4_xcmplx_0(k3_xcmplx_0(k12_euclid(A),k12_euclid(B))) ) & k4_euclid_3(A,k4_struct_0(k15_euclid(2)),B) != k7_xcmplx_0(k28_sin_cos,2) & k4_euclid_3(A,k4_struct_0(k15_euclid(2)),B) != k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos) ) & ~ ( ( k4_euclid_3(A,k4_struct_0(k15_euclid(2)),B) = k7_xcmplx_0(k28_sin_cos,2) | k4_euclid_3(A,k4_struct_0(k15_euclid(2)),B) = k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos) ) & k2_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(k17_euclid(A),k18_euclid(B))),k3_xcmplx_0(k18_euclid(A),k17_euclid(B))) != k3_xcmplx_0(k12_euclid(A),k12_euclid(B)) & k2_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(k17_euclid(A),k18_euclid(B))),k3_xcmplx_0(k18_euclid(A),k17_euclid(B))) != k4_xcmplx_0(k3_xcmplx_0(k12_euclid(A),k12_euclid(B))) ) ) ) ) ) )).
fof(t44_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ~ ( v2_euclid_4(B,A) & ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & C != D ) ) ) ) ) ) )).
fof(t44_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => k4_euclid_3(A,B,C) != k2_xcmplx_0(k3_xcmplx_0(2,k4_euclid_3(D,E,F)),k3_xcmplx_0(2,k28_sin_cos)) ) ) ) ) ) ) )).
fof(t44_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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))) ) ) ) )).
fof(t44_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => k9_euclid(3,B,A) = k1_euclid_8(k3_xcmplx_0(A,k1_funct_1(B,1)),k3_xcmplx_0(A,k1_funct_1(B,2)),k3_xcmplx_0(A,k1_funct_1(B,3))) ) ) )).
fof(t44_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ( ( r4_euclidlp(A,B,C) & r2_euclidlp(A,C,D) ) => r4_euclidlp(A,B,D) ) ) ) ) ) )).
fof(t44_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_exchsort(C) ) => ! [D] : ( ( 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(k9_funct_7(C,A,B),D) & m1_exchsort(C,k9_funct_7(D,A,B)) ) ) ) ) )).
fof(t44_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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)))) ) )).
fof(t44_fcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,k1_relset_1(k1_numbers,A)) => k1_funct_1(A,B) = k9_complex1(B) ) ) => v1_fcont_1(A) ) ) )).
fof(t44_fdiff_10,axiom,( ! [A] : ( ( 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,k18_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fdiff_9,k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fdiff_9,k18_sin_cos),A),B) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,k1_funct_1(k1_fdiff_9,B)),k1_funct_1(k16_sin_cos,B)),k1_square_1(k1_funct_1(k18_sin_cos,B)))) ) ) ) ) ) )).
fof(t44_fdiff_11,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,k1_relset_1(k1_numbers,k26_sin_cos)) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_sin_cos9)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_sin_cos9)),A),B) = k2_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k1_funct_1(k2_sin_cos9,B)),k1_square_1(k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k26_sin_cos,B)),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t44_fdiff_2,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) & r1_xxreal_0(k1_fdiff_1(A,B),k5_numbers) ) & ? [B] : ( v1_xreal_0(B) & r1_xxreal_0(k5_numbers,k1_fdiff_1(A,B)) ) ) | v3_rcomp_1(k2_relset_1(k1_numbers,A)) ) ) ) )).
fof(t44_fdiff_4,axiom,( ! [A] : ( ( 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)),k18_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)),k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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)),k18_sin_cos),A),B) = k2_xcmplx_0(k4_xcmplx_0(k1_funct_1(k18_sin_cos,B)),k3_xcmplx_0(B,k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t44_fdiff_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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,D,k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k16_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(4,A)))))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => ( k1_funct_1(D,E) = k7_xcmplx_0(E,2) & k1_funct_1(C,E) = k3_xcmplx_0(k3_xcmplx_0(2,A),E) ) ) ) ) => ( A = k5_numbers | ( r2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k16_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(4,A)))),B) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_1(k2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k16_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(4,A)))),B),E) = k1_square_1(k17_sin_cos(k3_xcmplx_0(A,E))) ) ) ) ) ) ) ) ) ) )).
fof(t44_fdiff_7,axiom,( ! [A] : ( ( 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,k22_sin_cos,k16_sin_cos))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k16_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k16_sin_cos),A),B) = k3_xcmplx_0(k1_funct_1(k22_sin_cos,B),k2_xcmplx_0(k1_funct_1(k16_sin_cos,B),k1_funct_1(k18_sin_cos,B))) ) ) ) ) ) )).
fof(t44_fdiff_9,axiom,( ! [A] : ( ( 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,k26_sin_cos,k2_fdiff_9))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k2_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k2_fdiff_9),A),B) = k6_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,B))),k1_funct_1(k16_sin_cos,B)),k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k26_sin_cos,B),k1_funct_1(k18_sin_cos,B)),k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t44_fib_num3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k1_nat_1(k1_fib_num3(A),k1_fib_num3(k1_nat_1(A,3))) = k2_nat_1(2,k1_fib_num3(k1_nat_1(A,2))) ) )).
fof(t44_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_finseq_1(B,A) => ! [C] : ( m1_finseq_1(C,A) => ! [D] : ( m1_finseq_1(D,A) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t44_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) | r2_hidden(k7_lattices(A,C),B) ) ) ) ) ) ) )).
fof(t44_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t44_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k1_lattice2(A)))) ) => ! [E] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t44_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : ( A = k10_finseq_1(B,C) <=> ( k3_finseq_1(A) = 2 & k1_funct_1(A,1) = B & k1_funct_1(A,2) = C ) ) ) )).
fof(t44_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ! [D] : ( ( 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),k4_ordinal1,B,D,C),B) ) ) ) ) ) )).
fof(t44_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => k3_finseq_1(k14_finseq_1(k2_finseq_1(A))) = A ) )).
fof(t44_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_hidden(B,k10_xtuple_0(A)) => r1_tarski(k10_xtuple_0(k6_finseq_4(A,B)),k10_xtuple_0(A)) ) ) )).
fof(t44_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t44_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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 ) ) ) ) ) ) )).
fof(t44_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t44_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t44_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_orders_2(A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_tarski(k9_fintopo3(A,B,k1_nat_1(C,1)),k9_fintopo3(A,B,C)) ) ) ) ) )).
fof(t44_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t44_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => r1_tarski(k6_flang_1(A,B,B),k8_flang_1(A,B)) ) )).
fof(t44_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( 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))) ) ) ) ) ) )).
fof(t44_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( 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))) ) ) ) )).
fof(t44_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v8_pre_topc(A) => v7_pre_topc(A) ) ) )).
fof(t44_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( ( ~ v2_struct_0(D) & l2_fsm_1(D,A,B) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( ( 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] : ( m1_subset_1(H,u1_struct_0(C)) => ! [I] : ( m1_subset_1(I,A) => ( k3_funct_2(u1_struct_0(C),u1_struct_0(D),G,k2_binop_1(u1_struct_0(C),A,u1_struct_0(C),u1_fsm_1(A,C),H,I)) = 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),G,H),I) & k2_binop_1(u1_struct_0(C),A,B,u3_fsm_1(A,B,C),H,I) = 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),G,H),I) ) ) ) => ( r5_fsm_1(A,B,C,E,F) <=> r5_fsm_1(A,B,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)) ) ) ) ) ) ) ) ) ) )).
fof(t44_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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) ) ) ) )).
fof(t44_funct_1,axiom,( ! [A] : k2_funct_1(k4_relat_1(A)) = k4_relat_1(A) )).
fof(t44_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k1_xboole_0,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_xboole_0,B))) ) => k7_relset_1(k1_xboole_0,B,C,A) = k1_xboole_0 ) )).
fof(t44_funct_3,axiom,( ! [A] : ! [B] : ( B != k1_xboole_0 => k10_xtuple_0(k7_funct_3(A,B)) = A ) )).
fof(t44_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ? [B] : ? [C] : r1_tarski(k9_xtuple_0(k2_funct_4(A)),k2_zfmisc_1(B,C)) ) )).
fof(t44_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) ) ) ) )).
fof(t44_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => k3_funct_7(A,k9_finseq_1(B)) = k3_relat_1(k6_partfun1(A),B) ) )).
fof(t44_funct_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t44_functor0,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => ! [C] : ( l1_functor0(C,A,B) => ( ( v10_functor0(C,A,B) & v5_functor0(C,A,B) ) => v7_functor0(C,A,B) ) ) ) ) )).
fof(t44_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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)) ) ) ) )).
fof(t44_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D,C)),k1_fuzzy_1(A,k2_fuzzy_2(A,B,D),k2_fuzzy_2(A,B,C))) ) ) ) ) )).
fof(t44_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_fvaluat1(C,A) => ( ( v3_fvaluat1(A) & r1_xxreal_0(k5_numbers,k3_funct_2(u1_struct_0(A),k6_numbers,C,B)) ) => r1_xxreal_0(k3_funct_2(u1_struct_0(A),k6_numbers,k5_fvaluat1(A,C),B),k3_funct_2(u1_struct_0(A),k6_numbers,C,B)) ) ) ) ) )).
fof(t44_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [D] : ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t44_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t44_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( ( ~ v1_xboole_0(F) & v1_relat_1(F) & v2_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ! [G] : ( m1_genealg1(G,F) => ! [H] : ( m1_genealg1(H,F) => ( k11_genealg1(F,G,H,k5_numbers,k5_numbers,k5_numbers,k5_numbers,E) = k7_genealg1(F,G,H,E) & k11_genealg1(F,G,H,k5_numbers,k5_numbers,k5_numbers,D,k5_numbers) = k7_genealg1(F,G,H,D) & k11_genealg1(F,G,H,k5_numbers,k5_numbers,C,k5_numbers,k5_numbers) = k7_genealg1(F,G,H,C) & k11_genealg1(F,G,H,k5_numbers,B,k5_numbers,k5_numbers,k5_numbers) = k7_genealg1(F,G,H,B) & k11_genealg1(F,G,H,A,k5_numbers,k5_numbers,k5_numbers,k5_numbers) = k7_genealg1(F,G,H,A) ) ) ) ) ) ) ) ) ) )).
fof(t44_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(k7_geomtrap(A,F,G))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k7_geomtrap(A,F,G))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k7_geomtrap(A,F,G))) => ! [K] : ( m1_subset_1(K,u1_struct_0(k7_geomtrap(A,F,G))) => ( ( B = H & D = I & C = J & E = K ) => ( r2_analoaf(k7_geomtrap(A,F,G),H,I,J,K) <=> r2_geomtrap(A,F,G,B,D,C,E) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t44_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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) ) )).
fof(t44_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t44_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r2_hidden(D,k1_relset_1(k4_ordinal1,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) ) ) ) ) ) )).
fof(t44_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( m1_subset_1(B,k6_glib_000(A)) & ? [C] : ( m1_subset_1(C,k6_glib_000(A)) & B != C & v11_glib_000(B,A) & v11_glib_000(C,A) ) ) ) )).
fof(t44_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_003(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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) ) ) ) )).
fof(t44_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ 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(k1_nat_1(A,1),k3_finseq_1(k2_goboard2(D))) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(k2_goboard2(D))) & r1_xxreal_0(1,C) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1))) = k2_topreal1(2,D,C) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1))) = k2_topreal1(2,D,k1_nat_1(C,1)) ) => ( r1_xxreal_0(k3_finseq_1(D),k1_nat_1(C,1)) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,1)) ) ) ) ) ) ) ) )).
fof(t44_gobrd14,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t44_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( m2_graph_1(E,A) => ! [F] : ( m2_graph_1(F,A) => ! [G] : ( m2_graph_1(G,A) => ( ( r1_graph_2(A,C,F) & r1_graph_2(A,D,G) & k1_funct_1(C,k3_finseq_1(C)) = k1_funct_1(D,1) & E = k8_finseq_1(u4_struct_0(A),F,G) & B = k4_graph_2(u1_struct_0(A),C,D) ) => r1_graph_2(A,B,E) ) ) ) ) ) ) ) ) )).
fof(t44_graph_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(k8_graph_3(B,D,E))) => ( F = C => ( C = D | k3_graph_3(k8_graph_3(B,D,E),F,A) = k3_graph_3(B,C,A) ) ) ) ) ) ) ) )).
fof(t44_graph_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ( r5_graph_5(B,A) => r6_graph_5(B,A) ) ) ) )).
fof(t44_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => r2_graphsp(k6_graphsp(k9_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),k15_graphsp(B),k18_graphsp(B))),A),C),k6_graphsp(k9_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),k15_graphsp(B),k18_graphsp(B))),k1_nat_1(A,1)),C),k1_nat_1(k2_nat_1(3,B),1),k1_nat_1(k2_nat_1(B,B),k2_nat_1(3,B))) ) ) ) )).
fof(t44_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( 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] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(F,k5_card_1(k3_polynom1(k15_pre_poly(A),C,D))) => r2_funct_2(k15_pre_poly(A),u1_struct_0(C),k6_groeb_3(A,B,C,k10_polynom1(A,C,E,D),F),k10_polynom1(A,C,E,k6_groeb_3(A,B,C,D,F))) ) ) ) ) ) ) ) )).
fof(t44_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & l1_struct_0(A) ) => r1_xxreal_0(1,k7_group_1(A)) ) )).
fof(t44_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,A) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t44_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => k1_group_1(B) = k1_group_1(A) ) ) )).
fof(t44_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t44_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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)) ) ) ) ) )).
fof(t44_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t44_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t44_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v2_group_9(C,A) & v4_group_9(C,A,B) & m1_group_9(C,A,B) ) => ! [D] : ( ( v2_group_9(D,A) & v4_group_9(D,A,B) & m1_group_9(D,A,B) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t44_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => k3_helly(A,B,C,D) = k3_helly(A,D,B,C) ) ) ) ) )).
fof(t44_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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) = k5_numbers => k9_complex1(k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(k1_complfld),D,C,B)) = k5_numbers ) ) ) ) ) )).
fof(t44_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(A,C) => ( r2_hidden(k5_numbers,C) | k1_funct_1(k2_fdiff_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_taylor_1(B)),C),A) = k4_xcmplx_0(k7_xcmplx_0(B,k1_funct_1(k1_taylor_1(k1_nat_1(B,1)),A))) ) ) ) ) ) )).
fof(t44_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(t44_hurwitz,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(A,k1_complfld) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(k1_complfld),k7_hurwitz(k5_vfunct_1(k4_ordinal1,k1_complfld,A)),k5_vfunct_1(k4_ordinal1,k1_complfld,k7_hurwitz(A))) ) )).
fof(t44_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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 ) ) )).
fof(t44_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u4_incsp_1(A)) => ~ ( B != C & ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t44_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & ~ v11_struct_0(C) & l1_msualg_1(C) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ( r3_pua2mss1(A,B,E,F) => ! [G] : ( ( 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] : ( ( 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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t44_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ ( ~ r1_xxreal_0(k3_int_1(A),k5_numbers) & v1_int_1(A) ) & ~ ( ~ v1_int_1(A) & r1_xxreal_0(k3_int_1(A),k5_numbers) ) ) ) )).
fof(t44_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => ! [F] : ( v1_int_1(F) => ~ ( A != k5_numbers & B != k5_numbers & C != k5_numbers & r1_int_2(A,B) & r1_int_2(A,C) & r1_int_2(B,C) & ! [G] : ( v1_int_1(G) => ! [H] : ( v1_int_1(H) => ? [I] : ( v1_int_1(I) & k5_int_1(k6_xcmplx_0(I,D),A) = k5_numbers & k5_int_1(k6_xcmplx_0(I,E),B) = k5_numbers & k5_int_1(k6_xcmplx_0(I,F),C) = k5_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)) & k5_int_1(k6_xcmplx_0(k3_xcmplx_0(A,G),k6_xcmplx_0(E,D)),B) = k5_numbers & k5_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) = k5_numbers ) ) ) ) ) ) ) ) ) ) ) )).
fof(t44_int_5,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t44_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(A,B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k2_xcmplx_0(1,k1_funct_1(k18_sin_cos,D)) != k5_numbers & k6_xcmplx_0(1,k1_funct_1(k18_sin_cos,D)) != k5_numbers & k1_funct_1(C,D) = k7_xcmplx_0(1,k6_xcmplx_0(1,k1_funct_1(k18_sin_cos,D))) ) ) ) & k9_xtuple_0(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k27_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) = k6_xcmplx_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k27_sin_cos),k2_fdiff_9),k2_seq_4(A)),k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k27_sin_cos),k2_fdiff_9),k3_seq_4(A))) ) ) ) ) )).
fof(t44_integr12,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,D) & r1_tarski(D,k2_rcomp_1(k4_xcmplx_0(1),1)) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => ( ~ r1_xxreal_0(k1_funct_1(k1_sin_cos6,E),k5_numbers) & k1_funct_1(C,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,B) & 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_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(k7_xcmplx_0(1,2))),k1_sin_cos6))) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos6,k3_taylor_1),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos6,k3_taylor_1),k3_seq_4(A))) ) ) ) ) ) )).
fof(t44_integr13,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(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)),k7_xcmplx_0(1,2))),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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)),k7_xcmplx_0(1,2))),A),B) = k7_xcmplx_0(k1_funct_1(k2_sin_cos9,B),k2_xcmplx_0(1,k1_square_1(B))) ) ) ) ) ) )).
fof(t44_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k2_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,D))),k1_funct_1(k18_sin_cos,D)),k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k26_sin_cos,D),k1_funct_1(k16_sin_cos,D)),k1_square_1(k1_funct_1(k18_sin_cos,D)))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_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) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_fdiff_9),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_fdiff_9),k3_seq_4(A))) ) ) ) ) )).
fof(t44_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t44_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [C] : ( m1_integra1(C,A) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t44_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( A = k1_rcomp_1(k3_xcmplx_0(k2_nat_1(2,B),k28_sin_cos),k3_xcmplx_0(k1_nat_1(k2_nat_1(2,B),1),k28_sin_cos)) => k2_integra5(A,k18_sin_cos) = k5_numbers ) ) ) )).
fof(t44_integra9,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t44_interva1,axiom,( ! [A] : ( ~ 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) ) ) )).
fof(t44_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(t44_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t44_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t44_jgraph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t44_jgraph_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(C,k5_numbers) & ~ v2_funct_1(k2_jgraph_2(A,B,C,D)) ) ) ) ) ) )).
fof(t44_jgraph_3,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k5_topmetr)) => ! [I] : ( m1_subset_1(I,u1_struct_0(k5_topmetr)) => ~ ( H = k5_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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t44_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r1_xxreal_0(A,k7_xcmplx_0(k18_euclid(B),k12_euclid(B))) & r1_xxreal_0(A,k7_xcmplx_0(k18_euclid(C),k12_euclid(C))) ) => ( r1_xxreal_0(1,A) | r1_xxreal_0(k5_numbers,k17_euclid(B)) | r1_xxreal_0(k5_numbers,k17_euclid(C)) | r1_xxreal_0(k7_xcmplx_0(k18_euclid(C),k12_euclid(C)),k7_xcmplx_0(k18_euclid(B),k12_euclid(B))) | ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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(k7_xcmplx_0(k18_euclid(E),k12_euclid(E)),k7_xcmplx_0(k18_euclid(D),k12_euclid(D))) ) ) ) ) ) ) ) ) )).
fof(t44_jgraph_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t44_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t44_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t44_jordan,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t44_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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)))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,B) ) => r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(C,B),k1_jordan1a(k1_jordan8(C,B)),1),k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(C,A),k1_jordan1a(k1_jordan8(C,A)),1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(C,A),k1_jordan1a(k1_jordan8(C,A)),k3_finseq_1(k1_jordan8(C,A))))) ) ) ) ) )).
fof(t44_jordan1g,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(C,1) & r1_xxreal_0(C,k3_finseq_1(k1_jordan8(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,1),k3_topreal1(2,k1_jordan1e(B,A))) ) ) ) ) )).
fof(t44_jordan1h,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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)) => k2_goboard2(k2_jordan9(B,A)) = k1_jordan8(B,A) ) ) ) )).
fof(t44_jordan1j,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => k3_jordan3(A,B) != k1_xboole_0 ) ) )).
fof(t44_jordan1k,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => r1_xxreal_0(k5_numbers,k5_jordan1k(A,C,B)) ) ) ) )).
fof(t44_jordan21,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( r1_tarski(A,B) & k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)) = k2_xcmplx_0(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(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)),2))))) ) => ( v1_xboole_0(k9_subset_1(u1_struct_0(k15_euclid(2)),A,k6_jordan6(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)),2)))) | r1_xxreal_0(k18_euclid(k2_jordan21(B)),k18_euclid(k2_jordan21(A))) ) ) ) ) )).
fof(t44_jordan23,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t44_jordan2c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k14_euclid(1)))) => ! [B] : ( v1_xreal_0(B) => ~ ( A = a_1_0_jordan2c(B) & v6_tbsp_1(A,k14_euclid(1)) ) ) ) )).
fof(t44_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)))) ) ) ) ) ) )).
fof(t44_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( 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)) ) ) ) ) ) ) )).
fof(t44_jordan5d,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(A)) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(k2_goboard2(A))) & E = a_2_0_jordan5d(A,B) & k17_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),A,D)) = k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),B,1)) & C = k1_xxreal_2(E) ) => r1_xxreal_0(k18_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),A,D)),k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),B,C))) ) ) ) ) ) ) )).
fof(t44_jordan6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(A),C)))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t44_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t44_kurato_1,axiom,( k2_pre_topc(k3_topmetr,k1_tops_1(k3_topmetr,k6_kurato_1)) != k1_tops_1(k3_topmetr,k6_kurato_1) )).
fof(t44_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k5_finsub_1(C)) => ! [E] : ( ( 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] : ( m1_subset_1(F,C) => ( r2_hidden(F,D) => r3_lattices(A,B,k3_funct_2(C,u1_struct_0(A),E,F)) ) ) ) ) ) ) ) ) )).
fof(t44_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t44_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => r1_tarski(k17_lexbfs(k6_glib_000(A),k4_ordinal1,k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),k13_lexbfs(A,k16_lexbfs(A),C)),B),k17_lexbfs(k6_glib_000(A),k4_ordinal1,k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),k13_lexbfs(A,k16_lexbfs(A),D)),B)) ) ) ) ) )).
fof(t44_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) = k4_xcmplx_0(k1_limfunc2(B,A)) ) ) ) ) )).
fof(t44_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,C) & ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ~ ( ~ 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_funct_1(B,E) != k5_numbers & k1_funct_1(B,F) != k5_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) = k5_numbers ) ) ) ) ) )).
fof(t44_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(A,k2_xcmplx_0(A,D)))) & k1_funct_1(B,E) = k2_limfunc2(B,A) ) ) ) ) | r6_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t44_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k24_lpspacc1(A,B,C))) => ( r2_hidden(D,E) => ( E = k17_lpspacc1(A,B,C,D) & k2_normsp_0(k24_lpspacc1(A,B,C),E) = k1_mesfunc6(A,B,C,k56_valued_1(A,k2_numbers,D)) ) ) ) ) ) ) ) )).
fof(t44_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t44_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [H] : ( ( v2_xxreal_0(H) & v1_xreal_0(H) ) => ( ( k5_lpspace2(A,B,C,D,H) = k5_lpspace2(A,B,C,F,H) & k5_lpspace2(A,B,C,E,H) = k5_lpspace2(A,B,C,G,H) ) => ( ! [I] : ( m2_subset_1(I,k1_zfmisc_1(A),B) => ~ ( k1_funct_1(C,k3_subset_1(A,I)) = k5_numbers & I = k1_relset_1(A,D) & r1_mesfunc6(A,B,D,I) ) ) | ! [I] : ( m2_subset_1(I,k1_zfmisc_1(A),B) => ~ ( k1_funct_1(C,k3_subset_1(A,I)) = k5_numbers & I = k1_relset_1(A,F) & r1_mesfunc6(A,B,F,I) ) ) | ! [I] : ( m2_subset_1(I,k1_zfmisc_1(A),B) => ~ ( k1_funct_1(C,k3_subset_1(A,I)) = k5_numbers & I = k1_relset_1(A,E) & r1_mesfunc6(A,B,E,I) ) ) | ! [I] : ( m2_subset_1(I,k1_zfmisc_1(A),B) => ~ ( k1_funct_1(C,k3_subset_1(A,I)) = k5_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,E,H)) | k5_lpspace2(A,B,C,k3_valued_1(A,k1_numbers,k1_numbers,D,E),H) = k5_lpspace2(A,B,C,k3_valued_1(A,k1_numbers,k1_numbers,F,G),H) ) ) ) ) ) ) ) ) ) ) )).
fof(t44_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_hilbert1)) => ( r8_ltlaxio1(B,A) => r8_ltlaxio1(B,k2_ltlaxio1(A)) ) ) ) )).
fof(t44_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( m1_subset_1(D,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(k3_hilbert1(B,k4_ltlaxio1(A,C)),k3_hilbert1(k3_hilbert1(A,D),k3_hilbert1(B,k4_ltlaxio1(D,C))))) ) ) ) ) )).
fof(t44_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t44_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t44_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( r1_matrix10(B,C) => r2_matrix10(B,C) ) ) ) ) )).
fof(t44_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(A)) ) => k6_matrix13(A,D,k3_matrix13(B),k3_matrix13(C)) = k2_matrlin(A,k13_matrix_0(A,k3_matrix_0(A,D,B,C))) ) ) ) ) )).
fof(t44_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(A),B,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,B) ) => k3_matrix_0(u1_struct_0(A),k4_matrix14(A,B,1),D,D) = k5_struct_0(A) ) ) ) ) ) )).
fof(t44_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ( 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_0(B))),k6_matrix13(u1_struct_0(A),C,D,k2_finseq_1(k1_matrix_0(C))))) ) ) ) ) ) ) )).
fof(t44_matrix16,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t44_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ( ~ v3_relat_1(B) <=> ( ~ r1_xxreal_0(k3_finseq_1(B),k5_numbers) & ~ r1_xxreal_0(k1_matrix_0(B),k5_numbers) ) ) ) ) )).
fof(t44_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) ) => k1_matrix_4(A,k2_matrix_3(A,B),C) = k1_matrix_4(A,k2_matrix_3(A,C),B) ) ) ) ) )).
fof(t44_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v4_matrix_6(C,A,B) & r1_matrix_6(A,B,C,D) ) => r1_matrix_6(A,B,k4_matrix_0(u1_struct_0(B),C),D) ) ) ) ) ) )).
fof(t44_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r2_matrix_8(A,B,C,D) => ( r1_xxreal_0(A,k5_numbers) | r2_matrix_8(A,B,D,C) ) ) ) ) ) ) )).
fof(t44_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => k17_rvsum_1(k8_finseq_1(k2_numbers,A,B)) = k2_xcmplx_0(k17_rvsum_1(A),k17_rvsum_1(B)) ) ) )).
fof(t44_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( 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_0(D))) => k16_matrix_0(k1_nat_1(A,k2_wsierp_1(k11_matrixj1(u1_struct_0(B),E))),u1_struct_0(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),k16_matrix_0(A,u1_struct_0(B),D)))) ) ) ) ) ) ) )).
fof(t44_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( ~ r1_xxreal_0(k3_finseq_1(A),k5_numbers) => k7_matrixr1(k5_numbers,A) = k8_matrixr1(k3_finseq_1(A),k1_matrix_0(A)) ) ) )).
fof(t44_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => k3_matrixr2(A,B) = k3_matrixr2(A,k4_matrix_0(k1_numbers,B)) ) ) )).
fof(t44_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( m1_matrlin(D,A,B) => ! [E] : ( m1_matrlin(E,A,C) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(A),k3_finseq_1(D),k3_finseq_1(E)) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(A))) ) => ( k8_matrix13(A,F) = k3_finseq_1(D) => v2_funct_1(k4_matrlin2(A,B,C,D,E,F)) ) ) ) ) ) ) ) )).
fof(t44_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & v4_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t44_matrprob,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(C) & k3_finseq_1(B) = k1_matrix_0(C) ) => ( r1_xxreal_0(k3_finseq_1(B),k5_numbers) | k22_rvsum_1(A,k11_matrixr1(C,B)) = k5_matrprob(k6_matrprob(A,B,C)) ) ) ) ) ) )).
fof(t44_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ? [D] : ( v3_card_1(D,B) & m2_finseq_1(D,k1_numbers) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(D)) => k1_funct_1(D,E) = k12_euclid(k2_matrtop1(k8_matrix_0(u1_struct_0(k2_vectsp_1),C,E))) ) ) & ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v3_card_1(E,A) & v1_finseq_1(E) & v3_valued_0(E) ) => r1_xxreal_0(k12_euclid(k1_funct_1(k3_matrtop1(A,B,C),E)),k3_xcmplx_0(k18_rvsum_1(D),k12_euclid(E))) ) ) ) ) ) )).
fof(t44_mcart_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t44_measure6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( v4_xxreal_2(A) => k2_seq_4(A) = k4_xcmplx_0(k3_seq_4(k3_measure6(A))) ) ) )).
fof(t44_member_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) )).
fof(t44_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) & v5_memstr_0(C,A,B,k5_numbers) ) => k8_memstr_0(A,B,C) = C ) ) ) )).
fof(t44_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t44_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ~ ( r1_mesfun7c(A,B,C) & ! [D] : ( ( v1_prob_2(D) & m2_finseq_1(D,B) ) => ! [E] : ( 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] : ( v7_ordinal1(F) => ( r2_hidden(F,k4_finseq_1(D)) => ! [G] : ( r2_hidden(G,k1_funct_1(D,F)) => k1_funct_1(C,G) = k1_funct_1(E,F) ) ) ) ) ) ) ) ) ) ) )).
fof(t44_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t44_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,k6_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) ) ) ) ) ) ) ) )).
fof(t44_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => r2_relset_1(A,k6_numbers,k1_mesfunc5(A,k56_valued_1(A,k1_numbers,B)),k10_mesfunc1(A,k1_mesfunc5(A,B))) ) ) )).
fof(t44_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(A),B) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ( ( k1_relset_1(A,k4_mesfunc5(A,k6_numbers,D,k5_numbers)) = C & v2_mesfunc9(D,A) & v1_mesfunc8(D,A,k6_numbers) & ! [E] : ( v7_ordinal1(E) => r1_mesfunc1(A,B,k4_mesfunc5(A,k6_numbers,k4_mesfunc9(A,D),E),C) ) & ! [E] : ( 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) ) ) ) ) ) )).
fof(t44_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_midsp_1(B,A) => k7_midsp_1(A,B,k6_midsp_1(A)) = B ) ) )).
fof(t44_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( ( k1_relset_1(A,C) = A & k1_relset_1(A,D) = A ) => r2_relset_1(A,A,k23_mmlquery(A,k20_mmlquery(A,C,D),B),k19_mmlquery(A,k23_mmlquery(A,C,B),k23_mmlquery(A,D,B))) ) ) ) ) )).
fof(t44_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k48_modelc_1(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k48_modelc_1(A,B,C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k48_modelc_1(A,B,C))) => ( ! [H] : ( m1_subset_1(H,A) => ( r3_modelc_1(A,B,C,H,F) => r3_modelc_1(A,B,C,H,G) ) ) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t44_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ~ ( r3_modelc_2(A,k8_modelc_2(B,C)) & ~ r2_modelc_2(A,B) & ~ r2_modelc_2(A,C) ) ) ) ) )).
fof(t44_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_3(B,A) & v3_modelc_3(B,A) & l1_modelc_3(B,A) ) => m1_subset_1(B,k23_modelc_3(A)) ) ) )).
fof(t44_moebius1,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k4_ordinal1)) ) => ( r1_xboole_0(A,B) => r8_pboole(k4_ordinal1,k4_moebius1(k4_subset_1(k4_ordinal1,A,B)),k11_pre_poly(k4_ordinal1,k4_moebius1(A),k4_moebius1(B))) ) ) ) )).
fof(t44_monoid_0,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_monoid_0)) <=> m1_subset_1(A,k4_ordinal1) ) )).
fof(t44_monoid_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t44_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => m1_msafree(k13_msafree(A,B),A,C) ) ) ) )).
fof(t44_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(t44_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msualg_4(C,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,B)) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t44_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_mycielsk(B,A) => ! [C] : ( 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))) ) ) ) ) ) ) )).
fof(t44_nat_1,axiom,( ! [A] : ( v1_finset_1(A) => ~ ( ~ r1_xxreal_0(k5_card_1(A),1) & ! [B] : ! [C] : ~ ( r2_hidden(B,A) & r2_hidden(C,A) & B != C ) ) ) )).
fof(t44_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( r1_int_2(A,B) => r1_xboole_0(k22_pre_poly(k8_newton,k12_nat_3(A)),k22_pre_poly(k8_newton,k12_nat_3(B))) ) ) ) )).
fof(t44_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(A,B) => r1_xxreal_0(k7_nat_d(A,1),B) ) ) ) )).
fof(t44_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ~ ( r2_hidden(E,C) & ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( v1_xreal_0(G) => ~ ( ~ r1_xxreal_0(G,k5_numbers) & ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ~ ( r2_hidden(H,C) & ~ r1_xxreal_0(G,k2_normsp_0(A,k5_algstr_0(A,H,E))) & r1_xxreal_0(F,k2_normsp_0(B,k5_algstr_0(B,k7_partfun1(u1_struct_0(B),D,H),k7_partfun1(u1_struct_0(B),D,E)))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t44_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_ndiff_1(A,B,C,D) => r1_nfcont_1(A,B,C,D) ) ) ) ) ) )).
fof(t44_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(1))) => ! [D] : ( m1_subset_1(D,k1_numbers) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t44_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_prvect_2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_prvect_2(A))) => ! [D] : ( m1_subset_1(D,k4_card_3(k4_prvect_2(A))) => ! [E] : ( m1_subset_1(E,k4_card_3(k4_prvect_2(A))) => ! [F] : ( ( 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(k2_normsp_0(k14_prvect_2(A),C),k2_normsp_0(k14_prvect_2(A),B)) ) ) ) ) ) ) )).
fof(t44_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_nat_d(B,A) <=> k5_nat_d(B,A) = A ) ) ) )).
fof(t44_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r5_nfcont_1(A,A,B,k1_partfun2(u1_struct_0(A),B)) ) ) )).
fof(t44_nfcont_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k4_ordinal1) => ( 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))) ) ) ) ) ) )).
fof(t44_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(k7_normform(A))) => ! [C] : ( 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)) ) ) )).
fof(t44_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t44_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(t44_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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) & r1_integra5(k3_integra5(B,C),k4_normsp_0(k1_numbers,k4_real_ns1(A),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)) ) => ( r1_integra5(k3_integra5(k3_xxreal_0(D,E),k4_xxreal_0(D,E)),k4_normsp_0(k1_numbers,k4_real_ns1(A),F)) & v1_comseq_2(k2_partfun1(k1_numbers,k1_numbers,k4_normsp_0(k1_numbers,k4_real_ns1(A),F),k3_integra5(k3_xxreal_0(D,E),k4_xxreal_0(D,E)))) & r1_xxreal_0(k2_normsp_0(k4_real_ns1(A),k6_integr18(k4_real_ns1(A),F,D,E)),k4_integra5(k3_xxreal_0(D,E),k4_xxreal_0(D,E),k4_normsp_0(k1_numbers,k4_real_ns1(A),F))) ) ) ) ) ) ) ) ) )).
fof(t44_orders_1,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t44_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m2_orders_1(C,k1_orders_1(u1_struct_0(A)),k6_partfun1(k1_orders_1(u1_struct_0(A)))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t44_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => k12_ordinal2(A,k1_ordinal1(B)) = k11_ordinal2(A,k12_ordinal2(A,B)) ) ) )).
fof(t44_ordinal3,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t44_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r2_hidden(A,B) => r2_hidden(k3_ordinal5(A),k3_ordinal5(B)) ) ) ) )).
fof(t44_ordinal6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( 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)))) ) ) ) ) )).
fof(t44_osafree,axiom,( ! [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) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( 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] : ( 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))) ) ) ) ) )).
fof(t44_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t44_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ r2_parsp_2(A,B,D,E,C) ) ) ) ) ) ) )).
fof(t44_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(t44_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,B) => v3_funct_1(k2_partfun1(A,B,k4_partfun2(A,B,C,D),C)) ) ) ) ) )).
fof(t44_pboole,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t44_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k26_pcs_0(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k26_pcs_0(A,B))) => ( r1_orders_2(k26_pcs_0(A,B),C,D) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,C) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_hidden(F,D) & r1_orders_2(A,E,F) ) ) ) ) ) ) ) ) )).
fof(t44_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m1_rcomp_1(C,k3_funct_2(k1_euclid(3),k1_numbers,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] : ( ( v9_ordinal1(D) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,E) = k1_tarski(k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(2,3),B)) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),C) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,2,k1_pdiff_3(3,3,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,2,k1_pdiff_3(3,3,A),B))))) & k8_pdiff_5(A,B) = k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,2,k1_pdiff_3(3,3,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,2,k1_pdiff_3(3,3,A),B))))) ) ) ) ) ) ) ) ) )).
fof(t44_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ~ ( 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 = k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_1(F,A),C) & D = k1_funct_1(k6_pdiff_1(A,F,C),I) & r2_hidden(J,k1_rcomp_1(H,I)) & E = k1_funct_1(k6_pdiff_1(A,F,C),J) & r1_xxreal_0(G,k12_euclid(k8_euclid(A,E,B))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t44_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t44_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ( A != k5_numbers => k3_nat_d(A,A) = 1 ) ) )).
fof(t44_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B))) => k10_pnproc_1(A,B,C,k12_pnproc_1(A,B)) = C ) ) )).
fof(t44_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k17_polyform(A,B))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t44_polynom5,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t44_polynom8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(k1_algseq_1(A,B),D) & r1_xxreal_0(k1_algseq_1(A,C),D) ) => ( r1_xxreal_0(D,k5_numbers) | ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_polynom8(A,E,k2_nat_1(2,D)) => ( k1_polynom8(A,k2_nat_1(2,D)) = k4_struct_0(A) | r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_polynom5(A,k6_polynom8(k2_nat_1(2,D),A,k2_polynom8(A,k6_polynom8(k2_nat_1(2,D),A,B,E),k6_polynom8(k2_nat_1(2,D),A,C,E)),k11_algstr_0(A,E)),k11_algstr_0(A,k1_polynom8(A,k2_nat_1(2,D)))),k13_polynom3(A,B,C)) ) ) ) ) ) ) ) ) ) )).
fof(t44_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => ( ~ r1_xxreal_0(A,k5_numbers) => k2_power(A,B) = k4_prepower(A,B) ) ) ) )).
fof(t44_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t44_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( A != k5_numbers => k3_prepower(A,k2_xcmplx_0(B,C)) = k3_xcmplx_0(k3_prepower(A,B),k3_prepower(A,C)) ) ) ) ) )).
fof(t44_prob_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( m2_prob_1(D,A,B) => ( v1_prob_2(C) => r2_funct_2(k4_ordinal1,k1_numbers,k8_prob_1(A,B,k2_prob_3(A,C),D),k3_series_1(k8_prob_1(A,B,C,D))) ) ) ) ) ) )).
fof(t44_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t44_pscomp_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t44_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t44_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( r1_qc_lang2(A,B,k1_qc_lang2(A)) <=> B = k12_qc_lang1(A) ) ) ) )).
fof(t44_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( ( ~ 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) ) ) ) ) )).
fof(t44_quatern2,axiom,( k28_quaterni(k4_struct_0(k15_quatern2)) = k5_numbers )).
fof(t44_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => r1_xxreal_0(k7_xcmplx_0(k2_xcmplx_0(k28_quaterni(k22_quaterni(A,B)),k28_quaterni(k25_quaterni(B,A))),2),k2_xcmplx_0(k28_quaterni(A),k28_quaterni(B))) ) ) )).
fof(t44_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ( k13_quaterni(k27_quaterni(A)) = k13_quaterni(A) & k14_quaterni(k27_quaterni(A)) = k4_xcmplx_0(k14_quaterni(A)) & k15_quaterni(k27_quaterni(A)) = k4_xcmplx_0(k15_quaterni(A)) & k16_quaterni(k27_quaterni(A)) = k4_xcmplx_0(k16_quaterni(A)) ) ) )).
fof(t44_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k19_quofield(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k19_quofield(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t44_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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)) ) ) ) ) )).
fof(t44_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & r1_xxreal_0(D,B) & C = k3_rcomp_1(A,D) ) ) & ! [D] : ( v1_xreal_0(D) => ~ ( r1_xxreal_0(A,D) & ~ r1_xxreal_0(B,D) & C = k4_rcomp_1(D,B) ) ) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t44_relat_1,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(t44_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ! [D] : ! [E] : ( ~ ( ? [F] : ? [G] : ( 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] : ! [G] : ~ ( r2_hidden(F,D) & r2_hidden(G,E) & r2_hidden(F,k1_relset_2(B,A,k3_relset_1(A,B,C),G)) ) ) ) ) )).
fof(t44_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r7_rewrite1(A,B,C) => r5_rewrite1(A,B,C) ) ) )).
fof(t44_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(A)) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t44_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_afinsq_1(D))) => ! [F] : ( ( ~ 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 ) ) ) ) )).
fof(t44_rfunct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t44_rfunct_2,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(t44_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : 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))) ) ) )).
fof(t44_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_seq_2(C) => ( ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k1_funct_1(C,k2_xcmplx_0(A,D)),B) ) <=> r1_xxreal_0(k1_funct_1(k4_rinfsup1(C),A),B) ) ) ) ) ) )).
fof(t44_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v1_rlaffin1(k5_rusub_4(A,C,B),A) => v1_rlaffin1(C,A) ) ) ) ) )).
fof(t44_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => k3_rlsub_1(A,k4_struct_0(A),B) = u1_struct_0(B) ) ) )).
fof(t44_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t44_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(t44_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k4_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B)) = B ) ) )).
fof(t44_rlvect_2,axiom,( ! [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) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_rlvect_2(D,A) => ( m2_rlvect_2(D,A,C) => m2_rlvect_2(k8_rlvect_2(A,B,D),A,C) ) ) ) ) ) )).
fof(t44_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_rmod_2(D,A,B) => r2_hidden(C,k3_rmod_2(A,B,C,D)) ) ) ) ) )).
fof(t44_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ( B = k1_rmod_3(A,B,C,D) => ( ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & ? [G] : ( m1_subset_1(G,u1_struct_0(B)) & ? [H] : ( m1_subset_1(H,u1_struct_0(B)) & ? [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) ) ) ) ) ) ) )).
fof(t44_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(t44_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_robbins1(A,k15_robbins1(A,B),B) = k16_robbins1(A,B) ) ) )).
fof(t44_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t44_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v1_orders_3(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( 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))) ) ) )).
fof(t44_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k2_rpr_1(A,k3_subset_1(A,B),B) = k5_numbers ) ) )).
fof(t44_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( k3_rusub_1(A,k1_rlvect_1(A,C,D),B) = u1_struct_0(B) => ( D = k5_numbers | r1_struct_0(B,C) ) ) ) ) ) ) )).
fof(t44_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t44_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( m1_rusub_1(D,A) => ( m1_rusub_1(B,C) => m1_rusub_1(B,k1_rusub_2(A,C,D)) ) ) ) ) ) )).
fof(t44_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ( u1_struct_0(A) = k6_domain_1(u1_struct_0(A),k4_struct_0(A)) => ( C = k5_numbers | v1_xboole_0(k6_bhsp_2(A,B,C)) ) ) ) ) ) )).
fof(t44_rvsum_1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) & v1_finseq_1(C) ) => k1_funct_1(k24_valued_1(C,B),A) = k3_xcmplx_0(B,k1_funct_1(C,A)) ) ) )).
fof(t44_rvsum_2,axiom,( ! [A] : ( m2_finseq_2(A,k2_numbers,k4_finseq_2(k5_numbers,k2_numbers)) => k20_rvsum_1(A) = 1 ) )).
fof(t44_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( v1_ami_2(E) & ~ v1_scmfsa_m(E) & m1_subset_1(E,u1_struct_0(k1_scmfsa_2)) ) => ( ( k1_funct_1(B,E) = k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),k5_card_1(D)),7)))) ) ) ) ) ) ) )).
fof(t44_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => ! [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(C,u1_struct_0(k1_ami_3)) ) => ! [D] : ( ( 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(k7_card_1(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(k7_card_1(3),k1_scmfsa_2,B,D) = k1_funct_4(D,k2_extpro_1(k7_card_1(2),k1_ami_3,A,C)) ) ) ) ) ) )).
fof(t44_scmfsa_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [B] : ( ( v1_ami_2(B) & ~ v1_scmfsa_m(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ( ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1))) & ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ( ~ ( r1_xxreal_0(k1_funct_1(C,D),k3_funct_2(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k4_ordinal1,C,k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k5_scmfsa_9(D,A,B,E),1))) & k1_funct_1(C,D) != k5_numbers ) & ( k1_funct_1(C,D) = k5_numbers => r1_xxreal_0(k1_funct_1(D,B),k5_numbers) ) & ( r1_xxreal_0(k1_funct_1(D,B),k5_numbers) => k1_funct_1(C,D) = k5_numbers ) ) ) ) ) => v7_amistd_1(k2_scmfsa_9(B,A),k7_card_1(3),k1_scmfsa_2) ) ) ) )).
fof(t44_scmpds_2,axiom,( ! [A] : ( ( 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] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t44_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),F)) = k5_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) ) ) ) ) ) ) ) )).
fof(t44_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ! [F] : ( v7_ordinal1(F) => ( r1_xxreal_0(k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),E)),k5_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)) = k1_nat_1(k5_card_1(C),3) ) ) ) ) ) ) ) )).
fof(t44_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( v4_scmyciel(B) => ( r1_tarski(A,B) => r1_tarski(A,k7_scmyciel(B,k3_tarski(A))) ) ) ) )).
fof(t44_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( ~ r1_semi_af1(A,B,C,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ r2_semi_af1(A,B,C,D,E) ) ) ) ) ) ) )).
fof(t44_seq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,k26_valued_1(k4_ordinal1,k1_numbers,B,A)),k26_valued_1(k4_ordinal1,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,B),k5_xcmplx_0(A))) ) ) )).
fof(t44_seq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v3_membered(B) ) => ( ( ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => r1_xxreal_0(A,C) ) ) & ! [C] : ( v1_xreal_0(C) => ( ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => r1_xxreal_0(C,D) ) ) => r1_xxreal_0(C,A) ) ) ) => A = k3_seq_4(B) ) ) ) )).
fof(t44_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( k2_xcmplx_0(k1_square_1(A),k1_square_1(B)) = k1_square_1(C) & r1_xxreal_0(3,D) & r1_xxreal_0(k1_newton(C,k1_nat_1(D,2)),k2_xcmplx_0(k1_newton(A,k1_nat_1(D,2)),k1_newton(B,k1_nat_1(D,2)))) ) ) ) ) ) )).
fof(t44_setfam_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t44_setlim_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ( v3_prob_1(C) => r1_tarski(k1_funct_1(C,A),k3_funct_2(k4_ordinal1,k9_setfam_1(B),k2_setlim_1(B,C),k1_nat_1(A,1))) ) ) ) )).
fof(t44_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => r1_tarski(k4_subset_1(B,k9_nat_1(k9_setfam_1(B),k2_setlim_1(B,C),A),k9_nat_1(k9_setfam_1(B),k2_setlim_1(B,D),A)),k9_nat_1(k9_setfam_1(B),k2_setlim_1(B,k2_setlim_2(B,C,D)),A)) ) ) ) )).
fof(t44_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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 ) ) )).
fof(t44_sf_mastr,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => k4_sf_mastr(k11_compos_1(k1_scmfsa_2,A)) = k3_sf_mastr(A) ) )).
fof(t44_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t44_simplex0,axiom,( ! [A] : ! [B] : ( v1_int_1(B) => ! [C] : ( m1_simplex0(C,A) => ( r1_xxreal_0(k2_xxreal_3(1),B) => r1_xxreal_0(k6_simplex0(k8_simplex0(A,C,B)),B) ) ) ) )).
fof(t44_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_series_1(k4_sin_cos(A)) & k4_series_1(k4_sin_cos(A)) = k3_complex1(k11_comseq_3(k3_sin_cos(A))) ) ) )).
fof(t44_sin_cos2,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(1,k1_funct_1(k5_sin_cos2,A)) & ~ r1_xxreal_0(k1_funct_1(k5_sin_cos2,A),k4_xcmplx_0(1)) ) ) )).
fof(t44_sin_cos3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1))) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,A),k1_funct_1(k3_sin_cos2,B)),k3_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,A),k1_funct_1(k1_sin_cos2,B))),k7_complex1)) ) ) )).
fof(t44_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => k4_sin_cos2(k3_xcmplx_0(3,A)) = k6_xcmplx_0(k3_xcmplx_0(4,k1_newton(k4_sin_cos2(A),3)),k3_xcmplx_0(3,k4_sin_cos2(A))) ) )).
fof(t44_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( k19_sin_cos(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A)) = 1 => r2_hidden(A,k4_numbers) ) ) )).
fof(t44_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) & k4_sin_cos7(A) != k3_xcmplx_0(k7_xcmplx_0(1,2),k2_sin_cos7(k7_xcmplx_0(k2_xcmplx_0(1,k1_square_1(A)),k6_xcmplx_0(1,k1_square_1(A))))) ) ) )).
fof(t44_sin_cos9,axiom,( k4_sin_cos9(k5_numbers) = k7_xcmplx_0(k28_sin_cos,2) & k1_funct_1(k2_sin_cos9,k5_numbers) = k7_xcmplx_0(k28_sin_cos,2) )).
fof(t44_sincos10,axiom,( k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k7_xcmplx_0(k28_sin_cos,2)))) = k1_rcomp_1(1,k3_square_1(2)) )).
fof(t44_sppol_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t44_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k9_pscomp_1(A) = k3_seq_4(k7_relset_1(u1_struct_0(k15_euclid(2)),k1_numbers,k5_pscomp_1,A)) ) )).
fof(t44_sprect_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t44_sprect_3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(k5_numbers,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,k13_matrix_0(u1_struct_0(k15_euclid(2)),k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),B,k6_xcmplx_0(1,D)),k1_rlvect_1(k15_euclid(2),C,D)))) ) ) ) ) ) )).
fof(t44_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t44_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(A,B) & r1_xxreal_0(k1_square_1(B),k1_square_1(A)) ) ) ) )).
fof(t44_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) ) => ( ( r3_stacks_1(A,B,D,F) & r3_stacks_1(B,C,E,G) ) => r3_stacks_1(A,C,k3_relat_1(D,E),k3_relat_1(F,G)) ) ) ) ) ) ) ) ) )).
fof(t44_stirl2_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( 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,k1_nat_1(B,1)))) ) ) )).
fof(t44_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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))) ) ) ) )).
fof(t44_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ~ ( r2_xboole_0(B,C) & ! [D] : ( m1_subset_1(D,A) => ~ ( r2_hidden(D,C) & r1_tarski(B,k7_subset_1(A,C,k1_tarski(D))) ) ) ) ) ) ) )).
fof(t44_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v6_supinf_2(A) => ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => k12_supinf_2(A,B) != k1_supinf_1 ) | k19_supinf_2(A) = k1_supinf_1 ) ) ) )).
fof(t44_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => m2_nat_lat(k12_tdlat_1(A),k4_tdlat_1(A)) ) )).
fof(t44_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(t44_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v4_tdlat_3(A) & l1_pre_topc(A) ) => k4_tdlat_1(A) = k12_tdlat_1(A) ) )).
fof(t44_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v3_tex_2(B,A) <=> v1_zfmisc_1(B) ) ) ) )).
fof(t44_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t44_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t44_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => r1_tmap_1(A,B,C,D) ) ) ) ) ) )).
fof(t44_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_borsuk_2(H,A,B,C) => ! [I] : ( m1_borsuk_2(I,A,C,D) => ! [J] : ( m1_borsuk_2(J,A,D,E) => ! [K] : ( m1_borsuk_2(K,A,E,F) => ! [L] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t44_topgen_3,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(t44_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) => v6_topgen_4(B,A) ) ) ) )).
fof(t44_topgen_5,axiom,( v7_topgen_1(k2_topgen_3) )).
fof(t44_topgrp_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t44_topreal6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(2))) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [D] : ( v1_xreal_0(D) => ( ( C = k8_metric_1(k14_euclid(2),B,D) & A = B ) => k8_pscomp_1(C) = k2_xcmplx_0(k17_euclid(A),D) ) ) ) ) ) )).
fof(t44_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => r1_tarski(k5_jgraph_6(A,B,C),k7_jgraph_6(A,B,C)) ) ) ) )).
fof(t44_toprealb,axiom,( v3_tops_2(k13_toprealb(k4_toprealb(k7_xcmplx_0(1,2))),k1_pre_topc(k2_topalg_2,k5_toprealb(k2_rcomp_1(k4_toprealb(k7_xcmplx_0(1,2)),k2_xcmplx_0(k4_toprealb(k7_xcmplx_0(1,2)),1)))),k11_toprealb(k3_funct_2(u1_struct_0(k2_topalg_2),u1_struct_0(k8_toprealb(2)),k12_toprealb,k4_toprealb(k7_xcmplx_0(1,2))))) )).
fof(t44_toprealc,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( ( 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))))) ) ) ) ) )).
fof(t44_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ( v3_toprns_1(B,A) => v2_toprns_1(B,A) ) ) ) )).
fof(t44_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t44_tops_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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))) ) ) ) ) ) )).
fof(t44_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t44_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t44_trees_1,axiom,( k7_trees_1(k2_trees_1(k5_numbers)) = 1 )).
fof(t44_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ! [C] : ( 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) ) ) ) )).
fof(t44_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => k2_trees_2(A,k5_numbers) = k1_tarski(k1_xboole_0) ) )).
fof(t44_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_connsp_1(A,B,C) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & ? [E] : ( 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) ) ) ) ) ) ) )).
fof(t44_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( m1_pre_topc(C,A) => ! [D] : ( m1_pre_topc(D,A) => ! [E] : ( m1_pre_topc(E,B) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t44_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( l1_turing_1(B) => ! [C] : ( m1_subset_1(C,k3_zfmisc_1(u2_turing_1(B),u1_turing_1(B),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1))) => ! [D] : ( m1_subset_1(D,u2_turing_1(B)) => ! [E] : ( 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),k1_enumset1(k4_xcmplx_0(1),k5_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),k1_enumset1(k4_xcmplx_0(1),k5_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),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),C)),k2_mcart_1(u2_turing_1(B),u1_turing_1(B),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),C),k3_mcart_1(u2_turing_1(B),u1_turing_1(B),k1_enumset1(k4_xcmplx_0(1),k5_numbers,1),C)) ) ) ) ) ) ) )).
fof(t44_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(k34_twoscomp(A,B),k35_twoscomp(A,B)))) => ! [D] : ( m1_subset_1(D,k6_margrel1) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t44_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ? [C] : ( m1_subset_1(C,u1_struct_0(k1_complfld)) & C = B & k2_polynom4(k1_complfld,k4_uniroots(A,k1_complfld),C) = k6_xcmplx_0(k1_newton(B,A),1) ) ) ) )).
fof(t44_uproots,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & v1_uproots(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( r1_polynom5(A,C,B) & r1_xxreal_0(k1_algseq_1(A,k5_uproots(A,B,C)),k5_numbers) ) ) ) ) )).
fof(t44_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t44_valued_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(B,k4_finseq_1(C)) => k1_funct_1(k14_finseq_1(k1_relset_1(k4_ordinal1,k61_valued_1(C,A))),B) = k1_nat_1(A,B) ) ) ) ) )).
fof(t44_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( ( 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) ) ) )).
fof(t44_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_vectsp_4(D,A,B) => r2_hidden(C,k3_vectsp_4(A,B,C,D)) ) ) ) ) )).
fof(t44_vectsp_5,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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)) ) ) ) )).
fof(t44_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t44_vfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,u1_struct_0(C)))) ) => ! [E] : ( v1_xreal_0(E) => ( r1_vfunct_1(B,C,D,A) => r1_vfunct_1(B,C,k4_vfunct_1(B,C,D,E),A) ) ) ) ) ) )).
fof(t44_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( r1_vfunct_2(A,B,C,E) => r1_vfunct_2(A,B,k2_vfunct_2(A,B,C,D),E) ) ) ) ) ) )).
fof(t44_waybel11,axiom,( ! [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) & v4_waybel11(A) & l1_waybel_9(A) ) => ! [B] : ( 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)))) ) ) ) )).
fof(t44_waybel12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ( v4_yellow_8(A) & v6_waybel_3(A) ) => v2_yellow_8(A) ) ) )).
fof(t44_waybel14,axiom,( ! [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) ) => ~ ( v2_waybel_8(k1_yellow_1(k5_waybel11(A))) & ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(k5_waybel11(A)))) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_yellow_1(k5_waybel11(A))))) & B = k1_yellow_0(k1_yellow_1(k5_waybel11(A)),C) & ! [D] : ( m1_subset_1(D,u1_struct_0(k1_yellow_1(k5_waybel11(A)))) => ( r2_hidden(D,C) => v6_waybel_6(D,k1_yellow_1(k5_waybel11(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)))) ) => B != a_1_0_waybel14(A) ) ) ) )).
fof(t44_waybel20,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t44_waybel21,axiom,( ! [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) & l1_waybel_9(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t44_waybel23,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t44_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v4_waybel11(C) & m1_yellow_9(C,k1_yellow_1(u1_pre_topc(B))) ) => ! [D] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k1_waybel26(A,C))) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t44_waybel27,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t44_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k8_waybel34(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k8_waybel34(A))) => ! [D] : ( 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))))) ) ) ) ) ) )).
fof(t44_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ( ( v1_lattice3(A) | v2_lattice3(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t44_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t44_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ( ! [B] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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) ) ) )).
fof(t44_waybel_4,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_setfam_1(a_2_2_waybel_4(A,B)) = k1_waybel_3(A,B) ) ) )).
fof(t44_waybel_7,axiom,( ! [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) & l1_orders_2(A) ) => ( v5_waybel_7(k1_waybel_4(A),A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v4_waybel_7(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t44_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( v2_wellord1(A) & r3_wellord1(A,B,C) ) => v2_wellord1(B) ) ) ) ) )).
fof(t44_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(k4_xboole_0(A,B),C) => r1_tarski(A,k2_xboole_0(B,C)) ) )).
fof(t44_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k5_xboolean(A,k9_xboolean(A,B)) = k6_xboolean(B,A) ) ) )).
fof(t44_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t44_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(B,k6_xcmplx_0(B,A)) ) ) ) )).
fof(t44_xtuple_0,axiom,( ! [A] : ! [B] : r1_tarski(k14_xtuple_0(k3_xboole_0(A,B)),k3_xboole_0(k14_xtuple_0(A),k14_xtuple_0(B))) )).
fof(t44_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => k3_xxreal_0(A,k2_xxreal_0) = k2_xxreal_0 ) )).
fof(t44_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(A,C) => ( r1_xxreal_0(B,D) | r1_tarski(k3_xxreal_1(C,D),k2_xxreal_1(A,B)) ) ) ) ) ) ) )).
fof(t44_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ( ( r1_tarski(A,B) & v3_xxreal_2(B) ) => v3_xxreal_2(A) ) ) ) )).
fof(t44_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k5_numbers,C) ) => k1_xxreal_3(k1_xxreal_3(A,B),C) = k1_xxreal_3(A,k1_xxreal_3(B,C)) ) ) ) ) )).
fof(t44_yellow10,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t44_yellow12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t44_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t44_yellow20,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(A,B) => r1_tarski(k2_funct_4(A),k2_funct_4(B)) ) ) ) )).
fof(t44_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_orders_2(A,k3_yellow_0(A),B) ) ) )).
fof(t44_yellow_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) => ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & D = a_3_0_yellow_2(A,B,C) & r1_yellow_0(k1_yellow_1(k7_waybel_0(A)),k7_domain_1(u1_struct_0(k1_yellow_1(k7_waybel_0(A))),B,C)) & k10_lattice3(k1_yellow_1(k7_waybel_0(A)),B,C) = k3_waybel_0(A,D) ) ) ) ) )).
fof(t44_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t44_yellow_4,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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))) ) ) ) ) )).
fof(t44_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t44_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m4_yellow_6(B,A) => ( k12_yellow_6(k13_yellow_6(A,B)) = B <=> v8_yellow_6(B,A) ) ) ) )).
fof(t44_yellow_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t44_yellow_9,axiom,( ! [A] : ( l1_waybel_9(A) => m1_yellow_9(A,A) ) )).
fof(t44_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v6_zf_lang(A) => A = k8_zf_lang(k23_zf_lang(A),k24_zf_lang(A)) ) ) )).
fof(t44_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ~ ( r2_zf_lang(A,B) & r1_zf_lang(B,A) ) ) ) )).
fof(t44_zfmisc_1,axiom,( ! [A] : ! [B] : ( k3_xboole_0(B,k1_tarski(A)) = k1_tarski(A) => r2_hidden(A,B) ) )).
fof(t44_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_struct_0(B,D) => r1_struct_0(C,D) ) ) => m1_zmodul01(B,C) ) ) ) ) )).
fof(t44_zmodul02,axiom,( ! [A] : ( ( ~ 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_struct_0(k31_zmodul02(A)) = k19_zmodul02(A) ) )).
fof(t45_abcmiz_0,axiom,( ! [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) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_abcmiz_0(A)) => ( r3_abcmiz_0(A,B,C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t45_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ( k3_finseq_1(k1_msualg_1(A,B)) = 2 => ! [C] : ( m1_subset_1(C,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [D] : ( m1_subset_1(D,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ( ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( 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)) ) ) ) ) ) ) )).
fof(t45_abcmiz_a,axiom,( ! [A] : ( ( 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 ) )).
fof(t45_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(D,E) & ~ r2_hidden(B,E) & r2_aff_1(A,B,C,E) & B != C & r1_aff_1(A,D,B,C) ) ) ) ) ) ) )).
fof(t45_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_1(D,A) & v1_aff_1(E,A) & r2_aff_4(A,D,E,C) & r2_aff_4(A,D,E,B) ) => ( D = E | r2_aff_4(A,D,C,B) ) ) ) ) ) ) ) )).
fof(t45_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( 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,k5_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 ) ) ) )).
fof(t45_afinsq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,A) & v1_funct_1(C) & v5_ordinal1(C) & v1_finset_1(C) ) => ! [D] : ( ( 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] : ( ( 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] : ( v7_ordinal1(F) => ( r2_hidden(F,k1_relset_1(k4_ordinal1,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) ) ) ) ) ) ) ) )).
fof(t45_afproj,axiom,( ! [A] : ( ( ~ 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) ) ) ) )).
fof(t45_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k4_struct_0(k5_afvect0(A,B)) = B ) ) )).
fof(t45_algspec1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => m2_algspec1(A,A) ) )).
fof(t45_algstr_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ( ( r1_tarski(B,C) & r1_funct_2(A,B,A,C,D,E) ) => r1_funct_2(u1_struct_0(k14_algstr_4(A)),u1_struct_0(k14_algstr_4(B)),u1_struct_0(k14_algstr_4(A)),u1_struct_0(k14_algstr_4(C)),k18_algstr_4(A,B,D),k18_algstr_4(A,C,E)) ) ) ) ) ) ) )).
fof(t45_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) )).
fof(t45_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r7_analmetr(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t45_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ~ ( r1_analmetr(A,J,K) & r2_analort(A,J,K,B,C,E,F) & r2_analort(A,J,K,E,F,H,I) & r2_analort(A,J,K,D,G,H,I) & ~ r2_analort(A,J,K,B,C,D,G) & E != F & H != I ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t45_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ( g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)) = g1_unialg_1(u1_struct_0(B),u1_unialg_1(B)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( ( C = D & v1_unialg_2(C,A) ) => v1_unialg_2(D,B) ) ) ) ) ) ) )).
fof(t45_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( ( v19_aofa_a00(F,A) & m1_subset_1(F,u1_struct_0(A)) ) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),F)) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),F)) => ! [I] : ( m2_subset_1(I,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => k15_aofa_a00(A,B,C,D,u8_aofa_a00(A),k33_aofa_a00(A,C,F,G,H),I) = k33_aofa_a00(A,D,F,k15_aofa_a00(A,B,C,D,F,G,I),k15_aofa_a00(A,B,C,D,F,H,I)) ) ) ) ) ) ) ) ) ) )).
fof(t45_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [E] : ( ( v1_aofa_i00(E,A,B,D) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),D) ) => ! [F] : ( v1_int_1(F) => ! [G] : ( 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) = k4_int_1(k21_aofa_i00(B,k4_numbers,C,G),F) & ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t45_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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))) ) ) )).
fof(t45_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ! [C] : ( ( v3_ordinal1(C) & v7_ordinal1(C) ) => ! [D] : ( ( v3_ordinal1(D) & v7_ordinal1(D) ) => ~ ( C != k1_xboole_0 & A != k1_xboole_0 & ~ ( k8_arytm_3(B,C) = k8_arytm_3(D,A) <=> k9_ordinal3(B,A) = k9_ordinal3(C,D) ) ) ) ) ) ) )).
fof(t45_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(10,A) & r1_xxreal_0(k2_power(2,k6_xcmplx_0(A,1)),k1_square_1(k2_nat_1(2,A))) ) ) )).
fof(t45_bcialg_1,axiom,( ! [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) ) => ( v12_bcialg_1(k4_bcialg_1(A),A) & m2_bcialg_1(k4_bcialg_1(A),A) ) ) )).
fof(t45_bcialg_2,axiom,( ! [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) ) => r1_tarski(k4_bcialg_2(A),k5_bcialg_2(A)) ) )).
fof(t45_bcialg_3,axiom,( ! [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) & v6_bcialg_3(A) & l2_bcialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v2_bcialg_3(B,A) => ( v11_bcialg_3(A) <=> ! [C] : ( 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) ) ) ) ) ) )).
fof(t45_bcialg_4,axiom,( ! [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) & l1_bcialg_4(A) ) => ( v4_bcialg_4(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_bcialg_1(A,B,C) => k1_bcialg_4(A,B,C) = C ) ) ) ) ) )).
fof(t45_bcialg_5,axiom,( ! [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) ) => ( ( ~ 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,k5_numbers,1,1,1) ) ) )).
fof(t45_bcialg_6,axiom,( ! [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] : ( ( ~ 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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( ( 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)))) ) => ( m2_bcialg_1(C,B) => m2_bcialg_1(k8_relset_1(u1_struct_0(A),u1_struct_0(B),D,C),A) ) ) ) ) ) )).
fof(t45_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( v3_bciideal(B,A) & m2_bcialg_1(B,A) ) ) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t45_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,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)) ) ) ) ) )).
fof(t45_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(C,k4_bhsp_2(A,B,D)) => r2_hidden(k5_algstr_0(A,C,B),k4_bhsp_2(A,k4_struct_0(A),D)) ) ) ) ) ) )).
fof(t45_bhsp_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(C)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(C),k5_bhsp_4(C,D,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)),k5_bhsp_4(C,k5_bhsp_4(C,D,B),A)) ) ) ) ) )).
fof(t45_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ 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] : ( ( 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)) ) ) ) ) )).
fof(t45_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t45_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k1_borsuk_4))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_topmetr)) => ( A = k3_rcomp_1(B,1) => v4_pre_topc(A,k1_borsuk_4) ) ) ) )).
fof(t45_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => k3_rcomp_1(A,k1_xxreal_0) != k1_numbers ) )).
fof(t45_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( ( 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,k5_numbers) = k5_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) ) ) ) ) ) ) )).
fof(t45_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( B = k1_funct_1(k12_toprealb,A) => k3_euclid_3(B) = k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k3_int_1(A)) ) ) ) )).
fof(t45_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t45_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t45_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t45_bvfunc26,axiom,( ! [A] : ( ~ 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)) ) )).
fof(t45_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k3_xboolean(k8_xboolean(A,B)) = k4_xboolean(A,B) ) ) )).
fof(t45_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t45_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t45_card_1,axiom,( k1_card_1(k4_ordinal1) = k4_ordinal1 )).
fof(t45_card_2,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => k5_card_1(k2_zfmisc_1(A,B)) = k2_nat_1(k5_card_1(A),k5_card_1(B)) ) ) )).
fof(t45_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_finset_1(B) ) => ! [C] : ( B = k16_funcop_1(C,A) => k3_card_fin(1,B) = k5_card_1(A) ) ) ) )).
fof(t45_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v11_cat_1(B,A) => ! [C] : ( m1_cat_1(C,A,B,B) => k4_cat_1(A,B) = C ) ) ) ) )).
fof(t45_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t45_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k23_cat_4(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k23_cat_4(A,B))) => C = D ) ) )).
fof(t45_catalan2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => r2_funct_2(k4_ordinal1,k1_numbers,k4_catalan2(A,k26_valued_1(k4_ordinal1,k1_numbers,B,C)),k26_valued_1(k4_ordinal1,k1_numbers,k4_catalan2(A,B),C)) ) ) ) )).
fof(t45_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => k4_struct_0(k9_cc0sp2(A)) = k1_cc0sp2(A,k5_numbers) ) )).
fof(t45_cfcont_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ! [C] : ( ( 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) ) ) ) )).
fof(t45_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t45_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ( ( v5_cgames_1(A) => ! [B] : ( v2_cgames_1(B) => ~ ( r2_hidden(B,k7_cgames_1(A)) & ~ v8_cgames_1(B) & ~ v9_cgames_1(B) ) ) ) & ( ! [B] : ( 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] : ( v2_cgames_1(B) => ~ ( r2_hidden(B,k6_cgames_1(A)) & ~ v8_cgames_1(B) & ~ v10_cgames_1(B) ) ) ) & ( ! [B] : ( v2_cgames_1(B) => ~ ( r2_hidden(B,k6_cgames_1(A)) & ~ v8_cgames_1(B) & ~ v10_cgames_1(B) ) ) => v6_cgames_1(A) ) ) ) )).
fof(t45_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( m1_chain_1(F,A) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k2_finseq_1(A))) => ! [H] : ( 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] : ( m2_subset_1(I,k4_ordinal1,k2_finseq_1(A)) => ( ( r2_hidden(I,G) & ~ r1_xxreal_0(k1_funct_1(C,I),k1_funct_1(B,I)) & m2_chain_1(k4_tarski(k1_funct_1(B,I),k1_funct_1(C,I)),k2_chain_1(A,F,I)) ) | ( ~ r2_hidden(I,G) & k1_funct_1(B,I) = k1_funct_1(C,I) & r2_hidden(k1_funct_1(B,I),k2_chain_1(A,F,I)) ) ) ) & ! [I] : ( m2_subset_1(I,k4_ordinal1,k2_finseq_1(A)) => ( ( r2_hidden(I,H) & ~ r1_xxreal_0(k1_funct_1(E,I),k1_funct_1(D,I)) & m2_chain_1(k4_tarski(k1_funct_1(D,I),k1_funct_1(E,I)),k2_chain_1(A,F,I)) ) | ( ~ r2_hidden(I,H) & k1_funct_1(D,I) = k1_funct_1(E,I) & r2_hidden(k1_funct_1(D,I),k2_chain_1(A,F,I)) ) ) ) ) => ( r1_tarski(G,H) & ! [I] : ( m2_subset_1(I,k4_ordinal1,k2_finseq_1(A)) => ( ~ ( ~ r2_hidden(I,G) & r2_hidden(I,H) ) => ( k1_funct_1(B,I) = k1_funct_1(D,I) & k1_funct_1(C,I) = k1_funct_1(E,I) ) ) ) & ! [I] : ( m2_subset_1(I,k4_ordinal1,k2_finseq_1(A)) => ~ ( ~ r2_hidden(I,G) & r2_hidden(I,H) & ~ ( k1_funct_1(B,I) = k1_funct_1(D,I) & k1_funct_1(C,I) = k1_funct_1(D,I) ) & ~ ( k1_funct_1(B,I) = k1_funct_1(E,I) & k1_funct_1(C,I) = k1_funct_1(E,I) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t45_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t45_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(D) & v1_finset_1(D) ) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t45_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ( v1_circcomb(A) => r1_tarski(u4_struct_0(A),u1_struct_0(A)) ) ) )).
fof(t45_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v4_msualg_1(E,A) & v4_msafree2(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( ( v4_msualg_1(F,B) & v4_msafree2(F,B) & l3_msualg_1(F,B) ) => ( r4_circtrm1(A,B,C,D,E,F) => ! [G] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(B,F))) => ! [H] : ( m1_subset_1(H,k4_card_3(u3_msualg_1(A,E))) => ( ( H = k3_relat_1(C,G) & ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ( r2_hidden(I,k2_msafree2(A)) => r1_facirc_1(B,F,G,k1_funct_1(C,I)) ) ) ) => k6_circuit2(A,E,H) = k3_relat_1(C,k6_circuit2(B,F,G)) ) ) ) ) ) ) ) ) ) ) )).
fof(t45_classes1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)))) ) ) )).
fof(t45_classes2,axiom,( ! [A] : ( v1_ordinal1(A) => k4_classes1(k1_card_1(k1_classes1(A))) = k1_classes1(A) ) )).
fof(t45_clvect_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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 ) ) ) )).
fof(t45_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(C,k4_clvect_2(A,B,D)) => r2_hidden(k5_algstr_0(A,C,B),k4_clvect_2(A,k4_struct_0(A),D)) ) ) ) ) ) )).
fof(t45_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k2_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => k6_clvect_3(A,B,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,C,D)) = k6_clvect_3(A,k6_clvect_3(A,B,D),C) ) ) ) ) )).
fof(t45_coh_sp,axiom,( ! [A] : ! [B] : ( 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 ) ) )).
fof(t45_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ~ ( ! [D] : ! [E] : ~ ( r2_hidden(D,C) & r2_hidden(E,C) & ! [F] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t45_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k9_complex1(A) = k5_numbers => A = k5_numbers ) ) )).
fof(t45_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k1_complex2(A,k6_xcmplx_0(B,C)) = k6_xcmplx_0(k1_complex2(A,B),k1_complex2(A,C)) ) ) ) )).
fof(t45_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ! [C] : ( 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) ) ) ) ) )).
fof(t45_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( v1_xcmplx_0(B) => k10_seq_4(A,k4_xcmplx_0(B)) = k9_seq_4(k10_seq_4(A,B)) ) ) )).
fof(t45_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(A)) => k1_funct_1(k11_compos_1(A,B),1) = k2_compos_1(A) ) ) )).
fof(t45_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t45_comptrig,axiom,( ! [A] : ( v1_xcmplx_0(A) => ~ ( ~ r1_xxreal_0(k4_complex1(A),k5_numbers) & r1_xxreal_0(k17_sin_cos(k1_comptrig(A)),k5_numbers) ) ) )).
fof(t45_comput_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v3_margrel1(B,A) & m2_rfunct_3(B,k3_finseq_2(A),A,k2_comput_1(A)) ) => ! [C] : ( ( v3_comput_1(C) & m2_finseq_1(C,k2_comput_1(A)) ) => ( ( k19_margrel1(B) = k3_finseq_1(C) & ! [D] : ( 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(k5_funct_6(C),B),A) & m2_rfunct_3(k3_relat_1(k5_funct_6(C),B),k3_finseq_2(A),A,k2_comput_1(A)) ) ) ) ) ) )).
fof(t45_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)),k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,A),k55_valued_1(k4_ordinal1,k2_numbers,B))) ) ) )).
fof(t45_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ? [C] : ( v7_ordinal1(C) & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => r1_xxreal_0(B,k9_complex1(k9_nat_1(k2_numbers,A,D))) ) ) ) & v2_comseq_2(k55_valued_1(k4_ordinal1,k2_numbers,A)) & k1_seq_2(k55_valued_1(k4_ordinal1,k2_numbers,A)) = k5_numbers ) ) ) )).
fof(t45_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t45_convex4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v1_xcmplx_0(C) => ( v2_convex4(B,A) => v2_convex4(k19_convex4(A,B,C),A) ) ) ) ) )).
fof(t45_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) )).
fof(t45_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t45_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t45_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t45_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k9_complex1(k12_csspace(A,B,C)),k3_xcmplx_0(k13_csspace(A,B),k13_csspace(A,C))) ) ) ) )).
fof(t45_dickson,axiom,( r7_relat_2(k10_dickson,k4_ordinal1) )).
fof(t45_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k9_diff_1(k18_sin_cos,A,B) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k17_sin_cos(k7_xcmplx_0(k2_xcmplx_0(A,B),2))),k17_sin_cos(k7_xcmplx_0(k6_xcmplx_0(A,B),2))),k6_xcmplx_0(A,B))) ) ) )).
fof(t45_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_square_1(D) ) => k1_funct_1(k3_diff_1(C,A),B) = k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,B),A),k1_square_1(A)) ) ) ) ) )).
fof(t45_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k4_diff_1(k4_diff_1(C,A),A),B) = k6_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k4_diff_1(C,A),B)),k1_funct_1(k4_diff_1(C,k3_xcmplx_0(2,A)),B)) ) ) ) )).
fof(t45_dilworth,axiom,( ! [A] : ( ( v4_dilworth(A) & l1_orders_2(A) ) => ! [B] : ( ( v2_dilworth(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t45_diraf,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t45_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( 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] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t45_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( 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] : ( 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) != k5_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) ) ) ) ) ) ) ) )).
fof(t45_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ( k3_graph_1(A,D) = k4_graph_1(A,C) => k18_ens_1(A,B,k1_cat_1(A,C,D)) = k1_partfun1(k2_cat_1(A,k4_graph_1(A,D),B),k2_cat_1(A,k3_graph_1(A,D),B),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,D),k18_ens_1(A,B,C)) ) ) ) ) ) )).
fof(t45_entropy1,axiom,( ! [A] : ( ( v1_matrprob(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( ( v1_matrprob(B) & m2_finseq_1(B,k1_numbers) ) => v1_matrprob(k2_entropy1(k1_numbers,k6_matrixr1(k9_matrixr1(A),k10_matrixr1(B)))) ) ) )).
fof(t45_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k5_enumset1(A,A,A,A,B,C,D) = k2_enumset1(A,B,C,D) )).
fof(t45_eqrel_1,axiom,( m1_eqrel_1(k1_xboole_0,k1_xboole_0) )).
fof(t45_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => k12_euclid(k21_euclid(A)) = k3_square_1(A) ) )).
fof(t45_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => k2_xcmplx_0(k1_square_1(k12_euclid(k3_rlvect_1(k15_euclid(A),B,C))),k1_square_1(k12_euclid(k5_algstr_0(k15_euclid(A),B,C)))) = k3_xcmplx_0(2,k2_xcmplx_0(k1_square_1(k12_euclid(B)),k1_square_1(k12_euclid(C)))) ) ) ) )).
fof(t45_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( A != B & C != B & ~ ( k22_rvsum_1(k5_algstr_0(k15_euclid(2),A,B),k5_algstr_0(k15_euclid(2),C,B)) = k5_numbers <=> ( k4_euclid_3(A,B,C) = k7_xcmplx_0(k28_sin_cos,2) | k4_euclid_3(A,B,C) = k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos) ) ) ) ) ) ) )).
fof(t45_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ~ ( v2_euclid_4(C,A) & ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ~ ( B != D & r2_hidden(D,C) ) ) ) ) ) ) )).
fof(t45_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => k4_euclid_3(A,B,C) != k2_xcmplx_0(k3_xcmplx_0(2,k4_euclid_3(D,E,F)),k3_xcmplx_0(4,k28_sin_cos)) ) ) ) ) ) ) )).
fof(t45_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => k1_rlvect_5(k10_funcsdom(k2_finseq_1(A))) = A ) )).
fof(t45_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => k3_finseq_1(k6_euclid(3,A)) = k3_finseq_1(A) ) )).
fof(t45_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ( r4_euclidlp(A,B,C) => r3_euclidlp(A,B,C) ) ) ) ) )).
fof(t45_exchsort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_orders_2(A,C,B) <=> ~ r3_orders_2(A,B,C) ) ) ) ) )).
fof(t45_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(B,u1_struct_0(k4_circcomb(A,C,B))) & ! [D] : ( r2_hidden(D,k10_xtuple_0(C)) => r2_hidden(D,u1_struct_0(k4_circcomb(A,C,B))) ) ) ) )).
fof(t45_fcont_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(B,C) = k9_complex1(C) ) ) => v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) ) )).
fof(t45_fdiff_10,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k16_sin_cos),A),B) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,k1_funct_1(k2_fdiff_9,B)),k1_funct_1(k18_sin_cos,B)),k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t45_fdiff_11,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,k1_relset_1(k1_numbers,k27_sin_cos)) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_sin_cos9)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_sin_cos9)),A),B) = k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k1_funct_1(k2_sin_cos9,B)),k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t45_fdiff_2,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) & r1_xxreal_0(k1_fdiff_1(A,B),k5_numbers) ) & ? [B] : ( v1_xreal_0(B) & r1_xxreal_0(k5_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] : ( v1_xreal_0(B) => ( 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) = k7_xcmplx_0(1,k1_fdiff_1(A,k1_funct_1(k2_partfun2(k1_numbers,k1_numbers,A),B))) ) ) ) ) ) ) )).
fof(t45_fdiff_4,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k16_sin_cos),A),B) = k2_xcmplx_0(k1_funct_1(k16_sin_cos,B),k3_xcmplx_0(B,k1_funct_1(k18_sin_cos,B))) ) ) ) ) ) )).
fof(t45_fdiff_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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,D,k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k16_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(4,A)))))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => ( k1_funct_1(D,E) = k7_xcmplx_0(E,2) & k1_funct_1(C,E) = k3_xcmplx_0(k3_xcmplx_0(2,A),E) ) ) ) ) => ( A = k5_numbers | ( r2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k16_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(4,A)))),B) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_1(k2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k16_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(4,A)))),B),E) = k1_square_1(k19_sin_cos(k3_xcmplx_0(A,E))) ) ) ) ) ) ) ) ) ) )).
fof(t45_fdiff_7,axiom,( ! [A] : ( ( 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,k22_sin_cos,k18_sin_cos))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k18_sin_cos),A),B) = k3_xcmplx_0(k1_funct_1(k22_sin_cos,B),k6_xcmplx_0(k1_funct_1(k18_sin_cos,B),k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t45_fdiff_9,axiom,( ! [A] : ( ( 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,k27_sin_cos,k2_fdiff_9))) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k2_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k2_fdiff_9),A),B) = k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B))),k1_funct_1(k16_sin_cos,B))),k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k27_sin_cos,B),k1_funct_1(k18_sin_cos,B)),k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t45_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(B,A) => r1_xxreal_0(k1_pre_ff(B),k1_pre_ff(A)) ) ) ) )).
fof(t45_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t45_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) ) ) ) ) )).
fof(t45_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ! [E] : ( ( ~ 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)) ) ) ) ) ) ) ) )).
fof(t45_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : ! [D] : ( A = k11_finseq_1(B,C,D) <=> ( k3_finseq_1(A) = 3 & k1_funct_1(A,1) = B & k1_funct_1(A,2) = C & k1_funct_1(A,3) = D ) ) ) )).
fof(t45_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( 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),k4_ordinal1,A,C,B),A) ) ) ) )).
fof(t45_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => r2_relset_1(k4_ordinal1,k4_ordinal1,k2_partfun1(k4_ordinal1,k4_ordinal1,k14_finseq_1(k2_finseq_1(k2_xcmplx_0(A,B))),k2_finseq_1(A)),k14_finseq_1(k2_finseq_1(A))) ) ) )).
fof(t45_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_finseq_4(A,B) <=> ( r2_hidden(B,k10_xtuple_0(A)) & ~ r2_hidden(B,k10_xtuple_0(k6_finseq_4(A,B))) ) ) ) )).
fof(t45_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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 ) ) ) ) )).
fof(t45_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => k2_rfinseq(A,1,k8_finseq_1(A,k12_finseq_1(A,B),C)) = C ) ) ) )).
fof(t45_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t45_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t45_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k9_fintopo3(A,B,C) = k3_subset_1(u1_struct_0(A),k7_fintopo3(A,k3_subset_1(u1_struct_0(A),B),C)) ) ) ) )).
fof(t45_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( m1_subset_1(C,k3_catalan2(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t45_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => k1_flang_2(A,B,k5_numbers,k5_numbers) = k4_flang_1(A,k2_flang_1(A)) ) )).
fof(t45_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( 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)) ) ) ) )).
fof(t45_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k21_fomodel0(k1_tarski(A)) = k10_xtuple_0(A) ) )).
fof(t45_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ~ ( ~ v7_pre_topc(A) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( r2_funct_2(k4_ordinal1,u1_struct_0(A),D,k8_funcop_1(u1_struct_0(A),k4_ordinal1,B)) & B != C & r1_frechet(A,D,C) ) ) ) ) ) ) )).
fof(t45_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & v8_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( ( ~ v2_struct_0(D) & v8_struct_0(D) & l2_fsm_1(D,A,B) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ~ ( D = k11_fsm_1(A,B,C) & E != F & r5_fsm_1(A,B,D,E,F) ) ) ) ) ) ) ) )).
fof(t45_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) ) )).
fof(t45_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( k9_xtuple_0(C) = k3_xboole_0(k9_xtuple_0(B),A) & ! [D] : ( r2_hidden(D,k9_xtuple_0(C)) => k1_funct_1(C,D) = k1_funct_1(B,D) ) ) => C = k5_relat_1(B,A) ) ) ) )).
fof(t45_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k1_xboole_0,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_xboole_0,B))) ) => k8_relset_1(k1_xboole_0,B,C,A) = k1_xboole_0 ) )).
fof(t45_funct_3,axiom,( ! [A] : ! [B] : r1_tarski(k10_xtuple_0(k8_funct_3(A,B)),B) )).
fof(t45_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t45_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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 ) ) ) )).
fof(t45_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k8_funct_6(k1_xboole_0,A) = k7_funcop_1(k9_xtuple_0(A),k1_tarski(k1_xboole_0)) ) )).
fof(t45_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(k9_xtuple_0(B),A) => k3_funct_7(A,k9_finseq_1(B)) = B ) ) )).
fof(t45_funct_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t45_functor0,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => ! [C] : ( l1_functor0(C,A,B) => ( ( v11_functor0(C,A,B) & v5_functor0(C,A,B) ) => v7_functor0(C,A,B) ) ) ) ) )).
fof(t45_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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))) ) ) )).
fof(t45_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D,C)),k2_fuzzy_1(A,k3_fuzzy_2(A,B,D),k3_fuzzy_2(A,B,C))) ) ) ) ) )).
fof(t45_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_fvaluat1(C,A) => ( ( v3_fvaluat1(A) & k3_funct_2(u1_struct_0(A),k6_numbers,C,B) = 1 ) => r2_funct_2(u1_struct_0(A),k6_numbers,k5_fvaluat1(A,C),C) ) ) ) ) )).
fof(t45_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [D] : ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t45_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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))) ) ) ) ) ) ) ) )).
fof(t45_genealg1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_genealg1(B,A) => ! [C] : ( m1_genealg1(C,A) => k11_genealg1(A,B,C,k5_numbers,k5_numbers,k5_numbers,k5_numbers,k5_numbers) = C ) ) ) )).
fof(t45_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(k7_geomtrap(A,D,E))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k7_geomtrap(A,D,E))) => ( ( r1_analmetr(A,D,E) & B = F & C = G ) => k1_geomtrap(A,B,C) = k9_geomtrap(k7_geomtrap(A,D,E),F,G) ) ) ) ) ) ) ) ) )).
fof(t45_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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) ) )).
fof(t45_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t45_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(C,D) & r1_xxreal_0(D,k3_finseq_1(B)) & r2_hidden(E,k1_relset_1(k4_ordinal1,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(k1_nat_1(C,E),1)) & r2_hidden(k6_xcmplx_0(k1_nat_1(C,E),1),k1_relset_1(k4_ordinal1,B)) ) ) ) ) ) ) ) )).
fof(t45_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) = k1_nat_1(k17_glib_000(A),1) ) ) ) )).
fof(t45_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_003(A) ) => ! [B] : ! [C] : ( 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)) ) ) )).
fof(t45_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ 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_0(k2_goboard2(D))) & r1_xxreal_0(1,C) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,2),B)) = k2_topreal1(2,D,C) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),B)) = k2_topreal1(2,D,k1_nat_1(C,1)) ) => ( r1_xxreal_0(k3_finseq_1(k2_goboard2(D)),k1_nat_1(A,1)) | r1_xxreal_0(k3_finseq_1(D),k1_nat_1(C,1)) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,2),B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,B) ) ) ) ) ) ) ) )).
fof(t45_graph_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( ( v3_graph_2(C,B) & m2_graph_1(C,B) ) => ( v3_graph_2(k2_partfun1(k4_ordinal1,u4_struct_0(B),C,k2_finseq_1(A)),B) & m2_graph_1(k2_partfun1(k4_ordinal1,u4_struct_0(B),C,k2_finseq_1(A)),B) ) ) ) ) )).
fof(t45_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t45_graph_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m2_finseq_1(C,u4_struct_0(B)) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ( ( r5_graph_5(B,A) & D = k9_graph_5(B,C,A) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k4_finseq_1(D)) => r1_xxreal_0(k5_numbers,k1_funct_1(D,E)) ) ) ) ) ) ) ) )).
fof(t45_graphsp,axiom,( ! [A] : ( 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] : ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( ~ r1_xxreal_0(k8_graphsp(A,B,C),D) & k7_graphsp(k6_graphsp(k9_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 ) ) ) ) ) )).
fof(t45_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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)) ) ) ) ) ) ) ) )).
fof(t45_group_1,axiom,( ~ v2_struct_0(g3_algstr_0(k1_numbers,k9_binop_2)) & v2_group_1(g3_algstr_0(k1_numbers,k9_binop_2)) & v3_group_1(g3_algstr_0(k1_numbers,k9_binop_2)) & v5_group_1(g3_algstr_0(k1_numbers,k9_binop_2)) & l3_algstr_0(g3_algstr_0(k1_numbers,k9_binop_2)) )).
fof(t45_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t45_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => k1_group_1(B) = k1_group_1(C) ) ) ) )).
fof(t45_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t45_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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)) ) ) ) ) )).
fof(t45_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t45_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( r1_struct_0(k10_group_6(A,B,C),D) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & D = k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,E) ) ) ) ) ) )).
fof(t45_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( ( 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) ) ) ) )).
fof(t45_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => k3_helly(A,B,C,D) = k3_helly(A,D,C,B) ) ) ) ) )).
fof(t45_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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(k1_square_1(k9_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))) ) ) ) ) )).
fof(t45_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( A != k5_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) = k4_xcmplx_0(k7_xcmplx_0(1,k1_square_1(A))) ) ) ) )).
fof(t45_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(t45_hurwitz,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(A,k1_complfld) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(B,k1_complfld) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(k1_complfld),k7_hurwitz(k8_polynom3(k1_complfld,A,B)),k8_polynom3(k1_complfld,k7_hurwitz(A),k7_hurwitz(B))) ) ) )).
fof(t45_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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 ) ) )).
fof(t45_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ~ ( ~ v3_incsp_1(k8_domain_1(u1_incsp_1(A),B,C,D),A) & ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => v4_incsp_1(k9_domain_1(u1_incsp_1(A),B,C,D,E),A) ) ) ) ) ) ) )).
fof(t45_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( A != k5_numbers => k1_int_1(k7_xcmplx_0(A,A)) = 1 ) ) )).
fof(t45_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => ! [F] : ( v1_int_1(F) => ~ ( A != k5_numbers & B != k5_numbers & C != k5_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] : ( v1_int_1(G) & k5_int_1(k6_xcmplx_0(G,D),A) = k5_numbers & k5_int_1(k6_xcmplx_0(G,E),B) = k5_numbers & k5_int_1(k6_xcmplx_0(G,F),C) = k5_numbers ) ) ) ) ) ) ) ) )).
fof(t45_int_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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) ) ) ) )).
fof(t45_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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(k4_xcmplx_0(1),1)) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(C,D) = k7_xcmplx_0(1,k2_xcmplx_0(1,k1_square_1(D))) ) ) & B = k9_xtuple_0(C) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,A)) ) => k2_integra5(A,C) = k6_xcmplx_0(k1_funct_1(k1_sin_cos9,k2_seq_4(A)),k1_funct_1(k1_sin_cos9,k3_seq_4(A))) ) ) ) ) )).
fof(t45_integr12,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,D) & r1_tarski(D,k2_rcomp_1(k4_xcmplx_0(1),1)) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => ( k1_funct_1(C,E) = 1 & ~ r1_xxreal_0(k1_funct_1(k3_sin_cos6,E),k5_numbers) ) ) ) & r1_tarski(D,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_sin_cos6,k3_taylor_1))) & D = k1_relset_1(k1_numbers,B) & 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_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(k7_xcmplx_0(1,2))),k3_sin_cos6))) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_sin_cos6,k3_taylor_1)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_sin_cos6,k3_taylor_1)),k3_seq_4(A))) ) ) ) ) ) )).
fof(t45_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,D) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => k1_funct_1(C,E) = 1 ) ) & r2_relset_1(k1_numbers,k1_numbers,B,k3_rfunct_1(k1_numbers,k1_numbers,k2_sin_cos9,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,C,k1_taylor_1(2)))) & r1_tarski(D,k2_rcomp_1(k4_xcmplx_0(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,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_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)),k7_xcmplx_0(1,2))),k2_seq_4(A)),k1_funct_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)),k7_xcmplx_0(1,2))),k3_seq_4(A))) ) ) ) ) ) )).
fof(t45_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k6_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,D))),k1_funct_1(k18_sin_cos,D)),k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k27_sin_cos,D),k1_funct_1(k16_sin_cos,D)),k1_square_1(k1_funct_1(k18_sin_cos,D)))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_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) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k1_fdiff_9)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k1_fdiff_9)),k3_seq_4(A))) ) ) ) ) )).
fof(t45_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t45_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [C] : ( m1_integra1(C,A) => ? [D] : ( m1_integra1(D,A) & r1_integra1(B,D) & r1_integra1(C,D) ) ) ) ) )).
fof(t45_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( A = k1_rcomp_1(k2_xcmplx_0(B,k3_xcmplx_0(k2_nat_1(2,C),k28_sin_cos)),k2_xcmplx_0(B,k3_xcmplx_0(k1_nat_1(k2_nat_1(2,C),1),k28_sin_cos))) => k2_integra5(A,k18_sin_cos) = k4_xcmplx_0(k3_xcmplx_0(2,k17_sin_cos(B))) ) ) ) ) )).
fof(t45_integra9,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( ~ 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] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => r1_xxreal_0(k5_numbers,k1_funct_1(k1_integra5(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,A,A),C),D)) ) ) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => r1_xxreal_0(k5_numbers,k1_funct_1(k1_integra5(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,B,B),C),D)) ) ) ) => k1_square_1(k2_integra9(C,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B))) = k2_xcmplx_0(k1_square_1(k2_integra9(C,A)),k1_square_1(k2_integra9(C,B))) ) ) ) ) )).
fof(t45_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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))) ) ) )).
fof(t45_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(t45_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => m1_isocat_1(k10_cat_1(A),A,A) ) )).
fof(t45_jgraph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t45_jgraph_2,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( m1_subset_1(G,u1_struct_0(k5_topmetr)) => ! [H] : ( m1_subset_1(H,u1_struct_0(k5_topmetr)) => ~ ( G = k5_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] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t45_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(B)) & ~ r1_xxreal_0(A,k7_xcmplx_0(k18_euclid(B),k12_euclid(B))) & ~ r1_xxreal_0(k5_numbers,k17_euclid(C)) & ~ r1_xxreal_0(A,k7_xcmplx_0(k18_euclid(C),k12_euclid(C))) & ~ r1_xxreal_0(k7_xcmplx_0(k18_euclid(C),k12_euclid(C)),k7_xcmplx_0(k18_euclid(B),k12_euclid(B))) & ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) & ? [E] : ( 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(k7_xcmplx_0(k18_euclid(E),k12_euclid(E)),k7_xcmplx_0(k18_euclid(D),k12_euclid(D))) ) ) ) ) ) ) )).
fof(t45_jgraph_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ 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(k5_numbers,k17_euclid(A)) | r1_xxreal_0(k5_numbers,k18_euclid(A)) | r1_xxreal_0(k5_numbers,k18_euclid(B)) | ( ~ r1_xxreal_0(k17_euclid(A),k17_euclid(B)) & ~ r1_xxreal_0(k18_euclid(B),k18_euclid(A)) ) ) ) ) ) ) )).
fof(t45_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t45_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t45_jordan,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t45_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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,B) & r1_xxreal_0(B,C) & r1_xxreal_0(1,A) & r1_xxreal_0(A,k1_matrix_0(k1_jordan8(D,C))) ) => r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(D,C),k1_jordan1a(k1_jordan8(D,C)),1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(D,C),k1_jordan1a(k1_jordan8(D,C)),A)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(D,B),k1_jordan1a(k1_jordan8(D,B)),1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(D,C),k1_jordan1a(k1_jordan8(D,C)),A))) ) ) ) ) ) )).
fof(t45_jordan1g,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,C) & ~ r1_xxreal_0(k3_finseq_1(k1_jordan8(B,A)),C) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,k1_matrix_0(k1_jordan8(B,A))),k3_topreal1(2,k2_jordan1e(B,A))) ) ) ) ) )).
fof(t45_jordan1h,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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)) => r2_hidden(k20_pscomp_1(B),k4_goboard5(k2_jordan9(B,A),1)) ) ) ) )).
fof(t45_jordan1j,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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 ) ) ) )).
fof(t45_jordan1k,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v2_compts_1(B,k15_euclid(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ( r2_hidden(C,B) => k5_jordan1k(A,C,B) = k5_numbers ) ) ) ) )).
fof(t45_jordan21,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( 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(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(B),k8_pscomp_1(B)),2))))) & k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)) = k2_xcmplx_0(k6_pscomp_1(B),k8_pscomp_1(B)) ) => ( v1_xboole_0(k9_subset_1(u1_struct_0(k15_euclid(2)),A,k6_jordan6(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)),2)))) | k1_jordan21(A) = k1_jordan21(B) ) ) ) ) )).
fof(t45_jordan2c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k14_euclid(1)))) => ! [B] : ( v1_xreal_0(B) => ~ ( A = a_1_1_jordan2c(B) & v6_tbsp_1(A,k14_euclid(1)) ) ) ) )).
fof(t45_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t45_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( 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)) ) ) ) ) ) ) )).
fof(t45_jordan5d,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(t45_jordan6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ! [F] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t45_knaster,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(t45_kurato_1,axiom,( 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)) )).
fof(t45_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k5_finsub_1(B)) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t45_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ! [C] : ( 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)) ) ) ) )).
fof(t45_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ! [E] : ( ( 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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),k13_lexbfs(A,k16_lexbfs(A),C)))) | r2_hidden(k7_nat_d(k15_glib_000(A),C),k17_lexbfs(k6_glib_000(A),k4_ordinal1,k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),k13_lexbfs(A,k16_lexbfs(A),B)),D)) ) ) ) ) ) )).
fof(t45_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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) = k2_xcmplx_0(k1_limfunc2(B,A),k1_limfunc2(C,A)) ) ) ) ) ) )).
fof(t45_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) = k5_numbers & ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,C) & ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ~ ( ~ 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_funct_1(B,E) != k5_numbers & k1_funct_1(B,F) != k5_numbers ) ) ) ) ) ) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,k9_subset_1(k1_numbers,k9_xtuple_0(B),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,C),A),k2_rcomp_1(A,k2_xcmplx_0(A,C))))) => r1_xxreal_0(k5_numbers,k1_funct_1(B,D)) ) ) ) ) | r2_limfunc3(k6_rfunct_1(k1_numbers,k1_numbers,B),A) ) ) ) ) )).
fof(t45_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k3_limfunc1(C))) & k1_funct_1(A,D) = k4_limfunc1(A) ) ) | v4_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).
fof(t45_lpspacc1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,C,k6_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,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => ! [G] : ( m1_subset_1(G,u1_struct_0(k24_lpspacc1(B,C,D))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k24_lpspacc1(B,C,D))) => ( ( ( r2_hidden(E,G) & r2_hidden(F,H) ) => r2_hidden(k2_valued_1(B,k2_numbers,k2_numbers,E,F),k1_algstr_0(k24_lpspacc1(B,C,D),G,H)) ) & ( r2_hidden(E,G) => r2_hidden(k25_valued_1(B,k2_numbers,E,A),k1_clvect_1(k24_lpspacc1(B,C,D),G,A)) ) ) ) ) ) ) ) ) ) ) )).
fof(t45_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t45_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [H] : ( ( v2_xxreal_0(H) & v1_xreal_0(H) ) => ( ( r2_hidden(D,k1_lpspace2(A,B,C,H)) & r2_hidden(F,k1_lpspace2(A,B,C,H)) & r2_hidden(E,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,F,H) & k5_lpspace2(A,B,C,E,H) = k5_lpspace2(A,B,C,G,H) ) => k5_lpspace2(A,B,C,k3_valued_1(A,k1_numbers,k1_numbers,D,E),H) = k5_lpspace2(A,B,C,k3_valued_1(A,k1_numbers,k1_numbers,F,G),H) ) ) ) ) ) ) ) ) ) )).
fof(t45_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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))) ) ) ) ) )).
fof(t45_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( m1_subset_1(D,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(k3_hilbert1(A,B),k3_hilbert1(k3_hilbert1(C,D),k3_hilbert1(k4_ltlaxio1(A,C),k4_ltlaxio1(B,D))))) ) ) ) ) )).
fof(t45_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t45_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( ( r1_matrix10(B,C) & r1_matrix10(C,D) ) => r1_matrix10(B,D) ) ) ) ) ) )).
fof(t45_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ! [D] : ( ( v7_ordinal1(D) & ~ v8_ordinal1(D) ) => ! [E] : ( ( v7_ordinal1(E) & ~ v8_ordinal1(E) ) => ! [F] : ( ( v1_matrix_0(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)) != k15_matrix_0(A,k3_matrix_0(A,F,B,D),k3_matrix_0(A,F,B,E),k3_matrix_0(A,F,C,D),k3_matrix_0(A,F,C,E)) ) ) ) ) ) ) ) )).
fof(t45_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(A),B,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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_0(u1_struct_0(A),k4_matrix14(A,B,1),D,E) = k4_struct_0(A) ) ) ) ) ) ) ) )).
fof(t45_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ( ( r1_tarski(D,k4_finseq_1(B)) & k4_finseq_1(B) = k4_finseq_1(C) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k7_subset_1(k4_ordinal1,k4_finseq_1(B),D)) => ( k7_matrix_0(u1_struct_0(A),B,E) = k5_finseq_2(u1_struct_0(A),k1_matrix_0(B),k4_struct_0(A)) & k7_matrix_0(u1_struct_0(A),C,E) = k5_finseq_2(u1_struct_0(A),k1_matrix_0(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_0(B))),k6_matrix13(u1_struct_0(A),C,D,k2_finseq_1(k1_matrix_0(C)))) ) ) ) ) ) ) )).
fof(t45_matrix16,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t45_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,C,k5_numbers,A) & m2_finseq_1(D,k3_finseq_2(C)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,C,k5_numbers,B) & m2_finseq_1(E,k3_finseq_2(C)) ) => D = E ) ) ) ) ) )).
fof(t45_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) ) => B = k1_matrix_4(A,k2_matrix_3(A,C),k1_matrix_4(A,k2_matrix_3(A,B),C)) ) ) ) ) )).
fof(t45_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_6(C,A,B) & v1_matrix_6(D,A,B) ) => ( v1_matrix_6(k4_matrix_3(B,C,D),A,B) & k1_matrix_6(A,B,k4_matrix_3(B,C,D)) = k4_matrix_3(B,k1_matrix_6(A,B,D),k1_matrix_6(A,B,C)) ) ) ) ) ) ) )).
fof(t45_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ( ( r2_matrix_8(A,B,C,D) & r2_matrix_8(A,B,D,E) ) => ( r1_xxreal_0(A,k5_numbers) | r2_matrix_8(A,B,C,E) ) ) ) ) ) ) ) )).
fof(t45_matrix_9,axiom,( ! [A] : ( ( 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(k4_ordinal1,3,2,1) & A != k3_finseq_4(k4_ordinal1,1,3,2) & A != k3_finseq_4(k4_ordinal1,2,1,3) ) ) )).
fof(t45_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ( k3_finseq_1(A) = 1 => k17_rvsum_1(A) = k9_matrix_5(A,1) ) ) )).
fof(t45_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v2_matrixj1(k1_xboole_0,A) & m2_finseq_1(k1_xboole_0,k3_finseq_2(k3_finseq_2(A))) ) ) )).
fof(t45_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( ~ r1_xxreal_0(k3_finseq_1(A),k5_numbers) => ( B = k9_matrixr1(A) <=> ( k8_matrix_0(k1_numbers,B,1) = A & k1_matrix_0(B) = 1 ) ) ) ) ) )).
fof(t45_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => k12_matrix_3(A,B,k4_matrix_3(B,C,D)) = k8_group_1(B,k12_matrix_3(A,B,C),k12_matrix_3(A,B,D)) ) ) ) ) )).
fof(t45_matrlin2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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,k3_matrix_1(B,A)),B,k6_prvect_1(B,A)) ) ) )).
fof(t45_matrprob,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => k22_rvsum_1(A,k5_finseq_2(k4_ordinal1,k3_finseq_1(A),1)) = k18_rvsum_1(A) ) )).
fof(t45_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ? [D] : ( v1_xreal_0(D) & ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v3_card_1(E,A) & v1_finseq_1(E) & v3_valued_0(E) ) => r1_xxreal_0(k12_euclid(k1_funct_1(k3_matrtop1(A,B,C),E)),k3_xcmplx_0(D,k12_euclid(E))) ) ) ) ) ) )).
fof(t45_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ ( ~ 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 ) )).
fof(t45_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v2_rcomp_1(A) <=> v2_rcomp_1(k3_measure6(A)) ) ) )).
fof(t45_member_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t45_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => k6_memstr_0(A,B,k8_memstr_0(A,B,C)) = k6_memstr_0(A,B,C) ) ) ) )).
fof(t45_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t45_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( r1_mesfun7c(A,B,C) <=> ? [D] : ( v1_prob_2(D) & m2_finseq_1(D,B) & ? [E] : ( m2_finseq_1(E,k2_numbers) & r3_mesfun7c(A,B,C,D,E) ) ) ) ) ) ) )).
fof(t45_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( v1_xcmplx_0(D) => ( r1_mesfun7c(A,B,C) => r1_mesfun7c(A,B,k25_valued_1(A,k2_numbers,C,D)) ) ) ) ) ) )).
fof(t45_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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))) ) ) )).
fof(t45_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ( ! [E] : ( v7_ordinal1(E) => r1_mesfunc5(A,B,C,k4_mesfunc5(A,k6_numbers,D,E)) ) => ! [E] : ( v7_ordinal1(E) => r1_mesfunc5(A,B,C,k4_mesfunc5(A,k6_numbers,k4_mesfunc9(A,D),E)) ) ) ) ) ) ) )).
fof(t45_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_midsp_1(B,A) => ? [C] : ( m1_midsp_1(C,A) & k7_midsp_1(A,B,C) = k6_midsp_1(A) ) ) ) )).
fof(t45_mmlquery,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(t45_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k48_modelc_1(A,B,C))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(A)) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t45_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r2_hidden(A,k13_modelc_2(B)) <=> r2_modelc_2(A,B) ) ) ) )).
fof(t45_modelc_3,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( m1_subset_1(A,k23_modelc_3(B)) <=> ? [C] : ( v1_modelc_3(C,B) & v3_modelc_3(C,B) & l1_modelc_3(C,B) & C = A ) ) ) )).
fof(t45_moebius1,axiom,( r8_pboole(k8_newton,k5_moebius1(1),k16_pre_poly(k8_newton)) )).
fof(t45_monoid_0,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_monoid_0)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_monoid_0)) => ( ( A = C & B = D ) => k6_algstr_0(k5_monoid_0,C,D) = k2_xcmplx_0(A,B) ) ) ) ) ) )).
fof(t45_monoid_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(B)) => ! [G] : ! [H] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t45_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & l3_msualg_1(D,A) ) => ! [E] : ( m1_msafree(E,A,C) => ( r8_pboole(u1_struct_0(A),E,k13_msafree(A,B)) => ! [F] : ( m2_pboole(F,u1_struct_0(A),E,u3_msualg_1(A,D)) => ? [G] : ( m2_pboole(G,u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D)) & r1_msualg_3(A,C,D,G) & r8_pboole(u1_struct_0(A),F,k1_msafree(u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D),E,G)) ) ) ) ) ) ) ) ) )).
fof(t45_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v2_relat_1(D) & m3_pboole(D,A,k1_mboolean(A,C)) ) => ( ! [E] : ( ( 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)) ) ) ) ) )).
fof(t45_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,B),D)) => ! [F] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t45_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_mycielsk(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t45_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(A,B) & ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(C,B) & A = C ) ) ) ) ) )).
fof(t45_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => r1_tarski(k22_pre_poly(k8_newton,k12_nat_3(A)),k22_pre_poly(k8_newton,k12_nat_3(k3_xcmplx_0(A,B)))) ) ) )).
fof(t45_nat_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => r1_xxreal_0(k3_wsierp_1(k14_finseq_1(a_1_0_nat_4(A))),k2_power(4,A)) ) )).
fof(t45_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => k7_nat_d(A,2) = k7_nat_d(k7_nat_d(A,1),1) ) )).
fof(t45_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ~ ( r2_hidden(E,C) & ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( v1_xreal_0(G) => ~ ( ~ r1_xxreal_0(G,k5_numbers) & ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ~ ( r2_hidden(H,C) & ~ r1_xxreal_0(G,k2_normsp_0(A,k5_algstr_0(A,H,E))) & r1_xxreal_0(F,k2_normsp_0(B,k5_algstr_0(B,k7_partfun1(u1_struct_0(B),D,H),k7_partfun1(u1_struct_0(B),D,E)))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t45_ndiff_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t45_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(1))) => ! [D] : ( m1_subset_1(D,k1_numbers) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [F] : ( ( 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(k4_ordinal1,1)) & ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t45_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_nat_d(B,C) & r1_nat_d(A,C) ) <=> r1_nat_d(k5_nat_d(B,A),C) ) ) ) ) )).
fof(t45_nfcont_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t45_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( 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) ) ) ) ) )).
fof(t45_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(k7_normform(A))) => ! [C] : ( 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)) ) ) )).
fof(t45_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t45_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t45_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( ( 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_xxreal_0(D,E) & r1_integr18(k4_real_ns1(A),k3_integra5(B,C),G) & r1_integra5(k3_integra5(B,C),k4_normsp_0(k1_numbers,k4_real_ns1(A),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] : ( v1_xreal_0(H) => ( r2_hidden(H,k3_integra5(D,E)) => r1_xxreal_0(k2_normsp_0(k4_real_ns1(A),k7_partfun1(u1_struct_0(k4_real_ns1(A)),G,H)),F) ) ) ) => ( r1_xxreal_0(k2_normsp_0(k4_real_ns1(A),k6_integr18(k4_real_ns1(A),G,D,E)),k3_xcmplx_0(F,k6_xcmplx_0(E,D))) & r1_xxreal_0(k2_normsp_0(k4_real_ns1(A),k6_integr18(k4_real_ns1(A),G,E,D)),k3_xcmplx_0(F,k6_xcmplx_0(E,D))) ) ) ) ) ) ) ) ) ) )).
fof(t45_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( 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))) ) ) ) )).
fof(t45_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m2_orders_1(B,k1_orders_1(u1_struct_0(A)),k6_partfun1(k1_orders_1(u1_struct_0(A)))) => m2_orders_2(k3_tarski(k4_orders_2(A,B)),A,B) ) ) )).
fof(t45_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( v4_ordinal1(B) => ( B = k5_ordinal1 | ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_ordinal2(C) ) => ( ( k9_xtuple_0(C) = B & ! [D] : ( v3_ordinal1(D) => ( r2_hidden(D,B) => k1_funct_1(C,D) = k12_ordinal2(A,D) ) ) ) => k12_ordinal2(A,B) = k8_ordinal2(C) ) ) ) ) ) ) )).
fof(t45_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( B != k1_xboole_0 => k3_tarski(k10_ordinal2(A,B)) = k10_ordinal2(A,k3_tarski(B)) ) ) ) )).
fof(t45_ordinal5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) ) => ( ! [B] : ( v3_ordinal1(B) => ( r2_hidden(B,k9_xtuple_0(A)) => k1_funct_1(A,B) = k3_ordinal5(B) ) ) => v2_ordinal2(A) ) ) )).
fof(t45_ordinal6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) ) => ( v2_ordinal6(A) => ! [B] : ( 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)) ) ) ) ) )).
fof(t45_osafree,axiom,( ! [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) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( 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) ) ) ) )).
fof(t45_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t45_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r3_parsp_2(A,B,B,C,D) => C = D ) ) ) ) ) )).
fof(t45_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => r2_hidden(C,k4_partfun1(A,B)) ) )).
fof(t45_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ( r1_tarski(k1_relset_1(A,C),k1_relset_1(A,D)) & ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,k1_relset_1(A,C)) => k7_partfun1(B,C,E) = k7_partfun1(B,D,E) ) ) ) => r1_relset_1(A,B,C,D) ) ) ) ) ) )).
fof(t45_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t45_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k26_pcs_0(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k26_pcs_0(A,B))) => ( ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,C) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_hidden(F,D) & r1_orders_2(A,E,F) ) ) ) ) => r1_orders_2(k26_pcs_0(A,B),C,D) ) ) ) ) ) )).
fof(t45_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m1_rcomp_1(C,k3_funct_2(k1_euclid(3),k1_numbers,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] : ( ( v9_ordinal1(D) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,E) = k1_tarski(k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(3,3),B)) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),C) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,3,k1_pdiff_3(3,3,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,3,k1_pdiff_3(3,3,A),B))))) & k9_pdiff_5(A,B) = k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),k1_pdiff_2(3,3,k1_pdiff_3(3,3,A),B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,k1_pdiff_2(3,3,k1_pdiff_3(3,3,A),B))))) ) ) ) ) ) ) ) ) )).
fof(t45_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(A)) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ~ ( 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] : ( m2_finseq_2(K,k1_numbers,k1_euclid(A)) => ( r2_hidden(K,C) => r3_pdiff_1(A,G,B,K) ) ) & ~ r1_xxreal_0(H,k5_numbers) & ! [K] : ( 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 = k1_funct_1(k6_pdiff_1(A,G,E),I) & J = k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_1(G,A),E) & ! [K] : ( 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) & k5_real_1(k7_partfun1(k1_numbers,B,F),k7_partfun1(k1_numbers,B,E)) = k3_xcmplx_0(k6_xcmplx_0(I,J),k10_pdiff_1(A,G,B,K)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t45_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ! [C] : ( ( 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] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(D,B) & ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( 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,k9_complex1(k5_real_1(k7_partfun1(k1_numbers,C,G),k7_partfun1(k1_numbers,C,D)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t45_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( v1_int_2(B) & v1_int_2(C) & A = k3_xcmplx_0(B,C) & r1_int_2(D,k1_euler_1(A)) & k4_nat_d(k3_xcmplx_0(D,E),k1_euler_1(A)) = 1 ) => ( B = C | ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ~ r1_xxreal_0(A,F) => k2_pepin(E,k2_pepin(D,F,A),A) = F ) ) ) ) ) ) ) ) ) )).
fof(t45_pnproc_1,axiom,( ! [A] : ! [B] : ( m2_pnproc_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_finseq_2(B))) => k11_pnproc_1(A,B,k12_pnproc_1(A,B),C) = C ) ) )).
fof(t45_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k17_polyform(A,B))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t45_polynom5,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k2_polynom4(A,k4_polynom5(A,B,k4_struct_0(A)),D) = B ) ) ) ) )).
fof(t45_polyred,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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),k11_polynom1(A,C,F,E),k8_polynom1(A,C)) ) ) ) ) ) ) ) )).
fof(t45_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(1,B) ) => k2_power(A,k7_xcmplx_0(1,B)) = k1_power(B,A) ) ) ) )).
fof(t45_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : ( r2_hidden(D,A) => r1_xxreal_0(k1_funct_1(B,D),k1_funct_1(C,D)) ) => r3_pre_poly(A,B,C) ) ) ) )).
fof(t45_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => k3_prepower(k3_prepower(A,B),C) = k3_prepower(A,k3_xcmplx_0(B,C)) ) ) ) )).
fof(t45_prob_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( m2_prob_1(D,A,B) => ( v1_prob_2(C) => ( v2_comseq_2(k3_series_1(k8_prob_1(A,B,C,D))) & k1_seq_2(k3_series_1(k8_prob_1(A,B,C,D))) = k1_rinfsup1(k3_series_1(k8_prob_1(A,B,C,D))) & k1_seq_2(k3_series_1(k8_prob_1(A,B,C,D))) = k1_funct_1(D,k1_kurato_0(A,C)) ) ) ) ) ) ) )).
fof(t45_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t45_pscomp_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(t45_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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,C,D) ) <=> r6_pboole(A,k3_pboole(A,k2_pzfmisc1(A,B,C),D),k2_pzfmisc1(A,B,C)) ) ) ) ) )).
fof(t45_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ( r1_qc_lang2(A,B,k14_qc_lang1(A,C,D)) <=> ( B = C | B = D ) ) ) ) ) ) )).
fof(t45_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( ( ~ 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))) ) ) ) ) )).
fof(t45_quatern2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_quatern2)) => ( k28_quaterni(A) = k5_numbers => A = k4_struct_0(k15_quatern2) ) ) )).
fof(t45_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => r1_xxreal_0(k7_xcmplx_0(k2_xcmplx_0(k28_quaterni(k22_quaterni(A,B)),k28_quaterni(k25_quaterni(A,B))),2),k2_xcmplx_0(k28_quaterni(A),k28_quaterni(B))) ) ) )).
fof(t45_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ( A = k5_numbers => k27_quaterni(A) = k5_numbers ) ) )).
fof(t45_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k19_quofield(A))) => ~ ( B != k4_struct_0(k19_quofield(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(k19_quofield(A))) => k8_group_1(k19_quofield(A),B,C) != k5_struct_0(k19_quofield(A)) ) ) ) ) )).
fof(t45_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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) ) ) ) ) ) )).
fof(t45_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(k9_nat_1(k1_numbers,k4_real_3(A),k5_numbers),k5_numbers) => ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,k5_real_3(A),B),k5_numbers) ) ) ) )).
fof(t45_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( r1_tarski(k9_xtuple_0(B),A) => k3_relat_1(k4_relat_1(A),B) = B ) ) )).
fof(t45_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) => ! [E] : ( 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)) ) ) ) ) )).
fof(t45_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r8_rewrite1(A,B,C) => r6_rewrite1(A,B,C) ) ) )).
fof(t45_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(A)) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t45_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ~ v1_xboole_0(F) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k8_afinsq_1(F))) => ! [H] : ( ( ~ v2_struct_0(H) & l1_rewrite3(H,G) ) => ( ( v2_rewrite3(H,F,G) & r2_hidden(k4_tarski(A,k4_tarski(B,D)),k1_rewrite3(F,G,H)) & r2_hidden(k4_tarski(A,k4_tarski(C,E)),k1_rewrite3(F,G,H)) ) => ( B = C & D = E ) ) ) ) ) )).
fof(t45_rfunct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t45_rfunct_2,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(t45_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : 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))) ) ) )).
fof(t45_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_seq_2(C) => ( ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(A,D) => r1_xxreal_0(k1_funct_1(C,D),B) ) ) <=> r1_xxreal_0(k1_funct_1(k4_rinfsup1(C),A),B) ) ) ) ) ) )).
fof(t45_rlaffin1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( v1_rlaffin1(k1_convex1(B,C,A),B) => ( A = k5_numbers | v1_rlaffin1(C,B) ) ) ) ) ) )).
fof(t45_rlsub_1,axiom,( ! [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) ) => ! [B] : ( 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) ) ) )).
fof(t45_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( ( r1_rlsub_2(A,B,C) & F = k3_rlvect_1(A,G,H) & F = k3_rlvect_1(A,D,E) & r1_struct_0(B,G) & r1_struct_0(B,D) & r1_struct_0(C,H) & r1_struct_0(C,E) ) => ( G = D & H = E ) ) ) ) ) ) ) ) ) ) )).
fof(t45_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_yellow13(B,A,k4_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t45_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t45_rlvect_2,axiom,( ! [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) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_rlvect_2(D,A) => r1_rlvect_2(A,k8_rlvect_2(A,k2_xcmplx_0(B,C),D),k7_rlvect_2(A,k8_rlvect_2(A,B,D),k8_rlvect_2(A,C,D))) ) ) ) ) )).
fof(t45_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => k3_rmod_2(A,B,k4_struct_0(B),C) = u1_struct_0(C) ) ) ) )).
fof(t45_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t45_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t45_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k9_robbins1(A,k15_robbins1(A,B),k11_robbins1(A,B)) = B ) ) )).
fof(t45_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t45_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ! [D] : ( 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) ) ) ) )).
fof(t45_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_xboole_0(B,C) => ( r1_xxreal_0(k1_rpr_1(A,C),k5_numbers) | k2_rpr_1(A,C,k3_subset_1(A,B)) = 1 ) ) ) ) ) )).
fof(t45_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t45_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(t45_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t45_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ~ ( u1_struct_0(A) != k6_domain_1(u1_struct_0(A),k4_struct_0(A)) & ~ r1_xxreal_0(C,k5_numbers) & v1_xboole_0(k6_bhsp_2(A,B,C)) ) ) ) ) )).
fof(t45_rvsum_1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) & v1_finseq_1(C) ) => k1_funct_1(k10_rvsum_1(C,B),A) = k3_xcmplx_0(B,k1_funct_1(C,A)) ) ) )).
fof(t45_rvsum_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xcmplx_0(C) => k19_rvsum_1(k2_finseq_2(k2_xcmplx_0(A,B),C)) = k3_xcmplx_0(k19_rvsum_1(k2_finseq_2(A,C)),k19_rvsum_1(k2_finseq_2(B,C))) ) ) ) )).
fof(t45_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( ( 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),k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),k5_card_1(D)),7)))) ) ) ) ) ) ) ) )).
fof(t45_scmfsa8c,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t45_scmfsa_2,axiom,( ! [A] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(A,u1_struct_0(k1_ami_3)) ) => ! [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(k7_card_1(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) ) ) ) )).
fof(t45_scmpds_2,axiom,( ! [A] : ( ( 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] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t45_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),F)) != k5_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) ) ) ) ) ) ) ) )).
fof(t45_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ! [G] : ( v7_ordinal1(G) => ( r1_xxreal_0(k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),F)),k5_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) ) ) ) ) ) ) ) ) )).
fof(t45_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : k3_tarski(k7_scmyciel(A,B)) = k3_xboole_0(k3_tarski(A),B) ) )).
fof(t45_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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 ) ) ) ) ) ) ) )).
fof(t45_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,k32_valued_1(k4_ordinal1,k1_numbers,A)),k26_valued_1(k4_ordinal1,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,A),k4_xcmplx_0(1))) ) )).
fof(t45_seq_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_membered(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => r1_xxreal_0(D,C) ) ) => r1_xxreal_0(k2_seq_4(A),C) ) ) ) ) )).
fof(t45_series_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_newton(k2_xcmplx_0(1,k7_xcmplx_0(1,A)),k1_nat_1(A,1)),k1_newton(k2_xcmplx_0(1,k7_xcmplx_0(1,k1_nat_1(A,1))),A)) ) ) )).
fof(t45_setfam_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( m1_setfam_1(B,A) <=> k5_setfam_1(A,B) = A ) ) )).
fof(t45_setlim_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ( v3_prob_1(C) => k1_funct_1(k2_setlim_1(B,C),A) = k1_funct_1(C,A) ) ) ) )).
fof(t45_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => r1_tarski(k9_nat_1(k9_setfam_1(B),k2_setlim_1(B,k3_setlim_2(B,C,D)),A),k7_subset_1(B,k9_nat_1(k9_setfam_1(B),k2_setlim_1(B,C),A),k9_nat_1(k9_setfam_1(B),k2_setlim_1(B,D),A))) ) ) ) )).
fof(t45_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( 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)) ) ) ) ) )).
fof(t45_sf_mastr,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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)) ) ) )).
fof(t45_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t45_simplex0,axiom,( ! [A] : ! [B] : ( v1_int_1(B) => ! [C] : ( 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) ) ) ) )).
fof(t45_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k4_series_1(k4_sin_cos(k2_xcmplx_0(A,B))) = k3_xcmplx_0(k4_series_1(k4_sin_cos(A)),k4_series_1(k4_sin_cos(B))) ) ) )).
fof(t45_sin_cos3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,k2_xcmplx_0(A,k3_xcmplx_0(k4_xcmplx_0(B),k7_complex1))) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,A),k1_funct_1(k3_sin_cos2,B)),k3_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,A),k1_funct_1(k1_sin_cos2,B)),k7_complex1)) ) ) )).
fof(t45_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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))) ) ) )).
fof(t45_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k2_sin_cos2(A) != k5_numbers => k1_sin_cos5(k3_xcmplx_0(2,A)) = k7_xcmplx_0(k2_xcmplx_0(1,k1_square_1(k1_sin_cos5(A))),k3_xcmplx_0(2,k1_sin_cos5(A))) ) ) )).
fof(t45_sin_cos6,axiom,( k7_relset_1(k1_numbers,k1_numbers,k16_sin_cos,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))) = k1_rcomp_1(k4_xcmplx_0(1),1) )).
fof(t45_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(1,k1_square_1(A)) => k4_sin_cos7(A) = k3_xcmplx_0(k7_xcmplx_0(1,2),k4_sin_cos7(k7_xcmplx_0(k3_xcmplx_0(2,A),k2_xcmplx_0(1,k1_square_1(A))))) ) ) )).
fof(t45_sin_cos9,axiom,( v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k1_sin_cos9,k7_relset_1(k1_numbers,k1_numbers,k26_sin_cos,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))))) )).
fof(t45_sincos10,axiom,( r1_tarski(k1_rcomp_1(1,k3_square_1(2)),k1_relset_1(k1_numbers,k1_sincos10)) )).
fof(t45_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t45_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k7_pscomp_1(A) = k2_seq_4(k7_relset_1(u1_struct_0(k15_euclid(2)),k1_numbers,k5_pscomp_1,A)) ) )).
fof(t45_sprect_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t45_sprect_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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,k13_matrix_0(u1_struct_0(k15_euclid(2)),k7_partfun1(u1_struct_0(k15_euclid(2)),C,A))) ) ) ) ) )).
fof(t45_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t45_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) => r1_xxreal_0(k4_xcmplx_0(A),k1_square_1(A)) ) ) )).
fof(t45_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r3_stacks_1(A,B,C,D) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t45_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k3_xcmplx_0(A,k3_stirl2_1(B,A)) = k1_card_1(a_2_3_stirl2_1(A,B)) ) ) )).
fof(t45_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t45_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ~ ( ~ v1_zfmisc_1(B) & ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & C != D ) ) ) ) ) )).
fof(t45_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ~ ( v6_supinf_2(A) & ? [B] : ( m1_subset_1(B,k4_ordinal1) & k12_supinf_2(A,B) = k1_supinf_1 ) & v7_supinf_2(A) ) ) )).
fof(t45_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(t45_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v4_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_tdlat_1(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t45_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t45_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t45_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t45_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ( r1_tmap_1(A,B,D,F) => r1_tmap_1(A,C,E,F) ) ) ) ) ) ) ) ) ) )).
fof(t45_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_borsuk_6(A,B,C) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t45_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k2_topgen_1(A,B) = k1_xboole_0 ) ) )).
fof(t45_topgen_3,axiom,( ! [A] : k2_tex_1(A) = k7_topgen_3(A,k11_arytm_3) )).
fof(t45_topgen_5,axiom,( v7_topgen_1(k3_topgen_5) )).
fof(t45_topgrp_1,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => v4_pre_topc(k5_group_2(A,C,B),A) ) ) ) )).
fof(t45_topreal3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( k3_finseq_1(B) = A => r2_hidden(B,u1_struct_0(k14_euclid(A))) ) ) ) )).
fof(t45_topreal6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(2))) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [D] : ( v1_xreal_0(D) => ( ( C = k8_metric_1(k14_euclid(2),B,D) & A = B ) => k9_pscomp_1(C) = k6_xcmplx_0(k18_euclid(A),D) ) ) ) ) ) )).
fof(t45_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(2))) => ( D = k19_euclid(A,B) => k9_metric_1(k14_euclid(2),D,C) = k7_jgraph_6(A,B,C) ) ) ) ) ) )).
fof(t45_toprealb,axiom,( ? [A] : ( 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(k5_numbers,1)),k7_relset_1(u1_struct_0(k2_topalg_2),u1_struct_0(k8_toprealb(2)),k12_toprealb,k2_rcomp_1(k7_xcmplx_0(1,2),k7_xcmplx_0(3,2)))) & m1_setfam_1(A,u1_struct_0(k8_toprealb(2))) & v1_tops_2(A,k8_toprealb(2)) & ! [B] : ( 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(k5_numbers,1)) => ( k5_setfam_1(u1_struct_0(k2_topalg_2),k3_toprealb(k5_numbers,1)) = k8_relset_1(u1_struct_0(k2_topalg_2),u1_struct_0(k8_toprealb(2)),k12_toprealb,B) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_topalg_2))) => ( r2_hidden(C,k3_toprealb(k5_numbers,1)) => ! [D] : ( ( 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(k7_xcmplx_0(1,2),k7_xcmplx_0(3,2))) => ( k5_setfam_1(u1_struct_0(k2_topalg_2),k3_toprealb(k7_xcmplx_0(1,2),k7_xcmplx_0(3,2))) = k8_relset_1(u1_struct_0(k2_topalg_2),u1_struct_0(k8_toprealb(2)),k12_toprealb,B) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_topalg_2))) => ( r2_hidden(C,k3_toprealb(k7_xcmplx_0(1,2),k7_xcmplx_0(3,2))) => ! [D] : ( ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t45_toprealc,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( ( 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))))) ) ) ) ) )).
fof(t45_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ~ ( v3_toprns_1(B,A) & k6_toprns_1(A,B) != k4_struct_0(k15_euclid(A)) & ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & r1_xxreal_0(k12_euclid(k9_nat_1(u1_struct_0(k15_euclid(A)),B,D)),k7_xcmplx_0(k12_euclid(k6_toprns_1(A,B)),2)) ) ) ) ) ) )).
fof(t45_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tops_1(B,A) <=> ! [C] : ( 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) ) ) ) ) ) )).
fof(t45_tops_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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))) ) ) ) ) ) )).
fof(t45_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t45_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t45_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ! [C] : ( m1_trees_1(C,k9_xtuple_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t45_trees_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => k2_trees_2(B,k1_nat_1(A,1)) = k3_tarski(a_2_3_trees_9(A,B)) ) ) )).
fof(t45_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_connsp_1(A,B,C) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & ? [E] : ( 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) ) ) ) ) ) ) )).
fof(t45_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ~ ( ~ r1_tsep_1(C,B) & ~ r1_tsep_1(D,B) & ? [E] : ( m1_pre_topc(E,B) & ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t45_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( l1_turing_1(B) => ! [C] : ( m1_subset_1(C,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k9_funct_2(k4_numbers,u1_turing_1(A)))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m2_funct_2(E,k4_numbers,u1_turing_1(A),k9_funct_2(k4_numbers,u1_turing_1(A))) => ! [F] : ( m1_subset_1(F,k3_zfmisc_1(u2_turing_1(B),k4_numbers,k9_funct_2(k4_numbers,u1_turing_1(B)))) => ! [G] : ( 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),k4_ordinal1,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)),k4_ordinal1,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)) ) ) ) ) ) ) ) ) ) )).
fof(t45_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t45_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => k7_uproots(k1_complfld,k4_uniroots(A,k1_complfld)) = k1_uproots(u1_struct_0(k1_complfld),k2_uniroots(A),1) ) )).
fof(t45_uproots,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) )).
fof(t45_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m1_valuat_1(E,A,B) => r2_valuat_1(A,B,E,k8_cqc_lang(A,k11_cqc_lang(A,C,D),D)) ) ) ) ) ) )).
fof(t45_valued_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(B,k4_finseq_1(C)) => k1_funct_1(k15_finseq_1(k61_valued_1(C,A)),B) = k1_funct_1(C,B) ) ) ) ) )).
fof(t45_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( ( 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)) ) ) ) ) )).
fof(t45_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => k3_vectsp_4(A,B,k4_struct_0(B),C) = u1_struct_0(C) ) ) ) )).
fof(t45_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m2_vectsp_4(E,A,B,C) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t45_vectsp_6,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t45_vfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( 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,k4_normsp_0(B,C,D),A)) & r1_vfunct_1(B,C,k5_vfunct_1(B,C,D),A) ) ) ) ) ) )).
fof(t45_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( r1_vfunct_2(A,B,C,D) => ( v1_comseq_2(k2_partfun1(A,k1_numbers,k4_normsp_0(A,B,C),D)) & r1_vfunct_2(A,B,k5_vfunct_1(A,B,C),D) ) ) ) ) ) )).
fof(t45_waybel11,axiom,( ! [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) & 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)))) ) ) )).
fof(t45_waybel14,axiom,( ! [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] : ( 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) ) ) )).
fof(t45_waybel21,axiom,( ! [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) & l1_waybel_9(A) ) => ! [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) & v2_waybel19(B) & l1_waybel_9(B) ) => ! [C] : ( ( 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] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => r3_waybel_0(A,B,C,D) ) ) ) ) ) ) )).
fof(t45_waybel23,axiom,( ! [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) ) => ( m1_waybel23(u1_struct_0(k1_waybel_8(A)),A) => v2_waybel_8(A) ) ) )).
fof(t45_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t45_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ( ( v1_lattice3(A) | v2_lattice3(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t45_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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))))) ) ) ) ) ) ) ) )).
fof(t45_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & v1_waybel_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t45_waybel_4,axiom,( ! [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) ) => ( v3_waybel_3(A) <=> ! [B] : ( ( 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) ) ) ) ) )).
fof(t45_waybel_7,axiom,( ! [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) & l1_orders_2(A) ) => ( v5_waybel_7(k1_waybel_4(A),A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v4_waybel_7(B,A) => v5_waybel_6(B,A) ) ) ) ) )).
fof(t45_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( v2_wellord1(A) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( ( r3_wellord1(A,B,C) & r3_wellord1(A,B,D) ) => C = D ) ) ) ) ) ) )).
fof(t45_xboole_1,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => B = k2_xboole_0(A,k4_xboole_0(B,A)) ) )).
fof(t45_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k5_xboolean(A,k9_xboolean(B,C)) = k4_xboolean(k6_xboolean(B,A),k6_xboolean(C,A)) ) ) ) )).
fof(t45_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t45_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,k5_numbers) => r1_xxreal_0(B,k6_xcmplx_0(B,A)) ) ) ) )).
fof(t45_xtuple_0,axiom,( ! [A] : ! [B] : r1_tarski(k4_xboole_0(k14_xtuple_0(A),k14_xtuple_0(B)),k14_xtuple_0(k4_xboole_0(A,B))) )).
fof(t45_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r2_hidden(A,k1_numbers) & r2_hidden(C,k1_numbers) & r1_xxreal_0(A,B) & r1_xxreal_0(B,C) ) => r2_hidden(B,k1_numbers) ) ) ) ) )).
fof(t45_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(D,B) ) => r1_tarski(k4_xxreal_1(C,D),k2_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t45_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ( ( r1_tarski(A,B) & v5_xxreal_2(B) ) => v5_xxreal_2(A) ) ) ) )).
fof(t45_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t45_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & l1_orders_2(B) ) => ! [C] : ( 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))) ) ) ) ) )).
fof(t45_yellow12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v8_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t45_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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)))) ) ) ) )).
fof(t45_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( 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 ) ) ) ) ) ) )).
fof(t45_yellow20,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t45_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v2_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_orders_2(A,B,k4_yellow_0(A)) ) ) )).
fof(t45_yellow_2,axiom,( ! [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] : ( ( ~ 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))) ) ) ) )).
fof(t45_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t45_yellow_4,axiom,( ! [A] : ( ( v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v12_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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))) ) ) ) ) )).
fof(t45_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_yellow_5(A,B,C) = k3_yellow_0(A) <=> r3_orders_2(A,B,C) ) ) ) ) )).
fof(t45_yellow_7,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,C,k7_funcop_1(A,B)) => k1_funct_6(D) = C ) ) ) )).
fof(t45_yellow_9,axiom,( ! [A] : ( l1_waybel_9(A) => ! [B] : ( m1_yellow_9(B,A) => m1_yellow_9(A,B) ) ) )).
fof(t45_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v11_zf_lang(A) => A = k13_zf_lang(k23_zf_lang(A),k24_zf_lang(A)) ) ) )).
fof(t45_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ~ ( r3_zf_lang(A,B) & r1_zf_lang(B,A) ) ) ) )).
fof(t45_zfmisc_1,axiom,( ! [A] : ! [B] : ( r2_hidden(A,B) => k3_xboole_0(B,k1_tarski(A)) = k1_tarski(A) ) )).
fof(t45_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_zmodul01(B) & m1_zmodul01(B,A) ) => ! [C] : ( ( v1_zmodul01(C) & m1_zmodul01(C,A) ) => ( u1_struct_0(B) = u1_struct_0(C) => B = C ) ) ) ) )).
fof(t45_zmodul02,axiom,( ! [A] : ( ( ~ 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_funct_2(k2_zfmisc_1(u1_struct_0(k31_zmodul02(A)),u1_struct_0(k31_zmodul02(A))),u1_struct_0(k31_zmodul02(A)),k2_zfmisc_1(k26_zmodul02(A),k26_zmodul02(A)),k26_zmodul02(A),u1_algstr_0(k31_zmodul02(A)),k29_zmodul02(A)) ) )).
fof(t46_abcmiz_0,axiom,( ! [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) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_abcmiz_0(A)) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t46_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_abcmiz_1(B,A,k13_abcmiz_1(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t46_abcmiz_a,axiom,( ! [A] : ( ( 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] : ( m1_abcmiz_1(B,k27_abcmiz_1,k14_abcmiz_1(k27_abcmiz_1)) => ! [C] : ( 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 ) ) ) )).
fof(t46_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) => ( ( r2_aff_1(A,C,E,G) & r1_aff_1(A,F,B,C) & r1_aff_1(A,F,D,E) & r2_hidden(F,G) & B = D ) => ( r2_hidden(B,G) | C = E ) ) ) ) ) ) ) ) ) )).
fof(t46_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_1(C,A) & v1_aff_1(D,A) & v1_aff_4(E,A) & r1_tarski(C,E) & r1_tarski(D,E) ) => ( C = D | ( r2_aff_4(A,C,D,B) <=> r1_tarski(B,E) ) ) ) ) ) ) ) ) )).
fof(t46_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( 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,k5_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 ) ) ) )).
fof(t46_afinsq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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] : ( ( 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] : ! [H] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t46_afproj,axiom,( ! [A] : ( ( ~ 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)) ) ) ) )).
fof(t46_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_afvect0(A,B))) => ? [D] : ( m1_subset_1(D,u1_struct_0(k5_afvect0(A,B))) & k3_rlvect_1(k5_afvect0(A,B),D,D) = C ) ) ) ) )).
fof(t46_algspec1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( m2_algspec1(B,A) => ! [C] : ( m2_algspec1(C,B) => m2_algspec1(C,A) ) ) ) )).
fof(t46_algstr_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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(u1_struct_0(k14_algstr_4(A)),u1_struct_0(k14_algstr_4(A)),k1_relset_1(u1_struct_0(k14_algstr_4(A)),k18_algstr_4(A,B,C)),k1_relset_1(u1_struct_0(k14_algstr_4(A)),k18_algstr_4(A,B,C)),k18_algstr_4(A,A,k6_partfun1(A)),k6_partfun1(k1_relset_1(u1_struct_0(k14_algstr_4(A)),k18_algstr_4(A,B,C)))) ) ) ) )).
fof(t46_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) )).
fof(t46_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_analmetr(A)))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t46_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ~ ( r1_analmetr(A,J,K) & r1_analort(A,J,K,B,C,E,F) & r1_analort(A,J,K,E,F,H,I) & r1_analort(A,J,K,B,C,D,G) & ~ r1_analort(A,J,K,D,G,H,I) & E != F & B != C ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t46_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ( g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)) = g1_unialg_1(u1_struct_0(B),u1_unialg_1(B)) => ! [C] : ( m1_freealg(C,A) => m1_freealg(C,B) ) ) ) ) )).
fof(t46_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( m2_pboole(E,u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,D)) => k15_aofa_a00(A,B,C,D,u8_aofa_a00(A),k21_aofa_a00(A,C),E) = k8_margrel1 ) ) ) ) ) )).
fof(t46_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [E] : ( ( v1_aofa_i00(E,A,B,D) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),D) ) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),E) => ! [G] : ( 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) = k4_int_1(k21_aofa_i00(B,k4_numbers,C,F),k3_funct_2(k9_funct_2(B,k4_numbers),k4_numbers,G,C)) & ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t46_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ! [C] : ( ( v3_ordinal1(C) & v7_ordinal1(C) ) => ! [D] : ( ( v3_ordinal1(D) & v7_ordinal1(D) ) => ~ ( C != k1_xboole_0 & A != k1_xboole_0 & k9_arytm_3(k8_arytm_3(B,C),k8_arytm_3(D,A)) != k8_arytm_3(k8_ordinal3(k9_ordinal3(B,A),k9_ordinal3(C,D)),k9_ordinal3(C,A)) ) ) ) ) ) )).
fof(t46_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(9,A) & r1_xxreal_0(k2_nat_1(2,k5_series_1(A,6)),k5_series_1(k1_nat_1(A,1),6)) ) ) )).
fof(t46_bcialg_1,axiom,( ! [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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( m2_bcialg_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & r1_bcialg_1(A,D,C) ) => r2_hidden(D,B) ) ) ) ) ) ) )).
fof(t46_bcialg_2,axiom,( ! [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) ) => r1_tarski(k4_bcialg_2(A),k6_bcialg_2(A)) ) )).
fof(t46_bcialg_3,axiom,( ! [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) & v6_bcialg_3(A) & l2_bcialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v2_bcialg_3(B,A) => ( v11_bcialg_3(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t46_bcialg_4,axiom,( ! [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) & l1_bcialg_4(A) ) => ( v4_bcialg_4(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t46_bcialg_5,axiom,( ! [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) ) => ( ( ~ 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,k5_numbers,1,1,1) ) ) )).
fof(t46_bcialg_6,axiom,( ! [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] : ( ( ~ 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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( ( 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)))) ) => ( ( v12_bcialg_1(C,B) & m2_bcialg_1(C,B) ) => ( v12_bcialg_1(k8_relset_1(u1_struct_0(A),u1_struct_0(B),D,C),A) & m2_bcialg_1(k8_relset_1(u1_struct_0(A),u1_struct_0(B),D,C),A) ) ) ) ) ) ) )).
fof(t46_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( v3_bciideal(B,A) & m2_bcialg_1(B,A) ) ) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t46_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( r2_hidden(C,k4_bhsp_2(A,B,E)) & r1_xxreal_0(E,D) ) => r2_hidden(C,k4_bhsp_2(A,B,D)) ) ) ) ) ) ) )).
fof(t46_bhsp_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(C)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(C),k5_bhsp_4(C,D,k26_valued_1(k4_ordinal1,k1_numbers,B,A)),k5_normsp_1(C,k5_bhsp_4(C,D,B),A)) ) ) ) ) )).
fof(t46_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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)) ) ) ) ) )).
fof(t46_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_topmetr)) => ! [F] : ( 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] : ( ( ~ v1_xboole_0(G) & m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k1_borsuk_4))) ) => ! [H] : ( ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(t46_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => k4_rcomp_1(k2_xxreal_0,A) != k1_numbers ) )).
fof(t46_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( ( 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,k5_numbers) = k5_numbers & k1_funct_1(E,1) = 1 ) => r4_borsuk_2(A,B,C,k2_borsuk_6(A,B,C,D,E),D) ) ) ) ) ) ) )).
fof(t46_borsuk_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(3))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(3))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(3))) => ( ( C = A & D = B ) => k1_binop_1(k13_euclid(3),C,D) = k3_square_1(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k6_xcmplx_0(k1_euclid_5(A),k1_euclid_5(B))),k1_square_1(k6_xcmplx_0(k2_euclid_5(A),k2_euclid_5(B)))),k1_square_1(k6_xcmplx_0(k3_euclid_5(A),k3_euclid_5(B))))) ) ) ) ) ) )).
fof(t46_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t46_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t46_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t46_bvfunc26,axiom,( ! [A] : ( ~ 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)) ) )).
fof(t46_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ( k8_xboolean(A,k3_xboolean(A)) = k8_margrel1 & k3_xboolean(k8_xboolean(A,k3_xboolean(A))) = k7_margrel1 ) ) )).
fof(t46_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t46_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)))) ) ) ) ) ) )).
fof(t46_card_1,axiom,( ! [A] : ( ( v1_finset_1(A) & v1_card_1(A) ) => ? [B] : ( v7_ordinal1(B) & A = k1_card_1(B) ) ) )).
fof(t46_card_2,axiom,( ! [A] : ( ( 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))) ) )).
fof(t46_card_fin,axiom,( ! [A] : ! [B] : ! [C] : ( v1_finset_1(C) => ! [D] : ( v1_finset_1(D) => ! [E] : ( ( 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) = k1_nat_1(k5_card_1(C),k5_card_1(D)) & k3_card_fin(2,E) = k5_card_1(k3_xboole_0(C,D)) ) ) ) ) ) ) )).
fof(t46_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v11_cat_1(B,A) & v11_cat_1(C,A) ) => r1_cat_1(A,B,C) ) ) ) ) )).
fof(t46_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t46_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u4_struct_0(k23_cat_4(A,B))) => ! [D] : ( m1_subset_1(D,u4_struct_0(k23_cat_4(A,B))) => C = D ) ) )).
fof(t46_catalan2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,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))) ) ) ) )).
fof(t46_cc0sp2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_cc0sp2(B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_cc0sp2(B))) => ( ( k2_normsp_0(k9_cc0sp2(B),C) = k5_numbers => C = k4_struct_0(k9_cc0sp2(B)) ) & ( C = k4_struct_0(k9_cc0sp2(B)) => k2_normsp_0(k9_cc0sp2(B),C) = k5_numbers ) & k2_normsp_0(k9_cc0sp2(B),k1_clvect_1(k9_cc0sp2(B),C,A)) = k3_xcmplx_0(k9_complex1(A),k2_normsp_0(k9_cc0sp2(B),C)) & r1_xxreal_0(k2_normsp_0(k9_cc0sp2(B),k1_algstr_0(k9_cc0sp2(B),C,D)),k2_xcmplx_0(k2_normsp_0(k9_cc0sp2(B),C),k2_normsp_0(k9_cc0sp2(B),D))) ) ) ) ) ) )).
fof(t46_cfcont_1,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(t46_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( 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,C,B),k1_cfunct_1(A,D,B)),k1_cfunct_1(A,k2_valued_1(A,k2_numbers,k2_numbers,C,D),B)) & r2_relset_1(A,k2_numbers,k46_valued_1(A,k2_numbers,k2_numbers,k1_cfunct_1(A,C,B),k1_cfunct_1(A,D,B)),k1_cfunct_1(A,k46_valued_1(A,k2_numbers,k2_numbers,C,D),B)) ) ) ) ) ) )).
fof(t46_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ( v8_cgames_1(A) <=> ( ? [B] : ( v2_cgames_1(B) & r2_hidden(B,k6_cgames_1(A)) & v5_cgames_1(B) ) & ? [B] : ( v2_cgames_1(B) & r2_hidden(B,k7_cgames_1(A)) & v6_cgames_1(B) ) ) ) ) )).
fof(t46_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( 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] : ( m2_subset_1(E,k4_ordinal1,k2_finseq_1(A)) => ~ r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) ) )).
fof(t46_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( 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] : ( ( v5_glib_001(E,A) & m3_glib_001(E,A) ) => ! [F] : ! [G] : ~ ( ~ 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 ) ) ) ) ) ) ) )).
fof(t46_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(D) & v1_finset_1(D) ) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t46_circcomb,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v1_circcomb(k5_circcomb(A,B)) & v2_circcomb(k5_circcomb(A,B)) ) ) )).
fof(t46_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v4_msualg_1(E,A) & v4_msafree2(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(B,F))) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t46_classes1,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(t46_classes2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => v3_ordinal1(k2_ordinal1(A)) ) )).
fof(t46_clvect_1,axiom,( ! [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) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) )).
fof(t46_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( r2_hidden(C,k4_clvect_2(A,B,E)) & r1_xxreal_0(E,D) ) => r2_hidden(C,k4_clvect_2(A,B,D)) ) ) ) ) ) ) )).
fof(t46_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [D] : ( v1_xcmplx_0(D) => k6_clvect_3(A,B,k25_valued_1(k4_ordinal1,k2_numbers,C,D)) = k6_clvect_1(A,k6_clvect_3(A,B,C),D) ) ) ) ) )).
fof(t46_coh_sp,axiom,( ! [A] : ! [B] : ( 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 ) ) )).
fof(t46_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t46_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => r1_xxreal_0(k5_numbers,k9_complex1(A)) ) )).
fof(t46_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k1_complex2(k2_xcmplx_0(A,B),k2_xcmplx_0(A,B)) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_complex2(A,A),k1_complex2(A,B)),k1_complex2(B,A)),k1_complex2(B,B)) ) ) )).
fof(t46_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_complfld)) => ~ ( B != k4_struct_0(k1_complfld) & ( k8_group_1(k1_complfld,A,B) = C | k8_group_1(k1_complfld,B,A) = C ) & A != k3_vectsp_1(k1_complfld,C,B) ) ) ) ) )).
fof(t46_complsp2,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( m2_finseq_1(C,k2_numbers) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ( ( k3_finseq_1(C) = k3_finseq_1(D) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k4_finseq_1(C)) => k9_matrix_5(A,k9_matrix_5(C,E)) = k9_matrix_5(B,k9_matrix_5(D,E)) ) ) ) => k4_finseqop(k2_numbers,k2_numbers,C,A) = k4_finseqop(k1_numbers,k1_numbers,D,B) ) ) ) ) ) )).
fof(t46_compos_1,axiom,( ! [A] : ! [B] : ( l1_compos_1(B) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ( r2_hidden(A,k2_afinsq_1(k11_compos_1(B,C))) <=> ( A = k5_numbers | A = 1 ) ) ) ) )).
fof(t46_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t46_comptrig,axiom,( ! [A] : ( v1_xcmplx_0(A) => ~ ( ~ r1_xxreal_0(k5_numbers,k4_complex1(A)) & r1_xxreal_0(k5_numbers,k17_sin_cos(k1_comptrig(A))) ) ) )).
fof(t46_comput_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v3_margrel1(B,A) & m2_rfunct_3(B,k3_finseq_2(A),A,k2_comput_1(A)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v3_margrel1(C,A) & m2_rfunct_3(C,k3_finseq_2(A),A,k2_comput_1(A)) ) => ( ( k19_margrel1(B) = k5_numbers & k19_margrel1(C) = k5_numbers & k1_funct_1(B,k1_xboole_0) = k1_funct_1(C,k1_xboole_0) ) => B = C ) ) ) ) )).
fof(t46_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,A)),k55_valued_1(k4_ordinal1,k2_numbers,k36_valued_1(k4_ordinal1,k2_numbers,A))) ) )).
fof(t46_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v2_comseq_2(A) <=> ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & r1_xxreal_0(B,k9_complex1(k6_xcmplx_0(k9_nat_1(k2_numbers,A,D),k9_nat_1(k2_numbers,A,C)))) ) ) ) ) ) ) )).
fof(t46_connsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t46_convex4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t46_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t46_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => r3_cqc_the1(A,B,k5_cqc_lang(A)) ) ) )).
fof(t46_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) )).
fof(t46_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t46_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k13_csspace(A,k3_rlvect_1(A,B,C)),k2_xcmplx_0(k13_csspace(A,B),k13_csspace(A,C))) ) ) ) )).
fof(t46_dickson,axiom,( r8_relat_2(k10_dickson,k4_ordinal1) )).
fof(t46_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k3_diff_1(k18_sin_cos,A),B) = k4_xcmplx_0(k3_xcmplx_0(2,k3_xcmplx_0(k17_sin_cos(k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(2,B),A),2)),k17_sin_cos(k7_xcmplx_0(A,2))))) ) ) )).
fof(t46_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_square_1(D) ) => k1_funct_1(k4_diff_1(C,A),B) = k3_xcmplx_0(A,k6_xcmplx_0(k3_xcmplx_0(2,B),A)) ) ) ) ) )).
fof(t46_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k5_diff_1(k4_diff_1(C,A),A),B) = k6_xcmplx_0(k1_funct_1(k5_diff_1(C,A),B),k1_funct_1(k4_diff_1(C,A),k6_xcmplx_0(B,k7_xcmplx_0(A,2)))) ) ) ) )).
fof(t46_diraf,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_analoaf(A) ) => ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) <=> ( ~ ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = C ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_analoaf(A,B,C,B,D) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_analoaf(A,B,D,C,E) & C != E ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_analoaf(A,B,C,D,E) & r2_analoaf(A,B,D,C,E) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_analoaf(A,D,B,B,E) & B != D & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_analoaf(A,C,B,B,F) & r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( ~ r2_analoaf(A,B,C,D,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_analoaf(A,B,C,B,F) & r2_analoaf(A,D,E,D,F) ) ) ) ) ) ) ) ) ) ) )).
fof(t46_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( 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] : ( 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)) ) ) ) ) )).
fof(t46_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( 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] : ( 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)) ) ) ) ) ) )).
fof(t46_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t46_entropy1,axiom,( ! [A] : ( ( v1_matrprob(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(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))) ) ) ) )).
fof(t46_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k6_enumset1(A,A,A,A,B,C,D,E) = k3_enumset1(A,B,C,D,E) )).
fof(t46_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r1_tarski(A,k8_relat_1(C,B)) => r1_tarski(k7_relat_1(C,A),B) ) ) )).
fof(t46_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => k12_euclid(k22_euclid(A)) = k3_square_1(A) ) )).
fof(t46_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => k6_xcmplx_0(k1_square_1(k12_euclid(k3_rlvect_1(k15_euclid(A),B,C))),k1_square_1(k12_euclid(k5_algstr_0(k15_euclid(A),B,C)))) = k3_xcmplx_0(4,k22_rvsum_1(B,C)) ) ) ) )).
fof(t46_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( A != B & C != B & ( k4_euclid_3(A,B,C) = k7_xcmplx_0(k28_sin_cos,2) | k4_euclid_3(A,B,C) = k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos) ) & k2_xcmplx_0(k1_square_1(k12_euclid(k5_algstr_0(k15_euclid(2),A,B))),k1_square_1(k12_euclid(k5_algstr_0(k15_euclid(2),C,B)))) != k1_square_1(k12_euclid(k5_algstr_0(k15_euclid(2),A,C))) ) ) ) ) )).
fof(t46_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => k4_euclid_3(A,B,C) != k6_xcmplx_0(k3_xcmplx_0(2,k4_euclid_3(D,E,F)),k3_xcmplx_0(4,k28_sin_cos)) ) ) ) ) ) ) )).
fof(t46_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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 ) ) ) )).
fof(t46_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => k7_euclid(3,A,B) = k1_euclid_8(k2_xcmplx_0(k1_funct_1(A,1),k1_funct_1(B,1)),k2_xcmplx_0(k1_funct_1(A,2),k1_funct_1(B,2)),k2_xcmplx_0(k1_funct_1(A,3),k1_funct_1(B,3))) ) ) )).
fof(t46_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ~ ( r2_euclidlp(A,B,C) & r4_euclidlp(A,B,C) ) ) ) ) )).
fof(t46_exchsort,axiom,( ! [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) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_exchsort(B) ) => ! [C] : ! [D] : ( r2_hidden(k4_tarski(C,D),k6_exchsort(A,B)) <=> ( r2_hidden(C,k9_xtuple_0(B)) & r2_hidden(D,k9_xtuple_0(B)) & r2_hidden(C,D) & r2_orders_2(A,k7_partfun1(u1_struct_0(A),B,D),k7_partfun1(u1_struct_0(A),B,C)) ) ) ) ) )).
fof(t46_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t46_fcont_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) )).
fof(t46_fdiff_10,axiom,( ! [A] : ( ( 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,k18_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k18_sin_cos),A),B) = k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,k1_funct_1(k2_fdiff_9,B)),k1_funct_1(k18_sin_cos,B)),k1_square_1(k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t46_fdiff_11,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,k1_relset_1(k1_numbers,k27_sin_cos)) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_sin_cos9)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_sin_cos9)),A),B) = k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k1_funct_1(k2_sin_cos9,B)),k1_square_1(k1_funct_1(k16_sin_cos,B)))),k7_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k27_sin_cos,B)),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t46_fdiff_4,axiom,( ! [A] : ( ( 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)),k18_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)),k18_sin_cos),k16_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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)),k18_sin_cos),k16_sin_cos),A),B) = k3_xcmplx_0(B,k1_funct_1(k16_sin_cos,B)) ) ) ) ) ) )).
fof(t46_fdiff_6,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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,k18_sin_cos,k1_taylor_1(A)),k7_xcmplx_0(1,A)))) => ( r1_xxreal_0(A,k5_numbers) | ( r2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(A)),k7_xcmplx_0(1,A)),B) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => k1_funct_1(k2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(A)),k7_xcmplx_0(1,A)),B),C) = k4_xcmplx_0(k3_xcmplx_0(k3_prepower(k1_funct_1(k18_sin_cos,C),k6_xcmplx_0(A,1)),k1_funct_1(k16_sin_cos,C))) ) ) ) ) ) ) ) )).
fof(t46_fdiff_7,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_funct_1(k18_sin_cos,A) != k5_numbers => ( r1_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),A) & k1_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),A) = k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,A))) ) ) ) )).
fof(t46_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(B,1) & ~ r1_xxreal_0(A,B) & r1_xxreal_0(k1_pre_ff(A),k1_pre_ff(B)) ) ) ) )).
fof(t46_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) <=> ~ r2_hidden(k7_lattices(A,C),B) ) ) ) ) ) )).
fof(t46_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) ) ) ) ) )).
fof(t46_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( B = k3_lattices(A,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) ) ) ) ) )).
fof(t46_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ~ ( A != k1_xboole_0 & ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : A != k7_finseq_1(C,k9_finseq_1(D)) ) ) ) )).
fof(t46_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => m2_finseq_1(k6_partfun1(k2_finseq_1(A)),k4_ordinal1) ) )).
fof(t46_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => k14_finseq_1(k2_finseq_1(A)) = k1_finseq_2(A) ) )).
fof(t46_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ~ ( r2_hidden(B,k10_xtuple_0(A)) & v2_funct_1(A) & r2_hidden(B,k10_xtuple_0(k6_finseq_4(A,B))) ) ) )).
fof(t46_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t46_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => k2_rfinseq(A,1,k2_finseq_4(A,B,C)) = k12_finseq_1(A,C) ) ) ) )).
fof(t46_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v3_card_1(E,D) & m2_finseq_1(E,A) ) => ! [F] : ( ( 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] : ( ( 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(k4_ordinal1,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))) ) ) ) ) ) ) ) ) )).
fof(t46_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v2_fintopo2(A) & ! [D] : ( 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)) ) ) ) ) )).
fof(t46_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => 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)) ) ) ) ) )).
fof(t46_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => ( ( v2_fintopo6(B,A) & r1_xxreal_0(1,C) ) => v2_fintopo6(k17_finseq_1(u1_struct_0(A),C,B),A) ) ) ) ) )).
fof(t46_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_catalan2(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_catalan2(A))) => ( ( r1_tarski(B,k8_flang_1(A,D)) & r1_tarski(C,k8_flang_1(A,D)) ) => r1_tarski(k6_flang_1(A,B,C),k8_flang_1(A,D)) ) ) ) ) )).
fof(t46_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => k1_flang_2(A,B,k5_numbers,1) = k4_subset_1(k8_afinsq_1(A),k4_flang_1(A,k2_flang_1(A)),B) ) )).
fof(t46_flang_3,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k5_afinsq_1(B),k1_flang_3(A,C,D)) <=> ( r2_hidden(k5_afinsq_1(B),C) & ( r2_hidden(k2_flang_1(A),C) | r1_xxreal_0(D,1) ) ) ) ) ) )).
fof(t46_fomodel0,axiom,( ! [A] : ( v4_funct_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => r1_tarski(k21_fomodel0(B),k21_fomodel0(A)) ) ) )).
fof(t46_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t46_funcop_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( 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))) ) ) ) )).
fof(t46_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(B,k9_xtuple_0(k5_relat_1(C,A))) => k1_funct_1(k5_relat_1(C,A),B) = k1_funct_1(C,B) ) ) )).
fof(t46_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k1_tarski(B),A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_tarski(B),A))) ) => ( A != k1_xboole_0 => r2_hidden(k1_funct_1(C,B),A) ) ) )).
fof(t46_funct_3,axiom,( ! [A] : ! [B] : ( A != k1_xboole_0 => k10_xtuple_0(k8_funct_3(A,B)) = B ) )).
fof(t46_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(t46_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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 ) ) ) )).
fof(t46_funct_6,axiom,( ! [A] : k8_funct_6(A,k1_xboole_0) = k1_xboole_0 )).
fof(t46_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => k4_funct_7(k9_finseq_1(B),A) = k10_finseq_1(A,k1_funct_1(B,A)) ) )).
fof(t46_funct_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t46_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( m2_functor0(C,A,B) => ( ( v15_functor0(C,A,B) & v5_functor0(C,A,B) ) => v7_functor0(C,A,B) ) ) ) ) )).
fof(t46_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D,C)),k1_fuzzy_1(A,k3_fuzzy_2(A,B,D),k3_fuzzy_2(A,B,C))) ) ) ) ) )).
fof(t46_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => r2_funct_2(u1_struct_0(A),k6_numbers,k5_fvaluat1(A,k5_fvaluat1(A,B)),k5_fvaluat1(A,B)) ) ) ) )).
fof(t46_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [D] : ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => D = k8_fvsum_1(A,B,k4_fvsum_1(A,B,D,C),C) ) ) ) ) )).
fof(t46_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t46_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( ( ~ v1_xboole_0(F) & v1_relat_1(F) & v2_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ! [G] : ( m1_genealg1(G,F) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t46_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t46_gfacirc1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ~ v1_facirc_1(k2_msafree2(k19_gfacirc1(A,B,C))) ) ) ) )).
fof(t46_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( m2_glib_000(F,A,B,D) => ! [G] : ( 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) ) ) ) ) )).
fof(t46_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m3_glib_001(D,B) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( C = D => k8_glib_001(A,C,E,F) = k8_glib_001(B,D,E,F) ) ) ) ) ) ) ) )).
fof(t46_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) = k1_nat_1(k17_glib_000(A),1) ) ) ) )).
fof(t46_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_003(A) ) => ! [B] : ! [C] : ( r2_hidden(B,k7_glib_000(A)) => r1_tarski(k11_glib_003(A),k11_glib_003(k12_glib_003(A,B,C))) ) ) )).
fof(t46_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ 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(k1_nat_1(A,1),k3_finseq_1(k2_goboard2(D))) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(k2_goboard2(D))) & r1_xxreal_0(1,C) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1))) = k2_topreal1(2,D,C) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),B)) = k2_topreal1(2,D,k1_nat_1(C,1)) ) => ( r1_xxreal_0(k3_finseq_1(D),k1_nat_1(C,1)) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,B) ) ) ) ) ) ) ) )).
fof(t46_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( ( 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 ) ) ) ) ) ) )).
fof(t46_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( ( v2_funct_1(E) & m2_graph_1(E,k8_graph_3(A,B,C)) ) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t46_graph_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_graph_1(C) ) => ! [D] : ( m2_finseq_1(D,u4_struct_0(C)) => ! [E] : ( m2_finseq_1(E,u4_struct_0(C)) => ~ ( r1_tarski(k10_xtuple_0(E),k10_xtuple_0(D)) & r6_graph_5(C,B) & r2_hidden(A,k4_finseq_1(E)) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( r2_hidden(F,k4_finseq_1(D)) & k1_funct_1(k9_graph_5(C,D,B),F) = k1_funct_1(k9_graph_5(C,E,B),A) ) ) ) ) ) ) ) ) )).
fof(t46_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(G,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] : ( ( 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,k3_polynom1(k15_pre_poly(A),C,F)) & r3_pre_poly(A,k3_termord(A,B,C,G),H) ) ) ) => r5_polyred(A,B,C,k6_polynom1(A,C,D,F),k6_polynom1(A,C,E,F),k1_groeb_1(A,C,G)) ) ) ) ) ) ) ) ) )).
fof(t46_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & v5_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t46_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v15_algstr_0(C) & v1_group_3(C,A) & m1_group_2(C,A) ) => ! [D] : ( ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) ) => ? [E] : ( 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))) ) ) ) ) ) )).
fof(t46_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => r1_struct_0(B,k1_group_1(A)) ) ) )).
fof(t46_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) )).
fof(t46_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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)) ) ) ) ) )).
fof(t46_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t46_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t46_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( 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)) ) ) ) ) )).
fof(t46_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t46_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_xxreal_0(k1_square_1(k9_complex1(k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(k1_complfld),B,C,D))),k3_xcmplx_0(k9_complex1(k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(k1_complfld),B,C,C)),k9_complex1(k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(k1_complfld),B,D,D)))) ) ) ) ) )).
fof(t46_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(t46_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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 ) ) )).
fof(t46_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u4_incsp_1(A)) => ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & ? [E] : ( 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) ) ) ) ) ) )).
fof(t46_int_1,axiom,( ! [A] : ( v1_int_1(A) => k4_int_1(A,k5_numbers) = k5_numbers ) )).
fof(t46_int_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => k5_nat_d(k6_nat_d(A,C),k6_nat_d(B,C)) = k6_nat_d(k5_nat_d(A,B),C) ) ) ) )).
fof(t46_int_5,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ( ( k3_finseq_1(A) = k3_finseq_1(C) & k3_finseq_1(B) = k3_finseq_1(D) ) => k8_rvsum_1(k8_finseq_1(k1_numbers,A,B),k8_finseq_1(k1_numbers,C,D)) = k8_finseq_1(k1_numbers,k8_rvsum_1(A,C),k8_rvsum_1(B,D)) ) ) ) ) ) )).
fof(t46_integr11,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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(k4_xcmplx_0(1),1)) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(D,E) = k7_xcmplx_0(A,k2_xcmplx_0(1,k1_square_1(E))) ) ) & C = k9_xtuple_0(D) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,D,B)) ) => k2_integra5(B,D) = k6_xcmplx_0(k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k1_sin_cos9,A),k2_seq_4(B)),k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k1_sin_cos9,A),k3_seq_4(B))) ) ) ) ) ) )).
fof(t46_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,D) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => k1_funct_1(C,E) = 1 ) ) & r2_relset_1(k1_numbers,k1_numbers,B,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,C,k1_taylor_1(2))))) & r1_tarski(D,k2_rcomp_1(k4_xcmplx_0(1),1)) & D = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,D),k1_sin_cos9),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,D),k1_sin_cos9),k3_seq_4(A))) ) ) ) ) ) )).
fof(t46_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k6_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,D))),k1_funct_1(k16_sin_cos,D)),k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k26_sin_cos,D),k1_funct_1(k18_sin_cos,D)),k1_square_1(k1_funct_1(k16_sin_cos,D)))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_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) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k2_fdiff_9),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k2_fdiff_9),k3_seq_4(A))) ) ) ) ) )).
fof(t46_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t46_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [C] : ( m1_integra1(C,A) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t46_integra8,axiom,( ! [A] : ( ( ~ 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)) = k6_xcmplx_0(k1_funct_1(k18_sin_cos,k2_seq_4(A)),k1_funct_1(k18_sin_cos,k3_seq_4(A))) ) )).
fof(t46_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( ~ r2_hidden(k4_xcmplx_0(A),B) => v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k6_rfunct_1(k1_numbers,k1_numbers,k1_fcont_1(1,A)),B)) ) ) ) )).
fof(t46_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t46_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( 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) ) ) )).
fof(t46_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m1_isocat_1(D,A,B) => ! [E] : ( m1_isocat_1(E,B,C) => m1_isocat_1(k9_cat_1(A,B,C,D,E),A,C) ) ) ) ) ) ) )).
fof(t46_jgraph_1,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( m1_subset_1(G,u1_struct_0(k5_topmetr)) => ! [H] : ( m1_subset_1(H,u1_struct_0(k5_topmetr)) => ~ ( G = k5_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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t46_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ~ r1_xxreal_0(k5_numbers,k17_euclid(B)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(C)) & ~ r1_xxreal_0(k7_xcmplx_0(k18_euclid(C),k12_euclid(C)),k7_xcmplx_0(k18_euclid(B),k12_euclid(B))) & ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) & ? [E] : ( 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(k7_xcmplx_0(k18_euclid(E),k12_euclid(E)),k7_xcmplx_0(k18_euclid(D),k12_euclid(D))) ) ) ) ) ) ) )).
fof(t46_jgraph_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ 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(k5_numbers,k18_euclid(A)) & r1_xxreal_0(k5_numbers,k18_euclid(B)) ) => ( A = B | r1_xxreal_0(k5_numbers,k17_euclid(B)) | ( ~ r1_xxreal_0(k17_euclid(B),k17_euclid(A)) & ~ r1_xxreal_0(k18_euclid(B),k18_euclid(A)) ) ) ) ) ) ) )).
fof(t46_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t46_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t46_jordan,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => r1_tarski(k1_jgraph_6(A,B,C,D),k2_jgraph_6(A,B,C,D)) ) ) ) ) )).
fof(t46_jordan1g,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( 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_0(k1_jordan8(B,A))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_topreal1(2,k2_jordan9(B,A))) & r1_xboole_0(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D)),k3_topreal1(2,k2_jordan1e(B,A))) ) ) ) ) ) )).
fof(t46_jordan1h,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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(B,A) ) => r1_tarski(k3_topreal1(2,k2_jordan9(C,A)),k2_pre_topc(k15_euclid(2),k3_goboard9(k2_jordan9(C,B)))) ) ) ) ) )).
fof(t46_jordan1k,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) & r2_hidden(D,B) & k5_jordan1k(A,C,B) = k1_topreal6(A,C,D) ) ) ) ) )).
fof(t46_jordan21,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( 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(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(B),k8_pscomp_1(B)),2))))) & k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)) = k2_xcmplx_0(k6_pscomp_1(B),k8_pscomp_1(B)) ) => ( v1_xboole_0(k9_subset_1(u1_struct_0(k15_euclid(2)),A,k6_jordan6(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)),2)))) | k2_jordan21(A) = k2_jordan21(B) ) ) ) ) )).
fof(t46_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k14_euclid(A)))) => ! [C] : ( v1_xreal_0(C) => ~ ( r1_xxreal_0(2,A) & B = a_2_2_jordan2c(A,C) & v6_tbsp_1(B,k14_euclid(A)) ) ) ) ) )).
fof(t46_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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))) ) ) ) )).
fof(t46_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( 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)) ) ) ) ) ) ) )).
fof(t46_jordan5d,axiom,( ! [A] : ( ( ~ 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_0(k2_goboard2(A))) & r1_xxreal_0(1,k3_jordan5d(A)) & r1_xxreal_0(k3_jordan5d(A),k1_matrix_0(k2_goboard2(A))) & r1_xxreal_0(1,k2_jordan5d(A)) & r1_xxreal_0(k2_jordan5d(A),k1_matrix_0(k2_goboard2(A))) & r1_xxreal_0(1,k1_jordan5d(A)) & r1_xxreal_0(k1_jordan5d(A),k1_matrix_0(k2_goboard2(A))) ) ) )).
fof(t46_jordan6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t46_knaster,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t46_kurato_1,axiom,( 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)))) )).
fof(t46_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k5_finsub_1(C)) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t46_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( 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)) ) ) )).
fof(t46_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(C,B) => ! [D] : ~ ( ~ r2_hidden(k7_nat_d(k15_glib_000(A),B),k17_lexbfs(k6_glib_000(A),k4_ordinal1,k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),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),k4_ordinal1,k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),k13_lexbfs(A,k16_lexbfs(A),C)),D)) ) ) ) ) ) )).
fof(t46_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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) = k6_xcmplx_0(k1_limfunc2(B,A),k1_limfunc2(C,A)) ) ) ) ) ) )).
fof(t46_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) = k5_numbers & ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,C) & ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ~ ( ~ 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_funct_1(B,E) != k5_numbers & k1_funct_1(B,F) != k5_numbers ) ) ) ) ) ) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,k9_subset_1(k1_numbers,k9_xtuple_0(B),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,C),A),k2_rcomp_1(A,k2_xcmplx_0(A,C))))) => r1_xxreal_0(k1_funct_1(B,D),k5_numbers) ) ) ) ) | r3_limfunc3(k6_rfunct_1(k1_numbers,k1_numbers,B),A) ) ) ) ) )).
fof(t46_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k3_limfunc1(C))) & k1_funct_1(A,D) = k4_limfunc1(A) ) ) | v5_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).
fof(t46_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( ? [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t46_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( ( v2_xxreal_0(G) & v1_xreal_0(G) ) => ( k5_lpspace2(A,B,C,D,G) = k5_lpspace2(A,B,C,E,G) => ( ! [H] : ( m2_subset_1(H,k1_zfmisc_1(A),B) => ~ ( k1_funct_1(C,k3_subset_1(A,H)) = k5_numbers & k1_relset_1(A,D) = H & r1_mesfunc6(A,B,D,H) ) ) | ! [H] : ( m2_subset_1(H,k1_zfmisc_1(A),B) => ~ ( k1_funct_1(C,k3_subset_1(A,H)) = k5_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) ) ) ) ) ) ) ) ) ) )).
fof(t46_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_hilbert1)) => ( r8_ltlaxio1(D,k3_hilbert1(C,k4_ltlaxio1(A,B))) => ( r8_ltlaxio1(D,k3_hilbert1(C,A)) & r8_ltlaxio1(D,k3_hilbert1(C,B)) ) ) ) ) ) ) )).
fof(t46_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(k3_hilbert1(A,B),k3_hilbert1(k3_hilbert1(A,C),k3_hilbert1(k3_hilbert1(C,A),k3_hilbert1(C,B))))) ) ) ) )).
fof(t46_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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) ) ) ) )).
fof(t46_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t46_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,k1_numbers,A,A) & m2_finseq_1(E,k3_finseq_2(k1_numbers)) ) => ( ( r1_matrix10(B,C) & r1_matrix10(D,E) ) => r1_matrix10(k4_matrix10(A,B,D),k4_matrix10(A,C,E)) ) ) ) ) ) ) )).
fof(t46_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( m1_matrix_2(D,k3_matrix_2(A)) => ! [E] : ( ( 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)) = k5_matrix_2(B,A,k12_matrix_3(A,B,C),D) ) ) ) ) ) ) )).
fof(t46_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(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_0(B))) = B ) ) )).
fof(t46_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(A),B,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ( ( C = 1 & ! [E] : ( v7_ordinal1(E) => ! [F] : ( 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_0(u1_struct_0(A),D,E,F) = k5_struct_0(A) ) & ( E != F => k3_matrix_0(u1_struct_0(A),D,E,F) = k4_struct_0(A) ) ) ) ) ) ) => D = k4_matrix14(A,B,C) ) ) ) ) ) )).
fof(t46_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(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,k17_matrix_0(u1_struct_0(B),A,C),k17_matrix_0(u1_struct_0(B),A,D))) ) ) ) ) ) ) )).
fof(t46_matrix16,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t46_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_subset_1(F,E) => ( r2_hidden(k4_tarski(A,B),k2_matrix_0(k11_matrix_0(E,C,D,F))) => k3_matrix_0(E,k11_matrix_0(E,C,D,F),A,B) = F ) ) ) ) ) ) ) )).
fof(t46_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(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) ) ) ) ) ) )).
fof(t46_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v4_matrix_6(C,A,B) & v4_matrix_6(D,A,B) ) => ( r1_xxreal_0(A,k5_numbers) | v4_matrix_6(k4_matrix_3(B,C,D),A,B) ) ) ) ) ) ) )).
fof(t46_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r2_matrix_8(A,B,C,D) => ( r1_xxreal_0(A,k5_numbers) | r2_matrix_8(A,B,k3_matrix_3(B,C,C),k3_matrix_3(B,D,D)) ) ) ) ) ) ) )).
fof(t46_matrix_9,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( ( v1_matrix_0(K) & v2_matrix_0(K,u1_struct_0(A),3,3) & m2_finseq_1(K,k3_finseq_2(u1_struct_0(A))) ) => ( K = k3_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t46_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( v7_ordinal1(C) => ( ( k3_finseq_1(A) = k1_nat_1(C,1) & B = k17_finseq_1(k2_numbers,C,A) ) => k17_rvsum_1(A) = k2_xcmplx_0(k17_rvsum_1(B),k7_partfun1(k2_numbers,A,k3_finseq_1(A))) ) ) ) ) )).
fof(t46_matrixj1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v2_matrixj1(B,A) & m2_finseq_1(B,k3_finseq_2(k3_finseq_2(A))) ) => k10_matrixj1(A,B) = k11_matrixj1(A,B) ) ) )).
fof(t46_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => ( r1_xxreal_0(k3_finseq_1(A),k5_numbers) | k9_matrixr1(k4_rvsum_1(A,B)) = k3_matrixr1(k9_matrixr1(A),k9_matrixr1(B)) ) ) ) ) )).
fof(t46_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => k3_matrixr2(A,k1_matrixr2(A,B,C)) = k3_xcmplx_0(k3_matrixr2(A,B),k3_matrixr2(A,C)) ) ) ) )).
fof(t46_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_matrlin(C,A,B) => ! [D] : ( m1_matrlin(D,A,k6_prvect_1(A,k3_finseq_1(C))) => ( D = k11_matrix13(A,k3_finseq_1(C),k3_finseq_1(C),k3_matrix_1(A,k3_finseq_1(C))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t46_matrprob,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(C) & k3_finseq_1(B) = k1_matrix_0(C) ) => k22_rvsum_1(k12_matrixr1(C,A),B) = k5_matrprob(k6_matrprob(A,B,C)) ) ) ) ) )).
fof(t46_matrtop1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(k2_vectsp_1),A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k2_vectsp_1))) ) => ~ ( k8_matrix13(k2_vectsp_1,C) = A & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v3_card_1(E,A) & v1_finseq_1(E) & v3_valued_0(E) ) => r1_xxreal_0(k12_euclid(E),k3_xcmplx_0(D,k12_euclid(k1_funct_1(k3_matrtop1(A,B,C),E)))) ) ) ) ) ) ) ) )).
fof(t46_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ~ 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) ) ) )).
fof(t46_measure6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ! [C] : ( v1_xreal_0(C) => ( r2_hidden(A,B) <=> r2_hidden(k2_xcmplx_0(C,A),k1_measure6(B,C)) ) ) ) ) )).
fof(t46_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( ( r2_hidden(C,A) & r2_hidden(D,B) ) => r2_hidden(k2_xcmplx_0(C,D),k9_member_1(A,B)) ) ) ) ) ) )).
fof(t46_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_partfun1(C,u1_struct_0(B)) ) => ( k5_memstr_0(A,B,C) = k5_numbers => k8_memstr_0(A,B,C) = C ) ) ) ) )).
fof(t46_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(A),B) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ( 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))) ) ) ) ) ) ) )).
fof(t46_mesfun7c,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(k6_complsp2(A))) => k12_supinf_2(k6_complsp2(A),B) = k3_complex1(k1_funct_1(A,B)) ) ) ) )).
fof(t46_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_partfun1(A,k6_numbers)) & v1_mesfunc8(E,A,k6_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( D = k1_relset_1(A,k4_mesfunc5(A,k6_numbers,E,k5_numbers)) & D = k1_relset_1(A,F) & ! [G] : ( v7_ordinal1(G) => r1_mesfunc1(A,B,k4_mesfunc5(A,k6_numbers,E,G),D) ) & r1_mesfunc5(A,B,C,F) & ! [G] : ( m1_subset_1(G,A) => ! [H] : ( v7_ordinal1(H) => ( r2_hidden(G,D) => r1_xxreal_0(k1_mesfunc9(k10_mesfunc1(A,k4_mesfunc5(A,k6_numbers,E,H)),G),k1_mesfunc9(F,G)) ) ) ) & ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(t46_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( r2_hidden(k8_relset_1(A,k6_numbers,D,k1_tarski(k1_supinf_1)),B) & r2_hidden(k8_relset_1(A,k6_numbers,D,k1_tarski(k2_supinf_1)),B) & r2_hidden(k8_relset_1(A,k6_numbers,E,k1_tarski(k1_supinf_1)),B) & r2_hidden(k8_relset_1(A,k6_numbers,E,k1_tarski(k2_supinf_1)),B) ) => ( ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ~ ( F = k1_relset_1(A,D) & r1_mesfunc1(A,B,D,F) ) ) | ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t46_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t46_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_midsp_1(B,A) => ! [C] : ( m1_midsp_1(C,A) => k7_midsp_1(A,B,C) = k7_midsp_1(A,C,B) ) ) ) )).
fof(t46_mmlquery,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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 ) ) ) )).
fof(t46_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k48_modelc_1(A,B,C))) => ! [F] : ( 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))) ) ) ) ) ) ) ) )).
fof(t46_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r2_modelc_2(A,B) => r1_tarski(k13_modelc_2(A),k13_modelc_2(B)) ) ) ) )).
fof(t46_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k25_modelc_2(k43_modelc_2)) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t46_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => k3_relat_1(k9_finseq_1(A),k5_moebius1(A)) = k9_finseq_1(A) ) )).
fof(t46_monoid_0,axiom,( k5_monoid_0 = g4_algstr_0(k4_ordinal1,k23_binop_2,k5_numbers) )).
fof(t46_monoid_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t46_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ( r2_msualg_3(A,k1_msafree3(A,B),C,k4_msafree4(A,B,C)) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,C),D)) => k1_funct_1(k2_msafree4(u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,C),k4_msafree4(A,B,C),D),E) = E ) ) ) ) ) ) )).
fof(t46_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t46_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t46_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ~ ( r2_hidden(B,k1_nat_1(A,1)) & ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(C,A) & B = C ) ) ) ) )).
fof(t46_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => k22_pre_poly(k8_newton,k12_nat_3(k3_xcmplx_0(A,B))) = k4_subset_1(k8_newton,k22_pre_poly(k8_newton,k12_nat_3(A)),k22_pre_poly(k8_newton,k12_nat_3(B))) ) ) )).
fof(t46_nat_4,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(2,A) => r1_xxreal_0(k3_wsierp_1(k14_finseq_1(a_1_1_nat_4(A))),k2_power(4,k6_xcmplx_0(A,1))) ) ) )).
fof(t46_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t46_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( v1_xreal_0(F) => ~ ( r2_hidden(E,C) & ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( v1_xreal_0(G) => ~ ( ~ r1_xxreal_0(G,k5_numbers) & ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ~ ( r2_hidden(H,C) & ~ r1_xxreal_0(G,k2_normsp_0(B,k5_algstr_0(B,H,E))) & r1_xxreal_0(F,k2_normsp_0(A,k5_algstr_0(A,k7_partfun1(u1_struct_0(A),D,H),k7_partfun1(u1_struct_0(A),D,E)))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t46_ndiff_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)))) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ( ( v3_nfcont_1(E,B) & r2_ndiff_1(A,B,C,D) & r1_tarski(E,A) ) => r2_ndiff_1(E,B,C,D) ) ) ) ) ) )).
fof(t46_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) = k4_struct_0(k4_real_ns1(A)) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ( ~ r1_xxreal_0(D,k9_complex1(E)) => r1_xxreal_0(k2_normsp_0(k4_real_ns1(A),k7_partfun1(u1_struct_0(k4_real_ns1(A)),B,E)),k3_xcmplx_0(C,k9_complex1(E))) ) ) ) ) ) ) ) ) ) )).
fof(t46_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_prvect_2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_prvect_2(A))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t46_newton,axiom,( ! [A] : ( v7_ordinal1(A) => k5_nat_d(A,1) = A ) )).
fof(t46_nfcont_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t46_nfcont_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k4_ordinal1) => ( 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) ) ) ) ) ) ) )).
fof(t46_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(k7_normform(A))) => ! [C] : ( m1_subset_1(C,k5_finsub_1(k7_normform(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t46_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t46_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t46_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( 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))) ) ) ) )).
fof(t46_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k1_relat_1(k2_wellord1(u1_orders_2(A),B)) = B ) ) )).
fof(t46_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ( k12_ordinal2(A,1) = A & k12_ordinal2(1,A) = 1 ) ) )).
fof(t46_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => k11_ordinal2(k10_ordinal2(A,B),C) = k10_ordinal2(k11_ordinal2(A,C),k11_ordinal2(B,C)) ) ) ) )).
fof(t46_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ( v4_ordinal1(A) => ( A = k1_xboole_0 | ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) ) => ( ( k9_xtuple_0(B) = A & ! [C] : ( v3_ordinal1(C) => ( r2_hidden(C,A) => k1_funct_1(B,C) = k3_ordinal5(C) ) ) ) => k3_ordinal5(A) = k3_card_3(B) ) ) ) ) ) )).
fof(t46_ordinal6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v3_ordinal6(A) ) => v1_ordinal6(a_1_1_ordinal6(A)) ) )).
fof(t46_osafree,axiom,( ! [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) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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)) ) ) )).
fof(t46_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t46_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r3_parsp_2(A,B,C,D,D) => B = C ) ) ) ) ) )).
fof(t46_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(C,k4_partfun1(A,B)) => ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ) )).
fof(t46_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t46_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t46_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k26_pcs_0(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k26_pcs_0(A,B))) => ( r1_pcs_0(k26_pcs_0(A,B),C,D) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r2_hidden(E,C) & r2_hidden(F,D) ) => r1_pcs_0(A,E,F) ) ) ) ) ) ) ) )).
fof(t46_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( 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) & k10_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) = k2_xcmplx_0(k1_pdiff_5(B,A),k1_pdiff_5(C,A)) ) ) ) ) ) )).
fof(t46_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_1(B,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( k3_finseq_1(B) = k2_xcmplx_0(A,1) & r1_xxreal_0(1,E) & r1_xxreal_0(E,A) & ! [F] : ( 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(k2_xcmplx_0(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(k2_xcmplx_0(A,1),E),k7_euclid(A,D,k7_partfun1(k1_euclid(A),B,k2_xcmplx_0(E,1)))),k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_1(k7_nat_d(k2_xcmplx_0(A,1),E),A),k7_euclid(A,D,C))) ) ) ) ) ) ) )).
fof(t46_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t46_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,1) => k3_pepin(1,A) = 1 ) ) )).
fof(t46_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_bspace)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t46_polynom5,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t46_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [G] : ( ( 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,k11_polynom1(A,C,G,E),k11_polynom1(A,C,G,F),D) ) ) ) ) ) ) ) ) )).
fof(t46_power,axiom,( ! [A] : ( v1_xreal_0(A) => k2_power(A,2) = k1_square_1(A) ) )).
fof(t46_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t46_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_int_1(C) => ( r1_xxreal_0(1,B) => ( r1_xxreal_0(A,k5_numbers) | k3_prepower(k2_prepower(B,A),C) = k2_prepower(B,k3_prepower(A,C)) ) ) ) ) ) )).
fof(t46_prob_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t46_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t46_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t46_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t46_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( ( ~ 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)) ) ) ) ) )).
fof(t46_quatern2,axiom,( k28_quaterni(k5_struct_0(k15_quatern2)) = 1 )).
fof(t46_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k7_quatern2(k23_quaterni(A,B)) = k23_quaterni(k7_quatern2(B),k7_quatern2(A)) ) ) )).
fof(t46_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ( k27_quaterni(A) = k5_numbers => A = k5_numbers ) ) )).
fof(t46_quofield,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t46_rcomp_3,axiom,( ! [A] : ( ( v13_struct_0(A,1) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t46_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(k9_nat_1(k1_numbers,k4_real_3(A),k5_numbers),k5_numbers) => ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,k5_real_3(A),k1_nat_1(B,2)),k4_real_1(k9_nat_1(k1_numbers,k4_real_3(A),k1_nat_1(B,2)),k9_nat_1(k1_numbers,k5_real_3(A),k1_nat_1(B,1)))) ) ) ) )).
fof(t46_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => k3_relat_1(k4_relat_1(k9_xtuple_0(A)),A) = A ) )).
fof(t46_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ! [D] : k7_relset_1(A,B,C,D) = k7_relset_1(A,B,C,k3_xboole_0(D,k9_xtuple_0(C))) ) )).
fof(t46_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ~ r2_hidden(B,k1_relat_1(A)) => r9_rewrite1(A,B) ) ) )).
fof(t46_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ( r2_hidden(C,k8_rewrite2(A,B,D)) <=> r3_rewrite2(A,B,D,C) ) ) ) ) )).
fof(t46_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ v2_struct_0(C) & l1_rewrite3(C,B) ) => ( v2_rewrite3(C,A,B) => v1_funct_1(k1_rewrite3(A,B,C)) ) ) ) ) )).
fof(t46_rfunct_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t46_rfunct_2,axiom,( ! [A] : ! [B] : ( ( 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))) ) )).
fof(t46_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( ! [C] : ( m1_subset_1(C,A) => ( r2_hidden(C,k1_relset_1(A,B)) => r1_xxreal_0(k5_numbers,k1_funct_1(B,C)) ) ) => r2_relset_1(A,k1_numbers,k18_rfunct_3(A,B),B) ) ) ) )).
fof(t46_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_seq_2(B) => k1_funct_1(k3_rinfsup1(B),A) = k3_xxreal_0(k3_funct_2(k4_ordinal1,k1_numbers,k3_rinfsup1(B),k1_nat_1(A,1)),k1_funct_1(B,A)) ) ) ) )).
fof(t46_rlaffin1,axiom,( ! [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) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t46_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_rlsub_1(A,B,k2_rlsub_1(A)) = u1_struct_0(A) ) ) )).
fof(t46_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ( A = k1_rlsub_2(A,B,C) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( 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) ) ) ) ) ) )).
fof(t46_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rltopsp1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( ~ v8_ordinal1(C) & v1_xreal_0(C) ) => k7_relset_1(u1_struct_0(A),u1_struct_0(A),k4_rltopsp1(A,C),B) = k1_convex1(A,B,C) ) ) ) )).
fof(t46_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t46_rlvect_2,axiom,( ! [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) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_rlvect_2(C,A) => ! [D] : ( 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))) ) ) ) ) )).
fof(t46_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(t46_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t46_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t46_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t46_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t46_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t46_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_xboole_0(B,C) => ( r1_xxreal_0(k1_rpr_1(A,B),k5_numbers) | r1_xxreal_0(1,k1_rpr_1(A,C)) | k2_rpr_1(A,k3_subset_1(A,C),B) = k7_xcmplx_0(k1_rpr_1(A,B),k6_xcmplx_0(1,k1_rpr_1(A,C))) ) ) ) ) ) )).
fof(t46_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t46_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ( A = k1_rusub_2(A,B,C) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( m1_subset_1(G,u1_struct_0(A)) & ? [H] : ( 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) ) ) ) ) ) )).
fof(t46_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ( C = k5_numbers => v1_xboole_0(k4_bhsp_2(A,B,C)) ) ) ) ) )).
fof(t46_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => k10_rvsum_1(k6_finseq_1(k1_numbers),A) = k6_finseq_1(k1_numbers) ) )).
fof(t46_rvsum_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xcmplx_0(C) => k19_rvsum_1(k2_finseq_2(k3_xcmplx_0(A,B),C)) = k19_rvsum_1(k2_finseq_2(B,k19_rvsum_1(k2_finseq_2(A,C)))) ) ) ) )).
fof(t46_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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] : ( ( 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(k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),k5_card_1(D)),7)))) ) & ( r1_xxreal_0(k5_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(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),k5_card_1(D)),7)))) ) ) ) ) ) ) ) )).
fof(t46_scmfsa8c,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t46_scmfsa_2,axiom,( ! [A] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(A,u1_struct_0(k1_ami_3)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ( C = k1_funct_4(B,A) => k1_funct_1(C,k4_struct_0(k1_scmfsa_2)) = k1_funct_1(A,k4_struct_0(k1_ami_3)) ) ) ) ) )).
fof(t46_scmpds_2,axiom,( ! [A] : ( ( 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] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t46_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => k5_card_1(k6_scmpds_6(A,B,C)) = k1_nat_1(k5_card_1(C),2) ) ) ) )).
fof(t46_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( r2_hidden(B,k3_tarski(A)) => k7_scmyciel(A,k1_tarski(B)) = k2_tarski(k1_xboole_0,k1_tarski(B)) ) ) )).
fof(t46_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_semi_af1(A,B,C,D,E) & r2_analoaf(A,B,E,C,D) ) ) ) ) ) ) )).
fof(t46_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_funct_2(k4_ordinal1,k1_numbers,k32_valued_1(k4_ordinal1,k1_numbers,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,A)),k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k32_valued_1(k4_ordinal1,k1_numbers,B),A)) & r2_funct_2(k4_ordinal1,k1_numbers,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,k32_valued_1(k4_ordinal1,k1_numbers,A)),k32_valued_1(k4_ordinal1,k1_numbers,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,A))) ) ) ) )).
fof(t46_seq_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_membered(A) ) => ! [B] : ( v1_xreal_0(B) => ( ( ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => r1_xxreal_0(C,B) ) ) & ! [C] : ( v1_xreal_0(C) => ( ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => r1_xxreal_0(D,C) ) ) => r1_xxreal_0(B,C) ) ) ) => B = k2_seq_4(A) ) ) ) )).
fof(t46_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( 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,k1_nat_1(D,C)),k1_newton(B,k1_nat_1(D,C))))) ) ) ) ) ) )).
fof(t46_setfam_1,axiom,( ! [A] : m1_subset_1(k1_tarski(k1_xboole_0),k1_zfmisc_1(k1_zfmisc_1(A))) )).
fof(t46_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(B) => r2_funct_2(k4_ordinal1,k9_setfam_1(A),k2_setlim_1(A,B),B) ) ) )).
fof(t46_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => r1_tarski(k9_nat_1(k9_setfam_1(B),k4_setlim_1(B,k1_setlim_2(B,C,D)),A),k9_subset_1(B,k9_nat_1(k9_setfam_1(B),k4_setlim_1(B,C),A),k9_nat_1(k9_setfam_1(B),k4_setlim_1(B,D),A))) ) ) ) )).
fof(t46_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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] : ( 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)) ) ) ) )).
fof(t46_sf_mastr,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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)) ) ) )).
fof(t46_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t46_simplex0,axiom,( ! [A] : ! [B] : ( v1_int_1(B) => ! [C] : ( 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)) ) ) ) )).
fof(t46_simplex1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_finset_1(C) & v1_rlaffin1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( ( 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] : ( 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] : ( 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] : ( v7_ordinal1(E) => k1_card_1(a_4_3_simplex1(A,B,C,D)) != k2_xcmplx_0(k3_xcmplx_0(2,E),1) ) ) ) ) ) ) )).
fof(t46_sin_cos,axiom,( k1_relset_1(k1_numbers,k22_sin_cos) = k1_numbers )).
fof(t46_sin_cos3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1))) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_sin_cos2,A),k1_funct_1(k18_sin_cos,B)),k3_xcmplx_0(k3_xcmplx_0(k1_funct_1(k3_sin_cos2,A),k1_funct_1(k16_sin_cos,B)),k7_complex1)) ) ) )).
fof(t46_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k19_sin_cos(k7_xcmplx_0(k6_xcmplx_0(A,B),2)) != k5_numbers => k7_xcmplx_0(k2_xcmplx_0(k17_sin_cos(A),k17_sin_cos(B)),k2_xcmplx_0(k19_sin_cos(A),k19_sin_cos(B))) = k1_sin_cos4(k7_xcmplx_0(k2_xcmplx_0(A,B),2)) ) ) ) )).
fof(t46_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k5_numbers,A) => r1_xxreal_0(k5_numbers,k2_sin_cos2(A)) ) ) )).
fof(t46_sin_cos6,axiom,( k7_relset_1(k1_numbers,k1_numbers,k16_sin_cos,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))) = k2_rcomp_1(k4_xcmplx_0(1),1) )).
fof(t46_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(k1_square_1(A),1) => k5_sin_cos7(A) = k4_sin_cos7(k7_xcmplx_0(1,A)) ) ) )).
fof(t46_sin_cos9,axiom,( v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k2_sin_cos9,k7_relset_1(k1_numbers,k1_numbers,k27_sin_cos,k2_rcomp_1(k5_numbers,k28_sin_cos)))) )).
fof(t46_sincos10,axiom,( r1_tarski(k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1)),k1_relset_1(k1_numbers,k2_sincos10)) )).
fof(t46_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(t46_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => k8_pscomp_1(A) = k2_seq_4(k7_relset_1(u1_struct_0(k15_euclid(2)),k1_numbers,k4_pscomp_1,A)) ) )).
fof(t46_sprect_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t46_sprect_3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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,k13_matrix_0(u1_struct_0(k15_euclid(2)),C)) ) ) ) ) )).
fof(t46_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t46_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(k1_square_1(A),k4_xcmplx_0(A)) ) ) )).
fof(t46_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) )).
fof(t46_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k3_stirl2_1(k1_nat_1(B,1),k1_nat_1(A,1)) = k2_xcmplx_0(k3_xcmplx_0(k1_nat_1(A,1),k3_stirl2_1(B,k1_nat_1(A,1))),k3_stirl2_1(B,A)) ) ) )).
fof(t46_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t46_subset_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_zfmisc_1(A) ) => ? [B] : ( m1_subset_1(B,A) & A = k1_tarski(B) ) ) )).
fof(t46_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ( v6_supinf_2(A) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_xxreal_0(k12_supinf_2(A,C),k12_supinf_2(B,C)) ) & v7_supinf_2(B) ) => v7_supinf_2(A) ) ) ) )).
fof(t46_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))))) ) ) )).
fof(t46_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v4_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_tdlat_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_tdlat_1(A))) => ! [D] : ( m1_subset_1(D,k1_tdlat_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t46_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ( v4_tex_2(B,A) <=> ( v1_tdlat_3(B) & ! [C] : ( ( ~ 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)) ) ) ) ) ) ) )).
fof(t46_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t46_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(t46_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ( ( F = G & r1_tmap_1(B,C,E,G) ) => r1_tmap_1(A,C,D,F) ) ) ) ) ) ) ) ) ) ) )).
fof(t46_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_borsuk_6(A,B,C) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t46_topalg_6,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(2,A) => v1_topalg_6(k4_mfold_2(A)) ) ) )).
fof(t46_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & v1_orders_4(A) & l1_pre_topc(A) ) => v7_topgen_1(A) ) )).
fof(t46_topgen_3,axiom,( ! [A] : k1_compts_1(A) = k7_topgen_3(A,A) )).
fof(t46_topgen_4,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v7_pre_topc(A) => v7_topgen_4(A) ) ) )).
fof(t46_topgen_5,axiom,( v7_pre_topc(k3_topgen_5) )).
fof(t46_topgrp_1,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => v4_pre_topc(k4_group_2(A,C,B),A) ) ) ) )).
fof(t46_topreal3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( k3_finseq_1(B) = A => r2_hidden(B,u1_struct_0(k15_euclid(A))) ) ) ) )).
fof(t46_topreal6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(2))) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [D] : ( v1_xreal_0(D) => ( ( C = k8_metric_1(k14_euclid(2),B,D) & A = B ) => k7_pscomp_1(C) = k2_xcmplx_0(k18_euclid(A),D) ) ) ) ) ) )).
fof(t46_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(2))) => ( D = k19_euclid(A,B) => k8_metric_1(k14_euclid(2),D,C) = k6_jgraph_6(A,B,C) ) ) ) ) ) )).
fof(t46_toprealc,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( ( 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))))) ) ) ) ) )).
fof(t46_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tops_1(B,A) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t46_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( ( ~ v2_struct_0(C) & l1_pre_topc(C) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t46_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t46_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t46_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => r1_xxreal_0(k6_trees_1(k4_trees_1(A,B)),k6_trees_1(A)) ) ) )).
fof(t46_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ! [C] : ( m1_trees_1(C,k9_xtuple_0(A)) => ! [D] : ( m1_trees_1(D,k9_xtuple_0(B)) => k1_funct_1(k7_trees_2(A,C,B),k8_finseq_1(k4_ordinal1,C,D)) = k1_funct_1(B,D) ) ) ) ) )).
fof(t46_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t46_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( m1_pre_topc(C,A) => ! [D] : ( m1_pre_topc(D,A) => ! [E] : ( m1_pre_topc(E,B) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t46_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( l1_turing_1(B) => ! [C] : ( 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)))) ) ) ) ) )).
fof(t46_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(k40_twoscomp(A,B),k41_twoscomp(A,B)))) => ! [D] : ( m1_subset_1(D,k6_margrel1) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t46_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => r2_funct_2(k4_ordinal1,u1_struct_0(k1_complfld),k4_uniroots(A,k1_complfld),k9_uproots(k1_complfld,k1_uproots(u1_struct_0(k1_complfld),k2_uniroots(A),1))) ) )).
fof(t46_uproots,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r2_funct_2(k4_ordinal1,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) ) ) ) ) ) )).
fof(t46_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t46_valued_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => k15_finseq_1(k61_valued_1(B,A)) = B ) ) )).
fof(t46_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( ( 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 ) ) ) ) ) ) )).
fof(t46_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(t46_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( r1_vectsp_5(A,B,C,D) <=> ! [E] : ( m2_vectsp_4(E,A,B,C) => ! [F] : ( m2_vectsp_4(F,A,B,D) => ? [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t46_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(t46_vfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ 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] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,u1_struct_0(D)))) ) => ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t46_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t46_waybel11,axiom,( ! [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) & v4_waybel11(A) & l1_waybel_9(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t46_waybel21,axiom,( ! [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) & l1_waybel_9(A) ) => ! [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) & v2_waybel19(B) & l1_waybel_9(B) ) => ! [C] : ( m1_waybel21(C,A,B) => ( v5_pre_topc(C,A,B) <=> ( v17_waybel_0(C,A,B) & v22_waybel_0(C,A,B) ) ) ) ) ) )).
fof(t46_waybel23,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( v2_waybel23(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( m1_waybel23(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( ~ r3_orders_2(A,D,C) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,B) & ~ r3_orders_2(A,E,C) & r1_waybel_3(A,E,D) ) ) ) ) ) ) ) ) )).
fof(t46_waybel27,axiom,( ! [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] : ( ( 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] : ( ( 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] : ( ( 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))))) ) ) ) ) ) )).
fof(t46_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_waybel34(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_waybel34(A))) => ! [D] : ( r2_hidden(D,k1_altcat_1(k9_waybel34(A),B,C)) <=> ? [E] : ( 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)) ) ) ) ) ) )).
fof(t46_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ( ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => v1_waybel_0(C,A) ) ) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & ! [E] : ( 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] : ( 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) ) ) ) ) ) )).
fof(t46_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( ~ 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))))) ) ) ) ) ) ) )).
fof(t46_waybel_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & v2_lattice3(A) & l1_orders_2(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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) ) ) )).
fof(t46_waybel_4,axiom,( ! [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) ) => ( v3_waybel_3(A) <=> ( v2_waybel_2(A) & ? [B] : ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t46_waybel_7,axiom,( ! [A] : ( ( 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] : ( 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) ) ) )).
fof(t46_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ( v2_wellord1(A) => ! [B] : ~ ( r2_hidden(B,k1_relat_1(A)) & r4_wellord1(A,k2_wellord1(A,k1_wellord1(A,B))) ) ) ) )).
fof(t46_xboole_1,axiom,( ! [A] : ! [B] : k4_xboole_0(A,k2_xboole_0(A,B)) = k1_xboole_0 )).
fof(t46_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( 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))) ) ) ) )).
fof(t46_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t46_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k6_xcmplx_0(B,A),B) ) ) ) )).
fof(t46_xtuple_0,axiom,( ! [A] : ! [B] : r1_tarski(k5_xboole_0(k14_xtuple_0(A),k14_xtuple_0(B)),k14_xtuple_0(k5_xboole_0(A,B))) )).
fof(t46_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r2_hidden(A,k1_numbers) & r1_xxreal_0(A,B) ) => ( r1_xxreal_0(C,B) | r2_hidden(B,k1_numbers) ) ) ) ) ) )).
fof(t46_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(D,B) ) => r1_tarski(k4_xxreal_1(C,D),k4_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t46_xxreal_2,axiom,( ~ v3_xxreal_2(k1_numbers) & ~ v4_xxreal_2(k1_numbers) )).
fof(t46_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(k3_xxreal_3(B,A),k5_numbers) ) ) ) )).
fof(t46_yellow10,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(t46_yellow12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v8_pre_topc(A) <=> ! [B] : ( 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)) ) ) ) ) )).
fof(t46_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ! [D] : ( ( 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),k5_numbers,1,C,B)) & v1_funct_2(k5_funct_4(u1_struct_0(A),k5_numbers,1,C,B),u1_struct_0(k9_waybel18),u1_struct_0(A)) & v5_pre_topc(k5_funct_4(u1_struct_0(A),k5_numbers,1,C,B),k9_waybel18,A) & m1_subset_1(k5_funct_4(u1_struct_0(A),k5_numbers,1,C,B),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k9_waybel18),u1_struct_0(A)))) ) ) ) ) ) )).
fof(t46_yellow18,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t46_yellow20,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(t46_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ! [C] : ( ( ! [D] : ( 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) ) ) )).
fof(t46_yellow_2,axiom,( ! [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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_yellow_1(k7_waybel_0(A))))) ) => ( r2_yellow_0(k1_yellow_1(k7_waybel_0(A)),B) & k2_yellow_0(k1_yellow_1(k7_waybel_0(A)),B) = k1_setfam_1(B) ) ) ) )).
fof(t46_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ 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))) ) ) ) ) )).
fof(t46_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t46_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t46_yellow_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) ) => ! [D] : ( 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)))) ) ) ) )).
fof(t46_yellow_9,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_yellow_9(B,A) => ! [C] : ( m1_yellow_9(C,B) => m1_yellow_9(C,A) ) ) ) )).
fof(t46_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( v9_zf_lang(B) => ( ~ ( A = k25_zf_lang(B) & ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => B != k11_zf_lang(A,C) ) ) & ( ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & B = k11_zf_lang(A,C) ) => A = k25_zf_lang(B) ) & ~ ( A = k26_zf_lang(B) & ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => B != k11_zf_lang(C,A) ) ) & ( ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & B = k11_zf_lang(C,A) ) => A = k26_zf_lang(B) ) ) ) ) ) )).
fof(t46_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r2_zf_lang(k6_zf_lang(A),B) => r3_zf_lang(A,B) ) ) ) )).
fof(t46_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r2_hidden(A,C) & r2_hidden(B,C) ) => k3_xboole_0(k2_tarski(A,B),C) = k2_tarski(A,B) ) )).
fof(t46_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_zmodul01(B) & m1_zmodul01(B,A) ) => ! [C] : ( ( v1_zmodul01(C) & m1_zmodul01(C,A) ) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_struct_0(B,D) <=> r1_struct_0(C,D) ) ) => B = C ) ) ) ) )).
fof(t46_zmodul02,axiom,( ! [A] : ( ( ~ 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_funct_2(k2_zfmisc_1(k4_numbers,u1_struct_0(k31_zmodul02(A))),u1_struct_0(k31_zmodul02(A)),k2_zfmisc_1(k4_numbers,k26_zmodul02(A)),k26_zmodul02(A),u1_zmodul01(k31_zmodul02(A)),k30_zmodul02(A)) ) )).
fof(t47_abcmiz_0,axiom,( ! [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) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_abcmiz_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t47_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_abcmiz_1(B,A,k13_abcmiz_1(A)) => ! [C] : ( m1_abcmiz_1(C,A,k13_abcmiz_1(A)) => ! [D] : ( m1_abcmiz_1(D,A,k12_abcmiz_1(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t47_abcmiz_a,axiom,( ! [A] : ( m1_abcmiz_1(A,k27_abcmiz_1,k12_abcmiz_1(k27_abcmiz_1)) => ! [B] : ( ( 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 ) ) )).
fof(t47_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t47_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t47_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( 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,k5_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 ) ) ) )).
fof(t47_afproj,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t47_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_tdgroup(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t47_algspec1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_instalg1(B) & l1_msualg_1(B) ) => ( r1_circcomb(A,B) => m2_algspec1(k2_circcomb(A,B),A) ) ) ) )).
fof(t47_algstr_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t47_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) )).
fof(t47_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v4_analmetr(B,A) => r6_analmetr(A,C,C,B) ) ) ) ) )).
fof(t47_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ~ ( r1_analmetr(A,J,K) & r2_analort(A,J,K,B,C,E,F) & r2_analort(A,J,K,E,F,H,I) & r2_analort(A,J,K,B,C,D,G) & ~ r2_analort(A,J,K,D,G,H,I) & E != F & B != C ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t47_aofa_000,axiom,( ! [A] : ( ( 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,k10_subset_1(3,k4_finseq_1(u1_unialg_1(A))))) = k4_finseq_2(3,u1_struct_0(A)) ) )).
fof(t47_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ( g1_unialg_1(u1_struct_0(A),u1_unialg_1(A)) = g1_unialg_1(u1_struct_0(B),u1_unialg_1(B)) => k1_unialg_1(A) = k1_unialg_1(B) ) ) ) )).
fof(t47_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( m2_pboole(E,u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,D)) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,C),u8_aofa_a00(A))) => k15_aofa_a00(A,B,C,D,u8_aofa_a00(A),k22_aofa_a00(A,C,F),E) = k22_aofa_a00(A,D,k15_aofa_a00(A,B,C,D,u8_aofa_a00(A),F,E)) ) ) ) ) ) ) )).
fof(t47_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [E] : ( ( v1_aofa_i00(E,A,B,D) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),D) ) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),E) => ! [G] : ( 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) = k4_int_1(k21_aofa_i00(B,k4_numbers,C,F),k21_aofa_i00(B,k4_numbers,C,G)) & ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t47_armstrng,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( B = a_2_2_armstrng(A,C) => k13_armstrng(A,B) = k1_tarski(C) ) ) ) ) )).
fof(t47_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ! [C] : ( ( v3_ordinal1(C) & v7_ordinal1(C) ) => ( C != k1_xboole_0 => k9_arytm_3(k8_arytm_3(A,C),k8_arytm_3(B,C)) = k8_arytm_3(k8_ordinal3(A,B),C) ) ) ) ) )).
fof(t47_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(30,A) & r1_xxreal_0(k5_series_1(2,A),k5_series_1(A,6)) ) ) )).
fof(t47_bcialg_1,axiom,( ! [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) ) => ( v13_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_bcialg_1(A,B) = B ) ) ) )).
fof(t47_bcialg_2,axiom,( ! [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) ) => k4_bcialg_2(A) = k3_xboole_0(k5_bcialg_2(A),k6_bcialg_2(A)) ) )).
fof(t47_bcialg_3,axiom,( ! [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) & v6_bcialg_3(A) & l2_bcialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v2_bcialg_3(B,A) => ( v11_bcialg_3(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t47_bcialg_4,axiom,( ! [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) & l1_bcialg_4(A) ) => ( v4_bcialg_4(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t47_bcialg_5,axiom,( ! [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) ) => ( ( ~ 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,k5_numbers,1,k5_numbers,k5_numbers) ) ) )).
fof(t47_bcialg_6,axiom,( ! [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] : ( ( ~ 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] : ( m2_bcialg_1(C,A) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t47_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( v3_bciideal(B,A) & m2_bcialg_1(B,A) ) ) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)))) ) ) ) ) )).
fof(t47_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(C,k5_bhsp_2(A,B,D)) <=> r1_xxreal_0(k3_bhsp_1(A,k5_algstr_0(A,B,C)),D) ) ) ) ) ) )).
fof(t47_bhsp_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(B),k5_bhsp_4(B,k5_vfunct_1(k4_ordinal1,B,C),A),k5_bhsp_4(B,C,k32_valued_1(k4_ordinal1,k1_numbers,A))) ) ) ) )).
fof(t47_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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)) ) ) ) ) )).
fof(t47_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_boolealg(A,k1_boolealg(A,B,k5_lattices(A)),B) ) ) )).
fof(t47_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_topmetr)) => ! [F] : ( m1_subset_1(F,u1_struct_0(k5_topmetr)) => ~ ( r1_topreal1(k15_euclid(A),C,D,B) & ~ r1_xxreal_0(F,E) & E != k5_numbers & ! [G] : ( ( ~ v1_xboole_0(G) & m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k1_borsuk_4))) ) => ! [H] : ( ( 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 ) ) ) ) ) ) ) ) ) ) )).
fof(t47_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => k2_rcomp_1(k2_xxreal_0,A) != k1_numbers ) )).
fof(t47_borsuk_6,axiom,( k1_funct_1(k3_borsuk_6,k5_numbers) = k5_numbers & k1_funct_1(k3_borsuk_6,1) = 1 )).
fof(t47_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(3))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(3))) => ( ( B = C & k3_euclid_5(B) = k5_numbers ) => r1_tarski(k4_card_3(k1_borsuk_7(1,2,3,k2_rcomp_1(k6_xcmplx_0(k1_euclid_5(B),k7_xcmplx_0(A,k3_square_1(2))),k2_xcmplx_0(k1_euclid_5(B),k7_xcmplx_0(A,k3_square_1(2)))),k2_rcomp_1(k6_xcmplx_0(k2_euclid_5(B),k7_xcmplx_0(A,k3_square_1(2))),k2_xcmplx_0(k2_euclid_5(B),k7_xcmplx_0(A,k3_square_1(2)))),k1_tarski(k5_numbers))),k8_metric_1(k14_euclid(3),C,A)) ) ) ) ) )).
fof(t47_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t47_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t47_bvfunc26,axiom,( ! [A] : ( ~ 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)) ) )).
fof(t47_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k8_xboolean(A,k4_xboolean(B,C)) = k3_xboolean(k4_xboolean(k4_xboolean(A,B),C)) ) ) ) )).
fof(t47_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t47_card_1,axiom,( 1 = k1_tarski(k5_ordinal1) )).
fof(t47_card_2,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( 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)) ) ) ) ) )).
fof(t47_card_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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)) ) )).
fof(t47_card_fin,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_finset_1(A) ) => ! [B] : ( ( v1_finset_1(k9_xtuple_0(A)) & r2_hidden(B,k9_xtuple_0(A)) ) => k3_card_fin(1,A) = k1_nat_1(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))) ) ) )).
fof(t47_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v11_cat_1(B,A) & r1_cat_1(A,B,C) ) => v11_cat_1(C,A) ) ) ) ) )).
fof(t47_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(B)) => ! [D] : ( 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))) ) ) ) )).
fof(t47_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k23_cat_4(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k23_cat_4(A,B))) => ! [E] : ( 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)) ) ) ) )).
fof(t47_catalan2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k3_funct_2(k4_ordinal1,k1_numbers,k4_catalan2(A,B),k5_numbers) = k4_real_1(k3_funct_2(k4_ordinal1,k1_numbers,A,k5_numbers),k3_funct_2(k4_ordinal1,k1_numbers,B,k5_numbers)) ) ) )).
fof(t47_cc0sp2,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t47_cfcont_1,axiom,( ! [A] : ! [B] : ( ( 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(k5_numbers)) = k1_xboole_0 ) => r2_cfcont_1(k2_cfunct_1(k2_numbers,B),A) ) ) )).
fof(t47_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( 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,C,B),k1_cfunct_1(A,E,D)),k1_cfunct_1(A,k2_valued_1(A,k2_numbers,k2_numbers,k19_valued_1(A,k2_numbers,k2_numbers,C,D),k19_valued_1(A,k2_numbers,k2_numbers,E,B)),k19_valued_1(A,k2_numbers,k2_numbers,B,D))) ) ) ) ) ) )).
fof(t47_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ( v7_cgames_1(A) <=> ( ! [B] : ( v2_cgames_1(B) => ~ ( r2_hidden(B,k6_cgames_1(A)) & ~ v8_cgames_1(B) & ~ v10_cgames_1(B) ) ) & ! [B] : ( v2_cgames_1(B) => ~ ( r2_hidden(B,k7_cgames_1(A)) & ~ v8_cgames_1(B) & ~ v9_cgames_1(B) ) ) ) ) ) )).
fof(t47_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m1_chain_1(D,A) => ( k3_chain_1(A,B,C) = k8_chain_1(A,D) <=> ! [E] : ( m2_subset_1(E,k4_ordinal1,k2_finseq_1(A)) => ( ~ r1_xxreal_0(k1_funct_1(B,E),k1_funct_1(C,E)) & m2_chain_1(k4_tarski(k1_funct_1(B,E),k1_funct_1(C,E)),k2_chain_1(A,D,E)) ) ) ) ) ) ) ) )).
fof(t47_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => ! [E] : ( 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] : ( ( 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 ) ) ) ) ) ) ) ) )).
fof(t47_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(D) & v1_finset_1(D) ) => ! [E] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t47_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_circcomb(A) & v2_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_circcomb(B) & v2_circcomb(B) & l1_msualg_1(B) ) => r1_circcomb(A,B) ) ) )).
fof(t47_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v4_msualg_1(E,A) & v4_msafree2(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(B,F))) => ! [H] : ( m1_subset_1(H,k4_card_3(u3_msualg_1(A,E))) => ( H = k3_relat_1(C,G) => ! [I] : ( v7_ordinal1(I) => k5_facirc_1(A,E,H,I) = k3_relat_1(C,k5_facirc_1(B,F,G,I)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t47_classes1,axiom,( ! [A] : ~ ( v1_ordinal1(A) & ! [B] : ( v3_ordinal1(B) => ~ r1_tarski(k1_classes1(A),k4_classes1(B)) ) ) )).
fof(t47_classes2,axiom,( ! [A] : ( v1_ordinal1(A) => v1_classes2(k1_classes1(A)) ) )).
fof(t47_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_clvect_1(B,A) => ! [C] : ( m1_clvect_1(C,A) => ( r1_tarski(u1_struct_0(B),u1_struct_0(C)) => m1_clvect_1(B,C) ) ) ) ) )).
fof(t47_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(C,k5_clvect_2(A,B,D)) <=> r1_xxreal_0(k13_csspace(A,k5_algstr_0(A,B,C)),D) ) ) ) ) ) )).
fof(t47_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => k6_clvect_3(A,k5_vfunct_1(k4_ordinal1,A,B),C) = k6_clvect_3(A,B,k31_valued_1(k4_ordinal1,k2_numbers,C)) ) ) ) )).
fof(t47_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t47_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( ~ ( A != k5_numbers & r1_xxreal_0(k9_complex1(A),k5_numbers) ) & ~ ( ~ r1_xxreal_0(k9_complex1(A),k5_numbers) & A = k5_numbers ) ) ) )).
fof(t47_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k1_complex2(k6_xcmplx_0(A,B),k6_xcmplx_0(A,B)) = k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k1_complex2(A,A),k1_complex2(A,B)),k1_complex2(B,A)),k1_complex2(B,B)) ) ) )).
fof(t47_complfld,axiom,( k2_complfld(k4_struct_0(k1_complfld)) = k4_struct_0(k1_complfld) )).
fof(t47_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( ( A = B & k3_finseq_1(A) = k3_finseq_1(B) ) => k4_finseqop(k2_numbers,k2_numbers,A,k1_binop_2) = k4_finseqop(k1_numbers,k1_numbers,B,k7_binop_2) ) ) ) )).
fof(t47_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(A)) => k2_afinsq_1(k11_compos_1(A,B)) = k7_domain_1(k4_ordinal1,k5_numbers,1) ) ) )).
fof(t47_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( v6_compos_0(D,u1_compos_1(A)) & m1_subset_1(D,u1_compos_1(A)) ) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t47_comptrig,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( r1_xxreal_0(k5_numbers,k4_complex1(A)) => r1_xxreal_0(k5_numbers,k17_sin_cos(k1_comptrig(A))) ) ) )).
fof(t47_comput_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v4_valued_0(A) & v2_margrel1(A) & v2_comput_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) & v2_comput_1(B) ) => ( ( k19_margrel1(A) = k5_numbers & k19_margrel1(B) = k5_numbers & k1_recdef_1(A,k1_xboole_0) = k1_recdef_1(B,k1_xboole_0) ) => A = B ) ) ) )).
fof(t47_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,A)),k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,B),k55_valued_1(k4_ordinal1,k2_numbers,A))) ) ) )).
fof(t47_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v2_comseq_2(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(C,D) & r1_xxreal_0(C,E) & r1_xxreal_0(B,k9_complex1(k6_xcmplx_0(k9_nat_1(k2_numbers,A,D),k9_nat_1(k2_numbers,A,E)))) ) ) ) ) ) ) ) )).
fof(t47_convex4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t47_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t47_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t47_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t47_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k13_csspace(A,k4_algstr_0(A,B)) = k13_csspace(A,B) ) ) )).
fof(t47_dickson,axiom,( ! [A] : ( 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)) ) ) ) )).
fof(t47_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k4_diff_1(k18_sin_cos,A),B) = k4_xcmplx_0(k3_xcmplx_0(2,k3_xcmplx_0(k17_sin_cos(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(2,B),A),2)),k17_sin_cos(k7_xcmplx_0(A,2))))) ) ) )).
fof(t47_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_square_1(D) ) => k1_funct_1(k5_diff_1(C,A),B) = k3_xcmplx_0(k3_xcmplx_0(2,A),B) ) ) ) ) )).
fof(t47_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(C,A),1),B) = k6_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(C,A),k5_numbers),B),k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(C,A),k5_numbers),k6_xcmplx_0(B,A))) ) ) ) )).
fof(t47_dilworth,axiom,( ! [A] : ( ( v4_dilworth(A) & l1_orders_2(A) ) => ! [B] : ( ( v2_dilworth(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v5_dilworth(C,A) & m1_eqrel_1(C,u1_struct_0(A)) ) => ~ ( k1_card_1(C) = k5_card_1(B) & ! [D] : ( ( 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] : ( r2_hidden(E,B) => r2_hidden(E,k1_funct_1(D,E)) ) ) ) ) ) ) ) )).
fof(t47_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t47_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( 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] : ( 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) ) ) ) ) ) )).
fof(t47_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t47_entropy1,axiom,( ! [A] : ( ( v4_partfun3(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( B = k4_entropy1(A) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => k1_funct_1(B,C) = k3_xcmplx_0(k1_funct_1(A,C),k3_power(2,k1_funct_1(A,C))) ) ) ) ) ) ) )).
fof(t47_enumset1,axiom,( ! [A] : k3_enumset1(A,A,A,A,A) = k1_tarski(A) )).
fof(t47_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) )).
fof(t47_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => r1_xxreal_0(1,k12_euclid(k22_euclid(A))) ) ) )).
fof(t47_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => k22_rvsum_1(B,C) = k3_xcmplx_0(k7_xcmplx_0(1,4),k6_xcmplx_0(k1_square_1(k12_euclid(k3_rlvect_1(k15_euclid(A),B,C))),k1_square_1(k12_euclid(k5_algstr_0(k15_euclid(A),B,C))))) ) ) ) )).
fof(t47_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => k4_euclid_3(A,B,C) != k6_xcmplx_0(k3_xcmplx_0(2,k4_euclid_3(D,E,F)),k3_xcmplx_0(6,k28_sin_cos)) ) ) ) ) ) ) )).
fof(t47_euclid_7,axiom,( m1_rlvect_3(k1_xboole_0,k10_funcsdom(k2_finseq_1(k5_numbers))) )).
fof(t47_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ( ( A = k1_funct_1(k6_euclid_8(C,D,E),I) & B = k1_funct_1(k6_euclid_8(F,G,H),J) & A = B ) => ( k1_funct_1(C,I) = k1_funct_1(F,J) & k1_funct_1(D,I) = k1_funct_1(G,J) & k1_funct_1(E,I) = k1_funct_1(H,J) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t47_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => r2_hidden(k2_euclid_4(A,B,C),k1_euclidlp(A)) ) ) ) )).
fof(t47_exchsort,axiom,( ! [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) ) => ! [B] : ( ( 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))) ) ) )).
fof(t47_facirc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : r2_hidden(k4_tarski(A,B),k3_msafree2(k5_circcomb(B,A))) ) )).
fof(t47_fcont_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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(B,A) & r1_tarski(k1_rcomp_1(B,A),k1_relset_1(k1_numbers,C)) ) => ( ( ~ v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A))) & ~ v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A))) ) | 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(B,A))),k7_relset_1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A)))) ) ) ) ) ) )).
fof(t47_fdiff_11,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k7_xcmplx_0(k3_xcmplx_0(k2_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k1_funct_1(k2_sin_cos9,B)),k1_funct_1(k16_sin_cos,B)),k1_square_1(k1_funct_1(k18_sin_cos,B))) ) ) ) ) ) )).
fof(t47_fdiff_4,axiom,( ! [A] : ( ( 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),k18_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),k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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),k18_sin_cos),A),B) = k3_xcmplx_0(B,k1_funct_1(k18_sin_cos,B)) ) ) ) ) ) )).
fof(t47_fdiff_6,axiom,( ! [A] : ( ( 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,k18_sin_cos,k1_taylor_1(3)),k7_xcmplx_0(1,3)),k18_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,k18_sin_cos,k1_taylor_1(3)),k7_xcmplx_0(1,3)),k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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,k18_sin_cos,k1_taylor_1(3)),k7_xcmplx_0(1,3)),k18_sin_cos),A),B) = k1_newton(k1_funct_1(k16_sin_cos,B),3) ) ) ) ) ) )).
fof(t47_fdiff_7,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_funct_1(k16_sin_cos,A) != k5_numbers => ( r1_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos,k16_sin_cos),A) & k1_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos,k16_sin_cos),A) = k4_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,A)))) ) ) ) )).
fof(t47_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => ( k1_pre_ff(A) = 1 <=> ( A = 1 | A = 2 ) ) ) )).
fof(t47_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( ( ~ 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) ) ) ) ) ) ) ) ) )).
fof(t47_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t47_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t47_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => k7_finseq_1(A,E) != C ) ) ) ) ) ) )).
fof(t47_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k2_finseq_1(A)) => k1_funct_1(k1_finseq_2(A),B) = B ) ) )).
fof(t47_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ( k5_relat_1(A,k2_finseq_1(B)) = A <=> r1_xxreal_0(k3_finseq_1(A),B) ) ) ) )).
fof(t47_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t47_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ~ ( r2_hidden(B,k10_xtuple_0(C)) & v1_xboole_0(k1_finseq_5(A,C,B)) ) ) ) ) )).
fof(t47_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => k2_rfinseq(A,1,k3_finseq_4(A,B,C,D)) = k2_finseq_4(A,C,D) ) ) ) ) )).
fof(t47_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v3_card_1(E,D) & m2_finseq_1(E,A) ) => ! [F] : ( ( 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] : ( ( 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(k4_ordinal1,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))) ) ) ) ) ) ) ) ) )).
fof(t47_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_fintopo2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v2_fintopo2(A) & ! [D] : ( 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)) ) ) ) ) )).
fof(t47_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k10_fintopo3(A,k5_numbers,B) = k1_fin_topo(A,B) ) ) )).
fof(t47_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( v2_fintopo6(B,A) => ( r1_xxreal_0(k3_finseq_1(B),C) | v2_fintopo6(k2_rfinseq(u1_struct_0(A),C,B),A) ) ) ) ) ) )).
fof(t47_flang_1,axiom,( ! [A] : ! [B] : ( 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)) ) ) ) )).
fof(t47_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => k1_flang_2(A,B,1,1) = B ) )).
fof(t47_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( 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) ) ) ) ) )).
fof(t47_fomodel0,axiom,( ! [A] : ( v4_funct_1(A) => ! [B] : ( v4_funct_1(B) => k21_fomodel0(k2_xboole_0(A,B)) = k2_xboole_0(k21_fomodel0(A),k21_fomodel0(B)) ) ) )).
fof(t47_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & v8_struct_0(C) & l2_fsm_1(C,A,B) ) => ( v5_fsm_1(C,A,B) <=> ? [D] : ( ~ 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)) ) ) ) ) ) )).
fof(t47_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t47_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(B,k3_xboole_0(k9_xtuple_0(C),A)) => k1_funct_1(k5_relat_1(C,A),B) = k1_funct_1(C,B) ) ) )).
fof(t47_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k1_tarski(B),A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_tarski(B),A))) ) => ( A != k1_xboole_0 => k2_relset_1(A,C) = k1_tarski(k1_funct_1(C,B)) ) ) )).
fof(t47_funct_3,axiom,( ! [A] : r1_tarski(k10_xtuple_0(k11_funct_3(A)),k2_zfmisc_1(A,A)) )).
fof(t47_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(t47_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t47_funct_6,axiom,( ! [A] : ! [B] : ! [C] : k8_funct_6(A,k7_funcop_1(B,C)) = k7_funcop_1(B,k1_funct_2(A,C)) )).
fof(t47_funct_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t47_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( m2_functor0(C,A,B) => ( ( v16_functor0(C,A,B) & v5_functor0(C,A,B) ) => v7_functor0(C,A,B) ) ) ) ) )).
fof(t47_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D),k2_fuzzy_1(A,B,C)),k2_fuzzy_1(A,B,k2_fuzzy_2(A,D,C))) ) ) ) ) )).
fof(t47_fvaluat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_fvaluat1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k6_fvaluat1(A,B)) <=> r1_xxreal_0(k5_numbers,k3_funct_2(u1_struct_0(A),k6_numbers,B,C)) ) ) ) ) )).
fof(t47_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [D] : ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => D = k4_fvsum_1(A,B,k8_fvsum_1(A,B,D,C),C) ) ) ) ) )).
fof(t47_gcd_1,axiom,( ! [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) & v3_gcd_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_gcd_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t47_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( ( ~ v1_xboole_0(F) & v1_relat_1(F) & v2_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ! [G] : ( m1_genealg1(G,F) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t47_geomtrap,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_geomtrap(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) <=> m1_subset_1(B,u1_struct_0(k2_diraf(A))) ) ) )).
fof(t47_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t47_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & ~ v4_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t47_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( ( r1_xxreal_0(C,D) & r1_xxreal_0(D,k3_finseq_1(B)) & k1_funct_1(B,C) = k1_funct_1(B,D) ) => k1_nat_1(k3_finseq_1(k20_glib_001(A,B,C,D)),D) = k1_nat_1(k3_finseq_1(B),C) ) ) ) ) ) )).
fof(t47_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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) ) ) ) )).
fof(t47_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & v2_glib_003(A) ) => ! [B] : ! [C] : ( 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))) = k1_nat_1(k5_card_1(k11_glib_003(A)),1) ) ) ) )).
fof(t47_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ 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(k1_nat_1(A,1),k3_finseq_1(k2_goboard2(D))) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(k2_goboard2(D))) & r1_xxreal_0(1,C) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1))) = k2_topreal1(2,D,C) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1))) = k2_topreal1(2,D,k1_nat_1(C,1)) ) => ( r1_xxreal_0(k3_finseq_1(D),k1_nat_1(C,1)) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,1)) ) ) ) ) ) ) ) )).
fof(t47_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( ( v3_graph_2(C,A) & m2_graph_1(C,A) ) => ( r1_graph_2(A,B,C) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t47_graph_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v6_graph_1(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) = k1_nat_1(k7_graph_3(B,C,A),1) ) ) ) ) ) ) ) )).
fof(t47_graph_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m2_finseq_1(C,u4_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u4_struct_0(B)) => ( ( k3_finseq_1(D) = 1 & r1_tarski(k10_xtuple_0(D),k10_xtuple_0(C)) & r5_graph_5(B,A) ) => r1_xxreal_0(k10_graph_5(B,D,A),k10_graph_5(B,C,A)) ) ) ) ) ) )).
fof(t47_graphsp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k3_finseq_2(k1_numbers)) => ( ( r1_xxreal_0(1,A) & r2_hidden(1,k4_finseq_1(B)) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,A) ) => k1_funct_1(B,C) = 1 ) ) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r1_xxreal_0(2,C) & r1_xxreal_0(C,A) ) => k1_funct_1(B,k1_nat_1(A,C)) = k4_xcmplx_0(1) ) ) ) => ( k1_funct_1(B,k1_nat_1(A,1)) = k4_xcmplx_0(1) | ( 1 = k14_graphsp(k7_graphsp(B,A),B,A) & k13_graphsp(B,A) = k1_xboole_0 & k6_domain_1(k4_ordinal1,1) = k13_graphsp(k6_graphsp(k9_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),k15_graphsp(A),k18_graphsp(A))),1),B),A) ) ) ) ) ) )).
fof(t47_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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,k11_polynom1(A,C,D,E),k11_polynom1(A,C,k6_termord(A,B,C,D),E),k1_groeb_1(A,C,E)) ) ) ) ) ) )).
fof(t47_group_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v5_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t47_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v15_algstr_0(C) & v1_group_3(C,A) & m1_group_2(C,A) ) => ! [D] : ( ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) ) => ? [E] : ( 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)) ) ) ) ) ) )).
fof(t47_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => r1_struct_0(C,k1_group_1(B)) ) ) ) )).
fof(t47_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t47_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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)) ) ) ) ) )).
fof(t47_group_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( r2_hidden(A,k4_group_5(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k2_group_5(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) ) ) ) )).
fof(t47_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t47_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t47_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => k3_helly(A,B,B,B) = B ) ) )).
fof(t47_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_xxreal_0(k4_hermitan(A,B,k3_rlvect_1(A,C,D)),k1_square_1(k2_xcmplx_0(k3_square_1(k4_hermitan(A,B,C)),k3_square_1(k4_hermitan(A,B,D))))) ) ) ) ) )).
fof(t47_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( A != k5_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) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(2,A),k1_square_1(k3_prepower(A,2)))) ) ) ) )).
fof(t47_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => r2_hidden(k3_hilbert1(k4_hilbert1(A,k4_hilbert1(C,B)),k4_hilbert1(A,k4_hilbert1(B,C))),k6_hilbert1) ) ) ) )).
fof(t47_hurwitz,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( 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)) ) ) )).
fof(t47_ideal_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t47_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => v4_incsp_1(k9_domain_1(u1_incsp_1(A),B,C,D,E),A) ) ) ) ) ) ) )).
fof(t47_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( A != k5_numbers => k4_int_1(A,A) = 1 ) ) )).
fof(t47_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( ( v7_ordinal1(D) & ~ v8_ordinal1(D) ) => ! [E] : ( ( v7_ordinal1(E) & ~ v8_ordinal1(E) ) => ! [F] : ( ( v7_ordinal1(F) & ~ v8_ordinal1(F) ) => ~ ( r1_int_1(k6_nat_d(D,E),k6_xcmplx_0(A,B)) & ! [G] : ( v1_int_1(G) => ! [H] : ( v1_int_1(H) => ? [I] : ( v1_int_1(I) & k5_int_1(k6_xcmplx_0(I,A),D) = k5_numbers & k5_int_1(k6_xcmplx_0(I,B),E) = k5_numbers & k5_int_1(k6_xcmplx_0(I,C),F) = k5_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)) & k5_int_1(k6_xcmplx_0(k3_xcmplx_0(k3_nat_d(D,k6_nat_d(D,E)),G),k4_int_1(k6_xcmplx_0(B,A),k6_nat_d(D,E))),k3_nat_d(E,k6_nat_d(D,E))) = k5_numbers & k5_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),k4_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))) = k5_numbers ) ) ) ) ) ) ) ) ) ) ) )).
fof(t47_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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(k4_xcmplx_0(1),1)) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(C,D) = k4_xcmplx_0(k7_xcmplx_0(1,k2_xcmplx_0(1,k1_square_1(D)))) ) ) & B = k9_xtuple_0(C) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,A)) ) => k2_integra5(A,C) = k6_xcmplx_0(k1_funct_1(k2_sin_cos9,k2_seq_4(A)),k1_funct_1(k2_sin_cos9,k3_seq_4(A))) ) ) ) ) )).
fof(t47_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,D) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => k1_funct_1(C,E) = 1 ) ) & r2_relset_1(k1_numbers,k1_numbers,B,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,C,k1_taylor_1(2))))) & r1_tarski(D,k2_rcomp_1(k4_xcmplx_0(1),1)) & D = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,D),k2_sin_cos9),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,D),k2_sin_cos9),k3_seq_4(A))) ) ) ) ) ) )).
fof(t47_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k2_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,D))),k1_funct_1(k16_sin_cos,D)),k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k27_sin_cos,D),k1_funct_1(k18_sin_cos,D)),k1_square_1(k1_funct_1(k16_sin_cos,D)))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_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) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k2_fdiff_9)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k2_fdiff_9)),k3_seq_4(A))) ) ) ) ) )).
fof(t47_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t47_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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_comseq_2(k2_partfun1(A,k1_numbers,B,A)) => r1_xxreal_0(k11_integra1(A,B),k10_integra1(A,B)) ) ) ) )).
fof(t47_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)) => k2_integra5(A,k32_valued_1(k1_numbers,k1_numbers,k16_sin_cos)) = k4_xcmplx_0(1) ) ) )).
fof(t47_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v3_rcomp_1(E) & m1_subset_1(E,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,E) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => ( k1_funct_1(C,F) = k2_xcmplx_0(A,F) & k1_funct_1(C,F) != k5_numbers ) ) ) & E = k1_relset_1(k1_numbers,C) & k1_relset_1(k1_numbers,C) = k1_relset_1(k1_numbers,D) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => k1_funct_1(D,F) = k4_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k2_xcmplx_0(A,F)))) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,D,B)) ) => k2_integra5(B,D) = k6_xcmplx_0(k1_funct_1(k6_rfunct_1(k1_numbers,k1_numbers,C),k2_seq_4(B)),k1_funct_1(k6_rfunct_1(k1_numbers,k1_numbers,C),k3_seq_4(B))) ) ) ) ) ) ) )).
fof(t47_interva1,axiom,( ! [A] : ( ~ 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))) ) )).
fof(t47_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(t47_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & 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] : ( m1_isocat_1(C,A,B) => ? [D] : ( 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)) ) ) ) ) ) )).
fof(t47_jgraph_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ 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(k5_numbers,k18_euclid(B)) & r1_xxreal_0(k17_euclid(B),k17_euclid(A)) ) ) ) ) )).
fof(t47_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t47_jordan,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t47_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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(C,D) => ( r1_xxreal_0(A,1) | r1_xxreal_0(k3_finseq_1(k1_jordan8(E,C)),k1_nat_1(A,1)) | r1_xxreal_0(B,1) | r1_xxreal_0(k1_matrix_0(k1_jordan8(E,C)),k1_nat_1(B,1)) | ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ( ( r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(k11_newton(2,k7_nat_d(D,C)),k6_xcmplx_0(A,2)),2),F) & r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(k11_newton(2,k7_nat_d(D,C)),k6_xcmplx_0(B,2)),2),G) ) => ( r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(k11_newton(2,k7_nat_d(D,C)),k6_xcmplx_0(A,1)),2),F) | r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(k11_newton(2,k7_nat_d(D,C)),k6_xcmplx_0(B,1)),2),G) | r1_tarski(k3_goboard5(k1_jordan8(E,D),F,G),k3_goboard5(k1_jordan8(E,C),A,B)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t47_jordan1h,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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(B,A) ) => r1_tarski(k2_goboard9(k2_jordan9(C,B)),k2_goboard9(k2_jordan9(C,A))) ) ) ) ) )).
fof(t47_jordan1k,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( r1_tarski(B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => r1_xxreal_0(k5_jordan1k(A,D,C),k5_jordan1k(A,D,B)) ) ) ) ) ) )).
fof(t47_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t47_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( 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)) ) ) ) ) ) ) )).
fof(t47_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(2),A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t47_knaster,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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) ) ) ) )).
fof(t47_kurato_1,axiom,( 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)))) )).
fof(t47_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k5_finsub_1(B)) => ! [D] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t47_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ! [C] : ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,B) & ! [E] : ( 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)) ) ) )).
fof(t47_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,B) => ( r1_xxreal_0(C,D) | ! [E] : ~ ( ~ r2_hidden(k7_nat_d(k15_glib_000(A),D),k17_lexbfs(k6_glib_000(A),k4_ordinal1,k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),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),k4_ordinal1,k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),k13_lexbfs(A,k16_lexbfs(A),B)),E)) ) ) ) ) ) ) ) )).
fof(t47_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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(k5_numbers)) = k1_xboole_0 ) => ( k1_limfunc2(B,A) = k5_numbers | ( r1_limfunc2(k6_rfunct_1(k1_numbers,k1_numbers,B),A) & k1_limfunc2(k6_rfunct_1(k1_numbers,k1_numbers,B),A) = k5_xcmplx_0(k1_limfunc2(B,A)) ) ) ) ) ) )).
fof(t47_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) = k5_numbers ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,k9_subset_1(k1_numbers,k9_xtuple_0(B),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,C),A),k2_rcomp_1(A,k2_xcmplx_0(A,C))))) & r1_xxreal_0(k1_funct_1(B,D),k5_numbers) ) ) ) ) | r2_limfunc3(k6_rfunct_1(k1_numbers,k1_numbers,B),A) ) ) ) ) )).
fof(t47_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k10_prob_1(C))) & k1_funct_1(A,D) = k5_limfunc1(A) ) ) | v7_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).
fof(t47_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( ( r2_hidden(D,k13_lpspacc1(A,B,C)) & r2_hidden(E,k13_lpspacc1(A,B,C)) ) => r1_xxreal_0(k1_mesfunc6(A,B,C,k55_valued_1(A,k2_numbers,k2_valued_1(A,k2_numbers,k2_numbers,D,E))),k3_supinf_2(k1_mesfunc6(A,B,C,k55_valued_1(A,k2_numbers,D)),k1_mesfunc6(A,B,C,k55_valued_1(A,k2_numbers,E)))) ) ) ) ) ) ) )).
fof(t47_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t47_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( ( v2_xxreal_0(G) & v1_xreal_0(G) ) => ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t47_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t47_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(k3_hilbert1(A,B),k3_hilbert1(k3_hilbert1(A,k1_ltlaxio1(C)),k3_hilbert1(A,k1_ltlaxio1(k3_hilbert1(B,C)))))) ) ) ) )).
fof(t47_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t47_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( r1_matrix10(B,C) => r1_matrix10(k4_matrix10(A,B,D),k4_matrix10(A,C,D)) ) ) ) ) ) )).
fof(t47_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ! [E] : ( ( v1_finset_1(E) & v1_setfam_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ( ( r2_hidden(B,k2_finseq_1(k5_card_1(D))) & r1_tarski(E,k2_finseq_1(k1_matrix_0(C))) ) => k7_matrix_0(A,k6_matrix13(A,C,D,E),B) = k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,A,k5_matrix13(E),k7_matrix_0(A,C,k1_funct_1(k5_matrix13(D),B))) ) ) ) ) ) ) )).
fof(t47_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(A),B,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,B) & ! [E] : ( v7_ordinal1(E) => ! [F] : ( 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_0(u1_struct_0(A),D,E,F) = k5_struct_0(A) ) & ( ( E = C & F = 1 ) => k3_matrix_0(u1_struct_0(A),D,E,F) = k5_struct_0(A) ) & ( ( E = 1 & F = 1 ) => k3_matrix_0(u1_struct_0(A),D,E,F) = k4_struct_0(A) ) & ( ( E = C & F = C ) => k3_matrix_0(u1_struct_0(A),D,E,F) = k4_struct_0(A) ) & ( ~ ( ( E = 1 | E = C ) & ( F = 1 | F = C ) ) => ( ( E = F => k3_matrix_0(u1_struct_0(A),D,E,F) = k5_struct_0(A) ) & ( E != F => k3_matrix_0(u1_struct_0(A),D,E,F) = k4_struct_0(A) ) ) ) ) ) ) ) ) => ( C = 1 | D = k4_matrix14(A,B,C) ) ) ) ) ) ) )).
fof(t47_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(D,k4_finseq_1(B)) & k7_matrix_0(u1_struct_0(A),B,D) = k5_finseq_2(u1_struct_0(A),k1_matrix_0(B),k4_struct_0(A)) & r2_hidden(D,k4_finseq_1(C)) & k7_matrix_0(u1_struct_0(A),C,D) = k5_finseq_2(u1_struct_0(A),k1_matrix_0(C),k4_struct_0(A)) ) => ( r1_xxreal_0(k3_finseq_1(B),1) | k4_matrix15(A,B,C) = k4_matrix15(A,k17_matrix_0(u1_struct_0(A),D,B),k17_matrix_0(u1_struct_0(A),D,C)) ) ) ) ) ) ) )).
fof(t47_matrix16,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t47_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( k3_finseq_1(k12_matrix_0(A,B,C,D)) = 2 & k1_matrix_0(k12_matrix_0(A,B,C,D)) = 2 & k2_matrix_0(k12_matrix_0(A,B,C,D)) = k2_zfmisc_1(k2_finseq_1(2),k2_finseq_1(2)) ) )).
fof(t47_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(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) ) ) ) ) ) )).
fof(t47_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v4_matrix_6(C,A,B) & r1_matrix_6(A,B,C,D) ) => r1_matrix_6(A,B,k4_matrix_0(u1_struct_0(B),C),D) ) ) ) ) ) )).
fof(t47_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r2_matrix_8(A,B,C,D) => ( r1_xxreal_0(A,k5_numbers) | r2_matrix_8(A,B,k3_matrix_3(B,k3_matrix_3(B,C,C),C),k3_matrix_3(B,k3_matrix_3(B,D,D),D)) ) ) ) ) ) ) )).
fof(t47_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ( ~ r1_xxreal_0(k3_finseq_1(A),k5_numbers) => k17_rvsum_1(k10_matrixc1(A)) = k17_rvsum_1(k11_matrixc1(A)) ) ) )).
fof(t47_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( ( v2_matrixj1(F,u1_struct_0(D)) & m2_finseq_1(F,k3_finseq_2(k3_finseq_2(u1_struct_0(D)))) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(D),C,C) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(D))) ) => ( ( r2_hidden(A,k4_finseq_1(G)) & r2_hidden(B,k2_finseq_1(C)) ) => k18_matrix_0(A,B,k2_wsierp_1(k10_matrixj1(u1_struct_0(D),k15_matrixj1(u1_struct_0(D),k16_matrixj1(u1_struct_0(D),C,G),F))),u1_struct_0(D),k20_matrixj1(u1_struct_0(D),E,k15_matrixj1(u1_struct_0(D),k16_matrixj1(u1_struct_0(D),C,G),F))) = k13_matrixj1(u1_struct_0(D),E,k3_matrixj1(u1_struct_0(D),k4_matrixj1(u1_struct_0(D),k18_matrix_0(A,B,C,u1_struct_0(D),G)),F)) ) ) ) ) ) ) ) ) )).
fof(t47_matrixr1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( ~ r1_xxreal_0(k3_finseq_1(B),k5_numbers) => k9_matrixr1(k10_rvsum_1(B,A)) = k7_matrixr1(A,k9_matrixr1(B)) ) ) ) )).
fof(t47_matrixr2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( ( v1_matrix_0(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),k5_numbers) | k12_matrixr1(C,k8_rvsum_1(A,B)) = k8_rvsum_1(k12_matrixr1(C,A),k12_matrixr1(C,B)) ) ) ) ) ) )).
fof(t47_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( ( 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] : ( m1_matrlin(E,A,B) => ! [F] : ( m1_matrlin(F,A,C) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_matrlin(H,A,k6_prvect_1(A,k3_finseq_1(F))) => ( H = k11_matrix13(A,k3_finseq_1(F),k3_finseq_1(F),k3_matrix_1(A,k3_finseq_1(F))) => ! [I] : ( ( v1_matrix_0(I) & v2_matrix_0(I,u1_struct_0(A),k3_finseq_1(E),k3_finseq_1(H)) & m2_finseq_1(I,k3_finseq_2(u1_struct_0(A))) ) => ( ( I = k1_matrlin2(A,B,C,D,E,F) & v13_vectsp_1(D,B,C) & v1_mod_2(D,A,B,C) ) => k3_funct_2(u1_struct_0(B),u1_struct_0(k6_prvect_1(A,k3_finseq_1(F))),k4_matrlin2(A,B,k6_prvect_1(A,k3_finseq_1(F)),E,H,I),G) = k9_matrlin(A,C,F,k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,G)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t47_matrprob,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(C) & k3_finseq_1(B) = k1_matrix_0(C) ) => ( r1_xxreal_0(k3_finseq_1(B),k5_numbers) | k22_rvsum_1(k12_matrixr1(C,A),B) = k22_rvsum_1(A,k11_matrixr1(C,B)) ) ) ) ) ) )).
fof(t47_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k4_zfmisc_1(k1_tarski(A),k1_tarski(B),k1_tarski(C),k1_tarski(D)) = k1_tarski(k6_xtuple_0(A,B,C,D)) )).
fof(t47_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => A = k1_measure6(A,k5_numbers) ) )).
fof(t47_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_membered(C) => ! [D] : ( v1_membered(D) => ( ( r1_tarski(A,B) & r1_tarski(C,D) ) => r1_tarski(k9_member_1(A,C),k9_member_1(B,D)) ) ) ) ) ) )).
fof(t47_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_partfun1(C,u1_struct_0(B)) ) => ! [D] : ( ( 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) = k5_numbers ) ) ) ) ) )).
fof(t47_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(A),B) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ( 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))) ) ) ) ) ) ) )).
fof(t47_mesfun7c,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(k7_complsp2(A))) => k12_supinf_2(k7_complsp2(A),B) = k4_complex1(k1_funct_1(A,B)) ) ) ) )).
fof(t47_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_partfun1(A,k1_numbers)) & v1_mesfunc8(E,A,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [F] : ( ( 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,k5_numbers)) & D = k1_relset_1(A,F) & ! [G] : ( v7_ordinal1(G) => r1_mesfunc6(A,B,k4_mesfunc5(A,k1_numbers,E,G),D) ) & r3_mesfunc6(A,B,C,F) & ! [G] : ( m1_subset_1(G,A) => ! [H] : ( v7_ordinal1(H) => ( r2_hidden(G,D) => r1_xxreal_0(k1_mesfunc9(k55_valued_1(A,k1_numbers,k4_mesfunc5(A,k1_numbers,E,H)),G),k1_mesfunc9(F,G)) ) ) ) & ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(t47_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ~ ( ? [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) & F = k1_relset_1(A,D) & r1_mesfunc1(A,B,D,F) ) & ? [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) & F = k1_relset_1(A,E) & r1_mesfunc1(A,B,E,F) ) & ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t47_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t47_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ~ ( r1_tarski(D,k1_relset_1(A,F)) & v6_supinf_2(F) & r1_mesfunc1(A,B,F,D) & v2_mesfunc9(E,A) & ! [G] : ( v7_ordinal1(G) => ( r1_mesfunc2(A,B,k4_mesfunc5(A,k6_numbers,E,G)) & v6_supinf_2(k4_mesfunc5(A,k6_numbers,E,G)) & r1_tarski(D,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,E,G))) ) ) & ! [G] : ( 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] : ( ( v1_funct_1(G) & v1_funct_2(G,k4_ordinal1,k6_numbers) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ~ ( ! [H] : ( v7_ordinal1(H) => k1_mesfunc9(G,H) = k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,E,H),D)) ) & v1_mesfunc9(G) & k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,F,D)) = k3_mesfunc9(G) ) ) ) ) ) ) ) ) ) )).
fof(t47_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_midsp_1(B,A) => ! [C] : ( m1_midsp_1(C,A) => ! [D] : ( m1_midsp_1(D,A) => ( k7_midsp_1(A,B,C) = k7_midsp_1(A,B,D) => C = D ) ) ) ) ) )).
fof(t47_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( 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) ) ) )).
fof(t47_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k48_modelc_1(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k48_modelc_1(A,B,C))) => ( ! [G] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t47_modelc_2,axiom,( ! [A] : ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( m1_subset_1(A,k1_zfmisc_1(k13_modelc_2(B))) => m1_subset_1(A,k1_zfmisc_1(k9_modelc_2)) ) ) )).
fof(t47_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k25_modelc_2(k43_modelc_2)) => ! [C] : ( ( 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] : ( ( 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] : ( v7_ordinal1(E) => ( ! [F] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t47_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => k3_relat_1(k9_finseq_1(A),k5_moebius1(k1_newton(A,B))) = k9_finseq_1(A) ) ) )).
fof(t47_monoid_0,axiom,( k23_binop_2 = k1_realset1(k9_binop_2,k4_ordinal1) & k23_binop_2 = k1_realset1(k20_binop_2,k4_ordinal1) )).
fof(t47_monoid_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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)) ) ) ) )).
fof(t47_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => r8_pboole(u1_struct_0(A),k8_pboole(k4_msafree4(A,B,C),k4_msafree4(A,B,C)),k4_msafree4(A,B,C)) ) ) ) )).
fof(t47_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( m3_pboole(E,A,k1_mboolean(A,D)) => ( ( r1_pboole(A,B,E) & r2_pboole(A,B,C) ) => r2_pboole(A,k4_mssubfam(A,D,E),C) ) ) ) ) ) )).
fof(t47_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,B),D)) => ! [G] : ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t47_mycielsk,axiom,( ! [A] : ( ( v1_mycielsk(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_xxreal_0(k2_mycielsk(k5_yellow_0(A,B)),k2_mycielsk(A)) ) ) )).
fof(t47_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(B,C) & r1_xxreal_0(C,k2_xcmplx_0(B,A)) & ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(k1_nat_1(B,k5_numbers),D) & r1_xxreal_0(D,k2_xcmplx_0(B,A)) & C = D ) ) ) ) ) ) )).
fof(t47_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( r1_int_2(A,B) => k5_card_1(k22_pre_poly(k8_newton,k12_nat_3(k3_xcmplx_0(A,B)))) = k2_xcmplx_0(k5_card_1(k22_pre_poly(k8_newton,k12_nat_3(A))),k5_card_1(k22_pre_poly(k8_newton,k12_nat_3(B)))) ) ) ) )).
fof(t47_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(k1_nat_1(A,2),B) | r1_xxreal_0(k1_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,k1_nat_1(k7_nat_d(A,1),1)) & ~ r1_xxreal_0(B,k7_nat_d(k1_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) ) ) ) ) )).
fof(t47_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(D,B) & ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( r2_hidden(G,B) & ~ r1_xxreal_0(F,k2_normsp_0(A,k5_algstr_0(A,G,D))) & r1_xxreal_0(E,k9_complex1(k6_xcmplx_0(k7_partfun1(k2_numbers,C,G),k7_partfun1(k2_numbers,C,D)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t47_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r1_ndiff_1(A,B,C,D) & ! [E] : ( m1_nfcont_1(E,A,D) => ~ ( r1_tarski(E,k1_relset_1(u1_struct_0(A),C)) & ? [F] : ( v1_funct_1(F) & v2_ndiff_1(F,A,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) & k7_partfun1(u1_struct_0(B),F,k4_struct_0(A)) = k4_struct_0(B) & r1_nfcont_1(A,B,F,k4_struct_0(A)) & ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( r2_hidden(G,E) => k5_algstr_0(B,k7_partfun1(u1_struct_0(B),C,G),k7_partfun1(u1_struct_0(B),C,D)) = k3_rlvect_1(B,k17_lopban_1(A,B,k3_ndiff_1(A,B,C,D),k5_algstr_0(A,G,D)),k7_partfun1(u1_struct_0(B),F,k5_algstr_0(A,G,D))) ) ) ) ) ) ) ) ) ) ) )).
fof(t47_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( 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] : ( ( 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))))) ) ) ) ) ) )).
fof(t47_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_prvect_2(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t47_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => r1_nat_d(k5_nat_d(B,A),k3_xcmplx_0(B,A)) ) ) )).
fof(t47_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ( ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & k2_relset_1(u1_struct_0(B),C) = k1_tarski(D) ) => r3_nfcont_1(A,B,C,k1_relset_1(u1_struct_0(A),C)) ) ) ) ) )).
fof(t47_nfcont_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k4_ordinal1) => ( 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)) ) ) ) ) ) )).
fof(t47_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(k7_normform(A))) => ! [C] : ( 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)) ) ) )).
fof(t47_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t47_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t47_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( 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))) ) ) ) )).
fof(t47_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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))) ) ) ) ) )).
fof(t47_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v4_ordinal1(A) => ( v1_xboole_0(A) | ( r2_hidden(B,k3_ordinal5(A)) <=> ? [C] : ( v3_ordinal1(C) & r2_hidden(C,A) & r2_hidden(B,k3_ordinal5(C)) ) ) ) ) ) )).
fof(t47_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t47_osafree,axiom,( ! [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) & v2_osalg_4(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m2_osafree(C,A,B) <=> r2_hidden(C,k30_osafree(A,B)) ) ) ) )).
fof(t47_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t47_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_parsp_2(A,B,C,C,B) => B = C ) ) ) ) )).
fof(t47_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k4_partfun1(A,B)) => ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ) )).
fof(t47_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,C) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t47_pboole,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(t47_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k26_pcs_0(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k26_pcs_0(A,B))) => ( ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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(k26_pcs_0(A,B),C,D) ) ) ) ) ) )).
fof(t47_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( 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) & k10_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) = k2_xcmplx_0(k2_pdiff_5(B,A),k2_pdiff_5(C,A)) ) ) ) ) ) )).
fof(t47_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(1)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ( ( v1_pdiff_7(C,A) & r2_hidden(D,C) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( 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] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ? [F] : ( m2_finseq_1(F,k1_euclid(1)) & k4_finseq_1(F) = k2_finseq_1(A) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( r2_hidden(G,k2_finseq_1(A)) => k1_funct_1(F,G) = k9_euclid(1,k11_pdiff_1(A,1,G,B,D),k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_1(G,A),E)) ) ) & k1_pdiff_6(A,1,k8_pdiff_1(A,1,B,D),E) = k5_euclid_7(1,F) ) ) ) ) ) ) ) ) )).
fof(t47_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( v1_xreal_0(D) => ( ( 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)) ) ) ) ) )).
fof(t47_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( k4_nat_d(k1_newton(A,B),C) = 1 & r1_int_2(A,C) ) => ( r1_xxreal_0(C,1) | r1_nat_d(k3_pepin(A,C),B) ) ) ) ) ) )).
fof(t47_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( 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)))))) ) ) ) )).
fof(t47_polynom5,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t47_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [G] : ( ( 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),k11_polynom1(A,C,G,E),k11_polynom1(A,C,G,F)) ) ) ) ) ) ) ) ) )).
fof(t47_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ( v1_abian(B) => k2_power(k4_xcmplx_0(A),B) = k2_power(A,B) ) ) ) )).
fof(t47_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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) ) ) )).
fof(t47_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => ( B = k5_numbers => k4_prepower(A,B) = 1 ) ) ) )).
fof(t47_prob_3,axiom,( ! [A] : ? [B] : ( m2_finseq_1(B,k9_setfam_1(A)) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k1_relset_1(k4_ordinal1,B)) => k4_prob_3(A,B,C) = A ) ) ) )).
fof(t47_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t47_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ 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))) ) ) ) ) ) ) )).
fof(t47_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t47_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ~ ( v2_qc_lang1(C,A) & r1_qc_lang2(A,B,C) ) ) ) ) )).
fof(t47_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( ( ~ 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))) ) ) ) ) )).
fof(t47_quatern2,axiom,( k7_quatern2(k5_struct_0(k15_quatern2)) = k5_struct_0(k15_quatern2) )).
fof(t47_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k7_quatern2(k27_quaterni(A)) = k27_quaterni(k7_quatern2(A)) ) )).
fof(t47_quaterni,axiom,( k27_quaterni(k18_quaterni) = k18_quaterni )).
fof(t47_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k19_quofield(A))) => ( B != k4_struct_0(k19_quofield(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( C != k4_struct_0(A) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t47_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( r1_tarski(k10_xtuple_0(B),A) => k3_relat_1(B,k4_relat_1(A)) = B ) ) )).
fof(t47_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ! [D] : 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))) ) )).
fof(t47_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_rewrite1(A) ) => ! [B] : ( v1_relat_1(B) => ( r1_tarski(B,A) => v1_rewrite1(B) ) ) ) )).
fof(t47_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => r2_hidden(C,k8_rewrite2(A,B,C)) ) ) )).
fof(t47_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ v2_struct_0(C) & l1_rewrite3(C,B) ) => ! [D] : ( m1_rewrite1(D,k1_rewrite3(A,B,C)) => ! [E] : ( v7_ordinal1(E) => ~ ( r2_hidden(E,k4_finseq_1(D)) & r2_hidden(k2_xcmplx_0(E,1),k4_finseq_1(D)) & ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,k8_afinsq_1(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(C)) => ! [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t47_rfunct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t47_rfunct_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),A)) ) )).
fof(t47_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( ! [C] : ( m1_subset_1(C,A) => ( r2_hidden(C,k1_relset_1(A,B)) => r1_xxreal_0(k1_funct_1(B,C),k5_numbers) ) ) => r2_relset_1(A,k1_numbers,k19_rfunct_3(A,B),k32_valued_1(A,k1_numbers,B)) ) ) ) )).
fof(t47_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_seq_2(B) => k1_funct_1(k4_rinfsup1(B),A) = k4_xxreal_0(k3_funct_2(k4_ordinal1,k1_numbers,k4_rinfsup1(B),k1_nat_1(A,1)),k1_funct_1(B,A)) ) ) ) )).
fof(t47_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t47_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t47_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t47_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v8_ordinal1(B) & v1_xreal_0(B) ) => k2_relset_1(u1_struct_0(A),k4_rltopsp1(A,B)) = k2_struct_0(A) ) ) )).
fof(t47_rlvect_1,axiom,( ! [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) ) => ! [B] : ( v1_xreal_0(B) => k1_rlvect_1(A,k4_rlvect_1(A,k6_finseq_1(u1_struct_0(A))),B) = k4_struct_0(A) ) ) )).
fof(t47_rlvect_2,axiom,( ! [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) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_rlvect_2(D,A) => r1_rlvect_2(A,k8_rlvect_2(A,B,k8_rlvect_2(A,C,D)),k8_rlvect_2(A,k3_xcmplx_0(B,C),D)) ) ) ) ) )).
fof(t47_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => k3_rmod_2(A,B,C,k2_rmod_2(A,B)) = u1_struct_0(B) ) ) ) )).
fof(t47_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t47_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_rmod_4(D,A,B) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t47_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k9_robbins1(A,B,k3_robbins1(A,C)) = k9_robbins1(A,C,k3_robbins1(A,B)) ) ) ) )).
fof(t47_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t47_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t47_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_xboole_0(B,C) => ( r1_xxreal_0(k1_rpr_1(A,B),k5_numbers) | r1_xxreal_0(1,k1_rpr_1(A,C)) | k2_rpr_1(A,k3_subset_1(A,C),k3_subset_1(A,B)) = k6_xcmplx_0(1,k7_xcmplx_0(k1_rpr_1(A,B),k6_xcmplx_0(1,k1_rpr_1(A,C)))) ) ) ) ) ) )).
fof(t47_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t47_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t47_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ( u1_struct_0(A) = k6_domain_1(u1_struct_0(A),k4_struct_0(A)) => ( r1_xxreal_0(C,k5_numbers) | k4_bhsp_2(A,B,C) = k6_domain_1(u1_struct_0(A),k4_struct_0(A)) ) ) ) ) ) )).
fof(t47_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k10_rvsum_1(k9_finseq_1(B),A) = k9_finseq_1(k3_xcmplx_0(A,B)) ) ) )).
fof(t47_rvsum_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k19_rvsum_1(k2_finseq_2(A,k3_xcmplx_0(B,C))) = k3_xcmplx_0(k19_rvsum_1(k2_finseq_2(A,B)),k19_rvsum_1(k2_finseq_2(A,C))) ) ) ) )).
fof(t47_scm_halt,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => r6_scmfsa7b(A,k1_scmfsa_m(B),C) ) ) ) ) )).
fof(t47_scmfsa8c,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t47_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(C,u1_struct_0(k1_ami_3)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(E,u1_struct_0(k1_scmfsa_2)) ) => ( ( E = k1_funct_4(D,C) & A = B ) => k1_funct_1(C,A) = k1_funct_1(E,B) ) ) ) ) ) ) )).
fof(t47_scmpds_2,axiom,( ! [A] : ( ( 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] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t47_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ( r2_hidden(k5_numbers,k9_xtuple_0(k6_scmpds_6(A,B,C))) & r2_hidden(1,k9_xtuple_0(k6_scmpds_6(A,B,C))) ) ) ) ) )).
fof(t47_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ( ! [B] : ! [C] : ( ( 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) ) ) )).
fof(t47_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_semi_af1(A,B,C,D,E) & r2_semi_af1(A,B,C,E,D) ) ) ) ) ) ) )).
fof(t47_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_funct_2(k4_ordinal1,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,A),k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,A)),k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C),A)) & r2_funct_2(k4_ordinal1,k1_numbers,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,A),k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,A)),k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C),A)) ) ) ) ) )).
fof(t47_seq_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_membered(A) ) => ! [B] : ( v3_membered(B) => ( ( r1_tarski(A,B) & v3_xxreal_2(B) ) => r1_xxreal_0(k3_seq_4(B),k3_seq_4(A)) ) ) ) )).
fof(t47_setfam_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( 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) ) ) ) )).
fof(t47_setlim_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ( v2_prob_1(C) => r1_tarski(k3_funct_2(k4_ordinal1,k9_setfam_1(B),k4_setlim_1(B,C),k1_nat_1(A,1)),k1_funct_1(C,A)) ) ) ) )).
fof(t47_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => k9_nat_1(k9_setfam_1(B),k4_setlim_1(B,k2_setlim_2(B,C,D)),A) = k4_subset_1(B,k9_nat_1(k9_setfam_1(B),k4_setlim_1(B,C),A),k9_nat_1(k9_setfam_1(B),k4_setlim_1(B,D),A)) ) ) ) )).
fof(t47_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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] : ( m1_subset_1(D,k5_finsub_1(A)) => ! [E] : ( 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)) ) ) ) ) )).
fof(t47_sf_mastr,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( 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)) ) ) )).
fof(t47_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t47_simplex0,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ v3_pencil_1(B) & v1_matroid0(B) & l1_pre_topc(B) ) => ! [C] : ( m3_simplex0(C,B,A) => ( ~ v1_xboole_0(C) => v7_ordinal1(A) ) ) ) ) )).
fof(t47_simplex1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_finset_1(C) & v1_rlaffin1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( ( 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] : ( 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] : ( 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] : ( m3_simplex0(E,k5_simplex1(A,B,k5_simplex0(u1_struct_0(B),k6_domain_1(k1_zfmisc_1(u1_struct_0(B)),C))),k6_xcmplx_0(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 ) ) ) ) ) ) )).
fof(t47_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => k1_funct_1(k22_sin_cos,A) = k3_complex1(k11_comseq_3(k3_sin_cos(A))) ) )).
fof(t47_sin_cos3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,k2_xcmplx_0(A,k3_xcmplx_0(k4_xcmplx_0(B),k7_complex1))) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_sin_cos2,A),k1_funct_1(k18_sin_cos,B)),k3_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(k1_funct_1(k3_sin_cos2,A),k1_funct_1(k16_sin_cos,B))),k7_complex1)) ) ) )).
fof(t47_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k19_sin_cos(k7_xcmplx_0(k2_xcmplx_0(A,B),2)) != k5_numbers => k7_xcmplx_0(k6_xcmplx_0(k17_sin_cos(A),k17_sin_cos(B)),k2_xcmplx_0(k19_sin_cos(A),k19_sin_cos(B))) = k1_sin_cos4(k7_xcmplx_0(k6_xcmplx_0(A,B),2)) ) ) ) )).
fof(t47_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(A,k5_numbers) => r1_xxreal_0(k2_sin_cos2(A),k5_numbers) ) ) )).
fof(t47_sin_cos6,axiom,( k7_relset_1(k1_numbers,k1_numbers,k16_sin_cos,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos))) = k1_rcomp_1(k4_xcmplx_0(1),1) )).
fof(t47_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(A,1) => ( r1_xxreal_0(A,k5_numbers) | k6_sin_cos7(A) = k2_sin_cos7(k7_xcmplx_0(1,A)) ) ) ) )).
fof(t47_sin_cos9,axiom,( v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k1_sin_cos9,k1_rcomp_1(k4_xcmplx_0(1),1))) )).
fof(t47_sincos10,axiom,( r1_tarski(k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1)),k1_relset_1(k1_numbers,k3_sincos10)) )).
fof(t47_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(t47_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( ( ~ 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] : ( ( ~ 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)) ) ) ) ) )).
fof(t47_sprect_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ 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))) ) ) ) ) ) ) ) )).
fof(t47_sprect_3,axiom,( ! [A] : ( ( v1_sprect_1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t47_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t47_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k1_square_1(B),k1_square_1(A)) & r1_xxreal_0(k5_numbers,A) ) => ( r1_xxreal_0(k4_xcmplx_0(A),B) & r1_xxreal_0(B,A) ) ) ) ) )).
fof(t47_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) ) )).
fof(t47_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => r1_tarski(k24_qc_lang1(A,B),k9_substut1(A,B)) ) ) )).
fof(t47_subset_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ~ ( v1_zfmisc_1(B) & ! [C] : ( m1_subset_1(C,A) => B != k1_tarski(C) ) ) ) ) )).
fof(t47_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v6_supinf_2(A) => ! [B] : ( v7_ordinal1(B) => ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( 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) ) ) ) ) )).
fof(t47_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))))) ) ) )).
fof(t47_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v4_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_tdlat_2(B,A) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t47_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( v3_tex_2(B,A) & ! [C] : ( ( ~ v2_struct_0(C) & v1_pre_topc(C) & m1_pre_topc(C,A) ) => ~ ( v4_tex_2(C,A) & B = u1_struct_0(C) ) ) ) ) ) )).
fof(t47_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( m1_pre_topc(B,A) => ~ v3_tex_3(B,A) ) => v1_tdlat_3(A) ) ) )).
fof(t47_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(t47_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ( ( G = k3_funct_2(u1_struct_0(A),u1_struct_0(B),D,F) & r1_tmap_1(A,B,D,F) & r1_tmap_1(B,C,E,G) ) => r1_tmap_1(A,C,k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),D,E),F) ) ) ) ) ) ) ) ) )).
fof(t47_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( r2_hidden(C,u1_struct_0(k5_topalg_1(A,B))) <=> ? [D] : ( 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) ) ) ) ) )).
fof(t47_topalg_6,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ( r1_xxreal_0(3,A) => v1_topalg_6(k7_toprealb(A,C,B)) ) ) ) ) )).
fof(t47_topgen_1,axiom,( ! [A] : ( 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 ) ) )).
fof(t47_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v7_topgen_4(A) => v6_pre_topc(A) ) ) )).
fof(t47_topgrp_1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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) ) ) )).
fof(t47_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(2))) => ( D = k19_euclid(A,B) => k10_metric_1(k14_euclid(2),D,C) = k5_jgraph_6(A,B,C) ) ) ) ) ) )).
fof(t47_toprealc,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( v3_membered(D) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(C)) => ( r2_hidden(A,k2_finseq_1(B)) => k1_funct_1(k3_funct_2(u1_struct_0(C),u1_struct_0(k15_euclid(B)),k14_toprealc(B,u1_struct_0(C),D,E),F),A) = k3_funct_2(u1_struct_0(C),D,E,F) ) ) ) ) ) ) )).
fof(t47_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t47_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t47_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t47_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t47_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => ~ ( B != k1_xboole_0 & r1_xxreal_0(k6_trees_1(A),k6_trees_1(k4_trees_1(A,B))) ) ) ) )).
fof(t47_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t47_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_trees_9(A) ) => ( v1_finset_1(A) <=> ? [B] : ( v7_ordinal1(B) & k2_trees_2(A,B) = k1_xboole_0 ) ) ) )).
fof(t47_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(B,C) => r2_tsep_1(A,B,C) ) ) ) ) )).
fof(t47_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ~ ( ~ r1_tsep_1(C,B) & ~ r1_tsep_1(D,B) & ? [E] : ( m1_pre_topc(E,B) & ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t47_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( l1_turing_1(B) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t47_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t47_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( 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)) ) ) ) )).
fof(t47_uproots,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r1_polynom5(A,C,B) => r2_funct_2(k4_ordinal1,u1_struct_0(A),C,k13_polynom3(A,k4_polynom5(A,k4_algstr_0(A,B),k5_struct_0(A)),k5_uproots(A,B,C))) ) ) ) ) )).
fof(t47_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [F] : ( m2_subset_1(F,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [G] : ( m1_valuat_1(G,A,B) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t47_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => k1_relset_1(k4_ordinal1,k2_xboole_0(A,k61_valued_1(B,k3_finseq_1(A)))) = k2_finseq_1(k1_nat_1(k3_finseq_1(A),k3_finseq_1(B))) ) ) )).
fof(t47_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( ( 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) ) ) ) )).
fof(t47_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => k3_vectsp_4(A,B,C,k2_vectsp_4(A,B)) = u1_struct_0(B) ) ) ) )).
fof(t47_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( k1_vectsp_5(A,B,C,D) = B <=> ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & ? [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t47_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t47_vfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ 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] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,u1_struct_0(D)))) ) => ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t47_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ! [E] : ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t47_waybel11,axiom,( ! [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) & v4_waybel11(A) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_tops_1(A,k6_waybel_0(A,B)) = k2_waybel_3(A,B) ) ) )).
fof(t47_waybel23,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r1_waybel_3(A,C,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,B) & r3_orders_2(A,C,E) & r1_waybel_3(A,E,D) ) ) ) ) ) ) ) ) ) )).
fof(t47_waybel27,axiom,( ! [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] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(t47_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ( ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => v2_waybel_0(C,A) ) ) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & ! [E] : ( 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] : ( 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) ) ) ) ) ) )).
fof(t47_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( C = a_2_0_waybel_1(A,B) => ! [D] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t47_waybel_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ! [D] : ( ( 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))) ) ) ) ) )).
fof(t47_waybel_4,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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) ) ) ) )).
fof(t47_wellord1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) ) )).
fof(t47_xboole_1,axiom,( ! [A] : ! [B] : k4_xboole_0(A,k3_xboole_0(A,B)) = k4_xboole_0(A,B) )).
fof(t47_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k9_xboolean(A,k7_xboolean(A,B)) = k4_xboolean(k3_xboolean(A),B) ) ) )).
fof(t47_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => k3_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(D,C)) = k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(A,C)),k3_xcmplx_0(B,D)),k3_xcmplx_0(B,C)) ) ) ) ) )).
fof(t47_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => r1_xxreal_0(k6_xcmplx_0(A,B),k5_numbers) ) ) ) )).
fof(t47_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r2_hidden(C,k1_numbers) & r1_xxreal_0(B,C) ) => ( r1_xxreal_0(B,A) | r2_hidden(B,k1_numbers) ) ) ) ) ) )).
fof(t47_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(C,A) & ~ r1_xxreal_0(B,D) & ~ r1_tarski(k1_xxreal_1(C,D),k4_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t47_xxreal_2,axiom,( v3_xxreal_2(k1_tarski(k1_xxreal_0)) )).
fof(t47_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ~ ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,C) & ~ r1_xxreal_0(B,k1_xxreal_3(C,A)) & r1_xxreal_0(k3_xxreal_3(B,A),C) ) ) ) ) )).
fof(t47_yellow10,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(t47_yellow12,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t47_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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(k5_numbers,1),k2_tarski(k1_xboole_0,1),u1_struct_0(k9_waybel18),u1_struct_0(k9_waybel18),k1_partfun1(k2_tarski(k5_numbers,1),u1_struct_0(A),u1_struct_0(A),k2_tarski(k1_xboole_0,1),k5_funct_4(u1_struct_0(A),k5_numbers,1,C,B),k5_funct_3(D,u1_struct_0(A))),k3_struct_0(k9_waybel18)) ) ) ) ) ) ) )).
fof(t47_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & m1_altcat_2(B,A) ) => m1_altcat_2(k1_yellow18(B),k1_yellow18(A)) ) ) )).
fof(t47_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ! [C] : ( ( r1_yellow_0(A,B) & ! [D] : ( 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) ) ) )).
fof(t47_yellow_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ( r2_yellow_0(k1_yellow_1(k7_waybel_0(A)),k1_xboole_0) & k2_yellow_0(k1_yellow_1(k7_waybel_0(A)),k1_xboole_0) = k2_struct_0(A) ) ) )).
fof(t47_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ 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))) ) ) ) ) )).
fof(t47_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t47_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k13_lattice3(A,B,C) = k13_lattice3(A,k1_yellow_5(A,B,C),C) ) ) ) )).
fof(t47_yellow_7,axiom,( ! [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] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) ) => ! [D] : ( 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)))) ) ) ) ) )).
fof(t47_yellow_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( ( C = D & v1_waybel11(C,A) ) => v1_waybel11(D,B) ) ) ) ) ) ) )).
fof(t47_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v9_zf_lang(A) => A = k11_zf_lang(k25_zf_lang(A),k26_zf_lang(A)) ) ) )).
fof(t47_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ( r2_zf_lang(k7_zf_lang(A,B),C) => ( r3_zf_lang(A,C) & r3_zf_lang(B,C) ) ) ) ) ) )).
fof(t47_zfmisc_1,axiom,( ! [A] : ! [B] : ~ ( r1_xboole_0(k1_tarski(A),B) & r2_hidden(A,B) ) )).
fof(t47_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_zmodul01(B) & m1_zmodul01(B,A) ) => ( u1_struct_0(B) = u1_struct_0(A) => B = A ) ) ) )).
fof(t47_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( m1_zmodul02(C,A) => k3_rlvect_1(k31_zmodul02(A),k1_rlvect_2(k31_zmodul02(A),B),k1_rlvect_2(k31_zmodul02(A),C)) = k22_zmodul02(A,B,C) ) ) ) )).
fof(t48_abcmiz_0,axiom,( ! [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) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_abcmiz_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t48_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( B != C => ! [D] : ( m1_abcmiz_1(D,A,B) => ! [E] : ( m1_abcmiz_1(E,A,C) => D != E ) ) ) ) ) ) )).
fof(t48_abcmiz_a,axiom,( ! [A] : ( ( v9_abcmiz_1(A,k27_abcmiz_1) & m1_abcmiz_1(A,k27_abcmiz_1,k12_abcmiz_1(k27_abcmiz_1)) ) => ! [B] : ( ( 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))) ) ) )).
fof(t48_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_aff_1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(B,D) & r5_aff_1(A,C,D) ) ) ) ) )).
fof(t48_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => r2_hidden(C,B) ) ) ) ) )).
fof(t48_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [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,k5_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 ) ) ) )).
fof(t48_afinsq_2,axiom,( ! [A] : ( ( 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,k15_binop_2) ) ) )).
fof(t48_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t48_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_tdgroup(A) & l1_analoaf(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t48_algspec1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_instalg1(B) & l1_msualg_1(B) ) => m2_algspec1(k2_circcomb(A,B),B) ) ) )).
fof(t48_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) )).
fof(t48_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t48_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t48_aofa_000,axiom,( ! [A] : ( ( 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,k10_subset_1(4,k4_finseq_1(u1_unialg_1(A))))) = k4_finseq_2(2,u1_struct_0(A)) ) )).
fof(t48_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v2_relat_1(D) & m1_msafree(D,A,B) ) => ! [E] : ( r2_hidden(E,k13_aofa_a00(A,B,C,D)) => m2_pboole(E,u1_struct_0(A),D,u3_msualg_1(A,C)) ) ) ) ) ) )).
fof(t48_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( m2_pboole(E,u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,D)) => ! [F] : ( v1_xboolean(F) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),u8_aofa_a00(A))) => ( k15_aofa_a00(A,B,C,D,u8_aofa_a00(A),k22_aofa_a00(A,C,G),E) = k3_xboolean(F) <=> k15_aofa_a00(A,B,C,D,u8_aofa_a00(A),G,E) = F ) ) ) ) ) ) ) ) )).
fof(t48_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_aofa_i00(E,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) ) => ! [F] : ( m3_aofa_i00(F,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_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) = k5_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) = k5_int_1(k2_xcmplx_0(k3_funct_2(k9_funct_2(B,k4_numbers),k4_numbers,F,C),1),2) & ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t48_armstrng,axiom,( ! [A] : ( l1_armstrng(A) => ( ~ v1_xboole_0(k13_armstrng(u1_armstrng(A),k5_armstrng(A))) & v11_armstrng(k13_armstrng(u1_armstrng(A),k5_armstrng(A))) ) ) )).
fof(t48_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => k10_arytm_3(A,k11_arytm_3) = k11_arytm_3 ) )).
fof(t48_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,9) & r1_xxreal_0(k2_power(2,A),k1_square_1(k3_xcmplx_0(2,A))) ) ) )).
fof(t48_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_1(A,C,B) = k1_bcialg_1(A,B,C) ) ) <=> v13_bcialg_1(A) ) ) )).
fof(t48_bcialg_2,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ! [C] : ( m4_bcialg_2(C,A,B) => ! [D] : ( m1_bcialg_2(D,A) => ( ! [E] : ( m2_bcialg_2(E,A) => m5_bcialg_2(E,A,B) ) => D = C ) ) ) ) ) )).
fof(t48_bcialg_3,axiom,( ! [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) & v6_bcialg_3(A) & l2_bcialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v2_bcialg_3(B,A) => ( v11_bcialg_3(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) ) ) )).
fof(t48_bcialg_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t48_bcialg_5,axiom,( ! [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) ) => ( ( ~ 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,k5_numbers,1,k5_numbers,k5_numbers) ) ) )).
fof(t48_bcialg_6,axiom,( ! [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] : ( ( ~ 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] : ( ( v12_bcialg_1(C,A) & m2_bcialg_1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t48_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( v3_bciideal(B,A) & m2_bcialg_1(B,A) ) ) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t48_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(C,k5_bhsp_2(A,B,D)) <=> r1_xxreal_0(k4_bhsp_1(A,B,C),D) ) ) ) ) ) )).
fof(t48_bhsp_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( ( v2_comseq_2(A) & v1_bhsp_2(C,B) ) => v1_bhsp_2(k5_bhsp_4(B,C,A),B) ) ) ) ) )).
fof(t48_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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))) ) ) ) ) ) )).
fof(t48_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t48_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( 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))))) ) ) ) ) ) ) ) )).
fof(t48_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( 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) ) ) ) )).
fof(t48_borsuk_6,axiom,( k1_funct_1(k4_borsuk_6,k5_numbers) = k5_numbers & k1_funct_1(k4_borsuk_6,1) = 1 )).
fof(t48_borsuk_7,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xreal_0(C) => k2_complex2(B,C) = k2_complex2(B,k2_xcmplx_0(C,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A))) ) ) ) )).
fof(t48_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t48_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t48_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t48_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k8_xboolean(A,k4_xboolean(B,C)) = k8_xboolean(k4_xboolean(A,B),C) ) ) ) )).
fof(t48_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t48_card_1,axiom,( 2 = k2_tarski(k5_ordinal1,1) )).
fof(t48_card_2,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(t48_card_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(A,k4_card_3(B)) => ( v1_relat_1(A) & v1_funct_1(A) ) ) ) )).
fof(t48_card_fin,axiom,( ! [A] : ! [B] : ( ( 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] : ( 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) ) ) ) )).
fof(t48_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v10_cat_1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_cat_1(D,A,C,B) & k2_cat_1(A,C,B) = k1_tarski(D) ) ) ) ) ) )).
fof(t48_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_cat_3(E,B,C,A) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t48_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k23_cat_4(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k23_cat_4(A,B))) => ! [E] : ( m1_subset_1(E,u4_struct_0(k23_cat_4(A,B))) => m1_cat_1(E,k23_cat_4(A,B),C,D) ) ) ) )).
fof(t48_cfcont_1,axiom,( ! [A] : ! [B] : ( ( 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(k5_numbers)) = k1_xboole_0 ) => r2_cfcont_1(k2_cfunct_1(k2_numbers,B),A) ) ) )).
fof(t48_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( 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,D),k1_cfunct_1(A,C,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,D,C))) ) ) ) ) ) )).
fof(t48_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ( v9_cgames_1(A) <=> ( ! [B] : ( v2_cgames_1(B) => ~ ( r2_hidden(B,k7_cgames_1(A)) & ~ v8_cgames_1(B) & ~ v9_cgames_1(B) ) ) & ? [B] : ( v2_cgames_1(B) & r2_hidden(B,k6_cgames_1(A)) & v5_cgames_1(B) ) ) ) ) )).
fof(t48_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_chain_1(C,B) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(k1_euclid(B)),k4_chain_1(B,C,A)) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(k1_euclid(B)),k4_chain_1(B,C,k1_nat_1(A,1))) => ( r2_hidden(E,k9_chain_1(B,C,A,D)) <=> r1_tarski(D,E) ) ) ) ) ) ) )).
fof(t48_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ~ ( r2_hidden(C,k2_chord(A,B)) & r2_hidden(C,B) ) ) )).
fof(t48_circcmb3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v8_struct_0(B) & m1_circcmb3(B,A) ) => ! [C] : ( m2_circcmb3(C,A,B) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( 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] : ( ( 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] : ( 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] : ( 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),k1_nat_1(1,k2_circcmb3(B,C,H))) ) ) ) ) ) ) ) ) ) ) )).
fof(t48_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t48_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v4_msualg_1(E,A) & v4_msafree2(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(B,F))) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t48_classes1,axiom,( ! [A] : ( v1_ordinal1(A) => r1_tarski(k3_tarski(A),A) ) )).
fof(t48_classes2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ( ~ v1_xboole_0(k1_classes1(A)) & v1_classes2(k1_classes1(A)) ) ) )).
fof(t48_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_clvect_1(B,A) => ! [C] : ( m1_clvect_1(C,A) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_struct_0(B,D) => r1_struct_0(C,D) ) ) => m1_clvect_1(B,C) ) ) ) ) )).
fof(t48_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(C,k5_clvect_2(A,B,D)) <=> r1_xxreal_0(k15_csspace(A,B,C),D) ) ) ) ) ) )).
fof(t48_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v2_comseq_2(C) & v1_clvect_2(B,A) ) => v1_clvect_2(k6_clvect_3(A,B,C),A) ) ) ) ) )).
fof(t48_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,A) ) => ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,A) ) => ! [E] : ! [F] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t48_complex1,axiom,( k9_complex1(k6_complex1) = 1 )).
fof(t48_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k3_complex1(k1_complex2(A,B)) = k5_numbers <=> ( k4_complex1(k1_complex2(A,B)) = k3_xcmplx_0(k9_complex1(A),k9_complex1(B)) | k4_complex1(k1_complex2(A,B)) = k4_xcmplx_0(k3_xcmplx_0(k9_complex1(A),k9_complex1(B))) ) ) ) ) )).
fof(t48_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ( k2_complfld(A) = k4_struct_0(k1_complfld) => A = k4_struct_0(k1_complfld) ) ) )).
fof(t48_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ( k6_complsp2(k10_seq_4(A,k7_complex1)) = k6_rvsum_1(k7_complsp2(A)) & k7_complsp2(k10_seq_4(A,k7_complex1)) = k6_complsp2(A) ) ) )).
fof(t48_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k2_afinsq_1(B)) => r2_hidden(C,k2_afinsq_1(k10_compos_1(A,B))) ) ) ) ) )).
fof(t48_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( v6_compos_0(D,u1_compos_1(A)) & m1_subset_1(D,u1_compos_1(A)) ) => ! [E] : ( ( v6_compos_0(E,u1_compos_1(A)) & m1_subset_1(E,u1_compos_1(A)) ) => ! [F] : ( ( 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) ) ) ) ) ) ) )).
fof(t48_comptrig,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( r1_xxreal_0(k4_complex1(A),k5_numbers) => r1_xxreal_0(k17_sin_cos(k1_comptrig(A)),k5_numbers) ) ) )).
fof(t48_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k3_finseq_2(k4_ordinal1)) & v1_funct_1(C) & v4_valued_0(C) & v2_margrel1(C) ) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ! [E] : ( m2_finseq_1(E,k4_ordinal1) => ~ ( r2_hidden(E,k1_relset_1(k3_finseq_2(k4_ordinal1),k6_comput_1(B,C,A,D))) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => E != k2_funct_7(k4_ordinal1,D,A,F) ) ) ) ) ) ) ) )).
fof(t48_comseq_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,k25_valued_1(k4_ordinal1,k2_numbers,B,A)),k26_valued_1(k4_ordinal1,k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,B),k9_complex1(A))) ) ) )).
fof(t48_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_convex4(B,A) <=> ! [C] : ( v1_xcmplx_0(C) => ( ? [D] : ( v1_xreal_0(D) & C = D & ~ r1_xxreal_0(D,k5_numbers) & ~ 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) ) ) ) ) ) )).
fof(t48_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t48_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) )).
fof(t48_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ( ( r6_cqc_the3(A,D,B) & r6_cqc_the3(A,E,C) ) => ( r1_cqc_the3(A,B,C) <=> r1_cqc_the3(A,k6_cqc_lang(A,E),k6_cqc_lang(A,D)) ) ) ) ) ) ) ) )).
fof(t48_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k6_xcmplx_0(k13_csspace(A,B),k13_csspace(A,C)),k13_csspace(A,k5_algstr_0(A,B,C))) ) ) ) )).
fof(t48_dickson,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t48_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k5_diff_1(k18_sin_cos,A),B) = k4_xcmplx_0(k3_xcmplx_0(2,k3_xcmplx_0(k17_sin_cos(B),k17_sin_cos(k7_xcmplx_0(A,2))))) ) ) )).
fof(t48_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => k1_funct_1(D,E) = k7_xcmplx_0(A,k1_square_1(E)) ) => ( B = C | B = k5_numbers | C = k5_numbers | k9_diff_1(D,B,C) = k4_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(A,k3_xcmplx_0(B,C)),k2_xcmplx_0(k7_xcmplx_0(1,B),k7_xcmplx_0(1,C)))) ) ) ) ) ) ) )).
fof(t48_dilworth,axiom,( ! [A] : ( ( v8_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( v2_dilworth(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v5_dilworth(C,A) & m1_eqrel_1(C,u1_struct_0(A)) ) => ( k5_card_1(C) = k5_card_1(B) => ! [D] : ~ ( r2_hidden(D,C) & ! [E] : ( m1_subset_1(E,B) => k9_subset_1(u1_struct_0(A),D,B) != k1_tarski(E) ) ) ) ) ) ) )).
fof(t48_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( 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) != k5_numbers & ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t48_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( 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] : ( 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) != k5_numbers & k6_ec_pf_2(A,k2_ec_pf_2(A,B),k3_ec_pf_2(A,B),D) != k5_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)) ) ) ) ) ) ) )).
fof(t48_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t48_entropy1,axiom,( ! [A] : ( ( v4_partfun3(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => ( ( k1_funct_1(A,B) = k5_numbers => k1_funct_1(k4_entropy1(A),B) = k5_numbers ) & ( ~ r1_xxreal_0(k1_funct_1(A,B),k5_numbers) => k1_funct_1(k4_entropy1(A),B) = k3_xcmplx_0(k1_funct_1(A,B),k3_power(2,k1_funct_1(A,B))) ) ) ) ) ) )).
fof(t48_enumset1,axiom,( ! [A] : ! [B] : k4_enumset1(A,A,A,A,A,B) = k2_tarski(A,B) )).
fof(t48_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) )).
fof(t48_euclid,axiom,( ! [A] : ( 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)))) ) ) )).
fof(t48_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => r1_xxreal_0(k22_rvsum_1(B,C),k2_xcmplx_0(k22_rvsum_1(B,B),k22_rvsum_1(C,C))) ) ) ) )).
fof(t48_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ~ ( r2_hidden(E,k9_euclid_3(A,B,C,D)) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ~ ( k2_xcmplx_0(k2_xcmplx_0(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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t48_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,k2_numbers) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t48_euclid_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => m1_rusub_3(k8_euclid_7(A),k7_real_ns1(A)) ) )).
fof(t48_euclid_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ( ( k1_funct_1(A,G) = k1_funct_1(D,H) & k1_funct_1(B,G) = k1_funct_1(E,H) & k1_funct_1(C,G) = k1_funct_1(F,H) ) => k1_funct_1(k6_euclid_8(A,B,C),G) = k1_funct_1(k6_euclid_8(D,E,F),H) ) ) ) ) ) ) ) ) ) )).
fof(t48_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t48_exchsort,axiom,( ! [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) ) => ! [B] : ( ( 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 ) ) ) )).
fof(t48_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) ) => ! [D] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t48_fcont_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k1_fcont_1(A,B),k5_numbers) = B ) ) )).
fof(t48_fdiff_11,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k2_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k1_funct_1(k2_sin_cos9,B)),k1_funct_1(k16_sin_cos,B)),k1_square_1(k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k1_fdiff_9,B)),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t48_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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(B,A),k1_relset_1(k1_numbers,C)) & r2_fdiff_1(C,k2_rcomp_1(B,A)) ) => ( ( ? [D] : ( v1_xreal_0(D) & r2_hidden(D,k2_rcomp_1(B,A)) & r1_xxreal_0(k1_fdiff_1(C,D),k5_numbers) ) & ? [D] : ( v1_xreal_0(D) & r2_hidden(D,k2_rcomp_1(B,A)) & r1_xxreal_0(k5_numbers,k1_fdiff_1(C,D)) ) ) | ( v2_funct_1(k2_partfun1(k1_numbers,k1_numbers,C,k2_rcomp_1(B,A))) & r2_fdiff_1(k2_partfun2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,C,k2_rcomp_1(B,A))),k1_relset_1(k1_numbers,k2_partfun2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,C,k2_rcomp_1(B,A))))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,k1_relset_1(k1_numbers,k2_partfun2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,C,k2_rcomp_1(B,A))))) => k1_fdiff_1(k2_partfun2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,C,k2_rcomp_1(B,A))),D) = k7_xcmplx_0(1,k1_fdiff_1(C,k1_funct_1(k2_partfun2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,C,k2_rcomp_1(B,A))),D))) ) ) ) ) ) ) ) ) )).
fof(t48_fdiff_4,axiom,( ! [A] : ( ( 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(k7_xcmplx_0(1,2))),2))) & ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & r1_xxreal_0(k1_funct_1(k16_sin_cos,B),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,k4_taylor_1(k7_xcmplx_0(1,2))),2),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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(k7_xcmplx_0(1,2))),2),A),B) = k3_xcmplx_0(k1_funct_1(k18_sin_cos,B),k6_prepower(k1_funct_1(k16_sin_cos,B),k4_xcmplx_0(k7_xcmplx_0(1,2)))) ) ) ) ) ) )).
fof(t48_fdiff_6,axiom,( ! [A] : ( ( 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)),k7_xcmplx_0(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)),k7_xcmplx_0(1,3))),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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)),k7_xcmplx_0(1,3))),A),B) = k1_newton(k1_funct_1(k18_sin_cos,B),3) ) ) ) ) ) )).
fof(t48_fdiff_7,axiom,( ! [A] : ( ( 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,k18_sin_cos),k1_taylor_1(2)))) & ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & k1_funct_1(k18_sin_cos,B) = k5_numbers ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_rfunct_1(k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),k1_taylor_1(2)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_rfunct_1(k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),k1_taylor_1(2)),A),B) = k7_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k16_sin_cos,B)),k3_prepower(k1_funct_1(k18_sin_cos,B),3)) ) ) ) ) ) )).
fof(t48_fib_num2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( ~ r1_xxreal_0(B,1) & A != k5_numbers & A != 1 & ~ ( k1_pre_ff(A) = k1_pre_ff(B) <=> A = B ) ) ) ) )).
fof(t48_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_lattices(A) & v10_lattices(A) & l3_lattices(A) ) => k6_filter_0(A,k1_filter_0(A)) = A ) )).
fof(t48_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t48_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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)))) ) ) ) ) )).
fof(t48_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t48_finseq_2,axiom,( k1_finseq_2(1) = k12_finseq_1(k4_ordinal1,1) )).
fof(t48_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k5_relat_1(k1_finseq_2(k2_xcmplx_0(B,A)),k2_finseq_1(B)) = k1_finseq_2(B) ) ) )).
fof(t48_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t48_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => r1_tarski(k10_xtuple_0(k1_finseq_5(A,C,B)),k10_xtuple_0(C)) ) ) ) )).
fof(t48_finseq_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ( ( r2_hidden(A,k4_finseq_1(C)) & ! [D] : ( 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 ) ) ) ) )).
fof(t48_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v3_card_1(E,C) & m2_finseq_1(E,A) ) => ! [F] : ( ( v3_card_1(F,C) & m2_finseq_1(F,A) ) => ! [G] : ( ( 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] : ( ( 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] : ( m1_subset_1(I,A) => ! [J] : ( m1_subset_1(J,A) => k3_funct_2(A,B,D,k5_binop_1(A,G,I,J)) = k5_binop_1(B,H,k3_funct_2(A,B,D,I),k3_funct_2(A,B,D,J)) ) ) => r2_relset_1(k4_ordinal1,B,k4_finseqop(A,B,k1_finseqop(A,A,A,G,E,F),D),k1_finseqop(B,B,B,H,k4_finseqop(A,B,E,D),k4_finseqop(A,B,F,D))) ) ) ) ) ) ) ) ) ) )).
fof(t48_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k10_fintopo3(A,k1_nat_1(C,1),B) = k12_fin_topo(A,k10_fintopo3(A,C,B)) ) ) ) )).
fof(t48_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t48_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => r2_hidden(k2_flang_1(A),k8_flang_1(A,B)) ) )).
fof(t48_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => k1_flang_2(A,B,k5_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)) ) )).
fof(t48_flang_3,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ( r2_hidden(B,k2_flang_3(A,C)) <=> ? [D] : ( v7_ordinal1(D) & ~ r1_xxreal_0(D,k5_numbers) & r2_hidden(B,k7_flang_1(A,C,D)) ) ) ) )).
fof(t48_fomodel0,axiom,( ! [A] : ! [B] : A = k2_xboole_0(k6_subset_1(A,B),k3_xboole_0(A,B)) )).
fof(t48_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & v8_struct_0(C) & l2_fsm_1(C,A,B) ) => ( r1_tarski(k12_fsm_1(A,B,C),u1_struct_0(C)) & ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ( r2_hidden(D,k12_fsm_1(A,B,C)) <=> v6_fsm_1(D,A,B,C) ) ) ) ) ) ) )).
fof(t48_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t48_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(B,A) => k1_funct_1(k5_relat_1(C,A),B) = k1_funct_1(C,B) ) ) )).
fof(t48_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k1_tarski(C),B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_tarski(C),B))) ) => ( B != k1_xboole_0 => r1_tarski(k7_relset_1(k1_tarski(C),B,D,A),k1_tarski(k1_funct_1(D,C))) ) ) )).
fof(t48_funct_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t48_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) )).
fof(t48_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t48_funct_6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => r2_wellord2(k4_card_3(k8_funct_6(A,B)),k1_funct_2(A,k4_card_3(B))) ) )).
fof(t48_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_funcop_1(C) & v1_finseq_1(C) ) => k1_funct_1(k4_funct_7(k7_finseq_1(B,C),A),k1_nat_1(k3_finseq_1(k7_finseq_1(B,C)),1)) = k1_funct_1(k4_funct_7(C,k1_funct_1(k4_funct_7(B,A),k1_nat_1(k3_finseq_1(B),1))),k1_nat_1(k3_finseq_1(C),1)) ) ) )).
fof(t48_funct_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t48_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ~ ( v21_functor0(C,A,B) & ! [D] : ( m2_functor0(D,B,A) => ~ ( D = k15_functor0(A,B,C) & v21_functor0(D,B,A) & v15_functor0(D,B,A) ) ) ) ) ) ) )).
fof(t48_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D),k1_fuzzy_1(A,B,C)),k1_fuzzy_1(A,B,k2_fuzzy_2(A,D,C))) ) ) ) ) )).
fof(t48_fvaluat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_fvaluat1(B,A) => r1_tarski(k6_fvaluat1(A,B),u1_struct_0(A)) ) ) )).
fof(t48_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t48_gcd_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t48_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( ( ~ v1_xboole_0(F) & v1_relat_1(F) & v2_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ! [G] : ( m1_genealg1(G,F) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t48_geomtrap,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_geomtrap(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_diraf(A))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k2_diraf(A))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k2_diraf(A))) => ! [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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t48_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t48_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & ~ v4_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( 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)))) => ( k1_nat_1(k15_glib_000(C),1) = k15_glib_000(A) & k1_nat_1(k17_glib_000(C),k5_card_1(k28_glib_000(A,B))) = k17_glib_000(A) ) ) ) ) )).
fof(t48_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_glib_001(A,C,D,B) => r1_glib_001(A,C,D,k20_glib_001(A,B,F,E)) ) ) ) ) ) )).
fof(t48_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( r1_glib_002(A,B) => m1_subset_1(B,k6_glib_000(A)) ) ) )).
fof(t48_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_003(A) ) => ! [B] : ! [C] : ! [D] : ( 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)) ) ) ) ) )).
fof(t48_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ 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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,1))) = k2_topreal1(2,D,C) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,2))) = k2_topreal1(2,D,k1_nat_1(C,1)) ) => ( r1_xxreal_0(k1_matrix_0(k2_goboard2(D)),k1_nat_1(B,1)) | r1_xxreal_0(k3_finseq_1(D),k1_nat_1(C,1)) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,2)) ) ) ) ) ) ) ) )).
fof(t48_graph_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v6_graph_1(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t48_graph_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m2_finseq_1(C,u4_struct_0(B)) => ( r5_graph_5(B,A) => r1_xxreal_0(k5_numbers,k10_graph_5(B,C,A)) ) ) ) ) )).
fof(t48_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ( k4_polynom1(A,C,F,k3_termord(A,B,C,k11_polynom1(A,C,D,E))) = k4_struct_0(C) => r5_polyred(A,B,C,k6_polynom1(A,C,k11_polynom1(A,C,D,E),F),k6_polynom1(A,C,k11_polynom1(A,C,k6_termord(A,B,C,D),E),F),k1_groeb_1(A,C,E)) ) ) ) ) ) ) ) )).
fof(t48_group_1,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(t48_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v15_algstr_0(C) & v1_group_3(C,A) & m1_group_2(C,A) ) => ! [D] : ( ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) ) => ? [E] : ( 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)))) ) ) ) ) ) )).
fof(t48_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ( D = B => k2_group_1(C,D) = k2_group_1(A,B) ) ) ) ) ) )).
fof(t48_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t48_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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)) ) ) ) ) )).
fof(t48_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t48_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t48_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( 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 ) ) )).
fof(t48_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => k3_helly(A,B,B,C) = B ) ) ) )).
fof(t48_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_xxreal_0(k9_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))),k1_square_1(k2_xcmplx_0(k3_square_1(k9_complex1(k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(k1_complfld),B,C,C))),k3_square_1(k9_complex1(k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(k1_complfld),B,D,D)))))) ) ) ) ) )).
fof(t48_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(t48_hurwitz,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(A,k1_complfld) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => ( v1_hurwitz(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ~ ( r1_xxreal_0(k5_numbers,k3_complex1(B)) & r1_xxreal_0(k9_complex1(k2_polynom4(k1_complfld,A,B)),k5_numbers) ) ) ) ) )).
fof(t48_ideal_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t48_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ~ ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => v4_incsp_1(k9_domain_1(u1_incsp_1(A),B,C,D,E),A) ) ) ) ) ) )).
fof(t48_int_1,axiom,( ! [A] : ( v1_int_1(A) => k5_int_1(A,A) = k5_numbers ) )).
fof(t48_int_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_finset_1(B) => ! [C] : ( m2_finseq_1(C,k1_zfmisc_1(B)) => ( ( k3_finseq_1(C) = A & ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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)) ) ) ) ) )).
fof(t48_integr11,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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(k4_xcmplx_0(1),1)) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(D,E) = k4_xcmplx_0(k7_xcmplx_0(A,k2_xcmplx_0(1,k1_square_1(E)))) ) ) & C = k9_xtuple_0(D) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,D,B)) ) => k2_integra5(B,D) = k6_xcmplx_0(k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k2_sin_cos9,A),k2_seq_4(B)),k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k2_sin_cos9,A),k3_seq_4(B))) ) ) ) ) ) )).
fof(t48_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,D) & r1_tarski(D,k2_rcomp_1(k4_xcmplx_0(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,k22_sin_cos),k3_valued_1(k1_numbers,k1_numbers,k1_numbers,C,k1_taylor_1(2)))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => k1_funct_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) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k22_sin_cos),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k22_sin_cos),k3_seq_4(A))) ) ) ) ) ) )).
fof(t48_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k3_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,k1_funct_1(k27_sin_cos,D)))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,D)))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k26_sin_cos))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k26_sin_cos)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k26_sin_cos)),k3_seq_4(A))) ) ) ) ) )).
fof(t48_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t48_integra1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => k9_member_1(k3_measure6(A),k3_measure6(B)) = k5_member_1(k9_member_1(A,B)) ) ) )).
fof(t48_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k28_sin_cos) => k2_integra5(A,k32_valued_1(k1_numbers,k1_numbers,k16_sin_cos)) = k4_xcmplx_0(2) ) ) )).
fof(t48_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v3_rcomp_1(E) & m1_subset_1(E,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,E) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => ( k1_funct_1(C,F) = k2_xcmplx_0(A,F) & k1_funct_1(C,F) != k5_numbers ) ) ) & k1_relset_1(k1_numbers,k26_valued_1(k1_numbers,k1_numbers,k6_rfunct_1(k1_numbers,k1_numbers,C),k4_xcmplx_0(1))) = E & k1_relset_1(k1_numbers,k26_valued_1(k1_numbers,k1_numbers,k6_rfunct_1(k1_numbers,k1_numbers,C),k4_xcmplx_0(1))) = k1_relset_1(k1_numbers,D) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => k1_funct_1(D,F) = k7_xcmplx_0(1,k1_square_1(k2_xcmplx_0(A,F))) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,D,B)) ) => k2_integra5(B,D) = k6_xcmplx_0(k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k6_rfunct_1(k1_numbers,k1_numbers,C),k4_xcmplx_0(1)),k2_seq_4(B)),k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k6_rfunct_1(k1_numbers,k1_numbers,C),k4_xcmplx_0(1)),k3_seq_4(B))) ) ) ) ) ) ) )).
fof(t48_interva1,axiom,( ! [A] : ( ~ 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))) ) )).
fof(t48_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(t48_jgraph_4,axiom,( ! [A] : ( 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))) ) )).
fof(t48_jgraph_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ 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),k5_numbers) & A != k18_pscomp_1(C) & r1_xxreal_0(k17_euclid(A),k17_euclid(B)) ) ) ) ) )).
fof(t48_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t48_jordan,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => r1_xboole_0(k2_jgraph_6(A,B,C,D),k3_jgraph_6(A,B,C,D)) ) ) ) ) )).
fof(t48_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ~ ( ~ r1_xxreal_0(C,1) & ~ r1_xxreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,1))),C) & ~ r1_xxreal_0(D,1) & ~ r1_xxreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,1))),D) & r1_xxreal_0(1,E) & r1_xxreal_0(E,F) & r1_xxreal_0(F,k1_matrix_0(k1_jordan8(B,k1_nat_1(A,1)))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),C,F),k8_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),D,E),k9_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) & r2_subset_1(k4_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),D,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),D,F)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),D,F),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),C,F))),k8_jordan6(B)) ) ) ) ) ) ) ) )).
fof(t48_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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(C,D) & r1_xxreal_0(3,A) ) => ( r1_xxreal_0(k3_finseq_1(k1_jordan8(E,C)),A) | r1_xxreal_0(B,1) | r1_xxreal_0(k1_matrix_0(k1_jordan8(E,C)),k1_nat_1(B,1)) | ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ( ( F = k2_xcmplx_0(k3_xcmplx_0(k11_newton(2,k7_nat_d(D,C)),k6_xcmplx_0(A,2)),2) & G = k2_xcmplx_0(k3_xcmplx_0(k11_newton(2,k7_nat_d(D,C)),k6_xcmplx_0(B,2)),2) ) => r1_tarski(k3_goboard5(k1_jordan8(E,D),k7_nat_d(F,1),G),k3_goboard5(k1_jordan8(E,C),k7_nat_d(A,1),B)) ) ) ) ) ) ) ) ) ) ) )).
fof(t48_jordan1h,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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(B,A) ) => r1_tarski(k3_goboard9(k2_jordan9(C,A)),k3_goboard9(k2_jordan9(C,B))) ) ) ) ) )).
fof(t48_jordan1j,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v7_ordinal1(D) => ( ( 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) ) ) ) ) ) ) ) )).
fof(t48_jordan1k,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ( ! [E] : ( 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)) ) ) ) ) ) )).
fof(t48_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t48_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t48_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( 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)) ) ) ) ) ) ) )).
fof(t48_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t48_knaster,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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) ) ) ) )).
fof(t48_kurato_1,axiom,( ! [A] : ( 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))) ) ) )).
fof(t48_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( v13_lattices(A) <=> v14_lattices(k1_lattice2(A)) ) ) )).
fof(t48_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( 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)) ) ) )).
fof(t48_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => ~ ( r2_hidden(C,k17_lexbfs(k6_glib_000(A),k4_ordinal1,k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),k13_lexbfs(A,k16_lexbfs(A),B)),D)) & ! [E] : ( 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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),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))) ) ) ) ) ) ) ) )).
fof(t48_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) = k9_complex1(k1_limfunc2(B,A)) ) ) ) ) )).
fof(t48_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) = k5_numbers ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,k9_subset_1(k1_numbers,k9_xtuple_0(B),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,C),A),k2_rcomp_1(A,k2_xcmplx_0(A,C))))) & r1_xxreal_0(k5_numbers,k1_funct_1(B,D)) ) ) ) ) | r3_limfunc3(k6_rfunct_1(k1_numbers,k1_numbers,B),A) ) ) ) ) )).
fof(t48_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k10_prob_1(C))) & k1_funct_1(A,D) = k5_limfunc1(A) ) ) | v8_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).
fof(t48_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t48_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( v2_xxreal_0(F) & v1_xreal_0(F) ) => ( ( 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))) ) ) ) ) ) ) ) )).
fof(t48_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t48_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( m1_subset_1(D,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(k3_hilbert1(A,k5_ltlaxio1(B,C)),k3_hilbert1(k3_hilbert1(C,D),k3_hilbert1(A,k5_ltlaxio1(B,D))))) ) ) ) ) )).
fof(t48_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(D,C) => r1_tarski(k4_mathmorp(A,B,C),k6_rusub_4(A,k3_mathmorp(A,B,D),C)) ) ) ) ) ) )).
fof(t48_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( r1_matrix10(B,C) => r1_matrix10(k5_matrix10(A,D,C),k5_matrix10(A,D,B)) ) ) ) ) ) )).
fof(t48_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( r1_xxreal_0(2,A) & ! [B] : ( v1_finset_1(B) => ! [C] : ( 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) = k3_matrix_2(A) & k5_card_1(C) = k5_card_1(B) ) ) ) ) ) )).
fof(t48_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ( r2_hidden(B,k2_finseq_1(k5_card_1(D))) => k7_matrix_0(A,k6_matrix13(A,C,D,k2_finseq_1(k1_matrix_0(C))),B) = k7_matrix_0(A,C,k1_funct_1(k5_matrix13(D),B)) ) ) ) ) ) )).
fof(t48_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,A) ) => ( ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,A) ) => ( k3_matrix_0(u1_struct_0(B),k4_matrix_3(B,k4_matrix14(B,A,D),C),D,E) = k3_matrix_0(u1_struct_0(B),C,1,E) & k3_matrix_0(u1_struct_0(B),k4_matrix_3(B,k4_matrix14(B,A,D),C),1,E) = k3_matrix_0(u1_struct_0(B),C,D,E) ) ) ) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ( 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_0(u1_struct_0(B),k4_matrix_3(B,k4_matrix14(B,A,D),C),E,F) = k3_matrix_0(u1_struct_0(B),C,E,F) ) ) ) ) ) ) ) ) ) ) )).
fof(t48_matrix16,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ( v4_matrix16(D,u1_struct_0(A)) => 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(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))) ) ) ) ) ) )).
fof(t48_matrix_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r2_hidden(k4_tarski(1,1),k2_matrix_0(k12_matrix_0(A,B,C,D))) & r2_hidden(k4_tarski(1,2),k2_matrix_0(k12_matrix_0(A,B,C,D))) & r2_hidden(k4_tarski(2,1),k2_matrix_0(k12_matrix_0(A,B,C,D))) & r2_hidden(k4_tarski(2,2),k2_matrix_0(k12_matrix_0(A,B,C,D))) ) )).
fof(t48_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(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) ) ) ) ) ) )).
fof(t48_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r1_matrix_6(A,B,C,D) => ( r1_xxreal_0(A,k5_numbers) | r1_matrix_6(A,B,k3_matrix_3(B,C,C),D) ) ) ) ) ) ) )).
fof(t48_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( v4_matrix_6(C,A,B) => r2_matrix_8(A,B,k4_matrix_3(B,D,C),k4_matrix_3(B,C,D)) ) ) ) ) ) )).
fof(t48_matrix_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_matrix_2(C,k3_matrix_2(B)) => ~ ( r2_hidden(A,k2_finseq_1(B)) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( r2_hidden(D,k2_finseq_1(B)) & A = k1_funct_1(C,D) ) ) ) ) ) ) )).
fof(t48_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => k11_matrixc1(A) = k10_matrixc1(k4_matrix_0(k2_numbers,A)) ) )).
fof(t48_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( ( v2_matrixj1(F,u1_struct_0(D)) & m2_finseq_1(F,k3_finseq_2(k3_finseq_2(u1_struct_0(D)))) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(D),C,C) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(D))) ) => ( ( r2_hidden(A,k4_finseq_1(G)) & r2_hidden(B,k2_finseq_1(C)) ) => k18_matrix_0(k1_nat_1(A,k2_wsierp_1(k10_matrixj1(u1_struct_0(D),F))),k1_nat_1(B,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),C,G)))),u1_struct_0(D),k20_matrixj1(u1_struct_0(D),E,k15_matrixj1(u1_struct_0(D),F,k16_matrixj1(u1_struct_0(D),C,G)))) = k13_matrixj1(u1_struct_0(D),E,k3_matrixj1(u1_struct_0(D),F,k4_matrixj1(u1_struct_0(D),k18_matrix_0(A,B,C,u1_struct_0(D),G)))) ) ) ) ) ) ) ) ) )).
fof(t48_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( B = k10_matrixr1(A) <=> ( k7_matrix_0(k1_numbers,B,1) = A & k3_finseq_1(B) = 1 ) ) ) ) )).
fof(t48_matrixr2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(A) = k1_matrix_0(C) & k3_finseq_1(B) = k3_finseq_1(A) ) => ( r1_xxreal_0(k3_finseq_1(A),k5_numbers) | r1_xxreal_0(k3_finseq_1(C),k5_numbers) | k11_matrixr1(C,k8_rvsum_1(A,B)) = k8_rvsum_1(k11_matrixr1(C,A),k11_matrixr1(C,B)) ) ) ) ) ) )).
fof(t48_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( m1_matrlin(D,A,B) => ! [E] : ( m1_matrlin(E,A,C) => ! [F] : ( ( 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)) ) ) ) ) ) ) )).
fof(t48_matrprob,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k3_finseq_1(A) = k1_matrix_0(C) ) => ( r1_xxreal_0(k3_finseq_1(A),k5_numbers) | r1_xxreal_0(k3_finseq_1(B),k5_numbers) | k22_rvsum_1(k11_matrixr1(C,A),B) = k22_rvsum_1(A,k11_matrixr1(k4_matrix_0(k1_numbers,C),B)) ) ) ) ) ) )).
fof(t48_mcart_1,axiom,( ! [A] : ! [B] : ( k2_zfmisc_1(A,B) != k1_xboole_0 => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ( C != k1_xtuple_0(C) & C != k2_xtuple_0(C) ) ) ) )).
fof(t48_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k1_measure6(k1_measure6(A,C),B) = k1_measure6(A,k2_xcmplx_0(B,C)) ) ) ) )).
fof(t48_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t48_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_hidden(k4_struct_0(B),k9_xtuple_0(k8_memstr_0(A,B,C))) ) ) ) )).
fof(t48_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(A),B) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ( 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))) ) ) ) ) ) ) )).
fof(t48_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( v1_prob_2(D) & m2_finseq_1(D,B) ) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t48_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_partfun1(A,k1_numbers)) & v1_mesfunc8(E,A,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [F] : ( ( 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,k5_numbers)) & D = k1_relset_1(A,F) & ! [G] : ( v7_ordinal1(G) => r1_mesfunc6(A,B,k4_mesfunc5(A,k1_numbers,E,G),D) ) & r3_mesfunc6(A,B,C,F) & ! [G] : ( m1_subset_1(G,A) => ! [H] : ( v7_ordinal1(H) => ( r2_hidden(G,D) => r1_xxreal_0(k1_mesfunc9(k55_valued_1(A,k1_numbers,k4_mesfunc5(A,k1_numbers,E,H)),G),k1_mesfunc9(F,G)) ) ) ) & ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k4_ordinal1,k1_numbers) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [H] : ( v7_ordinal1(H) => k1_mesfunc9(G,H) = k1_mesfunc6(A,B,C,k4_mesfunc5(A,k1_numbers,E,H)) ) & ( ! [H] : ( m1_subset_1(H,A) => ( r2_hidden(H,D) => v2_comseq_2(k10_seqfunc(A,E,H)) ) ) => ( v2_comseq_2(G) & k1_seq_2(G) = k7_mesfunc5(A,B,C,k8_mesfun7c(A,E)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t48_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t48_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t48_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_midsp_1(B,A) <=> r2_hidden(B,k10_midsp_1(A)) ) ) )).
fof(t48_mmlquery,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t48_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k48_modelc_1(A,B,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k48_modelc_1(A,B,C))) => ( ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(t48_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k25_modelc_2(k43_modelc_2)) => ! [C] : ( ( 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] : ( ( 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] : ( v7_ordinal1(E) => ( ! [F] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(t48_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( k11_nat_3(B,A) = k5_numbers => k1_recdef_1(k5_moebius1(B),A) = k5_numbers ) ) ) )).
fof(t48_monoid_0,axiom,( r3_binop_1(k4_ordinal1,k5_numbers,k23_binop_2) & v9_monoid_0(k23_binop_2,k4_ordinal1) )).
fof(t48_monoid_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( 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)))) ) ) ) )).
fof(t48_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( m3_pboole(E,A,k1_mboolean(A,D)) => ( ( r1_pboole(A,B,E) & r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A)) ) => r6_pboole(A,k3_pboole(A,k4_mssubfam(A,D,E),C),k1_pboole(A)) ) ) ) ) ) )).
fof(t48_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t48_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => k22_pre_poly(k8_newton,k12_nat_3(A)) = k22_pre_poly(k8_newton,k12_nat_3(k1_newton(A,B))) ) ) )).
fof(t48_nat_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ? [C] : ( m2_finseq_1(C,k4_ordinal1) & k3_finseq_1(C) = A & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k4_finseq_1(C)) => k1_recdef_1(C,D) = k1_int_1(k7_xcmplx_0(A,k1_newton(B,D))) ) ) & k11_nat_3(k7_newton(A),B) = k2_wsierp_1(C) ) ) ) )).
fof(t48_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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(k1_nat_1(k1_nat_1(B,1),1),A) & r1_xxreal_0(A,k1_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)) ) ) ) ) )).
fof(t48_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(D,B) & ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( r2_hidden(G,B) & ~ r1_xxreal_0(F,k2_normsp_0(A,k5_algstr_0(A,G,D))) & r1_xxreal_0(E,k9_complex1(k5_real_1(k7_partfun1(k1_numbers,C,G),k7_partfun1(k1_numbers,C,D)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t48_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( 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,k5_numbers) = k4_struct_0(k4_real_ns1(A)) => ! [D] : ( ( 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] : ( ( 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))))) ) ) ) ) ) ) ) ) )).
fof(t48_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_prvect_2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_prvect_2(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t48_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k6_nat_d(C,k6_nat_d(B,A)) = k6_nat_d(k6_nat_d(C,B),A) ) ) ) )).
fof(t48_nfcont_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t48_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(k7_normform(A))) => ! [C] : ( m1_subset_1(C,k5_finsub_1(k7_normform(A))) => k10_normform(A,B,C) = k10_normform(A,C,B) ) ) )).
fof(t48_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t48_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ 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] : ( ( 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) ) ) ) )).
fof(t48_ordeq_01,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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)) & 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),k1_relset_1(k1_numbers,D)) & r1_integra5(k3_integra5(A,B),D) & v1_comseq_2(k2_partfun1(k1_numbers,k1_numbers,D,k3_integra5(A,B))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k3_integra5(A,B)) => r1_xxreal_0(k1_funct_1(C,E),k1_funct_1(D,E)) ) ) ) => r1_xxreal_0(k4_integra5(A,B,C),k4_integra5(A,B,D)) ) ) ) ) ) )).
fof(t48_orders_1,axiom,( ! [A] : ( r1_orders_1(k6_partfun1(A),A) & r2_orders_1(k6_partfun1(A),A) ) )).
fof(t48_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t48_ordinal2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( r2_hidden(B,k10_xtuple_0(A)) => v3_ordinal1(B) ) ) )).
fof(t48_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ! [D] : ( v3_ordinal1(D) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t48_ordinal6,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t48_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => v15_lattices(k16_osalg_2(A,B)) ) ) )).
fof(t48_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r3_parsp_2(A,B,C,D,E) => r1_parsp_1(A,B,C,D,E) ) ) ) ) ) ) )).
fof(t48_partfun1,axiom,( ! [A] : k4_partfun1(k1_xboole_0,A) = k1_tarski(k1_xboole_0) )).
fof(t48_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( 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 ) ) ) ) ) ) )).
fof(t48_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t48_pcs_0,axiom,( ! [A] : ( l2_pcs_0(A) => ! [B] : ( r2_hidden(B,k27_pcs_0(A)) => ( v21_pcs_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).
fof(t48_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( 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) & k10_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) = k2_xcmplx_0(k3_pdiff_5(B,A),k3_pdiff_5(C,A)) ) ) ) ) ) )).
fof(t48_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_real_ns1(A)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_real_ns1(A))) => ( ( v3_nfcont_1(C,k4_real_ns1(A)) & r2_hidden(D,C) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( 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)),k14_pdiff_1(A,1,E,B,C),C) ) ) ) ) => ( r1_ndiff_1(k4_real_ns1(A),k4_real_ns1(1),B,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(A))) => ? [F] : ( m2_finseq_1(F,k1_euclid(1)) & k4_finseq_1(F) = k2_finseq_1(A) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( r2_hidden(G,k2_finseq_1(A)) => k1_funct_1(F,G) = k1_funct_1(k9_pdiff_1(A,1,G,B,D),k9_finseq_1(k1_funct_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) ) ) ) ) ) ) ) ) )).
fof(t48_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t48_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_int_2(A,C) & r1_nat_d(k3_pepin(A,C),B) ) => ( r1_xxreal_0(C,1) | k4_nat_d(k1_newton(A,B),C) = 1 ) ) ) ) ) )).
fof(t48_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( 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))) ) ) )).
fof(t48_polynom5,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k2_polynom4(A,k4_polynom5(A,k4_struct_0(A),k5_struct_0(A)),D) = D ) ) ) ) )).
fof(t48_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( 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,k8_polynom1(A,C)) => r1_rewrite1(k3_polyred(A,B,C,D),k11_polynom1(A,C,F,E),k8_polynom1(A,C)) ) ) ) ) ) ) ) )).
fof(t48_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ( ~ v1_abian(B) => k2_power(k4_xcmplx_0(A),B) = k4_xcmplx_0(k2_power(A,B)) ) ) ) )).
fof(t48_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t48_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => ( B = 1 => ( r1_xxreal_0(A,k5_numbers) | k4_prepower(A,B) = A ) ) ) ) )).
fof(t48_prob_3,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(t48_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t48_pscomp_1,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t48_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( r1_pboole(A,C,k4_pboole(A,D,k1_pzfmisc1(A,B))) => r1_pboole(A,C,D) ) ) ) ) )).
fof(t48_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( v3_qc_lang1(C,A) => ( r1_qc_lang2(A,B,C) <=> B = k18_qc_lang1(A,C) ) ) ) ) ) )).
fof(t48_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( ( ~ 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)) ) ) ) ) )).
fof(t48_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k17_quatern2(A,B) = k6_quaterni(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k13_quaterni(B)),k3_xcmplx_0(k14_quaterni(A),k14_quaterni(B))),k3_xcmplx_0(k15_quaterni(A),k15_quaterni(B))),k3_xcmplx_0(k16_quaterni(A),k16_quaterni(B))),k2_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k4_xcmplx_0(k14_quaterni(B))),k3_xcmplx_0(k14_quaterni(A),k13_quaterni(B))),k3_xcmplx_0(k15_quaterni(A),k16_quaterni(B))),k3_xcmplx_0(k16_quaterni(A),k15_quaterni(B))),k2_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k4_xcmplx_0(k15_quaterni(B))),k3_xcmplx_0(k13_quaterni(B),k15_quaterni(A))),k3_xcmplx_0(k14_quaterni(B),k16_quaterni(A))),k3_xcmplx_0(k16_quaterni(B),k14_quaterni(A))),k2_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k4_xcmplx_0(k16_quaterni(B))),k3_xcmplx_0(k16_quaterni(A),k13_quaterni(B))),k3_xcmplx_0(k14_quaterni(A),k15_quaterni(B))),k3_xcmplx_0(k15_quaterni(A),k14_quaterni(B)))) ) ) )).
fof(t48_quatern3,axiom,( k7_quatern2(k2_quatern2) = k2_quatern2 )).
fof(t48_quaterni,axiom,( k13_quaterni(k27_quaterni(k1_xcmplx_0)) = k5_numbers & k14_quaterni(k27_quaterni(k1_xcmplx_0)) = k4_xcmplx_0(1) & k15_quaterni(k27_quaterni(k1_xcmplx_0)) = k5_numbers & k16_quaterni(k27_quaterni(k1_xcmplx_0)) = k5_numbers )).
fof(t48_quofield,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t48_rcomp_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ! [C] : ( C = a_2_3_rcomp_3(A,B) => ! [D] : ( ( r7_orders_1(k1_wellord2(C),D) & r2_hidden(D,k1_relat_1(k1_wellord2(C))) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(E,D) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ! [G] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t48_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => k3_relat_1(A,k4_relat_1(k10_xtuple_0(A))) = A ) )).
fof(t48_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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) ) ) )).
fof(t48_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( r11_rewrite1(A,B) => r10_rewrite1(A,B) ) ) ) )).
fof(t48_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t48_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ v2_struct_0(C) & l1_rewrite3(C,B) ) => ! [D] : ( m1_rewrite1(D,k1_rewrite3(A,B,C)) => ! [E] : ( 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)))) ) ) ) ) ) ) ) )).
fof(t48_rfunct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t48_rfunct_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t48_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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,k5_numbers),B) ) ) )).
fof(t48_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_seq_2(B) => r1_xxreal_0(k1_funct_1(k3_rinfsup1(B),A),k3_funct_2(k4_ordinal1,k1_numbers,k3_rinfsup1(B),k1_nat_1(A,1))) ) ) ) )).
fof(t48_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t48_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rlsub_1(C,A) => ( r1_struct_0(C,B) <=> k3_rlsub_1(A,B,C) = u1_struct_0(C) ) ) ) ) )).
fof(t48_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t48_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v8_ordinal1(B) & v1_xreal_0(B) ) => 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,k5_xcmplx_0(B))) ) ) )).
fof(t48_rlvect_1,axiom,( ! [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) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t48_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => r1_rlvect_2(A,k8_rlvect_2(A,1,B),B) ) ) )).
fof(t48_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t48_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t48_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_rmod_4(E,A,B) => r1_rmod_4(A,B,k7_rmod_4(A,B,C,k7_rmod_4(A,B,D,E)),k7_rmod_4(A,B,k6_algstr_0(A,D,C),E)) ) ) ) ) ) )).
fof(t48_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k9_robbins1(A,k15_robbins1(A,B),B) = k11_robbins1(A,B) ) ) )).
fof(t48_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t48_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t48_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ~ ( ~ r1_xxreal_0(k1_rpr_1(A,k9_subset_1(A,C,D)),k5_numbers) & ~ r1_xxreal_0(k1_rpr_1(A,D),k5_numbers) & k1_rpr_1(A,k9_subset_1(A,k9_subset_1(A,B,C),D)) != k3_xcmplx_0(k3_xcmplx_0(k2_rpr_1(A,k9_subset_1(A,C,D),B),k2_rpr_1(A,D,C)),k1_rpr_1(A,D)) ) ) ) ) ) )).
fof(t48_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t48_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t48_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ~ ( u1_struct_0(A) != k6_domain_1(u1_struct_0(A),k4_struct_0(A)) & ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( D != B & r2_hidden(D,k4_bhsp_2(A,B,C)) ) ) ) ) ) ) )).
fof(t48_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k10_rvsum_1(k2_finseq_2(A,C),B) = k2_finseq_2(A,k3_xcmplx_0(B,C)) ) ) ) )).
fof(t48_rvsum_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k2_numbers) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k2_numbers) ) => k20_rvsum_1(k12_rvsum_2(A,B,C)) = k3_xcmplx_0(k20_rvsum_1(B),k20_rvsum_1(C)) ) ) ) )).
fof(t48_scm_halt,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => r5_scmfsa7b(A,k1_scmfsa_m(B),C) ) ) ) ) )).
fof(t48_scmfsa8c,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t48_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(C,u1_struct_0(k1_ami_3)) ) => ! [D] : ( ( 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(k7_card_1(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) ) ) ) ) ) )).
fof(t48_scmpds_2,axiom,( ! [A] : ( ( 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] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t48_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ( k1_funct_1(k6_scmpds_6(A,B,C),k5_numbers) = k7_scmpds_2(A,B,2) & k1_funct_1(k6_scmpds_6(A,B,C),1) = k3_scmpds_2(k1_nat_1(k5_card_1(C),1)) ) ) ) ) )).
fof(t48_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ( k1_funct_1(B,k2_scmp_gcd) = k5_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) ) ) ) ) )).
fof(t48_scmyciel,axiom,( v5_scmyciel(k1_tarski(k1_xboole_0)) )).
fof(t48_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r1_semi_af1(A,B,C,D) & D != B & D != C ) ) ) ) ) ) )).
fof(t48_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v9_ordinal1(A) & v9_ordinal1(C) ) => ( r2_funct_2(k4_ordinal1,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,A),k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,C)),k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C),k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,A)),k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,C))) & r2_funct_2(k4_ordinal1,k1_numbers,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,A),k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,C)),k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C),k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,A)),k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,C))) ) ) ) ) ) ) )).
fof(t48_seq_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_membered(A) ) => ! [B] : ( v3_membered(B) => ( ( r1_tarski(A,B) & v4_xxreal_2(B) ) => r1_xxreal_0(k2_seq_4(A),k2_seq_4(B)) ) ) ) )).
fof(t48_series_5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => k9_nat_1(k1_numbers,A,B) = k7_xcmplx_0(1,k1_square_1(k1_nat_1(B,1))) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => r1_xxreal_0(k9_nat_1(k1_numbers,k3_series_1(A),B),k6_xcmplx_0(2,k7_xcmplx_0(1,k1_nat_1(B,1)))) ) ) ) )).
fof(t48_setfam_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v3_setfam_1(B,A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t48_setlim_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ( v2_prob_1(C) => k1_funct_1(k4_setlim_1(B,C),A) = k1_funct_1(C,A) ) ) ) )).
fof(t48_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => r1_tarski(k7_subset_1(B,k9_nat_1(k9_setfam_1(B),k4_setlim_1(B,C),A),k9_nat_1(k9_setfam_1(B),k4_setlim_1(B,D),A)),k9_nat_1(k9_setfam_1(B),k4_setlim_1(B,k3_setlim_2(B,C,D)),A)) ) ) ) )).
fof(t48_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ! [D] : ( m1_subset_1(D,k5_finsub_1(A)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t48_sf_mastr,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_scmfsa_2)) ) => ~ r2_hidden(k2_scmfsa_m(A),A) ) )).
fof(t48_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t48_simplex0,axiom,( ! [A] : ( ( ~ v3_pencil_1(A) & v1_matroid0(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t48_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => k15_sin_cos(A) = k23_sin_cos(A) ) )).
fof(t48_sin_cos3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1))) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(k3_sin_cos2,A),k1_funct_1(k18_sin_cos,B)),k3_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_sin_cos2,A),k1_funct_1(k16_sin_cos,B)),k7_complex1)) ) ) )).
fof(t48_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k17_sin_cos(k7_xcmplx_0(k2_xcmplx_0(A,B),2)) != k5_numbers => k7_xcmplx_0(k2_xcmplx_0(k17_sin_cos(A),k17_sin_cos(B)),k6_xcmplx_0(k19_sin_cos(B),k19_sin_cos(A))) = k2_sin_cos4(k7_xcmplx_0(k6_xcmplx_0(A,B),2)) ) ) ) )).
fof(t48_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => k4_sin_cos2(k7_xcmplx_0(A,2)) = k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k4_sin_cos2(A),1),2)) ) )).
fof(t48_sin_cos6,axiom,( k7_relset_1(k1_numbers,k1_numbers,k16_sin_cos,k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos))) = k2_rcomp_1(k4_xcmplx_0(1),1) )).
fof(t48_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(A,1) => ( r1_xxreal_0(A,k5_numbers) | k7_sin_cos7(A) = k3_sin_cos7(k7_xcmplx_0(1,A)) ) ) ) )).
fof(t48_sin_cos9,axiom,( v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k2_sin_cos9,k1_rcomp_1(k4_xcmplx_0(1),1))) )).
fof(t48_sincos10,axiom,( r1_tarski(k1_rcomp_1(1,k3_square_1(2)),k1_relset_1(k1_numbers,k4_sincos10)) )).
fof(t48_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(t48_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( ( ~ 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] : ( ( ~ 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)) ) ) ) ) )).
fof(t48_sprect_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ 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))) ) ) ) ) ) ) ) )).
fof(t48_sprect_3,axiom,( ! [A] : ( ( v1_sprect_1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r2_hidden(B,k3_topreal1(2,A)) & r1_sprect_2(A,k13_matrix_0(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) ) ) ) ) ) )).
fof(t48_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t48_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k5_numbers,A) => ( r1_xxreal_0(k1_square_1(A),k1_square_1(B)) | ( ~ r1_xxreal_0(B,k4_xcmplx_0(A)) & ~ r1_xxreal_0(A,B) ) ) ) ) ) )).
fof(t48_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( v1_relat_1(B) & v1_funct_1(B) & ! [C] : ( 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) ) ) )).
fof(t48_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),D,k2_valuat_1(A,D)) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t48_subset_1,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ! [B] : ( m1_subset_1(B,A) => ? [C] : ( r2_hidden(C,A) & B != C ) ) ) )).
fof(t48_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => r2_hidden(k12_supinf_2(A,B),k1_numbers) ) => ! [B] : ( v7_ordinal1(B) => r2_hidden(k12_supinf_2(k18_supinf_2(A),B),k1_numbers) ) ) ) )).
fof(t48_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)))) ) ) )).
fof(t48_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v4_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_tdlat_2(B,A) => ! [C] : ( 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) ) ) ) ) ) ) ) )).
fof(t48_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) )).
fof(t48_tex_3,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( ( v1_tex_2(B,A) & m1_pre_topc(B,A) ) => ~ v1_tex_3(B,A) ) => v1_tdlat_3(A) ) ) )).
fof(t48_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(t48_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( v5_pre_topc(D,A,B) & r1_tmap_1(B,C,E,F) ) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( r2_hidden(G,k8_relset_1(u1_struct_0(A),u1_struct_0(B),D,k6_domain_1(u1_struct_0(B),F))) => r1_tmap_1(A,C,k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),D,E),G) ) ) ) ) ) ) ) ) ) )).
fof(t48_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t48_topgen_1,axiom,( ! [A] : ( 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 ) ) )).
fof(t48_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r1_topgen_4(A,B,D) & r1_tarski(B,C) ) => r1_topgen_4(A,C,D) ) ) ) ) ) )).
fof(t48_topgen_5,axiom,( ! [A] : ( ( v2_pre_topc(A) & v7_pre_topc(A) & l1_pre_topc(A) ) => ( v1_topgen_5(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(C,D) & r2_hidden(D,B) & ! [E] : ( ( 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) = k5_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(k4_ordinal1,1)) ) ) ) ) ) ) ) ) )).
fof(t48_topgrp_1,axiom,( ! [A] : ( ( ~ 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] : ( ( v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => v3_pre_topc(k5_group_2(A,C,B),A) ) ) ) )).
fof(t48_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k1_topreal9(2,k19_euclid(A,B),C) = k6_jgraph_6(A,B,C) ) ) ) )).
fof(t48_toprealc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v3_membered(B) => ! [C] : ( ( 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(k5_numbers)),A,k1_tarski(k5_numbers),k14_toprealc(k5_numbers,A,B,C),k7_funcop_1(A,k5_numbers)) ) ) ) )).
fof(t48_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_tops_1(B,A) <=> k1_tops_1(A,B) = k1_xboole_0 ) ) ) )).
fof(t48_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t48_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t48_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_diraf(A,B,C,D,E) & ~ r2_diraf(A,B,D,C,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r3_diraf(A,B,D,F) & r3_diraf(A,C,E,F) ) ) ) ) ) ) ) ) )).
fof(t48_trees_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_xboole_0(k7_finseq_1(A,C),k7_finseq_1(A,B)) => r2_xboole_0(C,B) ) ) ) ) )).
fof(t48_trees_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( v4_trees_3(B) => ( r2_hidden(k7_finseq_1(k9_finseq_1(A),C),k11_trees_3(B)) <=> ( ~ r1_xxreal_0(k3_finseq_1(B),A) & r2_hidden(C,k1_funct_1(B,k1_nat_1(A,1))) ) ) ) ) ) ) )).
fof(t48_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_trees_9(A) ) => ~ ( ~ v1_finset_1(A) & ! [B] : ( m1_trees_2(B,A) => v1_finset_1(B) ) ) ) )).
fof(t48_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t48_turing_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( l1_turing_1(B) => ! [C] : ( l1_turing_1(C) => ! [D] : ( m2_funct_2(D,k4_numbers,u1_turing_1(B),k9_funct_2(k4_numbers,u1_turing_1(B))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t48_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(k37_twoscomp(A,B),k38_twoscomp(A,B)))) => ! [D] : ( m1_subset_1(D,k6_margrel1) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t48_uniroots,axiom,( r2_funct_2(k4_ordinal1,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))) )).
fof(t48_uproots,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r2_funct_2(k4_ordinal1,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) ) ) ) ) ) )).
fof(t48_valued_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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),k1_relset_1(k4_ordinal1,k61_valued_1(C,A))) ) ) ) ) )).
fof(t48_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( v1_valued_2(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ( r2_hidden(A,k9_xtuple_0(k36_valued_2(C,E,D))) => k1_funct_1(k36_valued_2(C,E,D),A) = k13_valued_1(k1_funct_1(E,A),D) ) ) ) ) )).
fof(t48_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t48_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ! [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 ) ) ) ) ) ) ) ) ) ) ) )).
fof(t48_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) )).
fof(t48_vfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ 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] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,u1_struct_0(D)))) ) => ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t48_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t48_waybel11,axiom,( ! [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) & v4_waybel11(A) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k1_tops_1(A,B) = k3_tarski(a_2_4_waybel11(A,B)) ) ) )).
fof(t48_waybel21,axiom,( ! [A] : ( ( 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] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(t48_waybel23,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( ~ r3_orders_2(A,D,C) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,B) & ~ r3_orders_2(A,E,C) & r3_orders_2(A,E,D) ) ) ) ) ) ) ) ) ) ) )).
fof(t48_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( ( 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) ) ) ) ) ) )).
fof(t48_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) & B = k5_waybel_0(A,C) ) ) ) ) )).
fof(t48_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( C = a_2_1_waybel_1(A,B) => ! [D] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t48_waybel_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ! [D] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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)))) ) ) ) ) ) )).
fof(t48_waybel_4,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t48_wellord1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t48_xboole_1,axiom,( ! [A] : ! [B] : k4_xboole_0(A,k4_xboole_0(A,B)) = k3_xboole_0(A,B) )).
fof(t48_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k4_xboolean(k3_xboolean(A),k7_xboolean(A,B)) = k9_xboolean(A,B) ) ) )).
fof(t48_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k7_xcmplx_0(k7_xcmplx_0(A,B),C) = k7_xcmplx_0(k7_xcmplx_0(A,C),B) ) ) ) )).
fof(t48_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => r1_xxreal_0(k5_numbers,k6_xcmplx_0(B,A)) ) ) ) )).
fof(t48_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ~ ( ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(C,B) & ~ r2_hidden(B,k1_numbers) ) ) ) ) )).
fof(t48_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(D,B) => ( r1_xxreal_0(C,A) | r1_tarski(k2_xxreal_1(C,D),k4_xxreal_1(A,B)) ) ) ) ) ) ) )).
fof(t48_xxreal_2,axiom,( v4_xxreal_2(k1_tarski(k2_xxreal_0)) )).
fof(t48_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,C) ) => ( r1_xxreal_0(B,k1_xxreal_3(C,A)) | r1_xxreal_0(C,B) ) ) ) ) ) )).
fof(t48_yellow10,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t48_yellow12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v2_pre_topc(D) & l1_pre_topc(D) ) => ! [E] : ( 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)))) ) ) ) ) ) ) ) )).
fof(t48_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_yellow_9(D,k2_yellow_1(k1_tarski(k5_numbers))) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t48_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t48_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ! [C] : ( ( ! [D] : ( 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) ) ) )).
fof(t48_yellow_2,axiom,( ! [A] : ( ( 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(k1_yellow_1(k7_waybel_0(A))) ) )).
fof(t48_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t48_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t48_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_yellow_5(A,B,k13_lattice3(A,B,C)) = k3_yellow_0(A) ) ) ) )).
fof(t48_yellow_7,axiom,( ! [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) ) => ( v1_waybel_5(A) <=> ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) ) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t48_yellow_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_yellow_9(B,A) => ( u1_pre_topc(B) = k5_waybel11(A) => v2_pre_topc(B) ) ) ) )).
fof(t48_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( v10_zf_lang(B) => ( ~ ( A = k27_zf_lang(B) & ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => B != k12_zf_lang(A,C) ) ) & ( ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & B = k12_zf_lang(A,C) ) => A = k27_zf_lang(B) ) & ~ ( A = k28_zf_lang(B) & ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => B != k12_zf_lang(C,A) ) ) & ( ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & B = k12_zf_lang(C,A) ) => A = k28_zf_lang(B) ) ) ) ) ) )).
fof(t48_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ( r2_zf_lang(k8_zf_lang(C,B),A) => r3_zf_lang(B,A) ) ) ) ) )).
fof(t48_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( r1_xboole_0(k2_tarski(A,B),C) & r2_hidden(A,C) ) )).
fof(t48_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_zmodul01(B) & m1_zmodul01(B,A) ) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_struct_0(B,C) <=> r1_struct_0(A,C) ) ) => B = A ) ) ) )).
fof(t48_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( v1_int_1(C) => k1_zmodul01(k31_zmodul02(A),k1_rlvect_2(k31_zmodul02(A),B),C) = k23_zmodul02(A,C,B) ) ) ) )).
fof(t49_abcmiz_0,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t49_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t49_abcmiz_a,axiom,( ! [A] : ( ( v8_abcmiz_1(A,k27_abcmiz_1) & m1_abcmiz_1(A,k27_abcmiz_1,k13_abcmiz_1(k27_abcmiz_1)) ) => ! [B] : ( 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)) ) ) )).
fof(t49_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t49_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(A))) => ! [J] : ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A))) => ! [K] : ( m1_subset_1(K,k1_zfmisc_1(u1_struct_0(A))) => ( ( r2_hidden(H,I) & r2_hidden(H,K) & r2_hidden(H,J) & r2_hidden(B,I) & r2_hidden(E,I) & r2_hidden(C,K) & r2_hidden(F,K) & r2_hidden(D,J) & r2_hidden(G,J) & v1_aff_1(I,A) & v1_aff_1(K,A) & v1_aff_1(J,A) & r2_analoaf(A,B,C,E,F) & r2_analoaf(A,B,D,E,G) ) => ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) | H = B | H = C | H = D | I = K | I = J | r2_analoaf(A,C,D,F,G) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t49_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ( 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,k5_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 ) ) ) )).
fof(t49_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ( v10_incproj(k13_afproj(A)) => v2_aff_2(A) ) ) )).
fof(t49_afvect0,axiom,( ! [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) & 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)) ) ) )).
fof(t49_algspec1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_msualg_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t49_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) )).
fof(t49_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r6_analmetr(A,C,D,B) => r6_analmetr(A,D,C,B) ) ) ) ) ) )).
fof(t49_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r1_analmetr(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_analort(A,B,C,D,E,D,F) & ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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 ) ) ) ) ) ) ) ) ) ) ) )).
fof(t49_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ~ r2_hidden(k12_aofa_000(A),k18_aofa_000(A)) ) )).
fof(t49_aofa_a00,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_finseq_2(B,A),A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_2(B,A),A))) ) => ( 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(k13_finseq_1(A),A))) & ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v2_margrel1(D) ) => ( C = D => v8_comput_1(D,B) ) ) ) ) ) ) )).
fof(t49_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( m2_pboole(E,u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,D)) => k15_aofa_a00(A,B,C,D,u8_aofa_a00(A),k2_aofa_a01(A,C),E) = k7_margrel1 ) ) ) ) ) )).
fof(t49_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_aofa_i00(E,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) ) => ! [F] : ( 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) = k5_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) = k5_int_1(k2_xcmplx_0(k21_aofa_i00(B,k4_numbers,C,F),1),2) & ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t49_armstrng,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ~ ( ~ v1_xboole_0(B) & v11_armstrng(B) & ! [C] : ( ( 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) ) ) ) ) )).
fof(t49_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ! [C] : ( ( v3_ordinal1(C) & v7_ordinal1(C) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t49_asympt_1,axiom,( ? [A] : ( m1_subset_1(A,k4_ordinal1) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( r1_xxreal_0(A,B) & r1_xxreal_0(k6_xcmplx_0(k3_square_1(B),k3_power(2,B)),1) ) ) ) )).
fof(t49_bcialg_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t49_bcialg_2,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ! [C] : ( m4_bcialg_2(C,A,B) => ! [D] : ( m1_bcialg_2(D,A) => ( ! [E] : ( m3_bcialg_2(E,A) => m5_bcialg_2(E,A,B) ) => D = C ) ) ) ) ) )).
fof(t49_bcialg_4,axiom,( ! [A] : ( ( ~ 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) ) ) ) )).
fof(t49_bcialg_5,axiom,( ! [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) ) => ( ( ~ 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,k5_numbers,1,k5_numbers,1) ) ) ) )).
fof(t49_bcialg_6,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ! [C] : ( m5_bcialg_2(C,A,B) => v2_funct_2(k6_bcialg_6(A,B,C),u1_struct_0(k9_bcialg_2(A,C))) ) ) ) )).
fof(t49_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( v3_bciideal(B,A) & m2_bcialg_1(B,A) ) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_bcialg_1(A,B,C) = B => k1_bcialg_1(A,C,B) = C ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(t49_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_normsp_1(A,B,C),k6_bhsp_1(A,B,k5_vfunct_1(k4_ordinal1,A,C))) ) ) ) )).
fof(t49_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k5_numbers,C) => r2_hidden(B,k5_bhsp_2(A,B,C)) ) ) ) ) )).
fof(t49_bhsp_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( ( v1_comseq_2(A) & v2_bhsp_3(C,B) ) => v2_bhsp_3(k5_bhsp_4(B,C,A),B) ) ) ) ) )).
fof(t49_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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))) ) ) ) ) ) )).
fof(t49_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t49_borsuk_4,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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) ) ) ) )).
fof(t49_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => k5_measure6(k2_rcomp_1(A,k1_xxreal_0)) = k3_rcomp_1(A,k1_xxreal_0) ) )).
fof(t49_borsuk_6,axiom,( k1_funct_1(k5_borsuk_6,k5_numbers) = k5_numbers & k1_funct_1(k5_borsuk_6,1) = 1 )).
fof(t49_borsuk_7,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_xreal_0(B) => r2_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k1_jordan24(B),k1_jordan24(k2_xcmplx_0(B,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A)))) ) ) )).
fof(t49_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t49_bvfunc14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( v1_relat_1(H) & v1_funct_1(H) ) => ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ( 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 ) ) ) ) )).
fof(t49_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t49_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => k9_xboolean(k8_margrel1,A) = k7_margrel1 ) )).
fof(t49_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)))) ) ) ) ) ) )).
fof(t49_card_1,axiom,( 3 = k1_enumset1(k5_ordinal1,1,2) )).
fof(t49_card_2,axiom,( ! [A] : ! [B] : r1_xxreal_0(k5_card_1(k2_tarski(A,B)),2) )).
fof(t49_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(B,k8_card_3(A)) => ( r1_tarski(k9_xtuple_0(B),k9_xtuple_0(A)) & ! [C] : ( r2_hidden(C,k9_xtuple_0(B)) => r2_hidden(k1_funct_1(B,C),k1_funct_1(A,C)) ) ) ) ) ) )).
fof(t49_card_fin,axiom,( ! [A] : ! [B] : ( ( 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)))) ) )).
fof(t49_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v10_cat_1(B,A) => ! [C] : ( m1_cat_1(C,A,B,B) => k4_cat_1(A,B) = C ) ) ) ) )).
fof(t49_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_cat_3(D,B,C,A) => ( ( r1_cat_3(B,C,A,D) & ! [E] : ! [F] : ~ ( 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] : ( r2_hidden(E,A) => ! [F] : ( 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] : ( m1_cat_1(G,B,C,F) => ( G = k7_partfun1(u4_struct_0(B),D,E) => v1_cat_3(G,B,C,F) ) ) ) ) ) ) ) ) ) ) )).
fof(t49_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k23_cat_4(A,B))) => ! [D] : ( 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 ) ) )).
fof(t49_cfcont_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [C] : ( ( 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(k5_numbers)) = k1_xboole_0 & r2_cfcont_1(C,A) ) => r2_cfcont_1(k1_cfunct_1(k2_numbers,C,B),A) ) ) ) )).
fof(t49_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( 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,C,B),k1_cfunct_1(A,E,D)),k1_cfunct_1(A,k46_valued_1(A,k2_numbers,k2_numbers,k19_valued_1(A,k2_numbers,k2_numbers,C,D),k19_valued_1(A,k2_numbers,k2_numbers,E,B)),k19_valued_1(A,k2_numbers,k2_numbers,B,D))) ) ) ) ) ) )).
fof(t49_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ( v10_cgames_1(A) <=> ( ! [B] : ( v2_cgames_1(B) => ~ ( r2_hidden(B,k6_cgames_1(A)) & ~ v8_cgames_1(B) & ~ v10_cgames_1(B) ) ) & ? [B] : ( v2_cgames_1(B) & r2_hidden(B,k7_cgames_1(A)) & v6_cgames_1(B) ) ) ) ) )).
fof(t49_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_chain_1(C,B) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(k1_euclid(B)),k4_chain_1(B,C,A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k4_chain_1(B,C,k1_nat_1(A,1)))) => ( r2_hidden(D,k10_chain_1(B,C,A,E)) <=> ( r1_xxreal_0(k1_nat_1(A,1),B) & ~ v1_abian(k5_card_1(k9_subset_1(k4_chain_1(B,C,k1_nat_1(A,1)),k9_chain_1(B,C,A,D),E))) ) ) ) ) ) ) ) )).
fof(t49_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ( r2_hidden(C,k2_chord(A,B)) <=> ( ~ r2_hidden(C,B) & ? [D] : ( m1_subset_1(D,k6_glib_000(A)) & r2_hidden(D,B) & r1_chord(A,C,D) ) ) ) ) ) )).
fof(t49_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_circcmb3(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_xtuple_0(B) => r2_hidden(B,k3_msafree2(A)) ) ) ) )).
fof(t49_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_circcomb(B) & l1_msualg_1(B) ) => v1_circcomb(k2_circcomb(A,B)) ) ) )).
fof(t49_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v4_msualg_1(E,A) & v4_msafree2(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(B,F))) => ! [H] : ( m1_subset_1(H,k4_card_3(u3_msualg_1(A,E))) => ( H = k3_relat_1(C,G) => ! [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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t49_classes1,axiom,( ! [A] : ! [B] : ( ( v1_ordinal1(A) & v1_ordinal1(B) ) => v1_ordinal1(k2_xboole_0(A,B)) ) )).
fof(t49_classes2,axiom,( ! [A] : ( v3_ordinal1(A) => v1_classes2(k1_classes1(A)) ) )).
fof(t49_clvect_1,axiom,( ! [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) ) => ! [B] : ( ( v1_clvect_1(B) & m1_clvect_1(B,A) ) => ! [C] : ( ( v1_clvect_1(C) & m1_clvect_1(C,A) ) => ( u1_struct_0(B) = u1_struct_0(C) => B = C ) ) ) ) )).
fof(t49_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k5_numbers,C) => r2_hidden(B,k5_clvect_2(A,B,C)) ) ) ) ) )).
fof(t49_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v1_comseq_2(C) & v3_clvect_2(B,A) ) => v3_clvect_2(k6_clvect_3(A,B,C),A) ) ) ) ) )).
fof(t49_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( ( 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] : ! [E] : ~ ( r2_hidden(k4_tarski(D,E),k8_cohsp_1(A,B,C)) & ! [F] : D != k1_tarski(F) ) ) ) ) ) )).
fof(t49_complex1,axiom,( k9_complex1(k7_complex1) = 1 )).
fof(t49_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_complex2(A,k5_numbers) = A ) )).
fof(t49_complfld,axiom,( k2_complfld(k5_struct_0(k1_complfld)) = k5_struct_0(k1_complfld) )).
fof(t49_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => k8_complsp2(k10_seq_4(A,k7_complex1),B) = k3_xcmplx_0(k7_complex1,k8_complsp2(A,B)) ) ) ) )).
fof(t49_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) ) ) ) )).
fof(t49_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( v6_compos_0(D,u1_compos_1(A)) & m1_subset_1(D,u1_compos_1(A)) ) => ! [E] : ( ( v6_compos_0(E,u1_compos_1(A)) & m1_subset_1(E,u1_compos_1(A)) ) => ! [F] : ( ( v6_compos_0(F,u1_compos_1(A)) & m1_subset_1(F,u1_compos_1(A)) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t49_comptrig,axiom,( ! [A] : ( v1_xcmplx_0(A) => ~ ( ~ r1_xxreal_0(k3_complex1(A),k5_numbers) & r1_xxreal_0(k19_sin_cos(k1_comptrig(A)),k5_numbers) ) ) )).
fof(t49_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_convex4(B,A) => ! [C] : ( v1_xcmplx_0(C) => ( ? [D] : ( v1_xreal_0(D) & C = D & ~ r1_xxreal_0(D,k5_numbers) & ~ 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) ) ) ) ) ) )).
fof(t49_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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))))) ) ) ) ) ) )).
fof(t49_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t49_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => ( ( r6_cqc_the3(A,D,B) & r6_cqc_the3(A,E,C) ) => ( r5_cqc_the3(A,B,C) <=> r5_cqc_the3(A,k6_cqc_lang(A,D),k6_cqc_lang(A,E)) ) ) ) ) ) ) ) )).
fof(t49_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k13_csspace(A,B),k13_csspace(A,C))),k13_csspace(A,k5_algstr_0(A,B,C))) ) ) ) )).
fof(t49_dickson,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v3_dickson(A) => ( v4_dickson(A) <=> ! [B] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t49_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k9_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k16_sin_cos),A,B) = k7_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k19_sin_cos(k3_xcmplx_0(2,B)),k19_sin_cos(k3_xcmplx_0(2,A)))),k6_xcmplx_0(A,B)) ) ) )).
fof(t49_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( v1_xreal_0(F) => k1_funct_1(E,F) = k7_xcmplx_0(A,k1_square_1(F)) ) & r1_zfmisc_1(B,C,D) ) => ( B = k5_numbers | C = k5_numbers | D = k5_numbers | k10_diff_1(E,B,C,D) = k3_xcmplx_0(k7_xcmplx_0(A,k3_xcmplx_0(k3_xcmplx_0(B,C),D)),k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(1,B),k7_xcmplx_0(1,C)),k7_xcmplx_0(1,D))) ) ) ) ) ) ) ) )).
fof(t49_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k5_diff_1(C,A),B) = k6_xcmplx_0(k1_funct_1(k2_diff_1(C,k7_xcmplx_0(A,2)),B),k1_funct_1(k2_diff_1(C,k4_xcmplx_0(k7_xcmplx_0(A,2))),B)) ) ) ) )).
fof(t49_dilworth,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & v5_orders_2(A) & v4_dilworth(A) & l1_orders_2(A) ) => ! [B] : ( ( v2_dilworth(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( v5_dilworth(E,A) & m1_eqrel_1(E,u1_struct_0(A)) ) => k1_card_1(E) != k2_dilworth(A) ) ) ) ) ) ) )).
fof(t49_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( 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) = k5_numbers & ! [E] : ( 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) = k5_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) = k5_numbers ) ) ) ) ) ) ) )).
fof(t49_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( 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] : ( 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)) ) ) ) ) ) )).
fof(t49_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t49_entropy1,axiom,( ! [A] : ( ( v4_partfun3(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( B = k6_rvsum_1(k4_entropy1(A)) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => k1_funct_1(B,C) = k3_xcmplx_0(k1_funct_1(A,C),k3_power(2,k7_xcmplx_0(1,k1_funct_1(A,C)))) ) ) ) ) ) ) )).
fof(t49_enumset1,axiom,( ! [A] : ! [B] : ! [C] : k5_enumset1(A,A,A,A,A,B,C) = k1_enumset1(A,B,C) )).
fof(t49_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t49_euclid,axiom,( k1_euclid(k5_numbers) = k1_tarski(k4_struct_0(k15_euclid(k5_numbers))) )).
fof(t49_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => r1_xxreal_0(k9_complex1(k22_rvsum_1(B,C)),k3_xcmplx_0(k12_euclid(B),k12_euclid(C))) ) ) ) )).
fof(t49_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t49_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m1_subset_1(B,k2_numbers) => ! [C] : ( m1_subset_1(C,k2_numbers) => ( k2_xcmplx_0(k3_complex2(A,B),k3_complex2(B,C)) = k3_complex2(A,C) | k2_xcmplx_0(k3_complex2(A,B),k3_complex2(B,C)) = k2_xcmplx_0(k3_complex2(A,C),k3_xcmplx_0(2,k28_sin_cos)) ) ) ) ) )).
fof(t49_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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))) ) ) )).
fof(t49_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( v1_xreal_0(B) => k9_euclid(3,A,B) = k1_euclid_8(k3_xcmplx_0(B,k1_funct_1(A,1)),k3_xcmplx_0(B,k1_funct_1(A,2)),k3_xcmplx_0(B,k1_funct_1(A,3))) ) ) )).
fof(t49_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ( ~ ( ~ r1_xboole_0(B,C) & ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ~ ( r2_hidden(D,B) & r2_hidden(D,C) ) ) ) & ~ ( ? [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) & r2_hidden(D,B) & r2_hidden(D,C) ) & r1_xboole_0(B,C) ) ) ) ) ) )).
fof(t49_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( 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)) ) ) ) )).
fof(t49_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) ) => ! [D] : ( ( 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] : ( 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))) ) ) ) )).
fof(t49_fcont_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k1_fcont_1(A,B),1) = k2_xcmplx_0(A,B) ) ) )).
fof(t49_fdiff_11,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k2_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k1_funct_1(k2_sin_cos9,B)),k1_funct_1(k18_sin_cos,B)),k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t49_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r1_fdiff_1(B,A) => ! [C] : ( ( v1_funct_1(C) & v9_ordinal1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & v1_fdiff_1(C,k5_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v3_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,D) = k1_tarski(A) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,D)),k1_relset_1(k1_numbers,B)) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k32_valued_1(k4_ordinal1,k1_numbers,C),D)),k1_relset_1(k1_numbers,B)) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,k26_valued_1(k4_ordinal1,k1_numbers,C,2)),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,C),B),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,C),B)))) & k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,k26_valued_1(k4_ordinal1,k1_numbers,C,2)),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,C),B),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,C),B)))) = k1_fdiff_1(B,A) ) ) ) ) ) ) ) )).
fof(t49_fdiff_4,axiom,( ! [A] : ( ( 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)),k7_xcmplx_0(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)),k7_xcmplx_0(1,2)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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)),k7_xcmplx_0(1,2)),A),B) = k3_xcmplx_0(k1_funct_1(k16_sin_cos,B),k1_funct_1(k18_sin_cos,B)) ) ) ) ) ) )).
fof(t49_fdiff_6,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k16_sin_cos),A),B) = k7_xcmplx_0(k1_funct_1(k18_sin_cos,k3_power(k4_power,B)),B) ) ) ) ) ) )).
fof(t49_fdiff_7,axiom,( ! [A] : ( ( 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,k18_sin_cos,k16_sin_cos),k1_taylor_1(2)))) & ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & k1_funct_1(k16_sin_cos,B) = k5_numbers ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos,k16_sin_cos),k1_taylor_1(2)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos,k16_sin_cos),k1_taylor_1(2)),A),B) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k18_sin_cos,B)),k3_prepower(k1_funct_1(k16_sin_cos,B),3))) ) ) ) ) ) )).
fof(t49_fib_num2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( ~ r1_xxreal_0(A,1) & A != 4 & ~ v1_int_2(A) & ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ~ ( B != 1 & B != 2 & B != A & r1_nat_d(B,A) ) ) ) ) )).
fof(t49_fib_num3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k3_fib_num3(A,B,k1_nat_1(C,1)) = k1_nat_1(k2_nat_1(A,k1_pre_ff(C)),k2_nat_1(B,k1_pre_ff(k1_nat_1(C,1)))) ) ) ) )).
fof(t49_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t49_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => r1_filter_1(k7_filter_1(A,B),k7_filter_1(B,A)) ) ) )).
fof(t49_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v18_lattices(B,A) & v21_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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) ) ) ) )).
fof(t49_finseq_1,axiom,( ! [A] : r2_hidden(k1_xboole_0,k13_finseq_1(A)) )).
fof(t49_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => k1_finseq_2(k1_nat_1(A,1)) = k7_finseq_1(k1_finseq_2(A),k12_finseq_1(k4_ordinal1,k1_nat_1(A,1))) ) )).
fof(t49_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k5_relat_1(k1_finseq_2(B),k2_finseq_1(A)) = k1_finseq_2(A) <=> r1_xxreal_0(A,B) ) ) ) )).
fof(t49_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_hidden(B,k10_xtuple_0(A)) => ( k4_finseq_4(A,B) = k3_finseq_1(A) <=> k6_finseq_4(A,B) = k1_xboole_0 ) ) ) )).
fof(t49_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ~ ( r2_hidden(B,k10_xtuple_0(C)) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( k1_nat_1(D,1) = k4_finseq_4(C,B) & k2_finseq_5(A,C,B) = k2_rfinseq(A,D,C) ) ) ) ) ) ) )).
fof(t49_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ( B != C => k1_finseq_5(A,k2_finseq_4(A,B,C),C) = k2_finseq_4(A,B,C) ) ) ) ) )).
fof(t49_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( v3_card_1(F,D) & m2_finseq_1(F,A) ) => ! [G] : ( ( 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] : ( ( 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] : ( m1_subset_1(I,A) => ! [J] : ( m1_subset_1(J,A) => k3_funct_2(A,B,E,k5_binop_1(A,G,I,J)) = k5_binop_1(B,H,k3_funct_2(A,B,E,I),k3_funct_2(A,B,E,J)) ) ) => r2_relset_1(k4_ordinal1,B,k4_finseqop(A,B,k3_finseqop(A,A,A,G,C,F),E),k3_finseqop(B,B,B,H,k3_funct_2(A,B,E,C),k4_finseqop(A,B,F,E))) ) ) ) ) ) ) ) ) ) )).
fof(t49_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_fintopo6(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & ! [E] : ( m2_finseq_1(E,u1_struct_0(A)) => ~ r3_fintopo6(A,E,B,C,D) ) ) ) ) ) ) ) )).
fof(t49_flang_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_catalan2(A))) => ( k8_flang_1(A,C) = k1_tarski(B) => B = k2_flang_1(A) ) ) )).
fof(t49_flang_2,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(t49_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(C,k5_numbers) => r1_tarski(k7_flang_1(A,B,C),k2_flang_3(A,B)) ) ) ) )).
fof(t49_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ~ r1_xboole_0(k4_finseq_2(C,A),k4_finseq_2(D,B)) => C = D ) ) ) )).
fof(t49_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,B,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [F] : ( m1_subset_1(F,A) => ( ! [G] : ( m1_subset_1(G,B) => k3_funct_2(B,A,E,G) = k5_binop_1(A,C,k3_funct_2(B,A,D,G),F) ) => r2_funct_2(B,A,E,k9_funcop_1(A,B,C,D,F)) ) ) ) ) ) ) ) )).
fof(t49_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r2_hidden(B,k9_xtuple_0(C)) & r2_hidden(B,A) ) => r2_hidden(k1_funct_1(C,B),k10_xtuple_0(k5_relat_1(C,A))) ) ) )).
fof(t49_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,k1_tarski(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_tarski(C)))) ) => ( r2_hidden(B,A) => k1_funct_1(D,B) = C ) ) )).
fof(t49_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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)) ) ) ) )).
fof(t49_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) ) )).
fof(t49_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(A,B) => r1_tarski(k1_funct_2(C,A),k1_funct_2(C,B)) ) )).
fof(t49_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r2_hidden(B,k9_xtuple_0(k9_funct_6(A))) => ( v1_relat_1(k1_funct_1(k9_funct_6(A),B)) & v1_funct_1(k1_funct_1(k9_funct_6(A),B)) ) ) ) )).
fof(t49_funct_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t49_functor0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v16_functor0(C,A,B) & m2_functor0(C,A,B) ) => ~ ( v21_functor0(C,A,B) & ! [D] : ( m2_functor0(D,B,A) => ~ ( D = k15_functor0(A,B,C) & v21_functor0(D,B,A) & v16_functor0(D,B,A) ) ) ) ) ) ) )).
fof(t49_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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))) ) => k3_funct_2(A,k1_numbers,k3_fuzzy_2(A,C,D),B) = k6_xcmplx_0(1,k3_xcmplx_0(k6_xcmplx_0(1,k3_funct_2(A,k1_numbers,C,B)),k6_xcmplx_0(1,k3_funct_2(A,k1_numbers,D,B)))) ) ) ) ) )).
fof(t49_fvaluat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => r2_hidden(k4_struct_0(A),k6_fvaluat1(A,B)) ) ) ) )).
fof(t49_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t49_gcd_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t49_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( ( ~ v1_xboole_0(F) & v1_relat_1(F) & v2_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ! [G] : ( m1_genealg1(G,F) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t49_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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))) ) ) )).
fof(t49_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( 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)) ) ) ) ) )).
fof(t49_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => r1_xxreal_0(k3_finseq_1(k20_glib_001(A,B,D,C)),k3_finseq_1(B)) ) ) ) ) )).
fof(t49_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_003(A) & v3_glib_003(A) ) => ! [B] : ! [C] : k11_glib_003(A) = k11_glib_003(k13_glib_003(A,B,C)) ) )).
fof(t49_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ 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(k1_nat_1(A,1),k3_finseq_1(k2_goboard2(D))) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(k2_goboard2(D))) & r1_xxreal_0(1,C) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,1))) = k2_topreal1(2,D,C) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1))) = k2_topreal1(2,D,k1_nat_1(C,1)) ) => ( r1_xxreal_0(k3_finseq_1(D),k1_nat_1(C,1)) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1)) ) ) ) ) ) ) ) )).
fof(t49_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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))) ) ) ) )).
fof(t49_graph_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m2_finseq_1(C,u4_struct_0(B)) => ( ( C = k1_xboole_0 & r6_graph_5(B,A) ) => k10_graph_5(B,C,A) = k5_numbers ) ) ) ) )).
fof(t49_graphsp,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k3_finseq_2(k1_numbers)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r4_graphsp(A,C,D,E) & r4_graphsp(B,C,D,E) ) => A = B ) ) ) ) ) ) )).
fof(t49_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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)) ) ) ) ) ) ) ) )).
fof(t49_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k4_group_1(A),B,1) = B ) ) )).
fof(t49_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t49_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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)) ) ) )).
fof(t49_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t49_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,A) => ( r1_struct_0(k8_group_4(A,C,D),B) <=> ? [E] : ( m2_finseq_1(E,u1_struct_0(A)) & ? [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t49_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t49_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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)))) ) => ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k10_group_6(A,B,C))) & v1_group_6(C,A,k10_group_6(A,B,C)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k10_group_6(A,B,C))))) ) ) ) ) )).
fof(t49_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( ( 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)) ) ) ) )).
fof(t49_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => k3_helly(A,B,C,B) = B ) ) ) )).
fof(t49_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) = k2_xcmplx_0(k3_xcmplx_0(2,k4_hermitan(A,B,C)),k3_xcmplx_0(2,k4_hermitan(A,B,D))) ) ) ) ) )).
fof(t49_hfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( r1_xxreal_0(1,A) => ( r2_hidden(k5_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(k1_nat_1(A,1))),k4_xcmplx_0(A)),B)) ) ) ) ) )).
fof(t49_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(t49_hurwitz,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(A,k1_complfld) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => ( ( r1_xxreal_0(1,k2_hurwitz(k1_complfld,A)) & v1_hurwitz(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ( ~ ( ~ r1_xxreal_0(k5_numbers,k3_complex1(B)) & r1_xxreal_0(k9_complex1(k2_polynom4(k1_complfld,k7_hurwitz(A),B)),k9_complex1(k2_polynom4(k1_complfld,A,B))) ) & ~ ( ~ r1_xxreal_0(k3_complex1(B),k5_numbers) & r1_xxreal_0(k9_complex1(k2_polynom4(k1_complfld,A,B)),k9_complex1(k2_polynom4(k1_complfld,k7_hurwitz(A),B))) ) & ( k3_complex1(B) = k5_numbers => k9_complex1(k2_polynom4(k1_complfld,A,B)) = k9_complex1(k2_polynom4(k1_complfld,k7_hurwitz(A),B)) ) ) ) ) ) )).
fof(t49_ideal_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t49_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u4_incsp_1(A)) => ? [D] : ( m1_subset_1(D,u2_incsp_1(A)) & ~ r1_incsp_1(A,B,D) & r3_incsp_1(A,D,C) ) ) ) ) )).
fof(t49_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ~ ( ~ r1_xxreal_0(B,A) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( C = k6_xcmplx_0(B,A) & r1_xxreal_0(1,C) ) ) ) ) ) )).
fof(t49_int_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_finset_1(B) => ( r1_int_4(A,B) => ( k5_card_1(B) = A & ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & C != D & r2_hidden(k4_tarski(C,D),k1_int_4(A)) ) ) ) ) ) ) ) )).
fof(t49_int_5,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( 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),k2_nat_1(k3_nat_d(k7_nat_d(A,1),2),k3_nat_d(k7_nat_d(B,1),2))) ) ) ) )).
fof(t49_integr11,axiom,( ! [A] : ( ( 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),k27_sin_cos),k2_fdiff_9))) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( k2_xcmplx_0(1,k1_funct_1(k18_sin_cos,B)) != k5_numbers & k6_xcmplx_0(1,k1_funct_1(k18_sin_cos,B)) != k5_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),k27_sin_cos),k2_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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),k27_sin_cos),k2_fdiff_9),A),B) = k7_xcmplx_0(k1_funct_1(k18_sin_cos,B),k2_xcmplx_0(1,k1_funct_1(k18_sin_cos,B))) ) ) ) ) ) )).
fof(t49_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,D) & r1_tarski(D,k2_rcomp_1(k4_xcmplx_0(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,k22_sin_cos),k3_valued_1(k1_numbers,k1_numbers,k1_numbers,C,k1_taylor_1(2))))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => k1_funct_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) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k22_sin_cos),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k22_sin_cos),k3_seq_4(A))) ) ) ) ) ) )).
fof(t49_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k3_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,k1_funct_1(k26_sin_cos,D)))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,D)))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k26_sin_cos))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k26_sin_cos),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k26_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t49_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t49_integra1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( 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)) ) ) ) )).
fof(t49_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k7_xcmplx_0(k3_xcmplx_0(k28_sin_cos,3),2)) => k2_integra5(A,k32_valued_1(k1_numbers,k1_numbers,k16_sin_cos)) = k4_xcmplx_0(1) ) ) )).
fof(t49_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v3_rcomp_1(E) & m1_subset_1(E,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,E) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => ( k1_funct_1(C,F) = k6_xcmplx_0(A,F) & k1_funct_1(C,F) != k5_numbers ) ) ) & k1_relset_1(k1_numbers,C) = E & k1_relset_1(k1_numbers,C) = k1_relset_1(k1_numbers,D) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => k1_funct_1(D,F) = k7_xcmplx_0(1,k1_square_1(k6_xcmplx_0(A,F))) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,D,B)) ) => k2_integra5(B,D) = k6_xcmplx_0(k1_funct_1(k6_rfunct_1(k1_numbers,k1_numbers,C),k2_seq_4(B)),k1_funct_1(k6_rfunct_1(k1_numbers,k1_numbers,C),k3_seq_4(B))) ) ) ) ) ) ) )).
fof(t49_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ ! [B] : ( ( ~ 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)) ) ) )).
fof(t49_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(t49_jgraph_4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(B,k7_xcmplx_0(k17_euclid(A),k12_euclid(A))) => ( r1_xxreal_0(k18_euclid(A),k5_numbers) | k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k5_jgraph_4(B),A) = k19_euclid(k3_xcmplx_0(k12_euclid(A),k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k17_euclid(A),k12_euclid(A)),B),k6_xcmplx_0(1,B))),k3_xcmplx_0(k12_euclid(A),k3_square_1(k6_xcmplx_0(1,k1_square_1(k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k17_euclid(A),k12_euclid(A)),B),k6_xcmplx_0(1,B))))))) ) ) & ( r1_xxreal_0(k18_euclid(A),k5_numbers) => k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k5_jgraph_4(B),A) = A ) ) ) ) )).
fof(t49_jgraph_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ 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(k5_numbers,k18_euclid(B)) | r1_xxreal_0(k5_numbers,k17_euclid(B)) ) & r1_jordan6(C,A,B) & ~ r1_xxreal_0(k5_numbers,k18_euclid(A)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(A)) ) ) ) ) )).
fof(t49_jordan,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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) ) ) ) ) )).
fof(t49_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ~ ( ~ r1_xxreal_0(C,1) & ~ r1_xxreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,1))),C) & ~ r1_xxreal_0(D,1) & ~ r1_xxreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,1))),D) & r1_xxreal_0(1,E) & r1_xxreal_0(E,F) & r1_xxreal_0(F,k1_matrix_0(k1_jordan8(B,k1_nat_1(A,1)))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),C,F),k8_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),D,E),k9_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) & r2_subset_1(k4_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),D,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),D,F)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),D,F),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),C,F))),k9_jordan6(B)) ) ) ) ) ) ) ) )).
fof(t49_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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)))) ) => ( r1_xxreal_0(A,k3_finseq_1(k1_jordan8(C,B))) => r1_tarski(k3_goboard5(k1_jordan8(C,B),A,k5_numbers),k2_jordan2c(2,C)) ) ) ) ) )).
fof(t49_jordan1g,axiom,( ! [A] : ( ( v4_topreal1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( 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)) ) ) ) )).
fof(t49_jordan1h,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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)))) ) => ( ~ r1_xxreal_0(k3_jordan1h(B,A),2) & ~ r1_xxreal_0(k3_finseq_1(k1_jordan8(B,A)),k3_jordan1h(B,A)) ) ) ) )).
fof(t49_jordan1j,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( v7_ordinal1(D) => ( 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) ) ) ) ) )).
fof(t49_jordan1k,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( 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) ) ) ) )).
fof(t49_jordan21,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t49_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k14_euclid(A)))) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k14_euclid(A)))) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t49_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( 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)) ) ) ) ) ) ) )).
fof(t49_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t49_kurato_1,axiom,( ! [A] : ~ ( 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 ) )).
fof(t49_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( v14_lattices(A) <=> v13_lattices(k1_lattice2(A)) ) ) )).
fof(t49_lattice3,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t49_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),k14_lexbfs(A,k16_lexbfs(A)))) = k6_glib_000(A) ) )).
fof(t49_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_limfunc2(B,A) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,C) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,C) & ~ r1_xxreal_0(A,D) & r2_hidden(D,k1_relset_1(k1_numbers,B)) & k1_funct_1(B,D) != k5_numbers ) ) ) ) ) => ( k1_limfunc2(B,A) = k5_numbers | ( r1_limfunc2(k6_rfunct_1(k1_numbers,k1_numbers,B),A) & k1_limfunc2(k6_rfunct_1(k1_numbers,k1_numbers,B),A) = k5_xcmplx_0(k1_limfunc2(B,A)) ) ) ) ) ) )).
fof(t49_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,D),A),k2_rcomp_1(A,k2_xcmplx_0(A,D))))) & r1_xxreal_0(k1_limfunc3(B,A),k1_funct_1(B,E)) ) ) ) ) | r2_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t49_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k20_lpspace1(A,B,C))) => ( ? [E] : ( 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) & k2_normsp_0(k20_lpspace1(A,B,C),D) = k1_mesfunc6(A,B,C,k56_valued_1(A,k1_numbers,E)) ) & ! [E] : ( ( 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)) = k2_normsp_0(k20_lpspace1(A,B,C),D) ) ) ) ) ) ) ) )).
fof(t49_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v2_xxreal_0(E) & v1_xreal_0(E) ) => ( 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(k5_numbers,k1_mesfunc6(A,B,C,k2_mesfun6c(E,A,k56_valued_1(A,k1_numbers,D)))) ) ) ) ) ) ) ) )).
fof(t49_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t49_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(k3_hilbert1(A,C),k3_hilbert1(k3_hilbert1(B,C),k3_hilbert1(k5_ltlaxio1(A,B),C)))) ) ) ) )).
fof(t49_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(C,D) => r1_tarski(k5_mathmorp(A,B,C),k3_mathmorp(A,k6_rusub_4(A,B,D),C)) ) ) ) ) ) )).
fof(t49_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => r2_matrix10(k3_matrix10(A,k4_matrix10(A,B,C)),k4_matrix10(A,k3_matrix10(A,B),k3_matrix10(A,C))) ) ) ) )).
fof(t49_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(C,k2_finseq_1(A)) & r2_hidden(D,k2_finseq_1(A)) ) => ( r1_xxreal_0(D,C) | ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ( k7_matrix_0(u1_struct_0(B),E,C) = k7_matrix_0(u1_struct_0(B),E,D) => ! [F] : ( m1_matrix_2(F,k3_matrix_2(A)) => ! [G] : ( m1_matrix_2(G,k3_matrix_2(A)) => ! [H] : ( m1_matrix_2(H,k3_matrix_2(A)) => ( ( r2_funct_2(k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),G,k1_partfun1(k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),H,F)) & v4_matrix_2(H,k2_matrix_2(k3_matrix_2(A))) & k1_funct_1(H,C) = D ) => k3_funct_2(k3_matrix_2(A),u1_struct_0(B),k11_matrix_3(A,B,E),G) = k4_algstr_0(B,k3_funct_2(k3_matrix_2(A),u1_struct_0(B),k11_matrix_3(A,B,E),F)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t49_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ! [E] : ( ( v1_finset_1(E) & v1_setfam_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ( ( r2_hidden(B,k2_finseq_1(k5_card_1(E))) & r1_tarski(D,k2_finseq_1(k3_finseq_1(C))) ) => k8_matrix_0(A,k6_matrix13(A,C,D,E),B) = k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,A,k5_matrix13(D),k8_matrix_0(A,C,k1_funct_1(k5_matrix13(E),B))) ) ) ) ) ) ) )).
fof(t49_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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] : ( m1_subset_1(C,k4_ordinal1) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,A) ) => ( v1_matrix_6(k4_matrix14(B,A,C),A,B) & k1_matrix_6(A,B,k4_matrix14(B,A,C)) = k4_matrix14(B,A,C) ) ) ) ) ) )).
fof(t49_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),B,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ! [E] : ( ( v1_finset_1(E) & v1_setfam_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ~ ( k5_card_1(E) = B & r1_tarski(E,k2_finseq_1(A)) & k6_matrix13(u1_struct_0(C),D,k2_finseq_1(B),E) = k3_matrix_1(C,B) & ~ r1_xxreal_0(B,k5_numbers) & ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(C),k7_nat_d(A,B),A) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(C))) ) => ~ ( k6_matrix13(u1_struct_0(C),F,k2_finseq_1(k7_nat_d(A,B)),k7_subset_1(k4_ordinal1,k2_finseq_1(A),E)) = k3_matrix_1(C,k7_nat_d(A,B)) & k6_matrix13(u1_struct_0(C),F,k2_finseq_1(k7_nat_d(A,B)),E) = k2_matrix_3(C,k4_matrix_0(u1_struct_0(C),k6_matrix13(u1_struct_0(C),D,k2_finseq_1(B),k7_subset_1(k4_ordinal1,k2_finseq_1(A),E)))) & ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(C),A,G) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(C))) ) => ( ! [I] : ( v7_ordinal1(I) => ~ ( r2_hidden(I,k2_finseq_1(G)) & ! [J] : ( v7_ordinal1(J) => ~ ( r2_hidden(J,k2_finseq_1(k7_nat_d(A,B))) & k8_matrix_0(u1_struct_0(C),H,I) = k7_matrix_0(u1_struct_0(C),F,J) ) ) & k8_matrix_0(u1_struct_0(C),H,I) != k5_finseq_2(u1_struct_0(C),A,k4_struct_0(C)) ) ) => r2_hidden(H,k4_matrix15(C,D,k1_matrix_3(C,B,G))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t49_matrix16,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( 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),k5_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)) ) ) ) ) ) ) )).
fof(t49_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ( r2_hidden(k4_tarski(1,1),k2_matrix_0(k14_matrix_0(A,1,k13_matrix_0(A,B)))) & k3_matrix_0(A,k14_matrix_0(A,1,k13_matrix_0(A,B)),1,1) = B ) ) ) )).
fof(t49_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(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)) ) ) ) ) ) )).
fof(t49_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r1_matrix_6(A,B,C,D) => ( r1_xxreal_0(A,k5_numbers) | r1_matrix_6(A,B,k3_matrix_3(B,C,D),D) ) ) ) ) ) ) )).
fof(t49_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_6(D,A,B) & r2_matrix_8(A,B,C,D) ) => ( r1_xxreal_0(A,k5_numbers) | v1_matrix_6(C,A,B) ) ) ) ) ) ) )).
fof(t49_matrix_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( ? [D] : ( m1_subset_1(D,k4_ordinal1) & r2_hidden(D,k2_finseq_1(A)) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k2_finseq_1(A)) => k1_funct_1(k8_matrix_0(u1_struct_0(B),C,D),E) = k4_struct_0(B) ) ) ) => ! [D] : ( m1_matrix_2(D,k3_matrix_2(A)) => ? [E] : ( m1_subset_1(E,k4_ordinal1) & r2_hidden(E,k2_finseq_1(A)) & k1_funct_1(k10_matrix_3(A,B,C,D),E) = k4_struct_0(B) ) ) ) ) ) ) )).
fof(t49_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ( ~ r1_xxreal_0(k3_finseq_1(A),k5_numbers) => k12_matrixc1(A) = k12_matrixc1(k4_matrix_0(k2_numbers,A)) ) ) )).
fof(t49_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => k22_matrixj1(B,k16_matrixj1(u1_struct_0(B),A,C)) = k13_matrix_0(u1_struct_0(B),k12_matrix_3(A,B,C)) ) ) ) )).
fof(t49_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( ~ r1_xxreal_0(k3_finseq_1(A),k5_numbers) => ( k4_matrix_0(k1_numbers,k10_matrixr1(A)) = k9_matrixr1(A) & k4_matrix_0(k1_numbers,k9_matrixr1(A)) = k10_matrixr1(A) ) ) ) )).
fof(t49_matrixr2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(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),k5_numbers) | r1_xxreal_0(k1_matrix_0(B),k5_numbers) | k12_matrixr1(B,k6_rvsum_1(A)) = k6_rvsum_1(k12_matrixr1(B,A)) ) ) ) ) )).
fof(t49_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( m1_matrlin(D,A,B) => ! [E] : ( m1_matrlin(E,A,C) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(A),k3_finseq_1(D),k3_finseq_1(E)) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(A))) ) => k10_ranknull(A,B,C,k4_matrlin2(A,B,C,D,E,F)) = k8_matrix13(A,F) ) ) ) ) ) ) )).
fof(t49_matrprob,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k3_finseq_1(A) = k1_matrix_0(C) ) => ( r1_xxreal_0(k3_finseq_1(A),k5_numbers) | r1_xxreal_0(k3_finseq_1(B),k5_numbers) | k22_rvsum_1(A,k12_matrixr1(C,B)) = k22_rvsum_1(k12_matrixr1(k4_matrix_0(k1_numbers,C),A),B) ) ) ) ) ) )).
fof(t49_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(A,k2_zfmisc_1(B,C)) => ( A != k1_xtuple_0(A) & A != k2_xtuple_0(A) ) ) )).
fof(t49_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( v1_xreal_0(B) => ( v4_xxreal_2(A) <=> v4_xxreal_2(k1_measure6(A,B)) ) ) ) )).
fof(t49_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( 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))) ) ) ) )).
fof(t49_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( ( 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)))) ) ) ) ) )).
fof(t49_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(A),B) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( v1_xreal_0(E) => 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)) ) ) ) ) ) )).
fof(t49_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( r1_mesfun7c(A,B,C) <=> ? [D] : ( v1_prob_2(D) & m2_finseq_1(D,B) & ? [E] : ( 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] : ( v7_ordinal1(F) => ( r2_hidden(F,k4_finseq_1(D)) => ! [G] : ( r2_hidden(G,k1_funct_1(D,F)) => k12_supinf_2(k5_comseq_3(A,C),G) = k12_supinf_2(k6_complsp2(E),F) ) ) ) & ! [F] : ( v7_ordinal1(F) => ( r2_hidden(F,k4_finseq_1(D)) => ! [G] : ( r2_hidden(G,k1_funct_1(D,F)) => k12_supinf_2(k6_comseq_3(A,C),G) = k12_supinf_2(k7_complsp2(E),F) ) ) ) ) ) ) ) ) ) )).
fof(t49_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_partfun1(A,k1_numbers)) & v1_mesfunc8(E,A,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( ( D = k1_relset_1(A,k4_mesfunc5(A,k1_numbers,E,k5_numbers)) & ! [F] : ( v7_ordinal1(F) => r1_mesfunc6(A,B,k4_mesfunc5(A,k1_numbers,E,F),D) ) & v1_mesfun9c(E,A) & ! [F] : ( 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] : ( 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] : ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k6_numbers) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) & ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t49_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ? [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) & k1_relset_1(A,D) = E ) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t49_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t49_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,k10_midsp_1(A)) => ! [C] : ( m1_subset_1(C,k10_midsp_1(A)) => k11_midsp_1(A,B,C) = k11_midsp_1(A,C,B) ) ) ) )).
fof(t49_mmlquery,axiom,( ! [A] : ! [B] : ( ( v1_mmlquery(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( 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))) ) ) )).
fof(t49_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t49_modelc_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_modelc_2(A) & l1_modelc_2(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t49_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ( k11_nat_3(A,B) != k5_numbers => k1_recdef_1(k5_moebius1(A),B) = B ) ) ) )).
fof(t49_monoid_0,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k6_monoid_0)) <=> m1_subset_1(A,k1_numbers) ) )).
fof(t49_monoid_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t49_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_funct_1(u3_msualg_1(A,k3_equation(A)),C)) => r1_equation(A,B,C,k5_equation(A,C,D,D)) ) ) ) ) )).
fof(t49_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) => ! [D] : ( m3_pboole(D,A,k1_mboolean(A,B)) => ! [E] : ( m3_pboole(E,A,k1_mboolean(A,B)) => ( r6_pboole(A,E,k2_pboole(A,C,D)) => r6_pboole(A,k4_mssubfam(A,B,E),k3_pboole(A,k4_mssubfam(A,B,C),k4_mssubfam(A,B,D))) ) ) ) ) ) )).
fof(t49_msualg_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_msualg_4(C,A,B,B) => ! [D] : ( m1_msualg_4(D,A,B,B) => ( ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,k1_funct_1(B,E)) => ! [G] : ( 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) ) ) ) ) ) )).
fof(t49_mycielsk,axiom,( k7_mycielsk(k5_numbers) = k5_mycielsk(2) & ! [A] : ( v7_ordinal1(A) => k7_mycielsk(k2_xcmplx_0(A,1)) = k6_mycielsk(k7_nat_d(k3_xcmplx_0(3,k1_newton(2,A)),1),k7_mycielsk(A)) ) )).
fof(t49_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => r8_pboole(k8_newton,k12_nat_3(k3_xcmplx_0(A,B)),k11_pre_poly(k8_newton,k12_nat_3(A),k12_nat_3(B))) ) ) )).
fof(t49_nat_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ? [C] : ( m2_finseq_1(C,k1_numbers) & k3_finseq_1(C) = k2_nat_1(2,A) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k4_finseq_1(C)) => k1_funct_1(C,D) = k6_xcmplx_0(k1_int_1(k7_xcmplx_0(k2_nat_1(2,A),k1_newton(B,D))),k3_xcmplx_0(2,k1_int_1(k7_xcmplx_0(A,k1_newton(B,D))))) ) ) & k11_nat_3(k4_newton(A,k2_nat_1(2,A)),B) = k18_rvsum_1(C) ) ) ) )).
fof(t49_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t49_ncfcont1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(D,B) & ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( r2_hidden(G,B) & ~ r1_xxreal_0(F,k2_normsp_0(A,k5_algstr_0(A,G,D))) & r1_xxreal_0(E,k9_complex1(k6_xcmplx_0(k7_partfun1(k2_numbers,C,G),k7_partfun1(k2_numbers,C,D)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t49_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( 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,k5_numbers) = k4_struct_0(k4_real_ns1(A)) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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))))) ) ) ) ) ) ) ) ) ) )).
fof(t49_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(A)) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k4_finseq_1(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_prvect_2(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_prvect_2(A))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t49_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_nat_d(A,B) => k6_nat_d(A,B) = A ) ) ) )).
fof(t49_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ( ! [C] : ( 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)) ) ) ) )).
fof(t49_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(k7_normform(A))) => ! [C] : ( m1_subset_1(C,k5_finsub_1(k7_normform(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t49_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t49_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ 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] : ( ( 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) ) ) ) )).
fof(t49_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(A))) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A))) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A))))) ) => ( ( r1_xxreal_0(B,C) & ! [G] : ( m1_subset_1(G,u1_struct_0(k4_real_ns1(A))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k4_real_ns1(A))) => r1_xxreal_0(k2_normsp_0(k4_real_ns1(A),k5_algstr_0(k4_real_ns1(A),k10_funct_2(u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A)),F,G),k10_funct_2(u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A)),F,H))),k3_xcmplx_0(D,k2_normsp_0(k4_real_ns1(A),k5_algstr_0(k4_real_ns1(A),G,H)))) ) ) ) => ( r1_xxreal_0(D,k5_numbers) | ! [G] : ( m1_subset_1(G,u1_struct_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A)))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A)))) => ! [I] : ( ( v1_funct_1(I) & v1_nfcont_3(I,k4_real_ns1(A)) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [J] : ( ( v1_funct_1(J) & v1_nfcont_3(J,k4_real_ns1(A)) & m1_subset_1(J,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ( ( I = k3_funct_2(u1_struct_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A))),u1_struct_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A))),k6_ordeq_01(A,E,F,B,C),G) & J = k3_funct_2(u1_struct_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A))),u1_struct_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A))),k6_ordeq_01(A,E,F,B,C),H) ) => ! [K] : ( v1_xreal_0(K) => ( r2_hidden(K,k3_integra5(B,C)) => r1_xxreal_0(k2_normsp_0(k4_real_ns1(A),k5_algstr_0(k4_real_ns1(A),k7_partfun1(u1_struct_0(k4_real_ns1(A)),I,K),k7_partfun1(u1_struct_0(k4_real_ns1(A)),J,K))),k3_xcmplx_0(k3_xcmplx_0(D,k6_xcmplx_0(K,B)),k2_normsp_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A)),k5_algstr_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A)),G,H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t49_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ~ ( r4_orders_1(A,B) & B = k1_xboole_0 ) ) )).
fof(t49_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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))) ) ) ) ) )).
fof(t49_ordinal2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => r1_tarski(k10_xtuple_0(A),k4_ordinal2(A)) ) )).
fof(t49_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( ( r2_hidden(1,B) & v4_ordinal1(A) ) => ( A = k1_xboole_0 | ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_ordinal2(C) ) => ( ( k9_xtuple_0(C) = A & ! [D] : ( v3_ordinal1(D) => ( r2_hidden(D,A) => k1_funct_1(C,D) = k11_ordinal2(D,B) ) ) ) => k11_ordinal2(A,B) = k4_ordinal2(C) ) ) ) ) ) ) )).
fof(t49_ordinal5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ! [B] : ( r2_hidden(B,A) => ( v3_ordinal1(B) & v4_ordinal5(B) & ? [C] : ( v3_ordinal1(C) & v4_ordinal5(C) & r2_hidden(B,C) & r2_hidden(C,A) ) ) ) => ( v3_ordinal1(k3_tarski(A)) & v4_ordinal5(k3_tarski(A)) ) ) ) )).
fof(t49_ordinal6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t49_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t49_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r3_parsp_2(A,B,C,D,E) => r1_parsp_1(A,B,D,C,E) ) ) ) ) ) ) )).
fof(t49_partfun1,axiom,( ! [A] : k4_partfun1(A,k1_xboole_0) = k1_tarski(k1_xboole_0) )).
fof(t49_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t49_pboole,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(t49_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( 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) & k10_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) = k2_xcmplx_0(k4_pdiff_5(B,A),k4_pdiff_5(C,A)) ) ) ) ) ) )).
fof(t49_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_real_ns1(A)))) => ( v3_nfcont_1(C,k4_real_ns1(A)) => ( ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( 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)),k14_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) ) ) ) ) ) ) )).
fof(t49_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t49_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( v1_int_2(B) & r1_int_2(A,B) ) => r1_nat_d(k3_pepin(A,B),k7_nat_d(B,1)) ) ) ) )).
fof(t49_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ( v5_polyform(A) <=> ! [B] : ( v1_int_1(B) => k22_polyform(A,B) = k24_polyform(A,B) ) ) ) )).
fof(t49_polynom5,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k5_polynom5(A,k9_polynom3(A),B),k9_polynom3(A)) ) ) )).
fof(t49_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(G,C) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(H,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),k7_polynom1(A,C,E,F),G) & r1_rewrite1(k3_polyred(A,B,C,D),G,H) & ! [I] : ( ( v1_funct_1(I) & v1_funct_2(I,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(I,C) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [J] : ( ( v1_funct_1(J) & v1_funct_2(J,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(J,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),k7_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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t49_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) => r1_xxreal_0(k2_xcmplx_0(1,k3_xcmplx_0(B,A)),k2_power(k2_xcmplx_0(1,A),B)) ) ) ) )).
fof(t49_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t49_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(k5_numbers,A) => k4_prepower(A,B) = k1_newton(A,B) ) ) ) )).
fof(t49_prob_3,axiom,( ! [A] : ! [B] : ! [C] : ( m2_finseq_1(C,k9_setfam_1(B)) => ( r2_hidden(A,k5_prob_3(B,C)) <=> ? [D] : ( v7_ordinal1(D) & r2_hidden(D,k1_relset_1(k4_ordinal1,C)) & r2_hidden(A,k4_prob_3(B,C,D)) ) ) ) )).
fof(t49_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t49_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ~ ( ~ v1_xboole_0(A) & r1_pboole(A,C,k4_pboole(A,D,k1_pzfmisc1(A,B))) & C = B ) ) ) ) )).
fof(t49_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( v4_qc_lang1(C,A) => ( r1_qc_lang2(A,B,C) <=> ( B = k19_qc_lang1(A,C) | B = k20_qc_lang1(A,C) ) ) ) ) ) ) )).
fof(t49_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( ( ~ 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))) ) ) ) ) )).
fof(t49_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => k17_quatern2(A,A) = k1_square_1(k28_quaterni(A)) ) )).
fof(t49_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ( ( k28_quaterni(A) = k28_quaterni(B) & k7_quatern2(A) = k7_quatern2(B) ) => ( k28_quaterni(A) = k5_numbers | A = B ) ) ) ) )).
fof(t49_quaterni,axiom,( k13_quaterni(k27_quaterni(k11_quaterni)) = k5_numbers & k14_quaterni(k27_quaterni(k11_quaterni)) = k5_numbers & k15_quaterni(k27_quaterni(k11_quaterni)) = k4_xcmplx_0(1) & k16_quaterni(k27_quaterni(k11_quaterni)) = k5_numbers )).
fof(t49_quofield,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t49_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t49_relat_1,axiom,( k4_relat_1(k1_xboole_0) = k1_xboole_0 )).
fof(t49_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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)) ) ) )).
fof(t49_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( 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) ) ) )).
fof(t49_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ v2_struct_0(C) & l1_rewrite3(C,B) ) => ! [D] : ( m1_rewrite1(D,k1_rewrite3(A,B,C)) => ! [E] : ( 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))) ) ) ) ) ) ) ) )).
fof(t49_rfunct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( v1_xcmplx_0(C) => k5_relat_1(k24_valued_1(B,C),A) = k24_valued_1(k5_relat_1(B,A),C) ) ) )).
fof(t49_rfunct_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t49_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : 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)) ) ) ) )).
fof(t49_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_seq_2(B) => r1_xxreal_0(k3_funct_2(k4_ordinal1,k1_numbers,k4_rinfsup1(B),k1_nat_1(A,1)),k1_funct_1(k4_rinfsup1(B),A)) ) ) ) )).
fof(t49_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(B,k4_rlaffin1(A,B)) ) ) )).
fof(t49_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t49_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_2(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t49_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( ( v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v8_ordinal1(C) & v1_xreal_0(C) ) => v3_pre_topc(k1_convex1(A,B,C),A) ) ) ) )).
fof(t49_rlvect_1,axiom,( ! [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) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t49_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t49_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_rmod_2(D,A,B) => ( r1_struct_0(D,C) <=> k3_rmod_2(A,B,C,D) = u1_struct_0(D) ) ) ) ) ) )).
fof(t49_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t49_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_4(C,A,B) => r1_rmod_4(A,B,k7_rmod_4(A,B,k1_group_1(A),C),C) ) ) ) )).
fof(t49_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( 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) ) ) )).
fof(t49_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t49_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t49_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ~ ( ~ r1_xxreal_0(k1_rpr_1(A,C),k5_numbers) & ~ r1_xxreal_0(1,k1_rpr_1(A,C)) & k1_rpr_1(A,B) != k2_xcmplx_0(k3_xcmplx_0(k2_rpr_1(A,C,B),k1_rpr_1(A,C)),k3_xcmplx_0(k2_rpr_1(A,k3_subset_1(A,C),B),k1_rpr_1(A,k3_subset_1(A,C)))) ) ) ) ) )).
fof(t49_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t49_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_2(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t49_rusub_5,axiom,( ! [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_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) ) ) )).
fof(t49_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) & v1_finseq_1(C) ) => k10_rvsum_1(C,k3_xcmplx_0(A,B)) = k10_rvsum_1(k10_rvsum_1(C,B),A) ) ) ) )).
fof(t49_rvsum_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k2_numbers) ) => k20_rvsum_1(k10_rvsum_2(A,C,B)) = k3_xcmplx_0(k19_rvsum_1(k2_finseq_2(A,B)),k20_rvsum_1(C)) ) ) ) )).
fof(t49_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_m(B)),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_m(B)))),D) ) ) ) ) )).
fof(t49_scmfsa8c,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ~ r4_scmfsa7b(k4_compos_1(k1_scmfsa_2),A) ) )).
fof(t49_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => A != k4_struct_0(k1_scmfsa_2) ) )).
fof(t49_scmpds_2,axiom,( ! [A] : ( ( 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] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( 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)) = k4_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)) = 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))) & ! [F] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t49_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( 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)) = k5_numbers | ( r1_scmpds_6(k6_scmpds_6(D,E,C),B,A) & r2_scmpds_6(k6_scmpds_6(D,E,C),B,A) ) ) ) ) ) ) ) ) )).
fof(t49_scmyciel,axiom,( ! [A] : v5_scmyciel(k5_scmyciel(A)) )).
fof(t49_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t49_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,A),k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,B)),k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,B),k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,C))) ) ) ) ) )).
fof(t49_seq_4,axiom,( r3_binop_1(k2_numbers,k5_complex1,k3_binop_2) )).
fof(t49_series_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => k9_nat_1(k1_numbers,B,C) = k7_xcmplx_0(1,k1_square_1(k1_nat_1(C,1))) ) & r1_xxreal_0(2,k9_nat_1(k1_numbers,k3_series_1(B),A)) ) ) ) )).
fof(t49_setfam_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ~ ( A != k1_tarski(B) & ! [C] : ( m1_subset_1(C,A) => C = B ) ) ) )).
fof(t49_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v2_prob_1(B) => r2_funct_2(k4_ordinal1,k9_setfam_1(A),k4_setlim_1(A,B),B) ) ) )).
fof(t49_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => r1_tarski(k5_subset_1(B,k9_nat_1(k9_setfam_1(B),k4_setlim_1(B,C),A),k9_nat_1(k9_setfam_1(B),k4_setlim_1(B,D),A)),k9_nat_1(k9_setfam_1(B),k4_setlim_1(B,k4_setlim_2(B,C,D)),A)) ) ) ) )).
fof(t49_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ! [D] : ( ( 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] : ( m1_subset_1(E,k5_finsub_1(B)) => ( E != k1_xboole_0 => ! [F] : ( ( 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] : ( ( 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] : ( m1_subset_1(H,k5_finsub_1(C)) => ! [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)) ) ) ) ) ) ) ) ) ) )).
fof(t49_sf_mastr,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t49_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t49_simplex0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v3_pencil_1(B) & v1_matroid0(B) & m1_simplex0(B,A) ) => ! [C] : ( ( ~ v3_pencil_1(C) & m2_simplex0(C,A,B) ) => ! [D] : ( v1_int_1(D) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t49_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k23_sin_cos(k2_xcmplx_0(A,B)) = k3_xcmplx_0(k23_sin_cos(A),k23_sin_cos(B)) ) ) )).
fof(t49_sin_cos3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,k2_xcmplx_0(A,k3_xcmplx_0(k4_xcmplx_0(B),k7_complex1))) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(k3_sin_cos2,A),k1_funct_1(k18_sin_cos,B)),k3_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_sin_cos2,A),k1_funct_1(k16_sin_cos,B))),k7_complex1)) ) ) )).
fof(t49_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k17_sin_cos(k7_xcmplx_0(k6_xcmplx_0(A,B),2)) != k5_numbers => k7_xcmplx_0(k6_xcmplx_0(k17_sin_cos(A),k17_sin_cos(B)),k6_xcmplx_0(k19_sin_cos(B),k19_sin_cos(A))) = k2_sin_cos4(k7_xcmplx_0(k2_xcmplx_0(A,B),2)) ) ) ) )).
fof(t49_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k2_sin_cos2(k7_xcmplx_0(A,2)) != k5_numbers => k6_sin_cos2(k7_xcmplx_0(A,2)) = k7_xcmplx_0(k6_xcmplx_0(k4_sin_cos2(A),1),k2_sin_cos2(A)) ) ) )).
fof(t49_sin_cos6,axiom,( k7_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k5_numbers,k28_sin_cos)) = k1_rcomp_1(k4_xcmplx_0(1),1) )).
fof(t49_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k8_sin_cos7(A) = k1_sin_cos7(k7_xcmplx_0(1,A)) ) ) )).
fof(t49_sin_cos9,axiom,( ! [A] : ( r2_hidden(A,k1_rcomp_1(k4_xcmplx_0(1),1)) => r2_hidden(k1_funct_1(k1_sin_cos9,A),k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)),k7_xcmplx_0(k28_sin_cos,4))) ) )).
fof(t49_sincos10,axiom,( k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(1,k3_square_1(2))) = k2_partfun2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,4)))) )).
fof(t49_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( r1_topreal4(A,B,C) => r1_topreal4(A,C,B) ) ) ) ) )).
fof(t49_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( ( ~ 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] : ( ( ~ 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)) ) ) ) ) )).
fof(t49_sprect_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ 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))) ) ) ) ) ) ) ) )).
fof(t49_sprect_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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_0(k2_goboard2(C))) ) => r1_sprect_2(C,k13_matrix_0(u1_struct_0(k15_euclid(2)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,B))) ) ) ) ) )).
fof(t49_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t49_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k4_xcmplx_0(A),B) & r1_xxreal_0(B,A) ) => r1_xxreal_0(k1_square_1(B),k1_square_1(A)) ) ) ) )).
fof(t49_stacks_1,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t49_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),D,k2_valuat_1(A,D)) => ! [F] : ( 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 ) ) ) ) ) ) ) )).
fof(t49_subset_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(C,k3_xboole_0(A,B)) => k10_subset_1(C,A) = k10_subset_1(C,B) ) )).
fof(t49_supinf_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v6_supinf_2(A) => ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_xxreal_0(B,C) => k12_supinf_2(A,C) = k1_supinf_2 ) ) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r1_xxreal_0(C,B) & k12_supinf_2(A,C) = k1_supinf_1 ) ) ) ) | v7_supinf_2(A) ) ) ) )).
fof(t49_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)))) ) ) )).
fof(t49_tdlat_3,axiom,( ! [A] : ( ( ~ 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)) ) ) ) )).
fof(t49_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t49_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ~ ( ? [B] : ( ~ v2_struct_0(B) & m1_pre_topc(B,A) & v3_tex_3(B,A) ) & v1_tdlat_3(A) ) ) )).
fof(t49_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t49_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r1_tmap_1(A,B,D,F) & v5_pre_topc(E,B,C) ) => r1_tmap_1(A,C,k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),D,E),F) ) ) ) ) ) ) ) )).
fof(t49_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t49_topgen_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ( A = k3_numbers => k1_tops_1(k3_topmetr,A) = k1_xboole_0 ) ) )).
fof(t49_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_topgen_4(A,B,C) => r1_topgen_1(A,B,C) ) ) ) ) )).
fof(t49_topgen_5,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,k3_topmetr) ) => ! [C] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t49_topgrp_1,axiom,( ! [A] : ( ( ~ 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] : ( ( v3_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => v3_pre_topc(k4_group_2(A,C,B),A) ) ) ) )).
fof(t49_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k2_topreal9(2,k19_euclid(A,B),C) = k7_jgraph_6(A,B,C) ) ) ) )).
fof(t49_toprealc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( ( 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,k14_toprealc(A,u1_struct_0(B),u1_struct_0(k3_topmetr),D)) ) ) ) ) )).
fof(t49_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t49_tops_2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(t49_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_tops_3(B,A) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t49_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) != C ) ) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t49_trees_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ~ ( A != B & r1_tarski(k9_finseq_1(A),k7_finseq_1(k9_finseq_1(B),C)) ) ) ) ) )).
fof(t49_trees_3,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(k3_finseq_1(A),B) => k4_trees_1(k11_trees_3(A),k12_finseq_1(k4_ordinal1,B)) = k1_funct_1(A,k1_nat_1(B,1)) ) ) ) ) ) )).
fof(t49_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_trees_9(A) ) => ~ ( ~ v1_finset_1(A) & ! [B] : ( ( v2_trees_2(B,A) & m1_trees_2(B,A) ) => v1_finset_1(B) ) ) ) )).
fof(t49_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t49_turing_1,axiom,( ! [A] : ( 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] : ( m2_funct_2(B,k4_numbers,u1_turing_1(k18_turing_1),k9_funct_2(k4_numbers,u1_turing_1(k18_turing_1))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( A = k4_domain_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1,k9_funct_2(k4_numbers,u1_turing_1(k18_turing_1)),k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers),C,B) & r2_turing_1(k2_finseq_4(k4_ordinal1,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(k4_ordinal1,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))) ) ) ) ) ) ) )).
fof(t49_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t49_uproots,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & v1_uproots(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_polynom5(A,B,C) <=> r1_xxreal_0(1,k6_uproots(A,C,B)) ) ) ) ) )).
fof(t49_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => k7_finseq_1(A,B) = k2_xboole_0(A,k61_valued_1(B,k3_finseq_1(A))) ) ) )).
fof(t49_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( ( 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 ) ) ) ) ) ) )).
fof(t49_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_vectsp_4(D,A,B) => ( r1_struct_0(D,C) <=> k3_vectsp_4(A,B,C,D) = u1_struct_0(D) ) ) ) ) ) )).
fof(t49_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( B = k1_vectsp_5(A,B,C,D) => ( ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & ? [G] : ( m1_subset_1(G,u1_struct_0(B)) & ? [H] : ( m1_subset_1(H,u1_struct_0(B)) & ? [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) ) ) ) ) ) ) )).
fof(t49_vectsp_6,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) )).
fof(t49_vfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ 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] : ( ( 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)) ) ) ) ) )).
fof(t49_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ! [E] : ( ( 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)) ) ) ) ) )).
fof(t49_waybel21,axiom,( ! [A] : ( ( 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] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ( ? [C] : ( 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) ) ) ) )).
fof(t49_waybel23,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( ~ r3_orders_2(A,D,C) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,B) & ~ r3_orders_2(A,E,C) & r3_orders_2(A,E,D) ) ) ) ) ) ) ) ) ) )).
fof(t49_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k10_waybel34(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k10_waybel34(A))) => ! [D] : ( 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))))) ) ) ) ) ) )).
fof(t49_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) & B = k6_waybel_0(A,C) ) ) ) ) )).
fof(t49_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t49_waybel_2,axiom,( ! [A] : ( ( 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),k1_yellow_1(k7_waybel_0(A)),A) & v20_waybel_0(k2_yellow_2(A),k1_yellow_1(k7_waybel_0(A)),A) ) ) ) )).
fof(t49_waybel_4,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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] : ( 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 ) ) ) ) ) ) ) )).
fof(t49_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r3_wellord1(A,B,C) => ! [D] : ~ ( r2_hidden(D,k1_relat_1(A)) & ! [E] : ~ ( r2_hidden(E,k1_relat_1(B)) & k7_relat_1(C,k1_wellord1(A,D)) = k1_wellord1(B,E) ) ) ) ) ) ) )).
fof(t49_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : k3_xboole_0(A,k4_xboole_0(B,C)) = k4_xboole_0(k3_xboole_0(A,B),C) )).
fof(t49_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( 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))) ) ) ) )).
fof(t49_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(A,k5_numbers) = k5_numbers ) )).
fof(t49_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,A) & r1_xxreal_0(k5_numbers,k6_xcmplx_0(A,B)) ) ) ) )).
fof(t49_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( r1_xxreal_0(k4_xxreal_0(A,B),A) => k4_xxreal_0(A,B) = A ) ) ) )).
fof(t49_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(A,C) => ( r1_xxreal_0(B,D) | r1_tarski(k3_xxreal_1(C,D),k4_xxreal_1(A,B)) ) ) ) ) ) ) )).
fof(t49_xxreal_2,axiom,( ! [A] : ( ( v2_membered(A) & ~ v1_xboole_0(A) & v4_xxreal_2(A) ) => ~ ( A != k1_tarski(k2_xxreal_0) & ! [B] : ( m1_subset_1(B,k1_numbers) => ~ r2_hidden(B,A) ) ) ) )).
fof(t49_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,A) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(B,k1_xxreal_3(A,C)) ) ) ) ) ) )).
fof(t49_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & l1_orders_2(B) ) => ! [C] : ( 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))) ) ) ) ) )).
fof(t49_yellow12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v2_pre_topc(D) & l1_pre_topc(D) ) => ! [E] : ( m3_yellow_9(E,k2_borsuk_1(A,C),k2_borsuk_1(B,D)) => ! [F] : ( m3_yellow_9(F,A,B) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t49_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t49_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ! [C] : ( ( r2_yellow_0(A,B) & ! [D] : ( 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) ) ) )).
fof(t49_yellow_2,axiom,( ! [A] : ( ( ~ 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(k1_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))) ) ) )).
fof(t49_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t49_yellow_4,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t49_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_yellow_5(A,B,k12_lattice3(A,B,C)) = k1_yellow_5(A,B,C) ) ) ) )).
fof(t49_yellow_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t49_yellow_9,axiom,( ! [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] : ( m1_yellow_9(B,A) => ( u1_pre_topc(B) = k5_waybel11(A) => v4_waybel11(B) ) ) ) )).
fof(t49_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v10_zf_lang(A) => A = k12_zf_lang(k27_zf_lang(A),k28_zf_lang(A)) ) ) )).
fof(t49_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( 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)) ) ) ) )).
fof(t49_zfmisc_1,axiom,( ! [A] : ! [B] : ( ~ r2_hidden(A,B) => r1_xboole_0(k1_tarski(A),B) ) )).
fof(t49_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_zmodul01(C,A) => ( u1_struct_0(C) = B => v7_zmodul01(B,A) ) ) ) ) )).
fof(t49_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => k4_algstr_0(k31_zmodul02(A),k1_rlvect_2(k31_zmodul02(A),B)) = k24_zmodul02(A,B) ) ) )).
fof(t4_abcmiz_0,axiom,( ! [A] : ! [B] : ( A != B => ! [C] : ( 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) ) ) ) ) )).
fof(t4_abcmiz_1,axiom,( ! [A] : ! [B] : r1_tarski(k7_relset_1(A,A,k6_partfun1(A),B),B) )).
fof(t4_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => ( v1_abcmiz_a(A) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ( v2_abcmiz_1(B,A) <=> r2_hidden(B,k20_abcmiz_1) ) ) ) ) )).
fof(t4_abian,axiom,( ! [A] : ! [B] : ( 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 ) ) )).
fof(t4_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k4_xcmplx_0(k9_complex1(A)),A) & r1_xxreal_0(A,k9_complex1(A)) ) ) )).
fof(t4_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t4_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v8_aff_2(A) => v9_aff_2(A) ) ) )).
fof(t4_aff_3,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v4_aff_2(A) => v3_aff_3(A) ) ) )).
fof(t4_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t4_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => k1_nat_1(A,1) = k2_xboole_0(k1_tarski(k5_numbers),k2_finseq_1(A)) ) )).
fof(t4_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t4_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_analoaf(A,B,C,B,D) => C = D ) ) ) ) ) )).
fof(t4_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect01(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,E) => r2_analoaf(A,C,B,D,E) ) ) ) ) ) ) )).
fof(t4_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_unialg_1(C) & v3_unialg_1(C) & v4_unialg_1(C) & l1_unialg_1(C) ) => ! [D] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t4_algseq_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( k1_algseq_1(A,B) = k1_algseq_1(A,C) & ! [D] : ( 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(k4_ordinal1,u1_struct_0(A),B,C) ) ) ) ) )).
fof(t4_algspec1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t4_algstr_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_0)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_algstr_0)) => A = B ) ) )).
fof(t4_algstr_2,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t4_algstr_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_algstr_3(A) & l1_algstr_3(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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 & F = G ) ) ) ) ) ) ) ) ) ) )).
fof(t4_algstr_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t4_altcat_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k3_zfmisc_1(A,A,A)) & v1_funct_1(B) & v1_partfun1(B,k3_zfmisc_1(A,A,A)) ) => ! [C] : ( ( 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)) ) => ( ! [D] : ! [E] : ! [F] : ( ( r2_hidden(D,A) & r2_hidden(E,A) & r2_hidden(F,A) ) => k1_multop_1(B,D,E,F) = k1_multop_1(C,D,E,F) ) => r6_pboole(k3_zfmisc_1(A,A,A),C,B) ) ) ) )).
fof(t4_altcat_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( r1_pzfmisc1(A,B,C) => ! [E] : ( m2_pboole(E,A,B,C) => ! [F] : ( m2_pboole(F,A,C,D) => m2_pboole(k8_pboole(E,F),A,B,D) ) ) ) ) ) ) )).
fof(t4_altcat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_altcat_3(A,B,B,k8_altcat_1(A,B)) = k8_altcat_1(A,B) ) ) )).
fof(t4_altcat_5,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,u1_struct_0(k7_altcat_1(k1_tarski(k1_xboole_0)))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(k7_altcat_1(k1_tarski(k1_xboole_0)))))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_altcat_1(k1_tarski(k1_xboole_0)))) => ! [D] : ( m1_altcat_5(D,k7_altcat_1(k1_tarski(k1_xboole_0)),C,A,B) => ( r6_pboole(A,D,k7_funcop_1(A,k1_xboole_0)) => ( v2_altcat_5(D,k7_altcat_1(k1_tarski(k1_xboole_0)),A,B,C) & v3_altcat_5(D,k7_altcat_1(k1_tarski(k1_xboole_0)),A,B,C) ) ) ) ) ) )).
fof(t4_ami_2,axiom,( k5_card_3(k4_ordinal1,k4_card_3(k3_relat_1(k3_ami_2,k4_ami_2))) = k4_ordinal1 )).
fof(t4_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(C,u1_struct_0(k1_ami_3)) ) => ( k1_funct_1(k2_extpro_1(k7_card_1(2),k1_ami_3,k4_ami_3(A,B),C),k4_struct_0(k1_ami_3)) = k4_card_1(k5_memstr_0(k7_card_1(2),k1_ami_3,C)) & k1_funct_1(k2_extpro_1(k7_card_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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_ami_3)) ) => ( D != A => k1_funct_1(k2_extpro_1(k7_card_1(2),k1_ami_3,k4_ami_3(A,B),C),D) = k1_funct_1(C,D) ) ) ) ) ) ) )).
fof(t4_ami_4,axiom,( ! [A] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_ami_3)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ( r1_tarski(k1_ami_4,B) => ! [C] : ( v7_ordinal1(C) => ( k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,C)) = 2 => ( k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,k1_nat_1(C,1))) = 3 & k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,k1_nat_1(C,1)),k10_ami_3(k5_numbers)) = k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,C),k10_ami_3(2)) & k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,k1_nat_1(C,1)),k10_ami_3(1)) = k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,C),k10_ami_3(1)) & k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,k1_nat_1(C,1)),k10_ami_3(2)) = k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,C),k10_ami_3(2)) ) ) ) ) ) ) )).
fof(t4_ami_5,axiom,( ! [A] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => r2_hidden(B,k9_xtuple_0(A)) ) ) )).
fof(t4_ami_6,axiom,( ! [A] : ( 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) ) ) )).
fof(t4_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) & v3_funct_2(C,k4_ordinal1,k4_ordinal1) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(k3_funct_2(k4_ordinal1,k4_ordinal1,C,k1_nat_1(D,1)),k3_amistd_1(A,B,k3_funct_2(k4_ordinal1,k4_ordinal1,C,D))) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(k3_funct_2(k4_ordinal1,k4_ordinal1,C,E),k3_amistd_1(A,B,k3_funct_2(k4_ordinal1,k4_ordinal1,C,D))) => r1_xxreal_0(D,E) ) ) ) ) ) ) ) ) )).
fof(t4_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(k4_amistd_1(A))) => ( k2_compos_0(u1_compos_1(k4_amistd_1(A)),B) = k5_numbers => v2_extpro_1(B,A,k4_amistd_1(A)) ) ) ) )).
fof(t4_amistd_2,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ( v2_extpro_1(C,A,B) => v1_xboole_0(k2_amistd_1(A,B,C)) ) ) ) ) )).
fof(t4_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => r1_tarski(k2_amistd_4(A,B,C),k4_amistd_4(A,B,C)) ) ) ) )).
fof(t4_amistd_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_setfam_1(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_compos_1(C)) => ! [E] : ( ( 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)) ) => r6_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)) ) ) ) ) ) )).
fof(t4_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_analmetr(A,B,C,D,E) => r2_analmetr(A,C,B,D,E) ) ) ) ) ) ) )).
fof(t4_analoaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => k1_rlvect_1(A,k5_algstr_0(A,B,C),k6_xcmplx_0(D,E)) = k1_rlvect_1(A,k5_algstr_0(A,C,B),k6_xcmplx_0(E,D)) ) ) ) ) ) )).
fof(t4_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_analmetr(A,C,D) => k1_analort(A,C,D,k4_algstr_0(A,B)) = k4_algstr_0(A,k1_analort(A,C,D,B)) ) ) ) ) ) )).
fof(t4_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_anproj_1(A,B,E) & r1_anproj_1(A,C,F) & r1_anproj_1(A,D,G) & r2_anproj_1(A,B,C,D) ) => r2_anproj_1(A,E,F,G) ) ) ) ) ) ) ) ) )).
fof(t4_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & ? [I] : ( v1_xreal_0(I) & ? [J] : ( v1_xreal_0(J) & 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] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( 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 = k5_numbers & G = k5_numbers & H = k5_numbers & I = k5_numbers ) ) ) ) ) ) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( ~ v9_struct_0(F,A) & ~ v9_struct_0(G,A) & ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t4_aofa_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( ( 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) ) ) ) )).
fof(t4_aofa_a00,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_funcop_1(B) ) => k1_funct_6(k3_relat_1(B,A)) = k3_relat_1(B,k1_funct_6(A)) ) ) )).
fof(t4_aofa_a01,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => ( r2_hidden(D,k1_funct_1(k2_pboole(A,k2_aofa_a00(A,F,B),k2_aofa_a00(A,G,E)),C)) <=> ( ( C = F & D = B ) | ( C = G & D = E ) ) ) ) ) ) )).
fof(t4_aofa_i00,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [E] : ( ( 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] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t4_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(A,k5_numbers) = A ) )).
fof(t4_armstrng,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ( v2_finsub_1(B) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(A),B) => ( r1_armstrng(C,B) => ( C = A | ! [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) ) => r2_hidden(C,D) ) ) ) ) ) ) ) )).
fof(t4_arrow,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,k2_arrow(A)) => ( r1_arrow(D,B,C) | r1_arrow(D,C,B) ) ) ) ) ) )).
fof(t4_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => r2_hidden(k2_arytm_1(A,B),k1_numbers) ) ) )).
fof(t4_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ( ( r1_arytm_2(A,B) & r1_arytm_2(B,A) ) => A = B ) ) ) )).
fof(t4_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ( A = k11_arytm_3 => k8_arytm_2(A,B) = k11_arytm_3 ) ) ) )).
fof(t4_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(A) & v2_comseq_2(B) & r1_asympt_0(A,B) ) => r1_xxreal_0(k1_seq_2(A),k1_seq_2(B)) ) ) ) )).
fof(t4_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) ) ) )).
fof(t4_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t4_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t4_axioms,axiom,( ! [A] : ( v7_ordinal1(A) => A = a_1_0_axioms(A) ) )).
fof(t4_bagorder,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( C = D <=> ( k1_bagorder(A,k5_numbers,k1_nat_1(B,1),C) = k1_bagorder(A,k5_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) ) ) ) ) ) ) )).
fof(t4_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t4_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k1_bcialg_2(A,B,C,k1_nat_1(D,1)) = k1_bcialg_1(A,k1_bcialg_2(A,B,C,D),C) ) ) ) ) )).
fof(t4_bcialg_3,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)))) ) ) ) ) )).
fof(t4_bcialg_4,axiom,( ! [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) ) => ( v19_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_bcialg_1(A,B,C) = k4_struct_0(A) => B = C ) ) ) ) ) )).
fof(t4_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => k1_bcialg_2(B,k4_struct_0(B),C,A) = k4_struct_0(B) ) ) ) )).
fof(t4_bcialg_6,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => k3_bcialg_6(A,1,B) = B ) ) )).
fof(t4_bciideal,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t4_bhsp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t4_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_bhsp_2(B,A) & v1_bhsp_2(C,A) ) => v1_bhsp_2(k3_normsp_1(A,B,C),A) ) ) ) ) )).
fof(t4_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ? [D] : ( v7_ordinal1(D) & ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(D,E) => k1_normsp_1(A,B,E) = k1_normsp_1(A,C,E) ) ) ) => r1_bhsp_3(A,B,C) ) ) ) ) )).
fof(t4_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k1_bhsp_4(A,k5_vfunct_1(k4_ordinal1,A,B)),k5_vfunct_1(k4_ordinal1,A,k1_bhsp_4(A,B))) ) ) )).
fof(t4_bhsp_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B = k4_struct_0(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_bhsp_1(A,B,C) = k5_numbers ) ) ) ) )).
fof(t4_bhsp_6,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( 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] : ( m2_finseq_1(C,u1_struct_0(A)) => ( r1_xxreal_0(1,k3_finseq_1(C)) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ( ( k4_finseq_1(C) = k4_finseq_1(D) & ! [E] : ( v7_ordinal1(E) => ( 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,k9_binop_2) ) ) ) ) ) ) )).
fof(t4_bhsp_7,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_bhsp_5(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( m1_subset_1(C,k1_zfmisc_1(B)) => m1_bhsp_5(C,A) ) ) ) ) )).
fof(t4_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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] : ( ( 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))) ) ) ) ) ) ) )).
fof(t4_binari_2,axiom,( ! [A] : ( ( 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) = k4_xcmplx_0(1) ) ) )).
fof(t4_binari_3,axiom,( ! [A] : ( v7_ordinal1(A) => r2_hidden(k5_euclid(A),k3_finseq_2(k6_margrel1)) ) )).
fof(t4_binari_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(A,C) & r1_xxreal_0(C,B) & A != C & ~ ( r1_xxreal_0(k2_xcmplx_0(A,1),C) & r1_xxreal_0(C,B) ) ) ) ) ) )).
fof(t4_binarith,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k3_xboolean(k4_xboolean(A,B)) = k5_xboolean(k3_xboolean(A),k3_xboolean(B)) ) ) )).
fof(t4_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_algstr_0(A) & v1_algstr_1(A) & v1_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t4_binop_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ( v1_binop_1(B,A) => ( r3_binop_1(A,C,B) <=> ! [D] : ( m1_subset_1(D,A) => k3_binop_1(A,B,C,D) = D ) ) ) ) ) )).
fof(t4_binop_2,axiom,( k4_binop_1(k4_numbers,k20_binop_2) = k5_numbers )).
fof(t4_bintree1,axiom,( v1_bintree1(k2_trees_1(k5_numbers)) )).
fof(t4_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ( A = k3_finseq_2(k7_domain_1(k4_ordinal1,k5_numbers,1)) => k3_trees_1(A) = k1_xboole_0 ) ) )).
fof(t4_boole,axiom,( ! [A] : k4_xboole_0(k1_xboole_0,A) = k1_xboole_0 )).
fof(t4_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t4_boolmark,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => k7_relat_1(k1_funct_4(C,k7_funcop_1(A,B)),A) = k1_tarski(B) ) ) )).
fof(t4_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m2_connsp_2(D,A,C) => ( r1_tarski(B,C) => m2_connsp_2(D,A,B) ) ) ) ) ) )).
fof(t4_borsuk_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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)) ) ) ) )).
fof(t4_borsuk_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t4_borsuk_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(k5_numbers,D) & r1_xxreal_0(D,1) ) => ( r1_xxreal_0(C,A) | r1_xxreal_0(A,k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(1,D),B),k3_xcmplx_0(D,C))) ) ) ) ) ) ) )).
fof(t4_borsuk_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( 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 ) ) )).
fof(t4_borsuk_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_topmetr)) => ( r1_xxreal_0(k7_xcmplx_0(1,2),A) => m1_subset_1(k6_xcmplx_0(k3_xcmplx_0(2,A),1),u1_struct_0(k5_topmetr)) ) ) )).
fof(t4_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_int_1(C) & k3_int_1(k6_xcmplx_0(A,B)) = k2_xcmplx_0(k6_xcmplx_0(k3_int_1(A),k3_int_1(B)),C) & ( C = k5_numbers | C = 1 ) ) ) ) )).
fof(t4_brouwer,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_xreal_0(B) & ~ v3_xxreal_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( 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] : ( 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(k15_euclid(A),C,D),k3_topreal9(A,E,B)) ) ) ) ) ) ) ) )).
fof(t4_bspace,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k2_bspace)) => ( A = k5_numbers | A = 1 ) ) )).
fof(t4_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t4_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t4_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t4_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t4_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t4_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t4_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ( r2_hidden(C,B) => r1_setfam_1(C,k3_bvfunc_2(A,B)) ) ) ) ) )).
fof(t4_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t4_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t4_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t4_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t4_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t4_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) )).
fof(t4_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t4_c0sp1,axiom,( ! [A] : ( ( ~ 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] : ( v1_xreal_0(B) => k1_rlvect_1(A,k4_struct_0(A),B) = k4_struct_0(A) ) ) )).
fof(t4_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_c0sp2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_c0sp2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_c0sp2(A))) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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] : ( v1_xreal_0(H) => ( ( E = B & F = C ) => ( C = k1_rlvect_1(k3_c0sp2(A),B,H) <=> ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k1_numbers,F,I) = k3_xcmplx_0(H,k3_funct_2(u1_struct_0(A),k1_numbers,E,I)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t4_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)),k5_numbers) ) ) ) )).
fof(t4_calcul_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) <=> r1_tarski(k2_calcul_2(A,B),k2_calcul_2(A,C)) ) ) ) ) )).
fof(t4_cantor_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => r1_tarski(B,k2_cantor_1(A,B)) ) )).
fof(t4_card_1,axiom,( ! [A] : ! [B] : ( r2_wellord2(A,B) <=> k1_card_1(A) = k1_card_1(B) ) )).
fof(t4_card_2,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(t4_card_3,axiom,( ! [A] : ! [B] : k2_card_3(k16_funcop_1(A,B)) = k16_funcop_1(A,k2_zfmisc_1(B,k1_tarski(A))) )).
fof(t4_card_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( k2_nat_1(k1_newton(2,A),k1_nat_1(k3_xcmplx_0(2,D),1)) = k2_nat_1(k1_newton(2,B),k1_nat_1(k3_xcmplx_0(2,C),1)) => ( A = B & D = C ) ) ) ) ) ) )).
fof(t4_card_5,axiom,( ! [A] : ( v1_card_1(A) => ~ ( ~ v1_finset_1(A) & ! [B] : ( v3_ordinal1(B) => A != k3_card_1(B) ) ) ) )).
fof(t4_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_card_fil(k1_tarski(A),A) ) )).
fof(t4_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ! [C] : ! [D] : ~ ( ( 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)) ) ) ) )).
fof(t4_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( ~ ( ~ v1_card_lar(B,A) & ! [C] : ( v3_ordinal1(C) => ~ ( r2_hidden(C,A) & r1_tarski(B,C) ) ) ) & ~ ( ? [C] : ( v3_ordinal1(C) & r2_hidden(C,A) & r1_tarski(B,C) ) & v1_card_lar(B,A) ) ) ) ) )).
fof(t4_cardfin2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(k7_xcmplx_0(1,2),k9_complex1(k6_xcmplx_0(A,B))) => A = k1_cardfin2(B) ) ) ) )).
fof(t4_cat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t4_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m3_cat_2(B,A) => ! [C] : ( m1_subset_1(C,u4_struct_0(B)) => m1_subset_1(C,u4_struct_0(A)) ) ) ) )).
fof(t4_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( 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))) ) ) )).
fof(t4_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u4_struct_0(k5_cat_4(A,B))) => ! [D] : ( m1_subset_1(D,u4_struct_0(k5_cat_4(A,B))) => C = D ) ) )).
fof(t4_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m3_cat_2(B,A) => ! [C] : ( m3_cat_2(C,B) => m3_cat_2(C,A) ) ) ) )).
fof(t4_catalan1,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,1) => k1_nat_1(k7_nat_d(A,2),1) = k7_nat_d(A,1) ) ) )).
fof(t4_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => v1_catalan2(k8_funcop_1(k4_ordinal1,A,k5_numbers)) ) )).
fof(t4_catalg_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_catalg_1(C,A) => ( m1_catalg_1(C,B) => A = B ) ) )).
fof(t4_cayldick,axiom,( ! [A] : ! [B] : ( r2_hidden(A,B) => r2_hidden(k5_afinsq_1(A),k4_card_3(k5_afinsq_1(B))) ) )).
fof(t4_cayley,axiom,( k1_cayley(k1_xboole_0) = k1_tarski(k1_xboole_0) )).
fof(t4_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_cc0sp1(k3_cc0sp1(A),k8_cfuncdom(A)) ) )).
fof(t4_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t4_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_ordinal1) & v5_valued_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ( r2_relset_1(k4_ordinal1,k2_numbers,k9_comseq_3(B,k31_valued_1(k4_ordinal1,k2_numbers,A)),k31_valued_1(k4_ordinal1,k2_numbers,k9_comseq_3(B,A))) & r2_relset_1(k4_ordinal1,k1_numbers,k2_valued_0(k1_numbers,B,k55_valued_1(k4_ordinal1,k2_numbers,A)),k55_valued_1(k4_ordinal1,k2_numbers,k9_comseq_3(B,A))) ) ) ) )).
fof(t4_cfdiff_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( ( v3_normsp_1(B,A) & k6_normsp_1(A,B) = k4_struct_0(A) ) => ( v2_comseq_2(k5_normsp_0(A,B)) & k1_seq_2(k5_normsp_0(A,B)) = k5_numbers ) ) & ( ( v2_comseq_2(k5_normsp_0(A,B)) & k1_seq_2(k5_normsp_0(A,B)) = k5_numbers ) => ( v3_normsp_1(B,A) & k6_normsp_1(A,B) = k4_struct_0(A) ) ) ) ) ) )).
fof(t4_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ! [C] : ( m2_funct_2(C,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ! [D] : ( v1_xcmplx_0(D) => ( C = k1_funct_1(k3_cfuncdom(A),k4_tarski(D,B)) <=> ! [E] : ( m1_subset_1(E,A) => k3_funct_2(A,k2_numbers,C,E) = k3_xcmplx_0(D,k3_funct_2(A,k2_numbers,B,E)) ) ) ) ) ) ) )).
fof(t4_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( v1_xcmplx_0(C) => ( k1_relset_1(A,k25_valued_1(A,k2_numbers,B,C)) = k1_relset_1(A,B) & ! [D] : ( 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) = k3_xcmplx_0(C,k7_partfun1(k2_numbers,B,D)) ) ) ) ) ) ) )).
fof(t4_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ( v1_cgames_1(A) & l1_cgames_1(A) ) ) )).
fof(t4_chain_1,axiom,( ! [A] : ! [B] : ~ ( v1_zfmisc_1(A) & ~ v1_zfmisc_1(k2_xboole_0(A,k1_tarski(B))) & ! [C] : A != k1_tarski(C) ) )).
fof(t4_chord,axiom,( ! [A] : ( ( v1_int_1(A) & ~ v1_abian(A) ) => ! [B] : ( ( v1_int_1(B) & ~ v1_abian(B) ) => ( ~ r1_xxreal_0(A,B) => r1_xxreal_0(k2_xcmplx_0(B,2),A) ) ) ) )).
fof(t4_circcmb2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t4_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( 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)) ) ) ) ) ) )).
fof(t4_circcomb,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t4_circled1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t4_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) => ( ! [D] : ( 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] : ( r2_hidden(D,u4_struct_0(k1_circtrm1(A,B,C))) => m2_msaterm(D,A,B) ) ) ) ) ) )).
fof(t4_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_hidden(k1_funct_1(C,D),k1_funct_1(u3_msualg_1(A,B),D)) ) ) ) ) )).
fof(t4_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msafree2(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,k5_msafree2(A,B)),D)) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) & v6_trees_3(F) ) => ! [G] : ( ( 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] : ( m1_subset_1(H,k4_ordinal1) => ( 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) ) ) ) ) ) ) ) ) )).
fof(t4_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ( ( r1_ckspace1(A,D,B,C) & r1_ckspace1(A,E,B,C) & v1_pdiff_7(C,A) ) => r1_ckspace1(A,k3_valued_1(k1_euclid(A),k1_numbers,k1_numbers,D,E),B,C) ) ) ) ) ) ) )).
fof(t4_classes1,axiom,( ! [A] : ! [B] : ( r2_hidden(B,k1_classes1(A)) => r2_hidden(k9_setfam_1(B),k1_classes1(A)) ) )).
fof(t4_classes2,axiom,( ! [A] : ! [B] : ( ( v2_classes1(B) & r2_hidden(A,B) ) => r1_tarski(k1_classes1(A),B) ) )).
fof(t4_clopban1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m2_funct_2(C,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => ! [D] : ( m2_funct_2(D,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t4_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t4_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v9_clvect_1(B,A) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(D,E) & r1_xxreal_0(C,k2_normsp_0(A,k5_algstr_0(A,k1_normsp_0(A,B,E),k1_normsp_0(A,B,D)))) ) ) ) ) ) ) ) )).
fof(t4_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v9_clvect_1(C,A) => v9_clvect_1(k2_clopban3(A,C,B),A) ) ) ) ) )).
fof(t4_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_funcop_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v1_funcop_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( r1_pboole(A,D,k1_funct_6(C)) => k16_pralg_1(A,B,k16_pralg_1(A,C,D)) = k15_pralg_1(k8_pboole(C,B),D) ) ) ) ) )).
fof(t4_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) => ! [D] : ( 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))) ) ) ) )).
fof(t4_closure3,axiom,( ! [A] : ! [B] : ! [C] : ( ( r2_setfam_1(B,A) & r2_setfam_1(C,B) ) => r2_setfam_1(C,A) ) )).
fof(t4_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B = k4_algstr_0(A,B) => B = k4_struct_0(A) ) ) ) )).
fof(t4_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_clvect_2(B,A) & v1_clvect_2(C,A) ) => v1_clvect_2(k3_normsp_1(A,B,C),A) ) ) ) ) )).
fof(t4_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k1_bhsp_4(A,k5_vfunct_1(k4_ordinal1,A,B)) = k5_vfunct_1(k4_ordinal1,A,k1_bhsp_4(A,B)) ) ) )).
fof(t4_coh_sp,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ( r2_hidden(A,k3_tarski(B)) => r2_hidden(k1_tarski(A),B) ) ) )).
fof(t4_cohsp_1,axiom,( k1_coh_sp(k1_tarski(k1_xboole_0)) = k1_xboole_0 )).
fof(t4_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t4_combgras,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(t4_commacat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k3_cat_1(B,A))) => ! [D] : ( 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) ) ) )).
fof(t4_compact1,axiom,( ! [A] : ( l1_pre_topc(A) => r1_tarski(k2_struct_0(A),k2_struct_0(k1_compact1(A))) ) )).
fof(t4_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & v1_compl_sp(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ( ( v2_prob_1(B) & k1_seq_2(k1_compl_sp(A,B)) = k5_numbers ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ! [D] : ( v7_ordinal1(D) => r2_hidden(k2_tbsp_1(A,C,D),k9_nat_1(k9_setfam_1(u1_struct_0(A)),B,D)) ) => v3_tbsp_1(C,A) ) ) ) ) ) )).
fof(t4_complex1,axiom,( k3_complex1(k5_numbers) = k5_numbers & k4_complex1(k5_numbers) = k5_numbers )).
fof(t4_complex2,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_funct_1(k16_sin_cos,k6_xcmplx_0(A,k28_sin_cos)) = k4_xcmplx_0(k1_funct_1(k16_sin_cos,A)) & k1_funct_1(k18_sin_cos,k6_xcmplx_0(A,k28_sin_cos)) = k4_xcmplx_0(k1_funct_1(k18_sin_cos,A)) ) ) )).
fof(t4_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( ( A = C & B = D ) => k8_group_1(k1_complfld,A,B) = k3_xcmplx_0(C,D) ) ) ) ) ) )).
fof(t4_complsp1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_complsp1(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k12_seq_4(A))) => ( C = B => ( v1_seq_4(C,A) <=> v3_pre_topc(B,k1_complsp1(A)) ) ) ) ) ) )).
fof(t4_complsp2,axiom,( ! [A] : ( ( 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)) ) )).
fof(t4_compos_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_compos_0(B) & v2_compos_0(B) & v3_compos_0(B) ) => ! [C] : ( 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))) ) ) ) )).
fof(t4_compos_1,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_compos_1)) => k5_xtuple_0(A) = k5_numbers ) )).
fof(t4_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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)) ) ) ) ) )).
fof(t4_comptrig,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(k5_numbers,A) => ( B = k5_numbers | k1_newton(k1_power(B,A),B) = A ) ) ) ) )).
fof(t4_compts_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_compts_1(A) <=> ! [B] : ( 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 ) ) ) ) )).
fof(t4_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ( k1_funct_7(C,A,B) = k1_funct_7(D,A,B) => k2_finseq_3(A,C) = k2_finseq_3(A,D) ) ) ) ) )).
fof(t4_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v9_ordinal1(A) <=> ! [B] : ( m1_subset_1(B,k4_ordinal1) => k9_nat_1(k2_numbers,A,B) != k5_complex1 ) ) ) )).
fof(t4_comseq_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_funct_2(k4_ordinal1,k2_numbers,k2_comseq_2(k4_ordinal1,k25_valued_1(k4_ordinal1,k2_numbers,B,A)),k25_valued_1(k4_ordinal1,k2_numbers,k2_comseq_2(k4_ordinal1,B),k8_complex1(A))) ) ) )).
fof(t4_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(C,D) & r1_xxreal_0(C,E) & r1_xxreal_0(B,k9_complex1(k5_real_1(k9_nat_1(k1_numbers,A,D),k9_nat_1(k1_numbers,A,E)))) ) ) ) ) ) ) ) )).
fof(t4_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u4_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t4_conlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k11_conlat_1(A)))) => ( ~ v4_conlat_1(k16_lattice3(k11_conlat_1(A),B),A) & v6_conlat_1(k16_lattice3(k11_conlat_1(A),B),A) & l2_conlat_1(k16_lattice3(k11_conlat_1(A),B),A) & ~ v4_conlat_1(k15_lattice3(k11_conlat_1(A),B),A) & v6_conlat_1(k15_lattice3(k11_conlat_1(A),B),A) & l2_conlat_1(k15_lattice3(k11_conlat_1(A),B),A) ) ) ) )).
fof(t4_conmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t4_conmetr1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v6_conmetr1(A) => v2_conmetr1(A) ) ) )).
fof(t4_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t4_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( m1_connsp_2(B,A,C) => r2_hidden(C,B) ) ) ) ) )).
fof(t4_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v2_connsp_1(B,A) & k1_connsp_3(A,B) = k1_xboole_0 ) ) ) )).
fof(t4_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_convex1(B,A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(1,C) & ~ r1_tarski(k6_rusub_4(A,k1_convex1(A,B,C),k1_convex1(A,B,k6_xcmplx_0(1,C))),B) ) ) ) ) ) )).
fof(t4_convex2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ( B = a_3_2_convex2(A,C,D) => v1_convex1(B,A) ) ) ) ) ) )).
fof(t4_convex3,axiom,( ! [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) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t4_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => m2_convex4(k2_convex4(A),A,B) ) ) )).
fof(t4_convfun1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k6_numbers))) ) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k12_supinf_2(B,C) != k2_supinf_1 ) => ( v1_convfun1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_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,k6_xcmplx_0(1,E)))),k1_xxreal_3(k4_xxreal_3(E,k12_supinf_2(B,C)),k4_xxreal_3(k6_xcmplx_0(1,E),k12_supinf_2(B,D)))) ) ) ) ) ) ) ) ) )).
fof(t4_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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 ) ) ) ) )).
fof(t4_cqc_sim1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ~ 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)) ) ) )).
fof(t4_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => r2_hidden(k8_cqc_lang(A,C,k8_cqc_lang(A,k6_cqc_lang(A,C),D)),k1_cqc_the1(A,B)) ) ) ) ) )).
fof(t4_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t4_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t4_csspace,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace))) => ! [B] : ( m1_subset_1(B,u1_struct_0(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace))) => ! [C] : ( 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)) ) ) ) )).
fof(t4_csspace2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => r1_xxreal_0(k3_xcmplx_0(2,k9_complex1(k3_xcmplx_0(A,B))),k2_xcmplx_0(k1_square_1(k9_complex1(A)),k1_square_1(k9_complex1(B)))) ) ) )).
fof(t4_csspace3,axiom,( ~ 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) )).
fof(t4_csspace4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,u1_struct_0(k3_csspace4)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k3_csspace4)))) ) => ( v1_csspace3(A,k3_csspace4) => v9_clvect_1(A,k3_csspace4) ) ) )).
fof(t4_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_decomp_1(B,A) <=> B = k2_decomp_1(A,B) ) ) ) )).
fof(t4_descip_1,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t4_diff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k4_diff_1(C,A),B) = k6_xcmplx_0(k1_funct_1(C,B),k1_funct_1(C,k6_xcmplx_0(B,A))) ) ) ) )).
fof(t4_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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 != k5_numbers => k10_diff_1(C,k6_xcmplx_0(B,k3_xcmplx_0(2,A)),k6_xcmplx_0(B,A),B) = k7_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(C,A),2),B),k3_xcmplx_0(2,k1_square_1(A))) ) ) ) ) )).
fof(t4_diff_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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_funct_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,C),F),B),k2_xcmplx_0(A,1)),D) = k2_xcmplx_0(k3_xcmplx_0(C,k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(E,B),k2_xcmplx_0(A,1)),D)),k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(F,B),k2_xcmplx_0(A,1)),D)) ) ) ) ) ) ) )).
fof(t4_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & k6_xcmplx_0(k1_funct_1(k3_taylor_1,A),k1_funct_1(k3_taylor_1,B)) != k1_funct_1(k3_taylor_1,k7_xcmplx_0(A,B)) ) ) ) )).
fof(t4_dilworth,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) ) )).
fof(t4_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_analoaf(A,B,B,C,D) & r2_analoaf(A,C,D,B,B) ) ) ) ) ) )).
fof(t4_dirort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t4_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ( ( r1_dist_1(A,B,C) & r1_dist_1(A,C,D) ) => r1_dist_1(A,B,D) ) ) ) ) ) )).
fof(t4_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) => ! [C] : ( m1_dist_2(C,A,B) => ! [D] : ( m1_dist_2(D,A,B) => r1_dist_1(A,C,D) ) ) ) ) )).
fof(t4_domain_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ( ! [E] : ( r2_hidden(E,A) <=> ? [F] : ( m1_subset_1(F,B) & ? [G] : ( m1_subset_1(G,C) & ? [H] : ( m1_subset_1(H,D) & E = k3_xtuple_0(F,G,H) ) ) ) ) => A = k3_zfmisc_1(B,C,D) ) ) ) ) ) )).
fof(t4_dtconstr,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => k15_trees_3(k9_finseq_1(A)) = k9_finseq_1(k1_funct_1(A,k1_xboole_0)) ) )).
fof(t4_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( r1_tarski(B,k1_setfam_1(A)) <=> ! [C] : ( m1_subset_1(C,A) => r1_tarski(B,C) ) ) ) )).
fof(t4_e_siec,axiom,( 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)) )).
fof(t4_ec_pf_1,axiom,( ! [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] : ( ( ~ 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 ) ) ) )).
fof(t4_ec_pf_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k8_group_1(A,B,E) = k8_group_1(A,C,D) => ( C = k4_struct_0(A) | E = k4_struct_0(A) | k8_group_1(A,B,k11_algstr_0(A,C)) = k8_group_1(A,D,k11_algstr_0(A,E)) ) ) ) ) ) ) ) )).
fof(t4_endalg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_endalg(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_endalg(A))) => ! [D] : ( m2_funct_2(D,u1_struct_0(A),u1_struct_0(A),k1_endalg(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t4_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k2_ens_1(A)) => ? [C] : ( m1_subset_1(C,k1_ens_1(A)) & ? [D] : ( m1_subset_1(D,A) & ? [E] : ( 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))) ) ) ) ) ) )).
fof(t4_entropy1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,1) & ~ r1_xxreal_0(B,1) & r1_xxreal_0(k3_power(A,B),k5_numbers) ) ) ) )).
fof(t4_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_enumset1(A,B,C,D) = k2_xboole_0(k1_tarski(A),k1_enumset1(B,C,D)) )).
fof(t4_eqrel_1,axiom,( ! [A] : ( 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))) ) )).
fof(t4_equation,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r1_pzfmisc1(A,B,C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) & v1_funcop_1(D) ) => ( ( r6_pboole(A,k1_funct_6(D),B) & r2_pboole(A,k2_funct_6(D),C) ) => m2_pboole(D,A,B,C) ) ) ) ) ) )).
fof(t4_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => k12_euclid(k5_euclid(A)) = k5_numbers ) )).
fof(t4_euclid_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => k1_square_1(k12_euclid(A)) = k22_rvsum_1(A,A) ) )).
fof(t4_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( k2_euclid_3(A) = k2_euclid_3(B) => A = B ) ) ) )).
fof(t4_euclid_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(C)) => k9_euclid(C,D,k3_xcmplx_0(A,B)) = k9_euclid(C,k9_euclid(C,D,B),A) ) ) ) ) )).
fof(t4_euclid_5,axiom,( k4_struct_0(k15_euclid(3)) = k4_euclid_5(k5_numbers,k5_numbers,k5_numbers) )).
fof(t4_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( k2_xcmplx_0(k4_euclid_3(A,D,B),k4_euclid_3(B,D,C)) = k4_euclid_3(A,D,C) | k2_xcmplx_0(k4_euclid_3(A,D,B),k4_euclid_3(B,D,C)) = k2_xcmplx_0(k4_euclid_3(A,D,C),k3_xcmplx_0(2,k28_sin_cos)) ) ) ) ) ) )).
fof(t4_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t4_euclid_8,axiom,( k12_euclid(k2_euclid_8) = 1 )).
fof(t4_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) & v3_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) & v3_valued_0(C) ) => ( A != k5_numbers => r2_hidden(k1_euclid_9(A,B,C),k4_finseq_1(B)) ) ) ) ) )).
fof(t4_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t4_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t4_euler_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( 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))) ) ) )).
fof(t4_euler_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_int_2(C,D) & D = k4_nat_d(k3_xcmplx_0(A,B),C) ) => ( r1_xxreal_0(C,1) | r1_int_2(C,B) ) ) ) ) ) ) )).
fof(t4_exchsort,axiom,( ! [A] : k6_subset_1(k1_ordinal1(A),A) = k1_tarski(A) )).
fof(t4_extens_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v2_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( m2_pboole(E,A,B,C) => ! [F] : ( m2_pboole(F,A,C,D) => ! [G] : ( 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)) ) ) ) ) ) ) )).
fof(t4_extpro_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & ~ v1_setfam_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_memstr_0(C,B) & v3_memstr_0(C,B) & l1_extpro_1(C,B) ) => ! [D] : ( ( 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] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(C)) & v1_funct_1(E) ) => ! [F] : ( v7_ordinal1(F) => k5_extpro_1(B,C,E,D,k2_xcmplx_0(A,F)) = k5_extpro_1(B,C,E,k5_extpro_1(B,C,E,D,A),F) ) ) ) ) ) ) )).
fof(t4_extreal1,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ( ~ r1_xxreal_0(k5_numbers,A) => k3_extreal1(A) = k2_supinf_2(A) ) ) )).
fof(t4_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ~ ( A != k5_numbers & r1_xxreal_0(k3_extreal1(A),k5_numbers) ) ) )).
fof(t4_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ 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))) ) ) ) ) )).
fof(t4_facirc_2,axiom,( ! [A] : ! [B] : ( ( ~ 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)) ) ) )).
fof(t4_fcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r1_fcont_1(A,B) <=> ! [C] : ( m1_rcomp_1(C,k1_funct_1(A,B)) => ? [D] : ( m1_rcomp_1(D,B) & ! [E] : ( v1_xreal_0(E) => ( ( r2_hidden(E,k1_relset_1(k1_numbers,A)) & r2_hidden(E,D) ) => r2_hidden(k1_funct_1(A,E),C) ) ) ) ) ) ) ) )).
fof(t4_fcont_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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))) ) ) ) )).
fof(t4_fcont_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r2_hidden(k6_xcmplx_0(B,A),k2_rcomp_1(k4_xcmplx_0(C),C)) => ( ~ r1_xxreal_0(C,k5_numbers) & r2_hidden(B,k2_rcomp_1(k6_xcmplx_0(A,C),k2_xcmplx_0(A,C))) ) ) ) ) ) )).
fof(t4_fdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v2_fdiff_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(t4_fdiff_10,axiom,( ! [A] : ( ( 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,k26_sin_cos,k27_sin_cos))) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),A),B) = k3_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k26_sin_cos,B))))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,B)))) ) ) ) ) ) )).
fof(t4_fdiff_11,axiom,( ! [A] : ( ( 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,k18_sin_cos,k2_sin_cos9))) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k18_sin_cos,B),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(k18_sin_cos,B)) ) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k2_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k2_sin_cos9),A),B) = k7_xcmplx_0(k1_funct_1(k16_sin_cos,B),k2_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,B)))) ) ) ) ) ) )).
fof(t4_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v9_ordinal1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v1_fdiff_1(B,k5_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v3_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( k2_relset_1(k1_numbers,C) = k1_tarski(A) => ( v2_comseq_2(C) & k1_seq_2(C) = A & v2_comseq_2(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C)) & k1_seq_2(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C)) = A ) ) ) ) ) )).
fof(t4_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => ( k1_funct_1(D,E) = k2_xcmplx_0(A,E) & ~ r1_xxreal_0(k1_funct_1(D,E),k5_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] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_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) = k7_xcmplx_0(E,k2_xcmplx_0(A,E)) ) ) ) ) ) ) ) ) )).
fof(t4_fdiff_5,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( ~ r2_hidden(k5_numbers,A) => ( r2_fdiff_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A)),A),B) = k4_xcmplx_0(k7_xcmplx_0(1,k1_square_1(B))) ) ) ) ) ) )).
fof(t4_fdiff_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => ( k1_funct_1(C,E) = k1_square_1(A) & k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,C,D),E) != k5_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] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_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) = k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(4,k1_square_1(A)),E),k1_square_1(k6_xcmplx_0(k1_square_1(A),k1_newton(E,2)))) ) ) ) ) ) ) ) ) )).
fof(t4_fdiff_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,k2_rcomp_1(k4_xcmplx_0(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] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => k1_funct_1(k2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_sin_cos6,A),B),C) = k7_xcmplx_0(A,k3_square_1(k6_xcmplx_0(1,k1_square_1(C)))) ) ) ) ) ) ) )).
fof(t4_fdiff_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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] : ( v1_xreal_0(F) => ( r2_hidden(F,C) => ( k1_funct_1(D,F) = k2_xcmplx_0(F,A) & k1_funct_1(E,F) = k6_xcmplx_0(F,B) ) ) ) ) => ( r2_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,D,E),C) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,C) => k1_funct_1(k2_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,D,E),C),F) = k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(A),B),k1_square_1(k6_xcmplx_0(F,B))) ) ) ) ) ) ) ) ) ) )).
fof(t4_fdiff_9,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_fdiff_9,A),B) = k7_xcmplx_0(k1_funct_1(k16_sin_cos,B),k1_square_1(k1_funct_1(k18_sin_cos,B))) ) ) ) ) ) )).
fof(t4_ff_siec,axiom,( ! [A] : ( 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 ) )).
fof(t4_fib_fusc,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( r1_tarski(k3_fib_fusc,A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( ( v5_memstr_0(F,k7_card_1(2),k1_ami_3,k5_numbers) & m1_scm_1(F,k16_afinsq_1(2,B,D,E)) ) => ( k3_pre_ff(C) = k1_nat_1(k2_nat_1(D,k3_pre_ff(B)),k2_nat_1(E,k3_pre_ff(k1_nat_1(B,1)))) => ( r1_xxreal_0(C,k5_numbers) | ( r1_extpro_1(k7_card_1(2),k1_ami_3,A,F) & k1_funct_1(k6_extpro_1(k7_card_1(2),k1_ami_3,A,F),k10_ami_3(3)) = k3_pre_ff(C) & ( B = k5_numbers => k8_extpro_1(k7_card_1(2),k1_ami_3,A,F) = 1 ) & ( ~ r1_xxreal_0(B,k5_numbers) => k8_extpro_1(k7_card_1(2),k1_ami_3,A,F) = k2_xcmplx_0(k3_xcmplx_0(6,k2_xcmplx_0(k1_int_1(k3_power(2,B)),1)),1) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t4_fib_num2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_xreal_0(A) ) => ! [B] : ( v1_int_1(B) => k2_power(k3_xcmplx_0(k4_xcmplx_0(1),A),B) = k3_xcmplx_0(k2_power(k4_xcmplx_0(1),B),k2_power(A,B)) ) ) )).
fof(t4_fib_num3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => k1_nat_1(k7_nat_d(A,1),2) = k7_nat_d(k1_nat_1(A,2),1) ) )).
fof(t4_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ v1_abian(A) & B != k5_numbers & k2_power(k4_xcmplx_0(B),A) != k4_xcmplx_0(k2_power(B,A)) ) ) ) )).
fof(t4_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r1_xxreal_0(C,D) => r1_xxreal_0(k3_finseq_1(k2_rfinseq(A,D,B)),k3_finseq_1(k2_rfinseq(A,C,B))) ) ) ) ) ) )).
fof(t4_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v9_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t4_filter_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t4_fin_topo,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t4_finance1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => m2_subset_1(k3_rcomp_1(B,A),k1_zfmisc_1(k1_numbers),k12_prob_1) ) ) )).
fof(t4_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => r2_hidden(k1_nat_1(A,1),k2_finseq_1(k1_nat_1(A,1))) ) )).
fof(t4_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => m1_subset_1(k4_xxreal_0(k5_numbers,k6_xcmplx_0(A,B)),k4_ordinal1) ) ) )).
fof(t4_finseq_3,axiom,( k2_finseq_1(6) = k4_enumset1(1,2,3,4,5,6) )).
fof(t4_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => r1_finseq_4(A,B) ) <=> v2_funct_1(A) ) ) )).
fof(t4_finseq_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) <=> ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => k8_relat_1(A,k1_tarski(k1_funct_1(A,B))) = k1_tarski(B) ) ) ) )).
fof(t4_finseq_6,axiom,( ! [A] : ! [B] : ! [C] : k5_relat_1(k11_finseq_1(A,B,C),k2_finseq_1(1)) = k9_finseq_1(A) )).
fof(t4_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t4_finseq_8,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_xxreal_0(B,C) => k2_finseq_8(A,B,C) = k2_finseq_6(A,B,C) ) ) ) ) )).
fof(t4_finseqop,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => k4_funcop_1(B,k1_xboole_0,A) = k1_xboole_0 ) )).
fof(t4_finset_1,axiom,( ! [A] : ! [B] : ( v1_finset_1(A) => v1_finset_1(k6_subset_1(A,B)) ) )).
fof(t4_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t4_finsub_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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) ) ) )).
fof(t4_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t4_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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))) ) ) )).
fof(t4_fintopo5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t4_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v1_fintopo6(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t4_flang_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k3_catalan2(A)) => ! [D] : ( m1_subset_1(D,k3_catalan2(A)) => ( k1_flang_1(A,C,D) = k5_afinsq_1(B) <=> ( ( C = k2_flang_1(A) & D = k5_afinsq_1(B) ) | ( D = k2_flang_1(A) & C = k5_afinsq_1(B) ) ) ) ) ) )).
fof(t4_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => ! [C] : ( 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 ) ) ) )).
fof(t4_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ( k1_flang_3(A,B,C) = k1_xboole_0 <=> ( ~ r1_xxreal_0(C,k5_numbers) & B = k1_xboole_0 ) ) ) ) )).
fof(t4_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t4_fomodel1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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))) ) ) ) )).
fof(t4_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,D) => ! [F] : ( m1_subset_1(F,D) => ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) & v1_fomodel2(G,C,D) ) => ! [H] : ( ( 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(k4_ordinal1,k35_fomodel1(C),D,k9_funct_2(k35_fomodel1(C),D),k7_fomodel2(C,D,E,G),k1_nat_1(A,1)),H) = k1_funct_1(k9_nat_1(k9_funct_2(k35_fomodel1(C),D),k7_fomodel2(C,D,F,G),k2_xcmplx_0(k1_nat_1(A,1),B)),H) ) ) ) ) ) ) ) ) )).
fof(t4_fomodel3,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => r2_funct_2(k35_fomodel1(B),k35_fomodel1(B),k9_fomodel2(B,k35_fomodel1(B),k7_fomodel3(B,A)),k3_fomodel2(k35_fomodel1(B))) ) )).
fof(t4_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C))))) => ! [E] : ( 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) & v4_fomodel4(B,C,D,A) ) => ( ( ~ v7_fomodel4(E,C) & ~ v7_fomodel4(D,C) ) | v4_fomodel4(B,C,E,A) ) ) ) ) ) )).
fof(t4_fraenkel,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ! [D] : ( ( r1_tarski(C,B) & r1_tarski(D,A) ) => ( k1_funct_2(C,D) = k1_xboole_0 | ! [E] : ( m1_subset_1(E,k1_funct_2(C,D)) => ? [F] : ( m2_funct_2(F,B,A,k9_funct_2(B,A)) & k2_partfun1(B,A,F,C) = E ) ) ) ) ) )).
fof(t4_frechet,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t4_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t4_friends1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( ( r2_hidden(A,k4_finseq_1(C)) & B = k7_finseq_1(k1_rfinseq(A,C),k16_finseq_1(A,C)) ) => C = k7_finseq_1(k1_rfinseq(k7_nat_d(k3_finseq_1(B),A),B),k16_finseq_1(k7_nat_d(k3_finseq_1(B),A),B)) ) ) ) ) )).
fof(t4_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k3_fscirc_1(A,B,C),k5_fscirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( 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) ) ) ) ) )).
fof(t4_fscirc_2,axiom,( ! [A] : ! [B] : ! [C] : ( C = k4_tarski(k1_xboole_0,k1_margrel1(k6_margrel1,k4_finseq_2(k5_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(k5_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(k5_numbers,k6_margrel1),k8_margrel1),k1_xboole_0),k8_fscirc_1(A,B,C),k7_circcomb(k5_ordinal1,k6_margrel1,k1_margrel1(k6_margrel1,k4_finseq_2(k5_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) ) ) )).
fof(t4_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t4_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ( v1_fsm_2(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t4_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => ~ ( k1_afinsq_1(B) = 1 & ! [C] : ( m1_subset_1(C,A) => ~ ( k3_flang_1(A,C) = B & C = k1_funct_1(B,k5_numbers) ) ) ) ) ) )).
fof(t4_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( 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))) ) )).
fof(t4_funcop_1,axiom,( ! [A] : k1_funcop_1(k12_funct_3(A)) = k12_funct_3(A) )).
fof(t4_funcsdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( m2_funct_2(C,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [D] : ( v1_xreal_0(D) => ( C = k1_funct_1(k7_funcsdom(A),k4_tarski(D,B)) <=> ! [E] : ( m1_subset_1(E,A) => k3_funct_2(A,k1_numbers,C,E) = k3_xcmplx_0(D,k3_funct_2(A,k1_numbers,B,E)) ) ) ) ) ) ) )).
fof(t4_funct_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t4_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) ) ) )).
fof(t4_funct_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t4_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(B,C) => r1_relset_1(B,k1_tarski(A),k7_funcop_1(B,A),k7_funcop_1(C,A)) ) )).
fof(t4_funct_5,axiom,( ! [A] : ! [B] : ( r1_tarski(k9_xtuple_0(k2_zfmisc_1(A,B)),A) & r1_tarski(k10_xtuple_0(k2_zfmisc_1(A,B)),B) ) )).
fof(t4_funct_6,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t4_funct_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ! [F] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t4_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k7_xcmplx_0(k1_funct_1(B,C),k1_funct_1(B,k4_xcmplx_0(C))) = k4_xcmplx_0(1) ) ) ) => r2_funct_8(A,k1_numbers,k1_numbers,B) ) ) ) )).
fof(t4_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t4_functor0,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t4_functor1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_altcat_2(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & m1_altcat_2(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_altcat_2(C,A) ) => ! [D] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t4_functor2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( m2_functor0(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t4_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t4_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D) & r1_fuzzy_1(D,C) ) => r1_fuzzy_1(D,C) ) ) ) ) ) )).
fof(t4_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D) => r1_fuzzy_1(k1_fuzzy_2(A,B,C),k1_fuzzy_2(A,D,C)) ) ) ) ) ) )).
fof(t4_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ! [E] : ( r1_xxreal_0(k5_numbers,k1_binop_1(C,D,E)) & r1_xxreal_0(k1_binop_1(C,D,E),1) ) ) ) ) )).
fof(t4_fvaluat1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( B != k1_xxreal_0 & ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(k2_extreal1(A,B),k5_numbers) ) ) ) )).
fof(t4_fvsum_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t4_gate_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(k2_gate_1(A,B)) <=> ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) ) ) )).
fof(t4_gate_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ! [Q] : ! [R] : ! [S] : ! [T] : ! [U] : ! [V] : ! [W] : ~ ( ~ ( ~ 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) ) ) ) )).
fof(t4_gate_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ! [Q] : ! [R] : ! [S] : ! [T] : ! [U] : ! [V] : ! [W] : ~ ( ~ ( ~ 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) ) ) ) )).
fof(t4_gate_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ! [Q] : ! [R] : ! [S] : ! [T] : ! [U] : ! [V] : ! [W] : ! [X] : ! [Y] : ! [Z] : ! [A1] : ! [B1] : ! [C1] : ! [D1] : ! [E1] : ! [F1] : ! [G1] : ! [H1] : ! [I1] : ! [J1] : ! [K1] : ! [L1] : ! [M1] : ! [N1] : ! [O1] : ! [P1] : ! [Q1] : ! [R1] : ! [S1] : ! [T1] : ! [U1] : ! [V1] : ! [W1] : ! [X1] : ! [Y1] : ( v1_xboole_0(X1) => ( v1_xboole_0(A) | ( ~ v1_xboole_0(H1) & v1_xboole_0(k4_gate_1(Y1,G1)) ) | ( ~ v1_xboole_0(k4_gate_1(Y1,G1)) & v1_xboole_0(H1) ) | ( ~ v1_xboole_0(I1) & v1_xboole_0(k4_gate_1(R,k2_gate_1(B,H1))) ) | ( ~ v1_xboole_0(k4_gate_1(R,k2_gate_1(B,H1))) & v1_xboole_0(I1) ) | ( ~ v1_xboole_0(J1) & v1_xboole_0(k4_gate_1(S,k2_gate_1(C,H1))) ) | ( ~ v1_xboole_0(k4_gate_1(S,k2_gate_1(C,H1))) & v1_xboole_0(J1) ) | ( ~ v1_xboole_0(K1) & v1_xboole_0(k4_gate_1(T,k2_gate_1(D,H1))) ) | ( ~ v1_xboole_0(k4_gate_1(T,k2_gate_1(D,H1))) & v1_xboole_0(K1) ) | ( ~ v1_xboole_0(L1) & v1_xboole_0(k4_gate_1(U,k2_gate_1(E,H1))) ) | ( ~ v1_xboole_0(k4_gate_1(U,k2_gate_1(E,H1))) & v1_xboole_0(L1) ) | ( ~ v1_xboole_0(M1) & v1_xboole_0(k4_gate_1(V,k2_gate_1(F,H1))) ) | ( ~ v1_xboole_0(k4_gate_1(V,k2_gate_1(F,H1))) & v1_xboole_0(M1) ) | ( ~ v1_xboole_0(N1) & v1_xboole_0(k4_gate_1(W,k2_gate_1(G,H1))) ) | ( ~ v1_xboole_0(k4_gate_1(W,k2_gate_1(G,H1))) & v1_xboole_0(N1) ) | ( ~ v1_xboole_0(O1) & v1_xboole_0(k4_gate_1(X,k2_gate_1(H,H1))) ) | ( ~ v1_xboole_0(k4_gate_1(X,k2_gate_1(H,H1))) & v1_xboole_0(O1) ) | ( ~ v1_xboole_0(P1) & v1_xboole_0(k4_gate_1(Y,k2_gate_1(I,H1))) ) | ( ~ v1_xboole_0(k4_gate_1(Y,k2_gate_1(I,H1))) & v1_xboole_0(P1) ) | ( ~ v1_xboole_0(Q1) & v1_xboole_0(k4_gate_1(Z,k2_gate_1(J,H1))) ) | ( ~ v1_xboole_0(k4_gate_1(Z,k2_gate_1(J,H1))) & v1_xboole_0(Q1) ) | ( ~ v1_xboole_0(R1) & v1_xboole_0(k4_gate_1(A1,k2_gate_1(K,H1))) ) | ( ~ v1_xboole_0(k4_gate_1(A1,k2_gate_1(K,H1))) & v1_xboole_0(R1) ) | ( ~ v1_xboole_0(S1) & v1_xboole_0(k4_gate_1(B1,k2_gate_1(L,H1))) ) | ( ~ v1_xboole_0(k4_gate_1(B1,k2_gate_1(L,H1))) & v1_xboole_0(S1) ) | ( ~ v1_xboole_0(T1) & v1_xboole_0(k4_gate_1(C1,k2_gate_1(M,H1))) ) | ( ~ v1_xboole_0(k4_gate_1(C1,k2_gate_1(M,H1))) & v1_xboole_0(T1) ) | ( ~ v1_xboole_0(U1) & v1_xboole_0(k4_gate_1(D1,k2_gate_1(N,H1))) ) | ( ~ v1_xboole_0(k4_gate_1(D1,k2_gate_1(N,H1))) & v1_xboole_0(U1) ) | ( ~ v1_xboole_0(V1) & v1_xboole_0(k4_gate_1(E1,k2_gate_1(O,H1))) ) | ( ~ v1_xboole_0(k4_gate_1(E1,k2_gate_1(O,H1))) & v1_xboole_0(V1) ) | ( ~ v1_xboole_0(W1) & v1_xboole_0(k4_gate_1(F1,k2_gate_1(P,H1))) ) | ( ~ v1_xboole_0(k4_gate_1(F1,k2_gate_1(P,H1))) & v1_xboole_0(W1) ) | ( ~ ( ~ v1_xboole_0(W1) & v1_xboole_0(k4_gate_1(k4_gate_1(F1,k2_gate_1(P,G1)),k4_gate_1(X1,k2_gate_1(P,Y1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(F1,k2_gate_1(P,G1)),k4_gate_1(X1,k2_gate_1(P,Y1)))) & v1_xboole_0(W1) ) & ~ ( ~ v1_xboole_0(V1) & v1_xboole_0(k4_gate_1(k4_gate_1(E1,k2_gate_1(O,G1)),k4_gate_1(X1,k2_gate_1(O,Y1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(E1,k2_gate_1(O,G1)),k4_gate_1(X1,k2_gate_1(O,Y1)))) & v1_xboole_0(V1) ) & ~ ( ~ v1_xboole_0(U1) & v1_xboole_0(k4_gate_1(k4_gate_1(D1,k2_gate_1(N,G1)),k4_gate_1(X1,k2_gate_1(N,Y1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(D1,k2_gate_1(N,G1)),k4_gate_1(X1,k2_gate_1(N,Y1)))) & v1_xboole_0(U1) ) & ~ ( ~ v1_xboole_0(T1) & v1_xboole_0(k4_gate_1(k4_gate_1(C1,k2_gate_1(M,G1)),k4_gate_1(X1,k2_gate_1(M,Y1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(C1,k2_gate_1(M,G1)),k4_gate_1(X1,k2_gate_1(M,Y1)))) & v1_xboole_0(T1) ) & ~ ( ~ v1_xboole_0(S1) & v1_xboole_0(k4_gate_1(k4_gate_1(B1,k2_gate_1(L,G1)),k4_gate_1(X1,k2_gate_1(L,Y1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(B1,k2_gate_1(L,G1)),k4_gate_1(X1,k2_gate_1(L,Y1)))) & v1_xboole_0(S1) ) & ~ ( ~ v1_xboole_0(R1) & v1_xboole_0(k4_gate_1(k4_gate_1(A1,k2_gate_1(K,G1)),k4_gate_1(X1,k2_gate_1(K,Y1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(A1,k2_gate_1(K,G1)),k4_gate_1(X1,k2_gate_1(K,Y1)))) & v1_xboole_0(R1) ) & ~ ( ~ v1_xboole_0(Q1) & v1_xboole_0(k4_gate_1(k4_gate_1(Z,k2_gate_1(J,G1)),k4_gate_1(X1,k2_gate_1(J,Y1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(Z,k2_gate_1(J,G1)),k4_gate_1(X1,k2_gate_1(J,Y1)))) & v1_xboole_0(Q1) ) & ~ ( ~ v1_xboole_0(P1) & v1_xboole_0(k4_gate_1(k4_gate_1(Y,k2_gate_1(I,G1)),k4_gate_1(X1,k2_gate_1(I,Y1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(Y,k2_gate_1(I,G1)),k4_gate_1(X1,k2_gate_1(I,Y1)))) & v1_xboole_0(P1) ) & ~ ( ~ v1_xboole_0(O1) & v1_xboole_0(k4_gate_1(k4_gate_1(X,k2_gate_1(H,G1)),k4_gate_1(X1,k2_gate_1(H,Y1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(X,k2_gate_1(H,G1)),k4_gate_1(X1,k2_gate_1(H,Y1)))) & v1_xboole_0(O1) ) & ~ ( ~ v1_xboole_0(N1) & v1_xboole_0(k4_gate_1(k4_gate_1(W,k2_gate_1(G,G1)),k4_gate_1(X1,k2_gate_1(G,Y1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(W,k2_gate_1(G,G1)),k4_gate_1(X1,k2_gate_1(G,Y1)))) & v1_xboole_0(N1) ) & ~ ( ~ v1_xboole_0(M1) & v1_xboole_0(k4_gate_1(k4_gate_1(V,k2_gate_1(F,G1)),k4_gate_1(X1,k2_gate_1(F,Y1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(V,k2_gate_1(F,G1)),k4_gate_1(X1,k2_gate_1(F,Y1)))) & v1_xboole_0(M1) ) & ~ ( ~ v1_xboole_0(L1) & v1_xboole_0(k4_gate_1(k4_gate_1(U,k2_gate_1(E,G1)),k4_gate_1(X1,k2_gate_1(E,Y1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(U,k2_gate_1(E,G1)),k4_gate_1(X1,k2_gate_1(E,Y1)))) & v1_xboole_0(L1) ) & ~ ( ~ v1_xboole_0(K1) & v1_xboole_0(k4_gate_1(k4_gate_1(T,k2_gate_1(D,G1)),k4_gate_1(X1,k2_gate_1(D,Y1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(T,k2_gate_1(D,G1)),k4_gate_1(X1,k2_gate_1(D,Y1)))) & v1_xboole_0(K1) ) & ~ ( ~ v1_xboole_0(J1) & v1_xboole_0(k4_gate_1(k4_gate_1(S,k2_gate_1(C,G1)),k4_gate_1(X1,k2_gate_1(C,Y1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(S,k2_gate_1(C,G1)),k4_gate_1(X1,k2_gate_1(C,Y1)))) & v1_xboole_0(J1) ) & ~ ( ~ v1_xboole_0(I1) & v1_xboole_0(k4_gate_1(k4_gate_1(R,k2_gate_1(B,G1)),k4_gate_1(X1,k2_gate_1(B,Y1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(R,k2_gate_1(B,G1)),k4_gate_1(X1,k2_gate_1(B,Y1)))) & v1_xboole_0(I1) ) & ~ ( ~ v1_xboole_0(H1) & v1_xboole_0(k4_gate_1(k4_gate_1(X1,k2_gate_1(A,G1)),k4_gate_1(X1,k2_gate_1(A,Y1)))) ) & ~ ( ~ v1_xboole_0(k4_gate_1(k4_gate_1(X1,k2_gate_1(A,G1)),k4_gate_1(X1,k2_gate_1(A,Y1)))) & v1_xboole_0(H1) ) ) ) ) )).
fof(t4_gate_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ! [Q] : ! [R] : ! [S] : ~ ( ~ ( ~ 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) ) ) ) )).
fof(t4_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & l4_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t4_genealg1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_genealg1(B,A) => ! [C] : ( m1_genealg1(C,A) => k7_genealg1(A,B,C,k5_numbers) = C ) ) ) )).
fof(t4_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(k2_analmetr(A,F,G))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k2_analmetr(A,F,G))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k2_analmetr(A,F,G))) => ! [K] : ( m1_subset_1(K,u1_struct_0(k2_analmetr(A,F,G))) => ( ( H = B & I = D & J = C & K = E ) => ( r2_analoaf(k2_analmetr(A,F,G),H,I,J,K) <=> r1_geomtrap(A,B,D,C,E) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t4_gfacirc1,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( 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(k5_numbers,k5_numbers)) = 1 & k1_funct_1(k4_gfacirc1,k10_finseq_1(k5_numbers,1)) = k5_numbers & k1_funct_1(k4_gfacirc1,k10_finseq_1(1,k5_numbers)) = k5_numbers & k1_funct_1(k4_gfacirc1,k10_finseq_1(1,1)) = 1 ) ) ) )).
fof(t4_gfacirc2,axiom,( ! [A] : ! [B] : ! [C] : ( C = k4_tarski(k1_xboole_0,k1_margrel1(k6_margrel1,k4_finseq_2(k5_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(k5_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(k5_numbers,k6_margrel1),k7_margrel1),k1_xboole_0),k13_gfacirc1(A,B,C),k7_circcomb(k5_ordinal1,k6_margrel1,k1_margrel1(k6_margrel1,k4_finseq_2(k5_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) ) ) )).
fof(t4_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) ) )).
fof(t4_glib_001,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => k3_finseq_1(k15_finseq_1(C)) = k5_card_1(C) ) ) )).
fof(t4_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_002(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( 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) ) ) ) ) )).
fof(t4_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(t4_glib_004,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) => k2_uproots(A,C) = k1_funct_1(C,B) ) ) )).
fof(t4_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( ( 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] : ( 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),k5_numbers)) = k6_domain_1(k6_glib_000(A),C) ) ) ) )).
fof(t4_goboard1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ! [F] : ( ( ~ v3_relat_1(F) & v1_matrix_0(F) & v1_goboard1(F) & v2_goboard1(F) & v3_goboard1(F) & v4_goboard1(F) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( E = k3_matrix_0(u1_struct_0(k15_euclid(2)),F,A,D) & E = k3_matrix_0(u1_struct_0(k15_euclid(2)),F,B,C) & r2_hidden(k4_tarski(A,D),k2_matrix_0(F)) & r2_hidden(k4_tarski(B,C),k2_matrix_0(F)) ) => ( A = B & D = C ) ) ) ) ) ) ) )).
fof(t4_goboard2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ( ( k3_finseq_1(A) = k1_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)) ) ) ) ) )).
fof(t4_goboard4,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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] : ( v7_ordinal1(C) => ~ ( r2_hidden(C,k4_finseq_1(A)) & r2_hidden(k1_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,k1_nat_1(C,1)) ) ) & ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(k1_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,k1_nat_1(C,1)) ) ) & r1_goboard4(k1_goboard1(A),k1_funct_1(k1_goboard1(A),1),k1_funct_1(k1_goboard1(A),k3_finseq_1(A))) & r1_goboard4(k1_goboard1(B),k1_funct_1(k1_goboard1(A),1),k1_funct_1(k1_goboard1(A),k3_finseq_1(A))) & r1_goboard4(k2_goboard1(A),k1_funct_1(k2_goboard1(B),1),k1_funct_1(k2_goboard1(B),k3_finseq_1(B))) & r1_goboard4(k2_goboard1(B),k1_funct_1(k2_goboard1(B),1),k1_funct_1(k2_goboard1(B),k3_finseq_1(B))) & r1_xboole_0(k3_topreal1(2,A),k3_topreal1(2,B)) ) ) ) )).
fof(t4_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ~ ( v3_goboard1(D) & r1_xxreal_0(1,B) & ~ r1_xxreal_0(C,B) & r1_xxreal_0(C,k1_matrix_0(D)) & r1_xxreal_0(1,A) & r1_xxreal_0(A,k3_finseq_1(D)) & r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,A,C)),k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,A,B))) ) ) ) ) ) )).
fof(t4_goboard6,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( v1_xreal_0(D) & ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k8_metric_1(A,B,D),C) ) ) ) ) ) )).
fof(t4_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t4_goboard8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,2),k3_finseq_1(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(k2_goboard2(A))) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,2),k1_matrix_0(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,k1_nat_1(D,1)) ) => ( ( ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,D) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,k1_nat_1(D,2)) ) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,D) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,k1_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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_nat_1(D,1))),k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,k1_nat_1(D,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_nat_1(D,2))),k7_xcmplx_0(1,2))),k3_topreal1(2,A)) ) ) ) ) ) ) ) )).
fof(t4_goboard9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t4_gobrd10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( 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)) ) ) ) ) ) )).
fof(t4_gobrd11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t4_gobrd12,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t4_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_tarski(k9_matrix_0(D),k9_matrix_0(E)) & r2_hidden(k4_tarski(A,C),k2_matrix_0(D)) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(E)) & k3_matrix_0(u1_struct_0(k15_euclid(2)),D,A,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,B,1) ) => C = 1 ) ) ) ) ) ) )).
fof(t4_gobrd14,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_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_0(C),B) | v2_compts_1(k3_goboard5(C,A,B),k15_euclid(2)) ) ) ) ) ) )).
fof(t4_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( ( v1_henmodel(C,A) & m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) ) => ! [D] : ( 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)) ) ) ) ) ) ) ) )).
fof(t4_gr_cy_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t4_gr_cy_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(t4_gr_cy_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_gr_cy_3(A) ) => ( A != 7 => k4_nat_d(A,3) = 2 ) ) )).
fof(t4_graph_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m2_graph_1(C,B) => m2_graph_1(k2_partfun1(k4_ordinal1,u4_struct_0(B),C,k2_finseq_1(A)),B) ) ) ) )).
fof(t4_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( r2_hidden(B,u4_struct_0(A)) => ( v2_funct_1(k9_finseq_1(B)) & m2_graph_1(k9_finseq_1(B),A) ) ) ) )).
fof(t4_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( ( v7_graph_1(C,A) & m2_graph_1(C,A) ) => ( r3_graph_4(A,B,C) => r1_graph_2(A,B,C) ) ) ) ) )).
fof(t4_graph_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r1_xxreal_0(1,B) & ~ r1_xxreal_0(C,B) & r1_xxreal_0(C,k3_finseq_1(A)) & k1_funct_1(A,B) = k1_funct_1(A,C) ) ) ) <=> v2_funct_1(A) ) ) )).
fof(t4_graphsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u4_struct_0(A)) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t4_grcat_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_0)) => A = k1_xboole_0 ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_0)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_algstr_0)) => k3_rlvect_1(k3_algstr_0,A,B) = k1_xboole_0 ) ) & ! [A] : ( 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 )).
fof(t4_grfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r2_hidden(k4_tarski(A,B),k3_relat_1(C,D)) => ( r2_hidden(k4_tarski(A,k1_funct_1(C,A)),C) & r2_hidden(k4_tarski(k1_funct_1(C,A),B),D) ) ) ) ) )).
fof(t4_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t4_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( r1_tarski(D,E) => r1_relset_1(k8_struct_0(k12_polynom1(A,C)),u1_struct_0(k12_polynom1(A,C)),k3_polyred(A,B,C,D),k3_polyred(A,B,C,E)) ) ) ) ) ) ) )).
fof(t4_groeb_2,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t4_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(t4_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ! [C] : ( 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) ) ) ) )).
fof(t4_group_10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t4_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t4_group_12,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_group_7(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k1_group_7(A,B,C))) => ( D = k1_funct_7(k1_group_1(k2_group_7(A,B)),C,E) => k2_group_1(k2_group_7(A,B),D) = k1_funct_7(k1_group_1(k2_group_7(A,B)),C,k2_group_1(k1_group_7(A,B,C),E)) ) ) ) ) ) ) )).
fof(t4_group_14,axiom,( ! [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) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k20_prvect_1(k10_finseq_1(A,B)))) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & C = k10_finseq_1(D,E) ) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(k20_prvect_1(k10_finseq_1(A,B)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k20_prvect_1(k10_finseq_1(A,B)))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ( ( C = k10_finseq_1(E,G) & D = k10_finseq_1(F,H) ) => k3_rlvect_1(k20_prvect_1(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(k20_prvect_1(k10_finseq_1(A,B))) = k10_finseq_1(k4_struct_0(A),k4_struct_0(B)) & ! [C] : ( m1_subset_1(C,u1_struct_0(k20_prvect_1(k10_finseq_1(A,B)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( C = k10_finseq_1(D,E) => k4_algstr_0(k20_prvect_1(k10_finseq_1(A,B)),C) = k10_finseq_1(k4_algstr_0(A,D),k4_algstr_0(B,E)) ) ) ) ) ) ) ) )).
fof(t4_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t4_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t4_group_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_group_2(D,B) => ( r1_struct_0(D,C) => r1_struct_0(D,k5_group_1(B,A,C)) ) ) ) ) ) )).
fof(t4_group_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_group_2(C,B) => ! [D] : ( m1_group_2(D,B) => ( r2_hidden(A,k7_group_4(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & ? [F] : ( 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) ) ) ) ) ) ) )).
fof(t4_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t4_group_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( C = D => ! [E] : ( v1_int_1(E) => k5_group_1(B,E,C) = k5_group_1(A,E,D) ) ) ) ) ) ) )).
fof(t4_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => k1_group_1(B) = k1_group_1(C) ) ) )).
fof(t4_groupp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t4_grsolv_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ! [C] : ( ( v15_algstr_0(C) & m1_group_2(C,A) ) => ! [D] : ( ( v15_algstr_0(D) & v1_group_3(D,C) & m1_group_6(D,A,C) ) => ! [E] : ( ( v15_algstr_0(E) & m1_group_2(E,A) ) => ( r1_group_2(A,E,k10_group_2(A,C,B)) => ! [F] : ( ( v1_group_3(F,E) & m1_group_6(F,A,E) ) => ~ ( F = k10_group_2(A,D,B) & ! [G] : ( m1_group_2(G,k5_group_6(C,D)) => ~ r1_group_6(k5_group_6(E,F),G) ) ) ) ) ) ) ) ) ) )).
fof(t4_hahnban,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ( r1_rlsub_2(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t4_hahnban1,axiom,( 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) )).
fof(t4_hallmar1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ! [C] : ! [D] : ( r1_tarski(C,D) => r1_tarski(k1_hallmar1(A,B,C),k1_hallmar1(A,B,D)) ) ) ) )).
fof(t4_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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(k5_numbers,D) ) ) ) ) ) )).
fof(t4_heine,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => v1_compts_1(k4_topmetr(A,B)) ) ) ) )).
fof(t4_helly,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t4_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t4_hermitan,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => k3_xcmplx_0(A,k8_complex1(A)) = k2_xcmplx_0(k1_square_1(k9_complex1(A)),k3_xcmplx_0(k5_numbers,k7_complex1)) ) )).
fof(t4_hessenbe,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_collsp(A,B,C,D) ) ) ) ) ) )).
fof(t4_heyting1,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A)) => ! [C] : ( r1_tarski(C,B) => r2_hidden(C,k8_normform(A)) ) ) )).
fof(t4_heyting2,axiom,( ! [A] : ! [B] : ! [C] : ( m2_subset_1(C,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B)) => ! [D] : ( 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] : ~ ( r2_hidden(E,C) & ! [F] : ~ ( r2_hidden(F,D) & r1_tarski(F,E) ) ) ) ) ) )).
fof(t4_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_domain_1(k4_ordinal1,A)))) ) => ~ ! [C] : ( ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) ) => r2_hidden(k1_domain_1(k4_ordinal1,k4_ordinal1,k1_nat_1(k2_nat_1(2,C),1),A),B) ) ) ) )).
fof(t4_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => 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)),k3_xcmplx_0(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)) ) ) ) )).
fof(t4_hilbasis,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t4_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => r2_hidden(k3_hilbert1(B,k3_hilbert1(C,B)),k5_hilbert1(A)) ) ) ) )).
fof(t4_hilbert2,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ~ ( B != k1_xboole_0 & ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m1_subset_1(D,A) => B != k7_finseq_1(C,k9_finseq_1(D)) ) ) ) ) )).
fof(t4_hilbert3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) )).
fof(t4_holder_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( k2_xcmplx_0(k7_xcmplx_0(1,C),k7_xcmplx_0(1,D)) = 1 => ( r1_xxreal_0(C,1) | r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(B,k5_numbers) | ( r1_xxreal_0(k3_xcmplx_0(A,B),k2_xcmplx_0(k7_xcmplx_0(k6_prepower(A,C),C),k7_xcmplx_0(k6_prepower(B,D),D))) & ( k3_xcmplx_0(A,B) = k2_xcmplx_0(k7_xcmplx_0(k6_prepower(A,C),C),k7_xcmplx_0(k6_prepower(B,D),D)) => k6_prepower(A,C) = k6_prepower(B,D) ) & ( k6_prepower(A,C) = k6_prepower(B,D) => k3_xcmplx_0(A,B) = k2_xcmplx_0(k7_xcmplx_0(k6_prepower(A,C),C),k7_xcmplx_0(k6_prepower(B,D),D)) ) ) ) ) ) ) ) ) )).
fof(t4_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v4_aff_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( B != C & B != D & r1_aff_1(A,B,C,D) & ! [E] : ( ( 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 ) ) ) ) ) ) ) ) )).
fof(t4_hurwitz,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k4_ordinal1) => ( k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k4_group_1(A),k4_algstr_0(A,k1_group_1(A)),k2_nat_1(2,B)) = k1_group_1(A) & k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k4_group_1(A),k4_algstr_0(A,k1_group_1(A)),k1_nat_1(k2_nat_1(2,B),1)) = k4_algstr_0(A,k1_group_1(A)) ) ) ) )).
fof(t4_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => r1_xxreal_0(k6_xcmplx_0(B,A),C) ) ) ) ) )).
fof(t4_ideal_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t4_incproj,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_incproj(B,A) <=> m1_subset_1(B,u2_incsp_1(k3_incproj(A))) ) ) )).
fof(t4_incsp_1,axiom,( ! [A] : ( l2_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t4_index_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( m3_index_1(E,A,B,C,D) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(t4_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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] : ( m1_subset_1(D,u4_struct_0(A)) => k5_msualg_1(A,D,B) = k5_msualg_1(A,D,C) ) ) ) ) ) )).
fof(t4_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( v1_int_1(A) => ( v1_int_1(k2_xcmplx_0(A,1)) & v1_int_1(k6_xcmplx_0(A,1)) ) ) ) )).
fof(t4_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( ( A = k5_numbers | B = k5_numbers ) <=> k2_int_2(A,B) = k5_numbers ) ) ) )).
fof(t4_int_4,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( v1_xreal_0(B) => ( ( B = k5_numbers => ( v1_xboole_0(A) | k1_integra2(A,B) = k1_tarski(k5_numbers) ) ) & ~ ( k1_integra2(A,B) = k1_tarski(k5_numbers) & B != k5_numbers & A != k1_tarski(k5_numbers) ) ) ) ) )).
fof(t4_int_5,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ( k3_finseq_1(A) = 1 => ! [B] : ( m1_subset_1(B,k4_numbers) => k3_funct_2(k4_numbers,k4_numbers,k1_int_5(A),B) = k1_funct_1(A,1) ) ) ) )).
fof(t4_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t4_int_7,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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) ) => ( ( k22_pre_poly(A,B) = k1_xboole_0 & k22_pre_poly(A,C) = k1_xboole_0 ) => r6_pboole(A,B,C) ) ) ) )).
fof(t4_integr10,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( 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) = k2_xcmplx_0(k1_integr10(A,C,D),k1_integr10(B,C,D)) ) ) ) ) ) ) ) )).
fof(t4_integr11,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( r2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(k2_xcmplx_0(A,1))),k4_xcmplx_0(k7_xcmplx_0(1,k2_xcmplx_0(A,1)))),k1_numbers) & ! [B] : ( v1_xreal_0(B) => k1_funct_1(k2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(k2_xcmplx_0(A,1))),k4_xcmplx_0(k7_xcmplx_0(1,k2_xcmplx_0(A,1)))),k1_numbers),B) = k3_xcmplx_0(k3_prepower(k1_funct_1(k18_sin_cos,B),A),k1_funct_1(k16_sin_cos,B)) ) ) ) )).
fof(t4_integr12,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,D) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => ( ~ r1_xxreal_0(1,k1_funct_1(k22_sin_cos,E)) & k1_funct_1(C,E) = 1 ) ) ) & r1_tarski(D,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k2_sin_cos9))) & D = k1_relset_1(k1_numbers,B) & r2_relset_1(k1_numbers,k1_numbers,B,k3_rfunct_1(k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k22_sin_cos),k3_valued_1(k1_numbers,k1_numbers,k1_numbers,C,k41_valued_1(k1_numbers,k1_numbers,k22_sin_cos)))) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k2_sin_cos9),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k2_sin_cos9),k3_seq_4(A))) ) ) ) ) ) )).
fof(t4_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k22_sin_cos,k18_sin_cos),2)) & r1_tarski(C,k1_relset_1(k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)),k3_seq_4(A))) ) ) ) ) )).
fof(t4_integr14,axiom,( ! [A] : ( ( 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,k22_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,k22_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k22_sin_cos)),A),B) = k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k22_sin_cos,k1_funct_1(k2_fdiff_9,B)),k1_funct_1(k18_sin_cos,B)),k1_square_1(k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t4_integr15,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => ! [C] : ( m1_integra1(C,A) => ! [D] : ( v1_xreal_0(D) => ~ ( v1_seq_2(k2_partfun1(A,k1_numbers,B,A)) & ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( m1_integr15(E,A,B,C) => ~ r1_xxreal_0(k6_xcmplx_0(k6_integra1(A,B,C),D),k1_integr15(A,B,C,E)) ) ) ) ) ) ) )).
fof(t4_integr16,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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] : ( m1_integra1(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t4_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t4_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ( ( r1_xxreal_0(B,D) & r1_xxreal_0(D,E) & r1_xxreal_0(E,C) & r1_tarski(k3_integra5(B,C),k1_relset_1(k1_numbers,F)) & r1_tarski(k3_integra5(B,C),k1_relset_1(k1_numbers,G)) ) => r1_tarski(k3_integra5(D,E),k1_relset_1(k1_numbers,k7_integr15(A,k1_numbers,F,G))) ) ) ) ) ) ) ) ) )).
fof(t4_integra1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( m1_integra1(C,B) => ( r2_hidden(A,k4_finseq_1(C)) => r2_hidden(k1_funct_1(C,A),B) ) ) ) ) )).
fof(t4_integra2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( 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,k1_nat_1(D,1),E)) = k3_finseq_6(A,B,C,E) ) ) ) ) ) ) ) )).
fof(t4_integra3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [C] : ( m1_integra1(C,A) => ? [D] : ( 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)) ) ) ) ) )).
fof(t4_integra4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => ! [C] : ( v1_xreal_0(C) => ( k1_rvsum_1(B) = k1_seq_4(C) => ( v3_integra1(B,A) & k12_integra1(A,B) = k3_xcmplx_0(C,k3_integra1(A)) ) ) ) ) ) )).
fof(t4_integra5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t4_integra6,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) )).
fof(t4_integra7,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( r2_hidden(C,A) & r1_fdiff_1(k2_partfun1(k1_numbers,k1_numbers,B,A),C) ) => r1_fdiff_1(B,C) ) ) ) )).
fof(t4_integra8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k19_sin_cos(k2_xcmplx_0(A,k3_xcmplx_0(k1_nat_1(k2_nat_1(2,B),1),k28_sin_cos))) = k4_xcmplx_0(k19_sin_cos(A)) ) ) )).
fof(t4_integra9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( A != k5_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,k5_numbers),k18_sin_cos),k4_xcmplx_0(k7_xcmplx_0(1,A))),k1_numbers) & ! [B] : ( v1_xreal_0(B) => k1_funct_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,k5_numbers),k18_sin_cos),k4_xcmplx_0(k7_xcmplx_0(1,A))),k1_numbers),B) = k17_sin_cos(k3_xcmplx_0(A,B)) ) ) ) ) )).
fof(t4_interva1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ~ ( k1_interva1(A,B,C) = k1_xboole_0 & r1_tarski(B,C) ) ) ) )).
fof(t4_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => r2_hidden(k3_intpro_1(k4_intpro_1(B,C),C),k7_intpro_1(A)) ) ) ) )).
fof(t4_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,k5_numbers) => k2_power(B,k4_xcmplx_0(k1_nat_1(A,1))) = k7_xcmplx_0(k2_power(B,k4_xcmplx_0(A)),B) ) ) ) )).
fof(t4_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ( r1_nattra_1(A,B,C,D) => ! [E] : ( m1_nattra_1(E,A,B,C,D) => ( v1_nattra_1(E,A,B,C,D) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => r1_cat_1(B,k8_cat_1(A,B,C,F),k8_cat_1(A,B,D,F)) ) ) ) ) ) ) ) ) )).
fof(t4_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => k1_cat_1(A,k4_cat_1(A,k3_graph_1(A,B)),B) = B ) ) )).
fof(t4_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) => v2_isomichi(B,A) ) ) ) )).
fof(t4_jct_misc,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(A,B)))) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(k2_borsuk_1(A,B))) => ~ ( r2_hidden(D,C) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ! [F] : ( 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)) ) ) ) ) )).
fof(t4_jgraph_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => m2_finseq_1(k2_jgraph_1(B),u4_struct_0(k1_jgraph_1(A))) ) ) )).
fof(t4_jgraph_2,axiom,( k22_euclid(2) = k10_finseq_1(1,1) )).
fof(t4_jgraph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( v5_pre_topc(B,A,k3_topmetr) & v5_pre_topc(C,A,k3_topmetr) & E != k5_numbers & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,F) != k5_numbers ) & ! [F] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( v1_xreal_0(H) => ! [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) = k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(H,I),D),E) ) ) ) ) & v5_pre_topc(F,A,k3_topmetr) ) ) ) ) ) ) ) ) )).
fof(t4_jgraph_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_topmetr))) => ( ( r1_xxreal_0(k5_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) ) ) ) ) )).
fof(t4_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_topmetr))) => ( C = k1_rcomp_1(A,B) => v4_pre_topc(C,k5_topmetr) ) ) ) ) )).
fof(t4_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t4_jgraph_8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( m1_borsuk_2(G,k15_euclid(2),C,D) => ! [H] : ( 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] : ( 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] : ( 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] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t4_jordan,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( ( 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)) ) ) )).
fof(t4_jordan1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t4_jordan10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(k2_jordan9(E,D))) & r2_hidden(k4_tarski(A,B),k2_matrix_0(k1_jordan8(E,D))) & r2_hidden(k4_tarski(k1_nat_1(A,1),B),k2_matrix_0(k1_jordan8(E,D))) & k7_partfun1(u1_struct_0(k15_euclid(2)),k2_jordan9(E,D),C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,D),k1_nat_1(A,1),B) & k7_partfun1(u1_struct_0(k15_euclid(2)),k2_jordan9(E,D),k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,D),A,B) & r1_xxreal_0(k1_matrix_0(k1_jordan8(E,D)),B) ) ) ) ) ) ) )).
fof(t4_jordan11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_jordan1h(B,A) => k3_jordan1h(B,A) = k2_xcmplx_0(k3_xcmplx_0(k11_newton(2,k7_nat_d(A,k3_jordan11(B))),k6_xcmplx_0(k3_jordan1h(B,k3_jordan11(B)),2)),2) ) ) ) )).
fof(t4_jordan12,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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) ) ) ) ) )).
fof(t4_jordan14,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(A)) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k1_matrix_0(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_0(u1_struct_0(k15_euclid(2)),A,C,D))) & ~ r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),A,k1_nat_1(C,1),D)),k17_euclid(B)) & ~ r1_xxreal_0(k18_euclid(B),k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),A,C,D))) & ~ r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),A,C,k1_nat_1(D,1))),k18_euclid(B)) ) ) ) ) ) ) ) )).
fof(t4_jordan15,axiom,( ! [A] : ( ( 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)) ) )).
fof(t4_jordan16,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( r2_hidden(D,A) => r2_hidden(D,k4_jordan6(A,B,C,D)) ) ) ) ) ) )).
fof(t4_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r1_jordan6(A,k22_pscomp_1(A),B) => r2_hidden(B,k9_jordan6(A)) ) ) ) )).
fof(t4_jordan18,axiom,( ! [A] : ( 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))) ) )).
fof(t4_jordan19,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,k5_numbers) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( 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_0(k1_jordan8(A,B))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),C,D),k3_topreal1(2,k2_jordan9(A,B))) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),C,k1_matrix_0(k1_jordan8(A,B))),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),C,D)),k8_jordan6(k3_topreal1(2,k2_jordan9(A,B)))) ) ) ) ) ) ) )).
fof(t4_jordan1b,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t4_jordan1c,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t4_jordan1e,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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))) ) ) ) )).
fof(t4_jordan1g,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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)) ) ) )).
fof(t4_jordan1h,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r2_hidden(k4_tarski(A,B),k1_jordan1h) => r1_xxreal_0(A,B) ) ) ) )).
fof(t4_jordan1i,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(t4_jordan1j,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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)),k2_jordan9(B,A),k22_pscomp_1(k3_topreal1(2,k2_jordan9(B,A)))),k18_pscomp_1(k3_topreal1(2,k2_jordan9(B,A)))) ) ) )).
fof(t4_jordan1k,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( 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))) ) ) ) ) )).
fof(t4_jordan20,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v1_xreal_0(D) => ~ ( 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)) ) ) ) ) ) )).
fof(t4_jordan22,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( v2_compts_1(k2_kurato_2(k15_euclid(2),k2_jordan19(A),B),k15_euclid(2)) & v2_connsp_1(k2_kurato_2(k15_euclid(2),k2_jordan19(A),B),k15_euclid(2)) ) ) ) )).
fof(t4_jordan23,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ( v1_jordan23(B) <=> ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( 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 ) ) ) ) ) ) )).
fof(t4_jordan2b,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( 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)) ) ) ) ) )).
fof(t4_jordan2c,axiom,( ! [A] : ( v1_xreal_0(A) => k12_euclid(k1_jordan2b(A)) = k9_complex1(A) ) )).
fof(t4_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( r1_xxreal_0(2,B) & v4_topreal1(A) ) => v4_topreal1(k17_finseq_1(u1_struct_0(k15_euclid(2)),B,A)) ) ) ) )).
fof(t4_jordan4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(B,A) & k4_nat_d(B,A) = k5_numbers ) => ( r1_xxreal_0(B,k5_numbers) | B = A ) ) ) ) )).
fof(t4_jordan5a,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_borsuk_2(C,k15_euclid(2),A,B) => ! [D] : ( ( ~ v2_struct_0(D) & v1_compts_1(D) & m1_pre_topc(D,k15_euclid(2)) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t4_jordan5b,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,u1_struct_0(k17_borsuk_1)) => r2_hidden(k6_xcmplx_0(1,A),u1_struct_0(k17_borsuk_1)) ) ) )).
fof(t4_jordan5c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( ( 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] : ( v1_xreal_0(G) => ( ( 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,k5_numbers) = C & k1_funct_1(F,1) = D & r1_xxreal_0(k5_numbers,G) & r1_xxreal_0(G,1) & ! [H] : ( v1_xreal_0(H) => ~ ( r1_xxreal_0(H,1) & ~ r1_xxreal_0(H,G) & r2_hidden(k1_funct_1(F,H),B) ) ) ) => ! [H] : ( ( 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] : ( v1_xreal_0(I) => ( ( v3_tops_2(H,k5_topmetr,k1_pre_topc(k15_euclid(2),A)) & k1_funct_1(H,k5_numbers) = C & k1_funct_1(H,1) = D & k1_funct_1(H,I) = E & r1_xxreal_0(k5_numbers,I) & r1_xxreal_0(I,1) ) => ! [J] : ( v1_xreal_0(J) => ~ ( r1_xxreal_0(J,1) & ~ r1_xxreal_0(J,I) & r2_hidden(k1_funct_1(H,J),B) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t4_jordan5d,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( r2_hidden(A,k10_xtuple_0(B)) => ( r1_xxreal_0(k1_funct_1(k26_seq_4(B),1),A) & r1_xxreal_0(A,k1_funct_1(k26_seq_4(B),k3_finseq_1(k26_seq_4(B)))) ) ) ) ) )).
fof(t4_jordan6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t4_jordan7,axiom,( ! [A] : ( ( ~ 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) ) ) ) )).
fof(t4_jordan9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ~ ( r2_hidden(A,k4_finseq_1(k4_finseq_5(B,C))) & ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(D,k4_finseq_1(C)) & k2_xcmplx_0(A,D) = k1_nat_1(k3_finseq_1(C),1) & k7_partfun1(B,k4_finseq_5(B,C),A) = k7_partfun1(B,C,D) ) ) ) ) ) ) )).
fof(t4_jordan_a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(k15_euclid(A))) => ? [G] : ( 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) = k3_seq_4(G) ) ) => k3_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))) = k3_seq_4(k7_relset_1(u1_struct_0(k15_euclid(A)),k1_numbers,E,C)) ) ) ) ) ) ) )).
fof(t4_knaster,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t4_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( r2_hidden(C,k3_kurato_0(A,B)) <=> ? [D] : ( v7_ordinal1(D) & ! [E] : ( v7_ordinal1(E) => r2_hidden(C,k1_funct_1(B,k2_xcmplx_0(D,E))) ) ) ) ) )).
fof(t4_kurato_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t4_l_hospit,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( ? [C] : ( m1_rcomp_1(C,B) & r1_tarski(k7_subset_1(k1_numbers,C,k1_tarski(B)),k1_relset_1(k1_numbers,A)) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(B,C) & ~ r1_xxreal_0(D,B) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ~ ( ~ 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)) ) ) ) ) ) ) ) ) ) )).
fof(t4_lang1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t4_laplace,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(k3_finseq_1(B),1) => k1_matrix_0(B) = k1_matrix_0(k17_matrix_0(u1_struct_0(A),C,B)) ) ) ) ) )).
fof(t4_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t4_latsum_1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ! [D] : ( ( 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)) ) ) ) )).
fof(t4_lattice2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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,E,C),D) = D ) ) ) ) )).
fof(t4_lattice3,axiom,( ! [A] : ( v14_lattices(k1_lattice3(A)) & k6_lattices(k1_lattice3(A)) = A ) )).
fof(t4_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t4_lattice5,axiom,( ! [A] : ! [B] : ( 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))) ) ) )).
fof(t4_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v2_lattice6(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r3_lattices(A,C,B) & B != C & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r3_lattices(A,C,D) & r1_lattice6(A,B,D) ) ) ) ) ) ) )).
fof(t4_lattice7,axiom,( ! [A] : ( ( 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] : ( ( v6_orders_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t4_lattice8,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(t4_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_lattices(A) & v8_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_lattices(A,k4_lattices(A,B,C),B) ) ) ) )).
fof(t4_lexbfs,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(A,C) => r1_tarski(k2_finsub_1(k1_zfmisc_1(k4_ordinal1),k2_finseq_1(B),k2_finseq_1(k7_nat_d(B,A))),k2_finsub_1(k1_zfmisc_1(k4_ordinal1),k2_finseq_1(B),k2_finseq_1(k7_nat_d(B,C)))) ) ) ) ) )).
fof(t4_lfuzzy_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_lfuzzy_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k13_lattice3(A,B,C) = k2_lfuzzy_0(A,B,C) ) ) ) )).
fof(t4_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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) ) ) )).
fof(t4_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( v2_comseq_2(A) & ~ r1_xxreal_0(k1_seq_2(A),k5_numbers) & ! [B] : ( v7_ordinal1(B) => ? [C] : ( v7_ordinal1(C) & r1_xxreal_0(B,C) & r1_xxreal_0(k1_funct_1(A,C),k5_numbers) ) ) ) ) )).
fof(t4_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r1_tarski(k2_rcomp_1(A,k2_xcmplx_0(A,B)),k1_relset_1(k1_numbers,C)) => ( r1_xxreal_0(B,k5_numbers) | ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(D,E) & ~ r1_xxreal_0(E,A) & r2_hidden(E,k1_relset_1(k1_numbers,C)) ) ) ) ) ) ) ) ) ) )).
fof(t4_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(A,k5_numbers) => k7_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(B,A),k2_xcmplx_0(B,A)),k1_tarski(B)) = k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(B,A),B),k2_rcomp_1(B,k2_xcmplx_0(B,A))) ) ) ) )).
fof(t4_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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)) ) ) ) )).
fof(t4_lmod_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t4_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t4_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ~ ( v1_mod_3(C,A,B) & C = k1_xboole_0 ) ) ) ) ) )).
fof(t4_lopban_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m2_funct_2(C,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => ! [D] : ( m2_funct_2(D,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t4_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t4_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_normsp_1(B,A) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(D,E) & r1_xxreal_0(C,k2_normsp_0(A,k5_algstr_0(A,k5_rsspace3(A,B,E),k5_rsspace3(A,B,D)))) ) ) ) ) ) ) ) )).
fof(t4_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_normsp_1(C,A) => v3_normsp_1(k2_lopban_3(A,C,B),A) ) ) ) ) )).
fof(t4_lopban_5,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => r1_nfcont_1(A,B,C,D) ) ) ) ) ) )).
fof(t4_lopban_6,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t4_lopban_7,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_nfcont_1(A,B,C,D) <=> r1_nfcont_1(A,B,C,k4_struct_0(A)) ) ) ) ) ) )).
fof(t4_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(g3_lattices(k1_lopclset(A),k4_lopclset(A),k5_lopclset(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(g3_lattices(k1_lopclset(A),k4_lopclset(A),k5_lopclset(A)))) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k1_lopclset(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t4_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => v1_rlsub_1(k2_lp_space(A),k6_rsspace) ) ) )).
fof(t4_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_rfunct_3(B,A,k2_numbers,k3_rfunct_3(A,k2_numbers)) => ! [C] : ( m2_rfunct_3(C,A,k2_numbers,k3_rfunct_3(A,k2_numbers)) => ! [D] : ( m2_rfunct_3(D,A,k2_numbers,k3_rfunct_3(A,k2_numbers)) => ( r2_relset_1(A,k2_numbers,D,k2_lpspace1(A,k2_numbers,k9_lpspacc1(A),B,C)) <=> ( k1_relset_1(A,D) = k9_subset_1(A,k1_relset_1(A,B),k1_relset_1(A,C)) & ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,k1_relset_1(A,D)) => k1_funct_1(D,E) = k2_xcmplx_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) ) ) )).
fof(t4_lpspace1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(g1_rlvect_1(B,k10_subset_1(k4_struct_0(A),B),k1_ideal_1(A,B),k1_lpspace1(A,B)))) => ! [F] : ( m1_subset_1(F,u1_struct_0(g1_rlvect_1(B,k10_subset_1(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,k10_subset_1(k4_struct_0(A),B),k1_ideal_1(A,B),k1_lpspace1(A,B)),E,F) = k1_algstr_0(A,C,D) ) ) ) ) ) ) ) )).
fof(t4_lpspace2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k5_numbers,A) => ( r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(k5_numbers,k2_power(A,B)) ) ) ) ) )).
fof(t4_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ~ ( A != k2_hilbert1 & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( A != k1_hilbert2(B) & ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( m1_subset_1(D,k1_hilbert1) => ( A != k3_hilbert1(C,D) & ! [E] : ( m1_subset_1(E,k1_hilbert1) => ! [F] : ( m1_subset_1(F,k1_hilbert1) => A != k4_hilbert1(E,F) ) ) ) ) ) ) ) ) ) )).
fof(t4_ltlaxio2,axiom,( ! [A] : ( ( 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))) ) => k3_funct_2(k1_hilbert1,k6_margrel1,k12_ltlaxio1(A),k3_ltlaxio1) = 1 ) )).
fof(t4_ltlaxio3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) & v1_finseq_1(B) ) => ( r1_xboole_0(k10_xtuple_0(A),k10_xtuple_0(B)) => v2_funct_1(k7_finseq_1(A,B)) ) ) ) )).
fof(t4_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( v1_ltlaxio4(k4_ltlaxio1(k3_ltlaxio1,A)) => v1_ltlaxio4(A) ) ) )).
fof(t4_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => r2_hidden(k8_cqc_lang(A,B,B),k4_cqc_the1(A)) ) ) )).
fof(t4_margrel1,axiom,( ! [A] : m2_margrel1(k1_xboole_0,A) )).
fof(t4_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k1_xboole_0 => k1_mathmorp(A,B,C) = k1_xboole_0 ) ) ) ) )).
fof(t4_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( r2_hidden(k4_tarski(B,C),k2_matrix_0(D)) => k3_matrix_0(k1_numbers,k7_matrixr1(A,D),B,C) = k3_xcmplx_0(A,k3_matrix_0(k1_numbers,D,B,C)) ) ) ) ) ) )).
fof(t4_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_matrix_2(C,k3_matrix_2(k1_nat_1(A,2))) => ! [D] : ( m1_subset_1(D,k5_finsub_1(k2_sgraph1(k2_finseq_1(k1_nat_1(A,2))))) => ( ! [E] : ( 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) ) ) ) ) ) )).
fof(t4_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [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] : ( m1_subset_1(F,u1_struct_0(E)) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(E),B,C) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(E))) ) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(E),B,C) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(E))) ) => ( ( r2_hidden(A,k4_finseq_1(G)) & r2_hidden(D,k4_finseq_1(G)) & H = k2_matrix12(B,C,E,G,A,F) ) => ( ( D = A => k7_matrix_0(u1_struct_0(E),H,D) = k10_fvsum_1(k1_matrix_0(G),E,k7_matrix_0(u1_struct_0(E),G,A),F) ) & ( D != A => k7_matrix_0(u1_struct_0(E),H,D) = k7_matrix_0(u1_struct_0(E),G,D) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t4_matrix14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( 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)) ) ) ) ) ) ) )).
fof(t4_matrix15,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t4_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,B,A,A) & m2_finseq_1(D,k3_finseq_2(B)) ) => ( r1_matrix16(B,D,C) => ( r1_xxreal_0(A,k5_numbers) | C = k7_matrix_0(B,D,1) ) ) ) ) ) ) )).
fof(t4_matrix17,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r1_matrix17(u1_struct_0(B),D,C) => r1_matrix17(u1_struct_0(B),k2_matrix_3(B,D),k5_fvsum_1(B,C)) ) ) ) ) ) )).
fof(t4_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( ( k3_finseq_1(B) = A & k3_finseq_1(C) = A ) => v1_matrix_0(k10_finseq_1(B,C)) ) ) ) ) )).
fof(t4_matrix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => k5_matrix_1(B,A,k5_matrix_1(B,A,C,D),E) = k5_matrix_1(B,A,C,k5_matrix_1(B,A,D,E)) ) ) ) ) ) )).
fof(t4_matrix_2,axiom,( k3_matrix_2(1) = k1_tarski(k1_finseq_2(1)) )).
fof(t4_matrix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => k3_matrix_3(C,D,k1_matrix_3(C,A,B)) = D ) ) ) ) )).
fof(t4_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(D) & k3_matrix_3(A,B,D) = k3_matrix_3(A,C,D) ) => B = C ) ) ) ) ) )).
fof(t4_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k1_complfld))) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k1_complfld))) ) => ( k2_matrix_5(A) = k2_matrix_5(B) => A = B ) ) ) )).
fof(t4_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ( ( 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_3(B,D,E)) ) ) ) ) ) ) )).
fof(t4_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v3_matrix_8(C,A,B) => v1_matrix_6(C,A,B) ) ) ) ) )).
fof(t4_matrix_9,axiom,( ! [A] : ( v7_ordinal1(A) => r2_hidden(k3_finseq_5(k1_finseq_2(A)),k3_matrix_2(A)) ) )).
fof(t4_matrixc1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k2_numbers)) ) => k1_matrixc1(k7_matrix_5(A,B)) = k7_matrix_5(k8_complex1(A),k1_matrixc1(B)) ) ) )).
fof(t4_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t4_matrixj2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( m1_subset_1(D,u1_struct_0(C)) => ( r2_hidden(A,k2_finseq_1(B)) => ( A = B | k7_matrix_0(u1_struct_0(C),k2_matrixj2(C,D,B),A) = k4_fvsum_1(k1_matrix_0(k3_matrix_1(C,B)),C,k10_fvsum_1(k1_matrix_0(k3_matrix_1(C,B)),C,k7_matrix_0(u1_struct_0(C),k3_matrix_1(C,B),A),D),k7_matrix_0(u1_struct_0(C),k3_matrix_1(C,B),k1_nat_1(A,1))) ) ) ) ) ) ) )).
fof(t4_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( 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)) ) ) ) )).
fof(t4_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( k3_finseq_1(k6_matrixr1(B,C)) = k3_finseq_1(B) & k1_matrix_0(k6_matrixr1(B,C)) = k1_matrix_0(C) & k3_finseq_1(k6_matrixr1(B,C)) = A & k1_matrix_0(k6_matrixr1(B,C)) = A ) ) ) ) )).
fof(t4_matrlin,axiom,( ! [A] : ( ( 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)))) ) ) )).
fof(t4_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_matrlin(C,A,k2_vectsp_4(A,B)) => m1_matrlin(C,A,B) ) ) ) )).
fof(t4_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & l1_pre_topc(A) ) => ( v2_matroid0(A) <=> ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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) = k1_nat_1(k5_card_1(B),1) & ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t4_matrprob,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( ( r1_xxreal_0(1,k3_finseq_1(A)) & ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => r1_xxreal_0(k5_numbers,k1_funct_1(A,B)) ) ) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k9_nat_1(k1_numbers,B,1) = k1_funct_1(A,1) & ! [C] : ( v7_ordinal1(C) => ~ ( k5_numbers != C & ~ r1_xxreal_0(k3_finseq_1(A),C) & k9_nat_1(k1_numbers,B,k1_nat_1(C,1)) != k2_xcmplx_0(k9_nat_1(k1_numbers,B,C),k1_funct_1(A,k1_nat_1(C,1))) ) ) ) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(A)) => r1_xxreal_0(k1_funct_1(A,C),k9_nat_1(k1_numbers,B,C)) ) ) ) ) ) ) )).
fof(t4_matrtop1,axiom,( ! [A] : ( ( 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) ) )).
fof(t4_matrtop2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t4_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t4_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_algstr_0(A,k3_rlvect_1(A,B,C),C) = B ) ) ) )).
fof(t4_mboolean,axiom,( ! [A] : ! [B] : r6_pboole(B,k1_mboolean(B,k7_funcop_1(B,k1_tarski(A))),k7_funcop_1(B,k2_tarski(k1_xboole_0,k1_tarski(A)))) )).
fof(t4_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(A,k2_zfmisc_1(B,C)) => ( r2_hidden(k1_xtuple_0(A),B) & r2_hidden(k2_xtuple_0(A),C) ) ) )).
fof(t4_measure1,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) ) )).
fof(t4_measure3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ( ( k9_nat_1(B,C,k5_numbers) = k1_xboole_0 & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( k9_nat_1(B,C,k1_nat_1(E,1)) = k3_measure1(A,B,k9_nat_1(B,D,k5_numbers),k9_nat_1(B,D,E)) & r1_tarski(k9_nat_1(B,D,k1_nat_1(E,1)),k9_nat_1(B,D,E)) ) ) ) => k2_measure2(A,B,k1_measure3(A,B,C)) = k3_measure1(A,B,k9_nat_1(B,D,k5_numbers),k1_measure2(A,B,k1_measure3(A,B,D))) ) ) ) ) )).
fof(t4_measure4,axiom,( ! [A] : ! [B] : ( m1_measure4(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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))) ) ) ) )).
fof(t4_measure5,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ! [B] : ( m1_subset_1(B,k6_numbers) => ! [C] : ( m1_subset_1(C,k6_numbers) => ~ ( ~ r1_xxreal_0(C,A) & ~ r1_xxreal_0(C,B) & ! [D] : ( m1_subset_1(D,k6_numbers) => ~ ( ~ r1_xxreal_0(D,A) & ~ r1_xxreal_0(D,B) & ~ r1_xxreal_0(C,D) & r2_hidden(D,k1_numbers) ) ) ) ) ) ) )).
fof(t4_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ! [D] : ( m2_measure8(D,A,B) => v6_supinf_2(k2_measure8(A,B,C,D)) ) ) ) )).
fof(t4_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ( k4_member_1(A) = k4_member_1(B) => A = B ) ) ) )).
fof(t4_membered,axiom,( ! [A] : ( v4_membered(A) => r1_tarski(A,k3_numbers) ) )).
fof(t4_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( l1_memstr_0(B,A) => ! [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)) ) => r1_xboole_0(k1_tarski(k4_struct_0(B)),k9_xtuple_0(k6_memstr_0(A,B,C))) ) ) ) )).
fof(t4_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( k17_euclid(k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),A,C),k1_rlvect_1(k15_euclid(2),B,D))) = k2_xcmplx_0(k3_xcmplx_0(C,k17_euclid(A)),k3_xcmplx_0(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))) = k2_xcmplx_0(k3_xcmplx_0(C,k18_euclid(A)),k3_xcmplx_0(D,k18_euclid(B))) ) ) ) ) ) )).
fof(t4_mesfun10,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( m1_subset_1(B,k6_numbers) => ( ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(B,k12_supinf_2(A,C)) ) => r1_xxreal_0(B,k2_rinfsup2(A)) ) ) ) )).
fof(t4_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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))) ) ) ) )).
fof(t4_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( v7_ordinal1(C) => ( k1_relset_1(A,k4_mesfunc5(A,k6_numbers,k4_mesfun7c(A,B),C)) = k1_relset_1(A,k4_mesfunc5(A,k1_numbers,B,k5_numbers)) & ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,k4_mesfun7c(A,B),C))) => k12_supinf_2(k4_mesfunc5(A,k6_numbers,k4_mesfun7c(A,B),C),D) = k12_supinf_2(k3_rinfsup2(k1_mesfunc5(k4_ordinal1,k10_seqfunc(A,B,D))),C) ) ) ) ) ) ) )).
fof(t4_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [E] : ( v7_ordinal1(E) => ( ( v1_mesfunc8(D,A,k1_numbers) & r1_tarski(C,k1_relset_1(A,k4_mesfunc5(A,k1_numbers,D,k5_numbers))) & ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t4_mesfunc2,axiom,( ? [A] : ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k3_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k3_numbers))) & v2_funct_1(A) & k1_relset_1(k4_ordinal1,A) = k4_ordinal1 & k2_relset_1(k3_numbers,A) = k3_numbers ) )).
fof(t4_mesfunc3,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ( v1_prob_2(B) <=> ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t4_mesfunc5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(A,B) & ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k4_xxreal_3(k1_newton(2,A),A)) & r1_xxreal_0(k2_extreal1(k3_xxreal_3(C,1),k1_newton(2,A)),B) & ~ r1_xxreal_0(k2_extreal1(C,k1_newton(2,A)),B) ) ) ) ) ) )).
fof(t4_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( r2_hidden(D,k12_mesfunc1(B,C)) <=> ( r2_hidden(D,k1_relset_1(A,B)) & ? [E] : ( v1_xreal_0(E) & E = k12_supinf_2(B,D) & r1_xxreal_0(E,C) ) ) ) ) ) ) )).
fof(t4_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ~ ( ~ r1_xxreal_0(k1_xxreal_0,k12_supinf_2(C,k3_card_3(D))) & ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ~ ( r1_funct_2(k4_ordinal1,B,k4_ordinal1,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(k4_ordinal1,B,B,k6_numbers,E,C))) ) ) ) ) ) ) ) )).
fof(t4_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( v4_mesfunc5(B) & v4_mesfunc5(C) ) => v4_mesfunc5(k3_mesfunc1(A,B,C)) ) ) ) ) )).
fof(t4_metric_1,axiom,( ! [A] : ( l1_metric_1(A) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_xxreal_0(k1_metric_1(A,B,D),k2_xcmplx_0(k1_metric_1(A,B,C),k1_metric_1(A,C,D))) ) ) ) <=> v9_metric_1(A) ) ) )).
fof(t4_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_hidden(B,k1_metric_2(A,B)) ) ) )).
fof(t4_metric_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(D,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C))) => ! [E] : ( m1_subset_1(E,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C))) => ( k2_binop_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,k4_metric_3(A,B,C),D,E) = k5_numbers <=> D = E ) ) ) ) ) ) )).
fof(t4_metric_6,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t4_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( r1_borsuk_3(A,B) => k2_waybel23(A) = k2_waybel23(B) ) ) ) )).
fof(t4_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( v1_xreal_0(C) => u1_struct_0(k1_mfold_1(A,B,C)) = k1_topreal9(A,B,C) ) ) ) )).
fof(t4_mfold_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t4_midsp_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k2_midsp_1)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_midsp_1)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_midsp_1)) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(k2_midsp_1)) & k1_midsp_1(k2_midsp_1,E,A) = B ) ) ) ) ) ) )).
fof(t4_midsp_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( ~ v2_struct_0(D) & v13_algstr_0(D) & v3_rlvect_1(D) & v4_rlvect_1(D) & l2_algstr_0(D) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t4_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( ~ r1_xxreal_0(B,A) & B != k1_nat_1(A,1) & ~ r1_xxreal_0(k1_nat_1(A,2),B) ) ) ) )).
fof(t4_mmlquer2,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ! [D] : ( r2_hidden(k4_tarski(C,D),k1_toler_1(B,A)) <=> ( r2_hidden(C,A) & r2_hidden(D,A) & r2_hidden(k4_tarski(C,D),B) ) ) ) )).
fof(t4_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => r1_tarski(k4_mmlquery(A,C,B),B) ) ) )).
fof(t4_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t4_mod_3,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) => ( r1_struct_0(k1_mod_3(B,C,D),A) <=> ? [E] : ( m2_vectsp_6(E,B,C,D) & A = k4_vectsp_6(B,C,E) ) ) ) ) ) )).
fof(t4_mod_4,axiom,( ! [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) & 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)) ) ) )).
fof(t4_modal_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( r2_xboole_0(k8_finseq_1(k4_ordinal1,A,C),k8_finseq_1(k4_ordinal1,A,B)) => r2_xboole_0(C,B) ) ) ) ) )).
fof(t4_modcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ! [C] : ! [D] : ( ( r1_modcat_1(B,C,A) & r1_modcat_1(B,D,A) ) => C = D ) ) )).
fof(t4_modelc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_modelc_1(A) & l2_modelc_1(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t4_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v3_modelc_2(A) => A = k3_modelc_2(k10_modelc_2(A)) ) ) )).
fof(t4_modelc_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => k17_modelc_3(B,k7_modelc_3(B),A) = k5_numbers ) ) )).
fof(t4_moebius1,axiom,( ! [A] : ( ( ~ v1_int_2(A) & m1_subset_1(A,k4_ordinal1) ) => ~ ( A != 1 & ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ~ ( r1_nat_d(B,A) & B != A ) ) ) ) )).
fof(t4_monoid_0,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t4_monoid_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( 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))) ) ) ) ) ) ) )).
fof(t4_morph_01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = u1_struct_0(A) => k1_morph_01(A,C,B) = C ) ) ) ) )).
fof(t4_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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)))) ) ) )).
fof(t4_msafree1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v1_prob_2(B) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,C) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t4_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => r1_xboole_0(k2_msafree2(A),k1_msafree2(A)) ) )).
fof(t4_msafree3,axiom,( ! [A] : ! [B] : ( ( ~ v11_struct_0(B) & v1_instalg1(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(B)) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(t4_msafree4,axiom,( ! [A] : k3_trees_9(k4_trees_4(A,k1_xboole_0)) = k1_tarski(k4_trees_4(A,k1_xboole_0)) )).
fof(t4_msalimit,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_msalimit(C,A,B) => ! [D] : ( ( v1_msalimit(D,A,B,C) & m2_msalimit(D,A,B,C) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t4_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t4_msinst_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( ( v1_msualg_6(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v1_msualg_6(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v1_msualg_6(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( m2_pboole(F,u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D)) => ! [G] : ( m2_pboole(G,u1_struct_0(A),u3_msualg_1(A,D),u3_msualg_1(A,E)) => ! [H] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t4_msscyc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( r2_hidden(B,u4_struct_0(A)) => ( v7_graph_1(k9_finseq_1(B),A) & m1_graph_1(k9_finseq_1(B),A) ) ) ) )).
fof(t4_msscyc_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ( v5_msafree2(A) => v3_msscyc_1(k4_msscyc_2(A)) ) ) )).
fof(t4_mssubfam,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( ! [D] : ( r2_hidden(D,B) => r1_tarski(C,D) ) => r1_tarski(C,k8_setfam_1(A,B)) ) ) ) )).
fof(t4_mssublat,axiom,( ! [A] : k3_funct_2(k4_ordinal1,k3_finseq_2(k1_tarski(A)),k7_finseq_2(A),3) = k11_finseq_1(A,A,A) )).
fof(t4_msualg_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t4_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t4_msualg_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,C) => k8_pboole(D,k2_msualg_3(A,C)) = D ) ) ) )).
fof(t4_msualg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t4_msualg_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_msualg_4(C,A,B) & m1_msualg_4(C,A,B,B) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t4_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => m1_msualg_6(k2_msualg_3(u1_struct_0(A),u3_msualg_1(A,B)),A,B) ) ) )).
fof(t4_msualg_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) )).
fof(t4_msualg_8,axiom,( ! [A] : k6_lattices(k2_msualg_5(A)) = k1_eqrel_1(A) )).
fof(t4_msualg_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k8_eqrel_1(A,k1_eqrel_1(A)) = k1_tarski(A) ) )).
fof(t4_msuhom_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( 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)) ) ) )).
fof(t4_multop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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] : ( ( 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] : ! [J] : ! [K] : ( ( 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) ) ) ) ) )).
fof(t4_mycielsk,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( 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) ) ) )).
fof(t4_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t4_nagata_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => v1_pscomp_1(k2_nagata_2(u1_struct_0(A),B,C),A) ) ) ) ) )).
fof(t4_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => r1_xxreal_0(k3_xcmplx_0(B,A),k3_xcmplx_0(C,A)) ) ) ) ) )).
fof(t4_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => k3_nat_d(A,1) = A ) )).
fof(t4_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r1_nat_d(k1_newton(C,B),D) => ( r1_xxreal_0(B,A) | r1_nat_d(k1_newton(C,k2_xcmplx_0(A,1)),D) ) ) ) ) ) ) )).
fof(t4_nat_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(B,A) & C = k1_int_1(k7_xcmplx_0(A,2)) ) => r1_xxreal_0(k4_newton(B,A),k4_newton(C,A)) ) ) ) ) )).
fof(t4_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_finset_1(k1_tarski(A)) & m1_subset_1(k1_tarski(A),k1_zfmisc_1(k4_ordinal1)) ) ) )).
fof(t4_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_nat_d(B,C) & r1_nat_d(C,A) ) => r1_nat_d(B,A) ) ) ) ) )).
fof(t4_nat_lat,axiom,( k4_nat_lat = 1 )).
fof(t4_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m3_cat_2(B,A) => ( u1_graph_1(B) = k5_relat_1(u1_graph_1(A),u4_struct_0(B)) & u2_graph_1(B) = k5_relat_1(u2_graph_1(A),u4_struct_0(B)) & u1_cat_1(B) = k1_realset1(u1_cat_1(A),u4_struct_0(B)) ) ) ) )).
fof(t4_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( v7_ordinal1(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ( r1_tarski(k2_relset_1(u1_struct_0(A),D),k1_relset_1(u1_struct_0(A),E)) => r2_hidden(k1_normsp_1(A,D,C),k1_relset_1(u1_struct_0(A),E)) ) ) ) ) ) ) )).
fof(t4_ncfcont2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)))) ) => ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t4_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & ! [D] : ( m1_nfcont_1(D,A,C) => ~ r1_tarski(D,B) ) ) ) => v3_nfcont_1(B,A) ) ) ) )).
fof(t4_ndiff_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ~ ( ~ r1_xxreal_0(k2_normsp_0(A,k5_algstr_0(A,B,C)),k5_numbers) & B = C ) & ~ ( B != C & r1_xxreal_0(k2_normsp_0(A,k5_algstr_0(A,B,C)),k5_numbers) ) ) ) ) ) & ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_normsp_0(A,k5_algstr_0(A,B,C)) = k2_normsp_0(A,k5_algstr_0(A,C,B)) ) ) ) & ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_normsp_0(A,k5_algstr_0(A,B,C)) = k5_numbers <=> B = C ) ) ) ) & ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ~ ( k2_normsp_0(A,k5_algstr_0(A,B,C)) != k5_numbers & B = C ) & ~ ( B != C & k2_normsp_0(A,k5_algstr_0(A,B,C)) = k5_numbers ) ) ) ) ) & ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ~ r1_xxreal_0(k7_xcmplx_0(E,2),k2_normsp_0(A,k5_algstr_0(A,B,D))) & ~ r1_xxreal_0(k7_xcmplx_0(E,2),k2_normsp_0(A,k5_algstr_0(A,D,C))) & r1_xxreal_0(E,k2_normsp_0(A,k5_algstr_0(A,B,C))) ) ) ) ) ) ) & ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ~ r1_xxreal_0(k7_xcmplx_0(E,2),k2_normsp_0(A,k5_algstr_0(A,B,D))) & ~ r1_xxreal_0(k7_xcmplx_0(E,2),k2_normsp_0(A,k5_algstr_0(A,C,D))) & r1_xxreal_0(E,k2_normsp_0(A,k5_algstr_0(A,B,C))) ) ) ) ) ) ) & ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & r1_xxreal_0(C,k2_normsp_0(A,B)) ) ) => B = k4_struct_0(A) ) ) ) & ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_xxreal_0(D,k2_normsp_0(A,k5_algstr_0(A,B,C))) ) ) => B = C ) ) ) ) )).
fof(t4_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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)))) ) ) ) ) )).
fof(t4_ndiff_4,axiom,( ! [A] : ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t4_ndiff_5,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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,k5_numbers) = k4_struct_0(A) => ! [D] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) ) )).
fof(t4_neckla_2,axiom,( ! [A] : ( r2_hidden(A,k4_neckla_2) => ( ~ v2_struct_0(A) & v8_struct_0(A) & v1_orders_2(A) & l1_orders_2(A) ) ) )).
fof(t4_neckla_3,axiom,( ! [A] : ( v1_zfmisc_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ~ ( ~ v1_xboole_0(B) & ! [C] : B != k1_tarski(k4_tarski(C,C)) ) ) ) )).
fof(t4_necklace,axiom,( ! [A] : k1_card_1(k6_partfun1(A)) = k1_card_1(A) )).
fof(t4_net_1,axiom,( ! [A] : ! [B] : ( ( v1_net_1(B) & l1_petri(B) ) => ~ ( r2_hidden(A,u1_struct_0(B)) & r2_hidden(A,u4_struct_0(B)) ) ) )).
fof(t4_newton,axiom,( ! [A] : ( v1_xcmplx_0(A) => k1_newton(A,k5_numbers) = 1 ) )).
fof(t4_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_nfcont_1(C,A,B) => r2_hidden(B,C) ) ) ) )).
fof(t4_nfcont_2,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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)) ) ) ) ) ) )).
fof(t4_nfcont_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( v1_xreal_0(D) => ( r1_tarski(k2_relset_1(k1_numbers,C),k1_relset_1(k1_numbers,B)) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,C,k4_vfunct_1(k1_numbers,A,B,D)),k5_normsp_1(A,k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,C,B),D)) ) ) ) ) ) )).
fof(t4_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_euclid(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t4_normform,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_finsub_1(B) ) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(A,B)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t4_normsp_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_xxreal_0(k5_numbers,k2_normsp_0(A,B)) ) ) )).
fof(t4_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k2_normsp_2(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k2_normsp_2(A))))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_normsp_2(A))) => ( ( r1_funct_2(k4_ordinal1,u1_struct_0(A),k4_ordinal1,u1_struct_0(k2_normsp_2(A)),B,C) & D = E ) => ( r1_metric_6(k2_normsp_2(A),C,E) <=> ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( v7_ordinal1(G) => ? [H] : ( v7_ordinal1(H) & r1_xxreal_0(G,H) & r1_xxreal_0(F,k2_normsp_0(A,k5_algstr_0(A,k1_normsp_1(A,B,H),D))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t4_ntalgo_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ~ ( ~ r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k4_xcmplx_0(A),k4_xcmplx_0(k5_int_1(B,A))) ) ) ) )).
fof(t4_numbers,axiom,( r2_xboole_0(k4_numbers,k3_numbers) )).
fof(t4_numeral1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,1) => r1_xxreal_0(1,k1_afinsq_1(k2_numeral1(A,B))) ) ) ) )).
fof(t4_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t4_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => u1_struct_0(k6_openlatt(A)) = k1_openlatt(A) ) )).
fof(t4_oposet_1,axiom,( v3_necklace(k2_oposet_1) )).
fof(t4_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t4_ordeq_01,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_xxreal_0(D,k2_normsp_0(A,k5_algstr_0(A,B,C))) ) ) => B = C ) ) ) ) )).
fof(t4_orders_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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 ) ) )).
fof(t4_orders_2,axiom,( ! [A] : ( ( v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_orders_2(A,B,C) & r2_orders_2(A,C,B) ) ) ) ) )).
fof(t4_orders_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ~ ( k2_struct_0(A) = k1_tarski(B) & v3_orders_3(A) ) ) )).
fof(t4_orders_4,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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 ) ) ) ) ) ) )).
fof(t4_ordinal1,axiom,( ! [A] : ! [B] : ( r2_hidden(B,k1_ordinal1(A)) <=> ( r2_hidden(B,A) | B = A ) ) )).
fof(t4_ordinal2,axiom,( v4_ordinal1(k5_ordinal1) )).
fof(t4_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( r1_tarski(B,A) => v3_ordinal1(k3_tarski(B)) ) ) )).
fof(t4_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r1_ordinal2(B,A) => r1_ordinal2(k10_ordinal2(C,B),k1_ordinal3(C,A)) ) ) ) ) )).
fof(t4_ordinal5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) ) => ( v1_ordinal2(k1_ordinal4(A,B)) => ( v1_ordinal2(A) & v1_ordinal2(B) ) ) ) ) )).
fof(t4_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r1_ordinal1(A,B) <=> ~ r2_hidden(B,A) ) ) ) )).
fof(t4_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ~ ( ~ r1_orders_2(B,D,C) & r1_orders_2(B,E,C) & r1_orders_2(B,k3_rlvect_1(B,D,E),C) ) ) ) ) ) ) )).
fof(t4_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( r2_hidden(C,k6_dtconstr(k2_osafree(A,B))) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( r2_hidden(E,k1_funct_1(B,D)) & C = k4_tarski(E,D) ) ) ) ) ) )).
fof(t4_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_osalg_1(A) ) => ( v6_osalg_1(A) => v5_osalg_1(A) ) ) )).
fof(t4_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t4_osalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t4_osalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_orders_2(A,B,C) => k3_osalg_4(A,B) = k3_osalg_4(A,C) ) ) ) ) )).
fof(t4_papdesaf,axiom,( ! [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) ) => ! [B] : ( ( ~ v7_struct_0(B) & v2_analoaf(B) & l1_analoaf(B) ) => ( B = k2_analoaf(A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t4_pardepap,axiom,( ? [A] : ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t4_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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))) ) )).
fof(t4_parsp_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A))) => ! [E] : ( m1_subset_1(E,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) => ! [F] : ( m1_subset_1(F,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) => ! [G] : ( m1_subset_1(G,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t4_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,B) & v1_funct_1(C) ) => ( r2_hidden(A,k9_xtuple_0(C)) => r2_hidden(k1_funct_1(C,A),B) ) ) )).
fof(t4_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t4_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ( ( r1_setfam_1(C,B) & r1_setfam_1(B,C) ) => B = C ) ) ) ) )).
fof(t4_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t4_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r3_diraf(A,G,C,D) & r3_diraf(A,G,B,E) & r3_diraf(A,G,B,F) & r2_diraf(A,B,C,D,E) & r2_diraf(A,B,C,D,F) ) => ( r3_diraf(A,G,B,C) | E = F ) ) ) ) ) ) ) ) ) )).
fof(t4_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( 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)) ) ) ) )).
fof(t4_pcomps_1,axiom,( ! [A] : u1_pre_topc(k1_compts_1(A)) = k9_setfam_1(A) )).
fof(t4_pcomps_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v6_metric_1(B) & v7_metric_1(B) & v8_metric_1(B) & v9_metric_1(B) & l1_metric_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t4_pcs_0,axiom,( ! [A] : ( l1_pcs_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t4_pdiff_1,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(1))) => ! [C] : ( v1_xreal_0(C) => ( k1_funct_1(A,B) = C => k2_normsp_0(k4_real_ns1(1),B) = k9_complex1(C) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(1))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(1))) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( k1_funct_1(A,B) = D & k1_funct_1(A,C) = E ) => k1_funct_1(A,k3_rlvect_1(k4_real_ns1(1),B,C)) = k2_xcmplx_0(D,E) ) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(1))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( k1_funct_1(A,B) = C => k1_funct_1(A,k1_rlvect_1(k4_real_ns1(1),B,D)) = k3_xcmplx_0(D,C) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(1))) => ! [C] : ( v1_xreal_0(C) => ( k1_funct_1(A,B) = C => k1_funct_1(A,k4_algstr_0(k4_real_ns1(1),B)) = k4_xcmplx_0(C) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(1))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(1))) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( k1_funct_1(A,B) = D & k1_funct_1(A,C) = E ) => k1_funct_1(A,k5_algstr_0(k4_real_ns1(1),B,C)) = k6_xcmplx_0(D,E) ) ) ) ) ) ) ) ) )).
fof(t4_pdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(2)) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t4_pdiff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(2)) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t4_pdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t4_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t4_pdiff_6,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(B),k1_euclid(A)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(B),k1_euclid(A)))) ) => ! [E] : ( ( 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] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(B)),u1_struct_0(k4_real_ns1(A))))) ) => ( ( C = E & D = F ) => k7_integr15(A,k1_euclid(B),C,D) = k6_vfunct_1(u1_struct_0(k4_real_ns1(B)),k4_real_ns1(A),E,F) ) ) ) ) ) ) ) )).
fof(t4_pdiff_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( 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)) ) ) ) )).
fof(t4_pdiff_8,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(A))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k2_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)) = k9_complex1(k1_funct_1(k1_pdiff_1(C,A),B)) ) ) ) )).
fof(t4_pdiff_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ( ( 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 ) ) ) )).
fof(t4_pencil_1,axiom,( ! [A] : ( r1_ordinal1(2,k1_card_1(A)) <=> ~ v1_zfmisc_1(A) ) )).
fof(t4_pencil_2,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( 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) ) ) ) ) ) )).
fof(t4_pencil_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v6_pencil_1(A) & l1_pre_topc(A) ) => ( v10_pencil_1(A) => v9_pencil_1(A) ) ) )).
fof(t4_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => m1_vectsp_4(k2_vectsp_4(A,C),A,B) ) ) ) )).
fof(t4_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_nat_d(C,B) & r1_nat_d(A,B) & r1_int_2(C,A) ) => r1_nat_d(k3_xcmplx_0(C,A),B) ) ) ) ) )).
fof(t4_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( r2_hidden(C,k7_petri(A,B)) <=> ? [D] : ( m1_petri(D,u1_struct_0(A),u4_struct_0(A),u1_petri(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_hidden(E,B) & D = k4_tarski(E,C) ) ) ) ) ) )).
fof(t4_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => r2_pnproc_1(A,B,k2_pnproc_1(A,B,C)) ) ) )).
fof(t4_polyalg1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t4_polyeq_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( v1_xcmplx_0(F) => ( ! [G] : ( v1_xreal_0(G) => k2_polyeq_1(A,B,C,G) = k2_polyeq_1(D,E,F,G) ) => ( A = D & B = E & C = F ) ) ) ) ) ) ) ) )).
fof(t4_polyeq_2,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_newton(A,3) = k3_xcmplx_0(k1_square_1(A),A) & k3_xcmplx_0(k1_newton(A,3),A) = k1_newton(A,4) & k3_xcmplx_0(k1_square_1(A),k1_square_1(A)) = k1_newton(A,4) ) ) )).
fof(t4_polyeq_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( v1_xcmplx_0(F) => ( ! [G] : ( v1_xcmplx_0(G) => k2_polyeq_3(A,B,C,G) = k3_polyeq_1(A,G,E,F) ) => ( A = k5_numbers | ( k7_xcmplx_0(B,A) = k4_xcmplx_0(k2_xcmplx_0(E,F)) & k7_xcmplx_0(C,A) = k3_xcmplx_0(E,F) ) ) ) ) ) ) ) ) ) )).
fof(t4_polyeq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & v1_abian(C) & r1_xxreal_0(1,C) & k1_newton(A,C) = B & A != k1_power(C,B) & A != k4_xcmplx_0(k1_power(C,B)) ) ) ) ) )).
fof(t4_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( 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)) ) ) )).
fof(t4_polyform,axiom,( v1_abian(2) )).
fof(t4_polynom1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( 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)) ) ) )).
fof(t4_polynom2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ( k3_finseq_1(C) = k3_finseq_1(D) => ( ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( 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] : ( m1_subset_1(F,k4_ordinal1) => ( 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)) ) ) ) ) ) ) )).
fof(t4_polynom3,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r2_hidden(B,k4_finseq_1(A)) => r1_xxreal_0(k1_recdef_1(A,B),k2_wsierp_1(A)) ) ) ) )).
fof(t4_polynom4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v6_struct_0(A) & l5_algstr_0(A) ) => k1_algseq_1(A,k10_polynom3(A)) = 1 ) )).
fof(t4_polynom6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( m2_subset_1(C,k14_pre_poly(A),k15_pre_poly(A)) => ! [D] : ( m2_subset_1(D,k14_pre_poly(B),k15_pre_poly(B)) => ( A = k1_xboole_0 => k1_polynom6(A,B,C,D) = D ) ) ) ) ) )).
fof(t4_polyred,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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),k7_polynom1(A,B,C,k8_polynom1(A,B)),C) ) ) )).
fof(t4_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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))) ) ) )).
fof(t4_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ( ~ ( ~ ( r1_xxreal_0(1,B) & r1_xxreal_0(k5_numbers,A) ) & v1_abian(B) ) => ( k1_newton(k1_power(B,A),B) = A & k1_power(B,k1_newton(A,B)) = A ) ) ) ) )).
fof(t4_pralg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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))))) ) ) ) ) )).
fof(t4_pralg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t4_pre_ff,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r1_xxreal_0(k5_numbers,A) => ( r1_xxreal_0(B,A) | k4_int_1(A,B) = k5_numbers ) ) ) ) )).
fof(t4_pre_poly,axiom,( ! [A] : ! [B] : ( m2_finseq_2(B,A,k3_finseq_2(A)) => ! [C] : ( 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) ) ) )).
fof(t4_pre_topc,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t4_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_prelamb(A) ) => ! [B] : ( m1_prelamb(B,A) => ! [C] : ( 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)),k4_ordinal1),B,C)) = 1 & ! [D] : ( m1_trees_1(D,k9_xtuple_0(B)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( D = k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,k5_numbers)) & k1_xtuple_0(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k4_ordinal1),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)),k4_ordinal1),B,D)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),E,k12_finseq_1(u1_struct_0(A),G)),F) ) ) ) ) ) ) ) ) ) )).
fof(t4_prgcor_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(B,k4_nat_d(A,k2_nat_1(2,B))) & k4_nat_d(A,k2_nat_1(2,B)) != k4_nat_d(A,B) ) ) ) )).
fof(t4_prob_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(t4_prob_2,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [E] : ( m1_prob_1(E,A,B) => ( ( v2_prob_1(C) & ! [F] : ( v7_ordinal1(F) => k1_prob_2(A,B,D,F) = k5_prob_1(A,B,k1_prob_2(A,B,C,F),E) ) ) => v2_prob_1(D) ) ) ) ) ) )).
fof(t4_prob_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( v5_relat_1(D,C) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ! [E] : ( m2_prob_1(E,B,C) => r1_xxreal_0(k5_numbers,k1_funct_1(k8_prob_1(B,C,D,E),A)) ) ) ) ) ) )).
fof(t4_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => r2_hidden(k8_cqc_lang(A,C,k9_cqc_lang(A,B,C)),k4_cqc_the1(A)) ) ) ) )).
fof(t4_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t4_projpl_1,axiom,( ! [A] : ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ? [D] : ( m1_subset_1(D,u2_incsp_1(A)) & r4_incsp_1(A,k7_domain_1(u1_incsp_1(A),B,C),D) ) ) ) & ~ ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => r1_incsp_1(A,B,C) ) ) & ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ? [C] : ( m1_subset_1(C,u1_incsp_1(A)) & ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & ? [E] : ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u1_incsp_1(A)) => ! [G] : ( m1_subset_1(G,u2_incsp_1(A)) => ! [H] : ( m1_subset_1(H,u2_incsp_1(A)) => ! [I] : ( m1_subset_1(I,u2_incsp_1(A)) => ! [J] : ( 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] : ( m1_subset_1(K,u1_incsp_1(A)) => ~ r2_projpl_1(A,K,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t4_projred1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t4_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t4_prvect_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) ) )).
fof(t4_prvect_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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] : ( 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)))) ) ) ) ) ) ) )).
fof(t4_prvect_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( 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] : ( r2_hidden(C,A) => k1_funct_1(B,C) = k9_finseq_1(C) ) ) ) )).
fof(t4_pscomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k3_funct_2(u1_struct_0(A),k1_numbers,B,C),k2_pscomp_1(A,B)) ) ) ) )).
fof(t4_pua2mss1,axiom,( ! [A] : ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ( ! [E] : ( r2_hidden(E,B) => r1_tarski(E,k1_funct_1(D,E)) ) => ! [E] : ( m2_finseq_1(E,B) => ! [F] : ( m2_finseq_1(F,C) => ( r1_tarski(k4_card_3(E),k4_card_3(F)) <=> r2_relset_1(k4_ordinal1,C,k1_partfun1(k4_ordinal1,B,B,C,E,D),F) ) ) ) ) ) ) ) )).
fof(t4_pythtrip,axiom,( ! [A] : ( v1_int_1(A) => ( ~ v1_abian(A) => k4_nat_d(k1_pepin(A),4) = 1 ) ) )).
fof(t4_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => r1_tarski(k2_qc_lang1(A),k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))) ) )).
fof(t4_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t4_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t4_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => k10_xtuple_0(k1_qc_lang4(A,B)) = a_2_0_qc_lang4(A,B) ) ) )).
fof(t4_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_qc_trans(B,A) & m1_qc_lang1(B) ) => r1_tarski(k3_qc_lang1(A),k3_qc_lang1(B)) ) ) )).
fof(t4_qmax_1,axiom,( ! [A] : ( ( v2_qmax_1(A) & l1_qmax_1(A) ) => ! [B] : ( m1_subset_1(B,k5_qmax_1(A)) => ! [C] : ( m1_subset_1(C,k5_qmax_1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t4_quantal1,axiom,( ! [A] : ( ( ~ 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) ) ) ) )).
fof(t4_quatern2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k24_quaterni(k6_quaterni(A,B,C,D)) = k6_quaterni(k4_xcmplx_0(A),k4_xcmplx_0(B),k4_xcmplx_0(C),k4_xcmplx_0(D)) ) ) ) ) )).
fof(t4_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ( v1_xreal_0(B) => k23_quaterni(B,A) = k6_quaterni(k3_xcmplx_0(k13_quaterni(B),k13_quaterni(A)),k3_xcmplx_0(k13_quaterni(B),k14_quaterni(A)),k3_xcmplx_0(k13_quaterni(B),k15_quaterni(A)),k3_xcmplx_0(k13_quaterni(B),k16_quaterni(A))) ) ) ) )).
fof(t4_quaterni,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( r2_zfmisc_1(E,F,G,H) => k10_xtuple_0(k2_quaterni(E,F,G,H,A,B,C,D)) = k2_enumset1(A,B,C,D) ) )).
fof(t4_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r1_xxreal_0(k1_quin_1(B,C,D),k5_numbers) => ( r1_xxreal_0(k5_numbers,B) | r1_xxreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(A)),k3_xcmplx_0(C,A)),D),k5_numbers) ) ) ) ) ) ) )).
fof(t4_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A)) => ! [C] : ( m2_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t4_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( A != k5_numbers & k4_nat_d(k2_xcmplx_0(B,1),A) != k5_numbers & k4_nat_d(k2_xcmplx_0(B,1),A) != k2_xcmplx_0(k4_nat_d(B,A),1) ) ) ) )).
fof(t4_radix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(1,C) => ( r1_xxreal_0(B,k5_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) ) ) ) ) ) )).
fof(t4_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(2,A) => r1_tarski(k2_radix_3(A),k3_radix_1(A)) ) ) )).
fof(t4_radix_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(2,B) & r1_radix_1(1,A,B) ) => k7_radix_3(k2_xcmplx_0(1,1),B,k2_xcmplx_0(1,1),k10_radix_3(1,B,k10_radix_1(B,1,A))) = k5_radix_3(A,B) ) ) ) )).
fof(t4_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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) ) ) )).
fof(t4_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(2,B) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t4_ramsey_1,axiom,( ! [A] : ! [B] : ~ ( ~ v1_finset_1(A) & v1_finset_1(B) & v1_finset_1(k6_subset_1(A,B)) ) )).
fof(t4_random_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( v1_xreal_0(F) => ( ( r3_mesfunc6(A,B,C,D) & r1_tarski(E,k1_relset_1(A,D)) & ! [G] : ( m1_subset_1(G,A) => ( r2_hidden(G,E) => r1_xxreal_0(k12_supinf_2(D,G),F) ) ) ) => ( r1_xxreal_0(k1_xxreal_0,k3_funct_2(B,k6_numbers,C,E)) | r1_xxreal_0(k1_mesfunc6(A,B,C,k2_partfun1(A,k1_numbers,D,E)),k4_xxreal_3(F,k3_funct_2(B,k6_numbers,C,E))) ) ) ) ) ) ) ) ) )).
fof(t4_random_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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(k7_funcop_1(A,B),A,C) ) ) ) )).
fof(t4_random_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [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))) ) => ! [D] : ( v1_xreal_0(D) => ( m1_random_1(C,A,B) => r2_hidden(k8_relset_1(A,k1_numbers,C,k4_xxreal_1(k2_xxreal_0,D)),B) ) ) ) ) ) )).
fof(t4_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t4_rat_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,A) & ! [C] : ( v1_rat_1(C) => ~ ( ~ r1_xxreal_0(C,A) & ~ r1_xxreal_0(B,C) ) ) ) ) ) )).
fof(t4_ratfunc1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( 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)) ) ) ) )).
fof(t4_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,A) => k3_seq_4(k3_rcomp_1(A,B)) = A ) ) ) )).
fof(t4_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(A,B) & ~ v2_xxreal_0(B) & v2_xxreal_0(A) ) ) ) )).
fof(t4_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k4_nat_d(B,A) = k5_numbers => k7_xcmplx_0(B,A) = k3_nat_d(B,A) ) ) ) )).
fof(t4_real_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_real_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_real_lat)) => ! [C] : ( 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) ) ) ) ) )).
fof(t4_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(A))) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ( B = C => k4_algstr_0(k4_real_ns1(A),B) = k6_euclid(A,C) ) ) ) ) )).
fof(t4_realset1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m2_realset1(C,A,B) => ( v1_funct_1(k1_realset1(C,B)) & v1_funct_2(k1_realset1(C,B),k2_zfmisc_1(B,B),B) & m1_subset_1(k1_realset1(C,B),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B,B),B))) ) ) ) )).
fof(t4_realset2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(A),k8_struct_0(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k8_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t4_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t4_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v3_rearran1(B,k1_zfmisc_1(A)) & m2_finseq_1(B,k1_zfmisc_1(A)) ) => k3_finseq_1(B) != k5_numbers ) ) )).
fof(t4_recdef_2,axiom,( ! [A] : ( ? [B] : ? [C] : ? [D] : ? [E] : 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)) ) )).
fof(t4_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( 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) ) ) ) )).
fof(t4_relat_2,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( r5_relat_2(B,A) => r4_relat_2(k2_xboole_0(B,k4_relat_1(A)),A) ) ) )).
fof(t4_reloc,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(C,5) & k2_compos_0(u1_compos_1(k1_ami_3),A) = C ) ) => k5_compos_0(u1_compos_1(k1_ami_3),A,B) = A ) ) ) )).
fof(t4_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) ) )).
fof(t4_relset_2,axiom,( ! [A] : ! [B] : k10_eqrel_1(k3_xboole_0(A,B)) = k9_subset_1(k1_zfmisc_1(B),k10_eqrel_1(A),k10_eqrel_1(B)) )).
fof(t4_revrot_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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 ) ) ) )).
fof(t4_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( A != k1_xboole_0 => k1_rewrite1(k9_finseq_1(B),A) = A ) ) )).
fof(t4_rewrite2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( m1_rewrite1(C,B) => ~ ( r2_hidden(A,k4_finseq_1(C)) & ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t4_rewrite3,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( m1_rewrite1(B,A) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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),k5_numbers) | r1_xxreal_0(k3_finseq_1(D),k5_numbers) | ( m1_rewrite1(C,A) & m1_rewrite1(D,A) ) ) ) ) ) ) ) )).
fof(t4_rfinseq,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( r2_classes1(A,B) <=> ? [C] : ( 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) ) ) ) ) )).
fof(t4_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( v1_xreal_0(B) => ( A = k9_finseq_1(B) => ( k2_rfinseq2(A) = 1 & k4_rfinseq2(A) = B ) ) ) ) )).
fof(t4_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => k8_relat_1(k4_rfunct_1(A),k1_tarski(k5_numbers)) = k1_xboole_0 ) )).
fof(t4_rfunct_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_ordinal1) & v5_valued_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ( r2_relset_1(k4_ordinal1,k1_numbers,k2_valued_0(k1_numbers,B,k32_valued_1(k4_ordinal1,k1_numbers,A)),k32_valued_1(k4_ordinal1,k1_numbers,k2_valued_0(k1_numbers,B,A))) & r2_relset_1(k4_ordinal1,k1_numbers,k2_valued_0(k1_numbers,B,k56_valued_1(k4_ordinal1,k1_numbers,A)),k56_valued_1(k4_ordinal1,k1_numbers,k2_valued_0(k1_numbers,B,A))) ) ) ) )).
fof(t4_rfunct_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k5_numbers,A) => k1_rfunct_3(k3_xcmplx_0(A,B)) = k3_xcmplx_0(A,k1_rfunct_3(B)) ) ) ) )).
fof(t4_rfunct_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k4_finseq_1(B)) => k5_numbers = k1_funct_1(B,C) ) ) => B = k2_finseq_2(A,k5_numbers) ) ) ) )).
fof(t4_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k2_relset_1(k1_numbers,k32_valued_1(k4_ordinal1,k1_numbers,A)) = k5_member_1(k2_relset_1(k1_numbers,A)) ) )).
fof(t4_rinfsup2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( ( ~ 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) = k3_seq_4(B) ) ) ) ) )).
fof(t4_ring_1,axiom,( ! [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) ) => v2_ring_1(k6_domain_1(u1_struct_0(A),k4_struct_0(A)),A) ) )).
fof(t4_ringcat1,axiom,( ! [A] : ( ( v2_ringcat1(A) & v3_ringcat1(A) & l1_ringcat1(A) ) => ? [B] : ( ~ 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] : ( ~ 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] : ( 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) ) ) ) ) )).
fof(t4_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t4_rlaffin2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t4_rlaffin3,axiom,( ! [A] : ( v7_ordinal1(A) => k1_rlvect_5(k15_euclid(A)) = A ) )).
fof(t4_rlsub_1,axiom,( ! [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) ) => v1_rlsub_1(k6_domain_1(u1_struct_0(A),k4_struct_0(A)),A) ) )).
fof(t4_rlsub_2,axiom,( ! [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) ) => ! [B] : ( ( v1_rlvect_1(B) & m1_rlsub_1(B,A) ) => k1_rlsub_2(A,B,B) = B ) ) )).
fof(t4_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t4_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t4_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,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)) ) ) ) ) )).
fof(t4_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(t4_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( m1_rlsub_1(D,A) => ( m1_rlsub_1(C,D) => r1_tarski(k3_rlsub_1(A,B,C),k3_rlsub_1(A,B,D)) ) ) ) ) ) )).
fof(t4_rlvect_5,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( ( 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),k4_ordinal1,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)) ) ) ) ) ) ) )).
fof(t4_rlvect_x,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) => ! [E] : ( m2_rlvect_2(E,C,D) => ( A = B => r1_rlvect_2(C,k8_rlvect_2(C,A,E),k1_rlvect_x(C,B,E)) ) ) ) ) ) ) )).
fof(t4_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t4_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v2_vectsp_2(C,A) & m1_rmod_2(C,A,B) ) => k1_rmod_3(A,B,C,C) = C ) ) ) )).
fof(t4_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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),E,D,F))) = k3_rlvect_1(B,k3_rlvect_1(B,k5_vectsp_2(A,B,C,E),k5_vectsp_2(A,B,C,D)),k5_vectsp_2(A,B,C,F)) ) ) ) ) ) ) )).
fof(t4_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_robbins1(A,B,k3_robbins1(A,B)) = k5_robbins1(A,C,k3_robbins1(A,C)) ) ) ) )).
fof(t4_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) )).
fof(t4_robbins3,axiom,( ! [A] : ( ( ~ 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) ) ) ) )).
fof(t4_robbins4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v8_robbins3(A) & l4_robbins1(A) ) => ( v10_robbins1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_lattices(A,B,C) => r3_lattices(A,k3_robbins1(A,C),k3_robbins1(A,B)) ) ) ) ) ) )).
fof(t4_rolle,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,k5_numbers) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ~ ( r1_tarski(k1_rcomp_1(A,k2_xcmplx_0(A,B)),k1_relset_1(k1_numbers,C)) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,k1_rcomp_1(A,k2_xcmplx_0(A,B)))) & r2_fdiff_1(C,k2_rcomp_1(A,k2_xcmplx_0(A,B))) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(1,D) & k1_funct_1(C,k2_xcmplx_0(A,B)) = k2_xcmplx_0(k1_funct_1(C,A),k3_xcmplx_0(B,k1_fdiff_1(C,k2_xcmplx_0(A,k3_xcmplx_0(D,B))))) ) ) ) ) ) ) ) )).
fof(t4_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v1_roughs_1(A) & l1_orders_2(A) ) => ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( 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)) ) ) ) )).
fof(t4_rpr_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t4_rsspace,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace))) => ! [B] : ( m1_subset_1(B,u1_struct_0(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace))) => ! [C] : ( m1_subset_1(C,u1_struct_0(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace))) => k3_rlvect_1(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace),k3_rlvect_1(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace),A,B),C) = k3_rlvect_1(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace),A,k3_rlvect_1(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace),B,C)) ) ) ) )).
fof(t4_rsspace2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(k3_xcmplx_0(k2_xcmplx_0(A,B),k2_xcmplx_0(A,B)),k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,A),A),k3_xcmplx_0(k3_xcmplx_0(2,B),B))) ) ) & ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(k3_xcmplx_0(A,A),k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k6_xcmplx_0(A,B)),k6_xcmplx_0(A,B)),k3_xcmplx_0(k3_xcmplx_0(2,B),B))) ) ) )).
fof(t4_rsspace3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_series_1(A) & k4_series_1(k56_valued_1(k4_ordinal1,k1_numbers,A)) = k5_numbers ) => ! [B] : ( v7_ordinal1(B) => k1_funct_1(A,B) = k5_numbers ) ) ) )).
fof(t4_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => k4_struct_0(B) = k4_struct_0(A) ) ) )).
fof(t4_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_bhsp_1(B) & m1_rusub_1(B,A) ) => k1_rusub_2(A,B,B) = B ) ) )).
fof(t4_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t4_rusub_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_rusub_4(A) & v1_rlvect_3(B,A) ) => v1_finset_1(B) ) ) ) )).
fof(t4_rusub_5,axiom,( ! [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) ) => ! [B] : ( ( v2_rusub_4(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t4_rvsum_2,axiom,( ! [A] : ( ( 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) ) )).
fof(t4_scheme1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( A != k2_nat_1(5,B) & A != k1_nat_1(k2_nat_1(5,B),1) & A != k1_nat_1(k2_nat_1(5,B),2) & A != k1_nat_1(k2_nat_1(5,B),3) & A != k1_nat_1(k2_nat_1(5,B),4) ) ) ) )).
fof(t4_scm_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_ami_3)) ) => ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_ami_3)) ) => ( ( k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_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(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1))) = k1_nat_1(C,1) & k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1)),E) = k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B),F) & ! [G] : ( ( v1_ami_2(G) & m1_subset_1(G,u1_struct_0(k1_ami_3)) ) => ( G != E => k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1)),G) = k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B),G) ) ) ) ) ) ) ) ) ) ) )).
fof(t4_scm_comp,axiom,( ! [A] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( 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) ) ) )).
fof(t4_scm_halt,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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) ) => ( ( r1_tarski(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_3(k4_scmfsa_2(k5_numbers),1)),A) & r1_tarski(E,C) ) => ! [F] : ( v7_ordinal1(F) => ( ( r1_tarski(k6_compos_1(k1_scmfsa_2,E,F),D) & k5_memstr_0(k7_card_1(3),k1_scmfsa_2,B) = F & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,A) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,B) ) => ! [G] : ( v7_ordinal1(G) => ( k2_xcmplx_0(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,C,A,G)),F) = k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,D,B,G)) & k5_compos_0(u1_compos_1(k1_scmfsa_2),k3_extpro_1(k7_card_1(3),k1_scmfsa_2,C,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,C,A,G)),F) = k3_extpro_1(k7_card_1(3),k1_scmfsa_2,D,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,D,B,G)) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,C,A,G)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,D,B,G)) ) ) ) ) ) ) ) ) ) ) )).
fof(t4_scm_inst,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k2_scm_inst) => ! [C] : ( m1_subset_1(C,k2_scm_inst) => ( r2_hidden(A,k10_domain_1(k4_ordinal1,1,2,3,4,5)) => r2_hidden(k3_xtuple_0(A,k1_xboole_0,k2_finseq_4(k2_scm_inst,B,C)),k3_scm_inst) ) ) ) )).
fof(t4_scmbsort,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( m1_scmfsa_2(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmfsa_2)) ) => ( C != k1_nat_1(D,1) => k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k14_scmfsa_2(k4_scmfsa_2(C),E,B),k1_scmfsa_m(A)),k4_scmfsa_2(k1_nat_1(D,1))) = k1_funct_1(A,k4_scmfsa_2(k1_nat_1(D,1))) ) ) ) ) ) ) )).
fof(t4_scmfsa10,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( 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)) ) ) )).
fof(t4_scmfsa6a,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,u1_compos_1(k1_scmfsa_2)) => ( ( k2_xcmplx_0(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,A),C) = k5_memstr_0(k7_card_1(3),k1_scmfsa_2,B) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,A) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,B) ) => ( k2_xcmplx_0(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k2_extpro_1(k7_card_1(3),k1_scmfsa_2,D,A)),C) = k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k5_compos_0(u1_compos_1(k1_scmfsa_2),D,C),B)) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k2_extpro_1(k7_card_1(3),k1_scmfsa_2,D,A)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k5_compos_0(u1_compos_1(k1_scmfsa_2),D,C),B)) ) ) ) ) ) ) )).
fof(t4_scmfsa6c,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_scmfsa6c(C) & m1_subset_1(C,u1_compos_1(k1_scmfsa_2)) ) => r8_pboole(u1_struct_0(k1_scmfsa_2),k2_extpro_1(k7_card_1(3),k1_scmfsa_2,C,k1_scmfsa_m(A)),k1_scmfsa6b(k11_compos_1(k1_scmfsa_2,C),A,B)) ) ) ) )).
fof(t4_scmfsa7b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_scmfsa_2(C) => ! [D] : ( m2_finseq_1(D,k4_numbers) => ( k18_scmfsa_2(k1_scmfsa6b(k4_scmfsa_7(C,D),B,A),C) = D & ! [E] : ( ( 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] : ( m1_scmfsa_2(E) => ( E != C => k18_scmfsa_2(k1_scmfsa6b(k4_scmfsa_7(C,D),B,A),E) = k18_scmfsa_2(B,E) ) ) ) ) ) ) ) )).
fof(t4_scmfsa8a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_scmfsa7b(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => v1_scmfsa7b(k6_compos_1(k1_scmfsa_2,A,B)) ) ) )).
fof(t4_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,C) = k6_memstr_0(k7_card_1(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) ) ) ) ) ) ) ) )).
fof(t4_scmfsa8c,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ( ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => r6_scmfsa7b(A,k1_scmfsa_m(B),C) ) ) => v5_extpro_1(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)),k7_card_1(3),k1_scmfsa_2,A) ) ) )).
fof(t4_scmfsa9a,axiom,( k4_sf_mastr(k4_compos_1(k1_scmfsa_2)) = k1_xboole_0 )).
fof(t4_scmfsa_1,axiom,( k1_funct_1(k3_relat_1(k4_scmfsa_1,k5_scmfsa_1),k4_ordinal1) = k4_ordinal1 )).
fof(t4_scmfsa_2,axiom,( ! [A] : ( m1_scmfsa_2(A) => ? [B] : ( v7_ordinal1(B) & A = k5_scmfsa_2(B) ) ) )).
fof(t4_scmfsa_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( ~ 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(k7_card_1(3),k1_scmfsa_2)) & v1_finset_1(B) & v4_extpro_1(B,k7_card_1(3),k1_scmfsa_2,A) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ( ( r1_tarski(B,C) & r1_tarski(B,D) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( ( r1_tarski(A,E) & r1_tarski(A,F) ) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v1_ami_2(H) & m1_subset_1(H,u1_struct_0(k1_scmfsa_2)) ) => ! [I] : ( ( v1_ami_2(I) & m1_subset_1(I,u1_struct_0(k1_scmfsa_2)) ) => ( ( k3_extpro_1(k7_card_1(3),k1_scmfsa_2,E,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G)) = k7_scmfsa_2(H,I) & r2_hidden(H,k9_xtuple_0(B)) ) => k2_xcmplx_0(k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G),H),k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G),I)) = k2_xcmplx_0(k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,D,G),H),k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,D,G),I)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t4_scmfsa_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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 ) ) ) )).
fof(t4_scmfsa_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( v7_ordinal1(B) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(C,k7_card_1(3),k1_scmfsa_2,B) ) => ( k1_funct_1(C,k4_scmfsa_2(k5_numbers)) = 1 => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( v1_int_1(E) => ( ! [F] : ( v7_ordinal1(F) => ( 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_xcmplx_0(B,F)) ) ) => ( D = k4_scmfsa_2(k5_numbers) | ( ! [F] : ( v7_ordinal1(F) => ( r1_xxreal_0(F,k1_afinsq_1(k2_scmfsa_7(D,E))) => ( k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C,F)) = k2_xcmplx_0(B,F) & ! [G] : ( ( v1_ami_2(G) & m1_subset_1(G,u1_struct_0(k1_scmfsa_2)) ) => ( G != D => k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C,F),G) = k1_funct_1(C,G) ) ) & ! [G] : ( m1_scmfsa_2(G) => k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C,F),G) = k18_scmfsa_2(C,G) ) ) ) ) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C,k1_afinsq_1(k2_scmfsa_7(D,E))),D) = E ) ) ) ) ) ) ) ) ) )).
fof(t4_scmfsa_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => k5_card_1(k1_scmfsa_9(B,A)) = k1_nat_1(k5_card_1(A),6) ) ) )).
fof(t4_scmfsa_i,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k2_scm_inst) => ! [C] : ( m1_subset_1(C,k2_scm_inst) => ! [D] : ( 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(C,D,B)),k2_scmfsa_i) ) ) ) ) )).
fof(t4_scmfsa_m,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) ) => r2_hidden(k4_scmfsa_2(k5_numbers),k9_xtuple_0(k1_scmfsa_m(A))) ) )).
fof(t4_scmp_gcd,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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)) = k1_nat_1(k5_card_1(B),1) ) ) )).
fof(t4_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => r2_hidden(k3_xtuple_0(14,k1_xboole_0,k9_finseq_1(A)),k1_scmpds_i) ) )).
fof(t4_scmpds_5,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( ( 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) ) ) )).
fof(t4_scmpds_6,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( k5_memstr_0(2,k1_scmpds_2,A) = B => k17_scmpds_2(A,C) = k2_xcmplx_0(B,C) ) ) ) ) )).
fof(t4_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & 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))) ) ) )).
fof(t4_scmpds_8,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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_8(A,B,C)) = k1_nat_1(k5_card_1(C),2) ) ) ) )).
fof(t4_scmpds_i,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k7_card_1(15)) => ! [B] : ( m1_subset_1(B,k1_scmpds_i) => ! [C] : ( v1_int_1(C) => ( B = k3_xtuple_0(A,k1_xboole_0,k9_finseq_1(C)) => k4_scmpds_i(B) = C ) ) ) ) )).
fof(t4_scmring1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => k5_card_3(k4_ordinal1,k4_card_3(k3_relat_1(k3_ami_2,k1_scmring1(A)))) = k4_ordinal1 ) )).
fof(t4_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( ( 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)) ) ) ) ) )).
fof(t4_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( ( 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 ) ) ) )).
fof(t4_scmring4,axiom,( ! [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) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( 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(k7_card_1(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)) ) ) )).
fof(t4_scmringi,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k7_card_1(8)) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( m1_subset_1(C,k1_scmringi(B)) => ! [D] : ( m1_subset_1(D,k2_scm_inst) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t4_scmyciel,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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 ) ) )).
fof(t4_scpinvar,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_scmpds_2)) ) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ! [H] : ( m1_subset_1(H,k4_ordinal1) => ! [I] : ( m1_subset_1(I,k4_ordinal1) => ! [J] : ( m2_finseq_1(J,k4_numbers) => ( ( r1_scpisort(J,B,I) & k3_finseq_1(J) = G & k1_funct_1(B,E) = k5_numbers & k1_funct_1(B,D) = k5_numbers & k1_funct_1(B,k1_scmp_gcd(H)) = k4_xcmplx_0(G) & k1_funct_1(B,F) = k1_nat_1(I,1) & ! [K] : ( ( 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,k5_numbers) ) => ! [L] : ( ( v1_relat_1(L) & v4_relat_1(L,k4_ordinal1) & v5_relat_1(L,u1_compos_1(k1_scmpds_2)) & v1_funct_1(L) & v1_partfun1(L,k4_ordinal1) ) => ( ( k1_funct_1(K,D) = k5_numbers & ! [M] : ( m1_subset_1(M,k4_ordinal1) => ( ~ r1_xxreal_0(M,I) => k1_funct_1(K,k1_scmp_gcd(M)) = k1_funct_1(B,k1_scmp_gcd(M)) ) ) ) => ( ! [M] : ( 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) = k1_nat_1(k1_nat_1(I,1),k3_finseq_1(M)) ) ) | r1_xxreal_0(k5_numbers,k1_funct_1(K,k1_scmp_gcd(H))) | ( k1_funct_1(k6_scmpds_4(C,K,L),D) = k5_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] : ( 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) = k1_nat_1(k1_nat_1(I,1),k3_finseq_1(M)) & k1_funct_1(k6_scmpds_4(C,K,L),E) = k1_gr_cy_1(M) ) & ! [M] : ( m1_subset_1(M,k4_ordinal1) => ( ~ 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t4_scpisort,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) )).
fof(t4_scpqsort,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmpds_2)) => ! [C] : ( m1_subset_1(C,u1_compos_1(k1_scmpds_2)) => ! [D] : ( 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 ) ) ) ) )).
fof(t4_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,E) => r2_analoaf(A,C,B,D,E) ) ) ) ) ) ) )).
fof(t4_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v9_ordinal1(A) <=> ! [B] : ~ ( r2_hidden(B,k4_ordinal1) & k1_funct_1(A,B) = k5_numbers ) ) ) )).
fof(t4_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v7_ordinal1(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(D,B) & r1_xxreal_0(C,k9_complex1(k1_funct_1(A,D))) ) ) ) ) ) )).
fof(t4_seq_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v5_xxreal_2(A) <=> ? [B] : ( v1_xreal_0(B) & ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v1_xreal_0(C) => ~ ( r2_hidden(C,A) & r1_xxreal_0(B,k9_complex1(C)) ) ) ) ) ) )).
fof(t4_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( r2_relset_1(k4_ordinal1,k4_partfun1(A,k1_numbers),k6_seqfunc(A,B,C),k6_seqfunc(A,C,B)) & r2_relset_1(k4_ordinal1,k4_partfun1(A,k1_numbers),k6_seqfunc(A,k6_seqfunc(A,B,C),D),k6_seqfunc(A,B,k6_seqfunc(A,C,D))) ) ) ) ) ) )).
fof(t4_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v6_valued_0(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(C,B) & r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,A,C)) ) ) ) ) ) )).
fof(t4_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_series_1(A) => ( v2_comseq_2(A) & k1_seq_2(A) = k5_numbers ) ) ) )).
fof(t4_series_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(k3_xcmplx_0(A,B),k1_square_1(k7_xcmplx_0(k2_xcmplx_0(A,B),2))) ) ) )).
fof(t4_series_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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)) ) ) ) )).
fof(t4_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ~ ( ~ r1_xxreal_0(B,A) & r1_xxreal_0(k3_square_1(k7_xcmplx_0(A,B)),k7_xcmplx_0(A,B)) ) ) ) )).
fof(t4_setfam_1,axiom,( ! [A] : ( r2_hidden(k1_xboole_0,A) => k1_setfam_1(A) = k1_xboole_0 ) )).
fof(t4_setlim_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ( r2_hidden(A,k2_relset_1(B,C)) <=> ? [D] : ( v7_ordinal1(D) & A = k1_funct_1(C,D) ) ) ) ) )).
fof(t4_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => k8_nat_1(k9_setfam_1(B),k1_setlim_2(B,C,D),A) = k1_setlim_2(B,k8_nat_1(k9_setfam_1(B),C,A),k8_nat_1(k9_setfam_1(B),D,A)) ) ) ) )).
fof(t4_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( m1_subset_1(D,A) => r2_hidden(D,k8_relset_1(A,B,C,k1_tarski(k3_funct_2(A,B,C,D)))) ) ) ) ) )).
fof(t4_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ( k9_scmfsa_2(A,C) = k9_scmfsa_2(B,D) => ( A = B & C = D ) ) ) ) ) ) )).
fof(t4_sfmastr1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(D,k7_card_1(3),k1_scmfsa_2,k5_numbers) ) => ( ( r5_scmfsa7b(B,D,A) & r1_tarski(B,A) & r1_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D) ) => ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(E,k8_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D)) => r8_pboole(u1_struct_0(k1_scmfsa_2),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,D,E),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(B,C)),D,E)) ) ) ) ) ) ) ) )).
fof(t4_sfmastr2,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) => ( k1_funct_1(A,k4_scmfsa_2(k5_numbers)) = 1 => ( r5_scmfsa7b(C,A,B) <=> r5_scmfsa7b(C,k1_scmfsa_m(A),B) ) ) ) ) ) )).
fof(t4_sfmastr3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ~ ( A != B & r1_scmfsa7b(k6_scmfsa_2(C,B),A) ) ) ) ) )).
fof(t4_sgraph1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(1,A) => r1_tarski(k1_sgraph1(A,B),k2_finseq_1(B)) ) ) ) )).
fof(t4_sheffer1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k3_lattices(A,B,k1_sheffer1(A)) = k1_sheffer1(A) ) ) )).
fof(t4_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t4_simplex0,axiom,( ! [A] : k1_simplex0(k1_tarski(A)) = k9_setfam_1(A) )).
fof(t4_simplex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_simplex0(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t4_sin_cos,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ~ r1_xxreal_0(A,k5_numbers) => k9_nat_1(k2_numbers,k7_sin_cos(B),A) = k9_nat_1(k2_numbers,B,k7_nat_d(A,1)) ) ) ) )).
fof(t4_sin_cos2,axiom,( v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k18_sin_cos,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(t4_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,k2_xcmplx_0(A,B)) = k2_xcmplx_0(k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,B)),k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,B))) ) ) )).
fof(t4_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => k3_xcmplx_0(k17_sin_cos(A),k17_sin_cos(A)) = k6_xcmplx_0(1,k3_xcmplx_0(k19_sin_cos(A),k19_sin_cos(A))) ) )).
fof(t4_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( k17_sin_cos(A) != k5_numbers & k17_sin_cos(B) != k5_numbers & k17_sin_cos(C) != k5_numbers & k19_sin_cos(k2_xcmplx_0(k2_xcmplx_0(A,B),C)) != k4_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k17_sin_cos(A),k17_sin_cos(B)),k17_sin_cos(C)),k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_sin_cos4(A),k2_sin_cos4(B)),k2_sin_cos4(C)),k3_xcmplx_0(k3_xcmplx_0(k2_sin_cos4(A),k2_sin_cos4(B)),k2_sin_cos4(C))))) ) ) ) ) )).
fof(t4_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => r1_xxreal_0(k17_sin_cos(A),1) ) )).
fof(t4_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ r1_xxreal_0(k3_square_1(k2_xcmplx_0(k1_square_1(A),1)),k5_numbers) ) )).
fof(t4_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k5_numbers,A) => r1_xxreal_0(k5_numbers,k6_sin_cos2(A)) ) ) )).
fof(t4_sin_cos9,axiom,( r2_fdiff_1(k27_sin_cos,k2_rcomp_1(k5_numbers,k28_sin_cos)) & ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k2_rcomp_1(k5_numbers,k28_sin_cos)) => k1_fdiff_1(k27_sin_cos,A) = k4_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,A)))) ) ) )).
fof(t4_sincos10,axiom,( r1_tarski(k4_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)),k1_relset_1(k1_numbers,k2_fdiff_9)) )).
fof(t4_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_euclid(A)) => ! [C] : ( m1_subset_1(C,k1_euclid(A)) => ! [D] : ( m1_subset_1(D,k1_euclid(A)) => r1_xxreal_0(k6_xcmplx_0(k12_euclid(k8_euclid(A,C,B)),k12_euclid(k8_euclid(A,C,D))),k12_euclid(k8_euclid(A,D,B))) ) ) ) ) )).
fof(t4_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t4_sprect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( ~ 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 ) ) ) ) )).
fof(t4_sprect_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( 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,k1_nat_1(k7_nat_d(A,C),1)) ) ) ) ) ) ) ) )).
fof(t4_sprect_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( v1_xreal_0(D) => ( B = k3_rlvect_1(k15_euclid(A),k1_rlvect_1(k15_euclid(A),C,k6_xcmplx_0(1,D)),k1_rlvect_1(k15_euclid(A),B,D)) => ( r1_xxreal_0(1,D) | B = C ) ) ) ) ) ) )).
fof(t4_sprect_4,axiom,( ! [A] : ( ( v4_topreal1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v7_ordinal1(D) => ( ( 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,k1_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) ) ) ) ) ) ) )).
fof(t4_sprect_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t4_square_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k1_square_1(k2_xcmplx_0(A,B)) = k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k3_xcmplx_0(k3_xcmplx_0(2,A),B)),k1_square_1(B)) ) ) )).
fof(t4_stacks_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_stacks_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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 ) ) ) ) ) )).
fof(t4_stirl2_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k4_ordinal1)) => ( ~ r2_hidden(k3_nat_1(B),k9_subset_1(k4_ordinal1,B,A)) => k3_nat_1(B) = k3_nat_1(k7_subset_1(k4_ordinal1,B,A)) ) ) ) )).
fof(t4_struct_0,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t4_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_valuat_1(C,A,B) => ! [D] : ( m2_subset_1(D,k16_substut1(A),k38_substut1(A)) => ( v2_substut1(D,A) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t4_subset,axiom,( ! [A] : ! [B] : ! [C] : ( ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) ) => m1_subset_1(A,C) ) )).
fof(t4_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ~ ( B != k1_xboole_0 & ! [C] : ( m1_subset_1(C,A) => ~ r2_hidden(C,B) ) ) ) )).
fof(t4_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( m1_subset_1(D,k5_finsub_1(k4_partfun1(A,B))) => ( D = k1_tarski(k1_xboole_0) => k4_substlat(A,B,C,D) = C ) ) ) )).
fof(t4_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t4_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ( ! [C] : ( m1_subset_1(C,k1_substut1(A)) => ? [D] : ( m2_subset_1(D,k16_substut1(A),k38_substut1(A)) & k2_sublemma(A,D) = B & k19_substut1(A,D) = C ) ) => ! [C] : ( m1_subset_1(C,k1_substut1(A)) => ? [D] : ( m2_subset_1(D,k16_substut1(A),k38_substut1(A)) & k2_sublemma(A,D) = k6_cqc_lang(A,B) & k19_substut1(A,D) = C ) ) ) ) ) )).
fof(t4_supinf_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_setfam_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k6_numbers))) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_membered(B) ) => ( B = k5_setfam_1(k6_numbers,A) => m1_xxreal_2(k1_xxreal_2(B),k5_supinf_1(A)) ) ) ) )).
fof(t4_supinf_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( m1_subset_1(B,k6_numbers) => ( r2_hidden(B,A) <=> r2_hidden(k2_supinf_2(B),k6_supinf_2(A)) ) ) ) )).
fof(t4_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ~ ( ~ r1_orders_2(B,D,C) & r1_orders_2(B,E,C) & r1_orders_2(B,k3_rlvect_1(B,D,E),C) ) ) ) ) ) ) )).
fof(t4_sysrel,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r1_tarski(C,k2_zfmisc_1(A,B)) => r1_tarski(k2_relat_1(C),k2_zfmisc_1(B,A)) ) ) )).
fof(t4_t_0topsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) )).
fof(t4_t_1topsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => v7_pre_topc(k2_t_1topsp(A)) ) )).
fof(t4_tarski,axiom,( ! [A] : ? [B] : ( r2_hidden(A,B) & ! [C] : ! [D] : ( ( r2_hidden(C,B) & r1_tarski(D,C) ) => r2_hidden(D,B) ) & ! [C] : ~ ( r2_hidden(C,B) & ! [D] : ~ ( r2_hidden(D,B) & ! [E] : ( r1_tarski(E,C) => r2_hidden(E,D) ) ) ) & ! [C] : ~ ( r1_tarski(C,B) & ~ r2_tarski(C,B) & ~ r2_hidden(C,B) ) ) )).
fof(t4_taxonom1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( r1_relat_2(B,A) => k2_relset_1(A,B) = A ) ) )).
fof(t4_taxonom2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_taxonom1(B,A) => ( v3_orders_2(k1_yellow_1(k3_tarski(B))) & v4_orders_2(k1_yellow_1(k3_tarski(B))) & v5_orders_2(k1_yellow_1(k3_tarski(B))) & v1_taxonom2(k1_yellow_1(k3_tarski(B))) & v2_taxonom2(k1_yellow_1(k3_tarski(B))) & l1_orders_2(k1_yellow_1(k3_tarski(B))) ) ) ) )).
fof(t4_taylor_1,axiom,( ! [A] : ( v1_xreal_0(A) => k23_sin_cos(k4_xcmplx_0(A)) = k7_xcmplx_0(1,k23_sin_cos(A)) ) )).
fof(t4_taylor_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( r1_tarski(k2_rcomp_1(k4_xcmplx_0(C),C),k9_xtuple_0(B)) & r1_taylor_1(B,k1_nat_1(A,1),k2_rcomp_1(k4_xcmplx_0(C),C)) ) => ( r1_xxreal_0(C,k5_numbers) | ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,k2_rcomp_1(k4_xcmplx_0(C),C)) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ~ r1_xxreal_0(1,E) & k9_complex1(k6_xcmplx_0(k1_funct_1(B,D),k9_nat_1(k1_numbers,k3_series_1(k1_taylor_2(B,k2_rcomp_1(k4_xcmplx_0(C),C),D)),A))) = k9_complex1(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(B,k2_rcomp_1(k4_xcmplx_0(C),C)),k1_nat_1(A,1)),k3_xcmplx_0(E,D)),k1_newton(D,k1_nat_1(A,1))),k2_newton(k1_nat_1(A,1)))) ) ) ) ) ) ) ) ) ) )).
fof(t4_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) <=> ( k9_xtuple_0(B) = k4_ordinal1 & ! [C] : ( v7_ordinal1(C) => m1_subset_1(k1_funct_1(B,C),u1_struct_0(A)) ) ) ) ) ) )).
fof(t4_tdgroup,axiom,( ! [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) ) => ( u1_struct_0(k2_tdgroup(A)) = u1_struct_0(A) & u1_analoaf(k2_tdgroup(A)) = k1_tdgroup(A) ) ) )).
fof(t4_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)))) ) ) )).
fof(t4_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t4_tdlat_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t4_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [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) & v1_vectsp_2(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => r8_pboole(k15_pre_poly(A),k4_polynom7(A,B,k6_algstr_0(B,C,D)),k10_polynom1(A,B,k4_polynom7(A,B,C),k4_polynom7(A,B,D))) ) ) ) ) )).
fof(t4_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t4_tex_2,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ! [B] : ( m1_subset_1(B,A) => v1_subset_1(k6_domain_1(A,B),A) ) ) )).
fof(t4_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t4_tex_4,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t4_tietze,axiom,( ! [A] : ( ( v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) )).
fof(t4_tmap_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(A)) ) => ! [F] : ( ( ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(A)) ) => ! [G] : ( ( ~ 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] : ( ( v1_funct_1(H) & v1_funct_2(H,C,B) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(C,B))) ) => ! [I] : ( ( v1_funct_1(I) & v1_funct_2(I,D,B) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(D,B))) ) => ! [J] : ( ( 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] : ( ( v1_funct_1(K) & v1_funct_2(K,F,B) & m1_subset_1(K,k1_zfmisc_1(k2_zfmisc_1(F,B))) ) => ! [L] : ( ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t4_toler_1,axiom,( ! [A] : v7_relat_2(k1_eqrel_1(A)) )).
fof(t4_topalg_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k17_borsuk_1))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k17_borsuk_1)) => ( A = k4_rcomp_1(B,1) => v3_pre_topc(A,k17_borsuk_1) ) ) ) )).
fof(t4_topalg_2,axiom,( ! [A] : ( v1_xreal_0(A) => k7_partfun1(k1_numbers,k1_jordan2b(A),1) = A ) )).
fof(t4_topalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t4_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l3_algstr_0(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & l3_algstr_0(D) ) => ! [E] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) )).
fof(t4_topalg_5,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => k1_pre_topc(A,C) = k1_pre_topc(B,D) ) ) ) ) ) )).
fof(t4_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ( k2_xxreal_2(k1_relset_1(u1_struct_0(k5_topmetr),D)) = k5_numbers & k1_xxreal_2(k1_relset_1(u1_struct_0(k5_topmetr),D)) = 1 ) ) ) ) ) )).
fof(t4_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t4_topdim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v2_pre_topc(B) & v3_pcomps_1(B) & l1_pre_topc(B) ) => ( v5_waybel23(B) => ( ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t4_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t4_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => k2_topgen_2(A) = k3_tarski(a_1_0_topgen_2(A)) ) )).
fof(t4_topgen_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( ( r2_hidden(k11_arytm_3,B) & ! [C] : ! [D] : ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k2_xboole_0(C,D),B) ) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ( r1_tarski(C,B) => r2_hidden(k8_setfam_1(A,C),B) ) ) ) => ! [C] : ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) => ( v4_pre_topc(D,C) <=> r2_hidden(D,B) ) ) ) ) ) ) ) )).
fof(t4_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(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)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v3_pre_topc(C,A) & C != k1_xboole_0 & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(D,B) & r1_tarski(D,C) & D != k1_xboole_0 ) ) ) ) ) ) )).
fof(t4_topgen_5,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(A,k9_xtuple_0(k9_funct_6(B))) <=> ? [C] : ? [D] : ( 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)) ) ) ) )).
fof(t4_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( ( r1_tarski(B,D) & r1_tarski(C,E) ) => r1_tarski(k2_group_2(A,B,C),k2_group_2(A,D,E)) ) ) ) ) ) ) )).
fof(t4_topmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) ) )).
fof(t4_topmetr3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k7_metric_1)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k7_metric_1)))) ) => ( r1_funct_2(k4_ordinal1,k1_numbers,k4_ordinal1,u1_struct_0(k7_metric_1),A,B) => ( ( v2_comseq_2(A) => v2_tbsp_1(B,k7_metric_1) ) & ( v2_tbsp_1(B,k7_metric_1) => v2_comseq_2(A) ) & ( v2_comseq_2(A) => k1_seq_2(A) = k1_tbsp_1(k7_metric_1,B) ) ) ) ) ) )).
fof(t4_topreal1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r1_xxreal_0(k18_euclid(B),k18_euclid(C)) & r2_hidden(A,k1_rltopsp1(k15_euclid(2),B,C)) ) => ( r1_xxreal_0(k18_euclid(B),k18_euclid(A)) & r1_xxreal_0(k18_euclid(A),k18_euclid(C)) ) ) ) ) ) )).
fof(t4_topreal2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ ( v1_topreal2(A) & ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( B != C & r2_hidden(B,A) & r2_hidden(C,A) ) ) ) ) ) )).
fof(t4_topreal3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v1_xreal_0(B) => ( k17_euclid(k1_rlvect_1(k15_euclid(2),A,B)) = k3_xcmplx_0(B,k17_euclid(A)) & k18_euclid(k1_rlvect_1(k15_euclid(2),A,B)) = k3_xcmplx_0(B,k18_euclid(A)) ) ) ) )).
fof(t4_topreal4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( r1_topreal4(A,B,C) & B = C ) ) ) ) )).
fof(t4_topreal5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( ( 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] : ( m1_subset_1(H,u1_struct_0(A)) => k1_funct_1(G,H) != F ) ) ) ) ) ) ) ) ) )).
fof(t4_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => k19_rvsum_1(k2_finseq_2(1,A)) = A ) )).
fof(t4_topreal7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r1_xxreal_0(A,k1_nat_1(k3_finseq_1(B),k3_finseq_1(C))) => ( r1_xxreal_0(A,k3_finseq_1(B)) | r2_hidden(k6_xcmplx_0(A,k3_finseq_1(B)),k4_finseq_1(C)) ) ) ) ) ) )).
fof(t4_topreal8,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_hidden(B,k10_xtuple_0(A)) | k4_finseq_4(A,B) = k5_numbers ) ) )).
fof(t4_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ~ ( C != D & r2_hidden(C,k9_metric_1(B,E,A)) & r2_hidden(D,k9_metric_1(B,E,A)) & r1_xxreal_0(A,k5_numbers) ) ) ) ) ) ) )).
fof(t4_topreala,axiom,( ! [A] : ! [B] : k10_finseq_1(A,B) = k4_funct_4(1,2,A,B) )).
fof(t4_toprealb,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k6_xcmplx_0(B,A),1) => v4_taxonom2(k1_toprealb(A,B)) ) ) ) )).
fof(t4_toprealc,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t4_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => k9_nat_1(u1_struct_0(k15_euclid(A)),k1_toprns_1(A,C,D),B) = k3_rlvect_1(k15_euclid(A),k9_nat_1(u1_struct_0(k15_euclid(A)),C,B),k9_nat_1(u1_struct_0(k15_euclid(A)),D,B)) ) ) ) ) )).
fof(t4_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) )).
fof(t4_tops_2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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))) ) ) ) )).
fof(t4_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t4_tops_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( v3_pre_topc(E,A) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) ) => ! [F] : ( 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] : ( ( v1_xreal_0(G) & v2_xxreal_0(G) ) => ~ r1_tarski(k8_metric_1(B,F,G),k7_relset_1(u1_struct_0(A),u1_struct_0(k3_pcomps_1(B)),C,E)) ) ) ) ) ) ) ) ) ) )).
fof(t4_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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))) ) ) )).
fof(t4_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v11_aff_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t4_treal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(B,D) & r1_xxreal_0(C,B) ) => ( k4_topmetr(A,D) = k1_tsep_1(k3_topmetr,k4_topmetr(A,B),k4_topmetr(C,D)) & k4_topmetr(C,B) = k2_tsep_1(k3_topmetr,k4_topmetr(A,B),k4_topmetr(C,D)) ) ) ) ) ) ) )).
fof(t4_trees_1,axiom,( ! [A] : ! [B] : ( r3_xboole_0(k9_finseq_1(A),k9_finseq_1(B)) => A = B ) )).
fof(t4_trees_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(t4_trees_3,axiom,( ! [A] : ! [B] : ( ( v1_trees_3(A) & v1_trees_3(B) ) => v1_trees_3(k5_xboole_0(A,B)) ) )).
fof(t4_trees_4,axiom,( ! [A] : ! [B] : ( k1_trees_4(A) = k1_trees_4(B) => A = B ) )).
fof(t4_trees_9,axiom,( ! [A] : ( ( 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))) ) ) )).
fof(t4_trees_a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m4_trees_1(B,A) => r1_tarski(B,a_2_0_trees_a(A,B)) ) ) )).
fof(t4_triang_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t4_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_pre_topc(C,A) => ( r1_tarski(u1_struct_0(B),u1_struct_0(C)) <=> m1_pre_topc(B,C) ) ) ) ) )).
fof(t4_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t4_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t4_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ v1_tsp_2(B,A) ) ) )).
fof(t4_turing_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( k1_gr_cy_1(k4_turing_1(1,k2_finseq_4(k4_ordinal1,A,B))) = A & k1_gr_cy_1(k4_turing_1(2,k2_finseq_4(k4_ordinal1,A,B))) = k1_nat_1(A,B) ) ) ) )).
fof(t4_twoscomp,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( 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))) ) ) ) )).
fof(t4_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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] : ( m5_margrel1(C,u1_struct_0(A),k1_unialg_2(A)) => k2_unialg_2(A,B,C) = C ) ) ) ) ) )).
fof(t4_uniform1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & F = k1_funct_1(C,E) & ! [G] : ( v1_xreal_0(G) => ~ ( ~ r1_xxreal_0(G,k5_numbers) & ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(B)) => ~ ( I = k1_funct_1(C,H) & ~ r1_xxreal_0(G,k3_metric_1(A,E,H)) & r1_xxreal_0(D,k3_metric_1(B,F,I)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t4_uproots,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( r2_hidden(D,B) => k1_recdef_1(k1_uproots(A,B,C),D) = C ) ) ) )).
fof(t4_urysohn1,axiom,( ! [A] : ( v7_ordinal1(A) => ( k4_finseq_1(k5_urysohn1(A)) = k2_finseq_1(k1_nat_1(k1_newton(2,A),1)) & k10_xtuple_0(k5_urysohn1(A)) = k1_urysohn1(A) ) ) )).
fof(t4_urysohn2,axiom,( ! [A] : ( v1_xreal_0(A) => k1_integra2(k1_xboole_0,A) = k1_xboole_0 ) )).
fof(t4_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( 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)) ) ) ) )).
fof(t4_valued_0,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k3_numbers) ) => ( r1_tarski(A,B) => v5_relat_1(A,k3_numbers) ) ) ) )).
fof(t4_valued_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_membered(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t4_valued_2,axiom,( ! [A] : m1_subset_1(k9_valued_2(A),k1_zfmisc_1(k8_valued_2(A))) )).
fof(t4_vectmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v9_metric_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_vectmetr(A) & l1_vectmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k3_vectmetr(A,k3_rlvect_1(A,B,C)),k2_xcmplx_0(k3_vectmetr(A,B),k3_vectmetr(A,C))) ) ) ) )).
fof(t4_vectsp10,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t4_vectsp11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(D),C,C) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(D))) ) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(D),C,C) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(D))) ) => ( ( r2_hidden(A,k2_finseq_1(C)) & r2_hidden(B,k2_finseq_1(C)) ) => k2_laplace(A,B,C,D,k5_matrlin2(C,C,D,E,F)) = k5_matrlin2(k7_nat_d(C,1),k7_nat_d(C,1),D,k2_laplace(A,B,C,D,E),k2_laplace(A,B,C,D,F)) ) ) ) ) ) ) ) )).
fof(t4_vectsp_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t4_vectsp_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & B = k3_rlvect_1(A,C,D) & B = k3_rlvect_1(A,D,C) ) ) ) ) )).
fof(t4_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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) ) ) )).
fof(t4_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( v7_vectsp_1(C,A) & m1_vectsp_4(C,A,B) ) => k1_vectsp_5(A,B,C,C) = C ) ) ) )).
fof(t4_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( m2_vectsp_6(E,A,B,C) => ( r1_tarski(C,D) => m2_vectsp_6(E,A,B,D) ) ) ) ) ) ) )).
fof(t4_vectsp_7,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t4_vectsp_8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t4_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ? [E] : ( 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) ) ) ) ) ) )).
fof(t4_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t4_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t4_waybel10,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t4_waybel11,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t4_waybel12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t4_waybel13,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(t4_waybel14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t4_waybel15,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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)) ) ) ) ) ) )).
fof(t4_waybel16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t4_waybel17,axiom,( ! [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) & v4_waybel11(A) & l1_waybel_9(A) ) => ! [B] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t4_waybel18,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( 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(k1_funct_7(k12_pralg_1(A,B),C,D)) ) ) ) ) )).
fof(t4_waybel19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_waybel19(A) & l1_waybel_9(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t4_waybel20,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t4_waybel21,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ 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] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => r3_waybel_0(A,B,C,D) ) ) ) ) ) )).
fof(t4_waybel22,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => v22_waybel_0(k3_struct_0(A),A,A) ) )).
fof(t4_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & v8_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => k11_waybel_0(A,C) = k11_waybel_0(B,D) ) ) ) ) ) )).
fof(t4_waybel24,axiom,( ! [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] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) )).
fof(t4_waybel25,axiom,( ! [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] : ( ( 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] : ( ( v4_waybel11(C) & m1_yellow_9(C,A) ) => ! [D] : ( ( v4_waybel11(D) & m1_yellow_9(D,B) ) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t4_waybel26,axiom,( m1_yellow_9(k1_waybel25(k9_waybel18),k2_yellow_1(k1_tarski(k5_numbers))) )).
fof(t4_waybel27,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_waybel27(D) ) => ! [E] : ( ( 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)) ) ) ) ) )).
fof(t4_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => v1_waybel28(k3_struct_0(A),A) ) )).
fof(t4_waybel29,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v4_yellow_0(D,k5_yellow_1(k2_zfmisc_1(A,B),C)) & m1_yellow_0(D,k5_yellow_1(k2_zfmisc_1(A,B),C)) ) => ! [E] : ( ( ~ v2_struct_0(E) & v4_yellow_0(E,k5_yellow_1(A,k5_yellow_1(B,C))) & m1_yellow_0(E,k5_yellow_1(A,k5_yellow_1(B,C))) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t4_waybel30,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,k1_yellow_1(k7_waybel_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_yellow_1(k7_waybel_0(A))))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) => k1_yellow_0(k1_yellow_1(k7_waybel_0(A)),k4_yellow_4(k1_yellow_1(k7_waybel_0(A)),k6_domain_1(u1_struct_0(k1_yellow_1(k7_waybel_0(A))),C),B)) = k3_tarski(a_3_0_waybel30(A,B,C)) ) ) ) )).
fof(t4_waybel31,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v3_waybel_3(B) & l1_orders_2(B) ) => ( k1_yellow_1(u1_pre_topc(A)) = B => ! [C] : ( ( 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)))) ) ) ) ) ) )).
fof(t4_waybel32,axiom,( ! [A] : ( ( ~ 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] : ( m1_yellow_9(B,A) => ( v4_waybel11(B) => v2_pre_topc(B) ) ) ) )).
fof(t4_waybel33,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t4_waybel34,axiom,( ! [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] : ( ( 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] : ( ( 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))) ) ) ) )).
fof(t4_waybel35,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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) ) ) ) )).
fof(t4_waybel_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( ( C = D & v2_waybel_0(C,A) ) => v2_waybel_0(D,B) ) ) ) ) ) ) )).
fof(t4_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v2_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t4_waybel_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t4_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_waybel_3(A,k3_yellow_0(A),B) ) ) )).
fof(t4_waybel_4,axiom,( ! [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] : ( ( 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) ) ) )).
fof(t4_waybel_5,axiom,( ! [A] : ( ( 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),k1_yellow_1(k7_waybel_0(A)),A) => v3_waybel_3(A) ) ) )).
fof(t4_waybel_6,axiom,( ! [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] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t4_waybel_7,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) ) )).
fof(t4_waybel_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t4_waybel_9,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) )).
fof(t4_weierstr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) )).
fof(t4_wellfnd1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v12_waybel_0(B,A) & r2_hidden(C,B) ) => r1_tarski(k1_wellord1(u1_orders_2(A),C),B) ) ) ) )).
fof(t4_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ( r2_wellord1(A,k1_relat_1(A)) <=> v2_wellord1(A) ) ) )).
fof(t4_wellord2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r4_wellord1(k1_wellord2(A),k1_wellord2(B)) => A = B ) ) ) )).
fof(t4_wellset1,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) ) )).
fof(t4_wsierp_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( r1_int_1(A,B) & r1_int_1(A,C) ) => r1_int_1(A,k2_xcmplx_0(B,C)) ) ) ) ) )).
fof(t4_xboole_0,axiom,( ! [A] : ! [B] : ( ~ ( ~ r1_xboole_0(A,B) & ! [C] : ~ r2_hidden(C,k3_xboole_0(A,B)) ) & ~ ( ? [C] : r2_hidden(C,k3_xboole_0(A,B)) & r1_xboole_0(A,B) ) ) )).
fof(t4_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C)) )).
fof(t4_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k5_xboolean(A,k5_xboolean(A,B)) = k5_xboolean(A,B) ) ) )).
fof(t4_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k3_xcmplx_0(A,k3_xcmplx_0(B,C)) = k3_xcmplx_0(k3_xcmplx_0(A,B),C) ) ) ) )).
fof(t4_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(A,C) & ~ r1_xxreal_0(B,C) ) ) ) )).
fof(t4_xregular,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( r2_hidden(B,A) & ! [C] : ! [D] : ! [E] : ( ( r2_hidden(C,D) & r2_hidden(D,E) & r2_hidden(E,B) ) => r1_xboole_0(C,A) ) ) ) )).
fof(t4_xtuple_0,axiom,( ! [A] : ( v2_xtuple_0(A) => ! [B] : ( 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 ) ) ) )).
fof(t4_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ( r1_xxreal_0(k1_xxreal_0,A) => A = k1_xxreal_0 ) ) )).
fof(t4_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(C,k4_xxreal_1(A,B)) <=> ( ~ r1_xxreal_0(C,A) & ~ r1_xxreal_0(B,C) ) ) ) ) ) )).
fof(t4_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v2_membered(B) => ( r2_hidden(A,B) => r1_xxreal_0(A,k1_xxreal_2(B)) ) ) ) )).
fof(t4_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => k1_xxreal_3(A,k5_numbers) = A ) )).
fof(t4_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t4_yellow11,axiom,( k6_subset_1(3,2) = k6_domain_1(k4_ordinal1,2) )).
fof(t4_yellow12,axiom,( ! [A] : ! [B] : ( 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) ) )).
fof(t4_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => v8_pre_topc(A) ) )).
fof(t4_yellow14,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t4_yellow15,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k6_margrel1) => k3_finseq_1(k1_yellow15(A,k6_finseq_1(k9_setfam_1(A)),B)) = k5_numbers ) )).
fof(t4_yellow16,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & v4_waybel_0(B,A) & m1_yellow_0(B,A) ) => v24_waybel_0(B) ) ) )).
fof(t4_yellow17,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => k8_relat_1(k12_card_3(A,B),k1_funct_1(A,B)) = k4_card_3(A) ) ) )).
fof(t4_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t4_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_waybel_7(A,k1_yellow19(A,B),B) ) ) )).
fof(t4_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( m2_functor0(C,A,B) => ( v21_functor0(C,A,B) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t4_yellow21,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t4_yellow_0,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_orders_2(A,B,C) => ! [D] : ( ( r1_lattice3(A,D,C) => r1_lattice3(A,D,B) ) & ( r2_lattice3(A,D,B) => r2_lattice3(A,D,C) ) ) ) ) ) ) )).
fof(t4_yellow_1,axiom,( ! [A] : k2_yellow_1(A) = k1_yellow_1(k9_setfam_1(A)) )).
fof(t4_yellow_2,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ! [C] : ( ( 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)) ) ) ) )).
fof(t4_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => k12_lattice3(A,k1_yellow_0(A,B),C) = C ) ) ) ) )).
fof(t4_yellow_4,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t4_yellow_5,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_orders_2(A,D,k12_lattice3(A,B,C)) => r1_orders_2(A,D,B) ) ) ) ) ) )).
fof(t4_yellow_6,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => u1_struct_0(k3_yellow_6(A,B,C)) = u1_struct_0(A) ) ) ) )).
fof(t4_yellow_7,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_orders_2(A) <=> v3_orders_2(k7_lattice3(A)) ) ) )).
fof(t4_yellow_8,axiom,( ! [A] : ! [B] : ( ( r2_tarski(A,B) & v4_card_3(A) ) => v4_card_3(B) ) )).
fof(t4_yellow_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t4_zf_colla,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r1_ordinal1(B,C) => r1_tarski(k1_zf_colla(A,B),k1_zf_colla(A,C)) ) ) ) ) )).
fof(t4_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ! [D] : ( ( 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) ) ) ) ) )).
fof(t4_zf_fund2,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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) ) ) ) )).
fof(t4_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) <=> r2_hidden(A,k9_zf_lang) ) )).
fof(t4_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( k21_zf_lang(k7_zf_lang(A,B)) = A & k22_zf_lang(k7_zf_lang(A,B)) = B ) ) ) )).
fof(t4_zf_model,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t4_zf_refle,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => r2_zf_model(A,k10_zf_model) ) )).
fof(t4_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( k1_tarski(A) = k2_tarski(B,C) => A = B ) )).
fof(t4_zfmodel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_ordinal1(A) => ( r2_zf_model(A,k8_zf_model) <=> ! [B] : ( m1_subset_1(B,A) => r2_hidden(k3_tarski(B),A) ) ) ) ) )).
fof(t4_zfmodel2,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t4_zfrefle1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_zf_model(A) => r1_zfrefle1(A,k2_zfrefle1) ) ) )).
fof(t4_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(t4_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_zmodul02(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_zmodul02(A))) => ( ( B = D & C = E ) => ( k3_rlvect_1(A,B,C) = k3_rlvect_1(k15_zmodul02(A),D,E) & k5_algstr_0(A,B,C) = k5_algstr_0(k15_zmodul02(A),D,E) ) ) ) ) ) ) ) )).
fof(t50_abcmiz_0,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t50_abcmiz_1,axiom,( ! [A] : ( m1_subset_1(A,k2_abcmiz_1) => ! [B] : ( m1_subset_1(B,k2_abcmiz_1) => ! [C] : ( ( v1_instalg1(C) & v1_abcmiz_1(C) & v3_abcmiz_1(C) & l1_msualg_1(C) ) => ! [D] : ( ( 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 ) ) ) ) ) )).
fof(t50_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [C] : ( m1_subset_1(C,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t50_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t50_aff_4,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t50_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t50_afinsq_2,axiom,( ! [A] : ( ( 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(k4_ordinal1,A,k23_binop_2) ) ) )).
fof(t50_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t50_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_analoaf(A) & v2_tdgroup(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => A = k2_tdgroup(k5_afvect0(A,B)) ) ) )).
fof(t50_algspec1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_instalg1(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t50_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_altcat_4(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_altcat_4(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t50_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t50_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t50_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t50_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m2_pboole(C,u4_struct_0(A),k3_msafree4(k3_finseq_2(u1_struct_0(A)),u4_struct_0(A),u1_msualg_1(A),k6_finseq_2(u1_struct_0(A),B)),k3_msafree4(u1_struct_0(A),u4_struct_0(A),u2_msualg_1(A),B)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k1_msafree4(u4_struct_0(A),k3_msafree4(k3_finseq_2(u1_struct_0(A)),u4_struct_0(A),u1_msualg_1(A),k6_finseq_2(u1_struct_0(A),B)),D),k1_msafree4(u4_struct_0(A),k3_msafree4(u1_struct_0(A),u4_struct_0(A),u2_msualg_1(A),B),D)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_msafree4(u4_struct_0(A),k3_msafree4(k3_finseq_2(u1_struct_0(A)),u4_struct_0(A),u1_msualg_1(A),k6_finseq_2(u1_struct_0(A),B)),D),k1_msafree4(u4_struct_0(A),k3_msafree4(u1_struct_0(A),u4_struct_0(A),u2_msualg_1(A),B),D)))) ) => m2_pboole(k1_aofa_a00(u4_struct_0(A),C,D,E),u4_struct_0(A),k3_msafree4(k3_finseq_2(u1_struct_0(A)),u4_struct_0(A),u1_msualg_1(A),k6_finseq_2(u1_struct_0(A),B)),k3_msafree4(u1_struct_0(A),u4_struct_0(A),u2_msualg_1(A),B)) ) ) ) ) ) )).
fof(t50_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( m2_pboole(E,u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,D)) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,C),u8_aofa_a00(A))) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),u8_aofa_a00(A))) => k15_aofa_a00(A,B,C,D,u8_aofa_a00(A),k23_aofa_a00(A,C,F,G),E) = k23_aofa_a00(A,D,k15_aofa_a00(A,B,C,D,u8_aofa_a00(A),F,E),k15_aofa_a00(A,B,C,D,u8_aofa_a00(A),G,E)) ) ) ) ) ) ) ) )).
fof(t50_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_aofa_i00(E,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) ) => ! [F] : ( m3_aofa_i00(F,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_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,k5_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,k5_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,k5_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,k5_numbers)) => v1_abian(k3_funct_2(k9_funct_2(B,k4_numbers),k4_numbers,F,C)) ) ) ) ) ) ) ) ) )).
fof(t50_armstrng,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( ( v11_armstrng(B) & C = a_2_13_armstrng(A,B) ) => ( v1_xboole_0(B) | B = k13_armstrng(A,k10_armstrng(A,C)) ) ) ) ) )).
fof(t50_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => k9_arytm_3(A,k11_arytm_3) = A ) )).
fof(t50_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(C,k5_numbers) & C != 1 & k2_power(A,B) != k2_power(C,k3_xcmplx_0(B,k3_power(C,A))) ) ) ) ) )).
fof(t50_bcialg_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t50_bcialg_2,axiom,( ! [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] : ( 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) ) ) ) )).
fof(t50_bcialg_4,axiom,( ! [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) & l1_bcialg_4(A) ) => ( v8_bcialg_4(A) <=> ( v3_bcialg_4(A) & v4_bcialg_4(A) ) ) ) )).
fof(t50_bcialg_5,axiom,( ! [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) ) => ( ( ~ 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,k5_numbers,k5_numbers,k5_numbers) ) ) ) )).
fof(t50_bcialg_6,axiom,( ! [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] : ( ( ~ 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] : ( m2_bcialg_1(C,A) => ! [D] : ( m5_bcialg_2(D,A,C) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t50_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( m3_bciideal(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t50_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),B,k5_bhsp_1(A,B,k4_struct_0(A))) ) ) )).
fof(t50_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(C,k4_bhsp_2(A,B,D)) => r2_hidden(C,k5_bhsp_2(A,B,D)) ) ) ) ) ) )).
fof(t50_bhsp_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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),k1_seq_2(A)) ) ) ) ) ) )).
fof(t50_bilinear,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( ( 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))) ) ) ) ) ) )).
fof(t50_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ r4_boolealg(A,k4_lattices(A,B,C),k1_boolealg(A,B,C)) ) ) ) )).
fof(t50_borsuk_4,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)))) ) ) ) ) )).
fof(t50_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( 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) ) ) ) )).
fof(t50_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t50_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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) ) ) )).
fof(t50_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t50_bvfunc14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( v1_relat_1(H) & v1_funct_1(H) ) => ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ( 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) ) ) )).
fof(t50_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(t50_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => k9_xboolean(k7_margrel1,A) = k3_xboolean(A) ) )).
fof(t50_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)))) ) ) ) ) ) )).
fof(t50_card_1,axiom,( 4 = k2_enumset1(k5_ordinal1,1,2,3) )).
fof(t50_card_2,axiom,( ! [A] : ! [B] : ! [C] : r1_xxreal_0(k5_card_1(k1_enumset1(A,B,C)),3) )).
fof(t50_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => r2_hidden(k1_xboole_0,k8_card_3(A)) ) )).
fof(t50_card_fin,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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) ) ) )).
fof(t50_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v10_cat_1(B,A) & v10_cat_1(C,A) ) => r1_cat_1(A,B,C) ) ) ) ) )).
fof(t50_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t50_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k23_cat_4(A,B))) => v11_cat_1(C,k23_cat_4(A,B)) ) )).
fof(t50_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ( ( v1_partfun1(A,k2_numbers) & ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k7_partfun1(k2_numbers,A,k2_xcmplx_0(B,C)) = k2_xcmplx_0(k7_partfun1(k2_numbers,A,B),k7_partfun1(k2_numbers,A,C)) ) ) ) => ( ! [B] : ( v1_xcmplx_0(B) => ~ r1_cfcont_1(A,B) ) | r2_cfcont_1(A,k2_numbers) ) ) ) )).
fof(t50_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t50_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_chain_1(C,B) => ( ~ r1_xxreal_0(k1_nat_1(A,1),B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k4_chain_1(B,C,k1_nat_1(A,1)))) => k10_chain_1(B,C,A,D) = k5_chain_1(B,C,A) ) ) ) ) ) )).
fof(t50_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ( r5_glib_000(A,B) => ! [C] : k2_chord(A,C) = k2_chord(B,C) ) ) ) )).
fof(t50_circcmb3,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( v1_relat_1(B) => ~ r2_hidden(A,B) ) ) )).
fof(t50_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_circcomb(B) & l1_msualg_1(B) ) => v2_circcomb(k2_circcomb(A,B)) ) ) )).
fof(t50_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v4_msualg_1(E,A) & v4_msafree2(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( ( v4_msualg_1(F,B) & v4_msafree2(F,B) & l3_msualg_1(F,B) ) => ( r5_circtrm1(A,B,C,D,E,F) => ! [G] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t50_classes1,axiom,( ! [A] : ! [B] : ( ( v1_ordinal1(A) & v1_ordinal1(B) ) => v1_ordinal1(k3_xboole_0(A,B)) ) )).
fof(t50_classes2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => A = k4_classes1(k2_ordinal1(A)) ) )).
fof(t50_clvect_1,axiom,( ! [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) ) => ! [B] : ( ( v1_clvect_1(B) & m1_clvect_1(B,A) ) => ! [C] : ( ( v1_clvect_1(C) & m1_clvect_1(C,A) ) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_struct_0(B,D) <=> r1_struct_0(C,D) ) ) => B = C ) ) ) ) )).
fof(t50_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(C,k4_clvect_2(A,B,D)) => r2_hidden(C,k5_clvect_2(A,B,D)) ) ) ) ) ) )).
fof(t50_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) ) ) )).
fof(t50_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( r2_hidden(k4_tarski(B,C),k10_cohsp_1(A)) <=> r2_hidden(k4_tarski(k1_tarski(B),C),k7_cohsp_1(A)) ) ) )).
fof(t50_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k4_complex1(A) = k5_numbers => k9_complex1(A) = k9_complex1(k3_complex1(A)) ) ) )).
fof(t50_complex2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k2_complex2(B,A) = k5_numbers <=> B = k5_numbers ) ) ) )).
fof(t50_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => k2_complfld(k2_complfld(A)) = A ) )).
fof(t50_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => k8_complsp2(A,k10_seq_4(B,k7_complex1)) = k4_xcmplx_0(k3_xcmplx_0(k7_complex1,k8_complsp2(A,B))) ) ) ) )).
fof(t50_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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) ) ) ) )).
fof(t50_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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)) ) ) ) )).
fof(t50_comptrig,axiom,( ! [A] : ( v1_xcmplx_0(A) => ~ ( ~ r1_xxreal_0(k5_numbers,k3_complex1(A)) & r1_xxreal_0(k5_numbers,k19_sin_cos(k1_comptrig(A))) ) ) )).
fof(t50_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k3_finseq_2(k4_ordinal1)) & v1_funct_1(C) & v4_valued_0(C) & v2_margrel1(C) ) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ! [E] : ( m2_finseq_1(E,k4_ordinal1) => r1_partfun1(k6_comput_1(B,C,A,D),k6_comput_1(B,C,A,E)) ) ) ) ) ) )).
fof(t50_convex4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v2_convex4(B,A) & v2_convex4(C,A) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t50_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t50_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) )).
fof(t50_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t50_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k15_csspace(A,B,B) = k5_numbers ) ) )).
fof(t50_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k3_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k16_sin_cos),A),B) = k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k19_sin_cos(k3_xcmplx_0(2,B)),k19_sin_cos(k3_xcmplx_0(2,k2_xcmplx_0(B,A))))) ) ) )).
fof(t50_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => k1_funct_1(D,E) = k7_xcmplx_0(B,k1_square_1(E)) ) => ( C = k5_numbers | k2_xcmplx_0(C,A) = k5_numbers | k1_funct_1(k3_diff_1(D,A),C) = k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(B),A),k2_xcmplx_0(k3_xcmplx_0(2,C),A)),k1_square_1(k2_xcmplx_0(k1_square_1(C),k3_xcmplx_0(A,C)))) ) ) ) ) ) ) )).
fof(t50_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( ( 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] : ( v1_xreal_0(F) => k1_funct_1(D,F) = k1_funct_1(k5_diff_1(E,A),F) ) => k9_diff_1(D,B,C) = k6_xcmplx_0(k9_diff_1(E,k2_xcmplx_0(B,k7_xcmplx_0(A,2)),k2_xcmplx_0(C,k7_xcmplx_0(A,2))),k9_diff_1(E,k6_xcmplx_0(B,k7_xcmplx_0(A,2)),k6_xcmplx_0(C,k7_xcmplx_0(A,2)))) ) ) ) ) ) ) )).
fof(t50_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,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)) & r2_hidden(D,k8_eqrel_1(k6_ec_pf_1(A,B,C),k8_ec_pf_1(A,B,C))) & ! [E] : ( 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(k4_ordinal1,k4_ordinal1,k4_ordinal1,k5_numbers,1,k5_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] : ( 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] : ( m1_subset_1(F,u1_struct_0(k9_int_3(A))) => ! [G] : ( 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)),k4_ordinal1,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) ) ) ) ) ) ) ) ) )).
fof(t50_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( 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] : ( 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) != k5_numbers & k6_ec_pf_2(A,k2_ec_pf_2(A,B),k3_ec_pf_2(A,B),D) != k5_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)) ) ) ) ) ) ) )).
fof(t50_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t50_entropy1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v4_partfun3(C) & m2_finseq_1(C,k1_numbers) ) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(D,k4_finseq_1(C)) & k1_funct_1(C,D) = k3_xcmplx_0(A,B) ) => k1_funct_1(k4_entropy1(C),D) = k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(A,B),k3_power(2,A)),k3_xcmplx_0(k3_xcmplx_0(A,B),k3_power(2,B))) ) ) ) ) ) ) )).
fof(t50_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k6_enumset1(A,A,A,A,A,B,C,D) = k2_enumset1(A,B,C,D) )).
fof(t50_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t50_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => r1_xxreal_0(k12_euclid(k3_rlvect_1(k15_euclid(A),B,C)),k2_xcmplx_0(k12_euclid(B),k12_euclid(C))) ) ) ) )).
fof(t50_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t50_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,k2_numbers) => ! [E] : ( 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)) = k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(k17_euclid(A),k17_euclid(B)),k6_xcmplx_0(k17_euclid(C),k17_euclid(B))),k3_xcmplx_0(k6_xcmplx_0(k18_euclid(A),k18_euclid(B)),k6_xcmplx_0(k18_euclid(C),k18_euclid(B)))) & k4_complex1(k1_complex2(D,E)) = k2_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(k17_euclid(A),k17_euclid(B)),k6_xcmplx_0(k18_euclid(C),k18_euclid(B)))),k3_xcmplx_0(k6_xcmplx_0(k18_euclid(A),k18_euclid(B)),k6_xcmplx_0(k17_euclid(C),k17_euclid(B)))) & k9_complex1(D) = k3_square_1(k2_xcmplx_0(k1_square_1(k6_xcmplx_0(k17_euclid(A),k17_euclid(B))),k1_square_1(k6_xcmplx_0(k18_euclid(A),k18_euclid(B))))) & k12_euclid(k5_algstr_0(k15_euclid(2),A,B)) = k9_complex1(D) ) ) ) ) ) ) ) )).
fof(t50_euclid_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k1_rusub_4(k7_real_ns1(A)) = A ) )).
fof(t50_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k9_euclid(3,k1_euclid_8(A,B,C),D) = k1_euclid_8(k3_xcmplx_0(D,A),k3_xcmplx_0(D,B),k3_xcmplx_0(D,C)) ) ) ) ) )).
fof(t50_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t50_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( ( 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)) ) ) ) )).
fof(t50_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( 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) ) ) ) )).
fof(t50_fcont_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( A != k5_numbers => v2_funct_1(k1_fcont_1(A,B)) ) ) ) )).
fof(t50_fdiff_11,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k1_funct_1(k2_sin_cos9,B)),k1_funct_1(k18_sin_cos,B)),k1_square_1(k1_funct_1(k16_sin_cos,B)))),k7_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k2_fdiff_9,B)),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t50_fdiff_4,axiom,( ! [A] : ( ( 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)),k7_xcmplx_0(1,2))))) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k16_sin_cos,B),k5_numbers) & ~ r1_xxreal_0(1,k1_funct_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)),k7_xcmplx_0(1,2))),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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)),k7_xcmplx_0(1,2))),A),B) = k7_xcmplx_0(k1_newton(k1_funct_1(k18_sin_cos,B),3),k6_xcmplx_0(1,k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t50_fdiff_6,axiom,( ! [A] : ( ( 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,k18_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,k18_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_taylor_1,k18_sin_cos)),A),B) = k7_xcmplx_0(k1_funct_1(k16_sin_cos,k3_power(k4_power,B)),B) ) ) ) ) ) )).
fof(t50_fdiff_7,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k18_sin_cos)))) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => ( k1_funct_1(B,C) = k7_xcmplx_0(C,2) & k1_funct_1(k18_sin_cos,k1_funct_1(B,C)) != k5_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,k18_sin_cos)),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_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,k18_sin_cos)),A),C) = k7_xcmplx_0(1,k2_xcmplx_0(1,k1_funct_1(k18_sin_cos,C))) ) ) ) ) ) ) )).
fof(t50_fib_num2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( v1_int_2(k1_pre_ff(A)) => ( r1_xxreal_0(A,1) | A = 4 | v1_int_2(A) ) ) ) )).
fof(t50_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ v1_xboole_0(D) & v19_lattices(D,A) & v20_lattices(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k6_filter_0(A,D))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t50_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t50_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v18_lattices(B,A) & v21_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t50_finseq_1,axiom,( ! [A] : ( ( 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) ) )).
fof(t50_finseq_2,axiom,( k1_finseq_2(2) = k10_finseq_1(1,2) )).
fof(t50_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k5_relat_1(k1_finseq_2(B),k2_finseq_1(A)) = k1_finseq_2(B) <=> r1_xxreal_0(B,A) ) ) ) )).
fof(t50_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : ( ~ 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) ) ) ) )).
fof(t50_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t50_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t50_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( v3_card_1(F,D) & m2_finseq_1(F,A) ) => ! [G] : ( ( 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] : ( ( 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] : ( m1_subset_1(I,A) => ! [J] : ( m1_subset_1(J,A) => k3_funct_2(A,B,E,k5_binop_1(A,G,I,J)) = k5_binop_1(B,H,k3_funct_2(A,B,E,I),k3_funct_2(A,B,E,J)) ) ) => r2_relset_1(k4_ordinal1,B,k4_finseqop(A,B,k2_finseqop(A,A,A,G,F,C),E),k2_finseqop(B,B,B,H,k4_finseqop(A,B,F,E),k3_funct_2(A,B,E,C))) ) ) ) ) ) ) ) ) ) )).
fof(t50_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( ? [E] : ( 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] : ( m2_finseq_1(E,u1_struct_0(A)) => ~ r3_fintopo6(A,E,B,C,D) ) ) ) ) ) ) )).
fof(t50_flang_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_catalan2(A))) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(B,k7_flang_1(A,C,k1_nat_1(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))) ) ) ) ) )).
fof(t50_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => k1_flang_2(A,B,2,2) = k6_flang_1(A,B,B) ) )).
fof(t50_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => k2_flang_3(A,B) = k1_flang_3(A,B,1) ) )).
fof(t50_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( v3_fomodel0(C,A) & r1_tarski(B,C) ) => v3_fomodel0(B,A) ) ) )).
fof(t50_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t50_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) ) )).
fof(t50_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( ( 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) ) ) )).
fof(t50_funct_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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 ) ) ) )).
fof(t50_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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))) ) ) ) )).
fof(t50_funct_5,axiom,( ! [A] : k1_funct_2(k1_xboole_0,A) = k1_tarski(k1_xboole_0) )).
fof(t50_funct_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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(k9_funct_6(D),k1_funct_2(B,k1_funct_2(A,C))) ) ) ) )).
fof(t50_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => k3_funct_7(A,k10_finseq_1(B,C)) = k3_relat_1(k6_partfun1(A),k3_relat_1(B,C)) ) ) )).
fof(t50_funct_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t50_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D,C)),k3_fuzzy_2(A,k2_fuzzy_1(A,B,D),k2_fuzzy_1(A,B,C))) ) ) ) ) )).
fof(t50_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => r2_hidden(k5_struct_0(A),k6_fvaluat1(A,B)) ) ) ) )).
fof(t50_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t50_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( ( ~ v1_xboole_0(F) & v1_relat_1(F) & v2_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ! [G] : ( m1_genealg1(G,F) => ! [H] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t50_gfacirc1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => k2_msafree2(k19_gfacirc1(A,B,C)) = k1_enumset1(A,B,C) ) ) ) )).
fof(t50_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) => ! [C] : ( 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) => ( k1_nat_1(k15_glib_000(C),k5_card_1(B)) = k15_glib_000(A) & k1_nat_1(k17_glib_000(C),k5_card_1(k20_glib_000(A,B))) = k17_glib_000(A) ) ) ) ) ) )).
fof(t50_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => r2_relset_1(k4_ordinal1,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),k20_glib_001(A,B,C,C),B) ) ) ) )).
fof(t50_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_003(A) ) => ! [B] : ! [C] : ( r2_hidden(B,k7_glib_000(A)) => r2_hidden(B,k11_glib_003(k12_glib_003(A,B,C))) ) ) )).
fof(t50_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ 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(k1_nat_1(A,1),k3_finseq_1(k2_goboard2(D))) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(k2_goboard2(D))) & r1_xxreal_0(1,C) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1))) = k2_topreal1(2,D,C) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1))) = k2_topreal1(2,D,k1_nat_1(C,1)) ) => ( r1_xxreal_0(k3_finseq_1(D),k1_nat_1(C,1)) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),B) ) ) ) ) ) ) ) )).
fof(t50_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t50_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t50_graph_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( ~ 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] : ( m2_finseq_1(F,u4_struct_0(B)) => ~ ( r2_hidden(F,E) & ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t50_graphsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v7_graph_1(C,A) & m2_graph_1(C,A) ) => ! [D] : ( ( v7_graph_1(D,A) & m2_graph_1(D,A) ) => ( ( r5_graphsp(A,C,B) & r5_graphsp(A,D,B) ) => C = D ) ) ) ) ) )).
fof(t50_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k4_group_1(A),B,2) = k6_algstr_0(A,B,B) ) ) )).
fof(t50_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t50_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t50_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t50_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( 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))) ) ) ) )).
fof(t50_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t50_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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(A) => v8_struct_0(k10_group_6(A,B,C)) ) ) ) ) )).
fof(t50_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( 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) ) ) )).
fof(t50_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => k3_helly(A,B,C,C) = C ) ) ) )).
fof(t50_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k2_xcmplx_0(k9_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))),k9_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)))) = k2_xcmplx_0(k3_xcmplx_0(2,k9_complex1(k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(k1_complfld),B,C,C))),k3_xcmplx_0(2,k9_complex1(k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(k1_complfld),B,D,D)))) ) ) ) ) )).
fof(t50_hfdiff_1,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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)))) ) ) ) ) )).
fof(t50_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) )).
fof(t50_hurwitz,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ( ~ r1_xxreal_0(k9_complex1(A),k9_complex1(B)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(C,k1_complfld) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) ) ) ) ) ) ) )).
fof(t50_ideal_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t50_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u4_incsp_1(A)) => ~ ( r2_incsp_1(A,B,C) & ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u2_incsp_1(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t50_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( ~ r1_xxreal_0(B,A) => r1_xxreal_0(A,k6_xcmplx_0(B,1)) ) ) ) )).
fof(t50_int_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( r1_int_4(A,k1_xboole_0) <=> A = k5_numbers ) ) )).
fof(t50_int_5,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(t50_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(A,B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k2_xcmplx_0(1,k1_funct_1(k18_sin_cos,D)) != k5_numbers & k6_xcmplx_0(1,k1_funct_1(k18_sin_cos,D)) != k5_numbers & k1_funct_1(C,D) = k7_xcmplx_0(k1_funct_1(k18_sin_cos,D),k2_xcmplx_0(1,k1_funct_1(k18_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),k27_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) = k6_xcmplx_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k27_sin_cos),k2_fdiff_9),k2_seq_4(A)),k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k27_sin_cos),k2_fdiff_9),k3_seq_4(A))) ) ) ) ) )).
fof(t50_integr13,axiom,( ! [A] : ( ( 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,k22_sin_cos))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(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,k22_sin_cos)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k22_sin_cos)),A),B) = k7_xcmplx_0(k1_funct_1(k22_sin_cos,k1_funct_1(k2_sin_cos9,B)),k2_xcmplx_0(1,k1_square_1(B))) ) ) ) ) ) )).
fof(t50_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k3_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k27_sin_cos,D)))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,D)))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k27_sin_cos))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k27_sin_cos),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k27_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t50_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t50_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ 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)) = k2_xcmplx_0(k2_seq_4(A),k2_seq_4(B)) ) ) ) )).
fof(t50_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k3_xcmplx_0(k28_sin_cos,2)) => k2_integra5(A,k32_valued_1(k1_numbers,k1_numbers,k16_sin_cos)) = k5_numbers ) ) )).
fof(t50_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v3_rcomp_1(E) & m1_subset_1(E,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,E) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => ( k1_funct_1(C,F) = k2_xcmplx_0(A,F) & ~ r1_xxreal_0(k1_funct_1(C,F),k5_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] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => k1_funct_1(D,F) = k7_xcmplx_0(1,k2_xcmplx_0(A,F)) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,D,B)) ) => k2_integra5(B,D) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1),k2_seq_4(B)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1),k3_seq_4(B))) ) ) ) ) ) ) )).
fof(t50_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ ! [B] : ( ( ~ 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)) ) ) )).
fof(t50_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => r2_hidden(k3_intpro_1(k4_intpro_1(A,k4_intpro_1(C,B)),k4_intpro_1(A,k4_intpro_1(B,C))),k8_intpro_1) ) ) ) )).
fof(t50_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(D,C) & ~ v1_topreal2(k1_sppol_2(A,B,C,D)) ) ) ) ) ) )).
fof(t50_jgraph_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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,k5_numbers) | r1_xxreal_0(C,k5_numbers) | ( v3_tops_2(E,k15_euclid(2),k15_euclid(2)) & ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t50_jordan,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t50_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ r1_xxreal_0(C,1) & ~ r1_xxreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,1))),C) & r1_xxreal_0(1,D) & r1_xxreal_0(D,E) & r1_xxreal_0(E,k1_matrix_0(k1_jordan8(B,k1_nat_1(A,1)))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),C,E),k8_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),D),k9_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) & r2_subset_1(k4_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),E)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),E),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),C,E))),k8_jordan6(B)) ) ) ) ) ) ) )).
fof(t50_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( 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_0(k1_jordan8(C,B))),k2_jordan2c(2,C)) ) ) ) ) ) )).
fof(t50_jordan1g,axiom,( ! [A] : ( ( v4_topreal1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( ( 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)))) ) ) ) ) )).
fof(t50_jordan1h,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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)))) ) => ( 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)) ) ) ) )).
fof(t50_jordan1j,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => k17_finseq_1(A,k3_finseq_1(B),k4_graph_2(A,B,C)) = B ) ) )).
fof(t50_jordan1k,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t50_jordan21,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t50_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k3_finseq_1(A)) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(A)) & B != C & ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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] : ( m2_finseq_1(F,u1_struct_0(k15_euclid(2))) => ~ ( r3_jordan4(A,F,B,C) & F != D & F != E ) ) ) ) ) ) ) ) ) )).
fof(t50_jordan6,axiom,( ! [A] : ( 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(k7_xcmplx_0(k2_xcmplx_0(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(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)),2)),k22_pscomp_1(A),k18_pscomp_1(A)))) ) ) ) )).
fof(t50_kurato_1,axiom,( ! [A] : ~ ( 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 ) )).
fof(t50_lattice2,axiom,( ! [A] : ( ( ~ 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)) ) ) ) )).
fof(t50_lattice3,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t50_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),k14_lexbfs(A,k16_lexbfs(A)))),A) ) )).
fof(t50_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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)) ) ) ) ) )).
fof(t50_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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) = k3_xcmplx_0(k1_limfunc2(B,A),k1_limfunc2(C,A)) ) ) ) ) ) )).
fof(t50_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,D),A),k2_rcomp_1(A,k2_xcmplx_0(A,D))))) & r1_xxreal_0(k1_limfunc3(B,A),k1_funct_1(B,E)) ) ) ) ) | r3_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t50_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k20_lpspace1(A,B,C))) => ( r2_hidden(D,E) => ( E = k13_lpspace1(A,B,C,D) & k2_normsp_0(k20_lpspace1(A,B,C),E) = k1_mesfunc6(A,B,C,k56_valued_1(A,k1_numbers,D)) ) ) ) ) ) ) ) )).
fof(t50_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( v2_xxreal_0(F) & v1_xreal_0(F) ) => ( ? [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t50_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( m1_subset_1(D,k1_hilbert1) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t50_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(k3_hilbert1(C,k1_ltlaxio2(A,B)),k3_hilbert1(k3_hilbert1(C,k4_ltlaxio1(k1_ltlaxio1(A),k1_ltlaxio1(B))),k1_ltlaxio1(C)))) ) ) ) )).
fof(t50_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t50_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( r2_matrix10(B,C) => r2_matrix10(k5_matrix10(A,B,D),k5_matrix10(A,C,D)) ) ) ) ) ) )).
fof(t50_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(C,k2_finseq_1(A)) & r2_hidden(D,k2_finseq_1(A)) ) => ( r1_xxreal_0(D,C) | ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ( k7_matrix_0(u1_struct_0(B),E,C) = k7_matrix_0(u1_struct_0(B),E,D) => k12_matrix_3(A,B,E) = k4_struct_0(B) ) ) ) ) ) ) ) ) )).
fof(t50_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ( r2_hidden(B,k2_finseq_1(k5_card_1(D))) => k8_matrix_0(A,k6_matrix13(A,C,k2_finseq_1(k3_finseq_1(C)),D),B) = k8_matrix_0(A,C,k1_funct_1(k5_matrix13(D),B)) ) ) ) ) ) )).
fof(t50_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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] : ( m1_subset_1(C,k4_ordinal1) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,A) ) => k4_matrix_0(u1_struct_0(B),k4_matrix14(B,A,C)) = k4_matrix14(B,A,C) ) ) ) ) )).
fof(t50_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(D),C,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(D))) ) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(D),C,A) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(D))) ) => ! [G] : ( ( v1_finset_1(G) & v1_setfam_1(G) & m1_subset_1(G,k1_zfmisc_1(k4_ordinal1)) ) => ~ ( k5_card_1(G) = C & r1_tarski(G,k2_finseq_1(B)) & ~ r1_xxreal_0(C,k5_numbers) & k6_matrix13(u1_struct_0(D),E,k2_finseq_1(C),G) = k3_matrix_1(D,C) & ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(D),B,A) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(D))) ) => ~ ( k6_matrix13(u1_struct_0(D),H,k7_subset_1(k4_ordinal1,k2_finseq_1(B),G),k2_finseq_1(A)) = k1_matrix_3(D,k7_nat_d(B,C),A) & k6_matrix13(u1_struct_0(D),H,G,k2_finseq_1(A)) = F & r2_hidden(H,k4_matrix15(D,E,F)) ) ) ) ) ) ) ) ) ) ) )).
fof(t50_matrix16,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t50_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ( k3_matrix_0(A,k15_matrix_0(A,B,C,D,E),1,1) = B & k3_matrix_0(A,k15_matrix_0(A,B,C,D,E),1,2) = C & k3_matrix_0(A,k15_matrix_0(A,B,C,D,E),2,1) = D & k3_matrix_0(A,k15_matrix_0(A,B,C,D,E),2,2) = E ) ) ) ) ) ) )).
fof(t50_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(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_0(B)),B) = k2_matrix_3(A,B) ) ) )).
fof(t50_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r1_matrix_6(A,B,C,D) => ( r1_xxreal_0(A,k5_numbers) | r1_matrix_6(A,B,k3_matrix_3(B,C,C),k3_matrix_3(B,D,D)) ) ) ) ) ) ) )).
fof(t50_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r2_matrix_8(A,B,C,D) => ( r1_xxreal_0(A,k5_numbers) | r2_matrix_8(A,B,k4_matrix_0(u1_struct_0(B),C),k4_matrix_0(u1_struct_0(B),D)) ) ) ) ) ) ) )).
fof(t50_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k2_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(C) & k3_finseq_1(B) = k1_matrix_0(C) ) => ( r1_xxreal_0(k3_finseq_1(B),k5_numbers) | k4_matrix_0(k2_numbers,k13_matrixc1(A,B,C)) = k1_matrixc1(k13_matrixc1(B,A,k2_matrixc1(C))) ) ) ) ) ) )).
fof(t50_matrixj1,axiom,( ! [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] : ( ( v2_matrixj1(B,u1_struct_0(A)) & m2_finseq_1(B,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t50_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( 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)) ) ) ) )).
fof(t50_matrixr2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( k3_finseq_1(A) = k1_matrix_0(B) => ( r1_xxreal_0(k3_finseq_1(A),k5_numbers) | k11_matrixr1(B,k6_rvsum_1(A)) = k6_rvsum_1(k11_matrixr1(B,A)) ) ) ) ) )).
fof(t50_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( m1_matrlin(D,A,B) => ! [E] : ( m1_matrlin(E,A,C) => ! [F] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t50_matrprob,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & A = k5_finseq_2(k4_ordinal1,k3_finseq_1(A),1) ) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k2_finseq_1(k3_finseq_1(k12_matrixr1(B,A)))) => k1_funct_1(k12_matrixr1(B,A),C) = k18_rvsum_1(k8_matrix_0(k1_numbers,B,C)) ) ) ) ) ) )).
fof(t50_mcart_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k3_zfmisc_1(A,B,C)) => ! [E] : ! [F] : ! [G] : ( 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 ) ) ) ) ) ) )).
fof(t50_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( v1_xreal_0(B) => ( v3_xxreal_2(A) <=> v3_xxreal_2(k1_measure6(A,B)) ) ) ) )).
fof(t50_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_membered(C) => k9_member_1(k9_member_1(A,B),C) = k9_member_1(A,k9_member_1(B,C)) ) ) ) )).
fof(t50_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( ( 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,k5_numbers),D) ) ) ) ) ) )).
fof(t50_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_partfun1(A,k1_numbers)) & v1_mesfunc8(E,A,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [F] : ( ( 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,k5_numbers)) & ! [G] : ( 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] : ( v1_funct_1(G) & v1_funct_2(G,k4_ordinal1,k6_numbers) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) & ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t50_mesfunc5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v8_mesfunc5(A) => ( ~ v9_mesfunc5(A) & ~ v7_mesfunc5(A) ) ) ) )).
fof(t50_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( r2_mesfunc6(A,B,C) => r1_mesfunc6(A,B,C,D) ) ) ) ) ) )).
fof(t50_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,k10_midsp_1(A)) => ! [C] : ( m1_subset_1(C,k10_midsp_1(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t50_mmlquery,axiom,( ! [A] : ! [B] : ( 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 ) )).
fof(t50_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(t50_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_modelc_2(B) & l1_modelc_2(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t50_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k25_modelc_2(k43_modelc_2)) => ! [C] : ( ( 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] : ( r2_hidden(D,k22_modelc_3(A)) => ( v3_modelc_3(k10_modelc_3(D,A),A) | ! [E] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(t50_moebius1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ( r1_int_2(A,B) => r8_pboole(k8_newton,k5_moebius1(k2_nat_1(A,B)),k11_pre_poly(k8_newton,k5_moebius1(A),k5_moebius1(B))) ) ) ) )).
fof(t50_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & m2_monoid_0(A,k6_monoid_0) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( B = D & C = E ) => k6_algstr_0(A,B,C) = k3_xcmplx_0(D,E) ) ) ) ) ) ) )).
fof(t50_monoid_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t50_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_funct_1(u3_msualg_1(A,k3_equation(A)),C)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,k3_equation(A)),C)) => ( r1_equation(A,B,C,k5_equation(A,C,D,E)) => r1_equation(A,B,C,k5_equation(A,C,E,D)) ) ) ) ) ) ) )).
fof(t50_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) => ! [D] : ( m3_pboole(D,A,B) => ( r6_pboole(A,C,k1_pzfmisc1(A,D)) => r6_pboole(A,k4_mssubfam(A,B,C),D) ) ) ) ) )).
fof(t50_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msualg_4(C,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,B)) => ! [D] : ( m1_msualg_4(D,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,B)) => ( ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,B),E)) => ! [G] : ( 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)) ) ) ) ) ) ) )).
fof(t50_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => ( k1_dilworth(k7_mycielsk(A)) = 2 & k2_mycielsk(k7_mycielsk(A)) = k2_xcmplx_0(A,2) ) ) )).
fof(t50_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( r1_nat_d(B,A) => r8_pboole(k8_newton,k12_nat_3(k3_nat_d(A,B)),k12_pre_poly(k8_newton,k12_nat_3(A),k12_nat_3(B))) ) ) ) )).
fof(t50_nat_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ( B = k1_xboole_0 => k1_nat_4(B,A) = k1_xboole_0 ) ) ) )).
fof(t50_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,A) => r1_xxreal_0(k7_nat_d(B,C),A) ) ) ) ) )).
fof(t50_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ! [D] : ( ( 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) ) ) ) ) )).
fof(t50_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t50_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k4_finseq_1(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_prvect_2(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k11_prvect_2(A,C))) => ! [F] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t50_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_nat_d(C,B) & r1_nat_d(C,A) ) <=> r1_nat_d(C,k6_nat_d(B,A)) ) ) ) ) )).
fof(t50_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t50_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(k7_normform(A))) => ! [C] : ( 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)) ) ) )).
fof(t50_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t50_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,u4_struct_0(B),u4_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(B),u4_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u4_struct_0(A),u4_struct_0(C)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(A),u4_struct_0(C)))) ) => r2_funct_2(u4_struct_0(k2_oppcat_1(B)),u4_struct_0(C),k10_oppcat_1(B,C,k1_partfun1(u4_struct_0(B),u4_struct_0(A),u4_struct_0(A),u4_struct_0(C),D,E)),k1_partfun1(u4_struct_0(k2_oppcat_1(B)),u4_struct_0(A),u4_struct_0(A),u4_struct_0(C),k10_oppcat_1(B,A,D),E)) ) ) ) ) ) )).
fof(t50_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(A))) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A))) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A))))) ) => ( ( r1_xxreal_0(B,C) & ! [G] : ( m1_subset_1(G,u1_struct_0(k4_real_ns1(A))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k4_real_ns1(A))) => r1_xxreal_0(k2_normsp_0(k4_real_ns1(A),k5_algstr_0(k4_real_ns1(A),k10_funct_2(u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A)),F,G),k10_funct_2(u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A)),F,H))),k3_xcmplx_0(D,k2_normsp_0(k4_real_ns1(A),k5_algstr_0(k4_real_ns1(A),G,H)))) ) ) ) => ( r1_xxreal_0(D,k5_numbers) | ! [G] : ( m1_subset_1(G,u1_struct_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A)))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A)))) => ! [I] : ( m1_subset_1(I,k4_ordinal1) => ! [J] : ( ( v1_funct_1(J) & v1_nfcont_3(J,k4_real_ns1(A)) & m1_subset_1(J,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [K] : ( ( v1_funct_1(K) & v1_nfcont_3(K,k4_real_ns1(A)) & m1_subset_1(K,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ( ( J = k3_funct_2(u1_struct_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A))),u1_struct_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A))),k1_abian(u1_struct_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A))),k6_ordeq_01(A,E,F,B,C),k2_xcmplx_0(I,1)),G) & K = k3_funct_2(u1_struct_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A))),u1_struct_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A))),k1_abian(u1_struct_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A))),k6_ordeq_01(A,E,F,B,C),k2_xcmplx_0(I,1)),H) ) => ! [L] : ( v1_xreal_0(L) => ( r2_hidden(L,k3_integra5(B,C)) => r1_xxreal_0(k2_normsp_0(k4_real_ns1(A),k5_algstr_0(k4_real_ns1(A),k7_partfun1(u1_struct_0(k4_real_ns1(A)),J,L),k7_partfun1(u1_struct_0(k4_real_ns1(A)),K,L))),k3_xcmplx_0(k7_xcmplx_0(k1_newton(k3_xcmplx_0(D,k6_xcmplx_0(L,B)),k2_xcmplx_0(I,1)),k2_newton(k2_xcmplx_0(I,1))),k2_normsp_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A)),k5_algstr_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A)),G,H)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t50_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ~ ( r5_orders_1(A,B) & B = k1_xboole_0 ) ) )).
fof(t50_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v6_orders_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => r3_orders_1(u1_orders_2(A),B) ) ) )).
fof(t50_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ( r2_ordinal2(A,k5_ordinal1) => A = k5_ordinal1 ) ) )).
fof(t50_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => k11_ordinal2(k11_ordinal2(A,B),C) = k11_ordinal2(A,k11_ordinal2(B,C)) ) ) ) )).
fof(t50_ordinal5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ( ! [B] : ( r2_hidden(B,A) => ( v3_ordinal1(B) & v4_ordinal5(B) ) ) & ! [B] : ( v3_ordinal1(B) => ( r2_hidden(B,A) => r2_hidden(k2_ordinal5(B),A) ) ) ) => ( v3_ordinal1(k3_tarski(A)) & v4_ordinal5(k3_tarski(A)) ) ) ) )).
fof(t50_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v3_ordinal6(B) ) => ~ ( k9_xtuple_0(B) != k1_xboole_0 & ! [C] : ( v3_ordinal1(C) => ( r2_hidden(C,k9_xtuple_0(B)) => r1_abian(A,k1_funct_1(B,C)) ) ) & ! [C] : ( v3_ordinal1(C) => ~ ( r2_hidden(C,k9_xtuple_0(k7_ordinal6(B))) & A = k1_funct_1(k7_ordinal6(B),C) ) ) ) ) ) )).
fof(t50_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t50_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t50_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( r1_tarski(A,B) & r1_tarski(C,D) ) => r1_tarski(k4_partfun1(A,C),k4_partfun1(B,D)) ) )).
fof(t50_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ( r2_relset_1(A,B,E,k9_subset_1(k2_zfmisc_1(A,B),D,F)) & r2_hidden(C,k1_relset_1(A,E)) ) => ( k7_partfun1(B,E,C) = k7_partfun1(B,D,C) & k7_partfun1(B,E,C) = k7_partfun1(B,F,C) ) ) ) ) ) ) ) ) )).
fof(t50_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t50_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( 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) & k10_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) = k2_xcmplx_0(k5_pdiff_5(B,A),k5_pdiff_5(C,A)) ) ) ) ) ) )).
fof(t50_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_euclid(B)))) ) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t50_pepin,axiom,( k4_pepin(k5_numbers) = 3 )).
fof(t50_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( 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))))) ) ) ) )).
fof(t50_polynom5,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k5_polynom5(A,B,k9_polynom3(A)),k2_algseq_1(A,k3_funct_2(k4_ordinal1,u1_struct_0(A),B,k5_numbers))) ) ) )).
fof(t50_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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),k7_polynom1(A,C,E,F),k8_polynom1(A,C)) => r5_rewrite1(k3_polyred(A,B,C,D),E,F) ) ) ) ) ) ) ) )).
fof(t50_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & A != 1 & B != C & k2_power(A,B) = k2_power(A,C) ) ) ) ) )).
fof(t50_pre_poly,axiom,( k15_pre_poly(k1_xboole_0) = k1_tarski(k1_xboole_0) )).
fof(t50_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & B = k5_xcmplx_0(C) ) => k4_prepower(A,B) = k2_prepower(C,A) ) ) ) ) )).
fof(t50_prob_3,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k9_setfam_1(A)) => k1_relset_1(k4_ordinal1,k6_prob_3(A,B)) = k1_relset_1(k4_ordinal1,B) ) )).
fof(t50_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t50_pscomp_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t50_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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,C,k1_pzfmisc1(A,B)),C) & r1_pboole(A,B,C) ) ) ) )).
fof(t50_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( v5_qc_lang1(C,A) => ( r1_qc_lang2(A,B,C) <=> B = k22_qc_lang1(A,C) ) ) ) ) ) )).
fof(t50_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( ( ~ 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)) ) ) ) ) )).
fof(t50_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ( k13_quaterni(k17_quatern2(A,A)) = k1_square_1(k28_quaterni(A)) & k14_quaterni(k17_quatern2(A,A)) = k5_numbers & k15_quaterni(k17_quatern2(A,A)) = k5_numbers & k15_quaterni(k17_quatern2(A,A)) = k5_numbers ) ) )).
fof(t50_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => ! [D] : ( v1_quaterni(D) => k23_quaterni(k25_quaterni(A,B),k22_quaterni(C,D)) = k25_quaterni(k22_quaterni(k25_quaterni(k23_quaterni(A,C),k23_quaterni(B,C)),k23_quaterni(A,D)),k23_quaterni(B,D)) ) ) ) ) )).
fof(t50_quaterni,axiom,( k13_quaterni(k27_quaterni(k12_quaterni)) = k5_numbers & k14_quaterni(k27_quaterni(k12_quaterni)) = k5_numbers & k15_quaterni(k27_quaterni(k12_quaterni)) = k5_numbers & k16_quaterni(k27_quaterni(k12_quaterni)) = k4_xcmplx_0(1) )).
fof(t50_quofield,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t50_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k4_topmetr(A,A))))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t50_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => ! [D] : ( v1_relat_1(D) => ( ( r1_tarski(k10_xtuple_0(C),A) & k3_relat_1(C,D) = k4_relat_1(k9_xtuple_0(B)) & k3_relat_1(D,B) = k4_relat_1(A) ) => B = C ) ) ) ) )).
fof(t50_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ( k9_xtuple_0(C) = k7_relset_1(B,A,k3_relset_1(A,B,C),B) & k10_xtuple_0(C) = k7_relset_1(A,B,C,A) ) ) )).
fof(t50_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ( v7_rewrite1(A) <=> r11_rewrite1(A,A) ) ) )).
fof(t50_rewrite2,axiom,( ! [A] : ! [B] : ( 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) ) )).
fof(t50_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( ( ~ v2_struct_0(D) & l1_rewrite3(D,B) ) => ! [E] : ( ( ~ 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] : ( m1_rewrite1(F,k1_rewrite3(A,B,D)) => m1_rewrite1(F,k1_rewrite3(A,C,E)) ) ) ) ) ) ) ) )).
fof(t50_rfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( 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) ) ) ) ) ) ) )).
fof(t50_rfunct_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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(B,A))) | v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A))) ) => v2_funct_1(k2_partfun1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A))) ) ) ) ) )).
fof(t50_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k8_relset_1(A,k1_numbers,B,k1_tarski(k2_xcmplx_0(D,C))) = k8_relset_1(A,k1_numbers,k15_valued_1(A,k1_numbers,B,C),k1_tarski(D)) ) ) ) ) )).
fof(t50_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_seq_2(A) => v7_valued_0(k3_rinfsup1(A)) ) ) )).
fof(t50_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( v2_rusub_4(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => B = k4_rlaffin1(A,B) ) ) )).
fof(t50_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_rlsub_1(D,A) => ( k3_rlsub_1(A,k1_rlvect_1(A,B,C),D) = u1_struct_0(D) => ( C = k5_numbers | r1_struct_0(D,B) ) ) ) ) ) ) )).
fof(t50_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_2(C,A,B) => ! [D] : ( 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 ) ) ) ) )).
fof(t50_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v8_ordinal1(C) & v1_xreal_0(C) ) => v4_pre_topc(k1_convex1(A,B,C),A) ) ) ) )).
fof(t50_rlvect_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t50_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t50_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t50_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t50_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t50_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( 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) ) ) )).
fof(t50_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t50_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t50_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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),k5_numbers) | r1_xxreal_0(k1_rpr_1(A,D),k5_numbers) | k1_rpr_1(A,B) = k2_xcmplx_0(k3_xcmplx_0(k2_rpr_1(A,C,B),k1_rpr_1(A,C)),k3_xcmplx_0(k2_rpr_1(A,D,B),k1_rpr_1(A,D))) ) ) ) ) ) ) )).
fof(t50_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t50_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_2(C,A,B) => ! [D] : ( 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 ) ) ) ) )).
fof(t50_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_rusub_5(A)))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( B = k4_bhsp_2(A,D,C) => v3_pre_topc(B,k5_rusub_5(A)) ) ) ) ) ) )).
fof(t50_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) & v1_finseq_1(C) ) => k10_rvsum_1(C,k2_xcmplx_0(A,B)) = k4_rvsum_1(k10_rvsum_1(C,A),k10_rvsum_1(C,B)) ) ) ) )).
fof(t50_rvsum_2,axiom,( ! [A] : ( ( 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) ) )).
fof(t50_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ~ r4_scmfsa7b(C,D) => k1_funct_1(k1_scmfsa6b(C,B,A),D) = k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_m(B)),E),D) ) ) ) ) ) ) )).
fof(t50_scmfsa8c,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ r4_scmfsa7b(k1_scmfsa8a(B),A) ) ) )).
fof(t50_scmfsa_2,axiom,( ! [A] : ( m1_scmfsa_2(A) => A != k4_struct_0(k1_scmfsa_2) ) )).
fof(t50_scmpds_2,axiom,( ! [A] : ( ( 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] : ( v1_int_1(B) => ! [C] : ( ( 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)) = k5_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] : ( ( 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) ) ) ) ) ) ) )).
fof(t50_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( 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)) ) ) ) )).
fof(t50_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r2_semi_af1(A,B,C,D,E) & r2_semi_af1(A,B,C,F,G) ) => ( r1_semi_af1(A,D,E,F) | r2_semi_af1(A,D,E,F,G) ) ) ) ) ) ) ) ) ) )).
fof(t50_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k56_valued_1(k4_ordinal1,k1_numbers,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)),k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k56_valued_1(k4_ordinal1,k1_numbers,A),k56_valued_1(k4_ordinal1,k1_numbers,B))) ) ) )).
fof(t50_seq_4,axiom,( r1_finseqop(k2_numbers,k1_binop_2,k3_binop_2) )).
fof(t50_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( v7_ordinal1(C) => ( v2_prob_1(B) => r1_tarski(k3_funct_2(k4_ordinal1,k9_setfam_1(A),k2_setlim_1(A,B),k1_nat_1(C,1)),k1_funct_1(B,C)) ) ) ) )).
fof(t50_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => k9_nat_1(k9_setfam_1(B),k2_setlim_1(B,k5_setlim_2(B,D,C)),A) = k9_subset_1(B,C,k9_nat_1(k9_setfam_1(B),k2_setlim_1(B,D),A)) ) ) ) )).
fof(t50_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ! [D] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,k5_finsub_1(C)) => ! [H] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t50_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(t50_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t50_simplex0,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_pencil_1(C) & v1_matroid0(C) & l1_pre_topc(C) ) => ! [D] : ( m3_simplex0(D,C,B) => ( r1_xxreal_0(B,k6_simplex0(C)) => ( m4_simplex0(A,C,B,D) <=> ? [E] : ( r2_hidden(E,D) & k7_subset_1(u1_struct_0(C),D,k1_tarski(E)) = A ) ) ) ) ) ) )).
fof(t50_sin_cos,axiom,( k23_sin_cos(k5_numbers) = 1 )).
fof(t50_sin_cos3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xcmplx_0(B) => k2_comseq_3(k2_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,B),k3_xcmplx_0(k7_complex1,k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,B))),A) = k2_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,k3_xcmplx_0(A,B)),k3_xcmplx_0(k7_complex1,k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,k3_xcmplx_0(A,B)))) ) ) )).
fof(t50_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k7_xcmplx_0(k2_xcmplx_0(k19_sin_cos(A),k19_sin_cos(B)),k6_xcmplx_0(k19_sin_cos(A),k19_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))) ) ) )).
fof(t50_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k4_sin_cos2(k7_xcmplx_0(A,2)) != k5_numbers => k6_sin_cos2(k7_xcmplx_0(A,2)) = k7_xcmplx_0(k2_sin_cos2(A),k2_xcmplx_0(k4_sin_cos2(A),1)) ) ) )).
fof(t50_sin_cos6,axiom,( k7_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k2_rcomp_1(k5_numbers,k28_sin_cos)) = k2_rcomp_1(k4_xcmplx_0(1),1) )).
fof(t50_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k5_numbers,k2_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(k3_square_1(k2_xcmplx_0(k1_square_1(A),1)),k3_square_1(k2_xcmplx_0(k1_square_1(B),1))))) => k2_xcmplx_0(k1_sin_cos7(A),k1_sin_cos7(B)) = k1_sin_cos7(k2_xcmplx_0(k3_xcmplx_0(A,k3_square_1(k2_xcmplx_0(1,k1_square_1(B)))),k3_xcmplx_0(B,k3_square_1(k2_xcmplx_0(1,k1_square_1(A)))))) ) ) ) )).
fof(t50_sin_cos9,axiom,( ! [A] : ( r2_hidden(A,k1_rcomp_1(k4_xcmplx_0(1),1)) => r2_hidden(k1_funct_1(k2_sin_cos9,A),k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos))) ) )).
fof(t50_sincos10,axiom,( k2_partfun1(k1_numbers,k1_numbers,k2_sincos10,k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1))) = k2_partfun2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos),k28_sin_cos))) )).
fof(t50_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( r1_sppol_2(B,C,A) => r1_sppol_2(C,B,A) ) ) ) ) )).
fof(t50_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( ( ~ 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] : ( ( ~ 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)) ) ) ) ) )).
fof(t50_sprect_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ 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))) ) ) ) ) ) ) ) )).
fof(t50_sprect_3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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,k13_matrix_0(u1_struct_0(k15_euclid(2)),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),B,C),k7_xcmplx_0(1,2)))) ) ) ) ) )).
fof(t50_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t50_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k4_xcmplx_0(A)) & ~ r1_xxreal_0(A,B) & r1_xxreal_0(k1_square_1(A),k1_square_1(B)) ) ) ) )).
fof(t50_stirl2_1,axiom,( k7_newton(3) = 6 & k7_newton(4) = 24 )).
fof(t50_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_valuat_1(E,A,D) => ! [F] : ( 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] : ( m1_subset_1(G,D) => r1_valuat_1(A,D,B,E,k1_sublemma(A,D,F,k12_sublemma(A,D,C,G))) ) ) ) ) ) ) ) ) )).
fof(t50_subset_1,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ! [B] : ~ ! [C] : ( m1_subset_1(C,A) => C = B ) ) )).
fof(t50_supinf_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( v6_supinf_2(B) <=> ! [C] : r1_xxreal_0(k1_supinf_2,k1_funct_1(B,C)) ) ) )).
fof(t50_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)))) ) ) )).
fof(t50_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( k4_tdlat_1(A) = k8_tdlat_1(A) => v4_tdlat_3(A) ) ) )).
fof(t50_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t50_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ~ ( ? [B] : ( ~ v2_struct_0(B) & m1_pre_topc(B,A) & v1_tex_3(B,A) & v1_tex_2(B,A) ) & v1_tdlat_3(A) ) ) )).
fof(t50_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t50_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => r1_tmap_1(A,B,C,D) ) ) ) ) ) )).
fof(t50_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))))) ) ) ) ) ) ) )).
fof(t50_topgen_1,axiom,( ! [A] : ( 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 ) ) )).
fof(t50_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k4_topgen_4(A,B),k2_topgen_1(A,B)) ) ) )).
fof(t50_topgrp_1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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) ) ) )).
fof(t50_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k14_euclid(2))) => ( C = k4_struct_0(k15_euclid(2)) => ( r1_xxreal_0(A,k5_numbers) | r1_tarski(B,k8_metric_1(k14_euclid(2),C,k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k9_complex1(k8_pscomp_1(B)),k9_complex1(k7_pscomp_1(B))),k9_complex1(k6_pscomp_1(B))),k9_complex1(k9_pscomp_1(B))),A))) ) ) ) ) ) )).
fof(t50_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k3_topreal9(2,k19_euclid(A,B),C) = k5_jgraph_6(A,B,C) ) ) ) )).
fof(t50_toprealc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( ( 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,k14_toprealc(A,u1_struct_0(B),u1_struct_0(k3_topmetr),D)) ) ) ) ) )).
fof(t50_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_tops_1(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( r1_tarski(C,B) & v3_pre_topc(C,A) ) => C = k1_xboole_0 ) ) ) ) ) )).
fof(t50_tops_2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) )).
fof(t50_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_tops_3(B,A) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t50_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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 ) ) ) ) ) ) ) )).
fof(t50_trees_1,axiom,( k2_trees_1(1) = k2_tarski(k1_xboole_0,k12_finseq_1(k4_ordinal1,k5_numbers)) )).
fof(t50_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v4_trees_3(A) ) => ! [B] : ( ( 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 ) ) ) )).
fof(t50_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_2(B,A) => ! [C] : ( m1_trees_1(C,A) => ~ ( r2_hidden(C,B) & ~ v1_finset_1(B) & ! [D] : ( m1_trees_1(D,A) => ~ ( r2_hidden(D,B) & r2_xboole_0(C,D) ) ) ) ) ) ) )).
fof(t50_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t50_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(k40_twoscomp(A,B),k41_twoscomp(A,B)))) => ! [D] : ( m1_subset_1(D,k6_margrel1) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t50_uproots,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_uproots(A,B,k4_polynom5(A,k4_algstr_0(A,B),k5_struct_0(A))) = 1 ) ) )).
fof(t50_valued_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) ) => ( r1_xxreal_0(k3_finseq_1(B),A) => r1_xboole_0(B,k61_valued_1(C,A)) ) ) ) ) )).
fof(t50_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( ( 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)) ) ) ) ) )).
fof(t50_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t50_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t50_vfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ 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] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,u1_struct_0(D)))) ) => ! [F] : ( ( 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))) ) ) ) ) ) ) )).
fof(t50_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ! [F] : ( ( 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))) ) ) ) ) ) ) )).
fof(t50_waybel21,axiom,( ! [A] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & C = u1_struct_0(B) & v4_pre_topc(C,A) ) ) ) )).
fof(t50_waybel23,axiom,( ! [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] : ( ( ~ 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] : ( 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))) ) ) ) ) ) )).
fof(t50_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( ( 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) ) ) ) ) ) )).
fof(t50_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t50_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t50_waybel_2,axiom,( ! [A] : ( ( 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] : ( ( ~ 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] : ( ( ~ 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)) ) ) ) ) )).
fof(t50_waybel_4,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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] : ( 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 ) ) ) ) ) ) ) )).
fof(t50_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( v2_wellord1(A) & r3_wellord1(A,B,C) ) => ! [D] : ~ ( r2_hidden(D,k1_relat_1(A)) & ! [E] : ~ ( r2_hidden(E,k1_relat_1(B)) & r4_wellord1(k2_wellord1(A,k1_wellord1(A,D)),k2_wellord1(B,k1_wellord1(B,E))) ) ) ) ) ) ) )).
fof(t50_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : k3_xboole_0(A,k4_xboole_0(B,C)) = k4_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)) )).
fof(t50_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k7_xboolean(A,B) = k5_xboolean(k4_xboolean(A,B),k9_xboolean(A,B)) ) ) )).
fof(t50_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( A != k5_numbers & B != k5_numbers & k7_xcmplx_0(A,B) = k5_numbers ) ) ) )).
fof(t50_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,A) & r1_xxreal_0(k6_xcmplx_0(B,A),k5_numbers) ) ) ) )).
fof(t50_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( r1_xxreal_0(A,k3_xxreal_0(A,B)) => k3_xxreal_0(A,B) = A ) ) ) )).
fof(t50_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(C,D) & r1_tarski(k1_xxreal_1(C,D),k1_xxreal_1(A,B)) ) => ( r1_xxreal_0(A,C) & r1_xxreal_0(D,B) ) ) ) ) ) ) )).
fof(t50_xxreal_2,axiom,( ! [A] : ( ( v2_membered(A) & ~ v1_xboole_0(A) & v3_xxreal_2(A) ) => ~ ( A != k1_tarski(k1_xxreal_0) & ! [B] : ( m1_subset_1(B,k1_numbers) => ~ r2_hidden(B,A) ) ) ) )).
fof(t50_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(A,k1_xxreal_3(B,B)) ) ) ) ) )).
fof(t50_yellow10,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t50_yellow12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v2_pre_topc(D) & l1_pre_topc(D) ) => ! [E] : ( m3_yellow_9(E,A,B) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t50_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( r1_t_0topsp(A,B) <=> ? [C] : ( 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] : ( 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)) ) ) ) ) ) )).
fof(t50_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ( v21_functor0(C,A,B) => ! [D] : ( ( ~ v2_struct_0(D) & v2_altcat_1(D) & v3_altcat_2(D,A) & m1_altcat_2(D,A) ) => ! [E] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(t50_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t50_yellow_2,axiom,( ! [A] : ! [B] : ( ( ~ 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(k1_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))) ) ) ) )).
fof(t50_yellow_4,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v12_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t50_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k12_lattice3(A,k1_yellow_5(A,B,C),C) = k3_yellow_0(A) ) ) ) )).
fof(t50_yellow_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t50_yellow_9,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( ( C = D & v3_pre_topc(C,A) ) => v3_pre_topc(D,B) ) ) ) ) ) ) )).
fof(t50_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ~ r1_zf_lang(C,k4_zf_lang(A,B)) ) ) ) )).
fof(t50_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( 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)) ) ) ) )).
fof(t50_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( ~ r2_hidden(A,C) & ~ r2_hidden(B,C) & ~ r1_xboole_0(k2_tarski(A,B),C) ) )).
fof(t50_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( B != k1_xboole_0 & v7_zmodul01(B,A) & ! [C] : ( ( v1_zmodul01(C) & m1_zmodul01(C,A) ) => B != u1_struct_0(C) ) ) ) ) )).
fof(t50_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( m1_zmodul02(C,A) => k5_algstr_0(k31_zmodul02(A),k1_rlvect_2(k31_zmodul02(A),B),k1_rlvect_2(k31_zmodul02(A),C)) = k25_zmodul02(A,B,C) ) ) ) )).
fof(t51_abcmiz_0,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t51_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_abcmiz_1(B,A) & m1_subset_1(B,u4_struct_0(A)) ) => ! [C] : ( ( 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))) ) ) ) ) ) )).
fof(t51_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k38_abcmiz_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k38_abcmiz_1(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t51_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t51_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(A))) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(A))) => ! [J] : ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A))) => ( ( r5_aff_1(A,H,J) & r5_aff_1(A,H,I) & r2_hidden(B,H) & r2_hidden(E,H) & r2_hidden(C,J) & r2_hidden(F,J) & r2_hidden(D,I) & r2_hidden(G,I) & v1_aff_1(H,A) & v1_aff_1(J,A) & v1_aff_1(I,A) & r2_analoaf(A,B,C,E,F) & r2_analoaf(A,B,D,E,G) ) => ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) | H = J | H = I | r2_analoaf(A,C,D,F,G) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t51_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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 ) ) ) )).
fof(t51_afinsq_2,axiom,( ! [A] : ( ( 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) = k5_numbers ) ) )).
fof(t51_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ( v9_incproj(k13_afproj(A)) => v4_aff_2(A) ) ) )).
fof(t51_afvect0,axiom,( ! [A] : ( ( v1_analoaf(A) & l1_analoaf(A) ) => ( ( ~ v7_struct_0(A) & v2_tdgroup(A) & l1_analoaf(A) ) <=> ? [B] : ( ~ 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) ) ) ) )).
fof(t51_algspec1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_instalg1(B) & l1_msualg_1(B) ) => ( v2_struct_0(A) => m2_algspec1(B,A) ) ) ) )).
fof(t51_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_altcat_4(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_altcat_4(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t51_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & r2_hidden(D,B) & r6_analmetr(A,C,D,B) ) => C = D ) ) ) ) ) )).
fof(t51_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r1_analmetr(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_analort(A,B,C,D,E,D,F) & ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( 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 ) ) ) ) ) ) ) ) ) ) ) )).
fof(t51_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ r2_hidden(k14_aofa_000(A,B,C,D),k18_aofa_000(A)) ) ) ) ) )).
fof(t51_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v19_aofa_a00(E,A) & m1_subset_1(E,u1_struct_0(A)) ) => ! [F] : ( m2_pboole(F,u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,D)) => k15_aofa_a00(A,B,C,D,E,k27_aofa_a00(A,C,E),F) = k5_numbers ) ) ) ) ) ) )).
fof(t51_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_aofa_i00(E,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) ) => ! [F] : ( 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,k5_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,k5_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,k5_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,k5_numbers)) => v1_abian(k21_aofa_i00(B,k4_numbers,C,F)) ) ) ) ) ) ) ) ) )).
fof(t51_armstrng,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ~ ( ~ v1_xboole_0(B) & v11_armstrng(B) & ! [C] : ( l1_armstrng(C) => ~ ( u1_armstrng(C) = A & B = k13_armstrng(u1_armstrng(C),k5_armstrng(C)) ) ) ) ) ) )).
fof(t51_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( 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)) ) ) ) )).
fof(t51_asympt_1,axiom,( k7_newton(5) = 120 )).
fof(t51_bcialg_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t51_bcialg_2,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t51_bcialg_4,axiom,( ! [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) & l1_bcialg_4(A) ) => ( v8_bcialg_4(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t51_bcialg_5,axiom,( ! [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) ) => ( ( v8_bcialg_1(A) & m1_bcialg_5(A,1,k5_numbers,k5_numbers,k5_numbers) ) <=> ( v8_bcialg_1(A) & m1_bcialg_5(A,k5_numbers,k5_numbers,k5_numbers,k5_numbers) & v8_bcialg_1(A) & m1_bcialg_5(A,k5_numbers,1,k5_numbers,1) ) ) ) )).
fof(t51_bcialg_6,axiom,( ! [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] : ( ( v12_bcialg_1(B,A) & m2_bcialg_1(B,A) ) => ! [C] : ( m5_bcialg_2(C,A,B) => k5_bcialg_6(A,k9_bcialg_2(A,C),k6_bcialg_6(A,B,C)) = B ) ) ) )).
fof(t51_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( m4_bciideal(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t51_bhsp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => r2_funct_2(k4_ordinal1,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))) ) ) ) ) )).
fof(t51_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(C,k6_bhsp_2(A,B,D)) <=> k3_bhsp_1(A,k5_algstr_0(A,B,C)) = D ) ) ) ) ) )).
fof(t51_bhsp_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( ( v1_bhsp_3(C,B) & v3_bhsp_4(A) ) => v1_bhsp_3(k5_bhsp_4(B,C,A),B) ) ) ) ) )).
fof(t51_bilinear,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t51_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t51_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_borsuk_4))) => ~ ( ? [D] : ( m1_subset_1(D,u1_struct_0(k5_topmetr)) & ? [E] : ( 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] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ~ r1_topreal1(k15_euclid(A),D,E,B) ) ) ) ) ) ) )).
fof(t51_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => k5_measure6(k2_rcomp_1(k2_xxreal_0,A)) = k4_rcomp_1(k2_xxreal_0,A) ) )).
fof(t51_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t51_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t51_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t51_bvfunc14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( v1_relat_1(H) & v1_funct_1(H) ) => ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ( 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)) ) ) )).
fof(t51_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t51_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ( k9_xboolean(A,A) = k3_xboolean(A) & k3_xboolean(k9_xboolean(A,A)) = A ) ) )).
fof(t51_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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),C))) => 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)))) ) ) ) ) ) )).
fof(t51_card_1,axiom,( 5 = k3_enumset1(k5_ordinal1,1,2,3,4) )).
fof(t51_card_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : r1_xxreal_0(k5_card_1(k2_enumset1(A,B,C,D)),4) )).
fof(t51_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => r1_tarski(k4_card_3(A),k8_card_3(A)) ) )).
fof(t51_card_fin,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(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)) ) ) ) )).
fof(t51_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v10_cat_1(C,A) & r1_cat_1(A,B,C) ) => v10_cat_1(B,A) ) ) ) ) )).
fof(t51_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_cat_3(E,B,C,A) => ( r1_cat_3(B,C,A,E) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t51_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k23_cat_4(A,B))) => ! [D] : ( m1_subset_1(D,u4_struct_0(k23_cat_4(A,B))) => ! [E] : ( m1_subset_1(E,u4_struct_0(k23_cat_4(A,B))) => r4_cat_3(k23_cat_4(A,B),C,D,E) ) ) ) )).
fof(t51_cfcont_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t51_cfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t51_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_chain_1(C,B) => ( r1_xxreal_0(k1_nat_1(A,1),B) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(k1_euclid(B)),k4_chain_1(B,C,A)) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(k1_euclid(B)),k4_chain_1(B,C,k1_nat_1(A,1))) => ( r2_hidden(D,k10_chain_1(B,C,A,k6_domain_1(k4_chain_1(B,C,k1_nat_1(A,1)),E))) <=> r1_tarski(D,E) ) ) ) ) ) ) ) )).
fof(t51_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t51_circcmb3,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(t51_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ( ( v3_circcomb(A) & v3_circcomb(B) ) => v3_circcomb(k2_circcomb(A,B)) ) ) ) )).
fof(t51_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v4_msualg_1(E,A) & v4_msafree2(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( ( v4_msualg_1(F,B) & v4_msafree2(F,B) & l3_msualg_1(F,B) ) => ( r5_circtrm1(A,B,C,D,E,F) => ! [G] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(A,E))) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t51_classes1,axiom,( ! [A] : v1_ordinal1(k5_classes1(A)) )).
fof(t51_classes2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ( k2_ordinal1(A) != k1_xboole_0 & v4_ordinal1(k2_ordinal1(A)) ) ) )).
fof(t51_clvect_1,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_clvect_1(B) & m1_clvect_1(B,A) ) => ( u1_struct_0(B) = u1_struct_0(A) => B = A ) ) ) )).
fof(t51_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(C,k6_clvect_2(A,B,D)) <=> k13_csspace(A,k5_algstr_0(A,B,C)) = D ) ) ) ) ) )).
fof(t51_clvect_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( ( v2_clvect_2(C,B) & v3_clvect_3(A) ) => v2_clvect_2(k6_clvect_3(B,C,A),B) ) ) ) ) )).
fof(t51_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( k1_funct_1(A,k1_xboole_0) = k1_xboole_0 => ! [B] : ! [C] : ( ( 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)) ) ) ) )).
fof(t51_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k3_complex1(A) = k5_numbers => k9_complex1(A) = k9_complex1(k4_complex1(A)) ) ) )).
fof(t51_complex2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xcmplx_0(B) => k9_complex1(k2_complex2(B,A)) = k9_complex1(B) ) ) )).
fof(t51_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( 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)) ) ) )).
fof(t51_complsp2,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( 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,k5_seq_4(A)) = k4_finseqop(k1_numbers,k1_numbers,D,k3_rvsum_1(C)) ) ) ) ) ) )).
fof(t51_compos_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( l1_compos_1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t51_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t51_comptrig,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( r1_xxreal_0(k5_numbers,k3_complex1(A)) => r1_xxreal_0(k5_numbers,k19_sin_cos(k1_comptrig(A))) ) ) )).
fof(t51_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k3_finseq_2(k4_ordinal1)) & v1_funct_1(C) & v4_valued_0(C) & v2_margrel1(C) ) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => r1_tarski(k1_relset_1(k3_finseq_2(k4_ordinal1),k6_comput_1(B,C,A,D)),k4_finseq_2(k1_nat_1(1,k19_margrel1(B)),k4_ordinal1)) ) ) ) ) )).
fof(t51_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => k9_nat_1(k2_numbers,A,B) = k5_complex1 ) => v2_comseq_3(A) ) ) )).
fof(t51_convex4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k19_convex4(A,B,k6_complex1) = B ) ) )).
fof(t51_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t51_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t51_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t51_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_xxreal_0(k15_csspace(A,B,D),k2_xcmplx_0(k15_csspace(A,B,C),k15_csspace(A,C,D))) ) ) ) ) )).
fof(t51_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k4_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k16_sin_cos),A),B) = k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k19_sin_cos(k3_xcmplx_0(2,k6_xcmplx_0(B,A))),k19_sin_cos(k3_xcmplx_0(2,B)))) ) ) )).
fof(t51_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => k1_funct_1(D,E) = k7_xcmplx_0(B,k1_square_1(E)) ) => ( C = k5_numbers | k6_xcmplx_0(C,A) = k5_numbers | k1_funct_1(k4_diff_1(D,A),C) = k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(B),A),k6_xcmplx_0(k3_xcmplx_0(2,C),A)),k1_square_1(k6_xcmplx_0(k1_square_1(C),k3_xcmplx_0(C,A)))) ) ) ) ) ) ) )).
fof(t51_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k3_diff_1(k5_diff_1(C,A),A),B) = k6_xcmplx_0(k1_funct_1(k3_diff_1(C,A),k2_xcmplx_0(B,k7_xcmplx_0(A,2))),k1_funct_1(k5_diff_1(C,A),B)) ) ) ) )).
fof(t51_dilworth,axiom,( ! [A] : ( ( v8_struct_0(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ? [B] : ( v5_dilworth(B,A) & m1_eqrel_1(B,u1_struct_0(A)) & k5_card_1(B) = k2_dilworth(A) ) ) )).
fof(t51_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( 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(k4_ordinal1,k4_ordinal1,k4_ordinal1,k5_numbers,1,k5_numbers))),a_3_1_ec_pf_1(A,B,C)) ) ) ) ) )).
fof(t51_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( 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] : ( 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) != k5_numbers & k6_ec_pf_2(A,k2_ec_pf_2(A,B),k3_ec_pf_2(A,B),D) != k5_numbers & k5_ec_pf_2(A,k2_ec_pf_2(A,B),k3_ec_pf_2(A,B),C) != k5_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)) ) ) ) ) ) )).
fof(t51_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t51_entropy1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v4_partfun3(B) & m2_finseq_1(B,k1_numbers) ) => ( r1_xxreal_0(k5_numbers,A) => k4_entropy1(k10_rvsum_1(B,A)) = k4_rvsum_1(k10_rvsum_1(B,k3_xcmplx_0(A,k3_power(2,A))),k10_rvsum_1(k14_rvsum_1(B,k3_entropy1(2,B)),A)) ) ) ) )).
fof(t51_enumset1,axiom,( ! [A] : k4_enumset1(A,A,A,A,A,A) = k1_tarski(A) )).
fof(t51_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,B)))) => ( ! [E] : ( r2_hidden(E,D) => ( r1_tarski(E,C) & ? [F] : ( m1_subset_1(F,k1_zfmisc_1(A)) & ? [G] : ( 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) ) ) ) )).
fof(t51_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => r1_rvsum_1(B,k4_struct_0(k15_euclid(A))) ) ) )).
fof(t51_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( 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] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ~ ( 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)) & k2_xcmplx_0(k2_xcmplx_0(F,G),H) = 1 & ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ! [K] : ( v1_xreal_0(K) => ( ( 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)) & k2_xcmplx_0(k2_xcmplx_0(I,J),K) = 1 ) => ( I = F & J = G & K = H ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t51_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t51_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v5_euclid_7(B,A) & m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) ) => k1_card_1(B) = A ) ) )).
fof(t51_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => k6_euclid(3,A) = k1_euclid_8(k4_xcmplx_0(k1_funct_1(A,1)),k4_xcmplx_0(k1_funct_1(A,2)),k4_xcmplx_0(k1_funct_1(A,3))) ) )).
fof(t51_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ? [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) & ? [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) & B = k2_euclid_4(A,C,D) ) ) ) ) )).
fof(t51_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( 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,k9_funct_7(D,A,B))) ) ) ) )).
fof(t51_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( 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)) ) ) )).
fof(t51_fcont_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(D,C) & r1_xxreal_0(k1_funct_1(k1_fcont_1(A,B),D),k1_funct_1(k1_fcont_1(A,B),C)) ) ) ) ) ) )).
fof(t51_fdiff_11,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_sin_cos9)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_sin_cos9)),A),B) = k3_xcmplx_0(k1_funct_1(k22_sin_cos,B),k2_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k1_funct_1(k2_sin_cos9,B))) ) ) ) ) ) )).
fof(t51_fdiff_4,axiom,( ! [A] : ( ( 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)),k7_xcmplx_0(1,2)),k18_sin_cos))) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k16_sin_cos,B),k5_numbers) & ~ r1_xxreal_0(1,k1_funct_1(k18_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)),k7_xcmplx_0(1,2)),k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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)),k7_xcmplx_0(1,2)),k18_sin_cos),A),B) = k7_xcmplx_0(k1_newton(k1_funct_1(k16_sin_cos,B),3),k6_xcmplx_0(1,k1_funct_1(k18_sin_cos,B))) ) ) ) ) ) )).
fof(t51_fdiff_7,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k18_sin_cos,k16_sin_cos)))) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => ( k1_funct_1(B,C) = k7_xcmplx_0(C,2) & k1_funct_1(k16_sin_cos,k1_funct_1(B,C)) != k5_numbers ) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k3_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos,k16_sin_cos)),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k3_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos,k16_sin_cos)),A),C) = k4_xcmplx_0(k7_xcmplx_0(1,k6_xcmplx_0(1,k1_funct_1(k18_sin_cos,C)))) ) ) ) ) ) ) )).
fof(t51_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => ( r2_hidden(k3_xcmplx_0(2,A),k3_fib_num2) & ~ r2_hidden(k1_nat_1(k3_xcmplx_0(2,A),1),k3_fib_num2) ) ) )).
fof(t51_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ v1_xboole_0(D) & v19_lattices(D,A) & v20_lattices(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k6_filter_0(A,D))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t51_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t51_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v18_lattices(B,A) & v21_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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))) ) ) ) )).
fof(t51_finseq_1,axiom,( ! [A] : ( ? [B] : ( v7_ordinal1(B) & r1_tarski(A,k2_finseq_1(B)) ) => ( k14_finseq_1(A) = k1_xboole_0 <=> A = k1_xboole_0 ) ) )).
fof(t51_finseq_2,axiom,( k1_finseq_2(3) = k11_finseq_1(1,2,3) )).
fof(t51_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t51_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(t51_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t51_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ~ ( B != D & C != D & k1_finseq_5(A,k3_finseq_4(A,B,C,D),D) != k3_finseq_4(A,B,C,D) ) ) ) ) ) )).
fof(t51_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,B) & m2_finseq_1(C,A) ) => ! [D] : ( ( v3_card_1(D,B) & m2_finseq_1(D,A) ) => ! [E] : ( ( 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] : ( ( 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(k4_ordinal1,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))) ) ) ) ) ) ) ) )).
fof(t51_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t51_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( v7_ordinal1(C) => ( r1_tarski(k7_flang_1(A,B,k1_nat_1(C,1)),k6_flang_1(A,k8_flang_1(A,B),B)) & r1_tarski(k7_flang_1(A,B,k1_nat_1(C,1)),k6_flang_1(A,B,k8_flang_1(A,B))) ) ) ) )).
fof(t51_flang_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( k1_flang_2(A,C,D,E) = k1_tarski(B) => ( r1_xxreal_0(D,k5_numbers) | ! [F] : ( v7_ordinal1(F) => ( ( r1_xxreal_0(D,F) & r1_xxreal_0(F,E) ) => k7_flang_1(A,C,F) = k1_tarski(B) ) ) ) ) ) ) ) )).
fof(t51_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ( k2_flang_3(A,B) = k1_xboole_0 <=> B = k1_xboole_0 ) ) )).
fof(t51_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(A,B) <=> ! [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) ) ) ) ) ) )).
fof(t51_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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) ) ) ) )).
fof(t51_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( v2_funct_1(B) => v2_funct_1(k5_relat_1(B,A)) ) ) )).
fof(t51_funct_2,axiom,( ! [A] : ! [B] : ( ( 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 ) )).
fof(t51_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t51_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => r1_tarski(k2_funct_4(k2_funct_4(A)),A) ) )).
fof(t51_funct_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ! [G] : ! [H] : ( ( r2_hidden(G,A) & r2_hidden(H,B) & k1_funct_1(D,G) = E & k1_funct_1(k9_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) ) ) ) ) ) ) ) )).
fof(t51_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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) ) => k3_funct_7(A,k10_finseq_1(B,C)) = k3_relat_1(B,C) ) ) ) )).
fof(t51_funct_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t51_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D,C)),k3_fuzzy_2(A,k1_fuzzy_1(A,B,D),k1_fuzzy_1(A,B,C))) ) ) ) ) )).
fof(t51_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_fvaluat1(A,B))) => m1_subset_1(C,u1_struct_0(A)) ) ) ) ) )).
fof(t51_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v2_struct_0(C) & l3_algstr_0(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m2_finseq_2(F,u1_struct_0(C),k4_finseq_2(A,u1_struct_0(C))) => ( ( r2_hidden(B,k2_finseq_1(A)) & E = k1_funct_1(F,B) ) => k1_funct_1(k10_fvsum_1(A,C,F,D),B) = k6_algstr_0(C,D,E) ) ) ) ) ) ) ) )).
fof(t51_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( ( ~ v1_xboole_0(F) & v1_relat_1(F) & v2_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ! [G] : ( m1_genealg1(G,F) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t51_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k19_gfacirc1(A,B,C),k20_gfacirc1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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) ) ) ) ) ) ) )).
fof(t51_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( 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)) ) ) ) )).
fof(t51_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( ( 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))) ) ) ) ) ) )).
fof(t51_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_003(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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) ) ) ) )).
fof(t51_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ 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_0(k2_goboard2(D))) & r1_xxreal_0(1,C) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),B)) = k2_topreal1(2,D,C) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,2),B)) = k2_topreal1(2,D,k1_nat_1(C,1)) ) => ( r1_xxreal_0(k3_finseq_1(k2_goboard2(D)),k1_nat_1(A,1)) | r1_xxreal_0(k3_finseq_1(D),k1_nat_1(C,1)) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,2),B) ) ) ) ) ) ) ) )).
fof(t51_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t51_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => r2_hidden(k1_xboole_0,k9_graph_3(A)) ) )).
fof(t51_graph_5,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_graph_1(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( ( ~ 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] : ( m2_finseq_1(G,u4_struct_0(C)) => ~ ( r2_hidden(G,F) & ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t51_graphsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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 ) ) ) ) ) )).
fof(t51_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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)),k11_polynom1(A,C,D,E),k8_polynom1(A,C)) ) ) ) ) ) )).
fof(t51_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & v3_group_1(A) & v5_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k2_binop_1(u1_struct_0(A),k4_ordinal1,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),k4_ordinal1,u1_struct_0(A),k4_group_1(A),B,D),k2_binop_1(u1_struct_0(A),k4_ordinal1,u1_struct_0(A),k4_group_1(A),C,D)) ) ) ) ) )).
fof(t51_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t51_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_group_2(C,A) => ( r1_struct_0(C,B) => r1_struct_0(C,k2_group_1(A,B)) ) ) ) ) )).
fof(t51_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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))) ) ) ) ) )).
fof(t51_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t51_group_5,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t51_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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) & v5_group_1(A) & l3_algstr_0(A) ) => v5_group_1(k10_group_6(A,B,C)) ) ) ) ) )).
fof(t51_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ 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] : ( ( 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 ) ) ) ) )).
fof(t51_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( ( v5_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ( ( v5_glib_001(C,A) & m3_glib_001(C,A) ) => ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => ! [E] : ( m1_subset_1(E,k6_glib_000(A)) => ! [F] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t51_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( 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) ) ) )).
fof(t51_hurwitz,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(A,k1_complfld) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => ( r1_xxreal_0(1,k2_hurwitz(k1_complfld,A)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ( v1_hurwitz(A) => ( r1_xxreal_0(k5_numbers,k3_complex1(B)) | v1_hurwitz(k5_hurwitz(k1_complfld,k8_hurwitz(A,B),k3_hurwitz(k1_complfld,B,1))) ) ) ) ) ) )).
fof(t51_ideal_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t51_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ? [C] : ( m1_subset_1(C,u2_incsp_1(A)) & ? [D] : ( m1_subset_1(D,u2_incsp_1(A)) & ? [E] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t51_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k5_numbers,A) => ( r1_xxreal_0(k5_numbers,k2_int_1(A)) & r1_xxreal_0(k5_numbers,k1_int_1(A)) & m1_subset_1(k2_int_1(A),k4_ordinal1) & m1_subset_1(k1_int_1(A),k4_ordinal1) ) ) ) )).
fof(t51_int_5,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t51_integr11,axiom,( ! [A] : ( ( 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),k27_sin_cos),k2_fdiff_9))) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( k2_xcmplx_0(1,k1_funct_1(k18_sin_cos,B)) != k5_numbers & k6_xcmplx_0(1,k1_funct_1(k18_sin_cos,B)) != k5_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),k27_sin_cos),k2_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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),k27_sin_cos),k2_fdiff_9),A),B) = k7_xcmplx_0(k1_funct_1(k18_sin_cos,B),k6_xcmplx_0(k1_funct_1(k18_sin_cos,B),1)) ) ) ) ) ) )).
fof(t51_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,D) & r1_tarski(D,k2_rcomp_1(k4_xcmplx_0(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,k22_sin_cos),k3_valued_1(k1_numbers,k1_numbers,k1_numbers,C,k1_taylor_1(2)))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => k1_funct_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) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k22_sin_cos)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k22_sin_cos)),k3_seq_4(A))) ) ) ) ) ) )).
fof(t51_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k3_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k26_sin_cos,D)))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,D)))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos)),k3_seq_4(A))) ) ) ) ) )).
fof(t51_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_real_ns1(A))) => ! [E] : ( ( 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] : ( 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,k6_xcmplx_0(C,B)) ) ) ) ) ) ) ) )).
fof(t51_integra1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( m1_integra1(C,B) => ! [D] : ( ( 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] : ( ( 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_funct_1(k4_integra1(B,k3_valued_1(B,k1_numbers,k1_numbers,D,E),C),A),k2_xcmplx_0(k1_funct_1(k4_integra1(B,D,C),A),k1_funct_1(k4_integra1(B,E,C),A))) ) ) ) ) ) ) )).
fof(t51_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( A = k1_rcomp_1(k3_xcmplx_0(k2_nat_1(2,B),k28_sin_cos),k3_xcmplx_0(k1_nat_1(k2_nat_1(2,B),1),k28_sin_cos)) => k2_integra5(A,k32_valued_1(k1_numbers,k1_numbers,k16_sin_cos)) = k4_xcmplx_0(2) ) ) ) )).
fof(t51_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v3_rcomp_1(E) & m1_subset_1(E,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,E) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => ( k1_funct_1(C,F) = k6_xcmplx_0(F,A) & ~ r1_xxreal_0(k1_funct_1(C,F),k5_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] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => k1_funct_1(D,F) = k7_xcmplx_0(1,k6_xcmplx_0(F,A)) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,D,B)) ) => k2_integra5(B,D) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1),k2_seq_4(B)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1),k3_seq_4(B))) ) ) ) ) ) ) )).
fof(t51_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => k9_interva1(A,B,B) = k2_interva1(A,k1_subset_1(A),k1_subset_1(A)) ) ) )).
fof(t51_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(t51_jgraph_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ 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(k5_numbers,k17_euclid(A)) | r1_xxreal_0(k5_numbers,k17_euclid(B)) | r1_xxreal_0(k5_numbers,k18_euclid(A)) | r1_xxreal_0(k5_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) ) ) ) ) ) )).
fof(t51_jgraph_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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,k5_numbers) | r1_xxreal_0(C,k5_numbers) | ( v3_tops_2(E,k15_euclid(2),k15_euclid(2)) & ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t51_jordan,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t51_jordan15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ r1_xxreal_0(C,1) & ~ r1_xxreal_0(k3_finseq_1(k1_jordan8(B,k1_nat_1(A,1))),C) & r1_xxreal_0(1,D) & r1_xxreal_0(D,E) & r1_xxreal_0(E,k1_matrix_0(k1_jordan8(B,k1_nat_1(A,1)))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),C,E),k8_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),D),k9_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) & r2_subset_1(k4_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),E)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),E),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),C,E))),k9_jordan6(B)) ) ) ) ) ) ) )).
fof(t51_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(C,B) & r1_xboole_0(k4_topreal1(C),k3_topreal1(2,k2_jordan9(B,A))) ) ) ) ) )).
fof(t51_jordan1h,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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)))) ) => ( r1_jordan1h(B,A) => r1_xxreal_0(1,A) ) ) ) )).
fof(t51_jordan1j,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v7_ordinal1(D) => ( ( 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) ) ) ) ) ) ) ) )).
fof(t51_jordan1k,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t51_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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 ) ) ) )).
fof(t51_jordan4,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) ) )).
fof(t51_jordan6,axiom,( ! [A] : ( 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))) ) ) ) )).
fof(t51_kurato_1,axiom,( 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))))) )).
fof(t51_lattice2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t51_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t51_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => ! [E] : ( m1_subset_1(E,k6_glib_000(A)) => ( ( r2_hidden(D,k1_relset_1(k6_glib_000(A),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),k13_lexbfs(A,k16_lexbfs(A),B)))) & r2_hidden(E,k1_relset_1(k6_glib_000(A),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),k13_lexbfs(A,k16_lexbfs(A),B)))) & C = k7_nat_d(k15_glib_000(A),k1_recdef_1(k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),k13_lexbfs(A,k16_lexbfs(A),B)),E)) ) => ( r1_xxreal_0(k1_recdef_1(k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),k13_lexbfs(A,k16_lexbfs(A),B)),E),k1_recdef_1(k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),k13_lexbfs(A,k16_lexbfs(A),B)),D)) | r1_termord(k4_ordinal1,k4_bagorder(k4_ordinal1),k1_uproots(k4_ordinal1,k17_lexbfs(k6_glib_000(A),k4_ordinal1,k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),k13_lexbfs(A,k16_lexbfs(A),C)),D),1),k1_uproots(k4_ordinal1,k17_lexbfs(k6_glib_000(A),k4_ordinal1,k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),k13_lexbfs(A,k16_lexbfs(A),C)),E),1)) ) ) ) ) ) ) ) )).
fof(t51_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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)) ) ) ) ) )).
fof(t51_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(k6_xcmplx_0(A,D),A))) & k1_funct_1(B,E) = k1_limfunc2(B,A) ) ) ) ) | r2_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t51_lpspace1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,C,k6_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,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [G] : ( m1_subset_1(G,u1_struct_0(k20_lpspace1(B,C,D))) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t51_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v2_xxreal_0(E) & v1_xreal_0(E) ) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t51_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( m1_subset_1(D,k1_hilbert1) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t51_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => v1_ltlaxio1(k3_hilbert1(k3_hilbert1(C,k1_ltlaxio2(A,B)),k3_hilbert1(k3_hilbert1(C,k4_ltlaxio1(k1_ltlaxio1(B),k1_ltlaxio1(k4_hilbert1(A,B)))),k1_ltlaxio1(C)))) ) ) ) )).
fof(t51_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t51_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( r2_matrix10(k5_matrix10(A,B,D),k5_matrix10(A,C,D)) => r2_matrix10(B,C) ) ) ) ) ) )).
fof(t51_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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,k7_matrix_0(u1_struct_0(B),C,E))) = k4_struct_0(B) ) ) ) ) ) ) ) )).
fof(t51_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => k6_matrix13(A,C,k7_subset_1(k4_ordinal1,k2_finseq_1(k3_finseq_1(C)),k3_matrix13(B)),k2_finseq_1(k1_matrix_0(C))) = k1_matrlin(A,B,C) ) ) ) )).
fof(t51_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,A) ) => ( ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,A) ) => ( k3_matrix_0(u1_struct_0(B),k4_matrix_3(B,C,k4_matrix14(B,A,D)),E,D) = k3_matrix_0(u1_struct_0(B),C,E,1) & k3_matrix_0(u1_struct_0(B),k4_matrix_3(B,C,k4_matrix14(B,A,D)),E,1) = k3_matrix_0(u1_struct_0(B),C,E,D) ) ) ) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ( 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_0(u1_struct_0(B),k4_matrix_3(B,C,k4_matrix14(B,A,D)),E,F) = k3_matrix_0(u1_struct_0(B),C,E,F) ) ) ) ) ) ) ) ) ) ) )).
fof(t51_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),k5_numbers,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(C),k5_numbers,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(C))) ) => k4_matrix15(C,D,E) = k1_tarski(k1_xboole_0) ) ) ) ) ) )).
fof(t51_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( v5_matrix16(D,B) => v5_matrix16(k2_matrix13(A,A,B,D,C),B) ) ) ) ) ) )).
fof(t51_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(B)) ) => ( k3_finseq_1(C) = A => ( v1_matrix_0(C) & v2_matrix_0(C,B,A,k1_matrix_0(C)) & m2_finseq_1(C,k3_finseq_2(B)) ) ) ) ) ) )).
fof(t51_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) ) => k3_matrix_3(A,B,C) = k1_matrix_4(A,B,k2_matrix_3(A,C)) ) ) ) ) )).
fof(t51_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r1_matrix_6(A,B,C,D) => ( r1_xxreal_0(A,k5_numbers) | r1_matrix_6(A,B,k3_matrix_3(B,C,D),k3_matrix_3(B,D,D)) ) ) ) ) ) ) )).
fof(t51_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( v4_matrix_6(D,A,B) => r1_matrix_8(A,B,k4_matrix_3(B,k4_matrix_3(B,k4_matrix_0(u1_struct_0(B),D),C),D),C) ) ) ) ) ) )).
fof(t51_matrix_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( ? [D] : ( m1_subset_1(D,k4_ordinal1) & r2_hidden(D,k2_finseq_1(A)) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k2_finseq_1(A)) => k1_funct_1(k8_matrix_0(u1_struct_0(B),C,D),E) = k4_struct_0(B) ) ) ) => k7_setwiseo(k3_matrix_2(A),u1_struct_0(B),u1_algstr_0(B),k6_matrix_2(k3_matrix_2(A)),k11_matrix_3(A,B,C)) = k4_struct_0(B) ) ) ) ) )).
fof(t51_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k2_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(C) & k3_finseq_1(B) = k1_matrix_0(C) ) => k1_matrixc1(k13_matrixc1(A,B,C)) = k13_matrixc1(k1_complsp2(A),k1_complsp2(B),k1_matrixc1(C)) ) ) ) ) )).
fof(t51_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t51_matrixr1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_1(B,k1_numbers) => k10_matrixr1(k10_rvsum_1(B,A)) = k7_matrixr1(A,k10_matrixr1(B)) ) ) )).
fof(t51_matrixr2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(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),k5_numbers) | k12_matrixr1(k4_matrixr1(B),A) = k6_rvsum_1(k12_matrixr1(B,A)) ) ) ) ) )).
fof(t51_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t51_matrprob,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(A) = k1_matrix_0(B) & A = k5_finseq_2(k4_ordinal1,k3_finseq_1(A),1) ) => ( r1_xxreal_0(k1_matrix_0(B),k5_numbers) | ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k2_finseq_1(k3_finseq_1(k11_matrixr1(B,A)))) => k1_funct_1(k11_matrixr1(B,A),C) = k18_rvsum_1(k7_matrix_0(k1_numbers,B,C)) ) ) ) ) ) ) )).
fof(t51_mcart_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k3_zfmisc_1(B,C,D)) => ( ! [F] : ( m1_subset_1(F,B) => ! [G] : ( m1_subset_1(G,C) => ! [H] : ( m1_subset_1(H,D) => ( E = k3_xtuple_0(F,G,H) => A = F ) ) ) ) => A = k1_mcart_1(B,C,D,E) ) ) ) ) ) )).
fof(t51_measure6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( v3_xxreal_2(B) => k3_seq_4(k1_measure6(B,A)) = k2_xcmplx_0(A,k3_seq_4(B)) ) ) ) )).
fof(t51_member_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k9_member_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k2_xcmplx_0(A,B)) ) ) )).
fof(t51_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( v7_ordinal1(D) => k6_memstr_0(A,B,k9_memstr_0(A,B,C,D)) = k6_memstr_0(A,B,C) ) ) ) ) )).
fof(t51_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k4_partfun1(A,k2_numbers)) & v1_mesfunc8(F,A,k2_numbers) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k2_numbers)))) ) => ( ( D = k1_relset_1(A,k4_mesfunc5(A,k2_numbers,F,k5_numbers)) & D = k1_relset_1(A,E) & ! [G] : ( v7_ordinal1(G) => r1_mesfun6c(A,B,k4_mesfunc5(A,k2_numbers,F,G),D) ) & r3_mesfunc6(A,B,C,E) & ! [G] : ( m1_subset_1(G,A) => ! [H] : ( v7_ordinal1(H) => ( r2_hidden(G,D) => r1_xxreal_0(k1_mesfunc9(k55_valued_1(A,k2_numbers,k4_mesfunc5(A,k2_numbers,F,H)),G),k1_mesfunc9(E,G)) ) ) ) & ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(t51_mesfunc5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v9_mesfunc5(A) => ( ~ v8_mesfunc5(A) & ~ v7_mesfunc5(A) ) ) ) )).
fof(t51_mesfunc6,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( v6_supinf_2(B) <=> ! [C] : r1_xxreal_0(k5_numbers,k1_funct_1(B,C)) ) ) )).
fof(t51_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,k10_midsp_1(A)) => ? [C] : ( m1_subset_1(C,k10_midsp_1(A)) & k11_midsp_1(A,B,C) = k6_midsp_1(A) ) ) ) )).
fof(t51_mmlquery,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t51_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t51_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v2_struct_0(C) & v10_modelc_2(C) & l1_modelc_2(C) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t51_moebius1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k4_ordinal1)) ) => ( B = a_1_1_moebius1(A) => r8_pboole(k4_ordinal1,k4_moebius1(B),k16_pre_poly(k4_ordinal1)) ) ) ) )).
fof(t51_monoid_0,axiom,( ! [A] : ( ( ~ 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)) = k5_numbers | k4_binop_1(u1_struct_0(A),u2_algstr_0(A)) = 1 ) ) )).
fof(t51_monoid_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t51_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_funct_1(u3_msualg_1(A,k3_equation(A)),C)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,k3_equation(A)),C)) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,k3_equation(A)),C)) => ( ( r1_equation(A,B,C,k5_equation(A,C,D,E)) & r1_equation(A,B,C,k5_equation(A,C,E,F)) ) => r1_equation(A,B,C,k5_equation(A,C,D,F)) ) ) ) ) ) ) ) )).
fof(t51_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m3_pboole(C,A,k1_mboolean(A,B)) => ! [D] : ( m3_pboole(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t51_msualg_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_msualg_4(C,A,B,B) => ! [D] : ( ( v1_msualg_4(D,A,B) & m1_msualg_4(D,A,B,B) ) => ( r2_pboole(A,C,D) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,k1_funct_1(B,E)) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t51_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( v8_struct_0(B) & l1_orders_2(B) & k1_dilworth(B) = 2 & ~ r1_xxreal_0(k2_mycielsk(B),A) ) ) )).
fof(t51_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => r8_pboole(k8_newton,k12_nat_3(k1_newton(B,A)),k4_nat_3(k8_newton,k12_nat_3(B),A)) ) ) )).
fof(t51_nat_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => k1_nat_4(k8_finseq_1(k4_ordinal1,B,C),A) = k8_finseq_1(k4_ordinal1,k1_nat_4(B,A),k1_nat_4(C,A)) ) ) ) )).
fof(t51_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t51_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( 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) ) ) ) ) )).
fof(t51_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(k14_prvect_2(A))) => ! [E] : ! [F] : ( v1_xreal_0(F) => ! [G] : ( m1_subset_1(G,u1_struct_0(k16_lopban_1(k11_prvect_2(A,k5_ndiff_5(A,E)),B))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k11_prvect_2(A,k5_ndiff_5(A,E)))) => ! [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] : ( 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(k2_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] : ( 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] : ( 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(k2_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)))),k3_xcmplx_0(F,k2_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)))) ) ) ) ) ) ) ) ) ) )).
fof(t51_newton,axiom,( ! [A] : ( v7_ordinal1(A) => k6_nat_d(A,1) = 1 ) )).
fof(t51_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t51_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(k7_normform(A))) => ! [C] : ( 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)) ) ) )).
fof(t51_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t51_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,u4_struct_0(B),u4_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(B),u4_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u4_struct_0(A),u4_struct_0(C)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(A),u4_struct_0(C)))) ) => r2_funct_2(u4_struct_0(B),u4_struct_0(k2_oppcat_1(C)),k11_oppcat_1(B,C,k1_partfun1(u4_struct_0(B),u4_struct_0(A),u4_struct_0(A),u4_struct_0(C),D,E)),k1_partfun1(u4_struct_0(B),u4_struct_0(A),u4_struct_0(A),u4_struct_0(k2_oppcat_1(C)),D,k11_oppcat_1(A,C,E))) ) ) ) ) ) )).
fof(t51_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(A))) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A))) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A))))) ) => ! [G] : ( v7_ordinal1(G) => ( ( r1_xxreal_0(B,C) & ! [H] : ( m1_subset_1(H,u1_struct_0(k4_real_ns1(A))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k4_real_ns1(A))) => r1_xxreal_0(k2_normsp_0(k4_real_ns1(A),k5_algstr_0(k4_real_ns1(A),k10_funct_2(u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A)),F,H),k10_funct_2(u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A)),F,I))),k3_xcmplx_0(D,k2_normsp_0(k4_real_ns1(A),k5_algstr_0(k4_real_ns1(A),H,I)))) ) ) ) => ( r1_xxreal_0(D,k5_numbers) | ! [H] : ( m1_subset_1(H,u1_struct_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A)))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A)))) => r1_xxreal_0(k2_normsp_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A)),k5_algstr_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A)),k3_funct_2(u1_struct_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A))),u1_struct_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A))),k1_abian(u1_struct_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A))),k6_ordeq_01(A,E,F,B,C),k2_xcmplx_0(G,1)),H),k3_funct_2(u1_struct_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A))),u1_struct_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A))),k1_abian(u1_struct_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A))),k6_ordeq_01(A,E,F,B,C),k2_xcmplx_0(G,1)),I))),k3_xcmplx_0(k7_xcmplx_0(k1_newton(k3_xcmplx_0(D,k6_xcmplx_0(C,B)),k2_xcmplx_0(G,1)),k2_newton(k2_xcmplx_0(G,1))),k2_normsp_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A)),k5_algstr_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A)),H,I)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t51_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r4_orders_1(A,B) <=> r5_orders_1(k2_relat_1(A),B) ) ) )).
fof(t51_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r7_orders_1(u1_orders_2(A),B) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ r2_orders_2(A,C,B) ) ) ) ) )).
fof(t51_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r2_hidden(A,B) => B = k10_ordinal2(A,k5_ordinal3(B,A)) ) ) ) )).
fof(t51_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ~ ( v4_ordinal5(A) & ! [B] : ( v3_ordinal1(B) => A != k3_ordinal5(B) ) ) ) )).
fof(t51_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v3_ordinal1(B) & v4_ordinal1(B) & ~ v1_xboole_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & v3_ordinal6(C) ) => ( ( r1_ordinal1(B,k9_xtuple_0(k7_ordinal6(C))) & ! [D] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t51_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( 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 ) ) )).
fof(t51_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_parsp_2(A,B,C,D,E) => r3_parsp_2(A,B,C,D,E) ) ) ) ) ) ) )).
fof(t51_partfun1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_partfun1(A,B) <=> ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & k2_xboole_0(A,B) = C ) ) ) ) )).
fof(t51_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t51_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( ( r2_pboole(A,C,B) & r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A)) ) => r6_pboole(A,C,k1_pboole(A)) ) ) ) )).
fof(t51_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( 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) & k10_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) = k2_xcmplx_0(k6_pdiff_5(B,A),k6_pdiff_5(C,A)) ) ) ) ) ) )).
fof(t51_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t51_pepin,axiom,( k4_pepin(1) = 5 )).
fof(t51_polyform,axiom,( ! [A] : ( ( 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)))) ) )).
fof(t51_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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),k7_polynom1(A,C,E,F),k8_polynom1(A,C)) => r2_rewrite1(k3_polyred(A,B,C,D),E,F) ) ) ) ) ) ) ) )).
fof(t51_power,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & A != 1 & k3_power(A,1) != k5_numbers ) ) )).
fof(t51_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t51_prepower,axiom,( ! [A] : ( v1_rat_1(A) => k4_prepower(1,A) = 1 ) )).
fof(t51_prob_3,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k9_setfam_1(A)) => ! [C] : ( B != k1_xboole_0 => ( r2_hidden(C,k7_prob_3(A,B)) <=> ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,B)) => r2_hidden(C,k4_prob_3(A,B,D)) ) ) ) ) ) )).
fof(t51_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t51_pscomp_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t51_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t51_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ~ ( r1_qc_lang2(A,C,B) & r1_xxreal_0(k3_finseq_1(k11_qc_lang1(A,B)),k3_finseq_1(k11_qc_lang1(A,C))) ) ) ) ) )).
fof(t51_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( ( ~ 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)))) ) ) ) ) )).
fof(t51_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k28_quaterni(k17_quatern2(A,B)) = k3_xcmplx_0(k28_quaterni(A),k28_quaterni(B)) ) ) )).
fof(t51_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => ! [D] : ( v1_quaterni(D) => k23_quaterni(k22_quaterni(A,B),k22_quaterni(C,D)) = k22_quaterni(k22_quaterni(k22_quaterni(k23_quaterni(A,C),k23_quaterni(B,C)),k23_quaterni(A,D)),k23_quaterni(B,D)) ) ) ) ) )).
fof(t51_quaterni,axiom,( k27_quaterni(k1_xcmplx_0) = k24_quaterni(k1_xcmplx_0) )).
fof(t51_quofield,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) ) )).
fof(t51_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B))))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t51_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,k6_real_3(B),A)) ) ) )).
fof(t51_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r2_hidden(B,k9_xtuple_0(k5_relat_1(C,A))) <=> ( r2_hidden(B,A) & r2_hidden(B,k9_xtuple_0(C)) ) ) ) )).
fof(t51_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ! [E] : ( 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)) ) ) ) )).
fof(t51_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => k8_rewrite2(A,k6_rewrite2(k8_afinsq_1(A)),B) = k4_flang_1(A,B) ) )).
fof(t51_rfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t51_rfunct_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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(B,A))) => 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(B,A))),k7_relset_1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A)))) ) ) ) ) )).
fof(t51_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ( r2_classes1(C,D) <=> r2_classes1(k15_valued_1(A,k1_numbers,C,E),k15_valued_1(B,k1_numbers,D,E)) ) ) ) ) ) ) )).
fof(t51_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_seq_2(A) => v8_valued_0(k4_rinfsup1(A)) ) ) )).
fof(t51_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t51_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rlsub_1(C,A) => ( r1_struct_0(C,B) <=> k3_rlsub_1(A,k4_algstr_0(A,B),C) = u1_struct_0(C) ) ) ) ) )).
fof(t51_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_2(C,A,B) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t51_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( ~ v8_ordinal1(C) & v1_xreal_0(C) ) => k1_convex1(A,k1_tops_1(A,B),C) = k1_tops_1(A,k1_convex1(A,B,C)) ) ) ) )).
fof(t51_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( 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) ) ) )).
fof(t51_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => k3_rlvect_2(A,k9_rlvect_2(A,B)) = k3_rlvect_2(A,B) ) ) )).
fof(t51_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t51_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t51_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_4(C,A,B) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t51_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( 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 ) ) )).
fof(t51_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t51_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t51_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( 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),k5_numbers) | r1_xxreal_0(k1_rpr_1(A,D),k5_numbers) | r1_xxreal_0(k1_rpr_1(A,E),k5_numbers) | k1_rpr_1(A,B) = k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k2_rpr_1(A,C,B),k1_rpr_1(A,C)),k3_xcmplx_0(k2_rpr_1(A,D,B),k1_rpr_1(A,D))),k3_xcmplx_0(k2_rpr_1(A,E,B),k1_rpr_1(A,E))) ) ) ) ) ) ) ) )).
fof(t51_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t51_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_2(C,A,B) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t51_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_rusub_5(A)))) => ( v3_pre_topc(B,k5_rusub_5(A)) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k4_bhsp_2(A,C,D),B) ) ) ) ) ) ) ) )).
fof(t51_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t51_rvsum_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t51_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( 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) ) ) ) ) ) )).
fof(t51_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_m(B)),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_m(B)))),D) ) & ! [D] : ( m1_scmfsa_2(D) => k18_scmfsa_2(k1_scmfsa6b(C,B,A),D) = k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_m(B)),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_m(B)))),D) ) ) ) ) ) ) )).
fof(t51_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( m1_scmfsa_2(B) => A != B ) ) )).
fof(t51_scmpds_2,axiom,( ! [A] : ( ( 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] : ( 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] : ( ( 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) ) ) ) ) )).
fof(t51_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( 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)) = k5_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,k1_nat_1(k5_card_1(C),2))) ) ) ) ) ) ) ) )).
fof(t51_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ! [C] : ( ( 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)) ) ) ) )).
fof(t51_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_semi_af1(A,B,D,F) & r2_semi_af1(A,B,C,D,E) & r2_semi_af1(A,B,C,F,G) ) => ( D = F | r2_semi_af1(A,D,E,F,G) ) ) ) ) ) ) ) ) ) )).
fof(t51_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v9_ordinal1(A) => v9_ordinal1(k56_valued_1(k4_ordinal1,k1_numbers,A)) ) ) )).
fof(t51_seq_4,axiom,( v1_finseqop(k3_binop_2,k2_numbers) )).
fof(t51_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( v7_ordinal1(C) => ( v2_prob_1(B) => k1_funct_1(k2_setlim_1(A,B),C) = k3_funct_2(k4_ordinal1,k9_setfam_1(A),k2_setlim_1(A,B),k1_nat_1(C,1)) ) ) ) )).
fof(t51_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => k9_nat_1(k9_setfam_1(B),k2_setlim_1(B,k6_setlim_2(B,D,C)),A) = k4_subset_1(B,C,k9_nat_1(k9_setfam_1(B),k2_setlim_1(B,D),A)) ) ) ) )).
fof(t51_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => k3_funct_2(A,k5_finsub_1(A),B,C) = k1_tarski(C) ) ) ) ) )).
fof(t51_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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 ) ) ) ) ) )).
fof(t51_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t51_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ! [C] : ( ( 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)) ) ) )).
fof(t51_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => r1_xxreal_0(1,k1_funct_1(k22_sin_cos,A)) ) ) )).
fof(t51_sin_cos3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xcmplx_0(B) => k2_comseq_3(k6_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,B),k3_xcmplx_0(k7_complex1,k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,B))),A) = k6_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,k3_xcmplx_0(A,B)),k3_xcmplx_0(k7_complex1,k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,k3_xcmplx_0(A,B)))) ) ) )).
fof(t51_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k2_sin_cos2(k7_xcmplx_0(A,2)) != k5_numbers => k1_sin_cos5(k7_xcmplx_0(A,2)) = k7_xcmplx_0(k2_sin_cos2(A),k6_xcmplx_0(k4_sin_cos2(A),1)) ) ) )).
fof(t51_sin_cos6,axiom,( k7_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k28_sin_cos,k3_xcmplx_0(2,k28_sin_cos))) = k1_rcomp_1(k4_xcmplx_0(1),1) )).
fof(t51_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k6_xcmplx_0(k1_sin_cos7(A),k1_sin_cos7(B)) = k1_sin_cos7(k6_xcmplx_0(k3_xcmplx_0(A,k3_square_1(k2_xcmplx_0(1,k1_square_1(B)))),k3_xcmplx_0(B,k3_square_1(k2_xcmplx_0(1,k1_square_1(A)))))) ) ) )).
fof(t51_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) => k1_sin_cos4(k3_sin_cos9(A)) = A ) ) )).
fof(t51_sincos10,axiom,( k2_partfun1(k1_numbers,k1_numbers,k3_sincos10,k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1))) = k2_partfun2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4))))) )).
fof(t51_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t51_sprect_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(B,C) => ( r2_hidden(A,k1_rcomp_1(B,C)) <=> ? [D] : ( v1_xreal_0(D) & r1_xxreal_0(k5_numbers,D) & r1_xxreal_0(D,1) & A = k2_xcmplx_0(k3_xcmplx_0(D,B),k3_xcmplx_0(k6_xcmplx_0(1,D),C)) ) ) ) ) ) ) )).
fof(t51_sprect_2,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(t51_sprect_3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t51_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t51_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k1_square_1(A),1) => ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) ) ) )).
fof(t51_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( k4_newton(1,A) = A & k4_newton(2,A) = k7_xcmplx_0(k3_xcmplx_0(A,k6_xcmplx_0(A,1)),2) & k4_newton(3,A) = k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(A,k6_xcmplx_0(A,1)),k6_xcmplx_0(A,2)),6) & k4_newton(4,A) = k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(A,k6_xcmplx_0(A,1)),k6_xcmplx_0(A,2)),k6_xcmplx_0(A,3)),24) ) ) )).
fof(t51_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k16_substut1(A),k38_substut1(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t51_subset_1,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ! [B] : ( ( ~ v1_zfmisc_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ? [D] : ( m1_subset_1(D,A) & r2_hidden(D,B) & D != C ) ) ) )).
fof(t51_supinf_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ! [C] : ( r2_hidden(C,k1_relset_1(A,B)) => r1_xxreal_0(k1_supinf_2,k1_funct_1(B,C)) ) => v6_supinf_2(B) ) ) )).
fof(t51_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)))) ) ) )).
fof(t51_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( k4_tdlat_1(A) = k12_tdlat_1(A) => v4_tdlat_3(A) ) ) )).
fof(t51_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & ! [D] : ( 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) ) ) ) )).
fof(t51_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( v2_tops_1(B,A) & ! [C] : ( ( v1_pre_topc(C) & v3_tex_3(C,A) & m1_pre_topc(C,A) ) => B != u1_struct_0(C) ) ) ) ) )).
fof(t51_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t51_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ 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] : ( ( 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)))) ) ) ) ) ) ) )).
fof(t51_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ( r1_borsuk_6(A,B,C) => v2_funct_1(k6_topalg_1(A,B,C,D)) ) ) ) ) ) )).
fof(t51_topgen_1,axiom,( v1_tops_1(k3_numbers,k3_topmetr) & m1_subset_1(k3_numbers,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )).
fof(t51_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) )).
fof(t51_topgrp_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t51_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v6_metric_1(B) & v8_metric_1(B) & v9_metric_1(B) & l1_metric_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( ~ r1_xxreal_0(k5_numbers,A) => k10_metric_1(B,C,A) = k1_xboole_0 ) ) ) ) )).
fof(t51_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => r1_tarski(k6_jgraph_6(A,B,C),k7_jgraph_6(A,B,C)) ) ) ) )).
fof(t51_toprealc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( ( 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,k14_toprealc(A,u1_struct_0(B),u1_struct_0(k3_topmetr),D)) ) ) ) ) )).
fof(t51_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(B,A) => ( v2_tops_1(B,A) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( C != k1_xboole_0 & v3_pre_topc(C,A) & ! [D] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t51_tops_2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t51_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v3_tops_1(B,A) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t51_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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))) ) ) ) ) ) ) )).
fof(t51_trees_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ r2_xboole_0(k9_finseq_1(A),k9_finseq_1(B)) ) ) )).
fof(t51_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v4_trees_3(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v4_trees_3(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_trees_1(D) ) => ( r2_hidden(A,D) <=> r2_hidden(k7_finseq_1(k12_finseq_1(k4_ordinal1,k3_finseq_1(B)),A),k11_trees_3(k7_finseq_1(k7_finseq_1(B,k9_finseq_1(D)),C))) ) ) ) ) ) )).
fof(t51_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( v2_trees_2(B,A) & m1_trees_2(B,A) ) => ! [C] : ( m1_trees_1(C,A) => ~ ( r2_hidden(C,B) & ~ v1_finset_1(B) & ! [D] : ( m1_trees_1(D,A) => ~ ( r2_hidden(D,B) & r2_hidden(D,k1_trees_2(A,C)) ) ) ) ) ) ) )).
fof(t51_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( ( r1_tarski(D,C) & r1_tarski(E,B) & 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,E)) ) ) ) ) ) ) )).
fof(t51_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t51_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( k3_funct_2(k4_ordinal1,u1_struct_0(k1_complfld),k5_uniroots(A),k5_numbers) = 1 | k3_funct_2(k4_ordinal1,u1_struct_0(k1_complfld),k5_uniroots(A),k5_numbers) = k4_xcmplx_0(1) ) & v1_int_1(k3_funct_2(k4_ordinal1,u1_struct_0(k1_complfld),k5_uniroots(A),B)) ) ) ) )).
fof(t51_uproots,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r8_pboole(u1_struct_0(A),k7_uproots(A,k4_polynom5(A,k4_algstr_0(A,B),k5_struct_0(A))),k1_uproots(u1_struct_0(A),k6_domain_1(u1_struct_0(A),B),1)) ) ) )).
fof(t51_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_tarski(k61_valued_1(B,C),A) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,B)) => k1_funct_1(A,k1_nat_1(C,D)) = k1_funct_1(B,D) ) ) ) ) ) ) )).
fof(t51_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( ( 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)) ) ) ) ) )).
fof(t51_vectsp_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t51_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t51_vfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ 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] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,u1_struct_0(D)))) ) => ! [F] : ( ( 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))) ) ) ) ) ) )).
fof(t51_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ! [E] : ! [F] : ( ( 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))) ) ) ) ) ) )).
fof(t51_waybel21,axiom,( ! [A] : ( ( 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] : ( ( ~ 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] : ( ( ~ 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)) ) ) ) ) )).
fof(t51_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ( k1_relset_1(u1_struct_0(k1_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))) ) ) ) )).
fof(t51_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k11_waybel34(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k11_waybel34(A))) => ! [D] : ( r2_hidden(D,k1_altcat_1(k11_waybel34(A),B,C)) <=> ? [E] : ( 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)) ) ) ) ) ) )).
fof(t51_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( D != k1_xboole_0 => r1_yellow_0(A,D) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(B)) ) => ~ ( r1_yellow_0(A,E) & D = k1_yellow_0(A,E) ) ) ) ) & ! [D] : ( ( 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) ) ) ) ) )).
fof(t51_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( ~ 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) ) ) ) ) ) ) ) ) )).
fof(t51_waybel_2,axiom,( ! [A] : ( ( 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] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t51_waybel_4,axiom,( ! [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) & l1_orders_2(A) ) => v8_waybel_4(k1_waybel_4(A),A) ) )).
fof(t51_wellord1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v1_relat_1(D) => ! [E] : ( 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) ) ) ) ) )).
fof(t51_xboole_1,axiom,( ! [A] : ! [B] : k2_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B)) = A )).
fof(t51_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => k8_xboolean(A,A) = k3_xboolean(A) ) )).
fof(t51_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( B != k5_numbers => A = k7_xcmplx_0(A,k7_xcmplx_0(B,B)) ) ) ) )).
fof(t51_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(C,B) & r1_xxreal_0(C,k6_xcmplx_0(B,A)) ) ) ) ) )).
fof(t51_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_tarski(k4_xxreal_1(C,D),k1_xxreal_1(A,B)) => ( r1_xxreal_0(D,C) | ( r1_xxreal_0(A,C) & r1_xxreal_0(D,B) ) ) ) ) ) ) ) )).
fof(t51_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ( m1_xxreal_2(k2_xxreal_0,A) => r1_tarski(A,k1_tarski(k2_xxreal_0)) ) ) )).
fof(t51_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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),k5_numbers) ) ) ) )).
fof(t51_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & l1_orders_2(B) ) => ! [C] : ( 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))) ) ) ) ) )).
fof(t51_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t51_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v16_functor0(C,A,B) & m2_functor0(C,A,B) ) => ( v21_functor0(C,A,B) => ! [D] : ( ( ~ v2_struct_0(D) & v2_altcat_1(D) & v3_altcat_2(D,A) & m1_altcat_2(D,A) ) => ! [E] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(t51_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t51_yellow_2,axiom,( ! [A] : ( ( ~ 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),k1_yellow_1(k7_waybel_0(A)),A) ) )).
fof(t51_yellow_4,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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 ) ) ) ) )).
fof(t51_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k13_lattice3(A,B,k1_yellow_5(A,C,B)) = k13_lattice3(A,B,C) ) ) ) )).
fof(t51_yellow_7,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t51_yellow_9,axiom,( ! [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] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => u1_pre_topc(B) = k5_waybel11(A) ) ) )).
fof(t51_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ~ r1_zf_lang(C,k5_zf_lang(A,B)) ) ) ) )).
fof(t51_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,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)) ) ) ) )).
fof(t51_zfmisc_1,axiom,( ! [A] : ! [B] : ( r1_xboole_0(k1_tarski(A),B) | k3_xboole_0(k1_tarski(A),B) = k1_tarski(A) ) )).
fof(t51_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => k3_zmodul01(B) = k3_zmodul01(A) ) ) )).
fof(t51_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),k4_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_numbers))) ) => k20_zmodul02(A,k8_finseq_1(u1_struct_0(A),B,C),D) = k8_finseq_1(u1_struct_0(A),k20_zmodul02(A,B,D),k20_zmodul02(A,C,D)) ) ) ) ) )).
fof(t52_abcmiz_0,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t52_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_abcmiz_1(B,A) & m1_subset_1(B,u4_struct_0(A)) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t52_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m3_abcmiz_1(B,A) => ! [C] : ( m3_abcmiz_1(C,A) => ! [D] : ( m3_abcmiz_1(D,A) => ( ( r3_abcmiz_a(A,B,C) & r3_abcmiz_a(A,C,D) ) => r3_abcmiz_a(A,B,D) ) ) ) ) ) )).
fof(t52_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t52_aff_4,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t52_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ( ( r1_xxreal_0(B,k1_afinsq_1(C)) & r2_hidden(A,B) ) => ( k1_funct_1(k5_relat_1(C,B),A) = k1_funct_1(C,A) & r2_hidden(A,k2_afinsq_1(C)) ) ) ) ) ) )).
fof(t52_afinsq_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_afinsq_2(k5_afinsq_1(A)) = A ) )).
fof(t52_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ( v8_incproj(k13_afproj(A)) => v1_translac(A) ) ) )).
fof(t52_afvect0,axiom,( ! [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) & v12_vectsp_1(A) & v1_tdgroup(A) & l2_algstr_0(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_tdgroup(A))) => ( ( ! [E] : ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t52_algspec1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( ~ v11_struct_0(C) & v1_instalg1(C) & l1_msualg_1(C) ) => ! [D] : ( m2_algspec1(D,C) => ( r1_algspec1(D,A,B) => r1_algspec1(C,A,B) ) ) ) ) ) )).
fof(t52_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_altcat_4(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_altcat_4(A))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t52_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t52_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_analort(A,B,C))) <=> m1_subset_1(D,u1_struct_0(A)) ) ) ) ) )).
fof(t52_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ r2_hidden(k16_aofa_000(A,B,C),k18_aofa_000(A)) ) ) ) )).
fof(t52_aofa_a00,axiom,( ? [A] : ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v14_aofa_a00(A,10) & v15_aofa_a00(A) & l6_aofa_a00(A) & v13_aofa_a00(A) & v18_aofa_a00(A,4,1) & v16_aofa_a00(A) & u1_struct_0(A) = k2_tarski(k5_numbers,1) & ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & B = 1 & r1_aofa_a00(A,k1_funct_1(u7_aofa_a00(A),4),k1_xboole_0,B) ) ) )).
fof(t52_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v19_aofa_a00(E,A) & m1_subset_1(E,u1_struct_0(A)) ) => ! [F] : ( m2_pboole(F,u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,D)) => k15_aofa_a00(A,B,C,D,E,k28_aofa_a00(A,C,E),F) = 1 ) ) ) ) ) ) )).
fof(t52_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_aofa_i00(E,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_aofa_i00(G,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),E) => ! [H] : ( m1_aofa_i00(H,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),E) => ( ! [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] : ( ( v1_relat_1(I) & v1_funct_1(I) ) => ~ ( k1_funct_1(I,D) = k5_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,k5_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,k5_numbers),E) ) ) ) ) ) ) ) ) ) ) )).
fof(t52_armstrng,axiom,( ! [A] : ! [B] : ( 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) ) ) ) ) )).
fof(t52_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( 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)) ) ) ) )).
fof(t52_asympt_1,axiom,( k5_series_1(5,5) = 3125 )).
fof(t52_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v10_bcialg_1(B,A) ) ) ) )).
fof(t52_bcialg_2,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( B = k4_bcialg_1(A) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t52_bcialg_5,axiom,( ! [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_5(A) & l2_bcialg_1(A) ) => ( ( v8_bcialg_1(A) & m1_bcialg_5(A,k5_numbers,1,k5_numbers,1) ) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t52_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t52_bhsp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(C)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(C),k5_normsp_1(C,D,k2_xcmplx_0(A,B)),k6_bhsp_1(C,k5_normsp_1(C,D,A),k5_normsp_1(C,D,B))) ) ) ) ) )).
fof(t52_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(C,k6_bhsp_2(A,B,D)) <=> k4_bhsp_1(A,B,C) = D ) ) ) ) ) )).
fof(t52_bhsp_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ! [D] : ( v7_ordinal1(D) => k1_normsp_1(B,k1_bhsp_4(B,k5_bhsp_4(B,k1_bhsp_4(B,C),k47_valued_1(k4_ordinal1,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)),k1_nat_1(D,1)),k1_normsp_1(B,k5_bhsp_4(B,k1_bhsp_4(B,C),A),k1_nat_1(D,1))) ) ) ) ) )).
fof(t52_bilinear,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( ( 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))) ) ) ) ) ) )).
fof(t52_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ r4_boolealg(A,k1_boolealg(A,B,C),C) ) ) ) )).
fof(t52_borsuk_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(k5_topmetr)) & ? [E] : ( 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] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ~ r1_topreal1(k15_euclid(2),D,E,C) ) ) ) ) ) ) )).
fof(t52_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [C] : ( 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) ) ) ) ) )).
fof(t52_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( m1_borsuk_2(G,A,C,D) => ! [H] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(t52_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( B != k4_struct_0(k15_euclid(2)) & ! [C] : ( 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)) != k2_xcmplx_0(k2_xcmplx_0(A,k3_euclid_3(B)),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)) ) ) ) ) )).
fof(t52_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t52_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_eqrel_1(I,A) => ! [J] : ( m1_subset_1(J,A) => ! [K] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t52_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t52_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k3_xboolean(k9_xboolean(A,B)) = k5_xboolean(A,B) ) ) )).
fof(t52_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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),D))) & 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),C)),k12_finseq_1(k3_cqc_lang(A),D))) ) => 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,C))),k12_finseq_1(k3_cqc_lang(A),D))) ) ) ) ) ) ) )).
fof(t52_card_1,axiom,( 6 = k4_enumset1(k5_ordinal1,1,2,3,4,5) )).
fof(t52_card_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : r1_xxreal_0(k5_card_1(k3_enumset1(A,B,C,D,E)),5) )).
fof(t52_card_3,axiom,( ! [A] : ! [B] : ( ( 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))))) ) ) ) )).
fof(t52_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t52_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( 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))) ) ) )).
fof(t52_cat_4,axiom,( ! [A] : ! [B] : v6_cat_4(k23_cat_4(A,B)) )).
fof(t52_cfcont_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_numbers)) => ! [B] : ( ( 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)) ) ) ) )).
fof(t52_cfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t52_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_chain_1(C,B) => ( B = k1_nat_1(A,1) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t52_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( r2_hidden(B,k2_chord(A,k1_tarski(C))) <=> r2_hidden(C,k2_chord(A,k1_tarski(B))) ) ) )).
fof(t52_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) ) => ! [D] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(t52_circcomb,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t52_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v4_msualg_1(E,A) & v4_msafree2(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t52_classes1,axiom,( ! [A] : r1_tarski(A,k5_classes1(A)) )).
fof(t52_classes2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) ) => ~ ( ~ r2_hidden(A,B) & A != B & ~ r2_hidden(B,A) ) ) ) )).
fof(t52_clvect_1,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_clvect_1(B) & m1_clvect_1(B,A) ) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_struct_0(B,C) <=> r1_struct_0(A,C) ) ) => B = A ) ) ) )).
fof(t52_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(C,k6_clvect_2(A,B,D)) <=> k15_csspace(A,B,C) = D ) ) ) ) ) )).
fof(t52_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [D] : ( v7_ordinal1(D) => k1_normsp_0(A,k1_bhsp_4(A,k6_clvect_3(A,k1_bhsp_4(A,B),k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,C,k1_valued_0(k2_numbers,C,1)))),D) = k5_algstr_0(A,k1_normsp_0(A,k1_bhsp_4(A,k6_clvect_3(A,B,C)),k1_nat_1(D,1)),k1_normsp_0(A,k6_clvect_3(A,k1_bhsp_4(A,B),C),k1_nat_1(D,1))) ) ) ) ) )).
fof(t52_cohsp_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( 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))) ) ) ) )).
fof(t52_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k9_complex1(k4_xcmplx_0(A)) = k9_complex1(A) ) )).
fof(t52_complex2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( B != k5_numbers & ! [C] : ( v1_int_1(C) => k1_comptrig(k2_complex2(B,A)) != k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C),k2_xcmplx_0(A,k1_comptrig(B))) ) ) ) ) )).
fof(t52_complfld,axiom,( ! [A] : ( 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)) ) )).
fof(t52_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k10_seq_4(A,k2_xcmplx_0(B,C)) = k7_seq_4(k10_seq_4(A,B),k10_seq_4(A,C)) ) ) ) )).
fof(t52_compos_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( l1_compos_1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) ) ) )).
fof(t52_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( v6_compos_0(D,u1_compos_1(A)) & m1_subset_1(D,u1_compos_1(A)) ) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t52_comptrig,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( r1_xxreal_0(k3_complex1(A),k5_numbers) => ( A = k5_numbers | r1_xxreal_0(k19_sin_cos(k1_comptrig(A)),k5_numbers) ) ) ) )).
fof(t52_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k3_finseq_2(k4_ordinal1)) & v1_funct_1(C) & v4_valued_0(C) & v2_margrel1(C) ) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( v1_xboole_0(B) => v1_xboole_0(k6_comput_1(B,C,A,D)) ) ) ) ) ) )).
fof(t52_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_comseq_3(A) => ( v2_comseq_2(A) & k3_comseq_2(A) = k5_complex1 ) ) ) )).
fof(t52_convex4,axiom,( ! [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) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t52_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t52_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) )).
fof(t52_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ( r7_cqc_the3(A,B,C) => r5_cqc_the3(A,B,C) ) ) ) ) )).
fof(t52_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ~ ( B != C & k15_csspace(A,B,C) = k5_numbers ) & ~ ( k15_csspace(A,B,C) != k5_numbers & B = C ) ) ) ) ) )).
fof(t52_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k5_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k16_sin_cos),A),B) = k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k19_sin_cos(k6_xcmplx_0(k3_xcmplx_0(2,B),A)),k19_sin_cos(k2_xcmplx_0(k3_xcmplx_0(2,B),A)))) ) ) )).
fof(t52_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => k1_funct_1(D,E) = k7_xcmplx_0(B,k1_square_1(E)) ) => ( k2_xcmplx_0(C,k7_xcmplx_0(A,2)) = k5_numbers | k6_xcmplx_0(C,k7_xcmplx_0(A,2)) = k5_numbers | k1_funct_1(k5_diff_1(D,A),C) = k7_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,A),B),C)),k1_square_1(k6_xcmplx_0(k1_square_1(C),k1_square_1(k7_xcmplx_0(A,2))))) ) ) ) ) ) ) )).
fof(t52_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k4_diff_1(k5_diff_1(C,A),A),B) = k6_xcmplx_0(k1_funct_1(k5_diff_1(C,A),B),k1_funct_1(k4_diff_1(C,A),k6_xcmplx_0(B,k7_xcmplx_0(A,2)))) ) ) ) )).
fof(t52_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k9_int_3(A))) => ! [G] : ( 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)),k4_ordinal1,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)),k4_ordinal1,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)),k4_ordinal1,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)),k4_ordinal1,F,G,1)) <=> ( D = F & E = G ) ) ) ) ) ) ) ) ) ) ) )).
fof(t52_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( 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] : ( 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)) ) ) ) ) ) )).
fof(t52_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t52_entropy1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_matrprob(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => r1_xxreal_0(k1_funct_1(k4_entropy1(A),B),k5_numbers) ) ) ) )).
fof(t52_enumset1,axiom,( ! [A] : ! [B] : k5_enumset1(A,A,A,A,A,A,B) = k2_tarski(A,B) )).
fof(t52_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,B)))) => ( ! [E] : ( r2_hidden(E,D) => ( r1_tarski(E,C) & ? [F] : ( m1_subset_1(F,k1_zfmisc_1(A)) & ? [G] : ( 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) ) ) ) )).
fof(t52_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => r1_rvsum_1(k4_struct_0(k15_euclid(A)),B) ) ) )).
fof(t52_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ( ? [F] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & 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)) & k2_xcmplx_0(k2_xcmplx_0(F,G),H) = 1 ) ) ) => r2_hidden(E,k9_euclid_3(A,B,C,D)) ) ) ) ) ) ) )).
fof(t52_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ? [C] : ( 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] : ( 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) ) ) ) )).
fof(t52_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ( k1_funct_1(k6_euclid(3,A),1) = k4_xcmplx_0(k1_funct_1(A,1)) & k1_funct_1(k6_euclid(3,A),2) = k4_xcmplx_0(k1_funct_1(A,2)) & k1_funct_1(k6_euclid(3,A),3) = k4_xcmplx_0(k1_funct_1(A,3)) ) ) )).
fof(t52_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ? [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) & r2_hidden(C,B) ) ) ) )).
fof(t52_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( ~ 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] : ( ( 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,k9_funct_7(F,A,B))) ) ) ) ) ) )).
fof(t52_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(D) & v1_finset_1(D) ) => ! [E] : ( ( 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] : ( 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) ) ) ) ) )).
fof(t52_fcont_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(D,C) & r1_xxreal_0(k1_funct_1(k1_fcont_1(A,B),C),k1_funct_1(k1_fcont_1(A,B),D)) ) ) ) ) ) )).
fof(t52_fdiff_11,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_sin_cos9)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_sin_cos9)),A),B) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(k22_sin_cos,B),k6_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k1_funct_1(k2_sin_cos9,B))),k7_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k22_sin_cos,B)),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t52_fdiff_4,axiom,( ! [A] : ( ( 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)),k7_xcmplx_0(1,2))))) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k16_sin_cos,B),k5_numbers) & ~ r1_xxreal_0(k1_funct_1(k16_sin_cos,B),k4_xcmplx_0(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)),k7_xcmplx_0(1,2))),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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)),k7_xcmplx_0(1,2))),A),B) = k7_xcmplx_0(k1_newton(k1_funct_1(k18_sin_cos,B),3),k2_xcmplx_0(1,k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t52_fib_num2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( r2_hidden(k1_nat_1(k2_nat_1(2,A),1),k4_fib_num2) & ~ r2_hidden(k2_nat_1(2,A),k4_fib_num2) ) ) )).
fof(t52_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t52_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k7_filter_0(A,B,C) = k7_filter_0(A,B,D) => C = D ) ) ) ) ) )).
fof(t52_filter_2,axiom,( ! [A] : ( ( ~ 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)) ) ) ) )).
fof(t52_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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 ) ) ) )).
fof(t52_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( k3_finseq_1(A) = k2_xcmplx_0(C,D) & B = k5_relat_1(A,k2_finseq_1(C)) ) => k1_relset_1(k4_ordinal1,B) = k2_finseq_1(C) ) ) ) ) ) )).
fof(t52_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( r2_hidden(B,k10_xtuple_0(A)) & v2_funct_1(A) ) => v2_funct_1(k5_finseq_4(A,B)) ) ) )).
fof(t52_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t52_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t52_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( 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,k1_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 ) ) ) ) ) ) ) ) ) )).
fof(t52_flang_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) ) )).
fof(t52_flang_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( k1_flang_2(A,C,D,E) = k1_tarski(B) => ( D = E | B = k2_flang_1(A) ) ) ) ) ) )).
fof(t52_flang_3,axiom,( ! [A] : ! [B] : ( 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) ) )).
fof(t52_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ( ~ ( k1_funct_1(k9_fomodel0(B),A) != k1_xboole_0 & k1_funct_1(k9_fomodel0(C),A) != k1_xboole_0 & k1_funct_1(k9_fomodel0(B),A) != k1_funct_1(k9_fomodel0(C),A) ) & ( v5_relat_1(D,k3_finseq_2(k1_xboole_0)) => k1_funct_1(k9_fomodel0(B),D) = k1_xboole_0 ) & ( ( k1_funct_1(k9_fomodel0(B),D) = k1_xboole_0 & v5_relat_1(D,k3_finseq_2(B)) ) => v5_relat_1(D,k3_finseq_2(k1_xboole_0)) ) ) ) ) ) )).
fof(t52_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( ~ v2_struct_0(D) & l2_fsm_1(D,A,B) ) => ! [E] : ( ( ~ v2_struct_0(E) & l2_fsm_1(E,A,B) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ! [G] : ( ( ~ v2_struct_0(G) & v8_struct_0(G) & l2_fsm_1(G,A,B) ) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t52_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t52_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k6_relat_1(A,B) <=> ( ! [D] : ( r2_hidden(D,k9_xtuple_0(C)) <=> ( r2_hidden(D,k9_xtuple_0(B)) & r2_hidden(k1_funct_1(B,D),A) ) ) & ! [D] : ( r2_hidden(D,k9_xtuple_0(C)) => k1_funct_1(C,D) = k1_funct_1(B,D) ) ) ) ) ) )).
fof(t52_funct_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( 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 ) ) ) )).
fof(t52_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t52_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) ) )).
fof(t52_funct_5,axiom,( ! [A] : ! [B] : 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)) )).
fof(t52_funct_6,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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 | k9_funct_6(k9_funct_6(D)) = D ) ) ) )).
fof(t52_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => k4_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))) ) ) )).
fof(t52_funct_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t52_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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(k3_funct_2(k2_zfmisc_1(A,B),k1_numbers,k4_fuzzy_2(A,B),C),k3_funct_2(k2_zfmisc_1(A,B),k1_numbers,D,C)) & r1_xxreal_0(k3_funct_2(k2_zfmisc_1(A,B),k1_numbers,D,C),k3_funct_2(k2_zfmisc_1(A,B),k1_numbers,k5_fuzzy_2(A,B),C)) ) ) ) ) ) )).
fof(t52_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_fvaluat1(C,A) => ( v3_fvaluat1(A) => ( r1_xxreal_0(k5_numbers,k3_funct_2(u1_struct_0(A),k6_numbers,C,B)) <=> m1_subset_1(B,u1_struct_0(k7_fvaluat1(A,C))) ) ) ) ) ) )).
fof(t52_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k9_fvsum_1(A,k12_finseq_1(u1_struct_0(A),C),B) = k12_finseq_1(u1_struct_0(A),k6_algstr_0(A,B,C)) ) ) ) )).
fof(t52_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( ( ~ v1_xboole_0(F) & v1_relat_1(F) & v2_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ! [G] : ( m1_genealg1(G,F) => ! [H] : ( m1_genealg1(H,F) => ( k11_genealg1(F,G,H,A,A,C,D,E) = k9_genealg1(F,G,H,C,D,E) & k11_genealg1(F,G,H,A,B,A,D,E) = k9_genealg1(F,G,H,B,D,E) & k11_genealg1(F,G,H,A,B,C,A,E) = k9_genealg1(F,G,H,B,C,E) & k11_genealg1(F,G,H,A,B,C,D,A) = k9_genealg1(F,G,H,B,C,D) ) ) ) ) ) ) ) ) ) )).
fof(t52_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k19_gfacirc1(A,B,C),k20_gfacirc1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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) ) ) ) ) ) )).
fof(t52_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ! [C] : ( 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)) => k1_nat_1(k17_glib_000(C),1) = k17_glib_000(A) ) ) ) ) )).
fof(t52_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( ( r1_xxreal_0(C,D) & r1_xxreal_0(D,k3_finseq_1(B)) & k1_funct_1(B,C) = k1_funct_1(B,D) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k2_finseq_1(C)) => k1_funct_1(k20_glib_001(A,B,C,D),E) = k1_funct_1(B,E) ) ) ) ) ) ) ) )).
fof(t52_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_003(A) ) => ! [B] : ! [C] : ( 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)) ) ) )).
fof(t52_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ 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(k1_nat_1(A,1),k3_finseq_1(k2_goboard2(D))) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(k2_goboard2(D))) & r1_xxreal_0(1,C) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),B)) = k2_topreal1(2,D,C) & k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1))) = k2_topreal1(2,D,k1_nat_1(C,1)) ) => ( r1_xxreal_0(k3_finseq_1(D),k1_nat_1(C,1)) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),D,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),A,B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),B) & k7_partfun1(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(D),k1_nat_1(A,1),k1_nat_1(B,1)) ) ) ) ) ) ) ) )).
fof(t52_graph_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v3_graph_2(B,A) & m2_graph_1(B,A) ) => ( ( v2_funct_1(B) & m2_graph_1(B,A) ) <=> ~ ( k3_finseq_1(B) != k5_numbers & k3_finseq_1(B) != 1 & k1_funct_1(B,1) = k1_funct_1(B,2) ) ) ) ) )).
fof(t52_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) ) )).
fof(t52_graph_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m2_finseq_1(C,u4_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t52_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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] : ( ( 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] : ( ( 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_polynom1(k15_pre_poly(A),C,k6_termord(A,B,C,D))) & r2_hidden(G,k3_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) ) ) ) ) ) ) ) ) ) )).
fof(t52_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t52_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( B != k1_xboole_0 & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => r2_hidden(k2_group_1(A,C),B) ) ) & ! [C] : ( ( v15_algstr_0(C) & m1_group_2(C,A) ) => u1_struct_0(C) != B ) ) ) ) )).
fof(t52_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k4_group_3(A,B,k1_group_1(A)) = B ) ) )).
fof(t52_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t52_group_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_group_2(C,B) => ! [D] : ( m1_group_2(D,B) => ( r2_hidden(A,k5_group_5(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & ? [F] : ( 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) ) ) ) ) ) ) )).
fof(t52_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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_tarski(k7_struct_0(k10_group_6(A,B,C)),k7_struct_0(A)) ) ) ) )).
fof(t52_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(C)) => ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,F) = E ) ) ) ) ) ) )).
fof(t52_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( ( v5_glib_001(B,A) & m3_glib_001(B,A) ) => ! [C] : ( ( v5_glib_001(C,A) & m3_glib_001(C,A) ) => ! [D] : ( ( v5_glib_001(D,A) & m3_glib_001(D,A) ) => ! [E] : ( ( v5_glib_001(E,A) & m3_glib_001(E,A) ) => ! [F] : ( m1_subset_1(F,k6_glib_000(A)) => ! [G] : ( m1_subset_1(G,k6_glib_000(A)) => ! [H] : ( 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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t52_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( 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) ) ) )).
fof(t52_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_xxreal_0(1,B) & r2_hidden(A,C) ) => ( r2_hidden(k5_numbers,C) | k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_taylor_1(B)),C),2),A) = k3_xcmplx_0(k2_nat_1(B,k1_nat_1(B,1)),k1_funct_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_taylor_1(k1_nat_1(B,2))),A)) ) ) ) ) ) )).
fof(t52_hurwitz,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(A,k1_complfld) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => ~ ( r1_xxreal_0(1,k2_hurwitz(k1_complfld,A)) & ? [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) & ~ r1_xxreal_0(k5_numbers,k3_complex1(B)) & r1_xxreal_0(k9_complex1(k2_polynom4(k1_complfld,k7_hurwitz(A),B)),k9_complex1(k2_polynom4(k1_complfld,A,B))) ) & v1_hurwitz(A) ) ) )).
fof(t52_ideal_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t52_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ? [D] : ( m1_subset_1(D,u4_incsp_1(A)) & r2_incsp_1(A,B,D) & ~ r3_incsp_1(A,C,D) ) ) ) ) )).
fof(t52_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => r1_xxreal_0(A,k1_int_1(B)) ) ) ) )).
fof(t52_int_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k4_numbers)) ) => ( ( k5_card_1(B) = A & ! [C] : ( v1_int_1(C) => ! [D] : ( 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) ) ) ) )).
fof(t52_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(A,B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k2_xcmplx_0(1,k1_funct_1(k18_sin_cos,D)) != k5_numbers & k6_xcmplx_0(1,k1_funct_1(k18_sin_cos,D)) != k5_numbers & k1_funct_1(C,D) = k7_xcmplx_0(k1_funct_1(k18_sin_cos,D),k6_xcmplx_0(k1_funct_1(k18_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),k27_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) = k6_xcmplx_0(k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k27_sin_cos),k2_fdiff_9),k2_seq_4(A)),k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k27_sin_cos),k2_fdiff_9),k3_seq_4(A))) ) ) ) ) )).
fof(t52_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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,C,D),k3_taylor_1))) & r2_relset_1(k1_numbers,k1_numbers,B,k3_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,E),k3_valued_1(k1_numbers,k1_numbers,k1_numbers,C,D))) & r2_relset_1(k1_numbers,k1_numbers,D,k1_taylor_1(2)) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => k1_funct_1(C,F) = 1 ) ) & E = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_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),k7_xcmplx_0(1,2)),k2_seq_4(A)),k1_funct_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),k7_xcmplx_0(1,2)),k3_seq_4(A))) ) ) ) ) ) ) )).
fof(t52_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k2_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,D))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,D)))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),k2_seq_4(A)),k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t52_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( m1_subset_1(F,u1_struct_0(k4_real_ns1(A))) => ! [G] : ( ( 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] : ( 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,k6_xcmplx_0(E,D)) ) ) ) ) ) ) ) ) )).
fof(t52_integra1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( m1_integra1(C,B) => ! [D] : ( ( 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] : ( ( 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(k2_xcmplx_0(k1_funct_1(k5_integra1(B,D,C),A),k1_funct_1(k5_integra1(B,E,C),A)),k1_funct_1(k5_integra1(B,k3_valued_1(B,k1_numbers,k1_numbers,D,E),C),A)) ) ) ) ) ) ) )).
fof(t52_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( A = k1_rcomp_1(k2_xcmplx_0(B,k3_xcmplx_0(k2_nat_1(2,C),k28_sin_cos)),k2_xcmplx_0(B,k3_xcmplx_0(k1_nat_1(k2_nat_1(2,C),1),k28_sin_cos))) => k2_integra5(A,k32_valued_1(k1_numbers,k1_numbers,k16_sin_cos)) = k4_xcmplx_0(k3_xcmplx_0(2,k19_sin_cos(B))) ) ) ) ) )).
fof(t52_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v3_rcomp_1(E) & m1_subset_1(E,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,E) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => ( k1_funct_1(C,F) = k6_xcmplx_0(A,F) & ~ r1_xxreal_0(k1_funct_1(C,F),k5_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] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => k1_funct_1(D,F) = k7_xcmplx_0(1,k6_xcmplx_0(A,F)) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,D,B)) ) => k2_integra5(B,D) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1)),k2_seq_4(B)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k3_taylor_1)),k3_seq_4(B))) ) ) ) ) ) ) )).
fof(t52_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => r2_hidden(A,k4_interva1(A,B,k10_interva1(A,B))) ) ) )).
fof(t52_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(t52_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( 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] : ( 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) = k3_xcmplx_0(k12_euclid(D),k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k17_euclid(D),k12_euclid(D)),A),k6_xcmplx_0(1,A))) ) ) & ! [D] : ( 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(k5_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) ) ) ) ) ) )).
fof(t52_jgraph_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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(k7_xcmplx_0(2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(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(k4_xcmplx_0(1),1,k4_xcmplx_0(1),1)) ) ) ) ) ) ) ) ) )).
fof(t52_jordan,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t52_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(C,B) & r1_xboole_0(k5_topreal1(C),k3_topreal1(2,k2_jordan9(B,A))) ) ) ) ) )).
fof(t52_jordan1h,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( 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] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(k4_tarski(D,E),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k7_nat_d(k3_finseq_1(C),1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),D,E) & r2_hidden(k4_tarski(D,k1_nat_1(E,1)),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k3_finseq_1(C)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),D,k1_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),k1_nat_1(E,1)),k2_matrix_0(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) )).
fof(t52_jordan1j,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( v4_topreal1(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v7_ordinal1(D) => ( ( 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) ) ) ) ) ) ) ) )).
fof(t52_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ( ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k14_euclid(A)))) & C = a_2_3_jordan2c(A,B) ) & ! [C] : ( 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)) ) ) ) ) ) )).
fof(t52_jordan4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m2_finseq_1(E,u1_struct_0(k15_euclid(2))) => ( ( r1_jordan4(C,D,A,B) & r1_jordan4(C,E,A,B) ) => D = E ) ) ) ) ) ) )).
fof(t52_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( 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) ) ) ) )).
fof(t52_kurato_1,axiom,( 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)))) )).
fof(t52_lattice2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t52_lattice3,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t52_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => ~ ( r2_hidden(C,k17_lexbfs(k6_glib_000(A),k4_ordinal1,k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k5_finsub_1(k4_ordinal1),k6_glib_000(A),k13_lexbfs(A,k16_lexbfs(A),B)),D)) & ! [E] : ( m1_subset_1(E,k6_glib_000(A)) => ~ ( r2_hidden(E,k1_relset_1(k6_glib_000(A),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),k13_lexbfs(A,k16_lexbfs(A),B)))) & k1_recdef_1(k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),k13_lexbfs(A,k16_lexbfs(A),B)),E) = C & r2_hidden(D,k2_chord(A,k6_domain_1(k6_glib_000(A),E))) ) ) ) ) ) ) ) )).
fof(t52_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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)) ) ) ) ) )).
fof(t52_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r4_limfunc2(C,B) => ( r4_limfunc2(k26_valued_1(k1_numbers,k1_numbers,C,A),B) & k2_limfunc2(k26_valued_1(k1_numbers,k1_numbers,C,A),B) = k3_xcmplx_0(A,k2_limfunc2(C,B)) ) ) ) ) ) )).
fof(t52_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(k6_xcmplx_0(A,D),A))) & k1_funct_1(B,E) = k1_limfunc2(B,A) ) ) ) ) | r3_limfunc2(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t52_lpspace1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( m2_subset_1(D,k1_zfmisc_1(B),C) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ( ( D = k1_relset_1(B,E) & ! [F] : ( r2_hidden(F,k1_relset_1(B,E)) => k1_funct_1(E,F) = A ) ) => r1_mesfunc6(B,C,E,D) ) ) ) ) ) ) )).
fof(t52_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( v2_xxreal_0(F) & v1_xreal_0(F) ) => ! [G] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(t52_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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))) ) ) ) ) )).
fof(t52_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_hilbert1)) => ( ( r8_ltlaxio1(D,k3_hilbert1(A,B)) & r8_ltlaxio1(D,k3_hilbert1(A,C)) ) => r8_ltlaxio1(D,k3_hilbert1(A,k4_ltlaxio1(B,C))) ) ) ) ) ) )).
fof(t52_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t52_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(t52_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( r2_matrix10(B,k5_matrix10(A,C,D)) => r2_matrix10(D,k5_matrix10(A,C,B)) ) ) ) ) ) )).
fof(t52_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( 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_0(D),B,k7_matrix_0(u1_struct_0(B),D,F),C))) = k4_struct_0(B) ) ) ) ) ) ) ) ) )).
fof(t52_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(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(k4_ordinal1,k2_finseq_1(k1_matrix_0(C)),k3_matrix13(A))) = k16_matrix_0(A,u1_struct_0(B),C) ) ) ) )).
fof(t52_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( C = k2_matrix_1(B,A) <=> ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,A) & r1_xxreal_0(1,E) & r1_xxreal_0(E,A) ) => k3_matrix_0(u1_struct_0(B),C,D,E) = k4_struct_0(B) ) ) ) ) ) ) ) )).
fof(t52_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ( ~ v1_xboole_0(k4_matrix15(C,k1_matrix_3(C,B,A),D)) => D = k1_matrix_3(C,B,k1_matrix_0(D)) ) ) ) ) ) )).
fof(t52_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v5_matrix16(C,B) & v5_matrix16(D,B) ) => v5_matrix16(k3_matrix_3(B,C,D),B) ) ) ) ) ) )).
fof(t52_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,C,A,B) & m2_finseq_1(D,k3_finseq_2(C)) ) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k2_finseq_1(A)) => k1_funct_1(D,E) = k7_matrix_0(C,D,E) ) ) ) ) ) ) )).
fof(t52_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) ) => B = k1_matrix_4(A,B,k3_matrix_3(A,C,k2_matrix_3(A,C))) ) ) ) ) )).
fof(t52_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r1_matrix_6(A,B,C,D) => r1_matrix_6(A,B,k4_matrix_3(B,C,D),D) ) ) ) ) ) )).
fof(t52_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => k1_matrix_8(A,B,C) = k1_matrix_8(A,B,k4_matrix_0(u1_struct_0(B),C)) ) ) ) )).
fof(t52_matrix_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_matrix_2(C,k3_matrix_2(A)) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ? [E] : ( m1_subset_1(E,k4_ordinal1) & r2_hidden(E,k2_finseq_1(A)) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r2_hidden(F,k2_finseq_1(A)) => k1_funct_1(k8_matrix_0(u1_struct_0(B),D,E),F) = k4_struct_0(B) ) ) ) => k3_funct_2(k3_matrix_2(A),u1_struct_0(B),k1_matrix_9(A,B,D),C) = k4_struct_0(B) ) ) ) ) ) )).
fof(t52_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => ( r1_xxreal_0(k3_finseq_1(B),k5_numbers) | k8_complsp2(A,B) = k8_complex1(k8_complsp2(B,A)) ) ) ) ) )).
fof(t52_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),B,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(C),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(C))) ) => k12_matrix_3(k2_wsierp_1(k10_matrixj1(u1_struct_0(C),k17_matrixj1(u1_struct_0(C),B,A,D,E))),C,k20_matrixj1(u1_struct_0(C),k4_struct_0(C),k17_matrixj1(u1_struct_0(C),B,A,D,E))) = k8_group_1(C,k12_matrix_3(B,C,D),k12_matrix_3(A,C,E)) ) ) ) ) ) )).
fof(t52_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ~ ( ~ r1_xxreal_0(k3_finseq_1(B),k5_numbers) & ~ r1_xxreal_0(k1_matrix_0(B),k5_numbers) & ( k3_finseq_1(B) = k3_finseq_1(A) | k1_matrix_0(k4_matrix_0(k1_numbers,B)) = k3_finseq_1(A) ) & k11_matrixr1(k4_matrix_0(k1_numbers,B),A) != k12_matrixr1(B,A) ) ) ) )).
fof(t52_matrixr2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( k3_finseq_1(A) = k1_matrix_0(B) => ( r1_xxreal_0(k3_finseq_1(B),k5_numbers) | r1_xxreal_0(k3_finseq_1(A),k5_numbers) | k11_matrixr1(k4_matrixr1(B),A) = k6_rvsum_1(k11_matrixr1(B,A)) ) ) ) ) )).
fof(t52_mcart_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k3_zfmisc_1(B,C,D)) => ( ! [F] : ( m1_subset_1(F,B) => ! [G] : ( m1_subset_1(G,C) => ! [H] : ( m1_subset_1(H,D) => ( E = k3_xtuple_0(F,G,H) => A = G ) ) ) ) => A = k2_mcart_1(B,C,D,E) ) ) ) ) ) )).
fof(t52_measure6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( v4_xxreal_2(B) => k2_seq_4(k1_measure6(B,A)) = k2_xcmplx_0(A,k2_seq_4(B)) ) ) ) )).
fof(t52_member_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k9_member_1(k1_tarski(A),k2_tarski(B,C)) = k2_tarski(k2_xcmplx_0(A,B),k2_xcmplx_0(A,C)) ) ) ) )).
fof(t52_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( v7_ordinal1(D) => r2_hidden(k4_struct_0(B),k9_xtuple_0(k9_memstr_0(A,B,C,D))) ) ) ) ) )).
fof(t52_mesfunc5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( v7_ordinal1(C) => k9_nat_1(k6_numbers,A,C) = B ) => ( v7_mesfunc5(A) & k2_mesfunc5(A) = B ) ) ) ) )).
fof(t52_mesfunc6,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( ! [C] : ( r2_hidden(C,k1_relset_1(A,B)) => r1_xxreal_0(k5_numbers,k1_funct_1(B,C)) ) => v6_supinf_2(B) ) ) )).
fof(t52_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,k10_midsp_1(A)) => ! [C] : ( m1_subset_1(C,k10_midsp_1(A)) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t52_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => k19_mmlquery(A,B,k18_mmlquery(A,B)) = k1_xboole_0 ) )).
fof(t52_modelc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k30_modelc_1(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k48_modelc_1(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k48_modelc_1(A,B,C))) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(t52_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v2_struct_0(C) & v10_modelc_2(C) & l1_modelc_2(C) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t52_modelc_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k23_modelc_3(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k23_modelc_3(B)))) ) => ? [D] : ( 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) ) ) ) ) )).
fof(t52_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ~ r1_xxreal_0(k6_moebius1(A),k5_numbers) ) )).
fof(t52_monoid_0,axiom,( k7_monoid_0 = g3_algstr_0(k4_ordinal1,k24_binop_2) )).
fof(t52_monoid_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t52_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ( ( r2_hidden(D,k3_msualg_1(A,C,k3_equation(A))) & r2_hidden(E,k3_msualg_1(A,C,k3_equation(A))) & ! [F] : ( v7_ordinal1(F) => ( r2_hidden(F,k4_finseq_1(k1_msualg_1(A,C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( G = k1_funct_1(k1_msualg_1(A,C),F) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,k3_equation(A)),G)) => ! [I] : ( m1_subset_1(I,k1_funct_1(u3_msualg_1(A,k3_equation(A)),G)) => ( ( H = k1_funct_1(D,F) & I = k1_funct_1(E,F) ) => r1_equation(A,B,G,k5_equation(A,G,H,I)) ) ) ) ) ) ) ) ) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,k3_equation(A)),k2_msualg_1(A,C))) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,k3_equation(A)),k2_msualg_1(A,C))) => ( ( F = k4_trees_4(k4_tarski(C,u1_struct_0(A)),D) & G = k4_trees_4(k4_tarski(C,u1_struct_0(A)),E) ) => r1_equation(A,B,k2_msualg_1(A,C),k5_equation(A,k2_msualg_1(A,C),F,G)) ) ) ) ) ) ) ) ) ) )).
fof(t52_mssubfam,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m3_pboole(D,A,k1_mboolean(A,C)) => ( r1_pboole(A,B,k4_mssubfam(A,C,D)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t52_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t52_mycielsk,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( v8_struct_0(B) & l1_orders_2(B) & k2_dilworth(B) = 2 & ~ r1_xxreal_0(k3_mycielsk(B),A) ) ) )).
fof(t52_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( k22_pre_poly(k8_newton,k12_nat_3(A)) = k1_xboole_0 => A = 1 ) ) )).
fof(t52_nat_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => k1_nat_4(k3_pre_poly(k4_ordinal1,B),A) = k3_pre_poly(k4_ordinal1,k11_nat_3(B,A)) ) ) )).
fof(t52_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k7_nat_d(A,C),B) => r1_xxreal_0(A,k2_xcmplx_0(B,C)) ) ) ) ) )).
fof(t52_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( 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) ) ) ) ) )).
fof(t52_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_prvect_2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_prvect_2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_prvect_2(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_prvect_2(A))) => ! [F] : ( m2_subset_1(F,k4_ordinal1,k4_finseq_1(A)) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( m1_subset_1(H,u1_struct_0(k11_prvect_2(A,F))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k11_prvect_2(A,F))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k11_prvect_2(A,F))) => ~ ( ~ r1_xxreal_0(G,k2_normsp_0(k14_prvect_2(A),k5_algstr_0(k14_prvect_2(A),C,B))) & ~ r1_xxreal_0(G,k2_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,k2_normsp_0(k14_prvect_2(A),k5_algstr_0(k14_prvect_2(A),E,B))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t52_newton,axiom,( ! [A] : ( v7_ordinal1(A) => k6_nat_d(A,k5_numbers) = A ) )).
fof(t52_nfcont_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) ) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( ( r1_tarski(A,k1_relset_1(u1_struct_0(B),C)) & ! [F] : ( 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) ) ) ) ) ) )).
fof(t52_normform,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A)) => ! [C] : ( m2_subset_1(C,k5_finsub_1(k7_normform(A)),k8_normform(A)) => ! [D] : ( 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) ) ) ) )).
fof(t52_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t52_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,u4_struct_0(B),u4_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(B),u4_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u4_struct_0(A),u4_struct_0(C)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u4_struct_0(A),u4_struct_0(C)))) ) => r2_funct_2(u4_struct_0(k2_oppcat_1(B)),u4_struct_0(k2_oppcat_1(C)),k11_oppcat_1(k2_oppcat_1(B),C,k10_oppcat_1(B,C,k1_partfun1(u4_struct_0(B),u4_struct_0(A),u4_struct_0(A),u4_struct_0(C),D,E))),k1_partfun1(u4_struct_0(k2_oppcat_1(B)),u4_struct_0(k2_oppcat_1(A)),u4_struct_0(k2_oppcat_1(A)),u4_struct_0(k2_oppcat_1(C)),k11_oppcat_1(k2_oppcat_1(B),A,k10_oppcat_1(B,A,D)),k11_oppcat_1(k2_oppcat_1(A),C,k10_oppcat_1(A,C,E)))) ) ) ) ) ) )).
fof(t52_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_real_ns1(A))) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A))))) ) => ~ ( ~ r1_xxreal_0(C,B) & r5_nfcont_1(k4_real_ns1(A),k4_real_ns1(A),u1_struct_0(k4_real_ns1(A)),E) & ! [F] : ( v7_ordinal1(F) => ~ v1_nfcont_2(k1_abian(u1_struct_0(k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A))),k6_ordeq_01(A,D,E,B,C),k2_xcmplx_0(F,1)),k5_ordeq_01(k3_integra5(B,C),k4_real_ns1(A))) ) ) ) ) ) ) ) )).
fof(t52_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r4_orders_1(k2_relat_1(A),B) <=> r5_orders_1(A,B) ) ) )).
fof(t52_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r6_orders_1(u1_orders_2(A),B) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ r2_orders_2(A,B,C) ) ) ) ) )).
fof(t52_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => k5_ordinal3(k10_ordinal2(A,B),A) = B ) ) )).
fof(t52_ordinal5,axiom,( k4_ordinal5(k1_xboole_0) = k5_numbers )).
fof(t52_ordinal6,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_xboole_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v3_ordinal6(B) ) => ( ( ! [C] : ( 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)) ) ) ) ) )).
fof(t52_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t52_partfun1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_partfun1(A,B) <=> ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & r1_tarski(A,C) & r1_tarski(B,C) ) ) ) ) )).
fof(t52_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ( r2_hidden(C,k1_relset_1(A,F)) & r2_relset_1(A,B,E,k4_subset_1(k2_zfmisc_1(A,B),D,F)) ) => k7_partfun1(B,E,C) = k7_partfun1(B,F,C) ) ) ) ) ) ) ) )).
fof(t52_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t52_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( 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) & k10_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) = k6_xcmplx_0(k1_pdiff_5(B,A),k1_pdiff_5(C,A)) ) ) ) ) ) )).
fof(t52_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t52_pepin,axiom,( k4_pepin(2) = 17 )).
fof(t52_polyform,axiom,( ! [A] : ( ( 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)) ) )).
fof(t52_polyred,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & v3_ideal_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r11_polyred(A,B,C,C) ) ) ) )).
fof(t52_power,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & A != 1 & k3_power(A,A) != 1 ) ) )).
fof(t52_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t52_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k4_prepower(A,B),k5_numbers) ) ) ) )).
fof(t52_prob_3,axiom,( ! [A] : ! [B] : ! [C] : ( m2_finseq_1(C,k9_setfam_1(B)) => ( C != k1_xboole_0 => ( r2_hidden(A,k6_setfam_1(B,k2_relset_1(k9_setfam_1(B),C))) <=> ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,C)) => r2_hidden(A,k4_prob_3(B,C,D)) ) ) ) ) ) )).
fof(t52_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ( ( r2_hidden(k8_cqc_lang(A,D,B),k4_cqc_the1(A)) & r2_hidden(k8_cqc_lang(A,D,C),k4_cqc_the1(A)) ) => r2_hidden(k8_cqc_lang(A,D,k7_cqc_lang(A,B,C)),k4_cqc_the1(A)) ) ) ) ) ) )).
fof(t52_pscomp_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t52_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t52_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( r1_qc_lang2(A,C,B) => r2_qc_lang2(A,C,B) ) ) ) ) )).
fof(t52_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( ( ~ 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) ) ) ) ) )).
fof(t52_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ( k17_quatern2(A,A) = k5_numbers => A = k5_numbers ) ) )).
fof(t52_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k24_quaterni(k22_quaterni(A,B)) = k25_quaterni(k24_quaterni(A),B) ) ) )).
fof(t52_quaterni,axiom,( k27_quaterni(k11_quaterni) = k24_quaterni(k11_quaterni) )).
fof(t52_quofield,axiom,( ! [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] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) ) )).
fof(t52_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B))))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t52_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(k9_nat_1(k1_numbers,k4_real_3(A),1),k5_numbers) => ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,k6_real_3(A),B),k5_numbers) ) ) ) )).
fof(t52_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => r1_tarski(k9_xtuple_0(k5_relat_1(B,A)),A) ) )).
fof(t52_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ! [E] : ( 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)) ) ) ) )).
fof(t52_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ( v9_rewrite1(A) <=> r10_rewrite1(A,A) ) ) )).
fof(t52_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => r4_rewrite2(A,B,B,C) ) ) )).
fof(t52_rewrite3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(B)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k8_afinsq_1(B))) => ! [E] : ( ( ~ v2_struct_0(E) & l1_rewrite3(E,D) ) => ! [F] : ( m1_rewrite1(F,k1_rewrite3(B,D,E)) => ( k1_funct_1(F,k3_finseq_1(F)) = k4_tarski(A,C) => ! [G] : ( v7_ordinal1(G) => ~ ( r2_hidden(G,k4_finseq_1(F)) & ! [H] : ( m1_subset_1(H,k8_afinsq_1(B)) => k2_xtuple_0(k1_funct_1(F,G)) != k1_flang_1(B,H,C) ) ) ) ) ) ) ) ) ) )).
fof(t52_rfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t52_rfunct_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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(B,A))) => 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(B,A))),k7_relset_1(k1_numbers,k1_numbers,C,k1_rcomp_1(B,A)))) ) ) ) ) )).
fof(t52_rfunct_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(k5_numbers,D) & r1_xxreal_0(D,1) ) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( ( r2_hidden(E,k1_rcomp_1(A,B)) & r2_hidden(F,k1_rcomp_1(A,B)) ) => r1_xxreal_0(k1_funct_1(C,k2_xcmplx_0(k3_xcmplx_0(D,E),k3_xcmplx_0(k6_xcmplx_0(1,D),F))),k2_xcmplx_0(k3_xcmplx_0(D,k1_funct_1(C,E)),k3_xcmplx_0(k6_xcmplx_0(1,D),k1_funct_1(C,F)))) ) ) ) ) ) ) ) ) ) ) )).
fof(t52_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_comseq_2(B) => r1_xxreal_0(k1_funct_1(k3_rinfsup1(B),A),k1_funct_1(k4_rinfsup1(B),A)) ) ) ) )).
fof(t52_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t52_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t52_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_2(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t52_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( ~ v8_ordinal1(C) & v1_xreal_0(C) ) => k1_convex1(A,k2_pre_topc(A,B),C) = k2_pre_topc(A,k1_convex1(A,B,C)) ) ) ) )).
fof(t52_rlvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t52_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_rlvect_2(C,A) => ( m2_rlvect_2(C,A,B) => m2_rlvect_2(k9_rlvect_2(A,C),A,B) ) ) ) ) )).
fof(t52_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t52_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_4(C,A,B) => k2_rmod_4(A,B,k8_rmod_4(A,B,C)) = k2_rmod_4(A,B,C) ) ) ) )).
fof(t52_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k9_robbins1(A,k17_robbins1(A,B),B) = k3_robbins1(A,k15_robbins1(A,B)) ) ) )).
fof(t52_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t52_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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))) ) ) ) ) )).
fof(t52_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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),k5_numbers) | r1_xxreal_0(k1_rpr_1(A,D),k5_numbers) | k2_rpr_1(A,B,C) = k7_xcmplx_0(k3_xcmplx_0(k2_rpr_1(A,C,B),k1_rpr_1(A,C)),k2_xcmplx_0(k3_xcmplx_0(k2_rpr_1(A,C,B),k1_rpr_1(A,C)),k3_xcmplx_0(k2_rpr_1(A,D,B),k1_rpr_1(A,D)))) ) ) ) ) ) ) )).
fof(t52_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(k1_rlvect_1(A,C,D),k3_rusub_1(A,C,B)) => ( D = 1 | r1_struct_0(B,C) ) ) ) ) ) ) )).
fof(t52_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_2(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t52_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & ? [G] : ( v1_xreal_0(G) & 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)) ) ) ) ) ) ) ) )).
fof(t52_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => k10_rvsum_1(A,1) = A ) )).
fof(t52_rvsum_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t52_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k5_scmfsa6a(C,k8_scmfsa_2(D,k4_scmfsa_2(k5_numbers)))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_m(B)),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k5_scmfsa6a(C,k8_scmfsa_2(D,k4_scmfsa_2(k5_numbers)))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_m(B)))),D) = k6_xcmplx_0(k1_funct_1(B,D),1) ) ) ) ) ) )).
fof(t52_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_m(B)),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_m(B)))),D) ) ) ) ) )).
fof(t52_scmpds_2,axiom,( ! [A] : ( ( 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] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( 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)) != k5_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)) = k5_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) ) ) ) ) ) ) )).
fof(t52_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ( k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),E)) = k5_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,k1_nat_1(k5_card_1(C),2))) ) ) ) ) ) ) )).
fof(t52_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ~ ( r2_hidden(B,k3_tarski(A)) & ! [C] : ( ( v1_finset_1(C) & v4_scmyciel(C) & v5_scmyciel(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => k3_tarski(C) != k1_tarski(B) ) ) ) )).
fof(t52_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [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) ) ) ) ) ) ) ) ) ) ) )).
fof(t52_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,k56_valued_1(k4_ordinal1,k1_numbers,A)),k56_valued_1(k4_ordinal1,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,A))) ) )).
fof(t52_seq_4,axiom,( r2_funct_2(k2_numbers,k2_numbers,k5_finseqop(k2_numbers,k3_binop_2),k1_binop_2) )).
fof(t52_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( v7_ordinal1(C) => ( v2_prob_1(B) => k1_funct_1(k2_setlim_1(A,B),C) = k3_prob_1(A,B) ) ) ) )).
fof(t52_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => r1_tarski(k9_nat_1(k9_setfam_1(B),k2_setlim_1(B,k7_setlim_2(B,D,C)),A),k7_subset_1(B,C,k9_nat_1(k9_setfam_1(B),k2_setlim_1(B,D),A))) ) ) ) )).
fof(t52_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,A) => ( r2_hidden(B,k3_funct_2(A,k5_finsub_1(A),k11_setwiseo(A),C)) <=> B = C ) ) ) )).
fof(t52_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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 ) ) ) ) )).
fof(t52_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t52_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ! [C] : ( ( 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)) ) ) ) )).
fof(t52_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(k5_numbers,A) => ( ~ r1_xxreal_0(k1_funct_1(k22_sin_cos,A),k5_numbers) & r1_xxreal_0(k1_funct_1(k22_sin_cos,A),1) ) ) ) )).
fof(t52_sin_cos3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k2_numbers) => k15_sin_cos(k3_xcmplx_0(k3_xcmplx_0(k7_complex1,A),B)) = k2_comseq_3(k2_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,B),k3_xcmplx_0(k7_complex1,k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,B))),A) ) ) )).
fof(t52_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k4_sin_cos2(k7_xcmplx_0(A,2)) != k5_numbers => k1_sin_cos5(k7_xcmplx_0(A,2)) = k7_xcmplx_0(k2_xcmplx_0(k4_sin_cos2(A),1),k2_sin_cos2(A)) ) ) )).
fof(t52_sin_cos6,axiom,( k7_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k2_rcomp_1(k28_sin_cos,k3_xcmplx_0(2,k28_sin_cos))) = k2_rcomp_1(k4_xcmplx_0(1),1) )).
fof(t52_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(1,B) ) => k2_xcmplx_0(k2_sin_cos7(A),k2_sin_cos7(B)) = k2_sin_cos7(k2_xcmplx_0(k3_xcmplx_0(A,B),k3_square_1(k3_xcmplx_0(k6_xcmplx_0(k1_square_1(A),1),k6_xcmplx_0(k1_square_1(B),1))))) ) ) ) )).
fof(t52_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) => k2_sin_cos4(k4_sin_cos9(A)) = A ) ) )).
fof(t52_sincos10,axiom,( k2_partfun1(k1_numbers,k1_numbers,k4_sincos10,k1_rcomp_1(1,k3_square_1(2))) = k2_partfun2(k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(t52_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t52_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t52_sprect_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t52_sprect_3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r1_sprect_2(A,B) & r1_sprect_2(A,k13_matrix_0(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)) ) ) ) ) )).
fof(t52_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t52_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(1,k1_square_1(A)) => ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) ) ) ) )).
fof(t52_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k16_substut1(A),k38_substut1(A)) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t52_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))))) ) ) )).
fof(t52_tdlat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => v4_tdlat_3(A) ) )).
fof(t52_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ! [C] : ( 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) ) ) ) )).
fof(t52_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_pre_topc(C) & v1_tex_2(C,A) & v1_tex_3(C,A) & m1_pre_topc(C,A) ) => B != u1_struct_0(C) ) ) ) ) )).
fof(t52_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t52_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ 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] : ( ( 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)))) ) ) ) ) ) ) )).
fof(t52_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t52_topgen_1,axiom,( v1_tops_1(k1_borsuk_5,k3_topmetr) & m1_subset_1(k1_borsuk_5,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )).
fof(t52_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t52_topgen_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v7_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(C,D) & r2_hidden(D,B) & ! [E] : ( ( 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) = k5_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(k4_ordinal1,1)) ) ) ) ) ) => v1_topgen_5(A) ) ) ) )).
fof(t52_topgrp_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t52_topreal6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v7_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k10_metric_1(A,B,k5_numbers) = k1_tarski(B) ) ) )).
fof(t52_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => r1_xboole_0(k6_jgraph_6(A,B,C),k5_jgraph_6(A,B,C)) ) ) ) )).
fof(t52_toprealc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( ( 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,k14_toprealc(A,u1_struct_0(B),u1_struct_0(k3_topmetr),D)) ) ) ) ) )).
fof(t52_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_tops_1(B,A) <=> r1_tarski(B,k2_tops_1(A,B)) ) ) ) )).
fof(t52_tops_2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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)) ) ) ) ) ) )).
fof(t52_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v3_tops_1(B,A) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t52_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t52_trees_1,axiom,( k2_trees_1(2) = k1_enumset1(k1_xboole_0,k12_finseq_1(k4_ordinal1,k5_numbers),k12_finseq_1(k4_ordinal1,1)) )).
fof(t52_trees_3,axiom,( k11_trees_3(k1_xboole_0) = k2_trees_1(k5_numbers) )).
fof(t52_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t52_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(k40_twoscomp(A,B),k41_twoscomp(A,B)))) => ! [D] : ( m1_subset_1(D,k6_margrel1) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t52_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ( v1_int_1(B) => v1_int_1(k2_polynom4(k1_complfld,k5_uniroots(A),B)) ) ) ) )).
fof(t52_uproots,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & v1_uproots(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & v1_uproots(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k6_uproots(A,B,k13_polynom3(A,C,D)) = k1_nat_1(k6_uproots(A,B,C),k6_uproots(A,B,D)) ) ) ) ) )).
fof(t52_valued_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) ) => ( r1_tarski(C,B) => r1_tarski(k61_valued_1(C,A),k61_valued_1(B,A)) ) ) ) ) )).
fof(t52_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( ( 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)) ) ) ) ) )).
fof(t52_vectsp_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t52_vectsp_5,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_5(D,A,B,C) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t52_vfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,u1_struct_0(C)))) ) => ! [E] : ( v1_xreal_0(E) => ( 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)) ) ) ) ) ) )).
fof(t52_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t52_waybel21,axiom,( ! [A] : ( ( 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] : ( ( ~ 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] : ( ( ~ 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) ) ) ) )).
fof(t52_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( r2_hidden(C,k1_relset_1(u1_struct_0(k1_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))) ) ) ) ) )).
fof(t52_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => r3_yellow20(k4_waybel34(A),k5_waybel34(A),k6_waybel34(A),k8_waybel34(A),k9_waybel34(A)) ) )).
fof(t52_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( D != k1_xboole_0 => r1_yellow_0(A,D) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(B)) ) => ~ ( r1_yellow_0(A,E) & D = k1_yellow_0(A,E) ) ) ) ) & ! [D] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_lattice3(A,B,D) <=> r2_lattice3(A,C,D) ) ) ) ) ) ) )).
fof(t52_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( ~ 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) ) ) ) ) ) ) ) ) )).
fof(t52_waybel_2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t52_waybel_4,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r1_waybel_3(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r1_waybel_3(A,B,D) & r1_waybel_3(A,D,C) ) ) ) ) ) ) )).
fof(t52_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ~ ( v2_wellord1(A) & v2_wellord1(B) & ~ r4_wellord1(A,B) & ! [C] : ~ ( r2_hidden(C,k1_relat_1(A)) & r4_wellord1(k2_wellord1(A,k1_wellord1(A,C)),B) ) & ! [C] : ~ ( r2_hidden(C,k1_relat_1(B)) & r4_wellord1(A,k2_wellord1(B,k1_wellord1(B,C))) ) ) ) ) )).
fof(t52_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : k4_xboole_0(A,k4_xboole_0(B,C)) = k2_xboole_0(k4_xboole_0(A,B),k3_xboole_0(A,C)) )).
fof(t52_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k4_xboolean(A,k8_xboolean(A,B)) = k4_xboolean(A,k3_xboolean(B)) ) ) )).
fof(t52_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( A != k5_numbers => k7_xcmplx_0(A,k7_xcmplx_0(A,B)) = B ) ) ) )).
fof(t52_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(B,C) ) => r1_xxreal_0(B,k6_xcmplx_0(C,A)) ) ) ) ) )).
fof(t52_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_tarski(k2_xxreal_1(C,D),k1_xxreal_1(A,B)) => ( r1_xxreal_0(D,C) | ( r1_xxreal_0(A,C) & r1_xxreal_0(D,B) ) ) ) ) ) ) ) )).
fof(t52_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ( m2_xxreal_2(k1_xxreal_0,A) => r1_tarski(A,k1_tarski(k1_xxreal_0)) ) ) )).
fof(t52_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t52_yellow10,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(t52_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t52_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v11_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,B,C) & m2_functor0(E,B,C) ) => ! [F] : ( ( ~ v2_struct_0(F) & v2_altcat_1(F) & v3_altcat_2(F,A) & m1_altcat_2(F,A) ) => ! [G] : ( ( ~ v2_struct_0(G) & v2_altcat_1(G) & v3_altcat_2(G,B) & m1_altcat_2(G,B) ) => ! [H] : ( ( ~ 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) ) ) ) ) ) ) ) ) ) )).
fof(t52_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t52_yellow_2,axiom,( ! [A] : ( ( ~ 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,k1_yellow_1(k7_waybel_0(A))) ) )).
fof(t52_yellow_4,axiom,( ! [A] : ( ( v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(t52_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k13_lattice3(A,k12_lattice3(A,B,C),k1_yellow_5(A,B,C)) = B ) ) ) )).
fof(t52_yellow_9,axiom,( ! [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] : ( ( 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) ) ) ) )).
fof(t52_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r1_zf_lang(A,k6_zf_lang(B)) <=> A = B ) ) ) )).
fof(t52_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r2_zf_lang(A,B) <=> r2_hidden(A,k29_zf_lang(B)) ) ) ) )).
fof(t52_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( k3_xboole_0(k2_tarski(A,B),C) = k1_tarski(A) & r2_hidden(B,C) & A != B ) )).
fof(t52_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => k3_zmodul01(B) = k3_zmodul01(C) ) ) ) )).
fof(t52_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( m1_zmodul02(C,A) => k21_zmodul02(A,k22_zmodul02(A,B,C)) = k3_rlvect_1(A,k21_zmodul02(A,B),k21_zmodul02(A,C)) ) ) ) )).
fof(t53_abcmiz_0,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) ) )).
fof(t53_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ~ ( ! [C] : ( m1_subset_1(C,k2_abcmiz_1) => B != k35_abcmiz_1(C,A) ) & ! [C] : ( ( v2_abcmiz_1(C,A) & m1_subset_1(C,u4_struct_0(A)) ) => ! [D] : ( 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] : ( m1_abcmiz_1(C,A,k13_abcmiz_1(A)) => B != k30_abcmiz_1(A,k32_abcmiz_1(A),C) ) & ! [C] : ( m1_abcmiz_1(C,A,k13_abcmiz_1(A)) => ! [D] : ( m1_abcmiz_1(D,A,k12_abcmiz_1(A)) => B != k31_abcmiz_1(A,k33_abcmiz_1(A),C,D) ) ) ) ) ) )).
fof(t53_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [C] : ( m1_subset_1(C,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t53_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r1_aff_1(A,F,B,C) & r1_aff_1(A,F,D,E) & C = E ) => ( r1_aff_1(A,F,B,D) | ( C = F & E = F ) ) ) ) ) ) ) ) ) )).
fof(t53_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( r2_analoaf(A,B,D,E,G) & r2_analoaf(A,C,D,F,G) ) ) ) ) ) ) ) ) ) )).
fof(t53_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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 ) ) ) )).
fof(t53_afinsq_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k7_afinsq_2(k6_afinsq_1(A,B)) = k2_xcmplx_0(A,B) ) ) )).
fof(t53_afvect0,axiom,( ! [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) & v12_vectsp_1(A) & v1_tdgroup(A) & l2_algstr_0(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ( ! [D] : ( 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) ) ) ) ) )).
fof(t53_algspec1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( ~ v11_struct_0(C) & v1_instalg1(C) & l1_msualg_1(C) ) => ! [D] : ( m2_algspec1(D,C) => ( r1_algspec1(D,A,B) => m2_algspec1(k2_algspec1(D,A,B),k2_algspec1(C,A,B)) ) ) ) ) ) )).
fof(t53_altcat_4,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t53_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t53_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k6_analort(A,B,C))) <=> m1_subset_1(D,u1_struct_0(A)) ) ) ) ) )).
fof(t53_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ( ~ r2_hidden(B,k18_aofa_000(A)) & B != k12_aofa_000(A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => B != k14_aofa_000(A,C,D,E) ) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => B != k16_aofa_000(A,C,D) ) ) ) ) ) )).
fof(t53_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v19_aofa_a00(B,A) & m1_subset_1(B,u1_struct_0(A)) ) => ( B != u8_aofa_a00(A) & r1_aofa_a00(A,k1_funct_1(u7_aofa_a00(A),4),k1_xboole_0,B) & r1_aofa_a00(A,k1_funct_1(u7_aofa_a00(A),k2_xcmplx_0(4,1)),k1_xboole_0,B) & k1_funct_1(u7_aofa_a00(A),4) != k1_funct_1(u7_aofa_a00(A),k2_xcmplx_0(4,1)) & r1_aofa_a00(A,k1_funct_1(u7_aofa_a00(A),k2_xcmplx_0(4,2)),k12_finseq_1(u1_struct_0(A),B),B) & r1_aofa_a00(A,k1_funct_1(u7_aofa_a00(A),k2_xcmplx_0(4,3)),k2_finseq_4(u1_struct_0(A),B,B),B) & r1_aofa_a00(A,k1_funct_1(u7_aofa_a00(A),k2_xcmplx_0(4,4)),k2_finseq_4(u1_struct_0(A),B,B),B) & r1_aofa_a00(A,k1_funct_1(u7_aofa_a00(A),k2_xcmplx_0(4,5)),k2_finseq_4(u1_struct_0(A),B,B),B) & k1_funct_1(u7_aofa_a00(A),k2_xcmplx_0(4,3)) != k1_funct_1(u7_aofa_a00(A),k2_xcmplx_0(4,4)) & k1_funct_1(u7_aofa_a00(A),k2_xcmplx_0(4,3)) != k1_funct_1(u7_aofa_a00(A),k2_xcmplx_0(4,5)) & k1_funct_1(u7_aofa_a00(A),k2_xcmplx_0(4,4)) != k1_funct_1(u7_aofa_a00(A),k2_xcmplx_0(4,5)) & r1_aofa_a00(A,k1_funct_1(u7_aofa_a00(A),k2_xcmplx_0(4,6)),k2_finseq_4(u1_struct_0(A),B,B),u8_aofa_a00(A)) ) ) ) )).
fof(t53_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v19_aofa_a00(E,A) & m1_subset_1(E,u1_struct_0(A)) ) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,C),E)) => ! [G] : ( m2_pboole(G,u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,D)) => k15_aofa_a00(A,B,C,D,E,k29_aofa_a00(A,C,E,F),G) = k29_aofa_a00(A,D,E,k15_aofa_a00(A,B,C,D,E,F,G)) ) ) ) ) ) ) ) )).
fof(t53_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m2_funct_2(C,B,k4_numbers,k9_funct_2(B,k4_numbers)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_aofa_i00(E,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) & m1_aofa_000(E,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),D,k5_numbers)) ) => ! [F] : ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_aofa_i00(H,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),E) => ! [I] : ( m1_aofa_i00(I,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),E) => ( ( ! [J] : ( 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,k5_numbers),E,H,1)),F) ) ) ) & r2_hidden(C,F) ) => ( ! [J] : ( ( v1_relat_1(J) & v1_funct_1(J) ) => ~ ( k1_funct_1(J,D) = k5_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,k5_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,k5_numbers),E) ) ) ) ) ) ) ) ) ) ) )).
fof(t53_armstrng,axiom,( ! [A] : ! [B] : ( 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) ) ) ) ) )).
fof(t53_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => k10_arytm_3(A,k12_arytm_3) = A ) )).
fof(t53_asympt_1,axiom,( k5_series_1(4,4) = 256 )).
fof(t53_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) => k4_bcialg_1(A) = k1_tarski(k4_struct_0(A)) ) ) )).
fof(t53_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ 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,k1_nat_1(A,1),A,k1_nat_1(A,1)) ) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k1_bcialg_2(B,C,D,k1_nat_1(A,1)) = k1_bcialg_2(B,C,D,k1_nat_1(A,2)) ) ) ) ) ) )).
fof(t53_bcialg_6,axiom,( ! [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] : ( ( ~ 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] : ( m2_bcialg_1(C,A) => ! [D] : ( m5_bcialg_2(D,A,C) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t53_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) )).
fof(t53_bhsp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(C)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(C),k5_normsp_1(C,D,k3_xcmplx_0(A,B)),k5_normsp_1(C,k5_normsp_1(C,D,B),A)) ) ) ) ) )).
fof(t53_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(C,k6_bhsp_2(A,B,D)) => r2_hidden(C,k5_bhsp_2(A,B,D)) ) ) ) ) ) )).
fof(t53_bhsp_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ! [D] : ( v7_ordinal1(D) => k1_normsp_1(B,k1_bhsp_4(B,k5_bhsp_4(B,C,A)),k1_nat_1(D,1)) = k5_algstr_0(B,k1_normsp_1(B,k5_bhsp_4(B,k1_bhsp_4(B,C),A),k1_nat_1(D,1)),k1_normsp_1(B,k1_bhsp_4(B,k5_bhsp_4(B,k1_bhsp_4(B,C),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k1_valued_0(k1_numbers,A,1),A))),D)) ) ) ) ) )).
fof(t53_bilinear,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t53_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t53_borsuk_4,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ~ r1_topreal1(k15_euclid(2),C,D,B) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => B != k6_domain_1(u1_struct_0(k15_euclid(2)),C) ) ) ) ) )).
fof(t53_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t53_borsuk_6,axiom,( k6_borsuk_6 = a_0_12_borsuk_6 )).
fof(t53_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => 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)) ) )).
fof(t53_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t53_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_eqrel_1(I,A) => ! [J] : ( m1_subset_1(J,A) => ! [K] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t53_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t53_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ( k9_xboolean(A,k3_xboolean(A)) = k7_margrel1 & k3_xboolean(k9_xboolean(A,k3_xboolean(A))) = k8_margrel1 ) ) )).
fof(t53_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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))))) ) ) ) ) )).
fof(t53_card_1,axiom,( 7 = k5_enumset1(k5_ordinal1,1,2,3,4,5,6) )).
fof(t53_card_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : r1_xxreal_0(k5_card_1(k4_enumset1(A,B,C,D,E,F)),6) )).
fof(t53_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r2_hidden(B,k4_card_3(A)) & r2_hidden(C,k8_card_3(A)) ) => r2_hidden(k1_funct_4(B,C),k4_card_3(A)) ) ) ) ) )).
fof(t53_card_fin,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t53_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t53_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => v11_cat_1(k19_cat_4(A),A) ) )).
fof(t53_cfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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))) ) ) ) )).
fof(t53_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_chain_1(B,A) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k4_chain_1(A,B,k1_nat_1(k5_numbers,1))) => k5_card_1(k10_chain_1(A,B,k5_numbers,k6_domain_1(k4_chain_1(A,B,k1_nat_1(k5_numbers,1)),C))) = 2 ) ) ) )).
fof(t53_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k6_glib_000(A)) => ~ ( r2_hidden(C,k13_glib_001(A,B)) & ! [D] : ( ( v7_ordinal1(D) & ~ v1_abian(D) ) => ! [E] : ( ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(t53_circcmb3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(D) & v1_finset_1(D) ) => ! [E] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(t53_circcomb,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t53_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v4_msualg_1(E,A) & v4_msafree2(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t53_classes1,axiom,( ! [A] : ! [B] : ( ( r1_tarski(A,B) & v1_ordinal1(B) ) => r1_tarski(k5_classes1(A),B) ) )).
fof(t53_classes2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) ) => ( r1_tarski(A,B) | r2_hidden(B,A) ) ) ) )).
fof(t53_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_clvect_1(C,A) => ( u1_struct_0(C) = B => v6_clvect_1(B,A) ) ) ) ) )).
fof(t53_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(C,k6_clvect_2(A,B,D)) => r2_hidden(C,k5_clvect_2(A,B,D)) ) ) ) ) ) )).
fof(t53_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [D] : ( v7_ordinal1(D) => k1_normsp_0(A,k1_bhsp_4(A,k6_clvect_3(A,B,C)),k1_nat_1(D,1)) = k5_algstr_0(A,k1_normsp_0(A,k6_clvect_3(A,k1_bhsp_4(A,B),C),k1_nat_1(D,1)),k1_normsp_0(A,k1_bhsp_4(A,k6_clvect_3(A,k1_bhsp_4(A,B),k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k1_valued_0(k2_numbers,C,1),C))),D)) ) ) ) ) )).
fof(t53_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( ( 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] : ! [E] : ( r2_hidden(k2_tarski(D,E),A) => ! [F] : ! [G] : ( ( 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) ) ) ) ) ) )).
fof(t53_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k9_complex1(k8_complex1(A)) = k9_complex1(A) ) )).
fof(t53_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_complex2(A,k4_xcmplx_0(k1_comptrig(A))) = k9_complex1(A) ) )).
fof(t53_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( 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)) ) ) )).
fof(t53_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k10_seq_4(A,k6_xcmplx_0(B,C)) = k8_seq_4(k10_seq_4(A,B),k10_seq_4(A,C)) ) ) ) )).
fof(t53_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( 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)) ) ) )).
fof(t53_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( v6_compos_0(D,u1_compos_1(A)) & m1_subset_1(D,u1_compos_1(A)) ) => ! [E] : ( ( v6_compos_0(E,u1_compos_1(A)) & m1_subset_1(E,u1_compos_1(A)) ) => ! [F] : ( ( 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) ) ) ) ) ) ) )).
fof(t53_comptrig,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => k1_newton(k2_xcmplx_0(k19_sin_cos(A),k3_xcmplx_0(k17_sin_cos(A),k7_complex1)),B) = k2_xcmplx_0(k19_sin_cos(k3_xcmplx_0(B,A)),k3_xcmplx_0(k17_sin_cos(k3_xcmplx_0(B,A)),k7_complex1)) ) ) )).
fof(t53_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k3_finseq_2(k4_ordinal1)) & v1_funct_1(C) & v4_valued_0(C) & v2_margrel1(C) ) => ! [D] : ( m2_finseq_2(D,k4_ordinal1,k4_finseq_2(k1_nat_1(k19_margrel1(B),1),k4_ordinal1)) => ( ( v2_comput_1(B) & v2_comput_1(C) & k1_nat_1(k19_margrel1(B),2) = k19_margrel1(C) & r1_xxreal_0(1,A) & r1_xxreal_0(A,k1_nat_1(1,k19_margrel1(B))) ) => r2_hidden(D,k1_relset_1(k3_finseq_2(k4_ordinal1),k6_comput_1(B,C,A,D))) ) ) ) ) ) )).
fof(t53_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) )).
fof(t53_convex4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => k19_convex4(A,k19_convex4(A,B,D),C) = k19_convex4(A,B,k3_xcmplx_0(C,D)) ) ) ) ) )).
fof(t53_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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))) ) ) ) ) ) ) ) )).
fof(t53_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t53_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t53_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k5_numbers,k15_csspace(A,B,C)) ) ) ) )).
fof(t53_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k9_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),A,B) = k7_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k17_sin_cos(k3_xcmplx_0(2,A)),k17_sin_cos(k3_xcmplx_0(2,B)))),k6_xcmplx_0(A,B)) ) ) )).
fof(t53_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => 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) = k7_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,k19_sin_cos(k7_xcmplx_0(k2_xcmplx_0(A,B),2))),k17_sin_cos(k7_xcmplx_0(k6_xcmplx_0(A,B),2))),k3_xcmplx_0(k19_sin_cos(k7_xcmplx_0(k3_xcmplx_0(3,k2_xcmplx_0(A,B)),2)),k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(3,k6_xcmplx_0(A,B)),2))))),k6_xcmplx_0(A,B)) ) ) )).
fof(t53_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k5_diff_1(k5_diff_1(C,A),A),B) = k6_xcmplx_0(k1_funct_1(k3_diff_1(C,A),B),k1_funct_1(k4_diff_1(C,A),B)) ) ) ) )).
fof(t53_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ! [E] : ( ( 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(k4_ordinal1,k4_ordinal1,k4_ordinal1,k5_numbers,1,k5_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) ) ) ) ) ) )).
fof(t53_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( 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 = k5_int_1(3,A) & k5_ec_pf_2(A,k2_ec_pf_2(A,B),k3_ec_pf_2(A,B),D) = k5_numbers & k6_ec_pf_2(A,k2_ec_pf_2(A,B),k3_ec_pf_2(A,B),D) != k5_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))) = k5_numbers ) ) ) ) ) )).
fof(t53_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t53_entropy1,axiom,( ! [A] : ( ( v1_matrix_0(A) & v2_matrprob(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => k7_matrix_0(k1_numbers,k5_entropy1(A),B) = k4_entropy1(k7_matrix_0(k1_numbers,A,B)) ) ) ) )).
fof(t53_enumset1,axiom,( ! [A] : ! [B] : ! [C] : k6_enumset1(A,A,A,A,A,A,B,C) = k1_enumset1(A,B,C) )).
fof(t53_eqrel_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( 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)) ) ) ) )).
fof(t53_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ( r1_rvsum_1(B,B) <=> B = k4_struct_0(k15_euclid(A)) ) ) ) )).
fof(t53_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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) ) ) ) ) )).
fof(t53_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => k8_euclid(3,A,B) = k1_euclid_8(k6_xcmplx_0(k1_funct_1(A,1),k1_funct_1(B,1)),k6_xcmplx_0(k1_funct_1(A,2),k1_funct_1(B,2)),k6_xcmplx_0(k1_funct_1(A,3),k1_funct_1(B,3))) ) ) )).
fof(t53_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ~ ( v1_euclid_4(C,A) & ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ~ ( D != B & r2_hidden(D,C) ) ) ) ) ) ) )).
fof(t53_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( ( 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,k9_funct_7(E,A,B))) ) ) ) ) )).
fof(t53_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v1_xboole_0(D) & v1_finset_1(D) ) => ! [E] : ( ( 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] : ( 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))) ) ) ) )).
fof(t53_fcont_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(C,D) ) => r1_xxreal_0(k1_funct_1(k1_fcont_1(A,B),C),k1_funct_1(k1_fcont_1(A,B),D)) ) ) ) ) ) )).
fof(t53_fdiff_11,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(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),k22_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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),k22_sin_cos),A),B) = k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k1_funct_1(k2_sin_cos9,B)),k1_funct_1(k22_sin_cos,B))) ) ) ) ) ) )).
fof(t53_fdiff_4,axiom,( ! [A] : ( ( 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,k18_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)),k7_xcmplx_0(1,2))))) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k16_sin_cos,B),k5_numbers) & ~ r1_xxreal_0(k1_funct_1(k18_sin_cos,B),k4_xcmplx_0(1)) ) ) ) ) => ( r2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k18_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)),k7_xcmplx_0(1,2))),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k18_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)),k7_xcmplx_0(1,2))),A),B) = k7_xcmplx_0(k1_newton(k1_funct_1(k16_sin_cos,B),3),k2_xcmplx_0(1,k1_funct_1(k18_sin_cos,B))) ) ) ) ) ) )).
fof(t53_fib_num2,axiom,( k5_fib_num2(k5_numbers) = k1_xboole_0 )).
fof(t53_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t53_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k7_filter_0(A,B,k7_filter_0(A,B,C)) = C ) ) ) )).
fof(t53_filter_2,axiom,( ! [A] : ( ( ~ 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)) ) ) ) )).
fof(t53_finseq_2,axiom,( ! [A] : ( 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)))) ) ) )).
fof(t53_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( 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)))) ) ) ) ) )).
fof(t53_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( r2_hidden(B,k10_xtuple_0(A)) & v2_funct_1(A) ) => v2_funct_1(k6_finseq_4(A,B)) ) ) )).
fof(t53_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => k7_partfun1(A,k2_finseq_5(A,C,B),1) = B ) ) ) )).
fof(t53_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ( B != C => k2_finseq_5(A,k2_finseq_4(A,B,C),C) = k12_finseq_1(A,C) ) ) ) ) )).
fof(t53_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r3_fintopo6(A,B,C,D,E) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t53_flang_1,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(t53_flang_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k5_afinsq_1(B),k1_flang_2(A,C,D,E)) <=> ( r2_hidden(k5_afinsq_1(B),C) & r1_xxreal_0(D,E) & ( ( r2_hidden(k2_flang_1(A),C) & ~ r1_xxreal_0(E,k5_numbers) ) | ( r1_xxreal_0(D,1) & r1_xxreal_0(1,E) ) ) ) ) ) ) ) )).
fof(t53_flang_3,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(t53_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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(k9_fomodel0(B),D) = k1_funct_1(k9_fomodel0(C),D) ) ) ) ) ) )).
fof(t53_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( ~ v2_struct_0(D) & l2_fsm_1(D,A,B) ) => ! [E] : ( ( ~ v2_struct_0(E) & l2_fsm_1(E,A,B) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ! [G] : ( ( ~ v2_struct_0(G) & v8_struct_0(G) & l2_fsm_1(G,A,B) ) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t53_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t53_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(B,k9_xtuple_0(k6_relat_1(A,C))) <=> ( r2_hidden(B,k9_xtuple_0(C)) & r2_hidden(k1_funct_1(C,B),A) ) ) ) )).
fof(t53_funct_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t53_funct_3,axiom,( ! [A] : ! [B] : k13_funct_3(k9_funct_3(A,B),k10_funct_3(A,B)) = k4_relat_1(k2_zfmisc_1(A,B)) )).
fof(t53_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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 ) )).
fof(t53_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( r2_wellord2(A,C) & r2_wellord2(B,D) ) => ( r2_wellord2(k1_funct_2(A,B),k1_funct_2(C,D)) & k1_card_1(k1_funct_2(A,B)) = k1_card_1(k1_funct_2(C,D)) ) ) )).
fof(t53_funct_6,axiom,( k9_funct_6(k1_xboole_0) = k1_xboole_0 )).
fof(t53_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => k3_funct_7(A,k11_finseq_1(B,C,D)) = k3_relat_1(k6_partfun1(A),k3_relat_1(B,k3_relat_1(C,D))) ) ) ) )).
fof(t53_funct_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t53_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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)) ) ) ) ) )).
fof(t53_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k7_fvaluat1(A,B)))) => m2_xxreal_2(k5_numbers,k7_relset_1(u1_struct_0(A),k6_numbers,B,C)) ) ) ) ) )).
fof(t53_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t53_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( ( ~ v1_xboole_0(G) & v1_relat_1(G) & v2_relat_1(G) & v1_funct_1(G) & v1_finseq_1(G) ) => ! [H] : ( m1_genealg1(H,G) => ! [I] : ( m1_genealg1(I,G) => m1_genealg1(k6_genealg1(G,H,I,A,B,C,D,E,F),G) ) ) ) ) ) ) ) ) ) )).
fof(t53_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k19_gfacirc1(A,B,C),k20_gfacirc1(A,B,C)))) & ? [E] : ( m1_subset_1(E,k6_margrel1) & ? [F] : ( m1_subset_1(F,k6_margrel1) & ? [G] : ( 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) ) ) ) ) ) ) )).
fof(t53_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( 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) ) ) ) )).
fof(t53_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( ( r1_xxreal_0(C,D) & r1_xxreal_0(D,k3_finseq_1(B)) & k1_funct_1(B,C) = k1_funct_1(B,D) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( 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),k4_ordinal1) & r1_xxreal_0(k2_xcmplx_0(k6_xcmplx_0(E,C),D),k3_finseq_1(B)) ) ) ) ) ) ) ) ) )).
fof(t53_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_003(A) ) => ! [B] : ! [C] : ( r2_hidden(B,k6_glib_000(A)) => r1_tarski(k14_glib_003(A),k14_glib_003(k13_glib_003(A,B,C))) ) ) )).
fof(t53_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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_0(k2_goboard2(C)),k1_nat_1(B,1)) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1))),k3_topreal1(2,C)) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,2))),k3_topreal1(2,C)) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,1) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1)) & ( ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,2) = k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,2)) ) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,2) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,2)) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k7_nat_d(k3_finseq_1(C),1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,B) ) ) ) & ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(1,D) & ~ r1_xxreal_0(k3_finseq_1(C),k1_nat_1(D,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_nat_1(D,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1)) & ( ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,D) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,B) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_nat_1(D,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,2)) ) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,D) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,2)) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_nat_1(D,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,B) ) ) ) ) ) ) ) ) )).
fof(t53_graph_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,A) ) => ! [C] : ( m2_finseq_1(C,A) => k7_partfun1(A,k4_graph_2(A,B,C),1) = k7_partfun1(A,B,1) ) ) ) )).
fof(t53_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_2(B,u4_struct_0(A),k9_graph_3(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t53_graph_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m2_finseq_1(C,u4_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u4_struct_0(B)) => ( ( v2_funct_1(D) & r1_tarski(k10_xtuple_0(D),k10_xtuple_0(C)) & r5_graph_5(B,A) ) => r1_xxreal_0(k10_graph_5(B,D,A),k10_graph_5(B,C,A)) ) ) ) ) ) )).
fof(t53_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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),k7_polynom1(A,C,k11_polynom1(A,C,k5_termord(A,B,C,E),k6_termord(A,B,C,D)),k11_polynom1(A,C,k5_termord(A,B,C,D),k6_termord(A,B,C,E)))) ) ) ) ) ) ) )).
fof(t53_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => r1_tarski(k3_group_11(A,C,B),k8_group_2(A,C)) ) ) ) )).
fof(t53_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [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) ) => v5_group_1(B) ) ) ) )).
fof(t53_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t53_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t53_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => r2_hidden(k1_group_1(A),k5_group_5(A,B,C)) ) ) ) )).
fof(t53_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t53_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( 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))) ) ) )).
fof(t53_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_002(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => ! [E] : ( ~ v1_xboole_0(E) => ~ ( ! [F] : ( r2_hidden(F,E) => ( ? [G] : ( 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 ) ) ) ) ) ) )).
fof(t53_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( 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) ) ) )).
fof(t53_hfdiff_1,axiom,( ! [A] : ( ( 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,k18_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),k4_xcmplx_0(2)))) ) )).
fof(t53_hurwitz,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(A,k1_complfld) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => ( r1_xxreal_0(1,k2_hurwitz(k1_complfld,A)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ~ ( ~ r1_xxreal_0(k5_numbers,k3_complex1(B)) & ~ r1_xxreal_0(k9_complex1(k2_polynom4(k1_complfld,k7_hurwitz(A),B)),k9_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))) ) ) ) ) ) )).
fof(t53_ideal_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t53_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u4_incsp_1(A)) => ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & r2_incsp_1(A,D,C) & ~ r1_incsp_1(A,D,B) ) ) ) ) )).
fof(t53_int_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k5_numbers,k4_int_1(A,B)) ) ) )).
fof(t53_int_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_numbers)) ) => ( r1_int_4(A,C) => r1_int_4(A,k1_measure6(C,B)) ) ) ) ) )).
fof(t53_integr11,axiom,( ! [A] : ( ( 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),k26_sin_cos),k1_fdiff_9))) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( k2_xcmplx_0(1,k1_funct_1(k16_sin_cos,B)) != k5_numbers & k6_xcmplx_0(1,k1_funct_1(k16_sin_cos,B)) != k5_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),k26_sin_cos),k1_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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),k26_sin_cos),k1_fdiff_9),A),B) = k7_xcmplx_0(k1_funct_1(k16_sin_cos,B),k2_xcmplx_0(k1_funct_1(k16_sin_cos,B),1)) ) ) ) ) ) )).
fof(t53_integr13,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( 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,E,F),k3_taylor_1))) & r2_relset_1(k1_numbers,k1_numbers,C,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,E,F),A))) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,G) => ( k1_funct_1(D,H) = k7_xcmplx_0(H,A) & k1_funct_1(E,H) = 1 ) ) ) & r2_relset_1(k1_numbers,k1_numbers,F,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k1_taylor_1(2))) & G = k1_relset_1(k1_numbers,C) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,B)) ) => ( A = k5_numbers | k2_integra5(B,C) = k6_xcmplx_0(k1_funct_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,E,F),k3_taylor_1),k7_xcmplx_0(A,2)),k2_seq_4(B)),k1_funct_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,E,F),k3_taylor_1),k7_xcmplx_0(A,2)),k3_seq_4(B))) ) ) ) ) ) ) ) ) ) )).
fof(t53_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k6_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,D))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,D)))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),k2_seq_4(A)),k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t53_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t53_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [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))) ) => ! [D] : ( ( 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),k2_xcmplx_0(k6_integra1(A,C,B),k6_integra1(A,D,B))) ) ) ) ) ) )).
fof(t53_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => k2_integra5(A,k22_sin_cos) = k6_xcmplx_0(k1_funct_1(k22_sin_cos,k2_seq_4(A)),k1_funct_1(k22_sin_cos,k3_seq_4(A))) ) )).
fof(t53_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( 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] : ( v1_xreal_0(G) => ( r2_hidden(G,F) => ( k1_funct_1(D,G) = k2_xcmplx_0(A,G) & ~ r1_xxreal_0(k1_funct_1(D,G),k5_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] : ( v1_xreal_0(G) => ( r2_hidden(G,F) => k1_funct_1(E,G) = k7_xcmplx_0(G,k2_xcmplx_0(A,G)) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,E,B)) ) => k2_integra5(B,E) = k6_xcmplx_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,F),k26_valued_1(k1_numbers,k1_numbers,C,A)),k2_seq_4(B)),k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,F),k26_valued_1(k1_numbers,k1_numbers,C,A)),k3_seq_4(B))) ) ) ) ) ) ) ) )).
fof(t53_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => r2_hidden(k1_xboole_0,k3_interva1(A,B,k10_interva1(A,B))) ) ) )).
fof(t53_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(t53_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( 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] : ( 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) = k3_xcmplx_0(k12_euclid(D),k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k17_euclid(D),k12_euclid(D)),A),k2_xcmplx_0(1,A))) ) ) & ! [D] : ( 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(k5_numbers,k18_euclid(D)) & D != k4_struct_0(k15_euclid(2)) ) ) ) ) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) | v5_pre_topc(C,k1_pre_topc(k15_euclid(2),B),k3_topmetr) ) ) ) ) ) )).
fof(t53_jgraph_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ 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(k5_numbers,k18_euclid(A)) & r1_xxreal_0(k5_numbers,k18_euclid(B)) ) => ( r1_xxreal_0(k5_numbers,k17_euclid(A)) | r1_xxreal_0(k5_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) ) ) ) ) ) )).
fof(t53_jgraph_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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(k7_xcmplx_0(2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(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)) ) ) ) ) ) ) ) ) ) )).
fof(t53_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(C,B) & r1_xboole_0(k6_topreal1(C),k3_topreal1(2,k2_jordan9(B,A))) ) ) ) ) )).
fof(t53_jordan1h,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( 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] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(k4_tarski(D,E),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k7_nat_d(k3_finseq_1(C),1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),D,E) & r2_hidden(k4_tarski(k1_nat_1(D,1),E),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k3_finseq_1(C)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k1_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(k1_nat_1(D,1),k1_nat_1(E,1)),k2_matrix_0(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) )).
fof(t53_jordan1j,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v7_ordinal1(D) => ( ( 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) ) ) ) ) ) ) ) )).
fof(t53_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t53_jordan4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m2_finseq_1(E,u1_struct_0(k15_euclid(2))) => ( ( r2_jordan4(C,D,A,B) & r2_jordan4(C,E,A,B) ) => D = E ) ) ) ) ) ) )).
fof(t53_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( 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) ) ) ) )).
fof(t53_kurato_1,axiom,( 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)) )).
fof(t53_lattice2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k5_finsub_1(A)) => ! [C] : ( ( ~ v2_struct_0(C) & v10_lattices(C) & v13_lattices(C) & l3_lattices(C) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t53_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( v7_ordinal1(B) => v5_lexbfs(k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),k13_lexbfs(A,k16_lexbfs(A),B)),A) ) ) )).
fof(t53_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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)) ) ) ) ) )).
fof(t53_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) = k4_xcmplx_0(k2_limfunc2(B,A)) ) ) ) ) )).
fof(t53_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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) ) ) ) ) )).
fof(t53_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( 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)) = k5_numbers ) => r1_lpspace1(A,B,C,D,k8_lpspace1(A,k5_numbers)) ) ) ) ) ) )).
fof(t53_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v2_xxreal_0(D) & v1_xreal_0(D) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k12_lpspace2(A,B,C,D))) => ( ? [F] : ( 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] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ~ ( r2_hidden(F,E) & ! [G] : ( v1_xreal_0(G) => ~ ( r1_xxreal_0(k5_numbers,G) & G = k1_mesfunc6(A,B,C,k2_mesfun6c(D,A,k56_valued_1(A,k1_numbers,F))) & k2_normsp_0(k12_lpspace2(A,B,C,D),E) = k2_power(G,k2_extreal1(1,D)) ) ) ) ) ) ) ) ) ) ) )).
fof(t53_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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)))) ) ) ) )).
fof(t53_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( m1_subset_1(D,k1_hilbert1) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k1_hilbert1)) => ( ( r8_ltlaxio1(E,k3_hilbert1(A,B)) & r8_ltlaxio1(E,k3_hilbert1(C,D)) ) => r8_ltlaxio1(E,k3_hilbert1(k4_ltlaxio1(A,C),k4_ltlaxio1(B,D))) ) ) ) ) ) ) )).
fof(t53_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(t53_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( r2_matrix10(k5_matrix10(A,B,C),D) => r2_matrix10(k5_matrix10(A,B,D),C) ) ) ) ) ) )).
fof(t53_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( 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_0(D),B,k7_matrix_0(u1_struct_0(B),D,E),k10_fvsum_1(k1_matrix_0(D),B,k7_matrix_0(u1_struct_0(B),D,F),C)))) ) ) ) ) ) ) ) ) )).
fof(t53_matrix13,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & v1_setfam_1(B) & m1_subset_1(B,k1_zfmisc_1(k4_ordinal1)) ) => ( 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(k4_ordinal1)) ) ) )).
fof(t53_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ~ ( C != k2_matrix_1(B,A) & ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ~ ( v1_matrix_6(D,A,B) & v1_matrix_6(E,A,B) & k3_matrix_0(u1_struct_0(B),k4_matrix_3(B,k4_matrix_3(B,D,C),E),1,1) = k5_struct_0(B) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(F,A) => ( r1_xxreal_0(F,1) | k3_matrix_0(u1_struct_0(B),k4_matrix_3(B,k4_matrix_3(B,D,C),E),F,1) = k4_struct_0(B) ) ) ) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(F,A) => ( r1_xxreal_0(F,1) | k3_matrix_0(u1_struct_0(B),k4_matrix_3(B,k4_matrix_3(B,D,C),E),1,F) = k4_struct_0(B) ) ) ) ) ) ) ) ) ) ) )).
fof(t53_matrix15,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [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] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(E),D,B) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(E))) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(E),D,C) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(E))) ) => ( r2_hidden(A,k4_matrix15(E,F,G)) => ( r1_xxreal_0(D,k5_numbers) | ( v1_matrix_0(A) & v2_matrix_0(A,u1_struct_0(E),B,C) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(E))) ) ) ) ) ) ) ) ) ) )).
fof(t53_matrix16,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(A),B,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(A))) ) => ( ( r2_hidden(k4_tarski(C,D),k2_matrix_0(E)) & C = D & v5_matrix16(E,A) ) => k3_matrix_0(u1_struct_0(A),E,C,D) = k4_struct_0(A) ) ) ) ) ) ) )).
fof(t53_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ( ( k4_matrix_0(A,B) = k4_matrix_0(A,C) & k3_finseq_1(B) = k3_finseq_1(C) ) => B = C ) ) ) ) )).
fof(t53_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(D) & k1_matrix_4(A,B,D) = k3_matrix_3(A,C,k2_matrix_3(A,D)) ) => B = C ) ) ) ) ) )).
fof(t53_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r1_matrix_6(A,B,C,D) => r1_matrix_6(A,B,k4_matrix_3(B,C,C),D) ) ) ) ) ) )).
fof(t53_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => k1_matrix_8(A,B,k3_matrix_3(B,C,D)) = k3_rlvect_1(B,k1_matrix_8(A,B,C),k1_matrix_8(A,B,D)) ) ) ) ) )).
fof(t53_matrix_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( ? [D] : ( m1_subset_1(D,k4_ordinal1) & r2_hidden(D,k2_finseq_1(A)) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k2_finseq_1(A)) => k1_funct_1(k8_matrix_0(u1_struct_0(B),C,D),E) = k4_struct_0(B) ) ) ) => k12_matrix_3(A,B,C) = k4_struct_0(B) ) ) ) ) )).
fof(t53_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => ( r1_xxreal_0(k3_finseq_1(B),k5_numbers) | k8_complex1(k8_complsp2(A,B)) = k8_complsp2(k1_complsp2(A),k1_complsp2(B)) ) ) ) ) )).
fof(t53_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ~ ( ~ r1_xxreal_0(k3_finseq_1(B),k5_numbers) & ~ r1_xxreal_0(k1_matrix_0(B),k5_numbers) & ( k1_matrix_0(B) = k3_finseq_1(A) | k3_finseq_1(k4_matrix_0(k1_numbers,B)) = k3_finseq_1(A) ) & k11_matrixr1(B,A) != k12_matrixr1(k4_matrix_0(k1_numbers,B),A) ) ) ) )).
fof(t53_matrixr2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( k1_matrix_0(C) = k3_finseq_1(B) => ( r1_xxreal_0(k3_finseq_1(B),k5_numbers) | k11_matrixr1(C,k10_rvsum_1(B,A)) = k10_rvsum_1(k11_matrixr1(C,B),A) ) ) ) ) ) )).
fof(t53_matrprob,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_matrprob(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => r1_xxreal_0(k1_funct_1(A,B),1) ) ) ) )).
fof(t53_mcart_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k3_zfmisc_1(B,C,D)) => ( ! [F] : ( m1_subset_1(F,B) => ! [G] : ( m1_subset_1(G,C) => ! [H] : ( m1_subset_1(H,D) => ( E = k3_xtuple_0(F,G,H) => A = H ) ) ) ) => A = k3_mcart_1(B,C,D,E) ) ) ) ) ) )).
fof(t53_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( v1_xreal_0(B) => ( v2_rcomp_1(A) <=> v2_rcomp_1(k1_measure6(A,B)) ) ) ) )).
fof(t53_member_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => k9_member_1(k2_tarski(A,B),k2_tarski(C,D)) = k2_enumset1(k2_xcmplx_0(A,C),k2_xcmplx_0(A,D),k2_xcmplx_0(B,C),k2_xcmplx_0(B,D)) ) ) ) ) )).
fof(t53_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( v7_ordinal1(D) => k5_memstr_0(A,B,k9_memstr_0(A,B,C,D)) = k2_xcmplx_0(k5_memstr_0(A,B,C),D) ) ) ) ) )).
fof(t53_mesfunc6,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( v2_mesfunc5(B) <=> ! [C] : r1_xxreal_0(k12_supinf_2(B,C),k5_numbers) ) ) )).
fof(t53_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => u1_struct_0(k15_midsp_1(A)) = k10_midsp_1(A) ) )).
fof(t53_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( 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) ) ) )).
fof(t53_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_modelc_2(B) & l1_modelc_2(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t53_modelc_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k23_modelc_3(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k23_modelc_3(C)))) ) => ( ( v7_modelc_2(B) & r2_hidden(B,u1_modelc_3(C,k10_modelc_3(k3_funct_2(k4_ordinal1,k23_modelc_3(C),D,1),C))) & ! [E] : ( v7_ordinal1(E) => r6_modelc_3(C,k10_modelc_3(k1_funct_1(D,E),C),k10_modelc_3(k3_funct_2(k4_ordinal1,k23_modelc_3(C),D,k1_nat_1(E,1)),C)) ) & ! [E] : ( 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] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(t53_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => A = k6_moebius1(A) ) )).
fof(t53_monoid_0,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_monoid_0)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_monoid_0)) => ( ( A = C & B = D ) => k6_algstr_0(k7_monoid_0,C,D) = k3_xcmplx_0(A,B) ) ) ) ) ) )).
fof(t53_monoid_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) ) ) )).
fof(t53_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => r2_equation(A,B,k5_msafree4(A,B)) ) ) )).
fof(t53_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => r8_pboole(k8_newton,k12_nat_3(k3_int_2(B,A)),k5_nat_3(k8_newton,k12_nat_3(B),k12_nat_3(A))) ) ) )).
fof(t53_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(A,k2_xcmplx_0(B,C)) => r1_xxreal_0(k7_nat_d(A,C),B) ) ) ) ) )).
fof(t53_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ! [C] : ( ( 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) ) ) ) )).
fof(t53_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k14_prvect_2(A)))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_prvect_2(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k14_prvect_2(A))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k14_prvect_2(A))) => ! [H] : ! [I] : ( m1_subset_1(I,u1_struct_0(k11_prvect_2(A,k5_ndiff_5(A,H)))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k11_prvect_2(A,k5_ndiff_5(A,H)))) => ! [K] : ( v1_xreal_0(K) => ! [L] : ( v1_xreal_0(L) => ( ( 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] : ( m1_subset_1(M,u1_struct_0(k14_prvect_2(A))) => ( r2_hidden(M,D) => r1_ndiff_5(A,B,H,C,M) ) ) & ! [M] : ( m1_subset_1(M,u1_struct_0(k14_prvect_2(A))) => ( ~ r1_xxreal_0(K,k2_normsp_0(k14_prvect_2(A),k5_algstr_0(k14_prvect_2(A),M,E))) => r2_hidden(M,D) ) ) & ! [M] : ( m1_subset_1(M,u1_struct_0(k14_prvect_2(A))) => ( ~ r1_xxreal_0(K,k2_normsp_0(k14_prvect_2(A),k5_algstr_0(k14_prvect_2(A),M,E))) => r1_xxreal_0(k2_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,k2_normsp_0(k14_prvect_2(A),k5_algstr_0(k14_prvect_2(A),F,E))) | r1_xxreal_0(K,k2_normsp_0(k14_prvect_2(A),k5_algstr_0(k14_prvect_2(A),G,E))) | r1_xxreal_0(k2_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)))),k3_xcmplx_0(k2_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)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t53_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k5_nat_d(k6_nat_d(B,A),A) = A ) ) )).
fof(t53_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_numbers))) ) => ( ! [C] : ( 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) = k2_normsp_0(A,C) ) ) => r4_nfcont_1(A,B,k1_relset_1(u1_struct_0(A),B)) ) ) ) )).
fof(t53_normform,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k5_finsub_1(k7_normform(A)),k8_normform(A)) => ! [C] : ( m2_subset_1(C,k5_finsub_1(k7_normform(A)),k8_normform(A)) => ! [D] : ( 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)) ) ) ) )).
fof(t53_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t53_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_oppcat_1(C,A,B) => m2_cat_1(k10_oppcat_1(A,B,C),k2_oppcat_1(A),B) ) ) ) )).
fof(t53_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_real_ns1(A))) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A))))) ) => ( r5_nfcont_1(k4_real_ns1(A),k4_real_ns1(A),u1_struct_0(k4_real_ns1(A)),E) => ( r1_xxreal_0(C,B) | v1_ordeq_01(k6_ordeq_01(A,D,E,B,C)) ) ) ) ) ) ) ) )).
fof(t53_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ( r9_orders_1(A,B) & v4_relat_2(A) ) => r7_orders_1(A,B) ) ) )).
fof(t53_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r8_orders_1(u1_orders_2(A),B) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( B != C => r2_orders_2(A,C,B) ) ) ) ) ) )).
fof(t53_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t53_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => k4_ordinal5(k5_afinsq_1(A)) = A ) )).
fof(t53_ordinal6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v3_ordinal6(A) ) => ( ! [B] : ( 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)) ) ) ) )).
fof(t53_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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 ) ) ) ) ) ) ) )).
fof(t53_partfun1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(k9_xtuple_0(A),k9_xtuple_0(B)) => ( r1_partfun1(A,B) <=> ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) ) )).
fof(t53_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ~ ( r2_hidden(C,k1_relset_1(A,E)) & 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) & k7_partfun1(B,E,C) != k7_partfun1(B,F,C) ) ) ) ) ) ) ) )).
fof(t53_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t53_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( 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) & k10_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) = k6_xcmplx_0(k2_pdiff_5(B,A),k2_pdiff_5(C,A)) ) ) ) ) ) )).
fof(t53_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t53_pepin,axiom,( k4_pepin(3) = 257 )).
fof(t53_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ~ v1_xboole_0(k8_polyform(A,k5_numbers)) ) )).
fof(t53_polyred,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & v3_ideal_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r11_polyred(A,B,C,D) => r11_polyred(A,B,D,C) ) ) ) ) ) )).
fof(t53_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & A != 1 & ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(C,k5_numbers) & k2_xcmplx_0(k3_power(A,B),k3_power(A,C)) != k3_power(A,k3_xcmplx_0(B,C)) ) ) ) ) )).
fof(t53_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(t53_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => ! [C] : ( v1_rat_1(C) => ( ~ r1_xxreal_0(A,k5_numbers) => k3_xcmplx_0(k4_prepower(A,B),k4_prepower(A,C)) = k4_prepower(A,k2_xcmplx_0(B,C)) ) ) ) ) )).
fof(t53_prob_3,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(t53_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ( ( r2_hidden(k8_cqc_lang(A,B,D),k4_cqc_the1(A)) & r2_hidden(k8_cqc_lang(A,C,D),k4_cqc_the1(A)) ) => r2_hidden(k8_cqc_lang(A,k9_cqc_lang(A,B,C),D),k4_cqc_the1(A)) ) ) ) ) ) )).
fof(t53_pscomp_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(t53_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t53_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( r1_qc_lang2(A,C,B) => r3_qc_lang2(A,C,B) ) ) ) ) )).
fof(t53_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => k5_qc_lang3(A,k12_qc_lang1(A)) = k1_xboole_0 ) )).
fof(t53_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k17_quatern2(k22_quaterni(A,B),C) = k22_quaterni(k17_quatern2(A,C),k17_quatern2(B,C)) ) ) ) )).
fof(t53_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k24_quaterni(k25_quaterni(A,B)) = k22_quaterni(k24_quaterni(A),B) ) ) )).
fof(t53_quaterni,axiom,( k27_quaterni(k12_quaterni) = k24_quaterni(k12_quaterni) )).
fof(t53_quofield,axiom,( ! [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] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) ) ) )).
fof(t53_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(k4_real_1(k9_nat_1(k1_numbers,k4_real_3(B),k1_nat_1(A,2)),k9_nat_1(k1_numbers,k6_real_3(B),k1_nat_1(A,1))),k9_nat_1(k1_numbers,k6_real_3(B),k1_nat_1(A,2))) ) ) )).
fof(t53_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => r1_tarski(k5_relat_1(B,A),B) ) )).
fof(t53_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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)) ) ) ) )).
fof(t53_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_rewrite1(A) ) => ! [B] : ! [C] : ! [D] : ( ( r4_rewrite1(A,B,C) & r4_rewrite1(A,B,D) ) => C = D ) ) )).
fof(t53_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ( r4_rewrite2(A,B,C,D) => r4_rewrite2(A,C,B,D) ) ) ) ) )).
fof(t53_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(C))) => ! [G] : ( ( ~ v2_struct_0(G) & l1_rewrite3(G,F) ) => ! [H] : ( 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] : ( m1_subset_1(I,k8_afinsq_1(C)) => D != k1_flang_1(C,I,E) ) ) ) ) ) ) ) ) )).
fof(t53_rfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t53_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_comseq_2(B) => r1_xxreal_0(k1_funct_1(k3_rinfsup1(B),A),k2_rinfsup1(k4_rinfsup1(B))) ) ) ) )).
fof(t53_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t53_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t53_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_2(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t53_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v7_pre_topc(A) => k1_convex1(A,k2_pre_topc(A,B),k5_numbers) = k2_pre_topc(A,k1_convex1(A,B,k5_numbers)) ) ) ) )).
fof(t53_rlvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t53_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => r1_rlvect_2(A,k9_rlvect_2(A,k9_rlvect_2(A,B)),B) ) ) )).
fof(t53_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_rmod_2(E,A,B) => ( r2_hidden(D,k3_rmod_2(A,B,C,E)) <=> k3_rmod_2(A,B,C,E) = k3_rmod_2(A,B,D,E) ) ) ) ) ) ) )).
fof(t53_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t53_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( 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))) ) ) )).
fof(t53_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t53_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => r2_relset_1(k4_ordinal1,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)))) ) ) ) ) )).
fof(t53_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( 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),k5_numbers) | r1_xxreal_0(k1_rpr_1(A,D),k5_numbers) | r1_xxreal_0(k1_rpr_1(A,E),k5_numbers) | k2_rpr_1(A,B,C) = k7_xcmplx_0(k3_xcmplx_0(k2_rpr_1(A,C,B),k1_rpr_1(A,C)),k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k2_rpr_1(A,C,B),k1_rpr_1(A,C)),k3_xcmplx_0(k2_rpr_1(A,D,B),k1_rpr_1(A,D))),k3_xcmplx_0(k2_rpr_1(A,E,B),k1_rpr_1(A,E)))) ) ) ) ) ) ) ) )).
fof(t53_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( r1_struct_0(B,C) => r2_hidden(k1_rlvect_1(A,C,D),k3_rusub_1(A,C,B)) ) ) ) ) ) )).
fof(t53_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_2(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t53_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_rusub_5(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( B = k5_bhsp_2(A,C,D) => v4_pre_topc(B,k5_rusub_5(A)) ) ) ) ) ) )).
fof(t53_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => k11_rvsum_1(A,B,k5_numbers) = k5_finseq_2(k4_ordinal1,A,k5_numbers) ) ) )).
fof(t53_rvsum_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) ) ) )).
fof(t53_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_3(k4_scmfsa_2(k5_numbers),1)),B) & r1_tarski(C,A) & r1_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B) ) => ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(D,k8_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B)) => r8_pboole(u1_struct_0(k1_scmfsa_2),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B,D),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),B,D)) ) ) ) ) ) ) )).
fof(t53_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( 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(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_m(B)),E),D) ) ) ) ) ) ) ) )).
fof(t53_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_scmfsa_2(B) => A != B ) ) )).
fof(t53_scmpds_2,axiom,( ! [A] : ( ( 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] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( 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)),k5_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)),k5_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) ) ) ) ) ) ) )).
fof(t53_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( 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)) = k1_nat_1(k5_card_1(C),2) ) ) ) ) ) )).
fof(t53_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v5_scmyciel(A) ) => ! [B] : ! [C] : ( ( r2_hidden(B,k3_tarski(A)) & r2_hidden(C,k3_tarski(A)) ) => r2_hidden(k2_tarski(B,C),A) ) ) )).
fof(t53_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ r2_semi_af1(A,B,D,E,C) ) ) ) ) ) ) )).
fof(t53_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k56_valued_1(k4_ordinal1,k1_numbers,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,A)),k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k56_valued_1(k4_ordinal1,k1_numbers,B),k56_valued_1(k4_ordinal1,k1_numbers,A))) ) ) )).
fof(t53_seq_4,axiom,( r3_binop_1(k2_numbers,k6_complex1,k5_binop_2) )).
fof(t53_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v2_prob_1(B) => k1_kurato_0(A,k2_setlim_1(A,B)) = k3_prob_1(A,B) ) ) )).
fof(t53_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => k9_nat_1(k9_setfam_1(B),k2_setlim_1(B,k8_setlim_2(B,D,C)),A) = k7_subset_1(B,k9_nat_1(k9_setfam_1(B),k2_setlim_1(B,D),A),C) ) ) ) )).
fof(t53_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t53_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_scmfsa_2(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) ) => ( ( r2_hidden(k14_scmfsa_2(B,A,C),k2_relset_1(u1_compos_1(k1_scmfsa_2),D)) | r2_hidden(k15_scmfsa_2(B,A,C),k2_relset_1(u1_compos_1(k1_scmfsa_2),D)) ) => ( k5_sf_mastr(D) != A & k5_sf_mastr(D) != B ) ) ) ) ) ) )).
fof(t53_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t53_simplex0,axiom,( ! [A] : ! [B] : ( ( v1_matroid0(B) & m1_simplex0(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( v1_setfam_1(k9_xtuple_0(C)) & ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(D,k6_simplex0(B)) & ! [E] : ( 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) ) ) ) )).
fof(t53_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ~ r1_xxreal_0(k1_funct_1(k22_sin_cos,A),k5_numbers) ) )).
fof(t53_sin_cos3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k2_numbers) => k15_sin_cos(k4_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k7_complex1,A),B))) = k2_comseq_3(k6_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,B),k3_xcmplx_0(k7_complex1,k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,B))),A) ) ) )).
fof(t53_sin_cos6,axiom,( ! [A] : ( v1_int_1(A) => v5_valued_0(k5_relset_1(k1_numbers,k1_numbers,k16_sin_cos,k1_rcomp_1(k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A)),k2_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A))))) ) )).
fof(t53_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(1,B) ) => k2_xcmplx_0(k3_sin_cos7(A),k3_sin_cos7(B)) = k3_sin_cos7(k2_xcmplx_0(k3_xcmplx_0(A,B),k3_square_1(k3_xcmplx_0(k6_xcmplx_0(k1_square_1(A),1),k6_xcmplx_0(k1_square_1(B),1))))) ) ) ) )).
fof(t53_sin_cos9,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k1_sin_cos9,k1_rcomp_1(k4_xcmplx_0(1),1))) )).
fof(t53_sincos10,axiom,( k3_relat_1(k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(1,k3_square_1(2))),k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,4)))) = k1_partfun2(k1_numbers,k1_rcomp_1(1,k3_square_1(2))) )).
fof(t53_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t53_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t53_sprect_2,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(t53_sprect_3,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(t53_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t53_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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(k1_square_1(A),k1_square_1(B)),1) ) ) ) )).
fof(t53_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [E] : ( m2_subset_1(E,k16_substut1(A),k38_substut1(A)) => ! [F] : ( m1_substut1(F,A,k7_sublemma(A,E,B)) => ( v3_substut1(k7_sublemma(A,E,B),A) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t53_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))))) ) ) )).
fof(t53_tdlat_3,axiom,( ! [A] : ( ( ~ 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)) ) ) ) )).
fof(t53_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_tex_2(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) ) ) ) )).
fof(t53_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_tex_3(B,A) & m1_pre_topc(B,A) ) => ? [C] : ( ~ 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) ) ) ) )).
fof(t53_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_subset_1(k4_tex_4(A,B),k4_tex_4(A,C)) <=> ~ ( ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t53_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ( r2_hidden(F,u1_struct_0(C)) => k3_funct_2(u1_struct_0(A),u1_struct_0(B),D,F) = k1_funct_1(E,F) ) ) => r2_funct_2(u1_struct_0(C),u1_struct_0(B),k2_tmap_1(A,B,D,C),E) ) ) ) ) ) ) )).
fof(t53_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t53_topgen_1,axiom,( v2_tops_1(k3_numbers,k3_topmetr) & m1_subset_1(k3_numbers,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )).
fof(t53_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t53_topgen_5,axiom,( v7_pre_topc(k2_topgen_3) )).
fof(t53_topgrp_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_connsp_2(C,A,B) => m1_connsp_2(k1_group_2(A,C),A,k2_group_1(A,B)) ) ) ) )).
fof(t53_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v6_metric_1(B) & v8_metric_1(B) & v9_metric_1(B) & l1_metric_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( ~ r1_xxreal_0(k5_numbers,A) => k9_metric_1(B,C,A) = k1_xboole_0 ) ) ) ) )).
fof(t53_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t53_toprealc,axiom,( r2_funct_2(u1_struct_0(k2_borsuk_1(k15_euclid(k5_numbers),k15_euclid(k5_numbers))),u1_struct_0(k15_euclid(k5_numbers)),k15_toprealc(k5_numbers),k6_struct_0(k2_borsuk_1(k15_euclid(k5_numbers),k15_euclid(k5_numbers)),k15_euclid(k5_numbers),k4_struct_0(k15_euclid(k5_numbers)))) )).
fof(t53_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t53_tops_2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_struct_0(C) ) => ! [D] : ( ( 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] : ( ( 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))) ) ) ) ) ) ) )).
fof(t53_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t53_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t53_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => ( r2_hidden(B,k3_trees_1(A)) <=> ~ r2_hidden(k8_finseq_1(k4_ordinal1,B,k12_finseq_1(k4_ordinal1,k5_numbers)),A) ) ) ) )).
fof(t53_trees_3,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t53_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t53_twoscomp,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( 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)) ) ) ) )).
fof(t53_uproots,axiom,( ! [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) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & v1_uproots(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & v1_uproots(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r8_pboole(u1_struct_0(A),k7_uproots(A,k13_polynom3(A,B,C)),k11_pre_poly(u1_struct_0(A),k7_uproots(A,B),k7_uproots(A,C))) ) ) ) )).
fof(t53_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => r1_tarski(k61_valued_1(B,k3_finseq_1(A)),k7_finseq_1(A,B)) ) ) )).
fof(t53_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( ( 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)) ) ) ) ) )).
fof(t53_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t53_vectsp_5,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_5(D,A,B,C) => ! [E] : ( 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 ) ) ) ) ) )).
fof(t53_vfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( 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,k4_normsp_0(B,C,D),A)) & v3_funct_1(k2_partfun1(B,u1_struct_0(C),k5_vfunct_1(B,C,D),A)) ) ) ) ) ) )).
fof(t53_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( v3_funct_1(k2_partfun1(A,u1_struct_0(B),C,D)) => ( v3_funct_1(k2_partfun1(A,k1_numbers,k4_normsp_0(A,B,C),D)) & v3_funct_1(k2_partfun1(A,u1_struct_0(B),k5_vfunct_1(A,B,C),D)) ) ) ) ) ) )).
fof(t53_waybel21,axiom,( ! [A] : ( ( 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] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ( ! [C] : ( ( ~ 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) ) ) ) )).
fof(t53_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ( k1_relset_1(u1_struct_0(k1_yellow_1(k7_waybel_0(B))),k4_waybel23(A,B)) = k7_waybel_0(B) & m1_subset_1(k2_relset_1(u1_struct_0(k1_yellow_1(k7_waybel_0(A))),k4_waybel23(A,B)),k1_zfmisc_1(k7_waybel_0(A))) ) ) ) )).
fof(t53_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => r3_yellow20(k5_waybel34(A),k4_waybel34(A),k7_waybel34(A),k9_waybel34(A),k8_waybel34(A)) ) )).
fof(t53_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( D != k1_xboole_0 => r1_yellow_0(A,D) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(B)) ) => ~ ( r1_yellow_0(A,E) & D = k1_yellow_0(A,E) ) ) ) ) & ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t53_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t53_waybel_2,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t53_waybel_4,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_waybel_3(A,B,C) <=> ! [D] : ( ( ~ 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] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,D) & r1_waybel_3(A,B,E) ) ) ) ) ) ) ) ) )).
fof(t53_wellord1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ~ ( r1_tarski(A,k1_relat_1(B)) & v2_wellord1(B) & ~ r4_wellord1(B,k2_wellord1(B,A)) & ! [C] : ~ ( r2_hidden(C,k1_relat_1(B)) & r4_wellord1(k2_wellord1(B,k1_wellord1(B,C)),k2_wellord1(B,A)) ) ) ) )).
fof(t53_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : k4_xboole_0(A,k2_xboole_0(B,C)) = k3_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C)) )).
fof(t53_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k8_xboolean(A,k4_xboolean(A,B)) = k3_xboolean(k4_xboolean(A,B)) ) ) )).
fof(t53_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( k7_xcmplx_0(A,C) = k7_xcmplx_0(B,C) => ( C = k5_numbers | A = B ) ) ) ) ) )).
fof(t53_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(C,B) & r1_xxreal_0(k6_xcmplx_0(C,A),B) ) ) ) ) )).
fof(t53_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_tarski(k3_xxreal_1(C,D),k1_xxreal_1(A,B)) => ( r1_xxreal_0(D,C) | ( r1_xxreal_0(A,C) & r1_xxreal_0(D,B) ) ) ) ) ) ) ) )).
fof(t53_xxreal_2,axiom,( ! [A] : ( ( v2_membered(A) & ~ v1_xboole_0(A) ) => ( ~ ! [B] : ( m1_xxreal_2(B,A) => B = k1_xxreal_0 ) => v4_xxreal_2(A) ) ) )).
fof(t53_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ~ ( ~ ( C = k1_xxreal_0 & B = k1_xxreal_0 ) & ~ ( C = k2_xxreal_0 & B = k2_xxreal_0 ) & ~ r1_xxreal_0(k3_xxreal_3(C,B),A) & ~ ( A != k1_xxreal_0 & B != k1_xxreal_0 & C != k2_xxreal_0 & ~ r1_xxreal_0(C,k1_xxreal_3(A,B)) ) ) ) ) ) )).
fof(t53_yellow10,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(t53_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => v5_pre_topc(k1_yellow_9(A,B),B,A) ) ) )).
fof(t53_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v11_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v16_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,B,C) & m2_functor0(E,B,C) ) => ! [F] : ( ( ~ v2_struct_0(F) & v2_altcat_1(F) & v3_altcat_2(F,A) & m1_altcat_2(F,A) ) => ! [G] : ( ( ~ v2_struct_0(G) & v2_altcat_1(G) & v3_altcat_2(G,B) & m1_altcat_2(G,B) ) => ! [H] : ( ( ~ 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) ) ) ) ) ) ) ) ) ) )).
fof(t53_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_yellow_0(A,B) ) => v3_lattice3(A) ) ) )).
fof(t53_yellow_2,axiom,( ! [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] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t53_yellow_4,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) ) )).
fof(t53_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t53_yellow_9,axiom,( ! [A] : ( l1_pre_topc(A) => ? [B] : ( 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)))) ) ) )).
fof(t53_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ( r1_zf_lang(A,k7_zf_lang(B,C)) <=> ( A = B | A = C ) ) ) ) ) )).
fof(t53_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r2_hidden(A,k29_zf_lang(B)) => r1_tarski(k29_zf_lang(A),k29_zf_lang(B)) ) ) ) )).
fof(t53_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(A,C) => ( ( r2_hidden(B,C) & A != B ) | k3_xboole_0(k2_tarski(A,B),C) = k1_tarski(A) ) ) )).
fof(t53_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => m1_zmodul01(k3_zmodul01(B),A) ) ) )).
fof(t53_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( v1_int_1(B) => ! [C] : ( m1_zmodul02(C,A) => k21_zmodul02(A,k23_zmodul02(A,B,C)) = k1_zmodul01(A,k21_zmodul02(A,C),B) ) ) ) )).
fof(t54_abcmiz_0,axiom,( ! [A] : ( l2_abcmiz_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t54_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_abcmiz_1(B,A) & m1_subset_1(B,u4_struct_0(A)) ) => ! [C] : ( m1_abcmiz_1(C,A,k13_abcmiz_1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t54_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [C] : ( 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) ) ) ) ) )).
fof(t54_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r1_aff_1(A,F,D,E) & r2_analoaf(A,B,D,C,E) & C = F ) => ( r1_aff_1(A,F,B,D) | E = F ) ) ) ) ) ) ) ) )).
fof(t54_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( r2_analoaf(A,B,D,E,G) & r2_analoaf(A,C,D,F,G) ) ) ) ) ) ) ) ) ) )).
fof(t54_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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) ) ) )).
fof(t54_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_valued_0(A) & v1_finset_1(A) ) => ! [B] : ( ( 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)) = k2_xcmplx_0(k7_afinsq_2(A),k7_afinsq_2(B)) ) ) )).
fof(t54_algspec1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v11_struct_0(B) & v1_instalg1(B) & l1_msualg_1(B) ) => ( r1_circcomb(A,B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t54_altcat_4,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t54_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t54_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(k5_analort(A,F,G))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k5_analort(A,F,G))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k5_analort(A,F,G))) => ! [K] : ( m1_subset_1(K,u1_struct_0(k5_analort(A,F,G))) => ( ( B = H & D = I & C = J & E = K ) => ( r2_analoaf(k5_analort(A,F,G),H,I,J,K) <=> r1_analort(A,F,G,B,D,C,E) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t54_aofa_000,axiom,( k3_finseq_1(k19_aofa_000) = 4 & k4_finseq_1(k19_aofa_000) = k2_finseq_1(4) & k1_recdef_1(k19_aofa_000,1) = k5_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 )).
fof(t54_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v19_aofa_a00(E,A) & m1_subset_1(E,u1_struct_0(A)) ) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,C),E)) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),E)) => ! [H] : ( m2_pboole(H,u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,D)) => k15_aofa_a00(A,B,C,D,E,k30_aofa_a00(A,C,E,F,G),H) = k30_aofa_a00(A,D,E,k15_aofa_a00(A,B,C,D,E,F,H),k15_aofa_a00(A,B,C,D,E,G,H)) ) ) ) ) ) ) ) ) )).
fof(t54_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m3_aofa_i00(E,A,B,C,D) => ! [F] : ( m1_subset_1(F,B) => ! [G] : ( ( v1_aofa_i00(G,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),F,k5_numbers)) & m1_aofa_000(G,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),F,k5_numbers)) ) => ! [H] : ( 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,k5_numbers),H,G) => ! [I] : ( m1_aofa_i00(I,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),G) => ! [J] : ( m1_aofa_i00(J,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),G) => ( ! [K] : ( 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] : ( ( v1_relat_1(K) & v1_funct_1(K) ) => ~ ( k1_funct_1(K,F) = k5_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,k5_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,k5_numbers),G,I,1)),G) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t54_armstrng,axiom,( ! [A] : ! [B] : ( 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) ) ) ) ) )).
fof(t54_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ~ ( A != k11_arytm_3 & ! [B] : ( m1_subset_1(B,k5_arytm_3) => k10_arytm_3(A,B) != 1 ) ) ) )).
fof(t54_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ r1_xxreal_0(k2_xcmplx_0(k6_xcmplx_0(k1_square_1(A),A),1),k5_numbers) ) )).
fof(t54_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_bcialg_1(A,k2_bcialg_1(A,B)) = B ) ) ) )).
fof(t54_bcialg_5,axiom,( ! [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) ) => ( m1_bcialg_5(A,k5_numbers,1,k5_numbers,k5_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) ) ) ) )).
fof(t54_bcialg_6,axiom,( ! [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] : ( m1_bcialg_1(B,A) => ! [C] : ( ( v12_bcialg_1(C,A) & m2_bcialg_1(C,A) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t54_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( m4_bciideal(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t54_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k5_normsp_1(A,B,1),B) ) ) )).
fof(t54_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => r1_tarski(k4_bhsp_2(A,B,C),k5_bhsp_2(A,B,C)) ) ) ) )).
fof(t54_bhsp_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ! [D] : ( v7_ordinal1(D) => k3_bhsp_4(B,k5_bhsp_4(B,C,A),k1_nat_1(D,1)) = k5_algstr_0(B,k1_normsp_1(B,k5_bhsp_4(B,k1_bhsp_4(B,C),A),k1_nat_1(D,1)),k3_bhsp_4(B,k5_bhsp_4(B,k1_bhsp_4(B,C),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k1_valued_0(k1_numbers,A,1),A)),D)) ) ) ) ) )).
fof(t54_bilinear,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t54_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(t54_borsuk_4,axiom,( ! [A] : ( ( ~ 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(k5_numbers,1)) & ! [B] : ( ( ~ 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(k5_numbers,1)) & k3_seq_4(A) = k3_seq_4(B) & k2_seq_4(A) = k2_seq_4(B) ) ) ) ) )).
fof(t54_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t54_borsuk_6,axiom,( k7_borsuk_6 = a_0_13_borsuk_6 )).
fof(t54_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t54_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t54_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_eqrel_1(I,A) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t54_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t54_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k9_xboolean(A,k5_xboolean(B,C)) = k3_xboolean(k5_xboolean(k5_xboolean(A,B),C)) ) ) ) )).
fof(t54_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t54_card_1,axiom,( 8 = k6_enumset1(k5_ordinal1,1,2,3,4,5,6,7) )).
fof(t54_card_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : r1_xxreal_0(k5_card_1(k5_enumset1(A,B,C,D,E,F,G)),7) )).
fof(t54_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( k4_card_3(A) != k1_xboole_0 => ( r2_hidden(B,k8_card_3(A)) <=> ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & r2_hidden(C,k4_card_3(A)) & r1_tarski(B,C) ) ) ) ) ) )).
fof(t54_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k4_cat_1(A,B) = k4_cat_1(A,C) => B = C ) ) ) ) )).
fof(t54_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u4_struct_0(C)) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t54_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_cat_1(C,A,k19_cat_4(A),B) => ! [D] : ( m1_cat_1(D,A,k19_cat_4(A),B) => C = D ) ) ) ) )).
fof(t54_cfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t54_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( 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)) ) ) ) )).
fof(t54_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k6_glib_000(A)) => ~ ( r2_hidden(C,k13_glib_001(A,B)) & ! [D] : ( ( v7_ordinal1(D) & ~ v1_abian(D) ) => ! [E] : ( ( 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] : ~ ( r2_hidden(F,k14_glib_001(A,B)) & r1_glib_000(A,k1_funct_1(B,D),k1_funct_1(B,E),F) ) ) ) ) ) ) ) ) ) ) )).
fof(t54_circcomb,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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] : ( 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 ) ) ) ) ) ) )).
fof(t54_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v4_msualg_1(E,A) & v4_msafree2(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( ( v4_msualg_1(F,B) & v4_msafree2(F,B) & l3_msualg_1(F,B) ) => ( r5_circtrm1(A,B,C,D,E,F) => ! [G] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(A,E))) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t54_classes1,axiom,( ! [A] : ! [B] : ( ( ! [C] : ( ( r1_tarski(A,C) & v1_ordinal1(C) ) => r1_tarski(B,C) ) & r1_tarski(A,B) & v1_ordinal1(B) ) => k5_classes1(A) = B ) )).
fof(t54_classes2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) ) => r3_xboole_0(A,B) ) ) )).
fof(t54_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( B != k1_xboole_0 & v6_clvect_1(B,A) & ! [C] : ( ( v1_clvect_1(C) & m1_clvect_1(C,A) ) => B != u1_struct_0(C) ) ) ) ) )).
fof(t54_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => r1_tarski(k4_clvect_2(A,B,C),k5_clvect_2(A,B,C)) ) ) ) )).
fof(t54_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [D] : ( v7_ordinal1(D) => k2_clvect_3(A,k6_clvect_3(A,B,C),k1_nat_1(D,1)) = k5_algstr_0(A,k1_normsp_0(A,k6_clvect_3(A,k1_bhsp_4(A,B),C),k1_nat_1(D,1)),k2_clvect_3(A,k6_clvect_3(A,k1_bhsp_4(A,B),k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k1_valued_0(k2_numbers,C,1),C)),D)) ) ) ) ) )).
fof(t54_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( ( 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] : ! [E] : ( r2_hidden(k2_tarski(D,E),A) => ! [F] : ( ( 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 ) ) ) ) ) )).
fof(t54_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => r1_xxreal_0(k3_complex1(A),k9_complex1(A)) ) )).
fof(t54_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xreal_0(B) => ( k3_complex1(k2_complex2(A,B)) = k6_xcmplx_0(k3_xcmplx_0(k3_complex1(A),k19_sin_cos(B)),k3_xcmplx_0(k4_complex1(A),k17_sin_cos(B))) & k4_complex1(k2_complex2(A,B)) = k2_xcmplx_0(k3_xcmplx_0(k3_complex1(A),k17_sin_cos(B)),k3_xcmplx_0(k4_complex1(A),k19_sin_cos(B))) ) ) ) )).
fof(t54_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( 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)) ) ) )).
fof(t54_complsp2,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ( k6_complsp2(k10_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(k10_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))) ) ) ) )).
fof(t54_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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 ) ) )).
fof(t54_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( v6_compos_0(D,u1_compos_1(A)) & m1_subset_1(D,u1_compos_1(A)) ) => ! [E] : ( ( v6_compos_0(E,u1_compos_1(A)) & m1_subset_1(E,u1_compos_1(A)) ) => ! [F] : ( ( v6_compos_0(F,u1_compos_1(A)) & m1_subset_1(F,u1_compos_1(A)) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t54_comptrig,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( v7_ordinal1(B) => ( ~ ( A = k5_numbers & B = k5_numbers ) => k1_newton(A,B) = k2_xcmplx_0(k3_xcmplx_0(k1_newton(k9_complex1(A),B),k19_sin_cos(k3_xcmplx_0(B,k1_comptrig(A)))),k3_xcmplx_0(k3_xcmplx_0(k1_newton(k9_complex1(A),B),k17_sin_cos(k3_xcmplx_0(B,k1_comptrig(A)))),k7_complex1)) ) ) ) )).
fof(t54_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k3_finseq_2(k4_ordinal1)) & v1_funct_1(C) & v4_valued_0(C) & v2_margrel1(C) ) => ( v1_xboole_0(B) => v1_xboole_0(k7_comput_1(B,C,A)) ) ) ) ) )).
fof(t54_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) = k2_xcmplx_0(k11_comseq_3(A),k11_comseq_3(B)) ) ) ) ) )).
fof(t54_convex4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t54_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( m2_subset_1(E,k2_qc_lang1(A),k3_qc_lang1(A)) => ( ( r2_hidden(k13_cqc_lang(A,C,E),k3_cqc_lang(A)) & r3_cqc_the1(A,B,k13_cqc_lang(A,C,D)) ) => ( r2_hidden(D,k24_qc_lang1(A,C)) | r3_cqc_the1(A,B,k13_cqc_lang(A,C,E)) ) ) ) ) ) ) ) )).
fof(t54_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) )).
fof(t54_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t54_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ~ ( B != C & r1_xxreal_0(k15_csspace(A,B,C),k5_numbers) ) & ~ ( ~ r1_xxreal_0(k15_csspace(A,B,C),k5_numbers) & B = C ) ) ) ) ) )).
fof(t54_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k3_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),A),B) = k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k17_sin_cos(k3_xcmplx_0(2,k2_xcmplx_0(B,A))),k17_sin_cos(k3_xcmplx_0(2,B)))) ) ) )).
fof(t54_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => 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),k16_sin_cos),A),B) = k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,k19_sin_cos(k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(2,B),A),2))),k17_sin_cos(k7_xcmplx_0(A,2))),k3_xcmplx_0(k19_sin_cos(k7_xcmplx_0(k3_xcmplx_0(3,k2_xcmplx_0(k3_xcmplx_0(2,B),A)),2)),k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(3,A),2))))) ) ) )).
fof(t54_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(C,A),1),B) = k6_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(C,A),k5_numbers),k2_xcmplx_0(B,k7_xcmplx_0(A,2))),k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k8_diff_1(C,A),k5_numbers),k6_xcmplx_0(B,k7_xcmplx_0(A,2)))) ) ) ) )).
fof(t54_ec_pf_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v5_relat_1(C,k8_eqrel_1(A,B)) & v1_funct_1(C) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t54_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k9_int_3(A))) => ! [G] : ( 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] : ( 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] : ( 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 = k5_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)))) ) ) ) ) ) ) ) ) ) ) )).
fof(t54_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t54_entropy1,axiom,( ! [A] : ( ( v1_matrix_0(A) & v2_matrprob(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( B = k5_entropy1(A) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & k1_matrix_0(B) = k1_matrix_0(A) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k4_tarski(C,D),k2_matrix_0(B)) => k3_matrix_0(k1_numbers,B,C,D) = k3_xcmplx_0(k3_matrix_0(k1_numbers,A,C,D),k3_power(2,k3_matrix_0(k1_numbers,A,C,D))) ) ) ) ) ) ) ) )).
fof(t54_enumset1,axiom,( ! [A] : k5_enumset1(A,A,A,A,A,A,A) = k1_tarski(A) )).
fof(t54_eqrel_1,axiom,( ! [A] : ! [B] : ( 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)) ) )).
fof(t54_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t54_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) )).
fof(t54_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => k22_rvsum_1(A,B) = k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(A,1),k1_funct_1(B,1)),k3_xcmplx_0(k1_funct_1(A,2),k1_funct_1(B,2))),k3_xcmplx_0(k1_funct_1(A,3),k1_funct_1(B,3))) ) ) )).
fof(t54_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ~ ( ~ r2_hidden(B,C) & v1_euclid_4(C,A) & ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t54_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( ( 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,k9_funct_7(E,A,B))) ) ) ) ) ) )).
fof(t54_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ( 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) ) ) ) )).
fof(t54_fcont_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(C,D) ) => r1_xxreal_0(k1_funct_1(k1_fcont_1(A,B),D),k1_funct_1(k1_fcont_1(A,B),C)) ) ) ) ) ) )).
fof(t54_fdiff_11,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(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),k22_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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),k22_sin_cos),A),B) = k7_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(2,k2_xcmplx_0(1,k1_square_1(B))),k1_funct_1(k1_sin_cos9,B)),k1_funct_1(k2_sin_cos9,B)),k1_funct_1(k22_sin_cos,B)) ) ) ) ) ) )).
fof(t54_fdiff_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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)),k7_xcmplx_0(1,A)))) => ( r1_xxreal_0(A,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(A)),k7_xcmplx_0(1,A)),B) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => k1_funct_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)),k7_xcmplx_0(1,A)),B),C) = k3_xcmplx_0(k3_prepower(k1_funct_1(k16_sin_cos,C),k6_xcmplx_0(A,1)),k1_funct_1(k18_sin_cos,C)) ) ) ) ) ) ) ) )).
fof(t54_fib_num2,axiom,( k15_finseq_1(k5_relat_1(k2_fib_num2,k6_domain_1(k4_ordinal1,2))) = k12_finseq_1(k4_ordinal1,1) )).
fof(t54_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t54_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t54_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t54_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => r2_wellord2(k2_finseq_1(A),A) ) )).
fof(t54_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) )).
fof(t54_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k4_ordinal1) & k9_subset_1(k4_ordinal1,B,k1_relset_1(k4_ordinal1,A)) = k2_finseq_1(C) ) ) ) )).
fof(t54_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t54_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t54_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t54_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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,D,C) & r2_funct_2(A,A,E,k10_funcop_1(A,A,D,B,k6_partfun1(A))) ) => r7_binop_1(A,E,C) ) ) ) ) ) ) )).
fof(t54_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r3_fintopo6(A,B,C,D,E) => v2_funct_1(B) ) ) ) ) ) ) )).
fof(t54_flang_1,axiom,( ! [A] : ! [B] : ( 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)) ) ) ) )).
fof(t54_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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))) ) ) ) ) )).
fof(t54_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( 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))) ) ) )).
fof(t54_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ( ? [D] : ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) & B = D & v5_relat_1(D,k3_finseq_2(A)) ) => v5_relat_1(k1_funct_1(k9_fomodel0(C),B),A) ) ) )).
fof(t54_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( ~ v2_struct_0(D) & l2_fsm_1(D,A,B) ) => ! [E] : ( ( ~ v2_struct_0(E) & l2_fsm_1(E,A,B) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(E)) => ! [G] : ( ( ~ v2_struct_0(G) & v8_struct_0(G) & l2_fsm_1(G,A,B) ) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t54_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,B,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [F] : ( m1_subset_1(F,A) => ( ! [G] : ( m1_subset_1(G,B) => k3_funct_2(B,A,E,G) = k5_binop_1(A,C,F,k3_funct_2(B,A,D,G)) ) => r2_funct_2(B,A,E,k10_funcop_1(A,B,C,F,D)) ) ) ) ) ) ) ) )).
fof(t54_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(B,k9_xtuple_0(k6_relat_1(A,C))) => k1_funct_1(k6_relat_1(A,C),B) = k1_funct_1(C,B) ) ) )).
fof(t54_funct_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t54_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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 ) ) ) ) ) ) )).
fof(t54_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ! [F] : ( ( 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)) ) ) ) ) )).
fof(t54_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( k1_card_1(A) = k1_card_1(C) & k1_card_1(B) = k1_card_1(D) ) => k1_card_1(k1_funct_2(A,B)) = k1_card_1(k1_funct_2(C,D)) ) )).
fof(t54_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => k9_xtuple_0(k1_funct_6(A)) = k9_xtuple_0(A) ) )).
fof(t54_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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) ) => k3_funct_7(A,k11_finseq_1(B,C,D)) = k3_relat_1(B,k3_relat_1(C,D)) ) ) ) ) )).
fof(t54_funct_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t54_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ 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)) ) ) ) )).
fof(t54_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k7_fvaluat1(A,B))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t54_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t54_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( ( ~ v1_xboole_0(G) & v1_relat_1(G) & v2_relat_1(G) & v1_funct_1(G) & v1_finseq_1(G) ) => ! [H] : ( m1_genealg1(H,G) => ! [I] : ( m1_genealg1(I,G) => ( k12_genealg1(G,H,I,k5_numbers,B,C,D,E,F) = k11_genealg1(G,I,H,B,C,D,E,F) & k12_genealg1(G,H,I,A,k5_numbers,C,D,E,F) = k11_genealg1(G,I,H,A,C,D,E,F) & k12_genealg1(G,H,I,A,B,k5_numbers,D,E,F) = k11_genealg1(G,I,H,A,B,D,E,F) & k12_genealg1(G,H,I,A,B,C,k5_numbers,E,F) = k11_genealg1(G,I,H,A,B,C,E,F) & k12_genealg1(G,H,I,A,B,C,D,k5_numbers,F) = k11_genealg1(G,I,H,A,B,C,D,F) & k12_genealg1(G,H,I,A,B,C,D,E,k5_numbers) = k11_genealg1(G,I,H,A,B,C,D,E) ) ) ) ) ) ) ) ) ) ) )).
fof(t54_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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] : ( 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)) ) ) )).
fof(t54_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ! [C] : ( 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) ) ) )).
fof(t54_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( ( 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(k1_nat_1(k3_finseq_1(B),C),D) ) ) ) ) ) )).
fof(t54_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & v3_glib_003(A) ) => ! [B] : ! [C] : ( 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))) = k1_nat_1(k5_card_1(k14_glib_003(A)),1) ) ) ) )).
fof(t54_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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_nat_1(A,1),k3_finseq_1(k2_goboard2(C))) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(k2_goboard2(C))) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1))),k3_topreal1(2,C)) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1))),k3_topreal1(2,C)) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,1) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1)) & ( ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,2) = k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1)) ) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,2) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k7_nat_d(k3_finseq_1(C),1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,B) ) ) ) & ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(1,D) & ~ r1_xxreal_0(k3_finseq_1(C),k1_nat_1(D,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_nat_1(D,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1)) & ( ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,D) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,B) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_nat_1(D,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1)) ) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,D) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_nat_1(D,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,B) ) ) ) ) ) ) ) ) )).
fof(t54_graph_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t54_graph_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v6_graph_1(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_2(D,u4_struct_0(B),k12_graph_3(B,C,A)) => ! [E] : ( v1_finset_1(E) => ( E = u4_struct_0(B) => ( k7_graph_3(B,C,A) = k5_numbers | r1_xxreal_0(k3_finseq_1(D),k5_card_1(E)) ) ) ) ) ) ) )).
fof(t54_graph_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m2_finseq_1(C,u4_struct_0(B)) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t54_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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),k7_polynom1(A,C,k11_polynom1(A,C,k6_termord(A,B,C,D),E),k11_polynom1(A,C,k6_termord(A,B,C,E),D))) ) ) ) ) ) ) )).
fof(t54_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => r1_tarski(k8_group_2(A,C),k4_group_11(A,C,B)) ) ) ) )).
fof(t54_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => m1_group_2(A,A) ) )).
fof(t54_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t54_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t54_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t54_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( 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 ) ) ) ) ) )).
fof(t54_group_9,axiom,( ! [A] : ! [B] : ( ( ~ 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)))) ) )).
fof(t54_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( 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)) ) ) )).
fof(t54_hfdiff_1,axiom,( ! [A] : ( ( 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,k18_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,k18_sin_cos),A),k4_xcmplx_0(2)))) ) )).
fof(t54_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => k7_ideal_1(A,k2_struct_0(A)) = u1_struct_0(A) ) )).
fof(t54_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ? [C] : ( m1_subset_1(C,u2_incsp_1(A)) & ! [D] : ( m1_subset_1(D,u4_incsp_1(A)) => ~ ( r3_incsp_1(A,B,D) & r3_incsp_1(A,C,D) ) ) ) ) ) )).
fof(t54_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,1) & r1_xxreal_0(A,k4_int_1(A,B)) ) ) ) )).
fof(t54_int_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t54_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(A,B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k2_xcmplx_0(1,k1_funct_1(k16_sin_cos,D)) != k5_numbers & k6_xcmplx_0(1,k1_funct_1(k16_sin_cos,D)) != k5_numbers & k1_funct_1(C,D) = k7_xcmplx_0(k1_funct_1(k16_sin_cos,D),k2_xcmplx_0(1,k1_funct_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),k26_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) = k6_xcmplx_0(k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k26_sin_cos),k1_fdiff_9),k2_seq_4(A)),k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k26_sin_cos),k1_fdiff_9),k3_seq_4(A))) ) ) ) ) )).
fof(t54_integr13,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k6_xcmplx_0(k7_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k1_square_1(B)),k7_xcmplx_0(1,k3_xcmplx_0(B,k2_xcmplx_0(1,k1_square_1(B))))) ) ) ) ) ) )).
fof(t54_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k3_xcmplx_0(k1_funct_1(k18_sin_cos,k1_funct_1(k16_sin_cos,D)),k1_funct_1(k18_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) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k16_sin_cos),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k16_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t54_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( ( 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] : ( v1_xreal_0(H) => ( r2_hidden(H,k3_integra5(k3_xxreal_0(D,E),k4_xxreal_0(D,E))) => r1_xxreal_0(k2_normsp_0(k4_real_ns1(A),k7_partfun1(u1_struct_0(k4_real_ns1(A)),G,H)),F) ) ) ) => r1_xxreal_0(k2_normsp_0(k4_real_ns1(A),k6_integr18(k4_real_ns1(A),G,D,E)),k3_xcmplx_0(k3_xcmplx_0(A,F),k9_complex1(k6_xcmplx_0(E,D)))) ) ) ) ) ) ) ) ) )).
fof(t54_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [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))) ) => ! [D] : ( ( 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(k2_xcmplx_0(k7_integra1(A,C,B),k7_integra1(A,D,B)),k7_integra1(A,k3_valued_1(A,k1_numbers,k1_numbers,C,D),B)) ) ) ) ) ) )).
fof(t54_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,1) => k2_integra5(A,k22_sin_cos) = k6_xcmplx_0(k4_power,1) ) ) )).
fof(t54_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( 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] : ( v1_xreal_0(G) => ( r2_hidden(G,F) => ( k1_funct_1(D,G) = k2_xcmplx_0(A,G) & ~ r1_xxreal_0(k1_funct_1(D,G),k5_numbers) ) ) ) & k1_relset_1(k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_valued_1(k1_numbers,k1_numbers,C,k3_xcmplx_0(2,A)),k1_partfun2(k1_numbers,F))) = F & F = k1_relset_1(k1_numbers,E) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,F) => k1_funct_1(E,G) = k7_xcmplx_0(k6_xcmplx_0(A,G),k2_xcmplx_0(A,G)) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,E,B)) ) => k2_integra5(B,E) = k6_xcmplx_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_valued_1(k1_numbers,k1_numbers,C,k3_xcmplx_0(2,A)),k1_partfun2(k1_numbers,F)),k2_seq_4(B)),k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_valued_1(k1_numbers,k1_numbers,C,k3_xcmplx_0(2,A)),k1_partfun2(k1_numbers,F)),k3_seq_4(B))) ) ) ) ) ) ) ) )).
fof(t54_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_interva1(B,A) ) => r2_hidden(k1_xboole_0,k9_interva1(A,B,B)) ) ) )).
fof(t54_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => r2_hidden(k3_intpro_1(k5_intpro_1(A,A),A),k8_intpro_1) ) )).
fof(t54_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( 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] : ( 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) = k3_xcmplx_0(k12_euclid(D),k3_square_1(k6_xcmplx_0(1,k1_square_1(k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k17_euclid(D),k12_euclid(D)),A),k6_xcmplx_0(1,A)))))) ) ) & ! [D] : ( 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(k5_numbers,k18_euclid(D)) & r1_xxreal_0(A,k7_xcmplx_0(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) ) ) ) ) ) )).
fof(t54_jgraph_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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] : ( 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(k7_xcmplx_0(2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(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)) = k4_xcmplx_0(1) ) ) ) ) ) ) ) ) ) )).
fof(t54_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(C,B) & r1_xboole_0(k7_topreal1(C),k3_topreal1(2,k2_jordan9(B,A))) ) ) ) ) )).
fof(t54_jordan1g,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(B,k5_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,k2_jordan9(A,B))),k8_pscomp_1(k3_topreal1(2,k2_jordan9(A,B)))),2)),k18_pscomp_1(k3_topreal1(2,k2_jordan9(A,B))),k22_pscomp_1(k3_topreal1(2,k2_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,k2_jordan9(A,B))),k8_pscomp_1(k3_topreal1(2,k2_jordan9(A,B)))),2)),k22_pscomp_1(k3_topreal1(2,k2_jordan9(A,B))),k18_pscomp_1(k3_topreal1(2,k2_jordan9(A,B)))))) ) ) ) )).
fof(t54_jordan1h,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( 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] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(k4_tarski(k1_nat_1(E,1),D),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k7_nat_d(k3_finseq_1(C),1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k1_nat_1(E,1),D) & r2_hidden(k4_tarski(E,D),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k3_finseq_1(C)) = k3_matrix_0(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_0(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) )).
fof(t54_jordan1j,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t54_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( C = a_2_3_jordan2c(A,B) => v1_convex1(C,k15_euclid(A)) ) ) ) ) )).
fof(t54_jordan4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t54_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t54_kurato_1,axiom,( 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)))) )).
fof(t54_lattice2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k5_finsub_1(A)) => ! [C] : ( ( ~ v2_struct_0(C) & v10_lattices(C) & v13_lattices(C) & l3_lattices(C) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(C)) => ( ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t54_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & v6_chord(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k6_glib_000(A),k4_ordinal1))) ) => ( ( v5_lexbfs(B,A) & k1_relset_1(k6_glib_000(A),B) = k6_glib_000(A) ) => ! [C] : ( m3_chord(C,A) => ( k2_funct_1(C) = B => v7_chord(C,A) ) ) ) ) ) )).
fof(t54_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v4_limfunc1(A) & ! [C] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ~ 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)) ) ) ) ) )).
fof(t54_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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) = k2_xcmplx_0(k2_limfunc2(B,A),k2_limfunc2(C,A)) ) ) ) ) ) )).
fof(t54_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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) ) ) ) ) )).
fof(t54_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => k1_mesfunc6(A,B,C,k56_valued_1(A,k1_numbers,k8_lpspace1(A,k5_numbers))) = k5_numbers ) ) ) )).
fof(t54_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( ( v2_xxreal_0(G) & v1_xreal_0(G) ) => ! [H] : ( m1_subset_1(H,u1_struct_0(k12_lpspace2(A,B,C,G))) => ! [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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t54_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_hilbert1)) => ( r8_ltlaxio1(B,A) => r8_ltlaxio1(B,k6_ltlaxio1(A)) ) ) ) )).
fof(t54_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_hilbert1)) => ( ( r8_ltlaxio1(D,k3_hilbert1(A,B)) & r8_ltlaxio1(D,k3_hilbert1(A,C)) & r8_ltlaxio1(D,k3_hilbert1(C,A)) ) => r8_ltlaxio1(D,k3_hilbert1(C,B)) ) ) ) ) ) )).
fof(t54_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k4_mathmorp(A,B,D),k4_mathmorp(A,k4_subset_1(u1_struct_0(A),B,C),D)) ) ) ) ) )).
fof(t54_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,k1_numbers,A,A) & m2_finseq_1(E,k3_finseq_2(k1_numbers)) ) => ( ( r1_matrix10(B,C) & r2_matrix10(D,E) ) => r1_matrix10(k5_matrix10(A,B,E),k5_matrix10(A,C,D)) ) ) ) ) ) ) )).
fof(t54_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ~ r2_hidden(C,k3_matrix_2(A)) => k12_matrix_3(A,B,k4_matrix11(A,A,u1_struct_0(B),C,D)) = k4_struct_0(B) ) ) ) ) ) )).
fof(t54_matrix13,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & v1_setfam_1(B) & m1_subset_1(B,k1_zfmisc_1(k4_ordinal1)) ) => ( r1_tarski(A,B) => k14_finseq_1(A) = k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,k4_ordinal1,k14_finseq_1(k8_relat_1(k5_matrix13(B),A)),k5_matrix13(B)) ) ) )).
fof(t54_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ~ ( k4_matrix_3(B,D,C) = k3_matrix_1(B,A) & ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => k4_matrix_3(B,C,E) != k3_matrix_1(B,A) ) ) ) ) ) ) )).
fof(t54_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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(C,k5_numbers) & ~ r1_xxreal_0(A,k5_numbers) & k4_matrix15(D,k1_matrix_3(D,C,A),k1_matrix_3(D,C,B)) != a_3_1_matrix15(A,B,D) ) ) ) ) ) )).
fof(t54_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [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] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(F),D,D) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(F))) ) => ( ( v5_matrix16(G,F) & r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k2_finseq_1(D),k2_finseq_1(D))) & C = k2_xcmplx_0(A,1) & E = k2_xcmplx_0(B,1) ) => ( r1_xxreal_0(D,A) | r1_xxreal_0(D,B) | k3_matrix_0(u1_struct_0(F),G,C,E) = k3_matrix_0(u1_struct_0(F),G,A,B) ) ) ) ) ) ) ) ) ) )).
fof(t54_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ( ~ r1_xxreal_0(k1_matrix_0(B),k5_numbers) => ( k3_finseq_1(k4_matrix_0(A,B)) = k1_matrix_0(B) & k1_matrix_0(k4_matrix_0(A,B)) = k3_finseq_1(B) ) ) ) ) )).
fof(t54_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) & k1_matrix_0(C) = k1_matrix_0(D) & k1_matrix_4(A,D,B) = k3_matrix_3(A,D,k2_matrix_3(A,C)) ) => B = C ) ) ) ) ) )).
fof(t54_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r1_matrix_6(A,B,C,D) => r1_matrix_6(A,B,k4_matrix_3(B,C,C),k4_matrix_3(B,D,D)) ) ) ) ) ) )).
fof(t54_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => k1_matrix_8(A,B,k3_matrix_3(B,k3_matrix_3(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)) ) ) ) ) ) )).
fof(t54_matrix_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( ? [D] : ( m1_subset_1(D,k4_ordinal1) & r2_hidden(D,k2_finseq_1(A)) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k2_finseq_1(A)) => k1_funct_1(k8_matrix_0(u1_struct_0(B),C,D),E) = k4_struct_0(B) ) ) ) => k2_matrix_9(A,B,C) = k4_struct_0(B) ) ) ) ) )).
fof(t54_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ( ~ r1_xxreal_0(k1_matrix_0(A),k5_numbers) => k1_matrixc1(k4_matrix_0(k2_numbers,A)) = k4_matrix_0(k2_numbers,k1_matrixc1(A)) ) ) )).
fof(t54_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( k3_finseq_1(A) = k3_finseq_1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(A)) ) => k8_matrix_0(k1_numbers,k3_matrixr1(A,B),C) = k4_rvsum_1(k8_matrix_0(k1_numbers,A,C),k8_matrix_0(k1_numbers,B,C)) ) ) ) ) ) )).
fof(t54_matrixr2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(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_0(B) = k1_matrix_0(C) ) => ( r1_xxreal_0(k3_finseq_1(B),k5_numbers) | k12_matrixr1(k5_matrixr1(B,C),A) = k8_rvsum_1(k12_matrixr1(B,A),k12_matrixr1(C,A)) ) ) ) ) ) )).
fof(t54_matrprob,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ( r1_xxreal_0(1,k3_finseq_1(B)) & r1_xxreal_0(1,k1_matrix_0(B)) ) ) ) )).
fof(t54_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ~ ( r2_hidden(A,k3_zfmisc_1(B,C,D)) & ! [E] : ! [F] : ! [G] : ~ ( r2_hidden(E,B) & r2_hidden(F,C) & r2_hidden(G,D) & A = k3_xtuple_0(E,F,G) ) ) )).
fof(t54_measure6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( r2_hidden(A,B) <=> r2_hidden(k7_xcmplx_0(1,A),k4_measure6(B)) ) ) ) )).
fof(t54_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => k10_member_1(A,B) = a_2_2_member_1(A,B) ) ) )).
fof(t54_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t54_mesfunc5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => r1_xxreal_0(k9_nat_1(k6_numbers,A,B),k9_nat_1(k6_numbers,A,C)) ) ) ) => ( v10_mesfunc5(A) & k2_mesfunc5(A) = k8_supinf_2(k17_supinf_2(A)) ) ) ) )).
fof(t54_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( ! [C] : ( r2_hidden(C,k1_relset_1(A,B)) => r1_xxreal_0(k1_funct_1(B,C),k5_numbers) ) => v2_mesfunc5(B) ) ) ) )).
fof(t54_midsp_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t54_mmlquery,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : r1_xxreal_0(k24_mmlquery(A,B),k3_finseq_1(A)) ) )).
fof(t54_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v2_struct_0(C) & v10_modelc_2(C) & l1_modelc_2(C) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t54_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k23_modelc_3(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k23_modelc_3(B)))) ) => ~ ( v7_modelc_2(A) & r2_hidden(A,u1_modelc_3(B,k10_modelc_3(k3_funct_2(k4_ordinal1,k23_modelc_3(B),C,1),B))) & ! [D] : ( v7_ordinal1(D) => r6_modelc_3(B,k10_modelc_3(k1_funct_1(C,D),B),k10_modelc_3(k3_funct_2(k4_ordinal1,k23_modelc_3(B),C,k1_nat_1(D,1)),B)) ) & ? [D] : ( 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] : ( 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] : ( 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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t54_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => k6_moebius1(k1_newton(A,B)) = A ) ) )).
fof(t54_monoid_0,axiom,( k4_binop_1(u1_struct_0(k7_monoid_0),u2_algstr_0(k7_monoid_0)) = 1 )).
fof(t54_monoid_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t54_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m2_pboole(C,u1_struct_0(A),B,k7_funcop_1(u1_struct_0(A),k4_ordinal1)) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k1_msaterm(A,B)) & v1_funct_1(D) & v1_partfun1(D,k1_msaterm(A,B)) ) => ( ( ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_msafree4(F,u1_struct_0(A),B,k1_msafree4(u1_struct_0(A),B,E)) => k1_funct_1(D,k1_trees_4(k4_tarski(F,E))) = k1_trees_4(k4_tarski(k3_funct_2(k1_msafree4(u1_struct_0(A),B,E),k1_funct_1(k7_funcop_1(u1_struct_0(A),k4_ordinal1),E),k2_msafree4(u1_struct_0(A),B,k7_funcop_1(u1_struct_0(A),k4_ordinal1),C,E),F),E)) ) ) & ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( m1_msaterm(F,A,B,k2_msaterm(A,B,E)) => k1_msafree4(k1_msaterm(A,B),D,k6_msaterm(A,B,k2_msaterm(A,B,E),F)) = k4_trees_4(k2_msaterm(A,k7_funcop_1(u1_struct_0(A),k4_ordinal1),E),k3_relat_1(F,D)) ) ) ) => ! [E] : ( m1_subset_1(E,k3_card_3(u3_msualg_1(A,k1_msafree3(A,B)))) => k1_funct_1(D,E) = k6_msafree4(A,B,C,E) ) ) ) ) ) ) )).
fof(t54_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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))) ) ) ) )).
fof(t54_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => r8_pboole(k8_newton,k12_nat_3(k2_int_2(B,A)),k6_nat_3(k8_newton,k12_nat_3(B),k12_nat_3(A))) ) ) )).
fof(t54_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t54_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ! [C] : ( ( 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) ) ) ) )).
fof(t54_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k14_prvect_2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_prvect_2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_prvect_2(A))) => ! [E] : ( m1_subset_1(E,k4_card_3(k4_prvect_2(A))) => ! [F] : ( m1_subset_1(F,k4_card_3(k4_prvect_2(A))) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( ( C = E & F = k4_struct_0(k14_prvect_2(A)) & k3_finseq_1(B) = k1_nat_1(k3_finseq_1(A),1) & r1_xxreal_0(1,G) & r1_xxreal_0(G,k3_finseq_1(A)) & ! [H] : ( 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(k1_nat_1(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(k1_nat_1(k3_finseq_1(A),1),G)))),u1_struct_0(k14_prvect_2(A)),k4_ndiff_5(A,k5_ndiff_5(A,k7_nat_d(k1_nat_1(k3_finseq_1(A),1),G)),k3_rlvect_1(k14_prvect_2(A),D,k7_partfun1(u1_struct_0(k14_prvect_2(A)),B,k1_nat_1(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(k1_nat_1(k3_finseq_1(A),1),G)))),k3_ndiff_5(A,k5_ndiff_5(A,k7_nat_d(k1_nat_1(k3_finseq_1(A),1),G))),k3_rlvect_1(k14_prvect_2(A),D,C))) ) ) ) ) ) ) ) ) )).
fof(t54_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k6_nat_d(B,k5_nat_d(B,A)) = B ) ) )).
fof(t54_nfcont_1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ( r2_hidden(D,A) => k7_partfun1(k1_numbers,C,D) = k2_normsp_0(B,D) ) ) ) => r4_nfcont_1(B,C,A) ) ) ) )).
fof(t54_normform,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(k7_normform(A))) => r1_tarski(B,k10_normform(A,B,B)) ) )).
fof(t54_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t54_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_oppcat_1(C,A,B) => m2_cat_1(k11_oppcat_1(A,B,C),A,k2_oppcat_1(B)) ) ) ) )).
fof(t54_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(A))) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A))) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A))))) ) => ! [G] : ( ( v1_funct_1(G) & v1_nfcont_3(G,k4_real_ns1(A)) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [H] : ( ( v1_funct_1(H) & v1_nfcont_3(H,k4_real_ns1(A)) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ( ( k1_relset_1(k1_numbers,G) = k3_integra5(B,C) & k1_relset_1(k1_numbers,H) = k3_integra5(B,C) & D = k2_rcomp_1(B,C) & r5_nfcont_1(k4_real_ns1(A),k4_real_ns1(A),u1_struct_0(k4_real_ns1(A)),F) & H = k1_funct_1(k6_ordeq_01(A,E,F,B,C),G) ) => ( r1_xxreal_0(C,B) | ( k7_partfun1(u1_struct_0(k4_real_ns1(A)),H,B) = E & r2_ndiff_3(k4_real_ns1(A),H,D) & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,D) => k1_ndiff_3(k4_real_ns1(A),H,I) = k7_partfun1(u1_struct_0(k4_real_ns1(A)),k1_partfun1(k1_numbers,u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A)),G,F),I) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t54_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ( r8_orders_1(A,B) & v4_relat_2(A) ) => r6_orders_1(A,B) ) ) )).
fof(t54_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r9_orders_1(u1_orders_2(A),B) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( B != C => r2_orders_2(A,B,C) ) ) ) ) ) )).
fof(t54_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => k5_ordinal3(A,A) = k1_xboole_0 ) )).
fof(t54_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r3_parsp_2(A,B,C,D,E) ) ) ) ) ) )).
fof(t54_partfun1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(A,B) => r1_partfun1(A,B) ) ) ) )).
fof(t54_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t54_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t54_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( 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) & k10_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) = k6_xcmplx_0(k3_pdiff_5(B,A),k3_pdiff_5(C,A)) ) ) ) ) ) )).
fof(t54_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ! [C] : ( ( 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] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ( r2_hidden(D,B) => r1_pdiff_7(A,C,D) ) ) ) ) ) ) ) )).
fof(t54_pepin,axiom,( k4_pepin(4) = k1_nat_1(k2_nat_1(256,256),1) )).
fof(t54_polyform,axiom,( ! [A] : ( ( 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 ) )).
fof(t54_polynom5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l6_algstr_0(A) ) => v1_polynom5(k9_polynom3(A),A) ) )).
fof(t54_polyred,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_ideal_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t54_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & A != 1 & ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(C,k5_numbers) & k6_xcmplx_0(k3_power(A,B),k3_power(A,C)) != k3_power(A,k7_xcmplx_0(B,C)) ) ) ) ) )).
fof(t54_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(t54_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => ( ~ r1_xxreal_0(A,k5_numbers) => k7_xcmplx_0(1,k4_prepower(A,B)) = k4_prepower(A,k4_xcmplx_0(B)) ) ) ) )).
fof(t54_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t54_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t54_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ~ ( r3_qc_lang2(A,C,B) & r1_xxreal_0(k3_finseq_1(k11_qc_lang1(A,B)),k3_finseq_1(k11_qc_lang1(A,C))) ) ) ) ) )).
fof(t54_qc_lang3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_qc_lang1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(B),k8_qc_lang1(B,A)) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t54_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k17_quatern2(A,k22_quaterni(B,C)) = k22_quaterni(k17_quatern2(A,B),k17_quatern2(A,C)) ) ) ) )).
fof(t54_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k25_quaterni(C,k22_quaterni(A,B)) = k25_quaterni(k25_quaterni(C,A),B) ) ) ) )).
fof(t54_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k27_quaterni(k22_quaterni(A,B)) = k22_quaterni(k27_quaterni(A),k27_quaterni(B)) ) ) )).
fof(t54_quofield,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t54_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(k9_nat_1(k1_numbers,k4_real_3(A),1),k5_numbers) => ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,k6_real_3(A),k1_nat_1(B,2)),k4_real_1(k9_nat_1(k1_numbers,k4_real_3(A),k1_nat_1(B,2)),k9_nat_1(k1_numbers,k6_real_3(A),k1_nat_1(B,1)))) ) ) ) )).
fof(t54_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => r1_tarski(k9_xtuple_0(k5_relat_1(B,A)),k9_xtuple_0(B)) ) )).
fof(t54_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( 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)) ) ) ) )).
fof(t54_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_rewrite1(A) & v4_rewrite1(A) ) => ! [B] : r4_rewrite1(A,B,k2_rewrite1(A,B)) ) )).
fof(t54_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t54_rfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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(k5_numbers)) = k1_xboole_0 & v1_partfun1(B,A) ) ) ) ) )).
fof(t54_rfunct_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ! [C] : ( ( r2_rfunct_3(A,B) & r1_tarski(C,B) ) => r2_rfunct_3(A,C) ) ) )).
fof(t54_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_comseq_2(B) => r1_xxreal_0(k1_rinfsup1(k3_rinfsup1(B)),k1_funct_1(k4_rinfsup1(B),A)) ) ) ) )).
fof(t54_rlaffin1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(t54_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_rlsub_1(D,A) => ( r2_hidden(C,k3_rlsub_1(A,B,D)) <=> k3_rlsub_1(A,B,D) = k3_rlsub_1(A,C,D) ) ) ) ) ) )).
fof(t54_rlsub_2,axiom,( ! [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) ) => ( ~ 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))) ) ) )).
fof(t54_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_connsp_2(C,A,B) => ! [D] : ( ( ~ v8_ordinal1(D) & v1_xreal_0(D) ) => m1_connsp_2(k1_convex1(A,C,D),A,k1_rlvect_1(A,B,D)) ) ) ) ) )).
fof(t54_rlvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t54_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rlvect_2(C,A) => ! [D] : ( m1_rlvect_2(D,A) => k3_funct_2(u1_struct_0(A),k1_numbers,k10_rlvect_2(A,C,D),B) = k5_real_1(k3_funct_2(u1_struct_0(A),k1_numbers,C,B),k3_funct_2(u1_struct_0(A),k1_numbers,D,B)) ) ) ) ) )).
fof(t54_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t54_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_rmod_4(D,A,B) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t54_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & k3_robbins1(A,k5_robbins1(A,B,C)) = k3_robbins1(A,C) ) ) ) )).
fof(t54_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t54_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( 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) = k5_numbers ) ) )).
fof(t54_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_rpr_1(A,B,C) => ( r1_xxreal_0(k1_rpr_1(A,C),k5_numbers) | k2_rpr_1(A,C,B) = k1_rpr_1(A,B) ) ) ) ) ) )).
fof(t54_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t54_rusub_2,axiom,( ! [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_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))) ) ) )).
fof(t54_rusub_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k5_rusub_5(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( B = k6_bhsp_2(A,C,D) => v4_pre_topc(B,k5_rusub_5(A)) ) ) ) ) ) )).
fof(t54_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => k10_rvsum_1(A,k4_xcmplx_0(1)) = k6_rvsum_1(A) ) )).
fof(t54_rvsum_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t54_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_3(k4_scmfsa_2(k5_numbers),1)),B) & r1_tarski(C,A) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( r1_xxreal_0(D,k8_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B)) & k3_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),B,D)) = k2_compos_1(k1_scmfsa_2) ) ) ) ) ) ) )).
fof(t54_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ~ r4_scmfsa7b(C,D) => k1_funct_1(k1_scmfsa6b(C,B,A),D) = k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_m(B)),E),D) ) ) ) ) ) ) )).
fof(t54_scmpds_2,axiom,( ! [A] : ( ( 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] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ( ( r1_xxreal_0(k5_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(k5_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) ) ) ) ) ) ) )).
fof(t54_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),F)) != k5_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) ) ) ) ) ) ) ) )).
fof(t54_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v6_scmyciel(A) ) => ( k8_scmyciel(A) = k5_numbers => k3_tarski(A) = k1_xboole_0 ) ) )).
fof(t54_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r3_semi_af1(A,B,B,C,D) => C = D ) ) ) ) ) )).
fof(t54_seq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k56_valued_1(k4_ordinal1,k1_numbers,k26_valued_1(k4_ordinal1,k1_numbers,B,A)),k26_valued_1(k4_ordinal1,k1_numbers,k56_valued_1(k4_ordinal1,k1_numbers,B),k9_complex1(A))) ) ) )).
fof(t54_seq_4,axiom,( r6_binop_1(k2_numbers,k5_binop_2,k3_binop_2) )).
fof(t54_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => r1_tarski(k3_prob_1(A,B),k3_kurato_0(A,B)) ) )).
fof(t54_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => r1_tarski(k9_nat_1(k9_setfam_1(B),k2_setlim_1(B,k9_setlim_2(B,D,C)),A),k5_subset_1(B,C,k9_nat_1(k9_setfam_1(B),k2_setlim_1(B,D),A))) ) ) ) )).
fof(t54_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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] : ( m1_subset_1(D,k5_finsub_1(A)) => ! [E] : ( r2_hidden(E,k10_setwiseo(A,B,D,C)) <=> ? [F] : ( m1_subset_1(F,A) & r2_hidden(F,D) & r2_hidden(E,k3_funct_2(A,k5_finsub_1(B),C,F)) ) ) ) ) ) )).
fof(t54_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( m1_scmfsa_2(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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 ) ) ) ) )).
fof(t54_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t54_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_simplex0(D,A) => ! [E] : ( ( 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))) ) ) ) )).
fof(t54_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ~ r1_xxreal_0(k23_sin_cos(A),k5_numbers) ) )).
fof(t54_sin_cos3,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(1,k3_xcmplx_0(k4_xcmplx_0(1),k7_complex1)),2),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1)))),k3_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(1,k7_complex1),2),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,k2_xcmplx_0(A,k3_xcmplx_0(k1_real_1(B),k7_complex1))))) = k3_real_1(k4_real_1(k3_funct_2(k1_numbers,k1_numbers,k1_sin_cos2,A),k3_funct_2(k1_numbers,k1_numbers,k18_sin_cos,B)),k4_real_1(k3_funct_2(k1_numbers,k1_numbers,k3_sin_cos2,A),k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,B))) ) ) )).
fof(t54_sin_cos6,axiom,( ! [A] : ( v1_int_1(A) => v6_valued_0(k5_relset_1(k1_numbers,k1_numbers,k16_sin_cos,k1_rcomp_1(k2_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A)),k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A))))) ) )).
fof(t54_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(1,B) & r1_xxreal_0(k9_complex1(B),k9_complex1(A)) ) => k6_xcmplx_0(k2_sin_cos7(A),k2_sin_cos7(B)) = k2_sin_cos7(k6_xcmplx_0(k3_xcmplx_0(A,B),k3_square_1(k3_xcmplx_0(k6_xcmplx_0(k1_square_1(A),1),k6_xcmplx_0(k1_square_1(B),1))))) ) ) ) )).
fof(t54_sin_cos9,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k2_sin_cos9,k1_rcomp_1(k4_xcmplx_0(1),1))) )).
fof(t54_sincos10,axiom,( k3_relat_1(k2_partfun1(k1_numbers,k1_numbers,k2_sincos10,k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1))),k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos),k28_sin_cos))) = k1_partfun2(k1_numbers,k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1))) )).
fof(t54_sppol_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t54_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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) ) ) ) )).
fof(t54_sprect_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t54_sprect_3,axiom,( ! [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) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( ( 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))))) ) ) ) )).
fof(t54_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t54_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => k3_xcmplx_0(A,k3_square_1(B)) = k3_square_1(k3_xcmplx_0(k1_square_1(A),B)) ) ) ) )).
fof(t54_stirl2_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( 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] : ( 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)) ) ) ) )).
fof(t54_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_valuat_1(D,A,C) => ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [F] : ( m2_subset_1(F,k16_substut1(A),k38_substut1(A)) => ! [G] : ( m1_substut1(G,A,k7_sublemma(A,F,B)) => ( v3_substut1(k7_sublemma(A,F,B),A) => ( ! [H] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t54_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))))) ) ) )).
fof(t54_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_tex_2(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,k2_pre_topc(A,B)) & ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t54_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_tex_2(B,A) & v1_tex_3(B,A) & m1_pre_topc(B,A) ) => ? [C] : ( ~ v2_struct_0(C) & v1_pre_topc(C) & v3_tex_3(C,A) & m1_pre_topc(C,A) & r4_tsep_2(A,B,C) ) ) ) )).
fof(t54_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_subset_1(k4_tex_4(A,B),k4_tex_4(A,C)) <=> ~ ( ! [D] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t54_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( 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_pre_topc(u1_struct_0(C),u1_pre_topc(C)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) => r1_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),u1_struct_0(B),D,k2_tmap_1(A,B,D,C)) ) ) ) ) ) )).
fof(t54_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t54_topgen_1,axiom,( v2_tops_1(k1_borsuk_5,k3_topmetr) & m1_subset_1(k1_borsuk_5,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )).
fof(t54_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t54_topgen_5,axiom,( ! [A] : ( 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))) ) ) )).
fof(t54_topgrp_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_connsp_2(C,A,k6_algstr_0(A,B,k2_group_1(A,B))) => ? [D] : ( v3_pre_topc(D,A) & m1_connsp_2(D,A,B) & r1_tarski(k2_group_2(A,D,k1_group_2(A,D)),C) ) ) ) ) )).
fof(t54_topreal6,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k9_metric_1(A,B,k5_numbers) = k1_tarski(B) ) ) )).
fof(t54_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(B,k3_topreal9(2,k4_struct_0(k15_euclid(2)),A)) => k2_xcmplx_0(k1_square_1(k17_euclid(B)),k1_square_1(k18_euclid(B))) = k1_square_1(A) ) ) ) )).
fof(t54_toprealc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( ( 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(k15_toprealc(A),C,D) ) ) ) ) )).
fof(t54_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) )).
fof(t54_tops_2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) )).
fof(t54_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t54_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t54_trees_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => ( r2_hidden(B,k3_trees_1(A)) <=> ! [C] : ( v7_ordinal1(C) => ~ r2_hidden(k7_finseq_1(B,k9_finseq_1(C)),A) ) ) ) ) )).
fof(t54_trees_3,axiom,( ! [A] : ( v7_ordinal1(A) => k2_trees_1(A) = k11_trees_3(k2_finseq_2(A,k2_trees_1(k5_numbers))) ) )).
fof(t54_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_tsep_1(A,B,C) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t54_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ~ ( ~ r1_xxreal_0(A,B) & r1_nat_d(B,A) & ! [C] : ( m2_finseq_1(C,u1_struct_0(k14_polynom3(k1_complfld))) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(D,k1_complfld) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => ~ ( D = k3_group_4(k14_polynom3(k1_complfld),C) & k4_finseq_1(C) = k2_finseq_1(A) & ! [E] : ( ( ~ v8_ordinal1(E) & m1_subset_1(E,k4_ordinal1) ) => ( r2_hidden(E,k2_finseq_1(A)) => ( ( ~ ( r1_nat_d(E,A) & ~ r1_nat_d(E,B) & E != A ) => k1_funct_1(C,E) = k2_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(k4_ordinal1,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)) ) ) ) ) ) ) )).
fof(t54_valued_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) ) => ( r1_xboole_0(k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,C)) => r1_xboole_0(k1_relset_1(k4_ordinal1,k61_valued_1(B,A)),k1_relset_1(k4_ordinal1,k61_valued_1(C,A))) ) ) ) ) )).
fof(t54_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ( v2_relat_1(E) & ! [F] : ( 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 ) ) ) ) ) ) )).
fof(t54_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t54_vectsp_5,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_5(D,A,B,C) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t54_vfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( 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) ) ) ) ) )).
fof(t54_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( v3_funct_1(k2_partfun1(A,u1_struct_0(B),C,D)) => r1_vfunct_2(A,B,C,D) ) ) ) ) )).
fof(t54_waybel21,axiom,( ! [A] : ( ( 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] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & v5_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( 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] : ( ( ~ 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) ) ) ) ) ) ) ) )).
fof(t54_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( r2_hidden(C,k1_relset_1(u1_struct_0(k1_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))) ) ) ) ) )).
fof(t54_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => r3_yellow20(k4_waybel34(A),k5_waybel34(A),k6_waybel34(A),k10_waybel34(A),k11_waybel34(A)) ) )).
fof(t54_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( D != k1_xboole_0 => r1_yellow_0(A,D) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(B)) ) => ~ ( r1_yellow_0(A,E) & D = k1_yellow_0(A,E) ) ) ) ) & ! [D] : ( ( 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) ) ) ) ) )).
fof(t54_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t54_waybel_2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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)))) ) ) ) ) ) )).
fof(t54_waybel_4,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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) ) ) ) )).
fof(t54_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ( ( r4_wellord1(A,B) & v2_wellord1(A) ) => v2_wellord1(B) ) ) ) )).
fof(t54_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : k4_xboole_0(A,k3_xboole_0(B,C)) = k2_xboole_0(k4_xboole_0(A,B),k4_xboole_0(A,C)) )).
fof(t54_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k8_xboolean(A,k8_xboolean(B,C)) = k4_xboolean(k5_xboolean(k3_xboolean(A),B),k5_xboolean(k3_xboolean(A),C)) ) ) ) )).
fof(t54_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k7_xcmplx_0(A,B) != k5_numbers => B = k7_xcmplx_0(A,k7_xcmplx_0(A,B)) ) ) ) )).
fof(t54_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(B,C) & r1_xxreal_0(k6_xcmplx_0(C,A),B) ) ) ) ) )).
fof(t54_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(C,D) & r1_tarski(k1_xxreal_1(C,D),k2_xxreal_1(A,B)) ) => ( r1_xxreal_0(A,C) & ~ r1_xxreal_0(B,D) ) ) ) ) ) ) )).
fof(t54_xxreal_2,axiom,( ! [A] : ( ( v2_membered(A) & ~ v1_xboole_0(A) ) => ( ~ ! [B] : ( m2_xxreal_2(B,A) => B = k2_xxreal_0 ) => v3_xxreal_2(A) ) ) )).
fof(t54_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t54_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & l1_orders_2(B) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t54_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t54_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v11_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v16_functor0(E,B,C) & m2_functor0(E,B,C) ) => ! [F] : ( ( ~ v2_struct_0(F) & v2_altcat_1(F) & v3_altcat_2(F,A) & m1_altcat_2(F,A) ) => ! [G] : ( ( ~ v2_struct_0(G) & v2_altcat_1(G) & v3_altcat_2(G,B) & m1_altcat_2(G,B) ) => ! [H] : ( ( ~ 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) ) ) ) ) ) ) ) ) ) )).
fof(t54_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ( v1_lattice3(A) <=> ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => r1_yellow_0(A,B) ) ) ) )).
fof(t54_yellow_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t54_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( ~ 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))) ) ) ) )).
fof(t54_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_yellow_5(A,B,k1_yellow_5(A,B,C)) = k12_lattice3(A,B,C) ) ) ) )).
fof(t54_yellow_9,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( m3_yellow_9(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t54_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ( r1_zf_lang(B,k8_zf_lang(A,C)) <=> B = C ) ) ) ) )).
fof(t54_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => r2_hidden(A,k29_zf_lang(A)) ) )).
fof(t54_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( k3_xboole_0(k2_tarski(A,B),C) = k2_tarski(A,B) => r2_hidden(A,C) ) )).
fof(t54_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => m1_zmodul01(k3_zmodul01(A),B) ) ) )).
fof(t54_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => k21_zmodul02(A,k24_zmodul02(A,B)) = k4_algstr_0(A,k21_zmodul02(A,B)) ) ) )).
fof(t55_abcmiz_0,axiom,( ! [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) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_abcmiz_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t55_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_abcmiz_1(B,A) & m1_subset_1(B,u4_struct_0(A)) ) => ! [C] : ( m1_abcmiz_1(C,A,k13_abcmiz_1(A)) => ! [D] : ( m1_abcmiz_1(D,A,k12_abcmiz_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t55_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [C] : ( m1_subset_1(C,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t55_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_aff_1(A,F,B,C) & r1_aff_1(A,F,D,E) & r1_aff_1(A,F,D,G) & r2_analoaf(A,B,D,C,E) & r2_analoaf(A,B,D,C,G) ) => ( r1_aff_1(A,F,B,D) | E = G ) ) ) ) ) ) ) ) ) )).
fof(t55_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & ? [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) & ? [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t55_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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))) ) ) ) )).
fof(t55_afinsq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v3_valued_0(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( B = k2_partfun1(k4_ordinal1,k1_numbers,C,k1_nat_1(A,1)) => k7_afinsq_2(B) = k9_nat_1(k1_numbers,k3_series_1(C),A) ) ) ) ) )).
fof(t55_algspec1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_msualg_6(B,A) & l3_msualg_1(B,A) ) => m4_algspec1(B,A) ) ) )).
fof(t55_altcat_4,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t55_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t55_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(k6_analort(A,F,G))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k6_analort(A,F,G))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k6_analort(A,F,G))) => ! [K] : ( m1_subset_1(K,u1_struct_0(k6_analort(A,F,G))) => ( ( B = H & D = I & C = J & E = K ) => ( r2_analoaf(k6_analort(A,F,G),H,I,J,K) <=> r2_analort(A,F,G,B,D,C,E) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t55_aofa_000,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ( v12_aofa_000(A) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k4_finseq_1(u1_unialg_1(A))) => ~ ( B != 1 & B != 2 & B != 3 & B != 4 ) ) ) ) )).
fof(t55_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v17_aofa_a00(B,A) & v20_aofa_a00(B,4,1,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v19_aofa_a00(C,A) & m1_subset_1(C,u1_struct_0(A)) ) => ( k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C) = k4_numbers & k27_aofa_a00(A,B,C) = k5_numbers & k28_aofa_a00(A,B,C) = 1 & ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => ! [F] : ( m1_msafree4(F,u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) => ! [G] : ( m1_msafree4(G,u1_struct_0(A),u3_msualg_1(A,B),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),C)) => ( ( F = D & G = E ) => ( k29_aofa_a00(A,B,C,F) = k4_xcmplx_0(D) & k30_aofa_a00(A,B,C,F,G) = k2_xcmplx_0(D,E) & k31_aofa_a00(A,B,C,F,G) = k3_xcmplx_0(D,E) & ( E != k5_numbers => k32_aofa_a00(A,B,C,F,G) = k4_int_1(D,E) ) & k33_aofa_a00(A,B,C,F,G) = k5_xxreal_0(D,E,k7_margrel1,k8_margrel1) & ( k33_aofa_a00(A,B,C,F,G) = k8_margrel1 => r1_xxreal_0(D,E) ) & ( r1_xxreal_0(D,E) => k33_aofa_a00(A,B,C,F,G) = k8_margrel1 ) & ~ ( k33_aofa_a00(A,B,C,F,G) = k7_margrel1 & r1_xxreal_0(D,E) ) & ( ~ r1_xxreal_0(D,E) => k33_aofa_a00(A,B,C,F,G) = k7_margrel1 ) ) ) ) ) ) ) ) ) ) ) )).
fof(t55_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v19_aofa_a00(E,A) & m1_subset_1(E,u1_struct_0(A)) ) => ! [F] : ( m2_pboole(F,u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,D)) => k15_aofa_a00(A,B,C,D,E,k7_aofa_a01(A,B,C,E),F) = 2 ) ) ) ) ) ) )).
fof(t55_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_funct_2(B,k4_numbers))) => ! [D] : ( ( v1_aofa_i00(D,A,B,C) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),C) ) => ! [E] : ( m3_aofa_i00(E,A,B,C,D) => ! [F] : ( m1_subset_1(F,B) => ! [G] : ( ( v1_aofa_i00(G,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),F,k5_numbers)) & m1_aofa_000(G,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),F,k5_numbers)) ) => ! [H] : ! [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,k5_numbers),I,G,H) => ! [J] : ( m1_aofa_i00(J,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),G) => ! [K] : ( m1_aofa_i00(K,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),G) => ( ( ! [L] : ( 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,k5_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,k5_numbers),I,G,H) & r7_aofa_000(A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),F,k5_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,k5_numbers),k57_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),F,k5_numbers),G,J,1),G,H) ) => ( ! [L] : ( ( v1_relat_1(L) & v1_funct_1(L) ) => ~ ( k1_funct_1(L,F) = k5_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,k5_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,k5_numbers),G,J,1)),G,H) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t55_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( 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] : ( m1_subset_1(D,k1_zfmisc_1(A)) & ? [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) & r2_hidden(k6_armstrng(A,D,E),C) & r1_tarski(D,B) & ~ r1_tarski(E,B) ) ) ) ) ) )).
fof(t55_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ~ ( A != k11_arytm_3 & ! [C] : ( m1_subset_1(C,k5_arytm_3) => B != k10_arytm_3(A,C) ) ) ) ) )).
fof(t55_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(2,A) & r1_xxreal_0(k7_newton(A),1) ) ) )).
fof(t55_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_1(A,C,k1_bcialg_1(A,C,B)) = B ) ) ) ) )).
fof(t55_bcialg_6,axiom,( ! [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] : ( m1_bcialg_1(B,A) => ! [C] : ( ( v12_bcialg_1(C,A) & m2_bcialg_1(C,A) ) => ! [D] : ( m5_bcialg_2(D,A,C) => m1_bcialg_1(k10_bcialg_6(A,B,C,D),A) ) ) ) ) )).
fof(t55_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( m4_bciideal(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t55_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k5_normsp_1(A,B,k4_xcmplx_0(1)),k5_vfunct_1(k4_ordinal1,A,B)) ) ) )).
fof(t55_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => r1_tarski(k6_bhsp_2(A,B,C),k5_bhsp_2(A,B,C)) ) ) ) )).
fof(t55_bilinear,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) ) ) )).
fof(t55_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(t55_borsuk_4,axiom,( ! [A] : ( ( ~ 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(k5_numbers,1)) & ! [B] : ( m1_subset_1(B,u1_struct_0(k5_topmetr)) => ! [C] : ( 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(k5_numbers,1)) ) ) ) ) ) )).
fof(t55_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t55_borsuk_6,axiom,( k8_borsuk_6 = a_0_14_borsuk_6 )).
fof(t55_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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(k4_xcmplx_0(A)),B)) = B ) ) )).
fof(t55_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t55_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_eqrel_1(I,A) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t55_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(t55_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => k7_xboolean(k8_margrel1,A) = A ) )).
fof(t55_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t55_card_1,axiom,( 9 = k7_enumset1(k5_ordinal1,1,2,3,4,5,6,7,8) )).
fof(t55_card_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : r1_xxreal_0(k5_card_1(k6_enumset1(A,B,C,D,E,F,G,H)),8) )).
fof(t55_card_3,axiom,( ! [A] : ( ( 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)))) ) )).
fof(t55_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t55_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( k2_cat_1(A,D,B) != k1_xboole_0 & k2_cat_1(A,D,C) != k1_xboole_0 & ~ ! [E] : ( m1_cat_1(E,A,D,B) => ! [F] : ( m1_cat_1(F,A,D,C) => ( r2_cat_3(A,D,E,F) <=> ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( k2_cat_1(A,G,B) != k1_xboole_0 & k2_cat_1(A,G,C) != k1_xboole_0 & ~ ( k2_cat_1(A,G,D) != k1_xboole_0 & ! [H] : ( m1_cat_1(H,A,G,B) => ! [I] : ( m1_cat_1(I,A,G,C) => ? [J] : ( m1_cat_1(J,A,G,D) & ! [K] : ( m1_cat_1(K,A,G,D) => ( ( k5_cat_1(A,G,D,B,K,E) = H & k5_cat_1(A,G,D,C,K,F) = I ) <=> J = K ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t55_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_cat_1(A,k19_cat_4(A),B) != k1_xboole_0 ) ) )).
fof(t55_cfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t55_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_chain_1(C,B) => ! [D] : ( 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 ) ) ) ) )).
fof(t55_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_000(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t55_circcomb,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_card_1(D,A) & v1_finseq_1(D) ) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t55_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v4_msualg_1(E,A) & v4_msafree2(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( ( v4_msualg_1(F,B) & v4_msafree2(F,B) & l3_msualg_1(F,B) ) => ( r5_circtrm1(A,B,C,D,E,F) => ! [G] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(A,E))) => ! [H] : ( m1_subset_1(H,k4_card_3(u3_msualg_1(B,F))) => ( G = k3_relat_1(C,H) => ! [I] : ( m1_subset_1(I,k4_ordinal1) => k5_facirc_1(A,E,G,I) = k3_relat_1(C,k5_facirc_1(B,F,H,I)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t55_classes1,axiom,( ! [A] : ( v1_ordinal1(A) => k5_classes1(A) = A ) )).
fof(t55_classes2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t55_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_clvect_1(B,A) => k3_clvect_1(B) = k3_clvect_1(A) ) ) )).
fof(t55_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => r1_tarski(k6_clvect_2(A,B,C),k5_clvect_2(A,B,C)) ) ) ) )).
fof(t55_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t55_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => r1_xxreal_0(k4_complex1(A),k9_complex1(A)) ) )).
fof(t55_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xreal_0(C) => k2_complex2(k2_xcmplx_0(A,B),C) = k2_xcmplx_0(k2_complex2(A,C),k2_complex2(B,C)) ) ) ) )).
fof(t55_complfld,axiom,( ! [A] : ( 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)) ) ) )).
fof(t55_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( m2_finseq_1(C,k2_numbers) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k3_finseq_1(B) = k3_finseq_1(C) ) => k8_complsp2(k7_seq_4(A,B),C) = k2_xcmplx_0(k8_complsp2(A,C),k8_complsp2(B,C)) ) ) ) ) )).
fof(t55_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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 ) ) )).
fof(t55_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( v6_compos_0(D,u1_compos_1(A)) & m1_subset_1(D,u1_compos_1(A)) ) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t55_comptrig,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( B != k5_numbers => k1_newton(k2_xcmplx_0(k19_sin_cos(k7_xcmplx_0(k2_xcmplx_0(A,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)),B)),k3_xcmplx_0(k17_sin_cos(k7_xcmplx_0(k2_xcmplx_0(A,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)),B)),k7_complex1)),B) = k2_xcmplx_0(k19_sin_cos(A),k3_xcmplx_0(k17_sin_cos(A),k7_complex1)) ) ) ) ) )).
fof(t55_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k3_finseq_2(k4_ordinal1)) & v1_funct_1(C) & v4_valued_0(C) & v2_margrel1(C) ) => r1_tarski(k1_relset_1(k3_finseq_2(k4_ordinal1),k7_comput_1(B,C,A)),k4_finseq_2(k1_nat_1(k19_margrel1(B),1),k4_ordinal1)) ) ) ) )).
fof(t55_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v1_comseq_3(A) & v1_comseq_3(B) ) => ( v1_comseq_3(k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)) & k11_comseq_3(k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)) = k6_xcmplx_0(k11_comseq_3(A),k11_comseq_3(B)) ) ) ) ) )).
fof(t55_convex4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v2_convex4(B,A) <=> v2_convex4(k5_rusub_4(A,B,C),A) ) ) ) ) )).
fof(t55_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ( v2_cqc_the1(C,A) => r3_cqc_the1(A,B,C) ) ) ) ) )).
fof(t55_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t55_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k15_csspace(A,B,C) = k3_square_1(k9_complex1(k12_csspace(A,k5_algstr_0(A,B,C),k5_algstr_0(A,B,C)))) ) ) ) )).
fof(t55_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k4_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),A),B) = k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k17_sin_cos(k3_xcmplx_0(2,B)),k17_sin_cos(k3_xcmplx_0(2,k6_xcmplx_0(B,A))))) ) ) )).
fof(t55_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => 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),k16_sin_cos),A),B) = k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,k19_sin_cos(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(2,B),A),2))),k17_sin_cos(k7_xcmplx_0(A,2))),k3_xcmplx_0(k19_sin_cos(k7_xcmplx_0(k3_xcmplx_0(3,k6_xcmplx_0(k3_xcmplx_0(2,B),A)),2)),k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(3,A),2))))) ) ) )).
fof(t55_dilworth,axiom,( ! [A] : ( ( v8_struct_0(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( k7_struct_0(A) = k2_xcmplx_0(k3_xcmplx_0(B,C),1) & ! [D] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t55_ec_pf_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t55_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k9_int_3(A))) => ! [G] : ( 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] : ( 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] : ( 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 = k5_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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t55_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ( ( k4_graph_1(A,C) = k3_graph_1(A,B) & k3_graph_1(A,E) = k4_graph_1(A,D) ) => k21_ens_1(A,k1_cat_1(A,C,B),k1_cat_1(A,D,E)) = k1_partfun1(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)),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)),k21_ens_1(A,B,D),k21_ens_1(A,C,E)) ) ) ) ) ) ) )).
fof(t55_entropy1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_matrprob(A) & m2_finseq_1(A,k1_numbers) ) => r1_xxreal_0(k5_numbers,k6_entropy1(A)) ) )).
fof(t55_enumset1,axiom,( ! [A] : ! [B] : k6_enumset1(A,A,A,A,A,A,A,B) = k2_tarski(A,B) )).
fof(t55_eqrel_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( k5_setfam_1(A,B) = A => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t55_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t55_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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(k5_numbers,k10_euclid_3(2,A,B,C,D)) & r1_xxreal_0(k5_numbers,k11_euclid_3(2,A,B,C,D)) & r1_xxreal_0(k5_numbers,k12_euclid_3(2,A,B,C,D)) ) ) ) ) ) ) ) )).
fof(t55_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => k22_rvsum_1(A,A) = k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k1_funct_1(A,1)),k1_square_1(k1_funct_1(A,2))),k1_square_1(k1_funct_1(A,3))) ) )).
fof(t55_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ~ ( ~ r2_hidden(B,C) & v1_euclid_4(C,A) & ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t55_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( ( 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,k9_funct_7(E,A,B))) ) => r2_hidden(k4_tarski(A,C),k6_exchsort(D,E)) ) ) ) )).
fof(t55_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ( 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)) ) ) )).
fof(t55_fcont_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( A != k5_numbers => k2_relset_1(k1_numbers,k1_fcont_1(A,B)) = k1_numbers ) ) ) )).
fof(t55_fdiff_11,axiom,( ! [A] : ( ( 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),k22_sin_cos))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(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),k22_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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),k22_sin_cos),A),B) = k5_numbers ) ) ) ) ) )).
fof(t55_fdiff_4,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k22_sin_cos,B))) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(B,C) = k6_xcmplx_0(C,1) ) ) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,B),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,B),A),C) = k3_xcmplx_0(C,k1_funct_1(k22_sin_cos,C)) ) ) ) ) ) ) )).
fof(t55_fib_num2,axiom,( k5_fib_num2(2) = k12_finseq_1(k4_ordinal1,1) )).
fof(t55_fib_num3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k3_fib_num3(k1_nat_1(k2_nat_1(2,A),1),k1_nat_1(k2_nat_1(2,A),1),k1_nat_1(B,1)) = k2_nat_1(k1_nat_1(k2_nat_1(2,A),1),k1_pre_ff(k1_nat_1(B,2))) ) ) )).
fof(t55_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t55_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t55_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v18_lattices(B,A) & v21_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t55_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => k5_card_1(k2_finseq_1(A)) = k5_card_1(A) ) )).
fof(t55_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( r2_hidden(C,k2_finseq_1(A)) => k1_funct_1(k2_finseq_2(A,B),C) = B ) ) )).
fof(t55_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : k5_card_1(k8_relat_1(k7_finseq_1(A,B),C)) = k1_nat_1(k5_card_1(k8_relat_1(A,C)),k5_card_1(k8_relat_1(B,C))) ) ) )).
fof(t55_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t55_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t55_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ~ ( B != D & C != D & k2_finseq_5(A,k3_finseq_4(A,B,C,D),D) != k12_finseq_1(A,D) ) ) ) ) ) )).
fof(t55_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r3_fintopo6(A,B,C,D,E) & v1_fin_topo(A) ) => v4_fintopo6(B,A) ) ) ) ) ) ) )).
fof(t55_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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)) ) ) ) ) )).
fof(t55_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => r1_tarski(k2_flang_3(A,B),k8_flang_1(A,B)) ) )).
fof(t55_fomodel0,axiom,( ! [A] : ! [B] : k3_finseq_2(k3_xboole_0(A,B)) = k3_xboole_0(k3_finseq_2(A),k3_finseq_2(B)) )).
fof(t55_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( ~ v2_struct_0(D) & l2_fsm_1(D,A,B) ) => ! [E] : ( ( ~ v2_struct_0(E) & l2_fsm_1(E,A,B) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(E)) => ! [G] : ( ( ~ v2_struct_0(G) & v8_struct_0(G) & l2_fsm_1(G,A,B) ) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t55_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( 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)) ) ) ) ) )).
fof(t55_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => r1_tarski(k9_xtuple_0(k6_relat_1(A,B)),k9_xtuple_0(B)) ) )).
fof(t55_funct_2,axiom,( ! [A] : ! [B] : ( ( 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] : ! [D] : ( ( r2_hidden(C,A) & r2_hidden(D,A) & k1_funct_1(B,C) = k1_funct_1(B,D) ) => C = D ) ) ) )).
fof(t55_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t55_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ! [F] : ( ( 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)) ) ) ) )).
fof(t55_funct_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => k9_xtuple_0(k2_funct_6(A)) = k9_xtuple_0(A) ) )).
fof(t55_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => k4_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))))) ) ) ) )).
fof(t55_funct_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t55_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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) ) ) ) ) ) )).
fof(t55_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k7_fvaluat1(A,B))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t55_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t55_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( ( ~ v1_xboole_0(G) & v1_relat_1(G) & v2_relat_1(G) & v1_funct_1(G) & v1_finseq_1(G) ) => ! [H] : ( m1_genealg1(H,G) => ! [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t55_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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))) )).
fof(t55_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k7_glib_000(A))) => ! [C] : ( m2_glib_000(C,A,k6_glib_000(A),k6_subset_1(k7_glib_000(A),B)) => k1_nat_1(k17_glib_000(C),k5_card_1(B)) = k17_glib_000(A) ) ) ) )).
fof(t55_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( k1_funct_1(B,C) = k4_glib_001(A,B) => r2_relset_1(k4_ordinal1,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)) ) ) ) ) )).
fof(t55_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_003(A) ) => ! [B] : ! [C] : ! [D] : ( 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)) ) ) ) ) )).
fof(t55_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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_nat_1(A,1),k3_finseq_1(k2_goboard2(C))) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(k2_goboard2(C))) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1))),k3_topreal1(2,C)) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B)),k3_topreal1(2,C)) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,1) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1)) & ( ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,2) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k7_nat_d(k3_finseq_1(C),1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B) ) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,2) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k7_nat_d(k3_finseq_1(C),1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1)) ) ) ) & ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(1,D) & ~ r1_xxreal_0(k3_finseq_1(C),k1_nat_1(D,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_nat_1(D,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1)) & ( ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,D) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_nat_1(D,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B) ) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,D) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_nat_1(D,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1)) ) ) ) ) ) ) ) ) )).
fof(t55_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_graph_2(A,k1_xboole_0) = A ) )).
fof(t55_graph_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v6_graph_1(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => v1_abian(k7_graph_3(B,D,A)) ) => ( k7_graph_3(B,C,A) = k5_numbers | ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t55_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t55_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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)),k7_polynom1(A,C,k11_polynom1(A,C,k5_termord(A,B,C,E),k6_termord(A,B,C,D)),k11_polynom1(A,C,k5_termord(A,B,C,D),k6_termord(A,B,C,E))),k11_polynom1(A,C,E,k6_termord(A,B,C,D))) ) ) ) ) ) ) )).
fof(t55_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => r1_tarski(k3_group_11(A,C,B),k4_group_11(A,C,B)) ) ) ) )).
fof(t55_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t55_group_3,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C != k1_xboole_0 => k3_group_3(A,B,C) = B ) ) ) ) ) )).
fof(t55_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => r1_group_2(A,k8_group_4(A,B,B),B) ) ) )).
fof(t55_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t55_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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) => ( v1_funct_1(k2_funct_1(C)) & v1_funct_2(k2_funct_1(C),u1_struct_0(k10_group_6(A,B,C)),u1_struct_0(A)) & v1_group_6(k2_funct_1(C),k10_group_6(A,B,C),A) & m1_subset_1(k2_funct_1(C),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k10_group_6(A,B,C)),u1_struct_0(A)))) ) ) ) ) ) )).
fof(t55_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( ( ~ 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) ) ) ) ) )).
fof(t55_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,k1_complfld) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t55_hfdiff_1,axiom,( ! [A] : ( ( 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,k18_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),k18_sin_cos),A),4)) ) )).
fof(t55_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => k8_ideal_1(A,k2_struct_0(A)) = u1_struct_0(A) ) )).
fof(t55_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ? [C] : ( m1_subset_1(C,u4_incsp_1(A)) & ? [D] : ( m1_subset_1(D,u4_incsp_1(A)) & C != D & r3_incsp_1(A,B,C) & r3_incsp_1(A,B,D) ) ) ) ) )).
fof(t55_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r1_xxreal_0(k5_numbers,B) => r1_xxreal_0(k5_numbers,k5_int_1(A,B)) ) ) ) )).
fof(t55_integr11,axiom,( ! [A] : ( ( 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),k26_sin_cos),k1_fdiff_9))) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( k2_xcmplx_0(1,k1_funct_1(k16_sin_cos,B)) != k5_numbers & k6_xcmplx_0(1,k1_funct_1(k16_sin_cos,B)) != k5_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),k26_sin_cos),k1_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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),k26_sin_cos),k1_fdiff_9),A),B) = k7_xcmplx_0(k1_funct_1(k16_sin_cos,B),k6_xcmplx_0(k1_funct_1(k16_sin_cos,B),1)) ) ) ) ) ) )).
fof(t55_integr13,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k2_xcmplx_0(k7_xcmplx_0(k1_funct_1(k2_sin_cos9,B),k1_square_1(B)),k7_xcmplx_0(1,k3_xcmplx_0(B,k2_xcmplx_0(1,k1_square_1(B))))) ) ) ) ) ) )).
fof(t55_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k3_xcmplx_0(k1_funct_1(k18_sin_cos,k1_funct_1(k18_sin_cos,D)),k1_funct_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) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k16_sin_cos)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k16_sin_cos)),k3_seq_4(A))) ) ) ) ) )).
fof(t55_integr19,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( ~ v8_ordinal1(D) & m1_subset_1(D,k4_ordinal1) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(D))))) ) => ! [F] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t55_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => ! [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_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)) = k2_xcmplx_0(k12_integra1(A,B),k12_integra1(A,C)) ) ) ) ) ) )).
fof(t55_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => k2_integra5(A,k1_sin_cos2) = k6_xcmplx_0(k1_funct_1(k3_sin_cos2,k2_seq_4(A)),k1_funct_1(k3_sin_cos2,k3_seq_4(A))) ) )).
fof(t55_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( 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] : ( v1_xreal_0(G) => ( r2_hidden(G,F) => ( k1_funct_1(D,G) = k2_xcmplx_0(G,A) & ~ r1_xxreal_0(k1_funct_1(D,G),k5_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,k3_xcmplx_0(2,A)))) = F & F = k1_relset_1(k1_numbers,E) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,F) => k1_funct_1(E,G) = k7_xcmplx_0(k6_xcmplx_0(G,A),k2_xcmplx_0(G,A)) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,E,B)) ) => k2_integra5(B,E) = k6_xcmplx_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,F),k26_valued_1(k1_numbers,k1_numbers,C,k3_xcmplx_0(2,A))),k2_seq_4(B)),k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,F),k26_valued_1(k1_numbers,k1_numbers,C,k3_xcmplx_0(2,A))),k3_seq_4(B))) ) ) ) ) ) ) ) )).
fof(t55_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m2_interva1(B,A) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & B = k4_tarski(C,D) ) ) ) ) )).
fof(t55_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( 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) ) ) ) )).
fof(t55_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( 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] : ( 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) = k3_xcmplx_0(k12_euclid(D),k3_square_1(k6_xcmplx_0(1,k1_square_1(k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k17_euclid(D),k12_euclid(D)),A),k2_xcmplx_0(1,A)))))) ) ) & ! [D] : ( 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(k5_numbers,k18_euclid(D)) & r1_xxreal_0(k7_xcmplx_0(k17_euclid(D),k12_euclid(D)),A) & D != k4_struct_0(k15_euclid(2)) ) ) ) ) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) | v5_pre_topc(C,k1_pre_topc(k15_euclid(2),B),k3_topmetr) ) ) ) ) ) )).
fof(t55_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t55_jgraph_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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] : ( 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(k7_xcmplx_0(2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(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 ) ) ) ) ) ) ) ) ) )).
fof(t55_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(1,C) & ~ r1_xxreal_0(k3_finseq_1(k2_jordan9(B,A)),C) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k1_matrix_0(k1_jordan8(B,A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),k2_jordan9(B,A),C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),1,D) ) ) ) ) )).
fof(t55_jordan1g,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,k5_numbers) => k3_topreal1(2,k1_jordan1e(A,B)) = k8_jordan6(k3_topreal1(2,k2_jordan9(A,B))) ) ) ) )).
fof(t55_jordan1h,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( 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] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(k4_tarski(D,k1_nat_1(E,1)),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k7_nat_d(k3_finseq_1(C),1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),D,k1_nat_1(E,1)) & r2_hidden(k4_tarski(D,E),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k3_finseq_1(C)) = k3_matrix_0(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(k1_nat_1(D,1),E),k2_matrix_0(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) )).
fof(t55_jordan1j,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) )).
fof(t55_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(A))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( D = k8_metric_1(k14_euclid(A),B,C) => v1_convex1(D,k15_euclid(A)) ) ) ) ) ) )).
fof(t55_jordan4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t55_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t55_kurato_1,axiom,( k5_card_1(k5_kurato_1(k3_topmetr,k6_kurato_1)) = 7 )).
fof(t55_lattice2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k5_finsub_1(A)) => ! [C] : ( ( ~ v2_struct_0(C) & v10_lattices(C) & v13_lattices(C) & l3_lattices(C) ) => ! [D] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t55_lattice3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => k3_funct_2(k1_zfmisc_1(A),A,B,k6_domain_1(A,C)) = C ) & ! [C] : ( 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] : ( ( ~ v2_struct_0(C) & v3_lattices(C) & v10_lattices(C) & v4_lattice3(C) & l3_lattices(C) ) => ~ ( u1_struct_0(C) = A & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) => k15_lattice3(C,D) = k1_funct_1(B,D) ) ) ) ) ) ) )).
fof(t55_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),k14_lexbfs(A,k16_lexbfs(A)))),A) & m3_chord(k2_funct_1(k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),k14_lexbfs(A,k16_lexbfs(A)))),A) ) ) )).
fof(t55_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v4_limfunc1(A) & ! [C] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k3_limfunc1(D))) => r1_xxreal_0(C,k1_funct_1(B,E)) ) ) ) ) ) | v4_limfunc1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).
fof(t55_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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) = k6_xcmplx_0(k2_limfunc2(B,A),k2_limfunc2(C,A)) ) ) ) ) ) )).
fof(t55_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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) ) ) ) ) )).
fof(t55_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( 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)))) ) ) ) ) ) ) )).
fof(t55_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v2_xxreal_0(E) & v1_xreal_0(E) ) => ! [F] : ( 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] : ( v1_xreal_0(G) & r1_xxreal_0(k5_numbers,G) & G = k1_mesfunc6(A,B,C,k2_mesfun6c(E,A,k56_valued_1(A,k1_numbers,D))) & k2_normsp_0(k12_lpspace2(A,B,C,E),F) = k2_power(G,k2_extreal1(1,E)) ) ) ) ) ) ) ) ) ) )).
fof(t55_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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)) ) ) ) ) )).
fof(t55_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_hilbert1)) => ( r8_ltlaxio1(C,k3_hilbert1(A,k4_ltlaxio1(B,k1_ltlaxio1(B)))) => r8_ltlaxio1(C,k1_ltlaxio1(A)) ) ) ) ) )).
fof(t55_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( C = k4_mathmorp(A,C,D) => r1_tarski(k4_mathmorp(A,B,C),k4_mathmorp(A,B,D)) ) ) ) ) ) )).
fof(t55_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,k1_numbers,A,A) & m2_finseq_1(E,k3_finseq_2(k1_numbers)) ) => ( ( r2_matrix10(B,C) & r1_matrix10(D,E) ) => r1_matrix10(k5_matrix10(A,B,E),k5_matrix10(A,C,D)) ) ) ) ) ) ) )).
fof(t55_matrix13,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(C)) ) => ! [E] : ( ( v1_finset_1(E) & v1_setfam_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ! [F] : ( ( v1_finset_1(F) & v1_setfam_1(F) & m1_subset_1(F,k1_zfmisc_1(k4_ordinal1)) ) => r1_tarski(k2_zfmisc_1(k8_relat_1(k5_matrix13(E),A),k8_relat_1(k5_matrix13(F),B)),k2_matrix_0(k6_matrix13(C,D,E,F))) ) ) ) ) )).
fof(t55_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( ~ ( ? [D] : ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) & k4_matrix_3(B,D,C) = k3_matrix_1(B,A) ) & ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => k4_matrix_3(B,C,D) != k3_matrix_1(B,A) ) ) & ~ ( ? [D] : ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) & k4_matrix_3(B,C,D) = k3_matrix_1(B,A) ) & ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => k4_matrix_3(B,D,C) != k3_matrix_1(B,A) ) ) ) ) ) ) )).
fof(t55_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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(B,k5_numbers) & ~ v1_xboole_0(k4_matrix15(C,k1_matrix_3(C,B,k5_numbers),k1_matrix_3(C,B,A))) & A != k5_numbers ) ) ) ) )).
fof(t55_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( v5_matrix16(C,B) => v5_matrix16(k2_matrix_3(B,C),B) ) ) ) ) )).
fof(t55_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ( k4_matrix_0(A,B) = k4_matrix_0(A,C) => ( r1_xxreal_0(k1_matrix_0(B),k5_numbers) | r1_xxreal_0(k1_matrix_0(C),k5_numbers) | B = C ) ) ) ) ) )).
fof(t55_matrix_4,axiom,( ! [A] : ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) ) => k2_matrix_0(B) = k2_matrix_0(C) ) ) ) )).
fof(t55_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r1_matrix_6(A,B,C,D) => ( r1_xxreal_0(A,k5_numbers) | r1_matrix_6(A,B,k4_matrix_0(u1_struct_0(B),C),k4_matrix_0(u1_struct_0(B),D)) ) ) ) ) ) ) )).
fof(t55_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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,k2_matrix_1(B,A)) = k4_struct_0(B) ) ) )).
fof(t55_matrix_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),B,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(C),B,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(C))) ) => ( r2_hidden(A,k2_finseq_1(B)) => ! [F] : ( m1_matrix_2(F,k3_matrix_2(B)) => ? [G] : ( m1_subset_1(G,k4_ordinal1) & r2_hidden(G,k2_finseq_1(B)) & A = k1_funct_1(F,G) & k7_partfun1(u1_struct_0(C),k8_matrix_0(u1_struct_0(C),E,A),G) = k7_partfun1(u1_struct_0(C),k10_matrix_3(B,C,E,F),G) ) ) ) ) ) ) ) ) )).
fof(t55_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k2_numbers)) ) => ( ( k3_finseq_1(A) = k1_matrix_0(C) & k3_finseq_1(B) = k3_finseq_1(C) ) => ( r1_xxreal_0(k3_finseq_1(A),k5_numbers) | r1_xxreal_0(k3_finseq_1(B),k5_numbers) | k8_complsp2(A,k6_matrixc1(k2_matrixc1(C),B)) = k12_matrixc1(k13_matrixc1(A,B,k4_matrix_0(k2_numbers,C))) ) ) ) ) ) )).
fof(t55_matrixr1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( k1_matrix_0(A) = k1_matrix_0(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(A)) ) => k7_matrix_0(k1_numbers,k3_matrixr1(A,B),C) = k4_rvsum_1(k7_matrix_0(k1_numbers,A,C),k7_matrix_0(k1_numbers,B,C)) ) ) ) ) ) )).
fof(t55_matrixr2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(A) = k1_matrix_0(B) & k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) ) => ( r1_xxreal_0(k3_finseq_1(A),k5_numbers) | r1_xxreal_0(k3_finseq_1(B),k5_numbers) | k11_matrixr1(k5_matrixr1(B,C),A) = k8_rvsum_1(k11_matrixr1(B,A),k11_matrixr1(C,A)) ) ) ) ) ) )).
fof(t55_matrprob,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ? [C] : ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,B) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) & v2_matrprob(C) & k5_matrprob(C) = 1 ) ) ) )).
fof(t55_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( r2_hidden(k3_xtuple_0(A,B,C),k3_zfmisc_1(D,E,F)) <=> ( r2_hidden(A,D) & r2_hidden(B,E) & r2_hidden(C,F) ) ) )).
fof(t55_measure6,axiom,( ! [A] : ( ( v1_setfam_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( ( v2_rcomp_1(A) & v5_xxreal_2(A) ) => v2_rcomp_1(k4_measure6(A)) ) ) )).
fof(t55_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r2_hidden(C,A) & r2_hidden(D,B) ) => r2_hidden(k3_xxreal_3(C,D),k10_member_1(A,B)) ) ) ) ) ) )).
fof(t55_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( v7_ordinal1(D) => r1_tarski(k7_memstr_0(A,B,k2_xcmplx_0(k5_memstr_0(A,B,C),D)),k9_memstr_0(A,B,C,D)) ) ) ) ) )).
fof(t55_mesfunc5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k9_nat_1(k6_numbers,A,C),k9_nat_1(k6_numbers,B,C)) ) => r1_xxreal_0(k8_supinf_2(k17_supinf_2(A)),k8_supinf_2(k17_supinf_2(B))) ) ) ) )).
fof(t55_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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)) ) ) ) )).
fof(t55_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => k4_struct_0(k15_midsp_1(A)) = k14_midsp_1(A) ) )).
fof(t55_mmlquery,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( A != k1_xboole_0 & k24_mmlquery(A,B) = k3_finseq_1(A) ) <=> r2_hidden(B,k1_setfam_1(k10_xtuple_0(A))) ) ) )).
fof(t55_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v2_struct_0(C) & v10_modelc_2(C) & l1_modelc_2(C) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t55_modelc_3,axiom,( ! [A] : k3_tarski(k1_orders_1(A)) = A )).
fof(t55_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => r1_nat_d(k6_moebius1(A),A) ) )).
fof(t55_monoid_0,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,u1_struct_0(k8_monoid_0)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k8_monoid_0)) => ( ( A = C & B = D ) => k6_algstr_0(k8_monoid_0,C,D) = k3_xcmplx_0(A,B) ) ) ) ) ) )).
fof(t55_monoid_1,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(t55_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( k11_nat_3(B,A) = k5_numbers => k1_funct_1(k13_nat_3(B),A) = k5_numbers ) ) ) )).
fof(t55_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k2_xcmplx_0(B,C),A) => r1_xxreal_0(C,k7_nat_d(A,B)) ) ) ) ) )).
fof(t55_ncfcont1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ! [C] : ( ( 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) ) ) ) )).
fof(t55_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k14_prvect_2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_prvect_2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_prvect_2(A))) => ! [E] : ( m1_subset_1(E,k4_card_3(k4_prvect_2(A))) => ! [F] : ( m1_subset_1(F,k4_card_3(k4_prvect_2(A))) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( ( C = E & F = k4_struct_0(k14_prvect_2(A)) & k3_finseq_1(B) = k1_nat_1(k3_finseq_1(A),1) & r1_xxreal_0(1,G) & r1_xxreal_0(G,k3_finseq_1(A)) & ! [H] : ( 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(k1_nat_1(k3_finseq_1(A),1),H)))) ) ) ) => k5_algstr_0(k11_prvect_2(A,k5_ndiff_5(A,k7_nat_d(k1_nat_1(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(k1_nat_1(k3_finseq_1(A),1),G)))),k3_ndiff_5(A,k5_ndiff_5(A,k7_nat_d(k1_nat_1(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(k1_nat_1(k3_finseq_1(A),1),G)))),k3_ndiff_5(A,k5_ndiff_5(A,k7_nat_d(k1_nat_1(k3_finseq_1(A),1),G))),k3_rlvect_1(k14_prvect_2(A),D,k7_partfun1(u1_struct_0(k14_prvect_2(A)),B,k1_nat_1(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(k1_nat_1(k3_finseq_1(A),1),G)))),k3_ndiff_5(A,k5_ndiff_5(A,k7_nat_d(k1_nat_1(k3_finseq_1(A),1),G))),C) ) ) ) ) ) ) ) ) )).
fof(t55_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k6_nat_d(B,k5_nat_d(B,A)) = k5_nat_d(k6_nat_d(A,B),B) ) ) )).
fof(t55_normform,axiom,( ! [A] : ! [B] : ( 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) ) )).
fof(t55_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t55_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => m1_oppcat_1(k10_oppcat_1(A,B,C),k2_oppcat_1(A),B) ) ) ) )).
fof(t55_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(A))) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A))) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A))))) ) => ! [G] : ( ( v1_funct_1(G) & v1_nfcont_3(G,k4_real_ns1(A)) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ( ( D = k2_rcomp_1(B,C) & r5_nfcont_1(k4_real_ns1(A),k4_real_ns1(A),u1_struct_0(k4_real_ns1(A)),F) & k1_relset_1(k1_numbers,G) = k3_integra5(B,C) & r2_ndiff_3(k4_real_ns1(A),G,D) & k7_partfun1(u1_struct_0(k4_real_ns1(A)),G,B) = E & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,D) => k1_ndiff_3(k4_real_ns1(A),G,H) = k3_funct_2(u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A)),F,k7_partfun1(u1_struct_0(k4_real_ns1(A)),G,H)) ) ) ) => ( r1_xxreal_0(C,B) | r1_abian(G,k6_ordeq_01(A,E,F,B,C)) ) ) ) ) ) ) ) ) ) )).
fof(t55_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ( r7_orders_1(A,B) & v6_relat_2(A) ) => r9_orders_1(A,B) ) ) )).
fof(t55_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ~ ( ! [B] : ( ( v6_orders_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => r3_orders_2(A,D,C) ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r2_orders_2(A,B,C) ) ) ) ) )).
fof(t55_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r2_hidden(A,B) => ( k5_ordinal3(B,A) != k1_xboole_0 & r2_hidden(k1_xboole_0,k5_ordinal3(B,A)) ) ) ) ) )).
fof(t55_ordinal6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v3_ordinal6(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v3_ordinal6(B) ) => ( ( k9_xtuple_0(A) = k9_xtuple_0(B) & ! [C] : ( 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)) ) ) ) ) )).
fof(t55_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r3_parsp_2(A,B,C,B,C) ) ) ) )).
fof(t55_partfun1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( k9_xtuple_0(A) = k9_xtuple_0(B) & r1_partfun1(A,B) ) => A = B ) ) ) )).
fof(t55_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t55_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t55_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( 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) & k10_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) = k6_xcmplx_0(k4_pdiff_5(B,A),k4_pdiff_5(C,A)) ) ) ) ) ) )).
fof(t55_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t55_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ~ r1_xxreal_0(k4_pepin(A),2) ) )).
fof(t55_polyform,axiom,( ! [A] : ( ( 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)) ) )).
fof(t55_polynom5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_polynom5(A,k9_polynom3(A),B) ) ) )).
fof(t55_polyred,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & v1_ideal_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t55_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & A != 1 & ~ r1_xxreal_0(B,k5_numbers) & k3_power(A,k2_power(B,C)) != k3_xcmplx_0(C,k3_power(A,B)) ) ) ) ) )).
fof(t55_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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) ) ) ) )).
fof(t55_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => ! [C] : ( v1_rat_1(C) => ( ~ r1_xxreal_0(A,k5_numbers) => k7_xcmplx_0(k4_prepower(A,B),k4_prepower(A,C)) = k4_prepower(A,k6_xcmplx_0(B,C)) ) ) ) ) )).
fof(t55_prob_3,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k9_setfam_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ( ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,B)) => k1_prob_2(A,k9_setfam_1(A),C,D) = k4_prob_3(A,B,D) ) ) & ! [D] : ( v7_ordinal1(D) => ( ~ r2_hidden(D,k1_relset_1(k4_ordinal1,B)) => k1_prob_2(A,k9_setfam_1(A),C,D) = k1_xboole_0 ) ) ) => ( k1_prob_2(A,k9_setfam_1(A),C,k5_numbers) = k1_xboole_0 & k1_kurato_0(A,C) = k5_prob_3(A,B) ) ) ) ) )).
fof(t55_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t55_pscomp_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ 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))) ) ) ) ) ) ) )).
fof(t55_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t55_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ~ ( r3_qc_lang2(A,C,B) & ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ~ r1_qc_lang2(A,D,B) ) ) ) ) ) )).
fof(t55_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => k5_qc_lang3(A,k13_qc_lang1(A,B)) = k5_qc_lang3(A,B) ) ) )).
fof(t55_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k17_quatern2(k24_quaterni(A),B) = k24_quaterni(k17_quatern2(A,B)) ) ) )).
fof(t55_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k25_quaterni(C,k25_quaterni(A,B)) = k22_quaterni(k25_quaterni(C,A),B) ) ) ) )).
fof(t55_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => k27_quaterni(k24_quaterni(A)) = k24_quaterni(k27_quaterni(A)) ) )).
fof(t55_quofield,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => v1_quofield(k3_struct_0(A),A,A) ) )).
fof(t55_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B))))) => ! [E] : ( 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(k3_seq_4(k7_partfun1(k9_setfam_1(k1_numbers),E,k1_nat_1(C,1))),k2_seq_4(k7_partfun1(k9_setfam_1(k1_numbers),E,C)))) ) ) ) ) ) ) )).
fof(t55_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k9_xtuple_0(k5_relat_1(B,A)) = k3_xboole_0(k9_xtuple_0(B),A) ) )).
fof(t55_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ( k9_xtuple_0(C) = k7_relset_1(B,A,k3_relset_1(A,B,C),B) & k7_relset_1(B,A,k3_relset_1(A,B,C),k7_relset_1(A,B,C,A)) = k7_relset_1(B,A,k3_relset_1(A,B,C),k10_xtuple_0(C)) ) ) )).
fof(t55_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_rewrite1(A) & v4_rewrite1(A) ) => ! [B] : ! [C] : ( r2_rewrite1(A,B,C) => k2_rewrite1(A,B) = k2_rewrite1(A,C) ) ) )).
fof(t55_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( 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) ) ) )).
fof(t55_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ v2_struct_0(C) & l1_rewrite3(C,B) ) => ! [D] : ( m1_rewrite1(D,k1_rewrite3(A,B,C)) => ! [E] : ( v7_ordinal1(E) => ~ ( r2_hidden(E,k4_finseq_1(D)) & r2_hidden(k2_xcmplx_0(E,1),k4_finseq_1(D)) & ! [F] : ( m1_subset_1(F,k8_afinsq_1(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t55_rfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( 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(k5_numbers)) = k1_xboole_0 & v1_partfun1(C,A) ) <=> v1_partfun1(k3_rfunct_1(A,k1_numbers,B,C),A) ) ) ) ) )).
fof(t55_rfunct_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ! [C] : ( v1_xreal_0(C) => ( r2_rfunct_3(A,B) <=> r2_rfunct_3(k15_valued_1(k1_numbers,k1_numbers,A,C),B) ) ) ) )).
fof(t55_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_comseq_2(A) => r1_xxreal_0(k1_rinfsup1(k3_rinfsup1(A)),k2_rinfsup1(k4_rinfsup1(A))) ) ) )).
fof(t55_rlaffin1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( A != k5_numbers => k4_rlaffin1(B,k1_convex1(B,C,A)) = k1_convex1(B,k4_rlaffin1(B,C),A) ) ) ) ) )).
fof(t55_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t55_rlsub_2,axiom,( ! [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) ) => v13_lattices(g3_lattices(k3_rlsub_2(A),k5_rlsub_2(A),k6_rlsub_2(A))) ) )).
fof(t55_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_connsp_2(B,A,k4_struct_0(A)) => ! [C] : ( ( ~ v8_ordinal1(C) & v1_xreal_0(C) ) => m1_connsp_2(k1_convex1(A,B,C),A,k4_struct_0(A)) ) ) ) )).
fof(t55_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t55_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( 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))) ) ) ) )).
fof(t55_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t55_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_4(C,A,B) => ! [D] : ( 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))) ) ) ) ) )).
fof(t55_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_robbins1(A,k3_robbins1(A,B)) = B ) => v6_robbins1(A) ) ) )).
fof(t55_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t55_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( k1_rpr_1(A,C) = k5_numbers => r1_rpr_1(A,B,C) ) ) ) ) )).
fof(t55_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t55_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => v13_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A))) ) )).
fof(t55_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => k12_rvsum_1(k9_finseq_1(A)) = k9_finseq_1(k1_square_1(A)) ) )).
fof(t55_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( v7_ordinal1(D) => ( r1_xxreal_0(D,k8_extpro_1(k7_card_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(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(B),D),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),k1_scmfsa_m(B),D)) ) ) ) ) ) ) )).
fof(t55_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t55_scmfsa_2,axiom,( ! [A] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(A,u1_struct_0(k1_ami_3)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ( A = k5_relat_1(B,k1_ami_2) => k5_memstr_0(k7_card_1(3),k1_scmfsa_2,B) = k5_memstr_0(k7_card_1(2),k1_ami_3,A) ) ) ) )).
fof(t55_scmpds_2,axiom,( ! [A] : ( ( 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] : ( ( 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)) = k1_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] : ( ( 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) ) ) ) ) ) )).
fof(t55_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),F)) = k5_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) ) ) ) ) ) ) ) )).
fof(t55_scmyciel,axiom,( ! [A] : ( ( v1_scmyciel(A) & v4_scmyciel(A) ) => k8_scmyciel(A) = k5_numbers ) )).
fof(t55_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r3_semi_af1(A,B,C,D,D) => B = C ) ) ) ) ) )).
fof(t55_seq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => k9_nat_1(k1_numbers,k1_seq_1(A),B) = A ) ) )).
fof(t55_seq_4,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m1_subset_1(B,k2_numbers) => k3_funct_2(k2_numbers,k2_numbers,k5_seq_4(A),B) = k3_xcmplx_0(A,B) ) ) )).
fof(t55_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k3_kurato_0(A,B) = k4_kurato_0(A,k2_setlim_1(A,B)) ) )).
fof(t55_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => k9_nat_1(k9_setfam_1(B),k4_setlim_1(B,k5_setlim_2(B,D,C)),A) = k9_subset_1(B,C,k9_nat_1(k9_setfam_1(B),k4_setlim_1(B,D),A)) ) ) ) )).
fof(t55_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k5_finsub_1(A)) => k10_setwiseo(A,A,B,k11_setwiseo(A)) = B ) ) )).
fof(t55_sf_mastr,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k3_scmfsa_2)) ) => ~ r2_hidden(k3_scmfsa_m(A),A) ) )).
fof(t55_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t55_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ( m1_simplex0(C,A) => ! [D] : ( ( 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) ) ) ) )).
fof(t55_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => v2_comseq_3(k24_sin_cos(A)) ) )).
fof(t55_sin_cos3,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(1,k3_xcmplx_0(k4_xcmplx_0(1),k7_complex1)),2),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1)))),k3_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(1,k7_complex1),2),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,k2_xcmplx_0(A,k3_xcmplx_0(k1_real_1(B),k7_complex1))))) = k3_real_1(k4_real_1(k3_funct_2(k1_numbers,k1_numbers,k1_sin_cos2,A),k3_funct_2(k1_numbers,k1_numbers,k16_sin_cos,B)),k4_real_1(k3_funct_2(k1_numbers,k1_numbers,k3_sin_cos2,A),k3_funct_2(k1_numbers,k1_numbers,k18_sin_cos,B))) ) ) )).
fof(t55_sin_cos6,axiom,( ! [A] : ( v1_int_1(A) => v6_valued_0(k5_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A),k2_xcmplx_0(k28_sin_cos,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A))))) ) )).
fof(t55_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(1,B) & r1_xxreal_0(k9_complex1(B),k9_complex1(A)) ) => k6_xcmplx_0(k3_sin_cos7(A),k3_sin_cos7(B)) = k3_sin_cos7(k6_xcmplx_0(k3_xcmplx_0(A,B),k3_square_1(k3_xcmplx_0(k6_xcmplx_0(k1_square_1(A),1),k6_xcmplx_0(k1_square_1(B),1))))) ) ) ) )).
fof(t55_sin_cos9,axiom,( k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_sin_cos9,k1_rcomp_1(k4_xcmplx_0(1),1))) = k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)),k7_xcmplx_0(k28_sin_cos,4)) )).
fof(t55_sincos10,axiom,( k3_relat_1(k2_partfun1(k1_numbers,k1_numbers,k3_sincos10,k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1))),k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4))))) = k1_partfun2(k1_numbers,k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1))) )).
fof(t55_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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) ) ) ) )).
fof(t55_sprect_2,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(t55_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t55_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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),k3_square_1(k2_xcmplx_0(1,k1_square_1(A)))),k3_square_1(k2_xcmplx_0(1,k1_square_1(B)))) & r1_xxreal_0(k4_xcmplx_0(k3_square_1(k2_xcmplx_0(1,k1_square_1(B)))),k3_xcmplx_0(B,k3_square_1(k2_xcmplx_0(1,k1_square_1(A))))) ) ) ) ) )).
fof(t55_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( k1_card_1(B) = k1_nat_1(A,1) & r2_hidden(C,B) ) => k1_card_1(k6_subset_1(B,k1_tarski(C))) = A ) ) )).
fof(t55_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [E] : ( m2_subset_1(E,k16_substut1(A),k38_substut1(A)) => ! [F] : ( m1_substut1(F,A,k7_sublemma(A,E,B)) => ( v3_substut1(k7_sublemma(A,E,B),A) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t55_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))))) ) ) )).
fof(t55_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t55_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t55_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(t55_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(E,u1_struct_0(C)) => k7_relset_1(u1_struct_0(A),u1_struct_0(B),D,E) = k7_relset_1(u1_struct_0(C),u1_struct_0(B),k2_tmap_1(A,B,D,C),E) ) ) ) ) ) ) )).
fof(t55_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ( r1_borsuk_6(A,B,C) => ! [E] : ( ( 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))) ) ) ) ) ) ) ) )).
fof(t55_topgen_1,axiom,( ~ v2_tops_1(k1_numbers,k3_topmetr) & m1_subset_1(k1_numbers,k1_zfmisc_1(u1_struct_0(k3_topmetr))) )).
fof(t55_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_card_3(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ r1_topgen_4(A,B,C) ) ) ) ) )).
fof(t55_topgen_5,axiom,( ! [A] : ( 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))) ) ) )).
fof(t55_topgrp_1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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) ) ) )).
fof(t55_topreal6,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ( D = k9_metric_1(A,B,C) => v4_pre_topc(D,k3_pcomps_1(A)) ) ) ) ) ) )).
fof(t55_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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,k5_numbers) ) ) ) ) ) ) )).
fof(t55_toprealc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(B))) => ( r2_hidden(A,k4_finseq_1(D)) => k7_relset_1(u1_struct_0(k15_euclid(B)),u1_struct_0(k3_topmetr),k16_toprealc(B,A),k1_topreal9(B,D,C)) = k2_rcomp_1(k6_xcmplx_0(k7_partfun1(k1_numbers,D,A),C),k2_xcmplx_0(k7_partfun1(k1_numbers,D,A),C)) ) ) ) ) ) )).
fof(t55_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_tops_1(B,A) => v2_tops_1(B,A) ) ) ) )).
fof(t55_tops_2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) )).
fof(t55_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => k2_pre_topc(A,C) = k2_pre_topc(B,D) ) ) ) ) ) )).
fof(t55_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t55_trees_1,axiom,( r2_tarski(k4_ordinal1,k8_trees_1) )).
fof(t55_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( 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(k1_nat_1(k3_finseq_1(B),1))),k12_finseq_1(k4_ordinal1,k3_finseq_1(B)),A) ) ) )).
fof(t55_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ! [E] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t55_uniroots,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k14_polynom3(k1_complfld))) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(k1_complfld)) & v1_polynom1(D,k1_complfld) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k1_complfld)))) ) => ( ( D = k3_group_4(k14_polynom3(k1_complfld),C) & B = A & ! [E] : ( ( ~ v8_ordinal1(E) & m1_subset_1(E,k4_ordinal1) ) => ~ ( r2_hidden(E,k4_finseq_1(C)) & k1_funct_1(C,E) != k2_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)) ) ) ) ) ) )).
fof(t55_valued_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v2_finseq_1(D) ) => ( ( B = k2_xboole_0(C,D) & r1_xboole_0(C,D) ) => k2_xboole_0(k61_valued_1(C,A),k61_valued_1(D,A)) = k61_valued_1(B,A) ) ) ) ) ) )).
fof(t55_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( ( 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) ) ) ) )).
fof(t55_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_vectsp_4(E,A,B) => ( r2_hidden(D,k3_vectsp_4(A,B,C,E)) <=> k3_vectsp_4(A,B,C,E) = k3_vectsp_4(A,B,D,E) ) ) ) ) ) ) )).
fof(t55_vectsp_5,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_5(D,A,B,C) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t55_vfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( 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] : ( v1_xreal_0(E) => 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,k4_normsp_0(B,C,D),A)) ) ) ) ) ) )).
fof(t55_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( v3_funct_1(k2_partfun1(A,u1_struct_0(B),C,D)) => ( ! [E] : ( v1_xcmplx_0(E) => 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,k4_normsp_0(A,B,C),D)) ) ) ) ) ) )).
fof(t55_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( r2_hidden(C,k2_relset_1(u1_struct_0(k1_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))) ) ) ) ) )).
fof(t55_waybel34,axiom,( ! [A] : ( ~ v2_setfam_1(A) => r3_yellow20(k5_waybel34(A),k4_waybel34(A),k7_waybel34(A),k11_waybel34(A),k10_waybel34(A)) ) )).
fof(t55_waybel_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t55_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t55_waybel_2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ! [D] : ( ( 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))) ) ) ) ) )).
fof(t55_waybel_4,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_waybel_4(A,B,C) <=> ( r2_hidden(C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,B) & r2_orders_2(A,C,D) ) ) ) ) ) ) )).
fof(t55_xboole_1,axiom,( ! [A] : ! [B] : 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)) )).
fof(t55_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k8_xboolean(A,k5_xboolean(B,C)) = k4_xboolean(k3_xboolean(k4_xboolean(A,B)),k3_xboolean(k4_xboolean(A,C))) ) ) ) )).
fof(t55_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( C != k5_numbers => k7_xcmplx_0(A,B) = k7_xcmplx_0(k7_xcmplx_0(A,C),k7_xcmplx_0(B,C)) ) ) ) ) )).
fof(t55_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( A != B & r1_xxreal_0(k6_xcmplx_0(A,B),k5_numbers) & r1_xxreal_0(k6_xcmplx_0(B,A),k5_numbers) ) ) ) )).
fof(t55_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_tarski(k2_xxreal_1(C,D),k2_xxreal_1(A,B)) => ( r1_xxreal_0(D,C) | ( r1_xxreal_0(A,C) & r1_xxreal_0(D,B) ) ) ) ) ) ) ) )).
fof(t55_xxreal_2,axiom,( ! [A] : ( ( v2_membered(A) & ~ v1_xboole_0(A) ) => ! [B] : ( m1_xxreal_2(B,A) => ( r2_hidden(B,A) => B = k1_xxreal_2(A) ) ) ) )).
fof(t55_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ~ ( ~ ( C = k1_xxreal_0 & B = k2_xxreal_0 ) & ~ ( C = k2_xxreal_0 & B = k1_xxreal_0 ) & ~ r1_xxreal_0(k1_xxreal_3(C,B),A) & ~ ( A != k1_xxreal_0 & B != k2_xxreal_0 & C != k2_xxreal_0 & ~ r1_xxreal_0(C,k3_xxreal_3(A,B)) ) ) ) ) ) )).
fof(t55_yellow10,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t55_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ( r1_borsuk_1(A,B) => r1_waybel18(B,A) ) ) ) )).
fof(t55_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v11_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ! [D] : ( ( v16_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v16_functor0(E,B,C) & m2_functor0(E,B,C) ) => ! [F] : ( ( ~ v2_struct_0(F) & v2_altcat_1(F) & v3_altcat_2(F,A) & m1_altcat_2(F,A) ) => ! [G] : ( ( ~ v2_struct_0(G) & v2_altcat_1(G) & v3_altcat_2(G,B) & m1_altcat_2(G,B) ) => ! [H] : ( ( ~ 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) ) ) ) ) ) ) ) ) ) )).
fof(t55_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ( v2_lattice3(A) <=> ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => r2_yellow_0(A,B) ) ) ) )).
fof(t55_yellow_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t55_yellow_4,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t55_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_yellow_5(A,k13_lattice3(A,B,C),C) = k1_yellow_5(A,B,C) ) ) ) )).
fof(t55_yellow_9,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( m3_yellow_9(C,A,B) => m3_yellow_9(C,B,A) ) ) ) )).
fof(t55_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ~ ( v7_zf_lang(B) & r1_zf_lang(A,B) ) ) ) )).
fof(t55_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => 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))) ) ) )).
fof(t55_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(B,k4_xboole_0(C,k1_tarski(A))) <=> ( r2_hidden(B,C) & B != A ) ) )).
fof(t55_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => m1_zmodul01(k3_zmodul01(B),C) ) ) ) )).
fof(t55_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( m1_zmodul02(C,A) => k21_zmodul02(A,k25_zmodul02(A,B,C)) = k5_algstr_0(A,k21_zmodul02(A,B),k21_zmodul02(A,C)) ) ) ) )).
fof(t56_abcmiz_0,axiom,( ! [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) & l2_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_abcmiz_0(A)) => ( r3_abcmiz_0(A,B,C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t56_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_abcmiz_1(B,A,k13_abcmiz_1(A)) => ! [C] : ( m1_abcmiz_1(C,A,k13_abcmiz_1(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t56_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [C] : ( m1_subset_1(C,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t56_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t56_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t56_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( 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 ) ) )).
fof(t56_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v3_valued_0(A) & v1_finset_1(A) ) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ( r2_hidden(C,k1_relset_1(k4_ordinal1,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)) ) ) ) )).
fof(t56_algspec1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( m2_algspec1(B,A) => ! [C] : ( m4_algspec1(C,B) => m4_algspec1(C,A) ) ) ) )).
fof(t56_altcat_4,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t56_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t56_aofa_000,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_freealg(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_freealg(k19_aofa_000,A))) => ~ ( ! [C] : ( m1_subset_1(C,A) => B != k2_trees_4(A,C) ) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t56_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_aofa_a00(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l5_aofa_a00(B) ) => ( u1_struct_0(k36_aofa_a00(A,B)) = k2_xboole_0(u1_struct_0(A),u1_struct_0(B)) & u4_struct_0(k36_aofa_a00(A,B)) = k2_xboole_0(u4_struct_0(A),u4_struct_0(B)) & u1_msualg_1(k36_aofa_a00(A,B)) = k1_funct_4(u1_msualg_1(A),u1_msualg_1(B)) & u2_msualg_1(k36_aofa_a00(A,B)) = k1_funct_4(u2_msualg_1(A),u2_msualg_1(B)) ) ) ) )).
fof(t56_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v19_aofa_a00(E,A) & m1_subset_1(E,u1_struct_0(A)) ) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,C),E)) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),E)) => ! [H] : ( m2_pboole(H,u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,D)) => k15_aofa_a00(A,B,C,D,E,k34_aofa_a00(A,C,E,F,G),H) = k34_aofa_a00(A,D,E,k15_aofa_a00(A,B,C,D,E,F,H),k15_aofa_a00(A,B,C,D,E,G,H)) ) ) ) ) ) ) ) ) )).
fof(t56_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_aofa_i00(D,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [G] : ( m1_aofa_i00(G,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ( ? [H] : ( 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,k5_numbers),k13_aofa_000(A,k51_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,F,1),k17_aofa_000(A,k51_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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,k5_numbers),D,F,G),k57_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,G,1))),D) ) ) ) ) ) ) ) ) )).
fof(t56_armstrng,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ( ? [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) & ? [E] : ( 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)) ) ) ) )).
fof(t56_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( m1_subset_1(C,k5_arytm_3) => ( k10_arytm_3(A,B) = k10_arytm_3(A,C) => ( A = k11_arytm_3 | B = C ) ) ) ) ) )).
fof(t56_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r1_xxreal_0(B,A) => r1_xxreal_0(k7_newton(B),k7_newton(A)) ) ) ) )).
fof(t56_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t56_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( v8_bcialg_1(E) & m1_bcialg_5(E,A,B,C,D) ) => ( B = k5_numbers => ( r1_xxreal_0(C,k5_numbers) | ( v8_bcialg_1(E) & m1_bcialg_5(E,k5_numbers,k5_numbers,k5_numbers,k5_numbers) ) ) ) ) ) ) ) ) )).
fof(t56_bcialg_6,axiom,( ! [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] : ( m1_bcialg_1(B,A) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t56_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ! [C] : ( m2_bcialg_1(C,A) => ( ( r1_tarski(B,C) & m4_bciideal(B,A) ) => m4_bciideal(C,A) ) ) ) ) )).
fof(t56_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k4_normsp_1(A,C,B),k5_bhsp_1(A,C,k4_algstr_0(A,B))) ) ) ) )).
fof(t56_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => 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) ) ) ) )).
fof(t56_bilinear,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) )).
fof(t56_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_boolealg(A,k3_boolealg(A,B,k5_lattices(A)),B) ) ) )).
fof(t56_borsuk_4,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t56_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_xboole_0(k3_borsuk_5(A,B),k2_borsuk_5(A,B)) ) ) )).
fof(t56_borsuk_6,axiom,( 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(k5_numbers,1),k1_rcomp_1(k5_numbers,1)) )).
fof(t56_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => 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(k4_xcmplx_0(A)),k1_jordan24(A)),k3_struct_0(k15_euclid(2))) ) )).
fof(t56_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t56_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_eqrel_1(I,A) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t56_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t56_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => k7_xboolean(k7_margrel1,A) = k3_xboolean(A) ) )).
fof(t56_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t56_card_1,axiom,( 10 = k8_enumset1(k5_ordinal1,1,2,3,4,5,6,7,8,9) )).
fof(t56_card_2,axiom,( ! [A] : ! [B] : ( A != B => k5_card_1(k2_tarski(A,B)) = 2 ) )).
fof(t56_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(A,B) => r1_tarski(k8_card_3(A),k8_card_3(B)) ) ) ) )).
fof(t56_card_fin,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_finset_1(A) ) => ! [B] : ( v1_finset_1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( k9_xtuple_0(A) = B => ( ! [E] : ! [F] : ~ ( E != F & ! [G] : ( ( 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) = k2_nat_1(C,k4_newton(D,k5_card_1(B))) ) ) ) ) ) ) )).
fof(t56_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( 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] : ( 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] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( 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) ) ) ) ) )).
fof(t56_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( m1_subset_1(F,u4_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t56_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k24_cat_4(A,B) = k11_cat_3(A,k19_cat_4(A),B) ) ) )).
fof(t56_cfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => ! [D] : ( v1_xcmplx_0(D) => 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)) ) ) ) )).
fof(t56_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_chain_1(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(t56_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k6_glib_000(A))) ) => ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => ! [E] : ( m2_glib_000(E,A,C,k21_glib_000(A,C)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t56_circcomb,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( 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] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_card_1(D,A) & v1_finseq_1(D) ) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t56_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v4_msualg_1(E,A) & v4_msafree2(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( ( v4_msualg_1(F,B) & v4_msafree2(F,B) & l3_msualg_1(F,B) ) => ( r5_circtrm1(A,B,C,D,E,F) => ! [G] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(A,E))) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t56_classes1,axiom,( k5_classes1(k1_xboole_0) = k1_xboole_0 )).
fof(t56_classes2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => r2_hidden(k1_xboole_0,A) ) )).
fof(t56_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_clvect_1(B,A) => ! [C] : ( m1_clvect_1(C,A) => k3_clvect_1(B) = k3_clvect_1(C) ) ) ) )).
fof(t56_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => 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) ) ) ) )).
fof(t56_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k3_tarski(A),k3_tarski(B)))) => ~ ( ! [D] : ! [E] : ( r2_hidden(k2_tarski(D,E),A) => ! [F] : ! [G] : ( ( r2_hidden(k4_tarski(D,F),C) & r2_hidden(k4_tarski(E,G),C) ) => r2_hidden(k2_tarski(F,G),B) ) ) & ! [D] : ! [E] : ( r2_hidden(k2_tarski(D,E),A) => ! [F] : ( ( r2_hidden(k4_tarski(D,F),C) & r2_hidden(k4_tarski(E,F),C) ) => D = E ) ) & ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t56_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => r1_xxreal_0(k9_complex1(k2_xcmplx_0(A,B)),k2_xcmplx_0(k9_complex1(A),k9_complex1(B))) ) ) )).
fof(t56_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xreal_0(B) => k2_complex2(k4_xcmplx_0(A),B) = k4_xcmplx_0(k2_complex2(A,B)) ) ) )).
fof(t56_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ( B != k4_struct_0(k1_complfld) => k2_complfld(k3_vectsp_1(k1_complfld,A,B)) = k3_vectsp_1(k1_complfld,k2_complfld(A),k2_complfld(B)) ) ) ) )).
fof(t56_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => k8_complsp2(k9_seq_4(A),B) = k4_xcmplx_0(k8_complsp2(A,B)) ) ) ) )).
fof(t56_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => k2_compos_0(u1_compos_1(A),k2_compos_1(A)) = k5_numbers ) )).
fof(t56_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( v6_compos_0(D,u1_compos_1(A)) & m1_subset_1(D,u1_compos_1(A)) ) => ! [E] : ( ( v6_compos_0(E,u1_compos_1(A)) & m1_subset_1(E,u1_compos_1(A)) ) => ! [F] : ( ( 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) ) ) ) ) ) ) )).
fof(t56_comptrig,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( B != k5_numbers => A = k1_newton(k2_xcmplx_0(k3_xcmplx_0(k1_power(B,k9_complex1(A)),k19_sin_cos(k7_xcmplx_0(k2_xcmplx_0(k1_comptrig(A),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)),B))),k3_xcmplx_0(k3_xcmplx_0(k1_power(B,k9_complex1(A)),k17_sin_cos(k7_xcmplx_0(k2_xcmplx_0(k1_comptrig(A),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)),B))),k7_complex1)),B) ) ) ) ) )).
fof(t56_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k3_finseq_2(k4_ordinal1)) & v1_funct_1(C) & v4_valued_0(C) & v2_margrel1(C) ) => ( ( v2_comput_1(B) & v2_comput_1(C) & k1_nat_1(k19_margrel1(B),2) = k19_margrel1(C) & r1_xxreal_0(1,A) & r1_xxreal_0(A,k1_nat_1(1,k19_margrel1(B))) ) => ( k1_relset_1(k3_finseq_2(k4_ordinal1),k7_comput_1(B,C,A)) = k4_finseq_2(k1_nat_1(k19_margrel1(B),1),k4_ordinal1) & k19_margrel1(k7_comput_1(B,C,A)) = k1_nat_1(k19_margrel1(B),1) ) ) ) ) ) )).
fof(t56_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_comseq_3(A) => ! [B] : ( v1_xcmplx_0(B) => ( v1_comseq_3(k25_valued_1(k4_ordinal1,k2_numbers,A,B)) & k11_comseq_3(k25_valued_1(k4_ordinal1,k2_numbers,A,B)) = k3_xcmplx_0(B,k11_comseq_3(A)) ) ) ) ) )).
fof(t56_convex4,axiom,( ! [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) ) => v2_convex4(k17_convex4(A,k3_clvect_1(A)),A) ) )).
fof(t56_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => v2_cqc_the1(k5_cqc_lang(A),A) ) )).
fof(t56_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ! [E] : ( m2_subset_1(E,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t56_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t56_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)),k2_xcmplx_0(k15_csspace(A,B,D),k15_csspace(A,C,E))) ) ) ) ) ) )).
fof(t56_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k5_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),A),B) = k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k17_sin_cos(k2_xcmplx_0(k3_xcmplx_0(2,B),A)),k17_sin_cos(k6_xcmplx_0(k3_xcmplx_0(2,B),A)))) ) ) )).
fof(t56_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => 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),k16_sin_cos),A),B) = k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,k19_sin_cos(B)),k17_sin_cos(k7_xcmplx_0(A,2))),k3_xcmplx_0(k19_sin_cos(k3_xcmplx_0(3,B)),k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(3,A),2))))) ) ) )).
fof(t56_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(A,k1_relset_1(k1_numbers,k26_sin_cos)) & r2_hidden(B,k1_relset_1(k1_numbers,k26_sin_cos)) ) => k9_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k26_sin_cos),k16_sin_cos),A,B) = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k1_newton(k17_sin_cos(A),3),k1_square_1(k19_sin_cos(B))),k3_xcmplx_0(k1_newton(k17_sin_cos(B),3),k1_square_1(k19_sin_cos(A)))),k3_xcmplx_0(k3_xcmplx_0(k1_square_1(k19_sin_cos(A)),k1_square_1(k19_sin_cos(B))),k6_xcmplx_0(A,B))) ) ) ) )).
fof(t56_ec_pf_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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 ) ) ) ) )).
fof(t56_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k9_int_3(A))) => ! [G] : ( 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] : ( 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] : ( 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 = k5_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))) ) ) ) ) ) ) ) ) ) ) )).
fof(t56_ens_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t56_entropy1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_matrprob(A) & m2_finseq_1(A,k1_numbers) ) => ( ? [B] : ( v7_ordinal1(B) & r2_hidden(B,k4_finseq_1(A)) & k1_funct_1(A,B) = 1 ) => k6_entropy1(A) = k5_numbers ) ) )).
fof(t56_enumset1,axiom,( ! [A] : k6_enumset1(A,A,A,A,A,A,A,A) = k1_tarski(A) )).
fof(t56_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ~ ( ! [F] : ( m1_subset_1(F,A) => ! [G] : ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t56_euclid_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => r1_rvsum_1(B,C) ) => B = k4_struct_0(k15_euclid(A)) ) ) ) )).
fof(t56_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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(k5_numbers,k10_euclid_3(2,A,B,C,D)) & r1_xxreal_0(k5_numbers,k11_euclid_3(2,A,B,C,D)) & r1_xxreal_0(k5_numbers,k12_euclid_3(2,A,B,C,D)) & ~ ( k10_euclid_3(2,A,B,C,D) != k5_numbers & k11_euclid_3(2,A,B,C,D) != k5_numbers & k12_euclid_3(2,A,B,C,D) != k5_numbers ) ) ) ) ) ) ) ) )).
fof(t56_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => k12_euclid(A) = k3_square_1(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k1_funct_1(A,1)),k1_square_1(k1_funct_1(A,2))),k1_square_1(k1_funct_1(A,3)))) ) )).
fof(t56_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ( E = k2_euclid_4(A,C,D) => a_4_0_euclidlp(A,B,C,D) = k2_euclidlp(A,B,E) ) ) ) ) ) ) )).
fof(t56_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( ( 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,k9_funct_7(E,A,B))) ) => r2_hidden(k4_tarski(C,B),k6_exchsort(D,E)) ) ) ) )).
fof(t56_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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)) ) )).
fof(t56_fcont_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( A != k5_numbers => k2_funct_1(k1_fcont_1(A,B)) = k1_fcont_1(k5_xcmplx_0(A),k4_xcmplx_0(k7_xcmplx_0(B,A))) ) ) ) )).
fof(t56_fdiff_11,axiom,( ! [A] : ( ( 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),k22_sin_cos))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(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),k22_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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),k22_sin_cos),A),B) = k7_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k22_sin_cos,k6_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k1_funct_1(k2_sin_cos9,B)))),k2_xcmplx_0(1,k1_square_1(B))) ) ) ) ) ) )).
fof(t56_fdiff_4,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k22_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,B)),k3_taylor_1))) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(B,C) = 1 ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_rfunct_1(k1_numbers,k1_numbers,k22_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,B)),k3_taylor_1),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_rfunct_1(k1_numbers,k1_numbers,k22_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,B)),k3_taylor_1),A),C) = k7_xcmplx_0(1,k2_xcmplx_0(k1_funct_1(k22_sin_cos,C),1)) ) ) ) ) ) ) )).
fof(t56_fib_num2,axiom,( k5_fib_num2(4) = k10_finseq_1(1,3) )).
fof(t56_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_lattices(k6_filter_0(A,k2_filter_0(A,B))) = B ) ) )).
fof(t56_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r3_lattices(A,k4_lattices(A,k4_filter_0(A,B,D),k4_filter_0(A,C,D)),k4_filter_0(A,k3_lattices(A,B,C),D)) ) ) ) ) )).
fof(t56_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) | r2_hidden(k7_lattices(A,C),B) ) ) ) ) ) ) )).
fof(t56_finseq_1,axiom,( ! [A] : ~ ( v1_finset_1(A) & ! [B] : ( v7_ordinal1(B) => ~ r2_wellord2(A,k2_finseq_1(B)) ) ) )).
fof(t56_finseq_2,axiom,( ! [A] : k2_finseq_2(k5_numbers,A) = k1_xboole_0 )).
fof(t56_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : r1_tarski(k8_relat_1(A,C),k8_relat_1(k7_finseq_1(A,B),C)) ) ) )).
fof(t56_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t56_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t56_finseq_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t56_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,B) & m2_finseq_1(C,A) ) => ! [D] : ( ( 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(k4_ordinal1,A,k1_finseqop(A,A,A,D,k5_finseq_2(A,B,k4_binop_1(A,D)),C),C) & r2_relset_1(k4_ordinal1,A,k1_finseqop(A,A,A,D,C,k5_finseq_2(A,B,k4_binop_1(A,D))),C) ) ) ) ) ) ) )).
fof(t56_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t56_flang_1,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(t56_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => r1_tarski(k1_flang_2(A,k1_flang_2(A,B,E,F),C,D),k1_flang_2(A,B,k3_xcmplx_0(E,C),k3_xcmplx_0(F,D))) ) ) ) ) ) )).
fof(t56_flang_3,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(t56_fomodel0,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( 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)) ) ) )).
fof(t56_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & v8_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( ( ~ v2_struct_0(D) & v5_fsm_1(D,A,B) & l2_fsm_1(D,A,B) ) => ! [E] : ( ( ~ 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t56_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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) ) ) ) )).
fof(t56_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) ) )).
fof(t56_funct_2,axiom,( ! [A] : ! [B] : ( ( 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))) ) ) ) )).
fof(t56_funct_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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))) ) ) )).
fof(t56_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t56_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t56_funct_7,axiom,( k5_funct_7(k1_xboole_0) = k1_xboole_0 & k6_funct_7(k1_xboole_0) = k1_xboole_0 )).
fof(t56_funct_8,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k1_funct_1(k1_funct_8,A) = 1 ) ) )).
fof(t56_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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) ) ) ) ) ) )).
fof(t56_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => k4_struct_0(k7_fvaluat1(A,B)) = k4_struct_0(A) ) ) ) )).
fof(t56_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t56_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( ( ~ v1_xboole_0(G) & v1_relat_1(G) & v2_relat_1(G) & v1_funct_1(G) & v1_finseq_1(G) ) => ! [H] : ( m1_genealg1(H,G) => ! [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) ) ) ) ) ) ) ) ) ) ) )).
fof(t56_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t56_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( 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 ) ) ) ) )).
fof(t56_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( k3_glib_001(A,B) = k1_funct_1(B,C) => r2_relset_1(k4_ordinal1,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))) ) ) ) ) )).
fof(t56_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_003(A) & v3_glib_003(A) ) => ! [B] : ! [C] : k14_glib_003(A) = k14_glib_003(k12_glib_003(A,B,C)) ) )).
fof(t56_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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)),k1_nat_1(A,1)) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k1_matrix_0(k2_goboard2(C))) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B)),k3_topreal1(2,C)) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,2),B)),k3_topreal1(2,C)) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,1) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B) & ( ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,2) = k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,2),B) ) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,2) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,2),B) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k7_nat_d(k3_finseq_1(C),1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,B) ) ) ) & ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(1,D) & ~ r1_xxreal_0(k3_finseq_1(C),k1_nat_1(D,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_nat_1(D,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B) & ( ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,D) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,B) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_nat_1(D,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,2),B) ) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,D) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,2),B) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_nat_1(D,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,B) ) ) ) ) ) ) ) ) )).
fof(t56_graph_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => k3_graph_2(B,k9_finseq_1(A)) = B ) )).
fof(t56_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_graph_1(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( 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))) ) ) ) ) )).
fof(t56_graph_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t56_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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),k8_polynom1(A,C)) ) ) ) ) ) ) )).
fof(t56_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,A) => ( m1_group_2(C,D) => r1_tarski(k4_group_11(A,C,B),k4_group_11(A,D,B)) ) ) ) ) ) )).
fof(t56_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t56_group_3,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k4_group_3(A,B,C) = B ) ) ) ) )).
fof(t56_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => r1_group_2(A,k8_group_4(A,B,C),k8_group_4(A,C,B)) ) ) ) )).
fof(t56_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t56_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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) <=> r1_group_2(A,k9_group_6(A,B,C),k6_group_2(A)) ) ) ) ) )).
fof(t56_group_9,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(t56_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( 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)) ) ) )).
fof(t56_hfdiff_1,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k1_relset_1(k1_numbers,k26_sin_cos)) => ( r2_fdiff_1(k26_sin_cos,A) & r2_relset_1(k1_numbers,k1_numbers,k2_fdiff_1(k26_sin_cos,A),k5_relset_1(k1_numbers,k1_numbers,k41_valued_1(k1_numbers,k1_numbers,k6_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos)),A)) ) ) ) )).
fof(t56_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => k9_ideal_1(A,k2_struct_0(A)) = u1_struct_0(A) ) )).
fof(t56_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t56_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(B,k5_int_1(A,B)) ) ) ) )).
fof(t56_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(A,B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k2_xcmplx_0(1,k1_funct_1(k16_sin_cos,D)) != k5_numbers & k6_xcmplx_0(1,k1_funct_1(k16_sin_cos,D)) != k5_numbers & k1_funct_1(C,D) = k7_xcmplx_0(k1_funct_1(k16_sin_cos,D),k6_xcmplx_0(k1_funct_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),k26_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) = k6_xcmplx_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k26_sin_cos),k1_fdiff_9),k2_seq_4(A)),k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k26_sin_cos),k1_fdiff_9),k3_seq_4(A))) ) ) ) ) )).
fof(t56_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,D) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => k1_funct_1(C,E) = 1 ) ) & r2_relset_1(k1_numbers,k1_numbers,B,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,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)),k1_sin_cos9))) & r1_tarski(D,k2_rcomp_1(k4_xcmplx_0(1),1)) & D = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_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)),k2_seq_4(A)),k1_funct_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)),k3_seq_4(A))) ) ) ) ) ) )).
fof(t56_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k3_xcmplx_0(k1_funct_1(k16_sin_cos,k1_funct_1(k16_sin_cos,D)),k1_funct_1(k18_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) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)),k3_seq_4(A))) ) ) ) ) )).
fof(t56_integr19,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( ~ v8_ordinal1(D) & m1_subset_1(D,k4_ordinal1) ) => ! [E] : ( ( 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] : ( ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t56_integra1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( 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)) = k2_xcmplx_0(k6_xcmplx_0(B,A),1) ) ) ) ) )).
fof(t56_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,1) => k2_integra5(A,k1_sin_cos2) = k7_xcmplx_0(k1_square_1(k6_xcmplx_0(k4_power,1)),k3_xcmplx_0(2,k4_power)) ) ) )).
fof(t56_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( 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] : ( v1_xreal_0(G) => ( r2_hidden(G,F) => ( k1_funct_1(D,G) = k6_xcmplx_0(G,A) & ~ r1_xxreal_0(k1_funct_1(D,G),k5_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,k3_xcmplx_0(2,A)))) = F & F = k1_relset_1(k1_numbers,E) & ! [G] : ( v1_xreal_0(G) => ( r2_hidden(G,F) => k1_funct_1(E,G) = k7_xcmplx_0(k2_xcmplx_0(G,A),k6_xcmplx_0(G,A)) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,E,B)) ) => k2_integra5(B,E) = k6_xcmplx_0(k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,F),k26_valued_1(k1_numbers,k1_numbers,C,k3_xcmplx_0(2,A))),k2_seq_4(B)),k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,F),k26_valued_1(k1_numbers,k1_numbers,C,k3_xcmplx_0(2,A))),k3_seq_4(B))) ) ) ) ) ) ) ) )).
fof(t56_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m2_interva1(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(t56_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( 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) ) ) )).
fof(t56_jgraph_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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] : ( 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(k7_xcmplx_0(2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(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 ) ) ) ) ) ) ) ) ) )).
fof(t56_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(1,C) & ~ r1_xxreal_0(k3_finseq_1(k2_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)),k2_jordan9(B,A),C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),D,1) ) ) ) ) )).
fof(t56_jordan1g,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,k5_numbers) => k3_topreal1(2,k2_jordan1e(A,B)) = k9_jordan6(k3_topreal1(2,k2_jordan9(A,B))) ) ) ) )).
fof(t56_jordan1h,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( 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] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(k4_tarski(D,E),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k7_nat_d(k3_finseq_1(C),1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),D,E) & r2_hidden(k4_tarski(D,k1_nat_1(E,1)),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k3_finseq_1(C)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),D,k1_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,k1_nat_1(E,2)),k2_matrix_0(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) )).
fof(t56_jordan1j,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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) | k1_nat_1(k1_jordan3(A,B),1) = k4_finseq_4(A,B) ) ) ) ) )).
fof(t56_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(A))) => ~ ( C != D & r2_hidden(C,k8_metric_1(k14_euclid(A),E,B)) & r2_hidden(D,k8_metric_1(k14_euclid(A),E,B)) & ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))))) ) => ~ ( v5_pre_topc(F,k5_topmetr,k15_euclid(A)) & k1_funct_1(F,k5_numbers) = C & k1_funct_1(F,1) = D & r1_tarski(k2_relset_1(u1_struct_0(k15_euclid(A)),F),k8_metric_1(k14_euclid(A),E,B)) ) ) ) ) ) ) ) ) )).
fof(t56_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( ( v1_topreal2(A) & r2_hidden(B,A) ) => r1_jordan6(A,B,B) ) ) ) )).
fof(t56_kurato_1,axiom,( ! [A] : ( v1_setfam_1(A) => ! [B] : ( r1_tarski(B,A) => v1_setfam_1(B) ) ) )).
fof(t56_lattice2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t56_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => v2_lexbfs(k26_lexbfs(A)) ) )).
fof(t56_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v7_limfunc1(A) & ! [C] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ~ 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)) ) ) ) ) )).
fof(t56_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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(k5_numbers)) = k1_xboole_0 ) => ( k2_limfunc2(B,A) = k5_numbers | ( r4_limfunc2(k6_rfunct_1(k1_numbers,k1_numbers,B),A) & k2_limfunc2(k6_rfunct_1(k1_numbers,k1_numbers,B),A) = k5_xcmplx_0(k2_limfunc2(B,A)) ) ) ) ) ) )).
fof(t56_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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) ) ) ) ) )).
fof(t56_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => r2_hidden(k8_lpspace1(A,k5_numbers),k9_lpspace1(A,B,C)) ) ) ) )).
fof(t56_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_hilbert1)) => ( r8_ltlaxio1(C,B) => r8_ltlaxio1(k4_subset_1(k1_hilbert1,C,k6_domain_1(k1_hilbert1,A)),B) ) ) ) ) )).
fof(t56_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m2_finseq_1(B,k1_hilbert1) => ( ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => r8_ltlaxio1(k1_subset_1(k1_hilbert1),k3_hilbert1(A,k7_partfun1(k1_hilbert1,B,C))) ) ) => r8_ltlaxio1(k1_subset_1(k1_hilbert1),k3_hilbert1(A,k7_partfun1(k1_hilbert1,k2_ltlaxio2(B),k3_finseq_1(k2_ltlaxio2(B))))) ) ) ) )).
fof(t56_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( B = k1_xboole_0 => k6_mathmorp(k5_numbers,A,B) = k1_xboole_0 ) ) ) )).
fof(t56_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,k1_numbers,A,A) & m2_finseq_1(E,k3_finseq_2(k1_numbers)) ) => ( r2_matrix10(k5_matrix10(A,B,C),k5_matrix10(A,D,E)) => r2_matrix10(k5_matrix10(A,B,D),k5_matrix10(A,C,E)) ) ) ) ) ) ) )).
fof(t56_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( ( v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ! [E] : ( ( v1_finset_1(E) & v1_setfam_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ! [F] : ( ( v1_finset_1(F) & v1_setfam_1(F) & m1_subset_1(F,k1_zfmisc_1(k4_ordinal1)) ) => ! [G] : ( ( v1_finset_1(G) & v1_setfam_1(G) & m1_subset_1(G,k1_zfmisc_1(k4_ordinal1)) ) => ! [H] : ( ( v1_finset_1(H) & v1_setfam_1(H) & m1_subset_1(H,k1_zfmisc_1(k4_ordinal1)) ) => ( ( r1_tarski(C,D) & r1_tarski(F,G) & E = k8_relat_1(k5_matrix13(D),C) & H = k8_relat_1(k5_matrix13(G),F) ) => ( r1_tarski(k2_zfmisc_1(k10_xtuple_0(k5_matrix13(E)),k10_xtuple_0(k5_matrix13(H))),k2_matrix_0(k6_matrix13(A,B,D,G))) & k6_matrix13(A,k6_matrix13(A,B,D,G),E,H) = k6_matrix13(A,B,C,F) ) ) ) ) ) ) ) ) ) ) )).
fof(t56_matrix14,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( k4_matrix_3(B,C,D) = k3_matrix_1(B,A) => ( v1_matrix_6(C,A,B) & v1_matrix_6(D,A,B) ) ) ) ) ) ) )).
fof(t56_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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,k5_numbers),k1_matrix_3(B,A,k5_numbers)) = k1_tarski(k1_xboole_0) ) ) )).
fof(t56_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v5_matrix16(C,B) & v5_matrix16(D,B) ) => v5_matrix16(k1_matrix_4(B,C,D),B) ) ) ) ) ) )).
fof(t56_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(A)) ) => ~ ( ~ r1_xxreal_0(k1_matrix_0(B),k5_numbers) & ~ r1_xxreal_0(k1_matrix_0(C),k5_numbers) & ~ ( B = C <=> ( k4_matrix_0(A,B) = k4_matrix_0(A,C) & k1_matrix_0(B) = k1_matrix_0(C) ) ) ) ) ) ) )).
fof(t56_matrix_4,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t56_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_6(C,A,B) & v1_matrix_6(D,A,B) & v1_matrix_6(E,A,B) ) => ( v1_matrix_6(k4_matrix_3(B,k4_matrix_3(B,C,D),E),A,B) & k1_matrix_6(A,B,k4_matrix_3(B,k4_matrix_3(B,C,D),E)) = k4_matrix_3(B,k4_matrix_3(B,k1_matrix_6(A,B,E),k1_matrix_6(A,B,D)),k1_matrix_6(A,B,C)) ) ) ) ) ) ) ) )).
fof(t56_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => k1_matrix_8(A,B,k2_matrix_3(B,C)) = k4_algstr_0(B,k1_matrix_8(A,B,C)) ) ) ) )).
fof(t56_matrix_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ( ? [F] : ( m1_subset_1(F,k4_ordinal1) & r2_hidden(F,k2_finseq_1(A)) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( r2_hidden(G,k2_finseq_1(A)) => k1_funct_1(k8_matrix_0(u1_struct_0(B),D,F),G) = k8_group_1(B,C,k7_partfun1(u1_struct_0(B),k8_matrix_0(u1_struct_0(B),E,F),G)) ) ) & ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( r2_hidden(G,k2_finseq_1(A)) => ( G = F | k8_matrix_0(u1_struct_0(B),D,G) = k8_matrix_0(u1_struct_0(B),E,G) ) ) ) ) => ! [F] : ( m1_matrix_2(F,k3_matrix_2(A)) => ? [G] : ( m1_subset_1(G,k4_ordinal1) & 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)) ) ) ) ) ) ) ) ) )).
fof(t56_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k2_numbers)) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k3_finseq_1(A) = k1_matrix_0(C) ) => ( r1_xxreal_0(k3_finseq_1(A),k5_numbers) | r1_xxreal_0(k3_finseq_1(B),k5_numbers) | k8_complsp2(k6_matrixc1(C,A),B) = k12_matrixc1(k13_matrixc1(A,B,k4_matrix_0(k2_numbers,C))) ) ) ) ) ) )).
fof(t56_matrixj1,axiom,( ! [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] : ( m2_finseq_1(B,k4_ordinal1) => ( k10_matrixj1(u1_struct_0(A),k23_matrixj1(A,B)) = B & k11_matrixj1(u1_struct_0(A),k23_matrixj1(A,B)) = B ) ) ) )).
fof(t56_matrixr1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(B)) ) => k8_matrix_0(k1_numbers,k7_matrixr1(A,B),C) = k11_rvsum_1(k3_finseq_1(B),k8_matrix_0(k1_numbers,B,C),A) ) ) ) ) )).
fof(t56_matrixr2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(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)) ) ) ) )).
fof(t56_matrprob,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v4_matrprob(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( ~ v3_relat_1(k4_matrix_0(k1_numbers,A)) & v1_matrix_0(k4_matrix_0(k1_numbers,A)) & v4_matrprob(k4_matrix_0(k1_numbers,A)) & m2_finseq_1(k4_matrix_0(k1_numbers,A),k3_finseq_2(k1_numbers)) ) ) )).
fof(t56_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ! [E] : ( r2_hidden(E,D) <=> ? [F] : ? [G] : ? [H] : ( r2_hidden(F,A) & r2_hidden(G,B) & r2_hidden(H,C) & E = k3_xtuple_0(F,G,H) ) ) => D = k3_zfmisc_1(A,B,C) ) )).
fof(t56_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k1_numbers))) => ( v2_measure6(A) => v2_rcomp_1(k6_setfam_1(k1_numbers,A)) ) ) )).
fof(t56_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( v2_membered(C) => ! [D] : ( v2_membered(D) => ( ( r1_tarski(A,B) & r1_tarski(C,D) ) => r1_tarski(k10_member_1(A,C),k10_member_1(B,D)) ) ) ) ) ) )).
fof(t56_memstr_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_setfam_1(B) => ! [C] : ( ( ~ v2_struct_0(C) & v2_memstr_0(C,B) & v3_memstr_0(C,B) & l1_memstr_0(C,B) ) => ! [D] : ( ( 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_xcmplx_0(k5_memstr_0(B,C,D),A))) ) ) ) ) ) )).
fof(t56_mesfunc5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_nat_1(k6_numbers,A,B),k8_supinf_2(k17_supinf_2(A))) ) ) )).
fof(t56_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t56_midsp_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t56_mmlquery,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => r1_xxreal_0(k25_mmlquery(A),k3_finseq_1(A)) ) )).
fof(t56_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k30_modelc_1(k25_modelc_2(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k42_modelc_2(A,B))) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t56_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( 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))) ) ) ) ) )).
fof(t56_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( r1_nat_d(A,B) <=> r1_nat_d(A,k6_moebius1(B)) ) ) ) )).
fof(t56_monoid_0,axiom,( k8_monoid_0 = g4_algstr_0(k4_ordinal1,k24_binop_2,1) )).
fof(t56_monoid_1,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t56_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m2_pboole(C,u1_struct_0(A),B,k7_funcop_1(u1_struct_0(A),k4_ordinal1)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_msafree4(E,u1_struct_0(A),B,k1_msafree4(u1_struct_0(A),B,D)) => k6_msafree4(A,B,C,k1_trees_4(k4_tarski(E,D))) = k1_trees_4(k4_tarski(k3_funct_2(k1_msafree4(u1_struct_0(A),B,D),k1_funct_1(k7_funcop_1(u1_struct_0(A),k4_ordinal1),D),k2_msafree4(u1_struct_0(A),B,k7_funcop_1(u1_struct_0(A),k4_ordinal1),C,D),E),D)) ) ) ) ) ) )).
fof(t56_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( k11_nat_3(B,A) != k5_numbers => k1_funct_1(k13_nat_3(B),A) = k1_newton(A,k11_nat_3(B,A)) ) ) ) )).
fof(t56_nat_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(1,A) & ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ~ ( ~ r1_xxreal_0(B,A) & r1_xxreal_0(B,k2_nat_1(2,A)) ) ) ) ) )).
fof(t56_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(C,A) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(k7_nat_d(B,C),k7_nat_d(A,C)) ) ) ) ) )).
fof(t56_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ! [D] : ! [E] : ( ( 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) ) ) ) ) )).
fof(t56_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_nat_d(C,B) => r1_nat_d(k6_nat_d(C,A),k6_nat_d(B,A)) ) ) ) ) )).
fof(t56_normform,axiom,( ! [A] : m1_subset_1(k1_xboole_0,u1_struct_0(k12_normform(A))) )).
fof(t56_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t56_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => m1_oppcat_1(k11_oppcat_1(A,B,C),A,k2_oppcat_1(B)) ) ) ) )).
fof(t56_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(A))) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A))) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A))))) ) => ! [G] : ( ( v1_funct_1(G) & v1_nfcont_3(G,k4_real_ns1(A)) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [H] : ( ( v1_funct_1(H) & v1_nfcont_3(H,k4_real_ns1(A)) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ( ( D = k2_rcomp_1(B,C) & r5_nfcont_1(k4_real_ns1(A),k4_real_ns1(A),u1_struct_0(k4_real_ns1(A)),F) & k1_relset_1(k1_numbers,G) = k3_integra5(B,C) & r2_ndiff_3(k4_real_ns1(A),G,D) & k7_partfun1(u1_struct_0(k4_real_ns1(A)),G,B) = E & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,D) => k1_ndiff_3(k4_real_ns1(A),G,I) = k3_funct_2(u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A)),F,k7_partfun1(u1_struct_0(k4_real_ns1(A)),G,I)) ) ) & k1_relset_1(k1_numbers,H) = k3_integra5(B,C) & r2_ndiff_3(k4_real_ns1(A),H,D) & k7_partfun1(u1_struct_0(k4_real_ns1(A)),H,B) = E & ! [I] : ( v1_xreal_0(I) => ( r2_hidden(I,D) => k1_ndiff_3(k4_real_ns1(A),H,I) = k3_funct_2(u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A)),F,k7_partfun1(u1_struct_0(k4_real_ns1(A)),H,I)) ) ) ) => ( r1_xxreal_0(C,B) | r2_relset_1(k1_numbers,u1_struct_0(k4_real_ns1(A)),G,H) ) ) ) ) ) ) ) ) ) ) )).
fof(t56_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ( r6_orders_1(A,B) & v6_relat_2(A) ) => r8_orders_1(A,B) ) ) )).
fof(t56_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ( k5_ordinal3(A,k1_xboole_0) = A & k5_ordinal3(k1_xboole_0,A) = k1_xboole_0 ) ) )).
fof(t56_ordinal5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) & v1_ordinal2(A) ) => r1_ordinal1(k1_funct_1(A,k5_numbers),k4_ordinal5(A)) ) )).
fof(t56_ordinal6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v3_ordinal6(B) ) => ( ( r2_hidden(k9_xtuple_0(B),A) & ! [C] : ( 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)))) ) ) ) ) ) )).
fof(t56_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r3_parsp_2(A,F,G,B,C) & r3_parsp_2(A,F,G,D,E) ) => r3_parsp_2(A,B,C,D,E) ) ) ) ) ) ) ) ) )).
fof(t56_partfun1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_xboole_0(k9_xtuple_0(A),k9_xtuple_0(B)) => r1_partfun1(A,B) ) ) ) )).
fof(t56_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t56_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) )).
fof(t56_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( 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) & k10_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) = k6_xcmplx_0(k5_pdiff_5(B,A),k5_pdiff_5(C,A)) ) ) ) ) ) )).
fof(t56_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t56_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( v1_int_2(B) & ~ r1_xxreal_0(B,2) & r1_nat_d(B,k4_pepin(A)) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => B != k1_nat_1(k2_nat_1(C,k11_newton(2,k1_nat_1(A,1))),1) ) ) ) ) )).
fof(t56_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,k8_polyform(A,B)) => ! [D] : ( m1_subset_1(D,k8_polyform(A,k6_xcmplx_0(B,1))) => ( ( B = k5_numbers & D = k1_xboole_0 ) => k16_polyform(A,B,D,C) = k5_struct_0(k2_bspace) ) ) ) ) ) )).
fof(t56_polyred,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t56_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & A != 1 & ~ r1_xxreal_0(B,k5_numbers) & B != 1 & ~ r1_xxreal_0(C,k5_numbers) & k3_power(A,C) != k3_xcmplx_0(k3_power(A,B),k3_power(B,C)) ) ) ) ) )).
fof(t56_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(t56_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_rat_1(C) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & k4_prepower(k3_xcmplx_0(A,B),C) != k3_xcmplx_0(k4_prepower(A,C),k4_prepower(B,C)) ) ) ) ) )).
fof(t56_prob_3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( m1_prob_3(C,A,B) => ? [D] : ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k1_relset_1(k4_ordinal1,C)) => k1_prob_2(A,B,D,E) = k8_prob_3(A,B,C,E) ) ) & ! [E] : ( v7_ordinal1(E) => ( ~ r2_hidden(E,k1_relset_1(k4_ordinal1,C)) => k1_prob_2(A,B,D,E) = k1_xboole_0 ) ) ) ) ) )).
fof(t56_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t56_pscomp_1,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t56_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( ~ ( ~ r6_pboole(A,D,k1_pboole(A)) & ~ r6_pboole(A,D,k1_pzfmisc1(A,B)) & ~ r6_pboole(A,D,k1_pzfmisc1(A,C)) & ~ r6_pboole(A,D,k2_pzfmisc1(A,B,C)) ) => r6_pboole(A,k4_pboole(A,D,k2_pzfmisc1(A,B,C)),k1_pboole(A)) ) ) ) ) )).
fof(t56_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t56_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => k5_qc_lang3(A,k1_qc_lang2(A)) = k1_xboole_0 ) )).
fof(t56_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k24_quaterni(k17_quatern2(A,B)) = k17_quatern2(A,k24_quaterni(B)) ) ) )).
fof(t56_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => ! [D] : ( v1_quaterni(D) => k23_quaterni(k22_quaterni(A,B),k25_quaterni(C,D)) = k25_quaterni(k25_quaterni(k22_quaterni(k23_quaterni(A,C),k23_quaterni(B,C)),k23_quaterni(A,D)),k23_quaterni(B,D)) ) ) ) ) )).
fof(t56_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k27_quaterni(k25_quaterni(A,B)) = k25_quaterni(k27_quaterni(A),k27_quaterni(B)) ) ) )).
fof(t56_quofield,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t56_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B))))) => ! [D] : ( 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_seq_4(k7_partfun1(k9_setfam_1(k1_numbers),D,1)) = A ) ) ) ) ) )).
fof(t56_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( r1_tarski(A,k9_xtuple_0(B)) => k9_xtuple_0(k5_relat_1(B,A)) = A ) ) )).
fof(t56_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => k7_relset_1(B,A,k3_relset_1(A,B,C),B) = k7_relset_1(A,A,k7_relset_2(A,B,A,C,k3_relset_1(A,B,C)),A) ) )).
fof(t56_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t56_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(C))) => ! [G] : ( ( ~ v2_struct_0(G) & l1_rewrite3(G,F) ) => ! [H] : ( m1_rewrite1(H,k1_rewrite3(C,F,G)) => ! [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] : ( m1_subset_1(J,k8_afinsq_1(C)) => ~ ( r1_rewrite3(F,G,A,J,B) & D = k1_flang_1(C,J,E) ) ) ) ) ) ) ) ) ) ) )).
fof(t56_rfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t56_rfunct_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_numbers) => ( r2_rfunct_3(A,B) <=> r2_rfunct_3(k26_valued_1(k1_numbers,k1_numbers,A,C),B) ) ) ) ) )).
fof(t56_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_comseq_2(A) => ( v1_comseq_2(k4_rinfsup1(A)) & v1_comseq_2(k3_rinfsup1(A)) ) ) ) )).
fof(t56_rlaffin1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( 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) ) ) ) )).
fof(t56_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t56_rlsub_2,axiom,( ! [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) ) => v14_lattices(g3_lattices(k3_rlsub_2(A),k5_rlsub_2(A),k6_rlsub_2(A))) ) )).
fof(t56_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_connsp_2(B,A,k4_struct_0(A)) => ? [C] : ( 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) ) ) ) )).
fof(t56_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t56_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_rlvect_2(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t56_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t56_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_rmod_4(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t56_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ( v9_robbins1(A) => v6_robbins1(A) ) ) )).
fof(t56_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t56_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k3_roughs_1(A,B) = a_2_2_roughs_1(A,B) ) ) )).
fof(t56_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_rpr_1(A,B,C) => r1_rpr_1(A,k3_subset_1(A,B),C) ) ) ) ) )).
fof(t56_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t56_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => v14_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A))) ) )).
fof(t56_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => k12_rvsum_1(k2_finseq_2(A,B)) = k2_finseq_2(A,k1_square_1(B)) ) ) )).
fof(t56_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( m1_subset_1(D,k4_ordinal1) => ( ~ r1_xxreal_0(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(B)),D) => k3_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(B),D)) = k3_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),k1_scmfsa_m(B),D)) ) ) ) ) ) ) )).
fof(t56_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k5_numbers)) = 1 & ! [D] : ( v7_ordinal1(D) => k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_m(B)),D),k4_scmfsa_2(k5_numbers)) = 1 ) ) ) ) ) ) )).
fof(t56_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ( k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k6_scmfsa_2(A,B),C),k4_struct_0(k1_scmfsa_2)) = k4_card_1(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,C)) & k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k6_scmfsa_2(A,B),C),A) = k1_funct_1(C,B) & ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ( D != A => k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k6_scmfsa_2(A,B),C),D) = k1_funct_1(C,D) ) ) & ! [D] : ( m1_scmfsa_2(D) => r2_relset_1(k4_ordinal1,k4_numbers,k18_scmfsa_2(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k6_scmfsa_2(A,B),C),D),k18_scmfsa_2(C,D)) ) ) ) ) ) )).
fof(t56_scmpds_2,axiom,( ! [A] : ( ( 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] : ( v1_int_1(B) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t56_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => k5_card_1(k3_scmpds_6(A,B,C,D)) = k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),2) ) ) ) ) )).
fof(t56_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ! [C] : ( 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)) ) ) ) )).
fof(t56_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_semi_af1(A,B,C,C,B) => B = C ) ) ) ) )).
fof(t56_seq_4,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => r7_binop_1(k2_numbers,k5_seq_4(A),k3_binop_2) ) )).
fof(t56_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k4_kurato_0(A,B) = k4_kurato_0(A,k4_setlim_1(A,B)) ) )).
fof(t56_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => k9_nat_1(k9_setfam_1(B),k4_setlim_1(B,k6_setlim_2(B,D,C)),A) = k4_subset_1(B,C,k9_nat_1(k9_setfam_1(B),k4_setlim_1(B,D),A)) ) ) ) )).
fof(t56_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ! [D] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,k5_finsub_1(B)) => ! [G] : ( 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] : ( 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)) ) ) ) ) ) )).
fof(t56_sf_mastr,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t56_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t56_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_simplex0(D,A) => ! [E] : ( ( 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))) ) ) ) )).
fof(t56_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(A,k11_comseq_3(k24_sin_cos(A))) = k6_xcmplx_0(k6_xcmplx_0(k11_comseq_3(k3_sin_cos(A)),k6_complex1),A) ) )).
fof(t56_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A)) = k7_xcmplx_0(k6_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,k3_xcmplx_0(2,A)),1),2) ) )).
fof(t56_sin_cos6,axiom,( ! [A] : ( v1_int_1(A) => v5_valued_0(k5_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k2_xcmplx_0(k28_sin_cos,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A)),k2_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A))))) ) )).
fof(t56_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(1,k1_square_1(A)) & ~ r1_xxreal_0(1,k1_square_1(B)) & k2_xcmplx_0(k4_sin_cos7(A),k4_sin_cos7(B)) != k4_sin_cos7(k7_xcmplx_0(k2_xcmplx_0(A,B),k2_xcmplx_0(1,k3_xcmplx_0(A,B)))) ) ) ) )).
fof(t56_sin_cos9,axiom,( k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_sin_cos9,k1_rcomp_1(k4_xcmplx_0(1),1))) = k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos)) )).
fof(t56_sincos10,axiom,( k3_relat_1(k2_partfun1(k1_numbers,k1_numbers,k4_sincos10,k1_rcomp_1(1,k3_square_1(2))),k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k7_xcmplx_0(k28_sin_cos,2)))) = k1_partfun2(k1_numbers,k1_rcomp_1(1,k3_square_1(2))) )).
fof(t56_sppol_2,axiom,( k1_topreal1 = k1_sppol_2(k5_numbers,1,k5_numbers,1) )).
fof(t56_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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) ) ) ) )).
fof(t56_sprect_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t56_sprect_3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r1_sprect_2(A,B) & r1_sprect_2(A,k13_matrix_0(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)) ) ) ) ) )).
fof(t56_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t56_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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,k3_square_1(k2_xcmplx_0(1,k1_square_1(A)))),k3_square_1(k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) )).
fof(t56_stirl2_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) => ~ ( v1_finset_1(A) & ! [B] : ( v7_ordinal1(B) => ? [C] : ( v7_ordinal1(C) & r2_hidden(C,A) & ~ r1_xxreal_0(C,B) ) ) ) ) )).
fof(t56_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_valuat_1(D,A,C) => ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [F] : ( m2_subset_1(F,k16_substut1(A),k38_substut1(A)) => ! [G] : ( m1_substut1(G,A,k7_sublemma(A,F,B)) => ( v3_substut1(k7_sublemma(A,F,B),A) => ( ! [H] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t56_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ! [C] : ( 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)))) ) ) ) ) )).
fof(t56_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_tex_2(B,A) => v1_tops_1(B,A) ) ) ) )).
fof(t56_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( m1_pre_topc(B,A) => ~ v4_tex_3(B,A) ) => v3_tdlat_3(A) ) ) )).
fof(t56_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) => k3_tex_4(A,B) = B ) ) ) )).
fof(t56_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t56_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t56_topgen_1,axiom,( ? [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) & ? [B] : ( 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) ) ) )).
fof(t56_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_card_3(B) => k4_topgen_4(A,B) = k1_xboole_0 ) ) ) )).
fof(t56_topgen_5,axiom,( ! [A] : ( 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))) ) ) )).
fof(t56_topgrp_1,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_tops_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => v1_tops_1(k4_group_2(A,C,B),A) ) ) ) )).
fof(t56_topreal6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( v1_xreal_0(D) => ( C = k9_metric_1(k14_euclid(A),B,D) => v4_pre_topc(C,k15_euclid(A)) ) ) ) ) ) )).
fof(t56_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( m2_finseq_2(G,k1_numbers,k1_euclid(2)) => ! [H] : ( m2_finseq_2(H,k1_numbers,k1_euclid(2)) => ! [I] : ( m2_finseq_2(I,k1_numbers,k1_euclid(2)) => ~ ( G = E & H = F & I = k19_euclid(A,B) & D = k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(2,k22_rvsum_1(k5_algstr_0(k15_euclid(2),F,E),k5_algstr_0(k15_euclid(2),E,k19_euclid(A,B))))),k3_square_1(k1_quin_1(k18_rvsum_1(k11_euclid(2,k8_euclid(2,H,G))),k3_xcmplx_0(2,k22_rvsum_1(k5_algstr_0(k15_euclid(2),F,E),k5_algstr_0(k15_euclid(2),E,k19_euclid(A,B)))),k6_xcmplx_0(k18_rvsum_1(k11_euclid(2,k8_euclid(2,G,I))),k1_square_1(C))))),k3_xcmplx_0(2,k18_rvsum_1(k11_euclid(2,k8_euclid(2,H,G))))) & E != F & r2_hidden(E,k6_jgraph_6(A,B,C)) & ! [J] : ( m1_subset_1(J,u1_struct_0(k15_euclid(2))) => ~ ( k1_tarski(J) = k9_subset_1(u1_struct_0(k15_euclid(2)),k4_topreal9(k15_euclid(2),E,F),k5_jgraph_6(A,B,C)) & J = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),E,k6_xcmplx_0(1,D)),k1_rlvect_1(k15_euclid(2),F,D)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t56_toprealc,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( ( 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),k14_toprealc(B,u1_struct_0(A),u1_struct_0(k3_topmetr),C),k16_toprealc(B,B))) ) ) ) )).
fof(t56_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) )).
fof(t56_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t56_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t56_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t56_trees_3,axiom,( ! [A] : ( ( 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(k5_numbers)))) = k2_xboole_0(k11_trees_3(A),k2_trees_1(k1_nat_1(k3_finseq_1(A),1))) ) )).
fof(t56_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & ? [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(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) ) ) ) ) ) ) ) ) )).
fof(t56_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t56_valued_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_finseq_1(B) ) => k4_finseq_1(k15_finseq_1(B)) = k4_finseq_1(k15_finseq_1(k61_valued_1(B,A))) ) ) )).
fof(t56_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( v1_valued_2(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ( r2_hidden(A,k9_xtuple_0(k47_valued_2(C,E,D))) => k1_funct_1(k47_valued_2(C,E,D),A) = k24_valued_1(k1_funct_1(E,A),k5_xcmplx_0(D)) ) ) ) ) )).
fof(t56_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t56_vectsp_5,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_5(D,A,B,C) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t56_vfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ 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] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,u1_struct_0(D)))) ) => ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t56_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t56_waybel23,axiom,( ! [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] : ( ( 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(k1_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)))) ) ) ) )).
fof(t56_waybel34,axiom,( ! [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] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t56_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( D != k1_xboole_0 => r2_yellow_0(A,D) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(B)) ) => ~ ( r2_yellow_0(A,E) & D = k2_yellow_0(A,E) ) ) ) ) & ! [D] : ( ( 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) ) ) ) ) )).
fof(t56_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t56_waybel_2,axiom,( ! [A] : ( ( ~ 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) ) ) ) )).
fof(t56_waybel_4,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r5_waybel_4(A,B,C) <=> ( r2_hidden(C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,B) & r2_orders_2(A,D,C) ) ) ) ) ) ) )).
fof(t56_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r2_xboole_0(A,B) & r2_xboole_0(B,C) ) => r2_xboole_0(A,C) ) )).
fof(t56_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k6_xboolean(A,k8_xboolean(A,B)) = k8_xboolean(A,B) ) ) )).
fof(t56_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(1,k7_xcmplx_0(1,A)) = A ) )).
fof(t56_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(k5_numbers,C) => r1_xxreal_0(B,k6_xcmplx_0(A,C)) ) ) => r1_xxreal_0(B,A) ) ) ) )).
fof(t56_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_tarski(k4_xxreal_1(C,D),k2_xxreal_1(A,B)) => ( r1_xxreal_0(D,C) | ( r1_xxreal_0(A,C) & r1_xxreal_0(D,B) ) ) ) ) ) ) ) )).
fof(t56_xxreal_2,axiom,( ! [A] : ( ( v2_membered(A) & ~ v1_xboole_0(A) ) => ! [B] : ( m2_xxreal_2(B,A) => ( r2_hidden(B,A) => B = k2_xxreal_2(A) ) ) ) )).
fof(t56_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t56_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & l1_orders_2(B) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t56_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( r1_waybel18(A,B) <=> ? [C] : ( ~ v2_struct_0(C) & m1_pre_topc(C,B) & r1_borsuk_1(B,C) & r1_t_0topsp(C,A) ) ) ) ) )).
fof(t56_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( 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) ) ) ) )).
fof(t56_yellow_4,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t56_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k12_lattice3(A,B,C) = k3_yellow_0(A) <=> k1_yellow_5(A,B,C) = B ) ) ) ) )).
fof(t56_yellow_9,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( m3_yellow_9(C,A,B) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t56_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( v4_zf_lang(B) => ( r1_zf_lang(A,B) <=> A = k20_zf_lang(B) ) ) ) ) )).
fof(t56_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => 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))) ) ) )).
fof(t56_zfmisc_1,axiom,( ! [A] : ! [B] : ( k4_xboole_0(B,k1_tarski(A)) = B <=> ~ r2_hidden(A,B) ) )).
fof(t56_zmodul01,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t56_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( r1_tarski(B,C) & v1_zmodul02(C,A) ) => v1_zmodul02(B,A) ) ) ) ) )).
fof(t57_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l3_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_abcmiz_0(A)) => ( r5_abcmiz_0(A,B,C) => r3_abcmiz_0(A,B,C) ) ) ) ) )).
fof(t57_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( 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] : ( m1_abcmiz_1(C,A,k13_abcmiz_1(A)) => B != k30_abcmiz_1(A,k32_abcmiz_1(A),C) ) ) ) ) )).
fof(t57_abcmiz_a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k27_abcmiz_1)) => ? [C] : ( 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 ) ) ) )).
fof(t57_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,B) & r2_hidden(D,C) ) ) ) ) ) ) )).
fof(t57_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_aff_4(B,A) => r1_aff_4(A,B,B) ) ) ) )).
fof(t57_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t57_afinsq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xcmplx_0(B) => k7_afinsq_2(k7_funcop_1(A,B)) = k3_xcmplx_0(A,B) ) ) )).
fof(t57_algspec1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_instalg1(B) & l1_msualg_1(B) ) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t57_altcat_4,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t57_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( ( r2_hidden(H,D) & r2_hidden(H,E) & r2_hidden(F,D) & r2_hidden(G,E) & r2_hidden(F,C) & r2_hidden(G,C) & r10_analmetr(A,B,D) & r10_analmetr(A,B,E) & v4_analmetr(C,A) ) => ( F = G | r10_analmetr(A,B,C) ) ) ) ) ) ) ) ) ) ) )).
fof(t57_aofa_000,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_freealg(A) ) => k12_aofa_000(k7_freealg(k19_aofa_000,A)) = k4_trees_4(1,k1_xboole_0) ) )).
fof(t57_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ~ ( r2_hidden(D,A) & r2_hidden(C,A) & ! [E] : ( ( ~ v2_struct_0(E) & ~ v11_struct_0(E) & v12_aofa_a00(E) & v14_aofa_a00(E,4) & l5_aofa_a00(E) ) => ~ ( v21_aofa_a00(E,D,C,1) & v13_aofa_a00(E) & r1_tarski(A,u1_struct_0(E)) & r1_xboole_0(B,u4_struct_0(E)) & ~ r2_hidden(k1_funct_1(u2_msualg_1(E),k1_funct_1(u7_aofa_a00(E),2)),A) ) ) ) )).
fof(t57_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v19_aofa_a00(E,A) & m1_subset_1(E,u1_struct_0(A)) ) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,C),E)) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),E)) => ! [H] : ( m2_pboole(H,u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,D)) => k15_aofa_a00(A,B,C,D,E,k31_aofa_a00(A,C,E,F,G),H) = k31_aofa_a00(A,D,E,k15_aofa_a00(A,B,C,D,E,F,H),k15_aofa_a00(A,B,C,D,E,G,H)) ) ) ) ) ) ) ) ) )).
fof(t57_armstrng,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ( ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( r2_hidden(k6_armstrng(A,C,D),k12_armstrng(A,B)) <=> ! [E] : ( 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)) ) ) ) )).
fof(t57_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( 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)) ) ) ) )).
fof(t57_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(1,A) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( r1_xxreal_0(k7_newton(B),A) & ~ r1_xxreal_0(k7_newton(k1_nat_1(B,1)),A) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_xxreal_0(k7_newton(C),A) => ( r1_xxreal_0(k7_newton(k1_nat_1(C,1)),A) | C = B ) ) ) ) ) ) ) )).
fof(t57_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t57_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( v8_bcialg_1(E) & m1_bcialg_5(E,A,B,C,D) ) => ( C = k5_numbers => ( r1_xxreal_0(B,k5_numbers) | ( v8_bcialg_1(E) & m1_bcialg_5(E,k5_numbers,1,k5_numbers,1) ) ) ) ) ) ) ) ) )).
fof(t57_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ( m3_bciideal(B,A) => ( v3_bciideal(B,A) & m2_bcialg_1(B,A) & m4_bciideal(B,A) ) ) ) ) )).
fof(t57_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_normsp_1(A,B,C),k5_vfunct_1(k4_ordinal1,A,k3_normsp_1(A,C,B))) ) ) ) )).
fof(t57_bilinear,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t57_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_boolealg(A,k3_boolealg(A,B,B),k5_lattices(A)) ) ) )).
fof(t57_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t57_borsuk_6,axiom,( k9_subset_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)),k6_borsuk_6,k7_borsuk_6) = a_0_15_borsuk_6 )).
fof(t57_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t57_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t57_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_eqrel_1(I,A) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t57_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t57_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ( k7_xboolean(A,A) = k8_margrel1 & k3_xboolean(k7_xboolean(A,A)) = k7_margrel1 ) ) )).
fof(t57_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_finseq_1(D,k3_cqc_lang(A)) => ( ? [E] : ( 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)))) ) ) ) ) ) )).
fof(t57_card_1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t57_card_2,axiom,( ! [A] : ! [B] : ! [C] : ~ ( A != B & A != C & B != C & k5_card_1(k1_enumset1(A,B,C)) != 3 ) )).
fof(t57_card_3,axiom,( k8_card_3(k1_xboole_0) = k1_tarski(k1_xboole_0) )).
fof(t57_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( 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) ) ) ) ) ) )).
fof(t57_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,D,B) => ! [F] : ( m1_cat_1(F,A,D,C) => ( r2_cat_3(A,D,E,F) => ( k2_cat_1(A,D,B) = k1_xboole_0 | k2_cat_1(A,D,C) = k1_xboole_0 | k2_cat_1(A,B,C) = k1_xboole_0 | k2_cat_1(A,C,B) = k1_xboole_0 | ( v1_cat_3(E,A,D,B) & v1_cat_3(F,A,D,C) ) ) ) ) ) ) ) ) ) )).
fof(t57_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t57_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( 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) ) ) ) ) ) ) )).
fof(t57_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_chain_1(C,B) => k10_chain_1(B,C,A,k5_chain_1(B,C,k1_nat_1(A,1))) = k5_chain_1(B,C,A) ) ) ) )).
fof(t57_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) ) => ! [C] : ( m2_glib_000(C,A,B,k21_glib_000(A,B)) => ! [D] : ( 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t57_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t57_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v4_msualg_1(E,A) & v4_msafree2(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( ( v4_msualg_1(F,B) & v4_msafree2(F,B) & l3_msualg_1(F,B) ) => ( r5_circtrm1(A,B,C,D,E,F) => ! [G] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(A,E))) => ! [H] : ( m1_subset_1(H,k4_card_3(u3_msualg_1(B,F))) => ( G = k3_relat_1(C,H) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ( r1_facirc_1(A,E,G,I) <=> r1_facirc_1(B,F,H,k1_funct_1(C,I)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t57_classes1,axiom,( ! [A] : ( v3_ordinal1(A) => k5_classes1(A) = A ) )).
fof(t57_classes2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) ) => ( r2_hidden(A,B) => r2_hidden(k1_tarski(A),B) ) ) )).
fof(t57_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_clvect_1(B,A) => m1_clvect_1(k3_clvect_1(B),A) ) ) )).
fof(t57_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_funct_1(B) => v2_clvect_2(B,A) ) ) ) )).
fof(t57_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => k3_funct_2(A,B,C,D) = k7_relat_1(k11_cohsp_1(A,B,C),D) ) ) ) ) )).
fof(t57_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(A,B)),k2_xcmplx_0(k9_complex1(A),k9_complex1(B))) ) ) )).
fof(t57_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xreal_0(C) => k2_complex2(k6_xcmplx_0(A,B),C) = k6_xcmplx_0(k2_complex2(A,C),k2_complex2(B,C)) ) ) ) )).
fof(t57_complfld,axiom,( k9_complex1(k4_struct_0(k1_complfld)) = k5_numbers )).
fof(t57_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => k8_complsp2(A,k9_seq_4(B)) = k4_xcmplx_0(k8_complsp2(A,B)) ) ) ) )).
fof(t57_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( v6_compos_0(D,u1_compos_1(A)) & m1_subset_1(D,u1_compos_1(A)) ) => ! [E] : ( ( v6_compos_0(E,u1_compos_1(A)) & m1_subset_1(E,u1_compos_1(A)) ) => ! [F] : ( ( v6_compos_0(F,u1_compos_1(A)) & m1_subset_1(F,u1_compos_1(A)) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t57_comptrig,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( v7_ordinal1(C) => m1_comptrig(k2_xcmplx_0(k3_xcmplx_0(k1_power(B,k9_complex1(A)),k19_sin_cos(k7_xcmplx_0(k2_xcmplx_0(k1_comptrig(A),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)),B))),k3_xcmplx_0(k3_xcmplx_0(k1_power(B,k9_complex1(A)),k17_sin_cos(k7_xcmplx_0(k2_xcmplx_0(k1_comptrig(A),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)),B))),k7_complex1)),A,B) ) ) ) )).
fof(t57_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k3_finseq_2(k4_ordinal1)) & v1_funct_1(C) & v4_valued_0(C) & v2_margrel1(C) ) => ! [D] : ( m2_finseq_2(D,k4_ordinal1,k4_finseq_2(k1_nat_1(k19_margrel1(B),1),k4_ordinal1)) => ( r2_hidden(A,k4_finseq_1(D)) => ( r2_hidden(k8_comput_1(k1_nat_1(k19_margrel1(B),1),D,A,k5_numbers),k1_relset_1(k3_finseq_2(k4_ordinal1),k7_comput_1(B,C,A))) <=> r2_hidden(k2_finseq_3(A,D),k1_relset_1(k3_finseq_2(k4_ordinal1),B)) ) ) ) ) ) ) )).
fof(t57_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) )).
fof(t57_convex4,axiom,( ! [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) ) => v2_convex4(k17_convex4(A,k18_convex4(A)),A) ) )).
fof(t57_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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) ) ) )).
fof(t57_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t57_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)),k2_xcmplx_0(k15_csspace(A,B,D),k15_csspace(A,C,E))) ) ) ) ) ) )).
fof(t57_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k9_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k18_sin_cos),A,B) = k7_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k19_sin_cos(k3_xcmplx_0(2,A)),k19_sin_cos(k3_xcmplx_0(2,B)))),k6_xcmplx_0(A,B)) ) ) )).
fof(t57_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k9_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k18_sin_cos),k18_sin_cos),A,B) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,2),k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,k17_sin_cos(k7_xcmplx_0(k2_xcmplx_0(A,B),2))),k17_sin_cos(k7_xcmplx_0(k6_xcmplx_0(A,B),2))),k3_xcmplx_0(k17_sin_cos(k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(3,A),k3_xcmplx_0(3,B)),2)),k17_sin_cos(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(3,A),k3_xcmplx_0(3,B)),2))))),k6_xcmplx_0(A,B))) ) ) )).
fof(t57_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(B,k1_relset_1(k1_numbers,k26_sin_cos)) & r2_hidden(k2_xcmplx_0(B,A),k1_relset_1(k1_numbers,k26_sin_cos)) ) => k1_funct_1(k3_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k26_sin_cos),k16_sin_cos),A),B) = k6_xcmplx_0(k3_xcmplx_0(k1_newton(k1_funct_1(k16_sin_cos,k2_xcmplx_0(B,A)),3),k1_newton(k5_xcmplx_0(k1_funct_1(k18_sin_cos,k2_xcmplx_0(B,A))),2)),k3_xcmplx_0(k1_newton(k1_funct_1(k16_sin_cos,B),3),k1_newton(k5_xcmplx_0(k1_funct_1(k18_sin_cos,B)),2))) ) ) ) )).
fof(t57_ec_pf_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v5_relat_1(C,k8_eqrel_1(A,B)) & v1_funct_1(C) ) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( v2_funct_1(C) & v2_funct_2(C,k8_eqrel_1(A,B)) & k9_xtuple_0(C) = k4_finseq_1(D) & ! [E] : ( 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) ) ) ) ) ) )).
fof(t57_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k9_int_3(A))) => ! [G] : ( 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] : ( 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] : ( 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 = k5_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))))) ) ) ) ) ) ) ) ) ) ) )).
fof(t57_enumset1,axiom,( ! [A] : ! [B] : ! [C] : k1_enumset1(A,B,C) = k1_enumset1(A,C,B) )).
fof(t57_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( 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)))) ) ) ) ) ) ) )).
fof(t57_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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) = k5_numbers & r1_xxreal_0(k5_numbers,k11_euclid_3(2,A,B,C,D)) & r1_xxreal_0(k5_numbers,k12_euclid_3(2,A,B,C,D)) ) & ~ ( r1_xxreal_0(k5_numbers,k10_euclid_3(2,A,B,C,D)) & k11_euclid_3(2,A,B,C,D) = k5_numbers & r1_xxreal_0(k5_numbers,k12_euclid_3(2,A,B,C,D)) ) & ~ ( r1_xxreal_0(k5_numbers,k10_euclid_3(2,A,B,C,D)) & r1_xxreal_0(k5_numbers,k11_euclid_3(2,A,B,C,D)) & k12_euclid_3(2,A,B,C,D) = k5_numbers ) ) ) ) ) ) ) ) )).
fof(t57_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => k12_euclid(k9_euclid(3,B,A)) = k3_xcmplx_0(k9_complex1(A),k3_square_1(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k1_funct_1(B,1)),k1_square_1(k1_funct_1(B,2))),k1_square_1(k1_funct_1(B,3))))) ) ) )).
fof(t57_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ? [D] : ( 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) ) ) ) ) )).
fof(t57_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( ( 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,k9_funct_7(E,A,B))) ) => r2_hidden(k4_tarski(B,C),k6_exchsort(D,E)) ) ) ) )).
fof(t57_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) => ( C != k4_tarski(k10_finseq_1(A,B),D) => k2_msafree2(k8_facirc_1(A,B,C,D)) = k1_enumset1(A,B,C) ) ) )).
fof(t57_fcont_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(A,k5_numbers) => k7_relset_1(k1_numbers,k1_numbers,k1_fcont_1(A,B),k1_rcomp_1(k5_numbers,1)) = k1_rcomp_1(B,k2_xcmplx_0(A,B)) ) ) ) )).
fof(t57_fdiff_11,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k5_numbers ) ) ) ) ) )).
fof(t57_fdiff_4,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k22_sin_cos,B),k22_sin_cos),k3_taylor_1))) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => ( k1_funct_1(B,C) = 1 & ~ r1_xxreal_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,B),C),k5_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,k22_sin_cos,B),k22_sin_cos),k3_taylor_1),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_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,k22_sin_cos,B),k22_sin_cos),k3_taylor_1),A),C) = k7_xcmplx_0(1,k6_xcmplx_0(k1_funct_1(k22_sin_cos,C),1)) ) ) ) ) ) ) )).
fof(t57_fib_num2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k2_xboole_0(k3_xboole_0(k3_fib_num2,k2_finseq_1(k1_nat_1(k2_nat_1(2,A),2))),k6_domain_1(k4_ordinal1,k1_nat_1(k2_nat_1(2,A),4))) = k3_xboole_0(k3_fib_num2,k2_finseq_1(k1_nat_1(k2_nat_1(2,A),4))) ) )).
fof(t57_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t57_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t57_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t57_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => k5_card_1(k2_finseq_1(A)) = A ) )).
fof(t57_finseq_2,axiom,( ! [A] : k2_finseq_2(1,A) = k9_finseq_1(A) )).
fof(t57_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : k3_finseq_1(k1_finseq_3(A,B)) = k6_xcmplx_0(k3_finseq_1(A),k5_card_1(k8_relat_1(A,B))) ) )).
fof(t57_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t57_finseq_5,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t57_finseq_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t57_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,B) & m2_finseq_1(C,A) ) => ! [D] : ( ( 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(k4_ordinal1,A,k3_finseqop(A,A,A,D,k4_binop_1(A,D),C),C) ) ) ) ) ) )).
fof(t57_flang_1,axiom,( ! [A] : ! [B] : ( 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) ) )).
fof(t57_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(D,E) & r2_hidden(k2_flang_1(A),C) ) => ( r1_tarski(B,k6_flang_1(A,B,k1_flang_2(A,C,D,E))) & r1_tarski(B,k6_flang_1(A,k1_flang_2(A,C,D,E),B)) ) ) ) ) ) ) )).
fof(t57_flang_3,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(t57_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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) ) ) )).
fof(t57_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & v8_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( ( ~ v2_struct_0(D) & v5_fsm_1(D,A,B) & v7_fsm_1(D,A,B) & l2_fsm_1(D,A,B) ) => ! [E] : ( ( ~ v2_struct_0(E) & v5_fsm_1(E,A,B) & v7_fsm_1(E,A,B) & l2_fsm_1(E,A,B) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ! [H] : ( m1_subset_1(H,u1_struct_0(D)) => ! [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) ) ) ) ) ) ) ) ) ) ) )).
fof(t57_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t57_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( v2_funct_1(B) => v2_funct_1(k6_relat_1(A,B)) ) ) )).
fof(t57_funct_2,axiom,( ! [A] : ! [B] : ( ( 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] : ! [D] : ( ( r2_hidden(C,A) & r2_hidden(D,A) & k1_funct_1(B,C) = k1_funct_1(B,D) ) => C = D ) ) ) )).
fof(t57_funct_3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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)) ) ) ) )).
fof(t57_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ( ( r1_tarski(k9_xtuple_0(E),k2_zfmisc_1(A,C)) & r1_tarski(k9_xtuple_0(F),k2_zfmisc_1(B,D)) ) => r1_tarski(k9_xtuple_0(k3_funct_4(E,F)),k2_zfmisc_1(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D))) ) ) ) )).
fof(t57_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( r2_wellord2(k1_funct_2(C,k2_zfmisc_1(A,B)),k2_zfmisc_1(k1_funct_2(C,A),k1_funct_2(C,B))) & k1_card_1(k1_funct_2(C,k2_zfmisc_1(A,B))) = k1_card_1(k2_zfmisc_1(k1_funct_2(C,A),k1_funct_2(C,B))) ) )).
fof(t57_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( k5_funct_7(k7_finseq_1(k9_finseq_1(A),B)) = k9_xtuple_0(A) & k6_funct_7(k7_finseq_1(B,k9_finseq_1(A))) = k10_xtuple_0(A) ) ) ) )).
fof(t57_funct_8,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(k5_numbers,A) => k1_funct_1(k1_funct_8,A) = k4_xcmplx_0(1) ) ) )).
fof(t57_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => k5_struct_0(k7_fvaluat1(A,B)) = k5_struct_0(A) ) ) ) )).
fof(t57_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v5_group_1(B) & v5_vectsp_1(B) & v6_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( 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 ) ) ) )).
fof(t57_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( ( ~ v1_xboole_0(G) & v1_relat_1(G) & v2_relat_1(G) & v1_funct_1(G) & v1_finseq_1(G) ) => ! [H] : ( m1_genealg1(H,G) => ! [I] : ( m1_genealg1(I,G) => ( k12_genealg1(G,H,I,A,A,C,D,E,F) = k10_genealg1(G,H,I,C,D,E,F) & k12_genealg1(G,H,I,A,B,A,D,E,F) = k10_genealg1(G,H,I,B,D,E,F) & k12_genealg1(G,H,I,A,B,C,A,E,F) = k10_genealg1(G,H,I,B,C,E,F) & k12_genealg1(G,H,I,A,B,C,D,A,F) = k10_genealg1(G,H,I,B,C,D,F) & k12_genealg1(G,H,I,A,B,C,D,E,A) = k10_genealg1(G,H,I,B,C,D,E) ) ) ) ) ) ) ) ) ) ) )).
fof(t57_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t57_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ( r2_hidden(B,k26_glib_000(A,C)) <=> ? [D] : r2_glib_000(A,D,C,B) ) ) ) )).
fof(t57_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( k3_glib_001(A,k20_glib_001(A,B,D,C)) = k3_glib_001(A,B) & k4_glib_001(A,k20_glib_001(A,B,D,C)) = k4_glib_001(A,B) ) ) ) ) ) )).
fof(t57_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v3_glib_003(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : r2_hidden(B,k14_glib_003(k13_glib_003(A,B,C))) ) ) )).
fof(t57_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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_nat_1(A,1),k3_finseq_1(k2_goboard2(C))) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(k2_goboard2(C))) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B)),k3_topreal1(2,C)) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1))),k3_topreal1(2,C)) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,1) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B) & ( ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,2) = k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1)) ) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,2) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k7_nat_d(k3_finseq_1(C),1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,B) ) ) ) & ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(1,D) & ~ r1_xxreal_0(k3_finseq_1(C),k1_nat_1(D,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_nat_1(D,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B) & ( ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,D) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,B) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_nat_1(D,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1)) ) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,D) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_nat_1(D,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,B) ) ) ) ) ) ) ) ) )).
fof(t57_graph_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t57_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_graph_1(A) & v6_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_2(B,u4_struct_0(A),k9_graph_3(A)) => ( ! [C] : ( 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))) ) ) ) ) ) )).
fof(t57_graph_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v6_graph_1(B) & l1_graph_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ~ ( k4_graph_5(B,C,D) != k1_xboole_0 & ! [E] : ( m2_finseq_1(E,u4_struct_0(B)) => ~ ( r2_hidden(E,k4_graph_5(B,C,D)) & ! [F] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t57_groeb_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( r1_groeb_1(A,B,C,D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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),k8_polynom1(A,C)) ) ) ) ) ) ) ) ) ) )).
fof(t57_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,A) => ( m1_group_2(C,D) => r1_tarski(k4_group_11(A,B,C),k4_group_11(A,B,D)) ) ) ) ) ) )).
fof(t57_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ( r1_tarski(u1_struct_0(B),u1_struct_0(C)) => m1_group_2(B,C) ) ) ) ) )).
fof(t57_group_3,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t57_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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))) ) ) ) ) )).
fof(t57_group_5,axiom,( ! [A] : ( ( ~ 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] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => k5_group_5(A,B,C) = k6_domain_1(u1_struct_0(A),k1_group_1(A)) ) ) ) ) )).
fof(t57_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v15_algstr_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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 ) ) ) ) )).
fof(t57_group_9,axiom,( ! [A] : ! [B] : ( ( ~ 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))) ) )).
fof(t57_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( 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)) = k5_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) ) ) ) ) )).
fof(t57_hfdiff_1,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k1_relset_1(k1_numbers,k26_sin_cos)) => ( r2_fdiff_1(k6_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos),A) & r2_relset_1(k1_numbers,k1_numbers,k2_fdiff_1(k6_rfunct_1(k1_numbers,k1_numbers,k18_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,k18_sin_cos),k26_sin_cos),A)) ) ) ) )).
fof(t57_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t57_incsp_1,axiom,( ! [A] : ( ( v15_incsp_1(A) & l2_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u4_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u4_incsp_1(A)) => ~ ( B != C & ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & r2_incsp_1(A,D,B) & r2_incsp_1(A,D,C) ) & ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ~ ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t57_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( B != k5_numbers => A = k2_xcmplx_0(k3_xcmplx_0(k4_int_1(A,B),B),k5_int_1(A,B)) ) ) ) )).
fof(t57_integr11,axiom,( ! [A] : ( ( 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_sin_cos,k1_partfun2(k1_numbers,A)))) => ( r2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_partfun2(k1_numbers,A)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_partfun2(k1_numbers,A)),A),B) = k1_square_1(k1_funct_1(k26_sin_cos,B)) ) ) ) ) ) )).
fof(t57_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,D) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => k1_funct_1(C,E) = 1 ) ) & r2_relset_1(k1_numbers,k1_numbers,B,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,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)),k2_sin_cos9))) & r1_tarski(D,k2_rcomp_1(k4_xcmplx_0(1),1)) & D = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_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)),k2_seq_4(A)),k1_funct_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)),k3_seq_4(A))) ) ) ) ) ) )).
fof(t57_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k3_xcmplx_0(k1_funct_1(k16_sin_cos,k1_funct_1(k18_sin_cos,D)),k1_funct_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) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k18_sin_cos),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k18_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t57_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => k2_integra5(A,k3_sin_cos2) = k6_xcmplx_0(k1_funct_1(k1_sin_cos2,k2_seq_4(A)),k1_funct_1(k1_sin_cos2,k3_seq_4(A))) ) )).
fof(t57_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( 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] : ( v1_xreal_0(H) => ( r2_hidden(H,G) => ( k1_funct_1(E,H) = k2_xcmplx_0(H,B) & ~ r1_xxreal_0(k1_funct_1(E,H),k5_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,k6_xcmplx_0(A,B)))) = G & G = k1_relset_1(k1_numbers,F) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,G) => k1_funct_1(F,H) = k7_xcmplx_0(k2_xcmplx_0(H,A),k2_xcmplx_0(H,B)) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,F,C)) ) => k2_integra5(C,F) = k6_xcmplx_0(k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,G),k26_valued_1(k1_numbers,k1_numbers,D,k6_xcmplx_0(A,B))),k2_seq_4(C)),k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,G),k26_valued_1(k1_numbers,k1_numbers,D,k6_xcmplx_0(A,B))),k3_seq_4(C))) ) ) ) ) ) ) ) ) )).
fof(t57_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m2_interva1(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(t57_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( 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) ) ) ) )).
fof(t57_jgraph_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r1_xxreal_0(k18_euclid(B),k5_numbers) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) | r1_xxreal_0(1,A) | ! [C] : ( 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),k5_numbers) ) ) ) ) ) ) )).
fof(t57_jgraph_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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] : ( 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(k7_xcmplx_0(2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(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)) = k4_xcmplx_0(1) ) ) ) ) ) ) ) ) ) )).
fof(t57_jordan,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t57_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(1,C) & ~ r1_xxreal_0(k3_finseq_1(k2_jordan9(B,A)),C) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k1_matrix_0(k1_jordan8(B,A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),k2_jordan9(B,A),C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),k3_finseq_1(k1_jordan8(B,A)),D) ) ) ) ) )).
fof(t57_jordan1g,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,k5_numbers) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( 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_0(k1_jordan8(A,B))) & r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),C,D),k3_topreal1(2,k2_jordan9(A,B))) & r1_xboole_0(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),C,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),C,D)),k9_jordan6(k3_topreal1(2,k2_jordan9(A,B)))) ) ) ) ) ) ) )).
fof(t57_jordan1h,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( 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] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(k4_tarski(D,E),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k7_nat_d(k3_finseq_1(C),1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),D,E) & r2_hidden(k4_tarski(k1_nat_1(D,1),E),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k3_finseq_1(C)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k1_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(k1_nat_1(D,2),E),k2_matrix_0(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) )).
fof(t57_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k14_euclid(A))) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))))) ) => ~ ( v5_pre_topc(G,k5_topmetr,k15_euclid(A)) & k1_funct_1(G,k5_numbers) = D & k1_funct_1(G,1) = E & r2_hidden(C,k8_metric_1(k14_euclid(A),F,B)) & r2_hidden(E,k8_metric_1(k14_euclid(A),F,B)) & ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))))) ) => ~ ( v5_pre_topc(H,k5_topmetr,k15_euclid(A)) & k1_funct_1(H,k5_numbers) = D & k1_funct_1(H,1) = C & r1_tarski(k2_relset_1(u1_struct_0(k15_euclid(A)),H),k2_xboole_0(k2_relset_1(u1_struct_0(k15_euclid(A)),G),k8_metric_1(k14_euclid(A),F,B))) ) ) ) ) ) ) ) ) ) ) )).
fof(t57_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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 ) ) ) ) )).
fof(t57_kurato_1,axiom,( ! [A] : ( ( 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] : ( ( 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) ) ) ) )).
fof(t57_lattice2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t57_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : k1_recdef_1(k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k4_ordinal1,k6_glib_000(A),k18_lexbfs(A)),B) = k5_numbers ) )).
fof(t57_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v7_limfunc1(A) & ! [C] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k10_prob_1(D))) => r1_xxreal_0(C,k1_funct_1(B,E)) ) ) ) ) ) | v7_limfunc1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) ) )).
fof(t57_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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) = k9_complex1(k2_limfunc2(B,A)) ) ) ) ) )).
fof(t57_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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) ) ) ) ) ) )).
fof(t57_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v2_xxreal_0(E) & v1_xreal_0(E) ) => ( ( 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))) = k5_numbers ) => r1_lpspace1(A,B,C,D,k8_lpspace1(A,k5_numbers)) ) ) ) ) ) ) )).
fof(t57_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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)) ) ) ) ) )).
fof(t57_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m2_finseq_1(B,k1_hilbert1) => ( ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => r8_ltlaxio1(k1_subset_1(k1_hilbert1),k3_hilbert1(k7_partfun1(k1_hilbert1,B,C),A)) ) ) => r8_ltlaxio1(k1_subset_1(k1_hilbert1),k3_hilbert1(k1_ltlaxio1(k7_partfun1(k1_hilbert1,k2_ltlaxio2(k4_ltlaxio2(B)),k3_finseq_1(k2_ltlaxio2(k4_ltlaxio2(B))))),A)) ) ) ) )).
fof(t57_mathmorp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => k6_mathmorp(k5_numbers,k15_euclid(A),B) = k6_domain_1(u1_struct_0(k15_euclid(A)),k4_struct_0(k15_euclid(A))) ) ) )).
fof(t57_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,k1_numbers,A,A) & m2_finseq_1(E,k3_finseq_2(k1_numbers)) ) => ( r2_matrix10(k5_matrix10(A,B,C),k5_matrix10(A,D,E)) => r2_matrix10(k5_matrix10(A,E,C),k5_matrix10(A,D,B)) ) ) ) ) ) ) )).
fof(t57_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( ( v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ! [E] : ( ( v1_finset_1(E) & v1_setfam_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ! [F] : ( ( v1_finset_1(F) & v1_setfam_1(F) & m1_subset_1(F,k1_zfmisc_1(k4_ordinal1)) ) => ~ ( ( C = k1_xboole_0 => E = k1_xboole_0 ) & ( E = k1_xboole_0 => C = k1_xboole_0 ) & r1_tarski(k2_zfmisc_1(C,E),k2_matrix_0(k6_matrix13(A,B,D,F))) & ! [G] : ( ( v1_finset_1(G) & v1_setfam_1(G) & m1_subset_1(G,k1_zfmisc_1(k4_ordinal1)) ) => ! [H] : ( ( v1_finset_1(H) & v1_setfam_1(H) & m1_subset_1(H,k1_zfmisc_1(k4_ordinal1)) ) => ~ ( r1_tarski(G,D) & r1_tarski(H,F) & G = k7_relat_1(k5_matrix13(D),C) & H = k7_relat_1(k5_matrix13(F),E) & k5_card_1(G) = k5_card_1(C) & k5_card_1(H) = k5_card_1(E) & k6_matrix13(A,k6_matrix13(A,B,D,F),C,E) = k6_matrix13(A,B,G,H) ) ) ) ) ) ) ) ) ) ) )).
fof(t57_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( k3_finseq_1(B) = k3_finseq_1(C) => ( ( k1_matrix_0(B) = k5_numbers & k1_matrix_0(C) != k5_numbers ) | ( k8_matrix13(A,B) = k8_matrix13(A,k7_matrlin(u1_struct_0(A),B,C)) <=> ~ v1_xboole_0(k4_matrix15(A,B,C)) ) ) ) ) ) ) )).
fof(t57_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( r3_matrix16(B,D,C) => ( r1_xxreal_0(A,k5_numbers) | C = k7_matrix_0(u1_struct_0(B),D,1) ) ) ) ) ) ) )).
fof(t57_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ~ ( ~ r1_xxreal_0(k3_finseq_1(B),k5_numbers) & ~ r1_xxreal_0(k1_matrix_0(B),k5_numbers) & k4_matrix_0(A,k4_matrix_0(A,B)) != B ) ) ) )).
fof(t57_matrix_4,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t57_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ( ( v4_matrix_6(C,A,B) & v4_matrix_6(D,A,B) & v4_matrix_6(E,A,B) ) => ( r1_xxreal_0(A,k5_numbers) | v4_matrix_6(k4_matrix_3(B,k4_matrix_3(B,C,D),E),A,B) ) ) ) ) ) ) ) )).
fof(t57_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => k4_algstr_0(B,k1_matrix_8(A,B,k2_matrix_3(B,C))) = k1_matrix_8(A,B,C) ) ) ) )).
fof(t57_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k2_numbers)) ) => ( ( k3_finseq_1(A) = k1_matrix_0(C) & k3_finseq_1(B) = k3_finseq_1(C) ) => ( r1_xxreal_0(k1_matrix_0(C),k5_numbers) | r1_xxreal_0(k3_finseq_1(C),k5_numbers) | k8_complsp2(k6_matrixc1(C,A),B) = k8_complsp2(A,k6_matrixc1(k2_matrixc1(C),B)) ) ) ) ) ) )).
fof(t57_matrixj1,axiom,( ! [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] : ( m1_subset_1(B,k4_ordinal1) => k23_matrixj1(A,k13_matrix_0(k4_ordinal1,B)) = k16_matrixj1(u1_struct_0(A),B,k3_matrix_1(A,B)) ) ) )).
fof(t57_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k1_matrix_0(C) = k3_finseq_1(A) ) => ( r1_xxreal_0(k3_finseq_1(A),k5_numbers) | r1_xxreal_0(k3_finseq_1(C),k5_numbers) | k11_matrixr1(C,k4_rvsum_1(A,B)) = k4_rvsum_1(k11_matrixr1(C,A),k11_matrixr1(C,B)) ) ) ) ) ) )).
fof(t57_matrixr2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k1_matrix_0(B) = k3_finseq_1(C) ) => k12_matrixr1(k6_matrixr1(B,C),A) = k12_matrixr1(C,k12_matrixr1(B,A)) ) ) ) ) )).
fof(t57_matrprob,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v4_matrprob(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k4_tarski(B,C),k2_matrix_0(A)) => r1_xxreal_0(k3_matrix_0(k1_numbers,A,B,C),1) ) ) ) ) )).
fof(t57_mcart_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(B)) ) => ! [F] : ( ( ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(C)) ) => ! [G] : ( m1_subset_1(G,k3_zfmisc_1(A,B,C)) => ( r2_hidden(G,k3_zfmisc_1(D,E,F)) => ( r2_hidden(k1_mcart_1(A,B,C,G),D) & r2_hidden(k2_mcart_1(A,B,C,G),E) & r2_hidden(k3_mcart_1(A,B,C,G),F) ) ) ) ) ) ) ) ) ) )).
fof(t57_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( ( v2_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,B) => r1_tarski(k5_measure6(A),B) ) ) ) )).
fof(t57_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t57_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t57_mesfunc5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( m1_subset_1(B,k6_numbers) => ( ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k9_nat_1(k6_numbers,A,C),B) ) => r1_xxreal_0(k8_supinf_2(k17_supinf_2(A)),B) ) ) ) )).
fof(t57_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( v6_supinf_2(B) => ( ( r1_xxreal_0(k5_numbers,C) => v6_supinf_2(k26_valued_1(A,k1_numbers,B,C)) ) & ( r1_xxreal_0(C,k5_numbers) => v2_mesfunc5(k26_valued_1(A,k1_numbers,B,C)) ) ) ) ) ) ) )).
fof(t57_mmlquery,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( k24_mmlquery(A,B) = k3_finseq_1(A) => k25_mmlquery(A) = k3_finseq_1(A) ) ) )).
fof(t57_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k30_modelc_1(k25_modelc_2(A)))) ) => ! [C] : ( m1_subset_1(C,k25_modelc_2(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t57_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ? [B] : ( m2_orders_1(B,k1_orders_1(k1_modelc_3(A)),k6_partfun1(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)))) ) ) )).
fof(t57_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( ~ v1_moebius1(A) => k6_moebius1(A) = A ) ) )).
fof(t57_monoid_0,axiom,( k24_binop_2 = k1_realset1(k11_binop_2,k4_ordinal1) )).
fof(t57_monoid_1,axiom,( ! [A] : ( ( ~ 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)) ) ) ) )).
fof(t57_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m2_pboole(C,u1_struct_0(A),B,k7_funcop_1(u1_struct_0(A),k4_ordinal1)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( m1_msaterm(E,A,B,k2_msaterm(A,B,D)) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ( ( k4_finseq_1(F) = k4_finseq_1(E) & ! [G] : ( v7_ordinal1(G) => ! [H] : ( m1_subset_1(H,k3_card_3(u3_msualg_1(A,k1_msafree3(A,B)))) => ( ( r2_hidden(G,k4_finseq_1(E)) & H = k1_funct_1(E,G) ) => k1_funct_1(F,G) = k6_msafree4(A,B,C,H) ) ) ) ) => k6_msafree4(A,B,C,k6_msaterm(A,B,k2_msaterm(A,B,D),E)) = k4_trees_4(k2_msaterm(A,k7_funcop_1(u1_struct_0(A),k4_ordinal1),D),F) ) ) ) ) ) ) ) )).
fof(t57_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( k22_pre_poly(k8_newton,k13_nat_3(A)) = k1_xboole_0 => A = 1 ) ) )).
fof(t57_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t57_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ! [E] : ( ( 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) ) ) ) ) )).
fof(t57_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_nat_d(C,B) => r1_nat_d(k6_nat_d(A,C),k6_nat_d(A,B)) ) ) ) ) )).
fof(t57_normform,axiom,( ! [A] : k5_lattices(k12_normform(A)) = k1_xboole_0 )).
fof(t57_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t57_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m1_oppcat_1(D,B,A) => ! [E] : ( m2_cat_1(E,A,C) => m1_oppcat_1(k1_partfun1(u4_struct_0(B),u4_struct_0(A),u4_struct_0(A),u4_struct_0(C),D,E),B,C) ) ) ) ) ) )).
fof(t57_ordeq_01,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k4_real_ns1(A))) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A))) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A))))) ) => ~ ( ~ r1_xxreal_0(C,B) & D = k2_rcomp_1(B,C) & r5_nfcont_1(k4_real_ns1(A),k4_real_ns1(A),u1_struct_0(k4_real_ns1(A)),F) & ! [G] : ( ( v1_funct_1(G) & v1_nfcont_3(G,k4_real_ns1(A)) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ~ ( k1_relset_1(k1_numbers,G) = k3_integra5(B,C) & r2_ndiff_3(k4_real_ns1(A),G,D) & k7_partfun1(u1_struct_0(k4_real_ns1(A)),G,B) = E & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,D) => k1_ndiff_3(k4_real_ns1(A),G,H) = k3_funct_2(u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(A)),F,k7_partfun1(u1_struct_0(k4_real_ns1(A)),G,H)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t57_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( ( r2_hidden(C,B) & r8_orders_1(A,C) & r1_tarski(B,k1_relat_1(A)) & v1_relat_2(A) ) => r4_orders_1(A,B) ) ) )).
fof(t57_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => k5_ordinal3(A,k10_ordinal2(B,C)) = k5_ordinal3(k5_ordinal3(A,B),C) ) ) ) )).
fof(t57_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r2_hidden(1,B) => r2_hidden(A,k12_ordinal2(B,k1_ordinal1(k5_ordinal5(A,B)))) ) ) ) )).
fof(t57_ordinal6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ( ~ v4_card_3(A) <=> r2_hidden(k4_ordinal1,A) ) ) )).
fof(t57_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r3_parsp_2(A,B,C,D,E) => r3_parsp_2(A,D,E,B,C) ) ) ) ) ) ) )).
fof(t57_partfun1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r1_tarski(A,C) & r1_tarski(B,C) ) => r1_partfun1(A,B) ) ) ) ) )).
fof(t57_partfun2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ( v3_funct_1(k2_partfun1(B,C,D,A)) <=> ? [E] : ( m1_subset_1(E,C) & ! [F] : ( m1_subset_1(F,B) => ( r2_hidden(F,k9_subset_1(B,A,k1_relset_1(B,D))) => k1_funct_1(D,F) = E ) ) ) ) ) ) ) )).
fof(t57_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t57_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( 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) & k10_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) = k6_xcmplx_0(k6_pdiff_5(B,A),k6_pdiff_5(C,A)) ) ) ) ) ) )).
fof(t57_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t57_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ( A != k5_numbers => r1_int_2(3,k4_pepin(A)) ) ) )).
fof(t57_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,k8_polyform(A,B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k17_polyform(A,B))) => ! [E] : ( m1_subset_1(E,k8_polyform(A,k6_xcmplx_0(B,1))) => ! [F] : ( v7_ordinal1(F) => ( ( B = k5_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) ) ) ) ) ) ) ) )).
fof(t57_polynom5,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( k1_algseq_1(A,B) != k5_numbers => k1_algseq_1(A,k7_polynom5(A,B)) = k1_algseq_1(A,B) ) ) ) )).
fof(t57_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k12_polynom1(A,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k12_polynom1(A,C))) => ( r2_rewrite1(k3_polyred(A,B,C,D),E,F) => r11_polyred(k12_polynom1(A,C),k7_ideal_1(k12_polynom1(A,C),D),E,F) ) ) ) ) ) ) ) )).
fof(t57_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,1) & ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(C,B) & r1_xxreal_0(k3_power(A,C),k3_power(A,B)) ) ) ) ) )).
fof(t57_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t57_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => ( ~ r1_xxreal_0(A,k5_numbers) => k4_prepower(k7_xcmplx_0(1,A),B) = k7_xcmplx_0(1,k4_prepower(A,B)) ) ) ) )).
fof(t57_prob_3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( m1_prob_3(C,A,B) => r2_hidden(k5_prob_3(A,C),B) ) ) )).
fof(t57_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t57_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t57_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t57_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t57_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k17_quatern2(k24_quaterni(A),k24_quaterni(B)) = k17_quatern2(A,B) ) ) )).
fof(t57_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => ! [D] : ( v1_quaterni(D) => k23_quaterni(k25_quaterni(A,B),k25_quaterni(C,D)) = k22_quaterni(k25_quaterni(k25_quaterni(k23_quaterni(A,C),k23_quaterni(B,C)),k23_quaterni(A,D)),k23_quaterni(B,D)) ) ) ) ) )).
fof(t57_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ( k27_quaterni(k23_quaterni(A,B)) = k23_quaterni(k27_quaterni(A),k27_quaterni(B)) => k3_xcmplx_0(k15_quaterni(A),k16_quaterni(B)) = k3_xcmplx_0(k16_quaterni(A),k15_quaterni(B)) ) ) ) )).
fof(t57_quofield,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t57_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B))))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t57_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => r1_tarski(k3_relat_1(k5_relat_1(C,A),B),k3_relat_1(C,B)) ) ) )).
fof(t57_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( 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) ) )).
fof(t57_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ( v7_rewrite1(A) <=> v9_rewrite1(k18_finseq_1(A)) ) ) )).
fof(t57_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => r4_rewrite2(A,B,k7_rewrite2(A,B),C) ) ) )).
fof(t57_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_afinsq_1(D))) => ! [F] : ( ( ~ 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)) ) ) ) ) )).
fof(t57_rfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t57_rfunct_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( r1_tarski(B,k1_relset_1(k1_numbers,A)) => r2_rfunct_3(k26_valued_1(k1_numbers,k1_numbers,A,k5_numbers),B) ) ) )).
fof(t57_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_comseq_2(A) => ( v2_comseq_2(k3_rinfsup1(A)) & k1_seq_2(k3_rinfsup1(A)) = k1_rinfsup1(k3_rinfsup1(A)) ) ) ) )).
fof(t57_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t57_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t57_rlsub_2,axiom,( ! [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) ) => ( ~ 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))) ) ) )).
fof(t57_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( ( v2_compts_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v4_pre_topc(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( r1_xboole_0(B,C) & ! [D] : ( m1_connsp_2(D,A,k4_struct_0(A)) => ~ r1_xboole_0(k7_rusub_4(A,B,D),k7_rusub_4(A,C,D)) ) ) ) ) ) )).
fof(t57_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t57_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => r1_rlvect_2(A,k10_rlvect_2(A,B,B),k4_rlvect_2(A)) ) ) )).
fof(t57_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t57_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_4(C,A,B) => r1_rmod_4(A,B,k9_rmod_4(A,B,C,C),k3_rmod_4(A,B)) ) ) ) )).
fof(t57_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & k5_robbins1(A,B,C) = B ) ) => v6_robbins1(A) ) ) )).
fof(t57_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t57_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k4_roughs_1(A,B) = a_2_3_roughs_1(A,B) ) ) )).
fof(t57_rpr_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ~ ( r1_xboole_0(B,C) & r1_rpr_1(A,B,C) & k1_rpr_1(A,B) != k5_numbers & k1_rpr_1(A,C) != k5_numbers ) ) ) ) )).
fof(t57_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(C,k3_rusub_1(A,D,B)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r1_struct_0(B,E) & C = k3_rlvect_1(A,D,E) ) ) ) ) ) ) )).
fof(t57_rusub_2,axiom,( ! [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_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))) ) ) )).
fof(t57_rvsum_1,axiom,( ! [A] : ( ( 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) ) )).
fof(t57_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),k1_scmfsa_m(B),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(B)))) = k11_scmfsa_2(k5_numbers) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( r1_xxreal_0(D,k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(B))) & k3_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),k1_scmfsa_m(B),D)) = k2_compos_1(k1_scmfsa_2) ) ) ) ) ) ) ) )).
fof(t57_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ( ~ r4_scmfsa7b(C,D) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),E)),k2_afinsq_1(C)) => k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),k1_nat_1(E,1)),D) = k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),E),D) ) ) ) ) ) ) ) )).
fof(t57_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ( k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k7_scmfsa_2(A,B),C),k4_struct_0(k1_scmfsa_2)) = k4_card_1(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,C)) & k1_funct_1(k2_extpro_1(k7_card_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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ( D != A => k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k7_scmfsa_2(A,B),C),D) = k1_funct_1(C,D) ) ) & ! [D] : ( m1_scmfsa_2(D) => r2_relset_1(k4_ordinal1,k4_numbers,k18_scmfsa_2(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k7_scmfsa_2(A,B),C),D),k18_scmfsa_2(C,D)) ) ) ) ) ) )).
fof(t57_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ? [B] : ( 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] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmpds_2)) ) => k1_funct_1(B,C) = A ) ) ) )).
fof(t57_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ( r2_hidden(k5_numbers,k9_xtuple_0(k3_scmpds_6(A,B,C,D))) & r2_hidden(1,k9_xtuple_0(k3_scmpds_6(A,B,C,D))) ) ) ) ) ) )).
fof(t57_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v6_scmyciel(A) ) => ( k1_scmyciel(A) != k1_xboole_0 => r1_xxreal_0(2,k8_scmyciel(A)) ) ) )).
fof(t57_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r3_semi_af1(A,B,C,D,E) => r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) )).
fof(t57_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(B)) => ( r2_hidden(A,k2_finseq_1(B)) => r2_hidden(k1_funct_1(C,A),k2_numbers) ) ) ) ) )).
fof(t57_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k4_kurato_0(A,B) = k3_subset_1(A,k3_kurato_0(A,k2_prob_1(A,B))) ) )).
fof(t57_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => r1_tarski(k7_subset_1(B,C,k9_nat_1(k9_setfam_1(B),k4_setlim_1(B,D),A)),k9_nat_1(k9_setfam_1(B),k4_setlim_1(B,k7_setlim_2(B,D,C)),A)) ) ) ) )).
fof(t57_sf_mastr,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(t57_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t57_simplex0,axiom,( ! [A] : ! [B] : ! [C] : ( m1_simplex0(C,A) => ! [D] : ( ( 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) ) ) ) )).
fof(t57_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v1_xcmplx_0(C) => ~ ( ~ r1_xxreal_0(B,k9_complex1(C)) & r1_xxreal_0(A,k9_complex1(k11_comseq_3(k24_sin_cos(C)))) ) ) ) ) ) ) )).
fof(t57_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A)) = k7_xcmplx_0(k2_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,k3_xcmplx_0(2,A)),1),2) ) )).
fof(t57_sin_cos6,axiom,( ! [A] : ( v1_int_1(A) => v2_funct_1(k5_relset_1(k1_numbers,k1_numbers,k16_sin_cos,k1_rcomp_1(k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A)),k2_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A))))) ) )).
fof(t57_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(1,k1_square_1(A)) & ~ r1_xxreal_0(1,k1_square_1(B)) & k6_xcmplx_0(k4_sin_cos7(A),k4_sin_cos7(B)) != k4_sin_cos7(k7_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(1,k3_xcmplx_0(A,B)))) ) ) ) )).
fof(t57_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) & k3_sin_cos9(A) = k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)) ) => A = k4_xcmplx_0(1) ) ) )).
fof(t57_sincos10,axiom,( k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(1,k3_square_1(2))),k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,4)))) = k1_partfun2(k1_numbers,k1_rcomp_1(1,k3_square_1(2))) )).
fof(t57_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v5_topreal1(A) => v2_compts_1(A,k15_euclid(2)) ) ) )).
fof(t57_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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) ) ) ) )).
fof(t57_sprect_2,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(t57_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t57_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(B,A) => r1_xxreal_0(k3_xcmplx_0(B,k3_square_1(k2_xcmplx_0(1,k1_square_1(A)))),k3_xcmplx_0(A,k3_square_1(k2_xcmplx_0(1,k1_square_1(B))))) ) ) ) )).
fof(t57_stirl2_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ~ ( ( v1_xboole_0(B) => v1_xboole_0(A) ) & ~ r2_hidden(C,A) & ? [E] : ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) & ! [F] : ( ( 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 ) ) ) ) )).
fof(t57_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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) ) ) ) )).
fof(t57_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ! [C] : ( 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)) ) ) ) ) )).
fof(t57_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t57_tex_3,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( ( v1_tex_2(B,A) & m1_pre_topc(B,A) ) => ~ v2_tex_3(B,A) ) => v3_tdlat_3(A) ) ) )).
fof(t57_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) )).
fof(t57_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( 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] : ( 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_funct_2(u1_struct_0(C),u1_struct_0(B),k2_tmap_1(A,B,E,C),D) ) ) ) ) ) )).
fof(t57_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t57_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ~ ( v5_waybel23(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)))) ) => ~ v4_card_3(B) ) ) ) )).
fof(t57_topgen_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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))) ) ) ) )).
fof(t57_topgrp_1,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_tops_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => v1_tops_1(k5_group_2(A,C,B),A) ) ) ) )).
fof(t57_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v6_metric_1(B) & v8_metric_1(B) & v9_metric_1(B) & l1_metric_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => v6_tbsp_1(k9_metric_1(B,C,A),B) ) ) ) )).
fof(t57_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t57_toprealc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,k2_finseq_1(B)) => v5_pre_topc(k16_toprealc(B,A),k15_euclid(B),k3_topmetr) ) ) ) )).
fof(t57_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t57_tops_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_pre_topc(C) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t57_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t57_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t57_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v4_trees_3(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v4_trees_3(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_trees_1(C) ) => ! [D] : ( ( ~ 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(k4_ordinal1,k3_finseq_1(A)),C) ) ) ) ) )).
fof(t57_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ! [E] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t57_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( v1_int_1(C) => ( r1_nat_d(B,A) => ( r1_xxreal_0(A,B) | ! [D] : ( m1_subset_1(D,u1_struct_0(k1_complfld)) => ( D = C => ! [E] : ( v1_int_1(E) => ! [F] : ( v1_int_1(F) => ! [G] : ( 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,k4_int_1(F,G)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t57_valued_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) ) => ~ ( r2_hidden(B,k4_finseq_1(k15_finseq_1(C))) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( D = k1_funct_1(k14_finseq_1(k1_relset_1(k4_ordinal1,C)),B) & k1_funct_1(k14_finseq_1(k1_relset_1(k4_ordinal1,k61_valued_1(C,A))),B) = k1_nat_1(A,D) ) ) ) ) ) ) )).
fof(t57_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( ( 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)) ) ) ) ) )).
fof(t57_vectsp_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t57_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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))) ) ) ) )).
fof(t57_vfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( ~ 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] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,u1_struct_0(D)))) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) )).
fof(t57_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ! [F] : ( ( 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)) ) ) ) ) ) ) )).
fof(t57_waybel23,axiom,( ! [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] : ( ( v6_waybel23(B,A) & m1_waybel23(B,A) ) => ! [C] : ( r2_hidden(C,k2_relset_1(u1_struct_0(k1_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)))) ) ) ) ) )).
fof(t57_waybel34,axiom,( ! [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] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t57_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( D != k1_xboole_0 => r2_yellow_0(A,D) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(B)) ) => ~ ( r2_yellow_0(A,E) & D = k2_yellow_0(A,E) ) ) ) ) & ! [D] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_lattice3(A,B,D) <=> r1_lattice3(A,C,D) ) ) ) ) ) ) )).
fof(t57_waybel_1,axiom,( ! [A] : ( ( ~ 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,k1_yellow_1(k7_waybel_0(A)),k3_yellow_2(A),k2_yellow_2(A)),A,k1_yellow_1(k7_waybel_0(A))) & v18_waybel_0(k2_yellow_2(A),k1_yellow_1(k7_waybel_0(A)),A) ) ) )).
fof(t57_waybel_4,axiom,( ! [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] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ( v8_waybel_4(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ? [D] : ( 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) ) ) ) ) ) )).
fof(t57_xboole_1,axiom,( ! [A] : ! [B] : ~ ( r2_xboole_0(A,B) & r2_xboole_0(B,A) ) )).
fof(t57_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k8_xboolean(A,k8_xboolean(A,B)) = k6_xboolean(A,B) ) ) )).
fof(t57_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k7_xcmplx_0(1,k7_xcmplx_0(A,B)) = k7_xcmplx_0(B,A) ) ) )).
fof(t57_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_numbers) => r1_xxreal_0(k6_xcmplx_0(A,C),B) ) ) => r1_xxreal_0(A,B) ) ) ) )).
fof(t57_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_tarski(k3_xxreal_1(C,D),k2_xxreal_1(A,B)) => ( r1_xxreal_0(D,C) | ( r1_xxreal_0(A,C) & ~ r1_xxreal_0(B,D) ) ) ) ) ) ) ) )).
fof(t57_xxreal_2,axiom,( ! [A] : ( ( 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) ) ) ) )).
fof(t57_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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) ) ) ) ) ) ) )).
fof(t57_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v13_waybel_0(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t57_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v16_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( ~ v2_struct_0(D) & v2_altcat_1(D) & v3_altcat_2(D,A) & m1_altcat_2(D,A) ) => ! [E] : ( ( ~ v2_struct_0(E) & v2_altcat_1(E) & v3_altcat_2(E,B) & m1_altcat_2(E,B) ) => ( ( v21_functor0(C,A,B) & ! [F] : ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( k1_altcat_1(A,F,G) != k1_xboole_0 => ! [H] : ( m1_subset_1(H,u1_struct_0(D)) => ! [I] : ( m1_subset_1(I,u1_struct_0(D)) => ( ( H = F & I = G ) => ! [J] : ( m1_subset_1(J,u1_struct_0(E)) => ! [K] : ( m1_subset_1(K,u1_struct_0(E)) => ( ( J = k3_functor0(A,B,C,F) & K = k3_functor0(A,B,C,G) ) => ! [L] : ( 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) ) ) ) ) ) ) )).
fof(t57_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t57_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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)) ) ) ) )).
fof(t57_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t57_yellow_9,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ( u1_struct_0(A) = u1_struct_0(B) => ! [C] : ( m3_yellow_9(C,A,B) => ( m2_yellow_9(C,A) & m2_yellow_9(C,B) ) ) ) ) ) )).
fof(t57_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( v5_zf_lang(B) => ( r1_zf_lang(A,B) <=> ( A = k21_zf_lang(B) | A = k22_zf_lang(B) ) ) ) ) ) )).
fof(t57_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => 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))) ) ) )).
fof(t57_zfmisc_1,axiom,( ! [A] : ! [B] : ~ ( k4_xboole_0(B,k1_tarski(A)) = k1_xboole_0 & B != k1_xboole_0 & B != k1_tarski(A) ) )).
fof(t57_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_zmodul01(C,A) => ( r2_hidden(k4_struct_0(A),k5_zmodul01(A,B,C)) <=> r1_struct_0(C,B) ) ) ) ) )).
fof(t57_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_zmodul02(B,A) & r2_hidden(k4_struct_0(A),B) ) ) ) )).
fof(t58_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l3_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r5_abcmiz_0(A,B,k6_finseq_1(u1_abcmiz_0(A))) ) ) )).
fof(t58_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( 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] : ( m1_abcmiz_1(C,A,k13_abcmiz_1(A)) => ! [D] : ( m1_abcmiz_1(D,A,k12_abcmiz_1(A)) => B != k31_abcmiz_1(A,k33_abcmiz_1(A),C,D) ) ) ) ) ) )).
fof(t58_abcmiz_a,axiom,( ! [A] : ( m2_finseq_2(A,k2_abcmiz_1,k4_abcmiz_1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k27_abcmiz_1)) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t58_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_aff_1(D,A) & ~ r2_aff_1(A,B,C,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,D) & r1_aff_1(A,B,C,E) ) ) ) ) ) ) ) )).
fof(t58_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t58_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v5_ordinal1(D) & v1_funct_1(D) & v1_finset_1(D) ) => ( B = k2_xcmplx_0(k2_afinsq_1(C),A) => k5_relat_1(k1_ordinal4(C,D),B) = k1_ordinal4(C,k5_relat_1(D,A)) ) ) ) ) ) )).
fof(t58_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v3_valued_0(A) & v1_finset_1(A) ) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k1_relset_1(k4_ordinal1,A)) => r1_xxreal_0(k1_funct_1(A,C),B) ) ) => r1_xxreal_0(k7_afinsq_2(A),k3_xcmplx_0(k1_afinsq_1(A),B)) ) ) ) )).
fof(t58_algspec1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_instalg1(B) & l1_msualg_1(B) ) => ! [C] : ( l3_msualg_1(C,B) => ( m4_algspec1(C,A) => ! [D] : ( 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))))) ) ) ) ) ) ) )).
fof(t58_altcat_4,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t58_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r4_analmetr(A,C,D,B,B) & r4_analmetr(A,B,B,C,D) & r2_analoaf(A,C,D,B,B) & r2_analoaf(A,B,B,C,D) ) ) ) ) ) )).
fof(t58_aofa_000,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_freealg(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t58_aofa_a00,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,k5_numbers) => ! [C] : ( ( ~ v2_struct_0(C) & ~ v11_struct_0(C) & v14_aofa_a00(C,A) & l6_aofa_a00(C) ) => ! [D] : ! [E] : ! [F] : ( ( ~ v2_struct_0(F) & ~ v11_struct_0(F) & l5_aofa_a00(F) ) => ( v21_aofa_a00(F,D,E,B) => v21_aofa_a00(k36_aofa_a00(C,F),D,E,k2_xcmplx_0(A,B)) ) ) ) ) ) ) )).
fof(t58_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v19_aofa_a00(E,A) & m1_subset_1(E,u1_struct_0(A)) ) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,C),E)) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),E)) => ! [H] : ( m2_pboole(H,u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,D)) => k15_aofa_a00(A,B,C,D,E,k32_aofa_a00(A,C,E,F,G),H) = k32_aofa_a00(A,D,E,k15_aofa_a00(A,B,C,D,E,F,H),k15_aofa_a00(A,B,C,D,E,G,H)) ) ) ) ) ) ) ) ) )).
fof(t58_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_aofa_i00(D,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [G] : ( m1_aofa_i00(G,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [H] : ( m1_aofa_i00(H,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ( ? [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,k5_numbers),k13_aofa_000(A,k51_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,G,1),k17_aofa_000(A,k51_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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,k5_numbers),D,G,E),k57_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,H,1))),D) ) ) ) ) ) ) ) ) ) )).
fof(t58_armstrng,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t58_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & m1_subset_1(A,k5_arytm_3) ) => ! [B] : ( ( v3_ordinal1(B) & m1_subset_1(B,k5_arytm_3) ) => k9_arytm_3(A,B) = k8_ordinal3(A,B) ) ) )).
fof(t58_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(2,A) & r1_xxreal_0(A,k2_int_1(k7_xcmplx_0(A,2))) ) ) )).
fof(t58_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t58_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( v8_bcialg_1(E) & m1_bcialg_5(E,A,B,C,D) ) => ( D = k5_numbers => ( A = k5_numbers | ( v8_bcialg_1(E) & m1_bcialg_5(E,k5_numbers,k5_numbers,k5_numbers,k5_numbers) ) ) ) ) ) ) ) ) )).
fof(t58_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),B,k4_normsp_1(A,B,k4_struct_0(A))) ) ) )).
fof(t58_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t58_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ r4_boolealg(A,k4_lattices(A,B,C),k3_boolealg(A,B,C)) ) ) ) )).
fof(t58_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t58_borsuk_6,axiom,( k9_subset_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)),k8_borsuk_6,k7_borsuk_6) = a_0_16_borsuk_6 )).
fof(t58_borsuk_7,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xxreal_0(A) ) => ! [B] : ( v1_xreal_0(B) => 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) ) ) )).
fof(t58_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t58_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_eqrel_1(I,A) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t58_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t58_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k3_xboolean(k7_xboolean(A,B)) = k10_xboolean(A,B) ) ) )).
fof(t58_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t58_card_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_wellord2(A,B) => A = B ) ) ) )).
fof(t58_card_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ~ ( A != B & A != C & A != D & B != C & B != D & C != D & k5_card_1(k2_enumset1(A,B,C,D)) != 4 ) )).
fof(t58_card_3,axiom,( ! [A] : ! [B] : k4_partfun1(A,B) = k8_card_3(k7_funcop_1(A,B)) )).
fof(t58_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ~ ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,k4_numbers) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ~ ( k1_relset_1(k4_ordinal1,C) = k1_nat_1(k5_card_1(B),1) & k7_afinsq_2(C) = k1_card_1(a_2_1_card_fin(A,B)) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,C)) => k1_funct_1(C,D) = k3_xcmplx_0(k3_xcmplx_0(k1_newton(k4_xcmplx_0(1),D),k4_newton(D,k5_card_1(B))),k1_newton(k6_xcmplx_0(k5_card_1(B),D),k5_card_1(A))) ) ) ) ) ) ) ) )).
fof(t58_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t58_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ( ( r2_cat_3(A,B,D,E) & r2_hidden(C,k2_cat_1(A,B,B)) & k1_cat_1(A,C,D) = D & k1_cat_1(A,C,E) = E ) => C = k4_cat_1(A,B) ) ) ) ) ) ) )).
fof(t58_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_cat_1(A,k19_cat_4(A),B) = k1_tarski(k24_cat_4(A,B)) ) ) )).
fof(t58_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( v1_xcmplx_0(C) => ( v1_partfun1(B,A) <=> v1_partfun1(k25_valued_1(A,k2_numbers,B,C),A) ) ) ) ) )).
fof(t58_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_chain_1(B,k1_nat_1(A,1)) => k10_chain_1(k1_nat_1(A,1),B,A,k6_chain_1(k1_nat_1(A,1),B)) = k5_chain_1(k1_nat_1(A,1),B,A) ) ) )).
fof(t58_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ( r5_glib_000(A,B) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(B)) => ( C = D => ! [E] : ( m1_chord(E,A,k6_domain_1(k6_glib_000(A),C)) => ! [F] : ( m1_chord(F,B,k6_domain_1(k6_glib_000(B),D)) => r5_glib_000(E,F) ) ) ) ) ) ) ) ) )).
fof(t58_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ( v6_circcomb(B,A) <=> r1_tarski(k10_xtuple_0(u3_msualg_1(A,B)),k1_tarski(k6_margrel1)) ) ) ) )).
fof(t58_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( m3_msaterm(D,A,C) => ! [E] : ( ( ~ v2_struct_0(E) & ~ v11_struct_0(E) & v2_msafree2(E) & l1_msualg_1(E) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t58_classes1,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_tarski(k5_classes1(A),k5_classes1(B)) ) )).
fof(t58_classes2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) ) )).
fof(t58_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_clvect_1(B,A) => m1_clvect_1(k3_clvect_1(A),B) ) ) )).
fof(t58_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v2_clvect_2(B,A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & ? [F] : ( v7_ordinal1(F) & 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)))) ) ) ) ) ) ) ) ) )).
fof(t58_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ? [C] : ( 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 ) ) ) )).
fof(t58_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => r1_xxreal_0(k6_xcmplx_0(k9_complex1(A),k9_complex1(B)),k9_complex1(k2_xcmplx_0(A,B))) ) ) )).
fof(t58_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_complex2(A,k28_sin_cos) = k4_xcmplx_0(A) ) )).
fof(t58_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ( k9_complex1(A) = k5_numbers => A = k4_struct_0(k1_complfld) ) ) )).
fof(t58_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => k8_complsp2(k9_seq_4(A),k9_seq_4(B)) = k8_complsp2(A,B) ) ) ) )).
fof(t58_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( v6_compos_0(D,u1_compos_1(A)) & m1_subset_1(D,u1_compos_1(A)) ) => ! [E] : ( ( v6_compos_0(E,u1_compos_1(A)) & m1_subset_1(E,u1_compos_1(A)) ) => ! [F] : ( ( 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) ) ) ) ) ) ) )).
fof(t58_comptrig,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m1_comptrig(B,A,1) => B = A ) ) )).
fof(t58_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k3_finseq_2(k4_ordinal1)) & v1_funct_1(C) & v4_valued_0(C) & v2_margrel1(C) ) => ! [D] : ( m2_finseq_2(D,k4_ordinal1,k4_finseq_2(k1_nat_1(k19_margrel1(B),1),k4_ordinal1)) => ( ( r2_hidden(A,k4_finseq_1(D)) & r2_hidden(k8_comput_1(k1_nat_1(k19_margrel1(B),1),D,A,k5_numbers),k1_relset_1(k3_finseq_2(k4_ordinal1),k7_comput_1(B,C,A))) ) => k1_recdef_1(k7_comput_1(B,C,A),k8_comput_1(k1_nat_1(k19_margrel1(B),1),D,A,k5_numbers)) = k1_recdef_1(B,k2_finseq_3(A,D)) ) ) ) ) ) )).
fof(t58_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_comseq_3(A) => ! [B] : ( v7_ordinal1(B) => v1_comseq_3(k1_valued_0(k2_numbers,A,B)) ) ) ) )).
fof(t58_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( B = k1_xboole_0 => v2_convex4(B,A) ) ) ) )).
fof(t58_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) )).
fof(t58_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ! [E] : ( m2_subset_1(E,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t58_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t58_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k15_csspace(A,k5_algstr_0(A,B,D),k5_algstr_0(A,C,D)) = k15_csspace(A,B,C) ) ) ) ) )).
fof(t58_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k3_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k18_sin_cos),A),B) = k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k19_sin_cos(k3_xcmplx_0(2,k2_xcmplx_0(B,A))),k19_sin_cos(k3_xcmplx_0(2,B)))) ) ) )).
fof(t58_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k3_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k18_sin_cos),k18_sin_cos),A),B) = k4_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,2),k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,k17_sin_cos(k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(2,B),A),2))),k17_sin_cos(k7_xcmplx_0(A,2))),k3_xcmplx_0(k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(3,k2_xcmplx_0(k3_xcmplx_0(2,B),A)),2)),k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(3,A),2)))))) ) ) )).
fof(t58_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(B,k1_relset_1(k1_numbers,k26_sin_cos)) & r2_hidden(k6_xcmplx_0(B,A),k1_relset_1(k1_numbers,k26_sin_cos)) ) => k1_funct_1(k4_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k26_sin_cos),k16_sin_cos),A),B) = k6_xcmplx_0(k3_xcmplx_0(k1_newton(k1_funct_1(k16_sin_cos,B),3),k1_newton(k5_xcmplx_0(k1_funct_1(k18_sin_cos,B)),2)),k3_xcmplx_0(k1_newton(k1_funct_1(k16_sin_cos,k6_xcmplx_0(B,A)),3),k1_newton(k5_xcmplx_0(k1_funct_1(k18_sin_cos,k6_xcmplx_0(B,A))),2))) ) ) ) )).
fof(t58_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(A))) => ! [E] : ! [F] : ~ ( ~ 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t58_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k9_int_3(A))) => ! [G] : ( 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] : ( 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] : ( 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 = k5_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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t58_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t58_enumset1,axiom,( ! [A] : ! [B] : ! [C] : k1_enumset1(A,B,C) = k1_enumset1(B,A,C) )).
fof(t58_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t58_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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),k5_numbers) & ~ r1_xxreal_0(k11_euclid_3(2,A,B,C,D),k5_numbers) & ~ r1_xxreal_0(k12_euclid_3(2,A,B,C,D),k5_numbers) ) ) ) ) ) ) ) )).
fof(t58_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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_funct_1(C,1),k1_funct_1(C,2),k1_funct_1(C,3)),k2_xcmplx_0(A,B)) ) ) ) )).
fof(t58_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => r1_xxreal_0(k5_numbers,k3_euclidlp(A,B,C)) ) ) ) )).
fof(t58_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ 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] : ( ( 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,k9_funct_7(E,A,B))) ) ) ) ) )).
fof(t58_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) )).
fof(t58_fdiff_11,axiom,( ! [A] : ( ( 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(k4_xcmplx_0(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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k7_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k18_sin_cos,k6_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k1_funct_1(k2_sin_cos9,B)))),k2_xcmplx_0(1,k1_square_1(B))) ) ) ) ) ) )).
fof(t58_fib_num2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k2_xboole_0(k5_relat_1(k2_fib_num2,k3_xboole_0(k3_fib_num2,k2_finseq_1(k1_nat_1(k2_nat_1(2,A),2)))),k1_tarski(k1_domain_1(k4_ordinal1,k4_ordinal1,k1_nat_1(k2_nat_1(2,A),4),k3_funct_2(k4_ordinal1,k4_ordinal1,k2_fib_num2,k1_nat_1(k2_nat_1(2,A),4))))) = k5_relat_1(k2_fib_num2,k3_xboole_0(k3_fib_num2,k2_finseq_1(k1_nat_1(k2_nat_1(2,A),4)))) ) )).
fof(t58_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(t58_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t58_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) <=> ~ r2_hidden(k7_lattices(A,C),B) ) ) ) ) ) )).
fof(t58_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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 ) ) ) )).
fof(t58_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : k2_finseq_2(k1_nat_1(A,1),B) = k7_finseq_1(k2_finseq_2(A,B),k9_finseq_1(B)) ) )).
fof(t58_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : r1_xxreal_0(k3_finseq_1(k1_finseq_3(A,B)),k3_finseq_1(A)) ) )).
fof(t58_finseq_4,axiom,( ! [A] : ~ ( v1_finset_1(A) & ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ ( k10_xtuple_0(B) = A & v2_funct_1(B) ) ) ) )).
fof(t58_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t58_finseq_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_finseq_1(D,C) => ( r2_hidden(A,k4_finseq_1(D)) => ( r1_xxreal_0(A,B) | r2_hidden(k7_partfun1(C,D,A),k10_xtuple_0(k2_rfinseq(C,B,D))) ) ) ) ) ) ) )).
fof(t58_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,B) & m2_finseq_1(C,A) ) => ! [D] : ( ( 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(k4_ordinal1,A,k2_finseqop(A,A,A,D,C,k4_binop_1(A,D)),C) ) ) ) ) ) )).
fof(t58_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k8_afinsq_1(A))) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( v7_ordinal1(H) => ( ( r1_xxreal_0(G,H) & r1_xxreal_0(E,F) & r1_tarski(B,k1_flang_2(A,D,G,H)) & r1_tarski(C,k1_flang_2(A,D,E,F)) ) => r1_tarski(k6_flang_1(A,B,C),k1_flang_2(A,D,k2_xcmplx_0(G,E),k2_xcmplx_0(H,F))) ) ) ) ) ) ) ) ) )).
fof(t58_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t58_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ~ r2_hidden(C,k10_xtuple_0(B)) => r1_xboole_0(k2_zfmisc_1(A,k1_tarski(C)),B) ) )).
fof(t58_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & v8_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( ( ~ v2_struct_0(D) & v5_fsm_1(D,A,B) & v7_fsm_1(D,A,B) & l2_fsm_1(D,A,B) ) => ! [E] : ( ( ~ v2_struct_0(E) & v5_fsm_1(E,A,B) & v7_fsm_1(E,A,B) & l2_fsm_1(E,A,B) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ! [H] : ( m1_subset_1(H,u1_struct_0(E)) => ! [I] : ( m1_subset_1(I,u1_struct_0(E)) => ~ ( H = F & I = G & C = k13_fsm_1(A,B,D,E) & ~ r5_fsm_1(A,B,E,H,I) & r5_fsm_1(A,B,C,F,G) ) ) ) ) ) ) ) ) ) ) )).
fof(t58_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t58_funct_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t58_funct_2,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(t58_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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)))) ) ) ) ) )).
fof(t58_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ( ( k9_xtuple_0(E) = k2_zfmisc_1(A,C) & k9_xtuple_0(F) = k2_zfmisc_1(B,D) ) => k9_xtuple_0(k3_funct_4(E,F)) = k2_zfmisc_1(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) ) ) ) )).
fof(t58_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( B != C => ( r2_wellord2(k9_funct_2(A,k2_tarski(B,C)),k1_zfmisc_1(A)) & k1_card_1(k9_funct_2(A,k2_tarski(B,C))) = k1_card_1(k1_zfmisc_1(A)) ) ) )).
fof(t58_funct_7,axiom,( ! [A] : ! [B] : ( ( 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(k3_funct_7(A,B)),k6_funct_7(B)) ) ) )).
fof(t58_funct_8,axiom,( k1_funct_1(k1_funct_8,k5_numbers) = k5_numbers )).
fof(t58_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t58_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(t58_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) ) )).
fof(t58_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( 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 ) ) ) ) )).
fof(t58_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( 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(k4_ordinal1,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))) ) ) ) ) ) ) ) )).
fof(t58_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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_nat_1(A,1),k3_finseq_1(k2_goboard2(C))) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(k2_goboard2(C))) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1))),k3_topreal1(2,C)) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1))),k3_topreal1(2,C)) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,1) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1)) & ( ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,2) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k7_nat_d(k3_finseq_1(C),1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1)) ) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,2) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k7_nat_d(k3_finseq_1(C),1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B) ) ) ) & ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(1,D) & ~ r1_xxreal_0(k3_finseq_1(C),k1_nat_1(D,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_nat_1(D,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1)) & ( ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,D) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_nat_1(D,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1)) ) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),C,D) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_nat_1(D,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B) ) ) ) ) ) ) ) ) )).
fof(t58_graph_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( 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),k1_nat_1(k3_finseq_1(C),B)) = k7_partfun1(A,D,k1_nat_1(B,1)) ) ) ) ) ) ) )).
fof(t58_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_graph_1(A) & l1_graph_1(A) ) => ! [B] : ( ( v2_funct_1(B) & m2_graph_1(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t58_graph_5,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v6_graph_1(C) & l1_graph_1(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ~ ( k5_graph_5(C,D,E,A) != k1_xboole_0 & ! [F] : ( m2_finseq_1(F,u4_struct_0(C)) => ~ ( r2_hidden(F,k5_graph_5(C,D,E,A)) & ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t58_groeb_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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),k8_polynom1(A,C)) ) ) ) ) => ( r2_hidden(k8_polynom1(A,C),D) | ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(G,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,k8_polynom1(A,C)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t58_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ( m1_group_2(B,C) => r1_tarski(k4_group_11(A,B,B),k4_group_11(A,C,C)) ) ) ) ) )).
fof(t58_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_struct_0(B,D) => r1_struct_0(C,D) ) ) => m1_group_2(B,C) ) ) ) ) )).
fof(t58_group_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_group_2(D,B) => ( r1_struct_0(k6_group_3(B,D,C),A) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & A = k2_group_3(B,E,C) & r1_struct_0(D,E) ) ) ) ) ) )).
fof(t58_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t58_group_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ( r2_hidden(A,k6_group_5(B)) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(B)) & ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & A = k2_group_5(B,C,D) ) ) ) ) )).
fof(t58_group_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,B) => ? [E] : ( m1_subset_1(E,A) & k3_funct_2(A,B,C,E) = D ) ) ) ) ) ) )).
fof(t58_group_9,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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) ) ) ) )).
fof(t58_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( 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)) = k5_numbers => ( ( v5_bilinear(B,k1_complfld,A,A) & v6_bilinear(B,k1_complfld,A,A) ) | C = k4_struct_0(A) ) ) ) ) ) )).
fof(t58_hfdiff_1,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k1_relset_1(k1_numbers,k26_sin_cos)) => r2_relset_1(k1_numbers,k1_numbers,k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k26_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,k26_sin_cos,k6_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos)),k6_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos)),A),2)) ) ) )).
fof(t58_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t58_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => r2_int_1(k3_xcmplx_0(A,B),k5_numbers,A) ) ) )).
fof(t58_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(A,B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( ~ r1_xxreal_0(k1_funct_1(k18_sin_cos,D),k5_numbers) & k1_funct_1(C,D) = k1_square_1(k1_funct_1(k26_sin_cos,D)) ) ) ) & r1_tarski(B,k9_xtuple_0(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_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) = k6_xcmplx_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_partfun2(k1_numbers,B)),k2_seq_4(A)),k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_partfun2(k1_numbers,B)),k3_seq_4(A))) ) ) ) ) )).
fof(t58_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k2_xcmplx_0(k1_funct_1(k18_sin_cos,D),k7_xcmplx_0(k1_funct_1(k18_sin_cos,D),k1_square_1(k1_funct_1(k16_sin_cos,D)))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k27_sin_cos))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k27_sin_cos)),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k27_sin_cos)),k3_seq_4(A))) ) ) ) ) )).
fof(t58_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,1) => k2_integra5(A,k3_sin_cos2) = k7_xcmplx_0(k6_xcmplx_0(k1_square_1(k4_power),1),k3_xcmplx_0(2,k4_power)) ) ) )).
fof(t58_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( 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] : ( v1_xreal_0(H) => ( r2_hidden(H,G) => ( k1_funct_1(E,H) = k6_xcmplx_0(H,B) & ~ r1_xxreal_0(k1_funct_1(E,H),k5_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,k2_xcmplx_0(A,B)))) = G & G = k1_relset_1(k1_numbers,F) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,G) => k1_funct_1(F,H) = k7_xcmplx_0(k2_xcmplx_0(H,A),k6_xcmplx_0(H,B)) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,F,C)) ) => k2_integra5(C,F) = k6_xcmplx_0(k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,G),k26_valued_1(k1_numbers,k1_numbers,D,k2_xcmplx_0(A,B))),k2_seq_4(C)),k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,G),k26_valued_1(k1_numbers,k1_numbers,D,k2_xcmplx_0(A,B))),k3_seq_4(C))) ) ) ) ) ) ) ) ) )).
fof(t58_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m2_interva1(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(t58_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(t58_jgraph_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(k5_topmetr)) => ! [H] : ( 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(k7_xcmplx_0(2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(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(k4_xcmplx_0(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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t58_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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(k2_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)),k2_jordan9(D,B),A) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(D,B),C,k1_matrix_0(k1_jordan8(D,B))) ) => r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),k2_jordan9(D,B),A),k15_pscomp_1(k3_topreal1(2,k2_jordan9(D,B)))) ) ) ) ) ) )).
fof(t58_jordan1h,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( 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] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(k4_tarski(k1_nat_1(E,1),D),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k7_nat_d(k3_finseq_1(C),1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k1_nat_1(E,1),D) & r2_hidden(k4_tarski(E,D),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k3_finseq_1(C)) = k3_matrix_0(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_0(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) )).
fof(t58_jordan1j,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k3_topreal1(2,k1_jordan1e(B,A))) = k1_tarski(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k3_topreal1(2,k2_jordan1e(B,A))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D)) & r1_xboole_0(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k9_jordan6(B)) ) ) ) ) ) ) )).
fof(t58_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k14_euclid(A))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))))) ) => ~ ( v5_pre_topc(H,k5_topmetr,k15_euclid(A)) & r1_tarski(k2_relset_1(u1_struct_0(k15_euclid(A)),H),G) & k1_funct_1(H,k5_numbers) = D & k1_funct_1(H,1) = E & r2_hidden(C,k8_metric_1(k14_euclid(A),F,B)) & r2_hidden(E,k8_metric_1(k14_euclid(A),F,B)) & r1_tarski(k8_metric_1(k14_euclid(A),F,B),G) & ! [I] : ( ( v1_funct_1(I) & v1_funct_2(I,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A))))) ) => ~ ( v5_pre_topc(I,k5_topmetr,k15_euclid(A)) & r1_tarski(k2_relset_1(u1_struct_0(k15_euclid(A)),I),G) & k1_funct_1(I,k5_numbers) = D & k1_funct_1(I,1) = C ) ) ) ) ) ) ) ) ) ) ) )).
fof(t58_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t58_kurato_1,axiom,( r1_xboole_0(k3_kurato_1(k3_topmetr,k6_kurato_1),k4_kurato_1(k3_topmetr,k6_kurato_1)) )).
fof(t58_lattice2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k5_finsub_1(A)) => ! [C] : ( ( ~ v2_struct_0(C) & v10_lattices(C) & v14_lattices(C) & l3_lattices(C) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t58_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k9_funct_2(k6_glib_000(A),k4_ordinal1))) => ! [C] : ~ ( ~ r2_hidden(C,k1_relset_1(k6_glib_000(A),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),B))) & k1_relset_1(k6_glib_000(A),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),B)) != k6_glib_000(A) & ~ r1_xxreal_0(k1_recdef_1(k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k4_ordinal1,k6_glib_000(A),B),C),k1_recdef_1(k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k4_ordinal1,k6_glib_000(A),B),k19_lexbfs(A,B))) ) ) ) )).
fof(t58_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( ( v4_limfunc1(A) => ( r1_xxreal_0(B,k5_numbers) | v4_limfunc1(k26_valued_1(k1_numbers,k1_numbers,A,B)) ) ) & ( v4_limfunc1(A) => ( r1_xxreal_0(k5_numbers,B) | v5_limfunc1(k26_valued_1(k1_numbers,k1_numbers,A,B)) ) ) & ( v5_limfunc1(A) => ( r1_xxreal_0(B,k5_numbers) | v5_limfunc1(k26_valued_1(k1_numbers,k1_numbers,A,B)) ) ) & ( v5_limfunc1(A) => ( r1_xxreal_0(k5_numbers,B) | v4_limfunc1(k26_valued_1(k1_numbers,k1_numbers,A,B)) ) ) ) ) ) )).
fof(t58_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r4_limfunc2(B,A) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,A) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(C,D) & ~ r1_xxreal_0(D,A) & r2_hidden(D,k1_relset_1(k1_numbers,B)) & k1_funct_1(B,D) != k5_numbers ) ) ) ) ) => ( k2_limfunc2(B,A) = k5_numbers | ( r4_limfunc2(k6_rfunct_1(k1_numbers,k1_numbers,B),A) & k2_limfunc2(k6_rfunct_1(k1_numbers,k1_numbers,B),A) = k5_xcmplx_0(k2_limfunc2(B,A)) ) ) ) ) ) )).
fof(t58_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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) ) ) ) ) ) )).
fof(t58_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v2_xxreal_0(D) & v1_xreal_0(D) ) => k1_mesfunc6(A,B,C,k2_mesfun6c(D,A,k56_valued_1(A,k1_numbers,k8_lpspace1(A,k5_numbers)))) = k5_numbers ) ) ) ) )).
fof(t58_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) ) )).
fof(t58_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_hilbert1)) => r8_ltlaxio1(C,k3_hilbert1(k3_hilbert1(k2_ltlaxio1(A),k2_ltlaxio1(B)),k2_ltlaxio1(k3_hilbert1(A,B)))) ) ) ) )).
fof(t58_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t58_mathmorp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => k6_mathmorp(1,k15_euclid(A),B) = B ) ) )).
fof(t58_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,k1_numbers,A,A) & m2_finseq_1(E,k3_finseq_2(k1_numbers)) ) => ( r2_matrix10(k5_matrix10(A,B,C),k5_matrix10(A,D,E)) => r2_matrix10(k5_matrix10(A,E,D),k5_matrix10(A,C,B)) ) ) ) ) ) ) )).
fof(t58_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(D),C,C) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(D))) ) => k6_matrix13(u1_struct_0(D),E,k7_subset_1(k4_ordinal1,k2_finseq_1(C),k3_matrix13(A)),k7_subset_1(k4_ordinal1,k2_finseq_1(C),k3_matrix13(B))) = k18_matrix_0(A,B,C,u1_struct_0(D),E) ) ) ) ) ) )).
fof(t58_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ~ ( r2_hidden(D,k4_matrix15(A,B,k3_matrix15(u1_struct_0(A),C))) & ! [E] : ( m2_finseq_1(E,u1_struct_0(A)) => ~ ( D = k3_matrix15(u1_struct_0(A),E) & k3_finseq_1(E) = k1_matrix_0(B) ) ) ) ) ) ) )).
fof(t58_matrix16,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ( v6_matrix16(B,A) => v6_matrix16(k5_fvsum_1(A,B),A) ) ) ) )).
fof(t58_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => k7_matrix_0(A,B,C) = k8_matrix_0(A,k4_matrix_0(A,B),C) ) ) ) ) )).
fof(t58_matrix_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ( ~ r1_xxreal_0(k3_finseq_1(B),k5_numbers) => ! [C] : ( v7_ordinal1(C) => ( ( v1_matrix_0(B) & v2_matrix_0(B,A,C,k1_matrix_0(B)) & m2_finseq_1(B,k3_finseq_2(A)) ) <=> C = k3_finseq_1(B) ) ) ) ) ) )).
fof(t58_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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(k3_matrix_1(B,A),A,B) ) ) )).
fof(t58_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => k1_matrix_8(A,B,k3_matrix_3(B,C,k2_matrix_3(B,C))) = k4_struct_0(B) ) ) ) )).
fof(t58_matrixc1,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k2_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(C) & k3_finseq_1(B) = k1_matrix_0(C) ) => ( r1_xxreal_0(k1_matrix_0(C),k5_numbers) | r1_xxreal_0(k3_finseq_1(C),k5_numbers) | k8_complsp2(A,k6_matrixc1(C,B)) = k8_complsp2(k6_matrixc1(k2_matrixc1(C),A),B) ) ) ) ) ) )).
fof(t58_matrixj1,axiom,( ! [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] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => k23_matrixj1(A,k8_finseq_1(k4_ordinal1,B,C)) = k15_matrixj1(u1_struct_0(A),k23_matrixj1(A,B),k23_matrixj1(A,C)) ) ) ) )).
fof(t58_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( ( v1_matrix_0(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),k5_numbers) | k12_matrixr1(C,k4_rvsum_1(A,B)) = k4_rvsum_1(k12_matrixr1(C,A),k12_matrixr1(C,B)) ) ) ) ) ) )).
fof(t58_matrixr2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( k1_matrix_0(B) = k3_finseq_1(A) => ( r1_xxreal_0(k3_finseq_1(A),k5_numbers) | r1_xxreal_0(k3_finseq_1(B),k5_numbers) | k6_matrixr1(B,k9_matrixr1(A)) = k9_matrixr1(k11_matrixr1(B,A)) ) ) ) ) )).
fof(t58_matrprob,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ? [C] : ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,B) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) & v2_matrprob(C) & v5_matrprob(C) ) ) ) )).
fof(t58_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( r1_tarski(A,D) & r1_tarski(B,E) & r1_tarski(C,F) ) => r1_tarski(k3_zfmisc_1(A,B,C),k3_zfmisc_1(D,E,F)) ) )).
fof(t58_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => r1_tarski(A,k5_measure6(A)) ) )).
fof(t58_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( 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))) ) ) ) )).
fof(t58_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t58_mesfunc5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( m1_subset_1(B,k6_numbers) => ~ ( B != k1_supinf_1 & ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k9_nat_1(k6_numbers,A,C),B) ) & r1_xxreal_0(k1_supinf_1,k8_supinf_2(k17_supinf_2(A))) ) ) ) )).
fof(t58_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( ! [D] : ( 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)) ) => v6_supinf_2(k47_valued_1(A,k1_numbers,k1_numbers,B,C)) ) ) ) ) )).
fof(t58_mmlquery,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_1(C,k9_setfam_1(A)) => k27_mmlquery(A,C,B,k3_finseq_1(C)) = k26_mmlquery(A,C,B) ) ) )).
fof(t58_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k30_modelc_1(k25_modelc_2(A)))) ) => ! [C] : ( m1_subset_1(C,k25_modelc_2(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k42_modelc_2(A,B))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t58_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_3(B,A) & l1_modelc_3(B,A) ) => ! [C] : ( m2_orders_1(C,k1_orders_1(k1_modelc_3(A)),k6_partfun1(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)) ) ) ) ) )).
fof(t58_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => r1_xxreal_0(k6_moebius1(A),A) ) )).
fof(t58_monoid_0,axiom,( r3_binop_1(k4_ordinal1,1,k24_binop_2) & v9_monoid_0(k24_binop_2,k4_ordinal1) )).
fof(t58_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m3_pboole(C,u1_struct_0(A),B) => m1_msualg_2(k1_msafree3(A,C),A,k1_msafree3(A,B)) ) ) ) )).
fof(t58_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( r1_int_2(A,B) => r8_pboole(k8_newton,k13_nat_3(k3_xcmplx_0(A,B)),k11_pre_poly(k8_newton,k13_nat_3(A),k13_nat_3(B))) ) ) ) )).
fof(t58_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(A,B) => k7_nat_d(B,k7_nat_d(B,A)) = A ) ) ) )).
fof(t58_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ! [E] : ( ( 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) ) ) ) ) )).
fof(t58_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k6_nat_d(A,B),k5_numbers) ) ) ) )).
fof(t58_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t58_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,B,A) => ! [E] : ( m1_oppcat_1(E,A,C) => m1_oppcat_1(k1_partfun1(u4_struct_0(B),u4_struct_0(A),u4_struct_0(A),u4_struct_0(C),D,E),B,C) ) ) ) ) ) )).
fof(t58_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( ( r2_hidden(C,B) & r9_orders_1(A,C) & r1_tarski(B,k1_relat_1(A)) & v1_relat_2(A) ) => r5_orders_1(A,B) ) ) )).
fof(t58_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r1_ordinal1(A,B) => r1_ordinal1(k5_ordinal3(C,B),k5_ordinal3(C,A)) ) ) ) ) )).
fof(t58_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r2_hidden(k5_numbers,C) & r2_hidden(C,B) ) => k5_ordinal5(k11_ordinal2(C,k12_ordinal2(B,A)),B) = A ) ) ) ) )).
fof(t58_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ! [D] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t58_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r3_parsp_2(A,B,C,D,E) => r3_parsp_2(A,C,B,E,D) ) ) ) ) ) ) )).
fof(t58_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( ( r1_partfun1(C,E) & r1_relset_1(A,B,D,C) ) => r1_partfun1(D,E) ) ) ) ) )).
fof(t58_partfun2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ( v3_funct_1(k2_partfun1(B,C,D,A)) <=> ! [E] : ( m1_subset_1(E,B) => ! [F] : ( m1_subset_1(F,B) => ( ( r2_hidden(E,k9_subset_1(B,A,k1_relset_1(B,D))) & r2_hidden(F,k9_subset_1(B,A,k1_relset_1(B,D))) ) => k1_funct_1(D,E) = k1_funct_1(D,F) ) ) ) ) ) ) ) )).
fof(t58_pboole,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(t58_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( ( 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) & k10_pdiff_1(3,1,k26_valued_1(k1_euclid(3),k1_numbers,k1_pdiff_3(1,3,C),A),B) = k3_xcmplx_0(A,k1_pdiff_5(C,B)) ) ) ) ) ) )).
fof(t58_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t58_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ( r2_int_1(k11_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)) ) ) )).
fof(t58_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,k8_polyform(A,B)) => ! [D] : ( m1_subset_1(D,k8_polyform(A,k6_xcmplx_0(B,1))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k17_polyform(A,B))) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ( ( B = k5_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) ) ) ) ) ) ) ) ) ) )).
fof(t58_polynom5,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( k1_algseq_1(A,B) != k5_numbers => ! [C] : ( 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(k4_ordinal1,u1_struct_0(A),B,k7_nat_d(k1_algseq_1(A,B),1))) ) ) ) ) )).
fof(t58_polyred,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k12_polynom1(A,C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k12_polynom1(A,C))) => ( r11_polyred(k12_polynom1(A,C),k7_ideal_1(k12_polynom1(A,C),D),E,F) => r2_rewrite1(k3_polyred(A,B,C,D),E,F) ) ) ) ) ) ) ) )).
fof(t58_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) & ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(C,B) & r1_xxreal_0(k3_power(A,B),k3_power(A,C)) ) ) ) ) )).
fof(t58_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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) ) ) )).
fof(t58_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_rat_1(C) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & k4_prepower(k7_xcmplx_0(A,B),C) != k7_xcmplx_0(k4_prepower(A,C),k4_prepower(B,C)) ) ) ) ) )).
fof(t58_prob_3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( m1_prob_3(C,A,B) => r2_hidden(k7_prob_3(A,C),B) ) ) )).
fof(t58_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t58_pscomp_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t58_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t58_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( ( r2_qc_lang2(A,B,C) & r2_qc_lang2(A,C,B) ) => B = C ) ) ) ) )).
fof(t58_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => k5_qc_lang3(A,k15_qc_lang1(A,B,C)) = k5_qc_lang3(A,C) ) ) ) )).
fof(t58_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k17_quatern2(k25_quaterni(A,B),C) = k25_quaterni(k17_quatern2(A,C),k17_quatern2(B,C)) ) ) ) )).
fof(t58_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k24_quaterni(k22_quaterni(k22_quaterni(A,B),C)) = k25_quaterni(k25_quaterni(k24_quaterni(A),B),C) ) ) ) )).
fof(t58_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ( ( k14_quaterni(A) = k5_numbers & k15_quaterni(A) = k5_numbers & k16_quaterni(A) = k5_numbers ) => k27_quaterni(A) = A ) ) )).
fof(t58_quofield,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t58_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B))))) => ! [D] : ( 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) ) => k2_seq_4(k7_partfun1(k9_setfam_1(k1_numbers),D,k3_finseq_1(D))) = B ) ) ) ) ) )).
fof(t58_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ( ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,k4_real_3(A),B),k5_numbers) ) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k7_xcmplx_0(1,k9_nat_1(k1_numbers,k4_real_3(A),k1_nat_1(B,2))),k6_real_1(k9_nat_1(k1_numbers,k6_real_3(A),k1_nat_1(B,1)),k9_nat_1(k1_numbers,k6_real_3(A),B))) ) ) ) )).
fof(t58_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => r1_tarski(k3_relat_1(B,k5_relat_1(C,A)),k3_relat_1(B,C)) ) ) )).
fof(t58_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ! [F] : ( 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)))) ) ) ) )).
fof(t58_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ( v7_rewrite1(A) <=> v6_rewrite1(k18_finseq_1(A)) ) ) )).
fof(t58_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(A)) => ( ( r4_rewrite2(A,B,C,E) & r1_rewrite1(k7_rewrite2(A,k4_subset_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)),B,C)),E,D) ) => r1_rewrite1(k7_rewrite2(A,B),E,D) ) ) ) ) ) )).
fof(t58_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(C))) => ! [G] : ( ( ~ 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)) ) ) ) ) ) ) )).
fof(t58_rfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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) = k9_complex1(k1_funct_1(C,B)) ) ) ) ) ) )).
fof(t58_rfunct_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t58_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_comseq_2(A) => ( v2_comseq_2(k4_rinfsup1(A)) & k1_seq_2(k4_rinfsup1(A)) = k2_rinfsup1(k4_rinfsup1(A)) ) ) ) )).
fof(t58_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_rlaffin1(B,A) <=> ! [C] : ( 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 ) ) ) ) ) )).
fof(t58_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t58_rlsub_2,axiom,( ! [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) ) => v12_lattices(g3_lattices(k3_rlsub_2(A),k5_rlsub_2(A),k6_rlsub_2(A))) ) )).
fof(t58_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_yellow13(B,A,k4_struct_0(A)) => ! [C] : ( m1_connsp_2(C,A,k4_struct_0(A)) => ? [D] : ( m1_connsp_2(D,A,k4_struct_0(A)) & r2_hidden(D,B) & r1_tarski(k2_pre_topc(A,D),C) ) ) ) ) )).
fof(t58_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t58_rlvect_2,axiom,( ! [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) ) => u1_struct_0(k16_rlvect_2(A)) = k11_rlvect_2(A) ) )).
fof(t58_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_rmod_2(E,A,B) => ( r2_hidden(k5_algstr_0(B,D,C),k3_rmod_2(A,B,D,E)) <=> r1_struct_0(E,C) ) ) ) ) ) ) )).
fof(t58_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_4(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t58_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v5_robbins1(A) & l2_robbins1(A) ) => ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & k5_robbins1(A,B,C) = C ) ) ) )).
fof(t58_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t58_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k5_roughs_1(A,B) = a_2_4_roughs_1(A,B) ) ) )).
fof(t58_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(C,k3_rusub_1(A,D,B)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r1_struct_0(B,E) & C = k5_algstr_0(A,D,E) ) ) ) ) ) ) )).
fof(t58_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => v12_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A))) ) )).
fof(t58_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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),k1_square_1(A)) ) ) )).
fof(t58_scm_halt,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( 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(k5_numbers)) = 1 => ( r4_scmfsa7b(C,D) | r1_xxreal_0(k1_funct_1(A,D),k5_numbers) | r1_scmfsa8a(A,B,k1_scmfsa8c(k1_scmfsa8b(D,k1_scmfsa8a(2),k5_scmfsa6a(C,k8_scmfsa_2(D,k4_scmfsa_2(k5_numbers)))))) ) ) ) ) ) ) )).
fof(t58_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ( ~ r4_scmfsa7b(C,D) => ! [E] : ( v7_ordinal1(E) => ( ! [F] : ( v7_ordinal1(F) => ( ~ r1_xxreal_0(E,F) => r2_hidden(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),F)),k2_afinsq_1(C)) ) ) => ! [F] : ( v7_ordinal1(F) => ( r1_xxreal_0(F,E) => k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),F),D) = k1_funct_1(B,D) ) ) ) ) ) ) ) ) ) )).
fof(t58_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ( k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k8_scmfsa_2(A,B),C),k4_struct_0(k1_scmfsa_2)) = k4_card_1(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,C)) & k1_funct_1(k2_extpro_1(k7_card_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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ( D != A => k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k8_scmfsa_2(A,B),C),D) = k1_funct_1(C,D) ) ) & ! [D] : ( m1_scmfsa_2(D) => r2_relset_1(k4_ordinal1,k4_numbers,k18_scmfsa_2(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k8_scmfsa_2(A,B),C),D),k18_scmfsa_2(C,D)) ) ) ) ) ) )).
fof(t58_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ? [C] : ( 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,k4_ordinal1) = B & ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => k1_funct_1(C,D) = A ) ) ) ) )).
fof(t58_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => k1_funct_1(k3_scmpds_6(A,B,C,D),k5_numbers) = k8_scmpds_2(A,B,k1_nat_1(k5_card_1(C),2)) ) ) ) ) )).
fof(t58_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v6_scmyciel(A) ) => ! [B] : ( ( v4_scmyciel(B) & v6_scmyciel(B) ) => ( r1_tarski(A,B) => r1_xxreal_0(k8_scmyciel(A),k8_scmyciel(B)) ) ) ) )).
fof(t58_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r3_semi_af1(A,B,C,D,E) => r2_analoaf(A,B,D,C,E) ) ) ) ) ) ) )).
fof(t58_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k2_numbers) => ! [D] : ( m1_subset_1(D,k2_numbers) => ! [E] : ( m2_finseq_2(E,k2_numbers,k12_seq_4(B)) => ! [F] : ( m2_finseq_2(F,k2_numbers,k12_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(k13_seq_4(B,E,F),A) = k2_xcmplx_0(C,D) ) ) ) ) ) ) ) )).
fof(t58_setlim_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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 ) ) ) ) )).
fof(t58_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => k9_nat_1(k9_setfam_1(B),k4_setlim_1(B,k8_setlim_2(B,D,C)),A) = k7_subset_1(B,k9_nat_1(k9_setfam_1(B),k4_setlim_1(B,D),A),C) ) ) ) )).
fof(t58_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_scmfsa_2(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) ) => ~ ( ( r2_hidden(k14_scmfsa_2(B,A,C),k2_relset_1(u1_compos_1(k1_scmfsa_2),D)) | r2_hidden(k15_scmfsa_2(B,A,C),k2_relset_1(u1_compos_1(k1_scmfsa_2),D)) ) & k6_sf_mastr(D) = C ) ) ) ) ) )).
fof(t58_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t58_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ! [C] : ( m2_simplex0(C,A,B) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => m2_simplex0(k10_simplex0(A,C,D),A,k10_simplex0(A,B,D)) ) ) ) )).
fof(t58_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k6_xcmplx_0(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(k24_sin_cos(A))),k11_comseq_3(k3_sin_cos(B)))) ) ) )).
fof(t58_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,k3_xcmplx_0(2,A)) = k3_xcmplx_0(k3_xcmplx_0(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,k3_xcmplx_0(2,A)) = k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A)),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A)),1) ) ) )).
fof(t58_sin_cos6,axiom,( ! [A] : ( v1_int_1(A) => v2_funct_1(k5_relset_1(k1_numbers,k1_numbers,k16_sin_cos,k1_rcomp_1(k2_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A)),k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A))))) ) )).
fof(t58_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k3_power(k4_power,A) = k3_xcmplx_0(2,k4_sin_cos7(k7_xcmplx_0(k6_xcmplx_0(A,1),k2_xcmplx_0(A,1)))) ) ) )).
fof(t58_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) & k4_sin_cos9(A) = k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos) ) => A = k4_xcmplx_0(1) ) ) )).
fof(t58_sincos10,axiom,( k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_sincos10,k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1))),k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k1_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos),k28_sin_cos))) = k1_partfun2(k1_numbers,k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1))) )).
fof(t58_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal4(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) ) ) )).
fof(t58_sprect_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t58_sprect_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t58_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t58_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k5_numbers,A) => r1_xxreal_0(B,k3_square_1(k2_xcmplx_0(A,k1_square_1(B)))) ) ) ) )).
fof(t58_stirl2_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_xboole_0(B) => v1_xboole_0(A) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t58_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t58_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t58_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_tex_2(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( 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) ) ) ) ) ) )).
fof(t58_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ~ ( ? [B] : ( ~ v2_struct_0(B) & m1_pre_topc(B,A) & v4_tex_3(B,A) ) & v3_tdlat_3(A) ) ) )).
fof(t58_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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))) ) ) )).
fof(t58_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ( ( E = F & r1_tmap_1(A,B,C,E) ) => r1_tmap_1(D,B,k2_tmap_1(A,B,C,D),F) ) ) ) ) ) ) ) )).
fof(t58_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_group_6(k5_topalg_1(A,B),k5_topalg_1(A,C)) ) ) ) )).
fof(t58_topgen_4,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ~ v1_xboole_0(k1_topgen_3(k4_ordinal1,A,B)) & v4_card_3(k1_topgen_3(k4_ordinal1,A,B)) & m1_subset_1(k1_topgen_3(k4_ordinal1,A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) )).
fof(t58_topgen_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => ? [C] : ( 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] : ( 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) = k5_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 ) ) ) ) ) ) )).
fof(t58_topgrp_1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(t58_topreal6,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t58_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t58_toprealc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,k2_finseq_1(B)) => v1_t_0topsp(k16_toprealc(B,A),k15_euclid(B),k3_topmetr) ) ) ) )).
fof(t58_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t58_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) ) ) )).
fof(t58_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_tsep_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => k1_tops_1(A,C) = k1_tops_1(B,D) ) ) ) ) ) )).
fof(t58_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t58_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => k12_trees_3(A) = k5_trees_1(k2_trees_1(1),k14_trees_3(k5_numbers),A) ) )).
fof(t58_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_tsep_1(A,B,C) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t58_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_complfld)) => ( C = B => ! [D] : ( v1_int_1(D) => ( D = k2_polynom4(k1_complfld,k5_uniroots(A),C) => r1_int_1(D,k6_xcmplx_0(k11_newton(B,A),1)) ) ) ) ) ) ) )).
fof(t58_uproots,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k9_uproots(A,k1_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))) ) ) )).
fof(t58_valued_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) ) => ( r2_hidden(B,k4_finseq_1(k15_finseq_1(C))) => k1_funct_1(k15_finseq_1(k61_valued_1(C,A)),B) = k1_funct_1(k15_finseq_1(C),B) ) ) ) ) )).
fof(t58_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ( v2_relat_1(E) & ! [F] : ( 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 ) ) ) ) ) ) )).
fof(t58_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t58_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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))) ) ) ) )).
fof(t58_waybel23,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => v5_orders_3(k3_waybel23(A,B),k1_yellow_1(k7_waybel_0(B)),A) ) ) )).
fof(t58_waybel34,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t58_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( D != k1_xboole_0 => r2_yellow_0(A,D) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(B)) ) => ~ ( r2_yellow_0(A,E) & D = k2_yellow_0(A,E) ) ) ) ) & ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t58_waybel_1,axiom,( ! [A] : ( ( ~ 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(k1_yellow_1(k7_waybel_0(A))),u1_struct_0(A),u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A))),k2_yellow_2(A),k3_yellow_2(A)),k1_yellow_1(k7_waybel_0(A))) & r5_waybel_1(k1_yellow_2(k1_yellow_1(k7_waybel_0(A)),k1_yellow_1(k7_waybel_0(A)),k1_partfun1(u1_struct_0(k1_yellow_1(k7_waybel_0(A))),u1_struct_0(A),u1_struct_0(A),u1_struct_0(k1_yellow_1(k7_waybel_0(A))),k2_yellow_2(A),k3_yellow_2(A))),A) ) ) )).
fof(t58_waybel_4,axiom,( ! [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] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ? [D] : ( 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) ) ) ) )).
fof(t58_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r2_xboole_0(A,B) & r1_tarski(B,C) ) => r2_xboole_0(A,C) ) )).
fof(t58_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k8_xboolean(A,k8_xboolean(B,C)) = k4_xboolean(k6_xboolean(A,B),k6_xboolean(A,C)) ) ) ) )).
fof(t58_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k7_xcmplx_0(A,B) = 1 => A = B ) ) ) )).
fof(t58_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ ( ~ r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k4_xcmplx_0(A),k5_numbers) ) & ~ ( ~ r1_xxreal_0(k4_xcmplx_0(A),k5_numbers) & r1_xxreal_0(k5_numbers,A) ) ) ) )).
fof(t58_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(C,D) & r1_tarski(k1_xxreal_1(C,D),k3_xxreal_1(A,B)) ) => ( ~ r1_xxreal_0(C,A) & r1_xxreal_0(D,B) ) ) ) ) ) ) )).
fof(t58_xxreal_2,axiom,( ! [A] : ( ( 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) ) ) ) )).
fof(t58_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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 ) ) ) ) )).
fof(t58_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t58_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_yellow_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => m1_subset_1(C,u1_struct_0(A)) ) ) ) )).
fof(t58_yellow_4,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(k7_waybel_0(A)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( ( B = D & C = E ) => k12_lattice3(k1_yellow_1(k7_waybel_0(A)),B,C) = k4_yellow_4(A,D,E) ) ) ) ) ) ) )).
fof(t58_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t58_yellow_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m3_yellow_9(C,A,B) => ! [D] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) )).
fof(t58_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( v6_zf_lang(B) => ( r1_zf_lang(A,B) <=> A = k24_zf_lang(B) ) ) ) ) )).
fof(t58_zf_lang1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => k2_zf_model(k4_zf_lang(A,B)) = k2_tarski(A,B) ) ) )).
fof(t58_zfmisc_1,axiom,( ! [A] : ! [B] : ( k4_xboole_0(k1_tarski(A),B) = k1_tarski(A) <=> ~ r2_hidden(A,B) ) )).
fof(t58_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_zmodul01(C,A) => r2_hidden(B,k5_zmodul01(A,B,C)) ) ) ) )).
fof(t58_zmodul02,axiom,( ! [A] : ( ( ~ 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_zmodul02(k1_subset_1(u1_struct_0(A)),A) ) )).
fof(t59_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l3_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t59_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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) ) ) )).
fof(t59_abcmiz_a,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_abcmiz_1)) ) => ( k1_abcmiz_1(A) = A => ! [B] : ( m1_subset_1(B,u1_struct_0(k27_abcmiz_1)) => ? [C] : ( v2_abcmiz_1(C,k27_abcmiz_1) & m2_abcmiz_1(C,k27_abcmiz_1,B) & ? [D] : ( 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 ) ) ) ) ) )).
fof(t59_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( ~ r2_analoaf(A,B,C,D,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_aff_1(A,B,C,F) & r1_aff_1(A,D,E,F) ) ) ) ) ) ) ) ) )).
fof(t59_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_aff_4(B,A) & B = k1_xboole_0 ) ) ) )).
fof(t59_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ? [C] : ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) & B = k1_ordinal4(k5_relat_1(B,A),C) ) ) ) )).
fof(t59_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v3_valued_0(A) & v1_finset_1(A) ) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k1_relset_1(k4_ordinal1,A)) => r1_xxreal_0(B,k1_funct_1(A,C)) ) ) => r1_xxreal_0(k3_xcmplx_0(k1_afinsq_1(A),B),k7_afinsq_2(A)) ) ) ) )).
fof(t59_algspec1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( m4_algspec1(B,A) => ! [C] : ( ( ~ v2_struct_0(C) & l1_msualg_1(C) ) => ( l3_msualg_1(B,C) => l3_msualg_1(B,k2_circcomb(C,A)) ) ) ) ) )).
fof(t59_altcat_4,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t59_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t59_aofa_000,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_freealg(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_freealg(k19_aofa_000,A))) => ! [C] : ( 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) ) ) ) )).
fof(t59_aofa_a00,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ! [B] : ! [C] : ( ( ~ v2_struct_0(C) & ~ v11_struct_0(C) & l6_aofa_a00(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & ~ v11_struct_0(D) & l5_aofa_a00(D) ) => ( ( v18_aofa_a00(C,A,B) & r1_subset_1(u4_struct_0(C),u4_struct_0(D)) ) => v18_aofa_a00(k36_aofa_a00(C,D),A,B) ) ) ) ) ) )).
fof(t59_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v19_aofa_a00(E,A) & m1_subset_1(E,u1_struct_0(A)) ) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,C),E)) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),E)) => ! [H] : ( m2_pboole(H,u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,D)) => k15_aofa_a00(A,B,C,D,E,k35_aofa_a00(A,C,E,F,G),H) = k35_aofa_a00(A,D,E,k15_aofa_a00(A,B,C,D,E,F,H),k15_aofa_a00(A,B,C,D,E,G,H)) ) ) ) ) ) ) ) ) )).
fof(t59_armstrng,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(t59_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & m1_subset_1(A,k5_arytm_3) ) => ! [B] : ( ( v3_ordinal1(B) & m1_subset_1(B,k5_arytm_3) ) => k10_arytm_3(A,B) = k9_ordinal3(A,B) ) ) )).
fof(t59_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(3,A) & r1_xxreal_0(k7_newton(A),A) ) ) )).
fof(t59_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t59_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( ( v8_bcialg_1(E) & m1_bcialg_5(E,A,B,C,D) ) => ( A = k5_numbers => ( D = k5_numbers | ( v8_bcialg_1(E) & m1_bcialg_5(E,k5_numbers,1,k5_numbers,1) ) ) ) ) ) ) ) ) )).
fof(t59_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),B,k5_vfunct_1(k4_ordinal1,A,k5_vfunct_1(k4_ordinal1,A,B))) ) ) )).
fof(t59_bilinear,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t59_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t59_borsuk_5,axiom,( ! [A] : ( 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)) ) ) )).
fof(t59_borsuk_6,axiom,( ! [A] : ( 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),k7_xcmplx_0(1,2)) ) ) )).
fof(t59_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( C = k1_funct_1(k12_toprealb,B) => k1_funct_1(k10_borsuk_7(1,k4_xcmplx_0(k3_euclid_3(C))),k1_funct_1(k12_toprealb,A)) = k1_funct_1(k12_toprealb,k6_xcmplx_0(A,B)) ) ) ) ) )).
fof(t59_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t59_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_eqrel_1(I,A) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t59_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t59_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ( k7_xboolean(A,k3_xboolean(A)) = k7_margrel1 & k3_xboolean(k7_xboolean(A,k3_xboolean(A))) = k8_margrel1 ) ) )).
fof(t59_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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) ) ) )).
fof(t59_card_1,axiom,( ! [A] : ( v3_ordinal1(A) => ( v1_finset_1(A) <=> r2_hidden(A,k4_ordinal1) ) ) )).
fof(t59_card_2,axiom,( ! [A] : ~ ( k1_card_1(A) = 2 & ! [B] : ! [C] : ~ ( B != C & A = k2_tarski(B,C) ) ) )).
fof(t59_card_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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))) ) ) ) )).
fof(t59_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t59_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( m1_cat_1(F,A,C,B) => ( ( r2_cat_3(A,B,D,E) & k3_graph_1(A,F) = C & k4_graph_1(A,F) = B & v9_cat_1(F,A,C,B) ) => r2_cat_3(A,C,k1_cat_1(A,F,D),k1_cat_1(A,F,E)) ) ) ) ) ) ) ) )).
fof(t59_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t59_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t59_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_chain_1(C,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k4_chain_1(B,C,k1_nat_1(A,1)))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k4_chain_1(B,C,k1_nat_1(A,1)))) => k10_chain_1(B,C,A,k7_chain_1(B,C,k1_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)) ) ) ) ) ) )).
fof(t59_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) ) => ! [C] : ( m2_glib_000(C,A,B,k21_glib_000(A,B)) => ! [D] : ( 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] : ( m1_subset_1(E,k6_glib_000(C)) => ( D = E => ! [F] : ( m1_chord(F,A,k6_domain_1(k6_glib_000(A),D)) => ! [G] : ( m1_chord(G,C,k6_domain_1(k6_glib_000(C),E)) => r5_glib_000(F,G) ) ) ) ) ) ) ) ) ) ) )).
fof(t59_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t59_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( m3_msaterm(D,A,C) => ! [E] : ( ( ~ v2_struct_0(E) & ~ v11_struct_0(E) & v2_msafree2(E) & l1_msualg_1(E) ) => ! [F] : ( ( v4_msualg_1(F,E) & v4_msafree2(F,E) & l3_msualg_1(F,E) ) => ( r7_circtrm1(A,B,C,D,E,F) => ! [G] : ( m2_circtrm1(G,A,C,B,D,E,F) => ! [H] : ( 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] : ( m1_subset_1(I,k4_card_3(u3_msualg_1(E,F))) => ( r1_facirc_1(E,F,k5_facirc_1(E,F,I,k2_xcmplx_0(1,k6_trees_1(k9_xtuple_0(H)))),k1_funct_1(G,H)) & ! [J] : ( 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] : ( m1_circtrm1(K,A,C,D,B,J) => k1_funct_1(k5_facirc_1(E,F,I,k2_xcmplx_0(1,k6_trees_1(k9_xtuple_0(H)))),k1_funct_1(G,H)) = k7_circtrm1(A,B,C,H,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t59_classes1,axiom,( ! [A] : k5_classes1(k5_classes1(A)) = k5_classes1(A) )).
fof(t59_classes2,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) ) ) )).
fof(t59_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_clvect_1(B,A) => ! [C] : ( m1_clvect_1(C,A) => m1_clvect_1(k3_clvect_1(B),C) ) ) ) )).
fof(t59_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v2_clvect_2(B,A) & v2_clvect_2(C,A) ) => v2_clvect_2(k16_csspace(A,B,C),A) ) ) ) ) )).
fof(t59_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ! [D] : ~ ( r2_hidden(C,k3_tarski(A)) & r2_hidden(D,k3_tarski(B)) & ! [E] : ( ( 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)) ) ) ) ) )).
fof(t59_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => r1_xxreal_0(k6_xcmplx_0(k9_complex1(A),k9_complex1(B)),k9_complex1(k6_xcmplx_0(A,B))) ) ) )).
fof(t59_complex2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( r1_xxreal_0(k5_numbers,A) => k3_complex2(A,B) = k1_comptrig(B) ) ) ) )).
fof(t59_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ( ~ ( A != k4_struct_0(k1_complfld) & r1_xxreal_0(k9_complex1(A),k5_numbers) ) & ~ ( ~ r1_xxreal_0(k9_complex1(A),k5_numbers) & A = k4_struct_0(k1_complfld) ) ) ) )).
fof(t59_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( m2_finseq_1(C,k2_numbers) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k3_finseq_1(B) = k3_finseq_1(C) ) => k8_complsp2(k8_seq_4(A,B),C) = k6_xcmplx_0(k8_complsp2(A,C),k8_complsp2(B,C)) ) ) ) ) )).
fof(t59_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( v6_compos_0(D,u1_compos_1(A)) & m1_subset_1(D,u1_compos_1(A)) ) => ! [E] : ( ( v6_compos_0(E,u1_compos_1(A)) & m1_subset_1(E,u1_compos_1(A)) ) => ! [F] : ( ( v6_compos_0(F,u1_compos_1(A)) & m1_subset_1(F,u1_compos_1(A)) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t59_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k3_finseq_2(k4_ordinal1)) & v1_funct_1(C) & v4_valued_0(C) & v2_margrel1(C) ) => ! [D] : ( m2_finseq_2(D,k4_ordinal1,k4_finseq_2(k1_nat_1(k19_margrel1(B),1),k4_ordinal1)) => ( ( r2_hidden(A,k4_finseq_1(D)) & v2_comput_1(B) ) => k1_recdef_1(k7_comput_1(B,C,A),k8_comput_1(k1_nat_1(k19_margrel1(B),1),D,A,k5_numbers)) = k1_recdef_1(B,k2_finseq_3(A,D)) ) ) ) ) ) )).
fof(t59_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ? [B] : ( v7_ordinal1(B) & v1_comseq_3(k1_valued_0(k2_numbers,A,B)) ) => v1_comseq_3(A) ) ) )).
fof(t59_convex4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t59_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t59_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t59_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_xxreal_0(k15_csspace(A,k5_algstr_0(A,B,D),k5_algstr_0(A,C,D)),k2_xcmplx_0(k15_csspace(A,D,B),k15_csspace(A,D,C))) ) ) ) ) )).
fof(t59_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k4_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k18_sin_cos),A),B) = k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k19_sin_cos(k3_xcmplx_0(2,B)),k19_sin_cos(k3_xcmplx_0(2,k6_xcmplx_0(B,A))))) ) ) )).
fof(t59_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k4_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k18_sin_cos),k18_sin_cos),A),B) = k4_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,2),k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,k17_sin_cos(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(2,B),A),2))),k17_sin_cos(k7_xcmplx_0(A,2))),k3_xcmplx_0(k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(3,k6_xcmplx_0(k3_xcmplx_0(2,B),A)),2)),k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(3,A),2)))))) ) ) )).
fof(t59_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(k2_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k26_sin_cos)) & r2_hidden(k6_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k26_sin_cos)) ) => k1_funct_1(k5_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k26_sin_cos),k16_sin_cos),A),B) = k6_xcmplx_0(k3_xcmplx_0(k1_newton(k1_funct_1(k16_sin_cos,k2_xcmplx_0(B,k7_xcmplx_0(A,2))),3),k1_newton(k5_xcmplx_0(k1_funct_1(k18_sin_cos,k2_xcmplx_0(B,k7_xcmplx_0(A,2)))),2)),k3_xcmplx_0(k1_newton(k1_funct_1(k16_sin_cos,k6_xcmplx_0(B,k7_xcmplx_0(A,2))),3),k1_newton(k5_xcmplx_0(k1_funct_1(k18_sin_cos,k6_xcmplx_0(B,k7_xcmplx_0(A,2)))),2))) ) ) ) )).
fof(t59_ec_pf_1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_int_3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t59_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k9_int_3(A))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k9_int_3(A))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k9_int_3(A))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k9_int_3(A))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k9_int_3(A))) => ! [K] : ( 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] : ( 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 = k5_int_1(2,A) & D = k5_int_1(3,A) & E = k5_int_1(4,A) & F = k5_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)))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t59_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t59_entropy1,axiom,( ! [A] : ( ( v1_matrix_0(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)) ) )).
fof(t59_enumset1,axiom,( ! [A] : ! [B] : ! [C] : k1_enumset1(A,B,C) = k1_enumset1(B,C,A) )).
fof(t59_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t59_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t59_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => k22_rvsum_1(k9_euclid(3,B,A),C) = k3_xcmplx_0(A,k22_rvsum_1(B,C)) ) ) ) )).
fof(t59_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ( r2_hidden(B,C) <=> k3_euclidlp(A,B,C) = k5_numbers ) ) ) ) )).
fof(t59_exchsort,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r2_hidden(C,k6_subset_1(k1_ordinal1(B),A)) <=> ( r1_ordinal1(A,C) & r1_ordinal1(C,B) ) ) ) ) ) )).
fof(t59_facirc_1,axiom,( ! [A] : ( ( 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] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ~ v1_facirc_1(k2_msafree2(k8_facirc_1(B,C,D,A))) ) ) ) ) )).
fof(t59_fdiff_11,axiom,( ! [A] : ( ( 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),k18_sin_cos))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(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),k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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),k18_sin_cos),A),B) = k5_numbers ) ) ) ) ) )).
fof(t59_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( 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))) ) ) ) ) )).
fof(t59_filter_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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),E)) & r2_hidden(D,k6_eqrel_1(u1_struct_0(A),u1_struct_0(A),k9_filter_0(A,B),E)) ) => ( r2_hidden(k3_lattices(A,C,D),k6_eqrel_1(u1_struct_0(A),u1_struct_0(A),k9_filter_0(A,B),E)) & r2_hidden(k4_lattices(A,C,D),k6_eqrel_1(u1_struct_0(A),u1_struct_0(A),k9_filter_0(A,B),E)) ) ) ) ) ) ) ) )).
fof(t59_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( ( ~ 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) ) ) ) ) ) ) ) ) )).
fof(t59_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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 ) ) ) )).
fof(t59_finseq_2,axiom,( ! [A] : k2_finseq_2(2,A) = k10_finseq_1(A,A) )).
fof(t59_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( k3_finseq_1(k1_finseq_3(A,B)) = k3_finseq_1(A) => r1_xboole_0(B,k10_xtuple_0(A)) ) ) )).
fof(t59_finseq_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r2_hidden(B,k4_finseq_1(A)) & k2_xcmplx_0(B,C) = k1_nat_1(k3_finseq_1(A),1) ) => r2_hidden(C,k4_finseq_1(k3_finseq_5(A))) ) ) ) ) )).
fof(t59_finseq_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t59_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t59_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_catalan2(A))) => ! [D] : ( v7_ordinal1(D) => ( r1_tarski(B,k8_flang_1(A,C)) => r1_tarski(k7_flang_1(A,B,D),k8_flang_1(A,C)) ) ) ) ) )).
fof(t59_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => r1_tarski(k8_flang_1(A,k1_flang_2(A,B,C,D)),k8_flang_1(A,B)) ) ) ) )).
fof(t59_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => r1_tarski(B,k2_flang_3(A,B)) ) )).
fof(t59_fomodel0,axiom,( ! [A] : ( k3_xboole_0(k23_fomodel0(A),A) = k1_xboole_0 & ~ v1_finset_1(k23_fomodel0(A)) ) )).
fof(t59_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & v8_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(F,u1_struct_0(k11_fsm_1(A,B,C))) => ! [G] : ( m1_subset_1(G,F) => ! [H] : ( m1_subset_1(H,F) => ~ ( r2_hidden(G,u1_struct_0(D)) & r2_hidden(H,u1_struct_0(D)) & G != H ) ) ) ) ) ) ) ) ) ) )).
fof(t59_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(t59_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t59_funct_2,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(t59_funct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t59_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,C),E))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B,D),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,B),k2_zfmisc_1(C,D)),k2_zfmisc_1(E,F)))) ) ) ) )).
fof(t59_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( B != C => ( r2_wellord2(k1_funct_2(k2_tarski(B,C),A),k2_zfmisc_1(A,A)) & k1_card_1(k1_funct_2(k2_tarski(B,C),A)) = k1_card_1(k2_zfmisc_1(A,A)) ) ) )).
fof(t59_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t59_funct_8,axiom,( ! [A] : ( v1_xreal_0(A) => k1_funct_1(k1_funct_8,k4_xcmplx_0(A)) = k4_xcmplx_0(k1_funct_1(k1_funct_8,A)) ) )).
fof(t59_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => v1_vectsp_2(k7_fvaluat1(A,B)) ) ) ) )).
fof(t59_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(t59_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( C != k4_tarski(k10_finseq_1(A,B),k4_gfacirc1) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k22_gfacirc1(A,B,C),k23_gfacirc1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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 ) ) ) ) ) ) ) )).
fof(t59_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ( r2_hidden(B,k27_glib_000(A,C)) <=> ? [D] : r2_glib_000(A,C,D,B) ) ) ) )).
fof(t59_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m3_glib_001(D,B) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( C = D => k20_glib_001(A,C,E,F) = k20_glib_001(B,D,E,F) ) ) ) ) ) ) ) )).
fof(t59_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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_0(k2_goboard2(C)),k1_nat_1(B,1)) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1))),k3_topreal1(2,C)) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,2))),k3_topreal1(2,C)) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1))),k3_topreal1(2,C)) ) ) ) ) )).
fof(t59_graph_2,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( 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] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(B,E) & r1_xxreal_0(E,C) ) => r1_xxreal_0(k1_funct_1(A,D),k1_funct_1(A,E)) ) ) & ! [E] : ( v7_ordinal1(E) => ~ ( r1_xxreal_0(B,E) & ~ r1_xxreal_0(D,E) & r1_xxreal_0(k1_funct_1(A,E),k1_funct_1(A,D)) ) ) ) ) ) ) ) ) ) )).
fof(t59_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_graph_1(A) & v6_graph_1(A) & l1_graph_1(A) ) => ( ? [B] : ( v2_funct_1(B) & v1_msscyc_1(B,A) & m2_graph_1(B,A) & v1_graph_3(B,A) ) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v1_abian(k10_graph_1(A,B)) ) ) ) )).
fof(t59_graph_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v6_graph_1(B) & l1_graph_1(B) ) => ! [C] : ( ( v7_graph_1(C,B) & m2_graph_1(C,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ~ ( r1_graph_5(B,C,D,E) & r5_graph_5(B,A) & ! [F] : ( ( v7_graph_1(F,B) & v1_graph_4(F,B) & m2_graph_1(F,B) ) => ~ r7_graph_5(B,D,E,F,A) ) ) ) ) ) ) ) )).
fof(t59_groeb_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ( ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(G,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,k8_polynom1(A,C)) ) ) ) ) ) => ( r2_hidden(k8_polynom1(A,C),D) | r1_groeb_1(A,B,C,D) ) ) ) ) ) ) )).
fof(t59_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,A) => ( m1_group_2(C,D) => r1_tarski(k3_group_11(A,C,B),k3_group_11(A,D,B)) ) ) ) ) ) )).
fof(t59_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t59_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t59_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t59_group_5,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t59_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( 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))) ) ) )).
fof(t59_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( ( 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)))) ) => r3_group_9(A,k10_group_9(A,B,k13_group_9(A,B,C,D)),k14_group_9(A,B,C,D)) ) ) ) )).
fof(t59_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t59_hfdiff_1,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k1_relset_1(k1_numbers,k27_sin_cos)) => ( r2_fdiff_1(k27_sin_cos,A) & r2_relset_1(k1_numbers,k1_numbers,k2_fdiff_1(k27_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)),k4_xcmplx_0(1)),A)) ) ) ) )).
fof(t59_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t59_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => r1_xxreal_0(k5_numbers,k4_int_1(A,B)) ) ) ) )).
fof(t59_integr11,axiom,( ! [A] : ( ( 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,k27_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,k27_sin_cos),k1_partfun2(k1_numbers,A)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k27_sin_cos),k1_partfun2(k1_numbers,A)),A),B) = k1_square_1(k1_funct_1(k27_sin_cos,B)) ) ) ) ) ) )).
fof(t59_integr14,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k2_xcmplx_0(k1_funct_1(k16_sin_cos,D),k7_xcmplx_0(k1_funct_1(k16_sin_cos,D),k1_square_1(k1_funct_1(k18_sin_cos,D)))) ) ) & r1_tarski(C,k1_relset_1(k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k26_sin_cos))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k26_sin_cos),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k26_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t59_integra8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,C) & k9_xtuple_0(k26_sin_cos) = C & k9_xtuple_0(k26_sin_cos) = k9_xtuple_0(A) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => ( k1_funct_1(A,D) = k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,D))) & k1_funct_1(k18_sin_cos,D) != k5_numbers ) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,A,B)) ) => k2_integra5(B,A) = k6_xcmplx_0(k1_funct_1(k26_sin_cos,k2_seq_4(B)),k1_funct_1(k26_sin_cos,k3_seq_4(B))) ) ) ) ) )).
fof(t59_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( 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] : ( v1_xreal_0(H) => ( r2_hidden(H,G) => ( k1_funct_1(E,H) = k2_xcmplx_0(H,B) & ~ r1_xxreal_0(k1_funct_1(E,H),k5_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,k2_xcmplx_0(A,B)))) = G & G = k1_relset_1(k1_numbers,F) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,G) => k1_funct_1(F,H) = k7_xcmplx_0(k6_xcmplx_0(H,A),k2_xcmplx_0(H,B)) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,F,C)) ) => k2_integra5(C,F) = k6_xcmplx_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,G),k26_valued_1(k1_numbers,k1_numbers,D,k2_xcmplx_0(A,B))),k2_seq_4(C)),k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,G),k26_valued_1(k1_numbers,k1_numbers,D,k2_xcmplx_0(A,B))),k3_seq_4(C))) ) ) ) ) ) ) ) ) )).
fof(t59_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m2_interva1(B,A) => ! [C] : ( 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)) ) ) ) )).
fof(t59_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(t59_jgraph_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ 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(k5_numbers,k17_euclid(A)) & r1_xxreal_0(k5_numbers,k18_euclid(A)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(B)) & r1_xxreal_0(k5_numbers,k18_euclid(B)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(C)) & r1_xxreal_0(k5_numbers,k18_euclid(C)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(D)) & r1_xxreal_0(k5_numbers,k18_euclid(D)) & ! [F] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(k15_euclid(2))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k15_euclid(2))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k15_euclid(2))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k15_euclid(2))) => ~ ( v3_tops_2(F,k15_euclid(2),k15_euclid(2)) & ! [K] : ( 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(k5_numbers,k17_euclid(G)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(G)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(H)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(H)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(I)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(I)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(J)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(J)) & r1_jordan6(E,G,H) & r1_jordan6(E,H,I) & r1_jordan6(E,I,J) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t59_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t59_jgraph_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(k5_topmetr)) => ! [H] : ( 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(k7_xcmplx_0(2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(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(k4_xcmplx_0(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(k4_xcmplx_0(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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t59_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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(k2_jordan9(D,B))) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(k1_jordan8(D,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),k2_jordan9(D,B),A) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(D,B),1,C) ) => r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),k2_jordan9(D,B),A),k14_pscomp_1(k3_topreal1(2,k2_jordan9(D,B)))) ) ) ) ) ) )).
fof(t59_jordan1h,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( 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] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(k4_tarski(D,k1_nat_1(E,1)),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k7_nat_d(k3_finseq_1(C),1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),D,k1_nat_1(E,1)) & r2_hidden(k4_tarski(D,E),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k3_finseq_1(C)) = k3_matrix_0(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_0(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) )).
fof(t59_jordan1j,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k3_topreal1(2,k1_jordan1e(B,A))) = k1_tarski(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k3_topreal1(2,k2_jordan1e(B,A))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D)) & r1_xboole_0(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k8_jordan6(B)) ) ) ) ) ) ) )).
fof(t59_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( ( v2_connsp_1(B,k15_euclid(A)) & v3_pre_topc(B,k15_euclid(A)) & D = a_3_0_jordan2c(A,B,C) ) => v3_pre_topc(D,k15_euclid(A)) ) ) ) ) ) )).
fof(t59_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t59_kurato_1,axiom,( k5_card_1(k3_kurato_1(k3_topmetr,k6_kurato_1)) = 6 )).
fof(t59_lattice2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k5_finsub_1(A)) => ! [C] : ( ( ~ v2_struct_0(C) & v10_lattices(C) & v14_lattices(C) & l3_lattices(C) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(C)) => ( ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t59_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k9_funct_2(k6_glib_000(A),k4_ordinal1))) => ~ ( k1_relset_1(k6_glib_000(A),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),B)) != k6_glib_000(A) & r2_hidden(k19_lexbfs(A,B),k1_relset_1(k6_glib_000(A),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),B))) ) ) ) )).
fof(t59_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( ( v7_limfunc1(A) => ( r1_xxreal_0(B,k5_numbers) | v7_limfunc1(k26_valued_1(k1_numbers,k1_numbers,A,B)) ) ) & ( v7_limfunc1(A) => ( r1_xxreal_0(k5_numbers,B) | v8_limfunc1(k26_valued_1(k1_numbers,k1_numbers,A,B)) ) ) & ( v8_limfunc1(A) => ( r1_xxreal_0(B,k5_numbers) | v8_limfunc1(k26_valued_1(k1_numbers,k1_numbers,A,B)) ) ) & ( v8_limfunc1(A) => ( r1_xxreal_0(k5_numbers,B) | v7_limfunc1(k26_valued_1(k1_numbers,k1_numbers,A,B)) ) ) ) ) ) )).
fof(t59_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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) = k3_xcmplx_0(k2_limfunc2(B,A),k2_limfunc2(C,A)) ) ) ) ) ) )).
fof(t59_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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) ) ) ) ) ) )).
fof(t59_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( v2_xxreal_0(F) & v1_xreal_0(F) ) => ! [G] : ( ( v2_xxreal_0(G) & v1_xreal_0(G) ) => ( ( k3_supinf_2(k2_extreal1(1,F),k2_extreal1(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)) ) ) ) ) ) ) ) ) ) )).
fof(t59_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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) ) ) ) ) )).
fof(t59_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_hilbert1)) => r8_ltlaxio1(C,k3_hilbert1(k2_ltlaxio1(k4_ltlaxio1(A,B)),k4_ltlaxio1(k2_ltlaxio1(A),k2_ltlaxio1(B)))) ) ) ) )).
fof(t59_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t59_mathmorp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( 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)) ) ) )).
fof(t59_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( r2_matrix10(k4_matrix10(A,B,C),D) => r2_matrix10(B,k5_matrix10(A,D,C)) ) ) ) ) ) )).
fof(t59_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,A,D,C) & m2_finseq_1(E,k3_finseq_2(A)) ) => ! [F] : ( ( v1_finset_1(F) & v1_setfam_1(F) & m1_subset_1(F,k1_zfmisc_1(k4_ordinal1)) ) => ! [G] : ( ( v1_finset_1(G) & v1_setfam_1(G) & m1_subset_1(G,k1_zfmisc_1(k4_ordinal1)) ) => ! [H] : ( m2_finseq_1(H,A) => ! [I] : ( m2_finseq_1(I,A) => ( ( k3_finseq_1(H) = k1_matrix_0(E) & I = k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,A,k5_matrix13(G),H) & r1_tarski(k2_zfmisc_1(F,G),k2_matrix_0(E)) ) => k3_matrix11(B,k5_card_1(F),k5_card_1(G),A,k6_matrix13(A,E,F,G),I) = k6_matrix13(A,k3_matrix11(k1_funct_1(k5_matrix13(F),B),D,C,A,E,H),F,G) ) ) ) ) ) ) ) ) ) ) )).
fof(t59_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( 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_0(B) ) ) ) ) ) )).
fof(t59_matrix16,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ( v6_matrix16(B,A) => k3_matrix16(A,k5_fvsum_1(A,B)) = k2_matrix_3(A,k3_matrix16(A,B)) ) ) ) )).
fof(t59_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k2_finseq_1(k1_matrix_0(B))) => k7_matrix_0(A,k4_matrix_0(A,B),C) = k8_matrix_0(A,B,C) ) ) ) ) )).
fof(t59_matrix_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ( k1_matrix_0(D) = k1_matrix_0(E) => ( ! [F] : ( v7_ordinal1(F) => ~ r2_hidden(k4_tarski(A,F),k2_matrix_0(D)) ) | k7_matrix_0(u1_struct_0(B),k3_matrix_3(B,D,E),A) = k3_fvsum_1(B,k7_matrix_0(u1_struct_0(B),D,A),k7_matrix_0(u1_struct_0(B),E,A)) ) ) ) ) ) ) ) )).
fof(t59_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v4_matrix_6(C,A,B) & v4_matrix_6(D,A,B) ) => ( r1_xxreal_0(A,k5_numbers) | v4_matrix_6(k4_matrix_3(B,k1_matrix_6(A,B,C),D),A,B) ) ) ) ) ) ) )).
fof(t59_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => k1_matrix_8(A,B,k1_matrix_4(B,C,D)) = k5_algstr_0(B,k1_matrix_8(A,B,C),k1_matrix_8(A,B,D)) ) ) ) ) )).
fof(t59_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => k23_matrixj1(B,k17_finseq_1(k4_ordinal1,A,C)) = k18_matrixj1(u1_struct_0(B),A,k23_matrixj1(B,C)) ) ) ) )).
fof(t59_matrixr1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( k1_matrix_0(C) = k3_finseq_1(B) => ( r1_xxreal_0(k3_finseq_1(B),k5_numbers) | k11_matrixr1(C,k10_rvsum_1(B,A)) = k10_rvsum_1(k11_matrixr1(C,B),A) ) ) ) ) ) )).
fof(t59_matrixr2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(A) = k1_matrix_0(C) & k1_matrix_0(B) = k3_finseq_1(C) ) => ( r1_xxreal_0(k3_finseq_1(A),k5_numbers) | r1_xxreal_0(k3_finseq_1(C),k5_numbers) | k11_matrixr1(k6_matrixr1(B,C),A) = k11_matrixr1(B,k11_matrixr1(C,A)) ) ) ) ) ) )).
fof(t59_matrprob,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v6_matrprob(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k4_tarski(B,C),k2_matrix_0(A)) => r1_xxreal_0(k3_matrix_0(k1_numbers,A,B,C),1) ) ) ) ) )).
fof(t59_mcart_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k4_zfmisc_1(A,B,C,D)) => ! [F] : ! [G] : ! [H] : ! [I] : ( E = k6_xtuple_0(F,G,H,I) => ( k4_mcart_1(A,B,C,D,E) = F & k5_mcart_1(A,B,C,D,E) = G & k6_mcart_1(A,B,C,D,E) = H & k7_mcart_1(A,B,C,D,E) = I ) ) ) ) ) ) ) )).
fof(t59_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v2_rcomp_1(A) <=> A = k5_measure6(A) ) ) )).
fof(t59_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => k4_member_1(k8_member_1(A,B)) = k10_member_1(k4_member_1(A),B) ) ) )).
fof(t59_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_partfun1(C,u1_struct_0(B)) ) => ! [D] : ( 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) ) ) ) ) )).
fof(t59_mesfunc5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v3_mesfunc5(A) => ( ~ ( k8_supinf_2(k17_supinf_2(A)) != k1_supinf_1 & ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k9_nat_1(k6_numbers,A,C),B) ) ) ) ) & ~ ( ? [B] : ( v1_xreal_0(B) & ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k9_nat_1(k6_numbers,A,C),B) ) ) & k8_supinf_2(k17_supinf_2(A)) = k1_supinf_1 ) ) ) ) )).
fof(t59_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t59_mmlquery,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t59_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k30_modelc_1(k25_modelc_2(A)))) ) => ! [C] : ( m1_subset_1(C,k25_modelc_2(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t59_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_3(B,A) & l1_modelc_3(B,A) ) => ! [C] : ( m1_subset_1(C,k25_modelc_2(k43_modelc_2)) => ! [D] : ( m2_orders_1(D,k1_orders_1(k1_modelc_3(A)),k6_partfun1(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)) ) ) ) ) ) ) ) )).
fof(t59_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => r1_xxreal_0(k11_nat_3(k6_moebius1(B),A),k11_nat_3(B,A)) ) ) )).
fof(t59_monoid_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k9_monoid_0(A) = g3_algstr_0(k3_finseq_2(A),k11_monoid_0(A)) ) )).
fof(t59_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m2_pboole(C,u1_struct_0(A),B,k7_funcop_1(u1_struct_0(A),k4_ordinal1)) => ! [D] : ( 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_subset_1(k6_msafree4(A,B,C,D),k1_funct_1(u3_msualg_1(A,k1_msafree3(A,k2_funct_6(C))),k7_msaterm(A,B,D))) & m1_subset_1(k6_msafree4(A,B,C,D),k1_funct_1(u3_msualg_1(A,k3_equation(A)),k7_msaterm(A,B,D))) ) ) ) ) ) )).
fof(t59_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => k1_funct_1(k13_nat_3(k1_newton(A,B)),A) = k1_newton(A,B) ) ) )).
fof(t59_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,A) => k1_nat_1(k7_nat_d(B,k1_nat_1(A,1)),1) = k7_nat_d(B,A) ) ) ) )).
fof(t59_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t59_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k5_nat_d(B,A),k5_numbers) ) ) ) )).
fof(t59_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t59_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t59_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r7_orders_1(A,B) <=> r6_orders_1(k2_relat_1(A),B) ) ) )).
fof(t59_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r1_ordinal1(A,B) => r1_ordinal1(k5_ordinal3(A,C),k5_ordinal3(B,C)) ) ) ) ) )).
fof(t59_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( ( r2_hidden(k5_numbers,A) & r2_hidden(1,B) & C = k5_ordinal5(A,B) ) => r2_hidden(k6_ordinal3(A,k12_ordinal2(B,C)),B) ) ) ) ) )).
fof(t59_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v3_ordinal1(B) & v4_ordinal1(B) & ~ v1_xboole_0(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_classes2(C) ) => ( ( r2_hidden(B,C) & ! [D] : ( 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))) ) ) ) ) )).
fof(t59_partfun1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => r1_partfun1(k1_xboole_0,A) ) )).
fof(t59_partfun2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( ( 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] : ( m1_subset_1(F,B) => ~ ( r2_hidden(F,k1_relset_1(B,E)) & r2_hidden(F,A) & D = k1_funct_1(E,F) ) ) ) ) ) ) ) )).
fof(t59_pboole,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t59_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( ( 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) & k10_pdiff_1(3,2,k26_valued_1(k1_euclid(3),k1_numbers,k1_pdiff_3(1,3,C),A),B) = k3_xcmplx_0(A,k2_pdiff_5(C,B)) ) ) ) ) ) )).
fof(t59_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( v1_xreal_0(D) => ( ( 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] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t59_pepin,axiom,( v1_int_2(5) )).
fof(t59_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,k8_polyform(A,B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k17_polyform(A,B))) => ! [E] : ( m1_subset_1(E,k8_polyform(A,k6_xcmplx_0(B,1))) => ( ( B = k5_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) ) ) ) ) ) ) )).
fof(t59_polynom5,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( k1_algseq_1(A,B) != k5_numbers => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_polynom5(A,B,C) <=> r1_polynom5(A,k7_polynom5(A,B),C) ) ) ) ) ) )).
fof(t59_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(F,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(k7_polynom1(A,C,E,F),k7_ideal_1(k12_polynom1(A,C),D)) ) ) ) ) ) ) ) )).
fof(t59_power,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => k9_nat_1(k1_numbers,A,B) = k2_power(k2_xcmplx_0(1,k7_xcmplx_0(1,k1_nat_1(B,1))),k1_nat_1(B,1)) ) => v2_comseq_2(A) ) ) )).
fof(t59_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => r2_hidden(B,k18_pre_poly(A,B)) ) )).
fof(t59_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => ! [C] : ( v1_rat_1(C) => ( ~ r1_xxreal_0(A,k5_numbers) => k4_prepower(k4_prepower(A,B),C) = k4_prepower(A,k3_xcmplx_0(B,C)) ) ) ) ) )).
fof(t59_prob_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_prob_3(D,A,B) => k1_relset_1(k4_ordinal1,k1_partfun1(k4_ordinal1,k9_setfam_1(A),B,k1_numbers,D,C)) = k1_relset_1(k4_ordinal1,D) ) ) ) ) )).
fof(t59_pscomp_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t59_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t59_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ~ ( r3_qc_lang2(A,B,C) & r2_qc_lang2(A,C,B) ) ) ) ) )).
fof(t59_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t59_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k17_quatern2(A,k25_quaterni(B,C)) = k25_quaterni(k17_quatern2(A,B),k17_quatern2(A,C)) ) ) ) )).
fof(t59_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k24_quaterni(k25_quaterni(k25_quaterni(A,B),C)) = k22_quaterni(k22_quaterni(k24_quaterni(A),B),C) ) ) ) )).
fof(t59_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ( k13_quaterni(A) = k5_numbers => k27_quaterni(A) = k24_quaterni(A) ) ) )).
fof(t59_quofield,axiom,( ! [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) & v1_vectsp_2(A) & l6_algstr_0(A) ) => r2_quofield(A,k19_quofield(A)) ) )).
fof(t59_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B))))) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t59_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ( ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,k4_real_3(A),B),k5_numbers) ) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k9_nat_1(k1_numbers,k6_real_3(A),k1_nat_1(B,2)),k3_xcmplx_0(k3_xcmplx_0(2,k9_nat_1(k1_numbers,k4_real_3(A),k1_nat_1(B,2))),k9_nat_1(k1_numbers,k6_real_3(A),k1_nat_1(B,1)))) ) ) ) )).
fof(t59_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k5_relat_1(B,A) = k3_relat_1(k4_relat_1(A),B) ) )).
fof(t59_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t59_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r13_rewrite1(A,B,C) => r2_rewrite1(A,B,C) ) ) )).
fof(t59_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(A)) => ( ( r4_rewrite2(A,B,C,E) & r3_rewrite2(A,k4_subset_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)),B,C),E,D) ) => r3_rewrite2(A,B,E,D) ) ) ) ) ) )).
fof(t59_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(C))) => ! [G] : ( ( ~ v2_struct_0(G) & l1_rewrite3(G,F) ) => ! [H] : ( 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)) ) ) ) ) ) ) ) )).
fof(t59_rfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t59_rfunct_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ! [C] : ( v1_xreal_0(C) => ( r2_rfunct_3(A,B) => r2_rfunct_3(k18_rfunct_3(k1_numbers,k15_valued_1(k1_numbers,k1_numbers,A,C)),B) ) ) ) )).
fof(t59_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_seq_2(B) => k1_funct_1(k3_rinfsup1(B),A) = k4_xcmplx_0(k1_funct_1(k4_rinfsup1(k32_valued_1(k4_ordinal1,k1_numbers,B)),A)) ) ) ) )).
fof(t59_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k4_rlaffin1(A,B) = a_2_1_rlaffin1(A,B) ) ) )).
fof(t59_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_rlsub_1(D,A) => ( r1_struct_0(D,B) => r2_hidden(k1_rlvect_1(A,B,C),k3_rlsub_1(A,B,D)) ) ) ) ) ) )).
fof(t59_rlsub_2,axiom,( ! [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) ) => v16_lattices(g3_lattices(k3_rlsub_2(A),k5_rlsub_2(A),k6_rlsub_2(A))) ) )).
fof(t59_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_connsp_2(B,A,k4_struct_0(A)) => ? [C] : ( m1_connsp_2(C,A,k4_struct_0(A)) & r1_tarski(k2_pre_topc(A,C),B) ) ) ) )).
fof(t59_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t59_rlvect_2,axiom,( ! [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) ) => k4_struct_0(k16_rlvect_2(A)) = k4_rlvect_2(A) ) )).
fof(t59_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_rmod_2(E,A,B) => ( r2_hidden(C,k3_rmod_2(A,B,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r1_struct_0(E,F) & C = k5_algstr_0(B,D,F) ) ) ) ) ) ) ) )).
fof(t59_rmod_4,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_rmod_4(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t59_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v6_lattices(A) & v8_robbins1(A) & l4_robbins1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t59_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & l2_robbins1(A) ) => ( v5_robbins1(A) => v1_robbins2(A) ) ) )).
fof(t59_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t59_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ? [E] : ( 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)) ) ) ) ) ) )).
fof(t59_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => v16_lattices(g3_lattices(k3_rusub_2(A),k5_rusub_2(A),k6_rusub_2(A))) ) )).
fof(t59_rvsum_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) & v1_finseq_1(C) ) => k1_funct_1(k14_rvsum_1(B,C),A) = k3_xcmplx_0(k1_funct_1(B,A),k1_funct_1(C,A)) ) ) )).
fof(t59_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( 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),k5_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(k5_numbers)))))) ) ) ) ) ) )).
fof(t59_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( v7_ordinal1(D) => ( ! [E] : ( v7_ordinal1(E) => ( ~ r1_xxreal_0(D,E) => r2_hidden(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),E)),k2_afinsq_1(C)) ) ) => ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(E,D) => k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),E),k4_scmfsa_2(k5_numbers)) = k1_funct_1(B,k4_scmfsa_2(k5_numbers)) ) ) ) ) ) ) ) )).
fof(t59_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ( k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k9_scmfsa_2(A,B),C),k4_struct_0(k1_scmfsa_2)) = k4_card_1(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,C)) & k1_funct_1(k2_extpro_1(k7_card_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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ( D != A => k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k9_scmfsa_2(A,B),C),D) = k1_funct_1(C,D) ) ) & ! [D] : ( m1_scmfsa_2(D) => r2_relset_1(k4_ordinal1,k4_numbers,k18_scmfsa_2(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k9_scmfsa_2(A,B),C),D),k18_scmfsa_2(C,D)) ) ) ) ) ) )).
fof(t59_scmpds_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ( A = k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0) => v2_extpro_1(A,2,k1_scmpds_2) ) ) )).
fof(t59_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v3_scmpds_4(D) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( ( 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),F)),k5_numbers) | ( r1_scmpds_6(k3_scmpds_6(E,F,C,D),B,A) & r2_scmpds_6(k3_scmpds_6(E,F,C,D),B,A) ) ) ) ) ) ) ) ) ) )).
fof(t59_scmyciel,axiom,( ! [A] : ( v1_finset_1(A) => k8_scmyciel(k5_scmyciel(A)) = k5_card_1(A) ) )).
fof(t59_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t59_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ( k13_seq_4(A,B,k15_seq_4(A)) = B & B = k13_seq_4(A,k15_seq_4(A),B) ) ) ) )).
fof(t59_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(B) => k4_kurato_0(A,B) = k1_kurato_0(A,B) ) ) )).
fof(t59_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => r1_tarski(k5_subset_1(B,C,k9_nat_1(k9_setfam_1(B),k4_setlim_1(B,D),A)),k9_nat_1(k9_setfam_1(B),k4_setlim_1(B,k9_setlim_2(B,D,C)),A)) ) ) ) )).
fof(t59_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( m1_scmfsa_2(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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 ) ) ) ) )).
fof(t59_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t59_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ! [C] : ( m2_simplex0(C,A,B) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t59_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k6_xcmplx_0(k1_funct_1(k18_sin_cos,k2_xcmplx_0(A,B)),k1_funct_1(k18_sin_cos,A)) = k6_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(B,k1_funct_1(k16_sin_cos,A))),k3_xcmplx_0(B,k4_complex1(k3_xcmplx_0(k11_comseq_3(k24_sin_cos(k3_xcmplx_0(B,k7_complex1))),k2_xcmplx_0(k1_funct_1(k18_sin_cos,A),k3_xcmplx_0(k1_funct_1(k16_sin_cos,A),k7_complex1)))))) ) ) )).
fof(t59_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k6_xcmplx_0(k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A)),k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,B),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,B))) = k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,k2_xcmplx_0(A,B)),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,k6_xcmplx_0(A,B))) & k6_xcmplx_0(k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A)),k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,B),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,B))) = k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,k2_xcmplx_0(A,B)),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,k6_xcmplx_0(A,B))) & k6_xcmplx_0(k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A)),k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,B),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,B))) = k6_xcmplx_0(k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A)),k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,B),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,B))) ) ) ) )).
fof(t59_sin_cos6,axiom,( ! [A] : ( v1_int_1(A) => v2_funct_1(k5_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A),k2_xcmplx_0(k28_sin_cos,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A))))) ) )).
fof(t59_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k3_power(k4_power,A) = k4_sin_cos7(k7_xcmplx_0(k6_xcmplx_0(k1_square_1(A),1),k2_xcmplx_0(k1_square_1(A),1))) ) ) )).
fof(t59_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) & k3_sin_cos9(A) = k5_numbers ) => A = k5_numbers ) ) )).
fof(t59_sincos10,axiom,( k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k3_sincos10,k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1))),k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4))))) = k1_partfun2(k1_numbers,k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1))) )).
fof(t59_sppol_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal4(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( B != C & r2_hidden(B,A) & r2_hidden(C,A) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t59_sprect_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t59_sprect_2,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(t59_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t59_square_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => r1_xxreal_0(k3_square_1(k2_xcmplx_0(A,B)),k2_xcmplx_0(k3_square_1(A),k3_square_1(B))) ) ) ) )).
fof(t59_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [E] : ( ( v5_relat_1(E,k3_qc_lang1(A)) & v3_card_1(E,B) & m2_finseq_1(E,k2_qc_lang1(A)) ) => r2_relset_1(k4_ordinal1,C,k4_valuat_1(A,C,B,E,D),k4_relset_1(k4_ordinal1,k2_qc_lang1(A),k3_qc_lang1(A),C,E,k5_relset_1(k3_qc_lang1(A),C,D,k23_qc_lang1(A,E)))) ) ) ) ) ) )).
fof(t59_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t59_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v2_tex_2(B,A) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r1_tarski(B,C) & v3_tex_2(C,A) ) ) ) ) ) )).
fof(t59_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ~ ( ? [B] : ( ~ v2_struct_0(B) & m1_pre_topc(B,A) & v3_tex_3(B,A) & v1_borsuk_1(B,A) ) & v3_tdlat_3(A) ) ) )).
fof(t59_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k3_tex_4(A,B),k2_pre_topc(A,B)) ) ) )).
fof(t59_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => ( ( r1_tarski(E,u1_struct_0(D)) & m1_connsp_2(E,A,F) & F = G ) => ( r1_tmap_1(A,B,C,F) <=> r1_tmap_1(D,B,k2_tmap_1(A,B,C,D),G) ) ) ) ) ) ) ) ) ) )).
fof(t59_topalg_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_borsuk_2(D,k15_euclid(A),B,C) => ! [E] : ( m1_borsuk_2(E,k15_euclid(A),B,C) => r4_borsuk_2(k15_euclid(A),B,C,D,E) ) ) ) ) ) )).
fof(t59_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t59_topgen_5,axiom,( v1_topgen_5(k2_topgen_3) )).
fof(t59_topgrp_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t59_topreal6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( v1_xreal_0(D) => ( C = k10_metric_1(k14_euclid(A),B,D) => v4_pre_topc(C,k15_euclid(A)) ) ) ) ) ) )).
fof(t59_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t59_toprealc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k15_euclid(B)),u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(B)),u1_struct_0(k15_euclid(A))))) ) => ( v5_pre_topc(C,k15_euclid(B),k15_euclid(A)) => ( v1_funct_1(k20_valued_2(u1_struct_0(k15_euclid(B)),u1_struct_0(k15_euclid(A)),C)) & v1_funct_2(k20_valued_2(u1_struct_0(k15_euclid(B)),u1_struct_0(k15_euclid(A)),C),u1_struct_0(k15_euclid(B)),u1_struct_0(k15_euclid(A))) & v5_pre_topc(k20_valued_2(u1_struct_0(k15_euclid(B)),u1_struct_0(k15_euclid(A)),C),k15_euclid(B),k15_euclid(A)) & m1_subset_1(k20_valued_2(u1_struct_0(k15_euclid(B)),u1_struct_0(k15_euclid(A)),C),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(B)),u1_struct_0(k15_euclid(A))))) ) ) ) ) ) )).
fof(t59_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t59_tops_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) ) )).
fof(t59_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t59_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t59_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => k13_trees_3(A,B) = k5_trees_1(k5_trees_1(k2_trees_1(2),k14_trees_3(k5_numbers),A),k14_trees_3(1),B) ) ) )).
fof(t59_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ! [E] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t59_uniroots,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) ) => ( r1_nat_d(B,A) => ( r1_xxreal_0(A,B) | ! [D] : ( m1_subset_1(D,u1_struct_0(k1_complfld)) => ( D = C => ! [E] : ( v1_int_1(E) => ( E = k2_polynom4(k1_complfld,k5_uniroots(A),D) => r1_int_1(E,k4_int_1(k6_xcmplx_0(k11_newton(C,A),1),k6_xcmplx_0(k11_newton(C,B),1))) ) ) ) ) ) ) ) ) ) )).
fof(t59_uproots,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( m2_finseq_1(C,k3_finseq_2(u1_struct_0(k14_polynom3(A)))) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ( ( k3_finseq_1(C) = k5_card_1(k22_pre_poly(u1_struct_0(A),B)) & D = k19_finseq_1(k22_pre_poly(u1_struct_0(A),B)) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k4_finseq_1(C)) => k1_funct_1(C,E) = k8_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)) = k3_uproots(u1_struct_0(A),B) ) ) ) ) ) )).
fof(t59_valued_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_finseq_1(B) ) => k15_finseq_1(B) = k15_finseq_1(k61_valued_1(B,A)) ) ) )).
fof(t59_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_valued_0(D) ) => ! [E] : ( ( 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)) ) ) ) ) )).
fof(t59_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t59_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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))) ) ) ) )).
fof(t59_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => v5_orders_3(k4_waybel23(A,B),k1_yellow_1(k7_waybel_0(B)),k1_yellow_1(k7_waybel_0(A))) ) ) )).
fof(t59_waybel34,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t59_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ( D != k1_xboole_0 => r2_yellow_0(A,D) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(B)) ) => ~ ( r2_yellow_0(A,E) & D = k2_yellow_0(A,E) ) ) ) ) & ! [D] : ( ( 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) ) ) ) ) )).
fof(t59_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t59_waybel_4,axiom,( ! [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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => r1_waybel_4(A,k5_waybel_4(A,C,B),B) ) ) ) ) )).
fof(t59_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r1_tarski(A,B) & r2_xboole_0(B,C) ) => r2_xboole_0(A,C) ) )).
fof(t59_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k8_xboolean(A,k6_xboolean(A,B)) = k3_xboolean(k4_xboolean(A,B)) ) ) )).
fof(t59_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k7_xcmplx_0(1,A) = k7_xcmplx_0(1,B) => A = B ) ) ) )).
fof(t59_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,k4_xcmplx_0(B)) => r1_xxreal_0(k2_xcmplx_0(A,B),k5_numbers) ) ) ) )).
fof(t59_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_tarski(k4_xxreal_1(C,D),k3_xxreal_1(A,B)) => ( r1_xxreal_0(D,C) | ( r1_xxreal_0(A,C) & r1_xxreal_0(D,B) ) ) ) ) ) ) ) )).
fof(t59_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ( r1_tarski(A,B) => r1_xxreal_0(k1_xxreal_2(A),k1_xxreal_2(B)) ) ) ) )).
fof(t59_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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 ) ) ) ) )).
fof(t59_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t59_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_yellow_0(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( E = C & F = D & r1_orders_2(B,E,F) ) => r1_orders_2(A,C,D) ) ) ) ) ) ) ) )).
fof(t59_yellow_4,axiom,( ! [A] : ( ( v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( ~ 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))) ) ) ) )).
fof(t59_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t59_yellow_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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)))) ) ) ) ) ) ) )).
fof(t59_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => r2_zf_lang(A,A) ) )).
fof(t59_zf_lang1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => k2_zf_model(k5_zf_lang(A,B)) = k2_tarski(A,B) ) ) )).
fof(t59_zfmisc_1,axiom,( ! [A] : ! [B] : ( k4_xboole_0(k1_tarski(A),B) = k1_xboole_0 <=> r2_hidden(A,B) ) )).
fof(t59_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => k5_zmodul01(A,k4_struct_0(A),B) = u1_struct_0(B) ) ) )).
fof(t59_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( v6_zmodul01(A) => ( v1_zmodul02(k6_domain_1(u1_struct_0(A),B),A) <=> B != k4_struct_0(A) ) ) ) ) )).
fof(t5_abcmiz_0,axiom,( ! [A] : ( l1_abcmiz_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t5_abcmiz_1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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) ) ) ) )).
fof(t5_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v1_abcmiz_a(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t5_abian,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( ~ 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] : ( m2_subset_1(D,k1_zfmisc_1(A),C) => r1_xboole_0(D,k7_relat_1(B,D)) ) & v2_abian(B) ) ) ) )).
fof(t5_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k4_xcmplx_0(B),A) & r1_xxreal_0(A,B) ) <=> r1_xxreal_0(k9_complex1(A),B) ) ) ) )).
fof(t5_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) & r1_aff_1(A,C,D,B) & r1_aff_1(A,D,B,C) & r1_aff_1(A,D,C,B) ) ) ) ) ) ) )).
fof(t5_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v9_aff_2(A) => v10_aff_2(A) ) ) )).
fof(t5_aff_3,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v3_aff_3(A) => v4_aff_3(A) ) ) )).
fof(t5_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t5_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ( v1_finset_1(A) & v5_ordinal1(A) ) <=> ? [B] : ( v7_ordinal1(B) & k9_xtuple_0(A) = B ) ) ) )).
fof(t5_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ( k1_relset_1(k4_ordinal1,A) = k1_relset_1(k4_ordinal1,k1_afinsq_2(A)) & k10_xtuple_0(A) = k10_xtuple_0(k1_afinsq_2(A)) ) ) )).
fof(t5_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t5_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r2_analoaf(A,B,C,D,E) & r2_analoaf(A,B,C,D,F) ) => E = F ) ) ) ) ) ) ) )).
fof(t5_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect01(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_analoaf(A,B,B,C,C) ) ) ) )).
fof(t5_alg_1,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t5_algspec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t5_algstr_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_algstr_0)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_algstr_0)) => k1_algstr_0(k3_algstr_0,A,B) = k4_struct_0(k3_algstr_0) ) ) )).
fof(t5_algstr_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t5_algstr_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_algstr_3(A) & l1_algstr_3(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B != k4_struct_0(A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & k1_algstr_3(A,B,E,C) = D ) ) ) ) ) ) )).
fof(t5_algstr_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( v1_relat_1(D) & v5_relat_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) & v1_funct_1(D) ) => ~ r2_relset_1(u1_struct_0(A),u1_struct_0(A),k7_algstr_4(u1_struct_0(A),u1_struct_0(B),C),k6_algstr_4(A,D)) ) ) ) ) ) )).
fof(t5_altcat_1,axiom,( ! [A] : ( v4_funct_1(A) => ! [B] : ( v4_funct_1(B) => ! [C] : ( ( 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] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t5_altcat_2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,B) & v1_funct_1(D) & v1_partfun1(D,B) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,B) & v1_funct_1(E) & v1_partfun1(E,B) ) => ! [F] : ( m2_pboole(F,B,D,E) => m2_pboole(k3_relat_1(C,F),A,k3_relat_1(C,D),k3_relat_1(C,E)) ) ) ) ) ) )).
fof(t5_altcat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t5_altcat_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k1_xboole_0,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_xboole_0,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v7_altcat_3(C,A) => v5_altcat_5(C,A,k1_xboole_0,B) ) ) ) ) )).
fof(t5_ami_2,axiom,( ! [A] : ( 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 ) )).
fof(t5_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(C,u1_struct_0(k1_ami_3)) ) => ( k1_funct_1(k2_extpro_1(k7_card_1(2),k1_ami_3,k5_ami_3(A,B),C),k4_struct_0(k1_ami_3)) = k4_card_1(k5_memstr_0(k7_card_1(2),k1_ami_3,C)) & k1_funct_1(k2_extpro_1(k7_card_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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_ami_3)) ) => ( D != A => k1_funct_1(k2_extpro_1(k7_card_1(2),k1_ami_3,k5_ami_3(A,B),C),D) = k1_funct_1(C,D) ) ) ) ) ) ) )).
fof(t5_ami_4,axiom,( ! [A] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_ami_3)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ( r1_tarski(k1_ami_4,B) => ! [C] : ( v7_ordinal1(C) => ( k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,C)) = 3 => ( ( ~ r1_xxreal_0(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,C),k10_ami_3(1)),k5_numbers) => k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,k1_nat_1(C,1))) = k5_numbers ) & ( r1_xxreal_0(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,C),k10_ami_3(1)),k5_numbers) => k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,k1_nat_1(C,1))) = 4 ) & k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,k1_nat_1(C,1)),k10_ami_3(k5_numbers)) = k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,C),k10_ami_3(k5_numbers)) & k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,k1_nat_1(C,1)),k10_ami_3(1)) = k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,C),k10_ami_3(1)) ) ) ) ) ) ) )).
fof(t5_ami_5,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => r1_xxreal_0(k2_compos_0(u1_compos_1(k1_ami_3),A),8) ) )).
fof(t5_ami_6,axiom,( ! [A] : ( 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) ) ) )).
fof(t5_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( k1_ami_wstd(A,B,C) = k1_ami_wstd(A,B,D) => C = D ) ) ) ) ) )).
fof(t5_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t5_amistd_2,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(t5_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(t5_amistd_5,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_compos_1(B)) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( k5_memstr_0(A,B,D) = k2_xcmplx_0(E,F) => r6_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)) ) ) ) ) ) ) ) )).
fof(t5_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t5_analoaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( k1_rlvect_1(A,B,D) = C => ( D = k5_numbers | B = k1_rlvect_1(A,C,k5_xcmplx_0(D)) ) ) ) ) ) ) )).
fof(t5_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_analmetr(A,D,E) => k1_analort(A,D,E,k5_algstr_0(A,B,C)) = k5_algstr_0(A,k1_analort(A,D,E,B),k1_analort(A,D,E,C)) ) ) ) ) ) ) )).
fof(t5_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t5_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( 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 = k5_numbers & G = k5_numbers & H = k5_numbers & I = k5_numbers ) ) ) ) ) ) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t5_aofa_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( 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) ) ) ) ) )).
fof(t5_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( D = k1_funct_1(C,A) => k1_funct_1(D,B) = k4_funct_6(C,A,B) ) ) ) )).
fof(t5_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => k6_msualg_3(A,B,B,k2_msualg_3(u1_struct_0(A),u3_msualg_1(A,B))) = g3_msualg_1(A,u3_msualg_1(A,B),u4_msualg_1(A,B)) ) ) )).
fof(t5_aofa_i00,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( 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] : ( ( 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 ) ) ) ) ) ) ) ) )).
fof(t5_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(k5_numbers,A) = k5_numbers ) )).
fof(t5_armstrng,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1)) => k3_armstrng(A,k1_binari_3(A,k5_numbers),B) = k1_binari_3(A,k5_numbers) ) ) )).
fof(t5_arrow,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t5_arytm_0,axiom,( r1_xboole_0(k2_arytm_2,k2_zfmisc_1(k1_tarski(k11_arytm_3),k2_arytm_2)) )).
fof(t5_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ( ( r1_arytm_2(A,B) & B = k11_arytm_3 ) => A = k11_arytm_3 ) ) ) )).
fof(t5_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ( k7_arytm_2(A,B) = k11_arytm_3 => A = k11_arytm_3 ) ) ) )).
fof(t5_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ( r2_arytm_3(A,B) <=> ? [C] : ( v3_ordinal1(C) & v7_ordinal1(C) & B = k9_ordinal3(A,C) ) ) ) ) )).
fof(t5_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v5_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_limfunc1(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) => ( v2_comseq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,A)) & k1_seq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,A)) = k5_numbers ) ) ) ) )).
fof(t5_asympt_1,axiom,( r1_tarski(k6_asympt_0(k2_asympt_1),k6_asympt_0(k3_asympt_1(k7_xcmplx_0(1,2)))) & k6_asympt_0(k2_asympt_1) != k6_asympt_0(k3_asympt_1(k7_xcmplx_0(1,2))) )).
fof(t5_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(t5_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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)))) ) ) ) )).
fof(t5_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t5_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k1_bcialg_2(A,B,k4_struct_0(A),k1_nat_1(C,1)) = B ) ) ) )).
fof(t5_bcialg_3,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t5_bcialg_4,axiom,( ! [A] : ( ( ~ 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) ) => ( v19_bcialg_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_4(A,B,C) = k1_bcialg_1(A,B,k1_bcialg_1(A,k4_struct_0(A),C)) ) ) ) ) )).
fof(t5_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [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) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t5_bcialg_6,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => k3_bcialg_6(A,k4_xcmplx_0(1),B) = k2_bcialg_1(A,B) ) ) )).
fof(t5_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_subset_1(D,u1_struct_0(A),B) => ( r1_bcialg_1(A,C,D) => r2_hidden(C,B) ) ) ) ) ) )).
fof(t5_bhsp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( 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) = k2_xcmplx_0(k3_xcmplx_0(A,k2_bhsp_1(C,D,F)),k3_xcmplx_0(B,k2_bhsp_1(C,E,F))) ) ) ) ) ) ) )).
fof(t5_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_bhsp_2(C,A) => v1_bhsp_2(k5_normsp_1(A,C,B),A) ) ) ) ) )).
fof(t5_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_bhsp_3(B,A) & r1_bhsp_3(A,B,C) ) => v1_bhsp_3(C,A) ) ) ) ) )).
fof(t5_bhsp_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,u1_struct_0(C)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(C)))) ) => r2_funct_2(k4_ordinal1,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)))) ) ) ) ) ) )).
fof(t5_bhsp_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_xcmplx_0(k1_square_1(k3_bhsp_1(A,k3_rlvect_1(A,B,C))),k1_square_1(k3_bhsp_1(A,k5_algstr_0(A,B,C)))) = k2_xcmplx_0(k3_xcmplx_0(2,k1_square_1(k3_bhsp_1(A,B))),k3_xcmplx_0(2,k1_square_1(k3_bhsp_1(A,C)))) ) ) ) )).
fof(t5_bhsp_6,axiom,( ! [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_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] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v1_xboole_0(B) => ! [C] : ( ( 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),k9_binop_2,B,C) ) ) ) ) ) )).
fof(t5_bhsp_7,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m2_bhsp_5(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( m1_subset_1(C,k1_zfmisc_1(B)) => m2_bhsp_5(C,A) ) ) ) ) )).
fof(t5_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( ( 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))) ) ) ) ) ) ) )).
fof(t5_binari_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( r2_hidden(B,k2_finseq_1(A)) & B = 1 ) => k7_partfun1(k6_margrel1,k1_binari_2(A),B) = k8_margrel1 ) ) ) )).
fof(t5_binari_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ( B = k5_euclid(A) => k3_binarith(A,B) = k5_finseq_2(k4_ordinal1,A,1) ) ) ) )).
fof(t5_binari_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t5_binarith,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k3_xboolean(k5_xboolean(A,B)) = k4_xboolean(k3_xboolean(A),k3_xboolean(B)) ) ) )).
fof(t5_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_algstr_0(A) & v2_vectsp_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t5_binop_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ( v1_binop_1(B,A) => ( r3_binop_1(A,C,B) <=> ! [D] : ( m1_subset_1(D,A) => k3_binop_1(A,B,D,C) = D ) ) ) ) ) )).
fof(t5_binop_2,axiom,( k4_binop_1(k4_ordinal1,k23_binop_2) = k5_numbers )).
fof(t5_bintree1,axiom,( v1_bintree1(k2_trees_1(2)) )).
fof(t5_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_bintree1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_bintree2(C,A) => ( r2_hidden(C,k2_trees_2(A,B)) => m2_finseq_2(C,k6_margrel1,k4_finseq_2(B,k6_margrel1)) ) ) ) ) )).
fof(t5_boole,axiom,( ! [A] : k5_xboole_0(A,k1_xboole_0) = A )).
fof(t5_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r3_lattices(A,C,E) & r3_lattices(A,D,E) ) => r3_lattices(A,B,E) ) ) ) ) ) ) ) ) )).
fof(t5_boolmark,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m2_funct_2(B,u1_struct_0(A),k6_margrel1,k1_boolmark(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t5_borsuk_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( 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] : ( 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] : ~ ( r2_hidden(E,D) & ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t5_borsuk_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v3_funct_1(C) & m1_borsuk_2(C,A,B,B) ) => r2_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),k1_borsuk_2(A,B,B,B,C,C),C) ) ) ) )).
fof(t5_borsuk_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t5_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( A = k2_rcomp_1(B,C) => ( r1_xxreal_0(C,B) | r1_tarski(k1_rcomp_1(B,C),u1_struct_0(k5_topmetr)) ) ) ) ) ) )).
fof(t5_borsuk_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( r1_zfmisc_1(A,B,C) & r1_zfmisc_1(D,E,F) & r1_subset_1(k1_enumset1(A,B,C),k1_enumset1(D,E,F)) ) => r4_zfmisc_1(A,B,C,D,E,F) ) )).
fof(t5_borsuk_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_topmetr)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_topmetr)) => m1_subset_1(k3_xcmplx_0(A,B),u1_struct_0(k5_topmetr)) ) ) )).
fof(t5_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( k17_sin_cos(A) = k5_numbers & A != k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k1_int_1(k7_xcmplx_0(A,k3_xcmplx_0(2,k28_sin_cos)))) & A != k2_xcmplx_0(k28_sin_cos,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k1_int_1(k7_xcmplx_0(A,k3_xcmplx_0(2,k28_sin_cos))))) ) ) )).
fof(t5_brouwer,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_xreal_0(B) & ~ v3_xxreal_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( 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] : ( 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(k15_euclid(A),C,D),k3_topreal9(A,E,B)) ) ) ) ) ) ) ) ) )).
fof(t5_brouwer2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_numbers) => k2_tops_1(k15_euclid(A),k2_topreal9(A,B,C)) = k3_topreal9(A,B,C) ) ) ) ) )).
fof(t5_bspace,axiom,( k4_struct_0(k2_bspace) = k5_numbers )).
fof(t5_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) )).
fof(t5_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ( ( v2_bvfunc_2(B,A) & B = k2_tarski(C,D) ) => ( C = D | ! [E] : ! [F] : ~ ( r2_hidden(E,C) & r2_hidden(F,D) & r1_xboole_0(E,F) ) ) ) ) ) ) ) )).
fof(t5_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t5_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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),k9_bvfunc_1(A,k5_bvfunc_1(A,B,C),k2_bvfunc_1(A,B,C))) ) ) ) )).
fof(t5_bvfunc26,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(t5_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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,k12_bvfunc_1(A)),B) ) ) )).
fof(t5_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( m1_eqrel_1(D,A) => r2_bvfunc_1(A,k6_bvfunc_2(A,C,B,D),k5_bvfunc_2(A,D,B)) ) ) ) ) )).
fof(t5_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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))) ) ) ) ) ) )).
fof(t5_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t5_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t5_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t5_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t5_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t5_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t5_c0sp1,axiom,( ! [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) & 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) ) ) ) )).
fof(t5_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_c0sp2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_c0sp2(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_c0sp2(A))) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(H,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k1_numbers,G,H) = k4_real_1(k3_funct_2(u1_struct_0(A),k1_numbers,E,H),k3_funct_2(u1_struct_0(A),k1_numbers,F,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t5_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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(k4_ordinal1,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) ) ) ) ) )).
fof(t5_calcul_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) )).
fof(t5_cantor_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t5_card_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v2_wellord1(A) => r2_wellord2(k1_relat_1(A),k2_wellord2(A)) ) ) )).
fof(t5_card_2,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t5_card_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) ) )).
fof(t5_card_4,axiom,( r2_wellord2(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k4_ordinal1) & k1_card_1(k4_ordinal1) = k1_card_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1)) )).
fof(t5_card_5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ~ ( r1_tarski(B,A) & ! [C] : ( ( 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 ) ) ) ) )).
fof(t5_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_card_fil(B,A) => r2_hidden(A,B) ) ) )).
fof(t5_card_fin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => m1_subset_1(k7_xcmplx_0(k7_newton(A),k7_newton(k7_nat_d(A,B))),k4_ordinal1) ) ) )).
fof(t5_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v4_ordinal1(B) & ~ v1_finset_1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ~ ( k3_ordinal2(k8_subset_1(A,C,B)) != B & ! [D] : ( v3_ordinal1(D) => ~ ( r2_hidden(D,B) & r1_tarski(k8_subset_1(A,C,B),D) ) ) ) ) ) ) )).
fof(t5_cardfin2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,B) & ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,k2_rcomp_1(B,C)) & k23_sin_cos(B) = k2_xcmplx_0(k9_nat_1(k1_numbers,k3_series_1(k6_taylor_1(k22_sin_cos,k2_subset_1(k1_numbers),C,B)),A),k7_xcmplx_0(k3_xcmplx_0(k23_sin_cos(D),k1_newton(k6_xcmplx_0(B,C),k1_nat_1(A,1))),k2_newton(k1_nat_1(A,1)))) ) ) ) ) ) ) )).
fof(t5_cat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_cat_1(F,A,B,C) => ! [G] : ( m1_cat_1(G,A,D,E) => ( F = G => ( k2_cat_1(A,B,C) = k1_xboole_0 | k2_cat_1(A,D,E) = k1_xboole_0 | ( B = D & C = E ) ) ) ) ) ) ) ) ) ) )).
fof(t5_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m3_cat_2(B,A) => ! [C] : ( m1_subset_1(C,u4_struct_0(B)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ( C = D => ( k3_graph_1(B,C) = k3_graph_1(A,D) & k4_graph_1(B,C) = k4_graph_1(A,D) ) ) ) ) ) ) )).
fof(t5_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( 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))) ) ) )).
fof(t5_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k5_cat_4(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_cat_4(A,B))) => ! [E] : ( 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)) ) ) ) )).
fof(t5_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m3_cat_2(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t5_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(A,B) => v1_catalan2(k1_catalan2(k8_funcop_1(k4_ordinal1,B,k5_numbers),k8_funcop_1(k4_ordinal1,A,1))) ) ) ) )).
fof(t5_catalg_1,axiom,( ! [A] : k4_catalg_1(k3_catalg_1(A)) = A )).
fof(t5_cayldick,axiom,( ! [A] : ! [B] : ~ ( r2_hidden(A,k4_card_3(k5_afinsq_1(B))) & ! [C] : ~ ( r2_hidden(C,B) & A = k5_afinsq_1(C) ) ) )).
fof(t5_cayley,axiom,( ! [A] : ! [B] : ( 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))) ) ) )).
fof(t5_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_cc0sp1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_cc0sp1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_cc0sp1(A))) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(H,A) => k3_funct_2(A,k2_numbers,G,H) = k2_xcmplx_0(k3_funct_2(A,k2_numbers,E,H),k3_funct_2(A,k2_numbers,F,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t5_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t5_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_ordinal1) & v5_valued_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k36_valued_1(k4_ordinal1,k2_numbers,k9_comseq_3(B,A)),k9_comseq_3(B,k36_valued_1(k4_ordinal1,k2_numbers,A))) ) ) )).
fof(t5_cfdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_ordinal1) & v5_valued_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => ! [C] : ( v7_ordinal1(C) => k9_nat_1(k2_numbers,k9_comseq_3(B,A),C) = k3_funct_2(k4_ordinal1,k2_numbers,A,k9_nat_1(k4_ordinal1,B,C)) ) ) ) )).
fof(t5_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ! [C] : ( 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)) ) ) ) )).
fof(t5_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( 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) = k4_xcmplx_0(k7_partfun1(k2_numbers,B,C)) ) ) ) ) ) )).
fof(t5_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ! [B] : ( v2_cgames_1(B) => ( A = B <=> ( k6_cgames_1(A) = k6_cgames_1(B) & k7_cgames_1(A) = k7_cgames_1(B) ) ) ) ) )).
fof(t5_chain_1,axiom,( ! [A] : ( k1_card_1(A) = 2 <=> ? [B] : ? [C] : ( r2_hidden(B,A) & r2_hidden(C,A) & B != C & ! [D] : ~ ( r2_hidden(D,A) & D != B & D != C ) ) ) )).
fof(t5_chord,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v1_abian(A) ) => ~ ( 1 != A & ! [B] : ( ( v7_ordinal1(B) & ~ v1_abian(B) ) => k1_nat_1(B,2) != A ) ) ) )).
fof(t5_circcmb2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t5_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( 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)) ) ) ) ) ) )).
fof(t5_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ( r1_circcomb(A,B) => k2_circcomb(A,B) = k2_circcomb(B,A) ) ) ) )).
fof(t5_circled1,axiom,( ! [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) ) => v3_rltopsp1(k3_rusub_4(A,k1_rlsub_1(A)),A) ) )).
fof(t5_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t5_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,k5_msafree2(A,B)),C)) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_ordinal1) => ( ( r2_hidden(G,k1_relset_1(k4_ordinal1,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) ) ) ) ) ) ) ) ) ) )).
fof(t5_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msafree2(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t5_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) ) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ( ( r1_ckspace1(A,E,B,C) & v1_pdiff_7(C,A) ) => r1_ckspace1(A,k26_valued_1(k1_euclid(A),k1_numbers,E,D),B,C) ) ) ) ) ) ) )).
fof(t5_classes1,axiom,( ! [A] : ! [B] : ~ ( r1_tarski(B,k1_classes1(A)) & ~ r2_tarski(B,k1_classes1(A)) & ~ r2_hidden(B,k1_classes1(A)) ) )).
fof(t5_classes2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v2_classes1(B) & r2_hidden(A,B) ) => ( r2_hidden(k1_ordinal1(A),B) & r1_tarski(A,B) ) ) ) )).
fof(t5_clopban1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(t5_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t5_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_csspace3(B,A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(D,E) & r1_xxreal_0(C,k2_normsp_0(A,k5_algstr_0(A,k1_normsp_0(A,B,E),k1_normsp_0(A,B,D)))) ) ) ) ) ) ) ) )).
fof(t5_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v9_clvect_1(C,A) => v9_clvect_1(k3_clopban3(A,C,B),A) ) ) ) ) )).
fof(t5_closure1,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( ( r1_pboole(A,C,k1_funct_6(B)) & r1_pboole(A,D,k1_funct_6(B)) & r6_pboole(A,k16_pralg_1(A,B,C),k16_pralg_1(A,B,D)) ) => r6_pboole(A,C,D) ) ) ) ) ) )).
fof(t5_closure2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_closure2(B,C))) => m1_subset_1(k7_subset_1(k1_closure2(B,C),D,A),k1_zfmisc_1(k1_closure2(B,C))) ) ) )).
fof(t5_closure3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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))) ) ) )).
fof(t5_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( k3_rlvect_1(A,B,B) = k4_struct_0(A) => B = k4_struct_0(A) ) ) ) )).
fof(t5_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clvect_2(C,A) => v1_clvect_2(k6_clvect_1(A,C,B),A) ) ) ) ) )).
fof(t5_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t5_coh_sp,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( 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] : ! [D] : ( r2_hidden(k4_tarski(C,D),B) <=> r2_hidden(k2_tarski(C,D),A) ) ) ) ) )).
fof(t5_cohsp_1,axiom,( ! [A] : ( v1_cohsp_1(A) => ! [B] : ! [C] : ~ ( r2_hidden(B,A) & r2_hidden(C,A) & ! [D] : ~ ( r1_tarski(k2_xboole_0(B,C),D) & r2_hidden(D,A) ) ) ) )).
fof(t5_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_collsp(A,B,C,B) ) ) ) )).
fof(t5_combgras,axiom,( ! [A] : ! [B] : ! [C] : ( ( k6_subset_1(A,B) = k6_subset_1(A,C) & r1_tarski(B,A) & r1_tarski(C,A) ) => B = C ) )).
fof(t5_compact1,axiom,( ! [A] : ( l1_pre_topc(A) => m1_pre_topc(A,k1_compact1(A)) ) )).
fof(t5_compl_sp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v6_metric_1(B) & v8_metric_1(B) & v9_metric_1(B) & l1_metric_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( r1_xxreal_0(k5_numbers,A) => r1_xxreal_0(k3_tbsp_1(B,k9_metric_1(B,C,A)),k3_xcmplx_0(2,A)) ) ) ) ) )).
fof(t5_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( A = k5_numbers <=> k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A))) = k5_numbers ) ) )).
fof(t5_complex2,axiom,( ! [A] : ( v1_xreal_0(A) => ( k17_sin_cos(k6_xcmplx_0(A,k28_sin_cos)) = k4_xcmplx_0(k17_sin_cos(A)) & k19_sin_cos(k6_xcmplx_0(A,k28_sin_cos)) = k4_xcmplx_0(k19_sin_cos(A)) ) ) )).
fof(t5_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( v1_xcmplx_0(B) => ( A = B => ( A = k4_struct_0(k1_complfld) | k11_algstr_0(k1_complfld,A) = k5_xcmplx_0(B) ) ) ) ) )).
fof(t5_complsp1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_complsp1(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k12_seq_4(A))) => ( C = B => ( v2_seq_4(C,A) <=> v4_pre_topc(B,k1_complsp1(A)) ) ) ) ) ) )).
fof(t5_complsp2,axiom,( ! [A] : ( ( 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) ) )).
fof(t5_compos_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_compos_0(A) & v2_compos_0(A) & v3_compos_0(A) ) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ( ? [D] : ( v7_ordinal1(D) & k5_compos_0(A,B,D) = k5_compos_0(A,C,D) ) => B = C ) ) ) ) )).
fof(t5_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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)) ) ) ) ) )).
fof(t5_comptrig,axiom,( ~ r1_xxreal_0(k7_xcmplx_0(k28_sin_cos,2),k5_numbers) & ~ r1_xxreal_0(k28_sin_cos,k7_xcmplx_0(k28_sin_cos,2)) & ~ r1_xxreal_0(k28_sin_cos,k5_numbers) & ~ r1_xxreal_0(k7_xcmplx_0(k28_sin_cos,2),k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2))) & ~ r1_xxreal_0(k3_xcmplx_0(2,k28_sin_cos),k28_sin_cos) & ~ r1_xxreal_0(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k7_xcmplx_0(k28_sin_cos,2)) & ~ r1_xxreal_0(k5_numbers,k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2))) & ~ r1_xxreal_0(k3_xcmplx_0(2,k28_sin_cos),k5_numbers) & ~ r1_xxreal_0(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k28_sin_cos) & ~ r1_xxreal_0(k3_xcmplx_0(2,k28_sin_cos),k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos)) & ~ r1_xxreal_0(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k5_numbers) )).
fof(t5_compts_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_compts_1(A) <=> ! [B] : ( 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] : ( 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 ) ) ) ) ) ) )).
fof(t5_comput_1,axiom,( ! [A] : k4_finseq_2(k5_numbers,A) = k1_tarski(k1_xboole_0) )).
fof(t5_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & v9_ordinal1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r1_tarski(k2_relset_1(k2_numbers,A),k6_subset_1(k2_numbers,k1_tarski(k5_complex1))) ) )).
fof(t5_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_funct_2(k4_ordinal1,k2_numbers,k2_comseq_2(k4_ordinal1,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B)),k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k2_comseq_2(k4_ordinal1,A),k2_comseq_2(k4_ordinal1,B))) ) ) )).
fof(t5_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( 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))) ) ) )).
fof(t5_conmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t5_conmetr1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v4_conmetr1(A) => v3_conmetr1(A) ) ) )).
fof(t5_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t5_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( m1_connsp_2(C,A,B) & ! [D] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t5_connsp_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t5_convex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_convex1(B,A) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(1,C) & ~ r1_tarski(k7_rusub_4(A,k1_convex1(A,B,k6_xcmplx_0(1,C)),k1_convex1(A,B,C)),B) ) ) ) ) ) )).
fof(t5_convex2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ( B = a_3_3_convex2(A,C,D) => v1_convex1(B,A) ) ) ) ) ) )).
fof(t5_convex3,axiom,( ! [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) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t5_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m2_convex4(B,A,k1_subset_1(u1_struct_0(A))) => r2_funct_2(u1_struct_0(A),k2_numbers,B,k2_convex4(A)) ) ) )).
fof(t5_convfun1,axiom,( ! [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) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k6_numbers))) ) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k12_supinf_2(B,C) != k2_supinf_1 ) => ( v1_convfun1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ( ( r1_xxreal_0(k5_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,k6_xcmplx_0(1,E)))),k1_xxreal_3(k4_xxreal_3(E,k12_supinf_2(B,C)),k4_xxreal_3(k6_xcmplx_0(1,E),k12_supinf_2(B,D)))) ) ) ) ) ) ) ) ) )).
fof(t5_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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 ) ) ) ) ) )).
fof(t5_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ~ ( v2_qc_lang1(B,A) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_subset_1(D,k6_qc_lang1(A),k8_qc_lang1(A,C)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t5_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k9_qc_lang1(A),k3_cqc_lang(A)) => 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)))),k1_cqc_the1(A,B)) ) ) ) ) ) )).
fof(t5_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ( r2_hidden(D,k24_qc_lang1(A,k15_qc_lang1(A,C,B))) <=> ( r2_hidden(D,k24_qc_lang1(A,B)) & D != C ) ) ) ) ) ) )).
fof(t5_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => r1_cqc_the3(A,B,B) ) ) )).
fof(t5_csspace,axiom,( ! [A] : ( 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 ) )).
fof(t5_csspace2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( r1_xxreal_0(k3_xcmplx_0(k9_complex1(k2_xcmplx_0(A,B)),k9_complex1(k2_xcmplx_0(A,B))),k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k9_complex1(A)),k9_complex1(A)),k3_xcmplx_0(k3_xcmplx_0(2,k9_complex1(B)),k9_complex1(B)))) & r1_xxreal_0(k3_xcmplx_0(k9_complex1(A),k9_complex1(A)),k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k9_complex1(k6_xcmplx_0(A,B))),k9_complex1(k6_xcmplx_0(A,B))),k3_xcmplx_0(k3_xcmplx_0(2,k9_complex1(B)),k9_complex1(B)))) ) ) ) )).
fof(t5_csspace3,axiom,( u1_struct_0(k3_csspace3) = k1_csspace3 & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_csspace3)) <=> ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & v2_comseq_3(k2_csspace(A)) ) ) & k4_struct_0(k3_csspace3) = k6_csspace & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_csspace3)) => A = k2_csspace(A) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_csspace3)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_csspace3)) => k1_algstr_0(k3_csspace3,A,B) = k1_series_1(k2_numbers,k2_csspace(A),k2_csspace(B)) ) ) & ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_csspace3)) => k1_clvect_1(k3_csspace3,B,A) = k25_valued_1(k4_ordinal1,k2_numbers,k2_csspace(B),A) ) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_csspace3)) => ( k4_algstr_0(k3_csspace3,A) = k31_valued_1(k4_ordinal1,k2_numbers,k2_csspace(A)) & r2_funct_2(k4_ordinal1,k2_numbers,k2_csspace(k4_algstr_0(k3_csspace3,A)),k31_valued_1(k4_ordinal1,k2_numbers,k2_csspace(A))) ) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_csspace3)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_csspace3)) => k5_algstr_0(k3_csspace3,A,B) = k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k2_csspace(A),k2_csspace(B)) ) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_csspace3)) => v2_comseq_3(k2_csspace(A)) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_csspace3)) => k2_normsp_0(k3_csspace3,A) = k4_series_1(k55_valued_1(k4_ordinal1,k2_numbers,k2_csspace(A))) ) )).
fof(t5_csspace4,axiom,( ~ 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) )).
fof(t5_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_decomp_1(B,A) <=> B = k4_decomp_1(A,B) ) ) ) )).
fof(t5_descip_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t5_dickson,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v16_waybel_0(A) <=> r7_relat_2(u1_orders_2(A),u1_struct_0(A)) ) ) )).
fof(t5_diff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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_funct_1(k5_diff_1(C,A),B) = k6_xcmplx_0(k1_funct_1(C,k2_xcmplx_0(B,k7_xcmplx_0(A,2))),k1_funct_1(C,k6_xcmplx_0(B,k7_xcmplx_0(A,2)))) ) ) ) )).
fof(t5_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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) = k3_xcmplx_0(A,k10_diff_1(E,B,C,D)) ) ) ) ) ) )).
fof(t5_diff_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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_funct_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,C)),B),k2_xcmplx_0(A,1)),D) = k2_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(E,B),k2_xcmplx_0(A,1)),D),k3_xcmplx_0(C,k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(F,B),k2_xcmplx_0(A,1)),D))) ) ) ) ) ) ) )).
fof(t5_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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] : ( v1_xreal_0(G) => k1_funct_1(F,G) = k7_xcmplx_0(A,k1_square_1(G)) ) & r2_zfmisc_1(B,C,D,E) ) => ( B = k5_numbers | C = k5_numbers | D = k5_numbers | E = k5_numbers | k11_diff_1(F,B,C,D,E) = k7_xcmplx_0(k3_xcmplx_0(A,k6_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(k3_xcmplx_0(C,D),B)),k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(1,B),k7_xcmplx_0(1,D)),k7_xcmplx_0(1,C))),k3_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(k3_xcmplx_0(D,C),E)),k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(1,E),k7_xcmplx_0(1,C)),k7_xcmplx_0(1,D))))),k6_xcmplx_0(B,E)) ) ) ) ) ) ) ) ) )).
fof(t5_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t5_dirort,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dirort(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_analoaf(A,E,D,B,C) & E != D ) ) ) ) ) )).
fof(t5_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r1_dist_1(A,B,C) <=> r2_hidden(C,k5_dist_1(A,B)) ) ) ) ) )).
fof(t5_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m2_finseq_1(B,A) => ( ! [C] : k3_dist_1(A,B,C) = k5_numbers <=> v1_xboole_0(B) ) ) ) )).
fof(t5_domain_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ( A = k3_zfmisc_1(B,C,D) <=> ! [E] : ( r2_hidden(E,A) <=> ? [F] : ( m1_subset_1(F,B) & ? [G] : ( m1_subset_1(G,C) & ? [H] : ( m1_subset_1(H,D) & E = k3_xtuple_0(F,G,H) ) ) ) ) ) ) ) ) ) )).
fof(t5_dtconstr,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k5_trees_3(A))) => ! [C] : ( m1_trees_4(C,k5_trees_3(A),B) => ~ ( k3_finseq_1(k1_dtconstr(A,k5_trees_3(A),C)) = 1 & ! [D] : ( m1_subset_1(D,k5_trees_3(A)) => ~ ( C = k3_pre_poly(k5_trees_3(A),D) & r2_hidden(D,B) ) ) ) ) ) ) )).
fof(t5_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( v7_ordinal1(C) => k9_nat_1(k9_setfam_1(A),k4_dynkin(A,B),C) = k7_subset_1(A,k9_nat_1(k9_setfam_1(A),B,C),k3_tarski(k10_xtuple_0(k5_relat_1(B,C)))) ) ) ) )).
fof(t5_e_siec,axiom,( ! [A] : ! [B] : ( 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)))) ) )).
fof(t5_ec_pf_1,axiom,( ! [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] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) )).
fof(t5_ec_pf_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( 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) ) ) ) ) ) )).
fof(t5_endalg,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t5_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t5_entropy1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & A != 1 & ~ r1_xxreal_0(B,k5_numbers) & k4_xcmplx_0(k3_power(A,B)) != k3_power(A,k7_xcmplx_0(1,B)) ) ) ) )).
fof(t5_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_enumset1(A,B,C,D) = k2_xboole_0(k2_tarski(A,B),k2_tarski(C,D)) )).
fof(t5_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(t5_equation,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,C) => ! [E] : ( m3_pboole(E,A,B) => ! [F] : ( m3_pboole(F,A,B) => ! [G] : ( 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)) ) ) ) ) ) ) ) )).
fof(t5_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ( k12_euclid(B) = k5_numbers => B = k5_euclid(A) ) ) ) )).
fof(t5_euclid_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => k12_euclid(A) = k3_square_1(k22_rvsum_1(A,A)) ) )).
fof(t5_euclid_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_euclid_3(k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1))) = k19_euclid(A,B) ) ) )).
fof(t5_euclid_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(B)) => ~ ( k9_euclid(B,C,A) = k5_euclid(B) & A != k5_numbers & C != k5_euclid(B) ) ) ) ) )).
fof(t5_euclid_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(3))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(3))) => k3_rlvect_1(k15_euclid(3),A,B) = k4_euclid_5(k2_xcmplx_0(k1_euclid_5(A),k1_euclid_5(B)),k2_xcmplx_0(k2_euclid_5(A),k2_euclid_5(B)),k2_xcmplx_0(k3_euclid_5(A),k3_euclid_5(B))) ) ) )).
fof(t5_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => k1_euclid_6(A,B,C) = k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k12_euclid(k5_algstr_0(k15_euclid(2),A,B)),k12_euclid(k5_algstr_0(k15_euclid(2),C,B))),k17_sin_cos(k4_euclid_3(C,B,A))),2) ) ) ) )).
fof(t5_euclid_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => ( v5_valued_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(C,B) & r1_xxreal_0(1,B) & r1_xxreal_0(C,k3_finseq_1(A)) & r1_xxreal_0(k1_funct_1(A,C),k1_funct_1(A,B)) ) ) ) ) ) )).
fof(t5_euclid_8,axiom,( k12_euclid(k3_euclid_8) = 1 )).
fof(t5_euclid_9,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,B) & v1_finseq_1(C) & v3_valued_0(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_card_1(D,B) & v1_finseq_1(D) & v3_valued_0(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))) ) ) ) )).
fof(t5_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t5_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( ~ r5_analmetr(A,B,C,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r4_analmetr(A,E,B,C,D) & r4_analmetr(A,E,C,B,D) ) ) ) ) ) ) ) )).
fof(t5_euler_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k3_int_2(A,B) = 1 => ! [C] : ( v7_ordinal1(C) => k3_int_2(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) = C ) ) ) ) )).
fof(t5_euler_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k4_nat_d(k4_nat_d(A,B),B) = k4_nat_d(A,B) ) ) )).
fof(t5_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( v1_relat_1(B) => ! [C] : ( r2_hidden(C,k7_relat_1(A,B)) <=> ? [D] : ? [E] : ( r2_hidden(k4_tarski(D,E),B) & r2_hidden(k4_tarski(D,E),k9_xtuple_0(A)) & k1_binop_1(A,D,E) = C ) ) ) ) )).
fof(t5_extens_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r1_pzfmisc1(A,B,C) => ! [D] : ( m2_pboole(D,A,B,C) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t5_extpro_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(A,B) => ! [C] : ( ( ~ v1_xboole_0(C) & ~ v1_setfam_1(C) ) => ! [D] : ( ( ~ 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] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(D)) & v1_funct_1(E) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t5_extreal1,axiom,( k4_extreal1(k6_finseq_1(k6_numbers)) = k1_supinf_2 )).
fof(t5_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ( A = k5_numbers <=> k3_extreal1(A) = k5_numbers ) ) )).
fof(t5_facirc_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( v1_facirc_1(A) | r1_xboole_0(A,B) ) ) )).
fof(t5_facirc_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v1_msualg_1(B) & l1_msualg_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t5_fcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r1_fcont_1(A,B) <=> ! [C] : ( m1_rcomp_1(C,k1_funct_1(A,B)) => ? [D] : ( m1_rcomp_1(D,B) & r1_tarski(k7_relset_1(k1_numbers,k1_numbers,A,D),C) ) ) ) ) ) )).
fof(t5_fcont_2,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(t5_fdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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))) ) ) ) )).
fof(t5_fdiff_10,axiom,( ! [A] : ( ( 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,k26_sin_cos,k27_sin_cos))) => ( r2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),A),B) = k2_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t5_fdiff_11,axiom,( ! [A] : ( ( 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,k26_sin_cos,k1_sin_cos9))) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k26_sin_cos,B),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(k26_sin_cos,B)) ) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_sin_cos9),A),B) = 1 ) ) ) ) ) )).
fof(t5_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k2_relset_1(k1_numbers,B) = k1_tarski(A) & k2_relset_1(k1_numbers,C) = k1_tarski(A) ) => r2_relset_1(k4_ordinal1,k1_numbers,B,C) ) ) ) ) )).
fof(t5_fdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r4_fdiff_3(A,B) => r1_fdiff_3(A,B) ) ) ) )).
fof(t5_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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,k3_xcmplx_0(2,A)),k1_partfun2(k1_numbers,B)))) & C = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k3_taylor_1) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => ( k1_funct_1(D,E) = k2_xcmplx_0(A,E) & ~ r1_xxreal_0(k1_funct_1(D,E),k5_numbers) ) ) ) ) => ( r2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_valued_1(k1_numbers,k1_numbers,C,k3_xcmplx_0(2,A)),k1_partfun2(k1_numbers,B)),B) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_1(k2_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_valued_1(k1_numbers,k1_numbers,C,k3_xcmplx_0(2,A)),k1_partfun2(k1_numbers,B)),B),E) = k7_xcmplx_0(k6_xcmplx_0(A,E),k2_xcmplx_0(A,E)) ) ) ) ) ) ) ) ) )).
fof(t5_fdiff_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => ( k1_funct_1(D,F) = k1_square_1(A) & ~ r1_xxreal_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,D,E),F),k5_numbers) & A != k5_numbers ) ) ) ) => ( r2_fdiff_1(C,B) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => k1_funct_1(k2_fdiff_1(C,B),F) = k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(4,k1_square_1(A)),F),k6_xcmplx_0(k1_newton(A,4),k1_newton(F,4))) ) ) ) ) ) ) ) ) ) )).
fof(t5_fdiff_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,k2_rcomp_1(k4_xcmplx_0(1),1)) & r1_tarski(B,k1_relset_1(k1_numbers,k26_valued_1(k1_numbers,k1_numbers,k3_sin_cos6,A))) ) => ( r2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k3_sin_cos6,A),B) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => k1_funct_1(k2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k3_sin_cos6,A),B),C) = k4_xcmplx_0(k7_xcmplx_0(A,k3_square_1(k6_xcmplx_0(1,k1_square_1(C))))) ) ) ) ) ) ) )).
fof(t5_fdiff_8,axiom,( ! [A] : ( ( 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(k5_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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k4_xcmplx_0(k7_xcmplx_0(1,B)) ) ) ) ) ) ) )).
fof(t5_fdiff_9,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k2_fdiff_9,A),B) = k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k18_sin_cos,B),k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t5_ff_siec,axiom,( ! [A] : ( 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 ) )).
fof(t5_fib_fusc,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( r1_tarski(k3_fib_fusc,A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(B,k5_numbers) => ! [C] : ( ( v5_memstr_0(C,k7_card_1(2),k1_ami_3,k5_numbers) & m1_scm_1(C,k16_afinsq_1(2,B,1,k5_numbers)) ) => ( r1_extpro_1(k7_card_1(2),k1_ami_3,A,C) & k1_funct_1(k6_extpro_1(k7_card_1(2),k1_ami_3,A,C),k10_ami_3(3)) = k3_pre_ff(B) & ( B = k5_numbers => k8_extpro_1(k7_card_1(2),k1_ami_3,A,C) = 1 ) & ( ~ r1_xxreal_0(B,k5_numbers) => k8_extpro_1(k7_card_1(2),k1_ami_3,A,C) = k2_xcmplx_0(k3_xcmplx_0(6,k2_xcmplx_0(k1_int_1(k3_power(2,B)),1)),1) ) ) ) ) ) ) ) )).
fof(t5_fib_num,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k3_int_2(k1_pre_ff(A),k1_pre_ff(B)) = k1_pre_ff(k3_int_2(A,B)) ) ) )).
fof(t5_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => k2_power(C,k2_xcmplx_0(A,B)) = k3_xcmplx_0(k2_power(C,A),k2_power(C,B)) ) ) ) )).
fof(t5_fib_num3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k11_newton(k1_nat_1(A,B),2) = k1_nat_1(k1_nat_1(k1_nat_1(k2_nat_1(A,A),k2_nat_1(A,B)),k2_nat_1(A,B)),k2_nat_1(B,B)) ) ) )).
fof(t5_fib_num4,axiom,( ~ r1_xxreal_0(1,k9_complex1(k2_fib_num)) )).
fof(t5_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r1_xxreal_0(1,k3_finseq_1(C)) => k3_finseq_6(A,k1_finseq_8(A,B,C),k1_nat_1(k3_finseq_1(B),1),k1_nat_1(k3_finseq_1(B),k3_finseq_1(C))) = C ) ) ) ) )).
fof(t5_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t5_filter_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t5_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t5_finance1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => m2_subset_1(k3_prob_1(k1_numbers,k2_finance1(A,B)),k1_zfmisc_1(k1_numbers),k12_prob_1) ) ) )).
fof(t5_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(A,B) <=> r1_tarski(k2_finseq_1(A),k2_finseq_1(B)) ) ) ) )).
fof(t5_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( r2_hidden(A,k2_finseq_1(k1_nat_1(B,1))) & ~ r2_hidden(A,k2_finseq_1(B)) & A != k1_nat_1(B,1) ) ) ) )).
fof(t5_finseq_3,axiom,( k2_finseq_1(7) = k5_enumset1(1,2,3,4,5,6,7) )).
fof(t5_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r2_finseq_4(A,B) => r2_hidden(B,k10_xtuple_0(A)) ) ) )).
fof(t5_finseq_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( ( 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 ) ) )).
fof(t5_finseq_6,axiom,( ! [A] : ! [B] : ! [C] : k5_relat_1(k11_finseq_1(A,B,C),k2_finseq_1(2)) = k10_finseq_1(A,B) )).
fof(t5_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( v7_ordinal1(D) => k3_finseq_1(k1_finseq_7(A,B,D,C)) = k3_finseq_1(B) ) ) ) ) )).
fof(t5_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k3_finseq_8(A,B,1,C) = k17_finseq_1(A,C,B) ) ) ) )).
fof(t5_finseqop,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => k5_funcop_1(B,A,k1_xboole_0) = k1_xboole_0 ) )).
fof(t5_finset_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( v1_finset_1(A) => v1_finset_1(k7_relat_1(B,A)) ) ) )).
fof(t5_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( 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)) ) ) ) ) ) ) )).
fof(t5_finsub_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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) ) ) )).
fof(t5_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t5_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t5_fintopo4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_fintopo4(A,B,C) => r1_fintopo4(A,C,B) ) ) ) ) )).
fof(t5_fintopo5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t5_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_fin_topo(A) & r1_xboole_0(k9_fin_topo(A,B),C) ) => r1_xboole_0(B,k9_fin_topo(A,C)) ) ) ) ) )).
fof(t5_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k3_catalan2(A)) => ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v5_ordinal1(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)) ) ) ) ) ) )).
fof(t5_flang_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k8_afinsq_1(A))) => ~ ( ( r2_hidden(B,C) | r2_hidden(B,D) ) & B != k2_flang_1(A) & k6_flang_1(A,C,D) = k4_flang_1(A,k2_flang_1(A)) ) ) ) )).
fof(t5_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => r1_tarski(k1_flang_3(A,B,D),k1_flang_3(A,B,C)) ) ) ) ) )).
fof(t5_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m2_finseq_1(B,A) ) <=> r2_hidden(B,k6_subset_1(k3_finseq_2(A),k1_tarski(k1_xboole_0))) ) ) )).
fof(t5_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ~ ( r2_hidden(A,k35_fomodel1(B)) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ r2_hidden(A,k3_funct_2(k4_ordinal1,k9_setfam_1(k3_finseq_2(k15_fomodel1(B))),k28_fomodel1(B),C)) ) ) ) )).
fof(t5_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ~ v1_xboole_0(C) => ( v1_funct_1(k1_funct_5(k22_fomodel2(B,A,C))) & v1_funct_2(k1_funct_5(k22_fomodel2(B,A,C)),k15_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(k22_fomodel2(B,A,C)),k1_zfmisc_1(k2_zfmisc_1(k15_fomodel2(B,C),k3_rfunct_3(k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0)),k6_margrel1)))) ) ) ) ) )).
fof(t5_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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) != k31_fomodel2(B) => k13_fomodel2(B,k8_eqrel_1(A,C),k23_fomodel3(B,A,C,E),D) = k13_fomodel2(B,A,E,D) ) ) ) ) ) ) )).
fof(t5_fomodel4,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( 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(B,k1_funct_1(D,A)) => v5_fomodel4(B,1,C,k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(C)),k9_setfam_1(k1_fomodel4(C))),D),A) ) ) ) )).
fof(t5_fraenkel,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ! [D] : ( m2_funct_2(D,B,A,k9_funct_2(B,A)) => r2_relset_1(B,A,k2_partfun1(B,A,D,C),k2_partfun1(B,A,D,k3_xboole_0(B,C))) ) ) )).
fof(t5_frechet,axiom,( ! [A] : ( l1_pre_topc(A) => ( ( v4_pre_topc(k1_struct_0(A),A) & v4_pre_topc(k2_struct_0(A),A) & ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( 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) ) ) ) )).
fof(t5_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) )).
fof(t5_freealg,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_freealg(B) ) => ~ v1_xboole_0(k8_freealg(A,B)) ) ) )).
fof(t5_friends1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ~ ( k7_finseq_1(k1_rfinseq(A,C),k16_finseq_1(A,C)) = k7_finseq_1(k1_rfinseq(B,D),k16_finseq_1(B,D)) & ! [E] : ( v7_ordinal1(E) => C != k7_finseq_1(k1_rfinseq(E,D),k16_finseq_1(E,D)) ) ) ) ) ) ) )).
fof(t5_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k3_fscirc_1(A,B,C),k5_fscirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( 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) ) ) ) ) )).
fof(t5_fscirc_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t5_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ( 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) ) ) ) ) ) ) ) )).
fof(t5_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ( ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( 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) ) ) ) )).
fof(t5_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => ! [C] : ( v7_ordinal1(C) => ~ ( C != k5_numbers & r1_xxreal_0(k1_afinsq_1(B),k2_xcmplx_0(C,1)) & ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t5_ftacell1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( 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))) ) )).
fof(t5_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : k5_relat_1(k13_funct_3(A,B),C) = k13_funct_3(k5_relat_1(A,C),B) ) ) )).
fof(t5_funcsdom,axiom,( ! [A] : ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( 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)) ) ) )).
fof(t5_funct_1,axiom,( ! [A] : ( A != k1_xboole_0 => ! [B] : ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & k9_xtuple_0(C) = A & k10_xtuple_0(C) = k1_tarski(B) ) ) )).
fof(t5_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) ) ) ) )).
fof(t5_funct_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t5_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r1_relset_1(A,k1_tarski(C),k7_funcop_1(A,C),k7_funcop_1(B,D)) => r1_tarski(A,B) ) )).
fof(t5_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(C,k2_zfmisc_1(A,B)) => ( r1_tarski(k9_xtuple_0(C),A) & r1_tarski(k10_xtuple_0(C),B) ) ) )).
fof(t5_funct_6,axiom,( ! [A] : ! [B] : ! [C] : ( k2_zfmisc_1(B,C) != k1_xboole_0 => ( k1_funct_5(k7_funcop_1(k2_zfmisc_1(B,C),A)) = k7_funcop_1(B,k7_funcop_1(C,A)) & k3_funct_5(k7_funcop_1(k2_zfmisc_1(B,C),A)) = k7_funcop_1(C,k7_funcop_1(B,A)) ) ) )).
fof(t5_funct_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,B) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ! [F] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t5_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ~ ( r2_hidden(C,A) & k1_funct_1(B,C) = k5_numbers ) ) ) => ( r1_tarski(A,k1_relset_1(k1_numbers,B)) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k7_xcmplx_0(k1_funct_1(B,C),k1_funct_1(B,k4_xcmplx_0(C))) = 1 ) ) ) ) ) ) )).
fof(t5_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t5_functor0,axiom,( ! [A] : ! [B] : ! [C] : k2_funct_4(k7_funcop_1(k2_zfmisc_1(A,B),C)) = k7_funcop_1(k2_zfmisc_1(B,A),C) )).
fof(t5_functor1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l2_altcat_1(B) ) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t5_functor2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( m2_functor0(C,A,B) => ! [D] : ( m2_functor0(D,A,B) => ( r1_functor2(A,B,C,D) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t5_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t5_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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))) ) => ( k3_xxreal_0(k3_funct_2(A,k1_numbers,C,B),k3_funct_2(A,k1_numbers,D,B)) = k3_funct_2(A,k1_numbers,k1_fuzzy_1(A,C,D),B) & k4_xxreal_0(k3_funct_2(A,k1_numbers,C,B),k3_funct_2(A,k1_numbers,D,B)) = k3_funct_2(A,k1_numbers,k2_fuzzy_1(A,C,D),B) ) ) ) ) ) )).
fof(t5_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,D) => r1_fuzzy_1(k1_fuzzy_2(A,C,D),k1_fuzzy_2(A,C,B)) ) ) ) ) ) )).
fof(t5_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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,k1_fuzzy_4(A,B,k1_fuzzy_4(B,A,C)),C) ) ) ) )).
fof(t5_fvaluat1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( B != k1_xxreal_0 & ~ r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(k5_numbers,k2_extreal1(A,B)) ) ) ) )).
fof(t5_fvsum_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t5_gate_1,axiom,( ! [A] : ! [B] : ( ~ ( ~ 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)) ) ) )).
fof(t5_gate_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ! [Q] : ! [R] : ! [S] : ! [T] : ! [U] : ! [V] : ! [W] : ! [X] : ! [Y] : ! [Z] : ! [A1] : ! [B1] : ! [C1] : ! [D1] : ! [E1] : ! [F1] : ! [G1] : ! [H1] : ! [I1] : ! [J1] : ! [K1] : ! [L1] : ! [M1] : ! [N1] : ~ ( ~ ( ~ v1_xboole_0(A) & v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),k1_gate_1(H1),k1_gate_1(G1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),k1_gate_1(H1),k1_gate_1(G1))) & v1_xboole_0(A) ) & ~ ( ~ v1_xboole_0(B) & v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),k1_gate_1(H1),G1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),k1_gate_1(H1),G1)) & v1_xboole_0(B) ) & ~ ( ~ v1_xboole_0(C) & v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),H1,k1_gate_1(G1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),H1,k1_gate_1(G1))) & v1_xboole_0(C) ) & ~ ( ~ v1_xboole_0(D) & v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),H1,G1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),H1,G1)) & v1_xboole_0(D) ) & ~ ( ~ v1_xboole_0(E) & v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,k1_gate_1(H1),k1_gate_1(G1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,k1_gate_1(H1),k1_gate_1(G1))) & v1_xboole_0(E) ) & ~ ( ~ v1_xboole_0(F) & v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,k1_gate_1(H1),G1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,k1_gate_1(H1),G1)) & v1_xboole_0(F) ) & ~ ( ~ v1_xboole_0(G) & v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,H1,k1_gate_1(G1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,H1,k1_gate_1(G1))) & v1_xboole_0(G) ) & ~ ( ~ v1_xboole_0(H) & v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,H1,G1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,H1,G1)) & v1_xboole_0(H) ) & ~ ( ~ v1_xboole_0(I) & v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),k1_gate_1(H1),k1_gate_1(G1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),k1_gate_1(H1),k1_gate_1(G1))) & v1_xboole_0(I) ) & ~ ( ~ v1_xboole_0(J) & v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),k1_gate_1(H1),G1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),k1_gate_1(H1),G1)) & v1_xboole_0(J) ) & ~ ( ~ v1_xboole_0(K) & v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),H1,k1_gate_1(G1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),H1,k1_gate_1(G1))) & v1_xboole_0(K) ) & ~ ( ~ v1_xboole_0(L) & v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),H1,G1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),H1,G1)) & v1_xboole_0(L) ) & ~ ( ~ v1_xboole_0(M) & v1_xboole_0(k14_gate_1(J1,I1,k1_gate_1(H1),k1_gate_1(G1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(J1,I1,k1_gate_1(H1),k1_gate_1(G1))) & v1_xboole_0(M) ) & ~ ( ~ v1_xboole_0(N) & v1_xboole_0(k14_gate_1(J1,I1,k1_gate_1(H1),G1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(J1,I1,k1_gate_1(H1),G1)) & v1_xboole_0(N) ) & ~ ( ~ v1_xboole_0(O) & v1_xboole_0(k14_gate_1(J1,I1,H1,k1_gate_1(G1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(J1,I1,H1,k1_gate_1(G1))) & v1_xboole_0(O) ) & ~ ( ~ v1_xboole_0(P) & v1_xboole_0(k14_gate_1(J1,I1,H1,G1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(J1,I1,H1,G1)) & v1_xboole_0(P) ) & ~ ( ~ v1_xboole_0(Q) & v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),k1_gate_1(L1),k1_gate_1(K1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),k1_gate_1(L1),k1_gate_1(K1))) & v1_xboole_0(Q) ) & ~ ( ~ v1_xboole_0(R) & v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),k1_gate_1(L1),K1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),k1_gate_1(L1),K1)) & v1_xboole_0(R) ) & ~ ( ~ v1_xboole_0(S) & v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),L1,k1_gate_1(K1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),L1,k1_gate_1(K1))) & v1_xboole_0(S) ) & ~ ( ~ v1_xboole_0(T) & v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),L1,K1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),L1,K1)) & v1_xboole_0(T) ) & ~ ( ~ v1_xboole_0(U) & v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,k1_gate_1(L1),k1_gate_1(K1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,k1_gate_1(L1),k1_gate_1(K1))) & v1_xboole_0(U) ) & ~ ( ~ v1_xboole_0(V) & v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,k1_gate_1(L1),K1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,k1_gate_1(L1),K1)) & v1_xboole_0(V) ) & ~ ( ~ v1_xboole_0(W) & v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,L1,k1_gate_1(K1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,L1,k1_gate_1(K1))) & v1_xboole_0(W) ) & ~ ( ~ v1_xboole_0(X) & v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,L1,K1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,L1,K1)) & v1_xboole_0(X) ) & ~ ( ~ v1_xboole_0(Y) & v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),k1_gate_1(L1),k1_gate_1(K1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),k1_gate_1(L1),k1_gate_1(K1))) & v1_xboole_0(Y) ) & ~ ( ~ v1_xboole_0(Z) & v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),k1_gate_1(L1),K1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),k1_gate_1(L1),K1)) & v1_xboole_0(Z) ) & ~ ( ~ v1_xboole_0(A1) & v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),L1,k1_gate_1(K1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),L1,k1_gate_1(K1))) & v1_xboole_0(A1) ) & ~ ( ~ v1_xboole_0(B1) & v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),L1,K1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),L1,K1)) & v1_xboole_0(B1) ) & ~ ( ~ v1_xboole_0(C1) & v1_xboole_0(k14_gate_1(N1,M1,k1_gate_1(L1),k1_gate_1(K1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(N1,M1,k1_gate_1(L1),k1_gate_1(K1))) & v1_xboole_0(C1) ) & ~ ( ~ v1_xboole_0(D1) & v1_xboole_0(k14_gate_1(N1,M1,k1_gate_1(L1),K1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(N1,M1,k1_gate_1(L1),K1)) & v1_xboole_0(D1) ) & ~ ( ~ v1_xboole_0(E1) & v1_xboole_0(k14_gate_1(N1,M1,L1,k1_gate_1(K1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(N1,M1,L1,k1_gate_1(K1))) & v1_xboole_0(E1) ) & ~ ( ~ v1_xboole_0(F1) & v1_xboole_0(k14_gate_1(N1,M1,L1,K1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(N1,M1,L1,K1)) & v1_xboole_0(F1) ) & ~ ( ~ v1_xboole_0(K1) & v1_xboole_0(k1_gate_1(J1)) ) & ~ ( ~ v1_xboole_0(k1_gate_1(J1)) & v1_xboole_0(K1) ) & ~ ( ~ v1_xboole_0(L1) & v1_xboole_0(G1) ) & ~ ( ~ v1_xboole_0(G1) & v1_xboole_0(L1) ) & ~ ( ~ v1_xboole_0(M1) & v1_xboole_0(H1) ) & ~ ( ~ v1_xboole_0(H1) & v1_xboole_0(M1) ) & ~ ( ~ v1_xboole_0(N1) & v1_xboole_0(I1) ) & ~ ( ~ v1_xboole_0(I1) & v1_xboole_0(N1) ) & ~ ( ~ ( ~ v1_xboole_0(R) & v1_xboole_0(A) ) & ~ ( ~ v1_xboole_0(A) & v1_xboole_0(R) ) & ~ ( ~ v1_xboole_0(T) & v1_xboole_0(B) ) & ~ ( ~ v1_xboole_0(B) & v1_xboole_0(T) ) & ~ ( ~ v1_xboole_0(X) & v1_xboole_0(D) ) & ~ ( ~ v1_xboole_0(D) & v1_xboole_0(X) ) & ~ ( ~ v1_xboole_0(F1) & v1_xboole_0(H) ) & ~ ( ~ v1_xboole_0(H) & v1_xboole_0(F1) ) & ~ ( ~ v1_xboole_0(E1) & v1_xboole_0(P) ) & ~ ( ~ v1_xboole_0(P) & v1_xboole_0(E1) ) & ~ ( ~ v1_xboole_0(C1) & v1_xboole_0(O) ) & ~ ( ~ v1_xboole_0(O) & v1_xboole_0(C1) ) & ~ ( ~ v1_xboole_0(Y) & v1_xboole_0(M) ) & ~ ( ~ v1_xboole_0(M) & v1_xboole_0(Y) ) & ~ ( ~ v1_xboole_0(Q) & v1_xboole_0(I) ) & ~ ( ~ v1_xboole_0(I) & v1_xboole_0(Q) ) & ~ ( ~ v1_xboole_0(V) & v1_xboole_0(C) ) & ~ ( ~ v1_xboole_0(C) & v1_xboole_0(V) ) & ~ ( ~ v1_xboole_0(B1) & v1_xboole_0(F) ) & ~ ( ~ v1_xboole_0(F) & v1_xboole_0(B1) ) & ~ ( ~ v1_xboole_0(W) & v1_xboole_0(L) ) & ~ ( ~ v1_xboole_0(L) & v1_xboole_0(W) ) & ~ ( ~ v1_xboole_0(D1) & v1_xboole_0(G) ) & ~ ( ~ v1_xboole_0(G) & v1_xboole_0(D1) ) & ~ ( ~ v1_xboole_0(A1) & v1_xboole_0(N) ) & ~ ( ~ v1_xboole_0(N) & v1_xboole_0(A1) ) & ~ ( ~ v1_xboole_0(U) & v1_xboole_0(K) ) & ~ ( ~ v1_xboole_0(K) & v1_xboole_0(U) ) & ~ ( ~ v1_xboole_0(Z) & v1_xboole_0(E) ) & ~ ( ~ v1_xboole_0(E) & v1_xboole_0(Z) ) & ~ ( ~ v1_xboole_0(S) & v1_xboole_0(J) ) & ~ ( ~ v1_xboole_0(J) & v1_xboole_0(S) ) ) ) )).
fof(t5_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & l4_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t5_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( m1_genealg1(C,B) => ! [D] : ( m1_genealg1(D,B) => ( r1_xxreal_0(k3_finseq_1(C),A) => k7_genealg1(B,C,D,A) = C ) ) ) ) ) )).
fof(t5_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & k1_geomtrap(A,B,D) = C ) ) ) ) )).
fof(t5_gfacirc1,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( 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)) ) ) ) )).
fof(t5_gfacirc2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ! [G] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t5_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) ) => ( v1_glib_000(A) <=> ( r1_tarski(k5_glib_000,k1_relset_1(k4_ordinal1,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)))) ) ) ) )).
fof(t5_glib_001,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => k1_relset_1(k4_ordinal1,k15_finseq_1(C)) = k1_relset_1(k4_ordinal1,k14_finseq_1(k1_relset_1(k4_ordinal1,C))) ) ) )).
fof(t5_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ( ? [B] : ( m1_subset_1(B,k6_glib_000(A)) & ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ? [D] : ( m3_glib_001(D,A) & r1_glib_001(A,B,C,D) ) ) ) => v1_glib_002(A) ) ) )).
fof(t5_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(t5_glib_004,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : ( r2_hidden(D,A) => r1_xxreal_0(k1_funct_1(B,D),k1_funct_1(C,D)) ) => r1_xxreal_0(k2_uproots(A,B),k2_uproots(A,C)) ) ) ) )).
fof(t5_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) & v7_glib_003(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t5_goboard1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r2_hidden(C,k2_finseq_1(k1_matrix_0(D))) & r2_hidden(A,k4_finseq_1(D)) & r2_hidden(B,k2_finseq_1(k1_matrix_0(k16_matrix_0(C,u1_struct_0(k15_euclid(2)),D)))) ) => ( r1_xxreal_0(k1_matrix_0(D),1) | k3_matrix_0(u1_struct_0(k15_euclid(2)),k16_matrix_0(C,u1_struct_0(k15_euclid(2)),D),A,B) = k1_funct_1(k2_finseq_3(C,k7_matrix_0(u1_struct_0(k15_euclid(2)),D,A)),B) ) ) ) ) ) ) )).
fof(t5_goboard2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(k8_finseq_1(u1_struct_0(k15_euclid(2)),A,B))) & k1_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) ) ) ) ) ) ) )).
fof(t5_goboard4,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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_funct_1(k1_goboard1(A),1),k1_funct_1(k1_goboard1(A),k3_finseq_1(A))) & r1_goboard4(k1_goboard1(B),k1_funct_1(k1_goboard1(A),1),k1_funct_1(k1_goboard1(A),k3_finseq_1(A))) & r1_goboard4(k2_goboard1(A),k1_funct_1(k2_goboard1(B),1),k1_funct_1(k2_goboard1(B),k3_finseq_1(B))) & r1_goboard4(k2_goboard1(B),k1_funct_1(k2_goboard1(B),1),k1_funct_1(k2_goboard1(B),k3_finseq_1(B))) & r1_xboole_0(k3_topreal1(2,A),k3_topreal1(2,B)) ) ) ) )).
fof(t5_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( v2_goboard1(C) & r1_xxreal_0(1,B) & r1_xxreal_0(1,A) & r1_xxreal_0(A,k3_finseq_1(C)) ) => ( r1_xxreal_0(k1_matrix_0(C),B) | k2_goboard5(C,B) = a_3_0_goboard5(A,B,C) ) ) ) ) ) )).
fof(t5_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( r2_hidden(B,k1_tops_1(k15_euclid(A),C)) <=> ? [D] : ( v1_xreal_0(D) & ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k8_metric_1(k14_euclid(A),B,D),C) ) ) ) ) ) )).
fof(t5_goboard7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r2_hidden(C,k1_rltopsp1(k15_euclid(2),A,B)) & k17_euclid(A) = k17_euclid(B) ) => k17_euclid(C) = k17_euclid(B) ) ) ) ) )).
fof(t5_goboard8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,2),k3_finseq_1(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,2),k3_finseq_1(k2_goboard2(A))) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,2),k1_matrix_0(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_nat_1(D,1)) ) => ( ( ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,k1_nat_1(D,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_nat_1(D,2)) ) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,k1_nat_1(D,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,2),k1_nat_1(D,1))),k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_nat_1(D,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,2),k1_nat_1(D,2))),k7_xcmplx_0(1,2))),k3_topreal1(2,A)) ) ) ) ) ) ) ) )).
fof(t5_goboard9,axiom,( ! [A] : ( ( v1_convex1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( ( v1_convex1(B,k15_euclid(2)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => v1_convex1(k9_subset_1(u1_struct_0(k15_euclid(2)),A,B),k15_euclid(2)) ) ) )).
fof(t5_gobrd10,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r1_xxreal_0(B,A) & r1_xxreal_0(C,A) & ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ~ ( k1_funct_1(D,1) = B & k1_funct_1(D,k3_finseq_1(D)) = C & k3_finseq_1(D) = k1_nat_1(k1_nat_1(k7_nat_d(B,C),k7_nat_d(C,B)),1) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ( 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] : ( m1_subset_1(E,k4_ordinal1) => ~ ( r1_xxreal_0(1,E) & ~ r1_xxreal_0(k3_finseq_1(D),E) & k1_funct_1(D,k1_nat_1(E,1)) != k1_nat_1(k7_partfun1(k4_ordinal1,D,E),1) & k1_funct_1(D,E) != k1_nat_1(k7_partfun1(k4_ordinal1,D,k1_nat_1(E,1)),1) ) ) ) ) ) ) ) ) )).
fof(t5_gobrd11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t5_gobrd12,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t5_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_tarski(k9_matrix_0(D),k9_matrix_0(E)) & r2_hidden(k4_tarski(A,C),k2_matrix_0(D)) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(E)) & k3_matrix_0(u1_struct_0(k15_euclid(2)),D,A,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,B,k1_matrix_0(E)) ) => C = k1_matrix_0(D) ) ) ) ) ) ) )).
fof(t5_gobrd14,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r2_hidden(k4_tarski(A,B),k2_matrix_0(D)) & r2_hidden(k4_tarski(k2_xcmplx_0(A,C),B),k2_matrix_0(D)) ) => k1_topreal6(2,k3_matrix_0(u1_struct_0(k15_euclid(2)),D,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),D,k2_xcmplx_0(A,C),B)) = k6_xcmplx_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,k2_xcmplx_0(A,C),B)),k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,A,B))) ) ) ) ) ) )).
fof(t5_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)))) ) ) ) ) ) )).
fof(t5_gr_cy_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_struct_0(k5_group_4(A,k6_domain_1(u1_struct_0(A),B)),C) <=> ? [D] : ( v1_int_1(D) & C = k5_group_1(A,D,B) ) ) ) ) ) )).
fof(t5_gr_cy_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( v1_int_1(D) & C = k5_group_1(A,D,B) ) ) <=> A = k5_group_4(A,k6_domain_1(u1_struct_0(A),B)) ) ) ) )).
fof(t5_gr_cy_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_gr_cy_3(A) ) => ( A != 5 => k4_nat_d(A,4) = 3 ) ) )).
fof(t5_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ( r4_graph_1(B,A) => ( r1_relset_1(u4_struct_0(B),u1_struct_0(B),u1_graph_1(B),u1_graph_1(A)) & r1_relset_1(u4_struct_0(B),u1_struct_0(B),u2_graph_1(B),u2_graph_1(A)) ) ) ) ) )).
fof(t5_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v2_funct_1(B) & m2_graph_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( v2_funct_1(k2_graph_2(u4_struct_0(A),B,D,C)) & m2_graph_1(k2_graph_2(u4_struct_0(A),B,D,C),A) ) ) ) ) ) )).
fof(t5_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t5_graph_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r1_xxreal_0(1,B) & ~ r1_xxreal_0(C,B) & r1_xxreal_0(C,k3_finseq_1(A)) & k1_funct_1(A,B) = k1_funct_1(A,C) ) ) ) <=> k5_card_1(k10_xtuple_0(A)) = k3_finseq_1(A) ) ) )).
fof(t5_graphsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t5_grcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => u1_struct_0(k5_grcat_1(A,B)) = B ) ) )).
fof(t5_grfunc_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(k1_tarski(k4_tarski(A,B))) & v1_funct_1(k1_tarski(k4_tarski(A,B))) ) )).
fof(t5_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t5_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => k3_polynom1(k15_pre_poly(A),B,k5_vfunct_1(k15_pre_poly(A),B,C)) = k3_polynom1(k15_pre_poly(A),B,C) ) ) ) )).
fof(t5_groeb_2,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(t5_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t5_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( k6_algstr_0(A,C,B) = k1_group_1(A) & k6_algstr_0(A,B,C) = k1_group_1(A) ) => B = k2_group_1(A,C) ) ) ) ) )).
fof(t5_group_10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t5_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) )).
fof(t5_group_12,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_group_7(A,B))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t5_group_14,axiom,( ! [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) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k4_prvect_3(A,B))) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & C = k1_domain_1(u1_struct_0(A),u1_struct_0(B),D,E) ) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(k4_prvect_3(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_prvect_3(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( 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(k4_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(k4_prvect_3(A,B)) = k1_domain_1(u1_struct_0(A),u1_struct_0(B),k4_struct_0(A),k4_struct_0(B)) & ! [C] : ( m1_subset_1(C,u1_struct_0(k4_prvect_3(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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(k4_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)) ) ) ) ) ) ) ) )).
fof(t5_group_2,axiom,( ! [A] : ( ( ~ 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 ) )).
fof(t5_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t5_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t5_group_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_group_2(C,B) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(B)) & ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t5_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t5_group_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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] : ~ ( r2_hidden(D,A) & ! [E] : ( ( ~ 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)) ) ) ) )).
fof(t5_group_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( C = D & v8_struct_0(A) ) => k6_group_1(B,C) = k6_group_1(A,D) ) ) ) ) ) )).
fof(t5_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => r1_struct_0(C,k1_group_1(B)) ) ) )).
fof(t5_groupp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_group_1(A,k2_group_1(A,B)) = k6_group_1(A,B) ) ) )).
fof(t5_hahnban,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ( r1_rlsub_2(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t5_hahnban1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k3_rlvect_1(k1_complfld,k1_hahnban1(A,B),k1_hahnban1(C,D)) = k1_hahnban1(k2_xcmplx_0(A,C),k2_xcmplx_0(B,D)) ) ) ) ) )).
fof(t5_hallmar1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k4_finseq_1(B)) => k1_hallmar1(A,B,k1_tarski(C)) = k1_funct_1(B,C) ) ) ) ) )).
fof(t5_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [C] : ( r2_hidden(C,B) => k1_funct_1(k6_weierstr(A,B),C) = k5_numbers ) ) ) )).
fof(t5_helly,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t5_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t5_hermitan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ( A = k2_complfld(A) => k4_complex1(A) = k5_numbers ) ) )).
fof(t5_hessenbe,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_collsp(A,B,C,D) ) ) ) ) )).
fof(t5_heyting1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k12_normform(A))) => ! [C] : ( r1_tarski(C,B) => m1_subset_1(C,u1_struct_0(k12_normform(A))) ) ) )).
fof(t5_heyting2,axiom,( ! [A] : ! [B] : ! [C] : ( m2_subset_1(C,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B)) => ! [D] : ( m2_subset_1(D,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B)) => ( ! [E] : ~ ( r2_hidden(E,C) & ! [F] : ~ ( r2_hidden(F,D) & r1_tarski(F,E) ) ) => k3_substlat(A,B,k4_substlat(A,B,C,D)) = C ) ) ) )).
fof(t5_heyting3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_domain_1(k4_ordinal1,A)))) ) => ? [C] : ( m1_subset_1(C,k4_ordinal1) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( r1_xxreal_0(C,D) & r2_hidden(k1_domain_1(k4_ordinal1,k4_ordinal1,D,A),B) ) ) ) ) ) )).
fof(t5_hfdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => 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,k2_xcmplx_0(B,C))) ) ) ) )).
fof(t5_hilbasis,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t5_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => r2_hidden(k3_hilbert1(k4_hilbert1(B,C),B),k5_hilbert1(A)) ) ) ) )).
fof(t5_hilbert2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_trees_1(C) ) => ( r2_hidden(k9_finseq_1(A),k13_trees_3(B,C)) <=> ( A = k5_numbers | A = 1 ) ) ) ) )).
fof(t5_hilbert3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ ( C = k1_xboole_0 & B != k1_xboole_0 & A != k1_xboole_0 ) => ! [D] : ( ( 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)))) ) => k1_funct_6(D) = k7_funcop_1(A,B) ) ) )).
fof(t5_holder_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( k2_xcmplx_0(k7_xcmplx_0(1,C),k7_xcmplx_0(1,D)) = 1 & r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => ( r1_xxreal_0(C,1) | ( r1_xxreal_0(k3_xcmplx_0(A,B),k2_xcmplx_0(k7_xcmplx_0(k2_power(A,C),C),k7_xcmplx_0(k2_power(B,D),D))) & ( k3_xcmplx_0(A,B) = k2_xcmplx_0(k7_xcmplx_0(k2_power(A,C),C),k7_xcmplx_0(k2_power(B,D),D)) => k2_power(A,C) = k2_power(B,D) ) & ( k2_power(A,C) = k2_power(B,D) => k3_xcmplx_0(A,B) = k2_xcmplx_0(k7_xcmplx_0(k2_power(A,C),C),k7_xcmplx_0(k2_power(B,D),D)) ) ) ) ) ) ) ) ) )).
fof(t5_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( 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))) ) ) ) ) ) ) )).
fof(t5_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(C,A) & ~ r1_xxreal_0(C,B) & v1_int_2(C) & k4_nat_d(k3_xcmplx_0(A,B),C) = k5_numbers ) ) ) ) )).
fof(t5_ideal_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t5_incproj,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k3_incproj(A))) => ! [C] : ( m1_subset_1(C,u2_incsp_1(k3_incproj(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_incproj(E,A) => ( ( B = D & C = E ) => ( r1_incsp_1(k3_incproj(A),B,C) <=> r2_hidden(D,E) ) ) ) ) ) ) ) )).
fof(t5_incsp_1,axiom,( ! [A] : ( l2_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t5_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m3_index_1(B,u1_struct_0(A),u4_struct_0(A),u1_graph_1(A),u2_graph_1(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t5_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( l3_msualg_1(D,A) => ! [E] : ( 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] : ( m2_pboole(F,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [G] : ( 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] : ( 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] : ( m1_subset_1(I,k3_msualg_1(A,H,B)) & ? [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t5_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r1_xxreal_0(B,A) => r2_hidden(k6_xcmplx_0(A,B),k4_ordinal1) ) ) ) )).
fof(t5_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( ( A = k5_numbers & B = k5_numbers ) <=> k3_int_2(A,B) = k5_numbers ) ) ) )).
fof(t5_int_3,axiom,( ! [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) & l6_algstr_0(A) ) => v1_int_3(A) ) )).
fof(t5_int_4,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( v1_xreal_0(B) => ( B != k5_numbers => k1_card_1(A) = k1_card_1(k1_integra2(A,B)) ) ) ) )).
fof(t5_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t5_int_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r1_int_1(A,k3_xcmplx_0(D,k1_newton(B,C))) => ( A = B | r1_int_1(A,D) ) ) ) ) ) ) )).
fof(t5_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(B,1) & r1_int_2(A,B) & A = k5_numbers ) ) ) )).
fof(t5_integr10,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_tarski(k3_integra5(B,C),k1_relset_1(k1_numbers,A)) & r1_integr10(A,B,C) ) => ( r1_xxreal_0(C,B) | ! [D] : ( v1_xreal_0(D) => ( 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) = k3_xcmplx_0(D,k1_integr10(A,B,C)) ) ) ) ) ) ) ) )).
fof(t5_integr11,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( k2_xcmplx_0(B,A) != k5_numbers & k6_xcmplx_0(B,A) != k5_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(k2_xcmplx_0(B,A),k5_numbers),k16_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k2_xcmplx_0(B,A)))),k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k6_xcmplx_0(B,A),k5_numbers),k16_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k6_xcmplx_0(B,A))))),k1_numbers) & ! [C] : ( v1_xreal_0(C) => k1_funct_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(k2_xcmplx_0(B,A),k5_numbers),k16_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k2_xcmplx_0(B,A)))),k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k6_xcmplx_0(B,A),k5_numbers),k16_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k6_xcmplx_0(B,A))))),k1_numbers),C) = k3_xcmplx_0(k1_funct_1(k18_sin_cos,k3_xcmplx_0(B,C)),k1_funct_1(k18_sin_cos,k3_xcmplx_0(A,C))) ) ) ) ) ) )).
fof(t5_integr12,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k22_sin_cos,k3_rfunct_1(k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)),k3_rfunct_1(k1_numbers,k1_numbers,k22_sin_cos,k41_valued_1(k1_numbers,k1_numbers,k18_sin_cos)))) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k26_sin_cos),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k26_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t5_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k18_sin_cos,k16_sin_cos)) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k16_sin_cos),A)) ) => k2_integra5(A,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k16_sin_cos)) = k6_xcmplx_0(k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),k2_seq_4(A)),k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),k3_seq_4(A))) ) ) ) )).
fof(t5_integr14,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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_funct_1(k27_sin_cos,B) ) ) ) ) ) )).
fof(t5_integr15,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_integra1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) ) => ! [D] : ( m2_integr15(D,A,B,C) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( v2_seq_2(k2_partfun1(A,k1_numbers,B,A)) => r1_xxreal_0(k3_funct_2(k4_ordinal1,k1_numbers,k4_integra2(A,B,C),E),k3_funct_2(k4_ordinal1,k1_numbers,k3_integr15(A,B,C,D),E)) ) ) ) ) ) ) )).
fof(t5_integr16,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( 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))) ) ) )).
fof(t5_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(t5_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ( ( r1_xxreal_0(B,D) & r1_xxreal_0(D,E) & r1_xxreal_0(E,C) & r1_tarski(k3_integra5(B,C),k1_relset_1(k1_numbers,F)) & r1_tarski(k3_integra5(B,C),k1_relset_1(k1_numbers,G)) ) => r1_tarski(k3_integra5(D,E),k1_relset_1(k1_numbers,k8_integr15(A,k1_numbers,F,G))) ) ) ) ) ) ) ) ) )).
fof(t5_integra1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( m1_integra1(C,B) => ( r2_hidden(A,k4_finseq_1(C)) => ( A = 1 | ( r2_hidden(k6_xcmplx_0(A,1),k4_finseq_1(C)) & r2_hidden(k1_funct_1(C,k6_xcmplx_0(A,1)),B) & r2_hidden(k6_xcmplx_0(A,1),k4_ordinal1) ) ) ) ) ) ) )).
fof(t5_integra2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t5_integra3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => ! [C] : ( m1_integra1(C,A) => ( ~ r1_xxreal_0(k2_xxreal_2(k1_rvsum_1(k4_integra1(A,k7_rfunct_1(A,A),B))),k1_integra3(A,C)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ( r2_hidden(F,k4_finseq_1(C)) & r2_hidden(D,k9_subset_1(k1_numbers,k1_rvsum_1(B),k2_integra1(A,C,F))) & r2_hidden(E,k9_subset_1(k1_numbers,k1_rvsum_1(B),k2_integra1(A,C,F))) ) => D = E ) ) ) ) ) ) ) ) )).
fof(t5_integra4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ? [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))) & k1_rvsum_1(C) = k1_seq_4(B) & v1_comseq_2(k2_partfun1(A,k1_numbers,C,A)) ) ) ) )).
fof(t5_integra5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( ~ 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))) ) ) ) )).
fof(t5_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => k3_integra1(k3_integra5(A,B)) = k6_xcmplx_0(B,A) ) ) ) )).
fof(t5_integra7,axiom,( ! [A] : ! [B] : ( ( 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) ) ) )).
fof(t5_integra8,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k5_numbers,k17_sin_cos(k7_xcmplx_0(A,2))) => k17_sin_cos(k7_xcmplx_0(A,2)) = k3_square_1(k7_xcmplx_0(k6_xcmplx_0(1,k19_sin_cos(A)),2)) ) ) )).
fof(t5_integra9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( A != k5_numbers => k2_integra5(B,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,k5_numbers),k16_sin_cos)) = k6_xcmplx_0(k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,k5_numbers),k18_sin_cos),k4_xcmplx_0(k7_xcmplx_0(1,A))),k2_seq_4(B)),k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,k5_numbers),k18_sin_cos),k4_xcmplx_0(k7_xcmplx_0(1,A))),k3_seq_4(B))) ) ) ) )).
fof(t5_interva1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( k1_interva1(A,B,C) != k1_xboole_0 => r1_tarski(B,C) ) ) ) )).
fof(t5_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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)) ) ) ) )).
fof(t5_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k4_newton(k1_nat_1(A,1),B) = k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(B,A),k1_nat_1(A,1)),k4_newton(A,B)) ) ) )).
fof(t5_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ( v12_cat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ? [E] : ( m1_subset_1(E,u4_struct_0(A)) & k3_funct_2(u4_struct_0(A),u4_struct_0(B),C,E) = D ) ) ) ) ) ) )).
fof(t5_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_nattra_1(A,B))) <=> m2_cat_1(C,A,B) ) ) ) )).
fof(t5_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_tops_1(B,A) <=> ( v2_isomichi(B,A) & v1_isomichi(B,A) ) ) ) ) )).
fof(t5_jct_misc,axiom,( ! [A] : ( ( v1_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => v1_rcomp_1(k9_subset_1(k1_numbers,A,B)) ) ) )).
fof(t5_jgraph_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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))) ) ) ) ) )).
fof(t5_jgraph_2,axiom,( k17_euclid(k22_euclid(2)) = 1 & k18_euclid(k22_euclid(2)) = 1 )).
fof(t5_jgraph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( v1_xreal_0(D) & k3_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),B,C) = D & r1_xxreal_0(k5_numbers,D) ) ) & ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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_square_1(E) ) ) ) & v5_pre_topc(C,A,k3_topmetr) ) ) ) ) ) )).
fof(t5_jgraph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( v5_pre_topc(B,A,k3_topmetr) & v5_pre_topc(C,A,k3_topmetr) & E != k5_numbers & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,F) != k5_numbers ) & ! [F] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( v1_xreal_0(H) => ! [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) = k3_xcmplx_0(I,k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(H,I),D),E)) ) ) ) ) & v5_pre_topc(F,A,k3_topmetr) ) ) ) ) ) ) ) ) )).
fof(t5_jgraph_5,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_pre_topc(C) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t5_jgraph_6,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_pre_topc(C) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t5_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t5_jgraph_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(k17_borsuk_1)) => ! [H] : ( m1_subset_1(H,u1_struct_0(k17_borsuk_1)) => ~ ( G = k5_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] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t5_jordan,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( ( 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)) ) ) )).
fof(t5_jordan1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t5_jordan10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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,k2_jordan9(B,A))) ) ) )).
fof(t5_jordan11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_jordan1h(B,A) => r1_xxreal_0(k5_jordan11(B,A),k1_nat_1(k2_nat_1(k11_newton(2,k7_nat_d(A,k3_jordan11(B))),k7_nat_d(k4_jordan11(B),2)),2)) ) ) ) )).
fof(t5_jordan12,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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))) ) ) )).
fof(t5_jordan14,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t5_jordan15,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( ( 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_0(A)) ) => r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,E),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,F)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,C),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,D))) ) ) ) ) ) ) ) )).
fof(t5_jordan16,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ( r1_jordan5c(A,B,C,D,E) => ( r2_hidden(D,k5_jordan6(A,B,C,D,E)) & r2_hidden(E,k5_jordan6(A,B,C,D,E)) ) ) ) ) ) ) ) )).
fof(t5_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r1_jordan6(A,B,k18_pscomp_1(A)) => r2_hidden(B,k9_jordan6(A)) ) ) ) )).
fof(t5_jordan18,axiom,( ! [A] : ( 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))) ) )).
fof(t5_jordan19,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ~ ( r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),C),k9_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(k1_jordan8(B,k1_nat_1(A,1)))) & r2_subset_1(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,1),k1_jordan1a(k1_jordan8(B,1)),k1_matrix_0(k1_jordan8(B,1))),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),C)),k8_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) ) ) ) ) )).
fof(t5_jordan1b,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => k19_pscomp_1(A) != k22_pscomp_1(A) ) )).
fof(t5_jordan1c,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) ) )).
fof(t5_jordan1e,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v4_topreal1(A) => ! [B] : ( 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,k1_nat_1(k1_jordan3(A,B),1),k3_finseq_1(A)))) ) ) ) ) )).
fof(t5_jordan1f,axiom,( ! [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] : ( v7_ordinal1(B) => k7_partfun1(u1_struct_0(k15_euclid(2)),k1_jordan1e(A,B),1) = k18_pscomp_1(k3_topreal1(2,k2_jordan9(A,B))) ) ) )).
fof(t5_jordan1g,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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)) ) ) )).
fof(t5_jordan1h,axiom,( k1_relat_1(k1_jordan1h) = k1_numbers )).
fof(t5_jordan1i,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) ) )).
fof(t5_jordan1j,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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)))) ) => ( r2_hidden(k18_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))),k10_xtuple_0(k1_jordan1e(B,A))) & r2_hidden(k18_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))),k3_topreal1(2,k1_jordan1e(B,A))) ) ) ) )).
fof(t5_jordan1k,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(t5_jordan20,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v1_xreal_0(D) => ~ ( 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) ) ) ) ) ) )).
fof(t5_jordan22,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => r2_hidden(k1_domain_1(k4_ordinal1,k4_ordinal1,1,1),k2_matrix_0(k1_jordan8(A,B))) ) ) )).
fof(t5_jordan23,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ( v2_jordan23(B) <=> ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,C) & ~ r1_xxreal_0(k3_finseq_1(B),C) & k7_partfun1(A,B,C) = k7_partfun1(A,B,k1_nat_1(C,1)) ) ) ) ) )).
fof(t5_jordan24,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xreal_0(B) => k2_complex2(A,k4_xcmplx_0(B)) = k2_complex2(A,k6_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B)) ) ) )).
fof(t5_jordan2b,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k2_finseq_1(A)) => k7_partfun1(k1_numbers,k3_rlvect_1(k15_euclid(A),B,C),D) = k3_real_1(k7_partfun1(k1_numbers,B,D),k7_partfun1(k1_numbers,C,D)) ) ) ) ) ) )).
fof(t5_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)))) ) ) ) ) )).
fof(t5_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( 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)) ) ) ) )).
fof(t5_jordan4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t5_jordan5a,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( r2_hidden(A,k2_pcomps_1(k7_metric_1)) <=> v3_rcomp_1(A) ) ) )).
fof(t5_jordan5c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t5_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(A)) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k1_matrix_0(k2_goboard2(A))) ) => ( r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),1,B)),k17_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),A,C))) & r1_xxreal_0(k17_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),A,C)),k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k3_finseq_1(k2_goboard2(A)),B))) ) ) ) ) ) )).
fof(t5_jordan6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t5_jordan7,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t5_jordan9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( m2_finseq_1(C,A) => ( r1_goboard1(A,C,B) <=> r1_goboard1(A,k4_finseq_5(A,C),B) ) ) ) ) )).
fof(t5_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t5_knaster,axiom,( ! [A] : ! [B] : ( ( 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) ) )).
fof(t5_kolmog01,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(B)) ) => m1_dynkin(k1_kolmog01(A,B,D,C),A) ) ) ) ) )).
fof(t5_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( r2_hidden(C,k4_kurato_0(A,B)) <=> ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & r2_hidden(C,k1_funct_1(B,k2_xcmplx_0(D,E))) ) ) ) ) )).
fof(t5_kurato_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) )).
fof(t5_kurato_2,axiom,( ! [A] : ( ( ~ 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))) ) ) )).
fof(t5_lang1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => ! [B] : ( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ! [C] : ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t5_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),B,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(A,k2_finseq_1(k1_matrix_0(D))) => k1_matrix_0(k18_matrix_0(E,A,B,u1_struct_0(C),D)) = k7_nat_d(B,1) ) ) ) ) ) ) )).
fof(t5_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t5_latsum_1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ! [D] : ( ( 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)) ) ) ) )).
fof(t5_lattice2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(B,A) => k1_funct_4(A,B) = A ) ) ) )).
fof(t5_lattice3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k1_lattice3(A))) => k7_lattices(k1_lattice3(A),B) = k6_subset_1(A,B) ) )).
fof(t5_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t5_lattice5,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k2_msualg_5(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_msualg_5(A))) => ( r3_lattices(k2_msualg_5(A),B,C) <=> r1_tarski(B,C) ) ) ) )).
fof(t5_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ~ r1_lattice6(A,B,k6_lattices(A)) ) ) )).
fof(t5_lattice7,axiom,( ! [A] : ( ( 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] : ( ( v6_orders_2(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t5_lattice8,axiom,( ! [A] : ( ( 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] : ( ( 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) ) ) ) )).
fof(t5_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_lattices(A) & l2_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r1_lattices(A,B,C) & r1_lattices(A,C,D) ) => r1_lattices(A,B,D) ) ) ) ) ) )).
fof(t5_lexbfs,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,A) => k1_finsub_1(k1_zfmisc_1(k4_ordinal1),k2_finsub_1(k1_zfmisc_1(k4_ordinal1),k2_finseq_1(B),k2_finseq_1(k7_nat_d(B,A))),k6_domain_1(k4_ordinal1,k7_nat_d(B,A))) = k2_finsub_1(k1_zfmisc_1(k4_ordinal1),k2_finseq_1(B),k2_finseq_1(k7_nat_d(B,k1_nat_1(A,1)))) ) ) ) )).
fof(t5_lfuzzy_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_lfuzzy_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k12_lattice3(A,B,C) = k3_lfuzzy_0(A,B,C) ) ) ) )).
fof(t5_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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) ) ) ) ) ) )).
fof(t5_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( v2_comseq_2(A) & ~ r1_xxreal_0(k1_seq_2(A),k5_numbers) & ! [B] : ( v7_ordinal1(B) => ? [C] : ( v7_ordinal1(C) & r1_xxreal_0(B,C) & r1_xxreal_0(k1_funct_1(A,C),k7_xcmplx_0(k1_seq_2(A),2)) ) ) ) ) )).
fof(t5_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [D] : ( v7_ordinal1(D) => ( ~ r1_xxreal_0(k1_funct_1(B,D),k6_xcmplx_0(A,k7_xcmplx_0(1,k1_nat_1(D,1)))) & ~ r1_xxreal_0(A,k1_funct_1(B,D)) & r2_hidden(k1_funct_1(B,D),k1_relset_1(k1_numbers,C)) ) ) => ( v2_comseq_2(B) & k1_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))) ) ) ) ) ) )).
fof(t5_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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(k6_xcmplx_0(B,A),B),k2_rcomp_1(B,k2_xcmplx_0(B,A))),k9_xtuple_0(C)) => ( r1_xxreal_0(A,k5_numbers) | ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(B,D) & ~ r1_xxreal_0(E,B) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t5_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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)) ) ) ) )).
fof(t5_lmod_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t5_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => C = k4_struct_0(A) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => C = k4_struct_0(B) ) ) ) ) ) )).
fof(t5_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t5_lopban_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( 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) ) ) ) )).
fof(t5_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t5_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_rsspace3(B,A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(D,E) & r1_xxreal_0(C,k2_normsp_0(A,k5_algstr_0(A,k5_rsspace3(A,B,E),k5_rsspace3(A,B,D)))) ) ) ) ) ) ) ) )).
fof(t5_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_normsp_1(C,A) => v3_normsp_1(k3_lopban_3(A,C,B),A) ) ) ) ) )).
fof(t5_lopban_5,axiom,( ! [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) & v3_lopban_1(A) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k16_lopban_1(A,B)))) => ~ ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( v1_xreal_0(E) & r1_xxreal_0(k5_numbers,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(k16_lopban_1(A,B))) => ( r2_hidden(F,C) => r1_xxreal_0(k2_normsp_0(B,k17_lopban_1(A,B,F,D)),E) ) ) ) ) & ! [D] : ( v1_xreal_0(D) => ~ ( r1_xxreal_0(k5_numbers,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(k16_lopban_1(A,B))) => ( r2_hidden(E,C) => r1_xxreal_0(k2_normsp_0(k16_lopban_1(A,B),E),D) ) ) ) ) ) ) ) ) )).
fof(t5_lopban_6,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( v1_xreal_0(E) => 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) ) ) ) ) ) )).
fof(t5_lopban_7,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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)))) ) => ( r3_nfcont_1(A,B,C,u1_struct_0(A)) <=> r1_nfcont_1(A,B,C,k4_struct_0(A)) ) ) ) ) )).
fof(t5_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(g3_lattices(k1_lopclset(A),k4_lopclset(A),k5_lopclset(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(g3_lattices(k1_lopclset(A),k4_lopclset(A),k5_lopclset(A)))) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k1_lopclset(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t5_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => m1_rlsub_1(g1_rlvect_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A))),k6_rsspace) ) ) )).
fof(t5_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_rfunct_3(B,A,k2_numbers,k3_rfunct_3(A,k2_numbers)) => ! [C] : ( m2_rfunct_3(C,A,k2_numbers,k3_rfunct_3(A,k2_numbers)) => ! [D] : ( m2_rfunct_3(D,A,k2_numbers,k3_rfunct_3(A,k2_numbers)) => ( r2_relset_1(A,k2_numbers,D,k2_lpspace1(A,k2_numbers,k7_lpspacc1(A),B,C)) <=> ( k1_relset_1(A,D) = k9_subset_1(A,k1_relset_1(A,B),k1_relset_1(A,C)) & ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,k1_relset_1(A,D)) => k1_funct_1(D,E) = k3_xcmplx_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) ) ) )).
fof(t5_lpspace1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( ~ 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] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(g1_rlvect_1(B,k10_subset_1(k4_struct_0(A),B),k1_ideal_1(A,B),k1_lpspace1(A,B)))) => ( E = D => k1_rlvect_1(g1_rlvect_1(B,k10_subset_1(k4_struct_0(A),B),k1_ideal_1(A,B),k1_lpspace1(A,B)),E,C) = k1_rlvect_1(A,D,C) ) ) ) ) ) ) )).
fof(t5_lpspace2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => ( r1_xxreal_0(C,k5_numbers) | k2_power(k3_xcmplx_0(A,B),C) = k3_xcmplx_0(k2_power(A,C),k2_power(B,C)) ) ) ) ) ) )).
fof(t5_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => ( k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(C),k1_domain_1(k4_ordinal1,k1_hilbert1,B,k1_ltlaxio1(A))) = 1 <=> k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(C),k1_domain_1(k4_ordinal1,k1_hilbert1,B,A)) = k5_ordinal1 ) ) ) ) )).
fof(t5_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k1_hilbert1,k6_margrel1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_hilbert1,k6_margrel1))) ) => k3_funct_2(k1_hilbert1,k6_margrel1,k12_ltlaxio1(C),k5_ltlaxio1(A,B)) = k5_xboolean(k3_funct_2(k1_hilbert1,k6_margrel1,k12_ltlaxio1(C),A),k3_funct_2(k1_hilbert1,k6_margrel1,k12_ltlaxio1(C),B)) ) ) ) )).
fof(t5_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ( ~ v2_hilbert2(A) => k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,A) = k6_domain_1(k1_hilbert1,A) ) ) )).
fof(t5_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(C),k1_domain_1(k4_ordinal1,k1_hilbert1,D,k4_hilbert1(A,B))) = 1 <=> ? [E] : ( m1_subset_1(E,k4_ordinal1) & ~ r1_xxreal_0(E,D) & k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(C),k1_domain_1(k4_ordinal1,k1_hilbert1,E,B)) = 1 & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( ~ r1_xxreal_0(F,D) & ~ r1_xxreal_0(E,F) & k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(C),k1_domain_1(k4_ordinal1,k1_hilbert1,F,A)) != 1 ) ) ) ) ) ) ) ) )).
fof(t5_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => r2_hidden(k8_cqc_lang(A,C,k8_cqc_lang(A,B,C)),k4_cqc_the1(A)) ) ) ) )).
fof(t5_margrel1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => m1_margrel1(k1_xboole_0,A) ) )).
fof(t5_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( 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 ) ) )).
fof(t5_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => k2_matrix_0(B) = k2_matrix_0(k3_matrix10(A,B)) ) ) )).
fof(t5_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_matrix_2(C,k3_matrix_2(k1_nat_1(A,2))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t5_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [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] : ( m1_subset_1(G,u1_struct_0(F)) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,u1_struct_0(F),C,D) & m2_finseq_1(H,k3_finseq_2(u1_struct_0(F))) ) => ! [I] : ( ( v1_matrix_0(I) & v2_matrix_0(I,u1_struct_0(F),C,D) & m2_finseq_1(I,k3_finseq_2(u1_struct_0(F))) ) => ( ( r2_hidden(B,k4_finseq_1(H)) & r2_hidden(A,k4_finseq_1(H)) & r2_hidden(E,k4_finseq_1(H)) & I = k3_matrix12(C,D,F,H,B,A,G) ) => ( ( E = B => k7_matrix_0(u1_struct_0(F),I,E) = k4_fvsum_1(k1_matrix_0(H),F,k10_fvsum_1(k1_matrix_0(H),F,k7_matrix_0(u1_struct_0(F),H,A),G),k7_matrix_0(u1_struct_0(F),H,B)) ) & ( E != B => k7_matrix_0(u1_struct_0(F),I,E) = k7_matrix_0(u1_struct_0(F),H,E) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t5_matrix14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t5_matrix15,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t5_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( ~ v1_xboole_0(F) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,F,D,D) & m2_finseq_1(G,k3_finseq_2(F)) ) => ( ( v1_matrix16(G,F) & r2_hidden(k4_tarski(A,B),k2_zfmisc_1(k2_finseq_1(D),k2_finseq_1(D))) & C = k2_xcmplx_0(A,1) & E = k2_xcmplx_0(B,1) ) => ( r1_xxreal_0(D,A) | r1_xxreal_0(D,B) | k3_matrix_0(F,G,A,B) = k3_matrix_0(F,G,C,E) ) ) ) ) ) ) ) ) ) )).
fof(t5_matrix17,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(B),A,A) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(B))) ) => ( ( r1_matrix17(u1_struct_0(B),E,C) & r1_matrix17(u1_struct_0(B),F,D) ) => r1_matrix17(u1_struct_0(B),k3_matrix_3(B,E,F),k3_fvsum_1(B,C,D)) ) ) ) ) ) ) ) )).
fof(t5_matrix_0,axiom,( v1_matrix_0(k1_xboole_0) )).
fof(t5_matrix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => k5_matrix_1(B,A,C,k2_matrix_1(B,A)) = C ) ) ) )).
fof(t5_matrix_2,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(k1_finseq_2(A),u1_struct_0(k4_matrix_2(A))) ) )).
fof(t5_matrix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),A,B) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => k3_matrix_3(C,D,k2_matrix_3(C,D)) = k1_matrix_3(C,A,B) ) ) ) ) )).
fof(t5_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(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) ) ) ) )).
fof(t5_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => A = k2_matrix_5(k1_matrix_5(A)) ) )).
fof(t5_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ( ( r1_matrix_6(A,B,C,D) & r1_matrix_6(A,B,C,E) ) => ( r1_xxreal_0(A,k5_numbers) | r1_matrix_6(A,B,C,k3_matrix_3(B,D,E)) ) ) ) ) ) ) ) )).
fof(t5_matrix_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ( 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,k1_nat_1(C,1),k3_finseq_1(B))) ) ) ) ) ) )).
fof(t5_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( 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_3(B,C,C),k4_matrix_3(B,D,D)) ) ) ) ) ) )).
fof(t5_matrix_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( r2_hidden(B,k3_matrix_2(A)) => ( A = k5_numbers | r2_hidden(k3_finseq_5(B),k3_matrix_2(A)) ) ) ) ) )).
fof(t5_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k2_numbers)) ) => ( k3_finseq_1(k3_matrix_5(A,B)) = k3_finseq_1(A) & k1_matrix_0(k3_matrix_5(A,B)) = k1_matrix_0(A) ) ) ) )).
fof(t5_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( 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) ) ) ) )).
fof(t5_matrixj2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( m1_subset_1(C,u1_struct_0(B)) => k7_matrix_0(u1_struct_0(B),k2_matrixj2(B,C,A),A) = k10_fvsum_1(k1_matrix_0(k3_matrix_1(B,A)),B,k7_matrix_0(u1_struct_0(B),k3_matrix_1(B,A),A),C) ) ) ) )).
fof(t5_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => k8_rvsum_1(A,k5_euclid(k3_finseq_1(A))) = A ) )).
fof(t5_matrixr2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( k3_finseq_1(k7_matrixr1(A,B)) = k3_finseq_1(B) & k1_matrix_0(k7_matrixr1(A,B)) = k1_matrix_0(B) ) ) ) )).
fof(t5_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => ! [D] : ( m1_vectsp_6(D,A,B) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t5_matroid0,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ~ ( ~ r1_xxreal_0(k5_card_1(B),k5_card_1(A)) & ! [C] : ~ r2_hidden(C,k6_subset_1(B,A)) ) ) ) )).
fof(t5_matrprob,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => r1_xxreal_0(k5_numbers,k1_funct_1(A,B)) ) ) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => r1_xxreal_0(k1_funct_1(A,B),k18_rvsum_1(A)) ) ) ) ) )).
fof(t5_matrtop2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_vectsp_6(B,k2_vectsp_1,k6_prvect_1(k2_vectsp_1,A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t5_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(C))) => ( ( r2_hidden(A,k2_finseq_1(C)) & r2_hidden(B,k2_finseq_1(C)) ) => ( A = B | k13_fvsum_1(k2_vectsp_1,k1_matrtop1(D),k8_matrix_0(u1_struct_0(k2_vectsp_1),k1_matrtop3(C,A),B)) = k1_funct_1(D,B) ) ) ) ) ) ) )).
fof(t5_mazurulm,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_tarski(A),B,k7_funcop_1(k4_ordinal1,A)),k9_valued_1(k4_ordinal1,k1_numbers,B,A)) ) ) )).
fof(t5_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => r2_pboole(A,k1_pboole(A),B) ) )).
fof(t5_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r2_hidden(k1_xtuple_0(A),B) & r2_hidden(k2_xtuple_0(A),C) ) => ( ! [D] : ! [E] : A != k4_tarski(D,E) | r2_hidden(A,k2_zfmisc_1(B,C)) ) ) )).
fof(t5_measure1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(t5_measure3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ( ( k9_nat_1(B,C,k5_numbers) = k1_xboole_0 & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( k9_nat_1(B,C,k1_nat_1(E,1)) = k3_measure1(A,B,k9_nat_1(B,D,k5_numbers),k9_nat_1(B,D,E)) & r1_tarski(k9_nat_1(B,D,k1_nat_1(E,1)),k9_nat_1(B,D,E)) ) ) ) => k1_measure2(A,B,k1_measure3(A,B,D)) = k3_measure1(A,B,k9_nat_1(B,D,k5_numbers),k2_measure2(A,B,k1_measure3(A,B,C))) ) ) ) ) )).
fof(t5_measure4,axiom,( ! [A] : ! [B] : ( m1_measure4(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r2_hidden(C,k1_measure4(A,B)) <=> ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t5_measure5,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ! [B] : ( m1_subset_1(B,k6_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 ) ) ) ) )).
fof(t5_measure6,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => ~ ( ~ r1_xxreal_0(A,k1_supinf_2) & v1_xreal_0(k7_supinf_2(B)) & ! [C] : ( v1_xxreal_0(C) => ~ ( r2_hidden(C,B) & ~ r1_xxreal_0(k1_xxreal_3(k7_supinf_2(B),A),C) ) ) ) ) ) )).
fof(t5_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_xxreal_0(k12_supinf_2(A,C),k12_supinf_2(B,C)) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_xxreal_0(k12_supinf_2(k18_supinf_2(A),C),k19_supinf_2(B)) ) ) ) ) )).
fof(t5_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( m4_measure8(F,A,B,D) => r1_xxreal_0(k5_numbers,k1_mesfunc9(k4_measure8(A,B,D,C,F),E)) ) ) ) ) ) )).
fof(t5_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => k4_member_1(k2_xboole_0(A,B)) = k2_xboole_0(k4_member_1(A),k4_member_1(B)) ) ) )).
fof(t5_membered,axiom,( ! [A] : ( v5_membered(A) => r1_tarski(A,k4_numbers) ) )).
fof(t5_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v1_xreal_0(B) => ( k17_euclid(k1_rlvect_1(k15_euclid(2),A,k4_xcmplx_0(B))) = k4_xcmplx_0(k3_xcmplx_0(B,k17_euclid(A))) & k18_euclid(k1_rlvect_1(k15_euclid(2),A,k4_xcmplx_0(B))) = k4_xcmplx_0(k3_xcmplx_0(B,k18_euclid(A))) ) ) ) )).
fof(t5_mesfun10,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( m1_subset_1(B,k6_numbers) => ( ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k12_supinf_2(A,C),B) ) => r1_xxreal_0(k1_rinfsup2(A),B) ) ) ) )).
fof(t5_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t5_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( v7_ordinal1(C) => ( k1_relset_1(A,k4_mesfunc5(A,k6_numbers,k5_mesfun7c(A,B),C)) = k1_relset_1(A,k4_mesfunc5(A,k1_numbers,B,k5_numbers)) & ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,k5_mesfun7c(A,B),C))) => k12_supinf_2(k4_mesfunc5(A,k6_numbers,k5_mesfun7c(A,B),C),D) = k12_supinf_2(k4_rinfsup2(k1_mesfunc5(k4_ordinal1,k10_seqfunc(A,B,D))),C) ) ) ) ) ) ) )).
fof(t5_mesfun9c,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k6_numbers,k2_mesfunc9(k1_mesfunc5(k4_ordinal1,A)),k1_mesfunc5(k4_ordinal1,k3_series_1(A))) ) )).
fof(t5_mesfunc1,axiom,( r2_tarski(k4_ordinal1,k3_numbers) )).
fof(t5_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t5_mesfunc3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( ~ 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] : ( ( v1_prob_2(D) & m2_finseq_1(D,C) ) => ! [E] : ( m2_finseq_1(E,C) => ( ( k4_finseq_1(E) = k4_finseq_1(D) & ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t5_mesfunc4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( r1_mesfunc2(A,B,D) & ! [F] : ( r2_hidden(F,k9_xtuple_0(D)) => r1_xxreal_0(k1_supinf_2,k1_funct_1(D,F)) ) & r1_mesfunc2(A,B,E) & k9_xtuple_0(E) = k9_xtuple_0(D) & ! [F] : ( r2_hidden(F,k9_xtuple_0(E)) => r1_xxreal_0(k1_supinf_2,k1_funct_1(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] : ( r2_hidden(F,k9_xtuple_0(k3_mesfunc1(A,D,E))) => r1_xxreal_0(k1_supinf_2,k1_funct_1(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)) ) ) ) ) ) ) ) ) )).
fof(t5_mesfunc5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r1_xxreal_0(B,k4_xxreal_3(k1_newton(2,A),A)) & r1_xxreal_0(A,C) ) => r1_xxreal_0(k2_extreal1(B,k1_newton(2,A)),C) ) ) ) ) )).
fof(t5_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( r2_hidden(D,k13_mesfunc1(B,C)) <=> ( r2_hidden(D,k1_relset_1(A,B)) & ? [E] : ( v1_xreal_0(E) & E = k12_supinf_2(B,D) & ~ r1_xxreal_0(E,C) ) ) ) ) ) ) )).
fof(t5_mesfunc7,axiom,( k4_binop_1(k6_numbers,k1_mesfunc7) = 1 )).
fof(t5_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ~ ( v3_kurato_0(D,A) & ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ~ ( r1_funct_2(k4_ordinal1,B,k4_ordinal1,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(k4_ordinal1,B,B,k6_numbers,E,C))) ) ) ) ) ) ) ) )).
fof(t5_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( v3_mesfunc5(B) & v4_mesfunc5(C) ) => v3_mesfunc5(k4_mesfunc1(A,B,C)) ) ) ) ) )).
fof(t5_metric_1,axiom,( ! [A] : ( ( v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k5_numbers,k3_metric_1(A,B,C)) ) ) ) )).
fof(t5_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(B,k1_metric_2(A,C)) => r2_hidden(C,k1_metric_2(A,B)) ) ) ) ) )).
fof(t5_metric_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(D,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C))) => ! [E] : ( m1_subset_1(E,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C))) => k2_binop_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,k4_metric_3(A,B,C),D,E) = k2_binop_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,k4_metric_3(A,B,C),E,D) ) ) ) ) ) )).
fof(t5_metric_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => r1_xxreal_0(k2_binop_1(A,A,k1_numbers,B,D,E),k3_real_1(k2_binop_1(A,A,k1_numbers,B,C,D),k2_binop_1(A,A,k1_numbers,B,C,E))) ) ) ) ) ) ) ) )).
fof(t5_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ~ ( A != k5_numbers & m1_subset_1(B,u1_struct_0(k2_mfold_1(A))) & r1_xxreal_0(1,k12_euclid(B)) ) ) ) )).
fof(t5_mfold_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t5_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t5_midsp_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( ( ~ v2_struct_0(F) & v13_algstr_0(F) & v3_rlvect_1(F) & v4_rlvect_1(F) & l2_algstr_0(F) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t5_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( r2_hidden(D,k7_subset_1(k4_ordinal1,k2_finseq_1(A),k1_tarski(B))) & B = k1_nat_1(C,1) & ~ ( r1_xxreal_0(1,D) & r1_xxreal_0(D,C) ) & ~ ( r1_xxreal_0(k1_nat_1(B,1),D) & r1_xxreal_0(D,A) ) ) ) ) ) ) )).
fof(t5_mmlquer2,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => r1_tarski(k9_xtuple_0(k6_relat_1(A,B)),k9_xtuple_0(B)) ) )).
fof(t5_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( 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 ) ) ) )).
fof(t5_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ 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] : ( 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) ) ) ) ) ) )).
fof(t5_mod_3,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(t5_mod_4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t5_modal_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k2_zfmisc_1(k4_ordinal1,k4_ordinal1)) & v1_funct_1(A) & v3_trees_2(A) ) => r2_hidden(A,k4_partfun1(k3_finseq_2(k4_ordinal1),k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) )).
fof(t5_modcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) ) => ? [C] : ( r2_hidden(C,a_2_0_modcat_1(A,B)) & r1_modcat_1(C,k1_mod_2(A),A) ) ) ) )).
fof(t5_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_modelc_1(B) & l2_modelc_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t5_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v6_modelc_2(A) => A = k6_modelc_2(k10_modelc_2(A)) ) ) )).
fof(t5_modelc_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k13_modelc_2(C))) => ( ~ r2_hidden(B,D) => k17_modelc_3(C,k7_subset_1(k13_modelc_2(C),D,k1_tarski(B)),A) = k17_modelc_3(C,D,A) ) ) ) ) ) )).
fof(t5_moebius1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( A != 1 & ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ~ r1_nat_d(B,A) ) ) ) )).
fof(t5_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v1_group_1(A) <=> ! [B] : ( 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 ) ) ) ) )).
fof(t5_monoid_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t5_morph_01,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t5_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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] : ( 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] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(t5_msafree1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( ( v4_msualg_1(C,A) & v1_msafree1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( m2_pboole(E,u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D)) => ! [F] : ( 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) ) ) ) ) ) ) )).
fof(t5_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ( r2_hidden(E,k1_relset_1(k4_ordinal1,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)) ) ) ) ) ) )).
fof(t5_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [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] : ( 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))) ) ) ) ) )).
fof(t5_msafree4,axiom,( ! [A] : k4_trees_4(A,k1_xboole_0) = k1_trees_4(A) )).
fof(t5_msalimit,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_msalimit(C,A,B) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t5_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t5_msinst_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_msualg_6(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v1_msualg_6(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v1_msualg_6(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( m2_pboole(E,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [F] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t5_msscyc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t5_msscyc_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => v1_finset_1(a_4_0_msscyc_2(A,B,C,D)) ) ) ) ) ) )).
fof(t5_mssubfam,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ( ! [D] : ( r2_hidden(D,C) => r1_tarski(B,D) ) => ( C = k1_xboole_0 | r1_tarski(B,k8_setfam_1(A,C)) ) ) ) )).
fof(t5_mssublat,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k1_tarski(k5_numbers)) => ( B = k5_finseq_2(k4_ordinal1,A,k5_numbers) <=> k3_finseq_1(B) = A ) ) ) )).
fof(t5_msualg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ( v7_struct_0(A) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_subset_1(C,k10_xtuple_0(u3_msualg_1(A,B))) => ! [D] : ( m1_subset_1(D,k10_xtuple_0(u3_msualg_1(A,B))) => C = D ) ) ) ) ) )).
fof(t5_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t5_msualg_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,C) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t5_msualg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t5_msualg_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_msualg_4(C,A,B) & m1_msualg_4(C,A,B,B) ) => ! [D] : ( ( v1_msualg_4(D,A,B) & m1_msualg_4(D,A,B,B) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t5_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m2_pboole(C,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,B)) => ! [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,B)) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t5_msualg_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( 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)))) ) ) ) )).
fof(t5_msualg_8,axiom,( ! [A] : v4_lattice3(k2_msualg_5(A)) )).
fof(t5_msualg_9,axiom,( ! [A] : ! [B] : ? [C] : ( v1_relat_1(C) & v4_relat_1(C,B) & v1_funct_1(C) & v1_partfun1(C,B) & r6_pboole(B,k1_pzfmisc1(B,C),k7_funcop_1(B,k1_tarski(A))) ) )).
fof(t5_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_msualg_1(C) ) => ( ( r1_msuhom_1(A,B) & r1_msuhom_1(B,C) ) => r1_msuhom_1(A,C) ) ) ) ) )).
fof(t5_multop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( ( 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] : ( ( 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] : ( m1_subset_1(H,A) => ! [I] : ( m1_subset_1(I,B) => ! [J] : ( m1_subset_1(J,C) => ! [K] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t5_mycielsk,axiom,( ! [A] : ( ( v1_necklace(A) & l1_orders_2(A) ) => ! [B] : ! [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)) ) => r2_hidden(k4_tarski(C,B),u1_orders_2(A)) ) ) )).
fof(t5_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t5_nagata_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ! [D] : ( m1_subset_1(D,A) => r1_xxreal_0(k5_numbers,k3_funct_2(A,k1_numbers,k3_nagata_2(A,B,C),D)) ) ) ) ) ) )).
fof(t5_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ r1_xxreal_0(k1_nat_1(A,1),k5_numbers) ) )).
fof(t5_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(C,B) & A = k2_xcmplx_0(k7_nat_d(B,C),D) ) => C = k2_xcmplx_0(k7_nat_d(B,A),D) ) ) ) ) ) )).
fof(t5_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => ( r1_nat_d(C,k1_newton(A,B)) => r1_nat_d(C,A) ) ) ) ) )).
fof(t5_nat_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( B = k1_int_1(k7_xcmplx_0(A,2)) & r1_xxreal_0(2,A) ) => r1_xxreal_0(k7_xcmplx_0(k1_newton(2,A),A),k4_newton(B,A)) ) ) ) )).
fof(t5_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( v1_finset_1(k2_tarski(A,B)) & m1_subset_1(k2_tarski(A,B),k1_zfmisc_1(k4_ordinal1)) ) ) ) )).
fof(t5_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_nat_d(A,B) & r1_nat_d(B,A) ) => A = B ) ) ) )).
fof(t5_nat_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_nat_lat)) => ! [B] : ( 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) ) ) )).
fof(t5_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u4_struct_0(A))) ) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,B) => r2_hidden(k4_cat_1(A,D),C) ) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,C,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,C,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,B))) ) => ( ( r1_funct_2(C,B,C,u1_struct_0(A),D,k17_funct_3(u4_struct_0(A),u1_struct_0(A),u1_graph_1(A),C)) & r1_funct_2(C,B,C,u1_struct_0(A),E,k17_funct_3(u4_struct_0(A),u1_struct_0(A),u2_graph_1(A),C)) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(C,C),C))) ) => ( F = k1_realset1(u1_cat_1(A),C) => m3_cat_2(g1_cat_1(B,C,D,E,F),A) ) ) ) ) ) ) ) ) ) )).
fof(t5_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ( r1_tarski(k2_relset_1(u1_struct_0(A),D),k1_relset_1(u1_struct_0(A),E)) => r2_hidden(k1_normsp_1(A,D,C),k1_relset_1(u1_struct_0(A),E)) ) ) ) ) ) ) )).
fof(t5_ncfcont2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(D),u1_struct_0(C)))) ) => ! [F] : ( ( 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)) ) ) ) ) ) )).
fof(t5_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & ! [D] : ( m1_nfcont_1(D,A,C) => ~ r1_tarski(D,B) ) ) ) <=> v3_nfcont_1(B,A) ) ) ) )).
fof(t5_ndiff_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_ndiff_2(A,B,C,D,E) <=> ? [F] : ( m1_nfcont_1(F,A,D) & r1_tarski(F,k1_relset_1(u1_struct_0(A),C)) & ? [G] : ( m1_subset_1(G,u1_struct_0(B)) & ! [H] : ( ( v9_ordinal1(H) & v1_funct_1(H) & v1_funct_2(H,k4_ordinal1,k1_numbers) & v1_fdiff_1(H,k5_numbers) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [I] : ( ( v1_funct_1(I) & v3_funct_1(I) & v1_funct_2(I,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),k2_normsp_1(A,k2_ndiff_1(A,E,H),I),C),k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),I,C)),k37_valued_1(k4_ordinal1,k1_numbers,H)),B) & G = k6_normsp_1(B,k1_ndiff_1(B,k3_normsp_1(B,k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),k2_normsp_1(A,k2_ndiff_1(A,E,H),I),C),k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),I,C)),k37_valued_1(k4_ordinal1,k1_numbers,H))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t5_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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(k4_ordinal1,u1_struct_0(A),k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,D,k6_vfunct_1(k1_numbers,A,B,C)),k2_normsp_1(A,k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,D,B),k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,D,C))) & r2_funct_2(k4_ordinal1,u1_struct_0(A),k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,D,k2_vfunct_1(k1_numbers,A,B,C)),k3_normsp_1(A,k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,D,B),k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,D,C))) ) ) ) ) ) ) )).
fof(t5_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => r1_ndiff_4(A,C,D) ) ) ) ) ) ) ) )).
fof(t5_ndiff_5,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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,k5_numbers) = k4_struct_0(A) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) ) ) )).
fof(t5_neckla_2,axiom,( ! [A] : ( l1_orders_2(A) => ( r2_hidden(A,k4_neckla_2) => r2_hidden(u1_struct_0(A),k13_classes2) ) ) )).
fof(t5_neckla_3,axiom,( ! [A] : ( v3_card_1(A,1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => r3_relat_2(B,A) ) ) )).
fof(t5_necklace,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_xboole_0(k9_xtuple_0(A),k9_xtuple_0(B)) => k10_xtuple_0(k1_funct_4(A,B)) = k2_xboole_0(k10_xtuple_0(A),k10_xtuple_0(B)) ) ) ) )).
fof(t5_net_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t5_newton,axiom,( ! [A] : ( v1_xcmplx_0(A) => k1_newton(A,1) = A ) )).
fof(t5_nfcont_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t5_nfcont_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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)) ) ) ) ) )).
fof(t5_nfcont_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r1_tarski(k2_relset_1(k1_numbers,C),k1_relset_1(k1_numbers,B)) => ( r2_funct_2(k4_ordinal1,k1_numbers,k5_normsp_0(A,k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,C,B)),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,C,k4_normsp_0(k1_numbers,A,B))) & r2_funct_2(k4_ordinal1,u1_struct_0(A),k5_vfunct_1(k4_ordinal1,A,k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,C,B)),k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,C,k5_vfunct_1(k1_numbers,A,B))) ) ) ) ) ) )).
fof(t5_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,u1_struct_0(k4_real_ns1(A))))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,u1_struct_0(k4_real_ns1(A))))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,k1_euclid(A)))) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t5_normform,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_finsub_1(B) ) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(A,B)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t5_normsp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => r1_xxreal_0(k2_normsp_0(C,k3_rlvect_1(C,k1_rlvect_1(C,D,A),k1_rlvect_1(C,E,B))),k2_xcmplx_0(k3_xcmplx_0(k9_complex1(A),k2_normsp_0(C,D)),k3_xcmplx_0(k9_complex1(B),k2_normsp_0(C,E)))) ) ) ) ) ) )).
fof(t5_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k2_normsp_2(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k2_normsp_2(A))))) ) => ( r1_funct_2(k4_ordinal1,u1_struct_0(A),k4_ordinal1,u1_struct_0(k2_normsp_2(A)),B,C) => ( v2_tbsp_1(C,k2_normsp_2(A)) <=> v3_normsp_1(B,A) ) ) ) ) ) )).
fof(t5_ntalgo_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => ! [B] : ( m1_subset_1(B,k4_numbers) => ~ ( k1_int_2(B) != k5_numbers & r1_xxreal_0(k1_int_2(B),k1_int_2(k5_int_1(A,B))) ) ) ) )).
fof(t5_numbers,axiom,( r2_xboole_0(k4_numbers,k1_numbers) )).
fof(t5_numeral1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,1) => k1_numeral1(k2_numeral1(A,B),B) = A ) ) ) )).
fof(t5_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( 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) ) ) ) ) )).
fof(t5_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k6_openlatt(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t5_oposet_1,axiom,( v1_necklace(k1_oposet_1) )).
fof(t5_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_oppcat_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_oppcat_1(A))) => k2_cat_1(k2_oppcat_1(A),B,C) = k2_cat_1(A,k4_oppcat_1(A,C),k4_oppcat_1(A,B)) ) ) ) )).
fof(t5_orders_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) ) )).
fof(t5_orders_2,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t5_orders_3,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = C ) ) => v3_orders_3(A) ) ) )).
fof(t5_orders_4,axiom,( ! [A] : ( ( v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r1_orders_4(A,C,D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B))) => ( r1_orders_4(B,E,F) => ! [G] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t5_ordinal1,axiom,( ! [A] : A != k1_ordinal1(A) )).
fof(t5_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => r1_ordinal1(k3_tarski(A),A) ) )).
fof(t5_ordinal3,axiom,( ! [A] : v3_ordinal1(k3_tarski(k2_ordinal1(A))) )).
fof(t5_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r1_ordinal2(B,A) => r1_ordinal2(k11_ordinal2(B,C),k4_ordinal3(C,A)) ) ) ) ) )).
fof(t5_ordinal5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) ) => ( ~ v1_finset_1(A) <=> r1_ordinal1(k4_ordinal1,k9_xtuple_0(A)) ) ) )).
fof(t5_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( r2_hidden(C,k6_subset_1(A,B)) <=> ( r1_tarski(B,C) & r2_hidden(C,A) ) ) ) ) )).
fof(t5_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( ~ r1_orders_2(B,D,C) & E != k4_struct_0(A) & ~ ( ~ r1_orders_2(B,k4_vectsp_1(A,B,E,D),C) & ~ r1_orders_2(B,D,k4_vectsp_1(A,B,E,C)) ) ) ) ) ) ) ) )).
fof(t5_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t5_osalg_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t5_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t5_osalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( m2_pboole(E,u1_struct_0(A),B,C) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t5_osalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( r2_hidden(D,k1_funct_1(B,C)) => r2_hidden(D,k4_osalg_4(A,B,k3_osalg_4(A,C))) ) ) ) ) )).
fof(t5_papdesaf,axiom,( ! [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) ) => ! [B] : ( ( ~ v7_struct_0(B) & v2_analoaf(B) & l1_analoaf(B) ) => ~ ( B = k2_analoaf(A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & k3_rlvect_1(A,k1_rlvect_1(A,C,E),k1_rlvect_1(A,D,F)) = k4_struct_0(A) & ~ ( E = k5_numbers & F = k5_numbers ) ) ) ) ) ) ) ) )).
fof(t5_pardepap,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( r2_analoaf(A,B,C,B,D) & ~ ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t5_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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) ) )).
fof(t5_parsp_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_parsp_1(A))) => ! [F] : ( m1_subset_1(F,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) => ! [G] : ( m1_subset_1(G,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) => ! [H] : ( m1_subset_1(H,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) => ! [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)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t5_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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] : ( 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 ) ) ) )).
fof(t5_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t5_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ( r1_setfam_1(C,B) => r2_setfam_1(C,B) ) ) ) ) )).
fof(t5_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(k4_tarski(C,D),k4_partit1(A,B)) <=> r2_hidden(C,k15_bvfunc_1(A,D,B)) ) ) ) ) ) )).
fof(t5_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t5_pboole,axiom,( ! [A] : ! [B] : k1_funct_1(k1_pboole(A),B) = k1_xboole_0 )).
fof(t5_pcomps_1,axiom,( ! [A] : u1_struct_0(k1_compts_1(A)) = A )).
fof(t5_pcomps_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v6_metric_1(B) & v7_metric_1(B) & v8_metric_1(B) & v9_metric_1(B) & l1_metric_1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [D] : ( ( 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)))) ) ) ) ) ) ) )).
fof(t5_pcs_0,axiom,( ! [A] : ( l1_pcs_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t5_pdiff_1,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) ) )).
fof(t5_pdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(2)) => ( ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & B = k10_finseq_1(C,D) & r1_fdiff_1(k1_pdiff_2(2,1,A,B),C) ) ) <=> r3_pdiff_1(2,1,A,B) ) ) ) )).
fof(t5_pdiff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(2)) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t5_pdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t5_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t5_pdiff_6,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(B),k1_euclid(A)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(B),k1_euclid(A)))) ) => ! [E] : ( ( 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] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(B)),u1_struct_0(k4_real_ns1(A))))) ) => ( ( C = E & D = F ) => k8_integr15(A,k1_euclid(B),C,D) = k2_vfunct_1(u1_struct_0(k4_real_ns1(B)),k4_real_ns1(A),E,F) ) ) ) ) ) ) ) )).
fof(t5_pdiff_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(1))) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,B) ) => k2_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)) = k2_normsp_0(k4_real_ns1(1),C) ) ) ) ) )).
fof(t5_pdiff_8,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,A) ) => r1_xxreal_0(k9_complex1(k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_1(C,A),B)),k12_euclid(B)) ) ) ) ) )).
fof(t5_pdiff_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t5_pencil_1,axiom,( ! [A] : ( r1_ordinal1(3,k1_card_1(A)) <=> ? [B] : ? [C] : ? [D] : ( r2_hidden(B,A) & r2_hidden(C,A) & r2_hidden(D,A) & B != C & B != D & C != D ) ) )).
fof(t5_pencil_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_xxreal_0(k1_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))) ) ) ) ) )).
fof(t5_pencil_3,axiom,( ! [A] : ( ( ~ v3_pencil_1(A) & ~ v4_pencil_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_pre_topc(A)) => ~ ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_hidden(C,B) ) ) ) )).
fof(t5_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t5_pepin,axiom,( ! [A] : ( v1_int_1(A) => ( ~ r1_xxreal_0(A,1) => k5_int_1(1,A) = 1 ) ) )).
fof(t5_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u4_struct_0(A))) => k8_petri(A,B) = a_2_6_petri(A,B) ) ) )).
fof(t5_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => r1_pnproc_1(A,k3_pnproc_1(A,B,k1_pnproc_1(A)),B) ) )).
fof(t5_polyalg1,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k11_polynom3(A,k10_polynom3(A),B),B) ) ) )).
fof(t5_polyeq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k5_numbers,k1_quin_1(A,B,C)) => ( A = k5_numbers | ! [D] : ( v1_xreal_0(D) => ~ ( k2_polyeq_1(A,B,C,D) = k5_numbers & D != k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A)) & D != k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A)) ) ) ) ) ) ) ) )).
fof(t5_polyeq_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k2_xcmplx_0(A,B) != k5_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),k1_square_1(A)),k3_xcmplx_0(k3_xcmplx_0(3,k1_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),k1_square_1(A)),k3_xcmplx_0(k3_xcmplx_0(3,k1_square_1(B)),A))),k1_newton(B,3)),B)) ) ) ) )).
fof(t5_polyeq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k3_complex1(k3_polyeq_3(A)) = k6_xcmplx_0(k1_newton(k3_complex1(A),3),k3_xcmplx_0(k3_xcmplx_0(3,k3_complex1(A)),k1_square_1(k4_complex1(A)))) & k4_complex1(k3_polyeq_3(A)) = k2_xcmplx_0(k4_xcmplx_0(k1_newton(k4_complex1(A),3)),k3_xcmplx_0(k3_xcmplx_0(3,k1_square_1(k3_complex1(A))),k4_complex1(A))) ) ) )).
fof(t5_polyeq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( B != k5_numbers & k2_polyeq_1(B,C,k5_numbers,A) = k5_numbers & A != k5_numbers & A != k4_xcmplx_0(k7_xcmplx_0(C,B)) ) ) ) ) )).
fof(t5_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( 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)) ) ) )).
fof(t5_polyform,axiom,( ~ v1_abian(3) )).
fof(t5_polynom1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t5_polynom3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [C] : ( m2_finseq_2(C,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [D] : ( m2_finseq_2(D,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ( ( ( 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) ) ) ) ) ) ) )).
fof(t5_polynom4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( k1_algseq_1(A,B) = k5_numbers => r2_funct_2(k4_ordinal1,u1_struct_0(A),B,k9_polynom3(A)) ) ) ) )).
fof(t5_polynom5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k4_algstr_0(k1_complfld,k1_hahnban1(A,B)) = k1_hahnban1(k4_xcmplx_0(A),k4_xcmplx_0(B)) ) ) )).
fof(t5_polynom6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( m2_subset_1(C,k14_pre_poly(A),k15_pre_poly(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t5_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( 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),k10_polynom1(A,B,k8_polynom1(A,B),C),k8_polynom1(A,B)) ) ) ) )).
fof(t5_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t5_power,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => k1_power(A,k5_numbers) = k5_numbers ) ) )).
fof(t5_pralg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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] : ( m5_margrel1(C,u1_struct_0(A),k1_unialg_2(A)) => ! [D] : ( m5_margrel1(D,u1_struct_0(B),k1_unialg_2(B)) => ! [E] : ( m5_margrel1(E,u1_struct_0(k5_pralg_1(A,B)),k1_unialg_2(k5_pralg_1(A,B))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t5_pralg_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( 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)) ) ) )).
fof(t5_pralg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t5_pre_circ,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( m1_subset_1(D,k4_card_3(B)) => ( ( r1_tarski(k9_xtuple_0(C),k9_xtuple_0(B)) & ! [E] : ( r2_hidden(E,k9_xtuple_0(C)) => r2_hidden(k1_funct_1(C,E),k1_funct_1(B,E)) ) ) => m1_subset_1(k1_funct_4(D,C),k4_card_3(B)) ) ) ) ) )).
fof(t5_pre_ff,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ~ r1_xxreal_0(C,k5_numbers) => k4_int_1(k4_int_1(A,B),C) = k4_int_1(A,k3_xcmplx_0(B,C)) ) ) ) ) )).
fof(t5_pre_poly,axiom,( ! [A] : ! [B] : ( m2_finseq_2(B,A,k3_finseq_2(A)) => ! [C] : ( m2_finseq_2(C,A,k3_finseq_2(A)) => ! [D] : ( 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) ) ) ) )).
fof(t5_pre_topc,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t5_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_prelamb(A) ) => ! [B] : ( m1_prelamb(B,A) => ! [C] : ( 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)),k4_ordinal1),B,C)) = 2 & ! [D] : ( m1_trees_1(D,k9_xtuple_0(B)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( D = k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,k5_numbers)) & k1_xtuple_0(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k4_ordinal1),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)),k4_ordinal1),B,D)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k12_finseq_1(u1_struct_0(A),G),E),F) ) ) ) ) ) ) ) ) ) )).
fof(t5_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ~ ( k5_numbers != A & k5_numbers = k1_newton(A,B) ) ) ) )).
fof(t5_prgcor_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(B,k4_nat_d(A,k2_nat_1(2,B))) & k3_nat_d(A,B) != k2_nat_1(k3_nat_d(A,k2_nat_1(2,B)),2) ) ) ) )).
fof(t5_prgcor_2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( v7_ordinal1(C) => ( k3_finseq_1(A) = k3_finseq_1(B) => ( r1_xxreal_0(C,k3_finseq_1(A)) | k22_rvsum_1(A,B) = k2_prgcor_2(k11_afinsq_1(k1_numbers,A,C),k11_afinsq_1(k1_numbers,B,C)) ) ) ) ) ) )).
fof(t5_prob_1,axiom,( ! [A] : ! [B] : ( ( ~ 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) ) )).
fof(t5_prob_2,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [E] : ( m1_prob_1(E,A,B) => ( ! [F] : ( v7_ordinal1(F) => k1_prob_2(A,B,D,F) = k5_prob_1(A,B,k1_prob_2(A,B,C,F),E) ) => k9_subset_1(A,k3_prob_1(A,C),E) = k3_prob_1(A,D) ) ) ) ) ) )).
fof(t5_prob_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( v5_relat_1(D,C) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ! [E] : ( ( v5_relat_1(E,C) & v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ! [F] : ( m2_prob_1(F,B,C) => ( r1_tarski(k1_prob_2(B,C,D,A),k1_prob_2(B,C,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)) ) ) ) ) ) ) ) )).
fof(t5_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m1_prob_1(E,A,B) => k3_funct_2(B,k1_numbers,C,k3_measure1(A,B,D,E)) = k6_xcmplx_0(k3_funct_2(B,k1_numbers,C,k1_measure1(A,B,D,E)),k3_funct_2(B,k1_numbers,C,E)) ) ) ) ) ) )).
fof(t5_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t5_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( ~ r1_collsp(A,F,B,D) & r1_collsp(A,F,D,E) & D != E & r1_collsp(A,C,E,G) & r1_collsp(A,F,B,C) & F != C & G = D ) ) ) ) ) ) ) ) )).
fof(t5_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ( r4_projpl_1(A,B,C,D) <=> ? [E] : ( 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) ) ) ) ) ) ) )).
fof(t5_projred1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ? [C] : ( m1_subset_1(C,u2_incsp_1(A)) & ? [D] : ( m1_subset_1(D,u2_incsp_1(A)) & ? [E] : ( 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 ) ) ) ) ) )).
fof(t5_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t5_prvect_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) ) )).
fof(t5_prvect_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,k4_card_3(B)) => ! [G] : ( m2_subset_1(G,k4_ordinal1,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) ) ) ) ) ) )).
fof(t5_prvect_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ? [C] : ( 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] : ! [E] : ( ( r2_hidden(D,A) & r2_hidden(E,B) ) => k1_binop_1(C,D,E) = k10_finseq_1(D,E) ) ) ) ) )).
fof(t5_pscomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_xxreal_0(k3_funct_2(u1_struct_0(A),k1_numbers,B,D),C) ) => r1_xxreal_0(k2_pscomp_1(A,B),C) ) ) ) ) )).
fof(t5_pua2mss1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ~ ( r1_tarski(k10_xtuple_0(B),k3_tarski(A)) & ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ~ ( k9_xtuple_0(C) = k9_xtuple_0(B) & r1_tarski(k10_xtuple_0(C),A) & r2_hidden(B,k4_card_3(C)) ) ) ) ) )).
fof(t5_pythtrip,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( k1_pepin(A) = k1_pepin(B) => A = B ) ) ) )).
fof(t5_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => A = k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A)) ) )).
fof(t5_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ! [E] : ( m1_subset_1(E,k9_qc_lang1(A)) => ( k15_qc_lang1(A,B,D) = k15_qc_lang1(A,C,E) => ( B = C & D = E ) ) ) ) ) ) ) )).
fof(t5_qc_lang3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_qc_lang1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(B),k8_qc_lang1(B,A)) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t5_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => r2_hidden(B,k10_xtuple_0(k2_qc_lang4(A,B))) ) ) )).
fof(t5_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_qc_trans(B,A) & m1_qc_lang1(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v5_relat_1(D,k3_qc_lang1(A)) & v3_card_1(D,C) & m2_finseq_1(D,k2_qc_lang1(A)) ) => ( v5_relat_1(D,k3_qc_lang1(B)) & v3_card_1(D,C) & m2_finseq_1(D,k2_qc_lang1(B)) ) ) ) ) ) )).
fof(t5_qmax_1,axiom,( ! [A] : ( ( v2_qmax_1(A) & l1_qmax_1(A) ) => ! [B] : ( m1_subset_1(B,k5_qmax_1(A)) => r4_qmax_1(A,B,B) ) ) )).
fof(t5_quatern2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => k25_quaterni(k6_quaterni(A,B,C,D),k6_quaterni(E,F,G,H)) = k6_quaterni(k6_xcmplx_0(A,E),k6_xcmplx_0(B,F),k6_xcmplx_0(C,G),k6_xcmplx_0(D,H)) ) ) ) ) ) ) ) ) )).
fof(t5_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ( v1_xreal_0(A) => k23_quaterni(A,k3_quatern2) = k6_quaterni(k5_numbers,k13_quaterni(A),k5_numbers,k5_numbers) ) ) )).
fof(t5_quaterni,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( r1_tarski(k2_enumset1(B,C,D,E),A) <=> ( r2_hidden(B,A) & r2_hidden(C,A) & r2_hidden(D,A) & r2_hidden(E,A) ) ) )).
fof(t5_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(k5_numbers,k1_quin_1(B,C,D)) & r1_xxreal_0(k5_numbers,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(A)),k3_xcmplx_0(C,A)),D)) ) ) ) ) ) )).
fof(t5_quofield,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v6_struct_0(A) & v5_group_1(A) & l5_algstr_0(A) ) => ! [B] : ( 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)) ) ) )).
fof(t5_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( A != k5_numbers & B != k5_numbers & r1_xxreal_0(A,k3_nat_d(k4_nat_d(C,k1_newton(A,B)),k1_newton(A,k7_nat_d(B,1)))) ) ) ) ) )).
fof(t5_radix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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))) ) ) ) )).
fof(t5_radix_3,axiom,( r2_hidden(k5_numbers,k1_radix_3(k5_numbers)) )).
fof(t5_radix_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t5_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(A,k2_finseq_1(C)) => k4_radix_1(A,B,C,k10_radix_1(B,C,k5_numbers)) = k5_numbers ) ) ) ) )).
fof(t5_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k2_finseq_1(B)) => r1_xxreal_0(k5_numbers,k4_radix_1(D,C,B,k10_radix_1(C,B,A))) ) ) ) ) ) )).
fof(t5_ramsey_1,axiom,( ! [A] : k3_group_10(A,k5_numbers) = k1_tarski(k5_numbers) )).
fof(t5_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ? [C] : ( v1_prob_2(C) & m2_finseq_1(C,k1_random_1(A)) & ? [D] : ( 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] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(C)) => k1_funct_1(C,E) = k1_tarski(k1_funct_1(D,E)) ) ) & ! [E] : ( v7_ordinal1(E) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( 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)) ) => k12_supinf_2(B,F) = k12_supinf_2(B,G) ) ) ) ) ) ) ) ) )).
fof(t5_random_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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))) ) ) ) )).
fof(t5_random_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [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))) ) => ( m1_random_1(C,A,B) => ( ~ v1_xboole_0(a_3_0_random_3(A,B,C)) & v1_prob_1(a_3_0_random_3(A,B,C),k1_numbers) & v4_prob_1(a_3_0_random_3(A,B,C),k1_numbers) & m1_subset_1(a_3_0_random_3(A,B,C),k1_zfmisc_1(k1_zfmisc_1(k1_numbers))) ) ) ) ) ) )).
fof(t5_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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) = k5_numbers ) ) ) )).
fof(t5_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ? [B] : ( v1_int_1(B) & ? [C] : ( v7_ordinal1(C) & C != k5_numbers & A = k7_xcmplx_0(B,C) ) ) ) )).
fof(t5_ratfunc1,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k11_polynom3(A,k3_polynom5(A,B,D),C),k3_polynom5(A,k11_polynom3(A,B,C),D)) ) ) ) ) )).
fof(t5_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,A) => k2_seq_4(k3_rcomp_1(A,B)) = B ) ) ) )).
fof(t5_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => ( v8_ordinal1(B) | v3_xxreal_0(A) | v2_xxreal_0(B) ) ) ) ) )).
fof(t5_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k7_xcmplx_0(B,A) = k3_nat_d(B,A) => k4_nat_d(B,A) = k5_numbers ) ) ) )).
fof(t5_real_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_real_lat)) => ! [B] : ( 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 ) ) ) )).
fof(t5_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(A))) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t5_realset1,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m3_realset1(C,A,B) => ( v1_funct_1(k1_realset1(C,k6_subset_1(A,k6_domain_1(A,B)))) & v1_funct_2(k1_realset1(C,k6_subset_1(A,k6_domain_1(A,B))),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(k1_realset1(C,k6_subset_1(A,k6_domain_1(A,B))),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))))) ) ) ) ) )).
fof(t5_realset2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(A),k8_struct_0(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k8_struct_0(A)) => k6_algstr_0(A,B,C) = k6_algstr_0(A,C,B) ) ) ) )).
fof(t5_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_subset_1(D,u1_struct_0(A),k8_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t5_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_rearran1(B) & v2_rearran1(B) & m2_finseq_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( 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) ) ) ) ) ) )).
fof(t5_recdef_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( 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) ) ) )).
fof(t5_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( 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)) ) ) ) ) )).
fof(t5_relat_2,axiom,( ! [A] : ( 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)) ) ) ) )).
fof(t5_reloc,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_ami_3)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( k5_compos_0(u1_compos_1(k1_ami_3),A,C) = B => ( ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(k5_numbers,D) & r1_xxreal_0(D,5) & k2_compos_0(u1_compos_1(k1_ami_3),B) = D ) ) | A = B ) ) ) ) ) )).
fof(t5_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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))) ) ) )).
fof(t5_relset_2,axiom,( ! [A] : ! [B] : k10_eqrel_1(k6_subset_1(A,B)) = k7_subset_1(k1_zfmisc_1(A),k10_eqrel_1(A),k10_eqrel_1(B)) )).
fof(t5_revrot_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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))) = k13_matrix_0(A,k7_partfun1(A,B,k3_finseq_1(B))) ) ) ) )).
fof(t5_rewrite1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ~ ( A != k1_xboole_0 & ! [B] : ! [C] : ( ( 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) = k1_nat_1(k3_finseq_1(C),1) ) ) ) ) )).
fof(t5_rewrite2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t5_rewrite3,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( m1_rewrite1(B,A) => ~ ( ~ r1_xxreal_0(k3_finseq_1(B),1) & ! [C] : ( 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) ) ) ) ) ) )).
fof(t5_rfinseq,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( v1_finset_1(B) => ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & r2_classes1(k5_relat_1(A,B),C) ) ) ) )).
fof(t5_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( A = k10_finseq_1(B,C) => ( k3_rfinseq2(A) = k4_xxreal_0(B,C) & k1_rfinseq2(A) = k15_funcop_1(k4_ordinal1,B,k4_xxreal_0(B,C),1,2) ) ) ) ) ) )).
fof(t5_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ( k8_relat_1(k54_valued_1(A),k1_tarski(k5_numbers)) = k8_relat_1(A,k1_tarski(k5_numbers)) & k8_relat_1(k30_valued_1(A),k1_tarski(k5_numbers)) = k8_relat_1(A,k1_tarski(k5_numbers)) ) ) )).
fof(t5_rfunct_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_ordinal1) & v5_valued_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => r2_relset_1(k4_ordinal1,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,k2_valued_0(k1_numbers,B,A)),k2_valued_0(k1_numbers,B,k37_valued_1(k4_ordinal1,k1_numbers,A))) ) ) )).
fof(t5_rfunct_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(k1_rfunct_3(k2_xcmplx_0(A,B)),k2_xcmplx_0(k1_rfunct_3(A),k1_rfunct_3(B))) ) ) )).
fof(t5_rfunct_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => k14_rvsum_1(k2_finseq_2(A,k5_numbers),B) = k2_finseq_2(A,k5_numbers) ) ) )).
fof(t5_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_seq_2(A) <=> v4_xxreal_2(k2_relset_1(k1_numbers,A)) ) ) )).
fof(t5_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( v7_ordinal1(B) => ( ~ v1_xboole_0(a_2_0_rinfsup2(A,B)) & m1_subset_1(a_2_0_rinfsup2(A,B),k1_zfmisc_1(k6_numbers)) ) ) ) )).
fof(t5_ring_1,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t5_ringcat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) )).
fof(t5_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t5_rlaffin2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k1_rlaffin2(A,B),k3_convex1(A,B)) ) ) )).
fof(t5_rlaffin3,axiom,( ! [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_rlvect_5(A) & l1_rlvect_1(A) ) => ! [B] : ( ( v1_rlaffin1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => r1_xxreal_0(k5_card_1(B),k2_xcmplx_0(1,k1_rlvect_5(A))) ) ) )).
fof(t5_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( u1_struct_0(A) = B => v1_rlsub_1(B,A) ) ) ) )).
fof(t5_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => k1_rlsub_2(A,B,C) = k1_rlsub_2(A,C,B) ) ) ) )).
fof(t5_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k5_rusub_4(A,B,k4_struct_0(A)) = B ) ) )).
fof(t5_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t5_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k1_relset_1(k4_ordinal1,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)) ) ) ) ) ) )).
fof(t5_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t5_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t5_rlvect_5,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t5_rlvect_x,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m2_rlvect_2(C,A,B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t5_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( u1_struct_0(B) = C => v1_rmod_2(C,A,B) ) ) ) ) )).
fof(t5_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => k1_rmod_3(A,B,C,D) = k1_rmod_3(A,B,D,C) ) ) ) ) )).
fof(t5_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t5_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & v7_robbins1(A) & l2_robbins1(A) ) => ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k5_robbins1(A,B,C) = B & k5_robbins1(A,C,k3_robbins1(A,C)) = B ) ) ) ) )).
fof(t5_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) )).
fof(t5_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ( v10_lattices(A) <=> ( v2_robbins3(A) & v1_robbins3(A) & v3_robbins3(A) & v9_lattices(A) ) ) ) )).
fof(t5_robbins4,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t5_rolle,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,A) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k2_rcomp_1(A,B)) & k3_xcmplx_0(k6_xcmplx_0(k1_funct_1(C,B),k1_funct_1(C,A)),k1_fdiff_1(D,E)) = k3_xcmplx_0(k6_xcmplx_0(k1_funct_1(D,B),k1_funct_1(D,A)),k1_fdiff_1(C,E)) ) ) ) ) ) ) ) ) )).
fof(t5_roughs_1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( 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)) ) ) )).
fof(t5_rpr_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v3_card_1(B,1) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( v3_card_1(C,1) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ( r1_tarski(B,C) => B = C ) ) ) ) )).
fof(t5_rsspace,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace))) => k3_rlvect_1(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace),A,k4_struct_0(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace))) = A ) )).
fof(t5_rsspace2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(B) => ( ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & ~ r1_xxreal_0(k9_nat_1(k1_numbers,B,D),A) ) ) | r1_xxreal_0(k1_seq_2(B),A) ) ) ) ) )).
fof(t5_rsspace3,axiom,( ~ v2_struct_0(g1_normsp_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3),k2_rsspace3)) & v13_algstr_0(g1_normsp_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3),k2_rsspace3)) & v2_rlvect_1(g1_normsp_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3),k2_rsspace3)) & v3_rlvect_1(g1_normsp_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3),k2_rsspace3)) & v4_rlvect_1(g1_normsp_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3),k2_rsspace3)) & v5_rlvect_1(g1_normsp_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3),k2_rsspace3)) & v6_rlvect_1(g1_normsp_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3),k2_rsspace3)) & v7_rlvect_1(g1_normsp_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3),k2_rsspace3)) & v8_rlvect_1(g1_normsp_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3),k2_rsspace3)) & l1_rlvect_1(g1_normsp_1(k1_rsspace3,k9_rsspace(k6_rsspace,k1_rsspace3),k7_rsspace(k6_rsspace,k1_rsspace3),k8_rsspace(k6_rsspace,k1_rsspace3),k2_rsspace3)) )).
fof(t5_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => k3_funct_2(A,u1_struct_0(B),C,D) = k4_struct_0(B) ) => v1_rsspace4(C,A,B) ) ) ) ) )).
fof(t5_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => k4_struct_0(B) = k4_struct_0(C) ) ) ) )).
fof(t5_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => k1_rusub_2(A,B,C) = k1_rusub_2(A,C,B) ) ) ) )).
fof(t5_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_bhsp_1(B) & m1_rusub_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = u1_struct_0(B) => k1_rusub_3(A,C) = B ) ) ) ) )).
fof(t5_rusub_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_3(B,A) => ! [C] : ( m1_rusub_3(C,A) => ( v1_rusub_4(A) => k1_card_1(B) = k1_card_1(C) ) ) ) ) )).
fof(t5_rusub_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t5_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k3_rvsum_1(A),B) = k3_xcmplx_0(A,B) ) ) )).
fof(t5_rvsum_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k3_rvsum_2(k9_finseq_1(A),k9_finseq_1(B)) = k9_finseq_1(k2_xcmplx_0(A,B)) ) ) )).
fof(t5_scm_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_ami_3)) ) => ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_ami_3)) ) => ( ( k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_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(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1))) = k1_nat_1(C,1) & k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1)),E) = k2_xcmplx_0(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B),E),k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B),F)) & ! [G] : ( ( v1_ami_2(G) & m1_subset_1(G,u1_struct_0(k1_ami_3)) ) => ( G != E => k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1)),G) = k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B),G) ) ) ) ) ) ) ) ) ) ) )).
fof(t5_scm_comp,axiom,( ! [A] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(k1_scm_comp),k7_dtconstr(k1_scm_comp)) => ! [C] : ( m1_dtconstr(C,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t5_scm_halt,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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) ) => ( ( r1_tarski(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_3(k4_scmfsa_2(k5_numbers),1)),A) & r1_tarski(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_3(k4_scmfsa_2(k5_numbers),1)),B) & r1_tarski(E,C) & r1_tarski(E,D) & r8_pboole(u1_struct_0(k1_scmfsa_2),A,B) ) => ! [F] : ( v7_ordinal1(F) => ( r8_pboole(u1_struct_0(k1_scmfsa_2),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,C,A,F),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,D,B,F)) & k3_extpro_1(k7_card_1(3),k1_scmfsa_2,C,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,C,A,F)) = k3_extpro_1(k7_card_1(3),k1_scmfsa_2,D,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,D,B,F)) ) ) ) ) ) ) ) ) )).
fof(t5_scm_inst,axiom,( ! [A] : ( m1_subset_1(A,k3_scm_inst) => ! [B] : ( m1_subset_1(B,k2_scm_inst) => ! [C] : ( m1_subset_1(C,k2_scm_inst) => ! [D] : ( m2_subset_1(D,k4_ordinal1,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 ) ) ) ) ) ) )).
fof(t5_scmbsort,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ( B != k1_nat_1(C,1) => k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k6_scmfsa_2(k4_scmfsa_2(B),D),k1_scmfsa_m(A)),k4_scmfsa_2(k1_nat_1(C,1))) = k1_funct_1(A,k4_scmfsa_2(k1_nat_1(C,1))) ) ) ) ) ) )).
fof(t5_scmfsa10,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( 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)) ) ) )).
fof(t5_scmfsa6c,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [E] : ( ( v1_scmfsa6c(E) & m1_subset_1(E,u1_compos_1(k1_scmfsa_2)) ) => k1_funct_1(k1_scmfsa6b(k5_scmfsa6a(D,E),B,C),A) = k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,E,k1_scmfsa6b(D,B,C)),A) ) ) ) ) ) )).
fof(t5_scmfsa7b,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ~ r3_scmfsa7b(k2_compos_1(k1_scmfsa_2),A) ) )).
fof(t5_scmfsa8a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t5_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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(B),A) <=> r5_scmfsa7b(C,k1_funct_4(B,k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1))),k1_funct_4(A,D)) ) ) ) ) ) )).
fof(t5_scmfsa8c,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ( ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => r6_scmfsa7b(A,k1_scmfsa_m(B),C) ) ) => v5_extpro_1(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)),k7_card_1(3),k1_scmfsa_2,A) ) ) )).
fof(t5_scmfsa9a,axiom,( ! [A] : ( v7_ordinal1(A) => k2_sf_mastr(k1_scmfsa8a(A)) = k1_xboole_0 ) )).
fof(t5_scmfsa_1,axiom,( ! [A] : ( 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 ) )).
fof(t5_scmfsa_2,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t5_scmfsa_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( ~ 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(k7_card_1(3),k1_scmfsa_2)) & v1_finset_1(B) & v4_extpro_1(B,k7_card_1(3),k1_scmfsa_2,A) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ( ( r1_tarski(B,C) & r1_tarski(B,D) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( ( r1_tarski(A,E) & r1_tarski(A,F) ) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v1_ami_2(H) & m1_subset_1(H,u1_struct_0(k1_scmfsa_2)) ) => ! [I] : ( ( v1_ami_2(I) & m1_subset_1(I,u1_struct_0(k1_scmfsa_2)) ) => ( ( k3_extpro_1(k7_card_1(3),k1_scmfsa_2,E,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G)) = k8_scmfsa_2(H,I) & r2_hidden(H,k9_xtuple_0(B)) ) => k6_xcmplx_0(k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G),H),k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G),I)) = k6_xcmplx_0(k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,D,G),H),k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,D,G),I)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t5_scmfsa_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(B,k7_card_1(3),k1_scmfsa_2,k5_numbers) ) => ( k1_funct_1(B,k4_scmfsa_2(k5_numbers)) = 1 => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( v1_int_1(D) => ( r1_tarski(k2_scmfsa_7(C,D),A) => ( C = k4_scmfsa_2(k5_numbers) | ( ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(E,k1_afinsq_1(k2_scmfsa_7(C,D))) => ( k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B,E)) = E & ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_scmfsa_2)) ) => ( F != C => k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B,E),F) = k1_funct_1(B,F) ) ) & ! [F] : ( m1_scmfsa_2(F) => k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B,E),F) = k18_scmfsa_2(B,F) ) ) ) ) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B,k1_afinsq_1(k2_scmfsa_7(C,D))),C) = D ) ) ) ) ) ) ) ) )).
fof(t5_scmfsa_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => k5_card_1(k2_scmfsa_9(B,A)) = k1_nat_1(k5_card_1(A),6) ) ) )).
fof(t5_scmfsa_i,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k2_scm_inst) => ! [C] : ( 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) ) ) ) )).
fof(t5_scmfsa_m,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) ) => ( k1_funct_1(k1_scmfsa_m(A),k4_scmfsa_2(k5_numbers)) = 1 & k1_funct_1(k1_scmfsa_m(A),k4_struct_0(k1_scmfsa_2)) = k5_numbers ) ) )).
fof(t5_scmisort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_m(B)),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_m(B)))),D) ) ) ) ) ) )).
fof(t5_scmp_gcd,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmpds_2)) => k5_card_1(k4_scmpds_4(A,B)) = 2 ) ) )).
fof(t5_scmpds_2,axiom,( ! [A] : ( m2_subset_1(A,k1_ami_2,k2_ami_2) => r2_hidden(k3_xtuple_0(1,k1_xboole_0,k12_finseq_1(k2_ami_2,A)),k1_scmpds_i) ) )).
fof(t5_scmpds_3,axiom,( ! [A] : ( ( 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] : ( v7_ordinal1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmpds_2)) ) => k1_funct_1(A,C) = k1_funct_1(k1_funct_4(A,k7_memstr_0(2,k1_scmpds_2,B)),C) ) ) ) )).
fof(t5_scmpds_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( 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,k5_numbers) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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] : ( v7_ordinal1(E) => ( 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)) ) ) ) ) ) ) ) )).
fof(t5_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(B) & 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))) ) ) )).
fof(t5_scmpds_8,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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(k1_nat_1(k5_card_1(D),2),C) <=> r2_hidden(C,k9_xtuple_0(k1_scmpds_8(A,B,D))) ) ) ) ) ) )).
fof(t5_scmpds_9,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( v1_int_1(C) => k1_amistd_1(2,k1_scmpds_2,B,k6_scmpds_2(A,C)) = k1_tarski(k1_ordinal1(B)) ) ) ) )).
fof(t5_scmpds_i,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k7_card_1(15)) => ! [B] : ( m1_subset_1(B,k1_scmpds_i) => ! [C] : ( m1_subset_1(C,k2_scm_inst) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t5_scmring1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m2_subset_1(B,k1_ami_2,k2_ami_2) => k5_card_3(B,k4_card_3(k3_relat_1(k3_ami_2,k1_scmring1(A)))) = u1_struct_0(A) ) ) )).
fof(t5_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( v7_ordinal1(B) => r2_hidden(k3_xtuple_0(6,k9_finseq_1(B),k1_xboole_0),k1_scmringi(A)) ) ) )).
fof(t5_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => k2_compos_0(u1_compos_1(k1_scmring2(A)),k4_scmring2(A,B,C)) = 2 ) ) ) )).
fof(t5_scmring4,axiom,( ! [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) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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(k7_card_1(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(k7_card_1(2),k1_scmring2(A),C)),B) ) ) ) ) )).
fof(t5_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => r1_tarski(k1_scmringi(A),k3_zfmisc_1(k4_ordinal1,k13_finseq_1(k4_ordinal1),k10_xtuple_0(k1_scmringi(A)))) ) )).
fof(t5_scmyciel,axiom,( ! [A] : ! [B] : ~ ( r1_ordinal1(3,k1_card_1(A)) & ! [C] : ! [D] : ~ ( r2_hidden(C,A) & r2_hidden(D,A) & C != B & D != B & C != D ) ) )).
fof(t5_scpisort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t5_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_scmpds_2)) ) => ! [G] : ( v1_int_1(G) => ! [H] : ( 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] : ( ( 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,k5_numbers) ) => ! [J] : ( ( v1_relat_1(J) & v4_relat_1(J,k4_ordinal1) & v5_relat_1(J,u1_compos_1(k1_scmpds_2)) & v1_funct_1(J) & v1_partfun1(J,k4_ordinal1) ) => ( ( 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)),k5_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)),k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t5_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,E) => r2_analoaf(A,B,C,E,D) ) ) ) ) ) ) )).
fof(t5_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v9_ordinal1(A) <=> ! [B] : ( v7_ordinal1(B) => k9_nat_1(k1_numbers,A,B) != k5_numbers ) ) ) )).
fof(t5_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(A) & v2_comseq_2(B) ) => v2_comseq_2(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) ) ) )).
fof(t5_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( r2_relset_1(k4_ordinal1,k4_partfun1(A,k1_numbers),k8_seqfunc(A,B,C),k8_seqfunc(A,C,B)) & r2_relset_1(k4_ordinal1,k4_partfun1(A,k1_numbers),k8_seqfunc(A,k8_seqfunc(A,B,C),D),k8_seqfunc(A,B,k8_seqfunc(A,C,D))) ) ) ) ) ) )).
fof(t5_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v7_valued_0(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,A,k2_xcmplx_0(B,C))) ) ) ) ) )).
fof(t5_series_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_membered(A) & v7_membered(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => k1_valued_1(k2_series_1(B),k2_series_1(C)) = k2_series_1(k1_series_1(A,B,C)) ) ) ) )).
fof(t5_series_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(k1_square_1(k7_xcmplx_0(k2_xcmplx_0(A,B),2)),k7_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),2)) ) ) )).
fof(t5_series_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)) ) ) )).
fof(t5_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ~ ( ~ r1_xxreal_0(B,A) & r1_xxreal_0(k7_xcmplx_0(k2_xcmplx_0(B,k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),2))),k2_xcmplx_0(A,k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),2)))),k3_square_1(k7_xcmplx_0(A,B))) ) ) ) )).
fof(t5_setfam_1,axiom,( ! [A] : ! [B] : ( ! [C] : ( r2_hidden(C,A) => r1_tarski(B,C) ) => ( A = k1_xboole_0 | r1_tarski(B,k1_setfam_1(A)) ) ) )).
fof(t5_setlim_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => k2_relset_1(A,B) = a_2_0_setlim_1(A,B) ) ) )).
fof(t5_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => k8_nat_1(k9_setfam_1(B),k2_setlim_2(B,C,D),A) = k2_setlim_2(B,k8_nat_1(k9_setfam_1(B),C,A),k8_nat_1(k9_setfam_1(B),D,A)) ) ) ) )).
fof(t5_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( m1_subset_1(D,A) => k9_relat_1(C,D) = k1_tarski(k3_funct_2(A,B,C,D)) ) ) ) ) )).
fof(t5_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k5_finsub_1(A)) => ! [E] : ( m1_subset_1(E,k5_finsub_1(B)) => ! [F] : ( ( 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] : ( ( v1_funct_1(G) & v1_funct_2(G,A,C) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [H] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t5_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ( k10_scmfsa_2(A,C) = k10_scmfsa_2(B,D) => ( A = B & C = D ) ) ) ) ) ) )).
fof(t5_sfmastr1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k3_scmfsa6a(D,C)),k1_scmfsa_m(B)) = k2_xcmplx_0(k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,D),k1_scmfsa_m(B)),1),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(k1_funct_4(A,D),C),k1_scmfsa_m(k6_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,D),k1_scmfsa_m(B))))) ) ) ) ) ) )).
fof(t5_sfmastr2,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) => ( k1_funct_1(A,k4_scmfsa_2(k5_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) ) ) ) ) ) ) ) )).
fof(t5_sfmastr3,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & ~ v1_scmfsa_m(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( m1_scmfsa_2(D) => k1_funct_1(k2_extpro_1(k7_card_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))) ) ) ) ) )).
fof(t5_sgraph1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(B,A) => r1_xboole_0(k2_finseq_1(A),k1_sgraph1(B,C)) ) ) ) ) )).
fof(t5_sheffer1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k4_lattices(A,B,k2_sheffer1(A)) = k2_sheffer1(A) ) ) )).
fof(t5_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( 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) ) ) )).
fof(t5_simplex0,axiom,( ! [A] : ! [B] : k1_simplex0(k2_xboole_0(A,B)) = k2_xboole_0(k1_simplex0(A),k1_simplex0(B)) )).
fof(t5_simplex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_simplex0(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t5_simplex2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t5_sin_cos2,axiom,( v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k18_sin_cos,k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos))) )).
fof(t5_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,k6_xcmplx_0(A,B)) = k6_xcmplx_0(k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,B)),k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,B))) ) ) )).
fof(t5_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => k3_xcmplx_0(k19_sin_cos(A),k19_sin_cos(A)) = k6_xcmplx_0(1,k3_xcmplx_0(k17_sin_cos(A),k17_sin_cos(A))) ) )).
fof(t5_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => k17_sin_cos(k3_xcmplx_0(2,A)) = k3_xcmplx_0(k3_xcmplx_0(2,k17_sin_cos(A)),k19_sin_cos(A)) ) )).
fof(t5_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => r1_xxreal_0(k4_xcmplx_0(1),k19_sin_cos(A)) ) )).
fof(t5_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ r1_xxreal_0(k2_xcmplx_0(k3_square_1(k2_xcmplx_0(k1_square_1(A),1)),A),k5_numbers) ) )).
fof(t5_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ( k4_sin_cos2(A) = k7_xcmplx_0(1,k3_square_1(k6_xcmplx_0(1,k1_square_1(k6_sin_cos2(A))))) & k2_sin_cos2(A) = k7_xcmplx_0(k6_sin_cos2(A),k3_square_1(k6_xcmplx_0(1,k1_square_1(k6_sin_cos2(A))))) ) ) )).
fof(t5_sin_cos9,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k26_sin_cos,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(t5_sincos10,axiom,( r2_fdiff_1(k1_fdiff_9,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) & ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) => k1_fdiff_1(k1_fdiff_9,A) = k7_xcmplx_0(k1_funct_1(k16_sin_cos,A),k1_square_1(k1_funct_1(k18_sin_cos,A))) ) ) )).
fof(t5_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(A))) => ! [D] : ( m1_subset_1(D,k1_euclid(A)) => ! [E] : ( m1_subset_1(E,k1_euclid(A)) => ( ( D = B & E = C ) => k3_metric_1(k14_euclid(A),B,C) = k12_euclid(k8_euclid(A,D,E)) ) ) ) ) ) ) )).
fof(t5_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t5_sprect_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r3_connsp_1(A,C,B) => r1_tarski(B,C) ) ) ) ) )).
fof(t5_sprect_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t5_sprect_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( 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),k7_xcmplx_0(1,2)) => B = C ) ) ) ) )).
fof(t5_sprect_4,axiom,( ! [A] : ( ( v4_topreal1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( ( 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)))) ) ) ) )).
fof(t5_sprect_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t5_square_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k1_square_1(k6_xcmplx_0(A,B)) = k2_xcmplx_0(k6_xcmplx_0(k1_square_1(A),k3_xcmplx_0(k3_xcmplx_0(2,A),B)),k1_square_1(B)) ) ) )).
fof(t5_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ( r1_stacks_1(A,B) => k9_stacks_1(A,B) = k1_xboole_0 ) ) ) )).
fof(t5_stirl2_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( k3_nat_1(k6_domain_1(k4_ordinal1,A)) = A & k4_seq_4(k6_domain_1(k4_ordinal1,A)) = A ) ) )).
fof(t5_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v5_relat_1(D,k3_qc_lang1(A)) & v3_card_1(D,C) & m2_finseq_1(D,k2_qc_lang1(A)) ) => ( r2_hidden(B,k1_relset_1(k4_ordinal1,D)) => m2_subset_1(k1_funct_1(D,B),k2_qc_lang1(A),k3_qc_lang1(A)) ) ) ) ) ) )).
fof(t5_subset,axiom,( ! [A] : ! [B] : ! [C] : ~ ( r2_hidden(A,B) & m1_subset_1(B,k1_zfmisc_1(C)) & v1_xboole_0(C) ) )).
fof(t5_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,B) <=> ( r2_hidden(E,C) | r2_hidden(E,D) ) ) ) => B = k4_subset_1(A,C,D) ) ) ) ) )).
fof(t5_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ! [E] : ( ( r2_hidden(C,k1_substlat(A,B)) & r2_hidden(D,C) & r2_hidden(E,C) & r1_tarski(D,E) ) => D = E ) ) )).
fof(t5_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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))) ) ) ) )).
fof(t5_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ( ( ! [D] : ( m1_subset_1(D,k1_substut1(A)) => ? [E] : ( m2_subset_1(E,k16_substut1(A),k38_substut1(A)) & k2_sublemma(A,E) = B & k19_substut1(A,E) = D ) ) & ! [D] : ( m1_subset_1(D,k1_substut1(A)) => ? [E] : ( m2_subset_1(E,k16_substut1(A),k38_substut1(A)) & k2_sublemma(A,E) = C & k19_substut1(A,E) = D ) ) ) => ! [D] : ( m1_subset_1(D,k1_substut1(A)) => ? [E] : ( 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 ) ) ) ) ) ) )).
fof(t5_supinf_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_setfam_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k6_numbers))) ) => ! [B] : ( v2_membered(B) => ( B = k5_setfam_1(k6_numbers,A) => m1_xxreal_2(k1_xxreal_2(k5_supinf_1(A)),B) ) ) ) )).
fof(t5_supinf_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => ( r1_tarski(A,B) <=> r1_tarski(k6_supinf_2(A),k6_supinf_2(B)) ) ) ) )).
fof(t5_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( ~ r1_orders_2(B,D,C) & E != k4_struct_0(A) & ~ ( ~ r1_orders_2(B,k4_vectsp_1(A,B,E,D),C) & ~ r1_orders_2(B,D,k4_vectsp_1(A,B,E,C)) ) ) ) ) ) ) ) )).
fof(t5_sysrel,axiom,( ! [A] : ! [B] : k2_relat_1(k2_zfmisc_1(A,B)) = k2_zfmisc_1(B,A) )).
fof(t5_t_0topsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t5_t_1topsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t5_taxonom1,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(t5_taxonom2,axiom,( v3_taxonom2(k1_xboole_0) )).
fof(t5_taylor_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_xreal_0(B) => k6_prepower(k23_sin_cos(B),k7_xcmplx_0(1,A)) = k23_sin_cos(k7_xcmplx_0(B,A)) ) ) )).
fof(t5_taylor_2,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( k2_fdiff_1(k22_sin_cos,A) = k2_partfun1(k1_numbers,k1_numbers,k22_sin_cos,A) & k9_xtuple_0(k2_partfun1(k1_numbers,k1_numbers,k22_sin_cos,A)) = A ) ) )).
fof(t5_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v9_metric_1(A) & v8_metric_1(A) & v2_tbsp_1(B,A) ) => v3_tbsp_1(B,A) ) ) ) )).
fof(t5_tdgroup,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t5_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)))) ) ) )).
fof(t5_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)))))) ) ) ) )).
fof(t5_tdlat_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t5_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t5_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t5_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t5_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t5_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t5_tietze,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v1_series_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v1_series_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k1_funct_1(A,C),k1_funct_1(B,C)) ) => r1_xxreal_0(k4_series_1(A),k4_series_1(B)) ) ) ) )).
fof(t5_tmap_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,C,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,B))) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t5_toler_1,axiom,( ! [A] : v6_relat_2(k1_eqrel_1(A)) )).
fof(t5_topalg_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k17_borsuk_1))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k17_borsuk_1)) => ( A = k3_rcomp_1(k5_numbers,B) => v3_pre_topc(A,k17_borsuk_1) ) ) ) )).
fof(t5_topalg_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => k1_rcomp_1(A,B) = a_2_0_topalg_2(A,B) ) ) ) )).
fof(t5_topalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t5_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & l3_algstr_0(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v2_group_1(D) & v3_group_1(D) & l3_algstr_0(D) ) => ! [E] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) )).
fof(t5_topalg_5,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t5_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v3_funct_1(C) & m1_borsuk_2(C,A,B,B) ) => ! [D] : ( ( v3_funct_1(D) & m1_borsuk_2(D,A,B,B) ) => r3_borsuk_2(A,B,B,C,D) ) ) ) ) )).
fof(t5_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_topdim_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => r1_xxreal_0(k4_xcmplx_0(1),k2_topdim_1(A,B)) ) ) )).
fof(t5_topdim_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_topdim_1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t5_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t5_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_ordinal1(k1_topgen_2(A,B),k2_topgen_2(A)) ) ) )).
fof(t5_topgen_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( ! [C] : ( ( 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)) ) ) ) )).
fof(t5_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => r1_ordinal1(k4_topgen_1(A),k2_waybel23(A)) ) )).
fof(t5_topgen_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(A,k9_xtuple_0(k1_funct_1(k9_funct_6(C),B))) <=> ? [D] : ( 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)) ) ) ) )).
fof(t5_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t5_topmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( r2_hidden(B,C) => ! [D] : ( m1_connsp_2(D,A,B) => ! [E] : ( m1_subset_1(E,u1_struct_0(k1_pre_topc(A,C))) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t5_topmetr3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r1_tarski(k2_relset_1(k1_numbers,C),k1_rcomp_1(A,B)) => ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k2_topmetr(A,B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k2_topmetr(A,B))))) ) ) ) ) ) )).
fof(t5_topreal1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t5_topreal2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( v1_topreal2(A) <=> ( ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & B != C & r2_hidden(B,A) & r2_hidden(C,A) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( B != C & r2_hidden(B,A) & r2_hidden(C,A) & ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [E] : ( ( ~ 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) ) ) ) ) ) ) ) ) ) )).
fof(t5_topreal4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v1_topreal4(A) => v1_topreal2(A) ) ) )).
fof(t5_topreal5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( ( 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] : ( m1_subset_1(I,u1_struct_0(A)) => ~ ( r2_hidden(I,D) & k1_funct_1(H,I) = G ) ) ) ) ) ) ) ) ) ) ) )).
fof(t5_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => k19_rvsum_1(k2_finseq_2(2,A)) = k3_xcmplx_0(A,A) ) )).
fof(t5_topreal7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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 ) ) ) ) ) ) )).
fof(t5_topreal8,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & m2_finseq_1(C,B) ) => ! [D] : ( 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 ) ) ) ) )).
fof(t5_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ( r2_hidden(D,k1_topreal9(A,C,B)) <=> ~ r1_xxreal_0(B,k12_euclid(k5_algstr_0(k15_euclid(A),D,C))) ) ) ) ) ) )).
fof(t5_topreala,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v3_pre_topc(E,A) & m1_connsp_2(E,A,C) ) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t5_toprealb,axiom,( k1_pre_topc(k2_topalg_2,k5_toprealb(k2_subset_1(k1_numbers))) = k2_topalg_2 )).
fof(t5_toprealc,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t5_toprns_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(k15_euclid(B))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(B))))) ) => k9_nat_1(u1_struct_0(k15_euclid(B)),k2_toprns_1(A,B,D),C) = k1_rlvect_1(k15_euclid(B),k9_nat_1(u1_struct_0(k15_euclid(B)),D,C),A) ) ) ) ) )).
fof(t5_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t5_tops_2,axiom,( ! [A] : ! [B] : ( 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 ) ) ) )).
fof(t5_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) ) )).
fof(t5_tops_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v1_xreal_0(E) & v2_xxreal_0(E) ) => ? [F] : ( 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,k8_metric_1(B,D,E))) ) ) ) ) ) ) ) )).
fof(t5_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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,B,C),k1_transgeo(A,B,D)) | r2_funct_2(A,A,k1_transgeo(A,C,B),k1_transgeo(A,D,B)) ) => r2_funct_2(A,A,C,D) ) ) ) ) ) )).
fof(t5_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( 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 ) ) ) )).
fof(t5_treal_1,axiom,( k18_borsuk_1 = k1_treal_1(k5_numbers,1) & k19_borsuk_1 = k2_treal_1(k5_numbers,1) )).
fof(t5_trees_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ~ ( r2_xboole_0(A,B) & r1_xxreal_0(k5_card_1(B),k5_card_1(A)) ) ) ) )).
fof(t5_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ( ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( r2_hidden(C,A) <=> r2_hidden(C,B) ) ) => A = B ) ) ) )).
fof(t5_trees_3,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(t5_trees_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ( k9_xtuple_0(A) = k2_trees_1(k5_numbers) => A = k1_trees_4(k1_funct_1(A,k1_xboole_0)) ) ) )).
fof(t5_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => ( k4_trees_1(A,B) = k2_trees_1(k5_numbers) <=> r2_hidden(B,k3_trees_1(A)) ) ) ) )).
fof(t5_trees_a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m4_trees_1(B,A) => k6_subset_1(a_2_0_trees_a(A,B),a_2_1_trees_a(A,B)) = B ) ) )).
fof(t5_triang_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ! [C] : ( ( r1_tarski(B,C) & r2_hidden(C,k1_triang_1(A)) ) => r2_hidden(B,k1_triang_1(A)) ) ) )).
fof(t5_tsep_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t5_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tsep_2(A,B,k3_subset_1(u1_struct_0(A),B)) ) ) )).
fof(t5_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t5_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tsp_2(B,A) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t5_turing_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( k1_gr_cy_1(k4_turing_1(1,k3_finseq_4(k4_ordinal1,A,B,C))) = A & k1_gr_cy_1(k4_turing_1(2,k3_finseq_4(k4_ordinal1,A,B,C))) = k1_nat_1(A,B) & k1_gr_cy_1(k4_turing_1(3,k3_finseq_4(k4_ordinal1,A,B,C))) = k1_nat_1(k1_nat_1(A,B),C) ) ) ) ) )).
fof(t5_twoscomp,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( 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)) ) ) ) )).
fof(t5_uniform1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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)) ) ) ) ) ) )).
fof(t5_uniroots,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( C = A & D = B ) => ( k3_xcmplx_0(C,D) = k8_group_1(k1_complfld,A,B) & k2_xcmplx_0(C,D) = k1_algstr_0(k1_complfld,A,B) ) ) ) ) ) ) )).
fof(t5_uproots,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( C != k5_numbers => k22_pre_poly(A,k1_uproots(A,B,C)) = B ) ) ) )).
fof(t5_urysohn1,axiom,( ! [A] : ( v7_ordinal1(A) => r1_tarski(k1_urysohn1(A),k1_urysohn1(k1_nat_1(A,1))) ) )).
fof(t5_urysohn2,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ! [B] : ( m1_subset_1(B,k6_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 ) ) ) ) )).
fof(t5_urysohn3,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k2_urysohn1) => r2_hidden(A,k1_urysohn1(k3_urysohn3(A))) ) ) )).
fof(t5_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_funct_2(C,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [D] : ( 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 ) ) ) ) )).
fof(t5_valued_0,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k4_numbers) ) => ( r1_tarski(A,B) => v5_relat_1(A,k4_numbers) ) ) ) )).
fof(t5_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : k1_funct_1(k18_valued_1(A,B),C) = k3_xcmplx_0(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) )).
fof(t5_valued_2,axiom,( ! [A] : m1_subset_1(k11_valued_2(A),k1_zfmisc_1(k10_valued_2(A))) )).
fof(t5_vectmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v6_vectmetr(A) & l1_vectmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_metric_1(A,B,C) = k3_vectmetr(A,k5_algstr_0(A,C,B)) ) ) ) )).
fof(t5_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( r1_vectsp_5(A,B,C,D) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t5_vectsp11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(D),C,C) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(D))) ) => ( ( r2_hidden(A,k2_finseq_1(C)) & r2_hidden(B,k2_finseq_1(C)) ) => k2_laplace(A,B,C,D,k2_matrix13(C,C,D,F,E)) = k2_matrix13(k7_nat_d(C,1),k7_nat_d(C,1),D,k2_laplace(A,B,C,D,F),E) ) ) ) ) ) ) ) )).
fof(t5_vectsp_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t5_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t5_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( u1_struct_0(B) = C => v1_vectsp_4(C,A,B) ) ) ) ) )).
fof(t5_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => k1_vectsp_5(A,B,C,D) = k1_vectsp_5(A,B,D,C) ) ) ) ) )).
fof(t5_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => m2_vectsp_6(k2_vectsp_6(A,B),A,B,C) ) ) ) )).
fof(t5_vectsp_7,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => C != k4_vectsp_1(A,B,E,D) ) ) ) ) & ( ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t5_vectsp_8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t5_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( m2_finseq_1(E,u1_struct_0(B)) => ~ ( r1_tarski(k10_xtuple_0(E),u1_struct_0(k1_vectsp_7(A,B,D))) & ! [F] : ( m2_vectsp_6(F,A,B,D) => k4_rlvect_1(B,k3_vectsp_6(A,B,E,C)) != k4_vectsp_6(A,B,F) ) ) ) ) ) ) ) )).
fof(t5_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t5_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ( ( 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))) ) ) ) ) ) )).
fof(t5_waybel10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( 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)) ) ) ) )).
fof(t5_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t5_waybel12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t5_waybel13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t5_waybel14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t5_waybel15,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v3_orders_2(C) & v4_orders_2(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t5_waybel16,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k7_lattice3(A)))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t5_waybel17,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t5_waybel18,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => v5_pre_topc(k6_waybel18(A,B,C),k3_waybel18(A,B),k4_waybel18(A,B,C)) ) ) ) )).
fof(t5_waybel19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & v1_waybel19(A) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) => v12_waybel_0(B,A) ) ) ) )).
fof(t5_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ( r2_yellow_0(A,k1_xboole_0) => v2_yellow_0(A) ) ) )).
fof(t5_waybel21,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t5_waybel22,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t5_waybel23,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t5_waybel25,axiom,( ! [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] : ( ( 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] : ( ( v4_waybel11(C) & m1_yellow_9(C,A) ) => ! [D] : ( ( v4_waybel11(D) & m1_yellow_9(D,B) ) => ( r5_waybel_1(A,B) => r2_borsuk_3(C,D) ) ) ) ) ) )).
fof(t5_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ? [B] : ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k1_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(k1_yellow_1(u1_pre_topc(A))),u1_struct_0(k1_waybel26(A,k9_waybel18))))) & v23_waybel_0(B,k1_yellow_1(u1_pre_topc(A)),k1_waybel26(A,k9_waybel18)) & ! [C] : ( ( 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)) ) ) ) )).
fof(t5_waybel27,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v2_waybel27(D) ) => ! [E] : ( ( 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)) ) ) ) )).
fof(t5_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v7_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r1_orders_2(A,B,D) & r1_orders_2(A,C,D) ) ) ) ) )).
fof(t5_waybel29,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( l1_orders_2(C) => ! [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)) ) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t5_waybel30,axiom,( ! [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] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t5_waybel31,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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) ) => ( k1_yellow_1(u1_pre_topc(A)) = B => ! [C] : ( ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t5_waybel32,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) )).
fof(t5_waybel33,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ( u1_struct_0(A) = u1_struct_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & v4_orders_2(C) & v7_waybel_0(C) & l1_waybel_0(C,A) ) => ! [D] : ( ( ~ 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] : ( m2_yellow_6(E,A,C) => ? [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t5_waybel34,axiom,( ! [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] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(t5_waybel35,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( ( v4_waybel_4(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ( 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) ) ) ) )).
fof(t5_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t5_waybel_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t5_waybel_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t5_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t5_waybel_4,axiom,( ! [A] : ( ( 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(k1_yellow_1(k3_waybel_4(A))) = k4_waybel_4(A) ) )).
fof(t5_waybel_5,axiom,( ! [A] : ( ( 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),k1_yellow_1(k7_waybel_0(A)),A) & v18_waybel_0(k2_yellow_2(A),k1_yellow_1(k7_waybel_0(A)),A) ) => v4_waybel_1(k2_yellow_2(A),k1_yellow_1(k7_waybel_0(A)),A) ) ) )).
fof(t5_waybel_6,axiom,( ! [A] : ( ( 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] : ( ( v13_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_waybel_6(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & r1_xboole_0(k1_waybel_3(A,C),B) ) ) ) ) ) )).
fof(t5_waybel_7,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k2_yellow_1(A))) => k7_waybel_1(k2_yellow_1(A),B) = k6_subset_1(A,B) ) )).
fof(t5_waybel_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( 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))) ) ) )).
fof(t5_waybel_9,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) )).
fof(t5_wellfnd1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v12_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( C = k2_xboole_0(B,k1_tarski(D)) & r1_tarski(k1_wellord1(u1_orders_2(A),D),B) ) => v12_waybel_0(C,A) ) ) ) ) )).
fof(t5_wellord1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( r2_wellord1(B,A) => ! [C] : ~ ( r1_tarski(C,A) & C != k1_xboole_0 & ! [D] : ~ ( r2_hidden(D,C) & ! [E] : ( r2_hidden(E,C) => r2_hidden(k4_tarski(D,E),B) ) ) ) ) ) )).
fof(t5_wellord2,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( ( r4_wellord1(A,k1_wellord2(B)) & r4_wellord1(A,k1_wellord2(C)) ) => B = C ) ) ) ) )).
fof(t5_wsierp_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t5_xboole_0,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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) ) ) )).
fof(t5_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(k2_xboole_0(A,C),k2_xboole_0(B,C)) )).
fof(t5_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k5_xboolean(A,k4_xboolean(A,B)) = A ) ) )).
fof(t5_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( k3_xcmplx_0(A,C) = k3_xcmplx_0(B,C) => ( C = k5_numbers | A = B ) ) ) ) ) )).
fof(t5_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,A) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,A) & ~ r1_xxreal_0(B,C) ) ) ) ) ) )).
fof(t5_xtuple_0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( k6_xtuple_0(A,B,C,D) = k6_xtuple_0(E,F,G,H) => ( A = E & B = F & C = G & D = H ) ) )).
fof(t5_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => r1_xxreal_0(k2_xxreal_0,A) ) )).
fof(t5_xxreal_1,axiom,( ! [A] : ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ~ ( r2_hidden(A,k1_xxreal_1(B,C)) & ~ r2_hidden(A,k4_xxreal_1(B,C)) & A != B & A != C ) ) ) )).
fof(t5_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ( r1_tarski(B,A) => ! [C] : ( m2_xxreal_2(C,A) => m2_xxreal_2(C,B) ) ) ) ) )).
fof(t5_xxreal_3,axiom,( k2_xxreal_3(k2_xxreal_0) = k1_xxreal_0 )).
fof(t5_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & v1_yellow_0(B) & l1_orders_2(B) ) => ! [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))) ) ) ) ) )).
fof(t5_yellow11,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k12_lattice3(A,B,C) = C <=> k13_lattice3(A,B,C) = B ) ) ) ) )).
fof(t5_yellow12,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : r1_tarski(k7_relat_1(k13_funct_3(k10_funct_3(C,D),k9_funct_3(C,D)),k2_zfmisc_1(A,B)),k2_zfmisc_1(B,A)) )).
fof(t5_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => v7_pre_topc(A) ) )).
fof(t5_yellow14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( l1_struct_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t5_yellow15,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k6_margrel1) => k1_yellow15(A,k6_finseq_1(k9_setfam_1(A)),B) = k6_finseq_1(k9_setfam_1(A)) ) )).
fof(t5_yellow16,axiom,( ! [A] : ( ( ~ 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] : ( ( 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) ) ) ) )).
fof(t5_yellow17,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( ( r2_hidden(D,k1_funct_1(A,C)) & r2_hidden(C,k9_xtuple_0(A)) & r2_hidden(B,k4_card_3(A)) ) => r2_hidden(k1_funct_7(B,C,D),k8_relat_1(k12_card_3(A,C),k1_tarski(D))) ) ) ) )).
fof(t5_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t5_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => ! [D] : ( ( ~ v1_xboole_0(D) & v2_waybel_0(D,k2_yellow_1(k2_struct_0(A))) & v13_waybel_0(D,k2_yellow_1(k2_struct_0(A))) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k2_struct_0(A))))) ) => ( r2_waybel_7(A,D,C) => r2_hidden(B,D) ) ) ) ) ) ) ) )).
fof(t5_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( m2_functor0(C,A,B) => ( v21_functor0(C,A,B) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t5_yellow21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & v2_yellow21(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( 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)) ) ) ) ) ) )).
fof(t5_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ! [C] : ( 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) ) ) ) ) )).
fof(t5_yellow_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v4_yellow_0(k1_yellow_1(B),k2_yellow_1(A)) & m1_yellow_0(k1_yellow_1(B),k2_yellow_1(A)) ) ) )).
fof(t5_yellow_2,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r1_tarski(B,C) => r1_tarski(k2_wellord1(A,B),k2_wellord1(A,C)) ) ) )).
fof(t5_yellow_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => k13_lattice3(A,k2_yellow_0(A,B),C) = C ) ) ) ) )).
fof(t5_yellow_4,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t5_yellow_5,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_orders_2(A,k12_lattice3(A,B,C),k13_lattice3(A,B,D)) ) ) ) ) )).
fof(t5_yellow_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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 ) ) ) ) )).
fof(t5_yellow_7,axiom,( ! [A] : ( l1_orders_2(A) => ( v5_orders_2(A) <=> v5_orders_2(k7_lattice3(A)) ) ) )).
fof(t5_yellow_8,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t5_yoneda_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_oppcat_1(B,A,k9_nattra_1(A,k1_yoneda_1(A))) => ( ( v2_funct_1(k7_cat_1(A,k9_nattra_1(A,k1_yoneda_1(A)),B)) & v1_yoneda_1(B,A,k9_nattra_1(A,k1_yoneda_1(A))) ) => v2_funct_1(B) ) ) ) )).
fof(t5_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ! [D] : ( ( v8_zf_fund1(B,A) & r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k3_xboole_0(C,D),B) ) ) ) )).
fof(t5_zf_fund2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ( ( v8_zf_fund1(B,A) & v1_ordinal1(B) ) => v1_zf_fund2(B) ) ) ) )).
fof(t5_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ~ ( v2_zf_lang(A) & ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => A != k4_zf_lang(B,C) ) ) ) & ( ? [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) & ? [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) & A = k4_zf_lang(B,C) ) ) => v2_zf_lang(A) ) & ~ ( v3_zf_lang(A) & ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => A != k5_zf_lang(B,C) ) ) ) & ( ? [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) & ? [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) & A = k5_zf_lang(B,C) ) ) => v3_zf_lang(A) ) & ~ ( v4_zf_lang(A) & ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => A != k6_zf_lang(B) ) ) & ( ? [B] : ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) & A = k6_zf_lang(B) ) => v4_zf_lang(A) ) & ~ ( v5_zf_lang(A) & ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => A != k7_zf_lang(B,C) ) ) ) & ( ? [B] : ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) & ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & A = k7_zf_lang(B,C) ) ) => v5_zf_lang(A) ) & ~ ( v6_zf_lang(A) & ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => A != k8_zf_lang(B,C) ) ) ) & ( ? [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) & ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & A = k8_zf_lang(B,C) ) ) => v6_zf_lang(A) ) ) ) )).
fof(t5_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( k21_zf_lang(k10_zf_lang(A,B)) = A & k22_zf_lang(k10_zf_lang(A,B)) = B ) ) ) )).
fof(t5_zf_model,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t5_zf_refle,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r1_xboole_0(k1_enumset1(k2_zf_lang(k5_numbers),k2_zf_lang(1),k2_zf_lang(2)),k2_zf_model(B)) => r2_zf_model(A,k11_zf_model(B)) ) ) ) )).
fof(t5_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( k1_tarski(A) = k2_tarski(B,C) => B = C ) )).
fof(t5_zfmodel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_ordinal1(A) => ( r2_zf_model(A,k8_zf_model) <=> ! [B] : ( r2_hidden(B,A) => r2_hidden(k3_tarski(B),A) ) ) ) ) )).
fof(t5_zfmodel2,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t5_zfrefle1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ( r1_zfrefle1(A,k2_zfrefle1) & v1_ordinal1(A) ) => v1_zf_model(A) ) ) )).
fof(t5_zmodul01,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(t5_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_zmodul02(A))) => ! [D] : ( v1_int_1(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k1_int_3)) => ( ( B = C & D = E ) => k1_zmodul01(A,B,D) = k4_vectsp_1(k1_int_3,k15_zmodul02(A),E,C) ) ) ) ) ) ) )).
fof(t5_zmodul03,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( ( 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),k4_ordinal1,u1_struct_0(A),E,C) => k4_rlvect_1(A,k20_zmodul02(A,C,B)) = k4_rlvect_1(A,k20_zmodul02(A,D,B)) ) ) ) ) ) ) )).
fof(t60_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l3_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_abcmiz_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t60_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v6_abcmiz_1(B,A) & m1_abcmiz_1(B,A,k13_abcmiz_1(A)) ) => ? [C] : ( 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 ) ) ) )).
fof(t60_abcmiz_a,axiom,( ! [A] : ( ( v1_xboole_0(A) & m2_finseq_2(A,k2_abcmiz_1,k4_abcmiz_1) ) => m2_abcmiz_a(k1_xboole_0,A) ) )).
fof(t60_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t60_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v3_valued_0(A) & v1_finset_1(A) ) => ! [B] : ( v1_xreal_0(B) => ( v4_partfun3(A) => ( r1_xxreal_0(k1_afinsq_1(A),k5_numbers) | ! [C] : ~ ( r2_hidden(C,k1_relset_1(k4_ordinal1,A)) & k1_funct_1(A,C) = B ) | r1_xxreal_0(B,k7_afinsq_2(A)) ) ) ) ) )).
fof(t60_algspec1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_instalg1(B) & l1_msualg_1(B) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t60_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( F != G & ~ ( ~ ( r2_analoaf(A,F,G,B,C) & r2_analoaf(A,F,G,D,E) ) & ~ ( r2_analoaf(A,F,G,B,C) & r2_analoaf(A,D,E,F,G) ) & ~ ( r2_analoaf(A,B,C,F,G) & r2_analoaf(A,D,E,F,G) ) & ~ ( r2_analoaf(A,B,C,F,G) & r2_analoaf(A,F,G,D,E) ) ) & ~ r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) ) )).
fof(t60_aofa_000,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_freealg(A) ) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(k7_freealg(k19_aofa_000,A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t60_aofa_a00,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & l6_aofa_a00(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l5_aofa_a00(B) ) => ( r1_subset_1(u4_struct_0(A),u4_struct_0(B)) => v16_aofa_a00(k36_aofa_a00(A,B)) ) ) ) )).
fof(t60_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v19_aofa_a00(E,A) & m1_subset_1(E,u1_struct_0(A)) ) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,C),E)) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),E)) => ! [H] : ( m2_pboole(H,u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,D)) => k15_aofa_a00(A,B,C,D,u8_aofa_a00(A),k33_aofa_a00(A,C,E,F,G),H) = k33_aofa_a00(A,D,E,k15_aofa_a00(A,B,C,D,E,F,H),k15_aofa_a00(A,B,C,D,E,G,H)) ) ) ) ) ) ) ) ) )).
fof(t60_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_aofa_i00(D,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [G] : ( m1_aofa_i00(G,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [H] : ( m1_aofa_i00(H,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [I] : ( m1_aofa_i00(I,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ( ? [J] : ( v1_relat_1(J) & v1_funct_1(J) & k1_funct_1(J,C) = k5_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,k5_numbers),k13_aofa_000(A,k13_aofa_000(A,k51_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,F,k5_numbers),k51_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,G,1)),k17_aofa_000(A,k51_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_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,k5_numbers),D,H,F),k48_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,F,G)),k81_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,G,H)),k57_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,I,1))),D) ) ) ) ) ) ) ) ) ) ) )).
fof(t60_armstrng,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r2_hidden(C,k13_armstrng(A,k12_armstrng(A,B))) <=> r6_armstrng(A,C,B) ) ) ) ) )).
fof(t60_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ? [B] : ( m1_subset_1(B,k5_arytm_3) & A = k9_arytm_3(B,B) ) ) )).
fof(t60_asympt_1,axiom,( v4_asympt_0(k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k3_asympt_1(1),k1_seq_1(1))) )).
fof(t60_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t60_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,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)) ) ) ) ) )).
fof(t60_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t60_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( 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)) ) ) ) )).
fof(t60_borsuk_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr))) => ( r2_hidden(A,k8_borsuk_6) => r1_xxreal_0(k7_xcmplx_0(1,2),k1_xtuple_0(A)) ) ) )).
fof(t60_borsuk_7,axiom,( ! [A] : ( v1_int_1(A) => k1_funct_1(k12_borsuk_7,A) = k8_borsuk_7 ) )).
fof(t60_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t60_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_eqrel_1(I,A) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t60_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t60_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => ( r1_xxreal_0(A,k6_xboolean(B,C)) <=> r1_xxreal_0(k4_xboolean(A,B),C) ) ) ) ) )).
fof(t60_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( m2_subset_1(E,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [F] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t60_card_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k1_card_1(A) = k1_card_1(k9_xtuple_0(A)) ) )).
fof(t60_card_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => r1_ordinal1(k1_card_1(k10_xtuple_0(A)),k1_card_1(k9_xtuple_0(A))) ) )).
fof(t60_card_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t60_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( 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] : ( 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] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) )).
fof(t60_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t60_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t60_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t60_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_chain_1(B,k1_nat_1(A,1)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k4_chain_1(k1_nat_1(A,1),B,k1_nat_1(A,1)))) => k10_chain_1(k1_nat_1(A,1),B,A,k3_subset_1(k4_chain_1(k1_nat_1(A,1),B,k1_nat_1(A,1)),C)) = k10_chain_1(k1_nat_1(A,1),B,A,C) ) ) ) )).
fof(t60_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ( v4_glib_000(A) => v2_chord(A) ) ) )).
fof(t60_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_circcomb(A) & v2_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_circcomb(B) & v2_circcomb(B) & l1_msualg_1(B) ) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t60_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( m3_msaterm(D,A,C) => ! [E] : ( ( ~ v2_struct_0(E) & ~ v11_struct_0(E) & v2_msafree2(E) & l1_msualg_1(E) ) => ! [F] : ( ( v4_msualg_1(F,E) & v4_msafree2(F,E) & l3_msualg_1(F,E) ) => ( r7_circtrm1(A,B,C,D,E,F) => ! [G] : ( 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] : ( m1_subset_1(H,u1_struct_0(E)) => ~ ! [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_xcmplx_0(1,k6_trees_1(k9_xtuple_0(G)))),H) & ? [J] : ( m2_circtrm1(J,A,C,B,D,E,F) & ! [K] : ( 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] : ( m1_circtrm1(L,A,C,D,B,K) => k1_funct_1(k5_facirc_1(E,F,I,k2_xcmplx_0(1,k6_trees_1(k9_xtuple_0(G)))),H) = k7_circtrm1(A,B,C,G,L) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t60_classes1,axiom,( ! [A] : ! [B] : k5_classes1(k2_xboole_0(A,B)) = k2_xboole_0(k5_classes1(A),k5_classes1(B)) )).
fof(t60_classes2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) ) )).
fof(t60_clvect_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t60_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v2_clvect_2(B,A) & v2_clvect_2(C,A) ) => v2_clvect_2(k3_normsp_1(A,B,C),A) ) ) ) ) )).
fof(t60_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ! [D] : ( r2_hidden(C,k3_tarski(A)) => ! [E] : ( ( 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] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t60_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k9_complex1(k6_xcmplx_0(A,B)) = k9_complex1(k6_xcmplx_0(B,A)) ) ) )).
fof(t60_complex2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( k1_comptrig(B) = k1_comptrig(C) => ( B = k5_numbers | C = k5_numbers | k1_comptrig(k2_complex2(B,A)) = k1_comptrig(k2_complex2(C,A)) ) ) ) ) ) )).
fof(t60_complfld,axiom,( k9_complex1(k5_struct_0(k1_complfld)) = 1 )).
fof(t60_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( m2_finseq_1(C,k2_numbers) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k3_finseq_1(B) = k3_finseq_1(C) ) => k8_complsp2(A,k7_seq_4(B,C)) = k2_xcmplx_0(k8_complsp2(A,B),k8_complsp2(A,C)) ) ) ) ) )).
fof(t60_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( v6_compos_0(D,u1_compos_1(A)) & m1_subset_1(D,u1_compos_1(A)) ) => ! [E] : ( ( v6_compos_0(E,u1_compos_1(A)) & m1_subset_1(E,u1_compos_1(A)) ) => ! [F] : ( ( v6_compos_0(F,u1_compos_1(A)) & m1_subset_1(F,u1_compos_1(A)) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t60_comptrig,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( m1_subset_1(B,k2_numbers) => ! [C] : ( m1_comptrig(C,B,A) => ( C = k5_numbers => B = k5_numbers ) ) ) ) )).
fof(t60_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k3_finseq_2(k4_ordinal1)) & v1_funct_1(C) & v4_valued_0(C) & v2_margrel1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k3_finseq_2(k4_ordinal1)) & v1_funct_1(D) & v4_valued_0(D) & v2_margrel1(D) ) => ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(k1_nat_1(k19_margrel1(C),1),k4_ordinal1)) => ( r2_hidden(A,k4_finseq_1(E)) => ( r2_hidden(k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,k1_nat_1(B,1)),k1_relset_1(k3_finseq_2(k4_ordinal1),k7_comput_1(C,D,A))) <=> ( r2_hidden(k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,B),k1_relset_1(k3_finseq_2(k4_ordinal1),k7_comput_1(C,D,A))) & r2_hidden(k8_finseq_1(k4_ordinal1,k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,B),k12_finseq_1(k4_ordinal1,k1_recdef_1(k7_comput_1(C,D,A),k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,B)))),k1_relset_1(k3_finseq_2(k4_ordinal1),D)) ) ) ) ) ) ) ) ) )).
fof(t60_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_comseq_3(A) => ! [B] : ( v7_ordinal1(B) => k11_comseq_3(A) = k2_xcmplx_0(k9_nat_1(k2_numbers,k10_comseq_3(A),B),k11_comseq_3(k1_valued_0(k2_numbers,A,k1_nat_1(B,1)))) ) ) ) )).
fof(t60_convex4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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))) ) ) ) ) )).
fof(t60_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) )).
fof(t60_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) )).
fof(t60_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,B) & m2_finseq_1(C,k2_qc_lang1(A)) ) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k5_qc_lang1(A)) => ! [E] : ( 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)))) ) ) ) ) ) )).
fof(t60_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k16_csspace(A,B,k16_csspace(A,C,D)),k16_csspace(A,k16_csspace(A,B,C),D)) ) ) ) ) )).
fof(t60_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k5_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k18_sin_cos),A),B) = k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k19_sin_cos(k2_xcmplx_0(k3_xcmplx_0(2,B),A)),k19_sin_cos(k6_xcmplx_0(k3_xcmplx_0(2,B),A)))) ) ) )).
fof(t60_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_funct_1(k5_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k18_sin_cos),k18_sin_cos),A),B) = k4_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,2),k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,k17_sin_cos(B)),k17_sin_cos(k7_xcmplx_0(A,2))),k3_xcmplx_0(k17_sin_cos(k3_xcmplx_0(3,B)),k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(3,A),2)))))) ) ) )).
fof(t60_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(A,k1_relset_1(k1_numbers,k27_sin_cos)) & r2_hidden(B,k1_relset_1(k1_numbers,k27_sin_cos)) ) => k9_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k27_sin_cos),k18_sin_cos),A,B) = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k1_newton(k19_sin_cos(A),3),k1_square_1(k17_sin_cos(B))),k3_xcmplx_0(k1_newton(k19_sin_cos(B),3),k1_square_1(k17_sin_cos(A)))),k3_xcmplx_0(k3_xcmplx_0(k1_square_1(k17_sin_cos(A)),k1_square_1(k17_sin_cos(B))),k6_xcmplx_0(A,B))) ) ) ) )).
fof(t60_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k9_int_3(A))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k9_int_3(A))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k9_int_3(A))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k9_int_3(A))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k9_int_3(A))) => ! [K] : ( 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] : ( 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 = k5_int_1(2,A) & D = k5_int_1(3,A) & E = k5_int_1(4,A) & F = k5_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)))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t60_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t60_entropy1,axiom,( ! [A] : ( ( v1_matrprob(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( ( v1_matrprob(B) & m2_finseq_1(B,k1_numbers) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( C = k6_matrixr1(k9_matrixr1(A),k10_matrixr1(B)) => k5_matrprob(k5_entropy1(C)) = k2_xcmplx_0(k18_rvsum_1(k4_entropy1(A)),k18_rvsum_1(k4_entropy1(B))) ) ) ) ) )).
fof(t60_enumset1,axiom,( ! [A] : ! [B] : ! [C] : k1_enumset1(A,B,C) = k1_enumset1(C,B,A) )).
fof(t60_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(t60_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => k8_euclid(3,k9_euclid(3,C,A),k9_euclid(3,C,B)) = k9_euclid(3,k1_euclid_8(k1_funct_1(C,1),k1_funct_1(C,2),k1_funct_1(C,3)),k6_xcmplx_0(A,B)) ) ) ) )).
fof(t60_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t60_exchsort,axiom,( ! [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) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_exchsort(B) ) => ! [C] : ( m1_subset_1(C,k9_xtuple_0(B)) => ! [D] : ( m1_subset_1(D,k9_xtuple_0(B)) => r1_tarski(k6_subset_1(k1_ordinal1(D),C),k9_xtuple_0(B)) ) ) ) ) )).
fof(t60_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) )).
fof(t60_fdiff_11,axiom,( ! [A] : ( ( 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),k18_sin_cos))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(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),k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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),k18_sin_cos),A),B) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(2,k1_funct_1(k16_sin_cos,k6_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k1_funct_1(k2_sin_cos9,B)))),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t60_fib_num2,axiom,( k6_fib_num2(1) = k12_finseq_1(k4_ordinal1,1) )).
fof(t60_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( 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))) ) ) ) ) )).
fof(t60_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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))) ) ) ) )).
fof(t60_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(B,k2_finseq_1(A)) => r2_hidden(k2_xcmplx_0(B,C),k2_finseq_1(k2_xcmplx_0(A,C))) ) ) ) ) )).
fof(t60_finseq_2,axiom,( ! [A] : k2_finseq_2(3,A) = k11_finseq_1(A,A,A) )).
fof(t60_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : ( v7_ordinal1(C) => ( C = k6_xcmplx_0(k3_finseq_1(A),k5_card_1(k8_relat_1(A,B))) => k1_relset_1(k4_ordinal1,k1_finseq_3(A,B)) = k2_finseq_1(C) ) ) ) )).
fof(t60_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( k10_xtuple_0(A) = k4_finseq_1(A) => v2_funct_1(A) ) ) )).
fof(t60_finseq_5,axiom,( ! [A] : k3_finseq_5(k9_finseq_1(A)) = k9_finseq_1(A) )).
fof(t60_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t60_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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 ) ) ) ) ) ) )).
fof(t60_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t60_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => r1_tarski(k1_flang_2(A,k8_flang_1(A,B),C,D),k8_flang_1(A,B)) ) ) ) )).
fof(t60_flang_3,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(t60_fomodel0,axiom,( ! [A] : ! [B] : ( r1_tarski(k3_tarski(A),B) => r1_tarski(A,k9_setfam_1(B)) ) )).
fof(t60_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & v8_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(F,u1_struct_0(k11_fsm_1(A,B,C))) => ! [G] : ( m1_subset_1(G,F) => ! [H] : ( m1_subset_1(H,F) => ~ ( r2_hidden(G,u1_struct_0(E)) & r2_hidden(H,u1_struct_0(E)) & G != H ) ) ) ) ) ) ) ) ) ) )).
fof(t60_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,B,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(t60_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => r1_tarski(k7_relat_1(k6_relat_1(B,C),A),k7_relat_1(C,A)) ) )).
fof(t60_funct_2,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t60_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k2_zfmisc_1(A,C),E) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,C),E))) ) => ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,k2_zfmisc_1(B,D),F) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B,D),F))) ) => ~ ( E != 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,B),k2_zfmisc_1(C,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,B),k2_zfmisc_1(C,D)),k2_zfmisc_1(E,F)))) ) ) ) ) )).
fof(t60_funct_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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)))) ) ) ) ) ) )).
fof(t60_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_funct_7(B) ) => ( B != k1_xboole_0 => k9_xtuple_0(k3_funct_7(A,B)) = k3_xboole_0(k5_funct_7(B),A) ) ) )).
fof(t60_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => r2_funct_8(A,k1_numbers,k1_numbers,k1_funct_8) ) )).
fof(t60_fvaluat1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m1_fvaluat1(C,B) => ( v3_fvaluat1(B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t60_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t60_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( C != k4_tarski(k10_finseq_1(A,B),k4_gfacirc1) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k22_gfacirc1(A,B,C),k23_gfacirc1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( 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)) ) ) ) ) ) ) ) )).
fof(t60_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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)) ) ) )).
fof(t60_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( 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)) ) ) ) )).
fof(t60_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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_0(k2_goboard2(C)),k1_nat_1(B,1)) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1))),k3_topreal1(2,C)) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,2))),k3_topreal1(2,C)) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1))),k3_topreal1(2,C)) ) ) ) ) )).
fof(t60_graph_2,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(A)) ) => k8_graph_2(A,B,B) = B ) ) ) )).
fof(t60_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_graph_1(A) & v6_graph_1(A) & l1_graph_1(A) ) => ( ~ ( ? [B] : ( v2_funct_1(B) & m2_graph_1(B,A) & ~ v1_msscyc_1(B,A) & v1_graph_3(B,A) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( v1_abian(k10_graph_1(A,D)) <=> ( D != B & D != C ) ) ) ) ) ) ) & ~ ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & B != C & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( v1_abian(k10_graph_1(A,D)) <=> ( D != B & D != C ) ) ) ) ) & ! [B] : ( ( v2_funct_1(B) & m2_graph_1(B,A) ) => ~ ( ~ v1_msscyc_1(B,A) & v1_graph_3(B,A) ) ) ) ) ) )).
fof(t60_graph_5,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v6_graph_1(C) & l1_graph_1(C) ) => ! [D] : ( ( v7_graph_1(D,C) & m2_graph_1(D,C) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ~ ( r2_graph_5(C,E,F,D,A) & r5_graph_5(C,B) & ! [G] : ( ( v7_graph_1(G,C) & v1_graph_4(G,C) & m2_graph_1(G,C) ) => ~ r8_graph_5(C,E,F,G,A,B) ) ) ) ) ) ) ) )).
fof(t60_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,A) => ( m1_group_2(C,D) => r1_tarski(k3_group_11(A,B,D),k3_group_11(A,B,C)) ) ) ) ) ) )).
fof(t60_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ( ! [D] : ( 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)) ) ) ) ) )).
fof(t60_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t60_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t60_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t60_group_6,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) ) )).
fof(t60_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v2_group_9(C,A) & m1_group_9(C,A,B) ) => ! [D] : ( ( v2_group_9(D,A) & m1_group_9(D,A,B) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t60_hermitan,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_vectsp_1(A,k1_complfld) ) => ! [B] : ( ( ~ 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] : ( ( 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)) ) ) ) )).
fof(t60_hfdiff_1,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k1_relset_1(k1_numbers,k27_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),k27_sin_cos)),A)) ) ) ) )).
fof(t60_ideal_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( r2_hidden(C,k7_ideal_1(A,B)) <=> ? [D] : ( m1_ideal_1(D,A,B) & C = k4_rlvect_1(A,D) ) ) ) ) )).
fof(t60_int_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ! [B] : ( v1_int_1(B) => ( k5_int_1(B,A) = k5_numbers <=> r1_int_1(A,B) ) ) ) ) )).
fof(t60_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(A,B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( ~ r1_xxreal_0(k1_funct_1(k16_sin_cos,D),k5_numbers) & k1_funct_1(C,D) = k1_square_1(k1_funct_1(k27_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,k27_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) = k6_xcmplx_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k27_sin_cos),k1_partfun2(k1_numbers,B)),k2_seq_4(A)),k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k27_sin_cos),k1_partfun2(k1_numbers,B)),k3_seq_4(A))) ) ) ) ) )).
fof(t60_integra8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,C) & k9_xtuple_0(k27_sin_cos) = C & k9_xtuple_0(k27_sin_cos) = k9_xtuple_0(A) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => ( k1_funct_1(A,D) = k4_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,D)))) & k1_funct_1(k16_sin_cos,D) != k5_numbers ) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,A,B)) ) => k2_integra5(B,A) = k6_xcmplx_0(k1_funct_1(k27_sin_cos,k2_seq_4(B)),k1_funct_1(k27_sin_cos,k3_seq_4(B))) ) ) ) ) )).
fof(t60_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( 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] : ( v1_xreal_0(H) => ( r2_hidden(H,G) => ( k1_funct_1(E,H) = k6_xcmplx_0(H,B) & ~ r1_xxreal_0(k1_funct_1(E,H),k5_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,k6_xcmplx_0(B,A)))) = G & G = k1_relset_1(k1_numbers,F) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,G) => k1_funct_1(F,H) = k7_xcmplx_0(k6_xcmplx_0(H,A),k6_xcmplx_0(H,B)) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,F,C)) ) => k2_integra5(C,F) = k6_xcmplx_0(k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,G),k26_valued_1(k1_numbers,k1_numbers,D,k6_xcmplx_0(B,A))),k2_seq_4(C)),k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,G),k26_valued_1(k1_numbers,k1_numbers,D,k6_xcmplx_0(B,A))),k3_seq_4(C))) ) ) ) ) ) ) ) ) )).
fof(t60_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m2_interva1(B,A) => r2_interva1(A,k16_interva1(A,B,B),B) ) ) )).
fof(t60_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(t60_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [D] : ( ( 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,k4_xcmplx_0(1)) | r1_xxreal_0(1,A) | v5_pre_topc(D,k1_pre_topc(k15_euclid(2),B),k1_pre_topc(k15_euclid(2),C)) ) ) ) ) ) ) )).
fof(t60_jgraph_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ 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(k5_numbers,k18_euclid(A)) & r1_xxreal_0(k5_numbers,k18_euclid(B)) & r1_xxreal_0(k5_numbers,k18_euclid(C)) & ~ r1_xxreal_0(k18_euclid(D),k5_numbers) & ! [F] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(k15_euclid(2))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k15_euclid(2))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k15_euclid(2))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k15_euclid(2))) => ~ ( v3_tops_2(F,k15_euclid(2),k15_euclid(2)) & ! [K] : ( 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(k5_numbers,k17_euclid(G)) & r1_xxreal_0(k5_numbers,k18_euclid(G)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(H)) & r1_xxreal_0(k5_numbers,k18_euclid(H)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(I)) & r1_xxreal_0(k5_numbers,k18_euclid(I)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(J)) & r1_xxreal_0(k5_numbers,k18_euclid(J)) & r1_jordan6(E,G,H) & r1_jordan6(E,H,I) & r1_jordan6(E,I,J) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t60_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t60_jgraph_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(k5_topmetr)) => ! [H] : ( 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(k7_xcmplx_0(2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(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(k4_xcmplx_0(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(k4_xcmplx_0(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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t60_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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(k2_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)),k2_jordan9(D,B),A) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(D,B),C,1) ) => r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),k2_jordan9(D,B),A),k17_pscomp_1(k3_topreal1(2,k2_jordan9(D,B)))) ) ) ) ) ) )).
fof(t60_jordan1h,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( 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] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(k4_tarski(D,E),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k7_nat_d(k3_finseq_1(C),1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),D,E) & r2_hidden(k4_tarski(D,k1_nat_1(E,1)),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k3_finseq_1(C)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),D,k1_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(k1_nat_1(D,1),k1_nat_1(E,1)),k2_matrix_0(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) )).
fof(t60_jordan1j,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & ~ r1_xxreal_0(A,k5_numbers) & k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k8_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) = k1_tarski(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k9_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D)) & r1_xboole_0(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k9_jordan6(B)) ) ) ) ) ) ) )).
fof(t60_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( ( v2_connsp_1(C,k15_euclid(A)) & v3_pre_topc(C,k15_euclid(A)) & r2_hidden(B,C) & D = a_3_1_jordan2c(A,B,C) ) => v3_pre_topc(D,k15_euclid(A)) ) ) ) ) ) )).
fof(t60_jordan6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t60_kurato_1,axiom,( k5_card_1(k4_kurato_1(k3_topmetr,k6_kurato_1)) = 6 )).
fof(t60_lattice2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k5_finsub_1(A)) => ! [C] : ( ( ~ v2_struct_0(C) & v10_lattices(C) & v14_lattices(C) & l3_lattices(C) ) => ! [D] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t60_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k9_funct_2(k6_glib_000(A),k4_ordinal1))) => ! [C] : ! [D] : ( ~ r2_hidden(D,k2_chord(A,k1_tarski(C))) => k1_recdef_1(k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k4_ordinal1,k6_glib_000(A),B),D) = k1_recdef_1(k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k4_ordinal1,k6_glib_000(A),k20_lexbfs(A,B,C)),D) ) ) ) )).
fof(t60_limfunc1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t60_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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) ) ) ) ) ) )).
fof(t60_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( v2_xxreal_0(F) & v1_xreal_0(F) ) => ! [G] : ( ( v2_xxreal_0(G) & v1_xreal_0(G) ) => ~ ( k3_supinf_2(k2_extreal1(1,F),k2_extreal1(1,G)) = 1 & r2_hidden(D,k1_lpspace2(A,B,C,F)) & r2_hidden(E,k1_lpspace2(A,B,C,G)) & ! [H] : ( v1_xreal_0(H) => ~ ( H = k1_mesfunc6(A,B,C,k2_mesfun6c(F,A,k56_valued_1(A,k1_numbers,D))) & ? [I] : ( v1_xreal_0(I) & 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))),k3_xcmplx_0(k2_power(H,k2_extreal1(1,F)),k2_power(I,k2_extreal1(1,G)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t60_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( 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)))) ) ) ) )).
fof(t60_ltlaxio2,axiom,( ! [A] : ( m2_finseq_1(A,k1_hilbert1) => r8_ltlaxio1(k1_subset_1(k1_hilbert1),k3_hilbert1(k7_partfun1(k1_hilbert1,k2_ltlaxio2(k5_ltlaxio2(A)),k3_finseq_1(k2_ltlaxio2(k5_ltlaxio2(A)))),k2_ltlaxio1(k7_partfun1(k1_hilbert1,k2_ltlaxio2(A),k3_finseq_1(k2_ltlaxio2(A)))))) ) )).
fof(t60_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => r3_cqc_the1(A,C,k8_cqc_lang(A,B,B)) ) ) ) )).
fof(t60_mathmorp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( 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)) ) ) ) ) )).
fof(t60_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,k1_numbers,A,A) & m2_finseq_1(E,k3_finseq_2(k1_numbers)) ) => ( r2_matrix10(k4_matrix10(A,B,C),k4_matrix10(A,D,E)) => r2_matrix10(k5_matrix10(A,B,D),k5_matrix10(A,E,C)) ) ) ) ) ) ) )).
fof(t60_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,A,C,B) & m2_finseq_1(D,k3_finseq_2(A)) ) => ! [E] : ( ( v1_finset_1(E) & v1_setfam_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ! [F] : ( m2_finseq_1(F,A) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v1_finset_1(H) & v1_setfam_1(H) & m1_subset_1(H,k1_zfmisc_1(k4_ordinal1)) ) => ( r1_tarski(k2_zfmisc_1(H,E),k2_matrix_0(D)) => ( r2_hidden(G,H) | k6_matrix13(A,D,H,E) = k6_matrix13(A,k3_matrix11(G,C,B,A,D,F),H,E) ) ) ) ) ) ) ) ) ) ) )).
fof(t60_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( k1_matrix_0(B) = k5_numbers => ( v1_xboole_0(k6_matrix15(A,B,C)) | k3_finseq_1(B) = k5_numbers ) ) ) ) ) )).
fof(t60_matrix16,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t60_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => k1_funct_1(B,C) = k7_matrix_0(A,B,C) ) ) ) ) )).
fof(t60_matrix_4,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ( k3_finseq_1(C) = k3_finseq_1(D) => ( ! [E] : ( v7_ordinal1(E) => ~ r2_hidden(k4_tarski(E,B),k2_matrix_0(C)) ) | k8_matrix_0(u1_struct_0(A),k3_matrix_3(A,C,D),B) = k3_fvsum_1(A,k8_matrix_0(u1_struct_0(A),C,B),k8_matrix_0(u1_struct_0(A),D,B)) ) ) ) ) ) ) )).
fof(t60_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => k1_matrix_8(A,B,k3_matrix_3(B,k1_matrix_4(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)) ) ) ) ) ) )).
fof(t60_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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,k3_matrix_1(C,A),k3_matrix_1(C,B))) = k3_matrix_1(C,k2_xcmplx_0(A,B)) ) ) ) )).
fof(t60_matrixr1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( ( v1_matrix_0(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),k5_numbers) | r1_xxreal_0(k1_matrix_0(C),k5_numbers) | k12_matrixr1(C,k10_rvsum_1(B,A)) = k10_rvsum_1(k12_matrixr1(C,B),A) ) ) ) ) ) )).
fof(t60_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,B,C) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,k1_numbers,C,A) & m2_finseq_1(E,k3_finseq_2(k1_numbers)) ) => ( ~ r1_xxreal_0(B,k5_numbers) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ( r2_hidden(k4_tarski(F,G),k2_matrix_0(k6_matrixr1(D,E))) => k3_matrix_0(k1_numbers,k6_matrixr1(D,E),F,G) = k1_funct_1(k12_matrixr1(E,k7_matrix_0(k1_numbers,D,F)),G) ) ) ) ) ) ) ) ) ) )).
fof(t60_matrprob,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v6_matrprob(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) <=> ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => ( ~ v1_xboole_0(k7_matrix_0(k1_numbers,A,B)) & v1_matrprob(k7_matrix_0(k1_numbers,A,B)) & m2_finseq_1(k7_matrix_0(k1_numbers,A,B),k1_numbers) ) ) ) ) ) )).
fof(t60_mcart_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) => ( ! [G] : ( m1_subset_1(G,B) => ! [H] : ( m1_subset_1(H,C) => ! [I] : ( m1_subset_1(I,D) => ! [J] : ( m1_subset_1(J,E) => ( F = k6_xtuple_0(G,H,I,J) => A = G ) ) ) ) ) => A = k4_mcart_1(B,C,D,E,F) ) ) ) ) ) ) )).
fof(t60_measure6,axiom,( k5_measure6(k1_subset_1(k1_numbers)) = k1_xboole_0 )).
fof(t60_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => k4_member_1(k10_member_1(A,B)) = k8_member_1(k4_member_1(A),B) ) ) )).
fof(t60_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) ) )).
fof(t60_mesfunc5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( v1_xxreal_0(B) => ( ! [C] : ( v7_ordinal1(C) => k9_nat_1(k6_numbers,A,C) = B ) => ( v10_mesfunc5(A) & k2_mesfunc5(A) = B & k2_mesfunc5(A) = k8_supinf_2(k17_supinf_2(A)) ) ) ) ) )).
fof(t60_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( 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_funct_1(k3_valued_1(A,k1_numbers,k1_numbers,k3_valued_1(A,k1_numbers,k1_numbers,B,C),D),E) = k2_xcmplx_0(k2_xcmplx_0(k1_funct_1(B,E),k1_funct_1(C,E)),k1_funct_1(D,E)) ) ) ) ) ) )).
fof(t60_mmlquery,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k9_setfam_1(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t60_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k30_modelc_1(k25_modelc_2(A)))) ) => ! [C] : ( m1_subset_1(C,k25_modelc_2(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k42_modelc_2(A,B))) => ! [E] : ( 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] : ( v7_ordinal1(F) & ! [G] : ( 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) ) ) ) ) ) ) ) )).
fof(t60_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_3(B,A) & l1_modelc_3(B,A) ) => ! [C] : ( m1_subset_1(C,k25_modelc_2(k43_modelc_2)) => ! [D] : ( m2_orders_1(D,k1_orders_1(k1_modelc_3(A)),k6_partfun1(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))) ) ) ) ) ) ) ) )).
fof(t60_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ( k6_moebius1(A) = 1 <=> A = 1 ) ) )).
fof(t60_monoid_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k4_binop_1(u1_struct_0(k9_monoid_0(A)),u2_algstr_0(k9_monoid_0(A))) = k1_xboole_0 ) )).
fof(t60_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m2_pboole(C,u1_struct_0(A),B,k7_funcop_1(u1_struct_0(A),k4_ordinal1)) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k1_msaterm(A,B)) & v1_funct_1(D) & v1_partfun1(D,k1_msaterm(A,B)) ) => ( ( ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_msafree4(F,u1_struct_0(A),B,k1_msafree4(u1_struct_0(A),B,E)) => k1_funct_1(D,k1_trees_4(k4_tarski(F,E))) = k1_trees_4(k4_tarski(k3_funct_2(k1_msafree4(u1_struct_0(A),B,E),k1_funct_1(k7_funcop_1(u1_struct_0(A),k4_ordinal1),E),k2_msafree4(u1_struct_0(A),B,k7_funcop_1(u1_struct_0(A),k4_ordinal1),C,E),F),E)) ) ) & ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( m1_msaterm(F,A,B,k2_msaterm(A,B,E)) => k1_msafree4(k1_msaterm(A,B),D,k6_msaterm(A,B,k2_msaterm(A,B,E),F)) = k4_trees_4(k2_msaterm(A,k7_funcop_1(u1_struct_0(A),k4_ordinal1),E),k3_relat_1(F,D)) ) ) ) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( m1_msaterm(F,A,B,k2_msaterm(A,B,E)) => ( r2_hidden(k3_relat_1(F,D),k3_msualg_1(A,E,k1_msafree3(A,k2_funct_6(C)))) & r2_hidden(k3_relat_1(F,D),k3_msualg_1(A,E,k1_msafree3(A,k7_funcop_1(u1_struct_0(A),k4_ordinal1)))) ) ) ) ) ) ) ) ) )).
fof(t60_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => r8_pboole(k8_newton,k13_nat_3(k1_newton(A,B)),k9_nat_3(k8_newton,k13_nat_3(A),B)) ) ) )).
fof(t60_nat_d,axiom,( ! [A] : ( v1_finset_1(A) => ( v1_zfmisc_1(A) <=> ~ r1_xxreal_0(2,k5_card_1(A)) ) ) )).
fof(t60_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t60_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => r1_nat_d(k5_nat_d(k6_nat_d(B,C),k6_nat_d(B,A)),k6_nat_d(B,k5_nat_d(C,A))) ) ) ) )).
fof(t60_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t60_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_oppcat_1(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t60_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r7_orders_1(k2_relat_1(A),B) <=> r6_orders_1(A,B) ) ) )).
fof(t60_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r2_hidden(A,k10_ordinal2(B,C)) => ( C = k1_xboole_0 | r2_hidden(k5_ordinal3(A,B),C) ) ) ) ) ) )).
fof(t60_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( ( r2_hidden(k5_numbers,A) & r2_hidden(1,B) & C = k5_ordinal5(A,B) ) => r2_hidden(k5_numbers,k6_ordinal3(A,k12_ordinal2(B,C))) ) ) ) ) )).
fof(t60_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ! [D] : ( ( ~ 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] : ( 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)) ) ) ) ) ) )).
fof(t60_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => r1_partfun1(k3_partfun1(k1_xboole_0,A,B),C) ) )).
fof(t60_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t60_pboole,axiom,( ! [A] : ! [B] : ( ( 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)) ) )).
fof(t60_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( ( 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) & k10_pdiff_1(3,3,k26_valued_1(k1_euclid(3),k1_numbers,k1_pdiff_3(1,3,C),A),B) = k3_xcmplx_0(A,k3_pdiff_5(C,B)) ) ) ) ) ) )).
fof(t60_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) => ! [D] : ( ( 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] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ( r2_hidden(E,C) => r3_pdiff_1(A,B,D,E) ) ) ) ) ) ) ) ) ) )).
fof(t60_pepin,axiom,( v1_int_2(17) )).
fof(t60_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( m1_subset_1(B,k8_polyform(A,k5_numbers)) => k1_funct_1(k21_polyform(A,k5_numbers),k1_tarski(B)) = k1_tarski(k1_xboole_0) ) ) )).
fof(t60_polynom5,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( k1_algseq_1(A,B) != k5_numbers => ( v1_polynom5(B,A) <=> v1_polynom5(k7_polynom5(A,B),A) ) ) ) ) )).
fof(t60_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k12_polynom1(A,C)))) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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,k8_polynom1(A,C)) => r2_hidden(E,k7_ideal_1(k12_polynom1(A,C),D)) ) ) ) ) ) ) )).
fof(t60_power,axiom,( k2_power(2,2) = 4 )).
fof(t60_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & v2_pre_poly(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => r1_tarski(k18_pre_poly(A,B),k15_pre_poly(A)) ) )).
fof(t60_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k5_numbers,B) ) => r1_xxreal_0(1,k4_prepower(A,B)) ) ) ) )).
fof(t60_prob_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_prob_3(D,A,B) => m2_finseq_1(k1_partfun1(k4_ordinal1,k9_setfam_1(A),B,k1_numbers,D,C),k1_numbers) ) ) ) ) )).
fof(t60_pscomp_1,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t60_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( v2_relat_1(D) => ( ( ~ 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)) ) | r2_pboole(A,B,C) ) ) ) ) ) )).
fof(t60_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ~ ( r3_qc_lang2(A,B,C) & r3_qc_lang2(A,C,B) ) ) ) ) )).
fof(t60_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t60_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k17_quatern2(k22_quaterni(A,B),k22_quaterni(A,B)) = k22_quaterni(k22_quaterni(k22_quaterni(k17_quatern2(A,A),k17_quatern2(A,B)),k17_quatern2(B,A)),k17_quatern2(B,B)) ) ) )).
fof(t60_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k24_quaterni(k22_quaterni(k25_quaterni(A,B),C)) = k25_quaterni(k22_quaterni(k24_quaterni(A),B),C) ) ) ) )).
fof(t60_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ( k13_quaterni(k23_quaterni(A,k27_quaterni(A))) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k13_quaterni(A)),k1_square_1(k14_quaterni(A))),k1_square_1(k15_quaterni(A))),k1_square_1(k16_quaterni(A))) & k14_quaterni(k23_quaterni(A,k27_quaterni(A))) = k5_numbers & k15_quaterni(k23_quaterni(A,k27_quaterni(A))) = k5_numbers & k16_quaterni(k23_quaterni(A,k27_quaterni(A))) = k5_numbers ) ) )).
fof(t60_quofield,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t60_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B))))) => ! [D] : ( m1_rcomp_3(D,A,B,C) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t60_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ( ! [B] : ( v7_ordinal1(B) => k9_nat_1(k1_numbers,k4_real_3(A),B) != k5_numbers ) => ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k7_xcmplx_0(1,k3_xcmplx_0(k9_nat_1(k1_numbers,k4_real_3(A),k1_nat_1(B,1)),k1_square_1(k9_nat_1(k1_numbers,k6_real_3(A),B)))),k7_xcmplx_0(1,k1_square_1(k9_nat_1(k1_numbers,k6_real_3(A),B)))) ) ) ) )).
fof(t60_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( k5_relat_1(B,A) = k1_xboole_0 <=> r1_xboole_0(k9_xtuple_0(B),A) ) ) )).
fof(t60_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) => ! [E] : ( 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)) ) ) ) ) )).
fof(t60_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ( ! [B] : ! [C] : ~ r13_rewrite1(A,B,C) => v9_rewrite1(A) ) ) )).
fof(t60_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [D] : ( 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) ) ) ) ) )).
fof(t60_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_afinsq_1(C))) => ! [F] : ( ( ~ 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] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t60_rfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t60_rfunct_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( r2_rfunct_3(A,B) => r2_rfunct_3(k18_rfunct_3(k1_numbers,A),B) ) ) )).
fof(t60_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_seq_2(B) => k1_funct_1(k4_rinfsup1(B),A) = k4_xcmplx_0(k1_funct_1(k3_rinfsup1(k32_valued_1(k4_ordinal1,k1_numbers,B)),A)) ) ) ) )).
fof(t60_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v1_rlaffin1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( r1_tarski(C,B) & ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t60_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rlsub_1(C,A) => ( r2_hidden(k4_algstr_0(A,B),k3_rlsub_1(A,B,C)) <=> r1_struct_0(C,B) ) ) ) ) )).
fof(t60_rlsub_2,axiom,( ! [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) ) => ! [B] : ( ( v1_rlvect_1(B) & m1_rlsub_1(B,A) ) => ! [C] : ( ( v1_rlvect_1(C) & m1_rlsub_1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t60_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( 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)) ) ) )).
fof(t60_rlvect_1,axiom,( ! [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) ) => ! [B] : ( 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) ) ) )).
fof(t60_rlvect_2,axiom,( ! [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) ) => 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)) ) )).
fof(t60_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_rmod_2(E,A,B) => ( ? [F] : ( 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)) ) ) ) ) ) ) )).
fof(t60_rmod_4,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(t60_robbins1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t60_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t60_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( k3_rusub_1(A,D,B) = k3_rusub_1(A,C,B) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r1_struct_0(B,E) & k3_rlvect_1(A,D,E) = C ) ) ) ) ) ) ) )).
fof(t60_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_bhsp_1(B) & m1_rusub_1(B,A) ) => ! [C] : ( ( v1_bhsp_1(C) & m1_rusub_1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t60_rvsum_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) & v1_finseq_1(C) ) => k1_funct_1(k14_rvsum_1(B,C),A) = k3_xcmplx_0(k1_funct_1(B,A),k1_funct_1(C,A)) ) ) )).
fof(t60_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( 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(k5_numbers)) = 1 => ( r4_scmfsa7b(C,D) | ( r5_scmfsa7b(k2_scmfsa8c(D,C),B,A) & r6_scmfsa7b(k2_scmfsa8c(D,C),B,A) ) ) ) ) ) ) ) )).
fof(t60_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k5_numbers)) = 1 & ! [D] : ( v7_ordinal1(D) => k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_m(B)),D),k4_scmfsa_2(k5_numbers)) = 1 ) ) ) ) ) ) )).
fof(t60_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ( k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k10_scmfsa_2(A,B),C),k4_struct_0(k1_scmfsa_2)) = k4_card_1(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,C)) & ( A != B => k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k10_scmfsa_2(A,B),C),A) = k4_int_1(k1_funct_1(C,A),k1_funct_1(C,B)) ) & k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k10_scmfsa_2(A,B),C),B) = k5_int_1(k1_funct_1(C,A),k1_funct_1(C,B)) & ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ~ ( D != A & D != B & k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k10_scmfsa_2(A,B),C),D) != k1_funct_1(C,D) ) ) & ! [D] : ( m1_scmfsa_2(D) => r2_relset_1(k4_ordinal1,k4_numbers,k18_scmfsa_2(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k10_scmfsa_2(A,B),C),D),k18_scmfsa_2(C,D)) ) ) ) ) ) )).
fof(t60_scmpds_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ~ ( ? [B] : ( 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) ) ) )).
fof(t60_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v3_scmpds_4(D) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( ( r1_xxreal_0(k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,E),F)),k5_numbers) & r1_scmpds_6(D,B,A) & r2_scmpds_6(D,B,A) ) => ( r1_scmpds_6(k3_scmpds_6(E,F,C,D),B,A) & r2_scmpds_6(k3_scmpds_6(E,F,C,D),B,A) ) ) ) ) ) ) ) ) )).
fof(t60_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => v9_scmyciel(k1_subset_1(k3_tarski(A)),A) ) )).
fof(t60_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_semi_af1(A,B,C,D,E) => r3_semi_af1(A,B,C,D,E) ) ) ) ) ) ) )).
fof(t60_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k2_numbers) => ! [D] : ( m2_finseq_2(D,k2_numbers,k12_seq_4(B)) => ( ( r2_hidden(A,k2_finseq_1(B)) & C = k1_funct_1(D,A) ) => k1_funct_1(k16_seq_4(B,D),A) = k4_xcmplx_0(C) ) ) ) ) ) )).
fof(t60_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(B) => k3_kurato_0(A,B) = k1_kurato_0(A,B) ) ) )).
fof(t60_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) )).
fof(t60_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => ! [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(k7_card_1(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(k7_card_1(3),k1_scmfsa_2,B,C),A) = k1_funct_1(C,A) ) ) ) ) )).
fof(t60_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t60_simplex0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( m1_simplex0(C,A) => ! [D] : ( 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) ) ) ) ) )).
fof(t60_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k6_xcmplx_0(k1_funct_1(k16_sin_cos,k2_xcmplx_0(A,B)),k1_funct_1(k16_sin_cos,A)) = k2_xcmplx_0(k3_xcmplx_0(B,k1_funct_1(k18_sin_cos,A)),k3_xcmplx_0(B,k3_complex1(k3_xcmplx_0(k11_comseq_3(k24_sin_cos(k3_xcmplx_0(B,k7_complex1))),k2_xcmplx_0(k1_funct_1(k18_sin_cos,A),k3_xcmplx_0(k1_funct_1(k16_sin_cos,A),k7_complex1)))))) ) ) )).
fof(t60_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,k2_xcmplx_0(A,B)),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,k6_xcmplx_0(A,B))) = k2_xcmplx_0(k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A)),k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,B),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,B))) & k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,k2_xcmplx_0(A,B)),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,k6_xcmplx_0(A,B))) = k2_xcmplx_0(k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A)),k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,B),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,B))) & k2_xcmplx_0(k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A)),k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,B),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,B))) = k2_xcmplx_0(k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A)),k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,B),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,B))) ) ) ) )).
fof(t60_sin_cos6,axiom,( ! [A] : ( v1_int_1(A) => v2_funct_1(k5_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k2_xcmplx_0(k28_sin_cos,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A)),k2_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A))))) ) )).
fof(t60_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,1) => k3_power(k4_power,A) = k2_sin_cos7(k7_xcmplx_0(k2_xcmplx_0(k1_square_1(A),1),k3_xcmplx_0(2,A))) ) ) )).
fof(t60_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) & k4_sin_cos9(A) = k7_xcmplx_0(k28_sin_cos,2) ) => A = k5_numbers ) ) )).
fof(t60_sincos10,axiom,( k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k4_sincos10,k1_rcomp_1(1,k3_square_1(2))),k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k7_xcmplx_0(k28_sin_cos,2)))) = k1_partfun2(k1_numbers,k1_rcomp_1(1,k3_square_1(2))) )).
fof(t60_sprect_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t60_sprect_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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))) ) ) ) ) ) )).
fof(t60_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t60_stirl2_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t60_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_valuat_1(D,A,C) => ! [E] : ( m2_subset_1(E,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [F] : ( ( v5_relat_1(F,k3_qc_lang1(A)) & v3_card_1(F,B) & m2_finseq_1(F,k2_qc_lang1(A)) ) => ! [G] : ( m2_funct_2(G,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t60_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t60_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v3_tex_2(B,A) ) ) )).
fof(t60_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ~ ( ? [B] : ( ~ v2_struct_0(B) & m1_pre_topc(B,A) & v2_tex_3(B,A) & v1_tex_2(B,A) ) & v3_tdlat_3(A) ) ) )).
fof(t60_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(B,A) => k3_tex_4(A,B) = B ) ) ) )).
fof(t60_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => ( ( v3_pre_topc(E,A) & r2_hidden(F,E) & r1_tarski(E,u1_struct_0(D)) & F = G ) => ( r1_tmap_1(A,B,C,F) <=> r1_tmap_1(D,B,k2_tmap_1(A,B,C,D),G) ) ) ) ) ) ) ) ) ) )).
fof(t60_topalg_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t60_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( 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) ) ) ) ) )).
fof(t60_topgrp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t60_topreal6,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => v6_tbsp_1(k10_metric_1(A,B,C),A) ) ) ) )).
fof(t60_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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(k15_euclid(2),D,E),k5_jgraph_6(A,B,C)) = k2_tarski(D,E) ) ) ) ) ) ) )).
fof(t60_toprealc,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xxreal_0(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( 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))) ) ) ) )).
fof(t60_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t60_tops_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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)) ) ) ) ) ) ) )).
fof(t60_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t60_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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)) ) ) ) ) ) ) ) )).
fof(t60_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( r2_hidden(B,k12_trees_3(A)) <=> ~ ( B != k1_xboole_0 & ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ~ ( r2_hidden(C,A) & B = k7_finseq_1(k14_trees_3(k5_numbers),C) ) ) ) ) ) )).
fof(t60_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & ? [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) & ? [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(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) ) ) ) ) ) ) ) ) )).
fof(t60_uproots,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( m2_finseq_1(C,k3_finseq_2(u1_struct_0(k14_polynom3(A)))) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( k3_finseq_1(C) = k5_card_1(k22_pre_poly(u1_struct_0(A),B)) & D = k19_finseq_1(k22_pre_poly(u1_struct_0(A),B)) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r2_hidden(F,k4_finseq_1(C)) => k1_funct_1(C,F) = k8_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,k22_pre_poly(u1_struct_0(A),B)) => k5_card_1(k8_relset_1(k4_ordinal1,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(k4_ordinal1,u1_struct_0(A))),k4_polynom5(A,k4_algstr_0(A,E),k5_struct_0(A))))) = k1_recdef_1(B,E) ) & ( ~ r2_hidden(E,k22_pre_poly(u1_struct_0(A),B)) => k5_card_1(k8_relset_1(k4_ordinal1,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(k4_ordinal1,u1_struct_0(A))),k4_polynom5(A,k4_algstr_0(A,E),k5_struct_0(A))))) = k5_numbers ) ) ) ) ) ) ) ) )).
fof(t60_valued_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) ) => ( r1_tarski(k1_relset_1(k4_ordinal1,C),k2_finseq_1(B)) => r1_tarski(k1_relset_1(k4_ordinal1,k61_valued_1(C,A)),k2_finseq_1(k1_nat_1(A,B))) ) ) ) ) )).
fof(t60_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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)) ) ) ) )).
fof(t60_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t60_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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))) ) ) ) )).
fof(t60_waybel23,axiom,( ! [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] : ( ( v6_waybel23(B,A) & m1_waybel23(B,A) ) => v5_orders_3(k5_waybel23(A,B),A,k1_yellow_1(k7_waybel_0(k5_yellow_0(A,B)))) ) ) )).
fof(t60_waybel34,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t60_waybel_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t60_waybel_1,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v5_orders_3(k4_waybel_1(A,B),A,A) ) ) )).
fof(t60_waybel_4,axiom,( ! [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] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_waybel_4(A,k5_waybel_4(A,C,B),B) ) => v9_waybel_4(B,A) ) ) ) )).
fof(t60_xboole_1,axiom,( ! [A] : ! [B] : ~ ( r1_tarski(A,B) & r2_xboole_0(B,A) ) )).
fof(t60_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k8_xboolean(A,k6_xboolean(B,C)) = k4_xboolean(k6_xboolean(A,B),k6_xboolean(A,k3_xboolean(C))) ) ) ) )).
fof(t60_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( A != k5_numbers => k7_xcmplx_0(A,A) = 1 ) ) )).
fof(t60_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k4_xcmplx_0(A),B) => r1_xxreal_0(k5_numbers,k2_xcmplx_0(A,B)) ) ) ) )).
fof(t60_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_tarski(k2_xxreal_1(C,D),k3_xxreal_1(A,B)) => ( r1_xxreal_0(D,C) | ( ~ r1_xxreal_0(C,A) & r1_xxreal_0(D,B) ) ) ) ) ) ) ) )).
fof(t60_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ( r1_tarski(A,B) => r1_xxreal_0(k2_xxreal_2(B),k2_xxreal_2(A)) ) ) ) )).
fof(t60_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t60_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v5_orders_2(B) & v24_waybel_0(B) & l1_orders_2(B) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t60_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t60_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( 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)) ) ) )).
fof(t60_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t60_yellow_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( u1_struct_0(A) = u1_struct_0(B) => ! [C] : ( 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)))) ) ) ) ) ) )).
fof(t60_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ~ ( r1_zf_lang(B,A) & r1_xxreal_0(k3_finseq_1(A),k3_finseq_1(B)) ) ) ) )).
fof(t60_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => k2_zf_model(k6_zf_lang(A)) = k2_zf_model(A) ) )).
fof(t60_zfmisc_1,axiom,( ! [A] : ! [B] : ( k4_xboole_0(k1_tarski(A),B) = k1_xboole_0 | k4_xboole_0(k1_tarski(A),B) = k1_tarski(A) ) )).
fof(t60_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k5_zmodul01(A,B,k3_zmodul01(A)) = k6_domain_1(u1_struct_0(A),B) ) ) )).
fof(t60_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( v1_zmodul02(k7_domain_1(u1_struct_0(A),B,C),A) & B = k4_struct_0(A) ) ) ) ) )).
fof(t61_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l3_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_abcmiz_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t61_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v7_abcmiz_1(B,A) & m1_abcmiz_1(B,A,k13_abcmiz_1(A)) ) => ? [C] : ( 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 ) ) ) )).
fof(t61_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t61_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t61_afinsq_2,axiom,( ! [A] : ( ( 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) = k5_numbers <=> ( k1_afinsq_1(A) = k5_numbers | A = k8_funcop_1(k4_ordinal1,k1_afinsq_1(A),k5_numbers) ) ) ) ) )).
fof(t61_algspec1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_msafree1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k10_xtuple_0(u3_msualg_1(A,B))) => ! [D] : ( m1_subset_1(D,k10_xtuple_0(u3_msualg_1(A,B))) => ( C = D | r1_xboole_0(C,D) ) ) ) ) ) )).
fof(t61_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t61_aofa_000,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_freealg(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_freealg(k19_aofa_000,A))) => ! [C] : ( 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 ) ) ) ) )).
fof(t61_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( m2_subset_1(F,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_msafree4(H,u1_struct_0(A),u4_aofa_a00(A,B,C,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),G)) => k15_aofa_a00(A,B,C,D,G,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),G,H),F) = k1_funct_1(k1_msafree4(u1_struct_0(A),F,G),H) ) ) ) ) ) ) ) ) )).
fof(t61_arytm_3,axiom,( ! [A] : ~ r2_hidden(k4_tarski(k11_arytm_3,A),k5_arytm_3) )).
fof(t61_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(2,A) & r1_xxreal_0(k5_series_1(2,A),k1_nat_1(A,1)) ) ) )).
fof(t61_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t61_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,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))) ) ) ) ) )).
fof(t61_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t61_borsuk_5,axiom,( 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)) )).
fof(t61_borsuk_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_topmetr)) => r2_hidden(k4_tarski(k5_numbers,A),k6_borsuk_6) ) )).
fof(t61_borsuk_7,axiom,( ! [A] : ( 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(k5_numbers),k4_toprealb(A),k2_topalg_5(A),k12_borsuk_7)) ) )).
fof(t61_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t61_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_eqrel_1(I,A) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t61_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t61_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k7_xboolean(A,B) = k4_xboolean(k6_xboolean(A,B),k6_xboolean(B,A)) ) ) )).
fof(t61_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => k3_calcul_1(A,B) = k3_tarski(a_2_0_calcul_1(A,B)) ) ) )).
fof(t61_card_1,axiom,( ! [A] : ( v1_finset_1(k1_wellord2(A)) => v1_finset_1(A) ) )).
fof(t61_card_2,axiom,( ! [A] : ( ( v1_finset_1(A) & ! [B] : ! [C] : ~ ( 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) ) ) )).
fof(t61_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( k8_card_3(A) = k1_tarski(k1_xboole_0) <=> ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => k1_funct_1(A,B) = k1_xboole_0 ) ) ) )).
fof(t61_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ~ ( k9_xtuple_0(B) = A & v2_funct_1(B) & ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,k4_numbers) & v5_ordinal1(C) & 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(k4_ordinal1,C) = k1_nat_1(k5_card_1(A),1) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k1_relset_1(k4_ordinal1,C)) => k1_funct_1(C,D) = k7_xcmplx_0(k3_xcmplx_0(k1_newton(k4_xcmplx_0(1),D),k7_newton(k5_card_1(A))),k7_newton(D)) ) ) ) ) ) ) ) )).
fof(t61_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t61_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t61_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) )).
fof(t61_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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(k5_numbers)) = k1_xboole_0 & v1_partfun1(B,A) ) ) ) ) )).
fof(t61_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ( ( r5_glib_000(A,B) & v2_chord(A) ) => v2_chord(B) ) ) ) )).
fof(t61_circcomb,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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)) ) ) ) )).
fof(t61_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( m3_msaterm(D,A,C) => ! [E] : ( ( ~ v2_struct_0(E) & ~ v11_struct_0(E) & v2_msafree2(E) & l1_msualg_1(E) ) => ! [F] : ( ( v4_msualg_1(F,E) & v4_msafree2(F,E) & l3_msualg_1(F,E) ) => ( r8_circtrm1(A,B,C,D,E,F) => ! [G] : ( m2_circtrm1(G,A,C,B,D,E,F) => ! [H] : ( m1_subset_1(H,k4_card_3(u3_msualg_1(E,F))) => ! [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_xcmplx_0(1,k6_trees_1(k9_xtuple_0(I)))),k1_funct_1(G,I)) & ! [J] : ( 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] : ( m1_circtrm1(K,A,C,D,B,J) => k1_funct_1(k5_facirc_1(E,F,H,k2_xcmplx_0(1,k6_trees_1(k9_xtuple_0(I)))),k1_funct_1(G,I)) = k7_circtrm1(A,B,C,I,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t61_classes1,axiom,( ! [A] : ! [B] : r1_tarski(k5_classes1(k3_xboole_0(A,B)),k3_xboole_0(k5_classes1(A),k5_classes1(B))) )).
fof(t61_classes2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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) ) ) ) )).
fof(t61_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_clvect_1(C,A) => ( r2_hidden(k4_struct_0(A),k5_clvect_1(A,B,C)) <=> r1_struct_0(C,B) ) ) ) ) )).
fof(t61_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v2_clvect_2(C,A) => v2_clvect_2(k6_clvect_1(A,C,B),A) ) ) ) ) )).
fof(t61_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k11_cohsp_1(A,B,C))) => ? [E] : ( 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 ) ) ) ) ) )).
fof(t61_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k9_complex1(k6_xcmplx_0(A,B)) = k5_numbers <=> A = B ) ) ) )).
fof(t61_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_numbers) => k3_complex2(A,B) = k3_complex2(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) ) ) ) )).
fof(t61_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => k9_complex1(k4_algstr_0(k1_complfld,A)) = k9_complex1(A) ) )).
fof(t61_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( m2_finseq_1(C,k2_numbers) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k3_finseq_1(B) = k3_finseq_1(C) ) => k8_complsp2(A,k8_seq_4(B,C)) = k6_xcmplx_0(k8_complsp2(A,B),k8_complsp2(A,C)) ) ) ) ) )).
fof(t61_comptrig,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k5_numbers,A) & k19_sin_cos(A) = 1 ) => ( r1_xxreal_0(k3_xcmplx_0(2,k28_sin_cos),A) | A = k5_numbers ) ) ) )).
fof(t61_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k3_finseq_2(k4_ordinal1)) & v1_funct_1(C) & v4_valued_0(C) & v2_margrel1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k3_finseq_2(k4_ordinal1)) & v1_funct_1(D) & v4_valued_0(D) & v2_margrel1(D) ) => ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(k1_nat_1(k19_margrel1(C),1),k4_ordinal1)) => ( ( r2_hidden(A,k4_finseq_1(E)) & r2_hidden(k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,k1_nat_1(B,1)),k1_relset_1(k3_finseq_2(k4_ordinal1),k7_comput_1(C,D,A))) ) => k1_recdef_1(k7_comput_1(C,D,A),k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,k1_nat_1(B,1))) = k1_recdef_1(D,k8_finseq_1(k4_ordinal1,k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,B),k12_finseq_1(k4_ordinal1,k1_recdef_1(k7_comput_1(C,D,A),k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,B))))) ) ) ) ) ) ) )).
fof(t61_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_seq_2(k3_series_1(k55_valued_1(k4_ordinal1,k2_numbers,A))) <=> v2_comseq_3(A) ) ) )).
fof(t61_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( v1_xcmplx_0(D) => ( r1_tarski(B,C) => r1_tarski(k19_convex4(A,B,D),k19_convex4(A,C,D)) ) ) ) ) ) )).
fof(t61_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t61_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t61_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,B) & m2_finseq_1(C,k2_qc_lang1(A)) ) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k5_qc_lang1(A)) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t61_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => 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),k18_sin_cos),A,B) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,2),k2_xcmplx_0(k3_xcmplx_0(k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(3,k2_xcmplx_0(B,A)),2)),k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(3,k6_xcmplx_0(B,A)),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))))),k6_xcmplx_0(A,B))) ) ) )).
fof(t61_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k7_xcmplx_0(1,k17_sin_cos(D)) ) => ( k17_sin_cos(A) = k5_numbers | k17_sin_cos(B) = k5_numbers | k9_diff_1(C,A,B) = k4_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(2,k6_xcmplx_0(k17_sin_cos(B),k17_sin_cos(A))),k6_xcmplx_0(k19_sin_cos(k2_xcmplx_0(A,B)),k19_sin_cos(k6_xcmplx_0(A,B)))),k6_xcmplx_0(A,B))) ) ) ) ) ) )).
fof(t61_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(B,k1_relset_1(k1_numbers,k27_sin_cos)) & r2_hidden(k2_xcmplx_0(B,A),k1_relset_1(k1_numbers,k27_sin_cos)) ) => k1_funct_1(k3_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k27_sin_cos),k18_sin_cos),A),B) = k6_xcmplx_0(k3_xcmplx_0(k1_newton(k1_funct_1(k18_sin_cos,k2_xcmplx_0(B,A)),3),k1_newton(k5_xcmplx_0(k1_funct_1(k16_sin_cos,k2_xcmplx_0(B,A))),2)),k3_xcmplx_0(k1_newton(k1_funct_1(k18_sin_cos,B),3),k1_newton(k5_xcmplx_0(k1_funct_1(k16_sin_cos,B)),2))) ) ) ) )).
fof(t61_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k9_int_3(A))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k9_int_3(A))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k9_int_3(A))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k9_int_3(A))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k9_int_3(A))) => ! [K] : ( 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] : ( 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 = k5_int_1(2,A) & D = k5_int_1(3,A) & E = k5_int_1(4,A) & F = k5_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))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t61_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t61_entropy1,axiom,( ! [A] : ( ( v1_matrprob(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( ( v1_matrprob(B) & m2_finseq_1(B,k1_numbers) ) => k7_entropy1(k6_matrixr1(k9_matrixr1(A),k10_matrixr1(B))) = k2_xcmplx_0(k6_entropy1(A),k6_entropy1(B)) ) ) )).
fof(t61_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_enumset1(A,B,C,D) = k2_enumset1(A,B,D,C) )).
fof(t61_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => m1_subset_1(k3_tarski(C),k1_zfmisc_1(A)) ) ) ) )).
fof(t61_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => k22_rvsum_1(k9_euclid(3,B,A),C) = k3_xcmplx_0(A,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(B,1),k1_funct_1(C,1)),k3_xcmplx_0(k1_funct_1(B,2),k1_funct_1(C,2))),k3_xcmplx_0(k1_funct_1(B,3),k1_funct_1(C,3)))) ) ) ) )).
fof(t61_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t61_exchsort,axiom,( ! [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) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_exchsort(B) ) => ! [C] : ( m1_subset_1(C,k9_xtuple_0(B)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t61_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) ) )).
fof(t61_fdiff_11,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k2_sin_cos9),A),B) = k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(k2_sin_cos9,B),k1_funct_1(k1_sin_cos9,B)),k2_xcmplx_0(1,k1_square_1(B))) ) ) ) ) ) )).
fof(t61_fib_num2,axiom,( k6_fib_num2(3) = k10_finseq_1(1,2) )).
fof(t61_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k7_filter_0(A,B,C) = k7_filter_0(A,C,B) ) ) ) )).
fof(t61_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v20_lattices(B,A) & v21_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t61_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k2_xcmplx_0(B,C),k2_finseq_1(k2_xcmplx_0(A,C))) => ( r1_xxreal_0(B,k5_numbers) | ( r2_hidden(B,k2_finseq_1(A)) & r2_hidden(B,k2_finseq_1(k2_xcmplx_0(A,C))) ) ) ) ) ) ) )).
fof(t61_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => m2_finseq_1(k2_finseq_2(A,C),B) ) ) ) )).
fof(t61_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : r1_tarski(k1_relset_1(k4_ordinal1,k1_finseq_3(A,B)),k1_relset_1(k4_ordinal1,A)) ) )).
fof(t61_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t61_finseq_5,axiom,( ! [A] : ! [B] : k3_finseq_5(k10_finseq_1(A,B)) = k10_finseq_1(B,A) )).
fof(t61_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => r2_hidden(B,k10_xtuple_0(k2_finseq_5(A,C,B))) ) ) ) )).
fof(t61_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t61_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t61_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => ( r1_xxreal_0(D,k5_numbers) | k1_flang_2(A,k8_flang_1(A,B),C,D) = k8_flang_1(A,B) ) ) ) ) ) )).
fof(t61_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t61_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( r1_setfam_1(A,B) & r1_setfam_1(D,C) ) => r1_setfam_1(k2_xboole_0(A,D),k2_xboole_0(B,C)) ) )).
fof(t61_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & v8_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(F,u1_struct_0(k11_fsm_1(A,B,C))) => ? [G] : ( m1_subset_1(G,F) & ? [H] : ( m1_subset_1(H,F) & r2_hidden(G,u1_struct_0(D)) & r2_hidden(H,u1_struct_0(E)) & ! [I] : ( m1_subset_1(I,F) => ( I = G | I = H ) ) ) ) ) ) ) ) ) ) ) )).
fof(t61_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,B,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [F] : ( ( 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))) ) ) ) ) ) ) )).
fof(t61_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t61_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) => ( r1_tarski(A,B) => ( k7_relset_1(B,B,C,k8_relset_1(B,B,C,A)) = A & k8_relset_1(B,B,C,k7_relset_1(B,B,C,A)) = A ) ) ) )).
fof(t61_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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 ) ) ) ) )).
fof(t61_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( ~ v1_xboole_0(F) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k2_zfmisc_1(A,C),E) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,C),E))) ) => ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,k2_zfmisc_1(B,D),F) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(B,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,B),k2_zfmisc_1(C,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,B),k2_zfmisc_1(C,D)),k2_zfmisc_1(E,F)))) ) ) ) ) ) )).
fof(t61_funct_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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(k3_funct_5(D)) & v1_funct_2(k3_funct_5(D),B,k9_funct_2(A,C)) & m1_subset_1(k3_funct_5(D),k1_zfmisc_1(k2_zfmisc_1(B,k9_funct_2(A,C)))) ) ) ) ) ) )).
fof(t61_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_funct_7(A) ) => k9_xtuple_0(k3_funct_7(k5_funct_7(A),A)) = k5_funct_7(A) ) )).
fof(t61_funct_8,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k5_numbers,A) => k1_funct_1(k2_euclid,A) = A ) ) )).
fof(t61_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_fvaluat1(C,A) => ( v3_fvaluat1(A) => ( r2_hidden(B,k8_fvaluat1(A,C)) <=> ~ r1_xxreal_0(k3_funct_2(u1_struct_0(A),k6_numbers,C,B),k5_numbers) ) ) ) ) ) )).
fof(t61_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v2_struct_0(C) & l3_algstr_0(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m2_finseq_2(F,u1_struct_0(C),k4_finseq_2(A,u1_struct_0(C))) => ! [G] : ( 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(k12_fvsum_1(A,C,F,G),B) = k6_algstr_0(C,D,E) ) ) ) ) ) ) ) ) )).
fof(t61_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( C != k4_tarski(k10_finseq_1(A,B),k4_gfacirc1) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k22_gfacirc1(A,B,C),k23_gfacirc1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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 ) ) ) ) ) ) ) )).
fof(t61_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( 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 ) ) ) ) ) )).
fof(t61_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( 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)) ) ) ) ) )).
fof(t61_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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,B) & ~ r1_xxreal_0(k1_matrix_0(k2_goboard2(C)),B) & r1_xxreal_0(1,A) & ~ r1_xxreal_0(k3_finseq_1(k2_goboard2(C)),k1_nat_1(A,1)) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B)),k3_topreal1(2,C)) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,2),B)),k3_topreal1(2,C)) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1))),k3_topreal1(2,C)) ) ) ) ) )).
fof(t61_graph_2,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ! [B] : ( m2_finseq_1(B,k4_numbers) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(A)) & D = k8_graph_2(A,k1_nat_1(C,1),k3_finseq_1(A)) & r4_graph_2(A,C) & r3_graph_2(A,1,C) & B = k1_funct_7(k1_funct_7(A,k1_nat_1(C,1),k1_funct_1(A,D)),D,k1_funct_1(A,k1_nat_1(C,1))) ) => r3_graph_2(B,1,k1_nat_1(C,1)) ) ) ) ) ) )).
fof(t61_graph_5,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v6_graph_1(C) & l1_graph_1(C) ) => ! [D] : ( ( v7_graph_1(D,C) & m2_graph_1(D,C) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ( ( r5_graph_5(C,B) & r8_graph_5(C,E,F,D,A,B) & ! [G] : ( ( v7_graph_1(G,C) & m2_graph_1(G,C) ) => ! [H] : ( 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) ) ) ) ) ) ) ) )).
fof(t61_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ( m1_group_2(B,C) => r1_tarski(k3_group_11(A,B,C),k3_group_11(A,C,B)) ) ) ) ) )).
fof(t61_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t61_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => r1_group_2(A,k6_group_3(A,B,k1_group_1(A)),B) ) ) )).
fof(t61_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t61_group_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( r1_struct_0(k7_group_5(B,C,D),A) <=> ? [E] : ( m2_finseq_1(E,u1_struct_0(B)) & ? [F] : ( 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)) ) ) ) ) ) ) )).
fof(t61_group_6,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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 ) ) ) ) )).
fof(t61_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(t61_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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))) ) ) ) )).
fof(t61_hfdiff_1,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k1_relset_1(k1_numbers,k27_sin_cos)) => r2_relset_1(k1_numbers,k1_numbers,k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k27_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,k27_sin_cos,k6_rfunct_1(k1_numbers,k1_numbers,k16_sin_cos)),k6_rfunct_1(k1_numbers,k1_numbers,k16_sin_cos)),A),2)) ) ) )).
fof(t61_ideal_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( r2_hidden(C,k8_ideal_1(A,B)) <=> ? [D] : ( m2_ideal_1(D,A,B) & C = k4_rlvect_1(A,D) ) ) ) ) )).
fof(t61_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ v1_int_1(k7_xcmplx_0(A,B)) => k4_xcmplx_0(k1_int_1(k7_xcmplx_0(A,B))) = k2_xcmplx_0(k1_int_1(k7_xcmplx_0(k4_xcmplx_0(A),B)),1) ) ) ) )).
fof(t61_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(A,B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k1_funct_1(C,D) = k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,D))) & k1_funct_1(k18_sin_cos,D) != k5_numbers ) ) ) & k9_xtuple_0(k26_sin_cos) = B & B = k9_xtuple_0(C) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,A)) ) => k2_integra5(A,C) = k6_xcmplx_0(k1_funct_1(k26_sin_cos,k2_seq_4(A)),k1_funct_1(k26_sin_cos,k3_seq_4(A))) ) ) ) ) )).
fof(t61_integra8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( ( k9_xtuple_0(k5_sin_cos2) = k9_xtuple_0(A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,k1_numbers) => k1_funct_1(A,C) = k7_xcmplx_0(1,k1_square_1(k1_funct_1(k3_sin_cos2,C))) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,A,B)) ) => k2_integra5(B,A) = k6_xcmplx_0(k1_funct_1(k5_sin_cos2,k2_seq_4(B)),k1_funct_1(k5_sin_cos2,k3_seq_4(B))) ) ) ) )).
fof(t61_integra9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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))) = k6_xcmplx_0(k1_funct_1(k3_taylor_1,k2_seq_4(A)),k1_funct_1(k3_taylor_1,k3_seq_4(A))) ) ) ) )).
fof(t61_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m2_interva1(B,A) => r2_interva1(A,k17_interva1(A,B,B),B) ) ) )).
fof(t61_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) ) )).
fof(t61_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [D] : ( ( 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,k4_xcmplx_0(1)) | r1_xxreal_0(1,A) | v5_pre_topc(D,k1_pre_topc(k15_euclid(2),B),k1_pre_topc(k15_euclid(2),C)) ) ) ) ) ) ) )).
fof(t61_jgraph_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ 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(k5_numbers,k18_euclid(A)) & r1_xxreal_0(k5_numbers,k18_euclid(B)) & r1_xxreal_0(k5_numbers,k18_euclid(C)) & ~ r1_xxreal_0(k18_euclid(D),k5_numbers) & ! [F] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(k15_euclid(2))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k15_euclid(2))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k15_euclid(2))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k15_euclid(2))) => ~ ( v3_tops_2(F,k15_euclid(2),k15_euclid(2)) & ! [K] : ( 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(k5_numbers,k17_euclid(G)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(G)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(H)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(H)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(I)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(I)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(J)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(J)) & r1_jordan6(E,G,H) & r1_jordan6(E,H,I) & r1_jordan6(E,I,J) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t61_jgraph_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t61_jgraph_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(k5_topmetr)) => ! [H] : ( 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(k7_xcmplx_0(2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(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(k4_xcmplx_0(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)),k4_xcmplx_0(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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t61_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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(k2_jordan9(D,B))) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(k1_jordan8(D,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),k2_jordan9(D,B),A) = k3_matrix_0(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)),k2_jordan9(D,B),A),k16_pscomp_1(k3_topreal1(2,k2_jordan9(D,B)))) ) ) ) ) ) )).
fof(t61_jordan1h,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( 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] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(k4_tarski(D,E),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k7_nat_d(k3_finseq_1(C),1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),D,E) & r2_hidden(k4_tarski(k1_nat_1(D,1),E),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k3_finseq_1(C)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k1_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(k1_nat_1(D,1),k7_nat_d(E,1)),k2_matrix_0(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) )).
fof(t61_jordan1j,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( ~ 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_0(k1_jordan8(B,A))) & ~ r1_xxreal_0(A,k5_numbers) & k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k8_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) = k1_tarski(k3_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k9_jordan6(k3_topreal1(2,k2_jordan9(B,A)))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D)) & r1_xboole_0(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,A),C,E)),k8_jordan6(B)) ) ) ) ) ) ) )).
fof(t61_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( ( r2_hidden(B,D) & C = a_3_1_jordan2c(A,B,D) ) => r1_tarski(C,D) ) ) ) ) ) )).
fof(t61_jordan6,axiom,( ! [A] : ( ( ~ 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) ) ) )).
fof(t61_kurato_1,axiom,( 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)) )).
fof(t61_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => k5_lattices(A) = k6_lattices(k1_lattice2(A)) ) )).
fof(t61_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k9_funct_2(k6_glib_000(A),k4_ordinal1))) => ! [C] : ! [D] : ( r2_hidden(D,k1_relset_1(k6_glib_000(A),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),B))) => k1_recdef_1(k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k4_ordinal1,k6_glib_000(A),B),D) = k1_recdef_1(k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k4_ordinal1,k6_glib_000(A),k20_lexbfs(A,B,C)),D) ) ) ) )).
fof(t61_limfunc1,axiom,( ! [A] : ( ( 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)) ) ) )).
fof(t61_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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) = k5_numbers & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & v1_comseq_2(k2_partfun1(k1_numbers,k1_numbers,C,k2_rcomp_1(k6_xcmplx_0(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) = k5_numbers ) ) ) ) ) ) )).
fof(t61_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(k6_xcmplx_0(A,D),A))) & r1_xxreal_0(k1_limfunc2(B,A),k1_funct_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)) ) ) ) ) ) ) )).
fof(t61_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( ( v2_xxreal_0(F) & v1_xreal_0(F) ) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ( ( 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(k2_power(I,k2_extreal1(1,F)),k2_xcmplx_0(k2_power(G,k2_extreal1(1,F)),k2_power(H,k2_extreal1(1,F)))) ) ) ) ) ) ) ) ) ) ) )).
fof(t61_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_hilbert1)) => r8_ltlaxio1(C,k3_hilbert1(k5_ltlaxio1(k2_ltlaxio1(A),k2_ltlaxio1(B)),k2_ltlaxio1(k5_ltlaxio1(A,B)))) ) ) ) )).
fof(t61_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t61_mathmorp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t61_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,k1_numbers,A,A) & m2_finseq_1(E,k3_finseq_2(k1_numbers)) ) => ( r2_matrix10(k4_matrix10(A,B,C),k5_matrix10(A,D,E)) => r2_matrix10(k4_matrix10(A,B,E),k5_matrix10(A,D,C)) ) ) ) ) ) ) )).
fof(t61_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( ( v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ~ ( r1_tarski(k2_zfmisc_1(C,D),k2_matrix_0(B)) & ( k5_card_1(C) = k5_numbers => k5_card_1(D) = k5_numbers ) & ( k5_card_1(D) = k5_numbers => k5_card_1(C) = k5_numbers ) & k4_matrix_0(A,k6_matrix13(A,B,C,D)) != k6_matrix13(A,k4_matrix_0(A,B),D,C) ) ) ) ) ) )).
fof(t61_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ~ ( ~ ( k1_matrix_0(B) = k5_numbers & k3_finseq_1(B) != k5_numbers ) & v1_xboole_0(k6_matrix15(A,B,k5_finseq_2(u1_struct_0(A),k3_finseq_1(B),k4_struct_0(A)))) ) ) ) )).
fof(t61_matrix16,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t61_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ( ~ r2_hidden(C,k2_finseq_1(k1_matrix_0(B))) => k16_matrix_0(C,A,B) = B ) ) ) ) )).
fof(t61_matrix_4,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t61_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => k1_matrix_8(A,B,k1_matrix_4(B,k3_matrix_3(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)) ) ) ) ) ) )).
fof(t61_matrixj1,axiom,( ! [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] : ( m2_finseq_1(B,k4_ordinal1) => k20_matrixj1(u1_struct_0(A),k4_struct_0(A),k23_matrixj1(A,B)) = k3_matrix_1(A,k2_wsierp_1(B)) ) ) )).
fof(t61_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( k1_matrix_0(B) = k3_finseq_1(A) => ( r1_xxreal_0(k3_finseq_1(A),k5_numbers) | k3_finseq_1(k11_matrixr1(B,A)) = k3_finseq_1(B) ) ) ) ) )).
fof(t61_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(D,E),k2_matrix_0(k1_matrixr2(A,C,B))) => k3_matrix_0(k1_numbers,k1_matrixr2(A,C,B),D,E) = k1_funct_1(k12_matrixr1(B,k7_matrix_0(k1_numbers,C,D)),E) ) ) ) ) ) ) )).
fof(t61_matrprob,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v5_matrprob(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => k5_matrprob(A) = k3_finseq_1(A) ) )).
fof(t61_mcart_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) => ( ! [G] : ( m1_subset_1(G,B) => ! [H] : ( m1_subset_1(H,C) => ! [I] : ( m1_subset_1(I,D) => ! [J] : ( m1_subset_1(J,E) => ( F = k6_xtuple_0(G,H,I,J) => A = H ) ) ) ) ) => A = k5_mcart_1(B,C,D,E,F) ) ) ) ) ) ) )).
fof(t61_measure6,axiom,( k5_measure6(k2_subset_1(k1_numbers)) = k1_numbers )).
fof(t61_member_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k10_member_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k3_xxreal_3(A,B)) ) ) )).
fof(t61_mesfunc5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k6_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ( ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(D,E) => r1_xxreal_0(k9_nat_1(k6_numbers,A,D),k9_nat_1(k6_numbers,A,E)) ) ) ) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(D,E) => r1_xxreal_0(k9_nat_1(k6_numbers,B,D),k9_nat_1(k6_numbers,B,E)) ) ) ) & v3_mesfunc5(A) & v3_mesfunc5(B) & ! [D] : ( v7_ordinal1(D) => k3_supinf_2(k9_nat_1(k6_numbers,A,D),k9_nat_1(k6_numbers,B,D)) = k9_nat_1(k6_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))) ) ) ) ) ) )).
fof(t61_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t61_mmlquery,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_1(D,k9_setfam_1(A)) => r1_tarski(k27_mmlquery(A,D,B,C),k26_mmlquery(A,D,B)) ) ) ) )).
fof(t61_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k30_modelc_1(k25_modelc_2(A)))) ) => ! [C] : ( m1_subset_1(C,k25_modelc_2(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k42_modelc_2(A,B))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t61_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_3(B,A) & l1_modelc_3(B,A) ) => ! [C] : ( m1_subset_1(C,k25_modelc_2(k43_modelc_2)) => ! [D] : ( m2_orders_1(D,k1_orders_1(k1_modelc_3(A)),k6_partfun1(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))) ) ) ) ) ) ) ) )).
fof(t61_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => r1_xxreal_0(k11_nat_3(k6_moebius1(B),A),1) ) ) )).
fof(t61_monoid_0,axiom,( ! [A] : ( ~ 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 ) ) )).
fof(t61_nat_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => k8_nat_3(k8_newton,k13_nat_3(A)) = A ) )).
fof(t61_nat_d,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( A != k5_numbers => k4_int_1(k2_xcmplx_0(B,k3_xcmplx_0(A,C)),A) = k2_xcmplx_0(k4_int_1(B,A),C) ) & k5_int_1(k2_xcmplx_0(B,k3_xcmplx_0(A,C)),A) = k5_int_1(B,A) ) ) ) ) )).
fof(t61_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t61_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_nat_d(B,C) => r1_nat_d(k5_nat_d(B,k6_nat_d(A,C)),k6_nat_d(k5_nat_d(B,A),C)) ) ) ) ) )).
fof(t61_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t61_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(t61_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r9_orders_1(A,B) <=> r8_orders_1(k2_relat_1(A),B) ) ) )).
fof(t61_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r2_hidden(k10_ordinal2(A,B),C) => r2_hidden(B,k5_ordinal3(C,A)) ) ) ) ) )).
fof(t61_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( B != k5_numbers => r2_hidden(k7_ordinal3(A,k12_ordinal2(B,C)),k12_ordinal2(B,C)) ) ) ) ) )).
fof(t61_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( ( v3_ordinal1(C) & v4_ordinal1(C) & ~ v1_xboole_0(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_classes2(D) ) => ( ( r2_hidden(C,D) & r2_hidden(A,D) & r2_hidden(B,C) & ! [E] : ( 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)) ) ) ) ) ) )).
fof(t61_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_tarski(A)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k1_tarski(A)))) ) => r1_partfun1(C,D) ) ) )).
fof(t61_partfun2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,A) & v1_funct_1(C) ) => ( r1_tarski(B,C) => ! [D] : ( r2_hidden(D,k9_xtuple_0(B)) => k7_partfun1(A,B,D) = k7_partfun1(A,C,D) ) ) ) ) )).
fof(t61_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) )).
fof(t61_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( ( 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) & k10_pdiff_1(3,1,k26_valued_1(k1_euclid(3),k1_numbers,k1_pdiff_3(2,3,C),A),B) = k3_xcmplx_0(A,k4_pdiff_5(C,B)) ) ) ) ) ) )).
fof(t61_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t61_pepin,axiom,( v1_int_2(257) )).
fof(t61_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v1_int_1(B) => ( B = k4_xcmplx_0(1) => k1_vectsp_9(k2_bspace,k24_polyform(A,B)) = 1 ) ) ) )).
fof(t61_polynom5,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( k1_algseq_1(A,B) != k5_numbers => k6_polynom5(A,B) = k6_polynom5(A,k7_polynom5(A,B)) ) ) ) )).
fof(t61_power,axiom,( k2_power(2,3) = 8 )).
fof(t61_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(B,k5_numbers) ) => r1_xxreal_0(k4_prepower(A,B),1) ) ) ) )).
fof(t61_prob_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_prob_3(D,A,B) => k3_finseq_1(k9_prob_3(A,B,D,C)) = k3_finseq_1(D) ) ) ) ) )).
fof(t61_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t61_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ~ ( r2_qc_lang2(A,B,C) & r1_qc_lang2(A,C,B) ) ) ) ) )).
fof(t61_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t61_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k17_quatern2(k25_quaterni(A,B),k25_quaterni(A,B)) = k22_quaterni(k25_quaterni(k25_quaterni(k17_quatern2(A,A),k17_quatern2(A,B)),k17_quatern2(B,A)),k17_quatern2(B,B)) ) ) )).
fof(t61_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k24_quaterni(k25_quaterni(k22_quaterni(A,B),C)) = k22_quaterni(k25_quaterni(k24_quaterni(A),B),C) ) ) ) )).
fof(t61_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ( k13_quaterni(k22_quaterni(A,k27_quaterni(A))) = k3_xcmplx_0(2,k13_quaterni(A)) & k14_quaterni(k22_quaterni(A,k27_quaterni(A))) = k5_numbers & k15_quaterni(k22_quaterni(A,k27_quaterni(A))) = k5_numbers & k16_quaterni(k22_quaterni(A,k27_quaterni(A))) = k5_numbers ) ) )).
fof(t61_quofield,axiom,( ! [A] : ( ( ~ 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] : ( ~ 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] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) )).
fof(t61_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B))))) => ! [D] : ( m1_rcomp_3(D,A,B,C) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t61_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k5_relat_1(B,A) = k3_xboole_0(B,k2_zfmisc_1(A,k10_xtuple_0(B))) ) )).
fof(t61_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) => ! [E] : ( 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) ) ) ) ) )).
fof(t61_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t61_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ 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] : ( 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 ) ) ) ) ) ) )).
fof(t61_rfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,B) => ( ( r2_hidden(D,A) => k1_funct_1(C,D) = 1 ) & ( ~ r2_hidden(D,A) => k1_funct_1(C,D) = k5_numbers ) ) ) ) ) ) ) )).
fof(t61_rfunct_3,axiom,( r2_rfunct_3(k1_partfun2(k1_numbers,k2_subset_1(k1_numbers)),k1_numbers) )).
fof(t61_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_seq_2(A) => r2_funct_2(k4_ordinal1,k1_numbers,k3_rinfsup1(A),k32_valued_1(k4_ordinal1,k1_numbers,k4_rinfsup1(k32_valued_1(k4_ordinal1,k1_numbers,A)))) ) ) )).
fof(t61_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_rlsub_1(D,A) => ( r2_hidden(k3_rlvect_1(A,B,C),k3_rlsub_1(A,C,D)) <=> r1_struct_0(D,B) ) ) ) ) ) )).
fof(t61_rlsub_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( B = k1_algstr_0(A,C,D) <=> C = k5_algstr_0(A,B,D) ) ) ) ) ) )).
fof(t61_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t61_rlvect_1,axiom,( ! [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) ) => ! [B] : ( 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,k4_xcmplx_0(2)) ) ) )).
fof(t61_rlvect_2,axiom,( ! [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) ) => 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)) ) )).
fof(t61_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_rmod_2(E,A,B) => ~ ( k3_rmod_2(A,B,D,E) = k3_rmod_2(A,B,C,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ~ ( r1_struct_0(E,F) & k3_rlvect_1(B,D,F) = C ) ) ) ) ) ) ) ) )).
fof(t61_rmod_4,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_rmod_4(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t61_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v6_robbins1(A) & v10_robbins1(A) & l4_robbins1(A) ) => k7_robbins1(A) = k5_lattices(A) ) )).
fof(t61_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t61_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( k3_rusub_1(A,D,B) = k3_rusub_1(A,C,B) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r1_struct_0(B,E) & k5_algstr_0(A,D,E) = C ) ) ) ) ) ) ) )).
fof(t61_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_bhsp_1(B) & m1_rusub_1(B,A) ) => ( ! [C] : ( 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)) ) ) ) )).
fof(t61_rvsum_1,axiom,( ! [A] : ( ( 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) ) )).
fof(t61_scm_halt,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_3(k4_scmfsa_2(k5_numbers),1)),k7_card_1(3),k1_scmfsa_2,k2_scmfsa8c(B,A)) ) ) ) )).
fof(t61_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) => ( r5_scmfsa7b(C,B,A) => ! [D] : ( v7_ordinal1(D) => k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),D),k4_scmfsa_2(k5_numbers)) = k1_funct_1(B,k4_scmfsa_2(k5_numbers)) ) ) ) ) ) )).
fof(t61_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ( k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k10_scmfsa_2(A,A),B),k4_struct_0(k1_scmfsa_2)) = k4_card_1(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,B)) & k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k10_scmfsa_2(A,A),B),A) = k5_int_1(k1_funct_1(B,A),k1_funct_1(B,A)) & ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ( C != A => k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k10_scmfsa_2(A,A),B),C) = k1_funct_1(B,C) ) ) & ! [C] : ( m1_scmfsa_2(C) => r2_relset_1(k4_ordinal1,k4_numbers,k18_scmfsa_2(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k10_scmfsa_2(A,A),B),C),k18_scmfsa_2(B,C)) ) ) ) ) )).
fof(t61_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( 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) ) ) )).
fof(t61_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v3_scmpds_4(D) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( ( 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),F)),k5_numbers) | k6_scmpds_4(k3_scmpds_6(E,F,C,D),B,A) = k1_funct_4(k6_scmpds_4(C,B,A),k7_memstr_0(2,k1_scmpds_2,k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),2))) ) ) ) ) ) ) ) ) )).
fof(t61_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_tarski(A))) => ! [C] : ( B = k1_tarski(C) => v9_scmyciel(B,A) ) ) ) )).
fof(t61_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t61_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ( k13_seq_4(A,B,k16_seq_4(A,B)) = k15_seq_4(A) & k13_seq_4(A,k16_seq_4(A,B),B) = k15_seq_4(A) ) ) ) )).
fof(t61_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v2_prob_1(B) => k4_kurato_0(A,B) = k3_prob_1(A,B) ) ) )).
fof(t61_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) ) ) )).
fof(t61_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( v7_ordinal1(C) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ( ( r1_tarski(B,E) & ! [F] : ( v7_ordinal1(F) => ( ~ r1_xxreal_0(C,F) => r2_hidden(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,D,F)),k1_relset_1(k4_ordinal1,B)) ) ) ) => ( r2_hidden(A,k2_sf_mastr(B)) | k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,D,C),A) = k1_funct_1(D,A) ) ) ) ) ) ) ) )).
fof(t61_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t61_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => k11_simplex0(A,B,C,k5_numbers) = B ) ) )).
fof(t61_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k6_xcmplx_0(k1_funct_1(k22_sin_cos,k2_xcmplx_0(A,B)),k1_funct_1(k22_sin_cos,A)) = k2_xcmplx_0(k3_xcmplx_0(B,k1_funct_1(k22_sin_cos,A)),k3_xcmplx_0(k3_xcmplx_0(B,k1_funct_1(k22_sin_cos,A)),k3_complex1(k11_comseq_3(k24_sin_cos(B))))) ) ) )).
fof(t61_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k2_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,k3_xcmplx_0(2,A)),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,k3_xcmplx_0(2,B))) = k3_xcmplx_0(k3_xcmplx_0(2,k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,k2_xcmplx_0(A,B))),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,k6_xcmplx_0(A,B))) & k6_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,k3_xcmplx_0(2,A)),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,k3_xcmplx_0(2,B))) = k3_xcmplx_0(k3_xcmplx_0(2,k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,k6_xcmplx_0(A,B))),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,k2_xcmplx_0(A,B))) ) ) ) )).
fof(t61_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_int_1(C) => ( ( r1_xxreal_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C),A) & r1_xxreal_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C),B) & k17_sin_cos(A) = k17_sin_cos(B) & k19_sin_cos(A) = k19_sin_cos(B) ) => ( r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)),A) | r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)),B) | A = B ) ) ) ) ) )).
fof(t61_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,k7_xcmplx_0(k2_xcmplx_0(k1_square_1(A),1),k3_xcmplx_0(2,A))) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(1,A) | k3_power(k4_power,A) = k3_sin_cos7(k7_xcmplx_0(k2_xcmplx_0(k1_square_1(A),1),k3_xcmplx_0(2,A))) ) ) ) )).
fof(t61_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) & k3_sin_cos9(A) = k7_xcmplx_0(k28_sin_cos,4) ) => A = 1 ) ) )).
fof(t61_sincos10,axiom,( k3_relat_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k3_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))),k1_sincos10) = k1_partfun2(k1_numbers,k3_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) )).
fof(t61_sprect_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t61_sprect_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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))) ) ) ) ) ) )).
fof(t61_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t61_stirl2_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ~ ( r2_hidden(C,k10_xtuple_0(k3_relat_1(A,B))) & v2_funct_1(B) & ! [D] : ~ ( 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)) ) ) ) ) )).
fof(t61_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_valuat_1(D,A,C) => ( ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [F] : ( 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] : ( m2_funct_2(E,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t61_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t61_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_tdlat_3(B) & m1_pre_topc(B,A) ) => ? [C] : ( ~ v2_struct_0(C) & v1_pre_topc(C) & m1_pre_topc(C,A) & m1_pre_topc(B,C) & v4_tex_2(C,A) ) ) ) )).
fof(t61_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ~ ( ? [B] : ( ~ 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) ) ) )).
fof(t61_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) )).
fof(t61_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ v2_struct_0(D) & v1_tsep_1(D,A) & m1_pre_topc(D,A) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ( E = F => ( r1_tmap_1(A,B,C,E) <=> r1_tmap_1(D,B,k2_tmap_1(A,B,C,D),F) ) ) ) ) ) ) ) ) )).
fof(t61_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_topalg_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_topalg_1(A,B))) => ! [E] : ( m1_borsuk_2(E,A,B,B) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t61_topgen_4,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t61_topreal6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t61_topreal9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ! [G] : ( m2_finseq_2(G,k1_numbers,k1_euclid(2)) => ! [H] : ( m2_finseq_2(H,k1_numbers,k1_euclid(2)) => ! [I] : ( m2_finseq_2(I,k1_numbers,k1_euclid(2)) => ~ ( G = k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),E,k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(2),F,k7_xcmplx_0(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] : ( 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(k15_euclid(2),E,F),k5_jgraph_6(A,B,C)) & ( r2_hidden(F,k3_topreal9(2,k19_euclid(A,B),C)) => J = F ) & ( D = k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(2,k22_rvsum_1(k5_algstr_0(k15_euclid(2),F,k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),E,k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(2),F,k7_xcmplx_0(1,2)))),k5_algstr_0(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),E,k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(2),F,k7_xcmplx_0(1,2))),k19_euclid(A,B))))),k3_square_1(k1_quin_1(k18_rvsum_1(k11_euclid(2,k8_euclid(2,H,G))),k3_xcmplx_0(2,k22_rvsum_1(k5_algstr_0(k15_euclid(2),F,k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),E,k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(2),F,k7_xcmplx_0(1,2)))),k5_algstr_0(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),E,k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(2),F,k7_xcmplx_0(1,2))),k19_euclid(A,B)))),k6_xcmplx_0(k18_rvsum_1(k11_euclid(2,k8_euclid(2,G,I))),k1_square_1(C))))),k3_xcmplx_0(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,k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(2),F,k7_xcmplx_0(1,2))),k6_xcmplx_0(1,D)),k1_rlvect_1(k15_euclid(2),F,D)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t61_toprealc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_xreal_0(B) & ~ v3_xxreal_0(B) ) => ! [C] : ( ( 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))))) ) ) ) ) )).
fof(t61_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) )).
fof(t61_tops_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) )).
fof(t61_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t61_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t61_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( r2_hidden(B,A) <=> r2_hidden(k7_finseq_1(k14_trees_3(k5_numbers),B),k12_trees_3(A)) ) ) ) )).
fof(t61_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ! [E] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t61_uproots,axiom,( ! [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) ) => ! [B] : ( ( 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] : ( ( 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(k4_ordinal1,u1_struct_0(A),k9_uproots(A,k11_pre_poly(u1_struct_0(A),B,C)),k13_polynom3(A,k9_uproots(A,B),k9_uproots(A,C))) ) ) ) )).
fof(t61_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) ) => ~ ( r1_tarski(B,A) & ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v2_finseq_1(D) ) => D != k2_xboole_0(B,k61_valued_1(C,k3_finseq_1(A))) ) ) ) ) ) )).
fof(t61_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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)) ) ) ) )).
fof(t61_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_vectsp_4(E,A,B) => ( r2_hidden(k5_algstr_0(B,D,C),k3_vectsp_4(A,B,D,E)) <=> r1_struct_0(E,C) ) ) ) ) ) ) )).
fof(t61_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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))) ) ) ) )).
fof(t61_waybel23,axiom,( ! [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] : ( ( v6_waybel23(B,A) & m1_waybel23(B,A) ) => v18_waybel_0(k4_waybel23(A,k5_yellow_0(A,B)),k1_yellow_1(k7_waybel_0(k5_yellow_0(A,B))),k1_yellow_1(k7_waybel_0(A))) ) ) )).
fof(t61_waybel34,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(t61_waybel_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(B,k3_waybel_0(A,k11_waybel_0(A,B))) & ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t61_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t61_waybel_4,axiom,( ! [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] : ( ( 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) ) ) ) )).
fof(t61_xboole_1,axiom,( ! [A] : ( A != k1_xboole_0 => r2_xboole_0(k1_xboole_0,A) ) )).
fof(t61_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k5_xboolean(k3_xboolean(A),k8_xboolean(A,B)) = k8_xboolean(A,B) ) ) )).
fof(t61_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k7_xcmplx_0(B,A) = B => ( B = k5_numbers | A = 1 ) ) ) ) )).
fof(t61_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k4_xcmplx_0(B),A) & r1_xxreal_0(k5_numbers,k2_xcmplx_0(A,B)) ) ) ) )).
fof(t61_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_tarski(k3_xxreal_1(C,D),k3_xxreal_1(A,B)) => ( r1_xxreal_0(D,C) | ( r1_xxreal_0(A,C) & r1_xxreal_0(D,B) ) ) ) ) ) ) ) )).
fof(t61_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => ( ? [C] : ( v1_xxreal_0(C) & r2_hidden(C,A) & r1_xxreal_0(B,C) ) => r1_xxreal_0(B,k1_xxreal_2(A)) ) ) ) )).
fof(t61_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & r1_xxreal_0(k1_xxreal_3(B,C),A) ) ) => r1_xxreal_0(A,B) ) ) ) )).
fof(t61_yellow10,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t61_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t61_yellow_4,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t61_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t61_yellow_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( v2_pre_topc(B) & m1_yellow_9(B,A) ) => ! [C] : ( ( v2_pre_topc(C) & m1_yellow_9(C,A) ) => ! [D] : ( 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)))) ) ) ) ) ) )).
fof(t61_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r1_zf_lang(B,A) => r3_zf_lang(B,A) ) ) ) )).
fof(t61_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => k2_zf_model(k7_zf_lang(A,B)) = k4_subset_1(k1_zf_lang,k2_zf_model(A),k2_zf_model(B)) ) ) )).
fof(t61_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( k4_xboole_0(k2_tarski(A,B),C) = k1_tarski(A) <=> ( ~ r2_hidden(A,C) & ( r2_hidden(B,C) | A = B ) ) ) )).
fof(t61_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => k5_zmodul01(A,B,k4_zmodul01(A)) = u1_struct_0(A) ) ) )).
fof(t61_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ~ v1_zmodul02(k7_domain_1(u1_struct_0(A),B,k4_struct_0(A)),A) ) ) )).
fof(t62_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l3_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A))) => ( r6_abcmiz_0(A,B,C) => v1_finset_1(C) ) ) ) ) )).
fof(t62_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ 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 ) ) )).
fof(t62_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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 ) ) ) ) ) )).
fof(t62_afinsq_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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)) ) ) ) )).
fof(t62_afinsq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_valued_0(B) & v1_finset_1(B) ) => ! [C] : ( v1_xcmplx_0(C) => k24_valued_1(k5_relat_1(B,A),C) = k5_relat_1(k24_valued_1(B,C),A) ) ) ) )).
fof(t62_algspec1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v11_struct_0(B) & v1_instalg1(B) & l1_msualg_1(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t62_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( F != G & ~ ( ~ ( r2_analoaf(A,F,G,B,C) & r4_analmetr(A,F,G,D,E) ) & ~ ( r2_analoaf(A,F,G,D,E) & r4_analmetr(A,F,G,B,C) ) & ~ ( r2_analoaf(A,F,G,B,C) & r4_analmetr(A,D,E,F,G) ) & ~ ( r2_analoaf(A,F,G,D,E) & r4_analmetr(A,B,C,F,G) ) & ~ ( r2_analoaf(A,B,C,F,G) & r4_analmetr(A,D,E,F,G) ) & ~ ( r2_analoaf(A,D,E,F,G) & r4_analmetr(A,B,C,F,G) ) & ~ ( r2_analoaf(A,B,C,F,G) & r4_analmetr(A,F,G,D,E) ) & ~ ( r2_analoaf(A,D,E,F,G) & r4_analmetr(A,F,G,B,C) ) ) & ~ r4_analmetr(A,B,C,D,E) ) ) ) ) ) ) ) ) )).
fof(t62_aofa_000,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_freealg(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_freealg(k19_aofa_000,A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_freealg(k19_aofa_000,A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_freealg(k19_aofa_000,A))) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t62_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( ( v3_aofa_a01(G,A,B,C,u4_aofa_a00(A,B,C,E),F) & m1_msafree4(G,u1_struct_0(A),u4_aofa_a00(A,B,C,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),F)) ) => ! [H] : ( m2_pboole(H,u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,D)) => k15_aofa_a00(A,B,C,D,F,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),F,G),H) = k1_funct_1(k2_msafree4(u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,D),H,F),G) ) ) ) ) ) ) ) ) )).
fof(t62_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_aofa_i00(D,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [G] : ( m1_aofa_i00(G,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ( ? [H] : ( v1_relat_1(H) & v1_funct_1(H) & k1_funct_1(H,C) = k5_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,k5_numbers),k16_aofa_000(A,k78_aofa_i00(A,B,C,D,F,k5_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,k5_numbers),D,G,E),k83_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,G,F)),k48_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,E,F)),k48_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,F,G))),D,a_6_2_aofa_i00(A,B,C,D,E,F)) ) ) ) ) ) ) ) ) )).
fof(t62_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( m1_subset_1(C,k5_arytm_3) => ( k9_arytm_3(B,C) = k9_arytm_3(A,C) => B = A ) ) ) ) )).
fof(t62_asympt_1,axiom,( ! [A] : ( ( v1_xreal_0(A) & v1_asympt_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k9_nat_1(k1_numbers,B,k5_numbers) = k5_numbers & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ r1_xxreal_0(C,k5_numbers) => k9_nat_1(k1_numbers,B,C) = k3_power(A,C) ) ) ) => ( r1_xxreal_0(A,1) | v4_asympt_0(B) ) ) ) ) )).
fof(t62_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( k2_bcialg_1(A,B) = k4_struct_0(A) => B = k4_struct_0(A) ) ) ) ) )).
fof(t62_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,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)) ) ) ) ) )).
fof(t62_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t62_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t62_borsuk_6,axiom,( ! [A] : ( r2_hidden(k4_tarski(k5_numbers,A),k7_borsuk_6) => A = 1 ) )).
fof(t62_borsuk_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ( B != k4_struct_0(k15_euclid(A)) => k12_euclid(k9_toprealc(A,B,k12_euclid(B))) = 1 ) ) ) )).
fof(t62_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t62_bvfunc14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ( ( v1_relat_1(I) & v1_funct_1(I) ) => ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ! [Q] : ( 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 ) ) ) ) )).
fof(t62_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(t62_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k6_xboolean(A,B) = k6_xboolean(k3_xboolean(B),k3_xboolean(A)) ) ) )).
fof(t62_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => v1_finset_1(k3_calcul_1(A,B)) ) ) )).
fof(t62_card_1,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => k1_card_1(k7_funcop_1(B,A)) = B ) )).
fof(t62_card_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( r3_zfmisc_1(A,B,C,D,E) => k5_card_1(k3_enumset1(A,B,C,D,E)) = 5 ) )).
fof(t62_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( r1_tarski(B,k8_card_3(A)) & ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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)) ) ) )).
fof(t62_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => ? [B] : ( v1_relat_1(B) & v5_relat_1(B,k4_numbers) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) & k7_afinsq_2(B) = k1_card_1(a_1_1_card_fin(A)) & k1_relset_1(k4_ordinal1,B) = k1_nat_1(k5_card_1(A),1) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k1_relset_1(k4_ordinal1,B)) => k1_funct_1(B,C) = k7_xcmplx_0(k3_xcmplx_0(k1_newton(k4_xcmplx_0(1),C),k7_newton(k5_card_1(A))),k7_newton(C)) ) ) ) ) )).
fof(t62_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t62_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m2_cat_3(E,C,D,A) => ( r2_hidden(B,A) => k4_graph_1(C,k7_partfun1(u4_struct_0(C),E,B)) = D ) ) ) ) )).
fof(t62_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t62_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( 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(k5_numbers)) = k1_xboole_0 & v1_partfun1(C,A) ) <=> v1_partfun1(k1_cfunct_1(A,B,C),A) ) ) ) ) )).
fof(t62_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_chain_1(C,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k4_chain_1(B,C,k1_nat_1(A,1)))) => ( m3_chain_1(D,B,C,k1_nat_1(A,1)) <=> k10_chain_1(B,C,A,D) = k5_chain_1(B,C,A) ) ) ) ) ) )).
fof(t62_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_chord(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) => ! [C] : ( m2_glib_000(C,A,B,k21_glib_000(A,B)) => v2_chord(C) ) ) ) )).
fof(t62_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v6_circcomb(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v6_circcomb(D,B) & l3_msualg_1(D,B) ) => v6_circcomb(k3_circcomb(A,B,C,D),k2_circcomb(A,B)) ) ) ) ) )).
fof(t62_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m4_msaterm(C,A,B) => ! [D] : ( m3_msaterm(D,A,C) => ! [E] : ( ( ~ v2_struct_0(E) & ~ v11_struct_0(E) & v2_msafree2(E) & l1_msualg_1(E) ) => ! [F] : ( ( v4_msualg_1(F,E) & v4_msafree2(F,E) & l3_msualg_1(F,E) ) => ( r8_circtrm1(A,B,C,D,E,F) => ! [G] : ( 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] : ( m1_subset_1(H,u1_struct_0(E)) => ~ ! [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_xcmplx_0(1,k6_trees_1(k9_xtuple_0(G)))),H) & ? [J] : ( m2_circtrm1(J,A,C,B,D,E,F) & ! [K] : ( 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] : ( m1_circtrm1(L,A,C,D,B,K) => k1_funct_1(k5_facirc_1(E,F,I,k2_xcmplx_0(1,k6_trees_1(k9_xtuple_0(G)))),H) = k7_circtrm1(A,B,C,G,L) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t62_classes1,axiom,( ! [A] : ? [B] : ( v3_ordinal1(B) & r1_tarski(A,k4_classes1(B)) ) )).
fof(t62_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_clvect_1(C,A) => r2_hidden(B,k5_clvect_1(A,B,C)) ) ) ) )).
fof(t62_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v2_clvect_2(B,A) => v2_clvect_2(k5_vfunct_1(k4_ordinal1,A,B),A) ) ) ) )).
fof(t62_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ~ ( ! [D] : ! [E] : ~ ( r2_hidden(D,C) & r2_hidden(E,C) & ! [F] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t62_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( ~ ( A != B & r1_xxreal_0(k9_complex1(k6_xcmplx_0(A,B)),k5_numbers) ) & ~ ( ~ r1_xxreal_0(k9_complex1(k6_xcmplx_0(A,B)),k5_numbers) & A = B ) ) ) ) )).
fof(t62_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k1_comptrig(A) = k1_comptrig(B) => ( A = k5_numbers | B = k5_numbers | k1_comptrig(k4_xcmplx_0(A)) = k1_comptrig(k4_xcmplx_0(B)) ) ) ) ) )).
fof(t62_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => r1_xxreal_0(k9_complex1(k3_rlvect_1(k1_complfld,A,B)),k2_xcmplx_0(k9_complex1(A),k9_complex1(B))) ) ) )).
fof(t62_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( m2_finseq_1(C,k2_numbers) => ! [D] : ( m2_finseq_1(D,k2_numbers) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k3_finseq_1(B) = k3_finseq_1(C) & k3_finseq_1(C) = k3_finseq_1(D) ) => k8_complsp2(k7_seq_4(A,B),k7_seq_4(C,D)) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k8_complsp2(A,C),k8_complsp2(A,D)),k8_complsp2(B,C)),k8_complsp2(B,D)) ) ) ) ) ) )).
fof(t62_comptrig,axiom,( ! [A] : ( v1_xcmplx_0(A) => A = k2_xcmplx_0(k3_xcmplx_0(k9_complex1(A),k19_sin_cos(k1_comptrig(A))),k3_xcmplx_0(k3_xcmplx_0(k9_complex1(A),k17_sin_cos(k1_comptrig(A))),k7_complex1)) ) )).
fof(t62_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k3_finseq_2(k4_ordinal1)) & v1_funct_1(C) & v4_valued_0(C) & v2_margrel1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k3_finseq_2(k4_ordinal1)) & v1_funct_1(D) & v4_valued_0(D) & v2_margrel1(D) ) => ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(k1_nat_1(k19_margrel1(C),1),k4_ordinal1)) => ( ( v2_comput_1(C) & v2_comput_1(D) & k1_nat_1(k19_margrel1(C),2) = k19_margrel1(D) & r1_xxreal_0(1,A) & r1_xxreal_0(A,k1_nat_1(1,k19_margrel1(C))) ) => k1_recdef_1(k7_comput_1(C,D,A),k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,k1_nat_1(B,1))) = k1_recdef_1(D,k8_finseq_1(k4_ordinal1,k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,B),k12_finseq_1(k4_ordinal1,k1_recdef_1(k7_comput_1(C,D,A),k8_comput_1(k1_nat_1(k19_margrel1(C),1),E,A,B))))) ) ) ) ) ) ) )).
fof(t62_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_comseq_3(A) <=> ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & r1_xxreal_0(B,k9_complex1(k6_xcmplx_0(k9_nat_1(k2_numbers,k10_comseq_3(A),D),k9_nat_1(k2_numbers,k10_comseq_3(A),C)))) ) ) ) ) ) ) )).
fof(t62_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( ( v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( v1_xcmplx_0(C) => k19_convex4(A,B,C) = k1_xboole_0 ) ) ) )).
fof(t62_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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) ) ) ) )).
fof(t62_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t62_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => 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),k18_sin_cos),A),B) = k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k3_xcmplx_0(k17_sin_cos(k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(6,B),k3_xcmplx_0(3,A)),2)),k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(3,A),2))),k3_xcmplx_0(k17_sin_cos(k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(2,B),A),2)),k17_sin_cos(k7_xcmplx_0(A,2))))) ) ) )).
fof(t62_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k7_xcmplx_0(1,k17_sin_cos(D)) ) => ( k17_sin_cos(B) = k5_numbers | k17_sin_cos(k2_xcmplx_0(B,A)) = k5_numbers | k1_funct_1(k3_diff_1(C,A),B) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(2,k6_xcmplx_0(k17_sin_cos(B),k17_sin_cos(k2_xcmplx_0(B,A)))),k6_xcmplx_0(k19_sin_cos(k2_xcmplx_0(k3_xcmplx_0(2,B),A)),k19_sin_cos(A)))) ) ) ) ) ) )).
fof(t62_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(B,k1_relset_1(k1_numbers,k27_sin_cos)) & r2_hidden(k6_xcmplx_0(B,A),k1_relset_1(k1_numbers,k27_sin_cos)) ) => k1_funct_1(k4_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k27_sin_cos),k18_sin_cos),A),B) = k6_xcmplx_0(k3_xcmplx_0(k1_newton(k1_funct_1(k18_sin_cos,B),3),k1_newton(k5_xcmplx_0(k1_funct_1(k16_sin_cos,B)),2)),k3_xcmplx_0(k1_newton(k1_funct_1(k18_sin_cos,k6_xcmplx_0(B,A)),3),k1_newton(k5_xcmplx_0(k1_funct_1(k16_sin_cos,k6_xcmplx_0(B,A))),2))) ) ) ) )).
fof(t62_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k9_int_3(A))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k9_int_3(A))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k9_int_3(A))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k9_int_3(A))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k9_int_3(A))) => ! [K] : ( 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] : ( 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 = k5_int_1(2,A) & D = k5_int_1(3,A) & E = k5_int_1(4,A) & F = k5_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))))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t62_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(B)) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ( r1_tarski(k16_ens_1(B),A) => k3_funct_2(u4_struct_0(k6_cat_2(k2_oppcat_1(B),B)),u4_struct_0(k11_ens_1(A)),k25_ens_1(A,B),k8_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)) ) ) ) ) ) )).
fof(t62_entropy1,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v6_matrprob(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( B = k8_entropy1(A) <=> ( k3_finseq_1(B) = k3_finseq_1(A) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => k1_funct_1(B,C) = k4_xcmplx_0(k18_rvsum_1(k1_matrprob(k1_numbers,k5_entropy1(A),C))) ) ) ) ) ) ) )).
fof(t62_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_enumset1(A,B,C,D) = k2_enumset1(A,C,B,D) )).
fof(t62_eqrel_1,axiom,( ! [A] : ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( 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)) ) ) ) )).
fof(t62_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => k22_rvsum_1(A,k16_euclid(3)) = k5_numbers ) )).
fof(t62_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ~ ( ~ r2_hidden(B,C) & v1_euclid_4(C,A) & ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t62_exchsort,axiom,( ! [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) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_exchsort(B) ) => ! [C] : ( m1_subset_1(C,k9_xtuple_0(B)) => ! [D] : ( m1_subset_1(D,k9_xtuple_0(B)) => ! [E] : ( m1_subset_1(E,k9_xtuple_0(B)) => ( ( r1_ordinal1(C,E) & r1_ordinal1(E,D) ) => ( k1_binop_1(k7_exchsort(A,B,C,D),C,E) = k4_tarski(C,E) & k1_binop_1(k7_exchsort(A,B,C,D),E,D) = k4_tarski(E,D) ) ) ) ) ) ) ) )).
fof(t62_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ( m1_subset_1(E,k4_card_3(u3_msualg_1(k8_facirc_1(A,B,C,D),k10_facirc_1(A,B,C,D)))) => ( C != k4_tarski(k10_finseq_1(A,B),D) => ( k11_facirc_1(k8_facirc_1(A,B,C,D),k10_facirc_1(A,B,C,D),k5_facirc_1(k8_facirc_1(A,B,C,D),k10_facirc_1(A,B,C,D),E,2),k9_facirc_1(A,B,C,D)) = k1_funct_1(D,k10_finseq_1(k1_funct_1(D,k10_finseq_1(k1_funct_1(E,A),k1_funct_1(E,B))),k1_funct_1(E,C))) & k1_funct_1(k5_facirc_1(k8_facirc_1(A,B,C,D),k10_facirc_1(A,B,C,D),E,2),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(k5_facirc_1(k8_facirc_1(A,B,C,D),k10_facirc_1(A,B,C,D),E,2),A) = k1_funct_1(E,A) & k1_funct_1(k5_facirc_1(k8_facirc_1(A,B,C,D),k10_facirc_1(A,B,C,D),E,2),B) = k1_funct_1(E,B) & k1_funct_1(k5_facirc_1(k8_facirc_1(A,B,C,D),k10_facirc_1(A,B,C,D),E,2),C) = k1_funct_1(E,C) ) ) ) ) )).
fof(t62_fdiff_11,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A)),B),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A)),B)) ) ) ) ) => ( r2_hidden(k5_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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(k1_sin_cos9,k7_xcmplx_0(1,B)),k1_funct_1(k2_sin_cos9,k7_xcmplx_0(1,B))),k2_xcmplx_0(1,k1_square_1(B))) ) ) ) ) ) ) )).
fof(t62_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => k2_xboole_0(k3_xboole_0(k4_fib_num2,k2_finseq_1(k1_nat_1(k3_xcmplx_0(2,A),3))),k6_domain_1(k4_ordinal1,k1_nat_1(k3_xcmplx_0(2,A),5))) = k3_xboole_0(k4_fib_num2,k2_finseq_1(k1_nat_1(k3_xcmplx_0(2,A),5))) ) )).
fof(t62_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v3_filter_0(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t62_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t62_finseq_1,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_tarski(k13_finseq_1(A),k13_finseq_1(B)) ) )).
fof(t62_finseq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(t62_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( k1_relset_1(k4_ordinal1,k1_finseq_3(A,B)) = k1_relset_1(k4_ordinal1,A) => r1_xboole_0(B,k10_xtuple_0(A)) ) ) )).
fof(t62_finseq_4,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t62_finseq_5,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t62_finseq_6,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( 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))) ) ) ) ) )).
fof(t62_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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 ) ) ) ) )).
fof(t62_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => k8_flang_1(A,k8_flang_1(A,B)) = k8_flang_1(A,B) ) )).
fof(t62_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(C,D) & r2_hidden(k2_flang_1(A),B) ) => ( r1_xxreal_0(D,k5_numbers) | k8_flang_1(A,k1_flang_2(A,B,C,D)) = k8_flang_1(A,B) ) ) ) ) ) )).
fof(t62_flang_3,axiom,( ! [A] : ! [B] : ( 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) ) )).
fof(t62_fomodel0,axiom,( ! [A] : ! [B] : ( r1_setfam_1(A,B) => r1_setfam_1(k2_xboole_0(A,B),B) ) )).
fof(t62_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & v8_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( ( ~ v2_struct_0(D) & v8_struct_0(D) & l2_fsm_1(D,A,B) ) => ? [E] : ( ~ v2_struct_0(E) & v8_struct_0(E) & l2_fsm_1(E,A,B) & ? [F] : ( ~ 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) ) ) ) ) ) ) )).
fof(t62_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( 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))) ) ) ) ) ) ) )).
fof(t62_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ! [B] : ! [C] : 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) ) ) )).
fof(t62_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ! [E] : ( m1_subset_1(E,A) => k1_funct_1(C,E) = k1_funct_1(D,E) ) => r2_relset_1(A,B,C,D) ) ) ) )).
fof(t62_funct_3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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 ) ) ) ) ) )).
fof(t62_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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)) ) )).
fof(t62_funct_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( ( 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))) ) => k2_binop_1(A,B,C,F,D,E) = k3_funct_2(B,C,k10_funct_5(A,B,C,k9_funct_2(B,C),k11_funct_5(A,B,C,F),D),E) ) ) ) ) ) ) )).
fof(t62_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_funct_7(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(k10_xtuple_0(B),k5_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)) ) ) ) ) )).
fof(t62_funct_8,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(k5_numbers,A) => k1_funct_1(k2_euclid,A) = k4_xcmplx_0(A) ) ) )).
fof(t62_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => r2_hidden(k4_struct_0(A),k8_fvaluat1(A,B)) ) ) ) )).
fof(t62_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k11_fvsum_1(A,k12_finseq_1(u1_struct_0(A),B),k12_finseq_1(u1_struct_0(A),C)) = k12_finseq_1(u1_struct_0(A),k6_algstr_0(A,B,C)) ) ) ) )).
fof(t62_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( C != k4_tarski(k10_finseq_1(A,B),k4_gfacirc1) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k22_gfacirc1(A,B,C),k23_gfacirc1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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)) ) ) ) ) ) ) )).
fof(t62_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ! [D] : ( r1_glib_000(A,B,D,C) => r2_hidden(C,k28_glib_000(A,B)) ) ) ) )).
fof(t62_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( r1_glib_000(A,k4_glib_001(A,B),D,C) => k3_finseq_1(k10_glib_001(A,B,C)) = k1_nat_1(k3_finseq_1(B),2) ) ) ) )).
fof(t62_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ 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,B) & ~ r1_xxreal_0(k1_matrix_0(k2_goboard2(C)),B) & r1_xxreal_0(1,A) & ~ r1_xxreal_0(k3_finseq_1(k2_goboard2(C)),k1_nat_1(A,1)) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1))),k3_topreal1(2,C)) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,2),k1_nat_1(B,1))),k3_topreal1(2,C)) & r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(C),k1_nat_1(A,1),k1_nat_1(B,1))),k3_topreal1(2,C)) ) ) ) ) )).
fof(t62_graph_2,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ! [B] : ( m2_finseq_1(B,k4_numbers) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(A)) & D = k8_graph_2(A,k1_nat_1(C,1),k3_finseq_1(A)) & r4_graph_2(A,C) & B = k1_funct_7(k1_funct_7(A,k1_nat_1(C,1),k1_funct_1(A,D)),D,k1_funct_1(A,k1_nat_1(C,1))) ) => r4_graph_2(B,k1_nat_1(C,1)) ) ) ) ) ) )).
fof(t62_graph_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v6_graph_1(D) & l1_graph_1(D) ) => ! [E] : ( ( v7_graph_1(E,D) & m2_graph_1(E,D) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(D)) => ! [G] : ( 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] : ( ( v7_graph_1(H,D) & m2_graph_1(H,D) ) => ! [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) ) ) ) ) ) ) ) )).
fof(t62_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t62_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ( ! [C] : ( 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)) ) ) ) )).
fof(t62_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t62_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,A) => ( m1_group_2(B,C) => m1_group_2(B,k8_group_4(A,C,D)) ) ) ) ) ) )).
fof(t62_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( ( r1_tarski(B,D) & r1_tarski(C,E) ) => m1_group_2(k7_group_5(A,B,C),k7_group_5(A,D,E)) ) ) ) ) ) ) )).
fof(t62_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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)))) ) ) ) ) ) )).
fof(t62_group_9,axiom,( ! [A] : ! [B] : ( 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)))) ) )).
fof(t62_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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)) ) ) ) )).
fof(t62_hfdiff_1,axiom,( ! [A] : ( ( 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,k22_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,k22_sin_cos,k18_sin_cos),A),2)) ) )).
fof(t62_ideal_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( r2_hidden(C,k9_ideal_1(A,B)) <=> ? [D] : ( m3_ideal_1(D,A,B) & C = k4_rlvect_1(A,D) ) ) ) ) )).
fof(t62_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t62_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(A,B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => ( k1_funct_1(C,D) = k4_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,D)))) & k1_funct_1(k16_sin_cos,D) != k5_numbers ) ) ) & k9_xtuple_0(k27_sin_cos) = B & B = k9_xtuple_0(C) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,A)) ) => k2_integra5(A,C) = k6_xcmplx_0(k1_funct_1(k27_sin_cos,k2_seq_4(A)),k1_funct_1(k27_sin_cos,k3_seq_4(A))) ) ) ) ) )).
fof(t62_integra8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,k2_rcomp_1(k4_xcmplx_0(1),1)) & k9_xtuple_0(k2_fdiff_1(k1_sin_cos6,k2_rcomp_1(k4_xcmplx_0(1),1))) = k9_xtuple_0(A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,k2_rcomp_1(k4_xcmplx_0(1),1)) & k1_funct_1(A,C) = k7_xcmplx_0(1,k3_square_1(k6_xcmplx_0(1,k1_square_1(C)))) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,A,B)) ) => k2_integra5(B,A) = k6_xcmplx_0(k1_funct_1(k1_sin_cos6,k2_seq_4(B)),k1_funct_1(k1_sin_cos6,k3_seq_4(B))) ) ) ) )).
fof(t62_integra9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,D) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,D) & r1_xxreal_0(E,k5_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] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => k1_funct_1(C,E) = k7_xcmplx_0(A,E) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,B)) ) => k2_integra5(B,C) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_taylor_1(A),k3_taylor_1),k2_seq_4(B)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_taylor_1(A),k3_taylor_1),k3_seq_4(B))) ) ) ) ) ) )).
fof(t62_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m2_interva1(B,A) => ! [C] : ( m2_interva1(C,A) => r2_interva1(A,k16_interva1(A,B,C),k16_interva1(A,C,B)) ) ) ) )).
fof(t62_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(t62_jgraph_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ 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(k5_numbers,k18_euclid(A)) | r1_xxreal_0(k5_numbers,k17_euclid(A)) ) & ( r1_xxreal_0(k5_numbers,k18_euclid(B)) | r1_xxreal_0(k5_numbers,k17_euclid(B)) ) & ( r1_xxreal_0(k5_numbers,k18_euclid(C)) | r1_xxreal_0(k5_numbers,k17_euclid(C)) ) & ~ ( r1_xxreal_0(k18_euclid(D),k5_numbers) & r1_xxreal_0(k17_euclid(D),k5_numbers) ) & ! [F] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(k15_euclid(2))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k15_euclid(2))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k15_euclid(2))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k15_euclid(2))) => ~ ( v3_tops_2(F,k15_euclid(2),k15_euclid(2)) & ! [K] : ( 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(k5_numbers,k18_euclid(G)) & r1_xxreal_0(k5_numbers,k18_euclid(H)) & r1_xxreal_0(k5_numbers,k18_euclid(I)) & ~ r1_xxreal_0(k18_euclid(J),k5_numbers) & r1_jordan6(E,G,H) & r1_jordan6(E,H,I) & r1_jordan6(E,I,J) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t62_jgraph_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(k5_topmetr)) => ! [H] : ( 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(k7_xcmplx_0(2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(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(k4_xcmplx_0(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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t62_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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,k2_jordan9(B,A))) = k6_xcmplx_0(k6_pscomp_1(B),k7_xcmplx_0(k6_xcmplx_0(k8_pscomp_1(B),k6_pscomp_1(B)),k1_newton(2,A))) ) ) )).
fof(t62_jordan1h,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( 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] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(k4_tarski(k1_nat_1(E,1),D),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k7_nat_d(k3_finseq_1(C),1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),k1_nat_1(E,1),D) & r2_hidden(k4_tarski(E,D),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k3_finseq_1(C)) = k3_matrix_0(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,k1_nat_1(D,1)),k2_matrix_0(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) )).
fof(t62_jordan1j,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ~ ( r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),C),k8_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(k1_jordan8(B,k1_nat_1(A,1)))) & r1_xboole_0(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,1),k1_jordan1a(k1_jordan8(B,1)),1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),C)),k9_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) ) ) ) ) )).
fof(t62_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ( ( v2_connsp_1(C,k15_euclid(A)) & v3_pre_topc(C,k15_euclid(A)) & r2_hidden(D,C) & B = a_3_2_jordan2c(A,C,D) ) => r1_tarski(C,B) ) ) ) ) ) )).
fof(t62_jordan6,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ r1_xboole_0(k9_jordan6(A),k6_jordan6(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)),2))) ) )).
fof(t62_kurato_1,axiom,( k6_kurato_1 != k3_subset_1(u1_struct_0(k3_topmetr),k6_kurato_1) )).
fof(t62_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A) ) => k6_lattices(A) = k5_lattices(k1_lattice2(A)) ) )).
fof(t62_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k9_funct_2(k6_glib_000(A),k4_ordinal1))) => ! [C] : ! [D] : ( ( r2_hidden(D,k1_relset_1(k6_glib_000(A),k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k4_ordinal1,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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),B))) | k1_recdef_1(k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k4_ordinal1,k6_glib_000(A),k20_lexbfs(A,B,C)),D) = k1_nat_1(k1_recdef_1(k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k4_ordinal1,k6_glib_000(A),B),D),1) ) ) ) ) )).
fof(t62_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,B) & r2_hidden(C,k1_relset_1(k1_numbers,A)) ) ) => ( ! [B] : ( v1_xreal_0(B) => ~ ( 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) ) ) ) )).
fof(t62_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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) = k5_numbers & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & v1_comseq_2(k2_partfun1(k1_numbers,k1_numbers,C,k2_rcomp_1(A,k2_xcmplx_0(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) = k5_numbers ) ) ) ) ) ) )).
fof(t62_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(A,k2_xcmplx_0(A,D)))) & r1_xxreal_0(k1_funct_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)) ) ) ) ) ) ) )).
fof(t62_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_hilbert1)) => r8_ltlaxio1(C,k3_hilbert1(k2_ltlaxio1(k5_ltlaxio1(A,B)),k5_ltlaxio1(k2_ltlaxio1(A),k2_ltlaxio1(B)))) ) ) ) )).
fof(t62_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t62_mathmorp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t62_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,k1_numbers,A,A) & m2_finseq_1(E,k3_finseq_2(k1_numbers)) ) => ( r2_matrix10(k5_matrix10(A,B,C),k4_matrix10(A,D,E)) => r2_matrix10(k5_matrix10(A,B,E),k4_matrix10(A,D,C)) ) ) ) ) ) ) )).
fof(t62_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ~ r1_xxreal_0(A,k5_numbers) => k12_matrix_3(A,B,k4_matrix_3(B,C,D)) = k8_group_1(B,k12_matrix_3(A,B,C),k12_matrix_3(A,B,D)) ) ) ) ) ) )).
fof(t62_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( ( v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ( r1_tarski(k2_zfmisc_1(C,D),k2_matrix_0(B)) => ( ( k5_card_1(D) = k5_numbers & k5_card_1(C) != k5_numbers ) | k6_matrix13(A,B,C,D) = k4_matrix_0(A,k6_matrix13(A,k4_matrix_0(A,B),D,C)) ) ) ) ) ) ) )).
fof(t62_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( 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_0(B)),k7_matrix15(A,B)) ) ) ) ) )).
fof(t62_matrix16,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( v6_matrix16(C,A) => v6_matrix16(k9_fvsum_1(A,C,B),A) ) ) ) ) )).
fof(t62_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(B)) => k7_matrix_0(A,k16_matrix_0(C,A,B),D) = k2_finseq_3(C,k7_matrix_0(A,B,D)) ) ) ) ) ) )).
fof(t62_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(C) = k3_finseq_1(D) & k1_matrix_0(C) = k1_matrix_0(D) & k1_matrix_0(B) = k3_finseq_1(C) ) => ( r1_xxreal_0(k3_finseq_1(B),k5_numbers) | r1_xxreal_0(k3_finseq_1(C),k5_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)) ) ) ) ) ) ) )).
fof(t62_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => k1_matrix_8(A,B,k1_matrix_4(B,k1_matrix_4(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)) ) ) ) ) ) )).
fof(t62_matrixj1,axiom,( ! [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] : ( ( v1_matrixj1(B,u1_struct_0(A)) & m2_finseq_1(B,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t62_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(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_0(B) ) ) ) )).
fof(t62_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ~ r1_xxreal_0(A,k5_numbers) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(k4_tarski(D,E),k2_matrix_0(k1_matrixr2(A,B,C))) => k3_matrix_0(k1_numbers,k1_matrixr2(A,B,C),D,E) = k1_funct_1(k11_matrixr1(B,k8_matrix_0(k1_numbers,C,E)),D) ) ) ) ) ) ) ) )).
fof(t62_matrprob,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_matrprob(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(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_0(B) ) ) ) ) )).
fof(t62_mcart_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) => ( ! [G] : ( m1_subset_1(G,B) => ! [H] : ( m1_subset_1(H,C) => ! [I] : ( m1_subset_1(I,D) => ! [J] : ( m1_subset_1(J,E) => ( F = k6_xtuple_0(G,H,I,J) => A = I ) ) ) ) ) => A = k6_mcart_1(B,C,D,E,F) ) ) ) ) ) ) )).
fof(t62_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( r1_tarski(A,B) => r1_tarski(k5_measure6(A),k5_measure6(B)) ) ) ) )).
fof(t62_member_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) )).
fof(t62_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( v7_ordinal1(D) => r1_tarski(k6_memstr_0(A,B,C),k9_memstr_0(A,B,C,D)) ) ) ) ) )).
fof(t62_mesfunc5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_numbers,C) & v3_mesfunc5(A) & ! [D] : ( v7_ordinal1(D) => k9_nat_1(k6_numbers,B,D) = k4_xxreal_3(C,k9_nat_1(k6_numbers,A,D)) ) ) => ( k8_supinf_2(k17_supinf_2(B)) = k4_xxreal_3(C,k8_supinf_2(k17_supinf_2(A))) & v3_mesfunc5(B) ) ) ) ) ) )).
fof(t62_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( 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))) ) ) ) ) )).
fof(t62_mmlquery,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(t62_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k30_modelc_1(k25_modelc_2(A)))) ) => ! [C] : ( m1_subset_1(C,k25_modelc_2(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k42_modelc_2(A,B))) => ! [E] : ( 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] : ( v7_ordinal1(F) => ( ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t62_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k25_modelc_2(k43_modelc_2)) => ! [C] : ( m2_orders_1(C,k1_orders_1(k1_modelc_3(A)),k6_partfun1(k1_orders_1(k1_modelc_3(A)))) => r7_modelc_3(A,B,k26_modelc_3(B,A,C)) ) ) ) )).
fof(t62_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => k6_moebius1(k6_moebius1(A)) = k6_moebius1(A) ) )).
fof(t62_monoid_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k10_monoid_0(A))) => ! [C] : ( 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) ) ) ) )).
fof(t62_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ! [B] : ( v1_int_1(B) => ( r1_xxreal_0(k5_numbers,k5_int_1(B,A)) & ~ r1_xxreal_0(A,k5_int_1(B,A)) ) ) ) ) )).
fof(t62_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t62_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => r1_nat_d(k6_nat_d(A,B),k5_nat_d(A,B)) ) ) )).
fof(t62_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t62_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(t62_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r9_orders_1(k2_relat_1(A),B) <=> r8_orders_1(A,B) ) ) )).
fof(t62_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => r1_ordinal1(A,k10_ordinal2(B,k5_ordinal3(A,B))) ) ) )).
fof(t62_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ~ ( r2_hidden(k5_numbers,A) & ! [B] : ( v7_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ~ ( A = k10_ordinal2(k11_ordinal2(B,k12_ordinal2(k4_ordinal1,k5_ordinal5(A,k4_ordinal1))),C) & r2_hidden(k5_numbers,B) & r2_hidden(C,k12_ordinal2(k4_ordinal1,k5_ordinal5(A,k4_ordinal1))) ) ) ) ) ) )).
fof(t62_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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)))) ) ) ) ) )).
fof(t62_partfun1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => r1_partfun1(k5_relat_1(B,A),B) ) )).
fof(t62_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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)) ) ) ) )).
fof(t62_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( ( 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) & k10_pdiff_1(3,2,k26_valued_1(k1_euclid(3),k1_numbers,k1_pdiff_3(2,3,C),A),B) = k3_xcmplx_0(A,k5_pdiff_5(C,B)) ) ) ) ) ) )).
fof(t62_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t62_pepin,axiom,( v1_int_2(k1_nat_1(k2_nat_1(256,256),1)) )).
fof(t62_polyform,axiom,( ! [A] : ( ( 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 ) )).
fof(t62_polynom5,axiom,( r2_cfcont_1(k6_partfun1(k2_numbers),k2_numbers) )).
fof(t62_power,axiom,( k2_power(2,4) = 16 )).
fof(t62_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t62_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => ~ ( ~ r1_xxreal_0(A,1) & ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(k4_prepower(A,B),1) ) ) ) )).
fof(t62_prob_3,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( k3_finseq_1(A) = k5_numbers => k18_rvsum_1(A) = k5_numbers ) ) )).
fof(t62_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,A) & v1_funct_1(E) & v1_partfun1(E,A) ) => ( ( r2_pboole(A,B,D) & r2_pboole(A,C,E) ) => r2_pboole(A,k6_pboole(A,B,C),k6_pboole(A,D,E)) ) ) ) ) ) )).
fof(t62_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ~ ( r3_qc_lang2(A,B,C) & r1_qc_lang2(A,C,B) ) ) ) ) )).
fof(t62_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => k5_qc_lang3(A,k5_qc_lang2(A,B,C)) = k5_qc_lang3(A,C) ) ) ) )).
fof(t62_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => ( k22_quaterni(A,C) = k22_quaterni(B,C) => A = B ) ) ) ) )).
fof(t62_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => k24_quaterni(A) = k6_quaterni(k4_xcmplx_0(k13_quaterni(A)),k4_xcmplx_0(k14_quaterni(A)),k4_xcmplx_0(k15_quaterni(A)),k4_xcmplx_0(k16_quaterni(A))) ) )).
fof(t62_quofield,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( 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) ) ) ) ) ) ) )).
fof(t62_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B))))) => ! [E] : ( m1_rcomp_3(E,A,B,D) => ! [F] : ( 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(k2_seq_4(k7_partfun1(k9_setfam_1(k1_numbers),E,C)),k1_funct_1(F,k1_nat_1(C,1))) ) ) ) ) ) ) ) )).
fof(t62_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( r1_tarski(k9_xtuple_0(B),A) => k5_relat_1(B,A) = B ) ) )).
fof(t62_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) => ! [E] : ( 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)) ) ) ) ) )).
fof(t62_rewrite2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k8_afinsq_1(A),k8_afinsq_1(A)))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t62_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_afinsq_1(C))) => ! [F] : ( ( ~ 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] : ( 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)) ) ) ) ) ) ) ) )).
fof(t62_rfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => v1_partfun1(k7_rfunct_1(A,B),B) ) )).
fof(t62_rfunct_3,axiom,( ! [A] : ( v1_xreal_0(A) => 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) ) )).
fof(t62_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_seq_2(A) => r2_funct_2(k4_ordinal1,k1_numbers,k4_rinfsup1(A),k32_valued_1(k4_ordinal1,k1_numbers,k3_rinfsup1(k32_valued_1(k4_ordinal1,k1_numbers,A)))) ) ) )).
fof(t62_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ( v2_convex1(B,A) <=> ( k3_rlaffin1(A,B) = 1 & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k5_numbers,k3_funct_2(u1_struct_0(A),k1_numbers,B,C)) ) ) ) ) ) )).
fof(t62_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_rlsub_1(D,A) => ( r2_hidden(k5_algstr_0(A,C,B),k3_rlsub_1(A,C,D)) <=> r1_struct_0(D,B) ) ) ) ) ) )).
fof(t62_rlsub_2,axiom,( ! [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) ) => ! [B] : ( ( v1_rlvect_1(B) & m1_rlsub_1(B,A) ) => ( ! [C] : ( 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)) ) ) ) )).
fof(t62_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t62_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k4_rlvect_1(A,k3_finseq_4(u1_struct_0(A),C,B,D)) = k1_algstr_0(A,k1_algstr_0(A,k4_rlvect_1(A,k12_finseq_1(u1_struct_0(A),C)),k4_rlvect_1(A,k12_finseq_1(u1_struct_0(A),B))),k4_rlvect_1(A,k12_finseq_1(u1_struct_0(A),D))) ) ) ) ) )).
fof(t62_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( 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) ) ) ) )).
fof(t62_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_rmod_2(E,A,B) => ~ ( k3_rmod_2(A,B,D,E) = k3_rmod_2(A,B,C,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ~ ( r1_struct_0(E,F) & k5_algstr_0(B,D,F) = C ) ) ) ) ) ) ) ) )).
fof(t62_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t62_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_bhsp_1(B) & m1_rusub_1(B,A) ) => ! [C] : ( ( v1_bhsp_1(C) & m1_rusub_1(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k3_rusub_1(A,D,B) = k3_rusub_1(A,D,C) <=> B = C ) ) ) ) ) )).
fof(t62_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m2_rusub_1(D,A,B) & r2_hidden(C,D) ) ) ) ) )).
fof(t62_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k14_rvsum_1(k9_finseq_1(A),k9_finseq_1(B)) = k9_finseq_1(k3_xcmplx_0(A,B)) ) ) )).
fof(t62_scm_halt,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( 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),k5_numbers) & ! [E] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(E,u1_struct_0(k1_scmfsa_2)) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ! [G] : ( v7_ordinal1(G) => ~ ( r8_pboole(u1_struct_0(k1_scmfsa_2),E,k1_scmfsa_m(B)) & r8_pboole(k4_ordinal1,F,k1_funct_4(A,k1_scmfsa8c(k1_scmfsa8b(D,k1_scmfsa8a(2),k5_scmfsa6a(C,k8_scmfsa_2(D,k4_scmfsa_2(k5_numbers))))))) & G = k1_nat_1(k8_extpro_1(k7_card_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(k5_numbers))))),k1_scmfsa_m(B)),1) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,E,G),D) = k6_xcmplx_0(k1_funct_1(B,D),1) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,E,G),k4_scmfsa_2(k5_numbers)) = 1 & ! [H] : ( ( 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(k7_card_1(3),k1_scmfsa_2,F,E,G),H) = k1_funct_1(k1_scmfsa6b(C,B,A),H) ) ) & ! [H] : ( m1_scmfsa_2(H) => k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,E,G),H) = k18_scmfsa_2(k1_scmfsa6b(C,B,A),H) ) & k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,E,G)) = k5_numbers & ! [H] : ( v7_ordinal1(H) => ( r1_xxreal_0(H,G) => r2_hidden(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_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(k5_numbers))))))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t62_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) & v7_amistd_1(C,k7_card_1(3),k1_scmfsa_2) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k5_scmfsa6a(C,k8_scmfsa_2(D,k4_scmfsa_2(k5_numbers)))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_m(B)),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k5_scmfsa6a(C,k8_scmfsa_2(D,k4_scmfsa_2(k5_numbers)))),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_m(B)))),D) = k6_xcmplx_0(k1_funct_1(B,D),1) ) ) ) ) ) )).
fof(t62_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ( k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k11_scmfsa_2(A),B),k4_struct_0(k1_scmfsa_2)) = A & ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k11_scmfsa_2(A),B),C) = k1_funct_1(B,C) ) & ! [C] : ( m1_scmfsa_2(C) => r2_relset_1(k4_ordinal1,k4_numbers,k18_scmfsa_2(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k11_scmfsa_2(A),B),C),k18_scmfsa_2(B,C)) ) ) ) ) )).
fof(t62_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( 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) ) ) ) )).
fof(t62_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v2_compos_1(D,k1_scmpds_2) & v3_scmpds_4(D) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( ( r1_xxreal_0(k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,E),F)),k5_numbers) & r1_scmpds_6(D,B,A) & r2_scmpds_6(D,B,A) ) => k6_scmpds_4(k3_scmpds_6(E,F,C,D),B,A) = k1_funct_4(k6_scmpds_4(D,B,A),k7_memstr_0(2,k1_scmpds_2,k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),2))) ) ) ) ) ) ) ) )).
fof(t62_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ! [C] : ( ( 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))) ) ) ) ) )).
fof(t62_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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 ) ) ) ) ) ) ) )).
fof(t62_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => ( k13_seq_4(A,B,C) = k15_seq_4(A) => ( B = k16_seq_4(A,C) & C = k16_seq_4(A,B) ) ) ) ) ) )).
fof(t62_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v2_prob_1(B) => k3_kurato_0(A,B) = k3_prob_1(A,B) ) ) )).
fof(t62_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) ) ) )).
fof(t62_sf_mastr,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ( ~ r2_hidden(A,k3_sf_mastr(B)) => r2_relset_1(k4_ordinal1,k4_numbers,k18_scmfsa_2(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,B,C),A),k18_scmfsa_2(C,A)) ) ) ) ) )).
fof(t62_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t62_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => k11_simplex0(A,B,C,1) = k10_simplex0(A,B,C) ) ) )).
fof(t62_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_fdiff_1(k18_sin_cos,A) & k1_fdiff_1(k18_sin_cos,A) = k4_xcmplx_0(k1_funct_1(k16_sin_cos,A)) ) ) )).
fof(t62_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k2_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,k3_xcmplx_0(2,A)),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,k3_xcmplx_0(2,B))) = k3_xcmplx_0(k3_xcmplx_0(2,k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,k2_xcmplx_0(A,B))),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,k6_xcmplx_0(A,B))) & k6_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,k3_xcmplx_0(2,A)),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,k3_xcmplx_0(2,B))) = k3_xcmplx_0(k3_xcmplx_0(2,k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,k2_xcmplx_0(A,B))),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,k6_xcmplx_0(A,B))) ) ) ) )).
fof(t62_sin_cos6,axiom,( k2_relset_1(k1_numbers,k1_sin_cos6) = k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2)) )).
fof(t62_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k3_power(k4_power,A) = k1_sin_cos7(k7_xcmplx_0(k6_xcmplx_0(k1_square_1(A),1),k3_xcmplx_0(2,A))) ) ) )).
fof(t62_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) & k4_sin_cos9(A) = k7_xcmplx_0(k28_sin_cos,4) ) => A = 1 ) ) )).
fof(t62_sincos10,axiom,( k3_relat_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k4_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos)),k2_sincos10) = k1_partfun2(k1_numbers,k4_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos)) )).
fof(t62_sprect_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t62_sprect_2,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( 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))) ) ) ) ) ) ) )).
fof(t62_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t62_stirl2_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k4_ordinal1)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ( v2_stirl2_1(C,B,A) => k3_nat_1(k2_relset_1(A,C)) = k1_funct_1(C,k3_nat_1(k1_relset_1(B,C))) ) ) ) ) )).
fof(t62_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_valuat_1(E,A,D) => ( ( ! [F] : ( m2_funct_2(F,k3_qc_lang1(A),D,k2_valuat_1(A,D)) => ! [G] : ( 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] : ( m2_funct_2(F,k3_qc_lang1(A),D,k2_valuat_1(A,D)) => ! [G] : ( 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] : ( m2_funct_2(F,k3_qc_lang1(A),D,k2_valuat_1(A,D)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t62_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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 ) ) ) ) )).
fof(t62_tex_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) )).
fof(t62_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( v3_tops_1(B,A) & ! [C] : ( ( ~ v2_struct_0(C) & v1_pre_topc(C) & v4_tex_3(C,A) & m1_pre_topc(C,A) ) => B != u1_struct_0(C) ) ) ) ) )).
fof(t62_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) )).
fof(t62_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) )).
fof(t62_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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) ) ) ) )).
fof(t62_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)))) ) ) ) ) )).
fof(t62_topreal6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ( v5_tbsp_1(A) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => v6_tbsp_1(B,A) ) ) ) )).
fof(t62_toprealc,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_xreal_0(B) & ~ v3_xxreal_0(B) ) => ! [C] : ( ( 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))))) ) ) ) ) )).
fof(t62_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) )).
fof(t62_tops_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) ) ) ) )).
fof(t62_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t62_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t62_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => r1_tarski(k2_trees_1(1),k12_trees_3(A)) ) )).
fof(t62_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_connsp_1(A,B,C) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & ? [E] : ( 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)) ) ) ) ) ) ) )).
fof(t62_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( v1_valued_2(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_valued_0(E) ) => ( r2_hidden(A,k9_xtuple_0(k57_valued_2(C,D,E))) => k1_funct_1(k57_valued_2(C,D,E),A) = k13_valued_1(k1_funct_1(D,A),k1_funct_1(E,A)) ) ) ) ) )).
fof(t62_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_vectsp_4(E,A,B) => ( r2_hidden(C,k3_vectsp_4(A,B,D,E)) <=> ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r1_struct_0(E,F) & C = k5_algstr_0(B,D,F) ) ) ) ) ) ) ) )).
fof(t62_vectsp_5,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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))) ) ) ) )).
fof(t62_waybel23,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => r2_relset_1(u1_struct_0(k1_yellow_1(k7_waybel_0(B))),u1_struct_0(A),k3_waybel23(A,B),k1_partfun1(u1_struct_0(k1_yellow_1(k7_waybel_0(B))),u1_struct_0(k1_yellow_1(k7_waybel_0(A))),u1_struct_0(k1_yellow_1(k7_waybel_0(A))),u1_struct_0(A),k4_waybel23(A,B),k2_yellow_2(A))) ) ) )).
fof(t62_waybel34,axiom,( ! [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] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) )).
fof(t62_waybel_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(B,k4_waybel_0(A,k12_waybel_0(A,B))) & ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t62_waybel_1,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v5_waybel_1(k4_waybel_1(A,B),A,A) ) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_waybel_1(A,a_3_2_waybel_1(A,B,C)) ) ) ) ) )).
fof(t62_xboole_1,axiom,( ! [A] : ~ r2_xboole_0(A,k1_xboole_0) )).
fof(t62_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( 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))) ) ) ) )).
fof(t62_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k2_xcmplx_0(k7_xcmplx_0(A,C),k7_xcmplx_0(B,C)) = k7_xcmplx_0(k2_xcmplx_0(A,B),C) ) ) ) )).
fof(t62_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(B)) & r1_xxreal_0(k2_xcmplx_0(A,B),k5_numbers) ) ) ) )).
fof(t62_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(C,D) & r1_tarski(k1_xxreal_1(C,D),k4_xxreal_1(A,B)) ) => ( ~ r1_xxreal_0(C,A) & ~ r1_xxreal_0(B,D) ) ) ) ) ) ) )).
fof(t62_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v1_xxreal_0(B) => ( ? [C] : ( v1_xxreal_0(C) & r2_hidden(C,A) & r1_xxreal_0(C,B) ) => r1_xxreal_0(k2_xxreal_2(A),B) ) ) ) )).
fof(t62_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t62_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t62_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_yellow_0(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t62_yellow_4,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t62_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => k7_waybel_1(A,k3_yellow_0(A)) = k4_yellow_0(A) ) )).
fof(t62_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ~ ( r3_zf_lang(B,A) & r1_xxreal_0(k3_finseq_1(A),k3_finseq_1(B)) ) ) ) )).
fof(t62_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => k2_zf_model(k8_zf_lang(B,A)) = k7_subset_1(k1_zf_lang,k2_zf_model(A),k1_tarski(B)) ) ) )).
fof(t62_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( k4_xboole_0(k2_tarski(A,B),C) = k2_tarski(A,B) <=> ( ~ r2_hidden(A,C) & ~ r2_hidden(B,C) ) ) )).
fof(t62_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_zmodul01(C,A) => ( r2_hidden(k4_struct_0(A),k5_zmodul01(A,B,C)) <=> k5_zmodul01(A,B,C) = u1_struct_0(C) ) ) ) ) )).
fof(t62_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v6_zmodul01(A) => ( ( v1_zmodul02(k7_domain_1(u1_struct_0(A),B,C),A) => ( B = C | ( C != k4_struct_0(A) & ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => ~ ( E != k5_numbers & k1_zmodul01(A,B,E) = k1_zmodul01(A,C,D) ) ) ) ) ) ) & ( ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => ~ ( E != k5_numbers & k1_zmodul01(A,B,E) = k1_zmodul01(A,C,D) ) ) ) => ( C = k4_struct_0(A) | ( B != C & v1_zmodul02(k7_domain_1(u1_struct_0(A),B,C),A) ) ) ) ) ) ) ) ) )).
fof(t63_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l3_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r6_abcmiz_0(A,B,k1_subset_1(u1_abcmiz_0(A))) ) ) )).
fof(t63_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) )).
fof(t63_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t63_afinsq_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ( k1_funct_1(B,k5_numbers) = k5_numbers => ( r1_xxreal_0(k1_afinsq_1(B),k5_numbers) | k12_afinsq_1(A,B) = k1_xboole_0 ) ) ) ) )).
fof(t63_algspec1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v11_struct_0(B) & v1_instalg1(B) & l1_msualg_1(B) ) => ! [C] : ( ( v4_msualg_1(C,A) & v1_msafree1(C,A) & l3_msualg_1(C,A) ) => ( m4_algspec1(C,B) => m2_algspec1(A,B) ) ) ) ) )).
fof(t63_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( F != G & ~ ( ~ ( r4_analmetr(A,F,G,B,C) & r4_analmetr(A,F,G,D,E) ) & ~ ( r4_analmetr(A,F,G,B,C) & r4_analmetr(A,D,E,F,G) ) & ~ ( r4_analmetr(A,B,C,F,G) & r4_analmetr(A,D,E,F,G) ) & ~ ( r4_analmetr(A,B,C,F,G) & r4_analmetr(A,F,G,D,E) ) ) & ~ r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) ) )).
fof(t63_aofa_000,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_freealg(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_freealg(k19_aofa_000,A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_freealg(k19_aofa_000,A))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t63_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v19_aofa_a00(E,A) & m1_subset_1(E,u1_struct_0(A)) ) => ! [F] : ( v1_int_1(F) => ! [G] : ( v1_int_1(G) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,D),E)) => ! [I] : ( m1_subset_1(I,k1_funct_1(u3_msualg_1(A,D),E)) => ( ( H = F & I = G ) => k34_aofa_a00(A,D,E,H,I) = k6_xcmplx_0(F,G) ) ) ) ) ) ) ) ) ) ) )).
fof(t63_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ( k9_arytm_3(A,B) = k11_arytm_3 => A = k11_arytm_3 ) ) ) )).
fof(t63_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( r2_hidden(A,k6_asympt_0(B)) & r2_hidden(B,k6_asympt_0(A)) ) <=> k6_asympt_0(A) = k6_asympt_0(B) ) ) ) )).
fof(t63_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t63_bhsp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => r2_funct_2(k4_ordinal1,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))) ) ) ) ) )).
fof(t63_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t63_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t63_borsuk_6,axiom,( ! [A] : ( r2_hidden(k4_tarski(A,1),k8_borsuk_6) => A = 1 ) )).
fof(t63_borsuk_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v1_xreal_0(B) & ~ v3_xxreal_0(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t63_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t63_bvfunc14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ( ( v1_relat_1(I) & v1_funct_1(I) ) => ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ! [Q] : ( 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) ) ) )).
fof(t63_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))) ) ) ) ) )).
fof(t63_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k7_xboolean(A,B) = k7_xboolean(k3_xboolean(A),k3_xboolean(B)) ) ) )).
fof(t63_calcul_1,axiom,( ! [A] : ( 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)) ) ) )).
fof(t63_card_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v3_card_1(B,1) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : ( m1_subset_1(C,A) & B = k1_tarski(C) ) ) ) )).
fof(t63_card_2,axiom,( ! [A] : ! [B] : ( ( k1_card_1(A) = k5_numbers & k1_card_1(B) = k5_numbers ) => A = B ) )).
fof(t63_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r1_partfun1(B,C) & r2_hidden(B,k8_card_3(A)) & r2_hidden(C,k8_card_3(A)) ) => r2_hidden(k2_xboole_0(B,C),k8_card_3(A)) ) ) ) ) )).
fof(t63_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( 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)) ) ) ) ) )).
fof(t63_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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) ) ) ) )).
fof(t63_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => v4_cat_4(A) ) )).
fof(t63_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( 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) = k2_xcmplx_0(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) = k6_xcmplx_0(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) = k3_xcmplx_0(k7_partfun1(k2_numbers,C,B),k7_partfun1(k2_numbers,D,B)) ) ) ) ) ) ) )).
fof(t63_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_chain_1(C,B) => ( ~ r1_xxreal_0(A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k4_chain_1(B,C,A))) => m3_chain_1(D,B,C,A) ) ) ) ) ) )).
fof(t63_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_chord(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => v3_chord(B,A) ) ) )).
fof(t63_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t63_classes1,axiom,( ! [A] : k6_classes1(k9_setfam_1(A)) = k1_ordinal1(k6_classes1(A)) )).
fof(t63_classes2,axiom,( v2_classes1(k4_classes1(k4_ordinal1)) )).
fof(t63_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_clvect_1(B,A) => k5_clvect_1(A,k4_struct_0(A),B) = u1_struct_0(B) ) ) )).
fof(t63_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v2_clvect_2(C,A) => v2_clvect_2(k5_bhsp_1(A,C,B),A) ) ) ) ) )).
fof(t63_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t63_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(B,C)),k2_xcmplx_0(k9_complex1(k6_xcmplx_0(B,A)),k9_complex1(k6_xcmplx_0(A,C)))) ) ) ) )).
fof(t63_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( A != k5_numbers & B != k5_numbers & k3_complex2(A,B) != k3_complex2(k2_complex2(A,C),k2_complex2(B,C)) ) ) ) ) )).
fof(t63_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => r1_xxreal_0(k9_complex1(k5_algstr_0(k1_complfld,A,B)),k2_xcmplx_0(k9_complex1(A),k9_complex1(B))) ) ) )).
fof(t63_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( m2_finseq_1(C,k2_numbers) => ! [D] : ( m2_finseq_1(D,k2_numbers) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k3_finseq_1(B) = k3_finseq_1(C) & k3_finseq_1(C) = k3_finseq_1(D) ) => k8_complsp2(k8_seq_4(A,B),k8_seq_4(C,D)) = k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k8_complsp2(A,C),k8_complsp2(A,D)),k8_complsp2(B,C)),k8_complsp2(B,D)) ) ) ) ) ) )).
fof(t63_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k3_finseq_2(k4_ordinal1)) & v1_funct_1(C) & v4_valued_0(C) & v2_margrel1(C) ) => ( ( k1_nat_1(k19_margrel1(B),2) = k19_margrel1(C) & r1_xxreal_0(1,A) & r1_xxreal_0(A,k1_nat_1(k19_margrel1(B),1)) ) => r1_comput_1(k7_comput_1(B,C,A),B,C,A) ) ) ) ) )).
fof(t63_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v2_comseq_3(A) => v1_comseq_3(A) ) ) )).
fof(t63_convex4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( v2_convex4(B,A) => ( ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ~ ( C = E & D = F & r1_xxreal_0(k5_numbers,E) & r1_xxreal_0(k5_numbers,F) ) ) ) | k7_rusub_4(A,k19_convex4(A,B,C),k19_convex4(A,B,D)) = k19_convex4(A,B,k2_xcmplx_0(C,D)) ) ) ) ) ) ) )).
fof(t63_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t63_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t63_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t63_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => 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),k18_sin_cos),A),B) = k6_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,2),k3_xcmplx_0(k17_sin_cos(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(6,B),k3_xcmplx_0(3,A)),2)),k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(3,A),2)))),k3_xcmplx_0(k7_xcmplx_0(1,2),k3_xcmplx_0(k17_sin_cos(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(2,B),A),2)),k17_sin_cos(k7_xcmplx_0(A,2))))) ) ) )).
fof(t63_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k7_xcmplx_0(1,k17_sin_cos(D)) ) => ( k17_sin_cos(B) = k5_numbers | k17_sin_cos(k6_xcmplx_0(B,A)) = k5_numbers | k1_funct_1(k4_diff_1(C,A),B) = k7_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(2),k6_xcmplx_0(k17_sin_cos(k6_xcmplx_0(B,A)),k17_sin_cos(B))),k6_xcmplx_0(k19_sin_cos(k6_xcmplx_0(k3_xcmplx_0(2,B),A)),k19_sin_cos(A))) ) ) ) ) ) )).
fof(t63_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(k2_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k27_sin_cos)) & r2_hidden(k6_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k27_sin_cos)) ) => k1_funct_1(k5_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k27_sin_cos),k18_sin_cos),A),B) = k6_xcmplx_0(k3_xcmplx_0(k1_newton(k1_funct_1(k18_sin_cos,k2_xcmplx_0(B,k7_xcmplx_0(A,2))),3),k1_newton(k5_xcmplx_0(k1_funct_1(k16_sin_cos,k2_xcmplx_0(B,k7_xcmplx_0(A,2)))),2)),k3_xcmplx_0(k1_newton(k1_funct_1(k18_sin_cos,k6_xcmplx_0(B,k7_xcmplx_0(A,2))),3),k1_newton(k5_xcmplx_0(k1_funct_1(k16_sin_cos,k6_xcmplx_0(B,k7_xcmplx_0(A,2)))),2))) ) ) ) )).
fof(t63_ec_pf_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_ec_pf_2(A,5) ) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(k9_int_3(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_int_3(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_int_3(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k9_int_3(A))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k9_int_3(A))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k9_int_3(A))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k9_int_3(A))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k9_int_3(A))) => ! [K] : ( 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] : ( 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 = k5_int_1(2,A) & D = k5_int_1(3,A) & E = k5_int_1(4,A) & F = k5_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)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t63_entropy1,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v6_matrprob(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => k8_entropy1(A) = k6_rvsum_1(k3_matrprob(k5_entropy1(A))) ) )).
fof(t63_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_enumset1(A,B,C,D) = k2_enumset1(A,C,D,B) )).
fof(t63_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( D = k3_tarski(C) => k3_subset_1(A,D) = k3_tarski(k3_subset_1(B,C)) ) ) ) ) ) )).
fof(t63_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => k22_rvsum_1(k6_euclid(3,A),B) = k4_xcmplx_0(k22_rvsum_1(A,B)) ) ) )).
fof(t63_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ~ ( r1_xboole_0(B,C) & ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ~ ( r2_hidden(D,B) & ~ r2_hidden(D,C) ) ) ) ) ) ) )).
fof(t63_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v5_relat_1(C,u1_struct_0(B)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_exchsort(C) ) => ! [D] : ( m1_subset_1(D,k9_xtuple_0(C)) => ! [E] : ( m1_subset_1(E,k9_xtuple_0(C)) => ! [F] : ( m1_subset_1(F,k9_xtuple_0(C)) => ! [G] : ( 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)),D,E) => ( F = D | G = E | k1_binop_1(k7_exchsort(B,C,D,E),F,G) = k4_tarski(k1_funct_1(A,F),k1_funct_1(A,G)) ) ) ) ) ) ) ) ) ) )).
fof(t63_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ( m1_subset_1(E,k4_card_3(u3_msualg_1(k8_facirc_1(A,B,C,D),k10_facirc_1(A,B,C,D)))) => ( C != k4_tarski(k10_finseq_1(A,B),D) => v1_circuit2(k5_facirc_1(k8_facirc_1(A,B,C,D),k10_facirc_1(A,B,C,D),E,2),k8_facirc_1(A,B,C,D),k10_facirc_1(A,B,C,D)) ) ) ) )).
fof(t63_fdiff_11,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A)),B),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A)),B)) ) ) ) ) => ( r2_hidden(k5_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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k6_xcmplx_0(k1_funct_1(k1_sin_cos9,k7_xcmplx_0(1,B)),k7_xcmplx_0(B,k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) ) )).
fof(t63_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => k2_xboole_0(k5_relat_1(k2_fib_num2,k3_xboole_0(k4_fib_num2,k2_finseq_1(k1_nat_1(k3_xcmplx_0(2,A),3)))),k1_tarski(k1_domain_1(k4_ordinal1,k4_ordinal1,k1_nat_1(k3_xcmplx_0(2,A),5),k3_funct_2(k4_ordinal1,k4_ordinal1,k2_fib_num2,k1_nat_1(k3_xcmplx_0(2,A),5))))) = k5_relat_1(k2_fib_num2,k3_xboole_0(k4_fib_num2,k2_finseq_1(k1_nat_1(k3_xcmplx_0(2,A),5)))) ) )).
fof(t63_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)))) ) ) )).
fof(t63_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t63_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t63_finseq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t63_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : k10_xtuple_0(k1_finseq_3(A,B)) = k6_subset_1(k10_xtuple_0(A),B) ) )).
fof(t63_finseq_4,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ! [C] : ( ( 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 ) ) ) ) )).
fof(t63_finseq_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : k3_finseq_5(k7_finseq_1(A,k9_finseq_1(B))) = k7_finseq_1(k9_finseq_1(B),k3_finseq_5(A)) ) )).
fof(t63_finseq_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t63_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t63_flang_1,axiom,( ! [A] : ! [B] : ( 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) ) )).
fof(t63_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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) ) ) ) ) )).
fof(t63_flang_3,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ~ ( r2_hidden(B,C) & B != k2_flang_1(A) & k2_flang_3(A,C) = k4_flang_1(A,k2_flang_1(A)) ) ) )).
fof(t63_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_cohsp_1(B) & r1_setfam_1(A,B) ) => v1_cohsp_1(k2_xboole_0(A,B)) ) )).
fof(t63_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( ( ~ v2_struct_0(D) & l2_fsm_1(D,A,B) ) => ( r7_fsm_1(A,B,C,D) => r4_fsm_1(A,B,C,D) ) ) ) ) ) )).
fof(t63_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( 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)) ) ) ) ) ) ) )).
fof(t63_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t63_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ~ ( r2_hidden(E,k7_relset_1(A,B,D,C)) & ! [F] : ~ ( r2_hidden(F,A) & r2_hidden(F,C) & E = k1_funct_1(D,F) ) ) ) )).
fof(t63_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,A,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t63_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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 ) )).
fof(t63_funct_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( ( 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))) ) => k2_binop_1(A,B,C,F,D,E) = k3_funct_2(A,C,k10_funct_5(B,A,C,k9_funct_2(A,C),k12_funct_5(A,B,C,F),E),D) ) ) ) ) ) ) )).
fof(t63_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_funct_7(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(k6_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))) ) ) ) ) )).
fof(t63_funct_8,axiom,( ! [A] : ( v1_xreal_0(A) => k1_funct_1(k2_euclid,k4_xcmplx_0(A)) = k1_funct_1(k2_euclid,A) ) )).
fof(t63_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ~ ( v3_fvaluat1(A) & r2_hidden(k5_struct_0(A),k8_fvaluat1(A,B)) ) ) ) )).
fof(t63_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v5_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [D] : ( 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) ) ) ) ) )).
fof(t63_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : 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))) )).
fof(t63_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t63_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( r1_glib_000(A,k4_glib_001(A,B),D,C) => ( k1_funct_1(k10_glib_001(A,B,C),k1_nat_1(k3_finseq_1(B),1)) = C & k1_funct_1(k10_glib_001(A,B,C),k1_nat_1(k3_finseq_1(B),2)) = D & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k1_relset_1(k4_ordinal1,B)) => k1_funct_1(k10_glib_001(A,B,C),E) = k1_funct_1(B,E) ) ) ) ) ) ) )).
fof(t63_goboard7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t63_graph_2,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(C,B) => r3_graph_2(A,B,C) ) ) ) ) )).
fof(t63_graph_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v2_graph_1(D) & v6_graph_1(D) & l1_graph_1(D) ) => ! [E] : ( ( v7_graph_1(E,D) & m2_graph_1(E,D) ) => ! [F] : ( ( v7_graph_1(F,D) & m2_graph_1(F,D) ) => ! [G] : ( ( v7_graph_1(G,D) & m2_graph_1(G,D) ) => ! [H] : ( m1_subset_1(H,u1_struct_0(D)) => ! [I] : ( m1_subset_1(I,u1_struct_0(D)) => ! [J] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t63_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t63_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => k6_group_2(B) = k6_group_2(A) ) ) )).
fof(t63_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( 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))) ) ) ) ) )).
fof(t63_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t63_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( 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))) ) ) ) )).
fof(t63_group_6,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t63_group_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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,k12_finseq_1(A,C)) = k3_funct_2(A,k1_funct_2(B,B),D,C) ) ) ) )).
fof(t63_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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))) ) ) ) ) )).
fof(t63_hfdiff_1,axiom,( ! [A] : ( ( 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,k22_sin_cos,k18_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,k22_sin_cos,k32_valued_1(k1_numbers,k1_numbers,k16_sin_cos)),A),2)) ) )).
fof(t63_ideal_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) ) )).
fof(t63_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(B,A) => r1_xxreal_0(k2_int_1(B),A) ) ) ) )).
fof(t63_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(A,B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(C,D) = k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(k16_sin_cos,D),k1_square_1(k1_funct_1(k18_sin_cos,D))),k1_square_1(k1_funct_1(k18_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) = k6_xcmplx_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fdiff_9,k1_partfun2(k1_numbers,B)),k2_seq_4(A)),k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fdiff_9,k1_partfun2(k1_numbers,B)),k3_seq_4(A))) ) ) ) ) )).
fof(t63_integra8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,k2_rcomp_1(k4_xcmplx_0(1),1)) & k9_xtuple_0(k2_fdiff_1(k3_sin_cos6,k2_rcomp_1(k4_xcmplx_0(1),1))) = k9_xtuple_0(A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,k2_rcomp_1(k4_xcmplx_0(1),1)) & k1_funct_1(A,C) = k4_xcmplx_0(k7_xcmplx_0(1,k3_square_1(k6_xcmplx_0(1,k1_square_1(C))))) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,A,B)) ) => k2_integra5(B,A) = k6_xcmplx_0(k1_funct_1(k3_sin_cos6,k2_seq_4(B)),k1_funct_1(k3_sin_cos6,k3_seq_4(B))) ) ) ) )).
fof(t63_integra9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k4_xcmplx_0(k7_xcmplx_0(1,D)) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => ( r2_hidden(k5_numbers,C) | k2_integra5(A,B) = k6_xcmplx_0(k1_funct_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),k2_seq_4(A)),k1_funct_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),k3_seq_4(A))) ) ) ) ) ) )).
fof(t63_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m2_interva1(B,A) => ! [C] : ( m2_interva1(C,A) => r2_interva1(A,k17_interva1(A,B,C),k17_interva1(A,C,B)) ) ) ) )).
fof(t63_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) ) )).
fof(t63_jgraph_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ 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(k5_numbers,k18_euclid(A)) | r1_xxreal_0(k5_numbers,k17_euclid(A)) ) & ( r1_xxreal_0(k5_numbers,k18_euclid(B)) | r1_xxreal_0(k5_numbers,k17_euclid(B)) ) & ( r1_xxreal_0(k5_numbers,k18_euclid(C)) | r1_xxreal_0(k5_numbers,k17_euclid(C)) ) & ~ ( r1_xxreal_0(k18_euclid(D),k5_numbers) & r1_xxreal_0(k17_euclid(D),k5_numbers) ) & ! [F] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(k15_euclid(2))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k15_euclid(2))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k15_euclid(2))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k15_euclid(2))) => ~ ( v3_tops_2(F,k15_euclid(2),k15_euclid(2)) & ! [K] : ( 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(k5_numbers,k17_euclid(G)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(G)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(H)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(H)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(I)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(I)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(J)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(J)) & r1_jordan6(E,G,H) & r1_jordan6(E,H,I) & r1_jordan6(E,I,J) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t63_jgraph_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(k5_topmetr)) => ! [H] : ( 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(k7_xcmplx_0(2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(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(k4_xcmplx_0(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(k4_xcmplx_0(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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t63_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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,k2_jordan9(B,A))) = k6_xcmplx_0(k9_pscomp_1(B),k7_xcmplx_0(k6_xcmplx_0(k7_pscomp_1(B),k9_pscomp_1(B)),k1_newton(2,A))) ) ) )).
fof(t63_jordan1h,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( 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] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(k4_tarski(D,k1_nat_1(E,1)),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k7_nat_d(k3_finseq_1(C),1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(A,B),D,k1_nat_1(E,1)) & r2_hidden(k4_tarski(D,E),k2_matrix_0(k1_jordan8(A,B))) & k7_partfun1(u1_struct_0(k15_euclid(2)),C,k3_finseq_1(C)) = k3_matrix_0(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_0(k1_jordan8(A,B))) ) ) ) ) ) ) ) ) ) )).
fof(t63_jordan1j,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(C,D) & r1_xxreal_0(D,k1_matrix_0(k1_jordan8(B,k1_nat_1(A,1)))) & k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),D)),k8_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),D)) & k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),D)),k9_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),C)) & r1_xboole_0(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),D)),k9_jordan6(B)) ) ) ) ) ) )).
fof(t63_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ~ ( v2_connsp_1(B,k15_euclid(A)) & v3_pre_topc(B,k15_euclid(A)) & r2_hidden(C,B) & r2_hidden(D,B) & C != D & ! [E] : ( ( 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)) & r1_tarski(k2_relset_1(u1_struct_0(k15_euclid(A)),E),B) & k1_funct_1(E,k5_numbers) = C & k1_funct_1(E,1) = D ) ) ) ) ) ) ) )).
fof(t63_jordan6,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ r1_xboole_0(k8_jordan6(A),k6_jordan6(k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)),2))) ) )).
fof(t63_kurato_1,axiom,( 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)) )).
fof(t63_lattice2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t63_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k2_zfmisc_1(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k9_funct_2(k6_glib_000(A),k4_ordinal1))) => ! [C] : ( k1_relset_1(k6_glib_000(A),k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k4_ordinal1,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),k4_ordinal1),k4_ordinal1,k6_glib_000(A),k20_lexbfs(A,B,C))) = k6_glib_000(A) ) ) ) )).
fof(t63_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,B) & r2_hidden(C,k1_relset_1(k1_numbers,A)) ) ) => ( ! [B] : ( v1_xreal_0(B) => ~ ( 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) ) ) ) )).
fof(t63_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_limfunc2(C,A) & r1_limfunc2(D,A) & k1_limfunc2(C,A) = k1_limfunc2(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,E) & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,E) & ~ r1_xxreal_0(A,F) & r2_hidden(F,k1_relset_1(k1_numbers,B)) ) ) ) ) ) => ( ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(k6_xcmplx_0(A,E),A))) => ( r1_xxreal_0(k1_funct_1(C,F),k1_funct_1(B,F)) & r1_xxreal_0(k1_funct_1(B,F),k1_funct_1(D,F)) ) ) ) & ( ( r1_tarski(k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,C),k2_rcomp_1(k6_xcmplx_0(A,E),A)),k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,D),k2_rcomp_1(k6_xcmplx_0(A,E),A))) & r1_tarski(k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(k6_xcmplx_0(A,E),A)),k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,C),k2_rcomp_1(k6_xcmplx_0(A,E),A))) ) | ( r1_tarski(k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,D),k2_rcomp_1(k6_xcmplx_0(A,E),A)),k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,C),k2_rcomp_1(k6_xcmplx_0(A,E),A))) & r1_tarski(k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(k6_xcmplx_0(A,E),A)),k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,D),k2_rcomp_1(k6_xcmplx_0(A,E),A))) ) ) ) ) | ( r1_limfunc2(B,A) & k1_limfunc2(B,A) = k1_limfunc2(C,A) ) ) ) ) ) ) ) )).
fof(t63_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(k6_xcmplx_0(A,D),A))) & r1_xxreal_0(k1_funct_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)) ) ) ) ) ) ) )).
fof(t63_ltlaxio2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_hilbert1)) => r8_ltlaxio1(C,k3_hilbert1(k1_ltlaxio1(k4_hilbert1(A,B)),k2_ltlaxio1(k1_ltlaxio1(k1_ltlaxio2(A,B))))) ) ) ) )).
fof(t63_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t63_mathmorp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) => ! [D] : ( 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)) ) ) ) ) )).
fof(t63_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( r2_matrix10(B,C) => r2_matrix10(k2_matrix10(A,C),k2_matrix10(A,B)) ) ) ) ) )).
fof(t63_matrix13,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ! [E] : ( ( v1_finset_1(E) & v1_setfam_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ( r1_tarski(k2_zfmisc_1(D,E),k2_matrix_0(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) ) ) ) ) ) ) )).
fof(t63_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ( k8_matrix13(A,B) = k5_numbers => ( ( k1_matrix_0(B) = k5_numbers & k3_finseq_1(B) != k5_numbers ) | k7_matrix15(A,B) = k6_prvect_1(A,k1_matrix_0(B)) ) ) ) ) )).
fof(t63_matrix16,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t63_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(C,k2_finseq_1(k1_matrix_0(B))) & k1_matrix_0(B) = k1_nat_1(D,1) ) => k1_matrix_0(k16_matrix_0(C,A,B)) = D ) ) ) ) ) )).
fof(t63_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(C) = k3_finseq_1(D) & k1_matrix_0(C) = k1_matrix_0(D) & k3_finseq_1(B) = k1_matrix_0(C) ) => ( r1_xxreal_0(k3_finseq_1(C),k5_numbers) | r1_xxreal_0(k3_finseq_1(B),k5_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)) ) ) ) ) ) ) )).
fof(t63_matrixj1,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( 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))) ) ) ) )).
fof(t63_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) & k1_matrix_0(B) = k3_finseq_1(A) ) => ( r1_xxreal_0(k3_finseq_1(B),k5_numbers) | r1_xxreal_0(k3_finseq_1(A),k5_numbers) | k11_matrixr1(k3_matrixr1(B,C),A) = k4_rvsum_1(k11_matrixr1(B,A),k11_matrixr1(C,A)) ) ) ) ) ) )).
fof(t63_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ( ! [B] : ( v7_ordinal1(B) => ( r2_hidden(k4_tarski(B,B),k2_matrix_0(k4_matrixr2(A))) => k3_matrix_0(k1_numbers,k4_matrixr2(A),B,B) = 1 ) ) & ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k4_tarski(B,C),k2_matrix_0(k4_matrixr2(A))) => ( B = C | k3_matrix_0(k1_numbers,k4_matrixr2(A),B,C) = k5_numbers ) ) ) ) ) ) )).
fof(t63_matrprob,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v6_matrprob(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v6_matrprob(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( k1_matrix_0(A) = k3_finseq_1(B) => ( ~ v3_relat_1(k6_matrixr1(A,B)) & v1_matrix_0(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_0(k6_matrixr1(A,B)) = k1_matrix_0(B) ) ) ) ) )).
fof(t63_mcart_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_subset_1(F,k4_zfmisc_1(B,C,D,E)) => ( ! [G] : ( m1_subset_1(G,B) => ! [H] : ( m1_subset_1(H,C) => ! [I] : ( m1_subset_1(I,D) => ! [J] : ( m1_subset_1(J,E) => ( F = k6_xtuple_0(G,H,I,J) => A = J ) ) ) ) ) => A = k7_mcart_1(B,C,D,E,F) ) ) ) ) ) ) )).
fof(t63_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,k5_measure6(A)) <=> ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(t63_member_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) )).
fof(t63_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( v7_ordinal1(D) => k6_memstr_0(A,B,k10_memstr_0(A,B,C,D)) = k6_memstr_0(A,B,C) ) ) ) ) )).
fof(t63_mesfunc5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_numbers,C) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(D,E) => r1_xxreal_0(k9_nat_1(k6_numbers,A,D),k9_nat_1(k6_numbers,A,E)) ) ) ) & ! [D] : ( v7_ordinal1(D) => k9_nat_1(k6_numbers,B,D) = k4_xxreal_3(C,k9_nat_1(k6_numbers,A,D)) ) & v3_mesfunc5(A) ) => ( ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(D,E) => r1_xxreal_0(k9_nat_1(k6_numbers,B,D),k9_nat_1(k6_numbers,B,E)) ) ) ) & v3_mesfunc5(B) & v10_mesfunc5(B) & k2_mesfunc5(B) = k8_supinf_2(k17_supinf_2(B)) & k2_mesfunc5(B) = k4_xxreal_3(C,k2_mesfunc5(A)) ) ) ) ) ) )).
fof(t63_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t63_mmlquery,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k9_setfam_1(A)) => k26_mmlquery(A,B,1) = k5_prob_3(A,B) ) )).
fof(t63_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k25_modelc_2(k43_modelc_2)) => ( v2_modelc_2(A) => ( r7_modelc_2(B,A) <=> r2_hidden(A,k9_nat_1(k43_modelc_2,k27_modelc_2(k43_modelc_2,B),k5_numbers)) ) ) ) ) )).
fof(t63_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ( ( v5_modelc_3(B) & r2_modelc_2(A,B) ) => v5_modelc_3(A) ) ) ) )).
fof(t63_moebius1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => r1_tarski(a_2_4_moebius1(A,B),k2_finseq_1(A)) ) ) )).
fof(t63_monoid_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & m2_monoid_0(B,k9_monoid_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k6_algstr_0(B,C,D) = k7_finseq_1(C,D) ) ) ) ) )).
fof(t63_nat_d,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( ( r1_xxreal_0(k5_numbers,B) => ( r1_xxreal_0(A,B) | k5_int_1(B,A) = B ) ) & ( r1_xxreal_0(k4_xcmplx_0(A),B) => ( r1_xxreal_0(k5_numbers,B) | k5_int_1(B,A) = k2_xcmplx_0(A,B) ) ) ) ) ) )).
fof(t63_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t63_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,k5_numbers) => k4_nat_d(A,B) = k6_xcmplx_0(A,k2_nat_1(B,k3_nat_d(A,B))) ) ) ) )).
fof(t63_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t63_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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) ) ) )).
fof(t63_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ~ ( r2_orders_1(A,B) & k1_relat_1(A) = B & r4_orders_1(A,B) & ! [C] : ~ r6_orders_1(A,C) ) ) )).
fof(t63_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => k5_ordinal3(k11_ordinal2(A,C),k11_ordinal2(B,C)) = k11_ordinal2(k5_ordinal3(A,B),C) ) ) ) )).
fof(t63_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( ( r2_hidden(1,C) & r2_hidden(k5_ordinal5(B,C),k5_ordinal5(A,C)) ) => r2_hidden(B,A) ) ) ) ) )).
fof(t63_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) ) => ! [C] : ( ( ~ 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)) ) ) ) ) )).
fof(t63_partfun1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => r1_partfun1(k6_relat_1(A,B),B) ) )).
fof(t63_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) )).
fof(t63_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( ( 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) & k10_pdiff_1(3,3,k26_valued_1(k1_euclid(3),k1_numbers,k1_pdiff_3(2,3,C),A),B) = k3_xcmplx_0(A,k6_pdiff_5(C,B)) ) ) ) ) ) )).
fof(t63_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ! [C] : ( ( 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] : ( m1_subset_1(D,k4_ordinal1) => ( ( 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] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(D,B) & ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( 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] : ( m2_finseq_2(H,k1_numbers,k1_euclid(A)) => r1_xxreal_0(k9_complex1(k5_real_1(k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_7(A,C,G),H),k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_7(A,C,D),H))),k3_xcmplx_0(E,k12_euclid(H))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t63_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k4_nat_d(A,B) = k5_numbers => ( r1_xxreal_0(B,k5_numbers) | k3_nat_d(A,B) = k7_xcmplx_0(A,B) ) ) ) ) )).
fof(t63_polyform,axiom,( ! [A] : ( ( 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)))) ) )).
fof(t63_polynom5,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => r2_cfcont_1(k8_funcop_1(k2_numbers,k2_numbers,A),k2_numbers) ) )).
fof(t63_power,axiom,( k2_power(2,5) = 32 )).
fof(t63_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t63_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => ! [C] : ( v1_rat_1(C) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(C,B) ) => r1_xxreal_0(k4_prepower(A,C),k4_prepower(A,B)) ) ) ) ) )).
fof(t63_prob_3,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ~ ( r1_xxreal_0(1,k3_finseq_1(A)) & ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( k3_funct_2(k4_ordinal1,k1_numbers,B,1) = k1_funct_1(A,1) & ! [C] : ( v7_ordinal1(C) => ~ ( k5_numbers != C & ~ r1_xxreal_0(k3_finseq_1(A),C) & k3_funct_2(k4_ordinal1,k1_numbers,B,k1_nat_1(C,1)) != k2_xcmplx_0(k1_funct_1(B,C),k1_funct_1(A,k1_nat_1(C,1))) ) ) & k18_rvsum_1(A) = k3_funct_2(k4_ordinal1,k1_numbers,B,k3_finseq_1(A)) ) ) ) ) )).
fof(t63_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t63_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t63_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => k6_qc_lang3(A,k12_qc_lang1(A)) = k1_xboole_0 ) )).
fof(t63_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => ( k25_quaterni(A,C) = k25_quaterni(B,C) => A = B ) ) ) ) )).
fof(t63_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k25_quaterni(A,B) = k6_quaterni(k6_xcmplx_0(k13_quaterni(A),k13_quaterni(B)),k6_xcmplx_0(k14_quaterni(A),k14_quaterni(B)),k6_xcmplx_0(k15_quaterni(A),k15_quaterni(B)),k6_xcmplx_0(k16_quaterni(A),k16_quaterni(B))) ) ) )).
fof(t63_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B))))) => ! [E] : ( m1_rcomp_3(E,A,B,D) => ! [F] : ( 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),k3_seq_4(k7_partfun1(k9_setfam_1(k1_numbers),E,C))) ) ) ) ) ) ) ) )).
fof(t63_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => k6_real_1(k9_nat_1(k1_numbers,k5_real_3(B),k1_nat_1(A,2)),k9_nat_1(k1_numbers,k6_real_3(B),k1_nat_1(A,2))) = k6_real_1(k3_real_1(k4_real_1(k9_nat_1(k1_numbers,k4_real_3(B),k1_nat_1(A,2)),k9_nat_1(k1_numbers,k5_real_3(B),k1_nat_1(A,1))),k9_nat_1(k1_numbers,k5_real_3(B),A)),k3_real_1(k4_real_1(k9_nat_1(k1_numbers,k4_real_3(B),k1_nat_1(A,2)),k9_nat_1(k1_numbers,k6_real_3(B),k1_nat_1(A,1))),k9_nat_1(k1_numbers,k6_real_3(B),A))) ) ) )).
fof(t63_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => k5_relat_1(A,k9_xtuple_0(A)) = A ) )).
fof(t63_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) => ! [E] : ( 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)) ) ) ) ) )).
fof(t63_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( m2_rewrite1(B,A) => r12_rewrite1(A,B) ) ) )).
fof(t63_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_afinsq_1(C))) => ! [F] : ( ( ~ 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] : ( 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 ) ) ) ) ) ) ) )).
fof(t63_rfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ( r2_hidden(C,A) <=> k1_funct_1(k7_rfunct_1(A,B),C) = 1 ) ) ) )).
fof(t63_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( 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) ) ) ) )).
fof(t63_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v7_valued_0(B) => r1_xxreal_0(k1_funct_1(B,A),k3_funct_2(k4_ordinal1,k1_numbers,k3_rinfsup1(B),k1_nat_1(A,1))) ) ) ) )).
fof(t63_rlaffin1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_rlvect_2(C,B) => ( v2_convex1(C,B) => r1_xxreal_0(k1_funct_1(C,A),1) ) ) ) )).
fof(t63_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_rlsub_1(D,A) => ( r2_hidden(B,k3_rlsub_1(A,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r1_struct_0(D,E) & B = k3_rlvect_1(A,C,E) ) ) ) ) ) ) )).
fof(t63_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m2_rlsub_1(D,A,B) & r2_hidden(C,D) ) ) ) ) )).
fof(t63_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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) ) ) ) )).
fof(t63_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k4_rlvect_1(A,k3_finseq_4(u1_struct_0(A),C,B,D)) = k1_algstr_0(A,k4_rlvect_1(A,k2_finseq_4(u1_struct_0(A),C,B)),D) ) ) ) ) )).
fof(t63_rlvect_2,axiom,( ! [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) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t63_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( v2_vectsp_2(D,A) & m1_rmod_2(D,A,B) ) => ! [E] : ( ( 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 ) ) ) ) ) ) )).
fof(t63_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(t63_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_bhsp_1(B) & m1_rusub_1(B,A) ) => ! [C] : ( ( v1_bhsp_1(C) & m1_rusub_1(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k3_rusub_1(A,E,B) = k3_rusub_1(A,D,C) => B = C ) ) ) ) ) ) )).
fof(t63_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( r2_hidden(D,k3_rusub_1(A,C,B)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r1_struct_0(B,E) & D = k3_rlvect_1(A,C,E) ) ) ) ) ) )).
fof(t63_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t63_scmfsa8c,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ( ~ r3_scmfsa7b(A,k4_scmfsa_2(k5_numbers)) => v1_scmfsa7b(k11_compos_1(k1_scmfsa_2,A)) ) ) )).
fof(t63_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ( ( k1_funct_1(C,B) = k5_numbers => k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k12_scmfsa_2(A,B),C),k4_struct_0(k1_scmfsa_2)) = A ) & ( k1_funct_1(C,B) != k5_numbers => k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k12_scmfsa_2(A,B),C),k4_struct_0(k1_scmfsa_2)) = k4_card_1(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,C)) ) & ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k12_scmfsa_2(A,B),C),D) = k1_funct_1(C,D) ) & ! [D] : ( m1_scmfsa_2(D) => r2_relset_1(k4_ordinal1,k4_numbers,k18_scmfsa_2(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k12_scmfsa_2(A,B),C),D),k18_scmfsa_2(C,D)) ) ) ) ) ) )).
fof(t63_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmpds_2)) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t63_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => k5_memstr_0(2,k1_scmpds_2,k6_scmpds_4(k3_scmpds_6(E,F,C,D),B,A)) = k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),2) ) ) ) ) ) ) )).
fof(t63_scmyciel,axiom,( ! [A] : ( ( 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))) ) ) ) )).
fof(t63_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r3_semi_af1(A,B,C,D,E) ) ) ) ) ) )).
fof(t63_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => ( k16_seq_4(A,B) = k16_seq_4(A,C) => B = C ) ) ) ) )).
fof(t63_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(B) => ( v3_kurato_0(B,A) & k4_kurato_0(A,B) = k1_kurato_0(A,B) ) ) ) )).
fof(t63_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) )).
fof(t63_sf_mastr,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( v7_ordinal1(C) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ( ( r1_tarski(B,E) & ! [F] : ( v7_ordinal1(F) => ( ~ r1_xxreal_0(C,F) => r2_hidden(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,D,F)),k1_relset_1(k4_ordinal1,B)) ) ) ) => ( r2_hidden(A,k4_sf_mastr(B)) | r2_relset_1(k4_ordinal1,k4_numbers,k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,D,C),A),k18_scmfsa_2(D,A)) ) ) ) ) ) ) ) )).
fof(t63_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t63_simplex0,axiom,( ! [A] : ! [B] : ( m1_simplex0(B,A) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => k11_simplex0(A,B,C,k1_nat_1(D,E)) = k11_simplex0(A,k11_simplex0(A,B,C,E),C,D) ) ) ) ) )).
fof(t63_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_fdiff_1(k16_sin_cos,A) & k1_fdiff_1(k16_sin_cos,A) = k1_funct_1(k18_sin_cos,A) ) ) )).
fof(t63_sin_cos6,axiom,( k1_relset_1(k1_numbers,k1_sin_cos6) = k1_rcomp_1(k4_xcmplx_0(1),1) )).
fof(t63_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( B = k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k23_sin_cos(A),k23_sin_cos(k4_xcmplx_0(A)))) => A = k3_power(k4_power,k2_xcmplx_0(B,k3_square_1(k2_xcmplx_0(k1_square_1(B),1)))) ) ) ) )).
fof(t63_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) => ( r1_xxreal_0(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)),k3_sin_cos9(A)) & r1_xxreal_0(k3_sin_cos9(A),k7_xcmplx_0(k28_sin_cos,4)) ) ) ) )).
fof(t63_sincos10,axiom,( k3_relat_1(k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers)),k3_sincos10) = k1_partfun2(k1_numbers,k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers)) )).
fof(t63_sprect_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t63_sprect_2,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( 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))) ) ) ) ) ) ) )).
fof(t63_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t63_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [E] : ( m1_subset_1(E,C) => ! [F] : ( 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 ) ) ) ) ) ) ) )).
fof(t63_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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 ) ) ) ) )).
fof(t63_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) )).
fof(t63_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_pre_topc(C) & v1_tex_2(C,A) & v2_tex_3(C,A) & m1_pre_topc(C,A) ) => B != u1_struct_0(C) ) ) ) ) )).
fof(t63_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t63_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t63_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_topalg_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_topalg_1(A,B))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t63_topgen_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t63_topreal6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t63_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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))) ) ) ) )).
fof(t63_tops_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( ~ v2_struct_0(D) & v2_pre_topc(D) & l1_pre_topc(D) & v1_connsp_1(D) & ? [E] : ( 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) ) ) )).
fof(t63_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_tsep_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t63_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t63_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ( r1_tarski(A,B) => r1_tarski(k12_trees_3(A),k12_trees_3(B)) ) ) ) )).
fof(t63_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( r3_tsep_1(A,B,C) => r1_tsep_1(B,C) ) ) ) ) )).
fof(t63_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v2_finseq_1(D) ) => ~ ( r1_tarski(C,A) & r1_tarski(D,B) & ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v2_finseq_1(E) ) => ~ ( E = k2_xboole_0(C,k61_valued_1(D,k3_finseq_1(A))) & k4_finseq_1(k15_finseq_1(E)) = k2_finseq_1(k1_nat_1(k3_finseq_1(k15_finseq_1(C)),k3_finseq_1(k15_finseq_1(D)))) & k15_finseq_1(E) = k2_xboole_0(k15_finseq_1(C),k61_valued_1(k15_finseq_1(D),k3_finseq_1(k15_finseq_1(C)))) ) ) ) ) ) ) ) )).
fof(t63_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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) ) ) ) )).
fof(t63_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_vectsp_4(E,A,B) => ( ? [F] : ( 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)) ) ) ) ) ) ) )).
fof(t63_waybel23,axiom,( ! [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] : ( ( v6_waybel23(B,A) & m1_waybel23(B,A) ) => v3_waybel_1(k1_waybel_1(k1_yellow_1(k7_waybel_0(k5_yellow_0(A,B))),A,k3_waybel23(A,k5_yellow_0(A,B)),k5_waybel23(A,B)),k1_yellow_1(k7_waybel_0(k5_yellow_0(A,B))),A) ) ) )).
fof(t63_waybel34,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_yellow_0(D,A) => ! [E] : ( 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)))) ) ) ) ) ) ) ) )).
fof(t63_waybel_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t63_waybel_1,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v5_waybel_1(k4_waybel_1(A,B),A,A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( r1_yellow_0(A,B) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t63_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r1_tarski(A,B) & r1_xboole_0(B,C) ) => r1_xboole_0(A,C) ) )).
fof(t63_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( 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))) ) ) )).
fof(t63_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),D),C) = k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,C),k7_xcmplx_0(B,C)),k7_xcmplx_0(D,C)) ) ) ) ) )).
fof(t63_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => r1_xxreal_0(k5_numbers,k3_xcmplx_0(A,A)) ) )).
fof(t63_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_tarski(k4_xxreal_1(C,D),k4_xxreal_1(A,B)) => ( r1_xxreal_0(D,C) | ( r1_xxreal_0(A,C) & r1_xxreal_0(D,B) ) ) ) ) ) ) ) )).
fof(t63_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ( ! [C] : ( v1_xxreal_0(C) => ~ ( r2_hidden(C,A) & ! [D] : ( v1_xxreal_0(D) => ~ ( r2_hidden(D,B) & r1_xxreal_0(C,D) ) ) ) ) => r1_xxreal_0(k1_xxreal_2(A),k1_xxreal_2(B)) ) ) ) )).
fof(t63_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t63_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) ) )).
fof(t63_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t63_yellow_4,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t63_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => k7_waybel_1(A,k4_yellow_0(A)) = k3_yellow_0(A) ) )).
fof(t63_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ~ ( r3_zf_lang(B,A) & ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ~ r1_zf_lang(C,A) ) ) ) ) )).
fof(t63_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => k2_zf_model(k10_zf_lang(A,B)) = k4_subset_1(k1_zf_lang,k2_zf_model(A),k2_zf_model(B)) ) ) )).
fof(t63_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( k4_xboole_0(k2_tarski(A,B),C) = k1_xboole_0 <=> ( r2_hidden(A,C) & r2_hidden(B,C) ) ) )).
fof(t63_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_zmodul01(C,A) => ( r1_struct_0(C,B) <=> k5_zmodul01(A,B,C) = u1_struct_0(C) ) ) ) ) )).
fof(t63_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v6_zmodul01(A) => ( ( B != C & v1_zmodul02(k7_domain_1(u1_struct_0(A),B,C),A) ) <=> ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => ( k3_rlvect_1(A,k1_zmodul01(A,B,D),k1_zmodul01(A,C,E)) = k4_struct_0(A) => ( D = k5_numbers & E = k5_numbers ) ) ) ) ) ) ) ) ) )).
fof(t64_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & ~ v4_abcmiz_0(A) & l3_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A))) => ~ ( r6_abcmiz_0(A,B,C) & ! [D] : ( 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] : ( 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 ) ) ) ) ) ) ) ) )).
fof(t64_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( 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)) ) ) ) ) )).
fof(t64_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t64_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_afinsq_1(A) ) => r2_hidden(k5_numbers,k9_xtuple_0(A)) ) )).
fof(t64_afinsq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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(k4_ordinal1,B)) => k2_xcmplx_0(k7_afinsq_2(k5_relat_1(B,A)),k1_funct_1(B,A)) = k7_afinsq_2(k5_relat_1(B,k1_nat_1(A,1))) ) ) ) )).
fof(t64_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t64_aofa_000,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_freealg(A) ) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(k7_freealg(k19_aofa_000,A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_freealg(k19_aofa_000,A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t64_aofa_a00,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ( ( r1_xxreal_0(1,A) & r1_xxreal_0(1,B) ) => ! [E] : ( ( ~ v2_struct_0(E) & ~ v11_struct_0(E) & v14_aofa_a00(E,B) & l6_aofa_a00(E) ) => ! [F] : ( ( v4_msualg_1(F,E) & l3_msualg_1(F,E) ) => ! [G] : ( ( ~ v2_struct_0(G) & ~ v11_struct_0(G) & l5_aofa_a00(G) ) => ( v21_aofa_a00(G,C,D,A) => ! [H] : ( ( v4_msualg_1(H,G) & l3_msualg_1(H,G) ) => ( ( r1_partfun1(u3_msualg_1(E,F),u3_msualg_1(G,H)) & v22_aofa_a00(H,G,C,D,A) ) => ! [I] : ( ( ~ v2_struct_0(I) & ~ v11_struct_0(I) & l6_aofa_a00(I) ) => ( g6_aofa_a00(u1_struct_0(I),u4_struct_0(I),u1_msualg_1(I),u2_msualg_1(I),u8_aofa_a00(I),u7_aofa_a00(I)) = k36_aofa_a00(E,G) => ! [J] : ( ( v4_msualg_1(J,I) & l3_msualg_1(J,I) ) => ( J = k42_aofa_a00(E,G,F,H) => v22_aofa_a00(J,I,C,D,k2_xcmplx_0(B,A)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t64_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v19_aofa_a00(E,A) & m1_subset_1(E,u1_struct_0(A)) ) => ! [F] : ( v1_int_1(F) => ! [G] : ( v1_int_1(G) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,D),E)) => ! [I] : ( m1_subset_1(I,k1_funct_1(u3_msualg_1(A,D),E)) => ( ( H = F & I = G ) => ( G = k5_numbers | k35_aofa_a00(A,D,E,H,I) = k5_int_1(F,G) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t64_aofa_i00,axiom,( ! [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) & v2_aofa_i00(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_card_3(B) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_aofa_i00(D,A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) & m1_aofa_000(D,A,k9_funct_2(B,k4_numbers),k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers)) ) => ! [E] : ( m1_aofa_i00(E,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [F] : ( m1_aofa_i00(F,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ! [G] : ( m1_aofa_i00(G,B,u1_struct_0(A),k9_funct_2(B,k4_numbers),D) => ( ? [H] : ( v1_relat_1(H) & v1_funct_1(H) & k1_funct_1(H,C) = k5_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,k5_numbers),k16_aofa_000(A,k78_aofa_i00(A,B,C,D,F,k5_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,k5_numbers),D,G,k32_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,k42_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,E),k42_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,F))),k15_aofa_000(A,k79_aofa_i00(A,B,C,D,G,k5_numbers),k58_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,G,k4_xcmplx_0(1)))),k48_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,E,F)),k48_aofa_i00(A,B,k1_aofa_i00(k9_funct_2(B,k4_numbers),C,k5_numbers),D,F,G))),D,a_6_3_aofa_i00(A,B,C,D,E,F)) ) ) ) ) ) ) ) ) )).
fof(t64_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => r3_arytm_3(k11_arytm_3,A) ) )).
fof(t64_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(k5_numbers,C) ) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(k2_power(A,C),k2_power(B,C)) ) ) ) ) ) )).
fof(t64_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t64_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t64_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t64_borsuk_6,axiom,( r2_hidden(k4_tarski(k5_numbers,1),k7_borsuk_6) )).
fof(t64_borsuk_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(A))) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t64_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t64_bvfunc14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ( ( v1_relat_1(I) & v1_funct_1(I) ) => ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ! [Q] : ( 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)) ) ) )).
fof(t64_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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))))) ) ) ) ) )).
fof(t64_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ( ( A = k8_margrel1 & k6_xboolean(A,B) = k8_margrel1 ) => B = k8_margrel1 ) ) ) )).
fof(t64_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ~ ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => r2_hidden(C,k3_calcul_1(A,B)) ) ) ) )).
fof(t64_card_1,axiom,( ! [A] : ! [B] : ( r1_ordinal1(k1_card_1(A),k1_card_1(B)) <=> ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & r1_tarski(A,k7_relat_1(C,B)) ) ) )).
fof(t64_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => k6_card_3(k7_funcop_1(A,B)) = k2_card_2(A,B) ) ) )).
fof(t64_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( r1_tarski(C,B) & r2_hidden(B,k8_card_3(A)) ) => r2_hidden(C,k8_card_3(A)) ) ) ) )).
fof(t64_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( 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)) = k3_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)) = k4_graph_1(B,k3_funct_2(u4_struct_0(A),u4_struct_0(B),C,D)) ) ) ) ) ) )).
fof(t64_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t64_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t64_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( v1_xcmplx_0(D) => ( v1_partfun1(C,A) => k7_partfun1(k2_numbers,k25_valued_1(A,k2_numbers,C,D),B) = k3_xcmplx_0(D,k7_partfun1(k2_numbers,C,B)) ) ) ) ) ) )).
fof(t64_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_chain_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k4_chain_1(A,B,k5_numbers))) => ( m3_chain_1(C,A,B,k5_numbers) <=> v1_abian(k5_card_1(C)) ) ) ) ) )).
fof(t64_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v4_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => v3_chord(B,A) ) ) )).
fof(t64_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_circcomb(A) & v2_circcomb(A) & v3_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v1_circcomb(B) & v2_circcomb(B) & v3_circcomb(B) & l1_msualg_1(B) ) => ! [C] : ( ( v4_msafree2(C,A) & v4_circcomb(C,A) & v6_circcomb(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msafree2(D,B) & v4_circcomb(D,B) & v6_circcomb(D,B) & l3_msualg_1(D,B) ) => ! [E] : ( m1_subset_1(E,k4_card_3(u3_msualg_1(k2_circcomb(A,B),k3_circcomb(A,B,C,D)))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_circcomb(A,B))) => ( ! [G] : ( 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] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t64_classes1,axiom,( ! [A] : ( v3_ordinal1(A) => k6_classes1(k4_classes1(A)) = A ) )).
fof(t64_classes2,axiom,( k13_classes2 = k4_classes1(k4_ordinal1) )).
fof(t64_clvect_1,axiom,( ! [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) ) => ! [B] : ( 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) ) ) )).
fof(t64_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v2_clvect_2(C,A) => v2_clvect_2(k4_normsp_1(A,C,B),A) ) ) ) ) )).
fof(t64_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ! [D] : ! [E] : ! [F] : ( 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 ) ) ) ) ) ) ) )).
fof(t64_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k9_complex1(A),k9_complex1(B))),k9_complex1(k6_xcmplx_0(A,B))) ) ) )).
fof(t64_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(k5_numbers,C) & A != k5_numbers & B != k5_numbers & k3_complex2(A,B) != k3_complex2(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) ) ) ) )).
fof(t64_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => r1_xxreal_0(k6_xcmplx_0(k9_complex1(A),k9_complex1(B)),k9_complex1(k3_rlvect_1(k1_complfld,A,B))) ) ) )).
fof(t64_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => k8_complsp2(A,B) = k8_complex1(k8_complsp2(B,A)) ) ) )).
fof(t64_comseq_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( ~ r1_xxreal_0(1,k9_complex1(A)) => ( v1_comseq_3(k1_comseq_3(A)) & k11_comseq_3(k1_comseq_3(A)) = k7_xcmplx_0(k6_complex1,k6_xcmplx_0(k6_complex1,A)) ) ) ) )).
fof(t64_convex4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( v1_xcmplx_0(E) => ! [F] : ( v1_xcmplx_0(F) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t64_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ( ( r2_hidden(k13_cqc_lang(A,B,D),k3_cqc_lang(A)) & v2_cqc_the1(k13_cqc_lang(A,B,C),A) ) => ( r2_hidden(C,k24_qc_lang1(A,B)) | v2_cqc_the1(k13_cqc_lang(A,B,D),A) ) ) ) ) ) ) )).
fof(t64_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t64_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_normsp_1(A,B,C),k16_csspace(A,B,k5_vfunct_1(k4_ordinal1,A,C))) ) ) ) )).
fof(t64_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => 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),k18_sin_cos),A),B) = k2_xcmplx_0(k4_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,2),k3_xcmplx_0(k17_sin_cos(B),k17_sin_cos(k7_xcmplx_0(A,2))))),k3_xcmplx_0(k7_xcmplx_0(1,2),k3_xcmplx_0(k17_sin_cos(k3_xcmplx_0(3,B)),k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(3,A),2))))) ) ) )).
fof(t64_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k7_xcmplx_0(1,k17_sin_cos(D)) ) => ( k17_sin_cos(k2_xcmplx_0(B,k7_xcmplx_0(A,2))) = k5_numbers | k17_sin_cos(k6_xcmplx_0(B,k7_xcmplx_0(A,2))) = k5_numbers | k1_funct_1(k5_diff_1(C,A),B) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(2,k6_xcmplx_0(k17_sin_cos(k6_xcmplx_0(B,k7_xcmplx_0(A,2))),k17_sin_cos(k2_xcmplx_0(B,k7_xcmplx_0(A,2))))),k6_xcmplx_0(k19_sin_cos(k3_xcmplx_0(2,B)),k19_sin_cos(A)))) ) ) ) ) ) )).
fof(t64_entropy1,axiom,( ! [A] : ( ( v1_matrprob(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v6_matrprob(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( k3_finseq_1(A) = k3_finseq_1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( C = k6_matrixr1(k1_entropy1(A),B) => k5_matrprob(k5_entropy1(C)) = k2_xcmplx_0(k18_rvsum_1(k4_entropy1(A)),k18_rvsum_1(k14_rvsum_1(A,k3_matrprob(k5_entropy1(B))))) ) ) ) ) ) )).
fof(t64_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_enumset1(A,B,C,D) = k2_enumset1(A,D,C,B) )).
fof(t64_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t64_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => k22_rvsum_1(k6_euclid(3,A),k6_euclid(3,B)) = k22_rvsum_1(A,B) ) ) )).
fof(t64_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t64_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v5_relat_1(C,u1_struct_0(B)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_exchsort(C) ) => ! [D] : ( m1_subset_1(D,k9_xtuple_0(C)) => ! [E] : ( m1_subset_1(E,k9_xtuple_0(C)) => ! [F] : ( m1_subset_1(F,k9_xtuple_0(C)) => ( ( r2_hidden(F,D) & A = k5_exchsort(k9_xtuple_0(C),k9_xtuple_0(C),k6_partfun1(k9_xtuple_0(C)),D,E) ) => ( k1_binop_1(k7_exchsort(B,C,D,E),F,E) = k4_tarski(k1_funct_1(A,F),k1_funct_1(A,E)) & k1_binop_1(k7_exchsort(B,C,D,E),F,D) = k4_tarski(k1_funct_1(A,F),k1_funct_1(A,D)) ) ) ) ) ) ) ) ) )).
fof(t64_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( C != k4_tarski(k10_finseq_1(A,B),k1_facirc_1) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k8_facirc_1(A,B,C,k1_facirc_1),k10_facirc_1(A,B,C,k1_facirc_1)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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(k8_facirc_1(A,B,C,k1_facirc_1),k10_facirc_1(A,B,C,k1_facirc_1),k5_facirc_1(k8_facirc_1(A,B,C,k1_facirc_1),k10_facirc_1(A,B,C,k1_facirc_1),D,2),k9_facirc_1(A,B,C,k1_facirc_1)) = k2_binarith(k2_binarith(E,F),G) ) ) ) ) ) ) )).
fof(t64_fdiff_11,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A)),B),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A)),B)) ) ) ) ) => ( r2_hidden(k5_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] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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) = k2_xcmplx_0(k1_funct_1(k2_sin_cos9,k7_xcmplx_0(1,B)),k7_xcmplx_0(B,k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) ) )).
fof(t64_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t64_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( 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)) ) ) )).
fof(t64_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t64_finseq_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t64_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : r1_tarski(k10_xtuple_0(k1_finseq_3(A,B)),k10_xtuple_0(A)) ) )).
fof(t64_finseq_4,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t64_finseq_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t64_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t64_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( ( 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 ) ) ) ) ) ) ) )).
fof(t64_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( v7_ordinal1(C) => r1_tarski(k8_flang_1(A,k7_flang_1(A,B,C)),k8_flang_1(A,B)) ) ) )).
fof(t64_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t64_flang_3,axiom,( ! [A] : ! [B] : ( 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)) ) ) )).
fof(t64_fomodel0,axiom,( ! [A] : ! [B] : r1_setfam_1(k3_setfam_1(A,B),A) )).
fof(t64_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) )).
fof(t64_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t64_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ! [B] : ! [C] : 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) ) ) )).
fof(t64_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ! [E] : ~ ( r2_hidden(E,k7_relset_1(B,C,D,A)) & ! [F] : ( m1_subset_1(F,B) => ~ ( r2_hidden(F,A) & E = k1_funct_1(D,F) ) ) ) ) )).
fof(t64_funct_3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,A,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [G] : ( ( 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) ) ) ) ) ) ) ) ) )).
fof(t64_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( A != B => k10_xtuple_0(k4_funct_4(A,B,C,D)) = k2_tarski(C,D) ) )).
fof(t64_funct_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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,k13_funct_5(A,B,C,D)),D) ) ) ) ) )).
fof(t64_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => r1_funct_8(A,k1_numbers,k1_numbers,k2_euclid) ) )).
fof(t64_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t64_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => k11_fvsum_1(A,B,C) = k11_fvsum_1(A,C,B) ) ) ) )).
fof(t64_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : v1_relat_1(k3_msafree2(k25_gfacirc1(A,B,C))) )).
fof(t64_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ( r2_hidden(B,k28_glib_000(A,C)) <=> ? [D] : ( m1_subset_1(D,k6_glib_000(A)) & r1_glib_000(A,C,D,B) ) ) ) ) )).
fof(t64_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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)) ) ) ) )).
fof(t64_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_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_0(C),k1_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_0(u1_struct_0(k15_euclid(2)),C,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),k1_nat_1(B,1))),k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),k1_nat_1(B,2))),k7_xcmplx_0(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,k1_nat_1(B,1)))),k1_tarski(k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),k1_nat_1(B,1))),k7_xcmplx_0(1,2))))) ) ) ) ) ) )).
fof(t64_goboard7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t64_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,A) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t64_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => k6_group_2(B) = k6_group_2(C) ) ) ) )).
fof(t64_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_group_2(C,A) => k7_struct_0(C) = k7_struct_0(k6_group_3(A,C,B)) ) ) ) )).
fof(t64_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( v15_algstr_0(C) & m1_group_2(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t64_group_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_group_2(C,B) => ! [D] : ( m1_group_2(D,B) => ( r1_struct_0(k8_group_5(B,C,D),A) <=> ? [E] : ( m2_finseq_1(E,u1_struct_0(B)) & ? [F] : ( 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)) ) ) ) ) ) ) )).
fof(t64_group_6,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t64_group_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( ( 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))) ) ) ) ) )).
fof(t64_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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))) ) ) ) ) )).
fof(t64_hfdiff_1,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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)))) ) ) ) ) )).
fof(t64_ideal_1,axiom,( ! [A] : ( ( ~ 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] : ( 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) ) ) )).
fof(t64_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_xreal_0(B) => k3_int_1(k2_xcmplx_0(B,A)) = k3_int_1(B) ) ) )).
fof(t64_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(A,B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(C,D) = k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(k18_sin_cos,D),k1_square_1(k1_funct_1(k16_sin_cos,D))),k1_square_1(k1_funct_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) = k6_xcmplx_0(k1_funct_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)),k2_seq_4(A)),k1_funct_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)),k3_seq_4(A))) ) ) ) ) )).
fof(t64_integra8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( ( B = k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k3_square_1(2),2)),k7_xcmplx_0(k3_square_1(2),2)) & k9_xtuple_0(k2_fdiff_1(k1_sin_cos6,k2_rcomp_1(k4_xcmplx_0(1),1))) = k9_xtuple_0(A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,k2_rcomp_1(k4_xcmplx_0(1),1)) & k1_funct_1(A,C) = k7_xcmplx_0(1,k3_square_1(k6_xcmplx_0(1,k1_square_1(C)))) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,A,B)) ) => k2_integra5(B,A) = k7_xcmplx_0(k28_sin_cos,2) ) ) ) )).
fof(t64_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v3_rcomp_1(E) & m1_subset_1(E,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,E) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => ( k1_funct_1(C,F) = k2_xcmplx_0(A,F) & ~ r1_xxreal_0(k1_funct_1(C,F),k5_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(k7_xcmplx_0(3,2))),k7_xcmplx_0(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(k7_xcmplx_0(3,2))),k7_xcmplx_0(2,3))) = k1_relset_1(k1_numbers,D) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => k1_funct_1(D,F) = k6_prepower(k2_xcmplx_0(A,F),k7_xcmplx_0(1,2)) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,D,B)) ) => k2_integra5(B,D) = k6_xcmplx_0(k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(k7_xcmplx_0(3,2))),k7_xcmplx_0(2,3)),k2_seq_4(B)),k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(k7_xcmplx_0(3,2))),k7_xcmplx_0(2,3)),k3_seq_4(B))) ) ) ) ) ) ) )).
fof(t64_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m2_interva1(B,A) => ! [C] : ( m2_interva1(C,A) => ! [D] : ( 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))) ) ) ) ) )).
fof(t64_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(t64_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(2),B)))) => ! [D] : ( ( 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,k4_xcmplx_0(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)) ) ) ) ) ) ) )).
fof(t64_jgraph_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( r1_jordan6(k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(1),1),A,B) & r2_hidden(A,k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(1)),k19_euclid(k4_xcmplx_0(1),1))) & ~ ( r2_hidden(B,k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(1)),k19_euclid(k4_xcmplx_0(1),1))) & r1_xxreal_0(k18_euclid(A),k18_euclid(B)) ) & ~ r2_hidden(B,k1_rltopsp1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),1),k19_euclid(1,1))) & ~ r2_hidden(B,k1_rltopsp1(k15_euclid(2),k19_euclid(1,1),k19_euclid(1,k4_xcmplx_0(1)))) & ~ ( r2_hidden(B,k1_rltopsp1(k15_euclid(2),k19_euclid(1,k4_xcmplx_0(1)),k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(1)))) & B != k19_euclid(k4_xcmplx_0(1),k4_xcmplx_0(1)) ) ) ) ) )).
fof(t64_jgraph_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(k5_topmetr)) => ! [H] : ( 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(k7_xcmplx_0(2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(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(k4_xcmplx_0(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)),k4_xcmplx_0(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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t64_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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,k2_jordan9(B,A))) = k2_xcmplx_0(k8_pscomp_1(B),k7_xcmplx_0(k6_xcmplx_0(k8_pscomp_1(B),k6_pscomp_1(B)),k1_newton(2,A))) ) ) )).
fof(t64_jordan1j,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(C,D) & r1_xxreal_0(D,k1_matrix_0(k1_jordan8(B,k1_nat_1(A,1)))) & k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),D)),k8_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),D)) & k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),D)),k9_jordan6(k3_topreal1(2,k2_jordan9(B,k1_nat_1(A,1))))) = k1_tarski(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),C)) & r1_xboole_0(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),C),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(B,k1_nat_1(A,1)),k1_jordan1a(k1_jordan8(B,k1_nat_1(A,1))),D)),k8_jordan6(B)) ) ) ) ) ) )).
fof(t64_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( v1_xreal_0(C) => ( B = a_2_5_jordan2c(A,C) => ( v3_pre_topc(k3_subset_1(u1_struct_0(k15_euclid(A)),B),k15_euclid(A)) & v4_pre_topc(B,k15_euclid(A)) ) ) ) ) ) )).
fof(t64_jordan6,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => k17_euclid(k10_jordan6(A)) = k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)),2) ) )).
fof(t64_kurato_1,axiom,( k5_card_1(k2_kurato_1(k3_topmetr,k6_kurato_1)) = 14 )).
fof(t64_lattice2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k5_finsub_1(A)) => ! [C] : ( ( ~ v2_struct_0(C) & v10_lattices(C) & v11_lattices(C) & v13_lattices(C) & l3_lattices(C) ) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t64_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( 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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),k23_lexbfs(A,k26_lexbfs(A),B))))) => k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),k23_lexbfs(A,k26_lexbfs(A),k1_nat_1(B,1))) = k1_funct_4(k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),k23_lexbfs(A,k26_lexbfs(A),B))))))) ) ) ) )).
fof(t64_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,B) & r2_hidden(C,k1_relset_1(k1_numbers,A)) ) ) => ( ! [B] : ( v1_xreal_0(B) => ~ ( 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) ) ) ) )).
fof(t64_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_limfunc2(C,A) & r1_limfunc2(D,A) & k1_limfunc2(C,A) = k1_limfunc2(D,A) ) => ( ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & r1_tarski(k2_rcomp_1(k6_xcmplx_0(A,E),A),k9_subset_1(k1_numbers,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,C),k1_relset_1(k1_numbers,D)),k1_relset_1(k1_numbers,B))) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,k2_rcomp_1(k6_xcmplx_0(A,E),A)) => ( r1_xxreal_0(k1_funct_1(C,F),k1_funct_1(B,F)) & r1_xxreal_0(k1_funct_1(B,F),k1_funct_1(D,F)) ) ) ) ) ) | ( r1_limfunc2(B,A) & k1_limfunc2(B,A) = k1_limfunc2(C,A) ) ) ) ) ) ) ) )).
fof(t64_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(A,k2_xcmplx_0(A,D)))) & r1_xxreal_0(k2_limfunc2(B,A),k1_funct_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)) ) ) ) ) ) ) )).
fof(t64_lpspace2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v2_comseq_2(k5_normsp_0(A,k4_normsp_1(A,B,C))) & k1_seq_2(k5_normsp_0(A,k4_normsp_1(A,B,C))) = k5_numbers ) => ( v3_normsp_1(B,A) & k6_normsp_1(A,B) = C ) ) ) ) ) )).
fof(t64_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t64_mathmorp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) => ( A != k5_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)) ) ) ) ) ) )).
fof(t64_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( r2_matrix10(B,k2_matrix10(A,C)) => r2_matrix10(C,k2_matrix10(A,B)) ) ) ) ) )).
fof(t64_matrix13,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( 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(k4_ordinal1,C,k3_matrix13(k1_funct_1(k5_matrix13(C),E))),k7_subset_1(k4_ordinal1,D,k3_matrix13(k1_funct_1(k5_matrix13(D),F)))) & k5_card_1(k7_subset_1(k4_ordinal1,C,k3_matrix13(k1_funct_1(k5_matrix13(C),E)))) = k5_card_1(k7_subset_1(k4_ordinal1,D,k3_matrix13(k1_funct_1(k5_matrix13(D),F)))) ) ) ) ) ) ) ) ) )).
fof(t64_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ( k7_matrix15(A,B) = k6_prvect_1(A,k1_matrix_0(B)) => k8_matrix13(A,B) = k5_numbers ) ) ) )).
fof(t64_matrix16,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ( v6_matrix16(D,A) => 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(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))) ) ) ) ) ) )).
fof(t64_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k2_finseq_1(k1_matrix_0(B))) => ( r1_xxreal_0(k1_matrix_0(B),k5_numbers) | k1_matrix_0(B) = k1_nat_1(k1_matrix_0(k16_matrix_0(C,A,B)),1) ) ) ) ) ) )).
fof(t64_matrix_4,axiom,( ! [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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(A),B,C) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(A))) ) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(A),C,D) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(A))) ) => ( k1_matrix_0(E) = k3_finseq_1(F) => ( r1_xxreal_0(k3_finseq_1(E),k5_numbers) | r1_xxreal_0(k3_finseq_1(F),k5_numbers) | ( v1_matrix_0(k4_matrix_3(A,E,F)) & v2_matrix_0(k4_matrix_3(A,E,F),u1_struct_0(A),B,D) & m2_finseq_1(k4_matrix_3(A,E,F),k3_finseq_2(u1_struct_0(A))) ) ) ) ) ) ) ) ) ) )).
fof(t64_matrixj1,axiom,( ! [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] : ( ( v1_matrixj1(B,u1_struct_0(A)) & m2_finseq_1(B,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) => ! [C] : ( ( v1_matrixj1(C,u1_struct_0(A)) & m2_finseq_1(C,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t64_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) & k3_finseq_1(B) = k3_finseq_1(A) ) => ( r1_xxreal_0(k3_finseq_1(A),k5_numbers) | k12_matrixr1(k3_matrixr1(B,C),A) = k4_rvsum_1(k12_matrixr1(B,A),k12_matrixr1(C,A)) ) ) ) ) ) )).
fof(t64_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => k4_matrix_0(k1_numbers,k4_matrixr2(A)) = k4_matrixr2(A) ) )).
fof(t64_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ~ ( r2_hidden(A,k4_zfmisc_1(B,C,D,E)) & ! [F] : ! [G] : ! [H] : ! [I] : ~ ( r2_hidden(F,B) & r2_hidden(G,C) & r2_hidden(H,D) & r2_hidden(I,E) & A = k6_xtuple_0(F,G,H,I) ) ) )).
fof(t64_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,k5_measure6(A)) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( r1_tarski(k2_relset_1(k1_numbers,C),A) & v2_comseq_2(C) & k1_seq_2(C) = B ) ) ) ) ) )).
fof(t64_member_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t64_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( v7_ordinal1(D) => r2_hidden(k4_struct_0(B),k9_xtuple_0(k10_memstr_0(A,B,C,D))) ) ) ) ) )).
fof(t64_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k5_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)) ) ) ) ) ) )).
fof(t64_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( 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) ) ) )).
fof(t64_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k25_modelc_2(k43_modelc_2)) => ( r7_modelc_2(B,k3_modelc_2(A)) <=> ~ r7_modelc_2(B,A) ) ) ) )).
fof(t64_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v6_modelc_3(A) <=> ( v2_modelc_2(A) | ( v3_modelc_2(A) & v2_modelc_2(k10_modelc_2(A)) ) ) ) ) )).
fof(t64_moebius1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => r1_tarski(a_2_5_moebius1(A,B),k2_finseq_1(A)) ) ) )).
fof(t64_monoid_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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 ) ) )).
fof(t64_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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_msafree4(B,u1_struct_0(A)) ) => ! [C] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,C)) => ~ ( r1_msualg_3(A,k1_msafree3(A,B),C,D) & ! [E] : ( m2_pboole(E,u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,C)) => ~ ( r1_msualg_3(A,C,C,E) & r8_pboole(u1_struct_0(A),D,k3_msualg_3(u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,C),u3_msualg_1(A,C),k4_msafree4(A,B,C),E)) ) ) ) ) ) ) ) )).
fof(t64_nat_d,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( k5_int_1(B,A) = k5_int_1(C,A) => ( A = k5_numbers | r2_int_1(B,C,A) ) ) & ( r2_int_1(B,C,A) => k5_int_1(B,A) = k5_int_1(C,A) ) ) ) ) ) )).
fof(t64_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) => ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t64_newton,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r1_xxreal_0(k5_numbers,B) => r1_xxreal_0(k5_numbers,k5_int_1(A,B)) ) ) ) )).
fof(t64_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t64_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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) ) ) )).
fof(t64_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ~ ( r2_orders_1(A,B) & k1_relat_1(A) = B & r5_orders_1(A,B) & ! [C] : ~ r7_orders_1(A,C) ) ) )).
fof(t64_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => r1_ordinal1(k11_ordinal2(k6_ordinal3(A,B),B),A) ) ) )).
fof(t64_ordinal5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v6_ordinal5(A) ) => ( k4_ordinal5(A) = k5_numbers => A = k1_xboole_0 ) ) )).
fof(t64_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_classes2(C) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(t64_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => r1_partfun1(k5_relat_1(k6_relat_1(B,C),A),C) ) )).
fof(t64_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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))) ) ) ) )).
fof(t64_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( ( 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) & k10_pdiff_1(3,1,k26_valued_1(k1_euclid(3),k1_numbers,k1_pdiff_3(3,3,C),A),B) = k3_xcmplx_0(A,k7_pdiff_5(C,B)) ) ) ) ) ) )).
fof(t64_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( 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) & k10_pdiff_1(A,B,k20_valued_1(k1_euclid(A),k1_numbers,k1_numbers,C,D),E) = k2_xcmplx_0(k3_xcmplx_0(k10_pdiff_1(A,B,C,E),k1_funct_1(D,E)),k3_xcmplx_0(k1_funct_1(C,E),k10_pdiff_1(A,B,D,E))) ) ) ) ) ) ) ) )).
fof(t64_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,k5_numbers) => k3_nat_d(k1_newton(A,B),A) = k7_xcmplx_0(k1_newton(A,B),A) ) ) ) )).
fof(t64_polyform,axiom,( ! [A] : ( ( 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)))) ) )).
fof(t64_polynom5,axiom,( ! [A] : ( ( ~ 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))) ) )).
fof(t64_power,axiom,( k2_power(2,6) = 64 )).
fof(t64_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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 ) ) ) ) ) ) ) )).
fof(t64_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => ! [C] : ( v1_rat_1(C) => ~ ( ~ r1_xxreal_0(A,1) & ~ r1_xxreal_0(B,C) & r1_xxreal_0(k4_prepower(A,B),k4_prepower(A,C)) ) ) ) ) )).
fof(t64_prob_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_prob_3(D,A,B) => ! [E] : ( ( v5_relat_1(E,B) & v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ( ! [F] : ( v7_ordinal1(F) => ( r2_hidden(F,k1_relset_1(k4_ordinal1,D)) => k1_prob_2(A,B,E,F) = k8_prob_3(A,B,D,F) ) ) & ! [F] : ( v7_ordinal1(F) => ( ~ r2_hidden(F,k1_relset_1(k4_ordinal1,D)) => k1_prob_2(A,B,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(k4_ordinal1,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)) ) ) ) ) ) ) ) )).
fof(t64_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( 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))) ) ) ) ) )).
fof(t64_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ~ r3_qc_lang2(A,B,k12_qc_lang1(A)) ) ) )).
fof(t64_qc_lang3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_qc_lang1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(B),k8_qc_lang1(B,A)) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t64_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => ! [D] : ( v1_quaterni(D) => k23_quaterni(k25_quaterni(k22_quaterni(A,B),C),D) = k25_quaterni(k22_quaterni(k23_quaterni(A,D),k23_quaterni(B,D)),k23_quaterni(C,D)) ) ) ) ) )).
fof(t64_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ( k13_quaterni(k25_quaterni(A,k27_quaterni(A))) = k5_numbers & k14_quaterni(k25_quaterni(A,k27_quaterni(A))) = k3_xcmplx_0(2,k14_quaterni(A)) & k15_quaterni(k25_quaterni(A,k27_quaterni(A))) = k3_xcmplx_0(2,k15_quaterni(A)) & k16_quaterni(k25_quaterni(A,k27_quaterni(A))) = k3_xcmplx_0(2,k16_quaterni(A)) ) ) )).
fof(t64_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B))))) => ! [E] : ( m1_rcomp_3(E,A,B,D) => ! [F] : ( 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),k3_seq_4(k7_partfun1(k9_setfam_1(k1_numbers),E,k1_nat_1(C,1)))) ) ) ) ) ) ) ) ) )).
fof(t64_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => k5_real_1(k4_real_1(k9_nat_1(k1_numbers,k5_real_3(B),k1_nat_1(A,1)),k9_nat_1(k1_numbers,k6_real_3(B),A)),k4_real_1(k9_nat_1(k1_numbers,k5_real_3(B),A),k9_nat_1(k1_numbers,k6_real_3(B),k1_nat_1(A,1)))) = k1_newton(k4_xcmplx_0(1),A) ) ) )).
fof(t64_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => r1_tarski(k10_xtuple_0(k5_relat_1(B,A)),k10_xtuple_0(B)) ) )).
fof(t64_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(t64_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ( v1_relat_1(B) & v10_rewrite1(B) ) => ( r12_rewrite1(A,B) => m2_rewrite1(B,A) ) ) ) )).
fof(t64_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(C))) => ! [G] : ( ( ~ 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] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t64_rfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ( ~ r2_hidden(C,A) <=> k1_funct_1(k7_rfunct_1(A,B),C) = k5_numbers ) ) ) )).
fof(t64_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( 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) ) ) ) )).
fof(t64_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v7_valued_0(A) => r2_funct_2(k4_ordinal1,k1_numbers,k3_rinfsup1(A),A) ) ) )).
fof(t64_rlaffin1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_rlvect_2(C,B) => ( ( v2_convex1(C,B) & k1_funct_1(C,A) = 1 ) => k3_rlvect_2(B,C) = k1_tarski(A) ) ) ) )).
fof(t64_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_rlsub_1(D,A) => ( r2_hidden(B,k3_rlsub_1(A,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r1_struct_0(D,E) & B = k5_algstr_0(A,C,E) ) ) ) ) ) ) )).
fof(t64_rlsub_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k4_lattices(A,C,B) = B ) => B = k5_lattices(A) ) ) ) )).
fof(t64_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_connsp_2(B,A,k4_struct_0(A)) => ? [C] : ( m1_connsp_2(C,A,k4_struct_0(A)) & v3_rltopsp1(C,A) & r1_tarski(C,B) ) ) ) )).
fof(t64_rlvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t64_rlvect_2,axiom,( ! [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) ) => ! [B] : ( 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) ) ) )).
fof(t64_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v2_vectsp_2(E,A) & m1_rmod_2(E,A,B) ) => ! [F] : ( ( v2_vectsp_2(F,A) & m1_rmod_2(F,A,B) ) => ( k3_rmod_2(A,B,D,E) = k3_rmod_2(A,B,C,F) => E = F ) ) ) ) ) ) ) )).
fof(t64_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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) ) ) )).
fof(t64_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m2_rusub_1(C,A,B) => ( v1_rlsub_1(C,A) <=> C = u1_struct_0(B) ) ) ) ) )).
fof(t64_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k14_rvsum_1(k2_finseq_2(A,B),k2_finseq_2(A,C)) = k2_finseq_2(A,k3_xcmplx_0(B,C)) ) ) ) )).
fof(t64_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,C) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,D) ) => ! [F] : ( v7_ordinal1(F) => ( r8_pboole(u1_struct_0(k1_scmfsa_2),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,E),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,C),F),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,E),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D),F)) & k3_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,E),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,E),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,C),F)) = k3_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,E),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,E),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D),F)) ) ) ) ) ) ) ) ) )).
fof(t64_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ( ( ~ r1_xxreal_0(k1_funct_1(C,B),k5_numbers) => k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k13_scmfsa_2(A,B),C),k4_struct_0(k1_scmfsa_2)) = A ) & ( r1_xxreal_0(k1_funct_1(C,B),k5_numbers) => k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k13_scmfsa_2(A,B),C),k4_struct_0(k1_scmfsa_2)) = k4_card_1(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,C)) ) & ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k13_scmfsa_2(A,B),C),D) = k1_funct_1(C,D) ) & ! [D] : ( m1_scmfsa_2(D) => r2_relset_1(k4_ordinal1,k4_numbers,k18_scmfsa_2(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k13_scmfsa_2(A,B),C),D),k18_scmfsa_2(C,D)) ) ) ) ) ) )).
fof(t64_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmpds_2)) ) => ~ v2_extpro_1(k11_scmpds_2(C,A,B),2,k1_scmpds_2) ) ) ) )).
fof(t64_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v3_scmpds_4(D) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_scmpds_2)) ) => ! [G] : ( v1_int_1(G) => ( ~ r1_xxreal_0(k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,E),G)),k5_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) ) ) ) ) ) ) ) ) )).
fof(t64_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( ( v9_scmyciel(B,A) & m1_subset_1(B,k1_zfmisc_1(k3_tarski(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ( v9_scmyciel(C,A) & m1_subset_1(C,k1_zfmisc_1(k3_tarski(A))) ) ) ) ) )).
fof(t64_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r3_semi_af1(A,B,C,B,C) ) ) ) )).
fof(t64_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => ! [D] : ( m2_finseq_2(D,k2_numbers,k12_seq_4(A)) => ( ( k13_seq_4(A,C,B) = k13_seq_4(A,D,B) | k13_seq_4(A,C,B) = k13_seq_4(A,B,D) ) => C = D ) ) ) ) ) )).
fof(t64_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v2_prob_1(B) => ( v3_kurato_0(B,A) & k4_kurato_0(A,B) = k3_prob_1(A,B) ) ) ) )).
fof(t64_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_kurato_0(C,A) => k3_kurato_0(A,k3_setlim_2(A,B,C)) = k7_subset_1(A,k3_kurato_0(A,B),k3_kurato_0(A,C)) ) ) ) )).
fof(t64_sf_mastr,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(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(k7_card_1(3),k1_scmfsa_2,B) = k5_memstr_0(k7_card_1(3),k1_scmfsa_2,C) ) => ( k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k2_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B)) = k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k2_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C)) & k5_relat_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B),k1_sf_mastr(A)) = k5_relat_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C),k1_sf_mastr(A)) & k5_relat_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B),k3_sf_mastr(A)) = k5_relat_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C),k3_sf_mastr(A)) ) ) ) ) ) )).
fof(t64_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t64_simplex0,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_simplex0(C,A) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => k2_struct_0(k11_simplex0(A,C,D,B)) = k2_struct_0(C) ) ) ) )).
fof(t64_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_fdiff_1(k22_sin_cos,A) & k1_fdiff_1(k22_sin_cos,A) = k1_funct_1(k22_sin_cos,A) ) ) )).
fof(t64_sin_cos6,axiom,( k3_relat_1(k1_sin_cos6,k5_relset_1(k1_numbers,k1_numbers,k16_sin_cos,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2)))) = k6_partfun1(k1_rcomp_1(k4_xcmplx_0(1),1)) )).
fof(t64_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( B = k3_xcmplx_0(k7_xcmplx_0(1,2),k2_xcmplx_0(k23_sin_cos(A),k23_sin_cos(k4_xcmplx_0(A)))) & r1_xxreal_0(1,B) & A != k3_power(k4_power,k2_xcmplx_0(B,k3_square_1(k6_xcmplx_0(k1_square_1(B),1)))) & A != k4_xcmplx_0(k3_power(k4_power,k2_xcmplx_0(B,k3_square_1(k6_xcmplx_0(k1_square_1(B),1))))) ) ) ) )).
fof(t64_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) => ( r1_xxreal_0(k7_xcmplx_0(k28_sin_cos,4),k4_sin_cos9(A)) & r1_xxreal_0(k4_sin_cos9(A),k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos)) ) ) ) )).
fof(t64_sincos10,axiom,( k3_relat_1(k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k4_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))),k4_sincos10) = k1_partfun2(k1_numbers,k4_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) )).
fof(t64_sprect_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t64_sprect_2,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( 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))) ) ) ) ) ) ) )).
fof(t64_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t64_stirl2_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k4_ordinal1)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ( v1_finset_1(k2_relset_1(A,D)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,B,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,B,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) ) => ! [H] : ( ( 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,B,C) & v2_stirl2_1(F,B,C) ) => ( G = H & r2_funct_2(B,C,E,F) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t64_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),D,k2_valuat_1(A,D)) => ! [F] : ( m2_funct_2(F,k3_qc_lang1(A),D,k2_valuat_1(A,D)) => ! [G] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t64_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t64_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v2_tdlat_3(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) )).
fof(t64_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_tex_3(B,A) & m1_pre_topc(B,A) ) => ? [C] : ( ~ 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) ) ) ) )).
fof(t64_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t64_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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] : ( ( 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)))) ) ) ) ) ) ) ) ) )).
fof(t64_topalg_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_borsuk_2(D,k15_euclid(A),B,C) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t64_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t64_topreal6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t64_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t64_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)) ) ) ) )).
fof(t64_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t64_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t64_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ( k12_trees_3(A) = k12_trees_3(B) => A = B ) ) ) )).
fof(t64_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t64_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v2_finseq_1(D) ) => ~ ( r1_tarski(C,A) & r1_tarski(D,B) & ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v2_finseq_1(E) ) => ~ ( E = k2_xboole_0(C,k61_valued_1(D,k3_finseq_1(A))) & k7_finseq_1(k15_finseq_1(C),k15_finseq_1(D)) = k15_finseq_1(E) ) ) ) ) ) ) ) )).
fof(t64_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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)) ) ) ) )).
fof(t64_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_vectsp_4(E,A,B) => ~ ( k3_vectsp_4(A,B,D,E) = k3_vectsp_4(A,B,C,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ~ ( r1_struct_0(E,F) & k3_rlvect_1(B,D,F) = C ) ) ) ) ) ) ) ) )).
fof(t64_waybel23,axiom,( ! [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] : ( ( v6_waybel23(B,A) & m1_waybel23(B,A) ) => ( v4_waybel_1(k3_waybel23(A,k5_yellow_0(A,B)),k1_yellow_1(k7_waybel_0(k5_yellow_0(A,B))),A) & v5_waybel_1(k5_waybel23(A,B),k1_yellow_1(k7_waybel_0(k5_yellow_0(A,B))),A) ) ) ) )).
fof(t64_waybel34,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( 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] : ( ( ~ v2_struct_0(D) & v4_yellow_0(D,A) & v6_yellow_0(D,A) & m1_yellow_0(D,A) ) => ! [E] : ( ( ~ v2_struct_0(E) & v4_yellow_0(E,B) & v6_yellow_0(E,B) & m1_yellow_0(E,B) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t64_waybel_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t64_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v5_waybel_1(k4_waybel_1(A,B),A,A) ) <=> ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t64_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( r1_tarski(A,C) & r1_tarski(B,D) & r1_xboole_0(C,D) ) => r1_xboole_0(A,B) ) )).
fof(t64_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k4_xboolean(A,k8_xboolean(B,C)) = k5_xboolean(k4_xboolean(A,k3_xboolean(B)),k4_xboolean(A,k3_xboolean(C))) ) ) ) )).
fof(t64_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(k2_xcmplx_0(A,A),2) = A ) )).
fof(t64_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(k5_numbers,C) ) => r1_xxreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) ) ) ) )).
fof(t64_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_tarski(k2_xxreal_1(C,D),k4_xxreal_1(A,B)) => ( r1_xxreal_0(D,C) | ( ~ r1_xxreal_0(C,A) & r1_xxreal_0(D,B) ) ) ) ) ) ) ) )).
fof(t64_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ( ! [C] : ( v1_xxreal_0(C) => ~ ( r2_hidden(C,B) & ! [D] : ( v1_xxreal_0(D) => ~ ( r2_hidden(D,A) & r1_xxreal_0(D,C) ) ) ) ) => r1_xxreal_0(k2_xxreal_2(A),k2_xxreal_2(B)) ) ) ) )).
fof(t64_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(C,D) & r1_xxreal_0(k1_xxreal_3(B,C),k1_xxreal_3(A,D)) ) ) ) ) ) )).
fof(t64_yellow10,axiom,( ! [A] : ( ( v5_orders_2(A) & v3_yellow_0(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t64_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t64_yellow_4,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t64_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_yellow_5(A,B,B) = k3_yellow_0(A) ) ) )).
fof(t64_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ( ( r3_zf_lang(A,B) & r3_zf_lang(B,C) ) => r3_zf_lang(A,C) ) ) ) ) )).
fof(t64_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => k2_zf_model(k11_zf_lang(A,B)) = k4_subset_1(k1_zf_lang,k2_zf_model(A),k2_zf_model(B)) ) ) )).
fof(t64_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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) ) )).
fof(t64_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_int_1(C) => ! [D] : ( m1_zmodul01(D,A) => ( r1_struct_0(D,B) => k5_zmodul01(A,k1_zmodul01(A,B,C),D) = u1_struct_0(D) ) ) ) ) ) )).
fof(t64_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( r1_struct_0(k33_zmodul02(B,C),A) <=> ? [D] : ( m2_zmodul02(D,B,C) & A = k21_zmodul02(B,D) ) ) ) ) )).
fof(t65_abcmiz_0,axiom,( ! [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) & l3_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A))) => ~ ( r6_abcmiz_0(A,B,C) & ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t65_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v6_abcmiz_1(B,A) & v8_abcmiz_1(B,A) & m1_abcmiz_1(B,A,k13_abcmiz_1(A)) ) => ? [C] : ( v2_abcmiz_1(C,A) & m1_subset_1(C,u4_struct_0(A)) & k2_msualg_1(A,C) = k13_abcmiz_1(A) & ? [D] : ( 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) ) ) ) ) )).
fof(t65_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_aff_4(C,A) & ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t65_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k2_afinsq_1(A)) <=> ~ r1_xxreal_0(k5_card_1(A),B) ) ) ) )).
fof(t65_afinsq_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( k1_funct_1(C,B) = A & r2_hidden(B,k9_xtuple_0(C)) ) => k2_xboole_0(k1_tarski(B),k8_relat_1(k5_relat_1(C,k6_subset_1(k9_xtuple_0(C),k1_tarski(B))),k1_tarski(A))) = k8_relat_1(C,k1_tarski(A)) ) ) )).
fof(t65_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( r10_analmetr(A,C,B) & r10_analmetr(A,D,B) ) => r9_analmetr(A,C,D) ) ) ) ) ) )).
fof(t65_aofa_000,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_freealg(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_freealg(k19_aofa_000,A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_freealg(k19_aofa_000,A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_freealg(k19_aofa_000,A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k7_freealg(k19_aofa_000,A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k7_freealg(k19_aofa_000,A))) => ! [G] : ( 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 ) ) ) ) ) ) ) ) ) )).
fof(t65_aofa_a00,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( l6_aofa_a00(C) => ! [D] : ( l6_aofa_a00(D) => ( ( u8_aofa_a00(C) = u8_aofa_a00(D) & r1_xxreal_0(3,k3_finseq_1(u7_aofa_a00(D))) & ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,3) ) => ( k1_funct_1(u1_msualg_1(C),k1_funct_1(u7_aofa_a00(C),E)) = k1_funct_1(u1_msualg_1(D),k1_funct_1(u7_aofa_a00(D),E)) & k1_funct_1(u2_msualg_1(C),k1_funct_1(u7_aofa_a00(C),E)) = k1_funct_1(u2_msualg_1(D),k1_funct_1(u7_aofa_a00(D),E)) ) ) ) & v16_aofa_a00(C) ) => v16_aofa_a00(D) ) ) ) ) )).
fof(t65_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( ( ~ v2_struct_0(F) & v2_unialg_1(F) & v3_unialg_1(F) & v4_unialg_1(F) & v3_aofa_000(F) & v4_aofa_000(F) & v5_aofa_000(F) & v6_aofa_000(F) & ~ v10_aofa_000(F) & v11_aofa_000(F) & v12_aofa_000(F) & l3_aofa_a00(F,A,C,u4_aofa_a00(A,B,C,E)) ) => ! [G] : ( ( v3_aofa_a01(G,A,B,C,u4_aofa_a00(A,B,C,E),u8_aofa_a00(A)) & m1_msafree4(G,u1_struct_0(A),u4_aofa_a00(A,B,C,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u8_aofa_a00(A))) ) => ! [H] : ( m2_subset_1(H,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => ! [I] : ( m1_aofa_000(I,F,k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E)),k14_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E),u8_aofa_a00(A),G,k2_aofa_a01(A,D))) => ( ( v11_aofa_a00(E,A,B,C,D) & r2_hidden(I,k20_aofa_a00(A,B,C,D,E,F,u8_aofa_a00(A),G,k2_aofa_a01(A,D))) ) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( ( v3_aofa_a01(K,A,B,C,u4_aofa_a00(A,B,C,E),J) & m1_msafree4(K,u1_struct_0(A),u4_aofa_a00(A,B,C,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),J)) ) => ! [L] : ( m1_subset_1(L,k1_funct_1(u3_msualg_1(A,C),J)) => ( k1_funct_1(k1_msafree4(u1_struct_0(A),k3_aofa_a01(A,B,C,E,G,D,F,I,H,k12_aofa_a00(A,C,u4_aofa_a00(A,B,C,E),F,J,K,L)),J),K) = k15_aofa_a00(A,B,C,D,J,L,H) & ! [M] : ( ( v3_aofa_a01(M,A,B,C,u4_aofa_a00(A,B,C,E),J) & m1_msafree4(M,u1_struct_0(A),u4_aofa_a00(A,B,C,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),J)) ) => ( M != K => k1_funct_1(k1_msafree4(u1_struct_0(A),k3_aofa_a01(A,B,C,E,G,D,F,I,H,k12_aofa_a00(A,C,u4_aofa_a00(A,B,C,E),F,J,K,L)),J),M) = k1_funct_1(k1_msafree4(u1_struct_0(A),H,J),M) ) ) & ! [M] : ( m1_subset_1(M,u1_struct_0(A)) => ( J != M => ! [N] : ( ( v3_aofa_a01(N,A,B,C,u4_aofa_a00(A,B,C,E),M) & m1_msafree4(N,u1_struct_0(A),u4_aofa_a00(A,B,C,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),M)) ) => k1_funct_1(k1_msafree4(u1_struct_0(A),k3_aofa_a01(A,B,C,E,G,D,F,I,H,k12_aofa_a00(A,C,u4_aofa_a00(A,B,C,E),F,J,K,L)),M),N) = k1_funct_1(k1_msafree4(u1_struct_0(A),H,M),N) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t65_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ( r3_arytm_3(A,k11_arytm_3) => A = k11_arytm_3 ) ) )).
fof(t65_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(4,A) & r1_xxreal_0(k5_series_1(2,A),k1_nat_1(k2_nat_1(2,A),3)) ) ) )).
fof(t65_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t65_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)))) ) ) ) ) )).
fof(t65_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t65_borsuk_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_topmetr)) => r2_hidden(k4_tarski(A,1),k7_borsuk_6) ) )).
fof(t65_borsuk_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( 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] : ( 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)) ) ) ) ) )).
fof(t65_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t65_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_eqrel_1(I,A) => ! [J] : ( m1_eqrel_1(J,A) => ! [K] : ( m1_subset_1(K,A) => ! [L] : ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t65_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)))) ) ) ) ) )).
fof(t65_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ( B = k8_margrel1 => k6_xboolean(A,B) = k8_margrel1 ) ) ) )).
fof(t65_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( 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)))))) ) ) ) ) ) )).
fof(t65_card_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => r1_ordinal1(k1_card_1(k7_relat_1(B,A)),k1_card_1(A)) ) )).
fof(t65_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => k7_card_3(k7_funcop_1(B,A)) = k3_card_2(A,B) ) ) )).
fof(t65_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( r2_hidden(B,k8_card_3(A)) => r2_hidden(k5_relat_1(B,C),k8_card_3(A)) ) ) ) )).
fof(t65_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) => k8_cat_1(A,B,C,D) = E ) ) ) ) ) ) )).
fof(t65_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u4_struct_0(C)) => ! [F] : ( 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)) ) ) ) ) ) )).
fof(t65_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( k2_cat_1(A,B,D) != k1_xboole_0 & k2_cat_1(A,C,D) != k1_xboole_0 & k2_cat_1(A,k20_cat_4(A,B,C),D) = k1_xboole_0 ) ) ) ) ) )).
fof(t65_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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) = k4_xcmplx_0(k7_partfun1(k2_numbers,C,B)) & k1_funct_1(k55_valued_1(A,k2_numbers,C),B) = k9_complex1(k7_partfun1(k2_numbers,C,B)) ) ) ) ) ) )).
fof(t65_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_chain_1(B,A) => ! [C] : ( m3_chain_1(C,A,B,A) => m3_chain_1(k3_subset_1(k4_chain_1(A,B,A),C),A,B,A) ) ) ) )).
fof(t65_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ( r5_glib_000(A,B) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(B)) => ( ( C = D & v3_chord(C,A) ) => v3_chord(D,B) ) ) ) ) ) ) )).
fof(t65_classes1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => ( r1_tarski(A,k4_classes1(B)) <=> r1_ordinal1(k6_classes1(A),B) ) ) )).
fof(t65_classes2,axiom,( k16_classes2(k1_xboole_0) = k13_classes2 )).
fof(t65_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_clvect_1(A,B,k4_clvect_1(A)) = u1_struct_0(A) ) ) )).
fof(t65_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clvect_2(B,A) => v2_clvect_2(B,A) ) ) ) )).
fof(t65_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( r2_hidden(B,k13_cohsp_1(A)) <=> ( r1_tarski(B,k3_tarski(A)) & ! [C] : ( m1_subset_1(C,A) => ? [D] : r1_tarski(k3_xboole_0(B,C),k1_tarski(D)) ) ) ) ) )).
fof(t65_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k9_complex1(k3_xcmplx_0(A,B)) = k3_xcmplx_0(k9_complex1(A),k9_complex1(B)) ) ) )).
fof(t65_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( A != k5_numbers & B != k5_numbers & k3_complex2(A,B) != k3_complex2(k4_xcmplx_0(A),k4_xcmplx_0(B)) ) ) ) )).
fof(t65_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => r1_xxreal_0(k6_xcmplx_0(k9_complex1(A),k9_complex1(B)),k9_complex1(k5_algstr_0(k1_complfld,A,B))) ) ) )).
fof(t65_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => k8_complsp2(k7_seq_4(A,B),k7_seq_4(A,B)) = k2_xcmplx_0(k2_xcmplx_0(k8_complsp2(A,A),k3_xcmplx_0(2,k3_complex1(k8_complsp2(A,B)))),k8_complsp2(B,B)) ) ) ) )).
fof(t65_comput_1,axiom,( v6_comput_1(k2_comput_1(k4_ordinal1)) )).
fof(t65_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( v1_xcmplx_0(B) => ( ! [C] : ( v7_ordinal1(C) => k9_nat_1(k2_numbers,A,k1_nat_1(C,1)) = k3_xcmplx_0(B,k9_nat_1(k2_numbers,A,C)) ) => ( r1_xxreal_0(1,k9_complex1(B)) | ( v1_comseq_3(A) & k11_comseq_3(A) = k7_xcmplx_0(k9_nat_1(k2_numbers,A,k5_numbers),k6_xcmplx_0(k6_complex1,B)) ) ) ) ) ) )).
fof(t65_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ! [C] : ( 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) ) ) ) )).
fof(t65_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ! [E] : ( m2_subset_1(E,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t65_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),B,k5_bhsp_1(A,B,k4_struct_0(A))) ) ) )).
fof(t65_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k9_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),k18_sin_cos),A,B) = k7_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,2),k2_xcmplx_0(k3_xcmplx_0(k19_sin_cos(k7_xcmplx_0(k2_xcmplx_0(A,B),2)),k17_sin_cos(k7_xcmplx_0(k6_xcmplx_0(A,B),2))),k3_xcmplx_0(k19_sin_cos(k7_xcmplx_0(k3_xcmplx_0(3,k2_xcmplx_0(A,B)),2)),k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(3,k6_xcmplx_0(A,B)),2))))),k6_xcmplx_0(A,B)) ) ) )).
fof(t65_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k7_xcmplx_0(1,k19_sin_cos(D)) ) => ( A = B | k19_sin_cos(A) = k5_numbers | k19_sin_cos(B) = k5_numbers | k9_diff_1(C,A,B) = k7_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(2,k6_xcmplx_0(k19_sin_cos(B),k19_sin_cos(A))),k2_xcmplx_0(k19_sin_cos(k2_xcmplx_0(A,B)),k19_sin_cos(k6_xcmplx_0(A,B)))),k6_xcmplx_0(A,B)) ) ) ) ) ) )).
fof(t65_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( 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)),k11_cat_2(k2_oppcat_1(B),B,k11_ens_1(A),k25_ens_1(A,B),C),k24_ens_1(A,B,C)) ) ) ) ) )).
fof(t65_entropy1,axiom,( ! [A] : ( ( v1_matrprob(A) & m2_finseq_1(A,k1_numbers) ) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(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)) = k2_xcmplx_0(k6_entropy1(A),k18_rvsum_1(k14_rvsum_1(A,k8_entropy1(B)))) ) ) ) )).
fof(t65_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_enumset1(A,B,C,D) = k2_enumset1(B,A,C,D) )).
fof(t65_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_eqrel_1(B,A) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t65_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => k22_rvsum_1(k8_euclid(3,B,C),A) = k6_xcmplx_0(k22_rvsum_1(B,A),k22_rvsum_1(C,A)) ) ) ) )).
fof(t65_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t65_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v5_relat_1(C,u1_struct_0(B)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_exchsort(C) ) => ! [D] : ( m1_subset_1(D,k9_xtuple_0(C)) => ! [E] : ( m1_subset_1(E,k9_xtuple_0(C)) => ! [F] : ( m1_subset_1(F,k9_xtuple_0(C)) => ( ( r2_hidden(E,F) & A = k5_exchsort(k9_xtuple_0(C),k9_xtuple_0(C),k6_partfun1(k9_xtuple_0(C)),D,E) ) => ( k1_binop_1(k7_exchsort(B,C,D,E),D,F) = k4_tarski(k1_funct_1(A,D),k1_funct_1(A,F)) & k1_binop_1(k7_exchsort(B,C,D,E),E,F) = k4_tarski(k1_funct_1(A,E),k1_funct_1(A,F)) ) ) ) ) ) ) ) ) )).
fof(t65_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( C != k4_tarski(k10_finseq_1(A,B),k2_facirc_1) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k8_facirc_1(A,B,C,k2_facirc_1),k10_facirc_1(A,B,C,k2_facirc_1)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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(k8_facirc_1(A,B,C,k2_facirc_1),k10_facirc_1(A,B,C,k2_facirc_1),k5_facirc_1(k8_facirc_1(A,B,C,k2_facirc_1),k10_facirc_1(A,B,C,k2_facirc_1),D,2),k9_facirc_1(A,B,C,k2_facirc_1)) = k1_binarith(k1_binarith(E,F),G) ) ) ) ) ) ) )).
fof(t65_fdiff_11,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => ( ~ r1_xxreal_0(k1_funct_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A)),C),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A)),C)) ) ) ) ) => ( r2_hidden(k5_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] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_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) = k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,C),k1_funct_1(k1_sin_cos9,k7_xcmplx_0(1,C))),k7_xcmplx_0(k1_square_1(C),k2_xcmplx_0(1,k1_square_1(C)))) ) ) ) ) ) ) ) )).
fof(t65_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t65_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(t65_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( 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_xcmplx_0(k3_finseq_1(A),C)) = k1_funct_1(B,C) ) ) ) ) )).
fof(t65_finseq_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t65_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( k10_xtuple_0(k1_finseq_3(A,B)) = k10_xtuple_0(A) => r1_xboole_0(B,k10_xtuple_0(A)) ) ) )).
fof(t65_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(B),k1_card_1(A)) & B != k1_xboole_0 & ! [D] : ! [E] : ~ ( r2_hidden(D,A) & r2_hidden(E,A) & D != E & k1_funct_1(C,D) = k1_funct_1(C,E) ) ) ) )).
fof(t65_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t65_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ( r2_hidden(B,k6_subset_1(k10_xtuple_0(D),k10_xtuple_0(C))) => k2_finseq_5(A,k8_finseq_1(A,C,D),B) = k2_finseq_5(A,D,B) ) ) ) ) ) )).
fof(t65_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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) ) ) ) ) ) ) )).
fof(t65_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( v7_ordinal1(C) => r1_tarski(k7_flang_1(A,k8_flang_1(A,B),C),k8_flang_1(A,B)) ) ) )).
fof(t65_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( 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))) ) ) ) ) ) )).
fof(t65_flang_3,axiom,( ! [A] : ! [B] : ( 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) ) ) )).
fof(t65_fomodel0,axiom,( ! [A] : ( v1_cohsp_1(A) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k3_tarski(A))) ) => ? [C] : ( r2_hidden(C,A) & r1_tarski(B,C) ) ) ) )).
fof(t65_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & v8_struct_0(C) & v7_fsm_1(C,A,B) & l2_fsm_1(C,A,B) ) => ! [D] : ( ( ~ 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)) ) ) ) ) ) )).
fof(t65_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( ( 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)) ) ) ) ) ) )).
fof(t65_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) ) )).
fof(t65_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) ) )).
fof(t65_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( 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)) ) ) ) )).
fof(t65_funct_4,axiom,( ! [A] : ! [B] : ! [C] : k4_funct_4(A,B,C,C) = k7_funcop_1(k2_tarski(A,B),C) )).
fof(t65_funct_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,B) => k2_binop_1(A,B,C,k13_funct_5(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) ) ) ) ) ) ) )).
fof(t65_funct_7,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_funct_7(B,A) => ( B != k1_xboole_0 => ( k5_funct_7(B) = k1_funct_1(A,1) & r1_tarski(k6_funct_7(B),k1_funct_1(A,k3_finseq_1(A))) ) ) ) ) )).
fof(t65_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => r2_funct_8(A,k1_numbers,k1_numbers,k16_sin_cos) ) )).
fof(t65_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,k9_fvaluat1(A,B,C)) <=> ( r2_hidden(D,C) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(E,C) => r1_xxreal_0(k3_funct_2(u1_struct_0(A),k6_numbers,B,D),k3_funct_2(u1_struct_0(A),k6_numbers,B,E)) ) ) ) ) ) ) ) ) ) )).
fof(t65_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [D] : ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t65_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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) ) )).
fof(t65_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ! [D] : ! [E] : ~ ( r2_hidden(C,k28_glib_000(A,B)) & r1_glib_000(A,D,E,C) & B != D & B != E ) ) ) )).
fof(t65_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => r1_xxreal_0(1,k3_finseq_1(k11_glib_001(A,B))) ) ) )).
fof(t65_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(1,A) ) => ( r1_xxreal_0(k1_matrix_0(C),B) | r1_xxreal_0(k3_finseq_1(C),k1_nat_1(A,1)) | r1_tarski(k1_rltopsp1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),k1_nat_1(B,1))),k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,2),k1_nat_1(B,1))),k7_xcmplx_0(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,k1_nat_1(A,1),B))),k1_tarski(k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),k1_nat_1(B,1))),k7_xcmplx_0(1,2))))) ) ) ) ) ) )).
fof(t65_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t65_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => m1_group_2(k6_group_2(A),B) ) ) )).
fof(t65_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_group_2(C,A) => ( v8_struct_0(C) <=> v8_struct_0(k6_group_3(A,C,B)) ) ) ) ) )).
fof(t65_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => m1_group_2(k10_group_2(A,B,C),k8_group_4(A,B,C)) ) ) ) )).
fof(t65_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_group_2(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t65_group_6,axiom,( ! [A] : ( ( ~ 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)))) ) )).
fof(t65_group_9,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( m2_finseq_1(D,A) => ! [E] : ( 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) ) ) ) ) )).
fof(t65_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k6_vectsp10(k1_complfld,A,k13_bilinear(k1_complfld,A,A,B)))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k6_vectsp10(k1_complfld,A,k13_bilinear(k1_complfld,A,A,B)))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t65_hfdiff_1,axiom,( ! [A] : ( ( 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,k18_sin_cos,k16_sin_cos),A),k4_xcmplx_0(8))) ) )).
fof(t65_ideal_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t65_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(B,A) => ( r1_xxreal_0(k2_xcmplx_0(k1_int_1(B),1),A) | k1_int_1(A) = k1_int_1(B) ) ) ) ) )).
fof(t65_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,B) & ! [C] : ( v1_xreal_0(C) => ~ ( r2_hidden(C,B) & r1_xxreal_0(k1_funct_1(k16_sin_cos,C),k5_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(k27_sin_cos) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k27_sin_cos,A)) ) => k2_integra5(A,k27_sin_cos) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k3_taylor_1),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k3_taylor_1),k3_seq_4(A))) ) ) ) )).
fof(t65_integra8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( ( B = k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k3_square_1(2),2)),k7_xcmplx_0(k3_square_1(2),2)) & k9_xtuple_0(k2_fdiff_1(k3_sin_cos6,k2_rcomp_1(k4_xcmplx_0(1),1))) = k9_xtuple_0(A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,k2_rcomp_1(k4_xcmplx_0(1),1)) & k1_funct_1(A,C) = k4_xcmplx_0(k7_xcmplx_0(1,k3_square_1(k6_xcmplx_0(1,k1_square_1(C))))) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,A,B)) ) => k2_integra5(B,A) = k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)) ) ) ) )).
fof(t65_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v3_rcomp_1(E) & m1_subset_1(E,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,E) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => ( k1_funct_1(C,F) = k6_xcmplx_0(A,F) & ~ r1_xxreal_0(k1_funct_1(C,F),k5_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(k7_xcmplx_0(3,2))),k4_xcmplx_0(k7_xcmplx_0(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(k7_xcmplx_0(3,2))),k4_xcmplx_0(k7_xcmplx_0(2,3)))) = k1_relset_1(k1_numbers,D) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => k1_funct_1(D,F) = k6_prepower(k6_xcmplx_0(A,F),k7_xcmplx_0(1,2)) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,D,B)) ) => k2_integra5(B,D) = k6_xcmplx_0(k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(k7_xcmplx_0(3,2))),k4_xcmplx_0(k7_xcmplx_0(2,3))),k2_seq_4(B)),k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(k7_xcmplx_0(3,2))),k4_xcmplx_0(k7_xcmplx_0(2,3))),k3_seq_4(B))) ) ) ) ) ) ) )).
fof(t65_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m2_interva1(B,A) => ! [C] : ( m2_interva1(C,A) => ! [D] : ( 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))) ) ) ) ) )).
fof(t65_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(t65_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(2),B)))) => ! [D] : ( ( 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,k4_xcmplx_0(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)) ) ) ) ) ) ) )).
fof(t65_jgraph_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(k15_euclid(2))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k15_euclid(2))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k15_euclid(2))) => ! [J] : ( m1_subset_1(J,u1_struct_0(k15_euclid(2))) => ~ ( v3_tops_2(F,k15_euclid(2),k15_euclid(2)) & ! [K] : ( 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(k5_numbers,k17_euclid(G)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(G)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(H)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(H)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(I)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(I)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(J)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(J)) & r1_jordan6(E,G,H) & r1_jordan6(E,H,I) & r1_jordan6(E,I,J) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t65_jgraph_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(k5_topmetr)) => ! [H] : ( 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(k7_xcmplx_0(2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(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(k4_xcmplx_0(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))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t65_jordan,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( ( v1_xreal_0(D) & v2_xxreal_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)) ) ) ) ) ) )).
fof(t65_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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)))) ) => k2_xcmplx_0(k7_pscomp_1(k3_topreal1(2,k2_jordan9(C,B))),k9_pscomp_1(k3_topreal1(2,k2_jordan9(C,B)))) = k2_xcmplx_0(k7_pscomp_1(k3_topreal1(2,k2_jordan9(C,A))),k9_pscomp_1(k3_topreal1(2,k2_jordan9(C,A)))) ) ) ) )).
fof(t65_jordan1j,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) )).
fof(t65_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ( v3_pre_topc(B,k15_euclid(A)) => v1_connsp_2(k1_pre_topc(k15_euclid(A),B)) ) ) ) )).
fof(t65_jordan6,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => k17_euclid(k11_jordan6(A)) = k7_xcmplx_0(k2_xcmplx_0(k6_pscomp_1(A),k8_pscomp_1(A)),2) ) )).
fof(t65_lattice2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k5_finsub_1(A)) => ! [C] : ( ( ~ v2_struct_0(C) & v10_lattices(C) & v11_lattices(C) & v13_lattices(C) & l3_lattices(C) ) => ! [D] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(C)) => ( ! [G] : ( m1_subset_1(G,A) => ( r2_hidden(G,B) => k3_funct_2(A,u1_struct_0(C),E,G) = k4_lattices(C,F,k3_funct_2(A,u1_struct_0(C),D,G)) ) ) => k4_lattices(C,F,k2_lattice2(A,C,B,D)) = k2_lattice2(A,C,B,E) ) ) ) ) ) ) ) )).
fof(t65_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( 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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),k23_lexbfs(A,k26_lexbfs(A),B)))) = B ) ) ) )).
fof(t65_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,B) & r2_hidden(C,k1_relset_1(k1_numbers,A)) ) ) => ( ! [B] : ( v1_xreal_0(B) => ~ ( 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) ) ) ) )).
fof(t65_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r4_limfunc2(C,A) & r4_limfunc2(D,A) & k2_limfunc2(C,A) = k2_limfunc2(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(E,F) & ~ r1_xxreal_0(F,A) & r2_hidden(F,k1_relset_1(k1_numbers,B)) ) ) ) ) ) => ( ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(A,k2_xcmplx_0(A,E)))) => ( r1_xxreal_0(k1_funct_1(C,F),k1_funct_1(B,F)) & r1_xxreal_0(k1_funct_1(B,F),k1_funct_1(D,F)) ) ) ) & ( ( r1_tarski(k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,C),k2_rcomp_1(A,k2_xcmplx_0(A,E))),k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,D),k2_rcomp_1(A,k2_xcmplx_0(A,E)))) & r1_tarski(k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(A,k2_xcmplx_0(A,E))),k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,C),k2_rcomp_1(A,k2_xcmplx_0(A,E)))) ) | ( r1_tarski(k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,D),k2_rcomp_1(A,k2_xcmplx_0(A,E))),k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,C),k2_rcomp_1(A,k2_xcmplx_0(A,E)))) & r1_tarski(k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(A,k2_xcmplx_0(A,E))),k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,D),k2_rcomp_1(A,k2_xcmplx_0(A,E)))) ) ) ) ) | ( r4_limfunc2(B,A) & k2_limfunc2(B,A) = k2_limfunc2(C,A) ) ) ) ) ) ) ) )).
fof(t65_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k3_limfunc1(C))) & r1_xxreal_0(k4_limfunc1(A),k1_funct_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)) ) ) ) ) ) )).
fof(t65_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t65_mathmorp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) => ( A != k5_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)) ) ) ) ) ) )).
fof(t65_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( r2_matrix10(k2_matrix10(A,C),B) => r2_matrix10(k2_matrix10(A,B),C) ) ) ) ) )).
fof(t65_matrix13,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ! [E] : ( ( v1_finset_1(E) & v1_setfam_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ~ ( 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] : ( ( v1_finset_1(F) & v1_setfam_1(F) & m1_subset_1(F,k1_zfmisc_1(k4_ordinal1)) ) => ~ ( 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) ) ) ) ) ) ) ) ) )).
fof(t65_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(C),A,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(C))) ) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ( r2_hidden(G,k2_finseq_1(A)) => ( r1_xxreal_0(B,k5_numbers) | ( 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_0(E),C,k7_matrix_0(u1_struct_0(C),E,F),k10_fvsum_1(k1_matrix_0(E),C,k7_matrix_0(u1_struct_0(C),E,G),D)))) ) ) ) ) ) ) ) ) ) )).
fof(t65_matrix16,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t65_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(k1_matrix_0(B),1) & r2_hidden(C,k2_finseq_1(k1_matrix_0(B))) & v3_relat_1(k16_matrix_0(C,A,B)) ) ) ) ) )).
fof(t65_matrixj1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t65_matrixr1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ( k3_finseq_1(C) = B => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(B,k5_numbers) | k11_matrixr1(k8_matrixr1(A,B),C) = k5_euclid(A) ) ) ) ) ) )).
fof(t65_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(A,k5_numbers) => k3_matrixr1(k8_matrixr1(A,B),k8_matrixr1(A,B)) = k8_matrixr1(A,B) ) ) ) )).
fof(t65_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( r2_hidden(k6_xtuple_0(A,B,C,D),k4_zfmisc_1(E,F,G,H)) <=> ( r2_hidden(A,E) & r2_hidden(B,F) & r2_hidden(C,G) & r2_hidden(D,H) ) ) )).
fof(t65_measure6,axiom,( ! [A] : ! [B] : ! [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))) ) => k7_relset_1(A,k1_numbers,k32_valued_1(A,k1_numbers,C),B) = k3_measure6(k7_relset_1(A,k1_numbers,C,B)) ) )).
fof(t65_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => k11_member_1(A,B) = a_2_3_member_1(A,B) ) ) )).
fof(t65_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( 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) ) ) ) ) )).
fof(t65_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_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,k6_numbers,D,k1_relset_1(A,k3_mesfunc1(A,D,E)))),k5_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,E,k1_relset_1(A,k3_mesfunc1(A,D,E))))) ) ) ) ) ) ) ) )).
fof(t65_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k5_numbers,C) => ( r2_relset_1(A,k1_numbers,k18_rfunct_3(A,k26_valued_1(A,k1_numbers,B,k4_xcmplx_0(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,k4_xcmplx_0(C))),k26_valued_1(A,k1_numbers,k18_rfunct_3(A,B),C)) ) ) ) ) ) )).
fof(t65_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( 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) ) ) )).
fof(t65_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t65_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ~ ( 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) ) ) )).
fof(t65_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( ( r1_nat_d(A,B) & ~ v1_moebius1(A) ) <=> r1_nat_d(A,k6_moebius1(B)) ) ) ) )).
fof(t65_monoid_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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 ) ) ) ) )).
fof(t65_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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_msafree4(B,u1_struct_0(A)) ) => ! [C] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( m1_subset_1(E,k3_msualg_1(A,D,C)) => ! [F] : ( m1_subset_1(F,k3_msualg_1(A,D,k1_msafree3(A,B))) => ( F = E => k5_msualg_3(A,k1_msafree3(A,B),C,D,k4_msafree4(A,B,C),F) = E ) ) ) ) ) ) ) )).
fof(t65_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_int_1(B) => k5_int_1(k5_int_1(B,A),A) = k5_int_1(B,A) ) ) )).
fof(t65_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ! [D] : ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) )).
fof(t65_newton,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(B,k5_int_1(A,B)) ) ) ) )).
fof(t65_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t65_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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) ) ) )).
fof(t65_orders_1,axiom,( ! [A] : ~ ( A != k1_xboole_0 & ! [B] : ~ ( r1_tarski(B,A) & v6_ordinal1(B) & ! [C] : ~ ( r2_hidden(C,A) & ! [D] : ( r2_hidden(D,B) => r1_tarski(D,C) ) ) ) & ! [B] : ~ ( r2_hidden(B,A) & ! [C] : ~ ( r2_hidden(C,A) & C != B & r1_tarski(B,C) ) ) ) )).
fof(t65_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => A = k10_ordinal2(k11_ordinal2(k6_ordinal3(A,B),B),k7_ordinal3(A,B)) ) ) )).
fof(t65_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(k5_numbers,B) => v6_ordinal5(k5_afinsq_1(k11_ordinal2(B,k12_ordinal2(k4_ordinal1,A)))) ) ) ) )).
fof(t65_ordinal6,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_xboole_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes2(B) ) => ( ( r2_hidden(A,B) & ! [C] : ( 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)))) ) ) ) ) )).
fof(t65_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => r1_partfun1(k3_partfun1(C,A,B),C) ) )).
fof(t65_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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) ) ) )).
fof(t65_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( ( 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) & k10_pdiff_1(3,2,k26_valued_1(k1_euclid(3),k1_numbers,k1_pdiff_3(3,3,C),A),B) = k3_xcmplx_0(A,k8_pdiff_5(C,B)) ) ) ) ) ) )).
fof(t65_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( ( 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] : ( 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) = k2_xcmplx_0(k10_pdiff_1(A,B,D,F),k10_pdiff_1(A,B,E,F)) ) ) ) ) ) ) ) ) ) )).
fof(t65_pepin,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(A,1) & r1_xxreal_0(k1_newton(A,B),1) ) ) ) )).
fof(t65_polyform,axiom,( ! [A] : ( ( 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))) ) )).
fof(t65_polynom5,axiom,( 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))) )).
fof(t65_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => k20_pre_poly(A,k16_pre_poly(A)) = k3_pre_poly(k15_pre_poly(A),k16_pre_poly(A)) ) )).
fof(t65_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) & ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(1,k4_prepower(A,B)) ) ) ) )).
fof(t65_prob_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t65_pscomp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k3_funct_2(u1_struct_0(k15_euclid(2)),k1_numbers,k5_pscomp_1,k19_euclid(A,B)) = B & k3_funct_2(u1_struct_0(k15_euclid(2)),k1_numbers,k4_pscomp_1,k19_euclid(A,B)) = A ) ) ) )).
fof(t65_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t65_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_subset_1(D,k6_qc_lang1(A),k8_qc_lang1(A,C)) => ! [E] : ( ( v3_card_1(E,C) & m2_finseq_1(E,k2_qc_lang1(A)) ) => ~ r3_qc_lang2(A,B,k10_qc_lang1(A,D,E)) ) ) ) ) ) )).
fof(t65_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => k6_qc_lang3(A,k13_qc_lang1(A,B)) = k6_qc_lang3(A,B) ) ) )).
fof(t65_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => ! [D] : ( v1_quaterni(D) => k23_quaterni(k22_quaterni(k25_quaterni(A,B),C),D) = k22_quaterni(k25_quaterni(k23_quaterni(A,D),k23_quaterni(B,D)),k23_quaterni(C,D)) ) ) ) ) )).
fof(t65_quaterni,axiom,( k28_quaterni(k17_quaterni) = k5_numbers )).
fof(t65_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B))))) => ! [D] : ( m1_rcomp_3(D,A,B,C) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t65_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,k6_real_3(B),C) != k5_numbers ) => k5_real_1(k6_real_1(k9_nat_1(k1_numbers,k5_real_3(B),k1_nat_1(A,1)),k9_nat_1(k1_numbers,k6_real_3(B),k1_nat_1(A,1))),k6_real_1(k9_nat_1(k1_numbers,k5_real_3(B),A),k9_nat_1(k1_numbers,k6_real_3(B),A))) = k7_xcmplx_0(k1_newton(k4_xcmplx_0(1),A),k4_real_1(k9_nat_1(k1_numbers,k6_real_3(B),k1_nat_1(A,1)),k9_nat_1(k1_numbers,k6_real_3(B),A))) ) ) ) )).
fof(t65_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => k5_relat_1(k5_relat_1(C,A),B) = k5_relat_1(C,k3_xboole_0(A,B)) ) )).
fof(t65_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( m2_rewrite1(B,A) => ! [C] : ! [D] : ( r2_rewrite1(A,C,D) <=> k2_rewrite1(B,C) = k2_rewrite1(B,D) ) ) ) )).
fof(t65_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ 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] : ( m1_rewrite1(D,k1_rewrite3(A,B,C)) => ! [E] : ( 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))) ) ) ) ) ) ) ) )).
fof(t65_rfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ( r2_hidden(C,k6_subset_1(B,A)) <=> k1_funct_1(k7_rfunct_1(A,B),C) = k5_numbers ) ) ) )).
fof(t65_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ! [D] : ( ( 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(k7_finseq_1(k20_rfunct_3(A,D,k6_subset_1(C,k1_tarski(B))),k9_finseq_1(k1_funct_1(D,B))),k2_partfun1(A,k1_numbers,D,C)) ) ) ) ) )).
fof(t65_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v7_valued_0(B) & v1_seq_2(B) ) => r1_xxreal_0(k1_funct_1(B,A),k3_funct_2(k4_ordinal1,k1_numbers,k4_rinfsup1(B),k1_nat_1(A,1))) ) ) ) )).
fof(t65_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k3_convex1(A,B),k4_rlaffin1(A,B)) ) ) )).
fof(t65_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_rlsub_1(D,A) => ( ? [E] : ( 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)) ) ) ) ) ) )).
fof(t65_rlsub_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_lattices(A,C,B) = B ) => B = k6_lattices(A) ) ) ) )).
fof(t65_rltopsp1,axiom,( ! [A] : ( ( ~ 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] : ( m1_connsp_2(B,A,k4_struct_0(A)) => ~ ( v1_convex1(B,A) & ! [C] : ( m1_connsp_2(C,A,k4_struct_0(A)) => ~ ( v3_rltopsp1(C,A) & v1_convex1(C,A) & r1_tarski(C,B) ) ) ) ) ) )).
fof(t65_rlvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t65_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( 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) ) ) ) )).
fof(t65_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_rmod_2(D,A,B) => ? [E] : ( m2_rmod_2(E,A,B,D) & r2_hidden(C,E) ) ) ) ) ) )).
fof(t65_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t65_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_bhsp_1(B) & m1_rusub_1(B,A) ) => ! [C] : ( ( v1_bhsp_1(C) & m1_rusub_1(C,A) ) => ! [D] : ( m2_rusub_1(D,A,B) => ! [E] : ( m2_rusub_1(E,A,C) => ( D = E => B = C ) ) ) ) ) ) )).
fof(t65_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t65_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,C) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,D) ) => ( k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,E),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,C)) = k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,E),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D)) & r8_pboole(u1_struct_0(k1_scmfsa_2),k6_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,E),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,C)),k6_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,E),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,D))) ) ) ) ) ) ) ) )).
fof(t65_scmfsa_2,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ( k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k14_scmfsa_2(C,B,A),D),k4_struct_0(k1_scmfsa_2)) = k4_card_1(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,D)) & ? [E] : ( v7_ordinal1(E) & E = k1_int_2(k1_funct_1(D,B)) & k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k14_scmfsa_2(C,B,A),D),C) = k7_partfun1(k4_numbers,k18_scmfsa_2(D,A),E) ) & ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmfsa_2)) ) => ( E != C => k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k14_scmfsa_2(C,B,A),D),E) = k1_funct_1(D,E) ) ) & ! [E] : ( m1_scmfsa_2(E) => r2_relset_1(k4_ordinal1,k4_numbers,k18_scmfsa_2(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k14_scmfsa_2(C,B,A),D),E),k18_scmfsa_2(D,E)) ) ) ) ) ) ) )).
fof(t65_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmpds_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ~ v2_extpro_1(k12_scmpds_2(C,D,A,B),2,k1_scmpds_2) ) ) ) ) )).
fof(t65_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_scmpds_2)) ) => ! [G] : ( v1_int_1(G) => ( r1_xxreal_0(k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,E),G)),k5_numbers) => k1_funct_1(k6_scmpds_4(k3_scmpds_6(E,G,C,D),B,A),F) = k1_funct_1(k6_scmpds_4(D,B,A),F) ) ) ) ) ) ) ) ) )).
fof(t65_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => v10_scmyciel(k10_eqrel_1(k3_tarski(A)),A) ) )).
fof(t65_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r3_semi_af1(A,F,G,B,C) & r3_semi_af1(A,F,G,D,E) ) => r3_semi_af1(A,B,C,D,E) ) ) ) ) ) ) ) ) )).
fof(t65_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => k16_seq_4(A,k13_seq_4(A,B,C)) = k13_seq_4(A,k16_seq_4(A,B),k16_seq_4(A,C)) ) ) ) )).
fof(t65_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_setlim_1(B,A) => v3_kurato_0(B,A) ) ) )).
fof(t65_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) ) ) ) )).
fof(t65_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t65_simplex0,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_simplex0(C,A) => ! [D] : ( m2_simplex0(D,A,C) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => m2_simplex0(k11_simplex0(A,D,E,B),A,k11_simplex0(A,C,E,B)) ) ) ) ) )).
fof(t65_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_fdiff_1(k22_sin_cos,k1_numbers) & k1_fdiff_1(k22_sin_cos,A) = k1_funct_1(k22_sin_cos,A) ) ) )).
fof(t65_sin_cos6,axiom,( 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(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2)))) = k6_partfun1(k1_rcomp_1(k4_xcmplx_0(1),1)) )).
fof(t65_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( B = k7_xcmplx_0(k6_xcmplx_0(k23_sin_cos(A),k23_sin_cos(k4_xcmplx_0(A))),k2_xcmplx_0(k23_sin_cos(A),k23_sin_cos(k4_xcmplx_0(A)))) => A = k3_xcmplx_0(k7_xcmplx_0(1,2),k3_power(k4_power,k7_xcmplx_0(k2_xcmplx_0(1,B),k6_xcmplx_0(1,B)))) ) ) ) )).
fof(t65_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ~ ( ~ r1_xxreal_0(k3_sin_cos9(A),k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4))) & ~ r1_xxreal_0(k7_xcmplx_0(k28_sin_cos,4),k3_sin_cos9(A)) ) ) ) )).
fof(t65_sincos10,axiom,( k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k3_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))),k1_sincos10) = k1_partfun2(k1_numbers,k3_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) )).
fof(t65_sprect_1,axiom,( ! [A] : ( ( ~ 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) ) )).
fof(t65_sprect_2,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( 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))) ) ) ) ) ) ) )).
fof(t65_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t65_stirl2_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k4_ordinal1)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ( v1_finset_1(k2_relset_1(A,C)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,B,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k2_relset_1(A,C),k2_relset_1(A,C)) & v3_funct_2(F,k2_relset_1(A,C),k2_relset_1(A,C)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k2_relset_1(A,C),k2_relset_1(A,C)))) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k2_relset_1(A,C),k2_relset_1(A,C)) & v3_funct_2(G,k2_relset_1(A,C),k2_relset_1(A,C)) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k2_relset_1(A,C),k2_relset_1(A,C)))) ) => ( ( C = k1_partfun1(B,A,k2_relset_1(A,C),k2_relset_1(A,C),D,F) & C = k1_partfun1(B,A,k2_relset_1(A,C),k2_relset_1(A,C),E,G) & k2_relset_1(A,C) = k2_relset_1(A,D) & k2_relset_1(A,C) = k2_relset_1(A,E) & v2_stirl2_1(D,B,A) & v2_stirl2_1(E,B,A) ) => ( r2_funct_2(k2_relset_1(A,C),k2_relset_1(A,C),F,G) & r2_funct_2(B,A,D,E) ) ) ) ) ) ) ) ) ) ) )).
fof(t65_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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))) ) ) ) )).
fof(t65_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)))) ) ) ) ) )).
fof(t65_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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) ) ) )).
fof(t65_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_tex_2(B,A) & v2_tex_3(B,A) & m1_pre_topc(B,A) ) => ? [C] : ( ~ v2_struct_0(C) & v1_pre_topc(C) & v4_tex_3(C,A) & m1_pre_topc(C,A) & r4_tsep_2(A,B,C) ) ) ) )).
fof(t65_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t65_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ( r2_hidden(F,u1_struct_0(D)) => k3_funct_2(u1_struct_0(C),u1_struct_0(B),E,F) = k1_funct_1(k3_tmap_1(A,B,C,D,E),F) ) ) ) ) ) ) ) ) )).
fof(t65_topalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t65_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t65_topreal6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t65_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) ) )).
fof(t65_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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))) ) ) ) )).
fof(t65_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t65_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t65_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => k4_trees_1(k12_trees_3(A),k14_trees_3(k5_numbers)) = A ) )).
fof(t65_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t65_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_valued_0(D) ) => ! [E] : ( ( 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)) ) ) ) ) )).
fof(t65_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_vectsp_4(E,A,B) => ~ ( k3_vectsp_4(A,B,D,E) = k3_vectsp_4(A,B,C,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ~ ( r1_struct_0(E,F) & k5_algstr_0(B,D,F) = C ) ) ) ) ) ) ) ) )).
fof(t65_waybel23,axiom,( ! [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] : ( ( 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) ) ) )).
fof(t65_waybel34,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( ~ v2_struct_0(D) & v4_yellow_0(D,A) & v6_waybel34(D,A) & m1_yellow_0(D,A) ) => ! [E] : ( ( ~ v2_struct_0(E) & v4_yellow_0(E,B) & v6_waybel34(E,B) & m1_yellow_0(E,B) ) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t65_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) => ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t65_waybel_1,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ( ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( r1_yellow_0(A,B) => ! [C] : ( 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) ) ) )).
fof(t65_xboole_1,axiom,( ! [A] : r1_xboole_0(A,k1_xboole_0) )).
fof(t65_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k8_xboolean(A,k7_xboolean(A,B)) = k3_xboolean(k4_xboolean(A,B)) ) ) )).
fof(t65_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(k7_xcmplx_0(A,2),k7_xcmplx_0(A,2)) = A ) )).
fof(t65_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(C,k5_numbers) ) => r1_xxreal_0(k3_xcmplx_0(B,C),k3_xcmplx_0(A,C)) ) ) ) ) )).
fof(t65_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_tarski(k3_xxreal_1(C,D),k4_xxreal_1(A,B)) => ( r1_xxreal_0(D,C) | ( r1_xxreal_0(A,C) & ~ r1_xxreal_0(B,D) ) ) ) ) ) ) ) )).
fof(t65_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( m1_xxreal_2(C,A) => ! [D] : ( m1_xxreal_2(D,B) => m1_xxreal_2(k3_xxreal_0(C,D),k3_xboole_0(A,B)) ) ) ) ) )).
fof(t65_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k1_xxreal_3(C,A),B) ) => r1_xxreal_0(C,B) ) ) ) ) )).
fof(t65_yellow10,axiom,( ! [A] : ( ( v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t65_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t65_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_yellow_5(A,B,k3_yellow_0(A)) = B ) ) )).
fof(t65_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ( ( r2_zf_lang(A,B) & r2_zf_lang(B,C) ) => r2_zf_lang(A,C) ) ) ) ) )).
fof(t65_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => k2_zf_model(k12_zf_lang(A,B)) = k4_subset_1(k1_zf_lang,k2_zf_model(A),k2_zf_model(B)) ) ) )).
fof(t65_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( k4_xboole_0(C,k2_tarski(A,B)) = k1_xboole_0 <=> ~ ( C != k1_xboole_0 & C != k1_tarski(A) & C != k1_tarski(B) & C != k2_tarski(A,B) ) ) )).
fof(t65_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_zmodul01(D,A) => ( r1_struct_0(D,B) <=> k5_zmodul01(A,C,D) = k5_zmodul01(A,k3_rlvect_1(A,C,B),D) ) ) ) ) ) )).
fof(t65_zmodul02,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( r2_hidden(A,C) => r1_struct_0(k33_zmodul02(B,C),A) ) ) ) )).
fof(t66_abcmiz_0,axiom,( ! [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) & l3_abcmiz_0(A) ) => r1_relset_1(u1_struct_0(A),u1_struct_0(A),k11_abcmiz_0(A),u1_orders_2(A)) ) )).
fof(t66_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_trees_4(B,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A)))),k34_abcmiz_1(A)) => ! [C] : ( ( 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)) ) ) ) ) ) )).
fof(t66_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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 ) ) ) ) ) )).
fof(t66_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) ) => ( k9_xtuple_0(A) = k9_xtuple_0(B) => v1_afinsq_1(B) ) ) ) )).
fof(t66_afinsq_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( k1_funct_1(C,B) != A => k8_relat_1(k5_relat_1(C,k6_subset_1(k9_xtuple_0(C),k1_tarski(B))),k1_tarski(A)) = k8_relat_1(C,k1_tarski(A)) ) ) )).
fof(t66_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r10_analmetr(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,B) & r2_hidden(D,C) ) ) ) ) ) ) )).
fof(t66_aofa_000,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_freealg(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_freealg(k19_aofa_000,A))) => ! [C] : ( 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) ) ) ) )).
fof(t66_aofa_a00,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( ~ v2_struct_0(C) & l6_aofa_a00(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & l6_aofa_a00(D) ) => ( ( r1_xxreal_0(1,A) & u8_aofa_a00(C) = u8_aofa_a00(D) & r1_xxreal_0(k2_xcmplx_0(A,6),k3_finseq_1(u7_aofa_a00(D))) & ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(A,E) & r1_xxreal_0(E,k2_xcmplx_0(A,6)) ) => ( k1_funct_1(u1_msualg_1(C),k1_funct_1(u7_aofa_a00(C),E)) = k1_funct_1(u1_msualg_1(D),k1_funct_1(u7_aofa_a00(D),E)) & k1_funct_1(u2_msualg_1(C),k1_funct_1(u7_aofa_a00(C),E)) = k1_funct_1(u2_msualg_1(D),k1_funct_1(u7_aofa_a00(D),E)) ) ) ) & v18_aofa_a00(C,A,B) ) => ( k1_funct_1(u7_aofa_a00(D),A) = k1_funct_1(u7_aofa_a00(D),k2_xcmplx_0(A,1)) | k1_funct_1(u7_aofa_a00(D),k2_xcmplx_0(A,3)) = k1_funct_1(u7_aofa_a00(D),k2_xcmplx_0(A,4)) | k1_funct_1(u7_aofa_a00(D),k2_xcmplx_0(A,3)) = k1_funct_1(u7_aofa_a00(D),k2_xcmplx_0(A,5)) | k1_funct_1(u7_aofa_a00(D),k2_xcmplx_0(A,4)) = k1_funct_1(u7_aofa_a00(D),k2_xcmplx_0(A,5)) | v18_aofa_a00(D,A,B) ) ) ) ) ) )).
fof(t66_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( ( ~ v2_struct_0(F) & v2_unialg_1(F) & v3_unialg_1(F) & v4_unialg_1(F) & v3_aofa_000(F) & v4_aofa_000(F) & v5_aofa_000(F) & v6_aofa_000(F) & ~ v10_aofa_000(F) & v11_aofa_000(F) & v12_aofa_000(F) & l3_aofa_a00(F,A,C,u4_aofa_a00(A,B,C,E)) ) => ! [G] : ( ( v19_aofa_a00(G,A) & m1_subset_1(G,u1_struct_0(A)) ) => ! [H] : ( ( v3_aofa_a01(H,A,B,C,u4_aofa_a00(A,B,C,E),u8_aofa_a00(A)) & m1_msafree4(H,u1_struct_0(A),u4_aofa_a00(A,B,C,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u8_aofa_a00(A))) ) => ! [I] : ( m1_subset_1(I,k1_funct_1(u3_msualg_1(A,C),G)) => ! [J] : ( m1_subset_1(J,k1_funct_1(u3_msualg_1(A,C),G)) => ! [K] : ( m2_subset_1(K,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => ! [L] : ( m1_aofa_000(L,F,k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E)),k14_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E),u8_aofa_a00(A),H,k2_aofa_a01(A,D))) => ( ( v11_aofa_a00(E,A,B,C,D) & r2_hidden(L,k20_aofa_a00(A,B,C,D,E,F,u8_aofa_a00(A),H,k2_aofa_a01(A,D))) ) => ( ( ~ r1_xxreal_0(k15_aofa_a00(A,B,C,D,G,J,K),k15_aofa_a00(A,B,C,D,G,I,K)) => r2_hidden(k3_aofa_a01(A,B,C,E,H,D,F,L,K,k6_aofa_a01(A,B,C,E,F,H,G,J,I)),k14_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E),u8_aofa_a00(A),H,k2_aofa_a01(A,D))) ) & ~ ( r2_hidden(k3_aofa_a01(A,B,C,E,H,D,F,L,K,k6_aofa_a01(A,B,C,E,F,H,G,J,I)),k14_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E),u8_aofa_a00(A),H,k2_aofa_a01(A,D))) & r1_xxreal_0(k15_aofa_a00(A,B,C,D,G,J,K),k15_aofa_a00(A,B,C,D,G,I,K)) ) & ( r1_xxreal_0(k15_aofa_a00(A,B,C,D,G,I,K),k15_aofa_a00(A,B,C,D,G,J,K)) => r2_hidden(k3_aofa_a01(A,B,C,E,H,D,F,L,K,k5_aofa_a01(A,B,C,E,F,H,G,I,J)),k14_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E),u8_aofa_a00(A),H,k2_aofa_a01(A,D))) ) & ( r2_hidden(k3_aofa_a01(A,B,C,E,H,D,F,L,K,k5_aofa_a01(A,B,C,E,F,H,G,I,J)),k14_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E),u8_aofa_a00(A),H,k2_aofa_a01(A,D))) => r1_xxreal_0(k15_aofa_a00(A,B,C,D,G,I,K),k15_aofa_a00(A,B,C,D,G,J,K)) ) & ! [M] : ( ( v3_aofa_a01(M,A,B,C,u4_aofa_a00(A,B,C,E),G) & m1_msafree4(M,u1_struct_0(A),u4_aofa_a00(A,B,C,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),G)) ) => ( k1_funct_1(k1_msafree4(u1_struct_0(A),k3_aofa_a01(A,B,C,E,H,D,F,L,K,k6_aofa_a01(A,B,C,E,F,H,G,I,J)),G),M) = k1_funct_1(k1_msafree4(u1_struct_0(A),K,G),M) & k1_funct_1(k1_msafree4(u1_struct_0(A),k3_aofa_a01(A,B,C,E,H,D,F,L,K,k5_aofa_a01(A,B,C,E,F,H,G,I,J)),G),M) = k1_funct_1(k1_msafree4(u1_struct_0(A),K,G),M) ) ) & ! [M] : ( ( v3_aofa_a01(M,A,B,C,u4_aofa_a00(A,B,C,E),u8_aofa_a00(A)) & m1_msafree4(M,u1_struct_0(A),u4_aofa_a00(A,B,C,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u8_aofa_a00(A))) ) => ( M != H => ( k1_funct_1(k1_msafree4(u1_struct_0(A),k3_aofa_a01(A,B,C,E,H,D,F,L,K,k6_aofa_a01(A,B,C,E,F,H,G,I,J)),u8_aofa_a00(A)),M) = k1_funct_1(k1_msafree4(u1_struct_0(A),K,u8_aofa_a00(A)),M) & k1_funct_1(k1_msafree4(u1_struct_0(A),k3_aofa_a01(A,B,C,E,H,D,F,L,K,k5_aofa_a01(A,B,C,E,F,H,G,I,J)),u8_aofa_a00(A)),M) = k1_funct_1(k1_msafree4(u1_struct_0(A),K,u8_aofa_a00(A)),M) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t66_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ( ( r3_arytm_3(A,B) & r3_arytm_3(B,A) ) => A = B ) ) ) )).
fof(t66_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(6,A) & r1_xxreal_0(k5_series_1(2,A),k1_square_1(k1_nat_1(A,1))) ) ) )).
fof(t66_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t66_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t66_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t66_borsuk_6,axiom,( r2_hidden(k4_tarski(k7_xcmplx_0(1,2),k5_numbers),k8_borsuk_6) & r2_hidden(k4_tarski(1,1),k8_borsuk_6) )).
fof(t66_borsuk_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( 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)) ) ) ) )).
fof(t66_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t66_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_eqrel_1(I,A) => ! [J] : ( m1_eqrel_1(J,A) => ! [K] : ( m1_subset_1(K,A) => ! [L] : ( 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))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t66_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)) ) ) ) ) )).
fof(t66_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ( k3_xboolean(A) = k8_margrel1 => k6_xboolean(A,B) = k8_margrel1 ) ) ) )).
fof(t66_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( 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)))) ) ) ) ) ) )).
fof(t66_card_1,axiom,( ! [A] : ! [B] : ~ ( r2_hidden(k1_card_1(A),k1_card_1(B)) & k6_subset_1(B,A) = k1_xboole_0 ) )).
fof(t66_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( r2_hidden(B,k8_card_3(A)) => r2_hidden(k5_relat_1(B,C),k8_card_3(k5_relat_1(A,C))) ) ) ) )).
fof(t66_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( 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,k8_cat_1(A,B,C,D)) ) ) ) ) )).
fof(t66_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t66_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t66_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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) = k5_xcmplx_0(k7_partfun1(k2_numbers,C,B)) ) ) ) ) )).
fof(t66_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_chain_1(C,B) => ! [D] : ( 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))) ) ) ) ) )).
fof(t66_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) ) => ! [C] : ( m2_glib_000(C,A,B,k21_glib_000(A,B)) => ! [D] : ( 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] : ( m1_subset_1(E,k6_glib_000(C)) => ( D = E => ( v3_chord(D,A) <=> v3_chord(E,C) ) ) ) ) ) ) ) ) )).
fof(t66_classes1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => ( r2_hidden(A,k4_classes1(B)) <=> r2_hidden(k6_classes1(A),B) ) ) )).
fof(t66_classes2,axiom,( ! [A] : ( v3_ordinal1(A) => k16_classes2(k1_ordinal1(A)) = k1_classes1(k16_classes2(A)) ) )).
fof(t66_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t66_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r1_clvect_2(A,B,B) ) ) )).
fof(t66_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => k3_tarski(k13_cohsp_1(A)) = k3_tarski(A) ) )).
fof(t66_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k9_complex1(k5_xcmplx_0(A)) = k5_xcmplx_0(k9_complex1(A)) ) )).
fof(t66_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k3_complex2(A,B) = k5_numbers => ( B = k5_numbers | k3_complex2(A,k4_xcmplx_0(B)) = k28_sin_cos ) ) ) ) )).
fof(t66_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => k9_complex1(k5_algstr_0(k1_complfld,A,B)) = k9_complex1(k5_algstr_0(k1_complfld,B,A)) ) ) )).
fof(t66_complsp2,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => k8_complsp2(k8_seq_4(A,B),k8_seq_4(A,B)) = k2_xcmplx_0(k6_xcmplx_0(k8_complsp2(A,A),k3_xcmplx_0(2,k3_complex1(k8_complsp2(A,B)))),k8_complsp2(B,B)) ) ) ) )).
fof(t66_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_series_1(A) => ( ! [C] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(C,D) & ~ r1_xxreal_0(k9_complex1(k9_nat_1(k2_numbers,B,D)),k9_nat_1(k1_numbers,A,D)) ) ) | v2_comseq_3(B) ) ) ) ) )).
fof(t66_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_convex4(B,A) => v2_convex4(B,A) ) ) ) )).
fof(t66_csspace,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => r2_funct_2(k4_ordinal1,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))) ) ) ) ) )).
fof(t66_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => 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,k18_sin_cos),k18_sin_cos),A),B) = k3_xcmplx_0(k7_xcmplx_0(1,2),k2_xcmplx_0(k3_xcmplx_0(k19_sin_cos(k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(2,B),A),2)),k17_sin_cos(k7_xcmplx_0(A,2))),k3_xcmplx_0(k19_sin_cos(k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(6,B),k3_xcmplx_0(3,A)),2)),k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(3,A),2))))) ) ) )).
fof(t66_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k7_xcmplx_0(1,k19_sin_cos(D)) ) => ( k19_sin_cos(B) = k5_numbers | k19_sin_cos(k2_xcmplx_0(B,A)) = k5_numbers | k1_funct_1(k3_diff_1(C,A),B) = k7_xcmplx_0(k3_xcmplx_0(2,k6_xcmplx_0(k19_sin_cos(B),k19_sin_cos(k2_xcmplx_0(B,A)))),k2_xcmplx_0(k19_sin_cos(k2_xcmplx_0(k3_xcmplx_0(2,B),A)),k19_sin_cos(A))) ) ) ) ) ) )).
fof(t66_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_enumset1(A,B,C,D) = k2_enumset1(B,A,D,C) )).
fof(t66_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_eqrel_1(B,A) ) => ! [C] : ( 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)) ) ) ) )).
fof(t66_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => k22_rvsum_1(k7_euclid(3,B,C),A) = k2_xcmplx_0(k22_rvsum_1(B,A),k22_rvsum_1(C,A)) ) ) ) )).
fof(t66_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t66_exchsort,axiom,( ! [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) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_exchsort(B) ) => ! [C] : ( m1_subset_1(C,k9_xtuple_0(B)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t66_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( C != k4_tarski(k10_finseq_1(A,B),k3_facirc_1) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k8_facirc_1(A,B,C,k3_facirc_1),k10_facirc_1(A,B,C,k3_facirc_1)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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(k8_facirc_1(A,B,C,k3_facirc_1),k10_facirc_1(A,B,C,k3_facirc_1),k5_facirc_1(k8_facirc_1(A,B,C,k3_facirc_1),k10_facirc_1(A,B,C,k3_facirc_1),D,2),k9_facirc_1(A,B,C,k3_facirc_1)) = k10_margrel1(k10_margrel1(E,F),G) ) ) ) ) ) ) )).
fof(t66_fdiff_11,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => ( ~ r1_xxreal_0(k1_funct_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A)),C),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A)),C)) ) ) ) ) => ( r2_hidden(k5_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] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_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) = k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,C),k1_funct_1(k2_sin_cos9,k7_xcmplx_0(1,C))),k7_xcmplx_0(k1_square_1(C),k2_xcmplx_0(1,k1_square_1(C)))) ) ) ) ) ) ) ) )).
fof(t66_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) ) ) ) )).
fof(t66_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( 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)) ) ) ) )).
fof(t66_finseq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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 ) ) ) )).
fof(t66_finseq_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t66_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( k1_finseq_3(A,B) = k1_xboole_0 <=> r1_tarski(k10_xtuple_0(A),B) ) ) )).
fof(t66_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ~ ( r2_hidden(D,B) & ! [E] : ~ ( r2_hidden(E,A) & k1_funct_1(C,E) = D ) ) ) ) )).
fof(t66_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(D,k4_finseq_1(C)) & k2_xcmplx_0(D,A) = k1_nat_1(k3_finseq_1(C),1) ) => k7_partfun1(B,C,D) = k7_partfun1(B,k4_finseq_5(B,C),A) ) ) ) ) ) )).
fof(t66_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t66_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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] : ( ( 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] : ( m1_subset_1(E,A) => ( k5_binop_1(A,D,B,E) = B & k5_binop_1(A,D,E,B) = B ) ) ) ) ) ) ) )).
fof(t66_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(C,k5_numbers) => k7_flang_1(A,k8_flang_1(A,B),C) = k8_flang_1(A,B) ) ) ) )).
fof(t66_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) )).
fof(t66_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t66_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_funct_2(A,B))) => m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(k2_zfmisc_1(A,B)))) ) )).
fof(t66_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) ) )).
fof(t66_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t66_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => k7_relat_1(k6_relat_1(B,C),A) = k3_xboole_0(B,k7_relat_1(C,A)) ) )).
fof(t66_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) ) )).
fof(t66_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t66_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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) ) ) )).
fof(t66_funct_7,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m2_funct_7(B,A) => ( k9_xtuple_0(k3_funct_7(k1_funct_1(A,1),B)) = k1_funct_1(A,1) & r1_tarski(k10_xtuple_0(k3_funct_7(k1_funct_1(A,1),B)),k1_funct_1(A,k3_finseq_1(A))) ) ) ) )).
fof(t66_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => r1_funct_8(A,k1_numbers,k1_numbers,k18_sin_cos) ) )).
fof(t66_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t66_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v3_group_1(B) & v5_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t66_gfacirc1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => k2_msafree2(k25_gfacirc1(A,B,C)) = k1_enumset1(A,B,C) ) ) ) )).
fof(t66_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( r1_glib_000(A,B,C,D) => ( k29_glib_000(A,B,D) = C & k29_glib_000(A,C,D) = B ) ) ) ) ) )).
fof(t66_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( r1_xxreal_0(C,k3_finseq_1(B)) => ( k6_xcmplx_0(k2_nat_1(2,k3_nat_d(k1_nat_1(C,1),2)),1) = C & r1_xxreal_0(1,k3_nat_d(k1_nat_1(C,1),2)) & r1_xxreal_0(k3_nat_d(k1_nat_1(C,1),2),k3_finseq_1(k11_glib_001(A,B))) ) ) ) ) ) )).
fof(t66_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_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_0(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_0(u1_struct_0(k15_euclid(2)),B,A,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k1_nat_1(A,1),1)),k7_xcmplx_0(1,2)),k19_euclid(k5_numbers,1)),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,A,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k1_nat_1(A,1),2)),k7_xcmplx_0(1,2))),k2_xboole_0(k4_subset_1(u1_struct_0(k15_euclid(2)),k1_tops_1(k15_euclid(2),k3_goboard5(B,A,k5_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_0(u1_struct_0(k15_euclid(2)),B,A,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k1_nat_1(A,1),1)),k7_xcmplx_0(1,2))))) ) ) ) ) )).
fof(t66_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( v15_algstr_0(C) & v1_group_3(C,A) & m1_group_2(C,A) ) => ! [D] : ( ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) ) => ? [E] : ( 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))) ) ) ) ) ) )).
fof(t66_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => m1_group_2(B,k7_group_2(A)) ) ) )).
fof(t66_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v8_struct_0(C) & m1_group_2(C,A) ) => k7_group_1(C) = k7_group_1(k6_group_3(A,C,B)) ) ) ) )).
fof(t66_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( 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) ) ) ) )).
fof(t66_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t66_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t66_group_9,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(B)) => ! [E] : ( m1_subset_1(E,B) => ( ~ v1_xboole_0(D) => ( r2_hidden(E,k1_group_9(A,B,C,D)) <=> ? [F] : ( m2_finseq_1(F,A) & ? [G] : ( m1_subset_1(G,D) & k1_funct_1(k2_group_9(A,B,C,F),G) = E ) ) ) ) ) ) ) ) )).
fof(t66_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( 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)) ) ) )).
fof(t66_hfdiff_1,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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))) ) ) ) )).
fof(t66_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_hidden(B,k7_ideal_1(A,k6_domain_1(u1_struct_0(A),B))) ) ) )).
fof(t66_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(B,A) => ( r1_xxreal_0(k2_xcmplx_0(k1_int_1(B),1),A) | r1_xxreal_0(k3_int_1(B),k3_int_1(A)) ) ) ) ) )).
fof(t66_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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(k4_xcmplx_0(1),1)) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(C,D) = k7_xcmplx_0(k1_funct_1(k1_sin_cos6,D),k3_square_1(k6_xcmplx_0(1,k1_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)),k7_xcmplx_0(1,2)))) & B = k9_xtuple_0(C) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,A)) ) => k2_integra5(A,C) = k6_xcmplx_0(k1_funct_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)),k7_xcmplx_0(1,2)),k2_seq_4(A)),k1_funct_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)),k7_xcmplx_0(1,2)),k3_seq_4(A))) ) ) ) ) )).
fof(t66_integra8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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))) = k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k1_funct_1(A,k2_seq_4(C)),k1_funct_1(A,k3_seq_4(C))),k1_funct_1(B,k2_seq_4(C))),k1_funct_1(B,k3_seq_4(C))) ) ) ) ) ) )).
fof(t66_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v3_rcomp_1(E) & m1_subset_1(E,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,E) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => ( k1_funct_1(C,F) = k2_xcmplx_0(A,F) & ~ r1_xxreal_0(k1_funct_1(C,F),k5_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(k7_xcmplx_0(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(k7_xcmplx_0(1,2))),2)) = k1_relset_1(k1_numbers,D) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => k1_funct_1(D,F) = k6_prepower(k2_xcmplx_0(A,F),k4_xcmplx_0(k7_xcmplx_0(1,2))) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,D,B)) ) => k2_integra5(B,D) = k6_xcmplx_0(k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(k7_xcmplx_0(1,2))),2),k2_seq_4(B)),k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(k7_xcmplx_0(1,2))),2),k3_seq_4(B))) ) ) ) ) ) ) )).
fof(t66_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m2_interva1(B,A) => ! [C] : ( m2_interva1(C,A) => ! [D] : ( 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))) ) ) ) ) )).
fof(t66_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_intpro_1) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( 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) ) ) ) )).
fof(t66_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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) ) ) )).
fof(t66_jgraph_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ 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(k5_numbers,k17_euclid(A)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(B)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(C)) & ~ r1_xxreal_0(k5_numbers,k17_euclid(D)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(A)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(B)) & ~ r1_xxreal_0(k5_numbers,k18_euclid(C)) & ! [F] : ( ( 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] : ( 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(k4_xcmplx_0(1),k5_numbers) = k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,A) & k19_euclid(k5_numbers,1) = k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,B) & k19_euclid(1,k5_numbers) = k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,C) & k19_euclid(k5_numbers,k4_xcmplx_0(1)) = k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,D) ) ) ) ) ) ) ) ) )).
fof(t66_jgraph_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(k5_topmetr)) => ! [H] : ( 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(k7_xcmplx_0(2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(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(k4_xcmplx_0(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)),k4_xcmplx_0(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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t66_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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)))) ) => k2_xcmplx_0(k8_pscomp_1(k3_topreal1(2,k2_jordan9(C,B))),k6_pscomp_1(k3_topreal1(2,k2_jordan9(C,B)))) = k2_xcmplx_0(k8_pscomp_1(k3_topreal1(2,k2_jordan9(C,A))),k6_pscomp_1(k3_topreal1(2,k2_jordan9(C,A)))) ) ) ) )).
fof(t66_jordan1j,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) )).
fof(t66_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( v1_xreal_0(D) => ( ( C = a_2_5_jordan2c(A,D) & k3_subset_1(u1_struct_0(k15_euclid(A)),C) = B ) => v1_connsp_2(k1_pre_topc(k15_euclid(A),B)) ) ) ) ) ) )).
fof(t66_jordan6,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => r2_hidden(k10_jordan6(A),k9_jordan6(A)) ) )).
fof(t66_lattice2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k5_finsub_1(A)) => ! [C] : ( ( ~ v2_struct_0(C) & v10_lattices(C) & v11_lattices(C) & v13_lattices(C) & l3_lattices(C) ) => ! [D] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t66_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t66_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(B,C) & r2_hidden(C,k1_relset_1(k1_numbers,A)) ) ) => ( ! [B] : ( v1_xreal_0(B) => ~ ( 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) ) ) ) )).
fof(t66_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r4_limfunc2(C,A) & r4_limfunc2(D,A) & k2_limfunc2(C,A) = k2_limfunc2(D,A) ) => ( ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & r1_tarski(k2_rcomp_1(A,k2_xcmplx_0(A,E)),k9_subset_1(k1_numbers,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,C),k1_relset_1(k1_numbers,D)),k1_relset_1(k1_numbers,B))) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,k2_rcomp_1(A,k2_xcmplx_0(A,E))) => ( r1_xxreal_0(k1_funct_1(C,F),k1_funct_1(B,F)) & r1_xxreal_0(k1_funct_1(B,F),k1_funct_1(D,F)) ) ) ) ) ) | ( r4_limfunc2(B,A) & k2_limfunc2(B,A) = k2_limfunc2(C,A) ) ) ) ) ) ) ) )).
fof(t66_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k3_limfunc1(C))) & r1_xxreal_0(k1_funct_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)) ) ) ) ) ) )).
fof(t66_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t66_mathmorp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) => ( A != k5_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)) ) ) ) ) ) )).
fof(t66_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( v1_matrix10(B) => r1_matrix10(C,k4_matrix10(A,C,B)) ) ) ) ) )).
fof(t66_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ( ( r1_tarski(C,k4_finseq_1(B)) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k7_subset_1(k4_ordinal1,k4_finseq_1(B),C)) => k7_matrix_0(u1_struct_0(A),B,D) = k5_finseq_2(u1_struct_0(A),k1_matrix_0(B),k4_struct_0(A)) ) ) ) => ( v1_xboole_0(C) | r1_xxreal_0(k1_matrix_0(B),k5_numbers) | k7_matrix15(A,B) = k7_matrix15(A,k6_matrix13(u1_struct_0(A),B,C,k2_finseq_1(k1_matrix_0(B)))) ) ) ) ) ) )).
fof(t66_matrix16,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t66_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(C,k2_finseq_1(k1_matrix_0(B))) & r2_hidden(D,k4_finseq_1(B)) & r2_hidden(E,k2_finseq_1(k1_matrix_0(k16_matrix_0(C,A,B)))) ) => ( r1_xxreal_0(k1_matrix_0(B),1) | k3_matrix_0(A,k16_matrix_0(C,A,B),D,E) = k1_funct_1(k2_finseq_3(C,k7_matrix_0(A,B,D)),E) ) ) ) ) ) ) ) )).
fof(t66_matrixj1,axiom,( ! [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] : ( ( v1_matrixj1(B,u1_struct_0(A)) & m2_finseq_1(B,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t66_matrixr1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ( k3_finseq_1(C) = A => ( r1_xxreal_0(A,k5_numbers) | k12_matrixr1(k8_matrixr1(A,B),C) = k5_euclid(B) ) ) ) ) ) )).
fof(t66_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(A,k5_numbers) => k7_matrixr1(C,k8_matrixr1(A,B)) = k8_matrixr1(A,B) ) ) ) ) )).
fof(t66_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ! [F] : ( r2_hidden(F,E) <=> ? [G] : ? [H] : ? [I] : ? [J] : ( r2_hidden(G,A) & r2_hidden(H,B) & r2_hidden(I,C) & r2_hidden(J,D) & F = k6_xtuple_0(G,H,I,J) ) ) => E = k4_zfmisc_1(A,B,C,D) ) )).
fof(t66_measure6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ( v6_measure6(B,A) <=> v5_measure6(k32_valued_1(A,k1_numbers,B),A) ) ) ) )).
fof(t66_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( ( r2_hidden(C,A) & r2_hidden(D,B) ) => r2_hidden(k6_xcmplx_0(C,D),k11_member_1(A,B)) ) ) ) ) ) )).
fof(t66_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( ( 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] : ( 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) ) ) ) ) ) )).
fof(t66_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ( ( r1_mesfunc2(A,B,D) & v6_supinf_2(D) & r1_xxreal_0(k5_numbers,E) ) => k5_mesfunc5(A,B,C,k6_mesfunc1(A,D,E)) = k4_xxreal_3(E,k5_mesfunc5(A,B,C,D)) ) ) ) ) ) ) )).
fof(t66_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( 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)) ) ) ) )).
fof(t66_mmlquery,axiom,( ! [A] : ( l1_mmlquery(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(B,k30_mmlquery(A,C)) <=> r2_hidden(C,k31_mmlquery(A,B)) ) ) ) ) )).
fof(t66_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t66_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ( v6_modelc_2(A) & v5_modelc_3(A) ) => v5_modelc_3(k10_modelc_2(A)) ) ) )).
fof(t66_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => a_1_2_moebius1(A) = a_1_3_moebius1(A) ) )).
fof(t66_monoid_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ( r1_tarski(A,B) => m2_monoid_0(k9_monoid_0(A),k9_monoid_0(B)) ) ) ) )).
fof(t66_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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_msafree4(B,u1_struct_0(A)) ) => ! [C] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( m1_subset_1(E,k3_msualg_1(A,D,C)) => k3_funct_2(k3_msualg_1(A,D,C),k4_msualg_1(A,D,C),k5_msualg_1(A,D,C),E) = k1_funct_1(k2_msafree4(u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,C),k4_msafree4(A,B,C),k2_msualg_1(A,D)),k1_funct_1(k5_msualg_1(A,D,k1_msafree3(A,B)),E)) ) ) ) ) ) )).
fof(t66_nat_d,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => k5_int_1(k2_xcmplx_0(B,C),A) = k5_int_1(k2_xcmplx_0(k5_int_1(B,A),k5_int_1(C,A)),A) ) ) ) )).
fof(t66_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) )).
fof(t66_newton,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( B != k5_numbers => A = k2_xcmplx_0(k3_xcmplx_0(k4_int_1(A,B),B),k5_int_1(A,B)) ) ) ) )).
fof(t66_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t66_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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) ) ) )).
fof(t66_orders_1,axiom,( ! [A] : ~ ( A != k1_xboole_0 & ! [B] : ~ ( r1_tarski(B,A) & v6_ordinal1(B) & ! [C] : ~ ( r2_hidden(C,A) & ! [D] : ( r2_hidden(D,B) => r1_tarski(C,D) ) ) ) & ! [B] : ~ ( r2_hidden(B,A) & ! [C] : ~ ( r2_hidden(C,A) & C != B & r1_tarski(C,B) ) ) ) )).
fof(t66_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t66_ordinal5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t66_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => r2_hidden(A,k1_classes1(k2_xboole_0(k2_xboole_0(A,B),C))) ) ) ) )).
fof(t66_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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 ) ) ) )).
fof(t66_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t66_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( ( 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) & k10_pdiff_1(3,3,k26_valued_1(k1_euclid(3),k1_numbers,k1_pdiff_3(3,3,C),A),B) = k3_xcmplx_0(A,k9_pdiff_5(C,B)) ) ) ) ) ) )).
fof(t66_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( ( 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] : ( 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) = k6_xcmplx_0(k10_pdiff_1(A,B,D,F),k10_pdiff_1(A,B,E,F)) ) ) ) ) ) ) ) ) ) )).
fof(t66_pepin,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(A,1) & ~ r1_xxreal_0(B,C) & r1_xxreal_0(k1_newton(A,B),k1_newton(A,C)) ) ) ) ) )).
fof(t66_polyform,axiom,( ! [A] : ( ( 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)) ) )).
fof(t66_polynom5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_funct_2(u1_struct_0(A),u1_struct_0(A),k8_polynom5(A,B,k5_numbers),k8_funcop_1(u1_struct_0(A),u1_struct_0(A),B)) ) ) )).
fof(t66_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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),k4_ordinal1,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)) ) ) ) ) ) ) ) )).
fof(t66_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => ( ( r1_xxreal_0(A,1) & r1_xxreal_0(B,k5_numbers) ) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(1,k4_prepower(A,B)) ) ) ) ) )).
fof(t66_prob_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v2_prob_3(B,A) <=> ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(t66_pscomp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [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) => r1_xxreal_0(k7_pscomp_1(A),k7_pscomp_1(B)) ) ) ) )).
fof(t66_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( 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))) ) ) ) ) )).
fof(t66_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( r2_qc_lang2(A,B,C) <=> r3_qc_lang2(A,B,k13_qc_lang1(A,C)) ) ) ) ) )).
fof(t66_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => k6_qc_lang3(A,k1_qc_lang2(A)) = k1_xboole_0 ) )).
fof(t66_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => ! [D] : ( v1_quaterni(D) => k23_quaterni(k25_quaterni(k25_quaterni(A,B),C),D) = k25_quaterni(k25_quaterni(k23_quaterni(A,D),k23_quaterni(B,D)),k23_quaterni(C,D)) ) ) ) ) )).
fof(t66_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ( k28_quaterni(A) = k5_numbers => A = k5_numbers ) ) )).
fof(t66_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k4_topmetr(A,B))))) => ! [E] : ( m1_rcomp_3(E,A,B,D) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t66_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => k5_real_1(k4_real_1(k9_nat_1(k1_numbers,k5_real_3(B),k1_nat_1(A,2)),k9_nat_1(k1_numbers,k6_real_3(B),A)),k4_real_1(k9_nat_1(k1_numbers,k5_real_3(B),A),k9_nat_1(k1_numbers,k6_real_3(B),k1_nat_1(A,2)))) = k3_xcmplx_0(k1_newton(k4_xcmplx_0(1),A),k9_nat_1(k1_numbers,k4_real_3(B),k1_nat_1(A,2))) ) ) )).
fof(t66_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k5_relat_1(k5_relat_1(B,A),A) = k5_relat_1(B,A) ) )).
fof(t66_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ 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] : ( m1_rewrite1(D,k1_rewrite3(A,B,C)) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t66_rfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => k1_funct_1(k7_rfunct_1(A,A),B) = 1 ) ) )).
fof(t66_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ! [D] : ( ( 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(k7_finseq_1(k20_rfunct_3(A,D,k6_subset_1(C,k1_tarski(B))),k9_finseq_1(k1_funct_1(D,B))),k2_partfun1(A,k1_numbers,D,C)) ) ) ) ) )).
fof(t66_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v7_valued_0(B) & v1_seq_2(B) ) => k1_funct_1(k4_rinfsup1(B),A) = k3_funct_2(k4_ordinal1,k1_numbers,k4_rinfsup1(B),k1_nat_1(A,1)) ) ) ) )).
fof(t66_rlaffin1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( 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) ) ) ) )).
fof(t66_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_rlsub_1(D,A) => ~ ( k3_rlsub_1(A,C,D) = k3_rlsub_1(A,B,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r1_struct_0(D,E) & k3_rlvect_1(A,C,E) = B ) ) ) ) ) ) ) )).
fof(t66_rlvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t66_rlvect_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( m2_finseq_1(D,u1_struct_0(C)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(C)) => ( ( k3_finseq_1(D) = k3_finseq_1(E) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ( ( r2_hidden(F,k1_relset_1(k4_ordinal1,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)) ) ) ) ) ) ) )).
fof(t66_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m2_rmod_2(D,A,B,C) => ( v1_rmod_2(D,A,B) <=> D = u1_struct_0(C) ) ) ) ) ) )).
fof(t66_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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) ) ) ) ) ) )).
fof(t66_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => m2_rusub_1(k6_domain_1(u1_struct_0(A),B),A,k1_rusub_1(A)) ) ) )).
fof(t66_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) )).
fof(t66_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(C,k7_card_1(3),k1_scmfsa_2,k5_numbers) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(D,k7_card_1(3),k1_scmfsa_2,k5_numbers) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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) ) => ( ! [F] : ( v7_ordinal1(F) => ~ r8_pboole(u1_struct_0(k1_scmfsa_2),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C,F),D) ) | r8_pboole(u1_struct_0(k1_scmfsa_2),k6_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C),k6_extpro_1(k7_card_1(3),k1_scmfsa_2,B,D)) ) ) ) ) ) ) ) )).
fof(t66_scmfsa_2,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ( k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k15_scmfsa_2(C,B,A),D),k4_struct_0(k1_scmfsa_2)) = k4_card_1(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,D)) & ? [E] : ( v7_ordinal1(E) & E = k1_int_2(k1_funct_1(D,B)) & k18_scmfsa_2(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k15_scmfsa_2(C,B,A),D),A) = k1_funct_7(k18_scmfsa_2(D,A),E,k1_funct_1(D,C)) ) & ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmfsa_2)) ) => k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k15_scmfsa_2(C,B,A),D),E) = k1_funct_1(D,E) ) & ! [E] : ( m1_scmfsa_2(E) => ( E != A => r2_relset_1(k4_ordinal1,k4_numbers,k18_scmfsa_2(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k15_scmfsa_2(C,B,A),D),E),k18_scmfsa_2(D,E)) ) ) ) ) ) ) ) )).
fof(t66_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmpds_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ~ v2_extpro_1(k13_scmpds_2(C,D,A,B),2,k1_scmpds_2) ) ) ) ) )).
fof(t66_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => k5_card_1(k7_scmpds_6(A,B,C)) = k1_nat_1(k5_card_1(C),1) ) ) ) )).
fof(t66_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( ( v4_scmyciel(B) & v5_scmyciel(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t66_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r3_semi_af1(A,B,C,D,E) => r3_semi_af1(A,D,E,B,C) ) ) ) ) ) ) )).
fof(t66_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(B)) => ! [D] : ( m2_finseq_2(D,k2_numbers,k12_seq_4(B)) => ( r2_hidden(A,k2_finseq_1(B)) => k1_funct_1(k17_seq_4(B,C,D),A) = k6_xcmplx_0(k1_funct_1(C,A),k1_funct_1(D,A)) ) ) ) ) ) )).
fof(t66_setlim_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( v5_relat_1(D,C) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ( r2_hidden(A,k4_kurato_0(B,D)) <=> ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & r2_hidden(A,k1_funct_1(D,k2_xcmplx_0(E,F))) ) ) ) ) ) )).
fof(t66_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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)) ) ) ) )).
fof(t66_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t66_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_fdiff_1(k18_sin_cos,k1_numbers) & k1_fdiff_1(k18_sin_cos,A) = k4_xcmplx_0(k1_funct_1(k16_sin_cos,A)) ) ) )).
fof(t66_sin_cos6,axiom,( k4_relset_1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k5_relset_1(k1_numbers,k1_numbers,k16_sin_cos,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))),k1_sin_cos6) = k6_partfun1(k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))) )).
fof(t66_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( B = k7_xcmplx_0(k2_xcmplx_0(k23_sin_cos(A),k23_sin_cos(k4_xcmplx_0(A))),k6_xcmplx_0(k23_sin_cos(A),k23_sin_cos(k4_xcmplx_0(A)))) => ( A = k5_numbers | A = k3_xcmplx_0(k7_xcmplx_0(1,2),k3_power(k4_power,k7_xcmplx_0(k2_xcmplx_0(B,1),k6_xcmplx_0(B,1)))) ) ) ) ) )).
fof(t66_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ~ ( ~ r1_xxreal_0(k4_sin_cos9(A),k7_xcmplx_0(k28_sin_cos,4)) & ~ r1_xxreal_0(k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos),k4_sin_cos9(A)) ) ) ) )).
fof(t66_sincos10,axiom,( k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k4_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos)),k2_sincos10) = k1_partfun2(k1_numbers,k4_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos)) )).
fof(t66_sprect_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t66_sprect_2,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( 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))) ) ) ) ) ) ) )).
fof(t66_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t66_stirl2_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ~ ( ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k2_afinsq_1(B)) => v1_finset_1(k1_funct_1(B,C)) ) ) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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] : ( ( v1_relat_1(C) & v5_relat_1(C,k4_ordinal1) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ~ ( k2_afinsq_1(C) = k2_afinsq_1(B) & ! [D] : ( 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) ) ) ) ) ) )).
fof(t66_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),D,k2_valuat_1(A,D)) => ! [F] : ( m2_funct_2(F,k3_qc_lang1(A),D,k2_valuat_1(A,D)) => ! [G] : ( 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))) ) ) ) ) ) ) ) ) )).
fof(t66_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) ) ) ) ) )).
fof(t66_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ? [C] : ( 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) ) ) ) )).
fof(t66_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) ) )).
fof(t66_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( 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) ) ) ) ) )).
fof(t66_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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) => ! [F] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(C)) => ( r2_hidden(G,u1_struct_0(D)) => k3_funct_2(u1_struct_0(C),u1_struct_0(B),E,G) = k1_funct_1(F,G) ) ) => r2_funct_2(u1_struct_0(D),u1_struct_0(B),k3_tmap_1(A,B,C,D,E),F) ) ) ) ) ) ) ) ) )).
fof(t66_topgen_4,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t66_topreal6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => k3_seq_4(A) = k3_seq_4(k5_measure6(A)) ) )).
fof(t66_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t66_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t66_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => v1_transgeo(A) ) )).
fof(t66_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => k5_trees_1(k12_trees_3(A),k14_trees_3(k5_numbers),B) = k12_trees_3(B) ) ) )).
fof(t66_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t66_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_valued_0(D) ) => ! [E] : ( ( 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)) ) ) ) ) )).
fof(t66_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( v7_vectsp_1(D,A) & m1_vectsp_4(D,A,B) ) => ! [E] : ( ( 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 ) ) ) ) ) ) )).
fof(t66_waybel23,axiom,( ! [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] : ( ( v6_waybel23(B,A) & m1_waybel23(B,A) ) => ( v17_waybel_0(k3_waybel23(A,k5_yellow_0(A,B)),k1_yellow_1(k7_waybel_0(k5_yellow_0(A,B))),A) & v18_waybel_0(k3_waybel23(A,k5_yellow_0(A,B)),k1_yellow_1(k7_waybel_0(k5_yellow_0(A,B))),A) ) ) ) )).
fof(t66_waybel34,axiom,( ! [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] : ( ( 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] : ( ( 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))))) ) ) ) ) ) )).
fof(t66_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t66_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v9_waybel_1(A) => v2_waybel_1(A) ) ) )).
fof(t66_xboole_1,axiom,( ! [A] : ( ~ ( ~ r1_xboole_0(A,A) & A = k1_xboole_0 ) & ~ ( A != k1_xboole_0 & r1_xboole_0(A,A) ) ) )).
fof(t66_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( 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))) ) ) ) )).
fof(t66_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( A = k7_xcmplx_0(k2_xcmplx_0(A,B),2) => A = B ) ) ) )).
fof(t66_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,B) & r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(C,D) ) => r1_xxreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D)) ) ) ) ) ) )).
fof(t66_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r1_xxreal_0(A,B) & k1_xxreal_1(A,B) = k1_xxreal_1(C,D) ) => ( A = C & B = D ) ) ) ) ) ) )).
fof(t66_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( m2_xxreal_2(C,A) => ! [D] : ( m2_xxreal_2(D,B) => m2_xxreal_2(k4_xxreal_0(C,D),k3_xboole_0(A,B)) ) ) ) ) )).
fof(t66_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => k4_xxreal_3(A,k4_xxreal_3(B,C)) = k4_xxreal_3(k4_xxreal_3(A,B),C) ) ) ) )).
fof(t66_yellow10,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [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(B) ) ) ) )).
fof(t66_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t66_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t66_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( ( r2_zf_lang(A,B) & r2_zf_lang(B,A) ) => A = B ) ) ) )).
fof(t66_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => k2_zf_model(k13_zf_lang(B,A)) = k7_subset_1(k1_zf_lang,k2_zf_model(A),k1_tarski(B)) ) ) )).
fof(t66_zfmisc_1,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_tarski(k1_zfmisc_1(A),k1_zfmisc_1(B)) ) )).
fof(t66_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_zmodul01(D,A) => ( r1_struct_0(D,B) <=> k5_zmodul01(A,C,D) = k5_zmodul01(A,k5_algstr_0(A,C,B),D) ) ) ) ) ) )).
fof(t66_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( r1_struct_0(k3_zmodul01(A),B) <=> B = k4_struct_0(A) ) ) )).
fof(t67_abcmiz_0,axiom,( ! [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) & l3_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_rewrite1(k11_abcmiz_0(A),B,C) => r3_orders_2(A,B,C) ) ) ) ) )).
fof(t67_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v8_abcmiz_1(B,A) & m1_abcmiz_1(B,A,k13_abcmiz_1(A)) ) => k37_abcmiz_1(A,k37_abcmiz_1(A,B)) = B ) ) )).
fof(t67_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t67_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => k2_afinsq_1(A) = a_1_0_afinsq_1(A) ) )).
fof(t67_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r4_analmetr(A,B,C,D,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r5_analmetr(A,B,C,F) & r5_analmetr(A,D,E,F) ) ) ) ) ) ) ) ) )).
fof(t67_aofa_000,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_freealg(A) ) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(k7_freealg(k19_aofa_000,A))) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t67_aofa_a00,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ! [E] : ( ( ~ v2_struct_0(E) & l5_aofa_a00(E) ) => ! [F] : ( ( ~ v2_struct_0(F) & l5_aofa_a00(F) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k2_xcmplx_0(A,3),k3_finseq_1(u7_aofa_a00(E))) & ! [G] : ( v7_ordinal1(G) => ( ( r1_xxreal_0(A,G) & r1_xxreal_0(G,k2_xcmplx_0(A,3)) ) => ( k1_funct_1(u1_msualg_1(E),k1_funct_1(u7_aofa_a00(E),G)) = k1_funct_1(u1_msualg_1(F),k1_funct_1(u7_aofa_a00(F),k2_xcmplx_0(G,B))) & k1_funct_1(u2_msualg_1(E),k1_funct_1(u7_aofa_a00(E),G)) = k1_funct_1(u2_msualg_1(F),k1_funct_1(u7_aofa_a00(F),k2_xcmplx_0(G,B))) ) ) ) & v21_aofa_a00(F,C,D,k2_xcmplx_0(A,B)) ) => v21_aofa_a00(E,C,D,A) ) ) ) ) ) )).
fof(t67_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( m1_subset_1(C,k5_arytm_3) => ( ( r3_arytm_3(A,B) & r3_arytm_3(B,C) ) => r3_arytm_3(A,C) ) ) ) ) )).
fof(t67_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,6) & r1_xxreal_0(k2_power(2,A),k1_square_1(A)) ) ) )).
fof(t67_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k1_bcialg_1(A,C,B) = k1_bcialg_1(A,D,B) => C = D ) ) ) ) ) ) )).
fof(t67_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) )).
fof(t67_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t67_borsuk_6,axiom,( r2_hidden(k4_tarski(k7_xcmplx_0(1,2),k5_numbers),k7_borsuk_6) )).
fof(t67_borsuk_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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))) ) ) ) ) ) ) )).
fof(t67_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t67_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_eqrel_1(I,A) => ! [J] : ( m1_eqrel_1(J,A) => ! [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t67_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t67_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => ( k6_xboolean(C,k6_xboolean(B,A)) = k8_margrel1 => k6_xboolean(B,k6_xboolean(C,A)) = k8_margrel1 ) ) ) ) )).
fof(t67_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( 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)))))) ) ) ) ) ) )).
fof(t67_card_1,axiom,( ! [A] : ! [B] : ( r2_wellord2(A,k2_zfmisc_1(A,k1_tarski(B))) & k1_card_1(A) = k1_card_1(k2_zfmisc_1(A,k1_tarski(B))) ) )).
fof(t67_card_2,axiom,( ! [A] : ( v1_card_1(A) => ( r2_hidden(k5_numbers,A) <=> r1_ordinal1(1,A) ) ) )).
fof(t67_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ~ ( r2_hidden(C,k8_card_3(k1_funct_4(A,B))) & ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ~ ( r2_hidden(D,k8_card_3(A)) & r2_hidden(E,k8_card_3(B)) & C = k1_funct_4(D,E) ) ) ) ) ) ) ) )).
fof(t67_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ( k8_cat_1(A,B,C,k3_graph_1(A,D)) = k3_graph_1(B,k3_funct_2(u4_struct_0(A),u4_struct_0(B),C,D)) & k8_cat_1(A,B,C,k4_graph_1(A,D)) = k4_graph_1(B,k3_funct_2(u4_struct_0(A),u4_struct_0(B),C,D)) ) ) ) ) ) )).
fof(t67_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m2_cat_3(D,B,C,A) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t67_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_cat_1(F,A,B,D) => ! [G] : ( m1_cat_1(G,A,C,D) => ! [H] : ( m1_cat_1(H,A,D,E) => ~ ( k2_cat_1(A,B,D) != k1_xboole_0 & k2_cat_1(A,C,D) != k1_xboole_0 & k2_cat_1(A,D,E) != k1_xboole_0 & k29_cat_4(A,B,C,E,k5_cat_1(A,B,D,E,F,H),k5_cat_1(A,C,D,E,G,H)) != k5_cat_1(A,k20_cat_4(A,B,C),D,E,k29_cat_4(A,B,C,D,F,G),H) ) ) ) ) ) ) ) ) ) )).
fof(t67_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( 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) = k3_xcmplx_0(k7_partfun1(k2_numbers,C,B),k5_xcmplx_0(k7_partfun1(k2_numbers,D,B))) ) ) ) ) ) )).
fof(t67_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ( v3_chord(B,A) => ! [C] : ! [D] : ~ ( 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] : ~ r1_glib_000(A,C,D,E) ) ) ) ) )).
fof(t67_classes1,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_ordinal1(k6_classes1(A),k6_classes1(B)) ) )).
fof(t67_classes2,axiom,( k16_classes2(1) = k14_classes2 )).
fof(t67_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_clvect_1(C,A) => ( r1_struct_0(C,B) <=> k5_clvect_1(A,B,C) = u1_struct_0(C) ) ) ) ) )).
fof(t67_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r1_clvect_2(A,B,C) => r1_clvect_2(A,C,B) ) ) ) ) )).
fof(t67_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ! [C] : ~ ( B != C & r2_hidden(k2_tarski(B,C),A) & r2_hidden(k2_tarski(B,C),k13_cohsp_1(A)) ) ) )).
fof(t67_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k7_xcmplx_0(k9_complex1(A),k9_complex1(B)) = k9_complex1(k7_xcmplx_0(A,B)) ) ) )).
fof(t67_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( A != k5_numbers & B != k5_numbers & ~ ( k19_sin_cos(k3_complex2(A,B)) = k7_xcmplx_0(k3_complex1(k1_complex2(A,B)),k3_xcmplx_0(k9_complex1(A),k9_complex1(B))) & k17_sin_cos(k3_complex2(A,B)) = k4_xcmplx_0(k7_xcmplx_0(k4_complex1(k1_complex2(A,B)),k3_xcmplx_0(k9_complex1(A),k9_complex1(B)))) ) ) ) ) )).
fof(t67_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ( k9_complex1(k5_algstr_0(k1_complfld,A,B)) = k5_numbers <=> A = B ) ) ) )).
fof(t67_complsp2,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( m2_finseq_1(C,k2_numbers) => ( k3_finseq_1(B) = k3_finseq_1(C) => k8_complsp2(k10_seq_4(B,A),C) = k3_xcmplx_0(A,k8_complsp2(B,C)) ) ) ) ) )).
fof(t67_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,A),C)) & r1_xxreal_0(k9_nat_1(k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,A),C),k9_nat_1(k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,B),C)) ) ) & v2_comseq_3(B) ) => ( v2_comseq_3(A) & r1_xxreal_0(k4_series_1(k55_valued_1(k4_ordinal1,k2_numbers,A)),k4_series_1(k55_valued_1(k4_ordinal1,k2_numbers,B))) ) ) ) ) )).
fof(t67_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( B = a_3_1_convex4(A,C,D) => v2_convex4(B,A) ) ) ) ) ) )).
fof(t67_csspace,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(C)))) ) => r2_funct_2(k4_ordinal1,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))) ) ) ) ) )).
fof(t67_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => 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,k18_sin_cos),k18_sin_cos),A),B) = k3_xcmplx_0(k7_xcmplx_0(1,2),k2_xcmplx_0(k3_xcmplx_0(k19_sin_cos(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(2,B),A),2)),k17_sin_cos(k7_xcmplx_0(A,2))),k3_xcmplx_0(k19_sin_cos(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(6,B),k3_xcmplx_0(3,A)),2)),k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(3,A),2))))) ) ) )).
fof(t67_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k7_xcmplx_0(1,k19_sin_cos(D)) ) => ( k19_sin_cos(B) = k5_numbers | k19_sin_cos(k6_xcmplx_0(B,A)) = k5_numbers | k1_funct_1(k4_diff_1(C,A),B) = k7_xcmplx_0(k3_xcmplx_0(2,k6_xcmplx_0(k19_sin_cos(k6_xcmplx_0(B,A)),k19_sin_cos(B))),k2_xcmplx_0(k19_sin_cos(k6_xcmplx_0(k3_xcmplx_0(2,B),A)),k19_sin_cos(A))) ) ) ) ) ) )).
fof(t67_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_enumset1(A,B,C,D) = k2_enumset1(B,C,A,D) )).
fof(t67_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_eqrel_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => k8_relset_1(A,B,k13_eqrel_1(A,B),C) = k3_tarski(C) ) ) ) )).
fof(t67_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(3)) => k22_rvsum_1(k7_euclid(3,k9_euclid(3,D,A),k9_euclid(3,E,B)),C) = k2_xcmplx_0(k3_xcmplx_0(A,k22_rvsum_1(D,C)),k3_xcmplx_0(B,k22_rvsum_1(E,C))) ) ) ) ) ) )).
fof(t67_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t67_exchsort,axiom,( ! [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) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_exchsort(B) ) => ! [C] : ( m1_subset_1(C,k9_xtuple_0(B)) => ! [D] : ( m1_subset_1(D,k9_xtuple_0(B)) => ! [E] : ( m1_subset_1(E,k9_xtuple_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t67_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : v1_relat_1(k3_msafree2(k15_facirc_1(A,B,C))) )).
fof(t67_fdiff_11,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) & ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & k1_funct_1(k1_sin_cos9,B) = k5_numbers ) ) ) => ( r2_fdiff_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k6_rfunct_1(k1_numbers,k1_numbers,k1_sin_cos9),A),B) = k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(k1_square_1(k1_funct_1(k1_sin_cos9,B)),k2_xcmplx_0(1,k1_square_1(B))))) ) ) ) ) ) )).
fof(t67_fib_num2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => r1_int_2(k1_pre_ff(A),k1_pre_ff(k1_nat_1(A,1))) ) )).
fof(t67_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)))) ) ) ) ) )).
fof(t67_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v19_lattices(C,A) & v20_lattices(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ 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) ) ) ) ) ) )).
fof(t67_finseq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( 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 ) ) ) )).
fof(t67_finseq_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( ( r1_tarski(k2_zfmisc_1(k10_xtuple_0(B),k1_tarski(A)),k9_xtuple_0(D)) & C = k4_funcop_1(D,B,A) ) => k3_finseq_1(C) = k3_finseq_1(B) ) ) ) ) )).
fof(t67_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( k1_finseq_3(A,B) = A <=> r1_xboole_0(B,k10_xtuple_0(A)) ) ) )).
fof(t67_finseq_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => k7_partfun1(A,k8_finseq_1(A,B,k12_finseq_1(A,C)),k1_nat_1(k3_finseq_1(B),1)) = C ) ) ) )).
fof(t67_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => k5_finseq_5(A,C,B,k5_numbers) = k8_finseq_1(A,k12_finseq_1(A,B),C) ) ) ) )).
fof(t67_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ( r2_hidden(B,k6_subset_1(k10_xtuple_0(D),k10_xtuple_0(C))) => k1_finseq_5(A,k8_finseq_1(A,C,D),B) = k8_finseq_1(A,C,k1_finseq_5(A,D,B)) ) ) ) ) ) )).
fof(t67_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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)) ) ) ) ) ) ) ) ) )).
fof(t67_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t67_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k8_afinsq_1(A))) => ( ( r1_tarski(B,k2_flang_3(A,D)) & r1_tarski(C,k2_flang_3(A,D)) ) => r1_tarski(k6_flang_1(A,B,C),k2_flang_3(A,D)) ) ) ) ) )).
fof(t67_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m1_subset_1(D,B) => ~ ( ( r2_hidden(C,A) => r2_hidden(D,A) ) & ( r2_hidden(D,A) => r2_hidden(C,A) ) & ~ r2_hidden(k4_tarski(k3_funct_2(B,k6_margrel1,k10_fomodel0(A,B),C),k3_funct_2(B,k6_margrel1,k10_fomodel0(A,B),D)),k6_partfun1(k6_margrel1)) ) ) ) ) )).
fof(t67_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t67_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) )).
fof(t67_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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))) ) ) ) )).
fof(t67_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t67_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( A != C => k4_funct_4(A,C,B,D) = k2_tarski(k4_tarski(A,B),k4_tarski(C,D)) ) )).
fof(t67_funct_7,axiom,( ! [A] : ( v1_relat_1(A) => k8_funct_7(A,k5_numbers) = k6_partfun1(k1_relat_1(A)) ) )).
fof(t67_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => r2_funct_8(A,k1_numbers,k1_numbers,k1_sin_cos2) ) )).
fof(t67_fvaluat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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)) ) ) )).
fof(t67_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v3_group_1(B) & v5_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t67_gfacirc1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ~ v1_facirc_1(k2_msafree2(k25_gfacirc1(A,B,C))) ) ) ) )).
fof(t67_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( 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) ) ) ) )).
fof(t67_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => r2_relset_1(k4_ordinal1,k6_glib_000(A),k11_glib_001(A,k1_glib_001(A,B)),k12_finseq_1(k6_glib_000(A),B)) ) ) )).
fof(t67_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_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_0(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_0(u1_struct_0(k15_euclid(2)),B,A,k1_matrix_0(B)),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k1_nat_1(A,1),k1_matrix_0(B))),k7_xcmplx_0(1,2)),k19_euclid(k5_numbers,1)),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,A,k1_matrix_0(B)),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k1_nat_1(A,1),k7_nat_d(k1_matrix_0(B),1))),k7_xcmplx_0(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_0(B),1))),k1_tops_1(k15_euclid(2),k3_goboard5(B,A,k1_matrix_0(B)))),k1_tarski(k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,A,k1_matrix_0(B)),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k1_nat_1(A,1),k1_matrix_0(B))),k7_xcmplx_0(1,2))))) ) ) ) ) )).
fof(t67_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( v15_algstr_0(C) & v1_group_3(C,A) & m1_group_2(C,A) ) => ! [D] : ( ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) ) => ? [E] : ( 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)) ) ) ) ) ) )).
fof(t67_group_2,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t67_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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)) ) ) )).
fof(t67_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( 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) ) ) ) )).
fof(t67_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t67_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t67_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v15_algstr_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ? [C] : ( ~ 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)) ) ) )).
fof(t67_hermitan,axiom,( ! [A] : ( ( ~ 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] : ( ( 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)) ) ) )).
fof(t67_hfdiff_1,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ~ ( r2_hidden(C,A) & k1_funct_1(B,C) = k5_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)))) ) ) ) )).
fof(t67_ideal_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t67_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,B) & ~ r1_xxreal_0(k2_xcmplx_0(k1_int_1(B),1),A) & r1_xxreal_0(k3_int_1(A),k3_int_1(B)) ) ) ) )).
fof(t67_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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(k4_xcmplx_0(1),1)) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k1_funct_1(C,D) = k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k3_sin_cos6,D),k3_square_1(k6_xcmplx_0(1,k1_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,k3_sin_cos6,k1_taylor_1(2)),k7_xcmplx_0(1,2)))) & B = k9_xtuple_0(C) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,A)) ) => k2_integra5(A,C) = k6_xcmplx_0(k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_sin_cos6,k1_taylor_1(2)),k7_xcmplx_0(1,2)),k2_seq_4(A)),k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_sin_cos6,k1_taylor_1(2)),k7_xcmplx_0(1,2)),k3_seq_4(A))) ) ) ) ) )).
fof(t67_integra8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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))) = k6_xcmplx_0(k6_xcmplx_0(k1_funct_1(A,k2_seq_4(C)),k1_funct_1(A,k3_seq_4(C))),k6_xcmplx_0(k1_funct_1(B,k2_seq_4(C)),k1_funct_1(B,k3_seq_4(C)))) ) ) ) ) ) )).
fof(t67_integra9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v3_rcomp_1(E) & m1_subset_1(E,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,E) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => ( k1_funct_1(C,F) = k6_xcmplx_0(A,F) & ~ r1_xxreal_0(k1_funct_1(C,F),k5_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(k7_xcmplx_0(1,2))),k4_xcmplx_0(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(k7_xcmplx_0(1,2))),k4_xcmplx_0(2))) = k1_relset_1(k1_numbers,D) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,E) => k1_funct_1(D,F) = k6_prepower(k6_xcmplx_0(A,F),k4_xcmplx_0(k7_xcmplx_0(1,2))) ) ) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,D,B)) ) => k2_integra5(B,D) = k6_xcmplx_0(k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(k7_xcmplx_0(1,2))),k4_xcmplx_0(2)),k2_seq_4(B)),k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(k7_xcmplx_0(1,2))),k4_xcmplx_0(2)),k3_seq_4(B))) ) ) ) ) ) ) )).
fof(t67_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m2_interva1(B,A) => ! [C] : ( m2_interva1(C,A) => r2_interva1(A,k16_interva1(A,B,k17_interva1(A,B,C)),B) ) ) ) )).
fof(t67_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ( v9_intpro_1(A) => v8_intpro_1(A) ) ) )).
fof(t67_jgraph_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ 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] : ( ( 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] : ( 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(k4_xcmplx_0(1),k5_numbers) = k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,A) & k19_euclid(k5_numbers,1) = k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,B) & k19_euclid(1,k5_numbers) = k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,C) & k19_euclid(k5_numbers,k4_xcmplx_0(1)) = k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,D) ) ) ) ) ) ) ) ) )).
fof(t67_jgraph_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(k5_topmetr)) => ! [H] : ( 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(k7_xcmplx_0(2,k6_xcmplx_0(B,A)),k4_xcmplx_0(k7_xcmplx_0(k2_xcmplx_0(B,A),k6_xcmplx_0(B,A))),k7_xcmplx_0(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)),k4_xcmplx_0(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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t67_jordan,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( ( v1_xreal_0(D) & v2_xxreal_0(D) ) => ~ ( r2_hidden(C,k1_topreal9(A,B,D)) & v2_abian(k10_jordan(A,B,C,D)) ) ) ) ) ) )).
fof(t67_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( 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) ) => v5_pre_topc(B,k15_euclid(A),k3_topmetr) ) ) ) )).
fof(t67_jordan6,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => r2_hidden(k11_jordan6(A),k8_jordan6(A)) ) )).
fof(t67_lattice2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & r3_lattices(A,k4_lattices(A,B,D),C) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r3_lattices(A,k4_lattices(A,B,E),C) => r3_lattices(A,E,D) ) ) ) ) ) ) ) )).
fof(t67_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t67_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(B,C) & r2_hidden(C,k1_relset_1(k1_numbers,A)) ) ) => ( ! [B] : ( v1_xreal_0(B) => ~ ( 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) ) ) ) )).
fof(t67_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & 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_funct_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)) ) ) ) ) ) )).
fof(t67_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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))) ) ) ) ) ) ) )).
fof(t67_mathmorp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( C = k1_xboole_0 => k7_mathmorp(k15_euclid(A),B,C,D) = k3_mathmorp(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),B),D) ) ) ) ) ) )).
fof(t67_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( v2_matrix10(B) => r1_matrix10(k4_matrix10(A,B,C),C) ) ) ) ) )).
fof(t67_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( ( v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ( k5_card_1(C) = k5_card_1(D) => ( r1_tarski(k2_zfmisc_1(C,D),k2_matrix_0(B)) <=> ( r1_tarski(C,k2_finseq_1(k3_finseq_1(B))) & r1_tarski(D,k2_finseq_1(k1_matrix_0(B))) ) ) ) ) ) ) ) )).
fof(t67_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),B,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ! [E] : ( ( v1_finset_1(E) & v1_setfam_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ~ ( k5_card_1(E) = B & r1_tarski(E,k2_finseq_1(A)) & k6_matrix13(u1_struct_0(C),D,k2_finseq_1(B),E) = k3_matrix_1(C,B) & ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(k7_nat_d(A,B),k5_numbers) & ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(C),k7_nat_d(A,B),A) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(C))) ) => ~ ( k6_matrix13(u1_struct_0(C),F,k2_finseq_1(k7_nat_d(A,B)),k7_subset_1(k4_ordinal1,k2_finseq_1(A),E)) = k3_matrix_1(C,k7_nat_d(A,B)) & k6_matrix13(u1_struct_0(C),F,k2_finseq_1(k7_nat_d(A,B)),E) = k2_matrix_3(C,k4_matrix_0(u1_struct_0(C),k6_matrix13(u1_struct_0(C),D,k2_finseq_1(B),k7_subset_1(k4_ordinal1,k2_finseq_1(A),E)))) & k1_vectsp_7(C,k6_prvect_1(C,A),k9_matrix13(C,k7_nat_d(A,B),A,F)) = k7_matrix15(C,D) ) ) ) ) ) ) ) ) )).
fof(t67_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(C,k2_finseq_1(k1_matrix_0(B))) & k1_matrix_0(B) = k1_nat_1(E,1) & r1_xxreal_0(1,D) ) => ( r1_xxreal_0(E,k5_numbers) | r1_xxreal_0(C,D) | ( k8_matrix_0(A,k16_matrix_0(C,A,B),D) = k8_matrix_0(A,B,D) & r2_hidden(D,k2_finseq_1(k1_matrix_0(k16_matrix_0(C,A,B)))) & r2_hidden(D,k2_finseq_1(k1_matrix_0(B))) ) ) ) ) ) ) ) ) )).
fof(t67_matrixj1,axiom,( ! [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] : ( ( v1_matrixj1(B,u1_struct_0(A)) & m2_finseq_1(B,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) => ! [C] : ( ( v1_matrixj1(C,u1_struct_0(A)) & m2_finseq_1(C,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) => ! [D] : ( ( v1_matrixj1(D,u1_struct_0(A)) & m2_finseq_1(D,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) => ! [E] : ( ( 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)) ) ) ) ) ) ) )).
fof(t67_matrixr2,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => k4_matrix_3(A,B,k3_matrix_1(A,k1_matrix_0(B))) = B ) ) )).
fof(t67_mcart_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(A)) ) => ! [F] : ( ( ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(B)) ) => ! [G] : ( ( ~ v1_xboole_0(G) & m1_subset_1(G,k1_zfmisc_1(C)) ) => ! [H] : ( ( ~ v1_xboole_0(H) & m1_subset_1(H,k1_zfmisc_1(D)) ) => ! [I] : ( m1_subset_1(I,k4_zfmisc_1(A,B,C,D)) => ( r2_hidden(I,k4_zfmisc_1(E,F,G,H)) => ( r2_hidden(k4_mcart_1(A,B,C,D,I),E) & r2_hidden(k5_mcart_1(A,B,C,D,I),F) & r2_hidden(k6_mcart_1(A,B,C,D,I),G) & r2_hidden(k7_mcart_1(A,B,C,D,I),H) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t67_measure6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ( v5_measure6(B,A) <=> v6_measure6(k32_valued_1(A,k1_numbers,B),A) ) ) ) )).
fof(t67_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_membered(C) => ! [D] : ( v1_membered(D) => ( ( r1_tarski(A,B) & r1_tarski(C,D) ) => r1_tarski(k11_member_1(A,C),k11_member_1(B,D)) ) ) ) ) ) )).
fof(t67_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( 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)) ) ) ) ) )).
fof(t67_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( 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))) ) ) ) ) ) )).
fof(t67_mmlquery,axiom,( ! [A] : ( l1_mmlquery(A) => ! [B] : ( m2_finseq_1(B,u1_mmlquery(A)) => k35_mmlquery(A,B,k5_numbers) = k32_mmlquery(A,B) ) ) )).
fof(t67_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( 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) ) ) ) )).
fof(t67_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( 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)) ) ) ) ) )).
fof(t67_monoid_0,axiom,( ! [A] : ( ~ 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)) ) ) )).
fof(t67_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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_msafree4(B,u1_struct_0(A)) ) => ! [C] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,C)) => ( r1_msualg_3(A,k1_msafree3(A,B),C,D) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( m1_subset_1(F,k3_msualg_1(A,E,C)) => k1_funct_1(k2_msafree4(u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,C),D,k2_msualg_1(A,E)),k3_funct_2(k3_msualg_1(A,E,C),k4_msualg_1(A,E,C),k5_msualg_1(A,E,C),F)) = k1_funct_1(k2_msafree4(u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,C),D,k2_msualg_1(A,E)),k1_funct_1(k5_msualg_1(A,E,k1_msafree3(A,B)),F)) ) ) ) ) ) ) ) )).
fof(t67_nat_d,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => k5_int_1(k3_xcmplx_0(B,C),A) = k5_int_1(k3_xcmplx_0(k5_int_1(B,A),k5_int_1(C,A)),A) ) ) ) )).
fof(t67_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) => ! [F] : ( ( 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)) ) ) ) ) ) ) )).
fof(t67_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ ( r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(A,k5_numbers) ) & ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => k2_xcmplx_0(k3_xcmplx_0(C,B),k3_xcmplx_0(D,A)) != k6_nat_d(B,A) ) ) ) ) ) )).
fof(t67_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t67_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( 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(B),k10_oppcat_1(A,B,C),k1_partfun1(u4_struct_0(k2_oppcat_1(A)),u4_struct_0(A),u4_struct_0(A),u4_struct_0(B),k13_oppcat_1(A),C)) & r2_funct_2(u4_struct_0(A),u4_struct_0(k2_oppcat_1(B)),k11_oppcat_1(A,B,C),k1_partfun1(u4_struct_0(A),u4_struct_0(B),u4_struct_0(B),u4_struct_0(k2_oppcat_1(B)),C,k12_oppcat_1(B))) ) ) ) ) )).
fof(t67_orders_1,axiom,( ! [A] : ~ ( A != k1_xboole_0 & ! [B] : ( ( r1_tarski(B,A) & v6_ordinal1(B) ) => ( B = k1_xboole_0 | r2_hidden(k3_tarski(B),A) ) ) & ! [B] : ~ ( r2_hidden(B,A) & ! [C] : ~ ( r2_hidden(C,A) & C != B & r1_tarski(B,C) ) ) ) )).
fof(t67_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r2_hidden(A,k11_ordinal2(B,C)) => ( r2_hidden(k6_ordinal3(A,C),B) & r2_hidden(k7_ordinal3(A,C),C) ) ) ) ) ) )).
fof(t67_ordinal5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v6_ordinal5(A) ) => ~ ( A != k1_xboole_0 & ! [B] : ( ( v3_ordinal1(B) & v5_ordinal5(B) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t67_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t67_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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) ) ) ) ) )).
fof(t67_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) )).
fof(t67_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t67_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( 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) = k3_xcmplx_0(D,k10_pdiff_1(A,B,E,F)) ) ) ) ) ) ) ) ) ) )).
fof(t67_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( 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) ) ) ) )).
fof(t67_polynom5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ? [B] : ( 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)) ) ) )).
fof(t67_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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)) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( r2_hidden(E,k4_finseq_1(k21_pre_poly(A,B))) & k9_pre_poly(k15_pre_poly(A),k4_ordinal1,k4_finseq_2(2,k15_pre_poly(A)),k21_pre_poly(A,B),E) = k10_finseq_1(C,D) ) ) ) ) ) ) ) )).
fof(t67_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ? [B] : ( v5_relat_1(B,k3_numbers) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v2_comseq_2(B) & k1_seq_2(B) = A & ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k1_funct_1(B,C),A) ) ) ) )).
fof(t67_prob_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( v3_prob_3(B,A) <=> ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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) ) ) ) ) )).
fof(t67_pscomp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [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) => r1_xxreal_0(k8_pscomp_1(A),k8_pscomp_1(B)) ) ) ) )).
fof(t67_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,A) & v1_funct_1(E) & v1_partfun1(E,A) ) => ( ( r2_pboole(A,B,D) & r2_pboole(A,C,E) ) => r6_pboole(A,k3_pboole(A,k6_pboole(A,B,E),k6_pboole(A,D,C)),k6_pboole(A,B,C)) ) ) ) ) ) )).
fof(t67_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( r2_qc_lang2(A,k13_qc_lang1(A,B),C) => r3_qc_lang2(A,B,C) ) ) ) ) )).
fof(t67_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t67_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => ! [D] : ( v1_quaterni(D) => k23_quaterni(k22_quaterni(k22_quaterni(A,B),C),D) = k22_quaterni(k22_quaterni(k23_quaterni(A,D),k23_quaterni(B,D)),k23_quaterni(C,D)) ) ) ) ) )).
fof(t67_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => r1_xxreal_0(k5_numbers,k28_quaterni(A)) ) )).
fof(t67_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,k6_real_3(B),C) != k5_numbers ) => k5_real_1(k6_real_1(k9_nat_1(k1_numbers,k5_real_3(B),k1_nat_1(A,2)),k9_nat_1(k1_numbers,k6_real_3(B),k1_nat_1(A,2))),k6_real_1(k9_nat_1(k1_numbers,k5_real_3(B),A),k9_nat_1(k1_numbers,k6_real_3(B),A))) = k7_xcmplx_0(k3_xcmplx_0(k1_newton(k4_xcmplx_0(1),A),k9_nat_1(k1_numbers,k4_real_3(B),k1_nat_1(A,2))),k4_real_1(k9_nat_1(k1_numbers,k6_real_3(B),k1_nat_1(A,2)),k9_nat_1(k1_numbers,k6_real_3(B),A))) ) ) ) )).
fof(t67_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r1_tarski(A,B) => k5_relat_1(k5_relat_1(C,A),B) = k5_relat_1(C,A) ) ) )).
fof(t67_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ v2_struct_0(C) & l1_rewrite3(C,B) ) => ( v2_rewrite3(C,A,B) => ! [D] : ( m1_rewrite1(D,k1_rewrite3(A,B,C)) => ! [E] : ( m1_rewrite1(E,k1_rewrite3(A,B,C)) => ( k1_funct_1(D,1) = k1_funct_1(E,1) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t67_rfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ( k1_funct_1(k7_rfunct_1(A,B),C) != 1 <=> k1_funct_1(k7_rfunct_1(A,B),C) = k5_numbers ) ) ) )).
fof(t67_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ! [D] : ( 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) ) ) ) ) )).
fof(t67_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v7_valued_0(B) & v1_seq_2(B) ) => ( k1_funct_1(k4_rinfsup1(B),A) = k1_rinfsup1(B) & v3_funct_1(k4_rinfsup1(B)) ) ) ) ) )).
fof(t67_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k4_rlaffin1(A,k3_convex1(A,B)) = k4_rlaffin1(A,B) ) ) )).
fof(t67_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_rlsub_1(D,A) => ~ ( k3_rlsub_1(A,C,D) = k3_rlsub_1(A,B,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r1_struct_0(D,E) & k5_algstr_0(A,C,E) = B ) ) ) ) ) ) ) )).
fof(t67_rlvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t67_rlvect_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( m2_finseq_1(D,u1_struct_0(C)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(C)) => ( ( k3_finseq_1(D) = k3_finseq_1(E) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r2_hidden(F,k1_relset_1(k4_ordinal1,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)) ) ) ) ) ) ) )).
fof(t67_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v2_vectsp_2(C,A) & m1_rmod_2(C,A,B) ) => ! [D] : ( ( v2_vectsp_2(D,A) & m1_rmod_2(D,A,B) ) => ! [E] : ( m2_rmod_2(E,A,B,C) => ! [F] : ( m2_rmod_2(F,A,B,D) => ( E = F => C = D ) ) ) ) ) ) ) )).
fof(t67_rmod_4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) => ( r1_struct_0(k10_rmod_4(B,C,D),A) <=> ? [E] : ( m2_rmod_4(E,B,C,D) & A = k5_rmod_4(B,C,E) ) ) ) ) ) )).
fof(t67_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( m2_rusub_1(B,A,k1_rusub_1(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B != k6_domain_1(u1_struct_0(A),C) ) ) ) ) )).
fof(t67_rvsum_1,axiom,( ! [A] : ( ( 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) ) )).
fof(t67_scmfsa8c,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ( r4_scmfsa7b(k1_scmfsa8c(A),B) => r4_scmfsa7b(A,B) ) ) ) )).
fof(t67_scmfsa_2,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ( k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k16_scmfsa_2(B,A),C),k4_struct_0(k1_scmfsa_2)) = k4_card_1(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,C)) & k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k16_scmfsa_2(B,A),C),B) = k3_finseq_1(k18_scmfsa_2(C,A)) & ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ( D != B => k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k16_scmfsa_2(B,A),C),D) = k1_funct_1(C,D) ) ) & ! [D] : ( m1_scmfsa_2(D) => r2_relset_1(k4_ordinal1,k4_numbers,k18_scmfsa_2(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k16_scmfsa_2(B,A),C),D),k18_scmfsa_2(C,D)) ) ) ) ) ) )).
fof(t67_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmpds_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ~ v2_extpro_1(k14_scmpds_2(C,D,A,B),2,k1_scmpds_2) ) ) ) ) )).
fof(t67_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => r2_hidden(k5_numbers,k9_xtuple_0(k7_scmpds_6(A,B,C))) ) ) ) )).
fof(t67_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( ( v10_scmyciel(B,A) & m1_eqrel_1(B,k3_tarski(A)) ) => ! [C] : ( 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))) ) ) ) ) )).
fof(t67_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r3_semi_af1(A,B,C,D,E) => r3_semi_af1(A,C,B,E,D) ) ) ) ) ) ) )).
fof(t67_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => k17_seq_4(A,B,k15_seq_4(A)) = B ) ) )).
fof(t67_setlim_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( v5_relat_1(D,C) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ( r2_hidden(A,k3_kurato_0(B,D)) <=> ? [E] : ( v7_ordinal1(E) & ! [F] : ( v7_ordinal1(F) => r2_hidden(A,k1_funct_1(D,k2_xcmplx_0(E,F))) ) ) ) ) ) )).
fof(t67_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,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))) ) ) )).
fof(t67_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_sheffer1(A) ) => ( v1_sheffer2(A) => v10_sheffer1(A) ) ) )).
fof(t67_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_fdiff_1(k16_sin_cos,k1_numbers) & k1_fdiff_1(k16_sin_cos,A) = k1_funct_1(k18_sin_cos,A) ) ) )).
fof(t67_sin_cos6,axiom,( k3_relat_1(k5_relset_1(k1_numbers,k1_numbers,k16_sin_cos,k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))),k1_sin_cos6) = k6_partfun1(k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))) )).
fof(t67_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( B = k7_xcmplx_0(1,k7_xcmplx_0(k2_xcmplx_0(k23_sin_cos(A),k23_sin_cos(k4_xcmplx_0(A))),2)) & A != k3_power(k4_power,k7_xcmplx_0(k2_xcmplx_0(1,k3_square_1(k6_xcmplx_0(1,k1_square_1(B)))),B)) & A != k4_xcmplx_0(k3_power(k4_power,k7_xcmplx_0(k2_xcmplx_0(1,k3_square_1(k6_xcmplx_0(1,k1_square_1(B)))),B))) ) ) ) )).
fof(t67_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) => k3_sin_cos9(A) = k4_xcmplx_0(k3_sin_cos9(k4_xcmplx_0(A))) ) ) )).
fof(t67_sincos10,axiom,( k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers)),k3_sincos10) = k1_partfun2(k1_numbers,k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers)) )).
fof(t67_sprect_1,axiom,( ! [A] : ( ( ~ 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)) ) )).
fof(t67_sprect_2,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( 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))) ) ) ) ) ) ) )).
fof(t67_sprect_5,axiom,( ! [A] : ( ( ~ 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)))) ) ) )).
fof(t67_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_valuat_1(E,A,D) => ( ! [F] : ( m2_funct_2(F,k3_qc_lang1(A),D,k2_valuat_1(A,D)) => ! [G] : ( 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] : ( m2_funct_2(F,k3_qc_lang1(A),D,k2_valuat_1(A,D)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t67_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_tdlat_2(B,A) => v4_tops_1(k4_subset_1(u1_struct_0(A),k5_setfam_1(u1_struct_0(A),B),k1_tops_1(A,k2_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)))),A) ) ) ) )).
fof(t67_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => r1_borsuk_1(A,B) ) ) )).
fof(t67_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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) ) ) ) ) )).
fof(t67_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ( v2_pre_topc(B) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t67_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( 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)) ) ) ) ) )).
fof(t67_topgen_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ! [C] : ( ( 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,k5_numbers))),k8_relset_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr),k4_topgen_5(A,C),k3_rcomp_1(k5_numbers,B))) ) ) ) )).
fof(t67_topreal6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => k2_seq_4(A) = k2_seq_4(k5_measure6(A)) ) )).
fof(t67_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t67_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_tsep_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => ( v2_tops_1(C,A) <=> v2_tops_1(D,B) ) ) ) ) ) ) )).
fof(t67_transgeo,axiom,( ! [A] : ( ( ~ 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)) ) ) )).
fof(t67_trees_3,axiom,( k12_trees_3(k2_trees_1(k5_numbers)) = k2_trees_1(1) )).
fof(t67_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_tsep_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ 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) ) ) ) ) )).
fof(t67_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_valued_0(D) ) => ! [E] : ( ( 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)) ) ) ) ) )).
fof(t67_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v7_vectsp_1(E,A) & m1_vectsp_4(E,A,B) ) => ! [F] : ( ( v7_vectsp_1(F,A) & m1_vectsp_4(F,A,B) ) => ( k3_vectsp_4(A,B,D,E) = k3_vectsp_4(A,B,C,F) => E = F ) ) ) ) ) ) ) )).
fof(t67_waybel23,axiom,( ! [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] : ( ( v6_waybel23(B,A) & m1_waybel23(B,A) ) => v18_waybel_0(k5_waybel23(A,B),A,k1_yellow_1(k7_waybel_0(k5_yellow_0(A,B)))) ) ) )).
fof(t67_waybel34,axiom,( ! [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] : ( ( 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] : ( ( 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))))) ) ) ) ) ) ) )).
fof(t67_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) ) ) ) ) ) )).
fof(t67_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v9_waybel_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t67_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r1_tarski(A,B) & r1_tarski(A,C) & r1_xboole_0(B,C) ) => A = k1_xboole_0 ) )).
fof(t67_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k8_xboolean(A,k9_xboolean(B,C)) = k5_xboolean(k5_xboolean(k3_xboolean(A),B),C) ) ) ) )).
fof(t67_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,A),A),3) = A ) )).
fof(t67_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(B,A) & r1_xxreal_0(C,k5_numbers) & r1_xxreal_0(D,C) ) => r1_xxreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D)) ) ) ) ) ) )).
fof(t67_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( k4_xxreal_1(A,B) = k4_xxreal_1(C,D) => ( r1_xxreal_0(B,A) | ( A = C & B = D ) ) ) ) ) ) ) )).
fof(t67_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( 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))) ) ) )).
fof(t67_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k5_xxreal_3(k4_xxreal_3(A,B)) = k4_xxreal_3(k5_xxreal_3(A),k5_xxreal_3(B)) ) ) )).
fof(t67_yellow10,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( 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) ) ) ) ) )).
fof(t67_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( 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) ) ) ) ) )).
fof(t67_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ r1_yellow_5(A,k12_lattice3(A,B,C),k1_yellow_5(A,B,C)) ) ) ) )).
fof(t67_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ~ r3_zf_lang(C,k4_zf_lang(A,B)) ) ) ) )).
fof(t67_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,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)) ) ) ) )).
fof(t67_zfmisc_1,axiom,( ! [A] : r1_tarski(k1_tarski(A),k1_zfmisc_1(A)) )).
fof(t67_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_zmodul01(D,A) => ( r2_hidden(C,k5_zmodul01(A,B,D)) <=> k5_zmodul01(A,B,D) = k5_zmodul01(A,C,D) ) ) ) ) ) )).
fof(t67_zmodul02,axiom,( ! [A] : ( ( ~ 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) ) => k33_zmodul02(A,k1_subset_1(u1_struct_0(A))) = k3_zmodul01(A) ) )).
fof(t68_abcmiz_0,axiom,( ! [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) & l3_abcmiz_0(A) ) => v2_relat_2(k11_abcmiz_0(A)) ) )).
fof(t68_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v8_abcmiz_1(B,A) & m1_abcmiz_1(B,A,k13_abcmiz_1(A)) ) => ! [C] : ( ( 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 ) ) ) ) )).
fof(t68_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t68_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_finset_1(B) ) => ( ( r1_tarski(A,B) & k62_valued_1(A) = k62_valued_1(B) ) => A = B ) ) ) )).
fof(t68_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_valued_0(A) & v1_finset_1(A) ) => k7_afinsq_2(A) = k7_afinsq_2(k1_afinsq_2(A)) ) )).
fof(t68_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r6_analmetr(A,C,D,B) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r5_analmetr(A,C,D,E) & r2_hidden(E,B) ) ) ) ) ) ) ) )).
fof(t68_aofa_000,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_freealg(A) ) => ! [B] : ( 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] : ( m1_subset_1(C,A) => B != k4_trees_4(C,k1_xboole_0) ) ) ) ) )).
fof(t68_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(4,D) & r1_xxreal_0(k2_xcmplx_0(D,6),E) & r1_xxreal_0(1,C) ) => ! [F] : ( ( ~ v2_struct_0(F) & ~ v11_struct_0(F) & v13_aofa_a00(F) & v16_aofa_a00(F) & l6_aofa_a00(F) ) => ~ ( v21_aofa_a00(F,A,B,k2_xcmplx_0(E,C)) & v18_aofa_a00(F,D,B) & ! [G] : ( ( ~ v2_struct_0(G) & ~ v11_struct_0(G) & v16_aofa_a00(G) & l6_aofa_a00(G) ) => ! [H] : ( ( ~ v2_struct_0(H) & ~ v11_struct_0(H) & l5_aofa_a00(H) ) => ~ ( g6_aofa_a00(u1_struct_0(F),u4_struct_0(F),u1_msualg_1(F),u2_msualg_1(F),u8_aofa_a00(F),u7_aofa_a00(F)) = k36_aofa_a00(G,H) & v14_aofa_a00(G,E) & v18_aofa_a00(G,D,B) & v21_aofa_a00(H,A,B,C) & u1_struct_0(G) = u1_struct_0(H) & u4_struct_0(G) = k6_subset_1(u4_struct_0(F),k10_xtuple_0(u7_aofa_a00(H))) & u4_struct_0(H) = k10_xtuple_0(u7_aofa_a00(H)) & u7_aofa_a00(G) = k17_finseq_1(u4_struct_0(F),E,u7_aofa_a00(F)) & u7_aofa_a00(H) = k2_rfinseq(u4_struct_0(F),E,u7_aofa_a00(F)) ) ) ) ) ) ) ) ) ) )).
fof(t68_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v1_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_aofa_a01(D,A,B,C) & l4_aofa_a00(D,A,B,C) ) => ! [E] : ( ( ~ v2_struct_0(E) & v2_unialg_1(E) & v3_unialg_1(E) & v4_unialg_1(E) & v3_aofa_000(E) & v4_aofa_000(E) & v5_aofa_000(E) & v6_aofa_000(E) & ~ v10_aofa_000(E) & v11_aofa_000(E) & v12_aofa_000(E) & l3_aofa_a00(E,A,C,u4_aofa_a00(A,B,C,D)) ) => ( v5_aofa_a01(E,A,B,C,D) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_msafree4(G,u1_struct_0(A),u4_aofa_a00(A,B,C,D),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),F)) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),F)) => r2_hidden(k12_aofa_a00(A,C,u4_aofa_a00(A,B,C,D),E,F,G,H),k18_aofa_000(E)) ) ) ) ) ) ) ) ) ) )).
fof(t68_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ( ~ r3_arytm_3(B,A) <=> ( r3_arytm_3(A,B) & A != B ) ) ) ) )).
fof(t68_asympt_1,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k9_nat_1(k1_numbers,B,k5_numbers) = k5_numbers & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ r1_xxreal_0(C,k5_numbers) => k9_nat_1(k1_numbers,B,C) = k3_power(2,k2_power(C,A)) ) ) ) => ( v2_comseq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,k3_asympt_1(A))) & k1_seq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,k3_asympt_1(A))) = k5_numbers ) ) ) ) )).
fof(t68_bcialg_1,axiom,( ! [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) ) => ( v19_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k1_bcialg_1(A,B,C) = k1_bcialg_1(A,B,D) => C = D ) ) ) ) ) ) )).
fof(t68_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)))) ) ) ) )).
fof(t68_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k4_subset_1(k1_numbers,k3_rcomp_1(A,k1_xxreal_0),k1_seq_4(B)) != k1_numbers ) ) )).
fof(t68_borsuk_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_topmetr)) => r2_hidden(k4_tarski(1,A),k8_borsuk_6) ) )).
fof(t68_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t68_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_eqrel_1(I,A) => ! [J] : ( m1_eqrel_1(J,A) => ! [K] : ( 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) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t68_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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,k6_bvfunc26(A,B,C)),k5_bvfunc_1(A,B,k1_bvfunc_1(A,C))) ) ) ) )).
fof(t68_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => ( ( k6_xboolean(C,k6_xboolean(B,A)) = k8_margrel1 & B = k8_margrel1 ) => k6_xboolean(C,A) = k8_margrel1 ) ) ) ) )).
fof(t68_card_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) => k1_card_1(k9_xtuple_0(A)) = k1_card_1(k10_xtuple_0(A)) ) ) )).
fof(t68_card_2,axiom,( ! [A] : ( v1_card_1(A) => ( r2_hidden(1,A) <=> r1_ordinal1(2,A) ) ) )).
fof(t68_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( ( r1_xboole_0(k9_xtuple_0(B),k6_subset_1(k9_xtuple_0(C),k9_xtuple_0(D))) & r2_hidden(C,k8_card_3(A)) & r2_hidden(D,k8_card_3(B)) ) => r2_hidden(k1_funct_4(C,D),k8_card_3(k1_funct_4(A,B))) ) ) ) ) ) )).
fof(t68_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_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) ) ) ) ) ) )).
fof(t68_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( 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) ) ) ) ) )).
fof(t68_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,B,D) => ! [F] : ( m1_cat_1(F,A,B,D) => ! [G] : ( m1_cat_1(G,A,C,D) => ! [H] : ( m1_cat_1(H,A,C,D) => ( k29_cat_4(A,B,C,D,E,G) = k29_cat_4(A,B,C,D,F,H) => ( k2_cat_1(A,B,D) = k1_xboole_0 | k2_cat_1(A,C,D) = k1_xboole_0 | ( E = F & G = H ) ) ) ) ) ) ) ) ) ) ) )).
fof(t68_cfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => ( v1_comseq_2(k2_partfun1(B,k2_numbers,C,A)) <=> ? [D] : ( v1_xreal_0(D) & ! [E] : ( m1_subset_1(E,B) => ( r2_hidden(E,k9_subset_1(B,A,k1_relset_1(B,C))) => r1_xxreal_0(k9_complex1(k7_partfun1(k2_numbers,C,E)),D) ) ) ) ) ) ) )).
fof(t68_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ~ ( ~ v3_chord(B,A) & ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => ~ ( C != D & B != C & B != D & r1_chord(A,B,C) & r1_chord(A,B,D) & ~ r1_chord(A,C,D) ) ) ) ) ) ) )).
fof(t68_classes1,axiom,( ! [A] : ! [B] : ( r2_hidden(A,B) => r2_hidden(k6_classes1(A),k6_classes1(B)) ) )).
fof(t68_classes2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) ) => ( ( v4_ordinal1(A) & k9_xtuple_0(B) = A & ! [C] : ( 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)) ) ) ) ) )).
fof(t68_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t68_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( r2_clvect_2(A,B,C) & r2_clvect_2(A,C,D) ) => r2_clvect_2(A,B,D) ) ) ) ) ) )).
fof(t68_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ! [C] : ( 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)) ) ) ) )).
fof(t68_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k9_complex1(k3_xcmplx_0(A,A)) = k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A))) ) )).
fof(t68_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( r1_xxreal_0(k5_numbers,k4_complex2(A,B,C)) & ~ r1_xxreal_0(k3_xcmplx_0(2,k28_sin_cos),k4_complex2(A,B,C)) ) ) ) ) )).
fof(t68_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ( ~ ( A != B & r1_xxreal_0(k9_complex1(k5_algstr_0(k1_complfld,A,B)),k5_numbers) ) & ~ ( ~ r1_xxreal_0(k9_complex1(k5_algstr_0(k1_complfld,A,B)),k5_numbers) & A = B ) ) ) ) )).
fof(t68_complsp2,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k2_numbers) => ! [C] : ( m2_finseq_1(C,k2_numbers) => ( k3_finseq_1(B) = k3_finseq_1(C) => k8_complsp2(B,k10_seq_4(C,A)) = k3_xcmplx_0(k8_complex1(A),k8_complsp2(B,C)) ) ) ) ) )).
fof(t68_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v6_comput_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_comput_1(k4_ordinal1))) ) => r2_hidden(k3_comput_1(B,A),C) ) ) ) )).
fof(t68_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ~ ( ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,A),B),k5_numbers) ) & ? [B] : ( v7_ordinal1(B) & ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => r1_xxreal_0(1,k6_real_1(k9_nat_1(k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,A),k1_nat_1(C,1)),k9_nat_1(k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,A),C))) ) ) ) & v2_comseq_3(A) ) ) )).
fof(t68_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( B = a_3_2_convex4(A,C,D) => v2_convex4(B,A) ) ) ) ) ) )).
fof(t68_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t68_csspace,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(C)))) ) => r2_funct_2(k4_ordinal1,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)) ) ) ) ) )).
fof(t68_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => 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,k18_sin_cos),k18_sin_cos),A),B) = k3_xcmplx_0(k7_xcmplx_0(1,2),k2_xcmplx_0(k3_xcmplx_0(k19_sin_cos(B),k17_sin_cos(k7_xcmplx_0(A,2))),k3_xcmplx_0(k19_sin_cos(k3_xcmplx_0(3,B)),k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(3,A),2))))) ) ) )).
fof(t68_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k7_xcmplx_0(1,k19_sin_cos(D)) ) => ( k19_sin_cos(k2_xcmplx_0(B,k7_xcmplx_0(A,2))) = k5_numbers | k19_sin_cos(k6_xcmplx_0(B,k7_xcmplx_0(A,2))) = k5_numbers | k1_funct_1(k5_diff_1(C,A),B) = k7_xcmplx_0(k3_xcmplx_0(2,k6_xcmplx_0(k19_sin_cos(k6_xcmplx_0(B,k7_xcmplx_0(A,2))),k19_sin_cos(k2_xcmplx_0(B,k7_xcmplx_0(A,2))))),k2_xcmplx_0(k19_sin_cos(k3_xcmplx_0(2,B)),k19_sin_cos(A))) ) ) ) ) ) )).
fof(t68_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_enumset1(A,B,C,D) = k2_enumset1(B,C,D,A) )).
fof(t68_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_eqrel_1(B,A) ) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(A),B) => ? [D] : ( m1_subset_1(D,A) & k3_funct_2(A,B,k13_eqrel_1(A,B),D) = C ) ) ) ) )).
fof(t68_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => k22_rvsum_1(k7_euclid(3,A,B),k7_euclid(3,C,D)) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k22_rvsum_1(A,C),k22_rvsum_1(A,D)),k22_rvsum_1(B,C)),k22_rvsum_1(B,D)) ) ) ) ) )).
fof(t68_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(B)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t68_exchsort,axiom,( ! [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) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_exchsort(B) ) => ! [C] : ( m1_subset_1(C,k9_xtuple_0(B)) => ! [D] : ( m1_subset_1(D,k9_xtuple_0(B)) => ! [E] : ( m1_subset_1(E,k9_xtuple_0(B)) => ( ( r2_hidden(E,C) & r2_hidden(C,D) ) => ( k1_binop_1(k7_exchsort(A,B,C,D),E,C) = k4_tarski(E,D) & k1_binop_1(k7_exchsort(A,B,C,D),E,D) = k4_tarski(E,C) ) ) ) ) ) ) ) )).
fof(t68_facirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ~ v1_facirc_1(k2_msafree2(k15_facirc_1(A,B,C))) ) ) ) )).
fof(t68_fdiff_11,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) => ( r2_fdiff_1(k6_rfunct_1(k1_numbers,k1_numbers,k2_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k6_rfunct_1(k1_numbers,k1_numbers,k2_sin_cos9),A),B) = k7_xcmplx_0(1,k3_xcmplx_0(k1_square_1(k1_funct_1(k2_sin_cos9,B)),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t68_fib_num2,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( 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))) ) ) ) )).
fof(t68_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) ) ) ) )).
fof(t68_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m2_nat_lat(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => m1_subset_1(C,u1_struct_0(A)) ) ) ) )).
fof(t68_finseq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( 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 ) ) ) )).
fof(t68_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( m2_finseq_1(E,A) => ! [F] : ( m2_finseq_1(F,B) => m2_finseq_1(k3_funcop_1(D,E,F),C) ) ) ) ) ) ) )).
fof(t68_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( k1_finseq_3(A,k1_tarski(B)) = A <=> ~ r2_hidden(B,k10_xtuple_0(A)) ) ) )).
fof(t68_finseq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t68_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t68_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => k2_finseq_5(A,k2_finseq_5(A,C,B),B) = k2_finseq_5(A,C,B) ) ) ) )).
fof(t68_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t68_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( 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))) ) ) ) )).
fof(t68_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => r1_tarski(k7_flang_1(A,k1_flang_2(A,B,D,E),C),k8_flang_1(A,B)) ) ) ) ) )).
fof(t68_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => r1_tarski(k6_flang_1(A,B,B),k2_flang_3(A,B)) ) )).
fof(t68_fomodel0,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( r1_tarski(k9_xtuple_0(B),k9_xtuple_0(A)) & r1_tarski(A,B) ) => A = B ) ) ) )).
fof(t68_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t68_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => k8_relat_1(C,k6_subset_1(A,B)) = k6_subset_1(k8_relat_1(C,A),k8_relat_1(C,B)) ) )).
fof(t68_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ( 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_partfun1(C,A) ) ) ) )).
fof(t68_funct_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t68_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( k4_funct_4(A,B,C,D) = k4_funct_4(A,B,E,F) => ( A = B | ( C = E & D = F ) ) ) )).
fof(t68_funct_7,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v7_ordinal1(B) => k8_funct_7(A,k1_nat_1(B,1)) = k3_relat_1(A,k8_funct_7(A,B)) ) ) )).
fof(t68_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => r1_funct_8(A,k1_numbers,k1_numbers,k3_sin_cos2) ) )).
fof(t68_fvaluat1,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m2_fvaluat1(C,A,B) => ! [D] : ( ( 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] : ( m2_subset_1(E,u1_struct_0(A),B) => ! [F] : ( ( 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) ) ) ) ) ) ) ) )).
fof(t68_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t68_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( 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))) ) )).
fof(t68_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t68_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ( r1_glib_000(A,C,D,B) => k11_glib_001(A,k2_glib_001(A,C,D,B)) = k10_finseq_1(C,D) ) ) )).
fof(t68_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_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_0(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_0(u1_struct_0(k15_euclid(2)),B,1,A),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,k1_nat_1(A,1))),k7_xcmplx_0(1,2)),k19_euclid(1,k5_numbers)),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,A),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,2,k1_nat_1(A,1))),k7_xcmplx_0(1,2))),k2_xboole_0(k4_subset_1(u1_struct_0(k15_euclid(2)),k1_tops_1(k15_euclid(2),k3_goboard5(B,k5_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_0(u1_struct_0(k15_euclid(2)),B,1,A),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,k1_nat_1(A,1))),k7_xcmplx_0(1,2))))) ) ) ) ) )).
fof(t68_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( v15_algstr_0(C) & v1_group_3(C,A) & m1_group_2(C,A) ) => ! [D] : ( ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) ) => ? [E] : ( 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)) ) ) ) ) ) )).
fof(t68_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => v8_struct_0(k6_group_2(A)) ) )).
fof(t68_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t68_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t68_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t68_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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) => r1_group_6(A,k10_group_6(A,B,C)) ) ) ) ) )).
fof(t68_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(t68_hfdiff_1,axiom,( ! [A] : ( ( 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,k22_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,k22_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k16_sin_cos),k18_sin_cos)),2),A)) ) )).
fof(t68_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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))) ) ) ) ) )).
fof(t68_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k2_xcmplx_0(k1_int_1(B),1),A) & r1_xxreal_0(A,k2_xcmplx_0(B,1)) ) => k1_int_1(A) = k2_xcmplx_0(k1_int_1(B),1) ) ) ) )).
fof(t68_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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(k4_xcmplx_0(1),1)) & C = k47_valued_1(k1_numbers,k1_numbers,k1_numbers,D,E) & E = k1_taylor_1(2) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => ( k1_funct_1(D,F) = 1 & ~ r1_xxreal_0(k1_funct_1(C,F),k5_numbers) & F != k5_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(k7_xcmplx_0(1,2)))))) ) => k2_integra5(A,k1_sin_cos6) = k6_xcmplx_0(k1_funct_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(k7_xcmplx_0(1,2)))),k2_seq_4(A)),k1_funct_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(k7_xcmplx_0(1,2)))),k3_seq_4(A))) ) ) ) ) ) ) )).
fof(t68_integra8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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)) = k6_xcmplx_0(k3_xcmplx_0(C,k1_funct_1(A,k2_seq_4(B))),k3_xcmplx_0(C,k1_funct_1(A,k3_seq_4(B)))) ) ) ) ) ) )).
fof(t68_integra9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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)),k18_sin_cos),k16_sin_cos)) = C & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k3_xcmplx_0(D,k1_funct_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) = k6_xcmplx_0(k1_funct_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)),k18_sin_cos),k16_sin_cos),k2_seq_4(A)),k1_funct_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)),k18_sin_cos),k16_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t68_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m2_interva1(B,A) => ! [C] : ( m2_interva1(C,A) => r2_interva1(A,k17_interva1(A,B,k16_interva1(A,B,C)),B) ) ) ) )).
fof(t68_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => r1_tarski(k7_intpro_1(A),k11_intpro_1(A)) ) )).
fof(t68_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ! [C] : ( ( r2_hidden(B,C) & C = a_0_3_jgraph_4 ) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) | r1_xxreal_0(1,A) | r2_hidden(k1_funct_1(k5_jgraph_4(A),B),C) ) ) ) )).
fof(t68_jgraph_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ 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] : ( 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] : ( ( 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] : ( ( 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,k5_numbers) = A & k1_funct_1(G,1) = C & k1_funct_1(H,k5_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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t68_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t68_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t68_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( 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] : ( 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) ) & v5_pre_topc(B,k15_euclid(A),k3_topmetr) ) ) )).
fof(t68_jordan6,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => r2_hidden(k11_jordan6(A),A) ) )).
fof(t68_lattice2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( v8_struct_0(A) <=> v8_struct_0(k1_lattice2(A)) ) ) )).
fof(t68_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => v3_lexbfs(k26_lexbfs(A)) ) )).
fof(t68_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(B,C) & r2_hidden(C,k1_relset_1(k1_numbers,A)) ) ) => ( ! [B] : ( v1_xreal_0(B) => ~ ( 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) ) ) ) )).
fof(t68_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k10_prob_1(C))) & r1_xxreal_0(k1_funct_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)) ) ) ) ) ) )).
fof(t68_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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)) ) ) ) ) ) ) )).
fof(t68_mathmorp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( D = k1_xboole_0 => k7_mathmorp(k15_euclid(A),B,C,D) = k3_mathmorp(k15_euclid(A),B,C) ) ) ) ) ) )).
fof(t68_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( v4_matrix10(B) => r2_matrix10(C,k4_matrix10(A,B,C)) ) ) ) ) )).
fof(t68_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),B,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ! [E] : ( ( v1_finset_1(E) & v1_setfam_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ! [F] : ( ( v1_finset_1(F) & v1_setfam_1(F) & m1_subset_1(F,k1_zfmisc_1(k4_ordinal1)) ) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v7_ordinal1(H) & ~ v8_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_0(D)) ) => ( r2_hidden(H,E) | ( k5_card_1(E) = k5_card_1(k4_subset_1(k4_ordinal1,k7_subset_1(k4_ordinal1,E,k3_matrix13(G)),k3_matrix13(H))) & r1_tarski(k2_zfmisc_1(k4_subset_1(k4_ordinal1,k7_subset_1(k4_ordinal1,E,k3_matrix13(G)),k3_matrix13(H)),F),k2_matrix_0(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,k7_matrix_0(u1_struct_0(C),D,H)),E,F)) = k12_matrix_3(k5_card_1(k4_subset_1(k4_ordinal1,k7_subset_1(k4_ordinal1,E,k3_matrix13(G)),k3_matrix13(H))),C,k7_matrix13(u1_struct_0(C),D,k4_subset_1(k4_ordinal1,k7_subset_1(k4_ordinal1,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,k7_matrix_0(u1_struct_0(C),D,H)),E,F)) = k4_algstr_0(C,k12_matrix_3(k5_card_1(k4_subset_1(k4_ordinal1,k7_subset_1(k4_ordinal1,E,k3_matrix13(G)),k3_matrix13(H))),C,k7_matrix13(u1_struct_0(C),D,k4_subset_1(k4_ordinal1,k7_subset_1(k4_ordinal1,E,k3_matrix13(G)),k3_matrix13(H)),F))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t68_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ( ( k1_matrix_0(B) = k5_numbers => k3_finseq_1(B) = k5_numbers ) => k1_vectsp_9(A,k7_matrix15(A,B)) = k6_xcmplx_0(k1_matrix_0(B),k8_matrix13(A,B)) ) ) ) )).
fof(t68_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(C,k2_finseq_1(k1_matrix_0(B))) & k1_matrix_0(B) = k1_nat_1(E,1) & r1_xxreal_0(C,D) & r1_xxreal_0(D,E) ) => ( r1_xxreal_0(E,k5_numbers) | ( k8_matrix_0(A,k16_matrix_0(C,A,B),D) = k8_matrix_0(A,B,k1_nat_1(D,1)) & r2_hidden(D,k2_finseq_1(k1_matrix_0(k16_matrix_0(C,A,B)))) & r2_hidden(k1_nat_1(D,1),k2_finseq_1(k1_matrix_0(B))) ) ) ) ) ) ) ) ) )).
fof(t68_matrixj1,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t68_matrixr2,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => k4_matrix_3(A,k3_matrix_1(A,k3_finseq_1(B)),B) = B ) ) )).
fof(t68_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( r1_tarski(A,E) & r1_tarski(B,F) & r1_tarski(C,G) & r1_tarski(D,H) ) => r1_tarski(k4_zfmisc_1(A,B,C,D),k4_zfmisc_1(E,F,G,H)) ) )).
fof(t68_measure6,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ! [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))) ) => k8_relset_1(A,k1_numbers,k32_valued_1(A,k1_numbers,C),B) = k8_relset_1(A,k1_numbers,C,k3_measure6(B)) ) ) )).
fof(t68_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( 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)) ) ) ) )).
fof(t68_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t68_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( r1_mesfunc2(A,B,D) & v6_supinf_2(D) ) => r1_xxreal_0(k5_numbers,k5_mesfunc5(A,B,C,D)) ) ) ) ) ) )).
fof(t68_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => k10_relat_1(B,C) = k8_relset_1(A,k1_numbers,B,k1_tarski(C)) ) ) ) )).
fof(t68_mmlquery,axiom,( ! [A] : ( ( v3_mmlquery(A) & l1_mmlquery(A) ) => ! [B] : ( m2_finseq_1(B,u1_mmlquery(A)) => k36_mmlquery(A,B,k5_numbers) = k33_mmlquery(A,B) ) ) )).
fof(t68_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k25_modelc_2(k43_modelc_2)) => ( r7_modelc_2(C,k7_modelc_2(A,B)) <=> ? [D] : ( v7_ordinal1(D) & ! [E] : ( 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) ) ) ) ) ) )).
fof(t68_modelc_3,axiom,( ! [A] : ( m1_subset_1(A,k25_modelc_2(k43_modelc_2)) => ! [B] : ( ( v1_modelc_2(B) & v5_modelc_3(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r9_modelc_3(k43_modelc_2,k34_modelc_3(B),A) => r7_modelc_2(A,B) ) ) ) )).
fof(t68_monoid_0,axiom,( ! [A] : ! [B] : ( 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))) ) ) )).
fof(t68_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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_msafree4(B,u1_struct_0(A)) ) => ! [C] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,C)) => ( r1_msualg_3(A,k1_msafree3(A,B),C,D) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( m1_subset_1(F,k3_msualg_1(A,E,k1_msafree3(A,B))) => k1_funct_1(k2_msafree4(u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,C),D,k2_msualg_1(A,E)),k3_funct_2(k3_msualg_1(A,E,k1_msafree3(A,B)),k4_msualg_1(A,E,k1_msafree3(A,B)),k5_msualg_1(A,E,k1_msafree3(A,B)),F)) = k1_funct_1(k2_msafree4(u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,C),D,k2_msualg_1(A,E)),k1_funct_1(k5_msualg_1(A,E,k1_msafree3(A,B)),k5_msualg_3(A,k1_msafree3(A,B),C,E,k4_msafree4(A,B,C),F))) ) ) ) ) ) ) ) )).
fof(t68_nat_d,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ? [C] : ( v1_int_1(C) & ? [D] : ( v1_int_1(D) & k3_int_2(A,B) = k2_xcmplx_0(k3_xcmplx_0(C,A),k3_xcmplx_0(D,B)) ) ) ) ) )).
fof(t68_ncfcont1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t68_newton,axiom,( ! [A] : ( v7_ordinal1(A) => r1_tarski(k9_newton(A),k8_newton) ) )).
fof(t68_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t68_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_cat_1(E,A,B,C) => ! [F] : ( 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)) ) ) ) ) ) ) ) )).
fof(t68_orders_1,axiom,( ! [A] : ~ ( A != k1_xboole_0 & ! [B] : ( ( r1_tarski(B,A) & v6_ordinal1(B) ) => ( B = k1_xboole_0 | r2_hidden(k1_setfam_1(B),A) ) ) & ! [B] : ~ ( r2_hidden(B,A) & ! [C] : ~ ( r2_hidden(C,A) & C != B & r1_tarski(C,B) ) ) ) )).
fof(t68_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( B != k1_xboole_0 => k6_ordinal3(k11_ordinal2(A,B),B) = A ) ) ) )).
fof(t68_ordinal5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v5_ordinal1(A) & v1_ordinal2(A) & v6_ordinal5(A) ) => ! [B] : ( ( v3_ordinal1(B) & v5_ordinal5(B) ) => ( r2_hidden(k5_ordinal5(k1_funct_1(A,k5_numbers),k4_ordinal1),k5_ordinal5(B,k4_ordinal1)) => v6_ordinal5(k1_ordinal4(k5_afinsq_1(B),A)) ) ) ) )).
fof(t68_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => k13_ordinal6(k5_numbers,A) = k12_ordinal2(k4_ordinal1,A) ) )).
fof(t68_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t68_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) ) ) )).
fof(t68_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t68_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( ( 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] : ( 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) = k2_xcmplx_0(k3_xcmplx_0(k10_pdiff_1(A,B,D,F),k1_funct_1(E,F)),k3_xcmplx_0(k1_funct_1(D,F),k10_pdiff_1(A,B,E,F))) ) ) ) ) ) ) ) ) ) )).
fof(t68_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k17_polyform(A,k7_polyform(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k17_polyform(A,k7_polyform(A)))) => ~ ( B != C & B != k4_struct_0(k17_polyform(A,k7_polyform(A))) & C != k4_struct_0(k17_polyform(A,k7_polyform(A))) ) ) ) ) )).
fof(t68_polynom5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ? [B] : ( 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)) ) ) )).
fof(t68_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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(B,k4_finseq_1(k21_pre_poly(A,C))) & k9_pre_poly(k15_pre_poly(A),k4_ordinal1,k4_finseq_2(2,k15_pre_poly(A)),k21_pre_poly(A,C),B) = k10_finseq_1(D,E) ) => r6_pboole(A,D,k7_partfun1(k15_pre_poly(A),k20_pre_poly(A,C),B)) ) ) ) ) ) ) )).
fof(t68_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ? [B] : ( v5_relat_1(B,k3_numbers) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v2_comseq_2(B) & k1_seq_2(B) = A & ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(A,k1_funct_1(B,C)) ) ) ) )).
fof(t68_prob_3,axiom,( ! [A] : ( v2_prob_3(k9_setfam_1(A),A) & v3_prob_3(k9_setfam_1(A),A) ) )).
fof(t68_pscomp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [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) => r1_xxreal_0(k9_pscomp_1(B),k9_pscomp_1(A)) ) ) ) )).
fof(t68_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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))) ) ) ) ) )).
fof(t68_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t68_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => k6_qc_lang3(A,k15_qc_lang1(A,B,C)) = k6_qc_lang3(A,C) ) ) ) )).
fof(t68_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k23_quaterni(k25_quaterni(A,B),C) = k23_quaterni(k25_quaterni(B,A),k24_quaterni(C)) ) ) ) )).
fof(t68_quaterni,axiom,( k28_quaterni(k18_quaterni) = 1 )).
fof(t68_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r1_tarski(B,A) => k5_relat_1(k5_relat_1(C,A),B) = k5_relat_1(C,B) ) ) )).
fof(t68_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ v2_struct_0(C) & l1_rewrite3(C,B) ) => ( v2_rewrite3(C,A,B) => ! [D] : ( m1_rewrite1(D,k1_rewrite3(A,B,C)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t68_rfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ 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)) ) ) )).
fof(t68_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) )).
fof(t68_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v7_valued_0(A) & v1_seq_2(A) ) => k2_rinfsup1(k4_rinfsup1(A)) = k1_rinfsup1(A) ) ) )).
fof(t68_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t68_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_rlvect_1(C) & m1_rlsub_1(C,A) ) => ! [D] : ( ( v1_rlvect_1(D) & m1_rlsub_1(D,A) ) => ( k3_rlsub_1(A,B,C) = k3_rlsub_1(A,B,D) <=> C = D ) ) ) ) ) )).
fof(t68_rltopsp1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_hidden(B,k1_rltopsp1(A,B,C)) ) ) ) )).
fof(t68_rlvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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,D,C)) ) ) ) ) )).
fof(t68_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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)) ) ) ) )).
fof(t68_rmod_4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( 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) ) ) ) ) )).
fof(t68_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => m2_rusub_1(u1_struct_0(B),A,B) ) ) )).
fof(t68_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t68_scmfsa8c,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ~ r2_hidden(k2_compos_1(k1_scmfsa_2),k10_xtuple_0(k1_scmfsa8c(A))) ) )).
fof(t68_scmfsa_2,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ( k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k17_scmfsa_2(B,A),C),k4_struct_0(k1_scmfsa_2)) = k4_card_1(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,C)) & ? [D] : ( v7_ordinal1(D) & D = k1_int_2(k1_funct_1(C,B)) & k18_scmfsa_2(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k17_scmfsa_2(B,A),C),A) = k5_finseq_2(k4_ordinal1,D,k5_numbers) ) & ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k17_scmfsa_2(B,A),C),D) = k1_funct_1(C,D) ) & ! [D] : ( m1_scmfsa_2(D) => ( D != A => r2_relset_1(k4_ordinal1,k4_numbers,k18_scmfsa_2(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k17_scmfsa_2(B,A),C),D),k18_scmfsa_2(C,D)) ) ) ) ) ) ) )).
fof(t68_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmpds_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ~ v2_extpro_1(k15_scmpds_2(C,D,A,B),2,k1_scmpds_2) ) ) ) ) )).
fof(t68_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => k1_funct_1(k7_scmpds_6(A,B,C),k5_numbers) = k8_scmpds_2(A,B,k1_nat_1(k5_card_1(C),1)) ) ) ) )).
fof(t68_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v11_scmyciel(A) ) => ! [B] : ( ( v4_scmyciel(B) & v11_scmyciel(B) ) => ( r1_tarski(A,B) => r1_xxreal_0(k10_scmyciel(A),k10_scmyciel(B)) ) ) ) )).
fof(t68_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r3_semi_af1(A,B,C,D,E) => r3_semi_af1(A,B,D,C,E) ) ) ) ) ) ) )).
fof(t68_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => k17_seq_4(A,k15_seq_4(A),B) = k16_seq_4(A,B) ) ) )).
fof(t68_setlim_1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => r1_tarski(k3_prob_1(A,C),k3_kurato_0(A,C)) ) ) )).
fof(t68_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k4_kurato_0(A,k2_setlim_2(A,B,C)) = k4_subset_1(A,k4_kurato_0(A,B),k4_kurato_0(A,C)) ) ) )).
fof(t68_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_sheffer1(A) ) => ( v1_sheffer2(A) => v11_sheffer1(A) ) ) )).
fof(t68_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k1_rcomp_1(k5_numbers,1)) => ( ~ r1_xxreal_0(k1_funct_1(k18_sin_cos,A),k5_numbers) & r1_xxreal_0(k7_xcmplx_0(1,2),k1_funct_1(k18_sin_cos,A)) ) ) ) )).
fof(t68_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) => k17_sin_cos(k2_sin_cos6(A)) = A ) ) )).
fof(t68_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( B = k7_xcmplx_0(1,k7_xcmplx_0(k6_xcmplx_0(k23_sin_cos(A),k23_sin_cos(k4_xcmplx_0(A))),2)) & A != k5_numbers & A != k3_power(k4_power,k7_xcmplx_0(k2_xcmplx_0(1,k3_square_1(k2_xcmplx_0(1,k1_square_1(B)))),B)) & A != k3_power(k4_power,k7_xcmplx_0(k6_xcmplx_0(1,k3_square_1(k2_xcmplx_0(1,k1_square_1(B)))),B)) ) ) ) )).
fof(t68_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) => k4_sin_cos9(A) = k6_xcmplx_0(k28_sin_cos,k4_sin_cos9(k4_xcmplx_0(A))) ) ) )).
fof(t68_sincos10,axiom,( k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_fdiff_9,k4_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))),k4_sincos10) = k1_partfun2(k1_numbers,k4_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) )).
fof(t68_sprect_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => k17_pscomp_1(k3_topreal1(2,k1_sprect_1(A))) = k1_rltopsp1(k15_euclid(2),k10_pscomp_1(A),k13_pscomp_1(A)) ) )).
fof(t68_sprect_2,axiom,( ! [A] : ( ( ~ 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,k21_pscomp_1(k3_topreal1(2,A))),k4_finseq_4(A,k20_pscomp_1(k3_topreal1(2,A)))) ) ) )).
fof(t68_sprect_5,axiom,( ! [A] : ( ( ~ 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)) & 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)))) ) ) )).
fof(t68_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_valuat_1(C,A,B) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [F] : ( m2_funct_2(F,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ( r2_relset_1(k3_qc_lang1(A),B,k5_relset_1(k3_qc_lang1(A),B,E,k24_qc_lang1(A,D)),k5_relset_1(k3_qc_lang1(A),B,F,k24_qc_lang1(A,D))) => ( r1_valuat_1(A,B,D,C,E) <=> r1_valuat_1(A,B,D,C,F) ) ) ) ) ) ) ) ) )).
fof(t68_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => r1_tarski(C,k4_subset_1(u1_struct_0(A),k5_setfam_1(u1_struct_0(A),B),k1_tops_1(A,k2_pre_topc(A,k5_setfam_1(u1_struct_0(A),B))))) ) ) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v4_tops_1(C,A) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(D,B) => r1_tarski(D,C) ) ) ) => r1_tarski(k4_subset_1(u1_struct_0(A),k5_setfam_1(u1_struct_0(A),B),k1_tops_1(A,k2_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)))),C) ) ) ) ) ) )).
fof(t68_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_tex_2(B,A) & m1_pre_topc(B,A) ) => ? [C] : ( 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) ) ) ) )).
fof(t68_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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) & v3_pre_topc(B,A) & ! [C] : ( ( v1_pre_topc(C) & v1_tsep_1(C,A) & v1_tex_2(C,A) & v1_tex_3(C,A) & m1_pre_topc(C,A) ) => B != u1_struct_0(C) ) ) ) ) )).
fof(t68_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ( ! [C] : ( ( v1_tsep_1(C,A) & m1_pre_topc(C,A) ) => ( r1_tsep_1(B,C) | m1_pre_topc(B,C) ) ) => v2_tdlat_3(B) ) ) ) )).
fof(t68_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(C))) => ( r1_tarski(F,u1_struct_0(D)) => k7_relset_1(u1_struct_0(C),u1_struct_0(B),E,F) = k7_relset_1(u1_struct_0(D),u1_struct_0(B),k3_tmap_1(A,B,C,D,E),F) ) ) ) ) ) ) ) ) )).
fof(t68_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k2_borsuk_1(k3_topmetr,k3_topmetr)),u1_struct_0(k15_euclid(2))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_borsuk_1(k3_topmetr,k3_topmetr)),u1_struct_0(k15_euclid(2))))) ) => ( ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => k1_funct_1(C,k4_tarski(D,E)) = k10_finseq_1(D,E) ) ) => k7_relset_1(u1_struct_0(k2_borsuk_1(k3_topmetr,k3_topmetr)),u1_struct_0(k15_euclid(2)),C,k2_zfmisc_1(A,B)) = k4_card_3(k5_funct_4(k1_zfmisc_1(k1_numbers),1,2,A,B)) ) ) ) ) )).
fof(t68_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v5_tops_1(B,A) & v5_tops_1(C,A) ) => v5_tops_1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).
fof(t68_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( ( r1_tarski(C,D) & v3_tops_1(D,B) ) => v3_tops_1(C,A) ) ) ) ) ) )).
fof(t68_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t68_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( r2_hidden(C,k13_trees_3(A,B)) <=> ~ ( C != k1_xboole_0 & ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ( ~ ( r2_hidden(D,A) & C = k7_finseq_1(k14_trees_3(k5_numbers),D) ) & ~ ( r2_hidden(D,B) & C = k7_finseq_1(k14_trees_3(1),D) ) ) ) ) ) ) ) )).
fof(t68_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( ( A = k1_tsep_1(A,B,C) & r3_tsep_1(A,B,C) ) => ( v1_tsep_1(B,A) & m1_pre_topc(B,A) ) ) ) ) ) )).
fof(t68_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_valued_0(D) ) => k63_valued_2(A,B,C,k30_valued_1(D)) = k63_valued_2(A,k2_valued_2(k1_valued_2(B)),k16_valued_2(A,B,C),D) ) ) ) )).
fof(t68_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_vectsp_4(D,A,B) => ? [E] : ( m2_vectsp_4(E,A,B,D) & r2_hidden(C,E) ) ) ) ) ) )).
fof(t68_waybel23,axiom,( ! [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] : ( ( v6_waybel23(B,A) & m1_waybel23(B,A) ) => u1_struct_0(k1_waybel_8(k1_yellow_1(k7_waybel_0(k5_yellow_0(A,B))))) = a_2_0_waybel23(A,B) ) ) )).
fof(t68_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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) => v23_waybel_0(D,B,A) ) ) ) ) ) ) )).
fof(t68_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v9_waybel_1(A) => v2_yellow_0(A) ) ) )).
fof(t68_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ~ ( r1_tarski(C,A) & r1_tarski(C,B) & r1_xboole_0(A,B) ) ) )).
fof(t68_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k11_xboolean(k11_xboolean(A,B),B) = k11_xboolean(A,B) ) ) )).
fof(t68_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,3),k7_xcmplx_0(A,3)),k7_xcmplx_0(A,3)) = A ) )).
fof(t68_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(k3_xcmplx_0(B,C),k3_xcmplx_0(A,C)) ) ) ) ) )).
fof(t68_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( k3_xxreal_1(A,B) = k3_xxreal_1(C,D) => ( r1_xxreal_0(B,A) | ( A = C & B = D ) ) ) ) ) ) ) )).
fof(t68_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => r1_xxreal_0(k4_xxreal_0(k2_xxreal_2(A),k2_xxreal_2(B)),k2_xxreal_2(k3_xboole_0(A,B))) ) ) )).
fof(t68_xxreal_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( k4_xxreal_3(A,B) = k4_xxreal_3(A,C) => ( A = k5_numbers | B = C ) ) ) ) ) )).
fof(t68_yellow10,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) => ( v3_waybel_3(k3_yellow_3(A,B)) => ( v3_waybel_3(A) & v3_waybel_3(B) ) ) ) ) )).
fof(t68_yellow_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( r2_hidden(k1_yellow_0(A,C),u1_struct_0(B)) => k1_yellow_0(B,C) = k1_yellow_0(A,C) ) ) ) ) )).
fof(t68_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ r1_yellow_5(A,k1_yellow_5(A,B,C),C) ) ) ) )).
fof(t68_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ~ r3_zf_lang(C,k5_zf_lang(A,B)) ) ) ) )).
fof(t68_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => k2_zf_model(k16_zf_lang(B,C,D,A)) = k7_subset_1(k1_zf_lang,k2_zf_model(A),k1_enumset1(B,C,D)) ) ) ) ) )).
fof(t68_zfmisc_1,axiom,( ! [A] : ! [B] : r1_tarski(k2_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)),k1_zfmisc_1(k2_xboole_0(A,B))) )).
fof(t68_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_zmodul01(E,A) => ( ( r2_hidden(B,k5_zmodul01(A,C,E)) & r2_hidden(B,k5_zmodul01(A,D,E)) ) => k5_zmodul01(A,C,E) = k5_zmodul01(A,D,E) ) ) ) ) ) ) )).
fof(t68_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( k33_zmodul02(A,B) = k3_zmodul01(A) & B != k1_xboole_0 & B != k6_domain_1(u1_struct_0(A),k4_struct_0(A)) ) ) ) )).
fof(t69_abcmiz_0,axiom,( ! [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) & l3_abcmiz_0(A) ) => v3_rewrite1(k11_abcmiz_0(A)) ) )).
fof(t69_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v8_abcmiz_1(B,A) & m1_abcmiz_1(B,A,k13_abcmiz_1(A)) ) => k37_abcmiz_1(A,B) != B ) ) )).
fof(t69_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_4(C,A) & v1_aff_4(D,A) & r1_aff_4(A,C,D) ) => k3_aff_4(A,B,C) = k3_aff_4(A,B,D) ) ) ) ) ) )).
fof(t69_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => k62_valued_1(A) = k7_nat_d(k5_card_1(A),1) ) )).
fof(t69_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & v1_finset_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v5_ordinal1(D) & v1_finset_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v5_ordinal1(E) & v1_finset_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) ) => k1_ordinal4(D,E) = k3_relat_1(k1_ordinal4(B,C),A) ) ) ) ) ) ) )).
fof(t69_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r4_analmetr(A,B,E,C,D) & r5_analmetr(A,C,D,E) ) ) ) ) ) )).
fof(t69_aofa_000,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_freealg(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k7_freealg(k19_aofa_000,A))) => ! [C] : ( m1_subset_1(C,A) => ( m1_subset_1(k4_trees_4(C,B),u1_struct_0(k7_freealg(k19_aofa_000,A))) => B = k1_xboole_0 ) ) ) ) )).
fof(t69_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( m1_subset_1(C,k5_arytm_3) => ~ ( ( ( ~ r3_arytm_3(B,A) & r3_arytm_3(B,C) ) | ( r3_arytm_3(A,B) & ~ r3_arytm_3(C,B) ) ) & r3_arytm_3(C,A) ) ) ) ) )).
fof(t69_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ( v2_comseq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k2_asympt_1,k3_asympt_1(A))) & k1_seq_2(k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k2_asympt_1,k3_asympt_1(A))) = k5_numbers ) ) ) )).
fof(t69_bcialg_1,axiom,( ! [A] : ( ( ~ 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) & v19_bcialg_1(A) & l2_bcialg_1(A) ) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) & k1_bcialg_1(A,B,k4_struct_0(A)) = B ) ) ) ) ) ) )).
fof(t69_borsuk_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k4_subset_1(k1_numbers,k4_rcomp_1(k2_xxreal_0,A),k1_seq_4(B)) != k1_numbers ) ) )).
fof(t69_borsuk_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_topmetr)) => ( r1_xxreal_0(k7_xcmplx_0(1,2),A) => r2_hidden(k4_tarski(A,k5_numbers),k8_borsuk_6) ) ) )).
fof(t69_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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,k7_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) )).
fof(t69_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_eqrel_1(I,A) => ! [J] : ( m1_eqrel_1(J,A) => ! [K] : ( 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,E,B) = k2_partit1(A,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),K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t69_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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,k6_bvfunc26(A,B,C)),k5_bvfunc_1(A,B,k1_bvfunc_1(A,C))) ) ) ) )).
fof(t69_bvfunc_1,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => ( ( k6_xboolean(C,k6_xboolean(B,A)) = k8_margrel1 & B = k8_margrel1 & C = k8_margrel1 ) => A = k8_margrel1 ) ) ) ) )).
fof(t69_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( ( r1_xboole_0(k9_xtuple_0(C),k6_subset_1(k9_xtuple_0(B),k9_xtuple_0(D))) & r2_hidden(C,k8_card_3(A)) & r2_hidden(D,k8_card_3(B)) ) => r2_hidden(k1_funct_4(C,D),k8_card_3(k1_funct_4(A,B))) ) ) ) ) ) )).
fof(t69_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => m2_cat_1(k6_partfun1(u4_struct_0(A)),A,A) ) )).
fof(t69_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,u4_struct_0(k2_oppcat_1(B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u4_struct_0(k2_oppcat_1(B))))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_oppcat_1(B))) => ( m2_cat_3(C,k2_oppcat_1(B),D,A) <=> m1_cat_3(k5_cat_3(B,A,C),B,k4_oppcat_1(B,D),A) ) ) ) ) )).
fof(t69_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,B,D) => ! [F] : ( 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 & ( v8_cat_1(E,A,B,D) | v8_cat_1(F,A,C,D) ) & ~ v8_cat_1(k29_cat_4(A,B,C,D,E,F),A,k20_cat_4(A,B,C),D) ) ) ) ) ) ) ) )).
fof(t69_cfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,k2_numbers))) ) => ( ( r1_tarski(B,A) & v1_comseq_2(k2_partfun1(C,k2_numbers,D,A)) ) => v1_comseq_2(k2_partfun1(C,k2_numbers,D,B)) ) ) ) )).
fof(t69_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ~ ( B != C & ~ r1_chord(A,B,C) & ~ ! [D] : ( m2_chord(D,A,B,C) => m2_chord(D,A,C,B) ) ) ) ) ) )).
fof(t69_classes1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => ( r1_ordinal1(k6_classes1(A),B) <=> ! [C] : ( r2_hidden(C,A) => r2_hidden(k6_classes1(C),B) ) ) ) )).
fof(t69_classes2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ( r1_tarski(k13_classes2,A) & r1_tarski(k1_classes1(k1_xboole_0),A) & r1_tarski(k16_classes2(k1_xboole_0),A) ) ) )).
fof(t69_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( m1_clvect_1(D,A) => ( k5_clvect_1(A,k1_clvect_1(A,B,C),D) = u1_struct_0(D) => ( C = k5_numbers | r1_struct_0(D,B) ) ) ) ) ) ) )).
fof(t69_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r2_clvect_2(A,B,C) <=> ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(E,F) & r1_xxreal_0(D,k13_csspace(A,k5_algstr_0(A,k1_normsp_1(A,B,F),k1_normsp_1(A,C,F)))) ) ) ) ) ) ) ) ) )).
fof(t69_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ! [C] : ( r2_hidden(k4_tarski(B,C),k1_coh_sp(k13_cohsp_1(A))) <=> ( r2_hidden(B,k3_tarski(A)) & r2_hidden(C,k3_tarski(A)) & ~ ( B != C & r2_hidden(k4_tarski(B,C),k1_coh_sp(A)) ) ) ) ) )).
fof(t69_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k9_complex1(k3_xcmplx_0(A,A)) = k9_complex1(k3_xcmplx_0(A,k8_complex1(A))) ) )).
fof(t69_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k4_complex2(A,B,C) = k4_complex2(k6_xcmplx_0(A,B),k5_numbers,k6_xcmplx_0(C,B)) ) ) ) )).
fof(t69_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_complfld)) => r1_xxreal_0(k9_complex1(k5_algstr_0(k1_complfld,B,C)),k2_xcmplx_0(k9_complex1(k5_algstr_0(k1_complfld,B,A)),k9_complex1(k5_algstr_0(k1_complfld,A,C)))) ) ) ) )).
fof(t69_complsp2,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m1_subset_1(B,k2_numbers) => ! [C] : ( m2_finseq_1(C,k2_numbers) => ! [D] : ( m2_finseq_1(D,k2_numbers) => ! [E] : ( m2_finseq_1(E,k2_numbers) => ( ( k3_finseq_1(C) = k3_finseq_1(D) & k3_finseq_1(D) = k3_finseq_1(E) ) => k8_complsp2(k7_seq_4(k10_seq_4(C,A),k10_seq_4(D,B)),E) = k2_xcmplx_0(k3_xcmplx_0(A,k8_complsp2(C,E)),k3_xcmplx_0(B,k8_complsp2(D,E))) ) ) ) ) ) ) )).
fof(t69_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v6_comput_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_comput_1(k4_ordinal1))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,B) ) => r2_hidden(k4_comput_1(B,A),C) ) ) ) ) )).
fof(t69_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,A,C) = k1_power(C,k9_nat_1(k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,B),C)) ) & v2_comseq_2(A) ) => ( r1_xxreal_0(1,k1_seq_2(A)) | v2_comseq_3(B) ) ) ) ) )).
fof(t69_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( B = a_3_3_convex4(A,C,D) => v2_convex4(B,A) ) ) ) ) ) )).
fof(t69_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ( ~ r2_hidden(D,k24_qc_lang1(A,B)) => v2_cqc_the1(k10_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) ) ) ) ) ) )).
fof(t69_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k6_clvect_1(A,B,k6_complex1),B) ) ) )).
fof(t69_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(A,k9_xtuple_0(k26_sin_cos)) & r2_hidden(B,k9_xtuple_0(k26_sin_cos)) ) => k9_diff_1(k26_sin_cos,A,B) = k7_xcmplx_0(k17_sin_cos(k6_xcmplx_0(A,B)),k3_xcmplx_0(k3_xcmplx_0(k19_sin_cos(A),k19_sin_cos(B)),k6_xcmplx_0(A,B))) ) ) ) )).
fof(t69_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k7_xcmplx_0(1,k1_square_1(k17_sin_cos(D))) ) => ( A = B | k17_sin_cos(A) = k5_numbers | k17_sin_cos(B) = k5_numbers | k9_diff_1(C,A,B) = k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(16,k19_sin_cos(k7_xcmplx_0(k2_xcmplx_0(B,A),2))),k17_sin_cos(k7_xcmplx_0(k6_xcmplx_0(B,A),2))),k19_sin_cos(k7_xcmplx_0(k6_xcmplx_0(B,A),2))),k17_sin_cos(k7_xcmplx_0(k2_xcmplx_0(B,A),2))),k3_xcmplx_0(k1_square_1(k6_xcmplx_0(k19_sin_cos(k2_xcmplx_0(A,B)),k19_sin_cos(k6_xcmplx_0(A,B)))),k6_xcmplx_0(A,B))) ) ) ) ) ) )).
fof(t69_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_enumset1(A,B,C,D) = k2_enumset1(B,D,A,C) )).
fof(t69_eqrel_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_eqrel_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( r2_hidden(D,B) => ( r1_xboole_0(D,C) | r1_tarski(D,C) ) ) ) => C = k8_relset_1(A,B,k13_eqrel_1(A,B),k7_relset_1(A,B,k13_eqrel_1(A,B),C)) ) ) ) ) )).
fof(t69_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => k22_rvsum_1(k8_euclid(3,A,B),k8_euclid(3,C,D)) = k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k22_rvsum_1(A,C),k22_rvsum_1(A,D)),k22_rvsum_1(B,C)),k22_rvsum_1(B,D)) ) ) ) ) )).
fof(t69_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(B)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(B)) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(k1_euclid(B)),k1_euclidlp(B)) => ~ ( r2_hidden(C,E) & r2_hidden(D,E) & ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(B)) => ~ ( r2_hidden(F,E) & k8_euclid(B,F,C) = k9_euclid(B,k8_euclid(B,D,C),A) ) ) ) ) ) ) ) ) )).
fof(t69_exchsort,axiom,( ! [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) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_exchsort(B) ) => ! [C] : ( m1_subset_1(C,k9_xtuple_0(B)) => ! [D] : ( m1_subset_1(D,k9_xtuple_0(B)) => ! [E] : ( m1_subset_1(E,k9_xtuple_0(B)) => ( ( r2_hidden(C,E) & r2_hidden(E,D) ) => ( k1_binop_1(k7_exchsort(A,B,C,D),C,E) = k4_tarski(C,E) & k1_binop_1(k7_exchsort(A,B,C,D),E,D) = k4_tarski(E,D) ) ) ) ) ) ) ) )).
fof(t69_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k14_facirc_1(A,B,C),k16_facirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ( ( E = k1_funct_1(D,A) & F = k1_funct_1(D,B) ) => k1_funct_1(k6_circuit2(k14_facirc_1(A,B,C),k16_facirc_1(A,B,C),D),k4_tarski(k10_finseq_1(A,B),k3_facirc_1)) = k10_margrel1(E,F) ) ) ) ) )).
fof(t69_fdiff_11,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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,k1_sin_cos9),k1_taylor_1(A)),k7_xcmplx_0(1,A)))) & r1_tarski(B,k2_rcomp_1(k4_xcmplx_0(1),1)) & ! [C] : ( v1_xreal_0(C) => ~ ( r2_hidden(C,B) & k1_funct_1(k1_sin_cos9,C) = k5_numbers ) ) ) => ( r1_xxreal_0(A,k5_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,k1_sin_cos9),k1_taylor_1(A)),k7_xcmplx_0(1,A)),B) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => k1_funct_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,k1_sin_cos9),k1_taylor_1(A)),k7_xcmplx_0(1,A)),B),C) = k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(k3_prepower(k1_funct_1(k1_sin_cos9,C),k2_xcmplx_0(A,1)),k2_xcmplx_0(1,k1_square_1(C))))) ) ) ) ) ) ) ) )).
fof(t69_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ v1_xboole_0(D) & v19_lattices(D,A) & v20_lattices(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ( r1_filter_0(A,D,B,C) <=> r2_hidden(k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k8_filter_0(A,D)) ) ) ) ) ) )).
fof(t69_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => k6_filter_0(A,B) = k10_filter_2(A,B) ) ) )).
fof(t69_finseq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( ( v1_relat_1(H) & v1_funct_1(H) & v1_finseq_1(H) ) => ( H = 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)) => ( k3_finseq_1(H) = 7 & k1_funct_1(H,1) = A & k1_funct_1(H,2) = B & k1_funct_1(H,3) = C & k1_funct_1(H,4) = D & k1_funct_1(H,5) = E & k1_funct_1(H,6) = F & k1_funct_1(H,7) = G ) ) ) )).
fof(t69_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( 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] : ( m2_finseq_1(F,A) => ! [G] : ( m2_finseq_1(G,B) => ( D = k3_funcop_1(E,F,G) => k3_finseq_1(D) = k3_xxreal_0(k3_finseq_1(F),k3_finseq_1(G)) ) ) ) ) ) ) ) ) )).
fof(t69_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k1_finseq_3(A,k1_xboole_0) = A ) )).
fof(t69_finseq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ! [D] : ( m2_finseq_1(D,B) => ( r2_hidden(A,k4_finseq_1(D)) => k7_partfun1(B,k8_finseq_1(B,C,D),k2_xcmplx_0(k3_finseq_1(C),A)) = k7_partfun1(B,D,A) ) ) ) ) ) )).
fof(t69_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m2_finseq_1(D,B) => k3_finseq_1(k5_finseq_5(B,D,C,A)) = k1_nat_1(k3_finseq_1(D),1) ) ) ) ) )).
fof(t69_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ( ( r2_hidden(B,k10_xtuple_0(D)) & r2_hidden(C,k6_subset_1(k10_xtuple_0(D),k10_xtuple_0(k1_finseq_5(A,D,B)))) ) => k6_finseq_4(D,C) = k6_finseq_4(k6_finseq_4(D,B),C) ) ) ) ) ) )).
fof(t69_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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] : ( ( 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) ) => k3_funct_2(A,A,k10_funcop_1(A,A,D,B,k6_partfun1(A)),k4_binop_1(A,C)) = k4_binop_1(A,C) ) ) ) ) ) )).
fof(t69_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => k8_flang_1(A,B) = k8_flang_1(A,k7_subset_1(k3_catalan2(A),B,k4_flang_1(A,k2_flang_1(A)))) ) )).
fof(t69_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => r1_tarski(k1_flang_2(A,k7_flang_1(A,B,C),D,E),k8_flang_1(A,B)) ) ) ) ) )).
fof(t69_flang_3,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ( k2_flang_3(A,C) = k1_tarski(B) => B = k2_flang_1(A) ) ) )).
fof(t69_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(A,k32_fomodel0(B)) <=> r1_abian(A,B) ) ) )).
fof(t69_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r1_tarski(k2_zfmisc_1(k10_xtuple_0(B),k10_xtuple_0(C)),k9_xtuple_0(A)) => k9_xtuple_0(k3_funcop_1(A,B,C)) = k3_xboole_0(k9_xtuple_0(B),k9_xtuple_0(C)) ) ) ) ) )).
fof(t69_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => k8_relat_1(k5_relat_1(C,A),B) = k3_xboole_0(A,k8_relat_1(C,B)) ) )).
fof(t69_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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_partfun1(k3_partfun1(C,A,B),A) ) ) )).
fof(t69_funct_3,axiom,( ! [A] : ! [B] : k15_funct_3(k4_relat_1(A),k4_relat_1(B)) = k4_relat_1(k2_zfmisc_1(A,B)) )).
fof(t69_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( ( r1_tarski(k10_xtuple_0(C),k9_xtuple_0(A)) & r1_tarski(k10_xtuple_0(D),k9_xtuple_0(B)) & r1_partfun1(A,B) ) => k3_relat_1(k1_funct_4(C,D),k1_funct_4(A,B)) = k1_funct_4(k3_relat_1(C,A),k3_relat_1(D,B)) ) ) ) ) ) )).
fof(t69_funct_7,axiom,( ! [A] : ( v1_relat_1(A) => k8_funct_7(A,1) = A ) )).
fof(t69_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ( r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))) => r2_funct_8(A,k1_numbers,k1_numbers,k26_sin_cos) ) ) )).
fof(t69_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_fvaluat1(D,A) => ( ( v3_fvaluat1(A) & m1_subset_1(C,u1_struct_0(k7_fvaluat1(A,D))) ) => r1_xxreal_0(k3_funct_2(u1_struct_0(A),k6_numbers,D,B),k3_supinf_2(k3_funct_2(u1_struct_0(A),k6_numbers,D,B),k3_funct_2(u1_struct_0(A),k6_numbers,D,C))) ) ) ) ) ) )).
fof(t69_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v3_group_1(B) & v5_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [E] : ( 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) & k10_fvsum_1(A,B,k12_fvsum_1(A,B,D,E),C) = k12_fvsum_1(A,B,D,k10_fvsum_1(A,B,E,C)) ) ) ) ) ) ) )).
fof(t69_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(k4_tarski(k10_finseq_1(A,B),k4_gfacirc1),k3_msafree2(k25_gfacirc1(A,B,C))) & r2_hidden(k24_gfacirc1(A,B,C),k3_msafree2(k25_gfacirc1(A,B,C))) & r2_hidden(k4_tarski(k10_finseq_1(A,B),k3_gfacirc1),k3_msafree2(k25_gfacirc1(A,B,C))) & r2_hidden(k4_tarski(k10_finseq_1(B,C),k3_twoscomp),k3_msafree2(k25_gfacirc1(A,B,C))) & r2_hidden(k4_tarski(k10_finseq_1(C,A),k2_twoscomp),k3_msafree2(k25_gfacirc1(A,B,C))) & r2_hidden(k21_gfacirc1(A,B,C),k3_msafree2(k25_gfacirc1(A,B,C))) ) )).
fof(t69_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ( r2_hidden(B,k36_glib_000(A,C)) <=> ? [D] : r2_glib_000(A,B,C,D) ) ) ) )).
fof(t69_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( k3_glib_001(A,B) = k1_funct_1(k11_glib_001(A,B),1) & k4_glib_001(A,B) = k1_funct_1(k11_glib_001(A,B),k3_finseq_1(k11_glib_001(A,B))) ) ) ) )).
fof(t69_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_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_0(B),A) | r1_xxreal_0(k3_finseq_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_0(u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B),A),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B),k1_nat_1(A,1))),k7_xcmplx_0(1,2)),k19_euclid(1,k5_numbers)),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B),A),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k7_nat_d(k3_finseq_1(B),1),k1_nat_1(A,1))),k7_xcmplx_0(1,2))),k2_xboole_0(k4_subset_1(u1_struct_0(k15_euclid(2)),k1_tops_1(k15_euclid(2),k3_goboard5(B,k7_nat_d(k3_finseq_1(B),1),A)),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_0(u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B),A),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B),k1_nat_1(A,1))),k7_xcmplx_0(1,2))))) ) ) ) ) )).
fof(t69_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( v15_algstr_0(C) & v1_group_3(C,A) & m1_group_2(C,A) ) => ! [D] : ( ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) ) => ? [E] : ( 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,k4_group_11(A,B,C),k4_group_11(A,B,D)),k4_group_11(A,B,E)) ) ) ) ) ) )).
fof(t69_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => k7_group_1(k6_group_2(A)) = 1 ) )).
fof(t69_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_group_2(A,k6_group_3(A,k7_group_2(A),B),k7_group_2(A)) ) ) )).
fof(t69_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => u1_struct_0(k11_group_4(A)) = k1_group_3(A) ) )).
fof(t69_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( v1_group_3(C,A) & m1_group_2(C,A) ) => r1_group_2(A,k8_group_5(A,B,C),k8_group_5(A,C,B)) ) ) ) )).
fof(t69_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v15_algstr_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ( ( v7_struct_0(A) & v7_struct_0(B) ) => r2_group_6(A,B) ) ) ) )).
fof(t69_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( 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) ) ) ) )).
fof(t69_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_tarski(k7_ideal_1(A,k6_domain_1(u1_struct_0(A),B)),k7_ideal_1(A,k7_domain_1(u1_struct_0(A),B,C))) & r1_tarski(k7_ideal_1(A,k6_domain_1(u1_struct_0(A),C)),k7_ideal_1(A,k7_domain_1(u1_struct_0(A),B,C))) ) ) ) ) )).
fof(t69_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(k2_xcmplx_0(k1_int_1(B),1),A) & ~ r1_xxreal_0(k2_xcmplx_0(B,1),A) & r1_xxreal_0(k3_int_1(B),k3_int_1(A)) ) ) ) )).
fof(t69_integr11,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(B,C) & D = k47_valued_1(k1_numbers,k1_numbers,k1_numbers,E,F) & F = k1_taylor_1(2) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,C) => ( k1_funct_1(E,H) = k1_square_1(A) & ~ r1_xxreal_0(k1_funct_1(D,H),k5_numbers) & k1_funct_1(G,H) = k7_xcmplx_0(H,A) & ~ r1_xxreal_0(k1_funct_1(G,H),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(G,H)) & H != k5_numbers & ~ r1_xxreal_0(A,k5_numbers) ) ) ) & k9_xtuple_0(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,G,k1_sin_cos6)) = C & r1_tarski(C,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,C),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,G,k1_sin_cos6)),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k4_taylor_1(k7_xcmplx_0(1,2)))))) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,G,k1_sin_cos6),B)) ) => k2_integra5(B,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,G,k1_sin_cos6)) = k6_xcmplx_0(k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,C),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,G,k1_sin_cos6)),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k4_taylor_1(k7_xcmplx_0(1,2)))),k2_seq_4(B)),k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,C),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,G,k1_sin_cos6)),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k4_taylor_1(k7_xcmplx_0(1,2)))),k3_seq_4(B))) ) ) ) ) ) ) ) ) )).
fof(t69_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => k2_integra5(A,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)) = k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k18_sin_cos),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k18_sin_cos),k3_seq_4(A))),k1_funct_1(k16_sin_cos,k2_seq_4(A))),k1_funct_1(k16_sin_cos,k3_seq_4(A))) ) )).
fof(t69_integra9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & k1_relset_1(k1_numbers,k1_fdiff_9) = C & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k7_xcmplx_0(k1_funct_1(k16_sin_cos,D),k1_square_1(k1_funct_1(k18_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) = k6_xcmplx_0(k1_funct_1(k1_fdiff_9,k2_seq_4(A)),k1_funct_1(k1_fdiff_9,k3_seq_4(A))) ) ) ) ) )).
fof(t69_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m2_interva1(B,A) => r2_interva1(A,k16_interva1(A,k22_interva1(A),B),B) ) ) )).
fof(t69_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => ! [D] : ( m1_subset_1(D,k1_intpro_1) => ( r2_hidden(k3_intpro_1(B,k3_intpro_1(C,B)),k11_intpro_1(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))),k11_intpro_1(A)) & r2_hidden(k3_intpro_1(k4_intpro_1(B,C),B),k11_intpro_1(A)) & r2_hidden(k3_intpro_1(k4_intpro_1(B,C),C),k11_intpro_1(A)) & r2_hidden(k3_intpro_1(B,k3_intpro_1(C,k4_intpro_1(B,C))),k11_intpro_1(A)) & r2_hidden(k3_intpro_1(B,k5_intpro_1(B,C)),k11_intpro_1(A)) & r2_hidden(k3_intpro_1(C,k5_intpro_1(B,C)),k11_intpro_1(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))),k11_intpro_1(A)) & r2_hidden(k3_intpro_1(k2_intpro_1,B),k11_intpro_1(A)) & r2_hidden(k5_intpro_1(B,k3_intpro_1(B,k2_intpro_1)),k11_intpro_1(A)) ) ) ) ) ) )).
fof(t69_jgraph_5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ 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] : ( 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] : ( ( 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] : ( ( 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,k5_numbers) = A & k1_funct_1(G,1) = C & k1_funct_1(H,k5_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)) ) ) ) ) ) ) ) ) ) ) )).
fof(t69_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) = 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) & 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t69_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( 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)),A))))) => ( v3_connsp_1(B,k1_pre_topc(k15_euclid(2),k3_subset_1(u1_struct_0(k15_euclid(2)),A))) => v1_borsuk_2(k1_pre_topc(k1_pre_topc(k15_euclid(2),k3_subset_1(u1_struct_0(k15_euclid(2)),A)),B)) ) ) ) )).
fof(t69_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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))))) ) => ~ ( v5_pre_topc(B,k5_topmetr,k15_euclid(A)) & ! [C] : ( ( 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)))) ) => ~ ( ! [D] : ( m1_subset_1(D,u1_struct_0(k5_topmetr)) => k3_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr),C,D) = k12_euclid(k3_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)),B,D)) ) & v5_pre_topc(C,k5_topmetr,k3_topmetr) ) ) ) ) ) )).
fof(t69_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( v7_ordinal1(B) => ( k1_relset_1(k6_glib_000(A),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),k23_lexbfs(A,k26_lexbfs(A),B))) = k6_glib_000(A) <=> r1_xxreal_0(k15_glib_000(A),B) ) ) ) )).
fof(t69_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(B,C) & r2_hidden(C,k1_relset_1(k1_numbers,A)) ) ) => ( ! [B] : ( v1_xreal_0(B) => ~ ( v5_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) ) ) ) )).
fof(t69_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,C) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,C) & ~ r1_xxreal_0(A,D) & r2_hidden(D,k1_relset_1(k1_numbers,B)) & k1_funct_1(B,D) != k5_numbers ) ) ) ) => ( ( ~ r2_limfunc2(B,A) & ~ r3_limfunc2(B,A) ) | ( r1_limfunc2(k6_rfunct_1(k1_numbers,k1_numbers,B),A) & k1_limfunc2(k6_rfunct_1(k1_numbers,k1_numbers,B),A) = k5_numbers ) ) ) ) ) )).
fof(t69_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r2_limfunc3(B,A) & v3_limfunc1(C) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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))) ) ) ) ) ) ) ) => ( r1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) & k1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k4_limfunc1(C) ) ) ) ) ) )).
fof(t69_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( v1_mesfunc8(B,A,k1_numbers) => v1_mesfunc8(k5_seqfunc(A,B),A,k1_numbers) ) ) ) )).
fof(t69_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_cqc_lang(A))) => ( r3_cqc_the1(A,D,k8_cqc_lang(A,k6_cqc_lang(A,B),k6_cqc_lang(A,C))) <=> r3_cqc_the1(A,D,k8_cqc_lang(A,C,B)) ) ) ) ) ) )).
fof(t69_mathmorp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( r2_hidden(k4_struct_0(k15_euclid(A)),C) => r1_tarski(k7_mathmorp(k15_euclid(A),B,C,D),B) ) ) ) ) ) )).
fof(t69_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( v3_matrix10(B) => r2_matrix10(k4_matrix10(A,B,C),C) ) ) ) ) )).
fof(t69_matrix13,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( ( v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ( k5_card_1(C) = k5_card_1(D) => ( r1_tarski(k2_zfmisc_1(C,D),k2_matrix_0(B)) <=> r1_tarski(k2_zfmisc_1(D,C),k2_matrix_0(k4_matrix_0(A,B))) ) ) ) ) ) ) )).
fof(t69_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),B,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ( ( v2_funct_1(D) & r2_hidden(F,k4_finseq_1(D)) ) => ( ( E = F & G = k4_algstr_0(C,k1_group_1(C)) ) | k1_vectsp_7(C,k6_prvect_1(C,A),k9_matrix13(C,B,A,D)) = k1_vectsp_7(C,k6_prvect_1(C,A),k9_matrix13(C,B,A,k3_matrix11(E,B,A,u1_struct_0(C),D,k4_fvsum_1(k1_matrix_0(D),C,k7_matrix_0(u1_struct_0(C),D,E),k10_fvsum_1(k1_matrix_0(D),C,k7_matrix_0(u1_struct_0(C),D,F),G))))) ) ) ) ) ) ) ) ) ) )).
fof(t69_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( ( r2_hidden(C,k2_finseq_1(k1_matrix_0(B))) & k1_matrix_0(B) = k1_nat_1(F,1) & r2_hidden(E,k4_finseq_1(B)) & r1_xxreal_0(1,D) ) => ( r1_xxreal_0(F,k5_numbers) | r1_xxreal_0(C,D) | ( k3_matrix_0(A,k16_matrix_0(C,A,B),E,D) = k3_matrix_0(A,B,E,D) & r2_hidden(D,k2_finseq_1(k1_matrix_0(B))) ) ) ) ) ) ) ) ) ) )).
fof(t69_matrixj1,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => k25_matrixj1(A,k4_matrixj1(u1_struct_0(A),B),k4_matrixj1(u1_struct_0(A),C)) = k4_matrixj1(u1_struct_0(A),k3_matrix_3(A,B,C)) ) ) ) )).
fof(t69_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( A = k1_matrix_0(C) => k6_matrixr1(C,k4_matrixr2(A)) = C ) & ( B = k3_finseq_1(C) => k6_matrixr1(k4_matrixr2(B),C) = C ) ) ) ) ) )).
fof(t69_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( k13_mcart_1(k4_tarski(k4_tarski(A,B),C)) = A & k14_mcart_1(k4_tarski(k4_tarski(A,B),C)) = B & k15_mcart_1(k4_tarski(F,k4_tarski(D,E))) = D & k16_mcart_1(k4_tarski(F,k4_tarski(D,E))) = E ) )).
fof(t69_measure6,axiom,( ! [A] : ! [B] : ! [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))) ) => ! [D] : ( v1_xreal_0(D) => k7_relset_1(A,k1_numbers,k9_valued_1(A,k1_numbers,C,D),B) = k1_measure6(k7_relset_1(A,k1_numbers,C,B),D) ) ) )).
fof(t69_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_membered(C) => r1_tarski(k11_member_1(A,k3_xboole_0(B,C)),k3_xboole_0(k11_member_1(A,B),k11_member_1(A,C))) ) ) ) )).
fof(t69_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => k10_memstr_0(A,B,k10_memstr_0(A,B,C,D),E) = k10_memstr_0(A,B,C,k2_xcmplx_0(D,E)) ) ) ) ) ) )).
fof(t69_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( r1_mesfunc2(A,B,D) & v6_supinf_2(D) & r1_mesfunc2(A,B,E) & v6_supinf_2(E) & ! [F] : ( r2_hidden(F,k1_relset_1(A,k4_mesfunc1(A,D,E))) => r1_xxreal_0(k1_funct_1(E,F),k1_funct_1(D,F)) ) ) => ( k1_relset_1(A,k4_mesfunc1(A,D,E)) = k9_subset_1(A,k1_relset_1(A,D),k1_relset_1(A,E)) & k5_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,k1_relset_1(A,k4_mesfunc1(A,D,E)))) = k3_supinf_2(k5_mesfunc5(A,B,C,k4_mesfunc1(A,D,E)),k5_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,E,k1_relset_1(A,k4_mesfunc1(A,D,E))))) ) ) ) ) ) ) ) )).
fof(t69_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( ( 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,k14_mesfunc1(C,E)),k11_mesfunc1(C,F)),B) ) ) ) ) ) ) ) )).
fof(t69_mmlquery,axiom,( ! [A] : ( ( v3_mmlquery(A) & l1_mmlquery(A) ) => ! [B] : ( m2_finseq_1(B,u1_mmlquery(A)) => k37_mmlquery(A,B,k5_numbers,k5_numbers) = k34_mmlquery(A,B) ) ) )).
fof(t69_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k25_modelc_2(k43_modelc_2)) => ( r7_modelc_2(C,k8_modelc_2(A,B)) <=> ! [D] : ( v7_ordinal1(D) => ( ! [E] : ( v7_ordinal1(E) => ( ~ r1_xxreal_0(D,E) => r7_modelc_2(k29_modelc_2(k43_modelc_2,C,E),k3_modelc_2(A)) ) ) => r7_modelc_2(k29_modelc_2(k43_modelc_2,C,D),B) ) ) ) ) ) ) )).
fof(t69_monoid_0,axiom,( ! [A] : k4_binop_1(u1_struct_0(k12_monoid_0(A)),u2_algstr_0(k12_monoid_0(A))) = k6_partfun1(A) )).
fof(t69_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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_msafree4(B,u1_struct_0(A)) ) => ! [C] : ( ( 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)) & v1_msafree4(C,u1_struct_0(A)) ) => ! [D] : ( ( v5_msafree4(D,A,B) & l3_msualg_1(D,A) ) => ! [E] : ( m2_pboole(E,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,C)),u3_msualg_1(A,D)) => ~ ( r1_msualg_3(A,k1_msafree3(A,C),D,E) & ! [F] : ( m2_pboole(F,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,C)),u3_msualg_1(A,k1_msafree3(A,B))) => ~ ( r1_msualg_3(A,k1_msafree3(A,C),k1_msafree3(A,B),F) & r8_pboole(u1_struct_0(A),E,k3_msualg_3(u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,C)),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,D),F,k4_msafree4(A,B,D))) & ! [G] : ( m1_msafree(G,A,k1_msafree3(A,C)) => ( r8_pboole(u1_struct_0(A),G,k13_msafree(A,C)) => r8_pboole(u1_struct_0(A),k1_msafree(u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,C)),u3_msualg_1(A,k1_msafree3(A,B)),G,F),k1_msafree(u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,C)),u3_msualg_1(A,D),G,E)) ) ) ) ) ) ) ) ) ) ) )).
fof(t69_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k4_nat_d(B,A) = k6_xcmplx_0(A,1) => k4_nat_d(k1_nat_1(B,1),A) = k5_numbers ) ) ) )).
fof(t69_ncfcont1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)))) ) => ( r8_ncfcont1(B,C,E,D) => r8_ncfcont1(B,C,k4_vfunct_1(u1_struct_0(B),C,E,A),D) ) ) ) ) ) )).
fof(t69_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(A,B) => r1_tarski(k9_newton(A),k9_newton(B)) ) ) ) )).
fof(t69_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v7_o_ring_1(B,A) & v13_o_ring_1(C,A) ) => v13_o_ring_1(k6_algstr_0(A,B,C),A) ) ) ) ) )).
fof(t69_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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)) ) ) )).
fof(t69_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => k7_ordinal3(k11_ordinal2(A,B),B) = k1_xboole_0 ) ) )).
fof(t69_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => k12_ordinal6(B,k12_ordinal6(k1_ordinal1(B),A)) = k12_ordinal6(k1_ordinal1(B),A) ) ) )).
fof(t69_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( r2_hidden(D,k5_partfun1(A,B,C)) => ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ) ) )).
fof(t69_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => r6_pboole(A,k4_pboole(A,B,k3_pboole(A,C,D)),k2_pboole(A,k4_pboole(A,B,C),k4_pboole(A,B,D))) ) ) ) )).
fof(t69_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( 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,k20_valued_1(k1_euclid(3),k1_numbers,k1_numbers,k1_pdiff_3(1,3,B),k1_pdiff_3(1,3,C)),A) ) ) ) ) )).
fof(t69_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ! [C] : ( ( ~ v1_xboole_0(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ( ( v1_pdiff_7(B,A) & r1_tarski(k1_rvsum_1(C),k2_finseq_1(A)) & r4_pdiff_9(A,B,C,D) & r4_pdiff_9(A,B,C,E) ) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(F,k6_xcmplx_0(k3_finseq_1(C),1)) => ( r3_pdiff_9(A,B,k7_partfun1(k4_ordinal1,C,k1_nat_1(F,1)),k1_seqfunc(k1_euclid(A),k1_numbers,k4_pdiff_9(A,B,C,k3_valued_1(k1_euclid(A),k1_numbers,k1_numbers,D,E)),F)) & r2_relset_1(k1_euclid(A),k1_numbers,k1_seqfunc(k1_euclid(A),k1_numbers,k4_pdiff_9(A,B,C,k3_valued_1(k1_euclid(A),k1_numbers,k1_numbers,D,E)),F),k3_valued_1(k1_euclid(A),k1_numbers,k1_numbers,k1_seqfunc(k1_euclid(A),k1_numbers,k4_pdiff_9(A,B,C,D),F),k1_seqfunc(k1_euclid(A),k1_numbers,k4_pdiff_9(A,B,C,E),F))) ) ) ) ) ) ) ) ) ) )).
fof(t69_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => k10_polyform(A,k7_polyform(A)) = k9_finseq_1(A) ) )).
fof(t69_polynom5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k2_numbers,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) & r1_funct_2(k2_numbers,k2_numbers,u1_struct_0(k1_complfld),u1_struct_0(k1_complfld),C,k8_polynom5(k1_complfld,A,B)) & r1_funct_2(u1_struct_0(k1_complfld),u1_struct_0(k1_complfld),k2_numbers,k2_numbers,k8_polynom5(k1_complfld,A,k1_nat_1(B,1)),k19_valued_1(k2_numbers,k2_numbers,k2_numbers,C,k6_partfun1(k2_numbers))) ) ) ) )).
fof(t69_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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) ) => ( k9_pre_poly(k15_pre_poly(A),k4_ordinal1,k4_finseq_2(2,k15_pre_poly(A)),k21_pre_poly(A,B),1) = k10_finseq_1(k16_pre_poly(A),B) & k9_pre_poly(k15_pre_poly(A),k4_ordinal1,k4_finseq_2(2,k15_pre_poly(A)),k21_pre_poly(A,B),k3_finseq_1(k21_pre_poly(A,B))) = k10_finseq_1(B,k16_pre_poly(A)) ) ) ) )).
fof(t69_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v5_relat_1(B,k3_numbers) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(B) => ( r1_xxreal_0(A,k5_numbers) | v2_comseq_2(k5_prepower(A,B)) ) ) ) ) )).
fof(t69_prob_3,axiom,( ! [A] : ! [B] : ( ( v2_prob_3(B,A) & v3_prob_3(B,A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) <=> ( r1_tarski(B,k9_setfam_1(A)) & ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ( v1_setlim_1(C,A) & r1_tarski(k2_relset_1(k9_setfam_1(A),C),B) ) => r2_hidden(k4_kurato_0(A,C),B) ) ) ) ) )).
fof(t69_pscomp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [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) => r1_xxreal_0(k6_pscomp_1(B),k6_pscomp_1(A)) ) ) ) )).
fof(t69_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,A) & v1_funct_1(E) & v1_partfun1(E,A) ) => r6_pboole(A,k4_pboole(A,k6_pboole(A,B,C),k6_pboole(A,D,E)),k2_pboole(A,k6_pboole(A,k4_pboole(A,B,D),C),k6_pboole(A,B,k4_pboole(A,C,E)))) ) ) ) ) )).
fof(t69_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ( ( r2_qc_lang2(A,B,C) | r2_qc_lang2(A,B,D) ) <=> r3_qc_lang2(A,B,k14_qc_lang1(A,C,D)) ) ) ) ) ) )).
fof(t69_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => k6_qc_lang3(A,k3_qc_lang2(A,B,C)) = k4_subset_1(k4_qc_lang1(A),k6_qc_lang3(A,B),k6_qc_lang3(A,C)) ) ) ) )).
fof(t69_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k23_quaterni(C,k25_quaterni(A,B)) = k23_quaterni(k24_quaterni(C),k25_quaterni(B,A)) ) ) ) )).
fof(t69_quaterni,axiom,( k28_quaterni(k1_xcmplx_0) = 1 )).
fof(t69_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ( ! [B] : ( v7_ordinal1(B) => k9_nat_1(k1_numbers,k6_real_3(A),B) != k5_numbers ) => ! [B] : ( v7_ordinal1(B) => k9_complex1(k5_real_1(k6_real_1(k9_nat_1(k1_numbers,k5_real_3(A),k1_nat_1(B,1)),k9_nat_1(k1_numbers,k6_real_3(A),k1_nat_1(B,1))),k6_real_1(k9_nat_1(k1_numbers,k5_real_3(A),B),k9_nat_1(k1_numbers,k6_real_3(A),B)))) = k7_xcmplx_0(1,k9_complex1(k4_real_1(k9_nat_1(k1_numbers,k6_real_3(A),k1_nat_1(B,1)),k9_nat_1(k1_numbers,k6_real_3(A),B)))) ) ) ) )).
fof(t69_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r1_tarski(A,B) => r1_tarski(k5_relat_1(C,A),k5_relat_1(C,B)) ) ) )).
fof(t69_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( ( ~ v2_struct_0(C) & l1_rewrite3(C,B) ) => ( v2_rewrite3(C,A,B) => ! [D] : ( m1_rewrite1(D,k1_rewrite3(A,B,C)) => ! [E] : ( m1_rewrite1(E,k1_rewrite3(A,B,C)) => ( ( k1_funct_1(D,1) = k1_funct_1(E,1) & k2_xtuple_0(k1_funct_1(D,k3_finseq_1(D))) = k2_xtuple_0(k1_funct_1(E,k3_finseq_1(E))) ) => D = E ) ) ) ) ) ) ) )).
fof(t69_rfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => r2_relset_1(C,k1_numbers,k20_valued_1(C,k1_numbers,k1_numbers,k7_rfunct_1(A,C),k7_rfunct_1(B,C)),k7_rfunct_1(k3_xboole_0(A,B),C)) ) )).
fof(t69_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,A) => ( r2_hidden(C,k1_relset_1(A,B)) => k20_rfunct_3(A,B,k1_tarski(C)) = k9_finseq_1(k1_funct_1(B,C)) ) ) ) ) )).
fof(t69_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v8_valued_0(B) => r1_xxreal_0(k3_funct_2(k4_ordinal1,k1_numbers,k4_rinfsup1(B),k1_nat_1(A,1)),k1_funct_1(B,A)) ) ) ) )).
fof(t69_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(B,k4_rlaffin1(A,C)) => k4_rlaffin1(A,k4_subset_1(u1_struct_0(A),B,C)) = k4_rlaffin1(A,C) ) ) ) ) )).
fof(t69_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_rlvect_1(D) & m1_rlsub_1(D,A) ) => ! [E] : ( ( v1_rlvect_1(E) & m1_rlsub_1(E,A) ) => ( k3_rlsub_1(A,C,D) = k3_rlsub_1(A,B,E) => D = E ) ) ) ) ) ) )).
fof(t69_rltopsp1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_hidden(k1_rlvect_1(A,k3_rlvect_1(A,B,C),k7_xcmplx_0(1,2)),k1_rltopsp1(A,B,C)) ) ) ) )).
fof(t69_rlvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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),D,B,C)) ) ) ) ) )).
fof(t69_rlvect_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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) ) => k4_vectsp_1(A,C,B,k4_rlvect_1(C,k2_pre_poly(u1_struct_0(C)))) = k4_struct_0(C) ) ) ) )).
fof(t69_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ~ ( m2_rmod_2(C,A,B,k1_rmod_2(A,B)) & ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => C != k6_domain_1(u1_struct_0(B),D) ) ) ) ) ) )).
fof(t69_rmod_4,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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) ) => k10_rmod_4(A,B,k1_subset_1(u1_struct_0(B))) = k1_rmod_2(A,B) ) ) )).
fof(t69_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => m2_rusub_1(u1_struct_0(A),A,k2_rusub_1(A)) ) )).
fof(t69_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => k12_rvsum_1(k8_rvsum_1(A,B)) = k4_rvsum_1(k8_rvsum_1(k12_rvsum_1(A),k10_rvsum_1(k14_rvsum_1(A,B),2)),k12_rvsum_1(B)) ) ) )).
fof(t69_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) => ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(D,k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B))) => r8_pboole(u1_struct_0(k1_scmfsa_2),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),D),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),D)) ) ) ) ) ) ) )).
fof(t69_scmfsa_2,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( m1_subset_1(B,k4_card_3(k3_relat_1(k4_scmfsa_1,k5_scmfsa_1))) => ( B = A => k5_memstr_0(k7_card_1(3),k1_scmfsa_2,A) = k10_scmfsa_1(B) ) ) ) )).
fof(t69_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ~ ( A != k5_numbers & v2_extpro_1(k3_scmpds_2(A),2,k1_scmpds_2) ) ) )).
fof(t69_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ( ( 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,D),E)),k5_numbers) | ( r1_scmpds_6(k7_scmpds_6(D,E,C),B,A) & r2_scmpds_6(k7_scmpds_6(D,E,C),B,A) ) ) ) ) ) ) ) ) )).
fof(t69_scmyciel,axiom,( ! [A] : ( v1_finset_1(A) => k10_scmyciel(k5_scmyciel(A)) = k5_card_1(A) ) )).
fof(t69_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r3_semi_af1(A,B,C,D,E) => ( r3_semi_af1(A,D,E,B,C) & r3_semi_af1(A,C,B,E,D) & r3_semi_af1(A,B,D,C,E) & r3_semi_af1(A,E,D,C,B) & r3_semi_af1(A,C,E,B,D) & r3_semi_af1(A,D,B,E,C) & r3_semi_af1(A,E,C,D,B) ) ) ) ) ) ) ) )).
fof(t69_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => k17_seq_4(A,B,k16_seq_4(A,C)) = k13_seq_4(A,B,C) ) ) ) )).
fof(t69_setlim_1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => r1_tarski(k4_kurato_0(A,C),k1_kurato_0(A,C)) ) ) )).
fof(t69_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => r1_tarski(k7_subset_1(A,k4_kurato_0(A,B),k4_kurato_0(A,C)),k4_kurato_0(A,k3_setlim_2(A,B,C))) ) ) )).
fof(t69_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_sheffer1(A) ) => ( v1_sheffer2(A) => v12_sheffer1(A) ) ) )).
fof(t69_sin_cos,axiom,( r1_tarski(k1_rcomp_1(k5_numbers,1),k1_relset_1(k1_numbers,k26_sin_cos)) & r1_tarski(k2_rcomp_1(k5_numbers,1),k1_relset_1(k1_numbers,k26_sin_cos)) )).
fof(t69_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),A) & r1_xxreal_0(A,k7_xcmplx_0(k28_sin_cos,2)) ) => k2_sin_cos6(k17_sin_cos(A)) = A ) ) )).
fof(t69_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => k1_funct_1(k3_sin_cos2,k3_xcmplx_0(2,A)) = k2_xcmplx_0(1,k3_xcmplx_0(2,k1_square_1(k1_funct_1(k1_sin_cos2,A)))) ) )).
fof(t69_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) => k2_sin_cos4(k3_sin_cos9(A)) = k7_xcmplx_0(1,A) ) ) )).
fof(t69_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k5_numbers,A) => ( r1_xxreal_0(k7_xcmplx_0(k28_sin_cos,2),A) | k5_sincos10(k1_funct_1(k1_fdiff_9,A)) = A ) ) ) )).
fof(t69_sprect_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => k16_pscomp_1(k3_topreal1(2,k1_sprect_1(A))) = k1_rltopsp1(k15_euclid(2),k13_pscomp_1(A),k12_pscomp_1(A)) ) )).
fof(t69_sprect_2,axiom,( ! [A] : ( ( ~ 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,k21_pscomp_1(k3_topreal1(2,A))),1) ) ) )).
fof(t69_sprect_5,axiom,( ! [A] : ( ( ~ 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,k23_pscomp_1(k3_topreal1(2,A))),k4_finseq_4(A,k22_pscomp_1(k3_topreal1(2,A)))) ) ) )).
fof(t69_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [E] : ( m2_subset_1(E,k16_substut1(A),k38_substut1(A)) => ! [F] : ( m1_substut1(F,A,k7_sublemma(A,E,B)) => ! [G] : ( m1_subset_1(G,C) => ( v3_substut1(k7_sublemma(A,E,B),A) => r2_relset_1(k3_qc_lang1(A),C,k5_relset_1(k3_qc_lang1(A),C,k1_sublemma(A,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,D),k12_sublemma(A,C,B,G))),k24_qc_lang1(A,k2_sublemma(A,E))),k5_relset_1(k3_qc_lang1(A),C,k1_sublemma(A,C,D,k14_sublemma(A,C,k13_sublemma(A,E,B,F,C,D),k12_sublemma(A,C,B,G))),k24_qc_lang1(A,k2_sublemma(A,E)))) ) ) ) ) ) ) ) ) )).
fof(t69_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_tdlat_2(B,A) => v4_tops_1(k9_subset_1(u1_struct_0(A),k6_setfam_1(u1_struct_0(A),B),k2_pre_topc(A,k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B)))),A) ) ) ) )).
fof(t69_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_tex_2(B,A) & m1_pre_topc(B,A) ) => r1_borsuk_1(A,B) ) ) )).
fof(t69_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_borsuk_1(B,A) & v3_tex_3(B,A) & m1_pre_topc(B,A) ) => ? [C] : ( ~ v2_struct_0(C) & v1_pre_topc(C) & v1_tsep_1(C,A) & v1_tex_2(C,A) & v1_tex_3(C,A) & m1_pre_topc(C,A) & r4_tsep_2(A,B,C) ) ) ) )).
fof(t69_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ( ! [C] : ( ( v1_borsuk_1(C,A) & m1_pre_topc(C,A) ) => ( r1_tsep_1(B,C) | m1_pre_topc(B,C) ) ) => v2_tdlat_3(B) ) ) ) )).
fof(t69_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B))) => ( r1_tarski(k8_relset_1(u1_struct_0(C),u1_struct_0(B),E,F),u1_struct_0(D)) => k8_relset_1(u1_struct_0(C),u1_struct_0(B),E,F) = k8_relset_1(u1_struct_0(D),u1_struct_0(B),k3_tmap_1(A,B,C,D,E),F) ) ) ) ) ) ) ) ) )).
fof(t69_topreal6,axiom,( ! [A] : ( ( 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] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k1_funct_1(A,k4_tarski(B,C)) = k10_finseq_1(B,C) ) ) => v3_tops_2(A,k2_borsuk_1(k3_topmetr,k3_topmetr),k15_euclid(2)) ) ) )).
fof(t69_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v6_tops_1(B,A) & v6_tops_1(C,A) ) => v6_tops_1(k9_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).
fof(t69_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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 & v3_tops_1(D,A) ) => v3_tops_1(E,B) ) ) ) ) ) ) )).
fof(t69_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => v6_transgeo(k6_partfun1(u1_struct_0(A)),A) ) )).
fof(t69_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(C,A) <=> r2_hidden(k7_finseq_1(k14_trees_3(k5_numbers),C),k13_trees_3(A,B)) ) ) ) ) )).
fof(t69_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & 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) & r3_tsep_1(A,B,C) ) => ( v1_tsep_1(B,A) & m1_pre_topc(B,A) ) ) ) ) ) )).
fof(t69_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_valued_0(D) ) => k63_valued_2(A,B,C,k30_valued_1(D)) = k16_valued_2(k3_xboole_0(A,k9_xtuple_0(D)),k2_valued_2(k1_valued_2(B)),k63_valued_2(A,B,C,D)) ) ) ) )).
fof(t69_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m2_vectsp_4(D,A,B,C) => ( v1_vectsp_4(D,A,B) <=> D = u1_struct_0(C) ) ) ) ) ) )).
fof(t69_waybel23,axiom,( ! [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] : ( ( v6_waybel23(B,A) & m1_waybel23(B,A) ) => r5_waybel_1(k1_waybel_8(k1_yellow_1(k7_waybel_0(k5_yellow_0(A,B)))),k5_yellow_0(A,B)) ) ) )).
fof(t69_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ 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))) ) => r3_waybel_0(A,B,C,D) ) => v5_orders_3(C,A,B) ) ) ) ) )).
fof(t69_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v9_waybel_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k4_yellow_0(A) = k6_waybel_1(A,B,C) <=> r1_orders_2(A,B,C) ) ) ) ) ) )).
fof(t69_xboole_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ~ ( r1_tarski(B,A) & r1_xboole_0(B,A) ) ) )).
fof(t69_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k4_xboolean(A,k11_xboolean(A,B)) = k11_xboolean(A,B) ) ) )).
fof(t69_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,A),A),A),4) = A ) )).
fof(t69_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(k5_numbers,C) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) ) ) ) )).
fof(t69_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( k2_xxreal_1(A,B) = k2_xxreal_1(C,D) => ( r1_xxreal_0(B,A) | ( A = C & B = D ) ) ) ) ) ) ) )).
fof(t69_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => r1_tarski(A,k1_xxreal_1(k2_xxreal_2(A),k1_xxreal_2(A))) ) )).
fof(t69_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( A != k1_xxreal_0 & A != k2_xxreal_0 & k4_xxreal_3(A,B) = k1_xxreal_0 & B != k1_xxreal_0 & B != k2_xxreal_0 ) ) ) )).
fof(t69_yellow10,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & l1_orders_2(B) ) => ( v2_waybel_8(k3_yellow_3(A,B)) => ( v2_waybel_8(A) & v2_waybel_8(B) ) ) ) ) )).
fof(t69_yellow_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & v5_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( E = C & F = D ) => k12_lattice3(B,C,D) = k12_lattice3(A,E,F) ) ) ) ) ) ) ) )).
fof(t69_yellow_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v11_waybel_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ~ r1_yellow_5(A,B,C) => k1_yellow_5(A,k13_lattice3(A,B,C),C) = B ) ) ) ) )).
fof(t69_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r3_zf_lang(A,k6_zf_lang(B)) => r2_zf_lang(A,B) ) ) ) )).
fof(t69_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => k2_zf_model(k15_zf_lang(B,C,A)) = k7_subset_1(k1_zf_lang,k2_zf_model(A),k2_tarski(B,C)) ) ) ) )).
fof(t69_zfmisc_1,axiom,( ! [A] : ! [B] : ( k2_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) = k1_zfmisc_1(k2_xboole_0(A,B)) => r3_xboole_0(A,B) ) )).
fof(t69_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_int_1(C) => ! [D] : ( m1_zmodul01(D,A) => ( r1_struct_0(D,B) => r2_hidden(k1_zmodul01(A,B,C),k5_zmodul01(A,B,D)) ) ) ) ) ) )).
fof(t69_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( B = u1_struct_0(A) => k33_zmodul02(A,B) = A ) ) ) )).
fof(t6_abcmiz_0,axiom,( ! [A] : ( l1_abcmiz_0(A) => ! [B] : ( 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)) & v6_abcmiz_0(A) ) => v6_abcmiz_0(B) ) ) ) )).
fof(t6_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r2_hidden(A,k3_finseq_2(k1_tarski(C))) & r2_hidden(B,k3_finseq_2(k1_tarski(C))) & k1_card_1(A) = k1_card_1(B) ) => A = B ) )).
fof(t6_abcmiz_a,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & l1_msualg_1(A) ) => ( v1_abcmiz_a(A) <=> m1_instalg1(A,k27_abcmiz_1) ) ) )).
fof(t6_abian,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(A),k8_eqrel_1(A,k2_abian(A,B))) => ! [D] : ( m2_subset_1(D,A,C) => r2_hidden(k3_funct_2(A,A,B,D),C) ) ) ) ) )).
fof(t6_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ( A != k5_numbers => k3_xcmplx_0(k9_complex1(A),k9_complex1(k7_xcmplx_0(1,A))) = 1 ) ) )).
fof(t6_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_aff_1(A,B,B,C) & r1_aff_1(A,B,C,C) & r1_aff_1(A,B,C,B) ) ) ) ) )).
fof(t6_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v10_aff_2(A) => v7_aff_2(A) ) ) )).
fof(t6_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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_aff_1(A,D,E,F) | r2_aff_1(A,E,D,F) ) & ~ r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) )).
fof(t6_afinsq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ( r1_xxreal_0(k1_afinsq_1(B),A) => k2_afinsq_2(B,A) = k1_xboole_0 ) ) ) )).
fof(t6_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_aff_4(C,A) & r1_aff_4(A,B,C) & r1_aff_4(A,C,D) ) => r1_aff_4(A,B,D) ) ) ) ) ) )).
fof(t6_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_analoaf(A,B,B,C,C) ) ) ) )).
fof(t6_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect01(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,D) => B = C ) ) ) ) ) )).
fof(t6_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_unialg_1(C) & v3_unialg_1(C) & v4_unialg_1(C) & l1_unialg_1(C) ) => ! [D] : ( ( 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] : ( ( 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_alg_1(A,B,D) & r1_alg_1(B,C,E) ) => r1_alg_1(A,C,k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),D,E)) ) ) ) ) ) ) )).
fof(t6_algseq_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r2_funct_2(k4_ordinal1,u1_struct_0(A),B,k2_algseq_1(A,k4_struct_0(A))) <=> k1_algseq_1(A,B) = k5_numbers ) ) ) )).
fof(t6_algspec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,B,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,D))) ) => ( r1_partfun1(E,F) => r1_partfun1(k12_lang1(A,C,E),k12_lang1(B,D,F)) ) ) ) ) ) ) ) )).
fof(t6_algstr_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ( v4_algstr_1(A) <=> ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & k1_algstr_0(A,B,D) = C ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & k1_algstr_0(A,D,B) = C ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k1_algstr_0(A,B,C) = k1_algstr_0(A,B,D) => C = D ) ) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k1_algstr_0(A,C,B) = k1_algstr_0(A,D,B) => C = D ) ) ) ) ) ) ) )).
fof(t6_algstr_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_algstr_3(A) & l1_algstr_3(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k1_algstr_3(A,B,D,C) = k1_algstr_3(A,B,E,C) => ( B = k4_struct_0(A) | D = E ) ) ) ) ) ) ) )).
fof(t6_algstr_4,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( m1_algstr_4(B,A) => ! [C] : ( m1_algstr_4(C,A) => ( ( m1_algstr_4(B,C) & m1_algstr_4(C,B) ) => g3_algstr_0(u1_struct_0(B),u2_algstr_0(B)) = g3_algstr_0(u1_struct_0(C),u2_algstr_0(C)) ) ) ) ) )).
fof(t6_altcat_1,axiom,( ! [A] : ! [B] : ! [C] : r1_tarski(k10_xtuple_0(k6_altcat_1(k1_funct_2(A,B),k1_funct_2(B,C))),k1_funct_2(A,C)) )).
fof(t6_altcat_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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)) ) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,B) => k1_binop_1(k2_funct_4(C),E,D) = k1_binop_1(C,D,E) ) ) ) ) ) )).
fof(t6_altcat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t6_ami_2,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k3_ami_2,k4_ami_2))) => ! [B] : ( v7_ordinal1(B) => k1_funct_1(k6_ami_2(A,B),k4_ordinal1) = B ) ) )).
fof(t6_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(C,u1_struct_0(k1_ami_3)) ) => ( k1_funct_1(k2_extpro_1(k7_card_1(2),k1_ami_3,k6_ami_3(A,B),C),k4_struct_0(k1_ami_3)) = k4_card_1(k5_memstr_0(k7_card_1(2),k1_ami_3,C)) & ( A != B => k1_funct_1(k2_extpro_1(k7_card_1(2),k1_ami_3,k6_ami_3(A,B),C),A) = k4_int_1(k1_funct_1(C,A),k1_funct_1(C,B)) ) & k1_funct_1(k2_extpro_1(k7_card_1(2),k1_ami_3,k6_ami_3(A,B),C),B) = k5_int_1(k1_funct_1(C,A),k1_funct_1(C,B)) & ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_ami_3)) ) => ~ ( D != A & D != B & k1_funct_1(k2_extpro_1(k7_card_1(2),k1_ami_3,k6_ami_3(A,B),C),D) != k1_funct_1(C,D) ) ) ) ) ) ) )).
fof(t6_ami_4,axiom,( ! [A] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_ami_3)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ( r1_tarski(k1_ami_4,B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,C)) = 4 => k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,k2_xcmplx_0(C,D)) = k5_extpro_1(k7_card_1(2),k1_ami_3,B,A,C) ) ) ) ) ) ) )).
fof(t6_ami_5,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => ( k2_compos_0(u1_compos_1(k1_ami_3),A) = k5_numbers => A = k2_compos_1(k1_ami_3) ) ) )).
fof(t6_ami_6,axiom,( ! [A] : ( m1_subset_1(A,k1_compos_0(u1_compos_1(k1_ami_3))) => ( A = 3 => k3_compos_0(u1_compos_1(k1_ami_3),A) = k1_tarski(k1_xboole_0) ) ) )).
fof(t6_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( v7_ordinal1(C) => ? [D] : ( v7_ordinal1(D) & C = k1_ami_wstd(A,B,D) ) ) ) ) )).
fof(t6_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(k4_amistd_1(A))) => ( k2_compos_0(u1_compos_1(k4_amistd_1(A)),B) = 1 | k2_compos_0(u1_compos_1(k4_amistd_1(A)),B) = k5_numbers ) ) ) )).
fof(t6_amistd_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_setfam_1(B) => ! [C] : ( ( ~ v2_struct_0(C) & v2_memstr_0(C,B) & v3_memstr_0(C,B) & v3_extpro_1(C,B) & v3_amistd_1(C,B) & v2_amistd_2(C,B) & l1_extpro_1(C,B) ) => ! [D] : ( m1_subset_1(D,u1_compos_1(C)) => ( v4_amistd_1(D,B,C) => v4_amistd_1(k5_compos_0(u1_compos_1(C),D,A),B,C) ) ) ) ) ) )).
fof(t6_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_compos_1(B)) => k4_amistd_4(A,B,C) = k4_subset_1(u1_struct_0(B),k2_amistd_4(A,B,C),k5_amistd_4(A,B,C)) ) ) ) )).
fof(t6_amistd_5,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & v3_extpro_1(B,A) & v3_amistd_5(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) & ~ v2_compos_1(C,B) ) => ! [D] : ( ( 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) ) => r2_hidden(k4_struct_0(B),k9_xtuple_0(D)) ) ) ) ) )).
fof(t6_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( r2_analmetr(A,B,C,D,E) => r2_analmetr(A,k1_rlvect_1(A,B,F),k1_rlvect_1(A,C,G),D,E) ) ) ) ) ) ) ) ) )).
fof(t6_analoaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( ( k1_rlvect_1(A,B,D) = C => ( D = k5_numbers | B = k1_rlvect_1(A,C,k5_xcmplx_0(D)) ) ) & ( B = k1_rlvect_1(A,C,k5_xcmplx_0(D)) => ( D = k5_numbers | k1_rlvect_1(A,B,D) = C ) ) ) ) ) ) ) )).
fof(t6_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r1_analmetr(A,D,E) & k1_analort(A,D,E,B) = k1_analort(A,D,E,C) ) => B = C ) ) ) ) ) ) )).
fof(t6_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( ~ v9_struct_0(C,A) & ~ v9_struct_0(D,A) & ~ r1_anproj_1(A,C,D) & ~ ( r2_anproj_1(A,C,D,B) <=> ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & B = k3_rlvect_1(A,k1_rlvect_1(A,C,E),k1_rlvect_1(A,D,F)) ) ) ) ) ) ) ) ) )).
fof(t6_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_anproj_1(A,B,C,D) & r1_anproj_2(A,B,C,D) ) => ( r1_anproj_1(A,B,C) | r1_anproj_1(A,B,D) | r1_anproj_1(A,C,D) | ( ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & k1_rlvect_1(A,D,F) = k3_rlvect_1(A,B,k1_rlvect_1(A,C,E)) & E != k5_numbers & F != k5_numbers ) ) & ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & D = k3_rlvect_1(A,k1_rlvect_1(A,B,F),k1_rlvect_1(A,C,E)) & F != k5_numbers & E != k5_numbers ) ) ) ) ) ) ) ) ) )).
fof(t6_aofa_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => r2_hidden(B,k5_aofa_000(A,B)) ) ) )).
fof(t6_aofa_a00,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( k1_msafree4(A,k2_aofa_a00(A,B,D),B) = k1_tarski(D) & ( B != C => k1_msafree4(A,k2_aofa_a00(A,B,D),C) = k1_xboole_0 ) ) ) ) ) )).
fof(t6_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ( v4_msualg_1(B,A) & v4_msafree4(B,A,B) & l3_msualg_1(B,A) ) ) ) )).
fof(t6_aofa_i00,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( 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)))) ) <=> ( k9_xtuple_0(B) = A & k10_xtuple_0(B) = k1_card_1(A) & v2_funct_1(B) ) ) ) )).
fof(t6_arithm,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(A,1) = A ) )).
fof(t6_armstrng,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => k3_armstrng(A,k3_binarith(A,k1_binari_3(A,k5_numbers)),B) = B ) ) )).
fof(t6_arrow,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m2_subset_1(D,k2_arrow(A),k3_arrow(A)) => ( ( r1_arrow(D,B,C) & r1_arrow(D,C,B) ) => B = C ) ) ) ) ) )).
fof(t6_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ( k2_arytm_1(A,B) = k11_arytm_3 => A = B ) ) ) )).
fof(t6_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ( A = k11_arytm_3 => r1_arytm_2(A,B) ) ) ) )).
fof(t6_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => k7_arytm_2(A,k7_arytm_2(B,C)) = k7_arytm_2(k7_arytm_2(A,B),C) ) ) ) )).
fof(t6_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ( r2_hidden(k1_xboole_0,A) => r2_hidden(k7_ordinal3(B,A),A) ) ) ) )).
fof(t6_asympt_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_hidden(A,k6_asympt_0(B)) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) ) )).
fof(t6_asympt_1,axiom,( r2_hidden(k3_asympt_1(k7_xcmplx_0(1,2)),k7_asympt_0(k2_asympt_1)) & ~ r2_hidden(k2_asympt_1,k7_asympt_0(k3_asympt_1(k7_xcmplx_0(1,2)))) )).
fof(t6_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m2_funct_2(B,u1_struct_0(A),u1_struct_0(A),k1_autalg_1(A)) => ! [C] : ( m2_funct_2(C,u1_struct_0(A),u1_struct_0(A),k1_autalg_1(A)) => r2_hidden(k1_partfun1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),C,B),k1_autalg_1(A)) ) ) ) )).
fof(t6_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_funct_2(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) => m2_funct_2(k2_funct_1(B),u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) ) ) )).
fof(t6_bagorder,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( B != k1_xboole_0 & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & r4_waybel_4(B,C,u1_orders_2(A)) ) ) ) ) ) )).
fof(t6_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_bcialg_1(A,B,C) = k4_struct_0(A) => k2_bcialg_1(A,k1_bcialg_1(A,C,B)) = k4_struct_0(A) ) ) ) ) )).
fof(t6_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,k4_ordinal1) => k1_bcialg_2(A,k4_struct_0(A),k4_struct_0(A),B) = k4_struct_0(A) ) ) )).
fof(t6_bcialg_3,axiom,( ! [A] : ( ( ~ 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) & v1_bcialg_3(A) & l2_bcialg_1(A) ) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t6_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_4(A,B,C) = k1_bcialg_4(A,C,B) ) ) ) )).
fof(t6_bcialg_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [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) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ( k1_bcialg_2(C,D,E,B) = k1_bcialg_2(C,D,E,A) => ( r1_xxreal_0(A,B) | ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(B,F) => k1_bcialg_2(C,D,E,B) = k1_bcialg_2(C,D,E,F) ) ) ) ) ) ) ) ) ) )).
fof(t6_bcialg_6,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => k3_bcialg_6(A,2,B) = k1_bcialg_1(A,B,k2_bcialg_1(A,B)) ) ) )).
fof(t6_bciideal,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k5_bcialg_1(A)) => ! [D] : ( m2_subset_1(D,u1_struct_0(A),k5_bcialg_1(A)) => ( m2_subset_1(B,u1_struct_0(A),k7_bcialg_1(A,D)) => k6_bcialg_1(A,C,B) = k6_bcialg_1(A,C,D) ) ) ) ) ) )).
fof(t6_bhsp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => k2_bhsp_1(C,D,k3_rlvect_1(C,k1_rlvect_1(C,E,A),k1_rlvect_1(C,F,B))) = k2_xcmplx_0(k3_xcmplx_0(A,k2_bhsp_1(C,D,E)),k3_xcmplx_0(B,k2_bhsp_1(C,D,F))) ) ) ) ) ) ) )).
fof(t6_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_bhsp_2(B,A) => v1_bhsp_2(k5_vfunct_1(k4_ordinal1,A,B),A) ) ) ) )).
fof(t6_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_bhsp_2(B,A) & r1_bhsp_3(A,B,C) ) => v1_bhsp_2(C,A) ) ) ) ) )).
fof(t6_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_bhsp_4(B,A) & v1_bhsp_4(C,A) ) => ( v1_bhsp_4(k6_bhsp_1(A,B,C),A) & k2_bhsp_4(A,k6_bhsp_1(A,B,C)) = k3_rlvect_1(A,k2_bhsp_4(A,B),k2_bhsp_4(A,C)) ) ) ) ) ) )).
fof(t6_bhsp_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_bhsp_1(A,B,C) => k1_square_1(k3_bhsp_1(A,k3_rlvect_1(A,B,C))) = k2_xcmplx_0(k1_square_1(k3_bhsp_1(A,B)),k1_square_1(k3_bhsp_1(A,C))) ) ) ) ) )).
fof(t6_bhsp_6,axiom,( ! [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_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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v3_bhsp_6(B,A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( 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] : ( v1_xreal_0(E) & ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( ( v1_finset_1(F) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( ~ v1_xboole_0(F) & r1_tarski(F,B) & ! [G] : ( ( 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,k9_complex1(k5_real_1(k3_funct_2(u1_struct_0(A),k1_numbers,D,C),k5_bhsp_5(k1_numbers,u1_struct_0(A),k9_binop_2,G,D)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t6_bhsp_7,axiom,( ! [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_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] : ( m2_bhsp_5(B,A) => ! [C] : ( ( 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] : ( 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) ) ) ) => ( v1_bhsp_6(B,A) <=> r1_bhsp_6(A,B,C) ) ) ) ) ) ) )).
fof(t6_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( ( 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,k6_algstr_0(A,D,E)),k3_bilinear(A,B,C,k3_bilinear(A,B,C,F,E),D)) ) ) ) ) ) ) )).
fof(t6_binari_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k2_finseq_1(A)) => ( B = 1 | k7_partfun1(k6_margrel1,k1_binari_2(A),B) = k7_margrel1 ) ) ) ) )).
fof(t6_binari_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ( B = k5_euclid(A) => k6_binarith(A,B) = k5_numbers ) ) ) )).
fof(t6_binari_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k6_margrel1) ) => ( ( B = k5_euclid(A) & C = k5_euclid(A) ) => k7_binarith(A,B,C) = k5_euclid(A) ) ) ) ) )).
fof(t6_binarith,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k4_xboolean(A,B) = k3_xboolean(k5_xboolean(k3_xboolean(A),k3_xboolean(B))) ) ) )).
fof(t6_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => r2_relset_1(k4_ordinal1,u1_struct_0(A),k1_polynom1(A,C,B),k9_fvsum_1(A,C,B)) ) ) ) )).
fof(t6_binop_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ( v1_binop_1(B,A) => ( r3_binop_1(A,C,B) <=> r1_binop_1(A,C,B) ) ) ) ) )).
fof(t6_binop_2,axiom,( k4_binop_1(k2_numbers,k5_binop_2) = 1 )).
fof(t6_bintree1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( m1_trees_1(C,k13_trees_3(A,B)) => ( ! [D] : ( m1_trees_1(D,A) => ( C = k8_finseq_1(k4_ordinal1,k14_trees_3(k5_numbers),D) => ( r2_hidden(C,k3_trees_1(k13_trees_3(A,B))) <=> r2_hidden(D,k3_trees_1(A)) ) ) ) & ! [D] : ( m1_trees_1(D,B) => ( C = k8_finseq_1(k4_ordinal1,k14_trees_3(1),D) => ( r2_hidden(C,k3_trees_1(k13_trees_3(A,B))) <=> r2_hidden(D,k3_trees_1(B)) ) ) ) ) ) ) ) )).
fof(t6_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ( ! [B] : ( m1_trees_1(B,A) => k1_trees_2(A,B) = k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1)),k8_finseq_1(k4_ordinal1,B,k10_binarith(k4_ordinal1,k5_numbers)),k8_finseq_1(k4_ordinal1,B,k10_binarith(k4_ordinal1,1))) ) => k3_trees_1(A) = k1_xboole_0 ) ) )).
fof(t6_boole,axiom,( ! [A] : ( v1_xboole_0(A) => A = k1_xboole_0 ) )).
fof(t6_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_boolealg(A,B,k4_lattices(A,C,D)) <=> ( r3_lattices(A,B,C) & r3_lattices(A,B,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r3_lattices(A,E,C) & r3_lattices(A,E,D) ) => r3_lattices(A,E,B) ) ) ) ) ) ) ) ) )).
fof(t6_boolmark,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v4_petri(B,A) <=> ! [C] : ( 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] : ( 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) ) ) ) ) ) ) ) )).
fof(t6_borsuk_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( ( v3_pre_topc(C,A) & v3_pre_topc(D,B) ) => v3_pre_topc(k3_borsuk_1(A,B,C,D),k2_borsuk_1(A,B)) ) ) ) ) ) )).
fof(t6_borsuk_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v3_funct_1(C) & m1_borsuk_2(C,A,B,B) ) => r2_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),k2_borsuk_2(A,B,B,C),C) ) ) ) )).
fof(t6_borsuk_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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))) => r1_funct_2(u1_struct_0(B),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),u1_struct_0(A)),k2_tops_2(u1_struct_0(k2_borsuk_1(B,k1_pre_topc(A,k6_domain_1(u1_struct_0(A),C)))),u1_struct_0(B),D),k14_funct_3(u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),k3_struct_0(B),k6_struct_0(B,A,C))) ) ) ) ) ) )).
fof(t6_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( A = k4_rcomp_1(B,C) => ( r1_xxreal_0(C,B) | r1_tarski(k1_rcomp_1(B,C),u1_struct_0(k5_topmetr)) ) ) ) ) ) )).
fof(t6_borsuk_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( r4_zfmisc_1(A,B,C,D,E,F) & r1_subset_1(k4_enumset1(A,B,C,D,E,F),k1_tarski(G)) ) => r5_zfmisc_1(A,B,C,D,E,F,G) ) )).
fof(t6_borsuk_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_topmetr)) => m1_subset_1(k3_xcmplx_0(k7_xcmplx_0(1,2),A),u1_struct_0(k5_topmetr)) ) )).
fof(t6_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( k19_sin_cos(A) = k5_numbers & A != k2_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k1_int_1(k7_xcmplx_0(A,k3_xcmplx_0(2,k28_sin_cos))))) & A != k2_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(3,k28_sin_cos),2),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k1_int_1(k7_xcmplx_0(A,k3_xcmplx_0(2,k28_sin_cos))))) ) ) )).
fof(t6_brouwer,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xxreal_0(A) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(B))) => ( ( m1_subset_1(C,u1_struct_0(k2_brouwer(B,E,A))) & m1_subset_1(D,u1_struct_0(k2_brouwer(B,E,A))) ) => ( C = D | m1_subset_1(k3_brouwer(B,E,C,D,A),u1_struct_0(k7_toprealb(B,E,A))) ) ) ) ) ) ) ) )).
fof(t6_brouwer2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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)) & ~ v2_tops_1(B,k15_euclid(A)) & ! [C] : ( ( 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) ) ) ) ) ) )).
fof(t6_bspace,axiom,( k5_struct_0(k2_bspace) = 1 )).
fof(t6_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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,k9_bvfunc_1(A,B,C),k9_bvfunc_1(A,D,E)),k9_bvfunc_1(A,F,G)),k5_bvfunc_1(A,k5_bvfunc_1(A,B,D),F)),k5_bvfunc_1(A,k5_bvfunc_1(A,C,E),G)) ) ) ) ) ) ) ) )).
fof(t6_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ( ( v2_bvfunc_2(B,A) & B = k2_tarski(C,D) ) => ( C = D | k2_bvfunc_2(A,B) = k2_partit1(A,C,D) ) ) ) ) ) ) )).
fof(t6_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ( B = k1_enumset1(C,D,E) => ( D = E | E = C | k5_bvfunc_2(A,E,B) = k2_partit1(A,C,D) ) ) ) ) ) ) ) )).
fof(t6_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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,k1_bvfunc_1(A,B)),k11_bvfunc_1(A)) ) ) )).
fof(t6_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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,B,B),k1_bvfunc_1(A,B)) & r2_funct_2(A,k6_margrel1,k1_bvfunc_1(A,k5_bvfunc26(A,B,B)),B) ) ) ) )).
fof(t6_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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,B),B) ) ) )).
fof(t6_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( m1_eqrel_1(D,A) => r2_bvfunc_1(A,k7_bvfunc_2(A,C,B,D),k5_bvfunc_2(A,D,B)) ) ) ) ) )).
fof(t6_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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)),k5_bvfunc_1(A,C,D)) ) ) ) ) ) )).
fof(t6_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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,k1_bvfunc_1(A,B)),k12_bvfunc_1(A)) ) ) )).
fof(t6_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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,k2_bvfunc_1(A,B,k1_bvfunc_1(A,B))),k12_bvfunc_1(A)) ) ) )).
fof(t6_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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,B),k9_bvfunc_1(A,k9_bvfunc_1(A,D,C),k9_bvfunc_1(A,D,k2_bvfunc_1(A,B,C)))),k12_bvfunc_1(A)) ) ) ) ) )).
fof(t6_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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,C),D),k5_bvfunc_1(A,k9_bvfunc_1(A,B,D),k9_bvfunc_1(A,C,D))) ) ) ) ) )).
fof(t6_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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,k5_bvfunc_1(A,k2_bvfunc_1(A,B,C),k2_bvfunc_1(A,B,k1_bvfunc_1(A,C)))) ) ) ) )).
fof(t6_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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,B,k1_bvfunc_1(A,C))),k1_bvfunc_1(A,B)) ) ) ) )).
fof(t6_c0sp1,axiom,( ! [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) & v2_funcsdom(A) & v3_group_1(A) & v5_group_1(A) & v1_vectsp_1(A) & v3_vectsp_1(A) & l1_funcsdom(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v4_c0sp1(B,A) & v3_c0sp1(B,A) ) => ( v1_xboole_0(B) | m2_c0sp1(g1_funcsdom(B,k2_c0sp1(A,B),k1_c0sp1(A,B),k5_c0sp1(A,B),k4_c0sp1(A,B),k3_c0sp1(A,B)),A) ) ) ) ) )).
fof(t6_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => k4_struct_0(k3_c0sp2(A)) = k1_c0sp2(A,k5_numbers) ) )).
fof(t6_calcul_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( r1_xxreal_0(k3_finseq_1(A),k3_finseq_1(k7_finseq_1(A,B))) & r1_xxreal_0(k3_finseq_1(B),k3_finseq_1(k7_finseq_1(A,B))) & ( A != k1_xboole_0 => ( r1_xxreal_0(1,k3_finseq_1(A)) & ~ r1_xxreal_0(k3_finseq_1(k7_finseq_1(B,A)),k3_finseq_1(B)) ) ) ) ) ) )).
fof(t6_calcul_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => r2_wellord2(k2_calcul_2(A,B),B) ) ) )).
fof(t6_cantor_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => u1_pre_topc(A) = k1_cantor_1(u1_struct_0(A),u1_pre_topc(A)) ) )).
fof(t6_card_1,axiom,( ! [A] : ! [B] : ( v1_card_1(B) => ( r1_tarski(A,B) => r1_ordinal1(k1_card_1(A),B) ) ) )).
fof(t6_card_2,axiom,( ! [A] : ! [B] : ( r2_wellord2(k2_zfmisc_1(A,B),k2_zfmisc_1(k1_card_1(A),B)) & r2_wellord2(k2_zfmisc_1(A,B),k2_zfmisc_1(A,k1_card_1(B))) & r2_wellord2(k2_zfmisc_1(A,B),k2_zfmisc_1(k1_card_1(A),k1_card_1(B))) & k1_card_1(k2_zfmisc_1(A,B)) = k1_card_1(k2_zfmisc_1(k1_card_1(A),B)) & k1_card_1(k2_zfmisc_1(A,B)) = k1_card_1(k2_zfmisc_1(A,k1_card_1(B))) & k1_card_1(k2_zfmisc_1(A,B)) = k1_card_1(k2_zfmisc_1(k1_card_1(A),k1_card_1(B))) ) )).
fof(t6_card_3,axiom,( ! [A] : ! [B] : r1_tarski(k3_card_3(k7_funcop_1(A,B)),B) )).
fof(t6_card_4,axiom,( k2_card_2(k4_ordinal1,k4_ordinal1) = k4_ordinal1 )).
fof(t6_card_5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( r1_tarski(B,A) => r2_ordinal2(k3_ordinal2(B),k2_wellord2(k1_wellord2(B))) ) ) )).
fof(t6_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_card_fil(C,A) => ~ ( r2_hidden(B,C) & r2_hidden(k6_subset_1(A,B),C) ) ) ) ) )).
fof(t6_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ( r1_xxreal_0(k5_card_1(A),k5_card_1(B)) => k1_card_1(a_2_0_card_fin(A,B)) = k7_xcmplx_0(k7_newton(k5_card_1(B)),k7_newton(k7_nat_d(k5_card_1(B),k5_card_1(A)))) ) ) ) )).
fof(t6_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( v1_card_lar(B,A) <=> ! [C] : ( v3_ordinal1(C) => ~ ( r2_hidden(C,A) & ! [D] : ( v3_ordinal1(D) => ~ ( r2_hidden(D,B) & r1_ordinal1(C,D) ) ) ) ) ) ) ) )).
fof(t6_cardfin2,axiom,( ! [A] : ( ( v7_ordinal1(A) & v2_xxreal_0(A) ) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k7_xcmplx_0(1,2),k9_complex1(k4_xcmplx_0(k3_xcmplx_0(k2_newton(A),k7_xcmplx_0(k3_xcmplx_0(k23_sin_cos(B),k1_newton(k4_xcmplx_0(1),k1_nat_1(A,1))),k2_newton(k1_nat_1(A,1))))))) ) ) ) )).
fof(t6_cat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_cat_1(D,A,B,C) => ( k2_cat_1(A,B,C) = k1_tarski(D) => ! [E] : ( m1_cat_1(E,A,B,C) => D = E ) ) ) ) ) ) )).
fof(t6_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m3_cat_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t6_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u4_struct_0(C)) => ! [E] : ( m1_subset_1(E,u4_struct_0(C)) => r2_funct_2(k2_tarski(A,B),u1_struct_0(C),k2_cat_3(C,k2_tarski(A,B),k5_funct_4(u4_struct_0(C),A,B,D,E)),k5_funct_4(u1_struct_0(C),A,B,k3_graph_1(C,D),k3_graph_1(C,E))) ) ) ) )).
fof(t6_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k5_cat_4(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_cat_4(A,B))) => ! [E] : ( m1_subset_1(E,u4_struct_0(k5_cat_4(A,B))) => m1_cat_1(E,k5_cat_4(A,B),C,D) ) ) ) )).
fof(t6_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m3_cat_2(B,A) => ! [C] : ( m3_cat_2(C,A) => ( ~ r2_subset_1(u1_struct_0(B),u1_struct_0(C)) => ( m3_cat_2(k3_cat_5(B,C),B) & m3_cat_2(k3_cat_5(B,C),C) ) ) ) ) ) )).
fof(t6_catalan1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( ~ r1_xxreal_0(A,1) & r1_xxreal_0(k7_newton(k3_xcmplx_0(2,A)),k2_nat_1(k3_xcmplx_0(k7_newton(k7_nat_d(k3_xcmplx_0(2,A),2)),A),k1_nat_1(A,1))) ) ) )).
fof(t6_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ( v1_catalan2(B) => v1_catalan2(k5_relat_1(B,A)) ) ) ) )).
fof(t6_catalg_1,axiom,( ! [A] : k4_catalg_1(k3_catalg_1(A)) = A )).
fof(t6_cayldick,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( r2_hidden(A,C) & r2_hidden(B,D) ) => r2_hidden(k6_afinsq_1(A,B),k4_card_3(k6_afinsq_1(C,D))) ) )).
fof(t6_cayley,axiom,( ! [A] : k1_group_1(k2_cayley(A)) = k6_partfun1(A) )).
fof(t6_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_cc0sp1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_cc0sp1(A))) => ! [E] : ( ( 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] : ( ( v1_funct_1(F) & v1_funct_2(F,A,k2_numbers) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( ( E = C & F = D ) => ( D = k1_clvect_1(k3_cc0sp1(A),C,B) <=> ! [G] : ( m1_subset_1(G,A) => k3_funct_2(A,k2_numbers,F,G) = k3_xcmplx_0(B,k3_funct_2(A,k2_numbers,E,G)) ) ) ) ) ) ) ) ) ) )).
fof(t6_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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(k46_valued_1(u1_struct_0(A),k2_numbers,k2_numbers,B,C)) & v1_funct_2(k46_valued_1(u1_struct_0(A),k2_numbers,k2_numbers,B,C),u1_struct_0(A),k2_numbers) & v1_cc0sp2(k46_valued_1(u1_struct_0(A),k2_numbers,k2_numbers,B,C),A) & m1_subset_1(k46_valued_1(u1_struct_0(A),k2_numbers,k2_numbers,B,C),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k2_numbers))) ) ) ) ) )).
fof(t6_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_ordinal1) & v5_valued_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k9_comseq_3(C,k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,A)),k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k9_comseq_3(C,B),k9_comseq_3(C,A))) ) ) ) )).
fof(t6_cfdiff_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,k5_numbers) => m1_cfdiff_1(a_2_0_cfdiff_1(A,B),A) ) ) ) )).
fof(t6_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ! [C] : ( m2_funct_2(C,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ! [D] : ( m2_funct_2(D,A,k2_numbers,k9_funct_2(A,k2_numbers)) => r2_funct_2(A,k2_numbers,k1_funcsdom(A,k2_numbers,k1_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,k1_cfuncdom(A),B,C),D)) ) ) ) ) )).
fof(t6_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ( r1_tarski(k1_relset_1(A,k2_cfunct_1(A,B)),k1_relset_1(A,B)) & k9_subset_1(A,k1_relset_1(A,B),k7_subset_1(A,k1_relset_1(A,B),k8_relset_1(A,k2_numbers,B,k1_tarski(k5_numbers)))) = k7_subset_1(A,k1_relset_1(A,B),k8_relset_1(A,k2_numbers,B,k1_tarski(k5_numbers))) ) ) ) )).
fof(t6_cgames_1,axiom,( ! [A] : ( v2_cgames_1(A) => ( A = k3_cgames_1 <=> k8_cgames_1(A) = k1_xboole_0 ) ) )).
fof(t6_chain_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( v1_abian(B) <=> v1_abian(A) ) <=> v1_abian(k1_nat_1(B,A)) ) ) ) )).
fof(t6_chord,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v1_abian(A) ) => ( r1_xxreal_0(A,2) => A = 1 ) ) )).
fof(t6_circcmb2,axiom,( ! [A] : ( ~ v1_facirc_1(A) => ! [B] : ( v1_relat_1(B) => k4_xboole_0(A,B) = A ) ) )).
fof(t6_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ( v1_circcmb3(C,A,B) => ! [D] : ( r2_hidden(D,k2_msafree2(A)) => k1_funct_1(k1_circcmb3(A,B,C),D) = k1_funct_1(C,D) ) ) ) ) ) )).
fof(t6_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_msualg_1(C) ) => k2_circcomb(k2_circcomb(A,B),C) = k2_circcomb(A,k2_circcomb(B,C)) ) ) ) )).
fof(t6_circled1,axiom,( ! [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) ) => v3_rltopsp1(k3_rusub_4(A,k2_rlsub_1(A)),A) ) )).
fof(t6_circtrm1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_msaterm(A,B))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k1_msaterm(A,B))) ) => ( r1_partfun1(u1_msualg_1(k1_circtrm1(A,B,C)),u1_msualg_1(k1_circtrm1(A,B,D))) & r1_partfun1(u2_msualg_1(k1_circtrm1(A,B,C)),u2_msualg_1(k1_circtrm1(A,B,D))) ) ) ) ) ) )).
fof(t6_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,k5_msafree2(A,B)),C)) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,k5_msafree2(A,B)),D)) => ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) & v1_finseq_1(G) & v6_trees_3(G) ) => ! [H] : ( m1_subset_1(H,k4_ordinal1) => ( ( r2_hidden(C,k7_subset_1(u1_struct_0(A),k3_msafree2(A),k1_msafree2(A))) & E = k4_trees_4(k4_tarski(k4_msafree2(A,C),u1_struct_0(A)),G) & r2_hidden(k1_nat_1(H,1),k1_relset_1(k4_ordinal1,G)) & r2_hidden(k1_funct_1(G,k1_nat_1(H,1)),k1_funct_1(u3_msualg_1(A,k5_msafree2(A,B)),D)) ) => r2_hidden(k7_trees_2(E,k14_trees_3(H),F),k1_funct_1(u3_msualg_1(A,k5_msafree2(A,B)),C)) ) ) ) ) ) ) ) ) ) )).
fof(t6_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msafree2(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,k5_msafree2(A,B)),D)) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,k5_msafree2(A,B)),D)) => ! [G] : ( ( v1_relat_1(G) & v1_funct_1(G) & v3_trees_2(G) ) => ! [H] : ( ( v1_relat_1(H) & v1_funct_1(H) & v3_trees_2(H) ) => ( ( G = E & H = F & F = 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) ) => k9_xtuple_0(G) = k9_xtuple_0(H) ) ) ) ) ) ) ) ) ) )).
fof(t6_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ( ( r1_ckspace1(A,D,B,C) & r1_ckspace1(A,E,B,C) & v1_pdiff_7(C,A) ) => r1_ckspace1(A,k47_valued_1(k1_euclid(A),k1_numbers,k1_numbers,D,E),B,C) ) ) ) ) ) ) )).
fof(t6_classes1,axiom,( ! [A] : ! [B] : ( ( r1_tarski(B,k1_classes1(A)) & r2_hidden(k1_card_1(B),k1_card_1(k1_classes1(A))) ) => r2_hidden(B,k1_classes1(A)) ) )).
fof(t6_classes2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( r2_hidden(A,k1_classes1(B)) => ( r2_hidden(k1_ordinal1(A),k1_classes1(B)) & r1_tarski(A,k1_classes1(B)) ) ) ) )).
fof(t6_clopban1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m2_funct_2(C,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => k1_binop_1(k2_lopban_1(A,B),C,k1_funct_1(k2_clopban1(A,B),k4_tarski(k4_xcmplx_0(k6_complex1),C))) = k4_lopban_1(A,B) ) ) ) )).
fof(t6_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( 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)))) ) => ( 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_partfun1(u1_struct_0(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_partfun1(u1_struct_0(A))),B) ) ) ) )).
fof(t6_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ! [C] : ( v7_ordinal1(C) => k1_normsp_0(A,B,C) = k4_struct_0(A) ) => ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,k3_series_1(k5_normsp_0(A,B)),C) = k5_numbers ) ) ) ) )).
fof(t6_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v9_clvect_1(C,A) => k7_clvect_1(A,k2_clopban3(A,C,B)) = k6_algstr_0(A,B,k7_clvect_1(A,C)) ) ) ) ) )).
fof(t6_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,B))) => m1_subset_1(k5_subset_1(k1_closure2(A,B),C,D),k1_zfmisc_1(k1_closure2(A,B))) ) ) ) )).
fof(t6_closure3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( k5_relat_1(B,k1_closure3(A,B)) = k5_relat_1(C,k1_closure3(A,C)) => r8_pboole(A,B,C) ) ) ) ) )).
fof(t6_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xcmplx_0(C) => k1_clvect_1(A,k4_algstr_0(A,B),C) = k1_clvect_1(A,B,k4_xcmplx_0(C)) ) ) ) )).
fof(t6_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clvect_2(B,A) => v1_clvect_2(k5_vfunct_1(k4_ordinal1,A,B),A) ) ) ) )).
fof(t6_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_clvect_3(B,A) & v1_clvect_3(C,A) ) => ( v1_clvect_3(k16_csspace(A,B,C),A) & k1_clvect_3(A,k16_csspace(A,B,C)) = k3_rlvect_1(A,k1_clvect_3(A,B),k1_clvect_3(A,C)) ) ) ) ) ) )).
fof(t6_coh_sp,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ( r2_hidden(A,B) <=> ! [C] : ! [D] : ( ( r2_hidden(C,A) & r2_hidden(D,A) ) => r2_hidden(k2_tarski(C,D),B) ) ) ) )).
fof(t6_cohsp_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ! [B] : ! [C] : ~ ( r2_hidden(B,A) & r2_hidden(C,A) & ! [D] : ~ ( r1_tarski(k2_xboole_0(B,C),D) & r2_hidden(D,A) ) ) => v1_cohsp_1(A) ) ) )).
fof(t6_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t6_combgras,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ~ ( D != E & k7_relat_1(C,D) = k7_relat_1(C,E) ) ) ) ) ) ) )).
fof(t6_compact1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ( v8_pre_topc(A) & v5_compact1(A) ) <=> v8_pre_topc(k1_compact1(A)) ) ) )).
fof(t6_compl_sp,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ( C = B => ( ( v2_compl_sp(B,A) => v3_pre_topc(C,k3_pcomps_1(A)) ) & ( v3_pre_topc(C,k3_pcomps_1(A)) => v2_compl_sp(B,A) ) & ( v3_compl_sp(B,A) => v4_pre_topc(C,k3_pcomps_1(A)) ) & ( v4_pre_topc(C,k3_pcomps_1(A)) => v3_compl_sp(B,A) ) ) ) ) ) ) )).
fof(t6_complex1,axiom,( k3_complex1(k6_complex1) = 1 & k4_complex1(k6_complex1) = k5_numbers )).
fof(t6_complex2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(A,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) & r2_hidden(B,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) ) => ( ~ ( ~ r1_xxreal_0(B,A) & r1_xxreal_0(k17_sin_cos(B),k17_sin_cos(A)) ) & ~ ( ~ r1_xxreal_0(k17_sin_cos(B),k17_sin_cos(A)) & r1_xxreal_0(B,A) ) ) ) ) ) )).
fof(t6_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( ( A = C & B = D ) => ( B = k4_struct_0(k1_complfld) | k3_vectsp_1(k1_complfld,A,B) = k7_xcmplx_0(C,D) ) ) ) ) ) ) )).
fof(t6_complsp1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => v8_pre_topc(k1_complsp1(A)) ) )).
fof(t6_complsp2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t6_compos_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_compos_0(C) & v2_compos_0(C) & v3_compos_0(C) ) => ! [D] : ( m1_subset_1(D,C) => k5_compos_0(C,k5_compos_0(C,D,A),B) = k5_compos_0(C,D,k2_xcmplx_0(A,B)) ) ) ) ) )).
fof(t6_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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) ) => ( k5_card_1(B) = 1 => B = k4_compos_1(A) ) ) ) )).
fof(t6_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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,k3_compos_2(A,B,C),D) = k1_compos_2(A,B,k1_compos_2(A,C,D)) ) ) ) ) )).
fof(t6_comptrig,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,k2_rcomp_1(A,C)) & ~ r2_hidden(D,k2_rcomp_1(A,B)) & D != B & ~ r2_hidden(D,k2_rcomp_1(B,C)) ) ) ) ) ) )).
fof(t6_compts_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v8_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_compts_1(B,A) => ( B = k1_xboole_0 | ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,k3_subset_1(u1_struct_0(A),B)) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v3_pre_topc(D,A) & v3_pre_topc(E,A) & r2_hidden(C,D) & r1_tarski(B,E) & r1_xboole_0(D,E) ) ) ) ) ) ) ) ) ) ) )).
fof(t6_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( A != k5_numbers => k4_finseq_2(A,k1_xboole_0) = k1_xboole_0 ) ) )).
fof(t6_comseq_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ? [B] : ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) & k2_relset_1(k2_numbers,B) = k1_tarski(A) ) ) )).
fof(t6_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_funct_2(k4_ordinal1,k2_numbers,k36_valued_1(k4_ordinal1,k2_numbers,k2_comseq_2(k4_ordinal1,A)),k2_comseq_2(k4_ordinal1,k36_valued_1(k4_ordinal1,k2_numbers,A))) ) )).
fof(t6_conaffm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v5_conaffm(A) => v3_conaffm(A) ) ) )).
fof(t6_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u4_struct_0(A))) => r1_tarski(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))) ) ) )).
fof(t6_conmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k3_analmetr(A)))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k3_analmetr(A))) => ! [I] : ( m1_subset_1(I,u1_struct_0(k3_analmetr(A))) => ( ( D = H & E = I & F = G & r2_hidden(B,F) & r2_hidden(C,F) & r2_aff_1(k3_analmetr(A),H,I,G) ) => r2_analoaf(A,D,E,B,C) ) ) ) ) ) ) ) ) ) ) )).
fof(t6_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ! [F] : ( 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_connsp_1(A,C,D) ) => r1_connsp_1(B,E,F) ) ) ) ) ) ) ) )).
fof(t6_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( m1_connsp_2(C,A,B) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & v3_pre_topc(D,A) & r1_tarski(D,C) & r2_hidden(B,D) ) ) ) ) ) )).
fof(t6_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v2_connsp_1(B,A) & v2_connsp_1(C,A) & r1_tarski(k1_connsp_3(A,B),C) ) => C = k1_connsp_3(A,B) ) ) ) ) )).
fof(t6_convex1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_convex1(B,A) & v1_convex1(C,A) ) => ! [D] : ( v1_xreal_0(D) => v1_convex1(k7_rusub_4(A,k1_convex1(A,B,D),k1_convex1(A,C,k6_xcmplx_0(1,D))),A) ) ) ) ) ) )).
fof(t6_convex2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) )).
fof(t6_convex3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( B = k1_xboole_0 => v1_convex3(B,A) ) ) ) )).
fof(t6_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( ( 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))) ) => ( ( r2_hidden(C,k4_finseq_1(D)) & B = k1_funct_1(D,C) ) => k1_funct_1(k3_convex4(A,D,E),C) = k1_clvect_1(A,B,k3_funct_2(u1_struct_0(A),k2_numbers,E,B)) ) ) ) ) ) )).
fof(t6_convfun1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k4_convfun1),k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_convfun1),k6_numbers))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_convfun1))) => ( ( r1_tarski(C,k1_relset_1(k1_numbers,A)) & ! [D] : ( v1_xreal_0(D) => ( ( r2_hidden(D,C) => k12_supinf_2(B,D) = k12_supinf_2(A,D) ) & ( ~ r2_hidden(D,C) => k12_supinf_2(B,D) = k1_supinf_1 ) ) ) ) => ( v1_convfun1(B,k4_convfun1) <=> ( r2_rfunct_3(A,C) & v1_convex1(C,k4_convfun1) ) ) ) ) ) ) )).
fof(t6_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => m2_subset_1(k12_qc_lang1(A),k9_qc_lang1(A),k3_cqc_lang(A)) ) )).
fof(t6_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ~ ( v3_qc_lang1(B,A) & ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => B != k6_cqc_lang(A,C) ) ) ) ) )).
fof(t6_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t6_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ( r2_hidden(D,k24_qc_lang1(A,k5_qc_lang2(A,C,B))) <=> ( r2_hidden(D,k24_qc_lang1(A,B)) & D != C ) ) ) ) ) ) )).
fof(t6_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ( ( r1_cqc_the3(A,B,C) & r1_cqc_the3(A,C,D) ) => r1_cqc_the3(A,B,D) ) ) ) ) ) )).
fof(t6_csspace,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace))) => ? [B] : ( m1_subset_1(B,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,B) = k4_struct_0(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace)) ) ) )).
fof(t6_csspace2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_funct_2(k4_ordinal1,k2_numbers,k10_comseq_3(k2_comseq_2(k4_ordinal1,A)),k2_comseq_2(k4_ordinal1,k10_comseq_3(A))) ) )).
fof(t6_csspace3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_csspace3)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_csspace3)) => ! [C] : ( v1_xcmplx_0(C) => ( ( k2_normsp_0(k3_csspace3,A) = k5_numbers => A = k4_struct_0(k3_csspace3) ) & ( A = k4_struct_0(k3_csspace3) => k2_normsp_0(k3_csspace3,A) = k5_numbers ) & r1_xxreal_0(k5_numbers,k2_normsp_0(k3_csspace3,A)) & r1_xxreal_0(k2_normsp_0(k3_csspace3,k1_algstr_0(k3_csspace3,A,B)),k2_xcmplx_0(k2_normsp_0(k3_csspace3,A),k2_normsp_0(k3_csspace3,B))) & k2_normsp_0(k3_csspace3,k1_clvect_1(k3_csspace3,A,C)) = k3_xcmplx_0(k9_complex1(C),k2_normsp_0(k3_csspace3,A)) ) ) ) ) )).
fof(t6_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(D,A) => k3_funct_2(A,u1_struct_0(B),C,D) = k4_struct_0(B) ) => v1_csspace4(C,A,B) ) ) ) ) )).
fof(t6_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_decomp_1(B,A) <=> B = k5_decomp_1(A,B) ) ) ) )).
fof(t6_descip_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m2_finseq_2(C,A,k4_finseq_2(B,A)) => m2_finseq_2(k6_descip_1(C),A,k4_finseq_2(B,A)) ) ) ) )).
fof(t6_dickson,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ! [C] : ( ( r1_xboole_0(k1_wellord1(u1_orders_2(A),C),B) & r2_hidden(C,B) ) <=> r4_waybel_4(B,C,u1_orders_2(A)) ) ) )).
fof(t6_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( ( 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(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,D,E),A,B,C) = k2_xcmplx_0(k10_diff_1(D,A,B,C),k10_diff_1(E,A,B,C)) ) ) ) ) ) )).
fof(t6_diff_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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] : ( ( 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_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_valued_1(k1_numbers,k1_numbers,F,C),k26_valued_1(k1_numbers,k1_numbers,G,D)),B),k2_xcmplx_0(A,1)),E) = k6_xcmplx_0(k3_xcmplx_0(C,k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(F,B),k2_xcmplx_0(A,1)),E)),k3_xcmplx_0(D,k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(G,B),k2_xcmplx_0(A,1)),E))) ) ) ) ) ) ) ) )).
fof(t6_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(A,k1_relset_1(k1_numbers,k27_sin_cos)) & r2_hidden(B,k1_relset_1(k1_numbers,k27_sin_cos)) ) => k9_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k27_sin_cos),A,B) = k4_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k1_square_1(k19_sin_cos(B)),k1_square_1(k19_sin_cos(A))),k3_xcmplx_0(k1_square_1(k3_xcmplx_0(k17_sin_cos(A),k17_sin_cos(B))),k6_xcmplx_0(A,B)))) ) ) ) )).
fof(t6_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_dilworth(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t6_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_analoaf(A,B,C,B,D) <=> ( r2_analoaf(A,B,C,C,D) | r2_analoaf(A,B,D,D,C) ) ) ) ) ) ) )).
fof(t6_dirort,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dirort(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & B != E & ( r2_analoaf(A,C,D,B,E) | r2_analoaf(A,C,D,E,B) ) ) ) ) ) ) )).
fof(t6_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,A) => r2_hidden(B,k5_dist_1(A,B)) ) ) )).
fof(t6_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) => ( ~ v1_setfam_1(B) <=> B = k6_domain_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),k6_finseq_1(A)) ) ) ) )).
fof(t6_domain_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k3_zfmisc_1(B,C,D)) => ( A = k1_mcart_1(B,C,D,E) <=> ! [F] : ( m1_subset_1(F,B) => ! [G] : ( m1_subset_1(G,C) => ! [H] : ( m1_subset_1(H,D) => ( E = k4_domain_1(B,C,D,F,G,H) => A = F ) ) ) ) ) ) ) ) ) )).
fof(t6_dtconstr,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => k15_trees_3(k10_finseq_1(A,B)) = k10_finseq_1(k1_funct_1(A,k1_xboole_0),k1_funct_1(B,k1_xboole_0)) ) ) )).
fof(t6_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => v1_prob_2(k4_dynkin(A,B)) ) ) )).
fof(t6_e_siec,axiom,( ! [A] : ( u1_struct_0(k2_e_siec(A)) = A & u1_e_siec(k2_e_siec(A)) = k4_relat_1(A) & u2_e_siec(k2_e_siec(A)) = k4_relat_1(A) ) )).
fof(t6_ec_pf_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_ec_pf_1(B,A) => ! [C] : ( m1_ec_pf_1(C,A) => ( m1_ec_pf_1(B,C) <=> r1_tarski(u1_struct_0(B),u1_struct_0(C)) ) ) ) ) )).
fof(t6_ec_pf_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( B = k4_algstr_0(A,C) => k4_algstr_0(A,B) = C ) ) ) ) )).
fof(t6_endalg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => r1_tarski(k4_endalg(A,B),k4_autalg_1(u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,B))) ) ) )).
fof(t6_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => r1_tarski(k2_ens_1(A),k2_zfmisc_1(k2_zfmisc_1(A,A),k1_ens_1(A))) ) )).
fof(t6_entropy1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k5_numbers,C) ) => ( r1_xxreal_0(A,k5_numbers) | A = 1 | k3_xcmplx_0(k3_xcmplx_0(B,C),k3_power(A,k3_xcmplx_0(B,C))) = k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(B,C),k3_power(A,B)),k3_xcmplx_0(k3_xcmplx_0(B,C),k3_power(A,C))) ) ) ) ) ) )).
fof(t6_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_enumset1(A,B,C,D) = k2_xboole_0(k1_enumset1(A,B,C),k1_tarski(D)) )).
fof(t6_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v3_relat_2(D) & v1_partfun1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( r2_hidden(k4_tarski(B,C),D) => r2_hidden(k4_tarski(C,B),D) ) ) )).
fof(t6_equation,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m3_pboole(D,A,C) => ! [E] : ( m2_pboole(E,A,D,B) => ? [F] : ( m2_pboole(F,A,C,B) & r6_pboole(A,k1_msafree(A,C,B,D,F),E) ) ) ) ) ) )).
fof(t6_euclid,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => r1_xxreal_0(k5_numbers,k12_euclid(A)) ) )).
fof(t6_euclid_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => ( k22_rvsum_1(A,A) = k5_numbers <=> A = k5_euclid(k3_finseq_1(A)) ) ) )).
fof(t6_euclid_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(B)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(B)) => k9_euclid(B,k7_euclid(B,C,D),A) = k7_euclid(B,k9_euclid(B,C,A),k9_euclid(B,D,A)) ) ) ) ) )).
fof(t6_euclid_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => k3_rlvect_1(k15_euclid(3),k4_euclid_5(A,C,E),k4_euclid_5(B,D,F)) = k4_euclid_5(k2_xcmplx_0(A,B),k2_xcmplx_0(C,D),k2_xcmplx_0(E,F)) ) ) ) ) ) ) )).
fof(t6_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( B != A => k3_xcmplx_0(k12_euclid(k5_algstr_0(k15_euclid(2),C,B)),k17_sin_cos(k4_euclid_3(C,B,A))) = k3_xcmplx_0(k12_euclid(k5_algstr_0(k15_euclid(2),C,A)),k17_sin_cos(k4_euclid_3(B,A,C))) ) ) ) ) )).
fof(t6_euclid_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => ( v5_valued_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(B,C) & r1_xxreal_0(1,B) & r1_xxreal_0(C,k3_finseq_1(A)) ) => r1_xxreal_0(k1_funct_1(A,B),k1_funct_1(A,C)) ) ) ) ) ) )).
fof(t6_euclid_8,axiom,( k12_euclid(k4_euclid_8) = 1 )).
fof(t6_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ( B = k7_euclid(A,C,D) <=> C = k8_euclid(A,B,D) ) ) ) ) ) )).
fof(t6_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r4_analmetr(A,E,B,C,D) & r4_analmetr(A,E,C,B,D) & r4_analmetr(A,F,B,C,D) & r4_analmetr(A,F,C,B,D) ) => ( r5_analmetr(A,B,C,D) | E = F ) ) ) ) ) ) ) ) )).
fof(t6_euler_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( k3_int_2(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) = C => ( A = k5_numbers | C = k5_numbers | r1_int_2(A,B) ) ) ) ) ) )).
fof(t6_euler_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k4_nat_d(k2_xcmplx_0(C,A),B) = k4_nat_d(k1_nat_1(k4_nat_d(C,B),k4_nat_d(A,B)),B) ) ) ) )).
fof(t6_exchsort,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( k6_subset_1(A,B) != k1_xboole_0 => ( k2_ordinal2(k6_subset_1(A,B)) = B & k3_ordinal2(k6_subset_1(A,B)) = A & k3_tarski(k6_subset_1(A,B)) = k3_tarski(A) ) ) ) ) )).
fof(t6_extens_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,C) => ! [E] : ( m3_pboole(E,A,B) => ( v1_msualg_3(D) => v1_msualg_3(k1_msafree(A,B,C,E,D)) ) ) ) ) ) )).
fof(t6_extpro_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & ~ v1_setfam_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_memstr_0(C,B) & v3_memstr_0(C,B) & l1_extpro_1(C,B) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(C)) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ! [E] : ( ( 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)) ) => k5_extpro_1(B,C,D,E,k1_nat_1(A,1)) = k2_extpro_1(B,C,k3_compos_1(C,D,k5_memstr_0(B,C,k5_extpro_1(B,C,D,E,A))),k5_extpro_1(B,C,D,E,A)) ) ) ) ) ) )).
fof(t6_extreal1,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => k4_extreal1(k12_finseq_1(k6_numbers,A)) = A ) )).
fof(t6_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ~ ( k3_extreal1(A) = k2_xxreal_3(A) & A != k5_numbers & r1_xxreal_0(k5_numbers,A) ) ) )).
fof(t6_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_circcomb(A) & v2_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_circcomb(B) & v2_circcomb(B) & l1_msualg_1(B) ) => ( v1_relat_1(k3_msafree2(B)) => ( v1_facirc_1(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))) ) ) ) ) ) )).
fof(t6_facirc_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ( ( k1_funct_1(C,k5_numbers) = k5_circcomb(k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1),k1_xboole_0) & k1_funct_1(D,k5_numbers) = k7_circcomb(k5_ordinal1,k6_margrel1,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1),k1_xboole_0) & k1_funct_1(E,k5_numbers) = k4_tarski(k1_xboole_0,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1)) & ! [F] : ( v7_ordinal1(F) => ! [G] : ( ( ~ v2_struct_0(G) & l1_msualg_1(G) ) => ! [H] : ( ( v4_msualg_1(H,G) & l3_msualg_1(H,G) ) => ! [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,k19_facirc_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,k19_facirc_1(k1_funct_1(A,k1_nat_1(F,1)),k1_funct_1(B,k1_nat_1(F,1)),I),H,k20_facirc_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)) = k17_facirc_1(k1_funct_1(A,k1_nat_1(F,1)),k1_funct_1(B,k1_nat_1(F,1)),I) ) ) ) ) ) ) => ! [F] : ( v7_ordinal1(F) => ( k3_facirc_2(F,A,B) = k1_funct_1(C,F) & k4_facirc_2(F,A,B) = k1_funct_1(D,F) & k5_facirc_2(F,A,B) = k1_funct_1(E,F) ) ) ) ) ) ) ) ) )).
fof(t6_fcont_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ? [C] : ( m1_rcomp_1(C,A) & k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),C) = k1_seq_4(A) ) => r1_fcont_1(B,A) ) ) ) )).
fof(t6_fcont_2,axiom,( ! [A] : ! [B] : ( ( 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_2(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => v1_fcont_2(k2_partfun1(k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,B),A)) ) ) )).
fof(t6_fdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v3_fdiff_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v3_fdiff_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => v2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) )).
fof(t6_fdiff_10,axiom,( ! [A] : ( ( 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,k26_sin_cos,k27_sin_cos))) => ( r2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k27_sin_cos),A),B) = k6_xcmplx_0(k7_xcmplx_0(1,k1_square_1(k1_funct_1(k18_sin_cos,B))),k7_xcmplx_0(1,k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t6_fdiff_11,axiom,( ! [A] : ( ( 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,k26_sin_cos,k2_sin_cos9))) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k26_sin_cos,B),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(k26_sin_cos,B)) ) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k2_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k2_sin_cos9),A),B) = k4_xcmplx_0(1) ) ) ) ) ) )).
fof(t6_fdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( r1_fdiff_3(A,B) & k1_funct_1(A,B) != C & ? [D] : ( v1_xreal_0(D) & ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k1_rcomp_1(k6_xcmplx_0(B,D),B),k1_relset_1(k1_numbers,A)) ) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k1_rcomp_1(k6_xcmplx_0(B,D),B),k1_relset_1(k1_numbers,A)) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k1_rcomp_1(k6_xcmplx_0(B,D),B)) & k1_funct_1(A,E) = C ) ) ) ) ) ) ) ) )).
fof(t6_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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,k3_xcmplx_0(2,A))))) & C = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k3_taylor_1) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => ( k1_funct_1(D,E) = k2_xcmplx_0(E,A) & ~ r1_xxreal_0(k1_funct_1(D,E),k5_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,k3_xcmplx_0(2,A))),B) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_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,k3_xcmplx_0(2,A))),B),E) = k7_xcmplx_0(k6_xcmplx_0(E,A),k2_xcmplx_0(E,A)) ) ) ) ) ) ) ) ) )).
fof(t6_fdiff_6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(B,k9_xtuple_0(k26_valued_1(k1_numbers,k1_numbers,C,k7_xcmplx_0(1,k3_xcmplx_0(4,k1_square_1(A)))))) & 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] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => ( k1_funct_1(D,F) = k1_square_1(A) & ~ r1_xxreal_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,D,E),F),k5_numbers) & A != k5_numbers ) ) ) ) => ( r2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,C,k7_xcmplx_0(1,k3_xcmplx_0(4,k1_square_1(A)))),B) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => k1_funct_1(k2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,C,k7_xcmplx_0(1,k3_xcmplx_0(4,k1_square_1(A)))),B),F) = k7_xcmplx_0(F,k6_xcmplx_0(k1_newton(A,4),k1_newton(F,4))) ) ) ) ) ) ) ) ) ) )).
fof(t6_fdiff_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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_funct_1(B,A),k4_xcmplx_0(1)) | r1_xxreal_0(1,k1_funct_1(B,A)) | ( r1_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k1_sin_cos6),A) & k1_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k1_sin_cos6),A) = k7_xcmplx_0(k1_fdiff_1(B,A),k3_square_1(k6_xcmplx_0(1,k1_square_1(k1_funct_1(B,A))))) ) ) ) ) ) )).
fof(t6_fdiff_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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,k26_sin_cos))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(D,E) = k2_xcmplx_0(k3_xcmplx_0(A,E),B) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k26_sin_cos),C) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k26_sin_cos),C),E) = k7_xcmplx_0(A,k1_square_1(k1_funct_1(k18_sin_cos,k2_xcmplx_0(k3_xcmplx_0(A,E),B)))) ) ) ) ) ) ) ) ) )).
fof(t6_fdiff_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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_fdiff_9))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(D,E) = k2_xcmplx_0(k3_xcmplx_0(A,E),B) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k1_fdiff_9),C) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k1_fdiff_9),C),E) = k7_xcmplx_0(k3_xcmplx_0(A,k1_funct_1(k16_sin_cos,k2_xcmplx_0(k3_xcmplx_0(A,E),B))),k1_square_1(k1_funct_1(k18_sin_cos,k2_xcmplx_0(k3_xcmplx_0(A,E),B)))) ) ) ) ) ) ) ) ) )).
fof(t6_ff_siec,axiom,( u1_struct_0(k6_ff_siec) = k1_xboole_0 & u4_struct_0(k6_ff_siec) = k1_xboole_0 & k1_net_1(k6_ff_siec) = k1_xboole_0 )).
fof(t6_fib_num,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r1_xxreal_0(k5_numbers,k1_quin_1(B,C,D)) => ( B = k5_numbers | ( k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(A)),k3_xcmplx_0(C,A)),D) = k5_numbers <=> ( A = k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B)) | A = k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B)) ) ) ) ) ) ) ) ) )).
fof(t6_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_xreal_0(B) ) => ! [C] : ( ( v1_int_1(C) & ~ v1_abian(C) ) => k2_power(k2_power(B,C),A) = k2_power(B,k3_xcmplx_0(C,A)) ) ) ) )).
fof(t6_fib_num3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_xreal_0(B) ) => k2_power(k2_power(B,A),2) = k2_power(B,k2_nat_1(2,A)) ) ) )).
fof(t6_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_xreal_0(B) ) => ~ ( v1_abian(A) & r1_xxreal_0(k2_power(B,A),k5_numbers) ) ) ) )).
fof(t6_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,E) & r1_xxreal_0(E,k3_finseq_1(B)) ) => k3_finseq_6(A,k1_finseq_8(A,B,C),D,E) = k3_finseq_6(A,B,D,E) ) ) ) ) ) ) )).
fof(t6_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r3_lattices(A,B,D) & r3_lattices(A,C,D) ) => r3_lattices(A,k3_lattices(A,B,C),D) ) ) ) ) ) )).
fof(t6_filter_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m2_filter_1(D,A,B) => ( r1_binop_1(A,C,D) => r1_binop_1(k8_eqrel_1(A,B),k9_eqrel_1(A,B,C),k3_filter_1(A,B,D)) ) ) ) ) ) )).
fof(t6_filter_2,axiom,( ! [A] : ( l3_lattices(A) => ! [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)) => k1_lattice2(A) = k1_lattice2(B) ) ) ) )).
fof(t6_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k5_fin_topo(A,B) = k4_subset_1(u1_struct_0(A),k6_fin_topo(A,B),k7_fin_topo(A,B)) ) ) )).
fof(t6_finance1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k3_prob_1(k1_numbers,k2_finance1(A,B)) = k1_rcomp_1(A,B) ) ) )).
fof(t6_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k2_finseq_1(A) = k2_finseq_1(B) => A = B ) ) ) )).
fof(t6_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(A,k2_finseq_1(C)) => r2_hidden(A,k2_finseq_1(k2_xcmplx_0(C,B))) ) ) ) ) )).
fof(t6_finseq_3,axiom,( k2_finseq_1(8) = k6_enumset1(1,2,3,4,5,6,7,8) )).
fof(t6_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r2_finseq_4(A,B) <=> ? [C] : k1_tarski(C) = k8_relat_1(A,k1_tarski(B)) ) ) )).
fof(t6_finseq_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( r2_hidden(1,k4_finseq_1(A)) & r2_hidden(k3_finseq_1(A),k4_finseq_1(A)) ) ) )).
fof(t6_finseq_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( r2_hidden(C,k10_xtuple_0(A)) => k4_finseq_4(k7_finseq_1(A,B),C) = k4_finseq_4(A,C) ) ) ) )).
fof(t6_finseq_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : r1_tarski(k10_xtuple_0(k1_funct_7(A,B,C)),k2_xboole_0(k10_xtuple_0(A),k1_tarski(C))) ) ) )).
fof(t6_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_xxreal_0(k3_finseq_1(B),C) => k3_finseq_8(A,B,1,C) = B ) ) ) ) )).
fof(t6_finseqop,axiom,( ! [A] : ! [B] : ! [C] : r1_funct_2(A,k2_zfmisc_1(k1_tarski(B),k1_tarski(C)),A,k1_tarski(k4_tarski(B,C)),k14_funct_3(A,k1_tarski(B),k1_tarski(C),k7_funcop_1(A,B),k7_funcop_1(A,C)),k7_funcop_1(A,k4_tarski(B,C))) )).
fof(t6_finset_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ~ ( B != k1_xboole_0 & ! [C] : ~ ( r2_hidden(C,B) & ! [D] : ( ( r2_hidden(D,B) & r1_tarski(C,D) ) => D = C ) ) ) ) ) )).
fof(t6_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( 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(C)) ) | k1_finsop_1(A,k8_finseq_1(A,k12_finseq_1(A,B),C),D) = k5_binop_1(A,D,B,k1_finsop_1(A,C,D)) ) ) ) ) ) ) )).
fof(t6_finsub_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ( r2_hidden(k5_xboole_0(B,C),A) & r2_hidden(k2_xboole_0(B,C),A) ) ) ) => v4_finsub_1(A) ) ) )).
fof(t6_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( k1_fintopo2(A,B,C,D) = k8_margrel1 <=> ( r2_hidden(C,k1_fin_topo(A,B)) & r2_hidden(C,D) ) ) ) ) ) ) )).
fof(t6_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(B,C) => r1_tarski(k1_fintopo3(A,B),k1_fintopo3(A,C)) ) ) ) ) )).
fof(t6_fintopo4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_fintopo4(A,B,C) => r1_xboole_0(B,C) ) ) ) ) )).
fof(t6_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_fin_topo(A) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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) ) ) ) ) => v4_fin_topo(B,A) ) ) ) )).
fof(t6_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(k5_afinsq_1(B),k3_catalan2(A)) => r2_hidden(B,A) ) )).
fof(t6_flang_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k8_afinsq_1(A))) => ( r2_hidden(k5_afinsq_1(B),k6_flang_1(A,C,D)) <=> ( ( r2_hidden(k2_flang_1(A),C) & r2_hidden(k5_afinsq_1(B),D) ) | ( r2_hidden(k5_afinsq_1(B),C) & r2_hidden(k2_flang_1(A),D) ) ) ) ) ) )).
fof(t6_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(C,D) => r1_tarski(k1_flang_2(A,B,D,E),k1_flang_3(A,B,C)) ) ) ) ) ) )).
fof(t6_fomodel0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v5_relat_1(B,A) => ( v1_xboole_0(B) | k1_funct_1(k7_fomodel0(A),B) = k1_funct_1(B,1) ) ) ) ) )).
fof(t6_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => r1_tarski(k35_fomodel1(A),k6_subset_1(k3_finseq_2(k15_fomodel1(A)),k1_tarski(k1_xboole_0))) ) )).
fof(t6_fomodel2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r2_hidden(D,k2_xboole_0(k2_xboole_0(A,B),C)) <=> ~ ( ~ r2_hidden(D,A) & ~ r2_hidden(D,B) & ~ r2_hidden(D,C) ) ) )).
fof(t6_fomodel3,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( v10_fomodel1(C,B) & m1_subset_1(C,k1_fomodel1(B)) ) => ! [D] : ( ( v3_card_1(D,k1_int_2(k19_fomodel1(B,C))) & m2_subset_1(D,k3_finseq_2(k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0))),k3_fomodel0(k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0)),k35_fomodel1(B))) ) => ( ( ~ v7_fomodel1(C,B) => k1_funct_1(k4_fomodel3(B,C,A),D) = k1_fomodel3(B,C,D) ) & ( v7_fomodel1(C,B) => k1_funct_1(k4_fomodel3(B,C,A),D) = k1_funct_1(k10_fomodel0(A,k32_fomodel1(B)),k1_fomodel3(B,C,D)) ) ) ) ) ) )).
fof(t6_fomodel4,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( 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) => v9_fomodel4(C,B,k6_domain_1(k9_funct_2(k9_setfam_1(k1_fomodel4(B)),k9_setfam_1(k1_fomodel4(B))),k24_fomodel4(B)),A) ) ) ) )).
fof(t6_fraenkel,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & v1_finset_1(B) ) => v1_finset_1(k1_funct_2(A,B)) ) )).
fof(t6_frechet,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( 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) ) ) => ( v2_pre_topc(B) & l1_pre_topc(B) ) ) ) ) ) )).
fof(t6_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v8_pre_topc(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,k2_frechet(A,B)) & r2_hidden(D,k2_frechet(A,B)) ) => C = D ) ) ) ) ) ) )).
fof(t6_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(A,u1_struct_0(k4_fscirc_1(A,B,C))) & r2_hidden(B,u1_struct_0(k4_fscirc_1(A,B,C))) & r2_hidden(C,u1_struct_0(k4_fscirc_1(A,B,C))) ) )).
fof(t6_fscirc_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) ) => ! [D] : ! [E] : ( k1_fscirc_2(k1_nat_1(A,1),k7_finseq_1(B,k9_finseq_1(D)),k7_finseq_1(C,k9_finseq_1(E))) = k2_circcomb(k1_fscirc_2(A,B,C),k8_fscirc_1(D,E,k3_fscirc_2(A,B,C))) & k2_fscirc_2(k1_nat_1(A,1),k7_finseq_1(B,k9_finseq_1(D)),k7_finseq_1(C,k9_finseq_1(E))) = k3_circcomb(k1_fscirc_2(A,B,C),k8_fscirc_1(D,E,k3_fscirc_2(A,B,C)),k2_fscirc_2(A,B,C),k9_fscirc_1(D,E,k3_fscirc_2(A,B,C))) & k3_fscirc_2(k1_nat_1(A,1),k7_finseq_1(B,k9_finseq_1(D)),k7_finseq_1(C,k9_finseq_1(E))) = k6_fscirc_1(D,E,k3_fscirc_2(A,B,C)) ) ) ) ) )).
fof(t6_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( r1_fsm_1(A,B,C,E,F) => k1_funct_1(k2_fsm_1(A,B,E,k8_finseq_1(A,C,D)),k1_nat_1(k3_finseq_1(C),1)) = F ) ) ) ) ) ) ) )).
fof(t6_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ( v1_fsm_2(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ( ( k1_funct_1(C,1) = k1_funct_1(D,1) & k3_finseq_1(C) = k3_finseq_1(D) ) => k2_fsm_1(A,B,u2_fsm_1(A,B),C) = k2_fsm_1(A,B,u2_fsm_1(A,B),D) ) ) ) ) ) ) )).
fof(t6_fsm_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ! [D] : ( ( 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 ) ) ) ) )).
fof(t6_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( E != k4_tarski(k10_finseq_1(D,k12_gfacirc1(A,B,C)),k2_twoscomp) & ~ r2_hidden(E,k3_msafree2(k13_gfacirc1(A,B,C))) & ~ ( r2_hidden(A,k2_msafree2(k1_ftacell1(A,B,C,D,E))) & r2_hidden(B,k2_msafree2(k1_ftacell1(A,B,C,D,E))) & r2_hidden(C,k2_msafree2(k1_ftacell1(A,B,C,D,E))) & r2_hidden(D,k2_msafree2(k1_ftacell1(A,B,C,D,E))) & r2_hidden(E,k2_msafree2(k1_ftacell1(A,B,C,D,E))) ) ) ) ) ) ) )).
fof(t6_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : k5_relat_1(k13_funct_3(A,B),C) = k13_funct_3(A,k5_relat_1(B,C)) ) ) )).
fof(t6_funcsdom,axiom,( ! [A] : ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( m2_funct_2(C,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [D] : ( 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_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,k5_funcsdom(A),B,C),D)) ) ) ) )).
fof(t6_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( r1_tarski(k2_relset_1(B,D),C) => ( ( B = k1_xboole_0 & A != k1_xboole_0 ) | ( v1_funct_1(D) & v1_funct_2(D,A,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) ) ) ) )).
fof(t6_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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) & ! [E] : ! [F] : ( ( r2_hidden(E,A) & r2_hidden(F,B) ) => k1_binop_1(C,E,F) = k1_binop_1(D,E,F) ) ) => C = D ) ) ) )).
fof(t6_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r1_relset_1(A,k1_tarski(C),k7_funcop_1(A,C),k7_funcop_1(B,D)) => ( A = k1_xboole_0 | C = D ) ) )).
fof(t6_funct_5,axiom,( ! [A] : ! [B] : ( k9_xtuple_0(k1_tarski(k4_tarski(A,B))) = k1_tarski(A) & k10_xtuple_0(k1_tarski(k4_tarski(A,B))) = k1_tarski(B) ) )).
fof(t6_funct_6,axiom,( ! [A] : ! [B] : ! [C] : ( k2_funct_5(k7_funcop_1(B,k7_funcop_1(C,A))) = k7_funcop_1(k2_zfmisc_1(B,C),A) & k4_funct_5(k7_funcop_1(B,k7_funcop_1(C,A))) = k7_funcop_1(k2_zfmisc_1(C,B),A) ) )).
fof(t6_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => k5_relat_1(A,k1_tarski(B)) = k16_funcop_1(B,k1_funct_1(A,B)) ) ) )).
fof(t6_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k7_xcmplx_0(k1_funct_1(B,C),k1_funct_1(B,k4_xcmplx_0(C))) = 1 ) ) ) => r1_funct_8(A,k1_numbers,k1_numbers,B) ) ) ) )).
fof(t6_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) ) => ( v1_funct_9(B,A) => v1_funct_9(k30_valued_1(B),A) ) ) ) )).
fof(t6_functor0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( v2_funct_1(A) & v2_funct_1(B) ) => k2_funct_1(k15_funct_3(A,B)) = k15_funct_3(k2_funct_1(A),k2_funct_1(B)) ) ) ) )).
fof(t6_functor1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l1_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_altcat_2(C) & l1_altcat_1(C) ) => ! [D] : ( ( v8_functor0(D,A,B) & l2_functor0(D,A,B) ) => ! [E] : ( l2_functor0(E,B,C) => ( ( v4_functor0(D,A,B) & v4_functor0(E,B,C) ) => v4_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ) ) ) ) )).
fof(t6_functor2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( m2_functor0(C,A,B) => ! [D] : ( m2_functor0(D,A,B) => ! [E] : ( m2_functor0(E,A,B) => ! [F] : ( m2_functor0(F,A,B) => ( ( r1_functor2(A,B,C,D) & r1_functor2(A,B,D,E) & r1_functor2(A,B,E,F) ) => ! [G] : ( m1_functor2(G,A,B,C,D) => ! [H] : ( m1_functor2(H,A,B,D,E) => ! [I] : ( m1_functor2(I,A,B,E,F) => r8_pboole(u1_struct_0(A),k3_functor2(A,B,C,D,F,G,k3_functor2(A,B,D,E,F,H,I)),k3_functor2(A,B,C,E,F,k3_functor2(A,B,C,D,E,G,H),I)) ) ) ) ) ) ) ) ) ) ) )).
fof(t6_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_altcat_2(C) & l2_altcat_1(C) ) => ! [D] : ( ( v8_functor0(D,A,B) & v10_functor0(D,A,B) & l2_functor0(D,A,B) ) => ! [E] : ( ( v8_functor0(E,B,C) & v10_functor0(E,B,C) & l2_functor0(E,B,C) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,k1_altcat_1(A,F,G)) => ( k1_altcat_1(A,F,G) != k1_xboole_0 => k6_functor0(A,C,k13_functor0(A,B,C,D,E),F,G,H) = k6_functor0(B,C,E,k3_functor0(A,B,D,F),k3_functor0(A,B,D,G),k6_functor0(A,B,D,F,G,H)) ) ) ) ) ) ) ) ) ) )).
fof(t6_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,C,C),C) & r2_funct_2(A,k1_numbers,k1_fuzzy_1(A,C,C),C) & r2_funct_2(A,k1_numbers,k2_fuzzy_1(A,C,C),k1_fuzzy_1(A,C,C)) & r2_funct_2(A,k1_numbers,k1_fuzzy_1(A,B,D),k1_fuzzy_1(A,D,B)) & r2_funct_2(A,k1_numbers,k2_fuzzy_1(A,B,D),k2_fuzzy_1(A,D,B)) ) ) ) ) ) )).
fof(t6_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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,D) & r1_fuzzy_1(C,E) ) => r1_fuzzy_1(k1_fuzzy_2(A,B,E),k1_fuzzy_2(A,D,C)) ) ) ) ) ) ) )).
fof(t6_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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(B,A),k1_numbers,k3_fuzzy_1(k2_zfmisc_1(B,A),k1_fuzzy_4(B,A,C)),k1_fuzzy_4(B,A,k3_fuzzy_1(k2_zfmisc_1(A,B),C))) ) ) ) )).
fof(t6_fvaluat1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( B != k2_xxreal_0 & ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k5_numbers,k2_extreal1(A,B)) ) ) ) )).
fof(t6_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_algstr_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)) ) )).
fof(t6_gate_1,axiom,( ! [A] : ! [B] : ( ~ ( ~ v1_xboole_0(k4_gate_1(A,B)) & ~ ( ~ v1_xboole_0(A) & v1_xboole_0(B) ) & ~ ( v1_xboole_0(A) & ~ v1_xboole_0(B) ) ) & ~ ( ( ( ~ v1_xboole_0(A) & v1_xboole_0(B) ) | ( v1_xboole_0(A) & ~ v1_xboole_0(B) ) ) & v1_xboole_0(k4_gate_1(A,B)) ) ) )).
fof(t6_gate_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ! [Q] : ! [R] : ! [S] : ! [T] : ! [U] : ! [V] : ! [W] : ! [X] : ! [Y] : ! [Z] : ! [A1] : ! [B1] : ! [C1] : ! [D1] : ! [E1] : ! [F1] : ! [G1] : ! [H1] : ! [I1] : ! [J1] : ! [K1] : ! [L1] : ! [M1] : ! [N1] : ! [O1] : ~ ( ~ ( ~ v1_xboole_0(A) & v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),k1_gate_1(H1),k1_gate_1(G1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),k1_gate_1(H1),k1_gate_1(G1))) & v1_xboole_0(A) ) & ~ ( ~ v1_xboole_0(B) & v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),k1_gate_1(H1),G1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),k1_gate_1(H1),G1)) & v1_xboole_0(B) ) & ~ ( ~ v1_xboole_0(C) & v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),H1,k1_gate_1(G1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),H1,k1_gate_1(G1))) & v1_xboole_0(C) ) & ~ ( ~ v1_xboole_0(D) & v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),H1,G1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),k1_gate_1(I1),H1,G1)) & v1_xboole_0(D) ) & ~ ( ~ v1_xboole_0(E) & v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,k1_gate_1(H1),k1_gate_1(G1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,k1_gate_1(H1),k1_gate_1(G1))) & v1_xboole_0(E) ) & ~ ( ~ v1_xboole_0(F) & v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,k1_gate_1(H1),G1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,k1_gate_1(H1),G1)) & v1_xboole_0(F) ) & ~ ( ~ v1_xboole_0(G) & v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,H1,k1_gate_1(G1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,H1,k1_gate_1(G1))) & v1_xboole_0(G) ) & ~ ( ~ v1_xboole_0(H) & v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,H1,G1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(J1),I1,H1,G1)) & v1_xboole_0(H) ) & ~ ( ~ v1_xboole_0(I) & v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),k1_gate_1(H1),k1_gate_1(G1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),k1_gate_1(H1),k1_gate_1(G1))) & v1_xboole_0(I) ) & ~ ( ~ v1_xboole_0(J) & v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),k1_gate_1(H1),G1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),k1_gate_1(H1),G1)) & v1_xboole_0(J) ) & ~ ( ~ v1_xboole_0(K) & v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),H1,k1_gate_1(G1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),H1,k1_gate_1(G1))) & v1_xboole_0(K) ) & ~ ( ~ v1_xboole_0(L) & v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),H1,G1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(J1,k1_gate_1(I1),H1,G1)) & v1_xboole_0(L) ) & ~ ( ~ v1_xboole_0(M) & v1_xboole_0(k14_gate_1(J1,I1,k1_gate_1(H1),k1_gate_1(G1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(J1,I1,k1_gate_1(H1),k1_gate_1(G1))) & v1_xboole_0(M) ) & ~ ( ~ v1_xboole_0(N) & v1_xboole_0(k14_gate_1(J1,I1,k1_gate_1(H1),G1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(J1,I1,k1_gate_1(H1),G1)) & v1_xboole_0(N) ) & ~ ( ~ v1_xboole_0(O) & v1_xboole_0(k14_gate_1(J1,I1,H1,k1_gate_1(G1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(J1,I1,H1,k1_gate_1(G1))) & v1_xboole_0(O) ) & ~ ( ~ v1_xboole_0(P) & v1_xboole_0(k14_gate_1(J1,I1,H1,G1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(J1,I1,H1,G1)) & v1_xboole_0(P) ) & ~ ( ~ v1_xboole_0(Q) & v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),k1_gate_1(L1),k1_gate_1(K1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),k1_gate_1(L1),k1_gate_1(K1))) & v1_xboole_0(Q) ) & ~ ( ~ v1_xboole_0(R) & v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),k1_gate_1(L1),K1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),k1_gate_1(L1),K1)) & v1_xboole_0(R) ) & ~ ( ~ v1_xboole_0(S) & v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),L1,k1_gate_1(K1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),L1,k1_gate_1(K1))) & v1_xboole_0(S) ) & ~ ( ~ v1_xboole_0(T) & v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),L1,K1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),k1_gate_1(M1),L1,K1)) & v1_xboole_0(T) ) & ~ ( ~ v1_xboole_0(U) & v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,k1_gate_1(L1),k1_gate_1(K1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,k1_gate_1(L1),k1_gate_1(K1))) & v1_xboole_0(U) ) & ~ ( ~ v1_xboole_0(V) & v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,k1_gate_1(L1),K1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,k1_gate_1(L1),K1)) & v1_xboole_0(V) ) & ~ ( ~ v1_xboole_0(W) & v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,L1,k1_gate_1(K1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,L1,k1_gate_1(K1))) & v1_xboole_0(W) ) & ~ ( ~ v1_xboole_0(X) & v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,L1,K1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(k1_gate_1(N1),M1,L1,K1)) & v1_xboole_0(X) ) & ~ ( ~ v1_xboole_0(Y) & v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),k1_gate_1(L1),k1_gate_1(K1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),k1_gate_1(L1),k1_gate_1(K1))) & v1_xboole_0(Y) ) & ~ ( ~ v1_xboole_0(Z) & v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),k1_gate_1(L1),K1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),k1_gate_1(L1),K1)) & v1_xboole_0(Z) ) & ~ ( ~ v1_xboole_0(A1) & v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),L1,k1_gate_1(K1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),L1,k1_gate_1(K1))) & v1_xboole_0(A1) ) & ~ ( ~ v1_xboole_0(B1) & v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),L1,K1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(N1,k1_gate_1(M1),L1,K1)) & v1_xboole_0(B1) ) & ~ ( ~ v1_xboole_0(C1) & v1_xboole_0(k14_gate_1(N1,M1,k1_gate_1(L1),k1_gate_1(K1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(N1,M1,k1_gate_1(L1),k1_gate_1(K1))) & v1_xboole_0(C1) ) & ~ ( ~ v1_xboole_0(D1) & v1_xboole_0(k14_gate_1(N1,M1,k1_gate_1(L1),K1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(N1,M1,k1_gate_1(L1),K1)) & v1_xboole_0(D1) ) & ~ ( ~ v1_xboole_0(E1) & v1_xboole_0(k14_gate_1(N1,M1,L1,k1_gate_1(K1))) ) & ~ ( ~ v1_xboole_0(k14_gate_1(N1,M1,L1,k1_gate_1(K1))) & v1_xboole_0(E1) ) & ~ ( ~ v1_xboole_0(F1) & v1_xboole_0(k14_gate_1(N1,M1,L1,K1)) ) & ~ ( ~ v1_xboole_0(k14_gate_1(N1,M1,L1,K1)) & v1_xboole_0(F1) ) & ~ ( ~ v1_xboole_0(K1) & v1_xboole_0(k2_gate_1(k1_gate_1(J1),O1)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(k1_gate_1(J1),O1)) & v1_xboole_0(K1) ) & ~ ( ~ v1_xboole_0(L1) & v1_xboole_0(k2_gate_1(G1,O1)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(G1,O1)) & v1_xboole_0(L1) ) & ~ ( ~ v1_xboole_0(M1) & v1_xboole_0(k2_gate_1(H1,O1)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(H1,O1)) & v1_xboole_0(M1) ) & ~ ( ~ v1_xboole_0(N1) & v1_xboole_0(k2_gate_1(I1,O1)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(I1,O1)) & v1_xboole_0(N1) ) & ~ ( ~ ( ~ v1_xboole_0(R) & v1_xboole_0(k2_gate_1(A,O1)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(A,O1)) & v1_xboole_0(R) ) & ~ ( ~ v1_xboole_0(T) & v1_xboole_0(k2_gate_1(B,O1)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(B,O1)) & v1_xboole_0(T) ) & ~ ( ~ v1_xboole_0(X) & v1_xboole_0(k2_gate_1(D,O1)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(D,O1)) & v1_xboole_0(X) ) & ~ ( ~ v1_xboole_0(F1) & v1_xboole_0(k2_gate_1(H,O1)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(H,O1)) & v1_xboole_0(F1) ) & ~ ( ~ v1_xboole_0(E1) & v1_xboole_0(k2_gate_1(P,O1)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(P,O1)) & v1_xboole_0(E1) ) & ~ ( ~ v1_xboole_0(C1) & v1_xboole_0(k2_gate_1(O,O1)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(O,O1)) & v1_xboole_0(C1) ) & ~ ( ~ v1_xboole_0(Y) & v1_xboole_0(k2_gate_1(M,O1)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(M,O1)) & v1_xboole_0(Y) ) & ~ ( ~ v1_xboole_0(Q) & v1_xboole_0(k3_gate_1(k2_gate_1(I,O1),k1_gate_1(O1))) ) & ~ ( ~ v1_xboole_0(k3_gate_1(k2_gate_1(I,O1),k1_gate_1(O1))) & v1_xboole_0(Q) ) & ~ ( ~ v1_xboole_0(V) & v1_xboole_0(k2_gate_1(C,O1)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(C,O1)) & v1_xboole_0(V) ) & ~ ( ~ v1_xboole_0(B1) & v1_xboole_0(k2_gate_1(F,O1)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(F,O1)) & v1_xboole_0(B1) ) & ~ ( ~ v1_xboole_0(W) & v1_xboole_0(k2_gate_1(L,O1)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(L,O1)) & v1_xboole_0(W) ) & ~ ( ~ v1_xboole_0(D1) & v1_xboole_0(k2_gate_1(G,O1)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(G,O1)) & v1_xboole_0(D1) ) & ~ ( ~ v1_xboole_0(A1) & v1_xboole_0(k2_gate_1(N,O1)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(N,O1)) & v1_xboole_0(A1) ) & ~ ( ~ v1_xboole_0(U) & v1_xboole_0(k2_gate_1(K,O1)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(K,O1)) & v1_xboole_0(U) ) & ~ ( ~ v1_xboole_0(Z) & v1_xboole_0(k2_gate_1(E,O1)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(E,O1)) & v1_xboole_0(Z) ) & ~ ( ~ v1_xboole_0(S) & v1_xboole_0(k2_gate_1(J,O1)) ) & ~ ( ~ v1_xboole_0(k2_gate_1(J,O1)) & v1_xboole_0(S) ) ) ) )).
fof(t6_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_gcd_1(A,B,k6_algstr_0(A,B,C)) & ( v5_group_1(A) => r1_gcd_1(A,C,k6_algstr_0(A,B,C)) ) ) ) ) ) )).
fof(t6_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v2_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( m1_genealg1(D,C) => ! [E] : ( m1_genealg1(E,C) => m1_genealg1(k2_genealg1(C,D,E,A,B),C) ) ) ) ) ) )).
fof(t6_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k1_geomtrap(A,k1_geomtrap(A,B,C),k1_geomtrap(A,D,E)) = k1_geomtrap(A,k1_geomtrap(A,B,D),k1_geomtrap(A,C,E)) ) ) ) ) ) )).
fof(t6_gfacirc1,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k1_funct_1(k1_gfacirc1,k9_finseq_1(k1_funct_1(k14_twoscomp,k10_finseq_1(k1_funct_1(k4_gfacirc1,k10_finseq_1(A,B)),C)))) = k1_funct_1(k4_gfacirc1,k10_finseq_1(k1_funct_1(k4_gfacirc1,k10_finseq_1(A,B)),C)) ) ) ) )).
fof(t6_gfacirc2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_card_1(C,A) & v1_finseq_1(C) ) => ! [D] : ! [E] : ( k1_gfacirc2(k1_nat_1(A,1),k7_finseq_1(B,k9_finseq_1(D)),k7_finseq_1(C,k9_finseq_1(E))) = k2_circcomb(k1_gfacirc2(A,B,C),k13_gfacirc1(D,E,k3_gfacirc2(A,B,C))) & k2_gfacirc2(k1_nat_1(A,1),k7_finseq_1(B,k9_finseq_1(D)),k7_finseq_1(C,k9_finseq_1(E))) = k3_circcomb(k1_gfacirc2(A,B,C),k13_gfacirc1(D,E,k3_gfacirc2(A,B,C)),k2_gfacirc2(A,B,C),k14_gfacirc1(D,E,k3_gfacirc2(A,B,C))) & k3_gfacirc2(k1_nat_1(A,1),k7_finseq_1(B,k9_finseq_1(D)),k7_finseq_1(C,k9_finseq_1(E))) = k9_gfacirc1(D,E,k3_gfacirc2(A,B,C)) ) ) ) ) )).
fof(t6_glib_000,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ( k6_glib_000(k12_glib_000(A,B,C,D)) = A & k7_glib_000(k12_glib_000(A,B,C,D)) = B & r1_funct_2(k7_glib_000(k12_glib_000(A,B,C,D)),k6_glib_000(k12_glib_000(A,B,C,D)),B,A,k10_glib_000(k12_glib_000(A,B,C,D)),C) & r1_funct_2(k7_glib_000(k12_glib_000(A,B,C,D)),k6_glib_000(k12_glib_000(A,B,C,D)),B,A,k11_glib_000(k12_glib_000(A,B,C,D)),D) ) ) ) ) )).
fof(t6_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( r1_xxreal_0(C,k3_finseq_1(B)) => r2_hidden(k1_funct_1(B,C),k6_glib_000(A)) ) ) ) ) )).
fof(t6_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v4_glib_000(A) ) => v1_glib_002(A) ) )).
fof(t6_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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)) ) )).
fof(t6_glib_004,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : ( r2_hidden(D,A) => k1_funct_1(B,D) = k1_funct_1(C,D) ) => k2_uproots(A,B) = k2_uproots(A,C) ) ) ) )).
fof(t6_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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] : ( m1_subset_1(C,k6_glib_000(A)) => v13_glib_000(k5_glib_005(A,B,C)) ) ) ) )).
fof(t6_goboard1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r2_hidden(B,k2_finseq_1(k1_matrix_0(D))) & k1_matrix_0(D) = k1_nat_1(A,1) & r1_xxreal_0(1,C) ) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(B,C) | ( k8_matrix_0(u1_struct_0(k15_euclid(2)),k16_matrix_0(B,u1_struct_0(k15_euclid(2)),D),C) = k8_matrix_0(u1_struct_0(k15_euclid(2)),D,C) & r2_hidden(C,k2_finseq_1(k1_matrix_0(k16_matrix_0(B,u1_struct_0(k15_euclid(2)),D)))) & r2_hidden(C,k2_finseq_1(k1_matrix_0(D))) ) ) ) ) ) ) ) )).
fof(t6_goboard2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => r1_tarski(k3_topreal1(2,A),k3_topreal1(2,k8_finseq_1(u1_struct_0(k15_euclid(2)),A,B))) ) ) )).
fof(t6_goboard4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ~ ( r1_topreal4(A,C,E) & r1_topreal4(B,D,F) & ! [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(2))) => ( r2_hidden(G,k4_subset_1(u1_struct_0(k15_euclid(2)),A,B)) => ( r1_xxreal_0(k17_euclid(C),k17_euclid(G)) & r1_xxreal_0(k17_euclid(G),k17_euclid(E)) ) ) ) & ! [G] : ( m1_subset_1(G,u1_struct_0(k15_euclid(2))) => ( r2_hidden(G,k4_subset_1(u1_struct_0(k15_euclid(2)),A,B)) => ( r1_xxreal_0(k18_euclid(D),k18_euclid(G)) & r1_xxreal_0(k18_euclid(G),k18_euclid(F)) ) ) ) & r1_xboole_0(A,B) ) ) ) ) ) ) ) )).
fof(t6_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(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,k3_finseq_1(B)) ) => ( v3_relat_1(B) | k2_goboard5(B,k1_matrix_0(B)) = a_2_6_goboard5(A,B) ) ) ) ) )).
fof(t6_goboard6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k14_euclid(2))) => ( ( E = k19_euclid(A,B) & F = k19_euclid(C,D) ) => k3_metric_1(k14_euclid(2),E,F) = k3_square_1(k2_xcmplx_0(k1_square_1(k6_xcmplx_0(A,C)),k1_square_1(k6_xcmplx_0(B,D)))) ) ) ) ) ) ) ) )).
fof(t6_goboard7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r2_hidden(C,k1_rltopsp1(k15_euclid(2),A,B)) & k18_euclid(A) = k18_euclid(B) ) => k18_euclid(C) = k18_euclid(B) ) ) ) ) )).
fof(t6_goboard8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,2),k3_finseq_1(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,2),k3_finseq_1(k2_goboard2(A))) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,2),k1_matrix_0(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_nat_1(D,1)) ) => ( ( ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,k1_nat_1(D,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),D) ) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,k1_nat_1(D,1)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),D),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,2),k1_nat_1(D,1))),k7_xcmplx_0(1,2)),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_nat_1(D,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,2),k1_nat_1(D,2))),k7_xcmplx_0(1,2))),k3_topreal1(2,A)) ) ) ) ) ) ) ) )).
fof(t6_goboard9,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => k4_finseq_5(k1_numbers,k1_goboard1(A)) = k1_goboard1(k4_finseq_5(u1_struct_0(k15_euclid(2)),A)) ) )).
fof(t6_gobrd10,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r1_xxreal_0(B,A) & r1_xxreal_0(C,A) & ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ~ ( k1_funct_1(D,1) = B & k1_funct_1(D,k3_finseq_1(D)) = C & k3_finseq_1(D) = k1_nat_1(k1_nat_1(k7_nat_d(B,C),k7_nat_d(C,B)),1) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( ( 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] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(1,E) => ( r1_xxreal_0(k3_finseq_1(D),E) | r1_gobrd10(k7_partfun1(k4_ordinal1,D,E),k7_partfun1(k4_ordinal1,D,k1_nat_1(E,1))) ) ) ) ) ) ) ) ) ) )).
fof(t6_gobrd11,axiom,( ! [A] : ( ( ~ 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)) != k1_xboole_0 ) )).
fof(t6_gobrd12,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(B,k3_finseq_1(k2_goboard2(A))) & r1_xxreal_0(C,k1_matrix_0(k2_goboard2(A))) & r1_xxreal_0(D,k3_finseq_1(k2_goboard2(A))) & r1_xxreal_0(E,k1_matrix_0(k2_goboard2(A))) & r2_gobrd10(B,C,D,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))) <=> 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))) ) ) ) ) ) ) ) )).
fof(t6_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [F] : ( ( ~ v3_relat_1(F) & v1_matrix_0(F) & v1_goboard1(F) & v2_goboard1(F) & v3_goboard1(F) & v4_goboard1(F) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_tarski(k9_matrix_0(E),k9_matrix_0(F)) & r1_xxreal_0(1,A) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(E)) & r1_xxreal_0(1,B) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k1_matrix_0(F)) & k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),F,B,D) ) => ( r1_xxreal_0(k3_finseq_1(E),A) | r1_xxreal_0(k3_finseq_1(F),B) | r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),F,k1_nat_1(B,1),D)),k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),E,k1_nat_1(A,1),C))) ) ) ) ) ) ) ) ) )).
fof(t6_gobrd14,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r2_hidden(k4_tarski(A,B),k2_matrix_0(D)) & r2_hidden(k4_tarski(A,k2_xcmplx_0(B,C)),k2_matrix_0(D)) ) => k1_topreal6(2,k3_matrix_0(u1_struct_0(k15_euclid(2)),D,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),D,A,k2_xcmplx_0(B,C))) = k6_xcmplx_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,A,k2_xcmplx_0(B,C))),k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),D,A,B))) ) ) ) ) ) )).
fof(t6_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ( ( r1_henmodel(A,B,C) & r1_henmodel(A,B,D) ) <=> r1_henmodel(A,B,k7_cqc_lang(A,C,D)) ) ) ) ) ) )).
fof(t6_gr_cy_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ~ v4_group_1(B,A) ) ) )).
fof(t6_gr_cy_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,k4_ordinal1) & C = k5_group_1(A,D,B) ) ) <=> A = k5_group_4(A,k6_domain_1(u1_struct_0(A),B)) ) ) ) )).
fof(t6_gr_cy_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_gr_cy_3(A) ) => ( A != 7 => k4_nat_d(A,6) = 5 ) ) )).
fof(t6_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ 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)) ) => ( u1_graph_1(k5_graph_1(A,B)) = k2_xboole_0(u1_graph_1(A),u1_graph_1(B)) & u2_graph_1(k5_graph_1(A,B)) = k2_xboole_0(u2_graph_1(A),u2_graph_1(B)) ) ) ) ) )).
fof(t6_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(A)) ) => k1_graph_2(A,B,B) = k9_finseq_1(k1_funct_1(A,B)) ) ) ) )).
fof(t6_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v2_funct_1(B) & m2_graph_1(B,A) ) => ! [C] : ( ( v2_funct_1(C) & m2_graph_1(C,A) ) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(A)) => ( ( r1_xboole_0(k10_xtuple_0(B),k10_xtuple_0(C)) & r1_graph_2(A,D,B) & r1_graph_2(A,E,C) & k1_funct_1(D,k3_finseq_1(D)) = k1_funct_1(E,1) ) => ( v2_funct_1(k8_finseq_1(u4_struct_0(A),B,C)) & m2_graph_1(k8_finseq_1(u4_struct_0(A),B,C),A) ) ) ) ) ) ) ) )).
fof(t6_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( ( v7_graph_1(C,A) & m2_graph_1(C,A) ) => ( r3_graph_4(A,B,C) => r1_tarski(k2_graph_4(A,k10_xtuple_0(C)),k10_xtuple_0(B)) ) ) ) ) )).
fof(t6_graph_5,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( m2_finseq_1(C,u4_struct_0(B)) => ( r2_hidden(A,k4_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)) ) ) ) ) ) )).
fof(t6_graphsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u4_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u4_struct_0(A)) => ! [D] : ( ( 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(u2_graph_1(A),k1_funct_1(D,k3_finseq_1(D))) != 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(D,1)) != k1_funct_1(u1_graph_1(A),k1_funct_1(C,1)) ) ) ) ) ) ) )).
fof(t6_grcat_1,axiom,( r1_funct_2(u1_struct_0(k3_algstr_0),u1_struct_0(k3_algstr_0),k1_tarski(k5_ordinal1),k1_tarski(k5_ordinal1),k5_vectsp_1(k3_algstr_0),k8_funct_5) )).
fof(t6_grfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( C = k1_tarski(k4_tarski(A,B)) => k1_funct_1(C,A) = B ) ) )).
fof(t6_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_group_3(A,k2_group_5(A,B,k2_group_1(A,C)),C) = k2_group_5(A,C,B) ) ) ) )).
fof(t6_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,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_vfunct_1(k15_pre_poly(A),C,D)),k3_termord(A,B,C,D)) ) ) ) ) )).
fof(t6_groeb_2,axiom,( ! [A] : ! [B] : ( ( 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,k1_groeb_2(A,B,B),k16_pre_poly(A)) ) )).
fof(t6_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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) ) => ( ( r1_termord(A,B,C,D) & r2_termord(A,B,E,F) ) => r2_termord(A,B,k11_pre_poly(A,C,E),k11_pre_poly(A,D,F)) ) ) ) ) ) ) ) )).
fof(t6_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( k6_algstr_0(A,D,C) = k6_algstr_0(A,D,B) | k6_algstr_0(A,C,D) = k6_algstr_0(A,B,D) ) => C = B ) ) ) ) ) )).
fof(t6_group_10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( 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)))) ) => ( r1_subset_1(k13_group_10(A,B,E,C),k13_group_10(A,B,E,D)) | k13_group_10(A,B,E,C) = k13_group_10(A,B,E,D) ) ) ) ) ) ) )).
fof(t6_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,k7_group_4(A,B,C)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & D = k6_algstr_0(A,E,F) & r1_struct_0(B,E) & r1_struct_0(C,F) ) ) ) ) ) ) ) )).
fof(t6_group_12,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_group_7(A,B))) => ( r2_hidden(D,k1_group_12(A,B,C)) => r2_hidden(k2_group_1(k2_group_7(A,B),D),k1_group_12(A,B,C)) ) ) ) ) ) )).
fof(t6_group_14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( 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)))) ) => ! [E] : ( ( 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(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) & 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)))) ) ) ) ) ) ) )).
fof(t6_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => k1_group_2(A,k2_subset_1(u1_struct_0(A))) = u1_struct_0(A) ) )).
fof(t6_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,A) => ( m1_group_2(C,D) => ( r1_tarski(k13_group_2(A,C,B),k13_group_2(A,D,B)) & r1_tarski(k14_group_2(A,C,B),k14_group_2(A,D,B)) ) ) ) ) ) ) )).
fof(t6_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_group_4(A,k8_finseq_1(u1_struct_0(A),B,k12_finseq_1(u1_struct_0(A),C))) = k6_algstr_0(A,k3_group_4(A,B),C) ) ) ) )).
fof(t6_group_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_group_2(C,B) => ! [D] : ( m1_group_2(D,B) => ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v5_group_1(B) & l3_algstr_0(B) ) => ( r1_struct_0(k8_group_4(B,C,D),A) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & ? [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t6_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( B = a_1_0_group_6(A) => r1_group_2(A,k9_group_5(A),k5_group_4(A,B)) ) ) ) )).
fof(t6_group_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,B) & v1_funct_1(D) & v1_partfun1(D,B) & v1_group_7(D) & v2_group_7(D,B) ) => ! [E] : ( ( ~ v2_struct_0(E) & v2_group_1(E) & l3_algstr_0(E) ) => ( ( r2_hidden(A,B) & E = k1_funct_1(D,A) & C = k1_group_1(k2_group_7(B,D)) ) => k1_funct_1(C,A) = k1_group_1(E) ) ) ) ) )).
fof(t6_group_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_struct_0(B,C) => r1_tarski(k14_group_2(A,B,C),u1_struct_0(B)) ) ) ) ) )).
fof(t6_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ( E = D => k2_group_1(C,E) = k2_group_1(B,D) ) ) ) ) ) )).
fof(t6_groupp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_group_1(A,k2_group_3(A,B,C)) = k6_group_1(A,B) ) ) ) )).
fof(t6_grsolv_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ( ? [B] : ( m2_finseq_1(B,k1_group_3(A)) & ~ r1_xxreal_0(k3_finseq_1(B),k5_numbers) & k1_funct_1(B,1) = k7_group_2(A) & k1_funct_1(B,k3_finseq_1(B)) = k6_group_2(A) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(k1_nat_1(C,1),k4_finseq_1(B)) ) => ! [D] : ( ( v15_algstr_0(D) & m1_group_2(D,A) ) => ! [E] : ( ( v15_algstr_0(E) & m1_group_2(E,A) ) => ( ( D = k1_funct_1(B,C) & E = k1_funct_1(B,k1_nat_1(C,1)) ) => ( v15_algstr_0(E) & v1_group_3(E,D) & m1_group_6(E,A,D) & ! [F] : ( ( v1_group_3(F,D) & m1_group_6(F,A,D) ) => ( F = E => ( ~ v2_struct_0(k5_group_6(D,F)) & v2_group_1(k5_group_6(D,F)) & v3_group_1(k5_group_6(D,F)) & v1_gr_cy_1(k5_group_6(D,F)) & l3_algstr_0(k5_group_6(D,F)) ) ) ) ) ) ) ) ) ) ) => v1_grsolv_1(A) ) ) )).
fof(t6_hahnban,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ( r1_rlsub_2(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_struct_0(B,D) => k4_rlsub_2(A,D,B,C) = k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,k4_struct_0(A)) ) ) ) ) ) ) )).
fof(t6_hahnban1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k8_group_1(k1_complfld,k1_hahnban1(A,B),k1_hahnban1(C,D)) = k1_hahnban1(k6_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D)),k2_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(C,B))) ) ) ) ) )).
fof(t6_hallmar1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(D,k4_finseq_1(B)) ) => k1_hallmar1(A,B,k2_tarski(C,D)) = k2_xboole_0(k1_funct_1(B,C),k1_funct_1(B,D)) ) ) ) ) ) )).
fof(t6_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ( r2_hidden(B,k2_pre_topc(k3_pcomps_1(A),C)) <=> ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,C) & ~ r1_xxreal_0(D,k3_metric_1(A,B,E)) ) ) ) ) ) ) ) ) )).
fof(t6_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(C,k3_finseq_1(k1_helly(A,B))) => k1_funct_1(k1_helly(A,B),C) = k1_funct_1(A,C) ) ) ) ) )).
fof(t6_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ( ~ v1_henmodel(B,A) <=> ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => r1_henmodel(A,B,C) ) ) ) ) )).
fof(t6_hermitan,axiom,( k8_group_1(k1_complfld,k2_hahnban1,k2_complfld(k2_hahnban1)) = k1_group_1(k1_complfld) )).
fof(t6_hessenbe,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( ~ r1_collsp(A,B,C,E) & r1_collsp(A,B,C,D) & B != D & r1_collsp(A,B,D,E) ) ) ) ) ) ) )).
fof(t6_heyting1,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ! [C] : ( m2_subset_1(C,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => ( r2_hidden(C,k3_funct_2(k7_normform(A),u1_struct_0(k12_normform(A)),k4_heyting1(A),B)) => C = B ) ) ) )).
fof(t6_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => r1_tarski(k1_heyting2(A,B,C),A) ) ) )).
fof(t6_heyting3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v14_lattices(A) & l3_lattices(A) ) => k6_lattices(A) = k4_yellow_0(k3_lattice3(A)) ) )).
fof(t6_hfdiff_1,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r2_fdiff_1(k5_relset_1(k1_numbers,k1_numbers,B,A),A) => r2_fdiff_1(B,A) ) ) ) )).
fof(t6_hilbasis,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k16_pre_poly(k1_nat_1(A,1)) = k1_hilbasis(A,k5_numbers,k16_pre_poly(A)) ) )).
fof(t6_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => r2_hidden(k3_hilbert1(k4_hilbert1(B,C),C),k5_hilbert1(A)) ) ) ) )).
fof(t6_hilbert2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) ) => k1_funct_1(k6_trees_4(A,B,C),k1_xboole_0) = A ) ) )).
fof(t6_hilbert3,axiom,( ! [A] : k1_funct_1(k1_xboole_0,A) = k1_xboole_0 )).
fof(t6_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_aff_1(A,B,C,D) & ~ r2_hidden(B,D) & ! [E] : ( ( 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_homothet(A,E,D) & k3_funct_2(u1_struct_0(A),u1_struct_0(A),E,B) = C ) ) ) ) ) ) => v7_aff_2(A) ) ) )).
fof(t6_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => k2_idea_1(A,B,B) = k1_idea_1(A) ) ) )).
fof(t6_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_algstr_0(A) & v4_rlvect_1(A) & v2_vectsp_1(A) & l6_algstr_0(A) ) => v3_ideal_1(k6_domain_1(u1_struct_0(A),k4_struct_0(A)),A) ) )).
fof(t6_incproj,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & B != C & C != D & D != B ) ) ) ) )).
fof(t6_incsp_1,axiom,( ! [A] : ( l2_incsp_1(A) => ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_incsp_1(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_incsp_1(A))) => ( ( r1_tarski(D,C) & r4_incsp_1(A,C,B) ) => r4_incsp_1(A,D,B) ) ) ) ) ) )).
fof(t6_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m3_index_1(B,u1_struct_0(A),u4_struct_0(A),u1_graph_1(A),u2_graph_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)) <=> ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_funct_2(u4_struct_0(k2_index_1(u4_struct_0(A),k3_relat_1(u1_graph_1(A),k1_xtuple_0(B)),k4_cat_1(A,C))),u4_struct_0(k2_index_1(u4_struct_0(A),k3_relat_1(u2_graph_1(A),k1_xtuple_0(B)),k4_cat_1(A,C))),u4_struct_0(k2_index_1(u1_struct_0(A),k1_xtuple_0(B),C)),u4_struct_0(k2_index_1(u1_struct_0(A),k1_xtuple_0(B),C)),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),k4_cat_1(A,C)),k10_cat_1(k2_index_1(u1_struct_0(A),k1_xtuple_0(B),C))) ) & ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ( k3_graph_1(A,D) = k4_graph_1(A,C) => 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),k1_cat_1(A,C,D)) = k1_partfun1(u4_struct_0(k2_index_1(u4_struct_0(A),k3_relat_1(u1_graph_1(A),k1_xtuple_0(B)),C)),u4_struct_0(k2_index_1(u4_struct_0(A),k3_relat_1(u2_graph_1(A),k1_xtuple_0(B)),C)),u4_struct_0(k2_index_1(u4_struct_0(A),k3_relat_1(u1_graph_1(A),k1_xtuple_0(B)),D)),u4_struct_0(k2_index_1(u4_struct_0(A),k3_relat_1(u2_graph_1(A),k1_xtuple_0(B)),D)),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),C),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),D)) ) ) ) ) ) ) ) )).
fof(t6_instalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( l3_msualg_1(D,A) => ! [E] : ( 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)) & r1_pzfmisc1(u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) ) => ! [F] : ( m2_pboole(F,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ~ ( r1_msualg_3(A,B,C,F) & ! [G] : ( m2_pboole(G,u1_struct_0(A),u3_msualg_1(A,D),u3_msualg_1(A,E)) => ~ ( r8_pboole(u1_struct_0(A),G,F) & r1_msualg_3(A,D,E,G) ) ) ) ) ) ) ) ) ) ) )).
fof(t6_int_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( k2_xcmplx_0(B,A) = C => r1_xxreal_0(B,C) ) ) ) ) )).
fof(t6_int_2,axiom,( ! [A] : ( v7_ordinal1(A) => ( m1_subset_1(k4_xcmplx_0(A),k4_ordinal1) <=> A = k5_numbers ) ) )).
fof(t6_int_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k4_ordinal1))) ) => m1_int_3(B,A) ) ) )).
fof(t6_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r1_int_1(B,A) => ( A = k5_numbers | r1_xxreal_0(k1_int_2(B),k1_int_2(A)) ) ) ) ) )).
fof(t6_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ( ? [B] : ( v7_ordinal1(B) & r2_hidden(B,k4_finseq_1(A)) & k1_funct_1(A,B) = k5_numbers ) => k19_rvsum_1(A) = k5_numbers ) ) )).
fof(t6_int_7,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k8_newton) & v1_funct_1(B) & v1_partfun1(B,k8_newton) & v4_valued_0(B) & v2_pre_poly(B) ) => ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => ( ( v1_int_7(B) & r1_int_1(C,k8_nat_3(k8_newton,B)) & k8_nat_3(k8_newton,B) = k3_wsierp_1(A) & A = k3_relat_1(k19_finseq_1(k22_pre_poly(k8_newton,B)),B) ) => ( k8_nat_3(k8_newton,B) = 1 | r2_hidden(C,k22_pre_poly(k8_newton,B)) ) ) ) ) ) )).
fof(t6_int_8,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v7_ordinal1(C) => ( ( k5_int_1(k3_xcmplx_0(A,B),C) = 1 & k5_int_1(A,C) = 1 ) => k5_int_1(B,C) = 1 ) ) ) ) )).
fof(t6_integr10,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_tarski(k3_integra5(C,D),k1_relset_1(k1_numbers,A)) & r1_tarski(k3_integra5(C,D),k1_relset_1(k1_numbers,B)) & r2_integr10(A,C,D) & r2_integr10(B,C,D) ) => ( r1_xxreal_0(D,C) | ( r2_integr10(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B),C,D) & k2_integr10(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B),C,D) = k2_xcmplx_0(k2_integr10(A,C,D),k2_integr10(B,C,D)) ) ) ) ) ) ) ) )).
fof(t6_integr11,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( k2_xcmplx_0(B,A) != k5_numbers & k6_xcmplx_0(B,A) != k5_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,k1_fcont_1(k6_xcmplx_0(B,A),k5_numbers),k16_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k6_xcmplx_0(B,A)))),k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k2_xcmplx_0(B,A),k5_numbers),k16_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k2_xcmplx_0(B,A))))),k1_numbers) & ! [C] : ( v1_xreal_0(C) => k1_funct_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,k1_fcont_1(k6_xcmplx_0(B,A),k5_numbers),k16_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k6_xcmplx_0(B,A)))),k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k2_xcmplx_0(B,A),k5_numbers),k16_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k2_xcmplx_0(B,A))))),k1_numbers),C) = k3_xcmplx_0(k1_funct_1(k16_sin_cos,k3_xcmplx_0(B,C)),k1_funct_1(k16_sin_cos,k3_xcmplx_0(A,C))) ) ) ) ) ) )).
fof(t6_integr12,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k3_rfunct_1(k1_numbers,k1_numbers,k18_sin_cos,k16_sin_cos)),k3_rfunct_1(k1_numbers,k1_numbers,k22_sin_cos,k41_valued_1(k1_numbers,k1_numbers,k16_sin_cos)))) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k27_sin_cos),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k27_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t6_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,B) & B = k1_relset_1(k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k16_sin_cos)) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k16_sin_cos),A)) ) => k2_integra5(A,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k16_sin_cos)) = k6_xcmplx_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),k2_seq_4(A)),k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),k3_seq_4(A))) ) ) ) )).
fof(t6_integr14,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_fdiff_9,k1_taylor_1(A))),B) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => k1_funct_1(k2_fdiff_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))),B),C) = k7_xcmplx_0(k3_xcmplx_0(A,k1_funct_1(k18_sin_cos,C)),k3_prepower(k1_funct_1(k16_sin_cos,C),k2_xcmplx_0(A,1))) ) ) ) ) ) ) )).
fof(t6_integr15,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_integra1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) ) => ! [D] : ( m2_integr15(D,A,B,C) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( v1_seq_2(k2_partfun1(A,k1_numbers,B,A)) => r1_xxreal_0(k3_funct_2(k4_ordinal1,k1_numbers,k3_integr15(A,B,C,D),E),k3_funct_2(k4_ordinal1,k1_numbers,k3_integra2(A,B,C),E)) ) ) ) ) ) ) )).
fof(t6_integr16,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m1_subset_1(B,k2_numbers) => k2_integr16(k8_finseq_1(k2_numbers,A,k12_finseq_1(k2_numbers,B))) = k8_finseq_1(k1_numbers,k2_integr16(A),k12_finseq_1(k1_numbers,k4_complex1(B))) ) ) )).
fof(t6_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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,k6_vfunct_1(B,A,C,D)) & v1_integr18(C,A,B) & v1_integr18(D,A,B) ) => ( v1_integr18(E,A,B) & k4_integr18(A,B,E) = k3_rlvect_1(A,k4_integr18(A,B,C),k4_integr18(A,B,D)) ) ) ) ) ) ) ) )).
fof(t6_integr19,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(C,D) & r1_xxreal_0(D,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)) ) => ( r1_integra5(k3_integra5(C,D),k26_valued_1(k1_numbers,k1_numbers,F,E)) & v1_comseq_2(k2_partfun1(k1_numbers,k1_numbers,k26_valued_1(k1_numbers,k1_numbers,F,E),k3_integra5(C,D))) ) ) ) ) ) ) ) ) )).
fof(t6_integra1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( m1_integra1(C,B) => ( r2_hidden(A,k4_finseq_1(C)) => r1_tarski(k2_integra1(B,C,A),B) ) ) ) ) )).
fof(t6_integra2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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)) & r1_tarski(B,A) ) => v2_seq_2(k2_partfun1(A,k1_numbers,k2_partfun1(A,k1_numbers,C,B),B)) ) ) ) ) )).
fof(t6_integra3,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( ( k1_rvsum_1(A) = k1_rvsum_1(B) & v5_valued_0(A) & v5_valued_0(B) ) => A = B ) ) ) )).
fof(t6_integra4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,k1_integra1(A)) => ( k3_integra1(A) = k5_numbers => ( v3_integra1(B,A) & k12_integra1(A,B) = k5_numbers ) ) ) ) ) )).
fof(t6_integra5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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_partfun1(k1_integra5(B,A),A) ) ) ) )).
fof(t6_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k3_integra1(k3_integra5(k3_xxreal_0(A,B),k4_xxreal_0(A,B))) = k9_complex1(k6_xcmplx_0(B,A)) ) ) )).
fof(t6_integra7,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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_fdiff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,B,C),A) & r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) )).
fof(t6_integra8,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(k5_numbers,k17_sin_cos(k7_xcmplx_0(A,2))) => k17_sin_cos(k7_xcmplx_0(A,2)) = k4_xcmplx_0(k3_square_1(k7_xcmplx_0(k6_xcmplx_0(1,k19_sin_cos(A)),2))) ) ) )).
fof(t6_integra9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( A != k5_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,k5_numbers),k16_sin_cos),k7_xcmplx_0(1,A)),k1_numbers) & ! [B] : ( v1_xreal_0(B) => k1_funct_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,k5_numbers),k16_sin_cos),k7_xcmplx_0(1,A)),k1_numbers),B) = k19_sin_cos(k3_xcmplx_0(A,B)) ) ) ) ) )).
fof(t6_interva1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ( k1_interva1(A,B,C) = k1_interva1(A,D,E) => ( k1_interva1(A,B,C) = k1_xboole_0 | ( B = D & C = E ) ) ) ) ) ) ) )).
fof(t6_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => r2_hidden(k3_intpro_1(B,k5_intpro_1(B,C)),k7_intpro_1(A)) ) ) ) )).
fof(t6_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,k5_numbers) => k1_funct_1(k2_irrat_1(k1_nat_1(A,1)),B) = k3_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,k1_nat_1(A,1)),k1_funct_1(k2_irrat_1(A),B)),k1_funct_1(k1_irrat_1(A),B)) ) ) ) )).
fof(t6_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ( v12_cat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & k8_cat_1(A,B,C,E) = D ) ) ) ) ) ) )).
fof(t6_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(k9_nattra_1(A,B))) => ? [D] : ( m2_cat_1(D,A,B) & ? [E] : ( m2_cat_1(E,A,B) & ? [F] : ( m2_nattra_1(F,A,B,D,E) & r2_nattra_1(A,B,D,E) & k3_graph_1(k9_nattra_1(A,B),C) = D & k4_graph_1(k9_nattra_1(A,B),C) = E & C = k4_tarski(k4_tarski(D,E),F) ) ) ) ) ) ) )).
fof(t6_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_isomichi(B,A) => v2_isomichi(k3_subset_1(u1_struct_0(A),B),A) ) ) ) )).
fof(t6_jct_misc,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v2_connsp_1(C,A) => v6_xxreal_2(k7_relset_1(u1_struct_0(A),k1_numbers,B,C)) ) ) ) ) )).
fof(t6_jgraph_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( v7_graph_1(k3_jgraph_1(A,B),k1_jgraph_1(A)) & m2_graph_1(k3_jgraph_1(A,B),k1_jgraph_1(A)) ) ) ) )).
fof(t6_jgraph_2,axiom,( k1_relset_1(u1_struct_0(k15_euclid(2)),k4_pscomp_1) = u1_struct_0(k15_euclid(2)) & k1_relset_1(u1_struct_0(k15_euclid(2)),k4_pscomp_1) = k1_euclid(2) )).
fof(t6_jgraph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) != k5_numbers ) & ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( 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) = k1_square_1(k7_xcmplx_0(F,G)) ) ) ) ) & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).
fof(t6_jgraph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) = k1_square_1(E) ) ) ) & v5_pre_topc(C,A,k3_topmetr) ) ) ) ) ) )).
fof(t6_jgraph_5,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( l1_pre_topc(C) => ! [D] : ( ( 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] : ( ( 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) & v2_funct_1(D) ) => v2_funct_1(k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),D,E)) ) ) ) ) ) ) )).
fof(t6_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(k18_euclid(B),k18_euclid(A)) & r1_xxreal_0(k18_euclid(A),D) & r1_xxreal_0(k17_euclid(B),C) ) => ( r1_xxreal_0(D,k18_euclid(B)) | r1_xxreal_0(k17_euclid(B),k17_euclid(A)) | r1_jordan6(k1_sppol_2(k17_euclid(A),C,k18_euclid(B),D),A,B) ) ) ) ) ) ) )).
fof(t6_jgraph_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k1_topreala(A,B,C,D))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k1_topreala(A,B,C,D))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k1_topreala(A,B,C,D))) => ! [H] : ( m1_subset_1(H,u1_struct_0(k1_topreala(A,B,C,D))) => ! [I] : ( m1_borsuk_2(I,k1_topreala(A,B,C,D),E,F) => ! [J] : ( m1_borsuk_2(J,k1_topreala(A,B,C,D),H,G) => ! [K] : ( m1_subset_1(K,u1_struct_0(k15_euclid(2))) => ! [L] : ( m1_subset_1(L,u1_struct_0(k15_euclid(2))) => ! [M] : ( m1_subset_1(M,u1_struct_0(k15_euclid(2))) => ! [N] : ( m1_subset_1(N,u1_struct_0(k15_euclid(2))) => ~ ( k17_euclid(K) = A & k17_euclid(L) = B & k18_euclid(M) = C & k18_euclid(N) = D & E = K & F = L & G = M & H = N & ! [O] : ( m1_subset_1(O,u1_struct_0(k17_borsuk_1)) => ! [P] : ( m1_subset_1(P,u1_struct_0(k17_borsuk_1)) => k3_funct_2(u1_struct_0(k17_borsuk_1),u1_struct_0(k1_topreala(A,B,C,D)),I,O) != k3_funct_2(u1_struct_0(k17_borsuk_1),u1_struct_0(k1_topreala(A,B,C,D)),J,P) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t6_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r2_hidden(A,k1_rltopsp1(k15_euclid(2),B,C)) & v2_sppol_1(k1_rltopsp1(k15_euclid(2),B,C)) ) => v2_sppol_1(k1_rltopsp1(k15_euclid(2),A,C)) ) ) ) ) )).
fof(t6_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => a_4_0_jordan1(A,B,C,D) = k3_xboole_0(k3_xboole_0(k3_xboole_0(a_1_0_jordan1(A),a_1_1_jordan1(C)),a_1_2_jordan1(B)),a_1_3_jordan1(D)) ) ) ) ) )).
fof(t6_jordan10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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)))) ) => k7_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))) = k2_xcmplx_0(k7_pscomp_1(B),k7_xcmplx_0(k6_xcmplx_0(k7_pscomp_1(B),k9_pscomp_1(B)),k1_newton(2,A))) ) ) )).
fof(t6_jordan11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_jordan1h(B,A) => r1_tarski(k3_goboard5(k1_jordan8(B,A),k7_nat_d(k3_jordan1h(B,A),1),k5_jordan11(B,A)),k1_jordan2c(2,B)) ) ) ) )).
fof(t6_jordan12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(2))) => ( r2_jordan12(2,B,C) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ( D = k2_partfun1(k4_ordinal1,u1_struct_0(k15_euclid(2)),C,k2_finseq_1(A)) => r2_jordan12(2,B,D) ) ) ) ) ) ) )).
fof(t6_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( r1_jordan1h(A,B) => r2_hidden(k1_jordan14(A,B),k1_jordan2c(2,A)) ) ) ) )).
fof(t6_jordan15,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(B,k1_matrix_0(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,k3_finseq_1(A)) ) => r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,E,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,F,B)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,C,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,D,B))) ) ) ) ) ) ) ) )).
fof(t6_jordan16,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => r1_tarski(k1_jordan7(A,B,C),A) ) ) ) )).
fof(t6_jordan17,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ~ ( A != B & r1_topreal1(k15_euclid(2),C,D,E) & r1_jordan5c(E,C,D,A,B) & ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ~ ( A != F & B != F & r1_jordan5c(E,C,D,A,F) & r1_jordan5c(E,C,D,F,B) ) ) ) ) ) ) ) ) )).
fof(t6_jordan18,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => v3_xxreal_2(k7_relset_1(u1_struct_0(k15_euclid(2)),k1_numbers,k4_pscomp_1,k5_topreal1(A))) ) )).
fof(t6_jordan19,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(C)) & r1_goboard1(u1_struct_0(k15_euclid(2)),C,k1_jordan8(B,A)) & k1_topreal6(2,k7_partfun1(u1_struct_0(k15_euclid(2)),C,D),k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_nat_1(D,1))) != k7_xcmplx_0(k6_xcmplx_0(k7_pscomp_1(B),k9_pscomp_1(B)),k1_newton(2,A)) & k1_topreal6(2,k7_partfun1(u1_struct_0(k15_euclid(2)),C,D),k7_partfun1(u1_struct_0(k15_euclid(2)),C,k1_nat_1(D,1))) != k7_xcmplx_0(k6_xcmplx_0(k8_pscomp_1(B),k6_pscomp_1(B)),k1_newton(2,A)) ) ) ) ) ) )).
fof(t6_jordan1b,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ( r1_xxreal_0(1,A) => ( r1_xxreal_0(k3_finseq_1(C),A) | k8_finseq_1(B,k3_finseq_6(B,C,A,k7_nat_d(k3_finseq_1(C),1)),k13_matrix_0(B,k7_partfun1(B,C,k3_finseq_1(C)))) = k3_finseq_6(B,C,A,k3_finseq_1(C)) ) ) ) ) ) )).
fof(t6_jordan1c,axiom,( ! [A] : ( ( v2_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( k1_jordan2c(2,A) != k1_xboole_0 => r1_xxreal_0(k6_pscomp_1(A),k6_pscomp_1(k1_jordan2c(2,A))) ) ) )).
fof(t6_jordan1e,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( k2_xcmplx_0(A,B) = k2_xcmplx_0(C,D) & r1_xxreal_0(A,C) & r1_xxreal_0(B,D) ) => A = C ) ) ) ) ) )).
fof(t6_jordan1f,axiom,( ! [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] : ( v7_ordinal1(B) => k7_partfun1(u1_struct_0(k15_euclid(2)),k2_jordan1e(A,B),1) = k22_pscomp_1(k3_topreal1(2,k2_jordan9(A,B))) ) ) )).
fof(t6_jordan1g,axiom,( ! [A] : ( ( v1_matrix_0(A) & v2_goboard1(A) & v3_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(k4_tarski(B,D),k2_matrix_0(A)) & r2_hidden(k4_tarski(C,E),k2_matrix_0(A)) & k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,D)) = k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),A,C,E)) ) => D = E ) ) ) ) ) ) )).
fof(t6_jordan1h,axiom,( r3_orders_1(k1_jordan1h,k1_numbers) )).
fof(t6_jordan1j,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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_hidden(k19_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))),k10_xtuple_0(k1_jordan1e(B,A))) & r2_hidden(k19_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))),k3_topreal1(2,k1_jordan1e(B,A))) ) ) ) )).
fof(t6_jordan1k,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( r3_connsp_1(A,k1_struct_0(A),B) <=> v1_xboole_0(B) ) ) ) )).
fof(t6_jordan20,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v4_topreal1(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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,k2_topreal1(2,B,A)) & k18_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),B,A)) = k18_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),B,k1_nat_1(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,D) ) => ( r1_xxreal_0(k3_finseq_1(B),A) | r1_xxreal_0(k17_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),B,A)),k17_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),B,k1_nat_1(A,1)))) | r1_xxreal_0(k17_euclid(D),k17_euclid(C)) ) ) ) ) ) ) )).
fof(t6_jordan22,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => r2_hidden(k1_domain_1(k4_ordinal1,k4_ordinal1,1,2),k2_matrix_0(k1_jordan8(A,B))) ) ) )).
fof(t6_jordan23,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ( v3_jordan23(B) <=> ( k3_finseq_1(B) != 2 => ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,C) & ~ r1_xxreal_0(k3_finseq_1(B),C) & k7_partfun1(A,B,C) = k7_partfun1(A,B,k1_nat_1(C,1)) ) ) ) ) ) )).
fof(t6_jordan24,axiom,( ! [A] : ( v1_xreal_0(A) => r2_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k1_jordan24(k4_xcmplx_0(A)),k1_jordan24(k6_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),A))) ) )).
fof(t6_jordan2b,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k2_finseq_1(A)) => k7_partfun1(k1_numbers,k5_algstr_0(k15_euclid(A),B,C),D) = k5_real_1(k7_partfun1(k1_numbers,B,D),k7_partfun1(k1_numbers,C,D)) ) ) ) ) ) )).
fof(t6_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t6_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( v4_topreal1(A) & 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)) ) => ( B = C | v4_topreal1(k3_finseq_6(u1_struct_0(k15_euclid(2)),A,B,C)) ) ) ) ) ) )).
fof(t6_jordan4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(k3_finseq_1(B),C) => ( k1_funct_1(k2_rfinseq(A,C,B),k3_finseq_1(k2_rfinseq(A,C,B))) = k1_funct_1(B,k3_finseq_1(B)) & k7_partfun1(A,k2_rfinseq(A,C,B),k3_finseq_1(k2_rfinseq(A,C,B))) = k7_partfun1(A,B,k3_finseq_1(B)) ) ) ) ) ) )).
fof(t6_jordan5a,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(k3_topmetr)) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( v1_xreal_0(D) => ( ( r1_tmap_1(k3_topmetr,k3_topmetr,A,B) & A = C & B = D ) => r1_fcont_1(C,D) ) ) ) ) ) )).
fof(t6_jordan5c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( ( r2_hidden(D,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) ) => k2_jordan5c(A,B,C,D) = D ) ) ) ) ) )).
fof(t6_jordan5d,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(A)) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(k2_goboard2(A))) ) => ( r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),B,1)),k18_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),A,C))) & r1_xxreal_0(k18_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),A,C)),k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),B,k1_matrix_0(k2_goboard2(A))))) ) ) ) ) ) )).
fof(t6_jordan6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( B = a_1_2_jordan6(A) => v4_pre_topc(B,k15_euclid(2)) ) ) ) )).
fof(t6_jordan7,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( v1_topreal2(A) & r1_jordan6(A,B,C) ) => ( r2_hidden(B,k1_jordan7(A,B,C)) & r2_hidden(C,k1_jordan7(A,B,C)) ) ) ) ) ) )).
fof(t6_jordan9,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r1_goboard1(u1_struct_0(k15_euclid(2)),B,A) => ! [C] : ( v7_ordinal1(C) => ( ( 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),k9_matrix_0(A)) ) ) ) ) ) )).
fof(t6_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(B,k8_jordan6(A)) => r1_jordan6(A,B,k22_pscomp_1(A)) ) ) ) )).
fof(t6_knaster,axiom,( ! [A] : ! [B] : ( ( 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)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_tarski(k3_funct_2(k1_zfmisc_1(A),k9_setfam_1(A),B,C),C) => r1_tarski(k1_knaster(A,B),C) ) ) ) )).
fof(t6_kolmog01,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(A))) => ( ( v2_finsub_1(E) & r1_tarski(E,k1_kolmog01(A,B,D,C)) ) => r1_tarski(k9_prob_1(A,E),k1_kolmog01(A,B,D,C)) ) ) ) ) ) ) )).
fof(t6_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => r1_tarski(k3_kurato_0(A,B),k4_kurato_0(A,B)) ) )).
fof(t6_kurato_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,k2_kurato_1(A,B)) => ( r2_hidden(k3_subset_1(u1_struct_0(A),C),k2_kurato_1(A,B)) & r2_hidden(k2_pre_topc(A,C),k2_kurato_1(A,B)) ) ) ) ) ) )).
fof(t6_kurato_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => ( C = D => ( r2_hidden(C,k2_pre_topc(k15_euclid(A),B)) <=> ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & r1_xboole_0(k8_metric_1(k14_euclid(A),D,E),B) ) ) ) ) ) ) ) ) )).
fof(t6_lang1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => ! [B] : ( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => r3_lang1(A,B,B) ) ) )).
fof(t6_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => k1_card_1(k3_matrix_2(A)) = k7_newton(A) ) )).
fof(t6_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( m1_group_2(D,A) => ? [E] : ( v15_algstr_0(E) & m1_group_2(E,B) & u1_struct_0(E) = k7_relset_1(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(D)) ) ) ) ) ) )).
fof(t6_latsum_1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ! [D] : ( ( r2_hidden(k4_tarski(C,D),u1_orders_2(A)) => r2_hidden(k4_tarski(C,D),u1_orders_2(k1_latsum_1(A,B))) ) & ( r2_hidden(k4_tarski(C,D),u1_orders_2(B)) => r2_hidden(k4_tarski(C,D),u1_orders_2(k1_latsum_1(A,B))) ) ) ) ) )).
fof(t6_lattice2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => k7_funct_4(A,B,D,k2_partfun1(A,B,D,C)) = D ) ) ) )).
fof(t6_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ( k3_lattice3(A) = k3_lattice3(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)) ) ) ) )).
fof(t6_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & l3_lattices(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & D = k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,E) ) ) ) ) ) ) )).
fof(t6_lattice5,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k1_lattice5(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_lattice5(A))) => ( r3_orders_2(k1_lattice5(A),B,C) <=> r1_tarski(B,C) ) ) ) )).
fof(t6_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v14_lattices(A) & v1_lattice6(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B = k6_lattices(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ r1_lattice6(A,C,B) ) ) ) ) )).
fof(t6_lattice7,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( k1_lattice7(A,B) = 1 <=> B = k3_yellow_0(A) ) ) ) )).
fof(t6_lattice8,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( 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_yellow_0(k1_yellow_2(A,B,C)) ) ) ) )).
fof(t6_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & l2_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( r1_lattices(A,B,C) & r1_lattices(A,C,B) ) => B = C ) ) ) ) )).
fof(t6_lexbfs,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ~ ( B != C & k1_uproots(A,B,1) = k1_uproots(A,C,1) ) ) ) ) )).
fof(t6_lfuzzy_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_lfuzzy_0(A) & l1_orders_2(A) ) => ( ? [B] : ( v1_xreal_0(B) & r2_hidden(B,u1_struct_0(A)) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,u1_struct_0(A)) => r1_xxreal_0(B,C) ) ) ) <=> v1_yellow_0(A) ) ) )).
fof(t6_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ( ( v5_relat_1(E,k1_rcomp_1(k5_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] : ( ( v5_relat_1(F,k1_rcomp_1(k5_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] : ( ( v5_relat_1(G,k1_rcomp_1(k5_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(k3_fuzzy_4(A,B,C,D,F),k3_fuzzy_4(A,B,C,E,G)) ) ) ) ) ) ) ) ) )).
fof(t6_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ( v1_limfunc1(A) | v2_limfunc1(A) ) & ! [B] : ( v7_ordinal1(B) => ? [C] : ( v7_ordinal1(C) & r1_xxreal_0(B,C) & ~ v9_ordinal1(k1_valued_0(k1_numbers,A,C)) ) ) ) ) )).
fof(t6_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ~ r1_xxreal_0(k3_funct_2(k4_ordinal1,k1_numbers,B,D),k6_xcmplx_0(A,k7_xcmplx_0(1,k1_nat_1(D,1)))) & ~ r1_xxreal_0(A,k3_funct_2(k4_ordinal1,k1_numbers,B,D)) & r2_hidden(k3_funct_2(k4_ordinal1,k1_numbers,B,D),k9_xtuple_0(C)) ) ) => ( v2_comseq_2(B) & k1_seq_2(B) = A & r1_tarski(k10_xtuple_0(B),k6_subset_1(k9_xtuple_0(C),k1_tarski(A))) ) ) ) ) ) )).
fof(t6_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v5_limfunc1(A) & v8_limfunc1(B) & ! [C] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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)) ) ) ) )).
fof(t6_lmod_5,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( D != k4_struct_0(A) => k1_vectsp_6(A,B,k6_vectsp_6(A,B,D,C)) = k1_vectsp_6(A,B,C) ) ) ) ) ) )).
fof(t6_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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) => v7_struct_0(B) ) ) ) )).
fof(t6_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ( ( v1_mod_3(C,A,B) & C = k4_subset_1(u1_struct_0(B),D,E) & r1_xboole_0(D,E) ) => r1_vectsp_5(A,B,k1_mod_3(A,B,D),k1_mod_3(A,B,E)) ) ) ) ) ) ) )).
fof(t6_lopban_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m2_funct_2(C,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => k1_binop_1(k2_lopban_1(A,B),C,k1_funct_1(k3_lopban_1(A,B),k4_tarski(k4_xcmplx_0(1),C))) = k4_lopban_1(A,B) ) ) ) )).
fof(t6_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( 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)))) ) => ( 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_partfun1(u1_struct_0(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_partfun1(u1_struct_0(A))),B) ) ) ) )).
fof(t6_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ! [C] : ( v7_ordinal1(C) => k5_rsspace3(A,B,C) = k4_struct_0(A) ) => ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,k3_series_1(k5_normsp_0(A,B)),C) = k5_numbers ) ) ) ) )).
fof(t6_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_normsp_1(C,A) => k6_normsp_1(A,k2_lopban_3(A,C,B)) = k6_algstr_0(A,B,k6_normsp_1(A,C)) ) ) ) ) )).
fof(t6_lopban_5,axiom,( ! [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) & v3_lopban_1(A) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k16_lopban_1(A,B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k16_lopban_1(A,B))))) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ( v3_normsp_1(k2_lopban_5(A,B,C,E),B) & k3_funct_2(u1_struct_0(A),u1_struct_0(B),D,E) = k6_normsp_1(B,k2_lopban_5(A,B,C,E)) ) ) => ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => r1_xxreal_0(k2_normsp_0(B,k3_funct_2(u1_struct_0(A),u1_struct_0(B),D,E)),k3_xcmplx_0(k6_rinfsup1(k5_normsp_0(k16_lopban_1(A,B),C)),k2_normsp_0(A,E))) ) & ! [E] : ( m1_subset_1(E,u1_struct_0(k16_lopban_1(A,B))) => ( E = D => r1_xxreal_0(k2_normsp_0(k16_lopban_1(A,B),E),k6_rinfsup1(k5_normsp_0(k16_lopban_1(A,B),C))) ) ) ) ) ) ) ) ) )).
fof(t6_lopban_6,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k7_relset_1(u1_struct_0(A),u1_struct_0(B),C,k5_rusub_4(A,D,E)) = k5_rusub_4(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)) ) ) ) ) ) )).
fof(t6_lopban_7,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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) <=> r3_nfcont_1(A,B,C,u1_struct_0(A)) ) ) ) ) )).
fof(t6_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => m2_subset_1(k1_struct_0(A),k1_zfmisc_1(u1_struct_0(A)),k1_lopclset(A)) ) )).
fof(t6_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => ( v2_rlvect_1(g1_rlvect_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)))) & v3_rlvect_1(g1_rlvect_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)))) & v4_rlvect_1(g1_rlvect_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)))) & v13_algstr_0(g1_rlvect_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)))) & v5_rlvect_1(g1_rlvect_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)))) & v6_rlvect_1(g1_rlvect_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)))) & v7_rlvect_1(g1_rlvect_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)))) & v8_rlvect_1(g1_rlvect_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)))) ) ) ) )).
fof(t6_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k10_lpspacc1(A) != k11_lpspacc1(A) ) )).
fof(t6_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_rfunct_3(B,A,k1_numbers,k3_rfunct_3(A,k1_numbers)) => ! [C] : ( m2_rfunct_3(C,A,k1_numbers,k3_rfunct_3(A,k1_numbers)) => ! [D] : ( m2_rfunct_3(D,A,k1_numbers,k3_rfunct_3(A,k1_numbers)) => ( r2_relset_1(A,k1_numbers,D,k2_lpspace1(A,k1_numbers,k13_rfunct_3(A),B,C)) <=> ( k1_relset_1(A,D) = k9_subset_1(A,k1_relset_1(A,B),k1_relset_1(A,C)) & ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,k1_relset_1(A,D)) => k1_funct_1(D,E) = k2_xcmplx_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) ) ) )).
fof(t6_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( v6_supinf_2(D) => ( r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(C,k5_numbers) | r2_relset_1(A,k1_numbers,k2_mesfun6c(C,A,k2_mesfun6c(B,A,D)),k2_mesfun6c(k3_xcmplx_0(B,C),A,D)) ) ) ) ) ) ) )).
fof(t6_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(B),k1_domain_1(k4_ordinal1,k1_hilbert1,A,k3_ltlaxio1)) = 1 ) ) )).
fof(t6_ltlaxio2,axiom,( ! [A] : ( m2_finseq_1(A,k1_hilbert1) => ( ~ r1_xxreal_0(k3_finseq_1(A),k5_numbers) => k7_partfun1(k1_hilbert1,k2_ltlaxio2(A),1) = k7_partfun1(k1_hilbert1,A,1) ) ) )).
fof(t6_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => r2_hidden(A,k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,A)) ) )).
fof(t6_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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,C,D)),k4_cqc_the1(A)) ) ) ) ) )).
fof(t6_margrel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( m1_subset_1(C,k3_margrel1(A)) => ( r1_tarski(B,C) => m1_subset_1(B,k3_margrel1(A)) ) ) ) )).
fof(t6_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( 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 ) ) )).
fof(t6_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,B,B) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => k3_matrix10(B,k6_matrix10(B,A,C)) = k6_matrix10(B,k9_complex1(A),k3_matrix10(B,C)) ) ) ) )).
fof(t6_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_matrix_2(C,k3_matrix_2(k1_nat_1(A,2))) => ! [D] : ( m1_matrix_2(D,k3_matrix_2(k1_nat_1(A,2))) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( ( r2_hidden(E,k2_finseq_1(k1_nat_1(A,2))) & r2_hidden(F,k2_finseq_1(k1_nat_1(A,2))) & k1_funct_1(C,E) = k1_funct_1(D,E) & k1_funct_1(C,F) = k1_funct_1(D,F) ) => ( r1_xxreal_0(F,E) | k1_funct_1(k1_matrix11(A,B,C),k2_tarski(E,F)) = k1_funct_1(k1_matrix11(A,B,D),k2_tarski(E,F)) ) ) ) ) ) ) ) ) )).
fof(t6_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(D),C,C) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(D))) ) => ( ( r2_hidden(B,k4_finseq_1(k3_matrix_1(D,C))) & r2_hidden(A,k4_finseq_1(k3_matrix_1(D,C))) ) => k4_matrix_3(D,k1_matrix12(C,C,D,k3_matrix_1(D,C),B,A),E) = k1_matrix12(C,C,D,E,B,A) ) ) ) ) ) ) )).
fof(t6_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( m1_matrix_2(D,k3_matrix_2(A)) => ( D = k1_finseq_2(A) => k13_matrix_3(A,B,C) = k10_matrix_3(A,B,C,D) ) ) ) ) ) )).
fof(t6_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( k5_fvsum_1(A,k9_fvsum_1(A,C,B)) = k9_fvsum_1(A,C,k4_algstr_0(A,B)) & k5_fvsum_1(A,k9_fvsum_1(A,C,B)) = k9_fvsum_1(A,k5_fvsum_1(A,C),B) ) ) ) ) )).
fof(t6_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( v1_matrix16(D,u1_struct_0(B)) => v1_matrix16(k2_matrix13(A,A,B,D,C),u1_struct_0(B)) ) ) ) ) ) )).
fof(t6_matrix17,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,B,A,A) & m2_finseq_1(C,k3_finseq_2(B)) ) => ! [D] : ( m2_finseq_1(D,B) => ( r1_matrix17(B,C,D) => ( r1_xxreal_0(A,k5_numbers) | r1_matrix17(B,k4_matrix_0(B,C),D) ) ) ) ) ) ) )).
fof(t6_matrix_0,axiom,( v1_matrix_0(k10_finseq_1(k1_xboole_0,k1_xboole_0)) )).
fof(t6_matrix_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => k5_matrix_1(B,A,C,k4_matrix_1(B,A,C)) = k2_matrix_1(B,A) ) ) ) )).
fof(t6_matrix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_matrix_2(B,k3_matrix_2(A)) => ( k3_relat_1(k1_finseq_2(A),B) = B & k3_relat_1(B,k1_finseq_2(A)) = B ) ) ) )).
fof(t6_matrix_3,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( k3_finseq_1(B) = k3_finseq_1(C) => ( k3_finseq_1(k11_fvsum_1(A,B,C)) = k3_finseq_1(B) & k3_finseq_1(k11_fvsum_1(A,B,C)) = k3_finseq_1(C) ) ) ) ) ) )).
fof(t6_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) & B = k3_matrix_3(A,B,C) ) => C = k1_matrix_3(A,k3_finseq_1(B),k1_matrix_0(B)) ) ) ) ) )).
fof(t6_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k1_complfld))) ) => A = k1_matrix_5(k2_matrix_5(A)) ) )).
fof(t6_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => r1_matrix_6(A,B,C,k3_matrix_1(B,A)) ) ) ) )).
fof(t6_matrix_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( r1_xxreal_0(2,k3_finseq_1(B)) => B = k8_finseq_1(A,k17_finseq_1(A,k7_nat_d(k3_finseq_1(B),2),B),k3_finseq_6(A,B,k7_nat_d(k3_finseq_1(B),1),k3_finseq_1(B))) ) ) ) )).
fof(t6_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_8(C,A,B) & v1_matrix_8(D,A,B) & r1_matrix_6(A,B,C,D) & k4_matrix_3(B,C,D) = k2_matrix_1(B,A) ) => ( r1_xxreal_0(A,k5_numbers) | v1_matrix_8(k3_matrix_3(B,C,D),A,B) ) ) ) ) ) ) )).
fof(t6_matrix_9,axiom,( k3_matrix_2(2) = k2_tarski(k1_finseq_2(2),k3_finseq_5(k1_finseq_2(2))) )).
fof(t6_matrixc1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k2_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(k2_numbers)) ) => ( r2_hidden(k4_tarski(A,B),k2_matrix_0(C)) => k3_matrix_0(k2_numbers,k3_matrix_5(C,D),A,B) = k2_xcmplx_0(k3_matrix_0(k2_numbers,C,A,B),k3_matrix_0(k2_numbers,D,A,B)) ) ) ) ) ) )).
fof(t6_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ( r2_hidden(A,k4_finseq_1(B)) => ( k1_funct_1(B,A) = k5_numbers | k1_matrixj1(B,k2_wsierp_1(k17_finseq_1(k4_ordinal1,A,B))) = A ) ) ) ) )).
fof(t6_matrixj2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(B,u1_struct_0(C))) => ( r2_hidden(A,k2_finseq_1(B)) => ( ( A != B => k13_fvsum_1(C,k7_matrix_0(u1_struct_0(C),k2_matrixj2(C,D,B),A),E) = k3_rlvect_1(C,k8_group_1(C,D,k7_partfun1(u1_struct_0(C),E,A)),k7_partfun1(u1_struct_0(C),E,k1_nat_1(A,1))) ) & ( A = B => k13_fvsum_1(C,k7_matrix_0(u1_struct_0(C),k2_matrixj2(C,D,B),A),E) = k8_group_1(C,D,k7_partfun1(u1_struct_0(C),E,A)) ) ) ) ) ) ) ) ) )).
fof(t6_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => k8_rvsum_1(k5_euclid(k3_finseq_1(A)),A) = k6_rvsum_1(A) ) )).
fof(t6_matrixr2,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k1_matrix_0(A) = k1_matrix_0(B) ) => ( k3_finseq_1(k5_matrixr1(A,B)) = k3_finseq_1(A) & k1_matrix_0(k5_matrixr1(A,B)) = k1_matrix_0(A) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k4_tarski(C,D),k2_matrix_0(A)) => k3_matrix_0(k1_numbers,k5_matrixr1(A,B),C,D) = k5_real_1(k3_matrix_0(k1_numbers,A,C,D),k3_matrix_0(k1_numbers,B,C,D)) ) ) ) ) ) ) ) )).
fof(t6_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => ! [D] : ( m1_vectsp_6(D,A,B) => ! [E] : ( m1_vectsp_6(E,A,B) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B))) => ( ( v1_vectsp_7(F,A,B) & r1_tarski(k1_vectsp_6(A,B,C),F) & r1_tarski(k1_vectsp_6(A,B,D),F) & r1_tarski(k1_vectsp_6(A,B,E),F) & k4_vectsp_6(A,B,C) = k3_rlvect_1(B,k4_vectsp_6(A,B,D),k4_vectsp_6(A,B,E)) ) => r1_vectsp_6(A,B,C,k5_vectsp_6(A,B,D,E)) ) ) ) ) ) ) ) )).
fof(t6_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => r1_xxreal_0(k1_vectsp_9(A,k1_vectsp_7(A,B,C)),k5_card_1(C)) ) ) ) )).
fof(t6_matroid0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_taxonom2(A) & v1_setfam_1(A) ) => ! [B] : ( m2_orders_1(B,A,k6_partfun1(A)) => v2_funct_1(B) ) ) )).
fof(t6_matrtop2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k6_prvect_1(k2_vectsp_1,A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( B = C => k2_struct_0(k1_rlvect_3(k15_euclid(A),C)) = k2_struct_0(k1_vectsp_7(k2_vectsp_1,k6_prvect_1(k2_vectsp_1,A),B)) ) ) ) ) )).
fof(t6_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(B))) => ( r2_hidden(A,k2_finseq_1(B)) => k13_fvsum_1(k2_vectsp_1,k1_matrtop1(C),k8_matrix_0(u1_struct_0(k2_vectsp_1),k1_matrtop3(B,A),A)) = k4_xcmplx_0(k1_funct_1(C,A)) ) ) ) ) )).
fof(t6_mazurulm,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => k1_seq_2(k8_funcop_1(k1_numbers,k4_ordinal1,A)) = A ) )).
fof(t6_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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,k1_mboolean(A,B),k1_mboolean(A,C)) ) ) ) )).
fof(t6_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(B,k2_zfmisc_1(k1_tarski(A),C)) => ( k1_xtuple_0(B) = A & r2_hidden(k2_xtuple_0(B),C) ) ) )).
fof(t6_measure1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ! [D] : ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k6_subset_1(C,D),B) ) ) )).
fof(t6_measure3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ( ( k9_nat_1(B,D,k5_numbers) = k1_xboole_0 & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( k9_nat_1(B,D,k1_nat_1(F,1)) = k3_measure1(A,B,k9_nat_1(B,E,k5_numbers),k9_nat_1(B,E,F)) & r1_tarski(k9_nat_1(B,E,k1_nat_1(F,1)),k9_nat_1(B,E,F)) ) ) ) => ( r1_xxreal_0(k1_supinf_1,k12_supinf_2(C,k9_nat_1(B,E,k5_numbers))) | k12_supinf_2(C,k1_measure2(A,B,k1_measure3(A,B,E))) = k4_supinf_2(k12_supinf_2(C,k9_nat_1(B,E,k5_numbers)),k12_supinf_2(C,k2_measure2(A,B,k1_measure3(A,B,D)))) ) ) ) ) ) ) )).
fof(t6_measure4,axiom,( ! [A] : ! [B] : ( m1_measure4(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( ( r2_hidden(C,k1_measure4(A,B)) & r1_xboole_0(D,C) ) => k12_supinf_2(B,k4_subset_1(A,C,D)) = k3_supinf_2(k12_supinf_2(B,C),k12_supinf_2(B,D)) ) ) ) ) )).
fof(t6_measure5,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ! [B] : ( m1_subset_1(B,k6_numbers) => ( ( r1_xxreal_0(A,B) => k2_measure5(k1_xxreal_1(A,B)) = k4_supinf_2(B,A) ) & ( ~ r1_xxreal_0(A,B) => k2_measure5(k1_xxreal_1(A,B)) = k1_supinf_2 ) ) ) ) )).
fof(t6_measure6,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => ~ ( ~ r1_xxreal_0(A,k1_supinf_2) & v1_xreal_0(k8_supinf_2(B)) & ! [C] : ( v1_xxreal_0(C) => ~ ( r2_hidden(C,B) & ~ r1_xxreal_0(C,k3_xxreal_3(k8_supinf_2(B),A)) ) ) ) ) ) )).
fof(t6_measure7,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v6_supinf_2(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => r1_xxreal_0(k12_supinf_2(k18_supinf_2(A),B),k19_supinf_2(A)) ) ) ) )).
fof(t6_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ? [E] : ( v7_ordinal1(E) & ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [G] : ( m4_measure8(G,A,B,F) => r1_xxreal_0(k1_mesfunc9(k2_mesfunc9(k2_measure8(A,B,C,k8_measure8(A,B,F,G))),D),k1_mesfunc9(k2_mesfunc9(k4_measure8(A,B,F,C,G)),E)) ) ) ) ) ) ) )).
fof(t6_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => k4_member_1(k3_xboole_0(A,B)) = k3_xboole_0(k4_member_1(A),k4_member_1(B)) ) ) )).
fof(t6_membered,axiom,( ! [A] : ( v6_membered(A) => r1_tarski(A,k4_ordinal1) ) )).
fof(t6_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( l1_memstr_0(B,A) => ! [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)) ) => ( v4_memstr_0(C,A,B) <=> r1_tarski(k9_xtuple_0(C),k8_struct_0(B)) ) ) ) ) )).
fof(t6_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( k17_euclid(k5_algstr_0(k15_euclid(2),k1_rlvect_1(k15_euclid(2),A,C),k1_rlvect_1(k15_euclid(2),B,D))) = k6_xcmplx_0(k3_xcmplx_0(C,k17_euclid(A)),k3_xcmplx_0(D,k17_euclid(B))) & k18_euclid(k5_algstr_0(k15_euclid(2),k1_rlvect_1(k15_euclid(2),A,C),k1_rlvect_1(k15_euclid(2),B,D))) = k6_xcmplx_0(k3_xcmplx_0(C,k18_euclid(A)),k3_xcmplx_0(D,k18_euclid(B))) ) ) ) ) ) )).
fof(t6_mesfun10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & v1_mesfunc8(B,A,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(C,k1_relset_1(A,k1_mesfunc8(A,k1_valued_0(k4_partfun1(A,k6_numbers),B,D)))) => k12_supinf_2(k1_mesfunc8(A,k1_valued_0(k4_partfun1(A,k6_numbers),B,D)),C) = k2_rinfsup2(k1_valued_0(k6_numbers,k3_mesfunc5(A,B,C),D)) ) ) ) ) ) )).
fof(t6_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( 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,k46_valued_1(A,k2_numbers,k2_numbers,B,C)),k47_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,k46_valued_1(A,k2_numbers,k2_numbers,B,C)),k47_valued_1(A,k1_numbers,k1_numbers,k6_comseq_3(A,B),k6_comseq_3(A,C))) ) ) ) ) )).
fof(t6_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( m1_subset_1(C,A) => ( r2_hidden(C,k1_relset_1(A,k4_mesfunc5(A,k1_numbers,B,k5_numbers))) => r2_funct_2(k4_ordinal1,k6_numbers,k3_mesfunc5(A,k4_mesfun7c(A,B),C),k3_rinfsup2(k1_mesfunc5(k4_ordinal1,k10_seqfunc(A,B,C)))) ) ) ) ) )).
fof(t6_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,C) => v1_series_1(k10_seqfunc(A,D,E)) ) ) => ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,C) => v1_series_1(k10_seqfunc(A,k1_mesfun9c(A,k1_numbers,D,C),E)) ) ) ) ) ) ) ) )).
fof(t6_mesfunc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( C != k5_numbers => ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,k9_xtuple_0(k6_mesfunc1(A,B,C))) => k12_supinf_2(B,D) = k2_extreal1(k12_supinf_2(k6_mesfunc1(A,B,C),D),C) ) ) ) ) ) ) )).
fof(t6_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [F] : ( m1_subset_1(F,C) => ~ ( r1_mesfunc1(A,C,D,F) & r1_mesfunc1(A,C,E,F) & ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k3_numbers,C) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k3_numbers,C))) ) => ~ ! [H] : ( v1_rat_1(H) => k1_funct_1(G,H) = k9_subset_1(A,k9_subset_1(A,F,k15_mesfunc1(A,D,H)),k9_subset_1(A,F,k15_mesfunc1(A,E,k6_xcmplx_0(B,H)))) ) ) ) ) ) ) ) ) ) )).
fof(t6_mesfunc3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ( ( k4_finseq_1(D) = k4_finseq_1(C) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(D)) => k1_funct_1(D,E) = k3_xboole_0(B,k1_funct_1(C,E)) ) ) ) => k3_tarski(k2_relset_1(A,D)) = k3_xboole_0(B,k3_tarski(k2_relset_1(A,C))) ) ) ) ) )).
fof(t6_mesfunc4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [F] : ( m1_subset_1(F,k6_numbers) => ( ( r1_mesfunc2(A,B,D) & ! [G] : ( r2_hidden(G,k9_xtuple_0(D)) => r1_xxreal_0(k1_supinf_2,k1_funct_1(D,G)) ) & r1_xxreal_0(k1_supinf_2,F) & k9_xtuple_0(E) = k9_xtuple_0(D) & ! [G] : ( r2_hidden(G,k9_xtuple_0(E)) => k12_supinf_2(E,G) = k1_extreal1(F,k12_supinf_2(D,G)) ) ) => ( k9_xtuple_0(D) = k1_xboole_0 | r1_xxreal_0(k1_supinf_1,F) | k1_mesfunc3(A,B,C,E) = k1_extreal1(F,k1_mesfunc3(A,B,C,D)) ) ) ) ) ) ) ) ) )).
fof(t6_mesfunc5,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(k5_numbers,C) => ( k4_xxreal_3(C,k4_xxreal_0(A,B)) = k4_xxreal_0(k4_xxreal_3(C,A),k4_xxreal_3(C,B)) & k4_xxreal_3(C,k3_xxreal_0(A,B)) = k3_xxreal_0(k4_xxreal_3(C,A),k4_xxreal_3(C,B)) ) ) ) ) ) )).
fof(t6_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( r2_hidden(D,k14_mesfunc1(B,C)) <=> ( r2_hidden(D,k1_relset_1(A,B)) & ? [E] : ( v1_xreal_0(E) & E = k12_supinf_2(B,D) & r1_xxreal_0(C,E) ) ) ) ) ) ) )).
fof(t6_mesfunc7,axiom,( k2_mesfunc7(k6_finseq_1(k6_numbers)) = 1 )).
fof(t6_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ~ ( v3_kurato_0(D,A) & ~ r1_xxreal_0(k1_xxreal_0,k12_supinf_2(C,k3_card_3(D))) & ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ~ ( r1_funct_2(k4_ordinal1,B,k4_ordinal1,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(k4_ordinal1,B,B,k6_numbers,E,C))) ) ) ) ) ) ) ) )).
fof(t6_mesfunc9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( v4_mesfunc5(B) & v3_mesfunc5(C) ) => v4_mesfunc5(k4_mesfunc1(A,B,C)) ) ) ) ) )).
fof(t6_metric_1,axiom,( ! [A] : ( l1_metric_1(A) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( k1_metric_1(A,B,C) = k5_numbers => B = C ) & ( B = C => k1_metric_1(A,B,C) = k5_numbers ) & k1_metric_1(A,B,C) = k1_metric_1(A,C,B) & r1_xxreal_0(k1_metric_1(A,B,D),k2_xcmplx_0(k1_metric_1(A,B,C),k1_metric_1(A,C,D))) ) ) ) ) => ( v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) ) ) )).
fof(t6_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(B,k1_metric_2(A,C)) & r3_metric_2(A,C,D) ) => r2_hidden(B,k1_metric_2(A,D)) ) ) ) ) ) )).
fof(t6_metric_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(D,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C))) => ! [E] : ( m1_subset_1(E,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C))) => ! [F] : ( m1_subset_1(F,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C))) => r1_xxreal_0(k2_binop_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,k4_metric_3(A,B,C),D,F),k3_real_1(k2_binop_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,k4_metric_3(A,B,C),D,E),k2_binop_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,k4_metric_3(A,B,C),E,F))) ) ) ) ) ) ) )).
fof(t6_metric_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) => r1_pcomps_1(A,k1_metric_6(A,B)) ) ) ) )).
fof(t6_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ~ ( ~ v2_struct_0(A) & ~ v2_struct_0(B) & ~ ( r1_ordinal1(k2_waybel23(A),k2_waybel23(k2_borsuk_1(A,B))) & r1_ordinal1(k2_waybel23(B),k2_waybel23(k2_borsuk_1(A,B))) ) ) ) ) )).
fof(t6_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k2_mfold_1(A)),u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_mfold_1(A)),u1_struct_0(k15_euclid(A))))) ) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(k2_mfold_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ( C = D => k3_funct_2(u1_struct_0(k2_mfold_1(A)),u1_struct_0(k15_euclid(A)),B,C) = k1_rlvect_1(k15_euclid(A),D,k7_xcmplx_0(1,k6_xcmplx_0(1,k3_xcmplx_0(k12_euclid(D),k12_euclid(D))))) ) ) ) => ( A = k5_numbers | v3_tops_2(B,k2_mfold_1(A),k15_euclid(A)) ) ) ) ) )).
fof(t6_mfold_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( r1_metrizts(A,B,C,D) => r1_metrizts(B,A,D,C) ) ) ) ) ) )).
fof(t6_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k3_midsp_1(A,B,k3_midsp_1(A,C,D)) = k3_midsp_1(A,k3_midsp_1(A,B,C),k3_midsp_1(A,B,D)) ) ) ) ) )).
fof(t6_midsp_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ? [F] : ( m1_subset_1(F,A) & k2_binop_1(A,A,u1_struct_0(B),C,F,D) = E ) ) ) ) ) ) ) )).
fof(t6_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v2_struct_0(C) & v2_midsp_1(C) & l1_midsp_3(C,k1_nat_1(A,2)) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(C))) => ( r2_hidden(B,k2_finseq_1(k1_nat_1(A,1))) => ( k1_funct_1(k1_midsp_3(u1_struct_0(C),k1_nat_1(A,1),E,B,D),B) = D & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r2_hidden(F,k7_subset_1(k4_ordinal1,k4_finseq_1(E),k1_tarski(B))) => k1_funct_1(k1_midsp_3(u1_struct_0(C),k1_nat_1(A,1),E,B,D),F) = k1_funct_1(E,F) ) ) ) ) ) ) ) ) ) )).
fof(t6_mmlquer2,axiom,( ! [A] : ! [B] : ( ( v1_relat_2(B) & v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( v1_relat_2(k1_toler_1(B,C)) & v1_partfun1(k1_toler_1(B,C),C) & m1_subset_1(k1_toler_1(B,C),k1_zfmisc_1(k2_zfmisc_1(C,C))) ) ) ) )).
fof(t6_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [E] : ( v7_ordinal1(E) => ( r1_tarski(B,C) => ( E = k5_numbers | r1_tarski(k12_mmlquery(A,B,D,E),k4_mmlquery(A,D,C)) ) ) ) ) ) ) )).
fof(t6_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ 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] : ( ( 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_mod_2(g1_mod_2(A,B,C,D),A) & m1_mod_2(g1_mod_2(A,B,C,D),A,B,C) ) ) ) ) ) ) )).
fof(t6_mod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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_mod_3(A,B,k1_subset_1(u1_struct_0(B))) = k1_vectsp_4(A,B) ) ) )).
fof(t6_mod_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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)) & v3_group_1(k2_mod_4(A)) & v5_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)) ) ) )).
fof(t6_modal_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_trees_1(C) ) => ! [D] : ( m1_trees_1(D,A) => ( k5_trees_1(A,D,B) = k5_trees_1(A,D,C) => B = C ) ) ) ) ) )).
fof(t6_modcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ 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) ) => r2_hidden(k1_mod_2(B),k2_modcat_1(A,B)) ) ) )).
fof(t6_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_1(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v2_struct_0(C) & v10_modelc_1(C) & l2_modelc_1(C) ) => ! [D] : ( ( 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,k8_modelc_1(A,B)) = k2_lattices(C,k24_modelc_1(C,D,A),k24_modelc_1(C,D,B)) ) ) ) ) )).
fof(t6_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v4_modelc_2(A) => A = k4_modelc_2(k11_modelc_2(A),k12_modelc_2(A)) ) ) )).
fof(t6_modelc_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k13_modelc_2(C))) => ( ( k10_xtuple_0(A) = k1_modelc_3(C) & v2_funct_1(A) & r2_hidden(B,D) ) => k17_modelc_3(C,k7_subset_1(k13_modelc_2(C),D,k1_tarski(B)),A) = k6_xcmplx_0(k17_modelc_3(C,D,A),k3_finseq_1(B)) ) ) ) ) ) )).
fof(t6_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ( r1_nat_d(A,B) <=> ~ r1_xxreal_0(k11_nat_3(B,A),k5_numbers) ) ) ) )).
fof(t6_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v1_group_1(A) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k6_algstr_0(A,B,C) = C & k6_algstr_0(A,C,B) = C ) ) ) ) ) )).
fof(t6_monoid_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( v3_binop_1(C,B) => r2_funct_2(A,B,k3_monoid_1(A,B,B,B,C,D,D),D) ) ) ) ) )).
fof(t6_morph_01,axiom,( ! [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) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => k1_morph_01(A,B,C) = k1_setfam_1(a_3_2_morph_01(A,B,C)) ) ) ) )).
fof(t6_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_partfun1(B,u1_struct_0(A)) ) => ( r1_tarski(k2_lang1(k5_msafree(A,B)),k2_zfmisc_1(u4_struct_0(A),k1_tarski(u1_struct_0(A)))) & r1_tarski(k3_card_3(k3_msafree(u1_struct_0(A),B)),k1_lang1(k5_msafree(A,B))) & ( v2_relat_1(B) => ( k2_lang1(k5_msafree(A,B)) = k2_zfmisc_1(u4_struct_0(A),k1_tarski(u1_struct_0(A))) & k1_lang1(k5_msafree(A,B)) = k3_card_3(k3_msafree(u1_struct_0(A),B)) ) ) ) ) ) )).
fof(t6_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => m1_msafree(u3_msualg_1(A,B),A,B) ) ) )).
fof(t6_msafree3,axiom,( ! [A] : ! [B] : ( ( ~ v11_struct_0(B) & v1_instalg1(B) & l1_msualg_1(B) ) => ! [C] : ( ( 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_subset_1(A,k3_card_3(u3_msualg_1(B,k11_msafree(B,C)))) <=> m1_dtconstr(A,u1_struct_0(k5_msafree(B,C)),k5_trees_3(u1_struct_0(k5_msafree(B,C))),k1_msaterm(B,C)) ) ) ) )).
fof(t6_msafree4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finset_1(A) & v3_trees_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v3_trees_2(B) ) => ( r2_hidden(A,k3_trees_9(B)) => r1_xxreal_0(k6_trees_1(k9_xtuple_0(A)),k6_trees_1(k9_xtuple_0(B))) ) ) ) )).
fof(t6_msalimit,axiom,( ! [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))) ) )).
fof(t6_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( l3_msualg_1(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( r2_hidden(E,k1_funct_1(u3_msualg_1(A,C),D)) => m1_dtconstr(k1_trees_4(k4_tarski(E,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))) ) ) ) ) ) )).
fof(t6_msinst_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_altcat_1(C) & v11_altcat_1(C) & v12_altcat_1(C) & l2_altcat_1(C) ) => ( C = k4_msinst_1(B,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ( v3_msualg_1(D,B) & v1_msualg_6(D,B) & l3_msualg_1(D,B) ) ) ) ) ) ) )).
fof(t6_msscyc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( r2_hidden(B,u4_struct_0(A)) => ! [C] : ( ( v7_graph_1(C,A) & m1_graph_1(C,A) ) => ( C = k9_finseq_1(B) => k7_graph_2(A,C) = k10_finseq_1(k1_funct_1(u1_graph_1(A),B),k1_funct_1(u2_graph_1(A),B)) ) ) ) ) )).
fof(t6_msscyc_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ( ( v4_msscyc_1(A) & v3_msscyc_1(k4_msscyc_2(A)) ) => v5_msafree2(A) ) ) )).
fof(t6_mssubfam,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) => ( ( r2_hidden(B,D) & r1_tarski(B,C) ) => r1_tarski(k8_setfam_1(A,D),C) ) ) )).
fof(t6_mssublat,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( B = k1_funct_1(k7_finseq_2(k5_numbers),A) => k3_finseq_1(B) = A ) ) ) )).
fof(t6_msualg_1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v13_struct_0(A,1) & v5_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => k3_msualg_1(A,B,C) = k4_finseq_2(k3_finseq_1(k1_msualg_1(A,B)),k10_msualg_1(A,C)) ) ) ) )).
fof(t6_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( l3_msualg_1(D,A) => ( ( m1_msualg_2(B,A,C) & m1_msualg_2(C,A,D) ) => m1_msualg_2(B,A,D) ) ) ) ) ) )).
fof(t6_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r2_hidden(D,k3_msualg_1(A,B,C)) => ( k9_xtuple_0(D) = k4_finseq_1(k1_msualg_1(A,B)) & ! [E] : ( r2_hidden(E,k9_xtuple_0(k3_relat_1(k1_msualg_1(A,B),u3_msualg_1(A,C)))) => r2_hidden(k1_funct_1(D,E),k1_funct_1(k3_relat_1(k1_msualg_1(A,B),u3_msualg_1(A,C)),E)) ) ) ) ) ) ) ) )).
fof(t6_msualg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ( r2_msualg_3(A,B,C,D) => r6_msualg_3(A,k13_msualg_4(A,B,k17_msualg_4(A,B,C,D)),C) ) ) ) ) ) )).
fof(t6_msualg_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_msualg_4(C,A,B) & m1_msualg_4(C,A,B,B) ) => ! [D] : ( ( v1_msualg_4(D,A,B) & m1_msualg_4(D,A,B,B) ) => ! [E] : ( ( v1_msualg_4(E,A,B) & m1_msualg_4(E,A,B,B) ) => ( ( r2_pboole(A,k2_pboole(A,C,D),E) & ! [F] : ( ( v1_msualg_4(F,A,B) & m1_msualg_4(F,A,B,B) ) => ( r2_pboole(A,k2_pboole(A,C,D),F) => r2_pboole(A,E,F) ) ) ) => r8_pboole(A,E,k4_msualg_5(A,B,C,D)) ) ) ) ) ) ) )).
fof(t6_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_msualg_6(C,A,B) => ! [D] : ( m1_msualg_6(D,A,B) => m1_msualg_6(k1_msualg_6(u1_struct_0(A),u3_msualg_1(A,B),C,D),A,B) ) ) ) ) )).
fof(t6_msualg_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_msualg_5(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_msualg_5(A,B))) => ! [E] : ( ( v1_msualg_4(E,A,B) & m1_msualg_4(E,A,B,B) ) => ! [F] : ( ( v1_msualg_4(F,A,B) & m1_msualg_4(F,A,B,B) ) => ( ( C = E & D = F ) => ( r3_lattices(k5_msualg_5(A,B),C,D) <=> r2_pboole(A,E,F) ) ) ) ) ) ) ) ) )).
fof(t6_msualg_8,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_msualg_5(A)))) => m1_subset_1(k3_tarski(B),k1_zfmisc_1(k2_zfmisc_1(A,A))) ) )).
fof(t6_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_msualg_1(B) & l1_msualg_1(B) ) => ( ( r1_msuhom_1(A,B) & r1_msuhom_1(B,A) ) => A = B ) ) ) )).
fof(t6_multop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( ( 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] : ( ( 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] : ( m1_subset_1(H,A) => ! [I] : ( m1_subset_1(I,B) => ! [J] : ( m1_subset_1(J,C) => ! [K] : ( m1_subset_1(K,D) => k4_multop_1(A,B,C,D,E,F,H,I,J,K) = k4_multop_1(A,B,C,D,E,G,H,I,J,K) ) ) ) ) => r2_funct_2(k4_zfmisc_1(A,B,C,D),E,F,G) ) ) ) ) ) ) ) ) )).
fof(t6_mycielsk,axiom,( ! [A] : ( ( v1_necklace(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_orders_2(A,B,C) => r1_orders_2(A,C,B) ) ) ) ) )).
fof(t6_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_nagata_1(B,A) & r2_hidden(C,B) & r2_hidden(D,B) & C != D & ~ r1_xboole_0(C,D) ) ) ) ) ) )).
fof(t6_nagata_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,C) => k3_funct_2(A,k1_numbers,k3_nagata_2(A,B,C),D) = k5_numbers ) ) ) ) ) ) )).
fof(t6_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( A != k5_numbers & ! [B] : ( v7_ordinal1(B) => A != k1_nat_1(B,1) ) ) ) )).
fof(t6_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,k2_finseq_1(B)) => r2_hidden(k1_nat_1(k7_nat_d(B,A),1),k2_finseq_1(B)) ) ) ) )).
fof(t6_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => ( r1_nat_d(C,k1_newton(B,A)) => C = B ) ) ) ) )).
fof(t6_nat_4,axiom,( ! [A] : ( v7_ordinal1(A) => r1_xxreal_0(k7_xcmplx_0(k1_newton(4,A),k3_xcmplx_0(2,A)),k4_newton(A,k3_xcmplx_0(2,A))) ) )).
fof(t6_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( v2_funct_1(B) => v2_funct_1(k2_finseq_3(A,B)) ) ) ) )).
fof(t6_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_nat_d(A,k5_numbers) & r1_nat_d(1,A) ) ) )).
fof(t6_nat_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_nat_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_nat_lat)) => k1_binop_1(k1_nat_lat,B,A) = k1_binop_1(k1_nat_lat,A,B) ) ) )).
fof(t6_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) => ( 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,C),k1_relset_1(u1_struct_0(B),E)) ) ) ) ) ) ) )).
fof(t6_ncfcont2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)))) ) => ( ( r3_ncfcont2(A,C,D,E) & r3_ncfcont2(B,C,D,F) ) => r3_ncfcont2(k3_xboole_0(A,B),C,D,k3_vfunct_2(u1_struct_0(C),D,E,F)) ) ) ) ) ) )).
fof(t6_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v12_struct_0(B,k4_ordinal1,A) <=> ! [C] : ~ ( r2_hidden(C,k4_ordinal1) & k1_funct_1(B,C) = k4_struct_0(A) ) ) ) ) )).
fof(t6_ndiff_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_ndiff_1(A,B,C,D) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_ndiff_2(A,B,C,D,E) & k3_ndiff_2(A,B,C,D,E) = k17_lopban_1(A,B,k3_ndiff_1(A,B,C,D),E) & ? [F] : ( m1_nfcont_1(F,A,D) & r1_tarski(F,k1_relset_1(u1_struct_0(A),C)) & ! [G] : ( ( v9_ordinal1(G) & v1_funct_1(G) & v1_funct_2(G,k4_ordinal1,k1_numbers) & v1_fdiff_1(G,k5_numbers) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [H] : ( ( v1_funct_1(H) & v3_funct_1(H) & v1_funct_2(H,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( k2_relset_1(u1_struct_0(A),H) = k1_tarski(D) & r1_tarski(k2_relset_1(u1_struct_0(A),k2_normsp_1(A,k2_ndiff_1(A,E,G),H)),F) ) => ( v3_normsp_1(k1_ndiff_1(B,k3_normsp_1(B,k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),k2_normsp_1(A,k2_ndiff_1(A,E,G),H),C),k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),H,C)),k37_valued_1(k4_ordinal1,k1_numbers,G)),B) & k3_ndiff_2(A,B,C,D,E) = k6_normsp_1(B,k1_ndiff_1(B,k3_normsp_1(B,k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),k2_normsp_1(A,k2_ndiff_1(A,E,G),H),C),k8_funct_2(k4_ordinal1,u1_struct_0(B),u1_struct_0(A),H,C)),k37_valued_1(k4_ordinal1,k1_numbers,G))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t6_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_partfun1(B,k1_numbers) & v1_partfun1(C,k1_numbers) ) => ( r2_funct_2(k4_ordinal1,u1_struct_0(A),k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,D,k6_vfunct_1(k1_numbers,A,B,C)),k2_normsp_1(A,k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,D,B),k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,D,C))) & r2_funct_2(k4_ordinal1,u1_struct_0(A),k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,D,k2_vfunct_1(k1_numbers,A,B,C)),k3_normsp_1(A,k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,D,B),k8_funct_2(k4_ordinal1,u1_struct_0(A),k1_numbers,D,C))) ) ) ) ) ) ) )).
fof(t6_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ! [C] : ( ( 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) => v3_rcomp_1(B) ) ) ) ) )).
fof(t6_ndiff_5,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ( r1_ndiff_3(A,D,C) => ! [E] : ( ( 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,k7_partfun1(u1_struct_0(A),D,C)) => ( r1_ndiff_3(B,k1_partfun1(k1_numbers,u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),D,E),C) & k1_ndiff_3(B,k1_partfun1(k1_numbers,u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),D,E),C) = k17_lopban_1(A,B,k3_ndiff_1(A,B,E,k7_partfun1(u1_struct_0(A),D,C)),k1_ndiff_3(A,D,C)) ) ) ) ) ) ) ) ) )).
fof(t6_neckla_3,axiom,( ! [A] : ( ( v1_necklace(A) & v3_necklace(A) & l1_orders_2(A) ) => ~ ( k1_card_1(u1_struct_0(A)) = 2 & ! [B] : ! [C] : ~ ( u1_struct_0(A) = k2_tarski(B,C) & ( u1_orders_2(A) = k2_tarski(k4_tarski(B,C),k4_tarski(C,B)) | u1_orders_2(A) = k1_xboole_0 ) ) ) ) )).
fof(t6_necklace,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_funct_1(B) ) => ( ( r1_xboole_0(k9_xtuple_0(A),k9_xtuple_0(B)) & r1_xboole_0(k10_xtuple_0(A),k10_xtuple_0(B)) ) => k2_funct_1(k1_funct_4(A,B)) = k1_funct_4(k2_funct_1(A),k2_funct_1(B)) ) ) ) )).
fof(t6_net_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_net_1(C) & l1_petri(C) ) => ( ( r2_hidden(k4_tarski(A,B),k1_net_1(C)) & r2_hidden(B,u4_struct_0(C)) ) => r2_hidden(A,u1_struct_0(C)) ) ) )).
fof(t6_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xcmplx_0(B) => k1_newton(B,k1_nat_1(A,1)) = k3_xcmplx_0(k1_newton(B,A),B) ) ) )).
fof(t6_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( r2_hidden(C,k2_relset_1(u1_struct_0(A),B)) <=> ? [D] : ( v7_ordinal1(D) & C = k1_normsp_1(A,B,D) ) ) ) ) )).
fof(t6_nfcont_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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) => r2_nfcont_2(A,B,k4_normsp_0(u1_struct_0(B),C,D)) ) ) ) ) )).
fof(t6_nfcont_3,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(C)))) ) => ( ( r2_hidden(B,A) & r1_nfcont_3(C,D,B) ) => r1_nfcont_3(C,k2_partfun1(k1_numbers,u1_struct_0(C),D,A),B) ) ) ) ) )).
fof(t6_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,u1_struct_0(k4_real_ns1(A))))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k1_euclid(A)))) ) => ! [E] : ( v1_xreal_0(E) => ( C = D => k4_vfunct_1(B,k4_real_ns1(A),C,E) = k9_integr15(A,E,B,D) ) ) ) ) ) ) )).
fof(t6_normform,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_finsub_1(B) ) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(A,B)) => k1_normform(A,B,C,k2_normform(A,B,D,C)) = C ) ) ) ) )).
fof(t6_normsp_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_normsp_0(A,k5_algstr_0(A,B,C)) = k5_numbers <=> B = C ) ) ) ) )).
fof(t6_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k2_normsp_2(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k2_normsp_2(A))))) ) => ( ( r1_funct_2(k4_ordinal1,u1_struct_0(A),k4_ordinal1,u1_struct_0(k2_normsp_2(A)),B,C) & v2_tbsp_1(C,k2_normsp_2(A)) ) => k1_tbsp_1(k2_normsp_2(A),C) = k6_normsp_1(A,B) ) ) ) ) )).
fof(t6_ntalgo_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => ! [B] : ( m1_subset_1(B,k4_numbers) => ( k3_mcart_1(k4_numbers,k4_numbers,k4_numbers,k2_ntalgo_1(A,B)) = k3_int_2(A,B) & k2_xcmplx_0(k3_xcmplx_0(k1_mcart_1(k4_numbers,k4_numbers,k4_numbers,k2_ntalgo_1(A,B)),A),k3_xcmplx_0(k2_mcart_1(k4_numbers,k4_numbers,k4_numbers,k2_ntalgo_1(A,B)),B)) = k3_int_2(A,B) ) ) ) )).
fof(t6_numbers,axiom,( r2_xboole_0(k4_numbers,k2_numbers) )).
fof(t6_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v9_o_ring_1(B,A) => ( v11_o_ring_1(B,A) & v13_o_ring_1(B,A) ) ) ) ) )).
fof(t6_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k6_openlatt(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k6_openlatt(A))) => ( r3_lattices(k6_openlatt(A),B,C) <=> r1_tarski(B,C) ) ) ) ) )).
fof(t6_oposet_1,axiom,( v2_necklace(k2_oposet_1) )).
fof(t6_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_cat_1(A,B,C) != k1_xboole_0 => ! [D] : ( m1_cat_1(D,A,B,C) => k7_oppcat_1(k2_oppcat_1(A),k3_oppcat_1(A,C),k3_oppcat_1(A,B),k7_oppcat_1(A,B,C,D)) = D ) ) ) ) ) )).
fof(t6_ordeq_01,axiom,( ! [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) & v3_lopban_1(A) & l1_normsp_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( k3_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) = C & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k3_funct_2(u1_struct_0(A),u1_struct_0(A),B,D) = D => C = D ) ) ) ) ) ) ) )).
fof(t6_orders_1,axiom,( ! [A] : ( ~ ( ? [B] : ( B != k1_xboole_0 & r2_hidden(B,A) ) & k3_tarski(A) = k1_xboole_0 ) & ~ ( k3_tarski(A) != k1_xboole_0 & ! [B] : ~ ( B != k1_xboole_0 & r2_hidden(B,A) ) ) ) )).
fof(t6_orders_2,axiom,( ! [A] : ( ( v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r1_orders_2(A,B,C) & r2_orders_2(A,C,B) ) ) ) ) )).
fof(t6_orders_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( ( r2_hidden(D,k1_orders_3(A,B)) & r2_hidden(E,k1_orders_3(B,C)) ) => r2_hidden(k3_relat_1(D,E),k1_orders_3(A,C)) ) ) ) ) ) ) )).
fof(t6_ordinal1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_ordinal1(C) => ( ( r2_hidden(A,B) & r2_hidden(B,C) ) => r2_hidden(A,C) ) ) )).
fof(t6_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) ) => ( k9_xtuple_0(B) = k1_ordinal1(A) => k1_ordinal2(B) = k1_funct_1(B,A) ) ) ) )).
fof(t6_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( r1_tarski(B,A) => k2_ordinal1(B) = B ) ) )).
fof(t6_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_ordinal2(B) ) => ! [C] : ( v3_ordinal1(C) => ! [D] : ( v3_ordinal1(D) => ( ( k9_xtuple_0(A) = k9_xtuple_0(B) & r1_ordinal2(C,A) & r1_ordinal2(D,B) ) => ( ( ? [E] : ( v3_ordinal1(E) & r2_hidden(E,k9_xtuple_0(A)) & ~ r1_ordinal1(k1_funct_1(A,E),k1_funct_1(B,E)) ) & ? [E] : ( v3_ordinal1(E) & r2_hidden(E,k9_xtuple_0(A)) & ~ r2_hidden(k1_funct_1(A,E),k1_funct_1(B,E)) ) ) | r1_ordinal1(C,D) ) ) ) ) ) ) )).
fof(t6_ordinal5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_ordinal2(A) & v2_ordinal5(A) ) => ( ~ v1_xboole_0(k9_xtuple_0(A)) => r1_ordinal2(k3_card_3(A),A) ) ) )).
fof(t6_ordinal6,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r3_wellord1(k1_wellord2(A),k1_wellord2(B),C) => ! [D] : ! [E] : ( ( r2_hidden(D,A) & r2_hidden(E,A) ) => ( r1_tarski(D,E) <=> r1_tarski(k1_funct_1(C,D),k1_funct_1(C,E)) ) ) ) ) )).
fof(t6_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r1_orders_2(B,C,D) => r1_orders_2(B,k4_algstr_0(B,C),D) ) ) ) ) ) )).
fof(t6_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m1_trees_4(D,k5_trees_3(u1_struct_0(k2_osafree(A,B))),k4_dtconstr(k2_osafree(A,B))) => ( 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)) <=> ( k4_finseq_1(D) = k4_finseq_1(k1_msualg_1(A,C)) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(D)) => r2_hidden(k1_funct_1(D,E),k4_osafree(A,B,k7_partfun1(u1_struct_0(A),k1_msualg_1(A,C),E))) ) ) ) ) ) ) ) ) )).
fof(t6_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ! [C] : ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ( ( r2_osalg_1(A,B,C) & r2_osalg_1(A,C,B) ) => B = C ) ) ) ) )).
fof(t6_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_tarski(k1_msualg_2(A,B,C),k1_osalg_2(A,B,C)) ) ) ) )).
fof(t6_osalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( 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) ) => ! [D] : ( m2_pboole(D,u1_struct_0(A),B,C) => ( ( v1_msualg_3(D) & v2_msualg_3(D,u1_struct_0(A),B,C) & v1_osalg_3(D,A) ) => v1_osalg_3(k4_msualg_3(u1_struct_0(A),B,C,D),A) ) ) ) ) ) )).
fof(t6_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(k4_tarski(B,C),k1_osalg_4(A)) => B = C ) ) ) ) )).
fof(t6_papdesaf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ( v6_papdesaf(A) => v5_papdesaf(A) ) ) )).
fof(t6_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & 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_parsp_1(k9_parsp_1(A)) = k8_parsp_1(A) ) )).
fof(t6_parsp_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ~ ! [B] : ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A))) => r1_parsp_1(k9_parsp_1(A),B,C,B,D) ) ) ) ) )).
fof(t6_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => k3_relat_1(k4_relat_1(A),C) = C ) )).
fof(t6_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( r2_relset_1(A,A,C,k1_partfun2(A,B)) <=> ( k1_relset_1(A,C) = B & ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,B) => k7_partfun1(A,C,D) = D ) ) ) ) ) ) ) )).
fof(t6_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ( r1_setfam_1(C,B) => ! [D] : ( r2_hidden(D,B) => r1_partit1(A,C,D) ) ) ) ) ) )).
fof(t6_partit_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ( r2_relset_1(A,A,k4_partit1(A,D),k4_relset_1(A,A,A,A,k4_partit1(A,B),k4_partit1(A,C))) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ( r2_hidden(E,k15_bvfunc_1(A,F,D)) <=> ? [G] : ( m1_subset_1(G,A) & r2_hidden(E,k15_bvfunc_1(A,G,B)) & r2_hidden(G,k15_bvfunc_1(A,F,C)) ) ) ) ) ) ) ) ) ) )).
fof(t6_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t6_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ( ! [C] : ( r2_hidden(C,A) => k1_funct_1(B,C) = k1_xboole_0 ) => B = k1_pboole(A) ) ) )).
fof(t6_pcomps_1,axiom,( ! [A] : v1_compts_1(k1_compts_1(k1_tarski(A))) )).
fof(t6_pcomps_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v3_pcomps_1(A) => ! [B] : ( 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] : ( 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) ) ) ) ) ) ) )).
fof(t6_pcs_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pcs_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_pcs_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( r1_pcs_0(k8_pcs_0(A,B),k9_pcs_0(A,B,C,E),k9_pcs_0(A,B,D,F)) <=> ( r1_pcs_0(A,C,D) | r1_pcs_0(B,E,F) ) ) ) ) ) ) ) ) )).
fof(t6_pdiff_1,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( ( v1_funct_1(C) & v2_fdiff_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v1_funct_1(k1_partfun1(k1_euclid(1),k1_numbers,k1_numbers,k1_euclid(1),B,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_euclid(1),C,A))) & v2_ndiff_1(k1_partfun1(k1_euclid(1),k1_numbers,k1_numbers,k1_euclid(1),B,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_euclid(1),C,A)),k4_real_ns1(1),k4_real_ns1(1)) & m1_subset_1(k1_partfun1(k1_euclid(1),k1_numbers,k1_numbers,k1_euclid(1),B,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_euclid(1),C,A)),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(1)),u1_struct_0(k4_real_ns1(1))))) ) ) & ! [C] : ( ( v1_funct_1(C) & v3_fdiff_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v1_funct_1(k1_partfun1(k1_euclid(1),k1_numbers,k1_numbers,k1_euclid(1),B,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_euclid(1),C,A))) & v1_funct_2(k1_partfun1(k1_euclid(1),k1_numbers,k1_numbers,k1_euclid(1),B,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_euclid(1),C,A)),u1_struct_0(k4_real_ns1(1)),u1_struct_0(k4_real_ns1(1))) & v13_vectsp_1(k1_partfun1(k1_euclid(1),k1_numbers,k1_numbers,k1_euclid(1),B,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_euclid(1),C,A)),k4_real_ns1(1),k4_real_ns1(1)) & v1_lopban_1(k1_partfun1(k1_euclid(1),k1_numbers,k1_numbers,k1_euclid(1),B,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_euclid(1),C,A)),k4_real_ns1(1),k4_real_ns1(1)) & v2_lopban_1(k1_partfun1(k1_euclid(1),k1_numbers,k1_numbers,k1_euclid(1),B,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_euclid(1),C,A)),k4_real_ns1(1),k4_real_ns1(1)) & m1_subset_1(k1_partfun1(k1_euclid(1),k1_numbers,k1_numbers,k1_euclid(1),B,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_euclid(1),C,A)),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(1)),u1_struct_0(k4_real_ns1(1))))) ) ) ) ) ) ) )).
fof(t6_pdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(2)) => ( ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & B = k10_finseq_1(C,D) & r1_fdiff_1(k1_pdiff_2(2,2,A,B),D) ) ) <=> r3_pdiff_1(2,2,A,B) ) ) ) )).
fof(t6_pdiff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(2)) => ! [D] : ( ( 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) ) => k3_pdiff_3(D,C) = k1_fdiff_1(k1_pdiff_2(2,2,k1_pdiff_3(1,2,D),C),B) ) ) ) ) ) )).
fof(t6_pdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) ) => r1_fdiff_1(k1_pdiff_2(3,3,E,D),C) ) ) ) ) ) ) )).
fof(t6_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) ) => r1_fdiff_1(k1_pdiff_2(3,3,k1_pdiff_3(2,3,E),D),C) ) ) ) ) ) ) )).
fof(t6_pdiff_6,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(B),k1_euclid(A)))) ) => ! [D] : ( ( 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] : ( v1_xreal_0(E) => ( C = D => k9_integr15(A,E,k1_euclid(B),C) = k4_vfunct_1(u1_struct_0(k4_real_ns1(B)),k4_real_ns1(A),D,E) ) ) ) ) ) ) )).
fof(t6_pdiff_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( v1_xreal_0(D) => ( k45_valued_1(k1_funct_1(k6_pdiff_1(A,B,C),D),C) = k1_funct_1(k6_pdiff_1(A,B,k5_euclid(A)),k6_xcmplx_0(D,k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_1(B,A),C))) & k45_valued_1(C,k1_funct_1(k6_pdiff_1(A,B,C),D)) = k1_funct_1(k6_pdiff_1(A,B,k5_euclid(A)),k6_xcmplx_0(k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_1(B,A),C),D)) ) ) ) ) ) )).
fof(t6_pdiff_8,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k16_lopban_1(k4_real_ns1(A),k4_real_ns1(B)))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,B) ) => ( v1_funct_1(k4_pdiff_1(D,B)) & v1_funct_2(k4_pdiff_1(D,B),u1_struct_0(k4_real_ns1(B)),u1_struct_0(k4_real_ns1(1))) & v13_vectsp_1(k4_pdiff_1(D,B),k4_real_ns1(B),k4_real_ns1(1)) & v1_lopban_1(k4_pdiff_1(D,B),k4_real_ns1(B),k4_real_ns1(1)) & v2_lopban_1(k4_pdiff_1(D,B),k4_real_ns1(B),k4_real_ns1(1)) & m1_subset_1(k4_pdiff_1(D,B),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_real_ns1(B)),u1_struct_0(k4_real_ns1(1))))) & r1_xxreal_0(k1_funct_1(k15_lopban_1(k4_real_ns1(B),k4_real_ns1(1)),k4_pdiff_1(D,B)),1) ) ) ) ) ) ) )).
fof(t6_pdiff_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ( r2_hidden(C,k1_relset_1(k1_euclid(A),B)) => ( k1_funct_1(k3_pdiff_1(A,B),C) = k9_finseq_1(k1_funct_1(B,C)) & k7_partfun1(k1_euclid(1),k3_pdiff_1(A,B),C) = k12_finseq_1(k1_numbers,k7_partfun1(k1_numbers,B,C)) ) ) ) ) ) )).
fof(t6_pencil_1,axiom,( ! [A] : ( r1_ordinal1(3,k1_card_1(A)) => ! [B] : ! [C] : ? [D] : ( r2_hidden(D,A) & B != D & C != D ) ) )).
fof(t6_pencil_2,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(D,k4_finseq_1(B)) & r1_xxreal_0(C,D) & r1_xxreal_0(C,E) & r1_xxreal_0(E,k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k3_finseq_1(B),D),C),1)) ) => k1_funct_1(k1_pencil_2(A,B,C,D),E) = k1_funct_1(B,k1_nat_1(k1_nat_1(k7_nat_d(D,C),E),1)) ) ) ) ) ) )).
fof(t6_pencil_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k5_pencil_1(A,B))) => m1_pboole(C,A,k12_pralg_1(A,B)) ) ) ) )).
fof(t6_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m1_vectsp_4(E,A,B) => ! [F] : ( m1_vectsp_4(F,A,B) => ( ( m1_vectsp_4(C,A,D) & m1_vectsp_4(E,A,F) & k2_vectsp_4(A,C) = k2_vectsp_4(A,E) & k2_vectsp_4(A,D) = k2_vectsp_4(A,F) ) => k1_pencil_4(A,B,C,D) = k1_pencil_4(A,B,E,F) ) ) ) ) ) ) ) )).
fof(t6_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( A != k5_numbers => ( r1_nat_d(A,B) <=> k4_nat_d(B,A) = k5_numbers ) ) ) ) )).
fof(t6_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u4_struct_0(A))) => ! [C] : ( r2_hidden(C,k8_petri(A,B)) <=> ? [D] : ( m1_petri(D,u1_struct_0(A),u4_struct_0(A),u1_petri(A)) & ? [E] : ( m1_subset_1(E,u4_struct_0(A)) & r2_hidden(E,B) & D = k4_tarski(C,E) ) ) ) ) ) )).
fof(t6_petri_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri_2(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ~ ( v3_petri_2(A) & r2_hidden(B,k9_xtuple_0(u2_petri_2(A))) & ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_petri_2(A))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k8_petri(A,k6_domain_1(u4_struct_0(A),B)))) => ! [E] : ( 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)))) ) ) ) ) ) ) ) )).
fof(t6_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,k4_ordinal1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ( ( 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)) ) ) ) ) )).
fof(t6_polyalg1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_polynom5(A,k8_polynom3(A,C,D),B),k8_polynom3(A,k3_polynom5(A,C,B),k3_polynom5(A,D,B))) ) ) ) ) )).
fof(t6_polyeq_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k2_xcmplx_0(A,B) != k5_numbers => k1_newton(k2_xcmplx_0(A,B),4) = k2_xcmplx_0(k2_xcmplx_0(k1_newton(A,4),k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(4,B),k1_newton(A,3)),k3_xcmplx_0(k3_xcmplx_0(6,k1_square_1(B)),k1_square_1(A))),k3_xcmplx_0(k3_xcmplx_0(4,k1_newton(B,3)),A))),k1_newton(B,4)) ) ) ) )).
fof(t6_polyeq_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ( ! [I] : ( v1_xcmplx_0(I) => k4_polyeq_1(A,B,C,D,I) = k4_polyeq_1(E,F,G,H,I) ) => ( A = E & B = F & C = G & D = H ) ) ) ) ) ) ) ) ) ) )).
fof(t6_polyeq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k2_polyeq_1(B,k5_numbers,k5_numbers,A) = k5_numbers => ( B = k5_numbers | A = k5_numbers ) ) ) ) )).
fof(t6_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k1_newton(k6_xcmplx_0(A,B),4) = k2_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k1_newton(A,4),k3_xcmplx_0(k3_xcmplx_0(4,k1_newton(A,3)),B)),k3_xcmplx_0(k3_xcmplx_0(6,k1_newton(A,2)),k1_newton(B,2))),k3_xcmplx_0(k3_xcmplx_0(4,k1_newton(B,3)),A)),k1_newton(B,4)) ) ) )).
fof(t6_polyform,axiom,( v1_abian(4) )).
fof(t6_polynom1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k9_fvsum_1(A,k2_pre_poly(u1_struct_0(A)),B) = k2_pre_poly(u1_struct_0(A)) ) ) )).
fof(t6_polynom2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v7_struct_0(B) & v4_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( 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)))) ) => k1_polynom2(A,k16_pre_poly(A),B,C) = k5_struct_0(B) ) ) ) )).
fof(t6_polynom3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [C] : ( m2_finseq_2(C,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( r2_hidden(D,k2_finseq_1(A)) & k1_recdef_1(B,D) != k1_recdef_1(C,D) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(1,E) => ( r1_xxreal_0(D,E) | k1_recdef_1(B,E) = k1_recdef_1(C,E) ) ) ) ) ) ) ) ) ) )).
fof(t6_polynom4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(k1_algseq_1(A,B),D) & r1_xxreal_0(k1_algseq_1(A,C),D) ) => r1_xxreal_0(k1_algseq_1(A,k2_normsp_1(A,B,C)),D) ) ) ) ) ) )).
fof(t6_polynom5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k5_algstr_0(k1_complfld,k1_hahnban1(A,B),k1_hahnban1(C,D)) = k1_hahnban1(k6_xcmplx_0(A,C),k6_xcmplx_0(B,D)) ) ) ) ) )).
fof(t6_polynom6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( m2_subset_1(C,k14_pre_poly(k10_ordinal2(A,B)),k15_pre_poly(k10_ordinal2(A,B))) => ? [D] : ( m2_subset_1(D,k14_pre_poly(A),k15_pre_poly(A)) & ? [E] : ( m2_subset_1(E,k14_pre_poly(B),k15_pre_poly(B)) & r6_pboole(k10_ordinal2(A,B),C,k1_polynom6(A,B,D,E)) ) ) ) ) ) )).
fof(t6_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( 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)) & v3_polynom7(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) <=> ~ ( k3_polynom1(k15_pre_poly(A),B,C) != k1_xboole_0 & ! [D] : ( ( 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(k15_pre_poly(A),B,C) != k1_tarski(D) ) ) ) ) ) )).
fof(t6_polynom8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(C,k5_numbers) & ~ ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(A),B,C) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(A))) ) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(A),C,D) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(A))) ) => k4_matrix_3(A,k6_matrix_3(A,E,k1_polynom8(A,B)),F) = k6_matrix_3(A,k4_matrix_3(A,E,F),k1_polynom8(A,B)) ) ) ) ) ) ) ) )).
fof(t6_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(D,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,k11_polynom1(A,B,C,D)),k11_polynom1(A,B,k5_vfunct_1(k15_pre_poly(A),B,C),D)) & r2_funct_2(k15_pre_poly(A),u1_struct_0(B),k5_vfunct_1(k15_pre_poly(A),B,k11_polynom1(A,B,C,D)),k11_polynom1(A,B,C,k5_vfunct_1(k15_pre_poly(A),B,D))) ) ) ) ) ) )).
fof(t6_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ v1_xboole_0(D) & v6_orders_2(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,k1_yellow_0(A,D)) = k1_yellow_0(B,k7_relset_1(u1_struct_0(A),u1_struct_0(B),C,D)) ) ) ) ) ) ) )).
fof(t6_power,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( r1_xxreal_0(1,A) => k1_power(A,1) = 1 ) ) )).
fof(t6_pralg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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(k5_pralg_1(A,B),A) ) ) ) )).
fof(t6_pralg_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => r2_hidden(k9_funct_6(k11_pralg_2(A,B,C)),k1_funct_2(u4_struct_0(B),k1_funct_2(A,k10_xtuple_0(k2_funct_5(k11_pralg_2(A,B,C)))))) ) ) ) ) )).
fof(t6_pralg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_funct_1(u3_msualg_1(A,B),C) != k1_xboole_0 => k1_msualg_2(A,B,C) = a_3_0_pralg_3(A,B,C) ) ) ) ) )).
fof(t6_pre_ff,axiom,( ! [A] : ( v1_int_1(A) => ( k5_int_1(A,2) = k5_numbers | k5_int_1(A,2) = 1 ) ) )).
fof(t6_pre_poly,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k3_finseq_2(A)) => ! [C] : ( m2_finseq_1(C,k3_finseq_2(A)) => ( r1_relset_1(k4_ordinal1,k3_finseq_2(A),B,C) => r1_relset_1(k4_ordinal1,A,k5_pre_poly(A,B),k5_pre_poly(A,C)) ) ) ) )).
fof(t6_pre_topc,axiom,( ! [A] : ( l1_struct_0(A) => k2_struct_0(A) = k3_subset_1(u1_struct_0(A),k1_struct_0(A)) ) )).
fof(t6_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_prelamb(A) ) => ! [B] : ( m1_prelamb(B,A) => ! [C] : ( 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)),k4_ordinal1),B,C)) = 3 & ! [D] : ( m1_trees_1(D,k9_xtuple_0(B)) => ! [E] : ( m1_trees_1(E,k9_xtuple_0(B)) => ! [F] : ( m2_finseq_1(F,u1_struct_0(A)) => ! [G] : ( m2_finseq_1(G,u1_struct_0(A)) => ! [H] : ( m2_finseq_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ~ ( D = k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,k5_numbers)) & E = k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,1)) & k1_xtuple_0(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k4_ordinal1),B,C)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),G,k12_finseq_1(u1_struct_0(A),k2_prelamb(A,I,J))),F),H),K) & k1_xtuple_0(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k4_ordinal1),B,D)) = k6_prelamb(A,F,J) & k1_xtuple_0(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k4_ordinal1),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),K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t6_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k1_newton(A,B),k5_numbers) ) ) ) )).
fof(t6_prgcor_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k1_numbers) & ~ v1_xboole_0(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ( ( v7_ordinal1(k1_funct_1(A,k5_numbers)) & k1_afinsq_1(A) = C ) => ( r1_xxreal_0(C,k1_funct_1(A,k5_numbers)) | ( ? [D] : ( v1_relat_1(D) & v5_relat_1(D,k1_numbers) & v5_ordinal1(D) & v1_funct_1(D) & v1_finset_1(D) & r2_prgcor_2(A,D,B,C) ) & ! [D] : ( ( v1_relat_1(D) & v5_relat_1(D,k1_numbers) & ~ v1_xboole_0(D) & v5_ordinal1(D) & v1_funct_1(D) & v1_finset_1(D) ) => ( r2_prgcor_2(A,D,B,C) => k12_afinsq_1(k1_numbers,D) = k10_rvsum_1(k12_afinsq_1(k1_numbers,A),B) ) ) ) ) ) ) ) ) )).
fof(t6_prob_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k7_subset_1(A,C,D),B) ) ) ) ) )).
fof(t6_prob_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v2_prob_1(B) <=> ! [C] : ( v7_ordinal1(C) => r1_tarski(k1_prob_2(A,k9_setfam_1(A),B,k1_nat_1(C,1)),k1_prob_2(A,k9_setfam_1(A),B,C)) ) ) ) )).
fof(t6_prob_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( m2_prob_1(D,A,B) => ( v3_prob_1(C) => v7_valued_0(k8_prob_1(A,B,C,D)) ) ) ) ) ) )).
fof(t6_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_prob_1(D,A,B) => ! [E] : ( m1_prob_1(E,A,B) => ( ( r1_tarski(D,E) & k3_funct_2(B,k1_numbers,C,E) = k5_numbers ) => k3_funct_2(B,k1_numbers,C,D) = k5_numbers ) ) ) ) ) ) )).
fof(t6_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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)),k7_cqc_lang(A,k6_cqc_lang(A,B),k6_cqc_lang(A,C))),k4_cqc_the1(A)) ) ) ) )).
fof(t6_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ~ ( ~ r1_collsp(A,B,C,D) & ~ r1_collsp(A,C,D,E) & ~ r1_collsp(A,D,E,B) & ~ r1_collsp(A,E,B,C) ) => r1_projdes1(A,B,C,D,E) ) ) ) ) ) ) )).
fof(t6_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ( ~ r4_projpl_1(A,B,C,D) <=> ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t6_projred1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & ~ r1_incsp_1(A,D,B) & ~ r1_incsp_1(A,D,C) ) ) ) ) )).
fof(t6_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( r2_hidden(C,k1_projred2(A,B)) <=> ? [D] : ( m1_subset_1(D,u1_incsp_1(A)) & C = D & r1_incsp_1(A,D,B) ) ) ) ) )).
fof(t6_prvect_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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) => v1_binop_1(k2_prvect_1(B,C,A),k4_finseq_2(A,B)) ) ) ) ) )).
fof(t6_prvect_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => k14_prvect_2(A) = g1_normsp_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)),k13_prvect_2(A)) ) )).
fof(t6_prvect_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k2_zfmisc_1(k4_card_3(A),k4_card_3(B)),k4_card_3(k7_finseq_1(A,B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(k4_card_3(A),k4_card_3(B)),k4_card_3(k7_finseq_1(A,B))))) & v2_funct_1(C) & v2_funct_2(C,k4_card_3(k7_finseq_1(A,B))) & ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ( ( r2_hidden(D,k4_card_3(A)) & r2_hidden(E,k4_card_3(B)) ) => k1_binop_1(C,D,E) = k7_finseq_1(D,E) ) ) ) ) ) ) )).
fof(t6_pscomp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => r1_xxreal_0(k3_funct_2(u1_struct_0(B),k1_numbers,C,D),A) ) & ! [D] : ( v1_xreal_0(D) => ( ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => r1_xxreal_0(k3_funct_2(u1_struct_0(B),k1_numbers,C,E),D) ) => r1_xxreal_0(A,D) ) ) ) => A = k2_pscomp_1(B,C) ) ) ) ) )).
fof(t6_pua2mss1,axiom,( ! [A] : ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ? [D] : ( m2_finseq_1(D,B) & r2_hidden(C,k4_card_3(D)) ) ) ) )).
fof(t6_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( r6_pboole(A,D,k2_pzfmisc1(A,B,C)) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,A) & v1_funct_1(E) & v1_partfun1(E,A) ) => ( ( r6_pboole(A,E,B) | r6_pboole(A,E,C) ) => r1_pboole(A,E,D) ) ) ) ) ) ) )).
fof(t6_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => r1_tarski(k6_qc_lang1(A),k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))) ) )).
fof(t6_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v5_qc_lang1(B,A) => B = k15_qc_lang1(A,k21_qc_lang1(A,B),k22_qc_lang1(A,B)) ) ) ) )).
fof(t6_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v3_qc_lang1(B,A) => k24_qc_lang1(A,B) = k24_qc_lang1(A,k18_qc_lang1(A,B)) ) ) ) )).
fof(t6_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m1_trees_1(D,k9_xtuple_0(k2_qc_lang4(A,C))) => ~ ( r2_hidden(k7_finseq_1(D,k9_finseq_1(B)),k9_xtuple_0(k2_qc_lang4(A,C))) & ! [E] : ( m1_subset_1(E,k9_qc_lang1(A)) => ~ ( E = k1_funct_1(k2_qc_lang4(A,C),k7_finseq_1(D,k9_finseq_1(B))) & r1_qc_lang2(A,E,k3_trees_2(k9_qc_lang1(A),k2_qc_lang4(A,C),D)) ) ) ) ) ) ) ) )).
fof(t6_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [D] : ( ( v1_qc_trans(D,A) & m1_qc_lang1(D) ) => m2_subset_1(C,k6_qc_lang1(D),k8_qc_lang1(D,B)) ) ) ) ) )).
fof(t6_qmax_1,axiom,( ! [A] : ( ( v2_qmax_1(A) & l1_qmax_1(A) ) => ! [B] : ( m1_subset_1(B,k5_qmax_1(A)) => ! [C] : ( m1_subset_1(C,k5_qmax_1(A)) => ( r4_qmax_1(A,B,C) => r4_qmax_1(A,C,B) ) ) ) ) )).
fof(t6_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k6_algstr_0(A,k3_lattices(A,B,C),D) = k3_lattices(A,k6_algstr_0(A,B,D),k6_algstr_0(A,C,D)) & k6_algstr_0(A,D,k3_lattices(A,B,C)) = k3_lattices(A,k6_algstr_0(A,D,B),k6_algstr_0(A,D,C)) ) ) ) ) ) )).
fof(t6_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k22_quaterni(k25_quaterni(A,B),C) = k25_quaterni(k22_quaterni(A,C),B) ) ) ) )).
fof(t6_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ( v1_xreal_0(A) => k23_quaterni(A,k11_quaterni) = k6_quaterni(k5_numbers,k5_numbers,k13_quaterni(A),k5_numbers) ) ) )).
fof(t6_quaterni,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ( ( v1_relat_1(I) & v1_funct_1(I) ) => ( ( k9_xtuple_0(I) = k2_enumset1(A,B,C,D) & k1_funct_1(I,A) = E & k1_funct_1(I,B) = F & k1_funct_1(I,C) = G & k1_funct_1(I,D) = H ) => ( A = B | C = D | I = k2_quaterni(A,B,C,D,E,F,G,H) ) ) ) )).
fof(t6_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r1_xxreal_0(k5_numbers,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(A)),k3_xcmplx_0(C,A)),D)) => ( r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(k5_numbers,k6_xcmplx_0(k1_square_1(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,B),A),C)),k1_quin_1(B,C,D))) ) ) ) ) ) ) )).
fof(t6_quofield,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v6_struct_0(A) & l5_algstr_0(A) ) => ~ v1_xboole_0(k7_quofield(A)) ) )).
fof(t6_radix_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( r1_xxreal_0(k5_numbers,C) => ( r1_xxreal_0(B,k5_numbers) | k5_int_1(k5_int_1(A,k3_xcmplx_0(B,C)),C) = k5_int_1(A,C) ) ) ) ) ) )).
fof(t6_radix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ~ r1_xxreal_0(k1_radix_1(A),k5_numbers) ) )).
fof(t6_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => r2_hidden(k5_numbers,k1_radix_3(A)) ) )).
fof(t6_radix_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(2,B) & r1_radix_1(1,A,B) ) => k7_radix_3(1,B,k2_xcmplx_0(1,1),k10_radix_3(1,B,k10_radix_1(B,1,A))) = k6_xcmplx_0(A,k3_xcmplx_0(k5_radix_3(A,B),k1_radix_1(B))) ) ) ) )).
fof(t6_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(1,A) => k8_radix_1(A,B,k10_radix_1(B,A,k5_numbers)) = k5_numbers ) ) ) )).
fof(t6_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,A) & r1_radix_6(A,B,C) & r1_xxreal_0(k4_radix_1(A,B,A,k10_radix_1(B,A,C)),k5_numbers) ) ) ) ) )).
fof(t6_ramsey_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_finset_1(B) => ( ~ r1_xxreal_0(A,k5_card_1(B)) => v1_xboole_0(k3_group_10(B,A)) ) ) ) )).
fof(t6_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( r2_mesfunc6(A,k1_random_1(A),B) & m2_subset_1(k1_relset_1(A,B),k1_zfmisc_1(A),k1_random_1(A)) ) ) ) )).
fof(t6_random_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( r2_relset_1(A,k1_numbers,k2_mesfun6c(2,A,k3_valued_1(A,k1_numbers,k1_numbers,B,C)),k3_valued_1(A,k1_numbers,k1_numbers,k3_valued_1(A,k1_numbers,k1_numbers,k2_mesfun6c(2,A,B),k26_valued_1(A,k1_numbers,k20_valued_1(A,k1_numbers,k1_numbers,B,C),2)),k2_mesfun6c(2,A,C))) & r2_relset_1(A,k1_numbers,k2_mesfun6c(2,A,k47_valued_1(A,k1_numbers,k1_numbers,B,C)),k3_valued_1(A,k1_numbers,k1_numbers,k47_valued_1(A,k1_numbers,k1_numbers,k2_mesfun6c(2,A,B),k26_valued_1(A,k1_numbers,k20_valued_1(A,k1_numbers,k1_numbers,B,C),2)),k2_mesfun6c(2,A,C))) ) ) ) ) )).
fof(t6_random_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [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))) ) => ( m1_random_1(C,A,B) => a_3_0_random_3(A,B,C) = k12_prob_1 ) ) ) ) )).
fof(t6_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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) ) => ( k1_card_1(k2_struct_0(B)) = 2 => k1_vectsp_9(A,B) = 1 ) ) ) )).
fof(t6_ratfunc1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k11_polynom3(A,B,k3_polynom5(A,C,D)),k3_polynom5(A,k11_polynom3(A,B,C),D)) ) ) ) ) )).
fof(t6_rcomp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => v1_rcomp_1(k1_rcomp_1(A,B)) ) ) )).
fof(t6_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,A) => k3_seq_4(k4_rcomp_1(A,B)) = A ) ) ) )).
fof(t6_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => ( v8_ordinal1(A) | v2_xxreal_0(B) | v3_xxreal_0(A) ) ) ) ) )).
fof(t6_real_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k3_int_1(k7_xcmplx_0(B,A)) = k7_xcmplx_0(k4_nat_d(B,A),A) ) ) )).
fof(t6_real_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_real_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_real_lat)) => ( k1_binop_1(k1_real_lat,B,k1_binop_1(k2_real_lat,B,A)) = B & k1_binop_1(k1_real_lat,k1_binop_1(k2_real_lat,A,B),B) = B & k1_binop_1(k1_real_lat,B,k1_binop_1(k2_real_lat,A,B)) = B & k1_binop_1(k1_real_lat,k1_binop_1(k2_real_lat,B,A),B) = B ) ) ) )).
fof(t6_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( k4_finseq_1(B) = k2_finseq_1(A) => m2_finseq_2(B,k1_numbers,k1_euclid(A)) ) ) ) )).
fof(t6_realset2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(A),k8_struct_0(A)) => ( k6_algstr_0(A,B,k5_struct_0(A)) = B & k6_algstr_0(A,k5_struct_0(A),B) = B ) ) ) )).
fof(t6_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_subset_1(D,u1_struct_0(A),k8_struct_0(A)) => ! [E] : ( m2_subset_1(E,u1_struct_0(A),k8_struct_0(A)) => k1_binop_1(k4_realset2(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))) = k1_binop_1(k4_realset2(A),k5_binop_1(u1_struct_0(A),k4_realset2(A),B,C),k1_funct_1(k5_realset2(A),k5_binop_1(u1_struct_0(A),k4_realset2(A),D,E))) ) ) ) ) ) )).
fof(t6_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_rearran1(B) & v2_rearran1(B) & m2_finseq_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k6_xcmplx_0(k3_finseq_1(B),1)) & k1_funct_1(B,C) = k1_funct_1(B,k1_nat_1(C,1)) ) ) ) ) )).
fof(t6_recdef_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( r2_hidden(A,k4_zfmisc_1(B,C,D,E)) => A = k6_xtuple_0(k7_xtuple_0(A),k8_xtuple_0(A),k5_xtuple_0(A),k2_xtuple_0(A)) ) )).
fof(t6_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => k10_xtuple_0(k2_xboole_0(A,B)) = k2_xboole_0(k10_xtuple_0(A),k10_xtuple_0(B)) ) ) )).
fof(t6_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ( v3_relat_2(A) <=> A = k2_relat_1(A) ) ) )).
fof(t6_reloc,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( ~ 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(k7_card_1(2),k1_ami_3)) & v1_finset_1(C) & v4_extpro_1(C,k7_card_1(2),k1_ami_3,B) ) => ! [D] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ! [E] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(E,u1_struct_0(k1_ami_3)) ) => ( ( r2_hidden(k4_struct_0(k1_ami_3),k9_xtuple_0(C)) & r1_tarski(C,D) & r1_tarski(k9_memstr_0(k7_card_1(2),k1_ami_3,C,A),E) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_ami_3)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ! [G] : ( ( v1_relat_1(G) & v4_relat_1(G,k4_ordinal1) & v5_relat_1(G,u1_compos_1(k1_ami_3)) & v1_funct_1(G) & v1_partfun1(G,k4_ordinal1) ) => ( ( r1_tarski(B,F) & r1_tarski(k6_compos_1(k1_ami_3,B,A),G) ) => ! [H] : ( m1_subset_1(H,k4_ordinal1) => k1_nat_1(k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,F,D,H)),A) = k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,G,E,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t6_relset_2,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) <=> r1_tarski(k10_eqrel_1(A),k10_eqrel_1(B)) ) )).
fof(t6_revrot_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => r1_xxreal_0(1,k3_finseq_1(k2_finseq_5(A,C,B))) ) ) ) )).
fof(t6_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : m1_rewrite1(k9_finseq_1(B),A) ) )).
fof(t6_rewrite2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_rewrite2(B) ) => ( k1_rewrite2(k2_flang_1(A),B) = B & k2_rewrite2(k2_flang_1(A),B) = B ) ) )).
fof(t6_rewrite3,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( m1_rewrite1(B,A) => ~ ( ~ r1_xxreal_0(k3_finseq_1(B),1) & ! [C] : ( m1_rewrite1(C,A) => ~ ( k7_finseq_1(C,k9_finseq_1(k1_funct_1(B,k3_finseq_1(B)))) = B & k2_xcmplx_0(k3_finseq_1(C),1) = k3_finseq_1(B) ) ) ) ) ) )).
fof(t6_rfinseq,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(D,k2_finseq_1(C)) ) => ( k1_funct_1(k17_finseq_1(A,C,B),D) = k1_funct_1(B,D) & r2_hidden(D,k4_finseq_1(B)) ) ) ) ) ) ) )).
fof(t6_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( A = k10_finseq_1(B,C) => ( k4_rfinseq2(A) = k3_xxreal_0(B,C) & k2_rfinseq2(A) = k15_funcop_1(k4_ordinal1,B,k3_xxreal_0(B,C),1,2) ) ) ) ) ) )).
fof(t6_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => k9_xtuple_0(k4_rfunct_1(k4_rfunct_1(A))) = k9_xtuple_0(k5_relat_1(A,k9_xtuple_0(k4_rfunct_1(A)))) ) )).
fof(t6_rfunct_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_ordinal1) & v5_valued_0(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1))) ) => r2_relset_1(k4_ordinal1,k1_numbers,k2_valued_0(k1_numbers,C,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,A)),k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k2_valued_0(k1_numbers,C,B),k2_valued_0(k1_numbers,C,A))) ) ) ) )).
fof(t6_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( C != k5_numbers => k8_relset_1(A,k1_numbers,B,k1_tarski(k7_xcmplx_0(D,C))) = k8_relset_1(A,k1_numbers,k26_valued_1(A,k1_numbers,B,C),k1_tarski(D)) ) ) ) ) ) )).
fof(t6_rfunct_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( r1_rfunct_4(A,B) => r2_rfunct_3(A,B) ) ) )).
fof(t6_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_seq_2(A) <=> v3_xxreal_2(k2_relset_1(k1_numbers,A)) ) ) )).
fof(t6_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( v3_valued_0(A) => ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) ) ) )).
fof(t6_ring_1,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k6_eqrel_1(u1_struct_0(A),u1_struct_0(A),k1_ring_1(A,B),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) ) ) ) ) ) )).
fof(t6_ringcat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m1_ringcat1(D,B,C) => ! [E] : ( m1_ringcat1(E,A,B) => ( ( r1_ringcat1(A,B) & r1_ringcat1(B,C) ) => m1_ringcat1(k6_ringcat1(D,E),A,C) ) ) ) ) ) ) )).
fof(t6_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k5_rusub_4(A,B,k4_struct_0(A)) = B ) ) )).
fof(t6_rlaffin2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( k1_rlaffin2(A,B) = B <=> v1_zfmisc_1(B) ) ) ) )).
fof(t6_rlaffin3,axiom,( ! [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_rlvect_5(A) & l1_rlvect_1(A) ) => ! [B] : ( ( v1_rlaffin1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( k5_card_1(B) = k2_xcmplx_0(k1_rlvect_5(A),1) <=> k4_rlaffin1(A,B) = k2_struct_0(A) ) ) ) )).
fof(t6_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_rlsub_1(B,A) & v1_rlsub_1(C,A) & D = a_3_0_rlsub_1(A,B,C) ) => v1_rlsub_1(D,A) ) ) ) ) ) )).
fof(t6_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( m1_rlsub_1(D,A) => k1_rlsub_2(A,B,k1_rlsub_2(A,C,D)) = k1_rlsub_2(A,k1_rlsub_2(A,B,C),D) ) ) ) ) )).
fof(t6_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => k5_rusub_4(A,D,k1_algstr_0(A,B,C)) = k5_rusub_4(A,k5_rusub_4(A,D,C),B) ) ) ) ) )).
fof(t6_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_algstr_0(A,B,C) = k4_struct_0(A) => B = k4_algstr_0(A,C) ) ) ) ) )).
fof(t6_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)) & v3_funct_2(D,k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k1_relset_1(k4_ordinal1,C)) => k1_funct_1(C,E) = k1_funct_1(B,k1_funct_1(D,E)) ) ) ) => k4_rlvect_1(A,B) = k4_rlvect_1(A,C) ) ) ) ) ) )).
fof(t6_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_rlvect_3(B,A) & r2_hidden(k4_struct_0(A),B) ) ) ) )).
fof(t6_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m2_rlvect_2(E,A,k8_domain_1(u1_struct_0(A),B,C,D)) => ~ ( B != C & B != D & C != D & k6_rlvect_2(A,E) != k3_rlvect_1(A,k3_rlvect_1(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))) ) ) ) ) ) ) )).
fof(t6_rlvect_5,axiom,( ! [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) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ( v2_funct_1(B) => ! [C] : ( m1_rlvect_2(C,A) => ( r1_tarski(k3_rlvect_2(A,C),k10_xtuple_0(B)) => k4_rlvect_1(A,k5_rlvect_2(A,B,C)) = k6_rlvect_2(A,C) ) ) ) ) ) )).
fof(t6_rlvect_x,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m2_rlvect_2(D,B,C) => ( r1_tarski(k2_relset_1(k1_numbers,D),k4_numbers) => r1_tarski(k2_relset_1(k1_numbers,k1_rlvect_x(B,A,D)),k4_numbers) ) ) ) ) ) )).
fof(t6_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ( ( v1_rmod_2(C,A,B) & v1_rmod_2(D,A,B) & E = a_4_0_rmod_2(A,B,C,D) ) => v1_rmod_2(E,A,B) ) ) ) ) ) ) )).
fof(t6_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( m1_rmod_2(E,A,B) => k1_rmod_3(A,B,C,k1_rmod_3(A,B,D,E)) = k1_rmod_3(A,B,k1_rmod_3(A,B,C,D),E) ) ) ) ) ) )).
fof(t6_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => k1_rmod_4(A,B,k6_domain_1(u1_struct_0(B),C)) = C ) ) ) )).
fof(t6_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & v7_robbins1(A) & l2_robbins1(A) ) => v14_lattices(A) ) )).
fof(t6_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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,k3_robbins1(A,B),C)))) = C ) ) ) )).
fof(t6_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_oposet_1(A) & l2_qmax_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_robbins1(A,k3_robbins1(A,B)) = B ) ) )).
fof(t6_robbins4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_lattices(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & v1_robbins4(A) & l4_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_lattices(A,B,k4_lattices(A,k3_robbins1(A,B),k1_lattices(A,B,C))) = k1_lattices(A,B,C) ) ) ) )).
fof(t6_rolle,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,k5_numbers) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ~ ( r1_tarski(k1_rcomp_1(A,k2_xcmplx_0(A,B)),k1_relset_1(k1_numbers,C)) & r1_tarski(k1_rcomp_1(A,k2_xcmplx_0(A,B)),k1_relset_1(k1_numbers,D)) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,C,k1_rcomp_1(A,k2_xcmplx_0(A,B)))) & r2_fdiff_1(C,k2_rcomp_1(A,k2_xcmplx_0(A,B))) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,D,k1_rcomp_1(A,k2_xcmplx_0(A,B)))) & r2_fdiff_1(D,k2_rcomp_1(A,k2_xcmplx_0(A,B))) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k2_rcomp_1(A,k2_xcmplx_0(A,B))) & k1_fdiff_1(D,E) = k5_numbers ) ) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ~ r1_xxreal_0(1,E) & k7_xcmplx_0(k6_xcmplx_0(k1_funct_1(C,k2_xcmplx_0(A,B)),k1_funct_1(C,A)),k6_xcmplx_0(k1_funct_1(D,k2_xcmplx_0(A,B)),k1_funct_1(D,A))) = k7_xcmplx_0(k1_fdiff_1(C,k2_xcmplx_0(A,k3_xcmplx_0(E,B))),k1_fdiff_1(D,k2_xcmplx_0(A,k3_xcmplx_0(E,B)))) ) ) ) ) ) ) ) ) )).
fof(t6_roughs_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( v1_prob_2(B) & r1_tarski(A,B) ) => v1_prob_2(A) ) ) ) )).
fof(t6_rpr_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v3_card_1(B,1) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : ( m1_subset_1(C,A) & r2_hidden(C,A) & B = k6_domain_1(A,C) ) ) ) )).
fof(t6_rsspace,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace))) => ? [B] : ( m1_subset_1(B,u1_struct_0(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace))) & k3_rlvect_1(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace),A,B) = k4_struct_0(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace)) ) ) )).
fof(t6_rsspace2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,C,D) = k3_xcmplx_0(k6_xcmplx_0(k9_nat_1(k1_numbers,B,D),A),k6_xcmplx_0(k9_nat_1(k1_numbers,B,D),A)) ) => ( v2_comseq_2(C) & k1_seq_2(C) = k3_xcmplx_0(k6_xcmplx_0(k1_seq_2(B),A),k6_xcmplx_0(k1_seq_2(B),A)) ) ) ) ) ) ) )).
fof(t6_rsspace3,axiom,( u1_struct_0(k3_rsspace3) = k1_rsspace3 & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_rsspace3)) <=> ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & v2_series_1(k2_rsspace(A)) ) ) & k4_struct_0(k3_rsspace3) = k5_rsspace & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_rsspace3)) => A = k2_rsspace(A) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_rsspace3)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_rsspace3)) => k1_algstr_0(k3_rsspace3,A,B) = k1_series_1(k1_numbers,k2_rsspace(A),k2_rsspace(B)) ) ) & ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_rsspace3)) => k1_rlvect_1(k3_rsspace3,B,A) = k26_valued_1(k4_ordinal1,k1_numbers,k2_rsspace(B),A) ) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_rsspace3)) => ( k4_algstr_0(k3_rsspace3,A) = k32_valued_1(k4_ordinal1,k1_numbers,k2_rsspace(A)) & k2_rsspace(k4_algstr_0(k3_rsspace3,A)) = k32_valued_1(k4_ordinal1,k1_numbers,k2_rsspace(A)) ) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_rsspace3)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_rsspace3)) => k5_algstr_0(k3_rsspace3,A,B) = k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k2_rsspace(A),k2_rsspace(B)) ) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_rsspace3)) => v2_series_1(k2_rsspace(A)) ) & ! [A] : ( m1_subset_1(A,u1_struct_0(k3_rsspace3)) => k2_normsp_0(k3_rsspace3,A) = k4_series_1(k56_valued_1(k4_ordinal1,k1_numbers,k2_rsspace(A))) ) )).
fof(t6_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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(k4_rsspace4(A,B),k5_lopban_1(A,B)) ) ) )).
fof(t6_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( E = D & F = C ) => k3_rlvect_1(B,E,F) = k3_rlvect_1(A,D,C) ) ) ) ) ) ) ) )).
fof(t6_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ! [D] : ( m1_rusub_1(D,A) => k1_rusub_2(A,B,k1_rusub_2(A,C,D)) = k1_rusub_2(A,k1_rusub_2(A,B,C),D) ) ) ) ) )).
fof(t6_rusub_3,axiom,( ! [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_bhsp_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( B = u1_struct_0(A) => k1_rusub_3(A,B) = A ) ) ) )).
fof(t6_rusub_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => v1_rusub_4(k1_rusub_1(A)) ) )).
fof(t6_rusub_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ~ v1_xboole_0(k6_rusub_4(A,B,C)) ) ) ) )).
fof(t6_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => r7_binop_1(k1_numbers,k3_rvsum_1(A),k9_binop_2) ) )).
fof(t6_rvsum_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k3_rvsum_2(k2_finseq_2(A,B),k2_finseq_2(A,C)) = k2_finseq_2(A,k2_xcmplx_0(B,C)) ) ) ) )).
fof(t6_scm_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_ami_3)) ) => ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_ami_3)) ) => ( ( k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B)) = C & k3_compos_1(k1_ami_3,A,C) = k4_ami_3(E,F) ) => ( k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1))) = k1_nat_1(C,1) & k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1)),E) = k6_xcmplx_0(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B),E),k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B),F)) & ! [G] : ( ( v1_ami_2(G) & m1_subset_1(G,u1_struct_0(k1_ami_3)) ) => ( G != E => k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1)),G) = k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B),G) ) ) ) ) ) ) ) ) ) ) )).
fof(t6_scm_comp,axiom,( ! [A] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( m1_dtconstr(B,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [C] : ( m1_dtconstr(C,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ( k12_scm_comp(A,k5_scm_comp(B,C)) = k2_xcmplx_0(k12_scm_comp(A,B),k12_scm_comp(A,C)) & k12_scm_comp(A,k6_scm_comp(B,C)) = k6_xcmplx_0(k12_scm_comp(A,B),k12_scm_comp(A,C)) & k12_scm_comp(A,k7_scm_comp(B,C)) = k3_xcmplx_0(k12_scm_comp(A,B),k12_scm_comp(A,C)) & k12_scm_comp(A,k8_scm_comp(B,C)) = k4_int_1(k12_scm_comp(A,B),k12_scm_comp(A,C)) & k12_scm_comp(A,k9_scm_comp(B,C)) = k5_int_1(k12_scm_comp(A,B),k12_scm_comp(A,C)) ) ) ) ) )).
fof(t6_scm_halt,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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) ) => ( ( r1_tarski(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_3(k4_scmfsa_2(k5_numbers),1)),A) & r1_tarski(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_3(k4_scmfsa_2(k5_numbers),1)),B) & r1_tarski(E,C) & r1_tarski(E,D) & r8_pboole(u1_struct_0(k1_scmfsa_2),A,B) ) => ( k8_extpro_1(k7_card_1(3),k1_scmfsa_2,C,A) = k8_extpro_1(k7_card_1(3),k1_scmfsa_2,D,B) & r8_pboole(u1_struct_0(k1_scmfsa_2),k6_extpro_1(k7_card_1(3),k1_scmfsa_2,C,A),k6_extpro_1(k7_card_1(3),k1_scmfsa_2,D,B)) ) ) ) ) ) ) ) )).
fof(t6_scm_inst,axiom,( ! [A] : ( m1_subset_1(A,k3_scm_inst) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k7_card_1(9)) => ( A = k3_xtuple_0(C,k9_finseq_1(B),k1_xboole_0) => k6_scm_inst(A) = B ) ) ) ) )).
fof(t6_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_scmfsa_2(C) => ! [D] : ( ( v1_ami_2(D) & ~ v1_scmfsa_m(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ( k1_funct_1(k1_scmfsa6b(k4_compos_1(k1_scmfsa_2),B,A),D) = k1_funct_1(B,D) & k18_scmfsa_2(k1_scmfsa6b(k4_compos_1(k1_scmfsa_2),B,A),C) = k18_scmfsa_2(B,C) ) ) ) ) ) )).
fof(t6_scmfsa10,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => k10_scmfsa_2(A,B) = k3_xtuple_0(5,k1_xboole_0,k10_finseq_1(A,B)) ) ) )).
fof(t6_scmfsa6a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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)) ) ) )).
fof(t6_scmfsa6b,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(B,k7_card_1(3),k1_scmfsa_2,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_partfun1(D,k4_ordinal1) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & ~ v1_xboole_0(E) & v1_funct_1(E) & v1_finset_1(E) & v1_afinsq_1(E) & v7_amistd_1(E,k7_card_1(3),k1_scmfsa_2) ) => ( r1_tarski(E,C) => ! [F] : ( v7_ordinal1(F) => ( ( r1_tarski(k6_compos_1(k1_scmfsa_2,E,F),D) & k5_memstr_0(k7_card_1(3),k1_scmfsa_2,A) = F & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,B) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,A) ) => ! [G] : ( v7_ordinal1(G) => ( k2_xcmplx_0(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,C,B,G)),F) = k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,D,A,G)) & k5_compos_0(u1_compos_1(k1_scmfsa_2),k3_extpro_1(k7_card_1(3),k1_scmfsa_2,C,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,C,B,G)),F) = k3_extpro_1(k7_card_1(3),k1_scmfsa_2,D,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,D,A,G)) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,C,B,G)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,D,A,G)) ) ) ) ) ) ) ) ) ) ) )).
fof(t6_scmfsa6c,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [E] : ( ( v1_scmfsa6c(E) & m1_subset_1(E,u1_compos_1(k1_scmfsa_2)) ) => k18_scmfsa_2(k1_scmfsa6b(k5_scmfsa6a(D,E),B,C),A) = k18_scmfsa_2(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,E,k1_scmfsa6b(D,B,C)),A) ) ) ) ) ) )).
fof(t6_scmfsa7b,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ~ ( A != B & r3_scmfsa7b(k6_scmfsa_2(B,C),A) ) ) ) ) )).
fof(t6_scmfsa8a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_scmfsa7b(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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)) ) ) )).
fof(t6_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r5_scmfsa7b(C,B,A) <=> r5_scmfsa7b(C,k1_funct_4(B,k7_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_numbers)),k1_funct_4(A,C)) ) ) ) ) ) ) )).
fof(t6_scmfsa8c,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => ( r2_hidden(k2_compos_0(u1_compos_1(k1_scmfsa_2),B),k2_enumset1(k5_numbers,6,7,8)) => k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k2_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,A) ) ) ) )).
fof(t6_scmfsa9a,axiom,( ! [A] : ( v7_ordinal1(A) => k4_sf_mastr(k1_scmfsa8a(A)) = k1_xboole_0 ) )).
fof(t6_scmfsa_1,axiom,( ! [A] : ( 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) ) )).
fof(t6_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => k4_memstr_0(k7_card_1(3),k1_scmfsa_2,A) = k4_numbers ) )).
fof(t6_scmfsa_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( ~ 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(k7_card_1(3),k1_scmfsa_2)) & v1_finset_1(B) & v4_extpro_1(B,k7_card_1(3),k1_scmfsa_2,A) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ( ( r1_tarski(B,C) & r1_tarski(B,D) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( ( r1_tarski(A,E) & r1_tarski(A,F) ) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v1_ami_2(H) & m1_subset_1(H,u1_struct_0(k1_scmfsa_2)) ) => ! [I] : ( ( v1_ami_2(I) & m1_subset_1(I,u1_struct_0(k1_scmfsa_2)) ) => ( ( k3_extpro_1(k7_card_1(3),k1_scmfsa_2,E,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G)) = k9_scmfsa_2(H,I) & r2_hidden(H,k9_xtuple_0(B)) ) => k3_xcmplx_0(k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G),H),k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G),I)) = k3_xcmplx_0(k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,D,G),H),k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,D,G),I)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t6_scmfsa_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(B,k7_card_1(3),k1_scmfsa_2,k5_numbers) ) => ( k1_funct_1(B,k4_scmfsa_2(k5_numbers)) = 1 => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( v1_int_1(D) => ( r1_tarski(k1_scmfsa_7(C,D),A) => ( C = k4_scmfsa_2(k5_numbers) | ( r1_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B) & k1_funct_1(k6_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B),C) = D & ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmfsa_2)) ) => ( E != C => k1_funct_1(k6_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B),E) = k1_funct_1(B,E) ) ) & ! [E] : ( m1_scmfsa_2(E) => k18_scmfsa_2(k6_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B),E) = k18_scmfsa_2(B,E) ) ) ) ) ) ) ) ) ) )).
fof(t6_scmfsa_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => k5_card_1(k3_scmfsa_9(B,A)) = k1_nat_1(k5_card_1(A),11) ) ) )).
fof(t6_scmfsa_i,axiom,( r1_tarski(k2_scmfsa_i,k3_zfmisc_1(k4_ordinal1,k13_finseq_1(k4_ordinal1),k10_xtuple_0(k2_scmfsa_i))) )).
fof(t6_scmfsa_m,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ~ ( B != k4_scmfsa_2(k5_numbers) & ~ r2_hidden(B,k9_xtuple_0(A)) & r2_hidden(B,k9_xtuple_0(k1_scmfsa_m(A))) ) ) ) )).
fof(t6_scmisort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ( ( r1_tarski(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)),C) & r1_tarski(D,A) & r1_tarski(D,B) ) => ! [E] : ( v7_ordinal1(E) => ( r8_pboole(u1_struct_0(k1_scmfsa_2),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C,E),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,C,E)) & k3_extpro_1(k7_card_1(3),k1_scmfsa_2,A,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C,E)) = k3_extpro_1(k7_card_1(3),k1_scmfsa_2,B,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,C,E)) ) ) ) ) ) ) ) )).
fof(t6_scmp_gcd,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ( k1_funct_1(k3_scmpds_4(B,A),k5_card_1(B)) = A & r2_hidden(k5_card_1(B),k9_xtuple_0(k3_scmpds_4(B,A))) ) ) ) )).
fof(t6_scmpds_2,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k1_ami_2,k2_ami_2) => ! [C] : ( v1_int_1(C) => ( r2_hidden(A,k2_tarski(2,3)) => r2_hidden(k3_xtuple_0(A,k1_xboole_0,k3_scmpds_1(B,C)),k1_scmpds_i) ) ) ) )).
fof(t6_scmpds_3,axiom,( ! [A] : ( ( 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] : ( ( 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(k1_funct_4(A,k5_relat_1(B,k2_ami_2))) & v4_relat_1(k1_funct_4(A,k5_relat_1(B,k2_ami_2)),u1_struct_0(k1_scmpds_2)) & v1_funct_1(k1_funct_4(A,k5_relat_1(B,k2_ami_2))) & v5_funct_1(k1_funct_4(A,k5_relat_1(B,k2_ami_2)),k2_memstr_0(2,k1_scmpds_2)) & v1_partfun1(k1_funct_4(A,k5_relat_1(B,k2_ami_2)),u1_struct_0(k1_scmpds_2)) ) ) ) )).
fof(t6_scmpds_4,axiom,( ! [A] : ( ( 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] : ~ ( r2_hidden(B,k9_xtuple_0(A)) & ~ ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) & B != k4_struct_0(k1_scmpds_2) ) ) )).
fof(t6_scmpds_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( 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,k5_numbers) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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) ) ) ) ) ) ) )).
fof(t6_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( 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] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v2_scmpds_4(D) & v3_scmpds_4(D) ) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t6_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(E) & v1_funct_1(E) & v1_finset_1(E) & v1_afinsq_1(E) ) => ( ( r1_scmpds_6(E,C,A) & k6_memstr_0(2,k1_scmpds_2,C) = k6_memstr_0(2,k1_scmpds_2,D) ) => ! [F] : ( v7_ordinal1(F) => ( k5_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),F) = k5_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),F) & k3_extpro_1(2,k1_scmpds_2,k1_funct_4(A,k10_compos_1(k1_scmpds_2,E)),k5_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),F)) = k3_extpro_1(2,k1_scmpds_2,k1_funct_4(B,k10_compos_1(k1_scmpds_2,E)),k5_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),F)) ) ) ) ) ) ) ) ) )).
fof(t6_scmpds_8,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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_8(A,B,C),k5_numbers) = k9_scmpds_2(A,B,k1_nat_1(k5_card_1(C),2)) & k1_funct_1(k1_scmpds_8(A,B,C),k1_nat_1(k5_card_1(C),1)) = k3_scmpds_2(k4_xcmplx_0(k1_nat_1(k5_card_1(C),1))) ) ) ) ) )).
fof(t6_scmpds_9,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( v1_int_1(C) => k1_amistd_1(2,k1_scmpds_2,B,k5_scmpds_2(A,C)) = k1_tarski(k1_ordinal1(B)) ) ) ) )).
fof(t6_scmpds_i,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k7_card_1(15)) => ! [B] : ( m1_subset_1(B,k1_scmpds_i) => ! [C] : ( m1_subset_1(C,k2_scm_inst) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => ( B = k3_xtuple_0(A,k1_xboole_0,k11_finseq_1(C,D,E)) => ( k7_scmpds_i(B) = C & k8_scmpds_i(B) = D & k9_scmpds_i(B) = E ) ) ) ) ) ) ) )).
fof(t6_scmring1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k4_card_3(k3_relat_1(k3_ami_2,k1_scmring1(A)))) => ! [C] : ( v7_ordinal1(C) => k1_funct_1(k3_scmring1(A,B,C),k4_ordinal1) = C ) ) ) )).
fof(t6_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(B))) ) => ! [D] : ( v7_ordinal1(D) => r2_hidden(k3_xtuple_0(7,k9_finseq_1(D),k12_finseq_1(u1_struct_0(k1_scmring2(B)),C)),k1_scmringi(A)) ) ) ) ) )).
fof(t6_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => k2_compos_0(u1_compos_1(k1_scmring2(A)),k5_scmring2(A,B,C)) = 3 ) ) ) )).
fof(t6_scmring4,axiom,( ! [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) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( 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(k7_card_1(2),k1_scmring2(A))) & v1_partfun1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( ( 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(k7_card_1(2),k1_scmring2(A))) & v1_partfun1(C,u1_struct_0(k1_scmring2(A))) ) => ( ( k5_memstr_0(k7_card_1(2),k1_scmring2(A),B) = k5_memstr_0(k7_card_1(2),k1_scmring2(A),C) & ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmring2(A))) ) => k2_scmring2(A,B,D) = k2_scmring2(A,C,D) ) ) => r8_pboole(u1_struct_0(k1_scmring2(A)),B,C) ) ) ) ) )).
fof(t6_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => r2_hidden(k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0),k1_scmringi(A)) ) )).
fof(t6_scmyciel,axiom,( ! [A] : k9_bspace(k1_tarski(A)) = k1_tarski(k1_tarski(A)) )).
fof(t6_scpinvar,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_scmpds_2)) ) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ! [H] : ( m1_subset_1(H,k4_ordinal1) => ( ( k1_funct_1(B,D) = k5_numbers & k1_funct_1(B,E) = k5_numbers & k1_funct_1(B,F) = 1 & k1_funct_1(B,k1_scmp_gcd(H)) = G & ! [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,k5_numbers) ) => ! [J] : ( ( v1_relat_1(J) & v4_relat_1(J,k4_ordinal1) & v5_relat_1(J,u1_compos_1(k1_scmpds_2)) & v1_funct_1(J) & v1_partfun1(J,k4_ordinal1) ) => ! [K] : ( m1_subset_1(K,k4_ordinal1) => ( ( G = k2_xcmplx_0(k1_funct_1(I,k1_scmp_gcd(H)),K) & k1_funct_1(I,E) = k1_pre_ff(K) & k1_funct_1(I,F) = k1_pre_ff(k1_nat_1(K,1)) & k1_funct_1(I,D) = k5_numbers ) => ( r1_xxreal_0(k1_funct_1(I,k1_scmp_gcd(H)),k5_numbers) | ( k1_funct_1(k6_scmpds_4(C,I,J),D) = k5_numbers & r1_scmpds_6(C,I,J) & r2_scmpds_6(C,I,J) & k1_funct_1(k6_scmpds_4(C,I,J),k1_scmp_gcd(H)) = k6_xcmplx_0(k1_funct_1(I,k1_scmp_gcd(H)),1) & k1_funct_1(k6_scmpds_4(C,I,J),E) = k1_pre_ff(k1_nat_1(K,1)) & k1_funct_1(k6_scmpds_4(C,I,J),F) = k1_pre_ff(k1_nat_1(k1_nat_1(K,1),1)) ) ) ) ) ) ) ) => ( k1_funct_1(k6_scmpds_4(k2_scmpds_8(D,H,C),B,A),E) = k1_pre_ff(G) & k1_funct_1(k6_scmpds_4(k2_scmpds_8(D,H,C),B,A),F) = k1_pre_ff(k1_nat_1(G,1)) & r1_scmpds_6(k2_scmpds_8(D,H,C),B,A) & r2_scmpds_6(k2_scmpds_8(D,H,C),B,A) ) ) ) ) ) ) ) ) ) ) )).
fof(t6_scpisort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ( ( r1_scmpds_6(C,B,A) & r2_scmpds_6(C,B,A) ) => k1_funct_1(k6_scmpds_4(k1_scmpds_4(C,D),B,A),E) = k1_funct_1(k6_scmpds_4(D,k8_memstr_0(2,k1_scmpds_2,k6_scmpds_4(C,B,A)),A),E) ) ) ) ) ) ) )).
fof(t6_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_scmpds_2)) ) => ! [G] : ( v1_int_1(G) => ! [H] : ( v1_int_1(H) => ( ( r1_xxreal_0(H,k1_funct_1(B,E)) & ! [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,k5_numbers) ) => ! [J] : ( ( v1_relat_1(J) & v4_relat_1(J,k4_ordinal1) & v5_relat_1(J,u1_compos_1(k1_scmpds_2)) & v1_funct_1(J) & v1_partfun1(J,k4_ordinal1) ) => ( ( r1_xxreal_0(H,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)),k5_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(H,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)),k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t6_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,E) => ( r2_analoaf(A,C,B,D,E) & r2_analoaf(A,B,C,E,D) & r2_analoaf(A,C,B,E,D) & r2_analoaf(A,D,E,B,C) & r2_analoaf(A,E,D,B,C) & r2_analoaf(A,D,E,C,B) & r2_analoaf(A,E,D,C,B) ) ) ) ) ) ) ) )).
fof(t6_seq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ? [B] : ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) & k2_relset_1(k1_numbers,B) = k1_tarski(A) ) ) )).
fof(t6_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(A) & v2_comseq_2(B) ) => k1_seq_2(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) = k2_xcmplx_0(k1_seq_2(A),k1_seq_2(B)) ) ) ) )).
fof(t6_seq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v3_membered(C) => ( ( ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => r1_xxreal_0(D,A) ) ) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,C) & ~ r1_xxreal_0(E,k6_xcmplx_0(A,D)) ) ) ) ) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => r1_xxreal_0(D,B) ) ) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,C) & ~ r1_xxreal_0(E,k6_xcmplx_0(B,D)) ) ) ) ) ) => A = B ) ) ) ) )).
fof(t6_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( r2_relset_1(k4_ordinal1,k4_partfun1(A,k1_numbers),k8_seqfunc(A,k6_seqfunc(A,B,C),D),k6_seqfunc(A,k8_seqfunc(A,B,D),k8_seqfunc(A,C,D))) & r2_relset_1(k4_ordinal1,k4_partfun1(A,k1_numbers),k8_seqfunc(A,D,k6_seqfunc(A,B,C)),k6_seqfunc(A,k8_seqfunc(A,D,B),k8_seqfunc(A,D,C))) ) ) ) ) ) )).
fof(t6_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v7_valued_0(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,A,C)) ) ) ) ) ) )).
fof(t6_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k3_series_1(A),k3_series_1(B)),k3_series_1(k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B))) ) ) )).
fof(t6_series_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(k3_xcmplx_0(k3_xcmplx_0(2,A),B),k2_xcmplx_0(k1_square_1(A),k1_square_1(B))) ) ) )).
fof(t6_series_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k1_newton(k2_xcmplx_0(A,B),4) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_newton(A,4),k3_xcmplx_0(k3_xcmplx_0(4,k1_newton(A,3)),B)),k3_xcmplx_0(k3_xcmplx_0(6,k1_newton(A,2)),k1_newton(B,2))),k3_xcmplx_0(k3_xcmplx_0(4,k1_newton(B,3)),A)),k1_newton(B,4)) ) ) )).
fof(t6_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => ~ ( ~ r1_xxreal_0(B,A) & r1_xxreal_0(k7_xcmplx_0(k2_xcmplx_0(B,k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),2))),k2_xcmplx_0(A,k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),2)))),k7_xcmplx_0(A,B)) ) ) ) )).
fof(t6_setfam_1,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => ( A = k1_xboole_0 | r1_tarski(k1_setfam_1(B),k1_setfam_1(A)) ) ) )).
fof(t6_setlim_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => k2_relset_1(B,k8_nat_1(B,C,A)) = a_3_2_setlim_1(A,B,C) ) ) ) )).
fof(t6_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => k8_nat_1(k9_setfam_1(B),k3_setlim_2(B,C,D),A) = k3_setlim_2(B,k8_nat_1(k9_setfam_1(B),C,A),k8_nat_1(k9_setfam_1(B),D,A)) ) ) ) )).
fof(t6_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k5_finsub_1(A)) => ! [C] : ( r2_hidden(C,B) => m1_subset_1(C,A) ) ) ) )).
fof(t6_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k5_finsub_1(A)) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( 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] : ( ( v1_funct_1(G) & v1_funct_2(G,B,C) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ( ( v1_binop_1(F,C) & v2_binop_1(F,C) & v2_funct_1(E) ) => ( ( D = k1_xboole_0 & ~ v1_setwiseo(F,C) ) | k7_setwiseo(B,C,F,k8_setwiseo(A,B,E,D),G) = k7_setwiseo(A,C,F,D,k1_partfun1(A,B,B,C,E,G)) ) ) ) ) ) ) ) ) ) )).
fof(t6_sf_mastr,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k11_scmfsa_2(A) = k11_scmfsa_2(B) => A = B ) ) ) )).
fof(t6_sfmastr1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => r8_pboole(u1_struct_0(k1_scmfsa_2),k1_scmfsa6b(k3_scmfsa6a(D,C),B,A),k1_funct_4(k1_scmfsa6b(C,k1_scmfsa6b(D,B,A),A),k7_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_nat_1(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(C,k1_scmfsa6b(D,B,A),A)),k5_card_1(D))))) ) ) ) ) ) )).
fof(t6_sfmastr2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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(k4_subset_1(k2_scmfsa_2,k4_scmfsa_m(A),k2_sf_mastr(B)),k2_sf_mastr(k2_sfmastr2(A,B))) ) ) )).
fof(t6_sfmastr3,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( m1_scmfsa_2(D) => k18_scmfsa_2(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,k15_scmfsa_2(C,B,D),A),D) = k1_funct_7(k18_scmfsa_2(A,D),k1_int_2(k1_funct_1(A,B)),k1_funct_1(A,C)) ) ) ) ) )).
fof(t6_sgraph1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(A,B) => k1_sgraph1(A,B) = k1_xboole_0 ) ) ) )).
fof(t6_sheffer1,axiom,( ! [A] : ( ( ~ 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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k4_lattices(A,k3_lattices(A,k3_lattices(A,B,C),D),B) = B ) ) ) ) )).
fof(t6_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,B,B),B)),k5_sheffer1(A,B,B)) = B ) ) )).
fof(t6_simplex0,axiom,( ! [A] : ! [B] : ( r1_setfam_1(A,B) <=> r1_tarski(k1_simplex0(A),k1_simplex0(B)) ) )).
fof(t6_simplex1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_matroid0(C) & m1_simplex0(C,u1_struct_0(B)) ) => ( r2_hidden(A,k3_simplex1(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) & v3_pre_topc(D,C) & r2_hidden(A,k1_rlaffin2(B,k1_simplex1(B,C,D))) ) ) ) ) )).
fof(t6_simplex2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( l1_pre_topc(B) => ( v2_simplex0(B) => v1_simplex2(B,A) ) ) ) )).
fof(t6_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v7_ordinal1(C) => k1_newton(k2_xcmplx_0(B,A),C) = k9_nat_1(k2_numbers,k10_comseq_3(k8_sin_cos(C,B,A)),C) ) ) ) )).
fof(t6_sin_cos2,axiom,( v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k16_sin_cos,k2_rcomp_1(k28_sin_cos,k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos)))) )).
fof(t6_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,k2_xcmplx_0(A,B)) = k6_xcmplx_0(k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,B)),k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,B))) ) ) )).
fof(t6_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ( k19_sin_cos(A) != k5_numbers => k17_sin_cos(A) = k3_xcmplx_0(k19_sin_cos(A),k1_sin_cos4(A)) ) ) )).
fof(t6_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k19_sin_cos(A) != k5_numbers => k17_sin_cos(k3_xcmplx_0(2,A)) = k7_xcmplx_0(k3_xcmplx_0(2,k1_sin_cos4(A)),k2_xcmplx_0(1,k1_square_1(k1_sin_cos4(A)))) ) ) )).
fof(t6_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => r1_xxreal_0(k19_sin_cos(A),1) ) )).
fof(t6_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(1,A) ) => r1_xxreal_0(k5_numbers,k7_xcmplx_0(k2_xcmplx_0(A,1),B)) ) ) ) )).
fof(t6_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( k1_newton(k2_xcmplx_0(k4_sin_cos2(A),k2_sin_cos2(A)),B) = k2_xcmplx_0(k4_sin_cos2(k3_xcmplx_0(B,A)),k2_sin_cos2(k3_xcmplx_0(B,A))) & k1_newton(k6_xcmplx_0(k4_sin_cos2(A),k2_sin_cos2(A)),B) = k6_xcmplx_0(k4_sin_cos2(k3_xcmplx_0(B,A)),k2_sin_cos2(k3_xcmplx_0(B,A))) ) ) ) )).
fof(t6_sin_cos9,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k27_sin_cos,k2_rcomp_1(k5_numbers,k28_sin_cos))) )).
fof(t6_sincos10,axiom,( r2_fdiff_1(k1_fdiff_9,k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos)) & ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos)) => k1_fdiff_1(k1_fdiff_9,A) = k7_xcmplx_0(k1_funct_1(k16_sin_cos,A),k1_square_1(k1_funct_1(k18_sin_cos,A))) ) ) )).
fof(t6_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ~ ( v4_pre_topc(D,k15_euclid(A)) & r1_tarski(D,k1_rltopsp1(k15_euclid(A),B,C)) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(k3_rlvect_1(k15_euclid(A),k1_rlvect_1(k15_euclid(A),B,k6_xcmplx_0(1,E)),k1_rlvect_1(k15_euclid(A),C,E)),D) & ! [F] : ( v1_xreal_0(F) => ( ( r1_xxreal_0(k5_numbers,F) & r1_xxreal_0(F,1) & r2_hidden(k3_rlvect_1(k15_euclid(A),k1_rlvect_1(k15_euclid(A),B,k6_xcmplx_0(1,F)),k1_rlvect_1(k15_euclid(A),C,F)),D) ) => r1_xxreal_0(E,F) ) ) ) ) ) ) ) ) ) )).
fof(t6_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(A)) => k2_topreal1(2,k8_finseq_1(u1_struct_0(k15_euclid(2)),A,B),C) = k2_topreal1(2,A,C) ) ) ) ) )).
fof(t6_sprect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r3_connsp_1(A,B,C) & r3_connsp_1(A,B,D) & r3_connsp_1(A,B,E) & k4_subset_1(u1_struct_0(A),C,D) = B & E != C & E != D ) ) ) ) ) ) )).
fof(t6_sprect_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_finseq_1(D,C) => ( ( r2_hidden(A,k4_finseq_1(D)) & r2_hidden(B,k4_finseq_1(D)) & k3_finseq_1(k3_finseq_6(C,D,A,B)) = 1 ) => A = B ) ) ) ) ) )).
fof(t6_sprect_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ( ( r2_hidden(C,k1_rltopsp1(k15_euclid(A),B,D)) & r2_hidden(D,k1_rltopsp1(k15_euclid(A),B,C)) ) => C = D ) ) ) ) ) )).
fof(t6_sprect_4,axiom,( ! [A] : ( ( ~ 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) != k3_goboard9(A) ) )).
fof(t6_sprect_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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,D),k4_finseq_4(B,E)) ) => ( r1_xxreal_0(k4_finseq_4(B,D),k4_finseq_4(B,C)) | r1_xxreal_0(k4_finseq_4(k1_finseq_6(A,B,C),D),k4_finseq_4(k1_finseq_6(A,B,C),E)) ) ) ) ) ) ) ) )).
fof(t6_square_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k1_square_1(k2_xcmplx_0(A,1)) = k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k3_xcmplx_0(2,A)),1) ) )).
fof(t6_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ( ~ r1_stacks_1(A,B) => k9_stacks_1(A,B) = k1_stacks_1(u1_struct_0(A),k12_finseq_1(u1_struct_0(A),k6_stacks_1(A,B)),k9_stacks_1(A,k5_stacks_1(A,B))) ) ) ) )).
fof(t6_stirl2_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( k3_nat_1(k7_domain_1(k4_ordinal1,A,B)) = k4_nat_1(A,B) & k4_seq_4(k7_domain_1(k4_ordinal1,A,B)) = k4_nat_1(A,B) ) ) ) )).
fof(t6_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k16_substut1(A),k38_substut1(A)) => ( v4_substut1(B,A) => k39_substut1(A,B) = k10_qc_lang1(A,k16_qc_lang1(A,k2_sublemma(A,B)),k3_substut1(A,k26_substut1(A,B),k19_substut1(A,B))) ) ) ) )).
fof(t6_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,B) <=> ( r2_hidden(E,C) & r2_hidden(E,D) ) ) ) => B = k9_subset_1(A,C,D) ) ) ) ) )).
fof(t6_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( r2_hidden(D,k3_substlat(A,B,C)) => ( r2_hidden(D,C) & ! [E] : ( ( r2_hidden(E,C) & r1_tarski(E,D) ) => E = D ) ) ) ) )).
fof(t6_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( 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))) ) ) ) )).
fof(t6_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k1_substut1(A)) => r1_xboole_0(k9_xtuple_0(k7_substut1(A,C,k11_cqc_lang(A,C,B),D)),k6_domain_1(k3_qc_lang1(A),C)) ) ) ) ) )).
fof(t6_supinf_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_setfam_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k6_numbers))) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_membered(B) ) => ( B = k5_setfam_1(k6_numbers,A) => k1_xxreal_2(B) = k1_xxreal_2(k5_supinf_1(A)) ) ) ) )).
fof(t6_supinf_2,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ( r2_hidden(A,k1_numbers) <=> r2_hidden(k2_supinf_2(A),k1_numbers) ) ) )).
fof(t6_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r1_orders_2(B,C,D) => r1_orders_2(B,k4_algstr_0(B,C),D) ) ) ) ) ) )).
fof(t6_sysrel,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => k3_relat_1(k2_xboole_0(A,B),C) = k2_xboole_0(k3_relat_1(A,C),k3_relat_1(B,C)) ) ) ) )).
fof(t6_t_0topsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & 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),D) ) => r2_hidden(D,B) ) ) ) ) ) ) )).
fof(t6_t_1topsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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) => ! [D] : ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( D = k11_eqrel_1(u1_struct_0(A),E,k12_eqrel_1(u1_struct_0(A),k1_t_1topsp(A))) => r1_tarski(D,k8_relset_1(u1_struct_0(A),u1_struct_0(B),C,k6_domain_1(u1_struct_0(B),k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)))) ) ) ) ) ) ) )).
fof(t6_taxonom1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( ( r1_relat_2(D,A) & r1_rewrite1(D,B,C) & r2_hidden(B,A) ) => r2_hidden(k4_tarski(B,C),k18_finseq_1(D)) ) ) )).
fof(t6_taxonom2,axiom,( v3_taxonom2(k1_tarski(k1_xboole_0)) )).
fof(t6_taylor_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => k6_prepower(k23_sin_cos(A),k7_xcmplx_0(B,C)) = k23_sin_cos(k3_xcmplx_0(k7_xcmplx_0(B,C),A)) ) ) ) )).
fof(t6_taylor_2,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v7_ordinal1(B) => k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k22_sin_cos,A),B) = k2_partfun1(k1_numbers,k1_numbers,k22_sin_cos,A) ) ) )).
fof(t6_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_tbsp_1(B,A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(D,E) & r1_xxreal_0(C,k3_metric_1(A,k2_tbsp_1(A,B,k2_xcmplx_0(E,F)),k2_tbsp_1(A,B,E))) ) ) ) ) ) ) ) ) )).
fof(t6_tdgroup,axiom,( ~ ! [A] : ( m1_subset_1(A,u1_struct_0(k1_vectsp_1)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_vectsp_1)) => A = B ) ) )).
fof(t6_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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),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))) ) ) ) ) )).
fof(t6_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(k1_tops_1(A,k2_pre_topc(A,B)),B) => r1_tarski(k1_tops_1(A,k2_pre_topc(A,k9_subset_1(u1_struct_0(A),B,k2_pre_topc(A,k1_tops_1(A,B))))),k9_subset_1(u1_struct_0(A),B,k2_pre_topc(A,k1_tops_1(A,B)))) ) ) ) )).
fof(t6_tdlat_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v3_pre_topc(B,A) & v4_pre_topc(B,A) ) => k1_tops_1(A,k2_pre_topc(A,B)) = k2_pre_topc(A,k1_tops_1(A,B)) ) ) ) )).
fof(t6_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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) ) ) ) )).
fof(t6_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_tmap_1(A,k3_subset_1(u1_struct_0(A),B))))) => ( ( C = B & v2_tops_1(B,A) ) => ( v2_tops_1(C,k6_tmap_1(A,k3_subset_1(u1_struct_0(A),B))) & v4_pre_topc(C,k6_tmap_1(A,k3_subset_1(u1_struct_0(A),B))) ) ) ) ) ) )).
fof(t6_tex_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v1_subset_1(k6_domain_1(u1_struct_0(A),B),u1_struct_0(A)) ) ) )).
fof(t6_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( r4_tsep_2(A,B,C) => ( v1_tex_2(B,A) & v1_tex_2(C,A) ) ) ) ) ) )).
fof(t6_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v1_tex_4(k6_domain_1(u1_struct_0(A),B),A) ) ) )).
fof(t6_tmap_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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) ) ) ) )).
fof(t6_toler_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => k2_relset_1(A,B) = A ) )).
fof(t6_topalg_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v3_valued_0(B) ) => k10_rvsum_1(k6_rvsum_1(B),A) = k6_rvsum_1(k10_rvsum_1(B,A)) ) ) )).
fof(t6_topalg_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))))) => ( ( B = D & C = E ) => ( r1_connsp_1(A,B,C) <=> r1_connsp_1(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)),D,E) ) ) ) ) ) ) ) )).
fof(t6_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & l3_algstr_0(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v2_group_1(D) & v3_group_1(D) & l3_algstr_0(D) ) => ( ( r1_group_6(A,C) & r1_group_6(B,D) ) => r2_group_6(k2_group_7(k2_tarski(1,2),k10_finseq_1(A,B)),k2_group_7(k2_tarski(1,2),k10_finseq_1(C,D))) ) ) ) ) ) )).
fof(t6_topalg_5,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [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_1(A) ) => v1_connsp_1(B) ) ) ) )).
fof(t6_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_borsuk_2(G,A,C,D) => ! [H] : ( m1_borsuk_2(H,A,C,D) => ! [I] : ( m1_borsuk_2(I,B,E,F) => ! [J] : ( m1_borsuk_2(J,B,E,F) => ( ( r1_borsuk_6(B,E,F) & r1_borsuk_6(A,C,D) & r1_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),u1_struct_0(k5_topmetr),u1_struct_0(B),G,I) & r1_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),u1_struct_0(k5_topmetr),u1_struct_0(B),H,J) & r3_borsuk_2(B,E,F,I,J) ) => r3_borsuk_2(A,C,D,G,H) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t6_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_topdim_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( k2_topdim_1(A,B) = k4_xcmplx_0(1) <=> v1_xboole_0(B) ) ) ) )).
fof(t6_topdim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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),k5_numbers) ) ) ) ) ) ) )).
fof(t6_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( r1_tarski(B,C) => r1_tarski(k1_topgen_1(A,B),k1_topgen_1(A,C)) ) ) ) ) )).
fof(t6_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_frechet(A) <=> r1_ordinal1(k2_topgen_2(A),k4_ordinal1) ) ) )).
fof(t6_topgen_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( ! [C] : ( ( 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))) ) ) => g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) ) ) ) )).
fof(t6_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v7_topgen_1(A) <=> ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) & v1_tops_1(B,A) & v4_card_3(B) ) ) ) )).
fof(t6_topgen_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( 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)) ) => k1_funct_1(k1_funct_1(k9_funct_6(C),B),A) = k1_funct_1(D,B) ) ) ) )).
fof(t6_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_tarski(B,C) => r1_tarski(k4_group_2(A,D,B),k4_group_2(A,D,C)) ) ) ) ) ) )).
fof(t6_topmetr,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( v5_pre_topc(C,A,B) => ! [E] : ( ( 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))))) ) => ( E = C => v5_pre_topc(E,A,k1_pre_topc(B,D)) ) ) ) ) ) ) ) )).
fof(t6_topmetr3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k2_topmetr(A,B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k2_topmetr(A,B))))) ) => ( r1_xxreal_0(A,B) => ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k7_metric_1)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k7_metric_1)))) ) ) ) ) ) )).
fof(t6_topreal1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ( ( r2_hidden(D,k1_rltopsp1(k15_euclid(A),B,C)) & r2_hidden(E,k1_rltopsp1(k15_euclid(A),B,C)) ) => r1_tarski(k1_rltopsp1(k15_euclid(A),D,E),k1_rltopsp1(k15_euclid(A),B,C)) ) ) ) ) ) ) )).
fof(t6_topreal2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( v1_topreal2(A) <=> ? [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) & ? [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) & ? [D] : ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ? [E] : ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & B != C & r2_hidden(B,A) & r2_hidden(C,A) & 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) ) ) ) ) ) ) )).
fof(t6_topreal3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( ( k17_euclid(A) = k17_euclid(B) & k18_euclid(A) = k18_euclid(B) ) => A = B ) ) ) )).
fof(t6_topreal5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ~ r1_xxreal_0(B,A) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k3_topmetr)) & v5_pre_topc(E,k4_topmetr(A,B),k3_topmetr) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k3_topmetr)))) ) => ! [F] : ( v1_xreal_0(F) => ~ ( k1_funct_1(E,A) = C & k1_funct_1(E,B) = D & ~ r1_xxreal_0(F,C) & ~ r1_xxreal_0(D,F) & ! [G] : ( v1_xreal_0(G) => ~ ( k1_funct_1(E,G) = F & ~ r1_xxreal_0(G,A) & ~ r1_xxreal_0(B,G) ) ) ) ) ) ) ) ) ) ) )).
fof(t6_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => k19_rvsum_1(k2_finseq_2(k1_nat_1(B,1),A)) = k3_xcmplx_0(k19_rvsum_1(k2_finseq_2(B,A)),A) ) ) )).
fof(t6_topreal7,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( ( k3_finseq_1(A) = k3_finseq_1(B) | k4_finseq_1(A) = k4_finseq_1(B) ) => ( k3_finseq_1(k4_rvsum_1(A,B)) = k3_finseq_1(A) & k4_finseq_1(k4_rvsum_1(A,B)) = k4_finseq_1(A) ) ) ) ) )).
fof(t6_topreal8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_funct_1(B) & m2_finseq_1(B,A) ) => k4_finseq_4(B,k7_partfun1(A,B,k3_finseq_1(B))) = k3_finseq_1(B) ) ) )).
fof(t6_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ( r2_hidden(D,k2_topreal9(A,C,B)) <=> r1_xxreal_0(k12_euclid(k5_algstr_0(k15_euclid(A),D,C)),B) ) ) ) ) ) )).
fof(t6_topreala,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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_xboole_0(C) => v5_pre_topc(C,A,B) ) ) ) ) )).
fof(t6_toprealb,axiom,( ! [A] : ( ( 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_numbers => k1_pre_topc(k2_topalg_2,k5_toprealb(k1_relset_1(k1_numbers,A))) = k2_topalg_2 ) ) )).
fof(t6_toprealc,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_valued_0(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_valued_0(D) ) => ~ ( A != k5_numbers & B != k5_numbers & k45_valued_1(k14_valued_2(C,A),k14_valued_2(D,B)) != k14_valued_2(k45_valued_1(k24_valued_1(C,B),k24_valued_1(D,A)),k3_xcmplx_0(A,B)) ) ) ) ) ) )).
fof(t6_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => k9_nat_1(u1_struct_0(k15_euclid(A)),k3_toprns_1(A,C),B) = k4_algstr_0(k15_euclid(A),k9_nat_1(u1_struct_0(k15_euclid(A)),C,B)) ) ) ) )).
fof(t6_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k7_subset_1(u1_struct_0(A),k2_pre_topc(A,B),k2_pre_topc(A,C)),k2_pre_topc(A,k7_subset_1(u1_struct_0(A),B,C))) ) ) ) )).
fof(t6_tops_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( B != k1_xboole_0 => k6_setfam_1(A,k7_setfam_1(A,B)) = k3_subset_1(A,k5_setfam_1(A,B)) ) ) )).
fof(t6_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(C,A) => k1_tops_1(A,k4_subset_1(u1_struct_0(A),C,B)) = k1_tops_1(A,k4_subset_1(u1_struct_0(A),C,k1_tops_1(A,B))) ) ) ) ) )).
fof(t6_tops_4,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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))))) ) => ( v1_t_0topsp(C,k3_pcomps_1(A),k3_pcomps_1(B)) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( ( v1_xreal_0(F) & v2_xxreal_0(F) ) => ~ ( E = k1_funct_1(C,D) & ! [G] : ( ( v1_xreal_0(G) & v2_xxreal_0(G) ) => ~ r1_tarski(k8_metric_1(B,E,G),k7_relset_1(u1_struct_0(k3_pcomps_1(A)),u1_struct_0(k3_pcomps_1(B)),C,k8_metric_1(A,D,F))) ) ) ) ) ) ) ) ) ) )).
fof(t6_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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,k2_transgeo(A,k1_transgeo(A,C,B),D),k1_transgeo(A,k2_transgeo(A,C,D),k2_transgeo(A,B,D))) ) ) ) ) )).
fof(t6_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ~ ( F != G & r1_aff_1(A,F,G,H) & H != F & H != G ) ) ) ) & r2_analoaf(A,B,C,D,E) & r2_analoaf(A,B,D,C,E) ) => ( r1_aff_1(A,B,C,D) | r2_analoaf(A,B,E,C,D) ) ) ) ) ) ) ) )).
fof(t6_treal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(B,C) ) => ( k1_treal_1(A,B) = k1_treal_1(A,C) & k2_treal_1(B,C) = k2_treal_1(A,C) ) ) ) ) ) )).
fof(t6_trees_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r1_tarski(k7_finseq_1(B,k9_finseq_1(A)),C) => r2_xboole_0(B,C) ) ) ) )).
fof(t6_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ( r2_hidden(B,A) => A = k5_trees_1(A,B,k4_trees_1(A,B)) ) ) ) )).
fof(t6_trees_3,axiom,( ! [A] : ! [B] : ( ( v2_trees_3(A) & v2_trees_3(B) ) <=> v2_trees_3(k2_xboole_0(A,B)) ) )).
fof(t6_trees_4,axiom,( ! [A] : k1_trees_4(A) = k1_tarski(k4_tarski(k1_xboole_0,A)) )).
fof(t6_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( m1_trees_1(B,k9_xtuple_0(A)) => ( v1_zfmisc_1(k5_trees_2(A,B)) <=> r2_hidden(B,k3_trees_1(k9_xtuple_0(A))) ) ) ) )).
fof(t6_trees_a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( m4_trees_1(C,A) => r1_tarski(C,a_3_0_trees_a(A,B,C)) ) ) ) )).
fof(t6_triang_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_pre_poly(C,u1_struct_0(B),k1_triang_1(B)) ) => ( k5_card_1(C) = A => k4_finseq_1(k7_pre_poly(u1_struct_0(B),C,u1_orders_2(B))) = k2_finseq_1(A) ) ) ) ) )).
fof(t6_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_pre_topc(C,A) => ( ( m1_pre_topc(B,C) & m1_pre_topc(C,B) ) => g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) ) ) ) ) )).
fof(t6_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => r1_tsep_2(A,k1_struct_0(A),k2_struct_0(A)) ) )).
fof(t6_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_tsp_1(B,A) | v1_tsp_1(C,A) ) => v1_tsp_1(k9_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).
fof(t6_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tsp_2(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(C,A) => C = k3_tex_4(A,k9_subset_1(u1_struct_0(A),B,C)) ) ) ) ) ) )).
fof(t6_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( 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) => B = k9_turing_1(A,B) ) ) ) )).
fof(t6_twoscomp,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( m1_subset_1(B,k6_margrel1) => ( k1_funct_1(k2_twoscomp,k10_finseq_1(A,B)) = k1_funct_1(k13_twoscomp,k10_finseq_1(A,B)) & k1_funct_1(k3_twoscomp,k10_finseq_1(A,B)) = k1_funct_1(k12_twoscomp,k10_finseq_1(B,A)) & k1_funct_1(k4_twoscomp,k10_finseq_1(A,B)) = k1_funct_1(k11_twoscomp,k10_finseq_1(A,B)) ) ) ) )).
fof(t6_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( m5_margrel1(C,u1_struct_0(A),k1_unialg_2(A)) => ! [D] : ( m5_margrel1(D,u1_struct_0(B),k1_unialg_2(B)) => ! [E] : ( v7_ordinal1(E) => ( ( m1_unialg_2(A,B) & r2_hidden(E,k4_finseq_1(u1_unialg_1(A))) & C = k1_funct_1(u1_unialg_1(A),E) & D = k1_funct_1(u1_unialg_1(B),E) ) => k19_margrel1(C) = k19_margrel1(D) ) ) ) ) ) ) )).
fof(t6_unialg_3,axiom,( ! [A] : ( ( ~ 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] : ( m1_unialg_2(B,A) => k6_unialg_2(A) = k6_unialg_2(B) ) ) )).
fof(t6_uniform1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A))))) => ~ ( m1_setfam_1(B,u1_struct_0(k3_pcomps_1(A))) & v1_tops_2(B,k3_pcomps_1(A)) & v1_compts_1(k3_pcomps_1(A)) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( ~ r1_xxreal_0(C,k3_metric_1(A,D,E)) & ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ~ ( r2_hidden(D,F) & r2_hidden(E,F) & r2_hidden(F,B) ) ) ) ) ) ) ) ) ) ) )).
fof(t6_uniroots,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ~ ( k9_complex1(B) = 1 & B != k1_hahnban1(1,k5_numbers) & r1_xxreal_0(k9_complex1(k5_algstr_0(k1_complfld,k1_hahnban1(A,k5_numbers),B)),k6_xcmplx_0(A,1)) ) ) ) ) )).
fof(t6_uproots,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( v1_xboole_0(B) | C = k5_numbers ) => r6_pboole(A,k1_uproots(A,B,C),k16_pre_poly(A)) ) ) ) )).
fof(t6_urysohn1,axiom,( ! [A] : ( v7_ordinal1(A) => ( r2_hidden(k5_numbers,k1_urysohn1(A)) & r2_hidden(1,k1_urysohn1(A)) ) ) )).
fof(t6_urysohn2,axiom,( ! [A] : ( ( v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => v6_xxreal_2(k1_integra2(A,k5_numbers)) ) )).
fof(t6_urysohn3,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k2_urysohn1) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(k3_urysohn3(A),B) => r2_hidden(A,k1_urysohn1(B)) ) ) ) ) )).
fof(t6_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k3_qc_lang1(A)) & v3_card_1(D,B) & m2_finseq_1(D,k2_qc_lang1(A)) ) => ! [E] : ( m1_valuat_1(E,A,C) => ! [F] : ( m2_subset_1(F,k6_qc_lang1(A),k8_qc_lang1(A,B)) => r2_funct_2(k2_valuat_1(A,C),k6_margrel1,k8_valuat_1(A,C,E,k4_cqc_lang(B,A,F,D)),k5_valuat_1(A,C,B,D,k7_valuat_1(A,C,B,E,F))) ) ) ) ) ) ) )).
fof(t6_valued_0,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ( v1_relat_1(B) & v4_valued_0(B) ) => ( r1_tarski(A,B) => v4_valued_0(A) ) ) ) )).
fof(t6_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : k1_funct_1(k24_valued_1(A,B),C) = k3_xcmplx_0(B,k1_funct_1(A,C)) ) ) )).
fof(t6_valued_2,axiom,( ! [A] : m1_subset_1(k13_valued_2(A),k1_zfmisc_1(k12_valued_2(A))) )).
fof(t6_vectmetr,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k4_vectmetr(A)),u1_struct_0(k4_vectmetr(A))) & v2_funct_2(B,u1_struct_0(k4_vectmetr(A))) & v3_vectmetr(B,k4_vectmetr(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_vectmetr(A)),u1_struct_0(k4_vectmetr(A))))) ) => k10_xtuple_0(B) = k1_euclid(A) ) ) )).
fof(t6_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( r1_vectsp_5(A,B,C,D) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ( k4_vectsp_5(A,B,E,C,D) = k1_domain_1(u1_struct_0(B),u1_struct_0(B),F,G) => E = k3_rlvect_1(B,F,G) ) ) ) ) ) ) ) ) ) )).
fof(t6_vectsp11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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) ) => ( r2_hidden(A,k2_finseq_1(B)) => k2_laplace(A,A,B,C,k3_matrix_1(C,B)) = k3_matrix_1(C,k7_nat_d(B,1)) ) ) ) ) )).
fof(t6_vectsp_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t6_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ( B != k4_struct_0(A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_algstr_0(A,B,C) != k5_struct_0(A) ) ) ) ) )).
fof(t6_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ( ( v1_vectsp_4(C,A,B) & v1_vectsp_4(D,A,B) & E = a_4_0_vectsp_4(A,B,C,D) ) => v1_vectsp_4(E,A,B) ) ) ) ) ) ) )).
fof(t6_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m1_vectsp_4(E,A,B) => k1_vectsp_5(A,B,C,k1_vectsp_5(A,B,D,E)) = k1_vectsp_5(A,B,k1_vectsp_5(A,B,C,D),E) ) ) ) ) ) )).
fof(t6_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m2_vectsp_6(C,A,B,k1_subset_1(u1_struct_0(B))) => r2_funct_2(u1_struct_0(B),u1_struct_0(A),C,k2_vectsp_6(A,B)) ) ) ) )).
fof(t6_vectsp_7,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( ( C != D & v1_vectsp_7(k7_domain_1(u1_struct_0(B),C,D),A,B) ) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t6_vectsp_8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k1_vectsp_8(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_vectsp_8(A,B))) => ! [E] : ( ( v7_vectsp_1(E,A) & m1_vectsp_4(E,A,B) ) => ! [F] : ( ( v7_vectsp_1(F,A) & m1_vectsp_4(F,A,B) ) => ( ( C = E & D = F ) => ( r3_lattices(k1_vectsp_8(A,B),C,D) <=> r1_tarski(u1_struct_0(E),u1_struct_0(F)) ) ) ) ) ) ) ) ) )).
fof(t6_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ~ ( r1_tarski(k1_vectsp_6(A,B,C),u1_struct_0(k1_vectsp_7(A,B,D))) & ! [E] : ( m2_vectsp_6(E,A,B,D) => k4_vectsp_6(A,B,C) != k4_vectsp_6(A,B,E) ) ) ) ) ) ) )).
fof(t6_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( 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_1(A,B,k20_valued_1(A,k1_numbers,k1_numbers,C,D),E),k3_vfunct_1(A,B,C,k3_vfunct_1(A,B,D,E))) ) ) ) ) ) )).
fof(t6_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( 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),k1_vfunct_2(A,B,k19_valued_1(A,k2_numbers,k2_numbers,C,D),E),k1_vfunct_2(A,B,C,k1_vfunct_2(A,B,D,E))) ) ) ) ) ) )).
fof(t6_waybel10,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( m1_yellow_0(C,A) => ! [D] : ( ( 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)))) ) => ( k2_tmap_1(A,B,D,C) = k5_relset_1(u1_struct_0(A),u1_struct_0(B),D,u1_struct_0(C)) & ! [E] : ( r2_hidden(E,u1_struct_0(C)) => k1_funct_1(k2_tmap_1(A,B,D,C),E) = k1_funct_1(D,E) ) ) ) ) ) ) )).
fof(t6_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v12_waybel_0(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( r2_hidden(B,C) => r1_tarski(k5_waybel_0(A,B),C) ) ) ) ) )).
fof(t6_waybel12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v12_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => r2_hidden(k3_yellow_0(A),B) ) ) )).
fof(t6_waybel13,axiom,( ! [A] : ( ( 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] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & v7_yellow_0(B,A) & v4_waybel_0(B,A) & m1_yellow_0(B,A) ) => v2_waybel_8(B) ) ) )).
fof(t6_waybel14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v13_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( r2_hidden(k2_yellow_0(A,B),B) => B = k6_waybel_0(A,k2_yellow_0(A,B)) ) ) ) )).
fof(t6_waybel15,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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) & v23_waybel_0(C,A,B) ) => ( v3_waybel_1(k1_waybel_1(A,B,C,D),A,B) & v3_waybel_1(k1_waybel_1(B,A,D,C),B,A) ) ) ) ) ) ) )).
fof(t6_waybel16,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k7_lattice3(A)))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k7_lattice3(A)))) => ( ( B = D & C = E ) => k4_yellow_4(A,B,C) = k2_yellow_4(k7_lattice3(A),D,E) ) ) ) ) ) ) )).
fof(t6_waybel17,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_waybel17(A,B,C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k3_waybel17(A,B,C))) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( ( F = D & G = k1_nat_1(F,1) & G = E ) => ( ( k2_waybel_0(A,k3_waybel17(A,B,C),D) = B => k2_waybel_0(A,k3_waybel17(A,B,C),E) = C ) & ( k2_waybel_0(A,k3_waybel17(A,B,C),D) = C => k2_waybel_0(A,k3_waybel17(A,B,C),E) = B ) ) ) ) ) ) ) ) ) ) )).
fof(t6_waybel18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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))))) ) => ( v5_pre_topc(D,A,k3_waybel18(B,C)) <=> ! [E] : ( m1_subset_1(E,B) => v5_pre_topc(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)),A,k4_waybel18(B,C,E)) ) ) ) ) ) ) )).
fof(t6_waybel19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & v1_waybel19(A) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(B,A) => v13_waybel_0(B,A) ) ) ) )).
fof(t6_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ( r1_yellow_0(A,k1_xboole_0) => v1_yellow_0(A) ) ) )).
fof(t6_waybel21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ 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] : ( ( 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] : ( ( 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) => ( ( v17_waybel_0(E,A,B) => v17_waybel_0(F,C,D) ) & ( v22_waybel_0(E,A,B) => v22_waybel_0(F,C,D) ) ) ) ) ) ) ) ) ) ) )).
fof(t6_waybel22,axiom,( ! [A] : ( ( ~ 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) ) => ( ~ v2_struct_0(k1_yellow_1(k8_waybel_0(A))) & v4_yellow_0(k1_yellow_1(k8_waybel_0(A)),k2_yellow_1(u1_struct_0(A))) & v7_yellow_0(k1_yellow_1(k8_waybel_0(A)),k2_yellow_1(u1_struct_0(A))) & v4_waybel_0(k1_yellow_1(k8_waybel_0(A)),k2_yellow_1(u1_struct_0(A))) & m1_yellow_0(k1_yellow_1(k8_waybel_0(A)),k2_yellow_1(u1_struct_0(A))) ) ) )).
fof(t6_waybel23,axiom,( ! [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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_yellow_1(k7_waybel_0(A))))) => k1_yellow_0(k1_yellow_1(k7_waybel_0(A)),B) = k3_waybel_0(A,k11_waybel_0(A,k1_waybel23(A,B))) ) ) )).
fof(t6_waybel24,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_yellow_1(u1_struct_0(A),B)))) => ( v1_funct_1(k1_yellow_0(k5_yellow_1(u1_struct_0(A),B),C)) & v1_funct_2(k1_yellow_0(k5_yellow_1(u1_struct_0(A),B),C),u1_struct_0(A),u1_struct_0(B)) & m1_subset_1(k1_yellow_0(k5_yellow_1(u1_struct_0(A),B),C),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) ) ) ) )).
fof(t6_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( ( v2_waybel18(A) & r2_borsuk_3(A,B) ) => v2_waybel18(B) ) ) ) )).
fof(t6_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => r5_waybel_1(k1_yellow_1(u1_pre_topc(A)),k1_waybel26(A,k9_waybel18)) ) )).
fof(t6_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( ( 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)))) ) => u1_struct_0(k1_waybel28(A,B,C)) = u1_struct_0(B) ) ) ) )).
fof(t6_waybel29,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( l1_orders_2(C) => ! [D] : ( ( 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) => ! [E] : ( ( 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)))) ) => ( v23_waybel_0(E,B,C) => ! [F] : ( ( 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_relset_1(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)) => v23_waybel_0(F,A,C) ) ) ) ) ) ) ) ) ) )).
fof(t6_waybel30,axiom,( ! [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) & l1_waybel_9(A) ) => ! [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) ) => ! [C] : ( ( v2_pre_topc(C) & v2_waybel19(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)) ) ) ) ) )).
fof(t6_waybel31,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_yellow_0(B) & v1_lattice3(B) & v3_waybel_3(B) & l1_orders_2(B) ) => ( k1_yellow_1(u1_pre_topc(A)) = B => ( v8_struct_0(A) | k2_waybel23(A) = k1_waybel31(B) ) ) ) ) )).
fof(t6_waybel32,axiom,( ! [A] : ( ( ~ 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) ) => v2_waybel32(A) ) )).
fof(t6_waybel33,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( l1_waybel_0(C,A) => ! [D] : ~ ( r2_hidden(k4_tarski(C,D),k3_waybel28(A)) & ! [E] : ( ( ~ v2_struct_0(E) & v4_orders_2(E) & v6_waybel_0(E,B) & v7_waybel_0(E) & l1_waybel_0(E,B) ) => ~ ( r2_hidden(k4_tarski(E,D),k3_waybel28(B)) & g1_orders_2(u1_struct_0(C),u1_orders_2(C)) = g1_orders_2(u1_struct_0(E),u1_orders_2(E)) & r1_funct_2(u1_struct_0(C),u1_struct_0(A),u1_struct_0(E),u1_struct_0(B),u1_waybel_0(A,C),u1_waybel_0(B,E)) ) ) ) ) ) ) ) )).
fof(t6_waybel34,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => v3_waybel_1(k1_waybel_1(A,A,k3_struct_0(A),k3_struct_0(A)),A,A) ) )).
fof(t6_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & v3_waybel_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( ( 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_yellow_0(B,C) & k2_yellow_0(B,C) = k2_yellow_0(A,C) ) ) ) ) ) ) )).
fof(t6_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ( r5_waybel_1(A,B) => r5_waybel_1(B,A) ) ) ) )).
fof(t6_waybel_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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)))) ) => k3_tarski(a_2_2_waybel_2(A,B)) = k4_yellow_4(A,k4_yellow_3(A,A,B),k5_yellow_3(A,A,B)) ) ) )).
fof(t6_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( r1_waybel_3(A,B,C) & r1_waybel_3(A,C,B) ) => B = C ) ) ) ) )).
fof(t6_waybel_4,axiom,( ! [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] : ( ( v1_waybel_4(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ( ( v1_waybel_4(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ( v1_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)))) ) ) ) ) )).
fof(t6_waybel_5,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,C,k7_funcop_1(A,B)) => ! [E] : ( r2_hidden(E,A) => ( v1_funct_1(k1_funct_1(D,E)) & v1_funct_2(k1_funct_1(D,E),k1_funct_1(C,E),B) & m1_subset_1(k1_funct_1(D,E),k1_zfmisc_1(k2_zfmisc_1(k1_funct_1(C,E),B))) ) ) ) ) )).
fof(t6_waybel_6,axiom,( ! [A] : ( ( 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] : ( ( v13_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v1_waybel_6(B,A) <=> B = k3_tarski(a_2_0_waybel_6(A,B)) ) ) ) )).
fof(t6_waybel_7,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(A)))) => ( v12_waybel_0(B,k2_yellow_1(A)) <=> ! [C] : ! [D] : ( ( r1_tarski(C,D) & r2_hidden(D,B) ) => r2_hidden(C,B) ) ) ) )).
fof(t6_waybel_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_tarski(k2_waybel_8(A,B),k1_waybel_3(A,B)) ) ) )).
fof(t6_waybel_9,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k7_relset_1(u1_struct_0(A),u1_struct_0(A),k4_waybel_1(A,B),k6_waybel_0(A,B)) = k6_domain_1(u1_struct_0(A),B) ) ) )).
fof(t6_weddwitt,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m2_finseq_1(C,B) => ( ( v2_funct_1(C) & k2_relset_1(B,C) = B ) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( k3_finseq_1(D) = k3_finseq_1(C) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k4_finseq_1(D)) => k1_funct_1(D,E) = k1_card_1(k1_funct_1(C,E)) ) ) ) => k5_card_1(A) = k2_wsierp_1(D) ) ) ) ) ) ) )).
fof(t6_wellfnd1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v2_wellfnd1(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))) ) ) ) )).
fof(t6_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ( v2_wellord1(A) => ! [B] : ~ ( r1_tarski(B,k1_relat_1(A)) & B != k1_xboole_0 & ! [C] : ~ ( r2_hidden(C,B) & ! [D] : ( r2_hidden(D,B) => r2_hidden(k4_tarski(C,D),A) ) ) ) ) ) )).
fof(t6_wsierp_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( k3_int_2(B,C) = 1 & k3_int_2(A,C) = 1 ) => k3_int_2(k3_xcmplx_0(B,A),C) = 1 ) ) ) ) )).
fof(t6_xboole_0,axiom,( ! [A] : ! [B] : ~ ( r2_xboole_0(A,B) & ! [C] : ~ ( r2_hidden(C,B) & ~ r2_hidden(C,A) ) ) )).
fof(t6_xboole_1,axiom,( ! [A] : ! [B] : k2_xboole_0(A,k2_xboole_0(A,B)) = k2_xboole_0(A,B) )).
fof(t6_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k4_xboolean(A,k5_xboolean(A,B)) = A ) ) )).
fof(t6_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( k3_xcmplx_0(A,B) = k5_numbers & A != k5_numbers & B != k5_numbers ) ) ) )).
fof(t6_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(A,B) <=> r1_xxreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C)) ) ) ) ) )).
fof(t6_xregular,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( r2_hidden(B,A) & ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ( r2_hidden(C,D) & r2_hidden(D,E) & r2_hidden(E,F) & r2_hidden(F,G) & r2_hidden(G,B) ) => r1_xboole_0(C,A) ) ) ) )).
fof(t6_xtuple_0,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(k4_tarski(A,B),C) => r2_hidden(A,k3_tarski(k3_tarski(C))) ) )).
fof(t6_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ( r1_xxreal_0(A,k2_xxreal_0) => A = k2_xxreal_0 ) ) )).
fof(t6_xxreal_1,axiom,( ! [A] : ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ~ ( r2_hidden(A,k1_xxreal_1(B,C)) & ~ r2_hidden(A,k3_xxreal_1(B,C)) & A != B ) ) ) )).
fof(t6_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ( r1_tarski(B,A) => ! [C] : ( m1_xxreal_2(C,A) => m1_xxreal_2(C,B) ) ) ) ) )).
fof(t6_xxreal_3,axiom,( k2_xxreal_3(k1_xxreal_0) = k2_xxreal_0 )).
fof(t6_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v2_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & v2_yellow_0(B) & l1_orders_2(B) ) => ! [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))) ) ) ) ) )).
fof(t6_yellow11,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r3_orders_2(A,k13_lattice3(A,k12_lattice3(A,B,C),k12_lattice3(A,B,D)),k12_lattice3(A,B,k13_lattice3(A,C,D))) ) ) ) ) )).
fof(t6_yellow12,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(B)) => k7_relat_1(k13_funct_3(k10_funct_3(A,B),k9_funct_3(A,B)),k8_mcart_1(A,B,C,D)) = k8_mcart_1(B,A,D,C) ) ) )).
fof(t6_yellow13,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k3_waybel_0(B,k7_relset_1(u1_struct_0(A),u1_struct_0(B),C,D)),k3_waybel_0(B,k7_relset_1(u1_struct_0(A),u1_struct_0(B),C,k3_waybel_0(A,D)))) ) ) ) ) )).
fof(t6_yellow14,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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(A) ) ) ) ) )).
fof(t6_yellow15,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m2_finseq_1(C,k6_margrel1) => k3_finseq_1(k1_yellow15(A,k12_finseq_1(k1_zfmisc_1(A),B),C)) = 1 ) ) )).
fof(t6_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_yellow_0(B,A) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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_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)) => ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A)) & v11_quantal1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) ) ) ) ) )).
fof(t6_yellow17,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ! [E] : ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k1_funct_1(A,D))) => ( ( r2_hidden(E,k1_funct_1(A,C)) & r2_hidden(B,k4_card_3(A)) ) => ( C = D | ( r2_hidden(B,k8_relat_1(k12_card_3(A,D),F)) <=> r2_hidden(k1_funct_7(B,C,E),k8_relat_1(k12_card_3(A,D),F)) ) ) ) ) ) ) )).
fof(t6_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l2_altcat_1(B) ) => ( r2_yellow18(A,B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => m1_subset_1(C,u1_struct_0(B)) ) ) ) ) )).
fof(t6_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => m1_yellow19(k2_relset_1(u1_struct_0(A),u1_waybel_0(A,k4_waybel_9(A,B,C))),A,B) ) ) ) )).
fof(t6_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ( v21_functor0(C,A,B) => ! [D] : ( ( v15_functor0(D,B,A) & m2_functor0(D,B,A) ) => ( ( ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => k3_functor0(A,B,C,k3_functor0(B,A,D,E)) = E ) & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( k1_altcat_1(B,E,F) != k1_xboole_0 => ! [G] : ( m1_subset_1(G,k1_altcat_1(B,E,F)) => k6_functor0(A,B,C,k3_functor0(B,A,D,E),k3_functor0(B,A,D,F),k6_functor0(B,A,D,E,F,G)) = G ) ) ) ) ) => g2_functor0(B,A,u1_functor0(B,A,D),u2_functor0(B,A,D)) = k15_functor0(A,B,C) ) ) ) ) ) ) )).
fof(t6_yellow21,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_funct_1(C) ) => ! [D] : ( v1_relat_1(D) => ( r2_hidden(k4_tarski(A,B),k3_relat_1(k3_relat_1(C,D),k2_funct_1(C))) <=> ( r2_hidden(A,k9_xtuple_0(C)) & r2_hidden(B,k9_xtuple_0(C)) & r2_hidden(k4_tarski(k1_funct_1(C,A),k1_funct_1(C,B)),D) ) ) ) ) )).
fof(t6_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r2_lattice3(A,k1_xboole_0,B) & r1_lattice3(A,k1_xboole_0,B) ) ) ) )).
fof(t6_yellow_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_lattice3(k1_yellow_1(A)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(A))) => r1_tarski(k2_xboole_0(B,C),k10_lattice3(k1_yellow_1(A),B,C)) ) ) ) ) )).
fof(t6_yellow_2,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( ( v4_yellow_0(C,A) & m1_yellow_0(C,A) ) => ( r1_tarski(u1_struct_0(B),u1_struct_0(C)) => r1_relset_1(u1_struct_0(B),u1_struct_0(B),u1_orders_2(B),u1_orders_2(C)) ) ) ) ) )).
fof(t6_yellow_3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(B,C) => r1_tarski(k3_waybel_0(A,B),k3_waybel_0(A,C)) ) ) ) ) )).
fof(t6_yellow_4,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r2_yellow_4(A,B,k1_struct_0(A)) ) ) )).
fof(t6_yellow_5,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t6_yellow_6,axiom,( ! [A] : ( l1_orders_2(A) => ( v4_yellow_0(A,A) & m1_yellow_0(A,A) ) ) )).
fof(t6_yellow_7,axiom,( ! [A] : ( l1_orders_2(A) => ( v4_orders_2(A) <=> v4_orders_2(k7_lattice3(A)) ) ) )).
fof(t6_yellow_8,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => k8_setfam_1(u1_struct_0(A),k7_setfam_1(u1_struct_0(A),B)) = k3_subset_1(u1_struct_0(A),k5_setfam_1(u1_struct_0(A),B)) ) ) )).
fof(t6_yellow_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( u1_struct_0(k2_yellow_9(A,B)) = B & v4_yellow_0(k2_yellow_9(A,B),A) & m1_yellow_0(k2_yellow_9(A,B),A) & ! [C] : ( m1_subset_1(C,u1_struct_0(k2_yellow_9(A,B))) => k2_waybel_0(A,k2_yellow_9(A,B),C) = C ) ) ) ) )).
fof(t6_zf_colla,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ( ( r2_hidden(D,C) & r2_hidden(C,k1_zf_colla(A,B)) ) => ( r2_hidden(D,k1_zf_colla(A,B)) & ? [E] : ( v3_ordinal1(E) & r2_hidden(E,B) & r2_hidden(D,k1_zf_colla(A,E)) ) ) ) ) ) ) ) )).
fof(t6_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ! [D] : ( ( v8_zf_fund1(B,A) & r2_hidden(C,B) & r2_hidden(D,B) ) => ( r2_hidden(k2_tarski(C,D),B) & r2_hidden(k4_tarski(C,D),B) ) ) ) ) )).
fof(t6_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ~ ( v8_zf_lang(A) & ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => A != k10_zf_lang(B,C) ) ) ) & ( ? [B] : ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) & ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & A = k10_zf_lang(B,C) ) ) => v8_zf_lang(A) ) & ~ ( v9_zf_lang(A) & ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => A != k11_zf_lang(B,C) ) ) ) & ( ? [B] : ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) & ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & A = k11_zf_lang(B,C) ) ) => v9_zf_lang(A) ) & ~ ( v10_zf_lang(A) & ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => A != k12_zf_lang(B,C) ) ) ) & ( ? [B] : ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) & ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & A = k12_zf_lang(B,C) ) ) => v10_zf_lang(A) ) & ~ ( v11_zf_lang(A) & ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => A != k13_zf_lang(B,C) ) ) ) & ( ? [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) & ? [C] : ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) & A = k13_zf_lang(B,C) ) ) => v11_zf_lang(A) ) ) ) )).
fof(t6_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( k25_zf_lang(k11_zf_lang(A,B)) = A & k26_zf_lang(k11_zf_lang(A,B)) = B ) ) ) )).
fof(t6_zf_model,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( 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(C,A)) & ! [E] : ( ( 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] : ( m2_subset_1(F,k4_ordinal1,k1_zf_lang) => ( k3_funct_2(k1_zf_lang,A,E,F) != k3_funct_2(k1_zf_lang,A,D,F) => B = F ) ) => r2_hidden(E,k5_zf_model(C,A)) ) ) ) <=> r2_hidden(D,k5_zf_model(k8_zf_lang(B,C),A)) ) ) ) ) ) )).
fof(t6_zf_refle,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ( r2_hidden(k4_ordinal1,A) => v1_zf_model(A) ) ) )).
fof(t6_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ~ ( k2_tarski(A,B) = k2_tarski(C,D) & A != C & A != D ) )).
fof(t6_zfmodel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_ordinal1(A) => ( r2_zf_model(A,k9_zf_model) <=> ? [B] : ( m1_subset_1(B,A) & B != k1_xboole_0 & ! [C] : ( m1_subset_1(C,A) => ~ ( r2_hidden(C,B) & ! [D] : ( m1_subset_1(D,A) => ~ ( r2_xboole_0(C,D) & r2_hidden(D,B) ) ) ) ) ) ) ) ) )).
fof(t6_zfmodel2,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,D) => ! [F] : ( m1_subset_1(F,D) => ! [G] : ( m1_subset_1(G,D) => ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,k1_zf_lang,D) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang,D))) ) => ~ ( A != B & B != C & C != A & ~ ( r2_funct_2(k1_zf_lang,D,k2_zf_lang1(D,k2_zf_lang1(D,k2_zf_lang1(D,H,A,E),B,F),C,G),k2_zf_lang1(D,k2_zf_lang1(D,k2_zf_lang1(D,H,C,G),B,F),A,E)) & r2_funct_2(k1_zf_lang,D,k2_zf_lang1(D,k2_zf_lang1(D,k2_zf_lang1(D,H,A,E),B,F),C,G),k2_zf_lang1(D,k2_zf_lang1(D,k2_zf_lang1(D,H,B,F),C,G),A,E)) ) ) ) ) ) ) ) ) ) ) )).
fof(t6_zfrefle1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ? [B] : ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) & k2_zf_model(B) = k1_xboole_0 & ! [C] : ( ~ v1_xboole_0(C) => ( r2_zf_model(C,B) <=> r2_zf_model(C,A) ) ) ) ) )).
fof(t6_zmodul01,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => k1_zmodul01(B,k4_algstr_0(B,C),A) = k4_algstr_0(B,k1_zmodul01(B,C,A)) ) ) ) )).
fof(t6_zmodul02,axiom,( ! [A] : ( ( ~ 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_int_3) & v9_vectsp_1(A,k1_int_3) & v10_vectsp_1(A,k1_int_3) & v11_vectsp_1(A,k1_int_3) & l1_vectsp_1(A,k1_int_3) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k17_zmodul02(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k17_zmodul02(A))) => ( ( B = D & C = E ) => ( k3_rlvect_1(A,B,C) = k3_rlvect_1(k17_zmodul02(A),D,E) & k5_algstr_0(A,B,C) = k5_algstr_0(k17_zmodul02(A),D,E) ) ) ) ) ) ) ) )).
fof(t6_zmodul03,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( r1_xboole_0(k18_zmodul02(A,B),k2_relset_1(u1_struct_0(A),C)) => k4_rlvect_1(A,k20_zmodul02(A,C,B)) = k4_struct_0(A) ) ) ) ) )).
fof(t70_abcmiz_0,axiom,( ! [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) & l3_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A))) ) => ( ! [D] : ( 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) ) => D = C ) ) => ! [D] : ( ( 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) ) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,k3_finseq_1(D)) ) => r2_hidden(k4_tarski(k1_funct_1(k7_abcmiz_0(A,B,D),k1_nat_1(E,1)),k1_funct_1(k7_abcmiz_0(A,B,D),E)),k11_abcmiz_0(A)) ) ) ) ) ) ) ) ) )).
fof(t70_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ~ ( k2_msualg_1(A,B) = k6_abcmiz_1 & k1_msualg_1(A,B) = k1_xboole_0 & ! [C] : ( m1_abcmiz_1(C,A,k12_abcmiz_1(A)) => ~ ( C = k1_trees_4(k4_tarski(B,u1_struct_0(A))) & v9_abcmiz_1(C,A) ) ) ) ) ) )).
fof(t70_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => k64_valued_1(A) = k5_numbers ) )).
fof(t70_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_valued_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_finset_1(B) & v6_membered(B) ) => ! [C] : ( ( v1_finset_1(C) & v6_membered(C) ) => ( r1_afinsq_2(B,C) => k7_afinsq_2(k5_afinsq_2(A,k2_xboole_0(B,C))) = k2_xcmplx_0(k7_afinsq_2(k5_afinsq_2(A,B)),k7_afinsq_2(k5_afinsq_2(A,C))) ) ) ) ) )).
fof(t70_analmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( v4_analmetr(B,A) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r6_analmetr(A,C,D,B) & r2_hidden(D,B) ) ) ) ) ) ) )).
fof(t70_aofa_000,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_freealg(A) ) => ( k18_aofa_000(k7_freealg(k19_aofa_000,A)) = k12_freealg(k19_aofa_000,A) & k1_card_1(A) = k1_card_1(k12_freealg(k19_aofa_000,A)) ) ) )).
fof(t70_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( m1_subset_1(C,k5_arytm_3) => ~ ( ~ r3_arytm_3(B,A) & ~ r3_arytm_3(C,B) & r3_arytm_3(C,A) ) ) ) ) )).
fof(t70_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r1_xxreal_0(C,B) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,A,C)) ) ) => r1_xxreal_0(k5_numbers,k6_series_1(A,B)) ) ) ) )).
fof(t70_bcialg_1,axiom,( ! [A] : ( ( ~ 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) & v19_bcialg_1(A) & l2_bcialg_1(A) ) <=> ( v5_bcialg_1(A) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k1_bcialg_1(A,B,k1_bcialg_1(A,C,D)) = k1_bcialg_1(A,D,k1_bcialg_1(A,C,B)) & k1_bcialg_1(A,B,k4_struct_0(A)) = B ) ) ) ) ) ) ) )).
fof(t70_borsuk_5,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( B != C & k3_subset_1(u1_struct_0(A),B) = k3_subset_1(u1_struct_0(A),C) ) ) ) ) )).
fof(t70_borsuk_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_topmetr)) => ( r1_xxreal_0(A,k7_xcmplx_0(1,2)) => r2_hidden(k4_tarski(A,k5_numbers),k6_borsuk_6) ) ) )).
fof(t70_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ( v2_bvfunc_2(C,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,k7_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) )).
fof(t70_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_eqrel_1(I,A) => ! [J] : ( m1_eqrel_1(J,A) => ! [K] : ( 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,F,B) = k2_partit1(A,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),K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t70_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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,k6_bvfunc26(A,B,C)),k2_bvfunc_1(A,k1_bvfunc_1(A,B),C)) ) ) ) )).
fof(t70_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r2_hidden(B,k8_card_3(A)) & r2_hidden(C,k8_card_3(A)) ) => r2_hidden(k1_funct_4(B,C),k8_card_3(A)) ) ) ) ) )).
fof(t70_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,B,C) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(C),k7_cat_1(A,C,k9_cat_1(A,B,C,D,E)),F) = k3_funct_2(u1_struct_0(B),u1_struct_0(C),k7_cat_1(B,C,E),k3_funct_2(u1_struct_0(A),u1_struct_0(B),k7_cat_1(A,B,D),F)) ) ) ) ) ) ) )).
fof(t70_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(B)) => ! [D] : ( m2_cat_3(D,B,k3_graph_1(B,C),A) => r2_funct_2(A,u4_struct_0(k2_oppcat_1(B)),k6_cat_3(k2_oppcat_1(B),A,k4_cat_3(B,A,D),k5_oppcat_1(B,C)),k4_cat_3(B,A,k7_cat_3(B,A,D,C))) ) ) ) )).
fof(t70_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r1_cat_1(A,B,k20_cat_4(A,B,k19_cat_4(A))) & r1_cat_1(A,B,k20_cat_4(A,k19_cat_4(A),B)) ) ) ) )).
fof(t70_cfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => ( r1_xboole_0(A,k1_relset_1(B,C)) => v1_comseq_2(k2_partfun1(B,k2_numbers,C,A)) ) ) ) )).
fof(t70_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ~ ( B != C & ~ r1_chord(A,B,C) & ~ ! [D] : ( 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] : ( m3_glib_001(E,A) => ~ ( r1_glib_001(A,B,C,E) & ! [F] : ( m1_subset_1(F,k6_glib_000(A)) => ~ ( r2_hidden(F,D) & r2_hidden(F,k13_glib_001(A,E)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t70_classes1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => ( r1_ordinal1(B,k6_classes1(A)) <=> ! [C] : ( v3_ordinal1(C) => ~ ( r2_hidden(C,B) & ! [D] : ~ ( r2_hidden(D,A) & r1_ordinal1(C,k6_classes1(D)) ) ) ) ) ) )).
fof(t70_classes2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r2_hidden(A,B) <=> r2_hidden(k16_classes2(A),k16_classes2(B)) ) ) ) )).
fof(t70_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_clvect_1(C,A) => ( r1_struct_0(C,B) <=> k5_clvect_1(A,k4_algstr_0(A,B),C) = u1_struct_0(C) ) ) ) ) )).
fof(t70_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ? [D] : ( v7_ordinal1(D) & ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(D,E) => k1_normsp_1(A,B,E) = k1_normsp_1(A,C,E) ) ) ) => r2_clvect_2(A,B,C) ) ) ) ) )).
fof(t70_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => k13_cohsp_1(k13_cohsp_1(A)) = A ) )).
fof(t70_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(A,k5_numbers) => k9_complex1(A) = k4_xcmplx_0(A) ) ) )).
fof(t70_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => k4_complex2(A,B,C) = k4_complex2(k2_xcmplx_0(A,D),k2_xcmplx_0(B,D),k2_xcmplx_0(C,D)) ) ) ) ) )).
fof(t70_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k9_complex1(A),k9_complex1(B))),k9_complex1(k5_algstr_0(k1_complfld,A,B))) ) ) )).
fof(t70_complsp2,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ! [B] : ( m1_subset_1(B,k2_numbers) => ! [C] : ( m2_finseq_1(C,k2_numbers) => ! [D] : ( m2_finseq_1(D,k2_numbers) => ! [E] : ( m2_finseq_1(E,k2_numbers) => ( ( k3_finseq_1(C) = k3_finseq_1(D) & k3_finseq_1(D) = k3_finseq_1(E) ) => k8_complsp2(C,k7_seq_4(k10_seq_4(D,A),k10_seq_4(E,B))) = k2_xcmplx_0(k3_xcmplx_0(k8_complex1(A),k8_complsp2(C,D)),k3_xcmplx_0(k8_complex1(B),k8_complsp2(C,E))) ) ) ) ) ) ) )).
fof(t70_comput_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_comput_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_comput_1(k4_ordinal1))) ) => r2_hidden(k1_xboole_0,A) ) )).
fof(t70_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ~ ( ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,A,C) = k1_power(C,k9_nat_1(k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,B),C)) ) & ? [C] : ( v7_ordinal1(C) & ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => r1_xxreal_0(1,k9_nat_1(k1_numbers,A,D)) ) ) ) & v1_series_1(k55_valued_1(k4_ordinal1,k2_numbers,B)) ) ) ) )).
fof(t70_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( B = a_3_4_convex4(A,C,D) => v2_convex4(B,A) ) ) ) ) ) )).
fof(t70_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ( ~ r2_hidden(D,k24_qc_lang1(A,B)) => ( v2_cqc_the1(k9_cqc_lang(A,B,k11_cqc_lang(A,D,C)),A) <=> v2_cqc_the1(k11_cqc_lang(A,D,k9_cqc_lang(A,B,C)),A) ) ) ) ) ) ) )).
fof(t70_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k6_clvect_1(A,B,k4_xcmplx_0(k6_complex1)),k5_vfunct_1(k4_ordinal1,A,B)) ) ) )).
fof(t70_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(A,k9_xtuple_0(k27_sin_cos)) & r2_hidden(B,k9_xtuple_0(k27_sin_cos)) ) => k9_diff_1(k27_sin_cos,A,B) = k4_xcmplx_0(k7_xcmplx_0(k17_sin_cos(k6_xcmplx_0(A,B)),k3_xcmplx_0(k3_xcmplx_0(k17_sin_cos(A),k17_sin_cos(B)),k6_xcmplx_0(A,B)))) ) ) ) )).
fof(t70_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k7_xcmplx_0(1,k1_square_1(k17_sin_cos(D))) ) => ( k17_sin_cos(B) = k5_numbers | k17_sin_cos(k2_xcmplx_0(B,A)) = k5_numbers | k1_funct_1(k3_diff_1(C,A),B) = k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(16,k19_sin_cos(k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(2,B),A),2))),k17_sin_cos(k7_xcmplx_0(k4_xcmplx_0(A),2))),k19_sin_cos(k7_xcmplx_0(k4_xcmplx_0(A),2))),k17_sin_cos(k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(2,B),A),2))),k1_square_1(k6_xcmplx_0(k19_sin_cos(k2_xcmplx_0(k3_xcmplx_0(2,B),A)),k19_sin_cos(A)))) ) ) ) ) ) )).
fof(t70_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_enumset1(A,B,C,D) = k2_enumset1(B,D,C,A) )).
fof(t70_eqrel_1,axiom,( ! [A] : ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ! [D] : ! [E] : ( ( r2_hidden(C,D) & r2_hidden(D,B) & r2_hidden(C,E) & r2_hidden(E,B) ) => D = E ) ) )).
fof(t70_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ( k22_rvsum_1(A,A) = k5_numbers <=> A = k16_euclid(3) ) ) )).
fof(t70_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ~ ( r2_hidden(B,E) & r2_hidden(C,E) & r2_hidden(D,E) & B != C & ! [F] : ( v1_xreal_0(F) => k8_euclid(A,D,B) != k9_euclid(A,k8_euclid(A,C,B),F) ) ) ) ) ) ) ) )).
fof(t70_exchsort,axiom,( ! [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) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_exchsort(B) ) => ! [C] : ( m1_subset_1(C,k9_xtuple_0(B)) => ! [D] : ( m1_subset_1(D,k9_xtuple_0(B)) => ! [E] : ( m1_subset_1(E,k9_xtuple_0(B)) => ( ( r2_hidden(C,D) & r2_hidden(D,E) ) => ( k1_binop_1(k7_exchsort(A,B,C,D),C,E) = k4_tarski(D,E) & k1_binop_1(k7_exchsort(A,B,C,D),D,E) = k4_tarski(C,E) ) ) ) ) ) ) ) )).
fof(t70_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k14_facirc_1(A,B,C),k16_facirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ( ( E = k1_funct_1(D,B) & F = k1_funct_1(D,C) ) => k1_funct_1(k6_circuit2(k14_facirc_1(A,B,C),k16_facirc_1(A,B,C),D),k4_tarski(k10_finseq_1(B,C),k3_facirc_1)) = k10_margrel1(E,F) ) ) ) ) )).
fof(t70_fdiff_11,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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,k2_sin_cos9),k1_taylor_1(A)),k7_xcmplx_0(1,A)))) & r1_tarski(B,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r1_xxreal_0(A,k5_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,k2_sin_cos9),k1_taylor_1(A)),k7_xcmplx_0(1,A)),B) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => k1_funct_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,k2_sin_cos9),k1_taylor_1(A)),k7_xcmplx_0(1,A)),B),C) = k7_xcmplx_0(1,k3_xcmplx_0(k3_prepower(k1_funct_1(k2_sin_cos9,C),k2_xcmplx_0(A,1)),k2_xcmplx_0(1,k1_square_1(C)))) ) ) ) ) ) ) ) )).
fof(t70_fib_num2,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => m1_pythtrip(k8_domain_1(k4_ordinal1,k2_nat_1(k1_pre_ff(A),k1_pre_ff(k1_nat_1(A,3))),k2_nat_1(k2_nat_1(2,k1_pre_ff(k1_nat_1(A,1))),k1_pre_ff(k1_nat_1(A,2))),k1_nat_1(k1_pepin(k1_pre_ff(k1_nat_1(A,1))),k1_pepin(k1_pre_ff(k1_nat_1(A,2)))))) ) )).
fof(t70_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v2_struct_0(C) & v10_lattices(C) & v3_filter_0(C) & l3_lattices(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( ( ~ v1_xboole_0(E) & v19_lattices(E,C) & v20_lattices(E,C) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( r1_filter_0(C,E,D,D) & r1_filter_0(A,B,F,F) ) ) ) ) ) ) ) )).
fof(t70_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v20_lattices(B,A) & v21_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => k10_filter_2(A,B) = k11_filter_2(k1_lattice2(A),k10_filter_2(k1_lattice2(A),k3_filter_2(A,B))) ) ) )).
fof(t70_finseq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ( ( v1_relat_1(I) & v1_funct_1(I) & v1_finseq_1(I) ) => ( I = 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)) => ( k3_finseq_1(I) = 8 & k1_funct_1(I,1) = A & k1_funct_1(I,2) = B & k1_funct_1(I,3) = C & k1_funct_1(I,4) = D & k1_funct_1(I,5) = E & k1_funct_1(I,6) = F & k1_funct_1(I,7) = G & k1_funct_1(I,8) = H ) ) ) )).
fof(t70_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ! [E] : ( ( 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] : ( m2_finseq_1(F,A) => ! [G] : ( m2_finseq_1(G,B) => ( ( k3_finseq_1(F) = k3_finseq_1(G) & D = k3_funcop_1(E,F,G) ) => ( k3_finseq_1(D) = k3_finseq_1(F) & k3_finseq_1(D) = k3_finseq_1(G) ) ) ) ) ) ) ) ) ) )).
fof(t70_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k1_finseq_3(A,k10_xtuple_0(A)) = k1_xboole_0 ) )).
fof(t70_finseq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ( m2_finseq_1(D,C) => ( r2_hidden(A,k4_finseq_1(k17_finseq_1(C,B,D))) => k7_partfun1(C,k17_finseq_1(C,B,D),A) = k7_partfun1(C,D,A) ) ) ) ) )).
fof(t70_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m2_finseq_1(D,B) => k10_xtuple_0(k5_finseq_5(B,D,C,A)) = k2_xboole_0(k1_tarski(C),k10_xtuple_0(D)) ) ) ) ) )).
fof(t70_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r2_hidden(B,k10_xtuple_0(C)) => k10_xtuple_0(C) = k2_xboole_0(k10_xtuple_0(k1_finseq_5(A,C,B)),k10_xtuple_0(k2_finseq_5(A,C,B))) ) ) ) ) )).
fof(t70_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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] : ( ( 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) ) => k3_funct_2(A,A,k9_funcop_1(A,A,D,k6_partfun1(A),B),k4_binop_1(A,C)) = k4_binop_1(A,C) ) ) ) ) ) )).
fof(t70_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_catalan2(A))) => r1_tarski(k4_subset_1(k3_catalan2(A),k8_flang_1(A,B),k8_flang_1(A,C)),k8_flang_1(A,k4_subset_1(k3_catalan2(A),B,C))) ) ) )).
fof(t70_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => r1_tarski(k8_flang_1(A,k7_flang_1(A,B,C)),k8_flang_1(A,k1_flang_2(A,B,C,D))) ) ) ) ) )).
fof(t70_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => k6_flang_1(A,B,k2_flang_3(A,B)) = k6_flang_1(A,k2_flang_3(A,B),B) ) )).
fof(t70_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r2_hidden(A,k2_tarski(B,k1_funct_1(C,B))) & v1_partit_2(C) & r2_hidden(B,k9_xtuple_0(C)) ) => k2_tarski(A,k1_funct_1(C,A)) = k2_tarski(B,k1_funct_1(C,B)) ) ) )).
fof(t70_funcop_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( m1_subset_1(E,C) => k2_binop_1(B,C,k1_tarski(A),k7_funcop_1(k2_zfmisc_1(B,C),A),D,E) = A ) ) ) ) )).
fof(t70_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( r1_xboole_0(B,C) => r1_xboole_0(k8_relat_1(A,B),k8_relat_1(A,C)) ) ) )).
fof(t70_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ~ ( ( B = k1_xboole_0 => A = k1_xboole_0 ) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ? [E] : ( r2_hidden(E,k1_relset_1(A,C)) & k1_funct_1(D,E) != k1_funct_1(C,E) ) ) ) ) )).
fof(t70_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => k3_relat_1(k13_funct_3(B,D),k15_funct_3(A,C)) = k13_funct_3(k3_relat_1(B,A),k3_relat_1(D,C)) ) ) ) ) )).
fof(t70_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( r1_tarski(k9_xtuple_0(A),k2_xboole_0(B,C)) => k1_funct_4(k5_relat_1(A,B),k5_relat_1(A,C)) = A ) ) )).
fof(t70_funct_7,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v7_ordinal1(B) => k8_funct_7(A,k1_nat_1(B,1)) = k3_relat_1(k8_funct_7(A,B),A) ) ) )).
fof(t70_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ( r1_tarski(A,k1_relset_1(k1_numbers,k26_sin_cos)) => r2_funct_8(A,k1_numbers,k1_numbers,k26_sin_cos) ) ) )).
fof(t70_fvaluat1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_fvaluat1(D,B) => ( ( v3_fvaluat1(B) & m1_subset_1(C,u1_struct_0(k7_fvaluat1(B,D))) ) => m1_subset_1(k1_binop_1(k4_group_1(B),C,A),u1_struct_0(k7_fvaluat1(B,D))) ) ) ) ) ) )).
fof(t70_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v3_group_1(B) & v5_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => k10_fvsum_1(A,B,D,C) = k12_fvsum_1(A,B,k5_finseq_2(u1_struct_0(B),A,C),D) ) ) ) ) )).
fof(t70_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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) & ~ ( r2_hidden(A,k2_msafree2(k25_gfacirc1(A,B,C))) & r2_hidden(B,k2_msafree2(k25_gfacirc1(A,B,C))) & r2_hidden(C,k2_msafree2(k25_gfacirc1(A,B,C))) ) ) )).
fof(t70_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ( r2_hidden(B,k37_glib_000(A,C)) <=> ? [D] : r2_glib_000(A,C,B,D) ) ) ) )).
fof(t70_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( r1_xxreal_0(C,k3_finseq_1(B)) => k5_glib_001(A,B,C) = k1_funct_1(k11_glib_001(A,B),k3_nat_d(k1_nat_1(C,1),2)) ) ) ) ) )).
fof(t70_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( v15_algstr_0(C) & v1_group_3(C,A) & m1_group_2(C,A) ) => ! [D] : ( ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) ) => ? [E] : ( 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_group_11(A,B,E),k9_subset_1(u1_struct_0(A),k11_group_2(A,D,k4_group_11(A,B,C)),k11_group_2(A,C,k4_group_11(A,B,D)))) ) ) ) ) ) )).
fof(t70_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v8_struct_0(B) & v15_algstr_0(B) & m1_group_2(B,A) ) => ( k7_group_1(B) = 1 => r1_group_2(A,B,k6_group_2(A)) ) ) ) )).
fof(t70_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v15_algstr_0(C) & m1_group_2(C,A) ) => ( k6_group_3(A,C,B) = A => C = A ) ) ) ) )).
fof(t70_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => r1_funct_2(k2_zfmisc_1(u1_struct_0(k11_group_4(A)),u1_struct_0(k11_group_4(A))),u1_struct_0(k11_group_4(A)),k2_zfmisc_1(k1_group_3(A),k1_group_3(A)),k1_group_3(A),u2_lattices(k11_group_4(A)),k9_group_4(A)) ) )).
fof(t70_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( v15_algstr_0(C) & v1_group_3(C,A) & m1_group_2(C,A) ) => ! [D] : ( ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) ) => r1_group_2(A,k8_group_5(A,k8_group_4(A,B,C),D),k8_group_4(A,k8_group_5(A,B,D),k8_group_5(A,C,D))) ) ) ) ) )).
fof(t70_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => r2_group_6(k6_group_2(A),k6_group_2(B)) ) ) )).
fof(t70_group_9,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( m1_group_9(D,A,C) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t70_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_algstr_0(A) & v4_rlvect_1(A) & v2_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => k10_ideal_1(A,B,k4_struct_0(A)) = k6_domain_1(u1_struct_0(A),k4_struct_0(A)) ) ) )).
fof(t70_int_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(C,A) & r1_xxreal_0(C,B) & k3_int_1(A) = k3_int_1(B) ) => ( r1_xxreal_0(k2_xcmplx_0(C,1),A) | r1_xxreal_0(k2_xcmplx_0(C,1),B) | A = B ) ) ) ) ) )).
fof(t70_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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(k4_xcmplx_0(1),1)) & C = k47_valued_1(k1_numbers,k1_numbers,k1_numbers,D,E) & E = k1_taylor_1(2) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,B) => ( k1_funct_1(D,F) = 1 & ~ r1_xxreal_0(k1_funct_1(C,F),k5_numbers) & F != k5_numbers ) ) ) & k9_xtuple_0(k3_sin_cos6) = B & r1_tarski(B,k9_xtuple_0(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k3_sin_cos6),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(k7_xcmplx_0(1,2)))))) ) => k2_integra5(A,k3_sin_cos6) = k6_xcmplx_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k3_sin_cos6),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(k7_xcmplx_0(1,2)))),k2_seq_4(A)),k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k3_sin_cos6),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k4_taylor_1(k7_xcmplx_0(1,2)))),k3_seq_4(A))) ) ) ) ) ) ) )).
fof(t70_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)) => k2_integra5(A,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)) = 2 ) ) )).
fof(t70_integra9,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k1_relset_1(k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k2_fdiff_9))) => ( r2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k2_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k2_fdiff_9),A),B) = k7_xcmplx_0(k1_funct_1(k18_sin_cos,B),k1_square_1(k1_funct_1(k16_sin_cos,B))) ) ) ) ) ) )).
fof(t70_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m2_interva1(B,A) => r2_interva1(A,k17_interva1(A,k23_interva1(A),B),B) ) ) )).
fof(t70_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => ( ( r2_hidden(B,k11_intpro_1(A)) & r2_hidden(k3_intpro_1(B,C),k11_intpro_1(A)) ) => r2_hidden(C,k11_intpro_1(A)) ) ) ) ) )).
fof(t70_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ! [B] : ( ( 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,k5_jgraph_4(A)) & v5_pre_topc(B,k15_euclid(2),k15_euclid(2)) ) ) ) ) )).
fof(t70_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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 & k18_euclid(D) = H & 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(C),H) & r1_xxreal_0(E,k17_euclid(D)) & r1_xxreal_0(k17_euclid(D),F) & k1_funct_1(I,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t70_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m3_topgrp_1(B,k15_euclid(2)) => v1_topreal2(k7_relset_1(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),B,A)) ) ) )).
fof(t70_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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))))) ) => ! [C] : ( v1_xreal_0(C) => ~ ( v5_pre_topc(B,k5_topmetr,k15_euclid(A)) & r1_xxreal_0(k12_euclid(k10_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)),B,k5_numbers)),C) & r1_xxreal_0(C,k12_euclid(k10_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)),B,1))) & ! [D] : ( m1_subset_1(D,u1_struct_0(k5_topmetr)) => k12_euclid(k10_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)),B,D)) != C ) ) ) ) ) )).
fof(t70_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => k39_glib_000(k26_lexbfs(A)) = k15_glib_000(A) ) )).
fof(t70_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v4_limfunc1(B) & ! [C] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ r1_xxreal_0(D,C) & r2_hidden(D,k1_relset_1(k1_numbers,A)) ) ) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k3_limfunc1(C))) => r1_xxreal_0(k1_funct_1(B,D),k1_funct_1(A,D)) ) ) ) ) | v4_limfunc1(A) ) ) ) ) )).
fof(t70_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,A) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(C,D) & ~ r1_xxreal_0(D,A) & r2_hidden(D,k1_relset_1(k1_numbers,B)) & k1_funct_1(B,D) != k5_numbers ) ) ) ) => ( ( ~ r5_limfunc2(B,A) & ~ r6_limfunc2(B,A) ) | ( r4_limfunc2(k6_rfunct_1(k1_numbers,k1_numbers,B),A) & k2_limfunc2(k6_rfunct_1(k1_numbers,k1_numbers,B),A) = k5_numbers ) ) ) ) ) )).
fof(t70_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r3_limfunc3(B,A) & v6_limfunc1(C) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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))) ) ) ) ) ) ) ) => ( r1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) & k1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k5_limfunc1(C) ) ) ) ) ) )).
fof(t70_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ( r3_cqc_the1(A,C,k6_cqc_lang(A,k6_cqc_lang(A,B))) <=> r3_cqc_the1(A,C,B) ) ) ) ) )).
fof(t70_mathmorp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( r2_hidden(k4_struct_0(k15_euclid(A)),D) => k9_subset_1(u1_struct_0(k15_euclid(A)),k7_mathmorp(k15_euclid(A),B,C,D),B) = k1_xboole_0 ) ) ) ) ) )).
fof(t70_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( ( v3_matrix10(B) & r2_matrix10(D,C) ) => r2_matrix10(k4_matrix10(A,D,B),C) ) ) ) ) ) )).
fof(t70_matrix13,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ( ( r1_tarski(k2_zfmisc_1(C,D),k2_matrix_0(B)) & k5_card_1(C) = k5_card_1(D) ) => k12_matrix_3(k5_card_1(C),A,k7_matrix13(u1_struct_0(A),B,C,D)) = k12_matrix_3(k5_card_1(D),A,k7_matrix13(u1_struct_0(A),k4_matrix_0(u1_struct_0(A),B),D,C)) ) ) ) ) ) )).
fof(t70_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( m1_vectsp_4(C,B,k6_prvect_1(B,A)) => ? [D] : ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),k1_vectsp_9(B,C),A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) & ? [E] : ( v1_finset_1(E) & v1_setfam_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) & r1_tarski(E,k2_finseq_1(A)) & k1_vectsp_9(B,C) = k5_card_1(E) & k6_matrix13(u1_struct_0(B),D,k2_finseq_1(k1_vectsp_9(B,C)),E) = k3_matrix_1(B,k1_vectsp_9(B,C)) & k8_matrix13(B,D) = k1_vectsp_9(B,C) & m1_vectsp_7(k9_matrix13(B,k1_vectsp_9(B,C),A,D),B,C) ) ) ) ) ) )).
fof(t70_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( ( r2_hidden(C,k2_finseq_1(k1_matrix_0(B))) & k1_matrix_0(B) = k1_nat_1(F,1) & r2_hidden(E,k4_finseq_1(B)) & r1_xxreal_0(C,D) & r1_xxreal_0(D,F) ) => ( r1_xxreal_0(F,k5_numbers) | ( k3_matrix_0(A,k16_matrix_0(C,A,B),E,D) = k3_matrix_0(A,B,E,k1_nat_1(D,1)) & r2_hidden(k1_nat_1(D,1),k2_finseq_1(k1_matrix_0(B))) ) ) ) ) ) ) ) ) ) )).
fof(t70_matrixj1,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ! [E] : ( ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(A))) ) => k25_matrixj1(A,k5_matrixj1(u1_struct_0(A),B,D),k5_matrixj1(u1_struct_0(A),C,E)) = k5_matrixj1(u1_struct_0(A),k3_matrix_3(A,B,C),k3_matrix_3(A,D,E)) ) ) ) ) ) )).
fof(t70_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => k1_matrixr2(A,k4_matrixr2(A),B) = B ) ) )).
fof(t70_mcart_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r2_hidden(B,A) => ( r2_hidden(k1_xtuple_0(B),k9_xtuple_0(A)) & r2_hidden(k2_xtuple_0(B),k10_xtuple_0(A)) ) ) ) )).
fof(t70_measure6,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ! [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))) ) => ! [D] : ( v1_xreal_0(D) => k8_relset_1(A,k1_numbers,k9_valued_1(A,k1_numbers,C,D),B) = k8_relset_1(A,k1_numbers,C,k1_measure6(B,k4_xcmplx_0(D))) ) ) ) )).
fof(t70_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => k5_member_1(k9_member_1(A,B)) = k11_member_1(k5_member_1(A),B) ) ) )).
fof(t70_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => k10_memstr_0(A,B,k1_funct_4(C,k7_memstr_0(A,B,D)),E) = k1_funct_4(C,k7_memstr_0(A,B,k7_nat_d(D,E))) ) ) ) ) ) )).
fof(t70_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( r1_mesfunc2(A,B,D) & r1_mesfunc2(A,B,E) & v6_supinf_2(D) & v6_supinf_2(E) & ! [F] : ( r2_hidden(F,k1_relset_1(A,k4_mesfunc1(A,D,E))) => r1_xxreal_0(k1_funct_1(E,F),k1_funct_1(D,F)) ) ) => r1_xxreal_0(k5_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,E,k1_relset_1(A,k4_mesfunc1(A,D,E)))),k5_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,k1_relset_1(A,k4_mesfunc1(A,D,E))))) ) ) ) ) ) ) )).
fof(t70_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( r2_mesfunc6(A,B,C) => r2_mesfunc6(A,B,k2_partfun1(A,k1_numbers,C,D)) ) ) ) ) ) )).
fof(t70_mmlquery,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( l1_mmlquery(C) => ! [D] : ( m2_finseq_1(D,u1_mmlquery(C)) => ( r1_xxreal_0(A,B) => r1_tarski(k35_mmlquery(C,D,A),k35_mmlquery(C,D,B)) ) ) ) ) ) )).
fof(t70_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k25_modelc_2(k43_modelc_2)) => ( r7_modelc_2(C,k3_modelc_2(k5_modelc_2(A,B))) <=> r7_modelc_2(C,k4_modelc_2(k3_modelc_2(A),k3_modelc_2(B))) ) ) ) ) )).
fof(t70_modelc_3,axiom,( ! [A] : ( m1_subset_1(A,k25_modelc_2(k43_modelc_2)) => ! [B] : ( ( v1_modelc_2(B) & v5_modelc_3(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_3(C,B) & l1_modelc_3(C,B) ) => ( r8_modelc_2(A,k14_modelc_3(B,C)) => r8_modelc_2(k29_modelc_2(k43_modelc_2,A,1),k14_modelc_3(B,k12_modelc_3(B,C))) ) ) ) ) )).
fof(t70_monoid_0,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & m2_monoid_0(B,k12_monoid_0(A)) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k6_algstr_0(B,C,D) = k3_relat_1(C,D) ) ) ) )).
fof(t70_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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_msafree4(B,u1_struct_0(A)) ) => ! [C] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( m2_pboole(D,u1_struct_0(A),B,k7_funcop_1(u1_struct_0(A),k4_ordinal1)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,k1_msafree3(A,B)),E)) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,k3_equation(A)),E)) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,k3_equation(A)),E)) => ( ( G = k6_msafree4(A,B,D,F) & H = k6_msafree4(A,B,D,k3_funct_2(k1_funct_1(u3_msualg_1(A,k1_msafree3(A,B)),E),k1_funct_1(u3_msualg_1(A,C),E),k2_msafree4(u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,C),k4_msafree4(A,B,C),E),F)) ) => r1_equation(A,C,E,k5_equation(A,E,G,H)) ) ) ) ) ) ) ) ) ) )).
fof(t70_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(k6_xcmplx_0(A,1),k4_nat_d(B,A)) => k4_nat_d(k1_nat_1(B,1),A) = k1_nat_1(k4_nat_d(B,A),1) ) ) ) )).
fof(t70_ncfcont1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(B)))) ) => ( r9_ncfcont1(C,B,E,D) => r9_ncfcont1(C,B,k2_vfunct_2(u1_struct_0(C),B,E,A),D) ) ) ) ) ) )).
fof(t70_newton,axiom,( ! [A] : ( v7_ordinal1(A) => r1_tarski(k9_newton(A),k2_finseq_1(A)) ) )).
fof(t70_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v9_o_ring_1(B,A) & v3_o_ring_1(C,A) ) => v13_o_ring_1(k6_algstr_0(A,B,C),A) ) ) ) ) )).
fof(t70_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_oppcat_1(A))) => k4_cat_1(k2_oppcat_1(A),B) = k4_cat_1(A,k4_oppcat_1(A,B)) ) ) )).
fof(t70_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => r1_tarski(A,k2_zfmisc_1(k1_relat_1(A),k1_relat_1(A))) ) )).
fof(t70_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ( k6_ordinal3(k1_xboole_0,A) = k1_xboole_0 & k7_ordinal3(k1_xboole_0,A) = k1_xboole_0 & k7_ordinal3(A,k1_xboole_0) = A ) ) )).
fof(t70_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r2_hidden(B,C) => k12_ordinal6(B,k12_ordinal6(C,A)) = k12_ordinal6(C,A) ) ) ) ) )).
fof(t70_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( r2_hidden(D,k5_partfun1(A,B,C)) => v1_partfun1(D,A) ) ) ) )).
fof(t70_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => r6_pboole(A,k4_pboole(A,B,k3_pboole(A,B,C)),k4_pboole(A,B,C)) ) ) )).
fof(t70_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( 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,k20_valued_1(k1_euclid(3),k1_numbers,k1_numbers,k1_pdiff_3(2,3,B),k1_pdiff_3(2,3,C)),A) ) ) ) ) )).
fof(t70_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ! [C] : ( ( ~ v1_xboole_0(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ( ( v1_pdiff_7(B,A) & r1_tarski(k1_rvsum_1(C),k2_finseq_1(A)) & r4_pdiff_9(A,B,C,D) & r4_pdiff_9(A,B,C,E) ) => ( r4_pdiff_9(A,B,C,k3_valued_1(k1_euclid(A),k1_numbers,k1_numbers,D,E)) & r2_relset_1(k1_euclid(A),k1_numbers,k5_pdiff_9(A,B,C,k3_valued_1(k1_euclid(A),k1_numbers,k1_numbers,D,E)),k3_valued_1(k1_euclid(A),k1_numbers,k1_numbers,k5_pdiff_9(A,B,C,D),k5_pdiff_9(A,B,C,E))) ) ) ) ) ) ) ) )).
fof(t70_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => k15_polyform(A,k7_polyform(A),1) = A ) )).
fof(t70_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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),k4_ordinal1,k4_finseq_2(2,k15_pre_poly(A)),k21_pre_poly(A,C),B) = k10_finseq_1(D,E) => ( r1_xxreal_0(B,1) | r1_xxreal_0(k3_finseq_1(k21_pre_poly(A,C)),B) | ( D != k16_pre_poly(A) & E != k16_pre_poly(A) ) ) ) ) ) ) ) ) )).
fof(t70_prepower,axiom,( ! [A] : ( ( v5_relat_1(A,k3_numbers) & v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v5_relat_1(B,k3_numbers) & v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( v2_comseq_2(A) & v2_comseq_2(B) & k1_seq_2(A) = k1_seq_2(B) ) => ( r1_xxreal_0(C,k5_numbers) | ( v2_comseq_2(k5_prepower(C,A)) & v2_comseq_2(k5_prepower(C,B)) & k1_seq_2(k5_prepower(C,A)) = k1_seq_2(k5_prepower(C,B)) ) ) ) ) ) ) )).
fof(t70_prob_3,axiom,( ! [A] : ! [B] : ( ( ~ 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_xboole_0(B) & v1_prob_1(B,A) & v4_prob_1(B,A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) <=> ( v2_prob_3(B,A) & v3_prob_3(B,A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ) )).
fof(t70_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,A) & v1_funct_1(E) & v1_partfun1(E,A) ) => ( ( r6_pboole(A,k3_pboole(A,B,C),k1_pboole(A)) | r6_pboole(A,k3_pboole(A,D,E),k1_pboole(A)) ) => r6_pboole(A,k3_pboole(A,k6_pboole(A,B,D),k6_pboole(A,C,E)),k1_pboole(A)) ) ) ) ) ) )).
fof(t70_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ( r2_qc_lang2(A,k14_qc_lang1(A,B,C),D) => ( r3_qc_lang2(A,B,D) & r3_qc_lang2(A,C,D) ) ) ) ) ) ) )).
fof(t70_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => k6_qc_lang3(A,k2_qc_lang2(A,B,C)) = k4_subset_1(k4_qc_lang1(A),k6_qc_lang3(A,B),k6_qc_lang3(A,C)) ) ) ) )).
fof(t70_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => ! [D] : ( v1_quaterni(D) => k22_quaterni(k25_quaterni(k25_quaterni(A,B),C),D) = k22_quaterni(k25_quaterni(k25_quaterni(D,C),B),A) ) ) ) ) )).
fof(t70_quaterni,axiom,( k28_quaterni(k11_quaterni) = 1 )).
fof(t70_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => ( r1_tarski(B,C) => r1_tarski(k5_relat_1(B,A),k5_relat_1(C,A)) ) ) ) )).
fof(t70_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(C))) => ! [G] : ( ( ~ v2_struct_0(G) & l1_rewrite3(G,F) ) => ~ ( r1_rewrite1(k1_rewrite3(C,F,G),k4_tarski(A,D),k4_tarski(B,E)) & ! [H] : ( m1_subset_1(H,k8_afinsq_1(C)) => D != k1_flang_1(C,H,E) ) ) ) ) ) ) ) )).
fof(t70_rfunct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) ) => ( v1_seq_2(k5_relat_1(B,A)) <=> ? [C] : ( v1_xreal_0(C) & ! [D] : ( r2_hidden(D,k3_xboole_0(A,k9_xtuple_0(B))) => r1_xxreal_0(k1_funct_1(B,D),C) ) ) ) ) )).
fof(t70_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ! [D] : ( m1_subset_1(D,A) => ( ( v1_finset_1(k1_relset_1(A,k2_partfun1(A,k1_numbers,B,C))) & r2_hidden(D,k1_relset_1(A,k2_partfun1(A,k1_numbers,B,C))) & k1_funct_1(k20_rfunct_3(A,B,C),k3_finseq_1(k20_rfunct_3(A,B,C))) = k1_funct_1(B,D) ) => k20_rfunct_3(A,B,C) = k7_finseq_1(k20_rfunct_3(A,B,k6_subset_1(C,k1_tarski(D))),k9_finseq_1(k1_funct_1(B,D))) ) ) ) ) )).
fof(t70_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v8_valued_0(A) => r2_funct_2(k4_ordinal1,k1_numbers,k4_rinfsup1(A),A) ) ) )).
fof(t70_rlaffin1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v1_rlaffin1(E,B) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) ) => ( ( r2_hidden(C,k4_rlaffin1(B,E)) & r2_hidden(D,k4_rlaffin1(B,E)) ) => r1_rlvect_2(B,k5_rlaffin1(B,E,k3_rlvect_1(B,k1_rlvect_1(B,C,k6_xcmplx_0(1,A)),k1_rlvect_1(B,D,A))),k7_rlvect_2(B,k8_rlvect_2(B,k6_xcmplx_0(1,A),k5_rlaffin1(B,E,C)),k8_rlvect_2(B,A,k5_rlaffin1(B,E,D)))) ) ) ) ) ) ) )).
fof(t70_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m2_rlsub_1(C,A,B) => ( v1_rlsub_1(C,A) <=> C = u1_struct_0(B) ) ) ) ) )).
fof(t70_rltopsp1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_rltopsp1(A,B,B) = k6_domain_1(u1_struct_0(A),B) ) ) )).
fof(t70_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( k4_rlvect_1(A,k3_finseq_4(u1_struct_0(A),k4_struct_0(A),k4_struct_0(A),B)) = B & k4_rlvect_1(A,k3_finseq_4(u1_struct_0(A),k4_struct_0(A),B,k4_struct_0(A))) = B & k4_rlvect_1(A,k3_finseq_4(u1_struct_0(A),B,k4_struct_0(A),k4_struct_0(A))) = B ) ) ) )).
fof(t70_rlvect_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => k4_vectsp_1(A,C,B,k4_rlvect_1(C,k2_finseq_4(u1_struct_0(C),D,E))) = k3_rlvect_1(C,k4_vectsp_1(A,C,B,D),k4_vectsp_1(A,C,B,E)) ) ) ) ) ) )).
fof(t70_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => m2_rmod_2(u1_struct_0(C),A,B,C) ) ) ) )).
fof(t70_rmod_4,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ~ ( k10_rmod_4(A,B,C) = k1_rmod_2(A,B) & C != k1_xboole_0 & C != k6_domain_1(u1_struct_0(B),k4_struct_0(B)) ) ) ) ) )).
fof(t70_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( m2_rusub_1(B,A,k2_rusub_1(A)) => B = u1_struct_0(A) ) ) ) )).
fof(t70_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => k12_rvsum_1(k14_rvsum_1(A,B)) = k14_rvsum_1(k12_rvsum_1(A),k12_rvsum_1(B)) ) ) )).
fof(t70_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ~ r1_xxreal_0(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B)),D) => k3_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),D)) = k3_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),D)) ) ) ) ) ) ) )).
fof(t70_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => ( ( A = B & v2_extpro_1(A,k7_card_1(2),k1_ami_3) ) => v2_extpro_1(B,k7_card_1(3),k1_scmfsa_2) ) ) ) )).
fof(t70_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmpds_2)) ) => ~ v2_extpro_1(k7_scmpds_2(C,A,B),2,k1_scmpds_2) ) ) ) )).
fof(t70_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ( r1_xxreal_0(k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),E)),k5_numbers) => ( r1_scmpds_6(k7_scmpds_6(D,E,C),B,A) & r2_scmpds_6(k7_scmpds_6(D,E,C),B,A) ) ) ) ) ) ) ) )).
fof(t70_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v11_scmyciel(A) ) => ! [B] : ( ( v1_finset_1(B) & v10_scmyciel(B,A) & m1_eqrel_1(B,k3_tarski(A)) ) => ! [C] : ~ ( r2_hidden(C,B) & k5_card_1(B) = k10_scmyciel(A) & ! [D] : ( m1_subset_1(D,k3_tarski(A)) => ~ ( r2_hidden(D,C) & ! [E] : ( m1_card_lar(E,k3_tarski(A),B) => ~ ( E != C & ! [F] : ( m1_subset_1(F,k3_tarski(A)) => ~ ( r2_hidden(F,k4_scmyciel(A,D)) & r2_hidden(F,E) ) ) ) ) ) ) ) ) ) )).
fof(t70_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r3_semi_af1(A,B,C,E,F) & r3_semi_af1(A,C,D,F,G) ) => r3_semi_af1(A,B,D,E,G) ) ) ) ) ) ) ) ) )).
fof(t70_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => k16_seq_4(A,k17_seq_4(A,B,C)) = k17_seq_4(A,C,B) ) ) ) )).
fof(t70_setlim_1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => r1_tarski(k3_kurato_0(A,C),k4_kurato_0(A,C)) ) ) )).
fof(t70_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => r1_tarski(k5_subset_1(A,k4_kurato_0(A,B),k4_kurato_0(A,C)),k4_kurato_0(A,k4_setlim_2(A,B,C))) ) ) )).
fof(t70_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,B,B),B)) = k5_sheffer1(A,C,C) ) ) ) )).
fof(t70_sin_cos,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k26_sin_cos,k1_rcomp_1(k5_numbers,1))) )).
fof(t70_sin_cos6,axiom,( k2_sin_cos6(k4_xcmplx_0(1)) = k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)) )).
fof(t70_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => k1_square_1(k1_funct_1(k3_sin_cos2,A)) = k2_xcmplx_0(1,k1_square_1(k1_funct_1(k1_sin_cos2,A))) ) )).
fof(t70_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) => k1_sin_cos4(k4_sin_cos9(A)) = k7_xcmplx_0(1,A) ) ) )).
fof(t70_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(A,k28_sin_cos) => ( r1_xxreal_0(A,k7_xcmplx_0(k28_sin_cos,2)) | k6_sincos10(k1_funct_1(k1_fdiff_9,A)) = A ) ) ) )).
fof(t70_sprect_1,axiom,( ! [A] : ( ( ~ 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_relset_1(u1_struct_0(k15_euclid(2)),k1_numbers,k5_pscomp_1,k1_rltopsp1(k15_euclid(2),k10_pscomp_1(A),k11_pscomp_1(A))) = k1_rcomp_1(k9_pscomp_1(A),k7_pscomp_1(A)) ) )).
fof(t70_sprect_2,axiom,( ! [A] : ( ( ~ 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)) & 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)))) ) ) )).
fof(t70_sprect_5,axiom,( ! [A] : ( ( ~ 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)) & 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)))) ) ) )).
fof(t70_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_valuat_1(D,A,C) => ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [F] : ( m2_subset_1(F,k16_substut1(A),k38_substut1(A)) => ! [G] : ( m1_substut1(G,A,k7_sublemma(A,F,B)) => ( v3_substut1(k7_sublemma(A,F,B),A) => ( ! [H] : ( 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) ) <=> ! [H] : ( m1_subset_1(H,C) => r1_sublemma(A,F,C,k1_sublemma(A,C,E,k14_sublemma(A,C,k13_sublemma(A,F,B,G,C,E),k12_sublemma(A,C,B,H))),D) ) ) ) ) ) ) ) ) ) ) )).
fof(t70_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => r1_tarski(k9_subset_1(u1_struct_0(A),k6_setfam_1(u1_struct_0(A),B),k2_pre_topc(A,k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B)))),C) ) ) & ( B = k1_xboole_0 | ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v4_tops_1(C,A) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(D,B) => r1_tarski(C,D) ) ) ) => r1_tarski(C,k9_subset_1(u1_struct_0(A),k6_setfam_1(u1_struct_0(A),B),k2_pre_topc(A,k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B))))) ) ) ) ) ) ) )).
fof(t70_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_tex_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( D = E => k8_relset_1(u1_struct_0(A),u1_struct_0(B),C,D) = k2_pre_topc(A,E) ) ) ) ) ) ) ) )).
fof(t70_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_tsep_1(B,A) & v1_tex_2(B,A) & v1_tex_3(B,A) & m1_pre_topc(B,A) ) => ? [C] : ( ~ v2_struct_0(C) & v1_pre_topc(C) & v1_borsuk_1(C,A) & v3_tex_3(C,A) & m1_pre_topc(C,A) & r4_tsep_2(A,B,C) ) ) ) )).
fof(t70_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_tdlat_3(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( v1_tsep_1(C,A) & m1_pre_topc(C,A) ) => ( r1_tsep_1(B,C) | m1_pre_topc(B,C) ) ) ) ) )).
fof(t70_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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] : ( ( 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)))) ) => ( ( r2_funct_2(u1_struct_0(C),u1_struct_0(B),F,k2_tmap_1(A,B,E,C)) & m1_pre_topc(D,C) ) => r2_funct_2(u1_struct_0(D),u1_struct_0(B),k3_tmap_1(A,B,C,D,F),k2_tmap_1(A,B,E,D)) ) ) ) ) ) ) ) )).
fof(t70_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_tops_1(B,A) => k1_tops_1(A,k2_tops_1(A,B)) = k1_xboole_0 ) ) ) )).
fof(t70_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_tsep_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => ( v3_tops_1(C,A) <=> v3_tops_1(D,B) ) ) ) ) ) ) )).
fof(t70_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t70_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_hidden(C,B) <=> r2_hidden(k7_finseq_1(k14_trees_3(1),C),k13_trees_3(A,B)) ) ) ) ) )).
fof(t70_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( r3_tsep_1(A,C,D) => ( r1_tsep_1(C,B) | r1_tsep_1(D,B) | ( r3_tsep_1(A,k2_tsep_1(A,C,B),k2_tsep_1(A,D,B)) & r3_tsep_1(A,k2_tsep_1(A,B,C),k2_tsep_1(A,B,D)) ) ) ) ) ) ) ) )).
fof(t70_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_valued_0(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_valued_0(E) ) => k63_valued_2(k3_xboole_0(A,k9_xtuple_0(D)),k2_valued_2(k1_valued_2(B)),k63_valued_2(A,B,C,D),E) = k63_valued_2(A,B,C,k18_valued_1(D,E)) ) ) ) ) )).
fof(t70_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( v7_vectsp_1(C,A) & m1_vectsp_4(C,A,B) ) => ! [D] : ( ( v7_vectsp_1(D,A) & m1_vectsp_4(D,A,B) ) => ! [E] : ( m2_vectsp_4(E,A,B,C) => ! [F] : ( m2_vectsp_4(F,A,B,D) => ( E = F => C = D ) ) ) ) ) ) ) )).
fof(t70_waybel23,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( ( v6_waybel23(B,A) & m1_waybel23(B,A) ) => ( ! [C] : ( ( v6_waybel23(C,A) & m1_waybel23(C,A) ) => r1_tarski(B,C) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(k7_waybel_0(k5_yellow_0(A,B))))) => C = k9_subset_1(u1_struct_0(A),k1_waybel_3(A,k1_yellow_0(A,C)),B) ) ) ) ) )).
fof(t70_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ 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))) ) => r3_waybel_0(A,B,C,D) ) => v21_waybel_0(C,A,B) ) ) ) ) )).
fof(t70_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v9_waybel_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k4_yellow_0(A) = k6_waybel_1(A,B,B) ) ) ) )).
fof(t70_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ ( ~ r1_xboole_0(A,k2_xboole_0(B,C)) & r1_xboole_0(A,B) & r1_xboole_0(A,C) ) & ~ ( ~ ( r1_xboole_0(A,B) & r1_xboole_0(A,C) ) & r1_xboole_0(A,k2_xboole_0(B,C)) ) ) )).
fof(t70_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k9_xboolean(A,k7_xboolean(A,B)) = k11_xboolean(B,A) ) ) )).
fof(t70_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k7_xcmplx_0(A,4),k7_xcmplx_0(A,4)),k7_xcmplx_0(A,4)),k7_xcmplx_0(A,4)) = A ) )).
fof(t70_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(B,A) & ~ r1_xxreal_0(k5_numbers,C) & ~ r1_xxreal_0(C,D) & r1_xxreal_0(k3_xcmplx_0(B,D),k3_xcmplx_0(A,C)) ) ) ) ) ) )).
fof(t70_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( r1_xxreal_0(C,D) & k1_xxreal_1(C,D) = k3_xxreal_1(A,B) ) ) ) ) ) )).
fof(t70_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ( k1_xxreal_2(A) = k2_xxreal_2(A) => A = k1_tarski(k2_xxreal_2(A)) ) ) )).
fof(t70_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( A != k1_xxreal_0 & A != k2_xxreal_0 & k4_xxreal_3(A,B) = k2_xxreal_0 & B != k1_xxreal_0 & B != k2_xxreal_0 ) ) ) )).
fof(t70_yellow10,axiom,( ! [A] : ( ( 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] : ( ( 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) ) => ( v3_waybel_8(k3_yellow_3(A,B)) => ( v3_waybel_8(A) & v3_waybel_8(B) ) ) ) ) )).
fof(t70_yellow_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & v6_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( E = C & F = D ) => k13_lattice3(B,C,D) = k13_lattice3(A,E,F) ) ) ) ) ) ) ) )).
fof(t70_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ~ ( r3_zf_lang(A,k7_zf_lang(B,C)) & ~ r2_zf_lang(A,B) & ~ r2_zf_lang(A,C) ) ) ) ) )).
fof(t70_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => k2_zf_model(k17_zf_lang(B,C,D,A)) = k7_subset_1(k1_zf_lang,k2_zf_model(A),k1_enumset1(B,C,D)) ) ) ) ) )).
fof(t70_zfmisc_1,axiom,( ! [A] : ! [B] : k1_zfmisc_1(k3_xboole_0(A,B)) = k3_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)) )).
fof(t70_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_zmodul01(D,A) => ( r2_hidden(k3_rlvect_1(A,B,C),k5_zmodul01(A,C,D)) <=> r1_struct_0(D,B) ) ) ) ) ) )).
fof(t70_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(B,C) => m1_zmodul01(k33_zmodul02(A,B),k33_zmodul02(A,C)) ) ) ) ) )).
fof(t71_abcmiz_0,axiom,( ! [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) & l3_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A))) ) => ( ! [D] : ( 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) ) => D = C ) ) => ! [D] : ( ( 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) ) => m1_rewrite1(k4_finseq_5(u1_struct_0(A),k7_abcmiz_0(A,B,D)),k11_abcmiz_0(A)) ) ) ) ) ) ) )).
fof(t71_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ~ ( k2_msualg_1(A,B) = k7_abcmiz_1 & k1_msualg_1(A,B) = k1_xboole_0 & ! [C] : ( m1_abcmiz_1(C,A,k13_abcmiz_1(A)) => ~ ( C = k1_trees_4(k4_tarski(B,u1_struct_0(A))) & v6_abcmiz_1(C,A) ) ) ) ) ) )).
fof(t71_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => r1_xboole_0(k2_afinsq_1(A),k9_xtuple_0(k61_valued_1(B,k5_card_1(A)))) ) ) )).
fof(t71_afinsq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) => k6_afinsq_2(A,k4_afinsq_1(A),B) = k4_binop_1(A,B) ) ) ) )).
fof(t71_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => r1_tarski(k10_aofa_000(A),k18_aofa_000(A)) ) )).
fof(t71_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v21_aofa_a00(A,1,1,11) & l6_aofa_a00(A) ) => ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_aofa_a00(A,k1_funct_1(u7_aofa_a00(A),11),k10_finseq_1(B,C),D) => ( B = k37_aofa_a00(A) & ! [E] : ( ( v19_aofa_a00(E,A) & m1_subset_1(E,u1_struct_0(A)) ) => k37_aofa_a00(A) != E ) ) ) ) ) )).
fof(t71_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ( ( r2_hidden(A,k4_ordinal1) & r2_hidden(k9_arytm_3(A,B),k4_ordinal1) ) => r2_hidden(B,k4_ordinal1) ) ) ) )).
fof(t71_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r1_xxreal_0(D,C) => r1_xxreal_0(k9_nat_1(k1_numbers,A,D),k9_nat_1(k1_numbers,B,D)) ) ) => r1_xxreal_0(k6_series_1(A,C),k6_series_1(B,C)) ) ) ) ) )).
fof(t71_bcialg_1,axiom,( ! [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) ) => ( v14_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_bcialg_1(A,k2_bcialg_1(A,B),B) ) ) ) )).
fof(t71_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ( k1_numbers = k3_subset_1(u1_struct_0(k3_topmetr),A) => A = k1_xboole_0 ) ) )).
fof(t71_borsuk_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_topmetr)) => ( ~ r1_xxreal_0(k7_xcmplx_0(1,2),A) => ( ~ r2_hidden(k4_tarski(A,k5_numbers),k7_borsuk_6) & ~ r2_hidden(k4_tarski(A,k5_numbers),k8_borsuk_6) ) ) ) )).
fof(t71_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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,k7_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) )).
fof(t71_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_eqrel_1(I,A) => ! [J] : ( m1_eqrel_1(J,A) => ! [K] : ( 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,G,B) = k2_partit1(A,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),K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t71_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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,k6_bvfunc26(A,B,C)),k1_bvfunc_1(A,k5_bvfunc_1(A,B,k2_bvfunc_1(A,B,C)))) ) ) ) )).
fof(t71_card_2,axiom,( ! [A] : ( v3_ordinal1(A) => ? [B] : ( v7_ordinal1(B) & k11_ordinal2(A,k1_ordinal1(1)) = k10_ordinal2(A,B) ) ) )).
fof(t71_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ( ( r2_hidden(B,k9_xtuple_0(A)) & r2_hidden(D,k1_funct_1(A,B)) & r2_hidden(C,k9_xtuple_0(A)) & r2_hidden(E,k1_funct_1(A,C)) ) => r2_hidden(k4_funct_4(B,C,D,E),k8_card_3(A)) ) ) )).
fof(t71_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,B,C) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => k8_cat_1(A,C,k9_cat_1(A,B,C,D,E),F) = k8_cat_1(B,C,E,k8_cat_1(A,B,D,F)) ) ) ) ) ) ) )).
fof(t71_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( 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)))) ) => ( r1_cat_3(B,C,A,D) <=> r3_cat_3(k2_oppcat_1(B),k3_oppcat_1(B,C),A,k4_cat_3(B,A,D)) ) ) ) ) )).
fof(t71_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_cat_1(A,k20_cat_4(A,B,C),k20_cat_4(A,C,B)) ) ) ) )).
fof(t71_cfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => ! [D] : ( v1_xcmplx_0(D) => ( v1_comseq_2(k2_partfun1(B,k2_numbers,C,A)) => v1_comseq_2(k2_partfun1(B,k2_numbers,k25_valued_1(B,k2_numbers,C,D),A)) ) ) ) ) )).
fof(t71_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ~ ( B != C & ~ r1_chord(A,B,C) & ? [D] : ( m2_chord(D,A,B,C) & ? [E] : ( m3_glib_001(E,A) & r1_glib_001(A,B,C,E) & ! [F] : ( ( v7_ordinal1(F) & ~ v1_abian(F) ) => ~ ( ~ r1_xxreal_0(F,1) & ~ r1_xxreal_0(k3_finseq_1(E),F) & r2_hidden(k1_funct_1(E,F),D) ) ) ) ) ) ) ) ) )).
fof(t71_classes1,axiom,( ! [A] : ( k6_classes1(A) = k1_xboole_0 <=> A = k1_xboole_0 ) )).
fof(t71_classes2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( k16_classes2(A) = k16_classes2(B) => A = B ) ) ) )).
fof(t71_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_clvect_1(D,A) => ( r1_struct_0(D,B) <=> k5_clvect_1(A,C,D) = k5_clvect_1(A,k3_rlvect_1(A,C,B),D) ) ) ) ) ) )).
fof(t71_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v2_clvect_2(B,A) & r2_clvect_2(A,B,C) ) => v2_clvect_2(C,A) ) ) ) ) )).
fof(t71_cohsp_1,axiom,( k13_cohsp_1(k1_tarski(k1_xboole_0)) = k1_tarski(k1_xboole_0) )).
fof(t71_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => ( k9_complex1(A) = A | k9_complex1(A) = k4_xcmplx_0(A) ) ) )).
fof(t71_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k3_complex2(A,B) = k4_complex2(A,k5_numbers,B) ) ) )).
fof(t71_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => k9_complex1(k8_group_1(k1_complfld,A,B)) = k3_xcmplx_0(k9_complex1(A),k9_complex1(B)) ) ) )).
fof(t71_comput_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_comput_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_comput_1(k4_ordinal1))) ) => ! [B] : ( m1_comput_1(B,k3_finseq_2(k4_ordinal1),k4_ordinal1,k2_comput_1(k4_ordinal1),A) => ! [C] : ( ( v3_comput_1(C) & m2_finseq_1(C,A) ) => ( k19_margrel1(B) = k3_finseq_1(C) => r2_hidden(k3_relat_1(k5_funct_6(C),B),A) ) ) ) ) )).
fof(t71_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ~ ( ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,A,C) = k1_power(C,k9_nat_1(k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,B),C)) ) & v2_comseq_2(A) & ~ r1_xxreal_0(k1_seq_2(A),1) & v2_comseq_3(B) ) ) ) )).
fof(t71_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( B = a_3_5_convex4(A,C,D) => v2_convex4(B,A) ) ) ) ) ) )).
fof(t71_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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,k12_cqc_lang(A,D,C)),k12_cqc_lang(A,D,k7_cqc_lang(A,B,C))),A) & v2_cqc_the1(k8_cqc_lang(A,k12_cqc_lang(A,D,k7_cqc_lang(A,B,C)),k7_cqc_lang(A,B,k12_cqc_lang(A,D,C))),A) ) ) ) ) ) ) )).
fof(t71_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k4_normsp_1(A,C,B),k5_bhsp_1(A,C,k4_algstr_0(A,B))) ) ) ) )).
fof(t71_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(A,k9_xtuple_0(k2_fdiff_9)) & r2_hidden(B,k9_xtuple_0(k2_fdiff_9)) ) => k9_diff_1(k2_fdiff_9,A,B) = k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k19_sin_cos(k7_xcmplx_0(k2_xcmplx_0(B,A),2))),k17_sin_cos(k7_xcmplx_0(k6_xcmplx_0(B,A),2))),k3_xcmplx_0(k3_xcmplx_0(k17_sin_cos(B),k17_sin_cos(A)),k6_xcmplx_0(A,B))) ) ) ) )).
fof(t71_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k7_xcmplx_0(1,k1_square_1(k17_sin_cos(D))) ) => ( k17_sin_cos(B) = k5_numbers | k17_sin_cos(k6_xcmplx_0(B,A)) = k5_numbers | k1_funct_1(k4_diff_1(C,A),B) = k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(16,k19_sin_cos(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(2,B),A),2))),k17_sin_cos(k7_xcmplx_0(k4_xcmplx_0(A),2))),k19_sin_cos(k7_xcmplx_0(k4_xcmplx_0(A),2))),k17_sin_cos(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(2,B),A),2))),k1_square_1(k6_xcmplx_0(k19_sin_cos(k6_xcmplx_0(k3_xcmplx_0(2,B),A)),k19_sin_cos(A)))) ) ) ) ) ) )).
fof(t71_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_enumset1(A,B,C,D) = k2_enumset1(C,B,A,D) )).
fof(t71_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ( k12_euclid(A) = k5_numbers <=> A = k16_euclid(3) ) ) )).
fof(t71_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ( r5_euclidlp(A,B,C) => ( B = C | r1_xboole_0(B,C) ) ) ) ) ) )).
fof(t71_exchsort,axiom,( ! [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) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_exchsort(B) ) => ! [C] : ( m1_subset_1(C,k9_xtuple_0(B)) => ! [D] : ( m1_subset_1(D,k9_xtuple_0(B)) => ( r2_hidden(C,D) => v2_funct_1(k5_relat_1(k7_exchsort(A,B,C,D),k6_exchsort(A,k9_funct_7(B,C,D)))) ) ) ) ) ) )).
fof(t71_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k14_facirc_1(A,B,C),k16_facirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ( ( E = k1_funct_1(D,C) & F = k1_funct_1(D,A) ) => k1_funct_1(k6_circuit2(k14_facirc_1(A,B,C),k16_facirc_1(A,B,C),D),k4_tarski(k10_finseq_1(C,A),k3_facirc_1)) = k10_margrel1(E,F) ) ) ) ) )).
fof(t71_fdiff_11,axiom,( ! [A] : ( ( 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_cos9,k4_taylor_1(k7_xcmplx_0(1,2))),2))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) & ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & r1_xxreal_0(k1_funct_1(k1_sin_cos9,B),k5_numbers) ) ) ) => ( r2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k4_taylor_1(k7_xcmplx_0(1,2))),2),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k4_taylor_1(k7_xcmplx_0(1,2))),2),A),B) = k7_xcmplx_0(k6_prepower(k1_funct_1(k1_sin_cos9,B),k4_xcmplx_0(k7_xcmplx_0(1,2))),k2_xcmplx_0(1,k1_square_1(B))) ) ) ) ) ) )).
fof(t71_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ v1_xboole_0(D) & v19_lattices(D,A) & v20_lattices(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ( r1_filter_0(A,D,B,C) => r1_filter_0(A,D,C,B) ) ) ) ) ) )).
fof(t71_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( k10_filter_2(A,k5_filter_2(A)) = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) & k10_filter_2(A,k1_filter_0(A)) = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ) ) )).
fof(t71_finseq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ( ( v1_relat_1(J) & v1_funct_1(J) & v1_finseq_1(J) ) => ( J = 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)) => ( k3_finseq_1(J) = 9 & k1_funct_1(J,1) = A & k1_funct_1(J,2) = B & k1_funct_1(J,3) = C & k1_funct_1(J,4) = D & k1_funct_1(J,5) = E & k1_funct_1(J,6) = F & k1_funct_1(J,7) = G & k1_funct_1(J,8) = H & k1_funct_1(J,9) = I ) ) ) )).
fof(t71_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( m2_finseq_1(E,A) => ! [F] : ( m2_finseq_1(F,B) => ( k3_funcop_1(D,k6_finseq_1(A),F) = k6_finseq_1(C) & k3_funcop_1(D,E,k6_finseq_1(B)) = k6_finseq_1(C) ) ) ) ) ) ) ) )).
fof(t71_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : k1_finseq_3(k7_finseq_1(A,B),C) = k7_finseq_1(k1_finseq_3(A,C),k1_finseq_3(B,C)) ) ) )).
fof(t71_finseq_4,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(D,k2_finseq_1(C)) ) => ( r2_hidden(D,k4_finseq_1(B)) & k7_partfun1(A,k17_finseq_1(A,C,B),D) = k7_partfun1(A,B,D) ) ) ) ) ) )).
fof(t71_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m2_finseq_1(D,B) => r2_hidden(C,k10_xtuple_0(k5_finseq_5(B,D,C,A))) ) ) ) ) )).
fof(t71_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ( ( r2_hidden(B,k10_xtuple_0(D)) & r2_hidden(C,k6_subset_1(k10_xtuple_0(D),k10_xtuple_0(k1_finseq_5(A,D,B)))) ) => k2_finseq_5(A,k2_finseq_5(A,D,B),C) = k2_finseq_5(A,D,C) ) ) ) ) ) )).
fof(t71_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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) & v2_binop_1(D,B) & v1_finseqop(D,B) ) => ( r2_funct_2(A,B,k6_funcop_1(B,A,D,C,k1_partfun1(A,B,B,B,C,k5_finseqop(B,D))),k8_funcop_1(B,A,k4_binop_1(B,D))) & r2_funct_2(A,B,k6_funcop_1(B,A,D,k1_partfun1(A,B,B,B,C,k5_finseqop(B,D)),C),k8_funcop_1(B,A,k4_binop_1(B,D))) ) ) ) ) ) ) )).
fof(t71_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_catalan2(A))) => r1_tarski(k8_flang_1(A,k9_subset_1(k3_catalan2(A),B,C)),k9_subset_1(k3_catalan2(A),k8_flang_1(A,B),k8_flang_1(A,C))) ) ) )).
fof(t71_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => r1_tarski(k1_flang_2(A,k1_flang_2(A,B,E,F),C,D),k8_flang_1(A,B)) ) ) ) ) ) )).
fof(t71_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => k6_flang_1(A,k7_flang_1(A,B,C),k2_flang_3(A,B)) = k6_flang_1(A,k2_flang_3(A,B),k7_flang_1(A,B,C)) ) ) )).
fof(t71_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( v1_partit_2(C) & r2_hidden(A,k9_xtuple_0(C)) & r2_hidden(B,k9_xtuple_0(C)) ) => ( ( ~ r2_hidden(A,k2_tarski(B,k1_funct_1(C,B))) & ~ r2_hidden(k1_funct_1(C,A),k2_tarski(B,k1_funct_1(C,B))) ) | k2_tarski(A,k1_funct_1(C,A)) = k2_tarski(B,k1_funct_1(C,B)) ) ) ) )).
fof(t71_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : k1_binop_1(k13_funcop_1(A,B,C),A,B) = C )).
fof(t71_funct_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( r2_hidden(A,k10_xtuple_0(B)) <=> k8_relat_1(B,k1_tarski(A)) != k1_xboole_0 ) ) )).
fof(t71_funct_2,axiom,( ! [A] : ! [B] : r1_tarski(k1_funct_2(A,B),k4_partfun1(A,B)) )).
fof(t71_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => k3_relat_1(k15_funct_3(B,D),k15_funct_3(A,C)) = k15_funct_3(k3_relat_1(B,A),k3_relat_1(D,C)) ) ) ) ) )).
fof(t71_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : k5_relat_1(k1_funct_4(A,B),C) = k1_funct_4(k5_relat_1(A,C),k5_relat_1(B,C)) ) ) )).
fof(t71_funct_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_relat_1(B) => ( r1_tarski(k9_xtuple_0(k8_funct_7(B,A)),k1_relat_1(B)) & r1_tarski(k10_xtuple_0(k8_funct_7(B,A)),k1_relat_1(B)) ) ) ) )).
fof(t71_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ( r1_tarski(A,k1_relset_1(k1_numbers,k27_sin_cos)) => r2_funct_8(A,k1_numbers,k1_numbers,k27_sin_cos) ) ) )).
fof(t71_fvaluat1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m1_fvaluat1(C,B) => ( v3_fvaluat1(B) => ! [D] : ( m1_subset_1(D,u1_struct_0(k7_fvaluat1(B,C))) => ~ ( D != k4_struct_0(B) & k1_binop_1(k4_group_1(B),D,A) = k4_struct_0(B) ) ) ) ) ) ) )).
fof(t71_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => k4_rlvect_1(A,k8_finseq_1(u1_struct_0(A),C,k12_finseq_1(u1_struct_0(A),B))) = k1_algstr_0(A,k4_rlvect_1(A,C),B) ) ) ) )).
fof(t71_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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) & ? [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k25_gfacirc1(A,B,C),k26_gfacirc1(A,B,C)))) & ? [E] : ( m1_subset_1(E,k6_margrel1) & ? [F] : ( m1_subset_1(F,k6_margrel1) & ? [G] : ( 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(k25_gfacirc1(A,B,C),k26_gfacirc1(A,B,C),D,2),k24_gfacirc1(A,B,C)) = k9_margrel1(k2_binarith(k2_binarith(E,k9_margrel1(F)),G)) & k1_funct_1(k5_facirc_1(k25_gfacirc1(A,B,C),k26_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)) ) ) ) ) ) ) )).
fof(t71_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ( r2_hidden(B,k38_glib_000(A,C)) <=> ? [D] : r1_glib_000(A,C,B,D) ) ) ) )).
fof(t71_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k1_relset_1(k4_ordinal1,k11_glib_001(A,B))) <=> r2_hidden(k6_xcmplx_0(k2_nat_1(2,C),1),k1_relset_1(k4_ordinal1,B)) ) ) ) ) )).
fof(t71_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( v1_group_3(C,A) & m1_group_2(C,A) ) => ? [D] : ( v15_algstr_0(D) & m1_group_2(D,A) & u1_struct_0(D) = k4_group_11(A,B,C) ) ) ) ) )).
fof(t71_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => r1_ordinal1(k7_struct_0(B),k7_struct_0(A)) ) ) )).
fof(t71_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_group_2(C,A) => k17_group_2(A,C) = k17_group_2(A,k6_group_3(A,C,B)) ) ) ) )).
fof(t71_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => r1_funct_2(k2_zfmisc_1(u1_struct_0(k11_group_4(A)),u1_struct_0(k11_group_4(A))),u1_struct_0(k11_group_4(A)),k2_zfmisc_1(k1_group_3(A),k1_group_3(A)),k1_group_3(A),u1_lattices(k11_group_4(A)),k10_group_4(A)) ) )).
fof(t71_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( v15_algstr_0(C) & v1_group_3(C,A) & m1_group_2(C,A) ) => ! [D] : ( ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) ) => r1_group_2(A,k8_group_5(A,B,k8_group_4(A,C,D)),k8_group_4(A,k8_group_5(A,B,C),k8_group_5(A,B,D))) ) ) ) ) )).
fof(t71_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => r2_group_6(A,k5_group_6(A,k6_group_2(A))) ) )).
fof(t71_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( ( v2_group_9(D,A) & m1_group_9(D,A,B) ) => ! [E] : ( ( 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] : ( 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)) ) ) ) ) ) )).
fof(t71_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k10_ideal_1(A,B,k5_struct_0(A)) = B ) ) )).
fof(t71_integr11,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(B,C) & D = k47_valued_1(k1_numbers,k1_numbers,k1_numbers,E,F) & F = k1_taylor_1(2) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,C) => ( k1_funct_1(E,H) = k1_square_1(A) & ~ r1_xxreal_0(k1_funct_1(D,H),k5_numbers) & k1_funct_1(G,H) = k7_xcmplx_0(H,A) & ~ r1_xxreal_0(k1_funct_1(G,H),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(G,H)) & H != k5_numbers & ~ r1_xxreal_0(A,k5_numbers) ) ) ) & k9_xtuple_0(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,G,k3_sin_cos6)) = C & C = k9_xtuple_0(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,C),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,G,k3_sin_cos6)),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k4_taylor_1(k7_xcmplx_0(1,2))))) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,G,k3_sin_cos6),B)) ) => k2_integra5(B,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,G,k3_sin_cos6)) = k6_xcmplx_0(k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,C),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,G,k3_sin_cos6)),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k4_taylor_1(k7_xcmplx_0(1,2)))),k2_seq_4(B)),k1_funct_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,C),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,G,k3_sin_cos6)),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k4_taylor_1(k7_xcmplx_0(1,2)))),k3_seq_4(B))) ) ) ) ) ) ) ) ) )).
fof(t71_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k28_sin_cos) => k2_integra5(A,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)) = 2 ) ) )).
fof(t71_integra9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,C) & k1_relset_1(k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k2_fdiff_9)) = C & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => k1_funct_1(B,D) = k7_xcmplx_0(k1_funct_1(k18_sin_cos,D),k1_square_1(k1_funct_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) = k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k2_fdiff_9),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k2_fdiff_9),k3_seq_4(A))) ) ) ) ) )).
fof(t71_interva1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k21_interva1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k21_interva1(A))) => ! [D] : ( m2_interva1(D,A) => ! [E] : ( m2_interva1(E,A) => ( ( B = D & C = E ) => ( r3_lattices(k21_interva1(A),B,C) <=> ( r1_tarski(k14_interva1(A,D),k14_interva1(A,E)) & r1_tarski(k15_interva1(A,D),k15_interva1(A,E)) ) ) ) ) ) ) ) ) )).
fof(t71_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1)) => ( ( v9_intpro_1(A) & r1_tarski(B,A) ) => r1_tarski(k11_intpro_1(B),A) ) ) ) )).
fof(t71_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ~ v2_funct_1(k5_jgraph_4(A)) ) ) )).
fof(t71_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) = E & k17_euclid(C) = E & k18_euclid(D) = H & 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(C),H) & r1_xxreal_0(E,k17_euclid(D)) & 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t71_jordan,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( r1_jordan24(2,A,k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) => r1_tarski(A,k2_jgraph_6(k4_xcmplx_0(1),1,k4_xcmplx_0(3),3)) ) ) )).
fof(t71_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ( C = k9_finseq_1(B) => k12_euclid(C) = k9_complex1(B) ) ) ) ) )).
fof(t71_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => v3_lexbfs(k25_lexbfs(A,k26_lexbfs(A))) ) )).
fof(t71_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v5_limfunc1(B) & ! [C] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ r1_xxreal_0(D,C) & r2_hidden(D,k1_relset_1(k1_numbers,A)) ) ) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k3_limfunc1(C))) => r1_xxreal_0(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) | v5_limfunc1(A) ) ) ) ) )).
fof(t71_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_limfunc2(B,A) & k1_limfunc2(B,A) = k5_numbers ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(k6_xcmplx_0(A,C),A))) & r1_xxreal_0(k1_funct_1(B,D),k5_numbers) ) ) ) ) | r2_limfunc2(k6_rfunct_1(k1_numbers,k1_numbers,B),A) ) ) ) ) )).
fof(t71_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v3_limfunc1(A) & r1_limfunc3(B,k4_limfunc1(A)) & ! [C] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k3_limfunc1(C))) & k1_funct_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)) = k1_limfunc3(B,k4_limfunc1(A)) ) ) ) ) ) )).
fof(t71_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => k14_lpspace1(A,B,C) = k6_lpspace2(A,B,C,1) ) ) ) )).
fof(t71_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_cqc_lang(A))) => ( r3_cqc_the1(A,D,k8_cqc_lang(A,B,k6_cqc_lang(A,k6_cqc_lang(A,C)))) <=> r3_cqc_the1(A,D,k8_cqc_lang(A,B,C)) ) ) ) ) ) )).
fof(t71_mathmorp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( r2_hidden(k4_struct_0(k15_euclid(A)),C) => k8_mathmorp(k15_euclid(A),B,C,D) = B ) ) ) ) ) )).
fof(t71_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( ( v3_matrix10(B) & r1_matrix10(D,C) ) => r1_matrix10(k4_matrix10(A,D,B),C) ) ) ) ) ) )).
fof(t71_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => k12_matrix_3(A,B,k2_matrix13(A,A,B,D,C)) = k8_group_1(B,k1_laplace(B,k4_group_1(B),C,A),k12_matrix_3(A,B,D)) ) ) ) ) )).
fof(t71_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( v7_vectsp_1(C,B) & m1_vectsp_4(C,B,k6_prvect_1(B,A)) ) => ~ ( ~ r1_xxreal_0(A,k1_vectsp_9(B,C)) & ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),k7_nat_d(A,k1_vectsp_9(B,C)),A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_finset_1(E) & v1_setfam_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ~ ( k5_card_1(E) = k7_nat_d(A,k1_vectsp_9(B,C)) & r1_tarski(E,k2_finseq_1(A)) & k6_matrix13(u1_struct_0(B),D,k2_finseq_1(k7_nat_d(A,k1_vectsp_9(B,C))),E) = k3_matrix_1(B,k7_nat_d(A,k1_vectsp_9(B,C))) & C = k7_matrix15(B,D) ) ) ) ) ) ) ) )).
fof(t71_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( k1_matrix_0(B) = k1_nat_1(D,1) & r2_hidden(C,k2_finseq_1(D)) ) => ( r1_xxreal_0(D,k5_numbers) | ( k8_matrix_0(A,k16_matrix_0(1,A,B),C) = k8_matrix_0(A,B,k1_nat_1(C,1)) & r2_hidden(C,k2_finseq_1(k1_matrix_0(k16_matrix_0(1,A,B)))) & r2_hidden(k1_nat_1(C,1),k2_finseq_1(k1_matrix_0(B))) ) ) ) ) ) ) ) )).
fof(t71_matrixj1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ! [E] : ( ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(A))) ) => ! [F] : ( ( v1_matrix_0(F) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(A))) ) => ! [G] : ( ( v1_matrix_0(G) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(D) = k3_finseq_1(F) & k3_finseq_1(E) = k3_finseq_1(G) & k1_matrix_0(D) = k1_matrix_0(F) & k1_matrix_0(E) = k1_matrix_0(G) ) => k3_matrix_3(A,k13_matrixj1(u1_struct_0(A),B,k5_matrixj1(u1_struct_0(A),D,E)),k13_matrixj1(u1_struct_0(A),C,k5_matrixj1(u1_struct_0(A),F,G))) = k13_matrixj1(u1_struct_0(A),k3_rlvect_1(A,B,C),k25_matrixj1(A,k5_matrixj1(u1_struct_0(A),D,E),k5_matrixj1(u1_struct_0(A),F,G))) ) ) ) ) ) ) ) ) )).
fof(t71_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => k1_matrixr2(A,B,k4_matrixr2(A)) = B ) ) )).
fof(t71_mcart_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ! [B] : k9_relat_1(A,B) = a_2_0_mcart_1(A,B) ) )).
fof(t71_measure6,axiom,( ! [A] : ! [B] : ( ( v1_setfam_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => k8_relset_1(A,k1_numbers,k6_measure6(A,k1_numbers,C),B) = k8_relset_1(A,k1_numbers,C,k4_measure6(B)) ) ) )).
fof(t71_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => k5_member_1(k11_member_1(A,B)) = k9_member_1(k5_member_1(A),B) ) ) )).
fof(t71_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_partfun1(C,u1_struct_0(B)) ) => ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(D,k5_memstr_0(A,B,C)) => k2_xcmplx_0(k5_memstr_0(A,B,k10_memstr_0(A,B,C,D)),D) = k5_memstr_0(A,B,C) ) ) ) ) ) )).
fof(t71_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( r2_mesfunc6(A,B,C) => m2_subset_1(k1_relset_1(A,C),k1_zfmisc_1(A),B) ) ) ) ) )).
fof(t71_mmlquery,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_mmlquery(C) & l1_mmlquery(C) ) => ! [D] : ( m2_finseq_1(D,u1_mmlquery(C)) => ( r1_xxreal_0(A,B) => r1_tarski(k36_mmlquery(C,D,A),k36_mmlquery(C,D,B)) ) ) ) ) ) )).
fof(t71_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k25_modelc_2(k43_modelc_2)) => ( r7_modelc_2(C,k3_modelc_2(k4_modelc_2(A,B))) <=> r7_modelc_2(C,k5_modelc_2(k3_modelc_2(A),k3_modelc_2(B))) ) ) ) ) )).
fof(t71_modelc_3,axiom,( ! [A] : ( m1_subset_1(A,k25_modelc_2(k43_modelc_2)) => ! [B] : ( ( v1_modelc_2(B) & v5_modelc_3(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r7_modelc_2(A,k6_modelc_2(B)) => r8_modelc_2(A,k14_modelc_3(B,k11_modelc_3(B))) ) ) ) )).
fof(t71_monoid_0,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & m2_monoid_0(B,k12_monoid_0(A)) ) => ( m1_subset_1(k6_partfun1(A),u1_struct_0(B)) => ( v1_group_1(B) & k4_binop_1(u1_struct_0(B),u2_algstr_0(B)) = k6_partfun1(A) ) ) ) )).
fof(t71_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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_msafree4(B,u1_struct_0(A)) ) => ! [C] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( m2_pboole(D,u1_struct_0(A),B,k7_funcop_1(u1_struct_0(A),k4_ordinal1)) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( m1_subset_1(F,k3_msualg_1(A,E,k1_msafree3(A,B))) => ! [G] : ( m1_subset_1(G,k3_msualg_1(A,E,C)) => ( k5_msualg_3(A,k1_msafree3(A,B),C,E,k4_msafree4(A,B,C),F) = G => ! [H] : ( m1_dtconstr(H,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) => ! [I] : ( m1_dtconstr(I,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) => ( ( H = k3_funct_2(k3_msualg_1(A,E,k1_msafree3(A,B)),k4_msualg_1(A,E,k1_msafree3(A,B)),k5_msualg_1(A,E,k1_msafree3(A,B)),F) & I = k3_funct_2(k3_msualg_1(A,E,C),k4_msualg_1(A,E,C),k5_msualg_1(A,E,C),G) ) => ! [J] : ( m1_subset_1(J,k1_funct_1(u3_msualg_1(A,k3_equation(A)),k2_msualg_1(A,E))) => ! [K] : ( m1_subset_1(K,k1_funct_1(u3_msualg_1(A,k3_equation(A)),k2_msualg_1(A,E))) => ( ( J = k6_msafree4(A,B,D,H) & K = k6_msafree4(A,B,D,I) ) => r1_equation(A,C,k2_msualg_1(A,E),k5_equation(A,k2_msualg_1(A,E),J,K)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t71_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ! [D] : ( ( 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) => ( r11_ncfcont1(A,k4_normsp_0(u1_struct_0(A),B,D),C) & r7_ncfcont1(A,B,k5_vfunct_1(u1_struct_0(A),B,D),C) ) ) ) ) ) )).
fof(t71_newton,axiom,( ! [A] : ( v7_ordinal1(A) => v1_finset_1(k9_newton(A)) ) )).
fof(t71_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v9_o_ring_1(B,A) & v7_o_ring_1(C,A) ) => v13_o_ring_1(k6_algstr_0(A,B,C),A) ) ) ) ) )).
fof(t71_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( ( v1_relat_2(A) & r1_tarski(B,k1_relat_1(A)) ) => k1_relat_1(k2_wellord1(A,B)) = B ) ) )).
fof(t71_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ( k6_ordinal3(A,1) = A & k7_ordinal3(A,1) = k1_xboole_0 ) ) )).
fof(t71_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r1_ordinal1(A,B) <=> r1_ordinal1(k12_ordinal6(C,A),k12_ordinal6(C,B)) ) ) ) ) )).
fof(t71_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r2_hidden(D,k5_partfun1(A,B,C)) => r1_partfun1(C,D) ) ) ) )).
fof(t71_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) <=> r6_pboole(A,k4_pboole(A,B,C),B) ) ) ) )).
fof(t71_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( 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,k20_valued_1(k1_euclid(3),k1_numbers,k1_numbers,k1_pdiff_3(2,3,B),k1_pdiff_3(2,3,C)),A) ) ) ) ) )).
fof(t71_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ! [C] : ( ( ~ v1_xboole_0(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ( ( v1_pdiff_7(B,A) & r1_tarski(k1_rvsum_1(C),k2_finseq_1(A)) & r4_pdiff_9(A,B,C,D) & r4_pdiff_9(A,B,C,E) ) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(F,k6_xcmplx_0(k3_finseq_1(C),1)) => ( r3_pdiff_9(A,B,k7_partfun1(k4_ordinal1,C,k1_nat_1(F,1)),k1_seqfunc(k1_euclid(A),k1_numbers,k4_pdiff_9(A,B,C,k47_valued_1(k1_euclid(A),k1_numbers,k1_numbers,D,E)),F)) & r2_relset_1(k1_euclid(A),k1_numbers,k1_seqfunc(k1_euclid(A),k1_numbers,k4_pdiff_9(A,B,C,k47_valued_1(k1_euclid(A),k1_numbers,k1_numbers,D,E)),F),k47_valued_1(k1_euclid(A),k1_numbers,k1_numbers,k1_seqfunc(k1_euclid(A),k1_numbers,k4_pdiff_9(A,B,C,D),F),k1_seqfunc(k1_euclid(A),k1_numbers,k4_pdiff_9(A,B,C,E),F))) ) ) ) ) ) ) ) ) ) )).
fof(t71_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k17_polyform(A,k7_polyform(A)))) => ! [C] : ( m1_subset_1(C,k8_polyform(A,k7_polyform(A))) => ( B = k1_tarski(A) => k3_bspace(B,C) = k5_struct_0(k2_bspace) ) ) ) ) )).
fof(t71_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => k21_pre_poly(A,k16_pre_poly(A)) = k3_pre_poly(k3_finseq_2(k15_pre_poly(A)),k4_pre_poly(k15_pre_poly(A),k16_pre_poly(A),k16_pre_poly(A))) ) )).
fof(t71_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k6_prepower(A,k5_numbers) = 1 ) ) )).
fof(t71_prob_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v2_prob_3(k9_setfam_1(A),A) & v3_prob_3(k9_setfam_1(A),A) & m1_subset_1(k9_setfam_1(A),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) )).
fof(t71_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( v2_relat_1(C) => ( v2_relat_1(k6_pboole(A,k1_pzfmisc1(A,B),C)) & v2_relat_1(k6_pboole(A,C,k1_pzfmisc1(A,B))) ) ) ) ) )).
fof(t71_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ( r2_qc_lang2(A,B,C) <=> r3_qc_lang2(A,B,k15_qc_lang1(A,D,C)) ) ) ) ) ) )).
fof(t71_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => k6_qc_lang3(A,k4_qc_lang2(A,B,C)) = k4_subset_1(k4_qc_lang1(A),k6_qc_lang3(A,B),k6_qc_lang3(A,C)) ) ) ) )).
fof(t71_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => ! [D] : ( v1_quaterni(D) => k23_quaterni(k25_quaterni(A,B),k25_quaterni(C,D)) = k23_quaterni(k25_quaterni(B,A),k25_quaterni(D,C)) ) ) ) ) )).
fof(t71_quaterni,axiom,( k28_quaterni(k12_quaterni) = 1 )).
fof(t71_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => k9_nat_1(k1_numbers,k7_real_3(A),k5_numbers) = k9_nat_1(k1_numbers,k4_real_3(A),k5_numbers) ) )).
fof(t71_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ! [D] : ( v1_relat_1(D) => ( ( r1_tarski(C,D) & r1_tarski(A,B) ) => r1_tarski(k5_relat_1(C,A),k5_relat_1(D,B)) ) ) ) )).
fof(t71_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k8_afinsq_1(C)) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k8_afinsq_1(C))) => ! [H] : ( ( ~ v2_struct_0(H) & l1_rewrite3(H,G) ) => ( r1_rewrite1(k1_rewrite3(C,G,H),k4_tarski(A,D),k4_tarski(B,E)) => r1_rewrite1(k1_rewrite3(C,G,H),k4_tarski(A,k1_flang_1(C,D,F)),k4_tarski(B,k1_flang_1(C,E,F))) ) ) ) ) ) ) ) )).
fof(t71_rfunct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) ) => ( v2_seq_2(k5_relat_1(B,A)) <=> ? [C] : ( v1_xreal_0(C) & ! [D] : ( r2_hidden(D,k3_xboole_0(A,k9_xtuple_0(B))) => r1_xxreal_0(C,k1_funct_1(B,D)) ) ) ) ) )).
fof(t71_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v8_valued_0(B) & v2_seq_2(B) ) => r1_xxreal_0(k3_funct_2(k4_ordinal1,k1_numbers,k3_rinfsup1(B),k1_nat_1(A,1)),k1_funct_1(B,A)) ) ) ) )).
fof(t71_rlaffin1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( v1_rlaffin1(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,k3_convex1(B,D)) => ( v2_convex1(k5_rlaffin1(B,D,A),B) & r1_xxreal_0(k5_numbers,k3_funct_2(u1_struct_0(B),k1_numbers,k5_rlaffin1(B,D,A),C)) & r1_xxreal_0(k3_funct_2(u1_struct_0(B),k1_numbers,k5_rlaffin1(B,D,A),C),1) ) ) ) ) ) )).
fof(t71_rlsub_1,axiom,( ! [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) ) => ! [B] : ( ( v1_rlvect_1(B) & m1_rlsub_1(B,A) ) => ! [C] : ( ( v1_rlvect_1(C) & m1_rlsub_1(C,A) ) => ! [D] : ( m2_rlsub_1(D,A,B) => ! [E] : ( m2_rlsub_1(E,A,C) => ( D = E => B = C ) ) ) ) ) ) )).
fof(t71_rltopsp1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(k4_struct_0(A),k1_rltopsp1(A,B,C)) & ! [D] : ( v1_xreal_0(D) => ( B != k1_rlvect_1(A,C,D) & C != k1_rlvect_1(A,B,D) ) ) ) ) ) ) )).
fof(t71_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k4_rlvect_1(A,k3_finseq_4(u1_struct_0(A),k4_struct_0(A),C,B)) = k1_algstr_0(A,C,B) & k4_rlvect_1(A,k3_finseq_4(u1_struct_0(A),C,B,k4_struct_0(A))) = k1_algstr_0(A,C,B) & k4_rlvect_1(A,k3_finseq_4(u1_struct_0(A),C,k4_struct_0(A),B)) = k1_algstr_0(A,C,B) ) ) ) ) )).
fof(t71_rlvect_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => k4_vectsp_1(A,C,B,k4_rlvect_1(C,k3_finseq_4(u1_struct_0(C),D,E,F))) = k3_rlvect_1(C,k3_rlvect_1(C,k4_vectsp_1(A,C,B,D),k4_vectsp_1(A,C,B,E)),k4_vectsp_1(A,C,B,F)) ) ) ) ) ) ) )).
fof(t71_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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) ) => m2_rmod_2(u1_struct_0(B),A,B,k2_rmod_2(A,B)) ) ) )).
fof(t71_rmod_4,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( ( v2_vectsp_2(D,A) & m1_rmod_2(D,A,B) ) => ( C = u1_struct_0(D) => ( k4_struct_0(A) = k1_group_1(A) | k10_rmod_4(A,B,C) = D ) ) ) ) ) ) )).
fof(t71_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m2_rusub_1(C,A,B) => ( r2_hidden(k4_struct_0(A),C) <=> C = u1_struct_0(B) ) ) ) ) )).
fof(t71_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( r1_xxreal_0(D,k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B))) & k3_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),D)) = k2_compos_1(k1_scmfsa_2) ) ) ) ) ) ) )).
fof(t71_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ~ ( ? [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) & k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B),k4_struct_0(k1_scmfsa_2)) = k4_card_1(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,B)) ) & v2_extpro_1(A,k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(t71_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmpds_2)) ) => ~ v2_extpro_1(k8_scmpds_2(C,A,B),2,k1_scmpds_2) ) ) ) )).
fof(t71_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ( ( 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,D),E)),k5_numbers) | k6_scmpds_4(k7_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,k1_nat_1(k5_card_1(C),1))) ) ) ) ) ) ) ) )).
fof(t71_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v12_scmyciel(A) ) => ( k11_scmyciel(A) = 1 => v5_scmyciel(A) ) ) )).
fof(t71_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r3_semi_af1(A,C,B,E,F) & r3_semi_af1(A,D,B,E,G) ) => r3_semi_af1(A,C,D,G,F) ) ) ) ) ) ) ) ) )).
fof(t71_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => k16_seq_4(A,k17_seq_4(A,B,C)) = k13_seq_4(A,k16_seq_4(A,B),C) ) ) ) )).
fof(t71_setlim_1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k3_kurato_0(A,C) = k3_subset_1(A,k4_kurato_0(A,k2_prob_1(A,C))) ) ) )).
fof(t71_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ( v3_kurato_0(B,A) | v3_kurato_0(C,A) ) => k4_kurato_0(A,k1_setlim_2(A,B,C)) = k9_subset_1(A,k4_kurato_0(A,B),k4_kurato_0(A,C)) ) ) ) )).
fof(t71_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => C = k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,B,k5_sheffer1(A,B,B))) ) ) ) )).
fof(t71_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(A,k2_rcomp_1(k5_numbers,1)) & r2_hidden(B,k2_rcomp_1(k5_numbers,1)) & k1_funct_1(k26_sin_cos,A) = k1_funct_1(k26_sin_cos,B) ) => A = B ) ) ) )).
fof(t71_sin_cos6,axiom,( k2_sin_cos6(k5_numbers) = k5_numbers )).
fof(t71_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => k1_square_1(k1_funct_1(k1_sin_cos2,A)) = k6_xcmplx_0(k1_square_1(k1_funct_1(k3_sin_cos2,A)),1) ) )).
fof(t71_sin_cos9,axiom,( r2_fdiff_1(k1_sin_cos9,k7_relset_1(k1_numbers,k1_numbers,k26_sin_cos,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(t71_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),A) => ( r1_xxreal_0(k5_numbers,A) | k7_sincos10(k1_funct_1(k2_fdiff_9,A)) = A ) ) ) )).
fof(t71_sprect_1,axiom,( ! [A] : ( ( ~ 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_relset_1(u1_struct_0(k15_euclid(2)),k1_numbers,k4_pscomp_1,k1_rltopsp1(k15_euclid(2),k11_pscomp_1(A),k12_pscomp_1(A))) = k1_rcomp_1(k6_pscomp_1(A),k8_pscomp_1(A)) ) )).
fof(t71_sprect_2,axiom,( ! [A] : ( ( ~ 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,k23_pscomp_1(k3_topreal1(2,A))),k4_finseq_4(A,k22_pscomp_1(k3_topreal1(2,A)))) ) ) )).
fof(t71_sprect_5,axiom,( ! [A] : ( ( ~ 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,k25_pscomp_1(k3_topreal1(2,A))),k4_finseq_4(A,k24_pscomp_1(k3_topreal1(2,A)))) ) ) )).
fof(t71_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [E] : ( m2_subset_1(E,k16_substut1(A),k38_substut1(A)) => ! [F] : ( m1_substut1(F,A,k7_sublemma(A,E,B)) => k1_relset_1(k3_qc_lang1(A),k13_sublemma(A,E,B,F,C,D)) = k9_xtuple_0(k7_substut1(A,B,k11_cqc_lang(A,B,k2_sublemma(A,E)),F)) ) ) ) ) ) ) )).
fof(t71_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( r1_tarski(B,k5_tdlat_1(A)) <=> v2_tdlat_2(B,A) ) ) ) )).
fof(t71_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_tex_2(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,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),D)) = k2_pre_topc(A,k6_domain_1(u1_struct_0(A),E)) ) ) ) ) ) ) ) )).
fof(t71_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ( v4_tex_3(B,A) <=> ? [C] : ( ~ v2_struct_0(C) & v1_pre_topc(C) & v1_borsuk_1(C,A) & v3_tex_3(C,A) & m1_pre_topc(C,A) & m1_pre_topc(B,C) ) ) ) ) )).
fof(t71_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_tdlat_3(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( v1_borsuk_1(C,A) & m1_pre_topc(C,A) ) => ( r1_tsep_1(B,C) | m1_pre_topc(B,C) ) ) ) ) )).
fof(t71_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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)))) ) => ( m1_pre_topc(D,C) => r2_funct_2(u1_struct_0(D),u1_struct_0(B),k3_tmap_1(A,B,C,D,k2_tmap_1(A,B,E,C)),k2_tmap_1(A,B,E,D)) ) ) ) ) ) ) )).
fof(t71_topgen_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( ( 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(a_3_0_topgen_5(A,B,C),B) & v1_cantor_1(a_3_0_topgen_5(A,B,C),B) & m1_subset_1(a_3_0_topgen_5(A,B,C),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) ) ) ) )).
fof(t71_topreal6,axiom,( ! [A] : ( ( v1_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( v2_compts_1(k4_card_3(k5_funct_4(k1_zfmisc_1(k1_numbers),1,2,A,B)),k15_euclid(2)) & 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)))) ) ) ) )).
fof(t71_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_tops_1(B,A) => ( v4_tops_1(k1_tops_1(A,B),A) & v4_tops_1(k2_pre_topc(A,B),A) ) ) ) ) )).
fof(t71_tops_3,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => ( u1_struct_0(A) = u1_struct_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D <=> k3_subset_1(u1_struct_0(A),C) = k3_subset_1(u1_struct_0(B),D) ) ) ) ) ) ) )).
fof(t71_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( ( 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) ) ) ) ) )).
fof(t71_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => r1_tarski(k2_trees_1(2),k13_trees_3(A,B)) ) ) )).
fof(t71_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( m1_pre_topc(D,A) => ! [E] : ( m1_pre_topc(E,A) => ( ( m1_pre_topc(D,B) & m1_pre_topc(E,C) & r3_tsep_1(A,B,C) ) => r3_tsep_1(A,D,E) ) ) ) ) ) ) )).
fof(t71_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_valued_0(D) ) => k9_xtuple_0(k68_valued_2(B,C,D)) = k8_subset_1(A,k1_relset_1(A,C),k9_xtuple_0(D)) ) ) ) )).
fof(t71_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => m2_vectsp_4(k6_domain_1(u1_struct_0(B),C),A,B,k1_vectsp_4(A,B)) ) ) ) )).
fof(t71_waybel23,axiom,( ! [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) & 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] : ( ( v6_waybel23(B,A) & m1_waybel23(B,A) ) => r1_tarski(u1_struct_0(k1_waybel_8(A)),B) ) ) ) ) )).
fof(t71_waybel_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => r3_waybel_0(A,B,C,D) ) & ! [D] : ( ( ~ 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) ) ) => v17_waybel_0(C,A,B) ) ) ) ) )).
fof(t71_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v9_waybel_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( k4_yellow_0(A) = k6_waybel_1(A,B,C) & k4_yellow_0(A) = k6_waybel_1(A,C,B) ) => B = C ) ) ) ) ) )).
fof(t71_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( k2_xboole_0(A,B) = k2_xboole_0(C,B) & r1_xboole_0(A,B) & r1_xboole_0(C,B) ) => A = C ) )).
fof(t71_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k9_xboolean(A,k9_xboolean(A,B)) = k11_xboolean(B,A) ) ) )).
fof(t71_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_xcmplx_0(k7_xcmplx_0(A,4),k7_xcmplx_0(A,4)) = k7_xcmplx_0(A,2) ) )).
fof(t71_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(k5_numbers,D) & k2_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,D)) = k5_numbers & A != k5_numbers & C != k5_numbers ) ) ) ) ) )).
fof(t71_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( r1_xxreal_0(C,D) & k1_xxreal_1(C,D) = k2_xxreal_1(A,B) ) ) ) ) ) )).
fof(t71_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v2_membered(C) => ( ( r1_xxreal_0(A,B) & m1_xxreal_2(A,C) ) => m1_xxreal_2(B,C) ) ) ) ) )).
fof(t71_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(k5_numbers,C) ) => r1_xxreal_0(k4_xxreal_3(A,C),k4_xxreal_3(B,C)) ) ) ) ) )).
fof(t71_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ( r3_zf_lang(B,k8_zf_lang(A,C)) => r2_zf_lang(B,C) ) ) ) ) )).
fof(t71_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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,k8_zf_lang(B,A)) <=> ! [E] : ( m1_subset_1(E,C) => r1_zf_model(C,k2_zf_lang1(C,D,B,E),A) ) ) ) ) ) ) )).
fof(t71_zfmisc_1,axiom,( ! [A] : ! [B] : r1_tarski(k1_zfmisc_1(k4_xboole_0(A,B)),k2_xboole_0(k1_tarski(k1_xboole_0),k4_xboole_0(k1_zfmisc_1(A),k1_zfmisc_1(B)))) )).
fof(t71_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_zmodul01(D,A) => ( r2_hidden(k5_algstr_0(A,C,B),k5_zmodul01(A,C,D)) <=> r1_struct_0(D,B) ) ) ) ) ) )).
fof(t71_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( k33_zmodul02(A,B) = A & r1_tarski(B,C) ) => k33_zmodul02(A,C) = A ) ) ) ) )).
fof(t72_abcmiz_0,axiom,( ! [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) & l3_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A))) ) => ( r6_abcmiz_0(A,B,C) => r1_rewrite1(k11_abcmiz_0(A),k6_abcmiz_0(A,B,C),B) ) ) ) ) )).
fof(t72_abcmiz_1,axiom,( ! [A] : ! [B] : ( ( v1_instalg1(B) & v1_abcmiz_1(B) & v3_abcmiz_1(B) & l1_msualg_1(B) ) => ( m3_abcmiz_1(A,B) <=> ? [C] : ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k38_abcmiz_1(B))) & ? [D] : ( v9_abcmiz_1(D,B) & m1_abcmiz_1(D,B,k12_abcmiz_1(B)) & A = k1_domain_1(k1_zfmisc_1(k38_abcmiz_1(B)),k3_card_3(u3_msualg_1(B,k1_msafree3(B,k28_abcmiz_1(B)))),C,D) ) ) ) ) )).
fof(t72_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r2_hidden(B,k2_afinsq_1(A)) & r2_hidden(k1_ordinal1(B),k2_afinsq_1(A)) ) ) ) )).
fof(t72_afinsq_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => k8_afinsq_2(A,k5_afinsq_1(B)) = B ) )).
fof(t72_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ( v3_freealg(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k12_aofa_000(A) != k13_aofa_000(A,C,D) & k12_aofa_000(A) != k14_aofa_000(A,B,C,D) & k12_aofa_000(A) != k16_aofa_000(A,B,C) ) ) ) ) ) ) )).
fof(t72_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( ( v3_ordinal1(B) & m1_subset_1(B,k5_arytm_3) ) => ~ ( ~ r3_arytm_3(A,B) & ~ r3_arytm_3(k9_arytm_3(B,k12_arytm_3),A) & r2_hidden(A,k4_ordinal1) ) ) ) )).
fof(t72_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( ( k9_nat_1(k1_numbers,A,k5_numbers) = k5_numbers & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ r1_xxreal_0(C,k5_numbers) => k9_nat_1(k1_numbers,A,C) = B ) ) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k6_series_1(A,C) = k3_xcmplx_0(B,C) ) ) ) ) )).
fof(t72_bcialg_1,axiom,( ! [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) ) => ( v14_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t72_borsuk_5,axiom,( ! [A] : ( ( v2_compts_1(A,k3_topmetr) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( B = A => ( v4_xxreal_2(B) & v3_xxreal_2(B) ) ) ) ) )).
fof(t72_borsuk_6,axiom,( k9_subset_1(u1_struct_0(k2_borsuk_1(k5_topmetr,k5_topmetr)),k6_borsuk_6,k8_borsuk_6) = k1_tarski(k4_tarski(k7_xcmplx_0(1,2),k5_numbers)) )).
fof(t72_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ( v2_bvfunc_2(C,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,k7_bvfunc_2(A,k7_bvfunc_2(A,B,C,E),C,D))) ) ) ) ) ) ) )).
fof(t72_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_eqrel_1(I,A) => ! [J] : ( m1_eqrel_1(J,A) => ! [K] : ( 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,H,B) = k2_partit1(A,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),K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t72_card_2,axiom,( ! [A] : ( v3_ordinal1(A) => ( v4_ordinal1(A) => k11_ordinal2(A,k1_ordinal1(1)) = A ) ) )).
fof(t72_card_3,axiom,( ! [A] : ( ( v4_funct_1(A) & v2_card_3(A) ) => ( A = k1_tarski(k1_xboole_0) => k9_card_3(A) = k1_xboole_0 ) ) )).
fof(t72_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(A),k7_cat_1(A,A,k10_cat_1(A)),B) = B ) ) )).
fof(t72_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m2_cat_3(E,B,C,A) => ! [F] : ( m2_cat_3(F,B,D,A) => ( ( r3_cat_3(B,C,A,E) & r3_cat_3(B,D,A,F) & r2_funct_2(A,u1_struct_0(B),k2_cat_3(B,A,E),k2_cat_3(B,A,F)) ) => r1_cat_1(B,C,D) ) ) ) ) ) ) )).
fof(t72_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_cat_1(A,k20_cat_4(A,k20_cat_4(A,B,C),D),k20_cat_4(A,B,k20_cat_4(A,C,D))) ) ) ) ) )).
fof(t72_cfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => v2_seq_2(k2_partfun1(B,k1_numbers,k55_valued_1(B,k2_numbers,C),A)) ) ) )).
fof(t72_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ~ ( B != C & ~ r1_chord(A,B,C) & ? [D] : ( m2_chord(D,A,B,C) & D = k1_xboole_0 & ? [E] : ( m3_glib_001(E,A) & r1_glib_001(A,B,C,E) ) ) ) ) ) ) )).
fof(t72_classes1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => ~ ( k6_classes1(A) = k1_ordinal1(B) & ! [C] : ~ ( r2_hidden(C,A) & k6_classes1(C) = B ) ) ) )).
fof(t72_classes2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r1_ordinal1(A,B) <=> r1_tarski(k16_classes2(A),k16_classes2(B)) ) ) ) )).
fof(t72_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_clvect_1(D,A) => ( r1_struct_0(D,B) <=> k5_clvect_1(A,C,D) = k5_clvect_1(A,k5_algstr_0(A,C,B),D) ) ) ) ) ) )).
fof(t72_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_clvect_2(B,A) & r2_clvect_2(A,B,C) ) => v1_clvect_2(C,A) ) ) ) ) )).
fof(t72_cohsp_1,axiom,( ! [A] : ( k13_cohsp_1(k1_cohsp_1(A)) = k1_zfmisc_1(A) & k13_cohsp_1(k1_zfmisc_1(A)) = k1_cohsp_1(A) ) )).
fof(t72_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => k3_square_1(k1_square_1(A)) = k9_complex1(A) ) )).
fof(t72_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( k4_complex2(A,B,C) = k5_numbers => ( k1_comptrig(k6_xcmplx_0(A,B)) = k1_comptrig(k6_xcmplx_0(C,B)) & k4_complex2(C,B,A) = k5_numbers ) ) ) ) ) )).
fof(t72_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ( A != k4_struct_0(k1_complfld) => k9_complex1(k11_algstr_0(k1_complfld,A)) = k5_xcmplx_0(k9_complex1(A)) ) ) )).
fof(t72_comput_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_comput_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_comput_1(k4_ordinal1))) ) => ! [B] : ( m1_comput_1(B,k3_finseq_2(k4_ordinal1),k4_ordinal1,k2_comput_1(k4_ordinal1),A) => ! [C] : ( m1_comput_1(C,k3_finseq_2(k4_ordinal1),k4_ordinal1,k2_comput_1(k4_ordinal1),A) => ( k1_nat_1(k19_margrel1(B),2) = k19_margrel1(C) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,k1_nat_1(k19_margrel1(B),1)) ) => r2_hidden(k7_comput_1(B,C,D),A) ) ) ) ) ) ) )).
fof(t72_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( v8_valued_0(k55_valued_1(k4_ordinal1,k2_numbers,B)) & ! [C] : ( v7_ordinal1(C) => k9_nat_1(k1_numbers,A,C) = k3_xcmplx_0(k2_power(2,C),k9_nat_1(k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,B),k2_power(2,C))) ) ) => ( v2_comseq_3(B) <=> v1_series_1(A) ) ) ) ) )).
fof(t72_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( B = a_3_6_convex4(A,C,D) => v2_convex4(B,A) ) ) ) ) ) )).
fof(t72_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ( ~ r2_hidden(D,k24_qc_lang1(A,B)) => v2_cqc_the1(k10_cqc_lang(A,k7_cqc_lang(A,B,k12_cqc_lang(A,D,C)),k12_cqc_lang(A,D,k7_cqc_lang(A,B,C))),A) ) ) ) ) ) )).
fof(t72_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_normsp_1(A,B,C),k5_vfunct_1(k4_ordinal1,A,k3_normsp_1(A,C,B))) ) ) ) )).
fof(t72_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(A,k9_xtuple_0(k1_fdiff_9)) & r2_hidden(B,k9_xtuple_0(k1_fdiff_9)) ) => k9_diff_1(k1_fdiff_9,A,B) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k17_sin_cos(k7_xcmplx_0(k2_xcmplx_0(B,A),2))),k17_sin_cos(k7_xcmplx_0(k6_xcmplx_0(B,A),2))),k3_xcmplx_0(k3_xcmplx_0(k19_sin_cos(B),k19_sin_cos(A)),k6_xcmplx_0(A,B)))) ) ) ) )).
fof(t72_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k7_xcmplx_0(1,k1_square_1(k17_sin_cos(D))) ) => ( k17_sin_cos(k2_xcmplx_0(B,k7_xcmplx_0(A,2))) = k5_numbers | k17_sin_cos(k6_xcmplx_0(B,k7_xcmplx_0(A,2))) = k5_numbers | k1_funct_1(k5_diff_1(C,A),B) = k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(16,k19_sin_cos(B)),k17_sin_cos(k7_xcmplx_0(k4_xcmplx_0(A),2))),k19_sin_cos(k7_xcmplx_0(k4_xcmplx_0(A),2))),k17_sin_cos(B)),k1_square_1(k6_xcmplx_0(k19_sin_cos(k3_xcmplx_0(2,B)),k19_sin_cos(A)))) ) ) ) ) ) )).
fof(t72_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_enumset1(A,B,C,D) = k2_enumset1(C,B,D,A) )).
fof(t72_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => k22_rvsum_1(k8_euclid(3,A,B),k8_euclid(3,A,B)) = k2_xcmplx_0(k6_xcmplx_0(k22_rvsum_1(A,A),k3_xcmplx_0(2,k22_rvsum_1(A,B))),k22_rvsum_1(B,B)) ) ) )).
fof(t72_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ~ ( v1_euclid_4(C,A) & ! [D] : ( m2_subset_1(D,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ~ ( r2_hidden(B,D) & r5_euclidlp(A,D,C) ) ) ) ) ) ) )).
fof(t72_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( 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_xboole_0(k7_relat_1(k7_exchsort(C,D,A,B),k6_exchsort(C,k9_funct_7(D,A,B))),k6_exchsort(C,D)) ) ) ) )).
fof(t72_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(A,u1_struct_0(k15_facirc_1(A,B,C))) & r2_hidden(B,u1_struct_0(k15_facirc_1(A,B,C))) & r2_hidden(C,u1_struct_0(k15_facirc_1(A,B,C))) ) )).
fof(t72_fdiff_11,axiom,( ! [A] : ( ( 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,k2_sin_cos9,k4_taylor_1(k7_xcmplx_0(1,2))),2))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k4_taylor_1(k7_xcmplx_0(1,2))),2),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k4_taylor_1(k7_xcmplx_0(1,2))),2),A),B) = k4_xcmplx_0(k7_xcmplx_0(k6_prepower(k1_funct_1(k2_sin_cos9,B),k4_xcmplx_0(k7_xcmplx_0(1,2))),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t72_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v2_struct_0(C) & v10_lattices(C) & v3_filter_0(C) & l3_lattices(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( ( ~ v1_xboole_0(G) & v19_lattices(G,C) & v20_lattices(G,C) & m1_subset_1(G,k1_zfmisc_1(u1_struct_0(C))) ) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ( ( ( r1_filter_0(C,G,D,E) & r1_filter_0(C,G,E,F) ) => r1_filter_0(C,G,D,F) ) & ( ( r1_filter_0(A,B,H,I) & r1_filter_0(A,B,I,J) ) => r1_filter_0(A,B,H,J) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t72_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v20_lattices(B,A) & v21_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( u1_struct_0(k10_filter_2(A,B)) = B & u2_lattices(k10_filter_2(A,B)) = k1_realset1(u2_lattices(A),B) & u1_lattices(k10_filter_2(A,B)) = k1_realset1(u1_lattices(A),B) ) ) ) )).
fof(t72_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k16_finseq_1(k2_finseq_1(k5_numbers),A) = k1_xboole_0 ) )).
fof(t72_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( ( 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))) ) => ! [G] : ( m2_finseq_1(G,A) => ! [H] : ( m2_finseq_1(H,B) => ( ( G = k12_finseq_1(A,D) & H = k12_finseq_1(B,E) ) => k3_funcop_1(F,G,H) = k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)) ) ) ) ) ) ) ) ) ) )).
fof(t72_finseq_3,axiom,( ! [A] : k1_finseq_3(k1_xboole_0,A) = k1_xboole_0 )).
fof(t72_finseq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_finset_1(B) => ~ ( r1_xxreal_0(A,k5_card_1(B)) & ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(B)) ) => k5_card_1(C) != A ) ) ) ) )).
fof(t72_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m2_finseq_1(D,B) => ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(k17_finseq_1(B,A,D))) => k7_partfun1(B,k5_finseq_5(B,D,C,A),E) = k7_partfun1(B,D,E) ) ) ) ) ) ) )).
fof(t72_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r2_hidden(B,k10_xtuple_0(C)) => k4_finseq_4(k1_finseq_5(A,C,B),B) = k4_finseq_4(C,B) ) ) ) ) )).
fof(t72_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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))) ) => ( ( v2_binop_1(E,B) & v1_finseqop(E,B) & v1_setwiseo(E,B) & r2_funct_2(A,B,k6_funcop_1(B,A,E,C,D),k8_funcop_1(B,A,k4_binop_1(B,E))) ) => ( r2_funct_2(A,B,C,k1_partfun1(A,B,B,B,D,k5_finseqop(B,E))) & r2_funct_2(A,B,k1_partfun1(A,B,B,B,C,k5_finseqop(B,E)),D) ) ) ) ) ) ) ) )).
fof(t72_flang_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_catalan2(A))) => ( r2_hidden(k5_afinsq_1(B),k8_flang_1(A,C)) <=> r2_hidden(k5_afinsq_1(B),C) ) ) )).
fof(t72_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(k2_flang_1(A),B) & r1_xxreal_0(C,E) & r1_xxreal_0(D,E) ) => k1_flang_2(A,B,C,E) = k1_flang_2(A,B,D,E) ) ) ) ) ) )).
fof(t72_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k6_flang_1(A,k1_flang_2(A,B,C,D),k2_flang_3(A,B)) = k6_flang_1(A,k2_flang_3(A,B),k1_flang_2(A,B,C,D)) ) ) ) )).
fof(t72_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_partit_2(A) => r1_tarski(k3_relat_1(A,A),k6_partfun1(k9_xtuple_0(A))) ) ) )).
fof(t72_funcop_1,axiom,( ! [A] : ! [B] : k1_funct_1(k16_funcop_1(A,B),A) = B )).
fof(t72_funct_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( ! [C] : ~ ( r2_hidden(C,A) & k8_relat_1(B,k1_tarski(C)) = k1_xboole_0 ) => r1_tarski(A,k10_xtuple_0(B)) ) ) )).
fof(t72_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( r1_partfun1(C,D) => ( ( B = k1_xboole_0 & A != k1_xboole_0 ) | r2_relset_1(A,B,C,D) ) ) ) ) )).
fof(t72_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => k7_relat_1(k15_funct_3(C,D),k2_zfmisc_1(B,A)) = k2_zfmisc_1(k7_relat_1(C,B),k7_relat_1(D,A)) ) ) )).
fof(t72_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( r1_xboole_0(C,k9_xtuple_0(B)) => k5_relat_1(k1_funct_4(A,B),C) = k5_relat_1(A,C) ) ) ) )).
fof(t72_funct_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_relat_1(B) => ( A != k5_numbers => ( r1_tarski(k9_xtuple_0(k8_funct_7(B,A)),k9_xtuple_0(B)) & r1_tarski(k10_xtuple_0(k8_funct_7(B,A)),k10_xtuple_0(B)) ) ) ) ) )).
fof(t72_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ( r1_tarski(A,k1_rcomp_1(k4_xcmplx_0(1),1)) => r2_funct_8(A,k1_numbers,k1_numbers,k1_sin_cos9) ) ) )).
fof(t72_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_fvaluat1(C,A) => ( ( v3_fvaluat1(A) & k3_funct_2(u1_struct_0(A),k6_numbers,C,B) = k5_numbers ) => ( m1_subset_1(B,u1_struct_0(k7_fvaluat1(A,C))) & m1_subset_1(k11_algstr_0(A,B),u1_struct_0(k7_fvaluat1(A,C))) ) ) ) ) ) )).
fof(t72_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => k4_rlvect_1(A,k8_finseq_1(u1_struct_0(A),k12_finseq_1(u1_struct_0(A),B),C)) = k1_algstr_0(A,B,k4_rlvect_1(A,C)) ) ) ) )).
fof(t72_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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) & ~ ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k25_gfacirc1(A,B,C),k26_gfacirc1(A,B,C)))) => v1_circuit2(k5_facirc_1(k25_gfacirc1(A,B,C),k26_gfacirc1(A,B,C),D,2),k25_gfacirc1(A,B,C),k26_gfacirc1(A,B,C)) ) ) )).
fof(t72_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ! [D] : ! [E] : ( ( r1_glib_000(B,C,D,E) => r1_glib_000(A,C,D,E) ) & ( r2_glib_000(B,C,D,E) => r2_glib_000(A,C,D,E) ) & ( r3_glib_000(B,C,D,E) => r3_glib_000(A,C,D,E) ) & ( r4_glib_000(B,C,D,E) => r4_glib_000(A,C,D,E) ) ) ) ) )).
fof(t72_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_relset_1(k4_ordinal1,k6_glib_000(A),k11_glib_001(A,k8_glib_001(A,B,1,C)),k11_glib_001(A,B)) ) ) ) )).
fof(t72_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( v1_group_3(C,A) & m1_group_2(C,A) ) => ~ ( m1_group_2(C,B) & ! [D] : ( ( v15_algstr_0(D) & m1_group_2(D,A) ) => u1_struct_0(D) != k3_group_11(A,B,C) ) ) ) ) ) )).
fof(t72_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => r1_xxreal_0(k7_group_1(B),k7_group_1(A)) ) ) )).
fof(t72_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_group_2(C,A) => ( v1_finset_1(k15_group_2(A,C)) => k18_group_2(A,C) = k18_group_2(A,k6_group_3(A,C,B)) ) ) ) ) )).
fof(t72_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => k5_lattices(k11_group_4(A)) = k6_group_2(A) ) )).
fof(t72_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => r1_group_2(A,k9_group_5(A),k5_group_4(A,k6_group_5(A))) ) )).
fof(t72_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => v7_struct_0(k5_group_6(A,k7_group_2(A))) ) )).
fof(t72_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( 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) ) ) ) )).
fof(t72_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => k11_ideal_1(A,B,k11_ideal_1(A,C,D)) = k11_ideal_1(A,k11_ideal_1(A,B,C),D) ) ) ) ) )).
fof(t72_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(A,B) & r1_tarski(B,k2_rcomp_1(k4_xcmplx_0(1),1)) & D = k1_taylor_1(2) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_1(C,E) = 1 ) ) & B = k9_xtuple_0(k1_sin_cos9) & B = k9_xtuple_0(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),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),k7_xcmplx_0(1,2)))) ) => k2_integra5(A,k1_sin_cos9) = k6_xcmplx_0(k1_funct_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_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),k7_xcmplx_0(1,2))),k2_seq_4(A)),k1_funct_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_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),k7_xcmplx_0(1,2))),k3_seq_4(A))) ) ) ) ) ) )).
fof(t72_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k7_xcmplx_0(k3_xcmplx_0(k28_sin_cos,3),2)) => k2_integra5(A,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)) = k5_numbers ) ) )).
fof(t72_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => r1_tarski(A,k11_intpro_1(A)) ) )).
fof(t72_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,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))))) & k2_relset_1(u1_struct_0(k15_euclid(2)),k5_jgraph_4(A)) = u1_struct_0(k15_euclid(2)) ) ) ) )).
fof(t72_jgraph_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ 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] : ( ( 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))))) ) => ( ( E = k5_jgraph_6(k5_numbers,k5_numbers,1) & r2_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,k1_jgraph_3) & r1_jordan6(k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(1),1),A,B) & r1_jordan6(k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(1),1),B,C) & r1_jordan6(k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(1),1),C,D) ) => r1_jordan17(E,k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,A),k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,B),k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,C),k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,D)) ) ) ) ) ) ) ) )).
fof(t72_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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) = F & 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(C),H) & r1_xxreal_0(G,k18_euclid(D)) & r1_xxreal_0(k18_euclid(D),H) & k1_funct_1(I,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t72_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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(1,A) & r1_xxreal_0(A,k3_finseq_1(k1_jordan8(C,B))) ) => k9_pscomp_1(k3_topreal1(2,k2_jordan9(C,B))) = k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(C,B),A,1)) ) ) ) ) )).
fof(t72_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(1,A) & B = a_2_5_jordan2c(A,C) ) => ( r1_xxreal_0(C,k5_numbers) | r1_jordan2c(A,B,k1_jordan2c(A,B)) ) ) ) ) ) )).
fof(t72_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => k39_glib_000(k25_lexbfs(A,k26_lexbfs(A))) = k39_glib_000(k26_lexbfs(A)) ) )).
fof(t72_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v7_limfunc1(B) & ! [C] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ r1_xxreal_0(C,D) & r2_hidden(D,k1_relset_1(k1_numbers,A)) ) ) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k10_prob_1(C))) => r1_xxreal_0(k1_funct_1(B,D),k1_funct_1(A,D)) ) ) ) ) | v7_limfunc1(A) ) ) ) ) )).
fof(t72_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_limfunc2(B,A) & k1_limfunc2(B,A) = k5_numbers ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(k6_xcmplx_0(A,C),A))) & r1_xxreal_0(k5_numbers,k1_funct_1(B,D)) ) ) ) ) | r3_limfunc2(k6_rfunct_1(k1_numbers,k1_numbers,B),A) ) ) ) ) )).
fof(t72_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v6_limfunc1(A) & r1_limfunc3(B,k5_limfunc1(A)) & ! [C] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k10_prob_1(C))) & k1_funct_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)) = k1_limfunc3(B,k5_limfunc1(A)) ) ) ) ) ) )).
fof(t72_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => r1_funct_2(k2_zfmisc_1(k14_lpspace1(A,B,C),k14_lpspace1(A,B,C)),k14_lpspace1(A,B,C),k2_zfmisc_1(k6_lpspace2(A,B,C,1),k6_lpspace2(A,B,C,1)),k6_lpspace2(A,B,C,1),k15_lpspace1(A,B,C),k7_lpspace2(A,B,C,1)) ) ) ) )).
fof(t72_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_cqc_lang(A))) => ( r3_cqc_the1(A,D,k8_cqc_lang(A,k6_cqc_lang(A,k6_cqc_lang(A,B)),C)) <=> r3_cqc_the1(A,D,k8_cqc_lang(A,B,C)) ) ) ) ) ) )).
fof(t72_mathmorp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( r2_hidden(k4_struct_0(k15_euclid(A)),D) => k9_mathmorp(k15_euclid(A),B,C,D) = B ) ) ) ) ) )).
fof(t72_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( ( v2_matrix10(B) & r2_matrix10(D,C) ) => r1_matrix10(k4_matrix10(A,D,B),C) ) ) ) ) ) )).
fof(t72_matrix13,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ! [E] : ( ( v1_finset_1(E) & v1_setfam_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ( ( r1_tarski(k2_zfmisc_1(D,E),k2_matrix_0(C)) & k5_card_1(D) = k5_card_1(E) ) => k12_matrix_3(k5_card_1(D),A,k7_matrix13(u1_struct_0(A),k6_matrix_3(A,C,B),D,E)) = k8_group_1(A,k1_laplace(A,k4_group_1(A),B,k5_card_1(D)),k12_matrix_3(k5_card_1(D),A,k7_matrix13(u1_struct_0(A),C,D,E))) ) ) ) ) ) ) )).
fof(t72_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( k1_matrix_0(B) = k3_finseq_1(C) => ( ( k1_matrix_0(B) = k5_numbers & k3_finseq_1(B) != k5_numbers ) | ( k1_matrix_0(C) = k5_numbers & k3_finseq_1(C) != k5_numbers ) | m1_vectsp_4(k7_matrix15(A,C),A,k7_matrix15(A,k4_matrix_3(A,B,C))) ) ) ) ) ) )).
fof(t72_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( k1_matrix_0(B) = k1_nat_1(E,1) & r2_hidden(C,k2_finseq_1(E)) & r2_hidden(D,k4_finseq_1(B)) ) => ( r1_xxreal_0(E,k5_numbers) | ( k3_matrix_0(A,k16_matrix_0(1,A,B),D,C) = k3_matrix_0(A,B,D,k1_nat_1(C,1)) & r2_hidden(1,k2_finseq_1(k1_matrix_0(B))) ) ) ) ) ) ) ) ) )).
fof(t72_matrixj1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v2_matrixj1(D,u1_struct_0(A)) & m2_finseq_1(D,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) => ! [E] : ( ( v2_matrixj1(E,u1_struct_0(A)) & m2_finseq_1(E,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) => ( ( k10_matrixj1(u1_struct_0(A),D) = k10_matrixj1(u1_struct_0(A),E) & k11_matrixj1(u1_struct_0(A),D) = k11_matrixj1(u1_struct_0(A),E) ) => k3_matrix_3(A,k20_matrixj1(u1_struct_0(A),B,D),k20_matrixj1(u1_struct_0(A),C,E)) = k20_matrixj1(u1_struct_0(A),k3_rlvect_1(A,B,C),k25_matrixj1(A,D,E)) ) ) ) ) ) ) )).
fof(t72_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => k3_matrixr2(A,k4_matrixr2(A)) = 1 ) )).
fof(t72_mcart_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r2_hidden(B,A) => r2_hidden(k2_xtuple_0(B),k9_relat_1(A,k1_xtuple_0(B))) ) ) )).
fof(t72_measure6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,k3_measure6(A)) & ! [C] : ( v1_xreal_0(C) => ~ ( r2_hidden(C,A) & B = k4_xcmplx_0(C) ) ) ) ) ) )).
fof(t72_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_membered(C) => k9_member_1(A,k11_member_1(B,C)) = k11_member_1(k9_member_1(A,B),C) ) ) ) )).
fof(t72_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ( r2_hidden(k4_struct_0(B),k9_xtuple_0(D)) => k10_memstr_0(A,B,k1_funct_4(C,D),E) = k1_funct_4(C,k10_memstr_0(A,B,D,E)) ) ) ) ) ) ) )).
fof(t72_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( ( r2_mesfunc6(A,B,C) & r2_mesfunc6(A,B,D) ) => r2_mesfunc6(A,B,k3_valued_1(A,k1_numbers,k1_numbers,C,D)) ) ) ) ) ) )).
fof(t72_mmlquery,axiom,( ! [A] : ( ( v3_mmlquery(A) & l1_mmlquery(A) ) => ! [B] : ( m2_finseq_1(B,u1_mmlquery(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( ( r1_xxreal_0(C,E) & r1_xxreal_0(D,F) ) => r1_tarski(k37_mmlquery(A,B,C,D),k37_mmlquery(A,B,E,F)) ) ) ) ) ) ) ) )).
fof(t72_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k25_modelc_2(k43_modelc_2)) => ( r7_modelc_2(C,k8_modelc_2(A,B)) <=> r7_modelc_2(C,k3_modelc_2(k7_modelc_2(k3_modelc_2(A),k3_modelc_2(B)))) ) ) ) ) )).
fof(t72_modelc_3,axiom,( ! [A] : ( m1_subset_1(A,k25_modelc_2(k43_modelc_2)) => ! [B] : ( ( v1_modelc_2(B) & v5_modelc_3(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r7_modelc_2(A,B) <=> r8_modelc_2(A,k14_modelc_3(B,k12_modelc_3(B,k11_modelc_3(B)))) ) ) ) )).
fof(t72_monoid_0,axiom,( ! [A] : ! [B] : ( r1_tarski(B,A) => m2_monoid_0(k12_monoid_0(B),k12_monoid_0(A)) ) )).
fof(t72_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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_msafree4(B,u1_struct_0(A)) ) => ! [C] : ( m2_pboole(C,u1_struct_0(A),B,k7_funcop_1(u1_struct_0(A),k4_ordinal1)) => ~ ( v1_msualg_3(C) & ! [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,k3_equation(A)),u3_msualg_1(A,k1_msafree3(A,B))) => ~ ( r1_msualg_3(A,k3_equation(A),k1_msafree3(A,B),D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,k1_msafree3(A,B)),E)) => k1_funct_1(k2_msafree4(u1_struct_0(A),u3_msualg_1(A,k3_equation(A)),u3_msualg_1(A,k1_msafree3(A,B)),D,E),k6_msafree4(A,B,C,F)) = F ) ) ) ) ) ) ) ) )).
fof(t72_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( 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) => ( r11_ncfcont1(A,k4_normsp_0(u1_struct_0(A),B,D),C) & r8_ncfcont1(A,B,k5_vfunct_1(u1_struct_0(A),B,D),C) ) ) ) ) ) )).
fof(t72_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ? [B] : ( v7_ordinal1(B) & v1_int_2(B) & v1_int_2(B) & ~ r1_xxreal_0(B,A) ) ) )).
fof(t72_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v9_o_ring_1(B,A) & v11_o_ring_1(C,A) ) => v13_o_ring_1(k6_algstr_0(A,B,C),A) ) ) ) ) )).
fof(t72_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r1_relat_2(A,B) => v1_relat_2(k2_wellord1(A,B)) ) ) )).
fof(t72_ordinal3,axiom,( ! [A] : r1_tarski(k3_ordinal2(A),k1_ordinal1(k3_tarski(k2_ordinal1(A)))) )).
fof(t72_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( r2_hidden(A,B) <=> r2_hidden(k12_ordinal6(C,A),k12_ordinal6(C,B)) ) ) ) ) )).
fof(t72_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( v1_partfun1(C,A) <=> k5_partfun1(A,B,C) = k1_tarski(C) ) ) )).
fof(t72_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => r6_pboole(A,k4_pboole(A,k2_pboole(A,B,C),D),k2_pboole(A,k4_pboole(A,B,D),k4_pboole(A,C,D))) ) ) ) )).
fof(t72_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( 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,k20_valued_1(k1_euclid(3),k1_numbers,k1_numbers,k1_pdiff_3(2,3,B),k1_pdiff_3(2,3,C)),A) ) ) ) ) )).
fof(t72_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ! [C] : ( ( ~ v1_xboole_0(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ( ( v1_pdiff_7(B,A) & r1_tarski(k1_rvsum_1(C),k2_finseq_1(A)) & r4_pdiff_9(A,B,C,D) & r4_pdiff_9(A,B,C,E) ) => ( r4_pdiff_9(A,B,C,k47_valued_1(k1_euclid(A),k1_numbers,k1_numbers,D,E)) & r2_relset_1(k1_euclid(A),k1_numbers,k5_pdiff_9(A,B,C,k47_valued_1(k1_euclid(A),k1_numbers,k1_numbers,D,E)),k47_valued_1(k1_euclid(A),k1_numbers,k1_numbers,k5_pdiff_9(A,B,C,D),k5_pdiff_9(A,B,C,E))) ) ) ) ) ) ) ) )).
fof(t72_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( m1_subset_1(B,k8_polyform(A,k6_xcmplx_0(k7_polyform(A),1))) => ! [C] : ( m1_subset_1(C,k8_polyform(A,k7_polyform(A))) => ( C = A => k16_polyform(A,k7_polyform(A),B,C) = k5_struct_0(k2_bspace) ) ) ) ) )).
fof(t72_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( m2_finseq_1(C,k3_finseq_2(k4_finseq_2(3,k15_pre_poly(A)))) => ! [D] : ( m2_finseq_1(D,k3_finseq_2(k4_finseq_2(3,k15_pre_poly(A)))) => ~ ( k4_finseq_1(C) = k4_finseq_1(k21_pre_poly(A,B)) & k4_finseq_1(D) = k4_finseq_1(k21_pre_poly(A,B)) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(C)) => k1_funct_1(C,E) = k8_pre_poly(k21_pre_poly(A,k7_partfun1(k15_pre_poly(A),k9_pre_poly(k15_pre_poly(A),k4_ordinal1,k4_finseq_2(2,k15_pre_poly(A)),k21_pre_poly(A,B),E),1)),k5_finseq_2(k3_finseq_2(k15_pre_poly(A)),k3_finseq_1(k21_pre_poly(A,k7_partfun1(k15_pre_poly(A),k9_pre_poly(k15_pre_poly(A),k4_ordinal1,k4_finseq_2(2,k15_pre_poly(A)),k21_pre_poly(A,B),E),1))),k3_pre_poly(k15_pre_poly(A),k7_partfun1(k15_pre_poly(A),k9_pre_poly(k15_pre_poly(A),k4_ordinal1,k4_finseq_2(2,k15_pre_poly(A)),k21_pre_poly(A,B),E),2)))) ) ) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(D)) => k1_funct_1(D,E) = k8_pre_poly(k5_finseq_2(k3_finseq_2(k15_pre_poly(A)),k3_finseq_1(k21_pre_poly(A,k7_partfun1(k15_pre_poly(A),k9_pre_poly(k15_pre_poly(A),k4_ordinal1,k4_finseq_2(2,k15_pre_poly(A)),k21_pre_poly(A,B),E),2))),k3_pre_poly(k15_pre_poly(A),k7_partfun1(k15_pre_poly(A),k9_pre_poly(k15_pre_poly(A),k4_ordinal1,k4_finseq_2(2,k15_pre_poly(A)),k21_pre_poly(A,B),E),1))),k21_pre_poly(A,k7_partfun1(k15_pre_poly(A),k9_pre_poly(k15_pre_poly(A),k4_ordinal1,k4_finseq_2(2,k15_pre_poly(A)),k21_pre_poly(A,B),E),2))) ) ) & ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_finseq_1(k5_pre_poly(k4_finseq_2(3,k15_pre_poly(A)),C)),k4_finseq_1(k5_pre_poly(k4_finseq_2(3,k15_pre_poly(A)),C))) & v3_funct_2(E,k4_finseq_1(k5_pre_poly(k4_finseq_2(3,k15_pre_poly(A)),C)),k4_finseq_1(k5_pre_poly(k4_finseq_2(3,k15_pre_poly(A)),C))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_1(k5_pre_poly(k4_finseq_2(3,k15_pre_poly(A)),C)),k4_finseq_1(k5_pre_poly(k4_finseq_2(3,k15_pre_poly(A)),C))))) ) => k5_pre_poly(k4_finseq_2(3,k15_pre_poly(A)),D) != k1_partfun1(k4_finseq_1(k5_pre_poly(k4_finseq_2(3,k15_pre_poly(A)),C)),k4_finseq_1(k5_pre_poly(k4_finseq_2(3,k15_pre_poly(A)),C)),k4_ordinal1,k4_finseq_2(3,k15_pre_poly(A)),E,k5_pre_poly(k4_finseq_2(3,k15_pre_poly(A)),C)) ) ) ) ) ) ) )).
fof(t72_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k6_prepower(A,1) = A ) ) )).
fof(t72_prob_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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_xboole_0(k10_prob_3(A,B)) & v2_finsub_1(k10_prob_3(A,B)) & v1_prob_1(k10_prob_3(A,B),A) & m1_subset_1(k10_prob_3(A,B),k1_zfmisc_1(k1_zfmisc_1(A))) ) ) ) )).
fof(t72_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( r6_pboole(A,k6_pboole(A,k2_pzfmisc1(A,B,C),D),k2_pboole(A,k6_pboole(A,k1_pzfmisc1(A,B),D),k6_pboole(A,k1_pzfmisc1(A,C),D))) & r6_pboole(A,k6_pboole(A,D,k2_pzfmisc1(A,B,C)),k2_pboole(A,k6_pboole(A,D,k1_pzfmisc1(A,B)),k6_pboole(A,D,k1_pzfmisc1(A,C)))) ) ) ) ) )).
fof(t72_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ( r2_qc_lang2(A,k15_qc_lang1(A,D,C),B) => r3_qc_lang2(A,C,B) ) ) ) ) ) )).
fof(t72_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => k6_qc_lang3(A,k5_qc_lang2(A,B,C)) = k6_qc_lang3(A,C) ) ) ) )).
fof(t72_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => k25_quaterni(k25_quaterni(C,A),B) = k25_quaterni(k25_quaterni(C,B),A) ) ) ) )).
fof(t72_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => k28_quaterni(k24_quaterni(A)) = k28_quaterni(A) ) )).
fof(t72_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ( k9_nat_1(k1_numbers,k4_real_3(A),1) != k5_numbers => k9_nat_1(k1_numbers,k7_real_3(A),1) = k2_xcmplx_0(k9_nat_1(k1_numbers,k4_real_3(A),k5_numbers),k7_xcmplx_0(1,k9_nat_1(k1_numbers,k4_real_3(A),1))) ) ) )).
fof(t72_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => k5_relat_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k5_relat_1(C,A),k5_relat_1(C,B)) ) )).
fof(t72_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_afinsq_1(D))) => ! [F] : ( ( ~ v2_struct_0(F) & l1_rewrite3(F,E) ) => ( r1_rewrite3(E,F,A,B,C) => r1_rewrite1(k1_rewrite3(D,E,F),k4_tarski(A,B),k4_tarski(C,k2_flang_1(D))) ) ) ) ) )).
fof(t72_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) ) => ( v1_comseq_2(A) <=> ? [B] : ( v1_xreal_0(B) & ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => r1_xxreal_0(k9_complex1(k1_funct_1(A,C)),B) ) ) ) ) )).
fof(t72_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ! [E] : ( m1_subset_1(E,A) => ( ( v1_finset_1(k1_relset_1(A,k2_partfun1(A,k1_numbers,B,D))) & r2_hidden(E,k1_relset_1(A,k2_partfun1(A,k1_numbers,B,D))) ) => ( k1_funct_1(k20_rfunct_3(A,k15_valued_1(A,k1_numbers,B,C),D),k3_finseq_1(k20_rfunct_3(A,k15_valued_1(A,k1_numbers,B,C),D))) = k1_funct_1(k15_valued_1(A,k1_numbers,B,C),E) <=> k1_funct_1(k20_rfunct_3(A,B,D),k3_finseq_1(k20_rfunct_3(A,B,D))) = k1_funct_1(B,E) ) ) ) ) ) ) )).
fof(t72_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v8_valued_0(B) & v2_seq_2(B) ) => k1_funct_1(k3_rinfsup1(B),A) = k3_funct_2(k4_ordinal1,k1_numbers,k3_rinfsup1(B),k1_nat_1(A,1)) ) ) ) )).
fof(t72_rlaffin1,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( v1_rlaffin1(D,C) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) ) => ( r2_hidden(A,k3_convex1(C,D)) => ( k1_funct_1(k5_rlaffin1(C,D,A),B) = 1 <=> ( A = B & r2_hidden(A,D) ) ) ) ) ) )).
fof(t72_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => m2_rlsub_1(k6_domain_1(u1_struct_0(A),B),A,k1_rlsub_1(A)) ) ) )).
fof(t72_rltopsp1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_hidden(B,k5_rltopsp1(A,B,C)) ) ) ) )).
fof(t72_rlvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k4_rlvect_1(A,k3_finseq_4(u1_struct_0(A),B,B,B)) = k1_rlvect_1(A,B,3) ) ) )).
fof(t72_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( m2_rmod_2(C,A,B,k2_rmod_2(A,B)) => C = u1_struct_0(B) ) ) ) ) )).
fof(t72_rmod_4,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( C = u1_struct_0(B) => ( k4_struct_0(A) = k1_group_1(A) | k10_rmod_4(A,B,C) = B ) ) ) ) ) )).
fof(t72_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m2_rusub_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,C) <=> C = k3_rusub_1(A,D,B) ) ) ) ) ) )).
fof(t72_rvsum_1,axiom,( k18_rvsum_1(k6_finseq_1(k1_numbers)) = k5_numbers )).
fof(t72_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B),k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k8_memstr_0(k7_card_1(3),k1_scmfsa_2,B)))) = k11_scmfsa_2(k5_numbers) ) ) ) ) )).
fof(t72_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ~ v2_extpro_1(k6_scmfsa_2(A,B),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(t72_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmpds_2)) ) => ~ v2_extpro_1(k9_scmpds_2(C,A,B),2,k1_scmpds_2) ) ) ) )).
fof(t72_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ( r1_xxreal_0(k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),E)),k5_numbers) => k6_scmpds_4(k7_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,k1_nat_1(k5_card_1(C),1))) ) ) ) ) ) ) )).
fof(t72_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( ( v4_scmyciel(B) & v5_scmyciel(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ( v9_scmyciel(k3_tarski(B),k6_scmyciel(A)) & m1_subset_1(k3_tarski(B),k1_zfmisc_1(k3_tarski(k6_scmyciel(A)))) ) ) ) )).
fof(t72_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r3_semi_af1(A,B,D,D,E) & r3_semi_af1(A,C,D,D,F) ) => r3_semi_af1(A,B,C,F,E) ) ) ) ) ) ) ) )).
fof(t72_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => k17_seq_4(A,B,B) = k15_seq_4(A) ) ) )).
fof(t72_setlim_1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k4_kurato_0(A,C) = k3_subset_1(A,k3_kurato_0(A,k2_prob_1(A,C))) ) ) )).
fof(t72_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_kurato_0(C,A) => k4_kurato_0(A,k3_setlim_2(A,B,C)) = k7_subset_1(A,k4_kurato_0(A,B),k4_kurato_0(A,C)) ) ) ) )).
fof(t72_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,C,k5_sheffer1(A,B,k5_sheffer1(A,B,B)))) = C ) ) ) )).
fof(t72_sin_cos,axiom,( k1_funct_1(k16_sin_cos,k7_xcmplx_0(k28_sin_cos,4)) = k1_funct_1(k18_sin_cos,k7_xcmplx_0(k28_sin_cos,4)) )).
fof(t72_sin_cos6,axiom,( k2_sin_cos6(1) = k7_xcmplx_0(k28_sin_cos,2) )).
fof(t72_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => k2_sin_cos2(k3_xcmplx_0(5,A)) = k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(5,k2_sin_cos2(A)),k3_xcmplx_0(20,k1_newton(k2_sin_cos2(A),3))),k3_xcmplx_0(16,k1_newton(k2_sin_cos2(A),5))) ) )).
fof(t72_sin_cos9,axiom,( r2_fdiff_1(k2_sin_cos9,k7_relset_1(k1_numbers,k1_numbers,k27_sin_cos,k2_rcomp_1(k5_numbers,k28_sin_cos))) )).
fof(t72_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(A,k7_xcmplx_0(k28_sin_cos,2)) => ( r1_xxreal_0(A,k5_numbers) | k8_sincos10(k1_funct_1(k2_fdiff_9,A)) = A ) ) ) )).
fof(t72_sprect_1,axiom,( ! [A] : ( ( ~ 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_relset_1(u1_struct_0(k15_euclid(2)),k1_numbers,k5_pscomp_1,k1_rltopsp1(k15_euclid(2),k12_pscomp_1(A),k13_pscomp_1(A))) = k1_rcomp_1(k9_pscomp_1(A),k7_pscomp_1(A)) ) )).
fof(t72_sprect_2,axiom,( ! [A] : ( ( ~ 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)) & 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)))) ) ) )).
fof(t72_sprect_5,axiom,( ! [A] : ( ( ~ 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)) & k18_pscomp_1(k3_topreal1(2,A)) != k25_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)))) ) ) )).
fof(t72_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_valuat_1(D,A,C) => ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [F] : ( m2_subset_1(F,k16_substut1(A),k38_substut1(A)) => ! [G] : ( m1_substut1(G,A,k7_sublemma(A,F,B)) => ( ! [H] : ( m1_subset_1(H,C) => r1_sublemma(A,F,C,k1_sublemma(A,C,E,k14_sublemma(A,C,k13_sublemma(A,F,B,G,C,E),k12_sublemma(A,C,B,H))),D) ) <=> ! [H] : ( m1_subset_1(H,C) => r1_sublemma(A,F,C,k1_sublemma(A,C,k1_sublemma(A,C,E,k13_sublemma(A,F,B,G,C,E)),k12_sublemma(A,C,B,H)),D) ) ) ) ) ) ) ) ) ) )).
fof(t72_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v2_tdlat_2(B,A) => v1_tdlat_2(B,A) ) ) ) )).
fof(t72_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_tdlat_3(B) & m1_pre_topc(B,A) ) => ? [C] : ( 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) ) ) ) )).
fof(t72_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_tex_3(B,A) & m1_pre_topc(B,A) ) => ~ ( ~ ( v3_tex_3(B,A) & v1_borsuk_1(B,A) ) & ! [C] : ( ( ~ v2_struct_0(C) & v1_pre_topc(C) & v1_tex_2(C,A) & v2_tex_3(C,A) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & v1_pre_topc(D) & v1_borsuk_1(D,A) & v3_tex_3(D,A) & m1_pre_topc(D,A) ) => ~ ( k2_tsep_1(A,C,D) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & k1_tsep_1(A,C,D) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) ) ) ) ) ) ) )).
fof(t72_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = u1_struct_0(B) => ( v4_tex_4(B,A) <=> v3_tex_4(C,A) ) ) ) ) ) )).
fof(t72_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ v2_struct_0(E) & m1_pre_topc(E,A) ) => ( ( m1_pre_topc(D,C) & m1_pre_topc(E,D) ) => ! [F] : ( ( 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)))) ) => r2_funct_2(u1_struct_0(E),u1_struct_0(B),k3_tmap_1(A,B,D,E,k3_tmap_1(A,B,C,D,F)),k3_tmap_1(A,B,C,E,F)) ) ) ) ) ) ) ) )).
fof(t72_topgen_5,axiom,( v1_tops_2(a_0_2_topgen_5,k3_topmetr) & v1_cantor_1(a_0_2_topgen_5,k3_topmetr) & m1_subset_1(a_0_2_topgen_5,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k3_topmetr)))) )).
fof(t72_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( v9_rltopsp1(A,k15_euclid(2)) & v4_pre_topc(A,k15_euclid(2)) ) => v2_compts_1(A,k15_euclid(2)) ) ) )).
fof(t72_tops_3,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ( ( u1_struct_0(A) = u1_struct_0(B) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => ( v3_pre_topc(C,A) <=> v3_pre_topc(D,B) ) ) ) ) ) => g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) ) ) ) )).
fof(t72_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( r2_analoaf(A,C,D,E,F) <=> r2_analoaf(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)) ) ) ) ) ) ) ) ) )).
fof(t72_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_trees_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_trees_1(D) ) => ( ( r1_tarski(A,C) & r1_tarski(B,D) ) => r1_tarski(k13_trees_3(A,B),k13_trees_3(C,D)) ) ) ) ) ) )).
fof(t72_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( r3_tsep_1(A,B,D) => ( r1_tsep_1(B,C) | r3_tsep_1(A,k2_tsep_1(A,B,C),D) ) ) ) ) ) ) )).
fof(t72_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( v1_valued_2(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,C))) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_valued_0(E) ) => ( r2_hidden(A,k9_xtuple_0(k68_valued_2(C,D,E))) => k1_funct_1(k68_valued_2(C,D,E),A) = k14_valued_2(k1_funct_1(D,A),k1_funct_1(E,A)) ) ) ) ) )).
fof(t72_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ~ ( m2_vectsp_4(C,A,B,k1_vectsp_4(A,B)) & ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => C != k6_domain_1(u1_struct_0(B),D) ) ) ) ) ) )).
fof(t72_waybel23,axiom,( ! [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) & l1_orders_2(A) ) => ( v2_waybel_8(A) <=> ? [B] : ( v6_waybel23(B,A) & m1_waybel23(B,A) & ! [C] : ( ( v6_waybel23(C,A) & m1_waybel23(C,A) ) => r1_tarski(B,C) ) ) ) ) )).
fof(t72_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ 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))) ) => r4_waybel_0(A,B,C,D) ) => v5_orders_3(C,A,B) ) ) ) ) )).
fof(t72_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v9_waybel_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_orders_2(A,C,k6_waybel_1(A,B,C)) ) ) ) ) )).
fof(t72_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( k2_xboole_0(B,D) = k2_xboole_0(A,C) & r1_xboole_0(A,B) & r1_xboole_0(C,D) ) => A = D ) )).
fof(t72_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k10_xboolean(A,k10_xboolean(A,B)) = B ) ) )).
fof(t72_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k7_xcmplx_0(k2_xcmplx_0(A,A),4) = k7_xcmplx_0(A,2) ) )).
fof(t72_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(B,A) ) => r1_xxreal_0(k7_xcmplx_0(B,C),k7_xcmplx_0(A,C)) ) ) ) ) )).
fof(t72_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( r1_xxreal_0(C,D) & k1_xxreal_1(C,D) = k4_xxreal_1(A,B) ) ) ) ) ) )).
fof(t72_xxreal_2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v2_membered(C) => ( ( r1_xxreal_0(B,A) & m2_xxreal_2(A,C) ) => m2_xxreal_2(B,C) ) ) ) ) )).
fof(t72_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ~ ( ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(C,k5_numbers) & C != k1_xxreal_0 & r1_xxreal_0(k4_xxreal_3(B,C),k4_xxreal_3(A,C)) ) ) ) ) )).
fof(t72_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ~ ( v7_zf_lang(B) & r3_zf_lang(A,B) ) ) ) )).
fof(t72_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( ( 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(B,A)) <=> r1_zf_model(C,k2_zf_lang1(C,E,B,D),k8_zf_lang(B,A)) ) ) ) ) ) ) )).
fof(t72_zfmisc_1,axiom,( ! [A] : ! [B] : r1_tarski(k2_xboole_0(k1_zfmisc_1(k4_xboole_0(A,B)),k1_zfmisc_1(k4_xboole_0(B,A))),k1_zfmisc_1(k5_xboole_0(A,B))) )).
fof(t72_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_zmodul01(D,A) => ( r2_hidden(B,k5_zmodul01(A,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r1_struct_0(D,E) & B = k3_rlvect_1(A,C,E) ) ) ) ) ) ) )).
fof(t73_abcmiz_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( m1_rewrite1(C,B) => ( r2_hidden(k1_funct_1(C,1),A) => m2_finseq_1(C,A) ) ) ) ) )).
fof(t73_abcmiz_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_instalg1(C) & v1_abcmiz_1(C) & v3_abcmiz_1(C) & l1_msualg_1(C) ) => ( m3_abcmiz_1(k4_tarski(A,B),C) <=> ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k38_abcmiz_1(C))) & v9_abcmiz_1(B,C) & m1_abcmiz_1(B,C,k12_abcmiz_1(C)) ) ) ) )).
fof(t73_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => r1_tarski(A,k1_ordinal4(A,B)) ) ) )).
fof(t73_afinsq_2,axiom,( ! [A] : k8_afinsq_2(A,k4_afinsq_1(k8_afinsq_1(A))) = k4_afinsq_1(A) )).
fof(t73_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ( v3_freealg(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( k13_aofa_000(A,B,C) != B & k13_aofa_000(A,B,C) != C & ( k13_aofa_000(A,B,C) = k13_aofa_000(A,E,F) => ( B = E & C = F ) ) & k13_aofa_000(A,B,C) != k14_aofa_000(A,D,E,F) & k13_aofa_000(A,B,C) != k16_aofa_000(A,D,E) ) ) ) ) ) ) ) ) )).
fof(t73_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v16_aofa_a00(A) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v19_aofa_a00(B,A) & m1_subset_1(B,u1_struct_0(A)) ) => ( k37_aofa_a00(A) != B & r1_aofa_a00(A,k1_funct_1(u7_aofa_a00(A),11),k2_finseq_4(u1_struct_0(A),k37_aofa_a00(A),B),B) & r1_aofa_a00(A,k1_funct_1(u7_aofa_a00(A),k2_xcmplx_0(11,1)),k3_finseq_4(u1_struct_0(A),k37_aofa_a00(A),B,B),k37_aofa_a00(A)) & r1_aofa_a00(A,k1_funct_1(u7_aofa_a00(A),k2_xcmplx_0(11,2)),k12_finseq_1(u1_struct_0(A),k37_aofa_a00(A)),B) & r1_aofa_a00(A,k1_funct_1(u7_aofa_a00(A),k2_xcmplx_0(11,3)),k2_finseq_4(u1_struct_0(A),B,B),k37_aofa_a00(A)) ) ) ) )).
fof(t73_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ~ ( A != k11_arytm_3 & ! [B] : ( m1_subset_1(B,k5_arytm_3) => ~ ( ~ r3_arytm_3(A,B) & ~ r2_hidden(B,k4_ordinal1) ) ) ) ) )).
fof(t73_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k2_xcmplx_0(k7_series_1(A,B,C),k9_nat_1(k1_numbers,A,k1_nat_1(B,1))) = k7_series_1(A,k1_nat_1(B,1),C) ) ) ) )).
fof(t73_bcialg_1,axiom,( ! [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) ) => ( v14_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t73_borsuk_5,axiom,( ! [A] : ( ( v2_compts_1(A,k3_topmetr) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ! [C] : ( v1_xreal_0(C) => ( ( r2_hidden(C,B) & B = A ) => ( r1_xxreal_0(k3_seq_4(B),C) & r1_xxreal_0(C,k2_seq_4(B)) ) ) ) ) ) )).
fof(t73_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( m1_borsuk_2(G,A,C,D) => ! [H] : ( 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) ) => r3_borsuk_2(A,B,E,k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,C,D,F,G),H),k1_borsuk_2(A,B,C,E,F,k1_borsuk_2(A,C,D,E,G,H))) ) ) ) ) ) ) ) ) ) )).
fof(t73_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ( v2_bvfunc_2(C,A) => r1_bvfunc_1(A,k7_bvfunc_2(A,k7_bvfunc_2(A,k1_bvfunc_1(A,B),C,D),C,E),k7_bvfunc_2(A,k1_bvfunc_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) )).
fof(t73_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_eqrel_1(I,A) => ! [J] : ( m1_eqrel_1(J,A) => ! [K] : ( 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,I,B) = k2_partit1(A,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),K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t73_card_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_funct_1(A) ) => ! [B] : ( r2_hidden(B,k9_xtuple_0(k10_card_3(A))) => k1_funct_1(k10_card_3(A),B) = a_2_0_card_3(A,B) ) ) )).
fof(t73_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => r2_funct_2(u1_struct_0(A),u1_struct_0(A),k7_cat_1(A,A,k10_cat_1(A)),k6_partfun1(u1_struct_0(A))) ) )).
fof(t73_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m2_cat_3(D,B,C,A) => ( ( r3_cat_3(B,C,A,D) & ! [E] : ! [F] : ~ ( r2_hidden(E,A) & r2_hidden(F,A) & k2_cat_1(B,k3_graph_1(B,k7_partfun1(u4_struct_0(B),D,E)),k3_graph_1(B,k7_partfun1(u4_struct_0(B),D,F))) = k1_xboole_0 ) ) => ! [E] : ( r2_hidden(E,A) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( F = k3_graph_1(B,k7_partfun1(u4_struct_0(B),D,E)) => ( k2_cat_1(B,F,C) = k1_xboole_0 | ! [G] : ( m1_cat_1(G,B,F,C) => ( G = k7_partfun1(u4_struct_0(B),D,E) => v2_cat_3(G,B,F,C) ) ) ) ) ) ) ) ) ) ) )).
fof(t73_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( k2_cat_1(A,B,D) != k1_xboole_0 & k2_cat_1(A,C,E) != k1_xboole_0 & k2_cat_1(A,k20_cat_4(A,B,C),k20_cat_4(A,D,E)) = k1_xboole_0 ) ) ) ) ) ) )).
fof(t73_cfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => ( v1_comseq_2(k2_partfun1(B,k2_numbers,C,A)) => ( v1_comseq_2(k2_partfun1(B,k1_numbers,k55_valued_1(B,k2_numbers,C),A)) & v1_comseq_2(k2_partfun1(B,k2_numbers,k31_valued_1(B,k2_numbers,C),A)) ) ) ) ) )).
fof(t73_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ( ! [D] : ( m3_glib_001(D,A) => ~ r1_glib_001(A,B,C,D) ) => ( B = C | r1_chord(A,B,C) | m2_chord(k1_xboole_0,A,B,C) ) ) ) ) ) )).
fof(t73_classes1,axiom,( ! [A] : ( v3_ordinal1(A) => k6_classes1(A) = A ) )).
fof(t73_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_clvect_1(D,A) => ( r2_hidden(C,k5_clvect_1(A,B,D)) <=> k5_clvect_1(A,B,D) = k5_clvect_1(A,C,D) ) ) ) ) ) )).
fof(t73_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_clvect_2(C,A) & k1_clvect_2(A,C) = B & r2_clvect_2(A,C,D) ) => ( v1_clvect_2(D,A) & k1_clvect_2(A,D) = B ) ) ) ) ) ) )).
fof(t73_cohsp_1,axiom,( ! [A] : ! [B] : k14_cohsp_1(A,B) = k2_xboole_0(k2_zfmisc_1(A,k1_tarski(1)),k2_zfmisc_1(B,k1_tarski(2))) )).
fof(t73_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k3_xxreal_0(A,B) = k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(A,B),k9_complex1(k6_xcmplx_0(A,B))),2) ) ) )).
fof(t73_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( A != k5_numbers & B != k5_numbers & ~ ( k3_complex1(k1_complex2(A,B)) = k5_numbers <=> ( k4_complex2(A,k5_numbers,B) = k7_xcmplx_0(k28_sin_cos,2) | k4_complex2(A,k5_numbers,B) = k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos) ) ) ) ) ) )).
fof(t73_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ( B != k4_struct_0(k1_complfld) => k7_xcmplx_0(k9_complex1(A),k9_complex1(B)) = k9_complex1(k3_vectsp_1(k1_complfld,A,B)) ) ) ) )).
fof(t73_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_comput_1(k4_ordinal1))) => ( v6_comput_1(A) => r1_tarski(k9_comput_1,A) ) ) )).
fof(t73_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(1,C) => k9_nat_1(k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,A),C) = k7_xcmplx_0(1,k2_power(C,B)) ) ) => ( r1_xxreal_0(B,1) | v2_comseq_3(A) ) ) ) ) )).
fof(t73_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( B = a_3_7_convex4(A,C,D) => v2_convex4(B,A) ) ) ) ) ) )).
fof(t73_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ( ~ r2_hidden(D,k24_qc_lang1(A,B)) => ( v2_cqc_the1(k7_cqc_lang(A,B,k12_cqc_lang(A,D,C)),A) <=> v2_cqc_the1(k12_cqc_lang(A,D,k7_cqc_lang(A,B,C)),A) ) ) ) ) ) ) )).
fof(t73_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),B,k4_normsp_1(A,B,k4_struct_0(A))) ) ) )).
fof(t73_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k7_xcmplx_0(1,k1_square_1(k19_sin_cos(D))) ) => ( A = B | k19_sin_cos(A) = k5_numbers | k19_sin_cos(B) = k5_numbers | k9_diff_1(C,A,B) = k7_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(16),k17_sin_cos(k7_xcmplx_0(k2_xcmplx_0(B,A),2))),k17_sin_cos(k7_xcmplx_0(k6_xcmplx_0(B,A),2))),k19_sin_cos(k7_xcmplx_0(k2_xcmplx_0(B,A),2))),k19_sin_cos(k7_xcmplx_0(k6_xcmplx_0(B,A),2))),k1_square_1(k2_xcmplx_0(k19_sin_cos(k2_xcmplx_0(A,B)),k19_sin_cos(k6_xcmplx_0(A,B))))),k6_xcmplx_0(A,B)) ) ) ) ) ) )).
fof(t73_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_enumset1(A,B,C,D) = k2_enumset1(C,D,A,B) )).
fof(t73_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => k22_rvsum_1(k7_euclid(3,A,B),k7_euclid(3,A,B)) = k2_xcmplx_0(k2_xcmplx_0(k22_rvsum_1(A,A),k3_xcmplx_0(2,k22_rvsum_1(A,B))),k22_rvsum_1(B,B)) ) ) )).
fof(t73_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ~ ( ~ r2_hidden(B,C) & v1_euclid_4(C,A) & ! [D] : ( m2_subset_1(D,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ~ ( r2_hidden(B,D) & r5_euclidlp(A,D,C) & D != C ) ) ) ) ) ) )).
fof(t73_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( 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)) & v1_finset_1(k6_exchsort(C,D)) ) => r2_hidden(k1_card_1(k6_exchsort(C,k9_funct_7(D,A,B))),k1_card_1(k6_exchsort(C,D))) ) ) ) )).
fof(t73_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(k4_tarski(k10_finseq_1(A,B),k3_facirc_1),k3_msafree2(k15_facirc_1(A,B,C))) & r2_hidden(k4_tarski(k10_finseq_1(B,C),k3_facirc_1),k3_msafree2(k15_facirc_1(A,B,C))) & r2_hidden(k4_tarski(k10_finseq_1(C,A),k3_facirc_1),k3_msafree2(k15_facirc_1(A,B,C))) ) )).
fof(t73_fdiff_11,axiom,( ! [A] : ( ( 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_cos9,k4_taylor_1(k7_xcmplx_0(3,2))),k7_xcmplx_0(2,3)))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) & ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & r1_xxreal_0(k1_funct_1(k1_sin_cos9,B),k5_numbers) ) ) ) => ( r2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k4_taylor_1(k7_xcmplx_0(3,2))),k7_xcmplx_0(2,3)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k4_taylor_1(k7_xcmplx_0(3,2))),k7_xcmplx_0(2,3)),A),B) = k7_xcmplx_0(k6_prepower(k1_funct_1(k1_sin_cos9,B),k7_xcmplx_0(1,2)),k2_xcmplx_0(1,k1_square_1(B))) ) ) ) ) ) )).
fof(t73_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r3_lattices(A,D,B) & r3_lattices(A,D,C) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r3_lattices(A,E,B) & r3_lattices(A,E,C) ) => r3_lattices(A,E,D) ) ) ) => D = k4_lattices(A,B,C) ) ) ) ) ) )).
fof(t73_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v20_lattices(B,A) & v21_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k10_filter_2(A,B))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k10_filter_2(A,B))) => ( ( C = E & D = F ) => ( k3_lattices(A,C,D) = k3_lattices(k10_filter_2(A,B),E,F) & k4_lattices(A,C,D) = k4_lattices(k10_filter_2(A,B),E,F) ) ) ) ) ) ) ) ) )).
fof(t73_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => k16_finseq_1(k2_finseq_1(k5_numbers),A) = k16_finseq_1(k2_finseq_1(k5_numbers),B) ) ) )).
fof(t73_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,B) => ! [G] : ( m1_subset_1(G,B) => ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,k2_zfmisc_1(A,B),C) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C))) ) => ! [I] : ( m2_finseq_1(I,A) => ! [J] : ( m2_finseq_1(J,B) => ( ( I = k10_finseq_1(D,E) & J = k10_finseq_1(F,G) ) => k3_funcop_1(H,I,J) = k10_finseq_1(k2_binop_1(A,B,C,H,D,F),k2_binop_1(A,B,C,H,E,G)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t73_finseq_3,axiom,( ! [A] : ! [B] : ( k1_finseq_3(k9_finseq_1(A),B) = k9_finseq_1(A) <=> ~ r2_hidden(A,B) ) )).
fof(t73_finseq_4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( v2_funct_1(B) & r2_hidden(A,k10_xtuple_0(B)) ) => k1_card_1(k10_relat_1(B,A)) = 1 ) ) )).
fof(t73_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m2_finseq_1(D,B) => ( r1_xxreal_0(A,k3_finseq_1(D)) => k7_partfun1(B,k5_finseq_5(B,D,C,A),k1_nat_1(A,1)) = C ) ) ) ) ) )).
fof(t73_finseq_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => k17_finseq_1(B,A,k17_finseq_1(B,A,C)) = k17_finseq_1(B,A,C) ) ) ) )).
fof(t73_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,B) & m2_finseq_1(C,A) ) => ! [D] : ( ( 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) ) => ( r2_relset_1(k4_ordinal1,A,k1_finseqop(A,A,A,D,C,k4_finseqop(A,A,C,k5_finseqop(A,D))),k5_finseq_2(A,B,k4_binop_1(A,D))) & r2_relset_1(k4_ordinal1,A,k1_finseqop(A,A,A,D,k4_finseqop(A,A,C,k5_finseqop(A,D)),C),k5_finseq_2(A,B,k4_binop_1(A,D))) ) ) ) ) ) ) )).
fof(t73_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k3_catalan2(A)) => r2_hidden(B,k7_flang_1(A,k9_flang_1(A),k1_afinsq_1(B))) ) )).
fof(t73_flang_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ( r2_hidden(B,k2_flang_2(A,C)) <=> ? [D] : ( v7_ordinal1(D) & r1_xxreal_0(D,1) & r2_hidden(B,k7_flang_1(A,C,D)) ) ) ) )).
fof(t73_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ( r2_hidden(k2_flang_1(A),C) => ( r1_tarski(B,k6_flang_1(A,B,k2_flang_3(A,C))) & r1_tarski(B,k6_flang_1(A,k2_flang_3(A,C),B)) ) ) ) ) )).
fof(t73_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r1_tarski(D,B) => ( D = k1_xboole_0 | k3_relat_1(k2_zfmisc_1(A,D),k2_zfmisc_1(B,C)) = k2_zfmisc_1(A,C) ) ) )).
fof(t73_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r1_tarski(k16_funcop_1(A,B),C) <=> ( r2_hidden(A,k9_xtuple_0(C)) & k1_funct_1(C,A) = B ) ) ) )).
fof(t73_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ! [B] : ~ ( r2_hidden(B,k10_xtuple_0(A)) & ! [C] : k8_relat_1(A,k1_tarski(B)) != k1_tarski(C) ) <=> v2_funct_1(A) ) ) )).
fof(t73_funct_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( r1_partfun1(B,C) => r2_relset_1(A,A,B,C) ) ) ) )).
fof(t73_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => k8_relat_1(k15_funct_3(C,D),k2_zfmisc_1(B,A)) = k2_zfmisc_1(k8_relat_1(C,B),k8_relat_1(D,A)) ) ) )).
fof(t73_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( r1_xboole_0(k9_xtuple_0(A),C) => k5_relat_1(k1_funct_4(A,B),C) = k5_relat_1(B,C) ) ) ) )).
fof(t73_funct_7,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_tarski(k10_xtuple_0(A),k9_xtuple_0(A)) => ( k9_xtuple_0(k8_funct_7(A,B)) = k9_xtuple_0(A) & r1_tarski(k10_xtuple_0(k8_funct_7(A,B)),k9_xtuple_0(A)) ) ) ) ) )).
fof(t73_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => r1_funct_8(A,k1_numbers,k1_numbers,k55_valued_1(k1_numbers,k1_numbers,k16_sin_cos)) ) )).
fof(t73_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_fvaluat1(C,A) => ( ( v3_fvaluat1(A) & m1_subset_1(B,u1_struct_0(k7_fvaluat1(A,C))) & m1_subset_1(k11_algstr_0(A,B),u1_struct_0(k7_fvaluat1(A,C))) ) => ( B = k4_struct_0(A) | k3_funct_2(u1_struct_0(A),k6_numbers,C,B) = k5_numbers ) ) ) ) ) )).
fof(t73_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t73_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : k3_msafree2(k29_gfacirc1(A,B,C)) = k1_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)) )).
fof(t73_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ! [D] : ! [E] : ( r2_hidden(E,k25_glib_000(A,B)) => ( ( r1_glib_000(A,C,D,E) => r1_glib_000(B,C,D,E) ) & ( r2_glib_000(A,C,D,E) => r2_glib_000(B,C,D,E) ) & ( r3_glib_000(A,C,D,E) => r3_glib_000(B,C,D,E) ) & ( r4_glib_000(A,C,D,E) => r4_glib_000(B,C,D,E) ) ) ) ) ) )).
fof(t73_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( r1_glib_000(A,k4_glib_001(A,B),D,C) => k11_glib_001(A,k10_glib_001(A,B,C)) = k7_finseq_1(k11_glib_001(A,B),k9_finseq_1(D)) ) ) ) )).
fof(t73_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( v1_group_3(C,A) & m1_group_2(C,A) ) => ? [D] : ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) & u1_struct_0(D) = k4_group_11(A,B,C) ) ) ) ) )).
fof(t73_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ( k7_group_1(A) = k7_group_1(B) => g3_algstr_0(u1_struct_0(B),u2_algstr_0(B)) = g3_algstr_0(u1_struct_0(A),u2_algstr_0(A)) ) ) ) )).
fof(t73_group_3,axiom,( ! [A] : ( ( ~ 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] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_group_2(A,k6_group_3(A,B,C),B) ) ) ) ) )).
fof(t73_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => k6_lattices(k11_group_4(A)) = k7_group_2(A) ) )).
fof(t73_group_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ( r1_struct_0(k9_group_5(B),A) <=> ? [C] : ( m2_finseq_1(C,u1_struct_0(B)) & ? [D] : ( m2_finseq_1(D,k4_numbers) & k3_finseq_1(C) = k3_finseq_1(D) & r1_tarski(k10_xtuple_0(C),k6_group_5(B)) & A = k3_group_4(B,k4_group_4(B,D,C)) ) ) ) ) )).
fof(t73_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ 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) => k7_struct_0(A) = k7_struct_0(B) ) ) ) )).
fof(t73_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( 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) ) ) ) ) )).
fof(t73_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_algstr_0(A) & v4_rlvect_1(A) & v1_vectsp_1(A) & v1_algstr_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v3_ideal_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v3_ideal_1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => r1_tarski(B,k11_ideal_1(A,B,C)) ) ) ) )).
fof(t73_integr11,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(A,B) & r1_tarski(B,k2_rcomp_1(k4_xcmplx_0(1),1)) & D = k1_taylor_1(2) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_1(C,E) = 1 ) ) & k9_xtuple_0(k2_sin_cos9) = B & 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),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),k7_xcmplx_0(1,2)))) ) => k2_integra5(A,k2_sin_cos9) = k6_xcmplx_0(k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),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),k7_xcmplx_0(1,2))),k2_seq_4(A)),k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),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),k7_xcmplx_0(1,2))),k3_seq_4(A))) ) ) ) ) ) )).
fof(t73_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k3_xcmplx_0(k28_sin_cos,2)) => k2_integra5(A,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)) = k5_numbers ) ) )).
fof(t73_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1)) => ( r1_tarski(A,B) => r1_tarski(k11_intpro_1(A),k11_intpro_1(B)) ) ) ) )).
fof(t73_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ! [C] : ( ( ~ 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)),k5_jgraph_4(A),C) & ? [D] : ( 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)),k5_jgraph_4(A),B),D) ) ) ) ) ) ) )).
fof(t73_jgraph_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_compts_1(C,k15_euclid(2)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ( v1_topreal2(C) & r2_hidden(A,C) & r2_hidden(B,C) ) => ( r1_jordan6(C,A,B) | r1_jordan6(C,B,A) ) ) ) ) ) )).
fof(t73_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) = E & k17_euclid(C) = E & k17_euclid(D) = F & 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(C),H) & 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t73_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) )).
fof(t73_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v8_limfunc1(B) & ! [C] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ r1_xxreal_0(C,D) & r2_hidden(D,k1_relset_1(k1_numbers,A)) ) ) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k10_prob_1(C))) => r1_xxreal_0(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) | v8_limfunc1(A) ) ) ) ) )).
fof(t73_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r4_limfunc2(B,A) & k2_limfunc2(B,A) = k5_numbers ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(A,k2_xcmplx_0(A,C)))) & r1_xxreal_0(k1_funct_1(B,D),k5_numbers) ) ) ) ) | r5_limfunc2(k6_rfunct_1(k1_numbers,k1_numbers,B),A) ) ) ) ) )).
fof(t73_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_limfunc3(B,A) & r1_limfunc2(C,k1_limfunc3(B,A)) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,D),A),k2_rcomp_1(A,k2_xcmplx_0(A,D))))) & r1_xxreal_0(k1_limfunc3(B,A),k1_funct_1(B,E)) ) ) ) ) | ( r1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) & k1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k1_limfunc2(C,k1_limfunc3(B,A)) ) ) ) ) ) ) )).
fof(t73_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => k16_lpspace1(A,B,C) = k8_lpspace2(A,B,C,1) ) ) ) )).
fof(t73_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_cqc_lang(A))) => ( r3_cqc_the1(A,D,k8_cqc_lang(A,B,k6_cqc_lang(A,C))) => r3_cqc_the1(A,D,k8_cqc_lang(A,C,k6_cqc_lang(A,B))) ) ) ) ) ) )).
fof(t73_mathmorp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => k9_mathmorp(k15_euclid(A),B,D,C) = k3_subset_1(u1_struct_0(k15_euclid(A)),k8_mathmorp(k15_euclid(A),k3_subset_1(u1_struct_0(k15_euclid(A)),B),C,D)) ) ) ) ) )).
fof(t73_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( ( v4_matrix10(B) & r2_matrix10(C,D) ) => r2_matrix10(C,k4_matrix10(A,B,D)) ) ) ) ) ) )).
fof(t73_matrix13,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ( ( r1_tarski(k2_zfmisc_1(C,D),k2_matrix_0(B)) & k5_card_1(C) = k5_card_1(D) ) => ( r1_xxreal_0(k5_card_1(C),k3_finseq_1(B)) & r1_xxreal_0(k5_card_1(D),k1_matrix_0(B)) ) ) ) ) ) ) )).
fof(t73_matrix15,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( k1_matrix_0(B) = k3_finseq_1(C) => ( r1_xxreal_0(k8_matrix13(A,k4_matrix_3(A,B,C)),k8_matrix13(A,B)) & r1_xxreal_0(k8_matrix13(A,k4_matrix_3(A,B,C)),k8_matrix13(A,C)) ) ) ) ) ) )).
fof(t73_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( k1_matrix_0(B) = k1_nat_1(D,1) & r2_hidden(C,k2_finseq_1(D)) ) => ( r1_xxreal_0(D,k5_numbers) | ( k8_matrix_0(A,k16_matrix_0(k1_matrix_0(B),A,B),C) = k8_matrix_0(A,B,C) & r2_hidden(C,k2_finseq_1(k1_matrix_0(k16_matrix_0(k1_matrix_0(B),A,B)))) ) ) ) ) ) ) ) )).
fof(t73_matrixj1,axiom,( ! [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] : ( ( v1_matrixj1(B,u1_struct_0(A)) & m2_finseq_1(B,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) => ! [C] : ( ( v1_matrixj1(C,u1_struct_0(A)) & m2_finseq_1(C,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) => ( k11_matrixj1(u1_struct_0(A),B) = k10_matrixj1(u1_struct_0(A),C) => ( k10_matrixj1(u1_struct_0(A),k26_matrixj1(A,B,C)) = k10_matrixj1(u1_struct_0(A),B) & k11_matrixj1(u1_struct_0(A),k26_matrixj1(A,B,C)) = k11_matrixj1(u1_struct_0(A),C) ) ) ) ) ) )).
fof(t73_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k3_matrixr2(A,k5_matrixr2(A)) = k5_numbers ) ) )).
fof(t73_mcart_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( ( r2_hidden(C,B) & r2_hidden(A,B) & k1_xtuple_0(C) = k1_xtuple_0(A) & k2_xtuple_0(C) = k2_xtuple_0(A) ) => C = A ) ) )).
fof(t73_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_membered(C) => k11_member_1(A,k9_member_1(B,C)) = k11_member_1(k11_member_1(A,B),C) ) ) ) )).
fof(t73_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k4_struct_0(B),k9_xtuple_0(C)) => k10_memstr_0(A,B,k9_memstr_0(A,B,C,D),D) = C ) ) ) ) ) )).
fof(t73_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( v1_xreal_0(D) => ( r2_mesfunc6(A,B,C) => r2_mesfunc6(A,B,k26_valued_1(A,k1_numbers,C,D)) ) ) ) ) ) )).
fof(t73_mmlquery,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( l1_mmlquery(B) => ! [C] : ( m2_finseq_1(C,u1_mmlquery(B)) => r1_tarski(k32_mmlquery(B,C),k35_mmlquery(B,C,A)) ) ) ) )).
fof(t73_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k25_modelc_2(k43_modelc_2)) => ( ~ r7_modelc_2(B,k3_modelc_2(A)) <=> r7_modelc_2(B,A) ) ) ) )).
fof(t73_monoid_0,axiom,( ! [A] : ! [B] : ( m1_subset_1(A,u1_struct_0(k15_monoid_0(B))) <=> ( v1_funct_1(A) & v1_funct_2(A,B,B) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) ) )).
fof(t73_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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_msafree4(B,u1_struct_0(A)) ) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,C)) => ( r1_msualg_3(A,k1_msafree3(A,B),C,D) => ! [E] : ( m2_pboole(E,u1_struct_0(A),B,k7_funcop_1(u1_struct_0(A),k4_ordinal1)) => ( v1_msualg_3(E) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,k1_msafree3(A,B)),F)) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,k1_msafree3(A,B)),F)) => ! [I] : ( m1_subset_1(I,k1_funct_1(u3_msualg_1(A,k3_equation(A)),F)) => ! [J] : ( m1_subset_1(J,k1_funct_1(u3_msualg_1(A,k3_equation(A)),F)) => ( ( I = k6_msafree4(A,B,E,G) & J = k6_msafree4(A,B,E,H) & r1_equation(A,C,F,k5_equation(A,F,I,J)) ) => k3_funct_2(k1_funct_1(u3_msualg_1(A,k1_msafree3(A,B)),F),k1_funct_1(u3_msualg_1(A,C),F),k2_msafree4(u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,C),D,F),G) = k3_funct_2(k1_funct_1(u3_msualg_1(A,k1_msafree3(A,B)),F),k1_funct_1(u3_msualg_1(A,C),F),k2_msafree4(u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,C),D,F),H) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t73_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( 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) => ( r4_nfcont_1(B,k4_normsp_0(u1_struct_0(B),A,D),C) & r9_ncfcont1(B,A,k5_vfunct_1(u1_struct_0(B),A,D),C) ) ) ) ) ) )).
fof(t73_newton,axiom,( ! [A] : ( v7_ordinal1(A) => r1_tarski(k9_newton(A),k2_finseq_1(A)) ) )).
fof(t73_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v9_o_ring_1(B,A) & v13_o_ring_1(C,A) ) => v13_o_ring_1(k6_algstr_0(A,B,C),A) ) ) ) ) )).
fof(t73_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r8_relat_2(A,B) => v8_relat_2(k2_wellord1(A,B)) ) ) )).
fof(t73_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => r2_ordinal2(k1_ordinal1(A),1) ) )).
fof(t73_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ! [D] : ( v3_ordinal1(D) => ( r2_hidden(k12_ordinal6(A,B),k12_ordinal6(C,D)) <=> ~ ( ~ ( A = C & r2_hidden(B,D) ) & ~ ( r2_hidden(A,C) & r2_hidden(B,k12_ordinal6(C,D)) ) & ~ ( r2_hidden(C,A) & r2_hidden(k12_ordinal6(A,B),D) ) ) ) ) ) ) ) )).
fof(t73_partfun1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_xboole_0,A))) ) => k5_partfun1(k1_xboole_0,A,B) = k1_tarski(B) ) )).
fof(t73_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => r6_pboole(A,k4_pboole(A,k4_pboole(A,B,C),D),k4_pboole(A,B,k2_pboole(A,C,D))) ) ) ) )).
fof(t73_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ( ( r7_pdiff_5(B,A) & r7_pdiff_5(C,A) ) => r3_pdiff_1(3,1,k20_valued_1(k1_euclid(3),k1_numbers,k1_numbers,k1_pdiff_3(3,3,B),k1_pdiff_3(3,3,C)),A) ) ) ) ) )).
fof(t73_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( ~ v1_xboole_0(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ( ( v1_pdiff_7(B,A) & r1_tarski(k1_rvsum_1(D),k2_finseq_1(A)) & r4_pdiff_9(A,B,D,E) ) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(F,k6_xcmplx_0(k3_finseq_1(D),1)) => ( r3_pdiff_9(A,B,k7_partfun1(k4_ordinal1,D,k1_nat_1(F,1)),k1_seqfunc(k1_euclid(A),k1_numbers,k4_pdiff_9(A,B,D,k26_valued_1(k1_euclid(A),k1_numbers,E,C)),F)) & r2_relset_1(k1_euclid(A),k1_numbers,k1_seqfunc(k1_euclid(A),k1_numbers,k4_pdiff_9(A,B,D,k26_valued_1(k1_euclid(A),k1_numbers,E,C)),F),k26_valued_1(k1_euclid(A),k1_numbers,k1_seqfunc(k1_euclid(A),k1_numbers,k4_pdiff_9(A,B,D,E),F),C)) ) ) ) ) ) ) ) ) ) )).
fof(t73_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( m1_subset_1(B,k8_polyform(A,k6_xcmplx_0(k7_polyform(A),1))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k17_polyform(A,k7_polyform(A)))) => ( C = k1_tarski(A) => k19_polyform(A,k7_polyform(A),B,C) = k3_pre_poly(u1_struct_0(k2_bspace),k5_struct_0(k2_bspace)) ) ) ) ) )).
fof(t73_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v3_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v3_valued_0(C) ) => r1_tarski(k13_pre_poly(k11_pre_poly(A,B,C)),k2_xboole_0(k13_pre_poly(B),k13_pre_poly(C))) ) ) )).
fof(t73_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => k6_prepower(1,A) = 1 ) )).
fof(t73_prob_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_finsub_1(B) & v1_prob_1(B,A) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => k9_prob_1(A,B) = k10_prob_3(A,B) ) ) )).
fof(t73_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,A) & v1_funct_1(E) & v1_partfun1(E,A) ) => ( ( v2_relat_1(B) & v2_relat_1(D) & r6_pboole(A,k6_pboole(A,B,D),k6_pboole(A,C,E)) ) => ( r6_pboole(A,B,C) & r6_pboole(A,D,E) ) ) ) ) ) ) )).
fof(t73_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( r3_qc_lang2(A,k14_qc_lang1(A,B,k13_qc_lang1(A,C)),k2_qc_lang2(A,B,C)) & r3_qc_lang2(A,B,k2_qc_lang2(A,B,C)) & r3_qc_lang2(A,k13_qc_lang1(A,C),k2_qc_lang2(A,B,C)) & r3_qc_lang2(A,C,k2_qc_lang2(A,B,C)) ) ) ) ) )).
fof(t73_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k7_quatern2(A) = k6_quaterni(k7_xcmplx_0(k13_quaterni(A),k1_square_1(k28_quaterni(A))),k4_xcmplx_0(k7_xcmplx_0(k14_quaterni(A),k1_square_1(k28_quaterni(A)))),k4_xcmplx_0(k7_xcmplx_0(k15_quaterni(A),k1_square_1(k28_quaterni(A)))),k4_xcmplx_0(k7_xcmplx_0(k16_quaterni(A),k1_square_1(k28_quaterni(A))))) ) )).
fof(t73_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => k28_quaterni(k27_quaterni(A)) = k28_quaterni(A) ) )).
fof(t73_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ( ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,k4_real_3(A),B),k5_numbers) ) => k9_nat_1(k1_numbers,k7_real_3(A),2) = k2_xcmplx_0(k9_nat_1(k1_numbers,k4_real_3(A),k5_numbers),k7_xcmplx_0(1,k2_xcmplx_0(k9_nat_1(k1_numbers,k4_real_3(A),1),k7_xcmplx_0(1,k9_nat_1(k1_numbers,k4_real_3(A),2))))) ) ) )).
fof(t73_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => k5_relat_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k5_relat_1(C,A),k5_relat_1(C,B)) ) )).
fof(t73_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(C))) => ! [G] : ( ( ~ v2_struct_0(G) & l1_rewrite3(G,F) ) => ( r1_rewrite3(F,G,A,D,B) => r1_rewrite1(k1_rewrite3(C,F,G),k4_tarski(A,k1_flang_1(C,D,E)),k4_tarski(B,E)) ) ) ) ) ) ) )).
fof(t73_rfunct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) ) => ( v1_comseq_2(k5_relat_1(B,A)) <=> ? [C] : ( v1_xreal_0(C) & ! [D] : ( r2_hidden(D,k3_xboole_0(A,k9_xtuple_0(B))) => r1_xxreal_0(k9_complex1(k1_funct_1(B,D)),C) ) ) ) ) )).
fof(t73_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ! [E] : ( v1_finset_1(E) => ( E = k1_relset_1(A,k2_partfun1(A,k1_numbers,B,D)) => k20_rfunct_3(A,k15_valued_1(A,k1_numbers,B,C),D) = k8_rvsum_1(k20_rfunct_3(A,B,D),k2_finseq_2(k5_card_1(E),C)) ) ) ) ) ) )).
fof(t73_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v8_valued_0(B) & v2_seq_2(B) ) => ( k1_funct_1(k3_rinfsup1(B),A) = k2_rinfsup1(B) & v3_funct_1(k3_rinfsup1(B)) ) ) ) ) )).
fof(t73_rlaffin1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_rlaffin1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( ( r2_hidden(A,k4_rlaffin1(B,C)) & ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r2_hidden(D,C) => r1_xxreal_0(k5_numbers,k3_funct_2(u1_struct_0(B),k1_numbers,k5_rlaffin1(B,C,A),D)) ) ) ) => r2_hidden(A,k3_convex1(B,C)) ) ) ) )).
fof(t73_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( m2_rlsub_1(B,A,k1_rlsub_1(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B != k6_domain_1(u1_struct_0(A),C) ) ) ) ) )).
fof(t73_rltopsp1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_tarski(k1_rltopsp1(A,B,C),k5_rltopsp1(A,B,C)) ) ) ) )).
fof(t73_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ( k3_finseq_1(B) = k5_numbers => k4_rlvect_1(A,B) = k4_struct_0(A) ) ) ) )).
fof(t73_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m2_rmod_2(D,A,B,C) => ( r2_hidden(k4_struct_0(B),D) <=> D = u1_struct_0(C) ) ) ) ) ) )).
fof(t73_rmod_4,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( r1_tarski(C,D) => m1_rmod_2(k10_rmod_4(A,B,C),A,k10_rmod_4(A,B,D)) ) ) ) ) ) )).
fof(t73_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m2_rusub_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & r2_hidden(E,C) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_struct_0(B,F) & k3_rlvect_1(A,D,F) = E ) ) ) ) ) ) ) ) )).
fof(t73_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => k16_rvsum_1(k9_finseq_1(A)) = A ) )).
fof(t73_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(B,k7_card_1(3),k1_scmfsa_2,k5_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v6_amistd_1(C,k7_card_1(3),k1_scmfsa_2) ) => ( ( r1_tarski(C,A) & r1_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B) ) => ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(D,k8_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B)) => r8_pboole(u1_struct_0(k1_scmfsa_2),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B,D),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),B,D)) ) ) ) ) ) ) )).
fof(t73_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ~ v2_extpro_1(k7_scmfsa_2(A,B),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(t73_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => k5_memstr_0(2,k1_scmpds_2,k6_scmpds_4(k7_scmpds_6(D,E,C),B,A)) = k1_nat_1(k5_card_1(C),1) ) ) ) ) ) )).
fof(t73_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( ( v4_scmyciel(B) & v5_scmyciel(B) & m1_subset_1(B,k1_zfmisc_1(k6_scmyciel(A))) ) => ( v9_scmyciel(k3_tarski(B),A) & m1_subset_1(k3_tarski(B),k1_zfmisc_1(k3_tarski(A))) ) ) ) )).
fof(t73_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r3_semi_af1(A,C,B,E,F) & r3_semi_af1(A,D,B,E,G) ) => r2_analoaf(A,C,D,F,G) ) ) ) ) ) ) ) ) )).
fof(t73_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => ( k17_seq_4(A,B,C) = k15_seq_4(A) => B = C ) ) ) ) )).
fof(t73_setlim_1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [E] : ( ( v5_relat_1(E,B) & v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ! [F] : ( v7_ordinal1(F) => k1_funct_1(E,F) = k2_xboole_0(k1_funct_1(C,F),k1_funct_1(D,F)) ) => r1_tarski(k4_subset_1(A,k3_kurato_0(A,C),k3_kurato_0(A,D)),k3_kurato_0(A,E)) ) ) ) ) ) )).
fof(t73_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ( v3_kurato_0(B,A) & v3_kurato_0(C,A) ) => k4_kurato_0(A,k4_setlim_2(A,B,C)) = k5_subset_1(A,k4_kurato_0(A,B),k4_kurato_0(A,C)) ) ) ) )).
fof(t73_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(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))) ) ) ) ) ) )).
fof(t73_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k1_funct_1(k16_sin_cos,k2_xcmplx_0(A,B)) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,A),k1_funct_1(k18_sin_cos,B)),k3_xcmplx_0(k1_funct_1(k18_sin_cos,A),k1_funct_1(k16_sin_cos,B))) & k1_funct_1(k18_sin_cos,k2_xcmplx_0(A,B)) = k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,A),k1_funct_1(k18_sin_cos,B)),k3_xcmplx_0(k1_funct_1(k16_sin_cos,A),k1_funct_1(k16_sin_cos,B))) ) ) ) )).
fof(t73_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) & k2_sin_cos6(A) = k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)) ) => A = k4_xcmplx_0(1) ) ) )).
fof(t73_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => k4_sin_cos2(k3_xcmplx_0(5,A)) = k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(5,k4_sin_cos2(A)),k3_xcmplx_0(20,k1_newton(k4_sin_cos2(A),3))),k3_xcmplx_0(16,k1_newton(k4_sin_cos2(A),5))) ) )).
fof(t73_sin_cos9,axiom,( r2_fdiff_1(k1_sin_cos9,k2_rcomp_1(k4_xcmplx_0(1),1)) )).
fof(t73_sincos10,axiom,( k1_funct_1(k1_sincos10,1) = k5_numbers & k1_funct_1(k1_sincos10,k3_square_1(2)) = k7_xcmplx_0(k28_sin_cos,4) )).
fof(t73_sprect_1,axiom,( ! [A] : ( ( ~ 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_relset_1(u1_struct_0(k15_euclid(2)),k1_numbers,k4_pscomp_1,k1_rltopsp1(k15_euclid(2),k13_pscomp_1(A),k10_pscomp_1(A))) = k1_rcomp_1(k6_pscomp_1(A),k8_pscomp_1(A)) ) )).
fof(t73_sprect_2,axiom,( ! [A] : ( ( ~ 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,k24_pscomp_1(k3_topreal1(2,A)))) ) ) )).
fof(t73_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_valuat_1(D,A,C) => ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [F] : ( m2_subset_1(F,k16_substut1(A),k38_substut1(A)) => ! [G] : ( m1_substut1(G,A,k7_sublemma(A,F,B)) => ( ! [H] : ( m1_subset_1(H,C) => r1_sublemma(A,F,C,k1_sublemma(A,C,k1_sublemma(A,C,E,k13_sublemma(A,F,B,G,C,E)),k12_sublemma(A,C,B,H)),D) ) <=> ! [H] : ( m1_subset_1(H,C) => r1_valuat_1(A,C,k2_sublemma(A,F),D,k1_sublemma(A,C,k1_sublemma(A,C,E,k13_sublemma(A,F,B,G,C,E)),k12_sublemma(A,C,B,H))) ) ) ) ) ) ) ) ) ) )).
fof(t73_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v2_tdlat_2(B,A) => v2_tops_2(B,A) ) ) ) )).
fof(t73_tex_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_tdlat_3(B) & m1_pre_topc(B,A) ) => r1_borsuk_1(A,B) ) ) )).
fof(t73_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_tex_3(B,A) & m1_pre_topc(B,A) ) => ~ ( ~ ( v1_tex_3(B,A) & v1_tsep_1(B,A) ) & ! [C] : ( ( ~ v2_struct_0(C) & v1_pre_topc(C) & v1_tsep_1(C,A) & v1_tex_2(C,A) & v1_tex_3(C,A) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & v1_pre_topc(D) & v4_tex_3(D,A) & m1_pre_topc(D,A) ) => ~ ( r1_tsep_1(C,D) & k1_tsep_1(A,C,D) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) ) ) ) ) ) ) )).
fof(t73_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => m1_pre_topc(k1_tex_2(A,B),k5_tex_4(A,B)) ) ) )).
fof(t73_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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)))) ) => ( ( C = A & r1_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),u1_struct_0(B),E,G) ) => ( r2_funct_2(u1_struct_0(D),u1_struct_0(B),k3_tmap_1(A,B,C,D,G),F) <=> r2_funct_2(u1_struct_0(D),u1_struct_0(B),k2_tmap_1(A,B,E,D),F) ) ) ) ) ) ) ) ) ) )).
fof(t73_topgen_5,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( r2_hidden(B,D) & r2_hidden(C,D) & v1_tops_2(k2_xboole_0(D,k6_domain_1(k1_zfmisc_1(u1_struct_0(A)),k4_subset_1(u1_struct_0(A),B,C))),A) & v1_cantor_1(k2_xboole_0(D,k6_domain_1(k1_zfmisc_1(u1_struct_0(A)),k4_subset_1(u1_struct_0(A),B,C))),A) & m1_subset_1(k2_xboole_0(D,k6_domain_1(k1_zfmisc_1(u1_struct_0(A)),k4_subset_1(u1_struct_0(A),B,C))),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) => ( v1_tops_2(D,A) & v1_cantor_1(D,A) & m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) ) ) ) )).
fof(t73_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v9_rltopsp1(A,k15_euclid(2)) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(k15_euclid(2)),k1_numbers) & v1_pscomp_1(B,k15_euclid(2)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k15_euclid(2)),k1_numbers))) ) => r1_tarski(k5_measure6(k7_relset_1(u1_struct_0(k15_euclid(2)),k1_numbers,B,A)),k7_relset_1(u1_struct_0(k15_euclid(2)),k1_numbers,B,k2_pre_topc(k15_euclid(2),A))) ) ) ) )).
fof(t73_tops_3,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( l1_pre_topc(B) => ( ( u1_struct_0(A) = u1_struct_0(B) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => ( v4_pre_topc(C,A) <=> v4_pre_topc(D,B) ) ) ) ) ) => g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) ) ) ) )).
fof(t73_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_aff_1(A,C,D,E) <=> r1_aff_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),k3_funct_2(u1_struct_0(A),u1_struct_0(A),B,E)) ) ) ) ) ) ) ) )).
fof(t73_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_trees_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_trees_1(D) ) => ( k13_trees_3(A,B) = k13_trees_3(C,D) => ( A = C & B = D ) ) ) ) ) ) )).
fof(t73_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( ( r3_tsep_1(A,B,D) & r3_tsep_1(A,C,D) ) <=> r3_tsep_1(A,k1_tsep_1(A,B,C),D) ) ) ) ) ) )).
fof(t73_valued_2,axiom,( ! [A] : ! [B] : ( v1_valued_2(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_valued_0(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_valued_0(E) ) => k69_valued_2(k3_xboole_0(A,k9_xtuple_0(D)),k2_valued_2(k1_valued_2(B)),k63_valued_2(A,B,C,D),E) = k63_valued_2(A,B,C,k50_valued_1(D,E)) ) ) ) ) )).
fof(t73_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => m2_vectsp_4(u1_struct_0(C),A,B,C) ) ) ) )).
fof(t73_waybel23,axiom,( ! [A] : ( l1_pre_topc(A) => ! [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)))) ) => r1_ordinal1(k2_waybel23(A),k1_card_1(B)) ) ) )).
fof(t73_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ 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))) ) => r4_waybel_0(A,B,C,D) ) => v22_waybel_0(C,A,B) ) ) ) ) )).
fof(t73_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v9_waybel_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k4_yellow_0(A) = k6_waybel_1(A,B,k4_yellow_0(A)) ) ) ) )).
fof(t73_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r1_tarski(A,k2_xboole_0(B,C)) & r1_xboole_0(A,C) ) => r1_tarski(A,B) ) )).
fof(t73_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k10_xboolean(k10_xboolean(A,B),C) = k10_xboolean(A,k10_xboolean(B,C)) ) ) ) )).
fof(t73_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k3_xcmplx_0(A,B) = 1 => A = k7_xcmplx_0(1,B) ) ) ) )).
fof(t73_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(C,k5_numbers) & r1_xxreal_0(A,B) ) => r1_xxreal_0(k7_xcmplx_0(B,C),k7_xcmplx_0(A,C)) ) ) ) ) )).
fof(t73_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(D,C) & k2_xxreal_1(C,D) = k1_xxreal_1(A,B) ) ) ) ) ) )).
fof(t73_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ( v4_xxreal_2(A) <=> k1_xxreal_2(A) != k1_xxreal_0 ) ) )).
fof(t73_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( 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) != k5_numbers ) ) ) )).
fof(t73_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v4_zf_lang(A) => r3_zf_lang(k20_zf_lang(A),A) ) ) )).
fof(t73_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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,k13_zf_lang(B,A)) <=> ? [E] : ( m1_subset_1(E,C) & r1_zf_model(C,k2_zf_lang1(C,D,B,E),A) ) ) ) ) ) ) )).
fof(t73_zfmisc_1,axiom,( ! [A] : ! [B] : ( r2_hidden(B,A) => r1_tarski(B,k3_tarski(A)) ) )).
fof(t73_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_zmodul01(D,A) => ( r2_hidden(B,k5_zmodul01(A,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r1_struct_0(D,E) & B = k5_algstr_0(A,C,E) ) ) ) ) ) ) )).
fof(t73_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => m1_zmodul01(k33_zmodul02(A,k9_subset_1(u1_struct_0(A),B,C)),k7_zmodul01(A,k33_zmodul02(A,B),k33_zmodul02(A,C))) ) ) ) )).
fof(t74_abcmiz_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( r1_rewrite1(B,C,D) => r2_hidden(D,A) ) ) ) ) )).
fof(t74_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v9_abcmiz_1(B,A) & m1_abcmiz_1(B,A,k12_abcmiz_1(A)) ) => ? [C] : ( v2_abcmiz_1(C,A) & m1_subset_1(C,u4_struct_0(A)) & k2_msualg_1(A,C) = k12_abcmiz_1(A) & ? [D] : ( 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) ) ) ) ) )).
fof(t74_afinsq_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => k1_afinsq_1(k1_ordinal4(B,k5_afinsq_1(A))) = k1_nat_1(k1_afinsq_1(B),1) ) )).
fof(t74_afinsq_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k8_afinsq_1(A)) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,k8_afinsq_1(A)) & v1_funct_1(C) & v5_ordinal1(C) & v1_finset_1(C) ) => k8_afinsq_2(A,k1_ordinal4(B,C)) = k15_afinsq_1(A,k8_afinsq_2(A,B),k8_afinsq_2(A,C)) ) ) )).
fof(t74_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ( v3_freealg(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( k14_aofa_000(A,B,C,D) != B & k14_aofa_000(A,B,C,D) != C & k14_aofa_000(A,B,C,D) != D & k14_aofa_000(A,B,C,D) != k16_aofa_000(A,E,F) & ( k14_aofa_000(A,B,C,D) = k14_aofa_000(A,E,F,G) => ( B = E & C = F & D = G ) ) ) ) ) ) ) ) ) ) ) )).
fof(t74_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v19_aofa_a00(B,A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( ( v4_msualg_1(C,A) & v17_aofa_a00(C,A) & v20_aofa_a00(C,4,1,A) & v22_aofa_a00(C,A,1,1,11) & l3_msualg_1(C,A) ) => ( k1_msafree4(u1_struct_0(A),u3_msualg_1(A,C),k37_aofa_a00(A)) = k8_afinsq_1(k4_numbers) & ! [D] : ( m1_subset_1(D,k1_funct_1(u3_msualg_1(A,C),B)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,C),B)) => ( ( v1_int_1(D) & ~ v3_xxreal_0(D) ) => k41_aofa_a00(A,C,B,D,E) = k8_funcop_1(k1_funct_1(u3_msualg_1(A,C),B),D,E) ) ) ) & ! [D] : ( m1_msafree4(D,u1_struct_0(A),u3_msualg_1(A,C),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,C),k37_aofa_a00(A))) => ( k38_aofa_a00(A,C,D,B) = k1_card_1(D) & ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,C),B)) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ( ( F = D & r2_hidden(E,k9_xtuple_0(F)) ) => ( k39_aofa_a00(A,C,D,B,E) = k1_funct_1(F,E) & ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),B)) => k40_aofa_a00(A,C,D,B,E,G) = k1_funct_7(F,E,G) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t74_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ( r2_hidden(a_1_0_arytm_3(A),k5_arytm_3) <=> A = k11_arytm_3 ) ) )).
fof(t74_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(k1_nat_1(C,1),D) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(k1_nat_1(C,1),E) & r1_xxreal_0(E,D) ) => r1_xxreal_0(k9_nat_1(k1_numbers,A,E),k9_nat_1(k1_numbers,B,E)) ) ) ) => r1_xxreal_0(k7_series_1(A,D,C),k7_series_1(B,D,C)) ) ) ) ) ) )).
fof(t74_bcialg_1,axiom,( ! [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) ) => ( v14_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t74_borsuk_5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_connsp_1(A,k3_topmetr) & v2_compts_1(A,k3_topmetr) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ( ( A = B & r1_tarski(k1_rcomp_1(k3_seq_4(B),k2_seq_4(B)),B) ) => k1_rcomp_1(k3_seq_4(B),k2_seq_4(B)) = B ) ) ) )).
fof(t74_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( m1_borsuk_2(G,A,C,D) => ! [H] : ( m1_borsuk_2(H,A,D,E) => r4_borsuk_2(A,B,E,k1_borsuk_2(A,B,D,E,k1_borsuk_2(A,B,C,D,F,G),H),k1_borsuk_2(A,B,C,E,F,k1_borsuk_2(A,C,D,E,G,H))) ) ) ) ) ) ) ) ) )).
fof(t74_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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),k7_bvfunc_2(A,k1_bvfunc_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) )).
fof(t74_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_eqrel_1(I,A) => ! [J] : ( m1_eqrel_1(J,A) => ! [K] : ( 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,J,B) = k2_partit1(A,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),K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t74_card_2,axiom,( ! [A] : ( v1_card_1(A) => ( ~ v1_finset_1(A) => k1_card_2(A,A) = A ) ) )).
fof(t74_card_3,axiom,( ! [A] : ( ( v4_funct_1(A) & v2_card_3(A) ) => r1_tarski(A,k4_card_3(k10_card_3(A))) ) )).
fof(t74_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k8_cat_1(A,A,k10_cat_1(A),B) = B ) ) )).
fof(t74_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_cat_1(E,B,C,D) => ! [F] : ( m2_cat_3(F,B,C,A) => ( ( r3_cat_3(B,C,A,F) & k3_graph_1(B,E) = C & k4_graph_1(B,E) = D & v9_cat_1(E,B,C,D) ) => r3_cat_3(B,D,A,k7_cat_3(B,A,F,E)) ) ) ) ) ) ) )).
fof(t74_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k31_cat_4(A,B,C,B,C,k4_cat_1(A,B),k4_cat_1(A,C)) = k4_cat_1(A,k20_cat_4(A,B,C)) ) ) ) )).
fof(t74_cfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,k2_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,k2_numbers))) ) => ( ( v1_comseq_2(k2_partfun1(C,k2_numbers,D,A)) & v1_comseq_2(k2_partfun1(C,k2_numbers,E,B)) ) => v1_comseq_2(k2_partfun1(C,k2_numbers,k2_valued_1(C,k2_numbers,k2_numbers,D,E),k3_xboole_0(A,B))) ) ) ) ) )).
fof(t74_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ~ ( B != C & ~ r1_chord(A,B,C) & ~ ! [D] : ( m2_chord(D,A,B,C) => ! [E] : ( 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] : ( m1_subset_1(F,k6_glib_000(E)) => k9_subset_1(k6_glib_000(A),k1_glib_002(E,F),D) = k1_xboole_0 ) ) ) ) ) ) ) )).
fof(t74_classes1,axiom,( ! [A] : ( k6_classes1(k1_classes1(A)) != k1_xboole_0 & v4_ordinal1(k6_classes1(k1_classes1(A))) ) )).
fof(t74_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_clvect_1(C,A) => ( k5_clvect_1(A,B,C) = k5_clvect_1(A,k4_algstr_0(A,B),C) <=> r1_struct_0(C,B) ) ) ) ) )).
fof(t74_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v3_clvect_2(B,A) & v3_clvect_2(C,A) ) => v3_clvect_2(k16_csspace(A,B,C),A) ) ) ) ) )).
fof(t74_cohsp_1,axiom,( ! [A] : ( k14_cohsp_1(A,k1_xboole_0) = k2_zfmisc_1(A,k1_tarski(1)) & k14_cohsp_1(k1_xboole_0,A) = k2_zfmisc_1(A,k1_tarski(2)) ) )).
fof(t74_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k4_xxreal_0(A,B) = k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),k9_complex1(k6_xcmplx_0(A,B))),2) ) ) )).
fof(t74_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( A != k5_numbers & B != k5_numbers & ~ ( ~ ( ( k4_complex1(k1_complex2(A,B)) = k3_xcmplx_0(k9_complex1(A),k9_complex1(B)) | k4_complex1(k1_complex2(A,B)) = k4_xcmplx_0(k3_xcmplx_0(k9_complex1(A),k9_complex1(B))) ) & k4_complex2(A,k5_numbers,B) != k7_xcmplx_0(k28_sin_cos,2) & k4_complex2(A,k5_numbers,B) != k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos) ) & ~ ( ( k4_complex2(A,k5_numbers,B) = k7_xcmplx_0(k28_sin_cos,2) | k4_complex2(A,k5_numbers,B) = k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos) ) & k4_complex1(k1_complex2(A,B)) != k3_xcmplx_0(k9_complex1(A),k9_complex1(B)) & k4_complex1(k1_complex2(A,B)) != k4_xcmplx_0(k3_xcmplx_0(k9_complex1(A),k9_complex1(B))) ) ) ) ) ) )).
fof(t74_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => k1_binop_1(k4_group_1(k1_complfld),A,B) = k1_newton(A,B) ) ) )).
fof(t74_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(B,1) & ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(1,C) => k9_nat_1(k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,A),C) = k7_xcmplx_0(1,k2_power(C,B)) ) ) & v2_comseq_3(A) ) ) ) )).
fof(t74_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( B = a_3_8_convex4(A,C,D) => v2_convex4(B,A) ) ) ) ) ) )).
fof(t74_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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) & v2_cqc_the1(k8_cqc_lang(A,k8_cqc_lang(A,B,k11_cqc_lang(A,D,C)),k11_cqc_lang(A,D,k8_cqc_lang(A,B,C))),A) ) ) ) ) ) ) )).
fof(t74_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),B,k5_vfunct_1(k4_ordinal1,A,k5_vfunct_1(k4_ordinal1,A,B))) ) ) )).
fof(t74_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k7_xcmplx_0(1,k1_square_1(k19_sin_cos(D))) ) => ( k19_sin_cos(B) = k5_numbers | k19_sin_cos(k2_xcmplx_0(B,A)) = k5_numbers | k1_funct_1(k3_diff_1(C,A),B) = k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(16),k17_sin_cos(k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(2,B),A),2))),k17_sin_cos(k7_xcmplx_0(k4_xcmplx_0(A),2))),k19_sin_cos(k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(2,B),A),2))),k19_sin_cos(k7_xcmplx_0(k4_xcmplx_0(A),2))),k1_square_1(k2_xcmplx_0(k19_sin_cos(k2_xcmplx_0(k3_xcmplx_0(2,B),A)),k19_sin_cos(A)))) ) ) ) ) ) )).
fof(t74_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_enumset1(A,B,C,D) = k2_enumset1(C,D,B,A) )).
fof(t74_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => k5_euclid_8(A,B) = k6_euclid(3,k5_euclid_8(B,A)) ) ) )).
fof(t74_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [G] : ( m2_subset_1(G,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ( ( r2_hidden(B,F) & r2_hidden(C,F) & r2_hidden(D,G) & r2_hidden(E,G) & r6_euclidlp(A,F,G) ) => ( B = C | D = E | r4_euclidlp(A,k8_euclid(A,C,B),k8_euclid(A,E,D)) ) ) ) ) ) ) ) ) ) )).
fof(t74_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( v1_relat_1(D) & v5_relat_1(D,u1_struct_0(C)) & v1_funct_1(D) & v1_finset_1(D) & v1_exchsort(D) ) => ~ ( r2_hidden(k4_tarski(A,B),k6_exchsort(C,D)) & r1_xxreal_0(k5_card_1(k6_exchsort(C,D)),k5_card_1(k6_exchsort(C,k9_funct_7(D,A,B)))) ) ) ) )).
fof(t74_facirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ( r2_hidden(A,k2_msafree2(k15_facirc_1(A,B,C))) & r2_hidden(B,k2_msafree2(k15_facirc_1(A,B,C))) & r2_hidden(C,k2_msafree2(k15_facirc_1(A,B,C))) ) ) ) ) )).
fof(t74_fdiff_11,axiom,( ! [A] : ( ( 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,k2_sin_cos9,k4_taylor_1(k7_xcmplx_0(3,2))),k7_xcmplx_0(2,3)))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k4_taylor_1(k7_xcmplx_0(3,2))),k7_xcmplx_0(2,3)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k4_taylor_1(k7_xcmplx_0(3,2))),k7_xcmplx_0(2,3)),A),B) = k4_xcmplx_0(k7_xcmplx_0(k6_prepower(k1_funct_1(k2_sin_cos9,B),k7_xcmplx_0(1,2)),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t74_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r3_lattices(A,B,D) & r3_lattices(A,C,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r3_lattices(A,B,E) & r3_lattices(A,C,E) ) => r3_lattices(A,D,E) ) ) ) => D = k3_lattices(A,B,C) ) ) ) ) ) )).
fof(t74_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v20_lattices(B,A) & v21_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k10_filter_2(A,B))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k10_filter_2(A,B))) => ( ( C = E & D = F ) => ( r3_lattices(A,C,D) <=> r3_lattices(k10_filter_2(A,B),E,F) ) ) ) ) ) ) ) ) )).
fof(t74_finseq_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => m2_finseq_1(k12_finseq_1(A,B),A) ) ) )).
fof(t74_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,B) => ! [H] : ( m1_subset_1(H,B) => ! [I] : ( m1_subset_1(I,B) => ! [J] : ( ( v1_funct_1(J) & v1_funct_2(J,k2_zfmisc_1(A,B),C) & m1_subset_1(J,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C))) ) => ! [K] : ( m2_finseq_1(K,A) => ! [L] : ( m2_finseq_1(L,B) => ( ( K = k11_finseq_1(D,E,F) & L = k11_finseq_1(G,H,I) ) => k3_funcop_1(J,K,L) = k11_finseq_1(k2_binop_1(A,B,C,J,D,G),k2_binop_1(A,B,C,J,E,H),k2_binop_1(A,B,C,J,F,I)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t74_finseq_3,axiom,( ! [A] : ! [B] : ( k1_finseq_3(k9_finseq_1(A),B) = k1_xboole_0 <=> r2_hidden(A,B) ) )).
fof(t74_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( k7_finseq_4(A,B,C,D) = k7_finseq_1(k11_finseq_1(A,B,C),k9_finseq_1(D)) & k7_finseq_4(A,B,C,D) = k7_finseq_1(k10_finseq_1(A,B),k10_finseq_1(C,D)) & k7_finseq_4(A,B,C,D) = k7_finseq_1(k9_finseq_1(A),k11_finseq_1(B,C,D)) & k7_finseq_4(A,B,C,D) = 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)) ) )).
fof(t74_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m2_finseq_1(D,B) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(k1_nat_1(A,1),E) & r1_xxreal_0(E,k3_finseq_1(D)) ) => k7_partfun1(B,k5_finseq_5(B,D,C,A),k1_nat_1(E,1)) = k7_partfun1(B,D,E) ) ) ) ) ) ) )).
fof(t74_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r2_hidden(B,k10_xtuple_0(C)) => k1_finseq_5(A,k1_finseq_5(A,C,B),B) = k1_finseq_5(A,C,B) ) ) ) ) )).
fof(t74_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,B) & m2_finseq_1(C,A) ) => ! [D] : ( ( v3_card_1(D,B) & m2_finseq_1(D,A) ) => ! [E] : ( ( 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_finseqop(E,A) & v1_setwiseo(E,A) & r2_relset_1(k4_ordinal1,A,k1_finseqop(A,A,A,E,C,D),k5_finseq_2(A,B,k4_binop_1(A,E))) ) => ( r2_relset_1(k4_ordinal1,A,C,k4_finseqop(A,A,D,k5_finseqop(A,E))) & r2_relset_1(k4_ordinal1,A,k4_finseqop(A,A,C,k5_finseqop(A,E)),D) ) ) ) ) ) ) ) )).
fof(t74_flang_1,axiom,( ! [A] : k8_flang_1(A,k9_flang_1(A)) = k3_catalan2(A) )).
fof(t74_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(C,1) => r1_tarski(k7_flang_1(A,B,C),k2_flang_2(A,B)) ) ) ) )).
fof(t74_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => k6_flang_1(A,k2_flang_3(A,B),k2_flang_3(A,B)) = k1_flang_3(A,B,2) ) )).
fof(t74_fomodel0,axiom,( ! [A] : ( A != k1_xboole_0 => a_1_6_fomodel0(A) = A ) )).
fof(t74_funcop_1,axiom,( ! [A] : ! [B] : r2_hidden(A,k9_xtuple_0(k16_funcop_1(A,B))) )).
fof(t74_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => r1_tarski(k7_relat_1(B,k8_relat_1(B,A)),A) ) )).
fof(t74_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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 ) => ( r1_partfun1(C,D) <=> ! [E] : ( r2_hidden(E,k1_relset_1(A,C)) => k1_funct_1(C,E) = k1_funct_1(D,E) ) ) ) ) ) )).
fof(t74_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( k9_xtuple_0(B) = k9_xtuple_0(C) => k1_funct_4(k1_funct_4(A,B),C) = k1_funct_4(A,C) ) ) ) ) )).
fof(t74_funct_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_relat_1(B) => k3_relat_1(k6_partfun1(k1_relat_1(B)),k8_funct_7(B,A)) = k8_funct_7(B,A) ) ) )).
fof(t74_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => r1_funct_8(A,k1_numbers,k1_numbers,k55_valued_1(k1_numbers,k1_numbers,k18_sin_cos)) ) )).
fof(t74_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_fvaluat1(C,A) => ( ( v3_fvaluat1(A) & k3_funct_2(u1_struct_0(A),k6_numbers,C,B) = k5_numbers ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_ideal_1(D,k7_fvaluat1(A,C)) & v2_ideal_1(D,k7_fvaluat1(A,C)) & v3_ideal_1(D,k7_fvaluat1(A,C)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k7_fvaluat1(A,C)))) ) => ( r2_hidden(B,D) <=> D = u1_struct_0(k7_fvaluat1(A,C)) ) ) ) ) ) ) )).
fof(t74_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_2(B,u1_struct_0(A),k4_finseq_2(k5_numbers,u1_struct_0(A))) => k4_rlvect_1(A,B) = k4_struct_0(A) ) ) )).
fof(t74_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : k3_msafree2(k31_gfacirc1(A,B,C)) = k2_xboole_0(k1_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)),k1_tarski(k33_gfacirc1(A,B,C))) )).
fof(t74_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v9_glib_000(B,A) & m1_glib_000(B,A) ) => ! [C] : ( ( v9_glib_000(C,B) & m1_glib_000(C,B) ) => ( v9_glib_000(C,A) & m1_glib_000(C,A) ) ) ) ) )).
fof(t74_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m3_glib_001(D,B) => ( C = D => k11_glib_001(A,C) = k11_glib_001(B,D) ) ) ) ) ) )).
fof(t74_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( v1_group_3(C,A) & m1_group_2(C,A) ) => ~ ( m1_group_2(C,B) & ! [D] : ( ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) ) => u1_struct_0(D) != k3_group_11(A,B,C) ) ) ) ) ) )).
fof(t74_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_group_2(D,A) => ( ( r2_hidden(B,k8_group_2(A,D)) & r2_hidden(C,k8_group_2(A,D)) ) => r2_hidden(k6_algstr_0(A,B,C),k8_group_2(A,D)) ) ) ) ) ) )).
fof(t74_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_group_3(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & C = k2_group_3(A,B,D) ) ) ) ) ) )).
fof(t74_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_struct_0(k9_group_5(A),k2_group_5(A,B,C)) ) ) ) )).
fof(t74_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ( ( r1_group_6(A,B) & v8_struct_0(A) ) => v8_struct_0(B) ) ) ) )).
fof(t74_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v4_group_9(C,A,B) & m1_group_9(C,A,B) ) => ! [D] : ( ( 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)) ) ) ) ) ) )).
fof(t74_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_algstr_0(A) & v1_vectsp_1(A) & v1_algstr_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v3_ideal_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v3_ideal_1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => r1_tarski(C,k11_ideal_1(A,B,C)) ) ) ) )).
fof(t74_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( A = k1_rcomp_1(k3_xcmplx_0(k2_nat_1(2,B),k28_sin_cos),k3_xcmplx_0(k1_nat_1(k2_nat_1(2,B),1),k28_sin_cos)) => k2_integra5(A,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)) = 2 ) ) ) )).
fof(t74_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => k11_intpro_1(k11_intpro_1(A)) = k11_intpro_1(A) ) )).
fof(t74_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ! [B] : ( ( 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,k5_jgraph_4(A)) & v3_tops_2(B,k15_euclid(2),k15_euclid(2)) ) ) ) ) )).
fof(t74_jgraph_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( ( ~ v1_xboole_0(D) & v2_compts_1(D,k15_euclid(2)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ ( v1_topreal2(D) & r2_hidden(A,D) & r2_hidden(B,D) & r2_hidden(C,D) & ~ ( r1_jordan6(D,A,B) & r1_jordan6(D,B,C) ) & ~ ( r1_jordan6(D,A,C) & r1_jordan6(D,C,B) ) & ~ ( r1_jordan6(D,B,A) & r1_jordan6(D,A,C) ) & ~ ( r1_jordan6(D,B,C) & r1_jordan6(D,C,A) ) & ~ ( r1_jordan6(D,C,A) & r1_jordan6(D,A,B) ) & ~ ( r1_jordan6(D,C,B) & r1_jordan6(D,B,A) ) ) ) ) ) ) )).
fof(t74_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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 & k18_euclid(D) = G & 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(C),H) & ~ r1_xxreal_0(k17_euclid(D),E) & r1_xxreal_0(k17_euclid(D),F) & k1_funct_1(I,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t74_jordan,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( r1_jordan24(2,A,k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) => k9_subset_1(u1_struct_0(k15_euclid(2)),A,k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(3),3)) = k7_domain_1(u1_struct_0(k15_euclid(2)),k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) ) ) )).
fof(t74_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(D,B) & r2_hidden(C,k9_subset_1(u1_struct_0(k15_euclid(2)),k4_topreal1(D),k3_topreal1(2,k2_jordan9(B,A)))) & r1_xxreal_0(k18_euclid(C),k18_euclid(D)) ) ) ) ) ) )).
fof(t74_jordan2c,axiom,( ! [A] : ( ( ~ 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)))) ) => ~ v9_rltopsp1(k2_goboard9(k1_sprect_1(A)),k15_euclid(2)) ) )).
fof(t74_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(k15_glib_000(A),B) => k6_lexbfs(A,k25_lexbfs(A,k26_lexbfs(A)),B) = k19_lexbfs(A,k23_lexbfs(A,k26_lexbfs(A),B)) ) ) ) )).
fof(t74_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v4_limfunc1(B) => ( ! [C] : ( v1_xreal_0(C) => ~ ( r1_tarski(k3_limfunc1(C),k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k1_relset_1(k1_numbers,B))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,k3_limfunc1(C)) => r1_xxreal_0(k1_funct_1(B,D),k1_funct_1(A,D)) ) ) ) ) | v4_limfunc1(A) ) ) ) ) )).
fof(t74_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r4_limfunc2(B,A) & k2_limfunc2(B,A) = k5_numbers ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(A,k2_xcmplx_0(A,C)))) & r1_xxreal_0(k5_numbers,k1_funct_1(B,D)) ) ) ) ) | r6_limfunc2(k6_rfunct_1(k1_numbers,k1_numbers,B),A) ) ) ) ) )).
fof(t74_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_limfunc2(B,A) & r1_limfunc3(C,k1_limfunc2(B,A)) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,D) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(k6_xcmplx_0(A,D),A))) & k1_funct_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) = k1_limfunc3(C,k1_limfunc2(B,A)) ) ) ) ) ) ) )).
fof(t74_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => r1_funct_2(k2_zfmisc_1(k1_numbers,k14_lpspace1(A,B,C)),k14_lpspace1(A,B,C),k2_zfmisc_1(k1_numbers,k6_lpspace2(A,B,C,1)),k6_lpspace2(A,B,C,1),k17_lpspace1(A,B,C),k9_lpspace2(A,B,C,1)) ) ) ) )).
fof(t74_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_cqc_lang(A))) => ( r3_cqc_the1(A,D,k8_cqc_lang(A,k6_cqc_lang(A,B),C)) => r3_cqc_the1(A,D,k8_cqc_lang(A,k6_cqc_lang(A,C),B)) ) ) ) ) ) )).
fof(t74_mathmorp,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_convex1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ( ( r1_xxreal_0(k5_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,k6_xcmplx_0(1,E))),B) ) ) ) ) ) ) ) )).
fof(t74_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( ( v1_matrix10(B) & r2_matrix10(C,D) ) => r1_matrix10(C,k4_matrix10(A,B,D)) ) ) ) ) ) )).
fof(t74_matrix13,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ( r1_xxreal_0(k8_matrix13(A,B),k3_finseq_1(B)) & r1_xxreal_0(k8_matrix13(A,B),k1_matrix_0(B)) ) ) ) )).
fof(t74_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( k1_matrix_0(C) = k3_finseq_1(D) => ( k12_matrix_3(A,B,C) = k4_struct_0(B) | ( k1_matrix_0(D) = k5_numbers & k3_finseq_1(D) != k5_numbers ) | k7_matrix15(B,D) = k7_matrix15(B,k4_matrix_3(B,C,D)) ) ) ) ) ) ) )).
fof(t74_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( k1_matrix_0(B) = k1_nat_1(E,1) & r2_hidden(C,k2_finseq_1(E)) & r2_hidden(D,k4_finseq_1(B)) ) => ( r1_xxreal_0(E,k5_numbers) | ( r2_hidden(C,k2_finseq_1(k1_matrix_0(B))) & k3_matrix_0(A,k16_matrix_0(k1_matrix_0(B),A,B),D,C) = k3_matrix_0(A,B,D,C) & r2_hidden(k1_matrix_0(B),k2_finseq_1(k1_matrix_0(B))) ) ) ) ) ) ) ) ) )).
fof(t74_matrixj1,axiom,( ! [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] : ( ( v1_matrixj1(B,u1_struct_0(A)) & m2_finseq_1(B,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) => ! [C] : ( ( v1_matrixj1(C,u1_struct_0(A)) & m2_finseq_1(C,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) => ! [D] : ( ( v1_matrixj1(D,u1_struct_0(A)) & m2_finseq_1(D,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) => ! [E] : ( ( 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) => k26_matrixj1(A,k3_matrixj1(u1_struct_0(A),B,D),k3_matrixj1(u1_struct_0(A),C,E)) = k3_matrixj1(u1_struct_0(A),k26_matrixj1(A,B,C),k26_matrixj1(A,D,E)) ) ) ) ) ) ) )).
fof(t74_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k3_finseq_1(k6_matrixr2(A,B)) = A ) ) )).
fof(t74_mcart_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) ) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ( ( k1_xtuple_0(B) = k1_xtuple_0(C) & k2_xtuple_0(B) = k2_xtuple_0(C) ) => B = C ) ) ) ) )).
fof(t74_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_membered(C) => k11_member_1(A,k11_member_1(B,C)) = k9_member_1(k11_member_1(A,B),C) ) ) ) )).
fof(t74_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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)) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ( r2_hidden(k4_struct_0(B),k9_xtuple_0(D)) => k10_memstr_0(A,B,k1_funct_4(C,k9_memstr_0(A,B,D,E)),E) = k1_funct_4(C,D) ) ) ) ) ) ) )).
fof(t74_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( ! [D] : ( r2_hidden(D,k1_relset_1(A,k47_valued_1(A,k1_numbers,k1_numbers,B,C))) => r1_xxreal_0(k12_supinf_2(C,D),k12_supinf_2(B,D)) ) => v6_supinf_2(k47_valued_1(A,k1_numbers,k1_numbers,B,C)) ) ) ) ) )).
fof(t74_mmlquery,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v3_mmlquery(B) & l1_mmlquery(B) ) => ! [C] : ( m2_finseq_1(C,u1_mmlquery(B)) => r1_tarski(k33_mmlquery(B,C),k36_mmlquery(B,C,A)) ) ) ) )).
fof(t74_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k25_modelc_2(k43_modelc_2)) => ( r7_modelc_2(B,k6_modelc_2(k3_modelc_2(A))) <=> r7_modelc_2(B,k3_modelc_2(k6_modelc_2(A))) ) ) ) )).
fof(t74_monoid_0,axiom,( ! [A] : u2_algstr_0(k15_monoid_0(A)) = k1_realset1(k14_monoid_0(A),k1_funct_2(A,A)) )).
fof(t74_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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_msafree4(B,u1_struct_0(A)) ) => ! [C] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( m1_msafree(D,A,C) => ( r8_pboole(u1_struct_0(A),D,k13_msafree(A,B)) => v7_msafree4(D,A,C,k5_msafree4(A,C)) ) ) ) ) ) )).
fof(t74_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( 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)) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k7_partfun1(u1_struct_0(B),C,k3_rlvect_1(A,D,E)) = k3_rlvect_1(B,k7_partfun1(u1_struct_0(B),C,D),k7_partfun1(u1_struct_0(B),C,E)) ) ) ) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ r1_ncfcont1(A,B,C,D) ) | r7_ncfcont1(A,B,C,u1_struct_0(A)) ) ) ) ) ) )).
fof(t74_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(B,A) & r2_hidden(A,k9_newton(B)) ) ) ) )).
fof(t74_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v11_o_ring_1(B,A) & v1_o_ring_1(C,A) ) => v13_o_ring_1(k6_algstr_0(A,B,C),A) ) ) ) ) )).
fof(t74_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r4_relat_2(A,B) => v4_relat_2(k2_wellord1(A,B)) ) ) )).
fof(t74_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( v7_ordinal1(k10_ordinal2(A,B)) => ( r2_hidden(A,k4_ordinal1) & r2_hidden(B,k4_ordinal1) ) ) ) ) )).
fof(t74_ordinal6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v4_card_3(A) & v1_classes2(A) ) => k1_funct_1(k11_ordinal6(A),1) = k3_ordinal6(k6_ordinal6(A,k4_ordinal1)) ) )).
fof(t74_partfun1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_xboole_0,A))) ) => k5_partfun1(k1_xboole_0,A,B) = k1_tarski(k1_xboole_0) ) )).
fof(t74_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => r6_pboole(A,k4_pboole(A,k3_pboole(A,B,C),D),k3_pboole(A,k4_pboole(A,B,D),k4_pboole(A,C,D))) ) ) ) )).
fof(t74_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ( ( r8_pdiff_5(B,A) & r8_pdiff_5(C,A) ) => r3_pdiff_1(3,2,k20_valued_1(k1_euclid(3),k1_numbers,k1_numbers,k1_pdiff_3(3,3,B),k1_pdiff_3(3,3,C)),A) ) ) ) ) )).
fof(t74_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( ~ v1_xboole_0(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ( ( v1_pdiff_7(B,A) & r1_tarski(k1_rvsum_1(D),k2_finseq_1(A)) & r4_pdiff_9(A,B,D,E) ) => ( r4_pdiff_9(A,B,D,k26_valued_1(k1_euclid(A),k1_numbers,E,C)) & r2_relset_1(k1_euclid(A),k1_numbers,k5_pdiff_9(A,B,D,k26_valued_1(k1_euclid(A),k1_numbers,E,C)),k26_valued_1(k1_euclid(A),k1_numbers,k5_pdiff_9(A,B,D,E),C)) ) ) ) ) ) ) ) )).
fof(t74_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( m1_subset_1(B,k8_polyform(A,k6_xcmplx_0(k7_polyform(A),1))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k17_polyform(A,k7_polyform(A)))) => ( C = k1_tarski(A) => k4_rlvect_1(k2_bspace,k19_polyform(A,k7_polyform(A),B,C)) = k5_struct_0(k2_bspace) ) ) ) ) )).
fof(t74_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( 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) => k7_pre_poly(A,B,C) = k1_xboole_0 ) ) ) )).
fof(t74_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => ( ~ r1_xxreal_0(A,k5_numbers) => k6_prepower(A,B) = k4_prepower(A,B) ) ) ) )).
fof(t74_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( ( r2_pboole(A,B,k6_pboole(A,B,C)) | r2_pboole(A,B,k6_pboole(A,C,B)) ) => r6_pboole(A,B,k1_pboole(A)) ) ) ) )).
fof(t74_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( r3_qc_lang2(A,k14_qc_lang1(A,k13_qc_lang1(A,B),k13_qc_lang1(A,C)),k3_qc_lang2(A,B,C)) & r3_qc_lang2(A,k13_qc_lang1(A,B),k3_qc_lang2(A,B,C)) & r3_qc_lang2(A,k13_qc_lang1(A,C),k3_qc_lang2(A,B,C)) & r3_qc_lang2(A,B,k3_qc_lang2(A,B,C)) & r3_qc_lang2(A,C,k3_qc_lang2(A,B,C)) ) ) ) ) )).
fof(t74_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k5_quatern2(A,B) = k6_quaterni(k7_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(B),k13_quaterni(A)),k3_xcmplx_0(k14_quaterni(A),k14_quaterni(B))),k3_xcmplx_0(k15_quaterni(B),k15_quaterni(A))),k3_xcmplx_0(k16_quaterni(B),k16_quaterni(A))),k1_square_1(k28_quaterni(B))),k7_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k13_quaterni(B),k14_quaterni(A)),k3_xcmplx_0(k14_quaterni(B),k13_quaterni(A))),k3_xcmplx_0(k15_quaterni(B),k16_quaterni(A))),k3_xcmplx_0(k16_quaterni(B),k15_quaterni(A))),k1_square_1(k28_quaterni(B))),k7_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(B),k15_quaterni(A)),k3_xcmplx_0(k14_quaterni(B),k16_quaterni(A))),k3_xcmplx_0(k15_quaterni(B),k13_quaterni(A))),k3_xcmplx_0(k16_quaterni(B),k14_quaterni(A))),k1_square_1(k28_quaterni(B))),k7_xcmplx_0(k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k13_quaterni(B),k16_quaterni(A)),k3_xcmplx_0(k14_quaterni(B),k15_quaterni(A))),k3_xcmplx_0(k15_quaterni(B),k14_quaterni(A))),k3_xcmplx_0(k16_quaterni(B),k13_quaterni(A))),k1_square_1(k28_quaterni(B)))) ) ) )).
fof(t74_quaterni,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => r1_xxreal_0(k5_numbers,k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(C)),k1_square_1(D))) ) ) ) ) )).
fof(t74_real_3,axiom,( ! [A] : ( v1_xreal_0(A) => ( ! [B] : ( v7_ordinal1(B) => ~ r1_xxreal_0(k9_nat_1(k1_numbers,k4_real_3(A),B),k5_numbers) ) => k9_nat_1(k1_numbers,k7_real_3(A),3) = k2_xcmplx_0(k9_nat_1(k1_numbers,k4_real_3(A),k5_numbers),k7_xcmplx_0(1,k2_xcmplx_0(k9_nat_1(k1_numbers,k4_real_3(A),1),k7_xcmplx_0(1,k2_xcmplx_0(k9_nat_1(k1_numbers,k4_real_3(A),2),k7_xcmplx_0(1,k9_nat_1(k1_numbers,k4_real_3(A),3))))))) ) ) )).
fof(t74_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => k5_relat_1(C,k6_subset_1(A,B)) = k6_subset_1(k5_relat_1(C,A),k5_relat_1(C,B)) ) )).
fof(t74_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(E))) => ! [G] : ( ( ~ v2_struct_0(G) & l1_rewrite3(G,F) ) => ( r2_rewrite3(E,F,G,A,B,C,D) => r1_rewrite1(k1_rewrite3(E,F,G),k4_tarski(A,B),k4_tarski(C,D)) ) ) ) ) )).
fof(t74_rfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) ) => ( ( ( r1_tarski(B,A) & v1_seq_2(k5_relat_1(C,A)) ) => v1_seq_2(k5_relat_1(C,B)) ) & ( ( r1_tarski(B,A) & v2_seq_2(k5_relat_1(C,A)) ) => v2_seq_2(k5_relat_1(C,B)) ) & ( ( r1_tarski(B,A) & v1_comseq_2(k5_relat_1(C,A)) ) => v1_comseq_2(k5_relat_1(C,B)) ) ) ) )).
fof(t74_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( v1_finset_1(k1_relset_1(A,k2_partfun1(A,k1_numbers,B,C))) & ! [D] : ( m1_subset_1(D,A) => ( r2_hidden(D,k1_relset_1(A,k2_partfun1(A,k1_numbers,B,C))) => r1_xxreal_0(k5_numbers,k1_funct_1(B,D)) ) ) ) => k20_rfunct_3(A,k18_rfunct_3(A,B),C) = k20_rfunct_3(A,B,C) ) ) ) )).
fof(t74_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v8_valued_0(A) & v2_seq_2(A) ) => k1_rinfsup1(k3_rinfsup1(A)) = k2_rinfsup1(A) ) ) )).
fof(t74_rlaffin1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_rlaffin1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ( r2_hidden(A,C) => v1_convex1(k7_subset_1(u1_struct_0(B),k3_convex1(B,C),k1_tarski(A)),B) ) ) ) )).
fof(t74_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => m2_rlsub_1(u1_struct_0(B),A,B) ) ) )).
fof(t74_rltopsp1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r2_hidden(D,k5_rltopsp1(A,B,C)) & r2_hidden(E,k5_rltopsp1(A,B,C)) ) => r1_tarski(k5_rltopsp1(A,D,E),k5_rltopsp1(A,B,C)) ) ) ) ) ) ) )).
fof(t74_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ( k3_finseq_1(B) = 1 => k4_rlvect_1(A,B) = k1_funct_1(B,1) ) ) ) )).
fof(t74_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( m2_rmod_2(E,A,B,D) => ( r2_hidden(C,E) <=> E = k3_rmod_2(A,B,C,D) ) ) ) ) ) ) )).
fof(t74_rmod_4,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( ( k10_rmod_4(A,B,C) = B & r1_tarski(C,D) ) => k10_rmod_4(A,B,D) = B ) ) ) ) ) )).
fof(t74_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m2_rusub_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & r2_hidden(E,C) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_struct_0(B,F) & k5_algstr_0(A,D,F) = E ) ) ) ) ) ) ) ) )).
fof(t74_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => k16_rvsum_1(k7_finseq_1(B,k9_finseq_1(A))) = k2_xcmplx_0(k16_rvsum_1(B),A) ) ) )).
fof(t74_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ( ( r1_tarski(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)),B) & r1_tarski(C,A) ) => ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(D,k8_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B)) & k3_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k1_scmfsa8c(C)),B,D)) = k2_compos_1(k1_scmfsa_2) ) ) ) ) ) ) )).
fof(t74_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ~ v2_extpro_1(k8_scmfsa_2(A,B),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(t74_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ~ v2_extpro_1(k6_scmpds_2(B,A),2,k1_scmpds_2) ) ) )).
fof(t74_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( ~ r1_xxreal_0(k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),F)),k5_numbers) => k1_funct_1(k6_scmpds_4(k7_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) ) ) ) ) ) ) ) )).
fof(t74_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( ( v9_scmyciel(B,A) & m1_subset_1(B,k1_zfmisc_1(k3_tarski(A))) ) => ( v4_scmyciel(k7_scmyciel(k6_scmyciel(A),B)) & v5_scmyciel(k7_scmyciel(k6_scmyciel(A),B)) & m1_subset_1(k7_scmyciel(k6_scmyciel(A),B),k1_zfmisc_1(k6_scmyciel(A))) ) ) ) )).
fof(t74_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r3_semi_af1(A,B,D,D,E) & r3_semi_af1(A,C,D,D,F) ) => r2_analoaf(A,B,C,E,F) ) ) ) ) ) ) ) )).
fof(t74_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => ! [D] : ( m2_finseq_2(D,k2_numbers,k12_seq_4(A)) => k17_seq_4(A,k17_seq_4(A,B,C),D) = k17_seq_4(A,B,k13_seq_4(A,C,D)) ) ) ) ) )).
fof(t74_setlim_1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [E] : ( ( v5_relat_1(E,B) & v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ! [F] : ( v7_ordinal1(F) => k1_funct_1(E,F) = k3_xboole_0(k1_funct_1(C,F),k1_funct_1(D,F)) ) => k3_kurato_0(A,E) = k9_subset_1(A,k3_kurato_0(A,C),k3_kurato_0(A,D)) ) ) ) ) ) )).
fof(t74_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k3_kurato_0(A,k5_setlim_2(A,C,B)) = k9_subset_1(A,B,k3_kurato_0(A,C)) ) ) )).
fof(t74_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k5_sheffer1(A,k5_sheffer1(A,D,C),k5_sheffer1(A,k5_sheffer1(A,B,B),C)) = k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,D,D),B)),k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,D,D),B))) ) ) ) ) )).
fof(t74_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( k17_sin_cos(k2_xcmplx_0(A,B)) = k2_xcmplx_0(k3_xcmplx_0(k17_sin_cos(A),k19_sin_cos(B)),k3_xcmplx_0(k19_sin_cos(A),k17_sin_cos(B))) & k19_sin_cos(k2_xcmplx_0(A,B)) = k6_xcmplx_0(k3_xcmplx_0(k19_sin_cos(A),k19_sin_cos(B)),k3_xcmplx_0(k17_sin_cos(A),k17_sin_cos(B))) ) ) ) )).
fof(t74_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) & k2_sin_cos6(A) = k5_numbers ) => A = k5_numbers ) ) )).
fof(t74_sin_cos9,axiom,( r2_fdiff_1(k2_sin_cos9,k2_rcomp_1(k4_xcmplx_0(1),1)) )).
fof(t74_sincos10,axiom,( k1_funct_1(k2_sincos10,k4_xcmplx_0(k3_square_1(2))) = k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos) & k1_funct_1(k2_sincos10,k4_xcmplx_0(1)) = k28_sin_cos )).
fof(t74_sprect_1,axiom,( ! [A] : ( ( ~ 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(k3_topreal1(2,k1_sprect_1(A))) = k10_pscomp_1(A) ) )).
fof(t74_sprect_2,axiom,( ! [A] : ( ( ~ 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)) & 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)))) ) ) )).
fof(t74_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v5_relat_1(D,k3_qc_lang1(A)) & v3_card_1(D,B) & m2_finseq_1(D,k2_qc_lang1(A)) ) => ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),C))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),C))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),C))) ) => ( ( ! [I] : ( m2_subset_1(I,k2_qc_lang1(A),k3_qc_lang1(A)) => ~ ( r2_hidden(I,k1_relset_1(k3_qc_lang1(A),G)) & r2_hidden(I,k23_qc_lang1(A,D)) ) ) & ! [I] : ( m2_subset_1(I,k2_qc_lang1(A),k3_qc_lang1(A)) => ( r2_hidden(I,k1_relset_1(k3_qc_lang1(A),H)) => k1_funct_1(H,I) = k3_funct_2(k3_qc_lang1(A),C,E,I) ) ) & r1_xboole_0(k1_relset_1(k3_qc_lang1(A),F),k1_relset_1(k3_qc_lang1(A),H)) ) => r2_relset_1(k4_ordinal1,C,k4_valuat_1(A,C,B,D,k1_sublemma(A,C,E,F)),k4_valuat_1(A,C,B,D,k1_sublemma(A,C,E,k14_sublemma(A,C,k14_sublemma(A,C,F,G),H)))) ) ) ) ) ) ) ) ) ) )).
fof(t74_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_tdlat_2(B,A) => v2_tdlat_2(k1_pcomps_1(A,B),A) ) ) ) )).
fof(t74_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_tex_3(B,A) & m1_pre_topc(B,A) ) => ? [C] : ( ~ v2_struct_0(C) & v1_pre_topc(C) & v1_tsep_1(C,A) & v1_tex_2(C,A) & v1_tex_3(C,A) & m1_pre_topc(C,A) & ? [D] : ( ~ v2_struct_0(D) & v1_pre_topc(D) & v1_borsuk_1(D,A) & v3_tex_3(D,A) & m1_pre_topc(D,A) & r4_tsep_2(A,C,D) & m1_pre_topc(B,D) ) ) ) ) )).
fof(t74_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( m1_subset_1(C,u1_struct_0(k5_tex_4(A,B))) <=> g1_pre_topc(u1_struct_0(k5_tex_4(A,C)),u1_pre_topc(k5_tex_4(A,C))) = g1_pre_topc(u1_struct_0(k5_tex_4(A,B)),u1_pre_topc(k5_tex_4(A,B))) ) ) ) ) )).
fof(t74_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => ( ( F = G & m1_pre_topc(D,C) & r1_tmap_1(C,B,E,F) ) => r1_tmap_1(D,B,k3_tmap_1(A,B,C,D,E),G) ) ) ) ) ) ) ) ) )).
fof(t74_topgen_5,axiom,( v1_tops_2(k2_xboole_0(k2_xboole_0(a_0_3_topgen_5,a_0_4_topgen_5),a_0_5_topgen_5),k5_topmetr) & v1_cantor_1(k2_xboole_0(k2_xboole_0(a_0_3_topgen_5,a_0_4_topgen_5),a_0_5_topgen_5),k5_topmetr) & m1_subset_1(k2_xboole_0(k2_xboole_0(a_0_3_topgen_5,a_0_4_topgen_5),a_0_5_topgen_5),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k5_topmetr)))) )).
fof(t74_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => r1_tarski(k7_relset_1(u1_struct_0(k15_euclid(2)),k1_numbers,k4_pscomp_1,k2_pre_topc(k15_euclid(2),A)),k5_measure6(k7_relset_1(u1_struct_0(k15_euclid(2)),k1_numbers,k4_pscomp_1,A))) ) )).
fof(t74_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( ( u1_struct_0(A) = u1_struct_0(B) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => k1_tops_1(A,C) = k1_tops_1(B,D) ) ) ) ) => g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) ) ) ) )).
fof(t74_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)))) ) => ( ( v6_transgeo(D,A) & r1_aff_1(A,B,k3_funct_2(u1_struct_0(A),u1_struct_0(A),D,B),C) ) => r1_aff_1(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)) ) ) ) ) ) )).
fof(t74_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ( k4_trees_1(k13_trees_3(A,B),k14_trees_3(k5_numbers)) = A & k4_trees_1(k13_trees_3(A,B),k14_trees_3(1)) = B ) ) ) )).
fof(t74_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( r3_tsep_1(A,B,C) <=> ? [D] : ( ~ v2_struct_0(D) & v1_borsuk_1(D,A) & m1_pre_topc(D,A) & ? [E] : ( ~ v2_struct_0(E) & v1_borsuk_1(E,A) & m1_pre_topc(E,A) & m1_pre_topc(B,D) & m1_pre_topc(C,E) & r1_tsep_1(D,C) & r1_tsep_1(E,B) ) ) ) ) ) ) )).
fof(t74_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( v1_valued_2(C) => ! [D] : ( v1_valued_2(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [F] : ( ( 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) = k73_valued_2(B,A,D,C,F,E) ) ) ) ) )).
fof(t74_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => m2_vectsp_4(u1_struct_0(B),A,B,k2_vectsp_4(A,B)) ) ) )).
fof(t74_waybel23,axiom,( ! [A] : ( l1_pre_topc(A) => ? [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)))) & k1_card_1(B) = k2_waybel23(A) ) ) )).
fof(t74_waybel_0,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => r4_waybel_0(A,B,C,D) ) & ! [D] : ( ( ~ 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) ) ) => v18_waybel_0(C,A,B) ) ) ) ) )).
fof(t74_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v9_waybel_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => B = k6_waybel_1(A,k4_yellow_0(A),B) ) ) ) )).
fof(t74_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( ~ r1_xboole_0(A,k3_xboole_0(B,C)) & r1_xboole_0(A,B) ) )).
fof(t74_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k3_xboolean(k10_xboolean(A,B)) = k10_xboolean(k3_xboolean(A),B) ) ) )).
fof(t74_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k3_xcmplx_0(A,k7_xcmplx_0(B,C)) = k7_xcmplx_0(k3_xcmplx_0(A,B),C) ) ) ) )).
fof(t74_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(k7_xcmplx_0(B,C),k7_xcmplx_0(A,C)) ) ) ) ) )).
fof(t74_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(D,C) & k2_xxreal_1(C,D) = k3_xxreal_1(A,B) ) ) ) ) ) )).
fof(t74_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ( v3_xxreal_2(A) <=> k2_xxreal_2(A) != k2_xxreal_0 ) ) )).
fof(t74_xxreal_3,axiom,( k5_xxreal_3(k1_xxreal_0) = k5_numbers )).
fof(t74_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v5_zf_lang(A) => ( r3_zf_lang(k21_zf_lang(A),A) & r3_zf_lang(k22_zf_lang(A),A) ) ) ) )).
fof(t74_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( ( 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,k13_zf_lang(B,A)) <=> r1_zf_model(C,k2_zf_lang1(C,E,B,D),k13_zf_lang(B,A)) ) ) ) ) ) ) )).
fof(t74_zfmisc_1,axiom,( ! [A] : ! [B] : k3_tarski(k2_tarski(A,B)) = k2_xboole_0(A,B) )).
fof(t74_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_zmodul01(D,A) => ( ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_hidden(B,k5_zmodul01(A,E,D)) & r2_hidden(C,k5_zmodul01(A,E,D)) ) <=> r1_struct_0(D,k5_algstr_0(A,B,C)) ) ) ) ) ) )).
fof(t74_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( m1_zmodul01(D,A) => ( m1_zmodul01(B,D) => m1_zmodul01(k7_zmodul01(A,B,C),D) ) ) ) ) ) )).
fof(t75_abcmiz_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( ( v4_rewrite1(B) & v2_rewrite1(B) ) => ! [C] : ( m1_subset_1(C,A) => r2_hidden(k2_rewrite1(B,C),A) ) ) ) ) )).
fof(t75_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_trees_4(B,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A)))),k34_abcmiz_1(A)) => ! [C] : ( ( v2_abcmiz_1(C,A) & m1_subset_1(C,u4_struct_0(A)) ) => ( ( k2_msualg_1(A,C) = k12_abcmiz_1(A) & k3_finseq_1(B) = k3_finseq_1(k1_msualg_1(A,C)) ) => ( v9_abcmiz_1(k36_abcmiz_1(A,C,B),A) & m1_abcmiz_1(k36_abcmiz_1(A,C,B),A,k12_abcmiz_1(A)) ) ) ) ) ) )).
fof(t75_afinsq_1,axiom,( ! [A] : ! [B] : k6_afinsq_1(A,B) = k4_funct_4(k5_numbers,1,A,B) )).
fof(t75_afinsq_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => k8_afinsq_2(A,k6_afinsq_1(B,C)) = k15_afinsq_1(A,B,C) ) ) )).
fof(t75_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ( v3_freealg(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k16_aofa_000(A,B,C) != B & k16_aofa_000(A,B,C) != C & ( k16_aofa_000(A,B,C) = k16_aofa_000(A,D,E) => ( B = D & C = E ) ) ) ) ) ) ) ) ) )).
fof(t75_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v19_aofa_a00(B,A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( C = k10_subset_1(k1_funct_1(u7_aofa_a00(A),11),u4_struct_0(A)) => ( k1_msualg_1(A,C) = k2_finseq_4(u1_struct_0(A),k37_aofa_a00(A),B) & k2_msualg_1(A,C) = B ) ) ) ) ) )).
fof(t75_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_arytm_3)) => ~ ( ? [B] : ( m1_subset_1(B,k5_arytm_3) & r2_hidden(B,A) & B != k11_arytm_3 ) & ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( m1_subset_1(C,k5_arytm_3) => ( ( r2_hidden(B,A) & r3_arytm_3(C,B) ) => r2_hidden(C,A) ) ) ) & ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( m1_subset_1(C,k5_arytm_3) => ! [D] : ( m1_subset_1(D,k5_arytm_3) => ~ ( r2_hidden(B,A) & r2_hidden(C,A) & r2_hidden(D,A) & B != C & C != D & D != B ) ) ) ) ) ) )).
fof(t75_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => r1_xxreal_0(k2_int_1(k7_xcmplx_0(A,2)),A) ) )).
fof(t75_bcialg_1,axiom,( ! [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) ) => ( v14_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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))) ) ) ) ) ) )).
fof(t75_borsuk_5,axiom,( ! [A] : ( ( v2_connsp_1(A,k3_topmetr) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(B,C) & r1_xxreal_0(C,D) & r2_hidden(B,A) & r2_hidden(D,A) ) => r2_hidden(C,A) ) ) ) ) ) )).
fof(t75_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( m1_borsuk_2(G,A,C,D) => ! [H] : ( m1_borsuk_2(H,A,C,D) => ( ( r1_borsuk_6(A,B,C) & r1_borsuk_6(A,C,D) & r3_borsuk_2(A,B,C,E,F) & r3_borsuk_2(A,C,D,G,H) ) => r3_borsuk_2(A,B,D,k1_borsuk_2(A,B,C,D,E,G),k1_borsuk_2(A,B,C,D,F,H)) ) ) ) ) ) ) ) ) ) )).
fof(t75_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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),k7_bvfunc_2(A,k1_bvfunc_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) )).
fof(t75_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_eqrel_1(I,A) => ! [J] : ( m1_eqrel_1(J,A) => ! [K] : ( 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,K,B) = k2_partit1(A,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),J) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t75_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ~ ( ~ v1_finset_1(A) & ( r1_ordinal1(B,A) | r2_hidden(B,A) ) & ~ ( k1_card_2(A,B) = A & k1_card_2(B,A) = A ) ) ) ) )).
fof(t75_card_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_card_3(A) ) => A = k4_card_3(k10_card_3(A)) ) )).
fof(t75_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => v12_cat_1(k10_cat_1(A),A,A) ) )).
fof(t75_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_cat_3(C,A,B,k1_xboole_0) => ( r3_cat_3(A,B,k1_xboole_0,C) <=> v11_cat_1(B,A) ) ) ) ) )).
fof(t75_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_cat_1(G,A,B,D) => ! [H] : ( m1_cat_1(H,A,C,E) => ! [I] : ( m1_cat_1(I,A,D,F) => ! [J] : ( m1_cat_1(J,A,E,F) => ~ ( k2_cat_1(A,B,D) != k1_xboole_0 & k2_cat_1(A,C,E) != k1_xboole_0 & k2_cat_1(A,D,F) != k1_xboole_0 & k2_cat_1(A,E,F) != k1_xboole_0 & k5_cat_1(A,k20_cat_4(A,B,C),k20_cat_4(A,D,E),F,k31_cat_4(A,B,C,D,E,G,H),k29_cat_4(A,D,E,F,I,J)) != k29_cat_4(A,B,C,F,k5_cat_1(A,B,D,F,G,I),k5_cat_1(A,C,E,F,H,J)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t75_cfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,k2_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,k2_numbers))) ) => ( ( v1_comseq_2(k2_partfun1(C,k2_numbers,D,A)) & v1_comseq_2(k2_partfun1(C,k2_numbers,E,B)) ) => ( v1_comseq_2(k2_partfun1(C,k2_numbers,k19_valued_1(C,k2_numbers,k2_numbers,D,E),k3_xboole_0(A,B))) & v1_comseq_2(k2_partfun1(C,k2_numbers,k46_valued_1(C,k2_numbers,k2_numbers,D,E),k3_xboole_0(A,B))) ) ) ) ) ) )).
fof(t75_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ~ ( B != C & ~ r1_chord(A,B,C) & ? [D] : ( m2_chord(D,A,B,C) & ? [E] : ( 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] : ( m1_subset_1(F,k6_glib_000(E)) & ? [G] : ( m1_subset_1(G,k6_glib_000(E)) & F = B & G = C & k9_subset_1(k6_glib_000(E),k1_glib_002(E,F),k1_glib_002(E,G)) != k1_xboole_0 ) ) ) ) ) ) ) ) )).
fof(t75_classes1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_classes1(A,B) => k10_xtuple_0(A) = k10_xtuple_0(B) ) ) ) )).
fof(t75_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_clvect_1(E,A) => ( ( r2_hidden(B,k5_clvect_1(A,C,E)) & r2_hidden(B,k5_clvect_1(A,D,E)) ) => k5_clvect_1(A,C,E) = k5_clvect_1(A,D,E) ) ) ) ) ) ) )).
fof(t75_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_clvect_2(B,A) => v3_clvect_2(k5_vfunct_1(k4_ordinal1,A,B),A) ) ) ) )).
fof(t75_cohsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(C,k14_cohsp_1(A,B)) => ( C = k4_tarski(k1_xtuple_0(C),k2_xtuple_0(C)) & ( ( k2_xtuple_0(C) = 1 & r2_hidden(k1_xtuple_0(C),A) ) | ( k2_xtuple_0(C) = 2 & r2_hidden(k1_xtuple_0(C),B) ) ) ) ) )).
fof(t75_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => k1_square_1(k9_complex1(A)) = k1_square_1(A) ) )).
fof(t75_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ~ ( A != B & C != B & ( k4_complex2(A,B,C) = k7_xcmplx_0(k28_sin_cos,2) | k4_complex2(A,B,C) = k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos) ) & k2_xcmplx_0(k1_square_1(k9_complex1(k6_xcmplx_0(A,B))),k1_square_1(k9_complex1(k6_xcmplx_0(C,B)))) != k1_square_1(k9_complex1(k6_xcmplx_0(A,C))) ) ) ) ) )).
fof(t75_complfld,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_complfld(B,A,1) => B = A ) ) )).
fof(t75_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ( ! [C] : ( v7_ordinal1(C) => ( k9_nat_1(k2_numbers,B,C) != k5_complex1 & k9_nat_1(k1_numbers,A,C) = k6_real_1(k9_nat_1(k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,B),k1_nat_1(C,1)),k9_nat_1(k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,B),C)) ) ) & v2_comseq_2(A) ) => ( r1_xxreal_0(1,k1_seq_2(A)) | v2_comseq_3(B) ) ) ) ) )).
fof(t75_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( B = a_3_9_convex4(A,C,D) => v2_convex4(B,A) ) ) ) ) ) )).
fof(t75_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ( ~ r2_hidden(D,k24_qc_lang1(A,B)) => v2_cqc_the1(k10_cqc_lang(A,k8_cqc_lang(A,B,k11_cqc_lang(A,D,C)),k11_cqc_lang(A,D,k8_cqc_lang(A,B,C))),A) ) ) ) ) ) )).
fof(t75_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_normsp_1(A,B,k16_csspace(A,C,D)),k3_normsp_1(A,k3_normsp_1(A,B,C),D)) ) ) ) ) )).
fof(t75_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k7_xcmplx_0(1,k1_square_1(k19_sin_cos(D))) ) => ( k19_sin_cos(B) = k5_numbers | k19_sin_cos(k6_xcmplx_0(B,A)) = k5_numbers | k1_funct_1(k4_diff_1(C,A),B) = k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(16),k17_sin_cos(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(2,B),A),2))),k17_sin_cos(k7_xcmplx_0(k4_xcmplx_0(A),2))),k19_sin_cos(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(2,B),A),2))),k19_sin_cos(k7_xcmplx_0(k4_xcmplx_0(A),2))),k1_square_1(k2_xcmplx_0(k19_sin_cos(k6_xcmplx_0(k3_xcmplx_0(2,B),A)),k19_sin_cos(A)))) ) ) ) ) ) )).
fof(t75_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_enumset1(A,B,C,D) = k2_enumset1(D,B,C,A) )).
fof(t75_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => k5_euclid_8(k1_euclid_8(A,B,C),k1_euclid_8(D,E,F)) = k1_euclid_8(k6_xcmplx_0(k3_xcmplx_0(B,F),k3_xcmplx_0(C,E)),k6_xcmplx_0(k3_xcmplx_0(C,D),k3_xcmplx_0(A,F)),k6_xcmplx_0(k3_xcmplx_0(A,E),k3_xcmplx_0(B,D))) ) ) ) ) ) ) )).
fof(t75_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ~ ( r6_euclidlp(A,B,C) & B = C ) ) ) ) )).
fof(t75_exchsort,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v5_relat_1(C,u1_struct_0(B)) & v1_funct_1(C) & v1_exchsort(C) ) => m2_exchsort(k1_tarski(k4_tarski(A,C)),B,C) ) ) ) )).
fof(t75_facirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ( k2_msafree2(k15_facirc_1(A,B,C)) = k1_enumset1(A,B,C) & 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))) ) ) ) ) )).
fof(t75_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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) => v13_lattices(k10_filter_2(A,B)) ) ) ) )).
fof(t75_finseq_1,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => m2_finseq_1(k8_finseq_1(A,B,C),A) ) ) )).
fof(t75_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( ( 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] : ( m2_finseq_1(F,B) => m2_finseq_1(k5_funcop_1(E,D,F),C) ) ) ) ) ) ) )).
fof(t75_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : ( k1_finseq_3(k10_finseq_1(A,B),C) = k1_xboole_0 <=> ( r2_hidden(A,C) & r2_hidden(B,C) ) ) )).
fof(t75_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( k8_finseq_4(A,B,C,D,E) = k7_finseq_1(k11_finseq_1(A,B,C),k10_finseq_1(D,E)) & k8_finseq_4(A,B,C,D,E) = k7_finseq_1(k7_finseq_4(A,B,C,D),k9_finseq_1(E)) & k8_finseq_4(A,B,C,D,E) = 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)) & k8_finseq_4(A,B,C,D,E) = k7_finseq_1(k10_finseq_1(A,B),k11_finseq_1(C,D,E)) & k8_finseq_4(A,B,C,D,E) = k7_finseq_1(k9_finseq_1(A),k7_finseq_4(B,C,D,E)) ) )).
fof(t75_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m2_finseq_1(D,B) => ( r1_xxreal_0(1,A) => ( v1_xboole_0(D) | k7_partfun1(B,k5_finseq_5(B,D,C,A),1) = k7_partfun1(B,D,1) ) ) ) ) ) ) )).
fof(t75_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ( ( r2_hidden(B,k10_xtuple_0(D)) & r2_hidden(C,k10_xtuple_0(k1_finseq_5(A,D,B))) ) => k1_finseq_5(A,k1_finseq_5(A,D,B),C) = k1_finseq_5(A,D,C) ) ) ) ) ) )).
fof(t75_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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] : ( ( 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(E,B) & v1_setwiseo(E,B) & C = k4_binop_1(B,E) & v1_finseqop(E,B) & r6_binop_1(B,F,E) ) => r2_funct_2(A,B,k10_funcop_1(B,A,F,C,D),k8_funcop_1(B,A,C)) ) ) ) ) ) ) ) )).
fof(t75_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_catalan2(A))) => ( k8_flang_1(A,B) = k3_catalan2(A) => r1_tarski(k9_flang_1(A),B) ) ) )).
fof(t75_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => k2_flang_2(A,B) = k4_subset_1(k3_catalan2(A),k7_flang_1(A,B,k5_numbers),k7_flang_1(A,B,1)) ) )).
fof(t75_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => k6_flang_1(A,k2_flang_3(A,B),k7_flang_1(A,B,C)) = k1_flang_3(A,B,k2_xcmplx_0(C,1)) ) ) )).
fof(t75_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( k10_xtuple_0(A) = k9_xtuple_0(A) => ( v1_funct_1(A) & v1_funct_2(A,k9_xtuple_0(A),k9_xtuple_0(A)) & v2_funct_2(A,k9_xtuple_0(A)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k9_xtuple_0(A),k9_xtuple_0(A)))) ) ) ) )).
fof(t75_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(C,k9_xtuple_0(k16_funcop_1(A,B))) => C = A ) )).
fof(t75_funct_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( r1_tarski(A,k9_xtuple_0(B)) => r1_tarski(A,k8_relat_1(B,k7_relat_1(B,A))) ) ) )).
fof(t75_funct_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( r1_partfun1(B,C) <=> ! [D] : ( r2_hidden(D,k1_relset_1(A,B)) => k1_funct_1(B,D) = k1_funct_1(C,D) ) ) ) ) )).
fof(t75_funct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,B,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,D))) ) => ! [G] : ( m1_subset_1(G,A) => ! [H] : ( m1_subset_1(H,B) => k2_binop_1(A,B,k2_zfmisc_1(C,D),k16_funct_3(A,B,C,D,E,F),G,H) = k4_tarski(k3_funct_2(A,C,E,G),k3_funct_2(B,D,F,H)) ) ) ) ) ) ) ) ) )).
fof(t75_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : k1_funct_4(A,k5_relat_1(A,B)) = A ) )).
fof(t75_funct_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_relat_1(B) => k3_relat_1(k8_funct_7(B,A),k6_partfun1(k1_relat_1(B))) = k8_funct_7(B,A) ) ) )).
fof(t75_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => r2_funct_8(A,k1_numbers,k1_numbers,k37_valued_1(k1_numbers,k1_numbers,k16_sin_cos)) ) )).
fof(t75_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => m1_subset_1(k4_fvaluat1(A,B),u1_struct_0(k7_fvaluat1(A,B))) ) ) ) )).
fof(t75_fvsum_1,axiom,( ! [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) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => k4_rlvect_1(A,k5_fvsum_1(A,B)) = k4_algstr_0(A,k4_rlvect_1(A,B)) ) ) )).
fof(t75_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : v1_relat_1(k3_msafree2(k31_gfacirc1(A,B,C))) )).
fof(t75_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ( r1_xxreal_0(k15_glib_000(B),k15_glib_000(A)) & r1_xxreal_0(k17_glib_000(B),k17_glib_000(A)) ) ) ) )).
fof(t75_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,k3_finseq_1(B)) ) => ( r2_hidden(k3_nat_d(C,2),k1_relset_1(k4_ordinal1,k12_glib_001(A,B))) & k1_funct_1(B,C) = k1_funct_1(k12_glib_001(A,B),k3_nat_d(C,2)) ) ) ) ) ) )).
fof(t75_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( v1_group_3(C,A) & m1_group_2(C,A) ) => ~ ( m1_group_2(C,B) & ! [D] : ( ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) ) => ! [E] : ( ( v15_algstr_0(E) & v1_group_3(E,A) & m1_group_2(E,A) ) => ~ ( u1_struct_0(D) = k4_group_11(A,B,C) & u1_struct_0(E) = k3_group_11(A,B,C) & r1_tarski(k3_group_11(A,B,D),k3_group_11(A,B,E)) ) ) ) ) ) ) ) )).
fof(t75_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_group_2(C,A) => ( r2_hidden(B,k8_group_2(A,C)) => r2_hidden(k2_group_1(A,B),k8_group_2(A,C)) ) ) ) ) )).
fof(t75_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_group_3(A,B,B) ) ) )).
fof(t75_group_5,axiom,( ! [A] : ( ( ~ 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) ) <=> r1_group_2(A,k9_group_5(A),k6_group_2(A)) ) ) )).
fof(t75_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ 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) & v8_struct_0(A) ) => k7_struct_0(A) = k7_struct_0(B) ) ) ) )).
fof(t75_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( m1_group_9(D,A,B) => ( u1_struct_0(C) = u1_struct_0(D) => g1_group_9(A,u1_struct_0(C),u2_algstr_0(C),u1_group_9(A,C)) = g1_group_9(A,u1_struct_0(D),u2_algstr_0(D),u1_group_9(A,D)) ) ) ) ) )).
fof(t75_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( v1_ideal_1(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ( ( r1_tarski(B,D) & r1_tarski(C,D) ) => r1_tarski(k11_ideal_1(A,B,C),D) ) ) ) ) ) )).
fof(t75_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( A = k1_rcomp_1(k2_xcmplx_0(B,k3_xcmplx_0(k2_nat_1(2,C),k28_sin_cos)),k2_xcmplx_0(B,k3_xcmplx_0(k1_nat_1(k2_nat_1(2,C),1),k28_sin_cos))) => k2_integra5(A,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)) = k6_xcmplx_0(k3_xcmplx_0(2,k19_sin_cos(B)),k3_xcmplx_0(2,k17_sin_cos(B))) ) ) ) ) )).
fof(t75_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ( v9_intpro_1(A) <=> k11_intpro_1(A) = A ) ) )).
fof(t75_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r1_xxreal_0(A,k7_xcmplx_0(k17_euclid(B),k12_euclid(B))) => ( r1_xxreal_0(1,A) | r1_xxreal_0(k18_euclid(B),k5_numbers) | ! [C] : ( 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),k5_numbers) & r1_xxreal_0(k5_numbers,k17_euclid(C)) ) ) ) ) ) ) ) )).
fof(t75_jgraph_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( ( ~ v1_xboole_0(D) & v2_compts_1(D,k15_euclid(2)) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ ( v1_topreal2(D) & r2_hidden(A,D) & r2_hidden(B,D) & r2_hidden(C,D) & r1_jordan6(D,B,C) & ~ r1_jordan6(D,A,B) & ~ ( r1_jordan6(D,B,A) & r1_jordan6(D,A,C) ) & ~ r1_jordan6(D,C,A) ) ) ) ) ) )).
fof(t75_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) = E & k17_euclid(C) = E & k18_euclid(D) = G & 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(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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t75_jordan,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( r1_jordan24(2,A,k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) => k6_pscomp_1(A) = k4_xcmplx_0(1) ) ) )).
fof(t75_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(D,B) & r2_hidden(C,k9_subset_1(u1_struct_0(k15_euclid(2)),k5_topreal1(D),k3_topreal1(2,k2_jordan9(B,A)))) & r1_xxreal_0(k17_euclid(C),k17_euclid(D)) ) ) ) ) ) )).
fof(t75_jordan2c,axiom,( ! [A] : ( ( ~ 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)))) ) => r1_tarski(k2_goboard9(k1_sprect_1(A)),k2_jordan2c(2,k3_topreal1(2,k1_sprect_1(A)))) ) )).
fof(t75_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(k15_glib_000(A),B) & ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ~ ( C = k19_lexbfs(A,k23_lexbfs(A,k26_lexbfs(A),B)) & ! [D] : ( ( 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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),k23_lexbfs(A,k26_lexbfs(A),B)))) | k1_recdef_1(k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k4_ordinal1,k6_glib_000(A),k23_lexbfs(A,k26_lexbfs(A),k1_nat_1(B,1))),D) = k1_nat_1(k1_recdef_1(k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k4_ordinal1,k6_glib_000(A),k23_lexbfs(A,k26_lexbfs(A),B)),D),1) ) ) & ( ~ ( 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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),k23_lexbfs(A,k26_lexbfs(A),B)))) ) => k1_recdef_1(k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k4_ordinal1,k6_glib_000(A),k23_lexbfs(A,k26_lexbfs(A),k1_nat_1(B,1))),D) = k1_recdef_1(k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k4_ordinal1,k6_glib_000(A),k23_lexbfs(A,k26_lexbfs(A),B)),D) ) ) ) ) ) ) ) )).
fof(t75_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v5_limfunc1(B) => ( ! [C] : ( v1_xreal_0(C) => ~ ( r1_tarski(k3_limfunc1(C),k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k1_relset_1(k1_numbers,B))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,k3_limfunc1(C)) => r1_xxreal_0(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) | v5_limfunc1(A) ) ) ) ) )).
fof(t75_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_limfunc2(B,A) & k1_limfunc2(B,A) = k5_numbers & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,C) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,C) & ~ r1_xxreal_0(A,D) & r2_hidden(D,k1_relset_1(k1_numbers,B)) & k1_funct_1(B,D) != k5_numbers ) ) ) ) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(k6_xcmplx_0(A,C),A))) => r1_xxreal_0(k5_numbers,k1_funct_1(B,D)) ) ) ) ) | r2_limfunc2(k6_rfunct_1(k1_numbers,k1_numbers,B),A) ) ) ) ) )).
fof(t75_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_limfunc3(B,A) & r4_limfunc2(C,k1_limfunc3(B,A)) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,D),A),k2_rcomp_1(A,k2_xcmplx_0(A,D))))) & r1_xxreal_0(k1_funct_1(B,E),k1_limfunc3(B,A)) ) ) ) ) | ( r1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) & k1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k2_limfunc2(C,k1_limfunc3(B,A)) ) ) ) ) ) ) )).
fof(t75_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => k18_lpspace1(A,B,C) = k10_lpspace2(A,B,C,1) ) ) ) )).
fof(t75_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_cqc_lang(A))) => ( ( r3_cqc_the1(A,D,k8_cqc_lang(A,B,k6_cqc_lang(A,C))) & r3_cqc_the1(A,D,C) ) => r3_cqc_the1(A,D,k6_cqc_lang(A,B)) ) ) ) ) ) )).
fof(t75_mathmorp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( v1_convex1(B,k15_euclid(A)) => v1_convex1(k2_mathmorp(k15_euclid(A),B),k15_euclid(A)) ) ) ) )).
fof(t75_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( ( v4_matrix10(B) & r1_matrix10(C,D) ) => r1_matrix10(C,k4_matrix10(A,B,D)) ) ) ) ) ) )).
fof(t75_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m2_finseq_2(C,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [D] : ( m2_finseq_2(D,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [E] : ( ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ~ ( r1_tarski(k2_zfmisc_1(k10_xtuple_0(C),k10_xtuple_0(D)),k2_matrix_0(E)) & k12_matrix_3(A,B,k1_matrix13(u1_struct_0(B),E,A,A,C,D)) != k4_struct_0(B) & ! [F] : ( ( v1_finset_1(F) & v1_setfam_1(F) & m1_subset_1(F,k1_zfmisc_1(k4_ordinal1)) ) => ! [G] : ( ( v1_finset_1(G) & v1_setfam_1(G) & m1_subset_1(G,k1_zfmisc_1(k4_ordinal1)) ) => ~ ( F = k10_xtuple_0(C) & G = k10_xtuple_0(D) & k5_card_1(F) = k5_card_1(G) & k5_card_1(F) = A & k12_matrix_3(k5_card_1(F),B,k7_matrix13(u1_struct_0(B),E,F,G)) != k4_struct_0(B) ) ) ) ) ) ) ) ) ) )).
fof(t75_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( k1_matrix_0(C) = k3_finseq_1(D) => ( k12_matrix_3(A,B,C) = k4_struct_0(B) | k8_matrix13(B,k4_matrix_3(B,C,D)) = k8_matrix13(B,D) ) ) ) ) ) ) )).
fof(t75_matrix_0,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( m2_finseq_1(E,C) => ! [F] : ( ( v1_matrix_0(F) & m2_finseq_1(F,k3_finseq_2(C)) ) => ( ( r1_xboole_0(k10_xtuple_0(E),k10_xtuple_0(k8_matrix_0(C,F,A))) & r2_hidden(k7_partfun1(C,E,B),k10_xtuple_0(k7_matrix_0(C,F,D))) & r2_hidden(B,k4_finseq_1(E)) & r2_hidden(A,k2_finseq_1(k1_matrix_0(F))) & r2_hidden(D,k4_finseq_1(F)) ) => ( r1_xxreal_0(k1_matrix_0(F),1) | r2_hidden(k7_partfun1(C,E,B),k10_xtuple_0(k7_matrix_0(C,k16_matrix_0(A,C,F),D))) ) ) ) ) ) ) ) ) )).
fof(t75_matrixj1,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrixj1(C,u1_struct_0(A)) & m2_finseq_1(C,k3_finseq_2(k3_finseq_2(u1_struct_0(A)))) ) => k26_matrixj1(A,k4_matrixj1(u1_struct_0(A),B),C) = k4_matrixj1(u1_struct_0(A),k4_matrix_3(A,B,k2_matrixj1(u1_struct_0(A),C,1))) ) ) ) )).
fof(t75_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(B,A) ) => k1_funct_1(k6_matrixr2(A,B),B) = 1 ) ) ) )).
fof(t75_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : k9_xtuple_0(k9_xtuple_0(k2_tarski(k3_xtuple_0(A,B,C),k3_xtuple_0(D,E,F)))) = k2_tarski(A,D) )).
fof(t75_member_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k11_member_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k6_xcmplx_0(A,B)) ) ) )).
fof(t75_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( v2_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_finset_1(C) ) => r2_hidden(C,k11_memstr_0(A,B)) ) ) ) )).
fof(t75_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ~ ( r1_mesfunc2(A,B,D) & v6_supinf_2(D) & ! [F] : ( v7_ordinal1(F) => r1_mesfunc2(A,B,k4_mesfunc5(A,k6_numbers,E,F)) ) & ! [F] : ( v7_ordinal1(F) => k1_relset_1(A,k4_mesfunc5(A,k6_numbers,E,F)) = k1_relset_1(A,D) ) & ! [F] : ( v7_ordinal1(F) => v6_supinf_2(k4_mesfunc5(A,k6_numbers,E,F)) ) & ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ( r1_xxreal_0(F,G) => ! [H] : ( m1_subset_1(H,A) => ( r2_hidden(H,k1_relset_1(A,D)) => r1_xxreal_0(k12_supinf_2(k4_mesfunc5(A,k6_numbers,E,F),H),k12_supinf_2(k4_mesfunc5(A,k6_numbers,E,G),H)) ) ) ) ) ) & ! [F] : ( m1_subset_1(F,A) => ( r2_hidden(F,k1_relset_1(A,D)) => ( v10_mesfunc5(k3_mesfunc5(A,E,F)) & r1_xxreal_0(k12_supinf_2(D,F),k2_mesfunc5(k3_mesfunc5(A,E,F))) ) ) ) & ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k6_numbers) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ~ ( ! [G] : ( v7_ordinal1(G) => k9_nat_1(k6_numbers,F,G) = k5_mesfunc5(A,B,C,k4_mesfunc5(A,k6_numbers,E,G)) ) & v10_mesfunc5(F) & k8_supinf_2(k17_supinf_2(F)) = k2_mesfunc5(F) & r1_xxreal_0(k5_mesfunc5(A,B,C,D),k2_mesfunc5(F)) ) ) ) ) ) ) ) ) )).
fof(t75_mmlquery,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_mmlquery(C) & l1_mmlquery(C) ) => ! [D] : ( m2_finseq_1(D,u1_mmlquery(C)) => r1_tarski(k34_mmlquery(C,D),k37_mmlquery(C,D,A,B)) ) ) ) ) )).
fof(t75_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k25_modelc_2(k43_modelc_2)) => ( r7_modelc_2(C,k7_modelc_2(A,B)) <=> r7_modelc_2(C,k5_modelc_2(B,k4_modelc_2(A,k6_modelc_2(k7_modelc_2(A,B))))) ) ) ) ) )).
fof(t75_modelc_3,axiom,( ! [A] : ( m1_subset_1(A,k25_modelc_2(k43_modelc_2)) => ! [B] : ( ( v1_modelc_2(B) & v5_modelc_3(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r7_modelc_2(A,B) => r9_modelc_3(k43_modelc_2,k34_modelc_3(B),A) ) ) ) )).
fof(t75_monoid_0,axiom,( ! [A] : k4_binop_1(u1_struct_0(k15_monoid_0(A)),u2_algstr_0(k15_monoid_0(A))) = k6_partfun1(A) )).
fof(t75_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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_msafree4(B,u1_struct_0(A)) ) => ! [C] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => v8_msafree4(C,A,k5_msafree4(A,C)) ) ) ) )).
fof(t75_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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)) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k7_partfun1(u1_struct_0(B),C,k3_rlvect_1(A,D,E)) = k3_rlvect_1(B,k7_partfun1(u1_struct_0(B),C,D),k7_partfun1(u1_struct_0(B),C,E)) ) ) ) => ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ r2_ncfcont1(A,B,C,D) ) | r8_ncfcont1(A,B,C,u1_struct_0(A)) ) ) ) ) ) )).
fof(t75_newton,axiom,( ! [A] : ( v7_ordinal1(A) => v1_finset_1(k2_xboole_0(k9_newton(A),k1_tarski(A))) ) )).
fof(t75_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v11_o_ring_1(B,A) & v3_o_ring_1(C,A) ) => v13_o_ring_1(k6_algstr_0(A,B,C),A) ) ) ) ) )).
fof(t75_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r6_relat_2(A,B) => v6_relat_2(k2_wellord1(A,B)) ) ) )).
fof(t75_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( v7_ordinal1(k11_ordinal2(A,B)) => ( v1_xboole_0(k11_ordinal2(A,B)) | ( r2_hidden(A,k4_ordinal1) & r2_hidden(B,k4_ordinal1) ) ) ) ) ) )).
fof(t75_ordinal6,axiom,( ! [A] : ( v3_ordinal1(A) => v4_ordinal5(k13_ordinal6(1,A)) ) )).
fof(t75_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ~ r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) => r1_partfun1(C,D) ) ) ) )).
fof(t75_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => r6_pboole(A,k4_pboole(A,k2_pboole(A,B,C),C),k4_pboole(A,B,C)) ) ) )).
fof(t75_pdiff_5,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ( ( r9_pdiff_5(B,A) & r9_pdiff_5(C,A) ) => r3_pdiff_1(3,3,k20_valued_1(k1_euclid(3),k1_numbers,k1_numbers,k1_pdiff_3(3,3,B),k1_pdiff_3(3,3,C)),A) ) ) ) ) )).
fof(t75_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m2_finseq_1(E,k4_ordinal1) ) => ( r4_pdiff_9(A,B,k8_finseq_1(k4_ordinal1,E,D),C) <=> ( r4_pdiff_9(A,B,E,C) & r4_pdiff_9(A,B,D,k5_pdiff_9(A,B,E,C)) ) ) ) ) ) ) )).
fof(t75_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => k1_funct_1(k21_polyform(A,k7_polyform(A)),k1_tarski(A)) = k8_polyform(A,k6_xcmplx_0(k7_polyform(A),1)) ) )).
fof(t75_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r2_hidden(D,k4_finseq_1(k7_pre_poly(A,B,C))) & r2_hidden(E,k4_finseq_1(k7_pre_poly(A,B,C))) & k7_partfun1(A,k7_pre_poly(A,B,C),D) = k7_partfun1(A,k7_pre_poly(A,B,C),E) ) => D = E ) ) ) ) ) ) )).
fof(t75_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(A,k5_numbers) => k6_prepower(A,k2_xcmplx_0(B,C)) = k3_xcmplx_0(k6_prepower(A,B),k6_prepower(A,C)) ) ) ) ) )).
fof(t75_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,A) & v1_funct_1(E) & v1_partfun1(E,A) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,A) & v1_funct_1(F) & v1_partfun1(F,A) ) => ( ( r1_pboole(A,D,k6_pboole(A,B,C)) & r1_pboole(A,D,k6_pboole(A,E,F)) ) => r1_pboole(A,D,k6_pboole(A,k3_pboole(A,B,E),k3_pboole(A,C,F))) ) ) ) ) ) ) )).
fof(t75_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ~ ( v2_qc_lang1(C,A) & r3_qc_lang2(A,B,C) ) ) ) ) )).
fof(t75_quatern3,axiom,( k7_quatern2(k3_quatern2) = k24_quaterni(k3_quatern2) )).
fof(t75_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => r1_xxreal_0(k13_quaterni(A),k28_quaterni(A)) ) )).
fof(t75_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => k5_relat_1(A,k1_xboole_0) = k1_xboole_0 ) )).
fof(t75_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(C))) => ! [G] : ( ( ~ v2_struct_0(G) & l1_rewrite3(G,F) ) => ( r1_rewrite1(k1_rewrite3(C,F,G),k4_tarski(A,D),k4_tarski(B,E)) => r1_xxreal_0(k1_afinsq_1(E),k1_afinsq_1(D)) ) ) ) ) ) ) )).
fof(t75_rfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) ) => ( ( v1_seq_2(k5_relat_1(C,A)) & v2_seq_2(k5_relat_1(C,B)) ) => v1_comseq_2(k5_relat_1(C,k3_xboole_0(A,B))) ) ) )).
fof(t75_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_finset_1(E) => ( ( E = k1_relset_1(A,k2_partfun1(A,k1_numbers,B,C)) & k1_rvsum_1(k2_partfun1(A,k1_numbers,B,C)) = k1_tarski(D) ) => k20_rfunct_3(A,B,C) = k2_finseq_2(k5_card_1(E),D) ) ) ) ) ) )).
fof(t75_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_comseq_2(A) & v1_comseq_2(B) & ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) => ( ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k1_funct_1(k4_rinfsup1(A),C),k1_funct_1(k4_rinfsup1(B),C)) ) & ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k1_funct_1(k3_rinfsup1(A),C),k1_funct_1(k3_rinfsup1(B),C)) ) ) ) ) ) )).
fof(t75_rlaffin1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_rlaffin1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( ( r2_hidden(A,k4_rlaffin1(B,C)) & ! [E] : ( r2_hidden(E,D) => k1_funct_1(k5_rlaffin1(B,C,A),E) = k5_numbers ) ) => ( r2_hidden(A,k4_rlaffin1(B,k7_subset_1(u1_struct_0(B),C,D))) & r1_rlvect_2(B,k5_rlaffin1(B,C,A),k5_rlaffin1(B,k7_subset_1(u1_struct_0(B),C,D),A)) ) ) ) ) ) )).
fof(t75_rlsub_1,axiom,( ! [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) ) => m2_rlsub_1(u1_struct_0(A),A,k2_rlsub_1(A)) ) )).
fof(t75_rltopsp1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r2_hidden(D,k5_rltopsp1(A,B,C)) & r2_hidden(E,k5_rltopsp1(A,B,C)) ) => ( D = E | k5_rltopsp1(A,D,E) = k5_rltopsp1(A,B,C) ) ) ) ) ) ) ) )).
fof(t75_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( k3_finseq_1(B) = 2 & C = k1_funct_1(B,1) & D = k1_funct_1(B,2) ) => k4_rlvect_1(A,B) = k1_algstr_0(A,C,D) ) ) ) ) ) )).
fof(t75_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_rmod_2(E,A,B) => ! [F] : ( m2_rmod_2(F,A,B,E) => ~ ( r2_hidden(C,F) & r2_hidden(D,F) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ~ ( r1_struct_0(E,G) & k3_rlvect_1(B,C,G) = D ) ) ) ) ) ) ) ) ) )).
fof(t75_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ? [E] : ( m2_rusub_1(E,A,B) & r2_hidden(C,E) & r2_hidden(D,E) ) <=> r1_struct_0(B,k5_algstr_0(A,C,D)) ) ) ) ) ) )).
fof(t75_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => k16_rvsum_1(k7_finseq_1(A,B)) = k2_xcmplx_0(k16_rvsum_1(A),k16_rvsum_1(B)) ) ) )).
fof(t75_scmfsa8c,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) ) => ! [B] : ( ( v1_ami_2(B) & ~ v1_scmfsa_m(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => v1_scmfsa7b(k1_scmfsa8b(B,k1_scmfsa8a(2),k5_scmfsa6a(A,k8_scmfsa_2(B,k4_scmfsa_2(k5_numbers))))) ) ) )).
fof(t75_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ~ v2_extpro_1(k9_scmfsa_2(A,B),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(t75_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( r1_xxreal_0(k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),F)),k5_numbers) => k1_funct_1(k6_scmpds_4(k7_scmpds_6(D,F,C),k8_memstr_0(2,k1_scmpds_2,B),A),E) = k1_funct_1(B,E) ) ) ) ) ) ) ) )).
fof(t75_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( ( v9_scmyciel(B,k6_scmyciel(A)) & m1_subset_1(B,k1_zfmisc_1(k3_tarski(k6_scmyciel(A)))) ) => ( v4_scmyciel(k7_scmyciel(A,B)) & v5_scmyciel(k7_scmyciel(A,B)) & m1_subset_1(k7_scmyciel(A,B),k1_zfmisc_1(A)) ) ) ) )).
fof(t75_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_semi_af1(A,B,C,C) = B ) ) ) )).
fof(t75_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => ! [D] : ( m2_finseq_2(D,k2_numbers,k12_seq_4(A)) => k13_seq_4(A,B,k17_seq_4(A,C,D)) = k17_seq_4(A,k13_seq_4(A,B,C),D) ) ) ) ) )).
fof(t75_setlim_1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [E] : ( ( v5_relat_1(E,B) & v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ! [F] : ( v7_ordinal1(F) => k1_funct_1(E,F) = k2_xboole_0(k1_funct_1(C,F),k1_funct_1(D,F)) ) => k4_kurato_0(A,E) = k4_subset_1(A,k4_kurato_0(A,C),k4_kurato_0(A,D)) ) ) ) ) ) )).
fof(t75_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k3_kurato_0(A,k6_setlim_2(A,C,B)) = k4_subset_1(A,B,k3_kurato_0(A,C)) ) ) )).
fof(t75_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(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,C,k5_sheffer1(A,B,E)),k5_sheffer1(A,C,k5_sheffer1(A,B,E))) ) ) ) ) ) )).
fof(t75_sin_cos,axiom,( k1_funct_1(k18_sin_cos,k7_xcmplx_0(k28_sin_cos,2)) = k5_numbers & k1_funct_1(k16_sin_cos,k7_xcmplx_0(k28_sin_cos,2)) = 1 & k1_funct_1(k18_sin_cos,k28_sin_cos) = k4_xcmplx_0(1) & k1_funct_1(k16_sin_cos,k28_sin_cos) = k5_numbers & k1_funct_1(k18_sin_cos,k2_xcmplx_0(k28_sin_cos,k7_xcmplx_0(k28_sin_cos,2))) = k5_numbers & k1_funct_1(k16_sin_cos,k2_xcmplx_0(k28_sin_cos,k7_xcmplx_0(k28_sin_cos,2))) = k4_xcmplx_0(1) & k1_funct_1(k18_sin_cos,k3_xcmplx_0(2,k28_sin_cos)) = 1 & k1_funct_1(k16_sin_cos,k3_xcmplx_0(2,k28_sin_cos)) = k5_numbers )).
fof(t75_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) & k2_sin_cos6(A) = k7_xcmplx_0(k28_sin_cos,2) ) => A = 1 ) ) )).
fof(t75_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) => k1_fdiff_1(k1_sin_cos9,A) = k7_xcmplx_0(1,k2_xcmplx_0(1,k1_square_1(A))) ) ) )).
fof(t75_sincos10,axiom,( k1_funct_1(k3_sincos10,k4_xcmplx_0(1)) = k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)) & k1_funct_1(k3_sincos10,k4_xcmplx_0(k3_square_1(2))) = k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)) )).
fof(t75_sprect_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => k19_pscomp_1(k3_topreal1(2,k1_sprect_1(A))) = k11_pscomp_1(A) ) )).
fof(t75_sprect_2,axiom,( ! [A] : ( ( ~ 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,k18_pscomp_1(k3_topreal1(2,A)))) ) ) )).
fof(t75_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_valuat_1(D,A,C) => ! [E] : ( m2_subset_1(E,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [F] : ( ( v5_relat_1(F,k3_qc_lang1(A)) & v3_card_1(F,B) & m2_finseq_1(F,k2_qc_lang1(A)) ) => ! [G] : ( m2_funct_2(G,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),C))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),C))) ) => ! [J] : ( ( v1_funct_1(J) & m1_subset_1(J,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),C))) ) => ( ( ! [K] : ( m2_subset_1(K,k2_qc_lang1(A),k3_qc_lang1(A)) => ~ ( r2_hidden(K,k1_relset_1(k3_qc_lang1(A),I)) & r2_hidden(K,k24_qc_lang1(A,k4_cqc_lang(B,A,E,F))) ) ) & ! [K] : ( m2_subset_1(K,k2_qc_lang1(A),k3_qc_lang1(A)) => ( r2_hidden(K,k1_relset_1(k3_qc_lang1(A),J)) => k1_funct_1(J,K) = k3_funct_2(k3_qc_lang1(A),C,G,K) ) ) & r1_xboole_0(k1_relset_1(k3_qc_lang1(A),H),k1_relset_1(k3_qc_lang1(A),J)) ) => ( r1_valuat_1(A,C,k4_cqc_lang(B,A,E,F),D,k1_sublemma(A,C,G,H)) <=> r1_valuat_1(A,C,k4_cqc_lang(B,A,E,F),D,k1_sublemma(A,C,G,k14_sublemma(A,C,k14_sublemma(A,C,H,I),J))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t75_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v2_tdlat_2(B,A) => ( v5_tops_1(k2_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)),A) & v5_tops_1(k2_pre_topc(A,k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B))),A) ) ) ) ) )).
fof(t75_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & ~ v3_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_tex_2(B,A) & v2_tex_3(B,A) & m1_pre_topc(B,A) ) => ? [C] : ( v1_pre_topc(C) & v1_tsep_1(C,A) & v1_tex_2(C,A) & v1_tex_3(C,A) & m1_pre_topc(C,A) & ? [D] : ( v1_pre_topc(D) & v1_borsuk_1(D,A) & v3_tex_3(D,A) & m1_pre_topc(D,A) & r3_tsep_2(A,C,D) & m1_pre_topc(C,B) ) ) ) ) )).
fof(t75_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_subset_1(u1_struct_0(k5_tex_4(A,B)),u1_struct_0(k5_tex_4(A,C))) | g1_pre_topc(u1_struct_0(k5_tex_4(A,B)),u1_pre_topc(k5_tex_4(A,B))) = g1_pre_topc(u1_struct_0(k5_tex_4(A,C)),u1_pre_topc(k5_tex_4(A,C))) ) ) ) ) )).
fof(t75_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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)))) ) => ( m1_pre_topc(D,C) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => ( ( F = G & r1_tmap_1(C,B,k2_tmap_1(A,B,E,C),F) ) => r1_tmap_1(D,B,k2_tmap_1(A,B,E,D),G) ) ) ) ) ) ) ) ) ) )).
fof(t75_topgen_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k5_topmetr)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k5_topmetr)))) ) => ( v5_pre_topc(B,A,k5_topmetr) <=> ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(k5_numbers,C) & r1_xxreal_0(D,1) ) => ( r1_xxreal_0(1,C) | r1_xxreal_0(D,k5_numbers) | ( v3_pre_topc(k8_relset_1(u1_struct_0(A),u1_struct_0(k5_topmetr),B,k3_rcomp_1(k5_numbers,D)),A) & v3_pre_topc(k8_relset_1(u1_struct_0(A),u1_struct_0(k5_topmetr),B,k4_rcomp_1(C,1)),A) ) ) ) ) ) ) ) ) )).
fof(t75_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => r1_tarski(k7_relset_1(u1_struct_0(k15_euclid(2)),k1_numbers,k5_pscomp_1,k2_pre_topc(k15_euclid(2),A)),k5_measure6(k7_relset_1(u1_struct_0(k15_euclid(2)),k1_numbers,k5_pscomp_1,A))) ) )).
fof(t75_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( ( u1_struct_0(A) = u1_struct_0(B) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => k2_pre_topc(A,C) = k2_pre_topc(B,D) ) ) ) ) => g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) ) ) ) )).
fof(t75_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_analoaf(A,B,C,D,E) & ~ r2_analoaf(A,B,D,C,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_aff_1(A,B,D,F) & r1_aff_1(A,C,E,F) ) ) ) ) ) ) ) ) )).
fof(t75_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_trees_1(C) ) => ( k5_trees_1(k13_trees_3(B,C),k14_trees_3(k5_numbers),A) = k13_trees_3(A,C) & k5_trees_1(k13_trees_3(B,C),k14_trees_3(1),A) = k13_trees_3(B,A) ) ) ) ) )).
fof(t75_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( r3_tsep_1(A,B,C) <=> ? [D] : ( ~ v2_struct_0(D) & v1_borsuk_1(D,A) & m1_pre_topc(D,A) & ? [E] : ( ~ v2_struct_0(E) & v1_borsuk_1(E,A) & m1_pre_topc(E,A) & m1_pre_topc(B,D) & m1_pre_topc(C,E) & ( r1_tsep_1(D,E) | r1_tsep_1(k2_tsep_1(A,D,E),k1_tsep_1(A,B,C)) ) ) ) ) ) ) ) )).
fof(t75_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v1_valued_2(D) => ! [E] : ( v1_valued_2(E) => ! [F] : ( v1_valued_2(F) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,D))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(B,E))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(C,F))) ) => k73_valued_2(k3_xboole_0(A,B),C,k2_valued_2(k3_xboole_0(k1_valued_2(D),k1_valued_2(E))),F,k73_valued_2(A,B,D,E,G,H),I) = k73_valued_2(A,k3_xboole_0(B,C),D,k2_valued_2(k3_xboole_0(k1_valued_2(E),k1_valued_2(F))),G,k73_valued_2(B,C,E,F,H,I)) ) ) ) ) ) ) )).
fof(t75_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( m2_vectsp_4(C,A,B,k2_vectsp_4(A,B)) => C = u1_struct_0(B) ) ) ) ) )).
fof(t75_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ( v24_waybel_0(A) <=> ! [B] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => r1_yellow_0(A,B) ) ) ) )).
fof(t75_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v9_waybel_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_orders_2(A,B,C) => r1_orders_2(A,k6_waybel_1(A,C,D),k6_waybel_1(A,B,D)) ) ) ) ) ) ) )).
fof(t75_xboole_1,axiom,( ! [A] : ! [B] : ~ ( ~ r1_xboole_0(A,B) & r1_xboole_0(k3_xboole_0(A,B),B) ) )).
fof(t75_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k4_xboolean(A,k10_xboolean(B,C)) = k10_xboolean(k4_xboolean(A,B),k4_xboolean(A,C)) ) ) ) )).
fof(t75_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k3_xcmplx_0(k7_xcmplx_0(A,B),C) = k3_xcmplx_0(k7_xcmplx_0(C,B),A) ) ) ) )).
fof(t75_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(k5_numbers,C) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(k7_xcmplx_0(A,C),k7_xcmplx_0(B,C)) ) ) ) ) )).
fof(t75_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(D,C) & k2_xxreal_1(C,D) = k4_xxreal_1(A,B) ) ) ) ) ) )).
fof(t75_xxreal_2,axiom,( ! [A] : ( ( v2_membered(A) & v1_xxreal_2(A) & v2_xxreal_2(A) & v6_xxreal_2(A) ) => A = k1_xxreal_1(k2_xxreal_2(A),k1_xxreal_2(A)) ) )).
fof(t75_xxreal_3,axiom,( k5_xxreal_3(k2_xxreal_0) = k5_numbers )).
fof(t75_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v6_zf_lang(A) => r3_zf_lang(k24_zf_lang(A),A) ) ) )).
fof(t75_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( 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] : ( m2_subset_1(E,k4_ordinal1,k1_zf_lang) => ( r2_hidden(E,k2_zf_model(A)) => k3_funct_2(k1_zf_lang,B,D,E) = k3_funct_2(k1_zf_lang,B,C,E) ) ) & r1_zf_model(B,C,A) ) => r1_zf_model(B,D,A) ) ) ) ) ) )).
fof(t75_zfmisc_1,axiom,( ! [A] : ! [B] : ( ! [C] : ( r2_hidden(C,A) => r1_tarski(C,B) ) => r1_tarski(k3_tarski(A),B) ) )).
fof(t75_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_zmodul01(D,A) => ~ ( k5_zmodul01(A,C,D) = k5_zmodul01(A,B,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r1_struct_0(D,E) & k3_rlvect_1(A,C,E) = B ) ) ) ) ) ) ) )).
fof(t75_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( m1_zmodul01(D,A) => ( ( m1_zmodul01(B,C) & m1_zmodul01(B,D) ) => m1_zmodul01(B,k7_zmodul01(A,C,D)) ) ) ) ) ) )).
fof(t76_abcmiz_0,axiom,( ! [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) & l3_abcmiz_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r1_rewrite1(k11_abcmiz_0(A),B,C) & ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A))) ) => ~ ( r6_abcmiz_0(A,C,D) & B = k6_abcmiz_0(A,C,D) ) ) ) ) ) ) )).
fof(t76_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ( r1_subset_1(k34_abcmiz_1(A),k38_abcmiz_1(A)) & r1_subset_1(k34_abcmiz_1(A),k39_abcmiz_1(A)) & r1_subset_1(k39_abcmiz_1(A),k38_abcmiz_1(A)) ) ) )).
fof(t76_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => k1_ordinal4(A,B) = k1_funct_4(A,k61_valued_1(B,k5_card_1(A))) ) ) )).
fof(t76_afinsq_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => k8_afinsq_2(A,k7_afinsq_1(B,C,D)) = k15_afinsq_1(A,k15_afinsq_1(A,B,C),D) ) ) ) )).
fof(t76_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k12_aofa_000(A),k9_aofa_000(A,B,k1_nat_1(C,1))) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r2_hidden(D,k9_aofa_000(A,B,C)) & r2_hidden(E,k9_aofa_000(A,B,C)) & r2_hidden(F,k9_aofa_000(A,B,C)) ) => ( r2_hidden(k13_aofa_000(A,E,F),k9_aofa_000(A,B,k1_nat_1(C,1))) & r2_hidden(k14_aofa_000(A,D,E,F),k9_aofa_000(A,B,k1_nat_1(C,1))) & r2_hidden(k16_aofa_000(A,D,E),k9_aofa_000(A,B,k1_nat_1(C,1))) ) ) ) ) ) ) ) ) ) )).
fof(t76_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v19_aofa_a00(B,A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( C = k10_subset_1(k1_funct_1(u7_aofa_a00(A),12),u4_struct_0(A)) => ( k1_msualg_1(A,C) = k3_finseq_4(u1_struct_0(A),k37_aofa_a00(A),B,B) & k2_msualg_1(A,C) = k37_aofa_a00(A) ) ) ) ) ) )).
fof(t76_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( m1_subset_1(C,k5_arytm_3) => ( r3_arytm_3(k9_arytm_3(B,C),k9_arytm_3(A,C)) <=> r3_arytm_3(B,A) ) ) ) ) )).
fof(t76_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( k9_nat_1(k1_numbers,A,k5_numbers) = k5_numbers & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ~ r1_xxreal_0(D,k5_numbers) => k9_nat_1(k1_numbers,A,D) = B ) ) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k7_series_1(A,C,D) = k3_xcmplx_0(B,k6_xcmplx_0(C,D)) ) ) ) ) ) )).
fof(t76_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v20_bcialg_1(A) => ( k2_bcialg_1(A,B) = B & k1_bcialg_1(A,B,k1_bcialg_1(A,B,C)) = C & k1_bcialg_1(A,k1_bcialg_1(A,B,C),C) = B ) ) ) ) ) )).
fof(t76_borsuk_5,axiom,( ! [A] : ( ( v2_connsp_1(A,k3_topmetr) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => r1_tarski(k1_rcomp_1(B,C),A) ) ) ) ) )).
fof(t76_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ! [G] : ( m1_borsuk_2(G,A,C,D) => ! [H] : ( m1_borsuk_2(H,A,C,D) => ( ( r4_borsuk_2(A,B,C,E,F) & r4_borsuk_2(A,C,D,G,H) ) => r4_borsuk_2(A,B,D,k1_borsuk_2(A,B,C,D,E,G),k1_borsuk_2(A,B,C,D,F,H)) ) ) ) ) ) ) ) ) ) )).
fof(t76_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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),k7_bvfunc_2(A,k1_bvfunc_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) )).
fof(t76_bvfunc14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ( ( v1_relat_1(J) & v1_funct_1(J) ) => ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ! [Q] : ! [R] : ! [S] : ( J = k1_funct_4(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,L),k16_funcop_1(C,M)),k16_funcop_1(D,N)),k16_funcop_1(E,O)),k16_funcop_1(F,P)),k16_funcop_1(G,Q)),k16_funcop_1(H,R)),k16_funcop_1(I,S)),k16_funcop_1(A,K)) => ( A = B | A = C | A = D | A = E | A = F | A = G | A = H | A = I | B = C | B = D | B = E | B = F | B = G | B = H | B = 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 | ( k1_funct_1(J,A) = K & k1_funct_1(J,B) = L & k1_funct_1(J,C) = M & k1_funct_1(J,D) = N & k1_funct_1(J,E) = O & k1_funct_1(J,F) = P & k1_funct_1(J,G) = Q & k1_funct_1(J,H) = R & k1_funct_1(J,I) = S ) ) ) ) )).
fof(t76_card_2,axiom,( ! [A] : ! [B] : ~ ( ~ v1_finset_1(A) & ( r2_wellord2(A,B) | r2_wellord2(B,A) ) & ~ ( r2_wellord2(k2_xboole_0(A,B),A) & k1_card_1(k2_xboole_0(A,B)) = k1_card_1(A) ) ) )).
fof(t76_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( m1_subset_1(B,k4_card_3(A)) => ! [C] : ( m1_subset_1(C,k4_card_3(A)) => ! [D] : m1_subset_1(k1_funct_4(B,k5_relat_1(C,D)),k4_card_3(A)) ) ) ) )).
fof(t76_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( r2_hidden(F,k2_cat_1(A,D,E)) => r2_hidden(k1_funct_1(C,F),k2_cat_1(B,k8_cat_1(A,B,C,D),k8_cat_1(A,B,C,E))) ) ) ) ) ) ) )).
fof(t76_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => r3_cat_3(B,C,k1_tarski(A),k1_cat_3(u4_struct_0(B),A,k4_cat_1(B,C))) ) ) )).
fof(t76_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,B,D) => ! [F] : ( 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 & k5_cat_1(A,k20_cat_4(A,B,C),k20_cat_4(A,D,D),D,k31_cat_4(A,B,C,D,D,E,F),k30_cat_4(A,D)) != k29_cat_4(A,B,C,D,E,F) ) ) ) ) ) ) ) )).
fof(t76_cfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,k2_numbers))) ) => ( ( v1_comseq_2(k2_partfun1(C,k2_numbers,D,A)) & v1_comseq_2(k2_partfun1(C,k2_numbers,D,B)) ) => v1_comseq_2(k2_partfun1(C,k2_numbers,D,k2_xboole_0(A,B))) ) ) ) )).
fof(t76_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ~ ( B != C & ~ r1_chord(A,B,C) & ~ ! [D] : ( m2_chord(D,A,B,C) => ! [E] : ( 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))) => ( m1_subset_1(B,k6_glib_000(E)) & m1_subset_1(C,k6_glib_000(E)) ) ) ) ) ) ) ) )).
fof(t76_classes1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r2_classes1(A,B) & r2_classes1(A,C) ) => r2_classes1(B,C) ) ) ) ) )).
fof(t76_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_clvect_1(D,A) => ( ( r2_hidden(B,k5_clvect_1(A,C,D)) & r2_hidden(B,k5_clvect_1(A,k4_algstr_0(A,C),D)) ) => r1_struct_0(D,C) ) ) ) ) ) )).
fof(t76_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v3_clvect_2(B,A) & v3_clvect_2(C,A) ) => v3_clvect_2(k3_normsp_1(A,B,C),A) ) ) ) ) )).
fof(t76_cohsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(k4_tarski(C,1),k14_cohsp_1(A,B)) <=> r2_hidden(C,A) ) )).
fof(t76_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k4_xcmplx_0(k9_complex1(A)),A) & r1_xxreal_0(A,k9_complex1(A)) ) ) )).
fof(t76_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( A != B & B != C & k4_complex2(A,B,C) != k4_complex2(k2_complex2(A,D),k2_complex2(B,D),k2_complex2(C,D)) ) ) ) ) ) )).
fof(t76_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ~ ( ! [B] : ( v7_ordinal1(B) => k9_nat_1(k2_numbers,A,B) != k5_complex1 ) & ? [B] : ( v7_ordinal1(B) & ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => r1_xxreal_0(1,k6_real_1(k9_nat_1(k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,A),k1_nat_1(C,1)),k9_nat_1(k1_numbers,k55_valued_1(k4_ordinal1,k2_numbers,A),C))) ) ) ) & v2_comseq_3(A) ) ) )).
fof(t76_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ( B = a_3_10_convex4(A,C,D) => v2_convex4(B,A) ) ) ) ) ) )).
fof(t76_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ( ~ r2_hidden(D,k24_qc_lang1(A,B)) => ( v2_cqc_the1(k11_cqc_lang(A,D,k8_cqc_lang(A,B,C)),A) <=> v2_cqc_the1(k8_cqc_lang(A,B,k11_cqc_lang(A,D,C)),A) ) ) ) ) ) ) )).
fof(t76_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_normsp_1(A,k16_csspace(A,B,C),D),k16_csspace(A,B,k3_normsp_1(A,C,D))) ) ) ) ) )).
fof(t76_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k7_xcmplx_0(1,k1_square_1(k19_sin_cos(D))) ) => ( k19_sin_cos(k2_xcmplx_0(B,k7_xcmplx_0(A,2))) = k5_numbers | k19_sin_cos(k6_xcmplx_0(B,k7_xcmplx_0(A,2))) = k5_numbers | k1_funct_1(k5_diff_1(C,A),B) = k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(k4_xcmplx_0(16),k17_sin_cos(B)),k17_sin_cos(k7_xcmplx_0(k4_xcmplx_0(A),2))),k19_sin_cos(B)),k19_sin_cos(k7_xcmplx_0(k4_xcmplx_0(A),2))),k1_square_1(k2_xcmplx_0(k19_sin_cos(k3_xcmplx_0(2,B)),k19_sin_cos(A)))) ) ) ) ) ) )).
fof(t76_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_enumset1(A,B,C,D) = k2_enumset1(D,C,B,A) )).
fof(t76_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( 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)) ) ) ) ) )).
fof(t76_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ~ ( v1_euclid_4(D,A) & D = k2_euclid_4(A,B,C) & B = C ) ) ) ) ) )).
fof(t76_exchsort,axiom,( ! [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) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_exchsort(B) ) => ! [C] : ( ( v2_exchsort(C,k5_numbers) & m2_exchsort(C,A,B) ) => ( ( 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(C) ) ) ) ) )).
fof(t76_facirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k15_facirc_1(A,B,C),k18_facirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ( ( E = k1_funct_1(D,A) & F = k1_funct_1(D,B) ) => 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) ) ) ) ) ) ) ) )).
fof(t76_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v20_lattices(B,A) & v21_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v12_lattices(A) => v12_lattices(k10_filter_2(A,B)) ) ) ) )).
fof(t76_finseq_1,axiom,( ! [A] : ! [B] : ( k9_finseq_1(A) = k9_finseq_1(B) => A = B ) )).
fof(t76_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ! [F] : ( ( 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))) ) => ! [G] : ( m2_finseq_1(G,B) => ( E = k5_funcop_1(F,D,G) => k3_finseq_1(E) = k3_finseq_1(G) ) ) ) ) ) ) ) ) )).
fof(t76_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(A,C) => ( r2_hidden(B,C) | k1_finseq_3(k10_finseq_1(A,B),C) = k9_finseq_1(B) ) ) )).
fof(t76_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ( E = k7_finseq_4(A,B,C,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 ) ) ) )).
fof(t76_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m2_finseq_1(D,B) => ( v2_funct_1(D) => ( r2_hidden(C,k10_xtuple_0(D)) | v2_funct_1(k5_finseq_5(B,D,C,A)) ) ) ) ) ) ) )).
fof(t76_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r2_hidden(B,k10_xtuple_0(C)) => k8_finseq_1(A,k1_finseq_5(A,C,B),k2_rfinseq(A,1,k2_finseq_5(A,C,B))) = C ) ) ) ) )).
fof(t76_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v3_card_1(D,C) & m2_finseq_1(D,A) ) => ! [E] : ( ( 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] : ( ( 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(E,A) & v1_setwiseo(E,A) & B = k4_binop_1(A,E) & v1_finseqop(E,A) & r6_binop_1(A,F,E) ) => r2_relset_1(k4_ordinal1,A,k3_finseqop(A,A,A,F,B,D),k5_finseq_2(A,C,B)) ) ) ) ) ) ) ) )).
fof(t76_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => k2_flang_2(A,B) = k4_subset_1(k8_afinsq_1(A),k4_flang_1(A,k2_flang_1(A)),B) ) )).
fof(t76_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => k6_flang_1(A,k2_flang_3(A,B),B) = k1_flang_3(A,B,2) ) )).
fof(t76_fomodel0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => k32_fomodel0(k15_funct_3(A,B)) = k2_zfmisc_1(k32_fomodel0(A),k32_fomodel0(B)) ) ) )).
fof(t76_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ r2_hidden(B,A) => k5_relat_1(k16_funcop_1(B,C),A) = k1_xboole_0 ) )).
fof(t76_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(A,k10_xtuple_0(B)) => k7_relat_1(B,k8_relat_1(B,A)) = A ) ) )).
fof(t76_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ~ ( ( B = k1_xboole_0 => A = k1_xboole_0 ) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ~ r1_partfun1(C,D) ) ) ) )).
fof(t76_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,B,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,D))) ) => ~ ( ( C = k1_xboole_0 => A = k1_xboole_0 ) & ( D = k1_xboole_0 => B = k1_xboole_0 ) & k16_funct_3(A,B,C,D,E,F) != k13_funct_3(k3_relat_1(k9_funct_3(A,B),E),k3_relat_1(k10_funct_3(A,B),F)) ) ) ) )).
fof(t76_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( ( r1_tarski(k9_xtuple_0(A),C) & r1_tarski(k9_xtuple_0(B),D) & r1_xboole_0(C,D) ) => ( k5_relat_1(k1_funct_4(A,B),C) = A & k5_relat_1(k1_funct_4(A,B),D) = B ) ) ) ) )).
fof(t76_funct_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_relat_1(C) => k3_relat_1(k8_funct_7(C,A),k8_funct_7(C,B)) = k8_funct_7(C,k2_xcmplx_0(B,A)) ) ) ) )).
fof(t76_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => r1_funct_8(A,k1_numbers,k1_numbers,k37_valued_1(k1_numbers,k1_numbers,k18_sin_cos)) ) )).
fof(t76_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => v1_subset_1(k8_fvaluat1(A,B),u1_struct_0(k7_fvaluat1(A,B))) ) ) ) )).
fof(t76_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [D] : ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => k4_rlvect_1(B,k4_fvsum_1(A,B,C,D)) = k3_rlvect_1(B,k4_rlvect_1(B,C),k4_rlvect_1(B,D)) ) ) ) ) )).
fof(t76_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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) & k2_msafree2(k29_gfacirc1(A,B,C)) != k1_enumset1(A,B,C) ) )).
fof(t76_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( r1_tarski(k18_glib_000(B,C),k18_glib_000(A,C)) & r1_tarski(k19_glib_000(B,C),k19_glib_000(A,C)) & r1_tarski(k20_glib_000(B,C),k20_glib_000(A,C)) & r1_tarski(k21_glib_000(B,C),k21_glib_000(A,C)) ) ) ) )).
fof(t76_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k1_relset_1(k4_ordinal1,k12_glib_001(A,B))) <=> r2_hidden(k2_nat_1(2,C),k1_relset_1(k4_ordinal1,B)) ) ) ) ) )).
fof(t76_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( v1_group_3(C,A) & m1_group_2(C,A) ) => ~ ( m1_group_2(C,B) & ! [D] : ( ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) ) => ! [E] : ( ( v15_algstr_0(E) & v1_group_3(E,A) & m1_group_2(E,A) ) => ~ ( u1_struct_0(D) = k4_group_11(A,B,C) & u1_struct_0(E) = k3_group_11(A,B,C) & r1_tarski(k4_group_11(A,B,E),k4_group_11(A,B,D)) ) ) ) ) ) ) ) )).
fof(t76_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => k2_group_2(A,k8_group_2(A,B),k8_group_2(A,B)) = k8_group_2(A,B) ) ) )).
fof(t76_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_group_3(A,B,C) => r1_group_3(A,C,B) ) ) ) ) )).
fof(t76_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ( ( v1_finset_1(k15_group_2(A,B)) & k18_group_2(A,B) = 2 ) => m1_group_2(k9_group_5(A),B) ) ) ) )).
fof(t76_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v7_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ 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) => v7_struct_0(B) ) ) ) )).
fof(t76_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( ( v4_group_9(D,A,C) & m1_group_9(D,A,C) ) => ( v7_struct_0(k10_group_9(A,C,D)) => g1_group_9(A,u1_struct_0(C),u2_algstr_0(C),u1_group_9(A,C)) = g1_group_9(A,u1_struct_0(D),u2_algstr_0(D),u1_group_9(A,D)) ) ) ) ) )).
fof(t76_ideal_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k7_ideal_1(A,k7_domain_1(u1_struct_0(A),B,C)) = k12_ideal_1(A,k7_ideal_1(A,k6_domain_1(u1_struct_0(A),B)),k7_ideal_1(A,k6_domain_1(u1_struct_0(A),C))) ) ) ) )).
fof(t76_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => k2_integra5(A,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos2,k3_sin_cos2)) = k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k1_funct_1(k3_sin_cos2,k2_seq_4(A)),k1_funct_1(k3_sin_cos2,k3_seq_4(A))),k1_funct_1(k1_sin_cos2,k2_seq_4(A))),k1_funct_1(k1_sin_cos2,k3_seq_4(A))) ) )).
fof(t76_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ( v9_intpro_1(A) => r1_tarski(k12_intpro_1,A) ) ) )).
fof(t76_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(k18_euclid(B),k5_numbers) & ~ r1_xxreal_0(A,k7_xcmplx_0(k17_euclid(B),k12_euclid(B))) & ? [C] : ( 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),k5_numbers) & ~ r1_xxreal_0(k5_numbers,k17_euclid(C)) ) ) ) ) ) )).
fof(t76_jgraph_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ v1_xboole_0(E) & v2_compts_1(E,k15_euclid(2)) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ ( v1_topreal2(E) & r2_hidden(A,E) & r2_hidden(B,E) & r2_hidden(C,E) & r2_hidden(D,E) & r1_jordan6(E,B,C) & r1_jordan6(E,C,D) & ~ r1_jordan6(E,A,B) & ~ ( r1_jordan6(E,B,A) & r1_jordan6(E,A,C) ) & ~ ( r1_jordan6(E,C,A) & r1_jordan6(E,A,D) ) & ~ r1_jordan6(E,D,A) ) ) ) ) ) ) )).
fof(t76_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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 & k18_euclid(C) = H & k18_euclid(D) = H & r1_xxreal_0(G,k18_euclid(A)) & ~ r1_xxreal_0(k18_euclid(B),k18_euclid(A)) & r1_xxreal_0(k18_euclid(B),H) & r1_xxreal_0(E,k17_euclid(C)) & ~ r1_xxreal_0(k17_euclid(D),k17_euclid(C)) & r1_xxreal_0(k17_euclid(D),F) & k1_funct_1(I,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t76_jordan,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( r1_jordan24(2,A,k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) => k8_pscomp_1(A) = 1 ) ) )).
fof(t76_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(D,B) & r2_hidden(C,k9_subset_1(u1_struct_0(k15_euclid(2)),k6_topreal1(D),k3_topreal1(2,k2_jordan9(B,A)))) & r1_xxreal_0(k18_euclid(D),k18_euclid(C)) ) ) ) ) ) )).
fof(t76_jordan2c,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( v3_connsp_1(B,A) & v3_connsp_1(C,A) & v2_connsp_1(D,A) ) => ( r1_xboole_0(B,D) | r1_xboole_0(C,D) | B = C ) ) ) ) ) ) )).
fof(t76_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ r2_hidden(C,k1_relset_1(k6_glib_000(A),k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),k23_lexbfs(A,k26_lexbfs(A),B)))) => k1_recdef_1(k8_lexbfs(k3_rfunct_3(k6_glib_000(A),k4_ordinal1),k4_ordinal1,k6_glib_000(A),k23_lexbfs(A,k26_lexbfs(A),B)),C) = k5_card_1(k3_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),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),k23_lexbfs(A,k26_lexbfs(A),B))))) ) ) ) )).
fof(t76_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v7_limfunc1(B) => ( ! [C] : ( v1_xreal_0(C) => ~ ( r1_tarski(k10_prob_1(C),k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k1_relset_1(k1_numbers,B))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,k10_prob_1(C)) => r1_xxreal_0(k1_funct_1(B,D),k1_funct_1(A,D)) ) ) ) ) | v7_limfunc1(A) ) ) ) ) )).
fof(t76_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_limfunc2(B,A) & k1_limfunc2(B,A) = k5_numbers & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,C) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,C) & ~ r1_xxreal_0(A,D) & r2_hidden(D,k1_relset_1(k1_numbers,B)) & k1_funct_1(B,D) != k5_numbers ) ) ) ) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(k6_xcmplx_0(A,C),A))) => r1_xxreal_0(k1_funct_1(B,D),k5_numbers) ) ) ) ) | r3_limfunc2(k6_rfunct_1(k1_numbers,k1_numbers,B),A) ) ) ) ) )).
fof(t76_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r4_limfunc2(B,A) & r1_limfunc3(C,k2_limfunc2(B,A)) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(A,k2_xcmplx_0(A,D)))) & k1_funct_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) = k1_limfunc3(C,k2_limfunc2(B,A)) ) ) ) ) ) ) )).
fof(t76_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => r1_funct_2(u1_struct_0(k18_lpspace1(A,B,C)),k1_numbers,u1_struct_0(k10_lpspace2(A,B,C,1)),k1_numbers,k19_lpspace1(A,B,C),k11_lpspace2(A,B,C,1)) ) ) ) )).
fof(t76_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_cqc_lang(A))) => ( ( r3_cqc_the1(A,D,k8_cqc_lang(A,k6_cqc_lang(A,B),C)) & r3_cqc_the1(A,D,k6_cqc_lang(A,C)) ) => r3_cqc_the1(A,D,B) ) ) ) ) ) )).
fof(t76_mathmorp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( ( v1_convex1(B,k15_euclid(A)) & v1_convex1(C,k15_euclid(A)) ) => ( v1_convex1(k6_rusub_4(k15_euclid(A),B,C),k15_euclid(A)) & v1_convex1(k3_mathmorp(k15_euclid(A),B,C),k15_euclid(A)) ) ) ) ) ) )).
fof(t76_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( v4_matrix10(B) => r2_matrix10(k5_matrix10(A,C,B),C) ) ) ) ) )).
fof(t76_matrix13,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( k8_matrix13(A,B) = C <=> ( ? [D] : ( m2_finseq_2(D,k4_ordinal1,k4_finseq_2(C,k4_ordinal1)) & ? [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(C,k4_ordinal1)) & r1_tarski(k2_zfmisc_1(k10_xtuple_0(D),k10_xtuple_0(E)),k2_matrix_0(B)) & k12_matrix_3(C,A,k1_matrix13(u1_struct_0(A),B,C,C,D,E)) != k4_struct_0(A) ) ) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(D,k4_ordinal1)) => ! [F] : ( m2_finseq_2(F,k4_ordinal1,k4_finseq_2(D,k4_ordinal1)) => ( r1_tarski(k2_zfmisc_1(k10_xtuple_0(E),k10_xtuple_0(F)),k2_matrix_0(B)) => ( k12_matrix_3(D,A,k1_matrix13(u1_struct_0(A),B,D,D,E,F)) = k4_struct_0(A) | r1_xxreal_0(D,C) ) ) ) ) ) ) ) ) ) ) )).
fof(t76_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( k3_finseq_1(C) = k1_matrix_0(D) => ( k12_matrix_3(A,B,C) = k4_struct_0(B) | k8_matrix13(B,k4_matrix_3(B,D,C)) = k8_matrix13(B,D) ) ) ) ) ) ) )).
fof(t76_matrixj1,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => k26_matrixj1(A,k4_matrixj1(u1_struct_0(A),B),k4_matrixj1(u1_struct_0(A),C)) = k4_matrixj1(u1_struct_0(A),k4_matrix_3(A,B,C)) ) ) ) )).
fof(t76_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,A) ) => ( B = C | k1_funct_1(k6_matrixr2(A,B),C) = k5_numbers ) ) ) ) ) )).
fof(t76_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : k9_xtuple_0(k9_xtuple_0(k1_tarski(k3_xtuple_0(A,B,C)))) = k1_tarski(A) )).
fof(t76_member_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k11_member_1(k1_tarski(A),k2_tarski(B,C)) = k2_tarski(k6_xcmplx_0(A,B),k6_xcmplx_0(A,C)) ) ) ) )).
fof(t76_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( v2_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [C] : ( m2_subset_1(C,k8_card_3(k2_memstr_0(A,B)),k11_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)) & v1_finset_1(C) ) ) ) ) )).
fof(t76_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,k4_ordinal1,k6_numbers) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,k4_ordinal1,k6_numbers) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ( ! [I] : ( v7_ordinal1(I) => ( r1_mesfunc2(A,B,k4_mesfunc5(A,k6_numbers,E,I)) & k1_relset_1(A,k4_mesfunc5(A,k6_numbers,E,I)) = D ) ) & ! [I] : ( v7_ordinal1(I) => v6_supinf_2(k4_mesfunc5(A,k6_numbers,E,I)) ) & ! [I] : ( v7_ordinal1(I) => ! [J] : ( v7_ordinal1(J) => ( r1_xxreal_0(I,J) => ! [K] : ( m1_subset_1(K,A) => ( r2_hidden(K,D) => r1_xxreal_0(k12_supinf_2(k4_mesfunc5(A,k6_numbers,E,I),K),k12_supinf_2(k4_mesfunc5(A,k6_numbers,E,J),K)) ) ) ) ) ) & ! [I] : ( v7_ordinal1(I) => ( r1_mesfunc2(A,B,k4_mesfunc5(A,k6_numbers,F,I)) & k1_relset_1(A,k4_mesfunc5(A,k6_numbers,F,I)) = D ) ) & ! [I] : ( v7_ordinal1(I) => v6_supinf_2(k4_mesfunc5(A,k6_numbers,F,I)) ) & ! [I] : ( v7_ordinal1(I) => ! [J] : ( v7_ordinal1(J) => ( r1_xxreal_0(I,J) => ! [K] : ( m1_subset_1(K,A) => ( r2_hidden(K,D) => r1_xxreal_0(k12_supinf_2(k4_mesfunc5(A,k6_numbers,F,I),K),k12_supinf_2(k4_mesfunc5(A,k6_numbers,F,J),K)) ) ) ) ) ) & ! [I] : ( m1_subset_1(I,A) => ( r2_hidden(I,D) => ( v10_mesfunc5(k3_mesfunc5(A,E,I)) & v10_mesfunc5(k3_mesfunc5(A,F,I)) & k2_mesfunc5(k3_mesfunc5(A,E,I)) = k2_mesfunc5(k3_mesfunc5(A,F,I)) ) ) ) & ! [I] : ( v7_ordinal1(I) => ( k9_nat_1(k6_numbers,G,I) = k5_mesfunc5(A,B,C,k4_mesfunc5(A,k6_numbers,E,I)) & k9_nat_1(k6_numbers,H,I) = k5_mesfunc5(A,B,C,k4_mesfunc5(A,k6_numbers,F,I)) ) ) ) => ( v10_mesfunc5(G) & v10_mesfunc5(H) & k2_mesfunc5(G) = k2_mesfunc5(H) ) ) ) ) ) ) ) ) ) ) )).
fof(t76_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( ( r1_mesfunc6(A,B,C,E) & D = k9_subset_1(A,k1_relset_1(A,C),E) ) => r1_mesfunc6(A,B,k2_partfun1(A,k1_numbers,C,E),D) ) ) ) ) ) ) )).
fof(t76_mmlquery,axiom,( ! [A] : ( l1_mmlquery(A) => ! [B] : ( m2_finseq_1(B,u1_mmlquery(A)) => k34_mmlquery(A,B) = k15_mmlquery(u1_struct_0(A),k32_mmlquery(A,B),k33_mmlquery(A,B)) ) ) )).
fof(t76_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k25_modelc_2(k43_modelc_2)) => ( r7_modelc_2(C,k8_modelc_2(A,B)) <=> r7_modelc_2(C,k5_modelc_2(k4_modelc_2(A,B),k4_modelc_2(B,k6_modelc_2(k8_modelc_2(A,B))))) ) ) ) ) )).
fof(t76_modelc_3,axiom,( ! [A] : ( m1_subset_1(A,k25_modelc_2(k43_modelc_2)) => ! [B] : ( ( v1_modelc_2(B) & v5_modelc_3(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r9_modelc_3(k43_modelc_2,k34_modelc_3(B),A) <=> r7_modelc_2(A,B) ) ) ) )).
fof(t76_monoid_0,axiom,( ! [A] : ( u1_struct_0(k16_monoid_0(A)) = k1_funct_2(A,A) & u2_algstr_0(k16_monoid_0(A)) = k1_realset1(k14_monoid_0(A),k1_funct_2(A,A)) & k5_struct_0(k16_monoid_0(A)) = k6_partfun1(A) ) )).
fof(t76_msafree4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ? [C] : ( m1_msualg_4(C,A,B,B) & r6_pboole(A,C,k7_funcop_1(A,k1_xboole_0)) & v9_msafree4(C,A,B) ) ) )).
fof(t76_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ~ r3_ncfcont1(B,A,C,D) ) | r9_ncfcont1(B,A,C,u1_struct_0(B)) ) ) ) ) ) )).
fof(t76_newton,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,A) => r1_tarski(k2_xboole_0(k9_newton(A),k1_tarski(A)),k9_newton(B)) ) ) ) )).
fof(t76_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v11_o_ring_1(B,A) & v5_o_ring_1(C,A) ) => v13_o_ring_1(k6_algstr_0(A,B,C),A) ) ) ) ) )).
fof(t76_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( ( r6_relat_2(A,B) & r1_tarski(C,B) ) => r6_relat_2(A,C) ) ) )).
fof(t76_ordinal6,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal5(A) ) => ? [B] : ( v3_ordinal1(B) & A = k13_ordinal6(1,B) ) ) )).
fof(t76_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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) & r1_xboole_0(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) ) ) ) )).
fof(t76_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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)) => ( r2_pboole(A,k4_pboole(A,B,C),D) & r2_pboole(A,k4_pboole(A,B,D),C) ) ) ) ) ) )).
fof(t76_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r1_pdiff_5(A,B) => r1_fcont_1(k1_pdiff_2(3,1,k1_pdiff_3(1,3,A),B),k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(1,3),B)) ) ) ) )).
fof(t76_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ( r4_pdiff_9(A,C,k12_finseq_1(k4_ordinal1,B),D) <=> r3_pdiff_9(A,C,B,D) ) ) ) ) )).
fof(t76_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => v2_funct_1(k21_polyform(A,k7_polyform(A))) ) )).
fof(t76_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_subset_1(C,A) => ( ~ r2_hidden(C,B) => ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ( D = k2_xboole_0(k1_tarski(C),B) => ! [E] : ( ( 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] : ( m1_subset_1(F,k4_ordinal1) => ( ( r2_hidden(F,k4_finseq_1(k7_pre_poly(A,D,E))) & k7_partfun1(A,k7_pre_poly(A,D,E),F) = C ) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( ( r1_xxreal_0(1,G) & r1_xxreal_0(G,k6_xcmplx_0(F,1)) ) => k7_partfun1(A,k7_pre_poly(A,D,E),G) = k7_partfun1(A,k7_pre_poly(A,B,E),G) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t76_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(A,k5_numbers) => k6_prepower(A,k4_xcmplx_0(B)) = k7_xcmplx_0(1,k6_prepower(A,B)) ) ) ) )).
fof(t76_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,A) & v1_funct_1(E) & v1_partfun1(E,A) ) => ( ( r2_pboole(A,k6_pboole(A,B,D),k6_pboole(A,C,E)) & v2_relat_1(k6_pboole(A,B,D)) ) => ( r2_pboole(A,B,C) & r2_pboole(A,D,E) ) ) ) ) ) ) )).
fof(t76_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v3_qc_lang1(B,A) => r3_qc_lang2(A,k18_qc_lang1(A,B),B) ) ) ) )).
fof(t76_quatern3,axiom,( k7_quatern2(k11_quaterni) = k24_quaterni(k11_quaterni) )).
fof(t76_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => r1_xxreal_0(k14_quaterni(A),k28_quaterni(A)) ) )).
fof(t76_relat_1,axiom,( ! [A] : k5_relat_1(k1_xboole_0,A) = k1_xboole_0 )).
fof(t76_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(C))) => ! [G] : ( ( ~ v2_struct_0(G) & l1_rewrite3(G,F) ) => ( r1_rewrite1(k1_rewrite3(C,F,G),k4_tarski(A,E),k4_tarski(B,k1_flang_1(C,D,E))) => D = k2_flang_1(C) ) ) ) ) ) ) )).
fof(t76_rfunct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) ) => ( r1_xboole_0(A,k9_xtuple_0(B)) => v1_comseq_2(k5_relat_1(B,A)) ) ) )).
fof(t76_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ! [D] : ( ( v1_finset_1(k1_relset_1(A,k2_partfun1(A,k1_numbers,B,k2_xboole_0(C,D)))) & r1_xboole_0(C,D) ) => r2_classes1(k20_rfunct_3(A,B,k2_xboole_0(C,D)),k8_finseq_1(k1_numbers,k20_rfunct_3(A,B,C),k20_rfunct_3(A,B,D))) ) ) ) )).
fof(t76_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_seq_2(B) & v2_seq_2(C) ) => r1_xxreal_0(k2_xcmplx_0(k1_funct_1(k3_rinfsup1(B),A),k1_funct_1(k3_rinfsup1(C),A)),k1_funct_1(k3_rinfsup1(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C)),A)) ) ) ) ) )).
fof(t76_rlaffin1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_rlaffin1(C,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( ( r2_hidden(A,k3_convex1(B,C)) & ! [E] : ( r2_hidden(E,D) => k1_funct_1(k5_rlaffin1(B,C,A),E) = k5_numbers ) ) => r2_hidden(A,k3_convex1(B,k7_subset_1(u1_struct_0(B),C,D))) ) ) ) ) )).
fof(t76_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( m2_rlsub_1(B,A,k2_rlsub_1(A)) => B = u1_struct_0(A) ) ) ) )).
fof(t76_rltopsp1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ~ ( r2_hidden(D,k1_rltopsp1(A,B,C)) & ! [E] : ( v1_xreal_0(E) => ~ ( r1_xxreal_0(k5_numbers,E) & r1_xxreal_0(E,1) & D = k3_rlvect_1(A,k1_rlvect_1(A,B,k6_xcmplx_0(1,E)),k1_rlvect_1(A,C,E)) ) ) ) ) ) ) )).
fof(t76_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( k3_finseq_1(B) = 3 & D = k1_funct_1(B,1) & E = k1_funct_1(B,2) & C = k1_funct_1(B,3) ) => k4_rlvect_1(A,B) = k1_algstr_0(A,k1_algstr_0(A,D,E),C) ) ) ) ) ) ) )).
fof(t76_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_rmod_2(E,A,B) => ! [F] : ( m2_rmod_2(F,A,B,E) => ~ ( r2_hidden(C,F) & r2_hidden(D,F) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ~ ( r1_struct_0(E,G) & k5_algstr_0(B,C,G) = D ) ) ) ) ) ) ) ) ) )).
fof(t76_rmod_4,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => m1_rmod_2(k10_rmod_4(A,B,k9_subset_1(u1_struct_0(B),C,D)),A,k2_rmod_3(A,B,k10_rmod_4(A,B,C),k10_rmod_4(A,B,D))) ) ) ) ) )).
fof(t76_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_rusub_1(D,A,B) => ! [E] : ( m2_rusub_1(E,A,B) => ( ( r2_hidden(C,D) & r2_hidden(C,E) ) => D = E ) ) ) ) ) ) )).
fof(t76_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => k16_rvsum_1(k7_finseq_1(k9_finseq_1(A),B)) = k2_xcmplx_0(A,k16_rvsum_1(B)) ) ) )).
fof(t76_scmfsa8c,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => k1_funct_1(k1_scmfsa8b(C,k1_scmfsa8a(2),k5_scmfsa6a(A,k8_scmfsa_2(C,k4_scmfsa_2(k5_numbers)))),k1_nat_1(k5_card_1(k5_scmfsa6a(A,k8_scmfsa_2(C,k4_scmfsa_2(k5_numbers)))),3)) = k11_scmfsa_2(k1_nat_1(k5_card_1(k5_scmfsa6a(A,k8_scmfsa_2(C,k4_scmfsa_2(k5_numbers)))),5)) ) ) ) )).
fof(t76_scmfsa_2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ~ v2_extpro_1(k10_scmfsa_2(A,B),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(t76_scmpds_2,axiom,( k2_compos_1(k1_scmpds_2) = k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0) )).
fof(t76_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => k5_card_1(k8_scmpds_6(A,B,C)) = k1_nat_1(k5_card_1(C),2) ) ) ) )).
fof(t76_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v6_scmyciel(A) ) => k8_scmyciel(A) = k11_scmyciel(k6_scmyciel(A)) ) )).
fof(t76_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & k1_semi_af1(A,B,D,C) = C ) ) ) ) )).
fof(t76_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => ! [D] : ( m2_finseq_2(D,k2_numbers,k12_seq_4(A)) => k17_seq_4(A,B,k17_seq_4(A,C,D)) = k13_seq_4(A,k17_seq_4(A,B,C),D) ) ) ) ) )).
fof(t76_setlim_1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [E] : ( ( v5_relat_1(E,B) & v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ! [F] : ( v7_ordinal1(F) => k1_funct_1(E,F) = k3_xboole_0(k1_funct_1(C,F),k1_funct_1(D,F)) ) => r1_tarski(k4_kurato_0(A,E),k9_subset_1(A,k4_kurato_0(A,C),k4_kurato_0(A,D))) ) ) ) ) ) )).
fof(t76_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => r1_tarski(k3_kurato_0(A,k7_setlim_2(A,C,B)),k7_subset_1(A,B,k3_kurato_0(A,C))) ) ) )).
fof(t76_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => C = k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,k5_sheffer1(A,B,B),B)) ) ) ) )).
fof(t76_sin_cos,axiom,( k19_sin_cos(k7_xcmplx_0(k28_sin_cos,2)) = k5_numbers & k17_sin_cos(k7_xcmplx_0(k28_sin_cos,2)) = 1 & k19_sin_cos(k28_sin_cos) = k4_xcmplx_0(1) & k17_sin_cos(k28_sin_cos) = k5_numbers & k19_sin_cos(k2_xcmplx_0(k28_sin_cos,k7_xcmplx_0(k28_sin_cos,2))) = k5_numbers & k17_sin_cos(k2_xcmplx_0(k28_sin_cos,k7_xcmplx_0(k28_sin_cos,2))) = k4_xcmplx_0(1) & k19_sin_cos(k3_xcmplx_0(2,k28_sin_cos)) = 1 & k17_sin_cos(k3_xcmplx_0(2,k28_sin_cos)) = k5_numbers )).
fof(t76_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) => ( r1_xxreal_0(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k2_sin_cos6(A)) & r1_xxreal_0(k2_sin_cos6(A),k7_xcmplx_0(k28_sin_cos,2)) ) ) ) )).
fof(t76_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) => k1_fdiff_1(k2_sin_cos9,A) = k4_xcmplx_0(k7_xcmplx_0(1,k2_xcmplx_0(1,k1_square_1(A)))) ) ) )).
fof(t76_sincos10,axiom,( k1_funct_1(k4_sincos10,k3_square_1(2)) = k7_xcmplx_0(k28_sin_cos,4) & k1_funct_1(k4_sincos10,1) = k7_xcmplx_0(k28_sin_cos,2) )).
fof(t76_sprect_1,axiom,( ! [A] : ( ( ~ 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(k3_topreal1(2,k1_sprect_1(A))) = k11_pscomp_1(A) ) )).
fof(t76_sprect_2,axiom,( ! [A] : ( ( ~ 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(k3_finseq_1(A),k4_finseq_4(A,k18_pscomp_1(k3_topreal1(2,A)))) ) ) )).
fof(t76_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_valuat_1(D,A,C) => ( ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),C))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),C))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),C))) ) => ( ( ! [I] : ( m2_subset_1(I,k2_qc_lang1(A),k3_qc_lang1(A)) => ~ ( r2_hidden(I,k1_relset_1(k3_qc_lang1(A),G)) & r2_hidden(I,k24_qc_lang1(A,B)) ) ) & ! [I] : ( m2_subset_1(I,k2_qc_lang1(A),k3_qc_lang1(A)) => ( r2_hidden(I,k1_relset_1(k3_qc_lang1(A),H)) => k1_funct_1(H,I) = k3_funct_2(k3_qc_lang1(A),C,E,I) ) ) & r1_xboole_0(k1_relset_1(k3_qc_lang1(A),F),k1_relset_1(k3_qc_lang1(A),H)) ) => ( r1_valuat_1(A,C,B,D,k1_sublemma(A,C,E,F)) <=> r1_valuat_1(A,C,B,D,k1_sublemma(A,C,E,k14_sublemma(A,C,k14_sublemma(A,C,F,G),H))) ) ) ) ) ) ) => ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),C))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),C))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),C))) ) => ( ( ! [I] : ( m2_subset_1(I,k2_qc_lang1(A),k3_qc_lang1(A)) => ~ ( r2_hidden(I,k1_relset_1(k3_qc_lang1(A),G)) & r2_hidden(I,k24_qc_lang1(A,k6_cqc_lang(A,B))) ) ) & ! [I] : ( m2_subset_1(I,k2_qc_lang1(A),k3_qc_lang1(A)) => ( r2_hidden(I,k1_relset_1(k3_qc_lang1(A),H)) => k1_funct_1(H,I) = k3_funct_2(k3_qc_lang1(A),C,E,I) ) ) & r1_xboole_0(k1_relset_1(k3_qc_lang1(A),F),k1_relset_1(k3_qc_lang1(A),H)) ) => ( r1_valuat_1(A,C,k6_cqc_lang(A,B),D,k1_sublemma(A,C,E,F)) <=> r1_valuat_1(A,C,k6_cqc_lang(A,B),D,k1_sublemma(A,C,E,k14_sublemma(A,C,k14_sublemma(A,C,F,G),H))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t76_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => r1_tarski(C,k2_pre_topc(A,k5_setfam_1(u1_struct_0(A),B))) ) ) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v5_tops_1(C,A) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(D,B) => r1_tarski(D,C) ) ) ) => r1_tarski(k2_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)),C) ) ) ) ) ) )).
fof(t76_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_borsuk_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( m1_subset_1(C,u1_struct_0(B)) => m1_pre_topc(k5_tex_4(A,C),B) ) ) ) ) )).
fof(t76_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ! [H] : ( m1_subset_1(H,u1_struct_0(D)) => ( ( r1_tarski(F,u1_struct_0(D)) & m1_connsp_2(F,C,G) & G = H ) => ( r1_tmap_1(C,B,E,G) <=> r1_tmap_1(D,B,k3_tmap_1(A,B,C,D,E),H) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t76_topgen_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topgen_5))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_xreal_0(C) & v2_xxreal_0(C) ) => ~ ( A = k4_subset_1(u1_struct_0(k15_euclid(2)),k1_topreal9(2,k19_euclid(B,C),C),k6_domain_1(u1_struct_0(k15_euclid(2)),k19_euclid(B,k5_numbers))) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr)) & v5_pre_topc(D,k3_topgen_5,k5_topmetr) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k3_topgen_5),u1_struct_0(k5_topmetr)))) ) => ~ ( k1_funct_1(D,k19_euclid(B,k5_numbers)) = k5_numbers & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( ( r2_hidden(k19_euclid(E,F),k3_subset_1(u1_struct_0(k3_topgen_5),A)) => k1_funct_1(D,k19_euclid(E,F)) = 1 ) & ( r2_hidden(k19_euclid(E,F),k7_subset_1(u1_struct_0(k3_topgen_5),A,k6_domain_1(u1_struct_0(k15_euclid(2)),k19_euclid(B,k5_numbers)))) => k1_funct_1(D,k19_euclid(E,F)) = k7_xcmplx_0(k1_square_1(k12_euclid(k5_algstr_0(k15_euclid(2),k19_euclid(B,k5_numbers),k19_euclid(E,F)))),k3_xcmplx_0(k3_xcmplx_0(2,C),F)) ) ) ) ) ) ) ) ) ) ) )).
fof(t76_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v9_rltopsp1(A,k15_euclid(2)) => k5_measure6(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,k2_pre_topc(k15_euclid(2),A)) ) ) )).
fof(t76_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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_pre_topc(C,A) ) => v3_pre_topc(D,B) ) ) ) ) ) )).
fof(t76_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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) => ( ( r2_funct_2(u1_struct_0(A),u1_struct_0(A),B,k6_partfun1(u1_struct_0(A))) | ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) != C ) ) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_analoaf(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)) ) ) ) ) ) ) )).
fof(t76_trees_3,axiom,( k13_trees_3(k2_trees_1(k5_numbers),k2_trees_1(k5_numbers)) = k2_trees_1(2) )).
fof(t76_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( r3_tsep_1(A,B,C) <=> ? [D] : ( ~ v2_struct_0(D) & v1_tsep_1(D,A) & m1_pre_topc(D,A) & ? [E] : ( ~ v2_struct_0(E) & v1_tsep_1(E,A) & m1_pre_topc(E,A) & m1_pre_topc(B,D) & m1_pre_topc(C,E) & r1_tsep_1(D,C) & r1_tsep_1(E,B) ) ) ) ) ) ) )).
fof(t76_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( v1_valued_2(C) => ! [D] : ( v1_valued_2(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,D))) ) => k16_valued_2(k3_xboole_0(A,B),k2_valued_2(k3_xboole_0(k1_valued_2(C),k1_valued_2(D))),k73_valued_2(A,B,C,D,E,F)) = k73_valued_2(A,B,k2_valued_2(k1_valued_2(C)),k2_valued_2(k1_valued_2(D)),k16_valued_2(A,C,E),k16_valued_2(B,D,F)) ) ) ) ) )).
fof(t76_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m2_vectsp_4(D,A,B,C) => ( r2_hidden(k4_struct_0(B),D) <=> D = u1_struct_0(C) ) ) ) ) ) )).
fof(t76_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ( v25_waybel_0(A) <=> ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => r2_yellow_0(A,B) ) ) ) )).
fof(t76_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v9_waybel_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_orders_2(A,C,D) => r1_orders_2(A,k6_waybel_1(A,B,C),k6_waybel_1(A,B,D)) ) ) ) ) ) ) )).
fof(t76_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_xboole_0(B,C) => r1_xboole_0(k3_xboole_0(A,B),k3_xboole_0(A,C)) ) )).
fof(t76_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k4_xboolean(A,k10_xboolean(A,B)) = k4_xboolean(A,k3_xboolean(B)) ) ) )).
fof(t76_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t76_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(C,B)) ) ) ) ) )).
fof(t76_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(D,C) & k3_xxreal_1(C,D) = k1_xxreal_1(A,B) ) ) ) ) ) )).
fof(t76_xxreal_2,axiom,( ! [A] : ( ( v2_membered(A) & ~ v1_xxreal_2(A) & v2_xxreal_2(A) & v6_xxreal_2(A) ) => A = k3_xxreal_1(k2_xxreal_2(A),k1_xxreal_2(A)) ) )).
fof(t76_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => k6_xxreal_3(A,k1_xxreal_0) = k5_numbers ) )).
fof(t76_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ( r2_zf_lang(C,k4_zf_lang(A,B)) <=> C = k4_zf_lang(A,B) ) ) ) ) )).
fof(t76_zf_lang1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( k2_zf_lang(A) = k2_zf_lang(B) => A = B ) ) ) )).
fof(t76_zfmisc_1,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_tarski(k3_tarski(A),k3_tarski(B)) ) )).
fof(t76_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_zmodul01(D,A) => ~ ( k5_zmodul01(A,C,D) = k5_zmodul01(A,B,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r1_struct_0(D,E) & k5_algstr_0(A,C,E) = B ) ) ) ) ) ) ) )).
fof(t76_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( m1_zmodul01(D,A) => ( ( m1_zmodul01(B,D) & m1_zmodul01(C,D) ) => m1_zmodul01(k6_zmodul01(A,B,C),D) ) ) ) ) ) )).
fof(t77_abcmiz_0,axiom,( ! [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) ) => ( v8_rewrite1(k11_abcmiz_0(A)) & v4_rewrite1(k11_abcmiz_0(A)) ) ) )).
fof(t77_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ~ ( m1_abcmiz_1(B,A,k14_abcmiz_1(A)) & v8_abcmiz_1(B,A) & m1_abcmiz_1(B,A,k13_abcmiz_1(A)) ) & ~ ( m1_abcmiz_1(B,A,k14_abcmiz_1(A)) & m3_abcmiz_1(B,A) ) & ~ ( m3_abcmiz_1(B,A) & v8_abcmiz_1(B,A) & m1_abcmiz_1(B,A,k13_abcmiz_1(A)) ) ) ) )).
fof(t77_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ( k1_funct_4(A,k1_ordinal4(A,B)) = k1_ordinal4(A,B) & k1_funct_4(k1_ordinal4(A,B),A) = k1_ordinal4(A,B) ) ) ) )).
fof(t77_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ( r1_tarski(A,B) => k1_ordinal4(A,k2_afinsq_2(B,k1_afinsq_1(A))) = B ) ) ) )).
fof(t77_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v19_aofa_a00(B,A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( C = k10_subset_1(k1_funct_1(u7_aofa_a00(A),13),u4_struct_0(A)) => ( k1_msualg_1(A,C) = k12_finseq_1(u1_struct_0(A),k37_aofa_a00(A)) & k2_msualg_1(A,C) = B ) ) ) ) ) )).
fof(t77_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => r3_arytm_3(A,k9_arytm_3(A,B)) ) ) )).
fof(t77_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( v1_xreal_0(D) => ( ( v2_comseq_2(A) & k1_seq_2(A) = D & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r1_xxreal_0(C,E) => k9_nat_1(k1_numbers,A,E) = k9_nat_1(k1_numbers,B,E) ) ) ) => ( v2_comseq_2(B) & k1_seq_2(B) = D ) ) ) ) ) ) )).
fof(t77_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( v20_bcialg_1(A) & k1_bcialg_1(A,B,C) = k1_bcialg_1(A,B,D) ) => C = D ) ) ) ) ) )).
fof(t77_borsuk_5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_connsp_1(A,k3_topmetr) & v2_compts_1(A,k3_topmetr) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) ) => ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) ) )).
fof(t77_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ( ( r1_borsuk_6(A,B,C) & r3_borsuk_2(A,B,C,D,E) ) => r3_borsuk_2(A,C,B,k2_borsuk_2(A,B,C,D),k2_borsuk_2(A,B,C,E)) ) ) ) ) ) ) )).
fof(t77_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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),k6_bvfunc_2(A,k1_bvfunc_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) )).
fof(t77_bvfunc14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ( ( v1_relat_1(J) & v1_funct_1(J) ) => ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ! [Q] : ! [R] : ! [S] : ( J = k1_funct_4(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,L),k16_funcop_1(C,M)),k16_funcop_1(D,N)),k16_funcop_1(E,O)),k16_funcop_1(F,P)),k16_funcop_1(G,Q)),k16_funcop_1(H,R)),k16_funcop_1(I,S)),k16_funcop_1(A,K)) => k9_xtuple_0(J) = k7_enumset1(A,B,C,D,E,F,G,H,I) ) ) )).
fof(t77_card_2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ( v1_finset_1(A) | ( r2_wellord2(k2_xboole_0(A,B),A) & k1_card_1(k2_xboole_0(A,B)) = k1_card_1(A) ) ) ) )).
fof(t77_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( m1_subset_1(B,k8_card_3(A)) => ? [C] : ( m1_subset_1(C,k4_card_3(A)) & r1_tarski(B,C) ) ) ) )).
fof(t77_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k2_cat_1(A,D,E) != k1_xboole_0 => ! [F] : ( m1_cat_1(F,A,D,E) => r2_hidden(k3_funct_2(u4_struct_0(A),u4_struct_0(B),C,F),k2_cat_1(B,k8_cat_1(A,B,C,D),k8_cat_1(A,B,C,E))) ) ) ) ) ) ) ) )).
fof(t77_cat_4,axiom,( ! [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) & v6_cat_4(A) & l2_cat_4(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_cat_1(H,A,B,D) => ! [I] : ( m1_cat_1(I,A,C,E) => ! [J] : ( m1_cat_1(J,A,D,F) => ! [K] : ( m1_cat_1(K,A,E,G) => ~ ( k2_cat_1(A,B,D) != k1_xboole_0 & k2_cat_1(A,C,E) != k1_xboole_0 & k2_cat_1(A,D,F) != k1_xboole_0 & k2_cat_1(A,E,G) != k1_xboole_0 & k5_cat_1(A,k20_cat_4(A,B,C),k20_cat_4(A,D,E),k20_cat_4(A,F,G),k31_cat_4(A,B,C,D,E,H,I),k31_cat_4(A,D,E,F,G,J,K)) != k31_cat_4(A,B,C,F,G,k5_cat_1(A,B,D,F,H,J),k5_cat_1(A,C,E,G,I,K)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t77_cfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,k2_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,k2_numbers))) ) => ( ( v3_funct_1(k2_partfun1(C,k2_numbers,D,A)) & v3_funct_1(k2_partfun1(C,k2_numbers,E,B)) ) => ( v3_funct_1(k2_partfun1(C,k2_numbers,k2_valued_1(C,k2_numbers,k2_numbers,D,E),k3_xboole_0(A,B))) & v3_funct_1(k2_partfun1(C,k2_numbers,k46_valued_1(C,k2_numbers,k2_numbers,D,E),k3_xboole_0(A,B))) & v3_funct_1(k2_partfun1(C,k2_numbers,k19_valued_1(C,k2_numbers,k2_numbers,D,E),k3_xboole_0(A,B))) ) ) ) ) ) )).
fof(t77_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m2_chord(D,A,B,C) => ( D = k1_xboole_0 => v4_chord(D,A,B,C) ) ) ) ) ) )).
fof(t77_classes1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_classes1(A,B) <=> ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & k9_xtuple_0(C) = k9_xtuple_0(A) & k10_xtuple_0(C) = k9_xtuple_0(B) & v2_funct_1(C) & A = k3_relat_1(C,B) ) ) ) ) )).
fof(t77_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( m1_clvect_1(D,A) => ( r2_hidden(k1_clvect_1(A,B,C),k5_clvect_1(A,B,D)) => ( C = k6_complex1 | r1_struct_0(D,B) ) ) ) ) ) ) )).
fof(t77_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_clvect_2(C,A) => v3_clvect_2(k6_clvect_1(A,C,B),A) ) ) ) ) )).
fof(t77_cohsp_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(k4_tarski(C,2),k14_cohsp_1(A,B)) <=> r2_hidden(C,B) ) )).
fof(t77_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( k2_xcmplx_0(A,k3_xcmplx_0(B,k7_complex1)) = k2_xcmplx_0(C,k3_xcmplx_0(D,k7_complex1)) => ( A = C & B = D ) ) ) ) ) ) )).
fof(t77_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k4_complex2(A,B,A) = k5_numbers ) ) )).
fof(t77_convex4,axiom,( ! [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) ) => ! [B] : ( m1_convex4(B,A) => ~ ( v3_convex4(B,A) & k1_convex4(A,B) = k1_xboole_0 ) ) ) )).
fof(t77_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ( ~ r2_hidden(D,k24_qc_lang1(A,C)) => 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),C)),A) ) ) ) ) ) )).
fof(t77_csspace,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_normsp_1(A,B,k3_normsp_1(A,C,D)),k16_csspace(A,k3_normsp_1(A,B,C),D)) ) ) ) ) )).
fof(t77_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(A,k1_relset_1(k1_numbers,k26_sin_cos)) & r2_hidden(B,k1_relset_1(k1_numbers,k26_sin_cos)) ) => k9_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k16_sin_cos),A,B) = k7_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(1,k19_sin_cos(A)),k19_sin_cos(A)),k7_xcmplx_0(1,k19_sin_cos(B))),k19_sin_cos(B)),k6_xcmplx_0(A,B)) ) ) ) )).
fof(t77_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : k7_enumset1(A,B,C,D,E,F,G,H,I) = k2_xboole_0(k1_tarski(A),k6_enumset1(B,C,D,E,F,G,H,I)) )).
fof(t77_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => k5_euclid_8(A,k7_euclid(3,B,C)) = k7_euclid(3,k5_euclid_8(A,B),k5_euclid_8(A,C)) ) ) ) )).
fof(t77_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [G] : ( m2_subset_1(G,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ( ( r2_hidden(B,F) & r2_hidden(C,F) & r2_hidden(D,G) & r2_hidden(E,G) & r5_euclidlp(A,F,G) ) => ( B = C | D = E | r2_euclidlp(A,k8_euclid(A,C,B),k8_euclid(A,E,D)) ) ) ) ) ) ) ) ) ) )).
fof(t77_exchsort,axiom,( ! [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) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_exchsort(B) ) => ! [C] : ( ( v2_exchsort(C,k5_numbers) & m2_exchsort(C,A,B) ) => ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_finset_1(B) & v1_exchsort(B) & ! [D] : ( v3_ordinal1(D) => ( k6_exchsort(A,k1_funct_1(C,D)) != k1_xboole_0 => r2_hidden(k1_ordinal1(D),k9_xtuple_0(C)) ) ) ) => v6_exchsort(C,A,B) ) ) ) ) )).
fof(t77_facirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k15_facirc_1(A,B,C),k18_facirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ( ( E = k1_funct_1(D,B) & F = 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(B,C),k3_facirc_1)) = k10_margrel1(E,F) ) ) ) ) ) ) ) )).
fof(t77_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v20_lattices(B,A) & v21_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v11_lattices(A) => v11_lattices(k10_filter_2(A,B)) ) ) ) )).
fof(t77_finseq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( k10_finseq_1(A,B) = k10_finseq_1(C,D) => ( A = C & B = D ) ) )).
fof(t77_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( ( 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))) ) => k5_funcop_1(E,D,k6_finseq_1(B)) = k6_finseq_1(C) ) ) ) ) ) )).
fof(t77_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : ( k1_finseq_3(k10_finseq_1(A,B),C) = k9_finseq_1(B) => ( A = B | ( r2_hidden(A,C) & ~ r2_hidden(B,C) ) ) ) )).
fof(t77_finseq_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) ) => ( F = k8_finseq_4(A,B,C,D,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 ) ) ) )).
fof(t77_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => ( k17_finseq_1(A,D,k17_finseq_1(A,C,B)) = k17_finseq_1(A,C,B) & k17_finseq_1(A,C,k17_finseq_1(A,D,B)) = k17_finseq_1(A,C,B) ) ) ) ) ) ) )).
fof(t77_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( B != k1_xboole_0 => k2_rfinseq(A,1,k8_finseq_1(A,B,C)) = k8_finseq_1(A,k2_rfinseq(A,1,B),C) ) ) ) ) )).
fof(t77_finseqop,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( r2_hidden(k4_tarski(A,B),k9_xtuple_0(k6_finseqop(C,D,E))) => k1_binop_1(k6_finseqop(C,D,E),A,B) = k1_binop_1(C,k1_funct_1(D,A),k1_funct_1(E,B)) ) ) ) ) )).
fof(t77_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => r1_tarski(B,k2_flang_2(A,B)) ) )).
fof(t77_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => k6_flang_1(A,k2_flang_3(A,B),k1_flang_2(A,B,C,D)) = k1_flang_3(A,B,k2_xcmplx_0(C,1)) ) ) ) ) )).
fof(t77_fomodel0,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( ( k3_xboole_0(k10_xtuple_0(C),k10_xtuple_0(D)) = k1_xboole_0 & r1_tarski(k10_xtuple_0(C),k9_xtuple_0(D)) & r1_tarski(k10_xtuple_0(D),k9_xtuple_0(C)) ) => ( A = B | r1_tarski(k2_xboole_0(k2_zfmisc_1(k10_xtuple_0(C),k1_tarski(B)),k2_zfmisc_1(k10_xtuple_0(D),k1_tarski(A))),k3_relat_1(k3_relat_1(k2_xboole_0(C,D),k2_xboole_0(k2_zfmisc_1(k10_xtuple_0(C),k1_tarski(B)),k2_zfmisc_1(k10_xtuple_0(D),k1_tarski(A)))),k4_funct_4(A,B,B,A))) ) ) ) ) )).
fof(t77_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k1_tarski(A)) => ! [E] : ( m1_subset_1(E,k1_tarski(B)) => k2_binop_1(k1_tarski(A),k1_tarski(B),k1_tarski(C),k17_funcop_1(A,B,C),D,E) = C ) ) )).
fof(t77_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => k7_relat_1(B,k8_relat_1(B,A)) = k3_xboole_0(A,k7_relat_1(B,k9_xtuple_0(B))) ) )).
fof(t77_funct_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( ( r1_partfun1(B,D) & r1_partfun1(C,D) ) => r1_partfun1(B,C) ) ) ) ) )).
fof(t77_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [F] : ( ( 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) = k13_funct_3(k3_relat_1(k9_funct_3(A,B),E),k3_relat_1(k10_funct_3(A,B),F)) ) ) ) ) )).
fof(t77_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( r1_tarski(k9_xtuple_0(A),C) & r1_xboole_0(k9_xtuple_0(B),C) ) => k5_relat_1(k1_funct_4(A,B),C) = A ) ) ) )).
fof(t77_funct_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_relat_1(C) => ( B != k5_numbers => k8_funct_7(k8_funct_7(C,A),B) = k8_funct_7(C,k3_xcmplx_0(A,B)) ) ) ) ) )).
fof(t77_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => r2_funct_8(A,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k16_sin_cos)) ) )).
fof(t77_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => ! [C] : ( m1_subset_1(C,u1_struct_0(k7_fvaluat1(A,B))) => ( ~ r2_hidden(C,k8_fvaluat1(A,B)) => k1_funct_1(B,C) = k5_numbers ) ) ) ) ) )).
fof(t77_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [D] : ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => k4_rlvect_1(B,k8_fvsum_1(A,B,C,D)) = k5_algstr_0(B,k4_rlvect_1(B,C),k4_rlvect_1(B,D)) ) ) ) ) )).
fof(t77_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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) & k2_msafree2(k31_gfacirc1(A,B,C)) != k1_enumset1(A,B,C) ) )).
fof(t77_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ! [D] : ( r1_tarski(k22_glib_000(B,C,D),k22_glib_000(A,C,D)) & r1_tarski(k23_glib_000(B,C,D),k23_glib_000(A,C,D)) ) ) ) )).
fof(t77_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k1_relset_1(k4_ordinal1,k12_glib_001(A,B))) => r2_hidden(k1_funct_1(k12_glib_001(A,B),C),k7_glib_000(A)) ) ) ) ) )).
fof(t77_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( v1_group_3(C,A) & m1_group_2(C,A) ) => ~ ( m1_group_2(C,B) & ! [D] : ( ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) ) => ! [E] : ( ( v15_algstr_0(E) & v1_group_3(E,A) & m1_group_2(E,A) ) => ~ ( u1_struct_0(D) = k4_group_11(A,B,C) & u1_struct_0(E) = k3_group_11(A,B,C) & r1_tarski(k3_group_11(A,B,D),k4_group_11(A,B,E)) ) ) ) ) ) ) ) )).
fof(t77_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => k1_group_2(A,k8_group_2(A,B)) = k8_group_2(A,B) ) ) )).
fof(t77_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_group_3(A,B,C) & r2_group_3(A,C,D) ) => r2_group_3(A,B,D) ) ) ) ) ) )).
fof(t77_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r1_struct_0(k10_group_5(A),B) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_algstr_0(A,B,C) = k6_algstr_0(A,C,B) ) ) ) ) )).
fof(t77_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ 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) & v5_group_1(A) ) => v5_group_1(B) ) ) ) )).
fof(t77_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( ( v4_group_9(D,A,C) & m1_group_9(D,A,C) ) => ( u1_struct_0(C) = u1_struct_0(D) => v7_struct_0(k10_group_9(A,C,D)) ) ) ) ) )).
fof(t77_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v2_vectsp_1(A) & v6_vectsp_1(A) & v1_algstr_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ( r1_tarski(C,B) => k13_ideal_1(A,B,k12_ideal_1(A,C,D)) = k12_ideal_1(A,C,k13_ideal_1(A,B,D)) ) ) ) ) ) )).
fof(t77_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,1) => k2_integra5(A,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_sin_cos2,k3_sin_cos2)) = k6_xcmplx_0(k4_power,1) ) ) )).
fof(t77_intpro_1,axiom,( r1_tarski(k8_intpro_1,k12_intpro_1) )).
fof(t77_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r1_xxreal_0(A,k7_xcmplx_0(k17_euclid(B),k12_euclid(B))) & r1_xxreal_0(A,k7_xcmplx_0(k17_euclid(C),k12_euclid(C))) ) => ( r1_xxreal_0(1,A) | r1_xxreal_0(k18_euclid(B),k5_numbers) | r1_xxreal_0(k18_euclid(C),k5_numbers) | r1_xxreal_0(k7_xcmplx_0(k17_euclid(C),k12_euclid(C)),k7_xcmplx_0(k17_euclid(B),k12_euclid(B))) | ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( 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(k7_xcmplx_0(k17_euclid(E),k12_euclid(E)),k7_xcmplx_0(k17_euclid(D),k12_euclid(D))) ) ) ) ) ) ) ) ) )).
fof(t77_jgraph_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ 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] : ( ( 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))))) ) => ( ( E = k5_jgraph_6(k5_numbers,k5_numbers,1) & r2_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,k1_jgraph_3) & r1_jordan6(E,k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,A),k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,B)) & r1_jordan6(E,k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,B),k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,C)) & r1_jordan6(E,k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,C),k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,D)) ) => r1_jordan17(k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(1),1),A,B,C,D) ) ) ) ) ) ) ) )).
fof(t77_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) = E & k18_euclid(C) = H & k18_euclid(D) = H & r1_xxreal_0(G,k18_euclid(A)) & ~ r1_xxreal_0(k18_euclid(B),k18_euclid(A)) & r1_xxreal_0(k18_euclid(B),H) & r1_xxreal_0(E,k17_euclid(C)) & ~ 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t77_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(D,B) & r2_hidden(C,k9_subset_1(u1_struct_0(k15_euclid(2)),k7_topreal1(D),k3_topreal1(2,k2_jordan9(B,A)))) & r1_xxreal_0(k17_euclid(D),k17_euclid(C)) ) ) ) ) ) )).
fof(t77_jordan2c,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,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,k1_sprect_1(A))),B) => ( v9_rltopsp1(B,k15_euclid(2)) | B = k2_goboard9(k1_sprect_1(A)) ) ) ) ) )).
fof(t77_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( v7_ordinal1(B) => v6_lexbfs(k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k4_ordinal1),k23_lexbfs(A,k26_lexbfs(A),B)),A) ) ) )).
fof(t77_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v8_limfunc1(B) => ( ! [C] : ( v1_xreal_0(C) => ~ ( r1_tarski(k10_prob_1(C),k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,A),k1_relset_1(k1_numbers,B))) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,k10_prob_1(C)) => r1_xxreal_0(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) | v8_limfunc1(A) ) ) ) ) )).
fof(t77_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r4_limfunc2(B,A) & k2_limfunc2(B,A) = k5_numbers & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,A) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(C,D) & ~ r1_xxreal_0(D,A) & r2_hidden(D,k1_relset_1(k1_numbers,B)) & k1_funct_1(B,D) != k5_numbers ) ) ) ) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(A,k2_xcmplx_0(A,C)))) => r1_xxreal_0(k5_numbers,k1_funct_1(B,D)) ) ) ) ) | r5_limfunc2(k6_rfunct_1(k1_numbers,k1_numbers,B),A) ) ) ) ) )).
fof(t77_limfunc4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k1_limfunc3(B,A)) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(A,D) & ~ r1_xxreal_0(E,A) & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( ~ 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] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k4_subset_1(k1_numbers,k2_rcomp_1(k6_xcmplx_0(A,D),A),k2_rcomp_1(A,k2_xcmplx_0(A,D))))) & k1_funct_1(B,E) = k1_limfunc3(B,A) ) ) ) ) | ( r1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) & k1_limfunc3(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C),A) = k1_limfunc3(C,k1_limfunc3(B,A)) ) ) ) ) ) ) )).
fof(t77_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => k20_lpspace1(A,B,C) = k12_lpspace2(A,B,C,1) ) ) ) )).
fof(t77_mathmorp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( ( v1_convex1(B,k15_euclid(A)) & v1_convex1(C,k15_euclid(A)) ) => ( v1_convex1(k4_mathmorp(k15_euclid(A),B,C),k15_euclid(A)) & v1_convex1(k5_mathmorp(k15_euclid(A),B,C),k15_euclid(A)) ) ) ) ) ) )).
fof(t77_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( v1_matrix10(B) => r1_matrix10(k5_matrix10(A,C,B),C) ) ) ) ) )).
fof(t77_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( m2_finseq_2(D,k4_ordinal1,k4_finseq_2(B,k4_ordinal1)) => ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [F] : ( ( v1_matrix_0(F) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(C))) ) => ( ( B = k5_numbers | A = k5_numbers ) => k8_matrix13(C,k1_matrix13(u1_struct_0(C),F,B,A,D,E)) = k5_numbers ) ) ) ) ) ) ) )).
fof(t77_matrixj1,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ! [E] : ( ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(A))) ) => k26_matrixj1(A,k5_matrixj1(u1_struct_0(A),B,D),k5_matrixj1(u1_struct_0(A),C,E)) = k5_matrixj1(u1_struct_0(A),k4_matrix_3(A,B,C),k4_matrix_3(A,D,E)) ) ) ) ) ) )).
fof(t77_matrixr2,axiom,( k6_matrixr2(1,1) = k13_matrix_0(k4_ordinal1,1) & k6_matrixr2(2,1) = k2_finseq_4(k4_ordinal1,1,k5_numbers) & k6_matrixr2(2,2) = k2_finseq_4(k4_ordinal1,k5_numbers,1) & k6_matrixr2(3,1) = k3_finseq_4(k4_ordinal1,1,k5_numbers,k5_numbers) & k6_matrixr2(3,2) = k3_finseq_4(k4_ordinal1,k5_numbers,1,k5_numbers) & k6_matrixr2(3,3) = k3_finseq_4(k4_ordinal1,k5_numbers,k5_numbers,1) )).
fof(t77_member_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k11_member_1(k2_tarski(A,B),k1_tarski(C)) = k2_tarski(k6_xcmplx_0(A,C),k6_xcmplx_0(B,C)) ) ) ) )).
fof(t77_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_partfun1(C,u1_struct_0(B)) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => r2_hidden(k1_funct_1(C,D),k4_memstr_0(A,B,D)) ) ) ) ) )).
fof(t77_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( r1_mesfunc2(A,B,D) & v6_supinf_2(D) ) => k6_mesfunc5(A,B,C,D) = k5_mesfunc5(A,B,C,D) ) ) ) ) ) )).
fof(t77_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( ( r1_tarski(E,k1_relset_1(A,C)) & r1_mesfunc6(A,B,C,E) & r1_mesfunc6(A,B,D,E) ) => r1_mesfunc6(A,B,k3_valued_1(A,k1_numbers,k1_numbers,k18_rfunct_3(A,k3_valued_1(A,k1_numbers,k1_numbers,C,D)),k19_rfunct_3(A,C)),E) ) ) ) ) ) ) )).
fof(t77_mmlquery,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_mmlquery(C) & l1_mmlquery(C) ) => ! [D] : ( m2_finseq_1(D,u1_mmlquery(C)) => k37_mmlquery(C,D,A,B) = k15_mmlquery(u1_struct_0(C),k35_mmlquery(C,D,B),k36_mmlquery(C,D,A)) ) ) ) ) )).
fof(t77_modelc_2,axiom,( ! [A] : ( m1_subset_1(A,k25_modelc_2(k43_modelc_2)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k9_modelc_2)) => ( r8_modelc_2(A,k48_modelc_2(B)) <=> r8_modelc_2(k29_modelc_2(k43_modelc_2,A,1),B) ) ) ) )).
fof(t77_monoid_0,axiom,( ! [A] : ! [B] : ( m1_subset_1(A,u1_struct_0(k17_monoid_0(B))) <=> ( v1_funct_1(A) & v1_funct_2(A,B,B) & v3_funct_2(A,B,B) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) ) )).
fof(t77_msafree4,axiom,( ! [A] : r3_rewrite1(k1_xboole_0,A) )).
fof(t77_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ( ( v1_ncfcont1(k1_relset_1(u1_struct_0(A),C),A) & r7_ncfcont1(A,B,C,k1_relset_1(u1_struct_0(A),C)) ) => v1_ncfcont1(k2_relset_1(u1_struct_0(B),C),B) ) ) ) ) )).
fof(t77_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(B,A) & r2_hidden(A,k9_newton(B)) ) ) ) )).
fof(t77_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v11_o_ring_1(B,A) & v7_o_ring_1(C,A) ) => v13_o_ring_1(k6_algstr_0(A,B,C),A) ) ) ) ) )).
fof(t77_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( ( r2_wellord1(A,B) & r1_tarski(C,B) ) => r2_wellord1(A,C) ) ) )).
fof(t77_partfun1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ! [E] : ( ( r1_partfun1(A,B) & r2_hidden(k4_tarski(C,D),A) & r2_hidden(k4_tarski(C,E),B) ) => D = E ) ) ) )).
fof(t77_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => r6_pboole(A,k4_pboole(A,k2_pboole(A,B,C),k3_pboole(A,B,C)),k2_pboole(A,k4_pboole(A,B,C),k4_pboole(A,C,B))) ) ) )).
fof(t77_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r2_pdiff_5(A,B) => r1_fcont_1(k1_pdiff_2(3,2,k1_pdiff_3(1,3,A),B),k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(2,3),B)) ) ) ) )).
fof(t77_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => r2_relset_1(k1_euclid(A),k1_numbers,k5_pdiff_9(A,C,k12_finseq_1(k4_ordinal1,B),D),k3_pdiff_9(A,C,B,D)) ) ) ) )).
fof(t77_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => k1_vectsp_9(k2_bspace,k24_polyform(A,k6_xcmplx_0(k7_polyform(A),1))) = 1 ) )).
fof(t77_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_subset_1(C,A) => ( ~ r2_hidden(C,B) => ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ( D = k2_xboole_0(k1_tarski(C),B) => ! [E] : ( ( 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] : ( m1_subset_1(F,k4_ordinal1) => ( ( r2_hidden(F,k4_finseq_1(k7_pre_poly(A,D,E))) & k7_partfun1(A,k7_pre_poly(A,D,E),F) = C ) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( ( 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),k1_nat_1(G,1)) = k7_partfun1(A,k7_pre_poly(A,B,E),G) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t77_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(A,k5_numbers) => k6_prepower(A,k6_xcmplx_0(B,C)) = k7_xcmplx_0(k6_prepower(A,B),k6_prepower(A,C)) ) ) ) ) )).
fof(t77_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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,k6_pboole(A,B,B),k6_pboole(A,C,C)) ) ) ) )).
fof(t77_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v4_qc_lang1(B,A) => ( r3_qc_lang2(A,k19_qc_lang1(A,B),B) & r3_qc_lang2(A,k20_qc_lang1(A,B),B) ) ) ) ) )).
fof(t77_quatern3,axiom,( k7_quatern2(k12_quaterni) = k24_quaterni(k12_quaterni) )).
fof(t77_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => r1_xxreal_0(k15_quaterni(A),k28_quaterni(A)) ) )).
fof(t77_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => k5_relat_1(k3_relat_1(B,C),A) = k3_relat_1(k5_relat_1(B,A),C) ) ) )).
fof(t77_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(C))) => ! [G] : ( ( ~ v2_struct_0(G) & l1_rewrite3(G,F) ) => ~ ( ~ r2_hidden(k2_flang_1(C),k10_xtuple_0(k9_xtuple_0(u1_rewrite3(F,G)))) & r1_rewrite1(k1_rewrite3(C,F,G),k4_tarski(A,D),k4_tarski(B,E)) & r1_xxreal_0(k1_afinsq_1(D),k1_afinsq_1(E)) & ~ ( A = B & D = E ) ) ) ) ) ) ) )).
fof(t77_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ! [D] : ( v1_xreal_0(D) => ( v1_finset_1(k1_relset_1(A,k2_partfun1(A,k1_numbers,B,C))) => k21_rfunct_3(A,k26_valued_1(A,k1_numbers,B,D),C) = k3_xcmplx_0(D,k21_rfunct_3(A,B,C)) ) ) ) ) )).
fof(t77_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_seq_2(B) & v1_seq_2(C) ) => r1_xxreal_0(k1_funct_1(k4_rinfsup1(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C)),A),k2_xcmplx_0(k1_funct_1(k4_rinfsup1(B),A),k1_funct_1(k4_rinfsup1(C),A))) ) ) ) ) )).
fof(t77_rlaffin1,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( ( v1_rlaffin1(D,B) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( ( r1_tarski(C,D) & r2_hidden(A,k4_rlaffin1(B,C)) ) => r1_rlvect_2(B,k5_rlaffin1(B,C,A),k5_rlaffin1(B,D,A)) ) ) ) ) )).
fof(t77_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m2_rlsub_1(C,A,B) => ( r2_hidden(k4_struct_0(A),C) <=> C = u1_struct_0(B) ) ) ) ) )).
fof(t77_rlvect_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => k1_rlvect_1(B,C,k4_xcmplx_0(A)) = k4_algstr_0(B,k1_rlvect_1(B,C,A)) ) ) ) )).
fof(t77_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_rmod_2(E,A,B) => ( ? [F] : ( m2_rmod_2(F,A,B,E) & r2_hidden(C,F) & r2_hidden(D,F) ) <=> r1_struct_0(E,k5_algstr_0(B,C,D)) ) ) ) ) ) ) )).
fof(t77_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k16_rvsum_1(k10_finseq_1(A,B)) = k2_xcmplx_0(A,B) ) ) )).
fof(t77_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [D] : ( ( 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(k5_numbers)) = 1 => ( r4_scmfsa7b(C,D) | r1_xxreal_0(k1_funct_1(B,D),k5_numbers) | r1_scmfsa8a(B,A,k1_scmfsa8c(k1_scmfsa8b(D,k1_scmfsa8a(2),k5_scmfsa6a(C,k8_scmfsa_2(D,k4_scmfsa_2(k5_numbers)))))) ) ) ) ) ) ) )).
fof(t77_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => ~ v2_extpro_1(k11_scmfsa_2(A),k7_card_1(3),k1_scmfsa_2) ) )).
fof(t77_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ( r2_hidden(k5_numbers,k9_xtuple_0(k8_scmpds_6(A,B,C))) & r2_hidden(1,k9_xtuple_0(k8_scmpds_6(A,B,C))) ) ) ) ) )).
fof(t77_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v12_scmyciel(A) ) => k11_scmyciel(A) = k8_scmyciel(k6_scmyciel(A)) ) )).
fof(t77_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k1_semi_af1(A,k1_semi_af1(A,B,C,E),D,E) = k1_semi_af1(A,B,k1_semi_af1(A,C,D,E),E) ) ) ) ) ) )).
fof(t77_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => ! [D] : ( m2_finseq_2(D,k2_numbers,k12_seq_4(A)) => k13_seq_4(A,k17_seq_4(A,B,C),D) = k17_seq_4(A,k13_seq_4(A,B,D),C) ) ) ) ) )).
fof(t77_setlim_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( ~ 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] : ( ( v5_relat_1(D,C) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ( v3_funct_1(D) & k3_funct_1(D) = B ) => ( v3_kurato_0(D,A) & k4_kurato_0(A,D) = B & k3_kurato_0(A,D) = B & k4_kurato_0(A,D) = B ) ) ) ) ) )).
fof(t77_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k3_kurato_0(A,k8_setlim_2(A,C,B)) = k7_subset_1(A,k3_kurato_0(A,C),B) ) ) )).
fof(t77_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,B,B),B))) = C ) ) ) )).
fof(t77_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( k1_funct_1(k16_sin_cos,k2_xcmplx_0(A,k3_xcmplx_0(2,k28_sin_cos))) = k1_funct_1(k16_sin_cos,A) & k1_funct_1(k18_sin_cos,k2_xcmplx_0(A,k3_xcmplx_0(2,k28_sin_cos))) = k1_funct_1(k18_sin_cos,A) & k1_funct_1(k16_sin_cos,k6_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),A)) = k1_funct_1(k18_sin_cos,A) & k1_funct_1(k18_sin_cos,k6_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),A)) = k1_funct_1(k16_sin_cos,A) & k1_funct_1(k16_sin_cos,k2_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),A)) = k1_funct_1(k18_sin_cos,A) & k1_funct_1(k18_sin_cos,k2_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),A)) = k4_xcmplx_0(k1_funct_1(k16_sin_cos,A)) & k1_funct_1(k16_sin_cos,k2_xcmplx_0(k28_sin_cos,A)) = k4_xcmplx_0(k1_funct_1(k16_sin_cos,A)) & k1_funct_1(k18_sin_cos,k2_xcmplx_0(k28_sin_cos,A)) = k4_xcmplx_0(k1_funct_1(k18_sin_cos,A)) ) ) )).
fof(t77_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ~ ( ~ r1_xxreal_0(k2_sin_cos6(A),k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2))) & ~ r1_xxreal_0(k7_xcmplx_0(k28_sin_cos,2),k2_sin_cos6(A)) ) ) ) )).
fof(t77_sin_cos9,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k1_sin_cos9,k7_relset_1(k1_numbers,k1_numbers,k26_sin_cos,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2))))) )).
fof(t77_sincos10,axiom,( v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k7_relset_1(k1_numbers,k1_numbers,k1_fdiff_9,k3_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))))) )).
fof(t77_sprect_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => k21_pscomp_1(k3_topreal1(2,k1_sprect_1(A))) = k12_pscomp_1(A) ) )).
fof(t77_sprect_2,axiom,( ! [A] : ( ( ~ 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(k3_finseq_1(A),k4_finseq_4(A,k19_pscomp_1(k3_topreal1(2,A)))) ) ) )).
fof(t77_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_valuat_1(E,A,D) => ( ( ! [F] : ( m2_funct_2(F,k3_qc_lang1(A),D,k2_valuat_1(A,D)) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),D))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),D))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),D))) ) => ( ( ! [J] : ( m2_subset_1(J,k2_qc_lang1(A),k3_qc_lang1(A)) => ~ ( r2_hidden(J,k1_relset_1(k3_qc_lang1(A),H)) & r2_hidden(J,k24_qc_lang1(A,B)) ) ) & ! [J] : ( m2_subset_1(J,k2_qc_lang1(A),k3_qc_lang1(A)) => ( r2_hidden(J,k1_relset_1(k3_qc_lang1(A),I)) => k1_funct_1(I,J) = k3_funct_2(k3_qc_lang1(A),D,F,J) ) ) & r1_xboole_0(k1_relset_1(k3_qc_lang1(A),G),k1_relset_1(k3_qc_lang1(A),I)) ) => ( r1_valuat_1(A,D,B,E,k1_sublemma(A,D,F,G)) <=> r1_valuat_1(A,D,B,E,k1_sublemma(A,D,F,k14_sublemma(A,D,k14_sublemma(A,D,G,H),I))) ) ) ) ) ) ) & ! [F] : ( m2_funct_2(F,k3_qc_lang1(A),D,k2_valuat_1(A,D)) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),D))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),D))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),D))) ) => ( ( ! [J] : ( m2_subset_1(J,k2_qc_lang1(A),k3_qc_lang1(A)) => ~ ( r2_hidden(J,k1_relset_1(k3_qc_lang1(A),H)) & r2_hidden(J,k24_qc_lang1(A,C)) ) ) & ! [J] : ( m2_subset_1(J,k2_qc_lang1(A),k3_qc_lang1(A)) => ( r2_hidden(J,k1_relset_1(k3_qc_lang1(A),I)) => k1_funct_1(I,J) = k3_funct_2(k3_qc_lang1(A),D,F,J) ) ) & r1_xboole_0(k1_relset_1(k3_qc_lang1(A),G),k1_relset_1(k3_qc_lang1(A),I)) ) => ( r1_valuat_1(A,D,C,E,k1_sublemma(A,D,F,G)) <=> r1_valuat_1(A,D,C,E,k1_sublemma(A,D,F,k14_sublemma(A,D,k14_sublemma(A,D,G,H),I))) ) ) ) ) ) ) ) => ! [F] : ( m2_funct_2(F,k3_qc_lang1(A),D,k2_valuat_1(A,D)) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),D))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),D))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),D))) ) => ( ( ! [J] : ( m2_subset_1(J,k2_qc_lang1(A),k3_qc_lang1(A)) => ~ ( r2_hidden(J,k1_relset_1(k3_qc_lang1(A),H)) & r2_hidden(J,k24_qc_lang1(A,k7_cqc_lang(A,B,C))) ) ) & ! [J] : ( m2_subset_1(J,k2_qc_lang1(A),k3_qc_lang1(A)) => ( r2_hidden(J,k1_relset_1(k3_qc_lang1(A),I)) => k1_funct_1(I,J) = k3_funct_2(k3_qc_lang1(A),D,F,J) ) ) & r1_xboole_0(k1_relset_1(k3_qc_lang1(A),G),k1_relset_1(k3_qc_lang1(A),I)) ) => ( r1_valuat_1(A,D,k7_cqc_lang(A,B,C),E,k1_sublemma(A,D,F,G)) <=> r1_valuat_1(A,D,k7_cqc_lang(A,B,C),E,k1_sublemma(A,D,F,k14_sublemma(A,D,k14_sublemma(A,D,G,H),I))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t77_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ( v2_tops_2(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => r1_tarski(k2_pre_topc(A,k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B))),C) ) ) ) & ( B = k1_xboole_0 | ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v5_tops_1(C,A) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(D,B) => r1_tarski(C,D) ) ) ) => r1_tarski(C,k2_pre_topc(A,k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B)))) ) ) ) ) ) ) )).
fof(t77_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_tsep_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( m1_subset_1(C,u1_struct_0(B)) => m1_pre_topc(k5_tex_4(A,C),B) ) ) ) ) )).
fof(t77_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(C))) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ! [H] : ( m1_subset_1(H,u1_struct_0(D)) => ( ( v3_pre_topc(F,C) & r2_hidden(G,F) & r1_tarski(F,u1_struct_0(D)) & G = H ) => ( r1_tmap_1(C,B,E,G) <=> r1_tmap_1(D,B,k3_tmap_1(A,B,C,D,E),H) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t77_topreal6,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( v9_rltopsp1(A,k15_euclid(2)) => k5_measure6(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,k2_pre_topc(k15_euclid(2),A)) ) ) )).
fof(t77_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) => k1_tops_1(A,C) = k1_tops_1(B,D) ) ) ) ) ) )).
fof(t77_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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) = C ) => ( r1_aff_1(A,B,C,D) | k3_funct_2(u1_struct_0(A),u1_struct_0(A),E,D) = D ) ) ) ) ) ) ) )).
fof(t77_trees_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v5_trees_3(B) ) => ( ! [C] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) & v1_trees_1(C) ) => ( r2_hidden(C,k10_xtuple_0(B)) => r1_xxreal_0(k6_trees_1(C),A) ) ) => r1_xxreal_0(k6_trees_1(k11_trees_3(B)),k1_nat_1(A,1)) ) ) ) )).
fof(t77_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( r3_tsep_1(A,B,C) <=> ? [D] : ( ~ v2_struct_0(D) & v1_tsep_1(D,A) & m1_pre_topc(D,A) & ? [E] : ( ~ v2_struct_0(E) & v1_tsep_1(E,A) & m1_pre_topc(E,A) & m1_pre_topc(B,D) & m1_pre_topc(C,E) & ( r1_tsep_1(D,E) | r1_tsep_1(k2_tsep_1(A,D,E),k1_tsep_1(A,B,C)) ) ) ) ) ) ) ) )).
fof(t77_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( v1_valued_2(C) => ! [D] : ( v1_valued_2(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [F] : ( ( 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) = k16_valued_2(k3_xboole_0(B,A),k2_valued_2(k3_xboole_0(k1_valued_2(D),k1_valued_2(C))),k79_valued_2(B,A,D,C,F,E)) ) ) ) ) )).
fof(t77_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m2_vectsp_4(E,A,B,D) => ( r2_hidden(C,E) <=> E = k3_vectsp_4(A,B,C,D) ) ) ) ) ) ) )).
fof(t77_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v9_waybel_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k11_lattice3(A,B,k6_waybel_1(A,B,C)) = k11_lattice3(A,B,C) ) ) ) ) )).
fof(t77_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( ~ r1_xboole_0(A,B) & r1_tarski(A,C) & r1_xboole_0(A,k3_xboole_0(B,C)) ) )).
fof(t77_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k10_xboolean(A,k4_xboolean(A,B)) = k4_xboolean(A,k3_xboolean(B)) ) ) )).
fof(t77_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k7_xcmplx_0(A,k7_xcmplx_0(B,C)) = k7_xcmplx_0(k3_xcmplx_0(A,C),B) ) ) ) )).
fof(t77_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k3_xcmplx_0(A,B),C) => ( r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(A,k7_xcmplx_0(C,B)) ) ) ) ) ) )).
fof(t77_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(D,C) & k3_xxreal_1(C,D) = k2_xxreal_1(A,B) ) ) ) ) ) )).
fof(t77_xxreal_2,axiom,( ! [A] : ( ( v2_membered(A) & v1_xxreal_2(A) & ~ v2_xxreal_2(A) & v6_xxreal_2(A) ) => A = k2_xxreal_1(k2_xxreal_2(A),k1_xxreal_2(A)) ) )).
fof(t77_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => k6_xxreal_3(A,k2_xxreal_0) = k5_numbers ) )).
fof(t77_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ( r2_zf_lang(C,k5_zf_lang(A,B)) <=> C = k5_zf_lang(A,B) ) ) ) ) )).
fof(t77_zf_lang1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ? [B] : ( m1_subset_1(B,k4_ordinal1) & A = k2_zf_lang(B) ) ) )).
fof(t77_zfmisc_1,axiom,( ! [A] : ! [B] : k3_tarski(k2_xboole_0(A,B)) = k2_xboole_0(k3_tarski(A),k3_tarski(B)) )).
fof(t77_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_zmodul01(C) & m1_zmodul01(C,A) ) => ! [D] : ( ( v1_zmodul01(D) & m1_zmodul01(D,A) ) => ( k5_zmodul01(A,B,C) = k5_zmodul01(A,B,D) => C = D ) ) ) ) ) )).
fof(t77_zmodul02,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( m1_zmodul01(D,A) => ( m1_zmodul01(B,C) => m1_zmodul01(B,k6_zmodul01(A,C,D)) ) ) ) ) ) )).
fof(t78_abcmiz_0,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => r1_rewrite1(k11_abcmiz_0(A),B,k12_abcmiz_0(A,B)) ) ) )).
fof(t78_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v9_abcmiz_1(B,A) & m1_abcmiz_1(B,A,k12_abcmiz_1(A)) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k38_abcmiz_1(A))) ) => ( k41_abcmiz_1(A,k40_abcmiz_1(A,C,B)) = C & k42_abcmiz_1(A,k40_abcmiz_1(A,C,B)) = B ) ) ) ) )).
fof(t78_afinsq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => r1_xboole_0(k9_xtuple_0(k61_valued_1(B,A)),k9_xtuple_0(k61_valued_1(C,k1_nat_1(A,k5_card_1(B))))) ) ) ) )).
fof(t78_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ~ ( r1_tarski(A,B) & ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & v1_finset_1(C) ) => k1_ordinal4(A,C) != B ) ) ) ) )).
fof(t78_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v19_aofa_a00(B,A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( C = k10_subset_1(k1_funct_1(u7_aofa_a00(A),14),u4_struct_0(A)) => ( k1_msualg_1(A,C) = k2_finseq_4(u1_struct_0(A),B,B) & k2_msualg_1(A,C) = k37_aofa_a00(A) ) ) ) ) ) )).
fof(t78_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ~ ( k10_arytm_3(A,B) = k11_arytm_3 & A != k11_arytm_3 & B != k11_arytm_3 ) ) ) )).
fof(t78_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( r1_xxreal_0(1,A) => r1_xxreal_0(k2_xcmplx_0(k6_xcmplx_0(k1_square_1(A),A),1),k1_square_1(A)) ) ) )).
fof(t78_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( v20_bcialg_1(A) & k1_bcialg_1(A,C,B) = k1_bcialg_1(A,D,B) ) => C = D ) ) ) ) ) )).
fof(t78_borsuk_5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_connsp_1(A,k3_topmetr) & v2_compts_1(A,k3_topmetr) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) ) => ? [B] : ( v1_xreal_0(B) & ? [C] : ( v1_xreal_0(C) & r1_xxreal_0(B,C) & A = k1_rcomp_1(B,C) ) ) ) )).
fof(t78_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ( r4_borsuk_2(A,B,C,D,E) => r4_borsuk_2(A,C,B,k2_borsuk_2(A,B,C,D),k2_borsuk_2(A,B,C,E)) ) ) ) ) ) ) )).
fof(t78_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ( v2_bvfunc_2(C,A) => r1_bvfunc_1(A,k6_bvfunc_2(A,k6_bvfunc_2(A,k1_bvfunc_1(A,B),C,D),C,E),k6_bvfunc_2(A,k1_bvfunc_1(A,k6_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) )).
fof(t78_bvfunc14,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : ( ( v1_relat_1(J) & v1_funct_1(J) ) => ! [K] : ! [L] : ! [M] : ! [N] : ! [O] : ! [P] : ! [Q] : ! [R] : ! [S] : ( J = k1_funct_4(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,L),k16_funcop_1(C,M)),k16_funcop_1(D,N)),k16_funcop_1(E,O)),k16_funcop_1(F,P)),k16_funcop_1(G,Q)),k16_funcop_1(H,R)),k16_funcop_1(I,S)),k16_funcop_1(A,K)) => k10_xtuple_0(J) = k7_enumset1(k1_funct_1(J,A),k1_funct_1(J,B),k1_funct_1(J,C),k1_funct_1(J,D),k1_funct_1(J,E),k1_funct_1(J,F),k1_funct_1(J,G),k1_funct_1(J,H),k1_funct_1(J,I)) ) ) )).
fof(t78_card_2,axiom,( ! [A] : ! [B] : ~ ( ~ v1_finset_1(A) & ( r2_hidden(k1_card_1(B),k1_card_1(A)) | r1_ordinal1(k1_card_1(B),k1_card_1(A)) ) & ~ ( r2_wellord2(k2_xboole_0(A,B),A) & k1_card_1(k2_xboole_0(A,B)) = k1_card_1(A) ) ) )).
fof(t78_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( r2_hidden(B,k4_card_3(A)) => r2_hidden(k5_relat_1(B,C),k8_card_3(A)) ) ) ) )).
fof(t78_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k2_cat_1(A,D,E) != k1_xboole_0 => ! [F] : ( m1_cat_1(F,A,D,E) => m1_cat_1(k3_funct_2(u4_struct_0(A),u4_struct_0(B),C,F),B,k8_cat_1(A,B,C,D),k8_cat_1(A,B,C,E)) ) ) ) ) ) ) ) )).
fof(t78_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ( r2_cat_3(A,B,C,D) <=> r4_cat_3(k2_oppcat_1(A),k3_oppcat_1(A,B),k5_oppcat_1(A,C),k5_oppcat_1(A,D)) ) ) ) ) ) )).
fof(t78_cfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => ! [D] : ( v1_xcmplx_0(D) => ( v3_funct_1(k2_partfun1(B,k2_numbers,C,A)) => v3_funct_1(k2_partfun1(B,k2_numbers,k25_valued_1(B,k2_numbers,C,D),A)) ) ) ) ) )).
fof(t78_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ? [D] : ( m2_chord(D,A,B,C) & v4_chord(D,A,B,C) ) ) ) ) )).
fof(t78_classes1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_classes1(A,B) <=> ! [C] : k1_card_1(k8_relat_1(A,C)) = k1_card_1(k8_relat_1(B,C)) ) ) ) )).
fof(t78_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( m1_clvect_1(D,A) => ( r1_struct_0(D,B) => r2_hidden(k1_clvect_1(A,B,C),k5_clvect_1(A,B,D)) ) ) ) ) ) )).
fof(t78_cohsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r1_tarski(k14_cohsp_1(A,B),k14_cohsp_1(C,D)) <=> ( r1_tarski(A,C) & r1_tarski(B,D) ) ) )).
fof(t78_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(k3_square_1(k2_xcmplx_0(k1_square_1(A),k1_square_1(B))),k2_xcmplx_0(k9_complex1(A),k9_complex1(B))) ) ) )).
fof(t78_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( k4_complex2(A,B,C) != k5_numbers <=> k2_xcmplx_0(k4_complex2(A,B,C),k4_complex2(C,B,A)) = k3_xcmplx_0(2,k28_sin_cos) ) ) ) ) )).
fof(t78_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) & v2_comput_1(B) & v8_comput_1(B,1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k3_finseq_2(k4_ordinal1)) & v1_funct_1(C) & v4_valued_0(C) & v2_margrel1(C) ) => k1_recdef_1(k7_comput_1(B,C,2),k2_finseq_4(k4_ordinal1,A,k5_numbers)) = k1_recdef_1(B,k12_finseq_1(k4_ordinal1,A)) ) ) ) )).
fof(t78_convex4,axiom,( ! [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) ) => ! [B] : ( m1_convex4(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( v3_convex4(B,A) & ? [D] : ( v1_xreal_0(D) & D = k3_funct_2(u1_struct_0(A),k2_numbers,B,C) & r1_xxreal_0(D,k5_numbers) ) & r2_hidden(C,k1_convex4(A,B)) ) ) ) ) )).
fof(t78_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => v2_cqc_the1(k8_cqc_lang(A,k8_cqc_lang(A,k11_cqc_lang(A,D,B),C),k12_cqc_lang(A,D,k8_cqc_lang(A,B,C))),A) ) ) ) ) )).
fof(t78_csspace,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(B),k6_clvect_1(B,k3_normsp_1(B,C,D),A),k3_normsp_1(B,k6_clvect_1(B,C,A),k6_clvect_1(B,D,A))) ) ) ) ) )).
fof(t78_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k16_sin_cos),D) ) & r2_hidden(B,k1_relset_1(k1_numbers,k26_sin_cos)) & r2_hidden(k2_xcmplx_0(B,A),k1_relset_1(k1_numbers,k26_sin_cos)) ) => k1_funct_1(k3_diff_1(C,A),B) = k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(1,k19_sin_cos(k2_xcmplx_0(B,A))),k19_sin_cos(k2_xcmplx_0(B,A))),k7_xcmplx_0(1,k19_sin_cos(B))),k19_sin_cos(B)) ) ) ) ) )).
fof(t78_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : k7_enumset1(A,B,C,D,E,F,G,H,I) = k2_xboole_0(k2_tarski(A,B),k5_enumset1(C,D,E,F,G,H,I)) )).
fof(t78_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => k5_euclid_8(k7_euclid(3,A,B),C) = k7_euclid(3,k5_euclid_8(A,C),k5_euclid_8(B,C)) ) ) ) )).
fof(t78_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(A)) => ! [G] : ( m2_subset_1(G,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [H] : ( m2_subset_1(H,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ( ( r3_euclidlp(A,k8_euclid(A,C,B),k8_euclid(A,D,B)) & r2_hidden(E,k2_euclid_4(A,B,C)) & r2_hidden(F,k2_euclid_4(A,B,D)) & G = k2_euclid_4(A,C,D) & H = k2_euclid_4(A,E,F) ) => ( r5_euclidlp(A,G,H) <=> ? [I] : ( v1_xreal_0(I) & I != k5_numbers & k8_euclid(A,E,B) = k9_euclid(A,k8_euclid(A,C,B),I) & k8_euclid(A,F,B) = k9_euclid(A,k8_euclid(A,D,B),I) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t78_exchsort,axiom,( ! [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) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_exchsort(B) ) => ! [C] : ( ( v1_finset_1(C) & m2_exchsort(C,A,B) ) => ( m1_exchsort(k4_exchsort(C),B) & ! [D] : ( v3_ordinal1(D) => ( r2_hidden(D,k9_xtuple_0(C)) => m1_exchsort(k1_funct_1(C,D),B) ) ) ) ) ) ) )).
fof(t78_facirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k15_facirc_1(A,B,C),k18_facirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ( ( E = k1_funct_1(D,A) & F = 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(C,A),k3_facirc_1)) = k10_margrel1(F,E) ) ) ) ) ) ) ) )).
fof(t78_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v3_filter_0(A) & r3_lattices(A,B,C) ) => v3_filter_0(k10_filter_2(A,k9_filter_2(A,B,C))) ) ) ) ) )).
fof(t78_finseq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( k11_finseq_1(A,B,C) = k11_finseq_1(D,E,F) => ( A = D & B = E & C = F ) ) )).
fof(t78_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( ( 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))) ) => ! [G] : ( m2_finseq_1(G,B) => ( G = k12_finseq_1(B,E) => k5_funcop_1(F,D,G) = k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)) ) ) ) ) ) ) ) ) )).
fof(t78_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(B,C) => ( r2_hidden(A,C) | k1_finseq_3(k10_finseq_1(A,B),C) = k9_finseq_1(A) ) ) )).
fof(t78_finseq_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ( k7_partfun1(A,k9_finseq_4(A,B,C,D,E),1) = B & k7_partfun1(A,k9_finseq_4(A,B,C,D,E),2) = C & k7_partfun1(A,k9_finseq_4(A,B,C,D,E),3) = D & k7_partfun1(A,k9_finseq_4(A,B,C,D,E),4) = E ) ) ) ) ) ) )).
fof(t78_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => k17_finseq_1(A,B,k6_finseq_1(A)) = k6_finseq_1(A) ) ) )).
fof(t78_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r2_hidden(B,k10_xtuple_0(C)) => ( k4_finseq_4(C,B) = 1 | r2_hidden(B,k10_xtuple_0(k2_rfinseq(A,1,C))) ) ) ) ) ) )).
fof(t78_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( ( 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] : ( ( v1_funct_1(G) & v1_funct_2(G,A,C) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,B,D) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(B,D))) ) => ( v1_funct_1(k6_finseqop(F,G,H)) & v1_funct_2(k6_finseqop(F,G,H),k2_zfmisc_1(A,B),E) & m1_subset_1(k6_finseqop(F,G,H),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),E))) ) ) ) ) ) ) ) ) ) )).
fof(t78_flang_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ( r2_hidden(B,k2_flang_2(A,C)) <=> ( B = k2_flang_1(A) | r2_hidden(B,C) ) ) ) )).
fof(t78_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ( r1_tarski(B,k2_flang_3(A,C)) => ( r1_xxreal_0(D,k5_numbers) | r1_tarski(k7_flang_1(A,B,D),k2_flang_3(A,C)) ) ) ) ) ) )).
fof(t78_fomodel0,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(A,B) => k9_xtuple_0(k6_subset_1(B,A)) = k6_subset_1(k9_xtuple_0(B),k9_xtuple_0(A)) ) ) )).
fof(t78_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_funct_1(A) & ~ v1_xboole_0(A) ) => ? [B] : ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => k1_funct_1(A,C) = B ) ) )).
fof(t78_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => r1_tarski(k7_relat_1(C,k3_xboole_0(A,k8_relat_1(C,B))),k3_xboole_0(k7_relat_1(C,A),B)) ) )).
fof(t78_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ~ ( r1_partfun1(C,E) & r1_partfun1(D,E) ) ) ) ) ) )).
fof(t78_funct_3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => k13_funct_3(D,E) = k3_relat_1(k12_funct_3(A),k16_funct_3(A,A,B,C,D,E)) ) ) )).
fof(t78_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : k5_relat_1(A,k2_xboole_0(B,C)) = k1_funct_4(k5_relat_1(A,B),k5_relat_1(A,C)) ) )).
fof(t78_funct_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_relat_1(C) => ( r1_tarski(k10_xtuple_0(C),k9_xtuple_0(C)) => k8_funct_7(k8_funct_7(C,A),B) = k8_funct_7(C,k3_xcmplx_0(A,B)) ) ) ) ) )).
fof(t78_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => r1_funct_8(A,k1_numbers,k1_numbers,k32_valued_1(k1_numbers,k1_numbers,k18_sin_cos)) ) )).
fof(t78_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => v2_ring_1(k8_fvaluat1(A,B),k7_fvaluat1(A,B)) ) ) ) )).
fof(t78_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => k3_group_4(A,k8_finseq_1(u1_struct_0(A),k12_finseq_1(u1_struct_0(A),B),C)) = k8_group_1(A,B,k3_group_4(A,C)) ) ) ) )).
fof(t78_gfacirc1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ~ v1_facirc_1(k2_msafree2(k31_gfacirc1(A,B,C))) ) ) ) )).
fof(t78_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(B)) => ( C = D => ( r1_tarski(k26_glib_000(B,D),k26_glib_000(A,C)) & r1_tarski(k27_glib_000(B,D),k27_glib_000(A,C)) & r1_tarski(k28_glib_000(B,D),k28_glib_000(A,C)) ) ) ) ) ) ) )).
fof(t78_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ? [C] : ( v1_abian(C) & m1_subset_1(C,k4_ordinal1) & C = k6_xcmplx_0(k3_finseq_1(B),1) & k3_finseq_1(k12_glib_001(A,B)) = k3_nat_d(C,2) ) ) ) )).
fof(t78_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( v1_group_3(C,A) & m1_group_2(C,A) ) => ~ ( m1_group_2(C,B) & ! [D] : ( ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) ) => ! [E] : ( ( v15_algstr_0(E) & v1_group_3(E,A) & m1_group_2(E,A) ) => ~ ( u1_struct_0(D) = k4_group_11(A,B,C) & u1_struct_0(E) = k3_group_11(A,B,C) & r1_tarski(k3_group_11(A,B,E),k4_group_11(A,B,D)) ) ) ) ) ) ) ) )).
fof(t78_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( 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)) & ! [D] : ( ( v15_algstr_0(D) & m1_group_2(D,A) ) => u1_struct_0(D) != k2_group_2(A,k8_group_2(A,B),k8_group_2(A,C)) ) ) & ( ? [D] : ( m1_group_2(D,A) & u1_struct_0(D) = k2_group_2(A,k8_group_2(A,B),k8_group_2(A,C)) ) => 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)) ) ) ) ) ) )).
fof(t78_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ( r2_group_3(A,B,k1_group_1(A)) | r2_group_3(A,k1_group_1(A),B) ) => B = k1_group_1(A) ) ) ) )).
fof(t78_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ( v1_group_3(k10_group_5(A),A) & m1_group_2(k10_group_5(A),A) ) ) )).
fof(t78_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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)))) ) => r2_group_6(k5_group_6(A,k9_group_6(A,B,C)),k10_group_6(A,B,C)) ) ) ) )).
fof(t78_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( m1_group_9(D,A,B) => ! [E] : ( ( v2_group_9(E,A) & m1_group_9(E,A,C) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(B),u1_struct_0(C)) & v1_group_6(F,B,C) & v7_group_9(F,A,B,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)))) ) => ~ ( D = k13_group_9(A,B,C,F) & ! [G] : ( ( v2_group_9(G,A) & m1_group_9(G,A,B) ) => ~ ( u1_struct_0(G) = k8_relset_1(u1_struct_0(B),u1_struct_0(C),F,u1_struct_0(E)) & ( v4_group_9(E,A,C) => ( v4_group_9(D,A,G) & m1_group_9(D,A,G) & v4_group_9(G,A,B) ) ) ) ) ) ) ) ) ) ) )).
fof(t78_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_algstr_0(A) & v4_rlvect_1(A) & v2_vectsp_1(A) & v1_algstr_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => k14_ideal_1(A,k6_domain_1(u1_struct_0(A),k4_struct_0(A)),B) = k6_domain_1(u1_struct_0(A),k4_struct_0(A)) ) ) )).
fof(t78_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => k2_integra5(A,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)) = k6_xcmplx_0(k6_xcmplx_0(k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k18_sin_cos),k2_seq_4(A)),k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k18_sin_cos),k3_seq_4(A))),k6_xcmplx_0(k1_funct_1(k16_sin_cos,k2_seq_4(A)),k1_funct_1(k16_sin_cos,k3_seq_4(A)))) ) )).
fof(t78_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ( v10_intpro_1(A) => v9_intpro_1(A) ) ) )).
fof(t78_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(k18_euclid(B),k5_numbers) & ~ r1_xxreal_0(A,k7_xcmplx_0(k17_euclid(B),k12_euclid(B))) & ~ r1_xxreal_0(k18_euclid(C),k5_numbers) & ~ r1_xxreal_0(A,k7_xcmplx_0(k17_euclid(C),k12_euclid(C))) & ~ r1_xxreal_0(k7_xcmplx_0(k17_euclid(C),k12_euclid(C)),k7_xcmplx_0(k17_euclid(B),k12_euclid(B))) & ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) & ? [E] : ( 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(k7_xcmplx_0(k17_euclid(E),k12_euclid(E)),k7_xcmplx_0(k17_euclid(D),k12_euclid(D))) ) ) ) ) ) ) )).
fof(t78_jgraph_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( ( ~ 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] : ( ( 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))))) ) => ( ( E = k5_jgraph_6(k5_numbers,k5_numbers,1) & r2_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,k1_jgraph_3) ) => ( r1_jordan17(k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(1),1),A,B,C,D) <=> r1_jordan17(E,k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,A),k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,B),k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,C),k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),F,D)) ) ) ) ) ) ) ) ) )).
fof(t78_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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 & k18_euclid(C) = H & k17_euclid(D) = F & r1_xxreal_0(G,k18_euclid(A)) & ~ r1_xxreal_0(k18_euclid(B),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) & k1_funct_1(I,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t78_jordan2c,axiom,( ! [A] : ( ( ~ 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)))) ) => ( r1_tarski(k3_goboard9(k1_sprect_1(A)),k1_jordan2c(2,k3_topreal1(2,k1_sprect_1(A)))) & v9_rltopsp1(k3_goboard9(k1_sprect_1(A)),k15_euclid(2)) ) ) )).
fof(t78_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => v6_lexbfs(k7_lexbfs(k6_glib_000(A),k4_ordinal1,k9_funct_2(k6_glib_000(A),k5_finsub_1(k4_ordinal1)),k14_lexbfs(A,k16_lexbfs(A))),A) ) )).
fof(t78_limfunc2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r4_limfunc2(B,A) & k2_limfunc2(B,A) = k5_numbers & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,A) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(C,D) & ~ r1_xxreal_0(D,A) & r2_hidden(D,k1_relset_1(k1_numbers,B)) & k1_funct_1(B,D) != k5_numbers ) ) ) ) ) => ( ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k2_rcomp_1(A,k2_xcmplx_0(A,C)))) => r1_xxreal_0(k1_funct_1(B,D),k5_numbers) ) ) ) ) | r6_limfunc2(k6_rfunct_1(k1_numbers,k1_numbers,B),A) ) ) ) ) )).
fof(t78_mathmorp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(C)))) => ( v1_convex1(D,k15_euclid(C)) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(B,k5_numbers) | k6_mathmorp(k2_xcmplx_0(B,A),k15_euclid(C),D) = k6_rusub_4(k15_euclid(C),k6_mathmorp(B,k15_euclid(C),D),k6_mathmorp(A,k15_euclid(C),D)) ) ) ) ) ) ) )).
fof(t78_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( v3_matrix10(B) => r2_matrix10(C,k5_matrix10(A,C,B)) ) ) ) ) )).
fof(t78_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( m2_finseq_2(D,k4_ordinal1,k4_finseq_2(B,k4_ordinal1)) => ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [F] : ( ( v1_matrix_0(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_0(F)) => r1_xxreal_0(k8_matrix13(C,k1_matrix13(u1_struct_0(C),F,B,A,D,E)),k8_matrix13(C,F)) ) ) ) ) ) ) ) )).
fof(t78_matrixj1,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ! [D] : ( ( v1_matrix_0(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(A))) ) => ! [E] : ( ( v1_matrix_0(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(A))) ) => ( ( k1_matrix_0(B) = k3_finseq_1(D) & k1_matrix_0(C) = k3_finseq_1(E) ) => k4_matrix_3(A,k13_matrixj1(u1_struct_0(A),k4_struct_0(A),k5_matrixj1(u1_struct_0(A),B,C)),k13_matrixj1(u1_struct_0(A),k4_struct_0(A),k5_matrixj1(u1_struct_0(A),D,E))) = k13_matrixj1(u1_struct_0(A),k4_struct_0(A),k26_matrixj1(A,k5_matrixj1(u1_struct_0(A),B,C),k5_matrixj1(u1_struct_0(A),D,E))) ) ) ) ) ) ) )).
fof(t78_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,B) ) => k1_funct_1(k4_matrixr2(B),A) = k6_matrixr2(B,A) ) ) ) )).
fof(t78_member_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => k11_member_1(k2_tarski(A,B),k2_tarski(C,D)) = k2_enumset1(k6_xcmplx_0(A,C),k6_xcmplx_0(A,D),k6_xcmplx_0(B,C),k6_xcmplx_0(B,D)) ) ) ) ) )).
fof(t78_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_partfun1(C,u1_struct_0(B)) ) => ! [D] : ( ( 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) & k6_memstr_0(A,B,C) = k6_memstr_0(A,B,D) ) => C = D ) ) ) ) ) )).
fof(t78_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ~ ( ? [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) & F = k1_relset_1(A,D) & r1_mesfunc1(A,B,D,F) ) & ? [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) & F = k1_relset_1(A,E) & r1_mesfunc1(A,B,E,F) ) & v6_supinf_2(D) & v6_supinf_2(E) & ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ~ ( F = k1_relset_1(A,k3_mesfunc1(A,D,E)) & k6_mesfunc5(A,B,C,k3_mesfunc1(A,D,E)) = k3_supinf_2(k6_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,F)),k6_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,E,F))) ) ) ) ) ) ) ) ) )).
fof(t78_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( ( r1_tarski(E,k9_subset_1(A,k1_relset_1(A,C),k1_relset_1(A,D))) & r1_mesfunc6(A,B,C,E) & r1_mesfunc6(A,B,D,E) ) => r1_mesfunc6(A,B,k3_valued_1(A,k1_numbers,k1_numbers,k19_rfunct_3(A,k3_valued_1(A,k1_numbers,k1_numbers,C,D)),k18_rfunct_3(A,C)),E) ) ) ) ) ) ) )).
fof(t78_mmlquery,axiom,( ! [A] : ( l1_mmlquery(A) => ! [B] : ( m2_finseq_1(B,u1_mmlquery(A)) => ( B != k1_xboole_0 => k32_mmlquery(A,B) = k1_setfam_1(a_2_4_mmlquery(A,B)) ) ) ) )).
fof(t78_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( ( 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) ) ) & ( 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) ) ) & ( 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) ) ) & ( 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) ) ) & ( 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) ) ) & ( 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) ) ) & ( 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) ) ) ) ) )).
fof(t78_monoid_0,axiom,( ! [A] : ( k4_binop_1(u1_struct_0(k17_monoid_0(A)),u2_algstr_0(k17_monoid_0(A))) = k6_partfun1(A) & k1_group_1(k17_monoid_0(A)) = k6_partfun1(A) ) )).
fof(t78_msafree4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ! [D] : ( ( v3_msualg_6(D,A,k1_msafree3(A,B)) & v4_msualg_6(D,A,k1_msafree3(A,B)) & v9_msafree4(D,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B))) & v10_msafree4(D,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B))) & m1_msualg_4(D,u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,k1_msafree3(A,B))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(C,k1_msafree4(u1_struct_0(A),k9_msafree4(u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),D),E)) => k2_rewrite1(k7_msafree4(u1_struct_0(A),u3_msualg_1(A,k1_msafree3(A,B)),u3_msualg_1(A,k1_msafree3(A,B)),D,E),C) = C ) ) ) ) ) )).
fof(t78_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ( ( v1_ncfcont1(k1_relset_1(u1_struct_0(A),C),A) & r8_ncfcont1(A,B,C,k1_relset_1(u1_struct_0(A),C)) ) => v1_nfcont_1(k2_relset_1(u1_struct_0(B),C),B) ) ) ) ) )).
fof(t78_newton,axiom,( ! [A] : ( v7_ordinal1(A) => k9_newton(A) = a_1_1_newton(A) ) )).
fof(t78_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v11_o_ring_1(B,A) & v9_o_ring_1(C,A) ) => v13_o_ring_1(k6_algstr_0(A,B,C),A) ) ) ) ) )).
fof(t78_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v6_relat_2(A) => v6_relat_2(k2_relat_1(A)) ) ) )).
fof(t78_partfun1,axiom,( ! [A] : ( ( v4_funct_1(A) & ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) )).
fof(t78_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => r6_pboole(A,k4_pboole(A,k4_pboole(A,B,C),C),k4_pboole(A,B,C)) ) ) )).
fof(t78_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r3_pdiff_5(A,B) => r1_fcont_1(k1_pdiff_2(3,3,k1_pdiff_3(1,3,A),B),k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(3,3),B)) ) ) ) )).
fof(t78_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [F] : ( ( ~ v1_xboole_0(F) & m2_finseq_1(F,k4_ordinal1) ) => ( ( r5_pdiff_9(A,E,k1_nat_1(B,C),D) & r1_tarski(k1_rvsum_1(F),k2_finseq_1(A)) & k3_finseq_1(F) = C ) => r5_pdiff_9(A,k5_pdiff_9(A,D,F,E),B,D) ) ) ) ) ) ) )).
fof(t78_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ( v5_polyform(A) => k1_vectsp_9(k2_bspace,k22_polyform(A,k6_xcmplx_0(k7_polyform(A),1))) = 1 ) ) )).
fof(t78_pre_poly,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_subset_1(C,A) => ( ~ r2_hidden(C,B) => ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ( D = k1_finsub_1(k1_zfmisc_1(A),k6_domain_1(A,C),B) => ! [E] : ( ( 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] : ( m1_subset_1(F,k4_ordinal1) => ( ( r2_hidden(k1_nat_1(F,1),k4_finseq_1(k7_pre_poly(A,D,E))) & k7_partfun1(A,k7_pre_poly(A,D,E),k1_nat_1(F,1)) = C ) => k7_pre_poly(A,D,E) = k5_finseq_5(A,k7_pre_poly(A,B,E),C,F) ) ) ) ) ) ) ) ) ) ) )).
fof(t78_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & k6_prepower(k3_xcmplx_0(A,B),C) != k3_xcmplx_0(k6_prepower(A,C),k6_prepower(B,C)) ) ) ) ) )).
fof(t78_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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)) => r6_pboole(A,k3_pboole(A,k6_pboole(A,B,C),k6_pboole(A,C,B)),k1_pboole(A)) ) ) ) )).
fof(t78_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v5_qc_lang1(B,A) => r3_qc_lang2(A,k22_qc_lang1(A,B),B) ) ) ) )).
fof(t78_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k1_quatern3(A) = k6_quaterni(k6_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k1_square_1(k13_quaterni(A)),k1_square_1(k14_quaterni(A))),k1_square_1(k15_quaterni(A))),k1_square_1(k16_quaterni(A))),k3_xcmplx_0(2,k3_xcmplx_0(k13_quaterni(A),k14_quaterni(A))),k3_xcmplx_0(2,k3_xcmplx_0(k13_quaterni(A),k15_quaterni(A))),k3_xcmplx_0(2,k3_xcmplx_0(k13_quaterni(A),k16_quaterni(A)))) ) )).
fof(t78_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => r1_xxreal_0(k16_quaterni(A),k28_quaterni(A)) ) )).
fof(t78_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r2_hidden(B,k10_xtuple_0(k6_relat_1(A,C))) <=> ( r2_hidden(B,A) & r2_hidden(B,k10_xtuple_0(C)) ) ) ) )).
fof(t78_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_afinsq_1(C))) => ! [F] : ( ( ~ v2_struct_0(F) & l1_rewrite3(F,E) ) => ( r1_rewrite1(k1_rewrite3(C,E,F),k4_tarski(A,D),k4_tarski(B,D)) => ( r2_hidden(k2_flang_1(C),k10_xtuple_0(k9_xtuple_0(u1_rewrite3(E,F)))) | A = B ) ) ) ) ) ) )).
fof(t78_rfunct_1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) ) => ( ( ( v1_seq_2(k5_relat_1(C,A)) & r1_xxreal_0(k5_numbers,B) ) => v1_seq_2(k5_relat_1(k24_valued_1(C,B),A)) ) & ( ( v1_seq_2(k5_relat_1(C,A)) & r1_xxreal_0(B,k5_numbers) ) => v2_seq_2(k5_relat_1(k24_valued_1(C,B),A)) ) ) ) ) )).
fof(t78_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ! [E] : ( v1_finset_1(E) => ( ( E = k1_relset_1(A,k2_partfun1(A,k1_numbers,B,D)) & k1_relset_1(A,k2_partfun1(A,k1_numbers,B,D)) = k1_relset_1(A,k2_partfun1(A,k1_numbers,C,D)) ) => k21_rfunct_3(A,k3_valued_1(A,k1_numbers,k1_numbers,B,C),D) = k2_xcmplx_0(k21_rfunct_3(A,B,D),k21_rfunct_3(A,C,D)) ) ) ) ) ) )).
fof(t78_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_seq_2(B) & v4_partfun3(B) & v2_seq_2(C) & v4_partfun3(C) ) => r1_xxreal_0(k3_xcmplx_0(k1_funct_1(k3_rinfsup1(B),A),k1_funct_1(k3_rinfsup1(C),A)),k1_funct_1(k3_rinfsup1(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C)),A)) ) ) ) ) )).
fof(t78_rlaffin1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(C))) => ( ( r2_hidden(D,k4_rlaffin1(C,F)) & r2_hidden(E,k4_rlaffin1(C,F)) & k2_xcmplx_0(A,B) = 1 ) => r2_hidden(k3_rlvect_1(C,k1_rlvect_1(C,D,A),k1_rlvect_1(C,E,B)),k4_rlaffin1(C,F)) ) ) ) ) ) ) ) )).
fof(t78_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( m2_rlsub_1(D,A,C) => ( r2_hidden(B,D) <=> D = k3_rlsub_1(A,B,C) ) ) ) ) ) )).
fof(t78_rlvect_1,axiom,( ! [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) ) => k4_algstr_0(A,k4_rlvect_1(A,k6_finseq_1(u1_struct_0(A)))) = k4_struct_0(A) ) )).
fof(t78_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_rmod_2(D,A,B) => ! [E] : ( m2_rmod_2(E,A,B,D) => ! [F] : ( m2_rmod_2(F,A,B,D) => ( ( r2_hidden(C,E) & r2_hidden(C,F) ) => E = F ) ) ) ) ) ) ) )).
fof(t78_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k16_rvsum_1(k11_finseq_1(A,B,C)) = k2_xcmplx_0(k2_xcmplx_0(A,B),C) ) ) ) )).
fof(t78_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [D] : ( ( 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),k5_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(k5_numbers)))))) ) ) ) ) ) )).
fof(t78_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ~ v2_extpro_1(k12_scmfsa_2(A,B),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(t78_scmpds_2,axiom,( k8_struct_0(k1_scmpds_2) = k2_ami_2 )).
fof(t78_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ( k1_funct_1(k8_scmpds_6(A,B,C),k5_numbers) = k8_scmpds_2(A,B,2) & k1_funct_1(k8_scmpds_6(A,B,C),1) = k3_scmpds_2(k1_nat_1(k5_card_1(C),1)) ) ) ) ) )).
fof(t78_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( ( v7_scmyciel(B,k6_scmyciel(A)) & m1_eqrel_1(B,k3_tarski(k6_scmyciel(A))) ) => ( v10_scmyciel(B,A) & m1_eqrel_1(B,k3_tarski(A)) ) ) ) )).
fof(t78_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k1_semi_af1(A,B,C,D) = k1_semi_af1(A,C,B,D) ) ) ) ) )).
fof(t78_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => C = k17_seq_4(A,k13_seq_4(A,C,B),B) ) ) ) )).
fof(t78_setlim_1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(C) => k4_kurato_0(A,C) = k1_kurato_0(A,C) ) ) ) )).
fof(t78_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => r1_tarski(k3_kurato_0(A,k9_setlim_2(A,C,B)),k5_subset_1(A,B,k3_kurato_0(A,C))) ) ) )).
fof(t78_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,B,B),B)),k5_sheffer1(A,C,C)) = C ) ) ) )).
fof(t78_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ( k17_sin_cos(k2_xcmplx_0(A,k3_xcmplx_0(2,k28_sin_cos))) = k17_sin_cos(A) & k19_sin_cos(k2_xcmplx_0(A,k3_xcmplx_0(2,k28_sin_cos))) = k19_sin_cos(A) & k17_sin_cos(k6_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),A)) = k19_sin_cos(A) & k19_sin_cos(k6_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),A)) = k17_sin_cos(A) & k17_sin_cos(k2_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),A)) = k19_sin_cos(A) & k19_sin_cos(k2_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),A)) = k4_xcmplx_0(k17_sin_cos(A)) & k17_sin_cos(k2_xcmplx_0(k28_sin_cos,A)) = k4_xcmplx_0(k17_sin_cos(A)) & k19_sin_cos(k2_xcmplx_0(k28_sin_cos,A)) = k4_xcmplx_0(k19_sin_cos(A)) ) ) )).
fof(t78_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) => k2_sin_cos6(A) = k4_xcmplx_0(k2_sin_cos6(k4_xcmplx_0(A))) ) ) )).
fof(t78_sin_cos9,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k2_sin_cos9,k7_relset_1(k1_numbers,k1_numbers,k27_sin_cos,k2_rcomp_1(k5_numbers,k28_sin_cos)))) )).
fof(t78_sincos10,axiom,( v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k2_sincos10,k7_relset_1(k1_numbers,k1_numbers,k1_fdiff_9,k4_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos)))) )).
fof(t78_sprect_1,axiom,( ! [A] : ( ( ~ 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(k3_topreal1(2,k1_sprect_1(A))) = k13_pscomp_1(A) ) )).
fof(t78_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),D))) ) => ( ! [F] : ( m2_subset_1(F,k2_qc_lang1(A),k3_qc_lang1(A)) => ~ ( r2_hidden(F,k1_relset_1(k3_qc_lang1(A),E)) & r2_hidden(F,k24_qc_lang1(A,k11_cqc_lang(A,C,B))) ) ) => ! [F] : ( m2_subset_1(F,k2_qc_lang1(A),k3_qc_lang1(A)) => ~ ( r2_hidden(F,k7_subset_1(k3_qc_lang1(A),k1_relset_1(k3_qc_lang1(A),E),k6_domain_1(k3_qc_lang1(A),C))) & r2_hidden(F,k24_qc_lang1(A,B)) ) ) ) ) ) ) ) ) )).
fof(t78_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( r1_tarski(B,k9_tdlat_1(A)) <=> v3_tdlat_2(B,A) ) ) ) )).
fof(t78_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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) => v4_tex_4(k1_tex_2(A,B),A) ) ) ) )).
fof(t78_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ! [G] : ( m1_subset_1(G,u1_struct_0(C)) => ! [H] : ( m1_subset_1(H,u1_struct_0(D)) => ( ( v3_pre_topc(F,A) & r2_hidden(G,F) & r1_tarski(F,u1_struct_0(D)) & G = H ) => ( r1_tmap_1(C,B,E,G) <=> r1_tmap_1(D,B,k3_tmap_1(A,B,C,D,E),H) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t78_topreal6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( v9_rltopsp1(A,k15_euclid(2)) => k6_pscomp_1(A) = k6_pscomp_1(k2_pre_topc(k15_euclid(2),A)) ) ) )).
fof(t78_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( ( r1_tarski(C,D) & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) ) => r1_tarski(k1_tops_1(A,C),k1_tops_1(B,D)) ) ) ) ) ) )).
fof(t78_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)))) ) => ( ( v6_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))) ) ) ) ) ) ) )).
fof(t78_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v5_trees_3(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) ) => ~ ( r2_hidden(B,k10_xtuple_0(A)) & r1_xxreal_0(k6_trees_1(k11_trees_3(A)),k6_trees_1(B)) ) ) ) )).
fof(t78_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( ( r1_tsep_1(B,C) & r4_tsep_1(A,B,C) ) <=> r3_tsep_1(A,B,C) ) ) ) ) )).
fof(t78_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( v1_valued_2(C) => ! [D] : ( v1_valued_2(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,D))) ) => k16_valued_2(k3_xboole_0(A,B),k2_valued_2(k3_xboole_0(k1_valued_2(C),k1_valued_2(D))),k79_valued_2(A,B,C,D,E,F)) = k73_valued_2(A,B,k2_valued_2(k1_valued_2(C)),D,k16_valued_2(A,C,E),F) ) ) ) ) )).
fof(t78_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_vectsp_4(E,A,B) => ! [F] : ( m2_vectsp_4(F,A,B,E) => ~ ( r2_hidden(C,F) & r2_hidden(D,F) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ~ ( r1_struct_0(E,G) & k3_rlvect_1(B,C,G) = D ) ) ) ) ) ) ) ) ) )).
fof(t78_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v9_waybel_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k6_waybel_1(A,k10_lattice3(A,B,C),D) = k11_lattice3(A,k6_waybel_1(A,B,D),k6_waybel_1(A,C,D)) ) ) ) ) ) )).
fof(t78_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_xboole_0(A,B) => k3_xboole_0(A,k2_xboole_0(B,C)) = k3_xboole_0(A,C) ) )).
fof(t78_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k4_xboolean(k3_xboolean(A),k10_xboolean(A,B)) = k4_xboolean(k3_xboolean(A),B) ) ) )).
fof(t78_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k7_xcmplx_0(A,k3_xcmplx_0(B,C)) = k7_xcmplx_0(k7_xcmplx_0(A,B),C) ) ) ) )).
fof(t78_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(k3_xcmplx_0(A,B),C) => ( r1_xxreal_0(k5_numbers,B) | r1_xxreal_0(k7_xcmplx_0(C,B),A) ) ) ) ) ) )).
fof(t78_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(D,C) & k3_xxreal_1(C,D) = k4_xxreal_1(A,B) ) ) ) ) ) )).
fof(t78_xxreal_2,axiom,( ! [A] : ( ( v2_membered(A) & ~ v1_xboole_0(A) & ~ v1_xxreal_2(A) & ~ v2_xxreal_2(A) & v6_xxreal_2(A) ) => A = k4_xxreal_1(k2_xxreal_2(A),k1_xxreal_2(A)) ) )).
fof(t78_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ~ ( A != k2_xxreal_0 & A != k1_xxreal_0 & A != k5_numbers & k6_xxreal_3(A,A) != 1 ) ) )).
fof(t78_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r2_hidden(A,k29_zf_lang(B)) => r2_zf_lang(A,B) ) ) ) )).
fof(t78_zf_lang1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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,k4_zf_lang(A,A)) ) ) ) )).
fof(t78_zfmisc_1,axiom,( ! [A] : ! [B] : r1_tarski(k3_tarski(k3_xboole_0(A,B)),k3_xboole_0(k3_tarski(A),k3_tarski(B))) )).
fof(t78_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_zmodul01(D) & m1_zmodul01(D,A) ) => ! [E] : ( ( v1_zmodul01(E) & m1_zmodul01(E,A) ) => ( k5_zmodul01(A,C,D) = k5_zmodul01(A,B,E) => D = E ) ) ) ) ) ) )).
fof(t79_abcmiz_0,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => r3_orders_2(A,B,k12_abcmiz_0(A,B)) ) ) )).
fof(t79_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k38_abcmiz_1(A))) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k38_abcmiz_1(A))) ) => ! [D] : ( ( v9_abcmiz_1(D,A) & m1_abcmiz_1(D,A,k12_abcmiz_1(A)) ) => ! [E] : ( ( v9_abcmiz_1(E,A) & m1_abcmiz_1(E,A,k12_abcmiz_1(A)) ) => ( k40_abcmiz_1(A,B,D) = k40_abcmiz_1(A,C,E) => ( B = C & D = E ) ) ) ) ) ) ) )).
fof(t79_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( v7_ordinal1(C) => r1_tarski(k61_valued_1(A,C),k61_valued_1(k1_ordinal4(A,B),C)) ) ) ) )).
fof(t79_afinsq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,A) & v1_funct_1(C) & v5_ordinal1(C) & v1_finset_1(C) ) => ~ ( r1_tarski(B,C) & ! [D] : ( ( v1_relat_1(D) & v5_relat_1(D,A) & v1_funct_1(D) & v5_ordinal1(D) & v1_finset_1(D) ) => k1_ordinal4(B,D) != C ) ) ) ) ) )).
fof(t79_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ( v11_aofa_000(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( v7_ordinal1(C) & r2_hidden(B,k9_aofa_000(A,k18_aofa_000(A),C)) ) ) ) ) )).
fof(t79_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & v22_aofa_a00(D,A,1,1,11) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( ( v19_aofa_a00(F,A) & m1_subset_1(F,u1_struct_0(A)) ) => ! [G] : ( m2_subset_1(G,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),k37_aofa_a00(A))) => ! [I] : ( m1_subset_1(I,k1_funct_1(u3_msualg_1(A,C),F)) => k15_aofa_a00(A,B,C,D,F,k39_aofa_a00(A,C,H,F,I),G) = k39_aofa_a00(A,D,k15_aofa_a00(A,B,C,D,k37_aofa_a00(A),H,G),F,k15_aofa_a00(A,B,C,D,F,I,G)) ) ) ) ) ) ) ) ) ) )).
fof(t79_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( m1_subset_1(C,k5_arytm_3) => ~ ( r3_arytm_3(A,k10_arytm_3(B,C)) & ! [D] : ( m1_subset_1(D,k5_arytm_3) => ~ ( A = k10_arytm_3(B,D) & r3_arytm_3(D,C) ) ) ) ) ) ) )).
fof(t79_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( r1_xxreal_0(1,A) => r1_xxreal_0(k1_square_1(A),k3_xcmplx_0(2,k2_xcmplx_0(k6_xcmplx_0(k1_square_1(A),A),1))) ) ) )).
fof(t79_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v20_bcialg_1(A) & k1_bcialg_1(A,B,C) = k4_struct_0(A) ) => B = C ) ) ) ) )).
fof(t79_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( m1_borsuk_2(E,A,B,C) => ! [F] : ( m1_borsuk_2(F,A,B,C) => ( ( r3_borsuk_2(A,B,C,D,E) & r3_borsuk_2(A,B,C,E,F) ) => r3_borsuk_2(A,B,C,D,F) ) ) ) ) ) ) ) )).
fof(t79_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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),k7_bvfunc_2(A,k1_bvfunc_1(A,k7_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) )).
fof(t79_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_eqrel_1(I,A) => ! [J] : ( m1_eqrel_1(J,A) => ! [K] : ( m1_eqrel_1(K,A) => ! [L] : ( m1_subset_1(L,A) => ! [M] : ( m1_subset_1(M,A) => ~ ( v2_bvfunc_2(B,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 & k9_subset_1(A,k15_bvfunc_1(A,M,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)),k15_bvfunc_1(A,L,C)) = k1_xboole_0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t79_card_2,axiom,( ! [A] : ( ( v1_finset_1(A) & v1_card_1(A) ) => ! [B] : ( ( v1_finset_1(B) & v1_card_1(B) ) => v1_finset_1(k1_card_2(A,B)) ) ) )).
fof(t79_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( m1_subset_1(B,k4_card_3(A)) => ! [C] : ( m1_subset_1(C,k4_card_3(A)) => ! [D] : k5_relat_1(k1_funct_4(C,k11_card_3(A,B,D)),D) = k11_card_3(A,B,D) ) ) ) )).
fof(t79_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( k2_cat_1(A,D,E) != k1_xboole_0 & k2_cat_1(B,k8_cat_1(A,B,C,D),k8_cat_1(A,B,C,E)) = k1_xboole_0 ) ) ) ) ) ) )).
fof(t79_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u4_struct_0(C)) => ! [F] : ( m1_subset_1(F,u4_struct_0(C)) => ( A != B => ( r4_cat_3(C,D,E,F) <=> r3_cat_3(C,D,k2_tarski(A,B),k5_funct_4(u4_struct_0(C),A,B,E,F)) ) ) ) ) ) ) )).
fof(t79_cfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => ( v3_funct_1(k2_partfun1(B,k2_numbers,C,A)) => ( v3_funct_1(k2_partfun1(B,k1_numbers,k55_valued_1(B,k2_numbers,C),A)) & v3_funct_1(k2_partfun1(B,k2_numbers,k31_valued_1(B,k2_numbers,C),A)) ) ) ) ) )).
fof(t79_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ~ ( B != C & ~ r1_chord(A,B,C) & ? [D] : ( m2_chord(D,A,B,C) & v4_chord(D,A,B,C) & ? [E] : ( m2_chord(E,A,C,B) & D = E & ~ v4_chord(E,A,C,B) ) ) ) ) ) ) )).
fof(t79_classes1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r1_tarski(k10_xtuple_0(B),A) & r1_tarski(k10_xtuple_0(C),A) & ! [D] : ( m1_subset_1(D,A) => k1_card_1(k10_relat_1(B,D)) = k1_card_1(k10_relat_1(C,D)) ) ) => r2_classes1(B,C) ) ) ) ) )).
fof(t79_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_clvect_1(C,A) => ( r2_hidden(k4_algstr_0(A,B),k5_clvect_1(A,B,C)) <=> r1_struct_0(C,B) ) ) ) ) )).
fof(t79_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => ? [D] : ( v1_xreal_0(D) & ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ~ ( r1_xxreal_0(E,C) & r1_xxreal_0(D,k13_csspace(A,k1_normsp_1(A,B,E))) ) ) ) ) ) ) )).
fof(t79_cohsp_1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( r1_tarski(C,k14_cohsp_1(A,B)) & ! [D] : ! [E] : ~ ( C = k14_cohsp_1(D,E) & r1_tarski(D,A) & r1_tarski(E,B) ) ) )).
fof(t79_complex1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(k9_complex1(A),k3_square_1(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)))) ) ) )).
fof(t79_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ~ ( k4_complex2(A,B,C) != k5_numbers & k4_complex2(C,B,A) = k5_numbers ) ) ) ) )).
fof(t79_comput_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k3_finseq_2(k4_ordinal1)) & v1_funct_1(A) & v4_valued_0(A) & v2_margrel1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) ) => ( ( v2_comput_1(A) & k19_margrel1(A) = k5_numbers ) => k1_recdef_1(k7_comput_1(A,B,1),k12_finseq_1(k4_ordinal1,k5_numbers)) = k1_recdef_1(A,k1_xboole_0) ) ) ) )).
fof(t79_convex4,axiom,( ! [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) ) => ! [B] : ( m1_convex4(B,A) => ~ ( v3_convex4(B,A) & B = k2_convex4(A) ) ) ) )).
fof(t79_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ( ~ r2_hidden(D,k24_qc_lang1(A,C)) => ( v2_cqc_the1(k8_cqc_lang(A,k11_cqc_lang(A,D,B),C),A) <=> v2_cqc_the1(k12_cqc_lang(A,D,k8_cqc_lang(A,B,C)),A) ) ) ) ) ) ) )).
fof(t79_csspace,axiom,( ! [A] : ( l1_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) ) ) ) )).
fof(t79_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k16_sin_cos),D) ) & r2_hidden(B,k1_relset_1(k1_numbers,k26_sin_cos)) & r2_hidden(k6_xcmplx_0(B,A),k1_relset_1(k1_numbers,k26_sin_cos)) ) => k1_funct_1(k4_diff_1(C,A),B) = k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(1,k19_sin_cos(B)),k19_sin_cos(B)),k7_xcmplx_0(1,k19_sin_cos(k6_xcmplx_0(B,A)))),k19_sin_cos(k6_xcmplx_0(B,A))) ) ) ) ) )).
fof(t79_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : k7_enumset1(A,B,C,D,E,F,G,H,I) = k2_xboole_0(k1_enumset1(A,B,C),k4_enumset1(D,E,F,G,H,I)) )).
fof(t79_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => k5_euclid_8(k7_euclid(3,A,B),k7_euclid(3,C,D)) = k7_euclid(3,k7_euclid(3,k7_euclid(3,k5_euclid_8(A,C),k5_euclid_8(A,D)),k5_euclid_8(B,C)),k5_euclid_8(B,D)) ) ) ) ) )).
fof(t79_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( 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 & ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ~ ( r2_hidden(D,B) & ~ r2_hidden(D,C) ) ) ) ) ) ) )).
fof(t79_exchsort,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) & v1_finset_1(B) & v1_exchsort(B) & v2_exchsort(B,k5_numbers) ) => ( B != k1_xboole_0 => r2_hidden(k4_exchsort(B),A) ) ) )).
fof(t79_facirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k15_facirc_1(A,B,C),k18_facirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t79_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_lattices(k10_filter_2(A,k6_filter_2(A,B))) = B ) ) )).
fof(t79_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( C = k5_relat_1(B,k2_finseq_1(A)) => r1_xxreal_0(k3_finseq_1(C),k3_finseq_1(B)) ) ) ) ) )).
fof(t79_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( m1_subset_1(F,B) => ! [G] : ( ( 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] : ( m2_finseq_1(H,B) => ( H = k10_finseq_1(E,F) => k5_funcop_1(G,D,H) = k10_finseq_1(k2_binop_1(A,B,C,G,D,E),k2_binop_1(A,B,C,G,D,F)) ) ) ) ) ) ) ) ) ) )).
fof(t79_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : ( k1_finseq_3(k10_finseq_1(A,B),C) = k9_finseq_1(A) => ( A = B | ( ~ r2_hidden(A,C) & r2_hidden(B,C) ) ) ) )).
fof(t79_finseq_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ( k7_partfun1(A,k10_finseq_4(A,B,C,D,E,F),1) = B & k7_partfun1(A,k10_finseq_4(A,B,C,D,E,F),2) = C & k7_partfun1(A,k10_finseq_4(A,B,C,D,E,F),3) = D & k7_partfun1(A,k10_finseq_4(A,B,C,D,E,F),4) = E & k7_partfun1(A,k10_finseq_4(A,B,C,D,E,F),5) = F ) ) ) ) ) ) ) )).
fof(t79_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k4_finseq_5(A,k6_finseq_1(A)) = k6_finseq_1(A) ) )).
fof(t79_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => k4_finseq_4(k2_finseq_5(A,C,B),B) = 1 ) ) ) )).
fof(t79_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( v1_funct_1(C) & v1_funct_2(C,A,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [D] : ( ( 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(k6_finseqop(B,C,D)) & v1_funct_2(k6_finseqop(B,C,D),k2_zfmisc_1(A,A),A) & m1_subset_1(k6_finseqop(B,C,D),k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),A))) ) ) ) ) ) )).
fof(t79_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => k2_flang_2(A,B) = k1_flang_2(A,B,k5_numbers,1) ) )).
fof(t79_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => k6_flang_1(A,k2_flang_3(A,B),k2_flang_2(A,B)) = k6_flang_1(A,k2_flang_2(A,B),k2_flang_3(A,B)) ) )).
fof(t79_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : k3_funct_1(k7_funcop_1(A,B)) = B ) )).
fof(t79_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => k7_relat_1(C,k3_xboole_0(A,k8_relat_1(C,B))) = k3_xboole_0(k7_relat_1(C,A),B) ) )).
fof(t79_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( r1_partfun1(C,D) => ( ( B = k1_xboole_0 & A != k1_xboole_0 ) | r2_hidden(D,k5_partfun1(A,B,C)) ) ) ) ) )).
fof(t79_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k7_relat_1(k9_funct_3(k9_xtuple_0(A),k10_xtuple_0(A)),A) = k9_xtuple_0(A) ) )).
fof(t79_funct_4,axiom,( ! [A] : ! [B] : ! [C] : k17_funcop_1(A,B,C) = k16_funcop_1(k4_tarski(A,B),C) )).
fof(t79_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => r1_funct_8(A,k1_numbers,k1_numbers,k41_valued_1(k1_numbers,k1_numbers,k16_sin_cos)) ) )).
fof(t79_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_subset_1(C,u1_struct_0(k7_fvaluat1(A,B))) & 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)))) ) => r1_tarski(C,k8_fvaluat1(A,B)) ) ) ) ) )).
fof(t79_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k3_group_4(A,k3_finseq_4(u1_struct_0(A),B,C,D)) = k8_group_1(A,k8_group_1(A,B,C),D) ) ) ) ) )).
fof(t79_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(A,u1_struct_0(k31_gfacirc1(A,B,C))) & r2_hidden(B,u1_struct_0(k31_gfacirc1(A,B,C))) & r2_hidden(C,u1_struct_0(k31_gfacirc1(A,B,C))) & r2_hidden(k4_tarski(k10_finseq_1(A,B),k3_twoscomp),u1_struct_0(k31_gfacirc1(A,B,C))) & r2_hidden(k4_tarski(k10_finseq_1(B,C),k3_gfacirc1),u1_struct_0(k31_gfacirc1(A,B,C))) & r2_hidden(k4_tarski(k10_finseq_1(C,A),k4_twoscomp),u1_struct_0(k31_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(k31_gfacirc1(A,B,C))) ) )).
fof(t79_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(B)) => ( C = D => ( k26_glib_000(B,D) = k9_subset_1(k7_glib_000(A),k26_glib_000(A,C),k25_glib_000(A,B)) & k27_glib_000(B,D) = k9_subset_1(k7_glib_000(A),k27_glib_000(A,C),k25_glib_000(A,B)) & k28_glib_000(B,D) = k9_subset_1(k7_glib_000(A),k28_glib_000(A,C),k25_glib_000(A,B)) ) ) ) ) ) ) )).
fof(t79_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => r1_relset_1(k4_ordinal1,k7_glib_000(A),k12_glib_001(A,k8_glib_001(A,B,1,C)),k12_glib_001(A,B)) ) ) ) )).
fof(t79_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( v1_group_3(C,A) & m1_group_2(C,A) ) => ! [D] : ( ( v1_group_3(D,A) & m1_group_2(D,A) ) => ~ ( m1_group_2(C,D) & ! [E] : ( ( v15_algstr_0(E) & v1_group_3(E,A) & m1_group_2(E,A) ) => ! [F] : ( ( v15_algstr_0(F) & v1_group_3(F,A) & m1_group_2(F,A) ) => ~ ( u1_struct_0(E) = k4_group_11(A,C,B) & u1_struct_0(F) = k4_group_11(A,D,B) & r1_tarski(k4_group_11(A,C,E),k4_group_11(A,C,F)) ) ) ) ) ) ) ) ) )).
fof(t79_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( 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) & ! [D] : ( ( v15_algstr_0(D) & m1_group_2(D,A) ) => u1_struct_0(D) != k2_group_2(A,k8_group_2(A,B),k8_group_2(A,C)) ) ) ) ) ) )).
fof(t79_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_group_3(A,k8_group_2(A,k7_group_2(A)),B) = a_2_0_group_3(A,B) ) ) )).
fof(t79_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ( m1_group_2(B,k10_group_5(A)) => ( v1_group_3(B,A) & m1_group_2(B,A) ) ) ) ) )).
fof(t79_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(k5_group_6(A,k9_group_6(A,B,C))),u1_struct_0(k10_group_6(A,B,C))) & v1_group_6(D,k5_group_6(A,k9_group_6(A,B,C)),k10_group_6(A,B,C)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_group_6(A,k9_group_6(A,B,C))),u1_struct_0(k10_group_6(A,B,C))))) & v3_funct_2(D,u1_struct_0(k5_group_6(A,k9_group_6(A,B,C))),u1_struct_0(k10_group_6(A,B,C))) & r1_funct_2(u1_struct_0(A),u1_struct_0(B),u1_struct_0(A),u1_struct_0(k10_group_6(A,B,C)),C,k1_partfun1(u1_struct_0(A),u1_struct_0(k5_group_6(A,k9_group_6(A,B,C))),u1_struct_0(k5_group_6(A,k9_group_6(A,B,C))),u1_struct_0(k10_group_6(A,B,C)),k8_group_6(A,k9_group_6(A,B,C)),D)) ) ) ) ) )).
fof(t79_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( m1_group_9(D,A,B) => ! [E] : ( ( v2_group_9(E,A) & m1_group_9(E,A,B) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(B),u1_struct_0(C)) & v1_group_6(F,B,C) & v7_group_9(F,A,B,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)))) ) => ~ ( D = k13_group_9(A,B,C,F) & ! [G] : ( ( v2_group_9(G,A) & m1_group_9(G,A,C) ) => ~ ( u1_struct_0(G) = k7_relset_1(u1_struct_0(B),u1_struct_0(C),F,u1_struct_0(E)) & k8_relset_1(u1_struct_0(B),u1_struct_0(C),F,u1_struct_0(G)) = u1_struct_0(k19_group_9(A,B,E,D)) & ( ( v2_funct_2(F,u1_struct_0(C)) & v4_group_9(E,A,B) ) => v4_group_9(G,A,C) ) ) ) ) ) ) ) ) ) )).
fof(t79_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v7_algstr_0(A) & v4_rlvect_1(A) & v5_vectsp_1(A) & v1_algstr_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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))) ) => r1_tarski(k14_ideal_1(A,B,C),k13_ideal_1(A,B,C)) ) ) ) )).
fof(t79_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)) => k2_integra5(A,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)) = k5_numbers ) ) )).
fof(t79_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ( v10_intpro_1(A) => v8_intpro_1(A) ) ) )).
fof(t79_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & ~ r1_xxreal_0(k18_euclid(B),k5_numbers) & ~ r1_xxreal_0(k18_euclid(C),k5_numbers) & ~ r1_xxreal_0(k7_xcmplx_0(k17_euclid(C),k12_euclid(C)),k7_xcmplx_0(k17_euclid(B),k12_euclid(B))) & ? [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) & ? [E] : ( 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(k7_xcmplx_0(k17_euclid(E),k12_euclid(E)),k7_xcmplx_0(k17_euclid(D),k12_euclid(D))) ) ) ) ) ) ) )).
fof(t79_jgraph_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( r1_jordan17(k1_sppol_2(k4_xcmplx_0(1),1,k4_xcmplx_0(1),1),A,B,C,D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(2))))) ) => ! [F] : ( ( 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))))) ) => ~ ( v5_pre_topc(E,k5_topmetr,k15_euclid(2)) & v2_funct_1(E) & v5_pre_topc(F,k5_topmetr,k15_euclid(2)) & v2_funct_1(F) & k1_funct_1(E,k5_numbers) = A & k1_funct_1(E,1) = C & k1_funct_1(F,k5_numbers) = B & k1_funct_1(F,1) = D & r1_tarski(k2_relset_1(u1_struct_0(k15_euclid(2)),E),k2_jgraph_6(k4_xcmplx_0(1),1,k4_xcmplx_0(1),1)) & r1_tarski(k2_relset_1(u1_struct_0(k15_euclid(2)),F),k2_jgraph_6(k4_xcmplx_0(1),1,k4_xcmplx_0(1),1)) & r1_xboole_0(k2_relset_1(u1_struct_0(k15_euclid(2)),E),k2_relset_1(u1_struct_0(k15_euclid(2)),F)) ) ) ) ) ) ) ) ) )).
fof(t79_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) = E & k18_euclid(C) = H & k17_euclid(D) = F & r1_xxreal_0(G,k18_euclid(A)) & ~ r1_xxreal_0(k18_euclid(B),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_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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t79_jordan,axiom,( ! [A] : ( ( v2_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_jordan24(2,A,k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) => ( k18_pscomp_1(A) = k19_euclid(k4_xcmplx_0(1),k5_numbers) & k19_pscomp_1(A) = k19_euclid(k4_xcmplx_0(1),k5_numbers) ) ) ) )).
fof(t79_jordan2c,axiom,( ! [A] : ( ( ~ 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)))) ) => ( k2_goboard9(k1_sprect_1(A)) = k2_jordan2c(2,k3_topreal1(2,k1_sprect_1(A))) & k3_goboard9(k1_sprect_1(A)) = k1_jordan2c(2,k3_topreal1(2,k1_sprect_1(A))) ) ) )).
fof(t79_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( v2_matrix10(B) => r1_matrix10(C,k5_matrix10(A,C,B)) ) ) ) ) )).
fof(t79_matrix13,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ( r1_tarski(k2_zfmisc_1(C,D),k2_matrix_0(B)) => r1_xxreal_0(k8_matrix13(A,k6_matrix13(u1_struct_0(A),B,C,D)),k8_matrix13(A,B)) ) ) ) ) ) )).
fof(t79_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => k7_matrixr2(A,k4_matrixr2(A)) = k4_matrixr2(A) ) )).
fof(t79_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r2_hidden(C,A) & r2_hidden(D,B) ) => r2_hidden(k4_xxreal_3(C,D),k12_member_1(A,B)) ) ) ) ) ) )).
fof(t79_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_partfun1(C,u1_struct_0(B)) ) => ! [D] : ( v7_ordinal1(D) => k6_memstr_0(A,B,C) = k6_memstr_0(A,B,k1_funct_4(C,k7_memstr_0(A,B,D))) ) ) ) ) )).
fof(t79_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( v6_supinf_2(D) => ( ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ~ ( E = k1_relset_1(A,D) & r1_mesfunc1(A,B,D,E) ) ) | r1_xxreal_0(k5_numbers,k6_mesfunc5(A,B,C,D)) ) ) ) ) ) ) )).
fof(t79_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( ( r2_hidden(k1_relset_1(A,C),B) & r2_hidden(k1_relset_1(A,D),B) ) => r2_hidden(k1_relset_1(A,k3_valued_1(A,k1_numbers,k1_numbers,C,D)),B) ) ) ) ) ) )).
fof(t79_mmlquery,axiom,( ! [A] : ( l1_mmlquery(A) => ! [B] : ( m2_finseq_1(B,u1_mmlquery(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( B = k10_finseq_1(C,D) => k32_mmlquery(A,B) = k15_mmlquery(u1_struct_0(A),k31_mmlquery(A,C),k31_mmlquery(A,D)) ) ) ) ) ) )).
fof(t79_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k25_modelc_2(A)) => k29_modelc_2(A,B,k5_numbers) = B ) ) )).
fof(t79_monoid_0,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k17_monoid_0(A))) => k2_group_1(k17_monoid_0(A),B) = k2_funct_1(B) ) )).
fof(t79_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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) & r9_ncfcont1(B,A,C,k1_relset_1(u1_struct_0(B),C)) ) => v1_ncfcont1(k2_relset_1(u1_struct_0(A),C),A) ) ) ) ) )).
fof(t79_newton,axiom,( ~ v1_finset_1(k8_newton) )).
fof(t79_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v11_o_ring_1(B,A) & v11_o_ring_1(C,A) ) => v13_o_ring_1(k6_algstr_0(A,B,C),A) ) ) ) ) )).
fof(t79_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r1_relat_2(A,B) => r1_relat_2(k2_relat_1(A),B) ) ) )).
fof(t79_partfun1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r1_tarski(k10_xtuple_0(C),k9_xtuple_0(A)) & r1_tarski(k10_xtuple_0(C),k9_xtuple_0(B)) & r1_partfun1(A,B) ) => k3_relat_1(C,A) = k3_relat_1(C,B) ) ) ) ) )).
fof(t79_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => r6_pboole(A,k4_pboole(A,B,k2_pboole(A,C,D)),k3_pboole(A,k4_pboole(A,B,C),k4_pboole(A,B,D))) ) ) ) )).
fof(t79_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r4_pdiff_5(A,B) => r1_fcont_1(k1_pdiff_2(3,1,k1_pdiff_3(2,3,A),B),k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(1,3),B)) ) ) ) )).
fof(t79_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ( ( r5_pdiff_9(A,E,B,D) & r1_xxreal_0(C,B) ) => r5_pdiff_9(A,E,C,D) ) ) ) ) ) )).
fof(t79_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(B,1) & ~ r1_xxreal_0(k2_xcmplx_0(k7_polyform(A),2),B) & k1_funct_1(k28_polyform(A),B) != k1_funct_1(k29_polyform(A),k6_xcmplx_0(B,1)) ) ) ) )).
fof(t79_pre_poly,axiom,( ! [A] : ! [B] : ( ( 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 => r6_pboole(A,B,k16_pre_poly(A)) ) ) )).
fof(t79_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(A,k5_numbers) => k6_prepower(k7_xcmplx_0(1,A),B) = k7_xcmplx_0(1,k6_prepower(A,B)) ) ) ) )).
fof(t79_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,A) & v1_funct_1(E) & v1_partfun1(E,A) ) => ( v2_relat_1(B) => ( ( ~ r2_pboole(A,k6_pboole(A,B,C),k6_pboole(A,D,E)) & ~ r2_pboole(A,k6_pboole(A,C,B),k6_pboole(A,E,D)) ) | r2_pboole(A,C,E) ) ) ) ) ) ) )).
fof(t79_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( r2_qc_lang2(A,B,k12_qc_lang1(A)) <=> B = k12_qc_lang1(A) ) ) ) )).
fof(t79_quatern3,axiom,( k2_quatern3(k1_quatern2) = k5_numbers )).
fof(t79_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => r1_xxreal_0(k28_quaterni(k22_quaterni(A,B)),k2_xcmplx_0(k28_quaterni(A),k28_quaterni(B))) ) ) )).
fof(t79_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => r1_tarski(k10_xtuple_0(k6_relat_1(A,B)),A) ) )).
fof(t79_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_afinsq_1(C))) => ! [F] : ( ( ~ v2_struct_0(F) & l1_rewrite3(F,E) ) => ( r1_rewrite1(k1_rewrite3(C,E,F),k4_tarski(A,k3_flang_1(C,D)),k4_tarski(B,k2_flang_1(C))) => ( r2_hidden(k2_flang_1(C),k10_xtuple_0(k9_xtuple_0(u1_rewrite3(E,F)))) | r2_hidden(k4_tarski(k4_tarski(A,k3_flang_1(C,D)),k4_tarski(B,k2_flang_1(C))),k1_rewrite3(C,E,F)) ) ) ) ) ) ) )).
fof(t79_rfunct_1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) ) => ( ( ( v2_seq_2(k5_relat_1(C,A)) & r1_xxreal_0(k5_numbers,B) ) => v2_seq_2(k5_relat_1(k24_valued_1(C,B),A)) ) & ( ( v2_seq_2(k5_relat_1(C,A)) & r1_xxreal_0(B,k5_numbers) ) => v1_seq_2(k5_relat_1(k24_valued_1(C,B),A)) ) ) ) ) )).
fof(t79_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( v1_finset_1(k1_relset_1(A,k2_partfun1(A,k1_numbers,B,D))) & k1_relset_1(A,k2_partfun1(A,k1_numbers,B,D)) = k1_relset_1(A,k2_partfun1(A,k1_numbers,C,D)) ) => k21_rfunct_3(A,k47_valued_1(A,k1_numbers,k1_numbers,B,C),D) = k6_xcmplx_0(k21_rfunct_3(A,B,D),k21_rfunct_3(A,C,D)) ) ) ) ) )).
fof(t79_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_seq_2(B) & v4_partfun3(B) & v2_seq_2(C) & v4_partfun3(C) ) => r1_xxreal_0(k3_xcmplx_0(k1_funct_1(k3_rinfsup1(B),A),k1_funct_1(k3_rinfsup1(C),A)),k1_funct_1(k3_rinfsup1(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C)),A)) ) ) ) ) )).
fof(t79_rlaffin1,axiom,( ! [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) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( ( v1_rlaffin1(B,A) & r1_tarski(k4_rlaffin1(A,B),k4_rlaffin1(A,C)) ) => r1_xxreal_0(k5_card_1(B),k5_card_1(C)) ) ) ) ) )).
fof(t79_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_rlsub_1(D,A) => ! [E] : ( m2_rlsub_1(E,A,D) => ~ ( r2_hidden(B,E) & r2_hidden(C,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_struct_0(D,F) & k3_rlvect_1(A,B,F) = C ) ) ) ) ) ) ) ) )).
fof(t79_rlvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) )).
fof(t79_rvsum_1,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k4_finseq_2(k5_numbers,k1_numbers)) => k18_rvsum_1(A) = k5_numbers ) )).
fof(t79_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [D] : ( ( 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(k5_numbers)) = 1 => ( r4_scmfsa7b(C,D) | ( r5_scmfsa7b(k2_scmfsa8c(D,C),B,A) & r6_scmfsa7b(k2_scmfsa8c(D,C),B,A) ) ) ) ) ) ) ) )).
fof(t79_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ~ v2_extpro_1(k13_scmfsa_2(A,B),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(t79_scmpds_2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_compos_1(k1_scmpds_2)) => ( k2_compos_0(u1_compos_1(k1_scmpds_2),B) = k5_numbers => k2_extpro_1(2,k1_scmpds_2,B,A) = A ) ) ) )).
fof(t79_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ( ( r1_xxreal_0(k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),E)),k5_numbers) & r1_scmpds_6(C,B,A) & r2_scmpds_6(C,B,A) ) => ( r1_scmpds_6(k8_scmpds_6(D,E,C),B,A) & r2_scmpds_6(k8_scmpds_6(D,E,C),B,A) ) ) ) ) ) ) ) )).
fof(t79_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( ( v7_scmyciel(B,A) & m1_eqrel_1(B,k3_tarski(A)) ) => ( v10_scmyciel(B,k6_scmyciel(A)) & m1_eqrel_1(B,k3_tarski(k6_scmyciel(A))) ) ) ) )).
fof(t79_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_semi_af1(A,B,B,C) = C => B = C ) ) ) ) )).
fof(t79_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => k13_seq_4(A,B,k17_seq_4(A,C,B)) = C ) ) ) )).
fof(t79_setlim_1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(C) => k3_kurato_0(A,C) = k1_kurato_0(A,C) ) ) ) )).
fof(t79_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_kurato_0(C,A) => k3_kurato_0(A,k7_setlim_2(A,C,B)) = k7_subset_1(A,B,k3_kurato_0(A,C)) ) ) ) )).
fof(t79_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k5_sheffer1(A,k5_sheffer1(A,D,k5_sheffer1(A,k5_sheffer1(A,C,C),C)),k5_sheffer1(A,B,k5_sheffer1(A,B,B))) = D ) ) ) ) )).
fof(t79_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( r2_hidden(A,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) & r1_xxreal_0(k1_funct_1(k18_sin_cos,A),k5_numbers) ) ) )).
fof(t79_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,B) & k2_xcmplx_0(k1_square_1(A),k1_square_1(B)) = 1 ) => k19_sin_cos(k2_sin_cos6(A)) = B ) ) ) )).
fof(t79_sin_cos9,axiom,( v3_rcomp_1(k1_relset_1(k1_numbers,k1_sin_cos9)) )).
fof(t79_sincos10,axiom,( v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k3_sincos10,k7_relset_1(k1_numbers,k1_numbers,k2_fdiff_9,k3_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers)))) )).
fof(t79_sprect_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => k22_pscomp_1(k3_topreal1(2,k1_sprect_1(A))) = k12_pscomp_1(A) ) )).
fof(t79_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),C))) ) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ( ( ! [G] : ( m2_subset_1(G,k2_qc_lang1(A),k3_qc_lang1(A)) => ( r2_hidden(G,k9_xtuple_0(F)) => k1_funct_1(F,G) = k3_funct_2(k3_qc_lang1(A),C,D,G) ) ) & r1_xboole_0(k1_relset_1(k3_qc_lang1(A),E),k9_xtuple_0(F)) ) => ! [G] : ( m2_subset_1(G,k2_qc_lang1(A),k3_qc_lang1(A)) => ( r2_hidden(G,k6_subset_1(k9_xtuple_0(F),k6_domain_1(k3_qc_lang1(A),B))) => k1_funct_1(k5_relat_1(F,k6_subset_1(k9_xtuple_0(F),k6_domain_1(k3_qc_lang1(A),B))),G) = k3_funct_2(k3_qc_lang1(A),C,k1_sublemma(A,C,D,E),G) ) ) ) ) ) ) ) ) ) )).
fof(t79_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v3_tdlat_2(B,A) => v1_tdlat_2(B,A) ) ) ) )).
fof(t79_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_pre_topc(A,B)))) ) ) )).
fof(t79_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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_tsep_1(D,C) & m1_pre_topc(D,C) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => ( F = G => ( r1_tmap_1(C,B,E,F) <=> r1_tmap_1(D,B,k3_tmap_1(A,B,C,D,E),G) ) ) ) ) ) ) ) ) ) ) )).
fof(t79_topreal6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( v9_rltopsp1(A,k15_euclid(2)) => k8_pscomp_1(A) = k8_pscomp_1(k2_pre_topc(k15_euclid(2),A)) ) ) )).
fof(t79_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) & v4_pre_topc(C,A) ) => v4_pre_topc(D,B) ) ) ) ) ) )).
fof(t79_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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] : ( ( 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(D,A) & v6_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) ) ) ) ) ) ) )).
fof(t79_trees_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v5_trees_3(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) ) => ( ( r2_hidden(B,k10_xtuple_0(A)) & ! [C] : ( ( ~ v1_xboole_0(C) & v1_finset_1(C) & v1_trees_1(C) ) => ( r2_hidden(C,k10_xtuple_0(A)) => r1_xxreal_0(k6_trees_1(C),k6_trees_1(B)) ) ) ) => k6_trees_1(k11_trees_3(A)) = k1_nat_1(k6_trees_1(B),1) ) ) ) )).
fof(t79_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( m1_pre_topc(B,C) => r4_tsep_1(A,B,C) ) ) ) ) )).
fof(t79_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v1_valued_2(D) => ! [E] : ( v1_valued_2(E) => ! [F] : ( v1_valued_2(F) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,D))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(B,E))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(C,F))) ) => k79_valued_2(k3_xboole_0(A,B),C,k2_valued_2(k3_xboole_0(k1_valued_2(D),k1_valued_2(E))),F,k73_valued_2(A,B,D,E,G,H),I) = k73_valued_2(A,k3_xboole_0(B,C),D,k2_valued_2(k3_xboole_0(k1_valued_2(E),k1_valued_2(F))),G,k79_valued_2(B,C,E,F,H,I)) ) ) ) ) ) ) )).
fof(t79_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_vectsp_4(E,A,B) => ! [F] : ( m2_vectsp_4(F,A,B,E) => ~ ( r2_hidden(C,F) & r2_hidden(D,F) & ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ~ ( r1_struct_0(E,G) & k5_algstr_0(B,C,G) = D ) ) ) ) ) ) ) ) ) )).
fof(t79_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( ( v9_waybel_1(A) & v1_yellow_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r4_waybel_1(A,k7_waybel_1(A,B),a_2_2_waybel_1(A,B)) ) ) ) )).
fof(t79_xboole_1,axiom,( ! [A] : ! [B] : r1_xboole_0(k4_xboole_0(A,B),B) )).
fof(t79_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k5_xboolean(A,k10_xboolean(A,B)) = k5_xboolean(A,B) ) ) )).
fof(t79_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k7_xcmplx_0(A,k7_xcmplx_0(B,C)) = k3_xcmplx_0(A,k7_xcmplx_0(C,B)) ) ) ) )).
fof(t79_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(C,k3_xcmplx_0(A,B)) => ( r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(k7_xcmplx_0(C,B),A) ) ) ) ) ) )).
fof(t79_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(D,C) & k4_xxreal_1(C,D) = k1_xxreal_1(A,B) ) ) ) ) ) )).
fof(t79_xxreal_2,axiom,( ! [A] : ( ( v2_membered(A) & ~ v1_xxreal_2(A) & ~ v2_xxreal_2(A) & v6_xxreal_2(A) ) => ? [B] : ( v1_xxreal_0(B) & ? [C] : ( v1_xxreal_0(C) & r1_xxreal_0(B,C) & A = k4_xxreal_1(B,C) ) ) ) )).
fof(t79_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r1_xxreal_0(A,B) => ( r1_xxreal_0(C,k5_numbers) | r1_xxreal_0(k6_xxreal_3(A,C),k6_xxreal_3(B,C)) ) ) ) ) ) )).
fof(t79_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( r2_zf_lang(A,B) => r1_tarski(k29_zf_lang(A),k29_zf_lang(B)) ) ) ) )).
fof(t79_zf_lang1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( ~ v1_xboole_0(B) => r2_zf_model(B,k4_zf_lang(A,A)) ) ) )).
fof(t79_zfmisc_1,axiom,( ! [A] : ! [B] : ( ! [C] : ( r2_hidden(C,A) => r1_xboole_0(C,B) ) => r1_xboole_0(k3_tarski(A),B) ) )).
fof(t79_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m2_zmodul01(C,A,B) => ( v7_zmodul01(C,A) <=> C = u1_struct_0(B) ) ) ) ) )).
fof(t7_abcmiz_0,axiom,( ! [A] : ( l2_abcmiz_0(A) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( C = D => k2_abcmiz_0(A,C) = k2_abcmiz_0(B,D) ) ) ) ) ) ) )).
fof(t7_abcmiz_1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k3_card_3(u3_msualg_1(A,k1_msafree3(A,B)))) => ~ ( ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ~ ( C = k1_trees_4(k4_tarski(E,D)) & r2_hidden(E,k1_funct_1(B,D)) ) ) & ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( m2_finseq_1(E,k3_card_3(u3_msualg_1(A,k1_msafree3(A,B)))) => ~ ( C = k4_trees_4(k4_tarski(D,u1_struct_0(A)),E) & k3_finseq_1(E) = k3_finseq_1(k1_msualg_1(A,D)) & v6_trees_3(E) & m1_msaterm(E,A,k2_pboole(u1_struct_0(A),B,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_numbers))),k2_msaterm(A,k2_pboole(u1_struct_0(A),B,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_numbers))),D)) ) ) ) ) ) ) ) )).
fof(t7_abcmiz_a,axiom,( ! [A] : ( m1_subset_1(A,k2_abcmiz_1) => ( v7_ordinal1(k3_abcmiz_1(A)) => k3_abcmiz_1(A) = k5_numbers ) ) )).
fof(t7_abian,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(A),k8_eqrel_1(A,k2_abian(A,B))) => ! [D] : ( m2_subset_1(D,A,C) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => r2_hidden(k3_funct_2(A,A,k1_abian(A,B,E),D),C) ) ) ) ) ) )).
fof(t7_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => k9_complex1(k7_xcmplx_0(1,A)) = k7_xcmplx_0(1,k9_complex1(A)) ) )).
fof(t7_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r1_aff_1(A,B,C,D) & r1_aff_1(A,B,C,E) & r1_aff_1(A,B,C,F) ) => ( B = C | r1_aff_1(A,D,E,F) ) ) ) ) ) ) ) ) )).
fof(t7_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v11_aff_2(A) <=> v12_aff_2(A) ) ) )).
fof(t7_aff_3,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v6_aff_3(A) => v5_aff_3(A) ) ) )).
fof(t7_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) => ( ( r2_hidden(B,F) & r2_hidden(C,F) & r2_hidden(D,G) ) => ( ( ~ r5_aff_1(A,F,G) & ~ r5_aff_1(A,G,F) ) | B = C | ( ~ r2_analoaf(A,B,C,D,E) & ~ r2_analoaf(A,D,E,B,C) ) | r2_hidden(E,G) ) ) ) ) ) ) ) ) ) )).
fof(t7_afinsq_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ~ ( r2_hidden(A,B) & ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(C,k2_afinsq_1(B)) & A = k4_tarski(C,k1_funct_1(B,C)) ) ) ) ) )).
fof(t7_afinsq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ( ~ r1_xxreal_0(k1_afinsq_1(B),A) => k1_afinsq_1(k2_afinsq_2(B,A)) = k6_xcmplx_0(k1_afinsq_1(B),A) ) ) ) )).
fof(t7_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( r2_hidden(B,k1_afproj(A)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & B = C & v1_aff_1(C,A) ) ) ) )).
fof(t7_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_analoaf(A,B,C,D,E) => r2_analoaf(A,C,B,E,D) ) ) ) ) ) ) )).
fof(t7_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect01(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r2_analoaf(A,B,C,E,F) & r2_analoaf(A,B,C,C,D) & r2_analoaf(A,B,E,E,C) & r2_analoaf(A,B,F,F,C) ) => B = D ) ) ) ) ) ) ) )).
fof(t7_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) <=> ( r1_alg_1(A,B,C) & k2_relset_1(u1_struct_0(B),C) = u1_struct_0(B) & v2_funct_1(C) ) ) ) ) ) )).
fof(t7_algseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => k1_funct_1(k2_algseq_1(B,k4_struct_0(B)),A) = k4_struct_0(B) ) ) )).
fof(t7_algspec1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => k10_xtuple_0(k1_algspec1(A,B)) = k2_xboole_0(k6_subset_1(A,k9_xtuple_0(B)),k7_relat_1(B,A)) ) )).
fof(t7_algstr_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) <=> ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_algstr_0(A,B,k4_struct_0(A)) = B ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & k1_algstr_0(A,B,C) = k4_struct_0(A) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) ) )).
fof(t7_algstr_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_algstr_1(A) & v4_algstr_1(A) & v7_algstr_1(A) & v4_rlvect_1(A) & v2_vectsp_1(A) & v4_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_algstr_0(A,k1_algstr_2(A,C),B) = k1_algstr_2(A,k6_algstr_0(A,C,B)) ) ) ) )).
fof(t7_algstr_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_algstr_3(A) & l1_algstr_3(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B != k4_struct_0(A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & k1_algstr_3(A,E,B,C) = D ) ) ) ) ) ) )).
fof(t7_algstr_4,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( m1_algstr_4(B,A) => ( u1_struct_0(B) = u1_struct_0(A) => g3_algstr_0(u1_struct_0(B),u2_algstr_0(B)) = g3_algstr_0(u1_struct_0(A),u2_algstr_0(A)) ) ) ) )).
fof(t7_altcat_1,axiom,( ! [A] : 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))) )).
fof(t7_altcat_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,B) & v1_funct_1(D) & v1_partfun1(D,B) ) => ( ( r2_altcat_2(A,B,C,D) & r2_altcat_2(B,A,D,C) ) => C = D ) ) ) )).
fof(t7_altcat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_altcat_1(A,B,C)) => ! [F] : ( m1_subset_1(F,k1_altcat_1(A,C,D)) => ( ( v3_altcat_3(E,A,B,C) & v3_altcat_3(F,A,C,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 | ( v3_altcat_3(k5_altcat_1(A,B,C,D,E,F),A,B,D) & k1_altcat_3(A,B,D,k5_altcat_1(A,B,C,D,E,F)) = k5_altcat_1(A,D,C,B,k1_altcat_3(A,C,D,F),k1_altcat_3(A,B,C,E)) ) ) ) ) ) ) ) ) ) )).
fof(t7_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_altcat_1(A,B,C)) => ! [E] : ( m1_subset_1(E,k1_altcat_1(A,B,C)) => ( ( v9_altcat_3(D,A,B,C) & v9_altcat_3(E,A,B,C) ) => ( ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ v8_altcat_3(F,A) ) | D = E ) ) ) ) ) ) ) )).
fof(t7_altcat_5,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(k7_altcat_1(B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(k7_altcat_1(B))))) ) => ( ( r2_hidden(k4_card_3(C),B) & k4_card_3(C) = k1_xboole_0 ) => r6_pboole(A,k3_altcat_5(A,B,C),k7_funcop_1(A,k1_xboole_0)) ) ) ) )).
fof(t7_ami_2,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k3_ami_2,k4_ami_2))) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k1_ami_2,k2_ami_2) => k1_funct_1(k6_ami_2(A,B),C) = k1_funct_1(A,C) ) ) ) )).
fof(t7_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( v7_ordinal1(B) => ! [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(k7_card_1(2),k1_ami_3)) & v1_partfun1(C,u1_struct_0(k1_ami_3)) ) => ( k1_funct_1(k2_extpro_1(k7_card_1(2),k1_ami_3,k7_ami_3(B),C),k4_struct_0(k1_ami_3)) = B & k1_funct_1(k2_extpro_1(k7_card_1(2),k1_ami_3,k7_ami_3(B),C),A) = k1_funct_1(C,A) ) ) ) ) )).
fof(t7_ami_4,axiom,( ! [A] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(A,u1_struct_0(k1_ami_3)) & v5_memstr_0(A,k7_card_1(2),k1_ami_3,k5_numbers) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_ami_3)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ( r1_tarski(k1_ami_4,B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ( ( k1_funct_1(A,k10_ami_3(k5_numbers)) = C & k1_funct_1(A,k10_ami_3(1)) = D ) => ( r1_xxreal_0(C,k5_numbers) | r1_xxreal_0(D,k5_numbers) | k1_funct_1(k6_extpro_1(k7_card_1(2),k1_ami_3,B,A),k10_ami_3(k5_numbers)) = k3_int_2(C,D) ) ) ) ) ) ) ) )).
fof(t7_ami_5,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => ~ ( k2_compos_0(u1_compos_1(k1_ami_3),A) = 1 & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_ami_3)) ) => A != k2_ami_3(B,C) ) ) ) ) )).
fof(t7_ami_6,axiom,( ! [A] : ( m1_subset_1(A,k1_compos_0(u1_compos_1(k1_ami_3))) => ( A = 4 => k3_compos_0(u1_compos_1(k1_ami_3),A) = k1_tarski(k1_xboole_0) ) ) )).
fof(t7_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( k3_ami_wstd(A,B,C) = k3_ami_wstd(A,B,D) => C = D ) ) ) ) ) )).
fof(t7_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(k4_amistd_1(A))) => v2_amistd_1(B,A,k4_amistd_1(A)) ) ) )).
fof(t7_amistd_2,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( ( v3_amistd_2(C,A,B) & m1_subset_1(C,u1_compos_1(B)) ) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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)) ) => k2_xcmplx_0(k5_memstr_0(A,B,k2_extpro_1(A,B,C,E)),D) = k5_memstr_0(A,B,k2_extpro_1(A,B,k5_compos_0(u1_compos_1(B),C,D),k9_memstr_0(A,B,E,D))) ) ) ) ) ) )).
fof(t7_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ~ ( v1_zfmisc_1(k4_memstr_0(A,B,D)) & r2_hidden(D,k4_amistd_4(A,B,C)) ) ) ) ) ) )).
fof(t7_amistd_5,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_finset_1(C) & ~ v2_compos_1(C,B) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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(D,F) ) => ! [G] : ( ( v1_relat_1(G) & v4_relat_1(G,k4_ordinal1) & v5_relat_1(G,u1_compos_1(B)) & v1_funct_1(G) & v1_partfun1(G,k4_ordinal1) ) => ! [H] : ( ( v1_relat_1(H) & v4_relat_1(H,k4_ordinal1) & v5_relat_1(H,u1_compos_1(B)) & v1_funct_1(H) & v1_partfun1(H,k4_ordinal1) ) => ( ( r1_tarski(C,G) & r1_tarski(C,H) ) => ! [I] : ( v7_ordinal1(I) => ( k5_memstr_0(A,B,k5_extpro_1(A,B,G,E,I)) = k5_memstr_0(A,B,k5_extpro_1(A,B,H,F,I)) & k3_extpro_1(A,B,G,k5_extpro_1(A,B,G,E,I)) = k3_extpro_1(A,B,H,k5_extpro_1(A,B,H,F,I)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t7_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( r2_analmetr(A,B,C,D,E) => ( r2_analmetr(A,k1_rlvect_1(A,B,F),C,D,E) & r2_analmetr(A,B,k1_rlvect_1(A,C,G),D,E) ) ) ) ) ) ) ) ) ) )).
fof(t7_analoaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r1_analoaf(A,B,C,D,E) & B != C & D != E & ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( k1_rlvect_1(A,k5_algstr_0(A,C,B),F) = k1_rlvect_1(A,k5_algstr_0(A,E,D),G) & ~ r1_xxreal_0(F,k5_numbers) & ~ r1_xxreal_0(G,k5_numbers) ) ) ) ) ) ) ) ) ) )).
fof(t7_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_analmetr(A,C,D) => k1_analort(A,C,D,k1_analort(A,C,D,B)) = B ) ) ) ) ) )).
fof(t7_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( 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)) => ( r1_anproj_1(A,B,C) | v9_struct_0(B,A) | v9_struct_0(C,A) | ( D = F & E = G ) ) ) ) ) ) ) ) ) ) )).
fof(t7_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_anproj_1(A,B,C,D) & ~ r1_anproj_1(A,B,C) & r1_anproj_2(A,B,C,D) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => D != k3_rlvect_1(A,k1_rlvect_1(A,B,E),k1_rlvect_1(A,C,F)) ) ) ) ) ) ) ) )).
fof(t7_aofa_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( ( r1_tarski(k10_xtuple_0(A),k9_xtuple_0(A)) & r2_hidden(C,k5_aofa_000(A,B)) ) => r2_hidden(k1_funct_1(A,C),k5_aofa_000(A,B)) ) ) )).
fof(t7_aofa_a00,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( r2_hidden(D,k1_msafree4(A,C,B)) => m3_pboole(k2_aofa_a00(A,B,D),A,C) ) ) ) ) )).
fof(t7_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_aofa_a00(A,C,D,E) => ( v1_funct_1(k5_msualg_1(A,C,B)) & v1_funct_2(k5_msualg_1(A,C,B),k1_funct_1(k6_finseq_2(u1_struct_0(A),u3_msualg_1(A,B)),D),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),E)) & m1_subset_1(k5_msualg_1(A,C,B),k1_zfmisc_1(k2_zfmisc_1(k1_funct_1(k6_finseq_2(u1_struct_0(A),u3_msualg_1(A,B)),D),k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),E)))) & k3_msualg_1(A,C,B) = k1_funct_1(k6_finseq_2(u1_struct_0(A),u3_msualg_1(A,B)),D) & k4_msualg_1(A,C,B) = k1_msafree4(u1_struct_0(A),u3_msualg_1(A,B),E) ) ) ) ) ) ) )).
fof(t7_aofa_i00,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( 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))) ) <=> ( k9_xtuple_0(B) = k1_card_1(A) & k10_xtuple_0(B) = A & v2_funct_1(B) ) ) ) )).
fof(t7_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( k8_arytm_2(A,B) = k8_arytm_2(A,C) => ( A = k11_arytm_3 | B = C ) ) ) ) ) )).
fof(t7_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( r1_arytm_2(A,B) <=> r1_arytm_2(k7_arytm_2(A,C),k7_arytm_2(B,C)) ) ) ) ) )).
fof(t7_arytm_2,axiom,( v6_ordinal1(a_0_0_arytm_2) )).
fof(t7_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ( r2_arytm_3(B,A) <=> A = k9_ordinal3(B,k6_ordinal3(A,B)) ) ) ) )).
fof(t7_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_autalg_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_autalg_1(A))) => ! [D] : ( m2_funct_2(D,u1_struct_0(A),u1_struct_0(A),k1_autalg_1(A)) => ! [E] : ( m2_funct_2(E,u1_struct_0(A),u1_struct_0(A),k1_autalg_1(A)) => ( ( B = D & C = E ) => k6_algstr_0(k3_autalg_1(A),B,C) = k1_partfun1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),D,E) ) ) ) ) ) ) )).
fof(t7_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_funct_2(B,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) => ! [C] : ( m2_funct_2(C,u1_struct_0(A),u1_struct_0(A),k1_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),k1_autgroup(A)) ) ) ) )).
fof(t7_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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),C) ) ) ) ) )).
fof(t7_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => k1_bcialg_1(A,k1_bcialg_2(A,B,C,E),D) = k1_bcialg_2(A,k1_bcialg_1(A,B,D),C,E) ) ) ) ) ) )).
fof(t7_bcialg_3,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_bcialg_1(A,B,C) = B => k1_bcialg_1(A,C,B) = C ) ) ) ) ) )).
fof(t7_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_bcialg_1(A,B,C) => ( r1_bcialg_1(A,k1_bcialg_4(A,B,D),k1_bcialg_4(A,C,D)) & r1_bcialg_1(A,k1_bcialg_4(A,D,B),k1_bcialg_4(A,D,C)) ) ) ) ) ) ) )).
fof(t7_bcialg_5,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_5(A,B,C,k5_numbers,k5_numbers) = k1_bcialg_1(A,B,k1_bcialg_1(A,B,C)) ) ) ) )).
fof(t7_bcialg_6,axiom,( ! [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] : ( v7_ordinal1(B) => k3_bcialg_6(A,B,k4_struct_0(A)) = k4_struct_0(A) ) ) )).
fof(t7_bciideal,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k5_bcialg_1(A)) => ! [D] : ( m2_subset_1(D,u1_struct_0(A),k5_bcialg_1(A)) => ( m2_subset_1(C,u1_struct_0(A),k7_bcialg_1(A,D)) => k1_bcialg_1(A,B,C) = k1_bcialg_1(A,B,D) ) ) ) ) ) )).
fof(t7_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_bhsp_1(A,k4_algstr_0(A,B),C) = k2_bhsp_1(A,B,k4_algstr_0(A,C)) ) ) ) )).
fof(t7_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_bhsp_2(C,A) => v1_bhsp_2(k5_bhsp_1(A,C,B),A) ) ) ) ) )).
fof(t7_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_bhsp_2(C,A) & k1_bhsp_2(A,C) = B & r1_bhsp_3(A,C,D) ) => ( v1_bhsp_2(D,A) & k1_bhsp_2(A,D) = B ) ) ) ) ) ) )).
fof(t7_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_bhsp_4(B,A) & v1_bhsp_4(C,A) ) => ( v1_bhsp_4(k3_normsp_1(A,B,C),A) & k2_bhsp_4(A,k3_normsp_1(A,B,C)) = k5_algstr_0(A,k2_bhsp_4(A,B),k2_bhsp_4(A,C)) ) ) ) ) ) )).
fof(t7_bhsp_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ( ( r1_xxreal_0(1,k3_finseq_1(B)) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(D,k4_finseq_1(B)) ) => ( C = D | k1_funct_1(u1_bhsp_1(A),k4_tarski(k1_funct_1(B,C),k1_funct_1(B,D))) = k5_numbers ) ) ) ) ) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ( ( k4_finseq_1(B) = k4_finseq_1(C) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r2_hidden(D,k4_finseq_1(C)) => k1_funct_1(C,D) = k1_funct_1(u1_bhsp_1(A),k4_tarski(k1_funct_1(B,D),k1_funct_1(B,D))) ) ) ) => k2_bhsp_1(A,k1_finsop_1(u1_struct_0(A),B,u1_algstr_0(A)),k1_finsop_1(u1_struct_0(A),B,u1_algstr_0(A))) = k1_finsop_1(k1_numbers,C,k9_binop_2) ) ) ) ) ) )).
fof(t7_bhsp_6,axiom,( ! [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_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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_bhsp_6(B,A) => ! [C] : ( ( 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))) ) => ( v2_bhsp_6(C,A) => r1_bhsp_6(A,B,C) ) ) ) ) ) ) )).
fof(t7_bhsp_7,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_bhsp_6(B,A) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( ~ v1_xboole_0(D) & r1_tarski(D,B) & ! [E] : ( ( v1_finset_1(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( r1_tarski(D,E) & r1_tarski(E,B) & r1_xxreal_0(C,k9_complex1(k6_xcmplx_0(k2_bhsp_1(A,k2_bhsp_6(A,B),k2_bhsp_6(A,B)),k2_bhsp_1(A,k1_bhsp_6(A,E),k1_bhsp_6(A,E))))) ) ) ) ) ) ) ) ) ) )).
fof(t7_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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),k3_bilinear(A,B,C,D,k5_struct_0(A)),D) ) ) ) ) )).
fof(t7_binari_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => k1_binari_2(k1_nat_1(A,1)) = k9_binarith(A,1,k6_margrel1,k1_binari_2(A),k10_binarith(k6_margrel1,k7_margrel1)) ) )).
fof(t7_binari_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ( B = k5_euclid(A) => k6_binarith(A,k3_binarith(A,B)) = k6_xcmplx_0(k5_series_1(2,A),1) ) ) ) )).
fof(t7_binari_4,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ( B = k5_euclid(A) => k3_binari_2(A,B) = k5_numbers ) ) ) )).
fof(t7_binarith,axiom,( ! [A] : ( v1_xboolean(A) => k10_xboolean(k8_margrel1,A) = k3_xboolean(A) ) )).
fof(t7_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( k1_relset_1(k4_ordinal1,B) = k1_relset_1(k4_ordinal1,C) => k4_rlvect_1(A,k1_binom(A,B,C)) = k3_rlvect_1(A,k4_rlvect_1(A,B),k4_rlvect_1(A,C)) ) ) ) ) )).
fof(t7_binop_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ( v1_binop_1(B,A) => ( r3_binop_1(A,C,B) <=> r2_binop_1(A,C,B) ) ) ) ) )).
fof(t7_binop_2,axiom,( k4_binop_1(k1_numbers,k11_binop_2) = 1 )).
fof(t7_bintree1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( m1_trees_1(C,k13_trees_3(A,B)) => ( ( C = k1_xboole_0 => k1_trees_2(k13_trees_3(A,B),C) = k2_tarski(k8_finseq_1(k4_ordinal1,C,k14_trees_3(k5_numbers)),k8_finseq_1(k4_ordinal1,C,k14_trees_3(1))) ) & ! [D] : ( m1_trees_1(D,A) => ( C = k8_finseq_1(k4_ordinal1,k14_trees_3(k5_numbers),D) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ( r2_hidden(E,k1_trees_2(A,D)) <=> r2_hidden(k7_finseq_1(k14_trees_3(k5_numbers),E),k1_trees_2(k13_trees_3(A,B),C)) ) ) ) ) & ! [D] : ( m1_trees_1(D,B) => ( C = k8_finseq_1(k4_ordinal1,k14_trees_3(1),D) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ( r2_hidden(E,k1_trees_2(B,D)) <=> r2_hidden(k7_finseq_1(k14_trees_3(1),E),k1_trees_2(k13_trees_3(A,B),C)) ) ) ) ) ) ) ) ) )).
fof(t7_bintree2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ( ! [B] : ( m1_trees_1(B,A) => k1_trees_2(A,B) = k7_domain_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1)),k8_finseq_1(k4_ordinal1,B,k10_binarith(k4_ordinal1,k5_numbers)),k8_finseq_1(k4_ordinal1,B,k10_binarith(k4_ordinal1,1))) ) => v1_bintree1(A) ) ) )).
fof(t7_boole,axiom,( ! [A] : ! [B] : ~ ( r2_hidden(A,B) & v1_xboole_0(B) ) )).
fof(t7_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r2_boolealg(A,B,B) <=> B != k5_lattices(A) ) ) ) )).
fof(t7_boolmark,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(B)) ) => k7_partfun1(A,k8_finseq_1(A,B,C),D) = k7_partfun1(A,B,D) ) ) ) ) ) )).
fof(t7_bor_cant,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( v7_ordinal1(D) => k1_prob_2(A,B,k1_prob_3(A,k2_prob_1(A,C)),D) = k3_subset_1(A,k1_prob_2(A,B,k2_prob_3(A,C),D)) ) ) ) ) )).
fof(t7_borsuk_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => k1_tops_1(k2_borsuk_1(A,B),k3_borsuk_1(A,B,C,D)) = k3_borsuk_1(A,B,k1_tops_1(A,C),k1_tops_1(B,D)) ) ) ) ) )).
fof(t7_borsuk_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) => ! [D] : ( ( 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)))) ) => k8_relset_1(u1_struct_0(A),u1_struct_0(B),D,k5_setfam_1(u1_struct_0(B),C)) = k5_setfam_1(u1_struct_0(A),k6_funct_2(u1_struct_0(A),u1_struct_0(B),D,C)) ) ) ) ) )).
fof(t7_borsuk_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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))) => r1_funct_2(u1_struct_0(B),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(u1_struct_0(A),u1_struct_0(B)),k2_tops_2(u1_struct_0(k2_borsuk_1(k1_pre_topc(A,k6_domain_1(u1_struct_0(A),C)),B)),u1_struct_0(B),D),k14_funct_3(u1_struct_0(B),u1_struct_0(A),u1_struct_0(B),k6_struct_0(B,A,C),k3_struct_0(B))) ) ) ) ) ) )).
fof(t7_borsuk_4,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k5_topmetr))) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t7_borsuk_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( r5_zfmisc_1(A,B,C,D,E,F,G) => r5_zfmisc_1(G,A,B,C,D,E,F) ) )).
fof(t7_borsuk_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_topmetr)) => ( r1_xxreal_0(k7_xcmplx_0(1,2),A) => m1_subset_1(k6_xcmplx_0(A,k7_xcmplx_0(1,4)),u1_struct_0(k5_topmetr)) ) ) )).
fof(t7_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( k17_sin_cos(A) = k5_numbers & ! [B] : ( v1_int_1(B) => A != k3_xcmplx_0(k28_sin_cos,B) ) ) ) )).
fof(t7_brouwer,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_xreal_0(B) & ~ v3_xxreal_0(B) ) => ! [C] : ( ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(C))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(C))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(C))) => ! [G] : ( m1_subset_1(G,k1_euclid(C)) => ! [H] : ( m1_subset_1(H,k1_euclid(C)) => ! [I] : ( m1_subset_1(I,k1_euclid(C)) => ( ( G = D & H = E & I = F & m1_subset_1(D,u1_struct_0(k2_brouwer(C,F,B))) & m1_subset_1(E,u1_struct_0(k2_brouwer(C,F,B))) & A = k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(k22_rvsum_1(k5_algstr_0(k15_euclid(C),E,D),k5_algstr_0(k15_euclid(C),D,F))),k3_square_1(k6_xcmplx_0(k1_square_1(k22_rvsum_1(k5_algstr_0(k15_euclid(C),E,D),k5_algstr_0(k15_euclid(C),D,F))),k3_xcmplx_0(k18_rvsum_1(k11_euclid(C,k8_euclid(C,H,G))),k6_xcmplx_0(k18_rvsum_1(k11_euclid(C,k8_euclid(C,G,I))),k1_square_1(B)))))),k18_rvsum_1(k11_euclid(C,k8_euclid(C,H,G)))) ) => ( D = E | k3_brouwer(C,F,D,E,B) = k3_rlvect_1(k15_euclid(C),k1_rlvect_1(k15_euclid(C),D,k6_xcmplx_0(1,A)),k1_rlvect_1(k15_euclid(C),E,A)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t7_brouwer2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_convex1(B,k15_euclid(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ! [C] : ( ( v1_convex1(C,k15_euclid(A)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ~ ( v2_compts_1(B,k15_euclid(A)) & ~ v2_tops_1(B,k15_euclid(A)) & v2_compts_1(C,k15_euclid(A)) & ~ v2_tops_1(C,k15_euclid(A)) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(k1_pre_topc(k15_euclid(A),B)),u1_struct_0(k1_pre_topc(k15_euclid(A),C))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(A),B)),u1_struct_0(k1_pre_topc(k15_euclid(A),C))))) ) => ~ ( v3_tops_2(D,k1_pre_topc(k15_euclid(A),B),k1_pre_topc(k15_euclid(A),C)) & k7_relset_1(u1_struct_0(k1_pre_topc(k15_euclid(A),B)),u1_struct_0(k1_pre_topc(k15_euclid(A),C)),D,k2_tops_1(k15_euclid(A),B)) = k2_tops_1(k15_euclid(A),C) ) ) ) ) ) ) )).
fof(t7_bspace,axiom,( k3_rlvect_1(k2_bspace,k5_struct_0(k2_bspace),k5_struct_0(k2_bspace)) = k4_struct_0(k2_bspace) )).
fof(t7_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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,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)))) ) ) ) ) ) )).
fof(t7_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ( B = k2_tarski(C,D) => ( C = D | k5_bvfunc_2(A,C,B) = D ) ) ) ) ) ) )).
fof(t7_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ( B = k2_enumset1(C,D,E,F) => ( C = D | C = E | C = F | k5_bvfunc_2(A,C,B) = k2_partit1(A,k2_partit1(A,D,E),F) ) ) ) ) ) ) ) ) )).
fof(t7_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)),k9_bvfunc_1(A,C,k9_bvfunc_1(A,B,D))) ) ) ) ) )).
fof(t7_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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_bvfunc26(A,B,C)),k2_bvfunc_1(A,B,C)) ) ) ) )).
fof(t7_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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,B,C),D),k5_bvfunc_1(A,B,k5_bvfunc_1(A,C,D))) ) ) ) ) )).
fof(t7_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( m1_eqrel_1(D,A) => r2_funct_2(A,k6_margrel1,k6_bvfunc_2(A,k12_bvfunc_1(A),B,D),k12_bvfunc_1(A)) ) ) ) ) )).
fof(t7_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(E,A) => r1_bvfunc_1(A,k5_bvfunc_1(A,C,D),k5_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) )).
fof(t7_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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,k9_bvfunc_1(A,B,C),k9_bvfunc_1(A,C,B))) ) ) ) )).
fof(t7_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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,B),k12_bvfunc_1(A)) ) ) )).
fof(t7_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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,k5_bvfunc_1(A,B,C),D),k5_bvfunc_1(A,k9_bvfunc_1(A,B,D),k9_bvfunc_1(A,C,D))),k12_bvfunc_1(A)) ) ) ) ) )).
fof(t7_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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,C),D),k9_bvfunc_1(A,B,k9_bvfunc_1(A,C,D))) ) ) ) ) )).
fof(t7_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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,k5_bvfunc_1(A,B,C),k5_bvfunc_1(A,B,k1_bvfunc_1(A,C)))) ) ) ) )).
fof(t7_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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,k2_bvfunc_1(A,C,D)),k9_bvfunc_1(A,B,C)) ) ) ) ) )).
fof(t7_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ v2_struct_0(k12_funcsdom(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)) & v8_rlvect_1(k12_funcsdom(A)) & l1_rlvect_1(k12_funcsdom(A)) ) ) )).
fof(t7_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => k1_group_1(k3_c0sp2(A)) = k1_c0sp2(A,1) ) )).
fof(t7_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => k15_finseq_1(k2_partfun1(k4_ordinal1,k3_cqc_lang(A),k8_finseq_1(k3_cqc_lang(A),B,C),k1_relset_1(k4_ordinal1,B))) = k2_partfun1(k4_ordinal1,k3_cqc_lang(A),k8_finseq_1(k3_cqc_lang(A),B,C),k1_relset_1(k4_ordinal1,B)) ) ) ) )).
fof(t7_calcul_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => r1_tarski(k2_calcul_2(A,B),k2_finseq_1(k1_nat_1(A,B))) ) ) )).
fof(t7_cantor_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => u1_pre_topc(A) = k1_cantor_1(u1_struct_0(A),k2_cantor_1(u1_struct_0(A),u1_pre_topc(A))) ) )).
fof(t7_card_1,axiom,( ! [A] : ( v3_ordinal1(A) => r1_ordinal1(k1_card_1(A),A) ) )).
fof(t7_card_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( r2_wellord2(A,C) & r2_wellord2(B,D) ) => ( r2_wellord2(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) & k1_card_1(k2_zfmisc_1(A,B)) = k1_card_1(k2_zfmisc_1(C,D)) ) ) )).
fof(t7_card_3,axiom,( ! [A] : ! [B] : ( A != k1_xboole_0 => k3_card_3(k7_funcop_1(A,B)) = B ) )).
fof(t7_card_4,axiom,( ! [A] : ! [B] : ( ( v4_card_3(A) & v4_card_3(B) ) => v4_card_3(k2_zfmisc_1(A,B)) ) )).
fof(t7_card_5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( r1_tarski(B,A) => k1_card_1(B) = k1_card_1(k2_wellord2(k1_wellord2(B))) ) ) )).
fof(t7_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_card_fil(B,A) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ( ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( r2_hidden(D,C) <=> r2_hidden(k3_subset_1(A,D),B) ) ) => ( ~ r2_hidden(A,C) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => ( ( ( r2_hidden(D,C) & r2_hidden(E,C) ) => r2_hidden(k4_subset_1(A,D,E),C) ) & ( ( r2_hidden(D,C) & r1_tarski(E,D) ) => r2_hidden(E,C) ) ) ) ) ) ) ) ) ) )).
fof(t7_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => k1_card_1(a_1_0_card_fin(A)) = k7_newton(k5_card_1(A)) ) )).
fof(t7_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ~ ( v1_card_lar(B,A) & v1_xboole_0(B) ) ) ) )).
fof(t7_cardfin2,axiom,( ! [A] : ( v1_finset_1(A) => k2_cardfin2(A) = a_1_1_cardfin2(A) ) )).
fof(t7_cat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_cat_1(D,A,B,C) => ( ! [E] : ( m1_cat_1(E,A,B,C) => D = E ) => ( k2_cat_1(A,B,C) = k1_xboole_0 | k2_cat_1(A,B,C) = k1_tarski(D) ) ) ) ) ) ) )).
fof(t7_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m3_cat_2(B,A) => ! [C] : ( m1_subset_1(C,u4_struct_0(B)) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) )).
fof(t7_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u4_struct_0(C)) => ! [E] : ( m1_subset_1(E,u4_struct_0(C)) => r2_funct_2(k2_tarski(A,B),u1_struct_0(C),k3_cat_3(C,k2_tarski(A,B),k5_funct_4(u4_struct_0(C),A,B,D,E)),k5_funct_4(u1_struct_0(C),A,B,k4_graph_1(C,D),k4_graph_1(C,E))) ) ) ) )).
fof(t7_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k5_cat_4(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_cat_4(A,B))) => k2_cat_1(k5_cat_4(A,B),C,D) != k1_xboole_0 ) ) )).
fof(t7_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m3_cat_2(C,B) => ! [D] : ( m2_cat_1(D,A,B) => ( r1_tarski(k2_relset_1(u4_struct_0(B),D),u4_struct_0(C)) => m2_cat_1(D,A,C) ) ) ) ) ) )).
fof(t7_catalan1,axiom,( ! [A] : ( v7_ordinal1(A) => ~ r1_xxreal_0(4,k3_xcmplx_0(2,k6_xcmplx_0(2,k7_xcmplx_0(3,k1_nat_1(A,1))))) ) )).
fof(t7_catalan2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ( ( v1_catalan2(A) & v1_catalan2(B) ) => v1_catalan2(k1_catalan2(A,B)) ) ) ) )).
fof(t7_catalg_1,axiom,( ! [A] : ( ( v3_catalg_1(A) & l1_msualg_1(A) ) => ! [B] : ~ ( ( r2_hidden(B,u1_struct_0(A)) | r2_hidden(B,u4_struct_0(A)) ) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ~ ( B = k4_tarski(C,D) & r1_tarski(k10_xtuple_0(D),k4_catalg_1(A)) ) ) ) ) ) )).
fof(t7_cayldick,axiom,( ! [A] : ! [B] : ! [C] : ~ ( r2_hidden(A,k4_card_3(k6_afinsq_1(B,C))) & ! [D] : ! [E] : ~ ( r2_hidden(D,B) & r2_hidden(E,C) & A = k6_afinsq_1(D,E) ) ) )).
fof(t7_cayley,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k2_cayley(A))) => k2_group_1(k2_cayley(A),B) = k2_funct_1(B) ) )).
fof(t7_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_cc0sp1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_cc0sp1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_cc0sp1(A))) => ! [E] : ( ( 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] : ( ( 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] : ( ( 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 = k8_group_1(k3_cc0sp1(A),B,C) <=> ! [H] : ( m1_subset_1(H,A) => k3_funct_2(A,k2_numbers,G,H) = k3_xcmplx_0(k3_funct_2(A,k2_numbers,E,H),k3_funct_2(A,k2_numbers,F,H)) ) ) ) ) ) ) ) ) ) ) )).
fof(t7_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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(k19_valued_1(u1_struct_0(A),k2_numbers,k2_numbers,B,C)) & v1_funct_2(k19_valued_1(u1_struct_0(A),k2_numbers,k2_numbers,B,C),u1_struct_0(A),k2_numbers) & v1_cc0sp2(k19_valued_1(u1_struct_0(A),k2_numbers,k2_numbers,B,C),A) & m1_subset_1(k19_valued_1(u1_struct_0(A),k2_numbers,k2_numbers,B,C),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k2_numbers))) ) ) ) ) )).
fof(t7_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ! [C] : ( ( 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,A),k9_subset_1(k2_numbers,k1_relset_1(k2_numbers,B),k1_relset_1(k2_numbers,C))) => ( r2_relset_1(k4_ordinal1,k2_numbers,k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,A,k2_valued_1(k2_numbers,k2_numbers,k2_numbers,B,C)),k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,A,B),k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,A,C))) & r2_relset_1(k4_ordinal1,k2_numbers,k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,A,k46_valued_1(k2_numbers,k2_numbers,k2_numbers,B,C)),k46_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,A,B),k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,A,C))) & r2_relset_1(k4_ordinal1,k2_numbers,k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,A,k19_valued_1(k2_numbers,k2_numbers,k2_numbers,B,C)),k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,A,B),k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,A,C))) ) ) ) ) ) )).
fof(t7_cfdiff_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( m1_cfdiff_1(B,A) => r2_hidden(A,B) ) ) )).
fof(t7_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ! [C] : ( m2_funct_2(C,A,k2_numbers,k9_funct_2(A,k2_numbers)) => r2_funct_2(A,k2_numbers,k1_funcsdom(A,k2_numbers,k2_cfuncdom(A),B,C),k1_funcsdom(A,k2_numbers,k2_cfuncdom(A),C,B)) ) ) ) )).
fof(t7_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => k7_subset_1(A,k1_relset_1(A,k19_valued_1(A,k2_numbers,k2_numbers,B,C)),k8_relset_1(A,k2_numbers,k19_valued_1(A,k2_numbers,k2_numbers,B,C),k1_tarski(k5_numbers))) = k9_subset_1(A,k7_subset_1(A,k1_relset_1(A,B),k8_relset_1(A,k2_numbers,B,k1_tarski(k5_numbers))),k7_subset_1(A,k1_relset_1(A,C),k8_relset_1(A,k2_numbers,C,k1_tarski(k5_numbers)))) ) ) ) )).
fof(t7_cgames_1,axiom,( ! [A] : ( r2_hidden(A,k6_cgames_1(k4_cgames_1)) <=> A = k3_cgames_1 ) )).
fof(t7_chain_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ( r1_xboole_0(A,B) => ( ( v1_abian(k5_card_1(A)) <=> v1_abian(k5_card_1(B)) ) <=> v1_abian(k5_card_1(k2_xboole_0(A,B))) ) ) ) ) )).
fof(t7_chord,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v1_abian(A) ) => ~ ( r1_xxreal_0(A,4) & A != 1 & A != 3 ) ) )).
fof(t7_circcmb2,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r1_tarski(C,B) => ( v1_facirc_1(k4_xboole_0(B,C)) | k4_xboole_0(A,B) = k4_xboole_0(A,C) ) ) ) )).
fof(t7_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ( ( r1_xboole_0(k2_msafree2(A),k3_msafree2(B)) & r1_xboole_0(k2_msafree2(B),k3_msafree2(A)) ) => ! [C] : ( ( ~ v2_struct_0(C) & ~ v11_struct_0(C) & v2_msafree2(C) & l1_msualg_1(C) ) => ( C = k2_circcomb(A,B) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ( r2_circcomb(A,B,D,E) => ! [F] : ( ( v4_msualg_1(F,C) & v4_msafree2(F,C) & l3_msualg_1(F,C) ) => ( F = k3_circcomb(A,B,D,E) => ! [G] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(C,F))) => ! [H] : ( m1_subset_1(H,k4_card_3(u3_msualg_1(A,D))) => ! [I] : ( m1_subset_1(I,k4_card_3(u3_msualg_1(B,E))) => ( ( H = k5_relat_1(G,u1_struct_0(A)) & I = k5_relat_1(G,u1_struct_0(B)) & v1_circcmb3(H,A,D) & v1_circcmb3(I,B,E) ) => v1_circcmb3(G,C,F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t7_circcomb,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_funct_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_msafree2(C) & l1_msualg_1(C) ) => ( ( r1_tarski(u2_msualg_1(B),A) & r1_tarski(u2_msualg_1(C),A) ) => v2_msafree2(k2_circcomb(B,C)) ) ) ) ) )).
fof(t7_circled1,axiom,( ! [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) ) => ! [B] : ( ( v3_rltopsp1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v3_rltopsp1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => v3_rltopsp1(k9_subset_1(u1_struct_0(A),B,C),A) ) ) ) )).
fof(t7_circtrm1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v3_trees_3(B) ) => k9_trees_9(k2_xboole_0(A,B)) = k2_xboole_0(k9_trees_9(A),k9_trees_9(B)) ) ) )).
fof(t7_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_funct_1(u3_msualg_1(A,k5_msafree2(A,B)),C)) => ~ ( ~ r1_xxreal_0(k5_card_1(D),1) & ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => k1_funct_1(D,k1_xboole_0) != k4_tarski(E,u1_struct_0(A)) ) ) ) ) ) ) )).
fof(t7_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_msafree2(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,k5_msafree2(A,B)),D)) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,k5_msafree2(A,B)),D)) => ( F = 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) => k5_card_1(E) = k5_card_1(F) ) ) ) ) ) ) ) )).
fof(t7_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m2_finseq_1(E,k4_ordinal1) ) => r2_relset_1(k1_euclid(A),k1_numbers,k5_pdiff_9(A,B,k8_finseq_1(k4_ordinal1,E,D),C),k5_pdiff_9(A,B,D,k5_pdiff_9(A,B,E,C))) ) ) ) ) ) )).
fof(t7_classes1,axiom,( ! [A] : k3_classes1(A,k1_xboole_0) = k1_tarski(A) )).
fof(t7_classes2,axiom,( ! [A] : ! [B] : ( ( v1_classes1(B) & v1_ordinal1(A) & r2_hidden(A,B) ) => r1_tarski(A,B) ) )).
fof(t7_clopban1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( 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),k2_funcsdom(A,u1_struct_0(B),k2_numbers,k9_funct_2(A,u1_struct_0(B)),k2_clopban1(A,B),k1_domain_1(k2_numbers,k9_funct_2(A,u1_struct_0(B)),k6_complex1,C)),C) ) ) ) )).
fof(t7_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(k6_clopban1(A,A)),k8_clopban1(A,A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(k6_clopban1(A,A)),k8_clopban1(A,A)) => ! [D] : ( m2_subset_1(D,u1_struct_0(k6_clopban1(A,A)),k8_clopban1(A,A)) => k3_clopban2(A,k3_clopban2(A,D,C),B) = k3_clopban2(A,D,k3_clopban2(A,C,B)) ) ) ) ) )).
fof(t7_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( m2_valued_0(C,u1_struct_0(A),B) & v9_clvect_1(B,A) ) => v9_clvect_1(C,A) ) ) ) ) )).
fof(t7_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v9_clvect_1(C,A) => k7_clvect_1(A,k3_clopban3(A,C,B)) = k6_algstr_0(A,k7_clvect_1(A,C),B) ) ) ) ) )).
fof(t7_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,C) => ! [E] : ( m2_pboole(E,A,B,C) => ( ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,A) & v1_funct_1(F) & v1_partfun1(F,A) ) => ( r1_pboole(A,F,B) => r6_pboole(A,k16_pralg_1(A,D,F),k16_pralg_1(A,E,F)) ) ) => r6_pboole(A,D,E) ) ) ) ) ) )).
fof(t7_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r2_pboole(A,B,C) => m1_subset_1(k1_tarski(B),k1_zfmisc_1(k1_closure2(A,C))) ) ) ) )).
fof(t7_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xcmplx_0(C) => k1_clvect_1(A,k4_algstr_0(A,B),C) = k4_algstr_0(A,k1_clvect_1(A,B,C)) ) ) ) )).
fof(t7_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clvect_2(C,A) => v1_clvect_2(k5_bhsp_1(A,C,B),A) ) ) ) ) )).
fof(t7_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_clvect_3(B,A) & v1_clvect_3(C,A) ) => ( v1_clvect_3(k3_normsp_1(A,B,C),A) & k1_clvect_3(A,k3_normsp_1(A,B,C)) = k5_algstr_0(A,k1_clvect_3(A,B),k1_clvect_3(A,C)) ) ) ) ) ) )).
fof(t7_coh_sp,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ( r2_hidden(A,B) <=> ! [C] : ! [D] : ( ( r2_hidden(C,A) & r2_hidden(D,A) ) => r2_hidden(k4_tarski(C,D),k1_coh_sp(B)) ) ) ) )).
fof(t7_cohsp_1,axiom,( ! [A] : ( v2_cohsp_1(A) => ! [B] : ! [C] : ~ ( r2_hidden(B,A) & r2_hidden(C,A) & ! [D] : ~ ( r1_tarski(D,k3_xboole_0(B,C)) & r2_hidden(D,A) ) ) ) )).
fof(t7_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_collsp(A,B,C,D) => r1_collsp(A,C,B,D) ) ) ) ) ) )).
fof(t7_combgras,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ! [D] : ( ( k1_card_1(B) = k6_xcmplx_0(A,1) & k1_card_1(C) = k6_xcmplx_0(A,1) & k1_card_1(D) = k6_xcmplx_0(A,1) & k1_card_1(k3_xboole_0(B,C)) = k6_xcmplx_0(A,2) & k1_card_1(k3_xboole_0(B,D)) = k6_xcmplx_0(A,2) & k1_card_1(k3_xboole_0(C,D)) = k6_xcmplx_0(A,2) & r1_xxreal_0(2,A) ) => ( ~ ( r1_xxreal_0(3,A) & ~ ( k1_card_1(k3_xboole_0(k3_xboole_0(B,C),D)) = k6_xcmplx_0(A,2) & k1_card_1(k2_xboole_0(k2_xboole_0(B,C),D)) = k1_nat_1(A,1) ) & ~ ( k1_card_1(k3_xboole_0(k3_xboole_0(B,C),D)) = k6_xcmplx_0(A,3) & k1_card_1(k2_xboole_0(k2_xboole_0(B,C),D)) = A ) ) & ( A = 2 => ( k1_card_1(k3_xboole_0(k3_xboole_0(B,C),D)) = k6_xcmplx_0(A,2) & k1_card_1(k2_xboole_0(k2_xboole_0(B,C),D)) = k1_nat_1(A,1) ) ) ) ) ) )).
fof(t7_compact1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ~ ( ~ v1_compts_1(A) & ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_compact1(A)))) => ~ ( B = k2_struct_0(A) & v1_tops_1(B,k1_compact1(A)) ) ) ) & ~ ( ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_compact1(A)))) & B = k2_struct_0(A) & v1_tops_1(B,k1_compact1(A)) ) & v1_compts_1(A) ) ) ) )).
fof(t7_compl_sp,axiom,( ! [A] : ( l1_metric_1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(u1_struct_0(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(u1_struct_0(k3_pcomps_1(A)))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(u1_struct_0(k3_pcomps_1(A)))))) ) => ( r1_funct_2(k4_ordinal1,k9_setfam_1(u1_struct_0(k3_pcomps_1(A))),k4_ordinal1,k9_setfam_1(u1_struct_0(A)),C,B) => ( ( v6_compl_sp(B,A) => v4_compl_sp(C,k3_pcomps_1(A)) ) & ( v4_compl_sp(C,k3_pcomps_1(A)) => v6_compl_sp(B,A) ) & ( v7_compl_sp(B,A) => v5_compl_sp(C,k3_pcomps_1(A)) ) & ( v5_compl_sp(C,k3_pcomps_1(A)) => v7_compl_sp(B,A) ) ) ) ) ) ) )).
fof(t7_complex1,axiom,( k3_complex1(k7_complex1) = k5_numbers & k4_complex1(k7_complex1) = 1 )).
fof(t7_complex2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(A,k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos)) & r2_hidden(B,k2_rcomp_1(k7_xcmplx_0(k28_sin_cos,2),k28_sin_cos)) ) => ( ~ ( ~ r1_xxreal_0(B,A) & r1_xxreal_0(k17_sin_cos(A),k17_sin_cos(B)) ) & ~ ( ~ r1_xxreal_0(k17_sin_cos(A),k17_sin_cos(B)) & r1_xxreal_0(B,A) ) ) ) ) ) )).
fof(t7_complfld,axiom,( k4_struct_0(k1_complfld) = k5_complex1 )).
fof(t7_complsp1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => v9_pre_topc(k1_complsp1(A)) ) )).
fof(t7_complsp2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => ! [B] : ( ( 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) ) ) ) )).
fof(t7_compos_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_compos_0(A) & v2_compos_0(A) & v3_compos_0(A) ) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( r2_hidden(C,k4_finseq_1(k5_xtuple_0(B))) => r2_hidden(k1_funct_1(k5_xtuple_0(B),C),k1_funct_1(k10_card_3(k3_compos_0(A,k2_compos_0(A,B))),C)) ) ) ) )).
fof(t7_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => k62_valued_1(k4_compos_1(A)) = k5_numbers ) )).
fof(t7_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => ! [D] : ( ( v6_compos_0(D,u1_compos_1(A)) & m1_subset_1(D,u1_compos_1(A)) ) => k2_compos_2(A,k3_compos_2(A,B,C),D) = k1_compos_2(A,B,k3_compos_2(A,C,D)) ) ) ) ) )).
fof(t7_comptrig,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( r2_hidden(A,k2_rcomp_1(k5_numbers,k28_sin_cos)) & r1_xxreal_0(k1_funct_1(k16_sin_cos,A),k5_numbers) ) ) )).
fof(t7_compts_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v8_pre_topc(A) & v2_compts_1(B,A) ) => v4_pre_topc(B,A) ) ) ) )).
fof(t7_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ( r2_hidden(k1_xboole_0,k10_xtuple_0(A)) => k5_funct_6(A) = k1_xboole_0 ) ) )).
fof(t7_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B),C),k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,C))) ) ) ) )).
fof(t7_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_funct_2(k4_ordinal1,k2_numbers,k2_comseq_2(k4_ordinal1,k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,A)),k51_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k2_comseq_2(k4_ordinal1,B),k2_comseq_2(k4_ordinal1,A))) ) ) )).
fof(t7_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v1_xreal_0(D) => ( ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(E,C) => r1_xxreal_0(k9_nat_1(k1_numbers,A,E),k3_xcmplx_0(D,k9_nat_1(k1_numbers,B,E))) ) ) => r1_xxreal_0(k9_nat_1(k1_numbers,k3_series_1(A),C),k3_xcmplx_0(D,k9_nat_1(k1_numbers,k3_series_1(B),C))) ) ) ) ) ) )).
fof(t7_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( 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) = k3_funct_2(k9_setfam_1(u1_struct_0(A)),k9_setfam_1(u4_struct_0(A)),k1_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))) ) ) )).
fof(t7_conmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v5_conmetr(A) => v7_aff_2(k3_analmetr(A)) ) ) )).
fof(t7_connsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ( ( r1_connsp_1(A,B,D) & r1_tarski(C,B) & r1_tarski(E,D) ) => r1_connsp_1(A,C,E) ) ) ) ) ) ) )).
fof(t7_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( m1_connsp_2(D,A,C) & r1_tarski(D,B) ) ) ) ) ) ) ) )).
fof(t7_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_connsp_1(B,A) => k1_connsp_3(A,B) = B ) ) ) )).
fof(t7_convex1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v1_convex1(B,A) <=> v1_convex1(k5_rusub_4(A,B,C),A) ) ) ) ) )).
fof(t7_convex2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k2_convex1(A,B) != k1_xboole_0 ) ) )).
fof(t7_convex3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( v1_convex3(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ( v5_rlvect_1(A) & v6_rlvect_1(A) & v7_rlvect_1(A) & v8_rlvect_1(A) ) => ( v1_convex1(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) ) )).
fof(t7_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( ( 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))) ) => k3_convex4(A,k6_finseq_1(u1_struct_0(A)),B) = k6_finseq_1(u1_struct_0(A)) ) ) )).
fof(t7_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [D] : ( ( v3_card_1(D,B) & m2_finseq_1(D,k2_qc_lang1(A)) ) => ( m2_subset_1(k10_qc_lang1(A,C,D),k9_qc_lang1(A),k3_cqc_lang(A)) <=> ( a_3_0_cqc_lang(A,B,D) = k1_xboole_0 & a_3_1_cqc_lang(A,B,D) = k1_xboole_0 ) ) ) ) ) ) )).
fof(t7_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ~ ( v4_qc_lang1(B,A) & ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => B != k7_cqc_lang(A,C,D) ) ) ) ) ) )).
fof(t7_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t7_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ( r2_hidden(D,k24_qc_lang1(A,k2_qc_lang2(A,B,C))) <=> ( r2_hidden(D,k24_qc_lang1(A,B)) | r2_hidden(D,k24_qc_lang1(A,C)) ) ) ) ) ) ) )).
fof(t7_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ( r2_cqc_the3(A,B,C) <=> r1_tarski(C,k1_cqc_the1(A,B)) ) ) ) ) )).
fof(t7_csspace,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace))) => ! [C] : ( m1_subset_1(C,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),k3_rlvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),B,C),A) = k3_rlvect_1(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),k1_clvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),C,A)) ) ) ) )).
fof(t7_csspace2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( v7_ordinal1(B) => ( ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k5_numbers,k1_funct_1(k7_comseq_3(A),C)) & k1_funct_1(k8_comseq_3(A),C) = k5_numbers ) ) => k1_funct_1(k55_valued_1(k4_ordinal1,k2_numbers,k10_comseq_3(A)),B) = k1_funct_1(k3_series_1(k55_valued_1(k4_ordinal1,k2_numbers,A)),B) ) ) ) )).
fof(t7_csspace3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_csspace3(B,A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(D,E) & r1_xxreal_0(D,F) & r1_xxreal_0(C,k2_normsp_0(A,k5_algstr_0(A,k1_normsp_0(A,B,E),k1_normsp_0(A,B,F)))) ) ) ) ) ) ) ) ) )).
fof(t7_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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(k4_csspace4(A,B),k3_clopban1(A,B)) ) ) )).
fof(t7_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k9_subset_1(k1_zfmisc_1(u1_struct_0(A)),k6_decomp_1(A),k11_decomp_1(A)) = u1_pre_topc(A) ) )).
fof(t7_descip_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k3_finseq_1(k7_descip_1(A)) = k3_finseq_1(A) ) )).
fof(t7_dickson,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ! [D] : ( r4_waybel_4(k3_xboole_0(k1_wellord1(u1_orders_2(A),B),D),C,u1_orders_2(A)) => r4_waybel_4(D,C,u1_orders_2(A)) ) ) ) )).
fof(t7_diff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(k26_valued_1(k1_numbers,k1_numbers,E,C),B),k1_nat_1(A,1)),D) = k3_xcmplx_0(C,k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(E,B),k1_nat_1(A,1)),D)) ) ) ) ) ) )).
fof(t7_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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] : ( ( 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))) ) => k10_diff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_valued_1(k1_numbers,k1_numbers,F,A),k26_valued_1(k1_numbers,k1_numbers,G,B)),C,D,E) = k2_xcmplx_0(k3_xcmplx_0(A,k10_diff_1(F,C,D,E)),k3_xcmplx_0(B,k10_diff_1(G,C,D,E))) ) ) ) ) ) ) ) )).
fof(t7_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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,k6_diff_1(B,A),1),k3_diff_1(B,A)) ) ) )).
fof(t7_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(B,k1_relset_1(k1_numbers,k27_sin_cos)) & r2_hidden(k2_xcmplx_0(B,A),k1_relset_1(k1_numbers,k27_sin_cos)) ) => k1_funct_1(k3_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k27_sin_cos),A),B) = k7_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k19_sin_cos(k3_xcmplx_0(2,k2_xcmplx_0(B,A))),k19_sin_cos(k3_xcmplx_0(2,B)))),k1_square_1(k3_xcmplx_0(k17_sin_cos(k2_xcmplx_0(B,A)),k17_sin_cos(B)))) ) ) ) )).
fof(t7_dilworth,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & v1_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))) & ~ r1_orders_2(A,B,C) & ~ r1_orders_2(A,C,B) ) ) ) ) )).
fof(t7_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_analoaf(A,B,C,B,D) <=> ( r1_diraf(A,B,C,D) | r1_diraf(A,B,D,C) ) ) ) ) ) ) )).
fof(t7_dirort,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dirort(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_dirort(A,B,C,D,D) & r2_dirort(A,D,D,B,C) ) ) ) ) ) )).
fof(t7_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r1_dist_1(A,B,C) <=> k5_dist_1(A,B) = k5_dist_1(A,C) ) ) ) ) )).
fof(t7_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => m1_dist_1(k3_funct_2(k6_dist_1(A),k3_finseq_2(k1_numbers),k7_dist_1(A),B),A) ) ) )).
fof(t7_domain_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k3_zfmisc_1(B,C,D)) => ( A = k2_mcart_1(B,C,D,E) <=> ! [F] : ( m1_subset_1(F,B) => ! [G] : ( m1_subset_1(G,C) => ! [H] : ( m1_subset_1(H,D) => ( E = k4_domain_1(B,C,D,F,G,H) => A = G ) ) ) ) ) ) ) ) ) )).
fof(t7_dtconstr,axiom,( k11_mcart_1(k1_xboole_0) = k1_xboole_0 & k12_mcart_1(k1_xboole_0) = k1_xboole_0 )).
fof(t7_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k3_tarski(k10_xtuple_0(k4_dynkin(A,B))) = k3_tarski(k10_xtuple_0(B)) ) ) )).
fof(t7_e_siec,axiom,( ! [A] : ( u1_struct_0(k3_e_siec(A)) = A & u1_e_siec(k3_e_siec(A)) = k1_xboole_0 & u2_e_siec(k3_e_siec(A)) = k1_xboole_0 ) )).
fof(t7_ec_pf_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_ec_pf_1(B,A) => ! [C] : ( m1_ec_pf_1(C,A) => ( m1_ec_pf_1(B,C) <=> ! [D] : ( r1_struct_0(B,D) => r1_struct_0(C,D) ) ) ) ) ) )).
fof(t7_ec_pf_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(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,E,C),D),B) & 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,B,E),D),C) ) ) ) ) ) ) )).
fof(t7_endalg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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_endalg(A,B)) ) ) )).
fof(t7_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => r1_tarski(k2_ens_1(B),k2_ens_1(A)) ) ) )).
fof(t7_entropy1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ( ( k3_finseq_1(B) = k3_finseq_1(A) & k3_finseq_1(B) = k3_finseq_1(C) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(B)) => k1_funct_1(A,D) = k2_xcmplx_0(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) => k18_rvsum_1(A) = k2_xcmplx_0(k18_rvsum_1(B),k18_rvsum_1(C)) ) ) ) ) )).
fof(t7_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k3_enumset1(A,B,C,D,E) = k2_xboole_0(k1_tarski(A),k2_enumset1(B,C,D,E)) )).
fof(t7_eqrel_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v8_relat_2(C) & v1_partfun1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [D] : ! [E] : ( ( r2_hidden(k4_tarski(D,E),C) & r2_hidden(k4_tarski(E,B),C) ) => r2_hidden(k4_tarski(D,B),C) ) ) )).
fof(t7_equation,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( m2_pboole(E,A,B,C) => m3_pboole(k9_pboole(A,D,E),A,C) ) ) ) ) )).
fof(t7_euclid,axiom,( ! [A] : ( ( 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) ) )).
fof(t7_euclid_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => ( k22_rvsum_1(A,A) = k5_numbers <=> k12_euclid(A) = k5_numbers ) ) )).
fof(t7_euclid_3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k1_euclid_3(k2_xcmplx_0(A,B)) = k3_rlvect_1(k15_euclid(2),k1_euclid_3(A),k1_euclid_3(B)) ) ) )).
fof(t7_euclid_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(C)) => k9_euclid(C,D,k2_xcmplx_0(A,B)) = k7_euclid(C,k9_euclid(C,D,A),k9_euclid(C,D,B)) ) ) ) ) )).
fof(t7_euclid_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(3))) => k1_rlvect_1(k15_euclid(3),B,A) = k4_euclid_5(k3_xcmplx_0(A,k1_euclid_5(B)),k3_xcmplx_0(A,k2_euclid_5(B)),k3_xcmplx_0(A,k3_euclid_5(B))) ) ) )).
fof(t7_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( ( D = k12_euclid(k5_algstr_0(k15_euclid(2),A,B)) & E = k12_euclid(k5_algstr_0(k15_euclid(2),C,B)) & F = k12_euclid(k5_algstr_0(k15_euclid(2),C,A)) ) => k1_square_1(F) = k6_xcmplx_0(k2_xcmplx_0(k1_square_1(D),k1_square_1(E)),k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,D),E),k19_sin_cos(k4_euclid_3(A,B,C)))) ) ) ) ) ) ) ) )).
fof(t7_euclid_8,axiom,( r1_rvsum_1(k2_euclid_8,k3_euclid_8) )).
fof(t7_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ( B = k7_euclid(A,k7_euclid(A,C,D),E) <=> k8_euclid(A,B,C) = k7_euclid(A,D,E) ) ) ) ) ) ) )).
fof(t7_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r4_analmetr(A,B,C,D,E) & r4_analmetr(A,C,D,B,E) & r5_analmetr(A,B,C,D) & B != D & B != C & C != D ) ) ) ) ) ) )).
fof(t7_euler_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k3_int_2(A,B) = 1 => k3_int_2(k2_xcmplx_0(A,B),B) = 1 ) ) ) )).
fof(t7_euler_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k4_nat_d(k3_xcmplx_0(C,A),B) = k4_nat_d(k2_nat_1(C,k4_nat_d(A,B)),B) ) ) ) )).
fof(t7_extens_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,C) => ! [E] : ( m3_pboole(E,A,B) => r2_pboole(A,k1_funct_6(k1_msafree(A,B,C,E,D)),k1_funct_6(D)) ) ) ) ) )).
fof(t7_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) => ( 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) ) ) ) ) ) ) )).
fof(t7_extreal1,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ! [B] : ( m1_subset_1(B,k6_numbers) => k4_extreal1(k2_finseq_4(k6_numbers,A,B)) = k3_supinf_2(A,B) ) ) )).
fof(t7_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ( r1_xxreal_0(A,k5_numbers) => k3_extreal1(A) = k2_xxreal_3(A) ) ) )).
fof(t7_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_circcomb(A) & v2_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ 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_facirc_1(k2_msafree2(A)) | v1_facirc_1(k2_msafree2(B)) | k2_msafree2(k2_circcomb(A,B)) = k2_xboole_0(k2_msafree2(A),k2_msafree2(B)) ) ) ) ) )).
fof(t7_facirc_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( k3_facirc_2(k5_numbers,A,B) = k5_circcomb(k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1),k1_xboole_0) & k4_facirc_2(k5_numbers,A,B) = k7_circcomb(k5_ordinal1,k6_margrel1,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1),k1_xboole_0) & k5_facirc_2(k5_numbers,A,B) = k4_tarski(k1_xboole_0,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1)) ) ) ) )).
fof(t7_fcont_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r2_hidden(A,k9_subset_1(k1_numbers,k1_relset_1(k1_numbers,B),k1_relset_1(k1_numbers,C))) & r1_fcont_1(B,A) & r1_fcont_1(C,A) ) => ( r1_fcont_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,B,C),A) & r1_fcont_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,B,C),A) & r1_fcont_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t7_fcont_2,axiom,( ! [A] : ! [B] : ( ( 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)) => v1_fcont_2(k2_partfun1(k1_numbers,k1_numbers,k56_valued_1(k1_numbers,k1_numbers,B),A)) ) ) )).
fof(t7_fcont_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ~ ( r1_fcont_1(C,A) & k1_funct_1(C,A) != B & ? [D] : ( m1_rcomp_1(D,A) & r1_tarski(D,k1_relset_1(k1_numbers,C)) ) & ! [D] : ( m1_rcomp_1(D,A) => ~ ( r1_tarski(D,k1_relset_1(k1_numbers,C)) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,D) & k1_funct_1(C,E) = B ) ) ) ) ) ) ) ) )).
fof(t7_fdiff_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v2_fdiff_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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(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))) & v1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,B,A)) & v2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,B,A)) & m1_subset_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,B,A),k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) ) ) )).
fof(t7_fdiff_10,axiom,( ! [A] : ( ( 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,k16_sin_cos,k16_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k16_sin_cos),A),B) = k3_xcmplx_0(k1_funct_1(k18_sin_cos,k1_funct_1(k16_sin_cos,B)),k1_funct_1(k18_sin_cos,B)) ) ) ) ) )).
fof(t7_fdiff_11,axiom,( ! [A] : ( ( 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,k27_sin_cos,k1_sin_cos9))) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k27_sin_cos,B),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(k27_sin_cos,B)) ) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k1_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k1_sin_cos9),A),B) = k4_xcmplx_0(1) ) ) ) ) ) )).
fof(t7_fdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( r3_fdiff_3(A,B) => r2_fdiff_3(A,B) ) ) ) )).
fof(t7_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( 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,k1_partfun2(k1_numbers,B),k26_valued_1(k1_numbers,k1_numbers,C,k3_xcmplx_0(2,A))))) & C = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k3_taylor_1) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => ( k1_funct_1(D,E) = k6_xcmplx_0(E,A) & ~ r1_xxreal_0(k1_funct_1(D,E),k5_numbers) ) ) ) ) => ( r2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k26_valued_1(k1_numbers,k1_numbers,C,k3_xcmplx_0(2,A))),B) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,B) => k1_funct_1(k2_fdiff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k26_valued_1(k1_numbers,k1_numbers,C,k3_xcmplx_0(2,A))),B),E) = k7_xcmplx_0(k2_xcmplx_0(E,A),k6_xcmplx_0(E,A)) ) ) ) ) ) ) ) ) )).
fof(t7_fdiff_6,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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_rfunct_1(k1_numbers,k1_numbers,B,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,C,B)))) & B = k1_taylor_1(2) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => ( k1_funct_1(C,D) = 1 & D != k5_numbers ) ) ) ) => ( r2_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,B,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,C,B)),A) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,A) => k1_funct_1(k2_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,B,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,C,B)),A),D) = k7_xcmplx_0(k3_xcmplx_0(2,D),k1_square_1(k2_xcmplx_0(1,k1_square_1(D)))) ) ) ) ) ) ) ) )).
fof(t7_fdiff_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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_funct_1(B,A),k4_xcmplx_0(1)) | r1_xxreal_0(1,k1_funct_1(B,A)) | ( r1_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k3_sin_cos6),A) & k1_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k3_sin_cos6),A) = k4_xcmplx_0(k7_xcmplx_0(k1_fdiff_1(B,A),k3_square_1(k6_xcmplx_0(1,k1_square_1(k1_funct_1(B,A)))))) ) ) ) ) ) )).
fof(t7_fdiff_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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,k27_sin_cos))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(D,E) = k2_xcmplx_0(k3_xcmplx_0(A,E),B) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k27_sin_cos),C) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k27_sin_cos),C),E) = k4_xcmplx_0(k7_xcmplx_0(A,k1_square_1(k1_funct_1(k16_sin_cos,k2_xcmplx_0(k3_xcmplx_0(A,E),B))))) ) ) ) ) ) ) ) ) )).
fof(t7_fdiff_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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,k2_fdiff_9))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(D,E) = k2_xcmplx_0(k3_xcmplx_0(A,E),B) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k2_fdiff_9),C) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k2_fdiff_9),C),E) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(A,k1_funct_1(k18_sin_cos,k2_xcmplx_0(k3_xcmplx_0(A,E),B))),k1_square_1(k1_funct_1(k16_sin_cos,k2_xcmplx_0(k3_xcmplx_0(A,E),B))))) ) ) ) ) ) ) ) ) )).
fof(t7_ff_siec,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(A,u1_struct_0(C)) & ~ r2_hidden(B,u4_struct_0(C)) & r2_hidden(B,u1_struct_0(C)) ) ) & ( ( r2_hidden(k4_tarski(A,B),k1_net_1(C)) & r2_hidden(B,u4_struct_0(C)) ) => ( ~ r2_hidden(B,u1_struct_0(C)) & ~ r2_hidden(A,u4_struct_0(C)) & r2_hidden(A,u1_struct_0(C)) ) ) & ( ( r2_hidden(k4_tarski(A,B),k1_net_1(C)) & r2_hidden(A,u1_struct_0(C)) ) => ( ~ r2_hidden(B,u1_struct_0(C)) & ~ r2_hidden(A,u4_struct_0(C)) & r2_hidden(B,u4_struct_0(C)) ) ) & ( ( r2_hidden(k4_tarski(A,B),k1_net_1(C)) & r2_hidden(B,u1_struct_0(C)) ) => ( ~ r2_hidden(A,u1_struct_0(C)) & ~ r2_hidden(B,u4_struct_0(C)) & r2_hidden(A,u4_struct_0(C)) ) ) ) ) )).
fof(t7_fib_num,axiom,( ! [A] : ( v7_ordinal1(A) => k1_pre_ff(A) = k7_xcmplx_0(k6_xcmplx_0(k2_power(k1_fib_num,A),k2_power(k2_fib_num,A)),k3_square_1(5)) ) )).
fof(t7_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => k1_square_1(k2_power(k4_xcmplx_0(1),k4_xcmplx_0(A))) = 1 ) )).
fof(t7_fib_num3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k3_xcmplx_0(k2_xcmplx_0(A,B),k6_xcmplx_0(A,B)) = k6_xcmplx_0(k2_power(A,2),k2_power(B,2)) ) ) )).
fof(t7_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ v1_abian(A) & ~ r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k5_numbers,k2_power(B,A)) ) ) ) )).
fof(t7_filerec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(C,D) & r1_xxreal_0(C,k3_finseq_1(k17_finseq_1(A,E,B))) & r1_xxreal_0(D,k3_finseq_1(k17_finseq_1(A,E,B))) ) => k3_finseq_6(A,B,C,D) = k3_finseq_6(A,k17_finseq_1(A,E,B),C,D) ) ) ) ) ) ) )).
fof(t7_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_lattices(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r3_lattices(A,B,C) & r3_lattices(A,B,D) ) => r3_lattices(A,B,k4_lattices(A,C,D)) ) ) ) ) ) )).
fof(t7_filter_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m2_filter_1(D,A,B) => ( r2_binop_1(A,C,D) => r2_binop_1(k8_eqrel_1(A,B),k9_eqrel_1(A,B,C),k3_filter_1(A,B,D)) ) ) ) ) ) )).
fof(t7_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => k1_lattice2(k1_lattice2(A)) = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ) )).
fof(t7_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k8_fin_topo(A,C)) <=> r1_tarski(k1_fin_topo(A,B),C) ) ) ) ) )).
fof(t7_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(B,A) => k2_finseq_1(B) = k9_subset_1(k4_ordinal1,k2_finseq_1(A),k2_finseq_1(B)) ) ) ) )).
fof(t7_finseq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(A)) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) => A = B ) ) ) )).
fof(t7_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( k2_finseq_1(A) = k1_xboole_0 <=> ~ r2_hidden(A,k2_finseq_1(A)) ) ) )).
fof(t7_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r2_finseq_4(A,B) <=> ? [C] : ( r2_hidden(C,k9_xtuple_0(A)) & B = k1_funct_1(A,C) & ! [D] : ~ ( r2_hidden(D,k9_xtuple_0(A)) & D != C & k1_funct_1(A,D) = B ) ) ) ) )).
fof(t7_finseq_5,axiom,( ! [A] : ( ( v1_relat_1(A) & ~ v1_xboole_0(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ? [B] : ( v7_ordinal1(B) & k1_nat_1(B,1) = k3_finseq_1(A) ) ) )).
fof(t7_finseq_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( r2_hidden(C,k6_subset_1(k10_xtuple_0(B),k10_xtuple_0(A))) => k4_finseq_4(k7_finseq_1(A,B),C) = k1_nat_1(k3_finseq_1(A),k4_finseq_4(B,C)) ) ) ) )).
fof(t7_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(B)) ) => r2_hidden(C,k10_xtuple_0(k1_finseq_7(A,B,D,C))) ) ) ) ) ) )).
fof(t7_finseq_8,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ~ r1_xxreal_0(C,D) => k3_finseq_8(A,B,C,D) = k1_xboole_0 ) ) ) ) )).
fof(t7_finseqop,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ( r2_hidden(k4_tarski(C,D),k9_xtuple_0(A)) => k3_funcop_1(A,k7_funcop_1(B,C),k7_funcop_1(B,D)) = k7_funcop_1(B,k1_binop_1(A,C,D)) ) ) )).
fof(t7_finset_1,axiom,( ! [A] : ( ( v1_finset_1(A) & ! [B] : ( r2_hidden(B,A) => v1_finset_1(B) ) ) <=> v1_finset_1(k3_tarski(A)) ) )).
fof(t7_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)) & v3_funct_2(E,k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,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,k3_finseq_1(B)) ) | k1_finsop_1(A,B,D) = k1_finsop_1(A,C,D) ) ) ) ) ) ) ) )).
fof(t7_finsub_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) ) => r2_hidden(k1_xboole_0,A) ) )).
fof(t7_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( 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)) ) ) ) ) ) ) )).
fof(t7_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k9_fin_topo(A,k9_subset_1(u1_struct_0(A),B,C)),k9_subset_1(u1_struct_0(A),k9_fin_topo(A,B),k9_fin_topo(A,C))) ) ) ) )).
fof(t7_fintopo4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v1_fin_topo(A) => ( r1_fintopo4(A,B,C) <=> ( r1_xboole_0(k12_fin_topo(A,B),C) & r1_xboole_0(B,k12_fin_topo(A,C)) ) ) ) ) ) ) )).
fof(t7_fintopo5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( v3_orders_2(A) => r1_tarski(k10_fintopo3(A,C,B),k10_fintopo3(A,k1_nat_1(C,1),B)) ) ) ) ) )).
fof(t7_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_fintopo6(B,A) ) => ( v3_orders_2(A) => v3_orders_2(B) ) ) ) )).
fof(t7_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k3_catalan2(A)) => ! [C] : ( v7_ordinal1(C) => ~ ( k1_afinsq_1(B) = k1_nat_1(C,1) & ! [D] : ( m1_subset_1(D,k3_catalan2(A)) => ! [E] : ( m1_subset_1(E,A) => ~ ( k1_afinsq_1(D) = C & B = k1_ordinal4(D,k5_afinsq_1(E)) ) ) ) ) ) ) )).
fof(t7_flang_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(B,C) & B != k2_flang_1(A) & ~ r1_xxreal_0(D,k5_numbers) & k7_flang_1(A,C,D) = k4_flang_1(A,k2_flang_1(A)) ) ) ) )).
fof(t7_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,k2_xcmplx_0(D,1)) => k4_subset_1(k8_afinsq_1(A),k1_flang_2(A,B,C,D),k1_flang_3(A,B,k2_xcmplx_0(D,1))) = k1_flang_3(A,B,C) ) ) ) ) )).
fof(t7_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( v7_ordinal1(C) => ( v3_fomodel0(A,B) => v3_fomodel0(k7_relset_1(k3_finseq_2(k3_finseq_2(B)),k3_finseq_2(B),k9_fomodel0(B),k4_finseq_2(C,A)),B) ) ) ) )).
fof(t7_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => v12_fomodel1(k35_fomodel1(A),A) ) )).
fof(t7_fomodel2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k24_fomodel2(A,k5_numbers) = k32_fomodel1(A) ) )).
fof(t7_fomodel3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v6_struct_0(D) & v11_fomodel1(D) & l1_fomodel1(D) ) => ! [E] : ( ( v4_fomodel1(E,D) & m1_subset_1(E,k1_fomodel1(D)) ) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) & v1_fomodel2(F,D,B) ) => ! [G] : ( m2_subset_1(G,k6_subset_1(k3_finseq_2(k15_fomodel1(D)),k1_tarski(k1_xboole_0)),k35_fomodel1(D)) => k5_relat_1(k3_relat_1(k9_nat_1(k9_funct_2(k35_fomodel1(D),k35_fomodel1(D)),k7_fomodel2(D,k35_fomodel1(D),G,k34_fomodel2(D,k35_fomodel1(D),k7_fomodel3(D,A),E,G)),C),k9_fomodel2(D,B,F)),k9_nat_1(k9_setfam_1(k6_subset_1(k3_finseq_2(k15_fomodel1(D)),k1_tarski(k1_xboole_0))),k39_fomodel1(D),C)) = k5_relat_1(k9_nat_1(k9_funct_2(k35_fomodel1(D),B),k7_fomodel2(D,B,k3_funct_2(k35_fomodel1(D),B,k9_fomodel2(D,B,F),G),k5_fomodel2(F,E,k3_funct_2(k35_fomodel1(D),B,k9_fomodel2(D,B,F),G))),C),k9_nat_1(k9_setfam_1(k6_subset_1(k3_finseq_2(k15_fomodel1(D)),k1_tarski(k1_xboole_0))),k39_fomodel1(D),C)) ) ) ) ) ) ) )).
fof(t7_fomodel4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v6_struct_0(F) & v11_fomodel1(F) & l1_fomodel1(F) ) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(F)),k9_setfam_1(k1_fomodel4(F))))) => ! [H] : ( m1_subset_1(H,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(F)),k9_setfam_1(k1_fomodel4(F))))) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(F)),k9_setfam_1(k1_fomodel4(F))))) => ! [J] : ( v2_fomodel4(J,F) => ! [K] : ( v2_fomodel4(K,F) => ( ( v7_fomodel4(k4_subset_1(k9_funct_2(k9_setfam_1(k1_fomodel4(F)),k9_setfam_1(k1_fomodel4(F))),G,H),F) & v7_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) & v5_fomodel4(C,A,F,G,J) & v5_fomodel4(D,A,F,H,K) & v5_fomodel4(E,B,F,I,k2_tarski(C,D)) ) => v5_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)) ) ) ) ) ) ) ) ) ) )).
fof(t7_frechet,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k7_metric_1)) => ! [B] : ( v1_xreal_0(B) => k8_metric_1(k7_metric_1,A,B) = k2_rcomp_1(k6_xcmplx_0(A,B),k2_xcmplx_0(A,B)) ) ) )).
fof(t7_fscirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(k4_tarski(k10_finseq_1(A,B),k3_twoscomp),k3_msafree2(k4_fscirc_1(A,B,C))) & r2_hidden(k4_tarski(k10_finseq_1(B,C),k2_twoscomp),k3_msafree2(k4_fscirc_1(A,B,C))) & r2_hidden(k4_tarski(k10_finseq_1(A,C),k3_twoscomp),k3_msafree2(k4_fscirc_1(A,B,C))) ) )).
fof(t7_fscirc_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( k1_fscirc_2(k1_nat_1(A,1),B,C) = k2_circcomb(k1_fscirc_2(A,B,C),k8_fscirc_1(k1_funct_1(B,k1_nat_1(A,1)),k1_funct_1(C,k1_nat_1(A,1)),k3_fscirc_2(A,B,C))) & k2_fscirc_2(k1_nat_1(A,1),B,C) = k3_circcomb(k1_fscirc_2(A,B,C),k8_fscirc_1(k1_funct_1(B,k1_nat_1(A,1)),k1_funct_1(C,k1_nat_1(A,1)),k3_fscirc_2(A,B,C)),k2_fscirc_2(A,B,C),k9_fscirc_1(k1_funct_1(B,k1_nat_1(A,1)),k1_funct_1(C,k1_nat_1(A,1)),k3_fscirc_2(A,B,C))) & k3_fscirc_2(k1_nat_1(A,1),B,C) = k6_fscirc_1(k1_funct_1(B,k1_nat_1(A,1)),k1_funct_1(C,k1_nat_1(A,1)),k3_fscirc_2(A,B,C)) ) ) ) ) )).
fof(t7_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( r1_fsm_1(A,B,C,E,F) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( ( r1_xxreal_0(1,G) & r1_xxreal_0(G,k1_nat_1(k3_finseq_1(D),1)) ) => k1_funct_1(k2_fsm_1(A,B,E,k8_finseq_1(A,C,D)),k1_nat_1(k3_finseq_1(C),G)) = k1_funct_1(k2_fsm_1(A,B,F,D),G) ) ) ) ) ) ) ) ) ) )).
fof(t7_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ( ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ( ( k1_funct_1(C,1) = k1_funct_1(D,1) & k3_finseq_1(C) = k3_finseq_1(D) ) => 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) ) ) ) )).
fof(t7_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => ~ ( ~ r1_xxreal_0(k1_afinsq_1(B),k5_numbers) & ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => B != k1_flang_1(A,k3_flang_1(A,C),D) ) ) ) ) ) )).
fof(t7_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ! [E] : ! [F] : ( 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] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( m1_subset_1(H,k6_margrel1) => ! [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(k1_ftacell1(A,B,C,D,E),k2_ftacell1(A,B,C,D,E),F,2),k3_ftacell1(A,B,C,D,E)) = k1_binarith(k1_binarith(k10_margrel1(G,H),k10_margrel1(H,I)),k10_margrel1(I,G)) & k1_funct_1(k5_facirc_1(k1_ftacell1(A,B,C,D,E),k2_ftacell1(A,B,C,D,E),F,2),k4_ftacell1(A,B,C,D,E)) = k2_binarith(k2_binarith(G,H),I) ) ) ) ) ) ) ) ) ) )).
fof(t7_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(B,A) => k1_funct_1(k2_funcop_1(A,C),B) = C ) )).
fof(t7_funcsdom,axiom,( ! [A] : ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( m2_funct_2(C,A,k1_numbers,k9_funct_2(A,k1_numbers)) => r2_funct_2(A,k1_numbers,k1_funcsdom(A,k1_numbers,k6_funcsdom(A),B,C),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),C,B)) ) ) )).
fof(t7_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( k9_xtuple_0(B) = k9_xtuple_0(C) & k10_xtuple_0(B) = k1_tarski(A) & k10_xtuple_0(C) = k1_tarski(A) ) => B = C ) ) ) )).
fof(t7_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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) => ( ( B = k1_xboole_0 & A != k1_xboole_0 ) | ( v1_funct_1(D) & v1_funct_2(D,A,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) ) ) ) )).
fof(t7_funct_3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(A,k9_xtuple_0(k1_funct_3(B))) => k1_funct_1(k1_funct_3(B),A) = k7_relat_1(B,A) ) ) )).
fof(t7_funct_4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(A,k9_xtuple_0(B)) => r1_tarski(k16_funcop_1(A,k1_funct_1(B,A)),B) ) ) )).
fof(t7_funct_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( 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) ) )).
fof(t7_funct_6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r2_hidden(A,k9_xtuple_0(B)) & C = k1_funct_1(B,A) ) => ( r1_tarski(k10_xtuple_0(C),k10_xtuple_0(k2_funct_5(B))) & r1_tarski(k10_xtuple_0(C),k10_xtuple_0(k4_funct_5(B))) ) ) ) ) )).
fof(t7_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( r2_hidden(C,A) => k16_funcop_1(C,k1_funct_1(B,C)) = k5_relat_1(B,k1_tarski(C)) ) ) )).
fof(t7_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( 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) & r2_funct_8(A,k1_numbers,k1_numbers,B) ) => ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(B,C) = k5_numbers ) ) ) ) ) )).
fof(t7_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) ) => ( v1_funct_9(C,A) => v1_funct_9(k24_valued_1(C,B),A) ) ) ) ) )).
fof(t7_functor0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(k15_funct_3(A,A)) => v2_funct_1(A) ) ) )).
fof(t7_functor1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l1_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_altcat_2(C) & l1_altcat_1(C) ) => ! [D] : ( ( v8_functor0(D,A,B) & l2_functor0(D,A,B) ) => ! [E] : ( l2_functor0(E,B,C) => ( ( v17_functor0(D,A,B) & v17_functor0(E,B,C) ) => v17_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ) ) ) ) )).
fof(t7_functor2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => r2_functor2(A,B,C,C) ) ) ) )).
fof(t7_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_altcat_2(C) & l2_altcat_1(C) ) => ! [D] : ( ( v8_functor0(D,A,B) & v11_functor0(D,A,B) & l2_functor0(D,A,B) ) => ! [E] : ( ( v8_functor0(E,B,C) & v11_functor0(E,B,C) & l2_functor0(E,B,C) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,k1_altcat_1(A,F,G)) => ( k1_altcat_1(A,F,G) != k1_xboole_0 => k6_functor0(A,C,k13_functor0(A,B,C,D,E),F,G,H) = k8_functor0(B,C,E,k3_functor0(A,B,D,G),k3_functor0(A,B,D,F),k8_functor0(A,B,D,F,G,H)) ) ) ) ) ) ) ) ) ) )).
fof(t7_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,k2_fuzzy_1(A,B,D),C),k2_fuzzy_1(A,B,k2_fuzzy_1(A,D,C))) & r2_funct_2(A,k1_numbers,k1_fuzzy_1(A,k1_fuzzy_1(A,B,D),C),k1_fuzzy_1(A,B,k1_fuzzy_1(A,D,C))) ) ) ) ) ) )).
fof(t7_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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,k1_fuzzy_2(A,B,k4_fuzzy_1(A)),B) ) ) )).
fof(t7_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,k1_fuzzy_4(B,A,k2_fuzzy_1(k2_zfmisc_1(A,B),C,D)),k2_fuzzy_1(k2_zfmisc_1(B,A),k1_fuzzy_4(B,A,C),k1_fuzzy_4(B,A,D))) ) ) ) ) )).
fof(t7_fvaluat1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( ( r2_hidden(A,k1_numbers) & r2_hidden(B,k1_numbers) ) | r2_hidden(C,k1_numbers) ) => k2_extreal1(k1_xxreal_3(A,B),C) = k3_supinf_2(k2_extreal1(A,C),k2_extreal1(B,C)) ) ) ) ) )).
fof(t7_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_algstr_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => k4_binop_1(u1_struct_0(A),u1_algstr_0(A)) = k4_struct_0(A) ) )).
fof(t7_gate_1,axiom,( ! [A] : v1_xboole_0(k4_gate_1(A,A)) )).
fof(t7_gcd_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & l4_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_gcd_1(A,B,C) => r1_gcd_1(A,B,k6_algstr_0(A,C,D)) ) ) ) ) ) )).
fof(t7_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( m1_genealg1(C,B) => ! [D] : ( m1_genealg1(D,B) => k8_genealg1(B,C,D,k5_numbers,A) = k7_genealg1(B,D,C,A) ) ) ) ) )).
fof(t7_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k1_geomtrap(A,B,D) = k1_geomtrap(A,B,C) => D = C ) ) ) ) ) )).
fof(t7_gfacirc1,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k2_binarith(k2_binarith(k9_margrel1(A),B),k9_margrel1(C)) = k2_binarith(k2_binarith(A,k9_margrel1(B)),k9_margrel1(C)) ) ) ) )).
fof(t7_gfacirc2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( k1_gfacirc2(k1_nat_1(A,1),B,C) = k2_circcomb(k1_gfacirc2(A,B,C),k13_gfacirc1(k1_funct_1(B,k1_nat_1(A,1)),k1_funct_1(C,k1_nat_1(A,1)),k3_gfacirc2(A,B,C))) & k2_gfacirc2(k1_nat_1(A,1),B,C) = k3_circcomb(k1_gfacirc2(A,B,C),k13_gfacirc1(k1_funct_1(B,k1_nat_1(A,1)),k1_funct_1(C,k1_nat_1(A,1)),k3_gfacirc2(A,B,C)),k2_gfacirc2(A,B,C),k14_gfacirc1(k1_funct_1(B,k1_nat_1(A,1)),k1_funct_1(C,k1_nat_1(A,1)),k3_gfacirc2(A,B,C))) & k3_gfacirc2(k1_nat_1(A,1),B,C) = k9_gfacirc1(k1_funct_1(B,k1_nat_1(A,1)),k1_funct_1(C,k1_nat_1(A,1)),k3_gfacirc2(A,B,C)) ) ) ) ) )).
fof(t7_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ! [C] : ( v7_ordinal1(C) => k1_relset_1(k4_ordinal1,k13_glib_000(A,C,B)) = k2_xboole_0(k1_relset_1(k4_ordinal1,A),k1_tarski(C)) ) ) )).
fof(t7_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( r2_hidden(C,k1_relset_1(k4_ordinal1,B)) => r2_hidden(k1_funct_1(B,C),k7_glib_000(A)) ) ) ) ) )).
fof(t7_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ( ( r5_glib_000(A,B) & v1_glib_002(A) ) => v1_glib_002(B) ) ) ) )).
fof(t7_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( r5_glib_000(A,k13_glib_000(A,k2_glib_003,B)) & r5_glib_000(A,k13_glib_000(A,k3_glib_003,B)) & r5_glib_000(A,k13_glib_000(A,k4_glib_003,B)) ) ) )).
fof(t7_glib_004,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( ( 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) ) => ( C = D => k2_uproots(A,C) = k2_uproots(B,D) ) ) ) )).
fof(t7_goboard1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r2_hidden(B,k2_finseq_1(k1_matrix_0(D))) & k1_matrix_0(D) = k1_nat_1(A,1) & r1_xxreal_0(B,C) & r1_xxreal_0(C,A) ) => ( r1_xxreal_0(A,k5_numbers) | ( k8_matrix_0(u1_struct_0(k15_euclid(2)),k16_matrix_0(B,u1_struct_0(k15_euclid(2)),D),C) = k8_matrix_0(u1_struct_0(k15_euclid(2)),D,k1_nat_1(C,1)) & r2_hidden(C,k2_finseq_1(k1_matrix_0(k16_matrix_0(B,u1_struct_0(k15_euclid(2)),D)))) & r2_hidden(k1_nat_1(C,1),k2_finseq_1(k1_matrix_0(D))) ) ) ) ) ) ) ) )).
fof(t7_goboard2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ( v3_topreal1(A) => v3_topreal1(k17_finseq_1(u1_struct_0(k15_euclid(2)),B,A)) ) ) ) )).
fof(t7_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(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,k3_finseq_1(B)) ) => ( v3_relat_1(B) | k2_goboard5(B,k5_numbers) = a_2_7_goboard5(A,B) ) ) ) ) )).
fof(t7_goboard6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(2))) => ( ( E = k19_euclid(A,B) & r1_xxreal_0(k5_numbers,D) ) => ( r1_xxreal_0(C,D) | r2_hidden(k19_euclid(k2_xcmplx_0(A,D),B),k8_metric_1(k14_euclid(2),E,C)) ) ) ) ) ) ) ) )).
fof(t7_goboard7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( k17_euclid(A) = k17_euclid(B) & k17_euclid(B) = k17_euclid(C) & r1_xxreal_0(k18_euclid(A),k18_euclid(B)) & r1_xxreal_0(k18_euclid(B),k18_euclid(C)) ) => r2_hidden(B,k1_rltopsp1(k15_euclid(2),A,C)) ) ) ) ) )).
fof(t7_goboard8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,2),k3_finseq_1(A)) ) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,2),k3_finseq_1(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),1) ) => ( ( ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,2),1) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),2) ) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,2),1) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),1)),k7_xcmplx_0(1,2)),k19_euclid(k5_numbers,1)),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),2)),k7_xcmplx_0(1,2))),k3_topreal1(2,A)) ) ) ) ) ) ) )).
fof(t7_goboard9,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => k4_finseq_5(k1_numbers,k2_goboard1(A)) = k2_goboard1(k4_finseq_5(u1_struct_0(k15_euclid(2)),A)) ) )).
fof(t7_gobrd10,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ ( r1_xxreal_0(C,A) & r1_xxreal_0(D,B) & r1_xxreal_0(E,A) & r1_xxreal_0(F,B) & ! [G] : ( m2_finseq_1(G,k4_ordinal1) => ! [H] : ( m2_finseq_1(H,k4_ordinal1) => ~ ( ! [I] : ( m1_subset_1(I,k4_ordinal1) => ! [J] : ( m1_subset_1(J,k4_ordinal1) => ! [K] : ( m1_subset_1(K,k4_ordinal1) => ( ( r2_hidden(I,k4_finseq_1(G)) & J = k1_funct_1(G,I) & K = k1_funct_1(H,I) ) => ( r1_xxreal_0(J,A) & r1_xxreal_0(K,B) ) ) ) ) ) & k1_funct_1(G,1) = C & k1_funct_1(G,k3_finseq_1(G)) = E & k1_funct_1(H,1) = D & k1_funct_1(H,k3_finseq_1(H)) = F & k3_finseq_1(G) = k3_finseq_1(H) & k3_finseq_1(G) = k1_nat_1(k1_nat_1(k1_nat_1(k1_nat_1(k7_nat_d(C,E),k7_nat_d(E,C)),k7_nat_d(D,F)),k7_nat_d(F,D)),1) & ! [I] : ( m1_subset_1(I,k4_ordinal1) => ( r1_xxreal_0(1,I) => ( r1_xxreal_0(k3_finseq_1(G),I) | r2_gobrd10(k7_partfun1(k4_ordinal1,G,I),k7_partfun1(k4_ordinal1,H,I),k7_partfun1(k4_ordinal1,G,k1_nat_1(I,1)),k7_partfun1(k4_ordinal1,H,k1_nat_1(I,1))) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t7_gobrd11,axiom,( ! [A] : ( ( ~ 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))) ) => u1_struct_0(k15_euclid(2)) = k3_tarski(a_1_0_gobrd11(A)) ) )).
fof(t7_gobrd12,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( ( r2_hidden(D,k4_finseq_1(B)) & E = k1_funct_1(B,D) & F = k1_funct_1(C,D) ) => ( r1_xxreal_0(E,k3_finseq_1(k2_goboard2(A))) & r1_xxreal_0(F,k1_matrix_0(k2_goboard2(A))) ) ) ) ) ) ) => ( ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(D,k4_finseq_1(B)) & r1_tarski(k1_tops_1(k15_euclid(2),k3_goboard5(k2_goboard2(A),k7_partfun1(k4_ordinal1,B,D),k7_partfun1(k4_ordinal1,C,D))),k4_subset_1(u1_struct_0(k15_euclid(2)),k2_goboard9(A),k3_goboard9(A))) ) ) | ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(B)) => r1_tarski(k1_tops_1(k15_euclid(2),k3_goboard5(k2_goboard2(A),k7_partfun1(k4_ordinal1,B,D),k7_partfun1(k4_ordinal1,C,D))),k4_subset_1(u1_struct_0(k15_euclid(2)),k2_goboard9(A),k3_goboard9(A))) ) ) ) ) ) ) ) )).
fof(t7_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [F] : ( ( ~ v3_relat_1(F) & v1_matrix_0(F) & v1_goboard1(F) & v2_goboard1(F) & v3_goboard1(F) & v4_goboard1(F) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),E,k7_nat_d(A,1),C),k9_matrix_0(F)) & r1_xxreal_0(A,k3_finseq_1(E)) & r1_xxreal_0(1,C) & r1_xxreal_0(C,k1_matrix_0(E)) & r1_xxreal_0(B,k3_finseq_1(F)) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k1_matrix_0(F)) & k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),F,B,D) ) => ( r1_xxreal_0(A,1) | r1_xxreal_0(B,1) | r1_xxreal_0(k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),E,k7_nat_d(A,1),C)),k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),F,k7_nat_d(B,1),D))) ) ) ) ) ) ) ) ) )).
fof(t7_gobrd14,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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)))) ) => r1_xxreal_0(3,k7_nat_d(k3_finseq_1(k1_jordan8(B,A)),1)) ) ) )).
fof(t7_goedcpuc,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_qc_trans(B,A) & m1_qc_lang1(B) ) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k2_qc_lang1(A),k3_qc_lang1(A)) => ( k1_qc_trans(A,B,k9_cqc_lang(A,C,D)) = k9_cqc_lang(B,k1_qc_trans(A,B,C),k1_qc_trans(A,B,D)) & k1_qc_trans(A,B,k12_cqc_lang(A,E,C)) = k12_cqc_lang(B,k2_qc_trans(A,B,E),k1_qc_trans(A,B,C)) ) ) ) ) ) ) )).
fof(t7_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( ( v1_henmodel(D,A) & m1_subset_1(D,k1_zfmisc_1(k3_cqc_lang(A))) ) => ! [E] : ( m1_henmodel(E,A,D) => ( ( v1_goedelcp(D,A) & v2_goedelcp(D,A) ) => ( ( v1_goedelcp(D,A) & v2_goedelcp(D,A) & ~ ( r1_valuat_1(A,k1_henmodel(A),B,E,k3_henmodel(A)) <=> r1_henmodel(A,D,B) ) ) | ( v1_goedelcp(D,A) & v2_goedelcp(D,A) & ~ ( r1_valuat_1(A,k1_henmodel(A),C,E,k3_henmodel(A)) <=> r1_henmodel(A,D,C) ) ) | ( r1_valuat_1(A,k1_henmodel(A),k7_cqc_lang(A,B,C),E,k3_henmodel(A)) <=> r1_henmodel(A,D,k7_cqc_lang(A,B,C)) ) ) ) ) ) ) ) ) )).
fof(t7_gr_cy_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_group_1(A,B) = k7_group_1(k5_group_4(A,k6_domain_1(u1_struct_0(A),B))) ) ) )).
fof(t7_gr_cy_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ( v8_struct_0(A) & A = k5_group_4(A,k6_domain_1(u1_struct_0(A),B)) ) => ! [C] : ( ( v15_algstr_0(C) & m1_group_2(C,A) ) => ? [D] : ( m1_subset_1(D,k4_ordinal1) & r1_group_2(A,C,k5_group_4(A,k6_domain_1(u1_struct_0(A),k5_group_1(A,D,B)))) ) ) ) ) ) )).
fof(t7_gr_cy_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_gr_cy_3(A) ) => ( ~ r1_xxreal_0(A,7) => k4_nat_d(A,12) = 11 ) ) )).
fof(t7_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_graph_1(A) & l1_graph_1(A) ) => A = k5_graph_1(A,A) ) )).
fof(t7_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k1_graph_2(A,1,k3_finseq_1(A)) = A ) )).
fof(t7_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_graph_1(B,A) => ( B = k1_xboole_0 => v1_msscyc_1(B,A) ) ) ) )).
fof(t7_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( ( v7_graph_1(C,A) & m2_graph_1(C,A) ) => ( r3_graph_4(A,B,C) => ( C = k1_xboole_0 | r1_tarski(k10_xtuple_0(B),k2_xboole_0(k1_graph_4(A,k10_xtuple_0(C)),k2_graph_4(A,k10_xtuple_0(C)))) ) ) ) ) ) )).
fof(t7_graphsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v7_graph_1(B,A) & m2_graph_1(B,A) ) => ! [C] : ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_graph_5(A,D,E,B,C) <=> r2_graph_5(A,D,E,B,k2_xboole_0(C,k1_tarski(E))) ) ) ) ) ) )).
fof(t7_grcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_algstr_0(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_algstr_0(C) ) => ! [D] : ( ( 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] : ( ( 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)))) ) => ( ( v13_vectsp_1(D,A,B) & v13_vectsp_1(E,B,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) ) ) ) ) ) ) )).
fof(t7_grfunc_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( k9_xtuple_0(B) = k1_tarski(A) => B = k1_tarski(k4_tarski(A,k1_funct_1(B,A))) ) ) )).
fof(t7_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k2_group_3(A,k3_group_5(A,B,k2_group_1(A,C),D),C) = k3_group_5(A,C,B,k2_group_3(A,D,C)) ) ) ) ) )).
fof(t7_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,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,k7_polynom1(A,C,D,E)),k2_termord(A,B,k3_termord(A,B,C,D),k3_termord(A,B,C,E))) ) ) ) ) ) )).
fof(t7_groeb_2,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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) <=> r6_pboole(A,k2_groeb_2(A,B,C),B) ) ) ) )).
fof(t7_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [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) & v1_vectsp_2(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom7(C,A,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] : ( ( 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)))) ) => k2_polynom7(A,B,k10_polynom1(A,B,C,D)) = k11_pre_poly(A,k2_polynom7(A,B,C),k2_polynom7(A,B,D)) ) ) ) ) )).
fof(t7_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t7_group_10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( 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)))) ) => ( r1_group_10(A,B,D,C) => k13_group_10(A,B,D,C) = k6_domain_1(B,C) ) ) ) ) ) )).
fof(t7_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( v15_algstr_0(C) & v1_group_3(C,A) & m1_group_2(C,A) ) => ? [D] : ( v15_algstr_0(D) & m1_group_2(D,A) & u1_struct_0(D) = k7_group_4(A,B,C) ) ) ) ) )).
fof(t7_group_12,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_group_7(A,B))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_group_7(A,B))) => ( ( r1_struct_0(k2_group_12(A,B,C),E) & r1_struct_0(k2_group_12(A,B,D),F) ) => ( C = D | k6_algstr_0(k2_group_7(A,B),E,F) = k6_algstr_0(k2_group_7(A,B),F,E) ) ) ) ) ) ) ) ) )).
fof(t7_group_14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( 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)))) ) => ( 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)) & v13_vectsp_1(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)))) ) ) ) ) ) )).
fof(t7_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ~ ( B != k1_xboole_0 & k1_group_2(A,B) = k1_xboole_0 ) & ~ ( k1_group_2(A,B) != k1_xboole_0 & B = k1_xboole_0 ) ) ) ) )).
fof(t7_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_group_2(C,A) => k13_group_2(A,C,B) = k11_group_2(A,C,k6_domain_1(u1_struct_0(A),B)) ) ) ) )).
fof(t7_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_group_4(A,k8_finseq_1(u1_struct_0(A),k12_finseq_1(u1_struct_0(A),C),B)) = k6_algstr_0(A,C,k3_group_4(A,B)) ) ) ) )).
fof(t7_group_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( v15_algstr_0(C) & v1_group_3(C,B) & m1_group_2(C,B) ) => ! [D] : ( ( v15_algstr_0(D) & v1_group_3(D,B) & m1_group_2(D,B) ) => ( r1_struct_0(k8_group_4(B,C,D),A) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & ? [F] : ( 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) ) ) ) ) ) ) )).
fof(t7_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ( m1_group_6(k9_group_5(A),A,B) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_struct_0(B,k2_group_5(A,C,D)) ) ) ) ) ) )).
fof(t7_group_7,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) & v1_group_7(D) & v2_group_7(D,A) & v3_group_7(D,A) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_group_7(A,D))) => ( ( E = B & ! [F] : ~ ( r2_hidden(F,A) & ! [G] : ( ( ~ v2_struct_0(G) & v2_group_1(G) & v3_group_1(G) & l3_algstr_0(G) ) => ! [H] : ( m1_subset_1(H,u1_struct_0(G)) => ~ ( G = k1_funct_1(D,F) & k1_funct_1(C,F) = k2_group_1(G,H) & H = k1_funct_1(B,F) ) ) ) ) ) => C = k2_group_1(k2_group_7(A,D),E) ) ) ) ) ) )).
fof(t7_group_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ( B != k1_group_1(A) & k5_group_4(A,k6_domain_1(u1_struct_0(A),B)) = k6_group_2(A) ) ) ) )).
fof(t7_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t7_groupp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( v1_group_3(B,A) & r1_struct_0(B,D) ) => ! [E] : ( v7_ordinal1(E) => ? [F] : ( m1_subset_1(F,u1_struct_0(A)) & r1_struct_0(B,F) & k5_group_1(A,E,k6_algstr_0(A,C,D)) = k6_algstr_0(A,k5_group_1(A,E,C),F) ) ) ) ) ) ) ) )).
fof(t7_grsolv_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & v5_group_1(A) & l3_algstr_0(A) ) => v1_grsolv_1(A) ) )).
fof(t7_hahnban,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ( r1_rlsub_2(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_struct_0(C,D) => k4_rlsub_2(A,D,B,C) = k1_domain_1(u1_struct_0(A),u1_struct_0(A),k4_struct_0(A),D) ) ) ) ) ) ) )).
fof(t7_hahnban1,axiom,( ! [A] : ( v1_xreal_0(A) => k9_complex1(k1_hahnban1(A,k5_numbers)) = k9_complex1(A) ) )).
fof(t7_hallmar1,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m2_finseq_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r2_hidden(D,A) & r2_hidden(D,k4_finseq_1(C)) ) => r1_tarski(k1_funct_1(C,D),k1_hallmar1(B,C,A)) ) ) ) ) )).
fof(t7_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_funct_1(k6_weierstr(A,B),C) = k5_numbers <=> ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(E,B) & ~ r1_xxreal_0(D,k3_metric_1(A,C,E)) ) ) ) ) ) ) ) ) )).
fof(t7_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(C,k3_finseq_1(k1_helly(A,B))) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) ) )).
fof(t7_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ~ ( ~ v1_henmodel(B,A) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ~ ( r1_tarski(C,B) & v1_finset_1(C) & ~ v1_henmodel(C,A) ) ) ) ) ) )).
fof(t7_hermitan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ( A != k4_struct_0(k1_complfld) => ( k9_complex1(k1_hahnban1(k7_xcmplx_0(k3_complex1(A),k9_complex1(A)),k7_xcmplx_0(k1_real_1(k4_complex1(A)),k9_complex1(A)))) = 1 & k3_complex1(k8_group_1(k1_complfld,k1_hahnban1(k7_xcmplx_0(k3_complex1(A),k9_complex1(A)),k7_xcmplx_0(k1_real_1(k4_complex1(A)),k9_complex1(A))),A)) = k9_complex1(A) & k4_complex1(k8_group_1(k1_complfld,k1_hahnban1(k7_xcmplx_0(k3_complex1(A),k9_complex1(A)),k7_xcmplx_0(k1_real_1(k4_complex1(A)),k9_complex1(A))),A)) = k5_numbers ) ) ) )).
fof(t7_hessenbe,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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 ) ) ) ) ) ) ) )).
fof(t7_heyting1,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k2_zfmisc_1(k5_finsub_1(A),k5_finsub_1(A)),k7_normform(A)) => r2_hidden(B,k3_funct_2(k7_normform(A),u1_struct_0(k12_normform(A)),k4_heyting1(A),B)) ) )).
fof(t7_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ( C = k1_xboole_0 => k1_heyting2(A,B,C) = k1_xboole_0 ) ) ) )).
fof(t7_heyting3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => k5_lattices(A) = k3_yellow_0(k3_lattice3(A)) ) )).
fof(t7_hfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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_fdiff_1(C,B) ) ) ) ) )).
fof(t7_hilbasis,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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,k2_relset_1(k15_pre_poly(A),k20_pre_poly(A,B))) <=> r3_pre_poly(A,C,B) ) ) ) ) )).
fof(t7_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ( ( r2_hidden(B,k5_hilbert1(A)) & r2_hidden(k3_hilbert1(B,C),k5_hilbert1(A)) ) => r2_hidden(C,k5_hilbert1(A)) ) ) ) ) )).
fof(t7_hilbert2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) ) => ( k1_funct_1(k6_trees_4(A,B,C),k14_trees_3(k5_numbers)) = k1_funct_1(B,k1_xboole_0) & k1_funct_1(k6_trees_4(A,B,C),k14_trees_3(1)) = k1_funct_1(C,k1_xboole_0) ) ) ) )).
fof(t7_hilbert3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k1_partfun1(A,k2_tarski(k1_xboole_0,1),k2_tarski(k5_numbers,1),k4_ordinal1,k5_funct_3(B,A),k5_funct_4(k4_ordinal1,k5_numbers,1,1,k5_numbers)) = k5_funct_3(k3_subset_1(A,B),A) ) )).
fof(t7_holder_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( ~ r1_xxreal_0(A,1) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k1_numbers) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [G] : ( v7_ordinal1(G) => ( k9_nat_1(k1_numbers,D,G) = k2_power(k9_complex1(k9_nat_1(k1_numbers,B,G)),A) & k9_nat_1(k1_numbers,E,G) = k2_power(k9_complex1(k9_nat_1(k1_numbers,C,G)),A) & k9_nat_1(k1_numbers,F,G) = k2_power(k9_complex1(k3_real_1(k9_nat_1(k1_numbers,B,G),k9_nat_1(k1_numbers,C,G))),A) ) ) => ! [G] : ( v7_ordinal1(G) => r1_xxreal_0(k2_power(k9_nat_1(k1_numbers,k3_series_1(F),G),k7_xcmplx_0(1,A)),k2_xcmplx_0(k2_power(k9_nat_1(k1_numbers,k3_series_1(D),G),k7_xcmplx_0(1,A)),k2_power(k9_nat_1(k1_numbers,k3_series_1(E),G),k7_xcmplx_0(1,A)))) ) ) ) ) ) ) ) ) ) )).
fof(t7_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A))) => ! [K] : ( m1_subset_1(K,k1_zfmisc_1(u1_struct_0(A))) => ( ( r5_aff_1(A,K,J) & r2_hidden(D,K) & r2_hidden(F,K) & r2_hidden(E,K) & r2_hidden(G,K) & v7_aff_2(A) & r2_hidden(B,J) & r2_hidden(C,J) & r2_hidden(H,J) & r2_hidden(I,J) & r2_analoaf(A,D,B,E,H) & r2_analoaf(A,D,C,E,I) & r2_analoaf(A,F,B,G,H) ) => ( B = C | F = D | r2_analoaf(A,F,C,G,I) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t7_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k6_margrel1) ) => k2_idea_1(A,B,C) = k2_idea_1(A,C,B) ) ) ) )).
fof(t7_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ( ~ v1_xboole_0(k6_domain_1(u1_struct_0(A),k4_struct_0(A))) & v1_ideal_1(k6_domain_1(u1_struct_0(A),k4_struct_0(A)),A) & v2_ideal_1(k6_domain_1(u1_struct_0(A),k4_struct_0(A)),A) & v3_ideal_1(k6_domain_1(u1_struct_0(A),k4_struct_0(A)),A) & m1_subset_1(k6_domain_1(u1_struct_0(A),k4_struct_0(A)),k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(t7_incproj,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = C ) ) ) )).
fof(t7_incsp_1,axiom,( ! [A] : ( l2_incsp_1(A) => ! [B] : ( m1_subset_1(B,u4_incsp_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_incsp_1(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_incsp_1(A))) => ( ( r1_tarski(D,C) & r5_incsp_1(A,C,B) ) => r5_incsp_1(A,D,B) ) ) ) ) ) )).
fof(t7_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m3_index_1(B,u1_struct_0(A),u4_struct_0(A),u2_graph_1(A),u1_graph_1(A)) => ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => r1_funct_2(u4_struct_0(k2_index_1(u4_struct_0(A),k3_relat_1(u2_graph_1(A),k1_xtuple_0(B)),k4_cat_1(A,C))),u4_struct_0(k2_index_1(u4_struct_0(A),k3_relat_1(u1_graph_1(A),k1_xtuple_0(B)),k4_cat_1(A,C))),u4_struct_0(k2_index_1(u1_struct_0(A),k1_xtuple_0(B),C)),u4_struct_0(k2_index_1(u1_struct_0(A),k1_xtuple_0(B),C)),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),k4_cat_1(A,C)),k10_cat_1(k2_index_1(u1_struct_0(A),k1_xtuple_0(B),C))) ) & ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ( k3_graph_1(A,D) = k4_graph_1(A,C) => 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),k1_cat_1(A,C,D)) = k1_partfun1(u4_struct_0(k2_index_1(u4_struct_0(A),k3_relat_1(u2_graph_1(A),k1_xtuple_0(B)),D)),u4_struct_0(k2_index_1(u4_struct_0(A),k3_relat_1(u1_graph_1(A),k1_xtuple_0(B)),D)),u4_struct_0(k2_index_1(u4_struct_0(A),k3_relat_1(u2_graph_1(A),k1_xtuple_0(B)),C)),u4_struct_0(k2_index_1(u4_struct_0(A),k3_relat_1(u1_graph_1(A),k1_xtuple_0(B)),C)),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),D),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),C)) ) ) ) ) ) ) ) )).
fof(t7_instalg1,axiom,( ! [A] : ( l1_msualg_1(A) => ( v1_instalg1(A) <=> k9_xtuple_0(u2_msualg_1(A)) = u4_struct_0(A) ) ) )).
fof(t7_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( ~ r1_xxreal_0(B,A) => r1_xxreal_0(k2_xcmplx_0(A,1),B) ) ) ) )).
fof(t7_int_2,axiom,( ~ m1_subset_1(k4_xcmplx_0(1),k4_ordinal1) )).
fof(t7_int_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ! [B] : ( m1_subset_1(B,k7_card_1(A)) => ! [C] : ( m1_subset_1(C,k7_card_1(A)) => ( ( ~ r1_xxreal_0(A,k2_xcmplx_0(B,C)) => k5_binop_1(k7_card_1(A),k3_gr_cy_1(A),B,C) = k2_xcmplx_0(B,C) ) & ~ ( k5_binop_1(k7_card_1(A),k3_gr_cy_1(A),B,C) = k2_xcmplx_0(B,C) & r1_xxreal_0(A,k2_xcmplx_0(B,C)) ) & ( r1_xxreal_0(A,k2_xcmplx_0(B,C)) => k5_binop_1(k7_card_1(A),k3_gr_cy_1(A),B,C) = k6_xcmplx_0(k2_xcmplx_0(B,C),A) ) & ( k5_binop_1(k7_card_1(A),k3_gr_cy_1(A),B,C) = k6_xcmplx_0(k2_xcmplx_0(B,C),A) => r1_xxreal_0(A,k2_xcmplx_0(B,C)) ) ) ) ) ) ) )).
fof(t7_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( C != k5_numbers => ( r1_int_1(A,B) <=> r1_int_1(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) ) ) ) ) )).
fof(t7_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => ~ ( r1_int_1(C,k3_xcmplx_0(A,B)) & ~ r1_int_1(C,A) & ~ r1_int_1(C,B) ) ) ) ) )).
fof(t7_int_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => k5_int_1(k6_xcmplx_0(B,C),A) = k5_int_1(k6_xcmplx_0(k5_int_1(B,A),k5_int_1(C,A)),A) ) ) ) )).
fof(t7_int_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k8_newton) & v1_funct_1(A) & v1_partfun1(A,k8_newton) & v4_valued_0(A) & v2_pre_poly(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k8_newton) & v1_funct_1(B) & v1_partfun1(B,k8_newton) & v4_valued_0(B) & v2_pre_poly(B) ) => ( ( r1_tarski(k22_pre_poly(k8_newton,A),k22_pre_poly(k8_newton,B)) & k5_relat_1(A,k22_pre_poly(k8_newton,A)) = k5_relat_1(B,k22_pre_poly(k8_newton,A)) ) => r1_int_1(k8_nat_3(k8_newton,A),k8_nat_3(k8_newton,B)) ) ) ) )).
fof(t7_int_8,axiom,( ! [A] : ( ( v1_int_1(A) & ~ v1_abian(A) ) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(3,B) => k5_int_1(k1_newton(A,k11_newton(2,k7_nat_d(B,2))),k1_newton(2,B)) = 1 ) ) ) )).
fof(t7_integr10,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_tarski(k3_integra5(B,C),k1_relset_1(k1_numbers,A)) & r2_integr10(A,B,C) ) => ( r1_xxreal_0(C,B) | ! [D] : ( v1_xreal_0(D) => ( r2_integr10(k26_valued_1(k1_numbers,k1_numbers,A,D),B,C) & k2_integr10(k26_valued_1(k1_numbers,k1_numbers,A,D),B,C) = k3_xcmplx_0(D,k2_integr10(A,B,C)) ) ) ) ) ) ) ) )).
fof(t7_integr11,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( k2_xcmplx_0(B,A) != k5_numbers & k6_xcmplx_0(B,A) != k5_numbers & ~ ( r2_fdiff_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(k2_xcmplx_0(B,A),k5_numbers),k18_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k2_xcmplx_0(B,A))))),k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k6_xcmplx_0(B,A),k5_numbers),k18_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k6_xcmplx_0(B,A))))),k1_numbers) & ! [C] : ( v1_xreal_0(C) => k1_funct_1(k2_fdiff_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(k2_xcmplx_0(B,A),k5_numbers),k18_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k2_xcmplx_0(B,A))))),k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k6_xcmplx_0(B,A),k5_numbers),k18_sin_cos),k7_xcmplx_0(1,k3_xcmplx_0(2,k6_xcmplx_0(B,A))))),k1_numbers),C) = k3_xcmplx_0(k1_funct_1(k16_sin_cos,k3_xcmplx_0(B,C)),k1_funct_1(k18_sin_cos,k3_xcmplx_0(A,C))) ) ) ) ) ) )).
fof(t7_integr12,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,D) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => k1_funct_1(C,E) = 1 ) ) & r1_tarski(D,k2_rcomp_1(k4_xcmplx_0(1),1)) & D = 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,k22_sin_cos,k1_sin_cos9),k3_rfunct_1(k1_numbers,k1_numbers,k22_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,C,k1_taylor_1(2))))) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_sin_cos9),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k1_sin_cos9),k3_seq_4(A))) ) ) ) ) ) )).
fof(t7_integr13,axiom,( ! [A] : ( ( 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,k3_rfunct_1(k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),k22_sin_cos),k4_xcmplx_0(k7_xcmplx_0(1,2))))) => ( r2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k3_rfunct_1(k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),k22_sin_cos),k4_xcmplx_0(k7_xcmplx_0(1,2))),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k3_rfunct_1(k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),k22_sin_cos),k4_xcmplx_0(k7_xcmplx_0(1,2))),A),B) = k7_xcmplx_0(k1_funct_1(k16_sin_cos,B),k1_funct_1(k22_sin_cos,B)) ) ) ) ) ) )).
fof(t7_integr14,axiom,( ! [A] : ( ( 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_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_fdiff_9)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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_fdiff_9)),A),B) = k6_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(1,k1_funct_1(k18_sin_cos,B)),k1_square_1(B)),k7_xcmplx_0(k7_xcmplx_0(k1_funct_1(k16_sin_cos,B),B),k1_square_1(k1_funct_1(k18_sin_cos,B)))) ) ) ) ) ) )).
fof(t7_integr15,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_integra1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) ) => ! [D] : ( m1_subset_1(D,k1_numbers) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & v2_seq_2(k2_partfun1(A,k1_numbers,B,A)) & ! [E] : ( m2_integr15(E,A,B,C) => ~ ! [F] : ( m1_subset_1(F,k4_ordinal1) => r1_xxreal_0(k3_funct_2(k4_ordinal1,k1_numbers,k3_integr15(A,B,C,E),F),k3_real_1(k3_funct_2(k4_ordinal1,k1_numbers,k4_integra2(A,B,C),F),D)) ) ) ) ) ) ) ) )).
fof(t7_integr16,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( B = k1_integr16(A) => k18_rvsum_1(B) = k3_complex1(k17_rvsum_1(A)) ) ) ) )).
fof(t7_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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,k2_vfunct_1(B,A,C,D)) & v1_integr18(C,A,B) & v1_integr18(D,A,B) ) => ( v1_integr18(E,A,B) & k4_integr18(A,B,E) = k5_algstr_0(A,k4_integr18(A,B,C),k4_integr18(A,B,D)) ) ) ) ) ) ) ) )).
fof(t7_integr19,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(C,D) & r1_xxreal_0(D,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),k1_relset_1(k1_numbers,E)) & r1_tarski(k3_integra5(A,B),k1_relset_1(k1_numbers,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))) ) ) ) ) ) ) ) ) )).
fof(t7_integra1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v5_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => r1_xxreal_0(k5_numbers,k3_integra1(A)) ) )).
fof(t7_integra2,axiom,( ! [A] : ( v3_membered(A) => ! [B] : ( v1_xreal_0(B) => ( v1_xboole_0(A) <=> v1_xboole_0(k1_integra2(A,B)) ) ) ) )).
fof(t7_integra3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( m1_integra1(D,C) => ! [E] : ( m1_integra1(E,C) => ( ( r1_integra1(D,E) & r2_hidden(A,k4_finseq_1(D)) & r2_hidden(B,k4_finseq_1(D)) & r1_xxreal_0(A,B) ) => ( r1_xxreal_0(k13_integra1(C,D,E,A),k13_integra1(C,D,E,B)) & r2_hidden(k13_integra1(C,D,E,A),k4_finseq_1(E)) ) ) ) ) ) ) ) )).
fof(t7_integra4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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_comseq_2(k2_partfun1(A,k1_numbers,B,A)) & v3_integra1(B,A) & ! [C] : ( v1_xreal_0(C) => ~ ( r1_xxreal_0(k3_seq_4(k1_rvsum_1(B)),C) & r1_xxreal_0(C,k2_seq_4(k1_rvsum_1(B))) & k12_integra1(A,B) = k3_xcmplx_0(C,k3_integra1(A)) ) ) ) ) ) )).
fof(t7_integra5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v1_seq_2(k2_partfun1(k1_numbers,k1_numbers,B,A)) => v1_seq_2(k2_partfun1(A,k1_numbers,k1_integra5(B,A),A)) ) ) ) )).
fof(t7_integra6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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)) & r1_integra5(A,B) & v1_comseq_2(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => ( r1_integra5(A,k56_valued_1(k1_numbers,k1_numbers,B)) & r1_xxreal_0(k9_complex1(k2_integra5(A,B)),k2_integra5(A,k56_valued_1(k1_numbers,k1_numbers,B))) ) ) ) ) )).
fof(t7_integra7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ! [C] : ( ( 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) ) ) ) )).
fof(t7_integra8,axiom,( k17_sin_cos(k7_xcmplx_0(k28_sin_cos,4)) = k7_xcmplx_0(k3_square_1(2),2) )).
fof(t7_integra9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( A != k5_numbers => k2_integra5(B,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,k5_numbers),k18_sin_cos)) = k6_xcmplx_0(k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,k5_numbers),k16_sin_cos),k7_xcmplx_0(1,A)),k2_seq_4(B)),k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,k5_numbers),k16_sin_cos),k7_xcmplx_0(1,A)),k3_seq_4(B))) ) ) ) )).
fof(t7_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => k1_interva1(A,B,k1_subset_1(A)) = k1_xboole_0 ) ) )).
fof(t7_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => r2_hidden(k3_intpro_1(C,k5_intpro_1(B,C)),k7_intpro_1(A)) ) ) ) )).
fof(t7_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(B,k5_numbers) => k1_funct_1(k1_irrat_1(A),B) = k6_xcmplx_0(1,k7_xcmplx_0(A,B)) ) ) ) )).
fof(t7_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ( v2_funct_1(C) => v2_funct_1(k7_cat_1(A,B,C)) ) ) ) ) )).
fof(t7_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ! [C] : r1_isocat_1(k9_nattra_1(k3_cat_1(B,C),A),A) ) )).
fof(t7_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_isomichi(B,A) => v1_isomichi(k3_subset_1(u1_struct_0(A),B),A) ) ) ) )).
fof(t7_jct_misc,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r2_hidden(C,A) & r2_hidden(D,B) ) => r1_xxreal_0(k1_jct_misc(A,B),k9_complex1(k6_xcmplx_0(C,D))) ) ) ) ) ) )).
fof(t7_jgraph_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k1_jgraph_1(A))) => ( ( r1_xxreal_0(1,k3_finseq_1(B)) & B = C ) => r3_graph_4(k1_jgraph_1(A),C,k4_jgraph_1(A,B)) ) ) ) ) )).
fof(t7_jgraph_2,axiom,( k1_relset_1(u1_struct_0(k15_euclid(2)),k5_pscomp_1) = u1_struct_0(k15_euclid(2)) & k1_relset_1(u1_struct_0(k15_euclid(2)),k5_pscomp_1) = k1_euclid(2) )).
fof(t7_jgraph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) != k5_numbers ) & ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( 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(1,k1_square_1(k7_xcmplx_0(F,G))) ) ) ) ) & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).
fof(t7_jgraph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) = k9_complex1(E) ) ) ) & v5_pre_topc(C,A,k3_topmetr) ) ) ) ) ) )).
fof(t7_jgraph_5,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_pre_topc(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ! [E] : ( ( 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))))) ) => ! [F] : ( ( 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] : ( ( 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)))) ) => ( ( r2_relset_1(u1_struct_0(A),u1_struct_0(C),G,k1_partfun1(u1_struct_0(A),u1_struct_0(k1_pre_topc(B,D)),u1_struct_0(B),u1_struct_0(C),E,F)) & v5_pre_topc(E,A,k1_pre_topc(B,D)) & v5_pre_topc(F,B,C) ) => v5_pre_topc(G,A,C) ) ) ) ) ) ) ) ) )).
fof(t7_jgraph_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ~ ( v5_pre_topc(B,A,k3_topmetr) & ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) = k6_xcmplx_0(F,C) ) ) ) & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).
fof(t7_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( ( k18_euclid(A) = F & k18_euclid(B) = F & r1_xxreal_0(C,k17_euclid(A)) & r1_xxreal_0(k17_euclid(B),D) ) => ( r1_xxreal_0(D,C) | r1_xxreal_0(F,E) | r1_xxreal_0(k17_euclid(B),k17_euclid(A)) | r1_jordan6(k1_sppol_2(C,D,E,F),A,B) ) ) ) ) ) ) ) ) )).
fof(t7_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r2_hidden(A,k1_rltopsp1(k15_euclid(2),B,C)) & v1_sppol_1(k1_rltopsp1(k15_euclid(2),B,C)) ) => v1_sppol_1(k1_rltopsp1(k15_euclid(2),A,C)) ) ) ) ) )).
fof(t7_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => a_4_1_jordan1(A,B,C,D) = k2_xboole_0(k2_xboole_0(k2_xboole_0(a_1_1_jordan1(A),a_1_3_jordan1(B)),a_1_0_jordan1(C)),a_1_2_jordan1(D)) ) ) ) ) )).
fof(t7_jordan11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_jordan1h(B,A) => ( ~ r1_xxreal_0(k5_jordan11(B,A),1) & r1_xxreal_0(k5_jordan11(B,A),k1_matrix_0(k1_jordan8(B,A))) ) ) ) ) )).
fof(t7_jordan12,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k15_euclid(2))) => ( 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)) => r2_jordan12(2,k4_graph_2(u1_struct_0(k15_euclid(2)),A,B),C) ) ) ) ) ) )).
fof(t7_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_jordan1h(A,B) & r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(k1_jordan13(A,B))) ) => ( r1_xboole_0(k2_gobrd13(k1_jordan13(A,B),k1_jordan8(A,B),C),A) & ~ r1_xboole_0(k3_gobrd13(k1_jordan13(A,B),k1_jordan8(A,B),C),A) ) ) ) ) ) )).
fof(t7_jordan15,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(B,D) & r1_xxreal_0(D,E) & r1_xxreal_0(E,C) & r1_xxreal_0(C,k1_matrix_0(A)) ) => r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,k1_jordan1a(A),D),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,k1_jordan1a(A),E)),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,k1_jordan1a(A),B),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,k1_jordan1a(A),C))) ) ) ) ) ) ) )).
fof(t7_jordan16,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(B,A) & r2_hidden(C,A) & ~ r1_jordan6(A,B,C) & ~ r1_jordan6(A,C,B) ) ) ) ) )).
fof(t7_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(B,A) & ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( B != C & r1_jordan6(A,B,C) ) ) ) ) ) )).
fof(t7_jordan18,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => k3_seq_4(k7_relset_1(u1_struct_0(k15_euclid(2)),k1_numbers,k5_pscomp_1,k4_topreal1(A))) = k18_euclid(A) ) )).
fof(t7_jordan19,axiom,( ! [A] : ( ( v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(C,k8_metric_1(A,E,B)) & r2_hidden(D,k8_metric_1(A,E,B)) & r1_xxreal_0(k3_xcmplx_0(2,B),k3_metric_1(A,C,D)) ) ) ) ) ) ) )).
fof(t7_jordan1a,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => r1_xboole_0(k1_jordan2c(2,A),A) ) )).
fof(t7_jordan1b,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( v2_sppol_1(k1_rltopsp1(k15_euclid(2),A,B)) => ( A = B | v4_topreal1(k2_finseq_4(u1_struct_0(k15_euclid(2)),A,B)) ) ) ) ) )).
fof(t7_jordan1c,axiom,( ! [A] : ( ( v2_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( k1_jordan2c(2,A) != k1_xboole_0 => r1_xxreal_0(k8_pscomp_1(k1_jordan2c(2,A)),k8_pscomp_1(A)) ) ) )).
fof(t7_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & ~ r1_xxreal_0(k3_finseq_1(k2_jordan9(B,A)),C) & r2_hidden(k21_pscomp_1(B),k2_gobrd13(k2_jordan9(B,A),k1_jordan8(B,A),C)) ) ) ) )).
fof(t7_jordan1e,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ( v4_topreal1(A) => ! [B] : ( 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,k2_jordan3(A,B))) ) => k1_funct_1(A,1) = B ) ) ) ) )).
fof(t7_jordan1f,axiom,( ! [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] : ( v7_ordinal1(B) => k7_partfun1(u1_struct_0(k15_euclid(2)),k1_jordan1e(A,B),k3_finseq_1(k1_jordan1e(A,B))) = k22_pscomp_1(k3_topreal1(2,k2_jordan9(A,B))) ) ) )).
fof(t7_jordan1g,axiom,( ! [A] : ( ( v1_matrix_0(A) & v1_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(k4_tarski(B,D),k2_matrix_0(A)) & r2_hidden(k4_tarski(C,E),k2_matrix_0(A)) & k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,D)) = k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),A,C,E)) ) => B = C ) ) ) ) ) ) )).
fof(t7_jordan1h,axiom,( ! [A] : ( ( v1_finset_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => v5_valued_0(k7_pre_poly(k1_numbers,A,k1_jordan1h)) ) )).
fof(t7_jordan1j,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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_hidden(k20_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))),k10_xtuple_0(k1_jordan1e(B,A))) & r2_hidden(k20_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))),k3_topreal1(2,k1_jordan1e(B,A))) ) ) ) )).
fof(t7_jordan1k,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( r1_tarski(B,C) & r3_connsp_1(A,D,B) & r3_connsp_1(A,D,C) ) => B = C ) ) ) ) ) )).
fof(t7_jordan20,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v4_topreal1(B) & m2_finseq_1(B,u1_struct_0(k15_euclid(2))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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,k2_topreal1(2,B,A)) & k18_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),B,A)) = k18_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),B,k1_nat_1(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,D) ) => ( r1_xxreal_0(k3_finseq_1(B),A) | r1_xxreal_0(k17_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),B,k1_nat_1(A,1))),k17_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),B,A))) | r1_xxreal_0(k17_euclid(C),k17_euclid(D)) ) ) ) ) ) ) )).
fof(t7_jordan22,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => r2_hidden(k1_domain_1(k4_ordinal1,k4_ordinal1,2,1),k2_matrix_0(k1_jordan8(A,B))) ) ) )).
fof(t7_jordan23,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( k3_finseq_1(A) != 2 => ( v2_jordan23(A) <=> v3_jordan23(A) ) ) ) )).
fof(t7_jordan24,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ? [B] : ( m3_topgrp_1(B,k15_euclid(2)) & r1_jordan24(2,k7_relset_1(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),B,A),k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) ) ) )).
fof(t7_jordan2b,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r1_xxreal_0(B,A) => k17_finseq_1(k1_numbers,B,k5_euclid(A)) = k5_euclid(B) ) ) ) )).
fof(t7_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( r1_jordan2c(A,B,C) <=> ? [D] : ( 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)))) ) ) ) ) ) )).
fof(t7_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(B,k2_topreal1(2,A,C)) => r1_xxreal_0(k1_jordan3(A,B),C) ) ) ) ) )).
fof(t7_jordan4,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v7_ordinal1(B) => ( v4_topreal1(A) => ( r1_xxreal_0(k3_finseq_1(A),k1_nat_1(B,1)) | v4_topreal1(k2_rfinseq(u1_struct_0(k15_euclid(2)),B,A)) ) ) ) ) )).
fof(t7_jordan5a,axiom,( ! [A] : ( ( v1_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] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( A = B => v1_fcont_1(B) ) ) ) )).
fof(t7_jordan5b,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k17_borsuk_1),u1_struct_0(k1_pre_topc(k15_euclid(2),B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k17_borsuk_1),u1_struct_0(k1_pre_topc(k15_euclid(2),B))))) ) => ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(A)) & v4_topreal1(A) & B = k3_topreal1(2,A) & v3_tops_2(C,k17_borsuk_1,k1_pre_topc(k15_euclid(2),B)) & k1_funct_1(C,k5_numbers) = k7_partfun1(u1_struct_0(k15_euclid(2)),A,1) & k1_funct_1(C,1) = k7_partfun1(u1_struct_0(k15_euclid(2)),A,k3_finseq_1(A)) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,E) & r1_xxreal_0(k5_numbers,E) & r1_xxreal_0(E,1) & r1_xxreal_0(k5_numbers,F) & r1_xxreal_0(F,1) & k2_topreal1(2,A,D) = k7_relset_1(u1_struct_0(k17_borsuk_1),u1_struct_0(k1_pre_topc(k15_euclid(2),B)),C,k1_rcomp_1(E,F)) & k1_funct_1(C,E) = k7_partfun1(u1_struct_0(k15_euclid(2)),A,D) & k1_funct_1(C,F) = k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(D,1)) ) ) ) ) ) ) ) ) )).
fof(t7_jordan5c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( ( r1_tarski(A,B) & v4_pre_topc(A,k15_euclid(2)) & r1_topreal1(k15_euclid(2),C,D,A) ) => ( k1_jordan5c(A,B,C,D) = C & k2_jordan5c(A,B,C,D) = D ) ) ) ) ) ) )).
fof(t7_jordan6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( B = a_1_3_jordan6(A) => v4_pre_topc(B,k15_euclid(2)) ) ) ) )).
fof(t7_jordan7,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( ( r2_hidden(B,A) & v1_topreal2(A) ) => r2_hidden(B,k1_jordan7(A,B,k18_pscomp_1(A))) ) ) ) )).
fof(t7_jordan9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ~ ( r1_xxreal_0(A,k3_finseq_1(B)) & r2_hidden(C,k3_topreal1(2,k2_rfinseq(u1_struct_0(k15_euclid(2)),A,B))) & ! [D] : ( v7_ordinal1(D) => ~ ( r1_xxreal_0(k1_nat_1(A,1),D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(B)) & r2_hidden(C,k2_topreal1(2,B,D)) ) ) ) ) ) )).
fof(t7_jordan_a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( ~ v1_xboole_0(C) & v2_compts_1(C,k15_euclid(A)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) ) => ~ ( r1_subset_1(B,C) & r1_xxreal_0(k4_jordan1k(A,B,C),k5_numbers) ) ) ) ) )).
fof(t7_knaster,axiom,( ! [A] : ! [B] : ( ( 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)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_tarski(C,k3_funct_2(k1_zfmisc_1(A),k9_setfam_1(A),B,C)) => r1_tarski(C,k2_knaster(A,B)) ) ) ) )).
fof(t7_kolmog01,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(B)) ) => ( r1_tarski(D,k1_kolmog01(A,B,E,C)) <=> ! [F] : ( m1_prob_1(F,A,B) => ! [G] : ( m1_prob_1(G,A,B) => ( ( r2_hidden(F,D) & r2_hidden(G,E) ) => r1_prob_2(A,B,C,F,G) ) ) ) ) ) ) ) ) ) )).
fof(t7_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => r1_tarski(k2_kurato_0(A,B),k3_kurato_0(A,B)) ) )).
fof(t7_kurato_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_xxreal_0(k5_card_1(k2_kurato_1(A,B)),14) ) ) )).
fof(t7_kurato_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => ~ ( D = B & B != C & ! [E] : ( v1_xreal_0(E) => r2_hidden(C,k8_metric_1(k14_euclid(A),D,E)) ) ) ) ) ) ) )).
fof(t7_lang1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => ! [B] : ( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ! [C] : ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ( r2_lang1(A,B,C) => r3_lang1(A,B,C) ) ) ) ) )).
fof(t7_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( 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))) ) => k1_card_1(a_3_0_laplace(A,B,C)) = k7_newton(A) ) ) ) ) )).
fof(t7_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( m1_group_2(D,B) => ? [E] : ( v15_algstr_0(E) & m1_group_2(E,A) & u1_struct_0(E) = k8_relset_1(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(D)) ) ) ) ) ) )).
fof(t7_latsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B))) => ( r2_hidden(C,u1_struct_0(A)) | r2_hidden(C,k6_subset_1(u1_struct_0(B),u1_struct_0(A))) ) ) ) ) )).
fof(t7_lattice2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ! [F] : ( m1_subset_1(F,A) => ( r2_hidden(F,C) => k1_funct_1(E,F) = k1_funct_1(D,F) ) ) => k7_funct_4(A,B,D,k2_partfun1(A,B,E,C)) = D ) ) ) ) ) )).
fof(t7_lattice3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_lattices(A,B,C) <=> r3_orders_2(k3_lattice3(A),k4_lattice3(A,B),k4_lattice3(A,C)) ) ) ) ) )).
fof(t7_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( v20_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))) ) ) )).
fof(t7_lattice5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_lattice3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_lattice3(A))) => k12_lattice3(k3_lattice3(A),B,C) = k4_lattices(A,k5_lattice3(A,B),k5_lattice3(A,C)) ) ) ) )).
fof(t7_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ~ r1_lattice6(A,k5_lattices(A),B) ) ) )).
fof(t7_lattice7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => r1_xxreal_0(1,k1_lattice7(A,B)) ) ) )).
fof(t7_lattice8,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(A),u1_struct_0(k1_lattice5(D))) & v19_waybel_0(E,A,k1_lattice5(D)) & v20_waybel_0(E,A,k1_lattice5(D)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(k1_lattice5(D))))) ) => ( ( v2_funct_1(E) & r3_orders_2(k1_yellow_2(A,k1_lattice5(D),E),k3_funct_2(u1_struct_0(A),u1_struct_0(k1_yellow_2(A,k1_lattice5(D),E)),k2_waybel_1(A,k1_lattice5(D),E),B),k3_funct_2(u1_struct_0(A),u1_struct_0(k1_yellow_2(A,k1_lattice5(D),E)),k2_waybel_1(A,k1_lattice5(D),E),C)) ) => r3_orders_2(A,B,C) ) ) ) ) ) ) )).
fof(t7_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v7_lattices(A) & v8_lattices(A) & v9_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_lattices(A,B,C) => r1_lattices(A,k2_lattices(A,B,D),k2_lattices(A,C,D)) ) ) ) ) ) )).
fof(t7_lfuzzy_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_lfuzzy_0(A) & l1_orders_2(A) ) => ( ? [B] : ( v1_xreal_0(B) & r2_hidden(B,u1_struct_0(A)) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,u1_struct_0(A)) => r1_xxreal_0(C,B) ) ) ) <=> v2_yellow_0(A) ) ) )).
fof(t7_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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_lfuzzy_1(A,B,C),B) ) ) ) )).
fof(t7_limfunc1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_limfunc1(k1_valued_0(k1_numbers,B,A)) => v1_limfunc1(B) ) & ( v2_limfunc1(k1_valued_0(k1_numbers,B,A)) => v2_limfunc1(B) ) ) ) ) )).
fof(t7_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( v2_comseq_2(C) & k1_seq_2(C) = B & ~ r1_xxreal_0(A,k5_numbers) & ! [D] : ( m1_subset_1(D,k4_ordinal1) => ? [E] : ( m1_subset_1(E,k4_ordinal1) & r1_xxreal_0(D,E) & ~ ( ~ r1_xxreal_0(k3_funct_2(k4_ordinal1,k1_numbers,C,E),k6_xcmplx_0(B,A)) & ~ r1_xxreal_0(k2_xcmplx_0(B,A),k3_funct_2(k4_ordinal1,k1_numbers,C,E)) ) ) ) ) ) ) ) )).
fof(t7_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v7_limfunc1(A) & v4_limfunc1(B) & ! [C] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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))) ) ) ) => v7_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) )).
fof(t7_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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(B) <=> g1_vectsp_1(A,u1_struct_0(B),u1_algstr_0(B),u2_struct_0(B),u1_vectsp_1(A,B)) = k1_vectsp_4(A,B) ) ) ) )).
fof(t7_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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_binop_1(k5_vectsp_5(A,B),k3_vectsp_5(A,B)) & v2_binop_1(k5_vectsp_5(A,B),k3_vectsp_5(A,B)) & v1_setwiseo(k5_vectsp_5(A,B),k3_vectsp_5(A,B)) & k1_vectsp_4(A,B) = k4_binop_1(k3_vectsp_5(A,B),k5_vectsp_5(A,B)) ) ) ) )).
fof(t7_lopban_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m2_funct_2(C,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => k1_funct_1(k3_lopban_1(A,B),k1_domain_1(k4_ordinal1,k9_funct_2(A,u1_struct_0(B)),1,C)) = C ) ) ) )).
fof(t7_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(k8_lopban_1(A,A)),k10_lopban_1(A,A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(k8_lopban_1(A,A)),k10_lopban_1(A,A)) => ! [D] : ( m2_subset_1(D,u1_struct_0(k8_lopban_1(A,A)),k10_lopban_1(A,A)) => k3_lopban_2(A,k3_lopban_2(A,D,C),B) = k3_lopban_2(A,D,k3_lopban_2(A,C,B)) ) ) ) ) )).
fof(t7_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( m2_valued_0(C,u1_struct_0(A),B) & v3_normsp_1(B,A) ) => v3_normsp_1(C,A) ) ) ) ) )).
fof(t7_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v3_normsp_1(C,A) => k6_normsp_1(A,k3_lopban_3(A,C,B)) = k6_algstr_0(A,k6_normsp_1(A,C),B) ) ) ) ) )).
fof(t7_lopban_5,axiom,( ! [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) & v3_lopban_1(A) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k4_normsp_2(A)))) => ! [C] : ( ( ~ 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) & v3_lopban_1(C) & l1_normsp_1(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(k16_lopban_1(A,C))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k16_lopban_1(A,C))))) ) => ( ( v1_tops_1(B,k4_normsp_2(A)) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(E,B) => v3_normsp_1(k2_lopban_5(A,C,D,E),C) ) ) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ? [F] : ( v1_xreal_0(F) & r1_xxreal_0(k5_numbers,F) & ! [G] : ( v7_ordinal1(G) => r1_xxreal_0(k2_normsp_0(C,k5_rsspace3(C,k2_lopban_5(A,C,D,E),G)),F) ) ) ) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => v3_normsp_1(k2_lopban_5(A,C,D,E),C) ) ) ) ) ) ) )).
fof(t7_lopban_6,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k4_normsp_2(A)))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k4_normsp_2(A)))) => ( ( B = D & C = E ) => k7_rusub_4(A,B,C) = k7_rusub_4(k4_normsp_2(A),D,E) ) ) ) ) ) ) )).
fof(t7_lopban_7,axiom,( ! [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) & v3_lopban_1(A) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & 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] : ( ( 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)))) ) => ( 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)) & v13_vectsp_1(k2_funct_1(C),B,A) & v1_lopban_1(k2_funct_1(C),B,A) & v2_lopban_1(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)))) ) ) ) ) ) )).
fof(t7_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => m2_subset_1(k2_struct_0(A),k1_zfmisc_1(u1_struct_0(A)),k1_lopclset(A)) ) )).
fof(t7_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => ( ~ v2_struct_0(g1_rlvect_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)))) & v13_algstr_0(g1_rlvect_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)))) & v2_rlvect_1(g1_rlvect_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)))) & v3_rlvect_1(g1_rlvect_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)))) & v4_rlvect_1(g1_rlvect_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)))) & v5_rlvect_1(g1_rlvect_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)))) & v6_rlvect_1(g1_rlvect_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)))) & v7_rlvect_1(g1_rlvect_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)))) & v8_rlvect_1(g1_rlvect_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)))) & l1_rlvect_1(g1_rlvect_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)))) ) ) ) )).
fof(t7_lpspacc1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_rfunct_3(C,B,k2_numbers,k3_rfunct_3(B,k2_numbers)) => ! [D] : ( m2_rfunct_3(D,B,k2_numbers,k3_rfunct_3(B,k2_numbers)) => ( D = k1_binop_1(k8_lpspacc1(B),A,C) <=> ( k1_relset_1(B,D) = k1_relset_1(B,C) & ! [E] : ( m1_subset_1(E,B) => ( r2_hidden(E,k1_relset_1(B,C)) => k1_funct_1(D,E) = k3_xcmplx_0(A,k1_funct_1(C,E)) ) ) ) ) ) ) ) ) )).
fof(t7_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_rfunct_3(B,A,k1_numbers,k3_rfunct_3(A,k1_numbers)) => ! [C] : ( m2_rfunct_3(C,A,k1_numbers,k3_rfunct_3(A,k1_numbers)) => ! [D] : ( m2_rfunct_3(D,A,k1_numbers,k3_rfunct_3(A,k1_numbers)) => ( r2_relset_1(A,k1_numbers,D,k2_lpspace1(A,k1_numbers,k3_lpspace1(A),B,C)) <=> ( k1_relset_1(A,D) = k9_subset_1(A,k1_relset_1(A,B),k1_relset_1(A,C)) & ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,k1_relset_1(A,D)) => k1_funct_1(D,E) = k3_xcmplx_0(k1_funct_1(B,E),k1_funct_1(C,E)) ) ) ) ) ) ) ) ) )).
fof(t7_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( v6_supinf_2(D) => ( r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(C,k5_numbers) | r2_relset_1(A,k1_numbers,k20_valued_1(A,k1_numbers,k1_numbers,k2_mesfun6c(B,A,D),k2_mesfun6c(C,A,D)),k2_mesfun6c(k2_xcmplx_0(B,C),A,D)) ) ) ) ) ) ) )).
fof(t7_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => ( k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(D),k1_domain_1(k4_ordinal1,k1_hilbert1,C,k4_ltlaxio1(A,B))) = 1 <=> ( k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(D),k1_domain_1(k4_ordinal1,k1_hilbert1,C,A)) = 1 & k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(D),k1_domain_1(k4_ordinal1,k1_hilbert1,C,B)) = 1 ) ) ) ) ) ) )).
fof(t7_ltlaxio2,axiom,( ! [A] : ( m2_finseq_1(A,k1_hilbert1) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(1,B) => ( r1_xxreal_0(k3_finseq_1(A),B) | k7_partfun1(k1_hilbert1,k2_ltlaxio2(A),k1_nat_1(B,1)) = k4_ltlaxio1(k7_partfun1(k1_hilbert1,k2_ltlaxio2(A),B),k7_partfun1(k1_hilbert1,A,k1_nat_1(B,1))) ) ) ) ) )).
fof(t7_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ( r2_hidden(k3_hilbert1(A,B),k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,C)) => ( r2_hidden(A,k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,C)) & r2_hidden(B,k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,C)) ) ) ) ) ) )).
fof(t7_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => k12_ltlaxio3(k11_ltlaxio3(k6_finseq_1(k1_hilbert1),k12_finseq_1(k1_hilbert1,A))) = k4_ltlaxio1(k3_ltlaxio1,k1_ltlaxio1(A)) ) )).
fof(t7_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => r2_hidden(k8_cqc_lang(A,C,k8_cqc_lang(A,k8_cqc_lang(A,C,B),B)),k4_cqc_the1(A)) ) ) ) )).
fof(t7_margrel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => m1_subset_1(k1_tarski(B),k3_margrel1(A)) ) ) )).
fof(t7_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k6_rusub_4(A,B,k6_domain_1(u1_struct_0(A),C)) = k1_mathmorp(A,C,B) ) ) ) )).
fof(t7_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( v2_matrix10(B) => v1_matrix10(k2_matrix10(A,B)) ) ) ) )).
fof(t7_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,k5_finsub_1(k2_sgraph1(k2_finseq_1(k1_nat_1(A,2))))) => ! [D] : ( m1_matrix_2(D,k3_matrix_2(k1_nat_1(A,2))) => ! [E] : ( m1_matrix_2(E,k3_matrix_2(k1_nat_1(A,2))) => ! [F] : ( v1_finset_1(F) => ( F = a_5_0_matrix11(A,B,C,D,E) => ( ( k4_nat_d(k5_card_1(F),2) = k5_numbers => k7_setwiseo(k2_sgraph1(k2_finseq_1(k1_nat_1(A,2))),u1_struct_0(B),u2_algstr_0(B),C,k1_matrix11(A,B,D)) = k7_setwiseo(k2_sgraph1(k2_finseq_1(k1_nat_1(A,2))),u1_struct_0(B),u2_algstr_0(B),C,k1_matrix11(A,B,E)) ) & ( k4_nat_d(k5_card_1(F),2) = 1 => k7_setwiseo(k2_sgraph1(k2_finseq_1(k1_nat_1(A,2))),u1_struct_0(B),u2_algstr_0(B),C,k1_matrix11(A,B,D)) = k4_algstr_0(B,k7_setwiseo(k2_sgraph1(k2_finseq_1(k1_nat_1(A,2))),u1_struct_0(B),u2_algstr_0(B),C,k1_matrix11(A,B,E))) ) ) ) ) ) ) ) ) ) )).
fof(t7_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ( r2_hidden(C,k4_finseq_1(k3_matrix_1(B,A))) => k4_matrix_3(B,k2_matrix12(A,A,B,k3_matrix_1(B,A),C,D),E) = k2_matrix12(A,A,B,E,C,D) ) ) ) ) ) ) )).
fof(t7_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & v1_matrix_2(C,A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => k12_matrix_3(A,B,C) = k1_finsop_1(u1_struct_0(B),k13_matrix_3(A,B,C),u2_algstr_0(B)) ) ) ) )).
fof(t7_matrix14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(A)) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k3_finseq_1(D) = k3_finseq_1(E) ) => k11_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),k11_fvsum_1(A,B,C),k11_fvsum_1(A,D,E)) ) ) ) ) ) ) )).
fof(t7_matrix15,axiom,( ! [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) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(C,k4_finseq_1(B)) & r2_hidden(D,k4_finseq_1(B)) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(B)) => ( E = C | E = D | k1_funct_1(B,E) = k4_struct_0(A) ) ) ) ) => ( C = D | k4_rlvect_1(A,B) = k3_rlvect_1(A,k7_partfun1(u1_struct_0(A),B,C),k7_partfun1(u1_struct_0(A),B,D)) ) ) ) ) ) ) )).
fof(t7_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix16(C,u1_struct_0(B)) & v1_matrix16(D,u1_struct_0(B)) ) => v1_matrix16(k3_matrix_3(B,C,D),u1_struct_0(B)) ) ) ) ) ) )).
fof(t7_matrix17,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,B,A,A) & m2_finseq_1(C,k3_finseq_2(B)) ) => ( v4_matrix17(C,B) => ( r1_xxreal_0(A,k5_numbers) | v4_matrix17(k4_matrix_0(B,C),B) ) ) ) ) ) )).
fof(t7_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => v1_matrix_0(k2_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),k12_finseq_1(A,B),k12_finseq_1(A,C))) ) ) ) )).
fof(t7_matrix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_matrix_2(B,k3_matrix_2(A)) => ( k1_partfun1(k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_funct_2(k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),B),B) = k1_finseq_2(A) & k1_partfun1(k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),B,k2_funct_2(k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),B)) = k1_finseq_2(A) ) ) ) )).
fof(t7_matrix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(k4_tarski(C,D),k2_matrix_0(k3_matrix_1(B,A))) & D = C ) => k1_funct_1(k7_matrix_0(u1_struct_0(B),k3_matrix_1(B,A),C),D) = k5_struct_0(B) ) ) ) ) ) )).
fof(t7_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) & k1_matrix_4(A,B,C) = k1_matrix_3(A,k3_finseq_1(B),k1_matrix_0(B)) ) => B = C ) ) ) ) )).
fof(t7_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ( k3_finseq_1(A) = k3_finseq_1(k1_matrix_5(A)) & k1_matrix_0(A) = k1_matrix_0(k1_matrix_5(A)) ) ) )).
fof(t7_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ( ( r2_matrix_6(A,B,D,E) & r2_matrix_6(A,B,C,E) ) => C = D ) ) ) ) ) ) )).
fof(t7_matrix_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( r1_xxreal_0(1,k3_finseq_1(B)) => B = k8_finseq_1(A,k17_finseq_1(A,k7_nat_d(k3_finseq_1(B),1),B),k3_finseq_6(A,B,k3_finseq_1(B),k3_finseq_1(B))) ) ) ) )).
fof(t7_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_8(C,A,B) & v1_matrix_8(D,A,B) & k4_matrix_3(B,C,D) = k2_matrix_3(B,k4_matrix_3(B,D,C)) ) => v1_matrix_8(k3_matrix_3(B,C,D),A,B) ) ) ) ) ) )).
fof(t7_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k2_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k1_matrix_0(A) = k1_matrix_0(B) ) => k1_matrixc1(k3_matrix_5(A,B)) = k3_matrix_5(k1_matrixc1(A),k1_matrixc1(B)) ) ) ) )).
fof(t7_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ( r2_hidden(A,k2_finseq_1(k2_wsierp_1(B))) => ( k7_nat_d(k1_matrixj1(B,A),1) = k6_xcmplx_0(k1_matrixj1(B,A),1) & ~ r1_xxreal_0(A,k2_wsierp_1(k17_finseq_1(k4_ordinal1,k7_nat_d(k1_matrixj1(B,A),1),B))) ) ) ) ) )).
fof(t7_matrixj2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m2_finseq_2(E,u1_struct_0(C),k4_finseq_2(B,u1_struct_0(C))) => ( r2_hidden(A,k2_finseq_1(B)) => ( ( A = 1 => k13_fvsum_1(C,k8_matrix_0(u1_struct_0(C),k2_matrixj2(C,D,B),A),E) = k8_group_1(C,D,k7_partfun1(u1_struct_0(C),E,A)) ) & ( A != 1 => k13_fvsum_1(C,k8_matrix_0(u1_struct_0(C),k2_matrixj2(C,D,B),A),E) = k3_rlvect_1(C,k8_group_1(C,D,k7_partfun1(u1_struct_0(C),E,A)),k7_partfun1(u1_struct_0(C),E,k6_xcmplx_0(A,1))) ) ) ) ) ) ) ) ) )).
fof(t7_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => k8_rvsum_1(A,k6_rvsum_1(B)) = k4_rvsum_1(A,B) ) ) ) )).
fof(t7_matrixr2,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k1_matrix_0(A) = k1_matrix_0(B) ) => ( r1_xxreal_0(k3_finseq_1(A),k5_numbers) | k3_matrixr1(A,k5_matrixr1(B,B)) = A ) ) ) ) )).
fof(t7_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_vectsp_6(D,A,B) => ! [E] : ( m1_vectsp_6(E,A,B) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B))) => ( ( v1_vectsp_7(F,A,B) & r1_tarski(k1_vectsp_6(A,B,D),F) & r1_tarski(k1_vectsp_6(A,B,E),F) & k4_vectsp_6(A,B,D) = k4_vectsp_1(A,B,C,k4_vectsp_6(A,B,E)) ) => ( C = k4_struct_0(A) | r1_vectsp_6(A,B,D,k6_vectsp_6(A,B,C,E)) ) ) ) ) ) ) ) ) )).
fof(t7_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(A)) => k5_matrlin(A,B,k3_fvsum_1(A,D,E),C) = k3_fvsum_1(B,k5_matrlin(A,B,D,C),k5_matrlin(A,B,E,C)) ) ) ) ) ) )).
fof(t7_matroid0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_tdlat_3(A) & l1_pre_topc(A) ) => ( ~ v2_struct_0(A) & ~ v3_pencil_1(A) & v1_matroid0(A) & v2_matroid0(A) & l1_pre_topc(A) ) ) )).
fof(t7_matrtop1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( 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) & ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_finseq_1(k1_finseq_3(B,A)),k4_finseq_1(k1_finseq_3(B,A))) & v3_funct_2(E,k4_finseq_1(k1_finseq_3(B,A)),k4_finseq_1(k1_finseq_3(B,A))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_1(k1_finseq_3(B,A)),k4_finseq_1(k1_finseq_3(B,A))))) ) => k1_finseq_3(C,A) != k3_relat_1(E,k1_finseq_3(B,A)) ) ) ) ) ) )).
fof(t7_matrtop2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k6_prvect_1(k2_vectsp_1,A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( B = C => ( v1_vectsp_7(B,k2_vectsp_1,k6_prvect_1(k2_vectsp_1,A)) <=> v1_rlvect_3(C,k15_euclid(A)) ) ) ) ) ) )).
fof(t7_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,k2_finseq_1(B)) => ( v1_matrix_1(k1_matrtop3(B,A),k2_vectsp_1) & k1_matrix_6(B,k2_vectsp_1,k1_matrtop3(B,A)) = k1_matrtop3(B,A) ) ) ) ) )).
fof(t7_mazurulm,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_comseq_2(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k1_seq_2(k9_valued_1(k4_ordinal1,k1_numbers,B,A)) = k1_xxreal_3(A,k1_seq_2(B)) ) ) )).
fof(t7_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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,B),k1_mboolean(A,C)),k1_mboolean(A,k2_pboole(A,B,C))) ) ) )).
fof(t7_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(B,k2_zfmisc_1(C,k1_tarski(A))) => ( r2_hidden(k1_xtuple_0(B),C) & k2_xtuple_0(B) = A ) ) )).
fof(t7_measure1,axiom,( ! [A] : ! [B] : ( ( ~ 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) & r2_hidden(A,B) ) ) )).
fof(t7_measure2,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ( ( k9_nat_1(B,D,k5_numbers) = k9_nat_1(B,C,k5_numbers) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => k9_nat_1(B,D,k1_nat_1(F,1)) = k2_xboole_0(k9_nat_1(B,C,k1_nat_1(F,1)),k9_nat_1(B,D,F)) ) & k9_nat_1(B,E,k5_numbers) = k9_nat_1(B,C,k5_numbers) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => k9_nat_1(B,E,k1_nat_1(F,1)) = k6_subset_1(k9_nat_1(B,C,k1_nat_1(F,1)),k9_nat_1(B,D,F)) ) ) => ! [F] : ( m1_subset_1(F,k4_ordinal1) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ( r1_xxreal_0(F,G) => r1_tarski(k9_nat_1(B,E,F),k9_nat_1(B,D,G)) ) ) ) ) ) ) ) ) )).
fof(t7_measure3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ( ( k9_nat_1(B,D,k5_numbers) = k1_xboole_0 & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( k9_nat_1(B,D,k1_nat_1(F,1)) = k3_measure1(A,B,k9_nat_1(B,E,k5_numbers),k9_nat_1(B,E,F)) & r1_tarski(k9_nat_1(B,E,k1_nat_1(F,1)),k9_nat_1(B,E,F)) ) ) ) => ( r1_xxreal_0(k1_supinf_1,k12_supinf_2(C,k9_nat_1(B,E,k5_numbers))) | k12_supinf_2(C,k2_measure2(A,B,k1_measure3(A,B,D))) = k4_supinf_2(k12_supinf_2(C,k9_nat_1(B,E,k5_numbers)),k12_supinf_2(C,k1_measure2(A,B,k1_measure3(A,B,E)))) ) ) ) ) ) ) )).
fof(t7_measure4,axiom,( ! [A] : ! [B] : ! [C] : ( m1_measure4(C,B) => ( r2_hidden(A,k1_measure4(B,C)) => r2_hidden(k6_subset_1(B,A),k1_measure4(B,C)) ) ) )).
fof(t7_measure5,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ! [B] : ( m1_subset_1(B,k6_numbers) => ( ( ~ r1_xxreal_0(B,A) => k2_measure5(k2_xxreal_1(A,B)) = k4_supinf_2(B,A) ) & ( r1_xxreal_0(B,A) => k2_measure5(k2_xxreal_1(A,B)) = k1_supinf_2 ) ) ) ) )).
fof(t7_measure7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( v6_supinf_2(B) => v6_supinf_2(k1_measure7(A,B)) ) ) ) )).
fof(t7_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [E] : ( m4_measure8(E,A,B,D) => r1_xxreal_0(k7_supinf_2(k5_measure8(A,B,C,k5_setfam_1(A,k2_relset_1(k9_setfam_1(A),D)))),k19_supinf_2(k4_measure8(A,B,D,C,E))) ) ) ) ) )).
fof(t7_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => k4_member_1(k6_subset_1(A,B)) = k6_subset_1(k4_member_1(A),k4_member_1(B)) ) ) )).
fof(t7_membered,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_membered(A) ) => ? [B] : ( v1_xcmplx_0(B) & r2_hidden(B,A) ) ) )).
fof(t7_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( l1_memstr_0(B,A) => ! [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)) & v4_memstr_0(C,A,B) ) => k6_memstr_0(A,B,C) = C ) ) ) )).
fof(t7_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => k1_euclid_6(k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),A,k6_xcmplx_0(1,E)),k1_rlvect_1(k15_euclid(2),D,E)),B,C) = k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(1,E),k1_euclid_6(A,B,C)),k3_xcmplx_0(E,k1_euclid_6(D,B,C))) ) ) ) ) ) )).
fof(t7_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ( r2_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,k5_comseq_3(A,C),D),k5_comseq_3(A,k2_partfun1(A,k2_numbers,C,D))) & r2_relset_1(A,k1_numbers,k2_partfun1(A,k1_numbers,k6_comseq_3(A,C),D),k6_comseq_3(A,k2_partfun1(A,k2_numbers,C,D))) ) ) ) ) ) )).
fof(t7_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & v1_mesfunc8(B,A,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( ~ 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] : ( m2_subset_1(D,k1_zfmisc_1(A),C) => ! [E] : ( v7_ordinal1(E) => ( r1_mesfunc6(A,C,k4_mesfunc5(A,k1_numbers,B,E),D) => r1_mesfunc1(A,C,k4_mesfunc5(A,k6_numbers,k1_mesfun7c(A,B),E),D) ) ) ) ) ) ) )).
fof(t7_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => r2_funct_2(k4_ordinal1,k4_partfun1(A,k6_numbers),k4_mesfunc9(A,k1_mesfun7c(A,B)),k1_mesfun7c(A,k2_mesfun9c(A,B))) ) ) )).
fof(t7_mesfunc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( k9_xtuple_0(k9_mesfunc1(A,B,1)) = k6_subset_1(k9_xtuple_0(B),k8_relat_1(B,k1_tarski(k1_supinf_2))) & ! [C] : ( m1_subset_1(C,A) => ( r2_hidden(C,k9_xtuple_0(k9_mesfunc1(A,B,1))) => k12_supinf_2(k9_mesfunc1(A,B,1),C) = k2_extreal1(k8_mesfunc1,k12_supinf_2(B,C)) ) ) ) ) ) )).
fof(t7_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( 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_mesfunc1(A,B,k3_mesfunc1(A,C,D),E) ) ) ) ) ) ) )).
fof(t7_mesfunc3,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k4_finseq_1(B)) => ( r1_tarski(k1_funct_1(B,C),k3_tarski(k2_relset_1(A,B))) & k3_xboole_0(k1_funct_1(B,C),k3_tarski(k2_relset_1(A,B))) = k1_funct_1(B,C) ) ) ) ) )).
fof(t7_mesfunc5,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ! [B] : ( m1_subset_1(B,k6_numbers) => ! [C] : ( m1_subset_1(C,k6_numbers) => ( r1_xxreal_0(C,k5_numbers) => ( k4_xxreal_3(C,k3_xxreal_0(A,B)) = k4_xxreal_0(k1_extreal1(C,A),k1_extreal1(C,B)) & k4_xxreal_3(C,k4_xxreal_0(A,B)) = k3_xxreal_0(k1_extreal1(C,A),k1_extreal1(C,B)) ) ) ) ) ) )).
fof(t7_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( r2_hidden(D,k10_relat_1(B,C)) <=> ( r2_hidden(D,k1_relset_1(A,B)) & ? [E] : ( v1_xreal_0(E) & E = k12_supinf_2(B,D) & C = E ) ) ) ) ) ) )).
fof(t7_mesfunc7,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => k2_mesfunc7(k12_finseq_1(k6_numbers,A)) = A ) )).
fof(t7_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( m1_subset_1(C,A) => ( r2_hidden(C,k1_relset_1(A,k4_mesfunc5(A,k6_numbers,B,k5_numbers))) => r2_funct_2(k4_ordinal1,k6_numbers,k3_mesfunc5(A,k3_mesfunc8(A,B),C),k3_rinfsup2(k3_mesfunc5(A,B,C))) ) ) ) ) )).
fof(t7_mesfunc9,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ~ ( v7_mesfunc5(A) & ! [B] : ( v1_xreal_0(B) => ~ ( k2_mesfunc5(A) = B & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(D,E) & r1_xxreal_0(C,k3_extreal1(k4_supinf_2(k12_supinf_2(A,E),k2_mesfunc5(A)))) ) ) ) ) ) ) ) & ( v8_mesfunc5(A) => k2_mesfunc5(A) = k1_supinf_1 ) & ( v9_mesfunc5(A) => k2_mesfunc5(A) = k2_supinf_1 ) ) ) )).
fof(t7_metric_1,axiom,( ! [A] : ( ( v6_metric_1(A) & v7_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & r1_xxreal_0(k3_metric_1(A,B,C),k5_numbers) ) ) ) ) )).
fof(t7_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k1_metric_2(A,B)) => k1_metric_2(A,B) = k1_metric_2(A,C) ) ) ) ) )).
fof(t7_metric_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(E,k4_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),u1_struct_0(D))) => ! [F] : ( m1_subset_1(F,k4_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),u1_struct_0(D))) => ( k2_binop_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,k7_metric_3(A,B,C,D),E,F) = k5_numbers <=> E = F ) ) ) ) ) ) ) )).
fof(t7_metric_6,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) & k10_xtuple_0(C) = k6_domain_1(u1_struct_0(A),B) ) ) ) )).
fof(t7_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => r1_ordinal1(k1_card_1(k1_tops_2(A,B,C)),k1_card_1(C)) ) ) ) )).
fof(t7_mfold_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( r1_metrizts(A,B,C,D) => ( v1_xboole_0(C) <=> v1_xboole_0(D) ) ) ) ) ) ) )).
fof(t7_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k3_midsp_1(A,B,C) = B => B = C ) ) ) ) )).
fof(t7_midsp_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( ( ~ v2_struct_0(E) & v13_algstr_0(E) & v3_rlvect_1(E) & v4_rlvect_1(E) & l2_algstr_0(E) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(A,A),u1_struct_0(E)) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,A),u1_struct_0(E)))) ) => ( ( r1_midsp_2(A,E,F) & k2_binop_1(A,A,u1_struct_0(E),F,C,B) = k2_binop_1(A,A,u1_struct_0(E),F,D,B) ) => C = D ) ) ) ) ) ) ) )).
fof(t7_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( m1_midsp_3(B,A) <=> r2_hidden(B,k2_finseq_1(k1_nat_1(A,1))) ) ) ) )).
fof(t7_mmlquer2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) ) => ! [B] : ( ( 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)) ) ) )).
fof(t7_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => k12_mmlquery(A,B,C,1) = k4_mmlquery(A,C,B) ) ) )).
fof(t7_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ 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] : ( m1_mod_2(D,A,B,C) => ? [E] : ( 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)))) & g1_mod_2(A,u1_mod_2(A,D),u2_mod_2(A,D),u3_mod_2(A,D)) = g1_mod_2(A,B,C,E) & v13_vectsp_1(E,B,C) & v1_mod_2(E,A,B,C) ) ) ) ) ) )).
fof(t7_mod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ~ ( k1_mod_3(A,B,C) = k1_vectsp_4(A,B) & C != k1_xboole_0 & C != k6_domain_1(u1_struct_0(B),k4_struct_0(B)) ) ) ) ) )).
fof(t7_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ( g2_algstr_0(u1_struct_0(k3_mod_4(A,B)),u1_algstr_0(k3_mod_4(A,B)),u2_struct_0(k3_mod_4(A,B))) = g2_algstr_0(u1_struct_0(B),u1_algstr_0(B),u2_struct_0(B)) & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) <=> m1_subset_1(C,u1_struct_0(k3_mod_4(A,B))) ) ) ) ) )).
fof(t7_modal_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) & v3_trees_2(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,A) & v1_funct_1(C) & v3_trees_2(C) ) => ! [D] : ( ( v1_relat_1(D) & v5_relat_1(D,A) & v1_funct_1(D) & v3_trees_2(D) ) => ! [E] : ( m1_trees_1(E,k9_xtuple_0(B)) => ( k7_trees_2(B,E,C) = k7_trees_2(B,E,D) => C = D ) ) ) ) ) ) )).
fof(t7_modcat_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k2_modcat_1(A,B)) => ( ~ v2_struct_0(C) & v13_algstr_0(C) & v2_rlvect_1(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & v7_vectsp_1(C,B) & 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) ) ) ) ) )).
fof(t7_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_modelc_1(B) & l2_modelc_1(B) ) => ! [C] : ( ( 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,k9_modelc_1(A)) = k25_modelc_1(B,k24_modelc_1(B,C,A)) ) ) ) )).
fof(t7_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v5_modelc_2(A) => A = k5_modelc_2(k11_modelc_2(A),k12_modelc_2(A)) ) ) )).
fof(t7_modelc_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_modelc_2(C) & m2_finseq_1(C,k4_ordinal1) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k13_modelc_2(C))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k13_modelc_2(C))) => ( ( k10_xtuple_0(A) = k1_modelc_3(C) & v2_funct_1(A) & E = k2_xboole_0(D,k1_tarski(B)) ) => ( r2_hidden(B,D) | k17_modelc_3(C,E,A) = k2_xcmplx_0(k17_modelc_3(C,D,A),k3_finseq_1(B)) ) ) ) ) ) ) ) )).
fof(t7_moebius1,axiom,( k22_pre_poly(k8_newton,k13_nat_3(1)) = k1_xboole_0 )).
fof(t7_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v10_monoid_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_algstr_0(A,B,B) = B ) ) ) )).
fof(t7_monoid_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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) => v1_binop_1(k8_monoid_1(B,B,B,C,A),k9_funct_2(A,B)) ) ) ) )).
fof(t7_morph_01,axiom,( ! [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) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => k6_rusub_4(A,B,C) = a_3_3_morph_01(A,B,C) ) ) ) )).
fof(t7_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [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] : ( ~ ( r2_hidden(C,k1_lang1(k5_msafree(A,B))) & v2_relat_1(B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ~ ( r2_hidden(E,k1_funct_1(B,D)) & C = k4_tarski(E,D) ) ) ) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( r2_hidden(E,k1_funct_1(B,D)) => r2_hidden(k4_tarski(E,D),k1_lang1(k5_msafree(A,B))) ) ) ) ) ) )).
fof(t7_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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_finset_1(D) & v3_trees_2(D) ) ) ) ) ) )).
fof(t7_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_dtconstr(D,u1_struct_0(k5_msafree(A,B)),k5_trees_3(u1_struct_0(k5_msafree(A,B))),k1_msaterm(A,B)) => ( r2_hidden(D,k1_funct_1(u3_msualg_1(A,k11_msafree(A,B)),C)) <=> k7_msaterm(A,B,D) = C ) ) ) ) ) )).
fof(t7_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v6_trees_3(C) ) => ( v2_finset_1(C) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_trees_2(D) ) => ~ ( r2_hidden(A,k3_trees_9(D)) & r2_hidden(D,k10_xtuple_0(C)) & A = k4_trees_4(B,C) ) ) ) ) )).
fof(t7_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( l3_msualg_1(C,A) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( ( r2_hidden(F,k1_funct_1(u3_msualg_1(A,C),E)) & k1_funct_1(D,k1_xboole_0) = k4_tarski(F,E) ) => D = k1_trees_4(k4_tarski(F,E)) ) ) ) ) ) ) )).
fof(t7_msscyc_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => r1_xxreal_0(k3_finseq_1(k1_graph_2(C,A,B)),k3_finseq_1(C)) ) ) ) )).
fof(t7_mssubfam,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) => ( ( r2_hidden(B,D) & r1_xboole_0(B,C) ) => r1_xboole_0(k8_setfam_1(A,D),C) ) ) )).
fof(t7_mssublat,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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) => k6_msualg_1(A) = k6_msualg_1(B) ) ) ) )).
fof(t7_msualg_1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v13_struct_0(A,1) & v5_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => r1_tarski(k3_msualg_1(A,B,C),k3_finseq_2(k10_msualg_1(A,C))) ) ) ) )).
fof(t7_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ( ( m1_msualg_2(B,A,C) & m1_msualg_2(C,A,B) ) => 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)) ) ) ) ) )).
fof(t7_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( l3_msualg_1(C,A) => ( k3_msualg_1(A,B,C) != k1_xboole_0 => ! [D] : ( m1_subset_1(D,k3_msualg_1(A,B,C)) => D = k5_msualg_3(A,C,C,B,k2_msualg_3(u1_struct_0(A),u3_msualg_1(A,C)),D) ) ) ) ) ) )).
fof(t7_msualg_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_msualg_4(C,A,B) & m1_msualg_4(C,A,B,B) ) => r8_pboole(A,k4_msualg_5(A,B,C,C),C) ) ) ) )).
fof(t7_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r2_hidden(D,k3_msualg_1(A,B,C)) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( m1_subset_1(F,k1_funct_1(u3_msualg_1(A,C),k7_partfun1(u1_struct_0(A),k1_msualg_1(A,B),E))) => r2_hidden(k1_funct_7(D,E,F),k3_msualg_1(A,B,C)) ) ) ) ) ) ) ) )).
fof(t7_msualg_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_msualg_5(A,B)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,k6_pboole(A,B,B)))) => ( D = C => ! [E] : ( ( v1_msualg_4(E,A,B) & m1_msualg_4(E,A,B,B) ) => ! [F] : ( ( 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))) & r2_hidden(F,C) ) => r2_pboole(A,E,F) ) ) ) ) ) ) ) ) )).
fof(t7_msualg_8,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_msualg_5(A)))) => r1_tarski(k3_tarski(B),k15_lattice3(k2_msualg_5(A),B)) ) )).
fof(t7_msuhom_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,A) ) => k1_funct_1(k16_funcop_1(D,C),k7_partfun1(B,k5_finseq_2(B,A,D),E)) = C ) ) ) ) ) ) )).
fof(t7_mycielsk,axiom,( ! [A] : ! [B] : ( m1_eqrel_1(B,A) => r1_ordinal1(k1_card_1(B),k1_card_1(A)) ) )).
fof(t7_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_nagata_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( v3_pre_topc(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(C,D) & v1_zfmisc_1(k6_subset_1(k3_setfam_1(k6_domain_1(k1_zfmisc_1(u1_struct_0(A)),D),B),k1_tarski(k1_xboole_0))) ) ) ) ) ) )).
fof(t7_nagata_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) ) => r1_xxreal_0(k9_complex1(k5_real_1(k3_funct_2(u1_struct_0(A),k1_numbers,k3_nagata_2(u1_struct_0(A),B,E),C),k3_funct_2(u1_struct_0(A),k1_numbers,k3_nagata_2(u1_struct_0(A),B,E),D))),k2_binop_1(u1_struct_0(A),u1_struct_0(A),k1_numbers,B,C,D)) ) ) ) ) ) ) )).
fof(t7_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k2_xcmplx_0(A,B) = k5_numbers => ( A = k5_numbers & B = k5_numbers ) ) ) ) )).
fof(t7_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ r1_xxreal_0(A,B) => k1_nat_1(k7_nat_d(A,k1_nat_1(B,1)),1) = k7_nat_d(A,B) ) ) ) )).
fof(t7_nat_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ( r2_hidden(A,k1_rvsum_1(B)) => r1_nat_d(A,k3_wsierp_1(B)) ) ) ) )).
fof(t7_nat_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_nat_d(A,B) => ( r1_xxreal_0(B,k5_numbers) | A = 1 | A = B | ( ~ r1_xxreal_0(A,1) & ~ r1_xxreal_0(B,A) ) ) ) ) ) )).
fof(t7_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ ( v2_funct_1(B) & r2_hidden(A,k4_finseq_1(B)) & r2_hidden(k1_funct_1(B,A),k10_xtuple_0(k2_finseq_3(A,B))) ) ) ) )).
fof(t7_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_nat_d(A,B) => ( r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(A,B) ) ) ) ) )).
fof(t7_nat_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_nat_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_nat_lat)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_nat_lat)) => k1_binop_1(k2_nat_lat,A,k1_binop_1(k2_nat_lat,B,C)) = k1_binop_1(k2_nat_lat,k1_binop_1(k2_nat_lat,A,B),C) ) ) ) )).
fof(t7_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,B,C) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( k2_cat_1(A,F,G) != k1_xboole_0 => ! [H] : ( m1_cat_1(H,A,F,G) => k9_cat_3(A,F,G,C,k9_cat_1(A,B,C,D,E),H) = k9_cat_3(B,k8_cat_1(A,B,D,F),k8_cat_1(A,B,D,G),C,E,k9_cat_3(A,F,G,B,D,H)) ) ) ) ) ) ) ) ) ) )).
fof(t7_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( r2_hidden(C,k2_relset_1(u1_struct_0(A),B)) <=> ? [D] : ( v7_ordinal1(D) & C = k1_normsp_1(A,B,D) ) ) ) ) )).
fof(t7_ncfcont2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)))) ) => ! [F] : ( ( 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,k2_vfunct_1(u1_struct_0(C),D,E,F)) ) ) ) ) ) )).
fof(t7_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v12_struct_0(B,k4_ordinal1,A) <=> ! [C] : ( m1_subset_1(C,k4_ordinal1) => k1_normsp_1(A,B,C) != k4_struct_0(A) ) ) ) ) )).
fof(t7_ndiff_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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)))) ) => ( k7_partfun1(u1_struct_0(B),C,k4_struct_0(A)) = k4_struct_0(B) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ~ r1_xxreal_0(E,k2_normsp_0(A,F)) => r1_xxreal_0(k2_normsp_0(B,k7_partfun1(u1_struct_0(B),C,F)),k3_xcmplx_0(D,k2_normsp_0(A,F))) ) ) ) ) ) ) ) ) ) ) )).
fof(t7_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( 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)))) ) => ! [C] : ( ( 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)))) ) => ( v1_funct_1(k6_vfunct_1(k1_numbers,A,B,C)) & v1_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_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)))) ) ) ) ) )).
fof(t7_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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)) => ( ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => k2_relset_1(k1_euclid(A),C) != k1_tarski(D) ) | ( r2_ndiff_4(A,C,B) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,B) => k7_partfun1(k1_euclid(A),k2_ndiff_4(A,C,B),D) = k5_euclid(A) ) ) ) ) ) ) ) ) )).
fof(t7_neckla_3,axiom,( ! [A] : ( ( v3_necklace(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_necklace(B) & l1_orders_2(B) ) => ( r1_xboole_0(u1_struct_0(A),u1_struct_0(B)) => v3_necklace(k2_neckla_2(A,B)) ) ) ) )).
fof(t7_necklace,axiom,( ! [A] : ! [B] : ! [C] : k1_funct_4(k7_funcop_1(A,B),k7_funcop_1(A,C)) = k7_funcop_1(A,C) )).
fof(t7_net_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_net_1(C) & l1_petri(C) ) => ( ( r2_hidden(k4_tarski(A,B),k1_net_1(C)) & r2_hidden(A,u1_struct_0(C)) ) => r2_hidden(B,u4_struct_0(C)) ) ) )).
fof(t7_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k1_newton(k3_xcmplx_0(B,C),A) = k3_xcmplx_0(k1_newton(B,A),k1_newton(C,A)) ) ) ) )).
fof(t7_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( 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] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( r2_hidden(G,k1_relset_1(u1_struct_0(A),C)) & ~ r1_xxreal_0(F,k2_normsp_0(A,k5_algstr_0(A,G,D))) & r1_xxreal_0(E,k2_normsp_0(B,k5_algstr_0(B,k7_partfun1(u1_struct_0(B),C,G),k7_partfun1(u1_struct_0(B),C,D)))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t7_nfcont_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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) => r3_nfcont_1(B,C,D,A) ) ) ) ) )).
fof(t7_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_euclid(A)))) ) => r2_relset_1(B,k1_euclid(A),k9_integr15(A,k4_xcmplx_0(1),B,C),k2_nfcont_4(A,B,C)) ) ) ) )).
fof(t7_normform,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_finsub_1(B) ) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(A,B)) => k2_normform(A,B,C,k1_normform(A,B,D,C)) = C ) ) ) ) )).
fof(t7_normsp_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_normsp_0(A,k5_algstr_0(A,B,C)) = k2_normsp_0(A,k5_algstr_0(A,C,B)) ) ) ) )).
fof(t7_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_normsp_2(A)))) => ( v3_pre_topc(B,k3_normsp_2(A)) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,B) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(a_3_2_normsp_2(A,C,D),B) ) ) ) ) ) ) ) )).
fof(t7_ntalgo_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => ! [B] : ( m1_subset_1(B,k4_numbers) => ! [C] : ( m1_subset_1(C,k4_numbers) => ( ( C = k5_int_1(A,B) & k3_mcart_1(k4_numbers,k4_numbers,k4_numbers,k2_ntalgo_1(B,C)) = 1 ) => k5_int_1(k3_xcmplx_0(k3_ntalgo_1(A,B),A),B) = k5_int_1(1,B) ) ) ) ) )).
fof(t7_numbers,axiom,( r2_xboole_0(k4_ordinal1,k4_numbers) )).
fof(t7_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( ( v1_o_ring_1(B,A) & v1_o_ring_1(C,A) ) | ( v3_o_ring_1(B,A) & v1_o_ring_1(C,A) ) ) => v3_o_ring_1(k1_algstr_0(A,B,C),A) ) ) ) ) )).
fof(t7_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k6_openlatt(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k6_openlatt(A))) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k1_openlatt(A)) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(u1_struct_0(A)),k1_openlatt(A)) => ( ( B = D & C = E ) => ( r3_lattices(k6_openlatt(A),B,C) <=> r1_tarski(D,E) ) ) ) ) ) ) ) )).
fof(t7_oposet_1,axiom,( v4_orders_2(k2_oposet_1) )).
fof(t7_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_cat_1(A,B,C) != k1_xboole_0 => ! [D] : ( m1_cat_1(D,A,B,C) => k8_oppcat_1(A,C,B,k7_oppcat_1(A,B,C,D)) = D ) ) ) ) ) )).
fof(t7_ordeq_01,axiom,( ! [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) & v3_lopban_1(A) & l1_normsp_1(A) ) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & v1_nfcont_2(k1_abian(u1_struct_0(A),B,C),A) ) => v1_ordeq_01(B) ) ) ) )).
fof(t7_orders_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( r7_relat_2(B,A) <=> ( r1_relat_2(B,A) & r6_relat_2(B,A) ) ) ) )).
fof(t7_orders_2,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( ( r2_orders_2(A,B,C) & r1_orders_2(A,C,D) ) | ( r1_orders_2(A,B,C) & r2_orders_2(A,C,D) ) ) => r2_orders_2(A,B,D) ) ) ) ) ) )).
fof(t7_orders_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => r2_hidden(k6_partfun1(u1_struct_0(A)),k1_orders_3(A,A)) ) )).
fof(t7_ordinal1,axiom,( ! [A] : ( v1_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ( r2_xboole_0(A,B) => r2_hidden(A,B) ) ) ) )).
fof(t7_ordinal2,axiom,( ! [A] : r1_tarski(k2_ordinal1(A),A) )).
fof(t7_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => k2_ordinal1(k1_tarski(A)) = k1_tarski(A) ) )).
fof(t7_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_ordinal2(C) ) => ! [D] : ( ( v1_relat_1(D) & v5_ordinal1(D) & v1_funct_1(D) & v1_ordinal2(D) ) => ( ( k9_xtuple_0(C) = k9_xtuple_0(A) & k9_xtuple_0(A) = k9_xtuple_0(D) & r1_ordinal2(B,C) & r1_ordinal2(B,D) & ! [E] : ( v3_ordinal1(E) => ( r2_hidden(E,k9_xtuple_0(A)) => ( r1_ordinal1(k1_funct_1(C,E),k1_funct_1(A,E)) & r1_ordinal1(k1_funct_1(A,E),k1_funct_1(D,E)) ) ) ) ) => r1_ordinal2(B,A) ) ) ) ) ) )).
fof(t7_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(A,B) => r2_hidden(k11_ordinal2(C,k12_ordinal2(k4_ordinal1,A)),k12_ordinal2(k4_ordinal1,B)) ) ) ) ) )).
fof(t7_ordinal6,axiom,( ! [A] : ( v1_ordinal6(A) => ! [B] : ( v1_ordinal6(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r3_wellord1(k1_wellord2(A),k1_wellord2(B),C) => ! [D] : ! [E] : ( ( r2_hidden(D,A) & r2_hidden(E,A) ) => ( r2_hidden(D,E) <=> r2_hidden(k1_funct_1(C,D),k1_funct_1(C,E)) ) ) ) ) ) ) )).
fof(t7_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( r1_orders_2(B,k5_algstr_0(B,C,D),F) & r1_orders_2(B,k5_algstr_0(B,C,E),F) ) => r1_orders_2(B,k5_algstr_0(B,D,E),F) ) ) ) ) ) ) ) )).
fof(t7_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( 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),k3_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(D,k1_funct_1(k3_relat_1(u1_msualg_1(A),k6_finseq_2(u1_struct_0(A),k5_osafree(A,B))),C)) ) ) ) ) ) )).
fof(t7_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ! [C] : ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ( ( v1_orders_3(A) & r2_osalg_1(A,B,C) ) => B = C ) ) ) ) )).
fof(t7_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,u1_struct_0(A)) & v1_funct_1(B) & v1_partfun1(B,u1_struct_0(A)) ) => r2_pboole(u1_struct_0(A),B,k2_osalg_2(A,B)) ) ) )).
fof(t7_osalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,u1_struct_0(A)) & v1_funct_1(C) & v1_partfun1(C,u1_struct_0(A)) & v1_funcop_1(C) ) => ( v1_osalg_3(C,A) => ( v1_relat_1(k9_pboole(u1_struct_0(A),B,C)) & v4_relat_1(k9_pboole(u1_struct_0(A),B,C),u1_struct_0(A)) & v1_funct_1(k9_pboole(u1_struct_0(A),B,C)) & v1_partfun1(k9_pboole(u1_struct_0(A),B,C),u1_struct_0(A)) & v11_osalg_1(k9_pboole(u1_struct_0(A),B,C),A) ) ) ) ) ) )).
fof(t7_osalg_4,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k1_zfmisc_1(u1_struct_0(A)),k2_osalg_4(A)) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & B = k1_tarski(C) ) ) ) )).
fof(t7_papdesaf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r2_analoaf(A,C,B,B,E) & r3_diraf(A,B,D,F) & r2_diraf(A,C,D,E,F) ) => ( r3_diraf(A,B,C,D) | ( r2_analoaf(A,D,B,B,F) & r2_analoaf(A,C,D,F,E) ) ) ) ) ) ) ) ) ) )).
fof(t7_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_parsp_1(A))) => ( r1_parsp_1(k9_parsp_1(A),B,C,D,E) <=> 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),k8_parsp_1(A)) ) ) ) ) ) ) )).
fof(t7_parsp_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_parsp_1(A))) => ( ( r1_parsp_1(k9_parsp_1(A),C,D,B,E) & r1_parsp_1(k9_parsp_1(A),B,C,D,E) & r1_parsp_1(k9_parsp_1(A),B,D,C,E) ) => ( k3_rlvect_1(A,k1_group_1(A),k1_group_1(A)) = k4_struct_0(A) | r1_parsp_1(k9_parsp_1(A),B,C,B,D) ) ) ) ) ) ) ) )).
fof(t7_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => k3_relat_1(C,k4_relat_1(B)) = C ) )).
fof(t7_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( r2_hidden(C,k9_subset_1(A,k1_relset_1(A,D),B)) => k7_partfun1(A,D,C) = k7_partfun1(A,k1_partfun1(A,A,A,A,k1_partfun2(A,B),D),C) ) ) ) ) ) )).
fof(t7_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => r1_partit1(A,B,A) ) ) )).
fof(t7_partit_2,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( ( r1_relat_2(A,C) & r1_relat_2(B,C) ) => r1_relat_2(k3_relat_1(A,B),C) ) ) ) )).
fof(t7_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => v1_pasch(A) ) )).
fof(t7_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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) ) => r1_pboole(A,B,k2_pboole(A,C,D)) ) ) ) ) )).
fof(t7_pcomps_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v8_pre_topc(A) => v4_pre_topc(k6_domain_1(u1_struct_0(A),B),A) ) ) ) )).
fof(t7_pcomps_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v3_pcomps_1(A) => v2_pcomps_1(A) ) ) )).
fof(t7_pcs_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pcs_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_pcs_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k8_pcs_0(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k8_pcs_0(A,B))) => ( r1_pcs_0(k8_pcs_0(A,B),C,D) <=> ( r1_pcs_0(A,k10_pcs_0(A,B,C),k10_pcs_0(A,B,D)) | r1_pcs_0(B,k11_pcs_0(A,B,C),k11_pcs_0(A,B,D)) ) ) ) ) ) ) )).
fof(t7_pdiff_1,axiom,( ! [A] : ( ( 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] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(1))) => ! [D] : ( v1_xreal_0(D) => ( ( A = k2_pdiff_1(B) & C = k9_finseq_1(D) & r1_ndiff_1(k4_real_ns1(1),k4_real_ns1(1),A,C) ) => ( r1_fdiff_1(B,D) & k1_fdiff_1(B,D) = k1_funct_1(k3_relat_1(k2_funct_1(k1_pdiff_1(1,1)),k3_relat_1(k3_ndiff_1(k4_real_ns1(1),k4_real_ns1(1),A,C),k1_pdiff_1(1,1))),1) ) ) ) ) ) ) )).
fof(t7_pdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(2)) => ! [D] : ( ( 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) & ! [E] : ( m1_rcomp_1(E,A) => ~ ( r1_tarski(E,k1_relset_1(k1_numbers,k1_pdiff_2(2,1,D,C))) & ? [F] : ( v1_funct_1(F) & v3_fdiff_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [G] : ( v1_funct_1(G) & v2_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,E) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(2,1,D,C),H),k1_funct_1(k1_pdiff_2(2,1,D,C),A)) = k2_xcmplx_0(k1_funct_1(F,k6_xcmplx_0(H,A)),k1_funct_1(G,k6_xcmplx_0(H,A))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t7_pdiff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(2)) => ! [D] : ( ( 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) ) => k4_pdiff_3(D,C) = k1_fdiff_1(k1_pdiff_2(2,1,k1_pdiff_3(2,2,D),C),A) ) ) ) ) ) )).
fof(t7_pdiff_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & B = k11_finseq_1(C,D,E) & r1_fdiff_1(k1_pdiff_2(3,1,A,B),C) ) ) ) <=> r3_pdiff_1(3,1,A,B) ) ) ) )).
fof(t7_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) ) => r1_fdiff_1(k1_pdiff_2(3,1,k1_pdiff_3(3,3,E),D),A) ) ) ) ) ) ) )).
fof(t7_pdiff_6,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( 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)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k1_euclid(B),k1_euclid(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(B),k1_euclid(A)))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k16_lopban_1(k4_real_ns1(B),k4_real_ns1(A)))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k16_lopban_1(k4_real_ns1(B),k4_real_ns1(A)))) => ( ( C = E & D = F ) => k7_integr15(A,k1_euclid(B),C,D) = k3_rlvect_1(k16_lopban_1(k4_real_ns1(B),k4_real_ns1(A)),E,F) ) ) ) ) ) ) ) )).
fof(t7_pdiff_7,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_real_ns1(1))) => ( 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,B,C),D),C) = k3_funct_2(u1_struct_0(k4_real_ns1(1)),u1_struct_0(k4_real_ns1(A)),k7_pdiff_1(A,B,k4_struct_0(k4_real_ns1(A))),k5_algstr_0(k4_real_ns1(1),D,k3_funct_2(u1_struct_0(k4_real_ns1(A)),u1_struct_0(k4_real_ns1(1)),k4_pdiff_1(B,A),C))) & k5_algstr_0(k4_real_ns1(A),C,k3_funct_2(u1_struct_0(k4_real_ns1(1)),u1_struct_0(k4_real_ns1(A)),k7_pdiff_1(A,B,C),D)) = k3_funct_2(u1_struct_0(k4_real_ns1(1)),u1_struct_0(k4_real_ns1(A)),k7_pdiff_1(A,B,k4_struct_0(k4_real_ns1(A))),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(B,A),C),D)) ) ) ) ) ) )).
fof(t7_pdiff_8,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k16_lopban_1(k4_real_ns1(A),k4_real_ns1(B)))) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,B) ) => ( m1_subset_1(k3_relat_1(C,k4_pdiff_1(D,B)),u1_struct_0(k16_lopban_1(k4_real_ns1(A),k4_real_ns1(1)))) & r1_xxreal_0(k1_funct_1(k15_lopban_1(k4_real_ns1(A),k4_real_ns1(1)),k3_relat_1(C,k4_pdiff_1(D,B))),k3_xcmplx_0(k1_funct_1(k15_lopban_1(k4_real_ns1(B),k4_real_ns1(1)),k4_pdiff_1(D,B)),k1_funct_1(k15_lopban_1(k4_real_ns1(A),k4_real_ns1(B)),C))) ) ) ) ) ) ) )).
fof(t7_pdiff_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( ( 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,k3_valued_1(k1_euclid(A),k1_numbers,k1_numbers,B,C)),k7_integr15(1,k1_euclid(A),k3_pdiff_1(A,B),k3_pdiff_1(A,C))) & r2_relset_1(k1_euclid(A),k1_euclid(1),k3_pdiff_1(A,k47_valued_1(k1_euclid(A),k1_numbers,k1_numbers,B,C)),k8_integr15(1,k1_euclid(A),k3_pdiff_1(A,B),k3_pdiff_1(A,C))) ) ) ) ) )).
fof(t7_pencil_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v2_pralg_1(B) ) => ! [C] : ( m3_pboole(C,A,k12_pralg_1(A,B)) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k10_pralg_1(A,B,D)))) => m3_pboole(k1_funct_7(C,D,E),A,k12_pralg_1(A,B)) ) ) ) ) ) )).
fof(t7_pencil_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) & v2_pralg_1(B) ) => ! [C] : ( m1_subset_1(C,A) => k1_funct_1(k12_pralg_1(A,B),C) = k2_struct_0(k10_pralg_1(A,B,C)) ) ) ) )).
fof(t7_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m1_vectsp_4(E,A,B) => ! [F] : ( m1_vectsp_4(F,A,B) => ( ( m1_vectsp_4(C,A,D) & m1_vectsp_4(E,A,F) & k2_vectsp_4(A,C) = k2_vectsp_4(A,E) & k2_vectsp_4(A,D) = k2_vectsp_4(A,F) ) => k2_pencil_4(A,B,C,D) = k2_pencil_4(A,B,E,F) ) ) ) ) ) ) ) )).
fof(t7_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_nat_d(A,k4_nat_d(B,A)) => ( A = k5_numbers | r1_nat_d(A,B) ) ) ) ) )).
fof(t7_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u4_struct_0(A))) => k9_petri(A,B) = a_2_7_petri(A,B) ) ) )).
fof(t7_petri_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_petri(B) & v3_petri(B) & l1_petri_2(B) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ( ( r1_tarski(u1_struct_0(A),u1_struct_0(B)) & r1_relset_1(u1_struct_0(A),u4_struct_0(A),u1_petri(A),u1_petri(B)) & r1_relset_1(u4_struct_0(A),u1_struct_0(A),u2_petri(A),u2_petri(B)) & C = D ) => ( r1_tarski(k8_petri(A,k6_domain_1(u4_struct_0(A),C)),k8_petri(B,k6_domain_1(u4_struct_0(B),D))) & r1_tarski(k9_petri(A,k6_domain_1(u4_struct_0(A),C)),k9_petri(B,k6_domain_1(u4_struct_0(B),D))) ) ) ) ) ) ) )).
fof(t7_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => r1_pnproc_1(A,k3_pnproc_1(A,k2_pnproc_1(A,B,C),C),B) ) ) )).
fof(t7_polyalg1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_polynom5(A,D,k3_rlvect_1(A,B,C)),k8_polynom3(A,k3_polynom5(A,D,B),k3_polynom5(A,D,C))) ) ) ) ) )).
fof(t7_polyeq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(k5_numbers,k1_quin_1(A,B,C)) => ! [D] : ( v1_xreal_0(D) => k2_polyeq_1(A,B,C,D) != k5_numbers ) ) ) ) ) )).
fof(t7_polyeq_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ( ! [K] : ( v1_xreal_0(K) => k1_polyeq_2(A,B,C,D,E,K) = k1_polyeq_2(F,G,H,I,J,K) ) => ( E = J & k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(A,B),C),D) = k6_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(F,G),H),I) & k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C),D) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(F,G),H),I) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t7_polyeq_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xcmplx_0(D) => ~ ( A != k5_numbers & r1_xxreal_0(k5_numbers,k1_quin_1(A,B,C)) & k4_polyeq_1(k5_numbers,A,B,C,D) = k5_numbers & D != k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A)) & D != k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k3_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A)) & D != k4_xcmplx_0(k7_xcmplx_0(B,k3_xcmplx_0(2,A))) ) ) ) ) ) )).
fof(t7_polyeq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( B != k5_numbers & ~ v1_abian(E) & r1_xxreal_0(k5_numbers,k1_quin_1(B,C,D)) & k2_polyeq_1(B,C,D,k1_newton(A,E)) = k5_numbers & A != k1_power(E,k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B))) & A != k1_power(E,k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B))) ) ) ) ) ) ) )).
fof(t7_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => k1_newton(k1_polyeq_5(B,A),B) = A ) ) )).
fof(t7_polyform,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_abian(A) => k1_newton(k4_xcmplx_0(1),A) = 1 ) ) )).
fof(t7_polynom1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_polynom1(A,k2_pre_poly(u1_struct_0(A)),B) = k2_pre_poly(u1_struct_0(A)) ) ) )).
fof(t7_polynom3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [C] : ( m2_finseq_2(C,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ( r2_polynom3(A,B,C) | r1_polynom3(A,C,B) ) ) ) ) )).
fof(t7_polynom4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( k1_algseq_1(A,B) != k1_algseq_1(A,C) => k1_algseq_1(A,k2_normsp_1(A,B,C)) = k4_xxreal_0(k1_algseq_1(A,B),k1_algseq_1(A,C)) ) ) ) ) )).
fof(t7_polynom6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( m2_subset_1(C,k14_pre_poly(A),k15_pre_poly(A)) => ! [D] : ( m2_subset_1(D,k14_pre_poly(A),k15_pre_poly(A)) => ! [E] : ( m2_subset_1(E,k14_pre_poly(B),k15_pre_poly(B)) => ! [F] : ( m2_subset_1(F,k14_pre_poly(B),k15_pre_poly(B)) => ( r6_pboole(k10_ordinal2(A,B),k1_polynom6(A,B,C,E),k1_polynom6(A,B,D,F)) => ( r6_pboole(A,C,D) & r6_pboole(B,E,F) ) ) ) ) ) ) ) ) )).
fof(t7_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( 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_polynom1(k15_pre_poly(A),B,C) = k1_xboole_0 | k3_polynom1(k15_pre_poly(A),B,C) = k1_tarski(k2_polynom7(A,B,C)) ) ) ) )).
fof(t7_polynom8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( k9_nat_1(u1_struct_0(A),B,C) != k4_struct_0(A) => r1_xxreal_0(k1_nat_1(C,1),k1_algseq_1(A,B)) ) ) ) ) )).
fof(t7_polyred,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v5_vectsp_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( ( 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] : ( ( 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) ) => k4_polynom1(A,B,k10_polynom1(A,B,D,C),k11_pre_poly(A,k2_polynom7(A,B,D),E)) = k6_algstr_0(B,k4_polynom1(A,B,D,k2_polynom7(A,B,D)),k4_polynom1(A,B,C,E)) ) ) ) ) ) )).
fof(t7_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => v2_poset_1(k6_struct_0(A,B,C),A,B) ) ) ) )).
fof(t7_power,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(1,B) ) => r1_xxreal_0(k5_numbers,k1_power(B,A)) ) ) ) )).
fof(t7_pralg_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ v2_struct_0(C) & ~ v11_struct_0(C) & l1_msualg_1(C) ) => ! [D] : ( m1_pralg_2(D,A,C) => ! [E] : ( m1_subset_1(E,u4_struct_0(C)) => k1_funct_1(k12_pralg_2(A,C,D,E),B) = k5_msualg_1(C,E,k5_pralg_2(A,C,D,B)) ) ) ) ) ) )).
fof(t7_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ( k1_msualg_1(B,D) = k1_xboole_0 => r2_hidden(k1_funct_1(k9_funct_6(k11_pralg_2(A,B,C)),D),k1_funct_2(A,k1_funct_2(k1_tarski(k1_xboole_0),k3_tarski(a_4_0_pralg_3(A,B,C,D))))) ) ) ) ) ) )).
fof(t7_pre_circ,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : k4_card_3(k2_finseq_2(A,k1_tarski(B))) = k1_tarski(k2_finseq_2(A,B)) ) )).
fof(t7_pre_ff,axiom,( ! [A] : ( v1_int_1(A) => ( m1_subset_1(A,k4_ordinal1) => m1_subset_1(k4_int_1(A,2),k4_ordinal1) ) ) )).
fof(t7_pre_poly,axiom,( ! [A] : k2_wellord1(k1_xboole_0,A) = k1_xboole_0 )).
fof(t7_pre_topc,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k1_pre_topc(A,C)))) => ( ( B = D & r1_tarski(B,C) ) => k1_pre_topc(A,B) = k1_pre_topc(k1_pre_topc(A,C),D) ) ) ) ) ) )).
fof(t7_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_prelamb(A) ) => ! [B] : ( m1_prelamb(B,A) => ! [C] : ( 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)),k4_ordinal1),B,C)) = 4 & ! [D] : ( m1_trees_1(D,k9_xtuple_0(B)) => ! [E] : ( m1_trees_1(E,k9_xtuple_0(B)) => ! [F] : ( m2_finseq_1(F,u1_struct_0(A)) => ! [G] : ( m2_finseq_1(G,u1_struct_0(A)) => ! [H] : ( m2_finseq_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ~ ( D = k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,k5_numbers)) & E = k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,1)) & k1_xtuple_0(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k4_ordinal1),B,C)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),G,F),k12_finseq_1(u1_struct_0(A),k1_prelamb(A,J,I))),H),K) & k1_xtuple_0(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k4_ordinal1),B,D)) = k6_prelamb(A,F,J) & k1_xtuple_0(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k4_ordinal1),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),K) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t7_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => k1_newton(k7_xcmplx_0(1,A),B) = k7_xcmplx_0(1,k1_newton(A,B)) ) ) )).
fof(t7_prgcor_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,k3_finseq_1(B)) ) => r2_hidden(A,k4_finseq_1(B)) ) ) ) )).
fof(t7_prgcor_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k1_numbers) & ~ v1_xboole_0(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( v7_ordinal1(B) => ( ( v7_ordinal1(k1_funct_1(A,k5_numbers)) & k1_afinsq_1(A) = B ) => ( r1_xxreal_0(B,k1_funct_1(A,k5_numbers)) | ( ? [C] : ( v1_relat_1(C) & v5_relat_1(C,k1_numbers) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) & r3_prgcor_2(A,C,B) ) & ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,k1_numbers) & ~ v1_xboole_0(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ( r3_prgcor_2(A,C,B) => k12_afinsq_1(k1_numbers,C) = k6_rvsum_1(k12_afinsq_1(k1_numbers,A)) ) ) ) ) ) ) ) )).
fof(t7_prob_1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ! [D] : ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k2_xboole_0(k6_subset_1(C,D),D),B) ) ) )).
fof(t7_prob_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(B) <=> ! [C] : ( v7_ordinal1(C) => r1_tarski(k1_prob_2(A,k9_setfam_1(A),B,C),k1_prob_2(A,k9_setfam_1(A),B,k1_nat_1(C,1))) ) ) ) )).
fof(t7_prob_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( m2_prob_1(D,A,B) => ( v2_prob_1(C) => v8_valued_0(k8_prob_1(A,B,C,D)) ) ) ) ) ) )).
fof(t7_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( m2_prob_1(D,A,B) => ( ! [E] : ( m1_subset_1(E,k4_ordinal1) => k3_funct_2(B,k1_numbers,D,k1_prob_4(A,B,C,E)) = k5_numbers ) <=> k1_funct_1(D,k1_prob_1(A,C)) = k5_numbers ) ) ) ) ) )).
fof(t7_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( 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,B),k6_cqc_lang(A,C)),k6_cqc_lang(A,k9_cqc_lang(A,B,C))),k4_cqc_the1(A)) ) ) ) )).
fof(t7_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r1_projdes1(A,B,C,D,E) => ( r1_projdes1(A,C,D,E,B) & r1_projdes1(A,D,E,B,C) & r1_projdes1(A,E,B,C,D) & r1_projdes1(A,C,B,D,E) & r1_projdes1(A,D,C,E,B) & r1_projdes1(A,E,D,B,C) & r1_projdes1(A,B,E,C,D) & r1_projdes1(A,B,D,E,C) & r1_projdes1(A,C,E,B,D) & r1_projdes1(A,D,B,C,E) & r1_projdes1(A,E,C,D,B) & r1_projdes1(A,D,B,E,C) & r1_projdes1(A,E,C,B,D) & r1_projdes1(A,B,D,C,E) & r1_projdes1(A,C,E,D,B) & r1_projdes1(A,B,C,E,D) & r1_projdes1(A,B,E,D,C) & r1_projdes1(A,C,D,B,E) & r1_projdes1(A,C,B,E,D) & r1_projdes1(A,D,C,B,E) & r1_projdes1(A,D,E,C,B) & r1_projdes1(A,E,B,D,C) & r1_projdes1(A,E,D,C,B) ) ) ) ) ) ) ) )).
fof(t7_projpl_1,axiom,( ! [A] : ( 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] : ( m1_subset_1(B,u2_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => B = C ) ) ) ) )).
fof(t7_projred1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u2_incsp_1(A)) => ? [C] : ( m1_subset_1(C,u1_incsp_1(A)) & r1_incsp_1(A,C,B) ) ) ) )).
fof(t7_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ~ ( ~ r1_incsp_1(A,B,C) & ~ r1_incsp_1(A,B,D) & ~ v2_funct_1(k1_projred1(A,C,D,B)) ) ) ) ) ) )).
fof(t7_prvect_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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))) ) => ( v2_binop_1(C,B) => v2_binop_1(k2_prvect_1(B,C,A),k4_finseq_2(A,B)) ) ) ) ) )).
fof(t7_prvect_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_prvect_2(A))) => ! [C] : ( m1_subset_1(C,k4_card_3(k4_prvect_2(A))) => ( B = C => k2_normsp_0(k14_prvect_2(A),B) = k12_euclid(k12_prvect_2(A,C)) ) ) ) ) )).
fof(t7_prvect_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l2_algstr_0(B) ) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(k4_prvect_3(A,B))) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & C = k1_domain_1(u1_struct_0(A),u1_struct_0(B),D,E) ) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(k4_prvect_3(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_prvect_3(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( 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) ) => k1_algstr_0(k4_prvect_3(A,B),C,D) = k1_domain_1(u1_struct_0(A),u1_struct_0(B),k1_algstr_0(A,E,F),k1_algstr_0(B,G,H)) ) ) ) ) ) ) ) & k4_struct_0(k4_prvect_3(A,B)) = k1_domain_1(u1_struct_0(A),u1_struct_0(B),k4_struct_0(A),k4_struct_0(B)) ) ) ) )).
fof(t7_pscomp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,u1_struct_0(A),k1_numbers) & v1_comseq_2(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_numbers))) ) => r1_xxreal_0(k1_pscomp_1(A,B),k2_pscomp_1(A,B)) ) ) )).
fof(t7_pua2mss1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,B) => m1_eqrel_1(a_4_0_pua2mss1(A,B,C,D),k2_zfmisc_1(A,B)) ) ) ) ) )).
fof(t7_pythtrip,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ( r1_nat_d(B,C) | A = k5_numbers ) <=> r1_nat_d(k2_nat_1(A,B),k2_nat_1(A,C)) ) ) ) ) )).
fof(t7_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r1_pboole(A,B,k1_pzfmisc1(A,C)) => r6_pboole(A,B,C) ) ) ) )).
fof(t7_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => v1_qc_lang1(k9_qc_lang1(A),A) ) )).
fof(t7_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( k21_qc_lang1(A,k15_qc_lang1(A,B,C)) = B & k22_qc_lang1(A,k15_qc_lang1(A,B,C)) = C ) ) ) ) )).
fof(t7_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => k24_qc_lang1(A,k13_qc_lang1(A,B)) = k24_qc_lang1(A,B) ) ) )).
fof(t7_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m1_trees_1(D,k9_xtuple_0(k2_qc_lang4(A,B))) => ( r1_qc_lang2(A,C,k3_trees_2(k9_qc_lang1(A),k2_qc_lang4(A,B),D)) <=> ? [E] : ( v7_ordinal1(E) & r2_hidden(k7_finseq_1(D,k9_finseq_1(E)),k9_xtuple_0(k2_qc_lang4(A,B))) & C = k1_funct_1(k2_qc_lang4(A,B),k7_finseq_1(D,k9_finseq_1(E))) ) ) ) ) ) ) )).
fof(t7_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ( v1_qc_trans(B,A) & m1_qc_lang1(B) ) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => m2_subset_1(C,k9_qc_lang1(B),k3_cqc_lang(B)) ) ) ) )).
fof(t7_qmax_1,axiom,( ! [A] : ( ( v2_qmax_1(A) & l1_qmax_1(A) ) => ! [B] : ( m1_subset_1(B,k5_qmax_1(A)) => ! [C] : ( m1_subset_1(C,k5_qmax_1(A)) => ! [D] : ( m1_subset_1(D,k5_qmax_1(A)) => ( ( r4_qmax_1(A,B,C) & r4_qmax_1(A,C,D) ) => r4_qmax_1(A,B,D) ) ) ) ) ) )).
fof(t7_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => A = k25_quaterni(k22_quaterni(A,B),B) ) ) )).
fof(t7_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ( v1_xreal_0(A) => k23_quaterni(A,k12_quaterni) = k6_quaterni(k5_numbers,k5_numbers,k5_numbers,k13_quaterni(A)) ) ) )).
fof(t7_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ? [B] : ( v1_xreal_0(B) & ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & A = k6_quaterni(B,C,D,E) ) ) ) ) ) )).
fof(t7_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(A)),k3_xcmplx_0(C,A)),D),k5_numbers) & r1_xxreal_0(k6_xcmplx_0(k1_square_1(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,B),A),C)),k1_quin_1(B,C,D)),k5_numbers) ) ) ) ) ) )).
fof(t7_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A)) => ! [C] : ( m2_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A)) => ( ? [D] : ( m2_subset_1(D,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) & r2_hidden(B,D) & r2_hidden(C,D) ) => k8_group_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),C)) = k8_group_1(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)) ) ) ) ) )).
fof(t7_radix_1,axiom,( ! [A] : ( r2_hidden(A,k2_radix_1(k5_numbers)) <=> A = k5_numbers ) )).
fof(t7_radix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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) ) ) )).
fof(t7_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => r2_hidden(k5_numbers,k2_radix_3(A)) ) )).
fof(t7_radix_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(2,A) => k3_xcmplx_0(k1_newton(k1_radix_1(A),C),k7_radix_3(k2_xcmplx_0(C,1),A,k2_xcmplx_0(k2_xcmplx_0(C,1),1),k10_radix_3(k2_xcmplx_0(C,1),A,k10_radix_1(A,k2_xcmplx_0(C,1),B)))) = k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k1_newton(k1_radix_1(A),C),k4_radix_1(k2_xcmplx_0(C,1),A,k2_xcmplx_0(C,1),k10_radix_1(A,k2_xcmplx_0(C,1),B))),k3_xcmplx_0(k1_newton(k1_radix_1(A),k2_xcmplx_0(C,1)),k5_radix_3(k4_radix_1(k2_xcmplx_0(C,1),A,k2_xcmplx_0(C,1),k10_radix_1(A,k2_xcmplx_0(C,1),B)),A))),k3_xcmplx_0(k1_newton(k1_radix_1(A),C),k5_radix_3(k4_radix_1(C,A,k2_xcmplx_0(C,1),k10_radix_1(A,k2_xcmplx_0(C,1),B)),A))) ) ) ) ) )).
fof(t7_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( r2_hidden(1,k2_finseq_1(B)) & r1_xxreal_0(2,A) ) => k4_radix_1(1,A,B,k10_radix_1(A,B,1)) = 1 ) ) ) )).
fof(t7_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(2,C) & r1_radix_6(B,C,A) ) => r1_xxreal_0(k8_radix_1(k2_xcmplx_0(B,2),C,k6_radix_5(k2_xcmplx_0(B,2),B,C)),A) ) ) ) ) )).
fof(t7_ramsey_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(A,B) => r1_tarski(k3_group_10(A,C),k3_group_10(B,C)) ) )).
fof(t7_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k1_random_1(A),k6_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),k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ~ ( k1_relset_1(A,C) != k1_xboole_0 & ~ r1_xxreal_0(k1_xxreal_0,k3_funct_2(k1_zfmisc_1(A),k6_numbers,B,k1_relset_1(A,C))) & ~ r3_mesfunc6(A,k1_random_1(A),B,C) ) ) ) ) )).
fof(t7_random_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_random_1(E,A,B) => ( ( v6_supinf_2(E) & r1_random_1(A,B,E,C) & r3_mesfunc6(A,B,k2_prob_4(A,B,C),k2_mesfun6c(2,A,k7_random_1(A,B,E))) ) => ( r1_xxreal_0(D,k5_numbers) | r1_xxreal_0(k12_supinf_2(C,a_5_0_random_2(A,B,C,D,E)),k2_extreal1(k1_random_2(A,B,C,E),k2_power(D,2))) ) ) ) ) ) ) ) )).
fof(t7_random_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [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))) ) => ( r1_finance1(A,k1_numbers,B,k12_prob_1,C) <=> m1_random_1(C,A,B) ) ) ) ) )).
fof(t7_ranknull,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) & r1_tarski(k10_xtuple_0(C),k2_struct_0(B)) ) ) ) ) )).
fof(t7_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ~ r1_xxreal_0(k1_rat_1(A),k5_numbers) ) )).
fof(t7_ratfunc1,axiom,( ! [A] : ( ( ~ v7_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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(D,A) & ~ v1_ratfunc1(D,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r2_funct_2(k4_ordinal1,u1_struct_0(A),k11_polynom3(A,B,D),k11_polynom3(A,C,D)) => r2_funct_2(k4_ordinal1,u1_struct_0(A),B,C) ) ) ) ) ) )).
fof(t7_rcomp_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => v3_rcomp_1(k2_rcomp_1(A,B)) ) ) )).
fof(t7_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ~ r1_xxreal_0(B,A) => k2_seq_4(k4_rcomp_1(A,B)) = B ) ) ) )).
fof(t7_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,B) & ~ v2_xxreal_0(A) & ~ v3_xxreal_0(B) ) ) ) )).
fof(t7_real_3,axiom,( ! [A] : ( v1_rat_1(A) => ~ ( r1_xxreal_0(k5_numbers,A) & ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( C != k5_numbers & A = k7_xcmplx_0(B,C) ) ) ) ) ) )).
fof(t7_real_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_real_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_real_lat)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_real_lat)) => k1_binop_1(k1_real_lat,B,k1_binop_1(k2_real_lat,A,C)) = k1_binop_1(k2_real_lat,k1_binop_1(k1_real_lat,B,A),k1_binop_1(k1_real_lat,B,C)) ) ) ) )).
fof(t7_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ( ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k2_finseq_1(A)) => r1_xxreal_0(k5_numbers,k1_funct_1(B,C)) ) ) => ( r1_xxreal_0(k5_numbers,k18_rvsum_1(B)) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k2_finseq_1(A)) => r1_xxreal_0(k1_funct_1(B,C),k18_rvsum_1(B)) ) ) ) ) ) ) )).
fof(t7_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_subset_1(D,u1_struct_0(A),k8_struct_0(A)) => ! [E] : ( m2_subset_1(E,u1_struct_0(A),k8_struct_0(A)) => k1_binop_1(u1_algstr_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))) = k1_binop_1(k4_realset2(A),k5_binop_1(u1_struct_0(A),u1_algstr_0(A),k5_binop_1(u1_struct_0(A),k4_realset2(A),B,E),k5_binop_1(u1_struct_0(A),k4_realset2(A),C,D)),k1_funct_1(k5_realset2(A),k5_binop_1(u1_struct_0(A),k4_realset2(A),D,E))) ) ) ) ) ) )).
fof(t7_rearran1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_rearran1(C) & m2_finseq_1(C,k1_zfmisc_1(B)) ) => ~ ( r2_hidden(A,k4_finseq_1(C)) & k1_funct_1(C,A) = k1_xboole_0 ) ) ) ) )).
fof(t7_recdef_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( 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 ) )).
fof(t7_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( 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))) ) ) )).
fof(t7_relat_2,axiom,( ! [A] : ( 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))) ) ) )).
fof(t7_reloc,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( ~ 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(k7_card_1(2),k1_ami_3)) & v1_finset_1(C) & v4_extpro_1(C,k7_card_1(2),k1_ami_3,B) ) => ! [D] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ! [E] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(E,u1_struct_0(k1_ami_3)) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,u1_struct_0(k1_ami_3)) & v1_funct_1(F) & v5_funct_1(F,k2_memstr_0(k7_card_1(2),k1_ami_3)) & v1_partfun1(F,u1_struct_0(k1_ami_3)) ) => ( ( r2_hidden(k4_struct_0(k1_ami_3),k9_xtuple_0(C)) & r1_tarski(C,D) & r1_tarski(k9_memstr_0(k7_card_1(2),k1_ami_3,C,A),E) & r6_pboole(u1_struct_0(k1_ami_3),F,k1_funct_4(D,k6_memstr_0(k7_card_1(2),k1_ami_3,E))) ) => ! [G] : ( ( v1_relat_1(G) & v4_relat_1(G,k4_ordinal1) & v5_relat_1(G,u1_compos_1(k1_ami_3)) & v1_funct_1(G) & v1_partfun1(G,k4_ordinal1) ) => ! [H] : ( ( v1_relat_1(H) & v4_relat_1(H,k4_ordinal1) & v5_relat_1(H,u1_compos_1(k1_ami_3)) & v1_funct_1(H) & v1_partfun1(H,k4_ordinal1) ) => ( ( r1_tarski(B,G) & r1_tarski(k6_compos_1(k1_ami_3,B,A),H) ) => ! [I] : ( m1_subset_1(I,k4_ordinal1) => k6_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,G,F,I)) = k6_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,H,E,I)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t7_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) => ( ( r1_tarski(A,B) & r1_tarski(C,D) ) => m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(B,D))) ) ) )).
fof(t7_relset_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => r1_tarski(k9_subset_1(A,k8_setfam_1(A,B),k8_setfam_1(A,C)),k8_setfam_1(A,k9_subset_1(k1_zfmisc_1(A),B,C))) ) ) )).
fof(t7_revrot_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r2_hidden(B,k10_xtuple_0(C)) => r1_xxreal_0(k3_finseq_1(k2_finseq_5(A,C,B)),k3_finseq_1(C)) ) ) ) ) )).
fof(t7_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ! [C] : ( r2_hidden(k4_tarski(B,C),A) => m1_rewrite1(k10_finseq_1(B,C),A) ) ) )).
fof(t7_rewrite2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v1_rewrite2(C) ) => ( k1_rewrite2(A,k1_rewrite2(B,C)) = k1_rewrite2(k1_ordinal4(A,B),C) & k2_rewrite2(A,k2_rewrite2(B,C)) = k2_rewrite2(k1_ordinal4(B,A),C) ) ) ) ) )).
fof(t7_rewrite3,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( m1_rewrite1(B,A) => ~ ( ~ r1_xxreal_0(k3_finseq_1(B),1) & ! [C] : ( m1_rewrite1(C,A) => ~ ( k2_xcmplx_0(k3_finseq_1(C),1) = k3_finseq_1(B) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(C)) => k1_funct_1(C,D) = k1_funct_1(B,k2_xcmplx_0(D,1)) ) ) ) ) ) ) ) )).
fof(t7_rfinseq,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( k3_finseq_1(B) = k1_nat_1(C,1) & D = k1_funct_1(B,k1_nat_1(C,1)) ) => B = k7_finseq_1(k17_finseq_1(A,C,B),k9_finseq_1(D)) ) ) ) ) )).
fof(t7_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => ( r1_xxreal_0(k3_finseq_1(A),k5_numbers) | r1_xxreal_0(k3_rfinseq2(k4_rvsum_1(A,B)),k2_xcmplx_0(k3_rfinseq2(A),k3_rfinseq2(B))) ) ) ) ) )).
fof(t7_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( v1_xcmplx_0(B) => ( B != k5_numbers => k8_relat_1(k24_valued_1(A,B),k1_tarski(k5_numbers)) = k8_relat_1(A,k1_tarski(k5_numbers)) ) ) ) )).
fof(t7_rfunct_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(A) & ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k1_funct_1(A,B),k5_numbers) ) ) => r1_xxreal_0(k1_seq_2(A),k5_numbers) ) ) )).
fof(t7_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => k8_relset_1(A,k1_numbers,k26_valued_1(A,k1_numbers,B,k5_numbers),k1_tarski(k5_numbers)) = k1_relset_1(A,B) ) ) )).
fof(t7_rfunct_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r1_rfunct_4(C,k1_rcomp_1(A,B)) <=> ( r1_tarski(k1_rcomp_1(A,B),k9_xtuple_0(C)) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(1,D) & ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & r2_hidden(E,k1_rcomp_1(A,B)) & r2_hidden(F,k1_rcomp_1(A,B)) & E != F & r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(D,k1_funct_1(C,E)),k3_xcmplx_0(k6_xcmplx_0(1,D),k1_funct_1(C,F))),k1_funct_1(C,k2_xcmplx_0(k3_xcmplx_0(D,E),k3_xcmplx_0(k6_xcmplx_0(1,D),F)))) ) ) ) ) ) ) ) ) ) )).
fof(t7_rinfsup1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_seq_2(B) => ( A = k1_rinfsup1(B) <=> ( ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k1_funct_1(B,C),A) ) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k1_funct_1(B,D),k6_xcmplx_0(A,C)) ) ) ) ) ) ) ) ) )).
fof(t7_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( ( v5_valued_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(B,C) & r1_xxreal_0(k12_supinf_2(A,B),k12_supinf_2(A,C)) ) ) ) ) & ( ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(B,C) & r1_xxreal_0(k12_supinf_2(A,B),k12_supinf_2(A,C)) ) ) ) => v5_valued_0(A) ) & ( v6_valued_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(B,C) & r1_xxreal_0(k12_supinf_2(A,C),k12_supinf_2(A,B)) ) ) ) ) & ( ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( ~ r1_xxreal_0(B,C) & r1_xxreal_0(k12_supinf_2(A,C),k12_supinf_2(A,B)) ) ) ) => v6_valued_0(A) ) & ( v7_valued_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(C,B) => r1_xxreal_0(k12_supinf_2(A,C),k12_supinf_2(A,B)) ) ) ) ) & ( ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(C,B) => r1_xxreal_0(k12_supinf_2(A,C),k12_supinf_2(A,B)) ) ) ) => v7_valued_0(A) ) & ( v8_valued_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(C,B) => r1_xxreal_0(k12_supinf_2(A,B),k12_supinf_2(A,C)) ) ) ) ) & ( ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(C,B) => r1_xxreal_0(k12_supinf_2(A,B),k12_supinf_2(A,C)) ) ) ) => v8_valued_0(A) ) ) ) )).
fof(t7_ring_1,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_eqrel_1(u1_struct_0(A),u1_struct_0(A),k1_ring_1(A,k2_struct_0(A)),B) = u1_struct_0(A) ) ) )).
fof(t7_ringcat1,axiom,( ! [A] : ( ( v2_ringcat1(A) & v3_ringcat1(A) & l1_ringcat1(A) ) => ! [B] : ( ( v2_ringcat1(B) & v3_ringcat1(B) & l1_ringcat1(B) ) => ~ ( k1_ringcat1(B) = k2_ringcat1(A) & ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( 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_ringcat1(C,D,F) & B = g1_ringcat1(D,E,G) & k6_ringcat1(B,A) = g1_ringcat1(C,E,k1_partfun1(u1_struct_0(C),u1_struct_0(D),u1_struct_0(D),u1_struct_0(E),F,G)) ) ) ) ) ) ) ) ) ) )).
fof(t7_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => k1_card_1(C) = k1_card_1(k5_rusub_4(A,C,B)) ) ) ) )).
fof(t7_rlaffin2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_xboole_0(B,C) => r1_xboole_0(k3_convex1(A,B),k1_rlaffin2(A,C)) ) ) ) ) )).
fof(t7_rlaffin3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) => ( ( r1_xxreal_0(B,A) & C = a_3_0_rlaffin3(A,B,D) ) => ( v3_pre_topc(C,k15_euclid(A)) <=> v3_pre_topc(D,k15_euclid(B)) ) ) ) ) ) ) )).
fof(t7_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_rlsub_1(B,A) & v1_rlsub_1(C,A) ) => v1_rlsub_1(k9_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).
fof(t7_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ( m1_rlsub_1(B,k1_rlsub_2(A,B,C)) & m1_rlsub_1(C,k1_rlsub_2(A,B,C)) ) ) ) ) )).
fof(t7_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => k6_rusub_4(A,k5_rusub_4(A,C,B),D) = k5_rusub_4(A,k6_rusub_4(A,C,D),B) ) ) ) ) )).
fof(t7_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & k1_algstr_0(A,B,D) = C ) ) ) ) )).
fof(t7_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)) & v3_funct_2(D,k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B)))) ) => ( C = k1_partfun1(k1_relset_1(k4_ordinal1,B),k1_relset_1(k4_ordinal1,B),k4_ordinal1,u1_struct_0(A),D,B) => k4_rlvect_1(A,B) = k4_rlvect_1(A,C) ) ) ) ) ) )).
fof(t7_rlvect_3,axiom,( ! [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) ) => v1_rlvect_3(k1_subset_1(u1_struct_0(A)),A) ) )).
fof(t7_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( B != C & B != D & C != D & v1_rlvect_3(k8_domain_1(u1_struct_0(A),B,C,D),A) ) <=> ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ( 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 = k5_numbers & F = k5_numbers & G = k5_numbers ) ) ) ) ) ) ) ) ) ) )).
fof(t7_rlvect_5,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ? [D] : ( m1_rlvect_2(D,A) & k3_rlvect_2(A,D) = k9_subset_1(u1_struct_0(A),k10_xtuple_0(C),k3_rlvect_2(A,B)) & k5_rlvect_2(A,C,B) = k5_rlvect_2(A,C,D) ) ) ) ) )).
fof(t7_rlvect_x,axiom,( ! [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) ) => r1_tarski(k2_relset_1(k1_numbers,k4_rlvect_2(A)),k4_numbers) ) )).
fof(t7_rmod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( ( v1_rmod_2(C,A,B) & v1_rmod_2(D,A,B) ) => v1_rmod_2(k9_subset_1(u1_struct_0(B),C,D),A,B) ) ) ) ) ) )).
fof(t7_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( m1_rmod_2(D,A,B) => ( m1_rmod_2(C,A,k1_rmod_3(A,B,C,D)) & m1_rmod_2(D,A,k1_rmod_3(A,B,C,D)) ) ) ) ) ) )).
fof(t7_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( C != D => k1_rmod_4(A,B,k7_domain_1(u1_struct_0(B),C,D)) = k3_rlvect_1(B,C,D) ) ) ) ) ) )).
fof(t7_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & v7_robbins1(A) & l2_robbins1(A) ) => ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k4_robbins1(A,B,C) = B & k3_robbins1(A,k5_robbins1(A,C,k3_robbins1(A,C))) = B ) ) ) ) )).
fof(t7_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)),k3_robbins1(A,k1_lattices(A,B,C)))) = B ) ) ) )).
fof(t7_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_oposet_1(A) & v10_oposet_1(A) & l2_qmax_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_orders_2(A,B,C) => r3_orders_2(A,k3_robbins1(A,C),k3_robbins1(A,B)) ) ) ) ) )).
fof(t7_robbins4,axiom,( u1_struct_0(k14_lattice3(k1_robbins4)) = k4_enumset1(k5_numbers,1,k6_subset_1(3,1),2,k6_subset_1(3,2),3) )).
fof(t7_rolle,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( r2_hidden(D,k2_rcomp_1(A,B)) => k1_fdiff_1(C,D) = k5_numbers ) ) ) => v3_funct_1(k2_partfun1(k1_numbers,k1_numbers,C,k2_rcomp_1(A,B))) ) ) ) ) )).
fof(t7_roughs_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_2(D) & 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(C,k6_eqrel_1(A,A,D,B)) ) ) )).
fof(t7_rpr_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ? [B] : ( v3_card_1(B,1) & m1_subset_1(B,k1_zfmisc_1(A)) & v3_card_1(B,1) & m1_subset_1(B,k1_zfmisc_1(A)) ) ) )).
fof(t7_rsspace,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace))) => ! [C] : ( m1_subset_1(C,u1_struct_0(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace))) => k1_rlvect_1(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace),k3_rlvect_1(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace),B,C),A) = k3_rlvect_1(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace),k1_rlvect_1(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace),B,A),k1_rlvect_1(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace),C,A)) ) ) ) )).
fof(t7_rsspace2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(B) & v2_comseq_2(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [E] : ( v7_ordinal1(E) => k9_nat_1(k1_numbers,D,E) = k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(k9_nat_1(k1_numbers,B,E),A),k6_xcmplx_0(k9_nat_1(k1_numbers,B,E),A)),k9_nat_1(k1_numbers,C,E)) ) => ( v2_comseq_2(D) & k1_seq_2(D) = k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(k1_seq_2(B),A),k6_xcmplx_0(k1_seq_2(B),A)),k1_seq_2(C)) ) ) ) ) ) ) ) )).
fof(t7_rsspace3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_rsspace3)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_rsspace3)) => ! [C] : ( v1_xreal_0(C) => ( ( k2_normsp_0(k3_rsspace3,A) = k5_numbers => A = k4_struct_0(k3_rsspace3) ) & ( A = k4_struct_0(k3_rsspace3) => k2_normsp_0(k3_rsspace3,A) = k5_numbers ) & r1_xxreal_0(k5_numbers,k2_normsp_0(k3_rsspace3,A)) & r1_xxreal_0(k2_normsp_0(k3_rsspace3,k1_algstr_0(k3_rsspace3,A,B)),k2_xcmplx_0(k2_normsp_0(k3_rsspace3,A),k2_normsp_0(k3_rsspace3,B))) & k2_normsp_0(k3_rsspace3,k1_rlvect_1(k3_rsspace3,A,C)) = k3_xcmplx_0(k9_complex1(C),k2_normsp_0(k3_rsspace3,A)) ) ) ) ) )).
fof(t7_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & 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(k4_rsspace4(A,B),k9_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k7_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B)),k8_rsspace(k5_lopban_1(A,B),k4_rsspace4(A,B))),k5_lopban_1(A,B)) ) ) )).
fof(t7_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( v1_xreal_0(E) => ( D = C => k1_rlvect_1(B,D,E) = k1_rlvect_1(A,C,E) ) ) ) ) ) ) )).
fof(t7_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_rusub_1(C,A) => ( m1_rusub_1(B,k1_rusub_2(A,B,C)) & m1_rusub_1(C,k1_rusub_2(A,B,C)) ) ) ) ) )).
fof(t7_rusub_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(B,C) => m1_rusub_1(k1_rusub_3(A,B),k1_rusub_3(A,C)) ) ) ) ) )).
fof(t7_rusub_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ( v1_rusub_4(A) => v1_rusub_4(B) ) ) ) )).
fof(t7_rusub_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_xboole_0(B) | v1_xboole_0(C) ) => v1_xboole_0(k1_rusub_5(A,B,C)) ) ) ) ) )).
fof(t7_rvsum_1,axiom,( r1_finseqop(k1_numbers,k7_binop_2,k9_binop_2) )).
fof(t7_rvsum_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => k5_rvsum_2(k9_finseq_1(A)) = k9_finseq_1(k4_xcmplx_0(A)) ) )).
fof(t7_scm_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_ami_3)) ) => ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_ami_3)) ) => ( ( k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B)) = C & k3_compos_1(k1_ami_3,A,C) = k5_ami_3(E,F) ) => ( k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1))) = k1_nat_1(C,1) & k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1)),E) = k3_xcmplx_0(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B),E),k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B),F)) & ! [G] : ( ( v1_ami_2(G) & m1_subset_1(G,u1_struct_0(k1_ami_3)) ) => ( G != E => k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1)),G) = k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B),G) ) ) ) ) ) ) ) ) ) ) )).
fof(t7_scm_comp,axiom,( ! [A] : ( m2_subset_1(A,u1_struct_0(k1_scm_comp),k6_dtconstr(k1_scm_comp)) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k15_scm_comp(k3_scm_comp(A),B) = k5_afinsq_1(k2_ami_3(k10_ami_3(B),k4_scm_comp(A))) ) ) )).
fof(t7_scm_halt,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) => k1_funct_1(k1_scmfsa6b(C,A,B),k4_scmfsa_2(k5_numbers)) = 1 ) ) ) )).
fof(t7_scm_inst,axiom,( ! [A] : ( m1_subset_1(A,k3_scm_inst) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k2_scm_inst) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k7_card_1(9)) => ( A = k3_xtuple_0(D,k9_finseq_1(B),k12_finseq_1(k2_scm_inst,C)) => ( k7_scm_inst(A) = B & k8_scm_inst(A) = C ) ) ) ) ) ) )).
fof(t7_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ( r2_hidden(B,k10_xtuple_0(A)) => ( ( B != k6_scmfsa_2(C,D) & B != k7_scmfsa_2(C,D) & B != k8_scmfsa_2(C,D) & B != k9_scmfsa_2(C,D) & B != k10_scmfsa_2(C,D) ) | ( r2_hidden(C,k2_sf_mastr(A)) & r2_hidden(D,k2_sf_mastr(A)) ) ) ) ) ) ) ) )).
fof(t7_scmfsa10,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( v7_ordinal1(B) => k12_scmfsa_2(B,A) = k3_xtuple_0(7,k9_finseq_1(B),k9_finseq_1(A)) ) ) )).
fof(t7_scmfsa6a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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))) ) ) )).
fof(t7_scmfsa6b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(C,k7_card_1(3),k1_scmfsa_2,k5_numbers) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ( ( r1_tarski(D,A) & r1_tarski(D,B) ) => ! [E] : ( v7_ordinal1(E) => ( r8_pboole(u1_struct_0(k1_scmfsa_2),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C,E),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,C,E)) & k3_extpro_1(k7_card_1(3),k1_scmfsa_2,A,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C,E)) = k3_extpro_1(k7_card_1(3),k1_scmfsa_2,B,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,C,E)) ) ) ) ) ) ) ) )).
fof(t7_scmfsa6c,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( v1_scmfsa6c(D) & v2_scmfsa6c(D) & m1_subset_1(D,u1_compos_1(k1_scmfsa_2)) ) => ! [E] : ( ( v1_scmfsa6c(E) & m1_subset_1(E,u1_compos_1(k1_scmfsa_2)) ) => k1_funct_1(k1_scmfsa6b(k6_scmfsa6a(D,E),B,C),A) = k1_funct_1(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,E,k2_extpro_1(k7_card_1(3),k1_scmfsa_2,D,k1_scmfsa_m(B))),A) ) ) ) ) ) )).
fof(t7_scmfsa7b,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ~ ( A != B & r3_scmfsa7b(k7_scmfsa_2(B,C),A) ) ) ) ) )).
fof(t7_scmfsa8a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t7_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(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)) ) ) )).
fof(t7_scmfsa9a,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) => k2_sf_mastr(k1_scmfsa8b(A,B,C)) = k4_subset_1(k2_scmfsa_2,k4_subset_1(k2_scmfsa_2,k4_scmfsa_m(A),k2_sf_mastr(B)),k2_sf_mastr(C)) ) ) ) )).
fof(t7_scmfsa_2,axiom,( ! [A] : ( m1_scmfsa_2(A) => k4_memstr_0(k7_card_1(3),k1_scmfsa_2,A) = k3_finseq_2(k4_numbers) ) )).
fof(t7_scmfsa_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( ~ 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(k7_card_1(3),k1_scmfsa_2)) & v1_finset_1(B) & v4_extpro_1(B,k7_card_1(3),k1_scmfsa_2,A) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ( ( r1_tarski(B,C) & r1_tarski(B,D) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( ( r1_tarski(A,E) & r1_tarski(A,F) ) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v1_ami_2(H) & m1_subset_1(H,u1_struct_0(k1_scmfsa_2)) ) => ! [I] : ( ( v1_ami_2(I) & m1_subset_1(I,u1_struct_0(k1_scmfsa_2)) ) => ( ( k3_extpro_1(k7_card_1(3),k1_scmfsa_2,E,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G)) = k10_scmfsa_2(H,I) & r2_hidden(H,k9_xtuple_0(B)) ) => ( H = I | k4_int_1(k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G),H),k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G),I)) = k4_int_1(k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,D,G),H),k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,D,G),I)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t7_scmfsa_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(B,k7_card_1(3),k1_scmfsa_2,k5_numbers) ) => ( k1_funct_1(B,k4_scmfsa_2(k5_numbers)) = 1 => ! [C] : ( m1_scmfsa_2(C) => ! [D] : ( m2_finseq_1(D,k4_numbers) => ( r1_tarski(k4_scmfsa_7(C,D),A) => ( r1_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B) & k18_scmfsa_2(k6_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B),C) = D & ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmfsa_2)) ) => ~ ( E != k4_scmfsa_2(1) & E != k4_scmfsa_2(2) & k1_funct_1(k6_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B),E) != k1_funct_1(B,E) ) ) & ! [E] : ( m1_scmfsa_2(E) => ( E != C => k18_scmfsa_2(k6_extpro_1(k7_card_1(3),k1_scmfsa_2,A,B),E) = k18_scmfsa_2(B,E) ) ) ) ) ) ) ) ) ) )).
fof(t7_scmfsa_i,axiom,( ! [A] : ( m1_subset_1(A,k2_scmfsa_i) => ~ ( ~ ( r2_hidden(A,k3_scm_inst) & ~ ! [B] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(B,8) & k2_compos_0(k2_scmfsa_i,A) = B ) ) ) & ~ ( r2_hidden(A,a_0_0_scmfsa_i) & ( k2_compos_0(k2_scmfsa_i,A) = 9 | k2_compos_0(k2_scmfsa_i,A) = 10 ) ) & ~ ( r2_hidden(A,a_0_1_scmfsa_i) & ( k2_compos_0(k2_scmfsa_i,A) = 11 | k2_compos_0(k2_scmfsa_i,A) = 12 ) ) ) ) )).
fof(t7_scmfsa_m,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) ) => ! [B] : ( m1_scmfsa_2(B) => ~ ( ~ r2_hidden(B,k9_xtuple_0(A)) & r2_hidden(B,k9_xtuple_0(k1_scmfsa_m(A))) ) ) ) )).
fof(t7_scmisort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ( ( r1_tarski(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)),C) & r1_tarski(D,A) & r1_tarski(D,B) ) => ( k8_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C) = k8_extpro_1(k7_card_1(3),k1_scmfsa_2,B,C) & r8_pboole(u1_struct_0(k1_scmfsa_2),k6_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C),k6_extpro_1(k7_card_1(3),k1_scmfsa_2,B,C)) ) ) ) ) ) ) )).
fof(t7_scmp_gcd,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k3_scmpds_4(B,A),C),k5_card_1(B)) = A ) ) ) )).
fof(t7_scmpds_2,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k1_ami_2,k2_ami_2) => ! [C] : ( v1_int_1(C) => ! [D] : ( 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) ) ) ) ) )).
fof(t7_scmpds_3,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => ~ ( k5_memstr_0(2,k1_scmpds_2,A) = k5_memstr_0(2,k1_scmpds_2,B) & C != D & E = k5_memstr_0(2,k1_scmpds_2,A) & r1_xxreal_0(k5_numbers,k2_xcmplx_0(E,C)) & r1_xxreal_0(k5_numbers,k2_xcmplx_0(E,D)) & k17_scmpds_2(A,C) = k17_scmpds_2(B,D) ) ) ) ) ) ) )).
fof(t7_scmpds_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_scmpds_4(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ( r1_tarski(k10_compos_1(k1_scmpds_2,C),A) => ! [E] : ( v7_ordinal1(E) => ( 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) ) ) ) ) ) ) ) )).
fof(t7_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => k7_scmpds_2(A,B,C) != k2_compos_1(k1_scmpds_2) ) ) ) )).
fof(t7_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( 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,k5_numbers) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ( ( r1_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) ) => ! [E] : ( v7_ordinal1(E) => ( 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)) ) ) ) ) ) ) ) )).
fof(t7_scmpds_9,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => k1_amistd_1(2,k1_scmpds_2,B,k10_scmpds_2(A,C,D)) = k1_tarski(k1_ordinal1(B)) ) ) ) ) )).
fof(t7_scmpds_i,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k7_card_1(15)) => ! [B] : ( m1_subset_1(B,k1_scmpds_i) => ! [C] : ( m1_subset_1(C,k2_scm_inst) => ! [D] : ( m1_subset_1(D,k2_scm_inst) => ! [E] : ( v1_int_1(E) => ! [F] : ( v1_int_1(F) => ( B = k3_xtuple_0(A,k1_xboole_0,k7_finseq_4(C,D,E,F)) => ( k10_scmpds_i(B) = C & k11_scmpds_i(B) = D & k12_scmpds_i(B) = E & k13_scmpds_i(B) = F ) ) ) ) ) ) ) ) )).
fof(t7_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmring2(A))) <=> ~ ( B != k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0) & ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmring2(A))) ) => B != k3_scmring2(A,C,D) ) ) & ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmring2(A))) ) => B != k4_scmring2(A,C,D) ) ) & ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmring2(A))) ) => B != k5_scmring2(A,C,D) ) ) & ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmring2(A))) ) => B != k6_scmring2(A,C,D) ) ) & ! [C] : ( v7_ordinal1(C) => B != k8_scmring2(A,C) ) & ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => ! [D] : ( v7_ordinal1(D) => B != k9_scmring2(A,D,C) ) ) & ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => B != k7_scmring2(A,C,D) ) ) ) ) ) )).
fof(t7_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => k2_compos_0(u1_compos_1(k1_scmring2(A)),k6_scmring2(A,B,C)) = 4 ) ) ) )).
fof(t7_scmring4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(B))) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmring2(B))) ) => ! [E] : ( ( 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(k7_card_1(2),k1_scmring2(B))) & v1_partfun1(E,u1_struct_0(k1_scmring2(B))) ) => ! [F] : ( ( 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(k7_card_1(2),k1_scmring2(B))) & v1_partfun1(F,u1_struct_0(k1_scmring2(B))) ) => ! [G] : ( ( v1_relat_1(G) & v4_relat_1(G,k4_ordinal1) & v5_relat_1(G,u1_compos_1(k1_scmring2(B))) & v1_funct_1(G) & v1_partfun1(G,k4_ordinal1) ) => ! [H] : ( ( v1_relat_1(H) & v4_relat_1(H,k4_ordinal1) & v5_relat_1(H,u1_compos_1(k1_scmring2(B))) & v1_funct_1(H) & v1_partfun1(H,k4_ordinal1) ) => ! [I] : ( ( v1_relat_1(I) & v4_relat_1(I,k4_ordinal1) & 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] : ( ( 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(k7_card_1(2),k1_scmring2(B))) & ~ v1_xboole_0(J) & v1_finset_1(J) & v4_extpro_1(J,k7_card_1(2),k1_scmring2(B),I) ) => ( ( r1_tarski(J,E) & r1_tarski(J,F) & r1_tarski(I,G) & r1_tarski(I,H) & k3_extpro_1(k7_card_1(2),k1_scmring2(B),G,k5_extpro_1(k7_card_1(2),k1_scmring2(B),G,E,A)) = k3_scmring2(B,C,D) & r2_hidden(C,k9_xtuple_0(J)) ) => k2_scmring2(B,k5_extpro_1(k7_card_1(2),k1_scmring2(B),G,E,A),D) = k2_scmring2(B,k5_extpro_1(k7_card_1(2),k1_scmring2(B),H,F,A),D) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t7_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_scmringi(A)) => ~ ( ~ ( r2_hidden(B,k1_tarski(k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0))) & k4_xtuple_0(B) = k5_numbers ) & ~ ( r2_hidden(B,a_0_0_scmringi) & ~ ( k4_xtuple_0(B) != 1 & k4_xtuple_0(B) != 2 & k4_xtuple_0(B) != 3 & k4_xtuple_0(B) != 4 ) ) & ~ ( r2_hidden(B,a_0_1_scmringi) & k4_xtuple_0(B) = 6 ) & ~ ( r2_hidden(B,a_0_2_scmringi) & k4_xtuple_0(B) = 7 ) & ~ ( r2_hidden(B,a_1_1_scmringi(A)) & k4_xtuple_0(B) = 5 ) ) ) ) )).
fof(t7_scmyciel,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_eqrel_1(B,A) => ~ ( ~ r1_xxreal_0(k5_card_1(A),k5_card_1(B)) & ! [C] : ! [D] : ! [E] : ~ ( r2_hidden(C,B) & r2_hidden(D,C) & r2_hidden(E,C) & D != E ) ) ) ) )).
fof(t7_scpisort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ( ( r1_scmpds_6(D,k6_scmpds_4(C,B,A),A) & r2_scmpds_6(D,k6_scmpds_4(C,B,A),A) ) => k1_funct_1(k6_scmpds_4(k1_scmpds_4(C,D),B,A),E) = k1_funct_1(k6_scmpds_4(D,k8_memstr_0(2,k1_scmpds_2,k6_scmpds_4(C,B,A)),A),E) ) ) ) ) ) ) )).
fof(t7_scpqsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_scmpds_2)) ) => ! [G] : ( ( v1_ami_2(G) & m1_subset_1(G,u1_struct_0(k1_scmpds_2)) ) => ! [H] : ( ( v1_ami_2(H) & m1_subset_1(H,u1_struct_0(k1_scmpds_2)) ) => ! [I] : ( v1_int_1(I) => ! [J] : ( v1_int_1(J) => ! [K] : ( v1_int_1(K) => ( ( k1_funct_1(B,H) = k2_xcmplx_0(k6_xcmplx_0(k1_funct_1(B,G),J),k1_funct_1(B,E)) & r1_xxreal_0(K,k6_xcmplx_0(k1_funct_1(B,G),J)) & ! [L] : ( ( 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,k5_numbers) ) => ! [M] : ( ( v1_relat_1(M) & v4_relat_1(M,k4_ordinal1) & v5_relat_1(M,u1_compos_1(k1_scmpds_2)) & v1_funct_1(M) & v1_partfun1(M,k4_ordinal1) ) => ( ( k1_funct_1(L,H) = k2_xcmplx_0(k6_xcmplx_0(k1_funct_1(L,G),J),k1_funct_1(L,E)) & r1_xxreal_0(K,k6_xcmplx_0(k1_funct_1(L,G),J)) & k1_funct_1(L,F) = k1_funct_1(B,F) & k1_funct_1(L,D) = k1_funct_1(B,D) ) => ( r1_xxreal_0(k1_funct_1(L,k2_scmpds_2(k1_funct_1(B,D),I)),k5_numbers) | ( k1_funct_1(k6_scmpds_4(C,L,M),D) = k1_funct_1(L,D) & r1_scmpds_6(C,L,M) & r2_scmpds_6(C,L,M) & ~ r1_xxreal_0(k1_funct_1(L,k2_scmpds_2(k1_funct_1(B,D),I)),k1_funct_1(k6_scmpds_4(C,L,M),k2_scmpds_2(k1_funct_1(B,D),I))) & k1_funct_1(k6_scmpds_4(C,L,M),H) = k2_xcmplx_0(k6_xcmplx_0(k1_funct_1(k6_scmpds_4(C,L,M),G),J),k1_funct_1(k6_scmpds_4(C,L,M),E)) & r1_xxreal_0(K,k6_xcmplx_0(k1_funct_1(k6_scmpds_4(C,L,M),G),J)) & k1_funct_1(k6_scmpds_4(C,L,M),F) = k1_funct_1(L,F) ) ) ) ) ) ) => ( r1_scmpds_6(k2_scmpds_8(D,I,C),B,A) & r2_scmpds_6(k2_scmpds_8(D,I,C),B,A) & ( ~ r1_xxreal_0(k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),I)),k5_numbers) => r6_pboole(u1_struct_0(k1_scmpds_2),k6_scmpds_4(k2_scmpds_8(D,I,C),B,A),k6_scmpds_4(k2_scmpds_8(D,I,C),k8_memstr_0(2,k1_scmpds_2,k6_scmpds_4(C,B,A)),A)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t7_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_analoaf(A,B,C,B,D) => ( r2_analoaf(A,B,D,B,C) & r2_analoaf(A,C,B,B,D) & r2_analoaf(A,B,C,D,B) & r2_analoaf(A,B,D,C,B) & r2_analoaf(A,C,B,D,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,B,C,C,D) & r2_analoaf(A,C,B,D,C) & r2_analoaf(A,C,D,C,B) & r2_analoaf(A,B,C,D,C) & r2_analoaf(A,D,C,C,B) & r2_analoaf(A,C,D,B,C) & r2_analoaf(A,D,C,B,C) & r2_analoaf(A,D,B,D,C) & r2_analoaf(A,B,D,D,C) & r2_analoaf(A,D,B,C,D) & r2_analoaf(A,B,D,C,D) & r2_analoaf(A,D,C,D,B) & r2_analoaf(A,C,D,D,B) & r2_analoaf(A,D,C,B,D) & r2_analoaf(A,C,D,B,D) ) ) ) ) ) ) )).
fof(t7_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_funct_2(k4_ordinal1,k1_numbers,A,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C)) <=> ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,A,D) = k3_real_1(k9_nat_1(k1_numbers,B,D),k9_nat_1(k1_numbers,C,D)) ) ) ) ) ) )).
fof(t7_seq_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(B) => v2_comseq_2(k26_valued_1(k4_ordinal1,k1_numbers,B,A)) ) ) ) )).
fof(t7_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => r2_relset_1(k4_ordinal1,k4_partfun1(A,k1_numbers),k4_seqfunc(A,B),k2_seqfunc(A,B,k4_xcmplx_0(1))) ) ) )).
fof(t7_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v8_valued_0(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k9_nat_1(k1_numbers,A,k2_xcmplx_0(B,C)),k9_nat_1(k1_numbers,A,B)) ) ) ) ) )).
fof(t7_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_series_1(A) & v1_series_1(B) ) => ( v1_series_1(k1_series_1(k1_numbers,A,B)) & k4_series_1(k1_series_1(k1_numbers,A,B)) = k2_xcmplx_0(k4_series_1(A),k4_series_1(B)) ) ) ) ) )).
fof(t7_series_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(k3_xcmplx_0(A,B),k7_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),2)) ) ) )).
fof(t7_series_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k1_newton(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C),D),2) = k2_xcmplx_0(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)),k1_newton(D,2)),k2_xcmplx_0(k2_xcmplx_0(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,A),D))),k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,B),C),k3_xcmplx_0(k3_xcmplx_0(2,B),D))),k3_xcmplx_0(k3_xcmplx_0(2,C),D)) ) ) ) ) )).
fof(t7_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => r1_xxreal_0(k7_xcmplx_0(2,k2_xcmplx_0(k7_xcmplx_0(1,A),k7_xcmplx_0(1,B))),k3_square_1(k3_xcmplx_0(A,B))) ) ) )).
fof(t7_setfam_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r2_hidden(A,B) & r1_tarski(A,C) ) => r1_tarski(k1_setfam_1(B),C) ) )).
fof(t7_setlim_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ( r2_hidden(A,k6_setfam_1(B,k2_relset_1(k9_setfam_1(B),C))) <=> ! [D] : ( v7_ordinal1(D) => r2_hidden(A,k1_funct_1(C,D)) ) ) ) )).
fof(t7_setlim_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => k8_nat_1(k9_setfam_1(B),k4_setlim_2(B,C,D),A) = k4_setlim_2(B,k8_nat_1(k9_setfam_1(B),C,A),k8_nat_1(k9_setfam_1(B),D,A)) ) ) ) )).
fof(t7_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k5_finsub_1(A)) => ! [D] : ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ! [F] : ( 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) ) ) ) ) ) )).
fof(t7_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k5_finsub_1(A)) => ! [D] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [F] : ( ( 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) & k2_partfun1(A,B,E,C) = k2_partfun1(A,B,F,C) ) => ( ( C = k1_xboole_0 & ~ v1_setwiseo(D,B) ) | k7_setwiseo(A,B,D,C,E) = k7_setwiseo(A,B,D,C,F) ) ) ) ) ) ) ) ) )).
fof(t7_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( k12_scmfsa_2(C,A) = k12_scmfsa_2(D,B) => ( A = B & C = D ) ) ) ) ) ) )).
fof(t7_sfmastr1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmfsa_2)) ) => ~ ( ( v7_amistd_1(D,k7_card_1(3),k1_scmfsa_2) | ( r6_scmfsa7b(D,k1_scmfsa_m(B),A) & r5_scmfsa7b(D,k1_scmfsa_m(B),A) ) ) & ( v7_amistd_1(C,k7_card_1(3),k1_scmfsa_2) | ( r6_scmfsa7b(C,k1_scmfsa6b(D,B,A),A) & r5_scmfsa7b(C,k1_scmfsa6b(D,B,A),A) ) ) & k1_funct_1(k1_scmfsa6b(k3_scmfsa6a(D,C),B,A),E) != k1_funct_1(k1_scmfsa6b(C,k1_scmfsa6b(D,B,A),A),E) ) ) ) ) ) ) )).
fof(t7_sfmastr2,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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_sf_mastr(k2_sfmastr2(A,B)) = k4_sf_mastr(B) ) ) )).
fof(t7_sfmastr3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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_sf_mastr(k5_scmfsa8b(A,B,C,D)) = k4_subset_1(k2_scmfsa_2,k4_subset_1(k2_scmfsa_2,k5_scmfsa_m(A,B),k2_sf_mastr(C)),k2_sf_mastr(D)) ) ) ) ) )).
fof(t7_sgraph1,axiom,( ! [A] : ! [B] : ( r2_hidden(B,k2_sgraph1(A)) <=> ? [C] : ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(A)) & B = C & k5_card_1(C) = 2 ) ) )).
fof(t7_sheffer1,axiom,( ! [A] : ( ( ~ 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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k3_lattices(A,k4_lattices(A,k4_lattices(A,B,C),D),B) = B ) ) ) ) )).
fof(t7_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,k5_sheffer1(A,C,B))) = B ) ) ) )).
fof(t7_simplex0,axiom,( ! [A] : ( v1_classes1(A) => k1_simplex0(A) = A ) )).
fof(t7_simplex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_simplex0(B,u1_struct_0(A)) => ( v1_xboole_0(k3_simplex1(A,B)) <=> v4_simplex0(B) ) ) ) )).
fof(t7_simplex2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( l1_pre_topc(B) => ( v1_simplex2(B,A) => r1_xxreal_0(k5_numbers,k1_simplex2(A,B)) ) ) ) )).
fof(t7_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v7_ordinal1(C) => r2_funct_2(k4_ordinal1,k2_numbers,k9_sin_cos(C,B,A),k25_valued_1(k4_ordinal1,k2_numbers,k8_sin_cos(C,B,A),k7_xcmplx_0(k6_complex1,k2_newton(C)))) ) ) ) )).
fof(t7_sin_cos2,axiom,( v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k16_sin_cos,k2_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(2,k28_sin_cos)))) )).
fof(t7_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,k6_xcmplx_0(A,B)) = k2_xcmplx_0(k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k2_sin_cos3,B)),k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k1_sin_cos3,B))) ) ) )).
fof(t7_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( k19_sin_cos(A) != k5_numbers & k19_sin_cos(B) != k5_numbers & k1_sin_cos4(k2_xcmplx_0(A,B)) != k7_xcmplx_0(k2_xcmplx_0(k1_sin_cos4(A),k1_sin_cos4(B)),k6_xcmplx_0(1,k3_xcmplx_0(k1_sin_cos4(A),k1_sin_cos4(B)))) ) ) ) )).
fof(t7_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k19_sin_cos(k3_xcmplx_0(2,A)) = k6_xcmplx_0(k1_square_1(k19_sin_cos(A)),k1_square_1(k17_sin_cos(A))) & k19_sin_cos(k3_xcmplx_0(2,A)) = k6_xcmplx_0(k3_xcmplx_0(2,k1_square_1(k19_sin_cos(A))),1) & k19_sin_cos(k3_xcmplx_0(2,A)) = k6_xcmplx_0(1,k3_xcmplx_0(2,k1_square_1(k17_sin_cos(A)))) ) ) )).
fof(t7_sin_cos6,axiom,( k17_sin_cos(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2))) = k4_xcmplx_0(1) & k1_funct_1(k16_sin_cos,k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2))) = k4_xcmplx_0(1) )).
fof(t7_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(1,A) ) => r1_xxreal_0(k5_numbers,k7_xcmplx_0(k6_xcmplx_0(A,1),B)) ) ) ) )).
fof(t7_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ( k23_sin_cos(A) = k2_xcmplx_0(k4_sin_cos2(A),k2_sin_cos2(A)) & k23_sin_cos(k4_xcmplx_0(A)) = k6_xcmplx_0(k4_sin_cos2(A),k2_sin_cos2(A)) & k23_sin_cos(A) = k7_xcmplx_0(k2_xcmplx_0(k4_sin_cos2(k7_xcmplx_0(A,2)),k2_sin_cos2(k7_xcmplx_0(A,2))),k6_xcmplx_0(k4_sin_cos2(k7_xcmplx_0(A,2)),k2_sin_cos2(k7_xcmplx_0(A,2)))) & k23_sin_cos(k4_xcmplx_0(A)) = k7_xcmplx_0(k6_xcmplx_0(k4_sin_cos2(k7_xcmplx_0(A,2)),k2_sin_cos2(k7_xcmplx_0(A,2))),k2_xcmplx_0(k4_sin_cos2(k7_xcmplx_0(A,2)),k2_sin_cos2(k7_xcmplx_0(A,2)))) & k23_sin_cos(A) = k7_xcmplx_0(k2_xcmplx_0(1,k6_sin_cos2(k7_xcmplx_0(A,2))),k6_xcmplx_0(1,k6_sin_cos2(k7_xcmplx_0(A,2)))) & k23_sin_cos(k4_xcmplx_0(A)) = k7_xcmplx_0(k6_xcmplx_0(1,k6_sin_cos2(k7_xcmplx_0(A,2))),k2_xcmplx_0(1,k6_sin_cos2(k7_xcmplx_0(A,2)))) ) ) )).
fof(t7_sin_cos9,axiom,( v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k26_sin_cos,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(t7_sincos10,axiom,( r2_fdiff_1(k2_fdiff_9,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers)) & ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k5_numbers)) => k1_fdiff_1(k2_fdiff_9,A) = k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k18_sin_cos,A),k1_square_1(k1_funct_1(k16_sin_cos,A)))) ) ) )).
fof(t7_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ~ ( r1_tarski(k1_rltopsp1(k15_euclid(A),D,E),k1_rltopsp1(k15_euclid(A),B,C)) & r2_hidden(B,k1_rltopsp1(k15_euclid(A),D,E)) & B != D & B != E ) ) ) ) ) ) )).
fof(t7_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(1,C) => k2_topreal1(2,k8_finseq_1(u1_struct_0(k15_euclid(2)),A,B),k2_xcmplx_0(k3_finseq_1(A),C)) = k2_topreal1(2,B,C) ) ) ) ) )).
fof(t7_sprect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ( ( r3_connsp_1(A,B,C) & r3_connsp_1(A,B,D) & r3_connsp_1(A,B,E) & r3_connsp_1(A,B,F) & k4_subset_1(u1_struct_0(A),C,D) = B & k4_subset_1(u1_struct_0(A),E,F) = B ) => k2_tarski(C,D) = k2_tarski(E,F) ) ) ) ) ) ) ) )).
fof(t7_sprect_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t7_sprect_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k14_euclid(2))) => ! [C] : ( v1_xreal_0(C) => ( A = k8_metric_1(k14_euclid(2),B,C) => v2_connsp_1(A,k15_euclid(2)) ) ) ) ) )).
fof(t7_sprect_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_finseq_6(B,A) & m2_finseq_1(B,A) ) => ! [C] : ( m1_subset_1(C,A) => ~ ( r2_hidden(C,k10_xtuple_0(B)) & ~ r1_xxreal_0(k3_finseq_1(B),1) & r1_xxreal_0(k3_finseq_1(B),k4_finseq_4(B,C)) ) ) ) ) )).
fof(t7_square_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k1_square_1(k6_xcmplx_0(A,1)) = k2_xcmplx_0(k6_xcmplx_0(k1_square_1(A),k3_xcmplx_0(2,A)),1) ) )).
fof(t7_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ( ~ r1_stacks_1(A,B) => k9_stacks_1(A,k5_stacks_1(A,B)) = k2_stacks_1(u1_struct_0(A),1,k9_stacks_1(A,B)) ) ) ) )).
fof(t7_stirl2_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k3_nat_1(k8_domain_1(k4_ordinal1,A,B,C)) = k4_nat_1(A,k4_nat_1(B,C)) ) ) ) )).
fof(t7_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [D] : ( m2_subset_1(D,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [E] : ( ( v5_relat_1(E,k3_qc_lang1(A)) & v3_card_1(E,B) & m2_finseq_1(E,k2_qc_lang1(A)) ) => ! [F] : ( ( v5_relat_1(F,k3_qc_lang1(A)) & v3_card_1(F,B) & m2_finseq_1(F,k2_qc_lang1(A)) ) => ! [G] : ( m1_subset_1(G,k1_substut1(A)) => ! [H] : ( m1_subset_1(H,k1_substut1(A)) => ( r2_relset_1(k4_ordinal1,k2_qc_lang1(A),k26_substut1(A,k17_substut1(A,C,E,G)),k26_substut1(A,k17_substut1(A,D,F,H))) => r2_relset_1(k4_ordinal1,k2_qc_lang1(A),E,F) ) ) ) ) ) ) ) ) ) )).
fof(t7_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,B) <=> ( r2_hidden(E,C) & ~ r2_hidden(E,D) ) ) ) => B = k7_subset_1(A,C,D) ) ) ) ) )).
fof(t7_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( v1_finset_1(D) => ( ( r2_hidden(D,C) & ! [E] : ( v1_finset_1(E) => ( ( r2_hidden(E,C) & r1_tarski(E,D) ) => E = D ) ) ) => r2_hidden(D,k3_substlat(A,B,C)) ) ) ) )).
fof(t7_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ( m1_subset_1(k2_zfmisc_1(k9_qc_lang1(A),k1_substut1(A)),k1_zfmisc_1(k2_zfmisc_1(k13_finseq_1(k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))),k1_substut1(A)))) & ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [D] : ( ( v3_card_1(D,B) & m2_finseq_1(D,k2_qc_lang1(A)) ) => ! [E] : ( 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(k9_qc_lang1(A),k1_substut1(A))) ) ) ) ) & ! [B] : ( m1_subset_1(B,k1_substut1(A)) => r2_hidden(k1_domain_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_zfmisc_1(k4_ordinal1,k4_ordinal1))),k1_substut1(A),k12_finseq_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,k5_numbers,k5_numbers)),B),k2_zfmisc_1(k9_qc_lang1(A),k1_substut1(A))) ) & ! [B] : ( m2_finseq_1(B,k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))) => ! [C] : ( m1_subset_1(C,k1_substut1(A)) => ( r2_hidden(k1_domain_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A)))),k1_substut1(A),B,C),k2_zfmisc_1(k9_qc_lang1(A),k1_substut1(A))) => r2_hidden(k4_tarski(k7_finseq_1(k12_finseq_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,1,k5_numbers)),B),C),k2_zfmisc_1(k9_qc_lang1(A),k1_substut1(A))) ) ) ) & ! [B] : ( m2_finseq_1(B,k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))) => ! [C] : ( m2_finseq_1(C,k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))) => ! [D] : ( m1_subset_1(D,k1_substut1(A)) => ( ( r2_hidden(k1_domain_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A)))),k1_substut1(A),B,D),k2_zfmisc_1(k9_qc_lang1(A),k1_substut1(A))) & r2_hidden(k1_domain_1(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A)))),k1_substut1(A),C,D),k2_zfmisc_1(k9_qc_lang1(A),k1_substut1(A))) ) => r2_hidden(k4_tarski(k7_finseq_1(k7_finseq_1(k12_finseq_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,2,k5_numbers)),B),C),D),k2_zfmisc_1(k9_qc_lang1(A),k1_substut1(A))) ) ) ) ) & ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_finseq_1(C,k2_zfmisc_1(k4_ordinal1,k1_qc_lang1(A))) => ! [D] : ( m1_subset_1(D,k1_substut1(A)) => ( r2_hidden(k4_tarski(C,k1_funct_1(k15_substut1(A),k4_tarski(k7_finseq_1(k7_finseq_1(k12_finseq_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,3,k5_numbers)),k12_finseq_1(k3_qc_lang1(A),B)),C),D))),k2_zfmisc_1(k9_qc_lang1(A),k1_substut1(A))) => r2_hidden(k4_tarski(k7_finseq_1(k7_finseq_1(k12_finseq_1(k2_zfmisc_1(k4_ordinal1,k4_ordinal1),k1_domain_1(k4_ordinal1,k4_ordinal1,3,k5_numbers)),k12_finseq_1(k3_qc_lang1(A),B)),C),D),k2_zfmisc_1(k9_qc_lang1(A),k1_substut1(A))) ) ) ) ) ) ) )).
fof(t7_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k1_substut1(A)) => ( r2_hidden(C,k10_xtuple_0(k7_substut1(A,C,k11_cqc_lang(A,C,B),D))) => k35_substut1(A,k1_substut2(A,k11_cqc_lang(A,C,B),D)) = k2_qc_lang3(A,k13_substut1(A,k7_substut1(A,C,k11_cqc_lang(A,C,B),D),B)) ) ) ) ) ) )).
fof(t7_supinf_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_setfam_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k6_numbers))) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_membered(B) ) => ( B = k5_setfam_1(k6_numbers,A) => m2_xxreal_2(k2_xxreal_2(B),k6_supinf_1(A)) ) ) ) )).
fof(t7_supinf_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => r1_xxreal_0(k8_supinf_2(k5_supinf_2(A,B)),k3_supinf_2(k8_supinf_2(A),k8_supinf_2(B))) ) ) )).
fof(t7_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ~ ( ~ r1_orders_2(B,C,E) & r1_orders_2(B,k3_rlvect_1(B,C,D),E) & r1_orders_2(B,k3_rlvect_1(B,k4_vectsp_1(A,B,k3_rlvect_1(A,k1_group_1(A),k1_group_1(A)),C),D),E) ) ) ) ) ) ) )).
fof(t7_sysrel,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( v1_relat_1(E) => ( ( ( r1_xboole_0(C,D) & r1_tarski(E,k2_xboole_0(k2_zfmisc_1(C,D),k2_zfmisc_1(D,C))) & r2_hidden(k4_tarski(A,B),E) & r2_hidden(A,C) ) => ( ~ r2_hidden(A,D) & ~ r2_hidden(B,C) & r2_hidden(B,D) ) ) & ( ( r1_xboole_0(C,D) & r1_tarski(E,k2_xboole_0(k2_zfmisc_1(C,D),k2_zfmisc_1(D,C))) & r2_hidden(k4_tarski(A,B),E) & r2_hidden(B,D) ) => ( ~ r2_hidden(B,C) & ~ r2_hidden(A,D) & r2_hidden(A,C) ) ) & ( ( r1_xboole_0(C,D) & r1_tarski(E,k2_xboole_0(k2_zfmisc_1(C,D),k2_zfmisc_1(D,C))) & r2_hidden(k4_tarski(A,B),E) & r2_hidden(A,D) ) => ( ~ r2_hidden(A,C) & ~ r2_hidden(B,D) & r2_hidden(B,C) ) ) & ( ( r1_xboole_0(C,D) & r1_tarski(E,k2_xboole_0(k2_zfmisc_1(C,D),k2_zfmisc_1(D,C))) & r2_hidden(k4_tarski(A,B),E) & r2_hidden(B,C) ) => ( ~ r2_hidden(A,C) & ~ r2_hidden(B,D) & r2_hidden(A,D) ) ) ) ) )).
fof(t7_t_0topsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,k2_t_0topsp(A)) => ( r1_xboole_0(C,B) | r1_tarski(C,B) ) ) ) ) ) ) )).
fof(t7_t_1topsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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) => ! [D] : ~ ( r2_hidden(D,u1_struct_0(k2_t_1topsp(A))) & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ~ ( r2_hidden(E,k2_relset_1(u1_struct_0(B),C)) & r1_tarski(D,k8_relset_1(u1_struct_0(A),u1_struct_0(B),C,k6_domain_1(u1_struct_0(B),E))) ) ) ) ) ) ) ) )).
fof(t7_taxonom1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( r3_relat_2(B,A) => r3_relat_2(k18_finseq_1(B),A) ) ) )).
fof(t7_taxonom2,axiom,( v4_taxonom2(k1_xboole_0) )).
fof(t7_taylor_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_rat_1(B) => k4_prepower(k23_sin_cos(A),B) = k23_sin_cos(k3_xcmplx_0(B,A)) ) ) )).
fof(t7_taylor_2,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k22_sin_cos,A),B),C) = k1_funct_1(k22_sin_cos,C) ) ) ) ) )).
fof(t7_tdgroup,axiom,( ~ ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = C ) ) ) )).
fof(t7_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v3_pre_topc(B,A) | v3_pre_topc(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))) ) ) ) ) )).
fof(t7_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => k1_pcomps_1(A,B) = a_2_0_tdlat_2(A,B) ) ) )).
fof(t7_tdlat_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v4_tops_1(B,A) & r1_tarski(k2_pre_topc(A,k1_tops_1(A,B)),k1_tops_1(A,k2_pre_topc(A,B))) ) => ( v6_tops_1(B,A) & v5_tops_1(B,A) ) ) ) ) )).
fof(t7_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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) ) ) ) ) ) )).
fof(t7_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_tmap_1(A,k3_subset_1(u1_struct_0(A),B))))) => ( ( r1_tarski(C,B) & v2_tops_1(B,A) ) => v3_tops_1(C,k6_tmap_1(A,k3_subset_1(u1_struct_0(A),B))) ) ) ) ) )).
fof(t7_tex_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [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)) & v2_pre_topc(A) ) => v2_pre_topc(B) ) ) ) )).
fof(t7_tex_3,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_subset_1(B,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : ( ~ v2_struct_0(C) & v1_pre_topc(C) & v1_tex_2(C,A) & m1_pre_topc(C,A) & B = u1_struct_0(C) ) ) ) )).
fof(t7_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => v1_tex_4(B,A) ) ) )).
fof(t7_tietze,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v2_xxreal_0(B) & v1_xreal_0(B) ) => ! [C] : ( ( v2_xxreal_0(C) & v1_xreal_0(C) ) => ( ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k1_funct_1(A,D),k3_funct_2(k4_ordinal1,k1_numbers,A,k1_nat_1(D,1)))),k3_xcmplx_0(B,k2_power(C,D))) ) => ( r1_xxreal_0(1,C) | ( v2_comseq_2(A) & ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k1_seq_2(A),k1_funct_1(A,D))),k7_xcmplx_0(k3_xcmplx_0(B,k2_power(C,D)),k6_xcmplx_0(1,C))) ) ) ) ) ) ) ) )).
fof(t7_tmap_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v2_pre_topc(C) & l1_pre_topc(C) ) => ( B = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) => ( m1_pre_topc(B,A) <=> m1_pre_topc(C,A) ) ) ) ) ) )).
fof(t7_toler_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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) ) ) )).
fof(t7_topalg_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v3_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v3_valued_0(C) ) => k10_rvsum_1(k8_rvsum_1(B,C),A) = k8_rvsum_1(k10_rvsum_1(B,A),k10_rvsum_1(C,A)) ) ) ) )).
fof(t7_topalg_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( k9_xtuple_0(A) = k9_xtuple_0(B) => k11_mcart_1(k13_funct_3(A,B)) = A ) ) ) )).
fof(t7_topalg_5,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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_connsp_1(C,A) ) => v2_connsp_1(D,B) ) ) ) ) ) )).
fof(t7_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_borsuk_2(G,A,C,D) => ! [H] : ( m1_borsuk_2(H,A,C,D) => ! [I] : ( m1_borsuk_2(I,B,E,F) => ! [J] : ( m1_borsuk_2(J,B,E,F) => ( ( r1_borsuk_6(B,E,F) & r1_borsuk_6(A,C,D) & r1_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),u1_struct_0(k5_topmetr),u1_struct_0(B),G,I) & r1_funct_2(u1_struct_0(k5_topmetr),u1_struct_0(A),u1_struct_0(k5_topmetr),u1_struct_0(B),H,J) & k6_eqrel_1(k1_topalg_1(B,E,F),k1_topalg_1(B,E,F),k3_topalg_1(B,E,F),I) = k6_eqrel_1(k1_topalg_1(B,E,F),k1_topalg_1(B,E,F),k3_topalg_1(B,E,F),J) ) => k6_eqrel_1(k1_topalg_1(A,C,D),k1_topalg_1(A,C,D),k3_topalg_1(A,C,D),G) = k6_eqrel_1(k1_topalg_1(A,C,D),k1_topalg_1(A,C,D),k3_topalg_1(A,C,D),H) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t7_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_topdim_1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( r1_xxreal_0(k2_topdim_1(A,C),k6_xcmplx_0(B,1)) <=> r2_hidden(C,k13_prob_1(u1_struct_0(A),k4_ordinal1,k9_setfam_1(u1_struct_0(A)),k1_topdim_1(A),B)) ) ) ) ) )).
fof(t7_topdim_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( 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] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) => ~ ( m1_setfam_1(C,u1_struct_0(B)) & v2_topdim_1(C,B) & r1_xxreal_0(k3_topdim_1(B,C),k5_numbers) & r1_xxreal_0(k5_card_1(C),k1_xxreal_3(A,1)) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ( ( r2_hidden(D,C) & r2_hidden(E,C) ) => ( r1_xboole_0(D,E) | D = E ) ) ) ) ) ) ) ) ) )).
fof(t7_topgen_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => k1_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)),k1_topgen_1(A,B),k1_topgen_1(A,C)) ) ) ) )).
fof(t7_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)))) ) => ! [E] : ( ( 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)))) ) => ! [F] : ~ ( r2_hidden(B,F) & r2_hidden(F,E) & ! [G] : ( ( v3_pre_topc(G,A) & m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( r2_hidden(G,D) & r1_tarski(G,F) ) ) ) ) ) ) ) ) )).
fof(t7_topgen_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k9_setfam_1(A),k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) ) => ( ( k1_funct_1(B,k11_arytm_3) = k11_arytm_3 & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => r1_tarski(C,k3_funct_2(k1_zfmisc_1(A),k9_setfam_1(A),B,C)) ) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => k3_funct_2(k1_zfmisc_1(A),k9_setfam_1(A),B,k4_subset_1(A,C,D)) = k4_subset_1(A,k3_funct_2(k1_zfmisc_1(A),k9_setfam_1(A),B,C),k3_funct_2(k1_zfmisc_1(A),k9_setfam_1(A),B,D)) ) ) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k3_funct_2(k9_setfam_1(A),k9_setfam_1(A),B,k3_funct_2(k1_zfmisc_1(A),k9_setfam_1(A),B,C)) = k3_funct_2(k1_zfmisc_1(A),k9_setfam_1(A),B,C) ) ) => ! [C] : ( l1_pre_topc(C) => ( ( u1_struct_0(C) = A & u1_pre_topc(C) = k7_setfam_1(A,k1_topgen_3(k9_setfam_1(A),A,B)) ) => ( v2_pre_topc(C) & l1_pre_topc(C) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) => k2_pre_topc(C,D) = k1_funct_1(B,D) ) ) ) ) ) ) )).
fof(t7_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v5_waybel23(A) => v7_topgen_1(A) ) ) )).
fof(t7_topgen_5,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( D = k2_xboole_0(B,C) => k1_funct_1(k9_funct_6(D),A) = k2_xboole_0(k1_funct_1(k9_funct_6(B),A),k1_funct_1(k9_funct_6(C),A)) ) ) ) ) )).
fof(t7_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k1_group_2(A,B)) <=> r2_hidden(k2_group_1(A,C),B) ) ) ) ) )).
fof(t7_topmetr,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(k1_pre_topc(A,C)),u1_struct_0(B)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_pre_topc(A,C)),u1_struct_0(B)))) ) => ( ( v5_pre_topc(D,A,B) & E = k5_relset_1(u1_struct_0(A),u1_struct_0(B),D,C) ) => v5_pre_topc(E,k1_pre_topc(A,C),B) ) ) ) ) ) ) )).
fof(t7_topmetr3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k2_topmetr(A,B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k2_topmetr(A,B))))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(k7_metric_1)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k7_metric_1)))) ) => ( ( r1_funct_2(k4_ordinal1,u1_struct_0(k7_metric_1),k4_ordinal1,u1_struct_0(k2_topmetr(A,B)),D,C) & r1_xxreal_0(A,B) ) => ( ( v2_tbsp_1(D,k7_metric_1) => v2_tbsp_1(C,k2_topmetr(A,B)) ) & ( v2_tbsp_1(C,k2_topmetr(A,B)) => v2_tbsp_1(D,k7_metric_1) ) & ( v2_tbsp_1(D,k7_metric_1) => k1_tbsp_1(k7_metric_1,D) = k1_tbsp_1(k2_topmetr(A,B),C) ) ) ) ) ) ) ) )).
fof(t7_topreal1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ( ( r2_hidden(B,k1_rltopsp1(k15_euclid(A),D,E)) & r2_hidden(C,k1_rltopsp1(k15_euclid(A),D,E)) ) => k1_rltopsp1(k15_euclid(A),D,E) = k4_subset_1(u1_struct_0(k15_euclid(A)),k4_subset_1(u1_struct_0(k15_euclid(A)),k1_rltopsp1(k15_euclid(A),D,B),k1_rltopsp1(k15_euclid(A),B,C)),k1_rltopsp1(k15_euclid(A),C,E)) ) ) ) ) ) ) )).
fof(t7_topreal3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(2))) => ( ( C = A & D = B ) => k1_binop_1(k13_euclid(2),C,D) = k3_square_1(k2_xcmplx_0(k1_square_1(k6_xcmplx_0(k17_euclid(A),k17_euclid(B))),k1_square_1(k6_xcmplx_0(k18_euclid(A),k18_euclid(B))))) ) ) ) ) ) )).
fof(t7_topreal5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ~ r1_xxreal_0(B,A) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k3_topmetr)) & v5_pre_topc(E,k4_topmetr(A,B),k3_topmetr) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_topmetr(A,B)),u1_struct_0(k3_topmetr)))) ) => ! [F] : ( v1_xreal_0(F) => ~ ( k1_funct_1(E,A) = C & k1_funct_1(E,B) = D & ~ r1_xxreal_0(C,F) & ~ r1_xxreal_0(F,D) & ! [G] : ( v1_xreal_0(G) => ~ ( k1_funct_1(E,G) = F & ~ r1_xxreal_0(G,A) & ~ r1_xxreal_0(B,G) ) ) ) ) ) ) ) ) ) ) )).
fof(t7_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ( ( B != k5_numbers & A = k5_numbers ) <=> k19_rvsum_1(k2_finseq_2(B,A)) = k5_numbers ) ) ) )).
fof(t7_topreal7,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( ( k3_finseq_1(A) = k3_finseq_1(B) | k4_finseq_1(A) = k4_finseq_1(B) ) => ( k3_finseq_1(k8_rvsum_1(A,B)) = k3_finseq_1(A) & k4_finseq_1(k8_rvsum_1(A,B)) = k4_finseq_1(A) ) ) ) ) )).
fof(t7_topreal8,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => r1_xxreal_0(k3_finseq_1(A),k3_finseq_1(k3_graph_2(A,B))) ) ) )).
fof(t7_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ( r2_hidden(D,k3_topreal9(A,C,B)) <=> k12_euclid(k5_algstr_0(k15_euclid(A),D,C)) = B ) ) ) ) ) )).
fof(t7_topreala,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,B) ) => ! [D] : ( ( 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)))) ) => ( 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)))) ) ) ) ) ) )).
fof(t7_toprealb,axiom,( ! [A] : ( ( 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_funct_1(A) & v1_funct_2(A,u1_struct_0(k2_topalg_2),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_relset_1(k1_numbers,A))))) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_topalg_2),u1_struct_0(k1_pre_topc(k2_topalg_2,k5_toprealb(k2_relset_1(k1_numbers,A))))))) ) ) )).
fof(t7_toprealc,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_valued_0(C) ) => ( A != k5_numbers => k45_valued_1(k14_valued_2(B,A),C) = k14_valued_2(k45_valued_1(B,k24_valued_1(C,A)),A) ) ) ) ) )).
fof(t7_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => k3_xcmplx_0(k9_complex1(B),k12_euclid(C)) = k12_euclid(k1_rlvect_1(k15_euclid(A),C,B)) ) ) ) )).
fof(t7_tops_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v4_pre_topc(B,A) & v4_pre_topc(C,A) ) => 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)) ) ) ) ) )).
fof(t7_tops_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ( B != k1_xboole_0 => k5_setfam_1(A,k7_setfam_1(A,B)) = k3_subset_1(A,k6_setfam_1(A,B)) ) ) )).
fof(t7_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( r1_xboole_0(B,k1_tops_1(A,k2_pre_topc(A,B))) => k1_tops_1(A,k2_pre_topc(A,B)) = k1_xboole_0 ) ) ) )).
fof(t7_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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_funct_2(A,A,k2_transgeo(A,k2_funct_2(A,B),C),k2_funct_2(A,k2_transgeo(A,B,C))) ) ) ) )).
fof(t7_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( v11_aff_2(A) & ! [D] : ( ( 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 ) ) ) ) ) ) )).
fof(t7_treal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_topmetr(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_topmetr(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k4_topmetr(k5_numbers,1))) => k3_funct_2(u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k4_topmetr(A,B)),k3_treal_1(A,B,C,D),E) = k2_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(D,C),E),C) ) ) ) ) ) ) )).
fof(t7_trees_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r1_tarski(B,C) => r2_xboole_0(B,k7_finseq_1(C,k9_finseq_1(A))) ) ) ) )).
fof(t7_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( ( r2_hidden(C,A) & r2_hidden(D,A) ) => ( r1_tarski(C,D) | r2_hidden(D,k5_trees_1(A,C,B)) ) ) ) ) ) ) )).
fof(t7_trees_3,axiom,( ! [A] : ! [B] : ( ( v2_trees_3(A) & v2_trees_3(B) ) => v2_trees_3(k5_xboole_0(A,B)) ) )).
fof(t7_trees_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ( k3_trees_4(A,C) = k3_trees_4(B,D) => ( A = B & C = D ) ) ) ) )).
fof(t7_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) & v1_trees_9(A) ) => ! [B] : ( m1_trees_1(B,A) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k8_finseq_1(k4_ordinal1,B,k14_trees_3(C)),k1_trees_2(A,B)) <=> ~ r1_xxreal_0(k5_card_1(k1_trees_2(A,B)),C) ) ) ) ) )).
fof(t7_trees_a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( m4_trees_1(C,A) => ( C != k1_xboole_0 => k1_trees_a(A,B,C) = k2_xboole_0(a_2_1_trees_a(A,C),a_3_0_trees_a(A,B,C)) ) ) ) ) )).
fof(t7_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_pre_topc(C,B) => m1_pre_topc(C,A) ) ) ) )).
fof(t7_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ r1_tsep_2(A,B,B) ) ) )).
fof(t7_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_tsp_1(B,A) & v1_tsp_1(C,A) ) => ( ( ~ v3_pre_topc(B,A) & ~ v3_pre_topc(C,A) ) | v1_tsp_1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ) )).
fof(t7_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tsp_2(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => k2_pre_topc(A,C) = k3_tex_4(A,k9_subset_1(u1_struct_0(A),B,k2_pre_topc(A,C))) ) ) ) ) )).
fof(t7_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k9_funct_2(k4_numbers,u1_turing_1(A)))) => k9_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),k5_numbers) = B ) ) )).
fof(t7_twoscomp,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( m1_subset_1(B,k6_margrel1) => ( k1_funct_1(k8_twoscomp,k10_finseq_1(A,B)) = k1_funct_1(k7_twoscomp,k10_finseq_1(A,B)) & k1_funct_1(k9_twoscomp,k10_finseq_1(A,B)) = k1_funct_1(k6_twoscomp,k10_finseq_1(B,A)) & k1_funct_1(k10_twoscomp,k10_finseq_1(A,B)) = k1_funct_1(k5_twoscomp,k10_finseq_1(A,B)) ) ) ) )).
fof(t7_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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) => k4_finseq_1(u1_unialg_1(A)) = k4_finseq_1(u1_unialg_1(B)) ) ) ) )).
fof(t7_unialg_3,axiom,( ! [A] : ( ( ~ 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] : ( m1_unialg_2(B,A) => ! [C] : ( m1_unialg_2(C,A) => k6_unialg_2(B) = k6_unialg_2(C) ) ) ) )).
fof(t7_uniform1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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(k3_pcomps_1(A)),u1_struct_0(k3_pcomps_1(B)),u1_struct_0(A),u1_struct_0(B),D,C) & v1_compts_1(k3_pcomps_1(A)) & v5_pre_topc(D,k3_pcomps_1(A),k3_pcomps_1(B)) ) => v1_uniform1(C,A,B) ) ) ) ) ) )).
fof(t7_uproots,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r1_xboole_0(B,C) => r6_pboole(A,k1_uproots(A,k4_subset_1(A,B,C),D),k11_pre_poly(A,k1_uproots(A,B,D),k1_uproots(A,C,D))) ) ) ) ) )).
fof(t7_urysohn1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(B,k1_newton(2,A)) => ( r1_xxreal_0(B,k5_numbers) | r2_hidden(k7_xcmplx_0(k6_xcmplx_0(k2_nat_1(B,2),1),k11_newton(2,k1_nat_1(A,1))),k7_subset_1(k1_numbers,k1_urysohn1(k1_nat_1(A,1)),k1_urysohn1(A))) ) ) ) ) )).
fof(t7_urysohn2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ( v1_measure5(A) => ( B = k5_numbers | v1_measure5(k1_integra2(A,B)) ) ) ) ) )).
fof(t7_urysohn3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(A,k1_urysohn1(B)) => r1_xxreal_0(k3_urysohn3(A),B) ) ) ) )).
fof(t7_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [E] : ( ( v5_relat_1(E,k3_qc_lang1(A)) & v3_card_1(E,B) & m2_finseq_1(E,k2_qc_lang1(A)) ) => ! [F] : ( m2_subset_1(F,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [G] : ( m1_valuat_1(G,A,C) => ! [H] : ( m2_subset_1(H,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [I] : ( m1_subset_1(I,k3_margrel1(C)) => ( ( F = k4_cqc_lang(B,A,H,E) & r1_margrel1(C,I,k7_valuat_1(A,C,B,G,H)) ) => ( r2_hidden(k4_valuat_1(A,C,B,E,D),I) <=> k3_funct_2(k2_valuat_1(A,C),k6_margrel1,k8_valuat_1(A,C,G,F),D) = k8_margrel1 ) ) ) ) ) ) ) ) ) ) ) )).
fof(t7_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_valued_0(A) <=> ! [B] : v1_xcmplx_0(k1_funct_1(A,B)) ) ) )).
fof(t7_valued_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_membered(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( ( 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] : ( m1_subset_1(F,A) => k3_funct_2(A,k2_numbers,E,F) = k3_xcmplx_0(D,k3_funct_2(A,B,C,F)) ) => r2_funct_2(A,k2_numbers,E,k25_valued_1(A,B,C,D)) ) ) ) ) ) ) )).
fof(t7_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_valued_0(C) ) => ( k7_valued_1(C,A) = k7_valued_1(C,B) => ( C = k1_xboole_0 | A = B ) ) ) ) ) )).
fof(t7_vectmetr,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k1_group_1(k5_vectmetr(A)) = k3_struct_0(k4_vectmetr(A)) ) )).
fof(t7_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( r1_vectsp_5(A,B,C,D) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ( k4_vectsp_5(A,B,E,C,D) = k1_domain_1(u1_struct_0(B),u1_struct_0(B),F,G) => ( r1_struct_0(C,F) & r1_struct_0(D,G) ) ) ) ) ) ) ) ) ) ) )).
fof(t7_vectsp_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t7_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k6_algstr_0(A,C,B) = k5_struct_0(A) => k6_algstr_0(A,B,C) = k5_struct_0(A) ) ) ) ) )).
fof(t7_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( ( v1_vectsp_4(C,A,B) & v1_vectsp_4(D,A,B) ) => v1_vectsp_4(k9_subset_1(u1_struct_0(B),C,D),A,B) ) ) ) ) ) )).
fof(t7_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( m1_vectsp_4(C,A,k1_vectsp_5(A,B,C,D)) & m1_vectsp_4(D,A,k1_vectsp_5(A,B,C,D)) ) ) ) ) ) )).
fof(t7_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_6(C,A,B) => m2_vectsp_6(C,A,B,k1_vectsp_6(A,B,C)) ) ) ) )).
fof(t7_vectsp_7,axiom,( ! [A] : ! [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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) => ( r1_struct_0(k1_vectsp_7(B,C,D),A) <=> ? [E] : ( m2_vectsp_6(E,B,C,D) & A = k4_vectsp_6(B,C,E) ) ) ) ) ) )).
fof(t7_vectsp_8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k1_vectsp_8(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_vectsp_8(A,B))) => ! [E] : ( m1_vectsp_4(E,A,B) => ! [F] : ( m1_vectsp_4(F,A,B) => ( ( C = E & D = F ) => k3_lattices(k1_vectsp_8(A,B),C,D) = k1_vectsp_5(A,B,E,F) ) ) ) ) ) ) ) )).
fof(t7_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_6(D,A,B) => ( r1_tarski(k1_vectsp_6(A,B,D),u1_struct_0(C)) => ! [E] : ( m1_vectsp_6(E,A,C) => ( E = k2_partfun1(u1_struct_0(B),u1_struct_0(A),D,u1_struct_0(C)) => ( k1_vectsp_6(A,B,D) = k1_vectsp_6(A,C,E) & k4_vectsp_6(A,B,D) = k4_vectsp_6(A,C,E) ) ) ) ) ) ) ) ) )).
fof(t7_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( 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,k3_valued_1(A,k1_numbers,k1_numbers,D,E),C),k6_vfunct_1(A,B,k3_vfunct_1(A,B,D,C),k3_vfunct_1(A,B,E,C))) ) ) ) ) ) )).
fof(t7_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [E] : ( ( 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,k2_valued_1(A,k2_numbers,k2_numbers,D,E),C),k3_vfunct_2(A,B,k1_vfunct_2(A,B,D,C),k1_vfunct_2(A,B,E,C))) ) ) ) ) ) )).
fof(t7_waybel10,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_yellow_0(D,A) => v2_funct_1(k2_tmap_1(A,B,C,D)) ) ) ) ) ) )).
fof(t7_waybel11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v24_waybel_0(A) & v4_waybel11(A) & l1_waybel_9(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(B,A) <=> ( v2_waybel11(B,A) & v12_waybel_0(B,A) ) ) ) ) )).
fof(t7_waybel12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => r2_hidden(k3_yellow_0(A),k3_waybel_0(A,B)) ) ) )).
fof(t7_waybel13,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ v2_struct_0(C) & v4_yellow_0(C,k2_yellow_1(A)) & v7_yellow_0(C,k2_yellow_1(A)) & v4_waybel_0(C,k2_yellow_1(A)) & m1_yellow_0(C,k2_yellow_1(A)) ) => ( r2_hidden(B,u1_struct_0(k1_waybel_8(C))) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(k2_yellow_1(A))) & v1_finset_1(D) & B = k1_setfam_1(a_3_0_waybel13(A,C,D)) & r1_tarski(D,B) ) ) ) )).
fof(t7_waybel14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_waybel_3(A,B,C) <=> r1_tarski(k6_waybel_0(A,C),k2_waybel_3(A,B)) ) ) ) ) )).
fof(t7_waybel15,axiom,( ! [A] : v3_waybel_8(k2_yellow_1(A)) )).
fof(t7_waybel16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => k8_waybel_0(A) = k7_waybel_0(k7_lattice3(A)) ) )).
fof(t7_waybel17,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_waybel11(A,k3_waybel17(A,B,C)) = k12_lattice3(A,B,C) ) ) ) )).
fof(t7_waybel18,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => v2_waybel18(k4_waybel18(A,B,C)) ) => v2_waybel18(k3_waybel18(A,B)) ) ) ) )).
fof(t7_waybel19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_waybel_9(A) ) => ( v1_waybel19(A) <=> ( v1_tops_2(a_1_1_waybel19(A),A) & v1_cantor_1(a_1_1_waybel19(A),A) & m1_subset_1(a_1_1_waybel19(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ) ) )).
fof(t7_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(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))) ) ) ) ) )).
fof(t7_waybel21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ 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] : ( ( 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] : ( ( 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) => ( ( v18_waybel_0(E,A,B) => v18_waybel_0(F,C,D) ) & ( v21_waybel_0(E,A,B) => v21_waybel_0(F,C,D) ) ) ) ) ) ) ) ) ) ) )).
fof(t7_waybel22,axiom,( ! [A] : ( ( ~ 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] : ( r1_waybel22(A,B) => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(t7_waybel23,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k3_waybel_0(A,k3_waybel_0(A,B)) = k3_waybel_0(A,B) ) ) )).
fof(t7_waybel24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => k3_funct_2(u1_struct_0(B),u1_struct_0(C),k1_waybel24(A,B,C,D,E),F) = k1_binop_1(D,E,F) ) ) ) ) ) ) )).
fof(t7_waybel25,axiom,( ! [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] : ( ( 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] : ( ( v4_waybel11(C) & m1_yellow_9(C,A) ) => ! [D] : ( ( v4_waybel11(D) & m1_yellow_9(D,B) ) => ( ( r5_waybel_1(A,B) & v2_waybel18(C) ) => v2_waybel18(D) ) ) ) ) ) )).
fof(t7_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & v6_pre_topc(B) & v1_waybel25(B) & l1_pre_topc(B) ) => v24_waybel_0(k1_waybel26(A,B)) ) ) )).
fof(t7_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( ( 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)))) ) => k1_waybel28(A,B,C) = g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),k1_partfun1(u1_struct_0(B),u1_struct_0(B),u1_struct_0(B),u1_struct_0(A),C,u1_waybel_0(A,B))) ) ) ) )).
fof(t7_waybel29,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v2_pre_topc(C) & l1_pre_topc(C) ) => ! [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(C),u1_pre_topc(C)) & g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(D),u1_pre_topc(D)) ) => k2_borsuk_1(A,B) = k2_borsuk_1(C,D) ) ) ) ) ) )).
fof(t7_waybel30,axiom,( ! [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) & l1_waybel_9(A) ) => ! [B] : ( ( v4_waybel11(B) & m1_yellow_9(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( ( C = D & v4_pre_topc(D,B) ) => v4_pre_topc(C,A) ) ) ) ) ) )).
fof(t7_waybel31,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & v3_waybel_3(B) & l1_orders_2(B) ) => ( k1_yellow_1(u1_pre_topc(A)) = B => r1_ordinal1(k1_card_1(u1_struct_0(A)),k1_card_1(u1_struct_0(B))) ) ) ) )).
fof(t7_waybel32,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & v25_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = a_2_0_waybel32(A,B) => ( ~ v1_xboole_0(C) & v1_waybel_0(C,A) ) ) ) ) ) )).
fof(t7_waybel33,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_struct_0(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_waybel_0(C,A) ) => ! [D] : ( ( ~ v2_struct_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] : ( r1_waybel_0(A,C,E) => r1_waybel_0(B,D,E) ) ) ) ) ) ) )).
fof(t7_waybel34,axiom,( ! [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) ) => ( r2_funct_2(u1_struct_0(A),u1_struct_0(A),k1_waybel34(A,A,k3_struct_0(A)),k3_struct_0(A)) & r2_funct_2(u1_struct_0(A),u1_struct_0(A),k2_waybel34(A,A,k3_struct_0(A)),k3_struct_0(A)) ) ) )).
fof(t7_waybel35,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ( ( r1_yellow_0(A,C) & r2_hidden(k1_yellow_0(A,C),B) ) => ( r1_yellow_0(k5_yellow_0(A,B),C) & k1_yellow_0(A,C) = k1_yellow_0(k5_yellow_0(A,B),C) ) ) ) ) ) )).
fof(t7_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & v4_waybel_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( ( 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 | ( r1_yellow_0(B,C) & k1_yellow_0(B,C) = k1_yellow_0(A,C) ) ) ) ) ) ) )).
fof(t7_waybel_1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( l1_orders_2(C) => ( ( r5_waybel_1(A,B) & r5_waybel_1(B,C) ) => r5_waybel_1(A,C) ) ) ) ) )).
fof(t7_waybel_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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)))) ) => r1_yellow_0(A,k3_tarski(a_2_3_waybel_2(A,B))) ) ) )).
fof(t7_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(B,k1_waybel_3(A,C)) <=> r1_waybel_3(A,B,C) ) ) ) ) )).
fof(t7_waybel_4,axiom,( ! [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] : ( ( v2_waybel_4(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ( ( v2_waybel_4(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ( v2_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)))) ) ) ) ) )).
fof(t7_waybel_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ! [B] : ( r2_hidden(B,k1_relset_1(k4_card_3(k1_funct_6(A)),k2_pralg_2(A))) => ( v1_relat_1(B) & v1_funct_1(B) ) ) ) )).
fof(t7_waybel_6,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => v1_waybel_6(k2_waybel_3(A,B),A) ) ) )).
fof(t7_waybel_7,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(A)))) => ( v13_waybel_0(B,k2_yellow_1(A)) <=> ! [C] : ! [D] : ( ( r1_tarski(C,D) & r1_tarski(D,A) & r2_hidden(C,B) ) => r2_hidden(D,B) ) ) ) )).
fof(t7_waybel_8,axiom,( ! [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_8(A) <=> ( v3_waybel_3(A) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r1_waybel_3(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,u1_struct_0(k1_waybel_8(A))) & r3_orders_2(A,B,D) & r3_orders_2(A,D,C) ) ) ) ) ) ) ) ) )).
fof(t7_waybel_9,axiom,( ! [A] : ( ( v3_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k8_relset_1(u1_struct_0(A),u1_struct_0(A),k4_waybel_1(A,B),k6_domain_1(u1_struct_0(A),B)) = k6_waybel_0(A,B) ) ) )).
fof(t7_weddwitt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( r1_struct_0(k1_weddwitt(A,B),C) => r1_struct_0(A,C) ) ) ) )).
fof(t7_weierstr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) => ~ ( ? [F] : ( m1_subset_1(F,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) & r1_tarski(F,k6_funct_2(u1_struct_0(A),u1_struct_0(B),C,E)) & m1_setfam_1(F,D) & v1_finset_1(F) ) & ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) => ~ ( r1_tarski(F,E) & m1_setfam_1(F,k7_relset_1(u1_struct_0(A),u1_struct_0(B),C,D)) & v1_finset_1(F) ) ) ) ) ) ) ) ) )).
fof(t7_wellfnd1,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v2_wellfnd1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v2_wellfnd1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( v12_waybel_0(B,A) => ( v2_wellfnd1(k4_subset_1(u1_struct_0(A),B,C),A) & m1_subset_1(k4_subset_1(u1_struct_0(A),B,C),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) )).
fof(t7_wellord1,axiom,( ! [A] : ( v1_relat_1(A) => ~ ( v2_wellord1(A) & k1_relat_1(A) != k1_xboole_0 & ! [B] : ~ ( r2_hidden(B,k1_relat_1(A)) & ! [C] : ( r2_hidden(C,k1_relat_1(A)) => r2_hidden(k4_tarski(B,C),A) ) ) ) ) )).
fof(t7_wellord2,axiom,( ! [A] : ( v1_relat_1(A) => ~ ( v2_wellord1(A) & ! [B] : ( v3_ordinal1(B) => ~ r4_wellord1(A,k1_wellord2(B)) ) ) ) )).
fof(t7_wsierp_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( k3_int_2(A,B) = 1 & k3_int_2(C,B) = 1 ) => k3_int_2(k3_xcmplx_0(A,C),B) = 1 ) ) ) ) )).
fof(t7_xboole_0,axiom,( ! [A] : ~ ( A != k1_xboole_0 & ! [B] : ~ r2_hidden(B,A) ) )).
fof(t7_xboole_1,axiom,( ! [A] : ! [B] : r1_tarski(A,k2_xboole_0(A,B)) )).
fof(t7_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k4_xboolean(A,k5_xboolean(A,B)) = k5_xboolean(A,k4_xboolean(A,B)) ) ) )).
fof(t7_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k3_xcmplx_0(A,B) = B => ( B = k5_numbers | A = 1 ) ) ) ) )).
fof(t7_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t7_xregular,axiom,( ! [A] : ! [B] : ! [C] : ~ ( r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(C,A) ) )).
fof(t7_xtuple_0,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(k4_tarski(A,B),C) => r2_hidden(B,k3_tarski(k3_tarski(C))) ) )).
fof(t7_xxreal_0,axiom,( ~ r1_xxreal_0(k1_xxreal_0,k2_xxreal_0) )).
fof(t7_xxreal_1,axiom,( ! [A] : ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ~ ( r2_hidden(A,k1_xxreal_1(B,C)) & ~ r2_hidden(A,k2_xxreal_1(B,C)) & A != C ) ) ) )).
fof(t7_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( m2_xxreal_2(C,A) => ! [D] : ( m2_xxreal_2(D,B) => m2_xxreal_2(k3_xxreal_0(C,D),k2_xboole_0(A,B)) ) ) ) ) )).
fof(t7_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => k1_xxreal_3(A,k2_xxreal_3(A)) = k5_numbers ) )).
fof(t7_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_yellow_3(A,B))) => ( r1_lattice3(k3_yellow_3(A,B),k6_domain_1(u1_struct_0(k3_yellow_3(A,B)),D),C) <=> ( r1_lattice3(A,k6_domain_1(u1_struct_0(A),k8_yellow_3(A,B,D)),k8_yellow_3(A,B,C)) & r1_lattice3(B,k6_domain_1(u1_struct_0(B),k9_yellow_3(A,B,D)),k9_yellow_3(A,B,C)) ) ) ) ) ) ) )).
fof(t7_yellow11,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r3_orders_2(A,k13_lattice3(A,B,k12_lattice3(A,C,D)),k12_lattice3(A,k13_lattice3(A,B,C),k13_lattice3(A,B,D))) ) ) ) ) )).
fof(t7_yellow12,axiom,( ! [A] : ! [B] : v2_funct_1(k13_funct_3(k10_funct_3(A,B),k9_funct_3(A,B))) )).
fof(t7_yellow13,axiom,( ! [A] : ( ( v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( v5_orders_3(C,A,B) => k3_waybel_0(B,k7_relset_1(u1_struct_0(A),u1_struct_0(B),C,D)) = k3_waybel_0(B,k7_relset_1(u1_struct_0(A),u1_struct_0(B),C,k3_waybel_0(A,D))) ) ) ) ) ) )).
fof(t7_yellow14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( ( 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] : ( ( 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)))) ) => ( ( r1_yellow_2(u1_struct_0(A),B,E,F) & v5_orders_3(D,B,C) ) => r1_yellow_2(u1_struct_0(A),C,k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),E,D),k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),F,D)) ) ) ) ) ) ) ) )).
fof(t7_yellow15,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t7_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r1_yellow16(A,B,C) => k3_relat_1(k1_yellow_9(B,A),C) = k3_struct_0(A) ) ) ) ) )).
fof(t7_yellow17,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k1_funct_1(A,C))) => ( ( r2_hidden(D,k1_funct_1(A,B)) & r2_hidden(B,k9_xtuple_0(A)) & r2_hidden(C,k9_xtuple_0(A)) ) => ( k4_card_3(A) = k1_xboole_0 | E = k1_funct_1(A,C) | ( r1_tarski(k8_relat_1(k12_card_3(A,B),k1_tarski(D)),k8_relat_1(k12_card_3(A,C),E)) <=> ( B = C & r2_hidden(D,E) ) ) ) ) ) ) )).
fof(t7_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l2_altcat_1(B) ) => ( r2_yellow18(A,B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( E = C & F = D ) => k1_altcat_1(A,C,D) = k1_altcat_1(B,F,E) ) ) ) ) ) ) ) ) )).
fof(t7_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( r2_hidden(D,k2_relset_1(u1_struct_0(A),u1_waybel_0(A,k5_waybel_9(A,B,C)))) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & r1_orders_2(B,C,E) & D = k2_waybel_0(A,B,E) ) ) ) ) ) )).
fof(t7_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v16_functor0(C,A,B) & m2_functor0(C,A,B) ) => ( v21_functor0(C,A,B) => ! [D] : ( ( v16_functor0(D,B,A) & m2_functor0(D,B,A) ) => ( ( ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => k3_functor0(A,B,C,k3_functor0(B,A,D,E)) = E ) & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( k1_altcat_1(B,E,F) != k1_xboole_0 => ! [G] : ( m1_subset_1(G,k1_altcat_1(B,E,F)) => k8_functor0(A,B,C,k3_functor0(B,A,D,F),k3_functor0(B,A,D,E),k8_functor0(B,A,D,E,F,G)) = G ) ) ) ) ) => g2_functor0(B,A,u1_functor0(B,A,D),u2_functor0(B,A,D)) = k15_functor0(A,B,C) ) ) ) ) ) ) )).
fof(t7_yellow21,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => ~ ( r2_wellord2(A,B) & ! [C] : ( ( 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_wellord1(C,A) & k2_wellord2(C) = B ) ) ) ) )).
fof(t7_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( r1_lattice3(A,k1_tarski(C),B) => r1_orders_2(A,B,C) ) & ( r1_orders_2(A,B,C) => r1_lattice3(A,k1_tarski(C),B) ) & ( r2_lattice3(A,k1_tarski(C),B) => r1_orders_2(A,C,B) ) & ( r1_orders_2(A,C,B) => r2_lattice3(A,k1_tarski(C),B) ) ) ) ) ) )).
fof(t7_yellow_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v2_lattice3(k1_yellow_1(A)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(A))) => r1_tarski(k11_lattice3(k1_yellow_1(A),B,C),k3_xboole_0(B,C)) ) ) ) ) )).
fof(t7_yellow_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_yellow_0(C,B) ) => ( ( ( v1_waybel_0(A,C) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(C))) ) => ( v1_waybel_0(A,B) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(B))) ) ) & ( ( v2_waybel_0(A,C) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(C))) ) => ( v2_waybel_0(A,B) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(B))) ) ) ) ) ) )).
fof(t7_yellow_3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(B,C) => r1_tarski(k4_waybel_0(A,B),k4_waybel_0(A,C)) ) ) ) ) )).
fof(t7_yellow_4,axiom,( ! [A] : ( ( v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( r2_yellow_4(A,C,D) & r2_yellow_4(A,B,C) ) => r2_yellow_4(A,B,D) ) ) ) ) ) )).
fof(t7_yellow_5,axiom,( ! [A] : ( ( v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t7_yellow_6,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_yellow_0(B,A) => ! [C] : ( m1_yellow_0(C,B) => m1_yellow_0(C,A) ) ) ) )).
fof(t7_yellow_7,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( v16_waybel_0(A) <=> v16_waybel_0(k7_lattice3(A)) ) ) )).
fof(t7_yellow_8,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => k5_setfam_1(u1_struct_0(A),k7_setfam_1(u1_struct_0(A),B)) = k3_subset_1(u1_struct_0(A),k8_setfam_1(u1_struct_0(A),B)) ) ) )).
fof(t7_yellow_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( u1_struct_0(k3_yellow_9(A,B)) = B & v4_yellow_0(k3_yellow_9(A,B),k7_lattice3(A)) & m1_yellow_0(k3_yellow_9(A,B),k7_lattice3(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(k3_yellow_9(A,B))) => k2_waybel_0(A,k3_yellow_9(A,B),C) = C ) ) ) ) )).
fof(t7_zf_colla,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v3_ordinal1(B) => r1_tarski(k1_zf_colla(A,B),A) ) ) )).
fof(t7_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ( v8_zf_fund1(B,A) => r1_tarski(k4_ordinal1,B) ) ) ) )).
fof(t7_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ( k14_zf_lang(A,B,C) = k8_zf_lang(A,k8_zf_lang(B,C)) & k15_zf_lang(A,B,C) = k13_zf_lang(A,k13_zf_lang(B,C)) ) ) ) ) )).
fof(t7_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ( k27_zf_lang(k12_zf_lang(A,B)) = A & k28_zf_lang(k12_zf_lang(A,B)) = B ) ) ) )).
fof(t7_zf_model,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ( v2_zf_lang(A) => ! [C] : ( ( 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))) ) => ( k3_funct_2(k1_zf_lang,B,C,k18_zf_lang(A)) = k3_funct_2(k1_zf_lang,B,C,k19_zf_lang(A)) <=> r2_hidden(C,k5_zf_model(A,B)) ) ) ) ) ) )).
fof(t7_zf_refle,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( v3_ordinal1(B) & m1_subset_1(B,A) ) <=> r2_hidden(B,k2_ordinal1(A)) ) ) )).
fof(t7_zfmisc_1,axiom,( ! [A] : ! [B] : r1_tarski(k1_tarski(A),k2_tarski(A,B)) )).
fof(t7_zfmodel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_ordinal1(A) => ( r2_zf_model(A,k9_zf_model) <=> ? [B] : ( r2_hidden(B,A) & B != k1_xboole_0 & ! [C] : ~ ( r2_hidden(C,B) & ! [D] : ~ ( r2_xboole_0(C,D) & r2_hidden(D,B) ) ) ) ) ) ) )).
fof(t7_zfmodel2,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_subset_1(F,E) => ! [G] : ( m1_subset_1(G,E) => ! [H] : ( m1_subset_1(H,E) => ! [I] : ( m1_subset_1(I,E) => ! [J] : ( ( v1_funct_1(J) & v1_funct_2(J,k1_zf_lang,E) & m1_subset_1(J,k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang,E))) ) => ~ ( A != B & A != C & A != D & B != C & B != D & C != D & ~ ( r2_funct_2(k1_zf_lang,E,k2_zf_lang1(E,k2_zf_lang1(E,k2_zf_lang1(E,k2_zf_lang1(E,J,A,F),B,G),C,H),D,I),k2_zf_lang1(E,k2_zf_lang1(E,k2_zf_lang1(E,k2_zf_lang1(E,J,B,G),C,H),D,I),A,F)) & r2_funct_2(k1_zf_lang,E,k2_zf_lang1(E,k2_zf_lang1(E,k2_zf_lang1(E,k2_zf_lang1(E,J,A,F),B,G),C,H),D,I),k2_zf_lang1(E,k2_zf_lang1(E,k2_zf_lang1(E,k2_zf_lang1(E,J,C,H),D,I),A,F),B,G)) & r2_funct_2(k1_zf_lang,E,k2_zf_lang1(E,k2_zf_lang1(E,k2_zf_lang1(E,k2_zf_lang1(E,J,A,F),B,G),C,H),D,I),k2_zf_lang1(E,k2_zf_lang1(E,k2_zf_lang1(E,k2_zf_lang1(E,J,D,I),B,G),C,H),A,F)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t7_zfrefle1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ( r2_zfrefle1(A,B) <=> ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ( r2_zf_model(A,C) <=> r2_zf_model(B,C) ) ) ) ) ) )).
fof(t7_zmodul01,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => k1_zmodul01(B,k4_algstr_0(B,C),k4_xcmplx_0(A)) = k1_zmodul01(B,C,A) ) ) ) )).
fof(t7_zmodul02,axiom,( ! [A] : ( ( ~ 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_int_3) & v9_vectsp_1(A,k1_int_3) & v10_vectsp_1(A,k1_int_3) & v11_vectsp_1(A,k1_int_3) & l1_vectsp_1(A,k1_int_3) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k17_zmodul02(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_int_3)) => ! [E] : ( v1_int_1(E) => ( ( B = C & D = E ) => k4_vectsp_1(k1_int_3,A,D,B) = k1_zmodul01(k17_zmodul02(A),C,E) ) ) ) ) ) ) )).
fof(t7_zmodul03,axiom,( ! [A] : ( ( ~ 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] : ( m2_finseq_1(B,u1_struct_0(A)) => ( v2_funct_1(B) => ! [C] : ( m1_zmodul02(C,A) => ( r1_tarski(k18_zmodul02(A,C),k2_relset_1(u1_struct_0(A),B)) => k4_rlvect_1(A,k20_zmodul02(A,B,C)) = k21_zmodul02(A,C) ) ) ) ) ) )).
fof(t80_abcmiz_0,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( C = a_2_2_abcmiz_0(A,B) => ( r1_yellow_0(A,C) & k12_abcmiz_0(A,B) = k1_yellow_0(A,C) ) ) ) ) )).
fof(t80_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m3_abcmiz_1(B,A) => B = k40_abcmiz_1(A,k41_abcmiz_1(A,B),k42_abcmiz_1(A,B)) ) ) )).
fof(t80_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( v7_ordinal1(C) => r1_tarski(k61_valued_1(B,k1_nat_1(C,k5_card_1(A))),k61_valued_1(k1_ordinal4(A,B),C)) ) ) ) )).
fof(t80_afinsq_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & v1_finset_1(C) ) => ( r1_tarski(B,C) => r1_tarski(k1_ordinal4(A,B),k1_ordinal4(A,C)) ) ) ) ) )).
fof(t80_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(D)) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,k2_zfmisc_1(D,u1_struct_0(A)),D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(D,u1_struct_0(A)),D))) ) => ( ( v13_aofa_000(F,A,D) & r2_aofa_000(A,D,E,F) ) => ! [G] : ( m1_subset_1(G,D) => ( ~ r2_hidden(k2_binop_1(D,u1_struct_0(A),D,F,G,B),E) => k2_binop_1(D,u1_struct_0(A),D,F,G,k15_aofa_000(A,B,C)) = k2_binop_1(D,u1_struct_0(A),D,F,G,B) ) ) ) ) ) ) ) ) ) )).
fof(t80_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & v22_aofa_a00(D,A,1,1,11) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( ( v19_aofa_a00(F,A) & m1_subset_1(F,u1_struct_0(A)) ) => ! [G] : ( m2_subset_1(G,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),k37_aofa_a00(A))) => ! [I] : ( m1_subset_1(I,k1_funct_1(u3_msualg_1(A,C),F)) => ! [J] : ( m1_subset_1(J,k1_funct_1(u3_msualg_1(A,C),F)) => k15_aofa_a00(A,B,C,D,k37_aofa_a00(A),k40_aofa_a00(A,C,H,F,I,J),G) = k40_aofa_a00(A,D,k15_aofa_a00(A,B,C,D,k37_aofa_a00(A),H,G),F,k15_aofa_a00(A,B,C,D,F,I,G),k15_aofa_a00(A,B,C,D,F,J,G)) ) ) ) ) ) ) ) ) ) ) )).
fof(t80_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( m1_subset_1(C,k5_arytm_3) => ( r3_arytm_3(k10_arytm_3(B,C),k10_arytm_3(A,C)) => ( C = k11_arytm_3 | r3_arytm_3(B,A) ) ) ) ) ) )).
fof(t80_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(1,A) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ? [C] : ( m1_subset_1(C,k4_ordinal1) & r1_xxreal_0(B,C) & r1_xxreal_0(k6_xcmplx_0(k3_xcmplx_0(C,k3_power(2,k2_xcmplx_0(1,A))),k3_xcmplx_0(8,k3_power(2,C))),k3_xcmplx_0(8,k3_power(2,C))) ) ) ) ) )).
fof(t80_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( v20_bcialg_1(A) & k1_bcialg_1(A,k1_bcialg_1(A,B,C),D) = k4_struct_0(A) ) => ( C = k1_bcialg_1(A,B,D) & D = k1_bcialg_1(A,B,C) ) ) ) ) ) ) )).
fof(t80_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( ( v3_funct_1(E) & m1_borsuk_2(E,A,C,C) ) => ( r1_borsuk_6(A,B,C) => r3_borsuk_2(A,B,C,k1_borsuk_2(A,B,C,C,D,E),D) ) ) ) ) ) ) )).
fof(t80_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ( v2_bvfunc_2(C,A) => r2_funct_2(A,k6_margrel1,k6_bvfunc_2(A,k6_bvfunc_2(A,k1_bvfunc_1(A,B),C,D),C,E),k6_bvfunc_2(A,k1_bvfunc_1(A,k7_bvfunc_2(A,B,C,E)),C,D)) ) ) ) ) ) ) )).
fof(t80_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ! [G] : ( m1_eqrel_1(G,A) => ! [H] : ( m1_eqrel_1(H,A) => ! [I] : ( m1_eqrel_1(I,A) => ! [J] : ( m1_eqrel_1(J,A) => ! [K] : ( m1_eqrel_1(K,A) => ! [L] : ( m1_subset_1(L,A) => ! [M] : ( m1_subset_1(M,A) => ~ ( v2_bvfunc_2(B,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 & k15_bvfunc_1(A,L,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,E,F),G),H),I),J),K)) = k15_bvfunc_1(A,M,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,k2_partit1(A,E,F),G),H),I),J),K)) & r1_xboole_0(k15_bvfunc_1(A,M,k5_bvfunc_2(A,C,B)),k15_bvfunc_1(A,L,k5_bvfunc_2(A,D,B))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t80_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ( ~ v1_finset_1(A) => ( ~ v1_finset_1(k1_card_2(A,B)) & ~ v1_finset_1(k1_card_2(B,A)) ) ) ) ) )).
fof(t80_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(B,k4_card_3(A)) => r2_hidden(k3_relat_1(C,B),k4_card_3(k3_relat_1(C,A))) ) ) ) ) )).
fof(t80_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,B,C) => ( ( v13_cat_1(D,A,B) & v13_cat_1(E,B,C) ) => v13_cat_1(k9_cat_1(A,B,C,D,E),A,C) ) ) ) ) ) ) )).
fof(t80_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( m1_subset_1(F,u4_struct_0(A)) => ! [G] : ( m1_subset_1(G,u4_struct_0(A)) => ( ( r4_cat_3(A,B,D,E) & r4_cat_3(A,C,F,G) & k3_graph_1(A,D) = k3_graph_1(A,F) & k3_graph_1(A,E) = k3_graph_1(A,G) ) => r1_cat_1(A,B,C) ) ) ) ) ) ) ) ) )).
fof(t80_cfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => ( v3_funct_1(k2_partfun1(B,k2_numbers,C,A)) => v1_comseq_2(k2_partfun1(B,k2_numbers,C,A)) ) ) ) )).
fof(t80_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ~ ( B != C & ~ r1_chord(A,B,C) & ? [D] : ( m2_chord(D,A,B,C) & v4_chord(D,A,B,C) & ? [E] : ( m1_subset_1(E,k6_glib_000(A)) & r2_hidden(E,D) & ! [F] : ( m3_glib_001(F,A) => ~ ( r1_glib_001(A,B,C,F) & r2_hidden(E,k13_glib_001(A,F)) ) ) ) ) ) ) ) ) )).
fof(t80_classes1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( k9_xtuple_0(A) = k9_xtuple_0(B) => ( r2_classes1(A,B) <=> ? [C] : ( 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)))) & A = k3_relat_1(C,B) ) ) ) ) ) )).
fof(t80_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_clvect_1(D,A) => ( r2_hidden(k3_rlvect_1(A,B,C),k5_clvect_1(A,C,D)) <=> r1_struct_0(D,B) ) ) ) ) ) )).
fof(t80_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clvect_2(B,A) => v3_clvect_2(B,A) ) ) ) )).
fof(t80_cohsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( k14_cohsp_1(A,B) = k14_cohsp_1(C,D) <=> ( A = C & B = D ) ) )).
fof(t80_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k9_complex1(k7_xcmplx_0(1,A)) = k7_xcmplx_0(1,k9_complex1(A)) ) )).
fof(t80_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( k4_complex2(A,B,C) = k28_sin_cos => k4_complex2(C,B,A) = k28_sin_cos ) ) ) ) )).
fof(t80_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k3_finseq_2(k4_ordinal1)) & v1_funct_1(C) & v4_valued_0(C) & v2_margrel1(C) & v2_comput_1(C) & v8_comput_1(C,1) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k3_finseq_2(k4_ordinal1)) & v1_funct_1(D) & v4_valued_0(D) & v2_margrel1(D) & v2_comput_1(D) & v8_comput_1(D,3) ) => k1_recdef_1(k7_comput_1(C,D,2),k2_finseq_4(k4_ordinal1,A,k1_nat_1(B,1))) = k1_recdef_1(D,k3_finseq_4(k4_ordinal1,A,B,k1_recdef_1(k7_comput_1(C,D,2),k2_finseq_4(k4_ordinal1,A,B)))) ) ) ) ) )).
fof(t80_convex4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_convex4(C,A) => ( ( v3_convex4(C,A) & k1_convex4(A,C) = k6_domain_1(u1_struct_0(A),B) ) => ( ? [D] : ( v1_xreal_0(D) & D = k3_funct_2(u1_struct_0(A),k2_numbers,C,B) & D = 1 ) & k4_convex4(A,C) = k1_clvect_1(A,B,k3_funct_2(u1_struct_0(A),k2_numbers,C,B)) ) ) ) ) ) )).
fof(t80_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ( ~ r2_hidden(D,k24_qc_lang1(A,C)) => ( v2_cqc_the1(k8_cqc_lang(A,k8_cqc_lang(A,k12_cqc_lang(A,D,B),C),k11_cqc_lang(A,D,k8_cqc_lang(A,B,C))),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),C)),A) ) ) ) ) ) ) )).
fof(t80_csspace,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => k9_nat_1(k2_numbers,A,B) = k5_complex1 ) => ( v1_comseq_3(A) & k11_comseq_3(A) = k5_complex1 ) ) ) )).
fof(t80_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k16_sin_cos),D) ) & r2_hidden(k2_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k26_sin_cos)) & r2_hidden(k6_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k26_sin_cos)) ) => k1_funct_1(k5_diff_1(C,A),B) = k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(1,k19_sin_cos(k2_xcmplx_0(B,k7_xcmplx_0(A,2)))),k19_sin_cos(k2_xcmplx_0(B,k7_xcmplx_0(A,2)))),k7_xcmplx_0(1,k19_sin_cos(k6_xcmplx_0(B,k7_xcmplx_0(A,2))))),k19_sin_cos(k6_xcmplx_0(B,k7_xcmplx_0(A,2)))) ) ) ) ) )).
fof(t80_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [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)) )).
fof(t80_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => k5_euclid_8(A,k5_euclid_8(B,C)) = k8_euclid(3,k9_euclid(3,B,k22_rvsum_1(A,C)),k9_euclid(3,C,k22_rvsum_1(A,B))) ) ) ) )).
fof(t80_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ~ ( r6_euclidlp(A,C,D) & ! [E] : ( m2_subset_1(E,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ~ ( r2_hidden(B,E) & r6_euclidlp(A,E,D) & r5_euclidlp(A,E,C) ) ) ) ) ) ) ) )).
fof(t80_exchsort,axiom,( ! [A] : k4_exchsort(k5_afinsq_1(A)) = A )).
fof(t80_facirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k15_facirc_1(A,B,C),k18_facirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ( ( E = k1_funct_1(D,A) & F = k1_funct_1(D,B) ) => 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) ) ) ) ) ) ) ) )).
fof(t80_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v13_lattices(A) => ( v13_lattices(k10_filter_2(A,k6_filter_2(A,B))) & k5_lattices(k10_filter_2(A,k6_filter_2(A,B))) = k5_lattices(A) ) ) ) ) )).
fof(t80_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ~ ( C = k5_relat_1(B,k2_finseq_1(A)) & ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => B != k7_finseq_1(C,D) ) ) ) ) ) )).
fof(t80_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( m1_subset_1(F,B) => ! [G] : ( m1_subset_1(G,B) => ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,k2_zfmisc_1(A,B),C) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C))) ) => ! [I] : ( m2_finseq_1(I,B) => ( I = k11_finseq_1(E,F,G) => k5_funcop_1(H,D,I) = k11_finseq_1(k2_binop_1(A,B,C,H,D,E),k2_binop_1(A,B,C,H,D,F),k2_binop_1(A,B,C,H,D,G)) ) ) ) ) ) ) ) ) ) ) )).
fof(t80_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : ( k1_finseq_3(k10_finseq_1(A,B),C) = k10_finseq_1(A,B) <=> ( ~ r2_hidden(A,C) & ~ r2_hidden(B,C) ) ) )).
fof(t80_finseq_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ~ ( r1_tarski(B,C) & ! [D] : ( m2_finseq_1(D,A) => k8_finseq_1(A,B,D) != C ) ) ) ) ) )).
fof(t80_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t80_finseq_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => k2_rfinseq(B,A,k6_finseq_1(B)) = k6_finseq_1(B) ) ) )).
fof(t80_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,B) => ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,k2_zfmisc_1(C,D),E) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(C,D),E))) ) => ! [I] : ( ( v1_funct_1(I) & v1_funct_2(I,A,C) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [J] : ( ( v1_funct_1(J) & v1_funct_2(J,B,D) & m1_subset_1(J,k1_zfmisc_1(k2_zfmisc_1(B,D))) ) => k1_binop_1(k6_finseqop(H,I,J),F,G) = k2_binop_1(C,D,E,H,k3_funct_2(A,C,I,F),k3_funct_2(B,D,J,G)) ) ) ) ) ) ) ) ) ) ) )).
fof(t80_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ( k2_flang_2(A,B) = B <=> r2_hidden(k2_flang_1(A),B) ) ) )).
fof(t80_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => k6_flang_1(A,k2_flang_3(A,B),k2_flang_2(A,B)) = k2_flang_3(A,B) ) )).
fof(t80_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_funct_1(A) ) => A = k7_funcop_1(k9_xtuple_0(A),k3_funct_1(A)) ) )).
fof(t80_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => r1_tarski(k3_xboole_0(A,k8_relat_1(C,B)),k8_relat_1(C,k3_xboole_0(k7_relat_1(C,A),B))) ) )).
fof(t80_funct_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( r1_partfun1(B,C) => r2_hidden(C,k5_partfun1(A,A,B)) ) ) ) )).
fof(t80_funct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,A,k2_zfmisc_1(B,C)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k2_zfmisc_1(B,C)))) ) => ( ( k3_relat_1(D,k9_funct_3(B,C)) = k3_relat_1(E,k9_funct_3(B,C)) & k3_relat_1(D,k10_funct_3(B,C)) = k3_relat_1(E,k10_funct_3(B,C)) ) => r2_funct_2(A,k2_zfmisc_1(B,C),D,E) ) ) ) ) ) ) )).
fof(t80_funct_4,axiom,( ! [A] : ! [B] : ! [C] : k1_binop_1(k17_funcop_1(A,B,C),A,B) = C )).
fof(t80_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => r1_funct_8(A,k1_numbers,k1_numbers,k41_valued_1(k1_numbers,k1_numbers,k18_sin_cos)) ) )).
fof(t80_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => v4_ring_1(k8_fvaluat1(A,B),k7_fvaluat1(A,B)) ) ) ) )).
fof(t80_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_2(B,u1_struct_0(A),k4_finseq_2(k5_numbers,u1_struct_0(A))) => k3_group_4(A,B) = k5_struct_0(A) ) ) )).
fof(t80_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(k4_tarski(k10_finseq_1(A,B),k3_twoscomp),k3_msafree2(k31_gfacirc1(A,B,C))) & r2_hidden(k4_tarski(k10_finseq_1(B,C),k3_gfacirc1),k3_msafree2(k31_gfacirc1(A,B,C))) & r2_hidden(k4_tarski(k10_finseq_1(C,A),k4_twoscomp),k3_msafree2(k31_gfacirc1(A,B,C))) & r2_hidden(k33_gfacirc1(A,B,C),k3_msafree2(k31_gfacirc1(A,B,C))) ) )).
fof(t80_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(B)) => ! [E] : ( ( C = D & r2_hidden(E,k25_glib_000(A,B)) ) => k29_glib_000(A,C,E) = k29_glib_000(B,D,E) ) ) ) ) ) )).
fof(t80_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( 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)) ) ) ) )).
fof(t80_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( v1_group_3(C,A) & m1_group_2(C,A) ) => ? [D] : ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) & u1_struct_0(D) = k3_group_11(A,B,B) & r1_tarski(k3_group_11(A,C,B),k3_group_11(A,C,D)) ) ) ) ) )).
fof(t80_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ( ! [D] : ( m1_group_2(D,A) => ( D = k9_group_2(A,B,C) => u1_struct_0(D) = k3_xboole_0(u1_struct_0(B),u1_struct_0(C)) ) ) & ! [D] : ( ( v15_algstr_0(D) & m1_group_2(D,A) ) => ( u1_struct_0(D) = k3_xboole_0(u1_struct_0(B),u1_struct_0(C)) => r1_group_2(A,D,k9_group_2(A,B,C)) ) ) ) ) ) ) )).
fof(t80_group_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ( r2_hidden(A,k7_group_3(B,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(B)) & D = A & r2_group_3(B,C,D) ) ) ) ) )).
fof(t80_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => v5_group_1(k10_group_5(A)) ) )).
fof(t80_group_9,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v2_group_9(C,A) & v4_group_9(C,A,B) & m1_group_9(C,A,B) ) => ! [D] : ( ( v2_group_9(D,A) & m1_group_9(D,A,k10_group_9(A,B,C)) ) => ( u1_struct_0(B) = k8_relset_1(u1_struct_0(B),u1_struct_0(k10_group_9(A,B,C)),k12_group_9(A,B,C),u1_struct_0(D)) => D = k5_group_9(A,k10_group_9(A,B,C)) ) ) ) ) )).
fof(t80_ideal_1,axiom,( ! [A] : ( ( ~ 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_vectsp_1(A) & v1_algstr_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v3_ideal_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v3_ideal_1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v3_ideal_1(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => k14_ideal_1(A,B,k12_ideal_1(A,C,D)) = k12_ideal_1(A,k14_ideal_1(A,B,C),k14_ideal_1(A,B,D)) ) ) ) ) )).
fof(t80_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k28_sin_cos) => k2_integra5(A,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)) = 2 ) ) )).
fof(t80_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => r1_tarski(k11_intpro_1(A),k13_intpro_1(A)) ) )).
fof(t80_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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 & k18_euclid(C) = H & k18_euclid(D) = G & r1_xxreal_0(G,k18_euclid(A)) & ~ r1_xxreal_0(k18_euclid(B),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),E) & r1_xxreal_0(k17_euclid(D),F) & k1_funct_1(I,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t80_jordan,axiom,( ! [A] : ( ( v2_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_jordan24(2,A,k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) => ( k23_pscomp_1(A) = k19_euclid(1,k5_numbers) & k22_pscomp_1(A) = k19_euclid(1,k5_numbers) ) ) ) )).
fof(t80_jordan2c,axiom,( ! [A] : ( ( ~ 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)))) ) => ( k2_jordan2c(2,k3_topreal1(2,k1_sprect_1(A))) != k1_xboole_0 & r2_jordan2c(2,k3_topreal1(2,k1_sprect_1(A)),k2_jordan2c(2,k3_topreal1(2,k1_sprect_1(A)))) & k1_jordan2c(2,k3_topreal1(2,k1_sprect_1(A))) != k1_xboole_0 & r1_jordan2c(2,k3_topreal1(2,k1_sprect_1(A)),k1_jordan2c(2,k3_topreal1(2,k1_sprect_1(A)))) ) ) )).
fof(t80_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( v3_limfunc1(A) => ( v3_limfunc1(k26_valued_1(k1_numbers,k1_numbers,A,B)) & k4_limfunc1(k26_valued_1(k1_numbers,k1_numbers,A,B)) = k3_xcmplx_0(B,k4_limfunc1(A)) ) ) ) ) )).
fof(t80_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( r2_matrix10(B,C) => v4_matrix10(k5_matrix10(A,C,B)) ) ) ) ) )).
fof(t80_matrix13,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ! [E] : ( ( v1_finset_1(E) & v1_setfam_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ! [F] : ( ( v1_finset_1(F) & v1_setfam_1(F) & m1_subset_1(F,k1_zfmisc_1(k4_ordinal1)) ) => ( ( r1_tarski(C,D) & r1_tarski(E,F) ) => r1_xxreal_0(k8_matrix13(A,k6_matrix13(u1_struct_0(A),B,C,E)),k8_matrix13(A,k6_matrix13(u1_struct_0(A),B,D,F))) ) ) ) ) ) ) ) )).
fof(t80_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( ( k1_matrixr2(A,C,B) = k4_matrixr2(A) & k1_matrixr2(A,B,D) = k4_matrixr2(A) ) => ( C = D & v1_matrixr2(B,A) ) ) ) ) ) ) )).
fof(t80_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( v2_membered(C) => k12_member_1(k12_member_1(A,B),C) = k12_member_1(A,k12_member_1(B,C)) ) ) ) )).
fof(t80_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_partfun1(C,u1_struct_0(B)) ) => ! [D] : ( ( 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)) ) => ( k6_memstr_0(A,B,C) = k6_memstr_0(A,B,D) => k8_memstr_0(A,B,C) = k8_memstr_0(A,B,D) ) ) ) ) ) )).
fof(t80_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( v6_supinf_2(D) => ( ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ~ ( F = k1_relset_1(A,D) & r1_mesfunc1(A,B,D,F) ) ) | r1_xxreal_0(k5_numbers,k6_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,E))) ) ) ) ) ) ) ) )).
fof(t80_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( k1_relset_1(A,C) = D => ( r1_mesfunc6(A,B,C,E) <=> r1_mesfunc6(A,B,C,k5_prob_1(A,B,D,E)) ) ) ) ) ) ) ) )).
fof(t80_modelc_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t80_monoid_0,axiom,( ! [A] : ( l1_struct_0(A) => ( v4_funct_1(u1_struct_0(A)) => v1_monoid_0(A) ) ) )).
fof(t80_msafree4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( k1_rfinseq(k5_numbers,A) = A & ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(k3_finseq_1(A),B) => k1_rfinseq(B,A) = k1_xboole_0 ) ) ) ) )).
fof(t80_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ( v1_int_2(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( r1_nat_d(A,k3_xcmplx_0(B,C)) & ~ r1_nat_d(A,B) & ~ r1_nat_d(A,C) ) ) ) ) ) )).
fof(t80_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v11_o_ring_1(B,A) & v13_o_ring_1(C,A) ) => v13_o_ring_1(k6_algstr_0(A,B,C),A) ) ) ) ) )).
fof(t80_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r8_relat_2(A,B) => r8_relat_2(k2_relat_1(A),B) ) ) )).
fof(t80_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(D) & v5_relat_1(D,C) & v1_funct_1(D) ) => ( r2_hidden(A,k9_xtuple_0(k5_relat_1(D,B))) => k7_partfun1(C,k5_relat_1(D,B),A) = k7_partfun1(C,D,A) ) ) )).
fof(t80_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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),k4_pboole(A,C,B)) => r6_pboole(A,B,C) ) ) ) )).
fof(t80_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r5_pdiff_5(A,B) => r1_fcont_1(k1_pdiff_2(3,2,k1_pdiff_3(2,3,A),B),k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(2,3),B)) ) ) ) )).
fof(t80_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ( ( v1_pdiff_7(C,A) & r5_pdiff_9(A,D,B,C) & r5_pdiff_9(A,E,B,C) ) => ( r5_pdiff_9(A,k3_valued_1(k1_euclid(A),k1_numbers,k1_numbers,D,E),B,C) & r5_pdiff_9(A,k47_valued_1(k1_euclid(A),k1_numbers,k1_numbers,D,E),B,C) ) ) ) ) ) ) ) )).
fof(t80_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => k28_polyform(A) = k6_polyform(k6_polyform(k3_polyform(k4_xcmplx_0(1)),k29_polyform(A)),k3_polyform(k2_polyform(k4_xcmplx_0(1),k7_polyform(A)))) ) )).
fof(t80_pre_poly,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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(k2_orders_1(A),k22_pre_poly(A,B)) ) ) )).
fof(t80_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & k6_prepower(k7_xcmplx_0(A,B),C) != k7_xcmplx_0(k6_prepower(A,C),k6_prepower(B,C)) ) ) ) ) )).
fof(t80_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,A) & v1_funct_1(E) & v1_partfun1(E,A) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,A) & v1_funct_1(F) & v1_partfun1(F,A) ) => ! [G] : ( ( v1_relat_1(G) & v4_relat_1(G,A) & v1_funct_1(G) & v1_partfun1(G,A) ) => ( ( r2_pboole(A,B,k6_pboole(A,D,E)) & r2_pboole(A,C,k6_pboole(A,F,G)) ) => r2_pboole(A,k2_pboole(A,B,C),k6_pboole(A,k2_pboole(A,D,F),k2_pboole(A,E,G))) ) ) ) ) ) ) ) )).
fof(t80_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_subset_1(D,k6_qc_lang1(A),k8_qc_lang1(A,C)) => ! [E] : ( ( v3_card_1(E,C) & m2_finseq_1(E,k2_qc_lang1(A)) ) => ( r2_qc_lang2(A,B,k10_qc_lang1(A,D,E)) <=> B = k10_qc_lang1(A,D,E) ) ) ) ) ) ) )).
fof(t80_quatern3,axiom,( k2_quatern3(k2_quatern2) = 1 )).
fof(t80_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => r1_xxreal_0(k28_quaterni(k25_quaterni(A,B)),k2_xcmplx_0(k28_quaterni(A),k28_quaterni(B))) ) ) )).
fof(t80_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => r1_tarski(k6_relat_1(A,B),B) ) )).
fof(t80_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(E))) => ! [G] : ( ( ~ v2_struct_0(G) & l1_rewrite3(G,F) ) => ( ( v2_rewrite3(G,E,F) & r1_rewrite1(k1_rewrite3(E,F,G),A,k4_tarski(B,D)) & r1_rewrite1(k1_rewrite3(E,F,G),A,k4_tarski(C,D)) ) => B = C ) ) ) ) )).
fof(t80_rfunct_1,axiom,( ! [A] : ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) ) => ( v1_comseq_2(k5_relat_1(C,A)) => v1_comseq_2(k5_relat_1(k24_valued_1(C,B),A)) ) ) ) )).
fof(t80_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_finset_1(E) => ( E = k1_relset_1(A,k2_partfun1(A,k1_numbers,B,C)) => k21_rfunct_3(A,k15_valued_1(A,k1_numbers,B,D),C) = k6_xcmplx_0(k21_rfunct_3(A,B,C),k3_xcmplx_0(D,k5_card_1(E))) ) ) ) ) ) )).
fof(t80_rinfsup1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_seq_2(B) & v4_partfun3(B) & v1_seq_2(C) & v4_partfun3(C) ) => r1_xxreal_0(k1_funct_1(k4_rinfsup1(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C)),A),k3_xcmplx_0(k1_funct_1(k4_rinfsup1(B),A),k1_funct_1(k4_rinfsup1(C),A))) ) ) ) ) )).
fof(t80_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_rlsub_1(D,A) => ! [E] : ( m2_rlsub_1(E,A,D) => ~ ( r2_hidden(B,E) & r2_hidden(C,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_struct_0(D,F) & k5_algstr_0(A,B,F) = C ) ) ) ) ) ) ) ) )).
fof(t80_rlvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) )).
fof(t80_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => k16_rvsum_1(k2_finseq_2(A,B)) = k3_xcmplx_0(A,B) ) ) )).
fof(t80_scmfsa8c,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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) & v7_amistd_1(A,k7_card_1(3),k1_scmfsa_2) ) => ! [B] : ( ( 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(k7_card_1(3),k1_scmfsa_2,k16_funcop_1(k4_scmfsa_2(k5_numbers),1)),k7_card_1(3),k1_scmfsa_2,k2_scmfsa8c(B,A)) ) ) ) )).
fof(t80_scmfsa_2,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ~ v2_extpro_1(k14_scmfsa_2(C,B,A),k7_card_1(3),k1_scmfsa_2) ) ) ) )).
fof(t80_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( ( v10_scmyciel(B,A) & m1_eqrel_1(B,k3_tarski(A)) ) => ( v7_scmyciel(B,k6_scmyciel(A)) & m1_eqrel_1(B,k3_tarski(k6_scmyciel(A))) ) ) ) )).
fof(t80_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k1_semi_af1(A,B,D,C) = k1_semi_af1(A,B,E,C) => D = E ) ) ) ) ) ) )).
fof(t80_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => C = k13_seq_4(A,k17_seq_4(A,C,B),B) ) ) ) )).
fof(t80_setlim_1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_prob_1(C) => ( v3_kurato_0(C,A) & k4_kurato_0(A,C) = k1_kurato_0(A,C) ) ) ) ) )).
fof(t80_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_kurato_0(C,A) => k3_kurato_0(A,k9_setlim_2(A,C,B)) = k5_subset_1(A,B,k3_kurato_0(A,C)) ) ) ) )).
fof(t80_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,k5_sheffer1(A,C,C)),k5_sheffer1(A,D,k5_sheffer1(A,C,C))),k5_sheffer1(A,B,k5_sheffer1(A,B,B))) = k5_sheffer1(A,k5_sheffer1(A,C,C),D) ) ) ) ) )).
fof(t80_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( r2_hidden(A,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) & r1_xxreal_0(k19_sin_cos(A),k5_numbers) ) ) )).
fof(t80_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(B,k5_numbers) & k2_xcmplx_0(k1_square_1(A),k1_square_1(B)) = 1 ) => k19_sin_cos(k2_sin_cos6(A)) = k4_xcmplx_0(B) ) ) ) )).
fof(t80_sin_cos9,axiom,( v3_rcomp_1(k1_relset_1(k1_numbers,k2_sin_cos9)) )).
fof(t80_sincos10,axiom,( v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k4_sincos10,k7_relset_1(k1_numbers,k1_numbers,k2_fdiff_9,k4_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))))) )).
fof(t80_sprect_1,axiom,( ! [A] : ( ( ~ 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(k3_topreal1(2,k1_sprect_1(A))) = k10_pscomp_1(A) ) )).
fof(t80_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_valuat_1(E,A,D) => ( ! [F] : ( m2_funct_2(F,k3_qc_lang1(A),D,k2_valuat_1(A,D)) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),D))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),D))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),D))) ) => ( ( ! [J] : ( m2_subset_1(J,k2_qc_lang1(A),k3_qc_lang1(A)) => ~ ( r2_hidden(J,k1_relset_1(k3_qc_lang1(A),H)) & r2_hidden(J,k24_qc_lang1(A,B)) ) ) & ! [J] : ( m2_subset_1(J,k2_qc_lang1(A),k3_qc_lang1(A)) => ( r2_hidden(J,k1_relset_1(k3_qc_lang1(A),I)) => k1_funct_1(I,J) = k3_funct_2(k3_qc_lang1(A),D,F,J) ) ) & r1_xboole_0(k1_relset_1(k3_qc_lang1(A),G),k1_relset_1(k3_qc_lang1(A),I)) ) => ( r1_valuat_1(A,D,B,E,k1_sublemma(A,D,F,G)) <=> r1_valuat_1(A,D,B,E,k1_sublemma(A,D,F,k14_sublemma(A,D,k14_sublemma(A,D,G,H),I))) ) ) ) ) ) ) => ! [F] : ( m2_funct_2(F,k3_qc_lang1(A),D,k2_valuat_1(A,D)) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),D))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),D))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),D))) ) => ( ( ! [J] : ( m2_subset_1(J,k2_qc_lang1(A),k3_qc_lang1(A)) => ~ ( r2_hidden(J,k1_relset_1(k3_qc_lang1(A),H)) & r2_hidden(J,k24_qc_lang1(A,k11_cqc_lang(A,C,B))) ) ) & ! [J] : ( m2_subset_1(J,k2_qc_lang1(A),k3_qc_lang1(A)) => ( r2_hidden(J,k1_relset_1(k3_qc_lang1(A),I)) => k1_funct_1(I,J) = k3_funct_2(k3_qc_lang1(A),D,F,J) ) ) & r1_xboole_0(k1_relset_1(k3_qc_lang1(A),G),k1_relset_1(k3_qc_lang1(A),I)) ) => ( r1_valuat_1(A,D,k11_cqc_lang(A,C,B),E,k1_sublemma(A,D,F,G)) <=> r1_valuat_1(A,D,k11_cqc_lang(A,C,B),E,k1_sublemma(A,D,F,k14_sublemma(A,D,k14_sublemma(A,D,G,H),I))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t80_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v3_tdlat_2(B,A) => v1_tops_2(B,A) ) ) ) )).
fof(t80_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => m1_pre_topc(k1_pre_topc(A,C),B) ) ) ) ) )).
fof(t80_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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_tsep_1(D,A) & m1_pre_topc(D,A) & m1_pre_topc(D,C) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => ( F = G => ( r1_tmap_1(C,B,E,F) <=> r1_tmap_1(D,B,k3_tmap_1(A,B,C,D,E),G) ) ) ) ) ) ) ) ) ) ) )).
fof(t80_topreal6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( v9_rltopsp1(A,k15_euclid(2)) => k7_pscomp_1(A) = k7_pscomp_1(k2_pre_topc(k15_euclid(2),A)) ) ) )).
fof(t80_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( 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)) ) => k2_pre_topc(A,C) = k2_pre_topc(B,D) ) ) ) ) ) )).
fof(t80_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r2_analoaf(A,B,C,D,E) & r2_analoaf(A,B,C,D,F) & r2_analoaf(A,B,D,C,E) & r2_analoaf(A,B,D,C,F) ) => ( r1_aff_1(A,B,C,D) | E = F ) ) ) ) ) ) ) ) )).
fof(t80_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => k6_trees_1(k12_trees_3(A)) = k1_nat_1(k6_trees_1(A),1) ) )).
fof(t80_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_borsuk_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( v1_borsuk_1(C,A) & m1_pre_topc(C,A) ) => r4_tsep_1(A,B,C) ) ) ) )).
fof(t80_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v1_valued_2(D) => ! [E] : ( v1_valued_2(E) => ! [F] : ( v1_valued_2(F) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,D))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(B,E))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(C,F))) ) => k73_valued_2(k3_xboole_0(A,B),C,k2_valued_2(k3_xboole_0(k1_valued_2(D),k1_valued_2(E))),F,k79_valued_2(A,B,D,E,G,H),I) = k79_valued_2(A,k3_xboole_0(B,C),D,k2_valued_2(k3_xboole_0(k1_valued_2(E),k1_valued_2(F))),G,k79_valued_2(B,C,E,F,H,I)) ) ) ) ) ) ) )).
fof(t80_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_vectsp_4(E,A,B) => ( ? [F] : ( m2_vectsp_4(F,A,B,E) & r2_hidden(C,F) & r2_hidden(D,F) ) <=> r1_struct_0(E,k5_algstr_0(B,C,D)) ) ) ) ) ) ) )).
fof(t80_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( ( v9_waybel_1(A) & v1_yellow_0(A) ) => ( k7_waybel_1(A,k3_yellow_0(A)) = k4_yellow_0(A) & k7_waybel_1(A,k4_yellow_0(A)) = k3_yellow_0(A) ) ) ) )).
fof(t80_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_xboole_0(A,B) => r1_xboole_0(A,k4_xboole_0(B,C)) ) )).
fof(t80_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k5_xboolean(A,k10_xboolean(k3_xboolean(A),B)) = k5_xboolean(A,k3_xboolean(B)) ) ) )).
fof(t80_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k7_xcmplx_0(A,k7_xcmplx_0(B,C)) = k3_xcmplx_0(k7_xcmplx_0(C,B),A) ) ) ) )).
fof(t80_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(C,k3_xcmplx_0(A,B)) => ( r1_xxreal_0(k5_numbers,B) | r1_xxreal_0(A,k7_xcmplx_0(C,B)) ) ) ) ) ) )).
fof(t80_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(D,C) & k4_xxreal_1(C,D) = k3_xxreal_1(A,B) ) ) ) ) ) )).
fof(t80_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ( v6_xxreal_2(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r2_hidden(B,A) & r2_hidden(C,A) & r1_xxreal_0(B,D) & r1_xxreal_0(D,C) ) => r2_hidden(D,A) ) ) ) ) ) ) )).
fof(t80_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ~ ( ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(C,k5_numbers) & C != k1_xxreal_0 & r1_xxreal_0(k6_xxreal_3(B,C),k6_xxreal_3(A,C)) ) ) ) ) )).
fof(t80_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => k29_zf_lang(k4_zf_lang(A,B)) = k1_tarski(k4_zf_lang(A,B)) ) ) )).
fof(t80_zf_lang1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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,k5_zf_lang(A,A)) ) ) ) )).
fof(t80_zfmisc_1,axiom,( ! [A] : k3_tarski(k1_zfmisc_1(A)) = A )).
fof(t80_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_zmodul01(B) & m1_zmodul01(B,A) ) => ! [C] : ( ( v1_zmodul01(C) & m1_zmodul01(C,A) ) => ! [D] : ( m2_zmodul01(D,A,B) => ! [E] : ( m2_zmodul01(E,A,C) => ( D = E => B = C ) ) ) ) ) ) )).
fof(t81_abcmiz_0,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_abcmiz_0(A)) => ( ( r4_abcmiz_0(A,B,D) & r3_orders_2(A,k5_abcmiz_0(A,B,D),k12_abcmiz_0(A,C)) ) => r3_orders_2(A,B,k12_abcmiz_0(A,C)) ) ) ) ) ) )).
fof(t81_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m3_abcmiz_1(B,A) => ! [C] : ( m3_abcmiz_1(C,A) => ( ( k41_abcmiz_1(A,B) = k41_abcmiz_1(A,C) & k42_abcmiz_1(A,B) = k42_abcmiz_1(A,C) ) => B = C ) ) ) ) )).
fof(t81_afinsq_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ! [D] : ( v7_ordinal1(D) => ( r1_tarski(k61_valued_1(k1_ordinal4(B,C),D),A) => r1_tarski(k61_valued_1(B,D),A) ) ) ) ) )).
fof(t81_afinsq_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k8_afinsq_1(A)) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_relat_1(C,k8_afinsq_1(A)) & v1_funct_1(C) & v5_ordinal1(C) & v1_finset_1(C) ) => ( r1_tarski(B,C) => r1_tarski(k8_afinsq_2(A,B),k8_afinsq_2(A,C)) ) ) ) )).
fof(t81_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ( v13_aofa_000(k6_trees_3(B,u1_struct_0(A)),A,B) & v14_aofa_000(k6_trees_3(B,u1_struct_0(A)),A,B) & r2_aofa_000(A,B,C,k6_trees_3(B,u1_struct_0(A))) & r3_aofa_000(A,B,C,k6_trees_3(B,u1_struct_0(A))) ) ) ) ) )).
fof(t81_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & v22_aofa_a00(D,A,1,1,11) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( ( v19_aofa_a00(F,A) & m1_subset_1(F,u1_struct_0(A)) ) => ! [G] : ( m2_subset_1(G,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),k37_aofa_a00(A))) => k15_aofa_a00(A,B,C,D,F,k38_aofa_a00(A,C,H,F),G) = k38_aofa_a00(A,D,k15_aofa_a00(A,B,C,D,k37_aofa_a00(A),H,G),F) ) ) ) ) ) ) ) ) )).
fof(t81_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( m1_subset_1(C,k5_arytm_3) => ! [D] : ( m1_subset_1(D,k5_arytm_3) => ~ ( k9_arytm_3(A,B) = k9_arytm_3(C,D) & ~ r3_arytm_3(A,C) & ~ r3_arytm_3(B,D) ) ) ) ) ) )).
fof(t81_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(10,A) & r1_xxreal_0(k7_xcmplx_0(1,k2_power(2,k6_xcmplx_0(A,9))),k7_xcmplx_0(k5_series_1(2,k2_nat_1(2,A)),k7_newton(A))) ) ) )).
fof(t81_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v20_bcialg_1(A) => k1_bcialg_1(A,k1_bcialg_1(A,B,k1_bcialg_1(A,B,C)),k1_bcialg_1(A,C,B)) = B ) ) ) ) )).
fof(t81_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( ( v3_funct_1(E) & m1_borsuk_2(E,A,C,C) ) => r4_borsuk_2(A,B,C,k1_borsuk_2(A,B,C,C,D,E),D) ) ) ) ) ) )).
fof(t81_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => r1_bvfunc_1(A,k6_bvfunc_2(A,k7_bvfunc_2(A,k1_bvfunc_1(A,B),C,D),C,E),k7_bvfunc_2(A,k7_bvfunc_2(A,k1_bvfunc_1(A,B),C,E),C,D)) ) ) ) ) ) )).
fof(t81_card_2,axiom,( ! [A] : ( ( v1_finset_1(A) & v1_card_1(A) ) => ! [B] : ( ( v1_finset_1(B) & v1_card_1(B) ) => v1_finset_1(k2_card_2(A,B)) ) ) )).
fof(t81_card_3,axiom,( ! [A] : ( v1_finset_1(A) <=> r2_hidden(k1_card_1(A),k4_ordinal1) ) )).
fof(t81_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,A,B) => ! [E] : ( m2_cat_1(E,B,C) => ( ( v14_cat_1(D,A,B) & v14_cat_1(E,B,C) ) => v14_cat_1(k9_cat_1(A,B,C,D,E),A,C) ) ) ) ) ) ) )).
fof(t81_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( k2_cat_1(A,B,D) != k1_xboole_0 & k2_cat_1(A,C,D) != k1_xboole_0 & ~ ! [E] : ( m1_cat_1(E,A,B,D) => ! [F] : ( m1_cat_1(F,A,C,D) => ( r4_cat_3(A,D,E,F) <=> ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( k2_cat_1(A,B,G) != k1_xboole_0 & k2_cat_1(A,C,G) != k1_xboole_0 & ~ ( k2_cat_1(A,D,G) != k1_xboole_0 & ! [H] : ( m1_cat_1(H,A,B,G) => ! [I] : ( m1_cat_1(I,A,C,G) => ? [J] : ( m1_cat_1(J,A,D,G) & ! [K] : ( m1_cat_1(K,A,D,G) => ( ( k5_cat_1(A,B,D,G,E,K) = H & k5_cat_1(A,C,D,G,F,K) = I ) <=> J = K ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t81_cfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k2_numbers))) ) => ( v3_funct_1(k2_partfun1(B,k2_numbers,C,A)) => ( ! [D] : ( v1_xcmplx_0(D) => v1_comseq_2(k2_partfun1(B,k2_numbers,k25_valued_1(B,k2_numbers,C,D),A)) ) & v1_comseq_2(k2_partfun1(B,k2_numbers,k31_valued_1(B,k2_numbers,C),A)) & v1_comseq_2(k2_partfun1(B,k1_numbers,k55_valued_1(B,k2_numbers,C),A)) ) ) ) ) )).
fof(t81_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ~ ( B != C & ~ r1_chord(A,B,C) & ? [D] : ( m2_chord(D,A,B,C) & v4_chord(D,A,B,C) & ? [E] : ( 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] : ( m1_subset_1(F,k6_glib_000(E)) & F = B & ? [G] : ( m1_subset_1(G,k6_glib_000(A)) & r2_hidden(G,D) & ! [H] : ( m1_subset_1(H,k6_glib_000(A)) => ~ ( r2_hidden(H,k1_glib_002(E,F)) & r1_chord(A,G,H) ) ) ) ) ) ) ) ) ) ) )).
fof(t81_classes1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_classes1(A,B) => k1_card_1(k9_xtuple_0(A)) = k1_card_1(k9_xtuple_0(B)) ) ) ) )).
fof(t81_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_clvect_1(D,A) => ( r2_hidden(k5_algstr_0(A,C,B),k5_clvect_1(A,C,D)) <=> r1_struct_0(D,B) ) ) ) ) ) )).
fof(t81_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v3_clvect_2(B,A) & r2_clvect_2(A,B,C) ) => v3_clvect_2(C,A) ) ) ) ) )).
fof(t81_cohsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_xboole_0(k14_cohsp_1(A,B),k14_cohsp_1(C,D)) = k14_cohsp_1(k2_xboole_0(A,C),k2_xboole_0(B,D)) )).
fof(t81_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k2_xcmplx_0(A,B) = k2_xcmplx_0(k3_real_1(k3_complex1(A),k3_complex1(B)),k3_xcmplx_0(k3_real_1(k4_complex1(A),k4_complex1(B)),k7_complex1)) ) ) )).
fof(t81_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ~ ( A != B & A != C & B != C & k4_complex2(A,B,C) = k5_numbers & k4_complex2(B,C,A) = k5_numbers & k4_complex2(C,A,B) = k5_numbers ) ) ) ) )).
fof(t81_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k3_finseq_2(k4_ordinal1)) & v1_funct_1(B) & v4_valued_0(B) & v2_margrel1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k3_finseq_2(k4_ordinal1)) & v1_funct_1(C) & v4_valued_0(C) & v2_margrel1(C) ) => ( ( v2_comput_1(B) & v2_comput_1(C) & k19_margrel1(B) = k5_numbers & k19_margrel1(C) = 2 ) => k1_recdef_1(k7_comput_1(B,C,1),k12_finseq_1(k4_ordinal1,k1_nat_1(A,1))) = k1_recdef_1(C,k2_finseq_4(k4_ordinal1,A,k1_recdef_1(k7_comput_1(B,C,1),k12_finseq_1(k4_ordinal1,A)))) ) ) ) ) )).
fof(t81_convex4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_convex4(D,A) => ( ( v3_convex4(D,A) & k1_convex4(A,D) = k7_domain_1(u1_struct_0(A),B,C) ) => ( B = C | ( ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & E = k3_funct_2(u1_struct_0(A),k2_numbers,D,B) & F = k3_funct_2(u1_struct_0(A),k2_numbers,D,C) & k2_xcmplx_0(E,F) = 1 & r1_xxreal_0(k5_numbers,E) & r1_xxreal_0(k5_numbers,F) ) ) & 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))) ) ) ) ) ) ) ) )).
fof(t81_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ( ~ r2_hidden(D,k24_qc_lang1(A,C)) => v2_cqc_the1(k10_cqc_lang(A,k8_cqc_lang(A,k12_cqc_lang(A,D,B),C),k11_cqc_lang(A,D,k8_cqc_lang(A,B,C))),A) ) ) ) ) ) )).
fof(t81_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k18_sin_cos),D) ) & r2_hidden(A,k1_relset_1(k1_numbers,k26_sin_cos)) & r2_hidden(B,k1_relset_1(k1_numbers,k26_sin_cos)) ) => k9_diff_1(C,A,B) = k7_xcmplx_0(k6_xcmplx_0(k17_sin_cos(A),k17_sin_cos(B)),k6_xcmplx_0(A,B)) ) ) ) ) )).
fof(t81_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : k7_enumset1(A,B,C,D,E,F,G,H,I) = k2_xboole_0(k3_enumset1(A,B,C,D,E),k2_enumset1(F,G,H,I)) )).
fof(t81_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => k7_euclid_8(A,A,B) = k5_numbers ) ) )).
fof(t81_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ~ ( r2_hidden(B,D) & r6_euclidlp(A,C,D) & ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ~ ( B != E & r2_hidden(E,C) & ~ r2_hidden(E,D) ) ) ) ) ) ) ) )).
fof(t81_exchsort,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finset_1(B) & v1_exchsort(B) & v2_exchsort(B,k5_numbers) ) => k4_exchsort(k1_ordinal4(B,k5_afinsq_1(A))) = A ) )).
fof(t81_facirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k15_facirc_1(A,B,C),k18_facirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ( ( E = k1_funct_1(D,B) & F = k1_funct_1(D,C) ) => 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(E,F) ) ) ) ) ) ) ) )).
fof(t81_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v13_lattices(A) => v15_lattices(k10_filter_2(A,k6_filter_2(A,B))) ) ) ) )).
fof(t81_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(C,B) => k16_finseq_1(C,k16_finseq_1(B,A)) = k16_finseq_1(C,A) ) ) ) ) )).
fof(t81_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( 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] : ( m2_finseq_1(F,A) => m2_finseq_1(k4_funcop_1(E,F,D),C) ) ) ) ) ) ) )).
fof(t81_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ! [D] : ( v7_ordinal1(D) => ( ( k3_finseq_1(A) = k1_nat_1(D,1) & B = k5_relat_1(A,k2_finseq_1(D)) ) => ( r2_hidden(k1_funct_1(A,k1_nat_1(D,1)),C) <=> k1_finseq_3(A,C) = k1_finseq_3(B,C) ) ) ) ) ) )).
fof(t81_finseq_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_tarski(B,C) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(B)) ) => k1_funct_1(C,D) = k1_funct_1(B,D) ) ) ) ) ) )).
fof(t81_finseq_5,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ( r1_xxreal_0(2,k3_finseq_1(B)) => k17_finseq_1(A,2,B) = k10_finseq_1(k7_partfun1(A,B,1),k7_partfun1(A,B,2)) ) ) )).
fof(t81_finseq_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_finseq_1(D,C) => k2_rfinseq(C,k2_xcmplx_0(A,B),D) = k2_rfinseq(C,B,k2_rfinseq(C,A,D)) ) ) ) ) )).
fof(t81_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,A,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( k5_binop_1(A,k7_finseqop(A,D,k6_partfun1(A),E),B,C) = k5_binop_1(A,D,B,k3_funct_2(A,A,E,C)) & k5_binop_1(A,k7_finseqop(A,D,E,k6_partfun1(A)),B,C) = k5_binop_1(A,D,k3_funct_2(A,A,E,B),C) ) ) ) ) ) ) )).
fof(t81_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => k2_flang_2(A,k2_flang_2(A,B)) = k2_flang_2(A,B) ) )).
fof(t81_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ( r1_tarski(k2_flang_2(A,B),k2_flang_3(A,B)) <=> r2_hidden(k2_flang_1(A),B) ) ) )).
fof(t81_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : r1_tarski(k7_relset_1(A,k1_tarski(C),k7_funcop_1(A,C),B),k1_tarski(C)) )).
fof(t81_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( v2_funct_1(B) => r1_tarski(k8_relat_1(B,k7_relat_1(B,A)),A) ) ) )).
fof(t81_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( r2_hidden(D,k5_partfun1(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))) ) ) ) )).
fof(t81_funct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,A,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,B,D) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,D))) ) => ! [G] : ( ( ~ v1_xboole_0(G) & m1_subset_1(G,k1_zfmisc_1(A)) ) => ! [H] : ( ( ~ v1_xboole_0(H) & m1_subset_1(H,k1_zfmisc_1(B)) ) => r8_binop_1(G,H,k2_zfmisc_1(C,D),k17_funct_3(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D),k16_funct_3(A,B,C,D,E,F),k8_mcart_1(A,B,G,H)),k16_funct_3(G,H,C,D,k17_funct_3(A,C,E,G),k17_funct_3(B,D,F,H))) ) ) ) ) ) ) ) ) )).
fof(t81_funct_4,axiom,( ! [A] : ! [B] : ! [C] : k4_funct_4(A,A,B,C) = k16_funcop_1(A,C) )).
fof(t81_funct_7,axiom,( ! [A] : ( v1_relat_1(A) => ( r1_xboole_0(k10_xtuple_0(A),k9_xtuple_0(A)) => k8_funct_7(A,2) = k1_xboole_0 ) ) )).
fof(t81_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k1_relset_1(k1_numbers,k1_fdiff_9)) => r1_funct_8(A,k1_numbers,k1_numbers,k1_fdiff_9) ) ) )).
fof(t81_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => ! [C] : ( ( ~ 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)) & v4_ring_1(C,k7_fvaluat1(A,B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k7_fvaluat1(A,B)))) ) => C = k8_fvaluat1(A,B) ) ) ) ) )).
fof(t81_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v3_group_1(B) & v5_group_1(B) & v4_vectsp_1(B) & l6_algstr_0(B) ) => k3_group_4(B,k5_finseq_2(u1_struct_0(B),A,k1_group_1(B))) = k1_group_1(B) ) ) )).
fof(t81_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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(k31_gfacirc1(A,B,C))) & r2_hidden(B,k2_msafree2(k31_gfacirc1(A,B,C))) & r2_hidden(C,k2_msafree2(k31_gfacirc1(A,B,C))) ) ) )).
fof(t81_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(B)) => ( C = D => ( r1_xxreal_0(k32_glib_000(B,D),k32_glib_000(A,C)) & r1_xxreal_0(k33_glib_000(B,D),k33_glib_000(A,C)) & r1_xxreal_0(k35_glib_000(B,D),k35_glib_000(A,C)) ) ) ) ) ) ) )).
fof(t81_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ( r1_glib_000(A,C,D,B) <=> k12_glib_001(A,k2_glib_001(A,C,D,B)) = k9_finseq_1(B) ) ) )).
fof(t81_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( v1_group_3(C,A) & m1_group_2(C,A) ) => ? [D] : ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) & u1_struct_0(D) = k4_group_11(A,B,B) & r1_tarski(k4_group_11(A,C,B),k4_group_11(A,C,D)) ) ) ) ) )).
fof(t81_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => k8_group_2(A,k9_group_2(A,B,C)) = k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k8_group_2(A,B),k8_group_2(A,C)) ) ) ) )).
fof(t81_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(B,k7_group_3(A,C)) <=> r2_group_3(A,B,C) ) ) ) ) )).
fof(t81_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r1_struct_0(k10_group_5(A),B) <=> k7_group_3(A,B) = k6_domain_1(u1_struct_0(A),B) ) ) ) )).
fof(t81_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( v15_algstr_0(C) & v1_group_3(C,A) & m1_group_2(C,A) ) => r2_group_6(k5_group_6(k8_group_4(A,B,C),k1_group_6(A,k8_group_4(A,B,C),C)),k5_group_6(B,k2_group_6(A,B,C))) ) ) ) )).
fof(t81_group_9,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v2_group_9(C,A) & v4_group_9(C,A,B) & m1_group_9(C,A,B) ) => ! [D] : ( ( v2_group_9(D,A) & m1_group_9(D,A,k10_group_9(A,B,C)) ) => ( u1_struct_0(C) = k8_relset_1(u1_struct_0(B),u1_struct_0(k10_group_9(A,B,C)),k12_group_9(A,B,C),u1_struct_0(D)) => D = k4_group_9(A,k10_group_9(A,B,C)) ) ) ) ) )).
fof(t81_ideal_1,axiom,( ! [A] : ( ( ~ 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) & v5_vectsp_1(A) & v1_algstr_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v3_ideal_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v3_ideal_1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => r1_tarski(k15_ideal_1(A,k12_ideal_1(A,B,C),k13_ideal_1(A,B,C)),k15_ideal_1(A,B,C)) ) ) ) )).
fof(t81_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k7_xcmplx_0(k3_xcmplx_0(k28_sin_cos,3),2)) => k2_integra5(A,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)) = 2 ) ) )).
fof(t81_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => r1_tarski(k7_intpro_1(A),k13_intpro_1(A)) ) )).
fof(t81_jgraph_4,axiom,( ! [A] : ( 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)),k5_jgraph_4(A),k4_struct_0(k15_euclid(2))) ) )).
fof(t81_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) = E & k18_euclid(C) = H & k18_euclid(D) = G & r1_xxreal_0(G,k18_euclid(A)) & ~ r1_xxreal_0(k18_euclid(B),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),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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t81_jordan,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( r1_jordan24(2,A,k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) => v2_sppol_1(k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,3),k1_jordan21(A))) ) ) )).
fof(t81_jordan2c,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( k3_subset_1(u1_struct_0(A),B) != k1_xboole_0 => ( v2_tops_1(B,A) <=> ! [C] : ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(C,B) & r2_hidden(C,D) & v3_pre_topc(D,A) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r3_connsp_1(A,k3_subset_1(u1_struct_0(A),B),E) & ~ r1_xboole_0(D,E) ) ) ) ) ) ) ) ) )).
fof(t81_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v3_limfunc1(A) => ( v3_limfunc1(k32_valued_1(k1_numbers,k1_numbers,A)) & k4_limfunc1(k32_valued_1(k1_numbers,k1_numbers,A)) = k4_xcmplx_0(k4_limfunc1(A)) ) ) ) )).
fof(t81_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( ( v4_matrix10(B) & r1_matrix10(C,D) ) => r1_matrix10(k5_matrix10(A,C,B),D) ) ) ) ) ) )).
fof(t81_matrix13,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ~ ( r1_tarski(k10_xtuple_0(A),k10_xtuple_0(B)) & ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ~ ( k9_xtuple_0(C) = k9_xtuple_0(A) & r1_tarski(k10_xtuple_0(C),k9_xtuple_0(B)) & A = k3_relat_1(C,B) ) ) ) ) ) )).
fof(t81_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( v1_matrixr2(B,A) => k3_matrixr2(A,k7_matrixr2(A,B)) = k5_xcmplx_0(k3_matrixr2(A,B)) ) ) ) )).
fof(t81_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( v2_membered(C) => ! [D] : ( v2_membered(D) => ( ( r1_tarski(A,B) & r1_tarski(C,D) ) => r1_tarski(k12_member_1(A,C),k12_member_1(B,D)) ) ) ) ) ) )).
fof(t81_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => k2_memstr_0(A,k1_memstr_0(A)) = k16_funcop_1(k5_numbers,k4_ordinal1) ) )).
fof(t81_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ( ( v6_supinf_2(D) & r1_xboole_0(E,F) ) => ( ! [G] : ( m2_subset_1(G,k1_zfmisc_1(A),B) => ~ ( G = k1_relset_1(A,D) & r1_mesfunc1(A,B,D,G) ) ) | k6_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,k6_prob_1(A,B,E,F))) = k3_supinf_2(k6_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,E)),k6_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,F))) ) ) ) ) ) ) ) ) )).
fof(t81_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( ? [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) & k1_relset_1(A,C) = D ) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( r1_mesfunc6(A,B,C,E) => r1_mesfunc6(A,B,k26_valued_1(A,k1_numbers,C,D),E) ) ) ) ) ) ) ) )).
fof(t81_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => r2_funct_2(k4_ordinal1,A,k27_modelc_2(A,k26_modelc_2(A,B)),B) ) ) )).
fof(t81_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( ! [C] : ( m2_subset_1(C,u1_struct_0(A),B) => ! [D] : ( m2_subset_1(D,u1_struct_0(A),B) => r2_hidden(k6_algstr_0(A,C,D),B) ) ) & ! [C] : ( ( ~ v2_struct_0(C) & v15_algstr_0(C) & m2_monoid_0(C,A) ) => u1_struct_0(C) != B ) ) ) ) )).
fof(t81_msafree4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => k1_funct_7(k7_finseq_1(k7_finseq_1(C,k9_finseq_1(A)),D),k2_xcmplx_0(k3_finseq_1(C),1),B) = k7_finseq_1(k7_finseq_1(C,k9_finseq_1(B)),D) ) ) )).
fof(t81_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_numbers))) ) => ( ( v1_ncfcont1(k1_relset_1(u1_struct_0(A),B),A) & r11_ncfcont1(A,B,k1_relset_1(u1_struct_0(A),B)) ) => v1_rcomp_1(k2_relset_1(k1_numbers,B)) ) ) ) )).
fof(t81_newton,axiom,( ! [A] : ( v1_xcmplx_0(A) => ( k1_newton(A,2) = k3_xcmplx_0(A,A) & k1_square_1(A) = k1_newton(A,2) ) ) )).
fof(t81_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) )).
fof(t81_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r4_relat_2(A,B) => r4_relat_2(k2_relat_1(A),B) ) ) )).
fof(t81_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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),k3_pboole(A,B,D))) ) ) ) )).
fof(t81_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r6_pdiff_5(A,B) => r1_fcont_1(k1_pdiff_2(3,3,k1_pdiff_3(2,3,A),B),k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(3,3),B)) ) ) ) )).
fof(t81_pdiff_9,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_euclid(A))) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ( ( v1_pdiff_7(C,A) & r5_pdiff_9(A,D,B,C) ) => r5_pdiff_9(A,k26_valued_1(k1_euclid(A),k1_numbers,D,E),B,C) ) ) ) ) ) ) )).
fof(t81_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ( ~ v1_abian(k7_polyform(A)) => k16_rvsum_1(k28_polyform(A)) = k6_xcmplx_0(k16_rvsum_1(k29_polyform(A)),2) ) ) )).
fof(t81_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(k6_prepower(A,B),k5_numbers) ) ) ) )).
fof(t81_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( r2_qc_lang2(A,B,k1_qc_lang2(A)) <=> ( B = k1_qc_lang2(A) | B = k12_qc_lang1(A) ) ) ) ) )).
fof(t81_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k1_quatern3(A) = k2_quatern3(k24_quaterni(A)) ) )).
fof(t81_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => r1_xxreal_0(k6_xcmplx_0(k28_quaterni(A),k28_quaterni(B)),k28_quaterni(k22_quaterni(A,B))) ) ) )).
fof(t81_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => r1_tarski(k10_xtuple_0(k6_relat_1(A,B)),k10_xtuple_0(B)) ) )).
fof(t81_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(E))) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k8_afinsq_1(E))) => ! [H] : ( ( ~ v2_struct_0(H) & l1_rewrite3(H,F) ) => ! [I] : ( ( ~ v2_struct_0(I) & l1_rewrite3(I,G) ) => ( ( u1_struct_0(H) = u1_struct_0(I) & u1_rewrite3(F,H) = u1_rewrite3(G,I) & r3_rewrite3(E,F,H,A,B,C,D) ) => r3_rewrite3(E,G,I,A,B,C,D) ) ) ) ) ) ) )).
fof(t81_rfunct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) ) => v2_seq_2(k5_relat_1(k54_valued_1(B),A)) ) )).
fof(t81_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => k21_rfunct_3(A,B,k1_xboole_0) = k5_numbers ) ) )).
fof(t81_rinfsup1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_comseq_2(B) => ( r1_xxreal_0(k6_rinfsup1(B),A) <=> ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_numbers) => ! [D] : ( v7_ordinal1(D) => ~ ! [E] : ( v7_ordinal1(E) => r1_xxreal_0(k2_xcmplx_0(A,C),k1_funct_1(B,k2_xcmplx_0(D,E))) ) ) ) ) ) ) ) ) )).
fof(t81_rlaffin1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_rlvect_2(E,C) => ! [F] : ( 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,k6_xcmplx_0(1,A),F)),D) = B <=> A = k7_xcmplx_0(k6_xcmplx_0(k3_funct_2(u1_struct_0(C),k1_numbers,F,D),B),k5_real_1(k3_funct_2(u1_struct_0(C),k1_numbers,F,D),k3_funct_2(u1_struct_0(C),k1_numbers,E,D))) ) ) ) ) ) ) ) ) )).
fof(t81_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_rlsub_1(D,A) => ( ? [E] : ( m2_rlsub_1(E,A,D) & r2_hidden(B,E) & r2_hidden(C,E) ) <=> r1_struct_0(D,k5_algstr_0(A,B,C)) ) ) ) ) ) )).
fof(t81_rlvect_1,axiom,( ! [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) ) => ! [B] : ( 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) ) ) ) )).
fof(t81_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => k16_rvsum_1(k2_finseq_2(A,k5_numbers)) = k5_numbers ) )).
fof(t81_scmfsa8c,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ~ ( ~ r4_scmfsa7b(A,D) & ~ r4_scmfsa7b(B,D) & ~ ( ~ r4_scmfsa7b(k1_scmfsa8b(C,A,B),D) & ~ r4_scmfsa7b(k2_scmfsa8b(C,A,B),D) ) ) ) ) ) ) )).
fof(t81_scmfsa_2,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ~ v2_extpro_1(k15_scmfsa_2(C,B,A),k7_card_1(3),k1_scmfsa_2) ) ) ) )).
fof(t81_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ( ( r1_xxreal_0(k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),E)),k5_numbers) & r1_scmpds_6(C,B,A) & r2_scmpds_6(C,B,A) ) => k6_scmpds_4(k8_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,k1_nat_1(k5_card_1(C),2))) ) ) ) ) ) ) )).
fof(t81_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( ( v10_scmyciel(B,k6_scmyciel(A)) & m1_eqrel_1(B,k3_tarski(k6_scmyciel(A))) ) => ( v7_scmyciel(B,A) & m1_eqrel_1(B,k3_tarski(A)) ) ) ) )).
fof(t81_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r3_semi_af1(A,B,C,C,k2_semi_af1(A,B,C)) ) ) ) )).
fof(t81_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k2_numbers) => ! [D] : ( m1_subset_1(D,k2_numbers) => ! [E] : ( m2_finseq_2(E,k2_numbers,k12_seq_4(B)) => ( ( r2_hidden(A,k2_finseq_1(B)) & D = k1_funct_1(E,A) ) => k1_funct_1(k18_seq_4(B,E,C),A) = k3_xcmplx_0(C,D) ) ) ) ) ) ) )).
fof(t81_setlim_1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v2_prob_1(C) => k4_kurato_0(A,C) = k3_prob_1(A,C) ) ) ) )).
fof(t81_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k4_kurato_0(A,k5_setlim_2(A,C,B)) = k9_subset_1(A,B,k4_kurato_0(A,C)) ) ) )).
fof(t81_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,C,k5_sheffer1(A,B,B)) = k5_sheffer1(A,k5_sheffer1(A,B,B),C) ) ) ) )).
fof(t81_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k17_sin_cos(k6_xcmplx_0(A,B)) = k6_xcmplx_0(k3_xcmplx_0(k17_sin_cos(A),k19_sin_cos(B)),k3_xcmplx_0(k19_sin_cos(A),k17_sin_cos(B))) ) ) )).
fof(t81_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) => k19_sin_cos(k2_sin_cos6(A)) = k3_square_1(k6_xcmplx_0(1,k1_square_1(A))) ) ) )).
fof(t81_sin_cos9,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) => ( r2_fdiff_1(k1_sin_cos9,A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_sin_cos9,A),B) = k7_xcmplx_0(1,k2_xcmplx_0(1,k1_square_1(B))) ) ) ) ) ) )).
fof(t81_sincos10,axiom,( v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(1,k3_square_1(2)))) )).
fof(t81_sprect_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => k24_pscomp_1(k3_topreal1(2,k1_sprect_1(A))) = k13_pscomp_1(A) ) )).
fof(t81_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_valuat_1(C,A,B) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_funct_2(E,k3_qc_lang1(A),B,k2_valuat_1(A,B)) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),B))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),B))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),B))) ) => ( ( ! [I] : ( m2_subset_1(I,k2_qc_lang1(A),k3_qc_lang1(A)) => ~ ( r2_hidden(I,k1_relset_1(k3_qc_lang1(A),G)) & r2_hidden(I,k24_qc_lang1(A,D)) ) ) & ! [I] : ( m2_subset_1(I,k2_qc_lang1(A),k3_qc_lang1(A)) => ( r2_hidden(I,k1_relset_1(k3_qc_lang1(A),H)) => k1_funct_1(H,I) = k3_funct_2(k3_qc_lang1(A),B,E,I) ) ) & r1_xboole_0(k1_relset_1(k3_qc_lang1(A),F),k1_relset_1(k3_qc_lang1(A),H)) ) => ( r1_valuat_1(A,B,D,C,k1_sublemma(A,B,E,F)) <=> r1_valuat_1(A,B,D,C,k1_sublemma(A,B,E,k14_sublemma(A,B,k14_sublemma(A,B,F,G),H))) ) ) ) ) ) ) ) ) ) ) )).
fof(t81_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_tdlat_2(B,A) => v3_tdlat_2(k1_tdlat_2(A,B),A) ) ) ) )).
fof(t81_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k6_tex_4(A,B)))) ) ) )).
fof(t81_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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)))) ) => ( g1_pre_topc(u1_struct_0(D),u1_pre_topc(D)) = C => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,u1_struct_0(D)) => ( ( F = G & r1_tmap_1(D,B,k3_tmap_1(A,B,C,D,E),G) ) => r1_tmap_1(C,B,E,F) ) ) ) ) ) ) ) ) ) )).
fof(t81_topreal6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( v9_rltopsp1(A,k15_euclid(2)) => k9_pscomp_1(A) = k9_pscomp_1(k2_pre_topc(k15_euclid(2),A)) ) ) )).
fof(t81_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( ( r1_tarski(C,D) & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) ) => r1_tarski(k2_pre_topc(A,C),k2_pre_topc(B,D)) ) ) ) ) ) )).
fof(t81_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => v7_transgeo(k6_partfun1(u1_struct_0(A)),A) ) )).
fof(t81_trees_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) ) => k6_trees_1(k13_trees_3(A,B)) = k1_nat_1(k4_xxreal_0(k6_trees_1(A),k6_trees_1(B)),1) ) ) )).
fof(t81_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_tsep_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( v1_tsep_1(C,A) & m1_pre_topc(C,A) ) => r4_tsep_1(A,B,C) ) ) ) )).
fof(t81_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v1_valued_2(D) => ! [E] : ( v1_valued_2(E) => ! [F] : ( v1_valued_2(F) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,D))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(B,E))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(C,F))) ) => k79_valued_2(k3_xboole_0(A,B),C,k2_valued_2(k3_xboole_0(k1_valued_2(D),k1_valued_2(E))),F,k79_valued_2(A,B,D,E,G,H),I) = k79_valued_2(A,k3_xboole_0(B,C),D,k2_valued_2(k3_xboole_0(k1_valued_2(E),k1_valued_2(F))),G,k73_valued_2(B,C,E,F,H,I)) ) ) ) ) ) ) )).
fof(t81_vectsp_4,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m2_vectsp_4(E,A,B,D) => ! [F] : ( m2_vectsp_4(F,A,B,D) => ( ( r2_hidden(C,E) & r2_hidden(C,F) ) => E = F ) ) ) ) ) ) ) )).
fof(t81_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ( v9_waybel_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_orders_2(A,C,k7_waybel_1(A,B)) <=> r1_orders_2(A,B,k7_waybel_1(A,C)) ) ) ) ) ) )).
fof(t81_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_xboole_0(A,k4_xboole_0(B,C)) => r1_xboole_0(B,k4_xboole_0(A,C)) ) )).
fof(t81_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k10_xboolean(A,k4_xboolean(k3_xboolean(A),B)) = k5_xboolean(A,B) ) ) )).
fof(t81_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k7_xcmplx_0(A,k7_xcmplx_0(B,C)) = k3_xcmplx_0(C,k7_xcmplx_0(A,B)) ) ) ) )).
fof(t81_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(C,k3_xcmplx_0(A,B)) & r1_xxreal_0(k7_xcmplx_0(C,B),A) ) ) ) ) )).
fof(t81_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(D,C) & k4_xxreal_1(C,D) = k2_xxreal_1(A,B) ) ) ) ) ) )).
fof(t81_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ( v6_xxreal_2(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r2_hidden(B,A) & r1_xxreal_0(B,C) ) => ( r1_xxreal_0(k1_xxreal_2(A),C) | r2_hidden(C,A) ) ) ) ) ) ) )).
fof(t81_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => k4_xxreal_3(1,A) = A ) )).
fof(t81_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => k29_zf_lang(k5_zf_lang(A,B)) = k1_tarski(k5_zf_lang(A,B)) ) ) )).
fof(t81_zf_lang1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( ~ v1_xboole_0(B) => ( ~ r2_zf_model(B,k5_zf_lang(A,A)) & r2_zf_model(B,k6_zf_lang(k5_zf_lang(A,A))) ) ) ) )).
fof(t81_zfmisc_1,axiom,( ! [A] : r1_tarski(A,k1_zfmisc_1(k3_tarski(A))) )).
fof(t81_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => m2_zmodul01(k6_domain_1(u1_struct_0(A),B),A,k3_zmodul01(A)) ) ) )).
fof(t82_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m3_abcmiz_1(B,A) => ! [C] : ( ( v8_abcmiz_1(C,A) & m1_abcmiz_1(C,A,k13_abcmiz_1(A)) ) => ( k41_abcmiz_1(A,k43_abcmiz_1(A,B,C)) = 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,k43_abcmiz_1(A,B,C)) = k42_abcmiz_1(A,B) ) ) ) ) )).
fof(t82_afinsq_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v5_ordinal1(C) & v1_funct_1(C) & v1_finset_1(C) ) => ! [D] : ( v7_ordinal1(D) => ( r1_tarski(k61_valued_1(k1_ordinal4(B,C),D),A) => r1_tarski(k61_valued_1(C,k1_nat_1(D,k5_card_1(B))),A) ) ) ) ) )).
fof(t82_afinsq_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => k63_valued_1(k1_ordinal4(B,k5_afinsq_1(A))) = B ) )).
fof(t82_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(C)) => ! [E] : ( m1_subset_1(E,C) => ! [F] : ( m1_aofa_000(F,A,C,D) => ( r4_aofa_000(A,B,C,E,D,F) <=> ~ r1_xxreal_0(k1_supinf_1,k20_aofa_000(A,B,C,E,D,F)) ) ) ) ) ) ) ) )).
fof(t82_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & v22_aofa_a00(D,A,1,1,11) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( ( v19_aofa_a00(F,A) & m1_subset_1(F,u1_struct_0(A)) ) => ! [G] : ( m2_subset_1(G,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),F)) => ! [I] : ( m1_subset_1(I,k1_funct_1(u3_msualg_1(A,C),F)) => k15_aofa_a00(A,B,C,D,k37_aofa_a00(A),k41_aofa_a00(A,C,F,H,I),G) = k41_aofa_a00(A,D,F,k15_aofa_a00(A,B,C,D,F,H,G),k15_aofa_a00(A,B,C,D,F,I,G)) ) ) ) ) ) ) ) ) ) )).
fof(t82_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( m1_subset_1(C,k5_arytm_3) => ( r3_arytm_3(B,A) => r3_arytm_3(k10_arytm_3(B,C),k10_arytm_3(A,C)) ) ) ) ) )).
fof(t82_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( r1_xxreal_0(3,A) => r1_xxreal_0(k6_xcmplx_0(A,1),k3_xcmplx_0(2,k6_xcmplx_0(A,2))) ) ) )).
fof(t82_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v20_bcialg_1(A) => k1_bcialg_1(A,C,k1_bcialg_1(A,C,k1_bcialg_1(A,B,k1_bcialg_1(A,B,C)))) = C ) ) ) ) )).
fof(t82_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( ( v3_funct_1(E) & m1_borsuk_2(E,A,B,B) ) => ( r1_borsuk_6(A,B,C) => r3_borsuk_2(A,B,C,k1_borsuk_2(A,B,B,C,E,D),D) ) ) ) ) ) ) )).
fof(t82_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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),k7_bvfunc_2(A,k7_bvfunc_2(A,k1_bvfunc_1(A,B),C,E),C,D)) ) ) ) ) ) ) )).
fof(t82_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ! [C] : ( v1_card_1(C) => ! [D] : ( v1_card_1(D) => ( ~ ( ~ ( r2_hidden(A,B) & r2_hidden(C,D) ) & ~ ( r1_ordinal1(A,B) & r2_hidden(C,D) ) & ~ ( r2_hidden(A,B) & r1_ordinal1(C,D) ) & ~ ( r1_ordinal1(A,B) & r1_ordinal1(C,D) ) ) => ( r1_ordinal1(k1_card_2(A,C),k1_card_2(B,D)) & r1_ordinal1(k1_card_2(C,A),k1_card_2(B,D)) ) ) ) ) ) ) )).
fof(t82_card_3,axiom,( ! [A] : ( v3_ordinal1(A) => ( ~ v1_finset_1(A) <=> r1_ordinal1(k4_ordinal1,A) ) ) )).
fof(t82_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => r1_tarski(k7_relat_1(C,k2_cat_1(A,D,E)),k2_cat_1(B,k8_cat_1(A,B,C,D),k8_cat_1(A,B,C,E))) ) ) ) ) ) )).
fof(t82_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_cat_1(E,A,B,D) => ! [F] : ( m1_cat_1(F,A,C,D) => ( r4_cat_3(A,D,E,F) => ( k2_cat_1(A,B,D) = k1_xboole_0 | k2_cat_1(A,C,D) = k1_xboole_0 | k2_cat_1(A,B,C) = k1_xboole_0 | k2_cat_1(A,C,B) = k1_xboole_0 | ( v2_cat_3(E,A,B,D) & v2_cat_3(F,A,C,D) ) ) ) ) ) ) ) ) ) )).
fof(t82_cfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,k2_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,k2_numbers))) ) => ( ( v1_comseq_2(k2_partfun1(C,k2_numbers,D,A)) & v3_funct_1(k2_partfun1(C,k2_numbers,E,B)) ) => v1_comseq_2(k2_partfun1(C,k2_numbers,k2_valued_1(C,k2_numbers,k2_numbers,D,E),k3_xboole_0(A,B))) ) ) ) ) )).
fof(t82_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ~ ( B != C & ~ r1_chord(A,B,C) & ? [D] : ( m2_chord(D,A,B,C) & v4_chord(D,A,B,C) & ? [E] : ( 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] : ( m1_subset_1(F,k6_glib_000(E)) & F = C & ? [G] : ( m1_subset_1(G,k6_glib_000(A)) & r2_hidden(G,D) & ! [H] : ( m1_subset_1(H,k6_glib_000(A)) => ~ ( r2_hidden(H,k1_glib_002(E,F)) & r1_chord(A,G,H) ) ) ) ) ) ) ) ) ) ) )).
fof(t82_classes1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( r2_hidden(C,k10_xtuple_0(B)) => r2_hidden(k6_classes1(C),k6_classes1(k4_tarski(B,A))) ) ) )).
fof(t82_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_clvect_1(D,A) => ( r2_hidden(B,k5_clvect_1(A,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r1_struct_0(D,E) & B = k3_rlvect_1(A,C,E) ) ) ) ) ) ) )).
fof(t82_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v3_clvect_2(B,A) & m2_valued_0(C,u1_struct_0(A),B) ) => v3_clvect_2(C,A) ) ) ) ) )).
fof(t82_cohsp_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k3_xboole_0(k14_cohsp_1(A,B),k14_cohsp_1(C,D)) = k14_cohsp_1(k3_xboole_0(A,C),k3_xboole_0(B,D)) )).
fof(t82_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k3_xcmplx_0(A,B) = k2_xcmplx_0(k5_real_1(k4_real_1(k3_complex1(A),k3_complex1(B)),k4_real_1(k4_complex1(A),k4_complex1(B))),k3_xcmplx_0(k3_real_1(k4_real_1(k3_complex1(A),k4_complex1(B)),k4_real_1(k3_complex1(B),k4_complex1(A))),k7_complex1)) ) ) )).
fof(t82_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ~ ( A != B & B != C & ~ r1_xxreal_0(k4_complex2(A,B,C),k5_numbers) & ~ r1_xxreal_0(k28_sin_cos,k4_complex2(A,B,C)) & ~ ( k2_xcmplx_0(k2_xcmplx_0(k4_complex2(A,B,C),k4_complex2(B,C,A)),k4_complex2(C,A,B)) = k28_sin_cos & ~ r1_xxreal_0(k4_complex2(B,C,A),k5_numbers) & ~ r1_xxreal_0(k4_complex2(C,A,B),k5_numbers) ) ) ) ) ) )).
fof(t82_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k3_finseq_2(k4_ordinal1)) & v1_funct_1(D) & v4_valued_0(D) & v2_margrel1(D) & v2_comput_1(D) & v8_comput_1(D,2) ) => k1_recdef_1(k14_comput_1(D),k3_finseq_4(k4_ordinal1,A,B,C)) = k1_recdef_1(D,k2_finseq_4(k4_ordinal1,A,C)) ) ) ) ) )).
fof(t82_convex4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_convex4(E,A) => ( ( v3_convex4(E,A) & k1_convex4(A,E) = k8_domain_1(u1_struct_0(A),B,C,D) ) => ( B = C | C = D | D = B | ( ? [F] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & F = k3_funct_2(u1_struct_0(A),k2_numbers,E,B) & G = k3_funct_2(u1_struct_0(A),k2_numbers,E,C) & H = k3_funct_2(u1_struct_0(A),k2_numbers,E,D) & k2_xcmplx_0(k2_xcmplx_0(F,G),H) = 1 & r1_xxreal_0(k5_numbers,F) & r1_xxreal_0(k5_numbers,G) & r1_xxreal_0(k5_numbers,H) ) ) ) & 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))) ) ) ) ) ) ) ) ) )).
fof(t82_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ( ~ r2_hidden(D,k24_qc_lang1(A,C)) => ( v2_cqc_the1(k8_cqc_lang(A,k12_cqc_lang(A,D,B),C),A) <=> v2_cqc_the1(k11_cqc_lang(A,D,k8_cqc_lang(A,B,C)),A) ) ) ) ) ) ) )).
fof(t82_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k18_sin_cos),D) ) & r2_hidden(B,k1_relset_1(k1_numbers,k26_sin_cos)) & r2_hidden(k2_xcmplx_0(B,A),k1_relset_1(k1_numbers,k26_sin_cos)) ) => k1_funct_1(k3_diff_1(C,A),B) = k6_xcmplx_0(k17_sin_cos(k2_xcmplx_0(B,A)),k17_sin_cos(B)) ) ) ) ) )).
fof(t82_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : k7_enumset1(A,B,C,D,E,F,G,H,I) = k2_xboole_0(k4_enumset1(A,B,C,D,E,F),k1_enumset1(G,H,I)) )).
fof(t82_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => k7_euclid_8(B,A,B) = k5_numbers ) ) )).
fof(t82_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ( r2_hidden(B,k4_euclidlp(A,B,C,D)) & r2_hidden(C,k4_euclidlp(A,B,C,D)) & r2_hidden(D,k4_euclidlp(A,B,C,D)) ) ) ) ) ) )).
fof(t82_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_exchsort(A) ) => ! [B] : ( m1_exchsort(B,A) => r2_hidden(B,k1_funct_2(k9_xtuple_0(A),k10_xtuple_0(A))) ) ) )).
fof(t82_facirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k15_facirc_1(A,B,C),k18_facirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ( ( E = k1_funct_1(D,A) & F = k1_funct_1(D,C) ) => 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(F,E) ) ) ) ) ) ) ) )).
fof(t82_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_lattices(A,B,C) => ( v15_lattices(k10_filter_2(A,k9_filter_2(A,B,C))) & k6_lattices(k10_filter_2(A,k9_filter_2(A,B,C))) = C & k5_lattices(k10_filter_2(A,k9_filter_2(A,B,C))) = B ) ) ) ) ) )).
fof(t82_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => k2_finseq_1(A) = k6_subset_1(k1_nat_1(A,1),k1_tarski(k5_numbers)) ) )).
fof(t82_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) ) => ! [F] : ( ( 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))) ) => ! [G] : ( m2_finseq_1(G,A) => ( E = k4_funcop_1(F,G,D) => k3_finseq_1(E) = k3_finseq_1(G) ) ) ) ) ) ) ) ) )).
fof(t82_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ! [D] : ( v7_ordinal1(D) => ( ( k3_finseq_1(A) = k1_nat_1(D,1) & B = k5_relat_1(A,k2_finseq_1(D)) ) => ( ~ r2_hidden(k1_funct_1(A,k1_nat_1(D,1)),C) <=> k1_finseq_3(A,C) = k7_finseq_1(k1_finseq_3(B,C),k9_finseq_1(k1_funct_1(A,k1_nat_1(D,1)))) ) ) ) ) ) )).
fof(t82_finseq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(B,A) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ~ ( B = k1_nat_1(A,C) & r1_xxreal_0(1,C) ) ) ) ) ) )).
fof(t82_finseq_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m2_finseq_1(C,B) => ( r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) => k17_finseq_1(B,k1_nat_1(A,1),C) = k7_finseq_1(k17_finseq_1(B,A,C),k9_finseq_1(k7_partfun1(B,C,k1_nat_1(A,1)))) ) ) ) )).
fof(t82_finseq_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m2_finseq_1(D,B) => ( r2_hidden(C,k10_xtuple_0(D)) => ( r1_xxreal_0(k4_finseq_4(D,C),A) | k2_finseq_5(B,k2_rfinseq(B,A,D),C) = k2_finseq_5(B,D,C) ) ) ) ) ) ) )).
fof(t82_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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] : ( ( v1_funct_1(F) & v1_funct_2(F,B,B) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) => r2_funct_2(A,B,k6_funcop_1(B,A,k7_finseqop(B,E,k6_partfun1(B),F),C,D),k6_funcop_1(B,A,E,C,k1_partfun1(A,B,B,B,D,F))) ) ) ) ) ) ) )).
fof(t82_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ( r1_tarski(B,C) => r1_tarski(k2_flang_2(A,B),k2_flang_2(A,C)) ) ) ) )).
fof(t82_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ( r1_tarski(B,k2_flang_3(A,C)) => r1_tarski(k2_flang_3(A,B),k2_flang_3(A,C)) ) ) ) )).
fof(t82_funcop_1,axiom,( ! [A] : ! [B] : r3_wellord1(k1_tarski(k4_tarski(A,A)),k1_tarski(k4_tarski(B,B)),k16_funcop_1(A,B)) )).
fof(t82_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ! [B] : r1_tarski(k8_relat_1(A,k7_relat_1(A,B)),B) => v2_funct_1(A) ) ) )).
fof(t82_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => r1_tarski(k5_partfun1(A,B,C),k1_funct_2(A,B)) ) )).
fof(t82_funct_4,axiom,( ! [A] : ! [B] : k16_funcop_1(A,B) = k1_tarski(k4_tarski(A,B)) )).
fof(t82_funct_7,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( 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(k8_funct_7(C,B)) & v1_funct_2(k8_funct_7(C,B),A,A) & m1_subset_1(k8_funct_7(C,B),k1_zfmisc_1(k2_zfmisc_1(A,A))) ) ) ) )).
fof(t82_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & k1_funct_1(k18_sin_cos,B) = k5_numbers ) ) => r1_funct_8(A,k1_numbers,k1_numbers,k1_fdiff_9) ) ) )).
fof(t82_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => k6_fvaluat1(A,k5_fvaluat1(A,B)) = k6_fvaluat1(A,B) ) ) ) )).
fof(t82_fvsum_1,axiom,( ! [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) & 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] : ( m2_finseq_1(B,u1_struct_0(A)) => ( ? [C] : ( v7_ordinal1(C) & r2_hidden(C,k4_finseq_1(B)) & k1_funct_1(B,C) = k4_struct_0(A) ) <=> k3_group_4(A,B) = k4_struct_0(A) ) ) ) )).
fof(t82_gfacirc1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => k2_msafree2(k31_gfacirc1(A,B,C)) = k1_enumset1(A,B,C) ) ) ) )).
fof(t82_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(B)) => ( C = D => ( r1_tarski(k36_glib_000(B,D),k36_glib_000(A,C)) & r1_tarski(k37_glib_000(B,D),k37_glib_000(A,C)) & r1_tarski(k38_glib_000(B,D),k38_glib_000(A,C)) ) ) ) ) ) ) )).
fof(t82_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => r2_relset_1(k4_ordinal1,k7_glib_000(A),k12_glib_001(A,k6_glib_001(A,B)),k4_finseq_5(k7_glib_000(A),k12_glib_001(A,B))) ) ) )).
fof(t82_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( ( ~ v3_relat_1(D) & v1_matrix_0(D) & v1_goboard1(D) & v2_goboard1(D) & v3_goboard1(D) & v4_goboard1(D) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ~ ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(D)) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(D)) & r1_xboole_0(k1_rltopsp1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),D,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),D,k1_nat_1(A,1),k1_nat_1(B,1))),k7_xcmplx_0(1,2)),C),k1_tops_1(k15_euclid(2),k3_goboard5(D,A,B))) ) ) ) ) ) )).
fof(t82_group_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_group_2(C,B) => ! [D] : ( m1_group_2(D,B) => ( r1_struct_0(k9_group_2(B,C,D),A) <=> ( r1_struct_0(C,A) & r1_struct_0(D,A) ) ) ) ) ) )).
fof(t82_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r2_hidden(k2_group_3(A,B,C),k7_group_3(A,B)) ) ) ) )).
fof(t82_group_5,axiom,( ! [A] : ( ( ~ 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) ) <=> k10_group_5(A) = A ) ) )).
fof(t82_group_9,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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) & v6_group_9(B,A) ) => v6_group_9(C,A) ) ) ) )).
fof(t82_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k3_xcmplx_0(k28_sin_cos,2)) => k2_integra5(A,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)) = k5_numbers ) ) )).
fof(t82_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => ! [D] : ( m1_subset_1(D,k1_intpro_1) => ( r2_hidden(k3_intpro_1(B,k3_intpro_1(C,B)),k13_intpro_1(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))),k13_intpro_1(A)) & r2_hidden(k3_intpro_1(k4_intpro_1(B,C),B),k13_intpro_1(A)) & r2_hidden(k3_intpro_1(k4_intpro_1(B,C),C),k13_intpro_1(A)) & r2_hidden(k3_intpro_1(B,k3_intpro_1(C,k4_intpro_1(B,C))),k13_intpro_1(A)) & r2_hidden(k3_intpro_1(B,k5_intpro_1(B,C)),k13_intpro_1(A)) & r2_hidden(k3_intpro_1(C,k5_intpro_1(B,C)),k13_intpro_1(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))),k13_intpro_1(A)) & r2_hidden(k3_intpro_1(k2_intpro_1,B),k13_intpro_1(A)) & r2_hidden(k5_intpro_1(B,k3_intpro_1(B,k2_intpro_1)),k13_intpro_1(A)) ) ) ) ) ) )).
fof(t82_jgraph_4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(B,k7_xcmplx_0(k18_euclid(A),k12_euclid(A))) => ( r1_xxreal_0(k17_euclid(A),k5_numbers) | k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k7_jgraph_4(B),A) = k19_euclid(k3_xcmplx_0(k12_euclid(A),k3_square_1(k6_xcmplx_0(1,k1_square_1(k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k18_euclid(A),k12_euclid(A)),B),k6_xcmplx_0(1,B)))))),k3_xcmplx_0(k12_euclid(A),k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k18_euclid(A),k12_euclid(A)),B),k6_xcmplx_0(1,B)))) ) ) & ( r1_xxreal_0(k17_euclid(A),k5_numbers) => k3_funct_2(u1_struct_0(k15_euclid(2)),u1_struct_0(k15_euclid(2)),k7_jgraph_4(B),A) = A ) ) ) ) )).
fof(t82_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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) = F & k17_euclid(D) = F & r1_xxreal_0(G,k18_euclid(A)) & ~ r1_xxreal_0(k18_euclid(B),k18_euclid(A)) & r1_xxreal_0(k18_euclid(B),H) & 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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t82_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( ( r2_hidden(D,k15_pscomp_1(B)) & r2_hidden(C,k9_subset_1(u1_struct_0(k15_euclid(2)),k4_topreal1(D),k3_topreal1(2,k2_jordan9(B,A)))) ) => k18_euclid(C) = k7_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))) ) ) ) ) ) )).
fof(t82_jordan2c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( k3_subset_1(u1_struct_0(k15_euclid(2)),A) != k1_xboole_0 => ( ( v2_tops_1(A,k15_euclid(2)) & v1_jordan1(A) ) <=> ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ? [C] : ( 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) & A = k7_subset_1(u1_struct_0(k15_euclid(2)),k2_pre_topc(k15_euclid(2),B),B) & ! [D] : ( 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] : ( 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))) ) ) ) ) ) ) ) ) ) )).
fof(t82_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ r1_xxreal_0(D,C) & r2_hidden(D,k1_relset_1(k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) ) => ( v3_limfunc1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B)) & k4_limfunc1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B)) = k2_xcmplx_0(k4_limfunc1(A),k4_limfunc1(B)) ) ) ) ) )).
fof(t82_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( ( v3_matrix10(B) & r2_matrix10(C,D) ) => r2_matrix10(C,k5_matrix10(A,D,B)) ) ) ) ) ) )).
fof(t82_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( m2_finseq_2(D,k4_ordinal1,k4_finseq_2(B,k4_ordinal1)) => ! [E] : ( m2_finseq_2(E,k4_ordinal1,k4_finseq_2(A,k4_ordinal1)) => ! [F] : ( ( v1_matrix_0(F) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(C))) ) => ( k2_zfmisc_1(k10_xtuple_0(D),k10_xtuple_0(E)) = k2_matrix_0(F) => k8_matrix13(C,F) = k8_matrix13(C,k1_matrix13(u1_struct_0(C),F,B,A,D,E)) ) ) ) ) ) ) ) )).
fof(t82_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ~ ( v1_matrixr2(B,A) & k3_matrixr2(A,B) = k5_numbers ) ) ) )).
fof(t82_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( v2_membered(C) => k12_member_1(A,k2_xboole_0(B,C)) = k2_xboole_0(k12_member_1(A,B),k12_member_1(A,C)) ) ) ) )).
fof(t82_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( ( v6_supinf_2(D) & k12_supinf_2(C,E) = k5_numbers ) => ( ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ~ ( F = k1_relset_1(A,D) & r1_mesfunc1(A,B,D,F) ) ) | k6_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,E)) = k5_numbers ) ) ) ) ) ) ) )).
fof(t82_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( v6_supinf_2(D) => ( ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ~ ( E = k1_relset_1(A,D) & r1_mesfunc6(A,B,D,E) ) ) | k1_mesfunc6(A,B,C,D) = k6_mesfunc5(A,B,C,k1_mesfunc5(A,D)) ) ) ) ) ) ) )).
fof(t82_modelc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k25_modelc_2(A)) => k26_modelc_2(A,k27_modelc_2(A,B)) = B ) ) )).
fof(t82_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( ! [C] : ( m2_subset_1(C,u1_struct_0(A),B) => ! [D] : ( m2_subset_1(D,u1_struct_0(A),B) => r2_hidden(k6_algstr_0(A,C,D),B) ) ) & r2_hidden(k5_struct_0(A),B) & ! [C] : ( ( ~ v2_struct_0(C) & v22_algstr_0(C) & m3_monoid_0(C,A) ) => u1_struct_0(C) != B ) ) ) ) )).
fof(t82_msafree4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(k2_xcmplx_0(B,1),k3_finseq_1(A)) => k16_finseq_1(k2_xcmplx_0(B,1),A) = k7_finseq_1(k16_finseq_1(B,A),k9_finseq_1(k1_funct_1(A,k2_xcmplx_0(B,1)))) ) ) ) )).
fof(t82_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k4_int_1(B,A) = k3_nat_d(B,A) & k5_int_1(B,A) = k4_nat_d(B,A) ) ) ) )).
fof(t82_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v13_o_ring_1(B,A) & v9_o_ring_1(C,A) ) => v13_o_ring_1(k6_algstr_0(A,B,C),A) ) ) ) ) )).
fof(t82_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r6_relat_2(A,B) => r6_relat_2(k2_relat_1(A),B) ) ) )).
fof(t82_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( r2_pboole(A,k4_pboole(A,B,C),D) => r2_pboole(A,B,k2_pboole(A,C,D)) ) ) ) ) )).
fof(t82_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r7_pdiff_5(A,B) => r1_fcont_1(k1_pdiff_2(3,1,k1_pdiff_3(3,3,A),B),k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(1,3),B)) ) ) ) )).
fof(t82_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ( v1_abian(k7_polyform(A)) => k16_rvsum_1(k28_polyform(A)) = k16_rvsum_1(k29_polyform(A)) ) ) )).
fof(t82_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(B,C) ) => r1_xxreal_0(k6_prepower(A,B),k6_prepower(A,C)) ) ) ) ) )).
fof(t82_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( r2_hidden(B,k15_qc_lang2(A,C)) => r2_qc_lang2(A,B,C) ) ) ) ) )).
fof(t82_quatern3,axiom,( k4_quatern3(k1_quatern2) = k5_numbers )).
fof(t82_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => r1_xxreal_0(k6_xcmplx_0(k28_quaterni(A),k28_quaterni(B)),k28_quaterni(k25_quaterni(A,B))) ) ) )).
fof(t82_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k10_xtuple_0(k6_relat_1(A,B)) = k3_xboole_0(k10_xtuple_0(B),A) ) )).
fof(t82_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k8_afinsq_1(C))) => ! [E] : ( ( ~ v2_struct_0(E) & l1_rewrite3(E,D) ) => r3_rewrite3(C,D,E,A,B,A,B) ) ) ) )).
fof(t82_rfunct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) ) => ( v1_comseq_2(k5_relat_1(B,A)) => ( v1_comseq_2(k5_relat_1(k54_valued_1(B),A)) & v1_comseq_2(k5_relat_1(k30_valued_1(B),A)) ) ) ) )).
fof(t82_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,A) => ( r2_hidden(C,k1_relset_1(A,B)) => k21_rfunct_3(A,B,k1_tarski(C)) = k1_funct_1(B,C) ) ) ) ) )).
fof(t82_rinfsup1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_comseq_2(B) => ( r1_xxreal_0(A,k6_rinfsup1(B)) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(k1_funct_1(B,k2_xcmplx_0(D,E)),k6_xcmplx_0(A,C)) ) ) ) ) ) ) ) ) )).
fof(t82_rlaffin1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) ) ) ) )).
fof(t82_rlsub_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( m2_rlsub_1(D,A,C) => ! [E] : ( m2_rlsub_1(E,A,C) => ( ( r2_hidden(B,D) & r2_hidden(B,E) ) => D = E ) ) ) ) ) ) )).
fof(t82_rlvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) & k4_rlvect_1(A,k2_finseq_4(u1_struct_0(A),k4_algstr_0(A,C),B)) = k5_algstr_0(A,B,C) ) ) ) ) )).
fof(t82_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => ( ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k2_finseq_1(A)) => r1_xxreal_0(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) => r1_xxreal_0(k18_rvsum_1(B),k18_rvsum_1(C)) ) ) ) ) )).
fof(t82_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [D] : ( ( 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(B,k4_scmfsa_2(k5_numbers)) = 1 & ~ r1_xxreal_0(k1_funct_1(B,D),k5_numbers) & ! [E] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(E,u1_struct_0(k1_scmfsa_2)) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ! [G] : ( v7_ordinal1(G) => ~ ( r8_pboole(u1_struct_0(k1_scmfsa_2),E,k1_funct_4(B,k7_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_numbers))) & r8_pboole(k4_ordinal1,F,k1_funct_4(A,k1_scmfsa8c(k1_scmfsa8b(D,k1_scmfsa8a(2),k5_scmfsa6a(C,k8_scmfsa_2(D,k4_scmfsa_2(k5_numbers))))))) & G = k1_nat_1(k8_extpro_1(k7_card_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(k5_numbers))))),k1_funct_4(B,k7_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_numbers))),1) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,E,G),D) = k6_xcmplx_0(k1_funct_1(B,D),1) & k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,E,G),k4_scmfsa_2(k5_numbers)) = 1 & ! [H] : ( ( 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(k7_card_1(3),k1_scmfsa_2,F,E,G),H) = k1_funct_1(k1_scmfsa6b(C,B,A),H) ) ) & ! [H] : ( m1_scmfsa_2(H) => k18_scmfsa_2(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,E,G),H) = k18_scmfsa_2(k1_scmfsa6b(C,B,A),H) ) & k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,E,G)) = k5_numbers & ! [H] : ( v7_ordinal1(H) => ( r1_xxreal_0(H,G) => r2_hidden(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,E,H)),k2_afinsq_1(k1_scmfsa8c(k1_scmfsa8b(D,k1_scmfsa8a(2),k5_scmfsa6a(C,k8_scmfsa_2(D,k4_scmfsa_2(k5_numbers))))))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t82_scmfsa_2,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ~ v2_extpro_1(k16_scmfsa_2(B,A),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(t82_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ( ~ r1_xxreal_0(k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),E)),k5_numbers) => k6_scmpds_4(k8_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,k1_nat_1(k5_card_1(C),2))) ) ) ) ) ) ) )).
fof(t82_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v11_scmyciel(A) ) => k10_scmyciel(A) = k9_scmyciel(k6_scmyciel(A)) ) )).
fof(t82_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k2_semi_af1(A,B,D) = k2_semi_af1(A,C,D) => B = C ) ) ) ) ) )).
fof(t82_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k2_numbers) => ! [C] : ( m1_subset_1(C,k2_numbers) => ! [D] : ( m2_finseq_2(D,k2_numbers,k12_seq_4(A)) => k18_seq_4(A,k18_seq_4(A,D,C),B) = k10_seq_4(D,k3_xcmplx_0(B,C)) ) ) ) ) )).
fof(t82_setlim_1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v2_prob_1(C) => k3_kurato_0(A,C) = k3_prob_1(A,C) ) ) ) )).
fof(t82_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k4_kurato_0(A,k6_setlim_2(A,C,B)) = k4_subset_1(A,B,k4_kurato_0(A,C)) ) ) )).
fof(t82_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,C,B) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,B)),C) ) ) ) )).
fof(t82_sin_cos,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k19_sin_cos(k6_xcmplx_0(A,B)) = k2_xcmplx_0(k3_xcmplx_0(k19_sin_cos(A),k19_sin_cos(B)),k3_xcmplx_0(k17_sin_cos(A),k17_sin_cos(B))) ) ) )).
fof(t82_sin_cos6,axiom,( v5_valued_0(k5_relset_1(k1_numbers,k1_numbers,k1_sin_cos6,k1_rcomp_1(k4_xcmplx_0(1),1))) )).
fof(t82_sin_cos9,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) => ( r2_fdiff_1(k2_sin_cos9,A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k2_sin_cos9,A),B) = k4_xcmplx_0(k7_xcmplx_0(1,k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t82_sincos10,axiom,( v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k2_sincos10,k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1)))) )).
fof(t82_sprect_1,axiom,( ! [A] : ( ( v1_sprect_1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => k3_finseq_1(A) = 5 ) )).
fof(t82_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m1_subset_1(C,k1_substut1(A)) => r1_xboole_0(k1_relset_1(k3_qc_lang1(A),k5_relset_1(k3_qc_lang1(A),k3_qc_lang1(A),k2_substut1(A,C),k15_sublemma(A,B))),k1_relset_1(k3_qc_lang1(A),k5_relset_1(k3_qc_lang1(A),k3_qc_lang1(A),k2_substut1(A,C),k16_sublemma(A,B,C)))) ) ) ) )).
fof(t82_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v3_tdlat_2(B,A) => ( v6_tops_1(k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B)),A) & v6_tops_1(k1_tops_1(A,k2_pre_topc(A,k5_setfam_1(u1_struct_0(A),B))),A) ) ) ) ) )).
fof(t82_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => m1_pre_topc(k1_pre_topc(A,B),k6_tex_4(A,B)) ) ) )).
fof(t82_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( 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)))) ) => ( m1_pre_topc(D,C) => ( 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)) & v5_pre_topc(k3_tmap_1(A,B,C,D,E),D,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)))) ) ) ) ) ) ) ) )).
fof(t82_topgen_5,axiom,( v7_pre_topc(k3_topgen_5) )).
fof(t82_topreal6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( 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(k9_subset_1(u1_struct_0(k15_euclid(A)),B,C),k15_euclid(A)) ) ) ) ) )).
fof(t82_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( ( r1_tarski(D,C) & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & v2_tops_1(C,A) ) => v2_tops_1(D,B) ) ) ) ) ) )).
fof(t82_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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) => ( v7_transgeo(B,A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_analoaf(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)) ) ) ) ) ) ) )).
fof(t82_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( r4_tsep_1(A,B,C) => r4_tsep_1(A,k1_tsep_1(A,B,D),k1_tsep_1(A,C,D)) ) ) ) ) ) )).
fof(t82_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v1_valued_2(D) => ! [E] : ( v1_valued_2(E) => ! [F] : ( v1_valued_2(F) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,D))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(B,E))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(C,F))) ) => k79_valued_2(k3_xboole_0(A,B),C,k2_valued_2(k3_xboole_0(k1_valued_2(D),k1_valued_2(E))),F,k79_valued_2(A,B,D,E,G,H),I) = k79_valued_2(k3_xboole_0(A,C),B,k2_valued_2(k3_xboole_0(k1_valued_2(D),k1_valued_2(F))),E,k79_valued_2(A,C,D,F,G,I),H) ) ) ) ) ) ) )).
fof(t82_vectsp_4,axiom,( ! [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) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t82_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ( v9_waybel_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_orders_2(A,C,k7_waybel_1(A,B)) <=> k11_lattice3(A,B,C) = k3_yellow_0(A) ) ) ) ) ) )).
fof(t82_xboole_1,axiom,( ! [A] : ! [B] : r1_xboole_0(k4_xboole_0(A,B),k4_xboole_0(B,A)) )).
fof(t82_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k10_xboolean(A,k5_xboolean(A,B)) = k4_xboolean(k3_xboolean(A),B) ) ) )).
fof(t82_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k7_xcmplx_0(A,k7_xcmplx_0(B,C)) = k3_xcmplx_0(k7_xcmplx_0(A,B),C) ) ) ) )).
fof(t82_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(C,k3_xcmplx_0(A,B)) & r1_xxreal_0(A,k7_xcmplx_0(C,B)) ) ) ) ) )).
fof(t82_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( r1_xxreal_0(C,D) & r2_xboole_0(k1_xxreal_1(C,D),k1_xxreal_1(A,B)) & r1_xxreal_0(C,A) & r1_xxreal_0(B,D) ) ) ) ) ) )).
fof(t82_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ( v6_xxreal_2(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r2_hidden(B,A) & r1_xxreal_0(C,B) ) => ( r1_xxreal_0(C,k2_xxreal_2(A)) | r2_hidden(C,A) ) ) ) ) ) ) )).
fof(t82_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ~ ( k5_xxreal_3(A) = k5_numbers & A != k1_xxreal_0 & A != k2_xxreal_0 & A != k5_numbers ) ) )).
fof(t82_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => k29_zf_lang(k6_zf_lang(A)) = k2_xboole_0(k29_zf_lang(A),k1_tarski(k6_zf_lang(A))) ) )).
fof(t82_zf_lang1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ~ v1_xboole_0(C) => ( r2_zf_model(C,k4_zf_lang(A,B)) <=> ~ ( A != B & ! [D] : k1_tarski(D) != C ) ) ) ) ) )).
fof(t82_zfmisc_1,axiom,( ! [A] : ! [B] : ( ! [C] : ! [D] : ( ( r2_hidden(C,k2_xboole_0(A,B)) & r2_hidden(D,k2_xboole_0(A,B)) ) => ( C = D | r1_xboole_0(C,D) ) ) => k3_tarski(k3_xboole_0(A,B)) = k3_xboole_0(k3_tarski(A),k3_tarski(B)) ) )).
fof(t82_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( m2_zmodul01(B,A,k3_zmodul01(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B != k6_domain_1(u1_struct_0(A),C) ) ) ) ) )).
fof(t83_abcmiz_0,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_abcmiz_0(A)) => ( r4_abcmiz_0(A,B,C) => k12_abcmiz_0(A,k5_abcmiz_0(A,B,C)) = k12_abcmiz_0(A,B) ) ) ) ) )).
fof(t83_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m3_abcmiz_1(B,A) => ! [C] : ( ( v8_abcmiz_1(C,A) & m1_abcmiz_1(C,A,k13_abcmiz_1(A)) ) => k43_abcmiz_1(A,k43_abcmiz_1(A,B,C),C) = k43_abcmiz_1(A,B,C) ) ) ) )).
fof(t83_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k1_afinsq_1(k16_afinsq_1(A,B,C,D)) = 4 )).
fof(t83_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(C)) => ! [E] : ( m1_subset_1(E,C) => ! [F] : ( m1_aofa_000(F,A,C,D) => ( ~ r2_hidden(E,D) => ( r4_aofa_000(A,B,C,E,D,F) & k20_aofa_000(A,B,C,E,D,F) = k5_numbers ) ) ) ) ) ) ) ) )).
fof(t83_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & v22_aofa_a00(D,A,1,1,11) & l3_msualg_1(D,A) ) => ! [E] : ( ( v19_aofa_a00(E,A) & m1_subset_1(E,u1_struct_0(A)) ) => ! [F] : ( m2_pboole(F,u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,D)) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),k37_aofa_a00(A))) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),E)) => k15_aofa_a00(A,B,C,D,E,k39_aofa_a00(A,C,G,E,H),F) = k39_aofa_a00(A,D,k15_aofa_a00(A,B,C,D,k37_aofa_a00(A),G,F),E,k15_aofa_a00(A,B,C,D,E,H,F)) ) ) ) ) ) ) ) ) )).
fof(t83_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( m1_subset_1(C,k5_arytm_3) => ! [D] : ( m1_subset_1(D,k5_arytm_3) => ~ ( k10_arytm_3(A,B) = k10_arytm_3(C,D) & ~ r3_arytm_3(A,C) & ~ r3_arytm_3(B,D) ) ) ) ) ) )).
fof(t83_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(k5_numbers,A) => k2_power(A,k7_xcmplx_0(1,2)) = k3_square_1(A) ) ) )).
fof(t83_bcialg_1,axiom,( ! [A] : ( ( ~ 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) & v17_bcialg_1(A) & l2_bcialg_1(A) ) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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,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)) ) ) ) ) ) ) )).
fof(t83_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( ( v3_funct_1(E) & m1_borsuk_2(E,A,B,B) ) => r4_borsuk_2(A,B,C,k1_borsuk_2(A,B,B,C,E,D),D) ) ) ) ) ) )).
fof(t83_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ! [C] : ( v1_card_1(C) => ( ( r2_hidden(B,C) | r1_ordinal1(B,C) ) => ( r1_ordinal1(k1_card_2(A,B),k1_card_2(A,C)) & r1_ordinal1(k1_card_2(A,B),k1_card_2(C,A)) & r1_ordinal1(k1_card_2(B,A),k1_card_2(A,C)) & r1_ordinal1(k1_card_2(B,A),k1_card_2(C,A)) ) ) ) ) ) )).
fof(t83_card_3,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ( v1_finset_1(B) => ( v1_finset_1(A) | ( r2_hidden(B,A) & r1_ordinal1(B,A) ) ) ) ) ) )).
fof(t83_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k2_cat_1(A,D,E) != k1_xboole_0 => ! [F] : ( m1_cat_1(F,A,D,E) => k1_funct_1(k11_cat_1(A,B,C,D,E),F) = k3_funct_2(u4_struct_0(A),u4_struct_0(B),C,F) ) ) ) ) ) ) ) )).
fof(t83_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ( ( r4_cat_3(A,B,D,E) & r2_hidden(C,k2_cat_1(A,B,B)) & k1_cat_1(A,D,C) = D & k1_cat_1(A,E,C) = E ) => C = k4_cat_1(A,B) ) ) ) ) ) ) )).
fof(t83_cfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,k2_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,k2_numbers))) ) => ( ( v1_comseq_2(k2_partfun1(C,k2_numbers,D,A)) & v3_funct_1(k2_partfun1(C,k2_numbers,E,B)) ) => ( v1_comseq_2(k2_partfun1(C,k2_numbers,k46_valued_1(C,k2_numbers,k2_numbers,D,E),k3_xboole_0(A,B))) & v1_comseq_2(k2_partfun1(C,k2_numbers,k46_valued_1(C,k2_numbers,k2_numbers,E,D),k3_xboole_0(A,B))) & v1_comseq_2(k2_partfun1(C,k2_numbers,k19_valued_1(C,k2_numbers,k2_numbers,D,E),k3_xboole_0(A,B))) ) ) ) ) ) )).
fof(t83_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ~ ( v5_chord(B,A) & ! [C] : ( ( v7_ordinal1(C) & ~ v1_abian(C) ) => ! [D] : ( ( 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] : r1_glib_000(A,k1_funct_1(B,C),k1_funct_1(B,D),E) & ( v8_glib_001(B,A) => ( ~ ( C = 1 & D = k3_finseq_1(B) ) & ~ ( C = 1 & D = k6_xcmplx_0(k3_finseq_1(B),2) ) & ~ ( C = 3 & D = k3_finseq_1(B) ) ) ) ) ) ) ) ) ) )).
fof(t83_classes1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( k9_xtuple_0(A) = k9_xtuple_0(B) & r1_tarski(k10_xtuple_0(A),k9_xtuple_0(C)) & r1_tarski(k10_xtuple_0(B),k9_xtuple_0(C)) & r2_classes1(A,B) ) => r2_classes1(k3_relat_1(A,C),k3_relat_1(B,C)) ) ) ) ) )).
fof(t83_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_clvect_1(D,A) => ( r2_hidden(B,k5_clvect_1(A,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r1_struct_0(D,E) & B = k5_algstr_0(A,C,E) ) ) ) ) ) ) )).
fof(t83_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v1_clvect_2(B,A) & m2_valued_0(C,u1_struct_0(A),B) ) => v1_clvect_2(C,A) ) ) ) ) )).
fof(t83_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( r2_hidden(C,k15_cohsp_1(A,B)) <=> ? [D] : ( m1_subset_1(D,A) & ? [E] : ( m1_subset_1(E,B) & C = k14_cohsp_1(D,E) ) ) ) ) ) )).
fof(t83_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k4_xcmplx_0(A) = k2_xcmplx_0(k1_real_1(k3_complex1(A)),k3_xcmplx_0(k1_real_1(k4_complex1(A)),k7_complex1)) ) )).
fof(t83_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ~ ( A != B & B != C & ~ r1_xxreal_0(k4_complex2(A,B,C),k28_sin_cos) & ~ ( k2_xcmplx_0(k2_xcmplx_0(k4_complex2(A,B,C),k4_complex2(B,C,A)),k4_complex2(C,A,B)) = k3_xcmplx_0(5,k28_sin_cos) & ~ r1_xxreal_0(k4_complex2(B,C,A),k28_sin_cos) & ~ r1_xxreal_0(k4_complex2(C,A,B),k28_sin_cos) ) ) ) ) ) )).
fof(t83_comput_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v7_comput_1(A) & v8_comput_1(A,2) ) => r2_hidden(k14_comput_1(A),k9_comput_1) ) )).
fof(t83_convex4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_convex4(C,A,k6_domain_1(u1_struct_0(A),B)) => ( v3_convex4(C,A) => ( ? [D] : ( v1_xreal_0(D) & D = k3_funct_2(u1_struct_0(A),k2_numbers,C,B) & D = 1 ) & k4_convex4(A,C) = k1_clvect_1(A,B,k3_funct_2(u1_struct_0(A),k2_numbers,C,B)) ) ) ) ) ) )).
fof(t83_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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,k12_cqc_lang(A,D,k8_cqc_lang(A,B,C)),k8_cqc_lang(A,B,k12_cqc_lang(A,D,C))),A) ) ) ) ) ) )).
fof(t83_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k18_sin_cos),D) ) & r2_hidden(B,k1_relset_1(k1_numbers,k26_sin_cos)) & r2_hidden(k6_xcmplx_0(B,A),k1_relset_1(k1_numbers,k26_sin_cos)) ) => k1_funct_1(k4_diff_1(C,A),B) = k6_xcmplx_0(k17_sin_cos(B),k17_sin_cos(k6_xcmplx_0(B,A))) ) ) ) ) )).
fof(t83_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : k7_enumset1(A,B,C,D,E,F,G,H,I) = k2_xboole_0(k5_enumset1(A,B,C,D,E,F,G),k2_tarski(H,I)) )).
fof(t83_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => k7_euclid_8(A,B,B) = k5_numbers ) ) )).
fof(t83_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(A)) => ! [G] : ( m2_finseq_2(G,k1_numbers,k1_euclid(A)) => ( ( r2_hidden(B,k4_euclidlp(A,E,F,G)) & r2_hidden(C,k4_euclidlp(A,E,F,G)) & r2_hidden(D,k4_euclidlp(A,E,F,G)) ) => r1_tarski(k4_euclidlp(A,B,C,D),k4_euclidlp(A,E,F,G)) ) ) ) ) ) ) ) ) )).
fof(t83_exchsort,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v5_relat_1(C,B) ) => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) )).
fof(t83_facirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k15_facirc_1(A,B,C),k18_facirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t83_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( ( ~ v2_struct_0(A) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) ) => ( ~ v2_struct_0(k10_filter_2(A,k6_filter_2(A,B))) & v10_lattices(k10_filter_2(A,k6_filter_2(A,B))) & v15_lattices(k10_filter_2(A,k6_filter_2(A,B))) & v16_lattices(k10_filter_2(A,k6_filter_2(A,B))) & l3_lattices(k10_filter_2(A,k6_filter_2(A,B))) ) ) ) ) )).
fof(t83_finseq_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r2_hidden(C,k13_finseq_1(B)) & r2_hidden(A,k9_xtuple_0(C)) ) => r2_hidden(k1_funct_1(C,A),B) ) ) )).
fof(t83_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( 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))) ) => k4_funcop_1(E,k6_finseq_1(A),D) = k6_finseq_1(C) ) ) ) ) ) )).
fof(t83_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k1_relset_1(k4_ordinal1,A)) => ! [D] : ( v1_finset_1(D) => ~ ( D = a_3_0_finseq_3(A,B,C) & ~ r2_hidden(k1_funct_1(A,C),B) & k1_funct_1(k1_finseq_3(A,B),k6_xcmplx_0(C,k5_card_1(D))) != k1_funct_1(A,C) ) ) ) ) ) )).
fof(t83_finseq_4,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( ( 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) ) ) ) ) ) )).
fof(t83_finseq_5,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(k3_finseq_1(B),C) => k17_finseq_1(A,k1_nat_1(C,1),B) = k7_finseq_1(k17_finseq_1(A,C,B),k9_finseq_1(k1_funct_1(B,k1_nat_1(C,1)))) ) ) ) )).
fof(t83_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r2_hidden(B,k10_xtuple_0(C)) => ( k4_finseq_4(C,B) = 1 | k2_finseq_5(A,k2_rfinseq(A,1,C),B) = k2_finseq_5(A,C,B) ) ) ) ) ) )).
fof(t83_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,B) & m2_finseq_1(C,A) ) => ! [D] : ( ( v3_card_1(D,B) & m2_finseq_1(D,A) ) => ! [E] : ( ( 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] : ( ( v1_funct_1(F) & v1_funct_2(F,A,A) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => r2_relset_1(k4_ordinal1,A,k1_finseqop(A,A,A,k7_finseqop(A,E,k6_partfun1(A),F),C,D),k1_finseqop(A,A,A,E,C,k4_finseqop(A,A,D,F))) ) ) ) ) ) ) )).
fof(t83_flang_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ~ ( r2_hidden(B,C) & B != k2_flang_1(A) & k2_flang_2(A,C) = k4_flang_1(A,k2_flang_1(A)) ) ) )).
fof(t83_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ( r1_tarski(B,k2_flang_3(A,C)) => k2_flang_3(A,C) = k2_flang_3(A,k4_subset_1(k8_afinsq_1(A),C,B)) ) ) ) )).
fof(t83_funcop_1,axiom,( ! [A] : ! [B] : r4_wellord1(k1_tarski(k4_tarski(A,A)),k1_tarski(k4_tarski(B,B))) )).
fof(t83_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( v2_funct_1(B) => k7_relat_1(B,A) = k8_relat_1(k2_funct_1(B),A) ) ) )).
fof(t83_funct_2,axiom,( ! [A] : ! [B] : k5_partfun1(A,B,k3_partfun1(k1_xboole_0,A,B)) = k1_funct_2(A,B) )).
fof(t83_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ( B != D => k1_funct_1(k1_funct_4(A,k16_funcop_1(B,C)),D) = k1_funct_1(A,D) ) ) )).
fof(t83_funct_7,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => k8_funct_7(B,k5_numbers) = k6_partfun1(A) ) )).
fof(t83_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k1_relset_1(k1_numbers,k2_fdiff_9)) => r2_funct_8(A,k1_numbers,k1_numbers,k2_fdiff_9) ) ) )).
fof(t83_fvaluat1,axiom,( ! [A] : ( ( ~ 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] : ( m1_fvaluat1(B,A) => ( v3_fvaluat1(A) => k7_fvaluat1(A,k5_fvaluat1(A,B)) = k7_fvaluat1(A,B) ) ) ) )).
fof(t83_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v2_struct_0(C) & v3_group_1(C) & v5_group_1(C) & v4_vectsp_1(C) & l6_algstr_0(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => k3_group_4(C,k5_finseq_2(u1_struct_0(C),k2_xcmplx_0(A,B),D)) = k8_group_1(C,k3_group_4(C,k5_finseq_2(u1_struct_0(C),A,D)),k3_group_4(C,k5_finseq_2(u1_struct_0(C),B,D))) ) ) ) ) )).
fof(t83_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k31_gfacirc1(A,B,C),k32_gfacirc1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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(k31_gfacirc1(A,B,C),k32_gfacirc1(A,B,C),D),k4_tarski(k10_finseq_1(A,B),k3_twoscomp)) = k10_margrel1(k9_margrel1(E),F) & k1_funct_1(k6_circuit2(k31_gfacirc1(A,B,C),k32_gfacirc1(A,B,C),D),k4_tarski(k10_finseq_1(B,C),k3_gfacirc1)) = k10_margrel1(F,k9_margrel1(G)) & k1_funct_1(k6_circuit2(k31_gfacirc1(A,B,C),k32_gfacirc1(A,B,C),D),k4_tarski(k10_finseq_1(C,A),k4_twoscomp)) = k10_margrel1(k9_margrel1(G),k9_margrel1(E)) ) ) ) ) ) ) )).
fof(t83_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(B)) => ( ( C = D & v10_glib_000(C,A) ) => v10_glib_000(D,B) ) ) ) ) ) )).
fof(t83_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ( k4_glib_001(A,B) = k3_glib_001(A,C) => r2_relset_1(k4_ordinal1,k7_glib_000(A),k12_glib_001(A,k7_glib_001(A,B,C)),k8_finseq_1(k7_glib_000(A),k12_glib_001(A,B),k12_glib_001(A,C))) ) ) ) ) )).
fof(t83_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ~ ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) & r1_xboole_0(k1_rltopsp1(k15_euclid(2),B,k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_matrix_0(C)),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),k1_matrix_0(C))),k7_xcmplx_0(1,2)),k19_euclid(k5_numbers,1))),k1_tops_1(k15_euclid(2),k3_goboard5(C,A,k1_matrix_0(C)))) ) ) ) ) )).
fof(t83_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => r1_group_2(A,k9_group_2(A,B,B),B) ) ) )).
fof(t83_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_hidden(B,k7_group_3(A,B)) ) ) )).
fof(t83_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(C)) => ! [F] : ( m2_finseq_1(F,k4_numbers) => ( ( D = E & k3_finseq_1(D) = k3_finseq_1(F) ) => k3_group_4(B,k4_group_4(B,F,D)) = k3_group_4(C,k4_group_4(C,F,E)) ) ) ) ) ) ) )).
fof(t83_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_vectsp_1(A) & v1_algstr_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( r4_ideal_1(A,B,C) => r1_tarski(k13_ideal_1(A,B,C),k14_ideal_1(A,k11_ideal_1(A,B,C),k13_ideal_1(A,B,C))) ) ) ) ) )).
fof(t83_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( A = k1_rcomp_1(k3_xcmplx_0(k2_nat_1(2,B),k28_sin_cos),k3_xcmplx_0(k1_nat_1(k2_nat_1(2,B),1),k28_sin_cos)) => k2_integra5(A,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)) = 2 ) ) ) )).
fof(t83_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => ( ( r2_hidden(B,k13_intpro_1(A)) & r2_hidden(k3_intpro_1(B,C),k13_intpro_1(A)) ) => r2_hidden(C,k13_intpro_1(A)) ) ) ) ) )).
fof(t83_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) = E & k17_euclid(C) = F & k17_euclid(D) = F & r1_xxreal_0(G,k18_euclid(A)) & ~ r1_xxreal_0(k18_euclid(B),k18_euclid(A)) & r1_xxreal_0(k18_euclid(B),H) & 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t83_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ~ ( r1_jordan24(2,B,k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) & r2_hidden(A,B) & r1_xxreal_0(3,k18_euclid(A)) ) ) ) )).
fof(t83_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( ( r2_hidden(D,k16_pscomp_1(B)) & r2_hidden(C,k9_subset_1(u1_struct_0(k15_euclid(2)),k5_topreal1(D),k3_topreal1(2,k2_jordan9(B,A)))) ) => k17_euclid(C) = k8_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))) ) ) ) ) ) )).
fof(t83_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( ( r1_xxreal_0(1,A) & C = k6_domain_1(u1_struct_0(k15_euclid(A)),B) ) => v2_tops_1(C,k15_euclid(A)) ) ) ) ) )).
fof(t83_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ r1_xxreal_0(D,C) & r2_hidden(D,k1_relset_1(k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) ) => ( v3_limfunc1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B)) & k4_limfunc1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B)) = k6_xcmplx_0(k4_limfunc1(A),k4_limfunc1(B)) ) ) ) ) )).
fof(t83_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( ( v3_matrix10(B) & r1_matrix10(C,D) ) => r1_matrix10(C,k5_matrix10(A,D,B)) ) ) ) ) ) )).
fof(t83_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( k8_matrix13(B,C) = A <=> k12_matrix_3(A,B,C) != k4_struct_0(B) ) ) ) ) )).
fof(t83_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( v1_matrixr2(B,A) & v1_matrixr2(C,A) ) => ( v1_matrixr2(k1_matrixr2(A,B,C),A) & k7_matrixr2(A,k1_matrixr2(A,B,C)) = k1_matrixr2(A,k7_matrixr2(A,C),k7_matrixr2(A,B)) ) ) ) ) ) )).
fof(t83_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( v2_membered(C) => r1_tarski(k12_member_1(A,k3_xboole_0(B,C)),k3_xboole_0(k12_member_1(A,B),k12_member_1(A,C))) ) ) ) )).
fof(t83_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ( ( v6_supinf_2(D) & r1_tarski(E,F) ) => ( ! [G] : ( m2_subset_1(G,k1_zfmisc_1(A),B) => ~ ( G = k1_relset_1(A,D) & r1_mesfunc1(A,B,D,G) ) ) | r1_xxreal_0(k6_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,E)),k6_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,F))) ) ) ) ) ) ) ) ) )).
fof(t83_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( ( r2_mesfunc6(A,B,D) & v6_supinf_2(D) ) => ( k1_mesfunc6(A,B,C,D) = k6_mesfunc5(A,B,C,k1_mesfunc5(A,D)) & k1_mesfunc6(A,B,C,D) = k5_mesfunc5(A,B,C,k1_mesfunc5(A,D)) ) ) ) ) ) ) )).
fof(t83_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k25_modelc_2(k43_modelc_2)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_modelc_2)) => ~ ( r2_hidden(A,C) & r2_hidden(k3_modelc_2(A),C) & r8_modelc_2(B,C) ) ) ) ) )).
fof(t83_msafree4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(k2_xcmplx_0(B,1),k3_finseq_1(A)) => k1_rfinseq(B,A) = k7_finseq_1(k9_finseq_1(k1_funct_1(A,k2_xcmplx_0(B,1))),k1_rfinseq(k2_xcmplx_0(B,1),A)) ) ) ) )).
fof(t83_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( 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)) & v1_ncfcont1(C,A) & r7_ncfcont1(A,B,D,C) ) => v1_ncfcont1(k7_relset_1(u1_struct_0(A),u1_struct_0(B),D,C),B) ) ) ) ) ) )).
fof(t83_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(k1_newton(B,A),k5_numbers) ) ) ) )).
fof(t83_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v13_o_ring_1(B,A) & v3_o_ring_1(C,A) ) => v13_o_ring_1(k6_algstr_0(A,B,C),A) ) ) ) ) )).
fof(t83_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : k2_relat_1(k2_wellord1(A,B)) = k2_wellord1(k2_relat_1(A),B) ) )).
fof(t83_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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),k5_pboole(A,B,C)) ) ) )).
fof(t83_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r8_pdiff_5(A,B) => r1_fcont_1(k1_pdiff_2(3,2,k1_pdiff_3(3,3,A),B),k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(2,3),B)) ) ) ) )).
fof(t83_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ( k7_polyform(A) = 1 => k16_rvsum_1(k29_polyform(A)) = k11_polyform(A,k5_numbers) ) ) )).
fof(t83_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,1) & ~ r1_xxreal_0(C,B) & r1_xxreal_0(k6_prepower(A,C),k6_prepower(A,B)) ) ) ) ) )).
fof(t83_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( r2_qc_lang2(A,B,C) => r1_tarski(k15_qc_lang2(A,B),k15_qc_lang2(A,C)) ) ) ) ) )).
fof(t83_quatern3,axiom,( k4_quatern3(k2_quatern2) = 1 )).
fof(t83_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k28_quaterni(k25_quaterni(A,B)) = k28_quaterni(k25_quaterni(B,A)) ) ) )).
fof(t83_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( r1_tarski(A,k10_xtuple_0(B)) => k10_xtuple_0(k6_relat_1(A,B)) = A ) ) )).
fof(t83_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( ~ v1_xboole_0(G) => ! [H] : ( m1_subset_1(H,k1_zfmisc_1(k8_afinsq_1(G))) => ! [I] : ( ( ~ v2_struct_0(I) & l1_rewrite3(I,H) ) => ( ( r3_rewrite3(G,H,I,A,B,C,D) & r3_rewrite3(G,H,I,C,D,E,F) ) => r3_rewrite3(G,H,I,A,B,E,F) ) ) ) ) )).
fof(t83_rfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_valued_0(D) ) => ( ( ( v1_seq_2(k5_relat_1(C,A)) & v1_seq_2(k5_relat_1(D,B)) ) => v1_seq_2(k5_relat_1(k1_valued_1(C,D),k3_xboole_0(A,B))) ) & ( ( v2_seq_2(k5_relat_1(C,A)) & v2_seq_2(k5_relat_1(D,B)) ) => v2_seq_2(k5_relat_1(k1_valued_1(C,D),k3_xboole_0(A,B))) ) & ( ( v1_comseq_2(k5_relat_1(C,A)) & v1_comseq_2(k5_relat_1(D,B)) ) => v1_comseq_2(k5_relat_1(k1_valued_1(C,D),k3_xboole_0(A,B))) ) ) ) ) )).
fof(t83_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ! [D] : ( ( v1_finset_1(k1_relset_1(A,k2_partfun1(A,k1_numbers,B,k2_xboole_0(C,D)))) & r1_xboole_0(C,D) ) => k21_rfunct_3(A,B,k2_xboole_0(C,D)) = k2_xcmplx_0(k21_rfunct_3(A,B,C),k21_rfunct_3(A,B,D)) ) ) ) )).
fof(t83_rinfsup1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_comseq_2(B) => ( A = k6_rinfsup1(B) <=> ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_numbers) => ( ! [D] : ( v7_ordinal1(D) => ~ ! [E] : ( v7_ordinal1(E) => r1_xxreal_0(k2_xcmplx_0(A,C),k1_funct_1(B,k2_xcmplx_0(D,E))) ) ) & ? [D] : ( v7_ordinal1(D) & ! [E] : ( v7_ordinal1(E) => ~ r1_xxreal_0(k1_funct_1(B,k2_xcmplx_0(D,E)),k6_xcmplx_0(A,C)) ) ) ) ) ) ) ) ) ) )).
fof(t83_rlaffin1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(C))) => ( ( r2_hidden(D,G) & r2_hidden(E,G) & k3_rlvect_1(C,k1_rlvect_1(C,F,A),k1_rlvect_1(C,D,k6_xcmplx_0(1,A))) = k3_rlvect_1(C,k1_rlvect_1(C,F,B),k1_rlvect_1(C,E,k6_xcmplx_0(1,B))) ) => ( r2_hidden(F,k4_rlaffin1(C,G)) | A = 1 | ( A = B & D = E ) ) ) ) ) ) ) ) ) ) )).
fof(t83_rlvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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,k3_rlvect_1(A,B,C)) & k4_rlvect_1(A,k2_finseq_4(u1_struct_0(A),k4_algstr_0(A,C),k4_algstr_0(A,B))) = k4_algstr_0(A,k3_rlvect_1(A,B,C)) ) ) ) ) )).
fof(t83_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => ~ ( ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k2_finseq_1(A)) => r1_xxreal_0(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) & ? [D] : ( v7_ordinal1(D) & r2_hidden(D,k2_finseq_1(A)) & ~ r1_xxreal_0(k1_funct_1(C,D),k1_funct_1(B,D)) ) & r1_xxreal_0(k18_rvsum_1(C),k18_rvsum_1(B)) ) ) ) ) )).
fof(t83_scmfsa_2,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ~ v2_extpro_1(k17_scmfsa_2(B,A),k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(t83_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => k5_memstr_0(2,k1_scmpds_2,k6_scmpds_4(k8_scmpds_6(D,E,C),B,A)) = k1_nat_1(k5_card_1(C),2) ) ) ) ) ) )).
fof(t83_scmyciel,axiom,( ! [A] : ( ( v4_scmyciel(A) & v8_scmyciel(A) ) => k9_scmyciel(A) = k10_scmyciel(k6_scmyciel(A)) ) )).
fof(t83_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_analoaf(A,B,C,k2_semi_af1(A,B,D),k2_semi_af1(A,C,D)) ) ) ) ) )).
fof(t83_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k2_numbers) => ! [C] : ( m1_subset_1(C,k2_numbers) => ! [D] : ( m2_finseq_2(D,k2_numbers,k12_seq_4(A)) => k10_seq_4(D,k2_xcmplx_0(B,C)) = k13_seq_4(A,k18_seq_4(A,D,B),k18_seq_4(A,D,C)) ) ) ) ) )).
fof(t83_setlim_1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v2_prob_1(C) => ( v3_kurato_0(C,A) & k4_kurato_0(A,C) = k3_prob_1(A,C) ) ) ) ) )).
fof(t83_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => r1_tarski(k7_subset_1(A,B,k4_kurato_0(A,C)),k4_kurato_0(A,k7_setlim_2(A,C,B))) ) ) )).
fof(t83_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,C,B) = k5_sheffer1(A,B,C) ) ) ) )).
fof(t83_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_fdiff_1(k1_sin_cos6,k2_rcomp_1(k4_xcmplx_0(1),1)) & ~ ( ~ r1_xxreal_0(A,k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,A) & k1_fdiff_1(k1_sin_cos6,A) != k7_xcmplx_0(1,k3_square_1(k6_xcmplx_0(1,k1_square_1(A)))) ) ) ) )).
fof(t83_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(B,k2_rcomp_1(k4_xcmplx_0(1),1)) => ( r2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_sin_cos9,A),B) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => k1_funct_1(k2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_sin_cos9,A),B),C) = k7_xcmplx_0(A,k2_xcmplx_0(1,k1_square_1(C))) ) ) ) ) ) ) )).
fof(t83_sincos10,axiom,( v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k3_sincos10,k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1)))) )).
fof(t83_sprect_1,axiom,( ! [A] : ( ( v1_sprect_1(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)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,1) = k19_pscomp_1(k3_topreal1(2,A)) ) ) )).
fof(t83_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k1_substut1(A)) => r2_relset_1(k3_qc_lang1(A),k3_qc_lang1(A),k2_substut1(A,k7_substut1(A,C,k11_cqc_lang(A,C,B),D)),k7_subset_1(k2_zfmisc_1(k3_qc_lang1(A),k3_qc_lang1(A)),k2_substut1(A,D),k14_sublemma(A,k3_qc_lang1(A),k5_relset_1(k3_qc_lang1(A),k3_qc_lang1(A),k2_substut1(A,D),k15_sublemma(A,k11_cqc_lang(A,C,B))),k5_relset_1(k3_qc_lang1(A),k3_qc_lang1(A),k2_substut1(A,D),k16_sublemma(A,k11_cqc_lang(A,C,B),D))))) ) ) ) ) )).
fof(t83_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ( v1_tops_2(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => r1_tarski(C,k1_tops_1(A,k2_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)))) ) ) ) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v6_tops_1(C,A) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(D,B) => r1_tarski(D,C) ) ) ) => r1_tarski(k1_tops_1(A,k2_pre_topc(A,k5_setfam_1(u1_struct_0(A),B))),C) ) ) ) ) ) )).
fof(t83_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => g1_pre_topc(u1_struct_0(k5_tex_4(A,B)),u1_pre_topc(k5_tex_4(A,B))) = g1_pre_topc(u1_struct_0(k6_tex_4(A,k6_domain_1(u1_struct_0(A),B))),u1_pre_topc(k6_tex_4(A,k6_domain_1(u1_struct_0(A),B)))) ) ) )).
fof(t83_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ v2_struct_0(E) & m1_pre_topc(E,A) ) => ( ( m1_pre_topc(D,C) & m1_pre_topc(E,D) ) => ! [F] : ( ( 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)))) ) => ( ( v1_funct_1(k3_tmap_1(A,B,C,D,F)) & v1_funct_2(k3_tmap_1(A,B,C,D,F),u1_struct_0(D),u1_struct_0(B)) & v5_pre_topc(k3_tmap_1(A,B,C,D,F),D,B) & m1_subset_1(k3_tmap_1(A,B,C,D,F),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(D),u1_struct_0(B)))) ) => ( v1_funct_1(k3_tmap_1(A,B,C,E,F)) & v1_funct_2(k3_tmap_1(A,B,C,E,F),u1_struct_0(E),u1_struct_0(B)) & v5_pre_topc(k3_tmap_1(A,B,C,E,F),E,B) & m1_subset_1(k3_tmap_1(A,B,C,E,F),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(E),u1_struct_0(B)))) ) ) ) ) ) ) ) ) ) )).
fof(t83_topreal6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( 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(k7_subset_1(u1_struct_0(k15_euclid(A)),B,C),k15_euclid(A)) ) ) ) ) )).
fof(t83_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( ( r1_tarski(C,D) & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & v1_tops_1(C,A) ) => v1_tops_1(D,B) ) ) ) ) ) )).
fof(t83_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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] : ( ( 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(D,A) & v7_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) ) => ( r1_aff_1(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) ) ) ) ) ) ) ) )).
fof(t83_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ v2_struct_0(E) & m1_pre_topc(E,A) ) => ( ( m1_pre_topc(D,C) & m1_pre_topc(E,B) & r4_tsep_1(A,B,C) ) => ( r4_tsep_1(A,k1_tsep_1(A,B,D),k1_tsep_1(A,C,E)) & r4_tsep_1(A,k1_tsep_1(A,D,B),k1_tsep_1(A,E,C)) ) ) ) ) ) ) ) )).
fof(t83_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( v1_valued_2(C) => ! [D] : ( v1_valued_2(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [F] : ( ( 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) = k84_valued_2(B,A,D,C,F,E) ) ) ) ) )).
fof(t83_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ( v9_waybel_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_orders_2(A,B,C) => r1_orders_2(A,k7_waybel_1(A,C),k7_waybel_1(A,B)) ) ) ) ) ) )).
fof(t83_xboole_1,axiom,( ! [A] : ! [B] : ( r1_xboole_0(A,B) <=> k4_xboole_0(A,B) = A ) )).
fof(t83_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k10_xboolean(A,k4_xboolean(B,C)) = k4_xboolean(k5_xboolean(A,k4_xboolean(B,C)),k5_xboolean(k3_xboolean(A),k3_xboolean(k4_xboolean(B,C)))) ) ) ) )).
fof(t83_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => k7_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(C,D)) = k7_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(A,C),B),D) ) ) ) ) )).
fof(t83_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & ~ r1_xxreal_0(k3_xcmplx_0(A,B),C) & r1_xxreal_0(A,k7_xcmplx_0(C,B)) ) ) ) ) )).
fof(t83_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_tarski(k4_xxreal_1(C,D),k1_xxreal_1(A,B)) => ( r1_xxreal_0(D,C) | r1_tarski(k1_xxreal_1(C,D),k1_xxreal_1(A,B)) ) ) ) ) ) ) )).
fof(t83_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ( v6_xxreal_2(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( ~ r1_xxreal_0(B,k2_xxreal_2(A)) & ~ r1_xxreal_0(k1_xxreal_2(A),B) & ~ r2_hidden(B,A) ) ) ) ) )).
fof(t83_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & A != k1_xxreal_0 & k6_xxreal_3(k1_xxreal_0,A) != k1_xxreal_0 ) ) )).
fof(t83_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => k29_zf_lang(k7_zf_lang(B,A)) = k2_xboole_0(k2_xboole_0(k29_zf_lang(B),k29_zf_lang(A)),k1_tarski(k7_zf_lang(B,A))) ) ) )).
fof(t83_zf_lang1,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ~ v1_xboole_0(C) => ( r2_zf_model(C,k6_zf_lang(k5_zf_lang(A,B))) <=> ( A = B | ! [D] : ( r2_hidden(D,C) => r1_xboole_0(D,C) ) ) ) ) ) ) )).
fof(t83_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ~ ( r1_tarski(B,k2_zfmisc_1(C,D)) & r2_hidden(A,B) & ! [E] : ! [F] : ~ ( r2_hidden(E,C) & r2_hidden(F,D) & A = k4_tarski(E,F) ) ) )).
fof(t83_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => m2_zmodul01(u1_struct_0(B),A,B) ) ) )).
fof(t84_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m3_abcmiz_1(B,A) => ! [C] : ( ( v8_abcmiz_1(C,A) & m1_abcmiz_1(C,A,k13_abcmiz_1(A)) ) => ! [D] : ( ( v8_abcmiz_1(D,A) & m1_abcmiz_1(D,A,k13_abcmiz_1(A)) ) => k43_abcmiz_1(A,k43_abcmiz_1(A,B,D),C) = k43_abcmiz_1(A,k43_abcmiz_1(A,B,C),D) ) ) ) ) )).
fof(t84_afinsq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( k1_funct_1(k16_afinsq_1(A,B,C,D),k5_numbers) = A & k1_funct_1(k16_afinsq_1(A,B,C,D),1) = B & k1_funct_1(k16_afinsq_1(A,B,C,D),2) = C & k1_funct_1(k16_afinsq_1(A,B,C,D),3) = D ) )).
fof(t84_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(C)) => ! [E] : ( m1_subset_1(E,C) => ! [F] : ( m1_aofa_000(F,A,C,D) => ( r2_hidden(E,D) => ( ( r4_aofa_000(A,B,C,E,D,F) => r4_aofa_000(A,B,C,k2_binop_1(C,u1_struct_0(A),C,F,E,B),D,F) ) & ( r4_aofa_000(A,B,C,k2_binop_1(C,u1_struct_0(A),C,F,E,B),D,F) => r4_aofa_000(A,B,C,E,D,F) ) & k20_aofa_000(A,B,C,E,D,F) = k3_supinf_2(k8_mesfunc1,k20_aofa_000(A,B,C,k2_binop_1(C,u1_struct_0(A),C,F,E,B),D,F)) ) ) ) ) ) ) ) ) )).
fof(t84_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & v22_aofa_a00(D,A,1,1,11) & l3_msualg_1(D,A) ) => ! [E] : ( ( v19_aofa_a00(E,A) & m1_subset_1(E,u1_struct_0(A)) ) => ! [F] : ( m2_pboole(F,u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,D)) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),k37_aofa_a00(A))) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),E)) => ! [I] : ( m1_subset_1(I,k1_funct_1(u3_msualg_1(A,C),E)) => k15_aofa_a00(A,B,C,D,k37_aofa_a00(A),k40_aofa_a00(A,C,G,E,H,I),F) = k40_aofa_a00(A,D,k15_aofa_a00(A,B,C,D,k37_aofa_a00(A),G,F),E,k15_aofa_a00(A,B,C,D,E,H,F),k15_aofa_a00(A,B,C,D,E,I,F)) ) ) ) ) ) ) ) ) ) )).
fof(t84_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ( A = k11_arytm_3 <=> k9_arytm_3(A,B) = B ) ) ) )).
fof(t84_asympt_1,axiom,( ? [A] : ( m1_subset_1(A,k4_ordinal1) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( r1_xxreal_0(A,B) & r1_xxreal_0(k6_xcmplx_0(B,k3_xcmplx_0(k3_square_1(B),k3_power(2,B))),k7_xcmplx_0(B,2)) ) ) ) )).
fof(t84_bcialg_1,axiom,( ! [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) ) => ( v16_bcialg_1(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_1(A,B,C) = k1_bcialg_1(A,k1_bcialg_1(A,k1_bcialg_1(A,B,C),C),k2_bcialg_1(A,C)) ) ) ) ) )).
fof(t84_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( ( v3_funct_1(E) & m1_borsuk_2(E,A,B,B) ) => ( r1_borsuk_6(A,B,C) => r3_borsuk_2(A,B,B,k1_borsuk_2(A,B,C,B,D,k2_borsuk_2(A,B,C,D)),E) ) ) ) ) ) ) )).
fof(t84_card_2,axiom,( ! [A] : ! [B] : ( ( v4_card_3(A) & v4_card_3(B) ) => v4_card_3(k2_xboole_0(A,B)) ) )).
fof(t84_card_3,axiom,( ! [A] : ( ~ ( ~ v1_finset_1(A) & ! [B] : ~ ( r1_tarski(B,A) & k1_card_1(B) = k4_ordinal1 ) ) & ~ ( ? [B] : ( r1_tarski(B,A) & k1_card_1(B) = k4_ordinal1 ) & v1_finset_1(A) ) ) )).
fof(t84_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ( v13_cat_1(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k10_xtuple_0(k11_cat_1(A,B,C,D,E)) = k2_cat_1(B,k8_cat_1(A,B,C,D),k8_cat_1(A,B,C,E)) ) ) ) ) ) ) )).
fof(t84_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ! [F] : ( m1_cat_1(F,A,B,C) => ( ( r4_cat_3(A,B,D,E) & k3_graph_1(A,F) = B & k4_graph_1(A,F) = C & v9_cat_1(F,A,B,C) ) => r4_cat_3(A,C,k1_cat_1(A,D,F),k1_cat_1(A,E,F)) ) ) ) ) ) ) ) )).
fof(t84_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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) ) ) ) )).
fof(t84_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v5_glib_001(B,A) & m3_glib_001(B,A) ) => ( ? [C] : ( v7_ordinal1(C) & ~ v1_abian(C) & ? [D] : ( v7_ordinal1(D) & ~ v1_abian(D) & ~ r1_xxreal_0(D,k1_nat_1(C,2)) & r1_xxreal_0(D,k3_finseq_1(B)) & ? [E] : r1_glib_000(A,k1_funct_1(B,C),k1_funct_1(B,D),E) & ( v8_glib_001(B,A) => ( ~ ( C = 1 & D = k3_finseq_1(B) ) & ~ ( C = 1 & D = k6_xcmplx_0(k3_finseq_1(B),2) ) & ~ ( C = 3 & D = k3_finseq_1(B) ) ) ) ) ) => v5_chord(B,A) ) ) ) )).
fof(t84_classes1,axiom,( ! [A] : ! [B] : ( r2_hidden(k6_classes1(A),k6_classes1(k4_tarski(A,B))) & r2_hidden(k6_classes1(B),k6_classes1(k4_tarski(A,B))) ) )).
fof(t84_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_clvect_1(D,A) => ( ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_hidden(B,k5_clvect_1(A,E,D)) & r2_hidden(C,k5_clvect_1(A,E,D)) ) <=> r1_struct_0(D,k5_algstr_0(A,B,C)) ) ) ) ) ) )).
fof(t84_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( m2_valued_0(C,u1_struct_0(A),B) & v1_clvect_2(B,A) ) => k1_clvect_2(A,C) = k1_clvect_2(A,B) ) ) ) ) )).
fof(t84_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ! [D] : ( r2_hidden(k14_cohsp_1(C,D),k15_cohsp_1(A,B)) <=> ( r2_hidden(C,A) & r2_hidden(D,B) ) ) ) ) )).
fof(t84_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k6_xcmplx_0(A,B) = k2_xcmplx_0(k5_real_1(k3_complex1(A),k3_complex1(B)),k3_xcmplx_0(k5_real_1(k4_complex1(A),k4_complex1(B)),k7_complex1)) ) ) )).
fof(t84_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( k4_complex2(A,B,C) = k28_sin_cos => ( A = B | B = C | ( k4_complex2(B,C,A) = k5_numbers & k4_complex2(C,A,B) = k5_numbers ) ) ) ) ) ) )).
fof(t84_convex4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m2_convex4(D,A,k7_domain_1(u1_struct_0(A),B,C)) => ( v3_convex4(D,A) => ( B = C | ( ? [E] : ( v1_xreal_0(E) & ? [F] : ( v1_xreal_0(F) & E = k3_funct_2(u1_struct_0(A),k2_numbers,D,B) & F = k3_funct_2(u1_struct_0(A),k2_numbers,D,C) & r1_xxreal_0(k5_numbers,E) & r1_xxreal_0(k5_numbers,F) ) ) & 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))) ) ) ) ) ) ) ) )).
fof(t84_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => v2_cqc_the1(k8_cqc_lang(A,k8_cqc_lang(A,B,k12_cqc_lang(A,D,C)),k12_cqc_lang(A,D,k8_cqc_lang(A,B,C))),A) ) ) ) ) )).
fof(t84_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k18_sin_cos),D) ) & r2_hidden(k2_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k26_sin_cos)) & r2_hidden(k6_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k26_sin_cos)) ) => k1_funct_1(k5_diff_1(C,A),B) = k6_xcmplx_0(k17_sin_cos(k2_xcmplx_0(B,k7_xcmplx_0(A,2))),k17_sin_cos(k6_xcmplx_0(B,k7_xcmplx_0(A,2)))) ) ) ) ) )).
fof(t84_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : k7_enumset1(A,B,C,D,E,F,G,H,I) = k2_xboole_0(k6_enumset1(A,B,C,D,E,F,G,H),k1_tarski(I)) )).
fof(t84_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => k7_euclid_8(A,B,C) = k7_euclid_8(B,C,A) ) ) ) )).
fof(t84_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(A)) => ( r2_hidden(C,k4_euclidlp(A,D,E,F)) => ( ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ~ ( k2_xcmplx_0(k2_xcmplx_0(G,H),I) = k5_numbers & C = k7_euclid(A,k7_euclid(A,k9_euclid(A,D,G),k9_euclid(A,E,H)),k9_euclid(A,F,I)) ) ) ) ) | r2_hidden(k5_euclid(A),k4_euclidlp(A,D,E,F)) ) ) ) ) ) ) ) ) )).
fof(t84_exchsort,axiom,( ! [A] : ( ( v3_ordinal1(A) & v1_finset_1(A) ) => ! [B] : ~ ( r2_hidden(B,A) & B != k5_numbers & ! [C] : ( v3_ordinal1(C) => B != k1_ordinal1(C) ) ) ) )).
fof(t84_facirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t84_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( ~ v2_struct_0(A) & v10_lattices(A) & v15_lattices(A) & v16_lattices(A) & l3_lattices(A) & v12_lattices(A) & r3_lattices(A,B,C) ) => ( ~ v2_struct_0(k10_filter_2(A,k9_filter_2(A,B,C))) & v10_lattices(k10_filter_2(A,k9_filter_2(A,B,C))) & v15_lattices(k10_filter_2(A,k9_filter_2(A,B,C))) & v16_lattices(k10_filter_2(A,k9_filter_2(A,B,C))) & l3_lattices(k10_filter_2(A,k9_filter_2(A,B,C))) ) ) ) ) ) )).
fof(t84_finseq_1,axiom,( ! [A] : ( v3_finseq_1(A) => ? [B] : ( ~ v1_xboole_0(B) & r1_tarski(A,k13_finseq_1(B)) ) ) )).
fof(t84_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,B) => ! [F] : ( ( 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))) ) => ! [G] : ( m2_finseq_1(G,A) => ( G = k12_finseq_1(A,D) => k4_funcop_1(F,G,E) = k12_finseq_1(C,k2_binop_1(A,B,C,F,D,E)) ) ) ) ) ) ) ) ) )).
fof(t84_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : ( m2_finseq_1(A,C) => m2_finseq_1(k1_finseq_3(A,B),C) ) ) )).
fof(t84_finseq_4,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( v1_partfun1(C,A) & v3_relat_2(C) & v8_relat_2(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( k8_eqrel_1(A,B) = k8_eqrel_1(A,C) => B = C ) ) ) )).
fof(t84_finseq_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ( ( 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)) ) ) ) ) )).
fof(t84_finseq_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_finseq_1(D,C) => ( k2_xcmplx_0(A,B) = k3_finseq_1(D) => k4_finseq_5(C,k2_rfinseq(C,B,D)) = k17_finseq_1(C,A,k4_finseq_5(C,D)) ) ) ) ) ) )).
fof(t84_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,A,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( ( v2_binop_1(D,A) & v1_setwiseo(D,A) & v1_binop_1(D,A) & v1_finseqop(D,A) & r2_funct_2(A,A,E,k5_finseqop(A,D)) ) => ( k3_funct_2(A,A,E,k5_binop_1(A,k7_finseqop(A,D,k6_partfun1(A),E),B,C)) = k5_binop_1(A,k7_finseqop(A,D,E,k6_partfun1(A)),B,C) & k5_binop_1(A,k7_finseqop(A,D,k6_partfun1(A),E),B,C) = k3_funct_2(A,A,E,k5_binop_1(A,k7_finseqop(A,D,E,k6_partfun1(A)),B,C)) ) ) ) ) ) ) ) )).
fof(t84_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ( k2_flang_2(A,B) = k4_flang_1(A,k2_flang_1(A)) <=> ( B = k1_xboole_0 | B = k4_flang_1(A,k2_flang_1(A)) ) ) ) )).
fof(t84_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(C,k5_numbers) => r1_tarski(k1_flang_3(A,B,C),k2_flang_3(A,B)) ) ) ) )).
fof(t84_funcop_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(A,k9_xtuple_0(B)) => r1_tarski(k16_funcop_1(A,k1_funct_1(B,A)),B) ) ) )).
fof(t84_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( v2_funct_1(B) => k8_relat_1(B,A) = k7_relat_1(k2_funct_1(B),A) ) ) )).
fof(t84_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) => k5_partfun1(A,B,k3_partfun1(C,A,B)) = k1_tarski(C) ) ) )).
fof(t84_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ( 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 ) ) ) )).
fof(t84_funct_7,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => k8_funct_7(k8_funct_7(D,B),C) = k8_funct_7(D,k3_xcmplx_0(B,C)) ) ) ) )).
fof(t84_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & k1_funct_1(k16_sin_cos,B) = k5_numbers ) ) => r2_funct_8(A,k1_numbers,k1_numbers,k2_fdiff_9) ) ) )).
fof(t84_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v2_struct_0(C) & v3_group_1(C) & v5_group_1(C) & v4_vectsp_1(C) & l6_algstr_0(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => k3_group_4(C,k5_finseq_2(u1_struct_0(C),k3_xcmplx_0(A,B),D)) = k3_group_4(C,k5_finseq_2(u1_struct_0(C),B,k3_group_4(C,k5_finseq_2(u1_struct_0(C),A,D)))) ) ) ) ) )).
fof(t84_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k31_gfacirc1(A,B,C),k32_gfacirc1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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),k3_gfacirc1)) & G = k1_funct_1(D,k4_tarski(k10_finseq_1(C,A),k4_twoscomp)) ) => k1_twoscomp(k31_gfacirc1(A,B,C),k32_gfacirc1(A,B,C),k6_circuit2(k31_gfacirc1(A,B,C),k32_gfacirc1(A,B,C),D),k33_gfacirc1(A,B,C)) = k9_margrel1(k1_binarith(k1_binarith(E,F),G)) ) ) ) ) ) )).
fof(t84_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(B)) => ~ ( C = D & v11_glib_000(C,A) & ~ v11_glib_000(D,B) & ~ v10_glib_000(D,B) ) ) ) ) ) )).
fof(t84_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m3_glib_001(D,B) => ( C = D => k12_glib_001(A,C) = k12_glib_001(B,D) ) ) ) ) ) )).
fof(t84_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ~ ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) & 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_0(u1_struct_0(k15_euclid(2)),C,A,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),1)),k7_xcmplx_0(1,2)),k19_euclid(k5_numbers,1)),B),k1_tops_1(k15_euclid(2),k3_goboard5(C,A,k5_numbers))) ) ) ) ) )).
fof(t84_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,A) => r1_group_2(A,k10_group_2(A,k10_group_2(A,B,C),D),k10_group_2(A,B,k10_group_2(A,C,D))) ) ) ) ) )).
fof(t84_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(B,k7_group_3(A,C)) => r2_hidden(C,k7_group_3(A,B)) ) ) ) ) )).
fof(t84_group_9,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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] : ( ( v1_funct_1(E) & v1_funct_2(E,A,k1_funct_2(C,C)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_funct_2(C,C)))) ) => ! [F] : ( m2_finseq_1(F,A) => ( ( r1_tarski(B,C) & ! [G] : ( m1_subset_1(G,A) => ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,B,B) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) => ! [I] : ( ( v1_funct_1(I) & v1_funct_2(I,C,C) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(C,C))) ) => ( ( H = k1_funct_1(D,G) & I = k1_funct_1(E,G) ) => H = k2_partfun1(C,C,I,B) ) ) ) ) ) => k2_group_9(A,B,D,F) = k2_partfun1(C,C,k2_group_9(A,C,E,F),B) ) ) ) ) )).
fof(t84_ideal_1,axiom,( ! [A] : ( ( ~ 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) & v5_vectsp_1(A) & v6_vectsp_1(A) & v1_algstr_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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))) ) => ( r4_ideal_1(A,B,C) => k15_ideal_1(A,B,C) = k13_ideal_1(A,B,C) ) ) ) ) )).
fof(t84_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( A = k1_rcomp_1(k2_xcmplx_0(B,k3_xcmplx_0(k2_nat_1(2,C),k28_sin_cos)),k2_xcmplx_0(B,k3_xcmplx_0(k1_nat_1(k2_nat_1(2,C),1),k28_sin_cos))) => k2_integra5(A,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)) = k2_xcmplx_0(k3_xcmplx_0(2,k19_sin_cos(B)),k3_xcmplx_0(2,k17_sin_cos(B))) ) ) ) ) )).
fof(t84_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => r2_hidden(k3_intpro_1(k6_intpro_1(k3_intpro_1(B,C)),k3_intpro_1(k6_intpro_1(B),k6_intpro_1(C))),k13_intpro_1(A)) ) ) ) )).
fof(t84_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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) = F & k18_euclid(D) = G & r1_xxreal_0(G,k18_euclid(A)) & ~ r1_xxreal_0(k18_euclid(B),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),E) & r1_xxreal_0(k17_euclid(D),F) & k1_funct_1(I,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t84_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( ( r2_hidden(D,k17_pscomp_1(B)) & r2_hidden(C,k9_subset_1(u1_struct_0(k15_euclid(2)),k6_topreal1(D),k3_topreal1(2,k2_jordan9(B,A)))) ) => k18_euclid(C) = k9_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))) ) ) ) ) ) )).
fof(t84_jordan2c,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v1_xreal_0(C) => ( ( k17_euclid(A) = k18_euclid(B) & k4_xcmplx_0(k18_euclid(A)) = k17_euclid(B) & A = k1_rlvect_1(k15_euclid(2),B,C) ) => ( k17_euclid(A) = k5_numbers & k18_euclid(A) = k5_numbers & A = k4_struct_0(k15_euclid(2)) ) ) ) ) ) )).
fof(t84_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v3_limfunc1(A) & k8_relat_1(A,k1_tarski(k5_numbers)) = k1_xboole_0 ) => ( k4_limfunc1(A) = k5_numbers | ( v3_limfunc1(k6_rfunct_1(k1_numbers,k1_numbers,A)) & k4_limfunc1(k6_rfunct_1(k1_numbers,k1_numbers,A)) = k5_xcmplx_0(k4_limfunc1(A)) ) ) ) ) )).
fof(t84_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( ( v2_matrix10(B) & r2_matrix10(C,D) ) => r1_matrix10(C,k5_matrix10(A,D,B)) ) ) ) ) ) )).
fof(t84_matrix13,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => k8_matrix13(A,B) = k8_matrix13(A,k4_matrix_0(u1_struct_0(A),B)) ) ) )).
fof(t84_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( v1_matrixr2(B,A) => k7_matrixr2(A,k7_matrixr2(A,B)) = B ) ) ) )).
fof(t84_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => k12_member_1(A,k4_member_1(B)) = k4_member_1(k12_member_1(A,B)) ) ) )).
fof(t84_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ( ( v6_supinf_2(D) & E = k1_relset_1(A,D) & r1_mesfunc1(A,B,D,E) & k12_supinf_2(C,F) = k5_numbers ) => k6_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,k7_prob_1(A,B,E,F))) = k6_mesfunc5(A,B,C,D) ) ) ) ) ) ) ) )).
fof(t84_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( v6_supinf_2(D) => ( ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ~ ( E = k1_relset_1(A,D) & r1_mesfunc6(A,B,D,E) ) ) | r1_xxreal_0(k5_numbers,k1_mesfunc6(A,B,C,D)) ) ) ) ) ) ) )).
fof(t84_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( ( 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)) & v1_ncfcont1(C,A) & r8_ncfcont1(A,B,D,C) ) => v1_nfcont_1(k7_relset_1(u1_struct_0(A),u1_struct_0(B),D,C),B) ) ) ) ) ) )).
fof(t84_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => k1_newton(k5_numbers,A) = k5_numbers ) ) )).
fof(t84_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v13_o_ring_1(B,A) & v5_o_ring_1(C,A) ) => v13_o_ring_1(k6_algstr_0(A,B,C),A) ) ) ) ) )).
fof(t84_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => k2_wellord1(A,k1_xboole_0) = k1_xboole_0 ) )).
fof(t84_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => r6_pboole(A,k5_pboole(A,B,k1_pboole(A)),B) ) )).
fof(t84_pdiff_5,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( r9_pdiff_5(A,B) => r1_fcont_1(k1_pdiff_2(3,3,k1_pdiff_3(3,3,A),B),k3_funct_2(k1_euclid(3),k1_numbers,k1_pdiff_1(3,3),B)) ) ) ) )).
fof(t84_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ( k7_polyform(A) = 2 => k16_rvsum_1(k29_polyform(A)) = k6_xcmplx_0(k11_polyform(A,k5_numbers),k11_polyform(A,1)) ) ) )).
fof(t84_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(A,1) & r1_xxreal_0(B,C) ) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(k6_prepower(A,C),k6_prepower(A,B)) ) ) ) ) ) )).
fof(t84_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( r2_hidden(B,k15_qc_lang2(A,C)) => r1_tarski(k15_qc_lang2(A,B),k15_qc_lang2(A,C)) ) ) ) ) )).
fof(t84_quatern3,axiom,( k4_quatern3(k3_quatern2) = k24_quaterni(k3_quatern2) )).
fof(t84_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ( k28_quaterni(k25_quaterni(A,B)) = k5_numbers <=> A = B ) ) ) )).
fof(t84_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => r1_tarski(k3_relat_1(k6_relat_1(A,C),B),k3_relat_1(C,B)) ) ) )).
fof(t84_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_afinsq_1(D))) => ! [F] : ( ( ~ v2_struct_0(F) & l1_rewrite3(F,E) ) => ( r1_rewrite3(E,F,A,B,C) => r3_rewrite3(D,E,F,A,B,C,k2_flang_1(D)) ) ) ) ) )).
fof(t84_rfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_valued_0(D) ) => ( ( v1_comseq_2(k5_relat_1(C,A)) & v1_comseq_2(k5_relat_1(D,B)) ) => ( v1_comseq_2(k5_relat_1(k18_valued_1(C,D),k3_xboole_0(A,B))) & v1_comseq_2(k5_relat_1(k45_valued_1(C,D),k3_xboole_0(A,B))) ) ) ) ) )).
fof(t84_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ! [D] : ( ( v1_finset_1(k1_relset_1(A,k2_partfun1(A,k1_numbers,B,k2_xboole_0(C,D)))) & r1_xboole_0(k1_relset_1(A,k2_partfun1(A,k1_numbers,B,C)),k1_relset_1(A,k2_partfun1(A,k1_numbers,B,D))) ) => k21_rfunct_3(A,B,k2_xboole_0(C,D)) = k2_xcmplx_0(k21_rfunct_3(A,B,C),k21_rfunct_3(A,B,D)) ) ) ) )).
fof(t84_rinfsup1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_comseq_2(B) => ( r1_xxreal_0(A,k5_rinfsup1(B)) <=> ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_numbers) => ! [D] : ( v7_ordinal1(D) => ~ ! [E] : ( v7_ordinal1(E) => r1_xxreal_0(k1_funct_1(B,k2_xcmplx_0(D,E)),k6_xcmplx_0(A,C)) ) ) ) ) ) ) ) ) )).
fof(t84_rlaffin1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( ( v1_rlaffin1(F,B) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B))) ) => ( ( r2_hidden(C,F) & r2_hidden(D,k4_rlaffin1(B,F)) & r2_hidden(E,k4_rlaffin1(B,k7_subset_1(u1_struct_0(B),F,k6_domain_1(u1_struct_0(B),C)))) & D = k3_rlvect_1(B,k1_rlvect_1(B,C,A),k1_rlvect_1(B,E,k6_xcmplx_0(1,A))) ) => A = k3_funct_2(u1_struct_0(B),k1_numbers,k5_rlaffin1(B,F,D),C) ) ) ) ) ) ) ) )).
fof(t84_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ( ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => r1_xxreal_0(k5_numbers,k1_funct_1(A,B)) ) ) => r1_xxreal_0(k5_numbers,k16_rvsum_1(A)) ) ) )).
fof(t84_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ( A = k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0) => v2_extpro_1(A,k7_card_1(3),k1_scmfsa_2) ) ) )).
fof(t84_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( r1_xxreal_0(k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),F)),k5_numbers) => k1_funct_1(k6_scmpds_4(k8_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) ) ) ) ) ) ) ) )).
fof(t84_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => r1_tarski(A,k12_scmyciel(A)) ) )).
fof(t84_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_semi_af1(A,B,B) = B ) ) )).
fof(t84_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k2_numbers) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => ! [D] : ( m2_finseq_2(D,k2_numbers,k12_seq_4(A)) => k18_seq_4(A,k13_seq_4(A,C,D),B) = k13_seq_4(A,k18_seq_4(A,C,B),k18_seq_4(A,D,B)) ) ) ) ) )).
fof(t84_setlim_1,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_setlim_1(C,A) => v3_kurato_0(C,A) ) ) ) )).
fof(t84_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k4_kurato_0(A,k8_setlim_2(A,C,B)) = k7_subset_1(A,k4_kurato_0(A,C),B) ) ) )).
fof(t84_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,k5_sheffer1(A,C,B),k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,B)))) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,B)),C),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,B)),C)) ) ) ) )).
fof(t84_sin_cos6,axiom,( v1_fcont_1(k5_relset_1(k1_numbers,k1_numbers,k1_sin_cos6,k1_rcomp_1(k4_xcmplx_0(1),1))) )).
fof(t84_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(B,k2_rcomp_1(k4_xcmplx_0(1),1)) => ( r2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k2_sin_cos9,A),B) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => k1_funct_1(k2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k2_sin_cos9,A),B),C) = k4_xcmplx_0(k7_xcmplx_0(A,k2_xcmplx_0(1,k1_square_1(C)))) ) ) ) ) ) ) )).
fof(t84_sincos10,axiom,( v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k4_sincos10,k1_rcomp_1(1,k3_square_1(2)))) )).
fof(t84_sprect_1,axiom,( ! [A] : ( ( v1_sprect_1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,2) = k21_pscomp_1(k3_topreal1(2,A)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,2) = k22_pscomp_1(k3_topreal1(2,A)) ) ) )).
fof(t84_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k1_substut1(A)) => r1_xboole_0(k1_relset_1(k3_qc_lang1(A),k2_substut1(A,k7_substut1(A,C,B,D))),k4_subset_1(k3_qc_lang1(A),k1_relset_1(k3_qc_lang1(A),k5_relset_1(k3_qc_lang1(A),k3_qc_lang1(A),k2_substut1(A,D),k15_sublemma(A,B))),k1_relset_1(k3_qc_lang1(A),k5_relset_1(k3_qc_lang1(A),k3_qc_lang1(A),k2_substut1(A,D),k16_sublemma(A,B,D))))) ) ) ) ) )).
fof(t84_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,B) => r1_tarski(k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B)),C) ) ) & ( B = k1_xboole_0 | ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v6_tops_1(C,A) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(D,B) => r1_tarski(C,D) ) ) ) => r1_tarski(C,k1_tops_1(A,k6_setfam_1(u1_struct_0(A),B))) ) ) ) ) ) ) )).
fof(t84_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( r1_tarski(B,C) => m1_pre_topc(k6_tex_4(A,B),k6_tex_4(A,C)) ) ) ) ) )).
fof(t84_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,u1_struct_0(B)) => k1_funct_1(k4_tmap_1(A,B),C) = C ) ) ) ) )).
fof(t84_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k14_euclid(2))) => ( ( E = k19_euclid(A,C) & F = k19_euclid(B,D) ) => k3_metric_1(k14_euclid(2),E,F) = k3_square_1(k2_xcmplx_0(k1_square_1(k6_xcmplx_0(A,B)),k1_square_1(k6_xcmplx_0(C,D)))) ) ) ) ) ) ) ) )).
fof(t84_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( ( r1_tarski(D,C) & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & v3_tops_1(C,A) ) => v3_tops_1(D,B) ) ) ) ) ) )).
fof(t84_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( ( 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) & 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) ) ) ) ) ) )).
fof(t84_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( ~ r1_tsep_1(C,D) => ( ( ( r4_tsep_1(A,C,B) & r4_tsep_1(A,D,B) ) => r4_tsep_1(A,k2_tsep_1(A,C,D),B) ) & ( ( r4_tsep_1(A,B,C) & r4_tsep_1(A,B,D) ) => r4_tsep_1(A,B,k2_tsep_1(A,C,D)) ) ) ) ) ) ) ) )).
fof(t84_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v1_valued_2(D) => ! [E] : ( v1_valued_2(E) => ! [F] : ( v1_valued_2(F) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,D))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(B,E))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(C,F))) ) => k84_valued_2(k3_xboole_0(A,B),C,k2_valued_2(k3_xboole_0(k1_valued_2(D),k1_valued_2(E))),F,k84_valued_2(A,B,D,E,G,H),I) = k84_valued_2(A,k3_xboole_0(B,C),D,k2_valued_2(k3_xboole_0(k1_valued_2(E),k1_valued_2(F))),G,k84_valued_2(B,C,E,F,H,I)) ) ) ) ) ) ) )).
fof(t84_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ( v9_waybel_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k7_waybel_1(A,k10_lattice3(A,B,C)) = k11_lattice3(A,k7_waybel_1(A,B),k7_waybel_1(A,C)) ) ) ) ) )).
fof(t84_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( ~ r1_xboole_0(A,B) & r1_xboole_0(A,C) & r1_xboole_0(A,k4_xboole_0(B,C)) ) )).
fof(t84_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k10_xboolean(k3_xboolean(A),k6_xboolean(A,B)) = k4_xboolean(A,B) ) ) )).
fof(t84_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t84_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(k3_xcmplx_0(A,B),C) & r1_xxreal_0(k7_xcmplx_0(C,B),A) ) ) ) ) )).
fof(t84_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ~ r1_xxreal_0(C,B) => r1_tarski(k2_xxreal_1(C,A),k4_xxreal_1(B,A)) ) ) ) ) )).
fof(t84_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ( ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r2_hidden(B,A) & r2_hidden(C,A) ) => ( r1_xxreal_0(D,B) | r1_xxreal_0(C,D) | r2_hidden(D,A) ) ) ) ) ) => v6_xxreal_2(A) ) ) )).
fof(t84_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ~ ( ~ r1_xxreal_0(k5_numbers,A) & k2_xxreal_0 != A & k6_xxreal_3(k2_xxreal_0,A) != k1_xxreal_0 ) ) )).
fof(t84_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => k29_zf_lang(k8_zf_lang(A,B)) = k2_xboole_0(k29_zf_lang(B),k1_tarski(k8_zf_lang(A,B))) ) ) )).
fof(t84_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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))) ) => ( v2_zf_lang(A) => ( r1_zf_model(B,C,A) <=> k3_funct_2(k1_zf_lang,B,C,k18_zf_lang(A)) = k3_funct_2(k1_zf_lang,B,C,k19_zf_lang(A)) ) ) ) ) ) )).
fof(t84_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ~ ( r2_hidden(A,k3_xboole_0(k2_zfmisc_1(B,D),k2_zfmisc_1(C,E))) & ! [F] : ! [G] : ~ ( A = k4_tarski(F,G) & r2_hidden(F,k3_xboole_0(B,C)) & r2_hidden(G,k3_xboole_0(D,E)) ) ) )).
fof(t84_zmodul01,axiom,( ! [A] : ( ( ~ 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) ) => m2_zmodul01(u1_struct_0(A),A,k4_zmodul01(A)) ) )).
fof(t85_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => k1_abcmiz_1(k46_abcmiz_1(A,B)) = k46_abcmiz_1(A,B) ) ) )).
fof(t85_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(C)) => ! [E] : ( m1_subset_1(E,C) => ! [F] : ( m1_aofa_000(F,A,C,D) => r1_xxreal_0(k5_numbers,k20_aofa_000(A,B,C,E,D,F)) ) ) ) ) ) ) )).
fof(t85_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & v22_aofa_a00(D,A,1,1,11) & l3_msualg_1(D,A) ) => ! [E] : ( ( v19_aofa_a00(E,A) & m1_subset_1(E,u1_struct_0(A)) ) => ! [F] : ( m2_pboole(F,u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,D)) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),k37_aofa_a00(A))) => k15_aofa_a00(A,B,C,D,E,k38_aofa_a00(A,C,G,E),F) = k38_aofa_a00(A,D,k15_aofa_a00(A,B,C,D,k37_aofa_a00(A),G,F),E) ) ) ) ) ) ) ) )).
fof(t85_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( m1_subset_1(C,k5_arytm_3) => ! [D] : ( m1_subset_1(D,k5_arytm_3) => ( ( k9_arytm_3(A,B) = k9_arytm_3(C,D) & r3_arytm_3(A,C) ) => r3_arytm_3(D,B) ) ) ) ) ) )).
fof(t85_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => k9_nat_1(k1_numbers,A,B) = k2_power(k2_xcmplx_0(1,k7_xcmplx_0(1,k1_nat_1(B,1))),k1_nat_1(B,1)) ) => v7_valued_0(A) ) ) )).
fof(t85_bcialg_1,axiom,( ! [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) ) => ( ( ~ 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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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,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)) ) ) ) ) )).
fof(t85_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,B,C) => ! [E] : ( ( v3_funct_1(E) & m1_borsuk_2(E,A,B,B) ) => r4_borsuk_2(A,B,B,k1_borsuk_2(A,B,C,B,D,k2_borsuk_2(A,B,C,D)),E) ) ) ) ) ) )).
fof(t85_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r1_ordinal1(k1_card_1(k9_xtuple_0(C)),A) & ! [D] : ( r2_hidden(D,k9_xtuple_0(C)) => r1_ordinal1(k1_card_1(k1_funct_1(C,D)),B) ) ) => r1_ordinal1(k1_card_1(k3_card_3(C)),k2_card_2(A,B)) ) ) ) ) )).
fof(t85_card_3,axiom,( ! [A] : ! [B] : ( k1_card_1(A) = k1_card_1(B) <=> k2_card_1(A) = k2_card_1(B) ) )).
fof(t85_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ( v14_cat_1(C,A,B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => v2_funct_1(k11_cat_1(A,B,C,D,E)) ) ) ) ) ) ) )).
fof(t85_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ( ( r4_cat_3(A,B,C,D) & v11_cat_1(k3_graph_1(A,D),A) ) => r1_cat_1(A,k3_graph_1(A,C),B) ) ) ) ) ) )).
fof(t85_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ( r5_glib_000(A,B) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m3_glib_001(D,B) => ( ( C = D & v5_chord(C,A) ) => v5_chord(D,B) ) ) ) ) ) ) )).
fof(t85_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_clvect_1(D,A) => ~ ( k5_clvect_1(A,C,D) = k5_clvect_1(A,B,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r1_struct_0(D,E) & k3_rlvect_1(A,C,E) = B ) ) ) ) ) ) ) )).
fof(t85_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v2_clvect_2(B,A) & m2_valued_0(C,u1_struct_0(A),B) ) => v2_clvect_2(C,A) ) ) ) ) )).
fof(t85_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => k3_tarski(k15_cohsp_1(A,B)) = k14_cohsp_1(k3_tarski(A),k3_tarski(B)) ) ) )).
fof(t85_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k5_xcmplx_0(A) = k2_xcmplx_0(k7_xcmplx_0(k3_complex1(A),k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A)))),k3_xcmplx_0(k7_xcmplx_0(k1_real_1(k4_complex1(A)),k2_xcmplx_0(k1_square_1(k3_complex1(A)),k1_square_1(k4_complex1(A)))),k7_complex1)) ) )).
fof(t85_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ~ ( A != B & A != C & B != C & k4_complex2(A,B,C) = k5_numbers & ~ ( k4_complex2(B,C,A) = k5_numbers & k4_complex2(C,A,B) = k28_sin_cos ) & ~ ( k4_complex2(B,C,A) = k28_sin_cos & k4_complex2(C,A,B) = k5_numbers ) ) ) ) ) )).
fof(t85_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k1_recdef_1(k16_comput_1,k2_finseq_4(k4_ordinal1,A,B)) = k2_nat_1(A,B) ) ) )).
fof(t85_convex4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m2_convex4(E,A,k8_domain_1(u1_struct_0(A),B,C,D)) => ( v3_convex4(E,A) => ( B = C | C = D | D = B | ( ? [F] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & F = k3_funct_2(u1_struct_0(A),k2_numbers,E,B) & G = k3_funct_2(u1_struct_0(A),k2_numbers,E,C) & H = k3_funct_2(u1_struct_0(A),k2_numbers,E,D) & k2_xcmplx_0(k2_xcmplx_0(F,G),H) = 1 & r1_xxreal_0(k5_numbers,F) & r1_xxreal_0(k5_numbers,G) & r1_xxreal_0(k5_numbers,H) ) ) ) & 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))) ) ) ) ) ) ) ) ) )).
fof(t85_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ( ~ r2_hidden(D,k24_qc_lang1(A,B)) => v2_cqc_the1(k10_cqc_lang(A,k8_cqc_lang(A,B,k12_cqc_lang(A,D,C)),k12_cqc_lang(A,D,k8_cqc_lang(A,B,C))),A) ) ) ) ) ) )).
fof(t85_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k18_sin_cos),D) ) & r2_hidden(A,k1_relset_1(k1_numbers,k27_sin_cos)) & r2_hidden(B,k1_relset_1(k1_numbers,k27_sin_cos)) ) => k9_diff_1(C,A,B) = k7_xcmplx_0(k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(1,k17_sin_cos(A)),k17_sin_cos(A)),k7_xcmplx_0(1,k17_sin_cos(B))),k17_sin_cos(B)),k6_xcmplx_0(A,B)) ) ) ) ) )).
fof(t85_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ! [I] : ! [J] : k8_enumset1(A,B,C,D,E,F,G,H,I,J) = k2_xboole_0(k7_enumset1(A,B,C,D,E,F,G,H,I),k1_tarski(J)) )).
fof(t85_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => k7_euclid_8(A,B,C) = k22_rvsum_1(k5_euclid_8(A,B),C) ) ) ) )).
fof(t85_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(A)) => ( ( r2_hidden(E,k4_euclidlp(A,B,C,D)) & r2_hidden(F,k4_euclidlp(A,B,C,D)) ) => r1_tarski(k2_euclid_4(A,E,F),k4_euclidlp(A,B,C,D)) ) ) ) ) ) ) ) )).
fof(t85_exchsort,axiom,( ! [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) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_exchsort(B) & v2_exchsort(B,k5_numbers) ) => ? [C] : ( v2_exchsort(C,k5_numbers) & m2_exchsort(C,A,B) & v6_exchsort(C,A,B) ) ) ) )).
fof(t85_facirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => k2_msafree2(k19_facirc_1(A,B,C)) = k1_enumset1(A,B,C) ) ) ) )).
fof(t85_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( ~ v2_struct_0(A) & v10_lattices(A) & v17_lattices(A) & l3_lattices(A) & r3_lattices(A,B,C) ) => ( ~ v2_struct_0(k10_filter_2(A,k9_filter_2(A,B,C))) & v10_lattices(k10_filter_2(A,k9_filter_2(A,B,C))) & v17_lattices(k10_filter_2(A,k9_filter_2(A,B,C))) & l3_lattices(k10_filter_2(A,k9_filter_2(A,B,C))) ) ) ) ) ) )).
fof(t85_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( C = k5_relat_1(B,k2_finseq_1(A)) => r1_xxreal_0(k3_finseq_1(C),A) ) ) ) ) )).
fof(t85_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,B) => ! [G] : ( ( 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] : ( m2_finseq_1(H,A) => ( H = k10_finseq_1(D,E) => k4_funcop_1(G,H,F) = k10_finseq_1(k2_binop_1(A,B,C,G,D,F),k2_binop_1(A,B,C,G,E,F)) ) ) ) ) ) ) ) ) ) )).
fof(t85_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v2_funct_1(A) => v2_funct_1(k1_finseq_3(A,B)) ) ) )).
fof(t85_finseq_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ~ ( r2_hidden(C,B) & ! [D] : ( m1_subset_1(D,A) => ~ r2_hidden(D,C) ) ) ) ) )).
fof(t85_finseq_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_finseq_1(D,C) => ( k2_xcmplx_0(A,B) = k3_finseq_1(D) => k4_finseq_5(C,k17_finseq_1(C,B,D)) = k2_rfinseq(C,A,k4_finseq_5(C,D)) ) ) ) ) ) )).
fof(t85_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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_setwiseo(C,A) & v1_finseqop(C,A) ) => k5_binop_1(A,k7_finseqop(A,C,k6_partfun1(A),k5_finseqop(A,C)),B,B) = k4_binop_1(A,C) ) ) ) ) )).
fof(t85_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ( k2_flang_2(A,k8_flang_1(A,B)) = k8_flang_1(A,B) & k8_flang_1(A,k2_flang_2(A,B)) = k8_flang_1(A,B) ) ) )).
fof(t85_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ~ r1_xxreal_0(C,k5_numbers) => r1_tarski(k1_flang_2(A,B,C,D),k2_flang_3(A,B)) ) ) ) ) )).
fof(t85_funcop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,C,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,A))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,C,A) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,A))) ) => ! [F] : ( m1_subset_1(F,A) => ( v2_binop_1(B,A) => r2_funct_2(C,A,k6_funcop_1(A,C,B,k10_funcop_1(A,C,B,F,D),E),k10_funcop_1(A,C,B,F,k6_funcop_1(A,C,B,D,E))) ) ) ) ) ) ) )).
fof(t85_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( ( A = k10_xtuple_0(B) & k9_xtuple_0(C) = A & k9_xtuple_0(D) = A & k3_relat_1(B,C) = k3_relat_1(B,D) ) => C = D ) ) ) ) )).
fof(t85_funct_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => k5_partfun1(A,A,k3_partfun1(B,A,A)) = k1_tarski(B) ) )).
fof(t85_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r2_hidden(A,k9_xtuple_0(C)) & k1_funct_1(C,A) = B ) => r1_tarski(k16_funcop_1(A,B),C) ) ) )).
fof(t85_funct_7,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( v1_funct_1(k8_funct_7(C,B)) & m1_subset_1(k8_funct_7(C,B),k1_zfmisc_1(k2_zfmisc_1(A,A))) ) ) ) )).
fof(t85_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v3_group_1(B) & v5_group_1(B) & v4_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k3_group_4(B,k5_finseq_2(u1_struct_0(B),A,k8_group_1(B,C,D))) = k8_group_1(B,k3_group_4(B,k5_finseq_2(u1_struct_0(B),A,C)),k3_group_4(B,k5_finseq_2(u1_struct_0(B),A,D))) ) ) ) ) )).
fof(t85_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k31_gfacirc1(A,B,C),k32_gfacirc1(A,B,C)))) & ? [E] : ( m1_subset_1(E,k6_margrel1) & ? [F] : ( m1_subset_1(F,k6_margrel1) & ? [G] : ( 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(k31_gfacirc1(A,B,C),k32_gfacirc1(A,B,C),k5_facirc_1(k31_gfacirc1(A,B,C),k32_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)))) & k1_funct_1(k5_facirc_1(k31_gfacirc1(A,B,C),k32_gfacirc1(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(k31_gfacirc1(A,B,C),k32_gfacirc1(A,B,C),D,2),k4_tarski(k10_finseq_1(B,C),k3_gfacirc1)) = k10_margrel1(F,k9_margrel1(G)) & k1_funct_1(k5_facirc_1(k31_gfacirc1(A,B,C),k32_gfacirc1(A,B,C),D,2),k4_tarski(k10_finseq_1(C,A),k4_twoscomp)) = k10_margrel1(k9_margrel1(G),k9_margrel1(E)) ) ) ) ) ) ) )).
fof(t85_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_finset_1(C) & v1_glib_000(C) ) => ( ( r5_glib_000(A,B) & r5_glib_000(B,C) ) => r5_glib_000(A,C) ) ) ) ) )).
fof(t85_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( r2_hidden(C,k13_glib_001(A,B)) <=> ? [D] : ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) & r1_xxreal_0(D,k3_finseq_1(B)) & k1_funct_1(B,D) = C ) ) ) ) )).
fof(t85_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ~ ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k1_matrix_0(C)) & 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_0(u1_struct_0(k15_euclid(2)),C,1,A),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,1,k1_nat_1(A,1))),k7_xcmplx_0(1,2)),k19_euclid(1,k5_numbers)),B),k1_tops_1(k15_euclid(2),k3_goboard5(C,k5_numbers,A))) ) ) ) ) )).
fof(t85_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ( r1_group_2(A,k10_group_2(A,k6_group_2(A),B),k6_group_2(A)) & r1_group_2(A,k10_group_2(A,B,k6_group_2(A)),k6_group_2(A)) ) ) ) )).
fof(t85_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k7_group_3(A,B) = k7_group_3(A,C) <=> ~ r1_xboole_0(k7_group_3(A,B),k7_group_3(A,C)) ) ) ) ) )).
fof(t85_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( ( v2_group_9(D,A) & m1_group_9(D,A,C) ) => ! [E] : ( ( v2_group_9(E,A) & m1_group_9(E,A,C) ) => ! [F] : ( ( v2_group_9(F,A) & m1_group_9(F,A,B) ) => ! [G] : ( ( v2_group_9(G,A) & m1_group_9(G,A,B) ) => ( ( D = F & E = G ) => k16_group_9(A,B,F,G) = k16_group_9(A,C,D,E) ) ) ) ) ) ) ) )).
fof(t85_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v3_ideal_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(B,k16_ideal_1(A,B,C)) ) ) ) )).
fof(t85_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => k2_integra5(A,k26_valued_1(k1_numbers,k1_numbers,k16_sin_cos,B)) = k6_xcmplx_0(k3_xcmplx_0(B,k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k18_sin_cos),k2_seq_4(A))),k3_xcmplx_0(B,k1_funct_1(k32_valued_1(k1_numbers,k1_numbers,k18_sin_cos),k3_seq_4(A)))) ) ) )).
fof(t85_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => r2_hidden(k3_intpro_1(k6_intpro_1(B),B),k13_intpro_1(A)) ) ) )).
fof(t85_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( 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] : ( 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) = k3_xcmplx_0(k12_euclid(D),k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k18_euclid(D),k12_euclid(D)),A),k6_xcmplx_0(1,A))) ) ) & ! [D] : ( 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(k5_numbers,k17_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) ) ) ) ) ) )).
fof(t85_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) = E & k17_euclid(C) = F & k18_euclid(D) = G & r1_xxreal_0(G,k18_euclid(A)) & ~ r1_xxreal_0(k18_euclid(B),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),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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t85_jordan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( v2_compts_1(B,k15_euclid(2)) & v1_jordan21(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_jordan24(2,B,k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) & r2_hidden(A,k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,3),k1_jordan21(B))) ) => r1_xxreal_0(k18_euclid(k1_jordan21(B)),k18_euclid(A)) ) ) ) )).
fof(t85_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( ( r2_hidden(D,k14_pscomp_1(B)) & r2_hidden(C,k9_subset_1(u1_struct_0(k15_euclid(2)),k7_topreal1(D),k3_topreal1(2,k2_jordan9(B,A)))) ) => k17_euclid(C) = k6_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))) ) ) ) ) ) )).
fof(t85_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v3_limfunc1(A) => ( v3_limfunc1(k56_valued_1(k1_numbers,k1_numbers,A)) & k4_limfunc1(k56_valued_1(k1_numbers,k1_numbers,A)) = k9_complex1(k4_limfunc1(A)) ) ) ) )).
fof(t85_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,B,B) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,B,B) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( r1_matrix10(C,D) => ( r1_xxreal_0(A,k5_numbers) | r1_matrix10(k6_matrix10(B,A,C),k6_matrix10(B,A,D)) ) ) ) ) ) ) )).
fof(t85_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(C),B,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(C))) ) => ! [E] : ( ( 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)))) ) => k8_matrix13(C,D) = k8_matrix13(C,k4_matrix11(B,A,u1_struct_0(C),E,D)) ) ) ) ) ) )).
fof(t85_matrixr2,axiom,( k4_matrixr2(k5_numbers) = k5_matrixr2(k5_numbers) & k4_matrixr2(k5_numbers) = k1_xboole_0 )).
fof(t85_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => k6_member_1(k12_member_1(A,B)) = k12_member_1(k6_member_1(A),k6_member_1(B)) ) ) )).
fof(t85_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( v6_supinf_2(D) & v6_supinf_2(E) & ! [F] : ( m1_subset_1(F,A) => ( r2_hidden(F,k1_relset_1(A,E)) => r1_xxreal_0(k12_supinf_2(E,F),k12_supinf_2(D,F)) ) ) ) => ( ! [F] : ( 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) ) ) | r1_xxreal_0(k6_mesfunc5(A,B,C,E),k6_mesfunc5(A,B,C,D)) ) ) ) ) ) ) ) )).
fof(t85_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ( ( v6_supinf_2(D) & r1_xboole_0(E,F) ) => ( ! [G] : ( m2_subset_1(G,k1_zfmisc_1(A),B) => ~ ( G = k1_relset_1(A,D) & r1_mesfunc6(A,B,D,G) ) ) | k1_mesfunc6(A,B,C,k2_partfun1(A,k1_numbers,D,k6_prob_1(A,B,E,F))) = k3_supinf_2(k1_mesfunc6(A,B,C,k2_partfun1(A,k1_numbers,D,E)),k1_mesfunc6(A,B,C,k2_partfun1(A,k1_numbers,D,F))) ) ) ) ) ) ) ) ) )).
fof(t85_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( ( 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)) & v1_nfcont_1(C,B) & r9_ncfcont1(B,A,D,C) ) => v1_ncfcont1(k7_relset_1(u1_struct_0(B),u1_struct_0(A),D,C),A) ) ) ) ) ) )).
fof(t85_newton,axiom,( ! [A] : ( v7_ordinal1(A) => r1_xxreal_0(k1_nat_1(A,1),k1_newton(2,A)) ) )).
fof(t85_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v13_o_ring_1(B,A) & v7_o_ring_1(C,A) ) => v13_o_ring_1(k6_algstr_0(A,B,C),A) ) ) ) ) )).
fof(t85_orders_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ~ ( v1_finset_1(B) & r1_tarski(B,k10_xtuple_0(A)) & ! [C] : ~ ( r1_tarski(C,k9_xtuple_0(A)) & v1_finset_1(C) & k7_relat_1(A,C) = B ) ) ) )).
fof(t85_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => r6_pboole(A,k5_pboole(A,B,B),k1_pboole(A)) ) )).
fof(t85_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ( k7_polyform(A) = 3 => k16_rvsum_1(k29_polyform(A)) = k2_xcmplx_0(k6_xcmplx_0(k11_polyform(A,k5_numbers),k11_polyform(A,1)),k11_polyform(A,2)) ) ) )).
fof(t85_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k5_numbers,B) ) => r1_xxreal_0(1,k6_prepower(A,B)) ) ) ) )).
fof(t85_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => k15_qc_lang2(A,k12_qc_lang1(A)) = k1_tarski(k12_qc_lang1(A)) ) )).
fof(t85_quatern3,axiom,( k4_quatern3(k11_quaterni) = k24_quaterni(k11_quaterni) )).
fof(t85_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ! [C] : ( v1_quaterni(C) => r1_xxreal_0(k28_quaterni(k25_quaterni(B,C)),k2_xcmplx_0(k28_quaterni(k25_quaterni(B,A)),k28_quaterni(k25_quaterni(A,C)))) ) ) ) )).
fof(t85_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => r1_tarski(k3_relat_1(B,k6_relat_1(A,C)),k3_relat_1(B,C)) ) ) )).
fof(t85_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(C))) => ! [G] : ( ( ~ v2_struct_0(G) & l1_rewrite3(G,F) ) => ( r1_rewrite3(F,G,A,D,B) => r3_rewrite3(C,F,G,A,k1_flang_1(C,D,E),B,E) ) ) ) ) ) ) )).
fof(t85_rfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) ) => ( ( v1_seq_2(k5_relat_1(C,A)) & v1_seq_2(k5_relat_1(C,B)) ) => v1_seq_2(k5_relat_1(C,k2_xboole_0(A,B))) ) ) )).
fof(t85_rinfsup1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_comseq_2(B) => ( r1_xxreal_0(k5_rinfsup1(B),A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & r1_xxreal_0(k2_xcmplx_0(A,C),k1_funct_1(B,k2_xcmplx_0(D,E))) ) ) ) ) ) ) ) ) )).
fof(t85_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => ~ ( ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => r1_xxreal_0(k5_numbers,k1_funct_1(A,B)) ) ) & ? [B] : ( v7_ordinal1(B) & r2_hidden(B,k4_finseq_1(A)) & ~ r1_xxreal_0(k1_funct_1(A,B),k5_numbers) ) & r1_xxreal_0(k16_rvsum_1(A),k5_numbers) ) ) )).
fof(t85_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ( k2_compos_0(u1_compos_1(k1_scmfsa_2),A) = k5_numbers => A = k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0) ) ) )).
fof(t85_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( ~ r1_xxreal_0(k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,D),F)),k5_numbers) => k1_funct_1(k6_scmpds_4(k8_scmpds_6(D,F,C),k8_memstr_0(2,k1_scmpds_2,B),A),E) = k1_funct_1(B,E) ) ) ) ) ) ) ) )).
fof(t85_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( r2_hidden(B,k3_tarski(k12_scmyciel(A))) <=> ~ ( ~ r2_hidden(B,k3_tarski(A)) & ! [C] : ~ ( r2_hidden(C,k3_tarski(A)) & B = k4_tarski(C,k3_tarski(A)) ) & B != k3_tarski(A) ) ) ) )).
fof(t85_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => r2_analoaf(A,C,D,k1_semi_af1(A,C,E,B),k1_semi_af1(A,D,E,B)) ) ) ) ) ) )).
fof(t85_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => k18_seq_4(A,B,k6_complex1) = B ) ) )).
fof(t85_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => r1_tarski(k5_subset_1(A,B,k4_kurato_0(A,C)),k4_kurato_0(A,k9_setlim_2(A,C,B))) ) ) )).
fof(t85_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,k5_sheffer1(A,C,B),k5_sheffer1(A,C,B)) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,B)),C),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,B)),C)) ) ) ) )).
fof(t85_sin_cos6,axiom,( k2_relset_1(k1_numbers,k3_sin_cos6) = k1_rcomp_1(k5_numbers,k28_sin_cos) )).
fof(t85_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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_funct_1(B,A),k4_xcmplx_0(1)) | r1_xxreal_0(1,k1_funct_1(B,A)) | ( r1_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k1_sin_cos9),A) & k1_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k1_sin_cos9),A) = k7_xcmplx_0(k1_fdiff_1(B,A),k2_xcmplx_0(1,k1_square_1(k1_funct_1(B,A)))) ) ) ) ) ) )).
fof(t85_sincos10,axiom,( ! [A] : ( r2_hidden(A,k1_rcomp_1(1,k3_square_1(2))) => r2_hidden(k1_funct_1(k1_sincos10,A),k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,4))) ) )).
fof(t85_sprect_1,axiom,( ! [A] : ( ( v1_sprect_1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,3) = k24_pscomp_1(k3_topreal1(2,A)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,3) = k23_pscomp_1(k3_topreal1(2,A)) ) ) )).
fof(t85_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k16_substut1(A),k38_substut1(A)) => ! [D] : ( m1_substut1(D,A,k7_sublemma(A,C,B)) => ( v3_substut1(k7_sublemma(A,C,B),A) => r2_relset_1(k3_qc_lang1(A),k3_qc_lang1(A),k2_substut1(A,k19_substut1(A,k9_sublemma(A,k7_sublemma(A,C,B),D))),k14_sublemma(A,k3_qc_lang1(A),k14_sublemma(A,k3_qc_lang1(A),k2_substut1(A,k7_substut1(A,B,k11_cqc_lang(A,B,k2_sublemma(A,C)),D)),k5_relset_1(k3_qc_lang1(A),k3_qc_lang1(A),k2_substut1(A,D),k15_sublemma(A,k11_cqc_lang(A,B,k2_sublemma(A,C))))),k5_relset_1(k3_qc_lang1(A),k3_qc_lang1(A),k2_substut1(A,D),k16_sublemma(A,k11_cqc_lang(A,B,k2_sublemma(A,C)),D)))) ) ) ) ) ) )).
fof(t85_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => u1_struct_0(k4_tdlat_1(A)) = k1_tdlat_1(A) ) )).
fof(t85_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => g1_pre_topc(u1_struct_0(k6_tex_4(A,B)),u1_pre_topc(k6_tex_4(A,B))) = g1_pre_topc(u1_struct_0(k6_tex_4(A,k3_tex_4(A,B))),u1_pre_topc(k6_tex_4(A,k3_tex_4(A,B)))) ) ) )).
fof(t85_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ( r2_hidden(D,u1_struct_0(B)) => D = k1_funct_1(C,D) ) ) => r2_funct_2(u1_struct_0(B),u1_struct_0(A),k4_tmap_1(A,B),C) ) ) ) ) )).
fof(t85_topreal6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => k1_topreal6(2,A,B) = k3_square_1(k2_xcmplx_0(k1_square_1(k6_xcmplx_0(k17_euclid(A),k17_euclid(B))),k1_square_1(k6_xcmplx_0(k18_euclid(A),k18_euclid(B))))) ) ) )).
fof(t85_tops_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( ( r1_tarski(C,D) & g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & v1_tops_3(C,A) ) => v1_tops_3(D,B) ) ) ) ) ) )).
fof(t85_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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) => v7_transgeo(k2_funct_2(u1_struct_0(A),B),A) ) ) ) )).
fof(t85_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,A) ) => ( ( ( r4_tsep_1(A,B,D) & r4_tsep_1(A,C,D) ) => r4_tsep_1(A,k1_tsep_1(A,B,C),D) ) & ( ( r4_tsep_1(A,D,B) & r4_tsep_1(A,D,C) ) => r4_tsep_1(A,D,k1_tsep_1(A,B,C)) ) ) ) ) ) ) )).
fof(t85_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( v1_valued_2(C) => ! [D] : ( v1_valued_2(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,D))) ) => k84_valued_2(A,B,k2_valued_2(k1_valued_2(C)),D,k16_valued_2(A,C,E),F) = k16_valued_2(k3_xboole_0(A,B),k2_valued_2(k3_xboole_0(k1_valued_2(C),k1_valued_2(D))),k84_valued_2(A,B,C,D,E,F)) ) ) ) ) )).
fof(t85_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_yellow_0(A) & l1_orders_2(A) ) => ( v9_waybel_1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_orders_2(A,k10_lattice3(A,k7_waybel_1(A,B),k7_waybel_1(A,C)),k7_waybel_1(A,k11_lattice3(A,B,C))) ) ) ) ) )).
fof(t85_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(A,B) => r1_xboole_0(A,k4_xboole_0(C,B)) ) )).
fof(t85_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k6_xboolean(A,k10_xboolean(A,B)) = k5_xboolean(k3_xboolean(A),k3_xboolean(B)) ) ) )).
fof(t85_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => k3_xcmplx_0(k7_xcmplx_0(A,C),k7_xcmplx_0(B,D)) = k3_xcmplx_0(k7_xcmplx_0(A,D),k7_xcmplx_0(B,C)) ) ) ) ) )).
fof(t85_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A)) ) ) ) ) )).
fof(t85_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( r1_xxreal_0(B,A) => ( r1_tarski(k1_xxreal_1(A,B),k1_tarski(A)) & r1_tarski(k1_xxreal_1(A,B),k1_tarski(B)) ) ) ) ) )).
fof(t85_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ( ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(B,A) => ( r1_xxreal_0(C,B) | r1_xxreal_0(k1_xxreal_2(A),C) | r2_hidden(C,A) ) ) ) ) => v6_xxreal_2(A) ) ) )).
fof(t85_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ~ ( ~ r1_xxreal_0(k5_numbers,A) & k2_xxreal_0 != A & k6_xxreal_3(k1_xxreal_0,A) != k2_xxreal_0 ) ) )).
fof(t85_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v7_zf_lang(A) <=> k29_zf_lang(A) = k1_tarski(A) ) ) )).
fof(t85_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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))) ) => ( v3_zf_lang(A) => ( r1_zf_model(B,C,A) <=> r2_hidden(k3_funct_2(k1_zf_lang,B,C,k18_zf_lang(A)),k3_funct_2(k1_zf_lang,B,C,k19_zf_lang(A))) ) ) ) ) ) )).
fof(t85_zfmisc_1,axiom,( ! [A] : ! [B] : r1_tarski(k2_zfmisc_1(A,B),k1_zfmisc_1(k1_zfmisc_1(k2_xboole_0(A,B)))) )).
fof(t85_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( m2_zmodul01(B,A,k4_zmodul01(A)) => B = u1_struct_0(A) ) ) ) )).
fof(t86_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k2_abcmiz_1) => k45_abcmiz_1(A,k35_abcmiz_1(B,A)) = k6_domain_1(k2_abcmiz_1,B) ) ) )).
fof(t86_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & v22_aofa_a00(D,A,1,1,11) & l3_msualg_1(D,A) ) => ! [E] : ( ( v19_aofa_a00(E,A) & m1_subset_1(E,u1_struct_0(A)) ) => ! [F] : ( m2_pboole(F,u1_struct_0(A),k1_aofa_a01(A,B,C),u3_msualg_1(A,D)) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),E)) => ! [H] : ( m1_subset_1(H,k1_funct_1(u3_msualg_1(A,C),E)) => k15_aofa_a00(A,B,C,D,k37_aofa_a00(A),k41_aofa_a00(A,C,E,G,H),F) = k41_aofa_a00(A,D,E,k15_aofa_a00(A,B,C,D,E,G,F),k15_aofa_a00(A,B,C,D,E,H,F)) ) ) ) ) ) ) ) ) )).
fof(t86_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( m1_subset_1(C,k5_arytm_3) => ~ ( r3_arytm_3(A,B) & r3_arytm_3(B,k9_arytm_3(A,C)) & ! [D] : ( m1_subset_1(D,k5_arytm_3) => ~ ( B = k9_arytm_3(A,D) & r3_arytm_3(D,C) ) ) ) ) ) ) )).
fof(t86_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( r1_xxreal_0(1,A) => r1_xxreal_0(k2_power(k7_xcmplx_0(k1_nat_1(A,1),A),A),k2_power(k7_xcmplx_0(k1_nat_1(A,2),k1_nat_1(A,1)),k1_nat_1(A,1))) ) ) )).
fof(t86_bcialg_1,axiom,( ! [A] : ( ( ~ 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) & v15_bcialg_1(A) & l2_bcialg_1(A) ) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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,C) = k1_bcialg_1(A,k1_bcialg_1(A,k1_bcialg_1(A,B,C),C),k2_bcialg_1(A,C)) & 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)) ) ) ) ) ) ) )).
fof(t86_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,C,B) => ! [E] : ( ( v3_funct_1(E) & m1_borsuk_2(E,A,B,B) ) => ( r1_borsuk_6(A,C,B) => r3_borsuk_2(A,B,B,k1_borsuk_2(A,B,C,B,k2_borsuk_2(A,C,B,D),D),E) ) ) ) ) ) ) )).
fof(t86_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ! [C] : ( ( r1_ordinal1(k1_card_1(C),A) & ! [D] : ( r2_hidden(D,C) => r1_ordinal1(k1_card_1(D),B) ) ) => r1_ordinal1(k1_card_1(k3_tarski(C)),k2_card_2(A,B)) ) ) ) )).
fof(t86_card_3,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ( k2_card_1(B) = k2_card_1(A) => A = B ) ) ) )).
fof(t86_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( k2_cat_1(A,B,C) != k1_xboole_0 & ! [D] : ( m1_cat_1(D,A,B,C) => ~ r2_hidden(D,k2_cat_1(A,B,C)) ) ) ) ) ) )).
fof(t86_cat_3,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => ( ( r4_cat_3(A,B,C,D) & v11_cat_1(k3_graph_1(A,C),A) ) => r1_cat_1(A,k3_graph_1(A,D),B) ) ) ) ) ) )).
fof(t86_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) ) => ! [C] : ( m2_glib_000(C,A,B,k21_glib_000(A,B)) => ! [D] : ( m3_glib_001(D,A) => ! [E] : ( m3_glib_001(E,C) => ( D = E => ( v5_chord(E,C) <=> v5_chord(D,A) ) ) ) ) ) ) ) )).
fof(t86_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_clvect_1(D,A) => ~ ( k5_clvect_1(A,C,D) = k5_clvect_1(A,B,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r1_struct_0(D,E) & k5_algstr_0(A,C,E) = B ) ) ) ) ) ) ) )).
fof(t86_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( v7_ordinal1(D) => k1_valued_0(u1_struct_0(A),k16_csspace(A,B,C),D) = k16_csspace(A,k1_valued_0(u1_struct_0(A),B,D),k1_valued_0(u1_struct_0(A),C,D)) ) ) ) ) )).
fof(t86_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ! [D] : ( r2_hidden(k14_cohsp_1(C,D),k16_cohsp_1(A,B)) <=> ( ( r2_hidden(C,A) & D = k1_xboole_0 ) | ( C = k1_xboole_0 & r2_hidden(D,B) ) ) ) ) ) )).
fof(t86_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k7_xcmplx_0(A,B) = k2_xcmplx_0(k7_xcmplx_0(k3_real_1(k4_real_1(k3_complex1(A),k3_complex1(B)),k4_real_1(k4_complex1(A),k4_complex1(B))),k2_xcmplx_0(k1_square_1(k3_complex1(B)),k1_square_1(k4_complex1(B)))),k3_xcmplx_0(k7_xcmplx_0(k5_real_1(k4_real_1(k3_complex1(B),k4_complex1(A)),k4_real_1(k3_complex1(A),k4_complex1(B))),k2_xcmplx_0(k1_square_1(k3_complex1(B)),k1_square_1(k4_complex1(B)))),k7_complex1)) ) ) )).
fof(t86_complex2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( ( k2_xcmplx_0(k2_xcmplx_0(k4_complex2(A,B,C),k4_complex2(B,C,A)),k4_complex2(C,A,B)) = k28_sin_cos | k2_xcmplx_0(k2_xcmplx_0(k4_complex2(A,B,C),k4_complex2(B,C,A)),k4_complex2(C,A,B)) = k3_xcmplx_0(5,k28_sin_cos) ) <=> ( A != B & A != C & B != C ) ) ) ) ) )).
fof(t86_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v2_convex4(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( r1_tarski(B,C) => r1_tarski(k21_convex4(A,B),C) ) ) ) ) )).
fof(t86_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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,B,k12_cqc_lang(A,D,C)),A) <=> v2_cqc_the1(k12_cqc_lang(A,D,k8_cqc_lang(A,B,C)),A) ) ) ) ) ) ) )).
fof(t86_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k18_sin_cos),D) ) & r2_hidden(B,k1_relset_1(k1_numbers,k27_sin_cos)) & r2_hidden(k2_xcmplx_0(B,A),k1_relset_1(k1_numbers,k27_sin_cos)) ) => k1_funct_1(k3_diff_1(C,A),B) = k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(1,k17_sin_cos(k2_xcmplx_0(B,A))),k17_sin_cos(k2_xcmplx_0(B,A))),k7_xcmplx_0(1,k17_sin_cos(B))),k17_sin_cos(B)) ) ) ) ) )).
fof(t86_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( A != B & A != C & k4_xboole_0(k1_enumset1(A,B,C),k1_tarski(A)) != k2_tarski(B,C) ) )).
fof(t86_euclid_8,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(3)) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(3)) => k7_euclid_8(B,C,A) = k22_rvsum_1(k5_euclid_8(A,B),C) ) ) ) )).
fof(t86_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ( ( v1_euclidlp(B,A) & r2_hidden(C,B) ) => ( ! [D] : ( v1_xreal_0(D) => ~ ( D != 1 & r2_hidden(k9_euclid(A,C,D),B) ) ) | r2_hidden(k5_euclid(A),B) ) ) ) ) ) )).
fof(t86_exchsort,axiom,( ! [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) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,u1_struct_0(A)) & ~ v1_xboole_0(B) & v1_funct_1(B) & v1_finset_1(B) & v1_exchsort(B) & v2_exchsort(B,k5_numbers) ) => ? [C] : ( m1_exchsort(C,B) & v5_exchsort(C,A) ) ) ) )).
fof(t86_facirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => 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))) ) ) ) )).
fof(t86_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) <=> r2_hidden(k3_lattices(A,C,D),B) ) ) ) ) ) ) )).
fof(t86_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ( A = k7_finseq_1(A,B) | A = k7_finseq_1(B,A) ) => B = k1_xboole_0 ) ) ) )).
fof(t86_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,B) => ! [H] : ( ( v1_funct_1(H) & v1_funct_2(H,k2_zfmisc_1(A,B),C) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(A,B),C))) ) => ! [I] : ( m2_finseq_1(I,A) => ( I = k11_finseq_1(D,E,F) => k4_funcop_1(H,I,G) = k11_finseq_1(k2_binop_1(A,B,C,H,D,G),k2_binop_1(A,B,C,H,E,G),k2_binop_1(A,B,C,H,F,G)) ) ) ) ) ) ) ) ) ) ) )).
fof(t86_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v2_funct_1(A) => k3_finseq_1(k1_finseq_3(A,B)) = k6_xcmplx_0(k3_finseq_1(A),k5_card_1(k3_xboole_0(B,k10_xtuple_0(A)))) ) ) )).
fof(t86_finseq_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_eqrel_1(B,A) => r1_xxreal_0(k5_card_1(B),k5_card_1(A)) ) ) )).
fof(t86_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r2_finseq_4(C,B) => k3_finseq_5(k6_finseq_4(C,B)) = k5_finseq_4(k4_finseq_5(A,C),B) ) ) ) ) )).
fof(t86_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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_setwiseo(C,A) & v1_finseqop(C,A) ) => k5_binop_1(A,k7_finseqop(A,C,k6_partfun1(A),k5_finseqop(A,C)),B,k4_binop_1(A,C)) = B ) ) ) ) )).
fof(t86_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => r1_tarski(k2_flang_2(A,B),k8_flang_1(A,B)) ) )).
fof(t86_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => k6_flang_1(A,k8_flang_1(A,B),k2_flang_3(A,B)) = k6_flang_1(A,k2_flang_3(A,B),k8_flang_1(A,B)) ) )).
fof(t86_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(A,C) => k5_relat_1(k16_funcop_1(A,B),C) = k16_funcop_1(A,B) ) )).
fof(t86_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r1_tarski(k7_relat_1(C,A),k7_relat_1(C,B)) & r1_tarski(A,k9_xtuple_0(C)) & v2_funct_1(C) ) => r1_tarski(A,B) ) ) )).
fof(t86_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_tarski(B)))) ) => ! [D] : ( ( 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)))) ) => k5_partfun1(A,k1_tarski(B),C) = k1_tarski(D) ) ) )).
fof(t86_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( ( r2_hidden(A,k9_xtuple_0(E)) & r2_hidden(C,k9_xtuple_0(E)) & k1_funct_1(E,A) = B & k1_funct_1(E,C) = D ) => r1_tarski(k4_funct_4(A,C,B,D),E) ) ) )).
fof(t86_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v3_group_1(B) & v5_group_1(B) & v4_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => ! [D] : ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => k3_group_4(B,k12_fvsum_1(A,B,C,D)) = k8_group_1(B,k3_group_4(B,C),k3_group_4(B,D)) ) ) ) ) )).
fof(t86_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k31_gfacirc1(A,B,C),k32_gfacirc1(A,B,C)))) => v1_circuit2(k5_facirc_1(k31_gfacirc1(A,B,C),k32_gfacirc1(A,B,C),D,2),k31_gfacirc1(A,B,C),k32_gfacirc1(A,B,C)) ) ) )).
fof(t86_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( m1_glib_000(C,A) => ( ( k24_glib_000(A,B) = k24_glib_000(A,C) & k25_glib_000(A,B) = k25_glib_000(A,C) ) => r5_glib_000(B,C) ) ) ) ) )).
fof(t86_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( r2_hidden(k3_glib_001(A,B),k13_glib_001(A,B)) & r2_hidden(k4_glib_001(A,B),k13_glib_001(A,B)) ) ) ) )).
fof(t86_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ~ ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k1_matrix_0(C)) & r1_xboole_0(k1_rltopsp1(k15_euclid(2),B,k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k3_finseq_1(C),A),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k3_finseq_1(C),k1_nat_1(A,1))),k7_xcmplx_0(1,2)),k19_euclid(1,k5_numbers))),k1_tops_1(k15_euclid(2),k3_goboard5(C,k3_finseq_1(C),A))) ) ) ) ) )).
fof(t86_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & m1_group_2(B,A) ) => ( r1_group_2(A,k10_group_2(A,B,k7_group_2(A)),B) & r1_group_2(A,k10_group_2(A,k7_group_2(A),B),B) ) ) ) )).
fof(t86_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( k7_group_3(A,B) = k6_domain_1(u1_struct_0(A),k1_group_1(A)) <=> B = k1_group_1(A) ) ) ) )).
fof(t86_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( ( v2_group_9(D,A) & m1_group_9(D,A,C) ) => ! [E] : ( ( v2_group_9(E,A) & m1_group_9(E,A,C) ) => ! [F] : ( ( v2_group_9(F,A) & m1_group_9(F,A,B) ) => ! [G] : ( ( v2_group_9(G,A) & m1_group_9(G,A,B) ) => ( ( D = F & E = G ) => k19_group_9(A,B,F,G) = k19_group_9(A,C,D,E) ) ) ) ) ) ) ) )).
fof(t86_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => k2_integra5(A,k26_valued_1(k1_numbers,k1_numbers,k18_sin_cos,B)) = k6_xcmplx_0(k3_xcmplx_0(B,k1_funct_1(k16_sin_cos,k2_seq_4(A))),k3_xcmplx_0(B,k1_funct_1(k16_sin_cos,k3_seq_4(A)))) ) ) )).
fof(t86_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => r2_hidden(k3_intpro_1(k6_intpro_1(B),k6_intpro_1(k6_intpro_1(B))),k13_intpro_1(A)) ) ) )).
fof(t86_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( 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] : ( 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) = k3_xcmplx_0(k12_euclid(D),k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k18_euclid(D),k12_euclid(D)),A),k2_xcmplx_0(1,A))) ) ) & ! [D] : ( 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(k5_numbers,k17_euclid(D)) & D != k4_struct_0(k15_euclid(2)) ) ) ) ) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) | v5_pre_topc(C,k1_pre_topc(k15_euclid(2),B),k3_topmetr) ) ) ) ) ) )).
fof(t86_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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 & k18_euclid(C) = G & k18_euclid(D) = G & r1_xxreal_0(G,k18_euclid(A)) & ~ r1_xxreal_0(k18_euclid(B),k18_euclid(A)) & 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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t86_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(C,k15_pscomp_1(B)) & ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => k9_subset_1(u1_struct_0(k15_euclid(2)),k4_topreal1(C),k3_topreal1(2,k2_jordan9(B,A))) != k1_tarski(D) ) ) ) ) ) )).
fof(t86_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v3_limfunc1(A) & ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(C,B) & r2_hidden(C,k1_relset_1(k1_numbers,A)) & k1_funct_1(A,C) != k5_numbers ) ) ) => ( k4_limfunc1(A) = k5_numbers | ( v3_limfunc1(k6_rfunct_1(k1_numbers,k1_numbers,A)) & k4_limfunc1(k6_rfunct_1(k1_numbers,k1_numbers,A)) = k5_xcmplx_0(k4_limfunc1(A)) ) ) ) ) )).
fof(t86_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,B,B) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,B,B) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( ( r1_matrix10(C,D) & r1_xxreal_0(k5_numbers,A) ) => r2_matrix10(k6_matrix10(B,A,C),k6_matrix10(B,A,D)) ) ) ) ) ) )).
fof(t86_matrix13,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( B != k4_struct_0(A) => k8_matrix13(A,C) = k8_matrix13(A,k6_matrix_3(A,C,B)) ) ) ) ) )).
fof(t86_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( k3_finseq_1(B) = A => ( r1_xxreal_0(A,k5_numbers) | k11_matrixr1(k4_matrixr2(A),B) = B ) ) ) ) )).
fof(t86_member_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k12_member_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k4_xxreal_3(A,B)) ) ) )).
fof(t86_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ( ( r1_xxreal_0(k5_numbers,E) & v6_supinf_2(D) ) => ( ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ~ ( F = k1_relset_1(A,D) & r1_mesfunc1(A,B,D,F) ) ) | k6_mesfunc5(A,B,C,k6_mesfunc1(A,D,E)) = k4_xxreal_3(E,k6_mesfunc5(A,B,C,D)) ) ) ) ) ) ) ) )).
fof(t86_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( v6_supinf_2(D) => ( ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ~ ( F = k1_relset_1(A,D) & r1_mesfunc6(A,B,D,F) ) ) | r1_xxreal_0(k5_numbers,k1_mesfunc6(A,B,C,k2_partfun1(A,k1_numbers,D,E))) ) ) ) ) ) ) ) )).
fof(t86_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( 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_ncfcont1(k1_relset_1(u1_struct_0(A),B),A) & r11_ncfcont1(A,B,k1_relset_1(u1_struct_0(A),B)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) = k2_seq_4(k2_relset_1(k1_numbers,B)) & k7_partfun1(k1_numbers,B,D) = k3_seq_4(k2_relset_1(k1_numbers,B)) ) ) ) ) ) ) )).
fof(t86_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ~ r1_xxreal_0(k1_newton(2,A),A) ) )).
fof(t86_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v13_o_ring_1(B,A) & v11_o_ring_1(C,A) ) => v13_o_ring_1(k6_algstr_0(A,B,C),A) ) ) ) ) )).
fof(t86_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ( v1_finset_1(k1_relat_1(A)) => v1_finset_1(A) ) ) )).
fof(t86_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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),k2_pboole(A,k5_pboole(A,B,C),k3_pboole(A,B,C))) ) ) )).
fof(t86_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ( k7_polyform(A) = k5_numbers => v6_polyform(A) ) ) )).
fof(t86_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,1) & ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(k6_prepower(A,B),1) ) ) ) )).
fof(t86_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [D] : ( ( v3_card_1(D,B) & m2_finseq_1(D,k2_qc_lang1(A)) ) => k15_qc_lang2(A,k10_qc_lang1(A,C,D)) = k1_tarski(k10_qc_lang1(A,C,D)) ) ) ) ) )).
fof(t86_quatern3,axiom,( k4_quatern3(k12_quaterni) = k24_quaterni(k12_quaterni) )).
fof(t86_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k28_quaterni(A),k28_quaterni(B))),k28_quaterni(k25_quaterni(A,B))) ) ) )).
fof(t86_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k6_relat_1(A,B) = k3_relat_1(B,k4_relat_1(A)) ) )).
fof(t86_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k8_afinsq_1(C)) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k8_afinsq_1(C))) => ! [H] : ( ( ~ v2_struct_0(H) & l1_rewrite3(H,G) ) => ( r3_rewrite3(C,G,H,A,D,B,E) => r3_rewrite3(C,G,H,A,k1_flang_1(C,D,F),B,k1_flang_1(C,E,F)) ) ) ) ) ) ) ) )).
fof(t86_rfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) ) => ( ( v2_seq_2(k5_relat_1(C,A)) & v2_seq_2(k5_relat_1(C,B)) ) => v2_seq_2(k5_relat_1(C,k2_xboole_0(A,B))) ) ) )).
fof(t86_rinfsup1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_comseq_2(B) => ( A = k5_rinfsup1(B) <=> ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_numbers) => ( ! [D] : ( v7_ordinal1(D) => ~ ! [E] : ( v7_ordinal1(E) => r1_xxreal_0(k1_funct_1(B,k2_xcmplx_0(D,E)),k6_xcmplx_0(A,C)) ) ) & ? [D] : ( v7_ordinal1(D) & ! [E] : ( v7_ordinal1(E) => ~ r1_xxreal_0(k2_xcmplx_0(A,C),k1_funct_1(B,k2_xcmplx_0(D,E))) ) ) ) ) ) ) ) ) ) )).
fof(t86_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => r1_xxreal_0(k5_numbers,k18_rvsum_1(k12_rvsum_1(A))) ) )).
fof(t86_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) <=> ~ ( A != k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0) & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => A != k6_scmfsa_2(B,C) ) ) & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => A != k7_scmfsa_2(B,C) ) ) & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => A != k8_scmfsa_2(B,C) ) ) & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => A != k9_scmfsa_2(B,C) ) ) & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => A != k10_scmfsa_2(B,C) ) ) & ! [B] : ( v7_ordinal1(B) => A != k11_scmfsa_2(B) ) & ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => A != k12_scmfsa_2(B,C) ) ) & ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => A != k13_scmfsa_2(B,C) ) ) & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( m1_scmfsa_2(D) => A != k14_scmfsa_2(C,B,D) ) ) ) & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( m1_scmfsa_2(D) => A != k15_scmfsa_2(C,B,D) ) ) ) & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_scmfsa_2(C) => A != k16_scmfsa_2(B,C) ) ) & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( m1_scmfsa_2(C) => A != k17_scmfsa_2(B,C) ) ) ) ) )).
fof(t86_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => k5_card_1(k4_scmpds_6(A,B,C,D)) = k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),2) ) ) ) ) )).
fof(t86_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => k3_tarski(k12_scmyciel(A)) = k2_xboole_0(k2_xboole_0(k3_tarski(A),k2_zfmisc_1(k3_tarski(A),k1_tarski(k3_tarski(A)))),k1_tarski(k3_tarski(A))) ) )).
fof(t86_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( r2_analoaf(A,C,D,E,F) => r2_analoaf(A,C,D,k1_semi_af1(A,C,E,B),k1_semi_af1(A,D,F,B)) ) ) ) ) ) ) ) )).
fof(t86_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => k18_seq_4(A,B,k5_complex1) = k15_seq_4(A) ) ) )).
fof(t86_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_kurato_0(C,A) => k4_kurato_0(A,k7_setlim_2(A,C,B)) = k7_subset_1(A,B,k4_kurato_0(A,C)) ) ) ) )).
fof(t86_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,k5_sheffer1(A,C,B),k5_sheffer1(A,C,B)) = k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,B)),C)) ) ) ) )).
fof(t86_sin_cos6,axiom,( k1_relset_1(k1_numbers,k3_sin_cos6) = k1_rcomp_1(k4_xcmplx_0(1),1) )).
fof(t86_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( 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_funct_1(B,A),k4_xcmplx_0(1)) | r1_xxreal_0(1,k1_funct_1(B,A)) | ( r1_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k2_sin_cos9),A) & k1_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k2_sin_cos9),A) = k4_xcmplx_0(k7_xcmplx_0(k1_fdiff_1(B,A),k2_xcmplx_0(1,k1_square_1(k1_funct_1(B,A))))) ) ) ) ) ) )).
fof(t86_sincos10,axiom,( ! [A] : ( r2_hidden(A,k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1))) => r2_hidden(k1_funct_1(k2_sincos10,A),k1_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos),k28_sin_cos)) ) )).
fof(t86_sprect_1,axiom,( ! [A] : ( ( v1_sprect_1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,4) = k25_pscomp_1(k3_topreal1(2,A)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,4) = k18_pscomp_1(k3_topreal1(2,A)) ) ) )).
fof(t86_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [E] : ( m2_subset_1(E,k16_substut1(A),k38_substut1(A)) => ! [F] : ( m1_substut1(F,A,k7_sublemma(A,E,B)) => ~ ( v3_substut1(k7_sublemma(A,E,B),A) & ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),C))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(k3_qc_lang1(A),C))) ) => ~ ( ! [I] : ( m2_subset_1(I,k2_qc_lang1(A),k3_qc_lang1(A)) => ~ ( r2_hidden(I,k1_relset_1(k3_qc_lang1(A),G)) & r2_hidden(I,k24_qc_lang1(A,k11_cqc_lang(A,B,k2_sublemma(A,E)))) ) ) & ! [I] : ( m2_subset_1(I,k2_qc_lang1(A),k3_qc_lang1(A)) => ( r2_hidden(I,k1_relset_1(k3_qc_lang1(A),H)) => k1_funct_1(H,I) = k3_funct_2(k3_qc_lang1(A),C,D,I) ) ) & r1_xboole_0(k1_relset_1(k3_qc_lang1(A),k13_sublemma(A,E,B,F,C,D)),k1_relset_1(k3_qc_lang1(A),H)) & r2_funct_2(k3_qc_lang1(A),C,k1_sublemma(A,C,D,k3_sublemma(A,k9_sublemma(A,k7_sublemma(A,E,B),F),C,D)),k1_sublemma(A,C,D,k14_sublemma(A,C,k14_sublemma(A,C,k13_sublemma(A,E,B,F,C,D),G),H))) ) ) ) ) ) ) ) ) ) ) )).
fof(t86_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_tdlat_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_tdlat_1(A))) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k1_tdlat_1(A)) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(u1_struct_0(A)),k1_tdlat_1(A)) => ( ( B = D & C = E ) => ( k1_lattices(k4_tdlat_1(A),B,C) = k4_subset_1(u1_struct_0(A),k1_tops_1(A,k2_pre_topc(A,k4_subset_1(u1_struct_0(A),D,E))),k4_subset_1(u1_struct_0(A),D,E)) & k2_lattices(k4_tdlat_1(A),B,C) = k9_subset_1(u1_struct_0(A),k2_pre_topc(A,k1_tops_1(A,k9_subset_1(u1_struct_0(A),D,E))),k9_subset_1(u1_struct_0(A),D,E)) ) ) ) ) ) ) ) )).
fof(t86_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k6_tex_4(A,C)))) => m1_pre_topc(k6_tex_4(A,B),k6_tex_4(A,C)) ) ) ) ) )).
fof(t86_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( 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(C),u1_struct_0(B),k2_tmap_1(A,B,D,C),k1_partfun1(u1_struct_0(C),u1_struct_0(A),u1_struct_0(A),u1_struct_0(B),k4_tmap_1(A,C),D)) ) ) ) ) )).
fof(t86_topreal6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => k1_topreal6(A,B,B) = k5_numbers ) ) )).
fof(t86_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( ( 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(B,A) & v7_transgeo(C,A) ) => v7_transgeo(k1_transgeo(u1_struct_0(A),C,B),A) ) ) ) ) )).
fof(t86_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( ~ r1_tsep_1(B,C) => ( r4_tsep_1(A,B,C) <=> ~ ( ~ m1_pre_topc(B,C) & ~ m1_pre_topc(C,B) & ! [D] : ( ( ~ v2_struct_0(D) & v1_borsuk_1(D,A) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ v2_struct_0(E) & v1_borsuk_1(E,A) & m1_pre_topc(E,A) ) => ~ ( 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(k1_tsep_1(A,B,C),k1_tsep_1(A,D,E)) & ! [F] : ( ( ~ v2_struct_0(F) & v1_tsep_1(F,A) & 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,F,k1_tsep_1(A,B,C)),k2_tsep_1(A,B,C)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t86_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( v1_valued_2(C) => ! [D] : ( v1_valued_2(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,D))) ) => k84_valued_2(A,B,C,k2_valued_2(k1_valued_2(D)),E,k16_valued_2(B,D,F)) = k16_valued_2(k3_xboole_0(A,B),k2_valued_2(k3_xboole_0(k1_valued_2(C),k1_valued_2(D))),k84_valued_2(A,B,C,D,E,F)) ) ) ) ) )).
fof(t86_waybel_1,axiom,( ! [A] : ( ( 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) ) => ( ( v9_waybel_1(A) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k7_waybel_1(A,k7_waybel_1(A,B)) = B ) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r6_waybel_1(A,B,k7_waybel_1(A,B)) ) ) ) )).
fof(t86_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r1_tarski(A,B) & r1_xboole_0(A,C) ) => r1_tarski(A,k4_xboole_0(B,C)) ) )).
fof(t86_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k10_xboolean(A,k6_xboolean(A,B)) = k5_xboolean(k3_xboolean(A),k3_xboolean(B)) ) ) )).
fof(t86_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => ( r1_xxreal_0(k5_numbers,B) | r1_xxreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A)) ) ) ) ) )).
fof(t86_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => r1_xboole_0(k4_xxreal_1(A,B),k2_tarski(A,B)) ) ) )).
fof(t86_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ( ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( r2_hidden(B,A) => ( r1_xxreal_0(C,k2_xxreal_2(A)) | r1_xxreal_0(B,C) | r2_hidden(C,A) ) ) ) ) => v6_xxreal_2(A) ) ) )).
fof(t86_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & A != k1_xxreal_0 & k6_xxreal_3(k2_xxreal_0,A) != k2_xxreal_0 ) ) )).
fof(t86_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v4_zf_lang(A) => k29_zf_lang(A) = k2_xboole_0(k29_zf_lang(k20_zf_lang(A)),k1_tarski(A)) ) ) )).
fof(t86_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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))) ) => ( v4_zf_lang(A) => ( r1_zf_model(B,C,A) <=> ~ r1_zf_model(B,C,k20_zf_lang(A)) ) ) ) ) ) )).
fof(t86_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r2_hidden(k4_tarski(C,D),k2_zfmisc_1(A,B)) <=> ( r2_hidden(C,A) & r2_hidden(D,B) ) ) )).
fof(t86_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m2_zmodul01(C,A,B) => ( r2_hidden(k4_struct_0(A),C) <=> C = u1_struct_0(B) ) ) ) ) )).
fof(t87_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,k2_abcmiz_1) => k46_abcmiz_1(A,k35_abcmiz_1(B,A)) = k4_subset_1(k2_abcmiz_1,k6_domain_1(k2_abcmiz_1,B),k3_abcmiz_1(B)) ) ) )).
fof(t87_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v19_aofa_a00(D,A) & m1_subset_1(D,u1_struct_0(A)) ) => k10_aofa_a01(A,B,C,D,k5_numbers) = k27_aofa_a00(A,C,D) ) ) ) ) )).
fof(t87_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( m1_subset_1(C,k5_arytm_3) => ~ ( r3_arytm_3(A,k9_arytm_3(B,C)) & ! [D] : ( m1_subset_1(D,k5_arytm_3) => ! [E] : ( m1_subset_1(E,k5_arytm_3) => ~ ( A = k9_arytm_3(D,E) & r3_arytm_3(D,B) & r3_arytm_3(E,C) ) ) ) ) ) ) ) )).
fof(t87_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r1_xxreal_0(A,B) => r1_xxreal_0(k7_xcmplx_0(k4_newton(A,k1_nat_1(B,1)),k1_nat_1(B,1)),k4_newton(A,B)) ) ) ) )).
fof(t87_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_borsuk_2(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_borsuk_2(D,A,C,B) => ! [E] : ( ( v3_funct_1(E) & m1_borsuk_2(E,A,B,B) ) => r4_borsuk_2(A,B,B,k1_borsuk_2(A,B,C,B,k2_borsuk_2(A,C,B,D),D),E) ) ) ) ) ) )).
fof(t87_card_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( ( v1_finset_1(k9_xtuple_0(A)) & ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => v1_finset_1(k1_funct_1(A,B)) ) ) => v1_finset_1(k3_card_3(A)) ) ) )).
fof(t87_card_3,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ( r2_hidden(B,A) <=> r1_ordinal1(k2_card_1(B),A) ) ) ) )).
fof(t87_cat_1,axiom,( ! [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) & l1_cat_1(A) ) => u4_struct_0(A) = k3_tarski(a_1_0_cat_1(A)) ) )).
fof(t87_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ~ ( v8_glib_001(B,A) & v5_chord(B,A) & k15_glib_001(A,B) = 4 & ! [C] : ( ~ r1_glib_000(A,k1_funct_1(B,1),k1_funct_1(B,5),C) & ~ r1_glib_000(A,k1_funct_1(B,3),k1_funct_1(B,7),C) ) ) ) ) )).
fof(t87_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_clvect_1(C) & m1_clvect_1(C,A) ) => ! [D] : ( ( v1_clvect_1(D) & m1_clvect_1(D,A) ) => ( k5_clvect_1(A,B,C) = k5_clvect_1(A,B,D) <=> C = D ) ) ) ) ) )).
fof(t87_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => k1_valued_0(u1_struct_0(A),k5_vfunct_1(k4_ordinal1,A,B),C) = k5_vfunct_1(k4_ordinal1,A,k1_valued_0(u1_struct_0(A),B,C)) ) ) ) )).
fof(t87_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ~ ( r2_hidden(C,k16_cohsp_1(A,B)) & ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,B) => ~ ( C = k14_cohsp_1(D,E) & ( D = k1_xboole_0 | E = k1_xboole_0 ) ) ) ) ) ) ) )).
fof(t87_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => r3_cqc_the1(A,k6_domain_1(k3_cqc_lang(A),B),B) ) ) )).
fof(t87_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k18_sin_cos),D) ) & r2_hidden(B,k1_relset_1(k1_numbers,k27_sin_cos)) & r2_hidden(k6_xcmplx_0(B,A),k1_relset_1(k1_numbers,k27_sin_cos)) ) => k1_funct_1(k4_diff_1(C,A),B) = k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(1,k17_sin_cos(B)),k17_sin_cos(B)),k7_xcmplx_0(1,k17_sin_cos(k6_xcmplx_0(B,A)))),k17_sin_cos(k6_xcmplx_0(B,A))) ) ) ) ) )).
fof(t87_enumset1,axiom,( ! [A] : ! [B] : ! [C] : k2_xboole_0(k2_tarski(B,A),k2_tarski(C,A)) = k1_enumset1(A,B,C) )).
fof(t87_euclid_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( v1_xreal_0(D) => ( ( r1_fdiff_1(A,D) & r1_fdiff_1(B,D) & r1_fdiff_1(C,D) ) => k8_euclid_8(A,B,C,D) = k7_euclid(3,k7_euclid(3,k9_euclid(3,k2_euclid_8,k1_fdiff_1(A,D)),k9_euclid(3,k3_euclid_8,k1_fdiff_1(B,D))),k9_euclid(3,k4_euclid_8,k1_fdiff_1(C,D))) ) ) ) ) ) )).
fof(t87_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(D)) => ! [F] : ( m2_finseq_2(F,k1_numbers,k1_euclid(D)) => ! [G] : ( m2_finseq_2(G,k1_numbers,k1_euclid(D)) => ! [H] : ( m2_finseq_2(H,k1_numbers,k1_euclid(D)) => ~ ( r2_hidden(E,k4_euclidlp(D,F,G,H)) & E = k7_euclid(D,k7_euclid(D,k9_euclid(D,F,A),k9_euclid(D,G,B)),k9_euclid(D,H,C)) & k2_xcmplx_0(k2_xcmplx_0(A,B),C) != 1 & ~ r2_hidden(k5_euclid(D),k4_euclidlp(D,F,G,H)) ) ) ) ) ) ) ) ) ) )).
fof(t87_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( ~ v2_struct_0(D) & l1_msualg_1(D) ) => ( D = k19_facirc_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)) ) ) ) )).
fof(t87_finseq_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ~ ( k7_finseq_1(B,C) = k9_finseq_1(A) & ~ ( B = k9_finseq_1(A) & C = k1_xboole_0 ) & ~ ( B = k1_xboole_0 & C = k9_finseq_1(A) ) ) ) ) )).
fof(t87_finseq_2,axiom,( ! [A] : m1_finseq_2(k13_finseq_1(A),A) )).
fof(t87_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v1_finset_1(B) => ( ( v2_funct_1(A) & r1_tarski(B,k10_xtuple_0(A)) ) => k3_finseq_1(k1_finseq_3(A,B)) = k6_xcmplx_0(k3_finseq_1(A),k5_card_1(B)) ) ) ) )).
fof(t87_finseq_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ( r1_setfam_1(B,C) => r1_xxreal_0(k5_card_1(C),k5_card_1(B)) ) ) ) ) )).
fof(t87_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r2_finseq_4(C,B) => k4_finseq_5(A,k2_finseq_5(A,C,B)) = k1_finseq_5(A,k4_finseq_5(A,C),B) ) ) ) ) )).
fof(t87_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,A,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( v1_setwiseo(C,A) => k5_binop_1(A,k7_finseqop(A,C,k6_partfun1(A),D),k4_binop_1(A,C),B) = k3_funct_2(A,A,D,B) ) ) ) ) ) )).
fof(t87_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => k2_flang_2(A,k9_subset_1(k8_afinsq_1(A),B,C)) = k9_subset_1(k8_afinsq_1(A),k2_flang_2(A,B),k2_flang_2(A,C)) ) ) )).
fof(t87_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => r1_tarski(k7_flang_1(A,k2_flang_3(A,B),C),k1_flang_3(A,B,C)) ) ) )).
fof(t87_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r1_partfun1(k7_funcop_1(A,C),k7_funcop_1(B,D)) <=> ( C = D | r1_xboole_0(A,B) ) ) )).
fof(t87_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r1_tarski(k8_relat_1(C,A),k8_relat_1(C,B)) & r1_tarski(A,k10_xtuple_0(C)) ) => r1_tarski(A,B) ) ) )).
fof(t87_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( r1_relset_1(A,B,D,C) => r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) ) ) ) )).
fof(t87_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r1_tarski(A,C) & r1_tarski(B,C) ) => r1_tarski(k1_funct_4(A,B),C) ) ) ) ) )).
fof(t87_fvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v3_group_1(B) & v5_group_1(B) & v4_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(A,u1_struct_0(B))) => k3_group_4(B,k10_fvsum_1(A,B,D,C)) = k8_group_1(B,k3_group_4(B,k5_finseq_2(u1_struct_0(B),A,C)),k3_group_4(B,D)) ) ) ) ) )).
fof(t87_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : k3_msafree2(k34_gfacirc1(A,B,C)) = k2_xboole_0(k1_tarski(k4_tarski(k10_finseq_1(A,B),k4_gfacirc1)),k1_tarski(k36_gfacirc1(A,B,C))) )).
fof(t87_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ( r5_glib_000(A,B) <=> ( m1_glib_000(A,B) & m1_glib_000(B,A) ) ) ) ) )).
fof(t87_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( r1_xxreal_0(C,k3_finseq_1(B)) => r2_hidden(k5_glib_001(A,B,C),k13_glib_001(A,B)) ) ) ) ) )).
fof(t87_goboard6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ~ r1_xboole_0(k1_rltopsp1(k15_euclid(2),A,k5_algstr_0(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,1),k19_euclid(1,1))),k1_tops_1(k15_euclid(2),k3_goboard5(B,k5_numbers,k5_numbers))) ) ) )).
fof(t87_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => k10_group_2(A,k7_group_2(A),k7_group_2(A)) = A ) )).
fof(t87_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => k2_group_2(A,k7_group_3(A,B),C) = k2_group_2(A,C,k7_group_3(A,B)) ) ) ) )).
fof(t87_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( ( v2_group_9(D,A) & m1_group_9(D,A,B) ) => ! [E] : ( ( v2_group_9(E,A) & m1_group_9(E,A,B) ) => ( ( v4_group_9(D,A,C) & m1_group_9(D,A,C) & v4_group_9(E,A,C) & m1_group_9(E,A,C) ) => ( v4_group_9(k19_group_9(A,B,D,E),A,C) & m1_group_9(k19_group_9(A,B,D,E),A,C) ) ) ) ) ) ) )).
fof(t87_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_algstr_0(A) & v1_vectsp_1(A) & v1_algstr_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k14_ideal_1(A,k16_ideal_1(A,B,C),C),B) ) ) ) )).
fof(t87_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => k2_integra5(A,k26_valued_1(k1_numbers,k1_numbers,k1_sin_cos2,B)) = k6_xcmplx_0(k3_xcmplx_0(B,k1_funct_1(k3_sin_cos2,k2_seq_4(A))),k3_xcmplx_0(B,k1_funct_1(k3_sin_cos2,k3_seq_4(A)))) ) ) )).
fof(t87_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ( r2_hidden(B,k13_intpro_1(A)) => r2_hidden(k6_intpro_1(B),k13_intpro_1(A)) ) ) ) )).
fof(t87_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( 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] : ( 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) = k3_xcmplx_0(k12_euclid(D),k3_square_1(k6_xcmplx_0(1,k1_square_1(k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k18_euclid(D),k12_euclid(D)),A),k6_xcmplx_0(1,A)))))) ) ) & ! [D] : ( 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(k5_numbers,k17_euclid(D)) & r1_xxreal_0(A,k7_xcmplx_0(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) ) ) ) ) ) )).
fof(t87_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) = E & k18_euclid(C) = G & k18_euclid(D) = G & r1_xxreal_0(G,k18_euclid(A)) & ~ r1_xxreal_0(k18_euclid(B),k18_euclid(A)) & 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t87_jordan,axiom,( ! [A] : ( ( v2_compts_1(A,k15_euclid(2)) & v1_jordan21(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_jordan24(2,A,k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) => r1_tarski(k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,3),k1_jordan21(A)),k4_topreal1(k1_jordan21(A))) ) ) )).
fof(t87_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(C,k16_pscomp_1(B)) & ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => k9_subset_1(u1_struct_0(k15_euclid(2)),k5_topreal1(C),k3_topreal1(2,k2_jordan9(B,A))) != k1_tarski(D) ) ) ) ) ) )).
fof(t87_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k14_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ( ( D = C & r2_hidden(E,k8_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))) ) ) ) ) ) ) ) )).
fof(t87_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ r1_xxreal_0(D,C) & r2_hidden(D,k1_relset_1(k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) ) => ( v3_limfunc1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B)) & k4_limfunc1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B)) = k3_xcmplx_0(k4_limfunc1(A),k4_limfunc1(B)) ) ) ) ) )).
fof(t87_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,B,B) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,B,B) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( r1_matrix10(C,D) => ( r1_xxreal_0(k5_numbers,A) | r1_matrix10(k6_matrix10(B,A,D),k6_matrix10(B,A,C)) ) ) ) ) ) ) )).
fof(t87_matrix13,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) ) => ( ( D = k3_relat_1(E,C) & r1_tarski(k10_xtuple_0(E),k4_finseq_1(C)) ) => k3_relat_1(E,k9_fvsum_1(A,C,B)) = k9_fvsum_1(A,D,B) ) ) ) ) ) ) )).
fof(t87_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( ( v1_matrixr2(D,A) & k3_finseq_1(B) = A & k3_finseq_1(C) = A ) => ( r1_xxreal_0(A,k5_numbers) | ( k11_matrixr1(D,B) = C <=> B = k11_matrixr1(k7_matrixr2(A,D),C) ) ) ) ) ) ) ) )).
fof(t87_member_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => k12_member_1(k1_tarski(A),k2_tarski(B,C)) = k2_tarski(k4_xxreal_3(A,B),k4_xxreal_3(A,C)) ) ) ) )).
fof(t87_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,k1_relset_1(A,D)) => k5_numbers = k12_supinf_2(D,E) ) ) => ( ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ~ ( E = k1_relset_1(A,D) & r1_mesfunc1(A,B,D,E) ) ) | k6_mesfunc5(A,B,C,D) = k5_numbers ) ) ) ) ) ) )).
fof(t87_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ( ( v6_supinf_2(D) & r1_tarski(E,F) ) => ( ! [G] : ( m2_subset_1(G,k1_zfmisc_1(A),B) => ~ ( G = k1_relset_1(A,D) & r1_mesfunc6(A,B,D,G) ) ) | r1_xxreal_0(k1_mesfunc6(A,B,C,k2_partfun1(A,k1_numbers,D,E)),k1_mesfunc6(A,B,C,k2_partfun1(A,k1_numbers,D,F))) ) ) ) ) ) ) ) ) )).
fof(t87_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & 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) != k1_xboole_0 & v1_ncfcont1(k1_relset_1(u1_struct_0(A),C),A) & r7_ncfcont1(A,B,C,k1_relset_1(u1_struct_0(A),C)) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(D,k1_relset_1(u1_struct_0(A),C)) & r2_hidden(E,k1_relset_1(u1_struct_0(A),C)) & k7_partfun1(k1_numbers,k4_normsp_0(u1_struct_0(A),B,C),D) = k2_seq_4(k2_relset_1(k1_numbers,k4_normsp_0(u1_struct_0(A),B,C))) & k7_partfun1(k1_numbers,k4_normsp_0(u1_struct_0(A),B,C),E) = k3_seq_4(k2_relset_1(k1_numbers,k4_normsp_0(u1_struct_0(A),B,C))) ) ) ) ) ) ) ) )).
fof(t87_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ~ ( ~ ( A = k5_numbers & B != k5_numbers ) & k1_newton(A,B) = k5_numbers ) & ~ ( k1_newton(A,B) != k5_numbers & A = k5_numbers & B != k5_numbers ) ) ) ) )).
fof(t87_orders_1,axiom,( ! [A] : ( v1_relat_1(A) => ( ( v1_finset_1(k9_xtuple_0(A)) & v1_finset_1(k10_xtuple_0(A)) ) => v1_finset_1(A) ) ) )).
fof(t87_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => r6_pboole(A,k5_pboole(A,B,C),k4_pboole(A,k2_pboole(A,B,C),k3_pboole(A,B,C))) ) ) )).
fof(t87_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ( v5_polyform(A) => v6_polyform(A) ) ) )).
fof(t87_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(B,k5_numbers) ) => r1_xxreal_0(k6_prepower(A,B),1) ) ) ) )).
fof(t87_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => k15_qc_lang2(A,k1_qc_lang2(A)) = k2_tarski(k12_qc_lang1(A),k1_qc_lang2(A)) ) )).
fof(t87_quatern3,axiom,( k2_quatern3(k24_quaterni(k2_quatern2)) = 1 )).
fof(t87_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k28_quaterni(k23_quaterni(A,B)) = k3_xcmplx_0(k28_quaterni(A),k28_quaterni(B)) ) ) )).
fof(t87_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k6_relat_1(A,B) = k3_xboole_0(B,k2_zfmisc_1(k9_xtuple_0(B),A)) ) )).
fof(t87_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(E))) => ! [G] : ( ( ~ v2_struct_0(G) & l1_rewrite3(G,F) ) => ( r2_rewrite3(E,F,G,A,B,C,D) => r3_rewrite3(E,F,G,A,B,C,D) ) ) ) ) )).
fof(t87_rfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) ) => ( ( v1_comseq_2(k5_relat_1(C,A)) & v1_comseq_2(k5_relat_1(C,B)) ) => v1_comseq_2(k5_relat_1(C,k2_xboole_0(A,B))) ) ) )).
fof(t87_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_comseq_2(A) => r1_xxreal_0(k6_rinfsup1(A),k5_rinfsup1(A)) ) ) )).
fof(t87_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => k18_rvsum_1(k10_rvsum_1(B,A)) = k3_xcmplx_0(A,k16_rvsum_1(B)) ) ) )).
fof(t87_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ( v2_extpro_1(A,k7_card_1(3),k1_scmfsa_2) => A = k2_compos_1(k1_scmfsa_2) ) ) )).
fof(t87_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ( r2_hidden(k5_numbers,k9_xtuple_0(k4_scmpds_6(A,B,C,D))) & r2_hidden(1,k9_xtuple_0(k4_scmpds_6(A,B,C,D))) ) ) ) ) ) )).
fof(t87_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => r2_hidden(k3_tarski(A),k3_tarski(k12_scmyciel(A))) ) )).
fof(t87_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k3_semi_af1(A,B,C,D) = D <=> B = C ) ) ) ) ) )).
fof(t87_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => k10_seq_4(B,k4_xcmplx_0(k6_complex1)) = k16_seq_4(A,B) ) ) )).
fof(t87_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_kurato_0(C,A) => k4_kurato_0(A,k9_setlim_2(A,C,B)) = k5_subset_1(A,B,k4_kurato_0(A,C)) ) ) ) )).
fof(t87_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,k5_sheffer1(A,C,B),k5_sheffer1(A,C,B)) = k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,B,C)) ) ) ) )).
fof(t87_sin_cos6,axiom,( k3_relat_1(k3_sin_cos6,k5_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k5_numbers,k28_sin_cos))) = k6_partfun1(k1_rcomp_1(k4_xcmplx_0(1),1)) )).
fof(t87_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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_cos9))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => ( k1_funct_1(D,E) = k2_xcmplx_0(k3_xcmplx_0(A,E),B) & ~ r1_xxreal_0(k1_funct_1(D,E),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(D,E)) ) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k1_sin_cos9),C) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k1_sin_cos9),C),E) = k7_xcmplx_0(A,k2_xcmplx_0(1,k1_square_1(k2_xcmplx_0(k3_xcmplx_0(A,E),B)))) ) ) ) ) ) ) ) ) )).
fof(t87_sincos10,axiom,( ! [A] : ( r2_hidden(A,k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1))) => r2_hidden(k1_funct_1(k3_sincos10,A),k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4)))) ) )).
fof(t87_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_valuat_1(D,A,C) => ! [E] : ( m2_subset_1(E,k16_substut1(A),k38_substut1(A)) => ! [F] : ( m1_substut1(F,A,k7_sublemma(A,E,B)) => ( v3_substut1(k7_sublemma(A,E,B),A) => ! [G] : ( m2_funct_2(G,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ( r1_valuat_1(A,C,k11_cqc_lang(A,B,k2_sublemma(A,E)),D,k1_sublemma(A,C,G,k13_sublemma(A,E,B,F,C,G))) <=> r1_sublemma(A,k9_sublemma(A,k7_sublemma(A,E,B),F),C,k1_sublemma(A,C,G,k3_sublemma(A,k9_sublemma(A,k7_sublemma(A,E,B),F),C,G)),D) ) ) ) ) ) ) ) ) ) )).
fof(t87_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( k5_lattices(k4_tdlat_1(A)) = k1_struct_0(A) & k6_lattices(k4_tdlat_1(A)) = k2_struct_0(A) ) ) )).
fof(t87_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_tex_4(A,B)))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k6_tex_4(A,C)))) ) <=> g1_pre_topc(u1_struct_0(k6_tex_4(A,B)),u1_pre_topc(k6_tex_4(A,B))) = g1_pre_topc(u1_struct_0(k6_tex_4(A,C)),u1_pre_topc(k6_tex_4(A,C))) ) ) ) ) )).
fof(t87_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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) & m1_subset_1(k4_tmap_1(A,B),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) ) ) )).
fof(t87_topreal6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => r1_xxreal_0(k1_topreal6(A,B,D),k2_xcmplx_0(k1_topreal6(A,B,C),k1_topreal6(A,C,D))) ) ) ) ) )).
fof(t87_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( r2_analoaf(A,C,D,E,F) <=> r2_analoaf(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)) ) ) ) ) ) ) ) ) )).
fof(t87_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( A = k1_tsep_1(A,B,C) => ( r1_tsep_1(B,C) | ( r4_tsep_1(A,B,C) <=> ~ ( ~ m1_pre_topc(B,C) & ~ m1_pre_topc(C,B) & ! [D] : ( ( ~ v2_struct_0(D) & v1_borsuk_1(D,A) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ v2_struct_0(E) & v1_borsuk_1(E,A) & m1_pre_topc(E,A) ) => ~ ( m1_pre_topc(D,B) & m1_pre_topc(E,C) & ~ ( A != k1_tsep_1(A,D,E) & ! [F] : ( ( ~ v2_struct_0(F) & v1_tsep_1(F,A) & m1_pre_topc(F,A) ) => ~ ( A = k1_tsep_1(A,k1_tsep_1(A,D,E),F) & m1_pre_topc(F,k2_tsep_1(A,B,C)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t87_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v1_valued_2(D) => ! [E] : ( v1_valued_2(E) => ! [F] : ( v1_valued_2(F) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,D))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(B,E))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(C,F))) ) => k84_valued_2(A,k3_xboole_0(B,C),D,k2_valued_2(k3_xboole_0(k1_valued_2(E),k1_valued_2(F))),G,k73_valued_2(B,C,E,F,H,I)) = k73_valued_2(k3_xboole_0(A,B),k3_xboole_0(A,C),k2_valued_2(k3_xboole_0(k1_valued_2(D),k1_valued_2(E))),k2_valued_2(k3_xboole_0(k1_valued_2(D),k1_valued_2(F))),k84_valued_2(A,B,D,E,G,H),k84_valued_2(A,C,D,F,G,I)) ) ) ) ) ) ) )).
fof(t87_waybel_1,axiom,( ! [A] : ( ( 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) ) => ( v9_waybel_1(A) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k7_waybel_1(A,k7_waybel_1(A,B)) = B ) ) ) & ( ( v9_waybel_1(A) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k7_waybel_1(A,k7_waybel_1(A,B)) = B ) ) => ( v2_waybel_1(A) & v10_waybel_1(A) ) ) ) ) )).
fof(t87_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_xboole_0(B,C) => k2_xboole_0(k4_xboole_0(A,B),C) = k4_xboole_0(k2_xboole_0(A,C),B) ) )).
fof(t87_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k10_xboolean(k3_xboolean(A),k6_xboolean(B,A)) = k5_xboolean(k4_xboolean(A,k5_xboolean(A,k3_xboolean(B))),k4_xboolean(k3_xboolean(A),B)) ) ) )).
fof(t87_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( B != k5_numbers => k3_xcmplx_0(k7_xcmplx_0(A,B),B) = A ) ) ) )).
fof(t87_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) ) ) ) )).
fof(t87_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => r1_xboole_0(k2_xxreal_1(A,B),k1_tarski(B)) ) ) )).
fof(t87_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ( ! [B] : ( v1_xxreal_0(B) => ~ ( ~ r1_xxreal_0(B,k2_xxreal_2(A)) & ~ r1_xxreal_0(k1_xxreal_2(A),B) & ~ r2_hidden(B,A) ) ) => v6_xxreal_2(A) ) ) )).
fof(t87_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ~ ( A != k1_xxreal_0 & A != k2_xxreal_0 & A != k5_numbers & ~ ( k4_xxreal_3(A,k6_xxreal_3(1,A)) = 1 & k4_xxreal_3(k6_xxreal_3(1,A),A) = 1 ) ) ) )).
fof(t87_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v5_zf_lang(A) => k29_zf_lang(A) = k2_xboole_0(k2_xboole_0(k29_zf_lang(k21_zf_lang(A)),k29_zf_lang(k22_zf_lang(A))),k1_tarski(A)) ) ) )).
fof(t87_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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))) ) => ( v5_zf_lang(A) => ( r1_zf_model(B,C,A) <=> ( r1_zf_model(B,C,k21_zf_lang(A)) & r1_zf_model(B,C,k22_zf_lang(A)) ) ) ) ) ) ) )).
fof(t87_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D)) => r2_hidden(k4_tarski(B,A),k2_zfmisc_1(D,C)) ) )).
fof(t87_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( m2_zmodul01(D,A,C) => ( r2_hidden(B,D) <=> D = k5_zmodul01(A,B,C) ) ) ) ) ) )).
fof(t88_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_abcmiz_1(B,A) & m1_subset_1(B,u4_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) & v6_trees_3(D) ) => ( C = k4_trees_4(k4_tarski(B,u1_struct_0(A)),D) => k45_abcmiz_1(A,C) = k3_tarski(a_2_1_abcmiz_1(A,D)) ) ) ) ) ) )).
fof(t88_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(k13_aofa_000(A,B,C),k9_aofa_000(A,k18_aofa_000(A),D)) & ! [E] : ( v7_ordinal1(E) => ~ ( D = k1_nat_1(E,1) & r2_hidden(B,k9_aofa_000(A,k18_aofa_000(A),E)) & r2_hidden(C,k9_aofa_000(A,k18_aofa_000(A),E)) ) ) ) ) ) ) ) )).
fof(t88_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v19_aofa_a00(D,A) & m1_subset_1(D,u1_struct_0(A)) ) => ! [E] : ( v7_ordinal1(E) => ( k10_aofa_a01(A,B,C,D,k2_xcmplx_0(E,1)) = k30_aofa_a00(A,C,D,k10_aofa_a01(A,B,C,D,E),k28_aofa_a00(A,C,D)) & k10_aofa_a01(A,B,C,D,k4_xcmplx_0(k2_xcmplx_0(E,1))) = k29_aofa_a00(A,C,D,k10_aofa_a01(A,B,C,D,k2_xcmplx_0(E,1))) ) ) ) ) ) ) )).
fof(t88_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( m1_subset_1(C,k5_arytm_3) => ~ ( ~ r3_arytm_3(B,A) & ~ r3_arytm_3(C,A) & ! [D] : ( m1_subset_1(D,k5_arytm_3) => ~ ( r3_arytm_3(D,B) & r3_arytm_3(D,C) & ~ r3_arytm_3(D,A) ) ) ) ) ) ) )).
fof(t88_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => k9_nat_1(k1_numbers,A,B) = k3_power(2,k7_newton(B)) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k9_nat_1(k1_numbers,A,B) = k6_series_1(k2_asympt_1,B) ) ) ) )).
fof(t88_borsuk_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v3_funct_1(C) & m1_borsuk_2(C,A,B,B) ) => ! [D] : ( ( v3_funct_1(D) & m1_borsuk_2(D,A,B,B) ) => r3_borsuk_2(A,B,B,C,D) ) ) ) ) )).
fof(t88_card_3,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ( r2_hidden(B,k2_card_1(A)) <=> r1_ordinal1(B,A) ) ) ) )).
fof(t88_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ~ ( v1_chord(B,A) & v5_chord(B,A) ) ) ) )).
fof(t88_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_clvect_1(D) & m1_clvect_1(D,A) ) => ! [E] : ( ( v1_clvect_1(E) & m1_clvect_1(E,A) ) => ( k5_clvect_1(A,C,D) = k5_clvect_1(A,B,E) => D = E ) ) ) ) ) ) )).
fof(t88_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( v7_ordinal1(D) => 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)) ) ) ) ) )).
fof(t88_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => k3_tarski(k16_cohsp_1(A,B)) = k14_cohsp_1(k3_tarski(A),k3_tarski(B)) ) ) )).
fof(t88_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => k1_cqc_the1(A,k4_subset_1(k3_cqc_lang(A),k6_domain_1(k3_cqc_lang(A),B),k6_domain_1(k3_cqc_lang(A),C))) = k1_cqc_the1(A,k6_domain_1(k3_cqc_lang(A),k7_cqc_lang(A,B,C))) ) ) ) )).
fof(t88_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k18_sin_cos),D) ) & r2_hidden(k2_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k27_sin_cos)) & r2_hidden(k6_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k27_sin_cos)) ) => k1_funct_1(k5_diff_1(C,A),B) = k2_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(1,k17_sin_cos(k2_xcmplx_0(B,k7_xcmplx_0(A,2)))),k17_sin_cos(k2_xcmplx_0(B,k7_xcmplx_0(A,2)))),k7_xcmplx_0(1,k17_sin_cos(k6_xcmplx_0(B,k7_xcmplx_0(A,2))))),k17_sin_cos(k6_xcmplx_0(B,k7_xcmplx_0(A,2)))) ) ) ) ) )).
fof(t88_euclid_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( v1_xreal_0(G) => ( ( 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(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,A,D),k3_valued_1(k1_numbers,k1_numbers,k1_numbers,B,E),k3_valued_1(k1_numbers,k1_numbers,k1_numbers,C,F),G) = k7_euclid(3,k8_euclid_8(A,B,C,G),k8_euclid_8(D,E,F,G)) ) ) ) ) ) ) ) ) )).
fof(t88_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_finseq_2(E,k1_numbers,k1_euclid(A)) => ( r2_hidden(B,k4_euclidlp(A,C,D,E)) <=> ? [F] : ( v1_xreal_0(F) & ? [G] : ( v1_xreal_0(G) & ? [H] : ( v1_xreal_0(H) & k2_xcmplx_0(k2_xcmplx_0(F,G),H) = 1 & B = k7_euclid(A,k7_euclid(A,k9_euclid(A,C,F),k9_euclid(A,D,G)),k9_euclid(A,E,H)) ) ) ) ) ) ) ) ) ) )).
fof(t88_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : v1_relat_1(k3_msafree2(k19_facirc_1(A,B,C))) )).
fof(t88_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_card_1(B,A) & v1_finseq_1(B) ) => k4_finseq_1(B) = k2_finseq_1(A) ) ) )).
fof(t88_finseq_2,axiom,( ! [A] : ! [B] : ( m1_finseq_2(B,A) => r1_tarski(B,k3_finseq_2(A)) ) )).
fof(t88_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v2_funct_1(A) & r2_hidden(B,k10_xtuple_0(A)) ) => k3_finseq_1(k1_finseq_3(A,k1_tarski(B))) = k6_xcmplx_0(k3_finseq_1(A),1) ) ) )).
fof(t88_finseq_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ( r1_setfam_1(B,C) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),C) => ? [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) & r1_tarski(E,D) ) ) ) ) ) ) )).
fof(t88_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r2_finseq_4(C,B) => k4_finseq_5(A,k1_finseq_5(A,C,B)) = k2_finseq_5(A,k4_finseq_5(A,C),B) ) ) ) ) )).
fof(t88_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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(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))) ) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ! [F] : ( m1_subset_1(F,A) => ! [G] : ( m1_subset_1(G,A) => k5_binop_1(A,B,k5_binop_1(A,C,D,E),k5_binop_1(A,C,F,G)) = k5_binop_1(A,C,k5_binop_1(A,B,D,F),k5_binop_1(A,B,E,G)) ) ) ) ) ) ) ) ) )).
fof(t88_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => k4_subset_1(k8_afinsq_1(A),k2_flang_2(A,B),k2_flang_2(A,C)) = k2_flang_2(A,k4_subset_1(k8_afinsq_1(A),B,C)) ) ) )).
fof(t88_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => r1_tarski(k1_flang_2(A,k2_flang_3(A,B),C,D),k1_flang_3(A,B,C)) ) ) ) )).
fof(t88_funcop_1,axiom,( ! [A] : ! [B] : k10_xtuple_0(k16_funcop_1(A,B)) = k1_tarski(B) )).
fof(t88_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) <=> ! [B] : ? [C] : r1_tarski(k8_relat_1(A,k1_tarski(B)),k1_tarski(C)) ) ) )).
fof(t88_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ( r1_tarski(k1_relset_1(A,D),k1_relset_1(A,C)) & r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) ) => r1_relset_1(A,B,D,C) ) ) ) )).
fof(t88_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( r1_tarski(k3_xboole_0(C,k9_xtuple_0(A)),k3_xboole_0(C,k9_xtuple_0(B))) => k5_relat_1(k1_funct_4(A,k5_relat_1(B,C)),C) = k5_relat_1(B,C) ) ) ) )).
fof(t88_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ( r1_tarski(B,A) => ( r2_hidden(C,k9_xtuple_0(B)) | r1_tarski(B,k1_funct_7(A,C,D)) ) ) ) ) )).
fof(t88_fvsum_1,axiom,( ! [A] : ( ( ~ v2_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) & v6_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k13_fvsum_1(A,k12_finseq_1(u1_struct_0(A),B),k12_finseq_1(u1_struct_0(A),C)) = k8_group_1(A,B,C) ) ) ) )).
fof(t88_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(A,u1_struct_0(k34_gfacirc1(A,B,C))) & r2_hidden(B,u1_struct_0(k34_gfacirc1(A,B,C))) & r2_hidden(C,u1_struct_0(k34_gfacirc1(A,B,C))) & r2_hidden(k4_tarski(k10_finseq_1(A,B),k4_gfacirc1),u1_struct_0(k34_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(k34_gfacirc1(A,B,C))) ) )).
fof(t88_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( r5_glib_000(A,B) => ( ( r1_glib_000(A,F,G,E) => r1_glib_000(B,F,G,E) ) & ( r2_glib_000(A,F,G,E) => r2_glib_000(B,F,G,E) ) & ( r3_glib_000(A,C,D,E) => r3_glib_000(B,C,D,E) ) & ( r4_glib_000(A,C,D,E) => r4_glib_000(B,C,D,E) ) ) ) ) ) )).
fof(t88_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => k13_glib_001(A,k1_glib_001(A,B)) = k6_domain_1(k6_glib_000(A),B) ) ) )).
fof(t88_goboard6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ~ r1_xboole_0(k1_rltopsp1(k15_euclid(2),A,k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B),k1_matrix_0(B)),k19_euclid(1,1))),k1_tops_1(k15_euclid(2),k3_goboard5(B,k3_finseq_1(B),k1_matrix_0(B)))) ) ) )).
fof(t88_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ( m1_group_2(k10_group_2(A,B,C),B) & m1_group_2(k10_group_2(A,B,C),C) ) ) ) ) )).
fof(t88_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r3_group_3(A,B,C) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & C = k4_group_3(A,B,D) ) ) ) ) ) )).
fof(t88_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & v2_group_1(D) & v3_group_1(D) & v3_group_9(D,A) & l1_group_9(D,A) ) => ! [E] : ( ( 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] : ( ( 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)))) ) => u1_struct_0(k13_group_9(A,B,D,k11_group_9(A,B,C,D,E,F))) = k8_relset_1(u1_struct_0(B),u1_struct_0(C),E,u1_struct_0(k13_group_9(A,C,D,F))) ) ) ) ) ) )).
fof(t88_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v1_vectsp_1(A) & v1_algstr_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => k16_ideal_1(A,k16_ideal_1(A,B,C),D) = k16_ideal_1(A,B,k15_ideal_1(A,C,D)) ) ) ) ) )).
fof(t88_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => k2_integra5(A,k26_valued_1(k1_numbers,k1_numbers,k3_sin_cos2,B)) = k6_xcmplx_0(k3_xcmplx_0(B,k1_funct_1(k1_sin_cos2,k2_seq_4(A))),k3_xcmplx_0(B,k1_funct_1(k1_sin_cos2,k3_seq_4(A)))) ) ) )).
fof(t88_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1)) => ( ( v10_intpro_1(A) & r1_tarski(B,A) ) => r1_tarski(k13_intpro_1(B),A) ) ) ) )).
fof(t88_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( 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] : ( 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) = k3_xcmplx_0(k12_euclid(D),k3_square_1(k6_xcmplx_0(1,k1_square_1(k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(k18_euclid(D),k12_euclid(D)),A),k2_xcmplx_0(1,A)))))) ) ) & ! [D] : ( 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(k5_numbers,k17_euclid(D)) & r1_xxreal_0(k7_xcmplx_0(k18_euclid(D),k12_euclid(D)),A) & D != k4_struct_0(k15_euclid(2)) ) ) ) ) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) | v5_pre_topc(C,k1_pre_topc(k15_euclid(2),B),k3_topmetr) ) ) ) ) ) )).
fof(t88_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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) = 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(C),k17_euclid(B)) & ~ r1_xxreal_0(k17_euclid(D),k17_euclid(C)) & r1_xxreal_0(k17_euclid(D),F) & k1_funct_1(I,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t88_jordan,axiom,( ! [A] : ( ( v2_compts_1(A,k15_euclid(2)) & v1_jordan21(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_jordan24(2,A,k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) => r1_tarski(k1_rltopsp1(k15_euclid(2),k2_jordan21(A),k19_euclid(k5_numbers,k4_xcmplx_0(3))),k6_topreal1(k2_jordan21(A))) ) ) )).
fof(t88_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(C,k17_pscomp_1(B)) & ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => k9_subset_1(u1_struct_0(k15_euclid(2)),k6_topreal1(C),k3_topreal1(2,k2_jordan9(B,A))) != k1_tarski(D) ) ) ) ) ) )).
fof(t88_jordan2c,axiom,( ! [A] : ( ( ~ 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] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & r2_hidden(C,k3_topreal1(2,k1_sprect_1(A))) & ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t88_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,B,B) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,B,B) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( ( r1_matrix10(C,D) & r1_xxreal_0(A,k5_numbers) ) => r2_matrix10(k6_matrix10(B,A,D),k6_matrix10(B,A,C)) ) ) ) ) ) )).
fof(t88_matrix13,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(A)) => ! [F] : ( ( v1_relat_1(F) & v1_funct_1(F) ) => ( ( C = k3_relat_1(F,B) & r1_tarski(k10_xtuple_0(F),k4_finseq_1(B)) & E = k3_relat_1(F,D) & r1_tarski(k10_xtuple_0(F),k4_finseq_1(D)) ) => k3_relat_1(F,k3_fvsum_1(A,B,D)) = k3_fvsum_1(A,C,E) ) ) ) ) ) ) ) )).
fof(t88_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( k3_finseq_1(B) = A => k12_matrixr1(k4_matrixr2(A),B) = B ) ) ) )).
fof(t88_member_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => k12_member_1(k2_tarski(A,B),k2_tarski(C,D)) = k2_enumset1(k4_xxreal_3(A,C),k4_xxreal_3(A,D),k4_xxreal_3(B,C),k4_xxreal_3(B,D)) ) ) ) ) )).
fof(t88_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( v6_supinf_2(D) => ( ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ~ ( E = k1_relset_1(A,D) & r1_mesfunc1(A,B,D,E) ) ) | k7_mesfunc5(A,B,C,D) = k6_mesfunc5(A,B,C,D) ) ) ) ) ) ) )).
fof(t88_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( k3_funct_2(B,k6_numbers,C,E) = k5_numbers => ( ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ~ ( F = k1_relset_1(A,D) & r1_mesfunc6(A,B,D,F) ) ) | k1_mesfunc6(A,B,C,k2_partfun1(A,k1_numbers,D,E)) = k5_numbers ) ) ) ) ) ) ) )).
fof(t88_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & 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) != k1_xboole_0 & v1_ncfcont1(k1_relset_1(u1_struct_0(A),C),A) & r8_ncfcont1(A,B,C,k1_relset_1(u1_struct_0(A),C)) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(D,k1_relset_1(u1_struct_0(A),C)) & r2_hidden(E,k1_relset_1(u1_struct_0(A),C)) & k7_partfun1(k1_numbers,k4_normsp_0(u1_struct_0(A),B,C),D) = k2_seq_4(k2_relset_1(k1_numbers,k4_normsp_0(u1_struct_0(A),B,C))) & k7_partfun1(k1_numbers,k4_normsp_0(u1_struct_0(A),B,C),E) = k3_seq_4(k2_relset_1(k1_numbers,k4_normsp_0(u1_struct_0(A),B,C))) ) ) ) ) ) ) ) )).
fof(t88_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( k2_nat_1(k1_newton(2,A),k1_nat_1(k3_xcmplx_0(2,C),1)) = k2_nat_1(k1_newton(2,B),k1_nat_1(k3_xcmplx_0(2,D),1)) => ( A = B & C = D ) ) ) ) ) ) )).
fof(t88_orders_1,axiom,( ! [A] : ( v3_ordinal1(A) => k2_wellord2(k1_wellord2(A)) = A ) )).
fof(t88_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => r6_pboole(A,k4_pboole(A,k5_pboole(A,B,C),D),k2_pboole(A,k4_pboole(A,B,k2_pboole(A,C,D)),k4_pboole(A,C,k2_pboole(A,B,D)))) ) ) ) )).
fof(t88_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ( ( v5_polyform(A) & k7_polyform(A) = 1 ) => k12_polyform(A) = 2 ) ) )).
fof(t88_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,1) & ~ r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(1,k6_prepower(A,B)) ) ) ) )).
fof(t88_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => k15_qc_lang2(A,k13_qc_lang1(A,B)) = k2_xboole_0(k15_qc_lang2(A,B),k1_tarski(k13_qc_lang1(A,B))) ) ) )).
fof(t88_quatern3,axiom,( k4_quatern3(k24_quaterni(k2_quatern2)) = k4_xcmplx_0(1) )).
fof(t88_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => k28_quaterni(k23_quaterni(A,A)) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(k13_quaterni(A)),k1_square_1(k14_quaterni(A))),k1_square_1(k15_quaterni(A))),k1_square_1(k16_quaterni(A))) ) )).
fof(t88_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ( r1_tarski(k10_xtuple_0(B),A) => k6_relat_1(A,B) = B ) ) )).
fof(t88_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(C))) => ! [G] : ( ( ~ v2_struct_0(G) & l1_rewrite3(G,F) ) => ~ ( r3_rewrite3(C,F,G,A,D,B,E) & ! [H] : ( m1_subset_1(H,k8_afinsq_1(C)) => D != k1_flang_1(C,H,E) ) ) ) ) ) ) ) )).
fof(t88_rfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,k1_numbers))) ) => ( ( v3_funct_1(k2_partfun1(C,k1_numbers,D,A)) & v3_funct_1(k2_partfun1(C,k1_numbers,E,B)) ) => ( v3_funct_1(k2_partfun1(C,k1_numbers,k3_valued_1(C,k1_numbers,k1_numbers,D,E),k3_xboole_0(A,B))) & v3_funct_1(k2_partfun1(C,k1_numbers,k47_valued_1(C,k1_numbers,k1_numbers,D,E),k3_xboole_0(A,B))) & v3_funct_1(k2_partfun1(C,k1_numbers,k20_valued_1(C,k1_numbers,k1_numbers,D,E),k3_xboole_0(A,B))) ) ) ) ) ) )).
fof(t88_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_comseq_2(A) & k5_rinfsup1(A) = k6_rinfsup1(A) ) <=> v2_comseq_2(A) ) ) )).
fof(t88_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_valued_0(A) & v1_finseq_1(A) ) => k18_rvsum_1(k6_rvsum_1(A)) = k4_xcmplx_0(k16_rvsum_1(A)) ) )).
fof(t88_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ( k2_compos_0(u1_compos_1(k1_scmfsa_2),A) = k5_numbers => A = k2_compos_1(k1_scmfsa_2) ) ) )).
fof(t88_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => k1_funct_1(k4_scmpds_6(A,B,C,D),k5_numbers) = k9_scmpds_2(A,B,k1_nat_1(k5_card_1(C),2)) ) ) ) ) )).
fof(t88_scmyciel,axiom,( ! [A] : ( ( v1_scmyciel(A) & v4_scmyciel(A) ) => k12_scmyciel(A) = k2_tarski(k1_xboole_0,k1_tarski(k3_tarski(A))) ) )).
fof(t88_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r2_analoaf(A,D,k3_semi_af1(A,C,B,D),B,C) ) ) ) ) )).
fof(t88_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k2_numbers) => ! [D] : ( m2_finseq_2(D,k2_numbers,k12_seq_4(B)) => ( ( r2_hidden(A,k2_finseq_1(B)) & C = k1_funct_1(D,A) ) => k1_funct_1(k19_seq_4(B,D),A) = k9_complex1(C) ) ) ) ) ) )).
fof(t88_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ( v3_kurato_0(B,A) & v3_kurato_0(C,A) ) => ( v3_kurato_0(k1_setlim_2(A,B,C),A) & k4_kurato_0(A,k1_setlim_2(A,B,C)) = k9_subset_1(A,k4_kurato_0(A,B),k4_kurato_0(A,C)) ) ) ) ) )).
fof(t88_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,C),k5_sheffer1(A,k5_sheffer1(A,B,B),B)),k5_sheffer1(A,k5_sheffer1(A,D,C),k5_sheffer1(A,D,C))) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,D),k5_sheffer1(A,D,C)),k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,D,C))) ) ) ) ) )).
fof(t88_sin_cos6,axiom,( k4_relset_1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_sin_cos6,k5_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k5_numbers,k28_sin_cos))) = k6_partfun1(k1_rcomp_1(k4_xcmplx_0(1),1)) )).
fof(t88_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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,k2_sin_cos9))) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => ( k1_funct_1(D,E) = k2_xcmplx_0(k3_xcmplx_0(A,E),B) & ~ r1_xxreal_0(k1_funct_1(D,E),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(D,E)) ) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k2_sin_cos9),C) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k2_sin_cos9),C),E) = k4_xcmplx_0(k7_xcmplx_0(A,k2_xcmplx_0(1,k1_square_1(k2_xcmplx_0(k3_xcmplx_0(A,E),B))))) ) ) ) ) ) ) ) ) )).
fof(t88_sincos10,axiom,( ! [A] : ( r2_hidden(A,k1_rcomp_1(1,k3_square_1(2))) => r2_hidden(k1_funct_1(k4_sincos10,A),k1_rcomp_1(k7_xcmplx_0(k28_sin_cos,4),k7_xcmplx_0(k28_sin_cos,2))) ) )).
fof(t88_sprect_1,axiom,( ! [A] : ( ( v1_sprect_1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => r1_xboole_0(k2_goboard9(A),k3_goboard9(A)) ) )).
fof(t88_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_valuat_1(D,A,C) => ! [E] : ( m2_subset_1(E,k16_substut1(A),k38_substut1(A)) => ! [F] : ( m1_substut1(F,A,k7_sublemma(A,E,B)) => ( ( v3_substut1(k7_sublemma(A,E,B),A) & ! [G] : ( m2_funct_2(G,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ( r1_valuat_1(A,C,k39_substut1(A,E),D,G) <=> r1_sublemma(A,E,C,k1_sublemma(A,C,G,k3_sublemma(A,E,C,G)),D) ) ) ) => ! [G] : ( m2_funct_2(G,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ( r1_valuat_1(A,C,k39_substut1(A,k9_sublemma(A,k7_sublemma(A,E,B),F)),D,G) <=> r1_sublemma(A,k9_sublemma(A,k7_sublemma(A,E,B),F),C,k1_sublemma(A,C,G,k3_sublemma(A,k9_sublemma(A,k7_sublemma(A,E,B),F),C,G)),D) ) ) ) ) ) ) ) ) ) )).
fof(t88_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_tdlat_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_tdlat_1(A))) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k1_tdlat_1(A)) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(u1_struct_0(A)),k1_tdlat_1(A)) => ( ( B = D & C = E ) => ( r1_lattices(k4_tdlat_1(A),B,C) <=> r1_tarski(D,E) ) ) ) ) ) ) ) )).
fof(t88_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_tsep_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => m1_pre_topc(k6_tex_4(A,C),B) ) ) ) ) )).
fof(t88_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(u1_pre_topc(A),k5_tmap_1(A,B)) ) ) )).
fof(t88_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ( ( 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) & r1_xxreal_0(A,k17_euclid(F)) & r1_xxreal_0(k17_euclid(F),B) & r1_xxreal_0(C,k18_euclid(F)) & r1_xxreal_0(k18_euclid(F),D) ) => r1_xxreal_0(k1_topreal6(2,E,F),k2_xcmplx_0(k6_xcmplx_0(B,A),k6_xcmplx_0(D,C))) ) ) ) ) ) ) ) )).
fof(t88_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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)))) ) => ( v8_transgeo(E,A) => ( r1_aff_1(A,B,C,D) <=> r1_aff_1(A,k3_funct_2(u1_struct_0(A),u1_struct_0(A),E,B),k3_funct_2(u1_struct_0(A),u1_struct_0(A),E,C),k3_funct_2(u1_struct_0(A),u1_struct_0(A),E,D)) ) ) ) ) ) ) ) )).
fof(t88_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( ( A = k1_tsep_1(A,B,C) & r1_tsep_1(B,C) ) => ( r4_tsep_1(A,B,C) <=> ( v1_borsuk_1(B,A) & m1_pre_topc(B,A) & v1_borsuk_1(C,A) & m1_pre_topc(C,A) ) ) ) ) ) ) )).
fof(t88_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v1_valued_2(D) => ! [E] : ( v1_valued_2(E) => ! [F] : ( v1_valued_2(F) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,D))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(B,E))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(C,F))) ) => k84_valued_2(k3_xboole_0(B,C),A,k2_valued_2(k3_xboole_0(k1_valued_2(E),k1_valued_2(F))),D,k73_valued_2(B,C,E,F,H,I),G) = k73_valued_2(k3_xboole_0(B,A),k3_xboole_0(C,A),k2_valued_2(k3_xboole_0(k1_valued_2(E),k1_valued_2(D))),k2_valued_2(k3_xboole_0(k1_valued_2(F),k1_valued_2(D))),k84_valued_2(B,A,E,D,H,G),k84_valued_2(C,A,F,D,I,G)) ) ) ) ) ) ) )).
fof(t88_xboole_1,axiom,( ! [A] : ! [B] : ( r1_xboole_0(A,B) => k4_xboole_0(k2_xboole_0(A,B),B) = A ) )).
fof(t88_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k10_xboolean(A,k7_xboolean(A,B)) = k3_xboolean(B) ) ) )).
fof(t88_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( B != k5_numbers => A = k3_xcmplx_0(A,k7_xcmplx_0(B,B)) ) ) ) )).
fof(t88_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) ) ) ) )).
fof(t88_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => r1_xboole_0(k3_xxreal_1(A,B),k1_tarski(A)) ) ) )).
fof(t88_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ( ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r2_hidden(B,A) & r2_hidden(C,A) & r1_xxreal_0(B,D) & r1_xxreal_0(D,C) ) => r2_hidden(D,A) ) ) ) ) => v6_xxreal_2(A) ) ) )).
fof(t88_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( k2_xxreal_0 != B & B != k1_xxreal_0 & B != k5_numbers & ~ ( k6_xxreal_3(k4_xxreal_3(A,B),B) = A & k4_xxreal_3(A,k6_xxreal_3(B,B)) = A ) ) ) ) )).
fof(t88_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v6_zf_lang(A) => k29_zf_lang(A) = k2_xboole_0(k29_zf_lang(k24_zf_lang(A)),k1_tarski(A)) ) ) )).
fof(t88_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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))) ) => ( v6_zf_lang(A) => ( r1_zf_model(B,C,A) <=> ! [D] : ( m1_subset_1(D,B) => r1_zf_model(B,k2_zf_lang1(B,C,k23_zf_lang(A),D),k24_zf_lang(A)) ) ) ) ) ) ) )).
fof(t88_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ! [E] : ! [F] : ( r2_hidden(k4_tarski(E,F),k2_zfmisc_1(A,C)) <=> r2_hidden(k4_tarski(E,F),k2_zfmisc_1(B,D)) ) => k2_zfmisc_1(A,C) = k2_zfmisc_1(B,D) ) )).
fof(t88_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_zmodul01(D,A) => ! [E] : ( m2_zmodul01(E,A,D) => ~ ( r2_hidden(B,E) & r2_hidden(C,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_struct_0(D,F) & k3_rlvect_1(A,B,F) = C ) ) ) ) ) ) ) ) )).
fof(t89_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_abcmiz_1(B,A) & m1_subset_1(B,u4_struct_0(A)) ) => ! [C] : ( m1_subset_1(C,k3_card_3(u3_msualg_1(A,k1_msafree3(A,k28_abcmiz_1(A))))) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) & v6_trees_3(D) ) => ( C = k4_trees_4(k4_tarski(B,u1_struct_0(A)),D) => k46_abcmiz_1(A,C) = k3_tarski(a_2_2_abcmiz_1(A,D)) ) ) ) ) ) )).
fof(t89_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v7_ordinal1(E) => ~ ( r2_hidden(k14_aofa_000(A,B,C,D),k9_aofa_000(A,k18_aofa_000(A),E)) & ! [F] : ( v7_ordinal1(F) => ~ ( E = k1_nat_1(F,1) & r2_hidden(B,k9_aofa_000(A,k18_aofa_000(A),F)) & r2_hidden(C,k9_aofa_000(A,k18_aofa_000(A),F)) & r2_hidden(D,k9_aofa_000(A,k18_aofa_000(A),F)) ) ) ) ) ) ) ) ) )).
fof(t89_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v19_aofa_a00(D,A) & m1_subset_1(D,u1_struct_0(A)) ) => k10_aofa_a01(A,B,C,D,1) = k30_aofa_a00(A,C,D,k27_aofa_a00(A,C,D),k28_aofa_a00(A,C,D)) ) ) ) ) )).
fof(t89_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( m1_subset_1(C,k5_arytm_3) => ~ ( r3_arytm_3(A,B) & r3_arytm_3(B,C) & B != C & A = C ) ) ) ) )).
fof(t89_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( r1_xxreal_0(4,A) => r1_xxreal_0(k2_nat_1(2,A),k3_xcmplx_0(A,k3_power(2,A))) ) ) )).
fof(t89_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ! [C] : ( v1_card_1(C) => ! [D] : ( v1_card_1(D) => ( ~ ( ~ ( r2_hidden(A,B) & r2_hidden(C,D) ) & ~ ( r1_ordinal1(A,B) & r2_hidden(C,D) ) & ~ ( r2_hidden(A,B) & r1_ordinal1(C,D) ) & ~ ( r1_ordinal1(A,B) & r1_ordinal1(C,D) ) ) => ( r1_ordinal1(k2_card_2(A,C),k2_card_2(B,D)) & r1_ordinal1(k2_card_2(C,A),k2_card_2(B,D)) ) ) ) ) ) ) )).
fof(t89_card_3,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ( v1_finset_1(A) => ( ( ~ r1_ordinal1(B,A) & ~ r2_hidden(B,A) ) | v1_finset_1(B) ) ) ) ) )).
fof(t89_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ~ ( k3_finseq_1(B) = 5 & ~ r1_chord(A,k3_glib_001(A,B),k4_glib_001(A,B)) & v5_chord(B,A) ) ) ) )).
fof(t89_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_clvect_1(B,A) => ! [C] : ( m2_clvect_1(C,A,B) => ( v6_clvect_1(C,A) <=> C = u1_struct_0(B) ) ) ) ) )).
fof(t89_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( v7_ordinal1(D) => k1_valued_0(u1_struct_0(A),k6_clvect_1(A,C,B),D) = k6_clvect_1(A,k1_valued_0(u1_struct_0(A),C,D),B) ) ) ) ) )).
fof(t89_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ! [D] : ( r2_hidden(k4_tarski(k4_tarski(C,1),k4_tarski(D,1)),k1_coh_sp(k15_cohsp_1(A,B))) <=> r2_hidden(k4_tarski(C,D),k1_coh_sp(A)) ) ) ) )).
fof(t89_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ( r3_cqc_the1(A,k7_domain_1(k3_cqc_lang(A),B,C),D) <=> r3_cqc_the1(A,k6_domain_1(k3_cqc_lang(A),k7_cqc_lang(A,B,C)),D) ) ) ) ) ) )).
fof(t89_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k16_sin_cos),D) ) & r2_hidden(A,k1_relset_1(k1_numbers,k27_sin_cos)) & r2_hidden(B,k1_relset_1(k1_numbers,k27_sin_cos)) ) => k9_diff_1(C,A,B) = k7_xcmplx_0(k6_xcmplx_0(k19_sin_cos(A),k19_sin_cos(B)),k6_xcmplx_0(A,B)) ) ) ) ) )).
fof(t89_euclid_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( v1_xreal_0(G) => ( ( 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,A,D),k47_valued_1(k1_numbers,k1_numbers,k1_numbers,B,E),k47_valued_1(k1_numbers,k1_numbers,k1_numbers,C,F),G) = k8_euclid(3,k8_euclid_8(A,B,C,G),k8_euclid_8(D,E,F,G)) ) ) ) ) ) ) ) ) )).
fof(t89_euclidlp,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( m1_subset_1(G,k4_ordinal1) => ! [H] : ( m2_finseq_2(H,k1_numbers,k1_euclid(G)) => ! [I] : ( m2_finseq_2(I,k1_numbers,k1_euclid(G)) => ! [J] : ( m2_finseq_2(J,k1_numbers,k1_euclid(G)) => ! [K] : ( m2_finseq_2(K,k1_numbers,k1_euclid(G)) => ( ( r3_euclidlp(G,k8_euclid(G,J,I),k8_euclid(G,K,I)) & k2_xcmplx_0(k2_xcmplx_0(A,B),C) = 1 & H = k7_euclid(G,k7_euclid(G,k9_euclid(G,I,A),k9_euclid(G,J,B)),k9_euclid(G,K,C)) & k2_xcmplx_0(k2_xcmplx_0(D,E),F) = 1 & H = k7_euclid(G,k7_euclid(G,k9_euclid(G,I,D),k9_euclid(G,J,E)),k9_euclid(G,K,F)) ) => ( A = D & B = E & C = F ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t89_facirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ~ v1_facirc_1(k2_msafree2(k19_facirc_1(A,B,C))) ) ) ) )).
fof(t89_finseq_1,axiom,( ! [A] : ! [B] : ( r2_hidden(A,k4_finseq_1(k9_finseq_1(B))) => A = 1 ) )).
fof(t89_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_finseq_2(C,B) => m1_finseq_2(C,A) ) ) ) )).
fof(t89_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ( r1_xboole_0(k10_xtuple_0(A),k10_xtuple_0(B)) & v2_funct_1(A) & v2_funct_1(B) ) <=> v2_funct_1(k7_finseq_1(A,B)) ) ) ) )).
fof(t89_finseq_4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_eqrel_1(C,A) => ( ( r1_setfam_1(B,C) & k5_card_1(B) = k5_card_1(C) ) => B = C ) ) ) ) )).
fof(t89_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => k1_finseq_6(A,B,k7_partfun1(A,B,1)) = B ) ) )).
fof(t89_flang_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ( k2_flang_2(A,C) = k1_tarski(B) => B = k2_flang_1(A) ) ) )).
fof(t89_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ( r1_tarski(B,k2_flang_3(A,C)) => ( r1_xxreal_0(D,k5_numbers) | r1_tarski(k1_flang_3(A,B,D),k2_flang_3(A,C)) ) ) ) ) ) )).
fof(t89_funcop_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r2_hidden(C,D) => k3_relat_1(k16_funcop_1(B,C),k7_funcop_1(D,A)) = k16_funcop_1(B,A) ) )).
fof(t89_funct_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => ( r1_tarski(k10_xtuple_0(B),k9_xtuple_0(C)) => r1_tarski(k8_relat_1(B,A),k8_relat_1(k3_relat_1(B,C),k7_relat_1(C,A))) ) ) ) )).
fof(t89_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ( r1_tarski(k5_partfun1(A,B,C),k5_partfun1(A,B,D)) & ! [E] : B != k1_tarski(E) ) => r1_relset_1(A,B,D,C) ) ) ) )).
fof(t89_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : k1_funct_1(k1_funct_4(k1_funct_4(A,k16_funcop_1(B,C)),k16_funcop_1(E,D)),E) = D ) )).
fof(t89_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( k5_relat_1(A,C) = k5_relat_1(B,C) & r1_funct_7(A,B,C) ) => A = B ) ) ) )).
fof(t89_fvsum_1,axiom,( ! [A] : ( ( ~ v2_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) & v6_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k13_fvsum_1(A,k2_finseq_4(u1_struct_0(A),B,C),k2_finseq_4(u1_struct_0(A),D,E)) = k3_rlvect_1(A,k8_group_1(A,B,D),k8_group_1(A,C,E)) ) ) ) ) ) )).
fof(t89_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(k4_tarski(k10_finseq_1(A,B),k4_gfacirc1),k3_msafree2(k34_gfacirc1(A,B,C))) & r2_hidden(k36_gfacirc1(A,B,C),k3_msafree2(k34_gfacirc1(A,B,C))) ) )).
fof(t89_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ( r5_glib_000(A,B) => ( ( v2_glib_000(A) => v2_glib_000(B) ) & ( v3_glib_000(A) => v3_glib_000(B) ) & ( v4_glib_000(A) => v4_glib_000(B) ) & ( v5_glib_000(A) => v5_glib_000(B) ) & ( v6_glib_000(A) => v6_glib_000(B) ) & ( v7_glib_000(A) => v7_glib_000(B) ) & ( v8_glib_000(A) => v8_glib_000(B) ) ) ) ) ) )).
fof(t89_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ( r1_glib_000(A,C,D,B) => k13_glib_001(A,k2_glib_001(A,C,D,B)) = k2_tarski(C,D) ) ) )).
fof(t89_goboard6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ~ r1_xboole_0(k1_rltopsp1(k15_euclid(2),A,k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,1,k1_matrix_0(B)),k19_euclid(k4_xcmplx_0(1),1))),k1_tops_1(k15_euclid(2),k3_goboard5(B,k5_numbers,k1_matrix_0(B)))) ) ) )).
fof(t89_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( 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)) ) ) ) ) )).
fof(t89_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r3_group_3(A,B,B) ) ) )).
fof(t89_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_group_1(C) & v3_group_1(C) & v3_group_9(C,A) & l1_group_9(C,A) ) => ! [D] : ( m1_group_9(D,A,B) => ! [E] : ( m1_group_9(E,A,C) => ! [F] : ( ( v1_funct_1(F) & v1_funct_2(F,u1_struct_0(B),u1_struct_0(C)) & v1_group_6(F,B,C) & v7_group_9(F,A,B,C) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)))) ) => ( ( u1_struct_0(E) = k7_relset_1(u1_struct_0(B),u1_struct_0(C),F,u1_struct_0(D)) | u1_struct_0(D) = k8_relset_1(u1_struct_0(B),u1_struct_0(C),F,u1_struct_0(E)) ) => ( v1_funct_1(k2_partfun1(u1_struct_0(B),u1_struct_0(C),F,u1_struct_0(D))) & v1_funct_2(k2_partfun1(u1_struct_0(B),u1_struct_0(C),F,u1_struct_0(D)),u1_struct_0(D),u1_struct_0(E)) & v1_group_6(k2_partfun1(u1_struct_0(B),u1_struct_0(C),F,u1_struct_0(D)),D,E) & v7_group_9(k2_partfun1(u1_struct_0(B),u1_struct_0(C),F,u1_struct_0(D)),A,D,E) & m1_subset_1(k2_partfun1(u1_struct_0(B),u1_struct_0(C),F,u1_struct_0(D)),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(D),u1_struct_0(E)))) ) ) ) ) ) ) ) )).
fof(t89_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l4_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => k16_ideal_1(A,k13_ideal_1(A,C,D),B) = k13_ideal_1(A,k16_ideal_1(A,C,B),k16_ideal_1(A,D,B)) ) ) ) ) )).
fof(t89_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => k2_integra5(A,k26_valued_1(k1_numbers,k1_numbers,k22_sin_cos,B)) = k6_xcmplx_0(k3_xcmplx_0(B,k1_funct_1(k22_sin_cos,k2_seq_4(A))),k3_xcmplx_0(B,k1_funct_1(k22_sin_cos,k3_seq_4(A)))) ) ) )).
fof(t89_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => r1_tarski(A,k13_intpro_1(A)) ) )).
fof(t89_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) = 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(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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t89_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( r1_jordan24(2,A,k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) & r1_jordan2c(2,A,B) ) => r1_xboole_0(k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,3),k1_jordan21(A)),B) ) ) ) )).
fof(t89_jordan1a,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(C,k14_pscomp_1(B)) & ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => k9_subset_1(u1_struct_0(k15_euclid(2)),k7_topreal1(C),k3_topreal1(2,k2_jordan9(B,A))) != k1_tarski(D) ) ) ) ) ) )).
fof(t89_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( v6_limfunc1(A) => ( v6_limfunc1(k26_valued_1(k1_numbers,k1_numbers,A,B)) & k5_limfunc1(k26_valued_1(k1_numbers,k1_numbers,A,B)) = k3_xcmplx_0(B,k5_limfunc1(A)) ) ) ) ) )).
fof(t89_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,B,B) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,B,B) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( ( r2_matrix10(C,D) & r1_xxreal_0(k5_numbers,A) ) => r2_matrix10(k6_matrix10(B,A,C),k6_matrix10(B,A,D)) ) ) ) ) ) )).
fof(t89_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(D),C,B) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(D))) ) => ( E != k4_struct_0(D) => k8_matrix13(D,F) = k8_matrix13(D,k3_matrix11(A,C,B,u1_struct_0(D),F,k10_fvsum_1(k1_matrix_0(F),D,k7_matrix_0(u1_struct_0(D),F,A),E))) ) ) ) ) ) ) ) )).
fof(t89_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,A,A) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( ( v1_matrixr2(D,A) & k3_finseq_1(B) = A & k3_finseq_1(C) = A ) => ( k12_matrixr1(D,B) = C <=> B = k12_matrixr1(k7_matrixr2(A,D),C) ) ) ) ) ) ) )).
fof(t89_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( ( r2_hidden(C,A) & r2_hidden(D,B) ) => r2_hidden(k3_xcmplx_0(C,D),k13_member_1(A,B)) ) ) ) ) ) )).
fof(t89_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ( r1_mesfunc2(A,B,D) & v6_supinf_2(D) ) => ( k7_mesfunc5(A,B,C,D) = k6_mesfunc5(A,B,C,D) & k7_mesfunc5(A,B,C,D) = k5_mesfunc5(A,B,C,D) ) ) ) ) ) ) )).
fof(t89_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ( ( E = k1_relset_1(A,D) & r1_mesfunc6(A,B,D,E) & k3_funct_2(B,k6_numbers,C,F) = k5_numbers ) => k1_mesfunc6(A,B,C,k2_partfun1(A,k1_numbers,D,k7_prob_1(A,B,E,F))) = k1_mesfunc6(A,B,C,D) ) ) ) ) ) ) ) )).
fof(t89_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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) & r9_ncfcont1(B,A,C,k1_relset_1(u1_struct_0(B),C)) & ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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,k4_normsp_0(u1_struct_0(B),A,C),D) = k2_seq_4(k2_relset_1(k1_numbers,k4_normsp_0(u1_struct_0(B),A,C))) & k7_partfun1(k1_numbers,k4_normsp_0(u1_struct_0(B),A,C),E) = k3_seq_4(k2_relset_1(k1_numbers,k4_normsp_0(u1_struct_0(B),A,C))) ) ) ) ) ) ) ) )).
fof(t89_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => r1_nat_d(k1_newton(A,B),k1_newton(A,C)) ) ) ) ) )).
fof(t89_orders_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ r2_hidden(k1_xboole_0,A) => ! [B] : ( m2_orders_1(B,A,k6_partfun1(A)) => ! [C] : ( r2_hidden(C,A) => r2_hidden(k1_funct_1(B,C),C) ) ) ) ) )).
fof(t89_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => r6_pboole(A,k4_pboole(A,B,k5_pboole(A,C,D)),k2_pboole(A,k4_pboole(A,B,k2_pboole(A,C,D)),k3_pboole(A,k3_pboole(A,B,C),D))) ) ) ) )).
fof(t89_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ( ( v5_polyform(A) & k7_polyform(A) = 2 ) => k12_polyform(A) = k13_polyform(A) ) ) )).
fof(t89_prepower,axiom,( ! [A] : ( v1_rat_1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(B) & v2_comseq_2(C) & ! [D] : ( v7_ordinal1(D) => ( ~ r1_xxreal_0(k1_funct_1(B,D),k5_numbers) & k1_funct_1(C,D) = k4_prepower(k1_funct_1(B,D),A) ) ) ) => ( r1_xxreal_0(k1_seq_2(B),k5_numbers) | k1_seq_2(C) = k4_prepower(k1_seq_2(B),A) ) ) ) ) ) )).
fof(t89_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => k15_qc_lang2(A,k14_qc_lang1(A,C,B)) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A,C),k15_qc_lang2(A,B)),k1_tarski(k14_qc_lang1(A,C,B))) ) ) ) )).
fof(t89_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k3_quatern3(A) = k24_quaterni(k4_quatern3(k24_quaterni(A))) ) )).
fof(t89_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => k28_quaterni(k23_quaterni(A,A)) = k28_quaterni(k23_quaterni(A,k27_quaterni(A))) ) )).
fof(t89_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => k6_relat_1(k10_xtuple_0(A),A) = A ) )).
fof(t89_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(C))) => ! [G] : ( ( ~ v2_struct_0(G) & l1_rewrite3(G,F) ) => ( r3_rewrite3(C,F,G,A,D,B,E) => r1_xxreal_0(k1_afinsq_1(E),k1_afinsq_1(D)) ) ) ) ) ) ) )).
fof(t89_rfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ( v3_funct_1(k2_partfun1(B,k1_numbers,D,A)) => v3_funct_1(k2_partfun1(B,k1_numbers,k26_valued_1(B,k1_numbers,D,C),A)) ) ) ) ) )).
fof(t89_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(A) => ( k1_seq_2(A) = k5_rinfsup1(A) & k1_seq_2(A) = k6_rinfsup1(A) ) ) ) )).
fof(t89_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => k18_rvsum_1(k5_rvsum_1(A,B,C)) = k2_xcmplx_0(k18_rvsum_1(B),k18_rvsum_1(C)) ) ) ) )).
fof(t89_scmfsa_2,axiom,( k2_compos_1(k1_ami_3) = k2_compos_1(k1_scmfsa_2) )).
fof(t89_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v3_scmpds_4(D) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( ( r1_scmpds_6(C,B,A) & r2_scmpds_6(C,B,A) ) => ( r1_xxreal_0(k5_numbers,k1_funct_1(B,k2_scmpds_2(k1_funct_1(B,E),F))) | ( r1_scmpds_6(k4_scmpds_6(E,F,C,D),B,A) & r2_scmpds_6(k4_scmpds_6(E,F,C,D),B,A) ) ) ) ) ) ) ) ) ) )).
fof(t89_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( r1_semi_af1(A,F,k3_semi_af1(A,C,B,F),k3_semi_af1(A,E,D,F)) <=> r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) )).
fof(t89_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => k19_seq_4(A,k15_seq_4(A)) = k5_finseq_2(k4_ordinal1,A,k5_numbers) ) )).
fof(t89_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ( v3_kurato_0(B,A) & v3_kurato_0(C,A) ) => ( v3_kurato_0(k2_setlim_2(A,B,C),A) & k4_kurato_0(A,k2_setlim_2(A,B,C)) = k4_subset_1(A,k4_kurato_0(A,B),k4_kurato_0(A,C)) ) ) ) ) )).
fof(t89_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,C,B) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,C,B)),k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,C,B))) ) ) ) )).
fof(t89_sin_cos6,axiom,( k4_relset_1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k5_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k5_numbers,k28_sin_cos)),k3_sin_cos6) = k6_partfun1(k1_rcomp_1(k5_numbers,k28_sin_cos)) )).
fof(t89_sin_cos9,axiom,( ! [A] : ( ( 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,k3_taylor_1))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) & ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & r1_xxreal_0(k1_funct_1(k1_sin_cos9,B),k5_numbers) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k3_taylor_1),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k3_taylor_1),A),B) = k7_xcmplx_0(1,k3_xcmplx_0(k2_xcmplx_0(1,k1_square_1(B)),k1_funct_1(k1_sin_cos9,B))) ) ) ) ) ) )).
fof(t89_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,k3_square_1(2)) ) => k1_funct_1(k1_fdiff_9,k5_sincos10(A)) = A ) ) )).
fof(t89_sprect_1,axiom,( ! [A] : ( ( v1_sprect_1(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => k2_goboard9(A) != k3_goboard9(A) ) )).
fof(t89_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_valuat_1(C,A,B) => ! [D] : ( m2_subset_1(D,k16_substut1(A),k38_substut1(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t89_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k4_tdlat_1(A)))) => ? [C] : ( m1_subset_1(C,u1_struct_0(k4_tdlat_1(A))) & r4_lattice3(k4_tdlat_1(A),C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(k4_tdlat_1(A))) => ( r4_lattice3(k4_tdlat_1(A),D,B) => r1_lattices(k4_tdlat_1(A),C,D) ) ) ) ) ) )).
fof(t89_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_borsuk_1(B,A) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => m1_pre_topc(k6_tex_4(A,C),B) ) ) ) ) )).
fof(t89_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(a_2_1_tmap_1(A,B),k5_tmap_1(A,B)) ) ) )).
fof(t89_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( ( 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)))) ) => ( ( v8_transgeo(B,A) & v8_transgeo(C,A) ) => ( v8_transgeo(k2_funct_2(u1_struct_0(A),B),A) & v8_transgeo(k1_transgeo(u1_struct_0(A),C,B),A) & v8_transgeo(k6_partfun1(u1_struct_0(A)),A) ) ) ) ) ) )).
fof(t89_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( ~ r1_tsep_1(B,C) => ( r4_tsep_1(A,B,C) <=> ~ ( ~ m1_pre_topc(B,C) & ~ m1_pre_topc(C,B) & ! [D] : ( ( ~ v2_struct_0(D) & v1_tsep_1(D,A) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ v2_struct_0(E) & v1_tsep_1(E,A) & m1_pre_topc(E,A) ) => ~ ( 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(k1_tsep_1(A,B,C),k1_tsep_1(A,D,E)) & ! [F] : ( ( ~ v2_struct_0(F) & v1_borsuk_1(F,A) & 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,F,k1_tsep_1(A,B,C)),k2_tsep_1(A,B,C)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t89_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v1_valued_2(D) => ! [E] : ( v1_valued_2(E) => ! [F] : ( v1_valued_2(F) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,D))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(B,E))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(C,F))) ) => k84_valued_2(A,k3_xboole_0(B,C),D,k2_valued_2(k3_xboole_0(k1_valued_2(E),k1_valued_2(F))),G,k79_valued_2(B,C,E,F,H,I)) = k79_valued_2(k3_xboole_0(A,B),k3_xboole_0(A,C),k2_valued_2(k3_xboole_0(k1_valued_2(D),k1_valued_2(E))),k2_valued_2(k3_xboole_0(k1_valued_2(D),k1_valued_2(F))),k84_valued_2(A,B,D,E,G,H),k84_valued_2(A,C,D,F,G,I)) ) ) ) ) ) ) )).
fof(t89_xboole_1,axiom,( ! [A] : ! [B] : r1_xboole_0(k3_xboole_0(A,B),k4_xboole_0(A,B)) )).
fof(t89_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k10_xboolean(k3_xboolean(A),k7_xboolean(A,B)) = B ) ) )).
fof(t89_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( B != k5_numbers => A = k7_xcmplx_0(k3_xcmplx_0(A,B),B) ) ) ) )).
fof(t89_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A)) => ( r1_xxreal_0(k5_xcmplx_0(B),k5_numbers) | r1_xxreal_0(A,B) ) ) ) ) )).
fof(t89_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(D,A) => r1_xboole_0(k1_xxreal_1(C,D),k4_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t89_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ( ( v6_xxreal_2(A) & v6_xxreal_2(B) ) => ( r1_xboole_0(A,B) | v6_xxreal_2(k2_xboole_0(A,B)) ) ) ) ) )).
fof(t89_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ( k4_xxreal_3(k1_xxreal_0,A) != 1 & k4_xxreal_3(k2_xxreal_0,A) != 1 ) ) )).
fof(t89_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( v1_zf_lang(C) & m2_finseq_1(C,k4_ordinal1) ) => ( r2_hidden(B,k29_zf_lang(A)) => ( ( ~ r1_zf_lang(C,B) & ~ r3_zf_lang(C,B) & ~ r2_zf_lang(C,B) ) | r2_hidden(C,k29_zf_lang(A)) ) ) ) ) ) )).
fof(t89_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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))) ) => ( v8_zf_lang(A) => ( r1_zf_model(B,C,A) <=> ( r1_zf_model(B,C,k21_zf_lang(A)) | r1_zf_model(B,C,k22_zf_lang(A)) ) ) ) ) ) ) )).
fof(t89_zfmisc_1,axiom,( ! [A] : ! [B] : ( k2_zfmisc_1(A,B) = k1_xboole_0 <=> ( A = k1_xboole_0 | B = k1_xboole_0 ) ) )).
fof(t89_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_zmodul01(D,A) => ! [E] : ( m2_zmodul01(E,A,D) => ~ ( r2_hidden(B,E) & r2_hidden(C,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_struct_0(D,F) & k5_algstr_0(A,B,F) = C ) ) ) ) ) ) ) ) )).
fof(t8_abcmiz_0,axiom,( ! [A] : ( l2_abcmiz_0(A) => ! [B] : ( 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)) & v8_abcmiz_0(A) ) => v8_abcmiz_0(B) ) ) ) )).
fof(t8_abcmiz_1,axiom,( k1_abcmiz_1(k1_xboole_0) = k1_xboole_0 )).
fof(t8_abcmiz_a,axiom,( r1_subset_1(k2_abcmiz_1,k20_abcmiz_1) )).
fof(t8_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k5_numbers,k3_xcmplx_0(A,B)) => k3_square_1(k3_xcmplx_0(A,B)) = k3_xcmplx_0(k3_square_1(k9_complex1(A)),k3_square_1(k9_complex1(B))) ) ) ) )).
fof(t8_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r1_aff_1(A,B,C,D) & r2_analoaf(A,B,C,D,E) ) => ( B = C | r1_aff_1(A,B,C,E) ) ) ) ) ) ) ) )).
fof(t8_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v13_aff_2(A) <=> v14_aff_2(A) ) ) )).
fof(t8_aff_3,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v6_aff_3(A) <=> v8_aff_3(A) ) ) )).
fof(t8_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) => ! [H] : ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(A))) => ( ( r2_hidden(F,G) & r2_hidden(F,H) & r2_hidden(B,G) & r2_hidden(C,H) & r2_hidden(E,H) & v1_aff_1(G,A) & v1_aff_1(H,A) & F = D ) => ( F = B | F = C | G = H | ( ~ r2_analoaf(A,B,C,D,E) & ~ r2_analoaf(A,C,B,E,D) ) | F = E ) ) ) ) ) ) ) ) ) ) )).
fof(t8_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ( ( k2_afinsq_1(A) = k2_afinsq_1(B) & ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k2_afinsq_1(A)) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) => A = B ) ) ) )).
fof(t8_afinsq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v5_ordinal1(C) & v1_finset_1(C) ) => ( ~ r1_xxreal_0(k1_afinsq_1(C),k2_xcmplx_0(B,A)) => k1_funct_1(k2_afinsq_2(C,A),B) = k1_funct_1(C,k2_xcmplx_0(B,A)) ) ) ) ) )).
fof(t8_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( r2_hidden(B,k2_afproj(A)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & B = C & v1_aff_4(C,A) ) ) ) )).
fof(t8_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r2_analoaf(A,B,C,D,E) & r2_analoaf(A,B,D,F,E) ) => C = F ) ) ) ) ) ) ) )).
fof(t8_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect01(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_analoaf(A,B,D,B,E) & r2_analoaf(A,B,C,B,E) & C != D & C != E & D != E ) ) ) ) ) ) )).
fof(t8_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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) => ( k1_relset_1(u1_struct_0(A),C) = u1_struct_0(A) & k2_relset_1(u1_struct_0(B),C) = u1_struct_0(B) ) ) ) ) ) )).
fof(t8_algseq_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r2_funct_2(k4_ordinal1,u1_struct_0(A),B,k2_algseq_1(A,k4_struct_0(A))) <=> k10_xtuple_0(B) = k1_tarski(k4_struct_0(A)) ) ) ) )).
fof(t8_algspec1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( m1_subset_1(C,A) => k1_funct_1(k1_algspec1(A,B),C) = k1_funct_1(k1_funct_4(k6_partfun1(A),B),C) ) ) ) )).
fof(t8_algstr_1,axiom,( ! [A] : ( ( ~ v2_struct_0(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) & l2_algstr_0(A) ) <=> ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_algstr_0(A,B,k4_struct_0(A)) = B ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & k1_algstr_0(A,B,C) = k4_struct_0(A) ) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_algstr_0(A,B,C) = k1_algstr_0(A,C,B) ) ) ) ) ) )).
fof(t8_algstr_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_algstr_1(A) & v4_algstr_1(A) & v7_algstr_1(A) & v2_rlvect_1(A) & v4_rlvect_1(A) & v2_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) ) )).
fof(t8_algstr_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_algstr_3(A) & l1_algstr_3(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( k1_algstr_3(A,D,B,C) = k1_algstr_3(A,E,B,C) => ( B = k4_struct_0(A) | D = E ) ) ) ) ) ) ) )).
fof(t8_algstr_4,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( m1_algstr_4(B,A) => ( v2_algstr_4(u1_struct_0(B),A) & m1_subset_1(u1_struct_0(B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).
fof(t8_altcat_1,axiom,( ! [A] : ( v4_funct_1(A) => ! [B] : ( v4_funct_1(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t8_altcat_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,B) & v1_funct_1(E) & v1_partfun1(E,B) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,C) & v1_funct_1(F) & v1_partfun1(F,C) ) => ( ( r2_altcat_2(A,B,D,E) & r2_altcat_2(B,C,E,F) ) => r2_altcat_2(A,C,D,F) ) ) ) ) )).
fof(t8_altcat_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_altcat_3(A,B,C) & r2_altcat_3(A,C,D) ) => r2_altcat_3(A,B,D) ) ) ) ) ) )).
fof(t8_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_altcat_1(A,B,C)) => ( v7_altcat_3(B,A) => v4_altcat_3(D,A,B,C) ) ) ) ) ) )).
fof(t8_altcat_5,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(k7_altcat_1(B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(k7_altcat_1(B))))) ) => ( r2_hidden(k4_card_3(C),B) => ( v2_altcat_5(k3_altcat_5(A,B,C),k7_altcat_1(B),A,C,k2_altcat_5(A,B,C)) & v3_altcat_5(k3_altcat_5(A,B,C),k7_altcat_1(B),A,C,k2_altcat_5(A,B,C)) ) ) ) ) )).
fof(t8_ami_2,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k3_ami_2,k4_ami_2))) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k1_funct_1(k6_ami_2(A,B),C) = k1_funct_1(A,C) ) ) ) )).
fof(t8_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ( ( k1_funct_1(D,A) = k5_numbers => k1_funct_1(k2_extpro_1(k7_card_1(2),k1_ami_3,k8_ami_3(C,A),D),k4_struct_0(k1_ami_3)) = C ) & ( k1_funct_1(D,A) != k5_numbers => k1_funct_1(k2_extpro_1(k7_card_1(2),k1_ami_3,k8_ami_3(C,A),D),k4_struct_0(k1_ami_3)) = k4_card_1(k5_memstr_0(k7_card_1(2),k1_ami_3,D)) ) & k1_funct_1(k2_extpro_1(k7_card_1(2),k1_ami_3,k8_ami_3(C,A),D),B) = k1_funct_1(D,B) ) ) ) ) ) )).
fof(t8_ami_5,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => ~ ( k2_compos_0(u1_compos_1(k1_ami_3),A) = 2 & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_ami_3)) ) => A != k3_ami_3(B,C) ) ) ) ) )).
fof(t8_ami_6,axiom,( ! [A] : ( m1_subset_1(A,k1_compos_0(u1_compos_1(k1_ami_3))) => ( A = 5 => k3_compos_0(u1_compos_1(k1_ami_3),A) = k1_tarski(k1_xboole_0) ) ) )).
fof(t8_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r1_ami_wstd(A,B,k1_ami_wstd(A,B,C),k1_ami_wstd(A,B,D)) <=> r1_xxreal_0(C,D) ) ) ) ) ) )).
fof(t8_amistd_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_setfam_1(B) => ! [C] : ( v7_ordinal1(C) => ( C = A => k3_amistd_1(B,k4_amistd_1(B),C) = k2_tarski(A,k1_nat_1(A,1)) ) ) ) ) )).
fof(t8_amistd_2,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_extpro_1(A))) => k5_xtuple_0(B) = k5_numbers ) ) )).
fof(t8_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ~ ( v1_zfmisc_1(k4_memstr_0(A,B,D)) & r2_hidden(D,k5_amistd_4(A,B,C)) ) ) ) ) ) )).
fof(t8_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_analmetr(A,B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_analmetr(A,D,E,B,C) & E != k4_struct_0(A) ) ) ) ) ) ) )).
fof(t8_analoaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_analoaf(A,B,C,B,C) ) ) ) )).
fof(t8_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r1_analmetr(A,C,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => B != k1_analort(A,C,D,E) ) ) ) ) ) ) )).
fof(t8_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ( 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)) = k3_rlvect_1(A,k3_rlvect_1(A,k1_rlvect_1(A,B,H),k1_rlvect_1(A,C,I)),k1_rlvect_1(A,D,J)) => ( r2_anproj_1(A,B,C,D) | ( E = H & F = I & G = J ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ( ( r1_anproj_2(A,C,D,E) & r1_anproj_2(A,I,J,K) & r1_anproj_2(A,F,G,H) & r3_anproj_2(A,B,C,D,E,I,J,K) & r2_anproj_2(A,C,D,E,F,G,H) & r2_anproj_2(A,I,J,K,F,G,H) ) => ( v9_struct_0(B,A) | r1_anproj_1(A,B,I) | r1_anproj_1(A,B,J) | r1_anproj_1(A,B,K) | r1_anproj_1(A,C,I) | r1_anproj_1(A,D,J) | r1_anproj_1(A,E,K) | r2_anproj_1(A,B,C,D) | r2_anproj_1(A,B,C,E) | r2_anproj_1(A,B,D,E) | r2_anproj_1(A,F,G,H) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_aofa_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => r2_hidden(k1_funct_1(A,B),k5_aofa_000(A,B)) ) ) )).
fof(t8_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( k1_funct_1(k1_borsuk_7(A,B,C,D,E,F),C) = F & ( B != C => k1_funct_1(k1_borsuk_7(A,B,C,D,E,F),B) = E ) & ~ ( A != B & A != C & k1_funct_1(k1_borsuk_7(A,B,C,D,E,F),A) != D ) ) )).
fof(t8_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( l3_msualg_1(D,A) => ! [E] : ( ( v4_msualg_1(E,A) & 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,C),u4_msualg_1(A,C)) & 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)) ) => ! [F] : ( m2_pboole(F,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,D)) => ! [G] : ( m2_pboole(G,u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,E)) => ( ( r8_pboole(u1_struct_0(A),F,G) & r2_msualg_3(A,B,D,F) ) => r2_msualg_3(A,C,E,G) ) ) ) ) ) ) ) ) ) )).
fof(t8_aofa_i00,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( v1_funct_1(D) & v2_funct_1(D) & v1_funct_2(D,A,k1_card_1(A)) & v2_funct_2(D,k1_card_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_card_1(A)))) ) => ( v1_funct_1(k14_funct_7(A,k1_card_1(A),k14_funct_7(A,k1_card_1(A),D,B,k3_funct_2(A,k1_card_1(A),D,C)),C,k3_funct_2(A,k1_card_1(A),D,B))) & v2_funct_1(k14_funct_7(A,k1_card_1(A),k14_funct_7(A,k1_card_1(A),D,B,k3_funct_2(A,k1_card_1(A),D,C)),C,k3_funct_2(A,k1_card_1(A),D,B))) & v1_funct_2(k14_funct_7(A,k1_card_1(A),k14_funct_7(A,k1_card_1(A),D,B,k3_funct_2(A,k1_card_1(A),D,C)),C,k3_funct_2(A,k1_card_1(A),D,B)),A,k1_card_1(A)) & v2_funct_2(k14_funct_7(A,k1_card_1(A),k14_funct_7(A,k1_card_1(A),D,B,k3_funct_2(A,k1_card_1(A),D,C)),C,k3_funct_2(A,k1_card_1(A),D,B)),k1_card_1(A)) & m1_subset_1(k14_funct_7(A,k1_card_1(A),k14_funct_7(A,k1_card_1(A),D,B,k3_funct_2(A,k1_card_1(A),D,C)),C,k3_funct_2(A,k1_card_1(A),D,B)),k1_zfmisc_1(k2_zfmisc_1(A,k1_card_1(A)))) ) ) ) ) ) )).
fof(t8_armstrng,axiom,( ! [A] : ! [B] : ( r2_hidden(B,k4_armstrng(A)) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) & ? [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) & B = k4_tarski(C,D) ) ) ) )).
fof(t8_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ~ r2_hidden(k5_funct_4(k1_numbers,k5_numbers,1,A,B),k1_numbers) ) ) )).
fof(t8_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ! [C] : ( m1_subset_1(C,k2_arytm_2) => ( r1_arytm_2(A,B) => r1_arytm_2(k8_arytm_2(A,C),k8_arytm_2(B,C)) ) ) ) ) )).
fof(t8_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_arytm_2)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_arytm_2)) => ~ ( ? [C] : ( m1_subset_1(C,k2_arytm_2) & r2_hidden(C,B) ) & ! [C] : ( m1_subset_1(C,k2_arytm_2) => ! [D] : ( m1_subset_1(D,k2_arytm_2) => ( ( r2_hidden(C,A) & r2_hidden(D,B) ) => r1_arytm_2(C,D) ) ) ) & ! [C] : ( m1_subset_1(C,k2_arytm_2) => ? [D] : ( m1_subset_1(D,k2_arytm_2) & ? [E] : ( m1_subset_1(E,k2_arytm_2) & r2_hidden(D,A) & r2_hidden(E,B) & ~ ( r1_arytm_2(D,C) & r1_arytm_2(C,E) ) ) ) ) ) ) ) )).
fof(t8_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ! [B] : ( ( v3_ordinal1(B) & v7_ordinal1(B) ) => ( ( r2_arytm_3(A,B) & r2_arytm_3(B,A) ) => A = B ) ) ) )).
fof(t8_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(B,k5_numbers) => k9_nat_1(k1_numbers,A,B) = k2_power(B,k3_power(2,B)) ) ) & ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v4_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( r2_funct_2(k4_ordinal1,k1_numbers,B,A) & ~ v7_asympt_0(B) ) ) ) ) )).
fof(t8_autalg_1,axiom,( ! [A] : ( ( ~ 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_autalg_1(A)) ) )).
fof(t8_autgroup,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_autgroup(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_autgroup(A))) => ! [D] : ( m2_funct_2(D,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) => ! [E] : ( m2_funct_2(E,u1_struct_0(A),u1_struct_0(A),k1_autgroup(A)) => ( ( B = D & C = E ) => k6_algstr_0(k3_autgroup(A),B,C) = k1_partfun1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),E,D) ) ) ) ) ) ) )).
fof(t8_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_bcialg_1(A,B,k1_bcialg_1(A,B,k1_bcialg_1(A,B,C))) = k1_bcialg_1(A,B,C) ) ) ) )).
fof(t8_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k1_bcialg_2(A,B,k1_bcialg_1(A,B,k1_bcialg_1(A,B,C)),D) = k1_bcialg_2(A,B,C,D) ) ) ) ) )).
fof(t8_bcialg_3,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t8_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( k1_bcialg_4(A,k4_struct_0(A),B) = B & k1_bcialg_4(A,B,k4_struct_0(A)) = B ) ) ) )).
fof(t8_bcialg_5,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => k1_bcialg_5(A,B,C,D,E) = k1_bcialg_2(A,k1_bcialg_2(A,k1_bcialg_5(A,B,C,k5_numbers,k5_numbers),k1_bcialg_1(A,B,C),D),k1_bcialg_1(A,C,B),E) ) ) ) ) ) )).
fof(t8_bcialg_6,axiom,( ! [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] : ( m2_subset_1(B,u1_struct_0(A),k5_bcialg_1(A)) => k3_bcialg_6(A,k4_xcmplx_0(1),k3_bcialg_6(A,k4_xcmplx_0(1),B)) = B ) ) )).
fof(t8_bciideal,axiom,( ! [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] : ( m2_bcialg_1(B,A) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),B) => r1_tarski(k1_bciideal(A,C),B) ) ) ) )).
fof(t8_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_bhsp_1(A,k4_algstr_0(A,B),C) = k4_xcmplx_0(k2_bhsp_1(A,B,C)) ) ) ) )).
fof(t8_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_bhsp_2(C,A) => v1_bhsp_2(k4_normsp_1(A,C,B),A) ) ) ) ) )).
fof(t8_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => ? [D] : ( v1_xreal_0(D) & ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ~ ( r1_xxreal_0(E,C) & r1_xxreal_0(D,k3_bhsp_1(A,k1_normsp_1(A,B,E))) ) ) ) ) ) ) )).
fof(t8_bhsp_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ( v1_bhsp_4(C,B) => ( v1_bhsp_4(k5_normsp_1(B,C,A),B) & k2_bhsp_4(B,k5_normsp_1(B,C,A)) = k1_rlvect_1(B,k2_bhsp_4(B,C),A) ) ) ) ) ) )).
fof(t8_bhsp_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ( r1_xxreal_0(1,k3_finseq_1(C)) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ( ( k4_finseq_1(C) = k4_finseq_1(D) & ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( r2_hidden(E,k4_finseq_1(D)) => k1_funct_1(D,E) = k1_funct_1(u1_bhsp_1(A),k4_tarski(B,k1_funct_1(C,E))) ) ) ) => k2_bhsp_1(A,B,k1_finsop_1(u1_struct_0(A),C,u1_algstr_0(A))) = k1_finsop_1(k1_numbers,D,k9_binop_2) ) ) ) ) ) ) )).
fof(t8_bhsp_6,axiom,( ! [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_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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_bhsp_6(B,A) => ! [C] : ( ( 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))) ) => ( v2_bhsp_6(C,A) => r1_bhsp_6(A,B,C) ) ) ) ) ) ) )).
fof(t8_bhsp_7,axiom,( ! [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_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] : ( m2_bhsp_5(B,A) => ! [C] : ( ( 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] : ( 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) ) ) & v1_bhsp_6(B,A) ) => k2_bhsp_1(A,k2_bhsp_6(A,B),k2_bhsp_6(A,B)) = k3_bhsp_6(A,B,C) ) ) ) ) ) )).
fof(t8_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ( k1_relset_1(u1_struct_0(C),k7_bilinear(A,B,C,D,E)) = u1_struct_0(C) & r1_tarski(k2_relset_1(u1_struct_0(A),k7_bilinear(A,B,C,D,E)),u1_struct_0(A)) & ! [F] : ( m1_subset_1(F,u1_struct_0(C)) => k3_funct_2(u1_struct_0(C),u1_struct_0(A),k7_bilinear(A,B,C,D,E),F) = k2_binop_1(u1_struct_0(B),u1_struct_0(C),u1_struct_0(A),D,E,F) ) ) ) ) ) ) ) )).
fof(t8_binari_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => k3_binari_2(k2_xcmplx_0(A,1),k9_binarith(A,1,k6_margrel1,k1_binari_2(A),k10_binarith(k6_margrel1,k7_margrel1))) = 1 ) )).
fof(t8_binari_3,axiom,( ! [A] : ( v7_ordinal1(A) => k4_finseq_5(k1_numbers,k5_euclid(A)) = k5_euclid(A) ) )).
fof(t8_binari_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k2_xcmplx_0(B,C),k6_xcmplx_0(A,1)) => ( ~ r1_xxreal_0(A,B) & ~ r1_xxreal_0(A,C) ) ) ) ) ) )).
fof(t8_binarith,axiom,( ! [A] : ( v1_xboolean(A) => k10_xboolean(k7_margrel1,A) = A ) )).
fof(t8_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( k2_binom(A,B,k5_numbers) = k1_group_1(A) & k2_binom(A,B,1) = B ) ) ) )).
fof(t8_binop_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ( v1_binop_1(B,A) => ( r1_binop_1(A,C,B) <=> r2_binop_1(A,C,B) ) ) ) ) )).
fof(t8_binop_2,axiom,( k4_binop_1(k3_numbers,k17_binop_2) = 1 )).
fof(t8_bintree1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ( ( v1_bintree1(A) & v1_bintree1(B) ) <=> v1_bintree1(k13_trees_3(A,B)) ) ) ) )).
fof(t8_boole,axiom,( ! [A] : ! [B] : ~ ( v1_xboole_0(A) & A != B & v1_xboole_0(B) ) )).
fof(t8_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_boolealg(A,k3_lattices(A,k4_lattices(A,B,C),k4_lattices(A,B,D)),B) => r3_lattices(A,B,k3_lattices(A,C,D)) ) ) ) ) ) )).
fof(t8_bor_cant,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( ( v5_relat_1(D,B) & v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [E] : ( v7_ordinal1(E) => k3_funct_2(B,k1_numbers,C,k1_prob_2(A,B,k1_prob_3(A,k2_prob_1(A,D)),E)) = k6_xcmplx_0(1,k3_funct_2(B,k1_numbers,C,k1_prob_2(A,B,k2_prob_3(A,D),E))) ) ) ) ) ) )).
fof(t8_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_connsp_2(E,A,C) => ! [F] : ( m1_connsp_2(F,B,D) => m1_connsp_2(k3_borsuk_1(A,B,E,F),k2_borsuk_1(A,B),k4_borsuk_1(A,B,C,D)) ) ) ) ) ) ) )).
fof(t8_borsuk_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v2_pre_topc(D) & l1_pre_topc(D) ) => ! [E] : ( ( 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] : ( ( 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] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(C,D)))) => ! [H] : ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(k2_borsuk_1(C,D)))) => ( r2_hidden(H,k7_borsuk_1(C,D,G)) => 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),H),k2_borsuk_1(A,B)) ) ) ) ) ) ) ) ) ) )).
fof(t8_borsuk_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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))) => v3_tops_2(D,k2_borsuk_1(B,k1_pre_topc(A,k6_domain_1(u1_struct_0(A),C))),B) ) ) ) ) ) )).
fof(t8_borsuk_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( A != B => k5_measure6(k4_rcomp_1(A,B)) = k1_rcomp_1(A,B) ) ) ) )).
fof(t8_borsuk_5,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ( r5_zfmisc_1(A,B,C,D,E,F,G) => r5_zfmisc_1(A,B,E,C,F,G,D) ) )).
fof(t8_borsuk_6,axiom,( m1_borsuk_2(k3_struct_0(k5_topmetr),k17_borsuk_1,k18_borsuk_1,k19_borsuk_1) )).
fof(t8_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( k19_sin_cos(A) = k5_numbers & ! [B] : ( v1_int_1(B) => A != k2_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2),k3_xcmplx_0(k28_sin_cos,B)) ) ) ) )).
fof(t8_brouwer2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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)) => ( v2_tops_1(B,k15_euclid(A)) | ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k1_pre_topc(k15_euclid(A),B)),u1_struct_0(k1_pre_topc(k15_euclid(A),B))) & v5_pre_topc(C,k1_pre_topc(k15_euclid(A),B),k1_pre_topc(k15_euclid(A),B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(A),B)),u1_struct_0(k1_pre_topc(k15_euclid(A),B))))) ) => v2_abian(C) ) ) ) ) ) )).
fof(t8_bspace,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k2_bspace)) => ( A = k4_struct_0(k2_bspace) <=> A != k5_struct_0(k2_bspace) ) ) )).
fof(t8_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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,k5_bvfunc_1(A,B,C),k5_bvfunc_1(A,D,E)),k5_bvfunc_1(A,k5_bvfunc_1(A,k5_bvfunc_1(A,k2_bvfunc_1(A,B,D),k2_bvfunc_1(A,B,E)),k2_bvfunc_1(A,C,D)),k2_bvfunc_1(A,C,E))) ) ) ) ) ) )).
fof(t8_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [E] : ( m1_eqrel_1(E,A) => ( r1_bvfunc_1(A,B,C) => r1_bvfunc_1(A,k6_bvfunc_2(A,B,D,E),k7_bvfunc_2(A,C,D,E)) ) ) ) ) ) ) )).
fof(t8_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ( B = k2_enumset1(C,D,E,F) => ( C = D | D = E | D = F | k5_bvfunc_2(A,D,B) = k2_partit1(A,k2_partit1(A,C,E),F) ) ) ) ) ) ) ) ) )).
fof(t8_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)),k9_bvfunc_1(A,k9_bvfunc_1(A,B,C),k9_bvfunc_1(A,B,D))) ) ) ) ) )).
fof(t8_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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,B,k1_bvfunc_1(A,B)),k12_bvfunc_1(A)) & r2_funct_2(A,k6_margrel1,k1_bvfunc_1(A,k5_bvfunc26(A,B,k1_bvfunc_1(A,B))),k11_bvfunc_1(A)) ) ) ) )).
fof(t8_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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,k11_bvfunc_1(A)),B) ) ) )).
fof(t8_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( m1_eqrel_1(D,A) => r2_funct_2(A,k6_margrel1,k7_bvfunc_2(A,k12_bvfunc_1(A),B,D),k12_bvfunc_1(A)) ) ) ) ) )).
fof(t8_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( m1_eqrel_1(E,A) => r1_bvfunc_1(A,k6_bvfunc_1(A,C,D),k5_bvfunc_1(A,k1_bvfunc_1(A,k6_bvfunc_1(A,k7_bvfunc_2(A,k1_bvfunc_1(A,C),B,E),k7_bvfunc_2(A,D,B,E))),k1_bvfunc_1(A,k6_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,k1_bvfunc_1(A,D),B,E))))) ) ) ) ) ) )).
fof(t8_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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),k5_bvfunc_1(A,k1_bvfunc_1(A,B),C)) ) ) ) )).
fof(t8_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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,k1_bvfunc_1(A,C),k1_bvfunc_1(A,B)),k12_bvfunc_1(A)) ) ) ) ) )).
fof(t8_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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,D),k9_bvfunc_1(A,k9_bvfunc_1(A,C,D),k9_bvfunc_1(A,k5_bvfunc_1(A,B,C),D))),k12_bvfunc_1(A)) ) ) ) ) )).
fof(t8_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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,C),D),k9_bvfunc_1(A,B,k5_bvfunc_1(A,k1_bvfunc_1(A,C),D))) ) ) ) ) )).
fof(t8_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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,B,k5_bvfunc_1(A,k5_bvfunc_1(A,k5_bvfunc_1(A,k2_bvfunc_1(A,k2_bvfunc_1(A,B,C),D),k2_bvfunc_1(A,k2_bvfunc_1(A,B,C),k1_bvfunc_1(A,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,k1_bvfunc_1(A,C)),k1_bvfunc_1(A,D)))) ) ) ) ) )).
fof(t8_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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,k5_bvfunc_1(A,B,C),D),k9_bvfunc_1(A,B,D)) ) ) ) ) )).
fof(t8_c0sp1,axiom,( ! [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) & v2_funcsdom(A) & v3_group_1(A) & v5_group_1(A) & v1_vectsp_1(A) & v3_vectsp_1(A) & l1_funcsdom(A) ) => ! [B] : ( m2_c0sp1(B,A) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( v1_xreal_0(E) => ( C = D => k1_rlvect_1(B,C,E) = k1_rlvect_1(A,D,E) ) ) ) ) & k1_group_1(B) = k1_group_1(A) & k4_struct_0(B) = k4_struct_0(A) ) ) ) )).
fof(t8_c0sp2,axiom,( ! [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) & v3_group_1(A) & v5_group_1(A) & v1_vectsp_1(A) & v3_vectsp_1(A) & v2_funcsdom(A) & l1_funcsdom(A) ) => ! [B] : ( m2_c0sp1(B,A) => ! [C] : ( m2_c0sp1(C,A) => ( r1_tarski(u1_struct_0(B),u1_struct_0(C)) => m2_c0sp1(B,C) ) ) ) ) )).
fof(t8_calcul_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_finseq_1(B,k3_cqc_lang(A)) => ! [C] : ( m2_finseq_1(C,k3_cqc_lang(A)) => r2_calcul_1(A,B,k8_finseq_1(k3_cqc_lang(A),B,C)) ) ) ) )).
fof(t8_calcul_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => r1_xboole_0(k2_finseq_1(B),k2_calcul_2(B,A)) ) ) )).
fof(t8_cantor_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => r2_hidden(A,k2_cantor_1(A,B)) ) )).
fof(t8_card_1,axiom,( ! [A] : ! [B] : ( v1_card_1(B) => ( r2_hidden(A,B) => r2_hidden(k1_card_1(A),B) ) ) )).
fof(t8_card_2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ! [D] : ( 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)))) ) ) ) ) )).
fof(t8_card_3,axiom,( ! [A] : ! [B] : k3_card_3(k16_funcop_1(A,B)) = B )).
fof(t8_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => k7_setfam_1(A,B) = a_2_0_card_fil(A,B) ) ) )).
fof(t8_card_fin,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( v7_ordinal1(C) => ( k5_card_1(B) != C => v1_xboole_0(k1_card_fin(B,C,A,A)) ) ) ) )).
fof(t8_card_lar,axiom,( ! [A] : ( ( v3_ordinal1(A) & v4_ordinal1(A) & ~ v1_finset_1(A) ) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ~ ( v1_card_lar(C,A) & r2_hidden(B,A) & ! [D] : ( m1_subset_1(D,A) => ~ r2_hidden(D,a_3_0_card_lar(A,B,C)) ) ) ) ) ) )).
fof(t8_cardfin2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ? [B] : ( v1_xreal_0(B) & r2_hidden(B,k2_rcomp_1(k4_xcmplx_0(1),k5_numbers)) & k6_xcmplx_0(k5_card_1(k2_cardfin2(A)),k7_xcmplx_0(k2_newton(k5_card_1(A)),k4_power)) = k4_xcmplx_0(k3_xcmplx_0(k2_newton(k5_card_1(A)),k7_xcmplx_0(k3_xcmplx_0(k23_sin_cos(B),k1_newton(k4_xcmplx_0(1),k1_nat_1(k5_card_1(A),1))),k2_newton(k1_nat_1(k5_card_1(A),1))))) ) ) )).
fof(t8_cat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_cat_1(F,A,B,C) => ~ ( r2_tarski(k2_cat_1(A,B,C),k2_cat_1(A,D,E)) & k2_cat_1(A,B,C) = k1_tarski(F) & ! [G] : ( m1_cat_1(G,A,D,E) => k2_cat_1(A,D,E) != k1_tarski(G) ) ) ) ) ) ) ) ) )).
fof(t8_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => m3_cat_2(A,A) ) )).
fof(t8_cat_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u4_struct_0(B)) => r2_funct_2(A,u4_struct_0(k2_oppcat_1(B)),k4_cat_3(B,A,k8_funcop_1(u4_struct_0(B),A,C)),k8_funcop_1(u4_struct_0(k2_oppcat_1(B)),A,k5_oppcat_1(B,C))) ) ) )).
fof(t8_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k5_cat_4(A,B))) => v10_cat_1(C,k5_cat_4(A,B)) ) )).
fof(t8_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => m2_cat_1(C,A,k4_cat_5(A,B,C)) ) ) ) )).
fof(t8_catalan1,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,1) => k1_catalan1(A) = k7_xcmplx_0(k7_newton(k7_nat_d(k3_xcmplx_0(2,A),2)),k2_nat_1(k7_newton(k7_nat_d(A,1)),k7_newton(A))) ) ) )).
fof(t8_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ~ ( v1_catalan2(B) & r1_xxreal_0(k1_nat_1(k3_xcmplx_0(2,A),1),k3_xcmplx_0(2,k7_afinsq_2(k5_relat_1(B,k1_nat_1(k3_xcmplx_0(2,A),1))))) ) ) ) )).
fof(t8_catalg_1,axiom,( ! [A] : ( ( v3_catalg_1(A) & l1_msualg_1(A) ) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ( ( ( r2_hidden(k4_tarski(B,C),u1_struct_0(A)) & r2_hidden(k4_tarski(B,D),u1_struct_0(A)) ) | ( r2_hidden(k4_tarski(B,C),u4_struct_0(A)) & r2_hidden(k4_tarski(B,D),u4_struct_0(A)) ) ) => k3_finseq_1(C) = k3_finseq_1(D) ) ) ) ) )).
fof(t8_cayldick,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_cayldick)) => k8_group_1(k3_cayldick,A,A) = k1_square_1(k2_normsp_0(k3_cayldick,A)) ) )).
fof(t8_cayley,axiom,( ! [A] : ( v7_ordinal1(A) => k2_cayley(k2_finseq_1(A)) = k4_matrix_2(A) ) )).
fof(t8_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k4_struct_0(k3_cc0sp1(A)) = k8_funcop_1(k4_ordinal1,A,k5_numbers) ) )).
fof(t8_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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))) ) => ( v1_funct_1(k55_valued_1(u1_struct_0(A),k2_numbers,B)) & v1_funct_2(k55_valued_1(u1_struct_0(A),k2_numbers,B),u1_struct_0(A),k1_numbers) & m1_subset_1(k55_valued_1(u1_struct_0(A),k2_numbers,B),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_numbers))) & v1_pscomp_1(k55_valued_1(u1_struct_0(A),k2_numbers,B),A) ) ) ) )).
fof(t8_cfcont_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( 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,C)) => r2_relset_1(k4_ordinal1,k2_numbers,k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,B,k25_valued_1(k2_numbers,k2_numbers,C,A)),k25_valued_1(k4_ordinal1,k2_numbers,k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,B,C),A)) ) ) ) ) )).
fof(t8_cfdiff_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k2_numbers,k2_numbers))) ) => ( r2_cfdiff_1(B,A) => m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) ) )).
fof(t8_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ! [C] : ( m2_funct_2(C,A,k2_numbers,k9_funct_2(A,k2_numbers)) => ! [D] : ( 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,k2_cfuncdom(A),C,D)),k1_funcsdom(A,k2_numbers,k2_cfuncdom(A),k1_funcsdom(A,k2_numbers,k2_cfuncdom(A),B,C),D)) ) ) ) ) )).
fof(t8_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ~ ( r2_hidden(B,k1_relset_1(A,k2_cfunct_1(A,C))) & k7_partfun1(k2_numbers,C,B) = k5_numbers ) ) ) ) )).
fof(t8_cgames_1,axiom,( ! [A] : ( ( r2_hidden(A,k8_cgames_1(k5_cgames_1)) => A = k3_cgames_1 ) & ( A = k3_cgames_1 => r2_hidden(A,k8_cgames_1(k5_cgames_1)) ) & ( r2_hidden(A,k6_cgames_1(k5_cgames_1)) => A = k3_cgames_1 ) & ( A = k3_cgames_1 => r2_hidden(A,k6_cgames_1(k5_cgames_1)) ) & ( r2_hidden(A,k7_cgames_1(k5_cgames_1)) => A = k3_cgames_1 ) & ( A = k3_cgames_1 => r2_hidden(A,k7_cgames_1(k5_cgames_1)) ) ) )).
fof(t8_chain_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v1_finset_1(B) => ( ( v1_abian(k5_card_1(A)) <=> v1_abian(k5_card_1(B)) ) <=> v1_abian(k5_card_1(k5_xboole_0(A,B))) ) ) ) )).
fof(t8_chord,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v1_abian(A) ) => ~ ( r1_xxreal_0(A,6) & A != 1 & A != 3 & A != 5 ) ) )).
fof(t8_circcmb2,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r1_tarski(B,C) => ( v1_facirc_1(k4_xboole_0(A,B)) | k4_xboole_0(A,C) = k4_xboole_0(A,B) ) ) ) )).
fof(t8_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ( ( r1_xboole_0(k2_msafree2(A),k3_msafree2(B)) & r1_xboole_0(k2_msafree2(B),k3_msafree2(A)) ) => ! [C] : ( ( ~ v2_struct_0(C) & ~ v11_struct_0(C) & v2_msafree2(C) & l1_msualg_1(C) ) => ( C = k2_circcomb(A,B) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ( r2_circcomb(A,B,D,E) => ! [F] : ( ( v4_msualg_1(F,C) & v4_msafree2(F,C) & l3_msualg_1(F,C) ) => ( F = k3_circcomb(A,B,D,E) => ! [G] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(C,F))) => ! [H] : ( 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] : ( m1_subset_1(I,k4_card_3(u3_msualg_1(B,E))) => ( ( I = k5_relat_1(G,u1_struct_0(B)) & v1_circcmb3(I,B,E) ) => k2_circcmb3(C,F,G) = k5_nat_1(k2_circcmb3(A,D,H),k2_circcmb3(B,E,I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ( r1_xboole_0(k3_msafree2(A),k3_msafree2(B)) => v2_msafree2(k2_circcomb(A,B)) ) ) ) )).
fof(t8_circled1,axiom,( ! [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) ) => ! [B] : ( ( v3_rltopsp1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v3_rltopsp1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => v3_rltopsp1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) )).
fof(t8_circtrm1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v3_trees_3(B) ) => ! [C] : k12_trees_9(k2_xboole_0(A,B),C) = k2_xboole_0(k12_trees_9(A,C),k12_trees_9(B,C)) ) ) )).
fof(t8_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_card_3(u3_msualg_1(A,B))) => ! [D] : ( m1_subset_1(D,u4_struct_0(A)) => r2_hidden(k1_funct_1(k5_msualg_1(A,D,B),k3_circuit1(A,B,C,D)),k1_funct_1(u3_msualg_1(A,B),k2_msualg_1(A,D))) ) ) ) ) )).
fof(t8_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_msafree2(D,A,B) => k4_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,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),k4_circuit2(A,B,C,D)) ) ) ) ) )).
fof(t8_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m2_finseq_1(E,k4_ordinal1) ) => ( r1_pdiff_9(A,B,k5_pdiff_9(A,B,k8_finseq_1(k4_ordinal1,E,D),C)) <=> r1_pdiff_9(A,B,k5_pdiff_9(A,B,D,k5_pdiff_9(A,B,E,C))) ) ) ) ) ) ) )).
fof(t8_classes1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => k3_classes1(A,k1_ordinal1(B)) = k2_xboole_0(k2_xboole_0(a_2_0_classes1(A,B),a_2_1_classes1(A,B)),k8_subset_1(k1_zfmisc_1(k3_classes1(A,B)),k9_setfam_1(k3_classes1(A,B)),k1_classes1(A))) ) )).
fof(t8_classes2,axiom,( ! [A] : ! [B] : ( ( v1_ordinal1(A) & r2_hidden(A,k1_classes1(B)) ) => r1_tarski(A,k1_classes1(B)) ) )).
fof(t8_clopban1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m2_funct_2(C,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => k1_funct_1(k2_clopban1(A,B),k4_tarski(D,k1_funct_1(k2_clopban1(A,B),k4_tarski(E,C)))) = k1_funct_1(k2_clopban1(A,B),k4_tarski(k3_xcmplx_0(D,E),C)) ) ) ) ) ) )).
fof(t8_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(k6_clopban1(A,A)),k8_clopban1(A,A)) => ( k3_clopban2(A,k6_clopban2(A),B) = B & k3_clopban2(A,B,k6_clopban2(A)) = B ) ) ) )).
fof(t8_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( m2_valued_0(C,u1_struct_0(A),B) & v9_clvect_1(B,A) ) => k7_clvect_1(A,C) = k7_clvect_1(A,B) ) ) ) ) )).
fof(t8_clopban4,axiom,( ! [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) & 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v9_clvect_1(B,A) & v9_clvect_1(C,A) ) => k7_clvect_1(A,k4_clopban3(A,B,C)) = k6_algstr_0(A,k7_clvect_1(A,B),k7_clvect_1(A,C)) ) ) ) ) )).
fof(t8_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_pboole(C,A,B) => r6_pboole(A,C,k1_closure1(A,B,B,k2_msualg_3(A,B),C)) ) ) )).
fof(t8_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( ( r2_pboole(A,B,D) & r2_pboole(A,C,D) ) => m1_subset_1(k2_tarski(B,C),k1_zfmisc_1(k1_closure2(A,D))) ) ) ) ) )).
fof(t8_closure3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) => r6_pboole(A,k2_closure3(A,B,C),k2_mboolean(A,k5_closure2(A,B,C))) ) ) )).
fof(t8_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xcmplx_0(C) => k1_clvect_1(A,k4_algstr_0(A,B),k4_xcmplx_0(C)) = k1_clvect_1(A,B,C) ) ) ) )).
fof(t8_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clvect_2(C,A) => v1_clvect_2(k4_normsp_1(A,C,B),A) ) ) ) ) )).
fof(t8_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v1_xcmplx_0(C) => ( v1_clvect_3(B,A) => ( v1_clvect_3(k6_clvect_1(A,B,C),A) & k1_clvect_3(A,k6_clvect_1(A,B,C)) = k1_clvect_1(A,k1_clvect_3(A,B),C) ) ) ) ) ) )).
fof(t8_coh_sp,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ( ! [C] : ! [D] : ( ( r2_hidden(C,A) & r2_hidden(D,A) ) => r2_hidden(k2_tarski(C,D),B) ) => r1_tarski(A,k3_tarski(B)) ) ) )).
fof(t8_cohsp_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ! [B] : ! [C] : ~ ( r2_hidden(B,A) & r2_hidden(C,A) & ! [D] : ~ ( r1_tarski(D,k3_xboole_0(B,C)) & r2_hidden(D,A) ) ) => v2_cohsp_1(A) ) ) )).
fof(t8_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_collsp(A,B,C,D) => r1_collsp(A,C,D,B) ) ) ) ) ) )).
fof(t8_combgras,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( l1_incsp_1(B) => ( g1_incsp_1(u1_incsp_1(A),u2_incsp_1(A),u3_incsp_1(A)) = g1_incsp_1(u1_incsp_1(B),u2_incsp_1(B),u3_incsp_1(B)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u1_incsp_1(B)) => ( C = D => ! [E] : ( m1_subset_1(E,u2_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u2_incsp_1(B)) => ( ( E = F & r1_incsp_1(A,C,E) ) => r1_incsp_1(B,D,F) ) ) ) ) ) ) ) ) ) )).
fof(t8_compact1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ~ v1_compts_1(A) => v7_compact1(k1_yellow_9(k1_compact1(A),A),A,k1_compact1(A)) ) ) )).
fof(t8_compl_sp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v6_tbsp_1(B,A) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ( ( B = D & C = k2_pre_topc(k3_pcomps_1(A),D) ) => ( v6_tbsp_1(C,A) & k3_tbsp_1(A,B) = k3_tbsp_1(A,C) ) ) ) ) ) ) ) )).
fof(t8_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k3_complex1(k2_xcmplx_0(A,B)) = k3_real_1(k3_complex1(A),k3_complex1(B)) & k4_complex1(k2_xcmplx_0(A,B)) = k3_real_1(k4_complex1(A),k4_complex1(B)) ) ) ) )).
fof(t8_complex2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => k17_sin_cos(A) = k17_sin_cos(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B),A)) ) ) )).
fof(t8_complfld,axiom,( k1_group_1(k1_complfld) = k6_complex1 )).
fof(t8_complsp2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v1_valued_0(A) ) => m2_finseq_2(A,k2_numbers,k12_seq_4(k3_finseq_1(A))) ) )).
fof(t8_compos_0,axiom,( ! [A] : ( m1_subset_1(A,k2_tarski(k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0),k3_xtuple_0(1,k1_xboole_0,k1_xboole_0))) => k5_xtuple_0(A) = k1_xboole_0 ) )).
fof(t8_compos_1,axiom,( ! [A] : ( l1_compos_1(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(A)) & v1_funct_1(B) & v1_finset_1(B) ) => k5_compos_1(A,B,k5_numbers) = B ) ) )).
fof(t8_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => k3_compos_2(A,B,C) = k2_compos_2(A,k11_compos_1(A,B),C) ) ) ) )).
fof(t8_comptrig,axiom,( ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k1_rcomp_1(k5_numbers,k28_sin_cos)) => r1_xxreal_0(k5_numbers,k1_funct_1(k16_sin_cos,A)) ) ) )).
fof(t8_compts_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_compts_1(A) & v4_pre_topc(B,A) ) => v2_compts_1(B,A) ) ) ) )).
fof(t8_comput_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( k10_xtuple_0(B) = A => k10_xtuple_0(k5_funct_6(k9_finseq_1(B))) = k4_finseq_2(1,A) ) ) ) )).
fof(t8_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B),C),k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,C))) ) ) ) )).
fof(t8_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_comseq_2(A) <=> ? [B] : ( v1_xreal_0(B) & ~ r1_xxreal_0(B,k5_numbers) & ! [C] : ( v7_ordinal1(C) => ~ r1_xxreal_0(B,k9_complex1(k9_nat_1(k2_numbers,A,C))) ) ) ) ) )).
fof(t8_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v1_xreal_0(D) => ( ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(E,C) => r1_xxreal_0(k9_nat_1(k1_numbers,A,E),k3_xcmplx_0(D,k9_nat_1(k1_numbers,B,E))) ) ) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( r1_xxreal_0(k2_xcmplx_0(E,F),C) => r1_xxreal_0(k5_real_1(k9_nat_1(k1_numbers,k3_series_1(A),k2_xcmplx_0(E,F)),k9_nat_1(k1_numbers,k3_series_1(A),E)),k3_xcmplx_0(D,k5_real_1(k9_nat_1(k1_numbers,k3_series_1(B),k2_xcmplx_0(E,F)),k9_nat_1(k1_numbers,k3_series_1(B),E)))) ) ) ) ) ) ) ) ) )).
fof(t8_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( 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) = k3_funct_2(k9_setfam_1(u4_struct_0(A)),k9_setfam_1(u1_struct_0(A)),k2_conlat_1(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))) ) ) )).
fof(t8_conmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v11_aff_2(k3_analmetr(A)) => v8_conmetr(A) ) ) )).
fof(t8_connsp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( r1_connsp_1(A,B,C) & r1_connsp_1(A,B,D) ) => r1_connsp_1(A,B,k4_subset_1(u1_struct_0(A),C,D)) ) ) ) ) ) )).
fof(t8_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( m2_connsp_2(C,A,k6_domain_1(u1_struct_0(A),B)) <=> m1_connsp_2(C,A,B) ) ) ) ) )).
fof(t8_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_connsp_1(B,A) <=> ? [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) & v2_connsp_1(C,A) & C != k1_xboole_0 & B = k1_connsp_3(A,C) ) ) ) ) )).
fof(t8_convex1,axiom,( ! [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) ) => v1_convex1(k3_rusub_4(A,k1_rlsub_1(A)),A) ) )).
fof(t8_convex2,axiom,( ! [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) ) => ! [B] : ( ( v2_convex1(B,A) & m1_rlvect_2(B,A) ) => ! [C] : ( ( v2_convex1(C,A) & m1_rlvect_2(C,A) ) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(1,D) & ~ ( v2_convex1(k7_rlvect_2(A,k8_rlvect_2(A,D,B),k8_rlvect_2(A,k6_xcmplx_0(1,D),C)),A) & m1_rlvect_2(k7_rlvect_2(A,k8_rlvect_2(A,D,B),k8_rlvect_2(A,k6_xcmplx_0(1,D),C)),A) ) ) ) ) ) ) )).
fof(t8_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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))) ) => k3_convex4(A,k12_finseq_1(u1_struct_0(A),B),C) = k12_finseq_1(u1_struct_0(A),k1_clvect_1(A,B,k3_funct_2(u1_struct_0(A),k2_numbers,C,B))) ) ) ) )).
fof(t8_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( m2_subset_1(k13_qc_lang1(A,B),k9_qc_lang1(A),k3_cqc_lang(A)) <=> m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) ) ) ) )).
fof(t8_cqc_sim1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ~ ( v5_qc_lang1(B,A) & ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => B != k11_cqc_lang(A,C,D) ) ) ) ) ) )).
fof(t8_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t8_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ( r2_hidden(D,k24_qc_lang1(A,k14_qc_lang1(A,B,C))) <=> ( r2_hidden(D,k24_qc_lang1(A,B)) | r2_hidden(D,k24_qc_lang1(A,C)) ) ) ) ) ) ) )).
fof(t8_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => r2_cqc_the3(A,B,B) ) ) )).
fof(t8_csspace,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( m1_subset_1(C,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),C,k2_xcmplx_0(A,B)) = k3_rlvect_1(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),C,A),k1_clvect_1(g1_clvect_1(k1_csspace,k6_csspace,k4_csspace,k5_csspace),C,B)) ) ) ) )).
fof(t8_csspace2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v1_comseq_3(A) => k11_comseq_3(k2_comseq_2(k4_ordinal1,A)) = k8_complex1(k11_comseq_3(A)) ) ) )).
fof(t8_csspace3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,u1_struct_0(k3_csspace3)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k3_csspace3)))) ) => ( v1_csspace3(A,k3_csspace3) => v9_clvect_1(A,k3_csspace3) ) ) )).
fof(t8_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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(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))),k3_clopban1(A,B)) ) ) )).
fof(t8_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k9_subset_1(k1_zfmisc_1(u1_struct_0(A)),k7_decomp_1(A),k13_decomp_1(A)) = u1_pre_topc(A) ) )).
fof(t8_descip_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ( r1_xxreal_0(1,k3_finseq_1(B)) => m2_finseq_1(k7_descip_1(B),A) ) ) ) )).
fof(t8_dickson,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( v3_dickson(A) => ( r2_hidden(B,k6_eqrel_1(u1_struct_0(A),u1_struct_0(A),k1_dickson(A),C)) <=> ( r1_orders_2(A,B,C) & r1_orders_2(A,C,B) ) ) ) ) ) ) )).
fof(t8_diff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( ( 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_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,D,E),B),k1_nat_1(A,1)),C) = k2_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(D,B),k1_nat_1(A,1)),C),k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(E,B),k1_nat_1(A,1)),C)) ) ) ) ) ) )).
fof(t8_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( 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))) ) => k11_diff_1(k26_valued_1(k1_numbers,k1_numbers,F,A),B,C,D,E) = k3_xcmplx_0(A,k11_diff_1(F,B,C,D,E)) ) ) ) ) ) ) )).
fof(t8_diff_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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_funct_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,E,C),F),B),k2_xcmplx_0(A,1)),D) = k2_xcmplx_0(k3_xcmplx_0(C,k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(E,B),k2_xcmplx_0(A,1)),D)),k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(F,B),k2_xcmplx_0(A,1)),D)) ) ) ) ) ) ) )).
fof(t8_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(B,k1_relset_1(k1_numbers,k27_sin_cos)) & r2_hidden(k6_xcmplx_0(B,A),k1_relset_1(k1_numbers,k27_sin_cos)) ) => k1_funct_1(k4_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k27_sin_cos),A),B) = k7_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k19_sin_cos(k3_xcmplx_0(2,B)),k19_sin_cos(k3_xcmplx_0(2,k6_xcmplx_0(A,B))))),k1_square_1(k3_xcmplx_0(k17_sin_cos(B),k17_sin_cos(k6_xcmplx_0(B,A))))) ) ) ) )).
fof(t8_dilworth,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( r1_orders_2(A,B,C) | r1_orders_2(A,C,B) ) => ( v1_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))) ) ) ) ) ) )).
fof(t8_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_diraf(A,B,C,B) => B = C ) ) ) ) )).
fof(t8_dirort,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dirort(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_dirort(A,B,C,D,E) => r2_dirort(A,D,E,B,C) ) ) ) ) ) ) )).
fof(t8_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r1_dist_1(A,B,C) <=> k4_dist_1(A,B) = k4_dist_1(A,C) ) ) ) ) )).
fof(t8_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,A) & v1_funct_1(B) ) => ! [C] : ( ( 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(k3_dist_2(k3_relat_1(B,C)),k1_zfmisc_1(k9_xtuple_0(B))) ) ) ) )).
fof(t8_domain_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k3_zfmisc_1(B,C,D)) => ( A = k3_mcart_1(B,C,D,E) <=> ! [F] : ( m1_subset_1(F,B) => ! [G] : ( m1_subset_1(G,C) => ! [H] : ( m1_subset_1(H,D) => ( E = k4_domain_1(B,C,D,F,G,H) => A = H ) ) ) ) ) ) ) ) ) )).
fof(t8_dtconstr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => r1_xboole_0(k1_lang1(A),k2_lang1(A)) ) )).
fof(t8_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_xboole_0(B,C) => v1_prob_2(k1_dynkin(A,B,C,k1_subset_1(A))) ) ) ) ) )).
fof(t8_e_siec,axiom,( ! [A] : ( u1_struct_0(k4_e_siec(A)) = k1_tarski(A) & u1_e_siec(k4_e_siec(A)) = k4_relat_1(k1_tarski(A)) & u2_e_siec(k4_e_siec(A)) = k4_relat_1(k1_tarski(A)) ) )).
fof(t8_ec_pf_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v36_algstr_0(B) & m1_ec_pf_1(B,A) ) => ! [C] : ( ( v36_algstr_0(C) & m1_ec_pf_1(C,A) ) => ( B = C <=> u1_struct_0(B) = u1_struct_0(C) ) ) ) ) )).
fof(t8_ec_pf_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( k3_rlvect_1(A,k3_rlvect_1(A,k3_rlvect_1(A,B,C),D),E) = k3_rlvect_1(A,B,k3_rlvect_1(A,k3_rlvect_1(A,C,D),E)) & k3_rlvect_1(A,k3_rlvect_1(A,k3_rlvect_1(A,k3_rlvect_1(A,B,C),D),E),F) = k3_rlvect_1(A,B,k3_rlvect_1(A,k3_rlvect_1(A,k3_rlvect_1(A,C,D),E),F)) ) ) ) ) ) ) ) )).
fof(t8_endalg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_autalg_1(C,u1_struct_0(A),u3_msualg_1(A,B),k4_endalg(A,B)) => ! [D] : ( m1_autalg_1(D,u1_struct_0(A),u3_msualg_1(A,B),k4_endalg(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),k4_endalg(A,B)) ) ) ) ) )).
fof(t8_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k2_ens_1(A)) => B = k4_tarski(k1_domain_1(A,A,k3_ens_1(A,B),k4_ens_1(A,B)),k2_xtuple_0(B)) ) ) )).
fof(t8_entropy1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ( ( k3_finseq_1(B) = k3_finseq_1(A) & k3_finseq_1(B) = k3_finseq_1(C) & ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k4_finseq_1(B)) => k1_funct_1(A,D) = k6_xcmplx_0(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) => k18_rvsum_1(A) = k6_xcmplx_0(k18_rvsum_1(B),k18_rvsum_1(C)) ) ) ) ) )).
fof(t8_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k3_enumset1(A,B,C,D,E) = k2_xboole_0(k2_tarski(A,B),k1_enumset1(C,D,E)) )).
fof(t8_eqrel_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_2(B) & v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ~ ( ? [C] : r2_hidden(C,A) & B = k1_xboole_0 ) ) )).
fof(t8_equation,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( m2_pboole(E,A,B,C) => m3_pboole(k1_equation(A,D,E),A,B) ) ) ) ) )).
fof(t8_euclid,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v3_valued_0(B) ) => k12_euclid(k10_rvsum_1(B,A)) = k3_xcmplx_0(k9_complex1(A),k12_euclid(B)) ) ) )).
fof(t8_euclid_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => k22_rvsum_1(A,k5_euclid(k3_finseq_1(A))) = k5_numbers ) )).
fof(t8_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => k2_xcmplx_0(k17_euclid(k3_rlvect_1(k15_euclid(2),A,B)),k3_xcmplx_0(k18_euclid(k3_rlvect_1(k15_euclid(2),A,B)),k7_complex1)) = k2_xcmplx_0(k2_xcmplx_0(k17_euclid(A),k17_euclid(B)),k3_xcmplx_0(k2_xcmplx_0(k18_euclid(A),k18_euclid(B)),k7_complex1)) ) ) )).
fof(t8_euclid_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(B)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(B)) => ~ ( k9_euclid(B,C,A) = k9_euclid(B,D,A) & A != k5_numbers & C != D ) ) ) ) ) )).
fof(t8_euclid_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => k1_rlvect_1(k15_euclid(3),k4_euclid_5(B,C,D),A) = k4_euclid_5(k3_xcmplx_0(A,B),k3_xcmplx_0(A,C),k3_xcmplx_0(A,D)) ) ) ) ) )).
fof(t8_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( r2_hidden(C,k1_rltopsp1(k15_euclid(2),A,B)) => ( C = A | C = B | k4_euclid_3(A,C,B) = k28_sin_cos ) ) ) ) ) )).
fof(t8_euclid_7,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ( ( v1_rlvect_1(A) & v1_rlvect_1(B) & u1_struct_0(B) = u1_struct_0(A) ) => B = A ) ) ) )).
fof(t8_euclid_8,axiom,( r1_rvsum_1(k2_euclid_8,k4_euclid_8) )).
fof(t8_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(B))) => ( r2_hidden(A,k4_finseq_1(C)) => r1_xxreal_0(k1_square_1(k5_real_1(k7_partfun1(k1_numbers,C,A),k7_partfun1(k1_numbers,D,A))),k18_rvsum_1(k12_rvsum_1(k5_algstr_0(k15_euclid(B),C,D)))) ) ) ) ) ) )).
fof(t8_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => k6_euclid(A,k7_euclid(A,k7_euclid(A,B,C),D)) = k7_euclid(A,k7_euclid(A,k6_euclid(A,B),k6_euclid(A,C)),k6_euclid(A,D)) ) ) ) ) )).
fof(t8_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v1_euclmetr(A) <=> v3_conaffm(A) ) ) )).
fof(t8_euler_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k3_int_2(k2_xcmplx_0(A,k3_xcmplx_0(B,C)),B) = k3_int_2(A,B) ) ) ) )).
fof(t8_euler_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k4_nat_d(k3_xcmplx_0(C,A),B) = k4_nat_d(k3_xcmplx_0(k4_nat_d(C,B),A),B) ) ) ) )).
fof(t8_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( k9_xtuple_0(A) = k9_xtuple_0(B) & v1_exchsort(A) ) => v1_exchsort(B) ) ) ) )).
fof(t8_extens_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v2_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,C) => ! [E] : ( m3_pboole(E,A,B) => r2_pboole(A,k2_funct_6(k1_msafree(A,B,C,E,D)),k2_funct_6(D)) ) ) ) ) )).
fof(t8_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(B)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( 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] : ( v7_ordinal1(E) & k3_compos_1(B,C,k5_memstr_0(A,B,k5_extpro_1(A,B,C,D,E))) = k2_compos_1(B) ) => ! [E] : ( v7_ordinal1(E) => k6_extpro_1(A,B,C,D) = k6_extpro_1(A,B,C,k5_extpro_1(A,B,C,D,E)) ) ) ) ) ) ) )).
fof(t8_extreal1,axiom,( ! [A] : ( m2_finseq_1(A,k6_numbers) => ! [B] : ( m2_finseq_1(B,k6_numbers) => ~ ( ~ r2_hidden(k2_supinf_1,k2_relset_1(k6_numbers,A)) & ~ r2_hidden(k2_supinf_1,k2_relset_1(k6_numbers,B)) & k4_extreal1(k8_finseq_1(k6_numbers,A,B)) != k3_supinf_2(k4_extreal1(A),k4_extreal1(B)) ) ) ) )).
fof(t8_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k3_extreal1(k4_xxreal_3(A,B)) = k1_extreal1(k3_extreal1(A),k3_extreal1(B)) ) ) )).
fof(t8_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ~ ( r1_circcomb(A,B) & ~ v1_facirc_1(k2_msafree2(A)) & ~ v1_facirc_1(k2_msafree2(B)) & v1_facirc_1(k2_msafree2(k2_circcomb(A,B))) ) ) ) )).
fof(t8_facirc_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( C = k4_tarski(k1_xboole_0,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1)) => ( k3_facirc_2(1,A,B) = k2_circcomb(k5_circcomb(k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1),k1_xboole_0),k19_facirc_1(k1_funct_1(A,1),k1_funct_1(B,1),C)) & k4_facirc_2(1,A,B) = k3_circcomb(k5_circcomb(k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1),k1_xboole_0),k19_facirc_1(k1_funct_1(A,1),k1_funct_1(B,1),C),k7_circcomb(k5_ordinal1,k6_margrel1,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1),k1_xboole_0),k20_facirc_1(k1_funct_1(A,1),k1_funct_1(B,1),C)) & k5_facirc_2(1,A,B) = k17_facirc_1(k1_funct_1(A,1),k1_funct_1(B,1),C) ) ) ) ) )).
fof(t8_fcont_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r2_hidden(B,k1_relset_1(k1_numbers,C)) & r1_fcont_1(C,B) ) => r1_fcont_1(k26_valued_1(k1_numbers,k1_numbers,C,A),B) ) ) ) ) )).
fof(t8_fcont_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r1_tarski(A,k1_relset_1(k1_numbers,E)) & r1_tarski(B,k1_relset_1(k1_numbers,F)) & v1_fcont_2(k2_partfun1(k1_numbers,k1_numbers,E,A)) & v1_fcont_2(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)) ) => v1_fcont_2(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))) ) ) ) )).
fof(t8_fcont_3,axiom,( ! [A] : ! [B] : ( ( 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,B,A)) ) => v2_funct_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) ) )).
fof(t8_fdiff_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r2_fdiff_1(B,A) => m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) ) )).
fof(t8_fdiff_10,axiom,( ! [A] : ( ( 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,k18_sin_cos,k16_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k16_sin_cos),A),B) = k4_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,k1_funct_1(k18_sin_cos,B)),k1_funct_1(k16_sin_cos,B))) ) ) ) ) )).
fof(t8_fdiff_11,axiom,( ! [A] : ( ( 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,k27_sin_cos,k2_sin_cos9))) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k27_sin_cos,B),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(k27_sin_cos,B)) ) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k2_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k2_sin_cos9),A),B) = 1 ) ) ) ) ) )).
fof(t8_fdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ~ ( ? [C] : ( m1_rcomp_1(C,A) & r1_tarski(C,k1_relset_1(k1_numbers,B)) ) & ! [C] : ( ( v1_funct_1(C) & v9_ordinal1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & v1_fdiff_1(C,k5_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v3_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ~ ( k2_relset_1(k1_numbers,D) = k1_tarski(A) & r1_tarski(k2_relset_1(k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,D)),k1_relset_1(k1_numbers,B)) & r1_tarski(k1_tarski(A),k1_relset_1(k1_numbers,B)) ) ) ) ) ) ) )).
fof(t8_fdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( r2_fdiff_3(A,B) & k1_funct_1(A,B) != C & ? [D] : ( v1_xreal_0(D) & ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k1_rcomp_1(B,k2_xcmplx_0(B,D)),k1_relset_1(k1_numbers,A)) ) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k1_rcomp_1(B,k2_xcmplx_0(B,D)),k1_relset_1(k1_numbers,A)) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k1_rcomp_1(B,k2_xcmplx_0(B,D))) & k1_funct_1(A,E) = C ) ) ) ) ) ) ) ) )).
fof(t8_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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,k6_xcmplx_0(A,B))))) & D = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,E,k3_taylor_1) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,C) => ( k1_funct_1(E,F) = k2_xcmplx_0(F,B) & ~ r1_xxreal_0(k1_funct_1(E,F),k5_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,k6_xcmplx_0(A,B))),C) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,C) => k1_funct_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,k6_xcmplx_0(A,B))),C),F) = k7_xcmplx_0(k2_xcmplx_0(F,A),k2_xcmplx_0(F,B)) ) ) ) ) ) ) ) ) ) )).
fof(t8_fdiff_7,axiom,( ! [A] : ( ( 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_cos6,k3_taylor_1))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) & ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & r1_xxreal_0(k1_funct_1(k1_sin_cos6,B),k5_numbers) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos6,k3_taylor_1),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos6,k3_taylor_1),A),B) = k7_xcmplx_0(1,k3_xcmplx_0(k3_square_1(k6_xcmplx_0(1,k1_square_1(B))),k1_funct_1(k1_sin_cos6,B))) ) ) ) ) ) )).
fof(t8_fdiff_8,axiom,( ! [A] : ( ( 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)),k26_sin_cos))) => ( r2_hidden(k5_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)),k26_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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)),k26_sin_cos),A),B) = k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(k1_square_1(B),k1_square_1(k1_funct_1(k18_sin_cos,k7_xcmplx_0(1,B)))))) ) ) ) ) ) ) )).
fof(t8_fdiff_9,axiom,( ! [A] : ( ( 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_hidden(k5_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_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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_fdiff_9),A),B) = k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k16_sin_cos,k7_xcmplx_0(1,B)),k3_xcmplx_0(k1_square_1(B),k1_square_1(k1_funct_1(k18_sin_cos,k7_xcmplx_0(1,B)))))) ) ) ) ) ) ) )).
fof(t8_ff_siec,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ( r1_tarski(k1_net_1(A),k2_zfmisc_1(k2_net_1(A),k2_net_1(A))) & r1_tarski(k2_relat_1(k1_net_1(A)),k2_zfmisc_1(k2_net_1(A),k2_net_1(A))) ) ) )).
fof(t8_fib_num,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ r1_xxreal_0(1,k9_complex1(k6_xcmplx_0(k1_pre_ff(A),k7_xcmplx_0(k2_power(k1_fib_num,A),k3_square_1(5))))) ) )).
fof(t8_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_xreal_0(C) ) => k3_xcmplx_0(k2_power(C,k4_xcmplx_0(A)),k2_power(C,k4_xcmplx_0(B))) = k2_power(C,k6_xcmplx_0(k4_xcmplx_0(A),B)) ) ) ) )).
fof(t8_fib_num3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_xreal_0(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_xreal_0(C) ) => k2_power(k3_xcmplx_0(B,C),A) = k3_xcmplx_0(k2_power(B,A),k2_power(C,A)) ) ) ) )).
fof(t8_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( A != k5_numbers & r1_xxreal_0(k7_xcmplx_0(1,2),k2_power(k2_fib_num,A)) ) ) )).
fof(t8_filerec1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ( C = k9_finseq_1(A) => r2_hidden(A,B) ) ) ) )).
fof(t8_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) <=> r2_hidden(k4_lattices(A,C,D),B) ) ) ) ) ) ) )).
fof(t8_filter_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m2_filter_1(D,A,B) => ( r3_binop_1(A,C,D) => r3_binop_1(k8_eqrel_1(A,B),k9_eqrel_1(A,B,C),k3_filter_1(A,B,D)) ) ) ) ) ) )).
fof(t8_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k9_fin_topo(A,C)) <=> ~ r1_xboole_0(k1_fin_topo(A,B),C) ) ) ) ) )).
fof(t8_finance1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => m2_subset_1(k1_rcomp_1(B,A),k1_zfmisc_1(k1_numbers),k12_prob_1) ) ) )).
fof(t8_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k2_finseq_1(B) = k9_subset_1(k4_ordinal1,k2_finseq_1(B),k2_finseq_1(A)) => r1_xxreal_0(B,A) ) ) ) )).
fof(t8_finseq_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ ( r2_hidden(A,k10_xtuple_0(B)) & ! [C] : ( v7_ordinal1(C) => ~ ( r2_hidden(C,k4_finseq_1(B)) & k1_funct_1(B,C) = A ) ) ) ) )).
fof(t8_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ~ r2_hidden(k1_nat_1(A,1),k2_finseq_1(A)) ) )).
fof(t8_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) <=> ! [B] : ( r2_hidden(B,k10_xtuple_0(A)) => r2_finseq_4(A,B) ) ) ) )).
fof(t8_finseq_5,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => k3_finseq_1(k7_finseq_1(k9_finseq_1(A),B)) = k1_nat_1(1,k3_finseq_1(B)) ) )).
fof(t8_finseq_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( r2_hidden(C,k10_xtuple_0(A)) => k6_finseq_4(k7_finseq_1(A,B),C) = k7_finseq_1(k6_finseq_4(A,C),B) ) ) ) )).
fof(t8_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(B)) ) => k7_partfun1(A,k1_finseq_7(A,B,D,C),D) = C ) ) ) ) ) )).
fof(t8_finseq_8,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k3_finseq_8(A,B,k5_numbers,C) = k3_finseq_8(A,B,1,k1_nat_1(C,1)) ) ) )).
fof(t8_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( ( 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(k4_ordinal1,B,k4_finseqop(A,B,k8_finseq_1(A,D,k12_finseq_1(A,C)),E),k8_finseq_1(B,k4_finseqop(A,B,D,E),k12_finseq_1(B,k3_funct_2(A,B,E,C)))) ) ) ) ) ) )).
fof(t8_finset_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_finset_1(k9_xtuple_0(A)) => v1_finset_1(k10_xtuple_0(A)) ) ) )).
fof(t8_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( ( 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) ) => ( ( ~ v1_setwiseo(D,A) & ~ r1_xxreal_0(1,k3_finseq_1(B)) ) | k1_finsop_1(A,B,D) = k1_finsop_1(A,C,D) ) ) ) ) ) ) )).
fof(t8_finsub_1,axiom,( ! [A] : v4_finsub_1(k1_zfmisc_1(A)) )).
fof(t8_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k5_fin_topo(A,C)) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & k1_fintopo2(A,B,D,C) = k8_margrel1 & k2_fintopo2(A,B,E,C) = k8_margrel1 ) ) ) ) ) ) )).
fof(t8_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) )).
fof(t8_fintopo4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_fin_topo(A) & r1_xboole_0(k9_fin_topo(A,B),C) ) => r1_xboole_0(B,k9_fin_topo(A,C)) ) ) ) ) )).
fof(t8_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_fintopo6(B,A) ) => ( v1_fin_topo(A) => v1_fin_topo(B) ) ) ) )).
fof(t8_flang_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ~ ( A != k1_xboole_0 & ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : A != k1_ordinal4(k5_afinsq_1(C),B) ) ) ) )).
fof(t8_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(k2_flang_1(A),k7_flang_1(A,B,C)) <=> ( C = k5_numbers | r2_hidden(k2_flang_1(A),B) ) ) ) ) )).
fof(t8_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => k4_subset_1(k8_afinsq_1(A),k7_flang_1(A,B,C),k1_flang_3(A,B,k2_xcmplx_0(C,1))) = k1_flang_3(A,B,C) ) ) )).
fof(t8_fomodel0,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( v7_ordinal1(C) => ( v3_fomodel0(A,B) => v1_fomodel0(k9_fomodel0(B),k4_finseq_2(C,A)) ) ) ) )).
fof(t8_fomodel1,axiom,( ! [A] : ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ( r2_hidden(A,k35_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))) ) ) )).
fof(t8_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ~ v1_xboole_0(C) => ( r2_hidden(k22_fomodel2(B,A,C),k9_funct_2(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)),k15_fomodel2(B,C),k24_fomodel2(B,A)),k6_margrel1)) & r2_hidden(k9_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)),k15_fomodel2(B,C),k6_subset_1(k3_finseq_2(k1_fomodel1(B)),k1_tarski(k1_xboole_0))),k6_margrel1),k21_fomodel2(B,C),A),k9_funct_2(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)),k15_fomodel2(B,C),k24_fomodel2(B,A)),k6_margrel1)) ) ) ) ) )).
fof(t8_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => ! [C] : ( ( v4_fomodel1(C,B) & m1_subset_1(C,k1_fomodel1(B)) ) => ! [D] : ( ( 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] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_fomodel2(E,B,A) ) => ! [F] : ( m2_subset_1(F,k6_subset_1(k3_finseq_2(k15_fomodel1(B)),k1_tarski(k1_xboole_0)),k35_fomodel1(B)) => k13_fomodel2(B,A,E,k27_fomodel3(B,C,F,D)) = k13_fomodel2(B,A,k5_fomodel2(E,C,k3_funct_2(k35_fomodel1(B),A,k9_fomodel2(B,A,E),F)),D) ) ) ) ) ) ) )).
fof(t8_fomodel4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ! [E] : ! [F] : ( ( ~ v6_struct_0(F) & v11_fomodel1(F) & l1_fomodel1(F) ) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(F)),k9_setfam_1(k1_fomodel4(F))))) => ! [H] : ( m1_subset_1(H,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(F)),k9_setfam_1(k1_fomodel4(F))))) => ( ( v7_fomodel4(G,F) & v7_fomodel4(k4_subset_1(k9_funct_2(k9_setfam_1(k1_fomodel4(F)),k9_setfam_1(k1_fomodel4(F))),G,H),F) & v5_fomodel4(D,A,F,G,C) & v5_fomodel4(E,B,F,H,k1_tarski(D)) ) => v5_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),C) ) ) ) ) ) ) )).
fof(t8_frechet,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ( v3_pre_topc(A,k3_topmetr) <=> ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & r1_tarski(k2_rcomp_1(k6_xcmplx_0(B,C),k2_xcmplx_0(B,C)),A) ) ) ) ) ) ) )).
fof(t8_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ~ v2_frechet(B,A) => k2_frechet(A,B) = k1_xboole_0 ) ) ) )).
fof(t8_friends1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_2(B) & v3_relat_2(B) & v1_finset_1(B) & v3_friends1(B) ) => r1_nat_d(2,k5_card_1(k9_relat_1(B,A))) ) )).
fof(t8_fscirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ( r2_hidden(A,k2_msafree2(k4_fscirc_1(A,B,C))) & r2_hidden(B,k2_msafree2(k4_fscirc_1(A,B,C))) & r2_hidden(C,k2_msafree2(k4_fscirc_1(A,B,C))) ) ) ) ) )).
fof(t8_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( r1_fsm_1(A,B,C,E,F) => k2_fsm_1(A,B,E,k8_finseq_1(A,C,D)) = k7_finseq_1(k2_finseq_3(k1_nat_1(k3_finseq_1(C),1),k2_fsm_1(A,B,E,C)),k2_fsm_1(A,B,F,D)) ) ) ) ) ) ) ) )).
fof(t8_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ v2_struct_0(C) & l1_fsm_1(C,A) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => ( r1_fsm_2(A,C,D,B) => v2_fsm_2(D,A,C) ) ) ) ) ) )).
fof(t8_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ~ r2_hidden(k2_flang_1(A),k9_flang_1(A)) ) )).
fof(t8_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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,2),k12_gfacirc1(A,B,C)) = 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,2),A) = G & k1_funct_1(k5_facirc_1(k1_ftacell1(A,B,C,D,E),k2_ftacell1(A,B,C,D,E),F,2),B) = H & k1_funct_1(k5_facirc_1(k1_ftacell1(A,B,C,D,E),k2_ftacell1(A,B,C,D,E),F,2),C) = I & k1_funct_1(k5_facirc_1(k1_ftacell1(A,B,C,D,E),k2_ftacell1(A,B,C,D,E),F,2),D) = J & k1_funct_1(k5_facirc_1(k1_ftacell1(A,B,C,D,E),k2_ftacell1(A,B,C,D,E),F,2),E) = K ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_funcop_1,axiom,( ! [A] : ! [B] : ( A != k1_xboole_0 => k10_xtuple_0(k2_funcop_1(A,B)) = k1_tarski(B) ) )).
fof(t8_funcsdom,axiom,( ! [A] : ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( m2_funct_2(C,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [D] : ( 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,k6_funcsdom(A),C,D)),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k1_funcsdom(A,k1_numbers,k6_funcsdom(A),B,C),D)) ) ) ) )).
fof(t8_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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 ) => r2_hidden(C,k1_funct_2(A,B)) ) ) )).
fof(t8_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => k1_funct_1(k1_funct_3(A),k1_xboole_0) = k1_xboole_0 ) )).
fof(t8_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => r1_tarski(k5_relat_1(k6_relat_1(B,C),A),C) ) )).
fof(t8_funct_5,axiom,( ! [A] : ( ! [B] : ! [C] : ~ r2_hidden(k4_tarski(B,C),A) => ( k9_xtuple_0(A) = k1_xboole_0 & k10_xtuple_0(A) = k1_xboole_0 ) ) )).
fof(t8_funct_6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( k9_xtuple_0(k2_funct_5(k7_funcop_1(A,B))) = k2_zfmisc_1(A,k9_xtuple_0(B)) & r1_tarski(k10_xtuple_0(k2_funct_5(k7_funcop_1(A,B))),k10_xtuple_0(B)) & k9_xtuple_0(k4_funct_5(k7_funcop_1(A,B))) = k2_zfmisc_1(k9_xtuple_0(B),A) & r1_tarski(k10_xtuple_0(k4_funct_5(k7_funcop_1(A,B))),k10_xtuple_0(B)) ) ) )).
fof(t8_funct_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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)) ) => ! [D] : ! [E] : ( ( r2_hidden(D,A) & r2_hidden(E,B) ) => k17_funcop_1(D,E,k1_binop_1(C,D,E)) = k5_relat_1(C,k2_zfmisc_1(k1_tarski(D),k1_tarski(E))) ) ) )).
fof(t8_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(B,C) = k1_funct_1(B,k9_complex1(C)) ) ) ) ) ) )).
fof(t8_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) ) => ( v1_funct_9(C,A) => v1_funct_9(k7_valued_1(C,B),A) ) ) ) ) )).
fof(t8_functor0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) => v2_funct_1(k2_funct_4(A)) ) ) )).
fof(t8_functor1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l1_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_altcat_2(C) & l1_altcat_1(C) ) => ! [D] : ( ( v8_functor0(D,A,B) & l2_functor0(D,A,B) ) => ! [E] : ( l2_functor0(E,B,C) => ( ( v5_functor0(D,A,B) & v5_functor0(E,B,C) ) => v5_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ) ) ) ) )).
fof(t8_functor2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ! [E] : ( ( v15_functor0(E,A,B) & m2_functor0(E,A,B) ) => ( ( r2_functor2(A,B,C,D) & r2_functor2(A,B,D,E) ) => r2_functor2(A,B,C,E) ) ) ) ) ) ) )).
fof(t8_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_altcat_2(C) & l2_altcat_1(C) ) => ! [D] : ( ( v8_functor0(D,A,B) & v10_functor0(D,A,B) & l2_functor0(D,A,B) ) => ! [E] : ( ( v8_functor0(E,B,C) & v11_functor0(E,B,C) & l2_functor0(E,B,C) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,k1_altcat_1(A,F,G)) => ( k1_altcat_1(A,F,G) != k1_xboole_0 => k8_functor0(A,C,k13_functor0(A,B,C,D,E),F,G,H) = k8_functor0(B,C,E,k3_functor0(A,B,D,F),k3_functor0(A,B,D,G),k6_functor0(A,B,D,F,G,H)) ) ) ) ) ) ) ) ) ) )).
fof(t8_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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,k1_fuzzy_1(A,B,C)),B) & r2_funct_2(A,k1_numbers,k1_fuzzy_1(A,B,k2_fuzzy_1(A,B,C)),B) ) ) ) ) )).
fof(t8_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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,B,k1_fuzzy_1(A,B,C))) ) ) ) )).
fof(t8_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,k1_fuzzy_4(B,A,k1_fuzzy_1(k2_zfmisc_1(A,B),C,D)),k1_fuzzy_1(k2_zfmisc_1(B,A),k1_fuzzy_4(B,A,C),k1_fuzzy_4(B,A,D))) ) ) ) ) )).
fof(t8_fvaluat1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( B != k1_xxreal_0 & B != k2_xxreal_0 & B != k5_numbers & k4_xxreal_3(k2_extreal1(A,B),B) != A ) ) ) )).
fof(t8_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_algstr_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => v1_setwiseo(u1_algstr_0(A),u1_struct_0(A)) ) )).
fof(t8_gate_1,axiom,( ! [A] : ( ~ ( ~ v1_xboole_0(k4_gate_1(A,k1_xboole_0)) & v1_xboole_0(A) ) & ~ ( ~ v1_xboole_0(A) & v1_xboole_0(k4_gate_1(A,k1_xboole_0)) ) ) )).
fof(t8_gcd_1,axiom,( ! [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) & v1_vectsp_2(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_gcd_1(A,C,B) => ( C = k4_struct_0(A) | ( k1_gcd_1(A,B,C) = k4_struct_0(A) <=> B = k4_struct_0(A) ) ) ) ) ) ) )).
fof(t8_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( m1_genealg1(C,B) => ! [D] : ( m1_genealg1(D,B) => k8_genealg1(B,C,D,A,k5_numbers) = k7_genealg1(B,D,C,A) ) ) ) ) )).
fof(t8_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_analoaf(A,B,C,k1_geomtrap(A,D,B),k1_geomtrap(A,D,C)) ) ) ) ) )).
fof(t8_gfacirc1,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k1_funct_1(k4_gfacirc1,k10_finseq_1(k1_funct_1(k15_twoscomp,k10_finseq_1(A,B)),C)) = k1_funct_1(k4_gfacirc1,k10_finseq_1(k1_funct_1(k4_gfacirc1,k10_finseq_1(A,B)),C)) ) ) ) )).
fof(t8_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ! [C] : ( v7_ordinal1(C) => k1_funct_1(k13_glib_000(A,C,B),C) = B ) ) )).
fof(t8_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ~ ( r2_hidden(C,k1_relset_1(k4_ordinal1,B)) & ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ~ ( D = k6_xcmplx_0(C,1) & r2_hidden(k6_xcmplx_0(C,1),k1_relset_1(k4_ordinal1,B)) & r2_hidden(k1_nat_1(C,1),k1_relset_1(k4_ordinal1,B)) & r1_glib_000(A,k1_funct_1(B,D),k1_funct_1(B,k1_nat_1(C,1)),k1_funct_1(B,C)) ) ) ) ) ) ) )).
fof(t8_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => r2_hidden(B,k1_glib_002(A,B)) ) ) )).
fof(t8_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) & v1_glib_003(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_finset_1(C) & v1_glib_000(C) & v1_glib_003(C) ) => ( ( r5_glib_000(A,B) & k5_glib_003(A) = k5_glib_003(B) & v1_glib_003(A) & v4_glib_003(A,C) & m1_glib_000(A,C) ) => ( v1_glib_003(B) & v4_glib_003(B,C) & m1_glib_000(B,C) ) ) ) ) ) )).
fof(t8_glib_004,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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] : ( v1_xreal_0(D) => ( C = k1_funct_4(k16_pre_poly(A),k16_funcop_1(B,D)) => k2_uproots(A,C) = D ) ) ) )).
fof(t8_goboard1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r2_hidden(C,k2_finseq_1(k1_matrix_0(E))) & k1_matrix_0(E) = k1_nat_1(B,1) & r2_hidden(A,k4_finseq_1(E)) & r1_xxreal_0(1,D) ) => ( r1_xxreal_0(B,k5_numbers) | r1_xxreal_0(C,D) | ( k3_matrix_0(u1_struct_0(k15_euclid(2)),k16_matrix_0(C,u1_struct_0(k15_euclid(2)),E),A,D) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,D) & r2_hidden(D,k2_finseq_1(k1_matrix_0(E))) ) ) ) ) ) ) ) ) )).
fof(t8_goboard2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( 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)) ) ) ) ) )).
fof(t8_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( v1_goboard1(C) & r1_xxreal_0(1,A) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k1_matrix_0(C)) ) => ( r1_xxreal_0(k3_finseq_1(C),A) | k1_goboard5(C,A) = a_3_1_goboard5(A,B,C) ) ) ) ) ) )).
fof(t8_goboard6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(2))) => ( ( E = k19_euclid(A,B) & r1_xxreal_0(k5_numbers,D) ) => ( r1_xxreal_0(C,D) | r2_hidden(k19_euclid(A,k2_xcmplx_0(B,D)),k8_metric_1(k14_euclid(2),E,C)) ) ) ) ) ) ) ) )).
fof(t8_goboard7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r1_xxreal_0(k17_euclid(A),k17_euclid(B)) & r1_xxreal_0(k17_euclid(B),k17_euclid(C)) & k18_euclid(A) = k18_euclid(B) & k18_euclid(B) = k18_euclid(C) ) => r2_hidden(B,k1_rltopsp1(k15_euclid(2),A,C)) ) ) ) ) )).
fof(t8_goboard8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,2),k3_finseq_1(A)) ) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,2),k3_finseq_1(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),1) ) => ( ( ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,1) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),2) ) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,1) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,2),1)),k7_xcmplx_0(1,2)),k19_euclid(k5_numbers,1)),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,2),2)),k7_xcmplx_0(1,2))),k3_topreal1(2,A)) ) ) ) ) ) ) )).
fof(t8_goboard9,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(1,C) & k2_xcmplx_0(B,C) = k3_finseq_1(A) ) => k5_goboard5(A,B) = k4_goboard5(k1_goboard9(A),C) ) ) ) ) )).
fof(t8_gobrd11,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( B = a_1_1_gobrd11(A) & C = a_1_2_gobrd11(A) ) => B = k3_subset_1(u1_struct_0(k15_euclid(2)),C) ) ) ) ) )).
fof(t8_gobrd12,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) & ? [C] : ( v7_ordinal1(C) & r1_xxreal_0(B,k3_finseq_1(k2_goboard2(A))) & r1_xxreal_0(C,k1_matrix_0(k2_goboard2(A))) & 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))) ) ) ) )).
fof(t8_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [F] : ( ( ~ v3_relat_1(F) & v1_matrix_0(F) & v1_goboard1(F) & v2_goboard1(F) & v3_goboard1(F) & v4_goboard1(F) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r2_hidden(k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,k1_nat_1(C,1)),k9_matrix_0(F)) & r1_xxreal_0(1,A) & r1_xxreal_0(A,k3_finseq_1(E)) & r1_xxreal_0(1,C) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(F)) & r1_xxreal_0(1,D) & k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),F,B,D) ) => ( r1_xxreal_0(k1_matrix_0(E),C) | r1_xxreal_0(k1_matrix_0(F),D) | r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),F,B,k1_nat_1(D,1))),k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,k1_nat_1(C,1)))) ) ) ) ) ) ) ) ) )).
fof(t8_gobrd14,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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)))) ) => ( r1_xxreal_0(A,B) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ~ ( r1_xxreal_0(2,D) & r1_xxreal_0(D,k6_xcmplx_0(k3_finseq_1(k1_jordan8(C,A)),1)) & r1_xxreal_0(2,E) & r1_xxreal_0(E,k6_xcmplx_0(k3_finseq_1(k1_jordan8(C,A)),1)) & ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ~ ( r1_xxreal_0(2,F) & r1_xxreal_0(F,k6_xcmplx_0(k3_finseq_1(k1_jordan8(C,B)),1)) & r1_xxreal_0(2,G) & r1_xxreal_0(G,k6_xcmplx_0(k3_finseq_1(k1_jordan8(C,B)),1)) & r2_hidden(k4_tarski(F,G),k2_matrix_0(k1_jordan8(C,B))) & k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(C,A),D,E) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(C,B),F,G) & F = k1_nat_1(2,k2_nat_1(k11_newton(2,k7_nat_d(B,A)),k7_nat_d(D,2))) & G = k1_nat_1(2,k2_nat_1(k11_newton(2,k7_nat_d(B,A)),k7_nat_d(E,2))) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_goedcpuc,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_valuat_1(E,A,D) => ! [F] : ( m2_funct_2(F,k3_qc_lang1(A),D,k2_valuat_1(A,D)) => ( ( r1_valuat_1(A,D,B,E,F) | r1_valuat_1(A,D,C,E,F) ) <=> r1_valuat_1(A,D,k9_cqc_lang(A,B,C),E,F) ) ) ) ) ) ) ) )).
fof(t8_gr_cy_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_nat_d(k6_group_1(A,B),k7_group_1(A)) ) ) )).
fof(t8_gr_cy_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v2_struct_0(D) & v8_struct_0(D) & v2_group_1(D) & v3_group_1(D) & l3_algstr_0(D) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(D)) => ( ( D = k5_group_4(D,k6_domain_1(u1_struct_0(D),E)) & k7_group_1(D) = A & A = k3_xcmplx_0(B,C) ) => k6_group_1(D,k5_group_1(D,B,E)) = C ) ) ) ) ) ) )).
fof(t8_gr_cy_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v1_gr_cy_3(A) ) => ~ ( ~ r1_xxreal_0(A,5) & k4_nat_d(A,8) != 3 & k4_nat_d(A,8) != 7 ) ) )).
fof(t8_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ 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) = k5_graph_1(B,A) ) ) ) )).
fof(t8_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(B,C) & r1_xxreal_0(C,D) & r1_xxreal_0(D,k3_finseq_1(A)) ) => k7_finseq_1(k1_graph_2(A,k1_nat_1(B,1),C),k1_graph_2(A,k1_nat_1(C,1),D)) = k1_graph_2(A,k1_nat_1(B,1),D) ) ) ) ) ) )).
fof(t8_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v2_funct_1(C) & v1_msscyc_1(C,A) & m2_graph_1(C,A) ) => ( v2_funct_1(k8_finseq_1(u4_struct_0(A),k2_graph_2(u4_struct_0(A),C,k1_nat_1(B,1),k3_finseq_1(C)),k2_graph_2(u4_struct_0(A),C,1,B))) & v1_msscyc_1(k8_finseq_1(u4_struct_0(A),k2_graph_2(u4_struct_0(A),C,k1_nat_1(B,1),k3_finseq_1(C)),k2_graph_2(u4_struct_0(A),C,1,B)),A) & m2_graph_1(k8_finseq_1(u4_struct_0(A),k2_graph_2(u4_struct_0(A),C,k1_nat_1(B,1),k3_finseq_1(C)),k2_graph_2(u4_struct_0(A),C,1,B)),A) ) ) ) ) )).
fof(t8_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r3_graph_4(A,k12_finseq_1(u1_struct_0(A),B),k1_xboole_0) ) ) )).
fof(t8_graph_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t8_graphsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v7_graph_1(B,A) & m2_graph_1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( r8_graph_5(A,E,F,B,D,C) <=> r8_graph_5(A,E,F,B,k2_xboole_0(D,k1_tarski(F)),C) ) ) ) ) ) ) )).
fof(t8_grcat_1,axiom,( ! [A] : ( l1_grcat_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v13_algstr_0(C) & v3_rlvect_1(C) & v4_rlvect_1(C) & l2_algstr_0(C) ) => ! [D] : ( ( 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)))) ) => ( A = g1_grcat_1(B,C,D) => ( k7_grcat_1(A) = B & k8_grcat_1(A) = C & r1_funct_2(u1_struct_0(k7_grcat_1(A)),u1_struct_0(k8_grcat_1(A)),u1_struct_0(B),u1_struct_0(C),k9_grcat_1(A),D) ) ) ) ) ) ) )).
fof(t8_grfunc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( 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))) ) <=> ( A = B => C = D ) ) )).
fof(t8_grnilp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k6_algstr_0(A,k6_algstr_0(A,k3_group_5(A,B,C,k2_group_3(A,D,B)),k3_group_5(A,D,B,k2_group_3(A,C,D))),k3_group_5(A,C,D,k2_group_3(A,B,C))) = k1_group_1(A) ) ) ) ) )).
fof(t8_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom1(E,C) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ( r1_tarski(k3_polynom1(k15_pre_poly(A),C,E),k3_polynom1(k15_pre_poly(A),C,D)) => r1_polyred(A,B,C,E,D) ) ) ) ) ) ) )).
fof(t8_groeb_2,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : ( ( 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,k2_groeb_2(A,C,D)) => r3_pre_poly(A,k2_groeb_2(A,C,B),k2_groeb_2(A,C,D)) ) ) ) ) )).
fof(t8_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [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) & v1_vectsp_2(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( ( 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)))) ) => ! [E] : ( ( 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,k3_polynom1(k15_pre_poly(A),B,C)) <=> r2_hidden(k11_pre_poly(A,k2_polynom7(A,B,D),E),k3_polynom1(k15_pre_poly(A),B,k10_polynom1(A,B,D,C))) ) ) ) ) ) ) )).
fof(t8_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => k2_group_1(A,k1_group_1(A)) = k1_group_1(A) ) )).
fof(t8_group_10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( 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)))) ) => k1_card_1(k13_group_10(A,B,D,C)) = k17_group_2(A,k11_group_10(A,B,D,C)) ) ) ) ) )).
fof(t8_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v15_algstr_0(B) & v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( ( v15_algstr_0(C) & v1_group_3(C,A) & m1_group_2(C,A) ) => ? [D] : ( v15_algstr_0(D) & v1_group_3(D,A) & m1_group_2(D,A) & u1_struct_0(D) = k7_group_4(A,B,C) ) ) ) ) )).
fof(t8_group_14,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v1_prvect_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & ~ v1_xboole_0(B) & v1_finseq_1(B) & v1_prvect_1(B) ) => ? [C] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k20_prvect_1(k10_finseq_1(k20_prvect_1(A),k20_prvect_1(B)))),u1_struct_0(k20_prvect_1(k7_finseq_1(A,B)))) & v13_vectsp_1(C,k20_prvect_1(k10_finseq_1(k20_prvect_1(A),k20_prvect_1(B))),k20_prvect_1(k7_finseq_1(A,B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k20_prvect_1(k10_finseq_1(k20_prvect_1(A),k20_prvect_1(B)))),u1_struct_0(k20_prvect_1(k7_finseq_1(A,B)))))) & v3_funct_2(C,u1_struct_0(k20_prvect_1(k10_finseq_1(k20_prvect_1(A),k20_prvect_1(B)))),u1_struct_0(k20_prvect_1(k7_finseq_1(A,B)))) & ! [D] : ( m1_subset_1(D,u1_struct_0(k20_prvect_1(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k20_prvect_1(B))) => ? [F] : ( v1_relat_1(F) & v1_funct_1(F) & v1_finseq_1(F) & ? [G] : ( 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) ) ) ) ) ) ) ) )).
fof(t8_group_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( r2_hidden(A,k2_group_2(B,C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k6_algstr_0(B,E,F) & r2_hidden(E,C) & r2_hidden(F,D) ) ) ) ) ) ) )).
fof(t8_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_group_2(C,A) => k14_group_2(A,C,B) = k12_group_2(A,C,k6_domain_1(u1_struct_0(A),B)) ) ) ) )).
fof(t8_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & l3_algstr_0(A) ) => k3_group_4(A,k6_finseq_1(u1_struct_0(A))) = k1_group_1(A) ) )).
fof(t8_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( v1_group_3(C,A) & m1_group_2(C,A) ) => k7_group_4(A,B,C) = k7_group_4(A,C,B) ) ) ) )).
fof(t8_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( v1_group_3(C,A) & m1_group_2(C,A) ) => ( m1_group_6(C,A,B) => ( v1_group_3(C,B) & m1_group_6(C,A,B) ) ) ) ) ) )).
fof(t8_group_7,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,B) & v1_funct_1(E) & v1_partfun1(E,B) & v1_group_7(E) & v2_group_7(E,B) & v3_group_7(E,B) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(k2_group_7(B,E))) => ! [G] : ( ( ~ v2_struct_0(G) & v2_group_1(G) & v3_group_1(G) & l3_algstr_0(G) ) => ! [H] : ( m1_subset_1(H,u1_struct_0(G)) => ( ( r2_hidden(A,B) & G = k1_funct_1(E,A) & C = F & D = k2_group_1(k2_group_7(B,E),F) & k1_funct_1(C,A) = H ) => k1_funct_1(D,A) = k2_group_1(G,H) ) ) ) ) ) ) ) )).
fof(t8_group_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( v1_int_1(B) => k5_group_1(A,B,k1_group_1(A)) = k1_group_1(A) ) ) )).
fof(t8_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_group_9(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( r1_struct_0(C,D) => r1_struct_0(C,k2_group_1(B,D)) ) ) ) ) )).
fof(t8_groupp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( v1_group_3(B,A) & m1_group_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_group_6(A,B))) => ( D = k13_group_2(A,B,C) => ! [E] : ( v7_ordinal1(E) => k5_group_1(k5_group_6(A,B),E,D) = k13_group_2(A,B,k5_group_1(A,E,C)) ) ) ) ) ) ) )).
fof(t8_grsolv_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v15_algstr_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( v15_algstr_0(D) & m1_group_2(D,A) ) => u1_struct_0(k2_grsolv_1(A,B,C,D)) = k7_relset_1(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(D)) ) ) ) ) )).
fof(t8_hahnban,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_struct_0(C,D) => m1_subset_1(D,u1_struct_0(B)) ) ) ) ) ) )).
fof(t8_hahnban1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ( k3_complex1(k3_rlvect_1(k1_complfld,A,B)) = k3_real_1(k3_complex1(A),k3_complex1(B)) & k4_complex1(k3_rlvect_1(k1_complfld,A,B)) = k3_real_1(k4_complex1(A),k4_complex1(B)) ) ) ) )).
fof(t8_hallmar1,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m2_finseq_1(D,k1_zfmisc_1(B)) => ( ( r2_hidden(C,A) & r2_hidden(C,k4_finseq_1(D)) ) => k1_hallmar1(B,D,A) = k2_xboole_0(k1_hallmar1(B,D,k6_subset_1(A,k1_tarski(C))),k1_funct_1(D,C)) ) ) ) ) )).
fof(t8_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_pre_topc(k3_pcomps_1(A),B)) <=> k1_funct_1(k6_weierstr(A,B),C) = k5_numbers ) ) ) ) )).
fof(t8_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( 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(k1_helly(A,B))) ) & ~ ( ~ r1_xxreal_0(k3_finseq_1(A),k3_finseq_1(k1_helly(A,B))) & r1_tarski(A,B) ) ) ) ) )).
fof(t8_hermitan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ? [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) & k9_complex1(B) = 1 & k3_complex1(k8_group_1(k1_complfld,B,A)) = k9_complex1(A) & k4_complex1(k8_group_1(k1_complfld,B,A)) = k5_numbers ) ) )).
fof(t8_hessenbe,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( ~ r1_collsp(A,F,B,D) & r1_collsp(A,F,D,E) & D != E & r1_collsp(A,C,E,G) & r1_collsp(A,F,B,C) & F != C & G = D ) ) ) ) ) ) ) ) )).
fof(t8_heyting1,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,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)),k4_heyting1(A),B) = k3_funct_2(k7_normform(A),k5_finsub_1(k7_normform(A)),k11_setwiseo(k7_normform(A)),B) ) )).
fof(t8_heyting2,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m1_subset_1(B,k5_finsub_1(k4_partfun1(k1_xboole_0,A))) => k1_heyting2(k1_xboole_0,A,B) = k1_xboole_0 ) ) )).
fof(t8_heyting3,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ! [D] : ( m1_subset_1(D,k5_finsub_1(k4_partfun1(A,B))) => ( C = k1_xboole_0 => ( D = k1_xboole_0 | k3_heyting2(A,B,D,C) = k1_xboole_0 ) ) ) ) ) )).
fof(t8_hfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => r2_fdiff_1(k1_taylor_1(A),k1_numbers) ) )).
fof(t8_hilbasis,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => k22_pre_poly(A,k2_hilbasis(A,B)) = k6_domain_1(A,B) ) ) )).
fof(t8_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_hilbert1)) => ( ( v6_hilbert1(A) & r1_tarski(B,A) ) => r1_tarski(k5_hilbert1(B),A) ) ) ) )).
fof(t8_hilbert2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) ) => ( k5_trees_2(k6_trees_4(A,B,C),k14_trees_3(k5_numbers)) = B & k5_trees_2(k6_trees_4(A,B,C),k14_trees_3(1)) = C ) ) ) )).
fof(t8_hilbert3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k1_partfun1(A,k2_tarski(k1_xboole_0,1),k2_tarski(k5_numbers,1),k4_ordinal1,k5_funct_3(k3_subset_1(A,B),A),k5_funct_4(k4_ordinal1,k5_numbers,1,1,k5_numbers)) = k5_funct_3(B,A) ) )).
fof(t8_holder_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k9_nat_1(k1_numbers,A,C),k9_nat_1(k1_numbers,B,C)) ) & v2_comseq_2(B) & v7_valued_0(A) ) => ( v2_comseq_2(A) & r1_xxreal_0(k1_seq_2(A),k1_seq_2(B)) ) ) ) ) )).
fof(t8_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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] : ( ( 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_homothet(A,E,D) & k3_funct_2(u1_struct_0(A),u1_struct_0(A),E,B) = C ) ) ) ) ) ) ) )).
fof(t8_hurwitz,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => k6_algstr_0(A,B,k4_rlvect_1(A,C)) = k4_rlvect_1(A,k9_fvsum_1(A,C,B)) ) ) ) )).
fof(t8_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => k3_idea_1(A,k1_idea_1(A),B) = B ) ) )).
fof(t8_ideal_1,axiom,( ! [A] : ( ( ~ 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_xboole_0(k6_domain_1(u1_struct_0(A),k4_struct_0(A))) & v1_ideal_1(k6_domain_1(u1_struct_0(A),k4_struct_0(A)),A) & v2_ideal_1(k6_domain_1(u1_struct_0(A),k4_struct_0(A)),A) & m1_subset_1(k6_domain_1(u1_struct_0(A),k4_struct_0(A)),k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(t8_incproj,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k3_incproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k3_incproj(A))) => ! [D] : ( m1_subset_1(D,u2_incsp_1(k3_incproj(A))) => ! [E] : ( m1_subset_1(E,u2_incsp_1(k3_incproj(A))) => ~ ( r1_incsp_1(k3_incproj(A),B,D) & r1_incsp_1(k3_incproj(A),C,D) & r1_incsp_1(k3_incproj(A),B,E) & r1_incsp_1(k3_incproj(A),C,E) & B != C & D != E ) ) ) ) ) ) )).
fof(t8_incsp_1,axiom,( ! [A] : ( l2_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_incsp_1(A))) => ( ( r4_incsp_1(A,D,C) & r1_incsp_1(A,B,C) ) <=> r4_incsp_1(A,k4_subset_1(u1_incsp_1(A),D,k6_domain_1(u1_incsp_1(A),B)),C) ) ) ) ) ) )).
fof(t8_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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)) <=> m5_index_1(B,u1_struct_0(k2_oppcat_1(A)),u4_struct_0(k2_oppcat_1(A)),u1_graph_1(k2_oppcat_1(A)),u2_graph_1(k2_oppcat_1(A)),u1_cat_1(k2_oppcat_1(A)),k7_isocat_1(k2_oppcat_1(A))) ) ) )).
fof(t8_instalg1,axiom,( ! [A] : ( ( v1_instalg1(A) & l1_msualg_1(A) ) => r3_pua2mss1(A,A,k6_partfun1(u1_struct_0(A)),k6_partfun1(u4_struct_0(A))) ) )).
fof(t8_int_1,axiom,( ! [A] : ( v1_int_1(A) => ( ~ r1_xxreal_0(k5_numbers,A) => r1_xxreal_0(A,k4_xcmplx_0(1)) ) ) )).
fof(t8_int_2,axiom,( ! [A] : ( v1_int_1(A) => ( r1_int_1(A,k4_xcmplx_0(A)) & r1_int_1(k4_xcmplx_0(A),A) ) ) )).
fof(t8_int_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ! [B] : ( m1_subset_1(B,k7_card_1(A)) => ! [C] : ( m1_subset_1(C,k7_card_1(A)) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(k3_xcmplx_0(D,A),k3_xcmplx_0(B,C)) & ~ r1_xxreal_0(k3_xcmplx_0(k2_xcmplx_0(D,1),A),k3_xcmplx_0(B,C)) ) <=> k5_binop_1(k7_card_1(A),k7_int_3(A),B,C) = k6_xcmplx_0(k3_xcmplx_0(B,C),k3_xcmplx_0(D,A)) ) ) ) ) ) ) )).
fof(t8_int_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( k4_nat_d(A,C) = k4_nat_d(B,C) => k4_nat_d(k1_newton(A,D),C) = k4_nat_d(k1_newton(B,D),C) ) ) ) ) ) )).
fof(t8_int_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ! [C] : ( m2_finseq_1(C,k4_numbers) => ( k3_finseq_1(C) = k1_nat_1(A,1) => ( r1_xxreal_0(B,2) | r1_int_1(B,k1_funct_1(C,k1_nat_1(A,1))) | ! [D] : ( m2_finseq_1(D,k4_numbers) => ( ( ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(D)) => k5_int_1(k1_funct_1(k1_int_5(C),k1_funct_1(D,E)),B) = k5_numbers ) ) & ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ~ ( r2_hidden(E,k4_finseq_1(D)) & r2_hidden(F,k4_finseq_1(D)) & E != F & r2_int_1(k1_funct_1(D,E),k1_funct_1(D,F),B) ) ) ) ) => r1_xxreal_0(k3_finseq_1(D),A) ) ) ) ) ) ) ) )).
fof(t8_int_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( r1_int_1(A,B) => r1_int_1(k3_xcmplx_0(C,A),k3_xcmplx_0(C,B)) ) ) ) ) )).
fof(t8_int_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k8_newton) & v1_funct_1(A) & v1_partfun1(A,k8_newton) & v4_valued_0(A) & v2_pre_poly(A) ) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ( v1_int_7(A) => ( r1_int_1(B,k8_nat_3(k8_newton,A)) <=> r2_hidden(B,k22_pre_poly(k8_newton,A)) ) ) ) ) )).
fof(t8_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v7_ordinal1(B) & v1_int_2(B) ) => ( r1_xxreal_0(1,A) => k1_euler_1(k1_newton(B,A)) = k6_xcmplx_0(k1_newton(B,A),k1_newton(B,k7_nat_d(A,1))) ) ) ) )).
fof(t8_integr10,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ( r1_tarski(k2_limfunc1(C),k1_relset_1(k1_numbers,A)) & r1_tarski(k2_limfunc1(C),k1_relset_1(k1_numbers,B)) & r3_integr10(A,C) & r3_integr10(B,C) ) => ( r3_integr10(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B),C) & k3_integr10(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B),C) = k2_xcmplx_0(k3_integr10(A,C),k3_integr10(B,C)) ) ) ) ) ) )).
fof(t8_integr11,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( A != k5_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,k1_fcont_1(A,k5_numbers),k16_sin_cos),k7_xcmplx_0(1,k1_square_1(A))),k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,A),k5_numbers),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,k5_numbers),k18_sin_cos))),k1_numbers) & ! [B] : ( v1_xreal_0(B) => k1_funct_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,k1_fcont_1(A,k5_numbers),k16_sin_cos),k7_xcmplx_0(1,k1_square_1(A))),k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,A),k5_numbers),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,k5_numbers),k18_sin_cos))),k1_numbers),B) = k3_xcmplx_0(B,k1_funct_1(k16_sin_cos,k3_xcmplx_0(A,B))) ) ) ) ) )).
fof(t8_integr12,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v3_rcomp_1(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(A,D) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,D) => k1_funct_1(C,E) = 1 ) ) & r1_tarski(D,k2_rcomp_1(k4_xcmplx_0(1),1)) & D = k1_relset_1(k1_numbers,B) & r2_relset_1(k1_numbers,k1_numbers,B,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k2_sin_cos9),k3_rfunct_1(k1_numbers,k1_numbers,k22_sin_cos,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,C,k1_taylor_1(2))))) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k2_sin_cos9),k2_seq_4(A)),k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k22_sin_cos,k2_sin_cos9),k3_seq_4(A))) ) ) ) ) ) )).
fof(t8_integr13,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k16_sin_cos,k22_sin_cos)) & r1_tarski(C,k1_relset_1(k1_numbers,k26_valued_1(k1_numbers,k1_numbers,k3_rfunct_1(k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),k22_sin_cos),k4_xcmplx_0(k7_xcmplx_0(1,2))))) & C = k1_relset_1(k1_numbers,B) & v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k3_rfunct_1(k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),k22_sin_cos),k4_xcmplx_0(k7_xcmplx_0(1,2))),k2_seq_4(A)),k1_funct_1(k26_valued_1(k1_numbers,k1_numbers,k3_rfunct_1(k1_numbers,k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),k22_sin_cos),k4_xcmplx_0(k7_xcmplx_0(1,2))),k3_seq_4(A))) ) ) ) ) )).
fof(t8_integr14,axiom,( ! [A] : ( ( 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_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_fdiff_9)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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_fdiff_9)),A),B) = k2_xcmplx_0(k7_xcmplx_0(k7_xcmplx_0(1,k1_funct_1(k16_sin_cos,B)),k1_square_1(B)),k7_xcmplx_0(k7_xcmplx_0(k1_funct_1(k18_sin_cos,B),B),k1_square_1(k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t8_integr15,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_integra1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) ) => ! [D] : ( m1_subset_1(D,k1_numbers) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & v1_seq_2(k2_partfun1(A,k1_numbers,B,A)) & ! [E] : ( m2_integr15(E,A,B,C) => ~ ! [F] : ( m1_subset_1(F,k4_ordinal1) => r1_xxreal_0(k5_real_1(k3_funct_2(k4_ordinal1,k1_numbers,k3_integra2(A,B,C),F),D),k3_funct_2(k4_ordinal1,k1_numbers,k3_integr15(A,B,C,E),F)) ) ) ) ) ) ) ) )).
fof(t8_integr16,axiom,( ! [A] : ( m2_finseq_1(A,k2_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( B = k2_integr16(A) => k18_rvsum_1(B) = k4_complex1(k17_rvsum_1(A)) ) ) ) )).
fof(t8_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [D] : ( ( 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)))) ) => ( k2_partfun1(k1_numbers,u1_struct_0(A),C,B) = D => ( r1_integr18(A,B,C) <=> v1_integr18(D,A,B) ) ) ) ) ) ) )).
fof(t8_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ( ( r1_xxreal_0(B,C) & r1_integr15(A,k3_integra5(B,C),E) & v3_integr15(k2_partfun1(k1_numbers,k1_euclid(A),E,k3_integra5(B,C)),A) & r1_tarski(k3_integra5(B,C),k1_relset_1(k1_numbers,E)) & r2_hidden(D,k3_integra5(B,C)) ) => ( r1_integr15(A,k3_integra5(B,D),E) & r1_integr15(A,k3_integra5(D,C),E) & k12_integr15(B,C,A,E) = k7_euclid(A,k12_integr15(B,D,A,E),k12_integr15(D,C,A,E)) ) ) ) ) ) ) ) )).
fof(t8_integra1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t8_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => k1_integra2(B,A) = a_2_0_integra2(A,B) ) ) )).
fof(t8_integra3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v2_measure5(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( m1_integra1(D,C) => ! [E] : ( m1_integra1(E,C) => ~ ( r1_integra1(D,E) & r2_hidden(A,k4_finseq_1(D)) & r2_hidden(B,k4_finseq_1(D)) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(k13_integra1(C,D,E,B),k13_integra1(C,D,E,A)) ) ) ) ) ) ) )).
fof(t8_integra4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_integra1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) ) => ( ( v1_comseq_2(k2_partfun1(A,k1_numbers,B,A)) & v2_comseq_2(k2_integra3(A,C)) & k1_seq_2(k2_integra3(A,C)) = k5_numbers ) => ( v2_comseq_2(k4_integra2(A,B,C)) & k1_seq_2(k4_integra2(A,B,C)) = k11_integra1(A,B) ) ) ) ) ) )).
fof(t8_integra5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v2_seq_2(k2_partfun1(k1_numbers,k1_numbers,B,A)) => v2_seq_2(k2_partfun1(A,k1_numbers,k1_integra5(B,A),A)) ) ) ) )).
fof(t8_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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(k3_integra5(A,B),k9_xtuple_0(C)) & r1_integra5(k3_integra5(A,B),C) & v1_comseq_2(k2_partfun1(k1_numbers,k1_numbers,C,k3_integra5(A,B))) ) => r1_xxreal_0(k9_complex1(k4_integra5(A,B,C)),k4_integra5(A,B,k56_valued_1(k1_numbers,k1_numbers,C))) ) ) ) ) )).
fof(t8_integra7,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( ! [D] : ~ ( r2_hidden(D,A) & k1_funct_1(C,D) = k5_numbers ) & r2_fdiff_1(B,A) & r2_fdiff_1(C,A) ) => r2_fdiff_1(k3_rfunct_1(k1_numbers,k1_numbers,B,C),A) ) ) ) )).
fof(t8_integra8,axiom,( k17_sin_cos(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4))) = k4_xcmplx_0(k7_xcmplx_0(k3_square_1(2),2)) )).
fof(t8_integra9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k1_partfun2(k1_numbers,B),k16_sin_cos)) = k6_xcmplx_0(k1_funct_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,B)),k18_sin_cos),k16_sin_cos),k2_seq_4(A)),k1_funct_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,B)),k18_sin_cos),k16_sin_cos),k3_seq_4(A))) ) ) ) )).
fof(t8_interva1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k1_interva1(A,B,B) = k1_tarski(B) ) )).
fof(t8_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => ! [C] : ( m1_subset_1(C,k1_intpro_1) => ! [D] : ( m1_subset_1(D,k1_intpro_1) => 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))),k7_intpro_1(A)) ) ) ) ) )).
fof(t8_irrat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ( v2_comseq_2(k1_irrat_1(A)) & k1_seq_2(k1_irrat_1(A)) = 1 ) ) )).
fof(t8_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ( v12_cat_1(C,A,B) => v12_cat_1(k1_isocat_1(A,B,C),B,A) ) ) ) ) )).
fof(t8_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( ( ~ 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] : ( m2_cat_1(D,k6_cat_2(A,B),C) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => k8_cat_1(B,C,k10_cat_2(A,B,C,D,E),F) = k8_cat_1(k6_cat_2(A,B),C,D,k7_cat_2(A,B,E,F)) ) ) ) ) ) ) )).
fof(t8_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_isomichi(B,A) <=> r1_tarski(k1_tops_1(A,k2_pre_topc(A,B)),B) ) ) ) )).
fof(t8_jct_misc,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_numbers)) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(C,A) & r1_tarski(D,B) ) => r1_xxreal_0(k1_jct_misc(A,B),k1_jct_misc(C,D)) ) ) ) ) ) )).
fof(t8_jgraph_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r1_jgraph_1(A,B,C) => ( r1_xxreal_0(1,k3_finseq_1(C)) & r1_xxreal_0(k3_finseq_1(C),k3_finseq_1(B)) ) ) ) ) ) )).
fof(t8_jgraph_2,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => A = k19_euclid(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,k5_pscomp_1,A)) ) )).
fof(t8_jgraph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) != k5_numbers ) & ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( 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_square_1(k2_xcmplx_0(1,k1_square_1(k7_xcmplx_0(F,G)))) ) ) ) ) & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).
fof(t8_jgraph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) = k4_xcmplx_0(E) ) ) ) & v5_pre_topc(C,A,k3_topmetr) ) ) ) ) ) )).
fof(t8_jgraph_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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))))) ) => ( ( v3_tops_2(I,k4_topmetr(A,B),k4_topmetr(C,D)) & k1_funct_1(I,E) = G & k1_funct_1(I,F) = H & k1_funct_1(I,B) = D & r1_xxreal_0(C,D) & r1_xxreal_0(G,H) & r2_hidden(E,k1_rcomp_1(A,B)) & r2_hidden(F,k1_rcomp_1(A,B)) ) => r1_xxreal_0(E,F) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_jgraph_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ~ ( v5_pre_topc(B,A,k3_topmetr) & ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) = k6_xcmplx_0(C,F) ) ) ) & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).
fof(t8_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t8_jordan,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( r1_xxreal_0(k17_euclid(B),A) & r1_xxreal_0(A,k17_euclid(C)) & r1_xboole_0(k1_rltopsp1(k15_euclid(2),B,C),k6_jordan6(A)) ) ) ) ) )).
fof(t8_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( E = a_4_0_jordan1(A,B,C,D) => v1_convex1(E,k15_euclid(2)) ) ) ) ) ) ) )).
fof(t8_jordan10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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_hidden(k20_pscomp_1(B),k3_goboard9(k2_jordan9(B,A))) ) ) )).
fof(t8_jordan11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_jordan1h(B,A) => r2_hidden(k4_tarski(k3_jordan1h(B,A),k5_jordan11(B,A)),k2_matrix_0(k1_jordan8(B,A))) ) ) ) )).
fof(t8_jordan12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(2))) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) & r2_jordan12(2,B,C) ) => ( r2_hidden(k1_funct_1(C,A),k3_subset_1(u1_struct_0(k15_euclid(2)),k3_topreal1(2,B))) & r2_hidden(k1_funct_1(C,k1_nat_1(A,1)),k3_subset_1(u1_struct_0(k15_euclid(2)),k3_topreal1(2,B))) ) ) ) ) ) )).
fof(t8_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ( r1_jordan1h(A,B) => r1_subset_1(A,k3_topreal1(2,k1_jordan13(A,B))) ) ) ) )).
fof(t8_jordan15,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( k3_finseq_1(A) = k1_matrix_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(B,D) & r1_xxreal_0(D,E) & r1_xxreal_0(E,C) & r1_xxreal_0(C,k3_finseq_1(A)) ) => r1_tarski(k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,D,k1_jordan1a(A)),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,E,k1_jordan1a(A))),k1_rltopsp1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,B,k1_jordan1a(A)),k3_matrix_0(u1_struct_0(k15_euclid(2)),A,C,k1_jordan1a(A)))) ) ) ) ) ) ) ) )).
fof(t8_jordan16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,B) ) => ! [D] : ( ( 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] : ( ( 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) & v5_pre_topc(D,A,B) ) => v5_pre_topc(E,A,C) ) ) ) ) ) ) )).
fof(t8_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( B != C & r1_jordan6(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ~ ( D != B & D != C & r1_jordan6(A,B,D) & r1_jordan6(A,D,C) ) ) ) ) ) ) )).
fof(t8_jordan18,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => k2_seq_4(k7_relset_1(u1_struct_0(k15_euclid(2)),k1_numbers,k5_pscomp_1,k6_topreal1(A))) = k18_euclid(A) ) )).
fof(t8_jordan19,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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(k7_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))),k7_pscomp_1(B)) ) ) )).
fof(t8_jordan1a,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => r2_hidden(A,k6_jordan6(k17_euclid(A))) ) )).
fof(t8_jordan1b,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( v1_sppol_1(k1_rltopsp1(k15_euclid(2),A,B)) => ( A = B | v4_topreal1(k2_finseq_4(u1_struct_0(k15_euclid(2)),A,B)) ) ) ) ) )).
fof(t8_jordan1c,axiom,( ! [A] : ( ( v2_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( k1_jordan2c(2,A) != k1_xboole_0 => r1_xxreal_0(k9_pscomp_1(A),k9_pscomp_1(k1_jordan2c(2,A))) ) ) )).
fof(t8_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & ~ r1_xxreal_0(k3_finseq_1(k2_jordan9(B,A)),C) & r2_hidden(k21_pscomp_1(B),k4_goboard5(k2_jordan9(B,A),C)) ) ) ) )).
fof(t8_jordan1e,axiom,( ! [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] : ( v7_ordinal1(B) => k3_finseq_1(k1_jordan1e(A,B)) = k4_finseq_4(k1_finseq_6(u1_struct_0(k15_euclid(2)),k2_jordan9(A,B),k18_pscomp_1(k3_topreal1(2,k2_jordan9(A,B)))),k22_pscomp_1(k3_topreal1(2,k2_jordan9(A,B)))) ) ) )).
fof(t8_jordan1f,axiom,( ! [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] : ( v7_ordinal1(B) => k7_partfun1(u1_struct_0(k15_euclid(2)),k2_jordan1e(A,B),k3_finseq_1(k2_jordan1e(A,B))) = k18_pscomp_1(k3_topreal1(2,k2_jordan9(A,B))) ) ) )).
fof(t8_jordan1g,axiom,( ! [A] : ( ( ~ 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) != k20_pscomp_1(k3_topreal1(2,A)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k3_finseq_1(A)) != k20_pscomp_1(k3_topreal1(2,A)) ) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,1) != k21_pscomp_1(k3_topreal1(2,A)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k3_finseq_1(A)) != k21_pscomp_1(k3_topreal1(2,A)) ) ) & r1_xxreal_0(k17_euclid(k21_pscomp_1(k3_topreal1(2,A))),k17_euclid(k20_pscomp_1(k3_topreal1(2,A)))) ) ) )).
fof(t8_jordan1h,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( B = k1_rvsum_1(A) => k7_pre_poly(k1_numbers,B,k1_jordan1h) = k26_seq_4(A) ) ) ) )).
fof(t8_jordan1j,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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_hidden(k21_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))),k10_xtuple_0(k1_jordan1e(B,A))) & r2_hidden(k21_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))),k3_topreal1(2,k1_jordan1e(B,A))) ) ) ) )).
fof(t8_jordan1k,axiom,( ! [A] : ( v7_ordinal1(A) => ( r1_xxreal_0(1,A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k14_euclid(A)))) => ~ ( v6_tbsp_1(B,k14_euclid(A)) & v6_tbsp_1(k3_subset_1(u1_struct_0(k14_euclid(A)),B),k14_euclid(A)) ) ) ) ) )).
fof(t8_jordan20,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ~ ( r1_topreal1(k15_euclid(2),B,C,A) & r1_xxreal_0(k17_euclid(B),E) & r1_xxreal_0(E,k17_euclid(C)) & ! [F] : ( m1_subset_1(F,u1_struct_0(k15_euclid(2))) => ~ ( r2_hidden(F,A) & k17_euclid(F) = E ) ) ) ) ) ) ) ) )).
fof(t8_jordan22,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( 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(D,C) & r2_hidden(k4_tarski(A,B),k2_matrix_0(k1_jordan8(E,C))) & r2_hidden(k4_tarski(A,k1_nat_1(B,1)),k2_matrix_0(k1_jordan8(E,C))) & r1_xxreal_0(k1_topreal6(2,k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,C),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,C),A,k1_nat_1(B,1))),k1_topreal6(2,k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,D),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(E,D),A,k1_nat_1(B,1)))) ) ) ) ) ) ) )).
fof(t8_jordan23,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v1_jordan23(A) => v1_jordan23(k3_finseq_5(A)) ) ) )).
fof(t8_jordan24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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_funct_1(C) & v2_funct_2(C,u1_struct_0(B)) ) => ( v3_tops_2(C,A,B) <=> v2_jordan24(C,A,B) ) ) ) ) ) )).
fof(t8_jordan2b,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => k2_rfinseq(k1_numbers,B,k5_euclid(A)) = k5_euclid(k7_nat_d(A,B)) ) ) )).
fof(t8_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( r2_jordan2c(A,B,C) <=> ? [D] : ( 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)))) ) ) ) ) ) ) )).
fof(t8_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(B,k3_topreal1(2,A)) => ( r1_xxreal_0(1,k1_jordan3(A,B)) & ~ r1_xxreal_0(k3_finseq_1(A),k1_jordan3(A,B)) ) ) ) ) )).
fof(t8_jordan4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,C) & r1_xxreal_0(C,k3_finseq_1(B)) ) => k3_finseq_1(k3_finseq_6(A,B,D,C)) = k1_nat_1(k7_nat_d(C,D),1) ) ) ) ) ) )).
fof(t8_jordan5a,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(k5_topmetr)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_topmetr)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( B = D & C = E & ~ r1_xxreal_0(E,D) & F = k1_funct_1(A,B) & G = k1_funct_1(A,C) & r1_xxreal_0(G,F) ) ) ) ) ) ) ) | ! [B] : ( m1_subset_1(B,u1_struct_0(k5_topmetr)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_topmetr)) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ~ ( B = D & C = E & ~ r1_xxreal_0(E,D) & F = k1_funct_1(A,B) & G = k1_funct_1(A,C) & r1_xxreal_0(F,G) ) ) ) ) ) ) ) ) ) )).
fof(t8_jordan5b,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(k17_borsuk_1),u1_struct_0(k1_pre_topc(k15_euclid(2),B))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k17_borsuk_1),u1_struct_0(k1_pre_topc(k15_euclid(2),B))))) ) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( ( ~ v1_xboole_0(F) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(k17_borsuk_1))) ) => ~ ( v4_topreal1(A) & v3_tops_2(D,k17_borsuk_1,k1_pre_topc(k15_euclid(2),B)) & k1_funct_1(D,k5_numbers) = k7_partfun1(u1_struct_0(k15_euclid(2)),A,1) & k1_funct_1(D,1) = k7_partfun1(u1_struct_0(k15_euclid(2)),A,k3_finseq_1(A)) & r1_xxreal_0(1,E) & r1_xxreal_0(k1_nat_1(E,1),k3_finseq_1(A)) & k7_relset_1(u1_struct_0(k17_borsuk_1),u1_struct_0(k1_pre_topc(k15_euclid(2),B)),D,F) = k2_topreal1(2,A,E) & B = k3_topreal1(2,A) & C = k2_topreal1(2,A,E) & ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,u1_struct_0(k1_pre_topc(k17_borsuk_1,F)),u1_struct_0(k1_pre_topc(k15_euclid(2),C))) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_pre_topc(k17_borsuk_1,F)),u1_struct_0(k1_pre_topc(k15_euclid(2),C))))) ) => ~ ( G = k2_partfun1(u1_struct_0(k17_borsuk_1),u1_struct_0(k1_pre_topc(k15_euclid(2),B)),D,F) & v3_tops_2(G,k1_pre_topc(k17_borsuk_1,F),k1_pre_topc(k15_euclid(2),C)) ) ) ) ) ) ) ) ) ) )).
fof(t8_jordan5c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(2))) => ! [F] : ( ( 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] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ( ( r1_topreal1(k15_euclid(2),B,C,A) & v3_tops_2(F,k5_topmetr,k1_pre_topc(k15_euclid(2),A)) & k1_funct_1(F,k5_numbers) = B & k1_funct_1(F,1) = C & k1_funct_1(F,G) = D & r1_xxreal_0(k5_numbers,G) & r1_xxreal_0(G,1) & k1_funct_1(F,H) = E & r1_xxreal_0(k5_numbers,H) & r1_xxreal_0(H,1) & r1_xxreal_0(G,H) ) => r1_jordan5c(A,B,C,D,E) ) ) ) ) ) ) ) ) ) )).
fof(t8_jordan6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( B = a_1_4_jordan6(A) => v4_pre_topc(B,k15_euclid(2)) ) ) ) )).
fof(t8_jordan7,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( ( v1_topreal2(A) & r2_hidden(B,A) ) => ( B = k18_pscomp_1(A) | k1_jordan7(A,B,B) = k1_tarski(B) ) ) ) ) )).
fof(t8_jordan8,axiom,( ! [A] : ( ( ~ 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) <=> r1_xxreal_0(k8_pscomp_1(A),k6_pscomp_1(A)) ) ) )).
fof(t8_jordan9,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r1_goboard1(u1_struct_0(k15_euclid(2)),B,A) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(B)) ) => ( r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),B,C),k3_gobrd13(B,A,C)) & r2_hidden(k7_partfun1(u1_struct_0(k15_euclid(2)),B,C),k2_gobrd13(B,A,C)) ) ) ) ) ) ) )).
fof(t8_jordan_a,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r1_jordan6(A,B,C) & r1_jordan6(A,C,k22_pscomp_1(A)) ) => ( B = C | k1_jordan7(A,B,C) = k5_jordan6(k8_jordan6(A),k18_pscomp_1(A),k22_pscomp_1(A),B,C) ) ) ) ) ) )).
fof(t8_knaster,axiom,( ! [A] : ! [B] : ( ( 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)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r2_abian(k9_setfam_1(A),C,B) => ( r1_tarski(k1_knaster(A,B),C) & r1_tarski(C,k2_knaster(A,B)) ) ) ) ) )).
fof(t8_kolmog01,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(B)) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(B)) ) => ( r1_tarski(D,k1_kolmog01(A,B,E,C)) => r1_tarski(E,k1_kolmog01(A,B,D,C)) ) ) ) ) ) ) )).
fof(t8_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => r1_tarski(k4_kurato_0(A,B),k1_kurato_0(A,B)) ) )).
fof(t8_kurato_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k5_kurato_1(A,B) = k2_xboole_0(k2_xboole_0(k1_tarski(B),k1_enumset1(k1_tops_1(A,B),k1_tops_1(A,k2_pre_topc(A,B)),k1_tops_1(A,k2_pre_topc(A,k1_tops_1(A,B))))),k1_enumset1(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))))) ) ) )).
fof(t8_kurato_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( ~ v9_rltopsp1(B,k15_euclid(A)) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(A))) => ~ ( r2_hidden(D,B) & r2_hidden(E,B) & ~ r1_xxreal_0(k3_metric_1(k14_euclid(A),D,E),C) ) ) ) ) ) ) ) ) )).
fof(t8_lang1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_lang1(A) ) => ! [B] : ( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ! [C] : ( m2_finseq_2(C,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ! [D] : ( m2_finseq_2(D,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ( ( r3_lang1(A,C,B) & r3_lang1(A,D,C) ) => r3_lang1(A,D,B) ) ) ) ) ) )).
fof(t8_laplace,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & v12_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_matrix_2(C,k3_matrix_2(k1_nat_1(A,2))) => ! [D] : ( m1_subset_1(D,k5_finsub_1(k2_sgraph1(k2_finseq_1(k1_nat_1(A,2))))) => ! [E] : ( m1_subset_1(E,k5_finsub_1(k2_sgraph1(k2_finseq_1(k1_nat_1(A,2))))) => ( E = a_4_0_laplace(A,B,C,D) => 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_laplace(B,k4_group_1(B),k4_algstr_0(B,k1_group_1(B)),k5_card_1(E)) ) ) ) ) ) ) )).
fof(t8_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( m1_group_2(D,A) => ! [E] : ( m1_group_2(E,A) => ! [F] : ( m1_group_2(F,B) => ! [G] : ( m1_group_2(G,B) => ( ( u1_struct_0(F) = k7_relset_1(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(D)) & u1_struct_0(G) = k7_relset_1(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(E)) & m1_group_6(D,A,E) ) => m1_group_6(F,B,G) ) ) ) ) ) ) ) ) )).
fof(t8_latsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(k1_latsum_1(A,B))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k1_latsum_1(A,B))) => ( ( C = E & D = F & r1_latsum_1(A,B) & v4_orders_2(A) ) => ( r1_orders_2(A,C,D) <=> r1_orders_2(k1_latsum_1(A,B),E,F) ) ) ) ) ) ) ) ) )).
fof(t8_lattice2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [E] : ( m1_subset_1(E,k5_finsub_1(A)) => k7_funct_4(A,B,k2_partfun1(A,B,D,E),C) = C ) ) ) ) )).
fof(t8_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => k7_lattice3(k7_lattice3(A)) = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) )).
fof(t8_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( v20_lattices(B,A) & v21_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).
fof(t8_lattice5,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,u1_struct_0(k1_lattice5(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_lattice5(A))) => k12_lattice3(k1_lattice5(A),B,C) = k3_xboole_0(B,C) ) ) )).
fof(t8_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & v2_lattice6(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B = k5_lattices(A) <=> ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ r1_lattice6(A,B,C) ) ) ) ) )).
fof(t8_lattice7,axiom,( ! [A] : ( ( 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & r2_hidden(C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r2_hidden(D,B) & r2_orders_2(A,C,D) ) ) ) ) ) )).
fof(t8_lattice8,axiom,( ! [A] : ( ~ v1_zfmisc_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,k1_lattice5(A)) & v5_yellow_0(B,k1_lattice5(A)) & v6_yellow_0(B,k1_lattice5(A)) & v1_lattice8(B) & m1_yellow_0(B,k1_lattice5(A)) ) => ! [C] : ( ( 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)) & r1_xxreal_0(k2_lattice5(A,B),2) ) => ( C = k6_partfun1(A) | v1_yellow11(B) ) ) ) ) ) )).
fof(t8_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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) ) ) )).
fof(t8_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ( v3_lexbfs(A) => v13_glib_000(A) ) ) )).
fof(t8_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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,k2_lfuzzy_1(A,B,C)) ) ) ) )).
fof(t8_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_limfunc1(A) & v1_limfunc1(B) ) => v1_limfunc1(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) ) ) )).
fof(t8_limfunc3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,C) & ~ r1_xxreal_0(D,A) & ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ~ ( ~ 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] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(A,C) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,C) & ~ r1_xxreal_0(A,D) & r2_hidden(D,k9_xtuple_0(B)) ) ) ) ) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,A) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(C,D) & ~ r1_xxreal_0(D,A) & r2_hidden(D,k9_xtuple_0(B)) ) ) ) ) ) ) ) ) )).
fof(t8_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v7_limfunc1(A) & v5_limfunc1(B) & ! [C] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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)) ) ) ) )).
fof(t8_lmod_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v6_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) & v1_vectsp_2(B) & l6_algstr_0(B) ) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) => ( r1_struct_0(k1_lmod_5(B,C,D),A) <=> ? [E] : ( m2_vectsp_6(E,B,C,D) & A = k4_vectsp_6(B,C,E) ) ) ) ) ) )).
fof(t8_lmod_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) => m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) ) ) ) )).
fof(t8_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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_binop_1(k6_vectsp_5(A,B),k3_vectsp_5(A,B)) & v2_binop_1(k6_vectsp_5(A,B),k3_vectsp_5(A,B)) & v1_setwiseo(k6_vectsp_5(A,B),k3_vectsp_5(A,B)) & k2_vectsp_4(A,B) = k4_binop_1(k3_vectsp_5(A,B),k6_vectsp_5(A,B)) ) ) ) )).
fof(t8_lopban_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m2_funct_2(C,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => k1_funct_1(k3_lopban_1(A,B),k4_tarski(D,k1_funct_1(k3_lopban_1(A,B),k4_tarski(E,C)))) = k1_funct_1(k3_lopban_1(A,B),k4_tarski(k3_xcmplx_0(D,E),C)) ) ) ) ) ) )).
fof(t8_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(k8_lopban_1(A,A)),k10_lopban_1(A,A)) => ( k3_lopban_2(A,k6_lopban_2(A),B) = B & k3_lopban_2(A,B,k6_lopban_2(A)) = B ) ) ) )).
fof(t8_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( m2_valued_0(C,u1_struct_0(A),B) & v3_normsp_1(B,A) ) => k6_normsp_1(A,C) = k6_normsp_1(A,B) ) ) ) ) )).
fof(t8_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v3_normsp_1(B,A) & v3_normsp_1(C,A) ) => k6_normsp_1(A,k4_lopban_3(A,B,C)) = k6_algstr_0(A,k6_normsp_1(A,B),k6_normsp_1(A,C)) ) ) ) ) )).
fof(t8_lopban_6,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k4_normsp_2(A)))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k4_normsp_2(A))) => ( ( B = D & C = E ) => k5_rusub_4(A,B,C) = k5_rusub_4(k4_normsp_2(A),D,E) ) ) ) ) ) ) )).
fof(t8_lopban_7,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(B)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( ( v3_normsp_1(C,A) & k6_normsp_1(A,C) = E & v3_normsp_1(D,B) & k6_normsp_1(B,D) = F ) => ( v3_normsp_1(k2_lopban_7(A,B,C,D),k7_prvect_3(A,B)) & k6_normsp_1(k7_prvect_3(A,B),k2_lopban_7(A,B,C,D)) = k1_lopban_7(A,B,E,F) ) ) & ( ( v3_normsp_1(k2_lopban_7(A,B,C,D),k7_prvect_3(A,B)) & k6_normsp_1(k7_prvect_3(A,B),k2_lopban_7(A,B,C,D)) = k1_lopban_7(A,B,E,F) ) => ( v3_normsp_1(C,A) & k6_normsp_1(A,C) = E & v3_normsp_1(D,B) & k6_normsp_1(B,D) = F ) ) ) ) ) ) ) ) ) )).
fof(t8_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(u1_struct_0(A)),k1_lopclset(A)) => m2_subset_1(k3_subset_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A)),k1_lopclset(A)) ) ) )).
fof(t8_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => ( ~ v2_struct_0(g1_normsp_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)),k3_lp_space(A))) & v13_algstr_0(g1_normsp_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)),k3_lp_space(A))) & v2_rlvect_1(g1_normsp_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)),k3_lp_space(A))) & v3_rlvect_1(g1_normsp_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)),k3_lp_space(A))) & v4_rlvect_1(g1_normsp_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)),k3_lp_space(A))) & v5_rlvect_1(g1_normsp_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)),k3_lp_space(A))) & v6_rlvect_1(g1_normsp_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)),k3_lp_space(A))) & v7_rlvect_1(g1_normsp_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)),k3_lp_space(A))) & v8_rlvect_1(g1_normsp_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)),k3_lp_space(A))) & l1_rlvect_1(g1_normsp_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)),k3_lp_space(A))) ) ) ) )).
fof(t8_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => r3_binop_1(k3_rfunct_3(A,k2_numbers),k11_lpspacc1(A),k7_lpspacc1(A)) ) )).
fof(t8_lpspace1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k5_lpspace1(A) != k6_lpspace1(A) ) )).
fof(t8_lpspace2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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(1,A,B),B) ) ) )).
fof(t8_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => ( k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(D),k1_domain_1(k4_ordinal1,k1_hilbert1,C,k5_ltlaxio1(A,B))) = 1 <=> ( k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(D),k1_domain_1(k4_ordinal1,k1_hilbert1,C,A)) = 1 | k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(D),k1_domain_1(k4_ordinal1,k1_hilbert1,C,B)) = 1 ) ) ) ) ) ) )).
fof(t8_ltlaxio2,axiom,( ! [A] : ( m2_finseq_1(A,k1_hilbert1) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => k7_partfun1(k1_hilbert1,k4_ltlaxio2(A),B) = k1_ltlaxio1(k7_partfun1(k1_hilbert1,A,B)) ) ) ) )).
fof(t8_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ( r2_hidden(A,k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,B)) => r1_tarski(k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,A),k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,B)) ) ) ) )).
fof(t8_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( ( v3_ltlaxio3(C) & m1_subset_1(C,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) ) => ( r2_hidden(k1_ltlaxio2(A,B),k10_ltlaxio3(C)) => ( r2_hidden(A,k10_ltlaxio3(C)) & r2_hidden(B,k10_ltlaxio3(C)) & r2_hidden(k4_hilbert1(A,B),k10_ltlaxio3(C)) ) ) ) ) ) )).
fof(t8_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => r2_hidden(k8_cqc_lang(A,k8_cqc_lang(A,D,k8_cqc_lang(A,C,B)),k8_cqc_lang(A,C,k8_cqc_lang(A,D,B))),k4_cqc_the1(A)) ) ) ) ) )).
fof(t8_margrel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => m1_subset_1(k1_tarski(k10_finseq_1(B,C)),k3_margrel1(A)) ) ) ) )).
fof(t8_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = k1_xboole_0 => k3_mathmorp(A,B,C) = u1_struct_0(A) ) ) ) ) )).
fof(t8_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( ( v1_matrix10(B) & v1_matrix10(C) ) => v1_matrix10(k4_matrix10(A,B,C)) ) ) ) ) )).
fof(t8_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ~ r1_xxreal_0(D,C) => ( k1_funct_1(B,C) = D <=> ( r2_hidden(C,k9_xtuple_0(B)) & r2_hidden(D,k9_xtuple_0(B)) & k1_funct_1(B,C) = D & k1_funct_1(B,D) = C & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k9_xtuple_0(B)) => ( E = C | E = D | k1_funct_1(B,E) = E ) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( m1_subset_1(E,u1_struct_0(D)) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(D),C,C) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(D))) ) => ( ( r2_hidden(B,k4_finseq_1(k3_matrix_1(D,C))) & r2_hidden(A,k4_finseq_1(k3_matrix_1(D,C))) ) => k4_matrix_3(D,k3_matrix12(C,C,D,k3_matrix_1(D,C),B,A,E),F) = k3_matrix12(C,C,D,F,B,A,E) ) ) ) ) ) ) ) )).
fof(t8_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & v2_matrix_2(C,A,B) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => k12_matrix_3(A,B,C) = k1_finsop_1(u1_struct_0(B),k13_matrix_3(A,B,C),u2_algstr_0(B)) ) ) ) )).
fof(t8_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k3_finseq_1(B) = k3_finseq_1(C) => ( k11_fvsum_1(A,k9_fvsum_1(A,B,D),C) = k9_fvsum_1(A,k11_fvsum_1(A,B,C),D) & k11_fvsum_1(A,B,k9_fvsum_1(A,C,D)) = k9_fvsum_1(A,k11_fvsum_1(A,B,C),D) ) ) ) ) ) ) )).
fof(t8_matrix15,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(A,k2_finseq_1(B)) => k1_funct_1(k5_matrix13(k7_subset_1(k4_ordinal1,k2_finseq_1(k2_xcmplx_0(C,B)),k2_finseq_1(C))),A) = k2_xcmplx_0(C,A) ) ) ) ) )).
fof(t8_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix16(C,u1_struct_0(B)) & v1_matrix16(D,u1_struct_0(B)) & v1_matrix16(E,u1_struct_0(B)) ) => v1_matrix16(k3_matrix_3(B,k3_matrix_3(B,C,D),E),u1_struct_0(B)) ) ) ) ) ) ) )).
fof(t8_matrix17,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ( v5_matrix17(B,u1_struct_0(A)) => v5_matrix17(k5_fvsum_1(A,B),u1_struct_0(A)) ) ) ) )).
fof(t8_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => v1_matrix_0(k2_finseq_4(k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A)),k2_finseq_4(A,B,C),k2_finseq_4(A,D,E))) ) ) ) ) ) )).
fof(t8_matrix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_matrix_2(B,k3_matrix_2(A)) => m1_subset_1(k2_funct_2(k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),B),u1_struct_0(k4_matrix_2(A))) ) ) )).
fof(t8_matrix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k4_tarski(C,D),k2_matrix_0(k3_matrix_1(B,A))) => ( D = C | k1_funct_1(k7_matrix_0(u1_struct_0(B),k3_matrix_1(B,A),C),D) = k4_struct_0(B) ) ) ) ) ) ) )).
fof(t8_matrix_4,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(A))) ) => ( ( k3_finseq_1(B) = k3_finseq_1(C) & k1_matrix_0(B) = k1_matrix_0(C) & k3_matrix_3(A,B,C) = k1_matrix_3(A,k3_finseq_1(B),k1_matrix_0(B)) ) => C = k2_matrix_3(A,B) ) ) ) ) )).
fof(t8_matrix_5,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k1_complfld))) ) => ( k3_finseq_1(A) = k3_finseq_1(k2_matrix_5(A)) & k1_matrix_0(A) = k1_matrix_0(k2_matrix_5(A)) ) ) )).
fof(t8_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_6(A,B,k3_matrix_1(B,A)) = k3_matrix_1(B,A) & v1_matrix_6(k3_matrix_1(B,A),A,B) ) ) ) )).
fof(t8_matrix_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k4_matrix_2(2))) => ( ? [B] : ( m1_matrix_2(B,k3_matrix_2(2)) & B = A & v4_matrix_2(B,k2_matrix_2(k3_matrix_2(2))) ) => A = k10_finseq_1(2,1) ) ) )).
fof(t8_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,u1_struct_0(B),A,A) & m2_finseq_1(D,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_8(C,A,B) & v1_matrix_6(D,A,B) ) => v1_matrix_8(k4_matrix_3(B,k4_matrix_3(B,k1_matrix_6(A,B,D),C),D),A,B) ) ) ) ) ) )).
fof(t8_matrixc1,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k2_numbers)) ) => ( k3_finseq_1(k4_matrix_5(A)) = k3_finseq_1(A) & k1_matrix_0(k4_matrix_5(A)) = k1_matrix_0(A) ) ) )).
fof(t8_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( r2_hidden(A,k2_finseq_1(k2_wsierp_1(B))) => k1_matrixj1(k8_finseq_1(k4_ordinal1,B,C),A) = k1_matrixj1(B,A) ) ) ) ) )).
fof(t8_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => k6_rvsum_1(k8_rvsum_1(A,B)) = k8_rvsum_1(B,A) ) ) ) )).
fof(t8_matrixr2,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( ( k3_finseq_1(A) = k3_finseq_1(B) & k1_matrix_0(A) = k1_matrix_0(B) ) => ( r1_xxreal_0(k3_finseq_1(A),k5_numbers) | k5_matrixr1(k3_matrixr1(A,B),B) = A ) ) ) ) )).
fof(t8_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_vectsp_7(D,A,B) => ? [E] : ( m1_vectsp_6(E,A,B) & C = k4_vectsp_6(A,B,E) & r1_tarski(k1_vectsp_6(A,B,E),D) ) ) ) ) ) )).
fof(t8_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(A)) => k5_matrlin(A,B,E,k3_fvsum_1(B,C,D)) = k3_fvsum_1(B,k5_matrlin(A,B,E,C),k5_matrlin(A,B,E,D)) ) ) ) ) ) )).
fof(t8_matroid0,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_matroid0(A)))) => ( v3_pre_topc(B,k2_matroid0(A)) <=> ! [C] : ( m1_subset_1(C,A) => ? [D] : ( m1_subset_1(D,C) & r1_tarski(k8_subset_1(u1_struct_0(k2_matroid0(A)),B,C),k1_tarski(D)) ) ) ) ) )).
fof(t8_matrprob,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m2_finseq_1(C,B) => m2_finseq_1(k2_finseq_2(A,C),k3_finseq_2(B)) ) ) )).
fof(t8_matrtop1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v1_valued_0(C) ) => ! [D] : ( ( 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) => k16_rvsum_1(k1_finseq_3(C,A)) = k16_rvsum_1(k1_finseq_3(B,A)) ) ) ) ) )).
fof(t8_matrtop2,axiom,( ! [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] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_6(D,A,B) => m1_vectsp_6(k2_partfun1(u1_struct_0(B),u1_struct_0(A),D,u1_struct_0(C)),A,C) ) ) ) ) )).
fof(t8_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(C))) => ( r2_hidden(A,k2_finseq_1(C)) => ( A = B | k1_funct_1(k3_funct_2(u1_struct_0(k15_euclid(C)),u1_struct_0(k15_euclid(C)),k3_matrtop1(C,C,k1_matrtop3(C,A)),D),B) = k1_funct_1(D,B) ) ) ) ) ) ) )).
fof(t8_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k1_ndiff_1(A,k8_funcop_1(u1_struct_0(A),k4_ordinal1,B),C),k2_ndiff_1(A,B,C)) ) ) ) )).
fof(t8_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r6_pboole(A,k2_pboole(A,k1_mboolean(A,B),k1_mboolean(A,C)),k1_mboolean(A,k2_pboole(A,B,C))) => ! [D] : ( r2_hidden(D,A) => r3_xboole_0(k1_funct_1(B,D),k1_funct_1(C,D)) ) ) ) ) )).
fof(t8_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(C,k2_zfmisc_1(k1_tarski(A),k1_tarski(B))) => ( k1_xtuple_0(C) = A & k2_xtuple_0(C) = B ) ) )).
fof(t8_measure1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( 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)) ) ) ) ) ) )).
fof(t8_measure3,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_ordinal1,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ( ( k9_nat_1(B,D,k5_numbers) = k1_xboole_0 & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( k9_nat_1(B,D,k1_nat_1(F,1)) = k3_measure1(A,B,k9_nat_1(B,E,k5_numbers),k9_nat_1(B,E,F)) & r1_tarski(k9_nat_1(B,E,k1_nat_1(F,1)),k9_nat_1(B,E,F)) ) ) ) => ( r1_xxreal_0(k1_supinf_1,k12_supinf_2(C,k9_nat_1(B,E,k5_numbers))) | k12_supinf_2(C,k1_measure2(A,B,k1_measure3(A,B,E))) = k4_supinf_2(k12_supinf_2(C,k9_nat_1(B,E,k5_numbers)),k8_supinf_2(k17_supinf_2(k1_partfun1(k4_ordinal1,B,B,k6_numbers,D,C)))) ) ) ) ) ) ) )).
fof(t8_measure4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_measure4(D,C) => ( ( r2_hidden(A,k1_measure4(C,D)) & r2_hidden(B,k1_measure4(C,D)) ) => r2_hidden(k2_xboole_0(A,B),k1_measure4(C,D)) ) ) )).
fof(t8_measure5,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => ! [B] : ( m1_subset_1(B,k6_numbers) => ( ( ~ r1_xxreal_0(B,A) => k2_measure5(k3_xxreal_1(A,B)) = k4_supinf_2(B,A) ) & ( r1_xxreal_0(B,A) => k2_measure5(k3_xxreal_1(A,B)) = k1_supinf_2 ) ) ) ) )).
fof(t8_measure6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xxreal_0(B) => ( ? [C] : ( v1_xxreal_0(C) & r1_xxreal_0(B,C) & A = k2_rcomp_1(B,C) ) => B = k7_supinf_2(A) ) ) ) )).
fof(t8_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r2_hidden(C,B) => m3_measure8(k13_funct_7(k1_zfmisc_1(A),C,k1_subset_1(A),k1_subset_1(A)),A,C,B) ) ) ) )).
fof(t8_member_1,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => k4_member_1(k5_xboole_0(A,B)) = k5_xboole_0(k4_member_1(A),k4_member_1(B)) ) ) )).
fof(t8_membered,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_membered(A) ) => ? [B] : ( v1_xxreal_0(B) & r2_hidden(B,A) ) ) )).
fof(t8_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_partfun1(C,u1_struct_0(B)) ) => r1_tarski(k8_struct_0(B),k9_xtuple_0(C)) ) ) ) )).
fof(t8_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( k4_euclid_3(A,B,C) = k5_numbers & r1_zfmisc_1(A,B,C) & k4_euclid_3(B,C,A) != k28_sin_cos & k4_euclid_3(B,A,C) != k28_sin_cos ) ) ) ) )).
fof(t8_mesfun10,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( m1_subset_1(B,k6_numbers) => ( r2_hidden(B,k1_numbers) => k8_supinf_2(k5_supinf_2(k6_domain_1(k6_numbers,B),A)) = k3_supinf_2(k8_supinf_2(k6_domain_1(k6_numbers,B)),k8_supinf_2(A)) ) ) ) )).
fof(t8_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => r2_relset_1(A,k2_numbers,B,k2_valued_1(A,k1_numbers,k2_numbers,k5_comseq_3(A,B),k25_valued_1(A,k1_numbers,k6_comseq_3(A,B),k7_complex1))) ) ) )).
fof(t8_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( v7_ordinal1(C) => r2_funct_2(k4_ordinal1,k4_partfun1(A,k6_numbers),k8_nat_1(k4_partfun1(A,k6_numbers),k1_mesfun7c(A,B),C),k1_mesfun7c(A,k8_nat_1(k4_partfun1(A,k1_numbers),B,C))) ) ) ) )).
fof(t8_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( r2_hidden(E,k1_relset_1(A,k4_mesfunc5(A,k1_numbers,k2_mesfun9c(A,B),C))) & r1_xxreal_0(D,C) ) => ( r2_hidden(E,k1_relset_1(A,k4_mesfunc5(A,k1_numbers,k2_mesfun9c(A,B),D))) & r2_hidden(E,k1_relset_1(A,k4_mesfunc5(A,k1_numbers,B,D))) ) ) ) ) ) ) )).
fof(t8_mesfunc1,axiom,( ! [A] : ( v1_xreal_0(A) => ? [B] : ( m1_subset_1(B,k4_ordinal1) & r1_xxreal_0(A,B) ) ) )).
fof(t8_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => r2_relset_1(A,k6_numbers,k4_mesfunc1(A,B,C),k3_mesfunc1(A,B,k7_mesfunc1(A,C))) ) ) ) )).
fof(t8_mesfunc3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_prob_2(D) & m2_finseq_1(D,B) ) => k4_finseq_1(D) = k4_finseq_1(k4_finseqop(B,k6_numbers,D,C)) ) ) ) ) )).
fof(t8_mesfunc5,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( v2_mesfunc5(B) <=> ! [C] : r1_xxreal_0(k1_funct_1(B,C),k1_supinf_2) ) ) )).
fof(t8_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,C))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( v1_xreal_0(F) => ( ! [G] : ( v7_ordinal1(G) => k1_funct_1(D,G) = k3_xboole_0(B,k13_mesfunc1(E,k6_xcmplx_0(F,k2_extreal1(1,k1_nat_1(G,1))))) ) => k3_xboole_0(B,k14_mesfunc1(E,F)) = k6_setfam_1(A,k4_measure1(A,C,D)) ) ) ) ) ) ) )).
fof(t8_mesfunc7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v2_valued_0(A) ) => ! [B] : ( m1_subset_1(B,k6_numbers) => k2_mesfunc7(k7_finseq_1(A,k12_finseq_1(k6_numbers,B))) = k1_extreal1(k2_mesfunc7(A),B) ) ) )).
fof(t8_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & v1_mesfunc8(B,A,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => r2_relset_1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,k3_mesfunc8(A,B),C),k1_mesfunc8(A,k8_nat_1(k4_partfun1(A,k6_numbers),B,C))) ) ) ) )).
fof(t8_mesfunc9,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ~ ( v6_supinf_2(A) & v9_mesfunc5(A) ) ) )).
fof(t8_metric_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => ( k5_binop_1(k1_numbers,k6_metric_1,A,B) = k5_numbers <=> A = B ) ) ) )).
fof(t8_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k1_metric_2(A,B) = k1_metric_2(A,C) <=> r3_metric_2(A,B,C) ) ) ) ) )).
fof(t8_metric_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(E,k4_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),u1_struct_0(D))) => ! [F] : ( m1_subset_1(F,k4_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),u1_struct_0(D))) => k2_binop_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,k7_metric_3(A,B,C,D),E,F) = k2_binop_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,k7_metric_3(A,B,C,D),F,E) ) ) ) ) ) ) )).
fof(t8_metric_6,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_metric_6(B,A) <=> ? [C] : ( v1_xreal_0(C) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ~ r1_xxreal_0(C,k5_numbers) & ! [E] : ( v7_ordinal1(E) => r2_hidden(k2_tbsp_1(A,B,E),k8_metric_1(A,D,C)) ) ) ) ) ) ) )).
fof(t8_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( v1_cantor_1(C,A) & v1_tops_2(C,A) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) => ( v1_cantor_1(k1_tops_2(A,B,C),k1_pre_topc(A,B)) & v1_tops_2(k1_tops_2(A,B,C),k1_pre_topc(A,B)) & m1_subset_1(k1_tops_2(A,B,C),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(k1_pre_topc(A,B))))) ) ) ) ) )).
fof(t8_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => r2_borsuk_3(k2_mfold_1(A),k15_euclid(A)) ) )).
fof(t8_mfold_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(C))) => ( ( r1_metrizts(A,B,D,E) & r1_metrizts(B,C,E,F) ) => r1_metrizts(A,C,D,F) ) ) ) ) ) ) ) )).
fof(t8_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k3_midsp_1(A,C,B) = k3_midsp_1(A,D,B) => C = D ) ) ) ) ) )).
fof(t8_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ v2_struct_0(D) & v13_algstr_0(D) & v3_rlvect_1(D) & v4_rlvect_1(D) & l2_algstr_0(D) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(D)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(D)))) ) => ( ( r1_midsp_2(u1_struct_0(A),D,E) & v1_midsp_2(E,A,D) ) => k1_midsp_1(A,B,C) = k1_midsp_1(A,C,B) ) ) ) ) ) ) )).
fof(t8_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r1_xxreal_0(B,A) => m1_midsp_3(k1_nat_1(B,1),A) ) ) ) )).
fof(t8_mmlquer2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v6_relat_2(B) & v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ~ ( C != D & ~ r1_mmlquery(C,D,B) & ~ r1_mmlquery(D,C,B) ) ) ) ) ) )).
fof(t8_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ! [E] : ( v7_ordinal1(E) => ( r1_tarski(B,C) => r1_tarski(k14_mmlquery(A,B,D,E),k4_mmlquery(A,D,C)) ) ) ) ) ) )).
fof(t8_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ 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] : ( ( v2_mod_2(D,A) & m1_mod_2(D,A,B,C) ) => ? [E] : ( 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) ) ) ) ) ) )).
fof(t8_mod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( ( 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_mod_3(A,B,C) = D ) ) ) ) ) ) )).
fof(t8_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => r8_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)),u1_vectsp_2(k2_mod_4(A),k3_mod_4(A,B)),k4_mod_4(A,B,u1_vectsp_1(A,B))) ) ) )).
fof(t8_modal_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( r2_hidden(C,A) => ! [D] : ( m1_trees_1(D,k5_trees_1(A,C,B)) => ! [E] : ( 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) ) ) ) ) ) ) ) )).
fof(t8_modcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_modcat_1(B,A) => ! [C] : ( m4_modcat_1(C,A,k4_modcat_1(A,B)) => ! [D] : ( m4_modcat_1(D,A,k4_modcat_1(A,B)) => ~ ( k5_modcat_1(A,B,C) = k6_modcat_1(A,B,D) & ! [E] : ( ( v7_vectsp_1(E,A) & m2_modcat_1(E,A,B) ) => ! [F] : ( ( v7_vectsp_1(F,A) & m2_modcat_1(F,A,B) ) => ! [G] : ( ( v7_vectsp_1(G,A) & m2_modcat_1(G,A,B) ) => ~ ( m1_mod_2(C,A,F,G) & m1_mod_2(D,A,E,F) ) ) ) ) ) ) ) ) ) )).
fof(t8_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_modelc_1(B) & l2_modelc_1(B) ) => ! [C] : ( ( 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,k10_modelc_1(A)) = k26_modelc_1(B,k24_modelc_1(B,C,A)) ) ) ) )).
fof(t8_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v7_modelc_2(A) => A = k7_modelc_2(k11_modelc_2(A),k12_modelc_2(A)) ) ) )).
fof(t8_moebius1,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) ) => k22_pre_poly(k8_newton,k13_nat_3(A)) = k1_tarski(A) ) )).
fof(t8_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v11_monoid_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & k6_algstr_0(A,D,B) = C ) ) ) ) ) )).
fof(t8_monoid_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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))) ) => ( v2_binop_1(C,B) => v2_binop_1(k8_monoid_1(B,B,B,C,A),k9_funct_2(A,B)) ) ) ) )).
fof(t8_morph_01,axiom,( ! [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) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => k1_morph_01(A,B,C) = a_3_4_morph_01(A,B,C) ) ) ) )).
fof(t8_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [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)) => m1_trees_4(D,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k4_dtconstr(k5_msafree(A,B))) ) ) ) ) )).
fof(t8_msafree3,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v1_instalg1(A) & l1_msualg_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(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(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_numbers))))),k5_trees_3(u1_struct_0(k5_msafree(A,k2_pboole(u1_struct_0(A),B,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_numbers)))))),k1_msaterm(A,k2_pboole(u1_struct_0(A),B,k8_funcop_1(k1_zfmisc_1(k4_ordinal1),u1_struct_0(A),k6_domain_1(k4_ordinal1,k5_numbers))))) ) ) ) )).
fof(t8_msafree4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ( r2_hidden(B,A) => r1_tarski(k3_trees_9(B),k9_trees_9(A)) ) ) ) )).
fof(t8_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( l3_msualg_1(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,k1_funct_1(B,D)) => m1_dtconstr(k1_trees_4(k4_tarski(E,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))) ) ) ) ) ) )).
fof(t8_msscyc_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v2_struct_0(C) & ~ v11_struct_0(C) & l1_graph_1(C) ) => ! [D] : ( ( v7_graph_1(D,C) & m1_graph_1(D,C) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,B) & r1_xxreal_0(B,k3_finseq_1(D)) ) => ( v7_graph_1(k1_graph_2(D,A,B),C) & m1_graph_1(k1_graph_2(D,A,B),C) ) ) ) ) ) ) )).
fof(t8_mssubfam,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) => ( D = k4_subset_1(k1_zfmisc_1(A),B,C) => k8_setfam_1(A,D) = k9_subset_1(A,k8_setfam_1(A,B),k8_setfam_1(A,C)) ) ) ) ) )).
fof(t8_mssublat,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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] : ( 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)) => ! [D] : ( m1_subset_1(D,u4_struct_0(k6_msualg_1(B))) => ! [E] : ( m1_subset_1(E,u4_struct_0(k6_msualg_1(A))) => ( E = D => k5_msualg_1(k6_msualg_1(A),E,k9_msualg_1(A)) = k2_partfun1(k3_msualg_1(k6_msualg_1(B),D,k9_msualg_1(B)),k4_msualg_1(k6_msualg_1(B),D,k9_msualg_1(B)),k5_msualg_1(k6_msualg_1(B),D,k9_msualg_1(B)),k3_msualg_1(k6_msualg_1(A),E,k9_msualg_1(A))) ) ) ) ) ) ) ) ) )).
fof(t8_msualg_1,axiom,( ! [A] : ( ( ~ v11_struct_0(A) & v13_struct_0(A,1) & v5_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => m2_finseq_1(u4_msualg_1(A,B),k4_partfun1(k3_finseq_2(k10_msualg_1(A,B)),k10_msualg_1(A,B))) ) ) )).
fof(t8_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_msualg_2(C,A,B) => ! [D] : ( m1_msualg_2(D,A,B) => ( r2_pboole(u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D)) => m1_msualg_2(C,A,D) ) ) ) ) ) )).
fof(t8_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( ( v4_msualg_1(C,A) & l3_msualg_1(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,A) & l3_msualg_1(E,A) ) => ! [F] : ( m2_pboole(F,u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D)) => ! [G] : ( m2_pboole(G,u1_struct_0(A),u3_msualg_1(A,D),u3_msualg_1(A,E)) => ! [H] : ( m1_subset_1(H,k3_msualg_1(A,B,C)) => k5_msualg_3(A,C,E,B,k3_msualg_3(u1_struct_0(A),u3_msualg_1(A,C),u3_msualg_1(A,D),u3_msualg_1(A,E),F,G),H) = k5_msualg_3(A,D,E,B,G,k5_msualg_3(A,C,D,B,F,H)) ) ) ) ) ) ) ) ) )).
fof(t8_msualg_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_msualg_4(C,A,B) & m1_msualg_4(C,A,B,B) ) => ! [D] : ( ( v1_msualg_4(D,A,B) & m1_msualg_4(D,A,B,B) ) => ! [E] : ( ( v1_msualg_4(E,A,B) & m1_msualg_4(E,A,B,B) ) => r8_pboole(A,k4_msualg_5(A,B,k4_msualg_5(A,B,C,D),E),k4_msualg_5(A,B,C,k4_msualg_5(A,B,D,E))) ) ) ) ) ) )).
fof(t8_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( l3_msualg_1(C,A) => ! [D] : ( m2_pboole(D,u1_struct_0(A),u3_msualg_1(A,B),u3_msualg_1(A,C)) => ! [E] : ( m1_subset_1(E,u4_struct_0(A)) => ~ ( k3_msualg_1(A,E,B) != k1_xboole_0 & k3_msualg_1(A,E,C) != k1_xboole_0 & ? [F] : ( m1_subset_1(F,k4_ordinal1) & r2_hidden(F,k4_finseq_1(k1_msualg_1(A,E))) & ~ ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,B),k7_partfun1(u1_struct_0(A),k1_msualg_1(A,E),F))) => r2_hidden(k1_funct_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)),G),k1_funct_1(u3_msualg_1(A,C),k7_partfun1(u1_struct_0(A),k1_msualg_1(A,E),F))) ) ) ) ) ) ) ) ) )).
fof(t8_msualg_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_msualg_5(A,B)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_closure2(A,k6_pboole(A,B,B)))) => ( D = C => ( v1_xboole_0(C) | ( v1_msualg_4(k4_mssubfam(A,k6_pboole(A,B,B),k5_closure2(A,k6_pboole(A,B,B),D)),A,B) & m1_msualg_4(k4_mssubfam(A,k6_pboole(A,B,B),k5_closure2(A,k6_pboole(A,B,B),D)),A,B,B) ) ) ) ) ) ) ) )).
fof(t8_msualg_8,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_msualg_5(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( C = k3_tarski(B) => k15_lattice3(k2_msualg_5(A),B) = k1_msualg_5(A,C) ) ) ) )).
fof(t8_msualg_9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,k1_pzfmisc1(A,C)) => ! [E] : ( m2_pboole(E,A,B,k1_pzfmisc1(A,C)) => r6_pboole(A,D,E) ) ) ) ) )).
fof(t8_msuhom_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ! [E] : ( m2_pboole(E,A,C,D) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,B) & v1_funct_1(F) & v1_partfun1(F,B) ) => ! [G] : ( ( v1_relat_1(G) & v4_relat_1(G,B) & v1_funct_1(G) & v1_partfun1(G,B) ) => ( ( r6_pboole(B,F,k5_relat_1(C,B)) & r6_pboole(B,G,k5_relat_1(D,B)) ) => m2_pboole(k5_relat_1(E,B),B,F,G) ) ) ) ) ) ) ) )).
fof(t8_mycielsk,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_eqrel_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => r1_xxreal_0(k5_card_1(k1_mycielsk(A,B,C)),k5_card_1(B)) ) ) )).
fof(t8_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_nagata_1(B,A) <=> ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( v3_pre_topc(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & r2_hidden(C,D) & v1_zfmisc_1(k6_subset_1(k3_setfam_1(k6_domain_1(k1_zfmisc_1(u1_struct_0(A)),D),B),k1_tarski(k1_xboole_0))) ) ) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_hidden(C,B) & r2_hidden(D,B) & C != D & ~ r1_xboole_0(C,D) ) ) ) ) ) ) ) )).
fof(t8_nagata_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => v1_pscomp_1(k2_nagata_2(u1_struct_0(A),B,C),A) ) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => v1_pscomp_1(k3_nagata_2(u1_struct_0(A),B,C),A) ) ) ) ) )).
fof(t8_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(A,k1_nat_1(B,1)) & ~ r1_xxreal_0(A,B) & A != k1_nat_1(B,1) ) ) ) )).
fof(t8_nat_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(B,A) => k7_nat_d(B,A) = k5_numbers ) ) ) )).
fof(t8_nat_4,axiom,( ! [A] : ( v7_ordinal1(A) => ~ ( ? [B] : ( m1_subset_1(B,k4_ordinal1) & r1_nat_d(B,A) & ~ r1_xxreal_0(B,1) & ~ r1_xxreal_0(A,B) ) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => ~ ( r1_nat_d(B,A) & ~ r1_xxreal_0(B,1) & r1_xxreal_0(k2_nat_1(B,B),A) ) ) ) ) )).
fof(t8_nat_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( r2_hidden(C,k10_xtuple_0(B)) => ( r2_hidden(C,k10_xtuple_0(k2_finseq_3(A,B))) | C = k1_funct_1(B,A) ) ) ) ) )).
fof(t8_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_nat_d(B,C) & r1_nat_d(B,A) ) => r1_nat_d(B,k2_xcmplx_0(C,A)) ) ) ) ) )).
fof(t8_nat_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_nat_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_nat_lat)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_nat_lat)) => ( k1_binop_1(k2_nat_lat,A,k1_binop_1(k2_nat_lat,B,C)) = k1_binop_1(k2_nat_lat,k1_binop_1(k2_nat_lat,B,A),C) & k1_binop_1(k2_nat_lat,A,k1_binop_1(k2_nat_lat,B,C)) = k1_binop_1(k2_nat_lat,k1_binop_1(k2_nat_lat,A,C),B) & k1_binop_1(k2_nat_lat,A,k1_binop_1(k2_nat_lat,B,C)) = k1_binop_1(k2_nat_lat,k1_binop_1(k2_nat_lat,C,B),A) & k1_binop_1(k2_nat_lat,A,k1_binop_1(k2_nat_lat,B,C)) = k1_binop_1(k2_nat_lat,k1_binop_1(k2_nat_lat,C,A),B) ) ) ) ) )).
fof(t8_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m2_cat_1(D,A,B) => ( ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( k2_cat_1(A,E,F) != k1_xboole_0 => ! [G] : ( 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) ) ) ) ) ) )).
fof(t8_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( 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] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( r2_hidden(G,k1_relset_1(u1_struct_0(A),C)) & ~ r1_xxreal_0(F,k2_normsp_0(A,k5_algstr_0(A,G,D))) & r1_xxreal_0(E,k2_normsp_0(B,k5_algstr_0(B,k7_partfun1(u1_struct_0(B),C,G),k7_partfun1(u1_struct_0(B),C,D)))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_ncfcont2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(D),u1_struct_0(C)))) ) => ! [F] : ( ( 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,k2_vfunct_1(u1_struct_0(D),C,E,F)) ) ) ) ) ) )).
fof(t8_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k1_ndiff_1(A,B,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,C,D)),k2_normsp_1(A,k1_ndiff_1(A,B,C),k1_ndiff_1(A,B,D))) ) ) ) ) )).
fof(t8_ndiff_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v2_ndiff_1(D,B,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)))) ) => ( k7_partfun1(u1_struct_0(C),D,k4_struct_0(B)) = k4_struct_0(C) => ! [E] : ( ( 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) & v2_lopban_1(E,A,B) & m1_subset_1(E,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),E,D)) & v2_ndiff_1(k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),E,D),A,C) & m1_subset_1(k1_partfun1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(B),u1_struct_0(C),E,D),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(C)))) ) ) ) ) ) ) ) )).
fof(t8_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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)))) ) => ( v1_funct_1(k4_vfunct_1(k1_numbers,A,C,B)) & v1_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)))) ) ) ) ) )).
fof(t8_ndiff_4,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(k4_real_ns1(A))))) ) => ! [E] : ( m1_rcomp_1(E,B) => ( ( C = D & r1_ndiff_4(A,C,B) & r1_tarski(E,k1_relset_1(k1_numbers,C)) ) => ! [F] : ( ( v9_ordinal1(F) & v1_funct_1(F) & v1_funct_2(F,k4_ordinal1,k1_numbers) & v1_fdiff_1(F,k5_numbers) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [G] : ( ( v1_funct_1(G) & v3_funct_1(G) & v1_funct_2(G,k4_ordinal1,k1_numbers) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k1_rvsum_1(G) = k1_tarski(B) & r1_tarski(k1_rvsum_1(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,F,G)),E) ) => ( v3_normsp_1(k1_ndiff_1(k4_real_ns1(A),k3_normsp_1(k4_real_ns1(A),k8_funct_2(k4_ordinal1,u1_struct_0(k4_real_ns1(A)),k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,F,G),D),k8_funct_2(k4_ordinal1,u1_struct_0(k4_real_ns1(A)),k1_numbers,G,D)),k37_valued_1(k4_ordinal1,k1_numbers,F)),k4_real_ns1(A)) & k1_ndiff_4(A,C,B) = k6_normsp_1(k4_real_ns1(A),k1_ndiff_1(k4_real_ns1(A),k3_normsp_1(k4_real_ns1(A),k8_funct_2(k4_ordinal1,u1_struct_0(k4_real_ns1(A)),k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,F,G),D),k8_funct_2(k4_ordinal1,u1_struct_0(k4_real_ns1(A)),k1_numbers,G,D)),k37_valued_1(k4_ordinal1,k1_numbers,F))) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_ndiff_5,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_nfcont_1(C,A,B) => ! [D] : ( m1_nfcont_1(D,A,B) => m1_nfcont_1(k9_subset_1(u1_struct_0(A),C,D),A,B) ) ) ) ) )).
fof(t8_neckla_3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ( k1_neckla_2(A,B) = k1_neckla_2(B,A) & k2_neckla_2(A,B) = k2_neckla_2(B,A) ) ) ) )).
fof(t8_necklace,axiom,( ! [A] : ! [B] : k2_funct_1(k16_funcop_1(A,B)) = k16_funcop_1(B,A) )).
fof(t8_net_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_net_1(C) & l1_petri(C) ) => ( ( r2_hidden(k4_tarski(A,B),k1_net_1(C)) & r2_hidden(B,u1_struct_0(C)) ) => r2_hidden(A,u4_struct_0(C)) ) ) )).
fof(t8_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xcmplx_0(C) => k1_newton(C,k2_xcmplx_0(A,B)) = k3_xcmplx_0(k1_newton(C,A),k1_newton(C,B)) ) ) ) )).
fof(t8_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_numbers))) ) => ( r2_nfcont_1(A,C,B) <=> ( r2_hidden(B,k1_relset_1(u1_struct_0(A),C)) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_hidden(F,k1_relset_1(u1_struct_0(A),C)) & ~ r1_xxreal_0(E,k2_normsp_0(A,k5_algstr_0(A,F,B))) & r1_xxreal_0(D,k9_complex1(k5_real_1(k7_partfun1(k1_numbers,C,F),k7_partfun1(k1_numbers,C,B)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_nfcont_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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) => r4_nfcont_1(B,C,A) ) ) ) )).
fof(t8_nfcont_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ( r1_nfcont_3(B,C,A) <=> ( r2_hidden(A,k1_relset_1(k1_numbers,C)) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ~ ( r2_hidden(F,k1_relset_1(k1_numbers,C)) & ~ r1_xxreal_0(E,k9_complex1(k6_xcmplx_0(F,A))) & r1_xxreal_0(D,k2_normsp_0(B,k5_algstr_0(B,k7_partfun1(u1_struct_0(B),C,F),k7_partfun1(u1_struct_0(B),C,A)))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,u1_struct_0(k4_real_ns1(A))))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k1_euclid(A)))) ) => ( C = D => k5_vfunct_1(B,k4_real_ns1(A),C) = k2_nfcont_4(A,B,D) ) ) ) ) ) )).
fof(t8_normform,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_finsub_1(B) ) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(A,B)) => ! [E] : ( m1_subset_1(E,k2_zfmisc_1(A,B)) => k1_normform(A,B,C,k2_normform(A,B,D,E)) = k2_normform(A,B,k1_normform(A,B,C,D),k1_normform(A,B,C,E)) ) ) ) ) ) )).
fof(t8_normsp_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k6_xcmplx_0(k2_normsp_0(A,B),k2_normsp_0(A,C)),k2_normsp_0(A,k5_algstr_0(A,B,C))) ) ) ) )).
fof(t8_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ( v3_pre_topc(a_3_2_normsp_2(A,B,C),k3_normsp_2(A)) & m1_subset_1(a_3_2_normsp_2(A,B,C),k1_zfmisc_1(u1_struct_0(k3_normsp_2(A)))) ) ) ) ) )).
fof(t8_ntalgo_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => ! [B] : ( m1_subset_1(B,k4_numbers) => ( B != k5_numbers => r2_int_1(k5_int_1(A,B),A,B) ) ) ) )).
fof(t8_numbers,axiom,( r2_xboole_0(k4_ordinal1,k3_numbers) )).
fof(t8_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( ( v7_o_ring_1(B,A) & v1_o_ring_1(C,A) ) | ( v7_o_ring_1(B,A) & v5_o_ring_1(C,A) ) ) => v7_o_ring_1(k1_algstr_0(A,B,C),A) ) ) ) ) )).
fof(t8_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v13_lattices(k6_openlatt(A)) & k5_lattices(k6_openlatt(A)) = k1_xboole_0 ) ) )).
fof(t8_oposet_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( ( v1_necklace(A) & v4_orders_2(A) ) => v2_oposet_1(A) ) ) )).
fof(t8_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k2_oppcat_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k2_oppcat_1(A))) => ! [D] : ( m1_cat_1(D,k2_oppcat_1(A),B,C) => k5_oppcat_1(A,k6_oppcat_1(A,D)) = D ) ) ) ) )).
fof(t8_ordeq_01,axiom,( ! [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) & v3_lopban_1(A) & l1_normsp_1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k4_ordinal1) & v1_nfcont_2(k1_abian(u1_struct_0(A),B,C),A) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( k3_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) = C & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k3_funct_2(u1_struct_0(A),u1_struct_0(A),B,D) = D => C = D ) ) ) ) ) ) ) )).
fof(t8_orders_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( ( r1_relat_2(C,A) & r1_tarski(B,A) ) => r1_relat_2(C,B) ) ) )).
fof(t8_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v6_orders_2(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))) ) ) ) )).
fof(t8_orders_3,axiom,( ! [A] : ( l1_struct_0(A) => k2_orders_3(k1_tarski(A)) = k1_tarski(u1_struct_0(A)) ) )).
fof(t8_ordinal1,axiom,( ! [A] : ( v1_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( ( r1_tarski(A,B) & r2_hidden(B,C) ) => r2_hidden(A,C) ) ) ) ) )).
fof(t8_ordinal2,axiom,( ! [A] : ( v3_ordinal1(A) => k2_ordinal1(A) = A ) )).
fof(t8_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => ( A != k1_xboole_0 => r2_hidden(k1_xboole_0,A) ) ) )).
fof(t8_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ( ( v4_ordinal1(k9_xtuple_0(A)) & v2_ordinal2(A) ) => ( k9_xtuple_0(A) = k1_xboole_0 | ( r1_ordinal2(k4_ordinal2(A),A) & k8_ordinal2(A) = k4_ordinal2(A) ) ) ) ) )).
fof(t8_ordinal5,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_ordinal2(B) ) => ( ( r2_hidden(k5_numbers,A) & ! [C] : ( v3_ordinal1(C) => ( r2_hidden(C,k9_xtuple_0(B)) => k1_funct_1(B,C) = k12_ordinal2(A,C) ) ) ) => v2_ordinal5(B) ) ) ) )).
fof(t8_ordinal6,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(k4_tarski(B,C),k1_wellord2(A)) => r1_tarski(B,C) ) )).
fof(t8_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_orders_2(B,k5_algstr_0(B,E,k4_vectsp_1(A,B,F,D)),C) & r1_orders_2(B,k5_algstr_0(B,E,k4_vectsp_1(A,B,G,D)),C) ) => ( r1_orders_2(B,D,C) | F = G ) ) ) ) ) ) ) ) ) )).
fof(t8_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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(k5_osafree(A,B))) = k4_dtconstr(k2_osafree(A,B)) ) ) )).
fof(t8_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u4_struct_0(A)) => ( ( v1_orders_3(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)) ) => B = C ) ) ) ) )).
fof(t8_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [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] : ( ( 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) ) => ( r2_pboole(u1_struct_0(A),B,C) => r2_pboole(u1_struct_0(A),k2_osalg_2(A,B),C) ) ) ) ) )).
fof(t8_osalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => r1_osalg_3(A,B,B) ) ) )).
fof(t8_osalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_orders_3(A) & l1_orders_2(A) ) => v2_osalg_4(A) ) )).
fof(t8_papdesaf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( r2_analoaf(A,B,C,B,E) & r3_diraf(A,B,D,F) & r2_diraf(A,C,D,E,F) ) => ( r3_diraf(A,B,C,D) | ( r2_analoaf(A,B,D,B,F) & r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) ) ) ) )).
fof(t8_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A))) => ! [E] : ( 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),k8_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)) & ? [F] : ( m1_subset_1(F,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) & ? [G] : ( m1_subset_1(G,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) & ? [H] : ( m1_subset_1(H,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) & ? [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_parsp_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_parsp_1(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k9_parsp_1(A))) => ! [G] : ( m1_subset_1(G,u1_struct_0(k9_parsp_1(A))) => ( ( r1_parsp_1(k9_parsp_1(A),B,E,C,F) & r1_parsp_1(k9_parsp_1(A),B,E,D,G) & r1_parsp_1(k9_parsp_1(A),B,C,E,F) & r1_parsp_1(k9_parsp_1(A),B,D,E,G) ) => ( r1_parsp_1(k9_parsp_1(A),B,E,B,C) | r1_parsp_1(k9_parsp_1(A),B,E,B,D) | r1_parsp_1(k9_parsp_1(A),C,D,F,G) ) ) ) ) ) ) ) ) ) )).
fof(t8_partfun1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ( ( r2_hidden(D,k1_relset_1(A,C)) & r2_hidden(E,k1_relset_1(A,C)) & k1_funct_1(C,D) = k1_funct_1(C,E) ) => D = E ) ) ) => v2_funct_1(C) ) ) )).
fof(t8_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => ( r2_hidden(C,k1_relset_1(A,k1_partfun1(A,A,A,A,D,k1_partfun2(A,B)))) <=> ( r2_hidden(C,k1_relset_1(A,D)) & r2_hidden(k7_partfun1(A,D,C),B) ) ) ) ) ) ) )).
fof(t8_partit_2,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( r1_relat_2(A,B) => r1_tarski(B,k1_relat_1(A)) ) ) )).
fof(t8_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t8_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( r1_pboole(A,B,k3_pboole(A,C,D)) <=> ( r1_pboole(A,B,C) & r1_pboole(A,B,D) ) ) ) ) ) )).
fof(t8_pcomps_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(a_3_1_pcomps_1(A,B,C),B) ) ) ) )).
fof(t8_pcs_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( r1_relset_1(u1_struct_0(A),u1_struct_0(A),u1_orders_2(A),u1_orders_2(B)) & C = E & D = F & r1_orders_2(A,C,D) ) => r1_orders_2(B,E,F) ) ) ) ) ) ) ) )).
fof(t8_pdiff_1,axiom,( ! [A] : ( ( 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] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(1))) => ! [D] : ( v1_xreal_0(D) => ( ( A = k2_pdiff_1(B) & C = k9_finseq_1(D) & r1_fdiff_1(B,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(k4_ordinal1,1)) = k9_finseq_1(k1_fdiff_1(B,D)) ) ) ) ) ) ) )).
fof(t8_pdiff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(2)) => ! [D] : ( ( 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) & ! [E] : ( m1_rcomp_1(E,B) => ~ ( r1_tarski(E,k1_relset_1(k1_numbers,k1_pdiff_2(2,2,D,C))) & ? [F] : ( v1_funct_1(F) & v3_fdiff_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [G] : ( v1_funct_1(G) & v2_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,E) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(2,2,D,C),H),k1_funct_1(k1_pdiff_2(2,2,D,C),B)) = k2_xcmplx_0(k1_funct_1(F,k6_xcmplx_0(H,B)),k1_funct_1(G,k6_xcmplx_0(H,B))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_pdiff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(2)) => ! [D] : ( ( 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) ) => k5_pdiff_3(D,C) = k1_fdiff_1(k1_pdiff_2(2,2,k1_pdiff_3(2,2,D),C),B) ) ) ) ) ) )).
fof(t8_pdiff_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & B = k11_finseq_1(C,D,E) & r1_fdiff_1(k1_pdiff_2(3,2,A,B),D) ) ) ) <=> r3_pdiff_1(3,2,A,B) ) ) ) )).
fof(t8_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) ) => r1_fdiff_1(k1_pdiff_2(3,2,k1_pdiff_3(3,3,E),D),B) ) ) ) ) ) ) )).
fof(t8_pdiff_6,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( 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)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k1_euclid(B),k1_euclid(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(B),k1_euclid(A)))) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(k16_lopban_1(k4_real_ns1(B),k4_real_ns1(A)))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k16_lopban_1(k4_real_ns1(B),k4_real_ns1(A)))) => ( ( C = E & D = F ) => k8_integr15(A,k1_euclid(B),C,D) = k5_algstr_0(k16_lopban_1(k4_real_ns1(B),k4_real_ns1(A)),E,F) ) ) ) ) ) ) ) )).
fof(t8_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k4_real_ns1(A)))) => ( ( v3_nfcont_1(E,k4_real_ns1(A)) & r1_xxreal_0(1,C) & r1_xxreal_0(C,A) ) => ( r7_pdiff_1(A,B,C,D,E) <=> ( r1_tarski(E,k1_relset_1(u1_struct_0(k4_real_ns1(A)),D)) & ! [F] : ( m1_subset_1(F,u1_struct_0(k4_real_ns1(A))) => ( r2_hidden(F,E) => r2_pdiff_1(B,A,C,D,F) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_pdiff_8,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => v1_lopban_1(k4_pdiff_1(B,A),k4_real_ns1(A),k4_real_ns1(1)) ) ) )).
fof(t8_pdiff_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => r2_relset_1(k1_euclid(A),k1_euclid(1),k3_pdiff_1(A,k26_valued_1(k1_euclid(A),k1_numbers,B,C)),k9_integr15(1,C,k1_euclid(A),k3_pdiff_1(A,B))) ) ) ) )).
fof(t8_pencil_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_pencil_2(C,A,B) => ! [D] : ( m1_pencil_2(D,A,B) => ( r1_tarski(2,k1_card_1(k9_subset_1(u1_struct_0(k5_pencil_1(A,B)),C,D))) => C = D ) ) ) ) ) )).
fof(t8_pencil_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v11_pencil_1(C) & v14_pencil_1(C) ) => ? [D] : ( ~ v13_pencil_1(D) & v16_pencil_1(D,A) & m3_pboole(D,A,k12_pralg_1(A,C)) & k3_pencil_1(A,D) = B & m1_pencil_2(k4_card_3(D),A,C) ) ) ) ) )).
fof(t8_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( v7_ordinal1(C) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m1_vectsp_4(E,A,B) => ! [F] : ( m1_vectsp_4(F,A,B) => ( r2_hidden(F,k3_pencil_4(A,B,D,E,C)) => ( m1_vectsp_4(D,A,F) & m1_vectsp_4(F,A,E) ) ) ) ) ) ) ) ) )).
fof(t8_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( k4_nat_d(A,B) = C => ( r1_xxreal_0(B,k5_numbers) | r1_int_1(B,k6_xcmplx_0(A,C)) ) ) ) ) ) )).
fof(t8_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u4_struct_0(A))) => ! [C] : ( r2_hidden(C,k9_petri(A,B)) <=> ? [D] : ( m1_petri(D,u4_struct_0(A),u1_struct_0(A),u2_petri(A)) & ? [E] : ( m1_subset_1(E,u4_struct_0(A)) & r2_hidden(E,B) & D = k4_tarski(E,C) ) ) ) ) ) )).
fof(t8_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,k4_ordinal1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ( ( r2_pnproc_1(A,D,B) & r2_pnproc_1(A,B,C) ) => r2_pnproc_1(A,k3_pnproc_1(A,B,D),k3_pnproc_1(A,C,D)) ) ) ) ) )).
fof(t8_polyalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_polynom5(A,D,k6_algstr_0(A,B,C)),k3_polynom5(A,k3_polynom5(A,D,C),B)) ) ) ) ) )).
fof(t8_polyeq_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ( ! [K] : ( v1_xreal_0(K) => k1_polyeq_2(A,B,C,D,E,K) = k1_polyeq_2(F,G,H,I,J,K) ) => ( k6_xcmplx_0(A,F) = k6_xcmplx_0(H,C) & k6_xcmplx_0(B,G) = k6_xcmplx_0(I,D) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_polyeq_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xcmplx_0(D) => ~ ( A != k5_numbers & ~ r1_xxreal_0(k5_numbers,k1_quin_1(A,B,C)) & k4_polyeq_1(k5_numbers,A,B,C,D) = k5_numbers & D != k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,k3_xcmplx_0(2,A))),k3_xcmplx_0(k7_xcmplx_0(k3_square_1(k4_xcmplx_0(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A)),k7_complex1)) & D != k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,k3_xcmplx_0(2,A))),k3_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(k3_square_1(k4_xcmplx_0(k1_quin_1(A,B,C))),k3_xcmplx_0(2,A))),k7_complex1)) ) ) ) ) ) )).
fof(t8_polyeq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( B != k5_numbers & ~ r1_xxreal_0(k5_numbers,k7_xcmplx_0(C,B)) & ~ r1_xxreal_0(k7_xcmplx_0(D,B),k5_numbers) & v1_abian(E) & r1_xxreal_0(1,E) & r1_xxreal_0(k5_numbers,k1_quin_1(B,C,D)) & k2_polyeq_1(B,C,D,k1_newton(A,E)) = k5_numbers & A != k1_power(E,k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B))) & A != k4_xcmplx_0(k1_power(E,k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B)))) & A != k1_power(E,k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B))) & A != k4_xcmplx_0(k1_power(E,k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(C),k3_square_1(k1_quin_1(B,C,D))),k3_xcmplx_0(2,B)))) ) ) ) ) ) ) )).
fof(t8_polyeq_5,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k5_numbers,B) => k1_polyeq_5(A,B) = k1_power(A,B) ) ) ) )).
fof(t8_polyform,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ v1_abian(A) => k1_newton(k4_xcmplx_0(1),A) = k4_xcmplx_0(1) ) ) )).
fof(t8_polynom1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k9_fvsum_1(A,k3_pre_poly(u1_struct_0(A),C),B) = k3_pre_poly(u1_struct_0(A),k6_algstr_0(A,B,C)) ) ) ) )).
fof(t8_polynom2,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( 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] : ( ( 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] : ( ( 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)))) ) => k1_polynom2(A,k11_pre_poly(A,C,D),B,E) = k8_group_1(B,k1_polynom2(A,C,B,E),k1_polynom2(A,D,B,E)) ) ) ) ) ) )).
fof(t8_polynom3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k3_finseq_1(k6_polynom3(1,A)) = 1 ) )).
fof(t8_polynom4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => k1_algseq_1(A,k5_vfunct_1(k4_ordinal1,A,B)) = k1_algseq_1(A,B) ) ) )).
fof(t8_polynom5,axiom,( k1_polynom5(k6_finseq_1(u1_struct_0(k1_complfld))) = k6_finseq_1(k1_numbers) )).
fof(t8_polynom6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( ~ 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_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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),k10_polynom1(A,B,k6_polynom1(A,B,C,D),E),k6_polynom1(A,B,k10_polynom1(A,B,C,E),k10_polynom1(A,B,D,E))) ) ) ) ) ) )).
fof(t8_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( ( 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_polynom7(A,B,k1_polynom7(A,B,k4_struct_0(B),C)) = k4_struct_0(B) & k2_polynom7(A,B,k1_polynom7(A,B,k4_struct_0(B),C)) = k16_pre_poly(A) ) ) ) )).
fof(t8_polynom8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_struct_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( ~ r1_xxreal_0(k1_algseq_1(A,B),k5_numbers) & k1_funct_1(B,k6_xcmplx_0(k1_algseq_1(A,B),1)) = k4_struct_0(A) ) ) ) )).
fof(t8_polyred,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v5_algstr_0(B) & v2_vectsp_1(B) & v4_rlvect_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( 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),k5_polynom7(A,B,C,k4_struct_0(B)),k8_polynom1(A,B)) ) ) )).
fof(t8_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( ( ~ v1_xboole_0(D) & v6_orders_2(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => r3_orders_2(B,k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,k1_yellow_0(A,D)),k1_yellow_0(B,k7_relset_1(u1_struct_0(A),u1_struct_0(B),C,D))) ) => v2_poset_1(C,A,B) ) ) ) ) )).
fof(t8_power,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( ~ v1_abian(A) => k1_power(A,k4_xcmplx_0(1)) = k4_xcmplx_0(1) ) ) )).
fof(t8_pralg_1,axiom,( ! [A] : ( v7_ordinal1(A) => k19_margrel1(k7_pralg_1(A)) = A ) )).
fof(t8_pralg_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ! [E] : ( r2_hidden(E,k10_xtuple_0(k2_pralg_2(k12_pralg_2(A,B,C,D)))) => ( v1_relat_1(E) & v1_funct_1(E) ) ) ) ) ) ) )).
fof(t8_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_pralg_2(C,A,B) => ! [D] : ( m1_subset_1(D,u4_struct_0(B)) => ( k1_msualg_1(B,D) = k1_xboole_0 => r2_hidden(k1_pralg_3(B,k14_pralg_2(A,B,C),D),k1_funct_2(A,k3_tarski(a_4_0_pralg_3(A,B,C,D)))) ) ) ) ) ) )).
fof(t8_pre_ff,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(A,B) => ( r1_xxreal_0(C,1) | r1_xxreal_0(k2_power(C,A),k2_power(C,B)) ) ) ) ) ) )).
fof(t8_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( 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] : ( m2_finseq_1(D,A) => ( ( k2_relset_1(A,D) = B & ! [E] : ( v7_ordinal1(E) => ! [F] : ( 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) ) ) ) ) ) ) => D = k7_pre_poly(A,B,C) ) ) ) ) )).
fof(t8_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => u1_struct_0(k1_pre_topc(A,B)) = B ) ) )).
fof(t8_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_prelamb(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_prelamb(C,A) => ! [D] : ( m1_trees_1(D,k9_xtuple_0(C)) => ~ ( k2_xtuple_0(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k4_ordinal1),C,D)) = 5 & ! [E] : ( m1_trees_1(E,k9_xtuple_0(C)) => ! [F] : ( m2_finseq_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m2_finseq_1(I,u1_struct_0(A)) => ~ ( E = k8_finseq_1(k4_ordinal1,D,k12_finseq_1(k4_ordinal1,k5_numbers)) & k1_xtuple_0(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k4_ordinal1),C,D)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),F,k12_finseq_1(u1_struct_0(A),k3_prelamb(A,G,H))),I),B) & k1_xtuple_0(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k4_ordinal1),C,E)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),k8_finseq_1(u1_struct_0(A),F,k12_finseq_1(u1_struct_0(A),G)),k12_finseq_1(u1_struct_0(A),H)),I),B) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => k1_newton(k7_xcmplx_0(B,A),C) = k7_xcmplx_0(k1_newton(B,C),k1_newton(A,C)) ) ) ) )).
fof(t8_prgcor_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( r1_xxreal_0(k5_numbers,A) => ! [C] : ( m2_finseq_1(C,k4_numbers) => ! [D] : ( m2_finseq_1(D,k4_numbers) => ! [E] : ( m2_finseq_1(E,k4_numbers) => ! [F] : ( v1_int_1(F) => ( ( k3_finseq_1(C) = k2_xcmplx_0(A,1) & k3_finseq_1(D) = k2_xcmplx_0(A,1) & k3_finseq_1(E) = k2_xcmplx_0(A,1) ) => ( ( r1_xxreal_0(B,A) & ~ ( k1_funct_1(C,1) = B & r1_xxreal_0(1,F) & r1_xxreal_0(F,A) & ! [G] : ( v1_int_1(G) => ( r1_xxreal_0(1,G) => ( r1_xxreal_0(F,G) | ( k1_funct_1(C,k2_xcmplx_0(G,1)) = k3_xcmplx_0(k1_funct_1(C,G),2) & r1_xxreal_0(k1_funct_1(C,k2_xcmplx_0(G,1)),A) ) ) ) ) & k1_funct_1(C,k2_xcmplx_0(F,1)) = k3_xcmplx_0(k1_funct_1(C,F),2) & ~ r1_xxreal_0(k1_funct_1(C,k2_xcmplx_0(F,1)),A) & k1_funct_1(E,k2_xcmplx_0(F,1)) = k5_numbers & k1_funct_1(D,k2_xcmplx_0(F,1)) = A & ! [G] : ( v1_int_1(G) => ( ( r1_xxreal_0(1,G) & r1_xxreal_0(G,F) ) => ( ( r1_xxreal_0(k1_funct_1(C,k6_xcmplx_0(k2_xcmplx_0(F,1),G)),k1_funct_1(D,k6_xcmplx_0(k2_xcmplx_0(F,1),k6_xcmplx_0(G,1)))) => ( k1_funct_1(D,k6_xcmplx_0(k2_xcmplx_0(F,1),G)) = k6_xcmplx_0(k1_funct_1(D,k6_xcmplx_0(k2_xcmplx_0(F,1),k6_xcmplx_0(G,1))),k1_funct_1(C,k6_xcmplx_0(k2_xcmplx_0(F,1),G))) & k1_funct_1(E,k6_xcmplx_0(k2_xcmplx_0(F,1),G)) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(E,k6_xcmplx_0(k2_xcmplx_0(F,1),k6_xcmplx_0(G,1))),2),1) ) ) & ( ~ r1_xxreal_0(k1_funct_1(C,k6_xcmplx_0(k2_xcmplx_0(F,1),G)),k1_funct_1(D,k6_xcmplx_0(k2_xcmplx_0(F,1),k6_xcmplx_0(G,1)))) => ( k1_funct_1(D,k6_xcmplx_0(k2_xcmplx_0(F,1),G)) = k1_funct_1(D,k6_xcmplx_0(k2_xcmplx_0(F,1),k6_xcmplx_0(G,1))) & k1_funct_1(E,k6_xcmplx_0(k2_xcmplx_0(F,1),G)) = k3_xcmplx_0(k1_funct_1(E,k6_xcmplx_0(k2_xcmplx_0(F,1),k6_xcmplx_0(G,1))),2) ) ) ) ) ) & k1_prgcor_1(A,B) = k1_funct_1(E,1) ) ) | ( k3_finseq_1(C) = k2_xcmplx_0(A,1) & k3_finseq_1(D) = k2_xcmplx_0(A,1) & k3_finseq_1(E) = k2_xcmplx_0(A,1) & ( ~ r1_xxreal_0(B,A) => k1_prgcor_1(A,B) = k5_numbers ) & ( r1_xxreal_0(B,A) => ( r2_hidden(1,k1_relset_1(k4_ordinal1,C)) & k1_funct_1(C,1) = B & r1_xxreal_0(1,F) & r1_xxreal_0(F,A) & ! [G] : ( v1_int_1(G) => ( r1_xxreal_0(1,G) => ( r1_xxreal_0(F,G) | ( r2_hidden(k2_xcmplx_0(G,1),k1_relset_1(k4_ordinal1,C)) & r2_hidden(G,k1_relset_1(k4_ordinal1,C)) & k1_funct_1(C,k2_xcmplx_0(G,1)) = k3_xcmplx_0(k1_funct_1(C,G),2) & r1_xxreal_0(k1_funct_1(C,k2_xcmplx_0(G,1)),A) ) ) ) ) & r2_hidden(k2_xcmplx_0(F,1),k1_relset_1(k4_ordinal1,C)) & r2_hidden(F,k1_relset_1(k4_ordinal1,C)) & k1_funct_1(C,k2_xcmplx_0(F,1)) = k3_xcmplx_0(k1_funct_1(C,F),2) & ~ r1_xxreal_0(k1_funct_1(C,k2_xcmplx_0(F,1)),A) & r2_hidden(k2_xcmplx_0(F,1),k1_relset_1(k4_ordinal1,E)) & k1_funct_1(E,k2_xcmplx_0(F,1)) = k5_numbers & r2_hidden(k2_xcmplx_0(F,1),k1_relset_1(k4_ordinal1,D)) & k1_funct_1(D,k2_xcmplx_0(F,1)) = A & ! [G] : ( v1_int_1(G) => ( ( r1_xxreal_0(1,G) & r1_xxreal_0(G,F) ) => ( r2_hidden(k6_xcmplx_0(k2_xcmplx_0(F,1),k6_xcmplx_0(G,1)),k1_relset_1(k4_ordinal1,D)) & r2_hidden(k6_xcmplx_0(k2_xcmplx_0(F,1),G),k1_relset_1(k4_ordinal1,C)) & ( r1_xxreal_0(k1_funct_1(C,k6_xcmplx_0(k2_xcmplx_0(F,1),G)),k1_funct_1(D,k6_xcmplx_0(k2_xcmplx_0(F,1),k6_xcmplx_0(G,1)))) => ( r2_hidden(k6_xcmplx_0(k2_xcmplx_0(F,1),G),k1_relset_1(k4_ordinal1,D)) & r2_hidden(k6_xcmplx_0(k2_xcmplx_0(F,1),G),k1_relset_1(k4_ordinal1,C)) & k1_funct_1(D,k6_xcmplx_0(k2_xcmplx_0(F,1),G)) = k6_xcmplx_0(k1_funct_1(D,k6_xcmplx_0(k2_xcmplx_0(F,1),k6_xcmplx_0(G,1))),k1_funct_1(C,k6_xcmplx_0(k2_xcmplx_0(F,1),G))) & r2_hidden(k6_xcmplx_0(k2_xcmplx_0(F,1),G),k1_relset_1(k4_ordinal1,E)) & r2_hidden(k6_xcmplx_0(k2_xcmplx_0(F,1),k6_xcmplx_0(G,1)),k1_relset_1(k4_ordinal1,E)) & k1_funct_1(E,k6_xcmplx_0(k2_xcmplx_0(F,1),G)) = k2_xcmplx_0(k3_xcmplx_0(k1_funct_1(E,k6_xcmplx_0(k2_xcmplx_0(F,1),k6_xcmplx_0(G,1))),2),1) ) ) & ( ~ r1_xxreal_0(k1_funct_1(C,k6_xcmplx_0(k2_xcmplx_0(F,1),G)),k1_funct_1(D,k6_xcmplx_0(k2_xcmplx_0(F,1),k6_xcmplx_0(G,1)))) => ( r2_hidden(k6_xcmplx_0(k2_xcmplx_0(F,1),G),k1_relset_1(k4_ordinal1,D)) & r2_hidden(k6_xcmplx_0(k2_xcmplx_0(F,1),k6_xcmplx_0(G,1)),k1_relset_1(k4_ordinal1,D)) & k1_funct_1(D,k6_xcmplx_0(k2_xcmplx_0(F,1),G)) = k1_funct_1(D,k6_xcmplx_0(k2_xcmplx_0(F,1),k6_xcmplx_0(G,1))) & r2_hidden(k6_xcmplx_0(k2_xcmplx_0(F,1),G),k1_relset_1(k4_ordinal1,E)) & r2_hidden(k6_xcmplx_0(k2_xcmplx_0(F,1),k6_xcmplx_0(G,1)),k1_relset_1(k4_ordinal1,E)) & k1_funct_1(E,k6_xcmplx_0(k2_xcmplx_0(F,1),G)) = k3_xcmplx_0(k1_funct_1(E,k6_xcmplx_0(k2_xcmplx_0(F,1),k6_xcmplx_0(G,1))),2) ) ) ) ) ) & r2_hidden(1,k1_relset_1(k4_ordinal1,E)) & k1_prgcor_1(A,B) = k1_funct_1(E,1) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_prgcor_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k1_numbers) & ~ v1_xboole_0(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k1_numbers) & ~ v1_xboole_0(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( v7_ordinal1(C) => ( ( v7_ordinal1(k1_funct_1(B,k5_numbers)) & k1_afinsq_1(A) = C & k1_afinsq_1(B) = C & k1_funct_1(A,k5_numbers) = k1_funct_1(B,k5_numbers) ) => ( r1_xxreal_0(C,k1_funct_1(B,k5_numbers)) | ( ? [D] : ( v1_relat_1(D) & v5_relat_1(D,k1_numbers) & v5_ordinal1(D) & v1_funct_1(D) & v1_finset_1(D) & r4_prgcor_2(A,B,D,C) ) & ! [D] : ( ( v1_relat_1(D) & v5_relat_1(D,k1_numbers) & ~ v1_xboole_0(D) & v5_ordinal1(D) & v1_funct_1(D) & v1_finset_1(D) ) => ( r4_prgcor_2(A,B,D,C) => k12_afinsq_1(k1_numbers,D) = k4_rvsum_1(k12_afinsq_1(k1_numbers,A),k12_afinsq_1(k1_numbers,B)) ) ) ) ) ) ) ) ) )).
fof(t8_prob_1,axiom,( ! [A] : ( ~ v1_xboole_0(k2_tarski(k1_xboole_0,A)) & v2_finsub_1(k2_tarski(k1_xboole_0,A)) & v1_prob_1(k2_tarski(k1_xboole_0,A),A) & m1_subset_1(k2_tarski(k1_xboole_0,A),k1_zfmisc_1(k1_zfmisc_1(A))) ) )).
fof(t8_prob_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v2_prob_1(B) <=> v3_prob_1(k2_prob_1(A,B)) ) ) )).
fof(t8_prob_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => r1_tarski(k1_prob_2(B,k9_setfam_1(B),k1_prob_3(B,C),A),k1_prob_2(B,k9_setfam_1(B),C,A)) ) ) )).
fof(t8_prob_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( m2_prob_1(D,A,B) => ( ! [E] : ( r2_hidden(E,k4_measure1(A,k9_setfam_1(A),C)) => k1_funct_1(D,E) = k5_numbers ) <=> k1_funct_1(D,k5_setfam_1(A,k4_measure1(A,k9_setfam_1(A),C))) = k5_numbers ) ) ) ) ) )).
fof(t8_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => r2_hidden(k8_cqc_lang(A,k9_cqc_lang(A,B,C),k9_cqc_lang(A,C,B)),k4_cqc_the1(A)) ) ) ) )).
fof(t8_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,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_projdes1(A,B,C,D,H) ) => ( r1_collsp(A,B,C,D) | r1_projdes1(A,E,F,G,H) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ~ ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) & ! [D] : ( m1_subset_1(D,u1_incsp_1(A)) => ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ~ ( r4_incsp_1(A,k7_domain_1(u1_incsp_1(A),D,E),C) & r1_zfmisc_1(B,D,E) ) ) ) ) ) ) ) )).
fof(t8_projred1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ? [E] : ( m1_subset_1(E,u1_incsp_1(A)) & r1_incsp_1(A,E,D) & E != B & E != C ) ) ) ) ) )).
fof(t8_projred2,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ~ ( ~ r1_incsp_1(A,B,C) & ~ r1_incsp_1(A,B,D) & k2_funct_1(k1_projred1(A,C,D,B)) != k1_projred1(A,D,C,B) ) ) ) ) ) )).
fof(t8_prvect_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( 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))) ) => ( r3_binop_1(B,C,D) => r3_binop_1(k4_finseq_2(A,B),k5_finseq_2(B,A,C),k2_prvect_1(B,D,A)) ) ) ) ) ) )).
fof(t8_prvect_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m1_subset_1(B,k4_card_3(k4_prvect_2(A))) => ! [C] : ( m1_subset_1(C,k4_card_3(k4_prvect_2(A))) => ! [D] : ( m1_subset_1(D,k4_card_3(k4_prvect_2(A))) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r2_hidden(E,k9_xtuple_0(B)) & D = k12_prvect_1(k4_card_3(k4_prvect_2(A)),k13_prvect_1(k4_prvect_2(A),k6_prvect_2(A)),B,C) ) => r1_xxreal_0(k1_funct_1(k12_prvect_2(A,D),E),k1_funct_1(k7_euclid(k3_finseq_1(A),k12_prvect_2(A,B),k12_prvect_2(A,C)),E)) ) ) ) ) ) ) )).
fof(t8_prvect_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l2_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_prvect_3(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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(k4_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)) ) ) ) ) ) ) )).
fof(t8_pscomp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(k1_numbers)) => ( v3_rcomp_1(C) => v3_pre_topc(k8_relset_1(u1_struct_0(A),k1_numbers,B,C),A) ) ) ) ) ) )).
fof(t8_pua2mss1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => m1_eqrel_1(a_2_0_pua2mss1(A,B),k3_finseq_2(A)) ) ) )).
fof(t8_pythtrip,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k6_nat_d(k2_nat_1(A,B),k2_nat_1(A,C)) = k2_nat_1(A,k6_nat_d(B,C)) ) ) ) )).
fof(t8_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => r1_pboole(A,B,k1_pzfmisc1(A,B)) ) )).
fof(t8_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [D] : ( ( v3_card_1(D,B) & m2_finseq_1(D,k2_qc_lang1(A)) ) => k10_qc_lang1(A,C,D) = k7_finseq_1(k12_finseq_1(k8_qc_lang1(A,B),C),D) ) ) ) ) )).
fof(t8_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ( v3_qc_lang1(k1_qc_lang2(A),A) & k18_qc_lang1(A,k1_qc_lang2(A)) = k12_qc_lang1(A) ) ) )).
fof(t8_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => k24_qc_lang1(A,k1_qc_lang2(A)) = k1_xboole_0 ) )).
fof(t8_qc_lang4,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ( ( r2_hidden(C,k10_xtuple_0(k2_qc_lang4(A,B))) & r1_qc_lang2(A,D,C) ) => r2_hidden(D,k10_xtuple_0(k2_qc_lang4(A,B))) ) ) ) ) ) )).
fof(t8_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [F] : ( m2_subset_1(F,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [G] : ( ( v5_relat_1(G,k3_qc_lang1(A)) & v3_card_1(G,B) & m2_finseq_1(G,k2_qc_lang1(A)) ) => ! [H] : ( ( v1_qc_trans(H,A) & m1_qc_lang1(H) ) => ( k1_qc_trans(A,H,k5_cqc_lang(A)) = k5_cqc_lang(H) & k1_qc_trans(A,H,k4_cqc_lang(B,A,F,G)) = k4_cqc_lang(B,H,k3_qc_trans(A,H,B,F),k4_qc_trans(A,H,B,G)) & k1_qc_trans(A,H,k6_cqc_lang(A,C)) = k6_cqc_lang(H,k1_qc_trans(A,H,C)) & k1_qc_trans(A,H,k7_cqc_lang(A,C,D)) = k7_cqc_lang(H,k1_qc_trans(A,H,C),k1_qc_trans(A,H,D)) & k1_qc_trans(A,H,k11_cqc_lang(A,E,C)) = k11_cqc_lang(H,k2_qc_trans(A,H,E),k1_qc_trans(A,H,C)) ) ) ) ) ) ) ) ) ) )).
fof(t8_qmax_1,axiom,( ! [A] : ( ( v2_qmax_1(A) & l1_qmax_1(A) ) => ! [B] : ( m1_subset_1(B,k5_qmax_1(A)) => ! [C] : ( m1_subset_1(C,k5_qmax_1(A)) => ( r3_qmax_1(A,B,C) => r3_qmax_1(A,k8_qmax_1(A,C),k8_qmax_1(A,B)) ) ) ) ) )).
fof(t8_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v10_lattices(A) & v4_lattice3(A) & v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r3_lattices(A,B,C) => ( r3_lattices(A,k6_algstr_0(A,B,D),k6_algstr_0(A,C,D)) & r3_lattices(A,k6_algstr_0(A,D,B),k6_algstr_0(A,D,C)) ) ) ) ) ) ) )).
fof(t8_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => A = k22_quaterni(k25_quaterni(A,B),B) ) ) )).
fof(t8_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => k25_quaterni(A,k1_quatern2) = A ) )).
fof(t8_quaterni,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : ( r2_zfmisc_1(A,C,E,G) => k2_quaterni(A,C,E,G,B,D,F,H) = k2_enumset1(k4_tarski(A,B),k4_tarski(C,D),k4_tarski(E,F),k4_tarski(G,H)) ) )).
fof(t8_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r1_xxreal_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(A)),k3_xcmplx_0(C,A)),D),k5_numbers) => ( r1_xxreal_0(k5_numbers,B) | r1_xxreal_0(k5_numbers,k6_xcmplx_0(k1_square_1(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,B),A),C)),k1_quin_1(B,C,D))) ) ) ) ) ) ) )).
fof(t8_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_quofield(A)),k7_quofield(A)) => ( ~ r1_xboole_0(B,C) => B = C ) ) ) ) )).
fof(t8_radix_1,axiom,( k2_radix_1(k5_numbers) = k1_tarski(k5_numbers) )).
fof(t8_radix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_int_1(B) => k2_xcmplx_0(k12_radix_1(B,A),k3_xcmplx_0(k11_radix_1(B),k1_radix_1(A))) = B ) ) )).
fof(t8_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( r2_hidden(B,k2_radix_3(A)) => v1_int_1(B) ) ) )).
fof(t8_radix_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( r2_hidden(E,k2_finseq_1(A)) & r1_xxreal_0(2,B) ) => k1_radix_4(E,k2_xcmplx_0(k2_xcmplx_0(A,1),1),B,k10_radix_3(k2_xcmplx_0(A,1),B,k10_radix_1(B,k2_xcmplx_0(A,1),C)),k10_radix_3(k2_xcmplx_0(A,1),B,k10_radix_1(B,k2_xcmplx_0(A,1),D))) = k1_radix_4(E,k2_xcmplx_0(A,1),B,k10_radix_3(A,B,k10_radix_1(B,A,k4_nat_d(C,k1_newton(k1_radix_1(B),A)))),k10_radix_3(A,B,k10_radix_1(B,A,k4_nat_d(D,k1_newton(k1_radix_1(B),A))))) ) ) ) ) ) ) )).
fof(t8_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r2_hidden(A,k2_finseq_1(C)) & r1_xxreal_0(2,B) ) => ( r1_xxreal_0(A,1) | k4_radix_1(A,B,C,k10_radix_1(B,C,1)) = k5_numbers ) ) ) ) ) )).
fof(t8_radix_6,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ~ ( ~ r1_xxreal_0(k2_xcmplx_0(A,C),B) & ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v1_int_1(D) => ~ ( ~ r1_xxreal_0(k6_xcmplx_0(A,k3_xcmplx_0(D,C)),k4_xcmplx_0(C)) & ~ r1_xxreal_0(C,k6_xcmplx_0(B,k3_xcmplx_0(D,C))) ) ) ) ) ) ) )).
fof(t8_ramsey_1,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(A) & v1_finset_1(B) & k1_card_1(B) = A ) => k3_group_10(B,A) = k1_tarski(B) ) )).
fof(t8_random_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ? [C] : ( m2_subset_1(C,k1_zfmisc_1(A),k1_random_1(A)) & k1_relset_1(A,B) = C & r1_mesfunc6(A,k1_random_1(A),B,C) ) ) ) )).
fof(t8_random_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k1_zfmisc_1(A),k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_zfmisc_1(A),k1_numbers))) ) => ( ( ! [D] : ( r1_tarski(D,A) => ( r1_xxreal_0(k5_numbers,k12_supinf_2(C,D)) & r1_xxreal_0(k12_supinf_2(C,D),1) ) ) & k12_supinf_2(C,A) = 1 & ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => k12_supinf_2(C,D) = k5_bhsp_5(k1_numbers,A,k9_binop_2,D,B) ) ) => m2_prob_1(C,A,k1_random_1(A)) ) ) ) ) )).
fof(t8_random_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [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))) ) => k6_finance1(A,k1_numbers,B,k12_prob_1) = k3_random_2(A,B) ) ) ) )).
fof(t8_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => k5_algstr_0(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)) = k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,k5_algstr_0(B,E,F)) ) ) ) ) ) ) )).
fof(t8_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => r1_xxreal_0(1,k1_rat_1(A)) ) )).
fof(t8_ratfunc1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v1_group_1(A) & v1_vectsp_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( k2_hurwitz(A,B) = k5_numbers => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_polynom4(A,B,C) != k4_struct_0(A) ) ) ) ) )).
fof(t8_rcomp_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_numbers)) => ( v1_rcomp_1(A) => v2_rcomp_1(A) ) ) )).
fof(t8_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => k9_subset_1(k1_numbers,k1_rcomp_1(A,B),k4_subset_1(k1_numbers,k1_limfunc1(A),k2_limfunc1(B))) = k2_tarski(A,B) ) ) ) )).
fof(t8_real,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(A,B) & ~ v3_xxreal_0(B) & ~ v2_xxreal_0(A) ) ) ) )).
fof(t8_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( 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,C),k1_funcsdom(A,k1_numbers,k4_real_lat(A),C,B)) ) ) ) )).
fof(t8_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( v7_ordinal1(C) => ( r2_hidden(C,k2_finseq_1(A)) => r1_xxreal_0(k9_complex1(k1_funct_1(B,C)),k12_euclid(B)) ) ) ) ) )).
fof(t8_realset2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k3_rlvect_1(A,B,C) = k4_struct_0(A) => C = k3_funct_2(u1_struct_0(A),u1_struct_0(A),k5_vectsp_1(A),B) ) ) ) ) )).
fof(t8_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_binop_1(u1_struct_0(A),k1_realset3(A),B,B) = k4_struct_0(A) ) ) )).
fof(t8_rearran1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_rearran1(C) & m2_finseq_1(C,k1_zfmisc_1(B)) ) => ~ ( r1_xxreal_0(1,A) & r1_xxreal_0(A,k6_xcmplx_0(k3_finseq_1(C),1)) & k6_subset_1(k1_funct_1(C,k1_nat_1(A,1)),k1_funct_1(C,A)) = k1_xboole_0 ) ) ) ) )).
fof(t8_relat_1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( 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))) ) ) )).
fof(t8_relat_2,axiom,( ! [A] : ( v1_relat_1(A) => ( v8_relat_2(A) <=> r1_tarski(k3_relat_1(A,A),A) ) ) )).
fof(t8_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => r1_tarski(k1_relat_1(C),k2_xboole_0(A,B)) ) )).
fof(t8_relset_2,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => r1_tarski(k3_relat_1(k3_xboole_0(A,B),C),k3_xboole_0(k3_relat_1(A,C),k3_relat_1(B,C))) ) ) ) )).
fof(t8_revrot_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finseq_6(B,A) & m2_finseq_1(B,A) ) => v1_finseq_6(k4_finseq_5(A,B),A) ) ) )).
fof(t8_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( m1_rewrite1(B,A) => ! [C] : ( m1_rewrite1(C,A) => ( k1_funct_1(B,k3_finseq_1(B)) = k1_funct_1(C,1) => m1_rewrite1(k1_rewrite1(B,C),A) ) ) ) ) )).
fof(t8_rewrite2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v1_rewrite2(C) ) => k1_rewrite2(A,k2_rewrite2(B,C)) = k2_rewrite2(B,k1_rewrite2(A,C)) ) ) ) )).
fof(t8_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( m1_rewrite1(k10_finseq_1(A,B),C) => r2_hidden(k4_tarski(A,B),C) ) ) )).
fof(t8_rfinseq,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => k8_finseq_1(A,k17_finseq_1(A,C,B),k2_rfinseq(A,C,B)) = B ) ) ) )).
fof(t8_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => ( r1_xxreal_0(k3_finseq_1(A),k5_numbers) | r1_xxreal_0(k2_xcmplx_0(k4_rfinseq2(A),k4_rfinseq2(B)),k4_rfinseq2(k4_rvsum_1(A,B))) ) ) ) ) )).
fof(t8_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_valued_0(C) ) => k1_valued_1(k1_valued_1(A,B),C) = k1_valued_1(A,k1_valued_1(B,C)) ) ) ) )).
fof(t8_rfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ( r1_tarski(k2_relset_1(A,D),k9_subset_1(A,k1_relset_1(A,B),k1_relset_1(A,C))) => ( r2_relset_1(k4_ordinal1,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,A,D,k3_valued_1(A,k1_numbers,k1_numbers,B,C)),k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,A,D,B),k8_funct_2(k4_ordinal1,k1_numbers,A,D,C))) & r2_relset_1(k4_ordinal1,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,A,D,k47_valued_1(A,k1_numbers,k1_numbers,B,C)),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,A,D,B),k8_funct_2(k4_ordinal1,k1_numbers,A,D,C))) & r2_relset_1(k4_ordinal1,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,A,D,k20_valued_1(A,k1_numbers,k1_numbers,B,C)),k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,A,D,B),k8_funct_2(k4_ordinal1,k1_numbers,A,D,C))) ) ) ) ) ) ) )).
fof(t8_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_numbers) => k8_relset_1(A,k1_numbers,k56_valued_1(A,k1_numbers,B),k1_tarski(C)) = k8_relset_1(A,k1_numbers,B,k2_tarski(k4_xcmplx_0(C),C)) ) ) ) ) )).
fof(t8_rfunct_4,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r2_rfunct_3(B,A) <=> ( r1_tarski(A,k9_xtuple_0(B)) & ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ( r2_hidden(C,A) & r2_hidden(D,A) & r2_hidden(E,A) ) => ( r1_xxreal_0(D,C) | r1_xxreal_0(E,D) | r1_xxreal_0(k1_funct_1(B,D),k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(E,D),k6_xcmplx_0(E,C)),k1_funct_1(B,C)),k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(D,C),k6_xcmplx_0(E,C)),k1_funct_1(B,E)))) ) ) ) ) ) ) ) ) )).
fof(t8_rinfsup1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_seq_2(B) => ( A = k2_rinfsup1(B) <=> ( ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(A,k1_funct_1(B,C)) ) & ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k2_xcmplx_0(A,C),k1_funct_1(B,D)) ) ) ) ) ) ) ) ) )).
fof(t8_rinfsup2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( r1_xxreal_0(k12_supinf_2(k3_rinfsup2(B),A),k12_supinf_2(B,A)) & r1_xxreal_0(k12_supinf_2(B,A),k12_supinf_2(k4_rinfsup2(B),A)) ) ) ) )).
fof(t8_ring_1,axiom,( ! [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) & l6_algstr_0(A) ) => k8_eqrel_1(u1_struct_0(A),k1_ring_1(A,k2_struct_0(A))) = k1_tarski(u1_struct_0(A)) ) )).
fof(t8_ringcat1,axiom,( ! [A] : ( ( v2_ringcat1(A) & v3_ringcat1(A) & l1_ringcat1(A) ) => ! [B] : ( ( v2_ringcat1(B) & v3_ringcat1(B) & l1_ringcat1(B) ) => ( k1_ringcat1(B) = k2_ringcat1(A) => ( k1_ringcat1(k6_ringcat1(B,A)) = k1_ringcat1(A) & k2_ringcat1(k6_ringcat1(B,A)) = k2_ringcat1(B) ) ) ) ) )).
fof(t8_rlaffin1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_rusub_4(A,k1_struct_0(A),B) = k1_struct_0(A) ) ) )).
fof(t8_rlaffin2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k3_convex1(A,B) = k3_tarski(a_2_0_rlaffin2(A,B)) ) ) )).
fof(t8_rlaffin3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(B)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(k2_xcmplx_0(B,A))))) => ( D = a_2_0_rlaffin3(A,B) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(k2_xcmplx_0(B,A)),D)))) => ( E = a_4_0_rlaffin3(A,B,C,D) => ( v3_pre_topc(C,k15_euclid(B)) <=> v3_pre_topc(E,k1_pre_topc(k15_euclid(k2_xcmplx_0(B,A)),D)) ) ) ) ) ) ) ) ) )).
fof(t8_rlsub_1,axiom,( ! [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) ) => ! [B] : ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( m1_rlsub_1(D,A) => ( ( r1_struct_0(C,B) & m1_rlsub_1(C,D) ) => r1_struct_0(D,B) ) ) ) ) )).
fof(t8_rlsub_2,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( ( v1_rlvect_1(C) & m1_rlsub_1(C,A) ) => ( m1_rlsub_1(B,C) <=> k1_rlsub_2(A,B,C) = C ) ) ) ) )).
fof(t8_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_tarski(B,C) => r1_tarski(k5_rusub_4(A,B,D),k5_rusub_4(A,C,D)) ) ) ) ) ) )).
fof(t8_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( k1_algstr_0(A,B,D) = k1_algstr_0(A,B,E) | k1_algstr_0(A,D,B) = k1_algstr_0(A,E,B) ) => D = E ) ) ) ) ) ) )).
fof(t8_rlvect_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => k2_rlvect_2(A,k1_struct_0(A)) = k4_struct_0(A) ) )).
fof(t8_rlvect_3,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( v1_rlvect_3(k6_domain_1(u1_struct_0(A),B),A) <=> B != k4_struct_0(A) ) ) ) )).
fof(t8_rlvect_4,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m1_subset_1(C,u1_struct_0(B)) => ( r1_struct_0(k1_rlvect_3(B,k6_domain_1(u1_struct_0(B),C)),A) <=> ? [D] : ( v1_xreal_0(D) & A = k1_rlvect_1(B,C,D) ) ) ) ) )).
fof(t8_rlvect_5,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ~ ( r1_tarski(k10_xtuple_0(D),u1_struct_0(k1_rlvect_3(A,C))) & ! [E] : ( m2_rlvect_2(E,A,C) => k4_rlvect_1(A,k5_rlvect_2(A,D,B)) != k6_rlvect_2(A,E) ) ) ) ) ) ) )).
fof(t8_rlvect_x,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k2_rlvect_x(A,B),u1_struct_0(k1_rlvect_3(A,B))) ) ) )).
fof(t8_rmod_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m1_rmod_2(D,B,C) => ! [E] : ( m1_rmod_2(E,B,C) => ( ( r1_struct_0(D,A) & m1_rmod_2(D,B,E) ) => r1_struct_0(E,A) ) ) ) ) ) )).
fof(t8_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_rmod_2(C,A,B) => ! [D] : ( ( v2_vectsp_2(D,A) & m1_rmod_2(D,A,B) ) => ( m1_rmod_2(C,A,D) <=> k1_rmod_3(A,B,C,D) = D ) ) ) ) ) )).
fof(t8_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ~ ( C != D & D != E & C != E & k1_rmod_4(A,B,k8_domain_1(u1_struct_0(B),C,D,E)) != k3_rlvect_1(B,k3_rlvect_1(B,C,D),E) ) ) ) ) ) ) )).
fof(t8_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & v7_robbins1(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k7_robbins1(A) = k3_robbins1(A,k5_robbins1(A,B,k3_robbins1(A,B))) ) ) )).
fof(t8_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k3_robbins1(A,k1_lattices(A,B,k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,B,C)),B)))) = k3_robbins1(A,k1_lattices(A,B,C)) ) ) ) )).
fof(t8_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( ( r1_relat_2(u1_orders_2(A),u1_struct_0(A)) & v4_relat_2(u1_orders_2(A)) & v8_relat_2(u1_orders_2(A)) ) => ( v3_orders_2(A) & v5_orders_2(A) & v4_orders_2(A) ) ) ) )).
fof(t8_robbins4,axiom,( ! [A] : ( r2_hidden(A,u1_struct_0(k14_lattice3(k1_robbins4))) => r1_tarski(A,3) ) )).
fof(t8_rolle,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r2_fdiff_1(C,k2_rcomp_1(A,B)) & r2_fdiff_1(D,k2_rcomp_1(A,B)) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k2_rcomp_1(A,B)) => k1_fdiff_1(C,E) = k1_fdiff_1(D,E) ) ) ) => ( v3_funct_1(k2_partfun1(k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,C,D),k2_rcomp_1(A,B))) & ? [E] : ( v1_xreal_0(E) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,k2_rcomp_1(A,B)) => k1_funct_1(C,F) = k2_xcmplx_0(k1_funct_1(D,F),E) ) ) ) ) ) ) ) ) ) )).
fof(t8_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( r2_hidden(C,k3_roughs_1(A,B)) => r1_tarski(k6_eqrel_1(u1_struct_0(A),u1_struct_0(A),u1_orders_2(A),C),B) ) ) ) )).
fof(t8_rpr_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v3_card_1(B,1) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & m2_finseq_1(C,A) & k10_xtuple_0(C) = B & k3_finseq_1(C) = 1 ) ) ) )).
fof(t8_rsspace,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace))) => k1_rlvect_1(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace),C,k2_xcmplx_0(A,B)) = k3_rlvect_1(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace),k1_rlvect_1(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace),C,A),k1_rlvect_1(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace),C,B)) ) ) ) )).
fof(t8_rsspace3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_rsspace3(B,A) <=> ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ! [D] : ( v7_ordinal1(D) => ? [E] : ( v7_ordinal1(E) & ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(D,E) & r1_xxreal_0(D,F) & r1_xxreal_0(C,k2_normsp_0(A,k5_algstr_0(A,k5_rsspace3(A,B,E),k5_rsspace3(A,B,F)))) ) ) ) ) ) ) ) ) )).
fof(t8_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_rsspace4(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_rsspace4(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_rsspace4(A,B))) => ! [F] : ( ( 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] : ( ( 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] : ( ( 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 = k3_rlvect_1(k5_rsspace4(A,B),C,D) <=> ! [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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( E = C & F = D ) => k2_bhsp_1(B,E,F) = k2_bhsp_1(A,C,D) ) ) ) ) ) ) ) )).
fof(t8_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( ( v1_bhsp_1(C) & m1_rusub_1(C,A) ) => ( m1_rusub_1(B,C) <=> k1_rusub_2(A,B,C) = C ) ) ) ) )).
fof(t8_rusub_3,axiom,( ! [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_bhsp_1(A) & v2_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( k1_rusub_3(A,B) = A & r1_tarski(B,C) ) => k1_rusub_3(A,C) = A ) ) ) ) )).
fof(t8_rusub_4,axiom,( ! [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_bhsp_1(A) & v1_rusub_4(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => r1_xxreal_0(k1_rusub_4(B),k1_rusub_4(A)) ) ) )).
fof(t8_rusub_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ~ v1_xboole_0(k1_rusub_5(A,B,C)) ) ) ) )).
fof(t8_rvsum_1,axiom,( v1_finseqop(k9_binop_2,k1_numbers) )).
fof(t8_rvsum_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xcmplx_0(B) => k5_rvsum_2(k2_finseq_2(A,B)) = k2_finseq_2(A,k4_xcmplx_0(B)) ) ) )).
fof(t8_scm_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_ami_3)) ) => ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_ami_3)) ) => ( ( k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B)) = C & k3_compos_1(k1_ami_3,A,C) = k6_ami_3(E,F) ) => ( E = F | ( k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1))) = k1_nat_1(C,1) & k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1)),E) = k4_int_1(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B),E),k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B),F)) & k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1)),F) = k5_int_1(k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B),E),k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B),F)) & ! [G] : ( ( v1_ami_2(G) & m1_subset_1(G,u1_struct_0(k1_ami_3)) ) => ~ ( G != E & G != F & k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1)),G) != k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B),G) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_scm_comp,axiom,( ! [A] : ( m2_subset_1(A,u1_struct_0(k1_scm_comp),k7_dtconstr(k1_scm_comp)) => ! [B] : ( m1_dtconstr(B,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [C] : ( m1_dtconstr(C,u1_struct_0(k1_scm_comp),k5_trees_3(u1_struct_0(k1_scm_comp)),k4_dtconstr(k1_scm_comp)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,u1_struct_0(k1_scm_comp)) => ! [F] : ( m1_subset_1(F,u1_struct_0(k1_scm_comp)) => ( ( E = k1_bintree1(u1_struct_0(k1_scm_comp),B) & F = k1_bintree1(u1_struct_0(k1_scm_comp),C) & r1_lang1(k1_scm_comp,A,k4_pre_poly(u1_struct_0(k1_scm_comp),E,F)) ) => k15_scm_comp(k2_scm_comp(A,B,C),D) = k1_ordinal4(k1_ordinal4(k15_scm_comp(B,D),k15_scm_comp(C,k1_nat_1(D,1))),k13_scm_comp(A,D)) ) ) ) ) ) ) ) )).
fof(t8_scm_halt,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_3(k4_scmfsa_2(k5_numbers),1)),A) & r1_tarski(C,B) & r1_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A) ) => ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(E,k8_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A)) => r8_pboole(u1_struct_0(k1_scmfsa_2),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,E),k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,k3_scmfsa6a(C,D)),A,E)) ) ) ) ) ) ) ) )).
fof(t8_scm_inst,axiom,( r1_tarski(k3_scm_inst,k3_zfmisc_1(k4_ordinal1,k13_finseq_1(k4_ordinal1),k10_xtuple_0(k3_scm_inst))) )).
fof(t8_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(B,k10_xtuple_0(A)) => ( ( B != k12_scmfsa_2(D,C) & B != k13_scmfsa_2(D,C) ) | r2_hidden(C,k2_sf_mastr(A)) ) ) ) ) ) ) )).
fof(t8_scmfsa10,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( v7_ordinal1(B) => k13_scmfsa_2(B,A) = k3_xtuple_0(8,k9_finseq_1(B),k9_finseq_1(A)) ) ) )).
fof(t8_scmfsa6a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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) ) ) )).
fof(t8_scmfsa6b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(C,k7_card_1(3),k1_scmfsa_2,k5_numbers) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ( ( r1_tarski(D,A) & r1_tarski(D,B) ) => ( k8_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C) = k8_extpro_1(k7_card_1(3),k1_scmfsa_2,B,C) & r8_pboole(u1_struct_0(k1_scmfsa_2),k6_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C),k6_extpro_1(k7_card_1(3),k1_scmfsa_2,B,C)) ) ) ) ) ) ) )).
fof(t8_scmfsa6c,axiom,( ! [A] : ( m1_scmfsa_2(A) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_partfun1(C,k4_ordinal1) ) => ! [D] : ( ( v1_scmfsa6c(D) & v2_scmfsa6c(D) & m1_subset_1(D,u1_compos_1(k1_scmfsa_2)) ) => ! [E] : ( ( v1_scmfsa6c(E) & m1_subset_1(E,u1_compos_1(k1_scmfsa_2)) ) => k18_scmfsa_2(k1_scmfsa6b(k6_scmfsa6a(D,E),B,C),A) = k18_scmfsa_2(k2_extpro_1(k7_card_1(3),k1_scmfsa_2,E,k2_extpro_1(k7_card_1(3),k1_scmfsa_2,D,k1_scmfsa_m(B))),A) ) ) ) ) ) )).
fof(t8_scmfsa7b,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ~ ( A != B & r3_scmfsa7b(k8_scmfsa_2(B,C),A) ) ) ) ) )).
fof(t8_scmfsa8a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) & v1_afinsq_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_finset_1(B) & v1_afinsq_1(B) ) => ! [C] : ( r2_hidden(C,k2_afinsq_1(A)) => k1_funct_1(k3_scmfsa6a(A,B),C) = k1_funct_1(k2_scmfsa6a(A),C) ) ) ) )).
fof(t8_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_scmfsa6c(C) & v2_scmfsa6c(C) & m1_subset_1(C,u1_compos_1(k1_scmfsa_2)) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [E] : ( ( 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(k7_card_1(3),k1_scmfsa_2,C,k1_scmfsa_m(B)),A),E) ) ) ) ) ) )).
fof(t8_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k5_numbers,k2_afinsq_1(C)) ) ) ) ) )).
fof(t8_scmfsa9a,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => k4_sf_mastr(k1_scmfsa8b(C,A,B)) = k4_subset_1(k3_scmfsa_2,k4_sf_mastr(A),k4_sf_mastr(B)) ) ) ) )).
fof(t8_scmfsa_2,axiom,( ! [A] : ( 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)) ) ) )).
fof(t8_scmfsa_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( ~ 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(k7_card_1(3),k1_scmfsa_2)) & v1_finset_1(B) & v4_extpro_1(B,k7_card_1(3),k1_scmfsa_2,A) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ( ( r1_tarski(B,C) & r1_tarski(B,D) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( ( r1_tarski(A,E) & r1_tarski(A,F) ) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v1_ami_2(H) & m1_subset_1(H,u1_struct_0(k1_scmfsa_2)) ) => ! [I] : ( ( v1_ami_2(I) & m1_subset_1(I,u1_struct_0(k1_scmfsa_2)) ) => ( ( k3_extpro_1(k7_card_1(3),k1_scmfsa_2,E,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G)) = k10_scmfsa_2(H,I) & r2_hidden(I,k9_xtuple_0(B)) ) => k5_int_1(k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G),H),k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G),I)) = k5_int_1(k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,D,G),H),k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,D,G),I)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_scmfsa_i,axiom,( ! [A] : ( m1_subset_1(A,k1_compos_0(k2_scmfsa_i)) => ( ( A = 9 | A = 10 ) => k3_compos_0(k2_scmfsa_i,A) = k1_tarski(k1_xboole_0) ) ) )).
fof(t8_scmfsa_m,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ( ( k1_funct_1(A,k4_scmfsa_2(k5_numbers)) = 1 & k5_memstr_0(k7_card_1(3),k1_scmfsa_2,A) = k5_numbers ) => k1_scmfsa_m(A) = A ) ) )).
fof(t8_scmisort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( 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),k5_numbers) => ( r2_scm_halt(k2_scmfsa_9(D,C),B,A) & r1_scm_halt(k2_scmfsa_9(D,C),B,A) ) ) ) ) ) ) )).
fof(t8_scmp_gcd,axiom,( k5_card_1(k4_scmp_gcd) = 15 )).
fof(t8_scmpds_2,axiom,( ! [A] : ! [B] : ( m2_subset_1(B,k1_ami_2,k2_ami_2) => ! [C] : ( m2_subset_1(C,k1_ami_2,k2_ami_2) => ! [D] : ( v1_int_1(D) => ! [E] : ( 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) ) ) ) ) ) )).
fof(t8_scmpds_3,axiom,( ! [A] : ( ( 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] : ( ( 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] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( k5_memstr_0(2,k1_scmpds_2,A) = k5_memstr_0(2,k1_scmpds_2,B) & C != D & k17_scmpds_2(A,C) = k17_scmpds_2(B,D) ) ) ) ) ) )).
fof(t8_scmpds_4,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmpds_2)) => k4_scmpds_4(A,B) = k3_scmpds_4(k9_compos_1(k1_scmpds_2,A),B) ) ) )).
fof(t8_scmpds_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_scmpds_4(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) ) => ( r1_tarski(k10_compos_1(k1_scmpds_2,C),A) => ! [E] : ( v7_ordinal1(E) => ( 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) ) ) ) ) ) ) ) )).
fof(t8_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( 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,k5_numbers) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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) ) ) ) ) ) ) )).
fof(t8_scmpds_8,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( r1_xxreal_0(k5_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,k1_nat_1(k5_card_1(C),2))) ) ) ) ) ) ) ) )).
fof(t8_scmpds_9,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmpds_2)) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( v1_int_1(D) => ! [E] : ( v1_int_1(E) => k1_amistd_1(2,k1_scmpds_2,C,k16_scmpds_2(A,B,D,E)) = k1_tarski(k1_ordinal1(C)) ) ) ) ) ) )).
fof(t8_scmpds_i,axiom,( ! [A] : ( m1_subset_1(A,k1_scmpds_i) => ~ ( ~ ( r2_hidden(A,k1_tarski(k3_xtuple_0(k5_numbers,k1_xboole_0,k1_xboole_0))) & k4_xtuple_0(A) = k5_numbers ) & ~ ( r2_hidden(A,a_0_0_scmpds_i) & k4_xtuple_0(A) = 14 ) & ~ ( r2_hidden(A,a_0_1_scmpds_i) & k4_xtuple_0(A) = 1 ) & ~ ( r2_hidden(A,a_0_5_scmpds_i) & ( k4_xtuple_0(A) = 2 | k4_xtuple_0(A) = 3 ) ) & ~ ( r2_hidden(A,a_0_3_scmpds_i) & ~ ( k4_xtuple_0(A) != 4 & k4_xtuple_0(A) != 5 & k4_xtuple_0(A) != 6 & k4_xtuple_0(A) != 7 & k4_xtuple_0(A) != 8 ) ) & ~ ( r2_hidden(A,a_0_4_scmpds_i) & ~ ( 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 ) ) ) ) )).
fof(t8_scmring1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k4_card_3(k3_relat_1(k3_ami_2,k1_scmring1(A)))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => k1_funct_1(k3_scmring1(A,B,C),D) = k1_funct_1(B,D) ) ) ) ) )).
fof(t8_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & 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_struct_0(k1_scmring2(A)) = k4_ordinal1 ) )).
fof(t8_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(A))) ) => k2_compos_0(u1_compos_1(k1_scmring2(A)),k7_scmring2(A,C,B)) = 5 ) ) ) )).
fof(t8_scmring4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(B))) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmring2(B))) ) => ! [E] : ( ( 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(k7_card_1(2),k1_scmring2(B))) & v1_partfun1(E,u1_struct_0(k1_scmring2(B))) ) => ! [F] : ( ( 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(k7_card_1(2),k1_scmring2(B))) & v1_partfun1(F,u1_struct_0(k1_scmring2(B))) ) => ! [G] : ( ( v1_relat_1(G) & v4_relat_1(G,k4_ordinal1) & v5_relat_1(G,u1_compos_1(k1_scmring2(B))) & v1_funct_1(G) & v1_partfun1(G,k4_ordinal1) ) => ! [H] : ( ( v1_relat_1(H) & v4_relat_1(H,k4_ordinal1) & v5_relat_1(H,u1_compos_1(k1_scmring2(B))) & v1_funct_1(H) & v1_partfun1(H,k4_ordinal1) ) => ! [I] : ( ( v1_relat_1(I) & v4_relat_1(I,k4_ordinal1) & 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] : ( ( 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(k7_card_1(2),k1_scmring2(B))) & ~ v1_xboole_0(J) & v1_finset_1(J) & v4_extpro_1(J,k7_card_1(2),k1_scmring2(B),I) ) => ( ( r1_tarski(J,E) & r1_tarski(J,F) & r1_tarski(I,G) & r1_tarski(I,H) & k3_extpro_1(k7_card_1(2),k1_scmring2(B),G,k5_extpro_1(k7_card_1(2),k1_scmring2(B),G,E,A)) = k4_scmring2(B,C,D) & r2_hidden(C,k9_xtuple_0(J)) ) => k1_algstr_0(B,k2_scmring2(B,k5_extpro_1(k7_card_1(2),k1_scmring2(B),G,E,A),C),k2_scmring2(B,k5_extpro_1(k7_card_1(2),k1_scmring2(B),G,E,A),D)) = k1_algstr_0(B,k2_scmring2(B,k5_extpro_1(k7_card_1(2),k1_scmring2(B),H,F,A),C),k2_scmring2(B,k5_extpro_1(k7_card_1(2),k1_scmring2(B),H,F,A),D)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ! [C] : ( m1_subset_1(C,k2_scm_inst) => ! [D] : ( m1_subset_1(D,k2_scm_inst) => ( r2_hidden(B,k2_enumset1(1,2,3,4)) => r2_hidden(k3_xtuple_0(B,k1_xboole_0,k2_finseq_4(k2_scm_inst,C,D)),k1_scmringi(A)) ) ) ) ) )).
fof(t8_scmyciel,axiom,( ! [A] : k3_tarski(k2_tarski(k1_xboole_0,k1_tarski(A))) = k1_tarski(A) )).
fof(t8_scpinvar,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k4_scpinvar(A,B,C)) = k1_nat_1(k5_card_1(C),3) ) ) ) )).
fof(t8_scpisort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ( ( r1_scmpds_6(C,B,A) & r2_scmpds_6(C,B,A) ) => ( r1_scmpds_6(k1_scmpds_4(C,D),B,A) & r2_scmpds_6(k1_scmpds_4(C,D),B,A) ) ) ) ) ) ) )).
fof(t8_scpqsort,axiom,( ! [A] : ( m2_finseq_1(A,k4_numbers) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ( ( C = k6_xcmplx_0(D,1) & r3_graph_2(A,B,C) & r3_graph_2(A,k1_nat_1(D,1),E) & ! [F] : ( v7_ordinal1(F) => ( r1_xxreal_0(B,F) => ( r1_xxreal_0(D,F) | r1_xxreal_0(k1_funct_1(A,F),k1_funct_1(A,D)) ) ) ) & ! [F] : ( v7_ordinal1(F) => ( r1_xxreal_0(F,E) => ( r1_xxreal_0(F,D) | r1_xxreal_0(k1_funct_1(A,D),k1_funct_1(A,F)) ) ) ) ) => r3_graph_2(A,B,E) ) ) ) ) ) ) )).
fof(t8_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t8_seq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_funct_2(k4_ordinal1,k1_numbers,A,k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C)) <=> ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,A,D) = k4_real_1(k9_nat_1(k1_numbers,B,D),k9_nat_1(k1_numbers,C,D)) ) ) ) ) ) )).
fof(t8_seq_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(B) => k1_seq_2(k26_valued_1(k4_ordinal1,k1_numbers,B,A)) = k3_xcmplx_0(A,k1_seq_2(B)) ) ) ) )).
fof(t8_seq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v3_membered(C) => ( ( ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => r1_xxreal_0(A,D) ) ) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,C) & ~ r1_xxreal_0(k2_xcmplx_0(A,D),E) ) ) ) ) & ! [D] : ( v1_xreal_0(D) => ( r2_hidden(D,C) => r1_xxreal_0(B,D) ) ) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,C) & ~ r1_xxreal_0(k2_xcmplx_0(B,D),E) ) ) ) ) ) => A = B ) ) ) ) )).
fof(t8_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( r2_relset_1(k4_ordinal1,k4_partfun1(A,k1_numbers),k8_seqfunc(A,k7_seqfunc(A,B,C),D),k7_seqfunc(A,k8_seqfunc(A,B,D),k8_seqfunc(A,C,D))) & r2_relset_1(k4_ordinal1,k4_partfun1(A,k1_numbers),k7_seqfunc(A,k8_seqfunc(A,D,B),k8_seqfunc(A,D,C)),k8_seqfunc(A,D,k7_seqfunc(A,B,C))) ) ) ) ) ) )).
fof(t8_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v8_valued_0(A) <=> ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => r1_xxreal_0(k9_nat_1(k1_numbers,A,C),k9_nat_1(k1_numbers,A,B)) ) ) ) ) ) )).
fof(t8_series_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_series_1(A) & v1_series_1(B) ) => ( v1_series_1(k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) & k4_series_1(k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) = k6_xcmplx_0(k4_series_1(A),k4_series_1(B)) ) ) ) ) )).
fof(t8_series_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(k3_xcmplx_0(k3_xcmplx_0(2,k9_complex1(A)),k9_complex1(B)),k2_xcmplx_0(k1_square_1(A),k1_square_1(B))) ) ) )).
fof(t8_series_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => k1_newton(k2_xcmplx_0(k2_xcmplx_0(A,B),C),3) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_newton(A,3),k1_newton(B,3)),k1_newton(C,3)),k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,k1_newton(A,2)),B),k3_xcmplx_0(k3_xcmplx_0(3,k1_newton(A,2)),C))),k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,k1_newton(B,2)),A),k3_xcmplx_0(k3_xcmplx_0(3,k1_newton(B,2)),C))),k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(3,k1_newton(C,2)),A),k3_xcmplx_0(k3_xcmplx_0(3,k1_newton(C,2)),B))),k3_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(6,A),B),C)) ) ) ) )).
fof(t8_series_5,axiom,( ! [A] : ( ( v1_xreal_0(A) & v2_xxreal_0(A) ) => ! [B] : ( ( v1_xreal_0(B) & v2_xxreal_0(B) ) => r1_xxreal_0(k7_xcmplx_0(k2_xcmplx_0(A,B),2),k3_square_1(k7_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),2))) ) ) )).
fof(t8_setfam_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r2_hidden(A,B) & r1_xboole_0(A,C) ) => r1_xboole_0(k1_setfam_1(B),C) ) )).
fof(t8_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k3_prob_1(A,B) = k6_setfam_1(A,k2_relset_1(k9_setfam_1(A),B)) ) )).
fof(t8_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => r1_tarski(k1_prob_1(A,k1_setlim_2(A,B,C)),k9_subset_1(A,k1_prob_1(A,B),k1_prob_1(A,C))) ) ) )).
fof(t8_setwiseo,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k5_finsub_1(A)) => ! [C] : ( r1_tarski(C,B) => m1_subset_1(C,k5_finsub_1(A)) ) ) )).
fof(t8_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( k13_scmfsa_2(C,A) = k13_scmfsa_2(D,B) => ( A = B & C = D ) ) ) ) ) ) )).
fof(t8_sfmastr1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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] : ( m1_scmfsa_2(E) => ~ ( ( v7_amistd_1(D,k7_card_1(3),k1_scmfsa_2) | ( r6_scmfsa7b(D,k1_scmfsa_m(B),A) & r5_scmfsa7b(D,k1_scmfsa_m(B),A) ) ) & ( v7_amistd_1(C,k7_card_1(3),k1_scmfsa_2) | ( r6_scmfsa7b(C,k1_scmfsa6b(D,B,A),A) & r5_scmfsa7b(C,k1_scmfsa6b(D,B,A),A) ) ) & k18_scmfsa_2(k1_scmfsa6b(k3_scmfsa6a(D,C),B,A),E) != k18_scmfsa_2(k1_scmfsa6b(C,k1_scmfsa6b(D,B,A),A),E) ) ) ) ) ) ) )).
fof(t8_sfmastr2,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) & v1_scmfsa7b(D) ) => k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k3_sfmastr2(B,A,D,C),k5_numbers),k4_scmfsa_2(k5_numbers)) = 1 ) ) ) ) )).
fof(t8_sfmastr3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) => ~ ( ~ r4_scmfsa7b(C,A) & r4_scmfsa7b(k2_scmfsa_9(B,C),A) ) ) ) ) )).
fof(t8_sgraph1,axiom,( ! [A] : ! [B] : ( r2_hidden(B,k2_sgraph1(A)) <=> ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) & ? [C] : ? [D] : ( r2_hidden(C,A) & r2_hidden(D,A) & C != D & B = k2_tarski(C,D) ) ) ) )).
fof(t8_sheffer1,axiom,( ! [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) & l3_lattices(A) ) => v5_sheffer1(A) ) )).
fof(t8_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,C),B),B)),C) = k5_sheffer1(A,C,C) ) ) ) )).
fof(t8_simplex0,axiom,( ! [A] : ( r1_tarski(k1_simplex0(A),A) => v1_classes1(A) ) )).
fof(t8_simplex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k3_simplex1(A,k5_simplex0(u1_struct_0(A),k6_domain_1(k1_zfmisc_1(u1_struct_0(A)),B))) = k3_convex1(A,B) ) ) )).
fof(t8_simplex2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v6_metric_1(B) & l1_metric_1(B) ) => ! [C] : ( ( v1_simplex2(C,B) & m1_simplex0(C,A) ) => ! [D] : ( m2_simplex0(D,A,C) => r1_xxreal_0(k1_simplex2(B,D),k1_simplex2(B,C)) ) ) ) )).
fof(t8_sin_cos,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v7_ordinal1(C) => k7_xcmplx_0(k1_newton(k2_xcmplx_0(B,A),C),k2_newton(C)) = k9_nat_1(k2_numbers,k10_comseq_3(k9_sin_cos(C,B,A)),C) ) ) ) )).
fof(t8_sin_cos2,axiom,( v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k18_sin_cos,k2_rcomp_1(k28_sin_cos,k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos)))) )).
fof(t8_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k6_xcmplx_0(k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k4_sin_cos3,A)),k3_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A),k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A))) = 1 ) )).
fof(t8_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( k19_sin_cos(A) != k5_numbers & k19_sin_cos(B) != k5_numbers & k1_sin_cos4(k6_xcmplx_0(A,B)) != k7_xcmplx_0(k6_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)))) ) ) ) )).
fof(t8_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k19_sin_cos(A) != k5_numbers => k19_sin_cos(k3_xcmplx_0(2,A)) = k7_xcmplx_0(k6_xcmplx_0(1,k1_square_1(k1_sin_cos4(A))),k2_xcmplx_0(1,k1_square_1(k1_sin_cos4(A)))) ) ) )).
fof(t8_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => k1_funct_1(k16_sin_cos,A) = k1_funct_1(k16_sin_cos,k2_xcmplx_0(A,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B))) ) ) )).
fof(t8_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => r1_xxreal_0(1,k3_square_1(k7_xcmplx_0(k2_xcmplx_0(A,1),2))) ) ) )).
fof(t8_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => ( A != k5_numbers => ( k23_sin_cos(A) = k7_xcmplx_0(k2_xcmplx_0(k1_sin_cos5(k7_xcmplx_0(A,2)),1),k6_xcmplx_0(k1_sin_cos5(k7_xcmplx_0(A,2)),1)) & k23_sin_cos(k4_xcmplx_0(A)) = k7_xcmplx_0(k6_xcmplx_0(k1_sin_cos5(k7_xcmplx_0(A,2)),1),k2_xcmplx_0(k1_sin_cos5(k7_xcmplx_0(A,2)),1)) ) ) ) )).
fof(t8_sin_cos9,axiom,( v6_valued_0(k2_partfun1(k1_numbers,k1_numbers,k27_sin_cos,k2_rcomp_1(k5_numbers,k28_sin_cos))) )).
fof(t8_sincos10,axiom,( r2_fdiff_1(k2_fdiff_9,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) & ! [A] : ( v1_xreal_0(A) => ( r2_hidden(A,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2))) => k1_fdiff_1(k2_fdiff_9,A) = k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k18_sin_cos,A),k1_square_1(k1_funct_1(k16_sin_cos,A)))) ) ) )).
fof(t8_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ~ ( k1_rltopsp1(k15_euclid(A),B,C) = k1_rltopsp1(k15_euclid(A),D,E) & ~ ( B = D & C = E ) & ~ ( B = E & C = D ) ) ) ) ) ) ) )).
fof(t8_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ~ ( ~ v1_xboole_0(A) & ~ v1_xboole_0(B) & k2_topreal1(2,k8_finseq_1(u1_struct_0(k15_euclid(2)),A,B),k3_finseq_1(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)) ) ) ) )).
fof(t8_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => k3_topreal1(2,k3_finseq_4(u1_struct_0(k15_euclid(2)),A,B,C)) = k4_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),A,B),k1_rltopsp1(k15_euclid(2),B,C)) ) ) ) )).
fof(t8_sprect_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t8_sprect_3,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( v3_pre_topc(A,k15_euclid(2)) & r3_connsp_1(k15_euclid(2),A,B) ) => v3_pre_topc(B,k15_euclid(2)) ) ) ) )).
fof(t8_sprect_5,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(B,k10_xtuple_0(A)) => ( r1_xxreal_0(k4_finseq_4(A,B),1) | k4_finseq_4(k1_finseq_6(u1_struct_0(k15_euclid(2)),A,B),k7_partfun1(u1_struct_0(k15_euclid(2)),A,1)) = k6_xcmplx_0(k1_nat_1(k3_finseq_1(A),1),k4_finseq_4(A,B)) ) ) ) ) )).
fof(t8_square_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k3_xcmplx_0(k6_xcmplx_0(A,B),k2_xcmplx_0(A,B)) = k6_xcmplx_0(k1_square_1(A),k1_square_1(B)) ) ) )).
fof(t8_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k9_stacks_1(A,k7_stacks_1(A,B,C)) = k1_stacks_1(u1_struct_0(A),k12_finseq_1(u1_struct_0(A),C),k9_stacks_1(A,B)) ) ) ) )).
fof(t8_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => m1_subset_1(A,k1_zfmisc_1(k4_ordinal1)) ) )).
fof(t8_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [D] : ( ( v5_relat_1(D,k3_qc_lang1(A)) & v3_card_1(D,B) & m2_finseq_1(D,k2_qc_lang1(A)) ) => ! [E] : ( m1_subset_1(E,k1_substut1(A)) => k39_substut1(A,k4_sublemma(B,A,C,D,E)) = k10_qc_lang1(A,C,k3_substut1(A,D,E)) ) ) ) ) ) )).
fof(t8_subset_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( ! [E] : ( m1_subset_1(E,A) => ( r2_hidden(E,B) <=> ~ ( r2_hidden(E,C) <=> r2_hidden(E,D) ) ) ) => B = k5_subset_1(A,C,D) ) ) ) ) )).
fof(t8_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => r1_tarski(k3_substlat(A,B,C),C) ) )).
fof(t8_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k16_substut1(A)) => ? [C] : ( m1_subset_1(C,k9_qc_lang1(A)) & ? [D] : ( m1_subset_1(D,k1_substut1(A)) & B = k1_domain_1(k9_qc_lang1(A),k1_substut1(A),C,D) ) ) ) ) )).
fof(t8_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k1_substut1(A)) => ( ~ r2_hidden(C,k10_xtuple_0(k7_substut1(A,C,k11_cqc_lang(A,C,B),D))) => k35_substut1(A,k1_substut2(A,k11_cqc_lang(A,C,B),D)) = C ) ) ) ) ) )).
fof(t8_supinf_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_setfam_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k6_numbers))) ) => ! [B] : ( v2_membered(B) => ( B = k5_setfam_1(k6_numbers,A) => m2_xxreal_2(k2_xxreal_2(k6_supinf_1(A)),B) ) ) ) )).
fof(t8_supinf_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => r1_xxreal_0(k3_supinf_2(k7_supinf_2(A),k7_supinf_2(B)),k7_supinf_2(k5_supinf_2(A,B))) ) ) )).
fof(t8_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( r1_orders_2(B,E,D) & r1_orders_2(B,F,C) ) => ( r1_orders_2(B,E,C) | r1_orders_2(B,F,D) | ( ~ r1_orders_2(B,k3_rlvect_1(B,E,F),C) & ~ r1_orders_2(B,k3_rlvect_1(B,E,F),D) ) ) ) ) ) ) ) ) ) )).
fof(t8_sysrel,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v1_relat_1(D) => ( r1_tarski(D,k2_zfmisc_1(A,B)) => ( k5_relat_1(D,C) = k3_xboole_0(D,k2_zfmisc_1(C,B)) & k6_relat_1(C,D) = k3_xboole_0(D,k2_zfmisc_1(A,C)) ) ) ) )).
fof(t8_t_0topsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => v1_t_0topsp(k4_t_0topsp(A),A,k3_t_0topsp(A)) ) )).
fof(t8_taxonom1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( r1_relat_2(B,A) => r8_relat_2(k18_finseq_1(B),A) ) ) )).
fof(t8_taxonom2,axiom,( v4_taxonom2(k1_tarski(k1_xboole_0)) )).
fof(t8_taylor_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => k6_prepower(k23_sin_cos(B),A) = k23_sin_cos(k3_xcmplx_0(A,B)) ) ) )).
fof(t8_taylor_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(B,k5_numbers) => k3_funct_2(k4_ordinal1,k1_numbers,k1_taylor_2(k22_sin_cos,k2_rcomp_1(k4_xcmplx_0(B),B),C),A) = k7_xcmplx_0(k1_newton(C,A),k2_newton(A)) ) ) ) ) )).
fof(t8_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ( v1_compts_1(k3_pcomps_1(A)) => v4_tbsp_1(A) ) ) )).
fof(t8_tdgroup,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_tdgroup(A,B,C,D,D) => B = C ) ) ) ) ) )).
fof(t8_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k1_tops_1(A,k9_subset_1(u1_struct_0(A),B,k2_pre_topc(A,k3_subset_1(u1_struct_0(A),B)))) = k1_struct_0(A) ) ) )).
fof(t8_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => k1_pcomps_1(A,B) = k1_pcomps_1(A,k1_pcomps_1(A,B)) ) ) )).
fof(t8_tdlat_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v4_tops_1(B,A) & r1_tarski(k2_pre_topc(A,k1_tops_1(A,B)),k1_tops_1(A,k2_pre_topc(A,B))) ) => ( v3_pre_topc(B,A) & v4_pre_topc(B,A) ) ) ) ) )).
fof(t8_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( 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,D,E) ) => r1_termord(A,B,C,E) ) ) ) ) ) ) )).
fof(t8_tex_1,axiom,( ! [A] : ( ( v13_struct_0(A,1) & l1_pre_topc(A) ) => ( v3_tdlat_3(A) => ( v1_xboole_0(u1_pre_topc(A)) | v2_pre_topc(A) ) ) ) )).
fof(t8_tex_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = u1_struct_0(B) => ( v1_subset_1(C,u1_struct_0(A)) <=> v1_tex_2(B,A) ) ) ) ) ) )).
fof(t8_tex_3,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_tex_2(B,A) & m1_pre_topc(B,A) ) => ? [C] : ( ~ v2_struct_0(C) & v1_pre_topc(C) & v1_tex_2(C,A) & m1_pre_topc(C,A) & r4_tsep_2(A,B,C) ) ) ) )).
fof(t8_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v2_tex_4(B,A) => ( k6_setfam_1(u1_struct_0(A),B) = k1_xboole_0 | v1_tex_4(k5_setfam_1(u1_struct_0(A),B),A) ) ) ) ) )).
fof(t8_tietze,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v2_xxreal_0(B) & v1_xreal_0(B) ) => ! [C] : ( ( v2_xxreal_0(C) & v1_xreal_0(C) ) => ( ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k1_funct_1(A,D),k3_funct_2(k4_ordinal1,k1_numbers,A,k1_nat_1(D,1)))),k3_xcmplx_0(B,k2_power(C,D))) ) => ( r1_xxreal_0(1,C) | ( r1_xxreal_0(k6_xcmplx_0(k3_funct_2(k4_ordinal1,k1_numbers,A,k5_numbers),k7_xcmplx_0(B,k6_xcmplx_0(1,C))),k1_seq_2(A)) & r1_xxreal_0(k1_seq_2(A),k2_xcmplx_0(k3_funct_2(k4_ordinal1,k1_numbers,A,k5_numbers),k7_xcmplx_0(B,k6_xcmplx_0(1,C)))) ) ) ) ) ) ) )).
fof(t8_tmap_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v2_pre_topc(C) & l1_pre_topc(C) ) => ( C = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) => ( ( v1_borsuk_1(B,A) & m1_pre_topc(B,A) ) <=> ( v1_borsuk_1(C,A) & m1_pre_topc(C,A) ) ) ) ) ) ) )).
fof(t8_toler_1,axiom,( ! [A] : ! [B] : ( ( 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_relat_2(B,A) ) )).
fof(t8_topalg_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v3_valued_0(C) ) => k10_rvsum_1(C,k6_xcmplx_0(A,B)) = k8_rvsum_1(k10_rvsum_1(C,A),k10_rvsum_1(C,B)) ) ) ) )).
fof(t8_topalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_topalg_2(A) & m1_pre_topc(A,k2_topalg_2) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_tarski(k1_rcomp_1(B,C),u1_struct_0(A)) ) ) ) )).
fof(t8_topalg_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v1_connsp_1(g1_pre_topc(u1_struct_0(A),u1_pre_topc(A))) => v1_connsp_1(A) ) ) )).
fof(t8_topalg_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( k9_xtuple_0(A) = k9_xtuple_0(B) => k12_mcart_1(k13_funct_3(A,B)) = B ) ) ) )).
fof(t8_topalg_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_connsp_2(E,A,C) => ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & C = D ) => m1_connsp_2(E,B,D) ) ) ) ) ) ) )).
fof(t8_topalg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v7_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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)) ) ) ) )).
fof(t8_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ r1_xxreal_0(k5_card_1(B),k2_topdim_1(A,B)) ) ) )).
fof(t8_topdim_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( v2_pre_topc(B) & v3_pcomps_1(B) & l1_pre_topc(B) ) => ( v5_waybel23(B) => ( ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(B)))) ) => ~ ( m1_setfam_1(C,u1_struct_0(B)) & v2_topdim_1(C,B) & r1_xxreal_0(k3_topdim_1(B,C),k5_numbers) & r1_xxreal_0(k5_card_1(C),k1_xxreal_3(A,1)) ) ) | ( v3_topdim_1(B) & r1_xxreal_0(k4_topdim_1(B),A) ) ) ) ) ) )).
fof(t8_topgen_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( 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)) ) ) )).
fof(t8_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ! [E] : ~ ( r2_hidden(D,C) & r2_hidden(E,C) & ! [F] : ( ( v3_pre_topc(F,A) & m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( r2_hidden(F,C) & r1_tarski(F,k3_xboole_0(D,E)) ) ) ) ) ) ) )).
fof(t8_topgen_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( ( u1_struct_0(A) = u1_struct_0(B) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( C = D => k2_pre_topc(A,C) = k2_pre_topc(B,D) ) ) ) ) => u1_pre_topc(A) = u1_pre_topc(B) ) ) ) )).
fof(t8_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_connsp_1(A,B,C) => 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)) ) ) ) ) )).
fof(t8_topgen_5,axiom,( ! [A] : ! [B] : ( r2_tarski(k4_card_3(k10_finseq_1(A,B)),k2_zfmisc_1(A,B)) & k1_card_1(k4_card_3(k10_finseq_1(A,B))) = k2_card_2(k1_card_1(A),k1_card_1(B)) ) )).
fof(t8_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t8_topmetr,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v2_struct_0(B) & m1_topmetr(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => m1_subset_1(C,u1_struct_0(A)) ) ) ) )).
fof(t8_topmetr3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(k2_topmetr(A,B))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k2_topmetr(A,B))))) ) => ( ( r1_funct_2(k4_ordinal1,u1_struct_0(k2_topmetr(A,B)),k4_ordinal1,k1_numbers,D,C) & r1_xxreal_0(A,B) & v2_comseq_2(C) ) => ( v2_tbsp_1(D,k2_topmetr(A,B)) & k1_seq_2(C) = k1_tbsp_1(k2_topmetr(A,B),D) ) ) ) ) ) ) )).
fof(t8_topreal1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ( r2_hidden(B,k1_rltopsp1(k15_euclid(A),C,D)) => k9_subset_1(u1_struct_0(k15_euclid(A)),k1_rltopsp1(k15_euclid(A),C,B),k1_rltopsp1(k15_euclid(A),B,D)) = k1_tarski(B) ) ) ) ) ) )).
fof(t8_topreal3,axiom,( ! [A] : ( v7_ordinal1(A) => u1_struct_0(k15_euclid(A)) = u1_struct_0(k14_euclid(A)) ) )).
fof(t8_topreal4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(2))) => ( ( r2_hidden(A,k8_metric_1(k14_euclid(2),E,D)) & r2_hidden(B,k8_metric_1(k14_euclid(2),E,D)) & r2_hidden(k19_euclid(k17_euclid(A),k18_euclid(B)),k8_metric_1(k14_euclid(2),E,D)) & C = k3_finseq_4(u1_struct_0(k15_euclid(2)),A,k19_euclid(k17_euclid(A),k18_euclid(B)),B) ) => ( k17_euclid(A) = k17_euclid(B) | k18_euclid(A) = k18_euclid(B) | ( v4_topreal1(C) & 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 & r1_topreal4(k3_topreal1(2,C),A,B) & r1_tarski(k3_topreal1(2,C),k8_metric_1(k14_euclid(2),E,D)) ) ) ) ) ) ) ) ) )).
fof(t8_topreal5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(k5_numbers,k3_xcmplx_0(D,E)) & D = k1_funct_1(C,A) & E = k1_funct_1(C,B) & ! [F] : ( v1_xreal_0(F) => ~ ( k1_funct_1(C,F) = k5_numbers & ~ r1_xxreal_0(F,A) & ~ r1_xxreal_0(B,F) ) ) ) ) ) ) ) ) )).
fof(t8_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(C,B) => ( A = k5_numbers | k19_rvsum_1(k2_finseq_2(k7_nat_d(B,C),A)) = k7_xcmplx_0(k19_rvsum_1(k2_finseq_2(B,A)),k19_rvsum_1(k2_finseq_2(C,A))) ) ) ) ) ) )).
fof(t8_topreal7,axiom,( ! [A] : ( 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)) ) ) )).
fof(t8_topreal8,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( r2_hidden(C,k10_xtuple_0(A)) => k4_finseq_4(A,C) = k4_finseq_4(k3_graph_2(A,B),C) ) ) ) )).
fof(t8_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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)) ) ) ) ) )).
fof(t8_topreala,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( ( 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] : ( ( 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) => v5_pre_topc(F,k1_pre_topc(A,C),k1_pre_topc(B,D)) ) ) ) ) ) ) ) )).
fof(t8_toprealb,axiom,( ! [A] : ( ( 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_funct_1(A) & v1_funct_2(A,u1_struct_0(k2_topalg_2),u1_struct_0(k2_topalg_2)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_topalg_2),u1_struct_0(k2_topalg_2)))) ) ) )).
fof(t8_toprealc,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( 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)) ) ) ) )).
fof(t8_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => k5_toprns_1(A,k2_toprns_1(B,A,C)) = k26_valued_1(k4_ordinal1,k1_numbers,k5_toprns_1(A,C),k9_complex1(B)) ) ) ) )).
fof(t8_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t8_tops_2,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( 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) ) ) ) )).
fof(t8_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( k4_subset_1(u1_struct_0(A),B,k2_pre_topc(A,k1_tops_1(A,B))) = u1_struct_0(A) => k2_pre_topc(A,k1_tops_1(A,B)) = u1_struct_0(A) ) ) ) )).
fof(t8_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( ( 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] : ( ( 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,k2_transgeo(A,B,k1_transgeo(A,D,C)),k2_transgeo(A,k2_transgeo(A,B,D),C)) ) ) ) ) )).
fof(t8_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( 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 ) ) ) => v11_aff_2(A) ) ) )).
fof(t8_treal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_topmetr(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_topmetr(A,B))) => v5_pre_topc(k3_treal_1(A,B,C,D),k4_topmetr(k5_numbers,1),k4_topmetr(A,B)) ) ) ) ) ) )).
fof(t8_trees_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ( r2_xboole_0(B,k7_finseq_1(C,k9_finseq_1(A))) => r1_tarski(B,C) ) ) ) )).
fof(t8_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_trees_1(C) ) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ! [E] : ( m2_finseq_1(E,k4_ordinal1) => ( ( r2_hidden(D,A) & r2_hidden(E,A) ) => ( r3_xboole_0(D,E) | k5_trees_1(k5_trees_1(A,D,B),E,C) = k5_trees_1(k5_trees_1(A,E,C),D,B) ) ) ) ) ) ) ) )).
fof(t8_trees_3,axiom,( ! [A] : ! [B] : ( v2_trees_3(A) => ( v2_trees_3(k3_xboole_0(A,B)) & v2_trees_3(k3_xboole_0(B,A)) & v2_trees_3(k6_subset_1(A,B)) ) ) )).
fof(t8_trees_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(A,B) => k4_trees_1(k2_trees_1(A),k14_trees_3(B)) = k2_trees_1(k5_numbers) ) ) ) )).
fof(t8_trees_9,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) & v3_trees_9(A) ) => ? [B] : ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v6_trees_3(C) & A = k4_trees_4(B,C) ) ) )).
fof(t8_trees_a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( m4_trees_1(C,A) => ! [D] : ( m2_finseq_1(D,k4_ordinal1) => ( r2_hidden(D,C) => B = k4_trees_1(k1_trees_a(A,B,C),D) ) ) ) ) ) )).
fof(t8_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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 ) => ( v4_pre_topc(E,B) <=> v4_pre_topc(D,A) ) ) ) ) ) ) ) )).
fof(t8_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( r2_tsep_2(A,C,B) & r2_tsep_2(A,B,D) ) => C = D ) ) ) ) ) )).
fof(t8_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_tsp_1(B,A) & v1_tsp_1(C,A) ) => ( ( ~ v4_pre_topc(B,A) & ~ v4_pre_topc(C,A) ) | v1_tsp_1(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ) )).
fof(t8_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_tsp_2(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => k1_tops_1(A,C) = k3_tex_4(A,k9_subset_1(u1_struct_0(A),B,k1_tops_1(A,C))) ) ) ) ) )).
fof(t8_turing_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( l1_turing_1(B) => ! [C] : ( m1_subset_1(C,k3_zfmisc_1(u2_turing_1(B),k4_numbers,k9_funct_2(k4_numbers,u1_turing_1(B)))) => k9_nat_1(k3_zfmisc_1(u2_turing_1(B),k4_numbers,k9_funct_2(k4_numbers,u1_turing_1(B))),k10_turing_1(B,C),k1_nat_1(A,1)) = k9_turing_1(B,k9_nat_1(k3_zfmisc_1(u2_turing_1(B),k4_numbers,k9_funct_2(k4_numbers,u1_turing_1(B))),k10_turing_1(B,C),A)) ) ) ) )).
fof(t8_twoscomp,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( m1_subset_1(B,k6_margrel1) => k1_funct_1(k16_twoscomp,k10_finseq_1(A,B)) = k1_funct_1(k14_twoscomp,k10_finseq_1(A,B)) ) ) )).
fof(t8_unialg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => m1_unialg_2(A,A) ) )).
fof(t8_unialg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( v1_unialg_1(B) & m1_unialg_2(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k1_funct_1(k3_unialg_3(A),B)) <=> r1_struct_0(B,C) ) ) ) ) )).
fof(t8_uniform1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k2_topmetr(k5_numbers,1)),u1_struct_0(k14_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k2_topmetr(k5_numbers,1)),u1_struct_0(k14_euclid(A))))) ) => ( ( v5_pre_topc(B,k5_topmetr,k15_euclid(A)) & r1_funct_2(u1_struct_0(k2_topmetr(k5_numbers,1)),u1_struct_0(k14_euclid(A)),u1_struct_0(k5_topmetr),u1_struct_0(k15_euclid(A)),C,B) ) => v1_uniform1(C,k2_topmetr(k5_numbers,1),k14_euclid(A)) ) ) ) ) )).
fof(t8_uniroots,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k1_group_1(k1_complfld) = k2_binop_1(u1_struct_0(k1_complfld),k4_ordinal1,u1_struct_0(k1_complfld),k4_group_1(k1_complfld),k1_group_1(k1_complfld),A) ) )).
fof(t8_uproots,axiom,( ! [A] : ! [B] : ( ( 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) ) => ( r6_pboole(A,B,k16_pre_poly(A)) => k2_uproots(A,B) = k5_numbers ) ) )).
fof(t8_urysohn1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(k5_numbers,B) => ( r1_xxreal_0(k1_newton(2,A),B) | r2_hidden(k7_xcmplx_0(k1_nat_1(k2_nat_1(B,2),1),k11_newton(2,k1_nat_1(A,1))),k7_subset_1(k1_numbers,k1_urysohn1(k1_nat_1(A,1)),k1_urysohn1(A))) ) ) ) ) )).
fof(t8_urysohn2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ( v2_measure5(A) => ( B = k5_numbers | v2_measure5(k1_integra2(A,B)) ) ) ) ) )).
fof(t8_urysohn3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v10_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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] : ( m2_urysohn3(D,A,B,C) => ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,k2_urysohn1) => ! [F] : ( v7_ordinal1(F) => k1_funct_1(k2_urysohn3(k2_urysohn1,k9_setfam_1(u1_struct_0(A)),D,k3_urysohn3(E)),E) = k1_funct_1(k2_urysohn3(k2_urysohn1,k9_setfam_1(u1_struct_0(A)),D,k2_xcmplx_0(k3_urysohn3(E),F)),E) ) ) ) ) ) ) ) ) ) )).
fof(t8_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_funct_2(D,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ! [E] : ( ( v5_relat_1(E,k3_qc_lang1(A)) & v3_card_1(E,B) & m2_finseq_1(E,k2_qc_lang1(A)) ) => ! [F] : ( m2_subset_1(F,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [G] : ( m1_valuat_1(G,A,C) => ! [H] : ( m2_subset_1(H,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [I] : ( m1_subset_1(I,k3_margrel1(C)) => ( ( F = k4_cqc_lang(B,A,H,E) & r1_margrel1(C,I,k7_valuat_1(A,C,B,G,H)) ) => ( ~ r2_hidden(k4_valuat_1(A,C,B,E,D),I) <=> k3_funct_2(k2_valuat_1(A,C),k6_margrel1,k8_valuat_1(A,C,G,F),D) = k7_margrel1 ) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_valued_0(A) <=> ! [B] : v1_xxreal_0(k1_funct_1(A,B)) ) ) )).
fof(t8_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ( k9_xtuple_0(k30_valued_1(A)) = k9_xtuple_0(A) & ! [B] : k1_funct_1(k30_valued_1(A),B) = k4_xcmplx_0(k1_funct_1(A,B)) ) ) )).
fof(t8_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_valued_0(C) ) => ( k13_valued_1(C,A) = k13_valued_1(C,B) => ( C = k1_xboole_0 | A = B ) ) ) ) ) )).
fof(t8_vectmetr,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_vectmetr(A))) => ! [C] : ( ( 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) ) ) ) ) )).
fof(t8_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( r1_vectsp_5(A,B,C,D) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ( k4_vectsp_5(A,B,E,C,D) = k1_domain_1(u1_struct_0(B),u1_struct_0(B),F,G) => k4_vectsp_5(A,B,E,D,C) = k1_domain_1(u1_struct_0(B),u1_struct_0(B),G,F) ) ) ) ) ) ) ) ) ) )).
fof(t8_vectsp11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(B)) & v1_polynom1(D,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(B)))) & k1_algseq_1(B,D) = k1_nat_1(A,1) & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => k2_polynom4(B,D,E) = k12_matrix_3(A,B,k5_matrlin2(A,A,B,C,k2_matrix13(A,A,B,k3_matrix_1(B,A),E))) ) ) ) ) ) )).
fof(t8_vectsp_1,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t8_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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 ) ) ) ) ) ) )).
fof(t8_vectsp_4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m1_vectsp_4(D,B,C) => ! [E] : ( m1_vectsp_4(E,B,C) => ( ( r1_struct_0(D,A) & m1_vectsp_4(D,B,E) ) => r1_struct_0(E,A) ) ) ) ) ) )).
fof(t8_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( ( v7_vectsp_1(D,A) & m1_vectsp_4(D,A,B) ) => ( m1_vectsp_4(C,A,D) <=> k1_vectsp_5(A,B,C,D) = D ) ) ) ) ) )).
fof(t8_vectsp_6,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(C)) => ! [F] : ( ( 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)))) ) => ( ( r2_hidden(A,k9_xtuple_0(E)) & D = k1_funct_1(E,A) ) => k1_funct_1(k3_vectsp_6(B,C,E,F),A) = k4_vectsp_1(B,C,k3_funct_2(u1_struct_0(C),u1_struct_0(B),F,D),D) ) ) ) ) ) ) ) )).
fof(t8_vectsp_7,axiom,( ! [A] : ! [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] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) => ( r2_hidden(A,D) => r1_struct_0(k1_vectsp_7(B,C,D),A) ) ) ) ) )).
fof(t8_vectsp_8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k1_vectsp_8(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_vectsp_8(A,B))) => ! [E] : ( m1_vectsp_4(E,A,B) => ! [F] : ( m1_vectsp_4(F,A,B) => ( ( C = E & D = F ) => k4_lattices(k1_vectsp_8(A,B),C,D) = k2_vectsp_5(A,B,E,F) ) ) ) ) ) ) ) )).
fof(t8_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_6(D,A,C) => ? [E] : ( m1_vectsp_6(E,A,B) & k1_vectsp_6(A,C,D) = k1_vectsp_6(A,B,E) & k4_vectsp_6(A,C,D) = k4_vectsp_6(A,B,E) ) ) ) ) ) )).
fof(t8_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ( ( 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,E,k6_vfunct_1(A,B,C,D)),k6_vfunct_1(A,B,k3_vfunct_1(A,B,E,C),k3_vfunct_1(A,B,E,D))) ) ) ) ) ) )).
fof(t8_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [E] : ( ( 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,E,k3_vfunct_2(A,B,C,D)),k3_vfunct_2(A,B,k1_vfunct_2(A,B,E,C),k1_vfunct_2(A,B,E,D))) ) ) ) ) ) )).
fof(t8_waybel10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_yellow_0(C,A) ) => ! [D] : ( ( 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] : ( ( 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)))) ) => ( ( v2_funct_1(D) & E = k2_funct_1(D) ) => ( v1_funct_1(k2_tmap_1(B,A,E,k1_yellow_2(C,B,k2_tmap_1(A,B,D,C)))) & v1_funct_2(k2_tmap_1(B,A,E,k1_yellow_2(C,B,k2_tmap_1(A,B,D,C))),u1_struct_0(k1_yellow_2(C,B,k2_tmap_1(A,B,D,C))),u1_struct_0(C)) & m1_subset_1(k2_tmap_1(B,A,E,k1_yellow_2(C,B,k2_tmap_1(A,B,D,C))),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k1_yellow_2(C,B,k2_tmap_1(A,B,D,C))),u1_struct_0(C)))) & k2_tmap_1(B,A,E,k1_yellow_2(C,B,k2_tmap_1(A,B,D,C))) = k2_funct_1(k2_tmap_1(A,B,D,C)) ) ) ) ) ) ) ) )).
fof(t8_waybel11,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => v2_waybel11(k5_waybel_0(A,B),A) ) ) )).
fof(t8_waybel12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v2_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v13_waybel_0(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => r2_hidden(k4_yellow_0(A),B) ) ) )).
fof(t8_waybel13,axiom,( ! [A] : ( ( 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(k1_yellow_1(k7_waybel_0(A))) & v4_yellow_0(k1_yellow_1(k7_waybel_0(A)),k2_yellow_1(u1_struct_0(A))) & v7_yellow_0(k1_yellow_1(k7_waybel_0(A)),k2_yellow_1(u1_struct_0(A))) & v4_waybel_0(k1_yellow_1(k7_waybel_0(A)),k2_yellow_1(u1_struct_0(A))) & m1_yellow_0(k1_yellow_1(k7_waybel_0(A)),k2_yellow_1(u1_struct_0(A))) ) ) )).
fof(t8_waybel14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_waybel_3(A,B,C) <=> r1_tarski(k5_waybel_0(A,B),k1_waybel_3(A,C)) ) ) ) ) )).
fof(t8_waybel15,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => k7_relset_1(u1_struct_0(A),u1_struct_0(B),C,k1_waybel_3(A,D)) = k1_waybel_3(B,k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,D)) ) ) ) ) ) )).
fof(t8_waybel16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => k7_waybel_0(A) = k8_waybel_0(k7_lattice3(A)) ) )).
fof(t8_waybel17,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ( 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)))) ) => k1_waybel11(B,k6_waybel_9(A,B,E,k3_waybel17(A,C,D))) = k12_lattice3(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)) ) ) ) ) ) )).
fof(t8_waybel18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( v2_waybel18(A) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ( r1_borsuk_1(A,B) => v2_waybel18(B) ) ) ) ) )).
fof(t8_waybel19,axiom,( ! [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) & v1_waybel19(A) & l1_waybel_9(A) ) => ! [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) & v1_waybel19(B) & l1_waybel_9(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => r3_waybel_0(A,B,C,D) ) => v5_pre_topc(C,A,B) ) ) ) ) )).
fof(t8_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(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))) ) ) ) ) )).
fof(t8_waybel21,axiom,( ! [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] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & v7_yellow_0(B,A) & m1_yellow_0(B,A) ) => v17_waybel_0(k1_yellow_9(A,B),B,A) ) ) )).
fof(t8_waybel22,axiom,( ! [A] : ( ( ~ 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] : ( r1_waybel22(A,B) => ! [C] : ( m1_waybel16(C,A,A) => ( k2_partfun1(u1_struct_0(A),u1_struct_0(A),C,B) = k6_partfun1(B) => r2_funct_2(u1_struct_0(A),u1_struct_0(A),C,k3_struct_0(A)) ) ) ) ) )).
fof(t8_waybel23,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k4_waybel_0(A,k4_waybel_0(A,B)) = k4_waybel_0(A,B) ) ) )).
fof(t8_waybel24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(C),k2_waybel24(A,B,C,D,E),F) = k1_binop_1(D,F,E) ) ) ) ) ) ) )).
fof(t8_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( ~ 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)) & r1_waybel18(A,C) ) => r1_waybel18(B,D) ) ) ) ) ) )).
fof(t8_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( 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(k3_waybel26(A,B,C,D),k1_waybel26(A,B),k1_waybel26(A,C)) ) ) ) ) )).
fof(t8_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_orders_2(B) ) => ! [C] : ( ( 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)) & v7_waybel_0(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C)) & l1_waybel_0(g1_waybel_0(A,u1_struct_0(B),u1_orders_2(B),C),A) ) ) ) ) )).
fof(t8_waybel29,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ v1_xboole_0(C) & v1_waybel_0(C,k3_waybel24(A,B)) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_waybel24(A,B)))) ) => ( v1_funct_1(k1_yellow_0(k5_yellow_1(u1_struct_0(A),B),C)) & v1_funct_2(k1_yellow_0(k5_yellow_1(u1_struct_0(A),B),C),u1_struct_0(A),u1_struct_0(B)) & v5_pre_topc(k1_yellow_0(k5_yellow_1(u1_struct_0(A),B),C),A,B) & m1_subset_1(k1_yellow_0(k5_yellow_1(u1_struct_0(A),B),C),k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) ) ) ) )).
fof(t8_waybel30,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => r1_tarski(k5_waybel11(A),a_1_0_waybel30(A)) ) )).
fof(t8_waybel31,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v6_pre_topc(A) & l1_pre_topc(A) ) => ( v8_struct_0(A) => k2_waybel23(A) = k1_card_1(u1_struct_0(A)) ) ) )).
fof(t8_waybel32,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & v25_waybel_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => r3_orders_2(A,k2_yellow_0(A,B),C) ) ) ) ) )).
fof(t8_waybel33,axiom,( ! [A] : ( ( 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] : ( ( 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)) => k13_yellow_6(A,k3_waybel28(A)) = k13_yellow_6(B,k3_waybel28(B)) ) ) ) )).
fof(t8_waybel34,axiom,( ! [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] : ( ( 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] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v17_waybel_0(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & v17_waybel_0(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(C),u1_struct_0(A),k1_waybel34(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),k1_waybel34(B,C,E),k1_waybel34(A,B,D))) ) ) ) ) ) )).
fof(t8_waybel35,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & m1_waybel35(C,A,B) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(C)) => ( ( r1_yellow_0(A,D) & v2_waybel35(C,A,B) ) => r1_yellow_0(k5_yellow_0(A,C),D) ) ) ) ) ) )).
fof(t8_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ! [D] : ( r1_tarski(C,D) => ( ( r1_waybel_0(A,B,C) => r1_waybel_0(A,B,D) ) & ( r2_waybel_0(A,B,C) => r2_waybel_0(A,B,D) ) ) ) ) ) )).
fof(t8_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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) & v5_orders_3(D,B,A) & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( r3_orders_2(B,E,k3_funct_2(u1_struct_0(A),u1_struct_0(B),C,F)) <=> r3_orders_2(A,k3_funct_2(u1_struct_0(B),u1_struct_0(A),D,E),F) ) ) ) ) ) ) ) ) ) )).
fof(t8_waybel_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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)))) ) => r1_yellow_0(A,a_2_1_waybel_2(A,B)) ) ) )).
fof(t8_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(B,k2_waybel_3(A,C)) <=> r1_waybel_3(A,C,B) ) ) ) ) )).
fof(t8_waybel_4,axiom,( ! [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] : ( ( v3_waybel_4(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ( ( v3_waybel_4(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ( v3_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)))) ) ) ) ) )).
fof(t8_waybel_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(B,k1_relset_1(k4_card_3(k1_funct_6(A)),k2_pralg_2(A))) => ( k9_xtuple_0(B) = k9_xtuple_0(A) & k9_xtuple_0(A) = k9_xtuple_0(k1_funct_1(k2_pralg_2(A),B)) ) ) ) ) )).
fof(t8_waybel_6,axiom,( ! [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) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r1_waybel_3(A,B,C) & ! [D] : ( ( ~ v1_xboole_0(D) & v2_waybel_0(D,A) & v13_waybel_0(D,A) & v1_waybel_6(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( r2_hidden(C,D) & r1_tarski(D,k2_waybel_3(A,B)) ) ) ) ) ) ) )).
fof(t8_waybel_7,axiom,( ! [A] : ! [B] : ( ( v12_waybel_0(B,k2_yellow_1(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(A)))) ) => ( v1_waybel_0(B,k2_yellow_1(A)) <=> ! [C] : ! [D] : ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k2_xboole_0(C,D),B) ) ) ) )).
fof(t8_waybel_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( C = E & D = F & r1_waybel_3(A,C,D) ) => r1_waybel_3(B,E,F) ) ) ) ) ) ) ) ) )).
fof(t8_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => r1_waybel_0(A,B,k2_relset_1(u1_struct_0(A),u1_waybel_0(A,B))) ) ) )).
fof(t8_weddwitt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k6_algstr_0(A,B,C) = k6_algstr_0(A,C,B) <=> m1_subset_1(C,u1_struct_0(k1_weddwitt(A,B))) ) ) ) ) )).
fof(t8_weierstr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( v2_compts_1(D,A) & v5_pre_topc(C,A,B) ) => v2_compts_1(k7_relset_1(u1_struct_0(A),u1_struct_0(B),C,D),B) ) ) ) ) ) )).
fof(t8_wellfnd1,axiom,( ! [A] : ( l1_orders_2(A) => ( v1_wellfnd1(A) <=> k1_wellfnd1(A) = u1_struct_0(A) ) ) )).
fof(t8_wellord2,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => ( r1_tarski(A,B) => r1_ordinal1(k2_wellord2(k1_wellord2(A)),B) ) ) )).
fof(t8_wsierp_1,axiom,( ! [A] : ( v1_int_1(A) => ( k3_int_2(k5_numbers,A) = k1_int_2(A) & k3_int_2(1,A) = 1 ) ) )).
fof(t8_xboole_0,axiom,( ! [A] : ! [B] : ~ ( r2_xboole_0(A,B) & ! [C] : ~ ( r2_hidden(C,B) & r1_tarski(A,k4_xboole_0(B,k1_tarski(C))) ) ) )).
fof(t8_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r1_tarski(A,C) & r1_tarski(B,C) ) => r1_tarski(k2_xboole_0(A,B),C) ) )).
fof(t8_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k4_xboolean(A,k5_xboolean(B,C)) = k5_xboolean(k4_xboolean(A,B),k4_xboolean(A,C)) ) ) ) )).
fof(t8_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k3_xcmplx_0(A,k2_xcmplx_0(B,C)) = k2_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(A,C)) ) ) ) )).
fof(t8_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( 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)) ) ) ) ) ) )).
fof(t8_xregular,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ~ ( r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(C,D) & r2_hidden(D,A) ) )).
fof(t8_xtuple_0,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_tarski(k9_xtuple_0(A),k9_xtuple_0(B)) ) )).
fof(t8_xxreal_0,axiom,( ~ r2_hidden(k1_xxreal_0,k1_numbers) )).
fof(t8_xxreal_1,axiom,( ! [A] : ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ~ ( r2_hidden(A,k2_xxreal_1(B,C)) & ~ r2_hidden(A,k4_xxreal_1(B,C)) & A != B ) ) ) )).
fof(t8_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ! [C] : ( m1_xxreal_2(C,A) => ! [D] : ( m1_xxreal_2(D,B) => m1_xxreal_2(k4_xxreal_0(C,D),k2_xboole_0(A,B)) ) ) ) ) )).
fof(t8_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ( k1_xxreal_3(A,B) = k5_numbers => A = k2_xxreal_3(B) ) ) ) )).
fof(t8_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_yellow_3(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k3_yellow_3(A,B))) => ( r1_lattice3(k3_yellow_3(A,B),k7_domain_1(u1_struct_0(k3_yellow_3(A,B)),D,E),C) <=> ( r1_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)) & r1_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)) ) ) ) ) ) ) ) )).
fof(t8_yellow11,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r3_orders_2(A,B,D) => r3_orders_2(A,k13_lattice3(A,B,k12_lattice3(A,C,D)),k12_lattice3(A,k13_lattice3(A,B,C),D)) ) ) ) ) ) )).
fof(t8_yellow12,axiom,( ! [A] : ! [B] : k2_funct_1(k13_funct_3(k10_funct_3(A,B),k9_funct_3(A,B))) = k13_funct_3(k10_funct_3(B,A),k9_funct_3(B,A)) )).
fof(t8_yellow13,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => v2_funct_1(k3_yellow_2(A)) ) )).
fof(t8_yellow14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_waybel_9(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(k3_waybel24(A,B))) => ! [F] : ( m1_subset_1(F,u1_struct_0(k3_waybel24(A,B))) => ( ( E = C & F = D ) => ( r1_orders_2(k3_waybel24(A,B),E,F) <=> r1_yellow_2(u1_struct_0(A),B,C,D) ) ) ) ) ) ) ) ) )).
fof(t8_yellow15,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m2_finseq_1(D,k6_margrel1) => k3_finseq_1(k1_yellow15(A,k2_finseq_4(k1_zfmisc_1(A),B,C),D)) = 2 ) ) ) )).
fof(t8_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r1_yellow16(A,B,C) => r2_yellow16(A,B,C) ) ) ) ) )).
fof(t8_yellow17,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_waybel18(A,B))) => k1_funct_1(k6_waybel18(A,B,C),D) = k5_waybel18(A,B,D,C) ) ) ) ) )).
fof(t8_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l2_altcat_1(B) ) => ( r2_yellow18(A,B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( E = C & F = D ) => ! [G] : ( m1_subset_1(G,k1_altcat_1(A,C,D)) => m1_subset_1(G,k1_altcat_1(B,F,E)) ) ) ) ) ) ) ) ) ) )).
fof(t8_yellow19,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( m1_yellow19(C,A,B) => r1_waybel_0(A,B,C) ) ) ) )).
fof(t8_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ( v21_functor0(C,A,B) => ! [D] : ( ( v15_functor0(D,B,A) & m2_functor0(D,B,A) ) => ( ( ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k3_functor0(B,A,D,k3_functor0(A,B,C,E)) = E ) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( k1_altcat_1(A,E,F) != k1_xboole_0 => ! [G] : ( m1_subset_1(G,k1_altcat_1(A,E,F)) => k6_functor0(B,A,D,k3_functor0(A,B,C,E),k3_functor0(A,B,C,F),k6_functor0(A,B,C,E,F,G)) = G ) ) ) ) ) => g2_functor0(B,A,u1_functor0(B,A,D),u2_functor0(B,A,D)) = k15_functor0(A,B,C) ) ) ) ) ) ) )).
fof(t8_yellow21,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ( v2_yellow_0(A) <=> v5_yellow21(u1_orders_2(A)) ) ) )).
fof(t8_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r1_lattice3(A,k2_tarski(C,D),B) => ( r1_orders_2(A,B,C) & r1_orders_2(A,B,D) ) ) & ( ( r1_orders_2(A,B,C) & r1_orders_2(A,B,D) ) => r1_lattice3(A,k2_tarski(C,D),B) ) & ( r2_lattice3(A,k2_tarski(C,D),B) => ( r1_orders_2(A,C,B) & r1_orders_2(A,D,B) ) ) & ( ( r1_orders_2(A,C,B) & r1_orders_2(A,D,B) ) => r2_lattice3(A,k2_tarski(C,D),B) ) ) ) ) ) ) )).
fof(t8_yellow_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(A))) => ( r2_hidden(k2_xboole_0(B,C),A) => k10_lattice3(k1_yellow_1(A),B,C) = k2_xboole_0(B,C) ) ) ) ) )).
fof(t8_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & m1_yellow_0(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & v4_yellow_0(C,A) & m1_yellow_0(C,A) ) => ( r1_tarski(u1_struct_0(B),u1_struct_0(C)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(C))) => ( D = E => ( ( v2_waybel_0(D,B) => v2_waybel_0(E,C) ) & ( v1_waybel_0(D,B) => v1_waybel_0(E,C) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_yellow_3,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v2_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r3_waybel_0(A,B,C,k7_domain_1(u1_struct_0(A),D,E)) <=> 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)) ) ) ) ) ) ) )).
fof(t8_yellow_4,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( r2_yellow_4(A,C,B) & v13_waybel_0(C,A) ) => r1_tarski(B,C) ) ) ) ) )).
fof(t8_yellow_5,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r3_orders_2(A,B,C) => k13_lattice3(A,B,C) = C ) ) ) ) )).
fof(t8_yellow_6,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_waybel_0(B,A) => m1_yellow_6(B,A,B) ) ) )).
fof(t8_yellow_7,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( r1_lattice3(A,C,B) => r2_lattice3(k7_lattice3(A),C,k8_lattice3(A,B)) ) & ( r2_lattice3(k7_lattice3(A),C,k8_lattice3(A,B)) => r1_lattice3(A,C,B) ) & ( r2_lattice3(A,C,B) => r1_lattice3(k7_lattice3(A),C,k8_lattice3(A,B)) ) & ( r1_lattice3(k7_lattice3(A),C,k8_lattice3(A,B)) => r2_lattice3(A,C,B) ) ) ) ) )).
fof(t8_yellow_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( r1_tarski(C,B) & v4_pre_topc(B,A) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( r1_tarski(C,D) & v4_pre_topc(D,A) ) => r1_tarski(B,D) ) ) ) => B = k2_pre_topc(A,C) ) ) ) ) )).
fof(t8_yellow_9,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ( v2_struct_0(A) => u1_pre_topc(A) = k1_tarski(k1_xboole_0) ) ) )).
fof(t8_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ( v8_zf_fund1(B,A) => r1_tarski(k9_funct_2(C,k4_ordinal1),B) ) ) ) ) )).
fof(t8_zf_lang,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ( k16_zf_lang(A,B,C,D) = k8_zf_lang(A,k14_zf_lang(B,C,D)) & k17_zf_lang(A,B,C,D) = k13_zf_lang(A,k15_zf_lang(B,C,D)) ) ) ) ) ) )).
fof(t8_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ( k23_zf_lang(k8_zf_lang(B,A)) = B & k24_zf_lang(k8_zf_lang(B,A)) = A ) ) ) )).
fof(t8_zf_model,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ( v3_zf_lang(A) => ! [C] : ( ( 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(k3_funct_2(k1_zf_lang,B,C,k18_zf_lang(A)),k3_funct_2(k1_zf_lang,B,C,k19_zf_lang(A))) <=> r2_hidden(C,k5_zf_model(A,B)) ) ) ) ) ) )).
fof(t8_zf_refle,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) ) => ! [B] : ( v3_ordinal1(B) => ( v1_relat_1(k5_relat_1(A,k4_classes1(B))) & v5_ordinal1(k5_relat_1(A,k4_classes1(B))) & v1_funct_1(k5_relat_1(A,k4_classes1(B))) ) ) ) )).
fof(t8_zfmisc_1,axiom,( ! [A] : ! [B] : ( k2_xboole_0(k1_tarski(A),k1_tarski(B)) = k1_tarski(A) => A = B ) )).
fof(t8_zfmodel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_ordinal1(A) => ( r2_zf_model(A,k10_zf_model) <=> ! [B] : ( m1_subset_1(B,A) => r2_hidden(k3_xboole_0(A,k1_zfmisc_1(B)),A) ) ) ) ) )).
fof(t8_zfmodel2,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_subset_1(F,E) => ! [G] : ( m1_subset_1(G,E) => ! [H] : ( m1_subset_1(H,E) => ! [I] : ( m1_subset_1(I,E) => ! [J] : ( m1_subset_1(J,E) => ! [K] : ( ( v1_funct_1(K) & v1_funct_2(K,k1_zf_lang,E) & m1_subset_1(K,k1_zfmisc_1(k2_zfmisc_1(k1_zf_lang,E))) ) => ( r2_funct_2(k1_zf_lang,E,k2_zf_lang1(E,k2_zf_lang1(E,k2_zf_lang1(E,K,A,G),B,H),A,F),k2_zf_lang1(E,k2_zf_lang1(E,K,B,H),A,F)) & r2_funct_2(k1_zf_lang,E,k2_zf_lang1(E,k2_zf_lang1(E,k2_zf_lang1(E,k2_zf_lang1(E,K,A,G),B,H),C,I),A,F),k2_zf_lang1(E,k2_zf_lang1(E,k2_zf_lang1(E,K,B,H),C,I),A,F)) & r2_funct_2(k1_zf_lang,E,k2_zf_lang1(E,k2_zf_lang1(E,k2_zf_lang1(E,k2_zf_lang1(E,k2_zf_lang1(E,K,A,G),B,H),C,I),D,J),A,F),k2_zf_lang1(E,k2_zf_lang1(E,k2_zf_lang1(E,k2_zf_lang1(E,K,B,H),C,I),D,J),A,F)) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t8_zfrefle1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ( r2_zfrefle1(A,B) <=> ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k9_zf_lang)) => ( r1_zfrefle1(A,C) <=> r1_zfrefle1(B,C) ) ) ) ) ) )).
fof(t8_zmodul01,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k1_zmodul01(B,k5_algstr_0(B,C,D),A) = k5_algstr_0(B,k1_zmodul01(B,C,A),k1_zmodul01(B,D,A)) ) ) ) ) )).
fof(t8_zmodul02,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_zmodul02(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k3_funct_2(u1_struct_0(A),k4_numbers,B,C) = k5_numbers <=> ~ r2_hidden(C,k18_zmodul02(A,B)) ) ) ) ) )).
fof(t90_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_abcmiz_1(B,A) & m1_subset_1(B,u4_struct_0(A)) ) => ! [C] : ( 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)) => k45_abcmiz_1(A,k36_abcmiz_1(A,B,C)) = k3_tarski(a_2_3_abcmiz_1(A,C)) ) ) ) ) )).
fof(t90_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(k16_aofa_000(A,B,C),k9_aofa_000(A,k18_aofa_000(A),D)) & ! [E] : ( v7_ordinal1(E) => ~ ( D = k1_nat_1(E,1) & r2_hidden(B,k9_aofa_000(A,k18_aofa_000(A),E)) & r2_hidden(C,k9_aofa_000(A,k18_aofa_000(A),E)) ) ) ) ) ) ) ) )).
fof(t90_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & v22_aofa_a00(D,A,1,1,11) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( ( v19_aofa_a00(F,A) & m1_subset_1(F,u1_struct_0(A)) ) => ! [G] : ( m2_subset_1(G,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => ! [H] : ( v1_int_1(H) => k15_aofa_a00(A,B,C,D,F,k10_aofa_a01(A,B,C,F,H),G) = H ) ) ) ) ) ) ) ) )).
fof(t90_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( m1_subset_1(C,k5_arytm_3) => ~ ( ~ r3_arytm_3(k9_arytm_3(A,C),B) & C != k11_arytm_3 & ! [D] : ( m1_subset_1(D,k5_arytm_3) => ! [E] : ( m1_subset_1(E,k5_arytm_3) => ~ ( B = k9_arytm_3(D,E) & r3_arytm_3(D,A) & r3_arytm_3(E,C) & E != C ) ) ) ) ) ) ) )).
fof(t90_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(2,A) & r1_xxreal_0(k1_square_1(A),k1_nat_1(A,1)) ) ) )).
fof(t90_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ! [C] : ( v1_card_1(C) => ( ( r2_hidden(B,C) | r1_ordinal1(B,C) ) => ( r1_ordinal1(k2_card_2(A,B),k2_card_2(A,C)) & r1_ordinal1(k2_card_2(A,B),k2_card_2(C,A)) & r1_ordinal1(k2_card_2(B,A),k2_card_2(A,C)) & r1_ordinal1(k2_card_2(B,A),k2_card_2(C,A)) ) ) ) ) ) )).
fof(t90_card_3,axiom,( ! [A] : ( v4_card_3(A) <=> ? [B] : ( v1_relat_1(B) & v1_funct_1(B) & k9_xtuple_0(B) = k4_ordinal1 & r1_tarski(A,k10_xtuple_0(B)) ) ) )).
fof(t90_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ( v5_chord(B,A) <=> v5_chord(k6_glib_001(A,B),A) ) ) ) )).
fof(t90_clvect_1,axiom,( ! [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) ) => ! [B] : ( ( v1_clvect_1(B) & m1_clvect_1(B,A) ) => ! [C] : ( ( v1_clvect_1(C) & m1_clvect_1(C,A) ) => ! [D] : ( m2_clvect_1(D,A,B) => ! [E] : ( m2_clvect_1(E,A,C) => ( D = E => B = C ) ) ) ) ) ) )).
fof(t90_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => ( v1_clvect_2(B,A) => ( v1_clvect_2(k1_valued_0(u1_struct_0(A),B,C),A) & k1_clvect_2(A,k1_valued_0(u1_struct_0(A),B,C)) = k1_clvect_2(A,B) ) ) ) ) ) )).
fof(t90_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ! [D] : ( r2_hidden(k4_tarski(k4_tarski(C,2),k4_tarski(D,2)),k1_coh_sp(k15_cohsp_1(A,B))) <=> r2_hidden(k4_tarski(C,D),k1_coh_sp(B)) ) ) ) )).
fof(t90_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ( r3_cqc_the1(A,B,C) => r3_cqc_the1(A,B,k11_cqc_lang(A,D,C)) ) ) ) ) ) )).
fof(t90_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k16_sin_cos),D) ) & r2_hidden(B,k1_relset_1(k1_numbers,k27_sin_cos)) & r2_hidden(k2_xcmplx_0(B,A),k1_relset_1(k1_numbers,k27_sin_cos)) ) => k1_funct_1(k3_diff_1(C,A),B) = k6_xcmplx_0(k19_sin_cos(k2_xcmplx_0(B,A)),k19_sin_cos(B)) ) ) ) ) )).
fof(t90_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ( ( 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) = k9_euclid(3,k8_euclid_8(B,C,D,E),A) ) ) ) ) ) ) )).
fof(t90_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => r2_hidden(k4_euclidlp(A,B,C,D),k5_euclidlp(A)) ) ) ) ) )).
fof(t90_facirc_1,axiom,( ! [A] : ! [B] : ! [C] : ( r2_hidden(k12_facirc_1(A,B,C),k3_msafree2(k19_facirc_1(A,B,C))) & r2_hidden(k17_facirc_1(A,B,C),k3_msafree2(k19_facirc_1(A,B,C))) ) )).
fof(t90_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ~ ( r2_hidden(B,k2_finseq_1(A)) & ! [C] : ( v7_ordinal1(C) => ~ ( r1_xxreal_0(1,C) & r1_xxreal_0(C,A) & B = C ) ) ) ) )).
fof(t90_finseq_2,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,A) => m2_finseq_2(B,A,k4_finseq_2(k3_finseq_1(B),A)) ) )).
fof(t90_finseq_3,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => ( r1_tarski(A,k2_finseq_1(B)) => v2_funct_1(k14_finseq_1(A)) ) ) )).
fof(t90_finseq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ( r2_hidden(A,k4_finseq_1(C)) => k7_partfun1(B,C,1) = k7_partfun1(B,k17_finseq_1(B,A,C),1) ) ) ) ) )).
fof(t90_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( ( v1_finseq_6(C,A) & r2_hidden(B,k10_xtuple_0(C)) ) => k10_xtuple_0(k1_finseq_6(A,C,B)) = k10_xtuple_0(C) ) ) ) ) )).
fof(t90_flang_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ( r2_hidden(k5_afinsq_1(B),k2_flang_2(A,C)) <=> r2_hidden(k5_afinsq_1(B),C) ) ) )).
fof(t90_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => k6_flang_1(A,k2_flang_3(A,B),k1_flang_3(A,B,C)) = k1_flang_3(A,B,k2_xcmplx_0(C,1)) ) ) )).
fof(t90_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( k8_relat_1(C,A) = k8_relat_1(C,B) & r1_tarski(A,k10_xtuple_0(C)) & r1_tarski(B,k10_xtuple_0(C)) ) => A = B ) ) )).
fof(t90_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ( ! [E] : B != k1_tarski(E) & k5_partfun1(A,B,C) = k5_partfun1(A,B,D) ) => r2_relset_1(A,B,C,D) ) ) ) )).
fof(t90_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : k1_funct_1(k1_funct_4(k1_funct_4(A,k16_funcop_1(B,C)),k16_funcop_1(C,B)),B) = C ) )).
fof(t90_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ( r2_hidden(B,D) => r1_funct_7(A,k1_funct_7(A,B,C),D) ) ) )).
fof(t90_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => k13_fvsum_1(A,B,C) = k13_fvsum_1(A,C,B) ) ) ) )).
fof(t90_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( C != k4_tarski(k10_finseq_1(A,B),k4_gfacirc1) => ( r2_hidden(A,k2_msafree2(k34_gfacirc1(A,B,C))) & r2_hidden(B,k2_msafree2(k34_gfacirc1(A,B,C))) & r2_hidden(C,k2_msafree2(k34_gfacirc1(A,B,C))) ) ) )).
fof(t90_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ! [D] : ( r5_glib_000(A,B) => ( k14_glib_000(A) = k14_glib_000(B) & k16_glib_000(A) = k16_glib_000(B) & k18_glib_000(A,C) = k18_glib_000(B,C) & k19_glib_000(A,C) = k19_glib_000(B,C) & k20_glib_000(A,C) = k20_glib_000(B,C) & k21_glib_000(A,C) = k21_glib_000(B,C) & k23_glib_000(A,C,D) = k23_glib_000(B,C,D) ) ) ) ) )).
fof(t90_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => k13_glib_001(A,B) = k13_glib_001(A,k6_glib_001(A,B)) ) ) )).
fof(t90_goboard6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( ( ~ v3_relat_1(B) & v1_matrix_0(B) & v1_goboard1(B) & v2_goboard1(B) & v3_goboard1(B) & v4_goboard1(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ~ r1_xboole_0(k1_rltopsp1(k15_euclid(2),A,k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),B,k3_finseq_1(B),1),k19_euclid(1,k4_xcmplx_0(1)))),k1_tops_1(k15_euclid(2),k3_goboard5(B,k3_finseq_1(B),k5_numbers))) ) ) )).
fof(t90_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,A) => ( m1_group_2(B,C) => m1_group_2(k10_group_2(A,B,D),C) ) ) ) ) ) )).
fof(t90_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r3_group_3(A,B,C) => r3_group_3(A,C,B) ) ) ) ) )).
fof(t90_group_9,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( v2_group_9(D,A) & m1_group_9(D,A,B) ) => ! [E] : ( ( v2_group_9(E,A) & m1_group_9(E,A,B) ) => ! [F] : ( ( v2_group_9(F,A) & m1_group_9(F,A,B) ) => ! [G] : ( ( v1_funct_1(G) & v1_funct_2(G,u1_struct_0(B),u1_struct_0(C)) & v1_group_6(G,B,C) & v7_group_9(G,A,B,C) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(C)))) ) => ( ( D = k13_group_9(A,B,C,G) & v2_group_9(E,A) & v4_group_9(E,A,F) & m1_group_9(E,A,F) ) => ( v4_group_9(k19_group_9(A,B,E,k17_group_9(A,B,F,D)),A,F) & m1_group_9(k19_group_9(A,B,E,k17_group_9(A,B,F,D)),A,F) & v4_group_9(k19_group_9(A,B,E,D),A,k19_group_9(A,B,F,D)) & m1_group_9(k19_group_9(A,B,E,D),A,k19_group_9(A,B,F,D)) & ! [H] : ( ( v2_group_9(H,A) & v4_group_9(H,A,k19_group_9(A,B,F,D)) & m1_group_9(H,A,k19_group_9(A,B,F,D)) ) => ! [I] : ( ( v2_group_9(I,A) & v4_group_9(I,A,F) & m1_group_9(I,A,F) ) => ( ( H = k19_group_9(A,B,E,D) & I = k19_group_9(A,B,E,k17_group_9(A,B,F,D)) ) => r3_group_9(A,k10_group_9(A,k19_group_9(A,B,F,D),H),k10_group_9(A,F,I)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t90_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_algstr_0(A) & v4_rlvect_1(A) & v1_vectsp_1(A) & v1_algstr_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_ideal_1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v3_ideal_1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v3_ideal_1(D,A) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) ) => k16_ideal_1(A,B,k11_ideal_1(A,C,D)) = k13_ideal_1(A,k16_ideal_1(A,B,C),k16_ideal_1(A,B,D)) ) ) ) ) )).
fof(t90_integra8,axiom,( ! [A] : ( ( ~ 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,k16_sin_cos,k18_sin_cos)) = k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,k3_seq_4(A)),k1_funct_1(k18_sin_cos,k3_seq_4(A))),k3_xcmplx_0(k1_funct_1(k18_sin_cos,k2_seq_4(A)),k1_funct_1(k18_sin_cos,k2_seq_4(A))))) ) )).
fof(t90_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_intpro_1)) => ( r1_tarski(A,B) => r1_tarski(k13_intpro_1(A),k13_intpro_1(B)) ) ) ) )).
fof(t90_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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) = 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),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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t90_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( r1_jordan24(2,A,k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) & r1_jordan2c(2,A,B) ) => r1_xboole_0(k1_rltopsp1(k15_euclid(2),k2_jordan21(A),k19_euclid(k5_numbers,k4_xcmplx_0(3))),B) ) ) ) )).
fof(t90_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( 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)) ) ) ) )).
fof(t90_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v6_limfunc1(A) => ( v6_limfunc1(k32_valued_1(k1_numbers,k1_numbers,A)) & k5_limfunc1(k32_valued_1(k1_numbers,k1_numbers,A)) = k4_xcmplx_0(k5_limfunc1(A)) ) ) ) )).
fof(t90_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,B,B) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,B,B) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ( ( r2_matrix10(C,D) & r1_xxreal_0(A,k5_numbers) ) => r2_matrix10(k6_matrix10(B,A,D),k6_matrix10(B,A,C)) ) ) ) ) ) )).
fof(t90_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( k7_matrix_0(u1_struct_0(B),C,A) = k5_finseq_2(u1_struct_0(B),k1_matrix_0(C),k4_struct_0(B)) => k8_matrix13(B,k17_matrix_0(u1_struct_0(B),A,C)) = k8_matrix13(B,C) ) ) ) ) )).
fof(t90_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( v1_matrixr2(B,A) => ( r1_xxreal_0(A,k5_numbers) | ! [C] : ( m2_finseq_1(C,k1_numbers) => ~ ( k3_finseq_1(C) = A & ! [D] : ( m2_finseq_1(D,k1_numbers) => ~ ( k3_finseq_1(D) = A & k11_matrixr1(B,D) = C ) ) ) ) ) ) ) ) )).
fof(t90_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_membered(C) => k13_member_1(k13_member_1(A,B),C) = k13_member_1(A,k13_member_1(B,C)) ) ) ) )).
fof(t90_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( v6_supinf_2(D) => ( ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ~ ( E = k1_relset_1(A,D) & r1_mesfunc1(A,B,D,E) ) ) | r1_xxreal_0(k5_numbers,k7_mesfunc5(A,B,C,D)) ) ) ) ) ) ) )).
fof(t90_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( r3_mesfunc6(A,B,C,D) => ( ~ r1_xxreal_0(k1_mesfunc6(A,B,C,D),k2_supinf_1) & ~ r1_xxreal_0(k1_supinf_1,k1_mesfunc6(A,B,C,D)) ) ) ) ) ) ) )).
fof(t90_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => r2_relset_1(u1_struct_0(A),k1_numbers,k2_partfun1(u1_struct_0(A),k1_numbers,k4_normsp_0(u1_struct_0(A),B,D),C),k4_normsp_0(u1_struct_0(A),B,k2_partfun1(u1_struct_0(A),u1_struct_0(B),D,C))) ) ) ) )).
fof(t90_orders_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( ~ r2_hidden(k1_xboole_0,A) => ! [B] : ( m2_orders_1(B,A,k6_partfun1(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)))) ) ) ) ) )).
fof(t90_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => r6_pboole(A,k5_pboole(A,k5_pboole(A,B,C),D),k5_pboole(A,B,k5_pboole(A,C,D))) ) ) ) )).
fof(t90_polyform,axiom,( ! [A] : ( ( v2_polyform(A) & v3_polyform(A) & v4_polyform(A) & l1_polyform(A) ) => ( ( v5_polyform(A) & k7_polyform(A) = 3 ) => k2_xcmplx_0(k6_xcmplx_0(k12_polyform(A),k13_polyform(A)),k14_polyform(A)) = 2 ) ) )).
fof(t90_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v2_comseq_2(B) & v2_comseq_2(C) & ! [D] : ( v7_ordinal1(D) => k1_funct_1(C,D) = k6_prepower(A,k1_funct_1(B,D)) ) ) => ( r1_xxreal_0(A,k5_numbers) | k1_seq_2(C) = k6_prepower(A,k1_seq_2(B)) ) ) ) ) ) )).
fof(t90_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => k15_qc_lang2(A,k15_qc_lang1(A,C,B)) = k2_xboole_0(k15_qc_lang2(A,B),k1_tarski(k15_qc_lang1(A,C,B))) ) ) ) )).
fof(t90_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ( v1_xreal_0(A) => ( k13_quaterni(A) = A & k14_quaterni(A) = k5_numbers & k15_quaterni(A) = k5_numbers & k16_quaterni(A) = k5_numbers ) ) ) )).
fof(t90_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => k6_relat_1(B,k6_relat_1(A,C)) = k6_relat_1(k3_xboole_0(B,A),C) ) )).
fof(t90_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(C))) => ! [G] : ( ( ~ v2_struct_0(G) & l1_rewrite3(G,F) ) => ( r3_rewrite3(C,F,G,A,E,B,k1_flang_1(C,D,E)) => D = k2_flang_1(C) ) ) ) ) ) ) )).
fof(t90_rfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ( v3_funct_1(k2_partfun1(B,k1_numbers,C,A)) => v3_funct_1(k2_partfun1(B,k1_numbers,k32_valued_1(B,k1_numbers,C),A)) ) ) ) )).
fof(t90_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v1_comseq_2(A) => ( k5_rinfsup1(k32_valued_1(k4_ordinal1,k1_numbers,A)) = k4_xcmplx_0(k6_rinfsup1(A)) & k6_rinfsup1(k32_valued_1(k4_ordinal1,k1_numbers,A)) = k4_xcmplx_0(k5_rinfsup1(A)) ) ) ) )).
fof(t90_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => k18_rvsum_1(k9_rvsum_1(A,B,C)) = k6_xcmplx_0(k18_rvsum_1(B),k18_rvsum_1(C)) ) ) ) )).
fof(t90_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => ~ ( A = B & ~ v2_extpro_1(A,k7_card_1(2),k1_ami_3) & v2_extpro_1(B,k7_card_1(3),k1_scmfsa_2) ) ) ) )).
fof(t90_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v3_scmpds_4(D) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( ( r1_xxreal_0(k5_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) ) => ( r1_scmpds_6(k4_scmpds_6(E,F,C,D),B,A) & r2_scmpds_6(k4_scmpds_6(E,F,C,D),B,A) ) ) ) ) ) ) ) ) )).
fof(t90_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( r2_hidden(B,k1_scmyciel(k12_scmyciel(A))) <=> ~ ( ~ r2_hidden(B,k1_scmyciel(A)) & ! [C] : ( m1_subset_1(C,k3_tarski(A)) => ! [D] : ( m1_subset_1(D,k3_tarski(A)) => ~ ( B = k2_tarski(C,k4_tarski(D,k3_tarski(A))) & r2_hidden(k2_tarski(C,D),k1_scmyciel(A)) ) ) ) & ! [C] : ( m1_subset_1(C,k3_tarski(A)) => ~ ( B = k2_tarski(k3_tarski(A),k4_tarski(C,k3_tarski(A))) & r2_hidden(C,k3_tarski(A)) ) ) ) ) ) )).
fof(t90_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( r4_semi_af1(A,B,C,D,E,F) => ( F != B & B != D & D != F ) ) ) ) ) ) ) ) )).
fof(t90_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => k19_seq_4(A,k16_seq_4(A,B)) = k19_seq_4(A,B) ) ) )).
fof(t90_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ( v3_kurato_0(B,A) & v3_kurato_0(C,A) ) => ( v3_kurato_0(k3_setlim_2(A,B,C),A) & k4_kurato_0(A,k3_setlim_2(A,B,C)) = k7_subset_1(A,k4_kurato_0(A,B),k4_kurato_0(A,C)) ) ) ) ) )).
fof(t90_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,B,B),B))) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,B)),C),k5_sheffer1(A,k5_sheffer1(A,B,B),C)) ) ) ) )).
fof(t90_sin_cos6,axiom,( k3_relat_1(k5_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k5_numbers,k28_sin_cos)),k3_sin_cos6) = k6_partfun1(k1_rcomp_1(k5_numbers,k28_sin_cos)) )).
fof(t90_sin_cos9,axiom,( ! [A] : ( ( 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,k3_taylor_1))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) & ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & r1_xxreal_0(k1_funct_1(k2_sin_cos9,B),k5_numbers) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k3_taylor_1),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k3_taylor_1),A),B) = k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(k2_xcmplx_0(1,k1_square_1(B)),k1_funct_1(k2_sin_cos9,B)))) ) ) ) ) ) )).
fof(t90_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(k3_square_1(2)),A) & r1_xxreal_0(A,k4_xcmplx_0(1)) ) => k1_funct_1(k1_fdiff_9,k6_sincos10(A)) = A ) ) )).
fof(t90_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => v4_lattice3(k4_tdlat_1(A)) ) )).
fof(t90_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( r2_hidden(C,u1_pre_topc(A)) & r2_hidden(D,a_2_1_tmap_1(A,B)) ) => ( r2_hidden(k4_subset_1(u1_struct_0(A),C,D),k5_tmap_1(A,B)) & r2_hidden(k9_subset_1(u1_struct_0(A),C,D),k5_tmap_1(A,B)) ) ) ) ) ) ) )).
fof(t90_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,D) => r2_hidden(k3_funct_2(u1_struct_0(A),u1_struct_0(A),C,B),k7_relset_1(u1_struct_0(A),u1_struct_0(A),C,D)) ) ) ) ) ) )).
fof(t90_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( A = k1_tsep_1(A,B,C) => ( r1_tsep_1(B,C) | ( r4_tsep_1(A,B,C) <=> ~ ( ~ m1_pre_topc(B,C) & ~ m1_pre_topc(C,B) & ! [D] : ( ( ~ v2_struct_0(D) & v1_tsep_1(D,A) & m1_pre_topc(D,A) ) => ! [E] : ( ( ~ v2_struct_0(E) & v1_tsep_1(E,A) & m1_pre_topc(E,A) ) => ~ ( m1_pre_topc(D,B) & m1_pre_topc(E,C) & ~ ( A != k1_tsep_1(A,D,E) & ! [F] : ( ( ~ v2_struct_0(F) & v1_borsuk_1(F,A) & m1_pre_topc(F,A) ) => ~ ( A = k1_tsep_1(A,k1_tsep_1(A,D,E),F) & m1_pre_topc(F,k2_tsep_1(A,B,C)) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t90_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v1_valued_2(D) => ! [E] : ( v1_valued_2(E) => ! [F] : ( v1_valued_2(F) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,D))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(B,E))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(C,F))) ) => k84_valued_2(k3_xboole_0(B,C),A,k2_valued_2(k3_xboole_0(k1_valued_2(E),k1_valued_2(F))),D,k79_valued_2(B,C,E,F,H,I),G) = k79_valued_2(k3_xboole_0(B,A),k3_xboole_0(C,A),k2_valued_2(k3_xboole_0(k1_valued_2(E),k1_valued_2(D))),k2_valued_2(k3_xboole_0(k1_valued_2(F),k1_valued_2(D))),k84_valued_2(B,A,E,D,H,G),k84_valued_2(C,A,F,D,I,G)) ) ) ) ) ) ) )).
fof(t90_xboole_1,axiom,( ! [A] : ! [B] : r1_xboole_0(k4_xboole_0(A,k3_xboole_0(A,B)),B) )).
fof(t90_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k9_xboolean(A,k10_xboolean(A,B)) = k4_xboolean(k3_xboolean(A),k3_xboolean(B)) ) ) )).
fof(t90_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( B != k5_numbers => k3_xcmplx_0(A,C) = k3_xcmplx_0(k3_xcmplx_0(A,B),k7_xcmplx_0(C,B)) ) ) ) ) )).
fof(t90_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k5_xcmplx_0(B),k5_xcmplx_0(A)) => ( r1_xxreal_0(k5_numbers,k5_xcmplx_0(A)) | r1_xxreal_0(A,B) ) ) ) ) )).
fof(t90_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(D,A) => r1_xboole_0(k1_xxreal_1(C,D),k3_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t90_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ( ( v6_xxreal_2(A) & v1_xxreal_2(B) & v6_xxreal_2(B) & k1_xxreal_2(A) = k2_xxreal_2(B) ) => v6_xxreal_2(k2_xboole_0(A,B)) ) ) ) )).
fof(t90_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( k4_xxreal_3(A,B) != k1_xxreal_0 & k4_xxreal_3(A,B) != k2_xxreal_0 & ~ r2_hidden(A,k1_numbers) & ~ r2_hidden(B,k1_numbers) ) ) ) )).
fof(t90_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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))) ) => ( v9_zf_lang(A) => ( r1_zf_model(B,C,A) <=> ( r1_zf_model(B,C,k25_zf_lang(A)) => r1_zf_model(B,C,k26_zf_lang(A)) ) ) ) ) ) ) )).
fof(t90_zfmisc_1,axiom,( ! [A] : ! [B] : ( k2_zfmisc_1(A,B) = k2_zfmisc_1(B,A) => ( A = k1_xboole_0 | B = k1_xboole_0 | A = B ) ) )).
fof(t90_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_zmodul01(D,A) => ( ? [E] : ( m2_zmodul01(E,A,D) & r2_hidden(B,E) & r2_hidden(C,E) ) <=> r1_struct_0(D,k5_algstr_0(A,B,C)) ) ) ) ) ) )).
fof(t91_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v2_abcmiz_1(B,A) & m1_subset_1(B,u4_struct_0(A)) ) => ! [C] : ( 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)) => k46_abcmiz_1(A,k36_abcmiz_1(A,B,C)) = k3_tarski(a_2_4_abcmiz_1(A,C)) ) ) ) ) )).
fof(t91_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & v22_aofa_a00(D,A,1,1,11) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( ( v19_aofa_a00(F,A) & m1_subset_1(F,u1_struct_0(A)) ) => ! [G] : ( ( v3_aofa_a01(G,A,B,C,u4_aofa_a00(A,B,C,E),k37_aofa_a00(A)) & m1_msafree4(G,u1_struct_0(A),u4_aofa_a00(A,B,C,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),k37_aofa_a00(A))) ) => ! [H] : ( m2_subset_1(H,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => ! [I] : ( v1_int_1(I) => ( ( r2_hidden(I,k2_afinsq_1(k1_funct_1(k1_msafree4(u1_struct_0(A),H,k37_aofa_a00(A)),G))) & r2_hidden(k11_aofa_a01(A,B,C,E,F,G,I),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),F)) ) => k1_funct_1(k1_funct_1(k1_msafree4(u1_struct_0(A),H,k37_aofa_a00(A)),G),I) = k1_funct_1(k1_msafree4(u1_struct_0(A),H,F),k11_aofa_a01(A,B,C,E,F,G,I)) ) ) ) ) ) ) ) ) ) ) )).
fof(t91_arytm_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k5_arytm_3)) ) => ~ ( r2_hidden(A,k5_arytm_3) & ! [B] : ( m1_subset_1(B,k5_arytm_3) => ~ ( r2_hidden(B,A) & ! [C] : ( m1_subset_1(C,k5_arytm_3) => ( r2_hidden(C,A) => r3_arytm_3(C,B) ) ) ) ) ) ) )).
fof(t91_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(1,A) & r1_xxreal_0(k6_xcmplx_0(k5_series_1(2,k1_nat_1(A,1)),k5_series_1(2,A)),1) ) ) )).
fof(t91_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ! [C] : ( v1_card_1(C) => ! [D] : ( v1_card_1(D) => ~ ( ~ ( ~ ( r2_hidden(A,B) & r2_hidden(C,D) ) & ~ ( r1_ordinal1(A,B) & r2_hidden(C,D) ) & ~ ( r2_hidden(A,B) & r1_ordinal1(C,D) ) & ~ ( r1_ordinal1(A,B) & r1_ordinal1(C,D) ) ) & A != k5_numbers & ~ r1_ordinal1(k3_card_2(A,C),k3_card_2(B,D)) ) ) ) ) ) )).
fof(t91_card_3,axiom,( ! [A] : ! [B] : ( v4_card_3(A) => v4_card_3(k3_xboole_0(A,B)) ) )).
fof(t91_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v5_glib_001(B,A) & m3_glib_001(B,A) ) => ~ ( ~ v1_glib_001(B,A) & ~ v5_chord(B,A) & ? [C] : ( v7_ordinal1(C) & ~ v1_abian(C) & ? [D] : ( v7_ordinal1(D) & ~ v1_abian(D) & ~ r1_xxreal_0(D,C) & r1_xxreal_0(D,k3_finseq_1(B)) & ~ ( ? [E] : r1_glib_000(A,k1_funct_1(B,C),k1_funct_1(B,D),E) <=> k1_nat_1(C,2) = D ) ) ) ) ) ) )).
fof(t91_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => m2_clvect_1(k6_domain_1(u1_struct_0(A),B),A,k3_clvect_1(A)) ) ) )).
fof(t91_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clvect_2(B,A) => ( ! [D] : ( v7_ordinal1(D) => B != k1_valued_0(u1_struct_0(A),C,D) ) | v1_clvect_2(C,A) ) ) ) ) ) )).
fof(t91_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ! [D] : ( ( r2_hidden(C,k3_tarski(A)) & r2_hidden(D,k3_tarski(B)) ) => ( r2_hidden(k4_tarski(k4_tarski(C,1),k4_tarski(D,2)),k1_coh_sp(k15_cohsp_1(A,B))) & r2_hidden(k4_tarski(k4_tarski(D,2),k4_tarski(C,1)),k1_coh_sp(k15_cohsp_1(A,B))) ) ) ) ) )).
fof(t91_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( m2_subset_1(E,k2_qc_lang1(A),k3_qc_lang1(A)) => ( ~ r2_hidden(E,k24_qc_lang1(A,C)) => r3_cqc_the1(A,B,k8_cqc_lang(A,k11_cqc_lang(A,E,k8_cqc_lang(A,C,D)),k8_cqc_lang(A,C,k11_cqc_lang(A,E,D)))) ) ) ) ) ) ) )).
fof(t91_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k16_sin_cos),D) ) & r2_hidden(B,k1_relset_1(k1_numbers,k27_sin_cos)) & r2_hidden(k6_xcmplx_0(B,A),k1_relset_1(k1_numbers,k27_sin_cos)) ) => k1_funct_1(k4_diff_1(C,A),B) = k6_xcmplx_0(k19_sin_cos(B),k19_sin_cos(k6_xcmplx_0(B,A))) ) ) ) ) )).
fof(t91_euclid_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( v1_xreal_0(G) => ( ( 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(k3_xcmplx_0(k1_funct_1(D,G),k1_fdiff_1(A,G)),k3_xcmplx_0(k1_funct_1(E,G),k1_fdiff_1(B,G)),k3_xcmplx_0(k1_funct_1(F,G),k1_fdiff_1(C,G))),k1_euclid_8(k3_xcmplx_0(k1_funct_1(A,G),k1_fdiff_1(D,G)),k3_xcmplx_0(k1_funct_1(B,G),k1_fdiff_1(E,G)),k3_xcmplx_0(k1_funct_1(C,G),k1_fdiff_1(F,G)))) ) ) ) ) ) ) ) ) )).
fof(t91_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(k1_euclid(A)),k5_euclidlp(A)) => ( ( r2_hidden(B,E) & r2_hidden(C,E) & r2_hidden(D,E) ) => r1_tarski(k4_euclidlp(A,B,C,D),E) ) ) ) ) ) ) )).
fof(t91_facirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k19_facirc_1(A,B,C),k20_facirc_1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t91_finseq_1,axiom,( ! [A] : ! [B] : k4_finseq_1(k10_finseq_1(A,B)) = k2_tarski(1,2) )).
fof(t91_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : k4_finseq_2(A,B) = k1_funct_2(k2_finseq_1(A),B) ) )).
fof(t91_finseq_3,axiom,( ! [A] : v2_funct_1(k9_finseq_1(A)) )).
fof(t91_finseq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ( r2_hidden(A,k4_finseq_1(C)) => k7_partfun1(B,C,A) = k7_partfun1(B,k17_finseq_1(B,A,C),k3_finseq_1(k17_finseq_1(B,A,C))) ) ) ) ) )).
fof(t91_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r2_hidden(B,k10_xtuple_0(C)) => r2_hidden(B,k10_xtuple_0(k1_finseq_6(A,C,B))) ) ) ) ) )).
fof(t91_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => k6_flang_1(A,k2_flang_2(A,B),B) = k6_flang_1(A,B,k2_flang_2(A,B)) ) )).
fof(t91_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => k6_flang_1(A,k2_flang_3(A,B),k1_flang_3(A,B,C)) = k6_flang_1(A,k1_flang_3(A,B,C),k2_flang_3(A,B)) ) ) )).
fof(t91_funct_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k7_relat_1(k4_relat_1(A),B) = B ) )).
fof(t91_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(C,k1_funct_2(A,B)) => ( k9_xtuple_0(C) = A & r1_tarski(k10_xtuple_0(C),B) ) ) ) )).
fof(t91_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ~ ( F != E & F != B & k1_funct_1(k1_funct_4(k1_funct_4(A,k16_funcop_1(B,C)),k16_funcop_1(E,D)),F) != k1_funct_1(A,F) ) ) )).
fof(t91_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ! [D] : ( r2_hidden(B,D) | k5_relat_1(k1_funct_7(A,B,C),D) = k5_relat_1(A,D) ) ) )).
fof(t91_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( C != k4_tarski(k10_finseq_1(A,B),k4_gfacirc1) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k34_gfacirc1(A,B,C),k35_gfacirc1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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(k34_gfacirc1(A,B,C),k35_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(k34_gfacirc1(A,B,C),k35_gfacirc1(A,B,C),D),A) = E & k1_funct_1(k6_circuit2(k34_gfacirc1(A,B,C),k35_gfacirc1(A,B,C),D),B) = F & k1_funct_1(k6_circuit2(k34_gfacirc1(A,B,C),k35_gfacirc1(A,B,C),D),C) = G ) ) ) ) ) ) ) )).
fof(t91_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_finset_1(C) & v1_glib_000(C) ) => ( ( r5_glib_000(A,B) & m1_glib_000(C,A) ) => m1_glib_000(C,B) ) ) ) ) )).
fof(t91_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( m3_glib_001(C,A) => ( k4_glib_001(A,B) = k3_glib_001(A,C) => k13_glib_001(A,k7_glib_001(A,B,C)) = k4_subset_1(k6_glib_000(A),k13_glib_001(A,B),k13_glib_001(A,C)) ) ) ) ) )).
fof(t91_goboard6,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_pcomps_1(A))) => ! [D] : ( v1_xreal_0(D) => ( B = C => ( r1_xxreal_0(D,k5_numbers) | m1_connsp_2(k8_metric_1(A,B,D),k3_pcomps_1(A),C) ) ) ) ) ) ) )).
fof(t91_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,A) => ( ( m1_group_2(B,C) & m1_group_2(B,D) ) => m1_group_2(B,k10_group_2(A,C,D)) ) ) ) ) ) )).
fof(t91_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( r4_group_3(A,B,C) & r4_group_3(A,C,D) ) => r4_group_3(A,B,D) ) ) ) ) ) )).
fof(t91_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v2_group_9(C,A) & m1_group_9(C,A,B) ) => ! [D] : ( ( v2_group_9(D,A) & m1_group_9(D,A,B) ) => ! [E] : ( ( v2_group_9(E,A) & m1_group_9(E,A,B) ) => ! [F] : ( ( v2_group_9(F,A) & m1_group_9(F,A,B) ) => ! [G] : ( ( v4_group_9(G,A,k19_group_9(A,B,E,k17_group_9(A,B,C,D))) & m1_group_9(G,A,k19_group_9(A,B,E,k17_group_9(A,B,C,D))) ) => ! [H] : ( ( v4_group_9(H,A,k17_group_9(A,B,C,D)) & m1_group_9(H,A,k17_group_9(A,B,C,D)) ) => ( ( v4_group_9(E,A,C) & m1_group_9(E,A,C) & v4_group_9(F,A,D) & m1_group_9(F,A,D) & G = k19_group_9(A,B,E,k17_group_9(A,B,C,F)) & H = k19_group_9(A,B,k17_group_9(A,B,E,D),k17_group_9(A,B,F,C)) ) => r3_group_9(A,k10_group_9(A,k19_group_9(A,B,E,k17_group_9(A,B,C,D)),G),k10_group_9(A,k17_group_9(A,B,C,D),H)) ) ) ) ) ) ) ) ) )).
fof(t91_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v4_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k17_ideal_1(A,B)) <=> ? [D] : ( m1_subset_1(D,k4_ordinal1) & r2_hidden(k2_binom(A,C,D),k17_ideal_1(A,B)) ) ) ) ) ) )).
fof(t91_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)) => k2_integra5(A,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)) = k7_xcmplx_0(1,2) ) ) )).
fof(t91_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => k13_intpro_1(k13_intpro_1(A)) = k13_intpro_1(A) ) )).
fof(t91_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) = 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),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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t91_jordan2c,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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 ) ) ) ) ) ) )).
fof(t91_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ r1_xxreal_0(C,D) & r2_hidden(D,k1_relset_1(k1_numbers,k3_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) ) => ( v6_limfunc1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B)) & k5_limfunc1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B)) = k2_xcmplx_0(k5_limfunc1(A),k5_limfunc1(B)) ) ) ) ) )).
fof(t91_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,C,C) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,k1_numbers,C,C) & m2_finseq_1(E,k3_finseq_2(k1_numbers)) ) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,B) & v4_matrix10(D) & r2_matrix10(D,E) ) => r2_matrix10(k6_matrix10(C,A,D),k6_matrix10(C,B,E)) ) ) ) ) ) ) )).
fof(t91_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(D),C,B) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(D))) ) => ! [F] : ( m2_finseq_1(F,u1_struct_0(D)) => ( k3_finseq_1(F) = k1_matrix_0(E) => k8_matrix13(D,k17_matrix_0(u1_struct_0(D),A,E)) = k8_matrix13(D,k3_matrix11(A,C,B,u1_struct_0(D),E,k9_fvsum_1(D,F,k4_struct_0(D)))) ) ) ) ) ) ) ) )).
fof(t91_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( v1_matrixr2(B,A) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ~ ( k3_finseq_1(C) = A & ! [D] : ( m2_finseq_1(D,k1_numbers) => ~ ( k3_finseq_1(D) = A & k12_matrixr1(B,D) = C ) ) ) ) ) ) ) )).
fof(t91_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_membered(C) => ! [D] : ( v1_membered(D) => ( ( r1_tarski(A,B) & r1_tarski(C,D) ) => r1_tarski(k13_member_1(A,C),k13_member_1(B,D)) ) ) ) ) ) )).
fof(t91_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ( ( v6_supinf_2(D) & r1_xboole_0(E,F) ) => ( ! [G] : ( m2_subset_1(G,k1_zfmisc_1(A),B) => ~ ( G = k1_relset_1(A,D) & r1_mesfunc1(A,B,D,G) ) ) | k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,k6_prob_1(A,B,E,F))) = k3_supinf_2(k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,E)),k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,F))) ) ) ) ) ) ) ) ) )).
fof(t91_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( r3_mesfunc6(A,B,C,D) => r3_mesfunc6(A,B,C,k2_partfun1(A,k1_numbers,D,E)) ) ) ) ) ) ) )).
fof(t91_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => r2_relset_1(u1_struct_0(A),k1_numbers,k2_partfun1(u1_struct_0(A),k1_numbers,k4_normsp_0(u1_struct_0(A),B,D),C),k4_normsp_0(u1_struct_0(A),B,k2_partfun1(u1_struct_0(A),u1_struct_0(B),D,C))) ) ) ) )).
fof(t91_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( ( r2_pboole(A,k4_pboole(A,B,C),D) & r2_pboole(A,k4_pboole(A,C,B),D) ) => r2_pboole(A,k5_pboole(A,B,C),D) ) ) ) ) )).
fof(t91_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(A,k5_numbers) => k6_prepower(k6_prepower(A,B),C) = k6_prepower(A,k3_xcmplx_0(B,C)) ) ) ) ) )).
fof(t91_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => k15_qc_lang2(A,k2_qc_lang2(A,B,C)) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A,B),k15_qc_lang2(A,C)),k1_enumset1(k13_qc_lang1(A,C),k14_qc_lang1(A,B,k13_qc_lang1(A,C)),k2_qc_lang2(A,B,C))) ) ) ) )).
fof(t91_quaterni,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => k6_quaterni(A,B,k5_numbers,k5_numbers) = k5_arytm_0(A,B) ) ) )).
fof(t91_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => k6_relat_1(A,k6_relat_1(A,B)) = k6_relat_1(A,B) ) )).
fof(t91_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_afinsq_1(C))) => ! [F] : ( ( ~ v2_struct_0(F) & l1_rewrite3(F,E) ) => ( ~ r2_hidden(k2_flang_1(C),k10_xtuple_0(k9_xtuple_0(u1_rewrite3(E,F)))) => ( r3_rewrite3(C,E,F,A,D,B,D) <=> A = B ) ) ) ) ) ) )).
fof(t91_rfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ( v3_funct_1(k2_partfun1(B,k1_numbers,C,A)) => v3_funct_1(k2_partfun1(B,k1_numbers,k56_valued_1(B,k1_numbers,C),A)) ) ) ) )).
fof(t91_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_comseq_2(A) & v1_comseq_2(B) & ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k1_funct_1(A,C),k1_funct_1(B,C)) ) ) => ( r1_xxreal_0(k5_rinfsup1(A),k5_rinfsup1(B)) & r1_xxreal_0(k6_rinfsup1(A),k6_rinfsup1(B)) ) ) ) ) )).
fof(t91_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ( k18_rvsum_1(k13_rvsum_1(A,B)) = k5_numbers => B = k5_finseq_2(k4_ordinal1,A,k5_numbers) ) ) ) )).
fof(t91_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v2_compos_1(C,k1_scmpds_2) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v3_scmpds_4(D) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( ( r1_scmpds_6(C,B,A) & r2_scmpds_6(C,B,A) ) => ( r1_xxreal_0(k5_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,k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),2))) ) ) ) ) ) ) ) ) )).
fof(t91_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => k1_scmyciel(k12_scmyciel(A)) = k2_xboole_0(k2_xboole_0(k1_scmyciel(A),a_1_5_scmyciel(A)),a_1_6_scmyciel(A)) ) )).
fof(t91_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r4_semi_af1(A,B,C,D,F,E) & r4_semi_af1(A,B,C,D,G,E) ) => F = G ) ) ) ) ) ) ) ) )).
fof(t91_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k2_numbers) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => k19_seq_4(A,k18_seq_4(A,C,B)) = k11_rvsum_1(A,k19_seq_4(A,C),k9_complex1(B)) ) ) ) )).
fof(t91_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( ( v3_kurato_0(B,A) & v3_kurato_0(C,A) ) => ( v3_kurato_0(k4_setlim_2(A,B,C),A) & k4_kurato_0(A,k4_setlim_2(A,B,C)) = k5_subset_1(A,k4_kurato_0(A,B),k4_kurato_0(A,C)) ) ) ) ) )).
fof(t91_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,C,C)),B),k5_sheffer1(A,k5_sheffer1(A,C,C),B)) ) ) ) )).
fof(t91_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) => k19_sin_cos(k4_sin_cos6(A)) = A ) ) )).
fof(t91_sin_cos9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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_cos9,k1_taylor_1(A)))) & r1_tarski(B,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k1_taylor_1(A)),B) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k1_taylor_1(A)),B),C) = k7_xcmplx_0(k3_xcmplx_0(A,k3_prepower(k1_funct_1(k1_sin_cos9,C),k6_xcmplx_0(A,1))),k2_xcmplx_0(1,k1_square_1(C))) ) ) ) ) ) ) )).
fof(t91_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(k3_square_1(2)),A) & r1_xxreal_0(A,k4_xcmplx_0(1)) ) => k1_funct_1(k2_fdiff_9,k7_sincos10(A)) = A ) ) )).
fof(t91_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_tdlat_2(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k4_tdlat_1(A)))) => ( C = B => k15_lattice3(k4_tdlat_1(A),C) = k4_subset_1(u1_struct_0(A),k5_setfam_1(u1_struct_0(A),B),k1_tops_1(A,k2_pre_topc(A,k5_setfam_1(u1_struct_0(A),B)))) ) ) ) ) ) )).
fof(t91_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r2_hidden(B,k5_tmap_1(A,B)) ) ) )).
fof(t91_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k7_relset_1(u1_struct_0(A),u1_struct_0(A),C,D)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & r2_hidden(E,D) & k3_funct_2(u1_struct_0(A),u1_struct_0(A),C,E) = B ) ) ) ) ) ) )).
fof(t91_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( ( A = k1_tsep_1(A,B,C) & r1_tsep_1(B,C) ) => ( r4_tsep_1(A,B,C) <=> ( v1_tsep_1(B,A) & m1_pre_topc(B,A) & v1_tsep_1(C,A) & m1_pre_topc(C,A) ) ) ) ) ) ) )).
fof(t91_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( v1_valued_2(C) => ! [D] : ( v1_valued_2(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,D))) ) => k90_valued_2(A,B,k2_valued_2(k1_valued_2(C)),D,k16_valued_2(A,C,E),F) = k16_valued_2(k3_xboole_0(A,B),k2_valued_2(k3_xboole_0(k1_valued_2(C),k1_valued_2(D))),k90_valued_2(A,B,C,D,E,F)) ) ) ) ) )).
fof(t91_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : k5_xboole_0(k5_xboole_0(A,B),C) = k5_xboole_0(A,k5_xboole_0(B,C)) )).
fof(t91_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k9_xboolean(A,k10_xboolean(A,B)) = k9_xboolean(A,B) ) ) )).
fof(t91_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( C != k5_numbers => k7_xcmplx_0(A,B) = k7_xcmplx_0(k3_xcmplx_0(A,C),k3_xcmplx_0(B,C)) ) ) ) ) )).
fof(t91_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_xcmplx_0(B),k5_numbers) & ~ r1_xxreal_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) & r1_xxreal_0(B,A) ) ) ) )).
fof(t91_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(D,A) => r1_xboole_0(k3_xxreal_1(C,D),k4_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t91_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => ( ( v2_xxreal_2(A) & v6_xxreal_2(A) & v6_xxreal_2(B) & k1_xxreal_2(A) = k2_xxreal_2(B) ) => v6_xxreal_2(k2_xboole_0(A,B)) ) ) ) )).
fof(t91_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => k4_xxreal_3(k2_xxreal_3(1),A) = k2_xxreal_3(A) ) )).
fof(t91_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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))) ) => ( v10_zf_lang(A) => ( r1_zf_model(B,C,A) <=> ( r1_zf_model(B,C,k27_zf_lang(A)) <=> r1_zf_model(B,C,k28_zf_lang(A)) ) ) ) ) ) ) )).
fof(t91_zfmisc_1,axiom,( ! [A] : ! [B] : ( k2_zfmisc_1(A,A) = k2_zfmisc_1(B,B) => A = B ) )).
fof(t91_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( m2_zmodul01(D,A,C) => ! [E] : ( m2_zmodul01(E,A,C) => ( ( r2_hidden(B,D) & r2_hidden(B,E) ) => D = E ) ) ) ) ) ) )).
fof(t92_abcmiz_1,axiom,( ! [A] : ( l1_msualg_1(A) => ! [B] : r6_pboole(u1_struct_0(A),k2_msafree3(A,k4_trees_4(k4_tarski(B,u1_struct_0(A)),k1_xboole_0)),k1_pboole(u1_struct_0(A))) ) )).
fof(t92_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & v22_aofa_a00(D,A,1,1,11) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( ( v19_aofa_a00(F,A) & m1_subset_1(F,u1_struct_0(A)) ) => ! [G] : ( ( v3_aofa_a01(G,A,B,C,u4_aofa_a00(A,B,C,E),F) & m1_msafree4(G,u1_struct_0(A),u4_aofa_a00(A,B,C,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),F)) ) => ! [H] : ( ( v3_aofa_a01(H,A,B,C,u4_aofa_a00(A,B,C,E),k37_aofa_a00(A)) & m1_msafree4(H,u1_struct_0(A),u4_aofa_a00(A,B,C,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),k37_aofa_a00(A))) ) => ! [I] : ( m2_subset_1(I,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => ! [J] : ( v1_int_1(J) => ( ( r2_hidden(J,k2_afinsq_1(k1_funct_1(k1_msafree4(u1_struct_0(A),I,k37_aofa_a00(A)),H))) & r2_hidden(k39_aofa_a00(A,C,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),k37_aofa_a00(A),H),F,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),F,G)),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),F)) & J = k15_aofa_a00(A,B,C,D,F,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),F,G),I) ) => k1_funct_1(k1_funct_1(k1_msafree4(u1_struct_0(A),I,k37_aofa_a00(A)),H),k15_aofa_a00(A,B,C,D,F,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),F,G),I)) = k1_funct_1(k1_msafree4(u1_struct_0(A),I,F),k39_aofa_a00(A,C,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),k37_aofa_a00(A),H),F,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),F,G))) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t92_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ~ ! [C] : ( m1_subset_1(C,k5_arytm_3) => ( k9_arytm_3(A,C) != B & k9_arytm_3(B,C) != A ) ) ) ) )).
fof(t92_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ~ ( r1_xxreal_0(2,A) & r2_hidden(k6_xcmplx_0(k5_series_1(2,A),1),k5_asympt_1) ) ) )).
fof(t92_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ! [C] : ( v1_card_1(C) => ~ ( ( r2_hidden(B,C) | r1_ordinal1(B,C) ) & A != k5_numbers & ~ ( r1_ordinal1(k3_card_2(A,B),k3_card_2(A,C)) & r1_ordinal1(k3_card_2(B,A),k3_card_2(C,A)) ) ) ) ) ) )).
fof(t92_card_3,axiom,( ! [A] : ! [B] : ( v4_card_3(A) => v4_card_3(k6_subset_1(A,B)) ) )).
fof(t92_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v5_glib_001(B,A) & m3_glib_001(B,A) ) => ~ ( ~ v1_glib_001(B,A) & ~ v5_chord(B,A) & ? [C] : ( v7_ordinal1(C) & ~ v1_abian(C) & ? [D] : ( v7_ordinal1(D) & ~ v1_abian(D) & ~ r1_xxreal_0(D,C) & r1_xxreal_0(D,k3_finseq_1(B)) & ~ ( ~ v5_chord(k8_glib_001(A,B,C,D),A) & ~ v1_glib_001(k8_glib_001(A,B,C,D),A) ) ) ) ) ) ) )).
fof(t92_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( m2_clvect_1(B,A,k3_clvect_1(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B != k6_domain_1(u1_struct_0(A),C) ) ) ) ) )).
fof(t92_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v2_clvect_2(B,A) => ( ! [D] : ( v7_ordinal1(D) => B != k1_valued_0(u1_struct_0(A),C,D) ) | v2_clvect_2(C,A) ) ) ) ) ) )).
fof(t92_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ! [D] : ( r2_hidden(k4_tarski(k4_tarski(C,1),k4_tarski(D,1)),k1_coh_sp(k16_cohsp_1(A,B))) <=> r2_hidden(k4_tarski(C,D),k1_coh_sp(A)) ) ) ) )).
fof(t92_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ( ( v6_qc_lang1(C,A) & r3_cqc_the1(A,k4_subset_1(k3_cqc_lang(A),B,k6_domain_1(k3_cqc_lang(A),C)),D) ) => r3_cqc_the1(A,B,k8_cqc_lang(A,C,D)) ) ) ) ) ) )).
fof(t92_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k16_sin_cos),D) ) & r2_hidden(k2_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k27_sin_cos)) & r2_hidden(k6_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k27_sin_cos)) ) => k1_funct_1(k5_diff_1(C,A),B) = k6_xcmplx_0(k19_sin_cos(k2_xcmplx_0(B,k7_xcmplx_0(A,2))),k19_sin_cos(k6_xcmplx_0(B,k7_xcmplx_0(A,2)))) ) ) ) ) )).
fof(t92_euclid_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( v1_xreal_0(G) => ( ( r1_fdiff_1(A,G) & r1_fdiff_1(B,G) & r1_fdiff_1(C,G) & r1_fdiff_1(D,k1_funct_1(A,G)) & r1_fdiff_1(E,k1_funct_1(B,G)) & r1_fdiff_1(F,k1_funct_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(k3_xcmplx_0(k1_fdiff_1(D,k1_funct_1(A,G)),k1_fdiff_1(A,G)),k3_xcmplx_0(k1_fdiff_1(E,k1_funct_1(B,G)),k1_fdiff_1(B,G)),k3_xcmplx_0(k1_fdiff_1(F,k1_funct_1(C,G)),k1_fdiff_1(C,G))) ) ) ) ) ) ) ) ) )).
fof(t92_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(k1_euclid(A)),k5_euclidlp(A)) => ( ( r2_hidden(B,E) & r2_hidden(C,E) & r2_hidden(D,E) & r3_euclidlp(A,k8_euclid(A,C,B),k8_euclid(A,D,B)) ) => E = k4_euclidlp(A,B,C,D) ) ) ) ) ) ) )).
fof(t92_facirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( 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)) ) ) ) ) )).
fof(t92_finseq_1,axiom,( ! [A] : ( v1_finset_1(A) => k3_finseq_1(k19_finseq_1(A)) = k5_card_1(A) ) )).
fof(t92_finseq_2,axiom,( ! [A] : k4_finseq_2(k5_numbers,A) = k1_tarski(k6_finseq_1(A)) )).
fof(t92_finseq_3,axiom,( ! [A] : ! [B] : ( A != B <=> v2_funct_1(k10_finseq_1(A,B)) ) )).
fof(t92_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r2_hidden(B,k10_xtuple_0(C)) => k7_partfun1(A,k1_finseq_6(A,C,B),1) = B ) ) ) ) )).
fof(t92_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => k6_flang_1(A,k2_flang_2(A,B),B) = k1_flang_2(A,B,1,2) ) )).
fof(t92_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => k6_flang_1(A,k2_flang_3(A,B),k8_flang_1(A,B)) = k2_flang_3(A,B) ) )).
fof(t92_funct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( ( r1_tarski(A,k9_xtuple_0(C)) & r1_tarski(k7_relat_1(C,A),B) ) => r1_tarski(A,k8_relat_1(C,B)) ) ) )).
fof(t92_funct_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k9_setfam_1(A)))) ) => ? [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) & ! [D] : ( r2_hidden(D,A) => k9_relat_1(C,D) = k1_funct_1(B,D) ) ) ) )).
fof(t92_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_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_funct_4(A,B)) ) ) ) )).
fof(t92_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : ! [E] : ( k5_relat_1(A,E) = k5_relat_1(B,E) => k5_relat_1(k1_funct_7(A,C,D),E) = k5_relat_1(k1_funct_7(B,C,D),E) ) ) ) )).
fof(t92_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( C != k4_tarski(k10_finseq_1(A,B),k4_gfacirc1) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k34_gfacirc1(A,B,C),k35_gfacirc1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( m1_subset_1(G,k6_margrel1) => ! [H] : ( m1_subset_1(H,k6_margrel1) => ( ( E = k1_funct_1(D,k4_tarski(k10_finseq_1(A,B),k4_gfacirc1)) & F = k1_funct_1(D,A) & G = k1_funct_1(D,B) & H = k1_funct_1(D,C) ) => k1_twoscomp(k34_gfacirc1(A,B,C),k35_gfacirc1(A,B,C),k6_circuit2(k34_gfacirc1(A,B,C),k35_gfacirc1(A,B,C),D),k36_gfacirc1(A,B,C)) = k2_binarith(E,k9_margrel1(H)) ) ) ) ) ) ) ) )).
fof(t92_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v1_funct_1(C) & v1_finset_1(C) & v1_glib_000(C) ) => ( ( r5_glib_000(A,B) & m1_glib_000(A,C) ) => m1_glib_000(B,C) ) ) ) ) )).
fof(t92_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) ) => ( ( r1_xxreal_0(C,D) & r1_xxreal_0(D,k3_finseq_1(B)) ) => r1_tarski(k13_glib_001(A,k8_glib_001(A,B,C,D)),k13_glib_001(A,B)) ) ) ) ) ) )).
fof(t92_goboard6,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_pre_topc(k3_pcomps_1(A),B)) <=> ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_xboole_0(k8_metric_1(A,C,D),B) ) ) ) ) ) ) )).
fof(t92_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,A) => ( m1_group_2(B,C) => m1_group_2(k10_group_2(A,B,D),k10_group_2(A,C,D)) ) ) ) ) ) )).
fof(t92_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r4_group_3(A,k6_domain_1(u1_struct_0(A),B),k6_domain_1(u1_struct_0(A),C)) <=> r2_group_3(A,B,C) ) ) ) ) )).
fof(t92_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v2_group_9(C,A) & m1_group_9(C,A,B) ) => ! [D] : ( ( v2_group_9(D,A) & m1_group_9(D,A,B) ) => ! [E] : ( ( v2_group_9(E,A) & m1_group_9(E,A,B) ) => ! [F] : ( ( v2_group_9(F,A) & m1_group_9(F,A,B) ) => ( ( v4_group_9(E,A,C) & m1_group_9(E,A,C) & v4_group_9(F,A,D) & m1_group_9(F,A,D) ) => ( v4_group_9(k19_group_9(A,B,E,k17_group_9(A,B,C,F)),A,k19_group_9(A,B,E,k17_group_9(A,B,C,D))) & m1_group_9(k19_group_9(A,B,E,k17_group_9(A,B,C,F)),A,k19_group_9(A,B,E,k17_group_9(A,B,C,D))) ) ) ) ) ) ) ) )).
fof(t92_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k28_sin_cos) => k2_integra5(A,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)) = k5_numbers ) ) )).
fof(t92_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ( v10_intpro_1(A) <=> k13_intpro_1(A) = A ) ) )).
fof(t92_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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) = 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),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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t92_jordan2c,axiom,( ! [A] : ( 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)) ) ) )).
fof(t92_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ r1_xxreal_0(C,D) & r2_hidden(D,k1_relset_1(k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) ) => ( v6_limfunc1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B)) & k5_limfunc1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B)) = k6_xcmplx_0(k5_limfunc1(A),k5_limfunc1(B)) ) ) ) ) )).
fof(t92_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,C,C) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,k1_numbers,C,C) & m2_finseq_1(E,k3_finseq_2(k1_numbers)) ) => ( ( r1_xxreal_0(A,k5_numbers) & r1_xxreal_0(B,A) & v3_matrix10(D) & r2_matrix10(E,D) ) => r2_matrix10(k6_matrix10(C,A,D),k6_matrix10(C,B,E)) ) ) ) ) ) ) )).
fof(t92_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [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] : ( m1_subset_1(F,u1_struct_0(E)) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(E),D,C) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(E))) ) => ( r2_hidden(B,k2_finseq_1(k3_finseq_1(G))) => ( ( A = B & F = k4_algstr_0(E,k1_group_1(E)) ) | k8_matrix13(E,G) = k8_matrix13(E,k3_matrix11(A,D,C,u1_struct_0(E),G,k4_fvsum_1(k1_matrix_0(G),E,k7_matrix_0(u1_struct_0(E),G,A),k10_fvsum_1(k1_matrix_0(G),E,k7_matrix_0(u1_struct_0(E),G,B),F)))) ) ) ) ) ) ) ) ) ) )).
fof(t92_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( m2_finseq_1(C,k1_numbers) => ! [D] : ( m2_finseq_1(D,k1_numbers) => ( ( k3_finseq_1(C) = A & k3_finseq_1(D) = A & k12_matrixr1(B,C) = D ) => ! [E] : ( v7_ordinal1(E) => ( ( r1_xxreal_0(1,E) & r1_xxreal_0(E,A) ) => k1_funct_1(D,E) = k22_rvsum_1(C,k8_matrix_0(k1_numbers,B,E)) ) ) ) ) ) ) ) )).
fof(t92_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_membered(C) => k13_member_1(A,k2_xboole_0(B,C)) = k2_xboole_0(k13_member_1(A,B),k13_member_1(A,C)) ) ) ) )).
fof(t92_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( v6_supinf_2(D) => ( ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ~ ( F = k1_relset_1(A,D) & r1_mesfunc1(A,B,D,F) ) ) | r1_xxreal_0(k5_numbers,k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,E))) ) ) ) ) ) ) ) )).
fof(t92_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ( ( r3_mesfunc6(A,B,C,D) & r1_xboole_0(E,F) ) => k1_mesfunc6(A,B,C,k2_partfun1(A,k1_numbers,D,k6_prob_1(A,B,E,F))) = k3_supinf_2(k1_mesfunc6(A,B,C,k2_partfun1(A,k1_numbers,D,E)),k1_mesfunc6(A,B,C,k2_partfun1(A,k1_numbers,D,F))) ) ) ) ) ) ) ) )).
fof(t92_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ( ( v1_funct_1(D) & 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),k1_numbers,k2_partfun1(u1_struct_0(B),k1_numbers,k4_normsp_0(u1_struct_0(B),A,D),C),k4_normsp_0(u1_struct_0(B),A,k2_partfun1(u1_struct_0(B),u1_struct_0(A),D,C))) ) ) ) )).
fof(t92_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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),k5_pboole(A,B,k4_pboole(A,C,B))) ) ) )).
fof(t92_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => k15_qc_lang2(A,k3_qc_lang2(A,B,C)) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A,B),k15_qc_lang2(A,C)),k2_enumset1(k13_qc_lang1(A,C),k13_qc_lang1(A,B),k14_qc_lang1(A,k13_qc_lang1(A,B),k13_qc_lang1(A,C)),k3_qc_lang2(A,B,C))) ) ) ) )).
fof(t92_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k22_quaterni(A,B) = k22_quaterni(k22_quaterni(k19_quaterni(k2_xcmplx_0(k13_quaterni(A),k13_quaterni(B)),k21_quaterni(k2_xcmplx_0(k14_quaterni(A),k14_quaterni(B)),k1_xcmplx_0)),k21_quaterni(k2_xcmplx_0(k15_quaterni(A),k15_quaterni(B)),k11_quaterni)),k21_quaterni(k2_xcmplx_0(k16_quaterni(A),k16_quaterni(B)),k12_quaterni)) ) ) )).
fof(t92_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r1_tarski(A,B) => k6_relat_1(B,k6_relat_1(A,C)) = k6_relat_1(A,C) ) ) )).
fof(t92_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,C) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_afinsq_1(C))) => ! [F] : ( ( ~ v2_struct_0(F) & l1_rewrite3(F,E) ) => ( r3_rewrite3(C,E,F,A,k3_flang_1(C,D),B,k2_flang_1(C)) => ( 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)) ) ) ) ) ) ) )).
fof(t92_rfunct_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k1_numbers))) ) => ( v3_funct_1(k2_partfun1(B,k1_numbers,C,A)) => ( ! [D] : ( v1_xreal_0(D) => v1_comseq_2(k2_partfun1(B,k1_numbers,k26_valued_1(B,k1_numbers,C,D),A)) ) & v1_comseq_2(k2_partfun1(B,k1_numbers,k32_valued_1(B,k1_numbers,C),A)) & v1_comseq_2(k2_partfun1(B,k1_numbers,k56_valued_1(B,k1_numbers,C),A)) ) ) ) ) )).
fof(t92_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_comseq_2(A) & v1_comseq_2(B) ) => ( r1_xxreal_0(k2_xcmplx_0(k6_rinfsup1(A),k6_rinfsup1(B)),k6_rinfsup1(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B))) & r1_xxreal_0(k6_rinfsup1(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)),k2_xcmplx_0(k6_rinfsup1(A),k5_rinfsup1(B))) & r1_xxreal_0(k6_rinfsup1(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)),k2_xcmplx_0(k5_rinfsup1(A),k6_rinfsup1(B))) & r1_xxreal_0(k2_xcmplx_0(k6_rinfsup1(A),k5_rinfsup1(B)),k5_rinfsup1(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B))) & r1_xxreal_0(k2_xcmplx_0(k5_rinfsup1(A),k6_rinfsup1(B)),k5_rinfsup1(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B))) & r1_xxreal_0(k5_rinfsup1(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)),k2_xcmplx_0(k5_rinfsup1(A),k5_rinfsup1(B))) & ( ( v2_comseq_2(A) | v2_comseq_2(B) ) => ( k6_rinfsup1(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) = k2_xcmplx_0(k6_rinfsup1(A),k6_rinfsup1(B)) & k5_rinfsup1(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) = k2_xcmplx_0(k5_rinfsup1(A),k5_rinfsup1(B)) ) ) ) ) ) ) )).
fof(t92_rvsum_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k4_finseq_2(A,k1_numbers)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k4_finseq_2(A,k1_numbers)) => r1_xxreal_0(k1_square_1(k18_rvsum_1(k15_rvsum_1(A,B,C))),k3_xcmplx_0(k18_rvsum_1(k13_rvsum_1(A,B)),k18_rvsum_1(k13_rvsum_1(A,C)))) ) ) ) )).
fof(t92_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v2_compos_1(D,k1_scmpds_2) & v3_scmpds_4(D) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => ( ( r1_xxreal_0(k5_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,k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),2))) ) ) ) ) ) ) ) )).
fof(t92_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ~ r1_semi_af1(A,D,B,C) => r4_semi_af1(A,B,D,C,D,D) ) ) ) ) ) )).
fof(t92_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => k20_seq_4(k15_seq_4(A)) = k5_numbers ) )).
fof(t92_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_kurato_0(C,A) => ( v3_kurato_0(k5_setlim_2(A,C,B),A) & k4_kurato_0(A,k5_setlim_2(A,C,B)) = k9_subset_1(A,B,k4_kurato_0(A,C)) ) ) ) ) )).
fof(t92_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = k5_sheffer1(A,k5_sheffer1(A,C,B),k5_sheffer1(A,k5_sheffer1(A,C,C),B)) ) ) ) )).
fof(t92_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(A,k28_sin_cos) ) => k4_sin_cos6(k19_sin_cos(A)) = A ) ) )).
fof(t92_sin_cos9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( 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(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k1_taylor_1(A)),B) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_sin_cos9,k1_taylor_1(A)),B),C) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(A,k3_prepower(k1_funct_1(k2_sin_cos9,C),k6_xcmplx_0(A,1))),k2_xcmplx_0(1,k1_square_1(C)))) ) ) ) ) ) ) )).
fof(t92_sincos10,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,k3_square_1(2)) ) => k1_funct_1(k2_fdiff_9,k8_sincos10(A)) = A ) ) )).
fof(t92_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_tdlat_2(B,A) => ! [C] : ( 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) = k9_subset_1(u1_struct_0(A),k6_setfam_1(u1_struct_0(A),B),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) ) ) ) ) ) ) ) )).
fof(t92_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,u1_pre_topc(A)) <=> u1_pre_topc(A) = k5_tmap_1(A,B) ) ) ) )).
fof(t92_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(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) => C = D ) ) ) ) ) )).
fof(t92_tsep_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & m1_pre_topc(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( r3_tsep_1(A,B,C) <=> ? [D] : ( ~ v2_struct_0(D) & m1_pre_topc(D,A) & ? [E] : ( ~ v2_struct_0(E) & m1_pre_topc(E,A) & r4_tsep_1(A,D,E) & m1_pre_topc(B,D) & m1_pre_topc(C,E) & ( r1_tsep_1(D,E) | r1_tsep_1(k2_tsep_1(A,D,E),k1_tsep_1(A,B,C)) ) ) ) ) ) ) ) )).
fof(t92_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ( v1_valued_2(C) => ! [D] : ( v1_valued_2(D) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,C))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(B,D))) ) => k90_valued_2(A,B,C,k2_valued_2(k1_valued_2(D)),E,k16_valued_2(B,D,F)) = k16_valued_2(k3_xboole_0(A,B),k2_valued_2(k3_xboole_0(k1_valued_2(C),k1_valued_2(D))),k90_valued_2(A,B,C,D,E,F)) ) ) ) ) )).
fof(t92_xboole_1,axiom,( ! [A] : k5_xboole_0(A,A) = k1_xboole_0 )).
fof(t92_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k10_xboolean(A,k9_xboolean(A,B)) = k6_xboolean(B,A) ) ) )).
fof(t92_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( C != k5_numbers => k7_xcmplx_0(A,B) = k3_xcmplx_0(k7_xcmplx_0(A,k3_xcmplx_0(B,C)),C) ) ) ) ) )).
fof(t92_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k5_numbers,k5_xcmplx_0(A)) & ~ r1_xxreal_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) & r1_xxreal_0(B,A) ) ) ) )).
fof(t92_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(D,A) => r1_xboole_0(k3_xxreal_1(C,D),k3_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t92_xxreal_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ( ! [B] : ( m1_subset_1(B,k6_numbers) => ( r2_hidden(B,A) => r1_xxreal_0(B,k2_xxreal_0) ) ) => A = k1_tarski(k2_xxreal_0) ) ) )).
fof(t92_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k2_xxreal_3(k4_xxreal_3(A,B)) = k4_xxreal_3(k2_xxreal_3(A),B) ) ) )).
fof(t92_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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))) ) => ( v11_zf_lang(A) => ( r1_zf_model(B,C,A) <=> ? [D] : ( m1_subset_1(D,B) & r1_zf_model(B,k2_zf_lang1(B,C,k23_zf_lang(A),D),k24_zf_lang(A)) ) ) ) ) ) ) )).
fof(t92_zfmisc_1,axiom,( ! [A] : ( r1_tarski(A,k2_zfmisc_1(A,A)) => A = k1_xboole_0 ) )).
fof(t92_zmodul01,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( m1_zmodul01(C,B) => ! [D] : ( m1_zmodul01(D,B) => ( r1_struct_0(k6_zmodul01(B,C,D),A) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & r1_struct_0(C,E) & r1_struct_0(D,F) & A = k3_rlvect_1(B,E,F) ) ) ) ) ) ) )).
fof(t93_abcmiz_1,axiom,( ! [A] : ( l1_msualg_1(A) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) ) => r6_pboole(u1_struct_0(A),k2_msafree3(A,k4_trees_4(k4_tarski(B,u1_struct_0(A)),k9_finseq_1(C))),k2_msafree3(A,C)) ) ) )).
fof(t93_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ~ ( ~ r3_arytm_3(B,A) & ! [C] : ( m1_subset_1(C,k5_arytm_3) => ~ ( ~ r3_arytm_3(C,A) & ~ r3_arytm_3(B,C) ) ) ) ) ) )).
fof(t93_asympt_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k7_newton(A),B) ) => ( r1_xxreal_0(k7_newton(k1_nat_1(A,1)),B) | k6_asympt_1(B) = k7_newton(A) ) ) ) ) )).
fof(t93_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ( r1_ordinal1(A,k1_card_2(A,B)) & r1_ordinal1(B,k1_card_2(A,B)) ) ) ) )).
fof(t93_card_3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_card_3(A) ) => ? [B] : ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) & k2_relset_1(A,B) = A ) ) )).
fof(t93_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_glib_000(A))) ) => ! [C] : ( m2_glib_000(C,A,B,k21_glib_000(A,B)) => ! [D] : ( m3_glib_001(D,A) => ! [E] : ( m3_glib_001(E,C) => ( D = E => ( ~ ( ~ v5_chord(D,A) & v5_chord(E,C) ) & ~ ( ~ v5_chord(E,C) & v5_chord(D,A) ) ) ) ) ) ) ) ) )).
fof(t93_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_clvect_1(B,A) => m2_clvect_1(u1_struct_0(B),A,B) ) ) )).
fof(t93_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => ( v2_clvect_2(B,A) => v2_clvect_2(k1_valued_0(u1_struct_0(A),B,C),A) ) ) ) ) )).
fof(t93_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ! [D] : ( r2_hidden(k4_tarski(k4_tarski(C,2),k4_tarski(D,2)),k1_coh_sp(k16_cohsp_1(A,B))) <=> r2_hidden(k4_tarski(C,D),k1_coh_sp(B)) ) ) ) )).
fof(t93_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k26_sin_cos),D) ) & r2_hidden(A,k1_relset_1(k1_numbers,k26_sin_cos)) & r2_hidden(B,k1_relset_1(k1_numbers,k26_sin_cos)) ) => k9_diff_1(C,A,B) = k7_xcmplx_0(k6_xcmplx_0(k1_square_1(k19_sin_cos(B)),k1_square_1(k19_sin_cos(A))),k3_xcmplx_0(k1_square_1(k3_xcmplx_0(k19_sin_cos(A),k19_sin_cos(B))),k6_xcmplx_0(A,B))) ) ) ) ) )).
fof(t93_euclid_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( v1_xreal_0(G) => ( ( 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_funct_1(D,G) = k5_numbers | k1_funct_1(E,G) = k5_numbers | k1_funct_1(F,G) = k5_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(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(A,G),k1_funct_1(D,G)),k3_xcmplx_0(k1_fdiff_1(D,G),k1_funct_1(A,G))),k1_square_1(k1_funct_1(D,G))),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(B,G),k1_funct_1(E,G)),k3_xcmplx_0(k1_fdiff_1(E,G),k1_funct_1(B,G))),k1_square_1(k1_funct_1(E,G))),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k1_fdiff_1(C,G),k1_funct_1(F,G)),k3_xcmplx_0(k1_fdiff_1(F,G),k1_funct_1(C,G))),k1_square_1(k1_funct_1(F,G)))) ) ) ) ) ) ) ) ) ) )).
fof(t93_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k5_euclidlp(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k5_euclidlp(A)) => ( ( v1_euclidlp(B,A) & r1_tarski(B,C) ) => B = C ) ) ) ) )).
fof(t93_finseq_1,axiom,( ! [A] : k19_finseq_1(k1_tarski(A)) = k9_finseq_1(A) )).
fof(t93_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v3_card_1(C,k5_numbers) & m2_finseq_1(C,B) ) => ! [D] : ( ( v3_card_1(D,A) & m2_finseq_1(D,B) ) => ( k8_finseq_1(B,C,D) = D & k8_finseq_1(B,D,C) = D ) ) ) ) ) )).
fof(t93_finseq_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( A != B & B != C & C != A ) <=> v2_funct_1(k11_finseq_1(A,B,C)) ) )).
fof(t93_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => k1_finseq_6(A,k1_finseq_6(A,C,B),B) = k1_finseq_6(A,C,B) ) ) ) )).
fof(t93_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => k6_flang_1(A,k2_flang_2(A,B),k2_flang_2(A,B)) = k1_flang_2(A,B,k5_numbers,2) ) )).
fof(t93_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ( r1_tarski(C,k8_flang_1(A,B)) => ( r1_tarski(k6_flang_1(A,k2_flang_3(A,B),C),k2_flang_3(A,B)) & r1_tarski(k6_flang_1(A,C,k2_flang_3(A,B)),k2_flang_3(A,B)) ) ) ) ) )).
fof(t93_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( r1_tarski(A,k9_xtuple_0(B)) & v2_funct_1(B) ) => k8_relat_1(B,k7_relat_1(B,A)) = A ) ) )).
fof(t93_funct_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => k8_relset_1(A,A,k6_partfun1(A),B) = B ) )).
fof(t93_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => k1_funct_4(k1_funct_4(A,B),B) = k1_funct_4(A,B) ) ) )).
fof(t93_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : k1_funct_1(k1_funct_4(A,k16_funcop_1(B,C)),B) = C ) )).
fof(t93_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( C != k4_tarski(k10_finseq_1(A,B),k4_gfacirc1) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k34_gfacirc1(A,B,C),k35_gfacirc1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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(k34_gfacirc1(A,B,C),k35_gfacirc1(A,B,C),k5_facirc_1(k34_gfacirc1(A,B,C),k35_gfacirc1(A,B,C),D,2),k36_gfacirc1(A,B,C)) = k2_binarith(k2_binarith(E,k9_margrel1(F)),k9_margrel1(G)) & k1_funct_1(k5_facirc_1(k34_gfacirc1(A,B,C),k35_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(k34_gfacirc1(A,B,C),k35_gfacirc1(A,B,C),D,2),A) = E & k1_funct_1(k5_facirc_1(k34_gfacirc1(A,B,C),k35_gfacirc1(A,B,C),D,2),B) = F & k1_funct_1(k5_facirc_1(k34_gfacirc1(A,B,C),k35_gfacirc1(A,B,C),D,2),C) = G ) ) ) ) ) ) ) )).
fof(t93_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ! [C] : ! [D] : ( m2_glib_000(D,A,C,B) => ! [E] : ( m2_glib_000(E,A,C,B) => r5_glib_000(D,E) ) ) ) )).
fof(t93_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( r1_glib_000(A,k4_glib_001(A,B),D,C) => k13_glib_001(A,k10_glib_001(A,B,C)) = k2_xboole_0(k13_glib_001(A,B),k1_tarski(D)) ) ) ) )).
fof(t93_goboard6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => ( C = D => ! [E] : ( v1_xreal_0(E) => ( ~ r1_xxreal_0(E,k5_numbers) => ( r2_hidden(C,k2_pre_topc(k15_euclid(A),B)) <=> ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ~ r1_xxreal_0(E,F) & r1_xboole_0(k8_metric_1(k14_euclid(A),D,F),B) ) ) ) ) ) ) ) ) ) ) )).
fof(t93_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ( ( v8_struct_0(B) | v8_struct_0(C) ) => v8_struct_0(k10_group_2(A,B,C)) ) ) ) ) )).
fof(t93_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_group_2(C,A) => ~ ( r4_group_3(A,B,k8_group_2(A,C)) & ! [D] : ( ( v15_algstr_0(D) & m1_group_2(D,A) ) => u1_struct_0(D) != B ) ) ) ) ) )).
fof(t93_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v2_group_9(C,A) & m1_group_9(C,A,B) ) => ! [D] : ( ( v2_group_9(D,A) & m1_group_9(D,A,B) ) => ! [E] : ( ( v2_group_9(E,A) & m1_group_9(E,A,B) ) => ! [F] : ( ( v2_group_9(F,A) & m1_group_9(F,A,B) ) => ! [G] : ( ( v4_group_9(G,A,k19_group_9(A,B,E,k17_group_9(A,B,C,D))) & m1_group_9(G,A,k19_group_9(A,B,E,k17_group_9(A,B,C,D))) ) => ! [H] : ( ( v4_group_9(H,A,k19_group_9(A,B,F,k17_group_9(A,B,D,C))) & m1_group_9(H,A,k19_group_9(A,B,F,k17_group_9(A,B,D,C))) ) => ( ( G = k19_group_9(A,B,E,k17_group_9(A,B,C,F)) & H = k19_group_9(A,B,F,k17_group_9(A,B,D,E)) & v4_group_9(E,A,C) & m1_group_9(E,A,C) & v4_group_9(F,A,D) & m1_group_9(F,A,D) ) => r3_group_9(A,k10_group_9(A,k19_group_9(A,B,E,k17_group_9(A,B,C,D)),G),k10_group_9(A,k19_group_9(A,B,F,k17_group_9(A,B,D,C)),H)) ) ) ) ) ) ) ) ) )).
fof(t93_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ~ ( B != k6_domain_1(u1_struct_0(A),k4_struct_0(A)) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( C != k4_struct_0(A) & r2_hidden(C,B) ) ) ) ) ) )).
fof(t93_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k3_xcmplx_0(k28_sin_cos,k7_xcmplx_0(3,2))) => k2_integra5(A,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)) = k7_xcmplx_0(1,2) ) ) )).
fof(t93_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ( v10_intpro_1(A) => r1_tarski(k14_intpro_1,A) ) ) )).
fof(t93_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [D] : ( ( 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)),k7_jgraph_4(A),B) & C = k8_struct_0(k15_euclid(2)) & B = a_0_1_jgraph_4 ) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) | r1_xxreal_0(1,A) | v5_pre_topc(D,k1_pre_topc(k15_euclid(2),B),k1_pre_topc(k15_euclid(2),C)) ) ) ) ) ) ) )).
fof(t93_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) = 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),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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t93_jordan2c,axiom,( ! [A] : ( ( ~ 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] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & r2_hidden(C,k3_topreal1(2,k1_sprect_1(A))) & ! [D] : ( 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))) ) ) ) ) ) ) )).
fof(t93_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v6_limfunc1(A) & k8_relat_1(A,k1_tarski(k5_numbers)) = k1_xboole_0 ) => ( k5_limfunc1(A) = k5_numbers | ( v6_limfunc1(k6_rfunct_1(k1_numbers,k1_numbers,A)) & k5_limfunc1(k6_rfunct_1(k1_numbers,k1_numbers,A)) = k5_xcmplx_0(k5_limfunc1(A)) ) ) ) ) )).
fof(t93_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,C,C) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,k1_numbers,C,C) & m2_finseq_1(E,k3_finseq_2(k1_numbers)) ) => ( ( r1_xxreal_0(B,A) & v2_matrix10(D) & r1_matrix10(E,D) ) => ( r1_xxreal_0(k5_numbers,A) | r1_matrix10(k6_matrix10(C,A,D),k6_matrix10(C,B,E)) ) ) ) ) ) ) ) )).
fof(t93_matrix13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [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] : ( m1_subset_1(F,u1_struct_0(E)) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,u1_struct_0(E),D,C) & m2_finseq_1(G,k3_finseq_2(u1_struct_0(E))) ) => ( r2_hidden(B,k2_finseq_1(k3_finseq_1(G))) => ( B = A | k8_matrix13(E,k17_matrix_0(u1_struct_0(E),A,G)) = k8_matrix13(E,k3_matrix11(A,D,C,u1_struct_0(E),G,k10_fvsum_1(k1_matrix_0(G),E,k7_matrix_0(u1_struct_0(E),G,B),F))) ) ) ) ) ) ) ) ) ) )).
fof(t93_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ~ ( ! [C] : ( m2_finseq_1(C,k1_numbers) => ~ ( k3_finseq_1(C) = A & ! [D] : ( m2_finseq_1(D,k1_numbers) => ~ ( k3_finseq_1(D) = A & k12_matrixr1(B,D) = C ) ) ) ) & ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => k1_matrixr2(A,C,B) != k4_matrixr2(A) ) ) ) ) )).
fof(t93_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_membered(C) => r1_tarski(k13_member_1(A,k3_xboole_0(B,C)),k3_xboole_0(k13_member_1(A,B),k13_member_1(A,C))) ) ) ) )).
fof(t93_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ( ( v6_supinf_2(D) & r1_tarski(E,F) ) => ( ! [G] : ( m2_subset_1(G,k1_zfmisc_1(A),B) => ~ ( G = k1_relset_1(A,D) & r1_mesfunc1(A,B,D,G) ) ) | r1_xxreal_0(k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,E)),k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,F))) ) ) ) ) ) ) ) ) )).
fof(t93_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ( ( r3_mesfunc6(A,B,C,D) & F = k7_subset_1(A,k1_relset_1(A,D),E) ) => ( r3_mesfunc6(A,B,C,k2_partfun1(A,k1_numbers,D,E)) & k1_mesfunc6(A,B,C,D) = k3_supinf_2(k1_mesfunc6(A,B,C,k2_partfun1(A,k1_numbers,D,E)),k1_mesfunc6(A,B,C,k2_partfun1(A,k1_numbers,D,F))) ) ) ) ) ) ) ) ) )).
fof(t93_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( D != k1_xboole_0 & r1_tarski(D,k1_relset_1(u1_struct_0(A),C)) & v1_ncfcont1(D,A) & r7_ncfcont1(A,B,C,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_hidden(E,D) & r2_hidden(F,D) & k7_partfun1(k1_numbers,k4_normsp_0(u1_struct_0(A),B,C),E) = k2_seq_4(k7_relset_1(u1_struct_0(A),k1_numbers,k4_normsp_0(u1_struct_0(A),B,C),D)) & k7_partfun1(k1_numbers,k4_normsp_0(u1_struct_0(A),B,C),F) = k3_seq_4(k7_relset_1(u1_struct_0(A),k1_numbers,k4_normsp_0(u1_struct_0(A),B,C),D)) ) ) ) ) ) ) ) ) )).
fof(t93_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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),k5_pboole(A,B,k4_pboole(A,B,C))) ) ) )).
fof(t93_prepower,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(A,C) & r1_xxreal_0(1,B) ) => r1_xxreal_0(k1_newton(B,A),k1_newton(B,C)) ) ) ) ) )).
fof(t93_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => k15_qc_lang2(A,k4_qc_lang2(A,B,C)) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A,B),k15_qc_lang2(A,C)),k5_enumset1(k13_qc_lang1(A,C),k14_qc_lang1(A,B,k13_qc_lang1(A,C)),k2_qc_lang2(A,B,C),k13_qc_lang1(A,B),k14_qc_lang1(A,C,k13_qc_lang1(A,B)),k2_qc_lang2(A,C,B),k4_qc_lang2(A,B,C))) ) ) ) )).
fof(t93_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k23_quaterni(A,B) = k22_quaterni(k22_quaterni(k19_quaterni(k6_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k13_quaterni(B)),k3_xcmplx_0(k14_quaterni(A),k14_quaterni(B))),k3_xcmplx_0(k15_quaterni(A),k15_quaterni(B))),k3_xcmplx_0(k16_quaterni(A),k16_quaterni(B))),k21_quaterni(k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k14_quaterni(B)),k3_xcmplx_0(k14_quaterni(A),k13_quaterni(B))),k3_xcmplx_0(k15_quaterni(A),k16_quaterni(B))),k3_xcmplx_0(k16_quaterni(A),k15_quaterni(B))),k1_xcmplx_0)),k21_quaterni(k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k15_quaterni(B)),k3_xcmplx_0(k15_quaterni(A),k13_quaterni(B))),k3_xcmplx_0(k16_quaterni(A),k14_quaterni(B))),k3_xcmplx_0(k14_quaterni(A),k16_quaterni(B))),k11_quaterni)),k21_quaterni(k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k16_quaterni(B)),k3_xcmplx_0(k16_quaterni(A),k13_quaterni(B))),k3_xcmplx_0(k14_quaterni(A),k15_quaterni(B))),k3_xcmplx_0(k15_quaterni(A),k14_quaterni(B))),k12_quaterni)) ) ) )).
fof(t93_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r1_tarski(B,A) => k6_relat_1(B,k6_relat_1(A,C)) = k6_relat_1(B,C) ) ) )).
fof(t93_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( ~ v1_xboole_0(F) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k8_afinsq_1(F))) => ! [H] : ( ( ~ v2_struct_0(H) & l1_rewrite3(H,G) ) => ( ( v2_rewrite3(H,F,G) & r3_rewrite3(F,G,H,A,B,C,E) & r3_rewrite3(F,G,H,A,B,D,E) ) => C = D ) ) ) ) )).
fof(t93_rfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,k1_numbers))) ) => ( ( ( v1_seq_2(k2_partfun1(C,k1_numbers,D,A)) & v3_funct_1(k2_partfun1(C,k1_numbers,E,B)) ) => v1_seq_2(k2_partfun1(C,k1_numbers,k3_valued_1(C,k1_numbers,k1_numbers,D,E),k3_xboole_0(A,B))) ) & ( ( v2_seq_2(k2_partfun1(C,k1_numbers,D,A)) & v3_funct_1(k2_partfun1(C,k1_numbers,E,B)) ) => v2_seq_2(k2_partfun1(C,k1_numbers,k3_valued_1(C,k1_numbers,k1_numbers,D,E),k3_xboole_0(A,B))) ) & ( ( v1_comseq_2(k2_partfun1(C,k1_numbers,D,A)) & v3_funct_1(k2_partfun1(C,k1_numbers,E,B)) ) => v1_comseq_2(k2_partfun1(C,k1_numbers,k3_valued_1(C,k1_numbers,k1_numbers,D,E),k3_xboole_0(A,B))) ) ) ) ) ) )).
fof(t93_rinfsup1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_comseq_2(A) & v4_partfun3(A) & v1_comseq_2(B) & v4_partfun3(B) ) => ( r1_xxreal_0(k3_xcmplx_0(k6_rinfsup1(A),k6_rinfsup1(B)),k6_rinfsup1(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B))) & r1_xxreal_0(k5_rinfsup1(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)),k3_xcmplx_0(k5_rinfsup1(A),k5_rinfsup1(B))) ) ) ) ) )).
fof(t93_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( A != B & k4_scmfsa_2(A) = k4_scmfsa_2(B) ) ) ) )).
fof(t93_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( v1_int_1(F) => k5_memstr_0(2,k1_scmpds_2,k6_scmpds_4(k4_scmpds_6(E,F,C,D),B,A)) = k1_nat_1(k1_nat_1(k5_card_1(C),k5_card_1(D)),2) ) ) ) ) ) ) )).
fof(t93_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ! [C] : ~ ( r2_hidden(k2_tarski(B,C),k1_scmyciel(k12_scmyciel(A))) & ~ r2_hidden(k2_tarski(B,C),k1_scmyciel(A)) & ~ ( ( r2_hidden(B,k3_tarski(A)) | B = k3_tarski(A) ) & ? [D] : ( r2_hidden(D,k3_tarski(A)) & C = k4_tarski(D,k3_tarski(A)) ) ) & ~ ( ( r2_hidden(C,k3_tarski(A)) | C = k3_tarski(A) ) & ? [D] : ( r2_hidden(D,k3_tarski(A)) & B = k4_tarski(D,k3_tarski(A)) ) ) ) ) )).
fof(t93_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( r4_semi_af1(A,B,C,D,E,F) => r4_semi_af1(A,D,E,B,C,F) ) ) ) ) ) ) ) )).
fof(t93_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ( k20_seq_4(B) = k5_numbers => B = k15_seq_4(A) ) ) ) )).
fof(t93_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_kurato_0(C,A) => ( v3_kurato_0(k6_setlim_2(A,C,B),A) & k4_kurato_0(A,k6_setlim_2(A,C,B)) = k4_subset_1(A,B,k4_kurato_0(A,C)) ) ) ) ) )).
fof(t93_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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,k5_sheffer1(A,B,B),C)),k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,D,B)),k5_sheffer1(A,C,k5_sheffer1(A,D,B)))) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,C,k5_sheffer1(A,D,B))),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,D,B),k5_sheffer1(A,D,B)),k5_sheffer1(A,C,k5_sheffer1(A,D,B)))) ) ) ) ) )).
fof(t93_sin_cos6,axiom,( k4_sin_cos6(k4_xcmplx_0(1)) = k28_sin_cos )).
fof(t93_sin_cos9,axiom,( ! [A] : ( ( 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_cos9,k1_taylor_1(2)),k7_xcmplx_0(1,2)))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_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)),k7_xcmplx_0(1,2)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_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)),k7_xcmplx_0(1,2)),A),B) = k7_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k2_xcmplx_0(1,k1_square_1(B))) ) ) ) ) ) )).
fof(t93_sincos10,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(1,k3_square_1(2)))) )).
fof(t93_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => u1_struct_0(k8_tdlat_1(A)) = k5_tdlat_1(A) ) )).
fof(t93_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( u1_struct_0(k6_tmap_1(A,B)) = u1_struct_0(A) & u1_pre_topc(k6_tmap_1(A,B)) = k5_tmap_1(A,B) ) ) ) )).
fof(t93_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)))) ) => ( v8_transgeo(D,A) => k7_relset_1(u1_struct_0(A),u1_struct_0(A),D,k2_aff_1(A,B,C)) = k2_aff_1(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),D,C)) ) ) ) ) ) )).
fof(t93_tsep_1,axiom,( ! [A] : ( l1_pre_topc(A) => k1_pre_topc(A,k2_struct_0(A)) = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) ) )).
fof(t93_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v1_valued_2(D) => ! [E] : ( v1_valued_2(E) => ! [F] : ( v1_valued_2(F) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,D))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(B,E))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(C,F))) ) => k90_valued_2(k3_xboole_0(A,B),C,k2_valued_2(k3_xboole_0(k1_valued_2(D),k1_valued_2(E))),F,k84_valued_2(A,B,D,E,G,H),I) = k84_valued_2(A,k3_xboole_0(B,C),D,k2_valued_2(k3_xboole_0(k1_valued_2(E),k1_valued_2(F))),G,k90_valued_2(B,C,E,F,H,I)) ) ) ) ) ) ) )).
fof(t93_xboole_1,axiom,( ! [A] : ! [B] : k2_xboole_0(A,B) = k2_xboole_0(k5_xboole_0(A,B),k3_xboole_0(A,B)) )).
fof(t93_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k8_xboolean(A,k10_xboolean(A,B)) = k6_xboolean(A,B) ) ) )).
fof(t93_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k3_xcmplx_0(k6_xcmplx_0(B,A),k2_xcmplx_0(B,A)),k5_numbers) ) => ( r1_xxreal_0(k4_xcmplx_0(A),B) & r1_xxreal_0(B,A) ) ) ) ) )).
fof(t93_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(D,A) => r1_xboole_0(k4_xxreal_1(C,D),k1_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t93_xxreal_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ( ! [B] : ( m1_subset_1(B,k6_numbers) => ( r2_hidden(B,A) => r1_xxreal_0(k1_xxreal_0,B) ) ) => A = k1_tarski(k1_xxreal_0) ) ) )).
fof(t93_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( B = k2_xxreal_3(C) => k4_xxreal_3(A,k1_xxreal_3(B,C)) = k1_xxreal_3(k4_xxreal_3(A,B),k4_xxreal_3(A,C)) ) ) ) ) )).
fof(t93_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ~ v1_xboole_0(C) => ( r2_zf_model(C,k13_zf_lang(B,A)) <=> ! [D] : ( ( 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))) ) => ? [E] : ( m1_subset_1(E,C) & r1_zf_model(C,k2_zf_lang1(C,D,B,E),A) ) ) ) ) ) ) )).
fof(t93_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( C != k1_xboole_0 & ( r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) | r1_tarski(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) ) & ~ r1_tarski(A,B) ) )).
fof(t93_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r1_struct_0(B,D) | r1_struct_0(C,D) ) => r1_struct_0(k6_zmodul01(A,B,C),D) ) ) ) ) ) )).
fof(t94_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_abcmiz_1(B,A,k13_abcmiz_1(A)) => k45_abcmiz_1(A,k30_abcmiz_1(A,k32_abcmiz_1(A),B)) = k45_abcmiz_1(A,B) ) ) )).
fof(t94_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(C)) => ! [E] : ( m1_subset_1(E,C) => ! [F] : ( m1_aofa_000(F,A,C,D) => ( r2_hidden(B,k18_aofa_000(A)) => r2_hidden(k4_tarski(E,B),k21_aofa_000(A,C,D,F)) ) ) ) ) ) ) ) )).
fof(t94_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & v22_aofa_a00(D,A,1,1,11) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( ( v19_aofa_a00(F,A) & m1_subset_1(F,u1_struct_0(A)) ) => ! [G] : ( ( v3_aofa_a01(G,A,B,C,u4_aofa_a00(A,B,C,E),F) & m1_msafree4(G,u1_struct_0(A),u4_aofa_a00(A,B,C,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),F)) ) => ! [H] : ( ( v3_aofa_a01(H,A,B,C,u4_aofa_a00(A,B,C,E),u8_aofa_a00(A)) & m1_msafree4(H,u1_struct_0(A),u4_aofa_a00(A,B,C,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u8_aofa_a00(A))) ) => ! [I] : ( ( ~ v2_struct_0(I) & v2_unialg_1(I) & v3_unialg_1(I) & v4_unialg_1(I) & v3_aofa_000(I) & v4_aofa_000(I) & v5_aofa_000(I) & v6_aofa_000(I) & ~ v10_aofa_000(I) & v11_aofa_000(I) & v12_aofa_000(I) & v5_aofa_a01(I,A,B,C,E) & l3_aofa_a00(I,A,C,u4_aofa_a00(A,B,C,E)) ) => ! [J] : ( m1_aofa_000(J,I,k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E)),k14_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E),u8_aofa_a00(A),H,k2_aofa_a01(A,D))) => ( ( r2_hidden(J,k20_aofa_a00(A,B,C,D,E,I,u8_aofa_a00(A),H,k2_aofa_a01(A,D))) & v11_aofa_a00(E,A,B,C,D) ) => ! [K] : ( m1_subset_1(K,k1_funct_1(u3_msualg_1(A,C),F)) => ! [L] : ( m1_subset_1(L,k1_funct_1(u3_msualg_1(A,C),F)) => ! [M] : ( m1_subset_1(M,u1_struct_0(I)) => ! [N] : ( ( r7_aofa_000(I,k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E)),k14_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E),u8_aofa_a00(A),H,k2_aofa_a01(A,D)),k12_aofa_a00(A,C,u4_aofa_a00(A,B,C,E),I,F,G,K),J,N) & r7_aofa_000(I,k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E)),k14_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E),u8_aofa_a00(A),H,k2_aofa_a01(A,D)),k6_aofa_a01(A,B,C,E,I,H,F,L,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),F,G)),J,N) & r7_aofa_000(I,k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E)),k14_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E),u8_aofa_a00(A),H,k2_aofa_a01(A,D)),k12_aofa_a00(A,C,u4_aofa_a00(A,B,C,E),I,F,G,k30_aofa_a00(A,C,F,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),F,G),k28_aofa_a00(A,C,F))),J,N) & r7_aofa_000(I,k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E)),k14_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E),u8_aofa_a00(A),H,k2_aofa_a01(A,D)),M,J,N) & r6_aofa_000(I,k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E)),k14_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E),u8_aofa_a00(A),H,k2_aofa_a01(A,D)),M,J,N) & ! [O] : ( m2_subset_1(O,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => ( k1_funct_1(k1_msafree4(u1_struct_0(A),k3_aofa_a01(A,B,C,E,H,D,I,J,O,M),F),G) = k1_funct_1(k1_msafree4(u1_struct_0(A),O,F),G) & k1_funct_1(k1_msafree4(u1_struct_0(A),k3_aofa_a01(A,B,C,E,H,D,I,J,O,k6_aofa_a01(A,B,C,E,I,H,F,L,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),F,G))),F),G) = k1_funct_1(k1_msafree4(u1_struct_0(A),O,F),G) & k15_aofa_a00(A,B,C,D,F,L,k3_aofa_a01(A,B,C,E,H,D,I,J,O,k6_aofa_a01(A,B,C,E,I,H,F,L,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),F,G)))) = k15_aofa_a00(A,B,C,D,F,L,O) & k15_aofa_a00(A,B,C,D,F,L,k3_aofa_a01(A,B,C,E,H,D,I,J,O,k13_aofa_000(I,M,k12_aofa_a00(A,C,u4_aofa_a00(A,B,C,E),I,F,G,k30_aofa_a00(A,C,F,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),F,G),k28_aofa_a00(A,C,F)))))) = k15_aofa_a00(A,B,C,D,F,L,O) ) ) ) => r6_aofa_000(I,k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E)),k14_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E),u8_aofa_a00(A),H,k2_aofa_a01(A,D)),k17_aofa_000(I,k12_aofa_a00(A,C,u4_aofa_a00(A,B,C,E),I,F,G,K),k6_aofa_a01(A,B,C,E,I,H,F,L,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),F,G)),M,k12_aofa_a00(A,C,u4_aofa_a00(A,B,C,E),I,F,G,k30_aofa_a00(A,C,F,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),F,G),k28_aofa_a00(A,C,F)))),J,N) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t94_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ~ ! [B] : ( m1_subset_1(B,k5_arytm_3) => r3_arytm_3(B,A) ) ) )).
fof(t94_asympt_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(1,C) ) => ( r1_xxreal_0(A,1) | r1_xxreal_0(k3_power(B,C),k3_power(A,C)) ) ) ) ) ) )).
fof(t94_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ( B != k5_numbers => ( r1_ordinal1(A,k2_card_2(A,B)) & r1_ordinal1(A,k2_card_2(B,A)) ) ) ) ) )).
fof(t94_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( m1_subset_1(C,k4_card_3(A)) => ! [D] : ( m1_subset_1(D,k4_card_3(B)) => r2_hidden(k1_funct_4(C,D),k4_card_3(k1_funct_4(A,B))) ) ) ) ) )).
fof(t94_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ( ( r5_glib_000(A,B) & v6_chord(A) ) => v6_chord(B) ) ) ) )).
fof(t94_clvect_1,axiom,( ! [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) ) => m2_clvect_1(u1_struct_0(A),A,k4_clvect_1(A)) ) )).
fof(t94_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( v7_ordinal1(D) => ( r2_clvect_2(A,B,C) => r2_clvect_2(A,k1_valued_0(u1_struct_0(A),B,D),k1_valued_0(u1_struct_0(A),C,D)) ) ) ) ) ) )).
fof(t94_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ! [D] : ( ~ r2_hidden(k4_tarski(k4_tarski(C,1),k4_tarski(D,2)),k1_coh_sp(k16_cohsp_1(A,B))) & ~ r2_hidden(k4_tarski(k4_tarski(D,2),k4_tarski(C,1)),k1_coh_sp(k16_cohsp_1(A,B))) ) ) ) )).
fof(t94_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k26_sin_cos),D) ) & r2_hidden(B,k1_relset_1(k1_numbers,k26_sin_cos)) & r2_hidden(k2_xcmplx_0(B,A),k1_relset_1(k1_numbers,k26_sin_cos)) ) => k1_funct_1(k3_diff_1(C,A),B) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k19_sin_cos(k3_xcmplx_0(2,k2_xcmplx_0(B,A))),k19_sin_cos(k3_xcmplx_0(2,B)))),k1_square_1(k3_xcmplx_0(k19_sin_cos(k2_xcmplx_0(B,A)),k19_sin_cos(B))))) ) ) ) ) )).
fof(t94_euclid_8,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( v1_xreal_0(D) => ( ( r1_fdiff_1(A,D) & r1_fdiff_1(B,D) & r1_fdiff_1(C,D) ) => ( k1_funct_1(A,D) = k5_numbers | k1_funct_1(B,D) = k5_numbers | k1_funct_1(C,D) = k5_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(k7_xcmplx_0(k1_fdiff_1(A,D),k1_square_1(k1_funct_1(A,D))),k7_xcmplx_0(k1_fdiff_1(B,D),k1_square_1(k1_funct_1(B,D))),k7_xcmplx_0(k1_fdiff_1(C,D),k1_square_1(k1_funct_1(C,D))))) ) ) ) ) ) ) )).
fof(t94_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(A)) => ( r1_tarski(k2_euclid_4(A,B,C),k4_euclidlp(A,B,C,D)) & r1_tarski(k2_euclid_4(A,C,D),k4_euclidlp(A,B,C,D)) & r1_tarski(k2_euclid_4(A,D,B),k4_euclidlp(A,B,C,D)) ) ) ) ) ) )).
fof(t94_finseq_1,axiom,( ! [A] : ( v1_finset_1(A) => ( v1_funct_1(k2_funct_1(k19_finseq_1(A))) & v1_funct_2(k2_funct_1(k19_finseq_1(A)),A,k2_finseq_1(k5_card_1(A))) & m1_subset_1(k2_funct_1(k19_finseq_1(A)),k1_zfmisc_1(k2_zfmisc_1(A,k2_finseq_1(k5_card_1(A))))) ) ) )).
fof(t94_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k4_finseq_2(1,A) = a_1_0_finseq_2(A) ) )).
fof(t94_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v2_funct_1(A) & k10_xtuple_0(A) = k1_tarski(B) ) => k3_finseq_1(A) = 1 ) ) )).
fof(t94_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => k1_finseq_6(A,k12_finseq_1(A,B),B) = k12_finseq_1(A,B) ) ) )).
fof(t94_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => k7_flang_1(A,k2_flang_2(A,B),C) = k1_flang_2(A,k2_flang_2(A,B),k5_numbers,C) ) ) )).
fof(t94_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => r1_tarski(k2_flang_3(A,k9_subset_1(k8_afinsq_1(A),B,C)),k9_subset_1(k8_afinsq_1(A),k2_flang_3(A,B),k2_flang_3(A,C))) ) ) )).
fof(t94_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( r1_tarski(C,k9_xtuple_0(A)) & r1_tarski(C,k9_xtuple_0(B)) ) => ( k5_relat_1(A,C) = k5_relat_1(B,C) <=> ! [D] : ( r2_hidden(D,C) => k1_funct_1(A,D) = k1_funct_1(B,D) ) ) ) ) ) )).
fof(t94_funct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(B)) => ( r1_tarski(k7_relset_1(A,B,C,D),E) <=> r1_tarski(D,k8_relset_1(A,B,C,E)) ) ) ) ) ) ) )).
fof(t94_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( k5_relat_1(k1_funct_4(A,B),D) = k5_relat_1(C,D) => k5_relat_1(k1_funct_4(C,B),D) = k5_relat_1(k1_funct_4(A,B),D) ) ) ) ) )).
fof(t94_funct_7,axiom,( ! [A] : ! [B] : k1_funct_7(k9_finseq_1(A),1,B) = k9_finseq_1(B) )).
fof(t94_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ( C != k4_tarski(k10_finseq_1(A,B),k4_gfacirc1) => ! [D] : ( m1_subset_1(D,k4_card_3(u3_msualg_1(k34_gfacirc1(A,B,C),k35_gfacirc1(A,B,C)))) => ! [E] : ( m1_subset_1(E,k6_margrel1) => ! [F] : ( m1_subset_1(F,k6_margrel1) => ! [G] : ( 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(k34_gfacirc1(A,B,C),k35_gfacirc1(A,B,C),k5_facirc_1(k34_gfacirc1(A,B,C),k35_gfacirc1(A,B,C),D,2),k36_gfacirc1(A,B,C)) = k2_binarith(k2_binarith(k9_margrel1(E),F),k9_margrel1(G)) ) ) ) ) ) ) )).
fof(t94_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m2_glib_000(B,A,k6_glib_000(A),k21_glib_000(A,k6_glib_000(A))) => r5_glib_000(A,B) ) ) )).
fof(t94_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ( r1_glib_000(A,k4_glib_001(A,B),D,C) => ( r2_hidden(D,k13_glib_001(A,B)) | k5_card_1(k13_glib_001(A,k10_glib_001(A,B,C))) = k1_nat_1(k5_card_1(k13_glib_001(A,B)),1) ) ) ) ) )).
fof(t94_group_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_group_2(D,B) => ( r2_hidden(A,k11_group_2(B,D,C)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k6_algstr_0(B,E,F) & r2_hidden(E,C) & r1_struct_0(D,F) ) ) ) ) ) ) )).
fof(t94_group_3,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ( r2_hidden(A,k8_group_3(B,C)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) & A = D & r4_group_3(B,C,D) ) ) ) ) )).
fof(t94_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v8_group_9(C,A,B) & m2_finseq_1(C,k6_group_9(A,B)) ) => ! [D] : ( m2_finseq_1(D,k6_group_9(A,B)) => ! [E] : ( 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) ) => v8_group_9(D,A,B) ) ) ) ) ) )).
fof(t94_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v1_algstr_1(A) & v1_int_3(A) & l6_algstr_0(A) ) => v8_ideal_1(A) ) )).
fof(t94_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( A = k1_rcomp_1(k5_numbers,k3_xcmplx_0(k28_sin_cos,2)) => k2_integra5(A,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)) = k5_numbers ) ) )).
fof(t94_intpro_1,axiom,( r1_tarski(k12_intpro_1,k14_intpro_1) )).
fof(t94_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [D] : ( ( 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)),k7_jgraph_4(A),B) & C = k8_struct_0(k15_euclid(2)) & B = a_0_0_jgraph_4 ) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) | r1_xxreal_0(1,A) | v5_pre_topc(D,k1_pre_topc(k15_euclid(2),B),k1_pre_topc(k15_euclid(2),C)) ) ) ) ) ) ) )).
fof(t94_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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) = 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),k18_euclid(D)) & r1_xxreal_0(k18_euclid(C),H) & k1_funct_1(I,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t94_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ~ ( r1_jordan24(2,A,k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) & r1_xboole_0(k1_rltopsp1(k15_euclid(2),k19_euclid(k5_numbers,3),k19_euclid(k5_numbers,k4_xcmplx_0(3))),A) ) ) )).
fof(t94_jordan2c,axiom,( ! [A] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(t94_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( v6_limfunc1(A) => ( v6_limfunc1(k56_valued_1(k1_numbers,k1_numbers,A)) & k5_limfunc1(k56_valued_1(k1_numbers,k1_numbers,A)) = k9_complex1(k5_limfunc1(A)) ) ) ) )).
fof(t94_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,C,C) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,k1_numbers,C,C) & m2_finseq_1(E,k3_finseq_2(k1_numbers)) ) => ( ( r1_xxreal_0(k5_numbers,A) & v4_matrix10(D) & r1_matrix10(D,E) ) => ( r1_xxreal_0(B,A) | r1_matrix10(k6_matrix10(C,A,D),k6_matrix10(C,B,E)) ) ) ) ) ) ) ) )).
fof(t94_matrix13,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ( ~ ( ~ r1_xxreal_0(k8_matrix13(A,B),k5_numbers) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(k4_tarski(C,D),k2_matrix_0(B)) & k3_matrix_0(u1_struct_0(A),B,C,D) != k4_struct_0(A) ) ) ) ) & ~ ( ? [C] : ( v7_ordinal1(C) & ? [D] : ( v7_ordinal1(D) & r2_hidden(k4_tarski(C,D),k2_matrix_0(B)) & k3_matrix_0(u1_struct_0(A),B,C,D) != k4_struct_0(A) ) ) & r1_xxreal_0(k8_matrix13(A,B),k5_numbers) ) ) ) ) )).
fof(t94_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( k3_finseq_1(B) = A => ( r1_xxreal_0(A,k5_numbers) | k11_matrixr1(k4_matrix_0(k1_numbers,C),B) = k12_matrixr1(C,B) ) ) ) ) ) )).
fof(t94_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => k13_member_1(A,k5_member_1(B)) = k5_member_1(k13_member_1(A,B)) ) ) )).
fof(t94_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( k12_supinf_2(C,E) = k5_numbers => ( ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ~ ( F = k1_relset_1(A,D) & r1_mesfunc1(A,B,D,F) ) ) | k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,E)) = k5_numbers ) ) ) ) ) ) ) )).
fof(t94_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( ? [E] : ( 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) <=> r3_mesfunc6(A,B,C,k56_valued_1(A,k1_numbers,D)) ) ) ) ) ) ) )).
fof(t94_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( D != k1_xboole_0 & r1_tarski(D,k1_relset_1(u1_struct_0(A),C)) & v1_ncfcont1(D,A) & r8_ncfcont1(A,B,C,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r2_hidden(E,D) & r2_hidden(F,D) & k7_partfun1(k1_numbers,k4_normsp_0(u1_struct_0(A),B,C),E) = k2_seq_4(k7_relset_1(u1_struct_0(A),k1_numbers,k4_normsp_0(u1_struct_0(A),B,C),D)) & k7_partfun1(k1_numbers,k4_normsp_0(u1_struct_0(A),B,C),F) = k3_seq_4(k7_relset_1(u1_struct_0(A),k1_numbers,k4_normsp_0(u1_struct_0(A),B,C),D)) ) ) ) ) ) ) ) ) )).
fof(t94_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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),k5_pboole(A,B,k3_pboole(A,B,C))) ) ) )).
fof(t94_prepower,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_nat_d(A,B) & r1_nat_d(A,C) ) => r1_int_1(A,k6_xcmplx_0(B,C)) ) ) ) ) )).
fof(t94_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( ( B = k12_qc_lang1(A) | v2_qc_lang1(B,A) ) <=> k15_qc_lang2(A,B) = k1_tarski(B) ) ) ) )).
fof(t94_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => k24_quaterni(A) = k22_quaterni(k22_quaterni(k19_quaterni(k4_xcmplx_0(k13_quaterni(A)),k21_quaterni(k4_xcmplx_0(k14_quaterni(A)),k1_xcmplx_0)),k21_quaterni(k4_xcmplx_0(k15_quaterni(A)),k11_quaterni)),k21_quaterni(k4_xcmplx_0(k16_quaterni(A)),k12_quaterni)) ) )).
fof(t94_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r1_tarski(A,B) => r1_tarski(k6_relat_1(A,C),k6_relat_1(B,C)) ) ) )).
fof(t94_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_afinsq_1(D))) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(D))) => ! [G] : ( ( ~ v2_struct_0(G) & l1_rewrite3(G,E) ) => ! [H] : ( ( ~ v2_struct_0(H) & l1_rewrite3(H,F) ) => ( ( u1_struct_0(G) = u1_struct_0(H) & u1_rewrite3(E,G) = u1_rewrite3(F,H) & r4_rewrite3(D,E,G,A,B,C) ) => r4_rewrite3(D,F,H,A,B,C) ) ) ) ) ) ) )).
fof(t94_rfunct_1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(C,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(C,k1_numbers))) ) => ( ( ( v1_seq_2(k2_partfun1(C,k1_numbers,D,A)) & v3_funct_1(k2_partfun1(C,k1_numbers,E,B)) ) => v1_seq_2(k2_partfun1(C,k1_numbers,k47_valued_1(C,k1_numbers,k1_numbers,D,E),k3_xboole_0(A,B))) ) & ( ( v2_seq_2(k2_partfun1(C,k1_numbers,D,A)) & v3_funct_1(k2_partfun1(C,k1_numbers,E,B)) ) => v2_seq_2(k2_partfun1(C,k1_numbers,k47_valued_1(C,k1_numbers,k1_numbers,D,E),k3_xboole_0(A,B))) ) & ( ( v1_comseq_2(k2_partfun1(C,k1_numbers,D,A)) & v3_funct_1(k2_partfun1(C,k1_numbers,E,B)) ) => ( v1_comseq_2(k2_partfun1(C,k1_numbers,k47_valued_1(C,k1_numbers,k1_numbers,D,E),k3_xboole_0(A,B))) & v1_comseq_2(k2_partfun1(C,k1_numbers,k47_valued_1(C,k1_numbers,k1_numbers,E,D),k3_xboole_0(A,B))) & v1_comseq_2(k2_partfun1(C,k1_numbers,k20_valued_1(C,k1_numbers,k1_numbers,D,E),k3_xboole_0(A,B))) ) ) ) ) ) ) )).
fof(t94_rvsum_1,axiom,( k21_rvsum_1(k6_finseq_1(k1_numbers)) = 1 )).
fof(t94_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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(k7_card_1(3),k1_scmfsa_2,A))) ) ) )).
fof(t94_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & 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] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & v1_funct_1(D) & v1_finset_1(D) & v1_afinsq_1(D) & v3_scmpds_4(D) ) => ! [E] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_scmpds_2)) ) => ! [G] : ( v1_int_1(G) => ( ~ r1_xxreal_0(k5_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) ) ) ) ) ) ) ) ) )).
fof(t94_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ~ ( r2_hidden(k2_tarski(k3_tarski(A),B),k1_scmyciel(k12_scmyciel(A))) & ! [C] : ~ ( r2_hidden(C,k3_tarski(A)) & B = k4_tarski(C,k3_tarski(A)) ) ) ) )).
fof(t94_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r4_semi_af1(A,B,C,D,E,E) => E = C ) ) ) ) ) ) )).
fof(t94_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => r1_xxreal_0(k5_numbers,k20_seq_4(B)) ) ) )).
fof(t94_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_kurato_0(C,A) => ( v3_kurato_0(k7_setlim_2(A,C,B),A) & k4_kurato_0(A,k7_setlim_2(A,C,B)) = k7_subset_1(A,B,k4_kurato_0(A,C)) ) ) ) ) )).
fof(t94_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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,k5_sheffer1(A,B,B),C)),k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,D,B)),k5_sheffer1(A,C,k5_sheffer1(A,D,B)))) = k5_sheffer1(A,C,k5_sheffer1(A,D,B)) ) ) ) ) )).
fof(t94_sin_cos6,axiom,( k4_sin_cos6(k5_numbers) = k7_xcmplx_0(k28_sin_cos,2) )).
fof(t94_sin_cos9,axiom,( ! [A] : ( ( 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,k2_sin_cos9,k1_taylor_1(2)),k7_xcmplx_0(1,2)))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) ) => ( r2_fdiff_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)),k7_xcmplx_0(1,2)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_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)),k7_xcmplx_0(1,2)),A),B) = k4_xcmplx_0(k7_xcmplx_0(k1_funct_1(k2_sin_cos9,B),k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t94_sincos10,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k2_sincos10,k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1)))) )).
fof(t94_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k8_tdlat_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k8_tdlat_1(A))) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k5_tdlat_1(A)) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(u1_struct_0(A)),k5_tdlat_1(A)) => ( ( B = D & C = E ) => ( k1_lattices(k8_tdlat_1(A),B,C) = k4_subset_1(u1_struct_0(A),D,E) & k2_lattices(k8_tdlat_1(A),B,C) = k2_pre_topc(A,k1_tops_1(A,k9_subset_1(u1_struct_0(A),D,E))) ) ) ) ) ) ) ) )).
fof(t94_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_tmap_1(A,B)))) => ( C = B => v3_pre_topc(C,k6_tmap_1(A,B)) ) ) ) ) )).
fof(t94_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v8_transgeo(B,A) & v1_aff_1(C,A) ) => v1_aff_1(k7_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),A) ) ) ) ) )).
fof(t94_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v1_valued_2(D) => ! [E] : ( v1_valued_2(E) => ! [F] : ( v1_valued_2(F) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,D))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(B,E))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(C,F))) ) => k84_valued_2(k3_xboole_0(A,B),C,k2_valued_2(k3_xboole_0(k1_valued_2(D),k1_valued_2(E))),F,k90_valued_2(A,B,D,E,G,H),I) = k90_valued_2(k3_xboole_0(A,C),B,k2_valued_2(k3_xboole_0(k1_valued_2(D),k1_valued_2(F))),E,k84_valued_2(A,C,D,F,G,I),H) ) ) ) ) ) ) )).
fof(t94_xboole_1,axiom,( ! [A] : ! [B] : k2_xboole_0(A,B) = k5_xboole_0(k5_xboole_0(A,B),k3_xboole_0(A,B)) )).
fof(t94_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k10_xboolean(A,k8_xboolean(A,B)) = k6_xboolean(A,B) ) ) )).
fof(t94_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( k3_xcmplx_0(A,C) = k3_xcmplx_0(B,D) => ( C = k5_numbers | D = k5_numbers | k7_xcmplx_0(A,D) = k7_xcmplx_0(B,C) ) ) ) ) ) ) )).
fof(t94_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(k5_numbers,A) => ( r1_xxreal_0(k5_numbers,k3_xcmplx_0(k6_xcmplx_0(B,A),k2_xcmplx_0(B,A))) | ( ~ r1_xxreal_0(B,k4_xcmplx_0(A)) & ~ r1_xxreal_0(A,B) ) ) ) ) ) )).
fof(t94_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(D,A) => r1_xboole_0(k4_xxreal_1(C,D),k2_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t94_xxreal_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( v1_xxreal_0(B) => ~ ( ~ r1_xxreal_0(k1_xxreal_2(A),B) & ! [C] : ( m1_subset_1(C,k6_numbers) => ~ ( r2_hidden(C,A) & ~ r1_xxreal_0(C,B) ) ) ) ) ) )).
fof(t94_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => k4_xxreal_3(2,A) = k1_xxreal_3(A,A) ) )).
fof(t94_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( ~ v1_xboole_0(C) => ( r2_zf_model(C,A) => r2_zf_model(C,k13_zf_lang(B,A)) ) ) ) ) )).
fof(t94_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(A,B) => ( r1_tarski(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) & r1_tarski(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) ) ) )).
fof(t94_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( r1_struct_0(k7_zmodul01(A,B,C),D) <=> ( r1_struct_0(B,D) & r1_struct_0(C,D) ) ) ) ) ) )).
fof(t95_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_abcmiz_1(B,A,k13_abcmiz_1(A)) => k46_abcmiz_1(A,k30_abcmiz_1(A,k32_abcmiz_1(A),B)) = k46_abcmiz_1(A,B) ) ) )).
fof(t95_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r2_hidden(B,k18_aofa_000(A)) => v15_aofa_000(B,A) ) ) ) )).
fof(t95_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & v22_aofa_a00(D,A,1,1,11) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( ( v19_aofa_a00(F,A) & m1_subset_1(F,u1_struct_0(A)) ) => ! [G] : ( ( v3_aofa_a01(G,A,B,C,u4_aofa_a00(A,B,C,E),F) & m1_msafree4(G,u1_struct_0(A),u4_aofa_a00(A,B,C,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),F)) ) => ! [H] : ( ( v3_aofa_a01(H,A,B,C,u4_aofa_a00(A,B,C,E),F) & m1_msafree4(H,u1_struct_0(A),u4_aofa_a00(A,B,C,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),F)) ) => ! [I] : ( ( v3_aofa_a01(I,A,B,C,u4_aofa_a00(A,B,C,E),k37_aofa_a00(A)) & m1_msafree4(I,u1_struct_0(A),u4_aofa_a00(A,B,C,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),k37_aofa_a00(A))) ) => ! [J] : ( ( v3_aofa_a01(J,A,B,C,u4_aofa_a00(A,B,C,E),u8_aofa_a00(A)) & m1_msafree4(J,u1_struct_0(A),u4_aofa_a00(A,B,C,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u8_aofa_a00(A))) ) => ! [K] : ( ( ~ v2_struct_0(K) & v2_unialg_1(K) & v3_unialg_1(K) & v4_unialg_1(K) & v3_aofa_000(K) & v4_aofa_000(K) & v5_aofa_000(K) & v6_aofa_000(K) & ~ v10_aofa_000(K) & v11_aofa_000(K) & v12_aofa_000(K) & v5_aofa_a01(K,A,B,C,E) & l3_aofa_a00(K,A,C,u4_aofa_a00(A,B,C,E)) ) => ! [L] : ( m1_aofa_000(L,K,k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E)),k14_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E),u8_aofa_a00(A),J,k2_aofa_a01(A,D))) => ( ( r2_hidden(L,k20_aofa_a00(A,B,C,D,E,K,u8_aofa_a00(A),J,k2_aofa_a01(A,D))) & v11_aofa_a00(E,A,B,C,D) ) => ( H = G | r6_aofa_000(K,k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E)),k14_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E),u8_aofa_a00(A),J,k2_aofa_a01(A,D)),k13_aofa_000(K,k12_aofa_a00(A,C,u4_aofa_a00(A,B,C,E),K,F,G,k27_aofa_a00(A,C,F)),k17_aofa_000(K,k12_aofa_a00(A,C,u4_aofa_a00(A,B,C,E),K,F,H,k28_aofa_a00(A,C,F)),k6_aofa_a01(A,B,C,E,K,J,F,k38_aofa_a00(A,C,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),k37_aofa_a00(A),I),F),k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),F,H)),k15_aofa_000(K,k6_aofa_a01(A,B,C,E,K,J,F,k39_aofa_a00(A,C,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),k37_aofa_a00(A),I),F,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),F,H)),k39_aofa_a00(A,C,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),k37_aofa_a00(A),I),F,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),F,G))),k12_aofa_a00(A,C,u4_aofa_a00(A,B,C,E),K,F,G,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),F,H))),k12_aofa_a00(A,C,u4_aofa_a00(A,B,C,E),K,F,H,k30_aofa_a00(A,C,F,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),F,H),k28_aofa_a00(A,C,F))))),L,a_6_0_aofa_a01(A,B,C,D,E,I)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t95_arytm_3,axiom,( ! [A] : ( m1_subset_1(A,k5_arytm_3) => ! [B] : ( m1_subset_1(B,k5_arytm_3) => ~ ( B != k11_arytm_3 & ! [C] : ( m1_subset_1(C,k5_arytm_3) => ~ ( r2_hidden(C,k4_ordinal1) & r3_arytm_3(A,k10_arytm_3(C,B)) ) ) ) ) ) )).
fof(t95_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ! [C] : ( v1_card_1(C) => ! [D] : ( v1_card_1(D) => ( ( r2_hidden(A,B) & r2_hidden(C,D) ) => ( r2_hidden(k1_card_2(A,C),k1_card_2(B,D)) & r2_hidden(k1_card_2(C,A),k1_card_2(B,D)) ) ) ) ) ) ) )).
fof(t95_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( m1_subset_1(C,k4_card_3(k1_funct_4(A,B))) => r2_hidden(k11_card_3(k1_funct_4(A,B),C,k9_xtuple_0(B)),k4_card_3(B)) ) ) ) )).
fof(t95_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ( r1_xxreal_0(k5_card_1(k6_glib_000(A)),3) => v6_chord(A) ) ) )).
fof(t95_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( m2_clvect_1(B,A,k4_clvect_1(A)) => B = u1_struct_0(A) ) ) ) )).
fof(t95_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => ( v3_clvect_2(B,A) => v3_clvect_2(k1_valued_0(u1_struct_0(A),B,C),A) ) ) ) ) )).
fof(t95_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => k13_cohsp_1(k15_cohsp_1(A,B)) = k16_cohsp_1(k13_cohsp_1(A),k13_cohsp_1(B)) ) ) )).
fof(t95_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k26_sin_cos),D) ) & r2_hidden(B,k1_relset_1(k1_numbers,k26_sin_cos)) & r2_hidden(k6_xcmplx_0(B,A),k1_relset_1(k1_numbers,k26_sin_cos)) ) => k1_funct_1(k4_diff_1(C,A),B) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k19_sin_cos(k3_xcmplx_0(2,B)),k19_sin_cos(k3_xcmplx_0(2,k6_xcmplx_0(A,B))))),k1_square_1(k3_xcmplx_0(k19_sin_cos(B),k19_sin_cos(k6_xcmplx_0(B,A)))))) ) ) ) ) )).
fof(t95_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( v1_xreal_0(E) => ( ( 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,k3_xcmplx_0(A,k1_fdiff_1(B,E))),k9_euclid(3,k3_euclid_8,k3_xcmplx_0(A,k1_fdiff_1(C,E)))),k9_euclid(3,k4_euclid_8,k3_xcmplx_0(A,k1_fdiff_1(D,E)))) ) ) ) ) ) ) )).
fof(t95_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(k1_euclid(A)),k5_euclidlp(A)) => ( ( r2_hidden(B,D) & r2_hidden(C,D) ) => r1_tarski(k2_euclid_4(A,B,C),D) ) ) ) ) ) )).
fof(t95_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ r1_xxreal_0(A,k5_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))) ) ) ) )).
fof(t95_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v3_card_1(B,1) & m2_finseq_1(B,A) ) => ? [C] : ( m1_subset_1(C,A) & B = k12_finseq_1(A,C) ) ) ) )).
fof(t95_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v2_funct_1(A) & k10_xtuple_0(A) = k1_tarski(B) ) => A = k9_finseq_1(B) ) ) )).
fof(t95_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => k1_finseq_6(A,k2_finseq_4(A,B,C),B) = k2_finseq_4(A,B,C) ) ) ) )).
fof(t95_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => k7_flang_1(A,k2_flang_2(A,B),C) = k1_flang_2(A,B,k5_numbers,C) ) ) )).
fof(t95_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => r1_tarski(k4_subset_1(k8_afinsq_1(A),k2_flang_3(A,B),k2_flang_3(A,C)),k2_flang_3(A,k4_subset_1(k8_afinsq_1(A),B,C))) ) ) )).
fof(t95_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( k9_xtuple_0(A) = k9_xtuple_0(B) & ! [D] : ( r2_hidden(D,C) => k1_funct_1(A,D) = k1_funct_1(B,D) ) ) => k5_relat_1(A,C) = k5_relat_1(B,C) ) ) ) )).
fof(t95_funct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(A)) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,D,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(D,B))) ) => ( ! [F] : ( m1_subset_1(F,A) => ( r2_hidden(F,D) => k3_funct_2(A,B,C,F) = k1_funct_1(E,F) ) ) => k2_partfun1(A,B,C,D) = E ) ) ) ) ) ) )).
fof(t95_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( k5_relat_1(A,D) = k5_relat_1(C,D) => k5_relat_1(k1_funct_4(C,B),D) = k5_relat_1(k1_funct_4(A,B),D) ) ) ) ) )).
fof(t95_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => k1_funct_4(A,k16_funcop_1(B,k1_funct_1(A,B))) = A ) ) )).
fof(t95_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : k3_msafree2(k37_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(k36_gfacirc1(A,B,C))),k1_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))),k1_tarski(k33_gfacirc1(A,B,C))) )).
fof(t95_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ! [D] : ! [E] : ( m2_glib_000(E,A,C,D) => ( r5_glib_000(A,B) => m2_glib_000(E,B,C,D) ) ) ) ) )).
fof(t95_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ! [D] : ~ ( r2_hidden(C,k13_glib_001(A,B)) & r2_hidden(D,k13_glib_001(A,B)) & ! [E] : ( m3_glib_001(E,A) => ~ r1_glib_001(A,C,D,E) ) ) ) ) )).
fof(t95_group_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_group_2(D,B) => ( r2_hidden(A,k12_group_2(B,D,C)) <=> ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & ? [F] : ( m1_subset_1(F,u1_struct_0(B)) & A = k6_algstr_0(B,E,F) & r1_struct_0(D,E) & r2_hidden(F,C) ) ) ) ) ) ) )).
fof(t95_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k8_group_3(A,C)) <=> r4_group_3(A,B,C) ) ) ) ) )).
fof(t95_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v8_group_9(C,A,B) & m2_finseq_1(C,k6_group_9(A,B)) ) => ! [D] : ( ( v8_group_9(D,A,B) & m2_finseq_1(D,k6_group_9(A,B)) ) => ~ ( r4_group_9(A,B,C,D) & ! [E] : ( v7_ordinal1(E) => k3_finseq_1(C) != k2_xcmplx_0(k3_finseq_1(D),E) ) ) ) ) ) )).
fof(t95_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ( v8_ideal_1(A) => v6_ideal_1(A) ) ) )).
fof(t95_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( A = k1_rcomp_1(k3_xcmplx_0(k2_nat_1(2,B),k28_sin_cos),k3_xcmplx_0(k1_nat_1(k2_nat_1(2,B),1),k28_sin_cos)) => k2_integra5(A,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)) = k5_numbers ) ) ) )).
fof(t95_intpro_1,axiom,( r1_tarski(k8_intpro_1,k14_intpro_1) )).
fof(t95_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(2),B)))) => ! [D] : ( ( 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)),k7_jgraph_4(A),C) & B = k8_struct_0(k15_euclid(2)) & C = a_0_1_jgraph_4 ) => ( r1_xxreal_0(A,k4_xcmplx_0(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)) ) ) ) ) ) ) )).
fof(t95_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) = 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),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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t95_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_jordan24(2,A,k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) => ! [B] : ( ( v2_compts_1(B,k15_euclid(2)) & v1_jordan21(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( 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(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers),B) & r1_topreal1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_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(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_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) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( D = k1_connsp_1(k1_pre_topc(k15_euclid(2),k3_subset_1(u1_struct_0(k15_euclid(2)),A)),k2_connsp_3(k15_euclid(2),k3_subset_1(u1_struct_0(k15_euclid(2)),A),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k1_jordan21(k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k2_jordan21(B),k19_euclid(k5_numbers,k4_xcmplx_0(3))),C)),k2_jordan21(B)),k7_xcmplx_0(1,2)))) => ( r1_jordan2c(2,A,D) & ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( r1_jordan2c(2,A,E) => E = D ) ) ) ) ) ) ) ) ) ) )).
fof(t95_jordan2c,axiom,( ! [A] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(t95_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v6_limfunc1(A) & ! [B] : ( v1_xreal_0(B) => ? [C] : ( v1_xreal_0(C) & ~ r1_xxreal_0(B,C) & r2_hidden(C,k1_relset_1(k1_numbers,A)) & k1_funct_1(A,C) != k5_numbers ) ) ) => ( k5_limfunc1(A) = k5_numbers | ( v6_limfunc1(k6_rfunct_1(k1_numbers,k1_numbers,A)) & k5_limfunc1(k6_rfunct_1(k1_numbers,k1_numbers,A)) = k5_xcmplx_0(k5_limfunc1(A)) ) ) ) ) )).
fof(t95_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,C,C) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,k1_numbers,C,C) & m2_finseq_1(E,k3_finseq_2(k1_numbers)) ) => ( ( r1_xxreal_0(k5_numbers,A) & v1_matrix10(D) & r2_matrix10(D,E) ) => ( r1_xxreal_0(B,A) | r1_matrix10(k6_matrix10(C,A,D),k6_matrix10(C,B,E)) ) ) ) ) ) ) ) )).
fof(t95_matrix13,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ( k8_matrix13(A,B) = k5_numbers <=> B = k1_matrix_3(A,k3_finseq_1(B),k1_matrix_0(B)) ) ) ) )).
fof(t95_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( k3_finseq_1(B) = A => ( r1_xxreal_0(A,k5_numbers) | k12_matrixr1(k4_matrix_0(k1_numbers,C),B) = k11_matrixr1(C,B) ) ) ) ) ) )).
fof(t95_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_membered(C) => r1_tarski(k13_member_1(A,k9_member_1(B,C)),k9_member_1(k13_member_1(A,B),k13_member_1(A,C))) ) ) ) )).
fof(t95_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ( ( E = k1_relset_1(A,D) & r1_mesfunc1(A,B,D,E) & k12_supinf_2(C,F) = k5_numbers ) => k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,k7_prob_1(A,B,E,F))) = k7_mesfunc5(A,B,C,D) ) ) ) ) ) ) ) )).
fof(t95_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( r3_mesfunc6(A,B,C,D) => r1_xxreal_0(k3_extreal1(k1_mesfunc6(A,B,C,D)),k1_mesfunc6(A,B,C,k56_valued_1(A,k1_numbers,D))) ) ) ) ) ) )).
fof(t95_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) => ! [D] : ( 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) & r9_ncfcont1(B,A,C,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ~ ( r2_hidden(E,D) & r2_hidden(F,D) & k7_partfun1(k1_numbers,k4_normsp_0(u1_struct_0(B),A,C),E) = k2_seq_4(k7_relset_1(u1_struct_0(B),k1_numbers,k4_normsp_0(u1_struct_0(B),A,C),D)) & k7_partfun1(k1_numbers,k4_normsp_0(u1_struct_0(B),A,C),F) = k3_seq_4(k7_relset_1(u1_struct_0(B),k1_numbers,k4_normsp_0(u1_struct_0(B),A,C),D)) ) ) ) ) ) ) ) ) )).
fof(t95_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => r6_pboole(A,k4_pboole(A,C,B),k5_pboole(A,B,k2_pboole(A,B,C))) ) ) )).
fof(t95_prepower,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_nat_d(A,B) <=> r1_int_1(A,B) ) ) ) )).
fof(t95_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v3_qc_lang1(B,A) => k15_qc_lang2(A,B) = k2_xboole_0(k15_qc_lang2(A,k18_qc_lang1(A,B)),k1_tarski(B)) ) ) ) )).
fof(t95_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => k25_quaterni(A,B) = k22_quaterni(k22_quaterni(k19_quaterni(k6_xcmplx_0(k13_quaterni(A),k13_quaterni(B)),k21_quaterni(k6_xcmplx_0(k14_quaterni(A),k14_quaterni(B)),k1_xcmplx_0)),k21_quaterni(k6_xcmplx_0(k15_quaterni(A),k15_quaterni(B)),k11_quaterni)),k21_quaterni(k6_xcmplx_0(k16_quaterni(A),k16_quaterni(B)),k12_quaterni)) ) ) )).
fof(t95_relat_1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => ! [C] : ( v1_relat_1(C) => ( r1_tarski(B,C) => r1_tarski(k6_relat_1(A,B),k6_relat_1(A,C)) ) ) ) )).
fof(t95_rewrite3,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(B))) => ! [D] : ( ( ~ v2_struct_0(D) & l1_rewrite3(D,C) ) => r4_rewrite3(B,C,D,A,k2_flang_1(B),A) ) ) ) )).
fof(t95_rvsum_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k19_rvsum_1(k9_finseq_1(A)) = A ) )).
fof(t95_scmfsa_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_scmfsa_2(B) => ~ r2_hidden(B,k1_relset_1(u1_struct_0(k1_scmfsa_2),k7_memstr_0(k7_card_1(3),k1_scmfsa_2,A))) ) ) )).
fof(t95_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(D) & 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] : ( ( v1_ami_2(E) & m1_subset_1(E,u1_struct_0(k1_scmpds_2)) ) => ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_scmpds_2)) ) => ! [G] : ( v1_int_1(G) => ( r1_xxreal_0(k5_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) ) ) ) ) ) ) ) ) )).
fof(t95_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( r2_hidden(B,k3_tarski(A)) => r2_hidden(k1_tarski(k4_tarski(B,k3_tarski(A))),k12_scmyciel(A)) ) ) )).
fof(t95_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( F != C & r4_semi_af1(A,B,C,D,E,F) & r1_semi_af1(A,F,C,E) ) ) ) ) ) ) ) )).
fof(t95_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => k20_seq_4(k16_seq_4(A,B)) = k20_seq_4(B) ) ) )).
fof(t95_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_kurato_0(C,A) => ( v3_kurato_0(k8_setlim_2(A,C,B),A) & k4_kurato_0(A,k8_setlim_2(A,C,B)) = k7_subset_1(A,k4_kurato_0(A,C),B) ) ) ) ) )).
fof(t95_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,C,k5_sheffer1(A,B,k5_sheffer1(A,B,B)))) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),C),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,B)),C)) ) ) ) )).
fof(t95_sin_cos6,axiom,( k4_sin_cos6(1) = k5_numbers )).
fof(t95_sin_cos9,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k1_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k1_sin_cos9),A),B) = k2_xcmplx_0(k1_funct_1(k1_sin_cos9,B),k7_xcmplx_0(B,k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t95_sincos10,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k3_sincos10,k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1)))) )).
fof(t95_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( k5_lattices(k8_tdlat_1(A)) = k1_struct_0(A) & k6_lattices(k8_tdlat_1(A)) = k2_struct_0(A) ) ) )).
fof(t95_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(B,A) <=> g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = k6_tmap_1(A,B) ) ) ) )).
fof(t95_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( v8_transgeo(B,A) & r5_aff_1(A,C,D) ) => r5_aff_1(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)) ) ) ) ) ) )).
fof(t95_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v1_valued_2(D) => ! [E] : ( v1_valued_2(E) => ! [F] : ( v1_valued_2(F) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,D))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(B,E))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(C,F))) ) => k90_valued_2(k3_xboole_0(A,B),C,k2_valued_2(k3_xboole_0(k1_valued_2(D),k1_valued_2(E))),F,k90_valued_2(A,B,D,E,G,H),I) = k90_valued_2(A,k3_xboole_0(B,C),D,k2_valued_2(k3_xboole_0(k1_valued_2(E),k1_valued_2(F))),G,k84_valued_2(B,C,E,F,H,I)) ) ) ) ) ) ) )).
fof(t95_xboole_1,axiom,( ! [A] : ! [B] : k3_xboole_0(A,B) = k5_xboole_0(k5_xboole_0(A,B),k2_xboole_0(A,B)) )).
fof(t95_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k10_xboolean(A,k6_xboolean(A,B)) = k8_xboolean(A,B) ) ) )).
fof(t95_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( k7_xcmplx_0(A,D) = k7_xcmplx_0(B,C) => ( C = k5_numbers | D = k5_numbers | k3_xcmplx_0(A,C) = k3_xcmplx_0(B,D) ) ) ) ) ) ) )).
fof(t95_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( r1_xxreal_0(k5_numbers,k3_xcmplx_0(k6_xcmplx_0(B,A),k2_xcmplx_0(B,A))) & ~ r1_xxreal_0(B,k4_xcmplx_0(A)) & ~ r1_xxreal_0(A,B) ) ) ) )).
fof(t95_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(D,A) => r1_xboole_0(k2_xxreal_1(C,D),k1_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t95_xxreal_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( m1_subset_1(B,k6_numbers) => ~ ( ~ r1_xxreal_0(B,k2_xxreal_2(A)) & ! [C] : ( m1_subset_1(C,k6_numbers) => ~ ( r2_hidden(C,A) & ~ r1_xxreal_0(B,C) ) ) ) ) ) )).
fof(t95_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( v1_xreal_0(A) => k4_xxreal_3(A,k1_xxreal_3(B,C)) = k1_xxreal_3(k4_xxreal_3(A,B),k4_xxreal_3(A,C)) ) ) ) ) )).
fof(t95_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( ~ v1_xboole_0(D) => ( r2_zf_model(D,A) <=> r2_zf_model(D,k14_zf_lang(B,C,A)) ) ) ) ) ) )).
fof(t95_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( r1_tarski(A,C) & r1_tarski(B,D) ) => r1_tarski(k2_zfmisc_1(A,B),k2_zfmisc_1(C,D)) ) )).
fof(t95_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_zmodul01(B) & m1_zmodul01(B,A) ) => k6_zmodul01(A,B,B) = B ) ) )).
fof(t96_abcmiz_1,axiom,( ! [A] : ( l1_msualg_1(A) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_trees_2(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v3_trees_2(D) ) => r6_pboole(u1_struct_0(A),k2_msafree3(A,k4_trees_4(k4_tarski(B,u1_struct_0(A)),k10_finseq_1(C,D))),k2_pboole(u1_struct_0(A),k2_msafree3(A,C),k2_msafree3(A,D))) ) ) ) )).
fof(t96_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( m1_aofa_000(E,A,B,C) => r2_hidden(k4_tarski(D,k12_aofa_000(A)),k21_aofa_000(A,B,C,E)) ) ) ) ) ) )).
fof(t96_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_aofa_a01(D,A,B,C) & l4_aofa_a00(D,A,B,C) ) => ! [E] : ( ( v19_aofa_a00(E,A) & m1_subset_1(E,u1_struct_0(A)) ) => ! [F] : ( ( v3_aofa_a01(F,A,B,C,u4_aofa_a00(A,B,C,D),k37_aofa_a00(A)) & m1_msafree4(F,u1_struct_0(A),u4_aofa_a00(A,B,C,D),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),k37_aofa_a00(A))) ) => ( v7_aofa_a01(D,A,B,C) => ! [G] : ( m1_subset_1(G,k1_funct_1(u3_msualg_1(A,C),E)) => r2_hidden(k39_aofa_a00(A,C,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,D),k37_aofa_a00(A),F),E,G),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),E)) ) ) ) ) ) ) ) ) )).
fof(t96_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ! [C] : ( v1_card_1(C) => ( r2_hidden(k1_card_2(A,B),k1_card_2(A,C)) => r2_hidden(B,C) ) ) ) ) )).
fof(t96_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v1_funct_1(B) ) => ( r1_partfun1(A,B) => ! [C] : ( m1_subset_1(C,k4_card_3(k1_funct_4(A,B))) => r2_hidden(k11_card_3(k1_funct_4(A,B),C,k9_xtuple_0(A)),k4_card_3(A)) ) ) ) ) )).
fof(t96_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_clvect_1(B,A) => ! [C] : ( m2_clvect_1(C,A,B) => ( r2_hidden(k4_struct_0(A),C) <=> C = u1_struct_0(B) ) ) ) ) )).
fof(t96_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( v7_ordinal1(C) => ( v3_funct_1(B) => v3_funct_1(k1_valued_0(u1_struct_0(A),B,C)) ) ) ) ) )).
fof(t96_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( r2_hidden(C,k17_cohsp_1(A,B)) <=> ? [D] : ( m1_subset_1(D,A) & ? [E] : ( m1_subset_1(E,B) & r1_tarski(C,k2_zfmisc_1(D,E)) ) ) ) ) ) )).
fof(t96_diff_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => k1_funct_1(C,D) = k1_funct_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k26_sin_cos),D) ) & r2_hidden(k2_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k26_sin_cos)) & r2_hidden(k6_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k26_sin_cos)) ) => k1_funct_1(k5_diff_1(C,A),B) = k4_xcmplx_0(k7_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k19_sin_cos(k2_xcmplx_0(A,k3_xcmplx_0(2,B))),k19_sin_cos(k6_xcmplx_0(A,k3_xcmplx_0(2,B))))),k1_square_1(k3_xcmplx_0(k19_sin_cos(k2_xcmplx_0(B,k7_xcmplx_0(A,2))),k19_sin_cos(k6_xcmplx_0(B,k7_xcmplx_0(A,2))))))) ) ) ) ) )).
fof(t96_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [H] : ( v1_xreal_0(H) => ( ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t96_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ( r7_euclidlp(A,B,C) <=> ? [D] : ( m2_subset_1(D,k1_zfmisc_1(k1_euclid(A)),k5_euclidlp(A)) & r1_tarski(B,D) & r1_tarski(C,D) ) ) ) ) ) )).
fof(t96_finseq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v2_finseq_1(A) ) => ( A = k1_xboole_0 <=> k15_finseq_1(A) = k1_xboole_0 ) ) )).
fof(t96_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => r2_hidden(k12_finseq_1(A,B),k4_finseq_2(1,A)) ) ) )).
fof(t96_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : ( ( v2_funct_1(A) & k10_xtuple_0(A) = k2_tarski(B,C) ) => ( B = C | k3_finseq_1(A) = 2 ) ) ) )).
fof(t96_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => k1_finseq_6(A,k2_finseq_4(A,B,C),C) = k2_finseq_4(A,C,C) ) ) ) )).
fof(t96_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => k1_flang_2(A,k2_flang_2(A,B),C,D) = k1_flang_2(A,k2_flang_2(A,B),k5_numbers,D) ) ) ) ) )).
fof(t96_flang_3,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ( r2_hidden(k5_afinsq_1(B),k2_flang_3(A,C)) <=> r2_hidden(k5_afinsq_1(B),C) ) ) )).
fof(t96_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => r1_tarski(k10_xtuple_0(k5_relat_1(B,k1_tarski(A))),k1_tarski(k1_funct_1(B,A))) ) )).
fof(t96_funct_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( r1_tarski(C,B) => k7_relat_1(A,C) = k7_relat_1(k5_relat_1(A,B),C) ) ) )).
fof(t96_funct_4,axiom,( ! [A] : k16_funcop_1(A,A) = k6_partfun1(k1_tarski(A)) )).
fof(t96_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : ( v7_ordinal1(C) => k3_finseq_1(k1_funct_7(A,C,B)) = k3_finseq_1(A) ) ) )).
fof(t96_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : v1_relat_1(k3_msafree2(k37_gfacirc1(A,B,C))) )).
fof(t96_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ! [D] : ( m1_subset_1(D,k6_glib_000(A)) => ! [E] : ( m1_subset_1(E,k6_glib_000(B)) => ( ( D = E & r5_glib_000(A,B) ) => ( k26_glib_000(A,D) = k26_glib_000(B,E) & k27_glib_000(A,D) = k27_glib_000(B,E) & k28_glib_000(A,D) = k28_glib_000(B,E) & k29_glib_000(A,D,C) = k29_glib_000(B,E,C) & k30_glib_000(A,D) = k30_glib_000(B,E) & k31_glib_000(A,D) = k31_glib_000(B,E) & k34_glib_000(A,D) = k34_glib_000(B,E) & k36_glib_000(A,D) = k36_glib_000(B,E) & k37_glib_000(A,D) = k37_glib_000(B,E) & k38_glib_000(A,D) = k38_glib_000(B,E) ) ) ) ) ) ) )).
fof(t96_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( m3_glib_001(C,A) => ! [D] : ( m3_glib_001(D,B) => ( C = D => k13_glib_001(A,C) = k13_glib_001(B,D) ) ) ) ) ) )).
fof(t96_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_group_2(D,A) => k11_group_2(A,D,k2_group_2(A,B,C)) = k2_group_2(A,B,k11_group_2(A,D,C)) ) ) ) ) )).
fof(t96_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => r2_hidden(k4_group_3(A,C,B),k8_group_3(A,C)) ) ) ) )).
fof(t96_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v8_group_9(C,A,B) & m2_finseq_1(C,k6_group_9(A,B)) ) => ! [D] : ( ( v8_group_9(D,A,B) & m2_finseq_1(D,k6_group_9(A,B)) ) => ( ( k3_finseq_1(D) = k3_finseq_1(C) & r4_group_9(A,B,D,C) ) => C = D ) ) ) ) )).
fof(t96_integra8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( A = k1_rcomp_1(k2_xcmplx_0(B,k3_xcmplx_0(k2_nat_1(2,C),k28_sin_cos)),k2_xcmplx_0(B,k3_xcmplx_0(k1_nat_1(k2_nat_1(2,C),1),k28_sin_cos))) => k2_integra5(A,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos)) = k5_numbers ) ) ) ) )).
fof(t96_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k1_pre_topc(k15_euclid(2),B)))) => ! [D] : ( ( 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)),k7_jgraph_4(A),C) & B = k8_struct_0(k15_euclid(2)) & C = a_0_0_jgraph_4 ) => ( r1_xxreal_0(A,k4_xcmplx_0(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)) ) ) ) ) ) ) )).
fof(t96_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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) = H & 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(E,k17_euclid(B)) & 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,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t96_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_jordan24(2,A,k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers)) => ! [B] : ( ( v2_compts_1(B,k15_euclid(2)) & v1_jordan21(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [C] : ( ( 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(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_numbers),B) & r1_topreal1(k15_euclid(2),k19_euclid(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_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(k4_xcmplx_0(1),k5_numbers),k19_euclid(1,k5_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) ) => k1_jordan2c(2,A) = k1_connsp_1(k1_pre_topc(k15_euclid(2),k3_subset_1(u1_struct_0(k15_euclid(2)),A)),k2_connsp_3(k15_euclid(2),k3_subset_1(u1_struct_0(k15_euclid(2)),A),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k1_jordan21(k9_subset_1(u1_struct_0(k15_euclid(2)),k1_rltopsp1(k15_euclid(2),k2_jordan21(B),k19_euclid(k5_numbers,k4_xcmplx_0(3))),C)),k2_jordan21(B)),k7_xcmplx_0(1,2)))) ) ) ) ) ) )).
fof(t96_jordan2c,axiom,( ! [A] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(t96_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ r1_xxreal_0(C,D) & r2_hidden(D,k1_relset_1(k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B))) ) ) ) => ( v6_limfunc1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B)) & k5_limfunc1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B)) = k3_xcmplx_0(k5_limfunc1(A),k5_limfunc1(B)) ) ) ) ) )).
fof(t96_matrix10,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( v1_matrix_0(D) & v2_matrix_0(D,k1_numbers,C,C) & m2_finseq_1(D,k3_finseq_2(k1_numbers)) ) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,k1_numbers,C,C) & m2_finseq_1(E,k3_finseq_2(k1_numbers)) ) => ( ( r1_xxreal_0(A,B) & v1_matrix10(D) & r1_matrix10(D,E) ) => ( r1_xxreal_0(A,k5_numbers) | r1_matrix10(k6_matrix10(C,A,D),k6_matrix10(C,B,E)) ) ) ) ) ) ) ) )).
fof(t96_matrix13,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ( k8_matrix13(A,B) = 1 <=> ( ? [C] : ( v7_ordinal1(C) & ? [D] : ( v7_ordinal1(D) & r2_hidden(k4_tarski(C,D),k2_matrix_0(B)) & k3_matrix_0(u1_struct_0(A),B,C,D) != k4_struct_0(A) ) ) & ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ! [D] : ( ( v7_ordinal1(D) & ~ v8_ordinal1(D) ) => ! [E] : ( ( v7_ordinal1(E) & ~ v8_ordinal1(E) ) => ! [F] : ( ( v7_ordinal1(F) & ~ v8_ordinal1(F) ) => ( r1_tarski(k2_zfmisc_1(k4_matrix13(C,D),k4_matrix13(E,F)),k2_matrix_0(B)) => ( C = D | E = F | k12_matrix_3(k5_card_1(k4_matrix13(C,D)),A,k7_matrix13(u1_struct_0(A),B,k4_matrix13(C,D),k4_matrix13(E,F))) = k4_struct_0(A) ) ) ) ) ) ) ) ) ) ) )).
fof(t96_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ! [C] : ( m2_finseq_1(C,k1_numbers) => ~ ( k3_finseq_1(C) = A & ! [D] : ( m2_finseq_1(D,k1_numbers) => ~ ( k3_finseq_1(D) = A & k11_matrixr1(B,D) = C ) ) ) ) & ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => k1_matrixr2(A,B,C) != k4_matrixr2(A) ) ) ) ) )).
fof(t96_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => ! [C] : ( v1_membered(C) => r1_tarski(k13_member_1(A,k11_member_1(B,C)),k11_member_1(k13_member_1(A,B),k13_member_1(A,C))) ) ) ) )).
fof(t96_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( r1_mesfunc5(A,B,C,D) => ( r1_xxreal_0(k5_numbers,k6_mesfunc5(A,B,C,k1_mesfunc2(A,D))) & r1_xxreal_0(k5_numbers,k6_mesfunc5(A,B,C,k2_mesfunc2(A,D))) & ~ r1_xxreal_0(k7_mesfunc5(A,B,C,D),k2_supinf_1) & ~ r1_xxreal_0(k1_supinf_1,k7_mesfunc5(A,B,C,D)) ) ) ) ) ) ) )).
fof(t96_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ( ( k1_relset_1(A,D) = k1_relset_1(A,E) & r3_mesfunc6(A,B,C,E) & ! [F] : ( m1_subset_1(F,A) => ( r2_hidden(F,k1_relset_1(A,D)) => r1_xxreal_0(k9_complex1(k12_supinf_2(D,F)),k12_supinf_2(E,F)) ) ) ) => ( ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ~ ( F = k1_relset_1(A,D) & r1_mesfunc6(A,B,D,F) ) ) | ( r3_mesfunc6(A,B,C,D) & r1_xxreal_0(k1_mesfunc6(A,B,C,k56_valued_1(A,k1_numbers,D)),k1_mesfunc6(A,B,C,E)) ) ) ) ) ) ) ) ) )).
fof(t96_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),k1_numbers))) ) => ! [C] : ( 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) & r11_ncfcont1(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( r2_hidden(D,C) & r2_hidden(E,C) & k7_partfun1(k1_numbers,B,D) = k2_seq_4(k7_relset_1(u1_struct_0(A),k1_numbers,B,C)) & k7_partfun1(k1_numbers,B,E) = k3_seq_4(k7_relset_1(u1_struct_0(A),k1_numbers,B,C)) ) ) ) ) ) ) ) )).
fof(t96_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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),k5_pboole(A,k5_pboole(A,B,C),k3_pboole(A,B,C))) ) ) )).
fof(t96_prepower,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => k6_nat_d(A,B) = k6_nat_d(A,k1_int_2(k6_xcmplx_0(B,A))) ) ) )).
fof(t96_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v4_qc_lang1(B,A) => k15_qc_lang2(A,B) = k2_xboole_0(k2_xboole_0(k15_qc_lang2(A,k19_qc_lang1(A,B)),k15_qc_lang2(A,k20_qc_lang1(A,B))),k1_tarski(B)) ) ) ) )).
fof(t96_quaterni,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_square_1(A),k1_square_1(B)),k1_square_1(C)),k1_square_1(D)) = k5_numbers => ( A = k5_numbers & B = k5_numbers & C = k5_numbers & D = k5_numbers ) ) ) ) ) ) )).
fof(t96_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ! [D] : ( v1_relat_1(D) => ( ( r1_tarski(C,D) & r1_tarski(A,B) ) => r1_tarski(k6_relat_1(A,C),k6_relat_1(B,D)) ) ) ) )).
fof(t96_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(C)) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(C)) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k8_afinsq_1(C))) => ! [G] : ( ( ~ v2_struct_0(G) & l1_rewrite3(G,F) ) => ( r4_rewrite3(C,F,G,A,D,B) => r3_rewrite3(C,F,G,A,k1_flang_1(C,D,E),B,E) ) ) ) ) ) ) )).
fof(t96_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( v1_xcmplx_0(B) => k19_rvsum_1(k7_finseq_1(A,k9_finseq_1(B))) = k3_xcmplx_0(k19_rvsum_1(A),B) ) ) )).
fof(t96_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => k5_card_1(k9_scmpds_6(A,B,C)) = k1_nat_1(k5_card_1(C),1) ) ) ) )).
fof(t96_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ( r2_hidden(B,k3_tarski(A)) => r2_hidden(k2_tarski(k4_tarski(B,k3_tarski(A)),k3_tarski(A)),k12_scmyciel(A)) ) ) )).
fof(t96_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( r4_semi_af1(A,B,C,D,E,F) => ( F = C | r4_semi_af1(A,C,B,E,D,F) ) ) ) ) ) ) ) ) )).
fof(t96_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k2_numbers) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => k20_seq_4(k18_seq_4(A,C,B)) = k3_xcmplx_0(k9_complex1(B),k20_seq_4(C)) ) ) ) )).
fof(t96_setlim_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v3_kurato_0(C,A) => ( v3_kurato_0(k9_setlim_2(A,C,B),A) & k4_kurato_0(A,k9_setlim_2(A,C,B)) = k5_subset_1(A,B,k4_kurato_0(A,C)) ) ) ) ) )).
fof(t96_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,C),B),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,C,C)),B)) ) ) ) )).
fof(t96_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) & k4_sin_cos6(A) = k5_numbers ) => A = 1 ) ) )).
fof(t96_sin_cos9,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ( r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k2_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,A),k2_sin_cos9),A),B) = k6_xcmplx_0(k1_funct_1(k2_sin_cos9,B),k7_xcmplx_0(B,k2_xcmplx_0(1,k1_square_1(B)))) ) ) ) ) ) )).
fof(t96_sincos10,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k4_sincos10,k1_rcomp_1(1,k3_square_1(2)))) )).
fof(t96_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k8_tdlat_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k8_tdlat_1(A))) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(u1_struct_0(A)),k5_tdlat_1(A)) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(u1_struct_0(A)),k5_tdlat_1(A)) => ( ( B = D & C = E ) => ( r1_lattices(k8_tdlat_1(A),B,C) <=> r1_tarski(D,E) ) ) ) ) ) ) ) )).
fof(t96_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ~ r2_hidden(C,B) => r1_tmap_1(A,k6_tmap_1(A,B),k7_tmap_1(A,B),C) ) ) ) ) )).
fof(t96_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v1_aff_1(C,A) => v1_aff_1(k7_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),A) ) ) => v8_transgeo(B,A) ) ) ) )).
fof(t96_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v1_valued_2(D) => ! [E] : ( v1_valued_2(E) => ! [F] : ( v1_valued_2(F) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,D))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(B,E))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(C,F))) ) => k90_valued_2(k3_xboole_0(B,C),A,k2_valued_2(k3_xboole_0(k1_valued_2(E),k1_valued_2(F))),D,k73_valued_2(B,C,E,F,H,I),G) = k73_valued_2(k3_xboole_0(B,A),k3_xboole_0(C,A),k2_valued_2(k3_xboole_0(k1_valued_2(E),k1_valued_2(D))),k2_valued_2(k3_xboole_0(k1_valued_2(F),k1_valued_2(D))),k90_valued_2(B,A,E,D,H,G),k90_valued_2(C,A,F,D,I,G)) ) ) ) ) ) ) )).
fof(t96_xboole_1,axiom,( ! [A] : ! [B] : r1_tarski(k4_xboole_0(A,B),k5_xboole_0(A,B)) )).
fof(t96_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k8_xboolean(A,k10_xboolean(B,C)) = k7_xboolean(k4_xboolean(A,B),k4_xboolean(A,C)) ) ) ) )).
fof(t96_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => ( k3_xcmplx_0(A,C) = k7_xcmplx_0(B,D) => ( C = k5_numbers | D = k5_numbers | k3_xcmplx_0(A,D) = k7_xcmplx_0(B,C) ) ) ) ) ) ) )).
fof(t96_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,C) & ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(D,C) & r1_xxreal_0(k3_xcmplx_0(B,D),k3_xcmplx_0(A,C)) ) ) ) ) ) )).
fof(t96_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( r1_xxreal_0(D,A) => r1_xboole_0(k2_xxreal_1(C,D),k2_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t96_xxreal_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_numbers)) ) => ( ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ( ( r2_hidden(C,A) & r2_hidden(D,B) ) => r1_xxreal_0(C,D) ) ) ) => r1_xxreal_0(k1_xxreal_2(A),k2_xxreal_2(B)) ) ) ) )).
fof(t96_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(k5_numbers,C) ) => k4_xxreal_3(A,k1_xxreal_3(B,C)) = k1_xxreal_3(k4_xxreal_3(A,B),k4_xxreal_3(A,C)) ) ) ) ) )).
fof(t96_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( ~ v1_xboole_0(D) => ( r2_zf_model(D,A) => r2_zf_model(D,k15_zf_lang(B,C,A)) ) ) ) ) ) )).
fof(t96_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( k2_zfmisc_1(k2_xboole_0(A,B),C) = k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) & k2_zfmisc_1(C,k2_xboole_0(A,B)) = k2_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) ) )).
fof(t96_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => ! [D] : ( m1_zmodul01(D,A) => k6_zmodul01(A,B,k6_zmodul01(A,C,D)) = k6_zmodul01(A,k6_zmodul01(A,B,C),D) ) ) ) ) )).
fof(t97_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_abcmiz_1(B,A,k12_abcmiz_1(A)) => ! [C] : ( m1_abcmiz_1(C,A,k13_abcmiz_1(A)) => k45_abcmiz_1(A,k31_abcmiz_1(A,k33_abcmiz_1(A),C,B)) = k4_subset_1(k2_abcmiz_1,k45_abcmiz_1(A,C),k45_abcmiz_1(A,B)) ) ) ) )).
fof(t97_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(D)) => ! [F] : ( m1_subset_1(F,D) => ! [G] : ( m1_aofa_000(G,A,D,E) => ( ( v3_freealg(A) & r2_hidden(k4_tarski(F,k13_aofa_000(A,B,C)),k21_aofa_000(A,D,E,G)) ) => ( r2_hidden(k4_tarski(F,B),k21_aofa_000(A,D,E,G)) & r2_hidden(k4_tarski(k2_binop_1(D,u1_struct_0(A),D,G,F,B),C),k21_aofa_000(A,D,E,G)) ) ) ) ) ) ) ) ) ) )).
fof(t97_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v19_aofa_a00(B,A) & m1_subset_1(B,u1_struct_0(A)) ) => ! [C] : ( ( 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)) & v1_msafree4(C,u1_struct_0(A)) ) => ! [D] : ( ( v4_msualg_1(D,A) & v5_msafree4(D,A,C) & v3_aofa_a00(D,A,C) & v6_aofa_a01(D,A) & l1_aofa_a00(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,C,D) & l4_aofa_a00(E,A,C,D) ) => ! [F] : ( ( v3_aofa_a01(F,A,C,D,u4_aofa_a00(A,C,D,E),k37_aofa_a00(A)) & m1_msafree4(F,u1_struct_0(A),u4_aofa_a00(A,C,D,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,C,D,E),k37_aofa_a00(A))) ) => ! [G] : ( ( v3_aofa_a01(G,A,C,D,u4_aofa_a00(A,C,D,E),B) & m1_msafree4(G,u1_struct_0(A),u4_aofa_a00(A,C,D,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,C,D,E),B)) ) => ! [H] : ( ( v3_aofa_a01(H,A,C,D,u4_aofa_a00(A,C,D,E),B) & m1_msafree4(H,u1_struct_0(A),u4_aofa_a00(A,C,D,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,C,D,E),B)) ) => k39_aofa_a00(A,D,k4_aofa_a01(A,D,u4_aofa_a00(A,C,D,E),k37_aofa_a00(A),F),B,k4_aofa_a01(A,D,u4_aofa_a00(A,C,D,E),B,G)) != H ) ) ) ) ) ) ) ) )).
fof(t97_card_2,axiom,( ! [A] : ! [B] : ( ( k1_card_2(k1_card_1(A),k1_card_1(B)) = k1_card_1(A) & r2_hidden(k1_card_1(B),k1_card_1(A)) ) => k1_card_1(k6_subset_1(A,B)) = k1_card_1(A) ) )).
fof(t97_card_3,axiom,( ! [A] : ( ( v4_funct_1(A) & v2_card_3(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(B,A) => k9_xtuple_0(B) = k9_xtuple_0(k10_card_3(A)) ) ) ) )).
fof(t97_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v6_chord(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ~ ( B != C & ~ r1_chord(A,B,C) & ? [D] : ( m2_chord(D,A,B,C) & v4_chord(D,A,B,C) & ~ v1_xboole_0(D) & ~ ! [E] : ( m2_glib_000(E,A,D,k21_glib_000(A,D)) => v2_chord(E) ) ) ) ) ) ) )).
fof(t97_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_clvect_1(C,A) => ! [D] : ( m2_clvect_1(D,A,C) => ( r2_hidden(B,D) <=> D = k5_clvect_1(A,B,C) ) ) ) ) ) )).
fof(t97_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v4_clvect_2(A) & v2_clvect_2(B,A) ) => v3_clvect_2(B,A) ) ) ) )).
fof(t97_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ( m1_subset_1(C,k17_cohsp_1(A,B)) => ( r2_hidden(k9_xtuple_0(C),A) & r2_hidden(k10_xtuple_0(C),B) & r1_tarski(C,k2_zfmisc_1(k9_xtuple_0(C),k10_xtuple_0(C))) ) ) ) ) )).
fof(t97_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [H] : ( v1_xreal_0(H) => ( ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t97_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ( r5_euclidlp(A,B,C) => r7_euclidlp(A,B,C) ) ) ) ) )).
fof(t97_finseq_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ~ ( 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))) & v1_finseq_1(k2_tarski(k4_tarski(A,C),k4_tarski(B,D))) & ~ ( A = 1 & B = 1 & C = D ) & ~ ( A = 1 & B = 2 ) & ~ ( A = 2 & B = 1 ) ) )).
fof(t97_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k4_finseq_2(2,A) = a_1_1_finseq_2(A) ) )).
fof(t97_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : ~ ( v2_funct_1(A) & k10_xtuple_0(A) = k2_tarski(B,C) & B != C & A != k10_finseq_1(B,C) & A != k10_finseq_1(C,B) ) ) )).
fof(t97_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => k1_finseq_6(A,k3_finseq_4(A,B,C,D),B) = k3_finseq_4(A,B,C,D) ) ) ) ) )).
fof(t97_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => k1_flang_2(A,k2_flang_2(A,B),k5_numbers,C) = k1_flang_2(A,B,k5_numbers,C) ) ) )).
fof(t97_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(A,k9_xtuple_0(B)) => k10_xtuple_0(k5_relat_1(B,k1_tarski(A))) = k1_tarski(k1_funct_1(B,A)) ) ) )).
fof(t97_funct_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( r1_tarski(k8_relat_1(A,C),B) => k8_relat_1(A,C) = k8_relat_1(k5_relat_1(A,B),C) ) ) )).
fof(t97_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(A,B) => k1_funct_4(A,B) = B ) ) ) )).
fof(t97_funct_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,B) => ! [D] : ( m1_subset_1(D,B) => ( r2_hidden(A,k4_finseq_1(C)) => k2_funct_7(B,C,A,D) = k8_finseq_1(B,k8_finseq_1(B,k17_finseq_1(B,k7_nat_d(A,1),C),k12_finseq_1(B,D)),k2_rfinseq(B,A,C)) ) ) ) ) ) )).
fof(t97_gfacirc1,axiom,( ! [A] : ! [B] : ! [C] : ~ ( 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) & k2_msafree2(k37_gfacirc1(A,B,C)) != k1_enumset1(A,B,C) ) )).
fof(t97_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v1_finset_1(B) & v1_glib_000(B) ) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( m1_subset_1(D,k6_glib_000(B)) => ( ( C = D & r5_glib_000(A,B) ) => ( ( v10_glib_000(C,A) => v10_glib_000(D,B) ) & ( v11_glib_000(C,A) => v11_glib_000(D,B) ) ) ) ) ) ) ) )).
fof(t97_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( r2_hidden(C,k14_glib_001(A,B)) <=> ? [D] : ( v1_abian(D) & m1_subset_1(D,k4_ordinal1) & r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(B)) & k1_funct_1(B,D) = C ) ) ) ) )).
fof(t97_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_group_2(D,A) => k2_group_2(A,k11_group_2(A,D,B),C) = k2_group_2(A,B,k12_group_2(A,D,C)) ) ) ) ) )).
fof(t97_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => r2_hidden(B,k8_group_3(A,B)) ) ) )).
fof(t97_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v8_group_9(C,A,B) & m2_finseq_1(C,k6_group_9(A,B)) ) => ! [D] : ( ( v8_group_9(D,A,B) & m2_finseq_1(D,k6_group_9(A,B)) ) => ~ ( ~ v1_xboole_0(C) & r4_group_9(A,B,D,C) & v1_xboole_0(D) ) ) ) ) )).
fof(t97_integra8,axiom,( ! [A] : ( ( ~ 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,k16_sin_cos,k16_sin_cos)) = k2_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,k3_seq_4(A)),k1_funct_1(k16_sin_cos,k3_seq_4(A))),k3_xcmplx_0(k1_funct_1(k18_sin_cos,k2_seq_4(A)),k1_funct_1(k16_sin_cos,k2_seq_4(A)))),k2_integra5(A,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k18_sin_cos))) ) )).
fof(t97_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)),k7_jgraph_4(A),B)) = k12_euclid(B) ) ) )).
fof(t97_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) = H & 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(E,k17_euclid(B)) & 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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t97_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( 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))) ) => A = k2_tops_1(k15_euclid(2),B) ) ) ) ) )).
fof(t97_jordan2c,axiom,( ! [A] : ( ( ~ 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] : ( 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)) ) ) ) ) )).
fof(t97_matrix13,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ( k8_matrix13(A,B) = 1 <=> ( ? [C] : ( v7_ordinal1(C) & ? [D] : ( v7_ordinal1(D) & r2_hidden(k4_tarski(C,D),k2_matrix_0(B)) & k3_matrix_0(u1_struct_0(A),B,C,D) != k4_struct_0(A) ) ) & ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( v7_ordinal1(E) => ! [F] : ( v7_ordinal1(F) => ( r1_tarski(k2_zfmisc_1(k4_matrix13(C,D),k4_matrix13(E,F)),k2_matrix_0(B)) => k8_group_1(A,k3_matrix_0(u1_struct_0(A),B,C,E),k3_matrix_0(u1_struct_0(A),B,D,F)) = k8_group_1(A,k3_matrix_0(u1_struct_0(A),B,C,F),k3_matrix_0(u1_struct_0(A),B,D,E)) ) ) ) ) ) ) ) ) ) )).
fof(t97_matrixr2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ( ! [C] : ( m2_finseq_1(C,k1_numbers) => ~ ( k3_finseq_1(C) = A & ! [D] : ( m2_finseq_1(D,k1_numbers) => ! [E] : ( m2_finseq_1(E,k1_numbers) => ~ ( k3_finseq_1(D) = A & k3_finseq_1(E) = A & k11_matrixr1(B,D) = C & k12_matrixr1(B,E) = C ) ) ) ) ) => ( r1_xxreal_0(A,k5_numbers) | v1_matrixr2(B,A) ) ) ) ) )).
fof(t97_member_1,axiom,( ! [A] : ( v1_membered(A) => ! [B] : ( v1_membered(B) => k7_member_1(k13_member_1(A,B)) = k13_member_1(k7_member_1(A),k7_member_1(B)) ) ) )).
fof(t97_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( r1_mesfunc5(A,B,C,D) => ( r1_xxreal_0(k6_mesfunc5(A,B,C,k1_mesfunc2(A,k2_partfun1(A,k6_numbers,D,E))),k6_mesfunc5(A,B,C,k1_mesfunc2(A,D))) & r1_xxreal_0(k6_mesfunc5(A,B,C,k2_mesfunc2(A,k2_partfun1(A,k6_numbers,D,E))),k6_mesfunc5(A,B,C,k2_mesfunc2(A,D))) & r1_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,E)) ) ) ) ) ) ) ) )).
fof(t97_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ 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] : ! [D] : ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ( ( r13_ncfcont1(A,B,C,E) & r1_tarski(D,C) ) => r13_ncfcont1(A,B,D,E) ) ) ) ) )).
fof(t97_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( 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),k5_pboole(A,k5_pboole(A,B,C),k2_pboole(A,B,C))) ) ) )).
fof(t97_prepower,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( ( r1_xxreal_0(k5_numbers,A) & r1_xxreal_0(k5_numbers,B) ) => k3_int_2(A,B) = k3_int_2(A,k6_xcmplx_0(B,A)) ) ) ) )).
fof(t97_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v5_qc_lang1(B,A) => k15_qc_lang2(A,B) = k2_xboole_0(k15_qc_lang2(A,k22_qc_lang1(A,B)),k1_tarski(B)) ) ) ) )).
fof(t97_quaterni,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ( k13_quaterni(k23_quaterni(A,B)) = k6_xcmplx_0(k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k13_quaterni(B)),k3_xcmplx_0(k14_quaterni(A),k14_quaterni(B))),k3_xcmplx_0(k15_quaterni(A),k15_quaterni(B))),k3_xcmplx_0(k16_quaterni(A),k16_quaterni(B))) & k14_quaterni(k23_quaterni(A,B)) = k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k14_quaterni(B)),k3_xcmplx_0(k14_quaterni(A),k13_quaterni(B))),k3_xcmplx_0(k15_quaterni(A),k16_quaterni(B))),k3_xcmplx_0(k16_quaterni(A),k15_quaterni(B))) & k15_quaterni(k23_quaterni(A,B)) = k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k15_quaterni(B)),k3_xcmplx_0(k15_quaterni(A),k13_quaterni(B))),k3_xcmplx_0(k16_quaterni(A),k14_quaterni(B))),k3_xcmplx_0(k14_quaterni(A),k16_quaterni(B))) & k16_quaterni(k23_quaterni(A,B)) = k6_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k13_quaterni(A),k16_quaterni(B)),k3_xcmplx_0(k16_quaterni(A),k13_quaterni(B))),k3_xcmplx_0(k14_quaterni(A),k15_quaterni(B))),k3_xcmplx_0(k15_quaterni(A),k14_quaterni(B))) ) ) ) )).
fof(t97_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(t97_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_afinsq_1(D))) => ! [F] : ( ( ~ v2_struct_0(F) & l1_rewrite3(F,E) ) => ( r1_rewrite3(E,F,A,B,C) => r4_rewrite3(D,E,F,A,B,C) ) ) ) ) )).
fof(t97_rvsum_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) & v1_finseq_1(B) ) => k19_rvsum_1(k7_finseq_1(A,B)) = k3_xcmplx_0(k19_rvsum_1(A),k19_rvsum_1(B)) ) ) )).
fof(t97_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => r2_hidden(k5_numbers,k9_xtuple_0(k9_scmpds_6(A,B,C))) ) ) ) )).
fof(t97_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ! [C] : ~ r2_hidden(k2_tarski(k4_tarski(B,k3_tarski(A)),k4_tarski(C,k3_tarski(A))),k1_scmyciel(k12_scmyciel(A))) ) )).
fof(t97_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r4_semi_af1(A,B,C,D,E,C) => C = E ) ) ) ) ) ) )).
fof(t97_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => r1_xxreal_0(k20_seq_4(k13_seq_4(A,B,C)),k2_xcmplx_0(k20_seq_4(B),k20_seq_4(C))) ) ) ) )).
fof(t97_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => B = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,C),B),k5_sheffer1(A,C,B)) ) ) ) )).
fof(t97_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) & k4_sin_cos6(A) = k7_xcmplx_0(k28_sin_cos,2) ) => A = k5_numbers ) ) )).
fof(t97_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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_cos9))) & r1_tarski(C,k2_rcomp_1(k4_xcmplx_0(1),1)) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(D,E) = k2_xcmplx_0(k3_xcmplx_0(A,E),B) ) ) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k1_sin_cos9),C) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k1_sin_cos9),C),E) = k2_xcmplx_0(k3_xcmplx_0(A,k1_funct_1(k1_sin_cos9,E)),k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,E),B),k2_xcmplx_0(1,k1_square_1(E)))) ) ) ) ) ) ) ) ) )).
fof(t97_sincos10,axiom,( k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k1_sincos10,k1_rcomp_1(1,k3_square_1(2)))) = k1_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,4)) )).
fof(t97_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k8_tdlat_1(A)))) => ? [C] : ( m1_subset_1(C,u1_struct_0(k8_tdlat_1(A))) & r4_lattice3(k8_tdlat_1(A),C,B) & ! [D] : ( m1_subset_1(D,u1_struct_0(k8_tdlat_1(A))) => ( r4_lattice3(k8_tdlat_1(A),D,B) => r1_lattices(k8_tdlat_1(A),C,D) ) ) ) ) ) )).
fof(t97_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( r1_xboole_0(u1_struct_0(C),B) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => r1_tmap_1(C,k6_tmap_1(A,B),k2_tmap_1(A,k6_tmap_1(A,B),k7_tmap_1(A,B),C),D) ) ) ) ) ) )).
fof(t97_transgeo,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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)))) ) => ( ( v8_transgeo(D,A) & v1_aff_1(B,A) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(E,B) => k3_funct_2(u1_struct_0(A),u1_struct_0(A),D,E) = E ) ) & k3_funct_2(u1_struct_0(A),u1_struct_0(A),D,C) = C ) => ( r2_hidden(C,B) | r2_funct_2(u1_struct_0(A),u1_struct_0(A),D,k6_partfun1(u1_struct_0(A))) ) ) ) ) ) ) )).
fof(t97_valued_2,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( v1_valued_2(D) => ! [E] : ( v1_valued_2(E) => ! [F] : ( v1_valued_2(F) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,D))) ) => ! [H] : ( ( v1_funct_1(H) & m1_subset_1(H,k1_zfmisc_1(k2_zfmisc_1(B,E))) ) => ! [I] : ( ( v1_funct_1(I) & m1_subset_1(I,k1_zfmisc_1(k2_zfmisc_1(C,F))) ) => k90_valued_2(k3_xboole_0(B,C),A,k2_valued_2(k3_xboole_0(k1_valued_2(E),k1_valued_2(F))),D,k79_valued_2(B,C,E,F,H,I),G) = k79_valued_2(k3_xboole_0(B,A),k3_xboole_0(C,A),k2_valued_2(k3_xboole_0(k1_valued_2(E),k1_valued_2(D))),k2_valued_2(k3_xboole_0(k1_valued_2(F),k1_valued_2(D))),k90_valued_2(B,A,E,D,H,G),k90_valued_2(C,A,F,D,I,G)) ) ) ) ) ) ) )).
fof(t97_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( r1_tarski(k4_xboole_0(A,B),C) & r1_tarski(k4_xboole_0(B,A),C) ) => r1_tarski(k5_xboole_0(A,B),C) ) )).
fof(t97_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k10_xboolean(A,k4_xboolean(A,B)) = k11_xboolean(A,B) ) ) )).
fof(t97_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( C != k5_numbers => k7_xcmplx_0(A,B) = k3_xcmplx_0(C,k7_xcmplx_0(k7_xcmplx_0(A,C),B)) ) ) ) ) )).
fof(t97_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( r1_xxreal_0(k5_numbers,A) & ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(C,D) & r1_xxreal_0(k3_xcmplx_0(B,D),k3_xcmplx_0(A,C)) ) ) ) ) ) )).
fof(t97_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(A,C) & ~ r1_xxreal_0(D,C) & r1_tarski(k4_xxreal_1(C,D),k1_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t97_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ( ( r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(C,k5_numbers) ) => k4_xxreal_3(A,k1_xxreal_3(B,C)) = k1_xxreal_3(k4_xxreal_3(A,B),k4_xxreal_3(A,C)) ) ) ) ) )).
fof(t97_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ! [E] : ( ~ v1_xboole_0(E) => ( r2_zf_model(E,A) <=> r2_zf_model(E,k16_zf_lang(B,C,D,A)) ) ) ) ) ) ) )).
fof(t97_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : k2_zfmisc_1(k2_xboole_0(A,B),k2_xboole_0(C,D)) = k2_xboole_0(k2_xboole_0(k2_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(A,D)),k2_zfmisc_1(B,C)),k2_zfmisc_1(B,D)) )).
fof(t97_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( m1_zmodul01(C,A) => m1_zmodul01(B,k6_zmodul01(A,B,C)) ) ) ) )).
fof(t98_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_abcmiz_1(B,A,k12_abcmiz_1(A)) => ! [C] : ( m1_abcmiz_1(C,A,k13_abcmiz_1(A)) => k46_abcmiz_1(A,k31_abcmiz_1(A,k33_abcmiz_1(A),C,B)) = k4_subset_1(k2_abcmiz_1,k46_abcmiz_1(A,C),k46_abcmiz_1(A,B)) ) ) ) )).
fof(t98_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( ~ v1_xboole_0(E) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(E)) => ! [G] : ( m1_subset_1(G,E) => ! [H] : ( m1_aofa_000(H,A,E,F) => ( ( v3_freealg(A) & r2_hidden(k4_tarski(G,k14_aofa_000(A,B,C,D)),k21_aofa_000(A,E,F,H)) ) => ( r2_hidden(k4_tarski(G,B),k21_aofa_000(A,E,F,H)) & ( r2_hidden(k2_binop_1(E,u1_struct_0(A),E,H,G,B),F) => r2_hidden(k4_tarski(k2_binop_1(E,u1_struct_0(A),E,H,G,B),C),k21_aofa_000(A,E,F,H)) ) & ( ~ r2_hidden(k2_binop_1(E,u1_struct_0(A),E,H,G,B),F) => r2_hidden(k4_tarski(k2_binop_1(E,u1_struct_0(A),E,H,G,B),D),k21_aofa_000(A,E,F,H)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t98_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_aofa_a01(D,A,B,C) & l4_aofa_a00(D,A,B,C) ) => ! [E] : ( ( v19_aofa_a00(E,A) & m1_subset_1(E,u1_struct_0(A)) ) => ! [F] : ( ( v3_aofa_a01(F,A,B,C,u4_aofa_a00(A,B,C,D),E) & m1_msafree4(F,u1_struct_0(A),u4_aofa_a00(A,B,C,D),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),E)) ) => ! [G] : ( ( v3_aofa_a01(G,A,B,C,u4_aofa_a00(A,B,C,D),k37_aofa_a00(A)) & m1_msafree4(G,u1_struct_0(A),u4_aofa_a00(A,B,C,D),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,D),k37_aofa_a00(A))) ) => ( ~ v8_aofa_a01(C,A,B) => r8_pboole(u1_struct_0(A),k11_aofa_a00(A,C,E,k39_aofa_a00(A,C,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,D),k37_aofa_a00(A),G),E,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,D),E,F))),k2_pboole(u1_struct_0(A),k2_aofa_a00(u1_struct_0(A),E,F),k2_aofa_a00(u1_struct_0(A),k37_aofa_a00(A),G))) ) ) ) ) ) ) ) ) )).
fof(t98_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ! [C] : ( v1_card_1(C) => ( r2_hidden(k2_card_2(A,B),k2_card_2(A,C)) => r2_hidden(B,C) ) ) ) ) )).
fof(t98_card_3,axiom,( ! [A] : ( v4_funct_1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t98_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) ) => ( ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ~ ( B != C & ~ r1_chord(A,B,C) & ? [D] : ( m2_chord(D,A,B,C) & v4_chord(D,A,B,C) & ~ v1_xboole_0(D) & ~ ! [E] : ( m2_glib_000(E,A,D,k21_glib_000(A,D)) => v2_chord(E) ) ) ) ) ) => v6_chord(A) ) ) )).
fof(t98_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_clvect_1(D,A) => ! [E] : ( m2_clvect_1(E,A,D) => ~ ( r2_hidden(B,E) & r2_hidden(C,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_struct_0(D,F) & k3_rlvect_1(A,B,F) = C ) ) ) ) ) ) ) ) )).
fof(t98_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => k3_tarski(k17_cohsp_1(A,B)) = k2_zfmisc_1(k3_tarski(A),k3_tarski(B)) ) ) )).
fof(t98_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [H] : ( v1_xreal_0(H) => ( ( 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(k3_xcmplx_0(k1_funct_1(E,H),k1_fdiff_1(B,H)),k3_xcmplx_0(k1_funct_1(F,H),k1_fdiff_1(C,H)),k3_xcmplx_0(k1_funct_1(G,H),k1_fdiff_1(D,H))),A),k9_euclid(3,k1_euclid_8(k3_xcmplx_0(k1_funct_1(B,H),k1_fdiff_1(E,H)),k3_xcmplx_0(k1_funct_1(C,H),k1_fdiff_1(F,H)),k3_xcmplx_0(k1_funct_1(D,H),k1_fdiff_1(G,H))),A)) ) ) ) ) ) ) ) ) ) )).
fof(t98_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_subset_1(B,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ! [C] : ( 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) & r1_xboole_0(B,C) & ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t98_finseq_1,axiom,( ! [A] : ! [B] : k10_finseq_1(A,B) = k2_tarski(k4_tarski(1,A),k4_tarski(2,B)) )).
fof(t98_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v3_card_1(B,2) & m2_finseq_1(B,A) ) => ? [C] : ( m1_subset_1(C,A) & ? [D] : ( m1_subset_1(D,A) & B = k10_finseq_1(C,D) ) ) ) ) )).
fof(t98_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : ! [D] : ( ( 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 ) ) )).
fof(t98_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ( B != C => k1_finseq_6(A,k3_finseq_4(A,B,C,D),C) = k3_finseq_4(A,C,D,C) ) ) ) ) ) )).
fof(t98_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( r1_xxreal_0(C,D) => k1_flang_2(A,k2_flang_2(A,B),C,D) = k1_flang_2(A,B,k5_numbers,D) ) ) ) ) )).
fof(t98_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : k3_relat_1(k5_relat_1(A,C),k5_relat_1(B,k7_relat_1(A,C))) = k5_relat_1(k3_relat_1(A,B),C) ) ) )).
fof(t98_funct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( m1_subset_1(D,A) => k7_partfun1(B,C,D) = k3_funct_2(A,B,C,D) ) ) ) ) )).
fof(t98_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r1_tarski(A,B) => k1_funct_4(B,A) = B ) ) ) )).
fof(t98_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : k9_xtuple_0(k9_funct_7(A,B,C)) = k9_xtuple_0(A) ) )).
fof(t98_gfacirc1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => k2_msafree2(k37_gfacirc1(A,B,C)) = k1_enumset1(A,B,C) ) ) ) )).
fof(t98_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( m1_glib_000(C,A) => ~ ( r7_glib_000(B,C) & ~ r2_xboole_0(k24_glib_000(A,B),k24_glib_000(A,C)) & ~ r2_xboole_0(k25_glib_000(A,B),k25_glib_000(A,C)) ) ) ) ) )).
fof(t98_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( r2_hidden(C,k14_glib_001(A,B)) <=> ? [D] : ( ~ v1_abian(D) & m1_subset_1(D,k4_ordinal1) & ~ r1_xxreal_0(k3_finseq_1(B),D) & k1_funct_1(B,k1_nat_1(D,1)) = C ) ) ) ) )).
fof(t98_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_group_2(D,A) => k2_group_2(A,k12_group_2(A,D,B),C) = k12_group_2(A,D,k2_group_2(A,B,C)) ) ) ) ) )).
fof(t98_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k8_group_3(A,C)) => r2_hidden(C,k8_group_3(A,B)) ) ) ) ) )).
fof(t98_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v8_group_9(C,A,B) & m2_finseq_1(C,k6_group_9(A,B)) ) => ! [D] : ( ( 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(C,A,B) & v10_group_9(D,A,B) ) => C = D ) ) ) ) )).
fof(t98_integra8,axiom,( ! [A] : ( ( ~ 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_sin_cos2,k1_sin_cos2)) = k6_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(k3_sin_cos2,k2_seq_4(A)),k1_funct_1(k1_sin_cos2,k2_seq_4(A))),k3_xcmplx_0(k1_funct_1(k3_sin_cos2,k3_seq_4(A)),k1_funct_1(k1_sin_cos2,k3_seq_4(A)))),k2_integra5(A,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k3_sin_cos2,k3_sin_cos2))) ) )).
fof(t98_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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] : ( ( 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) = 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(D),E) & ~ r1_xxreal_0(k17_euclid(C),k17_euclid(D)) & r1_xxreal_0(k17_euclid(C),F) & k1_funct_1(I,k5_numbers) = A & k1_funct_1(I,1) = C & k1_funct_1(J,k5_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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t98_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ? [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) & ? [C] : ( 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] : ( 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] : ( 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))) ) ) ) ) ) ) ) )).
fof(t98_jordan2c,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r3_connsp_1(A,B,C) => v2_connsp_1(C,A) ) ) ) ) )).
fof(t98_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v3_limfunc1(A) & k4_limfunc1(A) = k5_numbers & ! [C] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ~ v1_comseq_2(k2_partfun1(k1_numbers,k1_numbers,B,k3_limfunc1(C))) ) | ( v3_limfunc1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B)) & k4_limfunc1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B)) = k5_numbers ) ) ) ) ) )).
fof(t98_matrix13,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ( k8_matrix13(A,B) = 1 <=> ? [C] : ( v7_ordinal1(C) & r2_hidden(C,k2_finseq_1(k3_finseq_1(B))) & ? [D] : ( v7_ordinal1(D) & r2_hidden(D,k2_finseq_1(k1_matrix_0(B))) & k3_matrix_0(u1_struct_0(A),B,C,D) != k4_struct_0(A) ) & ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(D,k2_finseq_1(k3_finseq_1(B))) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k7_matrix_0(u1_struct_0(A),B,D) != k10_fvsum_1(k1_matrix_0(B),A,k7_matrix_0(u1_struct_0(A),B,C),E) ) ) ) ) ) ) ) )).
fof(t98_member_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k13_member_1(k1_tarski(A),k1_tarski(B)) = k1_tarski(k3_xcmplx_0(A,B)) ) ) )).
fof(t98_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ( ( r1_mesfunc5(A,B,C,D) & r1_xboole_0(E,F) ) => k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,k6_prob_1(A,B,E,F))) = k3_supinf_2(k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,E)),k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,F))) ) ) ) ) ) ) ) )).
fof(t98_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( 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) & v6_supinf_2(D) & v6_supinf_2(E) ) => r3_mesfunc6(A,B,C,k3_valued_1(A,k1_numbers,k1_numbers,D,E)) ) ) ) ) ) ) )).
fof(t98_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ( ( r14_ncfcont1(A,B,C,E) & r1_tarski(D,C) ) => r14_ncfcont1(A,B,D,E) ) ) ) ) )).
fof(t98_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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,B,D) ) => r4_pboole(A,B,k2_pboole(A,C,D)) ) ) ) ) )).
fof(t98_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ( r1_xxreal_0(k5_numbers,A) => r1_xxreal_0(k5_numbers,k3_prepower(A,B)) ) ) ) )).
fof(t98_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k9_qc_lang1(A)) => ( r2_hidden(C,k15_qc_lang2(A,B)) => ( ( ~ r1_qc_lang2(A,D,C) & ~ r3_qc_lang2(A,D,C) & ~ r2_qc_lang2(A,D,C) ) | r2_hidden(D,k15_qc_lang2(A,B)) ) ) ) ) ) ) )).
fof(t98_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(t98_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k8_afinsq_1(D))) => ! [F] : ( ( ~ v2_struct_0(F) & l1_rewrite3(F,E) ) => ( r2_rewrite3(D,E,F,A,B,C,k2_flang_1(D)) => r4_rewrite3(D,E,F,A,B,C) ) ) ) ) )).
fof(t98_rvsum_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_valued_0(B) & v1_finseq_1(B) ) => k19_rvsum_1(k7_finseq_1(k9_finseq_1(A),B)) = k3_xcmplx_0(A,k19_rvsum_1(B)) ) ) )).
fof(t98_scmpds_6,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => k1_funct_1(k9_scmpds_6(A,B,C),k5_numbers) = k9_scmpds_2(A,B,k1_nat_1(k5_card_1(C),1)) ) ) ) )).
fof(t98_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ! [C] : ~ ( B != C & r2_hidden(k2_tarski(k4_tarski(B,k3_tarski(A)),k4_tarski(C,k3_tarski(A))),k12_scmyciel(A)) ) ) )).
fof(t98_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( ( r4_semi_af1(A,B,F,C,G,E) & r4_semi_af1(A,B,F,D,H,E) ) => r2_analoaf(A,C,D,G,H) ) ) ) ) ) ) ) ) ) )).
fof(t98_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => r1_xxreal_0(k20_seq_4(k17_seq_4(A,B,C)),k2_xcmplx_0(k20_seq_4(B),k20_seq_4(C))) ) ) ) )).
fof(t98_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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,k5_sheffer1(A,B,B),C)),k5_sheffer1(A,k5_sheffer1(A,C,k5_sheffer1(A,D,B)),k5_sheffer1(A,C,k5_sheffer1(A,D,B)))) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,B)),k5_sheffer1(A,k5_sheffer1(A,D,D),C)),k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,k5_sheffer1(A,D,D),C))) ) ) ) ) )).
fof(t98_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) & k4_sin_cos6(A) = k28_sin_cos ) => A = k4_xcmplx_0(1) ) ) )).
fof(t98_sin_cos9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( 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_sin_cos9))) & r1_tarski(C,k2_rcomp_1(k4_xcmplx_0(1),1)) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(D,E) = k2_xcmplx_0(k3_xcmplx_0(A,E),B) ) ) ) => ( r2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k2_sin_cos9),C) & ! [E] : ( v1_xreal_0(E) => ( r2_hidden(E,C) => k1_funct_1(k2_fdiff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,D,k2_sin_cos9),C),E) = k6_xcmplx_0(k3_xcmplx_0(A,k1_funct_1(k2_sin_cos9,E)),k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,E),B),k2_xcmplx_0(1,k1_square_1(E)))) ) ) ) ) ) ) ) ) )).
fof(t98_sincos10,axiom,( k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k2_sincos10,k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1)))) = k1_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,4),k28_sin_cos),k28_sin_cos) )).
fof(t98_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => v4_lattice3(k8_tdlat_1(A)) ) )).
fof(t98_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( u1_struct_0(C) = B => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => r1_tmap_1(C,k6_tmap_1(A,B),k2_tmap_1(A,k6_tmap_1(A,B),k7_tmap_1(A,B),C),D) ) ) ) ) ) )).
fof(t98_xboole_1,axiom,( ! [A] : ! [B] : k2_xboole_0(A,B) = k5_xboole_0(A,k4_xboole_0(B,A)) )).
fof(t98_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k4_xboolean(A,k10_xboolean(A,B)) = k11_xboolean(A,B) ) ) )).
fof(t98_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ( C != k5_numbers => k7_xcmplx_0(A,B) = k3_xcmplx_0(k7_xcmplx_0(A,C),k7_xcmplx_0(C,B)) ) ) ) ) )).
fof(t98_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(C,k5_numbers) & r1_xxreal_0(A,B) & ~ r1_xxreal_0(D,C) & r1_xxreal_0(k3_xcmplx_0(B,D),k3_xcmplx_0(A,C)) ) ) ) ) ) )).
fof(t98_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(A,C) & ~ r1_xxreal_0(D,C) & r1_tarski(k2_xxreal_1(C,D),k1_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t98_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k4_xxreal_3(A,k1_xxreal_3(k5_numbers,B)) = k1_xxreal_3(k4_xxreal_3(A,k5_numbers),k4_xxreal_3(A,B)) ) ) )).
fof(t98_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ! [C] : ( m2_subset_1(C,k4_ordinal1,k1_zf_lang) => ! [D] : ( m2_subset_1(D,k4_ordinal1,k1_zf_lang) => ! [E] : ( ~ v1_xboole_0(E) => ( r2_zf_model(E,A) => r2_zf_model(E,k17_zf_lang(B,C,D,A)) ) ) ) ) ) ) )).
fof(t98_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ( k2_zfmisc_1(k3_xboole_0(A,B),C) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,C)) & k2_zfmisc_1(C,k3_xboole_0(A,B)) = k3_xboole_0(k2_zfmisc_1(C,A),k2_zfmisc_1(C,B)) ) )).
fof(t98_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul01(B,A) => ! [C] : ( ( v1_zmodul01(C) & m1_zmodul01(C,A) ) => ( m1_zmodul01(B,C) <=> k6_zmodul01(A,B,C) = C ) ) ) ) )).
fof(t99_abcmiz_1,axiom,( ! [A] : ( ( v1_instalg1(A) & v1_abcmiz_1(A) & v3_abcmiz_1(A) & l1_msualg_1(A) ) => ! [B] : ( m1_abcmiz_1(B,A,k13_abcmiz_1(A)) => k45_abcmiz_1(A,k37_abcmiz_1(A,B)) = k45_abcmiz_1(A,B) ) ) )).
fof(t99_aofa_000,axiom,( ! [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) & l1_unialg_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(D)) => ! [F] : ( m1_subset_1(F,D) => ! [G] : ( 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(k4_tarski(F,B),k21_aofa_000(A,D,E,G)) & ? [H] : ( ~ v1_xboole_0(H) & m2_finseq_1(H,D) & k1_funct_1(H,1) = k2_binop_1(D,u1_struct_0(A),D,G,F,B) & ~ r2_hidden(k1_funct_1(H,k3_finseq_1(H)),E) & ! [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) & r2_hidden(k4_tarski(k1_funct_1(H,I),k13_aofa_000(A,C,B)),k21_aofa_000(A,D,E,G)) & k1_funct_1(H,k1_nat_1(I,1)) = k1_binop_1(G,k1_funct_1(H,I),k13_aofa_000(A,C,B)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t99_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v13_aofa_a00(A) & v16_aofa_a00(A) & v18_aofa_a00(A,4,1) & v21_aofa_a00(A,1,1,11) & v23_aofa_a00(A,11) & l6_aofa_a00(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v4_msualg_1(C,A) & v5_msafree4(C,A,B) & v3_aofa_a00(C,A,B) & v6_aofa_a01(C,A) & l1_aofa_a00(C,A) ) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree4(D,A,C) & v17_aofa_a00(D,A) & v20_aofa_a00(D,4,1,A) & v22_aofa_a00(D,A,1,1,11) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_aofa_a01(E,A,B,C) & l4_aofa_a00(E,A,B,C) ) => ! [F] : ( ( v19_aofa_a00(F,A) & m1_subset_1(F,u1_struct_0(A)) ) => ! [G] : ( ( v3_aofa_a01(G,A,B,C,u4_aofa_a00(A,B,C,E),F) & m1_msafree4(G,u1_struct_0(A),u4_aofa_a00(A,B,C,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),F)) ) => ! [H] : ( ( v3_aofa_a01(H,A,B,C,u4_aofa_a00(A,B,C,E),k37_aofa_a00(A)) & m1_msafree4(H,u1_struct_0(A),u4_aofa_a00(A,B,C,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),k37_aofa_a00(A))) ) => ! [I] : ( ( v3_aofa_a01(I,A,B,C,u4_aofa_a00(A,B,C,E),u8_aofa_a00(A)) & m1_msafree4(I,u1_struct_0(A),u4_aofa_a00(A,B,C,E),k1_msafree4(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u8_aofa_a00(A))) ) => ! [J] : ( m2_subset_1(J,k4_autalg_1(u1_struct_0(A),u4_aofa_a00(A,B,C,E),u3_msualg_1(A,D)),k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E))) => ! [K] : ( ( ~ v2_struct_0(K) & v2_unialg_1(K) & v3_unialg_1(K) & v4_unialg_1(K) & v3_aofa_000(K) & v4_aofa_000(K) & v5_aofa_000(K) & v6_aofa_000(K) & ~ v10_aofa_000(K) & v11_aofa_000(K) & v12_aofa_000(K) & v5_aofa_a01(K,A,B,C,E) & l3_aofa_a00(K,A,C,u4_aofa_a00(A,B,C,E)) ) => ! [L] : ( m1_aofa_000(L,K,k13_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E)),k14_aofa_a00(A,C,D,u4_aofa_a00(A,B,C,E),u8_aofa_a00(A),I,k2_aofa_a01(A,D))) => ( ( v7_aofa_a01(E,A,B,C) & v11_aofa_a00(E,A,B,C,D) & r2_hidden(L,k20_aofa_a00(A,B,C,D,E,K,u8_aofa_a00(A),I,k2_aofa_a01(A,D))) & v1_msafree4(B,u1_struct_0(A)) ) => ( v8_aofa_a01(C,A,B) | ! [M] : ( m1_subset_1(M,k1_funct_1(u3_msualg_1(A,C),F)) => r8_pboole(u1_struct_0(A),k3_aofa_a01(A,B,C,E,I,D,K,L,J,k13_aofa_a01(A,B,C,E,K,F,k39_aofa_a00(A,C,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),k37_aofa_a00(A),H),F,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),F,G)),M)),k3_aofa_a01(A,B,C,E,I,D,K,L,J,k12_aofa_a00(A,C,u4_aofa_a00(A,B,C,E),K,k37_aofa_a00(A),H,k40_aofa_a00(A,C,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),k37_aofa_a00(A),H),F,k4_aofa_a01(A,C,u4_aofa_a00(A,B,C,E),F,G),M)))) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t99_card_2,axiom,( ! [A] : ! [B] : ( ( v4_card_3(A) & v4_card_3(B) ) => v4_card_3(k5_xboole_0(A,B)) ) )).
fof(t99_card_3,axiom,( ! [A] : ( ( v4_funct_1(A) & v2_card_3(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t99_chord,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v2_glib_000(A) & v6_chord(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ( m1_subset_1(C,k6_glib_000(A)) => ~ ( B != C & ~ r1_chord(A,B,C) & ? [D] : ( m2_chord(D,A,B,C) & v4_chord(D,A,B,C) & ? [E] : ( 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] : ( m1_subset_1(F,k6_glib_000(E)) & B = F & ! [G] : ( m1_subset_1(G,k6_glib_000(A)) => ~ ( r2_hidden(G,k1_glib_002(E,F)) & ! [H] : ( m1_subset_1(H,k6_glib_000(A)) => ( r2_hidden(H,D) => r1_chord(A,G,H) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t99_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_clvect_1(D,A) => ! [E] : ( m2_clvect_1(E,A,D) => ~ ( r2_hidden(B,E) & r2_hidden(C,E) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_struct_0(D,F) & k5_algstr_0(A,B,F) = C ) ) ) ) ) ) ) ) )).
fof(t99_cohsp_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ! [C] : ! [D] : ! [E] : ! [F] : ( r2_hidden(k4_tarski(k4_tarski(C,E),k4_tarski(D,F)),k1_coh_sp(k17_cohsp_1(A,B))) <=> ( r2_hidden(k4_tarski(C,D),k1_coh_sp(A)) & r2_hidden(k4_tarski(E,F),k1_coh_sp(B)) ) ) ) ) )).
fof(t99_euclid_8,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [G] : ( ( v1_funct_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [H] : ( v1_xreal_0(H) => ( ( r1_fdiff_1(B,H) & r1_fdiff_1(C,H) & r1_fdiff_1(D,H) & r1_fdiff_1(E,k1_funct_1(B,H)) & r1_fdiff_1(F,k1_funct_1(C,H)) & r1_fdiff_1(G,k1_funct_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(k3_xcmplx_0(k1_fdiff_1(E,k1_funct_1(B,H)),k1_fdiff_1(B,H)),k3_xcmplx_0(k1_fdiff_1(F,k1_funct_1(C,H)),k1_fdiff_1(C,H)),k3_xcmplx_0(k1_fdiff_1(G,k1_funct_1(D,H)),k1_fdiff_1(D,H))),A) ) ) ) ) ) ) ) ) ) )).
fof(t99_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_subset_1(C,k1_zfmisc_1(k1_euclid(A)),k1_euclidlp(A)) => ? [D] : ( m2_subset_1(D,k1_zfmisc_1(k1_euclid(A)),k5_euclidlp(A)) & r2_hidden(B,D) & r1_tarski(C,D) ) ) ) ) )).
fof(t99_finseq_1,axiom,( ! [A] : ( ( 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))) ) )).
fof(t99_finseq_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => r2_hidden(k10_finseq_1(B,C),k4_finseq_2(2,A)) ) ) ) )).
fof(t99_finseq_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : ! [D] : ( ( v2_funct_1(A) & k10_xtuple_0(A) = k1_enumset1(B,C,D) ) => ( B = C | C = D | B = D | k3_finseq_1(A) = 3 ) ) ) )).
fof(t99_finseq_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ( C != D => k1_finseq_6(A,k3_finseq_4(A,B,C,D),D) = k3_finseq_4(A,D,C,D) ) ) ) ) ) )).
fof(t99_flang_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => k2_flang_2(A,k1_flang_2(A,B,1,C)) = k1_flang_2(A,B,k5_numbers,C) ) ) )).
fof(t99_funct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ! [D] : 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))) ) ) )).
fof(t99_funct_2,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( 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)) ) ) ) )).
fof(t99_funct_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : k9_xtuple_0(k6_funct_4(A,B,C)) = k9_xtuple_0(A) ) )).
fof(t99_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : r1_tarski(k10_xtuple_0(k1_funct_7(A,B,C)),k2_xboole_0(k10_xtuple_0(A),k1_tarski(C))) ) )).
fof(t99_gfacirc1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ~ v1_facirc_1(k2_msafree2(k37_gfacirc1(A,B,C))) ) ) ) )).
fof(t99_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_glib_000(B,A) => ! [C] : ( m1_glib_000(C,A) => ~ ( r7_glib_000(B,C) & ! [D] : ~ ( r2_hidden(D,k24_glib_000(A,C)) & ~ r2_hidden(D,k24_glib_000(A,B)) ) & ! [D] : ~ ( r2_hidden(D,k25_glib_000(A,C)) & ~ r2_hidden(D,k25_glib_000(A,B)) ) ) ) ) ) )).
fof(t99_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( 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)) ) ) )).
fof(t99_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,A) => k11_group_2(A,D,k11_group_2(A,C,B)) = k2_group_2(A,B,k12_group_2(A,C,k8_group_2(A,D))) ) ) ) ) )).
fof(t99_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( k8_group_3(A,B) = k8_group_3(A,C) <=> ~ r1_xboole_0(k8_group_3(A,B),k8_group_3(A,C)) ) ) ) ) )).
fof(t99_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( ( v8_group_9(C,A,B) & m2_finseq_1(C,k6_group_9(A,B)) ) => ! [D] : ( ( v8_group_9(D,A,B) & m2_finseq_1(D,k6_group_9(A,B)) ) => ! [E] : ( ( v8_group_9(E,A,B) & m2_finseq_1(E,k6_group_9(A,B)) ) => ! [F] : ( v7_ordinal1(F) => ( ( r2_hidden(F,k4_finseq_1(C)) & r2_hidden(k1_nat_1(F,1),k4_finseq_1(C)) & k1_funct_1(C,F) = k1_funct_1(C,k1_nat_1(F,1)) & D = k2_finseq_3(F,C) & v10_group_9(E,A,B) & r4_group_9(A,B,C,E) ) => r4_group_9(A,B,D,E) ) ) ) ) ) ) )).
fof(t99_integra8,axiom,( ! [A] : ( ( ~ 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_sin_cos2,k3_sin_cos2)) = k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k3_xcmplx_0(k1_funct_1(k3_sin_cos2,k2_seq_4(A)),k1_funct_1(k3_sin_cos2,k2_seq_4(A))),k3_xcmplx_0(k1_funct_1(k3_sin_cos2,k3_seq_4(A)),k1_funct_1(k3_sin_cos2,k3_seq_4(A))))) ) )).
fof(t99_jgraph_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ! [C] : ( ( r2_hidden(B,C) & C = a_0_0_jgraph_4 ) => ( r1_xxreal_0(A,k4_xcmplx_0(1)) | r1_xxreal_0(1,A) | r2_hidden(k1_funct_1(k7_jgraph_4(A),B),C) ) ) ) )).
fof(t99_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [J] : ( 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) = 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(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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t99_jordan,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => v1_jordan1(A) ) )).
fof(t99_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t99_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v6_limfunc1(A) & k5_limfunc1(A) = k5_numbers & ! [C] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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] : ( v1_xreal_0(C) => ~ v1_comseq_2(k2_partfun1(k1_numbers,k1_numbers,B,k10_prob_1(C))) ) | ( v6_limfunc1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B)) & k5_limfunc1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,A,B)) = k5_numbers ) ) ) ) ) )).
fof(t99_matrix13,axiom,( ! [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] : ( ( v1_matrix_0(B) & v1_matrix_1(B,A) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => ! [C] : ( C = a_2_1_matrix13(A,B) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ! [E] : ( ( v1_finset_1(E) & v1_setfam_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ( ( r1_tarski(k2_zfmisc_1(D,E),k2_matrix_0(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_tarski(D,C) & r1_tarski(E,C) ) ) ) ) ) ) ) ) )).
fof(t99_member_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => k13_member_1(k1_tarski(A),k2_tarski(B,C)) = k2_tarski(k3_xcmplx_0(A,B),k3_xcmplx_0(A,C)) ) ) ) )).
fof(t99_mesfunc5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ! [F] : ( m2_subset_1(F,k1_zfmisc_1(A),B) => ( ( r1_mesfunc5(A,B,C,D) & F = k7_subset_1(A,k1_relset_1(A,D),E) ) => ( r1_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,E)) & k7_mesfunc5(A,B,C,D) = k3_supinf_2(k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,E)),k7_mesfunc5(A,B,C,k2_partfun1(A,k6_numbers,D,F))) ) ) ) ) ) ) ) ) )).
fof(t99_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_numbers) & v10_valued_0(C) & v6_supinf_2(C) & v4_measure1(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,k6_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [E] : ( ( 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) ) => r2_hidden(k1_relset_1(A,k3_valued_1(A,k1_numbers,k1_numbers,D,E)),B) ) ) ) ) ) ) )).
fof(t99_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ! [D] : ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(A)))) ) => ( ( r15_ncfcont1(B,A,C,E) & r1_tarski(D,C) ) => r15_ncfcont1(B,A,D,E) ) ) ) ) )).
fof(t99_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( 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,C,D) ) => r4_pboole(A,B,D) ) ) ) ) )).
fof(t99_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => ( ~ r1_xxreal_0(A,k5_numbers) => k4_prepower(A,B) = k3_prepower(A,B) ) ) ) )).
fof(t99_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) )).
fof(t99_rewrite3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_subset_1(E,k8_afinsq_1(D)) => ! [F] : ( m1_subset_1(F,k8_afinsq_1(D)) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(k8_afinsq_1(D))) => ! [H] : ( ( ~ v2_struct_0(H) & l1_rewrite3(H,G) ) => ( ( r4_rewrite3(D,G,H,A,E,B) & r4_rewrite3(D,G,H,B,F,C) ) => r4_rewrite3(D,G,H,A,k1_flang_1(D,E,F),C) ) ) ) ) ) ) )).
fof(t99_rvsum_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k19_rvsum_1(k10_finseq_1(A,B)) = k3_xcmplx_0(A,B) ) ) )).
fof(t99_scmpds_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(C) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) & v3_scmpds_4(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ( ( r1_scmpds_6(C,B,A) & r2_scmpds_6(C,B,A) ) => ( r1_xxreal_0(k5_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) ) ) ) ) ) ) ) ) )).
fof(t99_scmyciel,axiom,( ! [A] : ( v4_scmyciel(A) => ! [B] : ! [C] : ( r2_hidden(k2_tarski(k4_tarski(B,k3_tarski(A)),C),k1_scmyciel(k12_scmyciel(A))) => ( B != C & r2_hidden(B,k3_tarski(A)) & ( r2_hidden(C,k3_tarski(A)) | C = k3_tarski(A) ) ) ) ) )).
fof(t99_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( ( r4_semi_af1(A,B,F,C,G,E) & r4_semi_af1(A,B,F,D,H,E) ) => ( r1_semi_af1(A,E,C,D) | r4_semi_af1(A,C,G,D,H,E) ) ) ) ) ) ) ) ) ) ) )).
fof(t99_seq_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k2_numbers,k12_seq_4(A)) => ! [C] : ( m2_finseq_2(C,k2_numbers,k12_seq_4(A)) => r1_xxreal_0(k6_xcmplx_0(k20_seq_4(B),k20_seq_4(C)),k20_seq_4(k13_seq_4(A,B,C))) ) ) ) )).
fof(t99_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_sheffer1(A) & v11_sheffer1(A) & v12_sheffer1(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k5_sheffer1(A,B,k5_sheffer1(A,D,C)) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,C),k5_sheffer1(A,C,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))) ) ) ) ) )).
fof(t99_sin_cos6,axiom,( ! [A] : ( v1_xreal_0(A) => ( ( r1_xxreal_0(k4_xcmplx_0(1),A) & r1_xxreal_0(A,1) ) => ( r1_xxreal_0(k5_numbers,k4_sin_cos6(A)) & r1_xxreal_0(k4_sin_cos6(A),k28_sin_cos) ) ) ) )).
fof(t99_sin_cos9,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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_cos9),k7_xcmplx_0(1,2)))) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => ( k1_funct_1(B,C) = k3_xcmplx_0(2,C) & ~ r1_xxreal_0(k1_funct_1(B,C),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_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_cos9),k7_xcmplx_0(1,2)),A) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(k2_fdiff_1(k26_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k1_sin_cos9),k7_xcmplx_0(1,2)),A),C) = k7_xcmplx_0(1,k2_xcmplx_0(1,k1_square_1(k3_xcmplx_0(2,C)))) ) ) ) ) ) ) )).
fof(t99_sincos10,axiom,( k2_relset_1(k1_numbers,k2_partfun1(k1_numbers,k1_numbers,k3_sincos10,k1_rcomp_1(k4_xcmplx_0(k3_square_1(2)),k4_xcmplx_0(1)))) = k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,4))) )).
fof(t99_tdlat_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v2_tdlat_2(B,A) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t99_tmap_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ( r1_xboole_0(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))))) ) ) ) ) ) )).
fof(t99_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : k4_xboole_0(k5_xboole_0(A,B),C) = k2_xboole_0(k4_xboole_0(A,k2_xboole_0(B,C)),k4_xboole_0(B,k2_xboole_0(A,C))) )).
fof(t99_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => k4_xboolean(k3_xboolean(A),k10_xboolean(A,B)) = k11_xboolean(B,A) ) ) )).
fof(t99_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k3_xcmplx_0(A,k7_xcmplx_0(1,B)) = k7_xcmplx_0(A,B) ) ) )).
fof(t99_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( ~ r1_xxreal_0(C,k5_numbers) & ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(B,A) & r1_xxreal_0(k7_xcmplx_0(C,A),k7_xcmplx_0(C,B)) ) ) ) ) )).
fof(t99_xxreal_1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ! [D] : ( v1_xxreal_0(D) => ~ ( ~ r1_xxreal_0(A,C) & ~ r1_xxreal_0(D,C) & r1_tarski(k3_xxreal_1(C,D),k1_xxreal_1(A,B)) ) ) ) ) ) )).
fof(t99_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => k5_xxreal_3(k2_xxreal_3(A)) = k2_xxreal_3(k5_xxreal_3(A)) ) )).
fof(t99_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_zf_lang(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( 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(A,B))) & r2_zf_model(C,k11_zf_lang(k12_zf_lang(A,B),k11_zf_lang(A,B))) ) ) ) ) ) )).
fof(t99_zfmisc_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : 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)) )).
fof(t99_zmodul01,axiom,( ! [A] : ( ( ~ 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] : ( ( v1_zmodul01(B) & m1_zmodul01(B,A) ) => k6_zmodul01(A,k3_zmodul01(A),B) = B ) ) )).
fof(t9_abcmiz_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_abcmiz_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & 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)) & v9_abcmiz_0(A) ) => v9_abcmiz_0(B) ) ) ) )).
fof(t9_abcmiz_1,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_tarski(k1_abcmiz_1(A),k1_abcmiz_1(B)) ) )).
fof(t9_abcmiz_a,axiom,( ! [A] : ( m1_subset_1(A,k2_abcmiz_1) => ( A != k9_abcmiz_1 & A != k10_abcmiz_1 ) ) )).
fof(t9_abian,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ ( ~ v1_abian(A) & ! [B] : ( m1_subset_1(B,k4_ordinal1) => A != k1_nat_1(k2_nat_1(2,B),1) ) ) & ~ ( ? [B] : ( m1_subset_1(B,k4_ordinal1) & A = k1_nat_1(k2_nat_1(2,B),1) ) & v1_abian(A) ) ) ) )).
fof(t9_absvalue,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( ( r1_xxreal_0(k9_complex1(A),C) & r1_xxreal_0(k9_complex1(B),D) ) => r1_xxreal_0(k9_complex1(k2_xcmplx_0(A,B)),k2_xcmplx_0(C,D)) ) ) ) ) ) )).
fof(t9_aff_1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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) ) ) ) ) ) ) )).
fof(t9_aff_2,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v2_aff_2(A) => v13_aff_2(A) ) ) )).
fof(t9_aff_3,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v5_aff_3(A) <=> v7_aff_3(A) ) ) )).
fof(t9_aff_4,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A))) => ! [H] : ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(A))) => ( ( r2_hidden(F,G) & r2_hidden(F,H) & r2_hidden(B,G) & r2_hidden(D,G) & r2_hidden(C,H) & r2_hidden(E,H) & v1_aff_1(G,A) & v1_aff_1(H,A) & B = D ) => ( F = B | F = C | G = H | ( ~ r2_analoaf(A,B,C,D,E) & ~ r2_analoaf(A,C,B,E,D) ) | C = E ) ) ) ) ) ) ) ) ) ) )).
fof(t9_afinsq_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ( ( k1_afinsq_1(A) = k1_afinsq_1(B) & ! [C] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(k1_afinsq_1(A),C) => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) ) => A = B ) ) ) )).
fof(t9_afinsq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => r1_tarski(k10_xtuple_0(k2_afinsq_2(B,A)),k10_xtuple_0(B)) ) ) )).
fof(t9_afproj,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_aff_1(B,A) => ! [C] : ( r2_hidden(C,k5_afproj(A,B)) <=> ? [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) & C = D & v1_aff_1(D,A) & r1_aff_4(A,B,D) ) ) ) ) ) )).
fof(t9_afvect0,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect0(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( ( r2_analoaf(A,C,D,F,G) & r2_analoaf(A,B,E,C,D) & r2_analoaf(A,B,H,F,G) ) => E = H ) ) ) ) ) ) ) ) ) )).
fof(t9_afvect01,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_afvect01(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ~ r1_afvect01(A,B,C) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( B != D & r2_analoaf(A,B,C,C,D) ) ) ) ) ) ) )).
fof(t9_alg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_unialg_1(B) & v3_unialg_1(B) & v4_unialg_1(B) & l1_unialg_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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) ) => r1_alg_1(B,A,D) ) ) ) ) ) )).
fof(t9_algspec1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r2_hidden(B,A) => ( ( r2_hidden(B,k9_xtuple_0(C)) => k1_funct_1(k1_algspec1(A,C),B) = k1_funct_1(C,B) ) & ( ~ r2_hidden(B,k9_xtuple_0(C)) => k1_funct_1(k1_algspec1(A,C),B) = B ) ) ) ) )).
fof(t9_algstr_1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k8_algstr_0)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k8_algstr_0)) => A = B ) ) )).
fof(t9_algstr_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_algstr_1(A) & v4_algstr_1(A) & v7_algstr_1(A) & v4_rlvect_1(A) & v2_vectsp_1(A) & v4_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k6_algstr_0(A,k2_algstr_2(A,C,D),B) = k2_algstr_2(A,k6_algstr_0(A,C,B),k6_algstr_0(A,D,B)) ) ) ) ) )).
fof(t9_algstr_4,axiom,( ! [A] : ( l3_algstr_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ! [C] : ( r2_hidden(C,k9_xtuple_0(B)) => ( v2_algstr_4(k1_funct_1(B,C),A) & m1_subset_1(k1_funct_1(B,C),k1_zfmisc_1(u1_struct_0(A))) ) ) => ( v2_algstr_4(k3_funct_6(B),A) & m1_subset_1(k3_funct_6(B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) )).
fof(t9_altcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)))) ) ) ) ) ) )).
fof(t9_altcat_2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ( r2_altcat_2(A,A,B,C) <=> r2_pboole(A,B,C) ) ) ) )).
fof(t9_altcat_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_altcat_1(A,C,B)) => ( v6_altcat_3(B,A) => v5_altcat_3(D,A,C,B) ) ) ) ) ) )).
fof(t9_altcat_5,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,u1_struct_0(k7_altcat_1(B))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(k7_altcat_1(B))))) ) => ( r2_hidden(k4_card_3(C),B) => v5_altcat_5(k2_altcat_5(A,B,C),k7_altcat_1(B),A,C) ) ) ) )).
fof(t9_ami_2,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k3_ami_2,k4_ami_2))) => ! [B] : ( m2_subset_1(B,k1_ami_2,k2_ami_2) => ! [C] : ( v1_int_1(C) => k1_funct_1(k7_ami_2(A,B,C),k4_ordinal1) = k1_funct_1(A,k4_ordinal1) ) ) ) )).
fof(t9_ami_3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_ami_3)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ( ( ~ r1_xxreal_0(k1_funct_1(D,A),k5_numbers) => k1_funct_1(k2_extpro_1(k7_card_1(2),k1_ami_3,k9_ami_3(C,A),D),k4_struct_0(k1_ami_3)) = C ) & ( r1_xxreal_0(k1_funct_1(D,A),k5_numbers) => k1_funct_1(k2_extpro_1(k7_card_1(2),k1_ami_3,k9_ami_3(C,A),D),k4_struct_0(k1_ami_3)) = k4_card_1(k5_memstr_0(k7_card_1(2),k1_ami_3,D)) ) & k1_funct_1(k2_extpro_1(k7_card_1(2),k1_ami_3,k9_ami_3(C,A),D),B) = k1_funct_1(D,B) ) ) ) ) ) )).
fof(t9_ami_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ~ ( ~ r1_xxreal_0(A,k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & k1_funct_1(k2_ami_4,k12_ami_3(k10_ami_3(k5_numbers),k10_ami_3(1),A,B)) != k11_ami_3(k10_ami_3(k5_numbers),k3_int_2(A,B)) ) ) ) )).
fof(t9_ami_5,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_ami_3)) => ~ ( k2_compos_0(u1_compos_1(k1_ami_3),A) = 3 & ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_ami_3)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_ami_3)) ) => A != k4_ami_3(B,C) ) ) ) ) )).
fof(t9_ami_6,axiom,( ! [A] : ( m1_subset_1(A,k1_compos_0(u1_compos_1(k1_ami_3))) => ( A = 6 => k9_xtuple_0(k10_card_3(k3_compos_0(u1_compos_1(k1_ami_3),A))) = k1_tarski(1) ) ) )).
fof(t9_ami_wstd,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r1_xxreal_0(k3_ami_wstd(A,B,C),k3_ami_wstd(A,B,D)) <=> r1_ami_wstd(A,B,C,D) ) ) ) ) ) )).
fof(t9_amistd_1,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( m1_subset_1(B,u1_compos_1(k4_amistd_1(A))) => ! [C] : ( ( 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)) ) ) ) ) )).
fof(t9_amistd_2,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( 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(k5_numbers) ) ) )).
fof(t9_amistd_4,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_compos_1(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ~ ( v1_zfmisc_1(k4_memstr_0(A,B,D)) & r2_hidden(D,k2_amistd_4(A,B,C)) ) ) ) ) ) )).
fof(t9_amistd_5,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ 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] : ( v7_ordinal1(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & v5_relat_1(D,u1_compos_1(B)) & v1_funct_1(D) & v1_finset_1(D) & ~ v2_compos_1(D,B) ) => ! [E] : ( ( 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) & v4_extpro_1(E,A,B,D) ) => ( r2_hidden(k4_struct_0(B),k9_xtuple_0(E)) => ! [F] : ( ( 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(k9_memstr_0(A,B,E,C),F) => ! [G] : ( ( v1_relat_1(G) & v4_relat_1(G,k4_ordinal1) & v5_relat_1(G,u1_compos_1(B)) & v1_funct_1(G) & v1_partfun1(G,k4_ordinal1) ) => ( r1_tarski(k6_compos_1(B,D,C),G) => ! [H] : ( v7_ordinal1(H) => r6_pboole(u1_struct_0(B),k5_extpro_1(A,B,G,F,H),k9_memstr_0(A,B,k5_extpro_1(A,B,k1_funct_4(G,D),k1_funct_4(F,E),H),C)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_analmetr,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ~ ( r1_analmetr(A,E,F) & r2_analmetr(A,D,B,E,F) & r2_analmetr(A,D,C,E,F) & D != k4_struct_0(A) & ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ~ ( k1_rlvect_1(A,B,G) = k1_rlvect_1(A,C,H) & ~ ( G = k5_numbers & H = k5_numbers ) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_analoaf,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_analoaf(A,B,C,D,D) & r1_analoaf(A,B,B,C,D) ) ) ) ) ) )).
fof(t9_analort,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_analmetr(A,C,D) => k2_analort(A,C,D,k4_algstr_0(A,B)) = k4_algstr_0(A,k2_analort(A,C,D,B)) ) ) ) ) ) )).
fof(t9_anproj_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ~ ( ~ r1_anproj_1(A,B,C) & D = k3_rlvect_1(A,k1_rlvect_1(A,B,F),k1_rlvect_1(A,C,G)) & E = k3_rlvect_1(A,k1_rlvect_1(A,B,H),k1_rlvect_1(A,C,I)) & k6_xcmplx_0(k3_xcmplx_0(F,I),k3_xcmplx_0(H,G)) = k5_numbers & ~ v9_struct_0(B,A) & ~ v9_struct_0(C,A) & ~ r1_anproj_1(A,D,E) & D != k4_struct_0(A) & E != k4_struct_0(A) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_anproj_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ! [J] : ( m1_subset_1(J,u1_struct_0(A)) => ! [K] : ( m1_subset_1(K,u1_struct_0(A)) => ( ( r1_anproj_2(A,C,D,E) & r1_anproj_2(A,I,J,K) & r1_anproj_2(A,F,G,H) & r4_anproj_2(A,B,C,D,E,I,J,K) & r5_anproj_2(A,B,C,D,E,I,J,K) & r2_anproj_1(A,C,J,H) & r2_anproj_1(A,I,D,H) & r2_anproj_1(A,C,K,G) & r2_anproj_1(A,E,I,G) & r2_anproj_1(A,D,K,F) & r2_anproj_1(A,E,J,F) ) => ( v9_struct_0(B,A) | r2_anproj_1(A,F,G,H) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_aofa_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r2_hidden(B,k9_xtuple_0(A)) => r1_tarski(k5_aofa_000(A,k1_funct_1(A,B)),k5_aofa_000(A,B)) ) ) )).
fof(t9_aofa_a00,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ! [G] : ! [H] : k9_xtuple_0(k4_aofa_a00(A,B,C,D,E,F,G,H)) = k2_enumset1(A,B,C,D) )).
fof(t9_aofa_a01,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( ( v5_msafree4(C,A,B) & l3_msualg_1(C,A) ) => ! [D] : ( ( v2_aofa_a01(D,A,B,C) & m1_msafree(D,A,C) ) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( ( v3_aofa_a01(F,A,B,C,D,E) & m1_subset_1(F,k1_msafree4(u1_struct_0(A),D,E)) ) <=> r2_hidden(F,k1_msafree4(u1_struct_0(A),k1_aofa_a01(A,B,C),E)) ) ) ) ) ) ) )).
fof(t9_aofa_i00,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ? [C] : ( 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)))) & k3_funct_2(A,k1_card_1(A),C,B) = k5_numbers ) ) ) )).
fof(t9_armstrng,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) => ~ ( r2_hidden(B,C) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(A)) => B != k4_tarski(D,E) ) ) ) ) )).
fof(t9_arytm_0,axiom,( ! [A] : ( m1_subset_1(A,k2_numbers) => ? [B] : ( m1_subset_1(B,k1_numbers) & ? [C] : ( m1_subset_1(C,k1_numbers) & A = k5_arytm_0(B,C) ) ) ) )).
fof(t9_arytm_1,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ~ ( ~ r1_arytm_2(A,B) & k1_arytm_1(A,B) = k11_arytm_3 ) ) ) )).
fof(t9_arytm_2,axiom,( ! [A] : ( m1_subset_1(A,k2_arytm_2) => ! [B] : ( m1_subset_1(B,k2_arytm_2) => ~ ( r1_arytm_2(A,B) & ! [C] : ( m1_subset_1(C,k2_arytm_2) => k7_arytm_2(A,C) != B ) ) ) ) )).
fof(t9_arytm_3,axiom,( ! [A] : ( ( v3_ordinal1(A) & v7_ordinal1(A) ) => ( r2_arytm_3(A,k1_xboole_0) & r2_arytm_3(1,A) ) ) )).
fof(t9_asympt_0,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & v2_asympt_0(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => k6_asympt_0(k1_asympt_0(A,B)) = k6_asympt_0(k5_asympt_0(A,B)) ) ) )).
fof(t9_asympt_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & v2_asympt_0(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ? [B] : ( m1_funct_2(B,k4_ordinal1,k1_numbers) & B = k1_tarski(k3_asympt_1(1)) & ~ ( r2_hidden(A,k15_asympt_0(B,k6_asympt_0(k1_seq_1(1)))) & ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(C,F) => ( r1_xxreal_0(1,k9_nat_1(k1_numbers,A,F)) & r1_xxreal_0(k9_nat_1(k1_numbers,A,F),k3_xcmplx_0(D,k9_nat_1(k1_numbers,k3_asympt_1(E),F))) ) ) ) ) ) ) ) ) & ( ? [C] : ( m1_subset_1(C,k4_ordinal1) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( m1_subset_1(E,k4_ordinal1) & ~ r1_xxreal_0(D,k5_numbers) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r1_xxreal_0(C,F) => ( r1_xxreal_0(1,k9_nat_1(k1_numbers,A,F)) & r1_xxreal_0(k9_nat_1(k1_numbers,A,F),k3_xcmplx_0(D,k9_nat_1(k1_numbers,k3_asympt_1(E),F))) ) ) ) ) ) ) => r2_hidden(A,k15_asympt_0(B,k6_asympt_0(k1_seq_1(1)))) ) ) ) )).
fof(t9_autalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( m2_funct_2(B,u1_struct_0(A),u1_struct_0(A),k1_autalg_1(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_autalg_1(A))) => ( B = C => k2_funct_1(B) = k2_group_1(k3_autalg_1(A),C) ) ) ) ) )).
fof(t9_autgroup,axiom,( ! [A] : ( ( ~ 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(k3_autgroup(A)) ) )).
fof(t9_bcialg_1,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_bcialg_1(A,k1_bcialg_1(A,B,C)) = k1_bcialg_1(A,k2_bcialg_1(A,B),k2_bcialg_1(A,C)) ) ) ) )).
fof(t9_bcialg_2,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => k2_bcialg_1(A,k1_bcialg_2(A,k4_struct_0(A),B,C)) = k1_bcialg_2(A,k4_struct_0(A),k2_bcialg_1(A,B),C) ) ) ) )).
fof(t9_bcialg_3,axiom,( ! [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) ) => ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( 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) ) ) ) ) ) )).
fof(t9_bcialg_4,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t9_bcialg_5,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => k1_bcialg_5(A,B,C,k1_nat_1(D,1),E) = k1_bcialg_1(A,k1_bcialg_5(A,B,C,D,E),k1_bcialg_1(A,B,C)) ) ) ) ) ) )).
fof(t9_bciideal,axiom,( ! [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) ) => ( m2_bcialg_1(k5_bcialg_1(A),A) => ! [B] : ( m2_subset_1(B,u1_struct_0(A),k4_bcialg_1(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k5_bcialg_1(A)) => ( r2_hidden(k1_bcialg_1(A,B,C),k5_bcialg_1(A)) => B = k4_struct_0(A) ) ) ) ) ) )).
fof(t9_bhsp_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k2_bhsp_1(A,B,k4_algstr_0(A,C)) = k4_xcmplx_0(k2_bhsp_1(A,B,C)) ) ) ) )).
fof(t9_bhsp_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_bhsp_2(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(E,F) & r1_xxreal_0(D,k3_bhsp_1(A,k5_algstr_0(A,k1_normsp_1(A,B,F),C))) ) ) ) ) ) ) ) ) )).
fof(t9_bhsp_3,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( ( v2_bhsp_3(B,A) & r1_bhsp_3(A,B,C) ) => v2_bhsp_3(C,A) ) ) ) ) )).
fof(t9_bhsp_4,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_bhsp_4(B,A) => ( v1_bhsp_2(B,A) & k1_bhsp_2(A,B) = k4_struct_0(A) ) ) ) ) )).
fof(t9_bhsp_5,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r2_hidden(D,B) & r2_hidden(E,B) ) => ( D = E | k1_funct_1(u1_bhsp_1(A),k4_tarski(k1_funct_1(C,D),k1_funct_1(C,E))) = k5_numbers ) ) ) ) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_hidden(E,B) => k1_funct_1(D,E) = k1_funct_1(u1_bhsp_1(A),k4_tarski(k1_funct_1(C,E),k1_funct_1(C,E))) ) ) ) => ! [E] : ( m2_finseq_1(E,u1_struct_0(A)) => ( ( v2_funct_1(E) & k10_xtuple_0(E) = B ) => k1_funct_1(u1_bhsp_1(A),k4_tarski(k1_finsop_1(u1_struct_0(A),k4_bhsp_5(u1_struct_0(A),u1_struct_0(A),C,E),u1_algstr_0(A)),k1_finsop_1(u1_struct_0(A),k4_bhsp_5(u1_struct_0(A),u1_struct_0(A),C,E),u1_algstr_0(A)))) = k1_finsop_1(k1_numbers,k4_bhsp_5(k1_numbers,u1_struct_0(A),D,E),k9_binop_2) ) ) ) ) ) ) ) ) )).
fof(t9_bhsp_6,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ~ v1_xboole_0(B) => v1_bhsp_6(B,A) ) ) ) )).
fof(t9_bilinear,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_vectsp_1(C,A) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(C)) => ( k1_relset_1(u1_struct_0(B),k8_bilinear(A,B,C,D,E)) = u1_struct_0(B) & r1_tarski(k2_relset_1(u1_struct_0(A),k8_bilinear(A,B,C,D,E)),u1_struct_0(A)) & ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => k3_funct_2(u1_struct_0(B),u1_struct_0(A),k8_bilinear(A,B,C,D,E),F) = k2_binop_1(u1_struct_0(B),u1_struct_0(C),u1_struct_0(A),D,F,E) ) ) ) ) ) ) ) )).
fof(t9_binari_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k3_binarith(k2_xcmplx_0(A,1),k9_binarith(A,1,k6_margrel1,B,k10_binarith(k6_margrel1,C))) = k9_binarith(A,1,k6_margrel1,k3_binarith(A,B),k10_binarith(k6_margrel1,k9_margrel1(C))) ) ) ) )).
fof(t9_binari_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ( B = k5_euclid(A) => k4_finseq_5(k6_margrel1,k3_binarith(A,B)) = k3_binarith(A,B) ) ) ) )).
fof(t9_binari_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( r1_xxreal_0(A,k2_xcmplx_0(B,C)) => ( r1_xxreal_0(k5_numbers,B) | r1_xxreal_0(k5_numbers,C) | ( ~ r1_xxreal_0(B,A) & ~ r1_xxreal_0(C,A) ) ) ) ) ) ) )).
fof(t9_binarith,axiom,( ! [A] : ( v1_xboolean(A) => k4_xboolean(A,A) = A ) )).
fof(t9_binom,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_group_1(A) & v3_group_1(A) & v5_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v7_ordinal1(D) => k2_binom(A,k8_group_1(A,B,C),D) = k8_group_1(A,k2_binom(A,B,D),k2_binom(A,C,D)) ) ) ) ) )).
fof(t9_binop_1,axiom,( ! [A] : ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,A) => ( ( r1_binop_1(A,C,B) & r2_binop_1(A,D,B) ) => C = D ) ) ) ) )).
fof(t9_binop_2,axiom,( k4_binop_1(k4_numbers,k22_binop_2) = 1 )).
fof(t9_bintree1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v3_trees_2(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v3_trees_2(B) ) => ! [C] : ( ( v2_bintree1(A) & v2_bintree1(B) ) <=> v2_bintree1(k6_trees_4(C,A,B)) ) ) ) )).
fof(t9_bintree2,axiom,( ~ v1_xboole_0(k3_finseq_2(k7_domain_1(k4_ordinal1,k5_numbers,1))) & v1_trees_1(k3_finseq_2(k7_domain_1(k4_ordinal1,k5_numbers,1))) )).
fof(t9_boolealg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r3_lattices(A,B,k5_lattices(A)) => r1_boolealg(A,B,k5_lattices(A)) ) ) ) )).
fof(t9_bor_cant,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v5_relat_1(C,B) & v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [D] : ( v7_ordinal1(D) => k1_prob_2(A,B,k9_bor_cant(A,k2_prob_1(A,C)),D) = k3_subset_1(A,k1_prob_2(A,B,k7_bor_cant(A,C),D)) ) ) ) ) )).
fof(t9_borsuk_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( m2_connsp_2(E,A,C) => ! [F] : ( m2_connsp_2(F,B,D) => m2_connsp_2(k3_borsuk_1(A,B,E,F),k2_borsuk_1(A,B),k3_borsuk_1(A,B,C,D)) ) ) ) ) ) ) )).
fof(t9_borsuk_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v2_pre_topc(D) & l1_pre_topc(D) ) => ! [E] : ( ( 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] : ( ( 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] : ( 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)) ) ) ) ) ) ) ) ) )).
fof(t9_borsuk_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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))) => v3_tops_2(D,k2_borsuk_1(k1_pre_topc(A,k6_domain_1(u1_struct_0(A),C)),B),B) ) ) ) ) ) )).
fof(t9_borsuk_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( A != B => k5_measure6(k3_rcomp_1(A,B)) = k1_rcomp_1(A,B) ) ) ) )).
fof(t9_borsuk_5,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_topmetr))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t9_borsuk_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k5_topmetr)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k5_topmetr)) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_topmetr)) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_topmetr)) => ( ( r1_xxreal_0(A,B) & r1_xxreal_0(C,D) ) => ( ~ v1_xboole_0(k8_mcart_1(k1_numbers,k1_numbers,k1_rcomp_1(A,B),k1_rcomp_1(C,D))) & 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)))) ) ) ) ) ) ) )).
fof(t9_borsuk_7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( k17_sin_cos(A) = k17_sin_cos(B) & ! [C] : ( v1_int_1(C) => ( A != k2_xcmplx_0(B,k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)) & A != k2_xcmplx_0(k6_xcmplx_0(k28_sin_cos,B),k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),C)) ) ) ) ) ) )).
fof(t9_brouwer,axiom,( ! [A] : ( ( v1_xreal_0(A) & ~ v3_xxreal_0(A) ) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k2_brouwer(B,C,A))) => ! [E] : ( ( 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) | k4_brouwer(B,C,A,D,E) = D ) ) ) ) ) ) ) )).
fof(t9_bspace,axiom,( ! [A] : ! [B] : ( k3_bspace(A,B) = k5_struct_0(k2_bspace) <=> r2_hidden(B,A) ) )).
fof(t9_bvfunc10,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( 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] : ( ( v1_funct_1(F) & v1_funct_2(F,A,k6_margrel1) & m1_subset_1(F,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,k2_bvfunc_1(A,D,E),F)),k2_bvfunc_1(A,k2_bvfunc_1(A,k2_bvfunc_1(A,k2_bvfunc_1(A,k2_bvfunc_1(A,k5_bvfunc_1(A,B,D),k5_bvfunc_1(A,B,E)),k5_bvfunc_1(A,B,F)),k5_bvfunc_1(A,C,D)),k5_bvfunc_1(A,C,E)),k5_bvfunc_1(A,C,F))) ) ) ) ) ) ) )).
fof(t9_bvfunc11,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( 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),k7_bvfunc_2(A,k6_bvfunc_2(A,B,C,E),C,D)) ) ) ) ) ) ) )).
fof(t9_bvfunc14,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( m1_eqrel_1(C,A) => ! [D] : ( m1_eqrel_1(D,A) => ! [E] : ( m1_eqrel_1(E,A) => ! [F] : ( m1_eqrel_1(F,A) => ( B = k2_enumset1(C,D,E,F) => ( C = E | D = E | E = F | k5_bvfunc_2(A,E,B) = k2_partit1(A,k2_partit1(A,C,D),F) ) ) ) ) ) ) ) ) )).
fof(t9_bvfunc25,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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))) ) ) ) )).
fof(t9_bvfunc26,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)),k1_bvfunc_1(A,k2_bvfunc_1(A,k2_bvfunc_1(A,B,C),D))) ) ) ) ) )).
fof(t9_bvfunc_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) )).
fof(t9_bvfunc_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A))) => ! [C] : ( ( 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] : ( m1_eqrel_1(D,A) => r2_funct_2(A,k6_margrel1,k6_bvfunc_2(A,k11_bvfunc_1(A),B,D),k11_bvfunc_1(A)) ) ) ) ) )).
fof(t9_bvfunc_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A))) => ! [C] : ( ( 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] : ( ( 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] : ( 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,k6_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E))) ) ) ) ) ) )).
fof(t9_bvfunc_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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),k5_bvfunc_1(A,k2_bvfunc_1(A,k1_bvfunc_1(A,B),C),k2_bvfunc_1(A,B,k1_bvfunc_1(A,C)))) ) ) ) )).
fof(t9_bvfunc_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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,C,D),k12_bvfunc_1(A)) ) => r2_funct_2(A,k6_margrel1,k9_bvfunc_1(A,B,D),k12_bvfunc_1(A)) ) ) ) ) ) )).
fof(t9_bvfunc_6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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,D),k9_bvfunc_1(A,C,D)),k9_bvfunc_1(A,k5_bvfunc_1(A,B,C),D)),k12_bvfunc_1(A)) ) ) ) ) )).
fof(t9_bvfunc_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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)),k9_bvfunc_1(A,k2_bvfunc_1(A,B,k1_bvfunc_1(A,C)),D)) ) ) ) ) )).
fof(t9_bvfunc_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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,B,k2_bvfunc_1(A,k2_bvfunc_1(A,k2_bvfunc_1(A,k5_bvfunc_1(A,k5_bvfunc_1(A,B,C),D),k5_bvfunc_1(A,k5_bvfunc_1(A,B,C),k1_bvfunc_1(A,D))),k5_bvfunc_1(A,k5_bvfunc_1(A,B,k1_bvfunc_1(A,C)),D)),k5_bvfunc_1(A,k5_bvfunc_1(A,B,k1_bvfunc_1(A,C)),k1_bvfunc_1(A,D)))) ) ) ) ) )).
fof(t9_bvfunc_9,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k6_margrel1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_margrel1))) ) => ! [C] : ( ( 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] : ( ( 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),C)) ) ) ) ) )).
fof(t9_c0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v4_c0sp1(k6_c0sp1(A),k12_funcsdom(A)) & v3_c0sp1(k6_c0sp1(A),k12_funcsdom(A)) ) ) )).
fof(t9_c0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v1_compts_1(A) & l1_pre_topc(A) ) => m2_c0sp1(k3_c0sp2(A),k7_c0sp1(u1_struct_0(A))) ) )).
fof(t9_calcul_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ~ r1_xxreal_0(k3_finseq_1(k7_finseq_1(k7_finseq_1(C,k9_finseq_1(A)),k9_finseq_1(B))),1) ) )).
fof(t9_calcul_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => k1_relset_1(k4_ordinal1,k7_finseq_1(A,B)) = k4_subset_1(k4_ordinal1,k1_relset_1(k4_ordinal1,A),k2_calcul_2(k3_finseq_1(A),k3_finseq_1(B))) ) ) )).
fof(t9_cantor_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A))) => ( r1_tarski(B,C) => r1_tarski(k1_cantor_1(A,B),k1_cantor_1(A,C)) ) ) ) )).
fof(t9_card_1,axiom,( ! [A] : ! [B] : ( r1_ordinal1(k1_card_1(A),k1_card_1(B)) <=> ? [C] : ( v1_relat_1(C) & v1_funct_1(C) & v2_funct_1(C) & k9_xtuple_0(C) = A & r1_tarski(k10_xtuple_0(C),B) ) ) )).
fof(t9_card_2,axiom,( ! [A] : ( v1_card_1(A) => ! [B] : ( v1_card_1(B) => ! [C] : ! [D] : ( 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)))) ) ) ) ) )).
fof(t9_card_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(B,k4_card_3(A)) <=> ( k9_xtuple_0(B) = k9_xtuple_0(A) & ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => r2_hidden(k1_funct_1(B,C),k1_funct_1(A,C)) ) ) ) ) ) )).
fof(t9_card_5,axiom,( ! [A] : ( v3_ordinal1(A) => ? [B] : ( v1_card_1(B) & r1_ordinal1(B,k1_card_1(A)) & r2_ordinal2(A,B) & ! [C] : ( v3_ordinal1(C) => ( r2_ordinal2(A,C) => r1_ordinal1(B,C) ) ) ) ) )).
fof(t9_card_fil,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) ) => k7_setfam_1(A,B) = a_2_1_card_fil(A,B) ) ) )).
fof(t9_card_fin,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ( ~ r1_xxreal_0(B,k5_card_1(A)) => v1_xboole_0(k1_card_fin(A,B,C,D)) ) ) ) )).
fof(t9_cardfin2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ~ r1_xxreal_0(k7_xcmplx_0(1,2),k9_complex1(k6_xcmplx_0(k5_card_1(k2_cardfin2(A)),k7_xcmplx_0(k2_newton(k5_card_1(A)),k4_power)))) ) )).
fof(t9_cat_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k3_cat_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_cat_1(A,B))) => ! [E] : ( 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)) ) ) ) )).
fof(t9_cat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m3_cat_2(B,A) => m2_cat_1(k10_cat_1(B),B,A) ) ) )).
fof(t9_cat_3,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u4_struct_0(C)) => ! [E] : ( m1_subset_1(E,u4_struct_0(C)) => ( A != B => r2_funct_2(k2_tarski(A,B),u4_struct_0(k2_oppcat_1(C)),k4_cat_3(C,k2_tarski(A,B),k5_funct_4(u4_struct_0(C),A,B,D,E)),k5_funct_4(u4_struct_0(k2_oppcat_1(C)),A,B,k5_oppcat_1(C,D),k5_oppcat_1(C,E))) ) ) ) ) )).
fof(t9_cat_4,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,u1_struct_0(k5_cat_4(A,B))) => ! [D] : ( m1_subset_1(D,u4_struct_0(k5_cat_4(A,B))) => ! [E] : ( m1_subset_1(E,u4_struct_0(k5_cat_4(A,B))) => r2_cat_3(k5_cat_4(A,B),C,D,E) ) ) ) )).
fof(t9_cat_5,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m3_cat_2(C,B) => ! [D] : ( m2_cat_1(D,A,C) => ! [E] : ( m2_cat_1(E,A,B) => ( r1_funct_2(u4_struct_0(A),u4_struct_0(C),u4_struct_0(A),u4_struct_0(B),D,E) => k4_cat_5(A,C,D) = k4_cat_5(A,B,E) ) ) ) ) ) ) )).
fof(t9_catalan1,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,1) => k1_catalan1(A) = k6_xcmplx_0(k2_nat_1(4,k4_newton(k7_nat_d(A,1),k7_nat_d(k3_xcmplx_0(2,A),3))),k4_newton(k7_nat_d(A,1),k7_nat_d(k3_xcmplx_0(2,A),1))) ) ) )).
fof(t9_catalan2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k4_ordinal1) & v1_funct_1(B) & v5_ordinal1(B) & v1_finset_1(B) ) => ( ( v1_catalan2(B) & r1_xxreal_0(A,k6_xcmplx_0(k1_afinsq_1(B),k3_xcmplx_0(2,k7_afinsq_2(B)))) ) => v1_catalan2(k1_catalan2(B,k8_funcop_1(k4_ordinal1,A,1))) ) ) ) )).
fof(t9_catalg_1,axiom,( ! [A] : ( ( v3_catalg_1(A) & l1_msualg_1(A) ) => ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) ) => ( ( k3_finseq_1(D) = k3_finseq_1(C) & r1_tarski(k10_xtuple_0(D),k4_catalg_1(A)) ) => ( ( r2_hidden(k4_tarski(B,C),u1_struct_0(A)) => r2_hidden(k4_tarski(B,D),u1_struct_0(A)) ) & ( r2_hidden(k4_tarski(B,C),u4_struct_0(A)) => r2_hidden(k4_tarski(B,D),u4_struct_0(A)) ) ) ) ) ) ) )).
fof(t9_cayldick,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_cayldick(A) ) => ( ( v3_rlvect_1(A) & v4_rlvect_1(A) & v13_algstr_0(A) & v3_cayldick(A) & v4_normsp_0(A) & v6_rlvect_1(A) & v8_rlvect_1(A) & v5_rlvect_1(A) & v2_vectsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_algstr_0(A,k2_cayldick(A,B),B) = k1_rlvect_1(A,k5_struct_0(A),k1_square_1(k2_normsp_0(A,B))) ) ) ) )).
fof(t9_cayley,axiom,( k2_cayley(k1_xboole_0) = k7_algstr_0 )).
fof(t9_cc0sp1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k1_group_1(k3_cc0sp1(A)) = k8_funcop_1(k2_numbers,A,k6_complex1) ) )).
fof(t9_cc0sp2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => m1_cc0sp1(k3_cc0sp2(A),k8_cfuncdom(u1_struct_0(A))) ) )).
fof(t9_cfcont_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( 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,B)) => r2_relset_1(k4_ordinal1,k2_numbers,k31_valued_1(k4_ordinal1,k2_numbers,k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,A,B)),k8_funct_2(k4_ordinal1,k2_numbers,k2_numbers,A,k31_valued_1(k2_numbers,k2_numbers,B))) ) ) ) )).
fof(t9_cfdiff_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k2_numbers)) => ( v6_cfdiff_1(A) => ! [B] : ( v1_xcmplx_0(B) => ~ ( r2_hidden(B,A) & ! [C] : ( m1_cfdiff_1(C,B) => ~ r1_tarski(C,A) ) ) ) ) ) )).
fof(t9_cfuncdom,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k2_numbers,k9_funct_2(A,k2_numbers)) => r2_funct_2(A,k2_numbers,k1_funcsdom(A,k2_numbers,k2_cfuncdom(A),k5_cfuncdom(A),B),B) ) ) )).
fof(t9_cfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => k8_relset_1(A,k2_numbers,k2_cfunct_1(A,B),k1_tarski(k5_numbers)) = k1_xboole_0 ) ) )).
fof(t9_cgames_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v2_cgames_1(B) => ( r2_hidden(B,k2_cgames_1(A)) <=> ! [C] : ~ ( r2_hidden(C,k8_cgames_1(B)) & ! [D] : ( v3_ordinal1(D) => ~ ( r2_hidden(D,A) & r2_hidden(C,k2_cgames_1(D)) ) ) ) ) ) ) )).
fof(t9_chain_1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m1_chain_1(C,A) => ( r2_hidden(B,k4_card_3(C)) <=> ! [D] : ( m2_subset_1(D,k4_ordinal1,k2_finseq_1(A)) => r2_hidden(k1_funct_1(B,D),k2_chain_1(A,C,D)) ) ) ) ) ) )).
fof(t9_chord,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v1_abian(A) ) => ~ ( r1_xxreal_0(A,8) & A != 1 & A != 3 & A != 5 & A != 7 ) ) )).
fof(t9_circcmb2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_msafree2(B) & l1_msualg_1(B) ) => ! [C] : ( ( ~ 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] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ! [F] : ( ( 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] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(B,E))) => ! [H] : ( m1_subset_1(H,k4_card_3(u3_msualg_1(C,F))) => ( G = k5_relat_1(H,u1_struct_0(B)) => k6_circuit2(B,E,G) = k5_relat_1(k6_circuit2(C,F,H),u1_struct_0(B)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_circcmb3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ v2_struct_0(C) & ~ v11_struct_0(C) & v2_msafree2(C) & l1_msualg_1(C) ) => ( C = k2_circcomb(A,B) => ! [D] : ( ( v4_msualg_1(D,A) & v4_msafree2(D,A) & l3_msualg_1(D,A) ) => ! [E] : ( ( v4_msualg_1(E,B) & v4_msafree2(E,B) & l3_msualg_1(E,B) ) => ( r2_circcomb(A,B,D,E) => ! [F] : ( ( v4_msualg_1(F,C) & v4_msafree2(F,C) & l3_msualg_1(F,C) ) => ( F = k3_circcomb(A,B,D,E) => ! [G] : ( m1_subset_1(G,k4_card_3(u3_msualg_1(C,F))) => ! [H] : ( 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] : ( 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) ) => v1_circcmb3(G,C,F) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_circcomb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_msualg_1(B) ) => ~ ( ~ ( v11_struct_0(A) & v11_struct_0(B) ) & v11_struct_0(k2_circcomb(A,B)) ) ) ) )).
fof(t9_circled1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(B,C) => r1_tarski(k1_circled1(A,C),k1_circled1(A,B)) ) ) ) ) )).
fof(t9_circtrm1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v3_trees_3(B) ) => ( ( ! [C] : ( m1_subset_1(C,A) => v1_finset_1(C) ) & ! [C] : ( m1_subset_1(C,B) => v1_finset_1(C) ) ) => ! [C] : k13_trees_9(k2_xboole_0(A,B),C) = k1_funct_4(k13_trees_9(A,C),k13_trees_9(B,C)) ) ) ) )).
fof(t9_circuit1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_funct_1(u3_msualg_1(A,k5_msafree2(A,B)),C)) => ~ ( k1_funct_1(D,k1_xboole_0) = k4_tarski(k4_msafree2(A,C),u1_struct_0(A)) & ! [E] : ( ( 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) ) ) ) ) ) ) )).
fof(t9_circuit2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_msafree2(A) & v5_msafree2(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v4_msafree2(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_msafree2(D,A,B) => ! [E] : ( ( v1_relat_1(E) & v1_funct_1(E) & v1_finseq_1(E) & v6_trees_3(E) ) => ( ( r2_hidden(C,k3_msafree2(A)) & k4_finseq_1(E) = k4_finseq_1(k1_msualg_1(A,k4_msafree2(A,C))) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r2_hidden(F,k4_finseq_1(E)) => k1_funct_1(E,F) = k4_circuit2(A,B,k7_partfun1(u1_struct_0(A),k1_msualg_1(A,k4_msafree2(A,C)),F),D) ) ) ) => k4_circuit2(A,B,C,D) = k4_trees_4(k4_tarski(k4_msafree2(A,C),u1_struct_0(A)),E) ) ) ) ) ) ) )).
fof(t9_ckspace1,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_euclid(A))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ! [F] : ( ( ~ v1_xboole_0(F) & m2_finseq_1(F,k4_ordinal1) ) => ( ( r1_ckspace1(A,C,k1_nat_1(D,E),B) & r1_tarski(k2_relset_1(k4_ordinal1,F),k2_finseq_1(A)) & k3_finseq_1(F) = E ) => r1_ckspace1(A,k5_pdiff_9(A,B,F,C),D,B) ) ) ) ) ) ) ) )).
fof(t9_classes1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => ( v4_ordinal1(B) => ( B = k1_xboole_0 | k3_classes1(A,B) = a_2_2_classes1(A,B) ) ) ) )).
fof(t9_classes2,axiom,( ! [A] : ( v2_classes1(A) => k2_ordinal1(A) = k1_card_1(A) ) )).
fof(t9_clopban1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m2_funct_2(C,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( v1_xcmplx_0(E) => k1_binop_1(k2_lopban_1(A,B),k1_funct_1(k2_clopban1(A,B),k4_tarski(D,C)),k1_funct_1(k2_clopban1(A,B),k4_tarski(E,C))) = k1_funct_1(k2_clopban1(A,B),k4_tarski(k2_xcmplx_0(D,E),C)) ) ) ) ) ) )).
fof(t9_clopban2,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(k6_clopban1(A,A)),k8_clopban1(A,A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(k6_clopban1(A,A)),k8_clopban1(A,A)) => ! [D] : ( m2_subset_1(D,u1_struct_0(k6_clopban1(A,A)),k8_clopban1(A,A)) => k3_clopban2(A,k2_clopban2(A,C,D),B) = k2_clopban2(A,k3_clopban2(A,C,B),k3_clopban2(A,D,B)) ) ) ) ) )).
fof(t9_clopban3,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( v9_clvect_1(B,A) => ( v9_clvect_1(k1_valued_0(u1_struct_0(A),B,D),A) & k7_clvect_1(A,k1_valued_0(u1_struct_0(A),B,D)) = k7_clvect_1(A,B) ) ) ) ) ) ) )).
fof(t9_clopban4,axiom,( ! [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) & 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r2_funct_2(k4_ordinal1,u1_struct_0(A),k1_bhsp_4(A,k2_clopban3(A,C,B)),k2_clopban3(A,k1_bhsp_4(A,C),B)) & r2_funct_2(k4_ordinal1,u1_struct_0(A),k1_bhsp_4(A,k3_clopban3(A,C,B)),k3_clopban3(A,k1_bhsp_4(A,C),B)) ) ) ) ) )).
fof(t9_closure1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_pboole(C,A,B) => ! [D] : ( m1_pboole(D,A,B) => ( r2_pboole(A,C,D) => r2_pboole(A,k1_closure1(A,B,B,k2_msualg_3(A,B),C),k1_closure1(A,B,B,k2_msualg_3(A,B),D)) ) ) ) ) )).
fof(t9_closure2,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_closure2(C,A,B,k2_closure2(A,B)) => ! [D] : ( m1_closure2(D,A,B,k2_closure2(A,B)) => r2_hidden(k3_pboole(A,C,D),k2_closure2(A,B)) ) ) ) )).
fof(t9_closure3,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_closure2(A,B))) => ! [D] : ( 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))) ) ) ) )).
fof(t9_clvect_1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( v1_xcmplx_0(D) => k1_clvect_1(A,k5_algstr_0(A,C,B),D) = k5_algstr_0(A,k1_clvect_1(A,C,D),k1_clvect_1(A,B,D)) ) ) ) ) )).
fof(t9_clvect_2,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clvect_2(B,A) <=> ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ! [E] : ( v7_ordinal1(E) => ? [F] : ( v7_ordinal1(F) & r1_xxreal_0(E,F) & r1_xxreal_0(D,k13_csspace(A,k5_algstr_0(A,k1_normsp_1(A,B,F),C))) ) ) ) ) ) ) ) ) )).
fof(t9_clvect_3,axiom,( ! [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) & v2_csspace(A) & l1_csspace(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( v1_clvect_3(B,A) => ( v1_clvect_2(B,A) & k1_clvect_2(A,B) = k4_struct_0(A) ) ) ) ) )).
fof(t9_coh_sp,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes1(A) & v1_coh_sp(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_classes1(B) & v1_coh_sp(B) ) => ( k1_coh_sp(A) = k1_coh_sp(B) => A = B ) ) ) )).
fof(t9_cohsp_1,axiom,( ! [A] : ( v1_cohsp_1(k1_tarski(A)) & v2_cohsp_1(k1_tarski(A)) ) )).
fof(t9_collsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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) ) => ( D = E | r1_collsp(A,B,C,F) ) ) ) ) ) ) ) ) )).
fof(t9_combgras,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( l1_incsp_1(B) => ( g1_incsp_1(u1_incsp_1(A),u2_incsp_1(A),u3_incsp_1(A)) = g1_incsp_1(u1_incsp_1(B),u2_incsp_1(B),u3_incsp_1(B)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_incsp_1(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_incsp_1(B))) => ( C = D => ! [E] : ( m1_subset_1(E,u2_incsp_1(A)) => ! [F] : ( m1_subset_1(F,u2_incsp_1(B)) => ( ( E = F & r4_incsp_1(A,C,E) ) => r4_incsp_1(B,D,F) ) ) ) ) ) ) ) ) ) )).
fof(t9_complex1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ( k3_complex1(k3_xcmplx_0(A,B)) = k5_real_1(k4_real_1(k3_complex1(A),k3_complex1(B)),k4_real_1(k4_complex1(A),k4_complex1(B))) & k4_complex1(k3_xcmplx_0(A,B)) = k3_real_1(k4_real_1(k3_complex1(A),k4_complex1(B)),k4_real_1(k3_complex1(B),k4_complex1(A))) ) ) ) )).
fof(t9_complex2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_int_1(B) => k19_sin_cos(A) = k19_sin_cos(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B),A)) ) ) )).
fof(t9_complfld,axiom,( k3_rlvect_1(k1_complfld,k1_group_1(k1_complfld),k1_group_1(k1_complfld)) != k4_struct_0(k1_complfld) )).
fof(t9_complsp2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_1(B,k2_numbers) => k9_matrix_5(k9_seq_4(B),A) = k4_xcmplx_0(k9_matrix_5(B,A)) ) ) )).
fof(t9_compos_0,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_compos_0(A) ) => ! [B] : ( m1_subset_1(B,k1_compos_0(A)) => ? [C] : ( m1_subset_1(C,A) & k2_compos_0(A,C) = B ) ) ) )).
fof(t9_compos_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( l1_compos_1(C) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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)) ) ) ) ) )).
fof(t9_compos_2,axiom,( ! [A] : ( ( v1_amistd_4(A) & l1_compos_1(A) ) => ! [B] : ( ( v6_compos_0(B,u1_compos_1(A)) & m1_subset_1(B,u1_compos_1(A)) ) => ! [C] : ( ( v6_compos_0(C,u1_compos_1(A)) & m1_subset_1(C,u1_compos_1(A)) ) => k3_compos_2(A,B,C) = k1_compos_2(A,B,k11_compos_1(A,C)) ) ) ) )).
fof(t9_comptrig,axiom,( ! [A] : ( v1_xreal_0(A) => ~ ( r2_hidden(A,k2_rcomp_1(k28_sin_cos,k3_xcmplx_0(2,k28_sin_cos))) & r1_xxreal_0(k5_numbers,k1_funct_1(k16_sin_cos,A)) ) ) )).
fof(t9_compts_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v2_compts_1(B,A) & r1_tarski(C,B) & v4_pre_topc(C,A) ) => v2_compts_1(C,A) ) ) ) ) )).
fof(t9_comput_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ~ v1_xboole_0(C) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(A,k1_nat_1(B,1)) ) => ! [D] : ( m2_finseq_2(D,C,k4_finseq_2(k1_nat_1(B,1),C)) => r2_hidden(k2_finseq_3(A,D),k4_finseq_2(B,C)) ) ) ) ) ) )).
fof(t9_comseq_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k2_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k2_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => r2_relset_1(k4_ordinal1,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,B),C),k2_valued_1(k4_ordinal1,k2_numbers,k2_numbers,k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,A,C),k19_valued_1(k4_ordinal1,k2_numbers,k2_numbers,B,C))) ) ) ) )).
fof(t9_comseq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( ? [B] : ( v1_xcmplx_0(B) & ! [C] : ( v7_ordinal1(C) => k9_nat_1(k2_numbers,A,C) = B ) ) => v2_comseq_2(A) ) ) )).
fof(t9_comseq_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [B] : ( v7_ordinal1(B) => r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,A,B)) ) => ( ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(B,C) => k9_complex1(k5_real_1(k9_nat_1(k1_numbers,k3_series_1(A),C),k9_nat_1(k1_numbers,k3_series_1(A),B))) = k5_real_1(k9_nat_1(k1_numbers,k3_series_1(A),C),k9_nat_1(k1_numbers,k3_series_1(A),B)) ) ) ) & ! [B] : ( v7_ordinal1(B) => k9_complex1(k9_nat_1(k1_numbers,k3_series_1(A),B)) = k9_nat_1(k1_numbers,k3_series_1(A),B) ) ) ) ) )).
fof(t9_conlat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_conlat_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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_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)) ) ) ) ) )).
fof(t9_conmetr1,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v13_aff_2(A) <=> v5_conmetr1(A) ) ) )).
fof(t9_connsp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( ( v4_pre_topc(B,A) & v4_pre_topc(C,A) ) | ( v3_pre_topc(B,A) & v3_pre_topc(C,A) ) ) => r1_connsp_1(A,k7_subset_1(u1_struct_0(A),B,C),k7_subset_1(u1_struct_0(A),C,B)) ) ) ) ) )).
fof(t9_connsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_pre_topc(A,B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k1_pre_topc(A,B)))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A))) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( ( v3_pre_topc(B,A) & m1_connsp_2(D,k1_pre_topc(A,B),C) & D = E & C = F ) => m1_connsp_2(E,A,F) ) ) ) ) ) ) ) )).
fof(t9_connsp_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_connsp_1(B,A) => ( B = k1_xboole_0 | v3_connsp_1(k1_connsp_3(A,B),A) ) ) ) ) )).
fof(t9_convex1,axiom,( ! [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) ) => v1_convex1(k3_rusub_4(A,k2_rlsub_1(A)),A) ) )).
fof(t9_convex2,axiom,( ! [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) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( v2_convex1(C,A) & m2_rlvect_2(C,A,B) ) => ! [D] : ( ( v2_convex1(D,A) & m2_rlvect_2(D,A,B) ) => ! [E] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ~ r1_xxreal_0(1,E) & ~ ( v2_convex1(k7_rlvect_2(A,k8_rlvect_2(A,E,C),k8_rlvect_2(A,k6_xcmplx_0(1,E),D)),A) & m2_rlvect_2(k7_rlvect_2(A,k8_rlvect_2(A,E,C),k8_rlvect_2(A,k6_xcmplx_0(1,E),D)),A,B) ) ) ) ) ) ) ) )).
fof(t9_convex3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_convex3(B,A) & v1_convex3(C,A) ) => v1_convex3(k9_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) )).
fof(t9_convex4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_clvect_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( 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))) ) => k3_convex4(A,k2_finseq_4(u1_struct_0(A),B,C),D) = k2_finseq_4(u1_struct_0(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))) ) ) ) ) )).
fof(t9_cqc_lang,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ( m2_subset_1(k14_qc_lang1(A,B,C),k9_qc_lang1(A),k3_cqc_lang(A)) <=> ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) & m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) ) ) ) ) ) )).
fof(t9_cqc_sim1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => k10_xtuple_0(A) = a_1_0_cqc_sim1(A) ) )).
fof(t9_cqc_the1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [E] : ( 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)) ) ) ) ) ) ) ) )).
fof(t9_cqc_the2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => ! [D] : ( m2_subset_1(D,k2_qc_lang1(A),k3_qc_lang1(A)) => ( r2_hidden(D,k24_qc_lang1(A,k3_qc_lang2(A,B,C))) <=> ( r2_hidden(D,k24_qc_lang1(A,B)) | r2_hidden(D,k24_qc_lang1(A,C)) ) ) ) ) ) ) )).
fof(t9_cqc_the3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k3_cqc_lang(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k3_cqc_lang(A))) => ( ( r2_cqc_the3(A,B,C) & r2_cqc_the3(A,C,D) ) => r2_cqc_the3(A,B,D) ) ) ) ) ) )).
fof(t9_csspace,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( m1_subset_1(C,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),C,k3_xcmplx_0(A,B)) = k1_clvect_1(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),C,B),A) ) ) ) )).
fof(t9_csspace2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k2_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k2_numbers))) ) => ( v2_comseq_3(A) => r1_xxreal_0(k9_complex1(k11_comseq_3(A)),k4_series_1(k55_valued_1(k4_ordinal1,k2_numbers,A))) ) ) )).
fof(t9_csspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(k5_csspace4(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_csspace4(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k5_csspace4(A,B))) => ! [F] : ( ( 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] : ( ( 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] : ( ( 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 = k3_rlvect_1(k5_csspace4(A,B),C,D) <=> ! [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)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_decomp_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => k9_subset_1(k1_zfmisc_1(u1_struct_0(A)),k8_decomp_1(A),k12_decomp_1(A)) = u1_pre_topc(A) ) )).
fof(t9_descip_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v8_ordinal1(B) & m1_subset_1(B,k4_ordinal1) ) => ! [C] : ( m2_finseq_2(C,A,k4_finseq_2(B,A)) => m2_finseq_2(k7_descip_1(C),A,k4_finseq_2(B,A)) ) ) ) )).
fof(t9_dickson,axiom,( ! [A] : ( l1_orders_2(A) => ( v3_dickson(A) => r2_orders_1(k2_dickson(A),k8_eqrel_1(u1_struct_0(A),k1_dickson(A))) ) ) )).
fof(t9_diff_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( ( 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] : ( ( 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_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(k47_valued_1(k1_numbers,k1_numbers,k1_numbers,D,E),B),k1_nat_1(A,1)),C) = k6_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(D,B),k1_nat_1(A,1)),C),k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k6_diff_1(E,B),k1_nat_1(A,1)),C)) ) ) ) ) ) )).
fof(t9_diff_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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))) ) => k11_diff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,E,F),A,B,C,D) = k2_xcmplx_0(k11_diff_1(E,A,B,C,D),k11_diff_1(F,A,B,C,D)) ) ) ) ) ) ) )).
fof(t9_diff_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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] : ( ( 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_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,E,k26_valued_1(k1_numbers,k1_numbers,F,C)),B),k2_xcmplx_0(A,1)),D) = k2_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(E,B),k2_xcmplx_0(A,1)),D),k3_xcmplx_0(C,k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k7_diff_1(F,B),k2_xcmplx_0(A,1)),D))) ) ) ) ) ) ) )).
fof(t9_diff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r2_hidden(k2_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k27_sin_cos)) & r2_hidden(k6_xcmplx_0(B,k7_xcmplx_0(A,2)),k1_relset_1(k1_numbers,k27_sin_cos)) ) => k1_funct_1(k5_diff_1(k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k27_sin_cos,k27_sin_cos),A),B) = k7_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(1,2),k6_xcmplx_0(k19_sin_cos(k2_xcmplx_0(A,k3_xcmplx_0(2,B))),k19_sin_cos(k6_xcmplx_0(A,k3_xcmplx_0(2,B))))),k1_square_1(k3_xcmplx_0(k17_sin_cos(k2_xcmplx_0(B,k7_xcmplx_0(A,2))),k17_sin_cos(k6_xcmplx_0(B,k7_xcmplx_0(A,2)))))) ) ) ) )).
fof(t9_dilworth,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( v1_dilworth(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(B)) => ( v1_dilworth(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) )).
fof(t9_diraf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( r1_diraf(A,B,C,D) => r1_diraf(A,D,C,B) ) ) ) ) ) )).
fof(t9_dirort,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dirort(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r2_dirort(A,B,C,D,E) => r2_dirort(A,C,B,E,D) ) ) ) ) ) ) )).
fof(t9_dist_1,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ( r2_hidden(C,k5_dist_1(A,B)) => k4_dist_1(A,B) = k4_dist_1(A,C) ) ) ) ) )).
fof(t9_dist_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_setfam_1(B) & m2_subset_1(B,k1_zfmisc_1(k3_finseq_2(A)),k6_dist_1(A)) ) => ! [C] : ( m1_dist_2(C,A,B) => ! [D] : ( ( 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] : ( ( ~ v1_xboole_0(E) & v1_finset_1(E) ) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(E)) => ( ( E = k4_finseq_1(C) & F = k3_dist_2(k1_partfun1(k4_ordinal1,A,A,k6_margrel1,C,D)) ) => k4_dist_2(A,B,C,D) = k1_rpr_1(E,F) ) ) ) ) ) ) ) )).
fof(t9_domain_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m1_subset_1(D,k3_zfmisc_1(A,B,C)) => ! [E] : ( m1_subset_1(E,k3_zfmisc_1(A,B,C)) => ( ( k1_mcart_1(A,B,C,D) = k1_mcart_1(A,B,C,E) & k2_mcart_1(A,B,C,D) = k2_mcart_1(A,B,C,E) & k3_mcart_1(A,B,C,D) = k3_mcart_1(A,B,C,E) ) => D = E ) ) ) ) ) ) )).
fof(t9_dtconstr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_dtconstr(A) & l1_lang1(A) ) => ! [B] : ( m1_dtconstr(B,u1_struct_0(A),k5_trees_3(u1_struct_0(A)),k4_dtconstr(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k6_dtconstr(A)) => ( k1_funct_1(B,k1_xboole_0) = C => B = k8_dtconstr(A,C) ) ) ) ) )).
fof(t9_dynkin,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ( v1_prob_2(B) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => v1_prob_2(k2_dynkin(A,B,C)) ) ) ) ) )).
fof(t9_e_siec,axiom,( ! [A] : ( u1_struct_0(k5_e_siec(A)) = k1_tarski(A) & u1_e_siec(k5_e_siec(A)) = k1_xboole_0 & u2_e_siec(k5_e_siec(A)) = k1_xboole_0 ) )).
fof(t9_ec_pf_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v36_algstr_0(B) & m1_ec_pf_1(B,A) ) => ! [C] : ( ( v36_algstr_0(C) & m1_ec_pf_1(C,A) ) => ( B = C <=> ! [D] : ( r1_struct_0(B,D) <=> r1_struct_0(C,D) ) ) ) ) ) )).
fof(t9_ec_pf_2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => k3_rlvect_1(A,k3_rlvect_1(A,k3_rlvect_1(A,k3_rlvect_1(A,k3_rlvect_1(A,B,C),D),E),F),G) = k3_rlvect_1(A,B,k3_rlvect_1(A,k3_rlvect_1(A,k3_rlvect_1(A,k3_rlvect_1(A,C,D),E),F),G)) ) ) ) ) ) ) ) )).
fof(t9_endalg,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( 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] : ( m2_funct_2(C,u1_struct_0(A),u1_struct_0(A),k1_endalg(A)) => ( B = k16_funcop_1(k5_numbers,C) => r2_hidden(B,k4_endalg(k6_msualg_1(A),k9_msualg_1(A))) ) ) ) ) )).
fof(t9_ens_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k2_ens_1(A)) => ( ~ ( k4_ens_1(A,B) = k1_xboole_0 & k3_ens_1(A,B) != k1_xboole_0 ) & v1_funct_1(k2_xtuple_0(B)) & v1_funct_2(k2_xtuple_0(B),k3_ens_1(A,B),k4_ens_1(A,B)) & m1_subset_1(k2_xtuple_0(B),k1_zfmisc_1(k2_zfmisc_1(k3_ens_1(A,B),k4_ens_1(A,B)))) ) ) ) )).
fof(t9_enumset1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : k3_enumset1(A,B,C,D,E) = k2_xboole_0(k1_enumset1(A,B,C),k2_tarski(D,E)) )).
fof(t9_eqrel_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,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_relat_2(B) & v3_relat_2(B) & v8_relat_2(B) & k1_relat_1(B) = A ) ) ) )).
fof(t9_equation,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,C) => ( v2_msualg_3(D,A,B,C) => r6_pboole(A,k9_pboole(A,B,D),C) ) ) ) ) )).
fof(t9_euclid,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => r1_xxreal_0(k12_euclid(k7_euclid(A,B,C)),k2_xcmplx_0(k12_euclid(B),k12_euclid(C))) ) ) ) )).
fof(t9_euclid_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => k22_rvsum_1(k5_euclid(k3_finseq_1(A)),A) = k5_numbers ) )).
fof(t9_euclid_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => k2_euclid_3(k3_rlvect_1(k15_euclid(2),A,B)) = k2_xcmplx_0(k2_euclid_3(A),k2_euclid_3(B)) ) ) )).
fof(t9_euclid_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ( r2_hidden(B,k2_euclid_4(A,B,C)) & r2_hidden(C,k2_euclid_4(A,B,C)) ) ) ) ) )).
fof(t9_euclid_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(3))) => ( k1_euclid_5(k1_rlvect_1(k15_euclid(3),B,A)) = k3_xcmplx_0(A,k1_euclid_5(B)) & k2_euclid_5(k1_rlvect_1(k15_euclid(3),B,A)) = k3_xcmplx_0(A,k2_euclid_5(B)) & k3_euclid_5(k1_rlvect_1(k15_euclid(3),B,A)) = k3_xcmplx_0(A,k3_euclid_5(B)) ) ) ) )).
fof(t9_euclid_6,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( r2_hidden(D,k1_rltopsp1(k15_euclid(2),B,C)) => ( D = B | k4_euclid_3(C,B,A) = k4_euclid_3(D,B,A) ) ) ) ) ) ) )).
fof(t9_euclid_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t9_euclid_8,axiom,( r1_rvsum_1(k3_euclid_8,k4_euclid_8) )).
fof(t9_euclid_9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k15_euclid(A))) => ( r2_hidden(C,k1_topreal9(A,D,B)) => ! [F] : ( ~ r1_xxreal_0(B,k9_complex1(k1_funct_1(k5_algstr_0(k15_euclid(A),C,D),F))) & ~ r1_xxreal_0(B,k9_complex1(k6_xcmplx_0(k1_funct_1(C,F),k1_funct_1(D,F)))) ) ) ) ) ) ) ) )).
fof(t9_euclidlp,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ( B = C <=> k8_euclid(A,B,C) = k5_euclid(A) ) ) ) ) )).
fof(t9_euclmetr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_analmetr(A) & l1_analmetr(A) ) => ( v7_euclmetr(A) <=> v4_conaffm(A) ) ) )).
fof(t9_euler_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( r1_int_2(A,B) & ! [C] : ( v7_ordinal1(C) => ~ ( ? [D] : ( v1_int_1(D) & ? [E] : ( v1_int_1(E) & C = k2_xcmplx_0(k3_xcmplx_0(D,A),k3_xcmplx_0(E,B)) & ~ r1_xxreal_0(C,k5_numbers) ) ) & ! [D] : ( v7_ordinal1(D) => ( ? [E] : ( v1_int_1(E) & ? [F] : ( v1_int_1(F) & D = k2_xcmplx_0(k3_xcmplx_0(E,A),k3_xcmplx_0(F,B)) & ~ r1_xxreal_0(D,k5_numbers) ) ) => r1_xxreal_0(C,D) ) ) ) ) ) ) ) )).
fof(t9_euler_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => k4_nat_d(k3_xcmplx_0(C,A),B) = k4_nat_d(k2_nat_1(k4_nat_d(C,B),k4_nat_d(A,B)),B) ) ) ) )).
fof(t9_exchsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v1_exchsort(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ! [D] : ( v3_ordinal1(D) => ( ( r1_ordinal1(B,C) & r1_ordinal1(C,D) & r2_hidden(B,k9_xtuple_0(A)) & r2_hidden(D,k9_xtuple_0(A)) ) => r2_hidden(C,k9_xtuple_0(A)) ) ) ) ) ) ) )).
fof(t9_extens_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,C) => ( v2_msualg_3(D,A,B,C) <=> r6_pboole(A,k2_funct_6(D),C) ) ) ) ) )).
fof(t9_extpro_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & ~ v1_setfam_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_extpro_1(B,A) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m1_subset_1(D,u1_compos_1(B)) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(B)) & v1_funct_1(E) ) => ( r1_tarski(k16_funcop_1(C,D),E) => ! [F] : ( ( 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(k16_funcop_1(k4_struct_0(B),C),F) => k3_extpro_1(A,B,E,F) = D ) ) ) ) ) ) ) ) )).
fof(t9_extreal2,axiom,( ! [A] : ( v1_xxreal_0(A) => ( r1_xxreal_0(k2_supinf_2(k3_extreal1(A)),A) & r1_xxreal_0(A,k3_extreal1(A)) ) ) )).
fof(t9_facirc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_circcomb(A) & v2_circcomb(A) & l1_msualg_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_circcomb(B) & v2_circcomb(B) & l1_msualg_1(B) ) => ~ ( ~ v1_facirc_1(k2_msafree2(A)) & ~ v1_facirc_1(k2_msafree2(B)) & v1_facirc_1(k2_msafree2(k2_circcomb(A,B))) ) ) ) )).
fof(t9_facirc_2,axiom,( ! [A] : ! [B] : ! [C] : ( C = k4_tarski(k1_xboole_0,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1)) => ( k3_facirc_2(1,k9_finseq_1(A),k9_finseq_1(B)) = k2_circcomb(k5_circcomb(k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1),k1_xboole_0),k19_facirc_1(A,B,C)) & k4_facirc_2(1,k9_finseq_1(A),k9_finseq_1(B)) = k3_circcomb(k5_circcomb(k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1),k1_xboole_0),k19_facirc_1(A,B,C),k7_circcomb(k5_ordinal1,k6_margrel1,k1_margrel1(k6_margrel1,k4_finseq_2(k5_numbers,k6_margrel1),k7_margrel1),k1_xboole_0),k20_facirc_1(A,B,C)) & k5_facirc_2(1,k9_finseq_1(A),k9_finseq_1(B)) = k17_facirc_1(A,B,C) ) ) )).
fof(t9_fcont_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( r2_hidden(A,k1_relset_1(k1_numbers,B)) & r1_fcont_1(B,A) ) => ( r1_fcont_1(k56_valued_1(k1_numbers,k1_numbers,B),A) & r1_fcont_1(k32_valued_1(k1_numbers,k1_numbers,B),A) ) ) ) ) )).
fof(t9_fcont_2,axiom,( ! [A] : ! [B] : ( ( 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_2(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) => v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,B,A)) ) ) )).
fof(t9_fcont_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v2_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)) => v5_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))) ) ) )).
fof(t9_fdiff_1,axiom,( ! [A] : ( ( v3_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r2_fdiff_1(B,A) <=> ( r1_tarski(A,k1_relset_1(k1_numbers,B)) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => r1_fdiff_1(B,C) ) ) ) ) ) ) )).
fof(t9_fdiff_10,axiom,( ! [A] : ( ( 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,k16_sin_cos,k18_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),A),B) = k4_xcmplx_0(k3_xcmplx_0(k1_funct_1(k16_sin_cos,k1_funct_1(k16_sin_cos,B)),k1_funct_1(k18_sin_cos,B))) ) ) ) ) )).
fof(t9_fdiff_11,axiom,( ! [A] : ( ( 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_sin_cos9))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => ( ~ r1_xxreal_0(k1_funct_1(k1_sin_cos9,B),k4_xcmplx_0(1)) & ~ r1_xxreal_0(1,k1_funct_1(k1_sin_cos9,B)) ) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k1_sin_cos9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos9,k1_sin_cos9),A),B) = k7_xcmplx_0(1,k3_xcmplx_0(k2_xcmplx_0(1,k1_square_1(B)),k2_xcmplx_0(1,k1_square_1(k1_funct_1(k1_sin_cos9,B))))) ) ) ) ) ) )).
fof(t9_fdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,C))) => ( r1_tarski(k2_relset_1(k1_numbers,A),k1_relset_1(k1_numbers,B)) & r1_tarski(k2_relset_1(k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,A,B)),k1_relset_1(k1_numbers,C)) ) ) ) ) ) )).
fof(t9_fdiff_3,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( ( ( r4_fdiff_3(A,B) & k1_fdiff_3(B,A) = C ) => ( ? [D] : ( v1_xreal_0(D) & ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k1_rcomp_1(k6_xcmplx_0(B,D),B),k1_relset_1(k1_numbers,A)) ) & ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v9_ordinal1(D) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k10_xtuple_0(E) = k1_tarski(B) & r1_tarski(k10_xtuple_0(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),k1_relset_1(k1_numbers,A)) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ r1_xxreal_0(k5_numbers,k3_funct_2(k4_ordinal1,k1_numbers,D,F)) ) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),A),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,A)))) & k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),A),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,A)))) = C ) ) ) ) ) ) & ( ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k1_numbers) & v9_ordinal1(D) & v1_fdiff_1(D,k5_numbers) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [E] : ( ( v1_funct_1(E) & v3_funct_1(E) & v1_funct_2(E,k4_ordinal1,k1_numbers) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( k10_xtuple_0(E) = k1_tarski(B) & r1_tarski(k10_xtuple_0(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E)),k1_relset_1(k1_numbers,A)) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ~ r1_xxreal_0(k5_numbers,k3_funct_2(k4_ordinal1,k1_numbers,D,F)) ) ) => ( v2_comseq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),A),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,A)))) & k1_seq_2(k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k37_valued_1(k4_ordinal1,k1_numbers,D),k47_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,D,E),A),k8_funct_2(k4_ordinal1,k1_numbers,k1_numbers,E,A)))) = C ) ) ) ) => ( ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & r1_tarski(k1_rcomp_1(k6_xcmplx_0(B,D),B),k1_relset_1(k1_numbers,A)) ) ) | ( r4_fdiff_3(A,B) & k1_fdiff_3(B,A) = C ) ) ) ) ) ) ) )).
fof(t9_fdiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v3_rcomp_1(C) & m1_subset_1(C,k1_zfmisc_1(k1_numbers)) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [E] : ( ( 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,k2_xcmplx_0(A,B))))) & D = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,E,k3_taylor_1) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,C) => ( k1_funct_1(E,F) = k6_xcmplx_0(F,B) & ~ r1_xxreal_0(k1_funct_1(E,F),k5_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,k2_xcmplx_0(A,B))),C) & ! [F] : ( v1_xreal_0(F) => ( r2_hidden(F,C) => k1_funct_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,k2_xcmplx_0(A,B))),C),F) = k7_xcmplx_0(k2_xcmplx_0(F,A),k6_xcmplx_0(F,B)) ) ) ) ) ) ) ) ) ) )).
fof(t9_fdiff_6,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( ( r1_tarski(B,k9_xtuple_0(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_taylor_1(A),k3_taylor_1))) & ! [C] : ( v1_xreal_0(C) => ~ ( r2_hidden(C,B) & r1_xxreal_0(C,k5_numbers) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_taylor_1(A),k3_taylor_1),B) & ! [C] : ( v1_xreal_0(C) => ( r2_hidden(C,B) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_taylor_1(A),k3_taylor_1),B),C) = k7_xcmplx_0(A,C) ) ) ) ) ) ) )).
fof(t9_fdiff_7,axiom,( ! [A] : ( ( 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_sin_cos6,k3_taylor_1))) & r1_tarski(A,k2_rcomp_1(k4_xcmplx_0(1),1)) & ! [B] : ( v1_xreal_0(B) => ~ ( r2_hidden(B,A) & r1_xxreal_0(k1_funct_1(k3_sin_cos6,B),k5_numbers) ) ) ) => ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_sin_cos6,k3_taylor_1),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k3_sin_cos6,k3_taylor_1),A),B) = k4_xcmplx_0(k7_xcmplx_0(1,k3_xcmplx_0(k3_square_1(k6_xcmplx_0(1,k1_square_1(B))),k1_funct_1(k3_sin_cos6,B)))) ) ) ) ) ) )).
fof(t9_fdiff_8,axiom,( ! [A] : ( ( 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)),k27_sin_cos))) => ( r2_hidden(k5_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)),k27_sin_cos),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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)),k27_sin_cos),A),B) = k7_xcmplx_0(1,k3_xcmplx_0(k1_square_1(B),k1_square_1(k1_funct_1(k16_sin_cos,k7_xcmplx_0(1,B))))) ) ) ) ) ) ) )).
fof(t9_fdiff_9,axiom,( ! [A] : ( ( 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_fdiff_9))) => ( r2_hidden(k5_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_fdiff_9),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_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_fdiff_9),A),B) = k7_xcmplx_0(k1_funct_1(k18_sin_cos,k7_xcmplx_0(1,B)),k3_xcmplx_0(k1_square_1(B),k1_square_1(k1_funct_1(k16_sin_cos,k7_xcmplx_0(1,B))))) ) ) ) ) ) ) )).
fof(t9_ff_siec,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ( r1_tarski(k10_xtuple_0(k5_relat_1(k1_net_1(A),u4_struct_0(A))),u1_struct_0(A)) & r1_tarski(k10_xtuple_0(k5_relat_1(k2_relat_1(k1_net_1(A)),u4_struct_0(A))),u1_struct_0(A)) & r1_tarski(k10_xtuple_0(k5_relat_1(k1_net_1(A),u1_struct_0(A))),u4_struct_0(A)) & r1_tarski(k10_xtuple_0(k5_relat_1(k2_relat_1(k1_net_1(A)),u1_struct_0(A))),u4_struct_0(A)) & r1_tarski(k10_xtuple_0(k4_relat_1(u4_struct_0(A))),u4_struct_0(A)) & r1_tarski(k9_xtuple_0(k4_relat_1(u4_struct_0(A))),u4_struct_0(A)) & r1_tarski(k10_xtuple_0(k4_relat_1(u1_struct_0(A))),u1_struct_0(A)) & r1_tarski(k9_xtuple_0(k4_relat_1(u1_struct_0(A))),u1_struct_0(A)) ) ) )).
fof(t9_fib_num,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v9_ordinal1(B) => k20_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B),k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,B,C)) = k52_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,C) ) ) ) ) )).
fof(t9_fib_num2,axiom,( ! [A] : ( v7_ordinal1(A) => k2_power(k4_xcmplx_0(1),k4_xcmplx_0(k3_xcmplx_0(2,A))) = 1 ) )).
fof(t9_fib_num4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(B,A) => ( v1_abian(B) | r1_xxreal_0(k5_numbers,C) | r1_xxreal_0(C,k4_xcmplx_0(1)) | r1_xxreal_0(k2_power(C,B),k2_power(C,A)) ) ) ) ) ) )).
fof(t9_filerec1,axiom,( ! [A] : ! [B] : ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( m2_finseq_1(D,C) => ( D = k10_finseq_1(A,B) => ( r2_hidden(A,C) & r2_hidden(B,C) ) ) ) ) )).
fof(t9_filter_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ( ( ~ v1_xboole_0(B) & v19_lattices(B,A) & v20_lattices(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) <=> ( ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k4_lattices(A,C,D),B) ) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r2_hidden(C,B) & r3_lattices(A,C,D) ) => r2_hidden(D,B) ) ) ) ) ) ) ) )).
fof(t9_filter_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m2_filter_1(C,A,B) => ! [D] : ( m2_filter_1(D,A,B) => ( r4_binop_1(A,C,D) => r4_binop_1(k8_eqrel_1(A,B),k3_filter_1(A,B,C),k3_filter_1(A,B,D)) ) ) ) ) ) )).
fof(t9_filter_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v13_lattices(A) & l3_lattices(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v10_lattices(B) & v13_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)) => k5_lattices(A) = k5_lattices(B) ) ) ) )).
fof(t9_fin_topo,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(B,k10_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) ) ) ) ) ) )).
fof(t9_finance1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [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))) ) => ( r1_finance1(A,k1_numbers,B,k12_prob_1,C) => ( ! [D] : ( v1_xreal_0(D) => ( m2_subset_1(a_3_0_finance1(A,C,D),k1_zfmisc_1(A),B) & m2_subset_1(a_3_1_finance1(A,C,D),k1_zfmisc_1(A),B) ) ) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( ~ r1_xxreal_0(E,D) => m2_subset_1(a_4_1_finance1(A,C,D,E),k1_zfmisc_1(A),B) ) ) ) & ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ( r1_xxreal_0(D,E) => m2_subset_1(a_4_2_finance1(A,C,D,E),k1_zfmisc_1(A),B) ) ) ) & ! [D] : ( v1_xreal_0(D) => k11_mesfunc1(C,D) = a_3_1_finance1(A,C,D) ) & ! [D] : ( v1_xreal_0(D) => k14_mesfunc1(C,D) = a_3_0_finance1(A,C,D) ) & ! [D] : ( v1_xreal_0(D) => k10_relat_1(C,D) = a_3_2_finance1(A,C,D) ) & ! [D] : ( v1_xreal_0(D) => m2_subset_1(k10_relat_1(C,D),k1_zfmisc_1(A),B) ) ) ) ) ) ) )).
fof(t9_finseq_1,axiom,( ! [A] : ( v7_ordinal1(A) => k2_xboole_0(k2_finseq_1(A),k1_tarski(k1_nat_1(A,1))) = k2_finseq_1(k1_nat_1(A,1)) ) )).
fof(t9_finseq_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( m2_finseq_1(C,B) => ( r2_hidden(A,k4_finseq_1(C)) => r2_hidden(k1_funct_1(C,A),B) ) ) ) )).
fof(t9_finseq_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( A != k5_numbers => r2_hidden(A,k2_finseq_1(k2_xcmplx_0(A,B))) ) ) ) )).
fof(t9_finseq_4,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( r1_finseq_4(A,B) <=> ( r2_hidden(B,k9_xtuple_0(A)) & r2_finseq_4(A,k1_funct_1(A,B)) ) ) ) )).
fof(t9_finseq_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ! [C] : ( ( r2_hidden(B,k10_xtuple_0(A)) & r2_hidden(C,k10_xtuple_0(A)) & k4_finseq_4(A,B) = k4_finseq_4(A,C) ) => B = C ) ) )).
fof(t9_finseq_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( r2_hidden(C,k6_subset_1(k10_xtuple_0(B),k10_xtuple_0(A))) => k6_finseq_4(k7_finseq_1(A,B),C) = k6_finseq_4(B,C) ) ) ) )).
fof(t9_finseq_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,k3_finseq_1(B)) ) => ! [E] : ( v7_ordinal1(E) => ( r1_xxreal_0(E,k6_xcmplx_0(k3_finseq_1(B),D)) => ( r1_xxreal_0(E,k5_numbers) | k1_funct_1(k1_finseq_7(A,B,D,C),k2_xcmplx_0(D,E)) = k1_funct_1(k2_rfinseq(A,D,B),E) ) ) ) ) ) ) ) ) )).
fof(t9_finseq_8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => k3_finseq_8(A,k1_finseq_8(A,B,C),k1_nat_1(k3_finseq_1(B),1),k1_nat_1(k3_finseq_1(B),k3_finseq_1(C))) = C ) ) ) )).
fof(t9_finseqop,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( ( 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(k4_ordinal1,B,k4_finseqop(A,B,k8_finseq_1(A,C,D),E),k8_finseq_1(B,k4_finseqop(A,B,C,E),k4_finseqop(A,B,D,E))) ) ) ) ) ) )).
fof(t9_finset_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( r1_tarski(A,k10_xtuple_0(B)) & v1_finset_1(k8_relat_1(B,A)) ) => v1_finset_1(A) ) ) )).
fof(t9_finsop_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( m2_finseq_1(C,A) => ! [D] : ( m2_finseq_1(D,A) => ! [E] : ( ( 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) & k3_finseq_1(B) = k3_finseq_1(C) & k3_finseq_1(B) = k3_finseq_1(D) & ! [F] : ( m1_subset_1(F,k4_ordinal1) => ( r2_hidden(F,k1_relset_1(k4_ordinal1,B)) => k1_funct_1(B,F) = k1_binop_1(E,k1_funct_1(C,F),k1_funct_1(D,F)) ) ) ) => ( ( ~ v1_setwiseo(E,A) & ~ r1_xxreal_0(1,k3_finseq_1(B)) ) | k1_finsop_1(A,B,E) = k5_binop_1(A,E,k1_finsop_1(A,C,E),k1_finsop_1(A,D,E)) ) ) ) ) ) ) ) )).
fof(t9_finsub_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_finsub_1(B) ) => ( ~ v1_xboole_0(k3_xboole_0(A,B)) & v4_finsub_1(k3_xboole_0(A,B)) ) ) ) )).
fof(t9_fintopo2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k3_fintopo2(A,B,C) = k8_margrel1 <=> r2_hidden(C,k1_fin_topo(A,B)) ) ) ) ) )).
fof(t9_fintopo3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => r1_tarski(k4_subset_1(u1_struct_0(A),k8_fin_topo(A,B),k8_fin_topo(A,C)),k8_fin_topo(A,k4_subset_1(u1_struct_0(A),B,C))) ) ) ) )).
fof(t9_fintopo4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_fin_topo(A) & r1_xboole_0(B,k9_fin_topo(A,C)) ) => r1_xboole_0(k9_fin_topo(A,B),C) ) ) ) ) )).
fof(t9_fintopo6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_fintopo6(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).
fof(t9_flang_1,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k3_catalan2(A)) => ! [C] : ( v7_ordinal1(C) => ~ ( k1_afinsq_1(B) = k1_nat_1(C,1) & ! [D] : ( m1_subset_1(D,k3_catalan2(A)) => ! [E] : ( m1_subset_1(E,A) => ~ ( k1_afinsq_1(D) = C & B = k1_ordinal4(k5_afinsq_1(E),D) ) ) ) ) ) ) )).
fof(t9_flang_2,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k8_afinsq_1(A))) => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(k5_afinsq_1(B),k7_flang_1(A,C,D)) <=> ( r2_hidden(k5_afinsq_1(B),C) & ( ( r2_hidden(k2_flang_1(A),C) & ~ r1_xxreal_0(D,1) ) | D = 1 ) ) ) ) ) )).
fof(t9_flang_3,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k8_afinsq_1(A))) => ! [C] : ( v7_ordinal1(C) => r1_tarski(k1_flang_3(A,B,C),k8_flang_1(A,B)) ) ) )).
fof(t9_fomodel0,axiom,( ! [A] : ! [B] : ( v7_ordinal1(B) => r1_tarski(k4_finseq_2(k2_xcmplx_0(B,1),A),k6_subset_1(k3_finseq_2(A),k1_tarski(k1_xboole_0))) ) )).
fof(t9_fomodel1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v11_fomodel1(A) & l1_fomodel1(A) ) => k7_subset_1(k15_fomodel1(A),k17_fomodel1(A),k9_fomodel1(A)) = k6_domain_1(k1_fomodel1(A),k18_fomodel1(A)) ) )).
fof(t9_fomodel2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v11_fomodel1(B) & l1_fomodel1(B) ) => k24_fomodel2(B,k1_nat_1(A,1)) = k2_xboole_0(k2_xboole_0(k27_fomodel2(B,A),k28_fomodel2(B,A)),k24_fomodel2(B,A)) ) ) )).
fof(t9_fomodel3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ v6_struct_0(C) & v11_fomodel1(C) & l1_fomodel1(C) ) => ! [D] : ( ( v4_fomodel1(D,C) & m1_subset_1(D,k1_fomodel1(C)) ) => ! [E] : ( ( v4_fomodel1(E,C) & m1_subset_1(E,k1_fomodel1(C)) ) => ! [F] : ( ( v4_fomodel2(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))) ) => ( ~ r2_hidden(E,k10_xtuple_0(F)) => ! [G] : ( m2_subset_1(G,k9_funct_2(k37_fomodel1(C),k3_rfunct_3(k3_finseq_2(A),k2_xboole_0(A,k6_margrel1))),k15_fomodel2(C,A)) => k25_fomodel2(C,A,k34_fomodel2(C,A,G,D,B),F) = k25_fomodel2(C,A,k34_fomodel2(C,A,G,E,B),k24_fomodel3(C,D,E,F)) ) ) ) ) ) ) ) ) )).
fof(t9_fomodel4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ! [D] : ( ( ~ v6_struct_0(D) & v11_fomodel1(D) & l1_fomodel1(D) ) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(k9_funct_2(k9_setfam_1(k1_fomodel4(D)),k9_setfam_1(k1_fomodel4(D))))) => ( v5_fomodel4(C,A,D,E,B) => v4_fomodel4(k1_tarski(C),D,E,B) ) ) ) ) )).
fof(t9_frechet,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,u1_struct_0(k3_topmetr)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k3_topmetr)))) ) => ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => r2_hidden(k3_funct_2(k4_ordinal1,u1_struct_0(k3_topmetr),A,B),k2_rcomp_1(k6_xcmplx_0(B,k7_xcmplx_0(1,4)),k2_xcmplx_0(B,k7_xcmplx_0(1,4)))) ) => v4_pre_topc(k2_relset_1(u1_struct_0(k3_topmetr),A),k3_topmetr) ) ) )).
fof(t9_frechet2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v4_pre_topc(B,A) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r1_tarski(k2_relset_1(u1_struct_0(A),C),B) => r1_tarski(k2_frechet(A,C),B) ) ) ) ) ) )).
fof(t9_friends1,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v2_relat_2(C) & v3_relat_2(C) & v1_finset_1(C) & v3_friends1(C) ) => ( ( r2_hidden(A,k1_relat_1(C)) & r2_hidden(B,k1_relat_1(C)) ) => ( r2_hidden(k4_tarski(A,B),C) | k5_card_1(k9_relat_1(C,A)) = k5_card_1(k9_relat_1(C,B)) ) ) ) )).
fof(t9_fscirc_1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ( k2_msafree2(k4_fscirc_1(A,B,C)) = k1_enumset1(A,B,C) & 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))) ) ) ) ) )).
fof(t9_fscirc_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => k3_msafree2(k1_fscirc_2(k1_nat_1(A,1),B,C)) = k2_xboole_0(k3_msafree2(k1_fscirc_2(A,B,C)),k3_msafree2(k8_fscirc_1(k1_funct_1(B,k1_nat_1(A,1)),k1_funct_1(C,k1_nat_1(A,1)),k3_fscirc_2(A,B,C)))) ) ) ) )).
fof(t9_fsm_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( ~ v2_struct_0(C) & l2_fsm_1(C,A,B) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(C)) => k4_fsm_1(A,B,C,D,k6_finseq_1(A)) = k6_finseq_1(B) ) ) ) ) )).
fof(t9_fsm_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_fsm_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ~ ( v2_fsm_2(C,A,B) & C != u2_fsm_1(A,B) & ! [D] : ( m1_subset_1(D,A) => ~ r1_fsm_2(A,B,C,D) ) ) ) ) ) )).
fof(t9_fsm_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => ( r2_hidden(B,k9_flang_1(A)) <=> k1_afinsq_1(B) = 1 ) ) ) )).
fof(t9_ftacell1,axiom,( ! [A] : ( ~ v1_xtuple_0(A) => ! [B] : ( ~ v1_xtuple_0(B) => ! [C] : ( ~ v1_xtuple_0(C) => ! [D] : ( ~ v1_xtuple_0(D) => ! [E] : ~ ( 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] : ( 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] : ( m1_subset_1(G,k6_margrel1) & ? [H] : ( m1_subset_1(H,k6_margrel1) & ? [I] : ( m1_subset_1(I,k6_margrel1) & ? [J] : ( m1_subset_1(J,k6_margrel1) & ? [K] : ( 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),k5_ftacell1(A,B,C,D,E)) = 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),k6_ftacell1(A,B,C,D,E)) = k2_binarith(k2_binarith(k2_binarith(k2_binarith(G,H),I),J),K) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_funcop_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( k10_xtuple_0(A) = k1_tarski(B) => A = k2_funcop_1(k9_xtuple_0(A),B) ) ) )).
fof(t9_funcsdom,axiom,( ! [A] : ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => r2_funct_2(A,k1_numbers,k1_funcsdom(A,k1_numbers,k6_funcsdom(A),k9_funcsdom(A),B),B) ) )).
fof(t9_funct_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ! [C] : ~ ( r2_hidden(C,A) & ! [D] : ~ ( r2_hidden(D,k9_xtuple_0(B)) & C = k1_funct_1(B,D) ) ) => r1_tarski(A,k10_xtuple_0(B)) ) ) )).
fof(t9_funct_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => r2_hidden(B,k1_funct_2(A,A)) ) )).
fof(t9_funct_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => r1_tarski(k10_xtuple_0(k1_funct_3(A)),k1_zfmisc_1(k10_xtuple_0(A))) ) )).
fof(t9_funct_4,axiom,( ! [A] : ! [B] : ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r1_tarski(C,D) => r1_tarski(k5_relat_1(k6_relat_1(B,C),A),k5_relat_1(k6_relat_1(B,D),A)) ) ) ) )).
fof(t9_funct_5,axiom,( ! [A] : ( ( k9_xtuple_0(A) = k1_xboole_0 | k10_xtuple_0(A) = k1_xboole_0 ) => ! [B] : ! [C] : ~ r2_hidden(k4_tarski(B,C),A) ) )).
fof(t9_funct_6,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( A != k1_xboole_0 => ( k10_xtuple_0(k2_funct_5(k7_funcop_1(A,B))) = k10_xtuple_0(B) & k10_xtuple_0(k4_funct_5(k7_funcop_1(A,B))) = k10_xtuple_0(B) ) ) ) )).
fof(t9_funct_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r1_tarski(k10_xtuple_0(C),k9_xtuple_0(A)) => k3_relat_1(k1_funct_4(B,C),A) = k1_funct_4(k3_relat_1(B,A),k3_relat_1(C,A)) ) ) ) ) )).
fof(t9_funct_8,axiom,( ! [A] : ( ( v1_funct_8(A) & m1_subset_1(A,k1_zfmisc_1(k2_numbers)) ) => ! [B] : ( ( 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] : ( v1_xreal_0(C) => ( r2_hidden(C,A) => k1_funct_1(B,C) = k1_funct_1(B,k9_complex1(C)) ) ) ) => r1_funct_8(A,k1_numbers,k1_numbers,B) ) ) ) )).
fof(t9_funct_9,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v3_valued_0(C) ) => ( v1_funct_9(C,A) => v1_funct_9(k13_valued_1(C,B),A) ) ) ) ) )).
fof(t9_functor0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( v2_funct_1(k2_funct_4(k15_funct_3(A,B))) => v2_funct_1(k15_funct_3(B,A)) ) ) ) )).
fof(t9_functor1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l1_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_altcat_2(C) & l1_altcat_1(C) ) => ! [D] : ( ( v8_functor0(D,A,B) & l2_functor0(D,A,B) ) => ! [E] : ( l2_functor0(E,B,C) => ( ( v18_functor0(D,A,B) & v18_functor0(E,B,C) ) => v18_functor0(k13_functor0(A,B,C,D,E),A,C) ) ) ) ) ) ) )).
fof(t9_functor2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v15_functor0(C,A,B) & m2_functor0(C,A,B) ) => ! [D] : ( ( v15_functor0(D,A,B) & m2_functor0(D,A,B) ) => ( r2_functor2(A,B,C,D) => ! [E] : ( m2_functor2(E,A,B,C,D) => ( r8_pboole(u1_struct_0(A),k3_functor2(A,B,C,D,D,E,k4_functor2(A,B,D)),E) & r8_pboole(u1_struct_0(A),k3_functor2(A,B,C,C,D,k4_functor2(A,B,C),E),E) ) ) ) ) ) ) ) )).
fof(t9_functor3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v1_altcat_2(B) & l2_altcat_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v1_altcat_2(C) & l2_altcat_1(C) ) => ! [D] : ( ( v8_functor0(D,B,C) & v10_functor0(D,B,C) & l2_functor0(D,B,C) ) => ! [E] : ( ( v8_functor0(E,A,B) & v11_functor0(E,A,B) & l2_functor0(E,A,B) ) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,k1_altcat_1(A,F,G)) => ( k1_altcat_1(A,F,G) != k1_xboole_0 => k8_functor0(A,C,k13_functor0(A,B,C,E,D),F,G,H) = k6_functor0(B,C,D,k3_functor0(A,B,E,G),k3_functor0(A,B,E,F),k8_functor0(A,B,E,F,G,H)) ) ) ) ) ) ) ) ) ) )).
fof(t9_fuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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,B,k2_fuzzy_1(A,D,C)),k2_fuzzy_1(A,k1_fuzzy_1(A,B,D),k1_fuzzy_1(A,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),k2_fuzzy_1(A,B,C))) ) ) ) ) ) )).
fof(t9_fuzzy_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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_2(A,B,C)),B) ) ) ) )).
fof(t9_fuzzy_4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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] : ( ( v5_relat_1(D,k1_rcomp_1(k5_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] : ! [F] : ( ( r2_hidden(E,A) & r2_hidden(F,B) & r1_xxreal_0(k1_funct_1(C,k4_tarski(E,F)),k1_funct_1(D,k4_tarski(E,F))) ) => r1_xxreal_0(k1_funct_1(k1_fuzzy_4(B,A,C),k4_tarski(F,E)),k1_funct_1(k1_fuzzy_4(B,A,D),k4_tarski(F,E))) ) ) ) ) ) )).
fof(t9_fvaluat1,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => ~ ( B != k2_xxreal_0 & B != k1_xxreal_0 & A != k5_numbers & B != k5_numbers & k2_extreal1(A,B) = k5_numbers ) ) ) )).
fof(t9_fvsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_group_1(A) & v6_vectsp_1(A) & l4_algstr_0(A) ) => v1_setwiseo(u2_algstr_0(A),u1_struct_0(A)) ) )).
fof(t9_gate_1,axiom,( ! [A] : ! [B] : ( ~ ( ~ v1_xboole_0(k4_gate_1(A,B)) & v1_xboole_0(k4_gate_1(B,A)) ) & ~ ( ~ v1_xboole_0(k4_gate_1(B,A)) & v1_xboole_0(k4_gate_1(A,B)) ) ) )).
fof(t9_gcd_1,axiom,( ! [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) & v1_vectsp_2(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( B != k4_struct_0(A) => k1_gcd_1(A,B,B) = k5_struct_0(A) ) ) ) )).
fof(t9_genealg1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v2_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => ! [D] : ( m1_genealg1(D,C) => ! [E] : ( m1_genealg1(E,C) => ( r1_xxreal_0(k3_finseq_1(D),A) => k8_genealg1(C,D,E,A,B) = k7_genealg1(C,D,E,B) ) ) ) ) ) ) )).
fof(t9_geomtrap,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_geomtrap(A,B,C,k1_geomtrap(A,D,B),k1_geomtrap(A,D,C)) ) ) ) ) )).
fof(t9_gfacirc1,axiom,( ! [A] : ( m1_subset_1(A,k6_margrel1) => ! [B] : ( m1_subset_1(B,k6_margrel1) => ! [C] : ( m1_subset_1(C,k6_margrel1) => k1_funct_1(k1_gfacirc1,k9_finseq_1(k1_funct_1(k4_gfacirc1,k10_finseq_1(k1_funct_1(k16_twoscomp,k10_finseq_1(A,B)),C)))) = k1_funct_1(k14_twoscomp,k10_finseq_1(k1_funct_1(k14_twoscomp,k10_finseq_1(A,B)),C)) ) ) ) )).
fof(t9_gfacirc2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) ) => k3_msafree2(k1_gfacirc2(k1_nat_1(A,1),B,C)) = k2_xboole_0(k3_msafree2(k1_gfacirc2(A,B,C)),k3_msafree2(k13_gfacirc1(k1_funct_1(B,k1_nat_1(A,1)),k1_funct_1(C,k1_nat_1(A,1)),k3_gfacirc2(A,B,C)))) ) ) ) )).
fof(t9_glib_000,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( C != D => k1_funct_1(A,D) = k1_funct_1(k13_glib_000(A,C,B),D) ) ) ) ) )).
fof(t9_glib_001,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m3_glib_001(B,A) => ! [C] : ( ( ~ v1_abian(C) & m1_subset_1(C,k4_ordinal1) ) => ( ~ r1_xxreal_0(k3_finseq_1(B),C) => r2_hidden(k1_funct_1(B,k1_nat_1(C,1)),k28_glib_000(A,k5_glib_001(A,B,C))) ) ) ) ) )).
fof(t9_glib_002,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) ) => ! [B] : ( m1_subset_1(B,k6_glib_000(A)) => ! [C] : ! [D] : ! [E] : ( ( r2_hidden(D,k1_glib_002(A,B)) & r1_glib_000(A,D,E,C) ) => r2_hidden(E,k1_glib_002(A,B)) ) ) ) )).
fof(t9_glib_003,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_finset_1(A) & v1_glib_000(A) & v1_glib_003(A) ) => ! [B] : ( ( v1_glib_003(B) & v4_glib_003(B,A) & m1_glib_000(B,A) ) => ! [C] : ( ( v1_glib_003(C) & v4_glib_003(C,B) & m1_glib_000(C,B) ) => ( v1_glib_003(C) & v4_glib_003(C,A) & m1_glib_000(C,A) ) ) ) ) )).
fof(t9_glib_005,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( 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] : ( m1_subset_1(C,k6_glib_000(A)) => ! [D] : ( r2_hidden(D,k1_relset_1(k6_glib_000(A),k6_glib_005(A,B,C))) <=> ? [E] : ( v5_glib_001(E,A) & m3_glib_001(E,A) & r1_glib_001(A,C,D,E) & r5_glib_005(A,B,E) ) ) ) ) ) )).
fof(t9_goboard1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r2_hidden(C,k2_finseq_1(k1_matrix_0(E))) & k1_matrix_0(E) = k1_nat_1(B,1) & r2_hidden(A,k4_finseq_1(E)) & r1_xxreal_0(C,D) & r1_xxreal_0(D,B) ) => ( r1_xxreal_0(B,k5_numbers) | ( k3_matrix_0(u1_struct_0(k15_euclid(2)),k16_matrix_0(C,u1_struct_0(k15_euclid(2)),E),A,D) = k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,k1_nat_1(D,1)) & r2_hidden(k1_nat_1(D,1),k2_finseq_1(k1_matrix_0(E))) ) ) ) ) ) ) ) ) )).
fof(t9_goboard2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ~ ( A != k1_xboole_0 & k1_goboard1(A) = k1_xboole_0 ) ) )).
fof(t9_goboard5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( v1_goboard1(B) & r1_xxreal_0(1,A) & r1_xxreal_0(A,k1_matrix_0(B)) ) => ( v3_relat_1(B) | k1_goboard5(B,k3_finseq_1(B)) = a_2_8_goboard5(A,B) ) ) ) ) )).
fof(t9_goboard6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(2))) => ( ( E = k19_euclid(A,B) & r1_xxreal_0(k5_numbers,D) ) => ( r1_xxreal_0(C,D) | r2_hidden(k19_euclid(k6_xcmplx_0(A,D),B),k8_metric_1(k14_euclid(2),E,C)) ) ) ) ) ) ) ) )).
fof(t9_goboard7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( ~ v3_relat_1(C) & v1_matrix_0(C) & v1_goboard1(C) & v2_goboard1(C) & v3_goboard1(C) & v4_goboard1(C) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(k1_nat_1(A,1),k3_finseq_1(C)) & r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,1),k1_matrix_0(C)) ) => k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),k1_nat_1(B,1))),k7_xcmplx_0(1,2)) = k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,A,k1_nat_1(B,1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),C,k1_nat_1(A,1),B)),k7_xcmplx_0(1,2)) ) ) ) ) )).
fof(t9_goboard8,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(k1_nat_1(B,2),k3_finseq_1(A)) ) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,2),k3_finseq_1(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,1)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_matrix_0(k2_goboard2(A))) ) => ( ( ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,2),k1_matrix_0(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k7_nat_d(k1_matrix_0(k2_goboard2(A)),1)) ) & ~ ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,k1_nat_1(B,2)) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,2),k1_matrix_0(k2_goboard2(A))) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,B) = k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k7_nat_d(k1_matrix_0(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_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,k7_nat_d(k1_matrix_0(k2_goboard2(A)),1)),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_matrix_0(k2_goboard2(A)))),k7_xcmplx_0(1,2)),k3_rlvect_1(k15_euclid(2),k1_rlvect_1(k15_euclid(2),k3_rlvect_1(k15_euclid(2),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),C,k1_matrix_0(k2_goboard2(A))),k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),k1_nat_1(C,1),k1_matrix_0(k2_goboard2(A)))),k7_xcmplx_0(1,2)),k19_euclid(k5_numbers,1))),k3_topreal1(2,A)) ) ) ) ) ) ) )).
fof(t9_goboard9,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,B) & r1_xxreal_0(1,C) & k2_xcmplx_0(B,C) = k3_finseq_1(A) ) => k5_goboard5(k1_goboard9(A),B) = k4_goboard5(A,C) ) ) ) ) )).
fof(t9_gobrd11,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( B = a_1_3_gobrd11(A) & C = a_1_4_gobrd11(A) ) => B = k3_subset_1(u1_struct_0(k15_euclid(2)),C) ) ) ) ) )).
fof(t9_gobrd12,axiom,( ! [A] : ( ( ~ 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] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(B,k3_finseq_1(k2_goboard2(A))) & r1_xxreal_0(C,k1_matrix_0(k2_goboard2(A))) ) => 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))) ) ) ) ) )).
fof(t9_gobrd13,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ! [E] : ( ( ~ v3_relat_1(E) & v1_matrix_0(E) & v1_goboard1(E) & v2_goboard1(E) & v3_goboard1(E) & v4_goboard1(E) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [F] : ( ( ~ v3_relat_1(F) & v1_matrix_0(F) & v1_goboard1(F) & v2_goboard1(F) & v3_goboard1(F) & v4_goboard1(F) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ( ( r1_tarski(k9_matrix_0(E),k9_matrix_0(F)) & r1_xxreal_0(1,A) & r1_xxreal_0(A,k3_finseq_1(E)) & r1_xxreal_0(C,k1_matrix_0(E)) & r1_xxreal_0(1,B) & r1_xxreal_0(B,k3_finseq_1(F)) & r1_xxreal_0(D,k1_matrix_0(F)) & k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,C) = k3_matrix_0(u1_struct_0(k15_euclid(2)),F,B,D) ) => ( r1_xxreal_0(C,1) | r1_xxreal_0(D,1) | r1_xxreal_0(k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),E,A,k7_nat_d(C,1))),k18_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),F,B,k7_nat_d(D,1)))) ) ) ) ) ) ) ) ) )).
fof(t9_gobrd14,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( ( 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_0(k1_jordan8(D,C))) & r2_hidden(k4_tarski(A,k1_nat_1(B,1)),k2_matrix_0(k1_jordan8(D,C))) ) => k1_topreal6(2,k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(D,C),A,B),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(D,C),A,k1_nat_1(B,1))) = k7_xcmplx_0(k6_xcmplx_0(k7_pscomp_1(D),k9_pscomp_1(D)),k1_newton(2,C)) ) ) ) ) ) )).
fof(t9_goedelcp,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( ~ v1_xboole_0(D) => ! [E] : ( m1_valuat_1(E,A,D) => ! [F] : ( m2_funct_2(F,k3_qc_lang1(A),D,k2_valuat_1(A,D)) => ( r1_valuat_1(A,D,k12_cqc_lang(A,C,B),E,F) <=> ? [G] : ( m1_subset_1(G,D) & r1_valuat_1(A,D,B,E,k1_sublemma(A,D,F,k12_sublemma(A,D,C,G))) ) ) ) ) ) ) ) ) )).
fof(t9_gr_cy_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k5_group_1(A,k7_group_1(A),B) = k1_group_1(A) ) ) )).
fof(t9_gr_cy_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( r1_nat_d(D,C) => r1_struct_0(k5_group_4(A,k6_domain_1(u1_struct_0(A),k5_group_1(A,D,B))),k5_group_1(A,C,B)) ) ) ) ) ) )).
fof(t9_gr_cy_3,axiom,( ! [A] : ( ( v7_ordinal1(A) & v1_int_2(A) & v2_gr_cy_3(A) ) => ~ ( ~ r1_xxreal_0(A,2) & k4_nat_d(A,4) != 1 & k4_nat_d(A,4) != 3 ) ) )).
fof(t9_graph_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_graph_1(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_graph_1(C) ) => ( ( r1_partfun1(u1_graph_1(A),u1_graph_1(B)) & r1_partfun1(u2_graph_1(A),u2_graph_1(B)) & r1_partfun1(u1_graph_1(A),u1_graph_1(C)) & r1_partfun1(u2_graph_1(A),u2_graph_1(C)) & r1_partfun1(u1_graph_1(B),u1_graph_1(C)) & r1_partfun1(u2_graph_1(B),u2_graph_1(C)) ) => k5_graph_1(k5_graph_1(A,B),C) = k5_graph_1(A,k5_graph_1(B,C)) ) ) ) ) )).
fof(t9_graph_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( r1_xxreal_0(B,k3_finseq_1(A)) => k7_finseq_1(k1_graph_2(A,1,B),k1_graph_2(A,k1_nat_1(B,1),k3_finseq_1(A))) = A ) ) ) )).
fof(t9_graph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v2_funct_1(B) & m2_graph_1(B,A) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(k1_nat_1(C,1),k4_finseq_1(B)) => ( k3_finseq_1(k8_finseq_1(u4_struct_0(A),k2_graph_2(u4_struct_0(A),B,k1_nat_1(C,1),k3_finseq_1(B)),k2_graph_2(u4_struct_0(A),B,1,C))) = k3_finseq_1(B) & k10_xtuple_0(k8_finseq_1(u4_struct_0(A),k2_graph_2(u4_struct_0(A),B,k1_nat_1(C,1),k3_finseq_1(B)),k2_graph_2(u4_struct_0(A),B,1,C))) = k10_xtuple_0(B) & k1_funct_1(k8_finseq_1(u4_struct_0(A),k2_graph_2(u4_struct_0(A),B,k1_nat_1(C,1),k3_finseq_1(B)),k2_graph_2(u4_struct_0(A),B,1,C)),1) = k1_funct_1(B,k1_nat_1(C,1)) ) ) ) ) ) )).
fof(t9_graph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v7_graph_1(B,A) & m2_graph_1(B,A) ) => ? [C] : ( m2_finseq_1(C,u1_struct_0(A)) & r3_graph_4(A,C,B) ) ) ) )).
fof(t9_graph_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( ( ~ 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) ) ) ) ) ) )).
fof(t9_graphsp,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( v7_graph_1(B,A) & m2_graph_1(B,A) ) => ! [C] : ( ( v7_graph_1(C,A) & m2_graph_1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ! [E] : ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r8_graph_5(A,F,G,B,E,D) & r8_graph_5(A,F,G,C,E,D) ) => k10_graph_5(A,B,D) = k10_graph_5(A,C,D) ) ) ) ) ) ) ) )).
fof(t9_grcat_1,axiom,( ! [A] : ( ( v2_grcat_1(A) & l1_grcat_1(A) ) => v13_vectsp_1(u3_grcat_1(A),u1_grcat_1(A),u2_grcat_1(A)) ) )).
fof(t9_grfunc_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v2_funct_1(A) <=> ! [B] : ! [C] : ! [D] : ( ( r2_hidden(k4_tarski(B,D),A) & r2_hidden(k4_tarski(C,D),A) ) => B = C ) ) ) )).
fof(t9_groeb_1,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(D,A,C) & v1_polynom1(D,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(C)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k15_pre_poly(A),u1_struct_0(C)) & v1_polynom7(E,A,C) & v1_polynom1(E,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) => r1_termord(A,B,k3_termord(A,B,C,E),k3_termord(A,B,C,D)) ) ) ) ) ) ) )).
fof(t9_groeb_2,axiom,( ! [A] : ! [B] : ( ( 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] : ( ( 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] : ( ( 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,C,B),k2_groeb_2(A,C,D)) => r3_pre_poly(A,k2_groeb_2(A,B,D),k2_groeb_2(A,C,D)) ) ) ) ) )).
fof(t9_groeb_3,axiom,( ! [A] : ( v3_ordinal1(A) => ! [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) & v1_vectsp_2(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(A),u1_struct_0(B)) & v1_polynom1(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(A),u1_struct_0(B)))) ) => ! [D] : ( ( 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)))) ) => k3_polynom1(k15_pre_poly(A),B,k10_polynom1(A,B,D,C)) = a_4_0_groeb_3(A,B,C,D) ) ) ) ) )).
fof(t9_group_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_group_1(A,C) = k2_group_1(A,B) => C = B ) ) ) ) )).
fof(t9_group_10,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v8_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => ! [D] : ( ( 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)))) ) => ( v2_group_10(B,C) => k4_nat_d(k5_card_1(k12_group_10(B,A,D)),C) = k4_nat_d(k5_card_1(A),C) ) ) ) ) ) )).
fof(t9_group_11,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_group_2(C,A) => ! [D] : ( m1_group_2(D,A) => ( u1_struct_0(B) = k7_group_4(A,C,D) => ( m1_group_2(C,B) & m1_group_2(D,B) ) ) ) ) ) ) )).
fof(t9_group_12,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,u1_struct_0(k2_group_7(k2_finseq_1(A),B))) => ! [D] : ( m2_finseq_1(D,u1_struct_0(k2_group_7(k2_finseq_1(A),B))) => ( ( k3_finseq_1(D) = A & ! [E] : ( m2_subset_1(E,k4_ordinal1,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) ) => ! [E] : ( v7_ordinal1(E) => ~ ( r1_xxreal_0(1,E) & r1_xxreal_0(E,A) & ! [F] : ( m1_subset_1(F,u1_struct_0(k2_group_7(k2_finseq_1(A),B))) => ~ ( F = k1_funct_1(D,E) & k1_funct_1(C,E) = k1_funct_1(F,E) ) ) ) ) ) ) ) ) ) )).
fof(t9_group_14,axiom,( ! [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) ) => ! [B] : ( ( ~ 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] : ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(k4_prvect_3(A,B)),u1_struct_0(k4_prvect_3(A,k20_prvect_1(k9_finseq_1(B))))) & v13_vectsp_1(C,k4_prvect_3(A,B),k4_prvect_3(A,k20_prvect_1(k9_finseq_1(B)))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k4_prvect_3(A,B)),u1_struct_0(k4_prvect_3(A,k20_prvect_1(k9_finseq_1(B))))))) & v3_funct_2(C,u1_struct_0(k4_prvect_3(A,B)),u1_struct_0(k4_prvect_3(A,k20_prvect_1(k9_finseq_1(B))))) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( 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(k4_ordinal1,u1_struct_0(B))),D,k12_finseq_1(u1_struct_0(B),E)) ) ) ) ) ) )).
fof(t9_group_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( B != k1_xboole_0 & C != k1_xboole_0 ) <=> k2_group_2(A,B,C) != k1_xboole_0 ) ) ) ) )).
fof(t9_group_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_group_2(D,A) => k11_group_2(A,D,k5_group_2(A,B,C)) = k2_group_2(A,C,k13_group_2(A,D,B)) ) ) ) ) )).
fof(t9_group_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_group_4(A,k12_finseq_1(u1_struct_0(A),B)) = B ) ) )).
fof(t9_group_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => k8_finseq_1(u1_struct_0(A),k1_group_5(A,C,B),k1_group_5(A,D,B)) = k1_group_5(A,k8_finseq_1(u1_struct_0(A),C,D),B) ) ) ) ) )).
fof(t9_group_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( ( v1_group_3(C,A) & m1_group_2(C,A) ) => ( v1_group_3(k10_group_2(A,B,C),B) & m1_group_6(k10_group_2(A,B,C),A,B) & v1_group_3(k10_group_2(A,C,B),B) & m1_group_6(k10_group_2(A,C,B),A,B) ) ) ) ) )).
fof(t9_group_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_int_1(C) => k5_group_1(A,k3_xcmplx_0(C,k6_group_1(A,B)),B) = k1_group_1(A) ) ) ) )).
fof(t9_group_9,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & v3_group_9(B,A) & l1_group_9(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ~ ( C != k1_xboole_0 & ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ( r2_hidden(D,C) => r2_hidden(k2_group_1(B,D),C) ) ) & ! [D] : ( m1_subset_1(D,A) => ! [E] : ( 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] : ( ( v2_group_9(D,A) & m1_group_9(D,A,B) ) => u1_struct_0(D) != C ) ) ) ) )).
fof(t9_groupp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_group_2(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( k13_group_2(A,B,C) = k13_group_2(A,B,D) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ~ ( C = k6_algstr_0(A,D,E) & r1_struct_0(B,E) ) ) ) ) ) ) ) )).
fof(t9_grsolv_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v15_algstr_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v15_algstr_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( ( v15_algstr_0(D) & m1_group_2(D,A) ) => ( v15_algstr_0(k10_group_6(D,B,k1_grsolv_1(A,B,C,D))) & m1_group_6(k10_group_6(D,B,k1_grsolv_1(A,B,C,D)),B,k10_group_6(A,B,C)) ) ) ) ) ) )).
fof(t9_hahnban,axiom,( ! [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) ) => ! [B] : ( m1_rlsub_1(B,A) => ! [C] : ( m1_rlsub_1(C,A) => ! [D] : ( m1_rlsub_1(D,A) => ! [E] : ( m1_rlsub_1(E,D) => ! [F] : ( m1_rlsub_1(F,D) => ( ( E = B & F = C ) => k1_rlsub_2(D,E,F) = k1_rlsub_2(A,B,C) ) ) ) ) ) ) ) )).
fof(t9_hahnban1,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ( k3_complex1(k8_group_1(k1_complfld,A,B)) = k5_real_1(k4_real_1(k3_complex1(A),k3_complex1(B)),k4_real_1(k4_complex1(A),k4_complex1(B))) & k4_complex1(k8_group_1(k1_complfld,A,B)) = k3_real_1(k4_real_1(k3_complex1(A),k4_complex1(B)),k4_real_1(k3_complex1(B),k4_complex1(A))) ) ) ) )).
fof(t9_hallmar1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_finset_1(C) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ! [E] : ( m2_finseq_1(E,k1_zfmisc_1(C)) => ( r2_hidden(D,k4_finseq_1(E)) => k1_hallmar1(C,E,k2_xboole_0(k2_xboole_0(k1_tarski(D),A),B)) = k2_xboole_0(k1_funct_1(E,D),k1_hallmar1(C,E,k2_xboole_0(A,B))) ) ) ) ) )).
fof(t9_hausdorf,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & v4_pre_topc(B,k3_pcomps_1(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) <=> k1_funct_1(k6_weierstr(A,B),C) = k5_numbers ) ) ) ) )).
fof(t9_helly,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ~ ( ~ r1_tarski(A,B) & ~ r1_tarski(B,A) & k1_funct_1(A,k1_nat_1(k3_finseq_1(k1_helly(A,B)),1)) = k1_funct_1(B,k1_nat_1(k3_finseq_1(k1_helly(A,B)),1)) ) ) ) )).
fof(t9_henmodel,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k3_cqc_lang(A))) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ( r1_henmodel(A,B,C) <=> ~ v1_henmodel(k4_subset_1(k3_cqc_lang(A),B,k6_domain_1(k3_cqc_lang(A),k6_cqc_lang(A,C))),A) ) ) ) ) )).
fof(t9_hermitan,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_complfld)) => ( k3_complex1(k5_algstr_0(k1_complfld,A,B)) = k5_real_1(k3_complex1(A),k3_complex1(B)) & k4_complex1(k5_algstr_0(k1_complfld,A,B)) = k5_real_1(k4_complex1(A),k4_complex1(B)) ) ) ) )).
fof(t9_hessenbe,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_collsp(A,B,C,F) & r1_collsp(A,C,D,E) & r1_collsp(A,E,F,G) ) => ( r1_collsp(A,B,C,D) | F = B | F = C | E = C | E = D | ( B != G & D != G ) ) ) ) ) ) ) ) ) ) )).
fof(t9_heyting2,axiom,( ! [A] : ! [B] : ( v1_finset_1(B) => ! [C] : ( m2_subset_1(C,k5_finsub_1(k4_partfun1(A,B)),k1_substlat(A,B)) => k4_substlat(A,B,C,k2_heyting2(A,B,C)) = k1_xboole_0 ) ) )).
fof(t9_heyting3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( ( r1_tarski(A,B) & r1_tarski(C,D) ) => r1_tarski(k1_substlat(A,C),k1_substlat(B,D)) ) )).
fof(t9_hfdiff_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v3_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( r2_hidden(A,B) => k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k16_sin_cos,B),2),A) = k4_xcmplx_0(k1_funct_1(k16_sin_cos,A)) ) ) ) )).
fof(t9_hilbasis,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ( k1_recdef_1(k2_hilbasis(A,B),B) = 1 & ! [C] : ( m1_subset_1(C,A) => ( B != C => k1_recdef_1(k2_hilbasis(A,B),C) = k5_numbers ) ) ) ) ) )).
fof(t9_hilbert1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_hilbert1)) => r1_tarski(A,k5_hilbert1(A)) ) )).
fof(t9_hilbert2,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ~ ( ~ v1_hilbert2(A) & ~ v2_hilbert2(A) & ~ v3_hilbert2(A) & A != k2_hilbert1 ) ) )).
fof(t9_hilbert3,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ! [F] : ( k4_funct_4(A,B,C,D) = k4_funct_4(A,B,E,F) => ( A = B | ( C = E & D = F ) ) ) )).
fof(t9_holder_1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( ! [D] : ( v7_ordinal1(D) => r1_xxreal_0(k9_nat_1(k1_numbers,A,D),k3_real_1(k9_nat_1(k1_numbers,B,D),k9_nat_1(k1_numbers,C,D))) ) & v2_comseq_2(B) & v2_comseq_2(C) & v7_valued_0(A) ) => ( v2_comseq_2(A) & r1_xxreal_0(k1_seq_2(A),k2_xcmplx_0(k1_seq_2(B),k1_seq_2(C))) ) ) ) ) ) )).
fof(t9_homothet,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ( v7_aff_2(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r2_aff_1(A,B,C,D) & ~ r2_hidden(B,D) & ! [E] : ( ( 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_homothet(A,E,D) & k3_funct_2(u1_struct_0(A),u1_struct_0(A),E,B) = C ) ) ) ) ) ) ) ) )).
fof(t9_hurwitz,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k5_vfunct_1(k4_ordinal1,A,k9_polynom3(A)),k9_polynom3(A)) ) )).
fof(t9_idea_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k6_margrel1) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k6_margrel1) ) => ! [D] : ( ( v3_card_1(D,A) & m2_finseq_1(D,k6_margrel1) ) => k3_idea_1(A,k3_idea_1(A,B,C),D) = k3_idea_1(A,B,k3_idea_1(A,C,D)) ) ) ) ) )).
fof(t9_ideal_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v2_vectsp_1(A) & l6_algstr_0(A) ) => ( ~ v1_xboole_0(k6_domain_1(u1_struct_0(A),k4_struct_0(A))) & v1_ideal_1(k6_domain_1(u1_struct_0(A),k4_struct_0(A)),A) & v3_ideal_1(k6_domain_1(u1_struct_0(A),k4_struct_0(A)),A) & m1_subset_1(k6_domain_1(u1_struct_0(A),k4_struct_0(A)),k1_zfmisc_1(u1_struct_0(A))) ) ) )).
fof(t9_incproj,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_collsp(A) & v3_collsp(A) & v4_collsp(A) & l1_collsp(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(k3_incproj(A))) => ! [C] : ( m1_subset_1(C,u1_incsp_1(k3_incproj(A))) => ? [D] : ( m1_subset_1(D,u2_incsp_1(k3_incproj(A))) & r1_incsp_1(k3_incproj(A),B,D) & r1_incsp_1(k3_incproj(A),C,D) ) ) ) ) )).
fof(t9_incsp_1,axiom,( ! [A] : ( l2_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u4_incsp_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_incsp_1(A))) => ( ( r5_incsp_1(A,D,C) & r2_incsp_1(A,B,C) ) <=> r5_incsp_1(A,k4_subset_1(u1_incsp_1(A),D,k6_domain_1(u1_incsp_1(A),B)),C) ) ) ) ) ) )).
fof(t9_index_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( 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] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ~ v1_xboole_0(k2_cat_1(A,C,D)) => ! [E] : ( m1_cat_1(E,A,C,D) => m2_cat_1(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),k2_index_1(u1_struct_0(A),k1_xtuple_0(B),C),k2_index_1(u1_struct_0(A),k1_xtuple_0(B),D)) ) ) ) ) ) ) )).
fof(t9_instalg1,axiom,( ! [A] : ( l1_msualg_1(A) => ! [B] : ( l1_msualg_1(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) ) => ( r3_pua2mss1(A,B,C,D) => ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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,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)))) ) ) ) ) ) ) )).
fof(t9_int_1,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ( k3_xcmplx_0(A,B) = 1 <=> ( ( A = 1 & B = 1 ) | ( A = k4_xcmplx_0(1) & B = k4_xcmplx_0(1) ) ) ) ) ) )).
fof(t9_int_2,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ( ( r1_int_1(A,B) & r1_int_1(B,C) ) => r1_int_1(A,C) ) ) ) ) )).
fof(t9_int_3,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(A,k5_numbers) => ! [B] : ( m1_subset_1(B,k7_card_1(A)) => ( ( B = k5_numbers => k1_funct_1(k8_int_3(A),B) = k5_numbers ) & ( k1_funct_1(k8_int_3(A),B) = k5_numbers => B = k5_numbers ) & ( B != k5_numbers => k1_funct_1(k8_int_3(A),B) = k6_xcmplx_0(A,B) ) & ~ ( k1_funct_1(k8_int_3(A),B) = k6_xcmplx_0(A,B) & B = k5_numbers ) ) ) ) ) )).
fof(t9_int_4,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => ( ( r2_int_1(k3_xcmplx_0(A,D),k3_xcmplx_0(B,D),C) & r1_int_2(D,C) ) => r2_int_1(A,B,C) ) ) ) ) ) )).
fof(t9_int_5,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v7_ordinal1(B) => r1_int_5(k1_pepin(A),B) ) ) )).
fof(t9_int_6,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k4_numbers) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => ( k1_funct_1(A,B) = k5_numbers | v1_int_1(k7_xcmplx_0(k19_rvsum_1(A),k1_funct_1(A,B))) ) ) ) ) )).
fof(t9_int_7,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( ( v7_ordinal1(C) & ~ v8_ordinal1(C) ) => ( C = k2_int_2(A,B) => k22_pre_poly(k8_newton,k13_nat_3(C)) = k4_subset_1(k8_newton,k22_pre_poly(k8_newton,k13_nat_3(A)),k22_pre_poly(k8_newton,k13_nat_3(B))) ) ) ) ) )).
fof(t9_int_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_int_2(A,B) => ( r1_xxreal_0(B,1) | r1_nat_d(k3_pepin(A,B),k1_euler_1(B)) ) ) ) ) )).
fof(t9_integr10,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( v1_xreal_0(B) => ( ( r1_tarski(k2_limfunc1(B),k1_relset_1(k1_numbers,A)) & r3_integr10(A,B) ) => ! [C] : ( v1_xreal_0(C) => ( r3_integr10(k26_valued_1(k1_numbers,k1_numbers,A,C),B) & k3_integr10(k26_valued_1(k1_numbers,k1_numbers,A,C),B) = k3_xcmplx_0(C,k3_integr10(A,B)) ) ) ) ) ) )).
fof(t9_integr11,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ( A != k5_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(A,k5_numbers),k18_sin_cos),k7_xcmplx_0(1,k1_square_1(A))),k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,A),k5_numbers),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,k5_numbers),k16_sin_cos))),k1_numbers) & ! [B] : ( v1_xreal_0(B) => k1_funct_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(A,k5_numbers),k18_sin_cos),k7_xcmplx_0(1,k1_square_1(A))),k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(k7_xcmplx_0(1,A),k5_numbers),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_fcont_1(A,k5_numbers),k16_sin_cos))),k1_numbers),B) = k3_xcmplx_0(B,k1_funct_1(k18_sin_cos,k3_xcmplx_0(A,B))) ) ) ) ) )).
fof(t9_integr12,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( ( 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,k16_sin_cos,k22_sin_cos),k18_sin_cos)) ) => k2_integra5(A,B) = k6_xcmplx_0(k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k22_sin_cos),k2_seq_4(A)),k1_funct_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k22_sin_cos),k3_seq_4(A))) ) ) ) ) )).
fof(t9_integr13,axiom,( ! [A] : ( ( 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,k3_rfunct_1(k1_numbers,k1_numbers,k47_valued_1(k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k18_sin_cos),k22_sin_cos),k7_xcmplx_0(1,2)))) => ( r2_fdiff_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,k18_sin_cos),k22_sin_cos),k7_xcmplx_0(1,2)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_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,k18_sin_cos),k22_sin_cos),k7_xcmplx_0(1,2)),A),B) = k7_xcmplx_0(k1_funct_1(k18_sin_cos,B),k1_funct_1(k22_sin_cos,B)) ) ) ) ) ) )).
fof(t9_integr14,axiom,( ! [A] : ( ( 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(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k2_fdiff_9)),A) & ! [B] : ( v1_xreal_0(B) => ( r2_hidden(B,A) => k1_funct_1(k2_fdiff_1(k32_valued_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k16_sin_cos,k2_fdiff_9)),A),B) = k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k18_sin_cos,B),k1_funct_1(k18_sin_cos,k1_funct_1(k16_sin_cos,B))),k1_square_1(k1_funct_1(k16_sin_cos,k1_funct_1(k16_sin_cos,B)))) ) ) ) ) ) )).
fof(t9_integr15,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_integra1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) ) => ! [D] : ( m2_integr15(D,A,B,C) => ( ( v1_comseq_2(B) & v3_integra1(B,A) & v2_comseq_2(k2_integra3(A,C)) & k1_seq_2(k2_integra3(A,C)) = k5_numbers ) => ( v2_comseq_2(k3_integr15(A,B,C,D)) & k1_seq_2(k3_integr15(A,B,C,D)) = k12_integra1(A,B) ) ) ) ) ) ) )).
fof(t9_integr16,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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] : ( m1_integra1(C,A) => ! [D] : ( m1_integr16(D,A,B,C) => ! [E] : ( m1_integr15(E,A,k5_comseq_3(A,B),C) => ( E = k1_integr16(D) => k3_complex1(k3_integr16(A,B,C,D)) = k1_integr15(A,k5_comseq_3(A,B),C,E) ) ) ) ) ) ) )).
fof(t9_integr18,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [D] : ( ( 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)))) ) => ( ( r1_tarski(B,k1_relset_1(k1_numbers,C)) & k2_partfun1(k1_numbers,u1_struct_0(A),C,B) = D ) => k5_integr18(A,B,C) = k4_integr18(A,B,D) ) ) ) ) ) )).
fof(t9_integr19,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(A)))) ) => ( ( r1_xxreal_0(B,D) & r1_xxreal_0(D,E) & r1_xxreal_0(E,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)) ) => ( r1_integr15(A,k3_integra5(D,E),F) & v3_integr15(k2_partfun1(k1_numbers,k1_euclid(A),F,k3_integra5(D,E)),A) ) ) ) ) ) ) ) ) )).
fof(t9_integra1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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)) ) ) ) )).
fof(t9_integra2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ( ( v4_xxreal_2(B) & r1_xxreal_0(k5_numbers,A) ) => v4_xxreal_2(k1_integra2(B,A)) ) ) ) )).
fof(t9_integra3,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_integra1(B,A) => r1_xxreal_0(k5_numbers,k1_integra3(A,B)) ) ) )).
fof(t9_integra4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_integra1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_integra1(A)))) ) => ( ( v1_comseq_2(k2_partfun1(A,k1_numbers,B,A)) & v2_comseq_2(k2_integra3(A,C)) & k1_seq_2(k2_integra3(A,C)) = k5_numbers ) => ( v2_comseq_2(k3_integra2(A,B,C)) & k1_seq_2(k3_integra2(A,B,C)) = k10_integra1(A,B) ) ) ) ) ) )).
fof(t9_integra5,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,B,A)) => v1_comseq_2(k2_partfun1(A,k1_numbers,k1_integra5(B,A),A)) ) ) ) )).
fof(t9_integra6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_measure5(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ! [C] : ( ( 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)) & r1_integra5(B,C) & v1_comseq_2(k2_partfun1(k1_numbers,k1_numbers,C,B)) ) => ( r1_integra5(B,k26_valued_1(k1_numbers,k1_numbers,C,A)) & k2_integra5(B,k26_valued_1(k1_numbers,k1_numbers,C,A)) = k3_xcmplx_0(A,k2_integra5(B,C)) ) ) ) ) ) )).
fof(t9_integra7,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( ! [C] : ~ ( r2_hidden(C,A) & k1_funct_1(B,C) = k5_numbers ) & r2_fdiff_1(B,A) ) => r2_fdiff_1(k6_rfunct_1(k1_numbers,k1_numbers,B),A) ) ) )).
fof(t9_integra8,axiom,( r1_tarski(k1_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k3_square_1(2),2)),k7_xcmplx_0(k3_square_1(2),2)),k2_rcomp_1(k4_xcmplx_0(1),1)) )).
fof(t9_integra9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( 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,k1_partfun2(k1_numbers,B),k18_sin_cos)) = k6_xcmplx_0(k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k16_sin_cos),k18_sin_cos),k2_seq_4(A)),k1_funct_1(k3_valued_1(k1_numbers,k1_numbers,k1_numbers,k20_valued_1(k1_numbers,k1_numbers,k1_numbers,k1_partfun2(k1_numbers,B),k16_sin_cos),k18_sin_cos),k3_seq_4(A))) ) ) ) )).
fof(t9_interva1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => m1_interva1(k1_xboole_0,A) ) )).
fof(t9_intpro_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k1_intpro_1)) => ! [B] : ( m1_subset_1(B,k1_intpro_1) => r2_hidden(k3_intpro_1(k2_intpro_1,B),k7_intpro_1(A)) ) ) )).
fof(t9_isocat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( 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)) ) ) ) ) )).
fof(t9_isocat_2,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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(k6_cat_2(A,B),k7_cat_2(A,B,C,E),k7_cat_2(A,B,D,F)) != k1_xboole_0 ) ) ) ) ) ) ) )).
fof(t9_isomichi,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_isomichi(B,A) <=> r1_tarski(B,k2_pre_topc(A,k1_tops_1(A,B))) ) ) ) )).
fof(t9_jct_misc,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_rcomp_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_rcomp_1(B) & m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) => ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & r2_hidden(C,A) & r2_hidden(D,B) & k1_jct_misc(A,B) = k9_complex1(k6_xcmplx_0(C,D)) ) ) ) ) )).
fof(t9_jgraph_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ~ ( r1_xxreal_0(1,k3_finseq_1(B)) & ! [C] : ( m2_finseq_1(C,A) => ~ r1_jgraph_1(A,B,C) ) ) ) ) )).
fof(t9_jgraph_2,axiom,( ! [A] : ( m1_subset_1(A,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))) => ( k3_subset_1(u1_struct_0(k15_euclid(2)),A) != k1_xboole_0 & k6_subset_1(u1_struct_0(k15_euclid(2)),A) != k1_xboole_0 ) ) ) )).
fof(t9_jgraph_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,D) != k5_numbers ) & ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( 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,k3_square_1(k2_xcmplx_0(1,k1_square_1(k7_xcmplx_0(F,G))))) ) ) ) ) & v5_pre_topc(D,A,k3_topmetr) ) ) ) ) ) ) )).
fof(t9_jgraph_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( ( 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] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( v5_pre_topc(B,A,k3_topmetr) & v5_pre_topc(C,A,k3_topmetr) & E != k5_numbers & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),C,F) != k5_numbers ) & ! [F] : ( ( 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] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( v1_xreal_0(H) => ! [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) = k3_xcmplx_0(I,k4_xcmplx_0(k3_square_1(k9_complex1(k6_xcmplx_0(1,k1_square_1(k7_xcmplx_0(k6_xcmplx_0(k7_xcmplx_0(H,I),D),E))))))) ) ) ) ) & v5_pre_topc(F,A,k3_topmetr) ) ) ) ) ) ) ) ) )).
fof(t9_jgraph_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [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))))) ) => ( ( v3_tops_2(I,k4_topmetr(A,B),k4_topmetr(C,D)) & k1_funct_1(I,E) = G & k1_funct_1(I,F) = H & k1_funct_1(I,B) = C & r1_xxreal_0(C,D) & r1_xxreal_0(H,G) & r2_hidden(E,k1_rcomp_1(A,B)) & r2_hidden(F,k1_rcomp_1(A,B)) ) => r1_xxreal_0(E,F) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_jgraph_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(B))) => ! [D] : ( ( 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] : ( ( 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] : ( m1_subset_1(F,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),u1_struct_0(k15_euclid(B)),E,F) = k1_rlvect_1(k15_euclid(B),C,k3_funct_2(u1_struct_0(A),u1_struct_0(k3_topmetr),D,F)) ) & v5_pre_topc(E,A,k15_euclid(B)) ) ) ) ) ) ) ) )).
fof(t9_jgraph_7,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ( ( k18_euclid(A) = F & k18_euclid(B) = E & r1_xxreal_0(C,k17_euclid(A)) & r1_xxreal_0(k17_euclid(A),D) & 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) ) ) ) ) ) ) ) ) )).
fof(t9_jordan,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( r1_xxreal_0(k18_euclid(B),A) & r1_xxreal_0(A,k18_euclid(C)) & r1_xboole_0(k1_rltopsp1(k15_euclid(2),B,C),k7_jordan6(A)) ) ) ) ) )).
fof(t9_jordan1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( 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)) ) ) ) )).
fof(t9_jordan10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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(B,k3_goboard9(k2_jordan9(B,A))) ) ) )).
fof(t9_jordan11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_topreal2(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( r1_jordan1h(B,A) => r2_hidden(k4_tarski(k7_nat_d(k3_jordan1h(B,A),1),k5_jordan11(B,A)),k2_matrix_0(k1_jordan8(B,A))) ) ) ) )).
fof(t9_jordan12,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r2_jordan12(2,A,B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(A)) & r1_xxreal_0(1,D) & r1_xxreal_0(k1_nat_1(D,1),k3_finseq_1(B)) ) => v1_zfmisc_1(k9_subset_1(u1_struct_0(k15_euclid(2)),k2_topreal1(2,A,C),k2_topreal1(2,B,D))) ) ) ) ) ) ) )).
fof(t9_jordan14,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( v7_ordinal1(B) => ~ ( r1_jordan1h(A,B) & r1_xboole_0(A,k2_goboard9(k1_jordan13(A,B))) ) ) ) )).
fof(t9_jordan16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,A) ) => ! [D] : ( ( ~ v2_struct_0(D) & m1_pre_topc(D,B) ) => ! [E] : ( ( 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) => ! [F] : ( ( 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(C),u1_struct_0(D),u1_struct_0(C),u1_struct_0(B),F,k2_tmap_1(A,B,E,C)) & v2_funct_2(F,u1_struct_0(D)) ) => v3_tops_2(F,C,D) ) ) ) ) ) ) ) ) )).
fof(t9_jordan17,axiom,( ! [A] : ( ( v1_topreal2(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(B,A) => r1_jordan17(A,B,B,B,B) ) ) ) )).
fof(t9_jordan18,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => k2_seq_4(k7_relset_1(u1_struct_0(k15_euclid(2)),k1_numbers,k4_pscomp_1,k7_topreal1(A))) = k17_euclid(A) ) )).
fof(t9_jordan19,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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(k8_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))),k8_pscomp_1(B)) ) ) )).
fof(t9_jordan1b,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( r1_sprect_2(B,A) => r1_sprect_2(B,k1_finseq_6(u1_struct_0(k15_euclid(2)),A,C)) ) ) ) ) )).
fof(t9_jordan1c,axiom,( ! [A] : ( ( v2_compts_1(A,k15_euclid(2)) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ( k1_jordan2c(2,A) != k1_xboole_0 => r1_xxreal_0(k7_pscomp_1(k1_jordan2c(2,A)),k7_pscomp_1(A)) ) ) )).
fof(t9_jordan1d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( 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] : ( v7_ordinal1(C) & r1_xxreal_0(1,C) & ~ r1_xxreal_0(k3_finseq_1(k2_jordan9(B,A)),C) & r2_hidden(k23_pscomp_1(B),k2_gobrd13(k2_jordan9(B,A),k1_jordan8(B,A),C)) ) ) ) )).
fof(t9_jordan1e,axiom,( ! [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] : ( v7_ordinal1(B) => k3_finseq_1(k2_jordan1e(A,B)) = k2_xcmplx_0(k6_xcmplx_0(k3_finseq_1(k1_finseq_6(u1_struct_0(k15_euclid(2)),k2_jordan9(A,B),k18_pscomp_1(k3_topreal1(2,k2_jordan9(A,B))))),k4_finseq_4(k1_finseq_6(u1_struct_0(k15_euclid(2)),k2_jordan9(A,B),k18_pscomp_1(k3_topreal1(2,k2_jordan9(A,B)))),k22_pscomp_1(k3_topreal1(2,k2_jordan9(A,B))))),1) ) ) )).
fof(t9_jordan1f,axiom,( ! [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] : ( v7_ordinal1(B) => ( ( k3_topreal1(2,k1_jordan1e(A,B)) = k8_jordan6(k3_topreal1(2,k2_jordan9(A,B))) & k3_topreal1(2,k2_jordan1e(A,B)) = k9_jordan6(k3_topreal1(2,k2_jordan9(A,B))) ) | ( k3_topreal1(2,k1_jordan1e(A,B)) = k9_jordan6(k3_topreal1(2,k2_jordan9(A,B))) & k3_topreal1(2,k2_jordan1e(A,B)) = k8_jordan6(k3_topreal1(2,k2_jordan9(A,B))) ) ) ) ) )).
fof(t9_jordan1g,axiom,( ! [A] : ( ( ~ 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) != k20_pscomp_1(k3_topreal1(2,A)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k3_finseq_1(A)) != k20_pscomp_1(k3_topreal1(2,A)) ) | ( k7_partfun1(u1_struct_0(k15_euclid(2)),A,1) != k21_pscomp_1(k3_topreal1(2,A)) & k7_partfun1(u1_struct_0(k15_euclid(2)),A,k3_finseq_1(A)) != k21_pscomp_1(k3_topreal1(2,A)) ) ) & k20_pscomp_1(k3_topreal1(2,A)) = k21_pscomp_1(k3_topreal1(2,A)) ) ) )).
fof(t9_jordan1h,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( 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))) ) => k3_finseq_1(k7_pre_poly(A,B,C)) = k5_card_1(B) ) ) ) )).
fof(t9_jordan1i,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( ~ r1_xxreal_0(k6_pscomp_1(k3_topreal1(2,A)),k17_euclid(B)) => r2_hidden(B,k2_goboard9(A)) ) ) ) )).
fof(t9_jordan1j,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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)))) ) => ( r2_hidden(k22_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))),k10_xtuple_0(k1_jordan1e(B,A))) & r2_hidden(k22_pscomp_1(k3_topreal1(2,k2_jordan9(B,A))),k3_topreal1(2,k1_jordan1e(B,A))) ) ) ) )).
fof(t9_jordan1k,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k3_pcomps_1(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_pcomps_1(A))) => r1_xxreal_0(k5_numbers,k3_funct_2(u1_struct_0(k3_pcomps_1(A)),u1_struct_0(k3_topmetr),k6_weierstr(A,B),C)) ) ) ) )).
fof(t9_jordan20,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ! [E] : ( v1_xreal_0(E) => ~ ( r1_topreal1(k15_euclid(2),B,C,A) & ~ 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) & ~ r5_jordan20(A,B,C,D,E) ) ) ) ) ) ) )).
fof(t9_jordan22,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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)))) ) => ~ ( ~ r1_xxreal_0(B,A) & r1_xxreal_0(k1_topreal6(2,k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(C,A),1,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(C,A),1,2)),k1_topreal6(2,k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(C,B),1,1),k3_matrix_0(u1_struct_0(k15_euclid(2)),k1_jordan8(C,B),1,2))) ) ) ) ) )).
fof(t9_jordan23,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ( v2_jordan23(A) => v2_jordan23(k3_finseq_5(A)) ) ) )).
fof(t9_jordan24,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ( k3_subset_1(A,B) = k1_xboole_0 <=> B = A ) ) )).
fof(t9_jordan2b,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k18_rvsum_1(k5_euclid(A)) = k5_numbers ) )).
fof(t9_jordan2c,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [C] : ( 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)) ) ) ) ) )).
fof(t9_jordan3,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ( r2_hidden(B,k3_topreal1(2,A)) => r2_hidden(B,k2_topreal1(2,A,k1_jordan3(A,B))) ) ) ) )).
fof(t9_jordan4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_finseq_1(B,A) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,C) & r1_xxreal_0(C,k3_finseq_1(B)) ) => k3_finseq_1(k3_finseq_6(A,B,C,D)) = k1_nat_1(k7_nat_d(C,D),1) ) ) ) ) ) )).
fof(t9_jordan5a,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k2_topmetr(C,D))) => ( ( r1_xxreal_0(C,D) & E = A & r1_tarski(k2_rcomp_1(k6_xcmplx_0(A,B),k2_xcmplx_0(A,B)),k1_rcomp_1(C,D)) ) => k2_rcomp_1(k6_xcmplx_0(A,B),k2_xcmplx_0(A,B)) = k8_metric_1(k2_topmetr(C,D),E,B) ) ) ) ) ) ) )).
fof(t9_jordan5b,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( r2_hidden(C,k1_rltopsp1(k15_euclid(2),A,B)) => ( A = B | r2_jordan3(A,B,C,C) ) ) ) ) ) )).
fof(t9_jordan5c,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k15_euclid(2))) => ( r2_hidden(D,A) => r1_jordan5c(A,B,C,D,D) ) ) ) ) ) )).
fof(t9_jordan5d,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m2_finseq_1(A,u1_struct_0(k15_euclid(2))) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( 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_0(k2_goboard2(A))) & ! [D] : ( v7_ordinal1(D) => ~ ( r2_hidden(D,k4_finseq_1(A)) & r2_hidden(k4_tarski(B,C),k2_matrix_0(k2_goboard2(A))) & k17_euclid(k7_partfun1(u1_struct_0(k15_euclid(2)),A,D)) = k17_euclid(k3_matrix_0(u1_struct_0(k15_euclid(2)),k2_goboard2(A),B,C)) ) ) ) ) ) ) )).
fof(t9_jordan6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( B = a_1_5_jordan6(A) => v4_pre_topc(B,k15_euclid(2)) ) ) ) )).
fof(t9_jordan7,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ~ ( v1_topreal2(A) & B != k18_pscomp_1(A) & C != k18_pscomp_1(A) & r2_hidden(k18_pscomp_1(A),k1_jordan7(A,B,C)) ) ) ) ) )).
fof(t9_jordan8,axiom,( ! [A] : ( ( ~ 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) <=> r1_xxreal_0(k7_pscomp_1(A),k9_pscomp_1(A)) ) ) )).
fof(t9_jordan9,axiom,( ! [A] : ( ( ~ v3_relat_1(A) & v1_matrix_0(A) & v1_goboard1(A) & v2_goboard1(A) & v3_goboard1(A) & v4_goboard1(A) & m2_finseq_1(A,k3_finseq_2(u1_struct_0(k15_euclid(2)))) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(k15_euclid(2))) => ( r1_goboard1(u1_struct_0(k15_euclid(2)),B,A) => ! [C] : ( v7_ordinal1(C) => ( ( r1_xxreal_0(1,C) & r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(B)) ) => ( k1_tops_1(k15_euclid(2),k3_gobrd13(B,A,C)) != k1_xboole_0 & k1_tops_1(k15_euclid(2),k2_gobrd13(B,A,C)) != k1_xboole_0 ) ) ) ) ) ) )).
fof(t9_knaster,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,B,A) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,A))) ) => ? [E] : ? [F] : ? [G] : ? [H] : ( r1_xboole_0(E,F) & r1_xboole_0(G,H) & k2_xboole_0(E,F) = A & k2_xboole_0(G,H) = B & k7_relset_1(A,B,C,E) = G & k7_relset_1(B,A,D,H) = F ) ) ) ) ) )).
fof(t9_kolmog01,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(k1_zfmisc_1(A))) => ( ( ~ v1_xboole_0(D) & m1_subset_1(D,k1_zfmisc_1(B)) & v2_finsub_1(D) ) => ! [E] : ( ( ~ v1_xboole_0(E) & m1_subset_1(E,k1_zfmisc_1(B)) ) => ( ( v2_finsub_1(E) & r1_tarski(D,k1_kolmog01(A,B,E,C)) ) => ! [F] : ( m1_subset_1(F,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [G] : ( ( ~ v1_xboole_0(G) & m1_subset_1(G,k1_zfmisc_1(B)) ) => ( ( F = E & k9_prob_1(A,F) = G ) => r1_tarski(k9_prob_1(A,D),k1_kolmog01(A,B,G,C)) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_kurato_0,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k3_kurato_0(A,B) = k3_subset_1(A,k4_kurato_0(A,k2_prob_1(A,B))) ) )).
fof(t9_kurato_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_hidden(C,k5_kurato_1(A,B)) => ( r2_hidden(k1_tops_1(A,C),k5_kurato_1(A,B)) & r2_hidden(k2_pre_topc(A,C),k5_kurato_1(A,B)) ) ) ) ) ) )).
fof(t9_kurato_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,u1_struct_0(k14_euclid(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(A))) => ~ ( ~ r1_xboole_0(k8_metric_1(k14_euclid(A),D,B),k8_metric_1(k14_euclid(A),E,C)) & r1_xxreal_0(k2_xcmplx_0(B,C),k3_metric_1(k14_euclid(A),D,E)) ) ) ) ) ) ) )).
fof(t9_lang1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_lang1(A) ) => ! [B] : ( m2_finseq_2(B,u1_struct_0(A),k3_finseq_2(u1_struct_0(A))) => ( r2_hidden(B,k3_lang1(A)) <=> ( r1_tarski(k2_relset_1(u1_struct_0(A),B),k1_lang1(A)) & r3_lang1(A,k3_pre_poly(u1_struct_0(A),u2_lang1(A)),B) ) ) ) ) )).
fof(t9_latsubgr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_group_1(B) & v3_group_1(B) & l3_algstr_0(B) ) => ! [C] : ( ( 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] : ( m1_group_2(D,B) => ! [E] : ( m1_group_2(E,B) => ! [F] : ( m1_group_2(F,A) => ! [G] : ( m1_group_2(G,A) => ( ( u1_struct_0(F) = k8_relset_1(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(D)) & u1_struct_0(G) = k8_relset_1(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(E)) & m1_group_6(D,B,E) ) => m1_group_6(F,A,G) ) ) ) ) ) ) ) ) )).
fof(t9_latsum_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_latsum_1(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k1_latsum_1(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( C = E & D = F & r1_latsum_1(A,B) & v4_orders_2(B) ) => ( r1_orders_2(k1_latsum_1(A,B),C,D) <=> r1_orders_2(B,E,F) ) ) ) ) ) ) ) ) )).
fof(t9_lattice2,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [D] : ( m1_subset_1(D,k5_finsub_1(A)) => k9_xtuple_0(k2_partfun1(A,B,C,D)) = D ) ) ) )).
fof(t9_lattice3,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_orders_2(A,B,C) <=> r1_orders_2(k7_lattice3(A),k8_lattice3(A,C),k8_lattice3(A,B)) ) ) ) ) )).
fof(t9_lattice4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k1_lattice4(A,k2_setwiseo(u1_struct_0(A),B)) = B ) ) )).
fof(t9_lattice5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_lattice3(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_lattice3(A))) => k13_lattice3(k3_lattice3(A),B,C) = k3_lattices(A,k5_lattice3(A,B),k5_lattice3(A,C)) ) ) ) )).
fof(t9_lattice6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v4_lattice3(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r3_lattices(A,B,k3_lattice6(A,B)) & r3_lattices(A,k4_lattice6(A,B),B) ) ) ) )).
fof(t9_lattice7,axiom,( ! [A] : ( ( 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] : ( m1_subset_1(B,u1_struct_0(A)) => ~ ( B != k3_yellow_0(A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ r2_lattice7(A,C,B) ) ) ) ) )).
fof(t9_lattice8,axiom,( ! [A] : ( ( 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) ) ) )).
fof(t9_lattices,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v10_lattices(A) & v11_lattices(A) & l3_lattices(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t9_lexbfs,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) & v2_lexbfs(A) & v3_lexbfs(A) ) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(k39_glib_000(A),B) => k1_funct_1(A,k39_glib_000(A)) = k1_funct_1(A,B) ) ) ) )).
fof(t9_lfuzzy_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v5_relat_1(B,k1_rcomp_1(k5_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] : ( ( v5_relat_1(C,k1_rcomp_1(k5_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,k1_fuzzy_4(A,A,k1_lfuzzy_1(k2_zfmisc_1(A,A),B,C)),k1_lfuzzy_1(k2_zfmisc_1(A,A),B,C)) ) ) ) ) )).
fof(t9_limfunc1,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( v1_limfunc1(A) & v2_seq_2(B) ) => v1_limfunc1(k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,A,B)) ) ) ) )).
fof(t9_limfunc4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( ( v8_limfunc1(A) & v7_limfunc1(B) & ! [C] : ( v1_xreal_0(C) => ? [D] : ( v1_xreal_0(D) & ~ 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))) ) ) ) => v7_limfunc1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,A,B)) ) ) ) )).
fof(t9_lmod_5,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & ~ v6_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) & v1_vectsp_2(B) & l6_algstr_0(B) ) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) => ( r2_hidden(A,D) => r1_struct_0(k1_lmod_5(B,C,D),A) ) ) ) ) )).
fof(t9_lmod_6,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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) ) => ( r2_hidden(A,k2_struct_0(C)) <=> r1_struct_0(C,A) ) ) ) )).
fof(t9_lmod_7,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( r1_tarski(C,D) => ( C = k1_xboole_0 | ! [E] : ( m9_lmod_7(E,A,B,C) => m9_lmod_7(E,A,B,D) ) ) ) ) ) ) ) )).
fof(t9_lopban_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & 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] : ( m2_funct_2(C,A,u1_struct_0(B),k9_funct_2(A,u1_struct_0(B))) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => k1_binop_1(k2_lopban_1(A,B),k1_funct_1(k3_lopban_1(A,B),k4_tarski(D,C)),k1_funct_1(k3_lopban_1(A,B),k4_tarski(E,C))) = k1_funct_1(k3_lopban_1(A,B),k4_tarski(k2_xcmplx_0(D,E),C)) ) ) ) ) ) )).
fof(t9_lopban_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m2_subset_1(B,u1_struct_0(k8_lopban_1(A,A)),k10_lopban_1(A,A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(k8_lopban_1(A,A)),k10_lopban_1(A,A)) => ! [D] : ( m2_subset_1(D,u1_struct_0(k8_lopban_1(A,A)),k10_lopban_1(A,A)) => k3_lopban_2(A,k2_lopban_2(A,C,D),B) = k2_lopban_2(A,k3_lopban_2(A,C,B),k3_lopban_2(A,D,B)) ) ) ) ) )).
fof(t9_lopban_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( v7_ordinal1(D) => ( v3_normsp_1(B,A) => ( v3_normsp_1(k1_valued_0(u1_struct_0(A),B,D),A) & k6_normsp_1(A,k1_valued_0(u1_struct_0(A),B,D)) = k6_normsp_1(A,B) ) ) ) ) ) ) )).
fof(t9_lopban_4,axiom,( ! [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) & l1_lopban_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r2_funct_2(k4_ordinal1,u1_struct_0(A),k1_bhsp_4(A,k2_lopban_3(A,C,B)),k2_lopban_3(A,k1_bhsp_4(A,C),B)) & r2_funct_2(k4_ordinal1,u1_struct_0(A),k1_bhsp_4(A,k3_lopban_3(A,C,B)),k3_lopban_3(A,k1_bhsp_4(A,C),B)) ) ) ) ) )).
fof(t9_lopban_6,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k4_normsp_2(A)))) => ( B = D => k1_convex1(A,B,C) = k1_convex1(k4_normsp_2(A),D,C) ) ) ) ) ) )).
fof(t9_lopban_7,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( 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)))) ) => m1_rlsub_1(k5_lopban_7(A,B,C),k7_prvect_3(A,B)) ) ) ) )).
fof(t9_lopclset,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( ~ v2_struct_0(g3_lattices(k1_lopclset(A),k4_lopclset(A),k5_lopclset(A))) & v10_lattices(g3_lattices(k1_lopclset(A),k4_lopclset(A),k5_lopclset(A))) & l3_lattices(g3_lattices(k1_lopclset(A),k4_lopclset(A),k5_lopclset(A))) ) ) )).
fof(t9_lp_space,axiom,( ! [A] : ( v1_xreal_0(A) => ( r1_xxreal_0(1,A) => m1_rlsub_1(g1_normsp_1(k2_lp_space(A),k9_rsspace(k6_rsspace,k2_lp_space(A)),k7_rsspace(k6_rsspace,k2_lp_space(A)),k8_rsspace(k6_rsspace,k2_lp_space(A)),k3_lp_space(A)),k6_rsspace) ) ) )).
fof(t9_lpspacc1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => r3_binop_1(k3_rfunct_3(A,k2_numbers),k10_lpspacc1(A),k9_lpspacc1(A)) ) )).
fof(t9_lpspace1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_rfunct_3(C,B,k1_numbers,k3_rfunct_3(B,k1_numbers)) => ! [D] : ( m2_rfunct_3(D,B,k1_numbers,k3_rfunct_3(B,k1_numbers)) => ( D = k1_binop_1(k4_lpspace1(B),A,C) <=> ( k1_relset_1(B,D) = k1_relset_1(B,C) & ! [E] : ( m1_subset_1(E,B) => ( r2_hidden(E,k1_relset_1(B,C)) => k1_funct_1(D,E) = k3_xcmplx_0(A,k1_funct_1(C,E)) ) ) ) ) ) ) ) ) )).
fof(t9_lpspace2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v2_xxreal_0(C) & v1_xreal_0(C) ) => ( ! [D] : ( v7_ordinal1(D) => ( k9_nat_1(k1_numbers,A,D) = k2_power(k9_nat_1(k1_numbers,B,D),C) & r1_xxreal_0(k5_numbers,k9_nat_1(k1_numbers,B,D)) ) ) => ( v2_comseq_2(A) <=> v2_comseq_2(B) ) ) ) ) ) )).
fof(t9_ltlaxio1,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_zfmisc_1(k10_ltlaxio1)))) ) => k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(C),k1_domain_1(k4_ordinal1,k1_hilbert1,B,k2_ltlaxio1(A))) = k3_funct_2(k2_zfmisc_1(k4_ordinal1,k1_hilbert1),k6_margrel1,k11_ltlaxio1(C),k1_domain_1(k4_ordinal1,k1_hilbert1,k1_nat_1(B,1),A)) ) ) ) )).
fof(t9_ltlaxio2,axiom,( ! [A] : ( m2_finseq_1(A,k1_hilbert1) => ! [B] : ( v7_ordinal1(B) => ( r2_hidden(B,k4_finseq_1(A)) => k7_partfun1(k1_hilbert1,k5_ltlaxio2(A),B) = k2_ltlaxio1(k7_partfun1(k1_hilbert1,A,B)) ) ) ) )).
fof(t9_ltlaxio3,axiom,( ! [A] : ( m1_subset_1(A,k1_hilbert1) => ! [B] : ( m1_subset_1(B,k1_hilbert1) => ! [C] : ( m1_subset_1(C,k1_hilbert1) => ( r2_hidden(k4_hilbert1(B,C),k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,k1_ltlaxio1(A))) => r2_hidden(k4_hilbert1(B,C),k3_funct_2(k1_hilbert1,k9_setfam_1(k1_hilbert1),k4_ltlaxio3,A)) ) ) ) ) )).
fof(t9_ltlaxio4,axiom,( ! [A] : ( m1_subset_1(A,k2_zfmisc_1(k1_ltlaxio3(k1_hilbert1),k1_ltlaxio3(k1_hilbert1))) => r1_tarski(k10_ltlaxio3(A),k5_setfam_1(k1_hilbert1,k7_ltlaxio3(k10_ltlaxio3(A)))) ) )).
fof(t9_lukasi_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( m2_subset_1(D,k9_qc_lang1(A),k3_cqc_lang(A)) => r2_hidden(k8_cqc_lang(A,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)) ) ) ) ) )).
fof(t9_margrel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => k4_margrel1(A) = k1_xboole_0 ) )).
fof(t9_mathmorp,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(B,C) => ( r1_tarski(k3_mathmorp(A,B,D),k3_mathmorp(A,C,D)) & r1_tarski(k6_rusub_4(A,B,D),k6_rusub_4(A,C,D)) ) ) ) ) ) ) )).
fof(t9_matrix10,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_matrix_0(B) & v2_matrix_0(B,k1_numbers,A,A) & m2_finseq_1(B,k3_finseq_2(k1_numbers)) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,k1_numbers,A,A) & m2_finseq_1(C,k3_finseq_2(k1_numbers)) ) => ( r1_matrix10(k2_matrix10(A,C),B) => v1_matrix10(k4_matrix10(A,B,C)) ) ) ) ) )).
fof(t9_matrix11,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_matrix_2(C,k3_matrix_2(k1_nat_1(A,2))) => ! [D] : ( m1_matrix_2(D,k3_matrix_2(k1_nat_1(A,2))) => ! [E] : ( m1_matrix_2(E,k3_matrix_2(k1_nat_1(A,2))) => ! [F] : ( v7_ordinal1(F) => ! [G] : ( v7_ordinal1(G) => ( ( r2_funct_2(k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),E,k1_partfun1(k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),k2_finseq_1(k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))),D,C)) & v4_matrix_2(D,k2_matrix_2(k3_matrix_2(k1_nat_1(A,2)))) & k1_funct_1(D,F) = G ) => ( r1_xxreal_0(G,F) | ! [H] : ( m1_subset_1(H,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),H) != k3_funct_2(k2_sgraph1(k2_finseq_1(k1_nat_1(A,2))),u1_struct_0(B),k1_matrix11(A,B,E),H) & ~ r2_hidden(F,H) & ~ r2_hidden(G,H) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_matrix12,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [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] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(D),B,C) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(D))) ) => k1_matrix12(B,C,D,E,A,A) = E ) ) ) ) ) )).
fof(t9_matrix13,axiom,( ! [A] : ( v1_finset_1(A) => ! [B] : ( v7_ordinal1(B) => k1_card_1(a_2_0_matrix13(A,B)) = k4_newton(B,k5_card_1(A)) ) ) )).
fof(t9_matrix14,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m2_finseq_1(B,u1_struct_0(A)) => ! [C] : ( m2_finseq_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k3_finseq_1(B) = k3_finseq_1(C) => k13_fvsum_1(A,k9_fvsum_1(A,B,D),C) = k8_group_1(A,D,k13_fvsum_1(A,B,C)) ) ) ) ) ) )).
fof(t9_matrix15,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) => ! [C] : ( ( v1_finset_1(C) & v1_setfam_1(C) & m1_subset_1(C,k1_zfmisc_1(k4_ordinal1)) ) => ! [D] : ( ( v1_finset_1(D) & v1_setfam_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ! [E] : ( ( v1_finset_1(E) & v1_setfam_1(E) & m1_subset_1(E,k1_zfmisc_1(k4_ordinal1)) ) => ! [F] : ( ( v1_finset_1(F) & v1_setfam_1(F) & m1_subset_1(F,k1_zfmisc_1(k4_ordinal1)) ) => ( ( r1_tarski(k2_zfmisc_1(C,D),k2_matrix_0(B)) & r1_tarski(k2_zfmisc_1(E,F),k2_matrix_0(B)) ) => ! [G] : ( ( v1_matrix_0(G) & v2_matrix_0(G,A,k5_card_1(C),k5_card_1(D)) & m2_finseq_1(G,k3_finseq_2(A)) ) => ! [H] : ( ( v1_matrix_0(H) & v2_matrix_0(H,A,k5_card_1(E),k5_card_1(F)) & m2_finseq_1(H,k3_finseq_2(A)) ) => ~ ( ! [I] : ( v7_ordinal1(I) => ! [J] : ( v7_ordinal1(J) => ! [K] : ( v7_ordinal1(K) => ! [L] : ( v7_ordinal1(L) => ! [M] : ( v7_ordinal1(M) => ! [N] : ( v7_ordinal1(N) => ( ( r2_hidden(k4_tarski(I,J),k3_xboole_0(k2_zfmisc_1(C,D),k2_zfmisc_1(E,F))) & K = k1_funct_1(k2_funct_1(k5_matrix13(C)),I) & L = k1_funct_1(k2_funct_1(k5_matrix13(D)),J) & M = k1_funct_1(k2_funct_1(k5_matrix13(E)),I) & N = k1_funct_1(k2_funct_1(k5_matrix13(F)),J) ) => k3_matrix_0(A,G,K,L) = k3_matrix_0(A,H,M,N) ) ) ) ) ) ) ) & ! [I] : ( ( v1_matrix_0(I) & v2_matrix_0(I,A,k3_finseq_1(B),k1_matrix_0(B)) & m2_finseq_1(I,k3_finseq_2(A)) ) => ~ ( k6_matrix13(A,I,C,D) = G & k6_matrix13(A,I,E,F) = H & ! [J] : ( v7_ordinal1(J) => ! [K] : ( v7_ordinal1(K) => ( r2_hidden(k4_tarski(J,K),k6_subset_1(k2_matrix_0(I),k2_xboole_0(k2_zfmisc_1(C,D),k2_zfmisc_1(E,F)))) => k3_matrix_0(A,I,J,K) = k3_matrix_0(A,B,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_matrix16,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( ( v1_matrix_0(E) & v2_matrix_0(E,u1_struct_0(B),A,A) & m2_finseq_1(E,k3_finseq_2(u1_struct_0(B))) ) => ! [F] : ( ( v1_matrix_0(F) & v2_matrix_0(F,u1_struct_0(B),A,A) & m2_finseq_1(F,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix16(E,u1_struct_0(B)) & v1_matrix16(F,u1_struct_0(B)) ) => v1_matrix16(k3_matrix_3(B,k2_matrix13(A,A,B,E,C),k2_matrix13(A,A,B,F,D)),u1_struct_0(B)) ) ) ) ) ) ) ) )).
fof(t9_matrix17,axiom,( ! [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] : ( m2_finseq_1(B,u1_struct_0(A)) => ( v5_matrix17(B,u1_struct_0(A)) => k1_matrix17(u1_struct_0(A),k5_fvsum_1(A,B)) = k2_matrix_3(A,k1_matrix17(u1_struct_0(A),B)) ) ) ) )).
fof(t9_matrix_0,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(A)) ) <=> ? [C] : ( v7_ordinal1(C) & ! [D] : ~ ( r2_hidden(D,k10_xtuple_0(B)) & ! [E] : ( m2_finseq_1(E,A) => ~ ( D = E & k3_finseq_1(E) = C ) ) ) ) ) ) ) )).
fof(t9_matrix_2,axiom,( ! [A] : ( v7_ordinal1(A) => k1_finseq_2(A) = k1_group_1(k4_matrix_2(A)) ) )).
fof(t9_matrix_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ( ( r2_hidden(k4_tarski(C,D),k2_matrix_0(k3_matrix_1(B,A))) & C = D ) => k1_funct_1(k8_matrix_0(u1_struct_0(B),k3_matrix_1(B,A),D),C) = k5_struct_0(B) ) ) ) ) ) )).
fof(t9_matrix_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [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) ) => k2_matrix_3(C,k1_matrix_3(C,A,B)) = k1_matrix_3(C,A,B) ) ) ) )).
fof(t9_matrix_5,axiom,( ! [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] : ( ( v1_matrix_0(B) & m2_finseq_1(B,k3_finseq_2(u1_struct_0(A))) ) => k6_matrix_3(A,B,k1_group_1(A)) = B ) ) )).
fof(t9_matrix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & 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_6(A,B,k1_matrix_6(A,B,k3_matrix_1(B,A))) = k3_matrix_1(B,A) ) ) )).
fof(t9_matrix_7,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_matrix_2(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_matrix_2(A))) => ! [D] : ( m1_matrix_2(D,k3_matrix_2(A)) => ! [E] : ( m1_matrix_2(E,k3_matrix_2(A)) => ( ( B = D & C = E ) => k6_algstr_0(k4_matrix_2(A),B,C) = k1_partfun1(k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),k2_finseq_1(k2_matrix_2(k3_matrix_2(A))),D,E) ) ) ) ) ) ) )).
fof(t9_matrix_8,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v6_struct_0(B) & v13_algstr_0(B) & v33_algstr_0(B) & v3_group_1(B) & v5_group_1(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v4_vectsp_1(B) & v5_vectsp_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( v1_matrix_0(C) & v2_matrix_0(C,u1_struct_0(B),A,A) & m2_finseq_1(C,k3_finseq_2(u1_struct_0(B))) ) => ( ( v1_matrix_6(C,A,B) & v1_matrix_8(C,A,B) ) => v1_matrix_8(k1_matrix_6(A,B,C),A,B) ) ) ) ) )).
fof(t9_matrix_9,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_matrix_2(F,k3_matrix_2(2)) => ( F = k1_finseq_2(2) => k10_matrix_3(2,A,k15_matrix_0(u1_struct_0(A),B,C,D,E),F) = k2_finseq_4(u1_struct_0(A),B,E) ) ) ) ) ) ) ) )).
fof(t9_matrixc1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_matrix_0(C) & m2_finseq_1(C,k3_finseq_2(k2_numbers)) ) => ( r2_hidden(k4_tarski(A,B),k2_matrix_0(C)) => k3_matrix_0(k2_numbers,k4_matrix_5(C),A,B) = k4_xcmplx_0(k3_matrix_0(k2_numbers,C,A,B)) ) ) ) ) )).
fof(t9_matrixj1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( r2_hidden(A,k7_subset_1(k4_ordinal1,k2_finseq_1(k1_nat_1(k2_wsierp_1(B),k2_wsierp_1(C))),k2_finseq_1(k2_wsierp_1(B)))) => ( k1_matrixj1(k8_finseq_1(k4_ordinal1,B,C),A) = k1_nat_1(k1_matrixj1(C,k7_nat_d(A,k2_wsierp_1(B))),k3_finseq_1(B)) & k7_nat_d(A,k2_wsierp_1(B)) = k6_xcmplx_0(A,k2_wsierp_1(B)) ) ) ) ) ) )).
fof(t9_matrixj2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => k5_matrlin2(A,A,B,k2_matrixj2(B,D,A),k2_matrix13(A,A,B,k3_matrix_1(B,A),C)) = k2_matrixj2(B,k3_rlvect_1(B,D,C),A) ) ) ) ) )).
fof(t9_matrixr1,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( k3_finseq_1(A) = k3_finseq_1(B) => k6_rvsum_1(k8_rvsum_1(A,B)) = k4_rvsum_1(k6_rvsum_1(A),B) ) ) ) )).
fof(t9_matrixr2,axiom,( ! [A] : ( ( v1_matrix_0(A) & m2_finseq_1(A,k3_finseq_2(k1_numbers)) ) => k7_matrixr1(k4_xcmplx_0(1),A) = k4_matrixr1(A) ) )).
fof(t9_matrlin,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(A)) => ( ( k3_finseq_1(D) = k3_finseq_1(E) & ! [F] : ( v7_ordinal1(F) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r2_hidden(F,k9_xtuple_0(D)) & G = k1_funct_1(E,F) ) => k1_funct_1(D,F) = k4_vectsp_1(A,B,G,C) ) ) ) ) => k4_rlvect_1(B,D) = k4_vectsp_1(A,B,k4_rlvect_1(A,E),C) ) ) ) ) ) ) )).
fof(t9_matrlin2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( m2_finseq_1(C,u1_struct_0(B)) => ! [D] : ( m2_finseq_1(D,u1_struct_0(B)) => ! [E] : ( m2_finseq_1(E,u1_struct_0(A)) => ! [F] : ( m2_finseq_1(F,u1_struct_0(A)) => ( ( k3_finseq_1(E) = k3_finseq_1(C) & k3_finseq_1(F) = k3_finseq_1(D) ) => k5_matrlin(A,B,k8_finseq_1(u1_struct_0(A),E,F),k8_finseq_1(u1_struct_0(B),C,D)) = k8_finseq_1(u1_struct_0(B),k5_matrlin(A,B,E,C),k5_matrlin(A,B,F,D)) ) ) ) ) ) ) ) )).
fof(t9_matrprob,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ! [D] : ( m2_finseq_1(D,C) => ! [E] : ( m2_finseq_1(E,C) => ? [F] : ( m2_finseq_1(F,k3_finseq_2(C)) & k3_finseq_1(F) = B & ! [G] : ( v7_ordinal1(G) => ( r2_hidden(G,k2_finseq_1(B)) => ( ( r2_hidden(G,k2_finseq_1(A)) => k1_matrprob(C,F,G) = D ) & ( ~ r2_hidden(G,k2_finseq_1(A)) => k1_matrprob(C,F,G) = E ) ) ) ) ) ) ) ) ) )).
fof(t9_matrtop1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v2_finseq_1(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v2_finseq_1(C) ) => ! [D] : ( ( 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) & ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k4_finseq_1(k15_finseq_1(k5_relat_1(C,k8_relat_1(D,A)))),k4_finseq_1(k15_finseq_1(k5_relat_1(C,k8_relat_1(D,A))))) & v3_funct_2(E,k4_finseq_1(k15_finseq_1(k5_relat_1(C,k8_relat_1(D,A)))),k4_finseq_1(k15_finseq_1(k5_relat_1(C,k8_relat_1(D,A))))) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k4_finseq_1(k15_finseq_1(k5_relat_1(C,k8_relat_1(D,A)))),k4_finseq_1(k15_finseq_1(k5_relat_1(C,k8_relat_1(D,A))))))) ) => k15_finseq_1(k5_relat_1(B,A)) != k3_relat_1(E,k15_finseq_1(k5_relat_1(C,k8_relat_1(D,A)))) ) ) ) ) ) )).
fof(t9_matrtop2,axiom,( ! [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] : ( ( ~ 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] : ( ( v1_vectsp_7(C,A,B) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( m1_vectsp_6(D,A,B) => ! [E] : ( m1_vectsp_6(E,A,B) => ( ( r1_tarski(k1_vectsp_6(A,B,D),C) & r1_tarski(k1_vectsp_6(A,B,E),C) & k4_vectsp_6(A,B,D) = k4_vectsp_6(A,B,E) ) => r1_vectsp_6(A,B,D,E) ) ) ) ) ) ) )).
fof(t9_matrtop3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(B))) => ( r2_hidden(A,k2_finseq_1(B)) => k1_funct_1(k3_funct_2(u1_struct_0(k15_euclid(B)),u1_struct_0(k15_euclid(B)),k3_matrtop1(B,B,k1_matrtop3(B,A)),C),A) = k4_xcmplx_0(k1_funct_1(C,A)) ) ) ) ) )).
fof(t9_mazurulm,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_normsp_1(A,k8_funcop_1(u1_struct_0(A),k4_ordinal1,B)) = B ) ) )).
fof(t9_mboolean,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => r6_pboole(A,k1_mboolean(A,k3_pboole(A,B,C)),k3_pboole(A,k1_mboolean(A,B),k1_mboolean(A,C))) ) ) )).
fof(t9_mcart_1,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( r2_hidden(C,k2_zfmisc_1(k2_tarski(A,B),D)) => ( ( k1_xtuple_0(C) = A | k1_xtuple_0(C) = B ) & r2_hidden(k2_xtuple_0(C),D) ) ) )).
fof(t9_measure1,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( 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,k2_finsub_1(B,E,D)) = k4_supinf_2(k12_supinf_2(C,E),k12_supinf_2(C,D)) ) ) ) ) ) ) )).
fof(t9_measure2,axiom,( ! [A] : ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) ) => ? [D] : ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,B))) & k9_nat_1(B,D,k5_numbers) = k1_xboole_0 & ! [E] : ( m1_subset_1(E,k4_ordinal1) => k9_nat_1(B,D,k1_nat_1(E,1)) = k3_measure1(A,B,k9_nat_1(B,C,k5_numbers),k9_nat_1(B,C,E)) ) ) ) ) )).
fof(t9_measure4,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ( m1_measure4(D,C) => ( ( r2_hidden(A,k1_measure4(C,D)) & r2_hidden(B,k1_measure4(C,D)) ) => r2_hidden(k3_xboole_0(A,B),k1_measure4(C,D)) ) ) )).
fof(t9_measure5,axiom,( ! [A] : ( ( v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( m1_subset_1(B,k6_numbers) => ! [C] : ( m1_subset_1(C,k6_numbers) => ( ( B = k2_supinf_1 & C = k1_supinf_1 ) => ( ( A != k1_measure5(B,C) & A != k1_xxreal_1(B,C) & A != k2_xxreal_1(B,C) & A != k3_xxreal_1(B,C) ) | k2_measure5(A) = k1_supinf_1 ) ) ) ) ) )).
fof(t9_measure6,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xxreal_0(B) => ( ? [C] : ( v1_xxreal_0(C) & r1_xxreal_0(B,C) & A = k3_xxreal_1(B,C) ) => B = k7_supinf_2(A) ) ) ) )).
fof(t9_measure8,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & v1_funct_2(C,B,k6_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,k6_numbers))) ) => ! [D] : ( r2_hidden(D,B) => r1_xxreal_0(k1_mesfunc9(k6_measure8(A,B,C),D),k1_mesfunc9(C,D)) ) ) ) )).
fof(t9_member_1,axiom,( ! [A] : ( v1_xxreal_0(A) => k4_member_1(k1_tarski(A)) = k1_tarski(k2_xxreal_3(A)) ) )).
fof(t9_membered,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_membered(A) ) => ? [B] : ( v1_xreal_0(B) & r2_hidden(B,A) ) ) )).
fof(t9_memstr_0,axiom,( ! [A] : ( ~ v1_setfam_1(A) => ! [B] : ( ( ~ v2_struct_0(B) & v2_memstr_0(B,A) & v3_memstr_0(B,A) & l1_memstr_0(B,A) ) => ! [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_partfun1(C,u1_struct_0(B)) ) => k9_xtuple_0(k6_memstr_0(A,B,C)) = k8_struct_0(B) ) ) ) )).
fof(t9_menelaus,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( r1_euclid_6(A,B,C) <=> k1_euclid_6(A,B,C) = k5_numbers ) ) ) ) )).
fof(t9_mesfun10,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( m1_subset_1(B,k6_numbers) => ( r2_hidden(B,k1_numbers) => k7_supinf_2(k5_supinf_2(k6_domain_1(k6_numbers,B),A)) = k3_supinf_2(k7_supinf_2(k6_domain_1(k6_numbers,B)),k7_supinf_2(A)) ) ) ) )).
fof(t9_mesfun6c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k2_numbers))) ) => ! [D] : ( m2_subset_1(D,k1_zfmisc_1(A),B) => ! [E] : ( m2_subset_1(E,k1_zfmisc_1(A),B) => ( ( r1_tarski(E,D) & r1_mesfun6c(A,B,C,D) ) => r1_mesfun6c(A,B,C,E) ) ) ) ) ) ) )).
fof(t9_mesfun7c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & v1_mesfunc8(B,A,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [C] : ( v7_ordinal1(C) => r2_relset_1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,k4_mesfun7c(A,B),C),k2_mesfun7c(A,k8_nat_1(k4_partfun1(A,k1_numbers),B,C))) ) ) ) )).
fof(t9_mesfun9c,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => v2_mesfunc9(k1_mesfun7c(A,B),A) ) ) )).
fof(t9_mesfunc1,axiom,( ! [A] : ( v1_xreal_0(A) => ? [B] : ( m1_subset_1(B,k4_ordinal1) & r1_xxreal_0(k4_xcmplx_0(B),A) ) ) )).
fof(t9_mesfunc2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => r2_relset_1(A,k6_numbers,k7_mesfunc1(A,B),k6_mesfunc1(A,B,k4_xcmplx_0(1))) ) ) )).
fof(t9_mesfunc5,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k6_numbers))) ) => ( ! [C] : ( r2_hidden(C,k1_relset_1(A,B)) => r1_xxreal_0(k12_supinf_2(B,C),k1_supinf_2) ) => v2_mesfunc5(B) ) ) )).
fof(t9_mesfunc6,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ! [C] : ( ( ~ 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] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,C) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,C))) ) => ! [E] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [F] : ( v1_xreal_0(F) => ( ! [G] : ( v7_ordinal1(G) => k1_funct_1(D,G) = k3_xboole_0(B,k11_mesfunc1(E,k2_xcmplx_0(F,k2_extreal1(1,k1_nat_1(G,1))))) ) => k3_xboole_0(B,k12_mesfunc1(E,F)) = k6_setfam_1(A,k4_measure1(A,C,D)) ) ) ) ) ) ) )).
fof(t9_mesfunc7,axiom,( ! [A] : ( m1_subset_1(A,k6_numbers) => k4_mesfunc7(A,1) = A ) )).
fof(t9_mesfunc8,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k4_partfun1(A,k6_numbers)) & v1_mesfunc8(B,A,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k6_numbers)))) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => r2_relset_1(A,k6_numbers,k4_mesfunc5(A,k6_numbers,k4_mesfunc8(A,B),C),k2_mesfunc8(A,k8_nat_1(k4_partfun1(A,k6_numbers),B,C))) ) ) ) )).
fof(t9_mesfunc9,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( v1_xxreal_0(B) => ( ( v10_mesfunc5(A) & ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k12_supinf_2(A,C),B) ) ) => r1_xxreal_0(k2_mesfunc5(A),B) ) ) ) )).
fof(t9_metric_1,axiom,( ! [A] : ( m1_subset_1(A,k1_numbers) => ! [B] : ( m1_subset_1(B,k1_numbers) => k5_binop_1(k1_numbers,k6_metric_1,A,B) = k5_binop_1(k1_numbers,k6_metric_1,B,A) ) ) )).
fof(t9_metric_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v6_metric_1(A) & v8_metric_1(A) & v9_metric_1(A) & l1_metric_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ~ r1_xboole_0(k1_metric_2(A,B),k1_metric_2(A,C)) <=> r3_metric_2(A,B,C) ) ) ) ) )).
fof(t9_metric_3,axiom,( ! [A] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( m1_subset_1(E,k4_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),u1_struct_0(D))) => ! [F] : ( m1_subset_1(F,k4_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),u1_struct_0(D))) => ! [G] : ( m1_subset_1(G,k4_zfmisc_1(u1_struct_0(A),u1_struct_0(B),u1_struct_0(C),u1_struct_0(D))) => r1_xxreal_0(k2_binop_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,k7_metric_3(A,B,C,D),E,G),k3_real_1(k2_binop_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,k7_metric_3(A,B,C,D),E,F),k2_binop_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,k7_metric_3(A,B,C,D),F,G))) ) ) ) ) ) ) ) )).
fof(t9_metric_6,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ( r1_metric_6(A,C,B) => v2_tbsp_1(C,A) ) ) ) ) )).
fof(t9_metrizts,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k1_pre_topc(A,B)))) => ( D = C => k1_pre_topc(k1_pre_topc(A,B),D) = k1_pre_topc(A,C) ) ) ) ) ) )).
fof(t9_mfold_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ! [D] : ( ( v1_xreal_0(D) & v2_xxreal_0(D) ) => ! [E] : ( ( v1_xreal_0(E) & v2_xxreal_0(E) ) => r2_borsuk_3(k1_mfold_1(A,B,D),k1_mfold_1(A,C,E)) ) ) ) ) ) )).
fof(t9_mfold_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ( ( v5_waybel23(A) & r1_mfold_2(A,B) ) => v5_waybel23(B) ) ) ) )).
fof(t9_midsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_midsp_1(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( k3_midsp_1(A,B,C) = k3_midsp_1(A,B,D) => C = D ) ) ) ) ) )).
fof(t9_midsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_midsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( ( ~ v2_struct_0(D) & v13_algstr_0(D) & v3_rlvect_1(D) & v4_rlvect_1(D) & l2_algstr_0(D) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(D)) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(D)))) ) => ~ ( r1_midsp_2(u1_struct_0(A),D,E) & v1_midsp_2(E,A,D) & ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => k1_midsp_1(A,F,B) != C ) ) ) ) ) ) ) )).
fof(t9_midsp_3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( ~ v2_struct_0(B) & v2_midsp_1(B) & l1_midsp_3(B,k1_nat_1(A,2)) ) => ! [C] : ( m2_finseq_2(C,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(B))) => ! [D] : ( m2_finseq_2(D,u1_struct_0(B),k4_finseq_2(k1_nat_1(A,1),u1_struct_0(B))) => ( ! [E] : ( m1_midsp_3(E,A) => k1_funct_1(C,E) = k1_funct_1(D,E) ) => C = D ) ) ) ) ) )).
fof(t9_mmlquer2,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( v1_relat_1(B) => ! [C] : ! [D] : ( r1_mmlquery(C,D,k1_mmlquer2(A,B)) <=> ( r1_mmlquery(C,D,A) | ( ~ r1_mmlquery(D,C,A) & r1_mmlquery(C,D,B) ) ) ) ) ) )).
fof(t9_mmlquery,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,A))) => k14_mmlquery(A,B,C,k5_numbers) = k4_mmlquery(A,C,B) ) ) )).
fof(t9_mod_2,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( v3_mod_2(B,A) & l1_mod_2(B,A) ) => ? [C] : ( ~ 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] : ( ~ 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(B,A,C,D) ) ) ) ) )).
fof(t9_mod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( 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_mod_3(A,B,C) = B ) ) ) ) ) )).
fof(t9_mod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_vectsp_2(B,A) ) => ( g2_algstr_0(u1_struct_0(k5_mod_4(A,B)),u1_algstr_0(k5_mod_4(A,B)),u2_struct_0(k5_mod_4(A,B))) = g2_algstr_0(u1_struct_0(B),u1_algstr_0(B),u2_struct_0(B)) & ! [C] : ( m1_subset_1(C,u1_struct_0(B)) <=> m1_subset_1(C,u1_struct_0(k5_mod_4(A,B))) ) ) ) ) )).
fof(t9_modal_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( m2_finseq_1(C,k4_ordinal1) => ( r2_hidden(C,A) => ! [D] : ( m1_trees_1(D,k5_trees_1(A,C,B)) => ! [E] : ( 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) ) ) ) ) ) ) ) ) )).
fof(t9_modcat_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_modcat_1(B,A) => ! [C] : ( m4_modcat_1(C,A,k4_modcat_1(A,B)) => ! [D] : ( m4_modcat_1(D,A,k4_modcat_1(A,B)) => ( k5_modcat_1(A,B,C) = k6_modcat_1(A,B,D) => r2_hidden(k8_mod_2(A,C,D),k4_modcat_1(A,B)) ) ) ) ) ) )).
fof(t9_modelc_1,axiom,( ! [A] : ( ( v1_modelc_1(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_1(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v2_struct_0(C) & v10_modelc_1(C) & l2_modelc_1(C) ) => ! [D] : ( ( 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,k11_modelc_1(A,B)) = k27_modelc_1(C,k24_modelc_1(C,D,A),k24_modelc_1(C,D,B)) ) ) ) ) )).
fof(t9_modelc_2,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ( v8_modelc_2(A) => A = k8_modelc_2(k11_modelc_2(A),k12_modelc_2(A)) ) ) )).
fof(t9_modelc_3,axiom,( ! [A] : ( ( v1_modelc_2(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ( v1_modelc_2(B) & m2_finseq_1(B,k4_ordinal1) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k13_modelc_2(B))) => ( ~ r2_hidden(A,C) => k18_modelc_3(B,k7_subset_1(k13_modelc_2(B),C,k1_tarski(A))) = k18_modelc_3(B,C) ) ) ) ) )).
fof(t9_moebius1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v7_ordinal1(C) & v1_int_2(C) ) => ( r1_xxreal_0(A,k11_nat_3(B,C)) => ( B = k5_numbers | r1_nat_d(k1_newton(C,A),B) ) ) ) ) ) )).
fof(t9_monoid_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ( v12_monoid_0(A) <=> ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & k6_algstr_0(A,B,D) = C ) ) ) ) ) )).
fof(t9_monoid_1,axiom,( ! [A] : ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( 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))) ) => ( r3_binop_1(B,C,D) => r3_binop_1(k9_funct_2(A,B),k5_monoid_1(B,A,C),k8_monoid_1(B,B,B,D,A)) ) ) ) ) )).
fof(t9_morph_01,axiom,( ! [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) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( k6_rusub_4(A,k6_subset_1(u1_struct_0(A),B),C) = k6_subset_1(u1_struct_0(A),k1_morph_01(A,B,C)) & k1_morph_01(A,k6_subset_1(u1_struct_0(A),B),C) = k6_subset_1(u1_struct_0(A),k6_rusub_4(A,B,C)) ) ) ) ) )).
fof(t9_msafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u4_struct_0(A)) => ! [D] : ( m1_trees_4(D,k5_trees_3(u1_struct_0(k5_msafree(A,B))),k4_dtconstr(k5_msafree(A,B))) => ( 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)) <=> ( k4_finseq_1(D) = k4_finseq_1(k1_msualg_1(A,C)) & ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k4_finseq_1(D)) => r2_hidden(k1_funct_1(D,E),k7_msafree(A,B,k7_partfun1(u1_struct_0(A),k1_msualg_1(A,C),E))) ) ) ) ) ) ) ) ) )).
fof(t9_msafree2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_funct_1(u3_msualg_1(A,k5_msafree2(A,B)),C)) => ~ ( r2_hidden(C,k2_msafree2(A)) & ! [E] : ( m1_subset_1(E,k1_funct_1(u3_msualg_1(A,B),C)) => D != k1_trees_4(k4_tarski(E,C)) ) ) ) ) ) ) )).
fof(t9_msafree3,axiom,( ! [A] : ( l1_msualg_1(A) => ! [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] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) ) => ! [D] : ( m3_pboole(D,u1_struct_0(A),B) => ( r6_pboole(u1_struct_0(A),D,k3_msafree3(A,B,C)) <=> ! [E] : ( r2_hidden(E,u1_struct_0(A)) => k1_funct_1(D,E) = k3_xboole_0(k1_funct_1(B,E),a_2_0_msafree3(C,E)) ) ) ) ) ) ) )).
fof(t9_msafree4,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v3_trees_3(A) ) => r1_tarski(A,k9_trees_9(A)) ) )).
fof(t9_msaterm,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( l3_msualg_1(C,A) => ! [D] : ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,k1_funct_1(B,E)) => ( k1_funct_1(D,k1_xboole_0) = k4_tarski(F,E) => D = k1_trees_4(k4_tarski(F,E)) ) ) ) ) ) ) ) )).
fof(t9_msscyc_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_graph_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v7_graph_1(B,A) & m1_graph_1(B,A) ) => k3_finseq_1(k7_graph_2(A,B)) = k1_nat_1(k3_finseq_1(B),1) ) ) )).
fof(t9_mssubfam,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( B = k1_tarski(C) => k8_setfam_1(A,B) = C ) ) ) )).
fof(t9_mssublat,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ 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) => m3_pboole(u3_msualg_1(k6_msualg_1(A),k9_msualg_1(A)),u1_struct_0(k6_msualg_1(B)),u3_msualg_1(k6_msualg_1(B),k9_msualg_1(B))) ) ) ) )).
fof(t9_msualg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_unialg_1(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => A = k12_msualg_1(k6_msualg_1(A),k9_msualg_1(A)) ) )).
fof(t9_msualg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => ! [C] : ( m1_msualg_2(C,A,B) => ! [D] : ( m1_msualg_2(D,A,B) => ( r8_pboole(u1_struct_0(A),u3_msualg_1(A,C),u3_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,D),u4_msualg_1(A,D)) ) ) ) ) ) )).
fof(t9_msualg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( l3_msualg_1(B,A) => r1_msualg_3(A,B,B,k2_msualg_3(u1_struct_0(A),u3_msualg_1(A,B))) ) ) )).
fof(t9_msualg_5,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_msualg_4(C,A,B) & m1_msualg_4(C,A,B,B) ) => ! [D] : ( ( v1_msualg_4(D,A,B) & m1_msualg_4(D,A,B,B) ) => r8_pboole(A,k3_pboole(A,C,k4_msualg_5(A,B,C,D)),C) ) ) ) ) )).
fof(t9_msualg_6,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & l1_msualg_1(A) ) => ! [B] : ( m1_subset_1(B,u4_struct_0(A)) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k4_finseq_1(k1_msualg_1(A,B))) => ! [D] : ( l3_msualg_1(D,A) => ! [E] : ( l3_msualg_1(E,A) => ! [F] : ( m2_pboole(F,u1_struct_0(A),u3_msualg_1(A,D),u3_msualg_1(A,E)) => ! [G] : ( m1_subset_1(G,k3_msualg_1(A,B,D)) => ! [H] : ( m1_subset_1(H,k3_msualg_1(A,B,D)) => ( ( r2_hidden(G,k3_msualg_1(A,B,D)) & r2_hidden(k5_msualg_3(A,D,E,B,F,G),k3_msualg_1(A,B,E)) ) => ! [I] : ( ( v1_relat_1(I) & v1_funct_1(I) ) => ! [J] : ( ( v1_relat_1(J) & v1_funct_1(J) ) => ! [K] : ( ( v1_relat_1(K) & v1_funct_1(K) ) => ( ( I = G & J = k5_msualg_3(A,D,E,B,F,G) & K = k5_msualg_3(A,D,E,B,F,H) ) => ! [L] : ( m1_subset_1(L,k1_funct_1(u3_msualg_1(A,D),k7_partfun1(u1_struct_0(A),k1_msualg_1(A,B),C))) => ( H = k1_funct_7(I,C,L) => ( k1_funct_1(K,C) = k1_funct_1(k1_msualg_3(u1_struct_0(A),u3_msualg_1(A,D),u3_msualg_1(A,E),F,k7_partfun1(u1_struct_0(A),k1_msualg_1(A,B),C)),L) & k5_msualg_3(A,D,E,B,F,H) = k1_funct_7(J,C,k1_funct_1(K,C)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_msualg_7,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => v4_lattice3(k5_msualg_5(A,B)) ) ) )).
fof(t9_msualg_8,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_msualg_5(A)))) => ! [C] : ( v1_relat_1(C) => ( C = k3_tarski(B) => C = k2_relat_1(C) ) ) ) )).
fof(t9_msualg_9,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v2_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( m2_pboole(D,A,B,k1_pzfmisc1(A,C)) => v2_msualg_3(D,A,B,k1_pzfmisc1(A,C)) ) ) ) )).
fof(t9_msuhom_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v1_msualg_1(A) & l1_msualg_1(A) ) => ! [B] : ( ( v3_msualg_1(B,A) & v4_msualg_1(B,A) & l3_msualg_1(B,A) ) => B = k1_msuhom_1(A,A,B) ) ) )).
fof(t9_mycielsk,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_eqrel_1(B,A) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( ! [D] : ~ ( r2_hidden(D,B) & r1_xboole_0(D,C) ) <=> k5_card_1(k1_mycielsk(A,B,C)) = k5_card_1(B) ) ) ) )).
fof(t9_nagata_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_nagata_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => k2_pre_topc(A,k9_subset_1(u1_struct_0(A),C,D)) = k9_subset_1(u1_struct_0(A),k2_pre_topc(A,C),k2_pre_topc(A,D)) ) ) ) ) ) ) )).
fof(t9_nagata_2,axiom,( ! [A] : ! [B] : ( ( 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) => r1_nagata_1(A,B) ) ) )).
fof(t9_nat_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ~ ( r1_xxreal_0(A,B) & r1_xxreal_0(B,k1_nat_1(A,1)) & A != B & B != k1_nat_1(A,1) ) ) ) )).
fof(t9_nat_2,axiom,( ! [A] : ( ( v7_ordinal1(A) & ~ v8_ordinal1(A) ) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ~ r1_xxreal_0(A,k7_nat_d(A,B)) ) ) )).
fof(t9_nat_3,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => k2_nat_3(A,k5_numbers) = k5_finseq_2(k4_ordinal1,k3_finseq_1(A),1) ) )).
fof(t9_nat_4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( v7_ordinal1(D) => ~ ( A = k2_xcmplx_0(k3_xcmplx_0(B,C),D) & ~ r1_xxreal_0(B,D) & ~ r1_xxreal_0(D,k5_numbers) & r1_nat_d(B,A) ) ) ) ) ) )).
fof(t9_nat_5,axiom,( ! [A] : ! [B] : ( m2_finseq_1(B,k4_ordinal1) => ! [C] : ( m2_finseq_1(C,A) => ( r1_tarski(k1_rvsum_1(B),k4_finseq_1(C)) => m2_finseq_1(k1_partfun1(k4_ordinal1,k4_ordinal1,k4_ordinal1,A,B,C),A) ) ) ) )).
fof(t9_nat_d,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_nat_d(B,C) => r1_nat_d(B,k3_xcmplx_0(C,A)) ) ) ) ) )).
fof(t9_nat_lat,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k3_nat_lat)) => ! [B] : ( m1_subset_1(B,u1_struct_0(k3_nat_lat)) => ! [C] : ( 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,A,B),C) ) ) ) )).
fof(t9_nattra_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & v2_cat_1(B) & v3_cat_1(B) & v4_cat_1(B) & v5_cat_1(B) & v6_cat_1(B) & l1_cat_1(B) ) => ! [C] : ( m2_cat_1(C,A,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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] : ( m1_cat_1(G,A,D,E) => ! [H] : ( 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)) ) ) ) ) ) ) ) ) ) )).
fof(t9_ncfcont1,axiom,( ! [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) & l2_clvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( 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] : ( v1_xreal_0(E) => ~ ( ~ r1_xxreal_0(E,k5_numbers) & ! [F] : ( v1_xreal_0(F) => ~ ( ~ r1_xxreal_0(F,k5_numbers) & ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ~ ( r2_hidden(G,k1_relset_1(u1_struct_0(A),C)) & ~ r1_xxreal_0(F,k2_normsp_0(A,k5_algstr_0(A,G,D))) & r1_xxreal_0(E,k2_normsp_0(B,k5_algstr_0(B,k7_partfun1(u1_struct_0(B),C,G),k7_partfun1(u1_struct_0(B),C,D)))) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_ncfcont2,axiom,( ! [A] : ! [B] : ! [C] : ( ( ~ 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] : ( ( ~ 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] : ( ( v1_funct_1(E) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)))) ) => ! [F] : ( ( v1_funct_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(C),u1_struct_0(D)))) ) => ( ( r3_ncfcont2(A,C,D,E) & r3_ncfcont2(B,C,D,F) ) => r3_ncfcont2(k3_xboole_0(A,B),C,D,k2_vfunct_1(u1_struct_0(C),D,E,F)) ) ) ) ) ) )).
fof(t9_ndiff_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k1_ndiff_1(A,k2_normsp_1(A,C,D),B),k2_normsp_1(A,k1_ndiff_1(A,C,B),k1_ndiff_1(A,D,B))) ) ) ) ) )).
fof(t9_ndiff_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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)))) ) => ! [E] : ( ( 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)) & 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)))) ) ) ) ) ) ) )).
fof(t9_ndiff_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ! [C] : ( ( 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) => m1_subset_1(B,k1_zfmisc_1(k1_numbers)) ) ) ) )).
fof(t9_ndiff_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( ~ v8_ordinal1(C) & m1_subset_1(C,k4_ordinal1) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_euclid(C)))) ) => ( r1_ndiff_4(C,D,A) => ( r1_ndiff_4(C,k9_integr15(C,B,k1_numbers,D),A) & k1_ndiff_4(C,k9_integr15(C,B,k1_numbers,D),A) = k9_euclid(C,k1_ndiff_4(C,D,A),B) ) ) ) ) ) ) )).
fof(t9_ndiff_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v2_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( r2_hidden(B,k4_card_3(A)) => ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) ) ) )).
fof(t9_neckla_3,axiom,( ! [A] : ( ( v3_necklace(A) & l1_orders_2(A) ) => ! [B] : ( l1_orders_2(B) => ! [C] : ( l1_orders_2(C) => ( ( A = k1_neckla_2(B,C) | A = k2_neckla_2(B,C) ) => ( v3_necklace(B) & v3_necklace(C) ) ) ) ) ) )).
fof(t9_necklace,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ~ ( ( 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) ) )).
fof(t9_net_1,axiom,( ! [A] : ( ( v1_net_1(A) & l1_petri(A) ) => ! [B] : ( m1_subset_1(B,k2_net_1(A)) => r1_tarski(k3_net_1(A,B),k2_net_1(A)) ) ) )).
fof(t9_newton,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v1_xcmplx_0(C) => k1_newton(k1_newton(C,A),B) = k1_newton(C,k3_xcmplx_0(A,B)) ) ) ) )).
fof(t9_nfcont_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [D] : ( 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] : ( m1_nfcont_1(E,B,k7_partfun1(u1_struct_0(B),C,D)) => ? [F] : ( m1_nfcont_1(F,A,D) & ! [G] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_nfcont_2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( ~ 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] : ( ( 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) => r1_nfcont_2(A,B,C,D) ) ) ) ) )).
fof(t9_nfcont_3,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(A)))) ) => ! [C] : ( v1_xreal_0(C) => ( r1_nfcont_3(A,B,C) <=> ( r2_hidden(C,k1_relset_1(k1_numbers,B)) & ! [D] : ( m1_nfcont_1(D,A,k7_partfun1(u1_struct_0(A),B,C)) => ? [E] : ( m1_rcomp_1(E,C) & ! [F] : ( v1_xreal_0(F) => ( ( r2_hidden(F,k1_relset_1(k1_numbers,B)) & r2_hidden(F,E) ) => r2_hidden(k7_partfun1(u1_struct_0(A),B,F),D) ) ) ) ) ) ) ) ) ) )).
fof(t9_nfcont_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(B,u1_struct_0(k4_real_ns1(A))))) ) => ! [D] : ( ( v1_funct_1(D) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,k1_euclid(A)))) ) => ( C = D => r2_relset_1(B,k1_numbers,k4_normsp_0(B,k4_real_ns1(A),C),k1_nfcont_4(A,B,D)) ) ) ) ) ) )).
fof(t9_normform,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v4_finsub_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v4_finsub_1(B) ) => ! [C] : ( m1_subset_1(C,k2_zfmisc_1(A,B)) => ! [D] : ( m1_subset_1(D,k2_zfmisc_1(A,B)) => ! [E] : ( m1_subset_1(E,k2_zfmisc_1(A,B)) => ( ( r1_normform(A,B,C,E) & r1_normform(A,B,D,E) ) => r1_normform(A,B,k1_normform(A,B,C,D),E) ) ) ) ) ) ) )).
fof(t9_normsp_1,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => r1_xxreal_0(k9_complex1(k6_xcmplx_0(k2_normsp_0(A,B),k2_normsp_0(A,C))),k2_normsp_0(A,k5_algstr_0(A,B,C))) ) ) ) )).
fof(t9_normsp_2,axiom,( ! [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) & l1_normsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( v1_xreal_0(C) => ( v4_pre_topc(a_3_3_normsp_2(A,B,C),k3_normsp_2(A)) & m1_subset_1(a_3_3_normsp_2(A,B,C),k1_zfmisc_1(u1_struct_0(k3_normsp_2(A)))) ) ) ) ) )).
fof(t9_ntalgo_1,axiom,( ! [A] : ( m1_subset_1(A,k4_numbers) => ! [B] : ( m1_subset_1(B,k4_numbers) => ( B != k5_numbers => k3_int_2(k5_int_1(A,B),B) = k3_int_2(A,B) ) ) ) )).
fof(t9_numbers,axiom,( r2_xboole_0(k4_ordinal1,k1_numbers) )).
fof(t9_o_ring_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( ( v9_o_ring_1(B,A) & ( v5_o_ring_1(C,A) | v9_o_ring_1(C,A) ) ) | ( v11_o_ring_1(B,A) & ~ ( ~ v1_o_ring_1(C,A) & ~ v5_o_ring_1(C,A) & ~ v9_o_ring_1(C,A) ) ) ) => v11_o_ring_1(k1_algstr_0(A,B,C),A) ) ) ) ) )).
fof(t9_openlatt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => k6_lattices(k6_openlatt(A)) = u1_struct_0(A) ) )).
fof(t9_oposet_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ( ( v3_necklace(A) & v4_orders_2(A) ) => v2_necklace(A) ) ) )).
fof(t9_oppcat_1,axiom,( ! [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) & l1_cat_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_cat_1(A,B,C) != k1_xboole_0 => ! [D] : ( 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) ) ) ) ) ) ) )).
fof(t9_ordeq_01,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v2_measure5(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_nfcont_3(C,B) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,u1_struct_0(B)))) ) => ( k1_relset_1(k1_numbers,C) = A => ( 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)))) ) ) ) ) ) )).
fof(t9_orders_1,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( ( r4_relat_2(C,A) & r1_tarski(B,A) ) => r4_relat_2(C,B) ) ) )).
fof(t9_orders_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( v6_orders_2(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))) ) <=> ( r3_orders_2(A,B,C) | r3_orders_2(A,C,B) ) ) ) ) ) )).
fof(t9_orders_3,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_struct_0(B) => k2_orders_3(k2_tarski(A,B)) = k2_tarski(u1_struct_0(A),u1_struct_0(B)) ) ) )).
fof(t9_ordinal1,axiom,( ! [A] : ! [B] : ( v3_ordinal1(B) => ( r2_hidden(A,B) => v3_ordinal1(A) ) ) )).
fof(t9_ordinal2,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_tarski(k2_ordinal1(A),k2_ordinal1(B)) ) )).
fof(t9_ordinal3,axiom,( ! [A] : ( v3_ordinal1(A) => k2_ordinal2(A) = k1_xboole_0 ) )).
fof(t9_ordinal4,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( v3_ordinal1(C) => ( ( v2_ordinal2(A) & r1_ordinal1(B,C) & r2_hidden(C,k9_xtuple_0(A)) ) => r1_ordinal1(k1_funct_1(A,B),k1_funct_1(A,C)) ) ) ) ) )).
fof(t9_ordinal6,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v5_ordinal1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v5_ordinal1(B) ) => r1_tarski(A,k1_ordinal4(A,B)) ) ) )).
fof(t9_ortsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( ( r1_orders_2(B,C,C) & r1_orders_2(B,D,D) ) => r1_orders_2(B,k3_rlvect_1(B,C,D),k5_algstr_0(B,C,D)) ) ) ) ) ) )).
fof(t9_osafree,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v1_relat_1(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] : ( m1_subset_1(C,u1_struct_0(A)) => k1_funct_1(u3_msualg_1(A,k8_osafree(A,B)),C) = a_3_0_osafree(A,B,C) ) ) ) )).
fof(t9_osalg_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ( v6_osalg_1(A) => v8_osalg_1(A) ) ) )).
fof(t9_osalg_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( 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) ) => r8_pboole(u1_struct_0(A),k2_osalg_2(A,B),B) ) ) )).
fof(t9_osalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v4_osalg_1(A) & v5_osalg_1(A) & l3_osalg_1(A) ) => ! [B] : ( ( v4_msualg_1(B,A) & v12_osalg_1(B,A) & l3_msualg_1(B,A) ) => ! [C] : ( ( v4_msualg_1(C,A) & v12_osalg_1(C,A) & l3_msualg_1(C,A) ) => ( r1_osalg_3(A,B,C) => r1_osalg_3(A,C,B) ) ) ) ) )).
fof(t9_osalg_4,axiom,( v1_partfun1(k1_xboole_0,k1_xboole_0) & v3_relat_2(k1_xboole_0) & v8_relat_2(k1_xboole_0) & m1_subset_1(k1_xboole_0,k1_zfmisc_1(k2_zfmisc_1(k1_xboole_0,k1_xboole_0))) )).
fof(t9_papdesaf,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => ( v6_papdesaf(A) => v4_aff_2(k2_diraf(A)) ) ) )).
fof(t9_parsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A))) => ! [E] : ( m1_subset_1(E,u1_struct_0(k9_parsp_1(A))) => ( r1_parsp_1(k9_parsp_1(A),B,C,D,E) <=> ( 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)) & ? [F] : ( m1_subset_1(F,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) & ? [G] : ( m1_subset_1(G,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) & ? [H] : ( m1_subset_1(H,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A))) & ? [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) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_parsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_parsp_1(A) & v1_parsp_2(A) & l1_parsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( B != C & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => r1_parsp_1(A,B,C,B,D) ) ) ) ) ) )).
fof(t9_partfun2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ( ! [D] : ( m1_subset_1(D,A) => ! [E] : ( m1_subset_1(E,A) => ( ( r2_hidden(D,k1_relset_1(A,C)) & r2_hidden(E,k1_relset_1(A,C)) & k7_partfun1(B,C,D) = k7_partfun1(B,C,E) ) => D = E ) ) ) => v2_funct_1(C) ) ) ) ) )).
fof(t9_partit1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_eqrel_1(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => ( ( r1_partit1(A,B,C) & r1_partit1(A,B,D) ) => ( r1_xboole_0(C,D) | r1_partit1(A,B,k9_subset_1(A,C,D)) ) ) ) ) ) ) )).
fof(t9_partit_2,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( r1_relat_2(B,A) => A = k1_relat_1(B) ) ) )).
fof(t9_pasch,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v2_analoaf(A) & l1_analoaf(A) ) => v2_pasch(A) ) )).
fof(t9_pboole,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( ( r1_pboole(A,B,C) & r2_pboole(A,C,D) ) => r1_pboole(A,B,D) ) ) ) ) )).
fof(t9_pcomps_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( ( r1_tarski(B,C) & v1_pcomps_1(C,A) ) => v1_pcomps_1(B,A) ) ) ) ) )).
fof(t9_pcs_0,axiom,( ! [A] : ( l1_pcs_0(A) => ! [B] : ( l1_pcs_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ( ( r1_relset_1(u1_struct_0(A),u1_struct_0(A),u1_pcs_0(A),u1_pcs_0(B)) & C = E & D = F & r1_pcs_0(A,C,D) ) => r1_pcs_0(B,E,F) ) ) ) ) ) ) ) )).
fof(t9_pdiff_1,axiom,( ! [A] : ( ( 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] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_real_ns1(1))) => ! [D] : ( v1_xreal_0(D) => ( ( A = k2_pdiff_1(B) & C = k9_finseq_1(D) ) => ( r1_ndiff_1(k4_real_ns1(1),k4_real_ns1(1),A,C) <=> r1_fdiff_1(B,D) ) ) ) ) ) ) )).
fof(t9_pdiff_2,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(2)) => ( r3_pdiff_1(2,1,A,B) <=> ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & B = k10_finseq_1(C,D) & ? [E] : ( m1_rcomp_1(E,C) & r1_tarski(E,k1_relset_1(k1_numbers,k1_pdiff_2(2,1,A,B))) & ? [F] : ( v1_funct_1(F) & v3_fdiff_1(F) & m1_subset_1(F,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ? [G] : ( v1_funct_1(G) & v2_fdiff_1(G) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) & ! [H] : ( v1_xreal_0(H) => ( r2_hidden(H,E) => k6_xcmplx_0(k1_funct_1(k1_pdiff_2(2,1,A,B),H),k1_funct_1(k1_pdiff_2(2,1,A,B),C)) = k2_xcmplx_0(k1_funct_1(F,k6_xcmplx_0(H,C)),k1_funct_1(G,k6_xcmplx_0(H,C))) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_pdiff_3,axiom,( ! [A] : ( m2_finseq_2(A,k1_numbers,k1_euclid(2)) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(2),k1_numbers))) ) => ( r1_pdiff_3(B,A) <=> r3_pdiff_1(2,1,k1_pdiff_3(1,2,B),A) ) ) ) )).
fof(t9_pdiff_4,axiom,( ! [A] : ( ( v1_funct_1(A) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(3),k1_numbers))) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(3)) => ( ? [C] : ( v1_xreal_0(C) & ? [D] : ( v1_xreal_0(D) & ? [E] : ( v1_xreal_0(E) & B = k11_finseq_1(C,D,E) & r1_fdiff_1(k1_pdiff_2(3,3,A,B),E) ) ) ) <=> r3_pdiff_1(3,3,A,B) ) ) ) )).
fof(t9_pdiff_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m2_finseq_2(D,k1_numbers,k1_euclid(3)) => ! [E] : ( ( 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) ) => r1_fdiff_1(k1_pdiff_2(3,3,k1_pdiff_3(3,3,E),D),C) ) ) ) ) ) ) )).
fof(t9_pdiff_6,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( ( 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)))) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k16_lopban_1(k4_real_ns1(B),k4_real_ns1(A)))) => ! [E] : ( v1_xreal_0(E) => ( C = D => k9_integr15(A,E,k1_euclid(B),C) = k1_rlvect_1(k16_lopban_1(k4_real_ns1(B),k4_real_ns1(A)),D,E) ) ) ) ) ) ) )).
fof(t9_pdiff_7,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k1_numbers) => ! [C] : ( m1_subset_1(C,k1_numbers) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(1,D) & r1_xxreal_0(D,A) ) => k1_finseq_7(k1_numbers,k5_euclid(A),D,k3_real_1(B,C)) = k3_valued_1(k4_ordinal1,k1_numbers,k1_numbers,k1_finseq_7(k1_numbers,k5_euclid(A),D,B),k1_finseq_7(k1_numbers,k5_euclid(A),D,C)) ) ) ) ) ) )).
fof(t9_pdiff_8,axiom,( ! [A] : ( ( ~ v8_ordinal1(A) & m1_subset_1(A,k4_ordinal1) ) => ! [B] : ( m2_finseq_2(B,k1_numbers,k1_euclid(A)) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_1(D,A),k9_euclid(A,B,C)) = k3_xcmplx_0(C,k3_funct_2(k1_euclid(A),k1_numbers,k1_pdiff_1(D,A),B)) ) ) ) ) )).
fof(t9_pdiff_9,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_euclid(A),k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,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,B),C) => r2_relset_1(k1_euclid(A),k1_numbers,k55_valued_1(k1_euclid(A),k1_numbers,B),k1_nfcont_4(1,k1_euclid(A),C)) ) ) ) ) )).
fof(t9_pencil_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( ~ v1_zfmisc_1(D) => ~ v13_pencil_1(k1_funct_7(B,C,D)) ) ) ) ) )).
fof(t9_pencil_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) & v11_pencil_1(C) & v14_pencil_1(C) ) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_pencil_1(A,C))) => ? [E] : ( ~ v13_pencil_1(E) & v16_pencil_1(E,A) & m3_pboole(E,A,k12_pralg_1(A,C)) & k3_pencil_1(A,E) = B & m1_pencil_2(k4_card_3(E),A,C) & r2_hidden(D,k4_card_3(E)) ) ) ) ) ) )).
fof(t9_pencil_4,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(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] : ( v7_ordinal1(C) => ! [D] : ( m1_vectsp_4(D,A,B) => ! [E] : ( m1_vectsp_4(E,A,B) => ! [F] : ( m1_vectsp_4(F,A,B) => ! [G] : ( m1_vectsp_4(G,A,B) => ( ( m1_vectsp_4(D,A,E) & m1_vectsp_4(F,A,G) & k2_vectsp_4(A,D) = k2_vectsp_4(A,F) & k2_vectsp_4(A,E) = k2_vectsp_4(A,G) ) => k3_pencil_4(A,B,D,E,C) = k3_pencil_4(A,B,F,G,C) ) ) ) ) ) ) ) ) )).
fof(t9_pepin,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ~ ( k3_xcmplx_0(A,C) != k5_numbers & ~ r1_xxreal_0(C,k4_nat_d(B,k3_xcmplx_0(A,C))) & k4_nat_d(B,k3_xcmplx_0(A,C)) != k4_nat_d(B,C) ) ) ) ) )).
fof(t9_petri,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & ~ v11_struct_0(A) & v2_petri(A) & v3_petri(A) & l1_petri(A) ) => k6_petri(A,k1_subset_1(u1_struct_0(A))) = k1_xboole_0 ) )).
fof(t9_pnproc_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,A,k4_ordinal1) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,A,k4_ordinal1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,A,k4_ordinal1) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,k4_ordinal1))) ) => ( 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)) ) ) ) ) )).
fof(t9_polyalg1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v4_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => r2_funct_2(k4_ordinal1,u1_struct_0(A),k3_polynom5(A,B,k5_struct_0(A)),B) ) ) )).
fof(t9_polyeq_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => k2_polyeq_1(k5_numbers,k5_numbers,k5_numbers,A) = k5_numbers ) )).
fof(t9_polyeq_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ! [F] : ( v1_xreal_0(F) => ! [G] : ( v1_xreal_0(G) => ! [H] : ( v1_xreal_0(H) => ! [I] : ( v1_xreal_0(I) => ! [J] : ( v1_xreal_0(J) => ( ! [K] : ( v1_xreal_0(K) => k1_polyeq_2(A,B,C,D,E,K) = k1_polyeq_2(F,G,H,I,J,K) ) => ( A = F & B = G & C = H & D = I & E = J ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_polyeq_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xcmplx_0(C) => ~ ( A != k5_numbers & r1_xxreal_0(k3_xcmplx_0(k3_xcmplx_0(4,A),B),k5_numbers) & k4_polyeq_1(A,k5_numbers,B,k5_numbers,C) = k5_numbers & C != k7_xcmplx_0(k3_square_1(k4_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(4,A),B))),k3_xcmplx_0(2,A)) & C != k7_xcmplx_0(k4_xcmplx_0(k3_square_1(k4_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(4,A),B)))),k3_xcmplx_0(2,A)) & C != k5_numbers ) ) ) ) )).
fof(t9_polyeq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ~ ( B != k5_numbers & ~ v1_abian(D) & k2_polyeq_1(B,C,k5_numbers,k1_newton(A,D)) = k5_numbers & A != k5_numbers & A != k1_power(D,k4_xcmplx_0(k7_xcmplx_0(C,B))) ) ) ) ) ) )).
fof(t9_polyeq_5,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( ( v7_ordinal1(B) & ~ v8_ordinal1(B) ) => ! [C] : ( v1_xreal_0(C) => ( ~ r1_xxreal_0(C,k5_numbers) => k1_polyeq_5(B,k7_xcmplx_0(A,C)) = k7_xcmplx_0(k1_polyeq_5(B,A),k1_polyeq_5(B,C)) ) ) ) ) )).
fof(t9_polyform,axiom,( ! [A] : ( v7_ordinal1(A) => v1_int_1(k1_newton(k4_xcmplx_0(1),A)) ) )).
fof(t9_polynom1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k1_polynom1(A,k3_pre_poly(u1_struct_0(A),C),B) = k3_pre_poly(u1_struct_0(A),k6_algstr_0(A,C,B)) ) ) ) )).
fof(t9_polynom2,axiom,( ! [A] : ( ( ~ 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] : ( v3_ordinal1(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k15_pre_poly(B),u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k15_pre_poly(B),u1_struct_0(A)))) ) => ( k3_polynom1(k15_pre_poly(B),A,C) = k1_xboole_0 => r2_funct_2(k15_pre_poly(B),u1_struct_0(A),C,k8_polynom1(B,A)) ) ) ) ) )).
fof(t9_polynom3,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => k3_finseq_1(k6_polynom3(2,A)) = k1_nat_1(A,1) ) )).
fof(t9_polynom4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [D] : ( m1_subset_1(D,k4_ordinal1) => ( ( r1_xxreal_0(k1_algseq_1(A,B),D) & r1_xxreal_0(k1_algseq_1(A,C),D) ) => r1_xxreal_0(k1_algseq_1(A,k3_normsp_1(A,B,C)),D) ) ) ) ) ) )).
fof(t9_polynom5,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k1_complfld)) => k1_polynom5(k12_finseq_1(u1_struct_0(k1_complfld),A)) = k9_finseq_1(k9_complex1(A)) ) )).
fof(t9_polynom6,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( v3_ordinal1(B) => ! [C] : ( m2_subset_1(C,k14_pre_poly(A),k15_pre_poly(A)) => ! [D] : ( m2_subset_1(D,k14_pre_poly(A),k15_pre_poly(A)) => ! [E] : ( m2_subset_1(E,k14_pre_poly(B),k15_pre_poly(B)) => ! [F] : ( m2_subset_1(F,k14_pre_poly(B),k15_pre_poly(B)) => ( ( r3_pre_poly(A,C,D) & r3_pre_poly(B,E,F) ) => r3_pre_poly(k10_ordinal2(A,B),k1_polynom6(A,B,C,E),k1_polynom6(A,B,D,F)) ) ) ) ) ) ) ) )).
fof(t9_polynom7,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & l2_struct_0(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( ( 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_polynom7(A,B,k1_polynom7(A,B,C,D)) = C ) ) ) )).
fof(t9_polynom8,axiom,( ! [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) & v3_rlvect_1(A) & v4_rlvect_1(A) & v1_vectsp_2(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ~ ( ~ r1_xxreal_0(k1_algseq_1(A,B),k5_numbers) & ~ r1_xxreal_0(k1_algseq_1(A,C),k5_numbers) & ~ r1_xxreal_0(k1_algseq_1(A,k11_polynom3(A,B,C)),k1_nat_1(k1_algseq_1(A,B),k1_algseq_1(A,C))) ) ) ) ) )).
fof(t9_polyred,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v5_vectsp_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l6_algstr_0(B) ) => ! [C] : ( ( 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] : ( m1_subset_1(D,u1_struct_0(B)) => ( r2_funct_2(k15_pre_poly(A),u1_struct_0(B),k5_vfunct_1(k15_pre_poly(A),B,k5_polynom7(A,B,C,D)),k5_polynom7(A,B,C,k4_algstr_0(B,D))) & r2_funct_2(k15_pre_poly(A),u1_struct_0(B),k5_vfunct_1(k15_pre_poly(A),B,k5_polynom7(A,B,C,D)),k5_polynom7(A,B,k5_vfunct_1(k15_pre_poly(A),B,C),D)) ) ) ) ) )).
fof(t9_poset_1,axiom,( ! [A] : ( ( ~ 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] : ( ( 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)))) ) => k3_poset_1(A,B) = k1_yellow_0(A,k2_poset_1(A,B)) ) ) )).
fof(t9_power,axiom,( ! [A] : ( v1_xreal_0(A) => k1_power(1,A) = A ) )).
fof(t9_pralg_1,axiom,( ! [A] : ( m2_finseq_1(A,k4_ordinal1) => ( v4_margrel1(k8_pralg_1(A),k1_tarski(k1_xboole_0)) & v5_margrel1(k8_pralg_1(A),k1_tarski(k1_xboole_0)) & v2_relat_1(k8_pralg_1(A)) ) ) )).
fof(t9_pralg_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & ~ v11_struct_0(B) & l1_msualg_1(B) ) => ! [C] : ( m1_subset_1(C,A) => ! [D] : ( m1_pralg_2(D,A,B) => ! [E] : ( m1_subset_1(E,u4_struct_0(B)) => ( k1_msualg_1(B,E) = k1_xboole_0 => k1_funct_1(k1_pralg_3(B,k14_pralg_2(A,B,D),E),C) = k1_pralg_3(B,k5_pralg_2(A,B,D,C),E) ) ) ) ) ) ) )).
fof(t9_pre_circ,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_finset_1(B) & v1_trees_1(B) ) => ! [C] : ( 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)) ) ) ) )).
fof(t9_pre_ff,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(B,A) => r1_xxreal_0(k1_int_1(B),k1_int_1(A)) ) ) ) )).
fof(t9_pre_poly,axiom,( ! [A] : ! [B] : ( ( v1_finset_1(B) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( ( 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)) ) ) ) )).
fof(t9_pre_topc,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( v1_funct_1(k5_relset_1(u1_struct_0(A),u1_struct_0(B),C,D)) & v1_funct_2(k5_relset_1(u1_struct_0(A),u1_struct_0(B),C,D),u1_struct_0(k1_pre_topc(A,D)),u1_struct_0(B)) & m1_subset_1(k5_relset_1(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(B)))) ) ) ) ) ) )).
fof(t9_prelamb,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_prelamb(A) ) => ! [B] : ( m1_prelamb(B,A) => ! [C] : ( 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)),k4_ordinal1),B,C)) = 6 & ! [D] : ( m1_trees_1(D,k9_xtuple_0(B)) => ! [E] : ( m1_trees_1(E,k9_xtuple_0(B)) => ! [F] : ( m2_finseq_1(F,u1_struct_0(A)) => ! [G] : ( m2_finseq_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ! [I] : ( m1_subset_1(I,u1_struct_0(A)) => ~ ( D = k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,k5_numbers)) & E = k8_finseq_1(k4_ordinal1,C,k12_finseq_1(k4_ordinal1,1)) & k1_xtuple_0(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k4_ordinal1),B,C)) = k6_prelamb(A,k8_finseq_1(u1_struct_0(A),F,G),k3_prelamb(A,H,I)) & k1_xtuple_0(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k4_ordinal1),B,D)) = k6_prelamb(A,F,H) & k1_xtuple_0(k3_trees_2(k2_zfmisc_1(k2_zfmisc_1(k3_finseq_2(u1_struct_0(A)),u1_struct_0(A)),k4_ordinal1),B,E)) = k6_prelamb(A,G,I) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_prepower,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(A,B) => ( r1_xxreal_0(A,k5_numbers) | r1_xxreal_0(k1_newton(A,C),k1_newton(B,C)) ) ) ) ) ) )).
fof(t9_prgcor_1,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ( ~ r1_xxreal_0(B,k5_numbers) => k1_prgcor_1(A,B) = k3_nat_d(A,B) ) ) ) )).
fof(t9_prgcor_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_relat_1(A,k1_numbers) & ~ v1_xboole_0(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v5_relat_1(B,k1_numbers) & ~ v1_xboole_0(B) & v5_ordinal1(B) & v1_funct_1(B) & v1_finset_1(B) ) => ! [C] : ( v7_ordinal1(C) => ( ( v7_ordinal1(k1_funct_1(B,k5_numbers)) & k1_afinsq_1(A) = C & k1_afinsq_1(B) = C & k1_funct_1(A,k5_numbers) = k1_funct_1(B,k5_numbers) ) => ( r1_xxreal_0(C,k1_funct_1(B,k5_numbers)) | ( ? [D] : ( v1_relat_1(D) & v5_relat_1(D,k1_numbers) & v5_ordinal1(D) & v1_funct_1(D) & v1_finset_1(D) & r5_prgcor_2(A,B,D,C) ) & ! [D] : ( ( v1_relat_1(D) & v5_relat_1(D,k1_numbers) & ~ v1_xboole_0(D) & v5_ordinal1(D) & v1_funct_1(D) & v1_finset_1(D) ) => ( r5_prgcor_2(A,B,D,C) => k12_afinsq_1(k1_numbers,D) = k8_rvsum_1(k12_afinsq_1(k1_numbers,A),k12_afinsq_1(k1_numbers,B)) ) ) ) ) ) ) ) ) )).
fof(t9_prob_1,axiom,( ! [A] : ( ~ v1_xboole_0(k9_setfam_1(A)) & v2_finsub_1(k9_setfam_1(A)) & v1_prob_1(k9_setfam_1(A),A) & m1_subset_1(k9_setfam_1(A),k1_zfmisc_1(k1_zfmisc_1(A))) ) )).
fof(t9_prob_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( m2_prob_1(C,A,B) => ! [D] : ( m2_prob_1(D,A,B) => ( ! [E] : ( m1_prob_1(E,A,B) => k3_funct_2(B,k1_numbers,C,E) = k3_funct_2(B,k1_numbers,D,E) ) => r2_funct_2(B,k1_numbers,C,D) ) ) ) ) ) )).
fof(t9_prob_3,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(B)))) ) => r1_tarski(k1_prob_2(B,k9_setfam_1(B),C,A),k1_prob_2(B,k9_setfam_1(B),k2_prob_3(B,C),A)) ) ) )).
fof(t9_prob_4,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k6_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ( r1_funct_2(k4_ordinal1,k1_numbers,k4_ordinal1,k6_numbers,A,B) => r1_funct_2(k4_ordinal1,k1_numbers,k4_ordinal1,k6_numbers,k3_series_1(A),k18_supinf_2(B)) ) ) ) )).
fof(t9_procal_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => r2_hidden(k9_cqc_lang(A,k6_cqc_lang(A,B),B),k4_cqc_the1(A)) ) ) )).
fof(t9_projdes1,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ! [H] : ( m1_subset_1(H,u1_struct_0(A)) => ( ( r1_projdes1(A,B,C,D,E) & r1_projdes1(A,B,C,D,G) & r1_projdes1(A,B,C,D,F) & r1_projdes1(A,E,F,G,H) ) => ( r1_collsp(A,E,F,G) | r1_projdes1(A,B,C,D,H) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_projpl_1,axiom,( ! [A] : ( l1_incsp_1(A) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u2_incsp_1(A)) => ! [D] : ( m1_subset_1(D,u2_incsp_1(A)) => ~ ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) & C != D & ! [E] : ( m1_subset_1(E,u1_incsp_1(A)) => ~ ( r1_incsp_1(A,E,C) & ~ r1_incsp_1(A,E,D) & B != E ) ) ) ) ) ) ) )).
fof(t9_projred1,axiom,( ! [A] : ( ( v6_incsp_1(A) & v1_incproj(A) & v2_incproj(A) & v3_incproj(A) & v4_incproj(A) & l1_incsp_1(A) ) => ! [B] : ( m1_subset_1(B,u1_incsp_1(A)) => ! [C] : ( m1_subset_1(C,u1_incsp_1(A)) => ? [D] : ( m1_subset_1(D,u2_incsp_1(A)) & ~ r1_incsp_1(A,B,D) & ~ r1_incsp_1(A,C,D) ) ) ) ) )).
fof(t9_projred2,axiom,( ! [A] : ( ( 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] : ( m1_projred2(B,A) => m1_projred2(k2_funct_1(B),A) ) ) )).
fof(t9_prvect_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,B,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(B,B))) ) => ( ( v1_setwiseo(C,B) & v2_binop_1(C,B) & r1_finseqop(B,D,C) ) => r1_finseqop(k4_finseq_2(A,B),k3_prvect_1(B,D,A),k2_prvect_1(B,C,A)) ) ) ) ) ) )).
fof(t9_prvect_2,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & ~ v1_xboole_0(A) & v1_finseq_1(A) & v2_prvect_2(A) ) => ! [B] : ( m1_subset_1(B,k4_card_3(k4_prvect_2(A))) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( r2_hidden(C,k9_xtuple_0(B)) => r1_xxreal_0(k5_numbers,k1_funct_1(k12_prvect_2(A,B),C)) ) ) ) ) )).
fof(t9_prvect_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_rlvect_1(B) ) => ( ! [C] : ( m1_subset_1(C,u1_struct_0(k5_prvect_3(A,B))) <=> ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(B)) & C = k1_domain_1(u1_struct_0(A),u1_struct_0(B),D,E) ) ) ) & ! [C] : ( m1_subset_1(C,u1_struct_0(k5_prvect_3(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_prvect_3(A,B))) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( 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) ) => k1_algstr_0(k5_prvect_3(A,B),C,D) = k1_domain_1(u1_struct_0(A),u1_struct_0(B),k1_algstr_0(A,E,F),k1_algstr_0(B,G,H)) ) ) ) ) ) ) ) & k4_struct_0(k5_prvect_3(A,B)) = k1_domain_1(u1_struct_0(A),u1_struct_0(B),k4_struct_0(A),k4_struct_0(B)) & ! [C] : ( m1_subset_1(C,u1_struct_0(k5_prvect_3(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( v1_xreal_0(F) => ( C = k1_domain_1(u1_struct_0(A),u1_struct_0(B),D,E) => k1_rlvect_1(k5_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)) ) ) ) ) ) ) ) ) )).
fof(t9_pscomp_1,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( 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_pscomp_1(k32_valued_1(u1_struct_0(A),k1_numbers,B),A) ) ) ) )).
fof(t9_pua2mss1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_eqrel_1(C,A) => m1_eqrel_1(a_3_0_pua2mss1(A,B,C),k4_finseq_2(B,A)) ) ) ) )).
fof(t9_pythtrip,axiom,( ! [A] : ~ ( ! [B] : ( m1_subset_1(B,k4_ordinal1) => ? [C] : ( m1_subset_1(C,k4_ordinal1) & r1_xxreal_0(B,C) & r2_hidden(C,A) ) ) & v1_finset_1(A) ) )).
fof(t9_pzfmisc1,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,A) & v1_funct_1(B) & v1_partfun1(B,A) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,A) & v1_funct_1(C) & v1_partfun1(C,A) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,A) & v1_funct_1(D) & v1_partfun1(D,A) ) => ( ( r6_pboole(A,B,C) | r6_pboole(A,B,D) ) => r1_pboole(A,B,k2_pzfmisc1(A,C,D)) ) ) ) ) )).
fof(t9_qc_lang1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ~ ( B != k12_qc_lang1(A) & ~ v2_qc_lang1(B,A) & ~ v3_qc_lang1(B,A) & ~ v4_qc_lang1(B,A) & ~ v5_qc_lang1(B,A) ) ) ) )).
fof(t9_qc_lang2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ! [C] : ( m1_subset_1(C,k9_qc_lang1(A)) => k3_qc_lang2(A,B,C) = k2_qc_lang2(A,k13_qc_lang1(A,B),C) ) ) ) )).
fof(t9_qc_lang3,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k9_qc_lang1(A)) => ( v4_qc_lang1(B,A) => k24_qc_lang1(A,B) = k4_subset_1(k3_qc_lang1(A),k24_qc_lang1(A,k19_qc_lang1(A,B)),k24_qc_lang1(A,k20_qc_lang1(A,B))) ) ) ) )).
fof(t9_qc_trans,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( ( v1_qc_trans(D,A) & m1_qc_lang1(D) ) => ! [E] : ( m1_valuat_1(E,D,C) => ! [F] : ( m1_valuat_1(F,A,C) => ! [G] : ( m2_funct_2(G,k3_qc_lang1(D),C,k2_valuat_1(D,C)) => ! [H] : ( m2_funct_2(H,k3_qc_lang1(A),C,k2_valuat_1(A,C)) => ( ( F = k5_relset_1(k6_qc_lang1(D),k3_margrel1(C),E,k6_qc_lang1(A)) & H = k5_relset_1(k3_qc_lang1(D),C,G,k3_qc_lang1(A)) ) => ( r1_valuat_1(D,C,k1_qc_trans(A,D,B),E,G) <=> r1_valuat_1(A,C,B,F,H) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_qmax_1,axiom,( ! [A] : ( ( v2_qmax_1(A) & l1_qmax_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k5_qmax_1(A))) => ! [C] : ( 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] : ( m1_subset_1(D,k5_qmax_1(A)) => ! [E] : ( m1_subset_1(E,k5_qmax_1(A)) => ! [F] : ( m1_subset_1(F,k5_qmax_1(A)) => ! [G] : ( 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) ) ) ) ) ) ) ) ) ) )).
fof(t9_quantal1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_group_1(A) & v10_lattices(A) & v4_lattice3(A) & v7_quantal1(A) & v8_quantal1(A) & l1_quantal1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( ( r3_lattices(A,B,C) & r3_lattices(A,D,E) ) => r3_lattices(A,k6_algstr_0(A,B,D),k6_algstr_0(A,C,E)) ) ) ) ) ) ) )).
fof(t9_quatern2,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_xreal_0(B) => k21_quaterni(k4_xcmplx_0(B),A) = k24_quaterni(k21_quaterni(B,A)) ) ) )).
fof(t9_quatern3,axiom,( ! [A] : ( v1_quaterni(A) => ! [B] : ( v1_quaterni(B) => ( v1_xreal_0(B) => k23_quaterni(B,A) = k23_quaterni(A,B) ) ) ) )).
fof(t9_quaterni,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(k5_arytm_3)) => ~ ( ? [B] : ( m1_subset_1(B,k5_arytm_3) & r2_hidden(B,A) & B != k11_arytm_3 ) & ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( m1_subset_1(C,k5_arytm_3) => ( ( r2_hidden(B,A) & r3_arytm_3(C,B) ) => r2_hidden(C,A) ) ) ) & ! [B] : ( m1_subset_1(B,k5_arytm_3) => ! [C] : ( m1_subset_1(C,k5_arytm_3) => ! [D] : ( m1_subset_1(D,k5_arytm_3) => ! [E] : ( m1_subset_1(E,k5_arytm_3) => ! [F] : ( m1_subset_1(F,k5_arytm_3) => ~ ( r2_hidden(B,A) & r2_hidden(C,A) & r2_hidden(D,A) & r2_hidden(E,A) & r2_hidden(F,A) & B != C & B != D & B != E & B != F & C != D & C != E & C != F & D != E & D != F & E != F ) ) ) ) ) ) ) ) )).
fof(t9_quin_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(k5_numbers,B) & ~ r1_xxreal_0(k5_numbers,k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(B,k1_square_1(A)),k3_xcmplx_0(C,A)),D)) & r1_xxreal_0(k6_xcmplx_0(k1_square_1(k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,B),A),C)),k1_quin_1(B,C,D)),k5_numbers) ) ) ) ) ) )).
fof(t9_quofield,axiom,( ! [A] : ( ( ~ 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] : ( m2_subset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A)) => ! [C] : ( m2_subset_1(C,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_quofield(A)) => k8_quofield(A,k10_quofield(A,B),k10_quofield(A,C)) = k10_quofield(A,k4_quofield(A,B,C)) ) ) ) )).
fof(t9_radix_1,axiom,( ! [A] : ( v7_ordinal1(A) => r1_tarski(k2_radix_1(A),k2_radix_1(k2_xcmplx_0(A,1))) ) )).
fof(t9_radix_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v3_card_1(C,k1_nat_1(B,1)) & m2_finseq_1(C,k3_radix_1(A)) ) => ! [D] : ( ( v3_card_1(D,B) & m2_finseq_1(D,k3_radix_1(A)) ) => ( ! [E] : ( v7_ordinal1(E) => ( r2_hidden(E,k2_finseq_1(B)) => k1_funct_1(C,E) = k1_funct_1(D,E) ) ) => k1_gr_cy_1(k7_radix_1(k1_nat_1(B,1),A,C)) = k1_gr_cy_1(k8_finseq_1(k4_numbers,k7_radix_1(B,A,D),k12_finseq_1(k4_numbers,k6_radix_1(k1_nat_1(B,1),A,k1_nat_1(B,1),C)))) ) ) ) ) ) )).
fof(t9_radix_3,axiom,( ! [A] : ( v7_ordinal1(A) => r1_tarski(k2_radix_3(A),k4_numbers) ) )).
fof(t9_radix_5,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( ( r1_xxreal_0(1,A) & r1_xxreal_0(2,B) ) => k8_radix_1(A,B,k10_radix_1(B,A,1)) = 1 ) ) ) )).
fof(t9_radix_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( r1_xxreal_0(2,B) => ! [C] : ( ( 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,k4_radix_6(A,B,C)),k8_radix_1(k2_xcmplx_0(A,2),B,k10_radix_1(B,k2_xcmplx_0(A,2),k5_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,k4_radix_5(k2_xcmplx_0(A,2),A,B))) ) ) ) ) )).
fof(t9_ramsey_1,axiom,( ! [A] : ! [B] : ! [C] : ( ( 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(A) & ~ v1_xboole_0(B) & ~ ( v3_funct_1(C) <=> ? [D] : ( m1_subset_1(D,B) & k10_xtuple_0(C) = k1_tarski(D) ) ) ) ) )).
fof(t9_random_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [C] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ? [D] : ( m2_finseq_1(D,A) & v2_funct_1(D) & k2_relset_1(A,D) = C & k5_bhsp_5(k1_numbers,A,k9_binop_2,C,B) = k18_rvsum_1(k4_bhsp_5(k1_numbers,A,B,D)) ) ) ) ) )).
fof(t9_random_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [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))) ) => ! [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(C) & v1_funct_2(C,A,k1_numbers) & v1_random_3(C,A,k1_numbers,B,k12_prob_1) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) <=> m1_random_1(C,A,B) ) ) ) ) )).
fof(t9_ranknull,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( 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)))) ) => k3_funct_2(u1_struct_0(B),u1_struct_0(C),D,k4_struct_0(B)) = k4_struct_0(C) ) ) ) ) )).
fof(t9_rat_1,axiom,( ! [A] : ( v1_rat_1(A) => ~ r1_xxreal_0(k5_xcmplx_0(k1_rat_1(A)),k5_numbers) ) )).
fof(t9_ratfunc1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(A)) & v1_polynom1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(A)))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( k2_polynom4(A,B,C) = k4_struct_0(A) <=> r1_hurwitz(A,B,k3_hurwitz(A,C,1)) ) ) ) ) )).
fof(t9_rcomp_3,axiom,( ! [A] : ( v1_xreal_0(A) => k2_seq_4(k1_limfunc1(A)) = A ) )).
fof(t9_real_lat,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m2_funct_2(B,A,k1_numbers,k9_funct_2(A,k1_numbers)) => ! [C] : ( 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,C),k1_funcsdom(A,k1_numbers,k5_real_lat(A),C,B)) ) ) ) )).
fof(t9_real_ns1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k4_real_ns1(A))) => ! [C] : ( m2_finseq_2(C,k1_numbers,k1_euclid(A)) => ( B = C => ! [D] : ( v7_ordinal1(D) => ( r2_hidden(D,k2_finseq_1(A)) => r1_xxreal_0(k9_complex1(k1_funct_1(C,D)),k2_normsp_0(k4_real_ns1(A),B)) ) ) ) ) ) ) )).
fof(t9_realset2,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => B = k3_funct_2(u1_struct_0(A),u1_struct_0(A),k5_vectsp_1(A),k3_funct_2(u1_struct_0(A),u1_struct_0(A),k5_vectsp_1(A),B)) ) ) )).
fof(t9_realset3,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => k5_binop_1(u1_struct_0(A),k4_realset2(A),B,k5_binop_1(u1_struct_0(A),k1_realset3(A),C,D)) = k5_binop_1(u1_struct_0(A),k1_realset3(A),k5_binop_1(u1_struct_0(A),k4_realset2(A),B,C),k5_binop_1(u1_struct_0(A),k4_realset2(A),B,D)) ) ) ) ) )).
fof(t9_rearran1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_rearran1(B) & v3_rearran1(B,k1_zfmisc_1(A)) & m2_finseq_1(B,k1_zfmisc_1(A)) ) => ? [C] : ( m1_subset_1(C,A) & k1_funct_1(B,1) = k1_tarski(C) ) ) ) )).
fof(t9_relat_1,axiom,( ! [A] : ! [B] : ! [C] : ( 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)) ) ) ) )).
fof(t9_relat_2,axiom,( ! [A] : ( 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))) ) ) )).
fof(t9_relset_1,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) => ( ! [D] : ~ ( r2_hidden(D,A) & ! [E] : ~ r2_hidden(k4_tarski(D,E),C) ) <=> k1_relset_1(A,C) = A ) ) )).
fof(t9_relset_2,axiom,( ! [A] : ! [B] : ! [C] : ( v1_relat_1(C) => ( r2_hidden(B,k9_relat_1(C,A)) <=> r2_hidden(k4_tarski(A,B),C) ) ) )).
fof(t9_revrot_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( m2_finseq_1(D,B) => ( ( r2_hidden(C,k10_xtuple_0(D)) & r1_xxreal_0(1,A) & 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,k1_nat_1(k7_nat_d(A,1),k4_finseq_4(D,C))) ) ) ) ) ) )).
fof(t9_rewrite1,axiom,( ! [A] : ( v1_relat_1(A) => ! [B] : ( m1_rewrite1(B,A) => m1_rewrite1(k3_finseq_5(B),k2_relat_1(A)) ) ) )).
fof(t9_rewrite2,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v1_rewrite2(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v1_rewrite2(C) ) => ( k1_rewrite2(A,k7_finseq_1(B,C)) = k7_finseq_1(k1_rewrite2(A,B),k1_rewrite2(A,C)) & k2_rewrite2(A,k7_finseq_1(B,C)) = k7_finseq_1(k2_rewrite2(A,B),k2_rewrite2(A,C)) ) ) ) ) )).
fof(t9_rewrite3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k8_afinsq_1(A)) => ! [C] : ( m1_subset_1(C,k8_afinsq_1(A)) => ! [D] : ( m1_subset_1(D,k8_afinsq_1(A)) => ( D = k1_flang_1(A,B,C) => ( r1_xxreal_0(k1_afinsq_1(B),k1_afinsq_1(D)) & r1_xxreal_0(k1_afinsq_1(C),k1_afinsq_1(D)) ) ) ) ) ) ) )).
fof(t9_rfinseq,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( m2_finseq_1(B,k1_numbers) => ( r2_classes1(A,B) => k18_rvsum_1(A) = k18_rvsum_1(B) ) ) ) )).
fof(t9_rfinseq2,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ! [B] : ( v1_xreal_0(B) => ~ ( ~ r1_xxreal_0(k3_finseq_1(A),k5_numbers) & ~ r1_xxreal_0(B,k5_numbers) & ~ ( k3_rfinseq2(k10_rvsum_1(A,B)) = k3_xcmplx_0(B,k3_rfinseq2(A)) & k1_rfinseq2(k10_rvsum_1(A,B)) = k1_rfinseq2(A) ) ) ) ) )).
fof(t9_rfunct_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_valued_0(C) ) => k18_valued_1(k18_valued_1(A,B),C) = k18_valued_1(A,k18_valued_1(B,C)) ) ) ) )).
fof(t9_rfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,A))) ) => ! [D] : ( v1_xreal_0(D) => ( r1_tarski(k2_relset_1(A,C),k1_relset_1(A,B)) => r2_relset_1(k4_ordinal1,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,A,C,k26_valued_1(A,k1_numbers,B,D)),k26_valued_1(k4_ordinal1,k1_numbers,k8_funct_2(k4_ordinal1,k1_numbers,A,C,B),D)) ) ) ) ) ) )).
fof(t9_rfunct_3,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,k1_numbers))) ) => k8_relset_1(A,k1_numbers,k56_valued_1(A,k1_numbers,B),k1_tarski(k5_numbers)) = k8_relset_1(A,k1_numbers,B,k1_tarski(k5_numbers)) ) ) )).
fof(t9_rfunct_4,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k1_numbers,k1_numbers))) ) => ( r1_rfunct_4(B,A) <=> ( r1_tarski(A,k9_xtuple_0(B)) & ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(C,A) & r2_hidden(D,A) & r2_hidden(E,A) & ~ r1_xxreal_0(D,C) & ~ r1_xxreal_0(E,D) & r1_xxreal_0(k2_xcmplx_0(k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(E,D),k6_xcmplx_0(E,C)),k1_funct_1(B,C)),k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(D,C),k6_xcmplx_0(E,C)),k1_funct_1(B,E))),k1_funct_1(B,D)) ) ) ) ) ) ) ) )).
fof(t9_rinfsup1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ! [C] : ( v7_ordinal1(C) => r1_xxreal_0(k1_funct_1(B,C),A) ) <=> ( v1_seq_2(B) & r1_xxreal_0(k1_rinfsup1(B),A) ) ) ) ) )).
fof(t9_rinfsup2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k6_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k6_numbers))) ) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( ( r1_funct_2(k4_ordinal1,k6_numbers,k4_ordinal1,k1_numbers,A,B) & v1_comseq_2(B) ) => ( r1_funct_2(k4_ordinal1,k6_numbers,k4_ordinal1,k1_numbers,k4_rinfsup2(A),k4_rinfsup1(B)) & k5_rinfsup2(A) = k5_rinfsup1(B) ) ) ) ) )).
fof(t9_ring_1,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k6_eqrel_1(u1_struct_0(A),u1_struct_0(A),k1_ring_1(A,k6_domain_1(u1_struct_0(A),k4_struct_0(A))),B) = k6_domain_1(u1_struct_0(A),B) ) ) )).
fof(t9_ringcat1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( ( ~ 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] : ( m1_ringcat1(E,A,B) => ! [F] : ( m1_ringcat1(F,B,C) => ! [G] : ( m1_ringcat1(G,C,D) => ( ( r1_ringcat1(A,B) & r1_ringcat1(B,C) & r1_ringcat1(C,D) ) => k6_ringcat1(G,k6_ringcat1(F,E)) = k6_ringcat1(k6_ringcat1(G,F),E) ) ) ) ) ) ) ) ) )).
fof(t9_rlaffin1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & l1_rlvect_1(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ( r1_tarski(C,D) => r1_tarski(k1_convex1(B,C,A),k1_convex1(B,D,A)) ) ) ) ) ) )).
fof(t9_rlaffin2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k3_convex1(A,B) = k2_xboole_0(k1_rlaffin2(A,B),k3_tarski(a_2_1_rlaffin2(A,B))) ) ) )).
fof(t9_rlaffin3,axiom,( ! [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) ) => ! [B] : ( ( v1_rlaffin1(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r1_tarski(C,B) => k9_subset_1(u1_struct_0(A),k3_convex1(A,B),k4_rlaffin1(A,C)) = k3_convex1(A,C) ) ) ) ) )).
fof(t9_rlsub_1,axiom,( ! [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) ) => ! [B] : ! [C] : ( m1_rlsub_1(C,A) => ( r1_struct_0(C,B) => r1_struct_0(A,B) ) ) ) )).
fof(t9_rlsub_2,axiom,( ! [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) ) => ! [B] : ( ( v1_rlvect_1(B) & m1_rlsub_1(B,A) ) => ( k1_rlsub_2(A,k1_rlsub_1(A),B) = B & k1_rlsub_2(A,B,k1_rlsub_1(A)) = B ) ) ) )).
fof(t9_rltopsp1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,B) => r2_hidden(k4_struct_0(A),k5_rusub_4(A,B,k4_algstr_0(A,C))) ) ) ) ) )).
fof(t9_rlvect_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( ( k1_algstr_0(A,B,C) = B | k1_algstr_0(A,C,B) = B ) => C = k4_struct_0(A) ) ) ) ) )).
fof(t9_rlvect_2,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k2_rlvect_2(A,k6_domain_1(u1_struct_0(A),B)) = B ) ) )).
fof(t9_rlvect_3,axiom,( ! [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) ) => ~ v1_rlvect_3(k6_domain_1(u1_struct_0(A),k4_struct_0(A)),A) ) )).
fof(t9_rlvect_4,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r1_struct_0(k1_rlvect_3(A,k6_domain_1(u1_struct_0(A),B)),B) ) ) )).
fof(t9_rlvect_5,axiom,( ! [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) ) => ! [B] : ( m1_rlvect_2(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r1_tarski(k3_rlvect_2(A,B),u1_struct_0(k1_rlvect_3(A,C))) & ! [D] : ( m2_rlvect_2(D,A,C) => k6_rlvect_2(A,B) != k6_rlvect_2(A,D) ) ) ) ) ) )).
fof(t9_rlvect_x,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ( ( r2_hidden(B,k2_rlvect_x(A,D)) & r2_hidden(C,k2_rlvect_x(A,D)) ) => r2_hidden(k3_rlvect_1(A,B,C),k2_rlvect_x(A,D)) ) ) ) ) ) )).
fof(t9_rmod_2,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m1_rmod_2(D,B,C) => ( r1_struct_0(D,A) => r1_struct_0(C,A) ) ) ) ) )).
fof(t9_rmod_3,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v2_vectsp_2(C,A) & m1_rmod_2(C,A,B) ) => ( k1_rmod_3(A,B,k1_rmod_2(A,B),C) = C & k1_rmod_3(A,B,C,k1_rmod_2(A,B)) = C ) ) ) ) )).
fof(t9_rmod_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( ( v1_finset_1(C) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) ) => ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) ) => ( r1_xboole_0(D,C) => k1_rmod_4(A,B,k4_subset_1(u1_struct_0(B),D,C)) = k3_rlvect_1(B,k1_rmod_4(A,B,D),k1_rmod_4(A,B,C)) ) ) ) ) ) )).
fof(t9_robbins1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v4_lattices(A) & v5_lattices(A) & v6_robbins1(A) & v7_robbins1(A) & l2_robbins1(A) ) => ( k3_robbins1(A,k6_lattices(A)) = k7_robbins1(A) & k6_lattices(A) = k3_robbins1(A,k7_robbins1(A)) ) ) )).
fof(t9_robbins2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_robbins2(A) & l2_robbins1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)),D)),k3_robbins1(A,k1_lattices(A,B,D)))) = D ) ) ) ) )).
fof(t9_robbins3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l3_lattices(A) ) => ! [B] : ( ( ~ 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)) & v4_lattices(A) ) => v4_lattices(B) ) ) ) )).
fof(t9_robbins4,axiom,( u1_struct_0(k2_robbins4) = k4_enumset1(k5_numbers,1,k6_subset_1(3,1),2,k6_subset_1(3,2),3) )).
fof(t9_rolle,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( 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] : ( v1_xreal_0(D) => ~ ( r2_hidden(D,k2_rcomp_1(A,B)) & r1_xxreal_0(k1_fdiff_1(C,D),k5_numbers) ) ) ) => v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,C,k2_rcomp_1(A,B))) ) ) ) ) )).
fof(t9_roughs_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_roughs_1(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r1_tarski(k6_eqrel_1(u1_struct_0(A),u1_struct_0(A),u1_orders_2(A),C),B) => r2_hidden(C,k3_roughs_1(A,B)) ) ) ) ) )).
fof(t9_rpr_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( v3_card_1(B,1) & m1_subset_1(B,k1_zfmisc_1(A)) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ( r1_xboole_0(B,C) | k9_subset_1(A,B,C) = B ) ) ) ) )).
fof(t9_rsspace,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace))) => k1_rlvect_1(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace),C,k3_xcmplx_0(A,B)) = k1_rlvect_1(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace),k1_rlvect_1(g1_rlvect_1(k1_rsspace,k5_rsspace,k3_rsspace,k4_rsspace),C,B),A) ) ) ) )).
fof(t9_rsspace4,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k5_rsspace4(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k5_rsspace4(A,B))) => ! [E] : ( ( 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] : ( ( 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] : ( v1_xreal_0(G) => ( D = k1_rlvect_1(k5_rsspace4(A,B),C,G) <=> ! [H] : ( 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) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_rusub_1,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_rusub_1(B,A) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( D = C => k4_algstr_0(A,C) = k4_algstr_0(B,D) ) ) ) ) ) )).
fof(t9_rusub_2,axiom,( ! [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_bhsp_1(A) & l1_bhsp_1(A) ) => ! [B] : ( ( v1_bhsp_1(B) & m1_rusub_1(B,A) ) => ( k1_rusub_2(A,k1_rusub_1(A),B) = B & k1_rusub_2(A,B,k1_rusub_1(A)) = B ) ) ) )).
fof(t9_rusub_4,axiom,( ! [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_bhsp_1(A) & v1_rusub_4(A) & l1_bhsp_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v1_rlvect_3(B,A) => k1_card_1(B) = k1_rusub_4(k1_rusub_3(A,B)) ) ) ) )).
fof(t9_rusub_5,axiom,( ! [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) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( B = k7_rusub_4(A,C,k6_domain_1(u1_struct_0(A),D)) <=> k1_rusub_5(A,B,k6_domain_1(u1_struct_0(A),D)) = C ) ) ) ) ) )).
fof(t9_rvsum_1,axiom,( r2_funct_2(k1_numbers,k1_numbers,k5_finseqop(k1_numbers,k9_binop_2),k7_binop_2) )).
fof(t9_rvsum_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v3_card_1(B,A) & m2_finseq_1(B,k2_numbers) ) => ! [C] : ( ( v3_card_1(C,A) & m2_finseq_1(C,k2_numbers) ) => ! [D] : ( ( v3_card_1(D,A) & m2_finseq_1(D,k2_numbers) ) => ( k4_rvsum_2(A,C,B) = k4_rvsum_2(A,D,B) => C = D ) ) ) ) ) )).
fof(t9_scm_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_ami_3)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( 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(k7_card_1(2),k1_ami_3)) & v1_partfun1(D,u1_struct_0(k1_ami_3)) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B)) = C & k3_compos_1(k1_ami_3,A,C) = k7_ami_3(E) ) => ( k5_memstr_0(k7_card_1(2),k1_ami_3,k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1))) = E & ! [F] : ( ( v1_ami_2(F) & m1_subset_1(F,u1_struct_0(k1_ami_3)) ) => k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,k1_nat_1(B,1)),F) = k1_funct_1(k5_extpro_1(k7_card_1(2),k1_ami_3,A,D,B),F) ) ) ) ) ) ) ) ) )).
fof(t9_scm_comp,axiom,( ! [A] : ( m2_subset_1(A,u1_struct_0(k1_scm_comp),k6_dtconstr(k1_scm_comp)) => k17_scm_comp(k3_scm_comp(A)) = k16_scm_comp(A) ) )).
fof(t9_scm_halt,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),A) & r1_tarski(k2_scmfsa6a(C),B) & r1_tarski(k8_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa_3(k4_scmfsa_2(k5_numbers),1)),A) ) => k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,A,k1_nat_1(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(B,C),A),1))) = k5_card_1(C) ) ) ) ) )).
fof(t9_scm_inst,axiom,( ! [A] : ( m1_subset_1(A,k3_scm_inst) => ~ ( ~ ( r2_hidden(A,k1_tarski(k3_xtuple_0(k1_scm_inst,k1_xboole_0,k1_xboole_0))) & k4_xtuple_0(A) = k5_numbers ) & ~ ( r2_hidden(A,a_0_0_scm_inst) & k4_xtuple_0(A) = 6 ) & ~ ( r2_hidden(A,a_0_1_scm_inst) & ( k4_xtuple_0(A) = 7 | k4_xtuple_0(A) = 8 ) ) & ~ ( r2_hidden(A,a_0_2_scm_inst) & ~ ( k4_xtuple_0(A) != 1 & k4_xtuple_0(A) != 2 & k4_xtuple_0(A) != 3 & k4_xtuple_0(A) != 4 & k4_xtuple_0(A) != 5 ) ) ) ) )).
fof(t9_scmbsort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_finset_1(A) ) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => ! [C] : ( m1_scmfsa_2(C) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( 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(E,D,C) & B != k15_scmfsa_2(E,D,C) ) | ( r2_hidden(D,k2_sf_mastr(A)) & r2_hidden(E,k2_sf_mastr(A)) ) ) ) ) ) ) ) ) )).
fof(t9_scmfsa10,axiom,( k5_xtuple_0(k2_compos_1(k1_scmfsa_2)) = k1_xboole_0 )).
fof(t9_scmfsa6a,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => ! [B] : ( m1_subset_1(B,u1_compos_1(k1_scmfsa_2)) => k6_scmfsa6a(A,B) = k5_scmfsa6a(k11_compos_1(k1_scmfsa_2,A),B) ) ) )).
fof(t9_scmfsa6b,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) & v1_scmfsa6b(C) ) => k1_funct_1(k1_scmfsa6b(C,A,B),k4_scmfsa_2(k5_numbers)) = 1 ) ) ) )).
fof(t9_scmfsa6c,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_ami_2(C) & ~ v1_scmfsa_m(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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) ) ) ) ) ) )).
fof(t9_scmfsa7b,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ~ ( A != B & r3_scmfsa7b(k9_scmfsa_2(B,C),A) ) ) ) ) )).
fof(t9_scmfsa8a,axiom,( ! [A] : ( v7_ordinal1(A) => k5_card_1(k1_scmfsa8a(A)) = 1 ) )).
fof(t9_scmfsa8b,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_scmfsa6c(C) & v2_scmfsa6c(C) & m1_subset_1(C,u1_compos_1(k1_scmfsa_2)) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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,k7_card_1(3),k1_scmfsa_2) ) => ! [E] : ( 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(k7_card_1(3),k1_scmfsa_2,C,k1_scmfsa_m(B)),A),E) ) ) ) ) ) )).
fof(t9_scmfsa8c,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) & v5_memstr_0(C,k7_card_1(3),k1_scmfsa_2,k5_numbers) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( ( ~ v1_xboole_0(E) & v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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] : ( v7_ordinal1(F) => ( ( r1_tarski(k6_compos_1(k1_scmfsa_2,E,F),B) & k5_memstr_0(k7_card_1(3),k1_scmfsa_2,D) = F & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,C) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,D) ) => ! [G] : ( v7_ordinal1(G) => ( k2_xcmplx_0(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C,G)),F) = k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,D,G)) & k5_compos_0(u1_compos_1(k1_scmfsa_2),k3_extpro_1(k7_card_1(3),k1_scmfsa_2,A,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C,G)),F) = k3_extpro_1(k7_card_1(3),k1_scmfsa_2,B,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,D,G)) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,A,C,G)) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,B,D,G)) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_scmfsa9a,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( ( v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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) ) => k2_sf_mastr(k2_scmfsa8b(A,B,C)) = k4_subset_1(k2_scmfsa_2,k4_subset_1(k2_scmfsa_2,k4_scmfsa_m(A),k2_sf_mastr(B)),k2_sf_mastr(C)) ) ) ) )).
fof(t9_scmfsa_1,axiom,( ! [A] : ( m1_subset_1(A,k4_card_3(k3_relat_1(k4_scmfsa_1,k5_scmfsa_1))) => ! [B] : ( v7_ordinal1(B) => k1_funct_1(k6_scmfsa_1(A,B),k4_ordinal1) = B ) ) )).
fof(t9_scmfsa_2,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmfsa_2)) => r1_xxreal_0(k2_compos_0(u1_compos_1(k1_scmfsa_2),A),12) ) )).
fof(t9_scmfsa_3,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & 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] : ( ( ~ 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(k7_card_1(3),k1_scmfsa_2)) & v1_finset_1(B) & v4_extpro_1(B,k7_card_1(3),k1_scmfsa_2,A) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ( ( r1_tarski(B,C) & r1_tarski(B,D) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(E) & v1_partfun1(E,k4_ordinal1) ) => ! [F] : ( ( v1_relat_1(F) & v4_relat_1(F,k4_ordinal1) & v5_relat_1(F,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(F) & v1_partfun1(F,k4_ordinal1) ) => ( ( r1_tarski(A,E) & r1_tarski(A,F) ) => ! [G] : ( v7_ordinal1(G) => ! [H] : ( ( v1_ami_2(H) & m1_subset_1(H,u1_struct_0(k1_scmfsa_2)) ) => ! [I] : ( v7_ordinal1(I) => ( k3_extpro_1(k7_card_1(3),k1_scmfsa_2,E,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G)) = k12_scmfsa_2(I,H) => ( I = k1_ordinal1(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G))) | ( k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,E,C,G),H) = k5_numbers <=> k1_funct_1(k5_extpro_1(k7_card_1(3),k1_scmfsa_2,F,D,G),H) = k5_numbers ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_scmfsa_9,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & 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] : ( v7_ordinal1(C) => ( ~ r1_xxreal_0(6,C) => r2_hidden(C,k2_afinsq_1(k1_scmfsa_9(A,B))) ) ) ) ) )).
fof(t9_scmfsa_i,axiom,( ! [A] : ( m1_subset_1(A,k1_compos_0(k2_scmfsa_i)) => ( ( A = 11 | A = 12 ) => k3_compos_0(k2_scmfsa_i,A) = k1_tarski(k1_xboole_0) ) ) )).
fof(t9_scmfsa_m,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) ) => k1_funct_1(k1_scmfsa_m(A),k4_scmfsa_2(k5_numbers)) = 1 ) )).
fof(t9_scmisort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( m1_subset_1(E,k4_ordinal1) => ( ( r1_scm_halt(C,D,A) & r2_scm_halt(C,D,A) & k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa_9(B,C)),k1_scmfsa_m(D),k1_nat_1(1,E))) = k1_nat_1(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(D),E)),4) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa_9(B,C)),k1_scmfsa_m(D),k1_nat_1(1,E))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(D),E)) ) => ( r1_xxreal_0(k8_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(D)),E) | ( k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa_9(B,C)),k1_scmfsa_m(D),k1_nat_1(k1_nat_1(1,E),1))) = k1_nat_1(k5_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(D),k1_nat_1(E,1))),4) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,k2_scmfsa_9(B,C)),k1_scmfsa_m(D),k1_nat_1(k1_nat_1(1,E),1))) = k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k5_extpro_1(k7_card_1(3),k1_scmfsa_2,k1_funct_4(A,C),k1_scmfsa_m(D),k1_nat_1(E,1))) ) ) ) ) ) ) ) ) )).
fof(t9_scmp_gcd,axiom,( ! [A] : ( v7_ordinal1(A) => ( ~ r1_xxreal_0(15,A) <=> r2_hidden(A,k9_xtuple_0(k4_scmp_gcd)) ) ) )).
fof(t9_scmpds_2,axiom,( ! [A] : ( v1_int_1(A) => k2_compos_0(u1_compos_1(k1_scmpds_2),k3_scmpds_2(A)) = 14 ) )).
fof(t9_scmpds_3,axiom,( ! [A] : ( ( 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) ) )).
fof(t9_scmpds_4,axiom,( ! [A] : ( m1_subset_1(A,u1_compos_1(k1_scmpds_2)) => ! [B] : ( 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)) ) ) )).
fof(t9_scmpds_7,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmpds_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( 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] : ( ( 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] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & v5_relat_1(E,u1_compos_1(k1_scmpds_2)) & ~ v1_xboole_0(E) & 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)) ) ) ) ) ) ) ) )).
fof(t9_scmpds_8,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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,k5_numbers) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmpds_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmpds_2)) ) => ! [E] : ( v1_int_1(E) => ( r1_xxreal_0(k5_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)) = k1_nat_1(k5_card_1(C),2) ) ) ) ) ) ) )).
fof(t9_scmpds_9,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( m1_subset_1(B,k4_ordinal1) => ! [C] : ( v1_int_1(C) => ! [D] : ( v1_int_1(D) => k1_amistd_1(2,k1_scmpds_2,B,k11_scmpds_2(A,C,D)) = k1_tarski(k1_ordinal1(B)) ) ) ) ) )).
fof(t9_scmring2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( 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(k7_card_1(2),k1_scmring2(A))) & v1_partfun1(B,u1_struct_0(k1_scmring2(A))) ) => ! [C] : ( m1_subset_1(C,k4_card_3(k3_relat_1(k3_ami_2,k1_scmring1(A)))) => ( C = B => k5_memstr_0(k7_card_1(2),k1_scmring2(A),B) = k2_scmring1(A,C) ) ) ) ) )).
fof(t9_scmring3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( v7_ordinal1(B) => k2_compos_0(u1_compos_1(k1_scmring2(A)),k8_scmring2(A,B)) = 6 ) ) )).
fof(t9_scmring4,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ 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] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmring2(B))) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmring2(B))) ) => ! [E] : ( ( 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(k7_card_1(2),k1_scmring2(B))) & v1_partfun1(E,u1_struct_0(k1_scmring2(B))) ) => ! [F] : ( ( 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(k7_card_1(2),k1_scmring2(B))) & v1_partfun1(F,u1_struct_0(k1_scmring2(B))) ) => ! [G] : ( ( v1_relat_1(G) & v4_relat_1(G,k4_ordinal1) & v5_relat_1(G,u1_compos_1(k1_scmring2(B))) & v1_funct_1(G) & v1_partfun1(G,k4_ordinal1) ) => ! [H] : ( ( v1_relat_1(H) & v4_relat_1(H,k4_ordinal1) & v5_relat_1(H,u1_compos_1(k1_scmring2(B))) & v1_funct_1(H) & v1_partfun1(H,k4_ordinal1) ) => ! [I] : ( ( v1_relat_1(I) & v4_relat_1(I,k4_ordinal1) & 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] : ( ( 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(k7_card_1(2),k1_scmring2(B))) & ~ v1_xboole_0(J) & v1_finset_1(J) & v4_extpro_1(J,k7_card_1(2),k1_scmring2(B),I) ) => ( ( r1_tarski(J,E) & r1_tarski(J,F) & r1_tarski(I,G) & r1_tarski(I,H) & k3_extpro_1(k7_card_1(2),k1_scmring2(B),G,k5_extpro_1(k7_card_1(2),k1_scmring2(B),G,E,A)) = k5_scmring2(B,C,D) & r2_hidden(C,k9_xtuple_0(J)) ) => k5_algstr_0(B,k2_scmring2(B,k5_extpro_1(k7_card_1(2),k1_scmring2(B),G,E,A),C),k2_scmring2(B,k5_extpro_1(k7_card_1(2),k1_scmring2(B),G,E,A),D)) = k5_algstr_0(B,k2_scmring2(B,k5_extpro_1(k7_card_1(2),k1_scmring2(B),H,F,A),C),k2_scmring2(B,k5_extpro_1(k7_card_1(2),k1_scmring2(B),H,F,A),D)) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_scmringi,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,k2_scm_inst) => r2_hidden(k3_xtuple_0(5,k1_xboole_0,k7_scmringi(A,C,B)),k1_scmringi(A)) ) ) ) )).
fof(t9_scmyciel,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ~ ( v3_card_1(B,1) & ! [C] : ~ ( r2_hidden(C,A) & B = k1_tarski(C) ) ) ) )).
fof(t9_scpinvar,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmpds_2)) ) => ! [B] : ( v1_int_1(B) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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(k1_nat_1(k5_card_1(D),3),C) <=> r2_hidden(C,k9_xtuple_0(k4_scpinvar(A,B,D))) ) ) ) ) ) )).
fof(t9_scpisort,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmpds_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & 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] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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(D,k6_scmpds_4(C,k8_memstr_0(2,k1_scmpds_2,B),A),A) & r2_scmpds_6(D,k6_scmpds_4(C,k8_memstr_0(2,k1_scmpds_2,B),A),A) ) => ( r1_scmpds_6(k1_scmpds_4(C,D),B,A) & r2_scmpds_6(k1_scmpds_4(C,D),B,A) ) ) ) ) ) ) )).
fof(t9_scpqsort,axiom,( k5_card_1(k1_scpqsort) = 38 )).
fof(t9_semi_af1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_semi_af1(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ~ r2_analoaf(A,B,C,B,D) => ( B != C & C != D & D != B ) ) ) ) ) ) )).
fof(t9_seq_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( r2_funct_2(k4_ordinal1,k1_numbers,B,k26_valued_1(k4_ordinal1,k1_numbers,C,A)) <=> ! [D] : ( v7_ordinal1(D) => k9_nat_1(k1_numbers,B,D) = k3_xcmplx_0(A,k9_nat_1(k1_numbers,C,D)) ) ) ) ) ) )).
fof(t9_seq_2,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v2_comseq_2(A) => v2_comseq_2(k32_valued_1(k4_ordinal1,k1_numbers,A)) ) ) )).
fof(t9_seq_4,axiom,( ! [A] : ( v1_xreal_0(A) => ( k3_seq_4(k1_seq_4(A)) = A & k2_seq_4(k1_seq_4(A)) = A ) ) )).
fof(t9_seqfunc,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( r2_relset_1(k4_ordinal1,k4_partfun1(A,k1_numbers),k2_seqfunc(A,k6_seqfunc(A,C,D),B),k6_seqfunc(A,k2_seqfunc(A,C,B),k2_seqfunc(A,D,B))) & r2_relset_1(k4_ordinal1,k4_partfun1(A,k1_numbers),k2_seqfunc(A,k7_seqfunc(A,C,D),B),k7_seqfunc(A,k2_seqfunc(A,C,B),k2_seqfunc(A,D,B))) ) ) ) ) ) )).
fof(t9_seqm_3,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,k4_ordinal1,k1_numbers) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ( v5_valued_0(A) => ! [B] : ( v7_ordinal1(B) => ~ ( ~ r1_xxreal_0(B,k5_numbers) & r1_xxreal_0(k9_nat_1(k1_numbers,A,B),k9_nat_1(k1_numbers,A,k5_numbers)) ) ) ) ) )).
fof(t9_series_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k1_numbers) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => r2_funct_2(k4_ordinal1,k1_numbers,k3_series_1(k26_valued_1(k4_ordinal1,k1_numbers,B,A)),k26_valued_1(k4_ordinal1,k1_numbers,k3_series_1(B),A)) ) ) )).
fof(t9_series_3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(k3_xcmplx_0(k3_xcmplx_0(4,A),B),k1_square_1(k2_xcmplx_0(A,B))) ) ) )).
fof(t9_series_4,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ( B != k5_numbers => k1_newton(k2_xcmplx_0(k1_newton(k7_xcmplx_0(1,B),k1_nat_1(A,1)),k1_newton(B,k1_nat_1(A,1))),2) = k2_xcmplx_0(k2_xcmplx_0(k1_newton(k7_xcmplx_0(1,B),k1_nat_1(k2_nat_1(2,A),2)),k1_newton(B,k1_nat_1(k2_nat_1(2,A),2))),2) ) ) ) )).
fof(t9_series_5,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => r1_xxreal_0(k2_xcmplx_0(A,B),k3_square_1(k3_xcmplx_0(2,k2_xcmplx_0(k1_square_1(A),k1_square_1(B))))) ) ) )).
fof(t9_setfam_1,axiom,( ! [A] : ! [B] : ~ ( A != k1_xboole_0 & B != k1_xboole_0 & k1_setfam_1(k2_xboole_0(A,B)) != k3_xboole_0(k1_setfam_1(A),k1_setfam_1(B)) ) )).
fof(t9_setlim_1,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => r1_tarski(k3_prob_1(A,B),k1_kurato_0(A,B)) ) )).
fof(t9_setlim_2,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k9_setfam_1(A)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k9_setfam_1(A)))) ) => k1_prob_1(A,k2_setlim_2(A,B,C)) = k4_subset_1(A,k1_prob_1(A,B),k1_prob_1(A,C)) ) ) )).
fof(t9_setwiseo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k5_finsub_1(A)) => ~ ( B != k1_xboole_0 & ! [C] : ( m1_subset_1(C,A) => ~ r2_hidden(C,B) ) ) ) ) )).
fof(t9_setwop_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,k5_finsub_1(A)) => ! [D] : ( m1_subset_1(D,B) => ! [E] : ( ( 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] : ( ( 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] : ( ( v1_funct_1(G) & v1_funct_2(G,A,B) & m1_subset_1(G,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) => ! [H] : ( ( 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(E,B) & v2_binop_1(E,B) & v1_setwiseo(E,B) & D = k4_binop_1(B,E) & k5_binop_1(B,F,D,D) = D & ! [I] : ( m1_subset_1(I,B) => ! [J] : ( m1_subset_1(J,B) => ! [K] : ( m1_subset_1(K,B) => ! [L] : ( m1_subset_1(L,B) => k5_binop_1(B,E,k5_binop_1(B,F,I,J),k5_binop_1(B,F,K,L)) = k5_binop_1(B,F,k5_binop_1(B,E,I,K),k5_binop_1(B,E,J,L)) ) ) ) ) ) => k5_binop_1(B,F,k7_setwiseo(A,B,E,C,G),k7_setwiseo(A,B,E,C,H)) = k7_setwiseo(A,B,E,C,k6_funcop_1(B,A,F,G,H)) ) ) ) ) ) ) ) ) ) )).
fof(t9_sf_mastr,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_ami_2(D) & m1_subset_1(D,u1_struct_0(k1_scmfsa_2)) ) => ! [E] : ( m1_scmfsa_2(E) => ! [F] : ( m1_scmfsa_2(F) => ( k14_scmfsa_2(C,A,E) = k14_scmfsa_2(D,B,F) => ( A = B & C = D & E = F ) ) ) ) ) ) ) ) )).
fof(t9_sfmastr1,axiom,( ! [A] : ( ( v1_relat_1(A) & v4_relat_1(A,k4_ordinal1) & v5_relat_1(A,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(A) & v1_partfun1(A,k4_ordinal1) ) => ! [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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( ~ v1_xboole_0(C) & v1_relat_1(C) & v4_relat_1(C,k4_ordinal1) & v5_relat_1(C,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(C) & v1_finset_1(C) & v1_afinsq_1(C) ) => ! [D] : ( ( ~ v1_xboole_0(D) & v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ~ ( ( v7_amistd_1(D,k7_card_1(3),k1_scmfsa_2) | ( r6_scmfsa7b(D,k1_scmfsa_m(B),A) & r5_scmfsa7b(D,k1_scmfsa_m(B),A) ) ) & ( v7_amistd_1(C,k7_card_1(3),k1_scmfsa_2) | ( r6_scmfsa7b(C,k1_scmfsa6b(D,B,A),A) & r5_scmfsa7b(C,k1_scmfsa6b(D,B,A),A) ) ) & k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(k3_scmfsa6a(D,C),B,A)) != k6_memstr_0(k7_card_1(3),k1_scmfsa_2,k1_scmfsa6b(C,k1_scmfsa6b(D,B,A),A)) ) ) ) ) ) )).
fof(t9_sfmastr2,axiom,( ! [A] : ( ( 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(k7_card_1(3),k1_scmfsa_2)) & v1_partfun1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_relat_1(B) & v4_relat_1(B,k4_ordinal1) & v5_relat_1(B,u1_compos_1(k1_scmfsa_2)) & v1_funct_1(B) & v1_partfun1(B,k4_ordinal1) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) & v1_scmfsa7b(D) ) => ( ~ ( k1_funct_1(A,k4_scmfsa_2(k5_numbers)) != 1 & v1_scmfsa_m(C) ) => k1_funct_1(k9_nat_1(k4_card_3(k2_memstr_0(k7_card_1(3),k1_scmfsa_2)),k3_sfmastr2(B,A,D,C),k5_numbers),k9_scmfsa_m(1,k4_subset_1(k2_scmfsa_2,k4_scmfsa_m(C),k2_sf_mastr(D)))) = k1_funct_1(A,C) ) ) ) ) ) )).
fof(t9_sfmastr3,axiom,( ! [A] : ( ( v1_ami_2(A) & m1_subset_1(A,u1_struct_0(k1_scmfsa_2)) ) => ! [B] : ( ( v1_ami_2(B) & m1_subset_1(B,u1_struct_0(k1_scmfsa_2)) ) => ! [C] : ( ( v1_ami_2(C) & m1_subset_1(C,u1_struct_0(k1_scmfsa_2)) ) => ! [D] : ( ( v1_relat_1(D) & v4_relat_1(D,k4_ordinal1) & 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) ) => ! [E] : ( ( v1_relat_1(E) & v4_relat_1(E,k4_ordinal1) & 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) ) => ~ ( C != A & ~ r4_scmfsa7b(D,C) & ~ r4_scmfsa7b(E,C) & r4_scmfsa7b(k5_scmfsa8b(A,B,D,E),C) ) ) ) ) ) ) )).
fof(t9_sgraph1,axiom,( ! [A] : r1_tarski(k2_sgraph1(A),k1_zfmisc_1(A)) )).
fof(t9_sheffer1,axiom,( ! [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) & l3_lattices(A) ) => v7_robbins1(A) ) )).
fof(t9_sheffer2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v1_sheffer2(A) & l1_sheffer1(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,B,C)),k5_sheffer1(A,B,C))),k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,B,C))) = k5_sheffer1(A,C,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,B,C)),C),C)) ) ) ) )).
fof(t9_simplex0,axiom,( ! [A] : ( ( v1_finset_1(A) & v6_ordinal1(A) ) => ( v1_xboole_0(A) | r2_hidden(k3_tarski(A),A) ) ) )).
fof(t9_simplex1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_rlvect_1(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => k3_simplex1(A,k5_simplex0(u1_struct_0(A),k4_subset_1(k1_zfmisc_1(u1_struct_0(A)),B,C))) = k4_subset_1(u1_struct_0(A),k3_simplex1(A,k5_simplex0(u1_struct_0(A),B)),k3_simplex1(A,k5_simplex0(u1_struct_0(A),C))) ) ) ) )).
fof(t9_simplex2,axiom,( ! [A] : ! [B] : ( ( ~ v2_struct_0(B) & v6_metric_1(B) & l1_metric_1(B) ) => ! [C] : ( ( v1_matroid0(C) & v1_simplex2(C,B) & m1_simplex0(C,A) ) => ! [D] : ( v1_int_1(D) => r1_xxreal_0(k1_simplex2(B,k9_simplex0(A,C,D)),k1_simplex2(B,C)) ) ) ) )).
fof(t9_sin_cos,axiom,( v2_comseq_3(k3_sin_cos(k5_complex1)) & k11_comseq_3(k3_sin_cos(k5_complex1)) = k6_complex1 )).
fof(t9_sin_cos2,axiom,( v5_valued_0(k2_partfun1(k1_numbers,k1_numbers,k18_sin_cos,k2_rcomp_1(k3_xcmplx_0(k7_xcmplx_0(3,2),k28_sin_cos),k3_xcmplx_0(2,k28_sin_cos)))) )).
fof(t9_sin_cos3,axiom,( ! [A] : ( v1_xcmplx_0(A) => k4_xcmplx_0(k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,A)) = k10_funct_2(k2_numbers,k2_numbers,k3_sin_cos3,k4_xcmplx_0(A)) ) )).
fof(t9_sin_cos4,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ~ ( k17_sin_cos(A) != k5_numbers & k17_sin_cos(B) != k5_numbers & k2_sin_cos4(k2_xcmplx_0(A,B)) != k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k2_sin_cos4(A),k2_sin_cos4(B)),1),k2_xcmplx_0(k2_sin_cos4(B),k2_sin_cos4(A))) ) ) ) )).
fof(t9_sin_cos5,axiom,( ! [A] : ( v1_xreal_0(A) => ( k19_sin_cos(A) != k5_numbers => k1_sin_cos4(k3_xcmplx_0(2,A)) = k7_xcmplx_0(k3_xcmplx_0(2,k1_sin_cos4(A)),k6_xcmplx_0(1,k1_square_1(k1_sin_cos4(A)))) ) ) )).
fof(t9_sin_cos6,axiom,( k19_sin_cos(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2))) = k5_numbers & k1_funct_1(k18_sin_cos,k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2))) = k5_numbers )).
fof(t9_sin_cos7,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( ( r1_xxreal_0(k5_numbers,B) & r1_xxreal_0(1,A) ) => r1_xxreal_0(k5_numbers,k7_xcmplx_0(k6_xcmplx_0(k1_square_1(A),1),B)) ) ) ) )).
fof(t9_sin_cos8,axiom,( ! [A] : ( v1_xreal_0(A) => k7_xcmplx_0(k2_xcmplx_0(k4_sin_cos2(A),k2_sin_cos2(A)),k6_xcmplx_0(k4_sin_cos2(A),k2_sin_cos2(A))) = k7_xcmplx_0(k2_xcmplx_0(1,k6_sin_cos2(A)),k6_xcmplx_0(1,k6_sin_cos2(A))) ) )).
fof(t9_sin_cos9,axiom,( v2_funct_1(k2_partfun1(k1_numbers,k1_numbers,k26_sin_cos,k2_rcomp_1(k4_xcmplx_0(k7_xcmplx_0(k28_sin_cos,2)),k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(t9_sincos10,axiom,( v1_fcont_1(k2_partfun1(k1_numbers,k1_numbers,k1_fdiff_9,k2_rcomp_1(k5_numbers,k7_xcmplx_0(k28_sin_cos,2)))) )).
fof(t9_sppol_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( ( r1_sppol_1(A,B,C) & r1_tarski(D,C) & r2_hidden(B,D) ) => r1_sppol_1(A,B,D) ) ) ) ) ) )).
fof(t9_sppol_2,axiom,( ! [A] : ( m2_finseq_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(k1_nat_1(C,1),k3_finseq_1(k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B))) => k2_topreal1(2,k1_finseq_5(u1_struct_0(k15_euclid(2)),A,B),C) = k2_topreal1(2,A,C) ) ) ) ) )).
fof(t9_sprect_1,axiom,( ! [A] : ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k15_euclid(2)))) => ( ( r1_tarski(A,B) & v1_sppol_1(B) ) => v1_sppol_1(A) ) ) ) )).
fof(t9_sprect_2,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ~ v1_xboole_0(C) => ! [D] : ( 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),k3_finseq_1(k3_finseq_6(C,D,A,B))) = k7_partfun1(C,D,B) ) ) ) ) ) )).
fof(t9_sprect_3,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( 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)) ) => ( r1_xboole_0(k1_rltopsp1(k15_euclid(2),A,B),k1_rltopsp1(k15_euclid(2),C,D)) | k18_euclid(A) = k18_euclid(C) ) ) ) ) ) ) )).
fof(t9_sprect_5,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(2))) => ( ( r2_hidden(B,k10_xtuple_0(A)) & r2_hidden(C,k10_xtuple_0(A)) ) => ( r1_xxreal_0(k4_finseq_4(A,C),k4_finseq_4(A,B)) | k4_finseq_4(k1_finseq_6(u1_struct_0(k15_euclid(2)),A,C),B) = k6_xcmplx_0(k1_nat_1(k3_finseq_1(A),k4_finseq_4(A,B)),k4_finseq_4(A,C)) ) ) ) ) ) )).
fof(t9_square_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => k1_square_1(k3_xcmplx_0(A,B)) = k3_xcmplx_0(k1_square_1(A),k1_square_1(B)) ) ) )).
fof(t9_stacks_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u4_struct_0(A)) => ( ~ r1_stacks_1(A,B) => k6_stacks_1(A,B) = k1_funct_1(k9_stacks_1(A,B),1) ) ) ) )).
fof(t9_stirl2_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k4_ordinal1)) ) => ( r1_tarski(B,A) => m1_subset_1(k6_xcmplx_0(A,1),k4_ordinal1) ) ) ) )).
fof(t9_sublemma,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( m2_subset_1(C,k6_qc_lang1(A),k8_qc_lang1(A,B)) => ! [D] : ( ( v5_relat_1(D,k3_qc_lang1(A)) & v3_card_1(D,B) & m2_finseq_1(D,k2_qc_lang1(A)) ) => ! [E] : ( m1_subset_1(E,k1_substut1(A)) => m2_subset_1(k10_qc_lang1(A,C,k3_substut1(A,D,E)),k9_qc_lang1(A),k3_cqc_lang(A)) ) ) ) ) ) )).
fof(t9_subset_1,axiom,( ! [A] : k2_subset_1(A) = k3_subset_1(A,k1_subset_1(A)) )).
fof(t9_substlat,axiom,( ! [A] : ! [B] : ! [C] : ( m1_subset_1(C,k5_finsub_1(k4_partfun1(A,B))) => ( C = k1_xboole_0 => k3_substlat(A,B,C) = k1_xboole_0 ) ) )).
fof(t9_substut1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m1_subset_1(B,k1_substut1(A)) => ! [C] : ( v7_ordinal1(C) => ! [D] : ( m2_subset_1(D,k6_qc_lang1(A),k8_qc_lang1(A,C)) => ! [E] : ( ( v3_card_1(E,C) & m2_finseq_1(E,k2_qc_lang1(A)) ) => k17_substut1(A,D,E,B) = k1_domain_1(k9_qc_lang1(A),k1_substut1(A),k10_qc_lang1(A,D,E),B) ) ) ) ) ) )).
fof(t9_substut2,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( m2_subset_1(B,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [C] : ( m2_subset_1(C,k2_qc_lang1(A),k3_qc_lang1(A)) => ! [D] : ( m1_subset_1(D,k1_substut1(A)) => k14_substut1(A,C,B,k7_substut1(A,C,k11_cqc_lang(A,C,B),D)) = 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)))) ) ) ) ) )).
fof(t9_supinf_1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_setfam_1(A) & m1_subset_1(A,k1_zfmisc_1(k1_zfmisc_1(k6_numbers))) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v2_membered(B) ) => ( B = k5_setfam_1(k6_numbers,A) => k2_xxreal_2(B) = k2_xxreal_2(k6_supinf_1(A)) ) ) ) )).
fof(t9_supinf_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & m1_subset_1(A,k1_zfmisc_1(k6_numbers)) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k6_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))) ) ) ) )).
fof(t9_symsp_1,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ~ ( C != k4_struct_0(B) & D != k4_struct_0(B) & ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ~ ( ~ r1_orders_2(B,E,C) & ~ r1_orders_2(B,E,D) ) ) ) ) ) ) ) )).
fof(t9_sysrel,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ( v1_relat_1(E) => ( ( r1_tarski(E,k2_zfmisc_1(A,B)) & A = k2_xboole_0(C,D) ) => E = k2_xboole_0(k5_relat_1(E,C),k5_relat_1(E,D)) ) ) )).
fof(t9_t_0topsp,axiom,( ! [A] : ( ( ~ 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)) & v6_pre_topc(k3_t_0topsp(A)) & l1_pre_topc(k3_t_0topsp(A)) ) ) )).
fof(t9_taxonom1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) => ( ( r1_relat_2(B,A) & r3_relat_2(B,A) ) => ( v1_partfun1(k13_lang1(A,B),A) & v3_relat_2(k13_lang1(A,B)) & v8_relat_2(k13_lang1(A,B)) & m1_subset_1(k13_lang1(A,B),k1_zfmisc_1(k2_zfmisc_1(A,A))) ) ) ) ) )).
fof(t9_taxonom2,axiom,( ! [A] : v4_taxonom2(k1_tarski(A)) )).
fof(t9_taylor_1,axiom,( ! [A] : ( v1_xreal_0(A) => ( k6_prepower(k23_sin_cos(1),A) = k23_sin_cos(A) & k2_power(k23_sin_cos(1),A) = k23_sin_cos(A) & k2_power(k4_power,A) = k23_sin_cos(A) & k6_prepower(k4_power,A) = k23_sin_cos(A) ) ) )).
fof(t9_taylor_2,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ! [D] : ( v1_xreal_0(D) => ( r2_hidden(C,k2_rcomp_1(k4_xcmplx_0(B),B)) => ( r1_xxreal_0(D,k5_numbers) | r1_xxreal_0(1,D) | r1_xxreal_0(k9_complex1(k7_xcmplx_0(k3_xcmplx_0(k1_funct_1(k1_seqfunc(k1_numbers,k1_numbers,k5_taylor_1(k22_sin_cos,k2_rcomp_1(k4_xcmplx_0(B),B)),k1_nat_1(A,1)),k3_xcmplx_0(D,C)),k1_newton(C,k1_nat_1(A,1))),k2_newton(k1_nat_1(A,1)))),k7_xcmplx_0(k3_xcmplx_0(k9_complex1(k1_funct_1(k22_sin_cos,k3_xcmplx_0(D,C))),k1_newton(k9_complex1(C),k1_nat_1(A,1))),k2_newton(k1_nat_1(A,1)))) ) ) ) ) ) ) )).
fof(t9_tbsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_metric_1(A) ) => ( ( v6_metric_1(A) & v9_metric_1(A) & v1_compts_1(k3_pcomps_1(A)) ) => v1_tbsp_1(A) ) ) )).
fof(t9_tdgroup,axiom,( ! [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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ! [G] : ( m1_subset_1(G,u1_struct_0(A)) => ( ( r1_tdgroup(A,B,C,F,G) & r1_tdgroup(A,D,E,F,G) ) => r1_tdgroup(A,B,C,D,E) ) ) ) ) ) ) ) ) )).
fof(t9_tdlat_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k2_pre_topc(A,k4_subset_1(u1_struct_0(A),B,k1_tops_1(A,k3_subset_1(u1_struct_0(A),B)))) = k2_struct_0(A) ) ) )).
fof(t9_tdlat_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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 ) ) ) )).
fof(t9_tdlat_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( 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)) = k1_tops_1(A,B) & k2_pre_topc(A,B) = k2_pre_topc(A,k1_tops_1(A,B)) ) ) ) ) )).
fof(t9_termord,axiom,( ! [A] : ( v3_ordinal1(A) => ! [B] : ( ( 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] : ( ( 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,k16_pre_poly(A),C) ) ) ) )).
fof(t9_tex_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v2_tdlat_3(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( ( v1_xboole_0(B) => k2_pre_topc(A,B) = k1_xboole_0 ) & ( ~ v1_xboole_0(B) => k2_pre_topc(A,B) = u1_struct_0(A) ) ) ) ) )).
fof(t9_tex_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_pre_topc(C,A) => ( ( g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) = g1_pre_topc(u1_struct_0(C),u1_pre_topc(C)) & v1_tex_2(B,A) ) => v1_tex_2(C,A) ) ) ) ) )).
fof(t9_tex_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( C = u1_struct_0(B) => ( v1_tex_3(B,A) <=> v1_tops_1(C,A) ) ) ) ) ) )).
fof(t9_tex_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v2_tex_4(B,A) => v1_tex_4(k6_setfam_1(u1_struct_0(A),B),A) ) ) ) )).
fof(t9_tietze,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k4_partfun1(A,k1_numbers)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k4_partfun1(A,k1_numbers)))) ) => ( r1_seqfunc(A,k1_numbers,C,B) => ! [D] : ( ( v2_xxreal_0(D) & v1_xreal_0(D) ) => ! [E] : ( ( v2_xxreal_0(E) & v1_xreal_0(E) ) => ( ! [F] : ( 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,k2_power(E,F)),B) ) => ( r1_xxreal_0(1,E) | ( r3_seqfunc(A,C,B) & ! [F] : ( v7_ordinal1(F) => r1_tietze(k47_valued_1(A,k1_numbers,k1_numbers,k11_seqfunc(A,C,B),k1_seqfunc(A,k1_numbers,C,F)),k7_xcmplx_0(k3_xcmplx_0(D,k2_power(E,F)),k6_xcmplx_0(1,E)),B) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_tmap_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( v2_pre_topc(C) & l1_pre_topc(C) ) => ( C = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) => ( ( v1_tsep_1(B,A) & m1_pre_topc(B,A) ) <=> ( v1_tsep_1(C,A) & m1_pre_topc(C,A) ) ) ) ) ) ) )).
fof(t9_toler_1,axiom,( ! [A] : ! [B] : ( ( v1_relat_2(B) & v3_relat_2(B) & v1_partfun1(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(A,A))) ) => r3_relat_2(B,A) ) )).
fof(t9_topalg_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) & v3_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) & v3_valued_0(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_finseq_1(C) & v3_valued_0(C) ) => ! [D] : ( ( v1_relat_1(D) & v1_funct_1(D) & v1_finseq_1(D) & v3_valued_0(D) ) => k8_rvsum_1(k4_rvsum_1(A,B),k4_rvsum_1(C,D)) = k4_rvsum_1(k8_rvsum_1(A,C),k8_rvsum_1(B,D)) ) ) ) ) )).
fof(t9_topalg_2,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => v2_topalg_2(k4_topmetr(A,B)) ) ) ) )).
fof(t9_topalg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ( ( r2_borsuk_3(A,B) & v1_borsuk_2(A) ) => v1_borsuk_2(B) ) ) ) )).
fof(t9_topalg_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v2_pre_topc(C) & l1_pre_topc(C) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(C),u1_struct_0(k2_borsuk_1(A,B))) & v5_pre_topc(D,C,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))))) ) => v5_pre_topc(k3_topalg_4(A,B,C,D),C,A) ) ) ) ) )).
fof(t9_topalg_5,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) => ! [E] : ( m2_connsp_2(E,A,C) => ( ( g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) = g1_pre_topc(u1_struct_0(B),u1_pre_topc(B)) & C = D ) => m2_connsp_2(E,B,D) ) ) ) ) ) ) )).
fof(t9_topalg_6,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k15_euclid(A)))) => ( ( r1_xxreal_0(2,A) & C = k7_subset_1(u1_struct_0(k15_euclid(A)),k2_struct_0(k15_euclid(A)),k1_tarski(B)) ) => v1_borsuk_2(k1_pre_topc(k15_euclid(A),C)) ) ) ) ) )).
fof(t9_topdim_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( ( v1_topdim_1(C,A) & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) ) => ( r1_xxreal_0(k2_topdim_1(A,C),B) <=> ! [D] : ( m1_subset_1(D,u1_struct_0(k1_pre_topc(A,C))) => ! [E] : ( ( v3_pre_topc(E,k1_pre_topc(A,C)) & m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k1_pre_topc(A,C)))) ) => ~ ( r2_hidden(D,E) & ! [F] : ( ( 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(D,F) & r1_tarski(F,E) & v1_topdim_1(k2_tops_1(k1_pre_topc(A,C),F),k1_pre_topc(A,C)) & r1_xxreal_0(k2_topdim_1(k1_pre_topc(A,C),k2_tops_1(k1_pre_topc(A,C),F)),k6_xcmplx_0(B,1)) ) ) ) ) ) ) ) ) ) )).
fof(t9_topdim_2,axiom,( ! [A] : ( ( v2_pre_topc(A) & v3_pcomps_1(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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)) ) ) ) ) ) )).
fof(t9_topgen_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_tops_1(A,B)) <=> ! [D] : ( 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) & k7_subset_1(u1_struct_0(A),D,B) != k1_xboole_0 ) ) ) ) ) ) ) )).
fof(t9_topgen_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ( r2_hidden(C,k2_pre_topc(A,B)) <=> ! [D] : ( ( 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] : ~ ( r2_hidden(E,D) & r1_xboole_0(E,B) ) ) ) ) ) ) )).
fof(t9_topgen_3,axiom,( ! [A] : ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k9_setfam_1(A),k9_setfam_1(A)) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k9_setfam_1(A),k9_setfam_1(A)))) ) => ( ( k1_funct_1(B,A) = A & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => r1_tarski(k3_funct_2(k1_zfmisc_1(A),k9_setfam_1(A),B,C),C) ) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(A)) => k3_funct_2(k1_zfmisc_1(A),k9_setfam_1(A),B,k9_subset_1(A,C,D)) = k9_subset_1(A,k3_funct_2(k1_zfmisc_1(A),k9_setfam_1(A),B,C),k3_funct_2(k1_zfmisc_1(A),k9_setfam_1(A),B,D)) ) ) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => k3_funct_2(k9_setfam_1(A),k9_setfam_1(A),B,k3_funct_2(k1_zfmisc_1(A),k9_setfam_1(A),B,C)) = k3_funct_2(k1_zfmisc_1(A),k9_setfam_1(A),B,C) ) ) => ! [C] : ( l1_pre_topc(C) => ( ( u1_struct_0(C) = A & u1_pre_topc(C) = k1_topgen_3(k9_setfam_1(A),A,B) ) => ( v2_pre_topc(C) & l1_pre_topc(C) & ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(C))) => k1_tops_1(C,D) = k1_funct_1(B,D) ) ) ) ) ) ) )).
fof(t9_topgen_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v1_pcomps_1(B,A) => r1_tarski(k2_tops_1(A,k5_setfam_1(u1_struct_0(A),B)),k5_setfam_1(u1_struct_0(A),k1_topgen_1(A,B))) ) ) ) )).
fof(t9_topgrp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( 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) ) ) )).
fof(t9_topmetr,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( ( v6_metric_1(B) & v7_metric_1(B) & v8_metric_1(B) & v9_metric_1(B) & l1_metric_1(B) ) => ! [C] : ( m1_topmetr(C,B) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ! [E] : ( m1_subset_1(E,u1_struct_0(C)) => ( D = E => k8_metric_1(C,E,A) = k8_subset_1(u1_struct_0(B),k8_metric_1(B,D,A),u1_struct_0(C)) ) ) ) ) ) ) )).
fof(t9_topmetr3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,k1_numbers) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,k1_numbers))) ) => ! [D] : ( ( v1_funct_1(D) & v1_funct_2(D,k4_ordinal1,u1_struct_0(k2_topmetr(A,B))) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k2_topmetr(A,B))))) ) => ( ( r1_funct_2(k4_ordinal1,u1_struct_0(k2_topmetr(A,B)),k4_ordinal1,k1_numbers,D,C) & r1_xxreal_0(A,B) & v7_valued_0(C) ) => v2_tbsp_1(D,k2_topmetr(A,B)) ) ) ) ) ) )).
fof(t9_topreal1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => ( B != C => r1_topreal1(k15_euclid(A),B,C,k1_rltopsp1(k15_euclid(A),B,C)) ) ) ) ) )).
fof(t9_topreal3,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(B,C) => a_3_0_topreal3(A,B,C) = k1_rltopsp1(k15_euclid(2),k19_euclid(A,B),k19_euclid(A,C)) ) ) ) ) )).
fof(t9_topreal4,axiom,( ! [A] : ( m1_subset_1(A,u1_struct_0(k15_euclid(2))) => ! [B] : ( m1_subset_1(B,u1_struct_0(k15_euclid(2))) => ! [C] : ( m2_finseq_1(C,u1_struct_0(k15_euclid(2))) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( m1_subset_1(E,u1_struct_0(k14_euclid(2))) => ( ( r2_hidden(A,k8_metric_1(k14_euclid(2),E,D)) & r2_hidden(B,k8_metric_1(k14_euclid(2),E,D)) & r2_hidden(k19_euclid(k17_euclid(B),k18_euclid(A)),k8_metric_1(k14_euclid(2),E,D)) & C = k3_finseq_4(u1_struct_0(k15_euclid(2)),A,k19_euclid(k17_euclid(B),k18_euclid(A)),B) ) => ( k17_euclid(A) = k17_euclid(B) | k18_euclid(A) = k18_euclid(B) | ( v4_topreal1(C) & 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 & r1_topreal4(k3_topreal1(2,C),A,B) & r1_tarski(k3_topreal1(2,C),k8_metric_1(k14_euclid(2),E,D)) ) ) ) ) ) ) ) ) )).
fof(t9_topreal5,axiom,( ! [A] : ( ( v1_funct_1(A) & v1_funct_2(A,u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr)) & m1_subset_1(A,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(k5_topmetr),u1_struct_0(k3_topmetr)))) ) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ~ ( v5_pre_topc(A,k5_topmetr,k3_topmetr) & k1_funct_1(A,k5_numbers) != k1_funct_1(A,1) & B = k1_funct_1(A,k5_numbers) & C = k1_funct_1(A,1) & ! [D] : ( v1_xreal_0(D) => ~ ( ~ r1_xxreal_0(D,k5_numbers) & ~ r1_xxreal_0(1,D) & k1_funct_1(A,D) = k7_xcmplx_0(k2_xcmplx_0(B,C),2) ) ) ) ) ) ) )).
fof(t9_topreal6,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v7_ordinal1(B) => ! [C] : ( v7_ordinal1(C) => ( r1_xxreal_0(C,B) => ( A = k5_numbers | k1_newton(A,k7_nat_d(B,C)) = k7_xcmplx_0(k1_newton(A,B),k1_newton(A,C)) ) ) ) ) ) )).
fof(t9_topreal7,axiom,( ! [A] : ( m2_finseq_1(A,k1_numbers) => ( k3_finseq_1(A) = k3_finseq_1(k3_euclid(A)) & k4_finseq_1(A) = k4_finseq_1(k3_euclid(A)) ) ) )).
fof(t9_topreal8,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => r1_xxreal_0(k3_finseq_1(B),k3_finseq_1(k3_graph_2(A,B))) ) ) )).
fof(t9_topreal9,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( 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) ) ) ) ) )).
fof(t9_topreala,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & m1_pre_topc(C,B) ) => ! [D] : ( ( 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] : ( ( 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) & v1_t_0topsp(D,A,B) ) => v1_t_0topsp(E,A,C) ) ) ) ) ) ) )).
fof(t9_toprealb,axiom,( ! [A] : ( m1_subset_1(A,k4_ordinal1) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k15_euclid(A))) => u1_struct_0(k7_toprealb(A,C,B)) = k3_topreal9(A,C,B) ) ) ) )).
fof(t9_toprealc,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_valued_0(B) ) => k39_valued_1(k45_valued_1(A,B)) = k39_valued_1(k45_valued_1(B,A)) ) ) )).
fof(t9_toprns_1,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( ( v1_funct_1(B) & v1_funct_2(B,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,k4_ordinal1,u1_struct_0(k15_euclid(A))) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(k4_ordinal1,u1_struct_0(k15_euclid(A))))) ) => k1_toprns_1(A,B,C) = k1_toprns_1(A,C,B) ) ) ) )).
fof(t9_tops_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( 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) ) ) ) ) )).
fof(t9_tops_2,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) => ( v2_tops_2(B,A) <=> v1_tops_2(k7_setfam_1(u1_struct_0(A),B),A) ) ) ) )).
fof(t9_tops_3,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => v2_tops_1(k1_struct_0(A),A) ) )).
fof(t9_transgeo,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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,k6_partfun1(A),B),k6_partfun1(A)) ) ) )).
fof(t9_translac,axiom,( ! [A] : ( ( ~ v7_struct_0(A) & v1_diraf(A) & v2_diraf(A) & l1_analoaf(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( 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] : ( ( 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) ) => ( r1_aff_1(A,B,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),k1_transgeo(u1_struct_0(A),D,C),k1_transgeo(u1_struct_0(A),C,D)) ) ) ) ) ) ) )).
fof(t9_treal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ( r1_xxreal_0(A,B) => ! [C] : ( m1_subset_1(C,u1_struct_0(k4_topmetr(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_topmetr(A,B))) => ( k3_funct_2(u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k4_topmetr(A,B)),k3_treal_1(A,B,C,D),k1_treal_1(k5_numbers,1)) = C & k3_funct_2(u1_struct_0(k4_topmetr(k5_numbers,1)),u1_struct_0(k4_topmetr(A,B)),k3_treal_1(A,B,C,D),k2_treal_1(k5_numbers,1)) = D ) ) ) ) ) ) )).
fof(t9_trees_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_finseq_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ( ~ ( ~ r2_xboole_0(k1_xboole_0,B) & k1_xboole_0 = B ) => r2_xboole_0(A,k7_finseq_1(A,B)) ) ) ) )).
fof(t9_trees_2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( m2_trees_2(B,A) => m4_trees_1(B,A) ) ) )).
fof(t9_trees_3,axiom,( ! [A] : ! [B] : ( ( v3_trees_3(A) & v3_trees_3(B) ) <=> v3_trees_3(k2_xboole_0(A,B)) ) )).
fof(t9_trees_4,axiom,( ! [A] : ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) & v1_finseq_1(B) ) => ! [C] : ( m1_subset_1(C,k4_ordinal1) => ( ~ r1_xxreal_0(k3_finseq_1(B),C) => k5_trees_2(k3_trees_4(A,B),k14_trees_3(C)) = k1_trees_4(k1_funct_1(B,k1_nat_1(C,1))) ) ) ) )).
fof(t9_trees_9,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_finset_1(A) & v1_trees_1(A) ) => ! [B] : ( m1_trees_1(B,A) => ( A = k4_trees_1(A,B) => B = k1_xboole_0 ) ) ) )).
fof(t9_trees_a,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_trees_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & v1_trees_1(B) ) => ! [C] : ( m1_trees_1(C,A) => k1_trees_a(A,B,k2_trees_a(A,C)) = k5_trees_1(A,C,B) ) ) ) )).
fof(t9_tsep_1,axiom,( ! [A] : ( ( v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_pre_topc(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) => ! [E] : ( 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 ) => ( v3_pre_topc(E,B) <=> v3_pre_topc(D,A) ) ) ) ) ) ) ) )).
fof(t9_tsep_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( r2_tsep_2(A,B,C) => ( r2_tsep_2(A,k2_pre_topc(A,B),k1_tops_1(A,C)) & r2_tsep_2(A,k1_tops_1(A,B),k2_pre_topc(A,C)) ) ) ) ) ) )).
fof(t9_tsp_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ( v2_tex_2(B,A) => v1_tsp_1(B,A) ) ) ) )).
fof(t9_tsp_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => ~ ( v1_tsp_1(B,A) & ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ~ ( r1_tarski(B,C) & v1_tsp_2(C,A) ) ) ) ) ) )).
fof(t9_turing_1,axiom,( ! [A] : ( l1_turing_1(A) => ! [B] : ( m1_subset_1(B,k3_zfmisc_1(u2_turing_1(A),k4_numbers,k9_funct_2(k4_numbers,u1_turing_1(A)))) => k9_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),1) = k9_turing_1(A,B) ) ) )).
fof(t9_twoscomp,axiom,( k1_funct_1(k2_twoscomp,k10_finseq_1(k5_numbers,k5_numbers)) = k5_numbers & k1_funct_1(k2_twoscomp,k10_finseq_1(k5_numbers,1)) = k5_numbers & k1_funct_1(k2_twoscomp,k10_finseq_1(1,k5_numbers)) = k5_numbers & k1_funct_1(k2_twoscomp,k10_finseq_1(1,1)) = 1 & k1_funct_1(k3_twoscomp,k10_finseq_1(k5_numbers,k5_numbers)) = k5_numbers & k1_funct_1(k3_twoscomp,k10_finseq_1(k5_numbers,1)) = 1 & k1_funct_1(k3_twoscomp,k10_finseq_1(1,k5_numbers)) = k5_numbers & k1_funct_1(k3_twoscomp,k10_finseq_1(1,1)) = k5_numbers & k1_funct_1(k4_twoscomp,k10_finseq_1(k5_numbers,k5_numbers)) = 1 & k1_funct_1(k4_twoscomp,k10_finseq_1(k5_numbers,1)) = k5_numbers & k1_funct_1(k4_twoscomp,k10_finseq_1(1,k5_numbers)) = k5_numbers & k1_funct_1(k4_twoscomp,k10_finseq_1(1,1)) = k5_numbers )).
fof(t9_unialg_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_unialg_1(A) & v3_unialg_1(A) & v4_unialg_1(A) & l1_unialg_1(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(k1_unialg_3(A))) ) => ~ v1_xboole_0(k7_relset_1(k1_unialg_3(A),k9_setfam_1(u1_struct_0(A)),k3_unialg_3(A),B)) ) ) )).
fof(t9_uniroots,axiom,( ! [A] : ( v7_ordinal1(A) => ! [B] : ( v7_ordinal1(B) => ( k19_sin_cos(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B),A)) = k19_sin_cos(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k4_nat_d(B,A)),A)) & k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),B),A)) = k17_sin_cos(k7_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(2,k28_sin_cos),k4_nat_d(B,A)),A)) ) ) ) )).
fof(t9_uproots,axiom,( ! [A] : ! [B] : ( ( 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) ) => ( k2_uproots(A,B) = k5_numbers => r6_pboole(A,B,k16_pre_poly(A)) ) ) )).
fof(t9_urysohn1,axiom,( ! [A] : ( v7_ordinal1(A) => r2_hidden(k7_xcmplx_0(1,k11_newton(2,k1_nat_1(A,1))),k7_subset_1(k1_numbers,k1_urysohn1(k1_nat_1(A,1)),k1_urysohn1(A))) ) )).
fof(t9_urysohn2,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v6_xxreal_2(A) & m1_subset_1(A,k1_zfmisc_1(k1_numbers)) ) => ! [B] : ( v1_xreal_0(B) => ( v3_measure5(A) => ( r1_xxreal_0(B,k5_numbers) | v3_measure5(k1_integra2(A,B)) ) ) ) ) )).
fof(t9_urysohn3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & v10_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( v4_pre_topc(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( ( 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] : ( m2_urysohn3(D,A,B,C) => ! [E] : ( v1_xreal_0(E) => ~ ( r2_hidden(E,k2_urysohn1) & ! [F] : ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A))) => ? [G] : ( v7_ordinal1(G) & r2_hidden(E,k1_urysohn1(G)) & F != k1_funct_1(k2_urysohn3(k2_urysohn1,k9_setfam_1(u1_struct_0(A)),D,G),E) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_valuat_1,axiom,( ! [A] : ( m1_qc_lang1(A) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m2_subset_1(C,k9_qc_lang1(A),k3_cqc_lang(A)) => ! [D] : ( 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,C)),k15_margrel1(k2_valuat_1(A,B),k8_valuat_1(A,B,D,C))) ) ) ) ) )).
fof(t9_valued_0,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ( v3_valued_0(A) <=> ! [B] : v1_xreal_0(k1_funct_1(A,B)) ) ) )).
fof(t9_valued_1,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_valued_0(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( ( k9_xtuple_0(A) = k9_xtuple_0(B) & ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => k1_funct_1(B,C) = k4_xcmplx_0(k1_funct_1(A,C)) ) ) => B = k30_valued_1(A) ) ) ) )).
fof(t9_valued_2,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) & v1_valued_0(C) ) => ( ( v2_relat_1(C) & k24_valued_1(C,A) = k24_valued_1(C,B) ) => ( C = k1_xboole_0 | A = B ) ) ) ) ) )).
fof(t9_vectsp10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v13_algstr_0(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & v3_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_4(D,A,B) => ( r1_vectsp_5(A,B,C,D) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ( r1_struct_0(C,E) => k4_vectsp_5(A,B,E,C,D) = k1_domain_1(u1_struct_0(B),u1_struct_0(B),E,k4_struct_0(B)) ) ) ) ) ) ) ) )).
fof(t9_vectsp11,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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] : ( m1_subset_1(C,u1_struct_0(B)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( D != k4_struct_0(A) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(B)) & v1_vectsp11(E,A,B) & m1_subset_1(E,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(B),u1_struct_0(B)))) ) => ! [F] : ( m1_vectsp11(F,A,B,E) => ( v1_vectsp11(k4_matrlin(A,B,B,E,D),A,B) & m1_vectsp11(k8_group_1(A,D,F),A,B,k4_matrlin(A,B,B,E,D)) & ( m2_vectsp11(C,A,B,E,F) => m2_vectsp11(C,A,B,k4_matrlin(A,B,B,E,D),k8_group_1(A,D,F)) ) & ( m2_vectsp11(C,A,B,k4_matrlin(A,B,B,E,D),k8_group_1(A,D,F)) => m2_vectsp11(C,A,B,E,F) ) ) ) ) ) ) ) ) ) )).
fof(t9_vectsp_1,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( 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)) ) ) ) ) )).
fof(t9_vectsp_2,axiom,( ! [A] : ( ( ~ 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] : ( m1_subset_1(B,u1_struct_0(A)) => ( B != k4_struct_0(A) => ( k6_algstr_0(A,B,k11_algstr_0(A,B)) = k5_struct_0(A) & k6_algstr_0(A,k11_algstr_0(A,B),B) = k5_struct_0(A) ) ) ) ) )).
fof(t9_vectsp_4,axiom,( ! [A] : ! [B] : ( ( ~ 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] : ( ( ~ 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] : ( m1_vectsp_4(D,B,C) => ( r1_struct_0(D,A) => r1_struct_0(C,A) ) ) ) ) )).
fof(t9_vectsp_5,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( v7_vectsp_1(C,A) & m1_vectsp_4(C,A,B) ) => ( k1_vectsp_5(A,B,k1_vectsp_4(A,B),C) = C & k1_vectsp_5(A,B,C,k1_vectsp_4(A,B)) = C ) ) ) ) )).
fof(t9_vectsp_6,axiom,( ! [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) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( ( 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)))) ) => k3_vectsp_6(A,B,k6_finseq_1(u1_struct_0(B)),C) = k6_finseq_1(u1_struct_0(B)) ) ) ) )).
fof(t9_vectsp_7,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(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_7(A,B,k1_subset_1(u1_struct_0(B))) = k1_vectsp_4(A,B) ) ) )).
fof(t9_vectsp_8,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ 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) ) => v4_lattice3(k1_vectsp_8(A,B)) ) ) )).
fof(t9_vectsp_9,axiom,( ! [A] : ( ( ~ v6_struct_0(A) & v13_algstr_0(A) & v33_algstr_0(A) & v3_group_1(A) & v5_group_1(A) & v4_vectsp_1(A) & v5_vectsp_1(A) & v2_rlvect_1(A) & v3_rlvect_1(A) & v4_rlvect_1(A) & l6_algstr_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v8_vectsp_1(B,A) & v9_vectsp_1(B,A) & v10_vectsp_1(B,A) & v11_vectsp_1(B,A) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & l1_vectsp_1(B,A) ) => ! [C] : ( m1_vectsp_4(C,A,B) => ! [D] : ( m1_vectsp_6(D,A,B) => ~ ( r1_tarski(k1_vectsp_6(A,B,D),u1_struct_0(C)) & ! [E] : ( m1_vectsp_6(E,A,C) => ~ ( k1_vectsp_6(A,C,E) = k1_vectsp_6(A,B,D) & k4_vectsp_6(A,C,E) = k4_vectsp_6(A,B,D) ) ) ) ) ) ) ) )).
fof(t9_vfunct_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ v2_struct_0(B) & v13_algstr_0(B) & v2_rlvect_1(B) & v3_rlvect_1(B) & v4_rlvect_1(B) & v5_rlvect_1(B) & v6_rlvect_1(B) & v7_rlvect_1(B) & v8_rlvect_1(B) & v3_normsp_0(B) & v4_normsp_0(B) & v2_normsp_1(B) & l1_normsp_1(B) ) => ! [C] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( v1_xreal_0(D) => ! [E] : ( ( 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,k26_valued_1(A,k1_numbers,E,D),C)) ) ) ) ) ) )).
fof(t9_vfunct_2,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( ~ 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] : ( ( v1_funct_1(C) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,u1_struct_0(B)))) ) => ! [D] : ( v1_xcmplx_0(D) => ! [E] : ( ( 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,k25_valued_1(A,k2_numbers,E,D),C)) ) ) ) ) ) )).
fof(t9_waybel10,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k6_yellow_1(A,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)))) ) ) ) ) )).
fof(t9_waybel11,axiom,( ! [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] : ( 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) ) ) )).
fof(t9_waybel12,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & v2_yellow_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => r2_hidden(k4_yellow_0(A),k4_waybel_0(A,B)) ) ) )).
fof(t9_waybel13,axiom,( ! [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] : ( ( ~ v1_xboole_0(B) & v1_waybel_0(B,k1_yellow_1(k7_waybel_0(A))) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_yellow_1(k7_waybel_0(A))))) ) => k1_yellow_0(k1_yellow_1(k7_waybel_0(A)),B) = k3_tarski(B) ) ) )).
fof(t9_waybel14,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & v3_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r3_orders_2(A,k1_yellow_0(A,k1_waybel_3(A,B)),B) & r3_orders_2(A,B,k2_yellow_0(A,k2_waybel_3(A,B))) ) ) ) )).
fof(t9_waybel15,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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_waybel_3(A) ) => v3_waybel_3(B) ) ) ) )).
fof(t9_waybel16,axiom,( ! [A] : ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k1_yellow_1(k8_waybel_0(k2_yellow_1(A)))))) ) => ( ~ v1_xboole_0(k1_setfam_1(B)) & v2_waybel_0(k1_setfam_1(B),k2_yellow_1(A)) & v13_waybel_0(k1_setfam_1(B),k2_yellow_1(A)) & m1_subset_1(k1_setfam_1(B),k1_zfmisc_1(u1_struct_0(k2_yellow_1(A)))) ) ) )).
fof(t9_waybel17,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v1_xboole_0(B) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => k4_waybel17(A,B) = k3_waybel11(A,B,k17_funct_3(u1_struct_0(A),u1_struct_0(A),k6_partfun1(u1_struct_0(A)),B)) ) ) )).
fof(t9_waybel18,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_pre_topc(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B)) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => u1_struct_0(k7_waybel18(A,B,C)) = k2_relset_1(u1_struct_0(B),C) ) ) ) )).
fof(t9_waybel19,axiom,( ! [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) & v1_waybel19(A) & l1_waybel_9(A) ) => ! [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) & v1_waybel19(B) & l1_waybel_9(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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_pre_topc(C,A,B) ) ) ) ) )).
fof(t9_waybel20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & v5_orders_2(C) & l1_orders_2(C) ) => ! [D] : ( ( ~ v2_struct_0(D) & v5_orders_2(D) & l1_orders_2(D) ) => ! [E] : ( ( 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] : ( ( 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)))) ) => ( ( v17_waybel_0(E,A,C) & v17_waybel_0(F,B,D) ) => v17_waybel_0(k1_waybel20(A,B,C,D,E,F),k3_yellow_3(A,B),k3_yellow_3(C,D)) ) ) ) ) ) ) ) )).
fof(t9_waybel21,axiom,( ! [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] : ( ( ~ v2_struct_0(B) & v4_yellow_0(B,A) & v8_yellow_0(B,A) & m1_yellow_0(B,A) ) => v18_waybel_0(k1_yellow_9(A,B),B,A) ) ) )).
fof(t9_waybel22,axiom,( ! [A] : r1_tarski(k1_waybel22(A),k8_waybel_0(k2_yellow_1(A))) )).
fof(t9_waybel23,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_waybel_0(A,k5_waybel_0(A,B)) = k5_waybel_0(A,B) ) ) )).
fof(t9_waybel24,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_orders_2(C) ) => ! [D] : ( ( 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] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => k3_funct_2(u1_struct_0(B),u1_struct_0(C),k1_waybel24(A,B,C,D,E),F) = k3_funct_2(u1_struct_0(A),u1_struct_0(C),k2_waybel24(A,B,C,D,F),E) ) ) ) ) ) ) )).
fof(t9_waybel25,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_pre_topc(B) ) => ! [C] : ( ( ~ v2_struct_0(C) & l1_pre_topc(C) ) => ( ( r2_borsuk_3(B,C) & r1_waybel18(B,A) ) => r1_waybel18(C,A) ) ) ) ) )).
fof(t9_waybel26,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_pre_topc(B) & l1_pre_topc(B) ) => ! [C] : ( ( 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(k3_waybel26(A,B,B,C)) ) ) ) ) )).
fof(t9_waybel27,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) ) => ! [B] : ! [C] : ( r1_tarski(k2_zfmisc_1(C,k1_tarski(B)),k9_xtuple_0(A)) => k5_card_3(B,k7_relat_1(k1_funct_5(A),C)) = k7_relat_1(A,k2_zfmisc_1(C,k1_tarski(B))) ) ) )).
fof(t9_waybel28,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v4_orders_2(B) & v7_waybel_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( ( 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)) & v7_waybel_0(k1_waybel28(A,B,C)) & l1_waybel_0(k1_waybel28(A,B,C),A) ) ) ) ) )).
fof(t9_waybel29,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( ~ 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) ) => ( v4_waybel_0(k3_waybel24(A,B),k5_yellow_1(u1_struct_0(A),B)) & m1_yellow_0(k3_waybel24(A,B),k5_yellow_1(u1_struct_0(A),B)) ) ) ) )).
fof(t9_waybel30,axiom,( ! [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) & l1_waybel_9(A) ) => k2_waybel19(A) = u1_pre_topc(A) ) )).
fof(t9_waybel31,axiom,( ! [A] : ( l1_pre_topc(A) => ! [B] : ( ( 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) ) => ( ( k1_yellow_1(u1_pre_topc(A)) = B & v8_struct_0(A) ) => k1_waybel31(B) = k1_card_1(u1_struct_0(B)) ) ) ) )).
fof(t9_waybel33,axiom,( ! [A] : ( ( 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] : ( ( 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)) => k4_waybel28(A) = k4_waybel28(B) ) ) ) )).
fof(t9_waybel34,axiom,( ! [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] : ( ( 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] : ( ( 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] : ( ( v1_funct_1(D) & v1_funct_2(D,u1_struct_0(A),u1_struct_0(B)) & v18_waybel_0(D,A,B) & m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(B)))) ) => ! [E] : ( ( v1_funct_1(E) & v1_funct_2(E,u1_struct_0(B),u1_struct_0(C)) & v18_waybel_0(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(C),u1_struct_0(A),k2_waybel34(C,A,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_waybel34(C,B,E),k2_waybel34(B,A,D))) ) ) ) ) ) )).
fof(t9_waybel35,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( 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] : ( ( ~ v1_xboole_0(C) & m1_waybel35(C,A,B) ) => ! [D] : ( m1_subset_1(D,k1_zfmisc_1(C)) => ( ( r2_yellow_0(A,k9_subset_1(u1_struct_0(A),k6_waybel_0(A,k1_yellow_0(A,D)),C)) & r1_yellow_0(A,D) & v2_waybel35(C,A,B) ) => ( k1_yellow_0(k5_yellow_0(A,C),D) = k2_yellow_0(A,k9_subset_1(u1_struct_0(A),k6_waybel_0(A,k1_yellow_0(A,D)),C)) & ( ~ r2_hidden(k1_yellow_0(A,D),C) => r2_orders_2(A,k1_yellow_0(A,D),k2_yellow_0(A,k9_subset_1(u1_struct_0(A),k6_waybel_0(A,k1_yellow_0(A,D)),C))) ) ) ) ) ) ) ) )).
fof(t9_waybel_0,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_struct_0(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_waybel_0(B,A) ) => ! [C] : ( r1_waybel_0(A,B,C) <=> ~ r2_waybel_0(A,B,k6_subset_1(u1_struct_0(A),C)) ) ) ) )).
fof(t9_waybel_1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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) => ( v4_waybel_1(C,A,B) & v5_waybel_1(D,A,B) ) ) ) ) ) ) )).
fof(t9_waybel_2,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v24_waybel_0(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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)))) ) => r3_orders_2(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)))) ) ) )).
fof(t9_waybel_3,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => r2_lattice3(A,k1_waybel_3(A,B),B) ) ) )).
fof(t9_waybel_4,axiom,( ! [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] : ( ( v4_waybel_4(B,A) & m1_subset_1(B,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ! [C] : ( ( v4_waybel_4(C,A) & m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))) ) => ( v4_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)))) ) ) ) ) )).
fof(t9_waybel_5,axiom,( ! [A] : ( ( v1_relat_1(A) & v1_funct_1(A) & v1_funcop_1(A) ) => ! [B] : ( ( v1_relat_1(B) & v1_funct_1(B) ) => ( r2_hidden(B,k1_relset_1(k4_card_3(k1_funct_6(A)),k2_pralg_2(A))) => ! [C] : ( r2_hidden(C,k9_xtuple_0(A)) => ( r2_hidden(k1_funct_1(B,C),k9_xtuple_0(k1_funct_1(A,C))) & k1_funct_1(k1_funct_1(k2_pralg_2(A),B),C) = k1_funct_1(k1_funct_1(A,C),k1_funct_1(B,C)) & r2_hidden(k1_funct_1(k1_funct_1(A,C),k1_funct_1(B,C)),k10_xtuple_0(k1_funct_1(k2_pralg_2(A),B))) ) ) ) ) ) )).
fof(t9_waybel_6,axiom,( ! [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] : ( ( v13_waybel_0(B,A) & v1_waybel_6(B,A) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ~ ( r2_hidden(C,k3_subset_1(u1_struct_0(A),B)) & ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ~ ( r3_orders_2(A,C,D) & r3_waybel_4(A,k3_subset_1(u1_struct_0(A),B),D) ) ) ) ) ) ) )).
fof(t9_waybel_7,axiom,( ! [A] : ! [B] : ( ( v13_waybel_0(B,k2_yellow_1(A)) & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(A)))) ) => ( v2_waybel_0(B,k2_yellow_1(A)) <=> ! [C] : ! [D] : ( ( r2_hidden(C,B) & r2_hidden(D,B) ) => r2_hidden(k3_xboole_0(C,D),B) ) ) ) )).
fof(t9_waybel_8,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ 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) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(B)) => ( ( C = D & v1_waybel_3(C,A) ) => v1_waybel_3(D,B) ) ) ) ) ) ) )).
fof(t9_waybel_9,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & l1_orders_2(A) ) => ( ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( ( ~ v2_struct_0(C) & v4_orders_2(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) ) ) )).
fof(t9_weddwitt,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v8_struct_0(A) & v2_group_1(A) & v3_group_1(A) & l3_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m2_subset_1(C,u1_struct_0(A),k7_group_3(A,B)) => k5_card_1(k8_relset_1(u1_struct_0(A),k7_group_3(A,B),k2_weddwitt(A,B),k1_tarski(C))) = k7_group_1(k1_weddwitt(A,B)) ) ) ) )).
fof(t9_weierstr,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_pre_topc(A) & l1_pre_topc(A) ) => ! [B] : ( ( 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] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( ( v2_compts_1(C,A) & v5_pre_topc(B,A,k3_topmetr) ) => v2_compts_1(k7_relset_1(u1_struct_0(A),u1_struct_0(k3_topmetr),B,C),k3_topmetr) ) ) ) ) )).
fof(t9_wellfnd1,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( r1_tarski(k1_wellord1(u1_orders_2(A),B),k1_wellfnd1(A)) => r2_hidden(B,k1_wellfnd1(A)) ) ) ) )).
fof(t9_wellord1,axiom,( ! [A] : ! [B] : ( v1_relat_1(B) => r1_tarski(k1_wellord1(B,A),k1_relat_1(B)) ) )).
fof(t9_wellord2,axiom,( ! [A] : ! [B] : ! [C] : ( ( r2_wellord2(A,B) & r2_wellord2(B,C) ) => r2_wellord2(A,C) ) )).
fof(t9_wsierp_1,axiom,( ! [A] : ( v1_int_1(A) => r1_int_2(1,A) ) )).
fof(t9_xboole_1,axiom,( ! [A] : ! [B] : ! [C] : ( r1_tarski(A,B) => r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,C)) ) )).
fof(t9_xboolean,axiom,( ! [A] : ( v1_xboolean(A) => ! [B] : ( v1_xboolean(B) => ! [C] : ( v1_xboolean(C) => k5_xboolean(A,k4_xboolean(B,C)) = k4_xboolean(k5_xboolean(A,B),k5_xboolean(A,C)) ) ) ) )).
fof(t9_xcmplx_1,axiom,( ! [A] : ( v1_xcmplx_0(A) => ! [B] : ( v1_xcmplx_0(B) => ! [C] : ( v1_xcmplx_0(C) => ! [D] : ( v1_xcmplx_0(D) => k3_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(A,B),C),D) = k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,D),k3_xcmplx_0(B,D)),k3_xcmplx_0(C,D)) ) ) ) ) )).
fof(t9_xreal_1,axiom,( ! [A] : ( v1_xreal_0(A) => ! [B] : ( v1_xreal_0(B) => ! [C] : ( v1_xreal_0(C) => ( r1_xxreal_0(A,B) <=> r1_xxreal_0(k6_xcmplx_0(A,C),k6_xcmplx_0(B,C)) ) ) ) ) )).
fof(t9_xregular,axiom,( ! [A] : ! [B] : ! [C] : ! [D] : ! [E] : ~ ( r2_hidden(A,B) & r2_hidden(B,C) & r2_hidden(C,D) & r2_hidden(D,E) & r2_hidden(E,A) ) )).
fof(t9_xtuple_0,axiom,( ! [A] : ! [B] : ( r1_tarski(A,B) => r1_tarski(k10_xtuple_0(A),k10_xtuple_0(B)) ) )).
fof(t9_xxreal_0,axiom,( ! [A] : ( v1_xxreal_0(A) => ~ ( r2_hidden(A,k1_numbers) & r1_xxreal_0(k1_xxreal_0,A) ) ) )).
fof(t9_xxreal_1,axiom,( ! [A] : ! [B] : ( v1_xxreal_0(B) => ! [C] : ( v1_xxreal_0(C) => ~ ( r2_hidden(A,k3_xxreal_1(B,C)) & ~ r2_hidden(A,k4_xxreal_1(B,C)) & A != C ) ) ) )).
fof(t9_xxreal_2,axiom,( ! [A] : ( v2_membered(A) => ! [B] : ( v2_membered(B) => k2_xxreal_2(k2_xboole_0(A,B)) = k3_xxreal_0(k2_xxreal_2(A),k2_xxreal_2(B)) ) ) )).
fof(t9_xxreal_3,axiom,( ! [A] : ( v1_xxreal_0(A) => ! [B] : ( v1_xxreal_0(B) => k2_xxreal_3(k1_xxreal_3(A,B)) = k1_xxreal_3(k2_xxreal_3(A),k2_xxreal_3(B)) ) ) )).
fof(t9_yellow10,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(k3_yellow_3(A,B))) => ! [D] : ( m1_subset_1(D,u1_struct_0(k3_yellow_3(A,B))) => ( r2_lattice3(k3_yellow_3(A,B),k6_domain_1(u1_struct_0(k3_yellow_3(A,B)),D),C) <=> ( r2_lattice3(A,k6_domain_1(u1_struct_0(A),k8_yellow_3(A,B,D)),k8_yellow_3(A,B,C)) & r2_lattice3(B,k6_domain_1(u1_struct_0(B),k9_yellow_3(A,B,D)),k9_yellow_3(A,B,C)) ) ) ) ) ) ) )).
fof(t9_yellow11,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & v2_lattice3(A) & l1_orders_2(A) ) => ( ~ ( ? [B] : ( 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) ) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( 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 ) ) ) ) ) ) ) & ~ ( ? [B] : ( m1_subset_1(B,u1_struct_0(A)) & ? [C] : ( m1_subset_1(C,u1_struct_0(A)) & ? [D] : ( m1_subset_1(D,u1_struct_0(A)) & ? [E] : ( m1_subset_1(E,u1_struct_0(A)) & ? [F] : ( 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 ) ) ) ) ) & ! [B] : ( ( 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) ) ) ) ) )).
fof(t9_yellow12,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v2_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(B)) => ! [F] : ( 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 ) => k12_lattice3(A,C,D) = k11_lattice3(B,E,F) ) ) ) ) ) ) ) )).
fof(t9_yellow13,axiom,( ! [A] : ( ( 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_funct_1(k2_yellow_2(A)) ) )).
fof(t9_yellow14,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( l1_orders_2(B) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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_2(C,u1_struct_0(B)) ) ) ) ) )).
fof(t9_yellow15,axiom,( ! [A] : ! [B] : ( m1_subset_1(B,k1_zfmisc_1(A)) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(A)) => ! [D] : ( 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) ) ) ) ) ) )).
fof(t9_yellow16,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_relat_1(C) & v1_funct_1(C) ) => ( r1_yellow16(A,B,C) => k10_xtuple_0(C) = u1_struct_0(A) ) ) ) ) )).
fof(t9_yellow17,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ( 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] : ( m1_subset_1(C,A) => ! [D] : ( m1_subset_1(D,u1_struct_0(k4_waybel18(A,B,C))) => ! [E] : ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(k4_waybel18(A,B,C)))) => ( ~ r1_xboole_0(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)),k8_relset_1(u1_struct_0(k3_waybel18(A,B)),u1_struct_0(k4_waybel18(A,B,C)),k6_waybel18(A,B,C),E)) => r2_hidden(D,E) ) ) ) ) ) ) )).
fof(t9_yellow18,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & l2_altcat_1(B) ) => ( r2_yellow18(A,B) <=> ( u1_struct_0(B) = u1_struct_0(A) & ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(B)) => ! [G] : ( m1_subset_1(G,u1_struct_0(B)) => ! [H] : ( m1_subset_1(H,u1_struct_0(B)) => ( ( F = C & G = D & H = E ) => ( k1_altcat_1(A,C,D) = k1_altcat_1(B,G,F) & ~ ( k1_altcat_1(A,C,D) != k1_xboole_0 & k1_altcat_1(A,D,E) != k1_xboole_0 & ? [I] : ( m1_subset_1(I,k1_altcat_1(A,C,D)) & ? [J] : ( m1_subset_1(J,k1_altcat_1(A,D,E)) & ? [K] : ( m1_subset_1(K,k1_altcat_1(B,G,F)) & ? [L] : ( m1_subset_1(L,k1_altcat_1(B,H,G)) & K = I & L = J & k5_altcat_1(B,H,G,F,L,K) != k5_altcat_1(A,C,D,E,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).
fof(t9_yellow20,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & v2_altcat_1(A) & v11_altcat_1(A) & v12_altcat_1(A) & l2_altcat_1(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & v2_altcat_1(B) & v11_altcat_1(B) & v12_altcat_1(B) & l2_altcat_1(B) ) => ! [C] : ( ( v16_functor0(C,A,B) & m2_functor0(C,A,B) ) => ( v21_functor0(C,A,B) => ! [D] : ( ( v16_functor0(D,B,A) & m2_functor0(D,B,A) ) => ( ( ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => k3_functor0(B,A,D,k3_functor0(A,B,C,E)) = E ) & ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ! [F] : ( m1_subset_1(F,u1_struct_0(A)) => ( k1_altcat_1(A,E,F) != k1_xboole_0 => ! [G] : ( m1_subset_1(G,k1_altcat_1(A,E,F)) => k8_functor0(B,A,D,k3_functor0(A,B,C,F),k3_functor0(A,B,C,E),k8_functor0(A,B,C,E,F,G)) = G ) ) ) ) ) => g2_functor0(B,A,u1_functor0(B,A,D),u2_functor0(B,A,D)) = k15_functor0(A,B,C) ) ) ) ) ) ) )).
fof(t9_yellow21,axiom,( ! [A] : ( ( ~ 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)) => ( v16_waybel_0(A) & v3_lattice3(A) & v3_waybel_3(A) ) ) ) )).
fof(t9_yellow_0,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ! [C] : ( r1_tarski(B,C) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r1_lattice3(A,C,D) => r1_lattice3(A,B,D) ) & ( r2_lattice3(A,C,D) => r2_lattice3(A,B,D) ) ) ) ) ) )).
fof(t9_yellow_1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k1_yellow_1(A))) => ! [C] : ( m1_subset_1(C,u1_struct_0(k1_yellow_1(A))) => ( r2_hidden(k3_xboole_0(B,C),A) => k11_lattice3(k1_yellow_1(A),B,C) = k3_xboole_0(B,C) ) ) ) ) )).
fof(t9_yellow_2,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( ( ~ v2_struct_0(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( ( 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) <=> ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => r1_orders_2(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),D,E)) ) ) ) ) ) ) )).
fof(t9_yellow_3,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( ( v3_orders_2(B) & v4_orders_2(B) & v5_orders_2(B) & v1_lattice3(B) & l1_orders_2(B) ) => ! [C] : ( ( v1_funct_1(C) & v1_funct_2(C,u1_struct_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] : ( m1_subset_1(D,u1_struct_0(A)) => ! [E] : ( m1_subset_1(E,u1_struct_0(A)) => ( r4_waybel_0(A,B,C,k7_domain_1(u1_struct_0(A),D,E)) <=> 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)) ) ) ) ) ) ) )).
fof(t9_yellow_4,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) => k1_yellow_4(A,B,k1_struct_0(A)) = k1_xboole_0 ) ) )).
fof(t9_yellow_5,axiom,( ! [A] : ( ( v3_orders_2(A) & v4_orders_2(A) & v5_orders_2(A) & v1_lattice3(A) & l1_orders_2(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ! [C] : ( m1_subset_1(C,u1_struct_0(A)) => ! [D] : ( m1_subset_1(D,u1_struct_0(A)) => ( ( r3_orders_2(A,B,D) & r3_orders_2(A,C,D) ) => r3_orders_2(A,k13_lattice3(A,B,C),D) ) ) ) ) ) )).
fof(t9_yellow_6,axiom,( ! [A] : ( l1_struct_0(A) => ! [B] : ( l1_waybel_0(B,A) => ! [C] : ( m1_yellow_6(C,A,B) => ! [D] : ( m1_yellow_6(D,A,C) => m1_yellow_6(D,A,B) ) ) ) ) )).
fof(t9_yellow_7,axiom,( ! [A] : ( l1_orders_2(A) => ! [B] : ( m1_subset_1(B,u1_struct_0(k7_lattice3(A))) => ! [C] : ( ( r1_lattice3(k7_lattice3(A),C,B) => r2_lattice3(A,C,k9_lattice3(A,B)) ) & ( r2_lattice3(A,C,k9_lattice3(A,B)) => r1_lattice3(k7_lattice3(A),C,B) ) & ( r2_lattice3(k7_lattice3(A),C,B) => r1_lattice3(A,C,k9_lattice3(A,B)) ) & ( r1_lattice3(A,C,k9_lattice3(A,B)) => r2_lattice3(k7_lattice3(A),C,B) ) ) ) ) )).
fof(t9_yellow_8,axiom,( ! [A] : ( l1_pre_topc(A) => ! [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)))) ) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ( v3_pre_topc(C,A) => C = k3_tarski(a_3_0_yellow_8(A,B,C)) ) ) ) ) )).
fof(t9_yellow_9,axiom,( ! [A] : ( ( v13_struct_0(A,1) & v2_pre_topc(A) & l1_pre_topc(A) ) => ( u1_pre_topc(A) = k9_setfam_1(u1_struct_0(A)) & ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => ( u1_struct_0(A) = k6_domain_1(u1_struct_0(A),B) & u1_pre_topc(A) = k2_tarski(k1_xboole_0,k6_domain_1(u1_struct_0(A),B)) ) ) ) ) )).
fof(t9_zf_fund1,axiom,( ! [A] : ( ( ~ v1_xboole_0(A) & v1_classes2(A) ) => ! [B] : ( m1_subset_1(B,A) => ! [C] : ( ( ~ v1_xboole_0(C) & m1_subset_1(C,k1_zfmisc_1(A)) ) => ! [D] : ( ( v1_finset_1(D) & m1_subset_1(D,k1_zfmisc_1(k4_ordinal1)) ) => ( ( v8_zf_fund1(C,A) & r2_hidden(B,C) ) => r2_hidden(k1_funct_2(D,B),C) ) ) ) ) ) )).
fof(t9_zf_lang,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ~ ( ~ v2_zf_lang(A) & ~ v3_zf_lang(A) & ~ v4_zf_lang(A) & ~ v5_zf_lang(A) & ~ v6_zf_lang(A) ) ) )).
fof(t9_zf_lang1,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( m2_subset_1(B,k4_ordinal1,k1_zf_lang) => ( k23_zf_lang(k13_zf_lang(B,A)) = B & k24_zf_lang(k13_zf_lang(B,A)) = A ) ) ) )).
fof(t9_zf_model,axiom,( ! [A] : ( ( v1_zf_lang(A) & m2_finseq_1(A,k4_ordinal1) ) => ! [B] : ( ~ v1_xboole_0(B) => ( v4_zf_lang(A) => ! [C] : ( ( 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(k20_zf_lang(A),B)) <=> r2_hidden(C,k5_zf_model(A,B)) ) ) ) ) ) )).
fof(t9_zf_refle,axiom,( ! [A] : ( ( v1_relat_1(A) & v5_ordinal1(A) & v1_funct_1(A) & v1_ordinal2(A) ) => ! [B] : ( v3_ordinal1(B) => ( v1_relat_1(k5_relat_1(A,k4_classes1(B))) & v5_ordinal1(k5_relat_1(A,k4_classes1(B))) & v1_funct_1(k5_relat_1(A,k4_classes1(B))) & v1_ordinal2(k5_relat_1(A,k4_classes1(B))) ) ) ) )).
fof(t9_zfmisc_1,axiom,( ! [A] : ! [B] : k2_xboole_0(k1_tarski(A),k2_tarski(A,B)) = k2_tarski(A,B) )).
fof(t9_zfmodel1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ( v1_ordinal1(A) => ( r2_zf_model(A,k10_zf_model) <=> ! [B] : ( r2_hidden(B,A) => r2_hidden(k3_xboole_0(A,k1_zfmisc_1(B)),A) ) ) ) ) )).
fof(t9_zfmodel2,axiom,( ! [A] : ( m2_subset_1(A,k4_ordinal1,k1_zf_lang) => ! [B] : ( ~ v1_xboole_0(B) => ! [C] : ( m1_subset_1(C,B) => ! [D] : ( ( v1_zf_lang(D) & m2_finseq_1(D,k4_ordinal1) ) => ! [E] : ( ( 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,k2_zf_model(D)) => ( r1_zf_model(B,E,D) <=> r1_zf_model(B,k2_zf_lang1(B,E,A,C),D) ) ) ) ) ) ) ) )).
fof(t9_zfrefle1,axiom,( ! [A] : ( ~ v1_xboole_0(A) => ! [B] : ( ~ v1_xboole_0(B) => ( r3_zfrefle1(A,B) => r2_zfrefle1(A,B) ) ) ) )).
fof(t9_zmodul01,axiom,( ! [A] : ( v1_int_1(A) => ! [B] : ( v1_int_1(B) => ! [C] : ( ( ~ 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] : ( m1_subset_1(D,u1_struct_0(C)) => k1_zmodul01(C,D,k6_xcmplx_0(A,B)) = k5_algstr_0(C,k1_zmodul01(C,D,A),k1_zmodul01(C,D,B)) ) ) ) ) )).
fof(t9_zmodul02,axiom,( ! [A] : ( ( ~ v2_struct_0(A) & l2_algstr_0(A) ) => ! [B] : ( m1_subset_1(B,u1_struct_0(A)) => k3_funct_2(u1_struct_0(A),k4_numbers,k19_zmodul02(A),B) = k5_numbers ) ) )).
fof(t9_zmodul03,axiom,( ! [A] : ( ( ~ 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] : ( m1_zmodul02(B,A) => ! [C] : ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) => ! [D] : ( m2_finseq_1(D,u1_struct_0(A)) => ~ ( r1_tarski(k2_relset_1(u1_struct_0(A),D),u1_struct_0(k33_zmodul02(A,C))) & ! [E] : ( m2_zmodul02(E,A,C) => k4_rlvect_1(A,k20_zmodul02(A,D,B)) != k21_zmodul02(A,E) ) ) ) ) ) ) )).
